LMFDB - Embedded newform 690.2.m.h.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	690.31
Dual form			690.2.m.h.601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 - 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(0.208237 + 0.133826i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.142315 - 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(0.208237 + 0.133826i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(0.841254 - 0.540641i) q^{10} +(0.108025 + 0.751334i) q^{11} +(-0.142315 - 0.989821i) q^{12} +(-2.45109 + 1.57522i) q^{13} +(0.162099 - 0.187072i) q^{14} +(-0.415415 + 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(6.73175 - 1.97662i) q^{17} +(0.654861 + 0.755750i) q^{18} +(7.70022 + 2.26099i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(-0.0352275 + 0.245013i) q^{21} +0.759060 q^{22} +(0.715117 + 4.74222i) q^{23} -1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(1.21036 + 2.65032i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(-0.162099 - 0.187072i) q^{28} +(-7.35741 + 2.16033i) q^{29} +(0.841254 + 0.540641i) q^{30} +(-1.32117 + 2.89295i) q^{31} +(0.654861 - 0.755750i) q^{32} +(-0.638562 + 0.410379i) q^{33} +(-0.998473 - 6.94453i) q^{34} +(0.0352275 + 0.245013i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-0.244627 + 0.282315i) q^{37} +(3.33383 - 7.30007i) q^{38} +(-2.45109 - 1.57522i) q^{39} +(-0.959493 + 0.281733i) q^{40} +(8.38273 + 9.67418i) q^{41} +(0.237505 + 0.0697379i) q^{42} +(-1.50964 - 3.30566i) q^{43} +(0.108025 - 0.751334i) q^{44} -1.00000 q^{45} +(4.79572 - 0.0329509i) q^{46} -3.48117 q^{47} +(-0.142315 + 0.989821i) q^{48} +(-2.88245 - 6.31169i) q^{49} +(0.959493 + 0.281733i) q^{50} +(4.59447 + 5.30230i) q^{51} +(2.79560 - 0.820862i) q^{52} +(8.29089 + 5.32823i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(-0.497078 + 0.573659i) q^{55} +(-0.208237 + 0.133826i) q^{56} +(1.14212 + 7.94361i) q^{57} +(1.09127 + 7.58997i) q^{58} +(11.5521 - 7.42412i) q^{59} +(0.654861 - 0.755750i) q^{60} +(1.29177 - 2.82859i) q^{61} +(2.67548 + 1.71943i) q^{62} +(-0.237505 + 0.0697379i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-2.79560 - 0.820862i) q^{65} +(0.315325 + 0.690465i) q^{66} +(1.45071 - 10.0899i) q^{67} -7.01595 q^{68} +(-4.01660 + 2.62048i) q^{69} +0.247532 q^{70} +(0.519931 - 3.61620i) q^{71} +(-0.415415 - 0.909632i) q^{72} +(-14.9793 - 4.39831i) q^{73} +(0.244627 + 0.282315i) q^{74} +(-0.959493 + 0.281733i) q^{75} +(-6.75131 - 4.33880i) q^{76} +(-0.0780530 + 0.170912i) q^{77} +(-1.90802 + 2.20197i) q^{78} +(-7.14726 + 4.59327i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(10.7687 - 6.92062i) q^{82} +(7.22752 - 8.34101i) q^{83} +(0.102829 - 0.225163i) q^{84} +(5.90219 + 3.79311i) q^{85} +(-3.48685 + 1.02383i) q^{86} +(-5.02148 - 5.79510i) q^{87} +(-0.728312 - 0.213852i) q^{88} +(-1.09693 - 2.40194i) q^{89} +(-0.142315 + 0.989821i) q^{90} -0.721215 q^{91} +(0.649886 - 4.75159i) q^{92} -3.18035 q^{93} +(-0.495422 + 3.44574i) q^{94} +(3.33383 + 7.30007i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-7.63862 - 8.81543i) q^{97} +(-6.65766 + 1.95487i) q^{98} +(-0.638562 - 0.410379i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$6$	0.959493	−	0.281733i	0.391711	−	0.115017i
$7$	0.208237	+	0.133826i	0.0787063	+	0.0505815i	0.579402	−	0.815042i	$-0.303286\pi$
$7$	0.208237	+	0.133826i	0.0787063	+	0.0505815i	−0.500696	+	0.865623i	$0.666922\pi$
$8$	−0.415415	+	0.909632i	−0.146871	+	0.321603i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	0.841254	−	0.540641i	0.266028	−	0.170966i
$11$	0.108025	+	0.751334i	0.0325709	+	0.226536i	0.999605	−	0.0281122i	$-0.00894956\pi$
$11$	0.108025	+	0.751334i	0.0325709	+	0.226536i	−0.967034	+	0.254648i	$0.918040\pi$
$12$	−0.142315	−	0.989821i	−0.0410828	−	0.285737i
$13$	−2.45109	+	1.57522i	−0.679811	+	0.436888i	−0.834450	−	0.551083i	$-0.814215\pi$
$13$	−2.45109	+	1.57522i	−0.679811	+	0.436888i	0.154639	+	0.987971i	$0.450578\pi$
$14$	0.162099	−	0.187072i	0.0433228	−	0.0499972i
$15$	−0.415415	+	0.909632i	−0.107260	+	0.234866i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	6.73175	−	1.97662i	1.63269	−	0.479401i	0.668301	−	0.743891i	$-0.267022\pi$
$17$	6.73175	−	1.97662i	1.63269	−	0.479401i	0.964388	+	0.264490i	$0.0852036\pi$
$18$	0.654861	+	0.755750i	0.154352	+	0.178132i
$19$	7.70022	+	2.26099i	1.76655	+	0.518706i	0.993317	−	0.115415i	$-0.0368198\pi$
$19$	7.70022	+	2.26099i	1.76655	+	0.518706i	0.773234	+	0.634121i	$0.218638\pi$
$20$	−0.415415	−	0.909632i	−0.0928896	−	0.203400i
$21$	−0.0352275	+	0.245013i	−0.00768727	+	0.0534661i
$22$	0.759060			0.161832
$23$	0.715117	+	4.74222i	0.149112	+	0.988820i
$23$	0.715117	+	4.74222i	0.149112	+	0.988820i
$24$	−1.00000			−0.204124
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$	1.21036	+	2.65032i	0.237371	+	0.519771i
$27$	−0.959493	−	0.281733i	−0.184655	−	0.0542195i
$28$	−0.162099	−	0.187072i	−0.0306338	−	0.0353533i
$29$	−7.35741	+	2.16033i	−1.36624	+	0.401163i	−0.880957	−	0.473196i	$-0.843100\pi$
$29$	−7.35741	+	2.16033i	−1.36624	+	0.401163i	−0.485279	+	0.874359i	$0.661282\pi$
$30$	0.841254	+	0.540641i	0.153591	+	0.0987071i
$31$	−1.32117	+	2.89295i	−0.237289	+	0.519589i	−0.990388	−	0.138317i	$-0.955831\pi$
$31$	−1.32117	+	2.89295i	−0.237289	+	0.519589i	0.753099	+	0.657907i	$0.228558\pi$
$32$	0.654861	−	0.755750i	0.115764	−	0.133599i
$33$	−0.638562	+	0.410379i	−0.111159	+	0.0714378i
$34$	−0.998473	−	6.94453i	−0.171237	−	1.19098i
$35$	0.0352275	+	0.245013i	0.00595453	+	0.0414147i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	−0.244627	+	0.282315i	−0.0402164	+	0.0464122i	−0.775501	−	0.631346i	$-0.782503\pi$
$37$	−0.244627	+	0.282315i	−0.0402164	+	0.0464122i	0.735285	+	0.677758i	$0.237048\pi$
$38$	3.33383	−	7.30007i	0.540819	−	1.18423i
$39$	−2.45109	−	1.57522i	−0.392489	−	0.252237i
$40$	−0.959493	+	0.281733i	−0.151709	+	0.0445458i
$41$	8.38273	+	9.67418i	1.30916	+	1.51085i	0.676662	+	0.736293i	$0.263426\pi$
$41$	8.38273	+	9.67418i	1.30916	+	1.51085i	0.632500	+	0.774560i	$0.282029\pi$
$42$	0.237505	+	0.0697379i	0.0366479	+	0.0107608i
$43$	−1.50964	−	3.30566i	−0.230218	−	0.504108i	0.758904	−	0.651202i	$-0.225735\pi$
$43$	−1.50964	−	3.30566i	−0.230218	−	0.504108i	−0.989122	+	0.147094i	$0.953008\pi$
$44$	0.108025	−	0.751334i	0.0162855	−	0.113268i
$45$	−1.00000			−0.149071
$46$	4.79572	−	0.0329509i	0.707090	−	0.00485834i
$47$	−3.48117			−0.507781			−0.253890	−	0.967233i	$-0.581710\pi$
$47$	−3.48117			−0.507781			−0.253890	+	0.967233i	$0.581710\pi$
$48$	−0.142315	+	0.989821i	−0.0205414	+	0.142868i
$49$	−2.88245	−	6.31169i	−0.411779	−	0.901670i
$50$	0.959493	+	0.281733i	0.135693	+	0.0398430i
$51$	4.59447	+	5.30230i	0.643354	+	0.742470i
$52$	2.79560	−	0.820862i	0.387680	−	0.113833i
$53$	8.29089	+	5.32823i	1.13884	+	0.731889i	0.967387	−	0.253304i	$-0.0815172\pi$
$53$	8.29089	+	5.32823i	1.13884	+	0.731889i	0.171454	+	0.985192i	$0.445154\pi$
$54$	−0.415415	+	0.909632i	−0.0565308	+	0.123785i
$55$	−0.497078	+	0.573659i	−0.0670260	+	0.0773522i
$56$	−0.208237	+	0.133826i	−0.0278269	+	0.0178832i
$57$	1.14212	+	7.94361i	0.151277	+	1.05216i
$58$	1.09127	+	7.58997i	0.143291	+	0.996611i
$59$	11.5521	−	7.42412i	1.50396	−	0.966537i	0.509610	−	0.860406i	$-0.329790\pi$
$59$	11.5521	−	7.42412i	1.50396	−	0.966537i	0.994352	−	0.106132i	$-0.0338465\pi$
$60$	0.654861	−	0.755750i	0.0845422	−	0.0975669i
$61$	1.29177	−	2.82859i	0.165395	−	0.362164i	−0.808728	−	0.588182i	$-0.799844\pi$
$61$	1.29177	−	2.82859i	0.165395	−	0.362164i	0.974123	+	0.226018i	$0.0725710\pi$
$62$	2.67548	+	1.71943i	0.339787	+	0.218368i
$63$	−0.237505	+	0.0697379i	−0.0299229	+	0.00878615i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−2.79560	−	0.820862i	−0.346751	−	0.101815i
$66$	0.315325	+	0.690465i	0.0388138	+	0.0849904i
$67$	1.45071	−	10.0899i	0.177232	−	1.23268i	−0.685899	−	0.727697i	$-0.740591\pi$
$67$	1.45071	−	10.0899i	0.177232	−	1.23268i	0.863131	−	0.504980i	$-0.168500\pi$
$68$	−7.01595			−0.850808
$69$	−4.01660	+	2.62048i	−0.483542	+	0.315469i
$70$	0.247532			0.0295858
$71$	0.519931	−	3.61620i	0.0617044	−	0.429164i	−0.935430	−	0.353512i	$-0.884987\pi$
$71$	0.519931	−	3.61620i	0.0617044	−	0.429164i	0.997134	−	0.0756515i	$-0.0241037\pi$
$72$	−0.415415	−	0.909632i	−0.0489571	−	0.107201i
$73$	−14.9793	−	4.39831i	−1.75319	−	0.514783i	−0.762041	−	0.647529i	$-0.775803\pi$
$73$	−14.9793	−	4.39831i	−1.75319	−	0.514783i	−0.991150	+	0.132745i	$0.957621\pi$
$74$	0.244627	+	0.282315i	0.0284373	+	0.0328184i
$75$	−0.959493	+	0.281733i	−0.110793	+	0.0325317i
$76$	−6.75131	−	4.33880i	−0.774428	−	0.497695i
$77$	−0.0780530	+	0.170912i	−0.00889497	+	0.0194773i
$78$	−1.90802	+	2.20197i	−0.216040	+	0.249324i
$79$	−7.14726	+	4.59327i	−0.804130	+	0.516783i	−0.876961	−	0.480561i	$-0.840433\pi$
$79$	−7.14726	+	4.59327i	−0.804130	+	0.516783i	0.0728311	+	0.997344i	$0.476797\pi$
$80$	0.142315	+	0.989821i	0.0159113	+	0.110665i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	10.7687	−	6.92062i	1.18920	−	0.764255i
$83$	7.22752	−	8.34101i	0.793324	−	0.915544i	−0.204672	−	0.978831i	$-0.565613\pi$
$83$	7.22752	−	8.34101i	0.793324	−	0.915544i	0.997995	+	0.0632862i	$0.0201581\pi$
$84$	0.102829	−	0.225163i	0.0112195	−	0.0245673i
$85$	5.90219	+	3.79311i	0.640182	+	0.411420i
$86$	−3.48685	+	1.02383i	−0.375997	+	0.110403i
$87$	−5.02148	−	5.79510i	−0.538359	−	0.621300i
$88$	−0.728312	−	0.213852i	−0.0776384	−	0.0227967i
$89$	−1.09693	−	2.40194i	−0.116274	−	0.254605i	0.842543	−	0.538629i	$-0.181058\pi$
$89$	−1.09693	−	2.40194i	−0.116274	−	0.254605i	−0.958817	+	0.284024i	$0.908330\pi$
$90$	−0.142315	+	0.989821i	−0.0150013	+	0.104336i
$91$	−0.721215			−0.0756038
$92$	0.649886	−	4.75159i	0.0677553	−	0.495388i
$93$	−3.18035			−0.329787
$94$	−0.495422	+	3.44574i	−0.0510989	+	0.355401i
$95$	3.33383	+	7.30007i	0.342044	+	0.748971i
$96$	0.959493	+	0.281733i	0.0979278	+	0.0287542i
$97$	−7.63862	−	8.81543i	−0.775584	−	0.895072i	0.221198	−	0.975229i	$-0.429003\pi$
$97$	−7.63862	−	8.81543i	−0.775584	−	0.895072i	−0.996782	+	0.0801571i	$0.974458\pi$
$98$	−6.65766	+	1.95487i	−0.672525	+	0.197471i
$99$	−0.638562	−	0.410379i	−0.0641779	−	0.0412446i
$100$	0.415415	−	0.909632i	0.0415415	−	0.0909632i
$101$	−4.48662	+	5.17784i	−0.446436	+	0.515214i	−0.933708	−	0.358036i	$-0.883447\pi$
$101$	−4.48662	+	5.17784i	−0.446436	+	0.515214i	0.487272	+	0.873250i	$0.337992\pi$
$102$	5.90219	−	3.79311i	0.584404	−	0.375574i
$103$	−0.722293	−	5.02366i	−0.0711696	−	0.494996i	−0.993964	−	0.109704i	$-0.965010\pi$
$103$	−0.722293	−	5.02366i	−0.0711696	−	0.494996i	0.922795	−	0.385292i	$-0.125899\pi$
$104$	−0.414651	−	2.88396i	−0.0406599	−	0.282796i
$105$	−0.208237	+	0.133826i	−0.0203219	+	0.0130601i
$106$	6.45391	−	7.44821i	0.626859	−	0.723434i
$107$	−7.89121	+	17.2793i	−0.762872	+	1.67046i	−0.0211256	+	0.999777i	$0.506725\pi$
$107$	−7.89121	+	17.2793i	−0.762872	+	1.67046i	−0.741747	+	0.670680i	$0.766002\pi$
$108$	0.841254	+	0.540641i	0.0809497	+	0.0520232i
$109$	−7.48610	+	2.19812i	−0.717039	+	0.210542i	−0.619845	−	0.784724i	$-0.712805\pi$
$109$	−7.48610	+	2.19812i	−0.717039	+	0.210542i	−0.0971933	+	0.995266i	$0.530987\pi$
$110$	0.497078	+	0.573659i	0.0473946	+	0.0546962i
$111$	−0.358424	−	0.105243i	−0.0340201	−	0.00998921i
$112$	0.102829	+	0.225163i	0.00971639	+	0.0212759i
$113$	−0.00792130	+	0.0550939i	−0.000745173	+	0.00518279i	−0.990191	−	0.139723i	$-0.955379\pi$
$113$	−0.00792130	+	0.0550939i	−0.000745173	+	0.00518279i	0.989445	+	0.144906i	$0.0462879\pi$
$114$	8.02530			0.751638
$115$	−3.11563	+	3.64594i	−0.290534	+	0.339986i
$116$	7.66802			0.711957
$117$	0.414651	−	2.88396i	0.0383345	−	0.266623i
$118$	−5.70451	−	12.4911i	−0.525142	−	1.14990i
$119$	1.66632	+	0.489277i	0.152752	+	0.0448520i
$120$	−0.654861	−	0.755750i	−0.0597803	−	0.0689902i
$121$	10.0016	−	2.93673i	0.909235	−	0.266976i
$122$	−2.61596	−	1.68118i	−0.236838	−	0.152207i
$123$	−5.31764	+	11.6440i	−0.479475	+	1.04990i
$124$	2.08269	−	2.40355i	0.187031	−	0.215845i
$125$	−0.841254	+	0.540641i	−0.0752440	+	0.0483564i
$126$	0.0352275	+	0.245013i	0.00313831	+	0.0218275i
$127$	−2.94522	−	20.4845i	−0.261346	−	1.81770i	−0.522766	−	0.852476i	$-0.675100\pi$
$127$	−2.94522	−	20.4845i	−0.261346	−	1.81770i	0.261420	−	0.965225i	$-0.415809\pi$
$128$	−0.841254	+	0.540641i	−0.0743570	+	0.0477863i
$129$	2.37980	−	2.74644i	0.209530	−	0.241810i
$130$	−1.21036	+	2.65032i	−0.106156	+	0.232449i
$131$	0.952898	+	0.612390i	0.0832551	+	0.0535048i	0.581606	−	0.813471i	$-0.302425\pi$
$131$	0.952898	+	0.612390i	0.0832551	+	0.0535048i	−0.498351	+	0.866975i	$0.666061\pi$
$132$	0.728312	−	0.213852i	0.0633915	−	0.0186134i
$133$	1.30089	+	1.50131i	0.112802	+	0.130180i
$134$	−9.78074	−	2.87188i	−0.844927	−	0.248093i
$135$	−0.415415	−	0.909632i	−0.0357532	−	0.0782887i
$136$	−0.998473	+	6.94453i	−0.0856184	+	0.595489i
$137$	−21.0104			−1.79504			−0.897519	−	0.440975i	$-0.854633\pi$
$137$	−21.0104			−1.79504			−0.897519	+	0.440975i	$0.854633\pi$
$138$	2.02219	+	4.34865i	0.172140	+	0.370182i
$139$	10.2677			0.870894			0.435447	−	0.900214i	$-0.356590\pi$
$139$	10.2677			0.870894			0.435447	+	0.900214i	$0.356590\pi$
$140$	0.0352275	−	0.245013i	0.00297727	−	0.0207073i
$141$	−1.44613	−	3.16658i	−0.121786	−	0.266674i
$142$	−3.50540	−	1.02928i	−0.294166	−	0.0863751i
$143$	−1.44830	−	1.67142i	−0.121113	−	0.139772i
$144$	−0.959493	+	0.281733i	−0.0799577	+	0.0234777i
$145$	−6.45074	−	4.14564i	−0.535705	−	0.344277i
$146$	−6.48532	+	14.2009i	−0.536729	+	1.17527i
$147$	4.54390	−	5.24394i	0.374775	−	0.432513i
$148$	0.314255	−	0.201959i	0.0258316	−	0.0166010i
$149$	−0.397912	−	2.76754i	−0.0325982	−	0.226726i	0.967009	−	0.254741i	$-0.0819903\pi$
$149$	−0.397912	−	2.76754i	−0.0325982	−	0.226726i	−0.999607	+	0.0280156i	$0.991081\pi$
$150$	0.142315	+	0.989821i	0.0116200	+	0.0808186i
$151$	1.73508	−	1.11507i	0.141199	−	0.0907428i	−0.468134	−	0.883657i	$-0.655074\pi$
$151$	1.73508	−	1.11507i	0.141199	−	0.0907428i	0.609333	+	0.792915i	$0.291437\pi$
$152$	−5.25545	+	6.06512i	−0.426274	+	0.491946i
$153$	−2.91453	+	6.38193i	−0.235626	+	0.515948i
$154$	0.158065	+	0.101582i	0.0127372	+	0.00818570i
$155$	−3.05153	+	0.896009i	−0.245105	+	0.0719692i
$156$	1.90802	+	2.20197i	0.152763	+	0.176298i
$157$	−17.5515	−	5.15359i	−1.40076	−	0.411301i	−0.507817	−	0.861465i	$-0.669547\pi$
$157$	−17.5515	−	5.15359i	−1.40076	−	0.411301i	−0.892946	+	0.450164i	$0.851366\pi$
$158$	3.52935	+	7.72821i	0.280780	+	0.614823i
$159$	−1.40257	+	9.75508i	−0.111231	+	0.773628i
$160$	1.00000			0.0790569
$161$	−0.485718	+	1.08321i	−0.0382799	+	0.0853687i
$162$	−1.00000			−0.0785674
$163$	1.40661	−	9.78316i	0.110174	−	0.766276i	−0.857575	−	0.514359i	$-0.828030\pi$
$163$	1.40661	−	9.78316i	0.110174	−	0.766276i	0.967749	−	0.251917i	$-0.0810611\pi$
$164$	−5.31764	−	11.6440i	−0.415238	−	0.909244i
$165$	−0.728312	−	0.213852i	−0.0566990	−	0.0166483i
$166$	−7.22752	−	8.34101i	−0.560965	−	0.647388i
$167$	17.4151	−	5.11355i	1.34762	−	0.395698i	0.473241	−	0.880933i	$-0.343084\pi$
$167$	17.4151	−	5.11355i	1.34762	−	0.395698i	0.874384	+	0.485235i	$0.161266\pi$
$168$	−0.208237	−	0.133826i	−0.0160659	−	0.0103249i
$169$	−1.87386	+	4.10318i	−0.144143	+	0.315630i
$170$	4.59447	−	5.30230i	0.352380	−	0.406668i
$171$	−6.75131	+	4.33880i	−0.516286	+	0.331797i
$172$	0.517181	+	3.59707i	0.0394347	+	0.274274i
$173$	−1.76194	−	12.2546i	−0.133958	−	0.931697i	−0.940324	−	0.340280i	$-0.889478\pi$
$173$	−1.76194	−	12.2546i	−0.133958	−	0.931697i	0.806366	−	0.591416i	$-0.201431\pi$
$174$	−6.45074	+	4.14564i	−0.489030	+	0.314280i
$175$	−0.162099	+	0.187072i	−0.0122535	+	0.0141413i
$176$	−0.315325	+	0.690465i	−0.0237685	+	0.0520458i
$177$	11.5521	+	7.42412i	0.868313	+	0.558031i
$178$	−2.53360	+	0.743931i	−0.189901	+	0.0557600i
$179$	1.92958	+	2.22685i	0.144224	+	0.166443i	0.823265	−	0.567657i	$-0.192150\pi$
$179$	1.92958	+	2.22685i	0.144224	+	0.166443i	−0.679042	+	0.734100i	$0.737604\pi$
$180$	0.959493	+	0.281733i	0.0715164	+	0.0209991i
$181$	8.75540	+	19.1716i	0.650783	+	1.42502i	0.890867	+	0.454265i	$0.150098\pi$
$181$	8.75540	+	19.1716i	0.650783	+	1.42502i	−0.240083	+	0.970752i	$0.577175\pi$
$182$	−0.102640	+	0.713874i	−0.00760815	+	0.0529158i
$183$	3.10960			0.229868
$184$	−4.61074	−	1.31949i	−0.339908	−	0.0972744i
$185$	−0.373556			−0.0274644
$186$	−0.452612	+	3.14798i	−0.0331871	+	0.230821i
$187$	2.21230	+	4.84427i	0.161780	+	0.354248i
$188$	3.34016	+	0.980759i	0.243606	+	0.0715292i
$189$	−0.162099	−	0.187072i	−0.0117910	−	0.0136075i
$190$	7.70022	−	2.26099i	0.558632	−	0.164029i
$191$	16.6713	+	10.7140i	1.20629	+	0.775236i	0.980034	−	0.198832i	$-0.0637148\pi$
$191$	16.6713	+	10.7140i	1.20629	+	0.775236i	0.226257	+	0.974068i	$0.427351\pi$
$192$	0.415415	−	0.909632i	0.0299800	−	0.0656470i
$193$	−9.62317	+	11.1057i	−0.692691	+	0.799408i	−0.987746	−	0.156073i	$-0.950117\pi$
$193$	−9.62317	+	11.1057i	−0.692691	+	0.799408i	0.295055	+	0.955480i	$0.404662\pi$
$194$	−9.81279	+	6.30630i	−0.704518	+	0.452766i
$195$	−0.414651	−	2.88396i	−0.0296938	−	0.206525i
$196$	0.987484	+	6.86810i	0.0705346	+	0.490579i
$197$	−9.47647	+	6.09016i	−0.675170	+	0.433906i	−0.832786	−	0.553595i	$-0.813256\pi$
$197$	−9.47647	+	6.09016i	−0.675170	+	0.433906i	0.157616	+	0.987501i	$0.449619\pi$
$198$	−0.497078	+	0.573659i	−0.0353258	+	0.0407682i
$199$	5.64551	−	12.3619i	0.400199	−	0.876314i	−0.597051	−	0.802203i	$-0.703661\pi$
$199$	5.64551	−	12.3619i	0.400199	−	0.876314i	0.997250	−	0.0741107i	$-0.0236118\pi$
$200$	−0.841254	−	0.540641i	−0.0594856	−	0.0382291i
$201$	9.78074	−	2.87188i	0.689880	−	0.202567i
$202$	4.48662	+	5.17784i	0.315678	+	0.364312i
$203$	−1.82119	−	0.534751i	−0.127823	−	0.0375322i
$204$	−2.91453	−	6.38193i	−0.204058	−	0.446824i
$205$	−1.82174	+	12.6705i	−0.127236	+	0.884945i
$206$	−5.07532			−0.353614
$207$	−4.05223	−	2.56504i	−0.281649	−	0.178283i
$208$	−2.91362			−0.202023
$209$	−0.866937	+	6.02968i	−0.0599673	+	0.417081i
$210$	0.102829	+	0.225163i	0.00709585	+	0.0155377i
$211$	−11.3184	−	3.32337i	−0.779188	−	0.228790i	−0.132132	−	0.991232i	$-0.542182\pi$
$211$	−11.3184	−	3.32337i	−0.779188	−	0.228790i	−0.647057	+	0.762442i	$0.724000\pi$
$212$	−6.45391	−	7.44821i	−0.443256	−	0.511545i
$213$	3.50540	−	1.02928i	0.240186	−	0.0705249i
$214$	15.9804	+	10.2700i	1.09240	+	0.702043i
$215$	1.50964	−	3.30566i	0.102957	−	0.225444i
$216$	0.654861	−	0.755750i	0.0445576	−	0.0514222i
$217$	−0.662268	+	0.425614i	−0.0449577	+	0.0288926i
$218$	1.11036	+	7.72273i	0.0752031	+	0.523049i
$219$	−2.22177	−	15.4528i	−0.150133	−	1.04420i
$220$	0.638562	−	0.410379i	0.0430518	−	0.0276677i
$221$	−13.3865	+	15.4489i	−0.900476	+	1.03920i
$222$	−0.155181	+	0.339798i	−0.0104150	+	0.0228058i
$223$	4.39442	+	2.82412i	0.294272	+	0.189117i	0.679443	−	0.733728i	$-0.262221\pi$
$223$	4.39442	+	2.82412i	0.294272	+	0.189117i	−0.385171	+	0.922845i	$0.625858\pi$
$224$	0.237505	−	0.0697379i	0.0158690	−	0.00465956i
$225$	−0.654861	−	0.755750i	−0.0436574	−	0.0503833i
$226$	0.0534058	+	0.0156813i	0.00355250	+	0.00104311i
$227$	−3.97630	−	8.70687i	−0.263916	−	0.577896i	0.730561	−	0.682847i	$-0.239259\pi$
$227$	−3.97630	−	8.70687i	−0.263916	−	0.577896i	−0.994477	+	0.104952i	$0.966531\pi$
$228$	1.14212	−	7.94361i	0.0756387	−	0.526079i
$229$	10.4808			0.692589			0.346295	−	0.938126i	$-0.387440\pi$
$229$	10.4808			0.692589			0.346295	+	0.938126i	$0.387440\pi$
$230$	3.16543	+	3.60278i	0.208722	+	0.237561i
$231$	−0.187892			−0.0123624
$232$	1.09127	−	7.58997i	0.0716455	−	0.498306i
$233$	−10.3733	−	22.7144i	−0.679580	−	1.48807i	−0.863087	−	0.505055i	$-0.831472\pi$
$233$	−10.3733	−	22.7144i	−0.679580	−	1.48807i	0.183507	−	0.983018i	$-0.441255\pi$
$234$	−2.79560	−	0.820862i	−0.182754	−	0.0536614i
$235$	−2.27968	−	2.63089i	−0.148710	−	0.171621i
$236$	−13.1758	+	3.86877i	−0.857673	+	0.251835i
$237$	−7.14726	−	4.59327i	−0.464265	−	0.298365i
$238$	0.721440	−	1.57973i	0.0467640	−	0.102399i
$239$	4.57194	−	5.27629i	0.295734	−	0.341295i	−0.588365	−	0.808596i	$-0.700228\pi$
$239$	4.57194	−	5.27629i	0.295734	−	0.341295i	0.884098	+	0.467301i	$0.154773\pi$
$240$	−0.841254	+	0.540641i	−0.0543027	+	0.0348982i
$241$	0.413617	+	2.87677i	0.0266434	+	0.185309i	0.998797	−	0.0490354i	$-0.0156147\pi$
$241$	0.413617	+	2.87677i	0.0266434	+	0.185309i	−0.972154	+	0.234345i	$0.924706\pi$
$242$	−1.48347	−	10.3177i	−0.0953608	−	0.663249i
$243$	0.841254	−	0.540641i	0.0539664	−	0.0346821i
$244$	−2.03635	+	2.35008i	−0.130364	+	0.150448i
$245$	2.88245	−	6.31169i	0.184153	−	0.403239i
$246$	10.7687	+	6.92062i	0.686587	+	0.441243i
$247$	−22.4355	+	6.58766i	−1.42754	+	0.419163i
$248$	−2.08269	−	2.40355i	−0.132251	−	0.152626i
$249$	10.5897	+	3.10941i	0.671093	+	0.197051i
$250$	0.415415	+	0.909632i	0.0262732	+	0.0575302i
$251$	−0.876307	+	6.09485i	−0.0553120	+	0.384703i	0.943296	+	0.331953i	$0.107708\pi$
$251$	−0.876307	+	6.09485i	−0.0553120	+	0.384703i	−0.998608	+	0.0527499i	$0.983201\pi$
$252$	0.247532			0.0155931
$253$	−3.48573	+	1.04957i	−0.219146	+	0.0659860i
$254$	−20.6951			−1.29853
$255$	−0.998473	+	6.94453i	−0.0625268	+	0.434884i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−25.3782	−	7.45171i	−1.58305	−	0.464825i	−0.632283	−	0.774737i	$-0.717882\pi$
$257$	−25.3782	−	7.45171i	−1.58305	−	0.464825i	−0.950765	+	0.309912i	$0.899700\pi$
$258$	−2.37980	−	2.74644i	−0.148160	−	0.170986i
$259$	−0.0887215	+	0.0260510i	−0.00551288	+	0.00161873i
$260$	2.45109	+	1.57522i	0.152010	+	0.0976911i
$261$	3.18541	−	6.97507i	0.197172	−	0.431746i
$262$	0.741769	−	0.856047i	0.0458266	−	0.0528867i
$263$	13.0195	−	8.36711i	0.802815	−	0.515938i	−0.0737181	−	0.997279i	$-0.523487\pi$
$263$	13.0195	−	8.36711i	0.802815	−	0.515938i	0.876533	+	0.481341i	$0.159850\pi$
$264$	−0.108025	−	0.751334i	−0.00664851	−	0.0462414i
$265$	1.40257	+	9.75508i	0.0861591	+	0.599250i
$266$	1.67117	−	1.07399i	0.102466	−	0.0658508i
$267$	1.72920	−	1.99560i	0.105825	−	0.122129i
$268$	−4.23460	+	9.27247i	−0.258669	+	0.566406i
$269$	22.1137	+	14.2116i	1.34830	+	0.866497i	0.997549	−	0.0699732i	$-0.0222914\pi$
$269$	22.1137	+	14.2116i	1.34830	+	0.866497i	0.350747	+	0.936470i	$0.385928\pi$
$270$	−0.959493	+	0.281733i	−0.0583929	+	0.0171457i
$271$	−10.3517	−	11.9466i	−0.628824	−	0.725702i	0.348533	−	0.937296i	$-0.386680\pi$
$271$	−10.3517	−	11.9466i	−0.628824	−	0.725702i	−0.977357	+	0.211595i	$0.932134\pi$
$272$	6.73175	+	1.97662i	0.408172	+	0.119850i
$273$	−0.299603	−	0.656040i	−0.0181328	−	0.0397053i
$274$	−2.99009	+	20.7965i	−0.180638	+	1.25636i
$275$	−0.759060			−0.0457730
$276$	4.59217	−	1.38273i	0.276416	−	0.0832303i
$277$	20.0951			1.20740			0.603699	−	0.797212i	$-0.293693\pi$
$277$	20.0951			1.20740			0.603699	+	0.797212i	$0.293693\pi$
$278$	1.46124	−	10.1632i	0.0876396	−	0.609547i
$279$	−1.32117	−	2.89295i	−0.0790962	−	0.173196i
$280$	−0.237505	−	0.0697379i	−0.0141937	−	0.00416763i
$281$	−11.6516	−	13.4466i	−0.695075	−	0.802160i	0.293003	−	0.956111i	$-0.405345\pi$
$281$	−11.6516	−	13.4466i	−0.695075	−	0.802160i	−0.988078	+	0.153952i	$0.950800\pi$
$282$	−3.34016	+	0.980759i	−0.198904	+	0.0584033i
$283$	7.90611	+	5.08095i	0.469969	+	0.302031i	0.754106	−	0.656753i	$-0.228071\pi$
$283$	7.90611	+	5.08095i	0.469969	+	0.302031i	−0.284137	+	0.958784i	$0.591707\pi$
$284$	−1.51767	+	3.32324i	−0.0900572	+	0.197198i
$285$	−5.25545	+	6.06512i	−0.311306	+	0.359266i
$286$	−1.86053	+	1.19569i	−0.110015	+	0.0707025i
$287$	0.450939	+	3.13635i	0.0266181	+	0.185133i
$288$	0.142315	+	0.989821i	0.00838598	+	0.0583258i
$289$	27.1081	−	17.4213i	1.59460	−	1.02478i
$290$	−5.02148	+	5.79510i	−0.294872	+	0.340300i
$291$	4.84561	−	10.6104i	0.284054	−	0.621992i
$292$	13.1334	+	8.44030i	0.768572	+	0.493931i
$293$	25.1073	−	7.37216i	1.46678	−	0.430686i	0.551731	−	0.834022i	$-0.313967\pi$
$293$	25.1073	−	7.37216i	1.46678	−	0.430686i	0.915052	+	0.403336i	$0.132149\pi$
$294$	−4.54390	−	5.24394i	−0.265006	−	0.305833i
$295$	13.1758	+	3.86877i	0.767126	+	0.225248i
$296$	−0.155181	−	0.339798i	−0.00901969	−	0.0197504i
$297$	0.108025	−	0.751334i	0.00626827	−	0.0435968i
$298$	−2.79600			−0.161968
$299$	−9.22286	−	10.4971i	−0.533372	−	0.607065i
$300$	1.00000			0.0577350
$301$	0.128019	−	0.890391i	0.00737888	−	0.0513213i
$302$	−0.856789	−	1.87611i	−0.0493027	−	0.107958i
$303$	−6.57374	−	1.93022i	−0.377651	−	0.110888i
$304$	5.25545	+	6.06512i	0.301421	+	0.347858i
$305$	2.98364	−	0.876075i	0.170843	−	0.0501639i
$306$	5.90219	+	3.79311i	0.337406	+	0.216837i
$307$	4.49329	−	9.83892i	0.256445	−	0.561537i	−0.736994	−	0.675900i	$-0.763755\pi$
$307$	4.49329	−	9.83892i	0.256445	−	0.561537i	0.993439	+	0.114363i	$0.0364825\pi$
$308$	0.123043	−	0.141999i	0.00701102	−	0.00809115i
$309$	4.26963	−	2.74392i	0.242891	−	0.156096i
$310$	0.452612	+	3.14798i	0.0257066	+	0.178793i
$311$	3.60527	+	25.0752i	0.204436	+	1.42189i	0.790918	+	0.611923i	$0.209604\pi$
$311$	3.60527	+	25.0752i	0.204436	+	1.42189i	−0.586481	+	0.809963i	$0.699487\pi$
$312$	2.45109	−	1.57522i	0.138766	−	0.0891794i
$313$	0.816373	−	0.942145i	0.0461441	−	0.0532532i	−0.732208	−	0.681081i	$-0.761510\pi$
$313$	0.816373	−	0.942145i	0.0461441	−	0.0532532i	0.778352	+	0.627828i	$0.216056\pi$
$314$	−7.59897	+	16.6394i	−0.428835	+	0.939017i
$315$	−0.208237	−	0.133826i	−0.0117328	−	0.00754024i
$316$	8.15182	−	2.39359i	0.458576	−	0.134650i
$317$	4.45714	+	5.14381i	0.250338	+	0.288905i	0.866985	−	0.498334i	$-0.166055\pi$
$317$	4.45714	+	5.14381i	0.250338	+	0.288905i	−0.616647	+	0.787240i	$0.711509\pi$
$318$	9.45618	+	2.77659i	0.530276	+	0.155703i
$319$	−2.41792	−	5.29450i	−0.135377	−	0.296435i
$320$	0.142315	−	0.989821i	0.00795564	−	0.0553327i
$321$	−18.9960			−1.06025
$322$	1.00306	+	0.634930i	0.0558982	+	0.0353833i
$323$	56.3051			3.13290
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	−1.21036	−	2.65032i	−0.0671388	−	0.147013i
$326$	−9.48340	−	2.78458i	−0.525237	−	0.154224i
$327$	−5.10932	−	5.89647i	−0.282546	−	0.326075i
$328$	−12.2823	+	3.60640i	−0.678174	+	0.199130i
$329$	−0.724909	−	0.465871i	−0.0399656	−	0.0256843i
$330$	−0.315325	+	0.690465i	−0.0173581	+	0.0380088i
$331$	10.4877	−	12.1034i	0.576454	−	0.665263i	−0.390384	−	0.920652i	$-0.627658\pi$
$331$	10.4877	−	12.1034i	0.576454	−	0.665263i	0.966839	+	0.255388i	$0.0822034\pi$
$332$	−9.28469	+	5.96691i	−0.509564	+	0.327477i
$333$	−0.0531625	−	0.369753i	−0.00291329	−	0.0202624i
$334$	−2.58307	−	17.9656i	−0.141339	−	0.983035i
$335$	8.57544	−	5.51110i	0.468527	−	0.301104i
$336$	−0.162099	+	0.187072i	−0.00884323	+	0.0102056i
$337$	−3.26141	+	7.14148i	−0.177660	+	0.389021i	−0.977422	−	0.211296i	$-0.932232\pi$
$337$	−3.26141	+	7.14148i	−0.177660	+	0.389021i	0.799762	+	0.600317i	$0.204959\pi$
$338$	3.79474	+	2.43873i	0.206407	+	0.132650i
$339$	−0.0534058	+	0.0156813i	−0.00290060	+	0.000851694i
$340$	−4.59447	−	5.30230i	−0.249170	−	0.287558i
$341$	−2.31629	−	0.680124i	−0.125434	−	0.0368308i
$342$	3.33383	+	7.30007i	0.180273	+	0.394742i
$343$	0.491026	−	3.41516i	0.0265129	−	0.184402i
$344$	3.63406			0.195935
$345$	−4.61074	−	1.31949i	−0.248234	−	0.0710392i
$346$	−12.3806			−0.665584
$347$	1.61998	−	11.2672i	0.0869653	−	0.604857i	−0.899005	−	0.437938i	$-0.855709\pi$
$347$	1.61998	−	11.2672i	0.0869653	−	0.604857i	0.985971	−	0.166919i	$-0.0533819\pi$
$348$	3.18541	+	6.97507i	0.170756	+	0.373903i
$349$	8.31575	+	2.44172i	0.445132	+	0.130702i	0.496614	−	0.867971i	$-0.334576\pi$
$349$	8.31575	+	2.44172i	0.445132	+	0.130702i	−0.0514823	+	0.998674i	$0.516395\pi$
$350$	0.162099	+	0.187072i	0.00866456	+	0.00999944i
$351$	2.79560	−	0.820862i	0.149218	−	0.0438144i
$352$	0.638562	+	0.410379i	0.0340355	+	0.0218733i
$353$	−8.62438	+	18.8848i	−0.459029	+	1.00513i	0.528678	+	0.848822i	$0.322688\pi$
$353$	−8.62438	+	18.8848i	−0.459029	+	1.00513i	−0.987708	+	0.156312i	$0.950040\pi$
$354$	8.99259	−	10.3780i	0.477951	−	0.551585i
$355$	3.07342	−	1.97517i	0.163120	−	0.104831i
$356$	0.375791	+	2.61368i	0.0199169	+	0.138525i
$357$	0.247154	+	1.71900i	0.0130808	+	0.0909789i
$358$	2.47879	−	1.59302i	0.131008	−	0.0841940i
$359$	6.37551	−	7.35773i	0.336487	−	0.388326i	−0.562139	−	0.827043i	$-0.690021\pi$
$359$	6.37551	−	7.35773i	0.336487	−	0.388326i	0.898625	+	0.438717i	$0.144567\pi$
$360$	0.415415	−	0.909632i	0.0218943	−	0.0479418i
$361$	38.1975	+	24.5480i	2.01039	+	1.29200i
$362$	20.2225	−	5.93787i	1.06287	−	0.312087i
$363$	6.82616	+	7.87780i	0.358280	+	0.413477i
$364$	0.692000	+	0.203190i	0.0362707	+	0.0106500i
$365$	−6.48532	−	14.2009i	−0.339457	−	0.743307i
$366$	0.442542	−	3.07795i	0.0231320	−	0.160887i
$367$	−20.5556			−1.07299			−0.536497	−	0.843902i	$-0.680253\pi$
$367$	−20.5556			−1.07299			−0.536497	+	0.843902i	$0.680253\pi$
$368$	−1.96224	+	4.37603i	−0.102289	+	0.228116i
$369$	−12.8008			−0.666382
$370$	−0.0531625	+	0.369753i	−0.00276379	+	0.0192226i
$371$	1.01342	+	2.21907i	0.0526139	+	0.115208i
$372$	3.05153	+	0.896009i	0.158214	+	0.0464559i
$373$	5.68881	+	6.56524i	0.294555	+	0.339935i	0.883667	−	0.468117i	$-0.155067\pi$
$373$	5.68881	+	6.56524i	0.294555	+	0.339935i	−0.589111	+	0.808052i	$0.700522\pi$
$374$	5.10980	−	1.50037i	0.264222	−	0.0775824i
$375$	−0.841254	−	0.540641i	−0.0434421	−	0.0279186i
$376$	1.44613	−	3.16658i	0.0745785	−	0.163304i
$377$	14.6307	−	16.8847i	0.753519	−	0.869607i
$378$	−0.208237	+	0.133826i	−0.0107106	+	0.00688327i
$379$	2.59439	+	18.0444i	0.133265	+	0.926879i	0.941258	+	0.337687i	$0.109645\pi$
$379$	2.59439	+	18.0444i	0.133265	+	0.926879i	−0.807993	+	0.589192i	$0.799446\pi$
$380$	−1.14212	−	7.94361i	−0.0585895	−	0.407499i
$381$	17.4098	−	11.1886i	0.891932	−	0.573210i
$382$	12.9775	−	14.9768i	0.663986	−	0.766281i
$383$	13.2788	−	29.0765i	0.678515	−	1.48574i	−0.185693	−	0.982608i	$-0.559453\pi$
$383$	13.2788	−	29.0765i	0.678515	−	1.48574i	0.864209	−	0.503134i	$-0.167820\pi$
$384$	−0.841254	−	0.540641i	−0.0429300	−	0.0275895i
$385$	−0.180281	+	0.0529352i	−0.00918796	+	0.00269783i
$386$	9.62317	+	11.1057i	0.489806	+	0.565267i
$387$	3.48685	+	1.02383i	0.177247	+	0.0520444i
$388$	4.84561	+	10.6104i	0.245998	+	0.538661i
$389$	3.11004	−	21.6308i	0.157685	−	1.09672i	−0.745200	−	0.666842i	$-0.767646\pi$
$389$	3.11004	−	21.6308i	0.157685	−	1.09672i	0.902885	−	0.429883i	$-0.141445\pi$
$390$	−2.91362			−0.147537
$391$	14.1876	+	30.5099i	0.717495	+	1.54295i
$392$	6.93873			0.350459
$393$	−0.161202	+	1.12118i	−0.00813155	+	0.0565562i
$394$	4.67953	+	10.2467i	0.235751	+	0.516223i
$395$	−8.15182	−	2.39359i	−0.410163	−	0.120435i
$396$	0.497078	+	0.573659i	0.0249791	+	0.0288275i
$397$	−31.7195	+	9.31368i	−1.59195	+	0.467440i	−0.953293	−	0.302048i	$-0.902330\pi$
$397$	−31.7195	+	9.31368i	−1.59195	+	0.467440i	−0.638662	+	0.769488i	$0.720512\pi$
$398$	−11.4327	−	7.34733i	−0.573068	−	0.368288i
$399$	−0.825230	+	1.80700i	−0.0413132	+	0.0904632i
$400$	−0.654861	+	0.755750i	−0.0327430	+	0.0377875i
$401$	0.766423	−	0.492550i	0.0382733	−	0.0245968i	−0.521364	−	0.853334i	$-0.674577\pi$
$401$	0.766423	−	0.492550i	0.0382733	−	0.0245968i	0.559638	+	0.828737i	$0.310940\pi$
$402$	−1.45071	−	10.0899i	−0.0723547	−	0.503238i
$403$	−1.31874	−	9.17202i	−0.0656910	−	0.456891i
$404$	5.76365	−	3.70407i	0.286752	−	0.184285i
$405$	0.654861	−	0.755750i	0.0325403	−	0.0375535i
$406$	−0.788491	+	1.72655i	−0.0391322	+	0.0856875i
$407$	−0.238538	−	0.153299i	−0.0118239	−	0.00759876i
$408$	−6.73175	+	1.97662i	−0.333271	+	0.0978573i
$409$	−5.07957	−	5.86214i	−0.251169	−	0.289864i	0.616138	−	0.787638i	$-0.288696\pi$
$409$	−5.07957	−	5.86214i	−0.251169	−	0.289864i	−0.867307	+	0.497774i	$0.834151\pi$
$410$	12.2823	+	3.60640i	0.606578	+	0.178107i
$411$	−8.72803	−	19.1117i	−0.430522	−	0.942712i
$412$	−0.722293	+	5.02366i	−0.0355848	+	0.247498i
$413$	3.39913			0.167260
$414$	−3.11563	+	3.64594i	−0.153125	+	0.179188i
$415$	11.0367			0.541772
$416$	−0.414651	+	2.88396i	−0.0203300	+	0.141398i
$417$	4.26535	+	9.33981i	0.208875	+	0.457373i
$418$	5.84492	+	1.71622i	0.285885	+	0.0839433i
$419$	−9.41388	−	10.8642i	−0.459898	−	0.530751i	0.477676	−	0.878536i	$-0.341479\pi$
$419$	−9.41388	−	10.8642i	−0.459898	−	0.530751i	−0.937574	+	0.347785i	$0.886934\pi$
$420$	0.237505	−	0.0697379i	0.0115891	−	0.00340286i
$421$	−5.71150	−	3.67056i	−0.278361	−	0.178892i	0.394010	−	0.919106i	$-0.371088\pi$
$421$	−5.71150	−	3.67056i	−0.278361	−	0.178892i	−0.672371	+	0.740214i	$0.734724\pi$
$422$	−4.90032	+	10.7302i	−0.238544	+	0.522338i
$423$	2.27968	−	2.63089i	0.110842	−	0.127918i
$424$	−8.29089	+	5.32823i	−0.402641	+	0.258762i
$425$	0.998473	+	6.94453i	0.0484331	+	0.336859i
$426$	−0.519931	−	3.61620i	−0.0251907	−	0.175205i
$427$	0.647534	−	0.416145i	0.0313364	−	0.0201387i
$428$	12.4397	−	14.3562i	0.601296	−	0.693933i
$429$	0.918737	−	2.01175i	0.0443570	−	0.0971283i
$430$	−3.05717	−	1.96472i	−0.147430	−	0.0947473i
$431$	−25.7963	+	7.57447i	−1.24256	+	0.364849i	−0.835978	−	0.548763i	$-0.815099\pi$
$431$	−25.7963	+	7.57447i	−1.24256	+	0.364849i	−0.406585	+	0.913613i	$0.633281\pi$
$432$	−0.654861	−	0.755750i	−0.0315070	−	0.0363610i
$433$	12.1982	+	3.58171i	0.586208	+	0.172126i	0.561369	−	0.827565i	$-0.310275\pi$
$433$	12.1982	+	3.58171i	0.586208	+	0.172126i	0.0248384	+	0.999691i	$0.492093\pi$
$434$	0.327031	+	0.716098i	0.0156980	+	0.0343738i
$435$	1.09127	−	7.58997i	0.0523225	−	0.363911i
$436$	7.80215			0.373655
$437$	−5.21553	+	38.1330i	−0.249493	+	1.82415i
$438$	−15.6117			−0.745954
$439$	0.489611	−	3.40532i	0.0233679	−	0.162527i	−0.974796	−	0.223098i	$-0.928383\pi$
$439$	0.489611	−	3.40532i	0.0233679	−	0.162527i	0.998164	+	0.0605709i	$0.0192921\pi$
$440$	−0.315325	−	0.690465i	−0.0150325	−	0.0329166i
$441$	6.65766	+	1.95487i	0.317031	+	0.0930888i
$442$	13.3865	+	15.4489i	0.636732	+	0.734828i
$443$	23.7826	−	6.98320i	1.12994	−	0.331782i	0.337259	−	0.941412i	$-0.390500\pi$
$443$	23.7826	−	6.98320i	1.12994	−	0.331782i	0.792686	+	0.609630i	$0.208682\pi$
$444$	0.314255	+	0.201959i	0.0149139	+	0.00958457i
$445$	1.09693	−	2.40194i	0.0519994	−	0.113863i
$446$	3.42076	−	3.94777i	0.161978	−	0.186932i
$447$	2.35214	−	1.51163i	0.111253	−	0.0714977i
$448$	−0.0352275	−	0.245013i	−0.00166434	−	0.0115758i
$449$	3.99444	+	27.7820i	0.188509	+	1.31111i	0.835870	+	0.548928i	$0.184964\pi$
$449$	3.99444	+	27.7820i	0.188509	+	1.31111i	−0.647360	+	0.762184i	$0.724127\pi$
$450$	−0.841254	+	0.540641i	−0.0396571	+	0.0254861i
$451$	−6.36299	+	7.34328i	−0.299622	+	0.345782i
$452$	0.0231222	−	0.0506305i	0.00108758	−	0.00238146i
$453$	1.73508	+	1.11507i	0.0815210	+	0.0523904i
$454$	−9.18414	+	2.69671i	−0.431033	+	0.126563i
$455$	−0.472295	−	0.545058i	−0.0221415	−	0.0255527i
$456$	−7.70022	−	2.26099i	−0.360596	−	0.105880i
$457$	0.128363	+	0.281076i	0.00600456	+	0.0131482i	0.912611	−	0.408830i	$-0.134063\pi$
$457$	0.128363	+	0.281076i	0.00600456	+	0.0131482i	−0.906606	+	0.421978i	$0.861336\pi$
$458$	1.49157	−	10.3741i	0.0696965	−	0.484750i
$459$	−7.01595			−0.327476
$460$	4.01660	−	2.62048i	0.187275	−	0.122181i
$461$	−20.4790			−0.953802			−0.476901	−	0.878957i	$-0.658240\pi$
$461$	−20.4790			−0.953802			−0.476901	+	0.878957i	$0.658240\pi$
$462$	−0.0267398	+	0.185979i	−0.00124405	+	0.00865254i
$463$	0.611236	+	1.33842i	0.0284065	+	0.0622017i	0.923303	−	0.384071i	$-0.125478\pi$
$463$	0.611236	+	1.33842i	0.0284065	+	0.0622017i	−0.894897	+	0.446273i	$0.852751\pi$
$464$	−7.35741	−	2.16033i	−0.341559	−	0.100291i
$465$	−2.08269	−	2.40355i	−0.0965824	−	0.111462i
$466$	−23.9595	+	7.03515i	−1.10990	+	0.325897i
$467$	15.8045	+	10.1569i	0.731343	+	0.470006i	0.852566	−	0.522620i	$-0.175045\pi$
$467$	15.8045	+	10.1569i	0.731343	+	0.470006i	−0.121223	+	0.992625i	$0.538682\pi$
$468$	−1.21036	+	2.65032i	−0.0559490	+	0.122511i
$469$	1.65238	−	1.90695i	0.0762999	−	0.0880548i
$470$	−2.92855	+	1.88206i	−0.135084	+	0.0868131i
$471$	−2.60329	−	18.1063i	−0.119953	−	0.834294i
$472$	1.95428	+	13.5923i	0.0899529	+	0.625636i
$473$	2.32057	−	1.49134i	0.106700	−	0.0685719i
$474$	−5.56368	+	6.42083i	−0.255548	+	0.294918i
$475$	−3.33383	+	7.30007i	−0.152967	+	0.334950i
$476$	−1.46098	−	0.938916i	−0.0669640	−	0.0430351i
$477$	−9.45618	+	2.77659i	−0.432969	+	0.127131i
$478$	−4.57194	−	5.27629i	−0.209115	−	0.241332i
$479$	−15.6248	−	4.58785i	−0.713914	−	0.209624i	−0.0954465	−	0.995435i	$-0.530428\pi$
$479$	−15.6248	−	4.58785i	−0.713914	−	0.209624i	−0.618467	+	0.785811i	$0.712246\pi$
$480$	0.415415	+	0.909632i	0.0189610	+	0.0415188i
$481$	0.154895	−	1.07732i	0.00706262	−	0.0491216i
$482$	2.90635			0.132381
$483$	−1.18709	+	0.00815640i	−0.0540147	+	0.000371129i
$484$	−10.4238			−0.473810
$485$	1.66003	−	11.5458i	0.0753781	−	0.524266i
$486$	−0.415415	−	0.909632i	−0.0188436	−	0.0412617i
$487$	16.4854	+	4.84054i	0.747024	+	0.219346i	0.633021	−	0.774134i	$-0.281815\pi$
$487$	16.4854	+	4.84054i	0.747024	+	0.219346i	0.114003	+	0.993480i	$0.463633\pi$
$488$	2.03635	+	2.35008i	0.0921814	+	0.106383i
$489$	9.48340	−	2.78458i	0.428854	−	0.125923i
$490$	−5.83723	−	3.75136i	−0.263699	−	0.169469i
$491$	5.64101	−	12.3521i	0.254575	−	0.557442i	−0.738591	−	0.674154i	$-0.764508\pi$
$491$	5.64101	−	12.3521i	0.254575	−	0.557442i	0.993166	+	0.116712i	$0.0372355\pi$
$492$	8.38273	−	9.67418i	0.377923	−	0.436146i
$493$	−45.2581	+	29.0856i	−2.03832	+	1.30995i
$494$	3.32770	+	23.1447i	0.149720	+	1.04133i
$495$	−0.108025	−	0.751334i	−0.00485538	−	0.0337699i
$496$	−2.67548	+	1.71943i	−0.120133	+	0.0772046i
$497$	0.592210	−	0.683447i	0.0265643	−	0.0306568i
$498$	4.58483	−	10.0394i	0.205451	−	0.449875i
$499$	5.08949	+	3.27081i	0.227837	+	0.146422i	0.649579	−	0.760294i	$-0.274945\pi$
$499$	5.08949	+	3.27081i	0.227837	+	0.146422i	−0.421743	+	0.906716i	$0.638581\pi$
$500$	0.959493	−	0.281733i	0.0429098	−	0.0125995i
$501$	11.8860	+	13.7171i	0.531026	+	0.612836i
$502$	5.90810	+	1.73477i	0.263691	+	0.0774268i
$503$	1.03572	+	2.26791i	0.0461804	+	0.101121i	0.931316	−	0.364212i	$-0.118662\pi$
$503$	1.03572	+	2.26791i	0.0461804	+	0.101121i	−0.885136	+	0.465333i	$0.845934\pi$
$504$	0.0352275	−	0.245013i	0.00156916	−	0.0109137i
$505$	−6.85126			−0.304877
$506$	0.542817	+	3.59962i	0.0241311	+	0.160023i
$507$	−4.51082			−0.200332
$508$	−2.94522	+	20.4845i	−0.130673	+	0.908851i
$509$	5.82961	+	12.7651i	0.258393	+	0.565801i	0.993718	−	0.111913i	$-0.0356978\pi$
$509$	5.82961	+	12.7651i	0.258393	+	0.565801i	−0.735325	+	0.677714i	$0.762971\pi$
$510$	6.73175	+	1.97662i	0.298087	+	0.0875262i
$511$	−2.53064	−	2.92051i	−0.111949	−	0.129196i
$512$	0.959493	−	0.281733i	0.0424040	−	0.0124509i
$513$	−6.75131	−	4.33880i	−0.298078	−	0.191563i
$514$	−10.9876	+	24.0594i	−0.484640	+	1.06121i
$515$	3.32362	−	3.83567i	0.146456	−	0.169020i
$516$	−3.05717	+	1.96472i	−0.134584	+	0.0864920i
$517$	−0.376055	−	2.61552i	−0.0165389	−	0.115030i
$518$	0.0131594	+	0.0915259i	0.000578192	+	0.00402142i
$519$	10.4152	−	6.69344i	0.457177	−	0.293810i
$520$	1.90802	−	2.20197i	0.0836720	−	0.0965626i
$521$	9.97156	−	21.8347i	0.436862	−	0.956594i	−0.555302	−	0.831649i	$-0.687397\pi$
$521$	9.97156	−	21.8347i	0.436862	−	0.956594i	0.992164	−	0.124945i	$-0.0398755\pi$
$522$	−6.45074	−	4.14564i	−0.282341	−	0.181450i
$523$	3.33252	−	0.978516i	0.145721	−	0.0427875i	−0.208059	−	0.978116i	$-0.566714\pi$
$523$	3.33252	−	0.978516i	0.145721	−	0.0427875i	0.353780	+	0.935329i	$0.384896\pi$
$524$	−0.741769	−	0.856047i	−0.0324043	−	0.0373966i
$525$	−0.237505	−	0.0697379i	−0.0103656	−	0.00304361i
$526$	−6.42908	−	14.0777i	−0.280321	−	0.613818i
$527$	−3.17550	+	22.0861i	−0.138327	+	0.962084i
$528$	−0.759060			−0.0330338
$529$	−21.9772	+	6.78248i	−0.955531	+	0.294890i
$530$	9.85540			0.428091
$531$	−1.95428	+	13.5923i	−0.0848084	+	0.589855i
$532$	−0.825230	−	1.80700i	−0.0357783	−	0.0783435i
$533$	−35.7858	−	10.5077i	−1.55006	−	0.455138i
$534$	−1.72920	−	1.99560i	−0.0748297	−	0.0863581i
$535$	−18.2265	+	5.35178i	−0.788000	+	0.231378i
$536$	8.57544	+	5.51110i	0.370403	+	0.238043i
$537$	−1.22404	+	2.68028i	−0.0528213	+	0.115662i
$538$	17.2141	−	19.8661i	0.742151	−	0.856488i
$539$	4.43081	−	2.84751i	0.190848	−	0.122651i
$540$	0.142315	+	0.989821i	0.00612426	+	0.0425951i
$541$	−5.39983	−	37.5567i	−0.232157	−	1.61469i	−0.688742	−	0.725007i	$-0.741837\pi$
$541$	−5.39983	−	37.5567i	−0.232157	−	1.61469i	0.456585	−	0.889680i	$-0.349073\pi$
$542$	−13.2982	+	8.54621i	−0.571205	+	0.367091i
$543$	−13.8020	+	15.9284i	−0.592301	+	0.683552i
$544$	2.91453	−	6.38193i	0.124959	−	0.273623i
$545$	−6.56358	−	4.21816i	−0.281153	−	0.180686i
$546$	−0.692000	+	0.203190i	−0.0296149	+	0.00869571i
$547$	0.900452	+	1.03918i	0.0385005	+	0.0444320i	0.774673	−	0.632362i	$-0.217914\pi$
$547$	0.900452	+	1.03918i	0.0385005	+	0.0444320i	−0.736173	+	0.676794i	$0.763369\pi$
$548$	20.1593	+	5.91931i	0.861164	+	0.252860i
$549$	1.29177	+	2.82859i	0.0551316	+	0.120721i
$550$	−0.108025	+	0.751334i	−0.00460622	+	0.0320370i
$551$	−61.5381			−2.62161
$552$	−0.715117	−	4.74222i	−0.0304374	−	0.201842i
$553$	−2.10303			−0.0894297
$554$	2.85983	−	19.8906i	0.121503	−	0.845070i
$555$	−0.155181	−	0.339798i	−0.00658705	−	0.0144236i
$556$	−9.85177	−	2.89274i	−0.417808	−	0.122680i
$557$	23.0787	+	26.6342i	0.977876	+	1.12853i	0.991693	+	0.128624i	$0.0410561\pi$
$557$	23.0787	+	26.6342i	0.977876	+	1.12853i	−0.0138178	+	0.999905i	$0.504398\pi$
$558$	−3.05153	+	0.896009i	−0.129181	+	0.0379311i
$559$	8.90742	+	5.72445i	0.376744	+	0.242118i
$560$	−0.102829	+	0.225163i	−0.00434530	+	0.00951488i
$561$	−3.48748	+	4.02476i	−0.147241	+	0.169926i
$562$	−14.9680	+	9.61933i	−0.631386	+	0.405767i
$563$	4.07707	+	28.3566i	0.171828	+	1.19509i	0.875019	+	0.484089i	$0.160849\pi$
$563$	4.07707	+	28.3566i	0.171828	+	1.19509i	−0.703191	+	0.711001i	$0.748242\pi$
$564$	0.495422	+	3.44574i	0.0208610	+	0.145092i
$565$	−0.0468245	+	0.0300923i	−0.00196992	+	0.00126599i
$566$	6.15439	−	7.10254i	0.258688	−	0.298542i
$567$	0.102829	−	0.225163i	0.00431839	−	0.00945596i
$568$	3.07342	+	1.97517i	0.128958	+	0.0828763i
$569$	−4.52820	+	1.32960i	−0.189832	+	0.0557397i	−0.375267	−	0.926917i	$-0.622449\pi$
$569$	−4.52820	+	1.32960i	−0.189832	+	0.0557397i	0.185435	+	0.982657i	$0.440631\pi$
$570$	5.25545	+	6.06512i	0.220127	+	0.254040i
$571$	11.3948	+	3.34582i	0.476859	+	0.140018i	0.511325	−	0.859388i	$-0.329155\pi$
$571$	11.3948	+	3.34582i	0.476859	+	0.140018i	−0.0344661	+	0.999406i	$0.510973\pi$
$572$	0.918737	+	2.01175i	0.0384143	+	0.0841156i
$573$	−2.82028	+	19.6155i	−0.117819	+	0.819447i
$574$	3.16860			0.132255
$575$	−4.79572	+	0.0329509i	−0.199995	+	0.00137415i
$576$	1.00000			0.0416667
$577$	−3.71665	+	25.8499i	−0.154726	+	1.07614i	0.753435	+	0.657522i	$0.228396\pi$
$577$	−3.71665	+	25.8499i	−0.154726	+	1.07614i	−0.908161	+	0.418621i	$0.862514\pi$
$578$	−13.3861	−	29.3115i	−0.556789	−	1.21920i
$579$	−14.0997	−	4.14006i	−0.585965	−	0.172055i
$580$	5.02148	+	5.79510i	0.208506	+	0.240628i
$581$	2.62128	−	0.769678i	0.108749	−	0.0319316i
$582$	−9.81279	−	6.30630i	−0.406753	−	0.261405i
$583$	−3.10765	+	6.80481i	−0.128706	+	0.281826i
$584$	10.2235	−	11.7985i	0.423050	−	0.488225i
$585$	2.45109	−	1.57522i	0.101340	−	0.0651274i
$586$	−3.72399	−	25.9009i	−0.153836	−	1.06996i
$587$	−1.89665	−	13.1915i	−0.0782833	−	0.544472i	−0.990790	−	0.135410i	$-0.956765\pi$
$587$	−1.89665	−	13.1915i	−0.0782833	−	0.544472i	0.912506	−	0.409062i	$-0.134144\pi$
$588$	−5.83723	+	3.75136i	−0.240723	+	0.154703i
$589$	−16.7142	+	19.2892i	−0.688697	+	0.794798i
$590$	5.70451	−	12.4911i	0.234851	−	0.514252i
$591$	−9.47647	−	6.09016i	−0.389810	−	0.250516i
$592$	−0.358424	+	0.105243i	−0.0147311	+	0.00432545i
$593$	−5.16759	−	5.96372i	−0.212208	−	0.244901i	0.639660	−	0.768658i	$-0.279075\pi$
$593$	−5.16759	−	5.96372i	−0.212208	−	0.244901i	−0.851867	+	0.523758i	$0.824530\pi$
$594$	−0.728312	−	0.213852i	−0.0298830	−	0.00877445i
$595$	0.721440	+	1.57973i	0.0295761	+	0.0647627i
$596$	−0.397912	+	2.76754i	−0.0162991	+	0.113363i
$597$	13.5900			0.556203
$598$	−11.7028	+	7.63509i	−0.478565	+	0.312222i
$599$	2.92435			0.119486			0.0597429	−	0.998214i	$-0.480972\pi$
$599$	2.92435			0.119486			0.0597429	+	0.998214i	$0.480972\pi$
$600$	0.142315	−	0.989821i	0.00580998	−	0.0404093i
$601$	−3.48553	−	7.63225i	−0.142178	−	0.311326i	0.825125	−	0.564950i	$-0.191105\pi$
$601$	−3.48553	−	7.63225i	−0.142178	−	0.311326i	−0.967303	+	0.253624i	$0.918377\pi$
$602$	−0.863109	−	0.253432i	−0.0351777	−	0.0103291i
$603$	6.67542	+	7.70385i	0.271844	+	0.313725i
$604$	−1.97894	+	0.581070i	−0.0805221	+	0.0236434i
$605$	8.76908	+	5.63555i	0.356514	+	0.229118i
$606$	−2.84612	+	6.23213i	−0.115616	+	0.253163i
$607$	−7.49717	+	8.65220i	−0.304301	+	0.351182i	−0.887219	−	0.461349i	$-0.847365\pi$
$607$	−7.49717	+	8.65220i	−0.304301	+	0.351182i	0.582918	+	0.812531i	$0.301911\pi$
$608$	6.75131	−	4.33880i	0.273802	−	0.175962i
$609$	−0.270125	−	1.87876i	−0.0109460	−	0.0761312i
$610$	−0.442542	−	3.07795i	−0.0179180	−	0.124622i
$611$	8.53267	−	5.48362i	0.345195	−	0.221843i
$612$	4.59447	−	5.30230i	0.185720	−	0.214333i
$613$	−1.49730	+	3.27864i	−0.0604755	+	0.132423i	−0.937457	−	0.348102i	$-0.886826\pi$
$613$	−1.49730	+	3.27864i	−0.0604755	+	0.132423i	0.876981	+	0.480525i	$0.159554\pi$
$614$	−9.09932	−	5.84778i	−0.367219	−	0.235997i
$615$	−12.2823	+	3.60640i	−0.495269	+	0.145424i
$616$	−0.123043	−	0.141999i	−0.00495754	−	0.00572131i
$617$	−17.5538	−	5.15427i	−0.706691	−	0.207503i	−0.0914125	−	0.995813i	$-0.529138\pi$
$617$	−17.5538	−	5.15427i	−0.706691	−	0.207503i	−0.615278	+	0.788310i	$0.710956\pi$
$618$	−2.10836	−	4.61667i	−0.0848108	−	0.185710i
$619$	2.19461	−	15.2638i	0.0882088	−	0.613506i	−0.896985	−	0.442061i	$-0.854247\pi$
$619$	2.19461	−	15.2638i	0.0882088	−	0.613506i	0.985194	−	0.171445i	$-0.0548435\pi$
$620$	3.18035			0.127726
$621$	0.649886	−	4.75159i	0.0260790	−	0.190675i
$622$	25.3331			1.01576
$623$	0.0930203	−	0.646970i	0.00372678	−	0.0259203i
$624$	−1.21036	−	2.65032i	−0.0484532	−	0.106098i
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$	−0.816373	−	0.942145i	−0.0326288	−	0.0376557i
$627$	−5.84492	+	1.71622i	−0.233424	+	0.0685394i
$628$	15.3886	+	9.88966i	0.614073	+	0.394640i
$629$	−1.08874	+	2.38401i	−0.0434109	+	0.0950566i
$630$	−0.162099	+	0.187072i	−0.00645818	+	0.00745314i
$631$	−17.5047	+	11.2496i	−0.696852	+	0.447840i	−0.840516	−	0.541787i	$-0.817748\pi$
$631$	−17.5047	+	11.2496i	−0.696852	+	0.447840i	0.143664	+	0.989627i	$0.454112\pi$
$632$	−1.20910	−	8.40949i	−0.0480955	−	0.334512i
$633$	−1.67877	−	11.6761i	−0.0667253	−	0.464084i
$634$	5.72577	−	3.67973i	0.227400	−	0.146141i
$635$	13.5524	−	15.6403i	0.537811	−	0.620667i
$636$	4.09408	−	8.96478i	0.162341	−	0.355477i
$637$	17.0075	+	10.9300i	0.673860	+	0.433064i
$638$	−5.58471	+	1.63982i	−0.221101	+	0.0649211i
$639$	2.39246	+	2.76104i	0.0946442	+	0.109225i
$640$	−0.959493	−	0.281733i	−0.0379273	−	0.0111365i
$641$	−15.0312	−	32.9137i	−0.593697	−	1.30001i	−0.933182	−	0.359403i	$-0.882980\pi$
$641$	−15.0312	−	32.9137i	−0.593697	−	1.30001i	0.339486	−	0.940611i	$-0.389747\pi$
$642$	−2.70341	+	18.8026i	−0.106695	+	0.742080i
$643$	−17.4582			−0.688485			−0.344243	−	0.938881i	$-0.611864\pi$
$643$	−17.4582			−0.688485			−0.344243	+	0.938881i	$0.611864\pi$
$644$	0.771217	−	0.902487i	0.0303902	−	0.0355630i
$645$	3.63406			0.143091
$646$	8.01305	−	55.7320i	0.315269	−	2.19274i
$647$	−14.0581	−	30.7830i	−0.552681	−	1.21020i	−0.955518	−	0.294931i	$-0.904703\pi$
$647$	−14.0581	−	30.7830i	−0.552681	−	1.21020i	0.402837	−	0.915272i	$-0.368024\pi$
$648$	0.959493	+	0.281733i	0.0376924	+	0.0110675i
$649$	6.82591	+	7.87752i	0.267941	+	0.309220i
$650$	−2.79560	+	0.820862i	−0.109652	+	0.0321968i
$651$	−0.662268	−	0.425614i	−0.0259563	−	0.0166811i
$652$	−4.10586	+	8.99059i	−0.160798	+	0.352099i
$653$	−4.81383	+	5.55546i	−0.188380	+	0.217402i	−0.842081	−	0.539351i	$-0.818670\pi$
$653$	−4.81383	+	5.55546i	−0.188380	+	0.217402i	0.653701	+	0.756753i	$0.273215\pi$
$654$	−6.56358	+	4.21816i	−0.256656	+	0.164943i
$655$	0.161202	+	1.12118i	0.00629867	+	0.0438082i
$656$	1.82174	+	12.6705i	0.0711270	+	0.494699i
$657$	13.1334	−	8.44030i	0.512381	−	0.329287i
$658$	−0.564294	+	0.651231i	−0.0219985	+	0.0253876i
$659$	17.2305	−	37.7295i	0.671204	−	1.46973i	−0.200498	−	0.979694i	$-0.564256\pi$
$659$	17.2305	−	37.7295i	0.671204	−	1.46973i	0.871702	−	0.490037i	$-0.163017\pi$
$660$	0.638562	+	0.410379i	0.0248560	+	0.0159740i
$661$	0.685134	−	0.201174i	0.0266486	−	0.00782474i	−0.268381	−	0.963313i	$-0.586489\pi$
$661$	0.685134	−	0.201174i	0.0266486	−	0.00782474i	0.295030	+	0.955488i	$0.404670\pi$
$662$	−10.4877	−	12.1034i	−0.407615	−	0.470412i
$663$	−19.6138	−	5.75912i	−0.761736	−	0.223666i
$664$	4.58483	+	10.0394i	0.177926	+	0.389603i
$665$	−0.282711	+	1.96630i	−0.0109631	+	0.0762498i
$666$	−0.373556			−0.0144750
$667$	−15.5062	−	33.3455i	−0.600401	−	1.29114i
$668$	−18.1504			−0.702259
$669$	−0.743403	+	5.17048i	−0.0287416	+	0.199902i
$670$	−4.23460	−	9.27247i	−0.163597	−	0.358227i
$671$	2.26476	+	0.664993i	0.0874301	+	0.0256718i
$672$	0.162099	+	0.187072i	0.00625311	+	0.00721647i
$673$	35.6868	−	10.4786i	1.37563	−	0.403920i	0.491381	−	0.870945i	$-0.336492\pi$
$673$	35.6868	−	10.4786i	1.37563	−	0.403920i	0.884244	+	0.467025i	$0.154674\pi$
$674$	6.60465	+	4.24455i	0.254401	+	0.163494i
$675$	0.415415	−	0.909632i	0.0159893	−	0.0350118i
$676$	2.95396	−	3.40905i	0.113614	−	0.131117i
$677$	−2.78383	+	1.78906i	−0.106991	+	0.0687590i	−0.593042	−	0.805171i	$-0.702073\pi$
$677$	−2.78383	+	1.78906i	−0.106991	+	0.0687590i	0.486051	+	0.873930i	$0.338437\pi$
$678$	0.00792130	+	0.0550939i	0.000304216	+	0.00211587i
$679$	−0.410911	−	2.85795i	−0.0157693	−	0.109678i
$680$	−5.90219	+	3.79311i	−0.226339	+	0.145459i
$681$	6.26824	−	7.23393i	0.240199	−	0.277205i
$682$	−1.00284	+	2.19592i	−0.0384009	+	0.0840862i
$683$	33.6342	+	21.6154i	1.28698	+	0.827091i	0.991732	−	0.128330i	$-0.0409616\pi$
$683$	33.6342	+	21.6154i	1.28698	+	0.827091i	0.295247	+	0.955421i	$0.404598\pi$
$684$	7.70022	−	2.26099i	0.294425	−	0.0864510i
$685$	−13.7589	−	15.8786i	−0.525700	−	0.606690i
$686$	−3.31052	−	0.972057i	−0.126396	−	0.0371133i
$687$	4.35387	+	9.53365i	0.166111	+	0.363731i
$688$	0.517181	−	3.59707i	0.0197173	−	0.137137i
$689$	−28.7149			−1.09395
$690$	−1.96224	+	4.37603i	−0.0747012	+	0.166593i
$691$	−7.75637			−0.295066			−0.147533	−	0.989057i	$-0.547133\pi$
$691$	−7.75637			−0.295066			−0.147533	+	0.989057i	$0.547133\pi$
$692$	−1.76194	+	12.2546i	−0.0669789	+	0.465848i
$693$	−0.0780530	−	0.170912i	−0.00296499	−	0.00649242i
$694$	−10.9220	−	3.20699i	−0.414594	−	0.121736i
$695$	6.72390	+	7.75980i	0.255052	+	0.294346i
$696$	7.35741	−	2.16033i	0.278882	−	0.0818871i
$697$	75.5526	+	48.5547i	2.86176	+	1.83914i
$698$	3.60033	−	7.88361i	0.136274	−	0.298399i
$699$	16.3525	−	18.8718i	0.618510	−	0.713799i
$700$	0.208237	−	0.133826i	0.00787063	−	0.00505815i
$701$	3.64777	+	25.3708i	0.137774	+	0.958243i	0.935022	+	0.354590i	$0.115380\pi$
$701$	3.64777	+	25.3708i	0.137774	+	0.958243i	−0.797247	+	0.603653i	$0.793711\pi$
$702$	−0.414651	−	2.88396i	−0.0156500	−	0.108848i
$703$	−2.52199	+	1.62079i	−0.0951187	+	0.0611291i
$704$	0.497078	−	0.573659i	0.0187343	−	0.0216206i
$705$	1.44613	−	3.16658i	0.0544644	−	0.119260i
$706$	17.4652	+	11.2242i	0.657310	+	0.422427i
$707$	−1.62721	+	0.477793i	−0.0611976	+	0.0179692i
$708$	−8.99259	−	10.3780i	−0.337962	−	0.390029i
$709$	−34.5180	−	10.1354i	−1.29635	−	0.380643i	−0.440447	−	0.897778i	$-0.645180\pi$
$709$	−34.5180	−	10.1354i	−1.29635	−	0.380643i	−0.855904	+	0.517136i	$0.826998\pi$
$710$	−1.51767	−	3.32324i	−0.0569572	−	0.124719i
$711$	1.20910	−	8.40949i	0.0453449	−	0.315381i
$712$	2.64056			0.0989591
$713$	−14.6638	−	4.19646i	−0.549163	−	0.157159i
$714$	1.73667			0.0649933
$715$	0.314745	−	2.18910i	0.0117708	−	0.0818677i
$716$	−1.22404	−	2.68028i	−0.0457446	−	0.100167i
$717$	6.69874	+	1.96693i	0.250169	+	0.0734562i
$718$	−6.37551	−	7.35773i	−0.237932	−	0.274588i
$719$	−30.6007	+	8.98517i	−1.14121	+	0.335090i	−0.797105	−	0.603840i	$-0.793636\pi$
$719$	−30.6007	+	8.98517i	−1.14121	+	0.335090i	−0.344107	+	0.938930i	$0.611818\pi$
$720$	−0.841254	−	0.540641i	−0.0313517	−	0.0201485i
$721$	0.521887	−	1.14277i	0.0194361	−	0.0425591i
$722$	29.7342	−	34.3151i	1.10659	−	1.27708i
$723$	−2.44498	+	1.57129i	−0.0909298	+	0.0584370i
$724$	−2.99946	−	20.8617i	−0.111474	−	0.775320i
$725$	−1.09127	−	7.58997i	−0.0405288	−	0.281884i
$726$	8.76908	−	5.63555i	0.325451	−	0.209155i
$727$	−17.0832	+	19.7151i	−0.633581	+	0.731191i	−0.978226	−	0.207542i	$-0.933454\pi$
$727$	−17.0832	+	19.7151i	−0.633581	+	0.731191i	0.344645	+	0.938733i	$0.387999\pi$
$728$	0.299603	−	0.656040i	0.0111040	−	0.0243145i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	−14.9793	+	4.39831i	−0.554408	+	0.162789i
$731$	−16.6966	−	19.2689i	−0.617545	−	0.712685i
$732$	−2.98364	−	0.876075i	−0.110278	−	0.0323807i
$733$	−0.598227	−	1.30993i	−0.0220960	−	0.0483835i	0.898262	−	0.439460i	$-0.144830\pi$
$733$	−0.598227	−	1.30993i	−0.0220960	−	0.0483835i	−0.920358	+	0.391076i	$0.872103\pi$
$734$	−2.92537	+	20.3464i	−0.107977	+	0.750998i
$735$	6.93873			0.255939
$736$	4.05223	+	2.56504i	0.149367	+	0.0945487i
$737$	7.73759			0.285018
$738$	−1.82174	+	12.6705i	−0.0670592	+	0.466407i
$739$	14.4421	+	31.6238i	0.531261	+	1.16330i	0.964997	+	0.262259i	$0.0844676\pi$
$739$	14.4421	+	31.6238i	0.531261	+	1.16330i	−0.433737	+	0.901040i	$0.642805\pi$
$740$	0.358424	+	0.105243i	0.0131759	+	0.00386880i
$741$	−15.3124	−	17.6714i	−0.562515	−	0.649177i
$742$	2.34071	−	0.687294i	0.0859301	−	0.0252314i
$743$	−16.2404	−	10.4371i	−0.595802	−	0.382898i	0.207707	−	0.978191i	$-0.433400\pi$
$743$	−16.2404	−	10.4371i	−0.595802	−	0.382898i	−0.803509	+	0.595293i	$0.797036\pi$
$744$	1.32117	−	2.89295i	0.0484363	−	0.106061i
$745$	1.83099	−	2.11307i	0.0670823	−	0.0774171i
$746$	7.30802	−	4.69658i	0.267565	−	0.171954i
$747$	1.57069	+	10.9244i	0.0574686	+	0.399703i
$748$	−0.757901	−	5.27132i	−0.0277116	−	0.192738i
$749$	−3.95567	+	2.54215i	−0.144537	+	0.0928883i
$750$	−0.654861	+	0.755750i	−0.0239121	+	0.0275961i
$751$	−0.479487	+	1.04993i	−0.0174967	+	0.0383125i	−0.918179	−	0.396167i	$-0.870340\pi$
$751$	−0.479487	+	1.04993i	−0.0174967	+	0.0383125i	0.900682	+	0.434479i	$0.143068\pi$
$752$	−2.92855	−	1.88206i	−0.106793	−	0.0686318i
$753$	−5.90810	+	1.73477i	−0.215303	+	0.0632187i
$754$	−14.6307	−	16.8847i	−0.532818	−	0.614905i
$755$	1.97894	+	0.581070i	0.0720212	+	0.0211473i
$756$	0.102829	+	0.225163i	0.00373984	+	0.00818910i
$757$	6.98665	−	48.5932i	0.253934	−	1.76615i	−0.320162	−	0.947363i	$-0.603737\pi$
$757$	6.98665	−	48.5932i	0.253934	−	1.76615i	0.574096	−	0.818788i	$-0.305354\pi$
$758$	18.2300			0.662142
$759$	−2.40275	−	2.73473i	−0.0872143	−	0.0992643i
$760$	−8.02530			−0.291108
$761$	1.69730	−	11.8050i	0.0615271	−	0.427931i	−0.935655	−	0.352915i	$-0.885190\pi$
$761$	1.69730	−	11.8050i	0.0615271	−	0.427931i	0.997182	−	0.0750153i	$-0.0239006\pi$
$762$	−8.59706	−	18.8249i	−0.311438	−	0.681955i
$763$	−1.85305	−	0.544105i	−0.0670850	−	0.0196979i
$764$	−12.9775	−	14.9768i	−0.469509	−	0.541842i
$765$	−6.73175	+	1.97662i	−0.243387	+	0.0714649i
$766$	−26.8908	−	17.2817i	−0.971604	−	0.624412i
$767$	−16.6208	+	36.3944i	−0.600141	+	1.31413i
$768$	−0.654861	+	0.755750i	−0.0236303	+	0.0272708i
$769$	10.1018	−	6.49202i	0.364279	−	0.234108i	−0.345677	−	0.938353i	$-0.612351\pi$
$769$	10.1018	−	6.49202i	0.364279	−	0.234108i	0.709957	+	0.704245i	$0.248714\pi$
$770$	0.0267398	+	0.185979i	0.000963635	+	0.00670223i
$771$	−3.76417	−	26.1804i	−0.135563	−	0.942863i
$772$	12.3622	−	7.94471i	0.444926	−	0.285936i
$773$	−6.98598	+	8.06225i	−0.251268	+	0.289979i	−0.867345	−	0.497707i	$-0.834176\pi$
$773$	−6.98598	+	8.06225i	−0.251268	+	0.289979i	0.616077	+	0.787686i	$0.288721\pi$
$774$	1.50964	−	3.30566i	0.0542630	−	0.118819i
$775$	−2.67548	−	1.71943i	−0.0961062	−	0.0617637i
$776$	11.1920	−	3.28627i	0.401769	−	0.117970i
$777$	−0.0605530	−	0.0698819i	−0.00217233	−	0.00250700i
$778$	−20.9680	−	6.15676i	−0.751740	−	0.220731i
$779$	42.6756	+	93.4466i	1.52901	+	3.34807i
$780$	−0.414651	+	2.88396i	−0.0148469	+	0.103262i
$781$	2.77314			0.0992307
$782$	32.2185	−	9.70113i	1.15213	−	0.346912i
$783$	7.66802			0.274033
$784$	0.987484	−	6.86810i	0.0352673	−	0.245289i
$785$	−7.59897	−	16.6394i	−0.271219	−	0.593887i
$786$	1.08683	+	0.319122i	0.0387659	+	0.0113827i
$787$	0.866171	+	0.999615i	0.0308757	+	0.0356324i	0.770977	−	0.636863i	$-0.219768\pi$
$787$	0.866171	+	0.999615i	0.0308757	+	0.0356324i	−0.740102	+	0.672495i	$0.765223\pi$
$788$	10.8084	−	3.17363i	0.385033	−	0.113056i
$789$	13.0195	+	8.36711i	0.463506	+	0.297877i
$790$	−3.52935	+	7.72821i	−0.125569	+	0.274957i
$791$	−0.00902250	+	0.0104125i	−0.000320803	+	0.000370227i
$792$	0.638562	−	0.410379i	0.0226903	−	0.0145822i
$793$	1.28940	+	8.96797i	0.0457879	+	0.318462i
$794$	4.70472	+	32.7221i	0.166964	+	1.16126i
$795$	−8.29089	+	5.32823i	−0.294047	+	0.188973i
$796$	−8.89958	+	10.2707i	−0.315437	+	0.364034i
$797$	1.78110	−	3.90007i	0.0630899	−	0.138148i	−0.875461	−	0.483289i	$-0.839442\pi$
$797$	1.78110	−	3.90007i	0.0630899	−	0.138148i	0.938551	+	0.345142i	$0.112169\pi$
$798$	1.67117	+	1.07399i	0.0591586	+	0.0380190i
$799$	−23.4344	+	6.88095i	−0.829048	+	0.243431i
$800$	0.654861	+	0.755750i	0.0231528	+	0.0267198i
$801$	2.53360	+	0.743931i	0.0895203	+	0.0262855i
$802$	−0.378463	−	0.828719i	−0.0133640	−	0.0292631i
$803$	1.68646	−	11.7296i	0.0595138	−	0.413927i
$804$	−10.1937			−0.359502
$805$	−1.13671	+	0.342269i	−0.0400638	+	0.0120634i
$806$	−9.26634			−0.326393
$807$	−3.74097	+	26.0190i	−0.131688	+	0.915914i
$808$	−2.84612	−	6.23213i	−0.100126	−	0.219246i
$809$	−31.4481	−	9.23399i	−1.10566	−	0.324650i	−0.322559	−	0.946549i	$-0.604543\pi$
$809$	−31.4481	−	9.23399i	−1.10566	−	0.324650i	−0.783097	+	0.621900i	$0.786361\pi$
$810$	−0.654861	−	0.755750i	−0.0230095	−	0.0265543i
$811$	−27.8690	+	8.18307i	−0.978612	+	0.287346i	−0.731651	−	0.681679i	$-0.761250\pi$
$811$	−27.8690	+	8.18307i	−0.978612	+	0.287346i	−0.246961	+	0.969026i	$0.579432\pi$
$812$	1.59677	+	1.02618i	0.0560355	+	0.0360118i
$813$	6.56670	−	14.3791i	0.230304	−	0.504296i
$814$	−0.185686	+	0.214294i	−0.00650831	+	0.00751099i
$815$	8.31475	−	5.34357i	0.291253	−	0.187177i
$816$	0.998473	+	6.94453i	0.0349536	+	0.243107i
$817$	−4.15053	−	28.8676i	−0.145209	−	1.00995i
$818$	−6.52537	+	4.19360i	−0.228154	+	0.146626i
$819$	0.472295	−	0.545058i	0.0165033	−	0.0190459i
$820$	5.31764	−	11.6440i	0.185700	−	0.406626i
$821$	−3.61651	−	2.32419i	−0.126217	−	0.0811148i	0.476009	−	0.879440i	$-0.342083\pi$
$821$	−3.61651	−	2.32419i	−0.126217	−	0.0811148i	−0.602226	+	0.798326i	$0.705719\pi$
$822$	−20.1593	+	5.91931i	−0.703137	+	0.206460i
$823$	−27.1084	−	31.2847i	−0.944938	−	1.09052i	−0.995777	−	0.0918102i	$-0.970735\pi$
$823$	−27.1084	−	31.2847i	−0.944938	−	1.09052i	0.0508381	−	0.998707i	$-0.483811\pi$
$824$	4.86973	+	1.42988i	0.169645	+	0.0498123i
$825$	−0.315325	−	0.690465i	−0.0109782	−	0.0240389i
$826$	0.483746	−	3.36453i	0.0168317	−	0.117067i
$827$	5.56761			0.193605			0.0968025	−	0.995304i	$-0.469138\pi$
$827$	5.56761			0.193605			0.0968025	+	0.995304i	$0.469138\pi$
$828$	3.16543	+	3.60278i	0.110006	+	0.125205i
$829$	32.3426			1.12330			0.561652	−	0.827374i	$-0.310166\pi$
$829$	32.3426			1.12330			0.561652	+	0.827374i	$0.310166\pi$
$830$	1.57069	−	10.9244i	0.0545195	−	0.379191i
$831$	8.34782	+	18.2792i	0.289583	+	0.634097i
$832$	2.79560	+	0.820862i	0.0969199	+	0.0284583i
$833$	−31.8798	−	36.7912i	−1.10457	−	1.27474i
$834$	9.85177	−	2.89274i	0.341139	−	0.100167i
$835$	15.2691	+	9.81283i	0.528408	+	0.339587i
$836$	2.53058	−	5.54119i	0.0875218	−	0.191646i
$837$	2.08269	−	2.40355i	0.0719883	−	0.0830789i
$838$	−12.0934	+	7.77193i	−0.417758	+	0.268477i
$839$	7.18407	+	49.9663i	0.248022	+	1.72503i	0.609619	+	0.792695i	$0.291322\pi$
$839$	7.18407	+	49.9663i	0.248022	+	1.72503i	−0.361597	+	0.932334i	$0.617768\pi$
$840$	−0.0352275	−	0.245013i	−0.00121546	−	0.00845374i
$841$	25.0681	−	16.1103i	0.864416	−	0.555526i
$842$	−4.44603	+	5.13099i	−0.153220	+	0.176825i
$843$	7.39125	−	16.1846i	0.254568	−	0.557427i
$844$	9.92359	+	6.37750i	0.341584	+	0.219523i
$845$	−4.32810	+	1.27084i	−0.148891	+	0.0437184i
$846$	−2.27968	−	2.63089i	−0.0783771	−	0.0904520i
$847$	2.47572	+	0.726936i	0.0850666	+	0.0249778i
$848$	4.09408	+	8.96478i	0.140591	+	0.307852i
$849$	−1.33748	+	9.30235i	−0.0459020	+	0.319256i
$850$	7.01595			0.240645
$851$	−1.51373	−	0.958186i	−0.0518901	−	0.0328462i
$852$	−3.65339			−0.125163
$853$	−4.94912	+	34.4219i	−0.169455	+	1.17858i	0.710560	+	0.703636i	$0.248441\pi$
$853$	−4.94912	+	34.4219i	−0.169455	+	1.17858i	−0.880015	+	0.474946i	$0.842468\pi$
$854$	−0.319756	−	0.700167i	−0.0109418	−	0.0239592i
$855$	−7.70022	−	2.26099i	−0.263342	−	0.0773242i
$856$	−12.4397	−	14.3562i	−0.425181	−	0.490685i
$857$	−14.4012	+	4.22858i	−0.491936	+	0.144445i	−0.518286	−	0.855207i	$-0.673430\pi$
$857$	−14.4012	+	4.22858i	−0.491936	+	0.144445i	0.0263500	+	0.999653i	$0.491612\pi$
$858$	−1.86053	−	1.19569i	−0.0635173	−	0.0408201i
$859$	13.9789	−	30.6096i	0.476955	−	1.04439i	−0.506335	−	0.862337i	$-0.669000\pi$
$859$	13.9789	−	30.6096i	0.476955	−	1.04439i	0.983290	−	0.182049i	$-0.0582728\pi$
$860$	−2.37980	+	2.74644i	−0.0811506	+	0.0936528i
$861$	−2.66560	+	1.71308i	−0.0908434	+	0.0583815i
$862$	3.82618	+	26.6117i	0.130320	+	0.906397i
$863$	1.75290	+	12.1917i	0.0596693	+	0.415009i	0.997661	+	0.0683522i	$0.0217741\pi$
$863$	1.75290	+	12.1917i	0.0596693	+	0.415009i	−0.937992	+	0.346657i	$0.887317\pi$
$864$	−0.841254	+	0.540641i	−0.0286200	+	0.0183930i
$865$	8.10755	−	9.35661i	0.275665	−	0.318134i
$866$	5.28124	−	11.5643i	0.179464	−	0.392971i
$867$	27.1081	+	17.4213i	0.920640	+	0.591660i
$868$	0.755351	−	0.221791i	0.0256383	−	0.00752808i
$869$	−4.22316	−	4.87379i	−0.143261	−	0.165332i
$870$	−7.35741	−	2.16033i	−0.249439	−	0.0732420i
$871$	12.3380	+	27.0165i	0.418057	+	0.915418i
$872$	1.11036	−	7.72273i	0.0376016	−	0.261525i
$873$	11.6645			0.394783
$874$	37.0026	+	10.5893i	1.25163	+	0.358189i
$875$	−0.247532			−0.00836811
$876$	−2.22177	+	15.4528i	−0.0750667	+	0.522100i
$877$	−5.93959	−	13.0059i	−0.200566	−	0.439178i	0.782447	−	0.622718i	$-0.213972\pi$
$877$	−5.93959	−	13.0059i	−0.200566	−	0.439178i	−0.983012	+	0.183540i	$0.941244\pi$
$878$	−3.30098	−	0.969255i	−0.111403	−	0.0327108i
$879$	17.1359	+	19.7759i	0.577980	+	0.667024i
$880$	−0.728312	+	0.213852i	−0.0245514	+	0.00720894i
$881$	−16.5872	−	10.6600i	−0.558837	−	0.359143i	0.230529	−	0.973065i	$-0.425954\pi$
$881$	−16.5872	−	10.6600i	−0.558837	−	0.359143i	−0.789366	+	0.613922i	$0.789591\pi$
$882$	2.88245	−	6.31169i	0.0970572	−	0.212526i
$883$	−19.0312	+	21.9632i	−0.640452	+	0.739121i	−0.979455	−	0.201665i	$-0.935365\pi$
$883$	−19.0312	+	21.9632i	−0.640452	+	0.739121i	0.339003	+	0.940785i	$0.389910\pi$
$884$	17.1967	−	11.0517i	0.578389	−	0.371708i
$885$	1.95428	+	13.5923i	0.0656923	+	0.456900i
$886$	−3.52750	−	24.5343i	−0.118509	−	0.824247i
$887$	−36.6781	+	23.5716i	−1.23153	+	0.791457i	−0.984129	−	0.177456i	$-0.943213\pi$
$887$	−36.6781	+	23.5716i	−1.23153	+	0.791457i	−0.247403	+	0.968913i	$0.579577\pi$
$888$	0.244627	−	0.282315i	0.00820914	−	0.00947386i
$889$	2.12805	−	4.65977i	0.0713724	−	0.156284i
$890$	−2.22138	−	1.42759i	−0.0744608	−	0.0478530i
$891$	0.728312	−	0.213852i	0.0243994	−	0.00716431i
$892$	−3.42076	−	3.94777i	−0.114536	−	0.132181i
$893$	−26.8058	−	7.87088i	−0.897021	−	0.263389i
$894$	−1.16150	−	2.54333i	−0.0388464	−	0.0850617i
$895$	−0.419338	+	2.91656i	−0.0140169	+	0.0974898i
$896$	−0.247532			−0.00826947
$897$	5.71722	−	12.7501i	0.190893	−	0.425713i
$898$	28.0677			0.936630
$899$	3.47063	−	24.1388i	0.115752	−	0.805073i
$900$	0.415415	+	0.909632i	0.0138472	+	0.0303211i
$901$	66.3441	+	19.4804i	2.21024	+	0.648985i
$902$	6.36299	+	7.34328i	0.211864	+	0.244505i
$903$	0.863109	−	0.253432i	0.0287225	−	0.00843367i
$904$	−0.0468245	−	0.0300923i	−0.00155736	−	0.00100085i
$905$	−8.75540	+	19.1716i	−0.291039	+	0.637287i
$906$	1.35064	−	1.55873i	0.0448721	−	0.0517852i
$907$	−30.1218	+	19.3581i	−1.00018	+	0.642775i	−0.934833	−	0.355088i	$-0.884451\pi$
$907$	−30.1218	+	19.3581i	−1.00018	+	0.642775i	−0.0653446	+	0.997863i	$0.520815\pi$
$908$	1.36222	+	9.47444i	0.0452068	+	0.314420i
$909$	−0.975037	−	6.78153i	−0.0323399	−	0.224929i
$910$	−0.606724	+	0.389918i	−0.0201127	+	0.0129257i
$911$	9.15072	−	10.5605i	0.303177	−	0.349885i	−0.583634	−	0.812017i	$-0.698370\pi$
$911$	9.15072	−	10.5605i	0.303177	−	0.349885i	0.886811	+	0.462132i	$0.152915\pi$
$912$	−3.33383	+	7.30007i	−0.110394	+	0.241729i
$913$	7.04764	+	4.52924i	0.233243	+	0.149896i
$914$	0.296483	−	0.0870551i	0.00980677	−	0.00287953i
$915$	2.03635	+	2.35008i	0.0673198	+	0.0776912i
$916$	−10.0562	−	2.95278i	−0.332267	−	0.0975625i
$917$	0.116475	+	0.255045i	0.00384635	+	0.00842233i
$918$	−0.998473	+	6.94453i	−0.0329545	+	0.229204i
$919$	−40.2758			−1.32858			−0.664288	−	0.747477i	$-0.731265\pi$
$919$	−40.2758			−1.32858			−0.664288	+	0.747477i	$0.731265\pi$
$920$	−2.02219	−	4.34865i	−0.0666695	−	0.143371i
$921$	10.8164			0.356412
$922$	−2.91447	+	20.2706i	−0.0959828	+	0.667575i
$923$	4.42192	+	9.68265i	0.145549	+	0.318708i
$924$	0.180281	+	0.0529352i	0.00593080	+	0.00174144i
$925$	−0.244627	−	0.282315i	−0.00804329	−	0.00928245i
$926$	1.41178	−	0.414537i	0.0463941	−	0.0136225i
$927$	4.26963	+	2.74392i	0.140233	+	0.0901222i
$928$	−3.18541	+	6.97507i	−0.104566	+	0.228968i
$929$	−2.03899	+	2.35312i	−0.0668972	+	0.0772035i	−0.788212	−	0.615404i	$-0.788993\pi$
$929$	−2.03899	+	2.35312i	−0.0668972	+	0.0772035i	0.721314	+	0.692608i	$0.243538\pi$
$930$	−2.67548	+	1.71943i	−0.0877326	+	0.0563823i
$931$	−7.92485	−	55.1186i	−0.259727	−	1.80644i
$932$	3.55375	+	24.7169i	0.116407	+	0.809628i
$933$	−21.3115	+	13.6961i	−0.697709	+	0.448390i
$934$	12.3027	−	14.1981i	0.402558	−	0.464576i
$935$	−2.21230	+	4.84427i	−0.0723500	+	0.158424i
$936$	2.45109	+	1.57522i	0.0801165	+	0.0514877i
$937$	−28.9296	+	8.49449i	−0.945089	+	0.277503i	−0.717741	−	0.696311i	$-0.754824\pi$
$937$	−28.9296	+	8.49449i	−0.945089	+	0.277503i	−0.227348	+	0.973814i	$0.573005\pi$
$938$	−1.65238	−	1.90695i	−0.0539522	−	0.0622641i
$939$	1.19614	+	0.351218i	0.0390345	+	0.0114616i
$940$	1.44613	+	3.16658i	0.0471676	+	0.103283i
$941$	1.89211	−	13.1599i	0.0616812	−	0.429002i	−0.935459	−	0.353434i	$-0.885014\pi$
$941$	1.89211	−	13.1599i	0.0616812	−	0.429002i	0.997141	−	0.0755680i	$-0.0240770\pi$
$942$	−18.2925			−0.596001
$943$	−39.8824	+	46.6709i	−1.29875	+	1.51981i
$944$	13.7321			0.446941
$945$	0.0352275	−	0.245013i	0.00114595	−	0.00797026i
$946$	−1.14591	−	2.50919i	−0.0372567	−	0.0815808i
$947$	13.6086	+	3.99584i	0.442220	+	0.129847i	0.495260	−	0.868745i	$-0.335073\pi$
$947$	13.6086	+	3.99584i	0.442220	+	0.129847i	−0.0530399	+	0.998592i	$0.516891\pi$
$948$	5.56368	+	6.42083i	0.180700	+	0.208539i
$949$	43.6439	−	12.8150i	1.41674	−	0.415993i
$950$	6.75131	+	4.33880i	0.219041	+	0.140769i
$951$	−2.82741	+	6.19117i	−0.0916852	+	0.200763i
$952$	−1.13728	+	1.31249i	−0.0368594	+	0.0425380i
$953$	−5.67873	+	3.64950i	−0.183952	+	0.118219i	−0.629376	−	0.777101i	$-0.716689\pi$
$953$	−5.67873	+	3.64950i	−0.183952	+	0.118219i	0.445424	+	0.895320i	$0.353053\pi$
$954$	1.40257	+	9.75508i	0.0454098	+	0.315832i
$955$	2.82028	+	19.6155i	0.0912620	+	0.634741i
$956$	−5.87324	+	3.77450i	−0.189954	+	0.122076i
$957$	3.81160	−	4.39883i	0.123212	−	0.142194i
$958$	−6.76478	+	14.8128i	−0.218560	+	0.478580i
$959$	−4.37515	−	2.81174i	−0.141281	−	0.0907957i
$960$	0.959493	−	0.281733i	0.0309675	−	0.00909288i
$961$	13.6770	+	15.7841i	0.441193	+	0.509164i
$962$	−1.04431	−	0.306638i	−0.0336700	−	0.00988639i
$963$	−7.89121	−	17.2793i	−0.254291	−	0.556819i
$964$	0.413617	−	2.87677i	0.0133217	−	0.0926546i
$965$	−14.6950			−0.473048
$966$	−0.160868	+	1.17617i	−0.00517584	+	0.0378427i
$967$	12.8606			0.413570			0.206785	−	0.978386i	$-0.433700\pi$
$967$	12.8606			0.413570			0.206785	+	0.978386i	$0.433700\pi$
$968$	−1.48347	+	10.3177i	−0.0476804	+	0.331624i
$969$	23.3900	+	51.2169i	0.751394	+	1.64532i
$970$	−11.1920	−	3.28627i	−0.359353	−	0.105516i
$971$	14.7941	+	17.0733i	0.474765	+	0.547908i	0.941731	−	0.336368i	$-0.109198\pi$
$971$	14.7941	+	17.0733i	0.474765	+	0.547908i	−0.466966	+	0.884275i	$0.654653\pi$
$972$	−0.959493	+	0.281733i	−0.0307758	+	0.00903658i
$973$	2.13811	+	1.37408i	0.0685448	+	0.0440511i
$974$	7.13739	−	15.6287i	0.228697	−	0.500776i
$975$	1.90802	−	2.20197i	0.0611054	−	0.0705194i
$976$	2.61596	−	1.68118i	0.0837349	−	0.0538131i
$977$	3.45157	+	24.0062i	0.110425	+	0.768026i	0.967507	+	0.252845i	$0.0813662\pi$
$977$	3.45157	+	24.0062i	0.110425	+	0.768026i	−0.857081	+	0.515181i	$0.827725\pi$
$978$	−1.40661	−	9.78316i	−0.0449783	−	0.312831i
$979$	1.68616	−	1.08363i	0.0538899	−	0.0346329i
$980$	−4.54390	+	5.24394i	−0.145150	+	0.167512i
$981$	3.24113	−	7.09708i	0.103481	−	0.226592i
$982$	−11.4236	−	7.34148i	−0.364541	−	0.234276i
$983$	3.79173	−	1.11335i	0.120937	−	0.0355104i	−0.220704	−	0.975341i	$-0.570835\pi$
$983$	3.79173	−	1.11335i	0.120937	−	0.0355104i	0.341641	+	0.939830i	$0.389017\pi$
$984$	−8.38273	−	9.67418i	−0.267232	−	0.308402i
$985$	−10.8084	−	3.17363i	−0.344384	−	0.101120i
$986$	22.3487	+	48.9367i	0.711726	+	1.55846i
$987$	0.122633	−	0.852931i	0.00390345	−	0.0271491i
$988$	23.3827			0.743902
$989$	14.5966	−	9.52299i	0.464144	−	0.302813i
$990$	−0.759060			−0.0241245
$991$	6.37800	−	44.3600i	0.202604	−	1.40914i	−0.593915	−	0.804528i	$-0.702419\pi$
$991$	6.37800	−	44.3600i	0.202604	−	1.40914i	0.796519	−	0.604613i	$-0.206672\pi$
$992$	1.32117	+	2.89295i	0.0419471	+	0.0918513i
$993$	15.3664	+	4.51198i	0.487637	+	0.143183i
$994$	−0.592210	−	0.683447i	−0.0187838	−	0.0216776i
$995$	13.0395	−	3.82876i	0.413381	−	0.121380i
$996$	−9.28469	−	5.96691i	−0.294197	−	0.189069i
$997$	18.0137	−	39.4446i	0.570501	−	1.24922i	−0.376029	−	0.926608i	$-0.622711\pi$
$997$	18.0137	−	39.4446i	0.570501	−	1.24922i	0.946530	−	0.322615i	$-0.104562\pi$
$998$	3.96183	−	4.57220i	0.125410	−	0.144730i
$999$	0.314255	−	0.201959i	0.00994259	−	0.00638971i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.h.31.2	✓	30
23.3	even	11	inner	690.2.m.h.601.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.h.31.2	✓	30	1.1	even	1	trivial
690.2.m.h.601.2	yes	30	23.3	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 - 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(0.208237 + 0.133826i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.142315 - 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(0.208237 + 0.133826i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(0.841254 - 0.540641i) q^{10} +(0.108025 + 0.751334i) q^{11} +(-0.142315 - 0.989821i) q^{12} +(-2.45109 + 1.57522i) q^{13} +(0.162099 - 0.187072i) q^{14} +(-0.415415 + 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(6.73175 - 1.97662i) q^{17} +(0.654861 + 0.755750i) q^{18} +(7.70022 + 2.26099i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(-0.0352275 + 0.245013i) q^{21} +0.759060 q^{22} +(0.715117 + 4.74222i) q^{23} -1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(1.21036 + 2.65032i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(-0.162099 - 0.187072i) q^{28} +(-7.35741 + 2.16033i) q^{29} +(0.841254 + 0.540641i) q^{30} +(-1.32117 + 2.89295i) q^{31} +(0.654861 - 0.755750i) q^{32} +(-0.638562 + 0.410379i) q^{33} +(-0.998473 - 6.94453i) q^{34} +(0.0352275 + 0.245013i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-0.244627 + 0.282315i) q^{37} +(3.33383 - 7.30007i) q^{38} +(-2.45109 - 1.57522i) q^{39} +(-0.959493 + 0.281733i) q^{40} +(8.38273 + 9.67418i) q^{41} +(0.237505 + 0.0697379i) q^{42} +(-1.50964 - 3.30566i) q^{43} +(0.108025 - 0.751334i) q^{44} -1.00000 q^{45} +(4.79572 - 0.0329509i) q^{46} -3.48117 q^{47} +(-0.142315 + 0.989821i) q^{48} +(-2.88245 - 6.31169i) q^{49} +(0.959493 + 0.281733i) q^{50} +(4.59447 + 5.30230i) q^{51} +(2.79560 - 0.820862i) q^{52} +(8.29089 + 5.32823i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(-0.497078 + 0.573659i) q^{55} +(-0.208237 + 0.133826i) q^{56} +(1.14212 + 7.94361i) q^{57} +(1.09127 + 7.58997i) q^{58} +(11.5521 - 7.42412i) q^{59} +(0.654861 - 0.755750i) q^{60} +(1.29177 - 2.82859i) q^{61} +(2.67548 + 1.71943i) q^{62} +(-0.237505 + 0.0697379i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-2.79560 - 0.820862i) q^{65} +(0.315325 + 0.690465i) q^{66} +(1.45071 - 10.0899i) q^{67} -7.01595 q^{68} +(-4.01660 + 2.62048i) q^{69} +0.247532 q^{70} +(0.519931 - 3.61620i) q^{71} +(-0.415415 - 0.909632i) q^{72} +(-14.9793 - 4.39831i) q^{73} +(0.244627 + 0.282315i) q^{74} +(-0.959493 + 0.281733i) q^{75} +(-6.75131 - 4.33880i) q^{76} +(-0.0780530 + 0.170912i) q^{77} +(-1.90802 + 2.20197i) q^{78} +(-7.14726 + 4.59327i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(10.7687 - 6.92062i) q^{82} +(7.22752 - 8.34101i) q^{83} +(0.102829 - 0.225163i) q^{84} +(5.90219 + 3.79311i) q^{85} +(-3.48685 + 1.02383i) q^{86} +(-5.02148 - 5.79510i) q^{87} +(-0.728312 - 0.213852i) q^{88} +(-1.09693 - 2.40194i) q^{89} +(-0.142315 + 0.989821i) q^{90} -0.721215 q^{91} +(0.649886 - 4.75159i) q^{92} -3.18035 q^{93} +(-0.495422 + 3.44574i) q^{94} +(3.33383 + 7.30007i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-7.63862 - 8.81543i) q^{97} +(-6.65766 + 1.95487i) q^{98} +(-0.638562 - 0.410379i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more