LMFDB - Embedded newform 460.2.w.a.3.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			3.6
Character	$\chi$	$=$	460.3
Dual form			460.2.w.a.307.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37121 + 0.346108i) q^{2} +(-0.338395 - 0.907273i) q^{3} +(1.76042 - 0.949171i) q^{4} +(1.81802 + 1.30185i) q^{5} +(0.778024 + 1.12694i) q^{6} +(1.65566 + 0.360166i) q^{7} +(-2.08538 + 1.91080i) q^{8} +(1.55862 - 1.35055i) q^{9} +O(q^{10})$	\(q+(-1.37121 + 0.346108i) q^{2} +(-0.338395 - 0.907273i) q^{3} +(1.76042 - 0.949171i) q^{4} +(1.81802 + 1.30185i) q^{5} +(0.778024 + 1.12694i) q^{6} +(1.65566 + 0.360166i) q^{7} +(-2.08538 + 1.91080i) q^{8} +(1.55862 - 1.35055i) q^{9} +(-2.94346 - 1.15588i) q^{10} +(0.111132 + 0.0159784i) q^{11} +(-1.45687 - 1.27599i) q^{12} +(1.27053 + 5.84051i) q^{13} +(-2.39490 + 0.0791732i) q^{14} +(0.565926 - 2.08998i) q^{15} +(2.19815 - 3.34188i) q^{16} +(0.488251 - 0.266605i) q^{17} +(-1.66975 + 2.39133i) q^{18} +(-3.08391 + 0.905517i) q^{19} +(4.43615 + 0.566195i) q^{20} +(-0.233497 - 1.62401i) q^{21} +(-0.157916 + 0.0165540i) q^{22} +(-4.63345 - 1.23738i) q^{23} +(2.43931 + 1.24541i) q^{24} +(1.61037 + 4.73357i) q^{25} +(-3.76360 - 7.56882i) q^{26} +(-4.30238 - 2.34928i) q^{27} +(3.25651 - 0.937457i) q^{28} +(0.0663376 - 0.225925i) q^{29} +(-0.0526446 + 3.06166i) q^{30} +(8.30577 - 3.79312i) q^{31} +(-1.85747 + 5.34320i) q^{32} +(-0.0231099 - 0.106234i) q^{33} +(-0.577219 + 0.534559i) q^{34} +(2.54113 + 2.81021i) q^{35} +(1.46192 - 3.85692i) q^{36} +(12.1163 + 0.866576i) q^{37} +(3.91527 - 2.30902i) q^{38} +(4.86900 - 3.12912i) q^{39} +(-6.27885 + 0.759015i) q^{40} +(2.30750 - 2.66300i) q^{41} +(0.882256 + 2.14604i) q^{42} +(2.65094 + 7.10743i) q^{43} +(0.210806 - 0.0773549i) q^{44} +(4.59180 - 0.426233i) q^{45} +(6.78169 + 0.0930288i) q^{46} +(1.86357 + 1.86357i) q^{47} +(-3.77584 - 0.863446i) q^{48} +(-3.75595 - 1.71528i) q^{49} +(-3.84647 - 5.93335i) q^{50} +(-0.407106 - 0.352759i) q^{51} +(7.78030 + 9.07581i) q^{52} +(-5.91404 - 1.28652i) q^{53} +(6.71256 + 1.73226i) q^{54} +(0.181239 + 0.173727i) q^{55} +(-4.14088 + 2.41255i) q^{56} +(1.86513 + 2.49152i) q^{57} +(-0.0127682 + 0.332750i) q^{58} +(4.44154 + 2.85440i) q^{59} +(-0.987479 - 4.21640i) q^{60} +(-1.18234 - 2.58896i) q^{61} +(-10.0761 + 8.07584i) q^{62} +(3.06695 - 1.67468i) q^{63} +(0.697652 - 7.96952i) q^{64} +(-5.29364 + 12.2722i) q^{65} +(0.0684570 + 0.137671i) q^{66} +(4.52429 - 6.04375i) q^{67} +(0.606473 - 0.932771i) q^{68} +(0.445299 + 4.62253i) q^{69} +(-4.45705 - 2.97387i) q^{70} +(1.24816 - 0.179458i) q^{71} +(-0.669678 + 5.79462i) q^{72} +(-7.30945 - 3.99126i) q^{73} +(-16.9139 + 3.00530i) q^{74} +(3.74970 - 3.06286i) q^{75} +(-4.56948 + 4.52124i) q^{76} +(0.178242 + 0.0664809i) q^{77} +(-5.59340 + 5.97587i) q^{78} +(6.02923 + 3.87475i) q^{79} +(8.34690 - 3.21392i) q^{80} +(0.204976 - 1.42564i) q^{81} +(-2.24238 + 4.45017i) q^{82} +(-14.9982 - 1.07269i) q^{83} +(-1.95252 - 2.63731i) q^{84} +(1.23473 + 0.150937i) q^{85} +(-6.09492 - 8.82826i) q^{86} +(-0.227424 + 0.0162657i) q^{87} +(-0.262285 + 0.179031i) q^{88} +(2.67945 + 1.22367i) q^{89} +(-6.14879 + 2.17371i) q^{90} +10.1275i q^{91} +(-9.33130 + 2.21963i) q^{92} +(-6.25203 - 6.25203i) q^{93} +(-3.20033 - 1.91034i) q^{94} +(-6.78544 - 2.36854i) q^{95} +(5.47630 - 0.122883i) q^{96} +(-0.895695 - 12.5234i) q^{97} +(5.74385 + 1.05205i) q^{98} +(0.194792 - 0.125185i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−1.37121	+	0.346108i	−0.969590	+	0.244735i
$2$	−1.37121	+	0.346108i	−0.969590	+	0.244735i
$3$	−0.338395	−	0.907273i	−0.195373	−	0.523814i	0.801913	−	0.597440i	$-0.203816\pi$
$3$	−0.338395	−	0.907273i	−0.195373	−	0.523814i	−0.997286	+	0.0736261i	$0.976543\pi$
$4$	1.76042	−	0.949171i	0.880209	−	0.474585i
$5$	1.81802	+	1.30185i	0.813042	+	0.582206i
$5$	1.81802	+	1.30185i	0.813042	+	0.582206i
$6$	0.778024	+	1.12694i	0.317627	+	0.460071i
$7$	1.65566	+	0.360166i	0.625779	+	0.136130i	0.514263	−	0.857633i	$-0.328066\pi$
$7$	1.65566	+	0.360166i	0.625779	+	0.136130i	0.111516	+	0.993763i	$0.464429\pi$
$8$	−2.08538	+	1.91080i	−0.737295	+	0.675571i
$9$	1.55862	−	1.35055i	0.519539	−	0.450183i
$10$	−2.94346	−	1.15588i	−0.930803	−	0.365521i
$11$	0.111132	+	0.0159784i	0.0335077	+	0.00481768i	0.159048	−	0.987271i	$-0.449157\pi$
$11$	0.111132	+	0.0159784i	0.0335077	+	0.00481768i	−0.125541	+	0.992088i	$0.540067\pi$
$12$	−1.45687	−	1.27599i	−0.420563	−	0.368345i
$13$	1.27053	+	5.84051i	0.352381	+	1.61987i	0.722838	+	0.691018i	$0.242837\pi$
$13$	1.27053	+	5.84051i	0.352381	+	1.61987i	−0.370457	+	0.928850i	$0.620799\pi$
$14$	−2.39490	+	0.0791732i	−0.640065	+	0.0211599i
$15$	0.565926	−	2.08998i	0.146121	−	0.539630i
$16$	2.19815	−	3.34188i	0.549537	−	0.835469i
$17$	0.488251	−	0.266605i	0.118418	−	0.0646613i	−0.418948	−	0.908010i	$-0.637601\pi$
$17$	0.488251	−	0.266605i	0.118418	−	0.0646613i	0.537366	+	0.843349i	$0.319419\pi$
$18$	−1.66975	+	2.39133i	−0.393564	+	0.563642i
$19$	−3.08391	+	0.905517i	−0.707497	+	0.207740i	−0.615634	−	0.788032i	$-0.711100\pi$
$19$	−3.08391	+	0.905517i	−0.707497	+	0.207740i	−0.0918624	+	0.995772i	$0.529282\pi$
$20$	4.43615	+	0.566195i	0.991953	+	0.126605i
$21$	−0.233497	−	1.62401i	−0.0509533	−	0.354388i
$22$	−0.157916	+	0.0165540i	−0.0336678	+	0.00352933i
$23$	−4.63345	−	1.23738i	−0.966142	−	0.258011i
$23$	−4.63345	−	1.23738i	−0.966142	−	0.258011i
$24$	2.43931	+	1.24541i	0.497921	+	0.254217i
$25$	1.61037	+	4.73357i	0.322074	+	0.946715i
$26$	−3.76360	−	7.56882i	−0.738103	−	1.48437i
$27$	−4.30238	−	2.34928i	−0.827994	−	0.452119i
$28$	3.25651	−	0.937457i	0.615422	−	0.177163i
$29$	0.0663376	−	0.225925i	0.0123186	−	0.0419533i	−0.953104	−	0.302642i	$-0.902131\pi$
$29$	0.0663376	−	0.225925i	0.0123186	−	0.0419533i	0.965423	+	0.260689i	$0.0839496\pi$
$30$	−0.0526446	+	3.06166i	−0.00961154	+	0.558981i
$31$	8.30577	−	3.79312i	1.49176	−	0.681264i	0.508100	−	0.861298i	$-0.330348\pi$
$31$	8.30577	−	3.79312i	1.49176	−	0.681264i	0.983660	+	0.180034i	$0.0576208\pi$
$32$	−1.85747	+	5.34320i	−0.328357	+	0.944554i
$33$	−0.0231099	−	0.106234i	−0.00402292	−	0.0184930i
$34$	−0.577219	+	0.534559i	−0.0989923	+	0.0916760i
$35$	2.54113	+	2.81021i	0.429529	+	0.475011i
$36$	1.46192	−	3.85692i	0.243653	−	0.642821i
$37$	12.1163	+	0.866576i	1.99191	+	0.142464i	0.999862	+	0.0166041i	$0.00528549\pi$
$37$	12.1163	+	0.866576i	1.99191	+	0.142464i	0.992048	+	0.125860i	$0.0401691\pi$
$38$	3.91527	−	2.30902i	0.635141	−	0.374572i
$39$	4.86900	−	3.12912i	0.779664	−	0.501060i
$40$	−6.27885	+	0.759015i	−0.992773	+	0.120011i
$41$	2.30750	−	2.66300i	0.360371	−	0.415890i	−0.546393	−	0.837529i	$-0.683999\pi$
$41$	2.30750	−	2.66300i	0.360371	−	0.415890i	0.906764	+	0.421639i	$0.138545\pi$
$42$	0.882256	+	2.14604i	0.136135	+	0.331141i
$43$	2.65094	+	7.10743i	0.404264	+	1.08387i	0.966448	+	0.256862i	$0.0826884\pi$
$43$	2.65094	+	7.10743i	0.404264	+	1.08387i	−0.562184	+	0.827012i	$0.690039\pi$
$44$	0.210806	−	0.0773549i	0.0317802	−	0.0116617i
$45$	4.59180	−	0.426233i	0.684505	−	0.0635391i
$46$	6.78169	+	0.0930288i	0.999906	+	0.0137163i
$47$	1.86357	+	1.86357i	0.271829	+	0.271829i	0.829836	−	0.558007i	$-0.188434\pi$
$47$	1.86357	+	1.86357i	0.271829	+	0.271829i	−0.558007	+	0.829836i	$0.688434\pi$
$48$	−3.77584	−	0.863446i	−0.544995	−	0.124628i
$49$	−3.75595	−	1.71528i	−0.536564	−	0.245040i
$50$	−3.84647	−	5.93335i	−0.543974	−	0.839102i
$51$	−0.407106	−	0.352759i	−0.0570062	−	0.0493962i
$52$	7.78030	+	9.07581i	1.07893	+	1.25859i
$53$	−5.91404	−	1.28652i	−0.812356	−	0.176717i	−0.212847	−	0.977085i	$-0.568274\pi$
$53$	−5.91404	−	1.28652i	−0.812356	−	0.176717i	−0.599509	+	0.800368i	$0.704637\pi$
$54$	6.71256	+	1.73226i	0.913464	+	0.235731i
$55$	0.181239	+	0.173727i	0.0244383	+	0.0234253i
$56$	−4.14088	+	2.41255i	−0.553349	+	0.322391i
$57$	1.86513	+	2.49152i	0.247043	+	0.330010i
$58$	−0.0127682	+	0.332750i	−0.00167654	+	0.0436923i
$59$	4.44154	+	2.85440i	0.578239	+	0.371612i	0.796829	−	0.604205i	$-0.206509\pi$
$59$	4.44154	+	2.85440i	0.578239	+	0.371612i	−0.218590	+	0.975817i	$0.570146\pi$
$60$	−0.987479	−	4.21640i	−0.127483	−	0.544334i
$61$	−1.18234	−	2.58896i	−0.151383	−	0.331482i	0.818714	−	0.574202i	$-0.194688\pi$
$61$	−1.18234	−	2.58896i	−0.151383	−	0.331482i	−0.970096	+	0.242720i	$0.921960\pi$
$62$	−10.0761	+	8.07584i	−1.27967	+	1.02563i
$63$	3.06695	−	1.67468i	0.386400	−	0.210990i
$64$	0.697652	−	7.96952i	0.0872065	−	0.996190i
$65$	−5.29364	+	12.2722i	−0.656596	+	1.52218i
$66$	0.0684570	+	0.137671i	0.00842648	+	0.0169461i
$67$	4.52429	−	6.04375i	0.552731	−	0.738362i	−0.433967	−	0.900929i	$-0.642887\pi$
$67$	4.52429	−	6.04375i	0.552731	−	0.738362i	0.986697	+	0.162567i	$0.0519774\pi$
$68$	0.606473	−	0.932771i	0.0735456	−	0.113115i
$69$	0.445299	+	4.62253i	0.0536077	+	0.556487i
$70$	−4.45705	−	2.97387i	−0.532719	−	0.355445i
$71$	1.24816	−	0.179458i	0.148129	−	0.0212978i	−0.0678513	−	0.997695i	$-0.521614\pi$
$71$	1.24816	−	0.179458i	0.148129	−	0.0212978i	0.215980	+	0.976398i	$0.430705\pi$
$72$	−0.669678	+	5.79462i	−0.0789224	+	0.682903i
$73$	−7.30945	−	3.99126i	−0.855506	−	0.467142i	−0.00927450	−	0.999957i	$-0.502952\pi$
$73$	−7.30945	−	3.99126i	−0.855506	−	0.467142i	−0.846232	+	0.532815i	$0.821134\pi$
$74$	−16.9139	+	3.00530i	−1.96620	+	0.349358i
$75$	3.74970	−	3.06286i	0.432978	−	0.353669i
$76$	−4.56948	+	4.52124i	−0.524155	+	0.518622i
$77$	0.178242	+	0.0664809i	0.0203126	+	0.00757620i
$78$	−5.59340	+	5.97587i	−0.633328	+	0.676634i
$79$	6.02923	+	3.87475i	0.678341	+	0.435943i	0.833924	−	0.551880i	$-0.186089\pi$
$79$	6.02923	+	3.87475i	0.678341	+	0.435943i	−0.155583	+	0.987823i	$0.549726\pi$
$80$	8.34690	−	3.21392i	0.933211	−	0.359328i
$81$	0.204976	−	1.42564i	0.0227751	−	0.158404i
$82$	−2.24238	+	4.45017i	−0.247629	+	0.491439i
$83$	−14.9982	−	1.07269i	−1.64627	−	0.117743i	−0.782841	−	0.622222i	$-0.786230\pi$
$83$	−14.9982	−	1.07269i	−1.64627	−	0.117743i	−0.863424	+	0.504479i	$0.831685\pi$
$84$	−1.95252	−	2.63731i	−0.213037	−	0.287754i
$85$	1.23473	+	0.150937i	0.133925	+	0.0163715i
$86$	−6.09492	−	8.82826i	−0.657232	−	0.951975i
$87$	−0.227424	+	0.0162657i	−0.0243824	+	0.00174387i
$88$	−0.262285	+	0.179031i	−0.0279597	+	0.0190848i
$89$	2.67945	+	1.22367i	0.284021	+	0.129708i	0.552332	−	0.833624i	$-0.313738\pi$
$89$	2.67945	+	1.22367i	0.284021	+	0.129708i	−0.268311	+	0.963332i	$0.586465\pi$
$90$	−6.14879	+	2.17371i	−0.648139	+	0.229129i
$91$			10.1275i			1.06165i
$92$	−9.33130	+	2.21963i	−0.972856	+	0.231413i
$93$	−6.25203	−	6.25203i	−0.648305	−	0.648305i
$94$	−3.20033	−	1.91034i	−0.330089	−	0.197037i
$95$	−6.78544	−	2.36854i	−0.696172	−	0.243007i
$96$	5.47630	−	0.122883i	0.558923	−	0.0125417i
$97$	−0.895695	−	12.5234i	−0.0909440	−	1.27156i	−0.814037	−	0.580813i	$-0.802735\pi$
$97$	−0.895695	−	12.5234i	−0.0909440	−	1.27156i	0.723093	−	0.690751i	$-0.242720\pi$
$98$	5.74385	+	1.05205i	0.580217	+	0.106273i
$99$	0.194792	−	0.125185i	0.0195774	−	0.0125816i
$100$	7.32789	+	6.80456i	0.732789	+	0.680456i
$101$	−2.20651	−	2.54645i	−0.219556	−	0.253381i	0.635277	−	0.772284i	$-0.280886\pi$
$101$	−2.20651	−	2.54645i	−0.219556	−	0.253381i	−0.854833	+	0.518903i	$0.826340\pi$
$102$	0.680319	+	0.342803i	0.0673616	+	0.0339426i
$103$	−5.43723	−	7.26329i	−0.535746	−	0.715673i	0.448241	−	0.893913i	$-0.352051\pi$
$103$	−5.43723	−	7.26329i	−0.535746	−	0.715673i	−0.983987	+	0.178239i	$0.942960\pi$
$104$	−13.8096	−	9.75199i	−1.35414	−	0.956261i
$105$	1.68972	−	3.25646i	0.164900	−	0.317798i
$106$	8.55465	−	0.282809i	0.830901	−	0.0274688i
$107$	6.04878	−	16.2174i	0.584758	−	1.56780i	−0.220825	−	0.975313i	$-0.570875\pi$
$107$	6.04878	−	16.2174i	0.584758	−	1.56780i	0.805583	−	0.592483i	$-0.201852\pi$
$108$	−9.80386	−	0.0520184i	−0.943377	−	0.00500547i
$109$	0.684860	−	2.33242i	0.0655977	−	0.223405i	−0.920170	−	0.391520i	$-0.871950\pi$
$109$	0.684860	−	2.33242i	0.0655977	−	0.223405i	0.985768	+	0.168114i	$0.0537677\pi$
$110$	−0.308644	−	0.175487i	−0.0294281	−	0.0167321i
$111$	−3.31388	−	11.2861i	−0.314540	−	1.07122i
$112$	4.84301	−	4.74130i	0.457621	−	0.448011i
$113$	−4.09915	+	5.47582i	−0.385616	+	0.515122i	−0.950784	−	0.309853i	$-0.899720\pi$
$113$	−4.09915	+	5.47582i	−0.385616	+	0.515122i	0.565169	+	0.824975i	$0.308811\pi$
$114$	−3.41982	−	2.77086i	−0.320295	−	0.259515i
$115$	−6.81281	−	8.28164i	−0.635298	−	0.772267i
$116$	−0.0976596	−	0.460689i	−0.00906747	−	0.0427739i
$117$	9.86816	+	7.38721i	0.912312	+	0.682948i
$118$	−7.07820	−	2.37673i	−0.651601	−	0.218796i
$119$	0.904398	−	0.265555i	0.0829060	−	0.0243434i
$120$	2.81337	+	5.43978i	0.256824	+	0.496582i
$121$	−10.5423	−	3.09551i	−0.958393	−	0.281410i
$122$	2.51729	+	3.14078i	0.227904	+	0.284353i
$123$	−3.19691	−	1.19239i	−0.288256	−	0.107514i
$124$	11.0213	−	14.5611i	0.989743	−	1.30762i
$125$	−3.23473	+	10.7022i	−0.289323	+	0.957231i
$126$	−3.62581	+	3.35783i	−0.323013	+	0.299140i
$127$	−13.4820	+	10.0925i	−1.19634	+	0.895567i	−0.996445	−	0.0842513i	$-0.973150\pi$
$127$	−13.4820	+	10.0925i	−1.19634	+	0.895567i	−0.199892	+	0.979818i	$0.564059\pi$
$128$	1.80169	+	11.1693i	0.159248	+	0.987239i
$129$	5.55132	−	4.81025i	0.488766	−	0.423518i
$130$	3.01118	−	18.6599i	0.264098	−	1.63658i
$131$	5.45344	+	8.48572i	0.476469	+	0.741400i	0.993409	−	0.114621i	$-0.0365654\pi$
$131$	5.45344	+	8.48572i	0.476469	+	0.741400i	−0.516940	+	0.856022i	$0.672929\pi$
$132$	−0.141518	−	0.165082i	−0.0123175	−	0.0143685i
$133$	−5.43203	+	0.388506i	−0.471016	+	0.0336878i
$134$	−4.11196	+	9.85313i	−0.355219	+	0.851181i
$135$	−4.76339	−	9.87209i	−0.409968	−	0.849654i
$136$	−0.508760	+	1.48893i	−0.0436258	+	0.127674i
$137$	−10.6458	+	10.6458i	−0.909529	+	0.909529i	−0.996234	−	0.0867048i	$-0.972366\pi$
$137$	−10.6458	+	10.6458i	−0.909529	+	0.909529i	0.0867048	+	0.996234i	$0.472366\pi$
$138$	−2.21049	−	6.18433i	−0.188169	−	0.526445i
$139$	−1.89476			−0.160711			−0.0803557	−	0.996766i	$-0.525606\pi$
$139$	−1.89476			−0.160711			−0.0803557	+	0.996766i	$0.525606\pi$
$140$	7.14081	+	2.53517i	0.603509	+	0.214261i
$141$	1.06014	−	2.32138i	0.0892800	−	0.195496i
$142$	−1.64937	+	0.678072i	−0.138412	+	0.0569025i
$143$	0.0478744	+	0.669371i	0.00400346	+	0.0559756i
$144$	−1.08730	−	8.17741i	−0.0906079	−	0.681451i
$145$	0.414724	−	0.324374i	0.0344409	−	0.0269378i
$146$	11.4042	+	2.94299i	0.943816	+	0.243563i
$147$	−0.285235	+	3.98811i	−0.0235258	+	0.328934i
$148$	22.1523	−	9.97492i	1.82091	−	0.819933i
$149$	−8.13521	−	1.16967i	−0.666463	−	0.0958229i	−0.199224	−	0.979954i	$-0.563842\pi$
$149$	−8.13521	−	1.16967i	−0.666463	−	0.0958229i	−0.467239	+	0.884131i	$0.654751\pi$
$150$	−4.08154	+	5.49762i	−0.333256	+	0.448879i
$151$	−11.2654	+	17.5292i	−0.916762	+	1.42651i	−0.0123146	+	0.999924i	$0.503920\pi$
$151$	−11.2654	+	17.5292i	−0.916762	+	1.42651i	−0.904447	+	0.426585i	$0.859716\pi$
$152$	4.70086	−	7.78109i	0.381290	−	0.631130i
$153$	0.400933	−	1.07494i	0.0324135	−	0.0869039i
$154$	−0.267416	−	0.0294681i	−0.0215490	−	0.00237461i
$155$	20.0381	+	3.91692i	1.60950	+	0.314615i
$156$	5.60141	−	10.1301i	0.448472	−	0.811055i
$157$	1.07513	−	1.96896i	0.0858049	−	0.157140i	−0.831253	−	0.555895i	$-0.812376\pi$
$157$	1.07513	−	1.96896i	0.0858049	−	0.157140i	0.917058	+	0.398755i	$0.130558\pi$
$158$	−9.60840	−	3.22632i	−0.764403	−	0.256672i
$159$	0.834059	+	5.80100i	0.0661451	+	0.460050i
$160$	−10.3330	+	7.29588i	−0.816892	+	0.576790i
$161$	−7.22574	−	3.71749i	−0.569468	−	0.292979i
$162$	0.212360	+	2.02579i	0.0166846	+	0.159161i
$163$	15.7721	+	11.8069i	1.23537	+	0.924786i	0.998902	−	0.0468532i	$-0.0149193\pi$
$163$	15.7721	+	11.8069i	1.23537	+	0.924786i	0.236468	+	0.971639i	$0.424010\pi$
$164$	1.53453	−	6.87821i	0.119827	−	0.537098i
$165$	0.0962873	−	0.223222i	0.00749595	−	0.0173778i
$166$	20.9369	−	3.72011i	1.62502	−	0.288736i
$167$	−6.30775	−	11.5518i	−0.488108	−	0.893904i	−0.999405	−	0.0344994i	$-0.989016\pi$
$167$	−6.30775	−	11.5518i	−0.488108	−	0.893904i	0.511296	−	0.859405i	$-0.329165\pi$
$168$	3.59010	+	2.94052i	0.276982	+	0.226866i
$169$	−20.6722	+	9.44066i	−1.59017	+	0.726204i
$170$	−1.74531	+	0.220383i	−0.133859	+	0.0169026i
$171$	−3.58368	+	5.57632i	−0.274051	+	0.426432i
$172$	11.4129	+	9.99587i	0.870228	+	0.762178i
$173$	6.26905	−	4.69295i	0.476627	−	0.356798i	−0.333794	−	0.942646i	$-0.608329\pi$
$173$	6.26905	−	4.69295i	0.476627	−	0.356798i	0.810421	+	0.585847i	$0.199238\pi$
$174$	0.306216	−	0.101017i	0.0232142	−	0.00765807i
$175$	0.961343	+	8.41717i	0.0726707	+	0.636278i
$176$	0.297684	−	0.336268i	0.0224387	−	0.0253471i
$177$	1.08673	−	4.99560i	0.0816834	−	0.375493i
$178$	−4.09761	−	0.750519i	−0.307129	−	0.0562538i
$179$	−9.84564	+	11.3625i	−0.735898	+	0.849271i	−0.993122	−	0.117080i	$-0.962647\pi$
$179$	−9.84564	+	11.3625i	−0.735898	+	0.849271i	0.257225	+	0.966352i	$0.417192\pi$
$180$	7.67893	−	5.10875i	0.572353	−	0.380784i
$181$	8.61922	−	18.8735i	0.640661	−	1.40285i	−0.258834	−	0.965922i	$-0.583338\pi$
$181$	8.61922	−	18.8735i	0.640661	−	1.40285i	0.899495	−	0.436931i	$-0.143934\pi$
$182$	−3.50520	−	13.8869i	−0.259823	−	1.02936i
$183$	−1.94879	+	1.94879i	−0.144059	+	0.144059i
$184$	12.0269	−	6.27321i	0.886636	−	0.462468i
$185$	20.8995	+	17.3491i	1.53656	+	1.27553i
$186$	10.7367	+	6.40895i	0.787253	+	0.469927i
$187$	0.0585205	−	0.0218270i	0.00427944	−	0.00159615i
$188$	5.04950	+	1.51181i	0.368272	+	0.110260i
$189$	−6.27714	−	5.43917i	−0.456594	−	0.395641i
$190$	10.1240	+	0.899270i	0.734473	+	0.0652399i
$191$	−4.75377	−	7.39702i	−0.343971	−	0.535229i	0.625567	−	0.780170i	$-0.284868\pi$
$191$	−4.75377	−	7.39702i	−0.343971	−	0.535229i	−0.969538	+	0.244941i	$0.921231\pi$
$192$	−7.46661	+	2.06389i	−0.538856	+	0.148948i
$193$	1.17551	−	16.4358i	0.0846151	−	1.18307i	−0.760808	−	0.648977i	$-0.775197\pi$
$193$	1.17551	−	16.4358i	0.0846151	−	1.18307i	0.845423	−	0.534097i	$-0.179348\pi$
$194$	5.56265	+	16.8622i	0.399375	+	1.21064i
$195$	12.9256	+	0.649928i	0.925619	+	0.0465423i
$196$	−8.24014	+	0.545418i	−0.588581	+	0.0389584i
$197$	−16.9419	+	3.68548i	−1.20706	+	0.262579i	−0.770703	−	0.637195i	$-0.780095\pi$
$197$	−16.9419	+	3.68548i	−1.20706	+	0.262579i	−0.436355	+	0.899774i	$0.643731\pi$
$198$	−0.223773	+	0.239074i	−0.0159029	+	0.0169903i
$199$	−3.04303	−	6.66332i	−0.215715	−	0.472350i	0.770580	−	0.637344i	$-0.219967\pi$
$199$	−3.04303	−	6.66332i	−0.215715	−	0.472350i	−0.986295	+	0.164994i	$0.947240\pi$
$200$	−12.4032	−	6.79422i	−0.877036	−	0.480424i
$201$	−7.01433	−	2.05959i	−0.494753	−	0.145273i
$202$	3.90692	+	2.72802i	0.274890	+	0.191943i
$203$	0.191203	−	0.350162i	0.0134198	−	0.0245765i
$204$	−1.05151	−	0.234591i	−0.0736201	−	0.0164246i
$205$	7.66190	−	1.83735i	0.535130	−	0.128326i
$206$	9.96945	+	8.07761i	0.694605	+	0.562794i
$207$	−8.89291	+	4.32910i	−0.618100	+	0.300894i
$208$	22.3111	+	8.59238i	1.54700	+	0.595774i
$209$	−0.357191	+	0.0513563i	−0.0247074	+	0.00355239i
$210$	−1.18987	+	5.05010i	−0.0821087	+	0.348490i
$211$	6.31565	+	21.5091i	0.434787	+	1.48075i	0.827699	+	0.561173i	$0.189650\pi$
$211$	6.31565	+	21.5091i	0.434787	+	1.48075i	−0.392912	+	0.919576i	$0.628532\pi$
$212$	−11.6323	+	3.34862i	−0.798911	+	0.229984i
$213$	−0.585189	−	1.07169i	−0.0400965	−	0.0734312i
$214$	−2.68116	+	24.3310i	−0.183281	+	1.66323i
$215$	−4.43338	+	16.3726i	−0.302354	+	1.11660i
$216$	13.4611	−	3.32186i	0.915914	−	0.226024i
$217$	15.1176	−	3.28864i	1.02625	−	0.223248i
$218$	−0.131817	+	3.43527i	−0.00892777	+	0.232666i
$219$	−1.14768	+	7.98229i	−0.0775530	+	0.539393i
$220$	0.483953	+	0.133805i	0.0326281	+	0.00902115i
$221$	2.17745	+	2.51291i	0.146471	+	0.169037i
$222$	8.45021	+	14.3286i	0.567141	+	0.961670i
$223$	1.84421	−	8.47771i	0.123498	−	0.567710i	−0.873261	−	0.487254i	$-0.837999\pi$
$223$	1.84421	−	8.47771i	0.123498	−	0.567710i	0.996758	−	0.0804559i	$-0.0256376\pi$
$224$	−4.99977	+	8.17751i	−0.334061	+	0.546383i
$225$	8.90286	+	5.20294i	0.593524	+	0.346863i
$226$	3.72556	−	8.92723i	0.247820	−	0.593831i
$227$	0.616241	−	0.229846i	0.0409014	−	0.0152554i	−0.328930	−	0.944354i	$-0.606688\pi$
$227$	0.616241	−	0.229846i	0.0409014	−	0.0152554i	0.369832	+	0.929099i	$0.379415\pi$
$228$	5.64829	+	2.61580i	0.374067	+	0.173235i
$229$		−	3.04009i		−	0.200895i	−0.994942	−	0.100447i	$-0.967973\pi$
$229$		−	3.04009i		−	0.200895i	0.994942	−	0.100447i	$-0.0320274\pi$
$230$	12.2081	+	8.99788i	0.804979	+	0.593303i
$231$		−	0.184211i		−	0.0121202i
$232$	0.293360	+	0.597899i	0.0192600	+	0.0392540i
$233$	5.04680	−	1.88236i	0.330627	−	0.123318i	−0.178668	−	0.983909i	$-0.557179\pi$
$233$	5.04680	−	1.88236i	0.330627	−	0.123318i	0.509295	+	0.860592i	$0.329906\pi$
$234$	−16.0881	−	6.71395i	−1.05171	−	0.438905i
$235$	0.961908	+	5.81408i	0.0627480	+	0.379269i
$236$	10.5283	+	0.809167i	0.685333	+	0.0526723i
$237$	1.47519	−	6.78135i	0.0958241	−	0.440496i
$238$	−1.14821	+	0.677150i	−0.0744272	+	0.0438931i
$239$	−4.89033	−	5.64375i	−0.316329	−	0.365064i	0.575211	−	0.818005i	$-0.304920\pi$
$239$	−4.89033	−	5.64375i	−0.316329	−	0.365064i	−0.891540	+	0.452942i	$0.850375\pi$
$240$	−5.74046	−	6.48534i	−0.370545	−	0.418627i
$241$	−0.0661110	+	0.459812i	−0.00425858	+	0.0296191i	−0.991840	−	0.127489i	$-0.959308\pi$
$241$	−0.0661110	+	0.459812i	−0.00425858	+	0.0296191i	0.987581	+	0.157108i	$0.0502172\pi$
$242$	15.5271	+	0.595800i	0.998119	+	0.0382995i
$243$	−15.7327	+	3.42245i	−1.00926	+	0.219550i
$244$	−4.53877	−	3.43541i	−0.290565	−	0.219930i
$245$	−4.59533	−	8.00810i	−0.293585	−	0.511619i
$246$	4.79633	+	0.528534i	0.305803	+	0.0336981i
$247$	−9.20687	−	16.8611i	−0.585819	−	1.07285i
$248$	−10.0728	+	23.7808i	−0.639624	+	1.51008i
$249$	4.10209	+	13.9704i	0.259960	+	0.885341i
$250$	0.731385	−	15.7945i	0.0462568	−	0.998930i
$251$	−28.0577	+	4.03408i	−1.77098	+	0.254629i	−0.949088	−	0.315010i	$-0.897992\pi$
$251$	−28.0577	+	4.03408i	−1.77098	+	0.254629i	−0.821895	+	0.569639i	$0.807083\pi$
$252$	3.80956	−	5.85921i	0.239980	−	0.369095i
$253$	−0.495155	−	0.211548i	−0.0311302	−	0.0132999i
$254$	14.9936	−	18.5052i	0.940780	−	1.16112i
$255$	−0.280885	−	1.17131i	−0.0175897	−	0.0733505i
$256$	−6.33628	−	14.6919i	−0.396017	−	0.918243i
$257$	14.0532	−	25.7366i	0.876617	−	1.60540i	0.0833573	−	0.996520i	$-0.473436\pi$
$257$	14.0532	−	25.7366i	0.876617	−	1.60540i	0.793259	−	0.608884i	$-0.208382\pi$
$258$	−5.94715	+	8.51720i	−0.370253	+	0.530258i
$259$	19.7483	+	5.79864i	1.22710	+	0.360310i
$260$	2.32937	+	26.6288i	0.144462	+	1.65145i
$261$	−0.201728	−	0.441723i	−0.0124867	−	0.0273420i
$262$	−10.4148	−	9.74820i	−0.643426	−	0.602246i
$263$	23.4201	−	5.09472i	1.44414	−	0.314154i	0.578855	−	0.815430i	$-0.303500\pi$
$263$	23.4201	−	5.09472i	1.44414	−	0.314154i	0.865287	+	0.501276i	$0.167136\pi$
$264$	0.251186	+	0.177381i	0.0154594	+	0.0109171i
$265$	−9.07697	−	10.0381i	−0.557594	−	0.616637i
$266$	7.31397	−	2.41279i	0.448448	−	0.147938i
$267$	0.203484	−	2.84508i	0.0124530	−	0.174116i
$268$	2.22810	−	14.9339i	0.136103	−	0.912231i
$269$	6.47449	+	10.0745i	0.394756	+	0.614253i	0.980565	−	0.196197i	$-0.0628591\pi$
$269$	6.47449	+	10.0745i	0.394756	+	0.614253i	−0.585808	+	0.810450i	$0.699223\pi$
$270$	9.94840	+	11.8880i	0.605441	+	0.723483i
$271$	−0.573207	−	0.496686i	−0.0348198	−	0.0301716i	0.637277	−	0.770635i	$-0.280061\pi$
$271$	−0.573207	−	0.496686i	−0.0348198	−	0.0301716i	−0.672097	+	0.740463i	$0.734606\pi$
$272$	0.182287	−	2.21771i	0.0110528	−	0.134469i
$273$	9.18839	−	3.42709i	0.556107	−	0.207417i
$274$	10.9130	−	18.2821i	0.659277	−	1.10446i
$275$	0.103329	+	0.551785i	0.00623097	+	0.0332739i
$276$	5.17148	+	7.71493i	0.311287	+	0.464384i
$277$	5.23951	−	5.23951i	0.314811	−	0.314811i	−0.531959	−	0.846770i	$-0.678544\pi$
$277$	5.23951	−	5.23951i	0.314811	−	0.314811i	0.846770	+	0.531959i	$0.178544\pi$
$278$	2.59811	−	0.655791i	0.155824	−	0.0393317i
$279$	7.82272	−	17.1294i	0.468334	−	1.02551i
$280$	−10.6690	−	1.00476i	−0.637593	−	0.0600458i
$281$	4.30361	−	4.96663i	0.256732	−	0.296285i	−0.612722	−	0.790299i	$-0.709925\pi$
$281$	4.30361	−	4.96663i	0.256732	−	0.296285i	0.869454	+	0.494014i	$0.164471\pi$
$282$	−0.650224	+	3.55002i	−0.0387203	+	0.211401i
$283$	−1.53876	+	7.07356i	−0.0914697	+	0.420479i	0.908527	+	0.417827i	$0.137208\pi$
$283$	−1.53876	+	7.07356i	−0.0914697	+	0.420479i	−0.999996	+	0.00265283i	$0.999156\pi$
$284$	2.02695	−	1.50064i	0.120277	−	0.0890465i
$285$	0.147246	+	6.95775i	0.00872213	+	0.412142i
$286$	−0.297320	−	0.901277i	−0.0175809	−	0.0532936i
$287$	4.77955	−	3.57793i	0.282128	−	0.211198i
$288$	4.32117	+	10.8366i	0.254627	+	0.638553i
$289$	−9.02358	+	14.0410i	−0.530799	+	0.825939i
$290$	−0.456404	+	0.588323i	−0.0268010	+	0.0345475i
$291$	−11.0591	+	5.05052i	−0.648295	+	0.296066i
$292$	−16.6561	−	0.0883756i	−0.974723	−	0.00517179i
$293$	−1.21309	−	2.22161i	−0.0708695	−	0.129788i	0.839842	−	0.542831i	$-0.182648\pi$
$293$	−1.21309	−	2.22161i	−0.0708695	−	0.129788i	−0.910711	+	0.413043i	$0.864466\pi$
$294$	−0.989200	−	5.56725i	−0.0576913	−	0.324689i
$295$	4.35878	+	10.9716i	0.253778	+	0.638790i
$296$	−26.9230	+	21.3448i	−1.56487	+	1.24064i
$297$	−0.440596	−	0.329826i	−0.0255660	−	0.0191385i
$298$	11.5599	−	1.21180i	0.669647	−	0.0701979i
$299$	1.34000	−	28.6339i	0.0774945	−	1.65594i
$300$	3.69387	−	8.95103i	0.213266	−	0.516788i
$301$	1.82918	+	12.7222i	0.105432	+	0.733298i
$302$	9.38014	−	27.9353i	0.539766	−	1.60749i
$303$	−1.56365	+	2.86361i	−0.0898293	+	0.164510i
$304$	−3.75276	+	12.2965i	−0.215236	+	0.705253i
$305$	1.22093	−	6.24599i	0.0699101	−	0.357645i
$306$	−0.177716	+	1.61273i	−0.0101593	+	0.0921939i
$307$	−7.54679	+	20.2337i	−0.430718	+	1.15480i	0.522533	+	0.852619i	$0.324987\pi$
$307$	−7.54679	+	20.2337i	−0.430718	+	1.15480i	−0.953251	+	0.302181i	$0.902285\pi$
$308$	0.376883	−	0.0521480i	0.0214749	−	0.00297141i
$309$	−4.74986	+	7.39092i	−0.270210	+	0.420455i
$310$	−28.8321	+	1.56443i	−1.63755	+	0.0888534i
$311$	5.87378	+	0.844523i	0.333072	+	0.0478885i	0.306822	−	0.951767i	$-0.400734\pi$
$311$	5.87378	+	0.844523i	0.333072	+	0.0478885i	0.0262498	+	0.999655i	$0.491643\pi$
$312$	−4.17461	+	15.8291i	−0.236340	+	0.896147i
$313$	−0.442394	+	6.18548i	−0.0250056	+	0.349624i	0.969511	+	0.245047i	$0.0788034\pi$
$313$	−0.442394	+	6.18548i	−0.0250056	+	0.349624i	−0.994517	+	0.104577i	$0.966651\pi$
$314$	−0.792758	+	3.07196i	−0.0447379	+	0.173361i
$315$	7.75596	+	0.948115i	0.436999	+	0.0534202i
$316$	14.2918	+	1.09841i	0.803975	+	0.0617907i
$317$	0.0978538	+	1.36818i	0.00549602	+	0.0768444i	0.999460	−	0.0328640i	$-0.0104628\pi$
$317$	0.0978538	+	1.36818i	0.00549602	+	0.0768444i	−0.993964	+	0.109708i	$0.965008\pi$
$318$	−3.15144	−	7.66571i	−0.176724	−	0.429871i
$319$	0.0109822	−	0.0240476i	0.000614885	−	0.00134641i
$320$	11.6435	−	13.5805i	0.650890	−	0.759172i
$321$	−16.7605			−0.935480
$322$	11.1946	+	2.59656i	0.623853	+	0.144701i
$323$	−1.26431	+	1.26431i	−0.0703478	+	0.0703478i
$324$	−0.992330	−	2.70427i	−0.0551294	−	0.150237i
$325$	−25.6005	+	15.4195i	−1.42006	+	0.855320i
$326$	−25.7133	−	10.7308i	−1.42413	−	0.594325i
$327$	−2.34790	+	0.167925i	−0.129839	+	0.00928626i
$328$	0.276444	+	9.96256i	0.0152640	+	0.550090i
$329$	2.41423	+	3.75662i	0.133101	+	0.207109i
$330$	−0.0547711	+	0.339409i	−0.00301505	+	0.0186838i
$331$	14.1998	−	12.3042i	0.780492	−	0.676300i	−0.170554	−	0.985348i	$-0.554556\pi$
$331$	14.1998	−	12.3042i	0.780492	−	0.676300i	0.951046	+	0.309048i	$0.100010\pi$
$332$	−27.4213	+	12.3475i	−1.50494	+	0.677655i
$333$	20.0550	−	15.0130i	1.09901	−	0.822708i
$334$	12.6474	+	13.6567i	0.692035	+	0.747263i
$335$	16.0933	−	5.09768i	0.879271	−	0.278516i
$336$	−5.94050	−	2.78950i	−0.324081	−	0.152180i
$337$	14.5838	+	5.43948i	0.794430	+	0.296307i	0.713721	−	0.700430i	$-0.247009\pi$
$337$	14.5838	+	5.43948i	0.794430	+	0.296307i	0.0807097	+	0.996738i	$0.474281\pi$
$338$	25.0783	−	20.0999i	1.36408	−	1.09329i
$339$	6.35520	+	1.86605i	0.345167	+	0.101350i
$340$	2.31691	−	0.906256i	0.125652	−	0.0491486i
$341$	0.983648	−	0.288825i	0.0532675	−	0.0156408i
$342$	2.98396	−	8.88663i	0.161354	−	0.480534i
$343$	−15.0957	−	11.3005i	−0.815091	−	0.610170i
$344$	−19.1091	−	9.75631i	−1.03030	−	0.526025i
$345$	−5.20829	+	8.98355i	−0.280405	+	0.483658i
$346$	−6.97190	+	8.60477i	−0.374812	+	0.462595i
$347$	8.76483	−	11.7084i	0.470521	−	0.628542i	−0.501014	−	0.865439i	$-0.667039\pi$
$347$	8.76483	−	11.7084i	0.470521	−	0.628542i	0.971535	+	0.236897i	$0.0761304\pi$
$348$	−0.384923	+	0.244499i	−0.0206340	+	0.0131065i
$349$	−0.803605	−	2.73683i	−0.0430160	−	0.146499i	0.935185	−	0.354160i	$-0.115233\pi$
$349$	−0.803605	−	2.73683i	−0.0430160	−	0.146499i	−0.978201	+	0.207661i	$0.933415\pi$
$350$	−4.23145	−	11.2090i	−0.226180	−	0.599144i
$351$	8.25471	−	28.1130i	0.440604	−	1.50056i
$352$	−0.291801	+	0.564123i	−0.0155530	+	0.0300679i
$353$	−2.77738	+	7.44644i	−0.147825	+	0.396334i	−0.989666	−	0.143392i	$-0.954199\pi$
$353$	−2.77738	+	7.44644i	−0.147825	+	0.396334i	0.841841	+	0.539725i	$0.181472\pi$
$354$	0.238889	+	7.22613i	0.0126968	+	0.384065i
$355$	2.50280	+	1.29866i	0.132835	+	0.0689257i
$356$	5.87843	−	0.389095i	0.311556	−	0.0206220i
$357$	−0.546975	−	0.730673i	−0.0289490	−	0.0386713i
$358$	9.56777	−	18.9880i	0.505673	−	1.00354i
$359$	−14.7339	−	17.0038i	−0.777623	−	0.897425i	0.219312	−	0.975655i	$-0.429619\pi$
$359$	−14.7339	−	17.0038i	−0.777623	−	0.897425i	−0.996935	+	0.0782300i	$0.975073\pi$
$360$	−8.76122	+	9.66290i	−0.461757	+	0.509279i
$361$	−7.29330	+	4.68712i	−0.383858	+	0.246690i
$362$	−5.28649	+	28.8626i	−0.277851	+	1.51698i
$363$	0.759005	+	10.6123i	0.0398374	+	0.557000i
$364$	9.61271	+	17.8286i	0.503843	+	0.934473i
$365$	−8.09267	−	16.7720i	−0.423590	−	0.877886i
$366$	1.99771	−	3.34669i	0.104422	−	0.174934i
$367$	−13.9399	−	13.9399i	−0.727658	−	0.727658i	0.242495	−	0.970153i	$-0.422034\pi$
$367$	−13.9399	−	13.9399i	−0.727658	−	0.727658i	−0.970153	+	0.242495i	$0.922034\pi$
$368$	−14.3202	+	12.7645i	−0.746492	+	0.665395i
$369$		−	7.26698i		−	0.378304i
$370$	−34.6622	−	16.5557i	−1.80200	−	0.860691i
$371$	−9.32826	−	4.26007i	−0.484299	−	0.221172i
$372$	−16.9404	−	5.07194i	−0.878320	−	0.262968i
$373$	−34.0698	+	2.43672i	−1.76407	+	0.126169i	−0.915346	−	0.402669i	$-0.868082\pi$
$373$	−34.0698	+	2.43672i	−1.76407	+	0.126169i	−0.848723	+	0.528838i	$0.822628\pi$
$374$	−0.0726892	+	0.0501837i	−0.00375867	+	0.00259494i
$375$	10.8044	−	0.686780i	0.557937	−	0.0354651i
$376$	−7.44716	−	0.325340i	−0.384058	−	0.0167781i
$377$	1.40380	+	0.100402i	0.0722995	+	0.00517097i
$378$	10.4898	+	5.28566i	0.539537	+	0.271865i
$379$	0.531178	−	3.69442i	0.0272848	−	0.189770i	−0.971621	−	0.236544i	$-0.923985\pi$
$379$	0.531178	−	3.69442i	0.0272848	−	0.189770i	0.998905	+	0.0467746i	$0.0148942\pi$
$380$	−14.1934	+	2.27092i	−0.728105	+	0.116495i
$381$	13.7189	+	8.81662i	0.702842	+	0.451689i
$382$	9.07857	+	8.49753i	0.464500	+	0.434771i
$383$	−32.6900	−	12.1927i	−1.67038	−	0.623020i	−0.676803	−	0.736164i	$-0.736635\pi$
$383$	−32.6900	−	12.1927i	−1.67038	−	0.623020i	−0.993579	+	0.113144i	$0.963908\pi$
$384$	9.52395	−	5.41427i	0.486017	−	0.276296i
$385$	0.237499	+	0.352908i	0.0121041	+	0.0179859i
$386$	4.07668	+	22.9437i	0.207498	+	1.16780i
$387$	13.7307	+	7.49754i	0.697972	+	0.381121i
$388$	−13.4637	−	21.1963i	−0.683515	−	1.07608i
$389$	17.6193	−	2.53327i	0.893334	−	0.128442i	0.319666	−	0.947530i	$-0.396429\pi$
$389$	17.6193	−	2.53327i	0.893334	−	0.128442i	0.573668	+	0.819088i	$0.305520\pi$
$390$	−17.9486	+	3.58245i	−0.908862	+	0.181405i
$391$	−2.59218	+	0.631152i	−0.131092	+	0.0319187i
$392$	11.1102	−	3.59986i	0.561148	−	0.181820i
$393$	5.85344	−	7.81928i	0.295267	−	0.394431i
$394$	21.9552	−	10.9173i	1.10609	−	0.550004i
$395$	5.91689	+	14.8935i	0.297711	+	0.749374i
$396$	0.224094	−	0.405270i	0.0112611	−	0.0203656i
$397$	−11.7422	+	6.41174i	−0.589325	+	0.321796i	−0.746095	−	0.665839i	$-0.768074\pi$
$397$	−11.7422	+	6.41174i	−0.589325	+	0.321796i	0.156770	+	0.987635i	$0.449892\pi$
$398$	6.47886	+	8.08357i	0.324756	+	0.405193i
$399$	2.19065	+	4.79686i	0.109670	+	0.240143i
$400$	19.3588	+	5.02345i	0.967942	+	0.251173i
$401$	−1.08626	−	0.698099i	−0.0542454	−	0.0348614i	0.513237	−	0.858247i	$-0.328446\pi$
$401$	−1.08626	−	0.698099i	−0.0542454	−	0.0348614i	−0.567482	+	0.823385i	$0.692083\pi$
$402$	10.3309	+	0.396415i	0.515261	+	0.0197714i
$403$	32.7065	+	43.6907i	1.62922	+	2.17639i
$404$	−6.30139	−	2.38846i	−0.313506	−	0.118830i
$405$	2.22862	−	2.32498i	0.110741	−	0.115529i
$406$	−0.140985	+	0.546321i	−0.00699697	+	0.0271135i
$407$	1.33267	+	0.289904i	0.0660579	+	0.0143700i
$408$	1.52303	−	0.0422613i	0.0754010	−	0.00209225i
$409$	0.0941485	+	0.0815801i	0.00465534	+	0.00403388i	0.657185	−	0.753729i	$-0.271747\pi$
$409$	0.0941485	+	0.0815801i	0.00465534	+	0.00403388i	−0.652530	+	0.757763i	$0.726292\pi$
$410$	−9.87013	+	5.17123i	−0.487451	+	0.255389i
$411$	13.2611	+	6.05614i	0.654122	+	0.298727i
$412$	−16.4659	−	7.62557i	−0.811217	−	0.375685i
$413$	6.32560	+	6.32560i	0.311262	+	0.311262i
$414$	10.6957	−	9.01401i	0.525665	−	0.443014i
$415$	−25.8705	−	21.4756i	−1.26993	−	1.05419i
$416$	−33.5670	−	4.05990i	−1.64576	−	0.199053i
$417$	0.641178	+	1.71906i	0.0313986	+	0.0841829i
$418$	0.472008	−	0.194047i	0.0230867	−	0.00949113i
$419$	−15.8292	+	18.2679i	−0.773307	+	0.892444i	−0.996607	−	0.0823055i	$-0.973772\pi$
$419$	−15.8292	+	18.2679i	−0.773307	+	0.892444i	0.223300	+	0.974750i	$0.428317\pi$
$420$	−0.116323	−	7.33656i	−0.00567598	−	0.357987i
$421$	−21.3229	+	13.7034i	−1.03922	+	0.667864i	−0.944793	−	0.327668i	$-0.893737\pi$
$421$	−21.3229	+	13.7034i	−1.03922	+	0.667864i	−0.0944234	+	0.995532i	$0.530101\pi$
$422$	−16.1045	−	27.3076i	−0.783956	−	1.32931i
$423$	5.42142	+	0.387747i	0.263598	+	0.0188529i
$424$	14.7913	−	8.61769i	0.718331	−	0.418512i
$425$	2.04826	+	1.88184i	0.0993552	+	0.0912826i
$426$	1.17334	+	1.26698i	0.0568483	+	0.0613851i
$427$	−1.02509	−	4.71226i	−0.0496075	−	0.228042i
$428$	−4.74470	−	34.2908i	−0.229344	−	1.65751i
$429$	0.591102	−	0.269947i	0.0285387	−	0.0130332i
$430$	0.412409	−	23.9846i	0.0198881	−	1.15664i
$431$	−0.786419	+	2.67830i	−0.0378805	+	0.129009i	−0.976263	−	0.216591i	$-0.930506\pi$
$431$	−0.786419	+	2.67830i	−0.0378805	+	0.129009i	0.938382	+	0.345600i	$0.112324\pi$
$432$	−17.3083	+	9.21397i	−0.832745	+	0.443307i
$433$	−27.2133	−	14.8596i	−1.30779	−	0.714107i	−0.334220	−	0.942495i	$-0.608473\pi$
$433$	−27.2133	−	14.8596i	−1.30779	−	0.714107i	−0.973570	+	0.228388i	$0.926655\pi$
$434$	−19.5912	+	9.74175i	−0.940408	+	0.467619i
$435$	−0.434636	−	0.266501i	−0.0208392	−	0.0127778i
$436$	−1.00822	−	4.75609i	−0.0482852	−	0.227775i
$437$	15.4096	−	0.379709i	0.737141	−	0.0181639i
$438$	−1.18902	−	11.3426i	−0.0568138	−	0.541970i
$439$	1.73634	+	12.0765i	0.0828710	+	0.576381i	0.988374	+	0.152041i	$0.0485846\pi$
$439$	1.73634	+	12.0765i	0.0828710	+	0.576381i	−0.905503	+	0.424340i	$0.860506\pi$
$440$	−0.709911	−	0.0159749i	−0.0338437	−	0.000761575i
$441$	−8.17065	+	2.39912i	−0.389079	+	0.114244i
$442$	−3.85547	−	2.69209i	−0.183386	−	0.128050i
$443$	21.4865	−	11.7325i	1.02085	−	0.557428i	0.120558	−	0.992706i	$-0.461532\pi$
$443$	21.4865	−	11.7325i	1.02085	−	0.557428i	0.900296	+	0.435278i	$0.143350\pi$
$444$	−16.5462	−	16.7227i	−0.785249	−	0.793626i
$445$	3.27826	+	5.71289i	0.155404	+	0.270817i
$446$	0.405403	+	12.2630i	0.0191964	+	0.580670i
$447$	1.69171	+	7.77667i	0.0800152	+	0.367824i
$448$	4.02542	−	12.9435i	0.190183	−	0.611524i
$449$	−0.488698	−	0.0702642i	−0.0230631	−	0.00331597i	0.130774	−	0.991412i	$-0.458254\pi$
$449$	−0.488698	−	0.0702642i	−0.0230631	−	0.00331597i	−0.153837	+	0.988096i	$0.549163\pi$
$450$	−14.0085	−	4.05296i	−0.660365	−	0.191059i
$451$	0.298989	−	0.259075i	0.0140788	−	0.0121994i
$452$	−2.01873	+	13.5305i	−0.0949530	+	0.636423i
$453$	19.7160	+	4.28894i	0.926336	+	0.201512i
$454$	−0.765443	+	0.528452i	−0.0359240	+	0.0248015i
$455$	−13.1845	+	18.4119i	−0.618098	+	0.863165i
$456$	−8.65033	−	1.63188i	−0.405089	−	0.0764199i
$457$	1.72579	+	4.62703i	0.0807292	+	0.216443i	0.971043	−	0.238903i	$-0.0767880\pi$
$457$	1.72579	+	4.62703i	0.0807292	+	0.216443i	−0.890314	+	0.455347i	$0.849515\pi$
$458$	1.05220	+	4.16860i	0.0491660	+	0.194786i
$459$	−2.72697			−0.127284
$460$	−19.8541	−	8.11264i	−0.925702	−	0.378254i
$461$	−20.0436			−0.933525			−0.466763	−	0.884383i	$-0.654580\pi$
$461$	−20.0436			−0.933525			−0.466763	+	0.884383i	$0.654580\pi$
$462$	0.0637569	+	0.252592i	0.00296624	+	0.0117516i
$463$	−10.1860	−	27.3096i	−0.473382	−	1.26919i	−0.926014	−	0.377489i	$-0.876788\pi$
$463$	−10.1860	−	27.3096i	−0.473382	−	1.26919i	0.452632	−	0.891697i	$-0.350485\pi$
$464$	−0.609194	−	0.718310i	−0.0282811	−	0.0333467i
$465$	−3.22708	−	19.5055i	−0.149652	−	0.904546i
$466$	−6.26871	+	4.32784i	−0.290393	+	0.200484i
$467$	−13.1512	−	2.86087i	−0.608566	−	0.132385i	−0.102287	−	0.994755i	$-0.532616\pi$
$467$	−13.1512	−	2.86087i	−0.608566	−	0.132385i	−0.506279	+	0.862370i	$0.668980\pi$
$468$	24.3838	+	3.63802i	1.12714	+	0.168167i
$469$	9.66743	−	8.37687i	0.446400	−	0.386808i
$470$	−3.33127	−	7.63938i	−0.153660	−	0.352378i
$471$	−2.15020	−	0.309153i	−0.0990761	−	0.0142450i
$472$	−14.7165	+	2.53438i	−0.677383	+	0.116655i
$473$	0.181039	+	0.832224i	0.00832419	+	0.0382657i
$474$	0.324283	+	9.80921i	0.0148948	+	0.450552i
$475$	−9.25255	−	13.1397i	−0.424536	−	0.602890i
$476$	1.34006	−	1.32592i	0.0614216	−	0.0607733i
$477$	−10.9552	+	5.98201i	−0.501606	+	0.273897i
$478$	8.65901	+	6.04616i	0.396054	+	0.276545i
$479$	28.1935	−	8.27837i	1.28820	−	0.378248i	0.435279	−	0.900296i	$-0.356650\pi$
$479$	28.1935	−	8.27837i	1.28820	−	0.378248i	0.852917	+	0.522047i	$0.174831\pi$
$480$	10.1160	+	6.90593i	0.461729	+	0.315211i
$481$	10.3328	+	71.8665i	0.471137	+	3.27683i
$482$	−0.0684926	−	0.653379i	−0.00311975	−	0.0297606i
$483$	−0.927616	+	7.81370i	−0.0422080	+	0.355536i
$484$	−21.4971	+	4.55708i	−0.977140	+	0.207140i
$485$	14.6753	−	23.9339i	0.666370	−	1.08678i
$486$	20.3883	−	10.1381i	0.924832	−	0.459874i
$487$	6.59040	+	3.59863i	0.298640	+	0.163070i	0.621582	−	0.783349i	$-0.286490\pi$
$487$	6.59040	+	3.59863i	0.298640	+	0.163070i	−0.322943	+	0.946419i	$0.604672\pi$
$488$	7.41262	+	3.13975i	0.335553	+	0.142130i
$489$	5.37484	−	18.3050i	0.243059	−	0.827782i
$490$	9.07281	+	9.39028i	0.409868	+	0.424210i
$491$	17.4056	−	7.94888i	0.785504	−	0.358728i	0.0180546	−	0.999837i	$-0.494253\pi$
$491$	17.4056	−	7.94888i	0.785504	−	0.358728i	0.767450	+	0.641109i	$0.221525\pi$
$492$	−6.75969	+	0.935316i	−0.304750	+	0.0421673i
$493$	−0.0278434	−	0.127994i	−0.00125401	−	0.00576457i
$494$	18.4603	+	19.9335i	0.830568	+	0.896852i
$495$	0.517109	+	0.0260014i	0.0232423	+	0.00116868i
$496$	5.58119	−	36.0947i	0.250603	−	1.62070i
$497$	2.13116	+	0.152423i	0.0955954	+	0.00683712i
$498$	−10.4601	−	17.7366i	−0.468728	−	0.794797i
$499$	−15.7764	+	10.1389i	−0.706247	+	0.453878i	−0.843829	−	0.536613i	$-0.819704\pi$
$499$	−15.7764	+	10.1389i	−0.706247	+	0.453878i	0.137581	+	0.990490i	$0.456067\pi$
$500$	4.46371	+	21.9106i	0.199623	+	0.979873i
$501$	−8.34611	+	9.63192i	−0.372877	+	0.430323i
$502$	37.0766	−	15.2425i	1.65481	−	0.680307i
$503$	3.81972	+	10.2411i	0.170313	+	0.456626i	0.993863	−	0.110617i	$-0.0352827\pi$
$503$	3.81972	+	10.2411i	0.170313	+	0.456626i	−0.823550	+	0.567243i	$0.808010\pi$
$504$	−3.19578	+	9.35270i	−0.142351	+	0.416603i
$505$	−0.696374	−	7.50203i	−0.0309883	−	0.333836i
$506$	0.752179	+	0.118699i	0.0334384	+	0.00527683i
$507$	15.5606	+	15.5606i	0.691071	+	0.691071i
$508$	−14.1545	+	30.5638i	−0.628004	+	1.35605i
$509$	17.7878	+	8.12343i	0.788431	+	0.360065i	0.768593	−	0.639739i	$-0.220957\pi$
$509$	17.7878	+	8.12343i	0.788431	+	0.360065i	0.0198388	+	0.999803i	$0.493685\pi$
$510$	0.790552	+	1.50890i	0.0350062	+	0.0668150i
$511$	−10.6644	−	9.24077i	−0.471766	−	0.408787i
$512$	13.7733	+	17.9526i	0.608701	+	0.793400i
$513$	15.3955	+	3.34908i	0.679726	+	0.147865i
$514$	−10.3623	+	40.1541i	−0.457060	+	1.77112i
$515$	−0.429253	−	20.2833i	−0.0189152	−	0.893787i
$516$	5.20690	−	13.7372i	0.229221	−	0.604746i
$517$	0.177326	+	0.236879i	0.00779877	+	0.0104179i
$518$	−29.0860	−	1.11608i	−1.27797	−	0.0490377i
$519$	−6.37920	−	4.09966i	−0.280016	−	0.179955i
$520$	−12.4105	−	35.7073i	−0.544235	−	1.56587i
$521$	10.7481	+	23.5351i	0.470883	+	1.03109i	0.984870	+	0.173292i	$0.0554405\pi$
$521$	10.7481	+	23.5351i	0.470883	+	1.03109i	−0.513987	+	0.857798i	$0.671832\pi$
$522$	0.429495	+	0.535874i	0.0187985	+	0.0234546i
$523$	15.5522	−	8.49215i	0.680050	−	0.371336i	−0.101797	−	0.994805i	$-0.532459\pi$
$523$	15.5522	−	8.49215i	0.680050	−	0.371336i	0.781848	+	0.623470i	$0.214277\pi$
$524$	17.6547	+	9.76217i	0.771250	+	0.426462i
$525$	7.31136	−	3.72053i	0.319094	−	0.162377i
$526$	−30.3504	+	15.0918i	−1.32334	+	0.658033i
$527$	3.04404	−	4.06636i	0.132600	−	0.177133i
$528$	−0.405821	−	0.156289i	−0.0176611	−	0.00680160i
$529$	19.9378	+	11.4667i	0.866860	+	0.498551i
$530$	15.9207	+	10.6227i	0.691550	+	0.461422i
$531$	10.7777	−	1.54959i	0.467711	−	0.0672466i
$532$	−9.19388	+	5.83985i	−0.398605	+	0.253190i
$533$	18.4850	+	10.0936i	0.800675	+	0.437202i
$534$	0.705685	+	3.97162i	0.0305380	+	0.171869i
$535$	32.1094	−	21.6089i	1.38821	−	0.934235i
$536$	2.11353	+	21.2486i	0.0912908	+	0.917799i
$537$	13.6406	+	5.08768i	0.588635	+	0.219549i
$538$	−12.3647	−	11.5734i	−0.533081	−	0.498963i
$539$	−0.390000	−	0.250638i	−0.0167985	−	0.0107957i
$540$	−17.7559	−	12.8577i	−0.764091	−	0.553309i
$541$	3.37007	−	23.4393i	0.144891	−	1.00774i	−0.779531	−	0.626364i	$-0.784543\pi$
$541$	3.37007	−	23.4393i	0.144891	−	1.00774i	0.924422	−	0.381372i	$-0.124548\pi$
$542$	0.957892	+	0.482669i	0.0411450	+	0.0207324i
$543$	−20.0401	−	1.43329i	−0.860002	−	0.0615086i
$544$	0.517614	+	3.10404i	0.0221925	+	0.133084i
$545$	4.28155	−	3.34879i	0.183401	−	0.143446i
$546$	−11.4130	+	7.87943i	−0.488433	+	0.337208i
$547$	7.66248	−	0.548032i	0.327624	−	0.0234321i	0.0934415	−	0.995625i	$-0.470213\pi$
$547$	7.66248	−	0.548032i	0.327624	−	0.0234321i	0.234183	+	0.972193i	$0.424759\pi$
$548$	−8.63636	+	28.8457i	−0.368927	+	1.23223i
$549$	−5.33932	−	2.43839i	−0.227877	−	0.104068i
$550$	−0.332662	−	0.720848i	−0.0141848	−	0.0307371i
$551$			0.756802i			0.0322409i
$552$	−9.76137	−	8.78887i	−0.415472	−	0.374079i
$553$	8.58677	+	8.58677i	0.365147	+	0.365147i
$554$	−5.37102	+	8.99788i	−0.228193	+	0.382283i
$555$	8.66806	−	24.8324i	0.367939	−	1.05408i
$556$	−3.33557	+	1.79845i	−0.141460	+	0.0762713i
$557$	2.98310	+	41.7092i	0.126398	+	1.76727i	0.525904	+	0.850544i	$0.323727\pi$
$557$	2.98310	+	41.7092i	0.126398	+	1.76727i	−0.399506	+	0.916731i	$0.630818\pi$
$558$	−4.79796	+	26.1954i	−0.203114	+	1.10894i
$559$	−38.1430	+	24.5130i	−1.61328	+	1.03679i
$560$	14.9771	−	2.31488i	0.632900	−	0.0978217i
$561$	−0.0396061	−	0.0457079i	−0.00167217	−	0.00192979i
$562$	−4.18216	+	8.29980i	−0.176414	+	0.350106i
$563$	2.53302	+	3.38371i	0.106754	+	0.142607i	0.850736	−	0.525593i	$-0.176156\pi$
$563$	2.53302	+	3.38371i	0.106754	+	0.142607i	−0.743983	+	0.668199i	$0.767065\pi$
$564$	−0.337099	−	5.09286i	−0.0141944	−	0.214448i
$565$	−14.5810	+	4.61865i	−0.613428	+	0.194308i
$566$	−0.338256	−	10.2319i	−0.0142180	−	0.430079i
$567$	0.852835	−	2.28654i	0.0358157	−	0.0960256i
$568$	−2.25998	+	2.75923i	−0.0948267	+	0.115775i
$569$	7.88448	−	26.8521i	0.330535	−	1.12570i	−0.611796	−	0.791015i	$-0.709553\pi$
$569$	7.88448	−	26.8521i	0.330535	−	1.12570i	0.942331	−	0.334683i	$-0.108629\pi$
$570$	−2.61004	−	9.48956i	−0.109322	−	0.397474i
$571$	2.62710	+	8.94710i	0.109941	+	0.374424i	0.996022	−	0.0891055i	$-0.0284008\pi$
$571$	2.62710	+	8.94710i	0.109941	+	0.374424i	−0.886081	+	0.463530i	$0.846583\pi$
$572$	0.719627	+	1.13293i	0.0300891	+	0.0473703i
$573$	−5.10246	+	6.81609i	−0.213158	+	0.284746i
$574$	−5.31540	+	6.56032i	−0.221861	+	0.273822i
$575$	−1.60434	−	23.9254i	−0.0669056	−	0.997759i
$576$	−9.67585	−	13.3636i	−0.403161	−	0.556818i
$577$	−20.3737	−	15.2515i	−0.848167	−	0.634930i	0.0841976	−	0.996449i	$-0.473167\pi$
$577$	−20.3737	−	15.2515i	−0.848167	−	0.634930i	−0.932365	+	0.361519i	$0.882258\pi$
$578$	7.51352	−	22.3762i	0.312521	−	0.930728i
$579$	−15.3095	+	4.49528i	−0.636242	+	0.186818i
$580$	0.422201	−	0.964678i	0.0175310	−	0.0400561i
$581$	−24.4455	−	7.17785i	−1.01417	−	0.297787i
$582$	13.4163	−	10.7529i	0.556123	−	0.445724i
$583$	−0.636685	−	0.237471i	−0.0263688	−	0.00983506i
$584$	22.8695	−	5.64361i	0.946347	−	0.233534i
$585$	8.32343	+	26.2769i	0.344131	+	1.08642i
$586$	2.43231	+	2.62643i	0.100478	+	0.108497i
$587$	37.8738	−	28.3520i	1.56322	−	1.17021i	0.652054	−	0.758173i	$-0.273908\pi$
$587$	37.8738	−	28.3520i	1.56322	−	1.17021i	0.911166	−	0.412039i	$-0.135183\pi$
$588$	3.28327	+	7.29149i	0.135400	+	0.300696i
$589$	−22.1795	+	19.2186i	−0.913890	+	0.791890i
$590$	−9.77414	−	13.5357i	−0.402395	−	0.557256i
$591$	9.07678	+	14.1237i	0.373369	+	0.580973i
$592$	29.5295	−	38.5864i	1.21365	−	1.58589i
$593$	5.23533	−	0.374438i	0.214989	−	0.0153763i	0.0365709	−	0.999331i	$-0.488357\pi$
$593$	5.23533	−	0.374438i	0.214989	−	0.0153763i	0.178418	+	0.983955i	$0.442902\pi$
$594$	0.718304	+	0.299766i	0.0294724	+	0.0122996i
$595$	1.98992	+	0.694608i	0.0815789	+	0.0284761i
$596$	−15.4316	+	5.66260i	−0.632103	+	0.231949i
$597$	−5.01570	+	5.01570i	−0.205279	+	0.205279i
$598$	8.07298	+	39.7268i	0.330129	+	1.62455i
$599$	41.8324			1.70923			0.854613	−	0.519265i	$-0.173794\pi$
$599$	41.8324			1.70923			0.854613	+	0.519265i	$0.173794\pi$
$600$	−1.96704	+	13.5522i	−0.0803040	+	0.553266i
$601$	15.0811	−	33.0230i	0.615171	−	1.34704i	−0.303810	−	0.952733i	$-0.598259\pi$
$601$	15.0811	−	33.0230i	0.615171	−	1.34704i	0.918980	−	0.394303i	$-0.129014\pi$
$602$	−6.91145	−	16.8117i	−0.281690	−	0.685195i
$603$	−1.11074	−	15.5302i	−0.0452328	−	0.632437i
$604$	−3.19351	+	41.5516i	−0.129942	+	1.69071i
$605$	−15.1362	−	19.3522i	−0.615376	−	0.786780i
$606$	1.15297	−	4.46780i	0.0468362	−	0.181492i
$607$	−1.45924	+	20.4028i	−0.0592286	+	0.828125i	0.877834	+	0.478964i	$0.158988\pi$
$607$	−1.45924	+	20.4028i	−0.0592286	+	0.828125i	−0.937063	+	0.349160i	$0.886467\pi$
$608$	0.889903	−	18.1599i	0.0360903	−	0.736482i
$609$	−0.382395	−	0.0549800i	−0.0154954	−	0.00222790i
$610$	0.487641	+	8.98712i	0.0197440	+	0.363878i
$611$	−8.51647	+	13.2519i	−0.344540	+	0.536114i
$612$	−0.314494	−	2.27290i	−0.0127127	−	0.0918766i
$613$	7.61073	−	20.4052i	0.307395	−	0.824157i	−0.687769	−	0.725929i	$-0.741410\pi$
$613$	7.61073	−	20.4052i	0.307395	−	0.824157i	0.995164	−	0.0982276i	$-0.0313173\pi$
$614$	3.34517	−	30.3566i	0.135000	−	1.22509i
$615$	−4.25973	−	6.32969i	−0.171769	−	0.255238i
$616$	−0.498735	+	0.201948i	−0.0200946	+	0.00813671i
$617$	12.9494	−	23.7150i	0.521322	−	0.954730i	−0.475846	−	0.879528i	$-0.657858\pi$
$617$	12.9494	−	23.7150i	0.521322	−	0.954730i	0.997168	−	0.0752016i	$-0.0239600\pi$
$618$	3.95498	−	11.7784i	0.159093	−	0.473798i
$619$	0.664828	+	4.62398i	0.0267217	+	0.185854i	0.998811	−	0.0487595i	$-0.0155268\pi$
$619$	0.664828	+	4.62398i	0.0267217	+	0.185854i	−0.972089	+	0.234613i	$0.924618\pi$
$620$	38.9933	−	12.1242i	1.56601	−	0.486918i
$621$	17.0279	+	16.2090i	0.683308	+	0.650443i
$622$	−8.34647	+	0.874946i	−0.334663	+	0.0350822i
$623$	3.99553	+	2.99102i	0.160078	+	0.119833i
$624$	0.245669	−	23.1499i	0.00983463	−	0.926736i
$625$	−19.8134	+	15.2456i	−0.792537	+	0.609823i
$626$	−1.53423	−	8.63470i	−0.0613201	−	0.345112i
$627$	0.167466	+	0.306691i	0.00668794	+	0.0122480i
$628$	0.0238059	−	4.48668i	0.000949958	−	0.179038i
$629$	6.14684	−	2.80717i	0.245091	−	0.111929i
$630$	−10.9632	+	1.38434i	−0.436783	+	0.0551532i
$631$	1.71526	−	2.66899i	0.0682834	−	0.106251i	−0.805433	−	0.592687i	$-0.798067\pi$
$631$	1.71526	−	2.66899i	0.0682834	−	0.106251i	0.873716	+	0.486436i	$0.161703\pi$
$632$	−19.9771	+	3.44034i	−0.794648	+	0.136849i
$633$	17.3775	−	13.0086i	0.690692	−	0.517045i
$634$	−0.607714	−	1.84218i	−0.0241354	−	0.0731625i
$635$	−37.6495	+	0.796774i	−1.49408	+	0.0316190i
$636$	6.97444	+	9.42053i	0.276554	+	0.373548i
$637$	5.24611	−	24.1160i	0.207858	−	0.955510i
$638$	−0.00673579	+	0.0367753i	−0.000266672	+	0.00145595i
$639$	1.70303	−	1.96541i	0.0673710	−	0.0777502i
$640$	−11.2653	+	22.6516i	−0.445300	+	0.895381i
$641$	4.80000	−	10.5105i	0.189589	−	0.415141i	−0.790838	−	0.612025i	$-0.790355\pi$
$641$	4.80000	−	10.5105i	0.189589	−	0.415141i	0.980427	+	0.196884i	$0.0630823\pi$
$642$	22.9821	−	5.80094i	0.907032	−	0.228945i
$643$	−20.0474	+	20.0474i	−0.790594	+	0.790594i	−0.981591	−	0.190997i	$-0.938828\pi$
$643$	−20.0474	+	20.0474i	−0.790594	+	0.790594i	0.190997	+	0.981591i	$0.438828\pi$
$644$	−16.2489	+	0.314133i	−0.640295	+	0.0123786i
$645$	16.3546	−	1.51811i	0.643962	−	0.0597757i
$646$	1.29604	−	2.17121i	0.0509920	−	0.0854251i
$647$	10.9058	−	4.06766i	0.428752	−	0.159916i	−0.125818	−	0.992053i	$-0.540156\pi$
$647$	10.9058	−	4.06766i	0.428752	−	0.159916i	0.554570	+	0.832137i	$0.312883\pi$
$648$	2.29666	+	3.36467i	0.0902213	+	0.132177i
$649$	0.447990	+	0.388186i	0.0175851	+	0.0152376i
$650$	29.7668	−	30.0039i	1.16755	−	1.17685i
$651$	−8.09944	−	12.6030i	−0.317442	−	0.493949i
$652$	38.9723	+	5.81459i	1.52627	+	0.227717i
$653$	−2.78478	+	38.9363i	−0.108977	+	1.52369i	0.589328	+	0.807894i	$0.299392\pi$
$653$	−2.78478	+	38.9363i	−0.108977	+	1.52369i	−0.698305	+	0.715800i	$0.746062\pi$
$654$	3.16133	−	1.04288i	0.123618	−	0.0407800i
$655$	−1.13270	+	22.5267i	−0.0442582	+	0.880192i
$656$	−3.82718	−	13.5651i	−0.149426	−	0.529626i
$657$	−16.7830	+	3.65092i	−0.654768	+	0.142436i
$658$	−4.61060	−	4.31552i	−0.179740	−	0.168236i
$659$	10.5226	+	23.0413i	0.409902	+	0.897561i	0.996170	+	0.0874430i	$0.0278696\pi$
$659$	10.5226	+	23.0413i	0.409902	+	0.897561i	−0.586267	+	0.810118i	$0.699403\pi$
$660$	−0.0423695	−	0.484357i	−0.00164923	−	0.0188536i
$661$	35.2123	+	10.3393i	1.36960	+	0.402151i	0.882137	−	0.470993i	$-0.156104\pi$
$661$	35.2123	+	10.3393i	1.36960	+	0.402151i	0.487462	+	0.873144i	$0.337923\pi$
$662$	−15.2123	+	21.7863i	−0.591243	+	0.846748i
$663$	1.54306	−	2.82590i	0.0599273	−	0.109749i
$664$	33.3267	−	26.4216i	1.29333	−	1.02536i
$665$	−10.3813	−	6.36538i	−0.402569	−	0.246839i
$666$	−22.3035	+	27.5272i	−0.864243	+	1.06666i
$667$	−0.586927	+	0.964729i	−0.0227259	+	0.0373545i
$668$	−22.0689	−	14.3488i	−0.853871	−	0.555173i
$669$	−8.31567	+	1.19561i	−0.321502	+	0.0462251i
$670$	−20.3029	+	12.5600i	−0.784370	+	0.485235i
$671$	−0.0900285	−	0.306609i	−0.00347551	−	0.0118365i
$672$	9.11113	+	1.76893i	0.351469	+	0.0682378i
$673$	4.22572	+	7.73883i	0.162890	+	0.298310i	0.946357	−	0.323123i	$-0.104733\pi$
$673$	4.22572	+	7.73883i	0.162890	+	0.298310i	−0.783467	+	0.621433i	$0.786551\pi$
$674$	−21.8801	−	2.41108i	−0.842788	−	0.0928715i
$675$	4.19207	−	24.1488i	0.161353	−	0.929490i
$676$	−27.4309	+	36.2409i	−1.05503	+	1.39388i
$677$	22.2214	−	4.83396i	0.854036	−	0.185784i	0.235824	−	0.971796i	$-0.424221\pi$
$677$	22.2214	−	4.83396i	0.854036	−	0.185784i	0.618212	+	0.786012i	$0.287857\pi$
$678$	−9.36015	−	0.359165i	−0.359474	−	0.0137936i
$679$	3.02756	−	21.0571i	0.116187	−	0.808098i
$680$	−2.86330	+	2.04456i	−0.109802	+	0.0784054i
$681$	−0.417066	−	0.481320i	−0.0159820	−	0.0184442i
$682$	−1.24882	+	0.736487i	−0.0478198	+	0.0282016i
$683$	−3.16483	+	14.5485i	−0.121099	+	0.556683i	0.876116	+	0.482101i	$0.160126\pi$
$683$	−3.16483	+	14.5485i	−0.121099	+	0.556683i	−0.997215	+	0.0745825i	$0.976238\pi$
$684$	−1.01590	+	13.2182i	−0.0388440	+	0.505410i
$685$	−33.2134	+	5.49498i	−1.26902	+	0.209952i
$686$	24.6105	+	10.2706i	0.939634	+	0.392133i
$687$	−2.75819	+	1.02875i	−0.105232	+	0.0392494i
$688$	29.5793	+	6.76410i	1.12770	+	0.257879i
$689$		−	36.1756i		−	1.37818i
$690$	4.03236	−	14.1209i	0.153509	−	0.537575i
$691$		−	15.2862i		−	0.581515i	−0.956797	−	0.290757i	$-0.906093\pi$
$691$		−	15.2862i		−	0.581515i	0.956797	−	0.290757i	$-0.0939073\pi$
$692$	6.58174	−	14.2120i	0.250200	−	0.540257i
$693$	0.367597	−	0.137106i	0.0139638	−	0.00520824i
$694$	−7.96602	+	19.0883i	−0.302386	+	0.724581i
$695$	−3.44470	−	2.46669i	−0.130665	−	0.0935670i
$696$	0.443186	−	0.468483i	0.0167989	−	0.0177578i
$697$	0.416671	−	1.91540i	0.0157825	−	0.0725511i
$698$	2.04915	+	3.47462i	0.0775613	+	0.131516i
$699$	−3.41563	−	3.94185i	−0.129191	−	0.149094i
$700$	9.68170	+	13.9053i	0.365934	+	0.525570i
$701$	1.93461	−	13.4555i	0.0730691	−	0.508207i	−0.920115	−	0.391649i	$-0.871905\pi$
$701$	1.93461	−	13.4555i	0.0730691	−	0.508207i	0.993184	−	0.116558i	$-0.0371860\pi$
$702$	−1.58881	+	41.4057i	−0.0599656	+	1.56276i
$703$	−38.1503	+	8.29909i	−1.43887	+	0.313006i
$704$	0.204872	−	0.874525i	0.00772141	−	0.0329599i
$705$	4.94945	−	2.84017i	0.186407	−	0.106967i
$706$	1.23109	−	11.1719i	0.0463327	−	0.420459i
$707$	−2.73608	−	5.01075i	−0.102901	−	0.188449i
$708$	−2.82859	−	9.82585i	−0.106305	−	0.369278i
$709$	7.24390	+	24.6705i	0.272050	+	0.926518i	0.976274	+	0.216540i	$0.0694771\pi$
$709$	7.24390	+	24.6705i	0.272050	+	0.926518i	−0.704223	+	0.709978i	$0.748705\pi$
$710$	−3.88134	−	0.914492i	−0.145664	−	0.0343203i
$711$	14.6303	−	2.10352i	0.548679	−	0.0788881i
$712$	−7.92587	+	2.56810i	−0.297035	+	0.0962436i
$713$	−43.1779	+	7.29785i	−1.61703	+	0.273307i
$714$	1.00291	+	0.812592i	0.0375329	+	0.0304105i
$715$	−0.784385	+	1.27925i	−0.0293344	+	0.0478414i
$716$	−6.54752	+	29.3479i	−0.244692	+	1.09678i
$717$	−3.46555	+	6.34669i	−0.129423	+	0.237021i
$718$	26.0883	+	18.2162i	0.973607	+	0.679822i
$719$	17.5106	+	5.14156i	0.653034	+	0.191748i	0.591435	−	0.806353i	$-0.298562\pi$
$719$	17.5106	+	5.14156i	0.653034	+	0.191748i	0.0615991	+	0.998101i	$0.480380\pi$
$720$	8.66905	−	16.2822i	0.323076	−	0.606800i
$721$	−6.38620	−	13.9838i	−0.237834	−	0.520785i
$722$	8.37837	−	8.95127i	0.311811	−	0.333132i
$723$	0.439547	−	0.0956175i	0.0163469	−	0.00355605i
$724$	−2.74070	−	41.4063i	−0.101857	−	1.53885i
$725$	1.17626	−	0.0498086i	0.0436853	−	0.00184985i
$726$	−4.71374	−	14.2889i	−0.174943	−	0.530312i
$727$	−1.04640	+	14.6306i	−0.0388088	+	0.542618i	0.940440	+	0.339958i	$0.110413\pi$
$727$	−1.04640	+	14.6306i	−0.0388088	+	0.542618i	−0.979249	+	0.202659i	$0.935042\pi$
$728$	−19.3516	−	21.1197i	−0.717219	−	0.782748i
$729$	6.09292	+	9.48078i	0.225664	+	0.351140i
$730$	16.9016	+	20.1969i	0.625558	+	0.747522i
$731$	3.18920	+	2.76346i	0.117957	+	0.102210i
$732$	−1.58095	+	5.28043i	−0.0584338	+	0.195170i
$733$	26.3423	−	9.82519i	0.972977	−	0.362902i	0.187823	−	0.982203i	$-0.439857\pi$
$733$	26.3423	−	9.82519i	0.972977	−	0.362902i	0.785153	+	0.619301i	$0.212584\pi$
$734$	23.9392	+	14.2898i	0.883613	+	0.527446i
$735$	−5.71049	+	6.87912i	−0.210635	+	0.253740i
$736$	15.2181	−	22.4591i	0.560945	−	0.827853i
$737$	0.599365	−	0.599365i	0.0220779	−	0.0220779i
$738$	2.51516	+	9.96454i	0.0925843	+	0.366800i
$739$	8.08897	−	17.7124i	0.297558	−	0.651561i	−0.700514	−	0.713639i	$-0.747046\pi$
$739$	8.08897	−	17.7124i	0.297558	−	0.651561i	0.998071	+	0.0620786i	$0.0197729\pi$
$740$	53.2591	+	10.7045i	1.95784	+	0.393504i
$741$	−12.1821	+	14.0589i	−0.447520	+	0.516465i
$742$	14.2654	+	2.61286i	0.523700	+	0.0959212i
$743$	6.61833	−	30.4240i	0.242803	−	1.11615i	−0.680702	−	0.732560i	$-0.738325\pi$
$743$	6.61833	−	30.4240i	0.242803	−	1.11615i	0.923505	−	0.383587i	$-0.125311\pi$
$744$	24.9843	+	1.09147i	0.915968	+	0.0400154i
$745$	−13.2672	−	12.7173i	−0.486073	−	0.465926i
$746$	45.8734	−	15.1331i	1.67955	−	0.554061i
$747$	−24.8251	+	18.5839i	−0.908304	+	0.679948i
$748$	0.0823030	−	0.0939706i	0.00300929	−	0.00343590i
$749$	15.8557	−	24.6719i	0.579353	−	0.901491i
$750$	−14.5774	+	4.68121i	−0.532291	+	0.170934i
$751$	11.1827	−	5.10696i	0.408062	−	0.186356i	−0.200799	−	0.979632i	$-0.564354\pi$
$751$	11.1827	−	5.10696i	0.408062	−	0.186356i	0.608861	+	0.793277i	$0.291627\pi$
$752$	10.3242	−	2.13141i	0.376485	−	0.0777245i
$753$	13.1546	+	24.0908i	0.479380	+	0.877919i
$754$	−1.95966	+	0.348195i	−0.0713664	+	0.0126805i
$755$	−43.3011	+	17.2026i	−1.57589	+	0.626068i
$756$	−16.2131	−	3.61714i	−0.589664	−	0.131554i
$757$	−40.1383	−	30.0472i	−1.45885	−	1.09208i	−0.976352	−	0.216187i	$-0.930638\pi$
$757$	−40.1383	−	30.0472i	−1.45885	−	1.09208i	−0.482500	−	0.875896i	$-0.660271\pi$
$758$	0.550313	+	5.24967i	0.0199883	+	0.190676i
$759$	−0.0243737	+	0.520828i	−0.000884708	+	0.0189049i
$760$	18.6761	−	8.02633i	0.677452	−	0.291146i
$761$	−1.31897	−	9.17366i	−0.0478127	−	0.332545i	−0.999662	−	0.0259799i	$-0.991729\pi$
$761$	−1.31897	−	9.17366i	−0.0478127	−	0.332545i	0.951850	−	0.306565i	$-0.0991797\pi$
$762$	−21.8630	−	7.34119i	−0.792013	−	0.265943i
$763$	1.97395	−	3.61502i	0.0714618	−	0.130873i
$764$	−15.3897	−	8.50970i	−0.556779	−	0.307870i
$765$	2.12832	−	1.43231i	0.0769494	−	0.0517852i
$766$	49.0448	+	5.40452i	1.77206	+	0.195273i
$767$	−11.0281	+	29.5675i	−0.398201	+	1.06762i
$768$	−11.1854	+	10.7204i	−0.403618	+	0.386839i
$769$	−2.94179	+	4.57752i	−0.106084	+	0.165070i	−0.890237	−	0.455498i	$-0.849461\pi$
$769$	−2.94179	+	4.57752i	−0.106084	+	0.165070i	0.784153	+	0.620567i	$0.213098\pi$
$770$	−0.447804	−	0.401710i	−0.0161378	−	0.0144766i
$771$	−28.1057	−	4.04098i	−1.01220	−	0.145532i
$772$	−13.5310	−	30.0496i	−0.486990	−	1.08151i
$773$	−2.02743	+	28.3472i	−0.0729217	+	1.01958i	0.820875	+	0.571108i	$0.193486\pi$
$773$	−2.02743	+	28.3472i	−0.0729217	+	1.01958i	−0.893797	+	0.448472i	$0.851968\pi$
$774$	−21.4226	−	5.52838i	−0.770020	−	0.198713i
$775$	31.3303	+	33.2077i	1.12542	+	1.19285i
$776$	25.7977	+	24.4047i	0.926084	+	0.876078i
$777$	−1.42180	−	19.8794i	−0.0510068	−	0.713168i
$778$	−23.2829	+	9.57182i	−0.834734	+	0.343166i
$779$	−4.70473	+	10.3019i	−0.168564	+	0.369105i
$780$	23.3713	−	11.1244i	0.836827	−	0.398318i
$781$	0.141578			0.00506607
$782$	3.33597	−	1.76261i	0.119294	−	0.0630309i
$783$	−0.816171	+	0.816171i	−0.0291676	+	0.0291676i
$784$	−13.9884	+	8.78146i	−0.499586	+	0.313624i
$785$	4.51790	−	2.17994i	0.161251	−	0.0778053i
$786$	−5.31997	+	12.7478i	−0.189757	+	0.454698i
$787$	−32.0353	+	2.29121i	−1.14194	+	0.0816729i	−0.629463	−	0.777030i	$-0.716725\pi$
$787$	−32.0353	+	2.29121i	−1.14194	+	0.0816729i	−0.512473	+	0.858703i	$0.671271\pi$
$788$	−26.3266	+	22.5687i	−0.937847	+	0.803977i
$789$	−12.5475	−	19.5244i	−0.446704	−	0.695085i
$790$	−13.2680	−	18.3742i	−0.472056	−	0.653725i
$791$	−8.75899	+	7.58970i	−0.311434	+	0.269859i
$792$	−0.167012	+	0.633270i	−0.00593451	+	0.0225023i
$793$	13.6186	−	10.1948i	0.483612	−	0.362028i
$794$	13.8819	−	12.8559i	0.492649	−	0.456238i
$795$	−6.03571	+	11.6321i	−0.214065	+	0.412550i
$796$	−11.6816	−	8.84187i	−0.414045	−	0.313392i
$797$	−4.68080	−	1.74585i	−0.165802	−	0.0618411i	0.265192	−	0.964196i	$-0.414565\pi$
$797$	−4.68080	−	1.74585i	−0.165802	−	0.0618411i	−0.430995	+	0.902354i	$0.641837\pi$
$798$	−4.66407	−	5.81929i	−0.165106	−	0.206001i
$799$	1.40672	+	0.413052i	0.0497663	+	0.0146127i
$800$	−28.2836	−	0.187948i	−0.999978	−	0.00664495i
$801$	5.82886	−	1.71151i	0.205953	−	0.0604731i
$802$	1.73111	+	0.581275i	0.0611276	+	0.0205255i
$803$	−0.748542	−	0.560352i	−0.0264155	−	0.0197744i
$804$	−14.3031	+	3.03205i	−0.504430	+	0.106932i
$805$	−8.29691	−	16.1653i	−0.292428	−	0.569752i
$806$	−59.9690	−	48.5891i	−2.11232	−	1.71148i
$807$	6.94938	−	9.28329i	0.244630	−	0.326787i
$808$	9.46718	+	1.09411i	0.333054	+	0.0384907i
$809$	14.1368	+	48.1454i	0.497022	+	1.69270i	0.700525	+	0.713628i	$0.252949\pi$
$809$	14.1368	+	48.1454i	0.497022	+	1.69270i	−0.203503	+	0.979074i	$0.565233\pi$
$810$	−2.25120	+	3.95938i	−0.0790991	+	0.139118i
$811$	5.79229	−	19.7267i	0.203395	−	0.692700i	−0.793103	−	0.609087i	$-0.791536\pi$
$811$	5.79229	−	19.7267i	0.203395	−	0.692700i	0.996498	−	0.0836126i	$-0.0266458\pi$
$812$	0.00423367	−	0.797916i	0.000148573	−	0.0280014i
$813$	−0.256660	+	0.688131i	−0.00900145	+	0.0241338i
$814$	−1.92770	+	0.0637280i	−0.0675660	+	0.00223366i
$815$	13.3032	+	41.9981i	0.465991	+	1.47113i
$816$	−2.07376	+	0.585080i	−0.0725960	+	0.0204819i
$817$	−14.6111	−	19.5182i	−0.511179	−	0.682855i
$818$	−0.157333	−	0.0792778i	−0.00550101	−	0.00277188i
$819$	13.6777	+	15.7849i	0.477936	+	0.551567i
$820$	11.7442	−	10.5070i	0.410125	−	0.366919i
$821$	32.4202	−	20.8352i	1.13147	−	0.727153i	0.165605	−	0.986192i	$-0.447042\pi$
$821$	32.4202	−	20.8352i	1.13147	−	0.727153i	0.965867	+	0.259040i	$0.0834060\pi$
$822$	−20.2798	−	3.71445i	−0.707339	−	0.129556i
$823$	−1.55589	−	21.7542i	−0.0542349	−	0.758303i	−0.949698	−	0.313167i	$-0.898610\pi$
$823$	−1.55589	−	21.7542i	−0.0542349	−	0.758303i	0.895463	−	0.445136i	$-0.146845\pi$
$824$	25.2175	+	4.75726i	0.878492	+	0.165727i
$825$	0.465653	−	0.280469i	0.0162120	−	0.00976467i
$826$	−10.8630	−	6.48437i	−0.377974	−	0.225620i
$827$	19.3236	+	19.3236i	0.671949	+	0.671949i	0.958165	−	0.286216i	$-0.0923976\pi$
$827$	19.3236	+	19.3236i	0.671949	+	0.671949i	−0.286216	+	0.958165i	$0.592398\pi$
$828$	−11.5462	+	16.0619i	−0.401258	+	0.558191i
$829$			20.1461i			0.699703i	0.936805	+	0.349851i	$0.113768\pi$
$829$			20.1461i			0.699703i	−0.936805	+	0.349851i	$0.886232\pi$
$830$	42.9066	+	20.4935i	1.48931	+	0.711340i
$831$	−6.52669	−	2.98064i	−0.226408	−	0.103397i
$832$	47.4325	−	6.05084i	1.64443	−	0.209775i
$833$	−2.29115	+	0.163866i	−0.0793836	+	0.00567763i
$834$	−1.47417	−	2.13528i	−0.0510463	−	0.0739386i
$835$	3.57111	−	29.2131i	0.123583	−	1.01096i
$836$	−0.580059	+	0.429444i	−0.0200618	+	0.0148526i
$837$	−44.6457	−	3.19312i	−1.54318	−	0.110370i
$838$	15.3825	−	30.5277i	0.531379	−	1.05456i
$839$	2.04608	−	14.2308i	0.0706385	−	0.491302i	−0.923535	−	0.383513i	$-0.874714\pi$
$839$	2.04608	−	14.2308i	0.0706385	−	0.491302i	0.994174	−	0.107788i	$-0.0343769\pi$
$840$	2.69874	+	10.0197i	0.0931155	+	0.345712i
$841$	24.3497	+	15.6486i	0.839645	+	0.539607i
$842$	24.4953	−	26.1703i	0.844164	−	0.901887i
$843$	−5.96242	−	2.22387i	−0.205357	−	0.0765940i
$844$	31.5340	+	31.8704i	1.08545	+	1.09703i
$845$	−49.8726	−	9.74880i	−1.71567	−	0.335369i
$846$	−7.56809	+	1.34471i	−0.260196	+	0.0462322i
$847$	−16.3396	−	8.92208i	−0.561434	−	0.306566i
$848$	−17.2993	+	16.9360i	−0.594062	+	0.581586i
$849$	6.93836	−	0.997585i	0.238124	−	0.0342370i
$850$	−3.45991	−	1.87147i	−0.118674	−	0.0641910i
$851$	−55.0681	−	19.0077i	−1.88771	−	0.651576i
$852$	−2.04740	−	1.33118i	−0.0701427	−	0.0456056i
$853$	13.8628	−	18.5186i	0.474655	−	0.634065i	−0.497762	−	0.867314i	$-0.665845\pi$
$853$	13.8628	−	18.5186i	0.474655	−	0.634065i	0.972417	+	0.233249i	$0.0749357\pi$
$854$	3.03656	+	6.10669i	0.103909	+	0.208967i
$855$	−13.7747	+	5.47242i	−0.471086	+	0.187153i
$856$	18.3743	+	45.3776i	0.628020	+	1.55097i
$857$	−48.5873	+	26.5307i	−1.65971	+	0.906271i	−0.673818	+	0.738897i	$0.735347\pi$
$857$	−48.5873	+	26.5307i	−1.65971	+	0.906271i	−0.985893	+	0.167374i	$0.946471\pi$
$858$	−0.717093	+	0.574739i	−0.0244811	+	0.0196213i
$859$	5.59627	+	12.2541i	0.190942	+	0.418105i	0.980755	−	0.195243i	$-0.0625496\pi$
$859$	5.59627	+	12.2541i	0.190942	+	0.418105i	−0.789813	+	0.613348i	$0.789822\pi$
$860$	7.73575	+	33.0306i	0.263787	+	1.12633i
$861$	−4.86353	−	3.12560i	−0.165749	−	0.106520i
$862$	0.151364	−	3.94469i	0.00515549	−	0.134357i
$863$	29.2298	+	39.0464i	0.994993	+	1.32915i	0.943818	+	0.330465i	$0.107206\pi$
$863$	29.2298	+	39.0464i	0.994993	+	1.32915i	0.0511746	+	0.998690i	$0.483703\pi$
$864$	20.5442	−	18.6248i	0.698928	−	0.633628i
$865$	17.5068	−	0.370494i	0.595247	−	0.0125972i
$866$	42.4582	+	10.9569i	1.44279	+	0.372329i
$867$	15.7925	+	3.43545i	0.536342	+	0.116674i
$868$	23.4919	−	20.1386i	0.797367	−	0.683549i
$869$	0.608130	+	0.526948i	0.0206294	+	0.0178755i
$870$	0.688215	+	0.214997i	0.0233327	+	0.00728909i
$871$	41.0468	+	18.7455i	1.39082	+	0.635166i
$872$	3.02860	+	6.17262i	0.102561	+	0.209031i
$873$	−18.3096	−	18.3096i	−0.619685	−	0.619685i
$874$	−20.9983	+	5.85404i	−0.710280	+	0.198016i
$875$	−9.21016	+	16.5541i	−0.311360	+	0.559630i
$876$	5.55616	+	15.1415i	0.187725	+	0.511584i
$877$	9.14859	+	24.5283i	0.308926	+	0.828262i	0.994921	+	0.100656i	$0.0320943\pi$
$877$	9.14859	+	24.5283i	0.308926	+	0.828262i	−0.685995	+	0.727606i	$0.740633\pi$
$878$	−6.56066	−	15.9584i	−0.221411	−	0.538571i
$879$	−1.60510	+	1.85239i	−0.0541387	+	0.0624794i
$880$	0.978964	−	0.223801i	0.0330009	−	0.00754432i
$881$	−43.0729	+	27.6813i	−1.45116	+	0.932606i	−0.451987	+	0.892024i	$0.649285\pi$
$881$	−43.0729	+	27.6813i	−1.45116	+	0.932606i	−0.999176	+	0.0405817i	$0.987079\pi$
$882$	10.3733	−	6.11762i	0.349287	−	0.205991i
$883$	34.4864	+	2.46651i	1.16056	+	0.0830048i	0.638304	−	0.769785i	$-0.279636\pi$
$883$	34.4864	+	2.46651i	1.16056	+	0.0830048i	0.522255	+	0.852789i	$0.325091\pi$
$884$	6.21840	+	2.35700i	0.209147	+	0.0792746i
$885$	8.47922	−	7.66733i	0.285026	−	0.257735i
$886$	−25.4017	+	23.5243i	−0.853387	+	0.790316i
$887$	1.35201	+	6.21508i	0.0453960	+	0.208682i	0.994258	−	0.107009i	$-0.0341273\pi$
$887$	1.35201	+	6.21508i	0.0453960	+	0.208682i	−0.948862	+	0.315691i	$0.897764\pi$
$888$	28.4762	+	17.2036i	0.955597	+	0.577314i
$889$	−25.9566	+	11.8540i	−0.870556	+	0.397570i
$890$	−6.47245	−	6.69893i	−0.216957	−	0.224549i
$891$	0.0455589	−	0.155159i	0.00152628	−	0.00519803i
$892$	−4.80021	−	16.6748i	−0.160723	−	0.558313i
$893$	−7.43455	−	4.05957i	−0.248788	−	0.135848i
$894$	−5.01125	−	10.0779i	−0.167601	−	0.337056i
$895$	−32.6918	+	7.83961i	−1.09277	+	0.262049i
$896$	−1.03984	+	19.1415i	−0.0347385	+	0.639472i
$897$	−26.4322	+	8.47382i	−0.882545	+	0.282933i
$898$	0.694426	−	0.0727955i	0.0231733	−	0.00242922i
$899$	−0.305976	−	2.12811i	−0.0102049	−	0.0709764i
$900$	20.6113	+	0.709021i	0.687042	+	0.0236340i
$901$	−3.23053	+	0.948570i	−0.107625	+	0.0316014i
$902$	−0.320308	+	0.458728i	−0.0106651	+	0.0152740i
$903$	10.9236	−	5.96472i	0.363513	−	0.198493i
$904$	−1.91493	−	19.2519i	−0.0636895	−	0.640307i
$905$	40.2403	−	23.0913i	1.33763	−	0.767581i
$906$	−28.5191	+	0.942813i	−0.947483	+	0.0313229i
$907$	−0.836700	−	3.84625i	−0.0277822	−	0.127713i	0.961167	−	0.275967i	$-0.0889981\pi$
$907$	−0.836700	−	3.84625i	−0.0277822	−	0.127713i	−0.988949	+	0.148255i	$0.952634\pi$
$908$	0.866679	−	0.989543i	0.0287618	−	0.0328392i
$909$	−6.87820	−	0.988935i	−0.228135	−	0.0328009i
$910$	11.7061	−	29.8098i	0.388055	−	0.988186i
$911$	−7.93258	+	6.87362i	−0.262818	+	0.227733i	−0.776294	−	0.630371i	$-0.782903\pi$
$911$	−7.93258	+	6.87362i	−0.262818	+	0.227733i	0.513476	+	0.858104i	$0.328357\pi$
$912$	12.4262	−	0.756297i	0.411473	−	0.0250435i
$913$	−1.64964	−	0.358858i	−0.0545953	−	0.0118765i
$914$	−3.96787	−	5.74731i	−0.131246	−	0.190104i
$915$	−6.07998	+	1.00590i	−0.200998	+	0.0332540i
$916$	−2.88557	−	5.35183i	−0.0953418	−	0.176830i
$917$	5.97275	+	16.0136i	0.197238	+	0.528815i
$918$	3.73925	−	0.943827i	0.123414	−	0.0311509i
$919$	−12.1553			−0.400966			−0.200483	−	0.979697i	$-0.564251\pi$
$919$	−12.1553			−0.400966			−0.200483	+	0.979697i	$0.564251\pi$
$920$	30.0319	+	4.25245i	0.990123	+	0.140199i
$921$	20.9113			0.689051
$922$	27.4840	−	6.93726i	0.905137	−	0.228466i
$923$	2.63395	+	7.06188i	0.0866974	+	0.232445i
$924$	−0.174848	−	0.324289i	−0.00575207	−	0.0106683i
$925$	15.4097	+	58.7490i	0.506669	+	1.93165i
$926$	23.4191	+	33.9217i	0.769601	+	1.11474i
$927$	−18.2840	−	3.97744i	−0.600525	−	0.130636i
$928$	1.08394	+	0.774105i	0.0355822	+	0.0254112i
$929$	33.1897	−	28.7591i	1.08892	−	0.943555i	0.0902919	−	0.995915i	$-0.471220\pi$
$929$	33.1897	−	28.7591i	1.08892	−	0.943555i	0.998628	+	0.0523607i	$0.0166746\pi$
$930$	11.1760	+	25.6292i	0.366475	+	0.840413i
$931$	13.1362	+	1.88870i	0.430522	+	0.0618997i
$932$	7.09781	−	8.10402i	0.232496	−	0.265456i
$933$	−1.22145	−	5.61491i	−0.0399884	−	0.183824i
$934$	19.0232	−	0.628889i	0.622459	−	0.0205779i
$935$	0.134807	+	0.0365031i	0.00440865	+	0.00119378i
$936$	−34.6944	+	3.45095i	−1.13402	+	0.112798i
$937$	1.10918	−	0.605657i	0.0362353	−	0.0197860i	−0.461029	−	0.887385i	$-0.652520\pi$
$937$	1.10918	−	0.605657i	0.0362353	−	0.0197860i	0.497265	+	0.867599i	$0.334338\pi$
$938$	−10.3567	+	14.8324i	−0.338160	+	0.484295i
$939$	5.76163	−	1.69177i	0.188024	−	0.0552087i
$940$	7.21191	+	9.32220i	0.235227	+	0.304057i
$941$	−6.48365	−	45.0947i	−0.211361	−	1.47005i	−0.768619	−	0.639707i	$-0.779056\pi$
$941$	−6.48365	−	45.0947i	−0.211361	−	1.47005i	0.557258	−	0.830339i	$-0.311853\pi$
$942$	3.05537	−	0.320290i	0.0995495	−	0.0104356i
$943$	−13.9868	+	9.48363i	−0.455474	+	0.308829i
$944$	19.3022	−	8.56867i	0.628234	−	0.278886i
$945$	−4.33095	−	18.0604i	−0.140886	−	0.587505i
$946$	−0.536281	−	1.07849i	−0.0174360	−	0.0350648i
$947$	−39.7557	−	21.7083i	−1.29189	−	0.705424i	−0.321484	−	0.946915i	$-0.604182\pi$
$947$	−39.7557	−	21.7083i	−1.29189	−	0.705424i	−0.970403	+	0.241491i	$0.922363\pi$
$948$	−3.83970	−	13.3382i	−0.124708	−	0.433206i
$949$	14.0242	−	47.7619i	0.455244	−	1.55042i
$950$	17.2349	+	14.8149i	0.559175	+	0.480657i
$951$	1.20820	−	0.551764i	0.0391784	−	0.0178922i
$952$	−1.37859	+	2.28191i	−0.0446805	+	0.0739572i
$953$	7.57666	+	34.8294i	0.245432	+	1.12823i	0.920581	+	0.390552i	$0.127716\pi$
$953$	7.57666	+	34.8294i	0.245432	+	1.12823i	−0.675149	+	0.737682i	$0.735920\pi$
$954$	12.9515	−	11.9943i	0.419319	−	0.388329i
$955$	0.987375	−	19.6366i	0.0319507	−	0.635426i
$956$	−13.9659	−	5.29359i	−0.451690	−	0.171207i
$957$	−0.0255341	−	0.00182623i	−0.000825400	−	5.90338e-5i
$958$	−35.7940	+	21.1094i	−1.15645	+	0.682013i
$959$	−21.4600	+	13.7915i	−0.692979	+	0.445350i
$960$	−16.2613	−	5.96824i	−0.524831	−	0.192624i
$961$	34.2974	−	39.5813i	1.10637	−	1.27682i
$962$	−39.0420	−	94.9676i	−1.25877	−	3.06188i
$963$	−12.4747	−	33.4459i	−0.401991	−	1.07778i
$964$	0.320057	+	0.872212i	0.0103083	+	0.0280921i
$965$	23.5340	−	28.3502i	0.757587	−	0.912625i
$966$	−1.43243	−	11.0353i	−0.0460876	−	0.355054i
$967$	36.5224	+	36.5224i	1.17448	+	1.17448i	0.981129	+	0.193353i	$0.0619364\pi$
$967$	36.5224	+	36.5224i	1.17448	+	1.17448i	0.193353	+	0.981129i	$0.438064\pi$
$968$	27.8997	−	13.6890i	0.896731	−	0.439981i
$969$	1.57491	+	0.719235i	0.0505932	+	0.0231052i
$970$	−11.8391	+	37.8976i	−0.380132	+	1.21682i
$971$	21.3285	+	18.4813i	0.684465	+	0.593093i	0.926102	−	0.377274i	$-0.123139\pi$
$971$	21.3285	+	18.4813i	0.684465	+	0.593093i	−0.241636	+	0.970367i	$0.577684\pi$
$972$	−24.4477	+	20.9580i	−0.784161	+	0.672228i
$973$	−3.13707	−	0.682428i	−0.100570	−	0.0218776i
$974$	−10.2823	−	2.65348i	−0.329467	−	0.0850230i
$975$	22.6528	+	18.0087i	0.725470	+	0.576741i
$976$	−11.2509	−	1.73969i	−0.360133	−	0.0556861i
$977$	16.1457	+	21.5682i	0.516548	+	0.690028i	0.980653	−	0.195753i	$-0.0627149\pi$
$977$	16.1457	+	21.5682i	0.516548	+	0.690028i	−0.464105	+	0.885780i	$0.653624\pi$
$978$	−1.03451	+	26.9603i	−0.0330800	+	0.862094i
$979$	0.278222	+	0.178802i	0.00889201	+	0.00571455i
$980$	−15.6908	−	9.73585i	−0.501223	−	0.311000i
$981$	−2.08261	−	4.56028i	−0.0664927	−	0.145599i
$982$	−21.1155	+	16.9238i	−0.673824	+	0.540059i
$983$	41.4516	−	22.6343i	1.32210	−	0.721922i	0.345794	−	0.938311i	$-0.387610\pi$
$983$	41.4516	−	22.6343i	1.32210	−	0.721922i	0.976307	+	0.216389i	$0.0694279\pi$
$984$	8.94521	−	3.62209i	0.285163	−	0.115468i
$985$	−35.5985	−	15.3555i	−1.13426	−	0.489268i
$986$	0.0824789	+	0.165870i	0.00262666	+	0.00528237i
$987$	2.59131	−	3.46159i	0.0824824	−	0.110184i
$988$	−32.2120	−	20.9437i	−1.02480	−	0.666309i
$989$	−3.48840	−	36.2122i	−0.110925	−	1.15148i
$990$	−0.718062	+	0.143322i	−0.0228215	+	0.00455507i
$991$	38.9237	−	5.59638i	1.23645	−	0.177775i	0.507084	−	0.861897i	$-0.330724\pi$
$991$	38.9237	−	5.59638i	1.23645	−	0.177775i	0.729368	+	0.684122i	$0.239814\pi$
$992$	4.83968	+	51.4250i	0.153660	+	1.63275i
$993$	−15.9684	−	8.71942i	−0.506743	−	0.276702i
$994$	−2.97501	+	0.528606i	−0.0943617	+	0.0167664i
$995$	3.14236	−	16.0756i	0.0996195	−	0.509631i
$996$	20.4817	+	20.7003i	0.648989	+	0.655913i
$997$	−25.7088	−	9.58887i	−0.814204	−	0.303683i	−0.0923492	−	0.995727i	$-0.529438\pi$
$997$	−25.7088	−	9.58887i	−0.814204	−	0.303683i	−0.721855	+	0.692044i	$0.756710\pi$
$998$	18.1235	−	19.3628i	0.573691	−	0.612919i
$999$	−50.0932	−	32.1929i	−1.58488	−	1.01854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.3.6	✓	1360
4.3	odd	2	inner	460.2.w.a.3.35	yes	1360
5.2	odd	4	inner	460.2.w.a.187.28	yes	1360
20.7	even	4	inner	460.2.w.a.187.68	yes	1360
23.8	even	11	inner	460.2.w.a.123.68	yes	1360
92.31	odd	22	inner	460.2.w.a.123.28	yes	1360
115.77	odd	44	inner	460.2.w.a.307.35	yes	1360
460.307	even	44	inner	460.2.w.a.307.6	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.3.6	✓	1360	1.1	even	1	trivial
460.2.w.a.3.35	yes	1360	4.3	odd	2	inner
460.2.w.a.123.28	yes	1360	92.31	odd	22	inner
460.2.w.a.123.68	yes	1360	23.8	even	11	inner
460.2.w.a.187.28	yes	1360	5.2	odd	4	inner
460.2.w.a.187.68	yes	1360	20.7	even	4	inner
460.2.w.a.307.6	yes	1360	460.307	even	44	inner
460.2.w.a.307.35	yes	1360	115.77	odd	44	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37121 + 0.346108i) q^{2} +(-0.338395 - 0.907273i) q^{3} +(1.76042 - 0.949171i) q^{4} +(1.81802 + 1.30185i) q^{5} +(0.778024 + 1.12694i) q^{6} +(1.65566 + 0.360166i) q^{7} +(-2.08538 + 1.91080i) q^{8} +(1.55862 - 1.35055i) q^{9} +O(q^{10})\)	\(q+(-1.37121 + 0.346108i) q^{2} +(-0.338395 - 0.907273i) q^{3} +(1.76042 - 0.949171i) q^{4} +(1.81802 + 1.30185i) q^{5} +(0.778024 + 1.12694i) q^{6} +(1.65566 + 0.360166i) q^{7} +(-2.08538 + 1.91080i) q^{8} +(1.55862 - 1.35055i) q^{9} +(-2.94346 - 1.15588i) q^{10} +(0.111132 + 0.0159784i) q^{11} +(-1.45687 - 1.27599i) q^{12} +(1.27053 + 5.84051i) q^{13} +(-2.39490 + 0.0791732i) q^{14} +(0.565926 - 2.08998i) q^{15} +(2.19815 - 3.34188i) q^{16} +(0.488251 - 0.266605i) q^{17} +(-1.66975 + 2.39133i) q^{18} +(-3.08391 + 0.905517i) q^{19} +(4.43615 + 0.566195i) q^{20} +(-0.233497 - 1.62401i) q^{21} +(-0.157916 + 0.0165540i) q^{22} +(-4.63345 - 1.23738i) q^{23} +(2.43931 + 1.24541i) q^{24} +(1.61037 + 4.73357i) q^{25} +(-3.76360 - 7.56882i) q^{26} +(-4.30238 - 2.34928i) q^{27} +(3.25651 - 0.937457i) q^{28} +(0.0663376 - 0.225925i) q^{29} +(-0.0526446 + 3.06166i) q^{30} +(8.30577 - 3.79312i) q^{31} +(-1.85747 + 5.34320i) q^{32} +(-0.0231099 - 0.106234i) q^{33} +(-0.577219 + 0.534559i) q^{34} +(2.54113 + 2.81021i) q^{35} +(1.46192 - 3.85692i) q^{36} +(12.1163 + 0.866576i) q^{37} +(3.91527 - 2.30902i) q^{38} +(4.86900 - 3.12912i) q^{39} +(-6.27885 + 0.759015i) q^{40} +(2.30750 - 2.66300i) q^{41} +(0.882256 + 2.14604i) q^{42} +(2.65094 + 7.10743i) q^{43} +(0.210806 - 0.0773549i) q^{44} +(4.59180 - 0.426233i) q^{45} +(6.78169 + 0.0930288i) q^{46} +(1.86357 + 1.86357i) q^{47} +(-3.77584 - 0.863446i) q^{48} +(-3.75595 - 1.71528i) q^{49} +(-3.84647 - 5.93335i) q^{50} +(-0.407106 - 0.352759i) q^{51} +(7.78030 + 9.07581i) q^{52} +(-5.91404 - 1.28652i) q^{53} +(6.71256 + 1.73226i) q^{54} +(0.181239 + 0.173727i) q^{55} +(-4.14088 + 2.41255i) q^{56} +(1.86513 + 2.49152i) q^{57} +(-0.0127682 + 0.332750i) q^{58} +(4.44154 + 2.85440i) q^{59} +(-0.987479 - 4.21640i) q^{60} +(-1.18234 - 2.58896i) q^{61} +(-10.0761 + 8.07584i) q^{62} +(3.06695 - 1.67468i) q^{63} +(0.697652 - 7.96952i) q^{64} +(-5.29364 + 12.2722i) q^{65} +(0.0684570 + 0.137671i) q^{66} +(4.52429 - 6.04375i) q^{67} +(0.606473 - 0.932771i) q^{68} +(0.445299 + 4.62253i) q^{69} +(-4.45705 - 2.97387i) q^{70} +(1.24816 - 0.179458i) q^{71} +(-0.669678 + 5.79462i) q^{72} +(-7.30945 - 3.99126i) q^{73} +(-16.9139 + 3.00530i) q^{74} +(3.74970 - 3.06286i) q^{75} +(-4.56948 + 4.52124i) q^{76} +(0.178242 + 0.0664809i) q^{77} +(-5.59340 + 5.97587i) q^{78} +(6.02923 + 3.87475i) q^{79} +(8.34690 - 3.21392i) q^{80} +(0.204976 - 1.42564i) q^{81} +(-2.24238 + 4.45017i) q^{82} +(-14.9982 - 1.07269i) q^{83} +(-1.95252 - 2.63731i) q^{84} +(1.23473 + 0.150937i) q^{85} +(-6.09492 - 8.82826i) q^{86} +(-0.227424 + 0.0162657i) q^{87} +(-0.262285 + 0.179031i) q^{88} +(2.67945 + 1.22367i) q^{89} +(-6.14879 + 2.17371i) q^{90} +10.1275i q^{91} +(-9.33130 + 2.21963i) q^{92} +(-6.25203 - 6.25203i) q^{93} +(-3.20033 - 1.91034i) q^{94} +(-6.78544 - 2.36854i) q^{95} +(5.47630 - 0.122883i) q^{96} +(-0.895695 - 12.5234i) q^{97} +(5.74385 + 1.05205i) q^{98} +(0.194792 - 0.125185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

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