LMFDB - Embedded newform 27.7.f.a.2.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, 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:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$102$
Relative dimension:	$17$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.10
Character	$\chi$	$=$	27.2
Dual form			27.7.f.a.14.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.51454 + 0.267054i) q^{2} +(26.8676 - 2.67034i) q^{3} +(-57.9178 - 21.0804i) q^{4} +(-139.142 - 165.822i) q^{5} +(41.4052 + 3.13078i) q^{6} +(-39.0374 + 14.2084i) q^{7} +(-167.329 - 96.6072i) q^{8} +(714.739 - 143.491i) q^{9} +O(q^{10})$	\(q+(1.51454 + 0.267054i) q^{2} +(26.8676 - 2.67034i) q^{3} +(-57.9178 - 21.0804i) q^{4} +(-139.142 - 165.822i) q^{5} +(41.4052 + 3.13078i) q^{6} +(-39.0374 + 14.2084i) q^{7} +(-167.329 - 96.6072i) q^{8} +(714.739 - 143.491i) q^{9} +(-166.452 - 288.303i) q^{10} +(-170.419 + 203.097i) q^{11} +(-1612.41 - 411.719i) q^{12} +(-454.269 - 2576.29i) q^{13} +(-62.9181 + 11.0942i) q^{14} +(-4181.21 - 4083.70i) q^{15} +(2794.14 + 2344.56i) q^{16} +(4585.03 - 2647.17i) q^{17} +(1120.82 - 26.4496i) q^{18} +(-3572.08 + 6187.02i) q^{19} +(4563.18 + 12537.2i) q^{20} +(-1010.90 + 485.990i) q^{21} +(-312.344 + 262.088i) q^{22} +(4130.38 - 11348.1i) q^{23} +(-4753.70 - 2148.78i) q^{24} +(-5423.46 + 30758.0i) q^{25} -4023.21i q^{26} +(18820.2 - 5763.87i) q^{27} +2560.48 q^{28} +(14932.5 + 2633.00i) q^{29} +(-5242.04 - 7301.54i) q^{30} +(-25151.2 - 9154.28i) q^{31} +(11554.2 + 13769.8i) q^{32} +(-4036.41 + 5911.82i) q^{33} +(7651.15 - 2784.79i) q^{34} +(7787.80 + 4496.29i) q^{35} +(-44420.9 - 6756.23i) q^{36} +(7676.10 + 13295.4i) q^{37} +(-7062.33 + 8416.55i) q^{38} +(-19084.7 - 68005.6i) q^{39} +(7262.72 + 41188.9i) q^{40} +(97509.7 - 17193.6i) q^{41} +(-1660.84 + 466.087i) q^{42} +(-67116.1 - 56317.1i) q^{43} +(14151.6 - 8170.46i) q^{44} +(-123244. - 98554.1i) q^{45} +(9286.20 - 16084.2i) q^{46} +(-58261.5 - 160072. i) q^{47} +(81332.6 + 55531.4i) q^{48} +(-88802.3 + 74514.0i) q^{49} +(-16428.1 + 45135.9i) q^{50} +(116120. - 83366.7i) q^{51} +(-27998.8 + 158789. i) q^{52} +8804.40i q^{53} +(30043.2 - 3703.61i) q^{54} +57390.4 q^{55} +(7904.71 + 1393.81i) q^{56} +(-79451.8 + 175769. i) q^{57} +(21912.7 + 7975.57i) q^{58} +(107143. + 127688. i) q^{59} +(156080. + 324660. i) q^{60} +(406882. - 148093. i) q^{61} +(-35647.8 - 20581.3i) q^{62} +(-25862.7 + 15756.9i) q^{63} +(-102897. - 178224. i) q^{64} +(-363998. + 433796. i) q^{65} +(-7692.08 + 7875.75i) q^{66} +(-50984.7 - 289149. i) q^{67} +(-321358. + 56664.1i) q^{68} +(80670.2 - 315927. i) q^{69} +(10594.2 + 8889.58i) q^{70} +(192176. - 110953. i) q^{71} +(-133459. - 45038.7i) q^{72} +(148533. - 257267. i) q^{73} +(8075.18 + 22186.4i) q^{74} +(-63581.2 + 840876. i) q^{75} +(337311. - 283038. i) q^{76} +(3767.01 - 10349.8i) q^{77} +(-10743.3 - 108094. i) q^{78} +(-123465. + 700204. i) q^{79} -789556. i q^{80} +(490261. - 205118. i) q^{81} +152274. q^{82} +(-372962. - 65763.2i) q^{83} +(68794.0 - 6837.35i) q^{84} +(-1.07693e6 - 391970. i) q^{85} +(-86610.4 - 103218. i) q^{86} +(408231. + 30867.6i) q^{87} +(48136.6 - 17520.3i) q^{88} +(-667826. - 385569. i) q^{89} +(-160339. - 182177. i) q^{90} +(54338.5 + 94117.0i) q^{91} +(-478446. + 570189. i) q^{92} +(-700197. - 178791. i) q^{93} +(-45491.5 - 257995. i) q^{94} +(1.52297e6 - 268541. i) q^{95} +(347205. + 339108. i) q^{96} +(576581. + 483809. i) q^{97} +(-154394. + 89139.4i) q^{98} +(-92662.2 + 169615. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) $ 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	1.51454	+	0.267054i	0.189318	+	0.0333818i	0.267503	−	0.963557i	$-0.413801\pi$
$2$	1.51454	+	0.267054i	0.189318	+	0.0333818i	−0.0781853	+	0.996939i	$0.524913\pi$
$3$	26.8676	−	2.67034i	0.995097	−	0.0989015i
$3$	26.8676	−	2.67034i	0.995097	−	0.0989015i
$4$	−57.9178	−	21.0804i	−0.904966	−	0.329381i
$5$	−139.142	−	165.822i	−1.11313	−	1.32658i	−0.939803	−	0.341716i	$-0.888992\pi$
$5$	−139.142	−	165.822i	−1.11313	−	1.32658i	−0.173329	−	0.984864i	$-0.555452\pi$
$6$	41.4052	+	3.13078i	0.191691	+	0.0144943i
$7$	−39.0374	+	14.2084i	−0.113812	+	0.0414240i	−0.398298	−	0.917256i	$-0.630399\pi$
$7$	−39.0374	+	14.2084i	−0.113812	+	0.0414240i	0.284487	+	0.958680i	$0.408177\pi$
$8$	−167.329	−	96.6072i	−0.326814	−	0.188686i
$9$	714.739	−	143.491i	0.980437	−	0.196833i
$10$	−166.452	−	288.303i	−0.166452	−	0.288303i
$11$	−170.419	+	203.097i	−0.128038	+	0.152590i	−0.826255	−	0.563297i	$-0.809533\pi$
$11$	−170.419	+	203.097i	−0.128038	+	0.152590i	0.698217	+	0.715887i	$0.253977\pi$
$12$	−1612.41	−	411.719i	−0.933105	−	0.238263i
$13$	−454.269	−	2576.29i	−0.206768	−	1.17264i	−0.894634	−	0.446800i	$-0.852563\pi$
$13$	−454.269	−	2576.29i	−0.206768	−	1.17264i	0.687866	−	0.725838i	$-0.258548\pi$
$14$	−62.9181	+	11.0942i	−0.0229294	+	0.00404306i
$15$	−4181.21	−	4083.70i	−1.23888	−	1.20999i
$16$	2794.14	+	2344.56i	0.682162	+	0.572402i
$17$	4585.03	−	2647.17i	0.933244	−	0.538809i	0.0454080	−	0.998969i	$-0.485541\pi$
$17$	4585.03	−	2647.17i	0.933244	−	0.538809i	0.887836	+	0.460160i	$0.152208\pi$
$18$	1120.82	−	26.4496i	0.192185	−	0.00453526i
$19$	−3572.08	+	6187.02i	−0.520787	+	0.902029i	0.478921	+	0.877858i	$0.341028\pi$
$19$	−3572.08	+	6187.02i	−0.520787	+	0.902029i	−0.999708	+	0.0241713i	$0.992305\pi$
$20$	4563.18	+	12537.2i	0.570397	+	1.56715i
$21$	−1010.90	+	485.990i	−0.109157	+	0.0524771i
$22$	−312.344	+	262.088i	−0.0293336	+	0.0246138i
$23$	4130.38	−	11348.1i	0.339474	−	0.932698i	−0.646070	−	0.763278i	$-0.723588\pi$
$23$	4130.38	−	11348.1i	0.339474	−	0.932698i	0.985544	−	0.169420i	$-0.0541893\pi$
$24$	−4753.70	−	2148.78i	−0.343873	−	0.155439i
$25$	−5423.46	+	30758.0i	−0.347101	+	1.96851i
$26$		−	4023.21i		−	0.228903i
$27$	18820.2	−	5763.87i	0.956163	−	0.292835i
$28$	2560.48			0.116640
$29$	14932.5	+	2633.00i	0.612263	+	0.107959i	0.471177	−	0.882039i	$-0.343829\pi$
$29$	14932.5	+	2633.00i	0.612263	+	0.107959i	0.141086	+	0.989997i	$0.454940\pi$
$30$	−5242.04	−	7301.54i	−0.194150	−	0.270427i
$31$	−25151.2	−	9154.28i	−0.844254	−	0.307283i	−0.116559	−	0.993184i	$-0.537186\pi$
$31$	−25151.2	−	9154.28i	−0.844254	−	0.307283i	−0.727695	+	0.685901i	$0.759408\pi$
$32$	11554.2	+	13769.8i	0.352608	+	0.420221i
$33$	−4036.41	+	5911.82i	−0.112319	+	0.164505i
$34$	7651.15	−	2784.79i	0.194666	−	0.0708526i
$35$	7787.80	+	4496.29i	0.181640	+	0.104870i
$36$	−44420.9	−	6756.23i	−0.952095	−	0.144810i
$37$	7676.10	+	13295.4i	0.151543	+	0.262480i	0.931795	−	0.362985i	$-0.118242\pi$
$37$	7676.10	+	13295.4i	0.151543	+	0.262480i	−0.780252	+	0.625465i	$0.784909\pi$
$38$	−7062.33	+	8416.55i	−0.128705	+	0.153385i
$39$	−19084.7	−	68005.6i	−0.321730	−	1.14644i
$40$	7262.72	+	41188.9i	0.113480	+	0.643577i
$41$	97509.7	−	17193.6i	1.41480	−	0.249468i	0.586591	−	0.809883i	$-0.300470\pi$
$41$	97509.7	−	17193.6i	1.41480	−	0.249468i	0.828212	+	0.560415i	$0.189358\pi$
$42$	−1660.84	+	466.087i	−0.0224171	+	0.00629099i
$43$	−67116.1	−	56317.1i	−0.844154	−	0.708329i	0.114340	−	0.993442i	$-0.463525\pi$
$43$	−67116.1	−	56317.1i	−0.844154	−	0.708329i	−0.958494	+	0.285113i	$0.907969\pi$
$44$	14151.6	−	8170.46i	0.166130	−	0.0959154i
$45$	−123244.	−	98554.1i	−1.35247	−	1.08153i
$46$	9286.20	−	16084.2i	0.0954036	−	0.165244i
$47$	−58261.5	−	160072.i	−0.561162	−	1.54178i	−0.817937	−	0.575308i	$-0.804882\pi$
$47$	−58261.5	−	160072.i	−0.561162	−	1.54178i	0.256775	−	0.966471i	$-0.417340\pi$
$48$	81332.6	+	55531.4i	0.735429	+	0.502129i
$49$	−88802.3	+	74514.0i	−0.754807	+	0.633359i
$50$	−16428.1	+	45135.9i	−0.131425	+	0.361087i
$51$	116120.	−	83366.7i	0.875380	−	0.628466i
$52$	−27998.8	+	158789.i	−0.199127	+	1.12930i
$53$			8804.40i			0.0591387i	0.999563	+	0.0295694i	$0.00941359\pi$
$53$			8804.40i			0.0591387i	−0.999563	+	0.0295694i	$0.990586\pi$
$54$	30043.2	−	3703.61i	0.190794	−	0.0235204i
$55$	57390.4			0.344946
$56$	7904.71	+	1393.81i	0.0450113	+	0.00793671i
$57$	−79451.8	+	175769.i	−0.429021	+	0.949113i
$58$	21912.7	+	7975.57i	0.112308	+	0.0408769i
$59$	107143.	+	127688.i	0.521684	+	0.621719i	0.960978	−	0.276624i	$-0.0892158\pi$
$59$	107143.	+	127688.i	0.521684	+	0.621719i	−0.439294	+	0.898343i	$0.644771\pi$
$60$	156080.	+	324660.i	0.722595	+	1.50306i
$61$	406882.	−	148093.i	1.79258	−	0.652446i	0.793546	−	0.608511i	$-0.208233\pi$
$61$	406882.	−	148093.i	1.79258	−	0.652446i	0.999034	−	0.0439349i	$-0.0139894\pi$
$62$	−35647.8	−	20581.3i	−0.149574	−	0.0863568i
$63$	−25862.7	+	15756.9i	−0.103431	+	0.0630156i
$64$	−102897.	−	178224.i	−0.392523	−	0.679869i
$65$	−363998.	+	433796.i	−1.32544	+	1.57960i
$66$	−7692.08	+	7875.75i	−0.0267554	+	0.0273943i
$67$	−50984.7	−	289149.i	−0.169518	−	0.961384i	−0.944283	−	0.329134i	$-0.893243\pi$
$67$	−50984.7	−	289149.i	−0.169518	−	0.961384i	0.774765	−	0.632249i	$-0.217868\pi$
$68$	−321358.	+	56664.1i	−1.02203	+	0.180211i
$69$	80670.2	−	315927.i	0.245565	−	0.961700i
$70$	10594.2	+	8889.58i	0.0308869	+	0.0259172i
$71$	192176.	−	110953.i	0.536937	−	0.310001i	−0.206900	−	0.978362i	$-0.566337\pi$
$71$	192176.	−	110953.i	0.536937	−	0.310001i	0.743837	+	0.668362i	$0.233004\pi$
$72$	−133459.	−	45038.7i	−0.357560	−	0.120667i
$73$	148533.	−	257267.i	0.381817	−	0.661327i	−0.609505	−	0.792782i	$-0.708632\pi$
$73$	148533.	−	257267.i	0.381817	−	0.661327i	0.991322	+	0.131456i	$0.0419651\pi$
$74$	8075.18	+	22186.4i	0.0199277	+	0.0547509i
$75$	−63581.2	+	840876.i	−0.150711	+	1.99319i
$76$	337311.	−	283038.i	0.768405	−	0.644769i
$77$	3767.01	−	10349.8i	0.00825134	−	0.0226704i
$78$	−10743.3	−	108094.i	−0.0226389	−	0.227781i
$79$	−123465.	+	700204.i	−0.250416	+	1.42018i	0.557154	+	0.830409i	$0.311893\pi$
$79$	−123465.	+	700204.i	−0.250416	+	1.42018i	−0.807570	+	0.589772i	$0.799218\pi$
$80$		−	789556.i		−	1.54210i
$81$	490261.	−	205118.i	0.922513	−	0.385965i
$82$	152274.			0.276175
$83$	−372962.	−	65763.2i	−0.652273	−	0.115013i	−0.162287	−	0.986744i	$-0.551887\pi$
$83$	−372962.	−	65763.2i	−0.652273	−	0.115013i	−0.489986	+	0.871730i	$0.662998\pi$
$84$	68794.0	−	6837.35i	0.116068	−	0.0115359i
$85$	−1.07693e6	−	391970.i	−1.75360	−	0.638257i
$86$	−86610.4	−	103218.i	−0.136168	−	0.162279i
$87$	408231.	+	30867.6i	0.619939	+	0.0468754i
$88$	48136.6	−	17520.3i	0.0706362	−	0.0257095i
$89$	−667826.	−	385569.i	−0.947312	−	0.546931i	−0.0550671	−	0.998483i	$-0.517537\pi$
$89$	−667826.	−	385569.i	−0.947312	−	0.546931i	−0.892245	+	0.451552i	$0.850871\pi$
$90$	−160339.	−	182177.i	−0.219943	−	0.249900i
$91$	54338.5	+	94117.0i	0.0721080	+	0.124895i
$92$	−478446.	+	570189.i	−0.614425	+	0.732243i
$93$	−700197.	−	178791.i	−0.870505	−	0.222279i
$94$	−45491.5	−	257995.i	−0.0547704	−	0.310619i
$95$	1.52297e6	−	268541.i	1.77632	−	0.313213i
$96$	347205.	+	339108.i	0.392439	+	0.383288i
$97$	576581.	+	483809.i	0.631750	+	0.530101i	0.901472	−	0.432837i	$-0.142487\pi$
$97$	576581.	+	483809.i	0.631750	+	0.530101i	−0.269722	+	0.962938i	$0.586932\pi$
$98$	−154394.	+	89139.4i	−0.164041	+	0.0947091i
$99$	−92662.2	+	169615.i	−0.0954986	+	0.174807i
$100$	962504.	−	1.66711e6i	0.962504	−	1.66711i
$101$	26379.9	+	72478.3i	0.0256041	+	0.0703467i	0.951836	−	0.306607i	$-0.0991938\pi$
$101$	26379.9	+	72478.3i	0.0256041	+	0.0703467i	−0.926232	+	0.376954i	$0.876972\pi$
$102$	198132.	−	95251.9i	0.186704	−	0.0897580i
$103$	−1.21933e6	+	1.02314e6i	−1.11586	+	0.936317i	−0.998388	−	0.0567592i	$-0.981923\pi$
$103$	−1.21933e6	+	1.02314e6i	−1.11586	+	0.936317i	−0.117471	+	0.993076i	$0.537479\pi$
$104$	−172876.	+	474972.i	−0.153686	+	0.422248i
$105$	221246.	+	100009.i	0.191121	+	0.0863911i
$106$	−2351.25	+	13334.6i	−0.00197416	+	0.0111960i
$107$			282600.i			0.230685i	0.993326	+	0.115343i	$0.0367966\pi$
$107$			282600.i			0.230685i	−0.993326	+	0.115343i	$0.963203\pi$
$108$	−1.21153e6	−	62904.8i	−0.961749	−	0.0499359i
$109$	1.61375e6			1.24611			0.623055	−	0.782178i	$-0.285891\pi$
$109$	1.61375e6			1.24611			0.623055	+	0.782178i	$0.285891\pi$
$110$	86920.1	+	15326.4i	0.0653044	+	0.0115149i
$111$	241742.	+	336718.i	0.176760	+	0.246205i
$112$	−142388.	−	51825.1i	−0.101349	−	0.0368881i
$113$	1.78286e6	+	2.12473e6i	1.23561	+	1.47254i	0.829295	+	0.558812i	$0.188742\pi$
$113$	1.78286e6	+	2.12473e6i	1.23561	+	1.47254i	0.406316	+	0.913732i	$0.366813\pi$
$114$	−167273.	+	244992.i	−0.112904	+	0.165362i
$115$	−2.45648e6	+	894087.i	−1.61518	+	0.587877i
$116$	−809352.	−	467280.i	−0.518518	−	0.299366i
$117$	−694358.	−	1.77619e6i	−0.433537	−	1.10900i
$118$	128173.	+	222002.i	0.0780099	+	0.135117i
$119$	−141375.	+	168485.i	−0.0838944	+	0.0999814i
$120$	305121.	+	1.08725e6i	0.176574	+	0.629198i
$121$	295422.	+	1.67542e6i	0.166758	+	0.945733i
$122$	655788.	−	115633.i	0.361147	−	0.0636799i
$123$	2.57394e6	−	722335.i	1.38319	−	0.388171i
$124$	1.26372e6	+	1.06039e6i	0.662808	+	0.556162i
$125$	2.92585e6	−	1.68924e6i	1.49804	−	0.864892i
$126$	−43378.1	+	16957.6i	−0.0216850	+	0.00847723i
$127$	−985200.	+	1.70642e6i	−0.480965	+	0.833055i	−0.999761	−	0.0218422i	$-0.993047\pi$
$127$	−985200.	+	1.70642e6i	−0.480965	+	0.833055i	0.518797	+	0.854898i	$0.326380\pi$
$128$	−501712.	−	1.37844e6i	−0.239235	−	0.657292i
$129$	−1.95364e6	−	1.33388e6i	−0.910070	−	0.621368i
$130$	−667138.	+	559795.i	−0.303659	+	0.254800i
$131$	114335.	−	314132.i	0.0508586	−	0.139733i	−0.911662	−	0.410940i	$-0.865201\pi$
$131$	114335.	−	314132.i	0.0508586	−	0.139733i	0.962521	+	0.271207i	$0.0874228\pi$
$132$	358403.	−	257310.i	0.155830	−	0.111876i
$133$	51536.6	−	292279.i	0.0219059	−	0.124235i
$134$		−	451543.i		−	0.187666i
$135$	−3.57445e6	−	2.31881e6i	−1.45281	−	0.942462i
$136$	−1.02294e6			−0.406663
$137$	268082.	+	47270.1i	0.104257	+	0.0183834i	0.225533	−	0.974235i	$-0.427588\pi$
$137$	268082.	+	47270.1i	0.104257	+	0.0183834i	−0.121276	+	0.992619i	$0.538699\pi$
$138$	206548.	−	456941.i	0.0785930	−	0.173869i
$139$	−1.35474e6	−	493086.i	−0.504443	−	0.183602i	0.0772483	−	0.997012i	$-0.475387\pi$
$139$	−1.35474e6	−	493086.i	−0.504443	−	0.183602i	−0.581691	+	0.813410i	$0.697609\pi$
$140$	−356269.	−	424585.i	−0.129836	−	0.154732i
$141$	−1.99280e6	−	4.14518e6i	−0.710895	−	1.47872i
$142$	320688.	−	116721.i	0.112000	−	0.0407647i
$143$	600652.	+	346787.i	0.205407	+	0.118592i
$144$	2.33350e6	+	1.27481e6i	0.781485	+	0.426932i
$145$	−1.64112e6	−	2.84250e6i	−0.538314	−	0.932388i
$146$	293664.	−	349975.i	0.0943610	−	0.112455i
$147$	−2.18693e6	+	2.23915e6i	−0.688467	+	0.704905i
$148$	−164311.	−	931855.i	−0.0506853	−	0.287451i
$149$	−1.88984e6	+	333230.i	−0.571303	+	0.100736i	−0.451834	−	0.892102i	$-0.649230\pi$
$149$	−1.88984e6	+	333230.i	−0.571303	+	0.100736i	−0.119469	+	0.992838i	$0.538119\pi$
$150$	−320856.	+	1.25656e6i	−0.0950685	+	0.372315i
$151$	3.00769e6	+	2.52375e6i	0.873579	+	0.733020i	0.964849	−	0.262806i	$-0.0846479\pi$
$151$	3.00769e6	+	2.52375e6i	0.873579	+	0.733020i	−0.0912693	+	0.995826i	$0.529092\pi$
$152$	1.19542e6	−	690177.i	0.340401	−	0.196530i
$153$	2.89725e6	−	2.54995e6i	0.808932	−	0.711962i
$154$	8469.24	−	14669.2i	0.00231890	−	0.00401646i
$155$	1.98159e6	+	5.44437e6i	0.532131	+	1.46202i
$156$	−328240.	+	4.34105e6i	−0.0864605	+	1.14346i
$157$	3.70259e6	−	3.10684e6i	0.956767	−	0.802823i	−0.0236572	−	0.999720i	$-0.507531\pi$
$157$	3.70259e6	−	3.10684e6i	0.956767	−	0.802823i	0.980424	+	0.196897i	$0.0630866\pi$
$158$	−373985.	+	1.02752e6i	−0.0948164	+	0.260506i
$159$	23510.7	+	236553.i	0.00584891	+	0.0588488i
$160$	675668.	−	3.83191e6i	0.164958	−	0.935524i
$161$			501688.i			0.120214i
$162$	797299.	−	179733.i	0.187532	−	0.0422749i
$163$	−1.82192e6			−0.420693			−0.210347	−	0.977627i	$-0.567459\pi$
$163$	−1.82192e6			−0.420693			−0.210347	+	0.977627i	$0.567459\pi$
$164$	−6.00999e6	−	1.05972e6i	−1.36252	−	0.240249i
$165$	1.54194e6	−	153252.i	0.343255	−	0.0341157i
$166$	−547303.	−	199202.i	−0.119648	−	0.0435481i
$167$	−2.29858e6	−	2.73934e6i	−0.493525	−	0.588161i	0.460585	−	0.887616i	$-0.347640\pi$
$167$	−2.29858e6	−	2.73934e6i	−0.493525	−	0.588161i	−0.954110	+	0.299455i	$0.903195\pi$
$168$	216103.	+	16340.2i	0.0455756	+	0.00344611i
$169$	−1.89517e6	+	689787.i	−0.392635	+	0.142907i
$170$	−1.52637e6	−	881253.i	−0.310681	−	0.179372i
$171$	−1.66532e6	+	4.93466e6i	−0.333049	+	0.986891i
$172$	2.70003e6	+	4.67660e6i	0.530620	+	0.919061i
$173$	2.22352e6	−	2.64989e6i	0.429441	−	0.511787i	−0.507320	−	0.861758i	$-0.669364\pi$
$173$	2.22352e6	−	2.64989e6i	0.429441	−	0.511787i	0.936761	+	0.349970i	$0.113808\pi$
$174$	610040.	+	155770.i	0.115801	+	0.0295690i
$175$	−225305.	−	1.27777e6i	−0.0420395	−	0.238418i
$176$	−952346.	+	167924.i	−0.174686	+	0.0308018i
$177$	3.21965e6	+	3.14457e6i	0.580615	+	0.567076i
$178$	−908481.	−	762306.i	−0.161085	−	0.135167i
$179$	−1.34247e6	+	775073.i	−0.234069	+	0.135140i	−0.612448	−	0.790511i	$-0.709815\pi$
$179$	−1.34247e6	+	775073.i	−0.234069	+	0.135140i	0.378379	+	0.925651i	$0.376482\pi$
$180$	5.06046e6	+	8.30606e6i	0.867707	+	1.42422i
$181$	−211118.	+	365667.i	−0.0356032	+	0.0616666i	−0.883278	−	0.468850i	$-0.844669\pi$
$181$	−211118.	+	365667.i	−0.0356032	+	0.0616666i	0.847675	+	0.530516i	$0.178002\pi$
$182$	57163.5	+	157055.i	0.00948210	+	0.0260519i
$183$	1.05365e7	−	5.06541e6i	1.71926	−	0.826536i
$184$	−1.78744e6	+	1.49984e6i	−0.286932	+	0.240764i
$185$	1.13661e6	−	3.12281e6i	0.179513	−	0.493209i
$186$	−1.01273e6	−	457778.i	−0.157382	−	0.0711403i
$187$	−243743.	+	1.38233e6i	−0.0372741	+	0.211392i
$188$			1.04992e7i			1.58009i
$189$	−652794.	+	492412.i	−0.0966920	+	0.0729362i
$190$	2.37832e6			0.346744
$191$	976604.	+	172202.i	0.140158	+	0.0247137i	0.243287	−	0.969954i	$-0.421774\pi$
$191$	976604.	+	172202.i	0.140158	+	0.0247137i	−0.103129	+	0.994668i	$0.532885\pi$
$192$	−3.24053e6	−	4.51367e6i	−0.457838	−	0.637715i
$193$	6.59133e6	+	2.39905e6i	0.916856	+	0.333708i	0.756987	−	0.653430i	$-0.226671\pi$
$193$	6.59133e6	+	2.39905e6i	0.916856	+	0.333708i	0.159869	+	0.987138i	$0.448893\pi$
$194$	744052.	+	886727.i	0.101906	+	0.121446i
$195$	−8.62139e6	+	1.26271e7i	−1.16272	+	1.70294i
$196$	6.71402e6	−	2.44370e6i	0.891691	−	0.324549i
$197$	−1.08756e7	−	6.27903e6i	−1.42251	−	0.821286i	−0.425996	−	0.904725i	$-0.640076\pi$
$197$	−1.08756e7	−	6.27903e6i	−1.42251	−	0.821286i	−0.996513	+	0.0834396i	$0.973409\pi$
$198$	−185637.	+	232143.i	−0.0239149	+	0.0299061i
$199$	−1.29797e6	−	2.24815e6i	−0.164704	−	0.285276i	0.771846	−	0.635810i	$-0.219334\pi$
$199$	−1.29797e6	−	2.24815e6i	−0.164704	−	0.285276i	−0.936550	+	0.350533i	$0.886000\pi$
$200$	3.87894e6	−	4.62274e6i	0.484868	−	0.577843i
$201$	−2.14196e6	−	7.63259e6i	−0.263769	−	0.939905i
$202$	20597.8	+	116816.i	0.00249901	+	0.0141726i
$203$	−620336.	+	109382.i	−0.0741547	+	0.0130755i
$204$	−8.48282e6	+	2.38057e6i	−0.999193	+	0.280408i
$205$	−1.64187e7	−	1.37769e7i	−1.90580	−	1.59916i
$206$	−2.11996e6	+	1.22396e6i	−0.242508	+	0.140012i
$207$	1.32378e6	−	8.70362e6i	0.149247	−	0.981271i
$208$	4.77096e6	−	8.26355e6i	0.530171	−	0.918283i
$209$	−647817.	−	1.77986e6i	−0.0709600	−	0.194961i
$210$	308379.	+	210552.i	0.0332987	+	0.0227353i
$211$	7.06217e6	−	5.92587e6i	0.751781	−	0.630819i	−0.184193	−	0.982890i	$-0.558967\pi$
$211$	7.06217e6	−	5.92587e6i	0.751781	−	0.630819i	0.935973	+	0.352071i	$0.114523\pi$
$212$	185600.	−	509931.i	0.0194791	−	0.0535185i
$213$	4.86702e6	−	3.49421e6i	0.503645	−	0.361585i
$214$	−75469.5	+	428009.i	−0.00770069	+	0.0436728i
$215$			1.89654e7i			1.90830i
$216$	−3.70598e6	−	853703.i	−0.367741	−	0.0847121i
$217$	1.11190e6			0.108815
$218$	2.44409e6	+	430959.i	0.235911	+	0.0415974i
$219$	3.30375e6	−	7.30880e6i	0.314539	−	0.695847i
$220$	−3.32393e6	−	1.20981e6i	−0.312164	−	0.113619i
$221$	−8.90270e6	−	1.06098e7i	−0.824793	−	0.982949i
$222$	276206.	+	574531.i	0.0252449	+	0.0525116i
$223$	6.34474e6	−	2.30930e6i	0.572136	−	0.208240i	−0.0397184	−	0.999211i	$-0.512646\pi$
$223$	6.34474e6	−	2.30930e6i	0.572136	−	0.208240i	0.611854	+	0.790970i	$0.290424\pi$
$224$	−646695.	−	373370.i	−0.0575381	−	0.0332196i
$225$	537151.	+	2.27621e7i	0.0471573	+	1.99832i
$226$	2.13280e6	+	3.69411e6i	0.184767	+	0.320025i
$227$	1.50061e6	−	1.78836e6i	0.128290	−	0.152890i	−0.698076	−	0.716024i	$-0.745960\pi$
$227$	1.50061e6	−	1.78836e6i	0.128290	−	0.152890i	0.826365	+	0.563134i	$0.190405\pi$
$228$	8.30695e6	−	8.50529e6i	0.700869	−	0.717604i
$229$	1.66872e6	+	9.46377e6i	0.138956	+	0.788057i	0.972023	+	0.234886i	$0.0754716\pi$
$229$	1.66872e6	+	9.46377e6i	0.138956	+	0.788057i	−0.833067	+	0.553172i	$0.813417\pi$
$230$	−3.95922e6	+	698116.i	−0.325406	+	0.0573779i
$231$	73573.1	−	288133.i	0.00596875	−	0.0233753i
$232$	−2.24427e6	−	1.88316e6i	−0.179726	−	0.150808i
$233$	1.15758e7	−	6.68327e6i	0.915128	−	0.528350i	0.0330507	−	0.999454i	$-0.489478\pi$
$233$	1.15758e7	−	6.68327e6i	0.915128	−	0.528350i	0.882078	+	0.471104i	$0.156144\pi$
$234$	−577296.	−	2.87554e6i	−0.0450558	−	0.224425i
$235$	−1.84370e7	+	3.19338e7i	−1.42065	+	2.46063i
$236$	−3.51378e6	−	9.65402e6i	−0.267324	−	0.734467i
$237$	−1.44742e6	+	1.91425e7i	−0.108730	+	1.43798i
$238$	−259113.	+	217422.i	−0.0192202	+	0.0161277i
$239$	−587742.	+	1.61481e6i	−0.0430520	+	0.118284i	−0.959356	−	0.282200i	$-0.908936\pi$
$239$	−587742.	+	1.61481e6i	−0.0430520	+	0.118284i	0.916304	+	0.400484i	$0.131158\pi$
$240$	−2.10838e6	−	2.12135e7i	−0.152516	−	1.53454i
$241$	194741.	−	1.10443e6i	0.0139125	−	0.0789019i	−0.977061	−	0.212960i	$-0.931690\pi$
$241$	194741.	−	1.10443e6i	0.0139125	−	0.0789019i	0.990974	+	0.134058i	$0.0428008\pi$
$242$			2.61639e6i			0.184611i
$243$	1.26244e7	−	6.82019e6i	0.879818	−	0.475311i
$244$	−2.66875e7			−1.83713
$245$	2.47122e7	+	4.35743e6i	1.68040	+	0.296300i
$246$	4.09124e6	−	406624.i	0.274821	−	0.0273141i
$247$	1.75622e7	+	6.39212e6i	1.16544	+	0.424184i
$248$	3.32414e6	+	3.96156e6i	0.217934	+	0.259723i
$249$	−1.01962e7	−	770966.i	−0.660451	−	0.0499387i
$250$	4.88244e6	−	1.77706e6i	0.312476	−	0.113732i
$251$	6.69282e6	+	3.86410e6i	0.423241	+	0.244358i	0.696463	−	0.717593i	$-0.254756\pi$
$251$	6.69282e6	+	3.86410e6i	0.423241	+	0.244358i	−0.273222	+	0.961951i	$0.588089\pi$
$252$	1.83007e6	−	367407.i	0.114358	−	0.0229586i
$253$	1.60088e6	+	2.77280e6i	0.0988546	+	0.171221i
$254$	−1.94783e6	+	2.32134e6i	−0.118864	+	0.141657i
$255$	−2.99812e7	−	7.65553e6i	−1.80812	−	0.461694i
$256$	1.89535e6	+	1.07491e7i	0.112972	+	0.640695i
$257$	−9.40272e6	+	1.65795e6i	−0.553929	+	0.0976727i	−0.443604	−	0.896223i	$-0.646300\pi$
$257$	−9.40272e6	+	1.65795e6i	−0.553929	+	0.0976727i	−0.110325	+	0.993896i	$0.535189\pi$
$258$	−2.60264e6	−	2.54195e6i	−0.151550	−	0.148016i
$259$	−488562.	−	409952.i	−0.0281203	−	0.0235958i
$260$	3.02266e7	−	1.74513e7i	1.71976	−	0.992906i
$261$	1.10506e7	−	260778.i	0.621535	−	0.0146673i
$262$	257055.	−	445233.i	0.0142930	−	0.0247561i
$263$	1.66284e6	+	4.56862e6i	0.0914079	+	0.251141i	0.976969	−	0.213382i	$-0.0684479\pi$
$263$	1.66284e6	+	4.56862e6i	0.0914079	+	0.251141i	−0.885561	+	0.464523i	$0.846226\pi$
$264$	1.24653e6	−	599270.i	0.0677472	−	0.0325695i
$265$	1.45997e6	−	1.22506e6i	0.0784522	−	0.0658292i
$266$	156109.	−	428905.i	0.00829434	−	0.0227885i
$267$	−1.89725e7	−	8.57601e6i	−0.996760	−	0.450559i
$268$	−3.14243e6	+	1.78216e7i	−0.163253	+	0.925855i
$269$			2.80600e7i			1.44155i	0.693167	+	0.720777i	$0.256215\pi$
$269$			2.80600e7i			1.44155i	−0.693167	+	0.720777i	$0.743785\pi$
$270$	−4.79440e6	−	4.46650e6i	−0.243581	−	0.226922i
$271$	4.70252e6			0.236278			0.118139	−	0.992997i	$-0.462307\pi$
$271$	4.70252e6			0.236278			0.118139	+	0.992997i	$0.462307\pi$
$272$	1.90176e7	+	3.35332e6i	0.945039	+	0.166636i
$273$	1.71127e6	+	2.38360e6i	0.0841067	+	0.117151i
$274$	393398.	+	143185.i	0.0191241	+	0.00696059i
$275$	−5.32260e6	−	6.34323e6i	−0.255933	−	0.305009i
$276$	−1.13321e7	+	1.65972e7i	−0.538993	+	0.789421i
$277$	−3.70873e6	+	1.34987e6i	−0.174496	+	0.0635114i	−0.427791	−	0.903878i	$-0.640708\pi$
$277$	−3.70873e6	+	1.34987e6i	−0.174496	+	0.0635114i	0.253295	+	0.967389i	$0.418486\pi$
$278$	−1.92013e6	−	1.10859e6i	−0.0893710	−	0.0515983i
$279$	−1.92901e7	−	2.93394e6i	−0.888221	−	0.135095i
$280$	−868748.	−	1.50472e6i	−0.0395749	−	0.0685457i
$281$	3.84499e6	−	4.58228e6i	0.173291	−	0.206520i	−0.672408	−	0.740181i	$-0.734740\pi$
$281$	3.84499e6	−	4.58228e6i	0.173291	−	0.206520i	0.845698	+	0.533661i	$0.179184\pi$
$282$	−1.91118e6	−	6.81023e6i	−0.0852226	−	0.303679i
$283$	−3.98329e6	−	2.25904e7i	−0.175745	−	0.996699i	−0.937281	−	0.348576i	$-0.886665\pi$
$283$	−3.98329e6	−	2.25904e7i	−0.175745	−	0.996699i	0.761536	−	0.648123i	$-0.224446\pi$
$284$	−1.34693e7	+	2.37500e6i	−0.588018	+	0.103683i
$285$	4.02015e7	−	1.12819e7i	1.73663	−	0.487358i
$286$	817102.	+	685630.i	0.0349283	+	0.0293084i
$287$	−3.56223e6	+	2.05665e6i	−0.150687	+	0.0869992i
$288$	1.02341e7	+	8.18388e6i	0.428423	+	0.342596i
$289$	1.94621e6	−	3.37093e6i	0.0806298	−	0.139655i
$290$	−1.72644e6	−	4.74335e6i	−0.0707876	−	0.194487i
$291$	1.67833e7	+	1.14591e7i	0.681080	+	0.465021i
$292$	−1.40260e7	+	1.17692e7i	−0.563360	+	0.472715i
$293$	4.23557e6	−	1.16371e7i	0.168387	−	0.462640i	−0.826583	−	0.562815i	$-0.809718\pi$
$293$	4.23557e6	−	1.16371e7i	0.168387	−	0.462640i	0.994970	+	0.100175i	$0.0319404\pi$
$294$	−3.91017e6	+	2.80725e6i	−0.153870	+	0.110469i
$295$	6.26550e6	−	3.55334e7i	0.244056	−	1.38411i
$296$		−	2.96627e6i		−	0.114376i
$297$	−2.03668e6	+	4.80459e6i	−0.0777417	+	0.183395i
$298$	−2.95123e6			−0.111520
$299$	−3.11123e7	−	5.48595e6i	−1.16391	−	0.205229i
$300$	2.14085e7	−	4.73614e7i	0.792906	−	1.75413i
$301$	3.42022e6	+	1.24486e6i	0.125416	+	0.0456478i
$302$	3.88129e6	+	4.62554e6i	0.140914	+	0.167935i
$303$	902308.	+	1.87688e6i	0.0324360	+	0.0674695i
$304$	−2.44867e7	+	8.91243e6i	−0.871584	+	0.317231i
$305$	−8.11713e7	−	4.68642e7i	−2.86090	−	1.65174i
$306$	5.06898e6	−	3.08827e6i	0.176912	−	0.107783i
$307$	−2.24913e6	−	3.89561e6i	−0.0777320	−	0.134636i	0.824539	−	0.565805i	$-0.191435\pi$
$307$	−2.24913e6	−	3.89561e6i	−0.0777320	−	0.134636i	−0.902271	+	0.431169i	$0.858101\pi$
$308$	−436354.	+	520026.i	−0.0149344	+	0.0177981i
$309$	−3.00284e7	+	3.07453e7i	−1.01779	+	1.04209i
$310$	1.54725e6	+	8.77491e6i	0.0519369	+	0.294549i
$311$	5.57853e7	−	9.83645e6i	1.85455	−	0.327007i	0.868792	−	0.495177i	$-0.164897\pi$
$311$	5.57853e7	−	9.83645e6i	1.85455	−	0.327007i	0.985758	+	0.168170i	$0.0537856\pi$
$312$	−3.37642e6	+	1.32230e7i	−0.111171	+	0.435378i
$313$	−2.41737e6	−	2.02842e6i	−0.0788335	−	0.0661492i	0.602519	−	0.798104i	$-0.294164\pi$
$313$	−2.41737e6	−	2.02842e6i	−0.0788335	−	0.0661492i	−0.681353	+	0.731955i	$0.738608\pi$
$314$	6.43741e6	−	3.71664e6i	0.207933	−	0.120050i
$315$	6.21142e6	+	2.09619e6i	0.198728	+	0.0670654i
$316$	2.19114e7	−	3.79516e7i	0.694398	−	1.20273i
$317$	−6.31032e6	−	1.73375e7i	−0.198095	−	0.544262i	0.800378	−	0.599495i	$-0.204632\pi$
$317$	−6.31032e6	−	1.73375e7i	−0.198095	−	0.544262i	−0.998473	+	0.0552333i	$0.982410\pi$
$318$	−27564.6	+	364548.i	−0.000857176	+	0.0113364i
$319$	−3.07953e6	+	2.58403e6i	−0.0948664	+	0.0796024i
$320$	−1.52362e7	+	4.18610e7i	−0.464971	+	1.27750i
$321$	754637.	+	7.59278e6i	0.0228151	+	0.229554i
$322$	−133978.	+	759827.i	−0.00401297	+	0.0227587i
$323$			3.78235e7i			1.12242i
$324$	−3.27188e7	+	1.54509e6i	−0.961972	+	0.0454274i
$325$	8.17050e7			2.38012
$326$	−2.75937e6	−	486551.i	−0.0796447	−	0.0140435i
$327$	4.33576e7	−	4.30926e6i	1.24000	−	0.123242i
$328$	−1.79772e7	−	6.54316e6i	−0.509448	−	0.185424i
$329$	4.54875e6	+	5.42099e6i	0.127733	+	0.152227i
$330$	2.37626e6	+	179677.i	0.0661231	+	0.00499976i
$331$	−1.95438e7	+	7.11338e6i	−0.538922	+	0.196152i	−0.597118	−	0.802154i	$-0.703688\pi$
$331$	−1.95438e7	+	7.11338e6i	−0.538922	+	0.196152i	0.0581956	+	0.998305i	$0.481465\pi$
$332$	2.02148e7	+	1.16710e7i	0.552402	+	0.318929i
$333$	7.39418e6	+	8.40128e6i	0.200243	+	0.227516i
$334$	−2.74974e6	−	4.76268e6i	−0.0737992	−	0.127824i
$335$	−4.08532e7	+	4.86870e7i	−1.08666	+	1.29503i
$336$	−3.96403e6	−	1.01219e6i	−0.104501	−	0.0266836i
$337$	−3.18396e6	−	1.80571e7i	−0.0831913	−	0.471801i	−0.997732	−	0.0673080i	$-0.978559\pi$
$337$	−3.18396e6	−	1.80571e7i	−0.0831913	−	0.471801i	0.914541	−	0.404493i	$-0.132552\pi$
$338$	−3.05453e6	+	538596.i	−0.0791032	+	0.0139480i
$339$	5.35750e7	+	5.23256e7i	1.37519	+	1.34312i
$340$	5.41104e7	+	4.54041e7i	1.37672	+	1.15520i
$341$	6.14544e6	−	3.54807e6i	0.154985	−	0.0894806i
$342$	−3.84001e6	+	7.02902e6i	−0.0959963	+	0.175718i
$343$	4.85161e6	−	8.40324e6i	0.120227	−	0.208240i
$344$	5.78981e6	+	1.59074e7i	0.142229	+	0.390772i
$345$	−6.36124e7	+	3.05816e7i	−1.54912	+	0.744738i
$346$	4.07528e6	−	3.41957e6i	0.0983850	−	0.0825548i
$347$	1.79916e7	−	4.94316e7i	0.430608	−	1.18308i	−0.514833	−	0.857290i	$-0.672146\pi$
$347$	1.79916e7	−	4.94316e7i	0.430608	−	1.18308i	0.945441	−	0.325794i	$-0.105632\pi$
$348$	−2.29932e7	−	1.03934e7i	−0.545583	−	0.246616i
$349$	5.13143e6	−	2.91018e7i	0.120715	−	0.684610i	−0.863046	−	0.505126i	$-0.831446\pi$
$349$	5.13143e6	−	2.91018e7i	0.120715	−	0.684610i	0.983761	−	0.179484i	$-0.0574429\pi$
$350$		−	1.99540e6i		−	0.0465400i
$351$	−2.33988e7	−	4.58678e7i	−0.541093	−	1.06068i
$352$	−4.76567e6			−0.109269
$353$	9.60660e6	+	1.69390e6i	0.218397	+	0.0385092i	0.281776	−	0.959480i	$-0.409077\pi$
$353$	9.60660e6	+	1.69390e6i	0.218397	+	0.0385092i	−0.0633791	+	0.997990i	$0.520188\pi$
$354$	4.03652e6	+	5.62239e6i	0.0909907	+	0.126739i
$355$	−4.51380e7	−	1.64289e7i	−1.00892	−	0.367218i
$356$	3.05511e7	+	3.64093e7i	0.677137	+	0.806980i
$357$	−3.34851e6	+	4.90430e6i	−0.0735948	+	0.107789i
$358$	−2.24021e6	+	815369.i	−0.0488246	+	0.0177707i
$359$	−5.89664e7	−	3.40442e7i	−1.27444	−	0.735801i	−0.298623	−	0.954371i	$-0.596527\pi$
$359$	−5.89664e7	−	3.40442e7i	−1.27444	−	0.735801i	−0.975821	+	0.218570i	$0.929861\pi$
$360$	1.11012e7	+	2.83972e7i	0.237937	+	0.608650i
$361$	−1.99653e6	−	3.45809e6i	−0.0424379	−	0.0735046i
$362$	−417400.	+	497438.i	−0.00879886	+	0.0104861i
$363$	1.24113e7	+	4.42258e7i	0.259475	+	0.924604i
$364$	−1.16315e6	−	6.59653e6i	−0.0241174	−	0.136776i
$365$	−6.33279e7	+	1.11664e7i	−1.30232	+	0.229633i
$366$	1.73107e7	−	4.85796e6i	0.353078	−	0.0990857i
$367$	4.51484e7	+	3.78840e7i	0.913365	+	0.766404i	0.972756	−	0.231831i	$-0.0744716\pi$
$367$	4.51484e7	+	3.78840e7i	0.913365	+	0.766404i	−0.0593916	+	0.998235i	$0.518916\pi$
$368$	3.81472e7	−	2.20243e7i	0.765454	−	0.441935i
$369$	6.72268e7	−	2.62807e7i	1.33802	−	0.523068i
$370$	2.55540e6	−	4.42609e6i	0.0504492	−	0.0873806i
$371$	−125097.	−	343701.i	−0.00244976	−	0.00673067i
$372$	3.67849e7	+	2.51156e7i	0.714563	+	0.487882i
$373$	2.78282e7	−	2.33506e7i	0.536239	−	0.449958i	−0.334010	−	0.942569i	$-0.608402\pi$
$373$	2.78282e7	−	2.33506e7i	0.536239	−	0.449958i	0.870249	+	0.492611i	$0.163958\pi$
$374$	−738317.	+	2.02851e6i	−0.0141133	+	0.0387759i
$375$	7.40999e7	−	5.31989e7i	1.40515	−	1.00881i
$376$	−5.71531e6	+	3.24131e7i	−0.107517	+	0.609758i
$377$		−	3.96664e7i		−	0.740285i
$378$	−1.12018e6	+	571446.i	−0.0207402	+	0.0105803i
$379$	−8.65793e7			−1.59036			−0.795181	−	0.606372i	$-0.792624\pi$
$379$	−8.65793e7			−1.59036			−0.795181	+	0.606372i	$0.792624\pi$
$380$	−9.38681e7	−	1.65515e7i	−1.71067	−	0.301638i
$381$	−2.19133e7	+	4.84782e7i	−0.396216	+	0.876539i
$382$	1.43312e6	+	521613.i	0.0257094	+	0.00935747i
$383$	−1.73191e6	−	2.06402e6i	−0.0308269	−	0.0367381i	0.750411	−	0.660972i	$-0.229856\pi$
$383$	−1.73191e6	−	2.06402e6i	−0.0308269	−	0.0367381i	−0.781238	+	0.624234i	$0.785411\pi$
$384$	−1.71607e7	−	3.56957e7i	−0.303069	−	0.630409i
$385$	−2.24037e6	+	815429.i	−0.0392589	+	0.0142891i
$386$	9.34217e6	+	5.39370e6i	0.162437	+	0.0937832i
$387$	−5.60515e7	−	3.06214e7i	−0.967062	−	0.528314i
$388$	−2.31954e7	−	4.01757e7i	−0.397107	−	0.687809i
$389$	−1.75469e7	+	2.09116e7i	−0.298093	+	0.355253i	−0.894213	−	0.447642i	$-0.852264\pi$
$389$	−1.75469e7	+	2.09116e7i	−0.298093	+	0.355253i	0.596120	+	0.802895i	$0.296708\pi$
$390$	−1.64296e7	+	1.68219e7i	−0.276970	+	0.283583i
$391$	−1.11025e7	−	6.29653e7i	−0.185733	−	1.05335i
$392$	2.20578e7	−	3.88938e6i	0.366187	−	0.0645687i
$393$	2.23306e6	−	8.74530e6i	0.0367895	−	0.144078i
$394$	−1.47947e7	−	1.24142e7i	−0.241890	−	0.202970i
$395$	1.33289e8	−	7.69543e7i	2.16273	−	1.24865i
$396$	8.94234e6	−	7.87038e6i	0.144001	−	0.126739i
$397$	8.39044e6	−	1.45327e7i	0.134095	−	0.232260i	−0.791156	−	0.611614i	$-0.790521\pi$
$397$	8.39044e6	−	1.45327e7i	0.134095	−	0.232260i	0.925251	+	0.379354i	$0.123854\pi$
$398$	−1.36545e6	−	3.75154e6i	−0.0216584	−	0.0595059i
$399$	604183.	−	7.99046e6i	0.00951151	−	0.125792i
$400$	−8.72677e7	+	7.32263e7i	−1.36356	+	1.14416i
$401$	−2.36419e7	+	6.49556e7i	−0.366648	+	1.00736i	0.609979	+	0.792418i	$0.291178\pi$
$401$	−2.36419e7	+	6.49556e7i	−0.366648	+	1.00736i	−0.976627	+	0.214940i	$0.931044\pi$
$402$	−1.20577e6	−	1.21319e7i	−0.0185604	−	0.186746i
$403$	−1.21586e7	+	6.89551e7i	−0.185768	+	1.05354i
$404$		−	4.75388e6i		−	0.0720949i
$405$	−1.02229e8	−	5.27559e7i	−1.53889	−	0.794157i
$406$	−968735.			−0.0144753
$407$	−4.00841e6	−	706791.i	−0.0594551	−	0.0104835i
$408$	−2.74840e7	+	2.73161e6i	−0.404669	+	0.0402196i
$409$	5.50721e7	+	2.00446e7i	0.804937	+	0.292973i	0.711531	−	0.702655i	$-0.248002\pi$
$409$	5.50721e7	+	2.00446e7i	0.804937	+	0.292973i	0.0934065	+	0.995628i	$0.470224\pi$
$410$	−2.11876e7	−	2.52504e7i	−0.307419	−	0.366368i
$411$	7.32896e6	+	554165.i	0.105564	+	0.00798203i
$412$	9.21890e7	−	3.35541e7i	1.31822	−	0.479793i
$413$	−5.99683e6	−	3.46227e6i	−0.0851278	−	0.0491486i
$414$	4.32927e6	−	1.28285e7i	0.0610117	−	0.180790i
$415$	4.09894e7	+	7.09958e7i	0.573492	+	0.993318i
$416$	3.02262e7	−	3.60222e7i	0.419860	−	0.500369i
$417$	−3.77154e7	−	9.63042e6i	−0.520128	−	0.132812i
$418$	−505825.	−	2.86868e6i	−0.00692583	−	0.0392783i
$419$	1.35444e8	−	2.38824e7i	1.84127	−	0.324665i	0.858976	−	0.512017i	$-0.171101\pi$
$419$	1.35444e8	−	2.38824e7i	1.84127	−	0.324665i	0.982293	+	0.187351i	$0.0599903\pi$
$420$	−1.07059e7	−	1.04562e7i	−0.144502	−	0.141133i
$421$	−2.50471e7	−	2.10170e7i	−0.335669	−	0.281659i	0.459336	−	0.888262i	$-0.348087\pi$
$421$	−2.50471e7	−	2.10170e7i	−0.335669	−	0.281659i	−0.795005	+	0.606603i	$0.792532\pi$
$422$	1.22785e7	−	7.08898e6i	0.163383	−	0.0943293i
$423$	−6.46107e7	−	1.06050e8i	−0.853657	−	1.40116i
$424$	850568.	−	1.47323e6i	0.0111586	−	0.0193273i
$425$	5.65548e7	+	1.55383e8i	0.736720	+	2.02412i
$426$	8.30444e6	−	3.99236e6i	0.107419	−	0.0516418i
$427$	−1.37794e7	+	1.15623e7i	−0.176989	+	0.148512i
$428$	5.95730e6	−	1.63675e7i	0.0759833	−	0.208762i
$429$	1.70641e7	+	7.71339e6i	0.216129	+	0.0976953i
$430$	−5.06480e6	+	2.87239e7i	−0.0637025	+	0.361275i
$431$			9.29626e7i			1.16112i	0.814218	+	0.580559i	$0.197166\pi$
$431$			9.29626e7i			1.16112i	−0.814218	+	0.580559i	$0.802834\pi$
$432$	6.60998e7	+	2.80199e7i	0.819877	+	0.347549i
$433$	3.06813e7			0.377929			0.188964	−	0.981984i	$-0.439487\pi$
$433$	3.06813e7			0.377929			0.188964	+	0.981984i	$0.439487\pi$
$434$	1.68402e6	+	296939.i	0.0206006	+	0.00363243i
$435$	−5.16834e7	−	7.19889e7i	−0.627890	−	0.874577i
$436$	−9.34648e7	−	3.40184e7i	−1.12769	−	0.410444i
$437$	5.54571e7	+	6.60912e7i	0.664527	+	0.791953i
$438$	6.95551e6	−	1.01872e7i	0.0827764	−	0.121236i
$439$	−6.92864e7	+	2.52182e7i	−0.818945	+	0.298072i	−0.717314	−	0.696751i	$-0.754628\pi$
$439$	−6.92864e7	+	2.52182e7i	−0.818945	+	0.298072i	−0.101631	+	0.994822i	$0.532406\pi$
$440$	−9.60306e6	−	5.54433e6i	−0.112733	−	0.0650865i
$441$	−5.27783e7	+	6.60004e7i	−0.615375	+	0.769539i
$442$	−1.06501e7	−	1.84465e7i	−0.123335	−	0.213623i
$443$	8.35391e7	−	9.95580e7i	0.960901	−	1.14516i	−0.0284484	−	0.999595i	$-0.509057\pi$
$443$	8.35391e7	−	9.95580e7i	0.960901	−	1.14516i	0.989349	−	0.145562i	$-0.0464989\pi$
$444$	−6.90303e6	−	2.45980e7i	−0.0788661	−	0.281029i
$445$	2.89863e7	+	1.64389e8i	0.328936	+	1.86549i
$446$	1.02261e7	−	1.80313e6i	0.115267	−	0.0203247i
$447$	−4.98857e7	+	1.39996e7i	−0.558539	+	0.156745i
$448$	6.54913e6	+	5.49537e6i	0.0728365	+	0.0611171i
$449$	−1.22386e8	+	7.06594e7i	−1.35205	+	0.780604i	−0.988536	−	0.150986i	$-0.951755\pi$
$449$	−1.22386e8	+	7.06594e7i	−1.35205	+	0.780604i	−0.363511	+	0.931590i	$0.618422\pi$
$450$	−5.26519e6	+	3.46176e7i	−0.0577799	+	0.379892i
$451$	−1.31255e7	+	2.27340e7i	−0.143082	+	0.247826i
$452$	−5.84693e7	−	1.60643e8i	−0.633158	−	1.73959i
$453$	8.75488e7	+	5.97757e7i	0.941793	+	0.643028i
$454$	2.75033e6	−	2.30780e6i	0.0293912	−	0.0246622i
$455$	8.04597e6	−	2.21061e7i	0.0854170	−	0.234681i
$456$	3.02751e7	−	2.17356e7i	0.319295	−	0.229233i
$457$	−2.12538e7	+	1.20536e8i	−0.222684	+	1.26290i	0.644380	+	0.764705i	$0.277115\pi$
$457$	−2.12538e7	+	1.20536e8i	−0.222684	+	1.26290i	−0.867064	+	0.498197i	$0.833996\pi$
$458$			1.47789e7i			0.153832i
$459$	7.10330e7	−	7.62476e7i	0.734551	−	0.788476i
$460$	1.61122e8			1.65532
$461$	−2.68646e7	−	4.73696e6i	−0.274207	−	0.0483500i	0.0348538	−	0.999392i	$-0.488903\pi$
$461$	−2.68646e7	−	4.73696e6i	−0.274207	−	0.0483500i	−0.309060	+	0.951042i	$0.600015\pi$
$462$	188377.	−	416741.i	0.00191030	−	0.00422611i
$463$	−1.46984e6	−	534978.i	−0.0148090	−	0.00539005i	0.334605	−	0.942358i	$-0.391397\pi$
$463$	−1.46984e6	−	534978.i	−0.0148090	−	0.00539005i	−0.349414	+	0.936968i	$0.613619\pi$
$464$	3.55502e7	+	4.23670e7i	0.355867	+	0.424106i
$465$	6.77789e7	+	1.40986e8i	0.674117	+	1.40222i
$466$	1.93168e7	−	7.03073e6i	0.190887	−	0.0694772i
$467$	−1.99016e7	−	1.14902e7i	−0.195406	−	0.112818i	0.399105	−	0.916905i	$-0.369321\pi$
$467$	−1.99016e7	−	1.14902e7i	−0.195406	−	0.112818i	−0.594511	+	0.804088i	$0.702654\pi$
$468$	2.77306e6	+	1.17510e8i	0.0270534	+	1.14640i
$469$	6.09866e6	+	1.05632e7i	0.0591175	+	0.102395i
$470$	−3.64516e7	+	4.34413e7i	−0.351094	+	0.418417i
$471$	9.11834e7	−	9.33605e7i	0.872676	−	0.893512i
$472$	−5.59250e6	−	3.17167e7i	−0.0531839	−	0.301621i
$473$	2.28757e7	−	4.03360e6i	0.216168	−	0.0381162i
$474$	−7.30428e6	+	2.86056e7i	−0.0685871	+	0.268606i
$475$	−1.70927e8	−	1.43425e8i	−1.59489	−	1.33827i
$476$	1.17399e7	−	6.77802e6i	0.108854	−	0.0628466i
$477$	1.26336e6	+	6.29284e6i	0.0116405	+	0.0579818i
$478$	−1.32140e6	+	2.28873e6i	−0.0120990	+	0.0209562i
$479$	4.95246e7	+	1.36068e8i	0.450624	+	1.23808i	0.932286	+	0.361722i	$0.117811\pi$
$479$	4.95246e7	+	1.36068e8i	0.450624	+	1.23808i	−0.481663	+	0.876357i	$0.659967\pi$
$480$	7.92111e6	−	1.04758e8i	0.0716246	−	0.947252i
$481$	3.07657e7	−	2.58155e7i	0.276460	−	0.231977i
$482$	589887.	−	1.62070e6i	0.00526778	−	0.0144731i
$483$	1.33968e6	+	1.34792e7i	0.0118894	+	0.119625i
$484$	1.82083e7	−	1.03264e8i	0.160596	−	0.910783i
$485$		−	1.62928e8i		−	1.42814i
$486$	2.09416e7	−	6.95805e6i	0.182432	−	0.0606148i
$487$	−6.21832e7			−0.538377			−0.269188	−	0.963088i	$-0.586755\pi$
$487$	−6.21832e7			−0.538377			−0.269188	+	0.963088i	$0.586755\pi$
$488$	−8.23898e7	−	1.45275e7i	−0.708947	−	0.125007i
$489$	−4.89506e7	+	4.86514e6i	−0.418631	+	0.0416072i
$490$	3.62640e7	+	1.31990e7i	0.308239	+	0.112190i
$491$	−7.87516e7	−	9.38525e7i	−0.665296	−	0.792869i	0.322839	−	0.946454i	$-0.395363\pi$
$491$	−7.87516e7	−	9.38525e7i	−0.665296	−	0.792869i	−0.988135	+	0.153585i	$0.950918\pi$
$492$	−1.64304e8	−	1.24235e7i	−1.37960	−	0.104316i
$493$	7.54359e7	−	2.74564e7i	0.629560	−	0.229141i
$494$	2.48916e7	+	1.43712e7i	0.206478	+	0.119210i
$495$	4.10191e7	−	8.23504e6i	0.338198	−	0.0678969i
$496$	−4.88130e7	−	8.45466e7i	−0.400028	−	0.692869i
$497$	−5.92557e6	+	7.06182e6i	−0.0482682	+	0.0575238i
$498$	−1.52367e7	−	3.89060e6i	−0.123368	−	0.0315013i
$499$	−1.81266e7	−	1.02801e8i	−0.145886	−	0.827362i	−0.966651	−	0.256096i	$-0.917564\pi$
$499$	−1.81266e7	−	1.02801e8i	−0.145886	−	0.827362i	0.820765	−	0.571266i	$-0.193547\pi$
$500$	−2.05069e8	+	3.61592e7i	−1.64055	+	0.289273i
$501$	−6.90722e7	−	6.74615e7i	−0.549276	−	0.536467i
$502$	9.10462e6	+	7.63969e6i	0.0719699	+	0.0603899i
$503$	−1.15416e8	+	6.66357e7i	−0.906909	+	0.523604i	−0.879435	−	0.476019i	$-0.842079\pi$
$503$	−1.15416e8	+	6.66357e7i	−0.906909	+	0.523604i	−0.0274734	+	0.999623i	$0.508746\pi$
$504$	5.84980e6	−	138046.i	0.0456930	−	0.00107828i
$505$	8.34798e6	−	1.44591e7i	0.0648198	−	0.112271i
$506$	1.68411e6	+	4.62705e6i	0.0129993	+	0.0357152i
$507$	−4.90768e7	+	2.35937e7i	−0.376576	+	0.181039i
$508$	9.30325e7	−	7.80635e7i	0.709649	−	0.595466i
$509$	4.17793e7	−	1.14788e8i	0.316816	−	0.870446i	−0.674420	−	0.738348i	$-0.735606\pi$
$509$	4.17793e7	−	1.14788e8i	0.316816	−	0.870446i	0.991237	−	0.132098i	$-0.0421714\pi$
$510$	−4.33633e7	−	1.96012e7i	−0.326898	−	0.147765i
$511$	−2.14299e6	+	1.21535e7i	−0.0160604	+	0.0910831i
$512$			1.10668e8i			0.824542i
$513$	−3.15659e7	+	1.37030e8i	−0.233811	+	1.01499i
$514$	−1.46836e7			−0.108129
$515$	3.39319e8	+	5.98311e7i	2.48420	+	0.438031i
$516$	8.50316e7	+	1.18439e8i	0.618915	+	0.862076i
$517$	4.24391e7	+	1.54466e7i	0.307110	+	0.111779i
$518$	−630468.	−	751362.i	−0.00453600	−	0.00540580i
$519$	5.26646e7	−	7.71338e7i	0.376719	−	0.551750i
$520$	1.02815e8	−	3.74217e7i	0.731219	−	0.266142i
$521$	5.16402e7	+	2.98145e7i	0.365153	+	0.210821i	0.671339	−	0.741151i	$-0.265720\pi$
$521$	5.16402e7	+	2.98145e7i	0.365153	+	0.210821i	−0.306186	+	0.951972i	$0.599053\pi$
$522$	1.68063e7	+	2.55616e6i	0.118157	+	0.0179712i
$523$	2.68599e7	+	4.65228e7i	0.187759	+	0.325207i	0.944503	−	0.328504i	$-0.106544\pi$
$523$	2.68599e7	+	4.65228e7i	0.187759	+	0.325207i	−0.756744	+	0.653711i	$0.773211\pi$
$524$	−1.32440e7	+	1.57836e7i	−0.0920506	+	0.109702i
$525$	−9.46550e6	−	3.37290e7i	−0.0654132	−	0.233091i
$526$	1.29837e6	+	7.36343e6i	0.00892158	+	0.0505968i
$527$	−1.39552e8	+	2.46067e7i	−0.953462	+	0.168121i
$528$	−2.51389e7	+	7.05482e6i	−0.170783	+	0.0479274i
$529$	1.68196e6	+	1.41133e6i	0.0113618	+	0.00953372i
$530$	2.53834e6	−	1.46551e6i	0.0170499	−	0.00984376i
$531$	9.49014e7	+	7.58895e7i	0.633853	+	0.506871i
$532$	−9.14623e6	+	1.58417e7i	−0.0607445	+	0.105213i
$533$	−8.85912e7	−	2.43402e8i	−0.585071	−	1.60747i
$534$	−2.64444e7	−	1.80554e7i	−0.173664	−	0.118572i
$535$	4.68613e7	−	3.93213e7i	0.306023	−	0.256783i
$536$	−1.94026e7	+	5.33083e7i	−0.125999	+	0.346179i
$537$	−3.39992e7	+	2.44092e7i	−0.219556	+	0.157627i
$538$	−7.49355e6	+	4.24980e7i	−0.0481217	+	0.272912i
$539$		−	3.07341e7i		−	0.196270i
$540$	1.58143e8	+	2.09651e8i	1.00431	+	1.33142i
$541$	−2.66154e8			−1.68090			−0.840449	−	0.541890i	$-0.817709\pi$
$541$	−2.66154e8			−1.68090			−0.840449	+	0.541890i	$0.817709\pi$
$542$	7.12216e6	+	1.25583e6i	0.0447315	+	0.00788738i
$543$	−4.69578e6	+	1.03884e7i	−0.0293297	+	0.0648855i
$544$	8.94275e7	+	3.25490e7i	0.555488	+	0.202181i
$545$	−2.24539e8	−	2.67596e8i	−1.38709	−	1.65306i
$546$	1.95524e6	+	4.06706e6i	0.0120122	+	0.0249863i
$547$	−1.02465e8	+	3.72940e7i	−0.626054	+	0.227865i	−0.635513	−	0.772090i	$-0.719211\pi$
$547$	−1.02465e8	+	3.72940e7i	−0.626054	+	0.227865i	0.00945911	+	0.999955i	$0.496989\pi$
$548$	−1.45303e7	−	8.38905e6i	−0.0882941	−	0.0509766i
$549$	2.69564e8	−	1.64232e8i	1.62909	−	0.992521i
$550$	−6.36731e6	−	1.10285e7i	−0.0382708	−	0.0662870i
$551$	−6.96304e7	+	8.29823e7i	−0.416240	+	0.496056i
$552$	−4.40193e7	+	4.50703e7i	−0.261713	+	0.267962i
$553$	−5.12907e6	−	2.90884e7i	−0.0303294	−	0.172006i
$554$	−5.97751e6	+	1.05400e6i	−0.0351553	+	0.00619883i
$555$	2.21991e7	−	8.69377e7i	0.129854	−	0.508545i
$556$	6.80692e7	+	5.71169e7i	0.396029	+	0.332307i
$557$	−1.42347e7	+	8.21838e6i	−0.0823723	+	0.0475577i	−0.540620	−	0.841267i	$-0.681810\pi$
$557$	−1.42347e7	+	8.21838e6i	−0.0823723	+	0.0475577i	0.458248	+	0.888824i	$0.348477\pi$
$558$	−2.84321e7	−	9.59506e6i	−0.163646	−	0.0552262i
$559$	−1.14600e8	+	1.98493e8i	−0.656070	+	1.13635i
$560$	1.12184e7	+	3.08222e7i	0.0638801	+	0.175509i
$561$	−2.85748e6	+	3.77909e7i	−0.0161844	+	0.214042i
$562$	7.04711e6	−	5.91322e6i	0.0397010	−	0.0333131i
$563$	−9.02079e7	+	2.47844e8i	−0.505498	+	1.38884i	0.380339	+	0.924847i	$0.375807\pi$
$563$	−9.02079e7	+	2.47844e8i	−0.505498	+	1.38884i	−0.885837	+	0.463997i	$0.846415\pi$
$564$	2.80365e7	+	2.82089e8i	0.156274	+	1.57235i
$565$	1.04258e8	−	5.91276e8i	0.578048	−	3.27827i
$566$		−	3.52778e7i		−	0.194559i
$567$	−1.62241e7	+	1.49731e7i	−0.0890045	+	0.0821416i
$568$	−4.28753e7			−0.233971
$569$	−2.91070e7	−	5.13234e6i	−0.158001	−	0.0278599i	0.0940880	−	0.995564i	$-0.470006\pi$
$569$	−2.91070e7	−	5.13234e6i	−0.158001	−	0.0278599i	−0.252089	+	0.967704i	$0.581118\pi$
$570$	6.38997e7	−	6.35092e6i	0.345044	−	0.0342935i
$571$	1.88924e8	+	6.87627e7i	1.01480	+	0.369355i	0.795273	−	0.606252i	$-0.207328\pi$
$571$	1.88924e8	+	6.87627e7i	1.01480	+	0.369355i	0.219523	+	0.975607i	$0.429550\pi$
$572$	−2.74781e7	−	3.27471e7i	−0.146824	−	0.174979i
$573$	2.66989e7	+	2.01878e6i	0.141915	+	0.0107306i
$574$	−5.94438e6	+	2.16358e6i	−0.0314319	+	0.0114403i
$575$	3.26645e8	+	1.88588e8i	1.71819	+	0.991999i
$576$	−9.91183e7	−	1.12618e8i	−0.518664	−	0.589307i
$577$	1.24276e8	+	2.15253e8i	0.646935	+	1.12052i	0.983851	+	0.178989i	$0.0572828\pi$
$577$	1.24276e8	+	2.15253e8i	0.646935	+	1.12052i	−0.336916	+	0.941535i	$0.609384\pi$
$578$	3.84783e6	−	4.58567e6i	0.0199266	−	0.0237476i
$579$	1.83500e8	+	4.68556e7i	0.945366	+	0.241394i
$580$	3.51291e7	+	1.99227e8i	0.180046	+	1.02109i
$581$	1.54938e7	−	2.73198e6i	0.0790006	−	0.0139299i
$582$	2.23588e7	+	2.18374e7i	0.113417	+	0.110772i
$583$	−1.78815e6	−	1.50043e6i	−0.00902397	−	0.00757201i
$584$	−4.97078e7	+	2.86988e7i	−0.249566	+	0.144087i
$585$	−1.97918e8	+	3.62282e8i	−0.988591	+	1.80958i
$586$	9.52269e6	−	1.64938e7i	0.0473224	−	0.0819648i
$587$	−3.40650e7	−	9.35927e7i	−0.168420	−	0.462730i	0.826555	−	0.562856i	$-0.190298\pi$
$587$	−3.40650e7	−	9.35927e7i	−0.168420	−	0.462730i	−0.994975	+	0.100126i	$0.968075\pi$
$588$	1.73864e8	−	8.35852e7i	0.855221	−	0.411147i
$589$	1.46480e8	−	1.22911e8i	0.716855	−	0.601513i
$590$	1.89787e7	−	5.21436e7i	0.0924083	−	0.253890i
$591$	−3.08969e8	−	1.39661e8i	−1.49676	−	0.676571i
$592$	−9.72377e6	+	5.51462e7i	−0.0468672	+	0.265797i
$593$			3.56564e8i			1.70991i	0.518702	+	0.854955i	$0.326415\pi$
$593$			3.56564e8i			1.70991i	−0.518702	+	0.854955i	$0.673585\pi$
$594$	−4.36773e6	+	6.73285e6i	−0.0208399	+	0.0321247i
$595$	4.76097e7			0.226019
$596$	1.16480e8	+	2.05386e7i	0.550190	+	0.0970134i
$597$	−4.08766e7	−	5.69363e7i	−0.192111	−	0.267588i
$598$	−4.56559e7	−	1.66174e7i	−0.213498	−	0.0777068i
$599$	2.30410e8	+	2.74591e8i	1.07206	+	1.27763i	0.958804	+	0.284068i	$0.0916843\pi$
$599$	2.30410e8	+	2.74591e8i	1.07206	+	1.27763i	0.113258	+	0.993566i	$0.463871\pi$
$600$	9.18737e7	−	1.34560e8i	0.425341	−	0.622964i
$601$	−1.66943e8	+	6.07624e7i	−0.769035	+	0.279906i	−0.696593	−	0.717467i	$-0.745301\pi$
$601$	−1.66943e8	+	6.07624e7i	−0.769035	+	0.279906i	−0.0724420	+	0.997373i	$0.523079\pi$
$602$	4.84761e6	+	2.79877e6i	0.0222197	+	0.0128286i
$603$	−7.79311e7	−	1.99350e8i	−0.355434	−	0.909209i
$604$	−1.20997e8	−	2.09573e8i	−0.549117	−	0.951098i
$605$	2.36717e8	−	2.82109e8i	1.06897	−	1.27394i
$606$	865355.	+	3.08357e6i	0.00388845	+	0.0138559i
$607$	4.55529e7	+	2.58343e8i	0.203681	+	1.15513i	0.899502	+	0.436916i	$0.143929\pi$
$607$	4.55529e7	+	2.58343e8i	0.203681	+	1.15513i	−0.695821	+	0.718215i	$0.744959\pi$
$608$	−1.26467e8	+	2.22995e7i	−0.562685	+	0.0992166i
$609$	−1.63749e7	+	4.59534e6i	−0.0724980	+	0.0203454i
$610$	−1.10422e8	−	9.26550e7i	−0.486481	−	0.408206i
$611$	−3.85925e8	+	2.22814e8i	−1.69192	+	0.976830i
$612$	−2.21556e8	+	8.66122e7i	−0.966562	+	0.377855i
$613$	4.90366e7	−	8.49340e7i	0.212882	−	0.368723i	−0.739733	−	0.672900i	$-0.765048\pi$
$613$	4.90366e7	−	8.49340e7i	0.212882	−	0.368723i	0.952615	+	0.304178i	$0.0983816\pi$
$614$	−2.36606e6	−	6.50070e6i	−0.0102217	−	0.0280838i
$615$	−4.77921e8	−	3.26310e8i	−2.05462	−	1.40283i
$616$	−1.63019e6	+	1.36789e6i	−0.00697423	+	0.00585208i
$617$	1.24365e8	−	3.41691e8i	0.529474	−	1.45472i	−0.330219	−	0.943905i	$-0.607122\pi$
$617$	1.24365e8	−	3.41691e8i	0.529474	−	1.45472i	0.859692	−	0.510812i	$-0.170655\pi$
$618$	−5.36899e7	+	3.85459e7i	−0.227471	+	0.163310i
$619$	2.40233e7	−	1.36243e8i	0.101289	−	0.574437i	−0.891349	−	0.453317i	$-0.850241\pi$
$619$	2.40233e7	−	1.36243e8i	0.101289	−	0.574437i	0.992638	−	0.121119i	$-0.0386484\pi$
$620$		−	3.57098e8i		−	1.49835i
$621$	1.23253e7	−	2.37381e8i	0.0514661	−	0.991221i
$622$	8.71160e7			0.362015
$623$	3.15485e7	+	5.56285e6i	0.130471	+	0.0230056i
$624$	1.06118e8	−	2.34762e8i	0.436752	−	0.966216i
$625$	−2.28645e8	−	8.32200e7i	−0.936530	−	0.340869i
$626$	−3.11951e6	−	3.71769e6i	−0.0127164	−	0.0151548i
$627$	−2.21582e7	−	4.60908e7i	−0.0898940	−	0.186987i
$628$	−2.79939e8	+	1.01889e8i	−1.13028	+	0.411387i
$629$	7.03903e7	+	4.06399e7i	0.282853	+	0.163305i
$630$	8.84766e6	+	4.83355e6i	0.0353840	+	0.0193306i
$631$	7.83312e7	+	1.35674e8i	0.311779	+	0.540017i	0.978748	−	0.205069i	$-0.0657418\pi$
$631$	7.83312e7	+	1.35674e8i	0.311779	+	0.540017i	−0.666969	+	0.745086i	$0.732408\pi$
$632$	8.83040e7	−	1.05237e8i	0.349808	−	0.416885i
$633$	1.73920e8	−	1.78072e8i	0.685706	−	0.702078i
$634$	−4.92719e6	−	2.79435e7i	−0.0193345	−	0.109651i
$635$	4.20044e8	−	7.40652e7i	1.64049	−	0.289263i
$636$	3.62494e6	−	1.41963e7i	0.0140906	−	0.0551826i
$637$	2.32309e8	+	1.94931e8i	0.898770	+	0.754158i
$638$	−5.35415e6	+	3.09122e6i	−0.0206172	+	0.0119033i
$639$	1.21435e8	−	1.06878e8i	0.465414	−	0.409623i
$640$	−1.58768e8	+	2.74994e8i	−0.605650	+	1.04902i
$641$	−3.57003e7	−	9.80859e7i	−0.135550	−	0.372419i	0.853283	−	0.521447i	$-0.174608\pi$
$641$	−3.57003e7	−	9.80859e7i	−0.135550	−	0.372419i	−0.988833	+	0.149028i	$0.952386\pi$
$642$	−884756.	+	1.17011e7i	−0.00334363	+	0.0442203i
$643$	−3.64814e8	+	3.06115e8i	−1.37227	+	1.15147i	−0.400291	+	0.916388i	$0.631091\pi$
$643$	−3.64814e8	+	3.06115e8i	−1.37227	+	1.15147i	−0.971976	+	0.235081i	$0.924465\pi$
$644$	1.05758e7	−	2.90567e7i	0.0395962	−	0.108790i
$645$	5.06441e7	+	5.09556e8i	0.188734	+	1.89895i
$646$	−1.01009e7	+	5.72853e7i	−0.0374683	+	0.212494i
$647$		−	3.97790e8i		−	1.46873i	−0.678756	−	0.734364i	$-0.737480\pi$
$647$		−	3.97790e8i		−	1.46873i	0.678756	−	0.734364i	$-0.262520\pi$
$648$	−1.01851e8	−	1.30407e7i	−0.374316	−	0.0479266i
$649$	−4.41923e7			−0.161664
$650$	1.23746e8	+	2.18197e7i	0.450599	+	0.0794527i
$651$	2.98742e7	−	2.96916e6i	0.108281	−	0.0107620i
$652$	1.05521e8	+	3.84067e7i	0.380713	+	0.138568i
$653$	−1.56138e8	−	1.86078e8i	−0.560751	−	0.668277i	0.408955	−	0.912555i	$-0.365893\pi$
$653$	−1.56138e8	−	1.86078e8i	−0.560751	−	0.668277i	−0.969705	+	0.244278i	$0.921449\pi$
$654$	6.68176e7	+	5.05228e6i	0.238868	+	0.0180615i
$655$	−6.79989e7	+	2.47496e7i	−0.241979	+	0.0880732i
$656$	3.12767e8	+	1.80576e8i	1.10792	+	0.639658i
$657$	6.92469e7	−	2.05192e8i	0.244177	−	0.723543i
$658$	5.44157e6	+	9.42508e6i	0.0191006	+	0.0330832i
$659$	−2.45150e8	+	2.92159e8i	−0.856596	+	1.02085i	0.142920	+	0.989734i	$0.454351\pi$
$659$	−2.45150e8	+	2.92159e8i	−0.856596	+	1.02085i	−0.999516	+	0.0311172i	$0.990093\pi$
$660$	−9.25366e7	−	2.36287e7i	−0.321871	−	0.0821880i
$661$	−3.14928e7	−	1.78605e8i	−0.109045	−	0.618427i	−0.989527	−	0.144347i	$-0.953892\pi$
$661$	−3.14928e7	−	1.78605e8i	−0.109045	−	0.618427i	0.880482	−	0.474080i	$-0.157219\pi$
$662$	−3.14996e7	+	5.55423e6i	−0.108575	+	0.0191448i
$663$	−2.67526e8	−	2.61287e8i	−0.917964	−	0.896557i
$664$	5.60539e7	+	4.70348e7i	0.191471	+	0.160663i
$665$	−5.56373e7	+	3.21222e7i	−0.189191	+	0.109230i
$666$	8.95519e6	+	1.46987e7i	0.0303146	+	0.0497573i
$667$	9.15565e7	−	1.58581e8i	0.308540	−	0.534407i
$668$	7.53823e7	+	2.07111e8i	0.252895	+	0.694823i
$669$	1.64301e8	−	7.89879e7i	0.548736	−	0.263805i
$670$	−7.48760e7	+	6.28284e7i	−0.248953	+	0.208897i
$671$	−3.92630e7	+	1.07874e8i	−0.129962	+	0.357068i
$672$	−1.83722e7	−	8.30466e6i	−0.0605415	−	0.0273662i
$673$	−7.18363e7	+	4.07404e8i	−0.235667	+	1.33653i	0.605538	+	0.795817i	$0.292958\pi$
$673$	−7.18363e7	+	4.07404e8i	−0.235667	+	1.33653i	−0.841205	+	0.540717i	$0.818153\pi$
$674$		−	2.81986e7i		−	0.0920974i
$675$	7.52146e7	+	6.10130e8i	0.244563	+	1.98386i
$676$	1.24305e8			0.402392
$677$	−1.58126e8	−	2.78819e7i	−0.509610	−	0.0898580i	−0.0870699	−	0.996202i	$-0.527750\pi$
$677$	−1.58126e8	−	2.78819e7i	−0.509610	−	0.0898580i	−0.422540	+	0.906344i	$0.638861\pi$
$678$	6.71677e7	+	9.35567e7i	0.215512	+	0.300183i
$679$	−2.93824e7	−	1.06943e7i	−0.0938594	−	0.0341620i
$680$	1.42334e8	+	1.69627e8i	0.452670	+	0.539471i
$681$	3.55424e7	−	5.20562e7i	0.112540	−	0.164828i
$682$	1.02550e7	−	3.73253e6i	0.0323284	−	0.0117666i
$683$	1.00171e8	+	5.78339e7i	0.314399	+	0.181518i	0.648893	−	0.760880i	$-0.275232\pi$
$683$	1.00171e8	+	5.78339e7i	0.314399	+	0.181518i	−0.334494	+	0.942398i	$0.608566\pi$
$684$	2.00476e8	−	2.50699e8i	0.626461	−	0.783403i
$685$	−2.94629e7	−	5.10313e7i	−0.0916651	−	0.158769i
$686$	9.59209e6	−	1.14314e7i	0.0297126	−	0.0354101i
$687$	7.01060e7	+	2.49813e8i	0.216215	+	0.770451i
$688$	−5.54928e7	−	3.14715e8i	−0.170401	−	0.966390i
$689$	2.26826e7	−	3.99956e6i	0.0693483	−	0.0122280i
$690$	−1.04511e8	+	2.93292e7i	−0.318136	+	0.0892797i
$691$	1.47889e7	+	1.24094e7i	0.0448232	+	0.0376111i	0.664924	−	0.746911i	$-0.268464\pi$
$691$	1.47889e7	+	1.24094e7i	0.0448232	+	0.0376111i	−0.620101	+	0.784522i	$0.712908\pi$
$692$	−1.84642e8	+	1.06603e8i	−0.557202	+	0.321701i
$693$	1.20732e6	−	7.93791e6i	0.00362763	−	0.0238510i
$694$	4.04500e7	−	7.00614e7i	0.121015	−	0.209604i
$695$	1.06736e8	+	2.93255e8i	0.317949	+	0.873557i
$696$	−6.53268e7	−	4.46031e7i	−0.193760	−	0.132293i
$697$	4.01570e8	−	3.36957e8i	1.18594	−	0.995123i
$698$	1.55435e7	−	4.27055e7i	0.0457071	−	0.125579i
$699$	2.93167e8	−	2.10475e8i	0.858387	−	0.616267i
$700$	−1.38867e7	+	7.87552e7i	−0.0404859	+	0.229607i
$701$		−	3.51261e8i		−	1.01971i	−0.860261	−	0.509854i	$-0.829699\pi$
$701$		−	3.51261e8i		−	1.01971i	0.860261	−	0.509854i	$-0.170301\pi$
$702$	−2.31892e7	−	7.57173e7i	−0.0670309	−	0.218869i
$703$	−1.09679e8			−0.315686
$704$	5.37324e7	+	9.47446e6i	0.153999	+	0.0271542i
$705$	−4.10083e8	+	9.07217e8i	−1.17032	+	2.58907i
$706$	1.40972e7	+	5.13097e6i	0.0400608	+	0.0145809i
$707$	−2.05961e6	−	2.45454e6i	−0.00582809	−	0.00694565i
$708$	−1.20186e8	−	2.49998e8i	−0.338653	−	0.704427i
$709$	5.49342e8	−	1.99944e8i	1.54136	−	0.561009i	0.574988	−	0.818162i	$-0.305007\pi$
$709$	5.49342e8	−	1.99944e8i	1.54136	−	0.561009i	0.966371	+	0.257153i	$0.0827843\pi$
$710$	−6.39760e7	−	3.69366e7i	−0.178748	−	0.103200i
$711$	1.22282e7	+	5.18179e8i	0.0340216	+	1.44169i
$712$	7.44976e7	+	1.29034e8i	0.206396	+	0.357489i
$713$	−2.07768e8	+	2.47608e8i	−0.573205	+	0.683119i
$714$	−6.38117e6	+	6.53353e6i	−0.0175310	+	0.0179495i
$715$	−2.60707e7	−	1.47854e8i	−0.0713237	−	0.404497i
$716$	9.40915e7	−	1.65909e7i	0.256337	−	0.0451991i
$717$	−1.14791e7	+	4.49555e7i	−0.0311424	+	0.121962i
$718$	−8.02153e7	−	6.73086e7i	−0.216712	−	0.181843i
$719$	1.35943e8	−	7.84865e7i	0.365737	−	0.211158i	−0.305857	−	0.952077i	$-0.598943\pi$
$719$	1.35943e8	−	7.84865e7i	0.365737	−	0.211158i	0.671594	+	0.740919i	$0.265610\pi$
$720$	−1.13295e8	−	5.64326e8i	−0.303537	−	1.51193i
$721$	3.30622e7	−	5.72655e7i	0.0882117	−	0.152787i
$722$	−2.10033e6	−	5.77060e6i	−0.00558053	−	0.0153324i
$723$	2.28302e6	−	3.01935e7i	0.00604081	−	0.0798911i
$724$	1.99359e7	−	1.67282e7i	0.0525315	−	0.0440791i
$725$	−1.61971e8	+	4.45013e8i	−0.425035	+	1.16777i
$726$	6.98666e6	+	7.02962e7i	0.0182583	+	0.183706i
$727$	−6.32999e7	+	3.58992e8i	−0.164740	+	0.934289i	0.784591	+	0.620013i	$0.212873\pi$
$727$	−6.32999e7	+	3.58992e8i	−0.164740	+	0.934289i	−0.949332	+	0.314276i	$0.898238\pi$
$728$		−	2.09980e7i		−	0.0544231i
$729$	3.20976e8	−	2.16954e8i	0.828495	−	0.559996i
$730$	−9.88947e7			−0.254217
$731$	−4.56810e8	−	8.05480e7i	−1.16946	−	0.206207i
$732$	−7.17031e8	+	7.12649e7i	−1.82812	+	0.181695i
$733$	−4.68800e8	−	1.70629e8i	−1.19035	−	0.433253i	−0.330506	−	0.943804i	$-0.607219\pi$
$733$	−4.68800e8	−	1.70629e8i	−1.19035	−	0.433253i	−0.859848	+	0.510550i	$0.829442\pi$
$734$	5.82620e7	+	6.94340e7i	0.147332	+	0.175584i
$735$	6.75594e8	+	5.10837e7i	1.70147	+	0.128653i
$736$	2.03985e8	−	7.42445e7i	0.511641	−	0.186222i
$737$	6.74140e7	+	3.89215e7i	0.168402	+	0.0972271i
$738$	1.08836e8	−	2.18500e7i	0.270772	−	0.0543604i
$739$	−1.71390e8	−	2.96856e8i	−0.424671	−	0.735552i	0.571719	−	0.820450i	$-0.306277\pi$
$739$	−1.71390e8	−	2.96856e8i	−0.424671	−	0.735552i	−0.996390	+	0.0848980i	$0.972944\pi$
$740$	−1.31660e8	+	1.56906e8i	−0.324907	+	0.387209i
$741$	4.88924e8	+	1.24844e8i	1.20167	+	0.306841i
$742$	−97677.4	−	553956.i	−0.000239102	−	0.00135601i
$743$	−3.76683e8	+	6.64193e7i	−0.918352	+	0.161930i	−0.612793	−	0.790243i	$-0.709954\pi$
$743$	−3.76683e8	+	6.64193e7i	−0.918352	+	0.161930i	−0.305558	+	0.952173i	$0.598843\pi$
$744$	9.98905e7	+	9.75610e7i	0.242552	+	0.236896i
$745$	3.18213e8	+	2.67012e8i	0.769571	+	0.645746i
$746$	4.83828e7	−	2.79338e7i	0.116540	−	0.0672844i
$747$	−2.76006e8	+	6.51332e6i	−0.662152	+	0.0156257i
$748$	4.32571e7	−	7.49236e7i	0.103360	−	0.179025i
$749$	−4.01530e6	−	1.10319e7i	−0.00955592	−	0.0262547i
$750$	1.26434e8	−	6.07833e7i	0.299696	−	0.144079i
$751$	−2.90458e8	+	2.43723e8i	−0.685747	+	0.575410i	−0.917679	−	0.397322i	$-0.869940\pi$
$751$	−2.90458e8	+	2.43723e8i	−0.685747	+	0.575410i	0.231932	+	0.972732i	$0.425495\pi$
$752$	2.12508e8	−	5.83861e8i	0.499714	−	1.37295i
$753$	1.90139e8	+	8.59471e7i	0.445334	+	0.201301i
$754$	1.05931e7	−	6.00765e7i	0.0247121	−	0.140149i
$755$		−	8.49902e8i		−	1.97482i
$756$	4.81886e7	−	1.47583e7i	0.111527	−	0.0341562i
$757$	6.82521e8			1.57336			0.786680	−	0.617361i	$-0.211798\pi$
$757$	6.82521e8			1.57336			0.786680	+	0.617361i	$0.211798\pi$
$758$	−1.31128e8	−	2.31214e7i	−0.301084	−	0.0530892i
$759$	5.04162e7	+

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.51454 + 0.267054i) q^{2} +(26.8676 - 2.67034i) q^{3} +(-57.9178 - 21.0804i) q^{4} +(-139.142 - 165.822i) q^{5} +(41.4052 + 3.13078i) q^{6} +(-39.0374 + 14.2084i) q^{7} +(-167.329 - 96.6072i) q^{8} +(714.739 - 143.491i) q^{9} +O(q^{10})\)	\(q+(1.51454 + 0.267054i) q^{2} +(26.8676 - 2.67034i) q^{3} +(-57.9178 - 21.0804i) q^{4} +(-139.142 - 165.822i) q^{5} +(41.4052 + 3.13078i) q^{6} +(-39.0374 + 14.2084i) q^{7} +(-167.329 - 96.6072i) q^{8} +(714.739 - 143.491i) q^{9} +(-166.452 - 288.303i) q^{10} +(-170.419 + 203.097i) q^{11} +(-1612.41 - 411.719i) q^{12} +(-454.269 - 2576.29i) q^{13} +(-62.9181 + 11.0942i) q^{14} +(-4181.21 - 4083.70i) q^{15} +(2794.14 + 2344.56i) q^{16} +(4585.03 - 2647.17i) q^{17} +(1120.82 - 26.4496i) q^{18} +(-3572.08 + 6187.02i) q^{19} +(4563.18 + 12537.2i) q^{20} +(-1010.90 + 485.990i) q^{21} +(-312.344 + 262.088i) q^{22} +(4130.38 - 11348.1i) q^{23} +(-4753.70 - 2148.78i) q^{24} +(-5423.46 + 30758.0i) q^{25} -4023.21i q^{26} +(18820.2 - 5763.87i) q^{27} +2560.48 q^{28} +(14932.5 + 2633.00i) q^{29} +(-5242.04 - 7301.54i) q^{30} +(-25151.2 - 9154.28i) q^{31} +(11554.2 + 13769.8i) q^{32} +(-4036.41 + 5911.82i) q^{33} +(7651.15 - 2784.79i) q^{34} +(7787.80 + 4496.29i) q^{35} +(-44420.9 - 6756.23i) q^{36} +(7676.10 + 13295.4i) q^{37} +(-7062.33 + 8416.55i) q^{38} +(-19084.7 - 68005.6i) q^{39} +(7262.72 + 41188.9i) q^{40} +(97509.7 - 17193.6i) q^{41} +(-1660.84 + 466.087i) q^{42} +(-67116.1 - 56317.1i) q^{43} +(14151.6 - 8170.46i) q^{44} +(-123244. - 98554.1i) q^{45} +(9286.20 - 16084.2i) q^{46} +(-58261.5 - 160072. i) q^{47} +(81332.6 + 55531.4i) q^{48} +(-88802.3 + 74514.0i) q^{49} +(-16428.1 + 45135.9i) q^{50} +(116120. - 83366.7i) q^{51} +(-27998.8 + 158789. i) q^{52} +8804.40i q^{53} +(30043.2 - 3703.61i) q^{54} +57390.4 q^{55} +(7904.71 + 1393.81i) q^{56} +(-79451.8 + 175769. i) q^{57} +(21912.7 + 7975.57i) q^{58} +(107143. + 127688. i) q^{59} +(156080. + 324660. i) q^{60} +(406882. - 148093. i) q^{61} +(-35647.8 - 20581.3i) q^{62} +(-25862.7 + 15756.9i) q^{63} +(-102897. - 178224. i) q^{64} +(-363998. + 433796. i) q^{65} +(-7692.08 + 7875.75i) q^{66} +(-50984.7 - 289149. i) q^{67} +(-321358. + 56664.1i) q^{68} +(80670.2 - 315927. i) q^{69} +(10594.2 + 8889.58i) q^{70} +(192176. - 110953. i) q^{71} +(-133459. - 45038.7i) q^{72} +(148533. - 257267. i) q^{73} +(8075.18 + 22186.4i) q^{74} +(-63581.2 + 840876. i) q^{75} +(337311. - 283038. i) q^{76} +(3767.01 - 10349.8i) q^{77} +(-10743.3 - 108094. i) q^{78} +(-123465. + 700204. i) q^{79} -789556. i q^{80} +(490261. - 205118. i) q^{81} +152274. q^{82} +(-372962. - 65763.2i) q^{83} +(68794.0 - 6837.35i) q^{84} +(-1.07693e6 - 391970. i) q^{85} +(-86610.4 - 103218. i) q^{86} +(408231. + 30867.6i) q^{87} +(48136.6 - 17520.3i) q^{88} +(-667826. - 385569. i) q^{89} +(-160339. - 182177. i) q^{90} +(54338.5 + 94117.0i) q^{91} +(-478446. + 570189. i) q^{92} +(-700197. - 178791. i) q^{93} +(-45491.5 - 257995. i) q^{94} +(1.52297e6 - 268541. i) q^{95} +(347205. + 339108. i) q^{96} +(576581. + 483809. i) q^{97} +(-154394. + 89139.4i) q^{98} +(-92662.2 + 169615. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more