LMFDB - Embedded newform 69.7.f.a.34.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(7,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.f (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			34.2
Character	$\chi$	$=$	69.34
Dual form			69.7.f.a.67.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.2621 + 7.88038i) q^{2} +(-2.21847 + 15.4298i) q^{3} +(61.6725 - 135.044i) q^{4} +(34.1338 + 116.249i) q^{5} +(-94.3895 - 206.684i) q^{6} +(289.705 - 251.031i) q^{7} +(175.202 + 1218.56i) q^{8} +(-233.157 - 68.4610i) q^{9} +O(q^{10})$	\(q+(-12.2621 + 7.88038i) q^{2} +(-2.21847 + 15.4298i) q^{3} +(61.6725 - 135.044i) q^{4} +(34.1338 + 116.249i) q^{5} +(-94.3895 - 206.684i) q^{6} +(289.705 - 251.031i) q^{7} +(175.202 + 1218.56i) q^{8} +(-233.157 - 68.4610i) q^{9} +(-1334.64 - 1156.47i) q^{10} +(-378.807 + 589.436i) q^{11} +(1946.88 + 1251.18i) q^{12} +(-1571.98 + 1814.16i) q^{13} +(-1574.18 + 5361.15i) q^{14} +(-1869.42 + 268.782i) q^{15} +(-5528.94 - 6380.74i) q^{16} +(-6084.37 + 2778.64i) q^{17} +(3398.50 - 997.888i) q^{18} +(-4436.13 - 2025.91i) q^{19} +(17803.8 + 2559.81i) q^{20} +(3230.65 + 5026.99i) q^{21} -10212.9i q^{22} +(11369.2 + 4333.26i) q^{23} -19190.8 q^{24} +(795.866 - 511.472i) q^{25} +(4979.50 - 34633.2i) q^{26} +(1573.59 - 3445.68i) q^{27} +(-16033.3 - 54604.6i) q^{28} +(-15744.5 - 34475.6i) q^{29} +(20805.0 - 18027.6i) q^{30} +(1346.38 + 9364.31i) q^{31} +(42481.0 + 12473.6i) q^{32} +(-8254.50 - 7152.56i) q^{33} +(52710.5 - 82019.2i) q^{34} +(39070.8 + 25109.3i) q^{35} +(-23624.6 + 27264.3i) q^{36} +(-5318.37 + 18112.7i) q^{37} +(70361.3 - 10116.4i) q^{38} +(-24504.7 - 28279.9i) q^{39} +(-135676. + 61961.1i) q^{40} +(-105405. + 30949.6i) q^{41} +(-79229.2 - 36182.8i) q^{42} +(-61950.6 - 8907.15i) q^{43} +(56237.7 + 87507.6i) q^{44} -29441.1i q^{45} +(-173558. + 36458.7i) q^{46} +60430.3 q^{47} +(110719. - 71155.0i) q^{48} +(4169.28 - 28998.0i) q^{49} +(-5728.41 + 12543.5i) q^{50} +(-29375.8 - 100045. i) q^{51} +(148043. + 324170. i) q^{52} +(68874.3 - 59679.9i) q^{53} +(7857.75 + 54651.8i) q^{54} +(-81451.5 - 23916.3i) q^{55} +(356652. + 309041. i) q^{56} +(41100.8 - 63954.2i) q^{57} +(464742. + 298672. i) q^{58} +(196221. - 226451. i) q^{59} +(-78994.5 + 269031. i) q^{60} +(-341176. + 49053.7i) q^{61} +(-90303.9 - 104216. i) q^{62} +(-84732.4 + 38696.0i) q^{63} +(-100744. + 29581.2i) q^{64} +(-264552. - 120817. i) q^{65} +(157583. + 22657.0i) q^{66} +(-230054. - 357971. i) q^{67} +993023. i q^{68} +(-92083.5 + 165811. i) q^{69} -676961. q^{70} +(-389290. + 250182. i) q^{71} +(42574.2 - 296110. i) q^{72} +(266926. - 584485. i) q^{73} +(-77520.6 - 264011. i) q^{74} +(6126.30 + 13414.7i) q^{75} +(-547175. + 474130. i) q^{76} +(38224.1 + 265855. i) q^{77} +(523336. + 153665. i) q^{78} +(213957. + 185394. i) q^{79} +(553031. - 860533. i) q^{80} +(49675.2 + 31924.3i) q^{81} +(1.04859e6 - 1.21014e6i) q^{82} +(-134936. + 459551. i) q^{83} +(878106. - 126253. i) q^{84} +(-530697. - 612457. i) q^{85} +(829837. - 378974. i) q^{86} +(566880. - 166451. i) q^{87} +(-784630. - 358329. i) q^{88} +(-1.17507e6 - 168949. i) q^{89} +(232007. + 361010. i) q^{90} +920184. i q^{91} +(1.28635e6 - 1.26810e6i) q^{92} -147476. q^{93} +(-741003. + 476214. i) q^{94} +(84088.5 - 584848. i) q^{95} +(-286707. + 627801. i) q^{96} +(77644.4 + 264433. i) q^{97} +(177391. + 388432. i) q^{98} +(128675. - 111497. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) $ 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−12.2621	+	7.88038i	−1.53276	+	0.985048i	−0.543419	+	0.839461i	$0.682871\pi$
$2$	−12.2621	+	7.88038i	−1.53276	+	0.985048i	−0.989346	+	0.145587i	$0.953493\pi$
$3$	−2.21847	+	15.4298i	−0.0821655	+	0.571474i
$3$	−2.21847	+	15.4298i	−0.0821655	+	0.571474i
$4$	61.6725	−	135.044i	0.963633	−	2.11006i
$5$	34.1338	+	116.249i	0.273070	+	0.929992i	0.975824	+	0.218559i	$0.0701355\pi$
$5$	34.1338	+	116.249i	0.273070	+	0.929992i	−0.702753	+	0.711433i	$0.748046\pi$
$6$	−94.3895	−	206.684i	−0.436989	−	0.956872i
$7$	289.705	−	251.031i	0.844620	−	0.731868i	−0.120769	−	0.992681i	$-0.538536\pi$
$7$	289.705	−	251.031i	0.844620	−	0.731868i	0.965389	+	0.260813i	$0.0839906\pi$
$8$	175.202	+	1218.56i	0.342192	+	2.38000i
$9$	−233.157	−	68.4610i	−0.319831	−	0.0939109i
$10$	−1334.64	−	1156.47i	−1.33464	−	1.15647i
$11$	−378.807	+	589.436i	−0.284604	+	0.442852i	−0.953892	−	0.300151i	$-0.902963\pi$
$11$	−378.807	+	589.436i	−0.284604	+	0.442852i	0.669288	+	0.743003i	$0.266599\pi$
$12$	1946.88	+	1251.18i	1.12667	+	0.724065i
$13$	−1571.98	+	1814.16i	−0.715511	+	0.825743i	−0.990760	−	0.135630i	$-0.956694\pi$
$13$	−1571.98	+	1814.16i	−0.715511	+	0.825743i	0.275249	+	0.961373i	$0.411240\pi$
$14$	−1574.18	+	5361.15i	−0.573679	+	1.95377i
$15$	−1869.42	+	268.782i	−0.553903	+	0.0796392i
$16$	−5528.94	−	6380.74i	−1.34984	−	1.55780i
$17$	−6084.37	+	2778.64i	−1.23842	+	0.565569i	−0.923518	−	0.383554i	$-0.874700\pi$
$17$	−6084.37	+	2778.64i	−1.23842	+	0.565569i	−0.314905	+	0.949123i	$0.601973\pi$
$18$	3398.50	−	997.888i	0.582732	−	0.171106i
$19$	−4436.13	−	2025.91i	−0.646761	−	0.295366i	0.0648971	−	0.997892i	$-0.479328\pi$
$19$	−4436.13	−	2025.91i	−0.646761	−	0.295366i	−0.711658	+	0.702526i	$0.752055\pi$
$20$	17803.8	+	2559.81i	2.22548	+	0.319976i
$21$	3230.65	+	5026.99i	0.348844	+	0.542813i
$22$		−	10212.9i		−	0.959136i
$23$	11369.2	+	4333.26i	0.934429	+	0.356149i
$23$	11369.2	+	4333.26i	0.934429	+	0.356149i
$24$	−19190.8			−1.38822
$25$	795.866	−	511.472i	0.0509355	−	0.0327342i
$26$	4979.50	−	34633.2i	0.283313	−	1.97048i
$27$	1573.59	−	3445.68i	0.0799467	−	0.175059i
$28$	−16033.3	−	54604.6i	−0.730382	−	2.48745i
$29$	−15744.5	−	34475.6i	−0.645557	−	1.41357i	−0.895389	−	0.445284i	$-0.853103\pi$
$29$	−15744.5	−	34475.6i	−0.645557	−	1.41357i	0.249832	−	0.968289i	$-0.419624\pi$
$30$	20805.0	−	18027.6i	0.770555	−	0.667689i
$31$	1346.38	+	9364.31i	0.0451943	+	0.314334i	0.999861	+	0.0166574i	$0.00530247\pi$
$31$	1346.38	+	9364.31i	0.0451943	+	0.314334i	−0.954667	+	0.297676i	$0.903788\pi$
$32$	42481.0	+	12473.6i	1.29642	+	0.380663i
$33$	−8254.50	−	7152.56i	−0.229694	−	0.199031i
$34$	52710.5	−	82019.2i	1.34110	−	2.08679i
$35$	39070.8	+	25109.3i	0.911272	+	0.585639i
$36$	−23624.6	+	27264.3i	−0.506357	+	0.584368i
$37$	−5318.37	+	18112.7i	−0.104996	+	0.357584i	−0.995186	−	0.0980060i	$-0.968754\pi$
$37$	−5318.37	+	18112.7i	−0.104996	+	0.357584i	0.890190	+	0.455590i	$0.150572\pi$
$38$	70361.3	−	10116.4i	1.28228	−	0.184364i
$39$	−24504.7	−	28279.9i	−0.413100	−	0.476743i
$40$	−135676.	+	61961.1i	−2.11994	+	0.968143i
$41$	−105405.	+	30949.6i	−1.52936	+	0.449059i	−0.934853	−	0.355034i	$-0.884469\pi$
$41$	−105405.	+	30949.6i	−1.52936	+	0.449059i	−0.594503	+	0.804094i	$0.702651\pi$
$42$	−79229.2	−	36182.8i	−1.06939	−	0.488375i
$43$	−61950.6	−	8907.15i	−0.779184	−	0.112030i	−0.258764	−	0.965940i	$-0.583315\pi$
$43$	−61950.6	−	8907.15i	−0.779184	−	0.112030i	−0.520419	+	0.853911i	$0.674224\pi$
$44$	56237.7	+	87507.6i	0.660191	+	1.02728i
$45$		−	29441.1i		−	0.323085i
$46$	−173558.	+	36458.7i	−1.78308	+	0.374565i
$47$	60430.3			0.582051			0.291025	−	0.956715i	$-0.406004\pi$
$47$	60430.3			0.582051			0.291025	+	0.956715i	$0.406004\pi$
$48$	110719.	−	71155.0i	1.00115	−	0.643401i
$49$	4169.28	−	28998.0i	0.0354383	−	0.246479i
$50$	−5728.41	+	12543.5i	−0.0458273	+	0.100348i
$51$	−29375.8	−	100045.i	−0.221452	−	0.754196i
$52$	148043.	+	324170.i	1.05288	+	2.30548i
$53$	68874.3	−	59679.9i	0.462625	−	0.400867i	−0.392120	−	0.919914i	$-0.628258\pi$
$53$	68874.3	−	59679.9i	0.462625	−	0.400867i	0.854746	+	0.519047i	$0.173713\pi$
$54$	7857.75	+	54651.8i	0.0499019	+	0.347075i
$55$	−81451.5	−	23916.3i	−0.489566	−	0.143749i
$56$	356652.	+	309041.i	2.03087	+	1.75975i
$57$	41100.8	−	63954.2i	0.221935	−	0.345338i
$58$	464742.	+	298672.i	2.38192	+	1.53077i
$59$	196221.	−	226451.i	0.955408	−	1.10260i	−0.0392355	−	0.999230i	$-0.512492\pi$
$59$	196221.	−	226451.i	0.955408	−	1.10260i	0.994643	−	0.103369i	$-0.0329623\pi$
$60$	−78994.5	+	269031.i	−0.365716	+	1.24551i
$61$	−341176.	+	49053.7i	−1.50310	+	0.216113i	−0.844165	−	0.536084i	$-0.819903\pi$
$61$	−341176.	+	49053.7i	−1.50310	+	0.216113i	−0.658938	+	0.752197i	$0.728994\pi$
$62$	−90303.9	−	104216.i	−0.378906	−	0.437281i
$63$	−84732.4	+	38696.0i	−0.338866	+	0.154755i
$64$	−100744.	+	29581.2i	−0.384310	+	0.112843i
$65$	−264552.	−	120817.i	−0.963319	−	0.439933i
$66$	157583.	+	22657.0i	0.548121	+	0.0788079i
$67$	−230054.	−	357971.i	−0.764902	−	1.19021i	−0.977058	−	0.212975i	$-0.931685\pi$
$67$	−230054.	−	357971.i	−0.764902	−	1.19021i	0.212156	−	0.977236i	$-0.431951\pi$
$68$			993023.i			3.15815i
$69$	−92083.5	+	165811.i	−0.280308	+	0.504739i
$70$	−676961.			−1.97365
$71$	−389290.	+	250182.i	−1.08767	+	0.699006i	−0.956318	−	0.292330i	$-0.905570\pi$
$71$	−389290.	+	250182.i	−1.08767	+	0.699006i	−0.131356	+	0.991335i	$0.541933\pi$
$72$	42574.2	−	296110.i	0.114064	−	0.793333i
$73$	266926.	−	584485.i	0.686154	−	1.50247i	−0.169835	−	0.985473i	$-0.554323\pi$
$73$	266926.	−	584485.i	0.686154	−	1.50247i	0.855989	−	0.516995i	$-0.172949\pi$
$74$	−77520.6	−	264011.i	−0.191303	−	0.651519i
$75$	6126.30	+	13414.7i	0.0145216	+	0.0317979i
$76$	−547175.	+	474130.i	−1.24648	+	1.08008i
$77$	38224.1	+	265855.i	0.0837270	+	0.582334i
$78$	523336.	+	153665.i	1.10280	+	0.323811i
$79$	213957.	+	185394.i	0.433955	+	0.376024i	0.844268	−	0.535921i	$-0.180035\pi$
$79$	213957.	+	185394.i	0.433955	+	0.376024i	−0.410314	+	0.911944i	$0.634581\pi$
$80$	553031.	−	860533.i	1.08014	−	1.68073i
$81$	49675.2	+	31924.3i	0.0934726	+	0.0600712i
$82$	1.04859e6	−	1.21014e6i	1.90180	−	2.19479i
$83$	−134936.	+	459551.i	−0.235990	+	0.803709i	0.753291	+	0.657687i	$0.228465\pi$
$83$	−134936.	+	459551.i	−0.235990	+	0.803709i	−0.989281	+	0.146022i	$0.953353\pi$
$84$	878106.	−	126253.i	1.48153	−	0.213011i
$85$	−530697.	−	612457.i	−0.864151	−	0.997284i
$86$	829837.	−	378974.i	1.30466	−	0.595818i
$87$	566880.	−	166451.i	0.860862	−	0.252772i
$88$	−784630.	−	358329.i	−1.15138	−	0.525815i
$89$	−1.17507e6	−	168949.i	−1.66683	−	0.239655i	−0.756639	−	0.653833i	$-0.773160\pi$
$89$	−1.17507e6	−	168949.i	−1.66683	−	0.239655i	−0.910196	+	0.414178i	$0.864069\pi$
$90$	232007.	+	361010.i	0.318254	+	0.495213i
$91$			920184.i			1.22110i
$92$	1.28635e6	−	1.26810e6i	1.65194	−	1.62851i
$93$	−147476.			−0.183347
$94$	−741003.	+	476214.i	−0.892147	+	0.573348i
$95$	84088.5	−	584848.i	0.0980766	−	0.682138i
$96$	−286707.	+	627801.i	−0.324060	+	0.709592i
$97$	77644.4	+	264433.i	0.0850737	+	0.289734i	0.991031	−	0.133636i	$-0.0426652\pi$
$97$	77644.4	+	264433.i	0.0850737	+	0.289734i	−0.905957	+	0.423370i	$0.860847\pi$
$98$	177391.	+	388432.i	0.188475	+	0.412703i
$99$	128675.	−	111497.i	0.132614	−	0.114910i
$100$	−19988.2	−	139021.i	−0.0199882	−	0.139021i
$101$	378043.	+	111003.i	0.366924	+	0.107739i	0.459997	−	0.887921i	$-0.347851\pi$
$101$	378043.	+	111003.i	0.366924	+	0.107739i	−0.0930723	+	0.995659i	$0.529669\pi$
$102$	1.14860e6	+	995269.i	1.08235	+	0.937865i
$103$	568879.	−	885193.i	0.520605	−	0.810077i	−0.477025	−	0.878890i	$-0.658285\pi$
$103$	568879.	−	885193.i	0.520605	−	0.810077i	0.997630	+	0.0688127i	$0.0219211\pi$
$104$	−2.48607e6	−	1.59770e6i	−2.21011	−	1.42035i
$105$	−474108.	+	547150.i	−0.409552	+	0.472649i
$106$	−374244.	+	1.27456e6i	−0.314222	+	1.07014i
$107$	−1.22079e6	+	175523.i	−0.996527	+	0.143279i	−0.621232	−	0.783626i	$-0.713368\pi$
$107$	−1.22079e6	+	175523.i	−0.996527	+	0.143279i	−0.375295	+	0.926905i	$0.622459\pi$
$108$	−368271.	−	425008.i	−0.292346	−	0.337385i
$109$	1.58621e6	−	724396.i	1.22484	−	0.559367i	0.305262	−	0.952268i	$-0.401256\pi$
$109$	1.58621e6	−	724396.i	1.22484	−	0.559367i	0.919581	+	0.392902i	$0.128529\pi$
$110$	1.18724e6	−	348604.i	0.891989	−	0.261912i
$111$	−267677.	−	122244.i	−0.195723	−	0.0893837i
$112$	−3.20352e6	−	460597.i	−2.28020	−	0.327844i
$113$	−569398.	−	886000.i	−0.394621	−	0.614042i	0.585917	−	0.810371i	$-0.300734\pi$
$113$	−569398.	−	886000.i	−0.394621	−	0.614042i	−0.980538	+	0.196329i	$0.937098\pi$
$114$			1.10810e6i			0.747938i
$115$	−115664.	+	1.46957e6i	−0.0760507	+	0.966266i
$116$	−5.62673e6			−3.60481
$117$	490716.	−	315364.i	0.306389	−	0.196904i
$118$	−621562.	+	4.32306e6i	−0.378302	+	2.63115i
$119$	−1.06515e6	+	2.33235e6i	−0.632076	+	1.38405i
$120$	−655054.	−	2.23091e6i	−0.379082	−	1.29104i
$121$	531994.	+	1.16490e6i	0.300296	+	0.657558i
$122$	3.79697e6	−	3.29010e6i	2.09102	−	1.81188i
$123$	−243709.	−	1.69503e6i	−0.130965	−	0.910884i
$124$	1.34763e6	+	395699.i	0.706814	+	0.207539i
$125$	1.51731e6	+	1.31476e6i	0.776865	+	0.673157i
$126$	734060.	−	1.14222e6i	0.366961	−	0.571002i
$127$	1.62908e6	+	1.04695e6i	0.795300	+	0.511109i	0.874079	−	0.485784i	$-0.161466\pi$
$127$	1.62908e6	+	1.04695e6i	0.795300	+	0.511109i	−0.0787787	+	0.996892i	$0.525102\pi$
$128$	−853362.	+	984833.i	−0.406915	+	0.469605i
$129$	274871.	−	936124.i	0.128044	−	0.436078i
$130$	4.19604e6	−	603300.i	1.90990	−	0.274602i
$131$	−1.56395e6	−	1.80490e6i	−0.695679	−	0.802857i	0.292483	−	0.956271i	$-0.405519\pi$
$131$	−1.56395e6	−	1.80490e6i	−0.695679	−	0.802857i	−0.988162	+	0.153414i	$0.950973\pi$
$132$	−1.47499e6	+	673604.i	−0.641307	+	0.292875i
$133$	−1.79373e6	+	526688.i	−0.762436	+	0.223871i
$134$	5.64190e6	+	2.57657e6i	2.34483	+	1.07085i
$135$	454270.	+	65314.1i	0.184634	+	0.0265464i
$136$	−4.45193e6	−	6.92734e6i	−1.76983	−	2.75391i
$137$			350111.i			0.136158i	0.997680	+	0.0680792i	$0.0216870\pi$
$137$			350111.i			0.136158i	−0.997680	+	0.0680792i	$0.978313\pi$
$138$	−177516.	−	2.75885e6i	−0.0675463	−	1.04976i
$139$	−816222.			−0.303923			−0.151962	−	0.988386i	$-0.548559\pi$
$139$	−816222.			−0.303923			−0.151962	+	0.988386i	$0.548559\pi$
$140$	5.80045e6	−	3.72772e6i	2.11387	−	1.35850i
$141$	−134063.	+	932426.i	−0.0478245	+	0.332627i
$142$	2.80200e6	−	6.13552e6i	0.978594	−	2.14282i
$143$	−473853.	−	1.61380e6i	−0.162045	−	0.551875i
$144$	852279.	+	1.86623e6i	0.285426	+	0.624997i
$145$	3.47034e6	−	3.00707e6i	1.13833	−	0.986368i
$146$	1.33290e6	+	9.27050e6i	0.428290	+	2.97882i
$147$	438184.	+	128662.i	0.137944	+	0.0405041i
$148$	2.11802e6	+	1.83527e6i	0.653347	+	0.566128i
$149$	−3.21081e6	+	4.99612e6i	−0.970636	+	1.51034i	−0.114607	+	0.993411i	$0.536561\pi$
$149$	−3.21081e6	+	4.99612e6i	−0.970636	+	1.51034i	−0.856029	+	0.516928i	$0.827075\pi$
$150$	−180835.	−	116215.i	−0.0535807	−	0.0344342i
$151$	−2.69016e6	+	3.10461e6i	−0.781353	+	0.901729i	−0.997206	−	0.0746967i	$-0.976201\pi$
$151$	−2.69016e6	+	3.10461e6i	−0.781353	+	0.901729i	0.215854	+	0.976426i	$0.430747\pi$
$152$	1.69147e6	−	5.76063e6i	0.481653	−	1.64036i
$153$	1.60884e6	−	231316.i	0.449199	−	0.0645851i
$154$	−2.56374e6	−	2.95872e6i	−0.701960	−	0.810106i
$155$	−1.04263e6	+	476155.i	−0.279987	+	0.127866i
$156$	−5.33030e6	+	1.56512e6i	−1.40403	+	0.412262i
$157$	−3.14341e6	−	1.43555e6i	−0.812273	−	0.370953i	−0.0344268	−	0.999407i	$-0.510961\pi$
$157$	−3.14341e6	−	1.43555e6i	−0.812273	−	0.370953i	−0.777846	+	0.628454i	$0.783688\pi$
$158$	−4.08454e6	−	587268.i	−1.03555	−	0.148890i
$159$	768053.	+	1.19511e6i	0.191073	+	0.297316i
$160$			5.36415e6i			1.30961i
$161$	4.38149e6	−	1.59865e6i	1.04989	−	0.383068i
$162$	−860699.			−0.202445
$163$	−4.30061e6	+	2.76383e6i	−0.993041	+	0.638189i	−0.932951	−	0.360004i	$-0.882775\pi$
$163$	−4.30061e6	+	2.76383e6i	−0.993041	+	0.638189i	−0.0600903	+	0.998193i	$0.519139\pi$
$164$	−2.32101e6	+	1.61430e7i	−0.526195	+	3.65976i
$165$	549721.	−	1.20372e6i	0.122374	−	0.267963i
$166$	−1.96683e6	−	6.69841e6i	−0.429975	−	1.46436i
$167$	−1.12077e6	−	2.45414e6i	−0.240639	−	0.526927i	0.750322	−	0.661072i	$-0.229898\pi$
$167$	−1.12077e6	−	2.45414e6i	−0.240639	−	0.526927i	−0.990962	+	0.134146i	$0.957171\pi$
$168$	−5.55966e6	+	4.81747e6i	−1.17252	+	1.01599i
$169$	−133131.	−	925949.i	−0.0275817	−	0.191835i
$170$	1.13339e7	+	3.32792e6i	2.30691	+	0.677371i
$171$	895618.	+	776058.i	0.179116	+	0.155205i
$172$	−5.02350e6	+	7.81672e6i	−0.987237	+	1.53617i
$173$	5.08942e6	+	3.27077e6i	0.982946	+	0.631701i	0.930256	−	0.366910i	$-0.119584\pi$
$173$	5.08942e6	+	3.27077e6i	0.982946	+	0.631701i	0.0526895	+	0.998611i	$0.483221\pi$
$174$	−5.63946e6	+	6.50828e6i	−1.07051	+	1.23543i
$175$	102171.	−	347963.i	0.0190640	−	0.0649260i
$176$	5.85544e6	−	841885.i	1.07404	−	0.154424i
$177$	3.05878e6	+	3.53002e6i	0.551605	+	0.636586i
$178$	1.57402e7	−	7.18830e6i	2.79094	−	1.27458i
$179$	−7.17605e6	+	2.10708e6i	−1.25120	+	0.367385i	−0.839212	−	0.543805i	$-0.816983\pi$
$179$	−7.17605e6	+	2.10708e6i	−1.25120	+	0.367385i	−0.411987	+	0.911190i	$0.635165\pi$
$180$	−3.97584e6	−	1.81571e6i	−0.681728	−	0.311335i
$181$	6.11930e6	+	879823.i	1.03197	+	0.148375i	0.637432	−	0.770506i	$-0.279997\pi$
$181$	6.11930e6	+	879823.i	1.03197	+	0.148375i	0.394535	+	0.918881i	$0.370906\pi$
$182$	−7.25141e6	−	1.12834e7i	−1.20284	−	1.87166i
$183$		−	5.37309e6i		−	0.876741i
$184$	−3.28842e6	+	1.46132e7i	−0.527879	+	2.34581i
$185$	−2.28712e6			−0.361222
$186$	1.80837e6	−	1.16217e6i	0.281027	−	0.180605i
$187$	666975.	−	4.63892e6i	0.101996	−	0.709401i
$188$	3.72689e6	−	8.16074e6i	0.560883	−	1.22816i
$189$	−409095.	−	1.39325e6i	−0.0605953	−	0.206369i
$190$	3.57773e6	+	7.83413e6i	0.521610	+	1.14217i
$191$	−1.10826e6	+	960317.i	−0.159054	+	0.137821i	−0.730752	−	0.682643i	$-0.760830\pi$
$191$	−1.10826e6	+	960317.i	−0.159054	+	0.137821i	0.571698	+	0.820464i	$0.306285\pi$
$192$	−232934.	−	1.62009e6i	−0.0329101	−	0.228895i
$193$	−240635.	−	70656.7i	−0.0334724	−	0.00982837i	0.264954	−	0.964261i	$-0.414643\pi$
$193$	−240635.	−	70656.7i	−0.0334724	−	0.00982837i	−0.298426	+	0.954433i	$0.596462\pi$
$194$	−3.03592e6	−	2.63064e6i	−0.415800	−	0.360293i
$195$	2.45108e6	−	3.81395e6i	0.330562	−	0.514364i
$196$	−3.65887e6	−	2.35142e6i	−0.485936	−	0.312292i
$197$	−8.18181e6	+	9.44232e6i	−1.07017	+	1.23504i	−0.0993895	+	0.995049i	$0.531689\pi$
$197$	−8.18181e6	+	9.44232e6i	−1.07017	+	1.23504i	−0.970776	+	0.239988i	$0.922856\pi$
$198$	−699184.	+	2.38120e6i	−0.0900733	+	0.306761i
$199$	8.52974e6	−	1.22639e6i	1.08237	−	0.155622i	0.422026	−	0.906584i	$-0.361319\pi$
$199$	8.52974e6	−	1.22639e6i	1.08237	−	0.155622i	0.660345	+	0.750962i	$0.270410\pi$
$200$	762697.	+	880199.i	0.0953371	+	0.110025i
$201$	6.03379e6	−	2.75554e6i	0.743022	−	0.339327i
$202$	−5.51035e6	+	1.61799e6i	−0.668537	+	0.196300i
$203$	−1.32157e7	−	6.03540e6i	−1.57980	−	0.721470i
$204$	−1.53221e7	−	2.20299e6i	−1.80480	−	0.259491i
$205$	−7.19573e6	−	1.11968e7i	−0.835243	−	1.29966i
$206$			1.53373e7i			1.75448i
$207$	−2.35415e6	−	1.78868e6i	−0.265413	−	0.201660i
$208$	2.02670e7			2.25217
$209$	2.87459e6	−	1.84738e6i	0.314874	−	0.202357i
$210$	1.50182e6	−	1.04454e7i	0.162166	−	1.12789i
$211$	−1.25269e6	+	2.74301e6i	−0.133351	+	0.291998i	−0.964514	−	0.264030i	$-0.914948\pi$
$211$	−1.25269e6	+	2.74301e6i	−0.133351	+	0.291998i	0.831163	+	0.556028i	$0.187675\pi$
$212$	−3.81176e6	−	1.29817e7i	−0.400054	−	1.36246i
$213$	−2.99662e6	−	6.56169e6i	−0.310094	−	0.679011i
$214$	1.35863e7	−	1.17726e7i	1.38631	−	1.20124i
$215$	−1.07916e6	−	7.50573e6i	−0.108585	−	0.755227i
$216$	4.47446e6	+	1.31382e6i	0.443997	+	0.130369i
$217$	2.74078e6	+	2.37490e6i	0.268223	+	0.232416i
$218$	−1.37417e7	+	2.13826e7i	−1.32639	+	2.06391i
$219$	8.42632e6	+	5.41527e6i	0.802242	+	0.515570i
$220$	−8.25307e6	+	9.52455e6i	−0.775082	+	0.894492i
$221$	4.52360e6	−	1.54060e7i	0.419090	−	1.42729i
$222$	4.24561e6	−	610427.i	0.388044	−	0.0557924i
$223$	−7.71343e6	−	8.90178e6i	−0.695558	−	0.802716i	0.292588	−	0.956239i	$-0.405484\pi$
$223$	−7.71343e6	−	8.90178e6i	−0.695558	−	0.802716i	−0.988145	+	0.153522i	$0.950938\pi$
$224$	1.54382e7	−	7.05039e6i	1.37358	−	0.627291i
$225$	−220578.	+	64767.4i	−0.0193648	+	0.00568603i
$226$	1.39640e7	+	6.37716e6i	1.20972	+	0.552462i
$227$	3.98776e6	+	573354.i	0.340919	+	0.0490168i	0.310648	−	0.950525i	$-0.399454\pi$
$227$	3.98776e6	+	573354.i	0.340919	+	0.0490168i	0.0302711	+	0.999542i	$0.490363\pi$
$228$	−6.10183e6	−	9.49463e6i	−0.514820	−	0.801076i
$229$			1.90215e7i			1.58394i	0.610561	+	0.791969i	$0.290944\pi$
$229$			1.90215e7i			1.58394i	−0.610561	+	0.791969i	$0.709056\pi$
$230$	−1.01625e7	−	1.89315e7i	−0.835250	−	1.55597i
$231$	−4.18688e6			−0.339668
$232$	3.92521e7	−	2.52258e7i	3.14340	−	2.02014i
$233$	241610.	−	1.68043e6i	0.0191006	−	0.132848i	−0.978040	−	0.208418i	$-0.933169\pi$
$233$	241610.	−	1.68043e6i	0.0191006	−	0.132848i	0.997140	+	0.0755703i	$0.0240777\pi$
$234$	−3.53203e6	+	7.73406e6i	−0.275662	+	0.603615i
$235$	2.06271e6	+	7.02496e6i	0.158941	+	0.541303i
$236$	−1.84794e7	−	4.04642e7i	−1.40589	−	3.07847i
$237$	−3.33525e6	+	2.89001e6i	−0.250544	+	0.217097i
$238$	−5.31883e6	−	3.69933e7i	−0.394535	−	2.74405i
$239$	−309846.	−	90979.0i	−0.0226962	−	0.00666419i	0.270365	−	0.962758i	$-0.412856\pi$
$239$	−309846.	−	90979.0i	−0.0226962	−	0.00666419i	−0.293061	+	0.956094i	$0.594674\pi$
$240$	1.20510e7	+	1.04422e7i	0.871742	+	0.755369i
$241$	682230.	−	1.06157e6i	0.0487393	−	0.0758399i	−0.816029	−	0.578011i	$-0.803829\pi$
$241$	682230.	−	1.06157e6i	0.0487393	−	0.0758399i	0.864768	+	0.502171i	$0.167465\pi$
$242$	−1.57033e7	−	1.00919e7i	−1.10801	−	0.712075i
$243$	−602788.	+	695654.i	−0.0420093	+	0.0484814i
$244$	−1.44168e7	+	4.90990e7i	−0.992426	+	3.37989i
$245$	3.51330e6	−	505137.i	0.238901	−	0.0343487i
$246$	1.63459e7	+	1.88642e7i	1.09800	+	1.26716i
$247$	1.06488e7	−	4.86315e6i	0.706660	−	0.322721i
$248$	−1.11751e7	+	3.28130e6i	−0.732648	+	0.215125i
$249$	−6.79142e6	−	3.10154e6i	−0.439909	−	0.200899i
$250$	−2.89663e7	−	4.16472e6i	−1.85384	−	0.266542i
$251$	9.87173e6	+	1.53607e7i	0.624270	+	0.971383i	0.999020	+	0.0442569i	$0.0140920\pi$
$251$	9.87173e6	+	1.53607e7i	0.624270	+	0.971383i	−0.374750	+	0.927126i	$0.622272\pi$
$252$			1.38291e7i			0.864155i
$253$	−6.86092e6	+	5.05994e6i	−0.423663	+	0.312452i
$254$	−2.82263e7			−1.72248
$255$	1.06274e7	−	6.82982e6i	0.640925	−	0.411897i
$256$	3.65950e6	−	2.54524e7i	0.218123	−	1.51708i
$257$	9.98733e6	−	2.18692e7i	0.588370	−	1.28835i	−0.348053	−	0.937475i	$-0.613157\pi$
$257$	9.98733e6	−	2.18692e7i	0.588370	−	1.28835i	0.936422	−	0.350875i	$-0.114116\pi$
$258$	4.00652e6	+	1.36450e7i	0.233296	+	0.794535i
$259$	3.00609e6	+	6.58241e6i	0.173022	+	0.378866i
$260$	−3.26311e7	+	2.82750e7i	−1.85657	+	1.60873i
$261$	1.31070e6	+	9.11611e6i	0.0737193	+	0.512729i
$262$	3.34006e7	+	9.80731e6i	1.85717	+	0.545313i
$263$	2.05520e7	+	1.78084e7i	1.12976	+	0.978944i	0.999921	−	0.0125904i	$-0.00400775\pi$
$263$	2.05520e7	+	1.78084e7i	1.12976	+	0.978944i	0.129841	+	0.991535i	$0.458553\pi$
$264$	7.26961e6	−	1.13117e7i	0.395093	−	0.614777i
$265$	9.28867e6	+	5.96947e6i	0.499133	+	0.320773i
$266$	1.78445e7	−	2.05936e7i	0.948111	−	1.09418i
$267$	5.21370e6	−	1.77562e7i	0.273913	−	0.932861i
$268$	−6.25299e7	+	8.99044e6i	−3.24850	+	0.467064i
$269$	1.53397e7	+	1.77030e7i	0.788061	+	0.909471i	0.997664	−	0.0683154i	$-0.0217624\pi$
$269$	1.53397e7	+	1.77030e7i	0.788061	+	0.909471i	−0.209602	+	0.977787i	$0.567217\pi$
$270$	−6.08501e6	+	2.77893e6i	−0.309150	+	0.141184i
$271$	−2.48744e7	+	7.30377e6i	−1.24981	+	0.366977i	−0.838693	−	0.544605i	$-0.816680\pi$
$271$	−2.48744e7	+	7.30377e6i	−1.24981	+	0.366977i	−0.411117	+	0.911582i	$0.634861\pi$
$272$	5.13699e7	+	2.34599e7i	2.55271	+	1.16579i
$273$	−1.41983e7	−	2.04140e6i	−0.697826	−	0.100332i
$274$	−2.75901e6	−	4.29310e6i	−0.134122	−	0.208699i
$275$			662862.i			0.0318731i
$276$	1.67128e7	+	2.26613e7i	0.794916	+	1.07785i
$277$	4.44841e6			0.209298			0.104649	−	0.994509i	$-0.466628\pi$
$277$	4.44841e6			0.209298			0.104649	+	0.994509i	$0.466628\pi$
$278$	1.00086e7	−	6.43214e6i	0.465843	−	0.299379i
$279$	327171.	−	2.27553e6i	0.0150648	−	0.104778i
$280$	−2.37518e7	+	5.20092e7i	−1.08199	+	2.36923i
$281$	−3.99055e6	−	1.35905e7i	−0.179851	−	0.612517i	−0.999229	−	0.0392629i	$-0.987499\pi$
$281$	−3.99055e6	−	1.35905e7i	−0.179851	−	0.612517i	0.819378	−	0.573254i	$-0.194319\pi$
$282$	−5.70398e6	−	1.24900e7i	−0.254350	−	0.556948i
$283$	−2.41588e6	+	2.09337e6i	−0.106590	+	0.0923607i	−0.706525	−	0.707688i	$-0.749738\pi$
$283$	−2.41588e6	+	2.09337e6i	−0.106590	+	0.0923607i	0.599935	+	0.800048i	$0.295193\pi$
$284$	9.77702e6	+	6.80007e7i	0.426827	+	2.96864i
$285$	8.83754e6	+	2.59493e6i	0.381765	+	0.112096i
$286$	1.85278e7	+	1.60544e7i	0.792000	+	0.686272i
$287$	−2.27669e7	+	3.54261e7i	−0.963073	+	1.49857i
$288$	−9.05079e6	−	5.81659e6i	−0.378887	−	0.243496i
$289$	1.34920e7	−	1.55706e7i	0.558963	−	0.645077i
$290$	−1.88569e7	+	6.42206e7i	−0.773171	+	2.63318i
$291$	−4.25239e6	+	611402.i	−0.172566	+	0.0248112i
$292$	−6.24693e7	−	7.20934e7i	−2.50910	−	2.89565i
$293$	2.46749e6	−	1.12687e6i	0.0980963	−	0.0447991i	−0.365763	−	0.930708i	$-0.619192\pi$
$293$	2.46749e6	−	1.12687e6i	0.0980963	−	0.0447991i	0.463859	+	0.885909i	$0.346464\pi$
$294$	−6.38697e6	+	1.87538e6i	−0.251335	+	0.0737986i
$295$	3.30224e7	+	1.50808e7i	1.28630	+	0.587434i
$296$	−2.30032e7	−	3.30736e6i	−0.886978	−	0.127528i
$297$	1.43492e6	+	2.23278e6i	0.0547720	+	0.0852269i
$298$		−	8.65655e7i		−	3.27112i
$299$	−2.57333e7	+	1.38137e7i	−0.962681	+	0.516770i
$300$	2.18940e6			0.0810890
$301$	−2.01833e7	+	1.29710e7i	−0.740105	+	0.475637i
$302$	8.52153e6	−	5.92686e7i	0.309383	−	2.15181i
$303$	−2.55143e6	+	5.58686e6i	−0.0917184	+	0.200835i
$304$	1.16003e7	+	3.95070e7i	0.412903	+	1.40622i
$305$	−1.73481e7	−	3.79870e7i	−0.611437	−	1.33886i
$306$	−1.79049e7	+	1.55147e7i	−0.624897	+	0.541476i
$307$	6.29011e6	+	4.37487e7i	0.217392	+	1.51199i	0.747613	+	0.664134i	$0.231200\pi$
$307$	6.29011e6	+	4.37487e7i	0.217392	+	1.51199i	−0.530222	+	0.847859i	$0.677891\pi$
$308$	3.82594e7	+	1.12340e7i	1.30944	+	0.384487i
$309$	1.23963e7	+	1.07415e7i	0.420162	+	0.364072i
$310$	9.03262e6	−	1.40550e7i	0.303200	−	0.471788i
$311$	5.85052e6	+	3.75990e6i	0.194497	+	0.124996i	0.634265	−	0.773116i	$-0.281303\pi$
$311$	5.85052e6	+	3.75990e6i	0.194497	+	0.124996i	−0.439768	+	0.898112i	$0.644939\pi$
$312$	3.01675e7	−	3.48151e7i	0.993288	−	1.14632i
$313$	−1.13999e6	+	3.88245e6i	−0.0371765	+	0.126611i	−0.975991	−	0.217813i	$-0.930108\pi$
$313$	−1.13999e6	+	3.88245e6i	−0.0371765	+	0.126611i	0.938814	+	0.344424i	$0.111926\pi$
$314$	4.98575e7	−	7.16843e6i	1.61043	−	0.231545i
$315$	−7.39061e6	−	8.52922e6i	−0.236455	−	0.272884i
$316$	3.82316e7	−	1.74598e7i	1.21161	−	0.553322i
$317$	5.18761e7	−	1.52322e7i	1.62851	−	0.478173i	0.665220	−	0.746647i	$-0.268338\pi$
$317$	5.18761e7	−	1.52322e7i	1.62851	−	0.478173i	0.963287	+	0.268475i	$0.0865195\pi$
$318$	−1.88359e7	−	8.60207e6i	−0.585741	−	0.267499i
$319$	2.62853e7	+	3.77926e6i	0.809731	+	0.116422i
$320$	−6.87758e6	−	1.07017e7i	−0.209887	−	0.326591i
$321$		−	1.92259e7i		−	0.581262i
$322$	−4.11284e7	+	5.41307e7i	−1.23190	+	1.62135i
$323$	3.26204e7			0.968013
$324$	7.37478e6	−	4.73948e6i	0.216827	−	0.139346i
$325$	−323192.	+	2.24785e6i	−0.00941479	+	0.0654813i
$326$	3.09545e7	−	6.77809e7i	0.893452	−	1.95639i
$327$	7.65833e6	+	2.60819e7i	0.219024	+	0.745926i
$328$	−5.61811e7	−	1.23019e8i	−1.59209	−	3.48620i
$329$	1.75069e7	−	1.51698e7i	0.491612	−	0.425984i
$330$	2.74504e6	+	1.90922e7i	0.0763848	+	0.531268i
$331$	−4.42588e7	−	1.29956e7i	−1.22044	−	0.358353i	−0.392805	−	0.919622i	$-0.628495\pi$
$331$	−4.42588e7	−	1.29956e7i	−1.22044	−	0.358353i	−0.827634	+	0.561269i	$0.810313\pi$
$332$	5.37377e7	+	4.65640e7i	1.46847	+	1.27244i
$333$	2.48003e6	−	3.85900e6i	0.0671621	−	0.104506i
$334$	3.30826e7	+	2.12609e7i	0.887892	+	0.570613i
$335$	3.37612e7	−	3.89625e7i	0.898014	−	1.03636i
$336$	1.42138e7	−	4.84078e7i	0.374708	−	1.27614i
$337$	3.76576e7	−	5.41434e6i	0.983927	−	0.141467i	0.368471	−	0.929639i	$-0.379881\pi$
$337$	3.76576e7	−	5.41434e6i	0.983927	−	0.141467i	0.615455	+	0.788172i	$0.288972\pi$
$338$	8.92931e6	+	1.03050e7i	0.231242	+	0.266868i
$339$	1.49340e7	−	6.82012e6i	0.383333	−	0.175062i
$340$	−1.15438e8	+	3.38957e7i	−2.93705	+	0.862397i
$341$	−6.02968e6	−	2.75366e6i	−0.152066	−	0.0694461i
$342$	−1.70978e7	−	2.45829e6i	−0.427427	−	0.0614547i
$343$	1.83108e7	+	2.84921e7i	0.453758	+	0.706062i
$344$		−	7.70510e7i		−	1.89279i
$345$	−2.24185e7	−	5.04486e6i	−0.545947	−	0.122855i
$346$	−8.81819e7			−2.12888
$347$	−5.43823e7	+	3.49494e7i	−1.30157	+	0.836471i	−0.993382	−	0.114853i	$-0.963360\pi$
$347$	−5.43823e7	+	3.49494e7i	−1.30157	+	0.836471i	−0.308192	+	0.951324i	$0.599724\pi$
$348$	1.24827e7	−	8.68192e7i	0.296191	−	2.06005i
$349$	−2.02816e7	+	4.44104e7i	−0.477117	+	1.04474i	0.506129	+	0.862458i	$0.331076\pi$
$349$	−2.02816e7	+	4.44104e7i	−0.477117	+	1.04474i	−0.983246	+	0.182283i	$0.941651\pi$
$350$	1.48925e6	+	5.07191e6i	0.0347346	+	0.118295i
$351$	3.77736e6	+	8.27127e6i	0.0873509	+	0.191272i
$352$	−2.34445e7	+	2.03148e7i	−0.537543	+	0.465783i
$353$	375160.	+	2.60930e6i	0.00852889	+	0.0593197i	0.993641	−	0.112591i	$-0.0359150\pi$
$353$	375160.	+	2.60930e6i	0.00852889	+	0.0593197i	−0.985113	+	0.171911i	$0.945006\pi$
$354$	−6.53250e7	−	1.91811e7i	−1.47255	−	0.432379i
$355$	−4.23713e7	−	3.67150e7i	−0.947081	−	0.820650i
$356$	−9.52849e7	+	1.48266e8i	−2.11190	+	3.28619i
$357$	−3.36246e7	−	2.16092e7i	−0.739015	−	0.474936i
$358$	7.13890e7	−	8.23872e7i	1.55590	−	1.79561i
$359$	−1.35863e6	+	4.62705e6i	−0.0293641	+	0.100005i	−0.972871	−	0.231347i	$-0.925687\pi$
$359$	−1.35863e6	+	4.62705e6i	−0.0293641	+	0.100005i	0.943507	+	0.331352i	$0.107505\pi$
$360$	3.58757e7	−	5.15815e6i	0.768941	−	0.110557i
$361$	−1.52336e7	−	1.75805e7i	−0.323802	−	0.373688i
$362$	−8.19689e7	+	3.74340e7i	−1.72792	+	0.789114i
$363$	−1.91544e7	+	5.62425e6i	−0.400451	+	0.117583i
$364$	1.24265e8	+	5.67501e7i	2.57659	+	1.17669i
$365$	7.70570e7	+	1.10791e7i	1.58465	+	0.227838i
$366$	4.23420e7	+	6.58855e7i	0.863632	+	1.34384i
$367$			8.31652e7i			1.68245i	0.540682	+	0.841227i	$0.318166\pi$
$367$			8.31652e7i			1.68245i	−0.540682	+	0.841227i	$0.681834\pi$
$368$	−3.52102e7	−	9.65023e7i	−0.706522	−	1.93640i
$369$	2.66947e7			0.531307
$370$	2.80450e7	−	1.80234e7i	0.553668	−	0.355821i
$371$	4.97173e6	−	3.45791e7i	0.0973611	−	0.677161i
$372$	−9.09523e6	+	1.99158e7i	−0.176679	+	0.386873i
$373$	−1.86274e7	−	6.34392e7i	−0.358944	−	1.22245i	−0.919087	−	0.394055i	$-0.871072\pi$
$373$	−1.86274e7	−	6.34392e7i	−0.358944	−	1.22245i	0.560143	−	0.828396i	$-0.310746\pi$
$374$	2.83779e7	+	6.21390e7i	0.542457	+	1.18782i
$375$	−2.36526e7	+	2.04951e7i	−0.448523	+	0.388647i
$376$	1.05875e7	+	7.36378e7i	0.199173	+	1.38528i
$377$	8.72942e7	+	2.56319e7i	1.62915	+	0.478362i
$378$	1.59957e7	+	1.38604e7i	0.296161	+	0.256625i
$379$	−1.29455e7	+	2.01436e7i	−0.237794	+	0.370014i	−0.939555	−	0.342398i	$-0.888761\pi$
$379$	−1.29455e7	+	2.01436e7i	−0.237794	+	0.370014i	0.701761	+	0.712412i	$0.252397\pi$
$380$	−7.37943e7	−	4.74247e7i	−1.34484	−	0.864278i
$381$	−1.97682e7	+	2.28137e7i	−0.357431	+	0.412498i
$382$	6.02201e6	−	2.05091e7i	0.108032	−	0.367922i
$383$	2.84044e7	−	4.08394e6i	0.505579	−	0.0726913i	0.115194	−	0.993343i	$-0.463251\pi$
$383$	2.84044e7	−	4.08394e6i	0.505579	−	0.0726913i	0.390385	+	0.920652i	$0.372342\pi$
$384$	−1.33026e7	−	1.53520e7i	−0.234932	−	0.271126i
$385$	−2.96006e7	+	1.35181e7i	−0.518702	+	0.236883i
$386$	3.50749e6	−	1.02989e6i	0.0609867	−	0.0179073i
$387$	1.38344e7	+	6.31796e6i	0.238686	+	0.109004i
$388$	4.04986e7	+	5.82281e6i	0.693337	+	0.0996868i
$389$	−5.39809e7	−	8.39960e7i	−0.917047	−	1.42695i	−0.904235	−	0.427035i	$-0.859558\pi$
$389$	−5.39809e7	−	8.39960e7i	−0.917047	−	1.42695i	−0.0128123	−	0.999918i	$-0.504078\pi$
$390$			6.60825e7i			1.11402i
$391$	−8.12150e7	+	5.22573e6i	−1.35865	+	0.0874212i
$392$	3.60662e7			0.598746
$393$	3.13187e7	−	2.01273e7i	0.515972	−	0.331595i
$394$	2.59173e7	−	1.80259e8i	0.423741	−	2.94718i
$395$	−1.42488e7	+	3.12005e7i	−0.231199	+	0.506255i
$396$	−7.12135e6	−	2.42531e7i	−0.114677	−	0.390554i
$397$	4.39187e6	+	9.61686e6i	0.0701905	+	0.153696i	0.941475	−	0.337082i	$-0.109440\pi$
$397$	4.39187e6	+	9.61686e6i	0.0701905	+	0.153696i	−0.871285	+	0.490778i	$0.836713\pi$
$398$	−9.49282e7	+	8.22558e7i	−1.50573	+	1.30472i
$399$	−4.14734e6	−	2.88454e7i	−0.0652907	−	0.454106i
$400$	−7.66387e6	−	2.25032e6i	−0.119748	−	0.0351612i
$401$	−7.02862e7	−	6.09033e7i	−1.09003	−	0.944513i	−0.0913428	−	0.995820i	$-0.529116\pi$
$401$	−7.02862e7	−	6.09033e7i	−1.09003	−	0.944513i	−0.998683	+	0.0513069i	$0.983661\pi$
$402$	−5.22723e7	+	8.13373e7i	−0.804625	+	1.25202i
$403$	−1.91048e7	−	1.22779e7i	−0.291896	−	0.187590i
$404$	3.83052e7	−	4.42065e7i	0.580916	−	0.670413i
$405$	−2.01557e6	+	6.86439e6i	−0.0303411	+	0.103332i
$406$	2.09614e8	−	3.01379e7i	3.13214	−	0.450334i
$407$	−8.66164e6	−	9.99607e6i	−0.128475	−	0.148268i
$408$	1.16764e8	−	5.33243e7i	1.71921	−	0.785135i
$409$	−8.58780e6	+	2.52161e6i	−0.125520	+	0.0368559i	−0.343889	−	0.939010i	$-0.611744\pi$
$409$	−8.58780e6	+	2.52161e6i	−0.125520	+	0.0368559i	0.218369	+	0.975866i	$0.429926\pi$
$410$	1.76470e8	+	8.05910e7i	2.56046	+	1.16932i
$411$	−5.40214e6	−	776711.i	−0.0778109	−	0.0111875i
$412$	−8.44558e7	−	1.31416e8i	−1.20764	−	1.87913i
$413$		−	1.14861e8i		−	1.63051i
$414$	4.29623e7	+	3.38138e6i	0.605461	+	0.0476533i
$415$	−5.80282e7			−0.811885
$416$	−8.94082e7	+	5.74592e7i	−1.24193	+	0.798141i
$417$	1.81076e6	−	1.25941e7i	0.0249720	−	0.173684i
$418$	−2.06904e7	+	4.53057e7i	−0.283296	+	0.620331i
$419$	−8.95103e6	−	3.04844e7i	−0.121683	−	0.414415i	0.876010	−	0.482292i	$-0.160196\pi$
$419$	−8.95103e6	−	3.04844e7i	−0.121683	−	0.414415i	−0.997694	+	0.0678770i	$0.978377\pi$
$420$	4.46498e7	+	9.77695e7i	0.602660	+	1.31964i
$421$	−6.42358e7	+	5.56606e7i	−0.860857	+	0.745937i	−0.968701	−	0.248231i	$-0.920151\pi$
$421$	−6.42358e7	+	5.56606e7i	−0.860857	+	0.745937i	0.107844	+	0.994168i	$0.465605\pi$
$422$	−6.25534e6	−	4.35068e7i	−0.0832364	−	0.578922i
$423$	−1.40897e7	−	4.13712e6i	−0.186158	−	0.0546609i
$424$	8.47904e7	+	7.34713e7i	1.11237	+	0.963874i
$425$	−3.42115e6	+	5.32341e6i	−0.0445662	+	0.0693463i
$426$	8.84536e7	+	5.68457e7i	1.14416	+	0.735307i
$427$	−8.65262e7	+	9.98566e7i	−1.11138	+	1.28261i
$428$	−5.15858e7	+	1.75685e8i	−0.657959	+	2.24080i
$429$	2.59518e7	−	3.73130e6i	0.328696	−	0.0472594i
$430$	7.23808e7	+	8.35319e7i	0.910370	+	1.05062i
$431$	4.36763e7	−	1.99463e7i	0.545524	−	0.249132i	−0.123537	−	0.992340i	$-0.539424\pi$
$431$	4.36763e7	−	1.99463e7i	0.545524	−	0.249132i	0.669061	+	0.743208i	$0.266697\pi$
$432$	−3.06863e7	+	9.01031e6i	−0.380621	+	0.111761i
$433$	5.96636e7	+	2.72474e7i	0.734929	+	0.335631i	0.747475	−	0.664290i	$-0.231266\pi$
$433$	5.96636e7	+	2.72474e7i	0.734929	+	0.335631i	−0.0125454	+	0.999921i	$0.503993\pi$
$434$	−5.23229e7	−	7.52290e6i	−0.640063	−	0.0920272i
$435$	3.86996e7	+	6.02177e7i	0.470152	+	0.731571i
$436$		−	2.58883e8i		−	3.12352i
$437$	−4.16565e7	−	4.22559e7i	−0.499158	−	0.506341i
$438$	−1.45999e8			−1.73751
$439$	8.04245e7	−	5.16857e7i	0.950594	−	0.610909i	0.0292139	−	0.999573i	$-0.490700\pi$
$439$	8.04245e7	−	5.16857e7i	0.950594	−	0.610909i	0.921380	+	0.388664i	$0.127063\pi$
$440$	1.48729e7	−	1.03444e8i	0.174598	−	1.21435i
$441$	−2.95733e6	+	6.47565e6i	−0.0344813	+	0.0755036i
$442$	6.59360e7	+	2.24558e8i	0.763583	+	2.60052i
$443$	−4.56657e7	−	9.99939e7i	−0.525266	−	1.15017i	−0.967407	−	0.253226i	$-0.918508\pi$
$443$	−4.56657e7	−	9.99939e7i	−0.525266	−	1.15017i	0.442142	−	0.896945i	$-0.354219\pi$
$444$	−3.30166e7	+	2.86090e7i	−0.377210	+	0.326854i
$445$	−2.04693e7	−	1.42367e8i	−0.232286	−	1.61559i
$446$	1.64732e8	+	4.83698e7i	1.85684	+	0.545217i
$447$	−6.99661e7	−	6.06259e7i	−0.783366	−	0.678791i
$448$	−2.17604e7	+	3.38598e7i	−0.242009	+	0.376574i
$449$	−5.11580e7	−	3.28772e7i	−0.565164	−	0.363209i	0.226645	−	0.973977i	$-0.427224\pi$
$449$	−5.11580e7	−	3.28772e7i	−0.565164	−	0.363209i	−0.791809	+	0.610769i	$0.790861\pi$
$450$	2.19436e6	−	2.53242e6i	0.0240807	−	0.0277906i
$451$	2.16853e7	−	7.38533e7i	0.236393	−	0.805082i
$452$	−1.54765e8	+	2.22519e7i	−1.67594	+	0.240963i
$453$	−4.19354e7	−	4.83961e7i	−0.451114	−	0.520614i
$454$	−5.34167e7	+	2.43946e7i	−0.570833	+	0.260691i
$455$	−1.06971e8	+	3.14094e7i	−1.13561	+	0.333446i
$456$	8.51329e7	+	3.88789e7i	0.897848	+	0.410033i
$457$	8.16909e7	+	1.17454e7i	0.855904	+	0.123060i	0.556278	−	0.830996i	$-0.312229\pi$
$457$	8.16909e7	+	1.17454e7i	0.855904	+	0.123060i	0.299626	+	0.954057i	$0.403138\pi$
$458$	−1.49897e8	−	2.33244e8i	−1.56026	−	2.42780i
$459$			2.53372e7i			0.262012i
$460$	1.91323e8	+	1.06252e8i	1.96560	+	1.09160i
$461$	1.30143e8			1.32837			0.664184	−	0.747569i	$-0.268779\pi$
$461$	1.30143e8			1.32837			0.664184	+	0.747569i	$0.268779\pi$
$462$	5.13400e7	−	3.29942e7i	0.520631	−	0.334589i
$463$	−1.61499e7	+	1.12325e8i	−0.162715	+	1.13171i	0.730774	+	0.682620i	$0.239160\pi$
$463$	−1.61499e7	+	1.12325e8i	−0.162715	+	1.13171i	−0.893488	+	0.449086i	$0.851750\pi$
$464$	−1.32930e8	+	2.91075e8i	−1.33066	+	2.91374i
$465$	−5.03392e6	−	1.71440e7i	−0.0500666	−	0.170511i
$466$	1.02798e7	+	2.25096e7i	0.101584	+	0.222439i
$467$	−5.77918e7	+	5.00769e7i	−0.567434	+	0.491684i	−0.890680	−	0.454630i	$-0.849771\pi$
$467$	−5.77918e7	+	5.00769e7i	−0.567434	+	0.491684i	0.323246	+	0.946315i	$0.395226\pi$
$468$	−1.23243e7	−	8.57175e7i	−0.120234	−	0.836242i
$469$	−1.56510e8	−	4.59553e7i	−1.51713	−	0.445469i
$470$	−8.06526e7	−	6.98859e7i	−0.776828	−	0.673125i
$471$	2.91238e7	−	4.53174e7i	0.278731	−	0.433713i
$472$	3.10322e8	+	1.99432e8i	2.95112	+	1.89657i
$473$	2.87175e7	−	3.31418e7i	0.271371	−	0.313179i
$474$	1.81228e7	−	6.17208e7i	0.170173	−	0.579557i
$475$	−4.56677e6	+	656602.i	−0.0426116	+	0.00612663i
$476$	2.49279e8	+	2.87684e8i	2.31135	+	2.66744i
$477$	−2.01443e7	+	9.19957e6i	−0.185608	+	0.0847642i
$478$	4.51632e6	−	1.32611e6i	0.0413524	−	0.0121422i
$479$	−2.01436e7	−	9.19927e6i	−0.183287	−	0.0837041i	0.321658	−	0.946856i	$-0.395760\pi$
$479$	−2.01436e7	−	9.19927e6i	−0.183287	−	0.0837041i	−0.504945	+	0.863152i	$0.668487\pi$
$480$	−8.27677e7	−	1.19002e7i	−0.748406	−	0.107605i
$481$	−2.44990e7	−	3.81211e7i	−0.220147	−	0.342555i
$482$			1.83933e7i			0.164255i
$483$	1.49466e7	+	7.11521e7i	0.132648	+	0.631460i
$484$	1.90123e8			1.67686
$485$	−2.80897e7	+	1.80522e7i	−0.246220	+	0.158236i
$486$	1.90943e6	−	1.32804e7i	0.0166340	−	0.115692i
$487$	−7.63460e6	+	1.67174e7i	−0.0660997	+	0.144738i	−0.939798	−	0.341729i	$-0.888987\pi$
$487$	−7.63460e6	+	1.67174e7i	−0.0660997	+	0.144738i	0.873699	+	0.486467i	$0.161715\pi$
$488$	−1.19550e8	−	4.07148e8i	−1.02870	−	3.50343i
$489$	−3.31046e7	−	7.24890e7i	−0.283114	−	0.619934i
$490$	−3.90999e7	+	3.38802e7i	−0.332343	+	0.287977i
$491$	2.12018e6	+	1.47462e7i	0.0179114	+	0.124576i	0.996815	−	0.0797446i	$-0.0254105\pi$
$491$	2.12018e6	+	1.47462e7i	0.0179114	+	0.124576i	−0.978904	+	0.204321i	$0.934501\pi$
$492$	−2.43934e8	−	7.16255e7i	−2.04822	−	0.601413i
$493$	1.91591e8	+	1.66014e8i	1.59895	+	1.38549i
$494$	−9.22536e7	+	1.43549e8i	−0.765248	+	1.19075i
$495$	1.73536e7	+	1.11525e7i	0.143079	+	0.0919510i
$496$	5.23072e7	−	6.03657e7i	0.428663	−	0.494704i
$497$	−4.99760e7	+	1.70203e8i	−0.407092	+	1.38643i
$498$	1.07718e8	−	1.54876e7i	0.872172	−	0.125399i
$499$	4.69154e7	+	5.41433e7i	0.377584	+	0.435755i	0.912454	−	0.409179i	$-0.134185\pi$
$499$	4.69154e7	+	5.41433e7i	0.377584	+	0.435755i	−0.534870	+	0.844934i	$0.679639\pi$
$500$	2.71127e8	−	1.23820e8i	2.16902	−	0.990556i
$501$	4.03533e7	−	1.18488e7i	0.320897	−	0.0942239i
$502$	−2.42097e8	−	1.10562e8i	−1.91372	−	0.873965i
$503$	6.95489e7	+	9.99963e6i	0.546496	+	0.0785742i	0.410032	−	0.912071i	$-0.365517\pi$
$503$	6.95489e7	+	9.99963e6i	0.546496	+	0.0785742i	0.136463	+	0.990645i	$0.456426\pi$
$504$	−6.19987e7	−	9.64718e7i	−0.484274	−	0.753544i
$505$			4.77361e7i			0.370657i
$506$	4.42551e7	−	1.16112e8i	0.341595	−	0.896245i
$507$	1.45825e7			0.111895
$508$	2.41853e8	−	1.55430e8i	1.84485	−	1.18561i
$509$	−2.77250e7	+	1.92832e8i	−0.210242	+	1.46226i	0.562107	+	0.827064i	$0.309991\pi$
$509$	−2.77250e7	+	1.92832e8i	−0.210242	+	1.46226i	−0.772349	+	0.635199i	$0.780918\pi$
$510$	−7.64930e7	+	1.67496e8i	−0.576648	+	1.26268i
$511$	−6.93941e7	−	2.36335e8i	−0.520068	−	1.77119i
$512$	1.21056e8	+	2.65076e8i	0.901938	+	1.97497i
$513$	−1.39613e7	+	1.20975e7i	−0.103413	+	0.0896076i
$514$	4.98719e7	+	3.46867e8i	0.367254	+	2.55431i
$515$	1.22321e8	+	3.59166e7i	0.895527	+	0.262951i
$516$	−1.09466e8	−	9.48528e7i	−0.796764	−	0.690400i
$517$	−2.28914e7	+	3.56198e7i	−0.165654	+	0.257762i
$518$	−8.87329e7	−	5.70252e7i	−0.638404	−	0.410277i
$519$	−6.17580e7	+	7.12725e7i	−0.441765	+	0.509824i
$520$	1.00872e8	−	3.43539e8i	0.717400	−	2.44324i
$521$	−1.05388e8	+	1.51525e7i	−0.745207	+	0.107145i	−0.504450	−	0.863441i	$-0.668305\pi$
$521$	−1.05388e8	+	1.51525e7i	−0.745207	+	0.107145i	−0.240757	+	0.970585i	$0.577396\pi$
$522$	−8.79104e7	−	1.01454e8i	−0.618057	−	0.713276i
$523$	−2.26461e8	+	1.03421e8i	−1.58303	+	0.722944i	−0.996227	−	0.0867886i	$-0.972340\pi$
$523$	−2.26461e8	+	1.03421e8i	−1.58303	+	0.722944i	−0.586799	+	0.809732i	$0.699612\pi$
$524$	−3.40193e8	+	9.98897e7i	−2.36446	+	0.694267i
$525$	5.14233e6	+	2.34842e6i	0.0355371	+	0.0162292i
$526$	−3.92348e8	−	5.64112e7i	−2.69597	−	0.387621i
$527$	−3.42120e7	−	5.32348e7i	−0.233747	−	0.363717i
$528$			9.22159e7i			0.626476i
$529$	1.10482e8	+	9.85315e7i	0.746316	+	0.665592i
$530$	−1.60940e8			−1.08103
$531$	−6.12532e7	+	3.93651e7i	−0.409115	+	0.262922i
$532$	−3.94981e7	+	2.74715e8i	−0.262326	+	1.82452i
$533$	1.09546e8	−	2.39873e8i	0.723463	−	1.58416i
$534$	7.59949e7	+	2.58815e8i	0.499069	+	1.69967i
$535$	−6.20745e7	−	1.35924e8i	−0.405370	−	0.887638i
$536$	3.95903e8	−	3.43052e8i	2.57095	−	2.22774i
$537$	−1.65919e7	−	1.15399e8i	−0.107146	−	0.745213i
$538$	−3.27603e8	−	9.61930e7i	−2.10379	−	0.617727i
$539$	1.55131e7	+	1.34422e7i	0.0990678	+	0.0858427i
$540$	3.68362e7	−	5.73183e7i	0.233934	−	0.364009i
$541$	6.52197e6	+	4.19141e6i	0.0411895	+	0.0264709i	0.561074	−	0.827766i	$-0.310388\pi$
$541$	6.52197e6	+	4.19141e6i	0.0411895	+	0.0264709i	−0.519884	+	0.854237i	$0.674025\pi$
$542$	2.47456e8	−	2.85579e8i	1.55417	−	1.79361i
$543$	−2.71510e7	+	9.24677e7i	−0.169584	+	0.577551i
$544$	−2.93130e8	+	4.21457e7i	−1.82081	+	0.261792i
$545$	1.38354e8	+	1.59669e8i	0.854675	+	0.986347i
$546$	1.90188e8	−	8.68558e7i	1.16843	−	0.533606i
$547$	9.02910e7	−	2.65118e7i	0.551674	−	0.161986i	0.00599749	−	0.999982i	$-0.498091\pi$
$547$	9.02910e7	−	2.65118e7i	0.551674	−	0.161986i	0.545676	+	0.837996i	$0.316273\pi$
$548$	4.72804e7	+	2.15922e7i	0.287302	+	0.131207i
$549$	8.29057e7	+	1.19200e7i	0.501034	+	0.0720378i
$550$	−5.22360e6	−	8.12809e6i	−0.0313966	−	0.0488540i
$551$			1.84835e8i			1.10492i
$552$	−2.18184e8	−	8.31587e7i	−1.29720	−	0.494414i
$553$	1.08524e8			0.641727
$554$	−5.45469e7	+	3.50551e7i	−0.320805	+	0.206169i
$555$	5.07391e6	−	3.52898e7i	0.0296800	−	0.206429i
$556$	−5.03384e7	+	1.10226e8i	−0.292870	+	0.641296i
$557$	−1.80667e7	−	6.15296e7i	−0.104547	−	0.356056i	0.890559	−	0.454869i	$-0.150314\pi$
$557$	−1.80667e7	−	6.15296e7i	−0.104547	−	0.356056i	−0.995106	+	0.0988125i	$0.968496\pi$
$558$	1.39202e7	+	3.04810e7i	0.0801205	+	0.175439i
$559$	1.13544e8	−	9.83863e7i	0.650022	−	0.563247i
$560$	−5.58044e7	−	3.88128e8i	−0.317764	−	2.21010i
$561$	7.00978e7	+	2.05826e7i	0.397023	+	0.116577i
$562$	1.56031e8	+	1.35202e8i	0.879028	+	0.761682i
$563$	5.31270e6	−	8.26673e6i	0.0297708	−	0.0463243i	−0.826049	−	0.563598i	$-0.809417\pi$
$563$	5.31270e6	−	8.26673e6i	0.0297708	−	0.0463243i	0.855820	+	0.517274i	$0.173053\pi$
$564$	1.17651e8	+	7.56094e7i	0.655778	+	0.421443i
$565$	8.35609e7	−	9.64344e7i	0.463295	−	0.534671i
$566$	1.31272e7	−	4.47072e7i	0.0723975	−	0.246563i
$567$	2.24051e7	−	3.22137e6i	0.122913	−	0.0176722i
$568$	−3.73066e8	−	4.30541e8i	−2.03582	−	2.34947i
$569$	8.22678e7	−	3.75704e7i	0.446574	−	0.203943i	−0.179418	−	0.983773i	$-0.557422\pi$
$569$	8.22678e7	−	3.75704e7i	0.446574	−	0.203943i	0.625992	+	0.779830i	$0.284694\pi$
$570$	−1.28816e8	+	3.78238e7i	−0.695577	+	0.204240i
$571$	−1.52664e8	−	6.97193e7i	−0.820028	−	0.374494i	−0.0391928	−	0.999232i	$-0.512479\pi$
$571$	−1.52664e8	−	6.97193e7i	−0.820028	−	0.374494i	−0.780835	+	0.624738i	$0.785206\pi$
$572$	−2.47157e8	−	3.55358e7i	−1.32064	−	0.189880i
$573$	−1.23588e7	−	1.92307e7i	−0.0656922	−	0.102219i
$574$		−	6.13811e8i		−	3.24563i
$575$	1.12647e7	−	2.36633e6i	0.0592538	−	0.0124472i
$576$	2.55144e7			0.133511
$577$	2.90838e8	−	1.86910e8i	1.51399	−	0.972983i	0.521159	−	0.853460i	$-0.325500\pi$
$577$	2.90838e8	−	1.86910e8i	1.51399	−	0.972983i	0.992831	−	0.119523i	$-0.0381365\pi$
$578$	−4.27382e7	+	2.97251e8i	−0.221326	+	1.53936i
$579$	1.62406e6	−	3.55619e6i	0.00836693	−	0.0183210i
$580$	−1.92062e8	−	6.54102e8i	−0.984366	−	3.35244i
$581$	7.62696e7	+	1.67007e8i	0.388887	+	0.851543i
$582$	4.73252e7	−	4.10076e7i	0.240062	−	0.208015i
$583$	9.08739e6	+	6.32042e7i	0.0458599	+	0.318963i
$584$	7.58996e8	+	2.22861e8i	3.81067	+	1.11891i
$585$	5.34108e7	+	4.62807e7i	0.266785	+	0.231170i
$586$	−2.13765e7	+	3.32625e7i	−0.106229	+	0.165296i
$587$	2.96523e8	+	1.90564e8i	1.46603	+	0.942162i	0.998300	+	0.0582930i	$0.0185657\pi$
$587$	2.96523e8	+	1.90564e8i	1.46603	+	0.942162i	0.467734	+	0.883869i	$0.345071\pi$
$588$	4.43990e7	−	5.12391e7i	0.218394	−	0.252040i
$589$	1.29985e7	−	4.42690e7i	0.0636134	−	0.216647i
$590$	−5.23768e8	+	7.53064e7i	−2.55025	+	0.366671i
$591$	−1.27542e8	−	1.47191e8i	−0.617860	−	0.713049i
$592$	1.44978e8	−	6.62090e7i	0.698772	−	0.319118i
$593$	3.35934e8	−	9.86392e7i	1.61098	−	0.473027i	0.652407	−	0.757869i	$-0.273759\pi$
$593$	3.35934e8	−	9.86392e7i	1.61098	−	0.473027i	0.958574	+	0.284842i	$0.0919413\pi$
$594$	−3.51903e7	−	1.60709e7i	−0.167905	−	0.0766797i
$595$	−3.07491e8	−	4.42105e7i	−1.45976	−	0.209882i
$596$	4.76677e8	+	7.41725e8i	2.25157	+	3.50351i
$597$			1.34333e8i			0.631334i
$598$	2.06688e8	−	3.72174e8i	0.966521	−	1.74037i
$599$	−2.35929e7			−0.109774			−0.0548871	−	0.998493i	$-0.517480\pi$
$599$	−2.35929e7			−0.109774			−0.0548871	+	0.998493i	$0.517480\pi$
$600$	−1.52733e7	+	9.81555e6i	−0.0707097	+	0.0454424i
$601$	740108.	−	5.14756e6i	0.00340935	−	0.0237125i	−0.988046	−	0.154161i	$-0.950733\pi$
$601$	740108.	−	5.14756e6i	0.00340935	−	0.0237125i	0.991455	+	0.130448i	$0.0416417\pi$
$602$	1.45274e8	−	3.18105e8i	0.665882	−	1.45808i
$603$	2.91316e7	+	9.92132e7i	0.132866	+	0.452499i
$604$	2.53350e8	+	5.54759e8i	1.14977	+	2.51764i
$605$	−1.17260e8	+	1.01606e8i	−0.529521	+	0.458833i
$606$	−1.27406e7	−	8.86130e7i	−0.0572497	−	0.398180i
$607$	−2.32210e6	−	681831.i	−0.0103828	−	0.00304867i	0.276537	−	0.961003i	$-0.410813\pi$
$607$	−2.32210e6	−	681831.i	−0.0103828	−	0.00304867i	−0.286920	+	0.957955i	$0.592631\pi$
$608$	−1.63181e8	−	1.41397e8i	−0.726038	−	0.629115i
$609$	1.22444e8	−	1.90526e8i	0.542106	−	0.843534i
$610$	5.12076e8	+	3.29091e8i	2.25603	+	1.44986i
$611$	−9.49950e7	+	1.09630e8i	−0.416463	+	0.480624i
$612$	6.79834e7	−	2.31530e8i	0.296585	−	1.01007i
$613$	1.64307e8	−	2.36238e7i	0.713306	−	0.102558i	0.223897	−	0.974613i	$-0.428122\pi$
$613$	1.64307e8	−	2.36238e7i	0.713306	−	0.102558i	0.489408	+	0.872055i	$0.337213\pi$
$614$	−4.21887e8	−	4.86883e8i	−1.82260	−	2.10339i
$615$	1.88727e8	−	8.61889e7i	0.811352	−	0.370532i
$616$	−3.17262e8	+	9.31567e7i	−1.35730	+	0.398540i
$617$	−1.59039e8	−	7.26304e7i	−0.677091	−	0.309217i	0.0470268	−	0.998894i	$-0.485025\pi$
$617$	−1.59039e8	−	7.26304e7i	−0.677091	−	0.309217i	−0.724117	+	0.689677i	$0.757753\pi$
$618$	−2.36652e8	−	3.40254e7i	−1.00264	−	0.144158i
$619$	1.40232e8	+	2.18205e8i	0.591256	+	0.920012i	0.999973	+	0.00735117i	$0.00233997\pi$
$619$	1.40232e8	+	2.18205e8i	0.591256	+	0.920012i	−0.408717	+	0.912661i	$0.634024\pi$
$620$			1.70167e8i			0.714004i
$621$	3.28215e7	−	3.23559e7i	0.137051	−	0.135107i
$622$	−1.01369e8			−0.421245
$623$	−3.82834e8	+	2.46032e8i	−1.58324	+	1.01749i
$624$	−4.49618e7	+	3.12716e8i	−0.185050	+	1.28705i
$625$	−9.49072e7	+	2.07818e8i	−0.388740	+	0.851222i
$626$	−1.66165e7	−	5.65906e7i	−0.0677356	−	0.230686i
$627$	2.21276e7	+	4.84526e7i	0.0897700	+	0.196569i
$628$	−3.87724e8	+	3.35965e8i	−1.56547	+	1.35648i
$629$	−1.79697e7	−	1.24982e8i	−0.0722088	−	0.502223i
$630$	1.57838e8	+	4.63455e7i	0.631234	+	0.185347i
$631$	1.87488e8	+	1.62459e8i	0.746251	+	0.646630i	0.942608	−	0.333902i	$-0.108366\pi$
$631$	1.87488e8	+	1.62459e8i	0.746251	+	0.646630i	−0.196357	+	0.980533i	$0.562911\pi$
$632$	−1.88428e8	+	2.93200e8i	−0.746440	+	1.16148i
$633$	−3.95450e7	−	2.54141e7i	−0.155912	−	0.100199i
$634$	−5.16075e8	+	5.95583e8i	−2.02509	+	2.33708i
$635$	−6.60998e7	+	2.25115e8i	−0.258154	+	0.879192i
$636$	2.08761e8	−	3.00153e7i	0.811479	−	0.116673i
$637$	4.60529e7	+	5.31479e7i	0.178172	+	0.205621i
$638$	−3.52095e8	+	1.60797e8i	−1.35581	+	0.619177i
$639$	1.07893e8	−	3.16804e7i	0.413516	−	0.121419i
$640$	−1.43614e8	−	6.55865e7i	−0.547845	−	0.250193i
$641$	−7.65178e7	−	1.10016e7i	−0.290528	−	0.0417717i	−0.00449029	−	0.999990i	$-0.501429\pi$
$641$	−7.65178e7	−	1.10016e7i	−0.290528	−	0.0417717i	−0.286038	+	0.958218i	$0.592338\pi$
$642$	1.51508e8	+	2.35750e8i	0.572571	+	0.890938i
$643$			3.08599e8i			1.16081i	0.814327	+	0.580406i	$0.197106\pi$
$643$			3.08599e8i			1.16081i	−0.814327	+	0.580406i	$0.802894\pi$
$644$	5.43296e7	−	6.90287e8i	0.203413	−	2.58447i
$645$	1.18206e8			0.440514
$646$	−3.99995e8	+	2.57061e8i	−1.48374	+	0.953539i
$647$	−311175.	+	2.16427e6i	−0.00114893	+	0.00799095i	−0.990388	−	0.138318i	$-0.955830\pi$
$647$	−311175.	+	2.16427e6i	−0.00114893	+	0.00799095i	0.989239	+	0.146309i	$0.0467394\pi$
$648$	−3.01984e7	+	6.61253e7i	−0.110984	+	0.243020i
$649$	5.91483e7	+	2.01441e8i	0.216376	+	0.736908i
$650$	−1.37509e7	−	3.01103e7i	−0.0500716	−	0.109641i
$651$	−4.27246e7	+	3.70211e7i	−0.154858	+	0.134186i
$652$	1.08010e8	+	7.51224e8i	0.389691	+	2.71036i
$653$	−4.55053e8	−	1.33616e8i	−1.63427	−	0.479864i	−0.669465	−	0.742844i	$-0.733477\pi$
$653$	−4.55053e8	−	1.33616e8i	−1.63427	−	0.479864i	−0.964801	+	0.262980i	$0.915295\pi$
$654$	−2.99443e8	−	2.59469e8i	−1.07048	−	0.927580i
$655$	1.56434e8	−	2.43416e8i	0.556681	−	0.866213i
$656$	7.80258e8	+	5.01442e8i	2.76393	+	1.77627i
$657$	−1.02250e8	+	1.18003e8i	−0.360551	+	0.416098i
$658$	−9.51279e7	+	3.23976e8i	−0.333910	+	1.13719i
$659$	−1.61050e8	+	2.31555e7i	−0.562736	+	0.0809092i	−0.417812	−	0.908534i	$-0.637203\pi$
$659$	−1.61050e8	+	2.31555e7i	−0.562736	+	0.0809092i	−0.144924	+	0.989443i	$0.546294\pi$
$660$	−1.28653e8	−	1.48473e8i	−0.447494	−	0.516435i
$661$	1.73202e8	−	7.90987e7i	0.599720	−	0.273883i	−0.0923346	−	0.995728i	$-0.529433\pi$
$661$	1.73202e8	−	7.90987e7i	0.599720	−	0.273883i	0.692055	+	0.721845i	$0.256706\pi$
$662$	6.45117e8	−	1.89423e8i	2.22364	−	0.652920i
$663$	2.27675e8	+	1.03976e8i	0.781224	+	0.356773i
$664$	−5.83631e8	−	8.39134e7i	−1.99358	−	0.286634i
$665$	−1.22454e8	−	1.90542e8i	−0.416397	−	0.647927i
$666$			6.68631e7i			0.226341i
$667$	−2.96103e7	−	4.60185e8i	−0.0997851	−	1.55080i
$668$	−4.00538e8			−1.34374
$669$	1.54465e8	−	9.92683e7i	0.515882	−	0.331537i
$670$	−1.06944e8	+	7.43814e8i	−0.355577	+	2.47309i
$671$	1.00326e8	−	2.19683e8i	0.332082	−	0.727158i
$672$	7.45369e7	+	2.53849e8i	0.245620	+	0.836504i
$673$	1.70904e7	+	3.74228e7i	0.0560670	+	0.122770i	0.935592	−	0.353083i	$-0.114867\pi$
$673$	1.70904e7	+	3.74228e7i	0.0560670	+	0.122770i	−0.879525	+	0.475853i	$0.842139\pi$
$674$	−4.19095e8	+	3.63148e8i	−1.36878	+	1.18605i
$675$	−510003.	−	3.54715e6i	−0.00165829	−	0.0115337i
$676$	−1.33254e8	−	3.91270e7i	−0.431361	−	0.126659i
$677$	−2.81853e8	−	2.44227e8i	−0.908357	−	0.787096i	0.0692360	−	0.997600i	$-0.477944\pi$
$677$	−2.81853e8	−	2.44227e8i	−0.908357	−	0.787096i	−0.977593	+	0.210505i	$0.932489\pi$
$678$	−1.29377e8	+	2.01315e8i	−0.415115	+	0.645931i
$679$	8.88746e7	+	5.71163e7i	0.283902	+	0.182453i
$680$	6.53335e8	−	7.53989e8i	2.07783	−	2.39794i
$681$	−1.76935e7	+	6.02584e7i	−0.0560236	+	0.190799i
$682$	9.56366e7	−	1.37505e7i	0.301489	−	0.0433475i
$683$	−9.10958e7	−	1.05130e8i	−0.285914	−	0.329963i	0.594565	−	0.804048i	$-0.297324\pi$
$683$	−9.10958e7	−	1.05130e8i	−0.285914	−	0.329963i	−0.880479	+	0.474085i	$0.842779\pi$
$684$	1.60037e8	−	7.30864e7i	0.500094	−	0.228385i
$685$	−4.07001e7	+	1.19506e7i	−0.126626	+	0.0371808i
$686$	−4.49058e8	−	2.05078e8i	−1.39101	−	0.635253i
$687$	−2.93498e8	−	4.21986e7i	−0.905179	−	0.130145i
$688$	2.85687e8	+	4.44538e8i	0.877254	+	1.36503i
$689$			2.18764e8i			0.668835i
$690$	3.14654e8	−	1.14806e8i	0.957825	−	0.349476i
$691$	1.17981e8			0.357583			0.178792	−	0.983887i	$-0.442781\pi$
$691$	1.17981e8			0.357583			0.178792	+	0.983887i	$0.442781\pi$
$692$	7.55575e8	−	4.85578e8i	2.28013	−	1.46535i
$693$	9.28846e6	−	6.46027e7i	0.0279090	−	0.194111i
$694$	3.91427e8	−	8.57107e8i	1.17104	−	2.56423i
$695$	−2.78607e7	−	9.48850e7i	−0.0829924	−	0.282646i
$696$	3.02149e8	+	6.61614e8i	0.896177	+	1.96235i
$697$	5.55324e8	−	4.81191e8i	1.64002	−	1.42108i
$698$	−1.01276e8	−	7.04393e8i	−0.297812	−	2.07133i
$699$	2.53927e7	+	7.45598e6i	0.0743495	+	0.0218310i
$700$	−4.06891e7	−	3.52573e7i	−0.118627	−	0.102791i
$701$	−2.32974e8	+	3.62514e8i	−0.676321	+	1.05238i	0.318218	+	0.948017i	$0.396915\pi$
$701$	−2.32974e8	+	3.62514e8i	−0.676321	+	1.05238i	−0.994540	+	0.104359i	$0.966721\pi$
$702$	−1.11499e8	−	7.16562e7i	−0.322300	−	0.207130i
$703$	6.02878e7	−	6.95758e7i	0.173526	−	0.200259i
$704$	2.07265e7	−	7.05880e7i	0.0594030	−	0.202308i
$705$	−1.12970e8	+	1.62426e7i	−0.322400	+	0.0463541i
$706$	−2.51625e7	−	2.90391e7i	−0.0715056	−	0.0825218i
$707$	1.37386e8	−	6.27421e7i	0.388762	−	0.177542i
$708$	6.65350e8	−	1.95364e8i	1.87478	−	0.550485i
$709$	4.02391e8	+	1.83766e8i	1.12904	+	0.515615i	0.890257	−	0.455458i	$-0.150524\pi$
$709$	4.02391e8	+	1.83766e8i	1.12904	+	0.515615i	0.238782	+	0.971073i	$0.423252\pi$
$710$	8.08891e8	+	1.16301e8i	2.26003	+	0.324944i
$711$	−3.71931e7	−	5.78737e7i	−0.103479	−	0.161017i
$712$		−	1.46149e9i		−	4.04907i
$713$	−2.52707e7	+	1.12299e8i	−0.0697186	+	0.309818i
$714$	5.82599e8			1.60057
$715$	1.71428e8	−	1.10170e8i	0.468989	−	0.301401i
$716$	−1.58017e8	+	1.09903e9i	−0.430491	+	2.99413i
$717$	2.09117e6	−	4.57903e6i	0.00567325	−	0.0124227i
$718$	−1.98033e7	−	6.74440e7i	−0.0535014	−	0.182209i
$719$	−3.40307e7	−	7.45169e7i	−0.0915555	−	0.200479i	0.858314	−	0.513124i	$-0.171512\pi$
$719$	−3.40307e7	−	7.45169e7i	−0.0915555	−	0.200479i	−0.949870	+	0.312646i	$0.898785\pi$
$720$	−1.87856e8	+	1.62778e8i	−0.503301	+	0.436112i
$721$	−5.74036e7	−	3.99251e8i	−0.153156	−	1.06522i
$722$	3.25337e8	+	9.55274e7i	0.864413	+	0.253815i
$723$	1.48663e7	+	1.28817e7i	0.0393358	+	0.0340847i
$724$	4.96207e8	−	7.72114e8i	1.30752	−	2.03454i
$725$	−3.01638e7	−	1.93851e7i	−0.0791540	−	0.0508692i
$726$	1.90553e8	−	2.19909e8i	0.497972	−	0.574690i
$727$	−1.15053e8	+	3.91833e8i	−0.299429	+	1.01976i	0.663089	+	0.748541i	$0.269245\pi$
$727$	−1.15053e8	+	3.91833e8i	−0.299429	+	1.01976i	−0.962518	+	0.271220i	$0.912573\pi$
$728$	−1.12130e9	+	1.61218e8i	−2.90621	+	0.417850i
$729$	−9.39654e6	−	1.08442e7i	−0.0242541	−	0.0279907i
$730$	−1.03219e9	+	4.71385e8i	−2.65333	+	1.21173i
$731$	4.01680e8	−	1.17944e8i	1.02832	−	0.301942i
$732$	−7.25604e8	−	3.31372e8i	−1.84998	−	0.844856i
$733$	−2.20767e8	−	3.17415e7i	−0.560561	−	0.0805965i	−0.143790	−	0.989608i	$-0.545929\pi$
$733$	−2.20767e8	−	3.17415e7i	−0.560561	−	0.0805965i	−0.416770	+	0.909012i	$0.636838\pi$
$734$	−6.55373e8	−	1.01978e9i	−1.65730	−	2.57881i
$735$			5.53302e7i			0.139348i
$736$	4.28924e8	+	3.25896e8i	1.07584	+	0.817421i
$737$	2.98147e8			0.744781
$738$	−3.27333e8	+	2.10364e8i	−0.814369	+	0.523363i
$739$	2.73451e7	−	1.90189e8i	0.0677557	−	0.471252i	−0.927489	−	0.373850i	$-0.878038\pi$
$739$	2.73451e7	−	1.90189e8i	0.0677557	−	0.471252i	0.995245	−	0.0974020i	$-0.0310533\pi$
$740$	−1.41053e8	+	3.08862e8i	−0.348085	+	0.762201i
$741$	5.14134e7	+	1.75098e8i	0.126363	+	0.430354i
$742$	2.11533e8	+	4.63192e8i	0.517805	+	1.13383i
$743$	9.19588e7	−	7.96828e7i	0.224196	−	0.194267i	−0.535519	−	0.844523i	$-0.679884\pi$
$743$	9.19588e7	−	7.96828e7i	0.224196	−	0.194267i	0.759715	+	0.650256i	$0.225339\pi$
$744$	−2.58382e7	−	1.79708e8i	−0.0627398	−	0.436365i
$745$	−6.90392e8	−	2.02717e8i	−1.66966	−	0.490255i
$746$	7.28337e8	+	6.31108e8i	1.75435	+	1.52015i
$747$	6.29226e7	−	9.79095e7i	0.150954	−	0.234889i
$748$	−5.85323e8	−	3.76165e8i	−1.39859	−	0.898821i
$749$	−3.09607e8	+	3.57305e8i	−0.736826	+	0.850343i
$750$	1.28522e8	−	4.37705e8i	0.304644	−	1.03752i
$751$	−4.45920e8	+	6.41136e7i	−1.05278	+	0.151367i	−0.646911	−	0.762566i	$-0.723939\pi$
$751$	−4.45920e8	+	6.41136e7i	−1.05278	+	0.151367i	−0.405867	+	0.913932i	$0.633030\pi$
$752$	−3.34115e8	−	3.85590e8i	−0.785675	−	0.906717i
$753$	−2.58913e8	+	1.18241e8i	−0.606413	+	0.276940i
$754$	−1.27240e9	+	3.73611e8i	−2.96832	+	0.871576i
$755$	−4.52733e8	−	2.06756e8i	−1.05197	−	0.480416i
$756$	−2.13380e8	−	3.06794e7i	−0.493842	−	0.0710038i
$757$	−2.40206e8	−	3.73768e8i	−0.553728	−	0.861618i	0.445709	−	0.895178i	$-0.352952\pi$
$757$	−2.40206e8	−	3.73768e8i	−0.553728	−	0.861618i	−0.999437	+	0.0335604i	$0.989315\pi$
$758$		−	3.49018e8i		−	0.801383i
$759$	−6.28531e7	−	1.17088e8i	−0.143748	−	0.267785i
$760$	7.27404e8			1.65705
$761$	−2.08670e8	+	1.34104e8i	−0.473484	+	0.304290i	−0.755533	−	0.655110i	$-0.772622\pi$
$761$	−2.08670e8	+	1.34104e8i	−0.473484	+	0.304290i	0.282049	+	0.959400i	$0.408986\pi$
$762$	6.26192e7	−	4.35526e8i	0.141528	−	0.984349i
$763$	2.77686e8	−	6.08047e8i	0.625144	−	1.36888i
$764$	6.13355e7	+	2.08890e8i	0.137541	+	0.468421i
$765$	8.18062e7	+	1.79131e8i	0.182727	+	0.400115i
$766$	−3.16115e8	+	2.73915e8i	−0.703330	+	0.609439i
$767$	1.02363e8	+	7.11951e8i	0.226860	+	1.57784i
$768$	3.84607e8	+	1.12931e8i	0.849050	+	0.249304i
$769$	−5.14688e8	−	4.45979e8i	−1.13179	−	0.980699i	−0.131843	−	0.991271i	$-0.542090\pi$
$769$	−5.14688e8	−	4.45979e8i	−1.13179	−	0.980699i	−0.999944	+	0.0105713i	$0.996635\pi$
$770$	2.56438e8	−	3.99025e8i	0.561707	−	0.874034i
$771$	3.15281e8	+	2.02619e8i	0.687914	+	0.442096i
$772$	−2.43823e7	+	2.81387e7i	−0.0529935	+	0.0611578i
$773$	−1.07277e7	+	3.65351e7i	−0.0232256	+	0.0790991i	−0.970290	−	0.241944i	$-0.922215\pi$
$773$	−1.07277e7	+	3.65351e7i	−0.0232256	+	0.0790991i	0.947065	+	0.321043i	$0.104033\pi$
$774$	−2.19427e8	+	3.15488e7i	−0.473225	+	0.0680394i
$775$	5.86113e6	+	6.76410e6i	0.0125915	+	0.0145313i
$776$	−3.08623e8	+	1.40943e8i	−0.660455	+	0.301620i
$777$	−1.08234e8	+	3.17804e7i	−0.230729	+	0.0677480i
$778$	1.32384e9	+	6.04578e8i	2.81124	+	1.28385i
$779$	5.30291e8	+	7.62443e7i	1.12176	+	0.161285i
$780$	−3.63887e8	−	5.66219e8i	−0.766800	−	1.19316i
$781$		−	3.24232e8i		−	0.680618i
$782$	9.54687e8	−	7.04084e8i	1.99637	−	1.47233i
$783$	−1.43567e8			−0.299068
$784$	−2.08080e8	+	1.33725e8i	−0.431800	+	0.277501i
$785$	5.95845e7	−	4.14419e8i	0.123175	−	0.856704i
$786$	−2.25423e8	+	4.93607e8i	−0.464227	+	1.01652i
$787$	7.35977e7	+	2.50651e8i	0.150987	+	0.514215i	0.999897	−	0.0143220i	$-0.00455898\pi$
$787$	7.35977e7	+	2.50651e8i	0.150987	+	0.514215i	−0.848910	+	0.528537i	$0.822741\pi$
$788$	7.70535e8	+	1.68724e9i	1.57476	+	3.44824i
$789$	−3.20374e8	+	2.77606e8i	−0.652268	+	0.565194i
$790$	−7.11515e7	−	4.94870e8i	−0.144312	−	1.00371i
$791$	−3.87370e8	−	1.13742e8i	−0.782703	−	0.229822i
$792$	1.58410e8	+	1.37263e8i	0.318866	+	0.276299i
$793$	4.47329e8	−	6.96058e8i	0.897031	−	1.39581i
$794$	−1.29638e8	−	8.33134e7i	−0.258983	−	0.166438i
$795$	−1.12714e8	+	1.30079e8i	−0.224325	+	0.258885i
$796$	3.60434e8	−	1.22752e9i	0.714638	−	2.43383i
$797$	3.85469e8	−	5.54220e7i	0.761402	−	0.109473i	0.249334	−	0.968418i	$-0.419788\pi$
$797$	3.85469e8	−	5.54220e7i	0.761402	−	0.109473i	0.512069	+	0.858945i	$0.328879\pi$
$798$	2.78168e8	+	3.21023e8i	0.547392	+	0.631724i
$799$	−3.67680e8	+	1.67914e8i	−0.720825	+	0.329190i
$800$	4.01891e7	−	1.18006e7i	0.0784944	−	0.0230480i
$801$	2.62408e8	+	1.19838e8i	0.510599	+	0.233183i
$802$	1.34180e9	+	1.92922e8i	2.60114	+	0.373988i
$803$	2.43403e8	+	3.78743e8i	0.470089	+	0.731472i
$804$		−	9.84768e8i		−	1.89481i
$805$	3.35399e8	+	4.54776e8i	0.642945	+	0.871787i
$806$	3.31020e8			0.632193
$807$	−3.07184e8	+	1.97415e8i	−0.584490	+	0.375629i
$808$	−6.90301e7	+	4.80115e8i	−0.130859	+	0.910147i
$809$	−1.21020e8	+	2.64998e8i	−0.228567	+	0.500492i	−0.988816	−	0.149140i	$-0.952350\pi$
$809$	−1.21020e8	+	2.64998e8i	−0.228567	+	0.500492i	0.760249	+	0.649631i	$0.225077\pi$
$810$	−2.93789e7	−	1.00055e8i	−0.0552816	−	0.188272i
$811$	−6.17178e7	−	1.35143e8i	−0.115704	−	0.253356i	0.842916	−	0.538045i	$-0.180837\pi$
$811$	−6.17178e7	−	1.35143e8i	−0.115704	−	0.253356i	−0.958620	+	0.284689i	$0.908110\pi$
$812$	−1.63009e9	+	1.41248e9i	−3.04469	+	2.63824i
$813$	−5.75126e7	−	4.00009e8i	−0.107027	−	0.744386i
$814$	1.84983e8	+	5.43159e7i	0.342972	+	0.100706i
$815$	−4.68089e8	−	4.05602e8i	−0.864681	−	0.749250i
$816$	−4.75943e8	+	7.40582e8i	−0.875961	+	1.36302i
$817$	2.56776e8	+	1.65020e8i	0.470856	+	0.302601i
$818$	8.54334e7	−	9.85954e7i	0.156087	−	0.180134i
$819$	6.29968e7	−	2.14547e8i	0.114674	−	0.390545i
$820$	−1.95583e9	+	2.81207e8i	−3.54724	+	0.510016i
$821$	−2.95233e8	−	3.40717e8i	−0.533500	−	0.615692i	0.423459	−	0.905915i	$-0.360816\pi$
$821$	−2.95233e8	−	3.40717e8i	−0.533500	−	0.615692i	−0.956959	+	0.290223i	$0.906270\pi$
$822$	7.23625e7	−	3.30468e7i	0.130286	−	0.0594996i
$823$	−8.43940e8	+	2.47803e8i	−1.51395	+	0.444536i	−0.930095	−	0.367320i	$-0.880275\pi$
$823$	−8.43940e8	+	2.47803e8i	−1.51395	+	0.444536i	−0.583857	+	0.811856i	$0.698457\pi$
$824$	1.17833e9	+	5.38125e8i	2.10613	+	0.961837i
$825$	−1.02278e7	−	1.47054e6i	−0.0182147	−	0.00261887i
$826$	9.05151e8	+	1.40844e9i	1.60613	+	2.49919i
$827$			1.57147e8i			0.277836i	0.990304	+	0.138918i	$0.0443624\pi$
$827$			1.57147e8i			0.277836i	−0.990304	+	0.138918i	$0.955638\pi$
$828$	−3.86736e8	+	2.07601e8i	−0.681277	+	0.365712i
$829$	4.12405e8			0.723870			0.361935	−	0.932203i	$-0.382116\pi$
$829$	4.12405e8			0.723870			0.361935	+	0.932203i	$0.382116\pi$
$830$	7.11549e8	−	4.57284e8i	1.24443	−	0.799746i
$831$	−9.86865e6	+	6.86380e7i	−0.0171971	+	0.119608i
$832$	1.04703e8	−	2.29267e8i	0.181798	−	0.398082i
$833$	5.52075e7	+	1.88020e8i	0.0955132	+	0.325288i
$834$	7.70428e7	+	1.68700e8i	0.132811	+	0.290815i
$835$	2.47035e8	−	2.14057e8i	0.424326	−	0.367681i
$836$	−7.21951e7	−	5.02128e8i	−0.123563	−	0.859401i
$837$	3.43851e7	+	1.00964e7i	0.0586400	+	0.0172183i
$838$	3.49987e8	+	3.03266e8i	0.594731	+	0.515337i
$839$	−1.42457e8	+	2.21668e8i	−0.241212	+	0.375334i	−0.940660	−	0.339350i	$-0.889793\pi$
$839$	−1.42457e8	+	2.21668e8i	−0.241212	+	0.375334i	0.699448	+	0.714684i	$0.253429\pi$
$840$	−7.49799e8	−	4.81867e8i	−1.26505	−	0.812997i
$841$	−5.51154e8	+	6.36065e8i	−0.926584	+	1.06933i
$842$	3.49040e8	−	1.18872e9i	0.584707	−	1.99133i
$843$	2.18552e8	−	3.14231e7i	0.364815	−	0.0524525i
$844$	2.93171e8	+	3.38337e8i	0.487633	+	0.562758i
$845$	1.03096e8	−	4.70825e7i	0.170873	−	0.0780351i
$846$	2.05372e8	−	6.03026e7i	0.339180	−	0.0995922i
$847$	4.46547e8	+	2.03931e8i	0.734882	+	0.335609i
$848$	−7.61604e8	−	1.09502e8i	−1.24894	−	0.179571i
$849$	−2.69407e7	−	4.19206e7i	−0.0440237	−	0.0685022i
$850$		−	9.22363e7i		−	0.150191i
$851$	−1.38953e8	+	1.82881e8i	−0.225465	+	0.296743i
$852$	−1.07093e9			−1.73157
$853$	−5.42533e8	+	3.48665e8i	−0.874136	+	0.561773i	−0.899015	−	0.437918i	$-0.855716\pi$
$853$	−5.42533e8	+	3.48665e8i	−0.874136	+	0.561773i	0.0248795	+	0.999690i	$0.492080\pi$
$854$	2.74087e8	−	1.90631e9i	0.440062	−	3.06070i
$855$	−5.96451e7	+	1.30605e8i	−0.0954281	+	0.208958i
$856$	−4.27770e8	−	1.45685e9i	−0.682007	−	2.32270i
$857$	3.12572e8	+	6.84438e8i	0.496602	+	1.08741i	0.977559	+	0.210662i	$0.0675620\pi$
$857$	3.12572e8	+	6.84438e8i	0.496602	+	1.08741i	−0.480957	+	0.876744i	$0.659711\pi$
$858$	−2.88819e8	+	2.50263e8i	−0.457261	+	0.396219i
$859$	−8.73801e7	−	6.07742e8i	−0.137858	−	0.958826i	−0.934902	−	0.354905i	$-0.884513\pi$
$859$	−8.73801e7	−	6.07742e8i	−0.137858	−	0.958826i	0.797044	−	0.603921i	$-0.206396\pi$
$860$	−1.08016e9	−	3.17163e8i	−1.69821	−	0.498640i
$861$	−4.96109e8	−	4.29881e8i	−0.777262	−	0.673502i
$862$	−3.78379e8	+	5.88769e8i	−0.590752	+	0.919228i
$863$	2.53219e8	+	1.62734e8i	0.393970	+	0.253189i	0.722596	−	0.691271i	$-0.242949\pi$
$863$	2.53219e8	+	1.62734e8i	0.393970	+	0.253189i	−0.328625	+	0.944460i	$0.606585\pi$
$864$	1.09828e8	−	1.26748e8i	0.170283	−	0.196517i
$865$	−2.06503e8	+	7.03283e8i	−0.319064	+	1.08663i
$866$	−9.46322e8	+	1.36061e8i	−1.45709	+	0.209497i
$867$	2.10319e8	+	2.42722e8i	0.322717	+	0.372435i
$868$	4.89747e8	−	2.23660e8i	0.748881	−	0.342002i
$869$	−1.90326e8	+	5.58849e7i	−0.290028	+	0.0851599i
$870$	−9.49077e8	−	4.33429e8i	−1.44126	−	0.658203i
$871$	1.01106e9	+	1.45368e8i	1.53010	+	0.219996i
$872$	1.16063e9	+	1.80597e9i	1.75042	+	2.72371i
$873$		−	6.69699e7i		−	0.100655i
$874$	8.43789e8	+	1.89878e8i	1.26386	+	0.284408i
$875$	7.69618e8			1.14882
$876$	1.25097e9	−	8.03951e8i	1.86095	−	1.19596i
$877$	−3.26432e6	+	2.27038e7i	−0.00483942	+	0.0336589i	−0.992098	−	0.125465i	$-0.959958\pi$
$877$	−3.26432e6	+	2.27038e7i	−0.00483942	+	0.0336589i	0.987259	+	0.159124i	$0.0508669\pi$
$878$	−5.78872e8	+	1.26755e9i	−0.855261	+	1.87276i
$879$	1.19132e7	+	4.05728e7i	0.0175414	+	0.0597404i
$880$	2.97737e8	+	6.51953e8i	0.436902	+	0.956683i
$881$	1.98203e8	−	1.71744e8i	0.289856	−	0.251161i	−0.497779	−	0.867304i	$-0.665851\pi$
$881$	1.98203e8	−	1.71744e8i	0.289856	−	0.251161i	0.787635	+	0.616143i	$0.211305\pi$
$882$	−1.47675e7	−	1.02710e8i	−0.0215229	−	0.149695i
$883$	1.53175e8	+	4.49763e7i	0.222488	+	0.0653284i	0.391077	−	0.920358i	$-0.372103\pi$
$883$	1.53175e8	+	4.49763e7i	0.222488	+	0.0653284i	−0.168589	+	0.985687i	$0.553921\pi$
$884$	−1.80150e9	−	1.56101e9i	−2.60782	−	2.25969i
$885$	−3.05953e8	+	4.76073e8i	−0.441393	+	0.686821i
$886$	1.34795e9	+	8.66274e8i	1.93808	+	1.24553i
$887$	6.26070e8	−	7.22523e8i	0.897123	−	1.03534i	−0.102054	−	0.994779i	$-0.532541\pi$
$887$	6.26070e8	−	7.22523e8i	0.897123	−	1.03534i	0.999177	−	0.0405566i	$-0.0129131\pi$
$888$	1.02064e8	−	3.47597e8i	0.145758	−	0.496406i
$889$	7.34768e8	−	1.05644e8i	1.04579	−	0.150362i
$890$	1.37291e9	+	1.58442e9i	1.94747	+	2.24750i
$891$	−3.76346e7	+	1.71872e7i	−0.0532053	+	0.0242980i
$892$	−1.67784e9	+	4.92658e8i	−2.36404	+	0.694146i
$893$	−2.68077e8	−	1.22426e8i	−0.376448	−	0.171918i
$894$	1.33569e9	+	1.92043e8i	1.86936	+	0.268773i
$895$	−4.89891e8	−	7.62286e8i	−0.683330	−	1.06328i
$896$			4.99531e8i			0.694446i
$897$	−1.56054e8	−	4.27705e8i	−0.216221	−	0.592608i
$898$	8.86390e8			1.22404
$899$	3.01642e8	−	1.93854e8i	0.415158	−	0.266806i
$900$	−4.85712e6	+	3.37820e7i	−0.00666272	+	0.0463402i
$901$	−2.53228e8	+	5.54492e8i	−0.346208	+	0.758090i
$902$	3.16085e8	+	1.07649e9i	0.430709	+	1.46686i
$903$	−1.55364e8	−	3.40201e8i	−0.211003	−	0.462032i
$904$	9.79883e8	−	8.49074e8i	1.32638	−	1.14932i
$905$	1.06596e8	+	7.41394e8i	0.143813	+	1.00024i
$906$	8.95597e8	+	2.62971e8i	1.20428	+	0.353609i
$907$	−5.74897e8	−	4.98151e8i	−0.770492	−	0.667635i	0.178144	−	0.984004i	$-0.442991\pi$
$907$	−5.74897e8	−	4.98151e8i	−0.770492	−	0.667635i	−0.948636	+	0.316369i	$0.897536\pi$
$908$	3.23363e8	−	5.03163e8i	0.431950	−	0.672127i
$909$	−8.05438e7	−	5.17624e7i	−0.107236	−	0.0689164i
$910$	1.06417e9	−	1.22811e9i	1.41217	−	1.62973i
$911$	3.72157e8	−	1.26745e9i	0.492234	−	1.67639i	−0.220843	−	0.975309i	$-0.570881\pi$
$911$	3.72157e8	−	1.26745e9i	0.492234	−	1.67639i	0.713077	−	0.701086i	$-0.247301\pi$
$912$	−6.35319e8	+	9.13451e7i	−0.837543	+	0.120421i
$913$	−2.19761e8	−	2.53617e8i	−0.288760	−	0.333247i
$914$	−1.09426e9	+	4.99732e8i	−1.43312	+	0.654484i
$915$	6.24617e8	−	1.83404e8i	0.815362	−	0.239412i
$916$	2.56874e9	+	1.17310e9i	3.34221	+	1.52634i
$917$	−9.06168e8	−	1.30287e8i	−1.17517	−	0.168964i
$918$	−1.99667e8	−	3.10688e8i	−0.258095	−	0.401603i
$919$		−	3.68887e8i		−	0.475277i	−0.971354	−	0.237638i	$-0.923627\pi$
$919$		−	3.68887e8i		−	0.475277i	0.971354	−	0.237638i	$-0.0763733\pi$
$920$	−1.81102e9	+	1.16529e8i	−2.32573	+	0.149648i
$921$	−6.88987e8			−0.881926
$922$	−1.59583e9	+	1.02558e9i	−2.03608	+	1.30851i
$923$	1.58086e8	−	1.09951e9i	0.201043	−	1.39829i
$924$	−2.58215e8	+	5.65413e8i	−0.327315	+	0.716720i
$925$	5.03144e6	+	1.71355e7i	0.00635721	+	0.0216507i
$926$	−6.87133e8	−	1.50461e9i	−0.865382	−	1.89492i
$927$	−1.93239e8	+	1.67443e8i	−0.242581	+	0.210197i
$928$	−2.38809e8	−	1.66095e9i	−0.298818	−	2.07832i
$929$	4.15354e8	+	1.21959e8i	0.518050	+	0.152113i	0.530297	−	0.847812i	$-0.322080\pi$
$929$	4.15354e8	+	1.21959e8i	0.518050	+	0.152113i	−0.0122474	+	0.999925i	$0.503899\pi$
$930$	1.96828e8	+	1.70552e8i	0.244702	+	0.212035i
$931$	−7.72429e7	+	1.20192e8i	−0.0957216	+	0.148946i
$932$	−2.12032e8	−	1.36264e8i	−0.261911	−	0.168320i
$933$	−7.09936e7	+	8.19310e7i	−0.0874127	+	0.100880i
$934$	3.14025e8	−	1.06947e9i	0.385410	−	1.31259i
$935$	5.62036e8	−	8.08086e7i	0.687589	−	0.0988604i
$936$	4.70264e8	+	5.42714e8i	0.573475	+	0.661825i
$937$	−1.16456e9	+	5.31835e8i	−1.41560	+	0.646484i	−0.968731	−	0.248114i	$-0.920189\pi$
$937$	−1.16456e9	+	5.31835e8i	−1.41560	+	0.646484i	−0.446872	+	0.894598i	$0.647462\pi$
$938$	2.28128e9	−	6.69845e8i	2.76421	−	0.811645i
$939$	−5.73764e7	−	2.62029e7i	−0.0693005	−	0.0316485i
$940$	1.07589e9	+	1.54690e8i	1.29534	+	0.186242i
$941$	−2.36533e8	−	3.68053e8i	−0.283872	−	0.441714i	0.669809	−	0.742534i	$-0.266376\pi$
$941$	−2.36533e8	−	3.68053e8i	−0.283872	−	0.441714i	−0.953681	+	0.300820i	$0.902740\pi$
$942$			7.85194e8i			0.939343i
$943$	−1.33248e9	−	1.04874e8i	−1.58901	−	0.125064i
$944$	−2.52982e9			−3.00727
$945$	1.48000e8	−	9.51138e7i	0.175374	−	0.112706i
$946$	−9.09676e7	+	6.32694e8i	−0.107452	+	0.747343i
$947$	1.83130e8	−	4.00999e8i	0.215630	−	0.472165i	−0.770647	−	0.637263i	$-0.780067\pi$
$947$	1.83130e8	−	4.00999e8i	0.215630	−	0.472165i	0.986277	+	0.165098i	$0.0527940\pi$
$948$	1.84585e8	+	6.28640e8i	0.216657	+	0.737865i
$949$	6.40748e8	+	1.40304e9i	0.749702	+	1.64162i
$950$	5.08240e7	−	4.40392e7i	0.0592786	−	0.0513652i
$951$	1.19944e8	+	8.34230e8i	0.139456	+	0.969938i
$952$	−3.02872e9	−	8.89312e8i	−3.51033	−	1.03073i
$953$	1.78693e8	+	1.54838e8i	0.206456	+	0.178895i	0.751951	−	0.659219i	$-0.229113\pi$
$953$	1.78693e8	+	1.54838e8i	0.206456	+	0.178895i	−0.545495	+	0.838114i	$0.683658\pi$
$954$	1.74515e8	−	2.71551e8i	0.200996	−	0.312756i
$955$	−1.49465e8	−	9.60554e7i	−0.171605	−	0.110284i
$956$	−3.13952e7	+	3.62319e7i	−0.0359326	+	0.0414685i
$957$	−1.16626e8	+	3.97192e8i	−0.133064	+	0.453174i
$958$	3.19497e8	−	4.59367e7i	0.363388	−	0.0522473i
$959$	8.78886e7	+	1.01429e8i	0.0996499	+	0.115002i
$960$	1.80383e8	−	8.23782e7i	0.203884	−	0.0931105i
$961$	7.65676e8	−	2.24823e8i	0.862730	−	0.253320i
$962$	6.00818e8	+	2.74385e8i	0.674867	+	0.308201i
$963$	2.96652e8	+	4.26521e7i	0.332176	+	0.0477597i
$964$	−1.01284e8	−	1.57601e8i	−0.113060	−	0.175925i
$965$		−	3.03853e7i		−	0.0338129i
$966$	−7.43983e8	−	7.54690e8i	−0.825338	−	0.837215i
$967$	1.49727e9			1.65585			0.827923	−	0.560842i	$-0.189522\pi$
$967$	1.49727e9			1.65585			0.827923	+	0.560842i	$0.189522\pi$
$968$	−1.32630e9	+	8.52359e8i	−1.46223	+	0.939716i
$969$	−7.23672e7	+	5.03325e8i	−0.0795373	+	0.553194i
$970$	2.02182e8	−	4.42716e8i	0.221527	−	0.485076i
$971$	3.24932e8	+	1.10662e9i	0.354924	+	1.20876i	0.922681	+	0.385563i	$0.125993\pi$
$971$	3.24932e8	+	1.10662e9i	0.354924	+	1.20876i	−0.567758	+	0.823196i	$0.692189\pi$
$972$	5.67685e7	+	1.24306e8i	0.0618171	+	0.135361i
$973$	−2.36463e8	+	2.04897e8i	−0.256700	+	0.222431i
$974$	−3.81235e7	−	2.65155e8i	−0.0412587	−	0.286961i
$975$	−3.39669e7	−	9.97357e6i	−0.0366473	−	0.0107606i
$976$	2.19934e9	+	1.90574e9i	2.36561	+	2.04981i
$977$	−8.42548e7	+	1.31103e8i	−0.0903464	+	0.140582i	−0.883485	−	0.468459i	$-0.844809\pi$
$977$	−8.42548e7	+	1.31103e8i	−0.0903464	+	0.140582i	0.793139	+	0.609041i	$0.208446\pi$
$978$	9.77174e8	+	6.27991e8i	1.04461	+	0.671332i
$979$	5.44709e8	−	6.28627e8i	0.580519	−	0.669954i
$980$	1.48459e8	−	5.05603e8i	0.157735	−	0.537195i
$981$	−4.19428e8	+	6.03046e7i	−0.444273	+	0.0638768i
$982$	−1.42204e8	−	1.64112e8i	−0.150168	−	0.173303i
$983$	−2.41905e8	+	1.10474e8i	−0.254674	+	0.116306i	−0.538661	−	0.842522i	$-0.681070\pi$
$983$	−2.41905e8	+	1.10474e8i	−0.254674	+	0.116306i	0.283988	+	0.958828i	$0.408342\pi$
$984$	2.02280e9	−	5.93948e8i	2.12309	−	0.623394i
$985$	−1.37694e9	−	6.28826e8i	−1.44080	−	0.657994i
$986$	−3.65756e9	−	5.25878e8i	−3.81559	−	0.548598i
$987$	1.95229e8	+	3.03782e8i	0.203045	+	0.315944i
$988$		−	1.73798e9i		−	1.80208i
$989$	−6.65731e8	−	3.69715e8i	−0.688193	−	0.382189i
$990$	−3.00678e8			−0.309882
$991$	8.74037e7	−	5.61709e7i	0.0898067	−	0.0577153i	−0.494967	−	0.868912i	$-0.664820\pi$
$991$	8.74037e7	−	5.61709e7i	0.0898067	−	0.0577153i	0.584773	+	0.811197i	$0.301183\pi$
$992$	−5.96105e7	+	4.14600e8i	−0.0610643	+	0.424712i
$993$	2.98706e8	−	6.54074e8i	0.305067	−	0.668004i
$994$	−7.28451e8	−	2.48088e9i	−0.741722	−	2.52607i
$995$	4.33719e8	+	9.49712e8i	0.440290	+	0.964102i
$996$	−8.37687e8	+	7.25860e8i	−0.847821	+	0.734641i
$997$	1.61848e8	+	1.12568e9i	0.163313	+	1.13587i	0.892334	+	0.451376i	$0.149067\pi$
$997$	1.61848e8	+	1.12568e9i	0.163313	+	1.13587i	−0.729020	+	0.684492i	$0.760024\pi$
$998$	−1.00195e9	−	2.94200e8i	−1.00799	−	0.295972i
$999$	5.40417e7	+	4.68274e7i	0.0542042	+	0.0469682i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.f.a.34.2	✓	240
23.21	odd	22	inner	69.7.f.a.67.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.f.a.34.2	✓	240	1.1	even	1	trivial
69.7.f.a.67.2	yes	240	23.21	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.2621 + 7.88038i) q^{2} +(-2.21847 + 15.4298i) q^{3} +(61.6725 - 135.044i) q^{4} +(34.1338 + 116.249i) q^{5} +(-94.3895 - 206.684i) q^{6} +(289.705 - 251.031i) q^{7} +(175.202 + 1218.56i) q^{8} +(-233.157 - 68.4610i) q^{9} +O(q^{10})\)	\(q+(-12.2621 + 7.88038i) q^{2} +(-2.21847 + 15.4298i) q^{3} +(61.6725 - 135.044i) q^{4} +(34.1338 + 116.249i) q^{5} +(-94.3895 - 206.684i) q^{6} +(289.705 - 251.031i) q^{7} +(175.202 + 1218.56i) q^{8} +(-233.157 - 68.4610i) q^{9} +(-1334.64 - 1156.47i) q^{10} +(-378.807 + 589.436i) q^{11} +(1946.88 + 1251.18i) q^{12} +(-1571.98 + 1814.16i) q^{13} +(-1574.18 + 5361.15i) q^{14} +(-1869.42 + 268.782i) q^{15} +(-5528.94 - 6380.74i) q^{16} +(-6084.37 + 2778.64i) q^{17} +(3398.50 - 997.888i) q^{18} +(-4436.13 - 2025.91i) q^{19} +(17803.8 + 2559.81i) q^{20} +(3230.65 + 5026.99i) q^{21} -10212.9i q^{22} +(11369.2 + 4333.26i) q^{23} -19190.8 q^{24} +(795.866 - 511.472i) q^{25} +(4979.50 - 34633.2i) q^{26} +(1573.59 - 3445.68i) q^{27} +(-16033.3 - 54604.6i) q^{28} +(-15744.5 - 34475.6i) q^{29} +(20805.0 - 18027.6i) q^{30} +(1346.38 + 9364.31i) q^{31} +(42481.0 + 12473.6i) q^{32} +(-8254.50 - 7152.56i) q^{33} +(52710.5 - 82019.2i) q^{34} +(39070.8 + 25109.3i) q^{35} +(-23624.6 + 27264.3i) q^{36} +(-5318.37 + 18112.7i) q^{37} +(70361.3 - 10116.4i) q^{38} +(-24504.7 - 28279.9i) q^{39} +(-135676. + 61961.1i) q^{40} +(-105405. + 30949.6i) q^{41} +(-79229.2 - 36182.8i) q^{42} +(-61950.6 - 8907.15i) q^{43} +(56237.7 + 87507.6i) q^{44} -29441.1i q^{45} +(-173558. + 36458.7i) q^{46} +60430.3 q^{47} +(110719. - 71155.0i) q^{48} +(4169.28 - 28998.0i) q^{49} +(-5728.41 + 12543.5i) q^{50} +(-29375.8 - 100045. i) q^{51} +(148043. + 324170. i) q^{52} +(68874.3 - 59679.9i) q^{53} +(7857.75 + 54651.8i) q^{54} +(-81451.5 - 23916.3i) q^{55} +(356652. + 309041. i) q^{56} +(41100.8 - 63954.2i) q^{57} +(464742. + 298672. i) q^{58} +(196221. - 226451. i) q^{59} +(-78994.5 + 269031. i) q^{60} +(-341176. + 49053.7i) q^{61} +(-90303.9 - 104216. i) q^{62} +(-84732.4 + 38696.0i) q^{63} +(-100744. + 29581.2i) q^{64} +(-264552. - 120817. i) q^{65} +(157583. + 22657.0i) q^{66} +(-230054. - 357971. i) q^{67} +993023. i q^{68} +(-92083.5 + 165811. i) q^{69} -676961. q^{70} +(-389290. + 250182. i) q^{71} +(42574.2 - 296110. i) q^{72} +(266926. - 584485. i) q^{73} +(-77520.6 - 264011. i) q^{74} +(6126.30 + 13414.7i) q^{75} +(-547175. + 474130. i) q^{76} +(38224.1 + 265855. i) q^{77} +(523336. + 153665. i) q^{78} +(213957. + 185394. i) q^{79} +(553031. - 860533. i) q^{80} +(49675.2 + 31924.3i) q^{81} +(1.04859e6 - 1.21014e6i) q^{82} +(-134936. + 459551. i) q^{83} +(878106. - 126253. i) q^{84} +(-530697. - 612457. i) q^{85} +(829837. - 378974. i) q^{86} +(566880. - 166451. i) q^{87} +(-784630. - 358329. i) q^{88} +(-1.17507e6 - 168949. i) q^{89} +(232007. + 361010. i) q^{90} +920184. i q^{91} +(1.28635e6 - 1.26810e6i) q^{92} -147476. q^{93} +(-741003. + 476214. i) q^{94} +(84088.5 - 584848. i) q^{95} +(-286707. + 627801. i) q^{96} +(77644.4 + 264433. i) q^{97} +(177391. + 388432. i) q^{98} +(128675. - 111497. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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