LMFDB - Embedded newform 552.2.x.a.35.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(35,552)]

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([11, 11, 11, 20]))

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

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

chi := DirichletCharacter("552.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.x (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:	$920$
Relative dimension:	$92$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			35.5
Character	$\chi$	$=$	552.35
Dual form			552.2.x.a.347.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40292 + 0.178405i) q^{2} +(1.61394 + 0.628649i) q^{3} +(1.93634 - 0.500576i) q^{4} +(-2.04785 + 0.601303i) q^{5} +(-2.37637 - 0.594005i) q^{6} +(-1.23389 + 1.06917i) q^{7} +(-2.62722 + 1.04772i) q^{8} +(2.20960 + 2.02920i) q^{9} +O(q^{10})$	\(q+(-1.40292 + 0.178405i) q^{2} +(1.61394 + 0.628649i) q^{3} +(1.93634 - 0.500576i) q^{4} +(-2.04785 + 0.601303i) q^{5} +(-2.37637 - 0.594005i) q^{6} +(-1.23389 + 1.06917i) q^{7} +(-2.62722 + 1.04772i) q^{8} +(2.20960 + 2.02920i) q^{9} +(2.76568 - 1.20892i) q^{10} +(-0.0524767 + 0.0816554i) q^{11} +(3.43983 + 0.409381i) q^{12} +(0.319231 + 0.276615i) q^{13} +(1.54030 - 1.72009i) q^{14} +(-3.68311 - 0.316911i) q^{15} +(3.49885 - 1.93857i) q^{16} +(-4.33039 + 1.97762i) q^{17} +(-3.46191 - 2.45259i) q^{18} +(-1.01461 + 2.22169i) q^{19} +(-3.66434 + 2.18943i) q^{20} +(-2.66356 + 0.949898i) q^{21} +(0.0590526 - 0.123918i) q^{22} +(-3.63595 + 3.12727i) q^{23} +(-4.89882 + 0.0393578i) q^{24} +(-0.374145 + 0.240448i) q^{25} +(-0.497203 - 0.331115i) q^{26} +(2.29051 + 4.66407i) q^{27} +(-1.85404 + 2.68794i) q^{28} +(1.17969 + 2.58317i) q^{29} +(5.22364 - 0.212488i) q^{30} +(1.50230 - 0.215997i) q^{31} +(-4.56274 + 3.34387i) q^{32} +(-0.136027 + 0.0987974i) q^{33} +(5.72235 - 3.54700i) q^{34} +(1.88393 - 2.93145i) q^{35} +(5.29432 + 2.82316i) q^{36} +(0.821456 - 2.79762i) q^{37} +(1.02705 - 3.29786i) q^{38} +(0.341325 + 0.647123i) q^{39} +(4.75015 - 3.72533i) q^{40} +(-2.47755 - 8.43777i) q^{41} +(3.56729 - 1.80782i) q^{42} +(-0.344197 + 2.39395i) q^{43} +(-0.0607382 + 0.184381i) q^{44} +(-5.74510 - 2.82686i) q^{45} +(4.54301 - 5.03598i) q^{46} -4.32833 q^{47} +(6.86561 - 0.929192i) q^{48} +(-0.616846 + 4.29026i) q^{49} +(0.481996 - 0.404078i) q^{50} +(-8.23221 + 0.469470i) q^{51} +(0.756606 + 0.375822i) q^{52} +(7.13420 + 8.23330i) q^{53} +(-4.04549 - 6.13466i) q^{54} +(0.0583648 - 0.198772i) q^{55} +(2.12151 - 4.10173i) q^{56} +(-3.03419 + 2.94784i) q^{57} +(-2.11586 - 3.41350i) q^{58} +(7.37884 + 6.39380i) q^{59} +(-7.29041 + 1.23003i) q^{60} +(-7.91046 + 1.13735i) q^{61} +(-2.06906 + 0.571044i) q^{62} +(-4.89598 - 0.141368i) q^{63} +(5.80457 - 5.50518i) q^{64} +(-0.820065 - 0.374511i) q^{65} +(0.173208 - 0.162872i) q^{66} +(-2.10802 + 1.35474i) q^{67} +(-7.39516 + 5.99704i) q^{68} +(-7.83416 + 2.76150i) q^{69} +(-2.12001 + 4.44868i) q^{70} +(8.83727 - 5.67937i) q^{71} +(-7.93114 - 3.01612i) q^{72} +(-3.27521 + 7.17171i) q^{73} +(-0.653322 + 4.07138i) q^{74} +(-0.755004 + 0.152863i) q^{75} +(-0.852514 + 4.80985i) q^{76} +(-0.0225532 - 0.156861i) q^{77} +(-0.594301 - 0.846965i) q^{78} +(-3.12348 - 2.70651i) q^{79} +(-5.99945 + 6.07377i) q^{80} +(0.764680 + 8.96746i) q^{81} +(4.98114 + 11.3955i) q^{82} +(3.11988 - 10.6253i) q^{83} +(-4.68208 + 3.17264i) q^{84} +(7.67883 - 6.65374i) q^{85} +(0.0557868 - 3.41991i) q^{86} +(0.280049 + 4.91069i) q^{87} +(0.0523159 - 0.269507i) q^{88} +(-3.13600 - 0.450889i) q^{89} +(8.56421 + 2.94089i) q^{90} -0.689646 q^{91} +(-5.47501 + 7.87555i) q^{92} +(2.56040 + 0.595809i) q^{93} +(6.07228 - 0.772198i) q^{94} +(0.741865 - 5.15978i) q^{95} +(-9.46610 + 2.52844i) q^{96} +(-11.4952 + 3.37528i) q^{97} +(0.0999771 - 6.12892i) q^{98} +(-0.281648 + 0.0739400i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9}+O(q^{10}) $ 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9	$ 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9} - 14 q^{10} - 6 q^{12} - 30 q^{16} - 16 q^{18} - 52 q^{19} - 32 q^{22} - 26 q^{24} - 112 q^{25} - 30 q^{27} - 34 q^{28} + 11 q^{30} - 30 q^{33} - 88 q^{34} - 18 q^{36} + 124 q^{40} - 3 q^{42} - 36 q^{43} - 110 q^{46} + 32 q^{49} - 30 q^{51} + 90 q^{52} - 39 q^{54} - 6 q^{57} - 68 q^{58} + 13 q^{60} + 28 q^{64} - 46 q^{66} - 100 q^{67} - 92 q^{70} + 29 q^{72} - 36 q^{73} + 14 q^{75} - 50 q^{76} - 86 q^{78} - 2 q^{81} - 12 q^{82} - 151 q^{84} - 42 q^{88} - 196 q^{90} - 136 q^{91} - 68 q^{94} - 175 q^{96} - 36 q^{97} - 54 q^{99}+O(q^{100}) $ 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9 - 14 * q^10 - 6 * q^12 - 30 * q^16 - 16 * q^18 - 52 * q^19 - 32 * q^22 - 26 * q^24 - 112 * q^25 - 30 * q^27 - 34 * q^28 + 11 * q^30 - 30 * q^33 - 88 * q^34 - 18 * q^36 + 124 * q^40 - 3 * q^42 - 36 * q^43 - 110 * q^46 + 32 * q^49 - 30 * q^51 + 90 * q^52 - 39 * q^54 - 6 * q^57 - 68 * q^58 + 13 * q^60 + 28 * q^64 - 46 * q^66 - 100 * q^67 - 92 * q^70 + 29 * q^72 - 36 * q^73 + 14 * q^75 - 50 * q^76 - 86 * q^78 - 2 * q^81 - 12 * q^82 - 151 * q^84 - 42 * q^88 - 196 * q^90 - 136 * q^91 - 68 * q^94 - 175 * q^96 - 36 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−1.40292	+	0.178405i	−0.992011	+	0.126152i
$2$	−1.40292	+	0.178405i	−0.992011	+	0.126152i
$3$	1.61394	+	0.628649i	0.931808	+	0.362950i
$3$	1.61394	+	0.628649i	0.931808	+	0.362950i
$4$	1.93634	−	0.500576i	0.968171	−	0.250288i
$5$	−2.04785	+	0.601303i	−0.915826	+	0.268911i	−0.705491	−	0.708719i	$-0.749274\pi$
$5$	−2.04785	+	0.601303i	−0.915826	+	0.268911i	−0.210335	+	0.977629i	$0.567455\pi$
$6$	−2.37637	−	0.594005i	−0.970151	−	0.242502i
$7$	−1.23389	+	1.06917i	−0.466368	+	0.404110i	−0.856093	−	0.516821i	$-0.827115\pi$
$7$	−1.23389	+	1.06917i	−0.466368	+	0.404110i	0.389726	+	0.920931i	$0.372570\pi$
$8$	−2.62722	+	1.04772i	−0.928862	+	0.370425i
$9$	2.20960	+	2.02920i	0.736534	+	0.676401i
$10$	2.76568	−	1.20892i	0.874586	−	0.382296i
$11$	−0.0524767	+	0.0816554i	−0.0158223	+	0.0246200i	−0.849075	−	0.528273i	$-0.822840\pi$
$11$	−0.0524767	+	0.0816554i	−0.0158223	+	0.0246200i	0.833252	+	0.552893i	$0.186476\pi$
$12$	3.43983	+	0.409381i	0.992992	+	0.118178i
$13$	0.319231	+	0.276615i	0.0885386	+	0.0767192i	0.698006	−	0.716092i	$-0.254071\pi$
$13$	0.319231	+	0.276615i	0.0885386	+	0.0767192i	−0.609467	+	0.792811i	$0.708617\pi$
$14$	1.54030	−	1.72009i	0.411663	−	0.459714i
$15$	−3.68311	−	0.316911i	−0.950976	−	0.0818261i
$16$	3.49885	−	1.93857i	0.874712	−	0.484643i
$17$	−4.33039	+	1.97762i	−1.05027	+	0.479644i	−0.864334	−	0.502918i	$-0.832260\pi$
$17$	−4.33039	+	1.97762i	−1.05027	+	0.479644i	−0.185939	+	0.982561i	$0.559533\pi$
$18$	−3.46191	−	2.45259i	−0.815979	−	0.578082i
$19$	−1.01461	+	2.22169i	−0.232768	+	0.509691i	−0.989587	−	0.143933i	$-0.954025\pi$
$19$	−1.01461	+	2.22169i	−0.232768	+	0.509691i	0.756819	+	0.653624i	$0.226752\pi$
$20$	−3.66434	+	2.18943i	−0.819372	+	0.489572i
$21$	−2.66356	+	0.949898i	−0.581237	+	0.207285i
$22$	0.0590526	−	0.123918i	0.0125901	−	0.0264193i
$23$	−3.63595	+	3.12727i	−0.758149	+	0.652082i
$23$	−3.63595	+	3.12727i	−0.758149	+	0.652082i
$24$	−4.89882	+	0.0393578i	−0.999968	+	0.00803387i
$25$	−0.374145	+	0.240448i	−0.0748289	+	0.0480896i
$26$	−0.497203	−	0.331115i	−0.0975095	−	0.0649369i
$27$	2.29051	+	4.66407i	0.440809	+	0.897601i
$28$	−1.85404	+	2.68794i	−0.350380	+	0.507974i
$29$	1.17969	+	2.58317i	0.219064	+	0.479682i	0.986975	−	0.160874i	$-0.0514312\pi$
$29$	1.17969	+	2.58317i	0.219064	+	0.479682i	−0.767911	+	0.640556i	$0.778704\pi$
$30$	5.22364	−	0.212488i	0.953701	−	0.0387948i
$31$	1.50230	−	0.215997i	0.269820	−	0.0387943i	−0.00607663	−	0.999982i	$-0.501934\pi$
$31$	1.50230	−	0.215997i	0.269820	−	0.0387943i	0.275897	+	0.961187i	$0.411025\pi$
$32$	−4.56274	+	3.34387i	−0.806585	+	0.591118i
$33$	−0.136027	+	0.0987974i	−0.0236792	+	0.0171984i
$34$	5.72235	−	3.54700i	0.981374	−	0.608305i
$35$	1.88393	−	2.93145i	0.318442	−	0.495506i
$36$	5.29432	+	2.82316i	0.882386	+	0.470526i
$37$	0.821456	−	2.79762i	0.135046	−	0.459926i	−0.864004	−	0.503484i	$-0.832051\pi$
$37$	0.821456	−	2.79762i	0.135046	−	0.459926i	0.999051	+	0.0435582i	$0.0138694\pi$
$38$	1.02705	−	3.29786i	0.166610	−	0.534984i
$39$	0.341325	+	0.647123i	0.0546558	+	0.103623i
$40$	4.75015	−	3.72533i	0.751065	−	0.589026i
$41$	−2.47755	−	8.43777i	−0.386929	−	1.31776i	−0.890964	−	0.454075i	$-0.849970\pi$
$41$	−2.47755	−	8.43777i	−0.386929	−	1.31776i	0.504035	−	0.863683i	$-0.331848\pi$
$42$	3.56729	−	1.80782i	0.550444	−	0.278953i
$43$	−0.344197	+	2.39395i	−0.0524896	+	0.365073i	0.946600	+	0.322411i	$0.104493\pi$
$43$	−0.344197	+	2.39395i	−0.0524896	+	0.365073i	−0.999090	+	0.0426627i	$0.986416\pi$
$44$	−0.0607382	+	0.184381i	−0.00915663	+	0.0277965i
$45$	−5.74510	−	2.82686i	−0.856429	−	0.421403i
$46$	4.54301	−	5.03598i	0.669830	−	0.742514i
$47$	−4.32833			−0.631352			−0.315676	−	0.948867i	$-0.602231\pi$
$47$	−4.32833			−0.631352			−0.315676	+	0.948867i	$0.602231\pi$
$48$	6.86561	−	0.929192i	0.990965	−	0.134117i
$49$	−0.616846	+	4.29026i	−0.0881208	+	0.612894i
$50$	0.481996	−	0.404078i	0.0681645	−	0.0571452i
$51$	−8.23221	+	0.469470i	−1.15274	+	0.0657389i
$52$	0.756606	+	0.375822i	0.104922	+	0.0521172i
$53$	7.13420	+	8.23330i	0.979957	+	1.13093i	0.991383	+	0.130996i	$0.0418176\pi$
$53$	7.13420	+	8.23330i	0.979957	+	1.13093i	−0.0114257	+	0.999935i	$0.503637\pi$
$54$	−4.04549	−	6.13466i	−0.550521	−	0.834821i
$55$	0.0583648	−	0.198772i	0.00786991	−	0.0268024i
$56$	2.12151	−	4.10173i	0.283499	−	0.548117i
$57$	−3.03419	+	2.94784i	−0.401888	+	0.390451i
$58$	−2.11586	−	3.41350i	−0.277826	−	0.448215i
$59$	7.37884	+	6.39380i	0.960643	+	0.832402i	0.985910	−	0.167278i	$-0.0534979\pi$
$59$	7.37884	+	6.39380i	0.960643	+	0.832402i	−0.0252662	+	0.999681i	$0.508043\pi$
$60$	−7.29041	+	1.23003i	−0.941188	+	0.158796i
$61$	−7.91046	+	1.13735i	−1.01283	+	0.145623i	−0.628694	−	0.777653i	$-0.716410\pi$
$61$	−7.91046	+	1.13735i	−1.01283	+	0.145623i	−0.384137	+	0.923276i	$0.625501\pi$
$62$	−2.06906	+	0.571044i	−0.262771	+	0.0725227i
$63$	−4.89598	−	0.141368i	−0.616836	−	0.0178107i
$64$	5.80457	−	5.50518i	0.725571	−	0.688147i
$65$	−0.820065	−	0.374511i	−0.101717	−	0.0464524i
$66$	0.173208	−	0.162872i	0.0213204	−	0.0200482i
$67$	−2.10802	+	1.35474i	−0.257535	+	0.165508i	−0.663037	−	0.748586i	$-0.730733\pi$
$67$	−2.10802	+	1.35474i	−0.257535	+	0.165508i	0.405502	+	0.914094i	$0.367097\pi$
$68$	−7.39516	+	5.99704i	−0.896795	+	0.727248i
$69$	−7.83416	+	2.76150i	−0.943123	+	0.332445i
$70$	−2.12001	+	4.44868i	−0.253389	+	0.531719i
$71$	8.83727	−	5.67937i	1.04879	−	0.674017i	0.101646	−	0.994821i	$-0.467589\pi$
$71$	8.83727	−	5.67937i	1.04879	−	0.674017i	0.947146	+	0.320803i	$0.103953\pi$
$72$	−7.93114	−	3.01612i	−0.934694	−	0.355453i
$73$	−3.27521	+	7.17171i	−0.383334	+	0.839385i	0.615357	+	0.788248i	$0.289012\pi$
$73$	−3.27521	+	7.17171i	−0.383334	+	0.839385i	−0.998692	+	0.0511367i	$0.983716\pi$
$74$	−0.653322	+	4.07138i	−0.0759471	+	0.473288i
$75$	−0.755004	+	0.152863i	−0.0871804	+	0.0176511i
$76$	−0.852514	+	4.80985i	−0.0977900	+	0.551728i
$77$	−0.0225532	−	0.156861i	−0.00257017	−	0.0178759i
$78$	−0.594301	−	0.846965i	−0.0672913	−	0.0958999i
$79$	−3.12348	−	2.70651i	−0.351419	−	0.304506i	0.461206	−	0.887293i	$-0.347417\pi$
$79$	−3.12348	−	2.70651i	−0.351419	−	0.304506i	−0.812625	+	0.582787i	$0.801962\pi$
$80$	−5.99945	+	6.07377i	−0.670758	+	0.679068i
$81$	0.764680	+	8.96746i	0.0849645	+	0.996384i
$82$	4.98114	+	11.3955i	0.550075	+	1.25842i
$83$	3.11988	−	10.6253i	0.342451	−	1.16628i	−0.590728	−	0.806870i	$-0.701160\pi$
$83$	3.11988	−	10.6253i	0.342451	−	1.16628i	0.933179	−	0.359411i	$-0.117022\pi$
$84$	−4.68208	+	3.17264i	−0.510856	+	0.346164i
$85$	7.67883	−	6.65374i	0.832886	−	0.721700i
$86$	0.0557868	−	3.41991i	0.00601564	−	0.368778i
$87$	0.280049	+	4.91069i	0.0300244	+	0.526481i
$88$	0.0523159	−	0.269507i	0.00557690	−	0.0287296i
$89$	−3.13600	−	0.450889i	−0.332416	−	0.0477941i	−0.0259136	−	0.999664i	$-0.508249\pi$
$89$	−3.13600	−	0.450889i	−0.332416	−	0.0477941i	−0.306502	+	0.951870i	$0.599159\pi$
$90$	8.56421	+	2.94089i	0.902747	+	0.309997i
$91$	−0.689646			−0.0722945
$92$	−5.47501	+	7.87555i	−0.570810	+	0.821082i
$93$	2.56040	+	0.595809i	0.265501	+	0.0617825i
$94$	6.07228	−	0.772198i	0.626308	−	0.0796461i
$95$	0.741865	−	5.15978i	0.0761137	−	0.529383i
$96$	−9.46610	+	2.52844i	−0.966129	+	0.258058i
$97$	−11.4952	+	3.37528i	−1.16716	+	0.342708i	−0.807210	−	0.590265i	$-0.799023\pi$
$97$	−11.4952	+	3.37528i	−1.16716	+	0.342708i	−0.359946	+	0.932973i	$0.617205\pi$
$98$	0.0999771	−	6.12892i	0.0100992	−	0.619114i
$99$	−0.281648	+	0.0739400i	−0.0283067	+	0.00743125i
$100$	−0.604110	+	0.652878i	−0.0604110	+	0.0652878i
$101$	15.1311	+	4.44290i	1.50560	+	0.442085i	0.927483	−	0.373867i	$-0.121968\pi$
$101$	15.1311	+	4.44290i	1.50560	+	0.442085i	0.578120	+	0.815951i	$0.303786\pi$
$102$	11.4653	−	2.12730i	1.13524	−	0.210634i
$103$	6.54991	−	10.1919i	0.645382	−	1.00423i	−0.352280	−	0.935895i	$-0.614593\pi$
$103$	6.54991	−	10.1919i	0.645382	−	1.00423i	0.997662	−	0.0683397i	$-0.0217702\pi$
$104$	−1.12850	−	0.392264i	−0.110659	−	0.0384646i
$105$	4.88340	−	3.54686i	0.476571	−	0.346138i
$106$	−11.4775	−	10.2778i	−1.11480	−	0.998273i
$107$	8.72468	−	1.25442i	0.843447	−	0.121269i	0.292972	−	0.956121i	$-0.405356\pi$
$107$	8.72468	−	1.25442i	0.843447	−	0.121269i	0.550475	+	0.834852i	$0.314447\pi$
$108$	6.76993	+	7.88467i	0.651437	+	0.758703i
$109$	−6.87741	+	3.14081i	−0.658736	+	0.300835i	−0.716595	−	0.697490i	$-0.754300\pi$
$109$	−6.87741	+	3.14081i	−0.658736	+	0.300835i	0.0578582	+	0.998325i	$0.481573\pi$
$110$	−0.0464188	+	0.289273i	−0.00442586	+	0.0275811i
$111$	3.08450	−	3.99878i	0.292768	−	0.379548i
$112$	−2.24453	+	6.13287i	−0.212088	+	0.579502i
$113$	−1.86023	−	2.89457i	−0.174995	−	0.272298i	0.742665	−	0.669663i	$-0.233561\pi$
$113$	−1.86023	−	2.89457i	−0.174995	−	0.272298i	−0.917661	+	0.397364i	$0.869925\pi$
$114$	3.73080	−	4.67689i	0.349421	−	0.438031i
$115$	5.56544	−	8.59050i	0.518980	−	0.801068i
$116$	3.57736	+	4.41137i	0.332150	+	0.409586i
$117$	0.144065	+	1.25899i	0.0133188	+	0.116394i
$118$	−11.4926	−	7.65354i	−1.05798	−	0.704565i
$119$	3.22881	−	7.07011i	0.295985	−	0.648116i
$120$	10.0084	−	3.02627i	0.913636	−	0.276260i
$121$	4.56565	+	9.99738i	0.415059	+	0.908853i
$122$	10.8948	−	3.00688i	0.986369	−	0.272230i
$123$	1.30577	−	15.1756i	0.117737	−	1.36833i
$124$	2.80084	−	1.17026i	0.251523	−	0.105092i
$125$	7.60997	−	8.78237i	0.680656	−	0.785519i
$126$	6.89387	−	0.675142i	0.614155	−	0.0601465i
$127$	1.23279	−	1.91826i	0.109393	−	0.170218i	−0.782241	−	0.622976i	$-0.785923\pi$
$127$	1.23279	−	1.91826i	0.109393	−	0.170218i	0.891634	+	0.452758i	$0.149560\pi$
$128$	−7.16116	+	8.75887i	−0.632963	+	0.774182i
$129$	−2.06046	+	3.64730i	−0.181414	+	0.321127i
$130$	1.21730	+	0.379104i	0.106764	+	0.0332496i
$131$	14.9415	−	12.9469i	1.30545	−	1.13118i	0.322645	−	0.946520i	$-0.395428\pi$
$131$	14.9415	−	12.9469i	1.30545	−	1.13118i	0.982803	−	0.184657i	$-0.0591176\pi$
$132$	−0.213939	+	0.259397i	−0.0186210	+	0.0225776i
$133$	−1.12345	−	3.82613i	−0.0974157	−	0.331767i
$134$	2.71568	−	2.27667i	0.234599	−	0.196674i
$135$	−7.49514	−	8.17403i	−0.645079	−	0.703508i
$136$	9.30488	−	9.73267i	0.797887	−	0.834570i
$137$			15.3942i			1.31522i	0.753359	+	0.657609i	$0.228432\pi$
$137$			15.3942i			1.31522i	−0.753359	+	0.657609i	$0.771568\pi$
$138$	10.4980	−	5.27180i	0.893649	−	0.448766i
$139$	16.8252			1.42709			0.713547	−	0.700607i	$-0.247087\pi$
$139$	16.8252			1.42709			0.713547	+	0.700607i	$0.247087\pi$
$140$	2.18052	−	6.61934i	0.184288	−	0.559437i
$141$	−6.98566	−	2.72100i	−0.588299	−	0.229149i
$142$	−11.3847	+	9.54429i	−0.955384	+	0.800939i
$143$	−0.0393393	+	0.0115510i	−0.00328971	+	0.000965947i
$144$	11.6648	+	2.81640i	0.972068	+	0.234700i
$145$	−3.96910	−	4.58059i	−0.329616	−	0.380397i
$146$	3.31537	−	10.6456i	0.274382	−	0.881037i
$147$	−3.69262	+	6.53644i	−0.304562	+	0.539116i
$148$	0.190199	−	5.82835i	0.0156343	−	0.479088i
$149$	3.93242	+	2.52721i	0.322156	+	0.207037i	0.691716	−	0.722170i	$-0.256855\pi$
$149$	3.93242	+	2.52721i	0.322156	+	0.207037i	−0.369560	+	0.929207i	$0.620491\pi$
$150$	1.03194	−	0.349151i	0.0842571	−	0.0285081i
$151$	−7.03192	−	6.09319i	−0.572250	−	0.495857i	0.319989	−	0.947421i	$-0.396321\pi$
$151$	−7.03192	−	6.09319i	−0.572250	−	0.495857i	−0.892239	+	0.451564i	$0.850866\pi$
$152$	0.337901	−	6.89991i	0.0274074	−	0.559656i
$153$	−13.5814	−	4.41747i	−1.09799	−	0.357131i
$154$	0.0596250	+	0.216039i	0.00480472	+	0.0174089i
$155$	−2.94660	+	1.34567i	−0.236676	+	0.108086i
$156$	0.984857	+	1.08219i	0.0788517	+	0.0866449i
$157$	16.6479	+	7.60285i	1.32865	+	0.606774i	0.948096	−	0.317985i	$-0.103006\pi$
$157$	16.6479	+	7.60285i	1.32865	+	0.606774i	0.380553	+	0.924759i	$0.375734\pi$
$158$	4.86484	+	3.23976i	0.387026	+	0.257742i
$159$	6.33831	+	17.7730i	0.502661	+	1.40949i
$160$	7.33312	−	9.59132i	0.579734	−	0.758261i
$161$	1.14277	−	7.74619i	0.0900632	−	0.610485i
$162$	−2.67263	−	12.4442i	−0.209981	−	0.977705i
$163$	18.1760	−	11.6810i	1.42365	−	0.914926i	0.423694	−	0.905806i	$-0.360733\pi$
$163$	18.1760	−	11.6810i	1.42365	−	0.914926i	0.999958	−	0.00912011i	$-0.00290306\pi$
$164$	−9.02113	−	15.0982i	−0.704432	−	1.17897i
$165$	0.219155	−	0.284115i	0.0170612	−	0.0221184i
$166$	−2.48131	+	15.4630i	−0.192587	+	1.20016i
$167$	−0.0564456	−	0.123599i	−0.00436789	−	0.00956435i	0.907435	−	0.420191i	$-0.138037\pi$
$167$	−0.0564456	−	0.123599i	−0.00436789	−	0.00956435i	−0.911803	+	0.410627i	$0.865310\pi$
$168$	6.00254	−	5.28626i	0.463106	−	0.407844i
$169$	−1.82470	−	12.6911i	−0.140362	−	0.976236i
$170$	−9.58568	+	10.7046i	−0.735188	+	0.821004i
$171$	−6.75015	+	2.85020i	−0.516197	+	0.217960i
$172$	0.531867	+	4.80780i	0.0405544	+	0.366591i
$173$	−14.8682	−	9.55521i	−1.13041	−	0.726469i	−0.164763	−	0.986333i	$-0.552686\pi$
$173$	−14.8682	−	9.55521i	−1.13041	−	0.726469i	−0.965645	+	0.259864i	$0.916322\pi$
$174$	−1.26898	−	6.83932i	−0.0962010	−	0.518488i
$175$	0.204573	−	0.696713i	0.0154643	−	0.0526665i
$176$	−0.0253132	+	0.387430i	−0.00190806	+	0.0292036i
$177$	7.88955	+	14.9579i	0.593015	+	1.12431i
$178$	4.47999	+	0.0730791i	0.335789	+	0.00547751i
$179$	−0.629147	−	2.14268i	−0.0470247	−	0.160151i	0.932633	−	0.360825i	$-0.117505\pi$
$179$	−0.629147	−	2.14268i	−0.0470247	−	0.160151i	−0.979658	+	0.200674i	$0.935687\pi$
$180$	−12.5395	−	2.59792i	−0.934642	−	0.193637i
$181$	10.5473	+	1.51647i	0.783974	+	0.112718i	0.522666	−	0.852537i	$-0.324937\pi$
$181$	10.5473	+	1.51647i	0.783974	+	0.112718i	0.261307	+	0.965256i	$0.415846\pi$
$182$	0.967515	−	0.123037i	0.0717170	−	0.00912008i
$183$	−13.4820	−	3.13728i	−0.996619	−	0.231915i
$184$	6.27594	−	12.0255i	0.462668	−	0.886531i
$185$			6.22305i			0.457528i
$186$	−3.69832	−	0.379080i	−0.271174	−	0.0277955i
$187$	0.0657611	−	0.457378i	0.00480892	−	0.0334468i
$188$	−8.38113	+	2.16666i	−0.611257	+	0.158020i
$189$	−7.81295	−	3.30601i	−0.568308	−	0.240477i
$190$	−0.120240	+	7.37109i	−0.00872312	+	0.534755i
$191$	11.7512	+	13.5616i	0.850284	+	0.981280i	0.999972	−	0.00745353i	$-0.00237255\pi$
$191$	11.7512	+	13.5616i	0.850284	+	0.981280i	−0.149689	+	0.988733i	$0.547827\pi$
$192$	12.8290	−	5.23599i	0.925857	−	0.377875i
$193$	8.78043	+	2.57817i	0.632029	+	0.185581i	0.582028	−	0.813169i	$-0.302259\pi$
$193$	8.78043	+	2.57817i	0.632029	+	0.185581i	0.0500010	+	0.998749i	$0.484078\pi$
$194$	15.5246	−	6.78603i	1.11460	−	0.487209i
$195$	−1.08810	−	1.11997i	−0.0779205	−	0.0802028i
$196$	0.953173	+	8.61619i	0.0680838	+	0.615442i
$197$	−10.2126	+	11.7859i	−0.727616	+	0.839714i	−0.992201	−	0.124649i	$-0.960220\pi$
$197$	−10.2126	+	11.7859i	−0.727616	+	0.839714i	0.264585	+	0.964362i	$0.414765\pi$
$198$	0.381937	−	0.153979i	0.0271431	−	0.0109428i
$199$	1.52966	−	0.219931i	0.108434	−	0.0155905i	−0.0878839	−	0.996131i	$-0.528010\pi$
$199$	1.52966	−	0.219931i	0.108434	−	0.0155905i	0.196318	+	0.980540i	$0.437101\pi$
$200$	0.731038	−	1.02371i	0.0516922	−	0.0723871i
$201$	−4.25387	+	0.861267i	−0.300045	+	0.0607491i
$202$	−22.0203	−	3.53354i	−1.54934	−	0.248619i
$203$	−4.21747	−	1.92606i	−0.296009	−	0.135183i
$204$	−15.7054	+	5.02990i	−1.09960	+	0.352163i
$205$	10.1473	+	15.7895i	0.708719	+	1.10279i
$206$	−7.37069	+	15.4669i	−0.513540	+	1.07763i
$207$	−14.3799	−	0.468049i	−0.999471	−	0.0325317i
$208$	1.65318	+	0.348982i	0.114627	+	0.0241975i
$209$	−0.128170	−	0.199436i	−0.00886567	−	0.0137953i
$210$	−6.21822	+	5.84716i	−0.429098	+	0.403493i
$211$	−1.32821	+	2.90836i	−0.0914375	+	0.200220i	−0.949825	−	0.312781i	$-0.898739\pi$
$211$	−1.32821	+	2.90836i	−0.0914375	+	0.200220i	0.858388	+	0.513002i	$0.171467\pi$
$212$	17.9356	+	12.3713i	1.23182	+	0.849664i
$213$	17.8332	−	3.61062i	1.22191	−	0.247396i
$214$	−12.0162	+	3.31638i	−0.821410	+	0.226703i
$215$	−0.734622	−	5.10941i	−0.0501008	−	0.348459i
$216$	−10.9043	−	9.85373i	−0.741944	−	0.670462i
$217$	−1.62273	+	1.87273i	−0.110158	+	0.127129i
$218$	9.08809	−	5.63326i	0.615523	−	0.381532i
$219$	−9.79447	+	9.51575i	−0.661849	+	0.643015i
$220$	0.0135137	−	0.414107i	0.000911095	−	0.0279191i
$221$	−1.92943	−	0.566532i	−0.129788	−	0.0381091i
$222$	−3.61389	+	6.16025i	−0.242548	+	0.413449i
$223$	4.75623	−	4.12130i	0.318501	−	0.275983i	−0.480906	−	0.876772i	$-0.659692\pi$
$223$	4.75623	−	4.12130i	0.318501	−	0.275983i	0.799408	+	0.600789i	$0.205147\pi$
$224$	2.05475	−	9.00433i	0.137289	−	0.601627i
$225$	−1.31463	−	0.227920i	−0.0876419	−	0.0151947i
$226$	3.12615	+	3.72896i	0.207948	+	0.248047i
$227$	−11.9138	−	1.71294i	−0.790745	−	0.113692i	−0.264904	−	0.964275i	$-0.585340\pi$
$227$	−11.9138	−	1.71294i	−0.790745	−	0.113692i	−0.525841	+	0.850583i	$0.676249\pi$
$228$	−4.39961	+	7.22688i	−0.291371	+	0.478612i
$229$			5.71969i			0.377968i	0.981980	+	0.188984i	$0.0605194\pi$
$229$			5.71969i			0.377968i	−0.981980	+	0.188984i	$0.939481\pi$
$230$	−6.27526	+	13.0446i	−0.413778	+	0.860139i
$231$	0.0622108	−	0.267342i	0.00409317	−	0.0175898i
$232$	−5.80575	−	5.55056i	−0.381166	−	0.364412i
$233$	3.81471	+	0.548473i	0.249910	+	0.0359316i	0.266131	−	0.963937i	$-0.414255\pi$
$233$	3.81471	+	0.548473i	0.249910	+	0.0359316i	−0.0162212	+	0.999868i	$0.505164\pi$
$234$	−0.426722	−	1.74056i	−0.0278957	−	0.113784i
$235$	8.86377	−	2.60264i	0.578208	−	0.169777i
$236$	17.4886	+	8.68693i	1.13841	+	0.565471i
$237$	−3.33967	−	6.33172i	−0.216935	−	0.411289i
$238$	−3.26840	+	10.4948i	−0.211859	+	0.680277i
$239$	−6.68260	−	1.96219i	−0.432262	−	0.126923i	0.0583611	−	0.998296i	$-0.481413\pi$
$239$	−6.68260	−	1.96219i	−0.432262	−	0.126923i	−0.490623	+	0.871372i	$0.663231\pi$
$240$	−13.5010	+	6.03116i	−0.871487	+	0.389310i
$241$	−21.3685	−	13.7327i	−1.37647	−	0.884601i	−0.377326	−	0.926080i	$-0.623156\pi$
$241$	−21.3685	−	13.7327i	−1.37647	−	0.884601i	−0.999139	+	0.0414796i	$0.986793\pi$
$242$	−8.18881	−	13.2109i	−0.526397	−	0.849232i
$243$	−4.40323	+	14.9536i	−0.282467	+	0.959277i
$244$	−14.7480	+	6.16209i	−0.944147	+	0.394487i
$245$	−1.31654	−	9.15671i	−0.0841104	−	0.585001i
$246$	0.875516	+	21.5230i	0.0558209	+	1.37226i
$247$	−0.938449	+	0.428575i	−0.0597121	+	0.0272696i
$248$	−3.72056	+	2.14146i	−0.236256	+	0.135983i
$249$	11.7149	−	15.1873i	0.742401	−	0.962458i
$250$	−9.10932	+	13.6786i	−0.576124	+	0.865110i
$251$	0.327359	+	0.509380i	0.0206627	+	0.0321518i	0.851431	−	0.524466i	$-0.175735\pi$
$251$	0.327359	+	0.509380i	0.0206627	+	0.0321518i	−0.830769	+	0.556618i	$0.812099\pi$
$252$	−9.55107	+	2.17707i	−0.601661	+	0.137143i
$253$	−0.0645559	−	0.461004i	−0.00405859	−	0.0289831i
$254$	−1.38728	+	2.91110i	−0.0870454	+	0.182659i
$255$	16.5760	−	5.91145i	1.03803	−	0.370190i
$256$	8.48388	−	13.5655i	0.530242	−	0.847846i
$257$	5.71769	+	2.61118i	0.356660	+	0.162881i	0.585684	−	0.810540i	$-0.300826\pi$
$257$	5.71769	+	2.61118i	0.356660	+	0.162881i	−0.229024	+	0.973421i	$0.573553\pi$
$258$	2.23996	−	5.48446i	0.139454	−	0.341447i
$259$	1.97756	+	4.33024i	0.122879	+	0.269068i
$260$	−1.77540	−	0.314678i	−0.110106	−	0.0195155i
$261$	−2.63512	+	8.10161i	−0.163110	+	0.501477i
$262$	−18.6519	+	20.8291i	−1.15232	+	1.28682i
$263$	−13.2402	+	15.2800i	−0.816427	+	0.942207i	−0.999161	−	0.0409552i	$-0.986960\pi$
$263$	−13.2402	+	15.2800i	−0.816427	+	0.942207i	0.182734	+	0.983162i	$0.441505\pi$
$264$	0.253860	−	0.402080i	0.0156240	−	0.0247463i
$265$	−19.5605	−	12.5708i	−1.20159	−	0.772215i
$266$	2.25871	+	5.16731i	0.138491	+	0.316828i
$267$	−4.77787	−	2.69915i	−0.292401	−	0.165185i
$268$	−3.40369	+	3.67846i	−0.207914	+	0.224698i
$269$	−6.29718	−	7.26733i	−0.383946	−	0.443097i	0.530574	−	0.847639i	$-0.321977\pi$
$269$	−6.29718	−	7.26733i	−0.383946	−	0.443097i	−0.914520	+	0.404542i	$0.867431\pi$
$270$	11.9733	+	10.1303i	0.728674	+	0.616510i
$271$	8.26992	+	28.1647i	0.502362	+	1.71089i	0.685742	+	0.727845i	$0.259478\pi$
$271$	8.26992	+	28.1647i	0.502362	+	1.71089i	−0.183381	+	0.983042i	$0.558704\pi$
$272$	−11.3176	+	15.3142i	−0.686230	+	0.928557i
$273$	−1.11305	−	0.433545i	−0.0673646	−	0.0262393i
$274$	−2.74642	−	21.5968i	−0.165917	−	1.30471i
$275$		−	0.0431688i		−	0.00260318i
$276$	−13.7873	+	9.26880i	−0.829897	+	0.557916i
$277$			19.6185i			1.17876i	0.807855	+	0.589381i	$0.200628\pi$
$277$			19.6185i			1.17876i	−0.807855	+	0.589381i	$0.799372\pi$
$278$	−23.6043	+	3.00171i	−1.41569	+	0.180030i
$279$	3.75778	+	2.57119i	0.224972	+	0.153933i
$280$	−1.87816	+	9.67540i	−0.112241	+	0.578216i
$281$	−7.18530	−	24.4709i	−0.428639	−	1.45981i	−0.837108	−	0.547038i	$-0.815755\pi$
$281$	−7.18530	−	24.4709i	−0.428639	−	1.45981i	0.408469	−	0.912772i	$-0.366063\pi$
$282$	10.2857	+	2.57105i	0.612506	+	0.153104i
$283$	−9.18250	−	10.5972i	−0.545843	−	0.629937i	0.414066	−	0.910247i	$-0.364108\pi$
$283$	−9.18250	−	10.5972i	−0.545843	−	0.629937i	−0.959910	+	0.280310i	$0.909563\pi$
$284$	14.2690	−	15.4209i	0.846712	−	0.915064i
$285$	4.44102	−	7.86121i	0.263063	−	0.465658i
$286$	0.0531289	−	0.0232235i	0.00314158	−	0.00137323i
$287$	12.0785	+	7.76237i	0.712970	+	0.458198i
$288$	−16.8672	−	1.87010i	−0.993910	−	0.110197i
$289$	3.70862	−	4.27998i	0.218154	−	0.251763i
$290$	6.38552	+	5.71807i	0.374970	+	0.335776i
$291$	−20.6743	−	1.77891i	−1.21195	−	0.104282i
$292$	−2.75195	+	15.5264i	−0.161045	+	0.908612i
$293$	12.7002	+	27.8095i	0.741952	+	1.62465i	0.780316	+	0.625385i	$0.215058\pi$
$293$	12.7002	+	27.8095i	0.741952	+	1.62465i	−0.0383640	+	0.999264i	$0.512215\pi$
$294$	4.01429	−	9.82885i	0.234118	−	0.573230i
$295$	−18.9554	−	8.65663i	−1.10362	−	0.504008i
$296$	0.772977	+	8.21062i	0.0449284	+	0.477233i
$297$	−0.501045	−	0.0577228i	−0.0290736	−	0.00334942i
$298$	−5.96772	−	2.84390i	−0.345701	−	0.164743i
$299$	−2.02576	−	0.00743680i	−0.117153	−	0.000430081i
$300$	−1.38543	+	0.673932i	−0.0799877	+	0.0389095i
$301$	−2.13484	−	3.32188i	−0.123050	−	0.191470i
$302$	10.9522	+	7.29370i	0.630231	+	0.419705i
$303$	21.6277	+	16.6827i	1.24248	+	0.958398i
$304$	0.756935	+	9.74027i	0.0434132	+	0.558643i
$305$	15.5155	−	7.08571i	0.888418	−	0.405727i
$306$	19.8417	+	3.77434i	1.13427	+	0.215765i
$307$	−2.07756	−	14.4497i	−0.118572	−	0.824690i	−0.959130	−	0.282967i	$-0.908681\pi$
$307$	−2.07756	−	14.4497i	−0.118572	−	0.824690i	0.840557	−	0.541723i	$-0.182228\pi$
$308$	−0.122191	−	0.292447i	−0.00696250	−	0.0166637i
$309$	16.9783	−	12.3315i	0.965860	−	0.701512i
$310$	3.89375	−	2.41354i	0.221150	−	0.137080i
$311$	−5.13320	−	3.29891i	−0.291077	−	0.187064i	0.386950	−	0.922101i	$-0.373529\pi$
$311$	−5.13320	−	3.29891i	−0.291077	−	0.187064i	−0.678027	+	0.735037i	$0.737165\pi$
$312$	−1.57474	−	1.34252i	−0.0891521	−	0.0760054i
$313$	−2.84349	−	0.834923i	−0.160723	−	0.0471926i	0.200381	−	0.979718i	$-0.435782\pi$
$313$	−2.84349	−	0.834923i	−0.160723	−	0.0471926i	−0.361104	+	0.932525i	$0.617600\pi$
$314$	−24.7120	−	7.69608i	−1.39458	−	0.434315i
$315$	10.1112	−	2.65447i	0.569704	−	0.149562i
$316$	−7.40295	−	3.67720i	−0.416448	−	0.206858i
$317$	1.29316	−	0.379705i	0.0726309	−	0.0213264i	−0.245215	−	0.969469i	$-0.578859\pi$
$317$	1.29316	−	0.379705i	0.0726309	−	0.0213264i	0.317846	+	0.948142i	$0.397040\pi$
$318$	−12.0629	−	23.8032i	−0.676454	−	1.33481i
$319$	−0.272836	−	0.0392279i	−0.0152759	−	0.00219634i
$320$	−8.57660	+	14.7641i	−0.479447	+	0.825337i
$321$	14.8697	+	3.46020i	0.829946	+	0.193130i
$322$	−0.221253	+	11.0711i	−0.0123299	+	0.616970i
$323$		−	11.6273i		−	0.646961i
$324$	5.96957	+	16.9813i	0.331643	+	0.943405i
$325$	−0.185950	−	0.0267356i	−0.0103146	−	0.00148302i
$326$	−23.4154	+	19.6301i	−1.29686	+	1.08721i
$327$	−13.0742	+	0.745600i	−0.723004	+	0.0412318i
$328$	15.3495	+	19.5721i	0.847534	+	1.08069i
$329$	5.34069	−	4.62774i	0.294442	−	0.255135i
$330$	−0.256768	+	0.437688i	−0.0141346	+	0.0240940i
$331$	10.9010	+	3.20081i	0.599171	+	0.175933i	0.567233	−	0.823557i	$-0.308014\pi$
$331$	10.9010	+	3.20081i	0.599171	+	0.175933i	0.0319382	+	0.999490i	$0.489832\pi$
$332$	0.722373	−	22.1360i	0.0396454	−	1.21487i
$333$	7.49203	−	4.51473i	0.410561	−	0.247406i
$334$	0.101239	+	0.163328i	0.00553956	+	0.00893692i
$335$	3.50229	−	4.04186i	0.191351	−	0.220830i
$336$	−7.47796	+	8.48706i	−0.407956	+	0.463007i
$337$	0.443075	+	3.08165i	0.0241358	+	0.167868i	0.998324	−	0.0578680i	$-0.0184303\pi$
$337$	0.443075	+	3.08165i	0.0241358	+	0.167868i	−0.974188	+	0.225736i	$0.927521\pi$
$338$	4.82406	+	17.4790i	0.262394	+	0.950730i
$339$	−1.18263	−	5.84109i	−0.0642315	−	0.317244i
$340$	11.5381	−	16.7278i	0.625744	−	0.907190i
$341$	−0.0611982	+	0.134005i	−0.00331407	+	0.00725679i
$342$	8.96140	−	5.20286i	0.484577	−	0.281338i
$343$	−10.0047	−	15.5677i	−0.540205	−	0.840576i
$344$	−1.60390	−	6.65004i	−0.0864766	−	0.358546i
$345$	14.3827	−	10.3658i	0.774338	−	0.558078i
$346$	22.5635	+	10.7526i	1.21302	+	0.578062i
$347$	5.57871	+	8.68064i	0.299481	+	0.466001i	0.958083	−	0.286490i	$-0.0924885\pi$
$347$	5.57871	+	8.68064i	0.299481	+	0.466001i	−0.658603	+	0.752491i	$0.728852\pi$
$348$	3.00044	+	9.36860i	0.160841	+	0.502209i
$349$	−9.50356	−	4.34013i	−0.508714	−	0.232322i	0.144487	−	0.989507i	$-0.453847\pi$
$349$	−9.50356	−	4.34013i	−0.508714	−	0.232322i	−0.653201	+	0.757185i	$0.726574\pi$
$350$	−0.162702	+	1.01393i	−0.00869677	+	0.0541966i
$351$	−0.558951	+	2.12250i	−0.0298346	+	0.113291i
$352$	−0.0336072	−	0.548047i	−0.00179127	−	0.0292110i
$353$	−13.6522	+	1.96289i	−0.726632	+	0.104474i	−0.495698	−	0.868495i	$-0.665088\pi$
$353$	−13.6522	+	1.96289i	−0.726632	+	0.104474i	−0.230935	+	0.972969i	$0.574178\pi$
$354$	−13.7369	−	19.5771i	−0.730110	−	1.04051i
$355$	−14.6824	+	16.9444i	−0.779260	+	0.899314i
$356$	−6.29808	+	0.696730i	−0.333798	+	0.0369266i
$357$	9.65572	−	9.38094i	0.511035	−	0.496492i
$358$	1.26491	+	2.89375i	0.0668524	+	0.152940i
$359$	20.9732	+	6.15828i	1.10692	+	0.325021i	0.783599	−	0.621267i	$-0.213382\pi$
$359$	20.9732	+	6.15828i	1.10692	+	0.325021i	0.323323	+	0.946289i	$0.395200\pi$
$360$	18.0554	+	1.40753i	0.951603	+	0.0741835i
$361$	8.53587	+	9.85092i	0.449257	+	0.518470i
$362$	−15.0675	−	0.245786i	−0.791930	−	0.0129182i
$363$	1.08384	+	19.0054i	0.0568871	+	0.997523i
$364$	−1.33539	+	0.345220i	−0.0699935	+	0.0180944i
$365$	2.39477	−	16.6560i	0.125348	−	0.871814i
$366$	19.4738	+	1.99608i	1.01791	+	0.104337i
$367$			25.4494i			1.32845i	0.747533	+	0.664224i	$0.231238\pi$
$367$			25.4494i			1.32845i	−0.747533	+	0.664224i	$0.768762\pi$
$368$	−6.65920	+	17.9904i	−0.347135	+	0.937815i
$369$	11.6475	−	23.6716i	0.606346	−	1.23229i
$370$	−1.11023	−	8.73041i	−0.0577179	−	0.453873i
$371$	−17.6057	−	2.53131i	−0.914041	−	0.131419i
$372$	5.25606	−	0.127983i	0.272514	−	0.00663563i
$373$	−7.36852	−	25.0949i	−0.381527	−	1.29936i	−0.896838	−	0.442359i	$-0.854142\pi$
$373$	−7.36852	−	25.0949i	−0.381527	−	1.29936i	0.515311	−	0.857003i	$-0.327677\pi$
$374$	−0.0106584	+	0.653395i	−0.000551133	+	0.0337863i
$375$	17.8031	−	9.39022i	0.919346	−	0.484909i
$376$	11.3715	−	4.53487i	0.586439	−	0.233868i
$377$	−0.337949	+	1.15095i	−0.0174052	+	0.0592768i
$378$	11.5507	+	3.24418i	0.594105	+	0.166863i
$379$	−10.4182	−	6.69536i	−0.535146	−	0.343918i	0.244992	−	0.969525i	$-0.421215\pi$
$379$	−10.4182	−	6.69536i	−0.535146	−	0.343918i	−0.780138	+	0.625607i	$0.784851\pi$
$380$	−1.14636	−	10.3625i	−0.0588069	−	0.531583i
$381$	3.19557	−	2.32097i	0.163714	−	0.118907i
$382$	−18.9053	−	16.9292i	−0.967281	−	0.866175i
$383$	−2.55041	−	17.7385i	−0.130320	−	0.906394i	−0.945137	−	0.326676i	$-0.894072\pi$
$383$	−2.55041	−	17.7385i	−0.130320	−	0.906394i	0.814817	−	0.579719i	$-0.196838\pi$
$384$	−17.0639	+	9.63443i	−0.870790	+	0.491655i
$385$	0.140506	+	0.307666i	0.00716086	+	0.0156801i
$386$	−12.7782	−	2.05047i	−0.650391	−	0.104366i
$387$	−5.61834	+	4.59122i	−0.285596	+	0.233385i
$388$	−20.5690	+	12.2899i	−1.04423	+	0.623925i
$389$	−15.9401	+	10.2441i	−0.808196	+	0.519396i	−0.878281	−	0.478145i	$-0.841309\pi$
$389$	−15.9401	+	10.2441i	−0.808196	+	0.519396i	0.0700846	+	0.997541i	$0.477673\pi$
$390$	1.72632	+	1.37710i	0.0874157	+	0.0697323i
$391$	9.56051	−	20.7328i	0.483496	−	1.04850i
$392$	−2.87440	−	11.9177i	−0.145179	−	0.601936i
$393$	32.2538	−	11.5026i	1.62699	−	0.580228i
$394$	12.2247	−	18.3567i	0.615872	−	0.924795i
$395$	8.02385	+	3.66437i	0.403724	+	0.184375i
$396$	−0.508354	+	0.284159i	−0.0255458	+	0.0142795i
$397$	−28.4449	+	12.9904i	−1.42761	+	0.651968i	−0.971301	−	0.237853i	$-0.923556\pi$
$397$	−28.4449	+	12.9904i	−1.42761	+	0.651968i	−0.456309	+	0.889821i	$0.650829\pi$
$398$	−2.10674	+	0.581444i	−0.105601	+	0.0291452i
$399$	0.592106	−	6.88140i	0.0296424	−	0.344501i
$400$	−0.842949	+	1.56660i	−0.0421474	+	0.0783299i
$401$	5.43043	+	4.70550i	0.271183	+	0.234981i	0.779826	−	0.625996i	$-0.215307\pi$
$401$	5.43043	+	4.70550i	0.271183	+	0.234981i	−0.508643	+	0.860977i	$0.669853\pi$
$402$	5.81416	−	1.96720i	0.289984	−	0.0981149i
$403$	0.539327	+	0.346604i	0.0268658	+	0.0172656i
$404$	31.5230	+	1.02870i	1.56833	+	0.0511799i
$405$	−6.95811	−	17.9042i	−0.345751	−	0.889667i
$406$	6.26038	+	1.94967i	0.310697	+	0.0967606i
$407$	0.185333	+	0.213886i	0.00918664	+	0.0106019i
$408$	21.1360	−	9.85845i	1.04639	−	0.488066i
$409$	−0.510769	+	0.149975i	−0.0252559	+	0.00741580i	−0.294336	−	0.955702i	$-0.595099\pi$
$409$	−0.510769	+	0.149975i	−0.0252559	+	0.00741580i	0.269080	+	0.963118i	$0.413280\pi$
$410$	−17.0528	−	20.3410i	−0.842176	−	1.00457i
$411$	−9.67757	+	24.8454i	−0.477359	+	1.22553i
$412$	7.58108	−	23.0137i	0.373493	−	1.13380i
$413$	−15.9408			−0.784395
$414$	20.2573	−	1.90882i	0.995590	−	0.0938132i
$415$			23.6351i			1.16020i
$416$	−2.38153	−	0.194656i	−0.116764	−	0.00954380i
$417$	27.1549	+	10.5771i	1.32978	+	0.517965i
$418$	0.215391	+	0.256925i	0.0105351	+	0.0125666i
$419$	3.27547	+	11.1552i	0.160017	+	0.544968i	0.999997	+	0.00235100i	$0.000748349\pi$
$419$	3.27547	+	11.1552i	0.160017	+	0.544968i	−0.839980	+	0.542617i	$0.817433\pi$
$420$	7.68047	−	9.31244i	0.374769	−	0.454401i
$421$	−21.5587	+	18.6807i	−1.05071	+	0.910444i	−0.996115	−	0.0880647i	$-0.971932\pi$
$421$	−21.5587	+	18.6807i	−1.05071	+	0.910444i	−0.0545936	+	0.998509i	$0.517386\pi$
$422$	1.34449	−	4.31715i	0.0654488	−	0.210156i
$423$	−9.56388	−	8.78305i	−0.465012	−	0.427047i
$424$	−27.3693	−	14.1561i	−1.32917	−	0.687479i
$425$	1.14467	−	1.78115i	0.0555249	−	0.0863984i
$426$	−24.3743	+	8.24693i	−1.18094	+	0.399565i
$427$	8.54464	−	9.86104i	0.413504	−	0.477209i
$428$	16.2660	−	6.79635i	0.786249	−	0.328514i
$429$	−0.0707527	−	0.00608788i	−0.00341597	−	0.000293925i
$430$	1.94216	+	7.03701i	0.0936592	+	0.339355i
$431$	9.63752	+	21.1032i	0.464223	+	1.01651i	0.986505	+	0.163734i	$0.0523538\pi$
$431$	9.63752	+	21.1032i	0.464223	+	1.01651i	−0.522281	+	0.852773i	$0.674919\pi$
$432$	17.0558	+	11.8786i	0.820597	+	0.571508i
$433$	10.4402	−	22.8608i	0.501723	−	1.09862i	−0.474183	−	0.880426i	$-0.657257\pi$
$433$	10.4402	−	22.8608i	0.501723	−	1.09862i	0.975906	−	0.218193i	$-0.0700162\pi$
$434$	1.94245	−	2.91679i	0.0932406	−	0.140010i
$435$	−3.52631	−	9.88796i	−0.169074	−	0.474092i
$436$	−11.7448	+	9.52434i	−0.562474	+	0.456133i
$437$	−3.25876	−	11.2509i	−0.155888	−	0.538206i
$438$	12.0432	−	15.0972i	0.575444	−	0.721371i
$439$	−12.7186	−	19.7905i	−0.607026	−	0.944551i	−0.999691	−	0.0248695i	$-0.992083\pi$
$439$	−12.7186	−	19.7905i	−0.607026	−	0.944551i	0.392664	−	0.919682i	$-0.371553\pi$
$440$	0.0549204	+	0.583368i	0.00261823	+	0.0278110i
$441$	−10.0688	+	8.22806i	−0.479466	+	0.391812i
$442$	2.80790	+	0.450575i	0.133558	+	0.0214317i
$443$	−30.7484	+	14.0423i	−1.46090	+	0.667171i	−0.978019	−	0.208516i	$-0.933137\pi$
$443$	−30.7484	+	14.0423i	−1.46090	+	0.667171i	−0.482881	+	0.875686i	$0.660410\pi$
$444$	3.97096	−	9.28704i	0.188453	−	0.440744i
$445$	6.69318	−	0.962334i	0.317287	−	0.0456190i
$446$	−5.93733	+	6.63037i	−0.281141	+	0.313957i
$447$	4.75796	+	6.55087i	0.225044	+	0.309846i
$448$	−1.27622	+	12.9989i	−0.0602957	+	0.614140i
$449$	−2.27145	+	3.53445i	−0.107197	+	0.166801i	−0.890708	−	0.454577i	$-0.849790\pi$
$449$	−2.27145	+	3.53445i	−0.107197	+	0.166801i	0.783511	+	0.621378i	$0.213427\pi$
$450$	1.88497	+	0.0852159i	0.0888585	+	0.00401711i
$451$	0.819003	+	0.240481i	0.0385653	+	0.0113238i
$452$	−5.05099	−	4.67369i	−0.237578	−	0.219832i
$453$	−7.51862	−	14.2547i	−0.353255	−	0.669742i
$454$	17.0196	+	0.277630i	0.798770	+	0.0130298i
$455$	1.41229	−	0.414686i	0.0662092	−	0.0194408i
$456$	4.88297	−	10.9236i	0.228666	−	0.511545i
$457$	−5.53353	+	38.4865i	−0.258847	+	1.80032i	0.282226	+	0.959348i	$0.408927\pi$
$457$	−5.53353	+	38.4865i	−0.258847	+	1.80032i	−0.541073	+	0.840976i	$0.681982\pi$
$458$	−1.02042	−	8.02424i	−0.0476813	−	0.374948i
$459$	−19.1426	−	15.6675i	−0.893498	−	0.731295i
$460$	6.47642	−	19.4201i	0.301964	−	0.905466i
$461$	−18.6591			−0.869040			−0.434520	−	0.900662i	$-0.643082\pi$
$461$	−18.6591			−0.869040			−0.434520	+	0.900662i	$0.643082\pi$
$462$	−0.0395813	+	0.386157i	−0.00184149	+	0.0179656i
$463$	36.2490	+	5.21182i	1.68463	+	0.242214i	0.917060	−	0.398748i	$-0.130555\pi$
$463$	36.2490	+	5.21182i	1.68463	+	0.242214i	0.767573	+	0.640962i	$0.221464\pi$
$464$	9.13523	+	6.75119i	0.424092	+	0.313416i
$465$	−5.60158	+	0.319449i	−0.259767	+	0.0148141i
$466$	−5.44957	−	0.0888953i	−0.252446	−	0.00411799i
$467$	7.77814	−	6.73980i	0.359930	−	0.311881i	−0.456058	−	0.889950i	$-0.650739\pi$
$467$	7.77814	−	6.73980i	0.359930	−	0.311881i	0.815988	+	0.578069i	$0.196194\pi$
$468$	0.909180	+	2.36572i	0.0420269	+	0.109356i
$469$	1.15261	−	3.92544i	0.0532227	−	0.181260i
$470$	−11.9708	+	5.23262i	−0.552171	+	0.241363i
$471$	22.0892	+	22.7362i	1.01782	+	1.04763i
$472$	−26.0848	−	9.06697i	−1.20065	−	0.417341i
$473$	−0.177416	−	0.153732i	−0.00815760	−	0.00706860i
$474$	5.81488	+	8.28705i	0.267086	+	0.380637i
$475$	−0.154590	−	1.07520i	−0.00709307	−	0.0493334i
$476$	2.71296	−	15.3064i	0.124348	−	0.701569i
$477$	−0.943297	+	32.6690i	−0.0431906	+	1.49581i
$478$	9.72519	+	1.56057i	0.444820	+	0.0713789i
$479$	14.7924	−	32.3908i	0.675880	−	1.47997i	−0.191070	−	0.981577i	$-0.561196\pi$
$479$	14.7924	−	32.3908i	0.675880	−	1.47997i	0.866950	−	0.498395i	$-0.166077\pi$
$480$	17.8648	−	10.8699i	0.815412	−	0.496139i
$481$	1.03610	−	0.665859i	0.0472420	−	0.0303606i
$482$	32.4282	+	15.4536i	1.47706	+	0.703890i
$483$	6.71400	−	11.7835i	0.305498	−	0.536167i
$484$	13.8451	+	17.0729i	0.629323	+	0.776041i
$485$	21.5108	−	13.8241i	0.976754	−	0.627722i
$486$	3.50955	−	21.7643i	0.159196	−	0.987247i
$487$	−5.29359	−	2.41750i	−0.239876	−	0.109547i	0.291850	−	0.956464i	$-0.405729\pi$
$487$	−5.29359	−	2.41750i	−0.239876	−	0.109547i	−0.531726	+	0.846916i	$0.678456\pi$
$488$	19.5909	−	11.2760i	0.886838	−	0.510442i
$489$	36.6782	−	7.42611i	1.65864	−	0.335820i
$490$	3.48060	+	12.6112i	0.157237	+	0.569717i
$491$	−41.8766	+	6.02094i	−1.88986	+	0.271721i	−0.987304	−	0.158843i	$-0.949224\pi$
$491$	−41.8766	+	6.02094i	−1.88986	+	0.271721i	−0.902560	+	0.430564i	$0.858315\pi$
$492$	−5.06809	−	30.0387i	−0.228487	−	1.35425i
$493$	−10.2171	−	8.85313i	−0.460153	−	0.398725i
$494$	1.24010	−	0.768679i	0.0557949	−	0.0345845i
$495$	0.532312	−	0.320774i	0.0239256	−	0.0144177i
$496$	4.83758	−	3.66805i	0.217214	−	0.164700i
$497$	−4.83201	+	16.4563i	−0.216745	+	0.738167i
$498$	−13.7255	+	23.3965i	−0.615054	+	1.04842i
$499$	21.3049	+	24.5871i	0.953736	+	1.10067i	0.994834	+	0.101515i	$0.0323690\pi$
$499$	21.3049	+	24.5871i	0.953736	+	1.10067i	−0.0410978	+	0.999155i	$0.513086\pi$
$500$	10.3393	−	20.8150i	0.462386	−	0.930877i
$501$	−0.0133997	−	0.234965i	−0.000598654	−	0.0104975i
$502$	−0.550132	−	0.656214i	−0.0245536	−	0.0292883i
$503$	−5.70991	+	39.7133i	−0.254592	+	1.77073i	0.315284	+	0.948997i	$0.397900\pi$
$503$	−5.70991	+	39.7133i	−0.254592	+	1.77073i	−0.569876	+	0.821731i	$0.693009\pi$
$504$	13.0109	−	4.75821i	0.579553	−	0.211948i
$505$	−33.6578			−1.49775
$506$	0.172812	+	0.635233i	0.00768244	+	0.0282395i
$507$	5.03327	−	21.6297i	0.223535	−	0.960609i
$508$	1.42687	−	4.33152i	0.0633073	−	0.192180i
$509$	4.55249	−	31.6633i	0.201786	−	1.40345i	−0.597196	−	0.802095i	$-0.703719\pi$
$509$	4.55249	−	31.6633i	0.201786	−	1.40345i	0.798982	−	0.601355i	$-0.205372\pi$
$510$	−22.2001	+	11.2505i	−0.983039	+	0.498182i
$511$	−3.62655	−	12.3509i	−0.160429	−	0.546371i
$512$	−9.48199	+	20.5449i	−0.419049	+	0.907964i
$513$	−12.6861	+	0.356578i	−0.560106	+	0.0157433i
$514$	−8.48728	−	2.64320i	−0.374358	−	0.116587i
$515$	−7.28484	+	24.8099i	−0.321008	+	1.09325i
$516$	−2.16401	+	8.09385i	−0.0952654	+	0.356312i
$517$	0.227136	−	0.353431i	0.00998945	−	0.0155439i
$518$	−3.54688	−	5.72216i	−0.155841	−	0.251417i
$519$	−17.9895	−	24.7684i	−0.789651	−	1.08721i
$520$	2.54688	+	0.124725i	0.111688	+	0.00546956i
$521$	43.6252	−	6.27236i	1.91126	−	0.274797i	0.918545	−	0.395317i	$-0.129365\pi$
$521$	43.6252	−	6.27236i	1.91126	−	0.274797i	0.992711	+	0.120520i	$0.0384561\pi$
$522$	2.25147	−	11.8360i	0.0985444	−	0.518047i
$523$	14.9603	+	32.7586i	0.654170	+	1.43243i	0.887857	+	0.460120i	$0.152194\pi$
$523$	14.9603	+	32.7586i	0.654170	+	1.43243i	−0.233687	+	0.972312i	$0.575079\pi$
$524$	22.4510	−	32.5490i	0.980778	−	1.42191i
$525$	0.768157	−	0.995848i	0.0335251	−	0.0434624i
$526$	15.8489	−	23.7987i	0.691044	−	1.03767i
$527$	−6.07836	+	3.90632i	−0.264777	+	0.170162i
$528$	−0.284411	+	0.609375i	−0.0123774	+	0.0265196i
$529$	3.44030	−	22.7412i	0.149578	−	0.988750i
$530$	29.6844	+	14.1460i	1.28941	+	0.614463i
$531$	3.32999	+	29.1009i	0.144509	+	1.26287i
$532$	−4.09066	−	6.84633i	−0.177352	−	0.296826i
$533$	1.54310	−	3.37892i	0.0668392	−	0.146357i
$534$	7.18449	+	2.93428i	0.310903	+	0.126979i
$535$	−17.1125	+	7.81504i	−0.739840	+	0.337874i
$536$	4.11883	−	5.76781i	0.177907	−	0.249131i
$537$	0.331586	−	3.85367i	0.0143090	−	0.166298i
$538$	10.1309	+	9.07200i	0.436776	+	0.391122i
$539$	−0.317952	−	0.275507i	−0.0136952	−	0.0118669i
$540$	−18.6049	−	12.0758i	−0.800626	−	0.519661i
$541$	−5.81967	+	9.05558i	−0.250207	+	0.389330i	−0.943525	−	0.331302i	$-0.892512\pi$
$541$	−5.81967	+	9.05558i	−0.250207	+	0.389330i	0.693317	+	0.720632i	$0.256148\pi$
$542$	−16.6267	−	38.0374i	−0.714180	−	1.63384i
$543$	16.0694	+	9.07803i	0.689602	+	0.389576i
$544$	13.1455	−	23.5036i	0.563609	−	1.00771i
$545$	12.1953	−	10.5673i	0.522390	−	0.452654i
$546$	1.63886	+	0.409653i	0.0701366	+	0.0175315i
$547$	16.8971	−	4.96143i	0.722468	−	0.212136i	0.100230	−	0.994964i	$-0.468042\pi$
$547$	16.8971	−	4.96143i	0.722468	−	0.212136i	0.622237	+	0.782829i	$0.286224\pi$
$548$	7.70598	+	29.8085i	0.329183	+	1.27336i
$549$	−19.7869	−	13.5388i	−0.844484	−	0.577823i
$550$	0.00770156	+	0.0605622i	0.000328395	+	0.00258238i
$551$	−6.93594			−0.295481
$552$	17.6888	−	15.4631i	0.752885	−	0.658152i
$553$	6.74777			0.286945
$554$	−3.50005	−	27.5231i	−0.148703	−	1.16934i
$555$	−3.91211	+	10.0436i	−0.166060	+	0.426328i
$556$	32.5794	−	8.42228i	1.38167	−	0.357184i
$557$	8.08020	−	2.37256i	0.342369	−	0.100529i	−0.106028	−	0.994363i	$-0.533813\pi$
$557$	8.08020	−	2.37256i	0.342369	−	0.100529i	0.448397	+	0.893834i	$0.351995\pi$
$558$	−5.73056	−	2.93676i	−0.242594	−	0.124323i
$559$	−0.772079	+	0.669011i	−0.0326555	+	0.0282961i
$560$	0.908753	−	13.9088i	0.0384018	−	0.587756i
$561$	0.393665	−	0.696840i	0.0166205	−	0.0294206i
$562$	14.4461	+	33.0487i	0.609372	+	1.39407i
$563$	−20.1878	+	31.4128i	−0.850815	+	1.32389i	0.0937594	+	0.995595i	$0.470112\pi$
$563$	−20.1878	+	31.4128i	−0.850815	+	1.32389i	−0.944574	+	0.328299i	$0.893525\pi$
$564$	−14.8887	−	1.77193i	−0.626927	−	0.0746118i
$565$	5.54998	+	4.80908i	0.233489	+	0.202320i
$566$	14.7729	+	13.2287i	0.620950	+	0.556045i
$567$	−10.5313	−	10.2473i	−0.442273	−	0.430346i
$568$	−17.2671	+	24.1799i	−0.724510	+	1.01457i
$569$	−34.3269	+	15.6766i	−1.43906	+	0.657196i	−0.973681	−	0.227917i	$-0.926809\pi$
$569$	−34.3269	+	15.6766i	−1.43906	+	0.657196i	−0.465377	+	0.885113i	$0.654081\pi$
$570$	−4.82789	+	11.8209i	−0.202218	+	0.495123i
$571$	1.03897	−	2.27502i	0.0434794	−	0.0952066i	−0.886646	−	0.462449i	$-0.846971\pi$
$571$	1.03897	−	2.27502i	0.0434794	−	0.0952066i	0.930125	+	0.367242i	$0.119698\pi$
$572$	−0.0703921	+	0.0420591i	−0.00294324	+	0.00175858i
$573$	10.4402	+	29.2749i	0.436146	+	1.22298i
$574$	−18.3299	−	8.73508i	−0.765077	−	0.364595i
$575$	0.608425	−	2.04431i	0.0253731	−	0.0852537i
$576$	23.9969	−	0.385613i	0.999871	−	0.0160672i
$577$	−15.1928	+	9.76385i	−0.632486	+	0.406474i	−0.817229	−	0.576312i	$-0.804491\pi$
$577$	−15.1928	+	9.76385i	−0.632486	+	0.406474i	0.184743	+	0.982787i	$0.440855\pi$
$578$	−4.43931	+	6.66609i	−0.184651	+	0.277273i
$579$	12.5503	+	9.68081i	0.521574	+	0.402321i
$580$	−9.97847	−	6.88275i	−0.414334	−	0.285791i
$581$	7.51073	+	16.4462i	0.311598	+	0.682304i
$582$	29.3217	−	1.19275i	1.21542	−	0.0494413i
$583$	−1.04667	+	0.150489i	−0.0433487	+	0.00623261i
$584$	1.09076	−	22.2732i	0.0451358	−	0.921670i
$585$	−1.05206	−	2.49160i	−0.0434973	−	0.103015i
$586$	−22.7786	−	36.7486i	−0.940977	−	1.51807i
$587$	−1.50900	+	2.34804i	−0.0622829	+	0.0969141i	−0.870998	−	0.491286i	$-0.836527\pi$
$587$	−1.50900	+	2.34804i	−0.0622829	+	0.0969141i	0.808715	+	0.588200i	$0.200163\pi$
$588$	−3.87819	+	14.5052i	−0.159934	+	0.598185i
$589$	−1.04437	+	3.55679i	−0.0430325	+	0.146555i
$590$	28.1372	+	8.76277i	1.15839	+	0.360758i
$591$	−23.8917	+	12.6017i	−0.982774	+	0.518364i
$592$	−2.54924	−	11.3809i	−0.104773	−	0.467752i
$593$	−1.77100	−	6.03146i	−0.0727261	−	0.247682i	0.915104	−	0.403217i	$-0.132108\pi$
$593$	−1.77100	−	6.03146i	−0.0727261	−	0.247682i	−0.987830	+	0.155535i	$0.950290\pi$
$594$	0.713222	−	0.00840889i	0.0292638	−	0.000345021i
$595$	−2.36084	+	16.4200i	−0.0967851	+	0.673155i
$596$	8.87957	+	2.92507i	0.363721	+	0.119816i
$597$	2.60703	+	0.606661i	0.106699	+	0.0248290i
$598$	2.84329	−	0.350973i	0.116271	−	0.0143524i
$599$	−43.1219			−1.76191			−0.880956	−	0.473198i	$-0.843100\pi$
$599$	−43.1219			−1.76191			−0.880956	+	0.473198i	$0.843100\pi$
$600$	1.82340	−	1.19264i	0.0744401	−	0.0486892i
$601$	−3.98054	+	27.6853i	−0.162370	+	1.12931i	0.731781	+	0.681540i	$0.238689\pi$
$601$	−3.98054	+	27.6853i	−0.162370	+	1.12931i	−0.894151	+	0.447766i	$0.852220\pi$
$602$	3.58764	+	4.27945i	0.146221	+	0.174417i
$603$	−7.40692	−	1.28415i	−0.301633	−	0.0522948i
$604$	−16.6663	−	8.27851i	−0.678143	−	0.336848i
$605$	−15.3612	−	17.7278i	−0.624523	−	0.720737i
$606$	−33.3181	−	19.5460i	−1.35346	−	0.794000i
$607$	1.17470	−	4.00065i	0.0476795	−	0.162381i	−0.932212	−	0.361913i	$-0.882124\pi$
$607$	1.17470	−	4.00065i	0.0476795	−	0.162381i	0.979891	+	0.199531i	$0.0639420\pi$
$608$	−2.79963	−	13.5297i	−0.113540	−	0.548703i
$609$	−5.59593	−	5.75984i	−0.226759	−	0.233401i
$610$	−20.5029	+	12.7087i	−0.830137	+	0.514561i
$611$	−1.38173	−	1.19728i	−0.0558990	−	0.0484368i
$612$	−28.5096	−	1.75521i	−1.15243	−	0.0709502i
$613$	−13.5383	+	1.94651i	−0.546806	+	0.0786188i	−0.410181	−	0.912004i	$-0.634535\pi$
$613$	−13.5383	+	1.94651i	−0.546806	+	0.0786188i	−0.136625	+	0.990623i	$0.543625\pi$
$614$	5.49255	+	19.9011i	0.221661	+	0.803143i
$615$	6.45108	+	31.8624i	0.260133	+	1.28482i
$616$	0.223598	+	0.388478i	0.00900902	+	0.0156522i
$617$	39.5493	+	18.0616i	1.59220	+	0.727131i	0.997070	−	0.0765010i	$-0.0243748\pi$
$617$	39.5493	+	18.0616i	1.59220	+	0.727131i	0.595126	+	0.803632i	$0.297102\pi$
$618$	−21.6191	+	20.3290i	−0.869647	+	0.817753i
$619$	1.18233	−	0.759839i	0.0475219	−	0.0305405i	−0.516664	−	0.856188i	$-0.672826\pi$
$619$	1.18233	−	0.759839i	0.0475219	−	0.0305405i	0.564186	+	0.825648i	$0.309190\pi$
$620$	−5.03201	+	4.08066i	−0.202090	+	0.163883i
$621$	−22.9140	−	9.79529i	−0.919508	−	0.393072i
$622$	7.78999	+	3.71230i	0.312350	+	0.148850i
$623$	4.35157	−	2.79658i	0.174342	−	0.112043i
$624$	2.44874	+	1.60250i	0.0980281	+	0.0641515i
$625$	−9.37943	+	20.5381i	−0.375177	+	0.821524i
$626$	4.13813	+	0.664033i	0.165393	+	0.0265401i
$627$	−0.0814829	−	0.402451i	−0.00325411	−	0.0160723i
$628$	36.0419	+	6.38818i	1.43823	+	0.254916i
$629$	1.97541	+	13.7393i	0.0787649	+	0.547822i
$630$	−13.7116	+	5.52789i	−0.546285	+	0.220237i
$631$	−27.8542	−	24.1358i	−1.10886	−	0.960833i	−0.109410	−	0.993997i	$-0.534896\pi$
$631$	−27.8542	−	24.1358i	−1.10886	−	0.960833i	−0.999450	+	0.0331641i	$0.989442\pi$
$632$	11.0417	+	3.83807i	0.439217	+	0.152670i
$633$	−3.97198	+	3.85895i	−0.157872	+	0.153380i
$634$	−1.74645	+	0.763401i	−0.0693603	+	0.0303185i
$635$	−1.37112	+	4.66960i	−0.0544112	+	0.185307i
$636$	21.1698	+	31.2417i	0.839439	+	1.23882i
$637$	−1.38366	+	1.19895i	−0.0548228	+	0.0475042i
$638$	0.389764	+	0.00635797i	0.0154309	+	0.000251715i
$639$	31.0514	+	5.38346i	1.22838	+	0.212966i
$640$	9.39825	−	22.2429i	0.371499	−	0.879227i
$641$	28.3088	+	4.07019i	1.11813	+	0.160763i	0.676506	−	0.736437i	$-0.263493\pi$
$641$	28.3088	+	4.07019i	1.11813	+	0.160763i	0.441624	+	0.897200i	$0.354402\pi$
$642$	−21.4782	−	2.20153i	−0.847679	−	0.0868876i
$643$	−42.5842			−1.67936			−0.839679	−	0.543083i	$-0.817257\pi$
$643$	−42.5842			−1.67936			−0.839679	+	0.543083i	$0.817257\pi$
$644$	−1.66475	−	15.5713i	−0.0656004	−	0.613596i
$645$	2.02639	−	8.70809i	0.0797889	−	0.342881i
$646$	2.07438	+	16.3121i	0.0816152	+	0.641792i
$647$	−0.0597864	+	0.415824i	−0.00235045	+	0.0163477i	−0.990963	−	0.134136i	$-0.957174\pi$
$647$	−0.0597864	+	0.415824i	−0.00235045	+	0.0163477i	0.988612	+	0.150484i	$0.0480832\pi$
$648$	−11.4044	−	22.7583i	−0.448006	−	0.894031i
$649$	−0.909306	+	0.266996i	−0.0356934	+	0.0104805i
$650$	0.265642	+	0.00433324i	0.0104193	+	0.000169964i
$651$	−3.79628	+	2.00235i	−0.148788	+	0.0784783i
$652$	29.3477	−	31.7168i	1.14934	−	1.24213i
$653$	32.9372	+	9.67122i	1.28893	+	0.378464i	0.853186	−	0.521606i	$-0.174667\pi$
$653$	32.9372	+	9.67122i	1.28893	+	0.378464i	0.435744	+	0.900071i	$0.356485\pi$
$654$	18.2090	−	3.37852i	0.712027	−	0.132111i
$655$	−22.8130	+	35.4977i	−0.891378	+	1.38701i
$656$	−25.0258	−	24.7196i	−0.977094	−	0.965137i
$657$	−21.7898	+	9.20056i	−0.850099	+	0.358948i
$658$	−6.66693	+	7.44513i	−0.259904	+	0.290241i
$659$	20.8082	−	2.99176i	0.810570	−	0.116542i	0.275447	−	0.961316i	$-0.411174\pi$
$659$	20.8082	−	2.99176i	0.810570	−	0.116542i	0.535124	+	0.844774i	$0.320265\pi$
$660$	0.282138	−	0.659849i	0.0109822	−	0.0256846i
$661$	33.9022	−	15.4826i	1.31864	−	0.602203i	0.373126	−	0.927781i	$-0.378286\pi$
$661$	33.9022	−	15.4826i	1.31864	−	0.602203i	0.945515	+	0.325577i	$0.105559\pi$
$662$	−15.8642	−	2.54568i	−0.616579	−	0.0989405i
$663$	−2.75783	−	2.12728i	−0.107105	−	0.0826168i
$664$	2.93576	+	31.1838i	0.113930	+	1.21017i
$665$	4.60133	+	7.15980i	0.178432	+	0.277645i
$666$	−9.70523	+	7.67040i	−0.376070	+	0.297222i
$667$	−12.3676	−	5.70305i	−0.478875	−	0.220823i
$668$	−0.171169	−	0.211074i	−0.00662271	−	0.00816670i
$669$	10.2671	−	3.66153i	0.396950	−	0.141563i
$670$	−4.19233	+	6.29521i	−0.161964	+	0.243205i
$671$	0.322244	−	0.705616i	0.0124401	−	0.0272400i
$672$	8.97680	−	13.2407i	0.346288	−	0.510772i
$673$	−19.3282	−	42.3228i	−0.745047	−	1.63142i	−0.775070	−	0.631875i	$-0.782286\pi$
$673$	−19.3282	−	42.3228i	−0.745047	−	1.63142i	0.0300237	−	0.999549i	$-0.490442\pi$
$674$	−1.17138	−	4.24425i	−0.0451199	−	0.163483i
$675$	−1.97845	−	1.19429i	−0.0761505	−	0.0459682i
$676$	−9.88609	−	23.6609i	−0.380234	−	0.910033i
$677$	−0.127143	+	0.146731i	−0.00488651	+	0.00563934i	−0.758188	−	0.652037i	$-0.773915\pi$
$677$	−0.127143	+	0.146731i	−0.00488651	+	0.00563934i	0.753301	+	0.657676i	$0.228460\pi$
$678$	2.70121	+	7.98357i	0.103739	+	0.306607i
$679$	10.5750	−	16.4551i	0.405832	−	0.631487i
$680$	−13.2027	+	25.5261i	−0.506301	+	0.978881i
$681$	−18.1513	−	10.2542i	−0.695558	−	0.392940i
$682$	0.0619486	−	0.198916i	0.00237213	−	0.00761689i
$683$	22.1620	−	19.2035i	0.848004	−	0.734800i	−0.118086	−	0.993003i	$-0.537676\pi$
$683$	22.1620	−	19.2035i	0.848004	−	0.734800i	0.966091	+	0.258203i	$0.0831304\pi$
$684$	−11.6439	+	8.89793i	−0.445215	+	0.340221i
$685$	−9.25660	−	31.5251i	−0.353677	−	1.20451i
$686$	16.8132	+	20.0552i	0.641930	+	0.765713i
$687$	−3.59567	+	9.23123i	−0.137184	+	0.352193i
$688$	3.43654	+	9.04330i	0.131017	+	0.344773i
$689$			4.60175i			0.175313i
$690$	−18.3284	+	17.1083i	−0.697750	+	0.651303i
$691$	35.6045			1.35446			0.677229	−	0.735772i	$-0.263181\pi$
$691$	35.6045			1.35446			0.677229	+	0.735772i	$0.263181\pi$
$692$	−33.5730	−	11.0595i	−1.27625	−	0.420419i
$693$	0.268468	−	0.392365i	0.0101983	−	0.0149047i
$694$	−9.37513	−	11.1829i	−0.355875	−	0.424498i
$695$	−34.4555	+	10.1170i	−1.30697	+	0.383761i
$696$	−5.88078	−	12.6081i	−0.222910	−	0.477907i
$697$	27.4155	+	31.6391i	1.03843	+	1.19842i
$698$	14.1070	+	4.39335i	0.533958	+	0.166291i
$699$	5.81192	+	3.28332i	0.219827	+	0.124186i
$700$	0.0473667	−	1.45148i	0.00179029	−	0.0548608i
$701$	−29.3291	−	18.8487i	−1.10775	−	0.711905i	−0.146945	−	0.989145i	$-0.546944\pi$
$701$	−29.3291	−	18.8487i	−1.10775	−	0.711905i	−0.960801	+	0.277240i	$0.910580\pi$
$702$	0.405495	−	3.07741i	0.0153044	−	0.116149i
$703$	5.38199	+	4.66352i	0.202986	+	0.175888i
$704$	0.144923	+	0.762868i	0.00546198	+	0.0287517i
$705$	15.9417	+	1.37170i	0.600400	+	0.0516611i
$706$	18.8027	−	5.18939i	0.707648	−	0.195305i
$707$	−23.4204	+	10.6957i	−0.880815	+	0.402255i
$708$	22.7644	+	25.0143i	0.855540	+	0.940096i
$709$	16.9129	+	7.72387i	0.635178	+	0.290076i	0.706862	−	0.707351i	$-0.250110\pi$
$709$	16.9129	+	7.72387i	0.635178	+	0.290076i	−0.0716841	+	0.997427i	$0.522837\pi$
$710$	17.5752	−	26.3909i	0.659585	−	0.990434i
$711$	−1.40959	−	12.3185i	−0.0528638	−	0.461979i
$712$	8.71137	−	2.10107i	0.326472	−	0.0787408i
$713$	−4.78679	+	5.48345i	−0.179267	+	0.205357i
$714$	−11.8725	+	14.8833i	−0.444319	+	0.556993i
$715$	0.0736152	−	0.0473096i	0.00275305	−	0.00176928i
$716$	−2.29082	−	3.83402i	−0.0856119	−	0.143284i
$717$	−9.55179	−	7.36787i	−0.356718	−	0.275158i
$718$	−30.5222	−	4.89781i	−1.13908	−	0.182785i
$719$	−16.0781	−	35.2061i	−0.599612	−	1.31297i	−0.929456	−	0.368932i	$-0.879723\pi$
$719$	−16.0781	−	35.2061i	−0.599612	−	1.31297i	0.329844	−	0.944035i	$-0.393004\pi$
$720$	−25.5813	+	1.24653i	−0.953359	+	0.0464555i
$721$	2.81499	+	19.5787i	0.104836	+	0.729148i
$722$	−13.7326	−	12.2972i	−0.511073	−	0.457653i
$723$	−25.8544	−	35.5970i	−0.961536	−	1.32387i
$724$	21.1823	−	2.34331i	0.787233	−	0.0870883i
$725$	−1.06249	−	0.682823i	−0.0394600	−	0.0253594i
$726$	−4.91120	−	26.4695i	−0.182272	−	0.982377i
$727$	13.7929	−	46.9742i	0.511550	−	1.74218i	−0.146507	−	0.989210i	$-0.546803\pi$
$727$	13.7929	−	46.9742i	0.511550	−	1.74218i	0.658056	−	0.752969i	$-0.271379\pi$
$728$	1.81185	−	0.722555i	0.0671517	−	0.0267797i
$729$	−16.5071	+	21.3662i	−0.611375	+	0.791341i
$730$	−0.388139	+	23.7942i	−0.0143657	+	0.880661i
$731$	−3.24381	−	11.0474i	−0.119977	−	0.408603i
$732$	−27.6762	+	0.673907i	−1.02294	+	0.0249083i
$733$	42.9143	+	6.17015i	1.58508	+	0.227900i	0.877796	−	0.479034i	$-0.159013\pi$
$733$	42.9143	+	6.17015i	1.58508	+	0.227900i	0.707280	+	0.706934i	$0.249922\pi$
$734$	−4.54032	−	35.7034i	−0.167586	−	1.31784i
$735$	3.63154	−	15.6060i	0.133952	−	0.575637i
$736$	6.13270	−	26.4271i	0.226054	−	0.974115i
$737$		−	0.243223i		−	0.00895924i
$738$	−12.1174	+	35.2872i	−0.446046	+	1.29894i
$739$	1.42744	−	9.92806i	0.0525092	−	0.365209i	−0.946577	−	0.322477i	$-0.895485\pi$
$739$	1.42744	−	9.92806i	0.0525092	−	0.365209i	0.999087	−	0.0427326i	$-0.0136063\pi$
$740$	3.11511	+	12.0500i	0.114514	+	0.442965i
$741$	−1.78402	+	0.101740i	−0.0655377	+	0.00373751i
$742$	25.1509	+	0.410270i	0.923317	+	0.0150615i
$743$	−11.1926	−	12.9170i	−0.410618	−	0.473878i	0.512338	−	0.858784i	$-0.328779\pi$
$743$	−11.1926	−	12.9170i	−0.410618	−	0.473878i	−0.922956	+	0.384906i	$0.874234\pi$
$744$	−7.35098	+	1.11726i	−0.269500	+	0.0409607i
$745$	−9.57262	−	2.81077i	−0.350714	−	0.102979i
$746$	14.8145	+	33.8914i	0.542396	+	1.24085i
$747$	28.4546	−	17.1469i	1.04110	−	0.627372i
$748$	−0.101616	−	0.918559i	−0.00371546	−	0.0335859i
$749$	−9.42413	+	10.8760i	−0.344350	+	0.397401i
$750$	−23.3009	+	16.3498i	−0.850829	+	0.597012i
$751$	14.5461	−	2.09141i	0.530794	−	0.0763166i	0.128293	−	0.991736i	$-0.459050\pi$
$751$	14.5461	−	2.09141i	0.530794	−	0.0763166i	0.402501	+	0.915420i	$0.368141\pi$
$752$	−15.1442	+	8.39078i	−0.552251	+	0.305980i
$753$	0.208116	+	1.02790i	0.00758417	+	0.0374588i
$754$	0.268778	−	1.67497i	0.00978831	−	0.0609989i
$755$	18.0642	+	8.24963i	0.657423	+	0.300235i
$756$	−16.7835	−	2.49060i	−0.610408	−	0.0905823i
$757$	5.96223	+	9.27742i	0.216701	+	0.337193i	0.932537	−	0.361075i	$-0.117590\pi$
$757$	5.96223	+	9.27742i	0.216701	+	0.337193i	−0.715836	+	0.698269i	$0.753954\pi$
$758$	15.8103	+	7.53437i	0.574257	+	0.273661i
$759$	0.185620	−	0.784616i	0.00673759	−	0.0284797i
$760$	3.45696	+	14.3332i	0.125397	+	0.519918i
$761$	−12.1788	−	18.9505i	−0.441480	−	0.686956i	0.547199	−	0.837002i	$-0.315694\pi$
$761$	−12.1788	−	18.9505i	−0.441480	−	0.686956i	−0.988679	+	0.150046i	$0.952058\pi$
$762$	−4.06904	+	3.82623i	−0.147406	+	0.138610i
$763$	5.12792	−	11.2286i	0.185643	−	0.406501i
$764$	29.5428	+	20.3775i	1.06882	+	0.737231i
$765$	30.4689	+	0.879770i	1.10161	+	0.0318082i
$766$	6.74265	+	24.4306i	0.243622	+	0.882713i
$767$	0.586931	+	4.08219i	0.0211928	+	0.147400i
$768$	22.2204	−	16.5606i	0.801810	−	0.597579i
$769$	13.0932	−	15.1104i	0.472153	−	0.544894i	−0.468856	−	0.883274i	$-0.655334\pi$
$769$	13.0932	−	15.1104i	0.472153	−	0.544894i	0.941009	+	0.338381i	$0.109879\pi$
$770$	−0.252008	−	0.406562i	−0.00908173	−	0.0146515i
$771$	7.58649	+	7.80871i	0.273221	+	0.281224i
$772$	18.2925	+	0.596946i	0.658361	+	0.0214846i
$773$	−1.97119	−	0.578795i	−0.0708989	−	0.0208178i	0.246091	−	0.969247i	$-0.420854\pi$
$773$	−1.97119	−	0.578795i	−0.0708989	−	0.0208178i	−0.316990	+	0.948429i	$0.602672\pi$
$774$	7.06295	−	7.44344i	0.253873	−	0.267549i
$775$	−0.510139	+	0.442038i	−0.0183248	+	0.0158785i
$776$	26.6639	−	20.9113i	0.957180	−	0.750672i
$777$	0.469454	+	8.23194i	0.0168416	+	0.295319i
$778$	20.5350	−	17.2154i	0.736217	−	0.617202i
$779$	21.2599	+	3.05671i	0.761715	+	0.109518i
$780$	−2.66757	−	1.62397i	−0.0955142	−	0.0581476i
$781$			1.01965i			0.0364858i
$782$	−9.71374	+	30.7921i	−0.347363	+	1.10112i
$783$	−9.34599	+	11.4189i	−0.333998	+	0.408080i
$784$	6.15872	+	16.2068i	0.219954	+	0.578813i
$785$	−38.6641	−	5.55905i	−1.37998	−	0.198411i
$786$	−43.1972	+	21.8914i	−1.54079	+	0.780840i
$787$	25.5658	−	7.50680i	0.911323	−	0.267589i	0.207725	−	0.978187i	$-0.433394\pi$
$787$	25.5658	−	7.50680i	0.911323	−	0.267589i	0.703598	+	0.710599i	$0.251576\pi$
$788$	−13.8753	+	27.9338i	−0.494287	+	0.995101i
$789$	−30.9747	+	16.3376i	−1.10273	+	0.581634i
$790$	−11.9105	−	3.70930i	−0.423758	−	0.131971i
$791$	5.39012	+	1.58268i	0.191651	+	0.0562737i
$792$	0.662482	−	0.489344i	0.0235403	−	0.0173881i
$793$	−2.83987	−	1.82507i	−0.100847	−	0.0648103i
$794$	37.5883	−	23.2991i	1.33396	−	0.826855i
$795$	−23.6668	−	32.5851i	−0.839376	−	1.15567i
$796$	2.85185	−	1.19157i	0.101081	−	0.0422341i
$797$	1.07448	+	7.47316i	0.0380600	+	0.264713i	0.999962	−	0.00868030i	$-0.00276306\pi$
$797$	1.07448	+	7.47316i	0.0380600	+	0.264713i	−0.961902	+	0.273393i	$0.911854\pi$
$798$	0.397005	+	9.75965i	0.0140538	+	0.345488i
$799$	18.7433	−	8.55979i	0.663091	−	0.302824i
$800$	0.903096	−	2.34819i	0.0319293	−	0.0830211i
$801$	−6.01437	−	7.35987i	−0.212507	−	0.260048i
$802$	−8.45793	−	5.63260i	−0.298660	−	0.198894i
$803$	−0.413736	−	0.643786i	−0.0146004	−	0.0227187i
$804$	−7.80581	+	3.79709i	−0.275290	+	0.133913i
$805$	2.31758	+	16.5502i	0.0816838	+	0.583317i
$806$	−0.818466	−	0.390038i	−0.0288292	−	0.0137385i
$807$	−5.59467	−	15.6877i	−0.196942	−	0.552235i
$808$	−44.4077	+	4.18070i	−1.56226	+	0.147077i
$809$	4.37897	+	1.99981i	0.153957	+	0.0703096i	0.490903	−	0.871214i	$-0.336667\pi$
$809$	4.37897	+	1.99981i	0.153957	+	0.0703096i	−0.336947	+	0.941524i	$0.609394\pi$
$810$	12.9558	+	23.8767i	0.455222	+	0.838942i
$811$	6.22189	+	13.6240i	0.218480	+	0.478405i	0.986858	−	0.161592i	$-0.0516629\pi$
$811$	6.22189	+	13.6240i	0.218480	+	0.478405i	−0.768378	+	0.639997i	$0.778936\pi$
$812$	−9.13061	−	1.61834i	−0.320422	−	0.0567926i
$813$	−4.35858	+	50.6551i	−0.152862	+	1.77655i
$814$	−0.298166	−	0.267000i	−0.0104507	−	0.00935833i
$815$	−30.1978	+	34.8502i	−1.05778	+	1.22075i
$816$	−27.8931	+	17.6013i	−0.976456	+	0.616170i
$817$	−4.96939	−	3.19363i	−0.173857	−	0.111731i
$818$	0.689809	−	0.301527i	0.0241186	−	0.0105426i
$819$	−1.52384	−	1.39943i	−0.0532474	−	0.0489001i
$820$	27.5525	+	25.4944i	0.962176	+	0.890304i
$821$	−4.41634	−	5.09673i	−0.154131	−	0.177877i	0.673432	−	0.739249i	$-0.264819\pi$
$821$	−4.41634	−	5.09673i	−0.154131	−	0.177877i	−0.827564	+	0.561372i	$0.810274\pi$
$822$	9.14426	−	36.5825i	0.318943	−	1.27596i
$823$	6.63846	+	22.6085i	0.231402	+	0.788084i	0.990548	+	0.137163i	$0.0437986\pi$
$823$	6.63846	+	22.6085i	0.231402	+	0.788084i	−0.759146	+	0.650920i	$0.774383\pi$
$824$	−6.52985	+	33.6387i	−0.227478	+	1.17186i
$825$	0.0271380	−	0.0696719i	0.000944825	−	0.00242566i
$826$	22.3636	−	2.84392i	0.778128	−	0.0989528i
$827$		−	48.7074i		−	1.69372i	−0.531815	−	0.846860i	$-0.678490\pi$
$827$		−	48.7074i		−	1.69372i	0.531815	−	0.846860i	$-0.321510\pi$
$828$	−28.0787	+	6.29191i	−0.975801	+	0.218659i
$829$		−	45.8470i		−	1.59233i	−0.605079	−	0.796165i	$-0.706858\pi$
$829$		−	45.8470i		−	1.59233i	0.605079	−	0.796165i	$-0.293142\pi$
$830$	−4.21663	−	33.1580i	−0.146361	−	1.15093i
$831$	−12.3331	+	31.6631i	−0.427832	+	1.09838i
$832$	3.37581	−	0.151792i	0.117035	−	0.00526242i
$833$	−5.81332	−	19.7984i	−0.201420	−	0.685972i
$834$	−39.9830	−	9.99425i	−1.38450	−	0.346073i
$835$	0.189912	+	0.219171i	0.00657219	+	0.00758471i
$836$	−0.348013	−	0.322017i	−0.0120363	−	0.0111372i
$837$	4.44845	+	6.51207i	0.153761	+	0.225090i
$838$	−6.58536	−	15.0655i	−0.227487	−	0.520428i
$839$	17.0418	+	10.9521i	0.588349	+	0.378109i	0.800683	−	0.599088i	$-0.204470\pi$
$839$	17.0418	+	10.9521i	0.588349	+	0.378109i	−0.212334	+	0.977197i	$0.568107\pi$
$840$	−9.11366	+	14.4348i	−0.314451	+	0.498048i
$841$	13.7099	−	15.8220i	0.472754	−	0.545588i
$842$	26.9123	−	30.0537i	0.927460	−	1.03572i
$843$	3.78695	−	44.0115i	0.130429	−	1.51584i
$844$	−1.11601	+	6.29646i	−0.0384145	+	0.216733i
$845$	11.3679	+	24.8922i	0.391067	+	0.856318i
$846$	14.9843	+	10.6156i	0.515169	+	0.364973i
$847$	−16.3225	−	7.45422i	−0.560847	−	0.256130i
$848$	40.9223	+	14.9769i	1.40528	+	0.514309i
$849$	−8.15811	−	22.8758i	−0.279986	−	0.785094i
$850$	−1.28812	+	2.70302i	−0.0441820	+	0.0927127i
$851$	5.76216	+	12.7409i	0.197524	+	0.436754i
$852$	32.7237	−	15.9182i	1.12110	−	0.545350i
$853$	15.8213	+	24.6185i	0.541713	+	0.842921i	0.998921	−	0.0464382i	$-0.0147870\pi$
$853$	15.8213	+	24.6185i	0.541713	+	0.842921i	−0.457209	+	0.889360i	$0.651151\pi$
$854$	−10.2281	+	15.3586i	−0.350000	+	0.525561i
$855$	12.1095	−	9.89567i	0.414135	−	0.338425i
$856$	−21.6074	+	12.4367i	−0.738525	+	0.425076i
$857$	−7.87293	+	3.59544i	−0.268934	+	0.122818i	−0.545318	−	0.838229i	$-0.683591\pi$
$857$	−7.87293	+	3.59544i	−0.268934	+	0.122818i	0.276384	+	0.961047i	$0.410864\pi$
$858$	0.100346	−	0.00408190i	0.00342576	−	0.000139354i
$859$	1.64522	+	11.4428i	0.0561343	+	0.390423i	0.998448	+	0.0556916i	$0.0177364\pi$
$859$	1.64522	+	11.4428i	0.0561343	+	0.390423i	−0.942314	+	0.334731i	$0.891355\pi$
$860$	−3.98013	−	9.52583i	−0.135721	−	0.324828i
$861$	14.6141	+	20.1211i	0.498048	+	0.685726i
$862$	−17.2856	−	27.8867i	−0.588749	−	0.949823i
$863$	41.2645	+	26.5191i	1.40466	+	0.902721i	0.999931	−	0.0117159i	$-0.00372936\pi$
$863$	41.2645	+	26.5191i	1.40466	+	0.902721i	0.404729	+	0.914437i	$0.367366\pi$
$864$	−26.0470	−	13.6218i	−0.886138	−	0.463422i
$865$	36.1934	+	10.6273i	1.23061	+	0.361340i
$866$	−10.5682	+	33.9343i	−0.359122	+	1.15314i
$867$	8.67610	−	4.57621i	0.294656	−	0.155416i
$868$	−2.20472	+	4.43855i	−0.0748331	+	0.150654i
$869$	0.384911	−	0.113020i	0.0130572	−	0.00383395i
$870$	6.71118	+	13.2429i	0.227530	+	0.448975i
$871$	−1.04768	−	0.150634i	−0.0354994	−	0.00510405i
$872$	14.7778	−	15.4572i	0.500439	−	0.523446i
$873$	−32.2488	−	15.8680i	−1.09146	−	0.537049i
$874$	6.57899	+	15.2027i	0.222538	+	0.514240i
$875$			18.9729i			0.641401i
$876$	−14.2021	+	23.3286i	−0.479845	+	0.788201i
$877$	15.7680	+	2.26710i	0.532447	+	0.0765544i	0.403294	−	0.915070i	$-0.367865\pi$
$877$	15.7680	+	2.26710i	0.532447	+	0.0765544i	0.129153	+	0.991625i	$0.458774\pi$
$878$	21.3739	+	25.4954i	0.721334	+	0.860428i
$879$	3.01491	+	52.8668i	0.101690	+	1.78315i
$880$	−0.181125	−	0.808618i	−0.00610572	−	0.0272585i
$881$	16.4264	−	14.2336i	0.553421	−	0.479542i	−0.332677	−	0.943041i	$-0.607952\pi$
$881$	16.4264	−	14.2336i	0.553421	−	0.479542i	0.886097	+	0.463499i	$0.153406\pi$
$882$	12.6577	−	13.3396i	0.426208	−	0.449167i
$883$	−39.7976	−	11.6856i	−1.33929	−	0.393252i	−0.467877	−	0.883794i	$-0.654981\pi$
$883$	−39.7976	−	11.6856i	−1.33929	−	0.393252i	−0.871418	+	0.490542i	$0.836799\pi$
$884$	−4.01963	−	0.131174i	−0.135195	−	0.00441187i
$885$	−25.1508	−	25.8875i	−0.845436	−	0.870200i
$886$	40.6322	−	25.1859i	1.36506	−	0.846136i
$887$	23.0819	−	26.6379i	0.775014	−	0.894413i	−0.221725	−	0.975109i	$-0.571169\pi$
$887$	23.0819	−	26.6379i	0.775014	−	0.894413i	0.996739	+	0.0806958i	$0.0257142\pi$
$888$	−3.91406	+	13.7374i	−0.131347	+	0.460996i
$889$	0.529823	+	3.68500i	0.0177697	+	0.123591i
$890$	−9.21828	+	2.54417i	−0.308997	+	0.0852809i
$891$	−0.772369	−	0.408142i	−0.0258753	−	0.0136733i
$892$	7.14668	−	10.3611i	0.239289	−	0.346916i
$893$	4.39158	−	9.61622i	0.146959	−	0.321794i
$894$	−7.84372	−	8.34148i	−0.262333	−	0.278981i
$895$	2.57680	+	4.00958i	0.0861328	+	0.134025i
$896$	−0.528646	−	18.4640i	−0.0176608	−	0.616840i
$897$	−3.26478	−	1.28549i	−0.109008	−	0.0429213i
$898$	2.55609	−	5.36378i	0.0852979	−	0.178992i
$899$	2.33021	+	3.62587i	0.0777167	+	0.120930i
$900$	−2.65966	+	0.216739i	−0.0886554	+	0.00722464i
$901$	−47.1762	−	21.5446i	−1.57167	−	0.717756i
$902$	−1.19189	−	0.191260i	−0.0396858	−	0.00636825i
$903$	−1.35721	−	6.70338i	−0.0451652	−	0.223074i
$904$	7.91992	+	5.65567i	0.263413	+	0.188105i
$905$	−22.5111	+	3.23661i	−0.748295	+	0.107589i
$906$	13.0911	+	18.6567i	0.434922	+	0.619828i
$907$	−0.282134	+	0.325600i	−0.00936810	+	0.0108114i	−0.760414	−	0.649438i	$-0.775004\pi$
$907$	−0.282134	+	0.325600i	−0.00936810	+	0.0108114i	0.751046	+	0.660250i	$0.229550\pi$
$908$	−23.9266	+	2.64690i	−0.794032	+	0.0878405i
$909$	24.4182	+	40.5211i	0.809901	+	1.34400i
$910$	−1.90734	+	0.833730i	−0.0632278	+	0.0276379i
$911$	−26.1897	−	7.68998i	−0.867702	−	0.254780i	−0.182564	−	0.983194i	$-0.558440\pi$
$911$	−26.1897	−	7.68998i	−0.867702	−	0.254780i	−0.685138	+	0.728414i	$0.740258\pi$
$912$	−4.90156	+	16.1960i	−0.162307	+	0.536305i
$913$	0.703894	+	0.812337i	0.0232955	+	0.0268844i
$914$	0.896862	−	54.9805i	0.0296656	−	1.81859i
$915$	29.4956	−	1.68209i	0.975094	−	0.0556080i
$916$	2.86314	+	11.0753i	0.0946007	+	0.365938i
$917$	−4.59375	+	31.9502i	−0.151699	+	1.05509i
$918$	29.6505	+	18.5650i	0.978614	+	0.612736i
$919$		−	3.77264i		−	0.124448i	−0.998062	−	0.0622240i	$-0.980181\pi$
$919$		−	3.77264i		−	0.124448i	0.998062	−	0.0622240i	$-0.0198193\pi$
$920$	−5.62122	+	28.4002i	−0.185326	+	0.936325i
$921$	5.73075	−	24.6270i	0.188835	−	0.811489i
$922$	26.1771	−	3.32888i	0.862098	−	0.109631i
$923$	4.39213	+	0.631492i	0.144569	+	0.0207858i
$924$	−0.0133633	−	0.548806i	−0.000439619	−	0.0180544i
$925$	0.365339	+	1.24423i	0.0120123	+	0.0409101i
$926$	−51.7841	−	0.844720i	−1.70173	−	0.0277592i
$927$	35.1541	−	9.22887i	1.15461	−	0.303116i
$928$	−14.0204	−	7.84158i	−0.460242	−	0.257412i
$929$	−10.4412	+	35.5595i	−0.342565	+	1.16667i	0.590523	+	0.807021i	$0.298922\pi$
$929$	−10.4412	+	35.5595i	−0.342565	+	1.16667i	−0.933088	+	0.359649i	$0.882897\pi$
$930$	7.80155	−	1.44751i	0.255823	−	0.0474658i
$931$	−8.90578	−	5.72339i	−0.291875	−	0.187577i
$932$	7.66114	−	0.847520i	0.250949	−	0.0277615i
$933$	−6.21082	−	8.55122i	−0.203333	−	0.279954i
$934$	−9.70966	+	10.8430i	−0.317710	+	0.354795i
$935$	0.140354	+	0.976184i	0.00459007	+	0.0319246i
$936$	−1.69756	−	3.15671i	−0.0554865	−	0.103180i
$937$	−1.25287	−	2.74341i	−0.0409295	−	0.0896232i	0.888063	−	0.459722i	$-0.152051\pi$
$937$	−1.25287	−	2.74341i	−0.0409295	−	0.0896232i	−0.928992	+	0.370099i	$0.879324\pi$
$938$	−0.916699	+	5.71269i	−0.0299313	+	0.186526i
$939$	−4.06434	−	3.13507i	−0.132635	−	0.102309i
$940$	15.8605	−	9.47658i	0.517312	−	0.309092i
$941$	−14.4081	+	9.25953i	−0.469691	+	0.301852i	−0.753993	−	0.656883i	$-0.771875\pi$
$941$	−14.4081	+	9.25953i	−0.469691	+	0.301852i	0.284302	+	0.958735i	$0.408238\pi$
$942$	−35.0456	−	27.9562i	−1.14185	−	0.910861i
$943$	35.3955	+	22.9313i	1.15264	+	0.746747i
$944$	38.2123	+	8.06653i	1.24370	+	0.262543i
$945$	17.9877	+	2.07227i	0.585139	+	0.0674109i
$946$	0.276326	+	0.184021i	0.00898415	+	0.00598304i
$947$	9.11646	+	4.16335i	0.296245	+	0.135291i	0.557993	−	0.829846i	$-0.311572\pi$
$947$	9.11646	+	4.16335i	0.296245	+	0.135291i	−0.261748	+	0.965136i	$0.584299\pi$
$948$	−9.63624	−	10.5886i	−0.312971	−	0.343903i
$949$	−3.02935	+	1.38346i	−0.0983368	+	0.0449089i
$950$	0.408697	+	1.48083i	0.0132599	+	0.0480445i
$951$	2.32578	+	0.200120i	0.0754185	+	0.00648934i
$952$	−1.07530	+	21.9576i	−0.0348508	+	0.711650i
$953$	−16.3017	−	14.1255i	−0.528063	−	0.457569i	0.349565	−	0.936912i	$-0.386329\pi$
$953$	−16.3017	−	14.1255i	−0.528063	−	0.457569i	−0.877628	+	0.479343i	$0.840875\pi$
$954$	−4.50497	−	46.0002i	−0.145854	−	1.48931i
$955$	−32.2192	−	20.7060i	−1.04259	−	0.670031i
$956$	−13.9220	−	0.454323i	−0.450271	−	0.0146939i
$957$	−0.415680	−	0.234829i	−0.0134370	−	0.00759096i
$958$	−14.9737	+	48.0805i	−0.483780	+	1.55341i
$959$	−16.4591	−	18.9948i	−0.531493	−	0.613375i
$960$	−23.1235	+	18.4367i	−0.746309	+	0.595041i
$961$	−27.5340	+	8.08473i	−0.888195	+	0.260798i
$962$	−1.33476	+	1.11899i	−0.0430345	+	0.0360777i
$963$	21.8235	+	14.9324i	0.703254	+	0.481189i
$964$	−48.2510	−	15.8947i	−1.55406	−	0.511933i
$965$	−19.5313			−0.628733
$966$	−7.31694	+	17.7290i	−0.235419	+	0.570422i
$967$			15.2482i			0.490349i	0.969479	+	0.245175i	$0.0788453\pi$
$967$			15.2482i			0.490349i	−0.969479	+	0.245175i	$0.921155\pi$
$968$	−22.4694	−	21.4818i	−0.722195	−	0.690451i
$969$	7.30949	−	18.7658i	0.234815	−	0.602843i
$970$	−27.7115	+	23.2317i	−0.889763	+	0.745926i
$971$	−1.45205	−	4.94523i	−0.0465986	−	0.158700i	0.932907	−	0.360118i	$-0.117263\pi$
$971$	−1.45205	−	4.94523i	−0.0465986	−	0.158700i	−0.979505	+	0.201417i	$0.935445\pi$
$972$	−1.04073	+	31.1595i	−0.0333816	+	0.999443i
$973$	−20.7605	+	17.9891i	−0.665551	+	0.576703i
$974$	7.85776	+	2.44715i	0.251779	+	0.0784116i
$975$	−0.283305	−	0.160047i	−0.00907301	−	0.00512560i
$976$	−25.4727	+	19.3144i	−0.815360	+	0.618240i
$977$	−24.5611	+	38.2178i	−0.785778	+	1.22269i	0.185006	+	0.982737i	$0.440770\pi$
$977$	−24.5611	+	38.2178i	−0.785778	+	1.22269i	−0.970784	+	0.239957i	$0.922867\pi$
$978$	−50.1315	+	16.9618i	−1.60303	+	0.542378i
$979$	0.201385	−	0.232410i	0.00643628	−	0.00742786i
$980$	−7.13289	−	17.0715i	−0.227852	−	0.545329i
$981$	−21.5697	−	7.01572i	−0.688667	−	0.223995i
$982$	57.6751	−	15.9179i	1.84049	−	0.507960i
$983$	−9.71220	−	21.2668i	−0.309771	−	0.678304i	0.689156	−	0.724613i	$-0.257981\pi$
$983$	−9.71220	−	21.2668i	−0.309771	−	0.678304i	−0.998927	+	0.0463089i	$0.985254\pi$
$984$	12.4692	+	41.2376i	0.397503	+	1.31461i
$985$	13.8269	−	30.2767i	0.440562	−	0.964696i
$986$	15.9131	+	10.5974i	0.506777	+	0.337490i
$987$	11.5288	−	4.11147i	0.366965	−	0.130869i
$988$	−1.60262	+	1.29963i	−0.0509863	+	0.0413468i
$989$	−6.23504	−	9.78067i	−0.198263	−	0.311007i
$990$	−0.689561	+	0.544986i	−0.0219157	+	0.0173208i
$991$	1.37477	+	2.13918i	0.0436710	+	0.0679534i	0.862403	−	0.506223i	$-0.168959\pi$
$991$	1.37477	+	2.13918i	0.0436710	+	0.0679534i	−0.818732	+	0.574176i	$0.805322\pi$
$992$	−6.13231	+	6.00901i	−0.194701	+	0.190786i
$993$	15.5813	+	12.0188i	0.494458	+	0.381405i
$994$	3.84300	−	23.9489i	0.121893	−	0.759612i
$995$	−3.00026	+	1.37017i	−0.0951147	+	0.0434374i
$996$	15.0816	−	35.2721i	0.477880	−	1.11764i
$997$	−9.10176	+	1.30864i	−0.288256	+	0.0414449i	−0.284926	−	0.958550i	$-0.591969\pi$
$997$	−9.10176	+	1.30864i	−0.288256	+	0.0414449i	−0.00332972	+	0.999994i	$0.501060\pi$
$998$	−34.2754	−	30.6927i	−1.08497	−	0.971561i
$999$	14.9299	−	2.57665i	0.472360	−	0.0815215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.x.a.35.5	✓	920
3.2	odd	2	inner	552.2.x.a.35.88	yes	920
8.3	odd	2	inner	552.2.x.a.35.63	yes	920
23.2	even	11	inner	552.2.x.a.347.30	yes	920
24.11	even	2	inner	552.2.x.a.35.30	yes	920
69.2	odd	22	inner	552.2.x.a.347.63	yes	920
184.163	odd	22	inner	552.2.x.a.347.88	yes	920
552.347	even	22	inner	552.2.x.a.347.5	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.x.a.35.5	✓	920	1.1	even	1	trivial
552.2.x.a.35.30	yes	920	24.11	even	2	inner
552.2.x.a.35.63	yes	920	8.3	odd	2	inner
552.2.x.a.35.88	yes	920	3.2	odd	2	inner
552.2.x.a.347.5	yes	920	552.347	even	22	inner
552.2.x.a.347.30	yes	920	23.2	even	11	inner
552.2.x.a.347.63	yes	920	69.2	odd	22	inner
552.2.x.a.347.88	yes	920	184.163	odd	22	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.x (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40292 + 0.178405i) q^{2} +(1.61394 + 0.628649i) q^{3} +(1.93634 - 0.500576i) q^{4} +(-2.04785 + 0.601303i) q^{5} +(-2.37637 - 0.594005i) q^{6} +(-1.23389 + 1.06917i) q^{7} +(-2.62722 + 1.04772i) q^{8} +(2.20960 + 2.02920i) q^{9} +O(q^{10})\)	\(q+(-1.40292 + 0.178405i) q^{2} +(1.61394 + 0.628649i) q^{3} +(1.93634 - 0.500576i) q^{4} +(-2.04785 + 0.601303i) q^{5} +(-2.37637 - 0.594005i) q^{6} +(-1.23389 + 1.06917i) q^{7} +(-2.62722 + 1.04772i) q^{8} +(2.20960 + 2.02920i) q^{9} +(2.76568 - 1.20892i) q^{10} +(-0.0524767 + 0.0816554i) q^{11} +(3.43983 + 0.409381i) q^{12} +(0.319231 + 0.276615i) q^{13} +(1.54030 - 1.72009i) q^{14} +(-3.68311 - 0.316911i) q^{15} +(3.49885 - 1.93857i) q^{16} +(-4.33039 + 1.97762i) q^{17} +(-3.46191 - 2.45259i) q^{18} +(-1.01461 + 2.22169i) q^{19} +(-3.66434 + 2.18943i) q^{20} +(-2.66356 + 0.949898i) q^{21} +(0.0590526 - 0.123918i) q^{22} +(-3.63595 + 3.12727i) q^{23} +(-4.89882 + 0.0393578i) q^{24} +(-0.374145 + 0.240448i) q^{25} +(-0.497203 - 0.331115i) q^{26} +(2.29051 + 4.66407i) q^{27} +(-1.85404 + 2.68794i) q^{28} +(1.17969 + 2.58317i) q^{29} +(5.22364 - 0.212488i) q^{30} +(1.50230 - 0.215997i) q^{31} +(-4.56274 + 3.34387i) q^{32} +(-0.136027 + 0.0987974i) q^{33} +(5.72235 - 3.54700i) q^{34} +(1.88393 - 2.93145i) q^{35} +(5.29432 + 2.82316i) q^{36} +(0.821456 - 2.79762i) q^{37} +(1.02705 - 3.29786i) q^{38} +(0.341325 + 0.647123i) q^{39} +(4.75015 - 3.72533i) q^{40} +(-2.47755 - 8.43777i) q^{41} +(3.56729 - 1.80782i) q^{42} +(-0.344197 + 2.39395i) q^{43} +(-0.0607382 + 0.184381i) q^{44} +(-5.74510 - 2.82686i) q^{45} +(4.54301 - 5.03598i) q^{46} -4.32833 q^{47} +(6.86561 - 0.929192i) q^{48} +(-0.616846 + 4.29026i) q^{49} +(0.481996 - 0.404078i) q^{50} +(-8.23221 + 0.469470i) q^{51} +(0.756606 + 0.375822i) q^{52} +(7.13420 + 8.23330i) q^{53} +(-4.04549 - 6.13466i) q^{54} +(0.0583648 - 0.198772i) q^{55} +(2.12151 - 4.10173i) q^{56} +(-3.03419 + 2.94784i) q^{57} +(-2.11586 - 3.41350i) q^{58} +(7.37884 + 6.39380i) q^{59} +(-7.29041 + 1.23003i) q^{60} +(-7.91046 + 1.13735i) q^{61} +(-2.06906 + 0.571044i) q^{62} +(-4.89598 - 0.141368i) q^{63} +(5.80457 - 5.50518i) q^{64} +(-0.820065 - 0.374511i) q^{65} +(0.173208 - 0.162872i) q^{66} +(-2.10802 + 1.35474i) q^{67} +(-7.39516 + 5.99704i) q^{68} +(-7.83416 + 2.76150i) q^{69} +(-2.12001 + 4.44868i) q^{70} +(8.83727 - 5.67937i) q^{71} +(-7.93114 - 3.01612i) q^{72} +(-3.27521 + 7.17171i) q^{73} +(-0.653322 + 4.07138i) q^{74} +(-0.755004 + 0.152863i) q^{75} +(-0.852514 + 4.80985i) q^{76} +(-0.0225532 - 0.156861i) q^{77} +(-0.594301 - 0.846965i) q^{78} +(-3.12348 - 2.70651i) q^{79} +(-5.99945 + 6.07377i) q^{80} +(0.764680 + 8.96746i) q^{81} +(4.98114 + 11.3955i) q^{82} +(3.11988 - 10.6253i) q^{83} +(-4.68208 + 3.17264i) q^{84} +(7.67883 - 6.65374i) q^{85} +(0.0557868 - 3.41991i) q^{86} +(0.280049 + 4.91069i) q^{87} +(0.0523159 - 0.269507i) q^{88} +(-3.13600 - 0.450889i) q^{89} +(8.56421 + 2.94089i) q^{90} -0.689646 q^{91} +(-5.47501 + 7.87555i) q^{92} +(2.56040 + 0.595809i) q^{93} +(6.07228 - 0.772198i) q^{94} +(0.741865 - 5.15978i) q^{95} +(-9.46610 + 2.52844i) q^{96} +(-11.4952 + 3.37528i) q^{97} +(0.0999771 - 6.12892i) q^{98} +(-0.281648 + 0.0739400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9}+O(q^{10}) \) 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9	\( 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9} - 14 q^{10} - 6 q^{12} - 30 q^{16} - 16 q^{18} - 52 q^{19} - 32 q^{22} - 26 q^{24} - 112 q^{25} - 30 q^{27} - 34 q^{28} + 11 q^{30} - 30 q^{33} - 88 q^{34} - 18 q^{36} + 124 q^{40} - 3 q^{42} - 36 q^{43} - 110 q^{46} + 32 q^{49} - 30 q^{51} + 90 q^{52} - 39 q^{54} - 6 q^{57} - 68 q^{58} + 13 q^{60} + 28 q^{64} - 46 q^{66} - 100 q^{67} - 92 q^{70} + 29 q^{72} - 36 q^{73} + 14 q^{75} - 50 q^{76} - 86 q^{78} - 2 q^{81} - 12 q^{82} - 151 q^{84} - 42 q^{88} - 196 q^{90} - 136 q^{91} - 68 q^{94} - 175 q^{96} - 36 q^{97} - 54 q^{99}+O(q^{100}) \) 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9 - 14 * q^10 - 6 * q^12 - 30 * q^16 - 16 * q^18 - 52 * q^19 - 32 * q^22 - 26 * q^24 - 112 * q^25 - 30 * q^27 - 34 * q^28 + 11 * q^30 - 30 * q^33 - 88 * q^34 - 18 * q^36 + 124 * q^40 - 3 * q^42 - 36 * q^43 - 110 * q^46 + 32 * q^49 - 30 * q^51 + 90 * q^52 - 39 * q^54 - 6 * q^57 - 68 * q^58 + 13 * q^60 + 28 * q^64 - 46 * q^66 - 100 * q^67 - 92 * q^70 + 29 * q^72 - 36 * q^73 + 14 * q^75 - 50 * q^76 - 86 * q^78 - 2 * q^81 - 12 * q^82 - 151 * q^84 - 42 * q^88 - 196 * q^90 - 136 * q^91 - 68 * q^94 - 175 * q^96 - 36 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

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