LMFDB - Embedded newform 552.2.bb.a.469.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			469.9
Character	$\chi$	$=$	552.469
Dual form			552.2.bb.a.133.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16747 - 0.798133i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.725969 + 1.86359i) q^{4} +(1.01697 - 0.146218i) q^{5} +(1.40498 - 0.161341i) q^{6} +(-1.00685 + 2.20469i) q^{7} +(0.639846 - 2.75510i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-1.16747 - 0.798133i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.725969 + 1.86359i) q^{4} +(1.01697 - 0.146218i) q^{5} +(1.40498 - 0.161341i) q^{6} +(-1.00685 + 2.20469i) q^{7} +(0.639846 - 2.75510i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-1.30398 - 0.640970i) q^{10} +(0.610660 - 2.07972i) q^{11} +(-1.76904 - 0.932999i) q^{12} +(2.65515 - 1.21257i) q^{13} +(2.93510 - 1.77031i) q^{14} +(-0.672820 + 0.776476i) q^{15} +(-2.94594 + 2.70582i) q^{16} +(1.68779 + 1.08468i) q^{17} +(-0.956157 + 1.04200i) q^{18} +(1.43551 + 2.23370i) q^{19} +(1.01078 + 1.78906i) q^{20} +(-0.682841 - 2.32554i) q^{21} +(-2.37282 + 1.94062i) q^{22} +(1.60458 + 4.51944i) q^{23} +(1.32065 + 2.50118i) q^{24} +(-3.78462 + 1.11127i) q^{25} +(-4.06759 - 0.703528i) q^{26} +(0.540641 + 0.841254i) q^{27} +(-4.83959 - 0.275817i) q^{28} +(1.40759 - 2.19026i) q^{29} +(1.40523 - 0.369512i) q^{30} +(-6.61993 + 7.63981i) q^{31} +(5.59889 - 0.807707i) q^{32} +(0.900419 + 1.97164i) q^{33} +(-1.10473 - 2.61341i) q^{34} +(-0.701568 + 2.38932i) q^{35} +(1.94794 - 0.453363i) q^{36} +(8.39353 + 1.20681i) q^{37} +(0.106873 - 3.75351i) q^{38} +(-1.21257 + 2.65515i) q^{39} +(0.247858 - 2.89541i) q^{40} +(0.836590 + 5.81861i) q^{41} +(-1.05890 + 3.26000i) q^{42} +(0.521422 - 0.451814i) q^{43} +(4.31906 - 0.371789i) q^{44} -1.02743i q^{45} +(1.73382 - 6.55697i) q^{46} +9.65777 q^{47} +(0.454459 - 3.97410i) q^{48} +(0.737099 + 0.850657i) q^{49} +(5.30537 + 1.72326i) q^{50} +(-1.98586 + 0.285523i) q^{51} +(4.18728 + 4.06783i) q^{52} +(5.93513 + 2.71048i) q^{53} +(0.0402504 - 1.41364i) q^{54} +(0.316930 - 2.20429i) q^{55} +(5.42993 + 4.18464i) q^{56} +(-2.54766 - 0.748059i) q^{57} +(-3.39144 + 1.43361i) q^{58} +(-5.37913 + 2.45657i) q^{59} +(-1.93548 - 0.690164i) q^{60} +(-3.53944 - 3.06694i) q^{61} +(13.8261 - 3.63566i) q^{62} +(2.03896 + 1.31036i) q^{63} +(-7.18119 - 3.52569i) q^{64} +(2.52290 - 1.62137i) q^{65} +(0.522421 - 3.02049i) q^{66} +(2.66755 + 9.08485i) q^{67} +(-0.796110 + 3.93279i) q^{68} +(-4.17226 - 2.36479i) q^{69} +(2.72605 - 2.22951i) q^{70} +(6.49915 - 1.90832i) q^{71} +(-2.63600 - 1.02543i) q^{72} +(0.0519881 - 0.0334107i) q^{73} +(-8.83600 - 8.10806i) q^{74} +(2.13250 - 3.31824i) q^{75} +(-3.12057 + 4.29681i) q^{76} +(3.97030 + 3.44028i) q^{77} +(3.53479 - 2.13202i) q^{78} +(1.99792 + 4.37484i) q^{79} +(-2.60029 + 3.18248i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(3.66733 - 7.46076i) q^{82} +(-2.91348 - 0.418896i) q^{83} +(3.83814 - 2.96081i) q^{84} +(1.87503 + 0.856296i) q^{85} +(-0.969352 + 0.111316i) q^{86} +(0.370526 + 2.57706i) q^{87} +(-5.33911 - 3.01313i) q^{88} +(-10.0908 - 11.6454i) q^{89} +(-0.820022 + 1.19949i) q^{90} +7.07466i q^{91} +(-7.25751 + 6.27124i) q^{92} -10.1089i q^{93} +(-11.2752 - 7.70818i) q^{94} +(1.78648 + 2.06171i) q^{95} +(-3.70243 + 4.27692i) q^{96} +(-1.41947 - 9.87263i) q^{97} +(-0.181603 - 1.58142i) q^{98} +(-1.97164 - 0.900419i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.16747	−	0.798133i	−0.825525	−	0.564365i
$2$	−1.16747	−	0.798133i	−0.825525	−	0.564365i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$4$	0.725969	+	1.86359i	0.362984	+	0.931795i
$5$	1.01697	−	0.146218i	0.454802	−	0.0653906i	0.0888926	−	0.996041i	$-0.471667\pi$
$5$	1.01697	−	0.146218i	0.454802	−	0.0653906i	0.365909	+	0.930651i	$0.380758\pi$
$6$	1.40498	−	0.161341i	0.573581	−	0.0658673i
$7$	−1.00685	+	2.20469i	−0.380553	+	0.833296i	0.618324	+	0.785923i	$0.287812\pi$
$7$	−1.00685	+	2.20469i	−0.380553	+	0.833296i	−0.998877	+	0.0473724i	$0.984915\pi$
$8$	0.639846	−	2.75510i	0.226220	−	0.974076i
$9$	0.142315	−	0.989821i	0.0474383	−	0.329940i
$10$	−1.30398	−	0.640970i	−0.412354	−	0.202693i
$11$	0.610660	−	2.07972i	0.184121	−	0.627058i	−0.814762	−	0.579796i	$-0.803132\pi$
$11$	0.610660	−	2.07972i	0.184121	−	0.627058i	0.998883	−	0.0472622i	$-0.0150496\pi$
$12$	−1.76904	−	0.932999i	−0.510679	−	0.269334i
$13$	2.65515	−	1.21257i	0.736406	−	0.336305i	−0.0116581	−	0.999932i	$-0.503711\pi$
$13$	2.65515	−	1.21257i	0.736406	−	0.336305i	0.748064	+	0.663627i	$0.230984\pi$
$14$	2.93510	−	1.77031i	0.784439	−	0.473136i
$15$	−0.672820	+	0.776476i	−0.173721	+	0.200485i
$16$	−2.94594	+	2.70582i	−0.736485	+	0.676454i
$17$	1.68779	+	1.08468i	0.409349	+	0.263073i	0.729070	−	0.684439i	$-0.239953\pi$
$17$	1.68779	+	1.08468i	0.409349	+	0.263073i	−0.319721	+	0.947512i	$0.603589\pi$
$18$	−0.956157	+	1.04200i	−0.225368	+	0.245602i
$19$	1.43551	+	2.23370i	0.329330	+	0.512447i	0.965949	−	0.258731i	$-0.0833043\pi$
$19$	1.43551	+	2.23370i	0.329330	+	0.512447i	−0.636620	+	0.771178i	$0.719668\pi$
$20$	1.01078	+	1.78906i	0.226017	+	0.400046i
$21$	−0.682841	−	2.32554i	−0.149008	−	0.507475i
$22$	−2.37282	+	1.94062i	−0.505886	+	0.413741i
$23$	1.60458	+	4.51944i	0.334577	+	0.942368i
$23$	1.60458	+	4.51944i	0.334577	+	0.942368i
$24$	1.32065	+	2.50118i	0.269576	+	0.510551i
$25$	−3.78462	+	1.11127i	−0.756924	+	0.222253i
$26$	−4.06759	−	0.703528i	−0.797721	−	0.137973i
$27$	0.540641	+	0.841254i	0.104046	+	0.161899i
$28$	−4.83959	−	0.275817i	−0.914596	−	0.0521246i
$29$	1.40759	−	2.19026i	0.261383	−	0.406720i	−0.685612	−	0.727967i	$-0.740465\pi$
$29$	1.40759	−	2.19026i	0.261383	−	0.406720i	0.946996	+	0.321246i	$0.104102\pi$
$30$	1.40523	−	0.369512i	0.256558	−	0.0674634i
$31$	−6.61993	+	7.63981i	−1.18897	+	1.37215i	−0.277535	+	0.960716i	$0.589517\pi$
$31$	−6.61993	+	7.63981i	−1.18897	+	1.37215i	−0.911440	+	0.411434i	$0.865028\pi$
$32$	5.59889	−	0.807707i	0.989754	−	0.142784i
$33$	0.900419	+	1.97164i	0.156743	+	0.343219i
$34$	−1.10473	−	2.61341i	−0.189459	−	0.448195i
$35$	−0.701568	+	2.38932i	−0.118587	+	0.403869i
$36$	1.94794	−	0.453363i	0.324656	−	0.0755605i
$37$	8.39353	+	1.20681i	1.37989	+	0.198398i	0.791988	−	0.610536i	$-0.209046\pi$
$37$	8.39353	+	1.20681i	1.37989	+	0.198398i	0.587899	+	0.808934i	$0.299955\pi$
$38$	0.106873	−	3.75351i	0.0173371	−	0.608900i
$39$	−1.21257	+	2.65515i	−0.194166	+	0.425164i
$40$	0.247858	−	2.89541i	0.0391897	−	0.457804i
$41$	0.836590	+	5.81861i	0.130653	+	0.908714i	0.944705	+	0.327922i	$0.106348\pi$
$41$	0.836590	+	5.81861i	0.130653	+	0.908714i	−0.814052	+	0.580793i	$0.802743\pi$
$42$	−1.05890	+	3.26000i	−0.163391	+	0.503028i
$43$	0.521422	−	0.451814i	0.0795161	−	0.0689011i	−0.614196	−	0.789154i	$-0.710520\pi$
$43$	0.521422	−	0.451814i	0.0795161	−	0.0689011i	0.693712	+	0.720253i	$0.255974\pi$
$44$	4.31906	−	0.371789i	0.651123	−	0.0560493i
$45$		−	1.02743i		−	0.153160i
$46$	1.73382	−	6.55697i	0.255638	−	0.966773i
$47$	9.65777			1.40873			0.704365	−	0.709838i	$-0.251232\pi$
$47$	9.65777			1.40873			0.704365	+	0.709838i	$0.251232\pi$
$48$	0.454459	−	3.97410i	0.0655956	−	0.573612i
$49$	0.737099	+	0.850657i	0.105300	+	0.121522i
$50$	5.30537	+	1.72326i	0.750292	+	0.243706i
$51$	−1.98586	+	0.285523i	−0.278076	+	0.0399813i
$52$	4.18728	+	4.06783i	0.580671	+	0.564106i
$53$	5.93513	+	2.71048i	0.815253	+	0.372314i	0.778996	−	0.627029i	$-0.215729\pi$
$53$	5.93513	+	2.71048i	0.815253	+	0.372314i	0.0362572	+	0.999342i	$0.488456\pi$
$54$	0.0402504	−	1.41364i	0.00547739	−	0.192372i
$55$	0.316930	−	2.20429i	0.0427348	−	0.297227i
$56$	5.42993	+	4.18464i	0.725605	+	0.559196i
$57$	−2.54766	−	0.748059i	−0.337445	−	0.0990828i
$58$	−3.39144	+	1.43361i	−0.445317	+	0.188242i
$59$	−5.37913	+	2.45657i	−0.700303	+	0.319818i	−0.733556	−	0.679629i	$-0.762141\pi$
$59$	−5.37913	+	2.45657i	−0.700303	+	0.319818i	0.0332528	+	0.999447i	$0.489413\pi$
$60$	−1.93548	−	0.690164i	−0.249869	−	0.0890998i
$61$	−3.53944	−	3.06694i	−0.453178	−	0.392681i	0.398145	−	0.917322i	$-0.369654\pi$
$61$	−3.53944	−	3.06694i	−0.453178	−	0.392681i	−0.851323	+	0.524641i	$0.824200\pi$
$62$	13.8261	−	3.63566i	1.75592	−	0.461729i
$63$	2.03896	+	1.31036i	0.256885	+	0.165090i
$64$	−7.18119	−	3.52569i	−0.897649	−	0.440711i
$65$	2.52290	−	1.62137i	0.312927	−	0.201106i
$66$	0.522421	−	3.02049i	0.0643056	−	0.371796i
$67$	2.66755	+	9.08485i	0.325893	+	1.10989i	0.945674	+	0.325116i	$0.105403\pi$
$67$	2.66755	+	9.08485i	0.325893	+	1.10989i	−0.619781	+	0.784775i	$0.712778\pi$
$68$	−0.796110	+	3.93279i	−0.0965426	+	0.476921i
$69$	−4.17226	−	2.36479i	−0.502281	−	0.284687i
$70$	2.72605	−	2.22951i	0.325826	−	0.266478i
$71$	6.49915	−	1.90832i	0.771307	−	0.226476i	0.127680	−	0.991815i	$-0.459247\pi$
$71$	6.49915	−	1.90832i	0.771307	−	0.226476i	0.643627	+	0.765339i	$0.277429\pi$
$72$	−2.63600	−	1.02543i	−0.310656	−	0.120848i
$73$	0.0519881	−	0.0334107i	0.00608475	−	0.00391043i	−0.537595	−	0.843203i	$-0.680667\pi$
$73$	0.0519881	−	0.0334107i	0.00608475	−	0.00391043i	0.543680	+	0.839293i	$0.317031\pi$
$74$	−8.83600	−	8.10806i	−1.02716	−	0.942543i
$75$	2.13250	−	3.31824i	0.246240	−	0.383157i
$76$	−3.12057	+	4.29681i	−0.357954	+	0.492878i
$77$	3.97030	+	3.44028i	0.452457	+	0.392056i
$78$	3.53479	−	2.13202i	0.400237	−	0.241403i
$79$	1.99792	+	4.37484i	0.224784	+	0.492208i	0.988099	−	0.153818i	$-0.0491570\pi$
$79$	1.99792	+	4.37484i	0.224784	+	0.492208i	−0.763315	+	0.646026i	$0.776430\pi$
$80$	−2.60029	+	3.18248i	−0.290721	+	0.355812i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	3.66733	−	7.46076i	0.404989	−	0.823903i
$83$	−2.91348	−	0.418896i	−0.319796	−	0.0459798i	−0.0194526	−	0.999811i	$-0.506192\pi$
$83$	−2.91348	−	0.418896i	−0.319796	−	0.0459798i	−0.300344	+	0.953831i	$0.597101\pi$
$84$	3.83814	−	2.96081i	0.418775	−	0.323050i
$85$	1.87503	+	0.856296i	0.203375	+	0.0928783i
$86$	−0.969352	+	0.111316i	−0.104528	+	0.0120035i
$87$	0.370526	+	2.57706i	0.0397245	+	0.276290i
$88$	−5.33911	−	3.01313i	−0.569151	−	0.321201i
$89$	−10.0908	−	11.6454i	−1.06962	−	1.23441i	−0.970947	−	0.239293i	$-0.923084\pi$
$89$	−10.0908	−	11.6454i	−1.06962	−	1.23441i	−0.0986775	−	0.995119i	$-0.531461\pi$
$90$	−0.820022	+	1.19949i	−0.0864379	+	0.126437i
$91$			7.07466i			0.741626i
$92$	−7.25751	+	6.27124i	−0.756648	+	0.653822i
$93$		−	10.1089i		−	1.04825i
$94$	−11.2752	−	7.70818i	−1.16294	−	0.795038i
$95$	1.78648	+	2.06171i	0.183289	+	0.211527i
$96$	−3.70243	+	4.27692i	−0.377877	+	0.436511i
$97$	−1.41947	−	9.87263i	−0.144125	−	1.00241i	−0.925607	−	0.378486i	$-0.876445\pi$
$97$	−1.41947	−	9.87263i	−0.144125	−	1.00241i	0.781482	−	0.623928i	$-0.214464\pi$
$98$	−0.181603	−	1.58142i	−0.0183446	−	0.159747i
$99$	−1.97164	−	0.900419i	−0.198158	−	0.0904955i
$100$	−4.81846	−	6.24624i	−0.481846	−	0.624624i
$101$	6.82621	+	0.981461i	0.679233	+	0.0976590i	0.473292	−	0.880905i	$-0.343065\pi$
$101$	6.82621	+	0.981461i	0.679233	+	0.0976590i	0.205941	+	0.978564i	$0.433975\pi$
$102$	2.54631	+	1.25164i	0.252123	+	0.123931i
$103$	2.60986	+	0.766324i	0.257157	+	0.0755082i	0.407770	−	0.913085i	$-0.366306\pi$
$103$	2.60986	+	0.766324i	0.257157	+	0.0755082i	−0.150613	+	0.988593i	$0.548125\pi$
$104$	−1.64186	−	8.09107i	−0.160997	−	0.793394i
$105$	−1.03446	−	2.26516i	−0.100953	−	0.221057i
$106$	−4.76576	−	7.90143i	−0.462891	−	0.767455i
$107$	−12.1400	−	10.5193i	−1.17362	−	1.01694i	−0.999481	−	0.0322215i	$-0.989742\pi$
$107$	−12.1400	−	10.5193i	−1.17362	−	1.01694i	−0.174135	−	0.984722i	$-0.555713\pi$
$108$	−1.17526	+	1.61826i	−0.113090	+	0.155717i
$109$	−6.11952	+	9.52216i	−0.586144	+	0.912057i	0.413855	+	0.910343i	$0.364182\pi$
$109$	−6.11952	+	9.52216i	−0.586144	+	0.912057i	−0.999999	+	0.00171447i	$0.999454\pi$
$110$	−2.12932	+	2.32049i	−0.203023	+	0.221250i
$111$	−7.13370	+	4.58455i	−0.677101	+	0.435146i
$112$	−2.99938	−	9.21924i	−0.283415	−	0.871137i
$113$	4.59360	−	1.34880i	0.432130	−	0.126885i	−0.0584316	−	0.998291i	$-0.518610\pi$
$113$	4.59360	−	1.34880i	0.432130	−	0.126885i	0.490561	+	0.871407i	$0.336792\pi$
$114$	2.37726	+	2.90670i	0.222651	+	0.272238i
$115$	2.29262	+	4.36151i	0.213788	+	0.406712i
$116$	5.10361	+	1.03312i	0.473858	+	0.0959226i
$117$	−0.822357	−	2.80069i	−0.0760269	−	0.258924i
$118$	8.24063	+	1.42529i	0.758612	+	0.131209i
$119$	−4.09073	+	2.62895i	−0.374996	+	0.240996i
$120$	1.70877	+	2.35052i	0.155989	+	0.214572i
$121$	5.30147	+	3.40705i	0.481952	+	0.309732i
$122$	1.68436	+	6.40550i	0.152495	+	0.579926i
$123$	−4.44263	−	3.84956i	−0.400579	−	0.347103i
$124$	−19.0433	−	6.79058i	−1.71014	−	0.609812i
$125$	−8.35924	+	3.81754i	−0.747674	+	0.341451i
$126$	−1.33458	−	3.15717i	−0.118894	−	0.281263i
$127$	8.54225	+	2.50823i	0.758002	+	0.222569i	0.637823	−	0.770183i	$-0.279835\pi$
$127$	8.54225	+	2.50823i	0.758002	+	0.222569i	0.120179	+	0.992752i	$0.461653\pi$
$128$	5.56986	+	9.84767i	0.492310	+	0.870420i
$129$	−0.0981887	+	0.682917i	−0.00864503	+	0.0601275i
$130$	−4.23948	−	0.120710i	−0.371827	−	0.0105870i
$131$	−9.49871	−	4.33792i	−0.829907	−	0.379006i	−0.0452800	−	0.998974i	$-0.514418\pi$
$131$	−9.49871	−	4.33792i	−0.829907	−	0.379006i	−0.784627	+	0.619969i	$0.787145\pi$
$132$	−3.02066	+	3.10936i	−0.262915	+	0.270635i
$133$	−6.36998	+	0.915865i	−0.552347	+	0.0794156i
$134$	4.13663	−	12.7353i	0.357350	−	1.10017i
$135$	0.672820	+	0.776476i	0.0579072	+	0.0668284i
$136$	4.06832	−	3.95601i	0.348856	−	0.339225i
$137$	−11.7602			−1.00474			−0.502371	−	0.864652i	$-0.667539\pi$
$137$	−11.7602			−1.00474			−0.502371	+	0.864652i	$0.667539\pi$
$138$	2.98357	+	6.09084i	0.253978	+	0.518487i
$139$		−	11.5192i		−	0.977045i	−0.872551	−	0.488522i	$-0.837536\pi$
$139$		−	11.5192i		−	0.977045i	0.872551	−	0.488522i	$-0.162464\pi$
$140$	−4.96203	+	0.427137i	−0.419368	+	0.0360996i
$141$	−7.29886	+	6.32450i	−0.614675	+	0.532619i
$142$	−9.11065	−	2.95927i	−0.764548	−	0.248337i
$143$	−0.900401	−	6.26242i	−0.0752953	−	0.523690i
$144$	2.25902	+	3.30103i	0.188252	+	0.275086i
$145$	1.11122	−	2.43324i	0.0922819	−	0.202069i
$146$	−0.0873607	−	0.00248741i	−0.00723002	−	0.000205859i
$147$	−1.11412	−	0.160187i	−0.0918914	−	0.0132120i
$148$	3.84444	+	16.5182i	0.316011	+	1.35779i
$149$	1.02668	−	3.49656i	0.0841090	−	0.286449i	−0.906689	−	0.421801i	$-0.861398\pi$
$149$	1.02668	−	3.49656i	0.0841090	−	0.286449i	0.990798	+	0.135352i	$0.0432164\pi$
$150$	−5.13803	+	2.17192i	−0.419518	+	0.177337i
$151$	3.44640	+	7.54657i	0.280464	+	0.614131i	0.996469	−	0.0839644i	$-0.0267582\pi$
$151$	3.44640	+	7.54657i	0.280464	+	0.614131i	−0.716004	+	0.698096i	$0.754031\pi$
$152$	7.07260	−	2.52576i	0.573663	−	0.204867i
$153$	1.31383	−	1.51624i	0.106217	−	0.122581i
$154$	−1.88940	−	7.18524i	−0.152252	−	0.579004i
$155$	−5.61518	+	8.73738i	−0.451022	+	0.701804i
$156$	−5.82839	−	0.332171i	−0.466645	−	0.0265950i
$157$	5.98129	+	9.30707i	0.477359	+	0.742785i	0.993514	−	0.113710i	$-0.0362736\pi$
$157$	5.98129	+	9.30707i	0.477359	+	0.742785i	−0.516155	+	0.856495i	$0.672637\pi$
$158$	1.15919	−	6.70210i	0.0922202	−	0.533190i
$159$	−6.26046	+	1.83824i	−0.496487	+	0.145782i
$160$	5.57579	−	1.64007i	0.440805	−	0.129659i
$161$	−11.5795	−	1.01280i	−0.912596	−	0.0798196i
$162$	0.895319	+	1.09472i	0.0703429	+	0.0860091i
$163$	−3.27094	−	11.1398i	−0.256199	−	0.872535i	−0.982674	−	0.185342i	$-0.940661\pi$
$163$	−3.27094	−	11.1398i	−0.256199	−	0.872535i	0.726475	−	0.687193i	$-0.241157\pi$
$164$	−10.2362	+	5.78319i	−0.799311	+	0.451591i
$165$	1.20399	+	1.87344i	0.0937302	+	0.145847i
$166$	3.06707	+	2.81439i	0.238051	+	0.218439i
$167$	−2.69173	−	1.72987i	−0.208292	−	0.133861i	0.432336	−	0.901713i	$-0.357690\pi$
$167$	−2.69173	−	1.72987i	−0.208292	−	0.133861i	−0.640628	+	0.767851i	$0.721326\pi$
$168$	−6.84402	+	0.393307i	−0.528028	+	0.0303443i
$169$	−2.93369	+	3.38566i	−0.225669	+	0.260435i
$170$	−1.50560	−	2.49622i	−0.115474	−	0.191451i
$171$	2.41526	−	1.10301i	0.184700	−	0.0843496i
$172$	1.22053	+	0.643713i	0.0930648	+	0.0490827i
$173$	3.42827	−	11.6756i	0.260647	−	0.887681i	−0.720342	−	0.693619i	$-0.756015\pi$
$173$	3.42827	−	11.6756i	0.260647	−	0.887681i	0.980989	−	0.194063i	$-0.0621665\pi$
$174$	1.62426	−	3.30437i	0.123135	−	0.250504i
$175$	1.36055	−	9.46281i	0.102848	−	0.715321i
$176$	3.82837	+	7.77905i	0.288574	+	0.586368i
$177$	2.45657	−	5.37913i	0.184647	−	0.404320i
$178$	2.48613	+	21.6495i	0.186343	+	1.62270i
$179$	−15.4335	+	2.21900i	−1.15355	+	0.165856i	−0.692432	−	0.721483i	$-0.743461\pi$
$179$	−15.4335	+	2.21900i	−1.15355	+	0.165856i	−0.461118	+	0.887339i	$0.652552\pi$
$180$	1.91470	−	0.745878i	0.142713	−	0.0555945i
$181$	10.6976	−	9.26950i	0.795144	−	0.688997i	−0.159351	−	0.987222i	$-0.550940\pi$
$181$	10.6976	−	9.26950i	0.795144	−	0.688997i	0.954495	+	0.298225i	$0.0963947\pi$
$182$	5.64652	−	8.25945i	0.418548	−	0.612231i
$183$	4.68335			0.346203
$184$	13.4782	−	1.52903i	0.993627	−	0.112721i
$185$	8.71240			0.640549
$186$	−8.06825	+	11.8018i	−0.591593	+	0.865353i
$187$	3.28649	−	2.84776i	0.240332	−	0.208249i
$188$	7.01124	+	17.9981i	0.511347	+	1.31265i
$189$	−2.39905	+	0.344931i	−0.174505	+	0.0250901i
$190$	−0.440144	−	3.83283i	−0.0319314	−	0.278063i
$191$	−0.0692543	+	0.151646i	−0.00501106	+	0.0109727i	−0.912121	−	0.409921i	$-0.865556\pi$
$191$	−0.0692543	+	0.151646i	−0.00501106	+	0.0109727i	0.907110	+	0.420894i	$0.138284\pi$
$192$	7.73602	−	2.03815i	0.558299	−	0.147090i
$193$	3.43482	−	23.8897i	0.247244	−	1.71962i	−0.366761	−	0.930315i	$-0.619533\pi$
$193$	3.43482	−	23.8897i	0.247244	−	1.71962i	0.614005	−	0.789302i	$-0.289558\pi$
$194$	−6.22248	+	12.6589i	−0.446748	+	0.908857i
$195$	−0.844910	+	2.87750i	−0.0605052	+	0.206062i
$196$	−1.05017	+	1.99120i	−0.0750119	+	0.142229i
$197$	9.24620	−	4.22260i	0.658765	−	0.300848i	−0.0578414	−	0.998326i	$-0.518422\pi$
$197$	9.24620	−	4.22260i	0.658765	−	0.300848i	0.716606	+	0.697478i	$0.245695\pi$
$198$	1.58318	+	2.62484i	0.112512	+	0.186540i
$199$	−10.0575	+	11.6070i	−0.712961	+	0.822800i	−0.990442	−	0.137931i	$-0.955955\pi$
$199$	−10.0575	+	11.6070i	−0.712961	+	0.822800i	0.277481	+	0.960731i	$0.410500\pi$
$200$	0.640074	+	11.1381i	0.0452601	+	0.787580i
$201$	−7.96531	−	5.11900i	−0.561830	−	0.361066i
$202$	−7.18605	−	6.59405i	−0.505609	−	0.463955i
$203$	3.41161	+	5.30857i	0.239448	+	0.372589i
$204$	−1.97377	−	3.49355i	−0.138191	−	0.244597i
$205$	1.70157	+	5.79501i	0.118843	+	0.404741i
$206$	−2.43530	−	2.97768i	−0.169676	−	0.207464i
$207$	4.70179	−	0.945061i	0.326797	−	0.0656863i
$208$	−4.54093	+	10.7565i	−0.314857	+	0.745828i
$209$	5.52209	−	1.62143i	0.381971	−	0.112157i
$210$	−0.600193	+	3.47014i	−0.0414172	+	0.239462i
$211$	10.1499	+	15.7936i	0.698751	+	1.08728i	0.991376	+	0.131051i	$0.0418350\pi$
$211$	10.1499	+	15.7936i	0.698751	+	1.08728i	−0.292625	+	0.956227i	$0.594529\pi$
$212$	−0.742513	+	13.0284i	−0.0509960	+	0.894793i
$213$	−3.66204	+	5.69825i	−0.250919	+	0.390438i
$214$	5.77721	+	21.9703i	0.394922	+	1.50186i
$215$	0.464206	−	0.535722i	0.0316586	−	0.0365359i
$216$	2.66367	−	0.951248i	0.181240	−	0.0647243i
$217$	−10.1782	−	22.2870i	−0.690938	−	1.51294i
$218$	14.7443	−	6.23264i	0.998610	−	0.422128i
$219$	−0.0174106	+	0.0592951i	−0.00117650	+	0.00400679i
$220$	4.33798	−	1.00962i	0.292467	−	0.0680687i
$221$	5.79657	+	0.833421i	0.389920	+	0.0560620i
$222$	11.9875	+	0.341317i	0.804545	+	0.0229077i
$223$	10.3139	−	22.5843i	0.690671	−	1.51236i	−0.160258	−	0.987075i	$-0.551232\pi$
$223$	10.3139	−	22.5843i	0.690671	−	1.51236i	0.850928	−	0.525282i	$-0.176040\pi$
$224$	−3.85650	+	13.1571i	−0.257673	+	0.879095i
$225$	0.561346	+	3.90425i	0.0374231	+	0.260283i
$226$	−6.43941	−	2.09162i	−0.428343	−	0.139132i
$227$	14.0159	−	12.1449i	0.930268	−	0.806082i	−0.0510059	−	0.998698i	$-0.516243\pi$
$227$	14.0159	−	12.1449i	0.930268	−	0.806082i	0.981274	+	0.192616i	$0.0616973\pi$
$228$	−0.455442	−	5.29085i	−0.0301624	−	0.350395i
$229$		−	18.3172i		−	1.21044i	−0.796059	−	0.605219i	$-0.793086\pi$
$229$		−	18.3172i		−	1.21044i	0.796059	−	0.605219i	$-0.206914\pi$
$230$	0.804491	−	6.92174i	0.0530466	−	0.456406i
$231$	−5.25345			−0.345652
$232$	−5.13374	−	5.27949i	−0.337047	−	0.346616i
$233$	9.25130	+	10.6766i	0.606073	+	0.699445i	0.973000	−	0.230804i	$-0.0741358\pi$
$233$	9.25130	+	10.6766i	0.606073	+	0.699445i	−0.366928	+	0.930250i	$0.619590\pi$
$234$	−1.27525	+	3.92607i	−0.0833654	+	0.256655i
$235$	9.82164	−	1.41214i	0.640693	−	0.0921178i
$236$	−8.48311	−	8.24110i	−0.552203	−	0.536450i
$237$	−4.37484	−	1.99792i	−0.284176	−	0.129779i
$238$	6.87405	+	0.195724i	0.445579	+	0.0126869i
$239$	2.26843	−	15.7773i	0.146733	−	1.02055i	−0.774789	−	0.632220i	$-0.782144\pi$
$239$	2.26843	−	15.7773i	0.146733	−	1.02055i	0.921522	−	0.388327i	$-0.126947\pi$
$240$	−0.118914	−	4.10798i	−0.00767586	−	0.265169i
$241$	12.0279	+	3.53171i	0.774784	+	0.227497i	0.645141	−	0.764063i	$-0.276799\pi$
$241$	12.0279	+	3.53171i	0.774784	+	0.227497i	0.129643	+	0.991561i	$0.458617\pi$
$242$	−3.47003	−	8.20890i	−0.223062	−	0.527688i
$243$	0.909632	−	0.415415i	0.0583529	−	0.0266489i
$244$	3.14600	−	8.82256i	0.201402	−	0.564807i
$245$	0.873987	+	0.757314i	0.0558370	+	0.0483830i
$246$	2.11417	+	8.04006i	0.134795	+	0.512615i
$247$	6.52002	+	4.19016i	0.414859	+	0.266614i
$248$	16.8127	+	23.1269i	1.06761	+	1.46856i
$249$	2.47618	−	1.59135i	0.156922	−	0.100847i
$250$	12.8061	+	2.21493i	0.809927	+	0.140084i
$251$	−7.35594	−	25.0520i	−0.464303	−	1.58127i	−0.775771	−	0.631014i	$-0.782639\pi$
$251$	−7.35594	−	25.0520i	−0.464303	−	1.58127i	0.311469	−	0.950256i	$-0.399179\pi$
$252$	−0.961755	+	4.75107i	−0.0605849	+	0.299290i
$253$	10.3790	−	0.577224i	0.652523	−	0.0362898i
$254$	−7.97091	−	9.74613i	−0.500139	−	0.611527i
$255$	−1.97780	+	0.580736i	−0.123855	+	0.0363671i
$256$	1.35711	−	15.9423i	0.0848197	−	0.996396i
$257$	−9.45715	+	6.07774i	−0.589921	+	0.379119i	−0.801280	−	0.598289i	$-0.795847\pi$
$257$	−9.45715	+	6.07774i	−0.589921	+	0.379119i	0.211359	+	0.977408i	$0.432211\pi$
$258$	0.659691	−	0.718917i	0.0410706	−	0.0447578i
$259$	−11.1117	+	17.2901i	−0.690445	+	1.07435i
$260$	4.85312	+	3.52459i	0.300978	+	0.218586i
$261$	−1.96764	−	1.70497i	−0.121794	−	0.105535i
$262$	7.62722	+	12.6456i	0.471211	+	0.781249i
$263$	−8.60999	−	18.8532i	−0.530915	−	1.16254i	−0.965139	−	0.261736i	$-0.915705\pi$
$263$	−8.60999	−	18.8532i	−0.530915	−	1.16254i	0.434225	−	0.900805i	$-0.357022\pi$
$264$	6.00821	−	1.21920i	0.369780	−	0.0750365i
$265$	6.43216	+	1.88865i	0.395124	+	0.116019i
$266$	8.16774	+	4.01485i	0.500796	+	0.246166i
$267$	15.2523	+	2.19294i	0.933424	+	0.134206i
$268$	−14.9939	+	11.5665i	−0.915897	+	0.706539i
$269$	−12.3799	−	5.65370i	−0.754814	−	0.344712i	0.000565241	−	1.00000i	$-0.499820\pi$
$269$	−12.3799	−	5.65370i	−0.754814	−	0.344712i	−0.755379	+	0.655288i	$0.772547\pi$
$270$	−0.165766	−	1.44351i	−0.0100882	−	0.0878493i
$271$	−1.10944	−	7.71634i	−0.0673938	−	0.468734i	−0.995372	−	0.0960992i	$-0.969363\pi$
$271$	−1.10944	−	7.71634i	−0.0673938	−	0.468734i	0.927978	−	0.372635i	$-0.121546\pi$
$272$	−7.90706	+	1.37146i	−0.479436	+	0.0831568i
$273$	−4.63292	−	5.34667i	−0.280397	−	0.323595i
$274$	13.7297	+	9.38620i	0.829440	+	0.567041i
$275$			8.54955i			0.515557i
$276$	1.37807	−	9.49215i	0.0829501	−	0.571360i
$277$			3.37614i			0.202853i	0.994843	+	0.101426i	$0.0323406\pi$
$277$			3.37614i			0.202853i	−0.994843	+	0.101426i	$0.967659\pi$
$278$	−9.19384	+	13.4483i	−0.551410	+	0.806575i
$279$	6.61993	+	7.63981i	0.396325	+	0.457383i
$280$	6.13393	+	3.46169i	0.366572	+	0.206876i
$281$	1.23126	+	8.56359i	0.0734508	+	0.510861i	0.993021	+	0.117936i	$0.0376278\pi$
$281$	1.23126	+	8.56359i	0.0734508	+	0.510861i	−0.919570	+	0.392925i	$0.871463\pi$
$282$	13.5690	−	1.55820i	0.808021	−	0.0927893i
$283$	29.2115	+	13.3404i	1.73644	+	0.793007i	0.992135	+	0.125170i	$0.0399477\pi$
$283$	29.2115	+	13.3404i	1.73644	+	0.793007i	0.744308	+	0.667837i	$0.232780\pi$
$284$	8.27451	+	10.7264i	0.491002	+	0.636493i
$285$	−2.70026	−	0.388239i	−0.159950	−	0.0229973i
$286$	−3.94705	+	8.02983i	−0.233394	+	0.474814i
$287$	−13.6706	−	4.01404i	−0.806948	−	0.236941i
$288$	−0.00268023	−	5.65685i	−0.000157934	−	0.333333i
$289$	−5.38995	−	11.8023i	−0.317056	−	0.694255i
$290$	−3.23936	+	1.95383i	−0.190222	+	0.114733i
$291$	7.53796	+	6.53168i	0.441883	+	0.382894i
$292$	0.100006	+	0.0726294i	0.00585239	+	0.00425031i
$293$	−16.3838	+	25.4937i	−0.957151	+	1.48936i	−0.0872163	+	0.996189i	$0.527797\pi$
$293$	−16.3838	+	25.4937i	−0.957151	+	1.48936i	−0.869935	+	0.493167i	$0.835839\pi$
$294$	1.17286	+	1.07623i	0.0684023	+	0.0627671i
$295$	−5.11120	+	3.28477i	−0.297586	+	0.191247i
$296$	8.69545	−	22.3529i	0.505413	−	1.29923i
$297$	2.07972	−	0.610660i	0.120677	−	0.0354341i
$298$	−3.98933	+	3.26269i	−0.231096	+	0.189003i
$299$	9.74051	+	10.0541i	0.563308	+	0.581445i
$300$	7.73197	+	1.56517i	0.446405	+	0.0903654i
$301$	0.471119	+	1.60448i	0.0271549	+	0.0924809i
$302$	1.99960	−	11.5611i	0.115064	−	0.665265i
$303$	−5.80163	+	3.72848i	−0.333295	+	0.214195i
$304$	−10.2729	−	2.69612i	−0.589193	−	0.154633i
$305$	−4.04793	−	2.60145i	−0.231784	−	0.148958i
$306$	−2.74402	+	0.721555i	−0.156865	+	0.0412486i
$307$	3.95949	+	3.43092i	0.225980	+	0.195813i	0.760490	−	0.649349i	$-0.224959\pi$
$307$	3.95949	+	3.43092i	0.225980	+	0.195813i	−0.534511	+	0.845162i	$0.679504\pi$
$308$	−3.52896	+	9.89654i	−0.201081	+	0.563908i
$309$	−2.47424	+	1.12995i	−0.140754	+	0.0642804i
$310$	13.5291	−	5.71897i	0.768403	−	0.324816i
$311$	3.07719	+	0.903545i	0.174492	+	0.0512354i	0.367811	−	0.929900i	$-0.380107\pi$
$311$	3.07719	+	0.903545i	0.174492	+	0.0512354i	−0.193320	+	0.981136i	$0.561925\pi$
$312$	6.53935	+	5.03963i	0.370218	+	0.285313i
$313$	−3.47809	+	24.1906i	−0.196593	+	1.36733i	0.617486	+	0.786582i	$0.288151\pi$
$313$	−3.47809	+	24.1906i	−0.196593	+	1.36733i	−0.814080	+	0.580753i	$0.802758\pi$
$314$	0.445304	−	15.6396i	0.0251299	−	0.882592i
$315$	2.26516	+	1.03446i	0.127627	+	0.0582854i
$316$	−6.70248	+	6.89931i	−0.377044	+	0.388116i
$317$	24.0752	−	3.46149i	1.35220	−	0.194416i	0.572155	−	0.820145i	$-0.306107\pi$
$317$	24.0752	−	3.46149i	1.35220	−	0.194416i	0.780041	+	0.625729i	$0.215198\pi$
$318$	8.77606	+	2.85059i	0.492137	+	0.159853i
$319$	−3.69555	−	4.26490i	−0.206911	−	0.238788i
$320$	−7.81856	−	2.53549i	−0.437071	−	0.141738i
$321$	16.0635			0.896576
$322$	12.7104	+	10.4244i	0.708324	+	0.580930i
$323$			5.32709i			0.296407i
$324$	−0.171528	−	1.99263i	−0.00952931	−	0.110702i
$325$	−8.70125	+	7.53968i	−0.482659	+	0.418226i
$326$	−5.07231	+	15.6160i	−0.280929	+	0.864890i
$327$	−1.61086	−	11.2038i	−0.0890809	−	0.619572i
$328$	16.5662	+	1.41813i	0.914713	+	0.0783029i
$329$	−9.72392	+	21.2924i	−0.536097	+	1.17389i
$330$	0.0896361	−	3.14812i	0.00493430	−	0.173298i
$331$	−20.1769	−	2.90100i	−1.10902	−	0.159453i	−0.436624	−	0.899644i	$-0.643826\pi$
$331$	−20.1769	−	2.90100i	−1.10902	−	0.159453i	−0.672397	+	0.740191i	$0.734735\pi$
$332$	−1.33445	−	5.73365i	−0.0732373	−	0.314675i
$333$	2.38905	−	8.13635i	0.130919	−	0.445869i
$334$	1.76185	+	4.16793i	0.0964040	+	0.228059i
$335$	4.04118	+	8.84895i	0.220793	+	0.483470i
$336$	8.30410	+	5.00326i	0.453026	+	0.272950i
$337$	−1.51183	+	1.74475i	−0.0823548	+	0.0950424i	−0.795431	−	0.606044i	$-0.792756\pi$
$337$	−1.51183	+	1.74475i	−0.0823548	+	0.0950424i	0.713077	+	0.701086i	$0.247301\pi$
$338$	6.12720	−	1.61118i	0.333276	−	0.0876366i
$339$	−2.58833	+	4.02753i	−0.140579	+	0.218745i
$340$	−0.234574	+	4.11592i	−0.0127216	+	0.223217i
$341$	11.8461	+	18.4329i	0.641503	+	0.998198i
$342$	−3.70010	−	0.639966i	−0.200078	−	0.0346054i
$343$	−18.8964	+	5.54848i	−1.02031	+	0.299590i
$344$	−0.911166	−	1.72566i	−0.0491268	−	0.0930415i
$345$	−4.58883	−	1.79486i	−0.247054	−	0.0966318i
$346$	−13.3211	+	10.8947i	−0.716147	+	0.585703i
$347$	−9.31307	−	31.7174i	−0.499952	−	1.70268i	−0.692523	−	0.721396i	$-0.743501\pi$
$347$	−9.31307	−	31.7174i	−0.499952	−	1.70268i	0.192571	−	0.981283i	$-0.438318\pi$
$348$	−4.53360	+	2.56137i	−0.243026	+	0.137304i
$349$	−3.73441	−	5.81085i	−0.199898	−	0.311048i	0.726804	−	0.686845i	$-0.241005\pi$
$349$	−3.73441	−	5.81085i	−0.199898	−	0.311048i	−0.926702	+	0.375798i	$0.877369\pi$
$350$	−9.14097	+	9.96164i	−0.488605	+	0.532472i
$351$	2.45556	+	1.57809i	0.131068	+	0.0842322i
$352$	1.73922	−	12.1373i	0.0927006	−	0.646923i
$353$	−14.9985	+	17.3092i	−0.798291	+	0.921277i	−0.998286	−	0.0585202i	$-0.981362\pi$
$353$	−14.9985	+	17.3092i	−0.798291	+	0.921277i	0.199995	+	0.979797i	$0.435907\pi$
$354$	−7.16122	+	4.31930i	−0.380615	+	0.229568i
$355$	6.33039	−	2.89099i	0.335982	−	0.153438i
$356$	14.3767	−	27.2594i	0.761963	−	1.44474i
$357$	1.36997	−	4.66569i	0.0725065	−	0.246934i
$358$	19.7891	+	9.72733i	1.04589	+	0.514106i
$359$	3.03567	−	21.1135i	0.160216	−	1.11433i	−0.738008	−	0.674792i	$-0.764233\pi$
$359$	3.03567	−	21.1135i	0.160216	−	1.11433i	0.898224	−	0.439537i	$-0.144858\pi$
$360$	−2.83066	−	0.657394i	−0.149189	−	0.0346477i
$361$	4.96415	−	10.8700i	0.261271	−	0.572104i
$362$	−19.8874	+	2.28377i	−1.04526	+	0.120032i
$363$	−6.23773	+	0.896850i	−0.327396	+	0.0470724i
$364$	−13.1843	+	5.13598i	−0.691043	+	0.269199i
$365$	0.0479850	−	0.0415792i	0.00251165	−	0.00217635i
$366$	−5.46766	−	3.73793i	−0.285799	−	0.195385i
$367$	23.9352			1.24941			0.624703	−	0.780862i	$-0.285220\pi$
$367$	23.9352			1.24941			0.624703	+	0.780862i	$0.285220\pi$
$368$	−16.9558	−	8.97230i	−0.883880	−	0.467714i
$369$	5.87844			0.306020
$370$	−10.1715	−	6.95365i	−0.528789	−	0.361503i
$371$	−11.9516	+	10.3561i	−0.620495	+	0.537662i
$372$	18.8389	−	7.33875i	0.976750	−	0.380497i
$373$	−20.7151	+	2.97839i	−1.07259	+	0.154215i	−0.655910	−	0.754839i	$-0.727715\pi$
$373$	−20.7151	+	2.97839i	−1.07259	+	0.154215i	−0.416678	+	0.909054i	$0.636806\pi$
$374$	−6.10976	+	0.701616i	−0.315928	+	0.0362797i
$375$	3.81754	−	8.35924i	0.197137	−	0.431670i
$376$	6.17949	−	26.6082i	0.318683	−	1.37221i
$377$	1.08154	−	7.52226i	0.0557020	−	0.387416i
$378$	3.07612	+	1.51206i	0.158218	+	0.0777722i
$379$	6.03407	−	20.5501i	0.309949	−	1.05559i	−0.646311	−	0.763074i	$-0.723689\pi$
$379$	6.03407	−	20.5501i	0.309949	−	1.05559i	0.956261	−	0.292516i	$-0.0944926\pi$
$380$	−2.54525	+	4.82600i	−0.130569	+	0.247569i
$381$	−8.09834	+	3.69839i	−0.414891	+	0.189474i
$382$	0.201886	−	0.121768i	0.0103294	−	0.00623017i
$383$	−14.2169	+	16.4071i	−0.726448	+	0.838366i	−0.992067	−	0.125712i	$-0.959878\pi$
$383$	−14.2169	+	16.4071i	−0.726448	+	0.838366i	0.265619	+	0.964078i	$0.414424\pi$
$384$	−10.6583	−	3.79490i	−0.543903	−	0.193657i
$385$	4.54069	+	2.91813i	0.231415	+	0.148721i
$386$	−23.0772	+	25.1490i	−1.17460	+	1.28005i
$387$	−0.373010	−	0.580414i	−0.0189611	−	0.0295041i
$388$	17.3680	−	9.81253i	0.881729	−	0.498156i
$389$	−3.39034	−	11.5464i	−0.171897	−	0.585427i	−0.999702	−	0.0244115i	$-0.992229\pi$
$389$	−3.39034	−	11.5464i	−0.171897	−	0.585427i	0.827805	−	0.561016i	$-0.189589\pi$
$390$	3.28303	−	2.68504i	0.166243	−	0.135962i
$391$	−2.19394	+	9.36831i	−0.110952	+	0.473776i
$392$	2.81528	−	1.48649i	0.142193	−	0.0750792i
$393$	10.0194	−	2.94196i	0.505411	−	0.148402i
$394$	−14.1649	−	2.44994i	−0.713615	−	0.123426i
$395$	2.67150	+	4.15694i	0.134418	+	0.209158i
$396$	0.246662	−	4.32801i	0.0123952	−	0.217491i
$397$	−9.88823	+	15.3864i	−0.496276	+	0.772221i	−0.995551	−	0.0942229i	$-0.969963\pi$
$397$	−9.88823	+	15.3864i	−0.496276	+	0.772221i	0.499275	+	0.866444i	$0.333600\pi$
$398$	21.0058	−	5.52359i	1.05293	−	0.276873i
$399$	4.21435	−	4.86362i	0.210981	−	0.243485i
$400$	8.14239	−	13.5142i	0.407119	−	0.675711i
$401$	7.03886	+	15.4129i	0.351504	+	0.769686i	0.999964	+	0.00843771i	$0.00268584\pi$
$401$	7.03886	+	15.4129i	0.351504	+	0.769686i	−0.648461	+	0.761248i	$0.724587\pi$
$402$	5.21362	+	12.3336i	0.260032	+	0.615146i
$403$	−8.31313	+	28.3119i	−0.414106	+	1.41032i
$404$	3.12657	+	13.4338i	0.155553	+	0.668355i
$405$	−1.01697	−	0.146218i	−0.0505335	−	0.00726562i
$406$	0.253992	−	8.92051i	0.0126054	−	0.442717i
$407$	7.63541	−	16.7192i	0.378473	−	0.828741i
$408$	−0.483998	+	5.65394i	−0.0239615	+	0.279912i
$409$	0.151385	+	1.05291i	0.00748550	+	0.0520628i	0.993222	−	0.116234i	$-0.0370823\pi$
$409$	0.151385	+	1.05291i	0.00748550	+	0.0520628i	−0.985736	+	0.168297i	$0.946173\pi$
$410$	2.63866	−	8.12358i	0.130314	−	0.401195i
$411$	8.88776	−	7.70129i	0.438401	−	0.379877i
$412$	0.466562	+	5.42004i	0.0229859	+	0.267026i
$413$		−	14.3327i		−	0.705267i
$414$	−6.24348	−	2.64933i	−0.306850	−	0.130207i
$415$	−3.02417			−0.148451
$416$	13.8865	−	8.93361i	0.680842	−	0.438006i
$417$	7.54346	+	8.70562i	0.369405	+	0.426316i
$418$	−7.74098	−	2.51439i	−0.378624	−	0.122983i
$419$	−14.1590	+	2.03575i	−0.691711	+	0.0994530i	−0.479200	−	0.877706i	$-0.659073\pi$
$419$	−14.1590	+	2.03575i	−0.691711	+	0.0994530i	−0.212511	+	0.977159i	$0.568164\pi$
$420$	3.47034	−	3.57225i	0.169335	−	0.174308i
$421$	8.83207	+	4.03347i	0.430449	+	0.196579i	0.618844	−	0.785514i	$-0.287601\pi$
$421$	8.83207	+	4.03347i	0.430449	+	0.196579i	−0.188395	+	0.982093i	$0.560329\pi$
$422$	0.755658	−	26.5396i	0.0367848	−	1.29193i
$423$	1.37444	−	9.55947i	0.0668278	−	0.464797i
$424$	11.2652	−	14.6176i	0.547088	−	0.709894i
$425$	−7.59301	−	2.22951i	−0.368315	−	0.108147i
$426$	8.82328	−	3.72973i	0.427489	−	0.180706i
$427$	10.3253	−	4.71542i	0.499678	−	0.228195i
$428$	10.7905	−	30.2606i	0.521579	−	1.46270i
$429$	4.78149	+	4.14319i	0.230853	+	0.200035i
$430$	−0.969523	+	0.254941i	−0.0467545	+	0.0122943i
$431$	−1.32506	−	0.851564i	−0.0638259	−	0.0410184i	0.508339	−	0.861157i	$-0.330260\pi$
$431$	−1.32506	−	0.851564i	−0.0638259	−	0.0410184i	−0.572165	+	0.820139i	$0.693896\pi$
$432$	−3.86897	−	1.01541i	−0.186146	−	0.0488538i
$433$	−10.9021	+	7.00639i	−0.523924	+	0.336705i	−0.775722	−	0.631074i	$-0.782614\pi$
$433$	−10.9021	+	7.00639i	−0.523924	+	0.336705i	0.251799	+	0.967780i	$0.418978\pi$
$434$	−5.90534	+	34.1430i	−0.283465	+	1.63891i
$435$	0.753625	+	2.56661i	0.0361336	+	0.123060i
$436$	−22.1880	−	4.49149i	−1.06261	−	0.215103i
$437$	−7.79170	+	10.0719i	−0.372728	+	0.481803i
$438$	0.0676517	−	0.0553292i	0.00323252	−	0.00264373i
$439$	−24.2250	+	7.11310i	−1.15620	+	0.339490i	−0.802954	−	0.596042i	$-0.796739\pi$
$439$	−24.2250	+	7.11310i	−1.15620	+	0.339490i	−0.353243	+	0.935532i	$0.614921\pi$
$440$	−5.87027	−	2.28358i	−0.279854	−	0.108866i
$441$	0.946899	−	0.608535i	0.0450904	−	0.0289779i
$442$	−6.10214	−	5.59943i	−0.290249	−	0.266338i
$443$	12.8860	−	20.0511i	0.612234	−	0.952655i	−0.387294	−	0.921956i	$-0.626590\pi$
$443$	12.8860	−	20.0511i	0.612234	−	0.952655i	0.999529	−	0.0306991i	$-0.00977337\pi$
$444$	−13.7226	−	9.96605i	−0.651244	−	0.472968i
$445$	−11.9648	−	10.3676i	−0.567186	−	0.491470i
$446$	−30.0664	+	18.1346i	−1.42369	+	0.858699i
$447$	1.51384	+	3.31485i	0.0716023	+	0.156787i
$448$	15.0034	−	12.2825i	0.708846	−	0.580293i
$449$	28.1760	+	8.27322i	1.32971	+	0.390437i	0.867987	−	0.496588i	$-0.165414\pi$
$449$	28.1760	+	8.27322i	1.32971	+	0.390437i	0.461721	+	0.887025i	$0.347232\pi$
$450$	2.46075	−	5.00612i	0.116001	−	0.235991i
$451$	12.6119	+	1.81332i	0.593873	+	0.0853860i
$452$	5.84843	+	7.58140i	0.275087	+	0.356599i
$453$	−7.54657	−	3.44640i	−0.354569	−	0.161926i
$454$	−26.0563	+	2.99219i	−1.22288	+	0.140430i
$455$	1.03444	+	7.19470i	0.0484954	+	0.337293i
$456$	−3.69109	+	6.54041i	−0.172851	+	0.306283i
$457$	18.1347	+	20.9286i	0.848306	+	0.978997i	0.999955	−	0.00943732i	$-0.00300404\pi$
$457$	18.1347	+	20.9286i	0.848306	+	0.978997i	−0.151650	+	0.988434i	$0.548459\pi$
$458$	−14.6196	+	21.3848i	−0.683129	+	0.999247i
$459$			2.00628i			0.0936451i
$460$	−6.46369	+	7.43883i	−0.301371	+	0.346837i
$461$			4.78122i			0.222683i	0.993782	+	0.111342i	$0.0355148\pi$
$461$			4.78122i			0.222683i	−0.993782	+	0.111342i	$0.964485\pi$
$462$	6.13325	+	4.19295i	0.285344	+	0.195074i
$463$	−12.0067	−	13.8565i	−0.558001	−	0.643967i	0.404728	−	0.914437i	$-0.367366\pi$
$463$	−12.0067	−	13.8565i	−0.558001	−	0.643967i	−0.962728	+	0.270470i	$0.912821\pi$
$464$	1.77975	+	10.2611i	0.0826229	+	0.476357i
$465$	−1.47810	−	10.2804i	−0.0685454	−	0.476744i
$466$	−2.27929	−	19.8483i	−0.105586	−	0.919456i
$467$	−11.0698	−	5.05539i	−0.512247	−	0.233936i	0.142484	−	0.989797i	$-0.454491\pi$
$467$	−11.0698	−	5.05539i	−0.512247	−	0.233936i	−0.654732	+	0.755862i	$0.727218\pi$
$468$	4.62233	−	3.56575i	0.213667	−	0.164827i
$469$	−22.7151	−	3.26594i	−1.04889	−	0.150807i
$470$	−12.5935	−	6.19034i	−0.580896	−	0.285539i
$471$	−10.6152	−	3.11690i	−0.489122	−	0.143619i
$472$	3.32628	+	16.3919i	0.153104	+	0.754497i
$473$	−0.621235	−	1.36031i	−0.0285644	−	0.0625473i
$474$	3.51288	+	5.82422i	0.161352	+	0.267515i
$475$	−7.91512	−	6.85849i	−0.363171	−	0.314689i
$476$	−7.86903	−	5.71491i	−0.360676	−	0.261942i
$477$	3.52755	−	5.48898i	0.161516	−	0.251323i
$478$	−15.2407	+	16.6090i	−0.697092	+	0.759677i
$479$	8.22767	−	5.28760i	0.375932	−	0.241597i	−0.339007	−	0.940784i	$-0.610091\pi$
$479$	8.22767	−	5.28760i	0.375932	−	0.241597i	0.714939	+	0.699187i	$0.246455\pi$
$480$	−3.13988	+	4.89085i	−0.143315	+	0.223236i
$481$	23.7494	−	6.97345i	1.08288	−	0.317962i
$482$	−11.2234	−	13.7230i	−0.511213	−	0.625066i
$483$	9.41448	−	6.81757i	0.428374	−	0.310210i
$484$	−2.50064	+	12.3532i	−0.113666	+	0.561508i
$485$	−2.88711	−	9.83259i	−0.131097	−	0.446475i
$486$	−1.39352	−	0.241023i	−0.0632115	−	0.0109330i
$487$	5.19604	−	3.33929i	0.235455	−	0.151318i	−0.417593	−	0.908634i	$-0.637126\pi$
$487$	5.19604	−	3.33929i	0.235455	−	0.151318i	0.653048	+	0.757316i	$0.273490\pi$
$488$	−10.7144	+	7.78914i	−0.485019	+	0.352598i
$489$	9.76702	+	6.27688i	0.441680	+	0.283850i
$490$	−0.415916	−	1.58170i	−0.0187892	−	0.0714538i
$491$	−4.30428	−	3.72968i	−0.194249	−	0.168318i	0.552306	−	0.833642i	$-0.313748\pi$
$491$	−4.30428	−	3.72968i	−0.194249	−	0.168318i	−0.746555	+	0.665324i	$0.768294\pi$
$492$	3.94880	−	11.0739i	0.178026	−	0.499250i
$493$	4.75144	−	2.16991i	0.213994	−	0.0977278i
$494$	−4.26762	−	10.0957i	−0.192009	−	0.454228i
$495$	−2.13675	−	0.627408i	−0.0960399	−	0.0281999i
$496$	−1.17000	−	40.4187i	−0.0525347	−	1.81485i
$497$	−2.33640	+	16.2500i	−0.104802	+	0.728913i
$498$	−4.16097	−	0.118475i	−0.186458	−	0.00530898i
$499$	−28.9187	−	13.2067i	−1.29458	−	0.591215i	−0.355423	−	0.934705i	$-0.615663\pi$
$499$	−28.9187	−	13.2067i	−1.29458	−	0.591215i	−0.939156	+	0.343491i	$0.888391\pi$
$500$	−13.1829	−	12.8068i	−0.589556	−	0.572737i
$501$	3.16710	−	0.455360i	0.141496	−	0.0203440i
$502$	−11.4070	+	35.1185i	−0.509120	+	1.56742i
$503$	5.74422	+	6.62919i	0.256122	+	0.295581i	0.869219	−	0.494427i	$-0.164622\pi$
$503$	5.74422	+	6.62919i	0.256122	+	0.295581i	−0.613097	+	0.790008i	$0.710077\pi$
$504$	4.91481	−	4.77912i	0.218923	−	0.212879i
$505$	7.08554			0.315302
$506$	−12.5779	−	7.60993i	−0.559155	−	0.338303i
$507$		−	4.47987i		−	0.198958i
$508$	1.52709	+	17.7402i	0.0677537	+	0.787092i
$509$	−14.3379	+	12.4239i	−0.635516	+	0.550678i	−0.911922	−	0.410363i	$-0.865402\pi$
$509$	−14.3379	+	12.4239i	−0.635516	+	0.550678i	0.276406	+	0.961041i	$0.410857\pi$
$510$	2.77253	+	0.900559i	0.122770	+	0.0398774i
$511$	0.0213162	+	0.148257i	0.000942973	+	0.00655852i
$512$	−14.3085	+	17.5290i	−0.632352	+	0.774681i
$513$	−1.10301	+	2.41526i	−0.0486993	+	0.106637i
$514$	15.8918	+	0.452484i	0.700956	+	0.0199582i
$515$	2.76619	+	0.397719i	0.121893	+	0.0175256i
$516$	−1.34396	+	0.312793i	−0.0591645	+	0.0137699i
$517$	5.89762	−	20.0854i	0.259377	−	0.883356i
$518$	26.7723	−	11.3171i	1.17631	−	0.497243i
$519$	5.05499	+	11.0689i	0.221890	+	0.485870i
$520$	−2.85277	−	7.98828i	−0.125102	−	0.350309i
$521$	−11.3464	+	13.0944i	−0.497094	+	0.573677i	−0.947747	−	0.319022i	$-0.896646\pi$
$521$	−11.3464	+	13.0944i	−0.497094	+	0.573677i	0.450653	+	0.892699i	$0.351191\pi$
$522$	0.936368	+	3.56094i	0.0409837	+	0.155858i
$523$	13.5899	−	21.1463i	0.594245	−	0.924663i	−0.405698	−	0.914007i	$-0.632972\pi$
$523$	13.5899	−	21.1463i	0.594245	−	0.924663i	0.999943	−	0.0106562i	$-0.00339204\pi$
$524$	1.18833	−	20.8509i	0.0519126	−	0.910876i
$525$	5.16859	+	8.04248i	0.225576	+	0.351003i
$526$	−4.99549	+	28.8825i	−0.217814	+	1.25934i
$527$	−19.4598	+	5.71390i	−0.847680	+	0.248901i
$528$	−7.98748	−	3.37197i	−0.347611	−	0.146746i
$529$	−17.8507	+	14.5036i	−0.776116	+	0.630590i
$530$	−6.00195	−	7.33866i	−0.260708	−	0.318771i
$531$	1.66603	+	5.67398i	0.0722996	+	0.246230i
$532$	−6.33120	−	11.2061i	−0.274493	−	0.485848i
$533$	9.27672	+	14.4349i	0.401819	+	0.625243i
$534$	−16.0563	−	14.7335i	−0.694824	−	0.637582i
$535$	−13.8841	−	8.92275i	−0.600261	−	0.385764i
$536$	26.7365	−	1.53648i	1.15484	−	0.0663656i
$537$	10.2107	−	11.7838i	0.440624	−	0.508507i
$538$	9.94072	+	16.4813i	0.428575	+	0.710559i
$539$	2.21924	−	1.01349i	0.0955896	−	0.0436543i
$540$	−0.958587	+	1.81756i	−0.0412510	+	0.0782153i
$541$	−0.951658	+	3.24105i	−0.0409150	+	0.139344i	−0.977418	−	0.211317i	$-0.932225\pi$
$541$	−0.951658	+	3.24105i	−0.0409150	+	0.139344i	0.936503	+	0.350661i	$0.114043\pi$
$542$	−4.86342	+	9.89407i	−0.208902	+	0.424987i
$543$	−2.01445	+	14.0108i	−0.0864485	+	0.601263i
$544$	10.3259	+	4.70975i	0.442717	+	0.201929i
$545$	−4.83104	+	10.5785i	−0.206939	+	0.453133i
$546$	1.14144	+	9.93976i	0.0488489	+	0.425382i
$547$	14.0126	−	2.01471i	0.599137	−	0.0861429i	0.163928	−	0.986472i	$-0.447584\pi$
$547$	14.0126	−	2.01471i	0.599137	−	0.0861429i	0.435209	+	0.900329i	$0.356674\pi$
$548$	−8.53753	−	21.9162i	−0.364705	−	0.936213i
$549$	−3.53944	+	3.06694i	−0.151059	+	0.130894i
$550$	6.82367	−	9.98133i	0.290962	−	0.425606i
$551$	6.91301			0.294504
$552$	−9.18485	+	9.98191i	−0.390933	+	0.424858i
$553$	−11.6568			−0.495697
$554$	2.69461	−	3.94154i	0.114483	−	0.167460i
$555$	−6.58440	+	5.70541i	−0.279492	+	0.242181i
$556$	21.4670	−	8.36257i	0.910406	−	0.354652i
$557$	5.49431	−	0.789962i	0.232801	−	0.0334718i	−0.0249267	−	0.999689i	$-0.507935\pi$
$557$	5.49431	−	0.789962i	0.232801	−	0.0334718i	0.257728	+	0.966218i	$0.417026\pi$
$558$	−1.63099	−	14.2028i	−0.0690451	−	0.601253i
$559$	0.836597	−	1.83189i	0.0353843	−	0.0774808i
$560$	−4.39829	−	8.93711i	−0.185862	−	0.377662i
$561$	−0.618876	+	4.30438i	−0.0261290	+	0.181731i
$562$	5.39743	−	10.9804i	0.227677	−	0.463182i
$563$	−6.93566	+	23.6207i	−0.292303	+	0.995493i	0.674138	+	0.738605i	$0.264515\pi$
$563$	−6.93566	+	23.6207i	−0.292303	+	0.995493i	−0.966441	+	0.256888i	$0.917303\pi$
$564$	−17.0850	−	9.01069i	−0.719409	−	0.379419i
$565$	4.47432	−	2.04336i	0.188236	−	0.0859646i
$566$	−23.4561	−	38.8892i	−0.985932	−	1.63464i
$567$	1.58720	−	1.83173i	0.0666561	−	0.0769252i
$568$	−1.09917	−	19.1269i	−0.0461201	−	0.802545i
$569$	−4.80997	−	3.09118i	−0.201645	−	0.129589i	0.435922	−	0.899985i	$-0.356422\pi$
$569$	−4.80997	−	3.09118i	−0.201645	−	0.129589i	−0.637566	+	0.770395i	$0.720059\pi$
$570$	2.84261	+	2.60842i	0.119064	+	0.109255i
$571$	5.33729	+	8.30499i	0.223359	+	0.347553i	0.934789	−	0.355204i	$-0.115589\pi$
$571$	5.33729	+	8.30499i	0.223359	+	0.347553i	−0.711430	+	0.702757i	$0.751952\pi$
$572$	11.0169	−	6.22430i	0.460641	−	0.260251i
$573$	−0.0469679	−	0.159958i	−0.00196211	−	0.00668234i
$574$	12.7562	+	15.5972i	0.532435	+	0.651015i
$575$	−11.0950	−	15.3213i	−0.462694	−	0.638941i
$576$	−4.51179	+	6.60634i	−0.187991	+	0.275264i
$577$	−23.5018	+	6.90074i	−0.978391	+	0.287281i	−0.731560	−	0.681777i	$-0.761207\pi$
$577$	−23.5018	+	6.90074i	−0.978391	+	0.287281i	−0.246831	+	0.969059i	$0.579389\pi$
$578$	−3.12723	+	18.0808i	−0.130076	+	0.752060i
$579$	13.0486	+	20.3040i	0.542280	+	0.843803i
$580$	5.34127	+	0.304409i	0.221784	+	0.0126399i
$581$	3.85698	−	6.00157i	0.160014	−	0.248987i
$582$	−3.58719	−	13.6418i	−0.148694	−	0.565472i
$583$	9.26139	−	10.6882i	0.383568	−	0.442661i
$584$	−0.0587856	−	0.164610i	−0.00243257	−	0.00681162i
$585$	−1.24582	−	2.72797i	−0.0515083	−	0.112788i
$586$	39.4749	−	16.6866i	1.63069	−	0.689319i
$587$	12.1303	−	41.3121i	0.500672	−	1.70513i	−0.189844	−	0.981814i	$-0.560798\pi$
$587$	12.1303	−	41.3121i	0.500672	−	1.70513i	0.690516	−	0.723317i	$-0.257383\pi$
$588$	−0.510296	−	2.19256i	−0.0210443	−	0.0904197i
$589$	−26.5681	−	3.81991i	−1.09472	−	0.157397i
$590$	8.58886	+	0.244549i	0.353598	+	0.0100679i
$591$	−4.22260	+	9.24620i	−0.173695	+	0.380338i
$592$	−27.9922	+	19.1562i	−1.15047	+	0.787314i
$593$	−4.54974	−	31.6442i	−0.186836	−	1.29947i	−0.840138	−	0.542373i	$-0.817526\pi$
$593$	−4.54974	−	31.6442i	−0.186836	−	1.29947i	0.653302	−	0.757097i	$-0.273383\pi$
$594$	−2.91539	−	0.946963i	−0.119620	−	0.0388544i
$595$	−3.77574	+	3.27170i	−0.154790	+	0.134126i
$596$	7.26149	−	0.625076i	0.297442	−	0.0256041i
$597$		−	15.3583i		−	0.628573i
$598$	−3.34721	−	19.5121i	−0.136878	−	0.797909i
$599$	21.9125			0.895322			0.447661	−	0.894203i	$-0.352257\pi$
$599$	21.9125			0.895322			0.447661	+	0.894203i	$0.352257\pi$
$600$	−7.77762	−	7.99843i	−0.317520	−	0.326534i
$601$	28.6823	+	33.1011i	1.16998	+	1.35022i	0.924666	+	0.380779i	$0.124344\pi$
$601$	28.6823	+	33.1011i	1.16998	+	1.35022i	0.245310	+	0.969445i	$0.421110\pi$
$602$	0.730574	−	2.24920i	0.0297760	−	0.0916706i
$603$	9.37201	−	1.34749i	0.381658	−	0.0548741i
$604$	−11.5617	+	11.9013i	−0.470441	+	0.484255i
$605$	5.88959	+	2.68969i	0.239446	+	0.109351i
$606$	9.74904	+	0.277583i	0.396028	+	0.0112760i
$607$	−3.51441	+	24.4433i	−0.142646	+	0.992122i	0.785223	+	0.619214i	$0.212548\pi$
$607$	−3.51441	+	24.4433i	−0.142646	+	0.992122i	−0.927868	+	0.372908i	$0.878361\pi$
$608$	9.84147	+	11.3468i	0.399124	+	0.460173i
$609$	−6.05470	−	1.77782i	−0.245349	−	0.0720409i
$610$	2.64954	+	6.26790i	0.107277	+	0.253780i
$611$	25.6428	−	11.7107i	1.03740	−	0.473764i
$612$	3.77946	+	1.34770i	0.152776	+	0.0544776i
$613$	−16.8090	−	14.5650i	−0.678908	−	0.588277i	0.245632	−	0.969363i	$-0.421005\pi$
$613$	−16.8090	−	14.5650i	−0.678908	−	0.588277i	−0.924539	+	0.381086i	$0.875550\pi$
$614$	−1.88425	−	7.16568i	−0.0760423	−	0.289183i
$615$	−5.08089	−	3.26529i	−0.204881	−	0.131669i
$616$	12.0187	−	8.73733i	0.484248	−	0.352037i
$617$	−10.9116	+	7.01248i	−0.439286	+	0.282312i	−0.741531	−	0.670918i	$-0.765900\pi$
$617$	−10.9116	+	7.01248i	−0.439286	+	0.282312i	0.302245	+	0.953230i	$0.402264\pi$
$618$	3.79044	+	0.655592i	0.152474	+	0.0263718i
$619$	−2.98294	−	10.1589i	−0.119894	−	0.408323i	0.877573	−	0.479442i	$-0.159161\pi$
$619$	−2.98294	−	10.1589i	−0.119894	−	0.408323i	−0.997468	+	0.0711196i	$0.977343\pi$
$620$	−20.3593	−	4.12132i	−0.817651	−	0.165516i
$621$	−2.93450	+	3.79325i	−0.117757	+	0.152218i
$622$	−2.87138	−	3.51087i	−0.115132	−	0.140773i
$623$	35.8345	−	10.5220i	1.43568	−	0.421554i
$624$	−3.61220	−	11.1029i	−0.144604	−	0.444471i
$625$	8.64830	−	5.55793i	0.345932	−	0.222317i
$626$	23.3679	−	25.4658i	0.933969	−	1.01782i
$627$	−3.11150	+	4.84159i	−0.124261	+	0.193355i
$628$	−13.0023	+	17.9033i	−0.518850	+	0.714420i
$629$	12.8575	+	11.1411i	0.512663	+	0.444225i
$630$	−1.81886	−	3.01560i	−0.0724652	−	0.120144i
$631$	−12.4476	−	27.2565i	−0.495532	−	1.08506i	−0.977896	−	0.209093i	$-0.932949\pi$
$631$	−12.4476	−	27.2565i	−0.495532	−	1.08506i	0.482364	−	0.875971i	$-0.339778\pi$
$632$	13.3315	−	2.70526i	0.530299	−	0.107609i
$633$	−18.0134	−	5.28922i	−0.715970	−	0.210228i
$634$	−30.8697	−	15.1740i	−1.22599	−	0.602636i
$635$	9.05394	+	1.30176i	0.359295	+	0.0516588i
$636$	−7.97062	−	10.3324i	−0.316056	−	0.409708i
$637$	2.98858	+	1.36484i	0.118412	+	0.0540770i
$638$	0.910492	+	7.92868i	0.0360467	+	0.313899i
$639$	−0.963973	−	6.70458i	−0.0381342	−	0.265229i
$640$	7.10427	+	9.20035i	0.280821	+	0.363676i
$641$	13.3789	+	15.4401i	0.528436	+	0.609848i	0.955723	−	0.294269i	$-0.0950760\pi$
$641$	13.3789	+	15.4401i	0.528436	+	0.609848i	−0.427287	+	0.904116i	$0.640531\pi$
$642$	−18.7536	−	12.8208i	−0.740146	−	0.505996i
$643$			14.5774i			0.574878i	0.957799	+	0.287439i	$0.0928039\pi$
$643$			14.5774i			0.574878i	−0.957799	+	0.287439i	$0.907196\pi$
$644$	−6.51895	−	22.3148i	−0.256882	−	0.879326i
$645$			0.708861i			0.0279114i
$646$	4.25173	−	6.21922i	0.167282	−	0.244692i
$647$	10.1372	+	11.6989i	0.398534	+	0.459933i	0.919179	−	0.393841i	$-0.128854\pi$
$647$	10.1372	+	11.6989i	0.398534	+	0.459933i	−0.520645	+	0.853773i	$0.674308\pi$
$648$	−1.39013	+	2.46324i	−0.0546095	+	0.0967651i
$649$	1.82414	+	12.6872i	0.0716039	+	0.498016i
$650$	16.1761	−	1.85759i	0.634479	−	0.0728606i
$651$	22.2870	+	10.1782i	0.873498	+	0.398913i
$652$	18.3854	−	14.1828i	0.720028	−	0.555442i
$653$	11.8275	+	1.70054i	0.462845	+	0.0665471i	0.369793	−	0.929114i	$-0.379429\pi$
$653$	11.8275	+	1.70054i	0.462845	+	0.0665471i	0.0930522	+	0.995661i	$0.470338\pi$
$654$	−7.06149	+	14.3658i	−0.276126	+	0.561746i
$655$	−10.2942	−	3.02264i	−0.402226	−	0.118104i
$656$	−18.2086	−	14.8776i	−0.710928	−	0.580873i
$657$	−0.0256720	−	0.0562138i	−0.00100156	−	0.00219311i
$658$	28.3466	−	17.0973i	1.10506	−	0.666521i
$659$	20.5239	+	17.7841i	0.799499	+	0.692770i	0.955501	−	0.294987i	$-0.0953152\pi$
$659$	20.5239	+	17.7841i	0.799499	+	0.692770i	−0.156002	+	0.987757i	$0.549861\pi$
$660$	−2.61727	+	3.60380i	−0.101877	+	0.140278i
$661$	−21.3763	+	33.2621i	−0.831440	+	1.29375i	0.122112	+	0.992516i	$0.461033\pi$
$661$	−21.3763	+	33.2621i	−0.831440	+	1.29375i	−0.953552	+	0.301229i	$0.902603\pi$
$662$	21.2405	+	19.4906i	0.825535	+	0.757525i
$663$	−4.92653	+	3.16609i	−0.191331	+	0.122961i
$664$	−3.01828	+	7.75892i	−0.117132	+	0.301105i
$665$	−6.34415	+	1.86281i	−0.246016	+	0.0722367i
$666$	−9.28303	+	7.59216i	−0.359710	+	0.294190i
$667$	12.1573	+	2.84710i	0.470733	+	0.110240i
$668$	1.26966	−	6.27212i	0.0491246	−	0.242676i
$669$	6.99485	+	23.8223i	0.270436	+	0.921022i
$670$	2.34468	−	13.5563i	0.0905830	−	0.523725i
$671$	−8.53976	+	5.48817i	−0.329674	+	0.211868i
$672$	−5.70151	−	12.4689i	−0.219941	−	0.480999i
$673$	13.7168	+	8.81527i	0.528745	+	0.339804i	0.777623	−	0.628731i	$-0.216425\pi$
$673$	13.7168	+	8.81527i	0.528745	+	0.339804i	−0.248878	+	0.968535i	$0.580062\pi$
$674$	3.15756	−	0.830296i	0.121625	−	0.0319818i
$675$	−2.98098	−	2.58303i	−0.114738	−	0.0994209i
$676$	−8.43925	−	3.00932i	−0.324587	−	0.115743i
$677$	−10.6833	+	4.87890i	−0.410593	+	0.187511i	−0.609993	−	0.792407i	$-0.708828\pi$
$677$	−10.6833	+	4.87890i	−0.410593	+	0.187511i	0.199400	+	0.979918i	$0.436101\pi$
$678$	6.23630	−	2.63618i	0.239504	−	0.101242i
$679$	23.1953	+	6.81076i	0.890154	+	0.261373i
$680$	3.55891	−	4.61799i	0.136478	−	0.177092i
$681$	−2.63933	+	18.3569i	−0.101139	+	0.703439i
$682$	0.881936	−	30.9746i	0.0337711	−	1.18608i
$683$	9.64670	+	4.40550i	0.369121	+	0.168572i	0.591335	−	0.806426i	$-0.298601\pi$
$683$	9.64670	+	4.40550i	0.369121	+	0.168572i	−0.222214	+	0.974998i	$0.571328\pi$
$684$	3.80897	+	3.70031i	0.145640	+	0.141485i
$685$	−11.9597	+	1.71955i	−0.456958	+	0.0657007i
$686$	26.4894	+	8.60414i	1.01137	+	0.328508i
$687$	11.9952	+	13.8432i	0.457647	+	0.528153i
$688$	−0.313550	+	2.74189i	−0.0119540	+	0.104534i
$689$	19.0453			0.725568
$690$	3.92478	+	5.75793i	0.149414	+	0.219201i
$691$		−	29.2917i		−	1.11431i	−0.830409	−	0.557154i	$-0.811893\pi$
$691$		−	29.2917i		−	1.11431i	0.830409	−	0.557154i	$-0.188107\pi$
$692$	24.2474	−	2.08724i	0.921748	−	0.0793450i
$693$	3.97030	−	3.44028i	0.150819	−	0.130685i
$694$	−14.4420	+	44.4622i	−0.548210	+	1.68776i
$695$	−1.68431	−	11.7146i	−0.0638895	−	0.444362i
$696$	7.33715	+	0.628088i	0.278114	+	0.0238076i
$697$	−4.89932	+	10.7280i	−0.185575	+	0.406353i
$698$	−0.278024	+	9.76454i	−0.0105234	+	0.369593i
$699$	−13.9833	−	2.01050i	−0.528898	−	0.0760440i
$700$	18.6225	−	4.33420i	0.703865	−	0.163817i
$701$	−8.83708	+	30.0963i	−0.333772	+	1.13672i	0.606155	+	0.795346i	$0.292711\pi$
$701$	−8.83708	+	30.0963i	−0.333772	+	1.13672i	−0.939927	+	0.341376i	$0.889107\pi$
$702$	−1.60726	−	3.80223i	−0.0606622	−	0.143506i
$703$	9.35339	+	20.4811i	0.352770	+	0.772458i
$704$	−11.7177	+	12.7819i	−0.441627	+	0.481734i
$705$	−6.49795	+	7.49903i	−0.244727	+	0.282430i
$706$	31.3254	−	8.23717i	1.17895	−	0.310010i
$707$	−9.03679	+	14.0615i	−0.339863	+	0.528838i
$708$	11.8079	+	0.672954i	0.443767	+	0.0252912i
$709$	−18.7996	−	29.2528i	−0.706035	−	1.09861i	−0.990176	−	0.139830i	$-0.955345\pi$
$709$	−18.7996	−	29.2528i	−0.706035	−	1.09861i	0.284140	−	0.958783i	$-0.408292\pi$
$710$	−9.69793	−	1.67735i	−0.363957	−	0.0629497i
$711$	4.61464	−	1.35498i	0.173063	−	0.0508158i
$712$	−38.5409	+	20.3500i	−1.44438	+	0.762647i
$713$	−45.1498	−	17.6597i	−1.69087	−	0.661362i
$714$	−5.32323	+	4.35363i	−0.199217	+	0.162930i
$715$	−1.83136	−	6.23703i	−0.0684888	−	0.233252i
$716$	−15.3395	−	27.1507i	−0.573264	−	1.01467i
$717$	8.61755	+	13.4092i	0.321828	+	0.500775i
$718$	−20.3954	+	22.2265i	−0.761151	+	0.829486i
$719$	−8.36136	−	5.37352i	−0.311826	−	0.200399i	0.375361	−	0.926879i	$-0.377519\pi$
$719$	−8.36136	−	5.37352i	−0.311826	−	0.200399i	−0.687188	+	0.726480i	$0.741155\pi$
$720$	2.78002	+	3.02673i	0.103605	+	0.112800i
$721$	−4.31725	+	4.98237i	−0.160783	+	0.185553i
$722$	−14.4712	+	8.72831i	−0.538561	+	0.324834i
$723$	−11.4028	+	5.20751i	−0.424077	+	0.193669i
$724$	25.0407	+	13.2065i	0.930629	+	0.490817i
$725$	−2.89325	+	9.85350i	−0.107453	+	0.365950i
$726$	7.99816	+	3.93149i	0.296840	+	0.145911i
$727$	−7.26615	+	50.5372i	−0.269487	+	1.87432i	0.183812	+	0.982961i	$0.441156\pi$
$727$	−7.26615	+	50.5372i	−0.269487	+	1.87432i	−0.453299	+	0.891359i	$0.649753\pi$
$728$	19.4914	+	4.52670i	0.722400	+	0.167771i
$729$	−0.415415	+	0.909632i	−0.0153857	+	0.0336901i
$730$	−0.0892067	+	0.0102441i	−0.00330169	+	0.000379150i
$731$	1.37012	−	0.196994i	0.0506758	−	0.00728608i
$732$	3.39996	+	8.72784i	0.125666	+	0.322590i
$733$	36.5128	−	31.6385i	1.34863	−	1.16860i	0.378615	−	0.925554i	$-0.376400\pi$
$733$	36.5128	−	31.6385i	1.34863	−	1.16860i	0.970016	−	0.243042i	$-0.0781452\pi$
$734$	−27.9436	−	19.1035i	−1.03142	−	0.705121i
$735$	−1.15645			−0.0426563
$736$	12.6342	+	24.0078i	0.465704	+	0.884940i
$737$	20.5229			0.755970
$738$	−6.86290	−	4.69178i	−0.252627	−	0.172707i
$739$	−5.40973	+	4.68756i	−0.199000	+	0.172435i	−0.748660	−	0.662954i	$-0.769303\pi$
$739$	−5.40973	+	4.68756i	−0.199000	+	0.172435i	0.549660	+	0.835388i	$0.314757\pi$
$740$	6.32493	+	16.2364i	0.232509	+	0.596860i
$741$	−7.67147	+	1.10299i	−0.281819	+	0.0405194i
$742$	22.2186	−	2.55148i	0.815672	−	0.0936679i
$743$	4.48450	−	9.81969i	0.164520	−	0.360249i	−0.809359	−	0.587314i	$-0.800185\pi$
$743$	4.48450	−	9.81969i	0.164520	−	0.360249i	0.973880	+	0.227064i	$0.0729127\pi$
$744$	−27.8511	−	6.46815i	−1.02107	−	0.237134i
$745$	0.532843	−	3.70600i	0.0195219	−	0.135777i
$746$	26.5614	+	13.0562i	0.972483	+	0.478023i
$747$	−0.829264	+	2.82421i	−0.0303412	+	0.103333i
$748$	7.69294	+	4.05728i	0.281282	+	0.148349i
$749$	35.4151	−	16.1735i	1.29404	−	0.590967i
$750$	−11.1286	+	6.71226i	−0.406361	+	0.245097i
$751$	−5.64133	+	6.51045i	−0.205855	+	0.237570i	−0.849284	−	0.527937i	$-0.822966\pi$
$751$	−5.64133	+	6.51045i	−0.205855	+	0.237570i	0.643429	+	0.765506i	$0.277511\pi$
$752$	−28.4512	+	26.1322i	−1.03751	+	0.952942i
$753$	21.9648	+	14.1159i	0.800443	+	0.514414i
$754$	−7.26642	+	7.91879i	−0.264627	+	0.288385i
$755$	4.60832	+	7.17069i	0.167714	+	0.260968i
$756$	−2.38445	−	4.22044i	−0.0867215	−	0.153496i
$757$	8.09763	+	27.5780i	0.294313	+	1.00234i	0.965359	+	0.260924i	$0.0840272\pi$
$757$	8.09763	+	27.5780i	0.294313	+	1.00234i	−0.671046	+	0.741416i	$0.734155\pi$
$758$	−23.4463	+	19.1757i	−0.851609	+	0.696492i
$759$	−7.46593	+	7.23304i	−0.270996	+	0.262543i
$760$	6.82329	−	3.60276i	0.247507	−	0.130686i
$761$	32.4398	−	9.52518i	1.17594	−	0.345288i	0.365333	−	0.930877i	$-0.380955\pi$
$761$	32.4398	−	9.52518i	1.17594	−	0.345288i	0.810608	+	0.585589i	$0.199137\pi$
$762$	12.4064	+	2.14580i	0.449435	+	0.0777340i
$763$	−14.8320	−	23.0790i	−0.536955	−	0.835518i
$764$	−0.332882	−	0.0189716i	−0.0120432	−	0.000686368i
$765$	1.11442	−	1.73408i	0.0402921	−	0.0626957i
$766$	29.6928	−	7.80788i	1.07285	−	0.282110i
$767$	−11.3036	+	13.0451i	−0.408151	+	0.471031i
$768$	9.41437	+	12.9371i	0.339712	+	0.466829i
$769$	−13.7721	−	30.1566i	−0.496633	−	1.08747i	−0.977549	−	0.210708i	$-0.932423\pi$
$769$	−13.7721	−	30.1566i	−0.496633	−	1.08747i	0.480916	−	0.876767i	$-0.340304\pi$
$770$	−2.97207	−	7.03090i	−0.107106	−	0.253376i
$771$	3.16716	−	10.7864i	0.114063	−	0.388462i
$772$	47.0142	−	10.9421i	1.69208	−	0.393814i
$773$	−15.6263	−	2.24672i	−0.562038	−	0.0808088i	−0.144560	−	0.989496i	$-0.546177\pi$
$773$	−15.6263	−	2.24672i	−0.562038	−	0.0808088i	−0.417478	+	0.908687i	$0.637086\pi$
$774$	−0.0277703	+	0.975327i	−0.000998185	+	0.0350574i
$775$	16.5641	−	36.2703i	0.594999	−	1.30287i
$776$	−28.1084	−	2.40618i	−1.00903	−	0.0863768i
$777$	−2.92496	−	20.3436i	−0.104932	−	0.729821i
$778$	−5.25747	+	16.1860i	−0.188489	+	0.580298i
$779$	−11.7961	+	10.2214i	−0.422640	+	0.366220i
$780$	−5.97586	+	0.514408i	−0.213970	+	0.0184188i
$781$		−	14.6817i		−	0.525353i
$782$	10.0385	−	9.18615i	0.358976	−	0.328496i
$783$	2.60356			0.0930438
$784$	−4.47317	−	0.511531i	−0.159756	−	0.0182690i
$785$	7.44364	+	8.59041i	0.265675	+	0.306605i
$786$	−14.0454	−	4.56215i	−0.500982	−	0.162727i
$787$	−40.4458	+	5.81523i	−1.44174	+	0.207291i	−0.818394	−	0.574658i	$-0.805135\pi$
$787$	−40.4458	+	5.81523i	−1.44174	+	0.207291i	−0.623343	+	0.781948i	$0.714226\pi$
$788$	14.5817	+	14.1657i	0.519450	+	0.504631i
$789$	18.8532	+	8.60999i	0.671193	+	0.306524i
$790$	0.198892	−	6.98531i	0.00707625	−	0.248526i
$791$	−1.65137	+	11.4855i	−0.0587159	+	0.408378i
$792$	−3.74230	+	4.85595i	−0.132977	+	0.172549i
$793$	−13.1166	−	3.85138i	−0.465784	−	0.136766i
$794$	23.8246	−	10.0710i	0.845503	−	0.357407i
$795$	−6.09791	+	2.78482i	−0.216270	+	0.0987674i
$796$	−28.9322	−	10.3168i	−1.02548	−	0.365670i
$797$	−14.2709	−	12.3658i	−0.505501	−	0.438019i	0.364402	−	0.931242i	$-0.381273\pi$
$797$	−14.2709	−	12.3658i	−0.505501	−	0.438019i	−0.869903	+	0.493223i	$0.835819\pi$
$798$	−8.80193	+	2.31451i	−0.311585	+	0.0819329i
$799$	16.3003	+	10.4756i	0.576663	+	0.370599i
$800$	−20.2921	+	9.27872i	−0.717435	+	0.328052i
$801$	−12.9630	+	8.33079i	−0.458024	+	0.294354i
$802$	4.08393	−	23.6121i	0.144208	−	0.833772i
$803$	−0.0377378	−	0.128523i	−0.00133174	−	0.00453548i
$804$	3.75714	−	18.5603i	0.132504	−	0.654572i
$805$	−11.9241	+	0.663154i	−0.420270	+	0.0233731i
$806$	32.3020	−	26.4183i	1.13779	−	0.930545i
$807$	13.0585	−	3.83431i	0.459680	−	0.134974i
$808$	7.07175	−	18.1789i	0.248783	−	0.639533i
$809$	39.8278	−	25.5958i	1.40027	−	0.899900i	0.400407	−	0.916337i	$-0.368869\pi$
$809$	39.8278	−	25.5958i	1.40027	−	0.899900i	0.999865	+	0.0164372i	$0.00523235\pi$
$810$	1.07058	+	0.982380i	0.0376162	+	0.0345173i
$811$	28.3135	−	44.0567i	0.994223	−	1.54704i	0.166395	−	0.986059i	$-0.446787\pi$
$811$	28.3135	−	44.0567i	0.994223	−	1.54704i	0.827828	−	0.560982i	$-0.189576\pi$
$812$	−7.41628	+	10.2117i	−0.260260	+	0.358360i
$813$	5.89159	+	5.10509i	0.206627	+	0.179043i
$814$	−22.2583	+	13.4251i	−0.780152	+	0.470550i
$815$	−4.95527	−	10.8505i	−0.173576	−	0.380077i
$816$	5.07764	−	6.21450i	0.177753	−	0.217551i
$817$	1.75773	+	0.516116i	0.0614951	+	0.0180566i
$818$	0.663621	−	1.35006i	0.0232030	−	0.0472037i
$819$	7.00265	+	1.00683i	0.244692	+	0.0351815i
$820$	−9.56425	+	7.37803i	−0.333998	+	0.257652i
$821$	−21.9105	−	10.0062i	−0.764683	−	0.349219i	−0.00540518	−	0.999985i	$-0.501721\pi$
$821$	−21.9105	−	10.0062i	−0.764683	−	0.349219i	−0.759278	+	0.650766i	$0.774448\pi$
$822$	−16.5228	+	1.89741i	−0.576300	+	0.0661796i
$823$	−5.26606	−	36.6263i	−0.183563	−	1.27671i	−0.848253	−	0.529592i	$-0.822345\pi$
$823$	−5.26606	−	36.6263i	−0.183563	−	1.27671i	0.664689	−	0.747120i	$-0.268564\pi$
$824$	3.78121	−	6.70011i	0.131725	−	0.233409i
$825$	−5.59876	−	6.46132i	−0.194924	−	0.224954i
$826$	−11.4394	+	16.7330i	−0.398028	+	0.582216i
$827$			55.0302i			1.91359i	0.290767	+	0.956794i	$0.406089\pi$
$827$			55.0302i			1.91359i	−0.290767	+	0.956794i	$0.593911\pi$
$828$	5.17456	+	8.07613i	0.179828	+	0.280665i
$829$		−	27.6689i		−	0.960981i	−0.877000	−	0.480491i	$-0.840459\pi$
$829$		−	27.6689i		−	0.960981i	0.877000	−	0.480491i	$-0.159541\pi$
$830$	3.53062	+	2.41369i	0.122550	+	0.0837803i
$831$	−2.21090	−	2.55152i	−0.0766954	−	0.0885112i
$832$	−23.3423	−	0.653553i	−0.809247	−	0.0226579i
$833$	0.321379	+	2.23524i	0.0111351	+	0.0774466i
$834$	−1.85852	−	16.1842i	−0.0643553	−	0.560414i
$835$	−2.99034	−	1.36564i	−0.103485	−	0.0472600i
$836$	7.03054	+	9.11380i	0.243156	+	0.315207i
$837$	−10.0060	−	1.43865i	−0.345859	−	0.0497270i
$838$	18.1550	+	8.92406i	0.627153	+	0.308276i
$839$	−36.6519	−	10.7620i	−1.26536	−	0.371544i	−0.420875	−	0.907119i	$-0.638277\pi$
$839$	−36.6519	−	10.7620i	−1.26536	−	0.371544i	−0.844488	+	0.535574i	$0.820095\pi$
$840$	−6.90264	+	1.40070i	−0.238164	+	0.0483287i
$841$	9.23113	+	20.2133i	0.318315	+	0.697012i
$842$	−7.09193	−	11.7581i	−0.244404	−	0.405212i
$843$	−6.53849	−	5.66563i	−0.225197	−	0.195135i
$844$	−22.0643	+	30.3810i	−0.759485	+	1.04576i
$845$	−2.48842	+	3.87206i	−0.0856044	+	0.133203i
$846$	−9.23435	+	10.0634i	−0.317483	+	0.345987i
$847$	−12.8493	+	8.25773i	−0.441507	+	0.283739i
$848$	−24.8186	+	8.07446i	−0.852275	+	0.277278i
$849$	−30.8127	+	9.04743i	−1.05749	+	0.310507i
$850$	7.08516	+	8.66311i	0.243019	+	0.297142i
$851$	8.01397	+	39.8705i	0.274715	+	1.36674i
$852$	−13.2777	−	2.68780i	−0.454888	−	0.0920824i
$853$	5.45637	+	18.5827i	0.186823	+	0.636259i	0.998630	+	0.0523336i	$0.0166659\pi$
$853$	5.45637	+	18.5827i	0.186823	+	0.636259i	−0.811807	+	0.583926i	$0.801516\pi$
$854$	−15.8181	−	2.73588i	−0.541283	−	0.0936198i
$855$	2.29496	−	1.47488i	0.0784861	−	0.0504400i
$856$	−36.7496	+	26.7161i	−1.25608	+	0.913138i
$857$	6.95858	+	4.47201i	0.237701	+	0.152761i	0.654068	−	0.756435i	$-0.273061\pi$
$857$	6.95858	+	4.47201i	0.237701	+	0.152761i	−0.416368	+	0.909196i	$0.636697\pi$
$858$	−2.27543	−	8.65331i	−0.0776820	−	0.295419i
$859$	−31.2800	−	27.1043i	−1.06726	−	0.924787i	−0.0699118	−	0.997553i	$-0.522272\pi$
$859$	−31.2800	−	27.1043i	−1.06726	−	0.924787i	−0.997349	+	0.0727664i	$0.976817\pi$
$860$	1.33536	+	0.476172i	0.0455356	+	0.0162373i
$861$	12.9602	−	5.91871i	0.441681	−	0.201709i
$862$	0.867305	+	2.05175i	0.0295405	+	0.0698828i
$863$	−6.12178	−	1.79752i	−0.208388	−	0.0611882i	0.175873	−	0.984413i	$-0.443725\pi$
$863$	−6.12178	−	1.79752i	−0.208388	−	0.0611882i	−0.384260	+	0.923225i	$0.625543\pi$
$864$	3.70648	+	4.27341i	0.126097	+	0.145384i
$865$	1.77926	−	12.3750i	0.0604966	−	0.420763i
$866$	18.3199	+	0.521621i	0.622537	+	0.0177254i
$867$	11.8023	+	5.38995i	0.400828	+	0.183052i
$868$	34.1449	−	35.1476i	1.15895	−	1.19299i
$869$	10.3185	−	1.48357i	0.350031	−	0.0503268i
$870$	1.16866	−	3.59793i	0.0396214	−	0.121981i
$871$	18.0987	+	20.8870i	0.613252	+	0.707730i
$872$	22.3190	+	22.9526i	0.755816	+	0.777274i
$873$	−9.97415			−0.337574
$874$	17.1353	−	5.53979i	0.579609	−	0.187386i
$875$		−	22.2733i		−	0.752974i
$876$	−0.123141	+	0.0106001i	−0.00416056	+	0.000358145i
$877$	25.4710	−	22.0707i	0.860094	−	0.745275i	−0.108454	−	0.994101i	$-0.534590\pi$
$877$	25.4710	−	22.0707i	0.860094	−	0.745275i	0.968548	+	0.248826i	$0.0800447\pi$
$878$	33.9592	+	11.0304i	1.14607	+	0.372259i
$879$	−4.31276	−	29.9959i	−0.145466	−	1.01174i
$880$	5.03076	+	7.35127i	0.169587	+	0.247811i
$881$	−18.6720	+	40.8860i	−0.629076	+	1.37748i	0.279654	+	0.960101i	$0.409780\pi$
$881$	−18.6720	+	40.8860i	−0.629076	+	1.37748i	−0.908730	+	0.417384i	$0.862947\pi$
$882$	−1.59117	−	0.0453051i	−0.0535774	−	0.00152550i
$883$	−9.51627	−	1.36823i	−0.320248	−	0.0460447i	−0.0196837	−	0.999806i	$-0.506266\pi$
$883$	−9.51627	−	1.36823i	−0.320248	−	0.0460447i	−0.300564	+	0.953762i	$0.597175\pi$
$884$	2.65497	+	11.4075i	0.0892964	+	0.383675i
$885$	1.71172	−	5.82959i	0.0575389	−	0.195960i
$886$	−31.0475	+	13.1242i	−1.04306	+	0.440917i
$887$	22.5337	+	49.3419i	0.756608	+	1.65674i	0.754114	+	0.656743i	$0.228067\pi$
$887$	22.5337	+	49.3419i	0.756608	+	1.65674i	0.00249386	+	0.999997i	$0.499206\pi$
$888$	8.06644	+	22.5875i	0.270692	+	0.757986i
$889$	−14.1306	+	16.3076i	−0.473926	+	0.546940i
$890$	5.69385	+	21.6533i	0.190858	+	0.725821i
$891$	−1.17185	+	1.82343i	−0.0392584	+	0.0610872i
$892$	49.5755	+	2.82540i	1.65991	+	0.0946015i
$893$	13.8639	+	21.5726i	0.463937	+	0.721900i
$894$	0.878328	−	5.07824i	0.0293757	−	0.169842i
$895$	−15.3709	+	4.51329i	−0.513791	+	0.150863i
$896$	−27.3191	+	2.36470i	−0.912667	+	0.0789990i
$897$	−13.9454	−	1.21973i	−0.465625	−	0.0407256i
$898$	−26.2915	−	32.1469i	−0.877358	−	1.07276i
$899$	7.41497	+	25.2531i	0.247303	+	0.842237i
$900$	−6.86840	+	3.88048i	−0.228947	+	0.129349i
$901$	7.07726	+	11.0124i	0.235778	+	0.366877i
$902$	−13.2768	−	12.1830i	−0.442068	−	0.405649i
$903$	−1.40676	−	0.904071i	−0.0468141	−	0.0300856i
$904$	−0.776893	−	13.5189i	−0.0258391	−	0.449631i
$905$	9.52372	−	10.9910i	0.316579	−	0.365352i
$906$	6.05970	+	10.0467i	0.201320	+	0.333780i
$907$	0.456788	−	0.208608i	0.0151674	−	0.00692672i	−0.407817	−	0.913064i	$-0.633710\pi$
$907$	0.456788	−	0.208608i	0.0151674	−	0.00692672i	0.422984	+	0.906137i	$0.360983\pi$
$908$	32.8081	+	17.3031i	1.08878	+	0.574224i
$909$	1.94294	−	6.61705i	0.0644433	−	0.219474i
$910$	4.53465	−	9.22521i	0.150322	−	0.305813i
$911$	−4.52980	+	31.5054i	−0.150079	+	1.04382i	0.766005	+	0.642835i	$0.222242\pi$
$911$	−4.52980	+	31.5054i	−0.150079	+	1.04382i	−0.916084	+	0.400987i	$0.868667\pi$
$912$	9.52935	−	4.68975i	0.315548	−	0.155293i
$913$	−2.65033	+	5.80342i	−0.0877132	+	0.192065i
$914$	−4.46794	−	38.9074i	−0.147786	−	1.28694i
$915$	4.76281	−	0.684789i	0.157454	−	0.0226384i
$916$	34.1358	−	13.2977i	1.12788	−	0.439370i
$917$	19.1276	−	16.5741i	0.631648	−	0.547326i
$918$	1.60128	−	2.34227i	0.0528500	−	0.0773064i
$919$	41.3843			1.36514			0.682570	−	0.730820i	$-0.260862\pi$
$919$	41.3843			1.36514			0.682570	+	0.730820i	$0.260862\pi$
$920$	13.4833	−	3.52573i	0.444532	−	0.116240i
$921$	−5.23915			−0.172636
$922$	3.81605	−	5.58192i	0.125675	−	0.183831i
$923$	14.9422	−	12.9475i	0.491830	−	0.426173i
$924$	−3.81384	−	9.79029i	−0.125466	−	0.322077i
$925$	−33.1074	+	4.76013i	−1.08857	+	0.156512i
$926$	2.95816	+	25.7600i	0.0972112	+	0.846527i
$927$	1.12995	−	2.47424i	0.0371123	−	0.0812646i
$928$	6.11187	−	13.3999i	0.200632	−	0.439874i
$929$	5.43677	−	37.8135i	0.178375	−	1.24062i	−0.682150	−	0.731213i	$-0.738955\pi$
$929$	5.43677	−	37.8135i	0.178375	−	1.24062i	0.860524	−	0.509410i	$-0.170136\pi$
$930$	−6.47951	+	13.1818i	−0.212471	+	0.432249i
$931$	−0.842001	+	2.86759i	−0.0275955	+	0.0939815i
$932$	−13.1806	+	24.9915i	−0.431745	+	0.818623i
$933$	−2.91728	+	1.33228i	−0.0955076	+	0.0436168i
$934$	8.88873	+	14.7372i	0.290848	+	0.482214i
$935$	2.92586	−	3.37662i	0.0956857	−	0.110427i
$936$	−8.24237	+	0.473667i	−0.269410	+	0.0154823i
$937$	−29.4858	−	18.9494i	−0.963260	−	0.619050i	−0.0383616	−	0.999264i	$-0.512214\pi$
$937$	−29.4858	−	18.9494i	−0.963260	−	0.619050i	−0.924898	+	0.380214i	$0.875850\pi$
$938$	23.9126	+	21.9426i	0.780773	+	0.716451i
$939$	−13.2129	−	20.5597i	−0.431188	−	0.670941i
$940$	9.76185	+	17.2783i	0.318396	+	0.563557i
$941$	7.31201	+	24.9024i	0.238365	+	0.811795i	0.988592	+	0.150616i	$0.0481257\pi$
$941$	7.31201	+	24.9024i	0.238365	+	0.811795i	−0.750228	+	0.661180i	$0.770056\pi$
$942$	9.90521	+	12.1112i	0.322729	+	0.394605i
$943$	−24.9545	+	13.1173i	−0.812630	+	0.427159i
$944$	9.19957	−	21.7918i	0.299420	−	0.709264i
$945$	−2.38932	+	0.701568i	−0.0777246	+	0.0228220i
$946$	−0.360439	+	2.08395i	−0.0117189	+	0.0677552i
$947$	−1.62569	−	2.52962i	−0.0528278	−	0.0822017i	0.813835	−	0.581096i	$-0.197376\pi$
$947$	−1.62569	−	2.52962i	−0.0528278	−	0.0822017i	−0.866663	+	0.498894i	$0.833740\pi$
$948$	0.547313	−	9.60334i	0.0177759	−	0.311902i
$949$	0.0975234	−	0.151749i	0.00316574	−	0.00492599i
$950$	3.76667	+	14.3244i	0.122207	+	0.464745i
$951$	−15.9280	+	18.3819i	−0.516501	+	0.596074i
$952$	4.62560	+	12.9525i	0.149916	+	0.419793i
$953$	−13.9398	−	30.5238i	−0.451553	−	0.988763i	−0.989332	−	0.145677i	$-0.953464\pi$
$953$	−13.9398	−	30.5238i	−0.451553	−	0.988763i	0.537779	−	0.843086i	$-0.319263\pi$
$954$	−8.49924	+	3.59276i	−0.275173	+	0.116320i
$955$	−0.0482560	+	0.164345i	−0.00156153	+	0.00531808i
$956$	31.0492	−	7.22638i	1.00420	−	0.233718i
$957$	5.58583	+	0.803121i	0.180564	+	0.0259612i
$958$	−13.8258	−	0.393659i	−0.446690	−	0.0127185i
$959$	11.8408	−	25.9276i	0.382358	−	0.837247i
$960$	7.56926	−	3.20387i	0.244297	−	0.103405i
$961$	−10.1314	−	70.4655i	−0.326820	−	2.27308i
$962$	−33.2924	−	10.8139i	−1.07339	−	0.348654i
$963$	−12.1400	+	10.5193i	−0.391205	+	0.338981i
$964$	2.15021	+	24.9790i	0.0692537	+	0.804518i
$965$		−	24.7973i		−	0.798252i
$966$	−16.4324	+	0.445299i	−0.528705	+	0.0143273i
$967$	−18.9487			−0.609348			−0.304674	−	0.952457i	$-0.598548\pi$
$967$	−18.9487			−0.609348			−0.304674	+	0.952457i	$0.598548\pi$
$968$	12.7789	−	12.4261i	0.410729	−	0.399390i
$969$	−3.48850	−	4.02595i	−0.112067	−	0.129332i
$970$	−4.47710	+	13.7835i	−0.143751	+	0.442563i
$971$	28.9214	−	4.15826i	0.928131	−	0.133445i	0.338361	−	0.941016i	$-0.390128\pi$
$971$	28.9214	−	4.15826i	0.928131	−	0.133445i	0.589770	+	0.807571i	$0.299218\pi$
$972$	1.43453	+	1.39360i	0.0460125	+	0.0446998i
$973$	25.3963	+	11.5981i	0.814167	+	0.371818i
$974$	−8.73142	−	0.248608i	−0.279773	−	0.00796593i
$975$	1.63853	−	11.3962i	0.0524749	−	0.364971i
$976$	18.7255	−	0.542049i	0.599390	−	0.0173506i
$977$	−14.3193	−	4.20452i	−0.458114	−	0.134515i	0.0445296	−	0.999008i	$-0.485821\pi$
$977$	−14.3193	−	4.20452i	−0.458114	−	0.134515i	−0.502644	+	0.864494i	$0.667639\pi$
$978$	−6.39291	−	15.1234i	−0.204423	−	0.483594i
$979$	−30.3813	+	13.8747i	−0.970989	+	0.443436i
$980$	−0.776836	+	2.17854i	−0.0248151	+	0.0695909i
$981$	8.55434	+	7.41238i	0.273119	+	0.236659i
$982$	2.04833	+	7.78967i	0.0653650	+	0.248578i
$983$	−33.5906	−	21.5874i	−1.07138	−	0.688531i	−0.118826	−	0.992915i	$-0.537913\pi$
$983$	−33.5906	−	21.5874i	−1.07138	−	0.688531i	−0.952549	+	0.304384i	$0.901549\pi$
$984$	−13.4485	+	9.77678i	−0.428724	+	0.311672i
$985$	8.78567	−	5.64621i	0.279935	−	0.179903i
$986$	−7.27903	−	1.25898i	−0.231812	−	0.0400940i
$987$	−6.59472	−	22.4596i	−0.209912	−	0.714896i
$988$	−3.07542	+	15.1926i	−0.0978420	+	0.483340i
$989$	2.87861	+	1.63156i	0.0915344	+	0.0518807i
$990$	1.99384	+	2.43789i	0.0633684	+	0.0774813i
$991$	20.0046	−	5.87387i	0.635466	−	0.186590i	0.0518962	−	0.998652i	$-0.483473\pi$
$991$	20.0046	−	5.87387i	0.635466	−	0.186590i	0.583570	+	0.812063i	$0.301655\pi$
$992$	−30.8936	+	48.1214i	−0.980871	+	1.52786i
$993$	17.1484	−	11.0206i	0.544188	−	0.349729i
$994$	15.6973	−	17.1066i	0.497890	−	0.542590i
$995$	−8.53104	+	13.2746i	−0.270452	+	0.420832i
$996$	4.76325	+	3.45932i	0.150929	+	0.109613i
$997$	20.8040	+	18.0268i	0.658871	+	0.570915i	0.918805	−	0.394712i	$-0.129156\pi$
$997$	20.8040	+	18.0268i	0.658871	+	0.570915i	−0.259935	+	0.965626i	$0.583701\pi$
$998$	23.2210	+	38.4994i	0.735047	+	1.21868i
$999$	3.52265	+	7.71354i	0.111452	+	0.244045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.469.9	yes	480
8.5	even	2	inner	552.2.bb.a.469.17	yes	480
23.18	even	11	inner	552.2.bb.a.133.17	yes	480
184.133	even	22	inner	552.2.bb.a.133.9	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.9	✓	480	184.133	even	22	inner
552.2.bb.a.133.17	yes	480	23.18	even	11	inner
552.2.bb.a.469.9	yes	480	1.1	even	1	trivial
552.2.bb.a.469.17	yes	480	8.5	even	2	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16747 - 0.798133i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.725969 + 1.86359i) q^{4} +(1.01697 - 0.146218i) q^{5} +(1.40498 - 0.161341i) q^{6} +(-1.00685 + 2.20469i) q^{7} +(0.639846 - 2.75510i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-1.16747 - 0.798133i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.725969 + 1.86359i) q^{4} +(1.01697 - 0.146218i) q^{5} +(1.40498 - 0.161341i) q^{6} +(-1.00685 + 2.20469i) q^{7} +(0.639846 - 2.75510i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-1.30398 - 0.640970i) q^{10} +(0.610660 - 2.07972i) q^{11} +(-1.76904 - 0.932999i) q^{12} +(2.65515 - 1.21257i) q^{13} +(2.93510 - 1.77031i) q^{14} +(-0.672820 + 0.776476i) q^{15} +(-2.94594 + 2.70582i) q^{16} +(1.68779 + 1.08468i) q^{17} +(-0.956157 + 1.04200i) q^{18} +(1.43551 + 2.23370i) q^{19} +(1.01078 + 1.78906i) q^{20} +(-0.682841 - 2.32554i) q^{21} +(-2.37282 + 1.94062i) q^{22} +(1.60458 + 4.51944i) q^{23} +(1.32065 + 2.50118i) q^{24} +(-3.78462 + 1.11127i) q^{25} +(-4.06759 - 0.703528i) q^{26} +(0.540641 + 0.841254i) q^{27} +(-4.83959 - 0.275817i) q^{28} +(1.40759 - 2.19026i) q^{29} +(1.40523 - 0.369512i) q^{30} +(-6.61993 + 7.63981i) q^{31} +(5.59889 - 0.807707i) q^{32} +(0.900419 + 1.97164i) q^{33} +(-1.10473 - 2.61341i) q^{34} +(-0.701568 + 2.38932i) q^{35} +(1.94794 - 0.453363i) q^{36} +(8.39353 + 1.20681i) q^{37} +(0.106873 - 3.75351i) q^{38} +(-1.21257 + 2.65515i) q^{39} +(0.247858 - 2.89541i) q^{40} +(0.836590 + 5.81861i) q^{41} +(-1.05890 + 3.26000i) q^{42} +(0.521422 - 0.451814i) q^{43} +(4.31906 - 0.371789i) q^{44} -1.02743i q^{45} +(1.73382 - 6.55697i) q^{46} +9.65777 q^{47} +(0.454459 - 3.97410i) q^{48} +(0.737099 + 0.850657i) q^{49} +(5.30537 + 1.72326i) q^{50} +(-1.98586 + 0.285523i) q^{51} +(4.18728 + 4.06783i) q^{52} +(5.93513 + 2.71048i) q^{53} +(0.0402504 - 1.41364i) q^{54} +(0.316930 - 2.20429i) q^{55} +(5.42993 + 4.18464i) q^{56} +(-2.54766 - 0.748059i) q^{57} +(-3.39144 + 1.43361i) q^{58} +(-5.37913 + 2.45657i) q^{59} +(-1.93548 - 0.690164i) q^{60} +(-3.53944 - 3.06694i) q^{61} +(13.8261 - 3.63566i) q^{62} +(2.03896 + 1.31036i) q^{63} +(-7.18119 - 3.52569i) q^{64} +(2.52290 - 1.62137i) q^{65} +(0.522421 - 3.02049i) q^{66} +(2.66755 + 9.08485i) q^{67} +(-0.796110 + 3.93279i) q^{68} +(-4.17226 - 2.36479i) q^{69} +(2.72605 - 2.22951i) q^{70} +(6.49915 - 1.90832i) q^{71} +(-2.63600 - 1.02543i) q^{72} +(0.0519881 - 0.0334107i) q^{73} +(-8.83600 - 8.10806i) q^{74} +(2.13250 - 3.31824i) q^{75} +(-3.12057 + 4.29681i) q^{76} +(3.97030 + 3.44028i) q^{77} +(3.53479 - 2.13202i) q^{78} +(1.99792 + 4.37484i) q^{79} +(-2.60029 + 3.18248i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(3.66733 - 7.46076i) q^{82} +(-2.91348 - 0.418896i) q^{83} +(3.83814 - 2.96081i) q^{84} +(1.87503 + 0.856296i) q^{85} +(-0.969352 + 0.111316i) q^{86} +(0.370526 + 2.57706i) q^{87} +(-5.33911 - 3.01313i) q^{88} +(-10.0908 - 11.6454i) q^{89} +(-0.820022 + 1.19949i) q^{90} +7.07466i q^{91} +(-7.25751 + 6.27124i) q^{92} -10.1089i q^{93} +(-11.2752 - 7.70818i) q^{94} +(1.78648 + 2.06171i) q^{95} +(-3.70243 + 4.27692i) q^{96} +(-1.41947 - 9.87263i) q^{97} +(-0.181603 - 1.58142i) q^{98} +(-1.97164 - 0.900419i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

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