LMFDB - Embedded newform 43.7.f.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(2,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([9]))

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

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

chi := DirichletCharacter("43.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.f (of order $14$, degree $6$, 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:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$126$
Relative dimension:	$21$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			2.2
Character	$\chi$	$=$	43.2
Dual form			43.7.f.a.22.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.62328 - 11.6769i) q^{2} +(-22.1545 + 46.0043i) q^{3} +(-64.8243 + 81.2871i) q^{4} +(43.4728 + 9.92237i) q^{5} +661.767 q^{6} +306.680i q^{7} +(505.038 + 115.272i) q^{8} +(-1171.05 - 1468.45i) q^{9} +O(q^{10})$	\(q+(-5.62328 - 11.6769i) q^{2} +(-22.1545 + 46.0043i) q^{3} +(-64.8243 + 81.2871i) q^{4} +(43.4728 + 9.92237i) q^{5} +661.767 q^{6} +306.680i q^{7} +(505.038 + 115.272i) q^{8} +(-1171.05 - 1468.45i) q^{9} +(-128.597 - 563.421i) q^{10} +(-52.9573 - 66.4064i) q^{11} +(-2303.41 - 4783.08i) q^{12} +(-263.570 + 1154.78i) q^{13} +(3581.06 - 1724.55i) q^{14} +(-1419.59 + 1780.11i) q^{15} +(-13.2846 - 58.2037i) q^{16} +(-1863.88 - 8166.18i) q^{17} +(-10561.8 + 21931.7i) q^{18} +(5004.02 + 3990.57i) q^{19} +(-3624.65 + 2890.56i) q^{20} +(-14108.6 - 6794.35i) q^{21} +(-477.624 + 991.796i) q^{22} +(-12375.5 - 15518.4i) q^{23} +(-16491.9 + 20680.2i) q^{24} +(-12286.2 - 5916.73i) q^{25} +(14966.3 - 3415.96i) q^{26} +(57209.2 - 13057.6i) q^{27} +(-24929.1 - 19880.3i) q^{28} +(3107.44 + 6452.67i) q^{29} +(28768.8 + 6566.30i) q^{30} +(8276.17 - 3985.59i) q^{31} +(25315.7 - 20188.6i) q^{32} +(4228.23 - 965.065i) q^{33} +(-84874.2 + 67684.9i) q^{34} +(-3042.99 + 13332.2i) q^{35} +195279. q^{36} -100299. i q^{37} +(18458.3 - 80871.2i) q^{38} +(-47285.4 - 37708.9i) q^{39} +(20811.6 + 10022.4i) q^{40} +(-11487.4 + 5532.06i) q^{41} +202951. i q^{42} +(-44777.2 + 65699.0i) q^{43} +8830.90 q^{44} +(-36338.4 - 75457.4i) q^{45} +(-111615. + 231771. i) q^{46} +(49831.3 - 62486.4i) q^{47} +(2971.94 + 678.325i) q^{48} +23596.4 q^{49} +176736. i q^{50} +(416973. + 95171.4i) q^{51} +(-76782.7 - 96282.4i) q^{52} +(49112.1 + 215174. i) q^{53} +(-474175. - 594597. i) q^{54} +(-1643.29 - 3412.33i) q^{55} +(-35351.5 + 154885. i) q^{56} +(-294445. + 141797. i) q^{57} +(57872.9 - 72570.3i) q^{58} +(-22744.7 - 99651.1i) q^{59} +(-52676.1 - 230789. i) q^{60} +(-48578.6 + 100875. i) q^{61} +(-93078.3 - 74227.5i) q^{62} +(450345. - 359138. i) q^{63} +(-381538. - 183739. i) q^{64} +(-22916.2 + 47586.0i) q^{65} +(-35045.4 - 43945.5i) q^{66} +(-94711.9 + 118765. i) q^{67} +(784630. + 377858. i) q^{68} +(988086. - 225524. i) q^{69} +(172790. - 39438.2i) q^{70} +(21411.2 + 17074.9i) q^{71} +(-422155. - 876615. i) q^{72} +(-529084. - 120760. i) q^{73} +(-1.17117e6 + 564007. i) q^{74} +(544390. - 434137. i) q^{75} +(-648764. + 148076. i) q^{76} +(20365.5 - 16240.9i) q^{77} +(-174422. + 764193. i) q^{78} -169739. q^{79} -2662.09i q^{80} +(-362054. + 1.58626e6i) q^{81} +(129194. + 103029. i) q^{82} +(-586495. - 282441. i) q^{83} +(1.46687e6 - 706409. i) q^{84} -373501. i q^{85} +(1.01895e6 + 153413. i) q^{86} -365695. q^{87} +(-19090.7 - 39642.2i) q^{88} +(-29735.1 + 61745.6i) q^{89} +(-676764. + 848635. i) q^{90} +(-354147. - 80831.6i) q^{91} +2.06368e6 q^{92} +469039. i q^{93} +(-1.00986e6 - 230494. i) q^{94} +(177942. + 223133. i) q^{95} +(367905. + 1.61190e6i) q^{96} +(-527551. - 661528. i) q^{97} +(-132689. - 275532. i) q^{98} +(-35498.9 + 155531. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9}+O(q^{10}) $ 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9} + 1955 q^{10} - 985 q^{11} - 455 q^{12} - 4485 q^{13} - 6771 q^{14} + 5017 q^{15} - 41935 q^{16} - 10409 q^{17} - 5110 q^{18} - 33397 q^{19} - 24507 q^{20} - 5448 q^{21} + 25193 q^{22} - 29017 q^{23} - 1885 q^{24} - 2080 q^{25} + 34713 q^{26} - 7 q^{27} + 28665 q^{28} + 17353 q^{29} - 290052 q^{30} + 13547 q^{31} + 458283 q^{32} - 94801 q^{33} - 191527 q^{34} + 183008 q^{35} + 956352 q^{36} + 304607 q^{38} - 381031 q^{39} + 66419 q^{40} + 313447 q^{41} - 323228 q^{43} + 281588 q^{44} - 1237551 q^{45} + 80948 q^{46} - 180133 q^{47} - 762055 q^{48} - 1861754 q^{49} + 999215 q^{51} + 471797 q^{52} + 1030011 q^{53} - 92099 q^{54} + 324233 q^{55} - 842713 q^{56} + 331037 q^{57} + 849461 q^{58} - 369609 q^{59} + 553323 q^{60} - 594727 q^{61} - 886711 q^{62} + 1914136 q^{63} - 3250219 q^{64} + 1473521 q^{65} - 427559 q^{66} + 122535 q^{67} - 602346 q^{68} + 4320057 q^{69} - 1694994 q^{70} - 770707 q^{71} - 391202 q^{72} + 476945 q^{73} - 3943812 q^{74} + 2061367 q^{75} - 2044462 q^{76} + 3016216 q^{77} + 239350 q^{78} + 5077268 q^{79} + 2388946 q^{81} + 5820437 q^{82} - 1324235 q^{83} + 3759618 q^{84} - 4967947 q^{86} - 3537894 q^{87} - 7289555 q^{88} - 4331495 q^{89} - 12825206 q^{90} + 1802976 q^{91} - 12038260 q^{92} + 6249341 q^{94} - 5313259 q^{95} + 7069598 q^{96} + 788975 q^{97} + 4724783 q^{98} - 2216971 q^{99}+O(q^{100}) \) 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9 + 1955 * q^10 - 985 * q^11 - 455 * q^12 - 4485 * q^13 - 6771 * q^14 + 5017 * q^15 - 41935 * q^16 - 10409 * q^17 - 5110 * q^18 - 33397 * q^19 - 24507 * q^20 - 5448 * q^21 + 25193 * q^22 - 29017 * q^23 - 1885 * q^24 - 2080 * q^25 + 34713 * q^26 - 7 * q^27 + 28665 * q^28 + 17353 * q^29 - 290052 * q^30 + 13547 * q^31 + 458283 * q^32 - 94801 * q^33 - 191527 * q^34 + 183008 * q^35 + 956352 * q^36 + 304607 * q^38 - 381031 * q^39 + 66419 * q^40 + 313447 * q^41 - 323228 * q^43 + 281588 * q^44 - 1237551 * q^45 + 80948 * q^46 - 180133 * q^47 - 762055 * q^48 - 1861754 * q^49 + 999215 * q^51 + 471797 * q^52 + 1030011 * q^53 - 92099 * q^54 + 324233 * q^55 - 842713 * q^56 + 331037 * q^57 + 849461 * q^58 - 369609 * q^59 + 553323 * q^60 - 594727 * q^61 - 886711 * q^62 + 1914136 * q^63 - 3250219 * q^64 + 1473521 * q^65 - 427559 * q^66 + 122535 * q^67 - 602346 * q^68 + 4320057 * q^69 - 1694994 * q^70 - 770707 * q^71 - 391202 * q^72 + 476945 * q^73 - 3943812 * q^74 + 2061367 * q^75 - 2044462 * q^76 + 3016216 * q^77 + 239350 * q^78 + 5077268 * q^79 + 2388946 * q^81 + 5820437 * q^82 - 1324235 * q^83 + 3759618 * q^84 - 4967947 * q^86 - 3537894 * q^87 - 7289555 * q^88 - 4331495 * q^89 - 12825206 * q^90 + 1802976 * q^91 - 12038260 * q^92 + 6249341 * q^94 - 5313259 * q^95 + 7069598 * q^96 + 788975 * q^97 + 4724783 * q^98 - 2216971 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{14}\right)$

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 $

$2$	−5.62328	−	11.6769i	−0.702910	−	1.45961i	−0.879784	−	0.475373i	$-0.842313\pi$
$2$	−5.62328	−	11.6769i	−0.702910	−	1.45961i	0.176875	−	0.984233i	$-0.443401\pi$
$3$	−22.1545	+	46.0043i	−0.820538	+	1.70386i	−0.117086	+	0.993122i	$0.537355\pi$
$3$	−22.1545	+	46.0043i	−0.820538	+	1.70386i	−0.703452	+	0.710743i	$0.748359\pi$
$4$	−64.8243	+	81.2871i	−1.01288	+	1.27011i
$5$	43.4728	+	9.92237i	0.347782	+	0.0793790i	0.392844	−	0.919605i	$-0.371491\pi$
$5$	43.4728	+	9.92237i	0.347782	+	0.0793790i	−0.0450617	+	0.998984i	$0.514348\pi$
$6$	661.767			3.06374
$7$			306.680i			0.894110i	0.894506	+	0.447055i	$0.147527\pi$
$7$			306.680i			0.894110i	−0.894506	+	0.447055i	$0.852473\pi$
$8$	505.038	+	115.272i	0.986403	+	0.225140i
$9$	−1171.05	−	1468.45i	−1.60638	−	2.01434i
$10$	−128.597	−	563.421i	−0.128597	−	0.563421i
$11$	−52.9573	−	66.4064i	−0.0397876	−	0.0498921i	0.761540	−	0.648118i	$-0.224444\pi$
$11$	−52.9573	−	66.4064i	−0.0397876	−	0.0498921i	−0.801327	+	0.598226i	$0.795872\pi$
$12$	−2303.41	−	4783.08i	−1.33299	−	2.76799i
$13$	−263.570	+	1154.78i	−0.119968	+	0.525615i	0.878854	+	0.477091i	$0.158309\pi$
$13$	−263.570	+	1154.78i	−0.119968	+	0.525615i	−0.998822	+	0.0485238i	$0.984548\pi$
$14$	3581.06	−	1724.55i	1.30505	−	0.628479i
$15$	−1419.59	+	1780.11i	−0.420619	+	0.527440i
$16$	−13.2846	−	58.2037i	−0.00324331	−	0.0142099i
$17$	−1863.88	−	8166.18i	−0.379377	−	1.66216i	−0.699386	−	0.714744i	$-0.746543\pi$
$17$	−1863.88	−	8166.18i	−0.379377	−	1.66216i	0.320009	−	0.947414i	$-0.396314\pi$
$18$	−10561.8	+	21931.7i	−1.81100	+	3.76059i
$19$	5004.02	+	3990.57i	0.729555	+	0.581801i	0.916245	−	0.400618i	$-0.131205\pi$
$19$	5004.02	+	3990.57i	0.729555	+	0.581801i	−0.186690	+	0.982419i	$0.559776\pi$
$20$	−3624.65	+	2890.56i	−0.453082	+	0.361321i
$21$	−14108.6	−	6794.35i	−1.52344	−	0.733652i
$22$	−477.624	+	991.796i	−0.0448557	+	0.0931439i
$23$	−12375.5	−	15518.4i	−1.01714	−	1.27545i	−0.960861	−	0.277033i	$-0.910649\pi$
$23$	−12375.5	−	15518.4i	−1.01714	−	1.27545i	−0.0562752	−	0.998415i	$-0.517922\pi$
$24$	−16491.9	+	20680.2i	−1.19299	+	1.49596i
$25$	−12286.2	−	5916.73i	−0.786318	−	0.378671i
$26$	14966.3	−	3415.96i	0.851518	−	0.194353i
$27$	57209.2	−	13057.6i	2.90653	−	0.663396i
$28$	−24929.1	−	19880.3i	−1.13562	−	0.905627i
$29$	3107.44	+	6452.67i	0.127412	+	0.264573i	0.954910	−	0.296895i	$-0.0959511\pi$
$29$	3107.44	+	6452.67i	0.127412	+	0.264573i	−0.827498	+	0.561468i	$0.810237\pi$
$30$	28768.8	+	6566.30i	1.06551	+	0.243196i
$31$	8276.17	−	3985.59i	0.277808	−	0.133785i	−0.289792	−	0.957090i	$-0.593586\pi$
$31$	8276.17	−	3985.59i	0.277808	−	0.133785i	0.567600	+	0.823304i	$0.307872\pi$
$32$	25315.7	−	20188.6i	0.772572	−	0.616106i
$33$	4228.23	−	965.065i	0.117657	−	0.0268544i
$34$	−84874.2	+	67684.9i	−2.15943	+	1.72209i
$35$	−3042.99	+	13332.2i	−0.0709736	+	0.310956i
$36$	195279.			4.18551
$37$		−	100299.i		−	1.98011i	−0.140670	−	0.990057i	$-0.544926\pi$
$37$		−	100299.i		−	1.98011i	0.140670	−	0.990057i	$-0.455074\pi$
$38$	18458.3	−	80871.2i	0.336389	−	1.47382i
$39$	−47285.4	−	37708.9i	−0.797138	−	0.635697i
$40$	20811.6	+	10022.4i	0.325182	+	0.156599i
$41$	−11487.4	+	5532.06i	−0.166675	+	0.0802667i	−0.515361	−	0.856973i	$-0.672342\pi$
$41$	−11487.4	+	5532.06i	−0.166675	+	0.0802667i	0.348686	+	0.937240i	$0.386628\pi$
$42$			202951.i			2.73932i
$43$	−44777.2	+	65699.0i	−0.563186	+	0.826330i
$43$	−44777.2	+	65699.0i	−0.563186	+	0.826330i
$44$	8830.90			0.103669
$45$	−36338.4	−	75457.4i	−0.398775	−	0.828064i
$46$	−111615.	+	231771.i	−1.14670	+	2.38114i
$47$	49831.3	−	62486.4i	0.479964	−	0.601855i	−0.481616	−	0.876383i	$-0.659950\pi$
$47$	49831.3	−	62486.4i	0.479964	−	0.601855i	0.961579	+	0.274527i	$0.0885213\pi$
$48$	2971.94	+	678.325i	0.0268730	+	0.00613359i
$49$	23596.4			0.200566
$50$			176736.i			1.41389i
$51$	416973.	+	95171.4i	3.14339	+	0.717457i
$52$	−76782.7	−	96282.4i	−0.546076	−	0.684758i
$53$	49112.1	+	215174.i	0.329884	+	1.44531i	0.819351	+	0.573293i	$0.194334\pi$
$53$	49112.1	+	215174.i	0.329884	+	1.44531i	−0.489467	+	0.872022i	$0.662809\pi$
$54$	−474175.	−	594597.i	−3.01132	−	3.77608i
$55$	−1643.29	−	3412.33i	−0.00987703	−	0.0205099i
$56$	−35351.5	+	154885.i	−0.201300	+	0.881953i
$57$	−294445.	+	141797.i	−1.58994	+	0.765673i
$58$	57872.9	−	72570.3i	0.296614	−	0.371942i
$59$	−22744.7	−	99651.1i	−0.110745	−	0.485206i	−0.999633	−	0.0270815i	$-0.991379\pi$
$59$	−22744.7	−	99651.1i	−0.110745	−	0.485206i	0.888888	−	0.458124i	$-0.151479\pi$
$60$	−52676.1	−	230789.i	−0.243871	−	1.06847i
$61$	−48578.6	+	100875.i	−0.214021	+	0.444418i	−0.980147	−	0.198271i	$-0.936467\pi$
$61$	−48578.6	+	100875.i	−0.214021	+	0.444418i	0.766127	+	0.642690i	$0.222182\pi$
$62$	−93078.3	−	74227.5i	−0.390547	−	0.311451i
$63$	450345.	−	359138.i	1.80104	−	1.43628i
$64$	−381538.	−	183739.i	−1.45545	−	0.700909i
$65$	−22916.2	+	47586.0i	−0.0834455	+	0.173276i
$66$	−35045.4	−	43945.5i	−0.121899	−	0.152856i
$67$	−94711.9	+	118765.i	−0.314906	+	0.394879i	−0.913943	−	0.405842i	$-0.866978\pi$
$67$	−94711.9	+	118765.i	−0.314906	+	0.394879i	0.599038	+	0.800721i	$0.295550\pi$
$68$	784630.	+	377858.i	2.49539	+	1.20172i
$69$	988086.	−	225524.i	3.00779	−	0.686508i
$70$	172790.	−	39438.2i	0.503761	−	0.114980i
$71$	21411.2	+	17074.9i	0.0598227	+	0.0477070i	0.652945	−	0.757406i	$-0.273533\pi$
$71$	21411.2	+	17074.9i	0.0598227	+	0.0477070i	−0.593122	+	0.805113i	$0.702105\pi$
$72$	−422155.	−	876615.i	−1.13103	−	2.34861i
$73$	−529084.	−	120760.i	−1.36005	−	0.310423i	−0.520574	−	0.853816i	$-0.674282\pi$
$73$	−529084.	−	120760.i	−1.36005	−	0.310423i	−0.839478	+	0.543393i	$0.817139\pi$
$74$	−1.17117e6	+	564007.i	−2.89019	+	1.39184i
$75$	544390.	−	434137.i	1.29041	−	1.02907i
$76$	−648764.	+	148076.i	−1.47790	+	0.337322i
$77$	20365.5	−	16240.9i	0.0446090	−	0.0355745i
$78$	−174422.	+	764193.i	−0.367551	+	1.61035i
$79$	−169739.			−0.344272			−0.172136	−	0.985073i	$-0.555067\pi$
$79$	−169739.			−0.344272			−0.172136	+	0.985073i	$0.555067\pi$
$80$		−	2662.09i		−	0.00519940i
$81$	−362054.	+	1.58626e6i	−0.681269	+	2.98483i
$82$	129194.	+	103029.i	0.234316	+	0.186860i
$83$	−586495.	−	282441.i	−1.02572	−	0.493962i	−0.156132	−	0.987736i	$-0.549903\pi$
$83$	−586495.	−	282441.i	−1.02572	−	0.493962i	−0.869590	+	0.493774i	$0.835617\pi$
$84$	1.46687e6	−	706409.i	2.47488	−	1.19184i
$85$		−	373501.i		−	0.608183i
$86$	1.01895e6	+	153413.i	1.60199	+	0.241195i
$87$	−365695.			−0.555343
$88$	−19090.7	−	39642.2i	−0.0280139	−	0.0581715i
$89$	−29735.1	+	61745.6i	−0.0421793	+	0.0875863i	−0.920994	−	0.389578i	$-0.872621\pi$
$89$	−29735.1	+	61745.6i	−0.0421793	+	0.0875863i	0.878814	+	0.477164i	$0.158335\pi$
$90$	−676764.	+	848635.i	−0.928346	+	1.16411i
$91$	−354147.	−	80831.6i	−0.469958	−	0.107265i
$92$	2.06368e6			2.65020
$93$			469039.i			0.583122i
$94$	−1.00986e6	−	230494.i	−1.21584	−	0.277508i
$95$	177942.	+	223133.i	0.207543	+	0.260251i
$96$	367905.	+	1.61190e6i	0.415836	+	1.82190i
$97$	−527551.	−	661528.i	−0.578028	−	0.724825i	0.403747	−	0.914871i	$-0.367708\pi$
$97$	−527551.	−	661528.i	−0.578028	−	0.724825i	−0.981775	+	0.190046i	$0.939136\pi$
$98$	−132689.	−	275532.i	−0.140980	−	0.292748i
$99$	−35498.9	+	155531.i	−0.0365855	+	0.160292i
$100$	1.27740e6	−	615163.i	1.27740	−	0.615163i
$101$	−502808.	+	630501.i	−0.488020	+	0.611958i	−0.963480	−	0.267779i	$-0.913710\pi$
$101$	−502808.	+	630501.i	−0.488020	+	0.611958i	0.475460	+	0.879737i	$0.342282\pi$
$102$	−1.23345e6	−	5.40411e6i	−1.16231	−	5.09241i
$103$	−305278.	−	1.33751e6i	−0.279373	−	1.22401i	−0.898589	−	0.438792i	$-0.855407\pi$
$103$	−305278.	−	1.33751e6i	−0.279373	−	1.22401i	0.619216	−	0.785221i	$-0.287451\pi$
$104$	−266226.	+	552824.i	−0.236674	+	0.491458i
$105$	−545924.	−	435360.i	−0.471590	−	0.376080i
$106$	2.23639e6	−	1.78346e6i	1.87771	−	1.49743i
$107$	1.33134e6	+	641140.i	1.08677	+	0.523361i	0.889475	−	0.456983i	$-0.151070\pi$
$107$	1.33134e6	+	641140.i	1.08677	+	0.523361i	0.197295	+	0.980344i	$0.436784\pi$
$108$	−2.64713e6	+	5.49683e6i	−2.10138	+	4.36356i
$109$	−13494.7	−	16921.8i	−0.0104204	−	0.0130668i	0.776594	−	0.630001i	$-0.216946\pi$
$109$	−13494.7	−	16921.8i	−0.0104204	−	0.0130668i	−0.787014	+	0.616935i	$0.788374\pi$
$110$	−30604.6	+	38376.9i	−0.0229937	+	0.0288332i
$111$	4.61417e6	+	2.22207e6i	3.37384	+	1.62476i
$112$	17849.9	−	4074.12i	0.0127052	−	0.00289988i
$113$	−1.69353e6	+	386536.i	−1.17370	+	0.267889i	−0.764541	−	0.644575i	$-0.777034\pi$
$113$	−1.69353e6	+	386536.i	−1.17370	+	0.267889i	−0.409157	+	0.912464i	$0.634177\pi$
$114$	3.31149e6	+	2.64083e6i	2.23516	+	1.78248i
$115$	−384018.	−	797421.i	−0.252498	−	0.524317i
$116$	−725957.	−	165695.i	−0.465090	−	0.106154i
$117$	2.00439e6	−	965263.i	1.25148	−	0.602682i
$118$	−1.03571e6	+	825952.i	−0.630366	+	0.502700i
$119$	2.50440e6	−	571614.i	1.48615	−	0.339205i
$120$	−922144.	+	735385.i	−0.533648	+	0.425570i
$121$	392604.	−	1.72011e6i	0.221615	−	0.970958i
$122$	1.45107e6			0.799113
$123$		−	651032.i		−	0.349854i
$124$	−212520.	+	931109.i	−0.111464	+	0.488355i
$125$	−1.02013e6	−	813529.i	−0.522308	−	0.416527i
$126$	−6.72602e6	−	3.23908e6i	−3.36238	−	1.61924i
$127$	−1.78481e6	+	859519.i	−0.871326	+	0.419609i	−0.815449	−	0.578829i	$-0.803510\pi$
$127$	−1.78481e6	+	859519.i	−0.871326	+	0.419609i	−0.0558773	+	0.998438i	$0.517796\pi$
$128$			3.41607e6i			1.62891i
$129$	−2.03042e6	−	3.51548e6i	−0.945839	−	1.63763i
$130$	684520.			0.311570
$131$	−951129.	−	1.97504e6i	−0.423083	−	0.878541i	−0.998171	−	0.0604494i	$-0.980747\pi$
$131$	−951129.	−	1.97504e6i	−0.423083	−	0.878541i	0.575088	−	0.818091i	$-0.304968\pi$
$132$	−195644.	+	406260.i	−0.0850640	+	0.176637i
$133$	−1.22383e6	+	1.53463e6i	−0.520194	+	0.652303i
$134$	1.91939e6	+	438089.i	0.797718	+	0.182074i
$135$	2.61660e6			1.06350
$136$		−	4.33909e6i		−	1.72497i
$137$	−4.11844e6	−	940007.i	−1.60166	−	0.365569i	−0.673924	−	0.738801i	$-0.735392\pi$
$137$	−4.11844e6	−	940007.i	−1.60166	−	0.365569i	−0.927738	+	0.373232i	$0.878250\pi$
$138$	−8.18969e6	−	1.02695e7i	−3.11624	−	3.90764i
$139$	530487.	+	2.32422e6i	0.197529	+	0.865431i	0.972402	+	0.233313i	$0.0749568\pi$
$139$	530487.	+	2.32422e6i	0.197529	+	0.865431i	−0.774873	+	0.632117i	$0.782186\pi$
$140$	−886478.	−	1.11161e6i	−0.323060	−	0.405105i
$141$	1.77066e6	+	3.67681e6i	0.631652	+	1.31164i
$142$	78979.6	−	346032.i	0.0275835	−	0.120851i
$143$	90642.4	−	43651.1i	0.0309973	−	0.0149275i
$144$	−69912.5	+	87667.5i	−0.0234135	+	0.0293597i
$145$	71063.3	+	311349.i	0.0233100	+	0.102128i
$146$	1.56509e6	+	6.85710e6i	0.502898	+	2.20334i
$147$	−522768.	+	1.08554e6i	−0.164572	+	0.341738i
$148$	8.15299e6	+	6.50179e6i	2.51496	+	2.00562i
$149$	2.10003e6	−	1.67472e6i	0.634844	−	0.506271i	−0.252369	−	0.967631i	$-0.581210\pi$
$149$	2.10003e6	−	1.67472e6i	0.634844	−	0.506271i	0.887213	+	0.461360i	$0.152638\pi$
$150$	−8.13061e6	−	3.91550e6i	−2.40907	−	1.16015i
$151$	506133.	−	1.05100e6i	0.147006	−	0.305260i	−0.814444	−	0.580243i	$-0.802958\pi$
$151$	506133.	−	1.05100e6i	0.147006	−	0.305260i	0.961449	+	0.274982i	$0.0886720\pi$
$152$	2.06722e6	+	2.59221e6i	0.588648	+	0.738141i
$153$	−9.80897e6	+	1.23001e7i	−2.73873	+	3.43426i
$154$	−304164.	−	146478.i	−0.0832809	−	0.0401060i
$155$	399334.	−	91145.4i	0.107236	−	0.0244760i
$156$	6.13049e6	−	1.39925e6i	1.61481	−	0.368570i
$157$	2.27653e6	+	1.81547e6i	0.588266	+	0.469127i	0.871818	−	0.489830i	$-0.162941\pi$
$157$	2.27653e6	+	1.81547e6i	0.588266	+	0.469127i	−0.283552	+	0.958957i	$0.591513\pi$
$158$	954491.	+	1.98202e6i	0.241992	+	0.502501i
$159$	−1.09870e7	−	2.50771e6i	−2.73330	−	0.623859i
$160$	1.30086e6	−	626461.i	0.317593	−	0.152945i
$161$	4.75917e6	−	3.79531e6i	1.14039	−	0.909432i
$162$	2.05585e7	−	4.69234e6i	4.83555	−	1.10368i
$163$	−2.54045e6	+	2.02594e6i	−0.586609	+	0.467805i	−0.871257	−	0.490827i	$-0.836695\pi$
$163$	−2.54045e6	+	2.02594e6i	−0.586609	+	0.467805i	0.284648	+	0.958632i	$0.408123\pi$
$164$	294980.	−	1.29239e6i	0.0668746	−	0.292997i
$165$	193388.			0.0430505
$166$			8.43666e6i			1.84436i
$167$	520527.	−	2.28058e6i	0.111762	−	0.489661i	−0.887805	−	0.460221i	$-0.847770\pi$
$167$	520527.	−	2.28058e6i	0.111762	−	0.489661i	0.999567	−	0.0294404i	$-0.00937251\pi$
$168$	−6.34219e6	−	5.05773e6i	−1.33755	−	1.06666i
$169$	3.08477e6	+	1.48555e6i	0.639090	+	0.307770i
$170$	−4.36131e6	+	2.10030e6i	−0.887708	+	0.427498i
$171$		−	1.20213e7i		−	2.40417i
$172$	−2.43783e6	−	7.89871e6i	−0.479091	−	1.55228i
$173$	2.87790e6			0.555823			0.277912	−	0.960607i	$-0.410358\pi$
$173$	2.87790e6			0.555823			0.277912	+	0.960607i	$0.410358\pi$
$174$	2.05640e6	+	4.27017e6i	0.390356	+	0.810582i
$175$	1.81454e6	−	3.76793e6i	0.338573	−	0.703055i
$176$	−3161.58	+	3964.49i	−0.000579917	+	0.000727193i
$177$	5.08828e6	+	1.16137e6i	0.917595	+	0.209435i
$178$	888203.			0.157490
$179$			9.01779e6i			1.57232i	0.618023	+	0.786160i	$0.287934\pi$
$179$			9.01779e6i			1.57232i	−0.618023	+	0.786160i	$0.712066\pi$
$180$	8.48932e6	+	1.93763e6i	1.45564	+	0.332241i
$181$	−4.04989e6	−	5.07840e6i	−0.682979	−	0.856429i	0.312646	−	0.949870i	$-0.398785\pi$
$181$	−4.04989e6	−	5.07840e6i	−0.682979	−	0.856429i	−0.995625	+	0.0934411i	$0.970213\pi$
$182$	1.04760e6	+	4.58986e6i	0.173773	+	0.761351i
$183$	−3.56443e6	−	4.46965e6i	−0.581617	−	0.729324i
$184$	−4.46127e6	−	9.26391e6i	−0.716151	−	1.48710i
$185$	995201.	−	4.36026e6i	0.157179	−	0.688648i
$186$	5.47689e6	−	2.63753e6i	0.851129	−	0.409882i
$187$	−443581.	+	556232.i	−0.0678340	+	0.0850612i
$188$	1.84906e6	+	8.10128e6i	0.278278	+	1.21921i
$189$	4.00451e6	+	1.75449e7i	0.593150	+	2.59876i
$190$	1.60487e6	−	3.33255e6i	0.233980	−	0.485865i
$191$	−6.91069e6	−	5.51109e6i	−0.991793	−	0.790929i	−0.0138721	−	0.999904i	$-0.504416\pi$
$191$	−6.91069e6	−	5.51109e6i	−0.991793	−	0.790929i	−0.977921	+	0.208975i	$0.932987\pi$
$192$	1.69056e7	−	1.34818e7i	2.38851	−	1.90477i
$193$	6.08812e6	+	2.93189e6i	0.846860	+	0.407826i	0.806411	−	0.591355i	$-0.201407\pi$
$193$	6.08812e6	+	2.93189e6i	0.846860	+	0.407826i	0.0404489	+	0.999182i	$0.487121\pi$
$194$	−4.75800e6	+	9.88009e6i	−0.651657	+	1.35318i
$195$	−1.68147e6	−	2.10849e6i	−0.226769	−	0.284360i
$196$	−1.52962e6	+	1.91809e6i	−0.203150	+	0.254742i
$197$	−2.54963e6	−	1.22784e6i	−0.333487	−	0.160599i	0.259645	−	0.965704i	$-0.416395\pi$
$197$	−2.54963e6	−	1.22784e6i	−0.333487	−	0.160599i	−0.593132	+	0.805105i	$0.702109\pi$
$198$	2.01573e6	−	460077.i	0.259679	−	0.0592700i
$199$	−2.10256e6	+	479895.i	−0.266802	+	0.0608958i	−0.353829	−	0.935310i	$-0.615121\pi$
$199$	−2.10256e6	+	479895.i	−0.266802	+	0.0608958i	0.0870270	+	0.996206i	$0.472263\pi$
$200$	−5.52297e6	−	4.40443e6i	−0.690372	−	0.550553i
$201$	−3.36541e6	−	6.98834e6i	−0.414429	−	0.860570i
$202$	1.01897e7	+	2.32573e6i	1.23625	+	0.282166i
$203$	−1.97891e6	+	952991.i	−0.236558	+	0.113920i
$204$	−3.47662e7	+	2.77251e7i	−4.09512	+	3.26575i
$205$	−554282.	+	126511.i	−0.0643382	+	0.0146848i
$206$	−1.39013e7	+	1.10859e7i	−1.59020	+	1.26814i
$207$	−8.29566e6	+	3.63457e7i	−0.935277	+	4.09771i
$208$	70713.7			0.00785802
$209$		−	543628.i		−	0.0595475i
$210$	−2.01375e6	+	8.82282e6i	−0.217444	+	0.952686i
$211$	−3.77448e6	−	3.01005e6i	−0.401800	−	0.320425i	0.401654	−	0.915792i	$-0.368435\pi$
$211$	−3.77448e6	−	3.01005e6i	−0.401800	−	0.320425i	−0.803454	+	0.595366i	$0.797007\pi$
$212$	−2.06745e7	−	9.95634e6i	−2.16984	−	1.04494i
$213$	−1.25987e6	+	606723.i	−0.130373	+	0.0627844i
$214$		−	1.91512e7i		−	1.95413i
$215$	−2.59848e6	+	2.41182e6i	−0.261459	+	0.242678i
$216$	3.03980e7			3.01637
$217$	1.22230e6	+	2.53813e6i	0.119619	+	0.248391i
$218$	−121709.	+	252732.i	−0.0117477	+	0.0243944i
$219$	1.72771e7	−	2.16648e7i	1.64489	−	2.06263i
$220$	383904.	+	87623.5i	0.0360541	+	0.00822911i
$221$	9.92138e6			0.919168
$222$		−	6.63744e7i		−	6.06654i
$223$	4.89056e6	+	1.11624e6i	0.441006	+	0.100657i	0.437258	−	0.899336i	$-0.355950\pi$
$223$	4.89056e6	+	1.11624e6i	0.441006	+	0.100657i	0.00374802	+	0.999993i	$0.498807\pi$
$224$	6.19142e6	+	7.76380e6i	0.550867	+	0.690765i
$225$	5.69936e6	+	2.49705e7i	0.500356	+	2.19220i
$226$	1.40367e7	+	1.76015e7i	1.21602	+	1.52484i
$227$	−1.02707e6	−	2.13273e6i	−0.0878054	−	0.182330i	0.852442	−	0.522822i	$-0.175121\pi$
$227$	−1.02707e6	−	2.13273e6i	−0.0878054	−	0.182330i	−0.940247	+	0.340492i	$0.889406\pi$
$228$	7.56091e6	−	3.31265e7i	0.637925	−	2.79493i
$229$	−1.89366e7	+	9.11938e6i	−1.57687	+	0.759379i	−0.998412	−	0.0563352i	$-0.982058\pi$
$229$	−1.89366e7	+	9.11938e6i	−1.57687	+	0.759379i	−0.578455	+	0.815714i	$0.696344\pi$
$230$	−7.15193e6	+	8.96823e6i	−0.587814	+	0.737095i
$231$	295966.	+	1.29671e6i	0.0240108	+	0.105198i
$232$	825567.	+	3.61705e6i	0.0661133	+	0.289661i
$233$	−4.96110e6	+	1.03018e7i	−0.392202	+	0.814417i	0.607594	+	0.794248i	$0.292135\pi$
$233$	−4.96110e6	+	1.03018e7i	−0.392202	+	0.814417i	−0.999797	+	0.0201691i	$0.993580\pi$
$234$	−2.25425e7	−	1.79770e7i	−1.75936	−	1.40304i
$235$	2.78632e6	−	2.22201e6i	0.214697	−	0.171215i
$236$	9.57476e6	+	4.61096e6i	0.728437	+	0.350797i
$237$	3.76049e6	−	7.80875e6i	0.282488	−	0.586592i
$238$	−2.07576e7	−	2.60292e7i	−1.53974	−	1.93077i
$239$	1.24191e7	−	1.55730e7i	0.909695	−	1.14072i	−0.0798950	−	0.996803i	$-0.525459\pi$
$239$	1.24191e7	−	1.55730e7i	0.909695	−	1.14072i	0.989590	−	0.143918i	$-0.0459701\pi$
$240$	122468.	+	58977.4i	0.00885907	+	0.00426630i
$241$	1.63723e7	−	3.73686e6i	1.16965	−	0.266966i	0.406788	−	0.913523i	$-0.366649\pi$
$241$	1.63723e7	−	3.73686e6i	1.16965	−	0.266966i	0.762866	+	0.646557i	$0.223792\pi$
$242$	−2.22932e7	+	5.08828e6i	−1.57299	+	0.359025i
$243$	−3.15086e7	−	2.51273e7i	−2.19589	−	1.75116i
$244$	−5.05072e6	−	1.04879e7i	−0.347684	−	0.721972i
$245$	1.02580e6	+	234133.i	0.0697534	+	0.0159208i
$246$	−7.60201e6	+	3.66094e6i	−0.510650	+	0.245916i
$247$	−5.92712e6	+	4.72672e6i	−0.393326	+	0.313667i
$248$	4.63921e6	−	1.05887e6i	0.304151	−	0.0694204i
$249$	2.59870e7	−	2.07240e7i	1.68329	−	1.34238i
$250$	−3.76297e6	+	1.64866e7i	−0.240830	+	1.05515i
$251$	1.45492e6			0.0920062			0.0460031	−	0.998941i	$-0.485352\pi$
$251$	1.45492e6			0.0920062			0.0460031	+	0.998941i	$0.485352\pi$
$252$			5.98882e7i			3.74231i
$253$	−375146.	+	1.64362e6i	−0.0231654	+	0.101494i
$254$	2.00730e7	+	1.60076e7i	1.22493	+	0.976847i
$255$	1.71827e7	+	8.27473e6i	1.03626	+	0.499038i
$256$	1.54705e7	−	7.45018e6i	0.922111	−	0.444065i
$257$		−	1.16981e7i		−	0.689154i	−0.938758	−	0.344577i	$-0.888022\pi$
$257$		−	1.16981e7i		−	0.689154i	0.938758	−	0.344577i	$-0.111978\pi$
$258$	−2.96321e7	+	4.34775e7i	−1.72545	+	2.53166i
$259$	3.07596e7			1.77044
$260$	−2.38260e6	−	4.94753e6i	−0.135560	−	0.281493i
$261$	5.83647e6	−	1.21196e7i	0.328268	−	0.681656i
$262$	−1.77138e7	+	2.22124e7i	−0.984935	+	1.23507i
$263$	2.01559e6	+	460046.i	0.110799	+	0.0252891i	0.277561	−	0.960708i	$-0.410474\pi$
$263$	2.01559e6	+	460046.i	0.110799	+	0.0252891i	−0.166762	+	0.985997i	$0.553331\pi$
$264$	2.24666e6			0.122103
$265$			9.84152e6i			0.528840i
$266$	2.48016e7	+	5.66080e6i	1.31775	+	0.300769i
$267$	−2.18180e6	−	2.73589e6i	−0.114625	−	0.143736i
$268$	−3.51443e6	−	1.53977e7i	−0.182579	−	0.799930i
$269$	8.82193e6	+	1.10624e7i	0.453218	+	0.568317i	0.954973	−	0.296692i	$-0.0958836\pi$
$269$	8.82193e6	+	1.10624e7i	0.453218	+	0.568317i	−0.501755	+	0.865010i	$0.667312\pi$
$270$	−1.47139e7	−	3.05537e7i	−0.747543	−	1.55229i
$271$	529052.	−	2.31793e6i	0.0265822	−	0.116464i	−0.959896	−	0.280356i	$-0.909548\pi$
$271$	529052.	−	2.31793e6i	0.0265822	−	0.116464i	0.986478	+	0.163892i	$0.0524047\pi$
$272$	−450541.	+	216969.i	−0.0223886	+	0.0107818i
$273$	1.15646e7	−	1.45015e7i	0.568383	−	0.712730i
$274$	1.21828e7	+	5.33763e7i	0.592237	+	2.59476i
$275$	257736.	+	1.12922e6i	0.0123930	+	0.0542974i
$276$	−4.57198e7	+	9.49381e7i	−2.17459	+	4.51558i
$277$	−1.20403e7	−	9.60181e6i	−0.566497	−	0.451766i	0.297885	−	0.954602i	$-0.403719\pi$
$277$	−1.20403e7	−	9.60181e6i	−0.566497	−	0.451766i	−0.864382	+	0.502835i	$0.832290\pi$
$278$	2.41565e7	−	1.92641e7i	1.12434	−	0.896634i
$279$	−1.55445e7	−	7.48583e6i	−0.715754	−	0.344689i
$280$	−3.07365e6	+	6.38251e6i	−0.140017	+	0.290748i
$281$	599696.	+	751995.i	0.0270279	+	0.0338919i	0.795162	−	0.606397i	$-0.207386\pi$
$281$	599696.	+	751995.i	0.0270279	+	0.0338919i	−0.768134	+	0.640289i	$0.778814\pi$
$282$	3.29767e7	−	4.13515e7i	1.47048	−	1.84393i
$283$	−1.18041e7	−	5.68457e6i	−0.520805	−	0.250806i	0.154964	−	0.987920i	$-0.450474\pi$
$283$	−1.18041e7	−	5.68457e6i	−0.520805	−	0.250806i	−0.675769	+	0.737114i	$0.736188\pi$
$284$	−2.77593e6	+	633589.i	−0.121186	+	0.0276600i
$285$	−1.42073e7	+	3.24273e6i	−0.613730	+	0.140080i
$286$	−1.01941e6	−	812956.i	−0.0435766	−	0.0347511i
$287$	−1.69657e6	−	3.52297e6i	−0.0717673	−	0.149026i
$288$	−5.92919e7	−	1.35330e7i	−2.48209	−	0.566522i
$289$	−4.14653e7	+	1.99686e7i	−1.71787	+	0.827285i
$290$	3.23596e6	−	2.58060e6i	0.132681	−	0.105810i
$291$	4.21208e7	−	9.61380e6i	1.70930	−	0.390136i
$292$	4.41137e7	−	3.51795e7i	1.77184	−	1.41300i
$293$	−83176.5	+	364420.i	−0.00330672	+	0.0144877i	−0.976554	−	0.215271i	$-0.930937\pi$
$293$	−83176.5	+	364420.i	−0.00330672	+	0.0144877i	0.973248	+	0.229759i	$0.0737937\pi$
$294$	1.56154e7			0.614483
$295$		−	4.55779e6i		−	0.177537i
$296$	1.15616e7	−	5.06547e7i	0.445803	−	1.95319i
$297$	−3.89676e6	−	3.10756e6i	−0.148742	−	0.118618i
$298$	−3.13645e7	−	1.51044e7i	−1.18520	−	0.570760i
$299$	2.11821e7	−	1.02007e7i	0.792418	−	0.381609i
$300$			7.23946e7i			2.68128i
$301$	−2.01486e7	−	1.37323e7i	−0.738830	−	0.503551i
$302$	−1.51185e7			−0.548892
$303$	−1.78663e7	−	3.70998e7i	−0.642254	−	1.33365i
$304$	165790.	−	344265.i	0.00590115	−	0.0122539i
$305$	−3.11276e6	+	3.90328e6i	−0.109710	+	0.137572i
$306$	1.98784e8	+	4.53713e7i	6.93774	+	1.58349i
$307$	−4.55776e7			−1.57520			−0.787600	−	0.616186i	$-0.788677\pi$
$307$	−4.55776e7			−1.57520			−0.787600	+	0.616186i	$0.788677\pi$
$308$			2.70826e6i			0.0926912i
$309$	6.82946e7	+	1.55878e7i	2.31479	+	0.528335i
$310$	−3.30986e6	−	4.15043e6i	−0.111103	−	0.139318i
$311$	243017.	+	1.06473e6i	0.00807897	+	0.0353963i	0.978807	−	0.204786i	$-0.0656499\pi$
$311$	243017.	+	1.06473e6i	0.00807897	+	0.0353963i	−0.970728	+	0.240182i	$0.922793\pi$
$312$	−1.95342e7	−	2.44951e7i	−0.643179	−	0.806520i
$313$	1.00947e7	+	2.09618e7i	0.329199	+	0.683589i	0.998219	−	0.0596557i	$-0.0190003\pi$
$313$	1.00947e7	+	2.09618e7i	0.329199	+	0.683589i	−0.669020	+	0.743244i	$0.733286\pi$
$314$	8.39743e6	−	3.67916e7i	0.271242	−	1.18839i
$315$	2.31413e7	−	1.11442e7i	0.740381	−	0.356549i
$316$	1.10032e7	−	1.37976e7i	0.348706	−	0.437263i
$317$	−6.28578e6	−	2.75398e7i	−0.197325	−	0.864536i	−0.972521	−	0.232816i	$-0.925206\pi$
$317$	−6.28578e6	−	2.75398e7i	−0.197325	−	0.864536i	0.775196	−	0.631721i	$-0.217651\pi$
$318$	3.25008e7	+	1.42395e8i	1.01068	+	4.42806i
$319$	263937.	−	548070.i	0.00813070	−	0.0168836i
$320$	−1.47634e7	−	1.17734e7i	−0.450543	−	0.359296i
$321$	−5.89904e7	+	4.70433e7i	−1.78347	+	1.42227i
$322$	−7.10795e7	−	3.42301e7i	−2.12900	−	1.02527i
$323$	2.32608e7	−	4.83017e7i	0.690268	−	1.43336i
$324$	−1.05473e8	−	1.32259e8i	−3.10103	−	3.88857i
$325$	1.00708e7	−	1.26283e7i	0.293368	−	0.367872i
$326$	3.79423e7	+	1.82721e7i	1.09514	+	0.527393i
$327$	1.07745e6	−	245920.i	0.0308143	−	0.00703317i
$328$	−6.43929e6	+	1.46972e6i	−0.182480	+	0.0416500i
$329$	1.91633e7	+	1.52822e7i	0.538125	+	0.429141i
$330$	−1.08748e6	−	2.25817e6i	−0.0302606	−	0.0628368i
$331$	2.76188e6	+	630381.i	0.0761589	+	0.0173828i	0.260431	−	0.965493i	$-0.416135\pi$
$331$	2.76188e6	+	630381.i	0.0761589	+	0.0173828i	−0.184272	+	0.982875i	$0.558993\pi$
$332$	6.09779e7	−	2.93654e7i	1.66632	−	0.802457i
$333$	−1.47284e8	+	1.17455e8i	−3.98862	+	3.18082i
$334$	−2.95570e7	+	6.74620e6i	−0.793271	+	0.181059i
$335$	−5.29582e6	+	4.22327e6i	−0.140864	+	0.112335i
$336$	−208029.	+	911434.i	−0.00548410	+	0.0240274i
$337$	1.77993e6			0.0465064			0.0232532	−	0.999730i	$-0.492598\pi$
$337$	1.77993e6			0.0465064			0.0232532	+	0.999730i	$0.492598\pi$
$338$		−	4.43740e7i		−	1.14915i
$339$	1.97369e7	−	8.64731e7i	0.506618	−	2.21964i
$340$	3.03608e7	+	2.42119e7i	0.772461	+	0.616017i
$341$	−702952.	−	338524.i	−0.0177281	−	0.00853741i
$342$	−1.40371e8	+	6.75993e7i	−3.50914	+	1.68991i
$343$			4.33171e7i			1.07344i
$344$	−3.01874e7	+	2.80190e7i	−0.741568	+	0.688298i
$345$	4.51925e7			1.10055
$346$	−1.61832e7	−	3.36048e7i	−0.390693	−	0.811283i
$347$	2.91803e7	−	6.05935e7i	0.698395	−	1.45023i	−0.185547	−	0.982635i	$-0.559406\pi$
$347$	2.91803e7	−	6.05935e7i	0.698395	−	1.45023i	0.883942	−	0.467596i	$-0.154880\pi$
$348$	2.37059e7	−	2.97263e7i	0.562496	−	0.705347i
$349$	1.24968e7	+	2.85231e6i	0.293983	+	0.0670997i	0.366969	−	0.930233i	$-0.380396\pi$
$349$	1.24968e7	+	2.85231e6i	0.293983	+	0.0670997i	−0.0729856	+	0.997333i	$0.523253\pi$
$350$	−5.42013e7			−1.26417
$351$			6.95054e7i			1.60730i
$352$	−2.68130e6	−	611989.i	−0.0614776	−	0.0140319i
$353$	−1.30683e7	−	1.63871e7i	−0.297095	−	0.372545i	0.610770	−	0.791808i	$-0.290860\pi$
$353$	−1.30683e7	−	1.63871e7i	−0.297095	−	0.372545i	−0.907865	+	0.419263i	$0.862289\pi$
$354$	−1.50517e7	−	6.59458e7i	−0.339294	−	1.48654i
$355$	761381.	+	954741.i	0.0170183	+	0.0213403i
$356$	−3.09156e6	−	6.41970e6i	−0.0685217	−	0.142287i
$357$	−2.91872e7	+	1.27877e8i	−0.641486	+	2.81053i
$358$	1.05299e8	−	5.07095e7i	2.29497	−	1.10520i
$359$	−2.08157e7	+	2.61021e7i	−0.449892	+	0.564147i	−0.954120	−	0.299423i	$-0.903206\pi$
$359$	−2.08157e7	+	2.61021e7i	−0.449892	+	0.564147i	0.504228	+	0.863571i	$0.331777\pi$
$360$	−9.65416e6	−	4.22976e7i	−0.206922	−	0.906585i
$361$	−1.35316e6	−	5.92859e6i	−0.0287626	−	0.126017i
$362$	−3.65261e7	+	7.58472e7i	−0.769976	+	1.59887i
$363$	7.04346e7	+	5.61697e7i	1.47254	+	1.17431i
$364$	2.95279e7	−	2.35477e7i	0.612249	−	0.488252i
$365$	−2.18025e7	−	1.04995e7i	−0.448361	−	0.215919i
$366$	−3.21477e7	+	6.67554e7i	−0.655703	+	1.36158i
$367$	5.93055e7	+	7.43667e7i	1.19977	+	1.50446i	0.812981	+	0.582290i	$0.197843\pi$
$367$	5.93055e7	+	7.43667e7i	1.19977	+	1.50446i	0.386786	+	0.922170i	$0.373585\pi$
$368$	−738823.	+	926455.i	−0.0148251	+	0.0185901i
$369$	2.15760e7	+	1.03904e7i	0.429429	+	0.206802i
$370$	−5.65104e7	+	1.28981e7i	−1.11564	+	0.254637i
$371$	−6.59896e7	+	1.50617e7i	−1.29227	+	0.294952i
$372$	−3.81268e7	−	3.04051e7i	−0.740630	−	0.590633i
$373$	−4.09825e7	−	8.51010e7i	−0.789717	−	1.63986i	−0.768297	−	0.640094i	$-0.778895\pi$
$373$	−4.09825e7	−	8.51010e7i	−0.789717	−	1.63986i	−0.0214205	−	0.999771i	$-0.506819\pi$
$374$	8.98942e6	+	2.05178e6i	0.171837	+	0.0392207i
$375$	6.00264e7	−	2.89072e7i	1.13828	−	0.548166i
$376$	3.23696e7	−	2.58139e7i	0.608939	−	0.485613i
$377$	−8.27042e6	+	1.88767e6i	−0.154349	+	0.0352291i
$378$	1.82351e8	−	1.45420e8i	3.37623	−	2.69246i
$379$	795780.	−	3.48654e6i	0.0146176	−	0.0640438i	−0.967093	−	0.254423i	$-0.918115\pi$
$379$	795780.	−	3.48654e6i	0.0146176	−	0.0640438i	0.981711	+	0.190379i	$0.0609717\pi$
$380$	−2.96728e7			−0.540764
$381$		−	1.01151e8i		−	1.82893i
$382$	−2.54915e7	+	1.11685e8i	−0.457304	+	2.00358i
$383$	−2.06159e7	−	1.64406e7i	−0.366949	−	0.292632i	0.422604	−	0.906314i	$-0.361116\pi$
$383$	−2.06159e7	−	1.64406e7i	−0.366949	−	0.292632i	−0.789553	+	0.613682i	$0.789688\pi$
$384$	−1.57154e8	−	7.56813e7i	−2.77544	−	1.33658i
$385$	1.04649e6	−	503964.i	0.0183381	−	0.00883116i
$386$		−	8.75769e7i		−	1.52275i
$387$	1.48913e8	−	1.11837e7i	2.56920	−	0.192954i
$388$	8.79718e7			1.50608
$389$	1.67178e7	+	3.47149e7i	0.284008	+	0.589749i	0.993352	−	0.115113i	$-0.0367231\pi$
$389$	1.67178e7	+	3.47149e7i	0.284008	+	0.589749i	−0.709344	+	0.704862i	$0.751009\pi$
$390$	−1.51652e7	+	3.14909e7i	−0.255655	+	0.530873i
$391$	−1.03659e8	+	1.29985e8i	−1.73412	+	2.17452i
$392$	1.19171e7	+	2.72000e6i	0.197839	+	0.0451555i
$393$	1.11932e8			1.84407
$394$			3.66762e7i			0.599647i
$395$	−7.37904e6	−	1.68422e6i	−0.119731	−	0.0273279i
$396$	−1.03415e7	−	1.29678e7i	−0.166531	−	0.208824i
$397$	1.60524e6	+	7.03299e6i	0.0256547	+	0.112401i	0.986134	−	0.165951i	$-0.0530692\pi$
$397$	1.60524e6	+	7.03299e6i	0.0256547	+	0.112401i	−0.960479	+	0.278351i	$0.910212\pi$
$398$	1.74269e7	+	2.18527e7i	0.276422	+	0.346622i
$399$	−4.34864e7	−	9.03004e7i	−0.684596	−	1.42158i
$400$	−181158.	+	793705.i	−0.00283059	+	0.0124016i
$401$	−1.07584e8	+	5.18097e7i	−1.66845	+	0.803485i	−0.670343	+	0.742052i	$0.733853\pi$
$401$	−1.07584e8	+	5.18097e7i	−1.66845	+	0.803485i	−0.998111	+	0.0614332i	$0.980433\pi$
$402$	−6.26772e7	+	7.85948e7i	−0.964788	+	1.20981i
$403$	2.42112e6	+	1.06076e7i	0.0369914	+	0.162070i
$404$	−1.86574e7	−	8.17436e7i	−0.282949	−	1.23968i
$405$	−3.14790e7	+	6.53668e7i	−0.473866	+	0.983993i
$406$	2.22559e7	+	1.77485e7i	0.332557	+	0.265206i
$407$	−6.66047e6	+	5.31155e6i	−0.0987920	+	0.0787840i
$408$	1.99617e8	+	9.61304e7i	2.93912	+	1.41540i
$409$	1.11807e7	−	2.32170e7i	0.163418	−	0.339341i	−0.803139	−	0.595791i	$-0.796839\pi$
$409$	1.11807e7	−	2.32170e7i	0.163418	−	0.339341i	0.966557	+	0.256450i	$0.0825529\pi$
$410$	4.59413e6	+	5.76086e6i	0.0666580	+	0.0835864i
$411$	1.34486e8	−	1.68641e8i	1.93710	−	2.42905i
$412$	1.28512e8	+	6.18881e7i	1.83760	+	0.884943i
$413$	3.05610e7	−	6.97534e6i	0.433828	−	0.0990183i
$414$	4.71052e8	−	1.07515e8i	6.63847	−	1.51519i
$415$	−2.26941e7	−	1.80979e7i	−0.317518	−	0.253212i
$416$	1.66408e7	+	3.45550e7i	0.231150	+	0.479989i
$417$	−1.18677e8	−	2.70872e7i	−1.63666	−	0.373556i
$418$	−6.34787e6	+	3.05697e6i	−0.0869159	+	0.0418565i
$419$	−4.64871e7	+	3.70723e7i	−0.631962	+	0.503973i	−0.886281	−	0.463148i	$-0.846720\pi$
$419$	−4.64871e7	+	3.70723e7i	−0.631962	+	0.503973i	0.254319	+	0.967120i	$0.418149\pi$
$420$	7.07783e7	−	1.61547e7i	0.955328	−	0.218047i
$421$	−4.28337e7	+	3.41588e7i	−0.574037	+	0.457779i	−0.866975	−	0.498352i	$-0.833939\pi$
$421$	−4.28337e7	+	3.41588e7i	−0.574037	+	0.457779i	0.292938	+	0.956132i	$0.405367\pi$
$422$	−1.39230e7	+	6.10005e7i	−0.185265	+	0.811700i
$423$	−1.50114e8			−1.98335
$424$			1.14332e8i			1.49993i
$425$	−2.54171e7	+	1.11360e8i	−0.331100	+	1.45064i
$426$	1.41692e7	+	1.12996e7i	0.183281	+	0.146162i
$427$	−3.09362e7	−	1.48981e7i	−0.397359	−	0.191358i
$428$	−1.38420e8	+	6.66594e7i	−1.76549	+	0.850217i
$429$			5.13702e6i			0.0650637i
$430$	4.27745e7	+	1.67797e7i	0.537996	+	0.211047i
$431$	−4.37330e7			−0.546233			−0.273116	−	0.961981i	$-0.588054\pi$
$431$	−4.37330e7			−0.546233			−0.273116	+	0.961981i	$0.588054\pi$
$432$	−1.52001e6	−	3.15632e6i	−0.0188536	−	0.0391499i
$433$	2.00011e7	−	4.15326e7i	0.246371	−	0.511594i	−0.740708	−	0.671827i	$-0.765510\pi$
$433$	2.00011e7	−	4.15326e7i	0.246371	−	0.511594i	0.987079	+	0.160232i	$0.0512243\pi$
$434$	2.27641e7	−	2.85453e7i	0.278472	−	0.349192i
$435$	−1.58978e7	−	3.62856e6i	−0.193138	−	0.0440826i
$436$	2.25031e6			0.0271509
$437$		−	1.27039e8i		−	1.52228i
$438$	−3.50130e8	−	7.99149e7i	−4.16684	−	0.951055i
$439$	9.58637e7	+	1.20209e8i	1.13308	+	1.42084i	0.892984	+	0.450089i	$0.148608\pi$
$439$	9.58637e7	+	1.20209e8i	1.13308	+	1.42084i	0.240096	+	0.970749i	$0.422821\pi$
$440$	−436580.	−	1.91278e6i	−0.00512514	−	0.0224547i
$441$	−2.76327e7	−	3.46503e7i	−0.322187	−	0.404009i
$442$	−5.57906e7	−	1.15850e8i	−0.646092	−	1.34162i
$443$	−2.04580e6	+	8.96325e6i	−0.0235317	+	0.103099i	−0.985330	−	0.170660i	$-0.945410\pi$
$443$	−2.04580e6	+	8.96325e6i	−0.0235317	+	0.103099i	0.961798	+	0.273759i	$0.0882671\pi$
$444$	−4.79736e8	+	2.31029e8i	−5.48092	+	2.63947i
$445$	−1.90533e6	+	2.38921e6i	−0.0216217	+	0.0271128i
$446$	−1.44668e7	−	6.33833e7i	−0.163068	−	0.714447i
$447$	3.05192e7	+	1.33713e8i	0.341704	+	1.49710i
$448$	5.63491e7	−	1.17010e8i	0.626690	−	1.30134i
$449$	3.17122e7	+	2.52896e7i	0.350338	+	0.279385i	0.782808	−	0.622263i	$-0.213787\pi$
$449$	3.17122e7	+	2.52896e7i	0.350338	+	0.279385i	−0.432470	+	0.901648i	$0.642358\pi$
$450$	2.59528e8	−	2.06967e8i	2.84805	−	2.27124i
$451$	975708.	+	469876.i	0.0106363	+	0.00512217i
$452$	7.83612e7	−	1.62719e8i	0.848567	−	1.76207i
$453$	3.71373e7	+	4.65686e7i	0.399499	+	0.500955i
$454$	−1.91281e7	+	2.39858e7i	−0.204411	+	0.256323i
$455$	−1.45937e7	−	7.02795e6i	−0.154928	−	0.0746095i
$456$	−1.65051e8	+	3.76719e7i	−1.74070	+	0.397304i
$457$	−3.60442e7	+	8.22686e6i	−0.377648	+	0.0861957i	−0.407131	−	0.913370i	$-0.633471\pi$
$457$	−3.60442e7	+	8.22686e6i	−0.377648	+	0.0861957i	0.0294835	+	0.999565i	$0.490614\pi$
$458$	2.12971e8	+	1.69839e8i	2.21679	+	1.76783i
$459$	−2.13262e8	−	4.42843e8i	−2.20534	−	4.57943i
$460$	8.97137e7	+	2.04766e7i	0.921691	+	0.210370i
$461$	−2.51027e7	+	1.20888e7i	−0.256223	+	0.123390i	−0.557586	−	0.830119i	$-0.688272\pi$
$461$	−2.51027e7	+	1.20888e7i	−0.256223	+	0.123390i	0.301364	+	0.953509i	$0.402558\pi$
$462$	1.34772e7	−	1.07477e7i	0.136670	−	0.108991i
$463$	9.57246e7	−	2.18485e7i	0.964452	−	0.220130i	0.288832	−	0.957380i	$-0.406733\pi$
$463$	9.57246e7	−	2.18485e7i	0.964452	−	0.220130i	0.675620	+	0.737250i	$0.263876\pi$
$464$	334288.	−	266586.i	0.00334632	−	0.00266860i
$465$	−4.65398e6	+	2.03904e7i	−0.0462877	+	0.202799i
$466$	1.48191e8			1.46441
$467$		−	5.28151e7i		−	0.518570i	−0.965801	−	0.259285i	$-0.916513\pi$
$467$		−	5.28151e7i		−	0.518570i	0.965801	−	0.259285i	$-0.0834869\pi$
$468$	−5.14697e7	+	2.25504e8i	−0.502128	+	2.19997i
$469$	−3.64228e7	−	2.90462e7i	−0.353065	−	0.281560i
$470$	−4.16143e7	−	2.00404e7i	−0.400820	−	0.193025i
$471$	−1.33955e8	+	6.45093e7i	−1.28202	+	0.617390i
$472$		−	5.29494e7i		−	0.503541i
$473$	6.73412e6	−	505750.i	0.0636352	−	0.00477917i
$474$	−1.12328e8			−1.05476
$475$	−3.78693e7	−	7.86364e7i	−0.353351	−	0.733741i
$476$	−1.15881e8	+	2.40630e8i	−1.07447	+	2.23115i
$477$	2.58460e8	−	3.24099e8i	2.38144	−	2.98623i
$478$	−2.51680e8	−	5.74443e7i	−2.30444	−	0.525973i
$479$	7.72113e7			0.702545			0.351273	−	0.936273i	$-0.385749\pi$
$479$	7.72113e7			0.702545			0.351273	+	0.936273i	$0.385749\pi$
$480$			7.37241e7i			0.666632i
$481$	1.15822e8	+	2.64357e7i	1.04078	+	0.237551i
$482$	−1.35700e8	−	1.70163e8i	−1.21183	−	1.51958i
$483$	6.91637e7	+	3.03026e8i	0.613814	+	2.68930i
$484$	1.14373e8	+	1.43419e8i	1.00876	+	1.26494i
$485$	−1.63702e7	−	3.39930e7i	−0.143492	−	0.297964i
$486$	−1.16226e8	+	5.09219e8i	−1.01250	+	4.43605i
$487$	−9.35749e7	+	4.50633e7i	−0.810163	+	0.390154i	−0.792638	−	0.609692i	$-0.791293\pi$
$487$	−9.35749e7	+	4.50633e7i	−0.810163	+	0.390154i	−0.0175251	+	0.999846i	$0.505579\pi$
$488$	−3.61620e7	+	4.53457e7i	−0.311167	+	0.390191i
$489$	−3.69197e7	−	1.61756e8i	−0.315741	−	1.38335i
$490$	−3.03444e6	−	1.32947e7i	−0.0257923	−	0.113003i
$491$	7.96220e7	−	1.65337e8i	0.672649	−	1.39677i	−0.232889	−	0.972503i	$-0.574818\pi$
$491$	7.96220e7	−	1.65337e8i	0.672649	−	1.39677i	0.905537	−	0.424266i	$-0.139468\pi$
$492$	5.29206e7	+	4.22027e7i	0.444354	+	0.354360i
$493$	4.69018e7	−	3.74030e7i	0.391425	−	0.312151i
$494$	8.85231e7	+	4.26305e7i	0.734304	+	0.353622i
$495$	−3.08647e6	+	6.40912e6i	−0.0254476	+	0.0528424i
$496$	−341922.	−	428757.i	−0.00280209	−	0.00351371i
$497$	−5.23652e6	+	6.56639e6i	−0.0426553	+	0.0534881i
$498$	−3.88123e8	−	1.86910e8i	−3.14254	−	1.51337i
$499$	1.02730e8	−	2.34473e7i	0.826787	−	0.188709i	0.211867	−	0.977298i	$-0.432046\pi$
$499$	1.02730e8	−	2.34473e7i	0.826787	−	0.188709i	0.614920	+	0.788590i	$0.289188\pi$
$500$	1.32259e8	−	3.01872e7i	1.05807	−	0.241498i
$501$	9.33845e7	+	7.44716e7i	0.742611	+	0.592213i
$502$	−8.18140e6	−	1.69889e7i	−0.0646720	−	0.134293i
$503$	−4.17692e7	−	9.53356e6i	−0.328211	−	0.0749119i	0.0552406	−	0.998473i	$-0.482407\pi$
$503$	−4.17692e7	−	9.53356e6i	−0.328211	−	0.0749119i	−0.383451	+	0.923561i	$0.625265\pi$
$504$	2.68840e8	−	1.29467e8i	2.09992	−	1.01127i
$505$	−2.81145e7	+	2.24206e7i	−0.218301	+	0.174089i
$506$	2.13019e7	−	4.86202e6i	0.164425	−	0.0375288i
$507$	−1.36683e8	+	1.09001e8i	−1.04880	+	0.836387i
$508$	4.58312e7	−	2.00800e8i	0.349599	−	1.53169i
$509$	1.10932e8			0.841206			0.420603	−	0.907245i	$-0.361819\pi$
$509$	1.10932e8			0.841206			0.420603	+	0.907245i	$0.361819\pi$
$510$		−	2.47170e8i		−	1.86331i
$511$	3.70346e7	−	1.62259e8i	0.277553	−	1.21604i
$512$	−3.05883e6	−	2.43934e6i	−0.0227901	−	0.0181745i
$513$	3.38383e8	+	1.62957e8i	2.50644	+	1.20704i
$514$	−1.36597e8	+	6.57817e7i	−1.00589	+	0.484413i
$515$		−	6.11744e7i		−	0.447866i
$516$	4.17384e8	+	6.28413e7i	3.03799	+	0.457400i
$517$	−6.78843e6			−0.0491244
$518$	−1.72970e8	−	3.59175e8i	−1.24446	−	2.58415i
$519$	−6.37584e7	+	1.32396e8i	−0.456074	+	0.947048i
$520$	−1.70589e7	+	2.13912e7i	−0.121322	+	0.152133i
$521$	−7.39068e7	−	1.68687e7i	−0.522602	−	0.119280i	−0.0469213	−	0.998899i	$-0.514941\pi$
$521$	−7.39068e7	−	1.68687e7i	−0.522602	−	0.119280i	−0.475681	+	0.879618i	$0.657798\pi$
$522$	−1.74338e8			−1.22569
$523$			2.19345e8i			1.53328i	0.642075	+	0.766642i	$0.278074\pi$
$523$			2.19345e8i			1.53328i	−0.642075	+	0.766642i	$0.721926\pi$
$524$	2.22202e8	+	5.07161e7i	1.54438	+	0.352494i
$525$	1.33141e8	+	1.66954e8i	0.920098	+	1.15377i
$526$	−5.96234e6	−	2.61227e7i	−0.0409694	−	0.179499i
$527$	−4.79728e7	−	6.01560e7i	−0.327766	−	0.411005i
$528$	−112341.	−	233278.i	−0.000763195	−	0.00158479i
$529$	−5.47261e7	+	2.39771e8i	−0.369681	+	1.61968i
$530$	1.14918e8	−	5.53416e7i	0.771899	−	0.371727i
$531$	−1.19698e8	+	1.50096e8i	−0.799470	+	1.00250i
$532$	−4.54120e7	−	1.98963e8i	−0.301603	−	1.32141i
$533$	−3.36054e6	−	1.47235e7i	−0.0221936	−	0.0972366i
$534$	−1.96777e7	+	4.08612e7i	−0.129226	+	0.268341i
$535$	5.15154e7	+	4.10822e7i	0.336415	+	0.268282i
$536$	−6.15234e7	+	4.90633e7i	−0.399527	+	0.318612i
$537$	−4.14858e8	−	1.99785e8i	−2.67902	−	1.29015i
$538$	7.95653e7	−	1.65219e8i	0.510948	−	1.06100i
$539$	−1.24960e6	−	1.56695e6i	−0.00798006	−	0.0100067i
$540$	−1.69620e8	+	2.12696e8i	−1.07720	+	1.35076i
$541$	1.70165e8	+	8.19473e7i	1.07468	+	0.517539i	0.885612	−	0.464426i	$-0.153739\pi$
$541$	1.70165e8	+	8.19473e7i	1.07468	+	0.517539i	0.189068	+	0.981964i	$0.439453\pi$
$542$	−3.00411e7	+	6.85669e6i	−0.188677	+	0.0430642i
$543$	3.23352e8	−	7.38030e7i	2.01965	−	0.460972i
$544$	−2.12049e8	−	1.69103e8i	−1.31716	−	1.05040i
$545$	−418748.	−	869538.i	−0.00258680	−	0.00537154i
$546$	−2.34363e8	−	5.34917e7i	−1.43983	−	0.328631i
$547$	−4.19073e7	+	2.01815e7i	−0.256051	+	0.123308i	−0.557507	−	0.830172i	$-0.688242\pi$
$547$	−4.19073e7	+	2.01815e7i	−0.256051	+	0.123308i	0.301455	+	0.953480i	$0.402528\pi$
$548$	3.43385e8	−	2.73841e8i	2.08660	−	1.66401i
$549$	2.05018e8	−	4.67940e7i	1.23901	−	0.282796i
$550$	1.17364e7	−	9.35945e6i	0.0705417	−	0.0562551i
$551$	−1.02001e7	+	4.46898e7i	−0.0609750	+	0.267149i
$552$	5.25018e8			3.12145
$553$		−	5.20556e7i		−	0.307817i
$554$	−4.44131e7	+	1.94586e8i	−0.261205	+	1.14441i
$555$	1.78543e8	+	1.42383e8i	1.04439	+	0.832874i
$556$	−2.23317e8	−	1.07544e8i	−1.29927	−	0.625694i
$557$	−2.16348e8	+	1.04188e8i	−1.25195	+	0.602907i	−0.938034	−	0.346543i	$-0.887355\pi$
$557$	−2.16348e8	+	1.04188e8i	−1.25195	+	0.602907i	−0.313916	+	0.949451i	$0.601641\pi$
$558$			2.23606e8i			1.28700i
$559$	−6.40657e7	−	6.90240e7i	−0.366767	−	0.395152i
$560$	816410.			0.00464883
$561$	−1.57618e7	−	3.27297e7i	−0.0892724	−	0.185376i
$562$	5.40868e6	−	1.12312e7i	0.0304707	−	0.0632731i
$563$	−1.69085e8	+	2.12026e8i	−0.947501	+	1.18813i	0.0345287	+	0.999404i	$0.489007\pi$
$563$	−1.69085e8	+	2.12026e8i	−0.947501	+	1.18813i	−0.982030	+	0.188725i	$0.939564\pi$
$564$	−4.13659e8	−	9.44151e7i	−2.30571	−	0.526264i
$565$	−7.74576e7			−0.429456
$566$			1.69801e8i			0.936464i
$567$	−4.86475e8	−	1.11035e8i	−2.66877	−	0.609130i
$568$	8.84523e6	+	1.10916e7i	0.0482685	+	0.0605268i
$569$	3.39675e7	+	1.48821e8i	0.184385	+	0.807845i	0.979509	+	0.201398i	$0.0645485\pi$
$569$	3.39675e7	+	1.48821e8i	0.184385	+	0.807845i	−0.795124	+	0.606447i	$0.792594\pi$
$570$	1.17756e8	+	1.47662e8i	0.635858	+	0.797341i
$571$	4.65435e7	+	9.66486e7i	0.250006	+	0.519143i	0.987770	−	0.155915i	$-0.0498326\pi$
$571$	4.65435e7	+	9.66486e7i	0.250006	+	0.519143i	−0.737764	+	0.675059i	$0.764118\pi$
$572$	−2.32756e6	+	1.01977e7i	−0.0124369	+	0.0544897i
$573$	4.06637e8	−	1.95826e8i	2.16144	−	1.04089i
$574$	−3.15969e7	+	3.96212e7i	−0.167074	+	0.209504i
$575$	6.02299e7	+	2.63884e8i	0.316817	+	1.38807i
$576$	1.76989e8	+	7.75440e8i	0.926145	+	4.05771i
$577$	5.64729e7	−	1.17267e8i	0.293977	−	0.610449i	−0.700705	−	0.713452i	$-0.747131\pi$
$577$	5.64729e7	−	1.17267e8i	0.293977	−	0.610449i	0.994681	+	0.103003i	$0.0328451\pi$
$578$	4.66342e8	+	3.71895e8i	2.41502	+	1.92591i
$579$	−2.69759e8	+	2.15126e8i	−1.38976	+	1.10830i
$580$	−2.99153e7	−	1.44064e7i	−0.153324	−	0.0738368i
$581$	8.66190e7	−	1.79866e8i	0.441656	−	0.917109i
$582$	−3.49116e8	−	4.37777e8i	−1.77093	−	2.22067i
$583$	1.16881e7	−	1.46564e7i	0.0589845	−	0.0739642i
$584$	−2.53287e8	−	1.21977e8i	−1.27167	−	0.612404i
$585$	9.67141e7	−	2.20744e7i	0.483083	−	0.110261i
$586$	4.72301e6	−	1.07800e6i	0.0234707	−	0.00535703i
$587$	1.39625e8	+	1.11348e8i	0.690319	+	0.550511i	0.904600	−	0.426261i	$-0.140169\pi$
$587$	1.39625e8	+	1.11348e8i	0.690319	+	0.550511i	−0.214281	+	0.976772i	$0.568741\pi$
$588$	−5.43523e7	−	1.12864e8i	−0.267353	−	0.555165i
$589$	5.73189e7	+	1.30827e7i	0.280512	+	0.0640251i
$590$	−5.32206e7	+	2.56297e7i	−0.259134	+	0.124792i
$591$	1.12972e8	−	9.00921e7i	0.547278	−	0.436440i
$592$	−5.83775e6	+	1.33243e6i	−0.0281372	+	0.00642213i
$593$	2.83085e8	−	2.25753e8i	1.35754	−	1.08260i	0.369366	−	0.929284i	$-0.379575\pi$
$593$	2.83085e8	−	2.25753e8i	1.35754	−	1.08260i	0.988177	−	0.153320i	$-0.0489965\pi$
$594$	−1.43740e7	+	6.29765e7i	−0.0685832	+	0.300483i
$595$	1.14545e8			0.543783
$596$			2.79268e8i			1.31912i
$597$	2.45039e7	−	1.07359e8i	0.115163	−	0.504562i
$598$	−2.38225e8	−	1.89978e8i	−1.11400	−	0.888383i
$599$	−5.89601e6	−	2.83937e6i	−0.0274333	−	0.0132112i	0.420117	−	0.907470i	$-0.361989\pi$
$599$	−5.89601e6	−	2.83937e6i	−0.0274333	−	0.0132112i	−0.447550	+	0.894259i	$0.647703\pi$
$600$	3.24982e8	−	1.56503e8i	1.50454	−	0.724550i
$601$		−	1.72793e8i		−	0.795982i	−0.917389	−	0.397991i	$-0.869707\pi$
$601$		−	1.72793e8i		−	0.795982i	0.917389	−	0.397991i	$-0.130293\pi$
$602$	−4.70488e7	+	3.12492e8i	−0.215655	+	1.43235i
$603$	2.85314e8			1.30128
$604$	5.26227e7	+	1.09272e8i	0.238815	+	0.495905i
$605$	3.41352e7	−	7.08824e7i	0.154147	−	0.320090i
$606$	−3.32741e8	+	4.17245e8i	−1.49516	+	1.87488i
$607$	3.71237e7	+	8.47323e6i	0.165991	+	0.0378864i	0.304709	−	0.952446i	$-0.401441\pi$
$607$	3.71237e7	+	8.47323e6i	0.165991	+	0.0378864i	−0.138718	+	0.990332i	$0.544298\pi$
$608$	2.07244e8			0.922085
$609$		−	1.12151e8i		−	0.496538i
$610$	6.30819e7	+	1.43980e7i	0.277917	+	0.0634328i
$611$	5.90238e7	+	7.40135e7i	0.258764	+	0.324480i
$612$	−3.63976e8	−	1.59469e9i	−1.58789	−	6.95698i
$613$	−1.50183e7	−	1.88323e7i	−0.0651987	−	0.0817566i	0.748163	−	0.663515i	$-0.230936\pi$
$613$	−1.50183e7	−	1.88323e7i	−0.0651987	−	0.0817566i	−0.813361	+	0.581759i	$0.802365\pi$
$614$	2.56295e8	+	5.32202e8i	1.10722	+	2.29917i
$615$	6.45979e6	−	2.83022e7i	0.0277711	−	0.121673i
$616$	1.21575e7	−	5.85473e6i	0.0520117	−	0.0250475i
$617$	2.16808e8	−	2.71868e8i	0.923037	−	1.15745i	−0.0641593	−	0.997940i	$-0.520437\pi$
$617$	2.16808e8	−	2.71868e8i	0.923037	−	1.15745i	0.987196	−	0.159512i	$-0.0509920\pi$
$618$	−2.02023e8	−	8.85121e8i	−0.855925	−	3.75005i
$619$	−6.36236e7	−	2.78753e8i	−0.268254	−	1.17530i	−0.912043	−	0.410095i	$-0.865496\pi$
$619$	−6.36236e7	−	2.78753e8i	−0.268254	−	1.17530i	0.643789	−	0.765203i	$-0.277361\pi$
$620$	−1.84776e7	+	3.83692e7i	−0.0775302	+	0.160993i
$621$	−9.10625e8	−	7.26199e8i	−3.80246	−	3.03236i
$622$	1.10661e7	−	8.82494e6i	0.0459859	−	0.0366725i
$623$	−1.89361e7	−	9.11916e6i	−0.0783118	−	0.0377130i
$624$	−1.56663e6	+	3.25314e6i	−0.00644781	+	0.0133890i
$625$	9.65729e7	+	1.21099e8i	0.395563	+	0.496020i
$626$	1.88002e8	−	2.35748e8i	0.766374	−	0.961002i
$627$	2.50093e7	+	1.20438e7i	0.101461	+	0.0488610i
$628$	−2.95149e8	+	6.73657e7i	−1.19169	+	0.271995i
$629$	−8.19057e8	+	1.86944e8i	−3.29126	+	0.751209i
$630$	−2.60259e8	−	2.07550e8i	−1.04084	−	0.830044i
$631$	1.59968e8	+	3.32176e8i	0.636714	+	1.32215i	0.930505	+	0.366280i	$0.119369\pi$
$631$	1.59968e8	+	3.32176e8i	0.636714	+	1.32215i	−0.293791	+	0.955870i	$0.594917\pi$
$632$	−8.57248e7	−	1.95661e7i	−0.339590	−	0.0775093i
$633$	2.22097e8	−	1.06956e8i	0.875654	−	0.421693i
$634$	−2.86232e8	+	2.28262e8i	−1.12318	+	0.895707i
$635$	−8.61191e7	+	1.96561e7i	−0.336340	+	0.0767673i
$636$	9.16069e8	−	7.30541e8i	3.56088	−	2.83971i
$637$	−6.21932e6	+	2.72486e7i	−0.0240616	+	0.105421i
$638$	−7.88393e6			−0.0303585
$639$		−	5.14369e7i		−	0.197139i
$640$	−3.38955e7	+	1.48506e8i	−0.129301	+	0.566505i
$641$	−1.18065e8	−	9.41534e7i	−0.448276	−	0.357488i	0.373181	−	0.927759i	$-0.378267\pi$
$641$	−1.18065e8	−	9.41534e7i	−0.448276	−	0.357488i	−0.821457	+	0.570270i	$0.806838\pi$
$642$	8.81037e8	+	4.24285e8i	3.32958	+	1.60344i
$643$	−1.95380e8	+	9.40899e7i	−0.734931	+	0.353924i	−0.763621	−	0.645664i	$-0.776581\pi$
$643$	−1.95380e8	+	9.40899e7i	−0.734931	+	0.353924i	0.0286905	+	0.999588i	$0.490866\pi$
$644$			6.32888e8i			2.36957i
$645$	−5.33862e7	−	1.72974e8i	−0.198953	−	0.644617i
$646$	−6.94813e8			−2.57733
$647$	1.88723e8	+	3.91887e8i	0.696806	+	1.44693i	0.885378	+	0.464873i	$0.153900\pi$
$647$	1.88723e8	+	3.91887e8i	0.696806	+	1.44693i	−0.188572	+	0.982059i	$0.560386\pi$
$648$	−3.65702e8	+	7.59389e8i	−1.34401	+	2.79087i
$649$	−5.41297e6	+	6.78765e6i	−0.0198016	+	0.0248305i
$650$	−2.04090e8	−	4.65822e7i	−0.743159	−	0.169621i
$651$	−1.43845e8			−0.521376
$652$		−	3.37837e8i		−	1.21889i
$653$	−9.14895e7	−	2.08819e7i	−0.328573	−	0.0749946i	0.0550524	−	0.998483i	$-0.482467\pi$
$653$	−9.14895e7	−	2.08819e7i	−0.328573	−	0.0749946i	−0.383625	+	0.923489i	$0.625325\pi$
$654$	−8.93036e6	−	1.11983e7i	−0.0319253	−	0.0400331i
$655$	−2.17511e7	−	9.52979e7i	−0.0774030	−	0.339125i
$656$	474593.	+	595120.i	0.00168116	+	0.00210811i
$657$	4.42255e8	+	9.18351e8i	1.55947	+	3.23827i
$658$	7.06879e7	−	3.09704e8i	0.248123	−	1.08710i
$659$	−4.42594e7	+	2.13142e7i	−0.154650	+	0.0744755i	−0.509608	−	0.860407i	$-0.670209\pi$
$659$	−4.42594e7	+	2.13142e7i	−0.154650	+	0.0744755i	0.354958	+	0.934882i	$0.384495\pi$
$660$	−1.25363e7	+	1.57200e7i	−0.0436050	+	0.0546790i
$661$	−1.68950e7	−	7.40216e7i	−0.0584996	−	0.256303i	0.937219	−	0.348742i	$-0.113391\pi$
$661$	−1.68950e7	−	7.40216e7i	−0.0584996	−	0.256303i	−0.995718	+	0.0924385i	$0.970534\pi$
$662$	−8.16994e6	−	3.57948e7i	−0.0281608	−	0.123380i
$663$	−2.19803e8	+	4.56426e8i	−0.754213	+	1.56614i
$664$	−2.63645e8	−	2.10250e8i	−0.900565	−	0.718176i
$665$	−6.84303e7	+	5.45714e7i	−0.232693	+	0.185567i
$666$	2.19972e9	+	1.05933e9i	7.44639	+	3.58599i
$667$	6.16789e7	−	1.28077e8i	0.207854	−	0.431614i
$668$	1.51639e8	+	1.90149e8i	0.508722	+	0.637918i
$669$	−1.59700e8	+	2.00257e8i	−0.533367	+	0.668821i
$670$	7.90944e7	+	3.80899e7i	0.262979	+	0.126644i
$671$	9.27130e6	−	2.11611e6i	0.0306883	−	0.00700441i
$672$	−4.94337e8	+	1.12829e8i	−1.62898	+	0.371803i
$673$	2.29129e8	+	1.82724e8i	0.751684	+	0.599448i	0.922564	−	0.385844i	$-0.126090\pi$
$673$	2.29129e8	+	1.82724e8i	0.751684	+	0.599448i	−0.170880	+	0.985292i	$0.554661\pi$
$674$	−1.00090e7	−	2.07840e7i	−0.0326898	−	0.0678811i
$675$	−7.80143e8	−	1.78063e8i	−2.53666	−	0.578977i
$676$	−3.20724e8	+	1.54452e8i	−1.03822	+	0.499982i
$677$	−1.85225e8	+	1.47712e8i	−0.596945	+	0.476048i	−0.874740	−	0.484592i	$-0.838968\pi$
$677$	−1.85225e8	+	1.47712e8i	−0.596945	+	0.476048i	0.277795	+	0.960640i	$0.410396\pi$
$678$	−1.12072e9	+	2.55797e8i	−3.59590	+	0.820741i
$679$	2.02877e8	−	1.61789e8i	0.648073	−	0.516821i
$680$	4.30540e7	−	1.88632e8i	0.136926	−	0.599914i
$681$	1.20869e8			0.382713
$682$			1.01119e7i			0.0318771i
$683$	−6.64455e6	+	2.91117e7i	−0.0208547	+	0.0913703i	−0.984284	−	0.176591i	$-0.943493\pi$
$683$	−6.64455e6	+	2.91117e7i	−0.0208547	+	0.0913703i	0.963430	+	0.267962i	$0.0863501\pi$
$684$	9.77180e8	+	7.79275e8i	3.05356	+	2.43513i
$685$	−1.69713e8	−	8.17293e7i	−0.528011	−	0.254277i
$686$	5.05808e8	−	2.43584e8i	1.56680	−	0.754531i
$687$		−	1.07320e9i		−	3.30987i
$688$	4.41878e6	+	1.73342e6i	0.0135686	+	0.00532276i
$689$	−2.61422e8			−0.799255
$690$	−2.54130e8	−	5.27707e8i	−0.773587	−	1.60637i
$691$	1.49143e8	−	3.09699e8i	0.452033	−	0.938655i	−0.543059	−	0.839695i	$-0.682734\pi$
$691$	1.49143e8	−	3.09699e8i	0.452033	−	0.938655i	0.995091	−	0.0989606i	$-0.0315518\pi$
$692$	−1.86558e8	+	2.33936e8i	−0.562982	+	0.705957i
$693$	−4.76982e7	−	1.08868e7i	−0.143318	−	0.0327115i
$694$	−8.71630e8			−2.60768
$695$			1.06304e8i			0.316661i
$696$	−1.84690e8	−	4.21543e7i	−0.547792	−	0.125030i
$697$	6.65870e7	+	8.34975e7i	0.196649	+	0.246590i
$698$	−3.69669e7	−	1.61963e8i	−0.108704	−	0.476265i
$699$	−3.64018e8	−	4.56464e8i	−1.06584	−	1.33652i
$700$	1.88658e8	+	3.91753e8i	0.550024	+	1.14214i
$701$	9.69740e7	−	4.24871e8i	0.281515	−	1.23340i	−0.614337	−	0.789044i	$-0.710577\pi$
$701$	9.69740e7	−	4.24871e8i	0.281515	−	1.23340i	0.895852	−	0.444353i	$-0.146566\pi$
$702$	8.11605e8	−	3.90848e8i	2.34603	−	1.12979i
$703$	4.00249e8	−	5.01896e8i	1.15203	−	1.44460i
$704$	8.00379e6	+	3.50669e7i	0.0229392	+	0.100503i
$705$	4.04927e7	+	1.77410e8i	0.115561	+	0.506304i
$706$	−1.17863e8	+	2.44746e8i	−0.334938	+	0.695507i
$707$	−1.93362e8	−	1.54201e8i	−0.547158	−	0.436344i
$708$	−4.24249e8	+	3.38327e8i	−1.19542	+	0.953316i
$709$	−4.56054e8	−	2.19624e8i	−1.27961	−	0.616228i	−0.334320	−	0.942460i	$-0.608507\pi$
$709$	−4.56054e8	−	2.19624e8i	−1.27961	−	0.616228i	−0.945290	+	0.326232i	$0.894221\pi$
$710$	6.86692e6	−	1.42593e7i	0.0191861	−	0.0398404i
$711$	1.98774e8	+	2.49254e8i	0.553032	+	0.693480i
$712$	−2.21349e7	+	2.77563e7i	−0.0613250	+	0.0768991i
$713$	−1.64272e8	−	7.91090e7i	−0.453204	−	0.218252i
$714$	1.65733e9	−	3.78275e8i	4.55318	−	1.03923i
$715$	4.37360e6	−	998245.i	0.0119652	−	0.00273098i
$716$	−7.33030e8	−	5.84572e8i	−1.99702	−	1.59257i
$717$	4.41288e8	+	9.16345e8i	1.19720	+	2.48600i
$718$	4.21843e8	+	9.62830e7i	1.13967	+	0.260121i
$719$	−1.56863e8	+	7.55411e7i	−0.422020	+	0.203234i	−0.632827	−	0.774294i	$-0.718105\pi$
$719$	−1.56863e8	+	7.55411e7i	−0.422020	+	0.203234i	0.210806	+	0.977528i	$0.432391\pi$
$720$	−3.90916e6	+	3.11745e6i	−0.0104734	+	0.00835222i
$721$	4.10188e8	−	9.36227e7i	1.09440	−	0.249790i
$722$	−6.16181e7	+	4.91388e7i	−0.163718	+	0.130561i
$723$	−1.90808e8	+	8.35983e8i	−0.504872	+	2.21199i
$724$	6.75340e8			1.77954
$725$		−	9.76648e7i		−	0.256286i
$726$	2.59812e8	−	1.13831e9i	0.678969	−	2.97476i
$727$	3.82706e8	+	3.05198e8i	0.996006	+	0.794288i	0.978644	−	0.205561i	$-0.0659019\pi$
$727$	3.82706e8	+	3.05198e8i	0.996006	+	0.794288i	0.0173617	+	0.999849i	$0.494473\pi$
$728$	−1.69540e8	−	8.16461e7i	−0.439418	−	0.211613i
$729$	7.85363e8	−	3.78211e8i	2.02716	−	0.976228i
$730$			3.13626e8i			0.806202i
$731$	6.19970e8	+	2.43204e8i	1.58715	+	0.622614i
$732$	5.94387e8			1.51543
$733$	−2.34423e8	−	4.86784e8i	−0.595234	−	1.23602i	−0.953217	−	0.302288i	$-0.902250\pi$
$733$	−2.34423e8	−	4.86784e8i	−0.595234	−	1.23602i	0.357983	−	0.933728i	$-0.383465\pi$
$734$	5.34878e8	−	1.11069e9i	1.35259	−	2.80869i
$735$	−3.34973e7	+	4.20043e7i	−0.0843622	+	0.105787i
$736$	−6.26587e8	−	1.43014e8i	−1.57162	−	0.358712i
$737$	1.29024e7			0.0322307
$738$		−	3.10368e8i		−	0.772161i
$739$	6.29271e8	+	1.43627e8i	1.55921	+	0.355879i	0.913220	−	0.407467i	$-0.133588\pi$
$739$	6.29271e8	+	1.43627e8i	1.55921	+	0.355879i	0.645990	+	0.763346i	$0.276445\pi$
$740$	2.89920e8	+	3.63548e8i	0.715455	+	0.897153i
$741$	−8.61372e7	−	3.77392e8i	−0.211707	−	0.927551i
$742$	5.46951e8	+	6.85855e8i	1.33886	+	1.67888i
$743$	−1.51569e8	−	3.14736e8i	−0.369525	−	0.767326i	0.630436	−	0.776241i	$-0.282876\pi$
$743$	−1.51569e8	−	3.14736e8i	−0.369525	−	0.767326i	−0.999960	+	0.00891585i	$0.997162\pi$
$744$	−5.40669e7	+	2.36882e8i	−0.131284	+	0.575193i
$745$	1.07911e8	−	5.19674e7i	0.260975	−	0.125679i
$746$	−7.63256e8	+	9.57092e8i	−1.83846	+	2.30535i
$747$	2.72065e8	+	1.19199e9i	0.652695	+	2.85965i
$748$	−1.64597e7	−	7.21148e7i	−0.0393294	−	0.172314i
$749$	−1.96625e8	+	4.08295e8i	−0.467942	+	0.971693i
$750$	−6.75090e8	−	5.38367e8i	−1.60021	−	1.27613i
$751$	2.46059e8	−	1.96225e8i	0.580924	−	0.463271i	−0.288403	−	0.957509i	$-0.593124\pi$
$751$	2.46059e8	−	1.96225e8i	0.580924	−	0.463271i	0.869327	+	0.494238i	$0.164553\pi$
$752$	−4.29893e6	−	2.07026e6i	−0.0101090	−	0.00486822i
$753$	−3.22330e7	+	6.69325e7i	−0.0754946	+	0.156766i
$754$	6.85489e7	+	8.59576e7i	0.159914	+	0.200526i
$755$	3.24314e7	−	4.06677e7i	0.0753571	−	0.0944949i
$756$	−1.68577e9	−	8.11822e8i	−3.90150	−	1.87886i
$757$	−2.19859e8	+	5.01815e7i	−0.506824	+	0.115679i	−0.468285	−	0.883578i	$-0.655128\pi$
$757$	−2.19859e8	+	5.01815e7i	−0.506824	+	0.115679i	−0.0385398	+	0.999257i	$0.512271\pi$
$758$	−4.51867e7	+	1.03136e7i	−0.103754	+	0.0236811i
$759$	−6.73026e7	−	5.36720e7i	−0.153924	−	0.122750i
$760$	6.41468e7	+	1.33202e8i	0.146128	+	0.303439i
$761$	−4.82134e8	−	1.10044e8i	−1.09399	−	0.249697i	−0.362799	−	0.931867i	$-0.618179\pi$
$761$	−4.82134e8	−	1.10044e8i	−1.09399	−	0.249697i	−0.731193	+	0.682171i	$0.761036\pi$
$762$	−1.18113e9	+	5.68801e8i	−2.66951	+	1.28557i
$763$	5.18959e6	−	4.13856e6i	0.0116831	−	0.00931698i
$764$	8.95961e8	−	2.04497e8i	2.00913	−	0.458572i
$765$	−5.48468e8	+	4.37389e8i	−1.22509	+	0.976975i
$766$	−7.60459e7	+	3.33179e8i	−0.169196	+	0.741295i
$767$	1.21069e8			0.268317
$768$			8.76763e8i			1.93552i
$769$	−1.73096e7	+	7.58383e7i	−0.0380634	+	0.166767i	−0.990387	−	0.138322i	$-0.955829\pi$
$769$	−1.73096e7	+	7.58383e7i	−0.0380634	+	0.166767i	0.952324	+	0.305089i	$0.0986862\pi$
$770$	−1.17694e7	−	9.38581e6i	−0.0257800	−	0.0205589i
$771$	5.38164e8	+	2.59166e8i	1.17423	+	0.565477i
$772$	−6.32983e8	+	3.04829e8i	−1.37575	+	0.662527i
$773$		−	4.41703e8i		−	0.956296i	−0.878279	−	0.478148i	$-0.841308\pi$
$773$		−	4.41703e8i		−	0.956296i	0.878279	−	0.478148i	$-0.158692\pi$
$774$	−9.67967e8	−	1.67594e9i	−2.08755	−	3.61440i
$775$	−1.25264e8			−0.269106
$776$	−1.90178e8	−	3.94908e8i	−0.406982	−	0.845106i
$777$	−6.81464e8	+	1.41507e9i	−1.45271	+	3.01659i
$778$	3.11352e8	−	3.90423e8i	0.661169	−	0.829080i
$779$	−7.95594e7	−	1.81589e7i	−0.168298	−	0.0384129i
$780$	2.80393e8			0.590859
$781$		−	2.32608e6i		−	0.00488283i
$782$	2.10072e9	+	4.79476e8i	4.39287	+	1.00264i
$783$	2.62031e8	+	3.28577e8i	0.545843	+	0.684465i
$784$	−313470.	−	1.37340e6i	−0.000650500	−	0.00285003i
$785$	8.09531e7	+	1.01512e8i	0.167350	+	0.209850i
$786$	−6.29426e8	−	1.30702e9i	−1.29621	−	2.69162i
$787$	−5.83105e7	+	2.55475e8i	−0.119625	+	0.524112i	0.879235	+	0.476388i	$0.158054\pi$
$787$	−5.83105e7	+	2.55475e8i	−0.119625	+	0.524112i	−0.998861	+	0.0477245i	$0.984803\pi$
$788$	2.65086e8	−	1.27659e8i	0.541761	−	0.260898i
$789$	−6.58186e7	+	8.25339e7i	−0.134004	+	0.168036i
$790$	2.18280e7	+	9.56347e7i	0.0442724	+	0.193970i
$791$	−1.18543e8	−	5.19370e8i	−0.239522	−	1.04942i
$792$	−3.58566e7	+	7.44569e7i	−0.0721761	+	0.149875i
$793$	−1.03684e8	−	8.26849e7i	−0.207917	−	0.165808i
$794$	7.30966e7	−	5.82926e7i	0.146028	−	0.116453i
$795$	−4.52753e8	−	2.18034e8i	−0.901072	−	0.433934i
$796$	9.72877e7	−	2.02020e8i	0.192894	−	0.400548i
$797$	−5.17123e8	−	6.48452e8i	−1.02145	−	1.28086i	−0.959178	−	0.282805i	$-0.908735\pi$
$797$	−5.17123e8	−	6.48452e8i	−1.02145	−	1.28086i	−0.0622771	−	0.998059i	$-0.519836\pi$
$798$	−8.09889e8	+	1.01557e9i	−1.59374	+	1.99848i
$799$	−6.03155e8	−	2.90464e8i	−1.18247	−	0.569446i
$800$	−4.30484e8	+	9.82551e7i	−0.840788	+	0.191904i
$801$	1.25492e8	−	2.86427e7i	0.244185	−	0.0557336i
$802$	1.20995e9	+	9.64901e8i	2.34554	+	1.87051i
$803$	1.99996e7	+	4.15296e7i	0.0386256	+	0.0802069i
$804$	7.86223e8	+	1.79450e8i	1.51279	+	0.345283i
$805$	2.44553e8	−	1.17770e8i	0.468797	−	0.225761i
$806$	1.10249e8	−	8.79205e7i	0.210557	−	0.167913i
$807$	−7.04362e8	+	1.60766e8i	−1.34022	+	0.305896i
$808$	−3.26616e8	+	2.60467e8i	−0.619160	+	0.493764i
$809$	1.09332e8	−	4.79014e8i	0.206491	−	0.904695i	−0.760390	−	0.649467i	$-0.774992\pi$
$809$	1.09332e8	−	4.79014e8i	0.206491	−	0.904695i	0.966881	−	0.255229i	$-0.0821507\pi$
$810$	9.40293e8			1.76933
$811$			3.41797e8i			0.640776i	0.947286	+	0.320388i	$0.103813\pi$
$811$			3.41797e8i			0.640776i	−0.947286	+	0.320388i	$0.896187\pi$
$812$	5.08153e7	−	2.22637e8i	0.0949132	−	0.415842i
$813$	9.49139e7	+	7.56913e7i	0.176628	+	0.140856i
$814$	9.94758e7	+	4.79050e7i	0.184435	+	0.0888194i
$815$	−1.30543e8	+	6.28660e7i	−0.241146	+	0.116130i
$816$		−	2.55337e7i		−	0.0469941i
$817$	−4.86243e8	+	1.50072e8i	−0.891634	+	0.275191i
$818$	−3.33974e8			−0.610173
$819$	2.96027e8	+	6.14706e8i	0.538864	+	1.11896i
$820$	2.56472e7	−	5.32570e7i	0.0465156	−	0.0965906i
$821$	−3.75106e8	+	4.70368e8i	−0.677835	+	0.849979i	−0.995153	−	0.0983408i	$-0.968646\pi$
$821$	−3.75106e8	+	4.70368e8i	−0.677835	+	0.849979i	0.317318	+	0.948319i	$0.397218\pi$
$822$	−2.72545e9	−	6.22065e8i	−4.90707	−	1.12001i
$823$	1.62153e8			0.290887			0.145444	−	0.989367i	$-0.453539\pi$
$823$	1.62153e8			0.290887			0.145444	+	0.989367i	$0.453539\pi$
$824$		−	7.10684e8i		−	1.27027i
$825$	−5.76589e7	−	1.31603e7i	−0.102684	−	0.0234370i
$826$	−2.53303e8	−	3.17632e8i	−0.449469	−	0.563617i
$827$	−2.38903e7	−	1.04670e8i	−0.0422382	−	0.185057i	0.949408	−	0.314045i	$-0.101684\pi$
$827$	−2.38903e7	−	1.04670e8i	−0.0422382	−	0.185057i	−0.991646	+	0.128988i	$0.958827\pi$
$828$	−2.41667e9	−	3.03041e9i	−4.25723	−	5.33840i
$829$	−1.15540e8	−	2.39920e8i	−0.202800	−	0.421118i	0.774619	−	0.632428i	$-0.217941\pi$
$829$	−1.15540e8	−	2.39920e8i	−0.202800	−	0.421118i	−0.977419	+	0.211310i	$0.932227\pi$
$830$	−8.37116e7	+	3.66765e8i	−0.146404	+	0.641436i
$831$	7.08472e8	−	3.41182e8i	1.23458	−	0.594543i
$832$	3.12740e8	−	3.92163e8i	0.543016	−	0.680921i
$833$	−4.39809e7	−	1.92693e8i	−0.0760903	−	0.333373i
$834$	3.51059e8	+	1.53809e9i	0.605177	+	2.65145i
$835$	4.52575e7	−	9.39781e7i	0.0777376	−	0.161424i
$836$	4.41900e7	+	3.52403e7i	0.0756319	+	0.0603144i
$837$	4.21431e8	−	3.36080e8i	0.718704	−	0.573147i
$838$	6.94297e8	+	3.34356e8i	1.17981	+	0.568168i
$839$	3.97897e8	−	8.26243e8i	0.673729	−	1.39901i	−0.230970	−	0.972961i	$-0.574190\pi$
$839$	3.97897e8	−	8.26243e8i	0.673729	−	1.39901i	0.904699	−	0.426052i	$-0.140096\pi$
$840$	−2.25528e8	−	2.82803e8i	−0.380507	−	0.477140i
$841$	3.38885e8	−	4.24949e8i	0.569725	−	0.714412i
$842$	6.39733e8	+	3.08079e8i	1.07167	+	0.516091i
$843$	−4.78810e7	+	1.09285e7i	−0.0799247	+	0.0182423i
$844$	4.89357e8	−	1.11692e8i	0.813951	−	0.185779i
$845$	1.19363e8	+	9.51889e7i	0.197834	+	0.157767i
$846$	8.44130e8	+	1.75285e9i	1.39411	+	2.89491i
$847$	5.27523e8	+	1.20404e8i	0.868143	+	0.198148i
$848$	1.18715e7	−	5.71701e6i	0.0194678	−	0.00937522i
$849$	5.23030e8	−	4.17103e8i	0.854680	−	0.681585i
$850$	1.44326e9	−	3.29414e8i	2.35010	−	0.536395i
$851$	−1.55647e9	+	1.24125e9i	−2.52553	+	2.01404i
$852$	3.23517e7	−	1.41742e8i	0.0523092	−	0.229181i
$853$	2.93676e8			0.473175			0.236587	−	0.971610i	$-0.423971\pi$
$853$	2.93676e8			0.473175			0.236587	+	0.971610i	$0.423971\pi$
$854$			4.45013e8i			0.714495i
$855$	1.19280e8	−	5.22601e8i	0.190840	−	0.836126i
$856$	5.98472e8	+	4.77266e8i	0.954163	+	0.760920i
$857$	−8.67914e8	−	4.17966e8i	−1.37891	−	0.664046i	−0.410139	−	0.912023i	$-0.634520\pi$
$857$	−8.67914e8	−	4.17966e8i	−1.37891	−	0.664046i	−0.968766	+	0.247977i	$0.920234\pi$
$858$	5.99842e7	−	2.88869e7i	0.0949675	−	0.0457339i
$859$			1.02609e9i			1.61884i	0.587228	+	0.809422i	$0.300219\pi$
$859$			1.02609e9i			1.61884i	−0.587228	+	0.809422i	$0.699781\pi$
$860$	−2.76053e7	−	3.67568e8i	−0.0434007	−	0.577886i
$861$	1.99659e8			0.312808
$862$	2.45923e8	+	5.10664e8i	0.383952	+	0.797285i
$863$	−2.40199e8	+	4.98779e8i	−0.373714	+	0.776025i	−0.999994	−	0.00357325i	$-0.998863\pi$
$863$	−2.40199e8	+	4.98779e8i	−0.373714	+	0.776025i	0.626280	+	0.779599i	$0.284577\pi$
$864$	1.18467e9	−	1.48553e9i	1.83678	−	2.30325i
$865$	1.25110e8	+	2.85556e7i	0.193305	+	0.0441207i
$866$	−5.97442e8			−0.919903
$867$		−	2.34998e9i		−	3.60584i
$868$	−2.85552e8	−	6.51755e7i	−0.436643	−	0.0996610i
$869$	8.98894e6	+	1.12718e7i	0.0136977	+	0.0171764i
$870$	4.70274e7	+	2.06040e8i	0.0714156	+	0.312892i
$871$	−1.12184e8	−	1.40674e8i	−0.169776	−	0.212892i
$872$	−4.86474e6	−	1.01017e7i	−0.00733685	−	0.0152351i
$873$	−3.53633e8	+	1.54937e9i	−0.531509	+	2.32869i
$874$	−1.48342e9	+	7.14378e8i	−2.22193	+	1.07002i
$875$	2.49493e8	−	3.12854e8i	0.372421	−	0.467001i
$876$	6.41092e8	+	2.80881e9i	0.953692	+	4.17840i
$877$	−1.76381e8	−	7.72778e8i	−0.261489	−	1.14566i	−0.919636	−	0.392771i	$-0.871517\pi$
$877$	−1.76381e8	−	7.72778e8i	−0.261489	−	1.14566i	0.658147	−	0.752890i	$-0.271341\pi$
$878$	8.64598e8	−	1.79536e9i	1.27741	−	2.65257i
$879$	−1.49222e7	−	1.19000e7i	−0.0219718	−	0.0175219i
$880$	−176780.	+	140977.i	−0.000259409	+	0.000206871i
$881$	5.49033e8	+	2.64400e8i	0.802916	+	0.386664i	0.789888	−	0.613251i	$-0.210139\pi$
$881$	5.49033e8	+	2.64400e8i	0.802916	+	0.386664i	0.0130283	+	0.999915i	$0.495853\pi$
$882$	−2.49220e8	+	5.17511e8i	−0.363226	+	0.754248i
$883$	5.49195e8	+	6.88668e8i	0.797709	+	1.00029i	0.999781	+	0.0209243i	$0.00666089\pi$
$883$	5.49195e8	+	6.88668e8i	0.797709	+	1.00029i	−0.202073	+	0.979371i	$0.564768\pi$
$884$	−6.43146e8	+	8.06480e8i	−0.931007	+	1.16745i
$885$	2.09678e8	+	1.00976e8i	0.302498	+	0.145676i
$886$	1.16167e8	−	2.65143e7i	0.167025	−	0.0381223i
$887$	4.91748e8	−	1.12238e8i	0.704647	−	0.160831i	0.144841	−	0.989455i	$-0.453733\pi$
$887$	4.91748e8	−	1.12238e8i	0.704647	−	0.160831i	0.559806	+	0.828624i	$0.310876\pi$
$888$	2.07419e9	+	1.65411e9i	2.96217	+	2.36225i
$889$	−2.63597e8	−	5.47365e8i	−0.375176	−	0.779062i
$890$	3.86126e7	+	8.81308e6i	0.0547721	+	0.0125014i
$891$	1.24511e8	−	5.99615e7i	0.176026	−	0.0847695i
$892$	−4.07763e8	+	3.25180e8i	−0.574531	+	0.458173i
$893$	4.98713e8	−	1.13828e8i	0.700320	−	0.159843i
$894$	1.38973e9	−	1.10827e9i	1.94500	−	1.55108i
$895$	−8.94779e7	+	3.92028e8i	−0.124809	+	0.546825i
$896$	−1.04764e9			−1.45642
$897$			1.20046e9i			1.66330i
$898$	1.16977e8	−	5.12509e8i	0.161537	−	0.707738i
$899$	5.14355e7	+	4.10184e7i	0.0707919	+	0.0564546i
$900$	−2.39924e9	−	1.15541e9i	−3.29114	−	1.58493i
$901$	1.66561e9	−	8.02117e8i	2.27719	−	1.09664i
$902$		−	1.40354e7i		−	0.0191252i
$903$	1.07813e9	−	6.22690e8i	1.46422	−	0.845685i
$904$	−8.99852e8			−1.21805
$905$	−1.25670e8	−	2.60957e8i	−0.169545	−	0.352065i
$906$	3.34942e8	−	6.95515e8i	0.450386	−	0.935237i
$907$	−2.66957e8	+	3.34754e8i	−0.357783	+	0.448646i	−0.927851	−	0.372952i	$-0.878346\pi$
$907$	−2.66957e8	+	3.34754e8i	−0.357783	+	0.448646i	0.570068	+	0.821598i	$0.306917\pi$
$908$	2.39942e8	+	5.47653e7i	0.320516	+	0.0731556i
$909$	1.51468e9			2.01664
$910$			2.09928e8i			0.278578i
$911$	−7.59856e8	−	1.73432e8i	−1.00502	−	0.229390i	−0.311827	−	0.950139i	$-0.600941\pi$
$911$	−7.59856e8	−	1.73432e8i	−1.00502	−	0.229390i	−0.693196	+	0.720749i	$0.743798\pi$
$912$	1.21647e7	+	1.52541e7i	0.0160368	+	0.0201095i
$913$	1.23033e7	+	5.39043e7i	0.0161663	+	0.0708290i
$914$	2.98751e8	+	3.74621e8i	0.391264	+	0.490630i
$915$	−1.10606e8	−	2.29676e8i	−0.144383	−	0.299814i
$916$	4.86263e8	−	2.13046e9i	0.632681	−	2.77196i
$917$	6.05705e8	−	2.91692e8i	0.785512	−	0.378283i
$918$	−3.97178e9	+	4.98046e9i	−5.13402	+	6.43786i
$919$	−2.29842e8	−	1.00700e9i	−0.296130	−	1.29743i	−0.875837	−	0.482607i	$-0.839690\pi$
$919$	−2.29842e8	−	1.00700e9i	−0.296130	−	1.29743i	0.579707	−	0.814825i	$-0.303167\pi$
$920$	−1.02024e8	−	4.46994e8i	−0.131020	−	0.574035i
$921$	1.00975e9	−	2.09677e9i	1.29251	−	2.68393i
$922$	2.82319e8	+	2.25142e8i	0.360203	+	0.287252i
$923$	−2.53610e7	+	2.02247e7i	−0.0322523	+	0.0257204i
$924$	−1.24592e8	−	6.00002e7i	−0.157933	−	0.0760566i
$925$	−5.93440e8	+	1.23229e9i	−0.749811	+	1.55700i
$926$	−7.93408e8	−	9.94902e8i	−0.999225	−	1.25299i
$927$	−1.60658e9	+	2.01458e9i	−2.01680	+	2.52898i
$928$	2.08937e8	+	1.00619e8i	0.261440	+	0.125903i
$929$	−1.05341e9	+	2.40434e8i	−1.31386	+	0.299881i	−0.821350	−	0.570424i	$-0.806779\pi$
$929$	−1.05341e9	+	2.40434e8i	−1.31386	+	0.299881i	−0.492513	+	0.870305i	$0.663922\pi$
$930$	2.64266e8	−	6.03171e7i	0.328544	−	0.0749879i
$931$	1.18077e8	+	9.41633e7i	0.146324	+	0.116690i
$932$	−5.15806e8	−	1.07108e9i	−0.637146	−	1.32305i
$933$	−5.43661e7	−	1.24087e7i	−0.0669396	−	0.0152785i
$934$	−6.16714e8	+	2.96994e8i	−0.756908	+	0.364508i
$935$	−2.48028e7	+	1.97796e7i	−0.0303435	+	0.0241982i
$936$	1.12356e9	−	2.56445e8i	1.37015	−	0.312728i
$937$	3.82926e8	−	3.05373e8i	0.465475	−	0.371204i	−0.362486	−	0.931989i	$-0.618072\pi$
$937$	3.82926e8	−	3.05373e8i	0.465475	−	0.371204i	0.827961	+	0.560785i	$0.189501\pi$
$938$	−1.34353e8	+	5.88639e8i	−0.162794	+	0.713248i
$939$	−1.18797e9			−1.43486
$940$			3.70532e8i			0.446110i
$941$	−1.21321e8	+	5.31541e8i	−0.145602	+	0.637922i	0.848475	+	0.529236i	$0.177521\pi$
$941$	−1.21321e8	+	5.31541e8i	−0.145602	+	0.637922i	−0.994076	+	0.108686i	$0.965336\pi$
$942$	1.50653e9	+	1.20142e9i	1.80229	+	1.43728i
$943$	2.28011e8	+	1.09804e8i	0.271908	+	0.130944i
$944$	−5.49791e6	+	2.64765e6i	−0.00653554	+	0.00314735i
$945$			8.02460e8i			0.950885i
$946$	−4.37734e7	−	7.57893e7i	−0.0517055	−	0.0895230i
$947$	1.01156e9			1.19109			0.595543	−	0.803323i	$-0.296937\pi$
$947$	1.01156e9			1.19109			0.595543	+	0.803323i	$0.296937\pi$
$948$	3.90979e8	+	8.11876e8i	0.458911	+	0.952939i
$949$	2.78901e8	−	5.79144e8i	0.326326	−	0.677623i
$950$	−7.05276e8	+	8.84388e8i	−0.822599	+	1.03151i
$951$	1.40621e9	+	3.20958e8i	1.63497	+	0.373170i
$952$	1.33071e9			1.54231
$953$		−	7.17377e8i		−	0.828837i	−0.910086	−	0.414418i	$-0.863985\pi$
$953$		−	7.17377e8i		−	0.828837i	0.910086	−	0.414418i	$-0.136015\pi$
$954$	−5.23785e9	−	1.19551e9i	−6.03265	−	1.37691i
$955$	−2.45743e8	−	3.08153e8i	−0.282145	−	0.353798i
$956$	4.60829e8	+	2.01902e9i	0.527431	+	2.31083i
$957$	1.93662e7	+	2.42845e7i	0.0220958	+	0.0277072i
$958$	−4.34180e8	−	9.01585e8i	−0.493826	−	1.02544i
$959$	2.88281e8	−	1.26304e9i	0.326859	−	1.43206i
$960$	8.68704e8	−	4.18346e8i	0.981879	−	0.472848i
$961$	−5.00739e8	+	6.27907e8i	−0.564211	+	0.707498i
$962$	−3.42616e8	−	1.50110e9i	−0.384842	−	1.68610i
$963$	−6.17586e8	−	2.70582e9i	−0.691542	−	3.02984i
$964$	−7.57561e8	+	1.57309e9i	−0.845642	+	1.75599i
$965$	2.35576e8	+	1.87866e8i	0.262150	+	0.209058i
$966$	3.14946e9	−	2.51161e9i	3.49386	−	2.78626i
$967$	−6.64226e8	−	3.19874e8i	−0.734575	−	0.353753i	0.0289065	−	0.999582i	$-0.490798\pi$
$967$	−6.64226e8	−	3.19874e8i	−0.734575	−	0.353753i	−0.763482	+	0.645829i	$0.776512\pi$
$968$	3.96560e8	−	8.23465e8i	0.437203	−	0.907861i
$969$	1.70675e9	+	2.14020e9i	1.87586	+	2.35225i
$970$	−3.04877e8	+	3.82304e8i	−0.334049	+	0.418884i
$971$	−7.22419e8	−	3.47899e8i	−0.789099	−	0.380010i	−0.00448131	−	0.999990i	$-0.501426\pi$
$971$	−7.22419e8	−	3.47899e8i	−0.789099	−	0.380010i	−0.784618	+	0.619980i	$0.787141\pi$
$972$	4.08505e9	−	9.32386e8i	4.44835	−	1.01531i
$973$	−7.12791e8	+	1.62690e8i	−0.773791	+	0.176613i
$974$	1.05240e9	+	8.39257e8i	1.13894	+	0.908277i
$975$	3.57846e8	+	7.43074e8i	0.386084	+	0.801712i
$976$	6.51662e6	+	1.48738e6i	0.00700927	+	0.00159982i
$977$	9.09718e7	−	4.38097e7i	0.0975491	−	0.0469772i	−0.384473	−	0.923136i	$-0.625617\pi$
$977$	9.09718e7	−	4.38097e7i	0.0975491	−	0.0469772i	0.482022	+	0.876159i	$0.339903\pi$
$978$	−1.68119e9	+	1.34070e9i	−1.79721	+	1.43323i
$979$	5.67499e6	−	1.29528e6i	0.00604808	−	0.00138043i
$980$	−8.55289e7	+	6.82070e7i	−0.0908730	+	0.0724688i
$981$	−9.04591e6	+	3.96327e7i	−0.00958176	+	0.0419804i
$982$	−2.37835e9			−2.51155
$983$			4.78710e8i			0.503978i	0.967730	+	0.251989i	$0.0810847\pi$
$983$			4.78710e8i			0.503978i	−0.967730	+	0.251989i	$0.918915\pi$
$984$	7.50456e7	−	3.28796e8i	0.0787662	−	0.345097i
$985$	−9.86565e7	−	7.86760e7i	−0.103233	−	0.0823253i
$986$	−7.00491e8	−	3.37339e8i	−0.730755	−	0.351913i
$987$	−1.12760e9	+	5.43026e8i	−1.17275	+	0.564767i
$988$		−	7.88205e8i		−	0.817276i
$989$	1.57368e9	−	1.18188e8i	1.62678	−	0.122175i
$990$	9.21944e7			0.0950165
$991$	−8.95764e7	−	1.86007e8i	−0.0920392	−	0.191121i	0.849867	−	0.526997i	$-0.176682\pi$
$991$	−8.95764e7	−	1.86007e8i	−0.0920392	−	0.191121i	−0.941906	+	0.335876i	$0.890968\pi$
$992$	1.29053e8	−	2.67982e8i	0.132201	−	0.274518i
$993$	−9.01883e7	+	1.13093e8i	−0.0921091	+	0.115501i
$994$	1.06121e8	+	2.42214e7i	0.108054	+	0.0246627i
$995$	−9.61657e7			−0.0976228
$996$			3.45583e9i			3.49763i
$997$	−5.13907e8	−	1.17296e8i	−0.518560	−	0.118358i	−0.0447727	−	0.998997i	$-0.514256\pi$
$997$	−5.13907e8	−	1.17296e8i	−0.518560	−	0.118358i	−0.473787	+	0.880639i	$0.657113\pi$
$998$	−8.51468e8	−	1.06771e9i	−0.856597	−	1.07414i
$999$	−1.30966e9	−	5.73801e9i	−1.31360	−	5.75526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.f.a.2.2	✓	126
43.22	odd	14	inner	43.7.f.a.22.2	yes	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.f.a.2.2	✓	126	1.1	even	1	trivial
43.7.f.a.22.2	yes	126	43.22	odd	14	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.f (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.62328 - 11.6769i) q^{2} +(-22.1545 + 46.0043i) q^{3} +(-64.8243 + 81.2871i) q^{4} +(43.4728 + 9.92237i) q^{5} +661.767 q^{6} +306.680i q^{7} +(505.038 + 115.272i) q^{8} +(-1171.05 - 1468.45i) q^{9} +O(q^{10})\)	\(q+(-5.62328 - 11.6769i) q^{2} +(-22.1545 + 46.0043i) q^{3} +(-64.8243 + 81.2871i) q^{4} +(43.4728 + 9.92237i) q^{5} +661.767 q^{6} +306.680i q^{7} +(505.038 + 115.272i) q^{8} +(-1171.05 - 1468.45i) q^{9} +(-128.597 - 563.421i) q^{10} +(-52.9573 - 66.4064i) q^{11} +(-2303.41 - 4783.08i) q^{12} +(-263.570 + 1154.78i) q^{13} +(3581.06 - 1724.55i) q^{14} +(-1419.59 + 1780.11i) q^{15} +(-13.2846 - 58.2037i) q^{16} +(-1863.88 - 8166.18i) q^{17} +(-10561.8 + 21931.7i) q^{18} +(5004.02 + 3990.57i) q^{19} +(-3624.65 + 2890.56i) q^{20} +(-14108.6 - 6794.35i) q^{21} +(-477.624 + 991.796i) q^{22} +(-12375.5 - 15518.4i) q^{23} +(-16491.9 + 20680.2i) q^{24} +(-12286.2 - 5916.73i) q^{25} +(14966.3 - 3415.96i) q^{26} +(57209.2 - 13057.6i) q^{27} +(-24929.1 - 19880.3i) q^{28} +(3107.44 + 6452.67i) q^{29} +(28768.8 + 6566.30i) q^{30} +(8276.17 - 3985.59i) q^{31} +(25315.7 - 20188.6i) q^{32} +(4228.23 - 965.065i) q^{33} +(-84874.2 + 67684.9i) q^{34} +(-3042.99 + 13332.2i) q^{35} +195279. q^{36} -100299. i q^{37} +(18458.3 - 80871.2i) q^{38} +(-47285.4 - 37708.9i) q^{39} +(20811.6 + 10022.4i) q^{40} +(-11487.4 + 5532.06i) q^{41} +202951. i q^{42} +(-44777.2 + 65699.0i) q^{43} +8830.90 q^{44} +(-36338.4 - 75457.4i) q^{45} +(-111615. + 231771. i) q^{46} +(49831.3 - 62486.4i) q^{47} +(2971.94 + 678.325i) q^{48} +23596.4 q^{49} +176736. i q^{50} +(416973. + 95171.4i) q^{51} +(-76782.7 - 96282.4i) q^{52} +(49112.1 + 215174. i) q^{53} +(-474175. - 594597. i) q^{54} +(-1643.29 - 3412.33i) q^{55} +(-35351.5 + 154885. i) q^{56} +(-294445. + 141797. i) q^{57} +(57872.9 - 72570.3i) q^{58} +(-22744.7 - 99651.1i) q^{59} +(-52676.1 - 230789. i) q^{60} +(-48578.6 + 100875. i) q^{61} +(-93078.3 - 74227.5i) q^{62} +(450345. - 359138. i) q^{63} +(-381538. - 183739. i) q^{64} +(-22916.2 + 47586.0i) q^{65} +(-35045.4 - 43945.5i) q^{66} +(-94711.9 + 118765. i) q^{67} +(784630. + 377858. i) q^{68} +(988086. - 225524. i) q^{69} +(172790. - 39438.2i) q^{70} +(21411.2 + 17074.9i) q^{71} +(-422155. - 876615. i) q^{72} +(-529084. - 120760. i) q^{73} +(-1.17117e6 + 564007. i) q^{74} +(544390. - 434137. i) q^{75} +(-648764. + 148076. i) q^{76} +(20365.5 - 16240.9i) q^{77} +(-174422. + 764193. i) q^{78} -169739. q^{79} -2662.09i q^{80} +(-362054. + 1.58626e6i) q^{81} +(129194. + 103029. i) q^{82} +(-586495. - 282441. i) q^{83} +(1.46687e6 - 706409. i) q^{84} -373501. i q^{85} +(1.01895e6 + 153413. i) q^{86} -365695. q^{87} +(-19090.7 - 39642.2i) q^{88} +(-29735.1 + 61745.6i) q^{89} +(-676764. + 848635. i) q^{90} +(-354147. - 80831.6i) q^{91} +2.06368e6 q^{92} +469039. i q^{93} +(-1.00986e6 - 230494. i) q^{94} +(177942. + 223133. i) q^{95} +(367905. + 1.61190e6i) q^{96} +(-527551. - 661528. i) q^{97} +(-132689. - 275532. i) q^{98} +(-35498.9 + 155531. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9}+O(q^{10}) \) 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9} + 1955 q^{10} - 985 q^{11} - 455 q^{12} - 4485 q^{13} - 6771 q^{14} + 5017 q^{15} - 41935 q^{16} - 10409 q^{17} - 5110 q^{18} - 33397 q^{19} - 24507 q^{20} - 5448 q^{21} + 25193 q^{22} - 29017 q^{23} - 1885 q^{24} - 2080 q^{25} + 34713 q^{26} - 7 q^{27} + 28665 q^{28} + 17353 q^{29} - 290052 q^{30} + 13547 q^{31} + 458283 q^{32} - 94801 q^{33} - 191527 q^{34} + 183008 q^{35} + 956352 q^{36} + 304607 q^{38} - 381031 q^{39} + 66419 q^{40} + 313447 q^{41} - 323228 q^{43} + 281588 q^{44} - 1237551 q^{45} + 80948 q^{46} - 180133 q^{47} - 762055 q^{48} - 1861754 q^{49} + 999215 q^{51} + 471797 q^{52} + 1030011 q^{53} - 92099 q^{54} + 324233 q^{55} - 842713 q^{56} + 331037 q^{57} + 849461 q^{58} - 369609 q^{59} + 553323 q^{60} - 594727 q^{61} - 886711 q^{62} + 1914136 q^{63} - 3250219 q^{64} + 1473521 q^{65} - 427559 q^{66} + 122535 q^{67} - 602346 q^{68} + 4320057 q^{69} - 1694994 q^{70} - 770707 q^{71} - 391202 q^{72} + 476945 q^{73} - 3943812 q^{74} + 2061367 q^{75} - 2044462 q^{76} + 3016216 q^{77} + 239350 q^{78} + 5077268 q^{79} + 2388946 q^{81} + 5820437 q^{82} - 1324235 q^{83} + 3759618 q^{84} - 4967947 q^{86} - 3537894 q^{87} - 7289555 q^{88} - 4331495 q^{89} - 12825206 q^{90} + 1802976 q^{91} - 12038260 q^{92} + 6249341 q^{94} - 5313259 q^{95} + 7069598 q^{96} + 788975 q^{97} + 4724783 q^{98} - 2216971 q^{99}+O(q^{100}) \) 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9 + 1955 * q^10 - 985 * q^11 - 455 * q^12 - 4485 * q^13 - 6771 * q^14 + 5017 * q^15 - 41935 * q^16 - 10409 * q^17 - 5110 * q^18 - 33397 * q^19 - 24507 * q^20 - 5448 * q^21 + 25193 * q^22 - 29017 * q^23 - 1885 * q^24 - 2080 * q^25 + 34713 * q^26 - 7 * q^27 + 28665 * q^28 + 17353 * q^29 - 290052 * q^30 + 13547 * q^31 + 458283 * q^32 - 94801 * q^33 - 191527 * q^34 + 183008 * q^35 + 956352 * q^36 + 304607 * q^38 - 381031 * q^39 + 66419 * q^40 + 313447 * q^41 - 323228 * q^43 + 281588 * q^44 - 1237551 * q^45 + 80948 * q^46 - 180133 * q^47 - 762055 * q^48 - 1861754 * q^49 + 999215 * q^51 + 471797 * q^52 + 1030011 * q^53 - 92099 * q^54 + 324233 * q^55 - 842713 * q^56 + 331037 * q^57 + 849461 * q^58 - 369609 * q^59 + 553323 * q^60 - 594727 * q^61 - 886711 * q^62 + 1914136 * q^63 - 3250219 * q^64 + 1473521 * q^65 - 427559 * q^66 + 122535 * q^67 - 602346 * q^68 + 4320057 * q^69 - 1694994 * q^70 - 770707 * q^71 - 391202 * q^72 + 476945 * q^73 - 3943812 * q^74 + 2061367 * q^75 - 2044462 * q^76 + 3016216 * q^77 + 239350 * q^78 + 5077268 * q^79 + 2388946 * q^81 + 5820437 * q^82 - 1324235 * q^83 + 3759618 * q^84 - 4967947 * q^86 - 3537894 * q^87 - 7289555 * q^88 - 4331495 * q^89 - 12825206 * q^90 + 1802976 * q^91 - 12038260 * q^92 + 6249341 * q^94 - 5313259 * q^95 + 7069598 * q^96 + 788975 * q^97 + 4724783 * q^98 - 2216971 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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