LMFDB - Embedded newform 552.2.x.a.35.12

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			35.12
Character	$\chi$	$=$	552.35
Dual form			552.2.x.a.347.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28905 - 0.581685i) q^{2} +(-0.724881 - 1.57307i) q^{3} +(1.32328 + 1.49964i) q^{4} +(0.385158 - 0.113093i) q^{5} +(0.0193752 + 2.44941i) q^{6} +(-0.150483 + 0.130394i) q^{7} +(-0.833459 - 2.70284i) q^{8} +(-1.94909 + 2.28058i) q^{9} +O(q^{10})$	\(q+(-1.28905 - 0.581685i) q^{2} +(-0.724881 - 1.57307i) q^{3} +(1.32328 + 1.49964i) q^{4} +(0.385158 - 0.113093i) q^{5} +(0.0193752 + 2.44941i) q^{6} +(-0.150483 + 0.130394i) q^{7} +(-0.833459 - 2.70284i) q^{8} +(-1.94909 + 2.28058i) q^{9} +(-0.562271 - 0.0782590i) q^{10} +(-1.50072 + 2.33517i) q^{11} +(1.39981 - 3.16868i) q^{12} +(1.46514 + 1.26955i) q^{13} +(0.269828 - 0.0805505i) q^{14} +(-0.457096 - 0.523901i) q^{15} +(-0.497835 + 3.96890i) q^{16} +(-5.46399 + 2.49532i) q^{17} +(3.83905 - 1.80601i) q^{18} +(-0.550420 + 1.20525i) q^{19} +(0.679271 + 0.427944i) q^{20} +(0.314201 + 0.142200i) q^{21} +(3.29283 - 2.13719i) q^{22} +(-1.77510 - 4.45523i) q^{23} +(-3.64760 + 3.27033i) q^{24} +(-4.07071 + 2.61609i) q^{25} +(-1.15015 - 2.48876i) q^{26} +(5.00037 + 1.41291i) q^{27} +(-0.394676 - 0.0531214i) q^{28} +(2.27022 + 4.97108i) q^{29} +(0.284473 + 0.941219i) q^{30} +(-7.69520 + 1.10640i) q^{31} +(2.95038 - 4.82651i) q^{32} +(4.76122 + 0.668018i) q^{33} +(8.49483 - 0.0382640i) q^{34} +(-0.0432130 + 0.0672408i) q^{35} +(-5.99925 + 0.0949157i) q^{36} +(-1.03608 + 3.52855i) q^{37} +(1.41059 - 1.23346i) q^{38} +(0.935038 - 3.22504i) q^{39} +(-0.626684 - 0.946762i) q^{40} +(0.737616 + 2.51209i) q^{41} +(-0.322305 - 0.366068i) q^{42} +(0.603362 - 4.19647i) q^{43} +(-5.48778 + 0.839551i) q^{44} +(-0.492792 + 1.09881i) q^{45} +(-0.303356 + 6.77554i) q^{46} +10.3020 q^{47} +(6.60422 - 2.09385i) q^{48} +(-0.990561 + 6.88951i) q^{49} +(6.76908 - 1.00439i) q^{50} +(7.88606 + 6.78642i) q^{51} +(0.0349291 + 3.87715i) q^{52} +(3.98112 + 4.59445i) q^{53} +(-5.62384 - 4.72995i) q^{54} +(-0.313924 + 1.06913i) q^{55} +(0.477856 + 0.298053i) q^{56} +(2.29493 - 0.00781571i) q^{57} +(-0.0348122 - 7.72851i) q^{58} +(2.26806 + 1.96528i) q^{59} +(0.180794 - 1.37875i) q^{60} +(12.8744 - 1.85106i) q^{61} +(10.5631 + 3.04998i) q^{62} +(-0.00406868 - 0.597338i) q^{63} +(-6.61069 + 4.50541i) q^{64} +(0.707886 + 0.323281i) q^{65} +(-5.74886 - 3.63064i) q^{66} +(-6.04275 + 3.88344i) q^{67} +(-10.9725 - 4.89199i) q^{68} +(-5.72164 + 6.02186i) q^{69} +(0.0948166 - 0.0615401i) q^{70} +(-0.954427 + 0.613373i) q^{71} +(7.78853 + 3.36732i) q^{72} +(-2.19756 + 4.81199i) q^{73} +(3.38806 - 3.94580i) q^{74} +(7.06607 + 4.50716i) q^{75} +(-2.53581 + 0.769460i) q^{76} +(-0.0786593 - 0.547087i) q^{77} +(-3.08126 + 3.61333i) q^{78} +(-6.79900 - 5.89137i) q^{79} +(0.257108 + 1.58495i) q^{80} +(-1.40207 - 8.89012i) q^{81} +(0.510424 - 3.66726i) q^{82} +(0.477157 - 1.62505i) q^{83} +(0.202529 + 0.659359i) q^{84} +(-1.82230 + 1.57903i) q^{85} +(-3.21879 + 5.05848i) q^{86} +(6.17422 - 7.17466i) q^{87} +(7.56237 + 2.10994i) q^{88} +(-7.02729 - 1.01037i) q^{89} +(1.27439 - 1.12977i) q^{90} -0.386020 q^{91} +(4.33227 - 8.55754i) q^{92} +(7.31856 + 11.3031i) q^{93} +(-13.2798 - 5.99254i) q^{94} +(-0.0756936 + 0.526461i) q^{95} +(-9.73112 - 1.14250i) q^{96} +(-11.3768 + 3.34052i) q^{97} +(5.28440 - 8.30470i) q^{98} +(-2.40048 - 7.97396i) 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 $

$2$	−1.28905	−	0.581685i	−0.911494	−	0.411314i
$2$	−1.28905	−	0.581685i	−0.911494	−	0.411314i
$3$	−0.724881	−	1.57307i	−0.418510	−	0.908212i
$3$	−0.724881	−	1.57307i	−0.418510	−	0.908212i
$4$	1.32328	+	1.49964i	0.661642	+	0.749820i
$5$	0.385158	−	0.113093i	0.172248	−	0.0505765i	−0.194471	−	0.980908i	$-0.562299\pi$
$5$	0.385158	−	0.113093i	0.172248	−	0.0505765i	0.366719	+	0.930332i	$0.380481\pi$
$6$	0.0193752	+	2.44941i	0.00790989	+	0.999969i
$7$	−0.150483	+	0.130394i	−0.0568772	+	0.0492843i	−0.682836	−	0.730572i	$-0.739253\pi$
$7$	−0.150483	+	0.130394i	−0.0568772	+	0.0492843i	0.625958	+	0.779856i	$0.284708\pi$
$8$	−0.833459	−	2.70284i	−0.294672	−	0.955598i
$9$	−1.94909	+	2.28058i	−0.649698	+	0.760192i
$10$	−0.562271	−	0.0782590i	−0.177806	−	0.0247477i
$11$	−1.50072	+	2.33517i	−0.452484	+	0.704079i	−0.990294	−	0.138987i	$-0.955615\pi$
$11$	−1.50072	+	2.33517i	−0.452484	+	0.704079i	0.537810	+	0.843066i	$0.319252\pi$
$12$	1.39981	−	3.16868i	0.404091	−	0.914719i
$13$	1.46514	+	1.26955i	0.406356	+	0.352110i	0.833929	−	0.551871i	$-0.186086\pi$
$13$	1.46514	+	1.26955i	0.406356	+	0.352110i	−0.427573	+	0.903981i	$0.640631\pi$
$14$	0.269828	−	0.0805505i	0.0721145	−	0.0215280i
$15$	−0.457096	−	0.523901i	−0.118022	−	0.135271i
$16$	−0.497835	+	3.96890i	−0.124459	+	0.992225i
$17$	−5.46399	+	2.49532i	−1.32521	+	0.605204i	−0.947214	−	0.320602i	$-0.896115\pi$
$17$	−5.46399	+	2.49532i	−1.32521	+	0.605204i	−0.377998	+	0.925806i	$0.623388\pi$
$18$	3.83905	−	1.80601i	0.904873	−	0.425681i
$19$	−0.550420	+	1.20525i	−0.126275	+	0.276504i	−0.962202	−	0.272337i	$-0.912203\pi$
$19$	−0.550420	+	1.20525i	−0.126275	+	0.276504i	0.835927	+	0.548841i	$0.184931\pi$
$20$	0.679271	+	0.427944i	0.151890	+	0.0956912i
$21$	0.314201	+	0.142200i	0.0685643	+	0.0310305i
$22$	3.29283	−	2.13719i	0.702034	−	0.455651i
$23$	−1.77510	−	4.45523i	−0.370133	−	0.928979i
$23$	−1.77510	−	4.45523i	−0.370133	−	0.928979i
$24$	−3.64760	+	3.27033i	−0.744563	+	0.667553i
$25$	−4.07071	+	2.61609i	−0.814142	+	0.523217i
$26$	−1.15015	−	2.48876i	−0.225564	−	0.488086i
$27$	5.00037	+	1.41291i	0.962321	+	0.271915i
$28$	−0.394676	−	0.0531214i	−0.0745867	−	0.0100390i
$29$	2.27022	+	4.97108i	0.421569	+	0.923107i	0.994620	+	0.103588i	$0.0330322\pi$
$29$	2.27022	+	4.97108i	0.421569	+	0.923107i	−0.573051	+	0.819519i	$0.694240\pi$
$30$	0.284473	+	0.941219i	0.0519374	+	0.171842i
$31$	−7.69520	+	1.10640i	−1.38210	+	0.198716i	−0.792939	−	0.609300i	$-0.791450\pi$
$31$	−7.69520	+	1.10640i	−1.38210	+	0.198716i	−0.589160	+	0.808016i	$0.700541\pi$
$32$	2.95038	−	4.82651i	0.521559	−	0.853215i
$33$	4.76122	+	0.668018i	0.828822	+	0.116287i
$34$	8.49483	−	0.0382640i	1.45685	−	0.00656222i
$35$	−0.0432130	+	0.0672408i	−0.00730433	+	0.0113658i
$36$	−5.99925	+	0.0949157i	−0.999875	+	0.0158193i
$37$	−1.03608	+	3.52855i	−0.170330	+	0.580090i	0.829439	+	0.558597i	$0.188660\pi$
$37$	−1.03608	+	3.52855i	−0.170330	+	0.580090i	−0.999769	+	0.0214932i	$0.993158\pi$
$38$	1.41059	−	1.23346i	0.228829	−	0.200093i
$39$	0.935038	−	3.22504i	0.149726	−	0.516419i
$40$	−0.626684	−	0.946762i	−0.0990875	−	0.149696i
$41$	0.737616	+	2.51209i	0.115196	+	0.392323i	0.996825	−	0.0796206i	$-0.0253709\pi$
$41$	0.737616	+	2.51209i	0.115196	+	0.392323i	−0.881629	+	0.471943i	$0.843553\pi$
$42$	−0.322305	−	0.366068i	−0.0497327	−	0.0564855i
$43$	0.603362	−	4.19647i	0.0920118	−	0.639956i	−0.890669	−	0.454652i	$-0.849764\pi$
$43$	0.603362	−	4.19647i	0.0920118	−	0.639956i	0.982681	−	0.185304i	$-0.0593271\pi$
$44$	−5.48778	+	0.839551i	−0.827315	+	0.126567i
$45$	−0.492792	+	1.09881i	−0.0734612	+	0.163801i
$46$	−0.303356	+	6.77554i	−0.0447274	+	0.998999i
$47$	10.3020			1.50271			0.751353	−	0.659901i	$-0.229402\pi$
$47$	10.3020			1.50271			0.751353	+	0.659901i	$0.229402\pi$
$48$	6.60422	−	2.09385i	0.953238	−	0.302222i
$49$	−0.990561	+	6.88951i	−0.141509	+	0.984215i
$50$	6.76908	−	1.00439i	0.957292	−	0.142042i
$51$	7.88606	+	6.78642i	1.10427	+	0.950290i
$52$	0.0349291	+	3.87715i	0.00484379	+	0.537665i
$53$	3.98112	+	4.59445i	0.546848	+	0.631097i	0.960146	−	0.279499i	$-0.0901685\pi$
$53$	3.98112	+	4.59445i	0.546848	+	0.631097i	−0.413297	+	0.910596i	$0.635623\pi$
$54$	−5.62384	−	4.72995i	−0.765308	−	0.643665i
$55$	−0.313924	+	1.06913i	−0.0423295	+	0.144161i
$56$	0.477856	+	0.298053i	0.0638561	+	0.0398290i
$57$	2.29493	−	0.00781571i	0.303971	−	0.00103522i
$58$	−0.0348122	−	7.72851i	−0.00457106	−	1.01480i
$59$	2.26806	+	1.96528i	0.295276	+	0.255858i	0.789881	−	0.613260i	$-0.210142\pi$
$59$	2.26806	+	1.96528i	0.295276	+	0.255858i	−0.494606	+	0.869117i	$0.664688\pi$
$60$	0.180794	−	1.37875i	0.0233405	−	0.177996i
$61$	12.8744	−	1.85106i	1.64840	−	0.237005i	0.745393	−	0.666625i	$-0.232262\pi$
$61$	12.8744	−	1.85106i	1.64840	−	0.237005i	0.903010	+	0.429620i	$0.141353\pi$
$62$	10.5631	+	3.04998i	1.34151	+	0.387348i
$63$	−0.00406868	−	0.597338i	−0.000512605	−	0.0752575i
$64$	−6.61069	+	4.50541i	−0.826337	+	0.563176i
$65$	0.707886	+	0.323281i	0.0878024	+	0.0400980i
$66$	−5.74886	−	3.63064i	−0.707636	−	0.446901i
$67$	−6.04275	+	3.88344i	−0.738239	+	0.474438i	−0.854938	−	0.518730i	$-0.826405\pi$
$67$	−6.04275	+	3.88344i	−0.738239	+	0.474438i	0.116699	+	0.993167i	$0.462769\pi$
$68$	−10.9725	−	4.89199i	−1.33061	−	0.593241i
$69$	−5.72164	+	6.02186i	−0.688805	+	0.724947i
$70$	0.0948166	−	0.0615401i	0.0113327	−	0.00735545i
$71$	−0.954427	+	0.613373i	−0.113270	+	0.0727940i	−0.596049	−	0.802948i	$-0.703264\pi$
$71$	−0.954427	+	0.613373i	−0.113270	+	0.0727940i	0.482779	+	0.875742i	$0.339627\pi$
$72$	7.78853	+	3.36732i	0.917887	+	0.396843i
$73$	−2.19756	+	4.81199i	−0.257205	+	0.563201i	−0.993549	−	0.113407i	$-0.963824\pi$
$73$	−2.19756	+	4.81199i	−0.257205	+	0.563201i	0.736343	+	0.676608i	$0.236551\pi$
$74$	3.38806	−	3.94580i	0.393854	−	0.458690i
$75$	7.06607	+	4.50716i	0.815919	+	0.520442i
$76$	−2.53581	+	0.769460i	−0.290877	+	0.0882631i
$77$	−0.0786593	−	0.547087i	−0.00896405	−	0.0623464i
$78$	−3.08126	+	3.61333i	−0.348884	+	0.409129i
$79$	−6.79900	−	5.89137i	−0.764948	−	0.662831i	0.182333	−	0.983237i	$-0.441635\pi$
$79$	−6.79900	−	5.89137i	−0.764948	−	0.662831i	−0.947280	+	0.320406i	$0.896181\pi$
$80$	0.257108	+	1.58495i	0.0287455	+	0.177203i
$81$	−1.40207	−	8.89012i	−0.155785	−	0.987791i
$82$	0.510424	−	3.66726i	0.0563669	−	0.404982i
$83$	0.477157	−	1.62505i	0.0523748	−	0.178372i	−0.929152	−	0.369699i	$-0.879461\pi$
$83$	0.477157	−	1.62505i	0.0523748	−	0.178372i	0.981526	+	0.191327i	$0.0612790\pi$
$84$	0.202529	+	0.659359i	0.0220978	+	0.0719419i
$85$	−1.82230	+	1.57903i	−0.197656	+	0.171270i
$86$	−3.21879	+	5.05848i	−0.347091	+	0.545470i
$87$	6.17422	−	7.17466i	0.661946	−	0.769204i
$88$	7.56237	+	2.10994i	0.806151	+	0.224921i
$89$	−7.02729	−	1.01037i	−0.744891	−	0.107099i	−0.240590	−	0.970627i	$-0.577341\pi$
$89$	−7.02729	−	1.01037i	−0.744891	−	0.107099i	−0.504301	+	0.863528i	$0.668250\pi$
$90$	1.27439	−	1.12977i	0.134333	−	0.119088i
$91$	−0.386020			−0.0404659
$92$	4.33227	−	8.55754i	0.451671	−	0.892185i
$93$	7.31856	+	11.3031i	0.758899	+	1.17207i
$94$	−13.2798	−	5.99254i	−1.36971	−	0.618083i
$95$	−0.0756936	+	0.526461i	−0.00776600	+	0.0540137i
$96$	−9.73112	−	1.14250i	−0.993178	−	0.116606i
$97$	−11.3768	+	3.34052i	−1.15514	+	0.339178i	−0.802540	−	0.596598i	$-0.796519\pi$
$97$	−11.3768	+	3.34052i	−1.15514	+	0.339178i	−0.352595	+	0.935776i	$0.614701\pi$
$98$	5.28440	−	8.30470i	0.533805	−	0.838902i
$99$	−2.40048	−	7.97396i	−0.241257	−	0.801414i
$100$	−9.30990	−	2.64277i	−0.930990	−	0.264277i
$101$	−11.3348	−	3.32820i	−1.12786	−	0.331169i	−0.335992	−	0.941865i	$-0.609072\pi$
$101$	−11.3348	−	3.32820i	−1.12786	−	0.331169i	−0.791865	+	0.610696i	$0.790890\pi$
$102$	−6.21794	−	13.3352i	−0.615668	−	1.32038i
$103$	6.94571	−	10.8077i	0.684381	−	1.06492i	−0.309112	−	0.951026i	$-0.600032\pi$
$103$	6.94571	−	10.8077i	0.684381	−	1.06492i	0.993493	−	0.113892i	$-0.0363318\pi$
$104$	2.21026	−	5.01815i	0.216734	−	0.492070i
$105$	0.137099	+	0.0192355i	0.0133795	+	0.00187719i
$106$	−2.45932	−	8.23822i	−0.238870	−	0.800167i
$107$	−4.71984	+	0.678611i	−0.456285	+	0.0656038i	−0.366625	−	0.930369i	$-0.619487\pi$
$107$	−4.71984	+	0.678611i	−0.456285	+	0.0656038i	−0.0896593	+	0.995972i	$0.528578\pi$
$108$	4.49805	+	9.36843i	0.432825	+	0.901478i
$109$	1.86623	−	0.852276i	0.178752	−	0.0816333i	−0.324029	−	0.946047i	$-0.605038\pi$
$109$	1.86623	−	0.852276i	0.178752	−	0.0816333i	0.502781	+	0.864414i	$0.332310\pi$
$110$	1.02656	−	1.19555i	0.0978785	−	0.113991i
$111$	6.30169	−	0.927962i	0.598130	−	0.0880782i
$112$	−0.442605	−	0.662166i	−0.0418223	−	0.0625688i
$113$	−2.13417	−	3.32083i	−0.200766	−	0.312397i	0.726243	−	0.687439i	$-0.241265\pi$
$113$	−2.13417	−	3.32083i	−0.200766	−	0.312397i	−0.927008	+	0.375041i	$0.877629\pi$
$114$	−2.96282	−	1.32485i	−0.277494	−	0.124084i
$115$	−1.18754	−	1.51521i	−0.110739	−	0.141294i
$116$	−4.45069	+	9.98267i	−0.413236	+	0.926867i
$117$	−5.75100	+	0.866890i	−0.531680	+	0.0801440i
$118$	−1.78046	−	3.85263i	−0.163904	−	0.354664i
$119$	0.496862	−	1.08797i	0.0455472	−	0.0997345i
$120$	−1.03505	+	1.67211i	−0.0944868	+	0.152642i
$121$	1.36873	+	2.99710i	0.124430	+	0.272463i
$122$	−17.6725	−	5.10276i	−1.59999	−	0.461982i
$123$	3.41701	−	2.98129i	0.308101	−	0.268814i
$124$	−11.8422	−	10.0759i	−1.06346	−	0.904846i
$125$	−2.58637	+	2.98483i	−0.231332	+	0.266971i
$126$	−0.342218	+	0.772363i	−0.0304872	+	0.0688076i
$127$	−5.83939	+	9.08627i	−0.518162	+	0.806276i	−0.997449	−	0.0713823i	$-0.977259\pi$
$127$	−5.83939	+	9.08627i	−0.518162	+	0.806276i	0.479287	+	0.877658i	$0.340895\pi$
$128$	11.1422	−	1.96235i	0.984843	−	0.173448i
$129$	−7.03871	+	2.09281i	−0.619724	+	0.184262i
$130$	−0.724451	−	0.828491i	−0.0635385	−	0.0726634i
$131$	−10.4203	+	9.02922i	−0.910424	+	0.788887i	−0.977952	−	0.208831i	$-0.933034\pi$
$131$	−10.4203	+	9.02922i	−0.910424	+	0.788887i	0.0675282	+	0.997717i	$0.478489\pi$
$132$	5.29866	+	8.02409i	0.461190	+	0.698407i
$133$	−0.0743290	−	0.253141i	−0.00644514	−	0.0219501i
$134$	10.0483	−	1.49096i	0.868043	−	0.128799i
$135$	2.08572	−	0.0213103i	0.179510	−	0.00183410i
$136$	11.2985	+	12.6885i	0.968835	+	1.08803i
$137$		−	15.5926i		−	1.33217i	−0.745877	−	0.666084i	$-0.767969\pi$
$137$		−	15.5926i		−	1.33217i	0.745877	−	0.666084i	$-0.232031\pi$
$138$	10.8783	−	4.43426i	0.926022	−	0.377470i
$139$	−11.0747			−0.939347			−0.469674	−	0.882840i	$-0.655628\pi$
$139$	−11.0747			−0.939347			−0.469674	+	0.882840i	$0.655628\pi$
$140$	−0.158020	+	0.0241748i	−0.0133551	+	0.00204314i
$141$	−7.46775	−	16.2058i	−0.628898	−	1.36478i
$142$	1.58709	−	0.235491i	0.133186	−	0.0197619i
$143$	−5.16337	+	1.51610i	−0.431783	+	0.126783i
$144$	−8.08105	−	8.87111i	−0.673421	−	0.739259i
$145$	1.43658	+	1.65791i	0.119302	+	0.137682i
$146$	5.63182	−	4.92459i	0.466093	−	0.407562i
$147$	11.5557	−	3.43585i	0.953099	−	0.283384i
$148$	−6.66258	+	3.11554i	−0.547661	+	0.256096i
$149$	3.88735	+	2.49825i	0.318464	+	0.204664i	0.690100	−	0.723714i	$-0.257567\pi$
$149$	3.88735	+	2.49825i	0.318464	+	0.204664i	−0.371636	+	0.928379i	$0.621203\pi$
$150$	−6.48675	−	9.92017i	−0.529641	−	0.809978i
$151$	−8.07078	−	6.99337i	−0.656791	−	0.569113i	0.261410	−	0.965228i	$-0.415813\pi$
$151$	−8.07078	−	6.99337i	−0.656791	−	0.569113i	−0.918201	+	0.396115i	$0.870358\pi$
$152$	3.71636	+	0.483170i	0.301436	+	0.0391903i
$153$	4.95906	−	17.3247i	0.400916	−	1.40062i
$154$	−0.216837	+	0.750976i	−0.0174732	+	0.0605154i
$155$	−2.83874	+	1.29641i	−0.228013	+	0.104130i
$156$	6.07371	−	2.86542i	0.486286	−	0.229417i
$157$	18.3860	+	8.39662i	1.46737	+	0.670123i	0.979250	−	0.202656i	$-0.0649574\pi$
$157$	18.3860	+	8.39662i	1.46737	+	0.670123i	0.488115	+	0.872779i	$0.337685\pi$
$158$	5.33731	+	11.5491i	0.424614	+	0.918800i
$159$	4.34156	−	9.59301i	0.344308	−	0.760775i
$160$	0.590520	−	2.19264i	0.0466847	−	0.173343i
$161$	0.848056	+	0.438973i	0.0668362	+	0.0345959i
$162$	−3.36392	+	12.2753i	−0.264295	+	0.964442i
$163$	20.4526	−	13.1441i	1.60197	−	1.02952i	0.635721	−	0.771919i	$-0.280703\pi$
$163$	20.4526	−	13.1441i	1.60197	−	1.02952i	0.966250	−	0.257606i	$-0.0829336\pi$
$164$	−2.79115	+	4.43037i	−0.217952	+	0.345954i
$165$	1.90937	−	0.281166i	0.148644	−	0.0218888i
$166$	−1.56034	+	1.81721i	−0.121106	+	0.141043i
$167$	3.66062	+	8.01563i	0.283267	+	0.620268i	0.996763	−	0.0803905i	$-0.0256167\pi$
$167$	3.66062	+	8.01563i	0.283267	+	0.620268i	−0.713496	+	0.700659i	$0.752889\pi$
$168$	0.122469	−	0.967753i	0.00944871	−	0.0746638i
$169$	−1.31522	−	9.14755i	−0.101171	−	0.703657i
$170$	3.26752	−	0.975440i	0.250608	−	0.0748128i
$171$	−1.67585	−	3.60442i	−0.128155	−	0.275637i
$172$	7.09161	−	4.64830i	0.540730	−	0.354430i
$173$	−15.3096	−	9.83889i	−1.16397	−	0.748037i	−0.191596	−	0.981474i	$-0.561366\pi$
$173$	−15.3096	−	9.83889i	−1.16397	−	0.748037i	−0.972372	+	0.233437i	$0.925003\pi$
$174$	−12.1323	+	5.65702i	−0.919744	+	0.428857i
$175$	0.271450	−	0.924473i	0.0205197	−	0.0698836i
$176$	−8.52093	−	7.11873i	−0.642289	−	0.536595i
$177$	1.44745	−	4.99241i	0.108797	−	0.375252i
$178$	8.47079	+	5.39009i	0.634912	+	0.404004i
$179$	0.563828	+	1.92022i	0.0421425	+	0.143524i	0.977877	−	0.209181i	$-0.0670799\pi$
$179$	0.563828	+	1.92022i	0.0421425	+	0.143524i	−0.935734	+	0.352706i	$0.885262\pi$
$180$	−2.29992	+	0.715028i	−0.171426	+	0.0532950i
$181$	−8.56209	−	1.23104i	−0.636415	−	0.0915027i	−0.183447	−	0.983030i	$-0.558726\pi$
$181$	−8.56209	−	1.23104i	−0.636415	−	0.0915027i	−0.452968	+	0.891527i	$0.649635\pi$
$182$	0.497598	+	0.224542i	0.0368844	+	0.0166442i
$183$	−12.2443	−	18.9106i	−0.905124	−	1.39791i
$184$	−10.5623	+	8.51105i	−0.778663	+	0.627443i
$185$			1.47622i			0.108534i
$186$	−2.85913	−	18.8273i	−0.209642	−	1.38048i
$187$	2.37293	−	16.5041i	0.173526	−	1.20690i
$188$	13.6325	+	15.4493i	0.994254	+	1.12676i
$189$	−0.936705	+	0.439399i	−0.0681352	+	0.0319616i
$190$	0.403807	−	0.634603i	0.0292952	−	0.0460389i
$191$	14.7985	+	17.0784i	1.07078	+	1.23575i	0.970579	+	0.240782i	$0.0774039\pi$
$191$	14.7985	+	17.0784i	1.07078	+	1.23575i	0.100203	+	0.994967i	$0.468051\pi$
$192$	11.8793	+	7.13319i	0.857314	+	0.514794i
$193$	−2.78412	−	0.817490i	−0.200405	−	0.0588443i	0.179989	−	0.983669i	$-0.442394\pi$
$193$	−2.78412	−	0.817490i	−0.200405	−	0.0588443i	−0.380395	+	0.924824i	$0.624212\pi$
$194$	16.6083	+	2.31161i	1.19241	+	0.165964i
$195$	−0.00459044	−	1.34789i	−0.000328728	−	0.0965247i
$196$	−11.6426	+	7.63129i	−0.831612	+	0.545092i
$197$	−9.23933	+	10.6628i	−0.658275	+	0.759690i	−0.982494	−	0.186292i	$-0.940353\pi$
$197$	−9.23933	+	10.6628i	−0.658275	+	0.759690i	0.324220	+	0.945982i	$0.394898\pi$
$198$	−1.54400	+	11.6751i	−0.109727	+	0.829716i
$199$	−1.04293	+	0.149951i	−0.0739316	+	0.0106298i	−0.179181	−	0.983816i	$-0.557345\pi$
$199$	−1.04293	+	0.149951i	−0.0739316	+	0.0106298i	0.105250	+	0.994446i	$0.466436\pi$
$200$	10.4636	+	8.82208i	0.739891	+	0.623815i
$201$	10.4892	+	6.69063i	0.739851	+	0.471921i
$202$	12.6752	+	10.8835i	0.891821	+	0.765761i
$203$	−0.989829	−	0.452040i	−0.0694724	−	0.0317270i
$204$	0.258313	+	20.8066i	0.0180856	+	1.45675i
$205$	0.568197	+	0.884132i	0.0396846	+	0.0617505i
$206$	−15.2400	+	9.89146i	−1.06182	+	0.689171i
$207$	13.6203	+	4.63541i	0.946677	+	0.322183i
$208$	−5.76811	+	5.18296i	−0.399947	+	0.359374i
$209$	−1.98844	−	3.09407i	−0.137543	−	0.214021i
$210$	−0.165538	−	0.104544i	−0.0114232	−	0.00721420i
$211$	−2.06460	+	4.52085i	−0.142133	+	0.311228i	−0.967289	−	0.253677i	$-0.918360\pi$
$211$	−2.06460	+	4.52085i	−0.142133	+	0.311228i	0.825156	+	0.564905i	$0.191087\pi$
$212$	−1.62187	+	12.0500i	−0.111391	+	0.827598i
$213$	1.65672	+	1.05676i	0.113517	+	0.0724078i
$214$	6.47884	+	1.87070i	0.442884	+	0.127879i
$215$	−0.242200	−	1.68454i	−0.0165179	−	0.114885i
$216$	−0.348724	−	14.6928i	−0.0237277	−	0.999718i
$217$	1.01373	−	1.16990i	0.0688163	−	0.0794182i
$218$	−2.90141	+	0.0130691i	−0.196508	+	0.000885148i
$219$	9.16256	−	0.0312044i	0.619149	−	0.00210860i
$220$	−2.01872	+	0.943987i	−0.136102	+	0.0636436i
$221$	−11.1734	−	3.28082i	−0.751607	−	0.220692i
$222$	−8.66295	−	2.46941i	−0.581419	−	0.165736i
$223$	−14.6503	+	12.6946i	−0.981057	+	0.850091i	−0.988704	−	0.149880i	$-0.952111\pi$
$223$	−14.6503	+	12.6946i	−0.981057	+	0.850091i	0.00764686	+	0.999971i	$0.497566\pi$
$224$	0.185367	+	1.11102i	0.0123854	+	0.0742331i
$225$	1.96801	−	14.3826i	0.131201	−	0.958838i
$226$	0.819365	+	5.52212i	0.0545034	+	0.367326i
$227$	2.00667	+	0.288516i	0.133187	+	0.0191495i	0.208586	−	0.978004i	$-0.433114\pi$
$227$	2.00667	+	0.288516i	0.133187	+	0.0191495i	−0.0753987	+	0.997153i	$0.524023\pi$
$228$	3.04857	+	3.43123i	0.201897	+	0.227239i
$229$		−	15.6797i		−	1.03614i	−0.855337	−	0.518071i	$-0.826650\pi$
$229$		−	15.6797i		−	1.03614i	0.855337	−	0.518071i	$-0.173350\pi$
$230$	0.649423	+	2.64396i	0.0428217	+	0.174338i
$231$	−0.803587	+	0.520310i	−0.0528722	+	0.0342339i
$232$	11.5439	−	10.2792i	0.757895	−	0.674864i
$233$	−11.3416	−	1.63068i	−0.743014	−	0.106829i	−0.239597	−	0.970873i	$-0.577015\pi$
$233$	−11.3416	−	1.63068i	−0.743014	−	0.106829i	−0.503418	+	0.864043i	$0.667924\pi$
$234$	7.91756	+	2.22781i	0.517587	+	0.145636i
$235$	3.96791	−	1.16508i	0.258838	−	0.0760016i
$236$	0.0540707	+	6.00189i	0.00351970	+	0.390690i
$237$	−4.33906	+	14.9658i	−0.281852	+	0.972136i
$238$	−1.27334	+	1.11343i	−0.0825382	+	0.0721732i
$239$	−10.4534	−	3.06941i	−0.676177	−	0.198543i	−0.0744251	−	0.997227i	$-0.523712\pi$
$239$	−10.4534	−	3.06941i	−0.676177	−	0.198543i	−0.601752	+	0.798683i	$0.705530\pi$
$240$	2.30687	−	1.55335i	0.148908	−	0.100268i
$241$	24.4070	+	15.6854i	1.57219	+	1.01039i	0.978637	+	0.205596i	$0.0659134\pi$
$241$	24.4070	+	15.6854i	1.57219	+	1.01039i	0.593558	+	0.804792i	$0.297723\pi$
$242$	−0.0209885	−	4.65957i	−0.00134919	−	0.299528i
$243$	−12.9684	+	8.64983i	−0.831926	+	0.554887i
$244$	19.8125	+	16.8575i	1.26836	+	1.07919i
$245$	0.397629	+	2.76557i	0.0254036	+	0.176686i
$246$	−6.13886	+	1.85540i	−0.391399	+	0.118296i
$247$	−2.33657	+	1.06708i	−0.148672	+	0.0678964i
$248$	9.40407	+	19.8768i	0.597159	+	1.26218i
$249$	−2.90219	+	0.427366i	−0.183919	+	0.0270832i
$250$	5.07018	−	2.34313i	0.320667	−	0.148193i
$251$	−8.30479	−	12.9225i	−0.524193	−	0.815661i	0.473690	−	0.880692i	$-0.342922\pi$
$251$	−8.30479	−	12.9225i	−0.524193	−	0.815661i	−0.997883	+	0.0650308i	$0.979285\pi$
$252$	0.890407	−	0.796550i	0.0560904	−	0.0501779i
$253$	13.0676	+	2.54090i	0.821554	+	0.159745i
$254$	12.8126	−	8.31594i	0.803934	−	0.521789i
$255$	3.80487	+	1.72199i	0.238270	+	0.107835i
$256$	−15.5043	−	3.95171i	−0.969020	−	0.246982i
$257$	−6.21776	−	2.83956i	−0.387853	−	0.177127i	0.211938	−	0.977283i	$-0.432022\pi$
$257$	−6.21776	−	2.83956i	−0.387853	−	0.177127i	−0.599791	+	0.800156i	$0.704750\pi$
$258$	10.2906	+	1.39657i	0.640664	+	0.0869469i
$259$	−0.304191	−	0.666085i	−0.0189015	−	0.0413885i
$260$	0.451930	+	1.48937i	0.0280275	+	0.0923665i
$261$	−15.7618	−	4.51170i	−0.975631	−	0.279267i
$262$	18.6844	−	5.57777i	1.15433	−	0.344596i
$263$	7.80719	−	9.00998i	0.481412	−	0.555579i	−0.462139	−	0.886808i	$-0.652918\pi$
$263$	7.80719	−	9.00998i	0.481412	−	0.555579i	0.943550	+	0.331229i	$0.107463\pi$
$264$	−2.16273	−	13.4256i	−0.133107	−	0.826288i
$265$	2.05296	+	1.31935i	0.126112	+	0.0810473i
$266$	−0.0514349	+	0.369547i	−0.00315368	+	0.0226584i
$267$	3.50457	+	11.7868i	0.214476	+	0.721341i
$268$	−13.8200	−	3.92305i	−0.844193	−	0.239638i
$269$	9.73466	+	11.2344i	0.593533	+	0.684974i	0.970458	−	0.241270i	$-0.0775640\pi$
$269$	9.73466	+	11.2344i	0.593533	+	0.684974i	−0.376925	+	0.926244i	$0.623019\pi$
$270$	−2.70099	−	1.18576i	−0.164377	−	0.0721632i
$271$	3.32100	+	11.3103i	0.201736	+	0.687050i	0.996757	+	0.0804683i	$0.0256416\pi$
$271$	3.32100	+	11.3103i	0.201736	+	0.687050i	−0.795021	+	0.606582i	$0.792540\pi$
$272$	−7.18351	−	22.9283i	−0.435564	−	1.39023i
$273$	0.279819	+	0.607236i	0.0169354	+	0.0367516i
$274$	−9.07000	+	20.0996i	−0.547939	+	1.21426i
$275$		−	13.4318i		−	0.809968i
$276$	−16.6020	−	0.611767i	−0.999322	−	0.0368240i
$277$		−	6.12252i		−	0.367866i	−0.982939	−	0.183933i	$-0.941117\pi$
$277$		−	6.12252i		−	0.367866i	0.982939	−	0.183933i	$-0.0588830\pi$
$278$	14.2759	+	6.44201i	0.856209	+	0.386366i
$279$	12.4754	−	19.7060i	0.746885	−	1.17977i
$280$	0.217757	+	0.0607555i	0.0130135	+	0.00363084i
$281$	2.39282	+	8.14921i	0.142744	+	0.486141i	0.999566	−	0.0294718i	$-0.00938254\pi$
$281$	2.39282	+	8.14921i	0.142744	+	0.486141i	−0.856822	+	0.515613i	$0.827564\pi$
$282$	0.199604	+	25.2339i	0.0118862	+	1.50266i
$283$	10.4348	+	12.0424i	0.620283	+	0.715845i	0.975761	−	0.218840i	$-0.0702272\pi$
$283$	10.4348	+	12.0424i	0.620283	+	0.715845i	−0.355477	+	0.934685i	$0.615682\pi$
$284$	−2.18282	−	0.619629i	−0.129526	−	0.0367682i
$285$	0.883028	−	0.262550i	0.0523060	−	0.0155521i
$286$	7.53772	+	1.04913i	0.445715	+	0.0620363i
$287$	−0.438560	−	0.281846i	−0.0258874	−	0.0166368i
$288$	5.25667	+	16.1359i	0.309752	+	0.950817i
$289$	12.4959	−	14.4211i	0.735055	−	0.848299i
$290$	−0.887445	−	2.97276i	−0.0521126	−	0.174566i
$291$	13.5017	+	15.4750i	0.791482	+	0.907158i
$292$	−10.1242	+	3.07208i	−0.592477	+	0.179780i
$293$	5.06078	+	11.0816i	0.295654	+	0.647392i	0.997916	−	0.0645269i	$-0.0205538\pi$
$293$	5.06078	+	11.0816i	0.295654	+	0.647392i	−0.702262	+	0.711918i	$0.747827\pi$
$294$	−16.8944	−	2.29281i	−0.985304	−	0.133719i
$295$	1.09582	+	0.500443i	0.0638010	+	0.0291369i
$296$	10.4006	−	0.140553i	0.604525	−	0.00816947i
$297$	−10.8035	+	9.55630i	−0.626885	+	0.554513i
$298$	−3.55778	−	5.48157i	−0.206097	−	0.317539i
$299$	3.05537	−	8.78109i	0.176697	−	0.507824i
$300$	2.59131	+	16.5608i	0.149609	+	0.956139i
$301$	0.456400	+	0.710172i	0.0263064	+	0.0409336i
$302$	6.33568	+	13.7094i	0.364577	+	0.788890i
$303$	2.98091	+	20.2430i	0.171249	+	1.16293i
$304$	−4.50951	−	2.78458i	−0.258638	−	0.159707i
$305$	4.74935	−	2.16895i	0.271947	−	0.124194i
$306$	−16.4700	+	19.4477i	−0.941525	+	1.11175i
$307$	0.121325	+	0.843831i	0.00692436	+	0.0481600i	0.992991	−	0.118193i	$-0.0377101\pi$
$307$	0.121325	+	0.843831i	0.00692436	+	0.0481600i	−0.986066	+	0.166353i	$0.946801\pi$
$308$	0.716345	−	0.841913i	0.0408175	−	0.0479724i
$309$	−22.0361	−	3.09176i	−1.25359	−	0.175884i
$310$	4.41337	−	0.0198795i	0.250663	−	0.00112908i
$311$	−23.0740	−	14.8288i	−1.30841	−	0.840861i	−0.314305	−	0.949322i	$-0.601772\pi$
$311$	−23.0740	−	14.8288i	−1.30841	−	0.840861i	−0.994101	+	0.108460i	$0.965408\pi$
$312$	−9.49608	+	0.160676i	−0.537609	+	0.00909651i
$313$	27.0988	+	7.95693i	1.53171	+	0.449752i	0.935575	−	0.353128i	$-0.114882\pi$
$313$	27.0988	+	7.95693i	1.53171	+	0.449752i	0.596140	+	0.802880i	$0.296700\pi$
$314$	−18.8163	−	21.5185i	−1.06186	−	1.21436i
$315$	−0.0691215	−	0.229609i	−0.00389456	−	0.0129370i
$316$	−0.162089	−	17.9920i	−0.00911822	−	1.01213i
$317$	14.6150	−	4.29134i	0.820858	−	0.241026i	0.155772	−	0.987793i	$-0.450213\pi$
$317$	14.6150	−	4.29134i	0.820858	−	0.241026i	0.665085	+	0.746767i	$0.268395\pi$
$318$	−11.1766	+	9.84042i	−0.626751	+	0.551823i
$319$	−15.0153	−	2.15887i	−0.840693	−	0.120873i
$320$	−2.03663	+	2.48291i	−0.113851	+	0.138799i
$321$	4.48883	+	6.93273i	0.250542	+	0.386947i
$322$	−0.837841	−	1.05916i	−0.0466910	−	0.0590246i
$323$		−	7.95896i		−	0.442848i
$324$	11.4766	−	13.8668i	0.637591	−	0.770375i
$325$	−9.28541	−	1.33504i	−0.515062	−	0.0740547i
$326$	−34.0101	+	5.04638i	−1.88364	+	0.279493i
$327$	−2.69348	−	2.31790i	−0.148950	−	0.128180i
$328$	6.17501	−	4.08738i	0.340958	−	0.225688i
$329$	−1.55028	+	1.34332i	−0.0854696	+	0.0740599i
$330$	−2.62482	−	0.748215i	−0.144491	−	0.0411879i
$331$	13.0971	+	3.84564i	0.719879	+	0.211376i	0.621097	−	0.783734i	$-0.286687\pi$
$331$	13.0971	+	3.84564i	0.719879	+	0.211376i	0.0987819	+	0.995109i	$0.468505\pi$
$332$	3.06840	−	1.43484i	0.168400	−	0.0787469i
$333$	−6.02772	−	9.24033i	−0.330317	−	0.506367i
$334$	−0.0561330	−	12.4619i	−0.00307146	−	0.681882i
$335$	−1.88822	+	2.17913i	−0.103165	+	0.119058i
$336$	−0.720796	+	1.17624i	−0.0393227	+	0.0641692i
$337$	−0.971241	−	6.75513i	−0.0529068	−	0.367975i	−0.999025	−	0.0441529i	$-0.985941\pi$
$337$	−0.971241	−	6.75513i	−0.0529068	−	0.367975i	0.946118	−	0.323822i	$-0.104968\pi$
$338$	−3.62561	+	12.5567i	−0.197207	+	0.682992i
$339$	−3.67688	+	5.76440i	−0.199701	+	0.313079i
$340$	−4.77939	−	0.643282i	−0.259199	−	0.0348869i
$341$	8.96471	−	19.6300i	0.485466	−	1.06302i
$342$	0.0636087	+	5.62109i	0.00343957	+	0.303954i
$343$	−1.50284	−	2.33847i	−0.0811460	−	0.126266i
$344$	−11.8453	+	1.86680i	−0.638654	+	0.100651i
$345$	−1.52271	+	2.96644i	−0.0819799	+	0.159708i
$346$	14.0117	+	21.5882i	0.753272	+	1.16059i
$347$	7.59929	+	11.8247i	0.407952	+	0.634785i	0.983058	−	0.183293i	$-0.0586758\pi$
$347$	7.59929	+	11.8247i	0.407952	+	0.634785i	−0.575107	+	0.818078i	$0.695039\pi$
$348$	18.9296	−	0.235011i	1.01474	−	0.0125979i
$349$	10.0859	+	4.60609i	0.539887	+	0.246558i	0.666645	−	0.745376i	$-0.267730\pi$
$349$	10.0859	+	4.60609i	0.539887	+	0.246558i	−0.126758	+	0.991934i	$0.540457\pi$
$350$	−0.887664	+	1.03379i	−0.0474476	+	0.0552584i
$351$	5.53247	+	8.41833i	0.295301	+	0.449337i
$352$	6.84301	+	14.1329i	0.364734	+	0.753285i
$353$	−13.1468	+	1.89023i	−0.699735	+	0.100607i	−0.482996	−	0.875623i	$-0.660451\pi$
$353$	−13.1468	+	1.89023i	−0.699735	+	0.100607i	−0.216740	+	0.976229i	$0.569542\pi$
$354$	−4.76984	+	5.59348i	−0.253514	+	0.297290i
$355$	−0.298237	+	0.344184i	−0.0158288	+	0.0182674i
$356$	−7.78391	−	11.8754i	−0.412546	−	0.629395i
$357$	−2.07163	+	0.00705520i	−0.109642	+	0.000373401i
$358$	0.390164	−	2.80323i	0.0206208	−	0.148155i
$359$	−35.4181	−	10.3997i	−1.86930	−	0.548875i	−0.998345	−	0.0575063i	$-0.981685\pi$
$359$	−35.4181	−	10.3997i	−1.86930	−	0.548875i	−0.870952	−	0.491369i	$-0.836497\pi$
$360$	3.38063	+	0.416127i	0.178175	+	0.0219318i
$361$	11.2927	+	13.0325i	0.594352	+	0.685919i
$362$	10.3209	+	6.56732i	0.542453	+	0.345170i
$363$	3.72247	−	4.32564i	0.195379	−	0.227037i
$364$	−0.510814	−	0.578890i	−0.0267739	−	0.0303421i
$365$	−0.302208	+	2.10190i	−0.0158183	+	0.110019i
$366$	4.78347	+	31.4990i	0.250036	+	1.64648i
$367$		−	0.463450i		−	0.0241919i	−0.999927	−	0.0120960i	$-0.996150\pi$
$367$		−	0.463450i		−	0.0241919i	0.999927	−	0.0120960i	$-0.00385036\pi$
$368$	18.5660	−	4.82721i	0.967822	−	0.251636i
$369$	−7.16670	−	3.21411i	−0.373084	−	0.167320i
$370$	0.858696	−	1.90292i	0.0446415	−	0.0989280i
$371$	−1.19818	−	0.172272i	−0.0622064	−	0.00894392i
$372$	−7.26600	+	25.9324i	−0.376725	+	1.34453i
$373$	−9.01629	−	30.7067i	−0.466846	−	1.58993i	−0.770690	−	0.637210i	$-0.780089\pi$
$373$	−9.01629	−	30.7067i	−0.466846	−	1.58993i	0.303845	−	0.952722i	$-0.401730\pi$
$374$	−12.6590	+	19.8943i	−0.654582	+	1.02871i
$375$	6.57016	+	1.90489i	0.339281	+	0.0983682i
$376$	−8.58632	−	27.8448i	−0.442806	−	1.43598i
$377$	−2.98485	+	10.1655i	−0.153728	+	0.523549i
$378$	1.46305	−	0.0215394i	0.0752511	−	0.00110787i
$379$	−26.9071	−	17.2921i	−1.38212	−	0.888238i	−0.382759	−	0.923848i	$-0.625026\pi$
$379$	−26.9071	−	17.2921i	−1.38212	−	0.888238i	−0.999366	+	0.0356106i	$0.988662\pi$
$380$	−0.889665	+	0.583144i	−0.0456388	+	0.0299147i
$381$	18.5262	+	2.59930i	0.949126	+	0.133166i
$382$	−9.14173	−	30.6229i	−0.467732	−	1.56680i
$383$	4.56444	+	31.7464i	0.233232	+	1.62216i	0.683971	+	0.729509i	$0.260251\pi$
$383$	4.56444	+	31.7464i	0.233232	+	1.62216i	−0.450739	+	0.892656i	$0.648840\pi$
$384$	−11.1637	−	16.1050i	−0.569695	−	0.821856i
$385$	−0.0921677	−	0.201819i	−0.00469730	−	0.0102857i
$386$	3.11334	+	2.67326i	0.158465	+	0.136066i
$387$	8.39437	+	9.55533i	0.426710	+	0.485725i
$388$	−20.0643	−	12.6406i	−1.01861	−	0.641728i
$389$	24.0864	−	15.4794i	1.22123	−	0.784836i	0.238727	−	0.971087i	$-0.423270\pi$
$389$	24.0864	−	15.4794i	1.22123	−	0.784836i	0.982502	+	0.186250i	$0.0596336\pi$
$390$	−0.778132	+	1.74017i	−0.0394023	+	0.0881169i
$391$	20.8163	+	19.9139i	1.05273	+	1.00709i
$392$	19.4468	−	3.06479i	0.982213	−	0.154795i
$393$	21.7570	+	9.84670i	1.09750	+	0.496700i
$394$	18.1123	−	8.37041i	0.912484	−	0.421695i
$395$	−3.28496	−	1.50019i	−0.165284	−	0.0754828i
$396$	8.78155	−	14.1517i	0.441289	−	0.711149i
$397$	9.54874	−	4.36076i	0.479238	−	0.218860i	−0.161124	−	0.986934i	$-0.551512\pi$
$397$	9.54874	−	4.36076i	0.479238	−	0.218860i	0.640361	+	0.768074i	$0.278785\pi$
$398$	1.43161	+	0.413365i	0.0717604	+	0.0207201i
$399$	−0.344329	+	0.300422i	−0.0172380	+	0.0150399i
$400$	−8.35644	−	17.4586i	−0.417822	−	0.872931i
$401$	22.9388	+	19.8766i	1.14551	+	0.992591i	0.999995	+	0.00323522i	$0.00102981\pi$
$401$	22.9388	+	19.8766i	1.14551	+	0.992591i	0.145516	+	0.989356i	$0.453516\pi$
$402$	−9.62923	−	14.7259i	−0.480262	−	0.734463i
$403$	−12.6792	−	8.14841i	−0.631595	−	0.405901i
$404$	−10.0081	−	21.4023i	−0.497921	−	1.06480i
$405$	−1.54542	−	3.26554i	−0.0767927	−	0.162266i
$406$	1.01299	+	1.15847i	0.0502739	+	0.0574938i
$407$	−6.68489	−	7.71478i	−0.331358	−	0.382407i
$408$	11.7699	−	26.9710i	0.582698	−	1.33526i
$409$	−25.5840	+	7.51214i	−1.26505	+	0.371451i	−0.844371	−	0.535759i	$-0.820025\pi$
$409$	−25.5840	+	7.51214i	−1.26505	+	0.371451i	−0.420677	+	0.907211i	$0.638207\pi$
$410$	−0.218146	−	1.47020i	−0.0107735	−	0.0726080i
$411$	−24.5283	+	11.3028i	−1.20989	+	0.557526i
$412$	25.3989	−	3.88565i	1.25131	−	0.191432i
$413$	−0.597564			−0.0294042
$414$	−14.8609	−	13.8980i	−0.730372	−	0.683049i
$415$		−	0.679862i		−	0.0333731i
$416$	10.4502	−	3.32586i	0.512364	−	0.163063i
$417$	8.02787	+	17.4213i	0.393127	+	0.853126i
$418$	0.763415	+	5.14504i	0.0373398	+	0.251652i
$419$	−2.69233	−	9.16924i	−0.131529	−	0.447947i	0.867221	−	0.497923i	$-0.165904\pi$
$419$	−2.69233	−	9.16924i	−0.131529	−	0.447947i	−0.998750	+	0.0499760i	$0.984086\pi$
$420$	0.152574	+	0.231053i	0.00744487	+	0.0112742i
$421$	27.2192	−	23.5856i	1.32658	−	1.14949i	0.349428	−	0.936963i	$-0.386376\pi$
$421$	27.2192	−	23.5856i	1.32658	−	1.14949i	0.977155	−	0.212527i	$-0.0681695\pi$
$422$	5.29108	−	4.62664i	0.257566	−	0.225221i
$423$	−20.0796	+	23.4946i	−0.976305	+	1.14235i
$424$	9.09998	−	14.5896i	0.441934	−	0.708534i
$425$	15.7144	−	24.4520i	0.762258	−	1.18610i
$426$	−1.52090	−	2.32590i	−0.0736876	−	0.112690i
$427$	−1.69601	+	1.95730i	−0.0820758	+	0.0947206i
$428$	−7.26337	−	6.18007i	−0.351088	−	0.298725i
$429$	6.12776	+	7.02334i	0.295851	+	0.339090i
$430$	−0.667664	+	2.31233i	−0.0321976	+	0.111511i
$431$	4.11716	+	9.01532i	0.198317	+	0.434253i	0.982497	−	0.186281i	$-0.0596434\pi$
$431$	4.11716	+	9.01532i	0.198317	+	0.434253i	−0.784180	+	0.620533i	$0.786916\pi$
$432$	−8.09706	+	19.1426i	−0.389570	+	0.920997i
$433$	13.0437	−	28.5616i	0.626839	−	1.37259i	−0.283601	−	0.958942i	$-0.591529\pi$
$433$	13.0437	−	28.5616i	0.626839	−	1.37259i	0.910439	−	0.413643i	$-0.135744\pi$
$434$	−1.98726	+	0.918391i	−0.0953914	+	0.0440842i
$435$	1.56665	−	3.46163i	0.0751151	−	0.165973i
$436$	3.74765	+	1.67086i	0.179480	+	0.0800197i
$437$	6.34672	+	0.312808i	0.303605	+	0.0149636i
$438$	−11.8291	−	5.28950i	−0.565218	−	0.252742i
$439$	20.1505	+	31.3547i	0.961729	+	1.49648i	0.865370	+	0.501133i	$0.167083\pi$
$439$	20.1505	+	31.3547i	0.961729	+	1.49648i	0.0963594	+	0.995347i	$0.469280\pi$
$440$	3.15132	−	0.0425866i	0.150233	−	0.00203024i
$441$	−13.7814	−	15.6873i	−0.656255	−	0.747016i
$442$	12.4947	+	10.7285i	0.594311	+	0.510305i
$443$	3.21184	−	1.46680i	0.152599	−	0.0696897i	−0.337651	−	0.941271i	$-0.609633\pi$
$443$	3.21184	−	1.46680i	0.152599	−	0.0696897i	0.490251	+	0.871582i	$0.336905\pi$
$444$	9.73054	+	8.22230i	0.461791	+	0.390213i
$445$	−2.82088	+	0.405581i	−0.133723	+	0.0192264i
$446$	26.2692	−	7.84203i	1.24388	−	0.371331i
$447$	1.11205	−	7.92600i	0.0525981	−	0.374887i
$448$	0.407317	−	1.53998i	0.0192439	−	0.0727573i
$449$	−8.84278	+	13.7596i	−0.417317	+	0.649357i	−0.984733	−	0.174074i	$-0.944307\pi$
$449$	−8.84278	+	13.7596i	−0.417317	+	0.649357i	0.567416	+	0.823431i	$0.307943\pi$
$450$	−10.9030	+	17.3950i	−0.513972	+	0.820010i
$451$	−6.97310	−	2.04749i	−0.328351	−	0.0964124i
$452$	2.15593	−	7.59489i	0.101407	−	0.357233i
$453$	−5.15070	+	17.7653i	−0.242001	+	0.834685i
$454$	−2.41887	−	1.53916i	−0.113523	−	0.0722364i
$455$	−0.148679	+	0.0436560i	−0.00697016	+	0.00204662i
$456$	−1.93386	−	6.19633i	−0.0905612	−	0.290170i
$457$	1.76341	−	12.2648i	0.0824889	−	0.573723i	−0.906098	−	0.423069i	$-0.860953\pi$
$457$	1.76341	−	12.2648i	0.0824889	−	0.573723i	0.988587	−	0.150654i	$-0.0481380\pi$
$458$	−9.12064	+	20.2118i	−0.426179	+	0.944438i
$459$	−30.8476	+	4.75739i	−1.43984	+	0.222056i
$460$	0.700815	−	3.78595i	0.0326757	−	0.176521i
$461$	22.6708			1.05588			0.527942	−	0.849280i	$-0.322964\pi$
$461$	22.6708			1.05588			0.527942	+	0.849280i	$0.322964\pi$
$462$	1.33852	−	0.203269i	0.0622735	−	0.00945693i
$463$	−1.19533	−	0.171862i	−0.0555515	−	0.00798710i	0.114483	−	0.993425i	$-0.463479\pi$
$463$	−1.19533	−	0.171862i	−0.0555515	−	0.00798710i	−0.170035	+	0.985438i	$0.554388\pi$
$464$	−20.8599	+	6.53549i	−0.968398	+	0.303402i
$465$	4.09709	+	3.52579i	0.189998	+	0.163505i
$466$	13.6713	+	8.69927i	0.633313	+	0.402986i
$467$	−6.05395	+	5.24578i	−0.280143	+	0.242746i	−0.783586	−	0.621283i	$-0.786612\pi$
$467$	−6.05395	+	5.24578i	−0.280143	+	0.242746i	0.503443	+	0.864028i	$0.332066\pi$
$468$	−8.91023	−	7.47728i	−0.411876	−	0.345637i
$469$	0.402952	−	1.37233i	0.0186066	−	0.0633683i
$470$	−5.79253	−	0.806226i	−0.267190	−	0.0371884i
$471$	−0.119228	−	35.0091i	−0.00549374	−	1.61313i
$472$	3.42151	−	7.76817i	0.157488	−	0.357559i
$473$	8.89398	+	7.70668i	0.408946	+	0.354353i
$474$	14.2987	−	16.7677i	0.656760	−	0.770167i
$475$	−0.912443	−	6.34618i	−0.0418657	−	0.291183i
$476$	2.28906	−	0.694588i	0.104919	−	0.0318364i
$477$	−18.2376	+	0.124223i	−0.835041	+	0.00568776i
$478$	11.6895	+	10.0372i	0.534667	+	0.459092i
$479$	6.01656	−	13.1744i	0.274904	−	0.601955i	−0.720944	−	0.692994i	$-0.756291\pi$
$479$	6.01656	−	13.1744i	0.274904	−	0.601955i	0.995847	+	0.0910386i	$0.0290187\pi$
$480$	−3.87722	+	0.660472i	−0.176970	+	0.0301463i
$481$	−5.99767	+	3.85447i	−0.273470	+	0.175749i
$482$	−22.3378	−	34.4165i	−1.01746	−	1.56763i
$483$	0.0757942	−	1.65225i	0.00344876	−	0.0751802i
$484$	−2.68334	+	6.01861i	−0.121970	+	0.273573i
$485$	−4.00406	+	2.57325i	−0.181815	+	0.116845i
$486$	21.7484	−	3.60649i	0.986528	−	0.163593i
$487$	−14.9371	−	6.82156i	−0.676867	−	0.309115i	0.0471594	−	0.998887i	$-0.484983\pi$
$487$	−14.9371	−	6.82156i	−0.676867	−	0.309115i	−0.724026	+	0.689773i	$0.757710\pi$
$488$	−15.7334	−	33.2548i	−0.712220	−	1.50537i
$489$	−35.5023	−	22.6455i	−1.60547	−	1.02406i
$490$	1.09613	−	3.79625i	0.0495181	−	0.171497i
$491$	37.2609	−	5.35730i	1.68156	−	0.241772i	0.765679	−	0.643223i	$-0.222403\pi$
$491$	37.2609	−	5.35730i	1.68156	−	0.241772i	0.915880	+	0.401452i	$0.131494\pi$
$492$	8.99253	+	1.17918i	0.405415	+	0.0531617i
$493$	−24.8089	−	21.4970i	−1.11734	−	0.968178i
$494$	3.63265	−	0.0163628i	0.163441	−	0.000736199i
$495$	−1.82636	−	2.79976i	−0.0820888	−	0.125840i
$496$	−0.560263	−	31.0923i	−0.0251566	−	1.39609i
$497$	0.0636446	−	0.216754i	0.00285485	−	0.00972273i
$498$	3.98966	+	1.13727i	0.178781	+	0.0509622i
$499$	−18.2401	−	21.0503i	−0.816541	−	0.942339i	0.182624	−	0.983183i	$-0.441541\pi$
$499$	−18.2401	−	21.0503i	−0.816541	−	0.942339i	−0.999166	+	0.0408440i	$0.986995\pi$
$500$	−7.89867	+	0.0711587i	−0.353239	+	0.00318231i
$501$	9.95563	−	11.5688i	0.444785	−	0.516855i
$502$	3.18843	+	21.4885i	0.142307	+	0.959078i
$503$	−0.704863	+	4.90243i	−0.0314283	+	0.218589i	−0.999483	−	0.0321504i	$-0.989764\pi$
$503$	−0.704863	+	4.90243i	−0.0314283	+	0.218589i	0.968055	+	0.250739i	$0.0806736\pi$
$504$	−1.61112	+	0.508853i	−0.0717649	+	0.0226661i
$505$	−4.74209			−0.211020
$506$	−15.3668	−	10.8766i	−0.683136	−	0.483523i
$507$	−13.4363	+	8.69982i	−0.596729	+	0.386372i
$508$	−21.3533	+	3.26674i	−0.947399	+	0.144938i
$509$	1.60036	−	11.1308i	0.0709349	−	0.493363i	−0.923122	−	0.384506i	$-0.874372\pi$
$509$	1.60036	−	11.1308i	0.0709349	−	0.493363i	0.994057	−	0.108857i	$-0.0347191\pi$
$510$	−3.90300	−	4.43296i	−0.172828	−	0.196295i
$511$	−0.296760	−	1.01067i	−0.0131279	−	0.0447094i
$512$	17.6871	+	14.1126i	0.781669	+	0.623694i
$513$	−4.45522	+	5.24901i	−0.196703	+	0.231749i
$514$	6.36326	+	7.27710i	0.280671	+	0.320979i
$515$	1.45292	−	4.94819i	0.0640233	−	0.218043i
$516$	−12.4527	−	7.78613i	−0.548199	−	0.342765i
$517$	−15.4605	+	24.0569i	−0.679950	+	1.05802i
$518$	0.00466455	+	1.03556i	0.000204948	+	0.0454998i
$519$	−4.37960	+	31.2151i	−0.192243	+	1.37019i
$520$	0.283782	−	2.18274i	0.0124447	−	0.0957196i
$521$	−15.8964	+	2.28555i	−0.696433	+	0.100132i	−0.481434	−	0.876482i	$-0.659884\pi$
$521$	−15.8964	+	2.28555i	−0.696433	+	0.100132i	−0.214999	+	0.976614i	$0.568975\pi$
$522$	17.6933	+	14.9842i	0.774416	+	0.655841i
$523$	−0.982742	−	2.15191i	−0.0429723	−	0.0940963i	0.886928	−	0.461907i	$-0.152835\pi$
$523$	−0.982742	−	2.15191i	−0.0429723	−	0.0940963i	−0.929901	+	0.367811i	$0.880107\pi$
$524$	−27.3296	−	3.67842i	−1.19390	−	0.160693i
$525$	−1.65103	+	0.243124i	−0.0720568	+	0.0106108i
$526$	−15.3048	+	7.07296i	−0.667321	+	0.308396i
$527$	39.2857	−	25.2474i	1.71131	−	1.09979i
$528$	−5.02160	+	18.5642i	−0.218537	+	0.807905i
$529$	−16.6981	+	15.8169i	−0.726003	+	0.687692i
$530$	−1.87891	−	2.89488i	−0.0816146	−	0.125746i
$531$	−8.90263	+	1.34196i	−0.386341	+	0.0582360i
$532$	0.281262	−	0.446445i	0.0121943	−	0.0193558i
$533$	−2.10851	+	4.61700i	−0.0913299	+	0.199985i
$534$	2.33866	−	17.2323i	0.101204	−	0.745715i
$535$	−1.74114	+	0.795152i	−0.0752760	+	0.0343774i
$536$	15.5327	+	13.0959i	0.670910	+	0.565657i
$537$	2.61194	−	2.27888i	0.112713	−	0.0983407i
$538$	−6.01356	−	20.1442i	−0.259263	−	0.868477i
$539$	−14.6016	−	12.6523i	−0.628935	−	0.544975i
$540$	2.79196	+	3.09963i	0.120147	+	0.133387i
$541$	−10.7882	+	16.7868i	−0.463822	+	0.721721i	−0.991837	−	0.127514i	$-0.959300\pi$
$541$	−10.7882	+	16.7868i	−0.463822	+	0.721721i	0.528015	+	0.849235i	$0.322936\pi$
$542$	2.29810	−	16.5112i	0.0987118	−	0.709219i
$543$	4.26999	+	14.3611i	0.183243	+	0.616295i
$544$	−4.07716	+	33.7342i	−0.174807	+	1.44634i
$545$	0.622405	−	0.539317i	0.0266609	−	0.0231018i
$546$	−0.00747921	−	0.945522i	−0.000320081	−	0.0404646i
$547$	−4.95562	+	1.45510i	−0.211887	+	0.0622156i	−0.385953	−	0.922518i	$-0.626127\pi$
$547$	−4.95562	+	1.45510i	−0.211887	+	0.0622156i	0.174066	+	0.984734i	$0.444309\pi$
$548$	23.3833	−	20.6335i	0.998885	−	0.881419i
$549$	−20.8720	+	32.9690i	−0.890795	+	1.40708i
$550$	−7.81308	+	17.3142i	−0.333151	+	0.738281i
$551$	−7.24098			−0.308476
$552$	21.0449	+	10.4457i	0.895730	+	0.444599i
$553$	1.79133			0.0761752
$554$	−3.56138	+	7.89221i	−0.151308	+	0.335308i
$555$	2.32220	−	1.07009i	0.0985718	−	0.0454226i
$556$	−14.6550	−	16.6081i	−0.621512	−	0.704341i
$557$	−23.8971	+	7.01682i	−1.01255	+	0.297312i	−0.745597	−	0.666397i	$-0.767836\pi$
$557$	−23.8971	+	7.01682i	−1.01255	+	0.297312i	−0.266955	+	0.963709i	$0.586018\pi$
$558$	−27.5441	+	18.1452i	−1.16604	+	0.768147i
$559$	6.21164	−	5.38241i	0.262724	−	0.227652i
$560$	−0.245359	−	0.204983i	−0.0103683	−	0.00866211i
$561$	−27.6822	+	8.23073i	−1.16874	+	0.347502i
$562$	1.65581	−	11.8966i	0.0698462	−	0.501827i
$563$	−24.9507	+	38.8241i	−1.05155	+	1.63624i	−0.329847	+	0.944034i	$0.606997\pi$
$563$	−24.9507	+	38.8241i	−1.05155	+	1.63624i	−0.721701	+	0.692205i	$0.756639\pi$
$564$	14.4209	−	32.6438i	0.607230	−	1.37455i
$565$	−1.19755	−	1.03769i	−0.0503814	−	0.0436557i
$566$	−6.44605	−	21.5930i	−0.270948	−	0.907619i
$567$	1.37021	+	1.15499i	0.0575432	+	0.0485050i
$568$	2.45332	+	2.06844i	0.102939	+	0.0867899i
$569$	14.8806	−	6.79574i	0.623827	−	0.284892i	−0.0783153	−	0.996929i	$-0.524954\pi$
$569$	14.8806	−	6.79574i	0.623827	−	0.284892i	0.702143	+	0.712036i	$0.252227\pi$
$570$	−1.29099	−	0.175205i	−0.0540734	−	0.00733851i
$571$	−13.6242	+	29.8328i	−0.570155	+	1.24847i	0.376560	+	0.926392i	$0.377107\pi$
$571$	−13.6242	+	29.8328i	−0.570155	+	1.24847i	−0.946715	+	0.322073i	$0.895620\pi$
$572$	−9.10621	−	5.73696i	−0.380750	−	0.239874i
$573$	16.1383	−	35.6589i	0.674188	−	1.48967i
$574$	0.401380	+	0.618416i	0.0167533	+	0.0258122i
$575$	18.8812	+	13.4921i	0.787399	+	0.562661i
$576$	2.60992	−	23.8577i	0.108747	−	0.994069i
$577$	2.06792	−	1.32897i	0.0860886	−	0.0553258i	−0.496888	−	0.867814i	$-0.665524\pi$
$577$	2.06792	−	1.32897i	0.0860886	−	0.0553258i	0.582977	+	0.812489i	$0.301888\pi$
$578$	−24.4964	+	11.3208i	−1.01892	+	0.470881i
$579$	0.732185	+	4.97219i	0.0304286	+	0.206637i
$580$	−0.585252	+	4.34824i	−0.0243012	+	0.180551i
$581$	0.140093	+	0.306760i	0.00581202	+	0.0127266i
$582$	−8.40274	−	27.8017i	−0.348305	−	1.15242i
$583$	−16.7033	+	2.40158i	−0.691782	+	0.0994632i
$584$	14.8376	+	1.92907i	0.613985	+	0.0798253i
$585$	−2.11700	+	0.984284i	−0.0875273	+	0.0406951i
$586$	−0.0776034	−	17.2284i	−0.00320577	−	0.711700i
$587$	−3.11772	+	4.85126i	−0.128682	+	0.200233i	−0.899616	−	0.436682i	$-0.856153\pi$
$587$	−3.11772	+	4.85126i	−0.128682	+	0.200233i	0.770934	+	0.636915i	$0.219790\pi$
$588$	20.4440	+	12.7828i	0.843098	+	0.527153i
$589$	2.90210	−	9.88365i	0.119579	−	0.407249i
$590$	−1.12146	−	1.28252i	−0.0461698	−	0.0528003i
$591$	23.4707	+	6.80487i	0.965454	+	0.279915i
$592$	−13.4887	−	5.86872i	−0.554381	−	0.241203i
$593$	−5.56648	−	18.9577i	−0.228588	−	0.778499i	−0.991284	−	0.131742i	$-0.957943\pi$
$593$	−5.56648	−	18.9577i	−0.228588	−	0.778499i	0.762696	−	0.646757i	$-0.223875\pi$
$594$	19.4850	−	6.03427i	0.799480	−	0.247589i
$595$	0.0683282	−	0.475233i	0.00280118	−	0.0194827i
$596$	1.39760	+	9.13551i	0.0572479	+	0.374205i
$597$	0.991887	+	1.53191i	0.0405952	+	0.0626969i
$598$	−9.04635	+	9.54198i	−0.369933	+	0.390201i
$599$	15.5645			0.635949			0.317974	−	0.948099i	$-0.396997\pi$
$599$	15.5645			0.635949			0.317974	+	0.948099i	$0.396997\pi$
$600$	6.29285	−	22.8550i	0.256905	−	0.933051i
$601$	1.38423	−	9.62752i	0.0564639	−	0.392715i	−0.941918	−	0.335844i	$-0.890979\pi$
$601$	1.38423	−	9.62752i	0.0564639	−	0.392715i	0.998382	−	0.0568709i	$-0.0181123\pi$
$602$	−0.175224	−	1.18093i	−0.00714161	−	0.0481309i
$603$	2.92140	−	21.3501i	0.118969	−	0.869445i
$604$	−0.192408	−	21.3575i	−0.00782899	−	0.869024i
$605$	0.866125	+	0.999562i	0.0352130	+	0.0406380i
$606$	7.93253	−	27.8282i	0.322237	−	1.13044i
$607$	−10.4188	+	35.4833i	−0.422888	+	1.44022i	0.422642	+	0.906297i	$0.361103\pi$
$607$	−10.4188	+	35.4833i	−0.422888	+	1.44022i	−0.845530	+	0.533927i	$0.820716\pi$
$608$	4.19322	+	6.21256i	0.170057	+	0.251953i
$609$	0.00641875	+	1.88474i	0.000260101	+	0.0763737i
$610$	−7.38378	+	0.0332594i	−0.298961	+	0.00134663i
$611$	15.0939	+	13.0789i	0.610634	+	0.529117i
$612$	32.5430	−	15.4887i	1.31547	−	0.626092i
$613$	28.8025	−	4.14118i	1.16332	−	0.167261i	0.466512	−	0.884515i	$-0.345510\pi$
$613$	28.8025	−	4.14118i	1.16332	−	0.167261i	0.696812	+	0.717254i	$0.254601\pi$
$614$	0.334451	−	1.15831i	0.0134973	−	0.0467456i
$615$	0.978926	−	1.53470i	0.0394741	−	0.0618853i
$616$	−1.41313	+	0.668578i	−0.0569366	+	0.0269378i
$617$	16.1050	+	7.35491i	0.648363	+	0.296098i	0.712320	−	0.701855i	$-0.247645\pi$
$617$	16.1050	+	7.35491i	0.648363	+	0.296098i	−0.0639565	+	0.997953i	$0.520372\pi$
$618$	26.6072	+	16.8035i	1.07030	+	0.675936i
$619$	−15.0836	+	9.69363i	−0.606260	+	0.389620i	−0.807453	−	0.589932i	$-0.799155\pi$
$619$	−15.0836	+	9.69363i	−0.606260	+	0.389620i	0.201193	+	0.979552i	$0.435518\pi$
$620$	−5.70061	−	2.54157i	−0.228942	−	0.102072i
$621$	−2.58129	−	24.7858i	−0.103584	−	0.994621i
$622$	21.1178	+	32.5368i	0.846746	+	1.30461i
$623$	1.18923	−	0.764273i	0.0476456	−	0.0306200i
$624$	12.3344	+	5.31661i	0.493769	+	0.212835i
$625$	9.39208	−	20.5658i	0.375683	−	0.822632i
$626$	−30.3032	−	26.0198i	−1.21116	−	1.03996i
$627$	−3.42580	+	5.37078i	−0.136813	+	0.214488i
$628$	11.7381	+	38.6835i	0.468399	+	1.54364i
$629$	−3.14376	−	21.8653i	−0.125350	−	0.871827i
$630$	−0.0444593	+	0.336184i	−0.00177130	+	0.0133939i
$631$	19.3990	+	16.8093i	0.772262	+	0.669168i	0.949066	−	0.315078i	$-0.102031\pi$
$631$	19.3990	+	16.8093i	0.772262	+	0.669168i	−0.176804	+	0.984246i	$0.556576\pi$
$632$	−10.2567	+	23.2868i	−0.407991	+	0.926301i
$633$	8.60820	−	0.0293164i	0.342145	−	0.00116522i
$634$	−21.3356	−	2.96957i	−0.847344	−	0.117936i
$635$	−1.22150	+	4.16004i	−0.0484736	+	0.165086i
$636$	20.1312	−	6.18351i	0.798253	−	0.245192i
$637$	−10.1979	+	8.83651i	−0.404055	+	0.350115i
$638$	18.0996	+	11.5170i	0.716570	+	0.455964i
$639$	0.461423	−	3.37217i	0.0182536	−	0.133401i
$640$	4.06959	−	2.01591i	0.160865	−	0.0796860i
$641$	49.7479	+	7.15266i	1.96492	+	0.282513i	0.999784	+	0.0207744i	$0.00661319\pi$
$641$	49.7479	+	7.15266i	1.96492	+	0.282513i	0.965139	+	0.261739i	$0.0842959\pi$
$642$	−1.75365	−	11.5477i	−0.0692109	−	0.455751i
$643$	−2.05111			−0.0808878			−0.0404439	−	0.999182i	$-0.512877\pi$
$643$	−2.05111			−0.0808878			−0.0404439	+	0.999182i	$0.512877\pi$
$644$	0.463920	+	1.85266i	0.0182810	+	0.0730052i
$645$	−2.47433	+	1.60209i	−0.0974267	+	0.0630822i
$646$	−4.62961	+	10.2595i	−0.182150	+	0.403654i
$647$	−0.548424	+	3.81437i	−0.0215608	+	0.149959i	−0.997758	−	0.0669267i	$-0.978681\pi$
$647$	−0.548424	+	3.81437i	−0.0215608	+	0.149959i	0.976197	+	0.216885i	$0.0695897\pi$
$648$	−22.8600	+	11.1991i	−0.898026	+	0.439942i
$649$	−7.99297	+	2.34695i	−0.313752	+	0.0921258i
$650$	11.1928	+	7.12211i	0.439016	+	0.279352i
$651$	−2.57517	−	0.746622i	−0.100929	−	0.0292624i
$652$	46.7760	+	13.2781i	1.83189	+	0.520012i
$653$	−33.4030	−	9.80801i	−1.30716	−	0.383817i	−0.447318	−	0.894375i	$-0.647621\pi$
$653$	−33.4030	−	9.80801i	−1.30716	−	0.383817i	−0.859843	+	0.510558i	$0.829439\pi$
$654$	2.12374	+	4.55464i	0.0830446	+	0.178101i
$655$	−2.99231	+	4.65613i	−0.116919	+	0.181930i
$656$	−10.3374	+	1.67692i	−0.403609	+	0.0654727i
$657$	−6.69086	−	14.3907i	−0.261035	−	0.561436i
$658$	2.77977	−	0.829834i	0.108367	−	0.0323503i
$659$	43.5266	−	6.25819i	1.69556	−	0.243784i	0.774322	−	0.632791i	$-0.218091\pi$
$659$	43.5266	−	6.25819i	1.69556	−	0.243784i	0.921235	+	0.389007i	$0.127182\pi$
$660$	2.94829	+	2.49130i	0.114762	+	0.0969738i
$661$	−22.7455	+	10.3875i	−0.884697	+	0.404027i	−0.805336	−	0.592818i	$-0.798015\pi$
$661$	−22.7455	+	10.3875i	−0.884697	+	0.404027i	−0.0793607	+	0.996846i	$0.525288\pi$
$662$	−14.6458	−	12.5756i	−0.569224	−	0.488764i
$663$	2.93846	+	19.9548i	0.114120	+	0.774980i
$664$	−4.78993	+	0.0647306i	−0.185885	+	0.00251203i
$665$	−0.0572568	−	0.0890932i	−0.00222032	−	0.00345489i
$666$	2.39506	+	15.4175i	0.0928066	+	0.597414i
$667$	18.1174	−	18.9385i	0.701510	−	0.733301i
$668$	−7.17652	+	16.0966i	−0.277668	+	0.622795i
$669$	30.5892	+	13.8439i	1.18265	+	0.535236i
$670$	3.70157	−	1.71064i	0.143004	−	0.0660880i
$671$	−14.9984	+	32.8419i	−0.579006	+	1.26785i
$672$	1.61334	−	1.09695i	0.0622360	−	0.0423159i
$673$	3.08133	+	6.74717i	0.118776	+	0.260084i	0.959677	−	0.281106i	$-0.0907012\pi$
$673$	3.08133	+	6.74717i	0.118776	+	0.260084i	−0.840900	+	0.541190i	$0.817974\pi$
$674$	−2.67738	+	9.27263i	−0.103129	+	0.357168i
$675$	−24.0514	+	7.32984i	−0.925737	+	0.282126i
$676$	11.9776	−	14.0772i	0.460677	−	0.541429i
$677$	21.4153	−	24.7146i	0.823057	−	0.949858i	−0.176349	−	0.984328i	$-0.556429\pi$
$677$	21.4153	−	24.7146i	0.823057	−	0.949858i	0.999406	+	0.0344694i	$0.0109741\pi$
$678$	8.09273	−	5.29180i	0.310800	−	0.203230i
$679$	1.27642	−	1.98615i	0.0489846	−	0.0762216i
$680$	5.78667	+	3.60932i	0.221909	+	0.138411i
$681$	−1.00074	−	3.36577i	−0.0383486	−	0.128977i
$682$	−22.9744	+	20.0893i	−0.879735	+	0.769260i
$683$	−10.3802	+	8.99449i	−0.397187	+	0.344165i	−0.830440	−	0.557108i	$-0.811911\pi$
$683$	−10.3802	+	8.99449i	−0.397187	+	0.344165i	0.433253	+	0.901272i	$0.357366\pi$
$684$	3.18771	−	7.28285i	0.121885	−	0.278467i
$685$	−1.76341	−	6.00562i	−0.0673764	−	0.229463i
$686$	0.576983	+	3.88858i	0.0220293	+	0.148467i
$687$	−24.6652	+	11.3659i	−0.941037	+	0.433637i
$688$	16.3550	+	4.48383i	0.623529	+	0.170944i
$689$			11.7857i			0.449001i
$690$	3.68838	−	2.93815i	0.140414	−	0.111853i
$691$	4.88465			0.185821			0.0929105	−	0.995674i	$-0.470383\pi$
$691$	4.88465			0.185821			0.0929105	+	0.995674i	$0.470383\pi$
$692$	−5.50419	−	35.9785i	−0.209238	−	1.36770i
$693$	1.40099	+	0.886936i	0.0532192	+	0.0336919i
$694$	−2.91758	−	19.6630i	−0.110750	−	0.746399i
$695$	−4.26552	+	1.25247i	−0.161800	+	0.0475089i
$696$	−24.5379	−	10.7082i	−0.930107	−	0.405892i
$697$	−10.2988	−	11.8855i	−0.390095	−	0.450194i
$698$	−10.3219	−	11.8043i	−0.390691	−	0.446799i
$699$	5.65616	+	19.0232i	0.213936	+	0.719524i
$700$	1.74558	−	0.816264i	0.0659768	−	0.0308519i
$701$	32.9820	+	21.1962i	1.24571	+	0.800570i	0.986262	−	0.165187i	$-0.0528227\pi$
$701$	32.9820	+	21.1962i	1.24571	+	0.800570i	0.259449	+	0.965757i	$0.416459\pi$
$702$	−2.23480	−	14.0698i	−0.0843470	−	0.531029i
$703$	−3.68252	−	3.19092i	−0.138889	−	0.120348i
$704$	−0.600083	−	22.1984i	−0.0226165	−	0.836634i
$705$	−4.70902	−	5.39725i	−0.177352	−	0.203272i
$706$	18.0464	+	5.21072i	0.679185	+	0.196108i
$707$	2.13967	−	0.977156i	0.0804707	−	0.0367498i
$708$	9.40220	−	4.43572i	0.353356	−	0.166704i
$709$	29.0019	+	13.2447i	1.08919	+	0.497417i	0.877332	−	0.479884i	$-0.159321\pi$
$709$	29.0019	+	13.2447i	1.08919	+	0.497417i	0.211858	+	0.977300i	$0.432048\pi$
$710$	0.584648	−	0.270189i	0.0219415	−	0.0101400i
$711$	26.6876	−	4.02282i	1.00086	−	0.150868i
$712$	3.12608	+	19.8357i	0.117155	+	0.743376i
$713$	18.5890	+	32.3199i	0.696164	+	1.21039i
$714$	2.67453	+	1.19594i	0.100092	+	0.0447569i
$715$	−1.81725	+	1.16788i	−0.0679614	+	0.0436761i
$716$	−2.13354	+	3.38654i	−0.0797340	+	0.126561i
$717$	2.74911	+	18.6689i	0.102668	+	0.697204i
$718$	39.6063	+	34.0079i	1.47809	+	1.26916i
$719$	8.25097	+	18.0671i	0.307709	+	0.673789i	0.998800	−	0.0489789i	$-0.0155967\pi$
$719$	8.25097	+	18.0671i	0.307709	+	0.673789i	−0.691091	+	0.722768i	$0.742869\pi$
$720$	−4.11574	−	2.50287i	−0.153384	−	0.0932764i
$721$	0.364055	+	2.53206i	0.0135581	+	0.0942987i
$722$	−6.97602	−	23.3682i	−0.259620	−	0.869676i
$723$	6.98209	−	49.7640i	0.259667	−	1.85074i
$724$	−9.48397	−	14.4691i	−0.352469	−	0.537739i
$725$	−22.2462	−	14.2968i	−0.826203	−	0.530968i
$726$	−7.31460	+	3.41065i	−0.271470	+	0.126581i
$727$	8.82626	−	30.0595i	0.327348	−	1.11484i	−0.617292	−	0.786734i	$-0.711770\pi$
$727$	8.82626	−	30.0595i	0.327348	−	1.11484i	0.944640	−	0.328110i	$-0.106412\pi$
$728$	0.321732	+	1.04335i	0.0119242	+	0.0386691i
$729$	23.0074	+	14.1302i	0.852124	+	0.523339i
$730$	1.61221	−	2.53366i	0.0596704	−	0.0937750i
$731$	7.17478	+	24.4351i	0.265369	+	0.903764i
$732$	12.1564	−	43.3861i	0.449312	−	1.60360i
$733$	−27.9125	−	4.01322i	−1.03097	−	0.148232i	−0.393994	−	0.919113i	$-0.628907\pi$
$733$	−27.9125	−	4.01322i	−1.03097	−	0.148232i	−0.636979	+	0.770881i	$0.719816\pi$
$734$	−0.269582	+	0.597409i	−0.00995046	+	0.0220508i
$735$	4.06220	−	2.63021i	0.149837	−	0.0970167i
$736$	−26.7404	−	4.57709i	−0.985665	−	0.168714i
$737$		−	19.9388i		−	0.734454i
$738$	7.36862	+	8.31190i	0.271242	+	0.305965i
$739$	−4.34492	+	30.2196i	−0.159830	+	1.11165i	0.739113	+	0.673581i	$0.235245\pi$
$739$	−4.34492	+	30.2196i	−0.159830	+	1.11165i	−0.898944	+	0.438064i	$0.855664\pi$
$740$	−2.21380	+	1.95346i	−0.0813809	+	0.0718107i
$741$	3.37232	+	2.90208i	0.123885	+	0.106611i
$742$	1.44430	+	0.919030i	0.0530220	+	0.0337387i
$743$	−27.6592	−	31.9204i	−1.01472	−	1.17104i	−0.985188	−	0.171481i	$-0.945145\pi$
$743$	−27.6592	−	31.9204i	−1.01472	−	1.17104i	−0.0295284	−	0.999564i	$-0.509401\pi$
$744$	24.4507	−	29.2015i	0.896406	−	1.07058i
$745$	1.77978	+	0.522589i	0.0652059	+	0.0191462i
$746$	−6.23919	+	44.8270i	−0.228433	+	1.64123i
$747$	2.77602	+	4.25556i	0.101569	+	0.155703i
$748$	27.8903	−	18.2811i	1.01977	−	0.668423i
$749$	0.621769	−	0.717559i	0.0227189	−	0.0262190i
$750$	−7.36119	−	6.27726i	−0.268793	−	0.229213i
$751$	50.8756	−	7.31481i	1.85648	−	0.266921i	0.878825	−	0.477145i	$-0.158328\pi$
$751$	50.8756	−	7.31481i	1.85648	−	0.266921i	0.977653	+	0.210224i	$0.0674192\pi$
$752$	−5.12871	+	40.8877i	−0.187025	+	1.49102i
$753$	−14.3080	+	22.4313i	−0.521413	+	0.817441i
$754$	9.76073	−	11.3675i	0.355465	−	0.413981i
$755$	−3.89942	−	1.78081i	−0.141915	−	0.0648102i
$756$	−1.89847	−	0.823268i	−0.0690466	−	0.0299420i
$757$	0.0555103	+	0.0863758i	0.00201756	+	0.00313938i	0.842261	−	0.539070i	$-0.181224\pi$
$757$	0.0555103	+	0.0863758i	0.00201756	+	0.00313938i	−0.840243	+	0.542210i	$0.817588\pi$
$758$	24.6259	+	37.9418i	0.894454	+	1.37811i
$759$	−5.47545	−	22.3981i	−0.198746	−	0.813000i
$760$	1.48603	−	0.234195i	0.0539038	−	0.00849516i
$761$	23.3048	+	36.2630i	0.844799	+	1.31453i	0.947479	+	0.319819i	$0.103622\pi$
$761$	23.3048	+	36.2630i	0.844799	+	1.31453i	−0.102679	+	0.994715i	$0.532742\pi$
$762$	−22.3692	−	14.1270i	−0.810349	−	0.511768i
$763$	−0.169703	+	0.371598i	−0.00614366	+	0.0134527i
$764$	−6.02878	+	44.7920i	−0.218114	+	1.62052i
$765$	−0.0492703	−	7.23356i	−0.00178137	−	0.261530i
$766$	12.5826	−	43.5776i	0.454629	−	1.57452i
$767$	0.827993	+	5.75882i	0.0298971	+	0.207939i
$768$	5.02248	+	27.2539i	0.181233	+	0.983440i
$769$	−34.5424	+	39.8640i	−1.24563	+	1.43753i	−0.389294	+	0.921114i	$0.627281\pi$
$769$	−34.5424	+	39.8640i	−1.24563	+	1.43753i	−0.856336	+	0.516420i	$0.827264\pi$
$770$	0.00141333	+	0.313767i	5.09327e−5	+	0.0113074i
$771$	0.0403204	+	11.8393i	0.00145210	+	0.426382i
$772$	−2.45824	−	5.25694i	−0.0884740	−	0.189202i
$773$	−26.5957	−	7.80920i	−0.956581	−	0.280878i	−0.234057	−	0.972223i	$-0.575200\pi$
$773$	−26.5957	−	7.80920i	−0.956581	−	0.280878i	−0.722524	+	0.691345i	$0.757018\pi$
$774$	−5.26254	−	17.2002i	−0.189158	−	0.618247i
$775$	28.4305	−	24.6352i	1.02125	−	0.884922i
$776$	18.5110	+	27.9654i	0.664504	+	1.00390i
$777$	−0.827295	+	0.961345i	−0.0296790	+	0.0344881i
$778$	−40.0526	+	5.94296i	−1.43596	+	0.213066i
$779$	−3.43370	−	0.493692i	−0.123025	−	0.0176883i
$780$	2.01528	−	1.79053i	0.0721586	−	0.0641113i
$781$		−	3.14925i		−	0.112689i
$782$	−15.2496	−	37.7785i	−0.545325	−	1.35096i
$783$	4.32822	+	28.0649i	0.154678	+	1.00296i
$784$	−26.8506	−	7.36127i	−0.958951	−	0.262903i
$785$	8.03112	+	1.15470i	0.286643	+	0.0412130i
$786$	−22.3182	−	25.3486i	−0.796063	−	0.904155i
$787$	−18.9100	+	5.55247i	−0.674067	+	0.197924i	−0.600813	−	0.799389i	$-0.705157\pi$
$787$	−18.9100	+	5.55247i	−0.674067	+	0.197924i	−0.0732539	+	0.997313i	$0.523338\pi$
$788$	−28.2165	+	0.254201i	−1.00517	+	0.00905554i
$789$	−19.8326	−	5.75008i	−0.706059	−	0.204708i
$790$	3.36183	+	3.84463i	0.119608	+	0.136786i
$791$	0.754172	+	0.221445i	0.0268153	+	0.00787368i
$792$	−19.5517	+	13.1341i	−0.694738	+	0.466699i
$793$	21.2128	+	13.6327i	0.753290	+	0.484110i
$794$	−14.8454	+	0.0668692i	−0.526842	+	0.00237310i
$795$	0.587287	−	4.18582i	0.0208289	−	0.148456i
$796$	−1.60497	−	1.36560i	−0.0568867	−	0.0484023i
$797$	−1.32100	−	9.18773i	−0.0467921	−	0.325446i	−0.999750	−	0.0223444i	$-0.992887\pi$
$797$	−1.32100	−	9.18773i	−0.0467921	−	0.325446i	0.952958	−	0.303102i	$-0.0980221\pi$
$798$	0.618607	−	0.186967i	0.0218985	−	0.00661856i
$799$	−56.2902	+	25.7069i	−1.99140	+	0.909444i
$800$	0.616430	+	27.3658i	0.0217941	+	0.967527i
$801$	16.0011	−	14.0570i	0.565370	−	0.496678i
$802$	−18.0073	−	38.9651i	−0.635860	−	1.37590i
$803$	−7.93887	−	12.3531i	−0.280156	−	0.435932i
$804$	3.84666	+	24.5836i	0.135661	+	0.866997i
$805$	0.376280	+	0.0731649i	0.0132621	+	0.00257872i
$806$	11.6042	+	17.8790i	0.408742	+	0.629760i
$807$	10.6160	−	23.4569i	0.373701	−	0.825722i
$808$	0.451501	+	33.4101i	0.0158837	+	1.17536i
$809$	−3.73896	−	1.70752i	−0.131455	−	0.0600334i	0.348602	−	0.937271i	$-0.386657\pi$
$809$	−3.73896	−	1.70752i	−0.131455	−	0.0600334i	−0.480056	+	0.877238i	$0.659384\pi$
$810$	0.0926089	+	5.10838i	0.00325395	+	0.179490i
$811$	11.3925	+	24.9461i	0.400045	+	0.875977i	0.997266	+	0.0738996i	$0.0235445\pi$
$811$	11.3925	+	24.9461i	0.400045	+	0.875977i	−0.597221	+	0.802077i	$0.703728\pi$
$812$	−0.631929	−	2.08256i	−0.0221764	−	0.0730836i
$813$	15.3845	−	13.4228i	0.539559	−	0.470757i
$814$	4.12957	+	13.8332i	0.144741	+	0.484854i
$815$	6.39098	−	7.37558i	0.223866	−	0.258355i
$816$	−30.8606	+	27.9205i	−1.08034	+	0.977411i
$817$	4.72570	+	3.03703i	0.165331	+	0.106252i
$818$	37.3487	+	5.19833i	1.30587	+	0.181755i
$819$	0.752389	−	0.880348i	0.0262906	−	0.0307619i
$820$	−0.573993	+	2.02205i	−0.0200447	+	0.0706130i
$821$	13.4913	+	15.5698i	0.470849	+	0.543389i	0.940648	−	0.339385i	$-0.110219\pi$
$821$	13.4913	+	15.5698i	0.470849	+	0.543389i	−0.469799	+	0.882774i	$0.655673\pi$
$822$	38.1928	−	0.302110i	1.33213	−	0.0105373i
$823$	−7.52222	−	25.6183i	−0.262208	−	0.892999i	−0.980377	−	0.197131i	$-0.936838\pi$
$823$	−7.52222	−	25.6183i	−0.262208	−	0.892999i	0.718169	−	0.695869i	$-0.244980\pi$
$824$	−35.0005	−	9.76534i	−1.21930	−	0.340192i
$825$	−21.1291	+	9.73646i	−0.735622	+	0.338980i
$826$	0.770289	+	0.347594i	0.0268018	+	0.0120944i
$827$			24.5320i			0.853062i	0.904473	+	0.426531i	$0.140264\pi$
$827$			24.5320i			0.853062i	−0.904473	+	0.426531i	$0.859736\pi$
$828$	11.0721	+	26.5595i	0.384783	+	0.923007i
$829$		−	15.3545i		−	0.533285i	−0.963796	−	0.266642i	$-0.914086\pi$
$829$		−	15.3545i		−	0.533285i	0.963796	−	0.266642i	$-0.0859143\pi$
$830$	−0.395466	+	0.876374i	−0.0137268	+	0.0304194i
$831$	−9.63114	+	4.43810i	−0.334101	+	0.153956i
$832$	−15.4054	−	1.79155i	−0.534087	−	0.0621109i
$833$	−11.7791	−	40.1160i	−0.408122	−	1.38994i
$834$	−0.214575	−	27.1266i	−0.00743013	−	0.939318i
$835$	2.31642	+	2.67330i	0.0801631	+	0.0925132i
$836$	2.00872	−	7.07627i	0.0694729	−	0.244738i
$837$	−40.0421	−	5.34022i	−1.38406	−	0.184585i
$838$	−1.86307	+	13.3857i	−0.0643586	+	0.462400i
$839$	−26.0862	−	16.7646i	−0.900596	−	0.578778i	0.00637102	−	0.999980i	$-0.497972\pi$
$839$	−26.0862	−	16.7646i	−0.900596	−	0.578778i	−0.906967	+	0.421202i	$0.861608\pi$
$840$	−0.0622756	−	0.386588i	−0.00214871	−	0.0133386i
$841$	−0.566822	+	0.654147i	−0.0195456	+	0.0225568i
$842$	−48.8062	+	14.5699i	−1.68197	+	0.502112i
$843$	11.0848	−	9.67128i	0.381779	−	0.333097i
$844$	−9.51170	+	2.88621i	−0.327406	+	0.0993476i
$845$	−1.54109	−	3.37451i	−0.0530150	−	0.116087i
$846$	39.5500	−	18.6056i	1.35976	−	0.639674i
$847$	−0.596773	−	0.272537i	−0.0205054	−	0.00936449i
$848$	−20.2169	+	13.5134i	−0.694250	+	0.464051i
$849$	11.3795	−	25.1439i	0.390544	−	0.862937i
$850$	−34.4799	+	22.3790i	−1.18265	+	0.767593i
$851$	17.5596	−	1.64756i	0.601936	−	0.0564778i
$852$	0.607564	+	3.88288i	0.0208148	+	0.133025i
$853$	27.8701	+	43.3667i	0.954254	+	1.48485i	0.872745	+	0.488176i	$0.162337\pi$
$853$	27.8701	+	43.3667i	0.954254	+	1.48485i	0.0815087	+	0.996673i	$0.474026\pi$
$854$	3.32478	−	1.53651i	0.113771	−	0.0525783i
$855$	−1.05310	−	1.19875i	−0.0360153	−	0.0409963i
$856$	5.76797	+	12.1914i	0.197145	+	0.416693i
$857$	−26.7796	+	12.2298i	−0.914772	+	0.417763i	−0.816466	−	0.577394i	$-0.804070\pi$
$857$	−26.7796	+	12.2298i	−0.914772	+	0.417763i	−0.0983064	+	0.995156i	$0.531343\pi$
$858$	−3.81360	−	12.6179i	−0.130194	−	0.430766i
$859$	7.38583	+	51.3696i	0.252001	+	1.75271i	0.586163	+	0.810193i	$0.300638\pi$
$859$	7.38583	+	51.3696i	0.252001	+	1.75271i	−0.334162	+	0.942516i	$0.608453\pi$
$860$	2.20570	−	2.59234i	0.0752138	−	0.0883980i
$861$	−0.125458	+	0.894191i	−0.00427561	+	0.0304739i
$862$	−0.0631337	−	14.0161i	−0.00215034	−	0.477389i
$863$	9.51640	+	6.11582i	0.323942	+	0.208185i	0.692497	−	0.721421i	$-0.256511\pi$
$863$	9.51640	+	6.11582i	0.323942	+	0.208185i	−0.368554	+	0.929606i	$0.620147\pi$
$864$	21.5724	−	19.9657i	0.733909	−	0.679248i
$865$	−7.00932	−	2.05812i	−0.238324	−	0.0699782i
$866$	−33.4278	+	29.2300i	−1.13592	+	0.993276i
$867$	−31.7434	−	9.20340i	−1.07806	−	0.312564i
$868$	3.09588	−	0.0278906i	0.105081	−	0.000946670i
$869$	23.9607	−	7.03550i	0.812812	−	0.238663i
$870$	−4.03306	+	3.55091i	−0.136734	+	0.120387i
$871$	−13.7837	−	1.98179i	−0.467042	−	0.0671505i
$872$	−3.85899	−	4.33377i	−0.130682	−	0.146760i
$873$	14.5561	−	32.4566i	0.492648	−	1.09849i
$874$	−7.99926	−	4.09502i	−0.270579	−	0.138516i
$875$		−	0.786413i		−	0.0265856i
$876$	12.1715	+	13.6992i	0.411236	+	0.462855i
$877$	1.69622	+	0.243880i	0.0572774	+	0.00823525i	0.170894	−	0.985289i	$-0.445334\pi$
$877$	1.69622	+	0.243880i	0.0572774	+	0.00823525i	−0.113617	+	0.993525i	$0.536244\pi$
$878$	−7.73632	−	52.1390i	−0.261088	−	1.75960i
$879$	13.7636	−	15.9938i	0.464235	−	0.539456i
$880$	−4.08698	−	1.77818i	−0.137772	−	0.0599425i
$881$	−4.23484	+	3.66951i	−0.142675	+	0.123629i	−0.723275	−	0.690561i	$-0.757364\pi$
$881$	−4.23484	+	3.66951i	−0.142675	+	0.123629i	0.580599	+	0.814190i	$0.302818\pi$
$882$	8.63972	+	28.2381i	0.290914	+	0.950828i
$883$	48.9427	+	14.3709i	1.64705	+	0.483618i	0.968100	−	0.250565i	$-0.0806164\pi$
$883$	48.9427	+	14.3709i	1.64705	+	0.483618i	0.678952	+	0.734183i	$0.262435\pi$
$884$	−9.86560	−	21.0976i	−0.331816	−	0.709588i
$885$	−0.00710606	−	2.08656i	−0.000238868	−	0.0701389i
$886$	−4.99343	+	0.0224923i	−0.167757	+	0.000755644i
$887$	13.0974	−	15.1152i	0.439769	−	0.507520i	−0.491989	−	0.870602i	$-0.663730\pi$
$887$	13.0974	−	15.1152i	0.439769	−	0.507520i	0.931757	+	0.363082i	$0.118275\pi$
$888$	−7.76033	−	16.2590i	−0.260420	−	0.545618i
$889$	−0.306068	−	2.12875i	−0.0102652	−	0.0713959i
$890$	3.87217	+	1.11805i	0.129795	+	0.0374771i
$891$	22.8640	+	10.0675i	0.765973	+	0.337275i
$892$	−38.4238	−	5.17165i	−1.28652	−	0.173160i
$893$	−5.67045	+	12.4165i	−0.189754	+	0.415504i
$894$	−6.04392	+	9.57013i	−0.202139	+	0.320073i
$895$	0.434326	+	0.675824i	0.0145179	+	0.0225903i
$896$	−1.42084	+	1.74818i	−0.0474668	+	0.0584026i
$897$	−16.0280	+	1.55895i	−0.535161	+	0.0520517i
$898$	19.4025	−	12.5931i	0.647471	−	0.420237i
$899$	−22.9698	−	35.7417i	−0.766086	−	1.19205i
$900$	24.1729	−	16.0809i	0.805763	−	0.536031i
$901$	−33.2174	−	15.1699i	−1.10663	−	0.505382i
$902$	7.79766	+	6.69546i	0.259634	+	0.222934i
$903$	0.786314	−	1.23274i	0.0261669	−	0.0410230i
$904$	−7.19693	+	8.53609i	−0.239366	+	0.283906i
$905$	−3.43698	+	0.494163i	−0.114249	+	0.0164265i
$906$	16.9733	−	19.9042i	0.563900	−	0.661272i
$907$	29.1406	−	33.6301i	0.967598	−	1.11667i	−0.0255343	−	0.999674i	$-0.508129\pi$
$907$	29.1406	−	33.6301i	0.967598	−	1.11667i	0.993133	−	0.116994i	$-0.0373258\pi$
$908$	2.22273	+	3.39107i	0.0737638	+	0.112537i
$909$	29.6829	−	19.3630i	0.984518	−	0.642229i
$910$	0.217048	+	0.0302095i	0.00719506	+	0.00100144i
$911$	−31.3847	−	9.21537i	−1.03982	−	0.305319i	−0.283123	−	0.959084i	$-0.591370\pi$
$911$	−31.3847	−	9.21537i	−1.03982	−	0.305319i	−0.756698	+	0.653765i	$0.773189\pi$
$912$	−1.11148	+	9.11225i	−0.0368047	+	0.301737i
$913$	3.07867	+	3.55298i	0.101889	+	0.117586i
$914$	−9.40736	+	14.7841i	−0.311168	+	0.489016i
$915$	−6.85463	−	5.89882i	−0.226607	−	0.195009i
$916$	23.5139	−	20.7487i	0.776920	−	0.685556i
$917$	0.390715	−	2.71748i	0.0129026	−	0.0897392i
$918$	42.5314	+	11.8111i	1.40374	+	0.389825i
$919$		−	17.7330i		−	0.584959i	−0.956272	−	0.292479i	$-0.905520\pi$
$919$		−	17.7330i		−	0.584959i	0.956272	−	0.292479i	$-0.0944803\pi$
$920$	−3.10561	+	4.47261i	−0.102389	+	0.147458i
$921$	1.23946	−	0.802530i	0.0408416	−	0.0264443i
$922$	−29.2237	−	13.1873i	−0.962432	−	0.434300i
$923$	−2.17707	−	0.313016i	−0.0716593	−	0.0103031i
$924$	−1.84365	−	0.516573i	−0.0606517	−	0.0169940i
$925$	−5.01343	−	17.0742i	−0.164841	−	0.561396i
$926$	1.44086	+	0.916841i	0.0473496	+	0.0301293i
$927$	11.1100	+	36.9055i	0.364901	+	1.21214i
$928$	30.6910	+	3.70936i	1.00748	+	0.121766i
$929$	−7.08237	+	24.1203i	−0.232365	+	0.791363i	0.757924	+	0.652342i	$0.226214\pi$
$929$	−7.08237	+	24.1203i	−0.232365	+	0.791363i	−0.990290	+	0.139021i	$0.955605\pi$
$930$	−3.23044	−	6.92813i	−0.105930	−	0.227182i
$931$	−7.75837	−	4.98600i	−0.254270	−	0.163410i
$932$	−12.5628	−	19.1662i	−0.411507	−	0.627809i
$933$	−6.60075	+	47.0461i	−0.216099	+	1.54022i
$934$	10.8552	−	3.24056i	0.355193	−	0.106034i
$935$	−0.952537	−	6.62504i	−0.0311513	−	0.216662i
$936$	7.13628	+	14.8215i	0.233257	+	0.484456i
$937$	5.00599	+	10.9616i	0.163538	+	0.358099i	0.973605	−	0.228238i	$-0.0732965\pi$
$937$	5.00599	+	10.9616i	0.163538	+	0.358099i	−0.810067	+	0.586337i	$0.800569\pi$
$938$	−1.31769	+	1.53461i	−0.0430240	+	0.0501067i
$939$	−7.12662	−	48.3961i	−0.232568	−	1.57935i
$940$	6.99788	+	4.40869i	0.228246	+	0.143796i
$941$	−29.0899	+	18.6949i	−0.948302	+	0.609437i	−0.920737	−	0.390183i	$-0.872412\pi$
$941$	−29.0899	+	18.6949i	−0.948302	+	0.609437i	−0.0275652	+	0.999620i	$0.508775\pi$
$942$	−20.2106	+	45.1977i	−0.658496	+	1.47262i
$943$	9.88259	−	7.74545i	0.321821	−	0.252227i
$944$	−8.92912	+	8.02330i	−0.290618	+	0.261136i
$945$	−0.311086	+	0.275172i	−0.0101196	+	0.00895136i
$946$	−6.98190	−	15.1078i	−0.227001	−	0.491196i
$947$	28.1979	+	12.8775i	0.916309	+	0.418464i	0.817030	−	0.576596i	$-0.195619\pi$
$947$	28.1979	+	12.8775i	0.916309	+	0.418464i	0.0992788	+	0.995060i	$0.468346\pi$
$948$	−28.1852	+	13.2971i	−0.915412	+	0.431868i
$949$	−9.32879	+	4.26032i	−0.302825	+	0.138296i
$950$	−2.51530	+	8.71128i	−0.0816070	+	0.282631i
$951$	−17.3447	−	19.8796i	−0.562440	−	0.644641i
$952$	−3.35474	−	0.436155i	−0.108728	−	0.0141359i
$953$	−25.2603	−	21.8882i	−0.818263	−	0.709029i	0.141470	−	0.989943i	$-0.454817\pi$
$953$	−25.2603	−	21.8882i	−0.818263	−	0.709029i	−0.959733	+	0.280914i	$0.909362\pi$
$954$	23.5814	+	10.4484i	0.763475	+	0.338279i
$955$	7.63120	+	4.90427i	0.246940	+	0.158699i
$956$	−9.22988	−	19.7381i	−0.298515	−	0.638375i
$957$	7.48823	+	25.1850i	0.242060	+	0.814115i
$958$	−15.4190	+	13.4827i	−0.498165	+	0.435607i
$959$	2.03319	+	2.34642i	0.0656550	+	0.0757699i
$960$	5.38211	+	1.40394i	0.173707	+	0.0453121i
$961$	28.2478	−	8.29429i	0.911218	−	0.267558i
$962$	9.97336	−	1.47983i	0.321554	−	0.0477118i
$963$	7.65180	−	12.0866i	0.246576	−	0.389487i
$964$	8.77494	+	57.3580i	0.282622	+	1.84738i
$965$	−1.16478			−0.0374955
$966$	−1.05879	+	2.08575i	−0.0340662	+	0.0671078i
$967$		−	45.9808i		−	1.47864i	−0.673352	−	0.739322i	$-0.735146\pi$
$967$		−	45.9808i		−	1.47864i	0.673352	−	0.739322i	$-0.264854\pi$
$968$	6.95989	−	6.19741i	0.223699	−	0.199192i
$969$	−12.5200	+	5.76930i	−0.402200	+	0.185337i
$970$	6.65825	−	0.987942i	0.213783	−	0.0317209i
$971$	1.67938	+	5.71946i	0.0538940	+	0.183546i	0.982041	−	0.188668i	$-0.0604169\pi$
$971$	1.67938	+	5.71946i	0.0538940	+	0.183546i	−0.928147	+	0.372214i	$0.878599\pi$
$972$	−30.1326	−	8.00180i	−0.966502	−	0.256658i
$973$	1.66656	−	1.44408i	0.0534274	−	0.0462951i
$974$	15.2867	+	17.4820i	0.489817	+	0.560160i
$975$	4.63071	+	15.5743i	0.148301	+	0.498778i
$976$	0.937346	+	52.0189i	0.0300037	+	1.66508i
$977$	14.9363	−	23.2413i	0.477853	−	0.743554i	−0.515719	−	0.856758i	$-0.672475\pi$
$977$	14.9363	−	23.2413i	0.477853	−	0.743554i	0.993572	+	0.113204i	$0.0361114\pi$
$978$	32.5916	+	49.8422i	1.04216	+	1.59378i
$979$	12.9054	−	14.8936i	0.412458	−	0.476001i
$980$	−3.62118	+	4.25594i	−0.115674	+	0.135951i
$981$	−1.69377	+	5.91724i	−0.0540778	+	0.188923i
$982$	−51.1473	−	14.7683i	−1.63217	−	0.471274i
$983$	−9.71208	−	21.2665i	−0.309767	−	0.678296i	0.689160	−	0.724610i	$-0.257980\pi$
$983$	−9.71208	−	21.2665i	−0.309767	−	0.678296i	−0.998927	+	0.0463138i	$0.985253\pi$
$984$	−10.9059	−	6.75085i	−0.347667	−	0.215209i
$985$	−2.35272	+	5.15174i	−0.0749639	+	0.164148i
$986$	19.4753	+	42.1417i	0.620221	+	1.34206i
$987$	3.23691	+	1.46495i	0.103032	+	0.0466297i
$988$	−4.69217	−	2.09197i	−0.149278	−	0.0665543i
$989$	−19.7673	+	4.76103i	−0.628562	+	0.151392i
$990$	0.725686	+	4.67139i	0.0230638	+	0.148466i
$991$	24.5422	+	38.1884i	0.779608	+	1.21309i	0.972735	+	0.231920i	$0.0745009\pi$
$991$	24.5422	+	38.1884i	0.779608	+	1.21309i	−0.193126	+	0.981174i	$0.561863\pi$
$992$	−17.3637	+	40.4053i	−0.551299	+	1.28287i
$993$	−3.44435	−	23.3902i	−0.109303	−	0.742266i
$994$	−0.208123	+	0.242385i	−0.00660127	+	0.00768797i
$995$	−0.384736	+	0.175703i	−0.0121969	+	0.00557015i
$996$	−4.48132	−	3.78672i	−0.141996	−	0.119987i
$997$	50.7876	−	7.30215i	1.60846	−	0.231261i	0.721265	−	0.692659i	$-0.243561\pi$
$997$	50.7876	−	7.30215i	1.60846	−	0.231261i	0.887194	+	0.461397i	$0.152652\pi$
$998$	11.2678	+	37.7448i	0.356676	+	1.19479i
$999$	−10.1663	+	16.1802i	−0.321647	+	0.511918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.x.a.35.12	✓	920
3.2	odd	2	inner	552.2.x.a.35.81	yes	920
8.3	odd	2	inner	552.2.x.a.35.48	yes	920
23.2	even	11	inner	552.2.x.a.347.45	yes	920
24.11	even	2	inner	552.2.x.a.35.45	yes	920
69.2	odd	22	inner	552.2.x.a.347.48	yes	920
184.163	odd	22	inner	552.2.x.a.347.81	yes	920
552.347	even	22	inner	552.2.x.a.347.12	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.x.a.35.12	✓	920	1.1	even	1	trivial
552.2.x.a.35.45	yes	920	24.11	even	2	inner
552.2.x.a.35.48	yes	920	8.3	odd	2	inner
552.2.x.a.35.81	yes	920	3.2	odd	2	inner
552.2.x.a.347.12	yes	920	552.347	even	22	inner
552.2.x.a.347.45	yes	920	23.2	even	11	inner
552.2.x.a.347.48	yes	920	69.2	odd	22	inner
552.2.x.a.347.81	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)

\(f(q)\)	\(=\)	\(q+(-1.28905 - 0.581685i) q^{2} +(-0.724881 - 1.57307i) q^{3} +(1.32328 + 1.49964i) q^{4} +(0.385158 - 0.113093i) q^{5} +(0.0193752 + 2.44941i) q^{6} +(-0.150483 + 0.130394i) q^{7} +(-0.833459 - 2.70284i) q^{8} +(-1.94909 + 2.28058i) q^{9} +O(q^{10})\)	\(q+(-1.28905 - 0.581685i) q^{2} +(-0.724881 - 1.57307i) q^{3} +(1.32328 + 1.49964i) q^{4} +(0.385158 - 0.113093i) q^{5} +(0.0193752 + 2.44941i) q^{6} +(-0.150483 + 0.130394i) q^{7} +(-0.833459 - 2.70284i) q^{8} +(-1.94909 + 2.28058i) q^{9} +(-0.562271 - 0.0782590i) q^{10} +(-1.50072 + 2.33517i) q^{11} +(1.39981 - 3.16868i) q^{12} +(1.46514 + 1.26955i) q^{13} +(0.269828 - 0.0805505i) q^{14} +(-0.457096 - 0.523901i) q^{15} +(-0.497835 + 3.96890i) q^{16} +(-5.46399 + 2.49532i) q^{17} +(3.83905 - 1.80601i) q^{18} +(-0.550420 + 1.20525i) q^{19} +(0.679271 + 0.427944i) q^{20} +(0.314201 + 0.142200i) q^{21} +(3.29283 - 2.13719i) q^{22} +(-1.77510 - 4.45523i) q^{23} +(-3.64760 + 3.27033i) q^{24} +(-4.07071 + 2.61609i) q^{25} +(-1.15015 - 2.48876i) q^{26} +(5.00037 + 1.41291i) q^{27} +(-0.394676 - 0.0531214i) q^{28} +(2.27022 + 4.97108i) q^{29} +(0.284473 + 0.941219i) q^{30} +(-7.69520 + 1.10640i) q^{31} +(2.95038 - 4.82651i) q^{32} +(4.76122 + 0.668018i) q^{33} +(8.49483 - 0.0382640i) q^{34} +(-0.0432130 + 0.0672408i) q^{35} +(-5.99925 + 0.0949157i) q^{36} +(-1.03608 + 3.52855i) q^{37} +(1.41059 - 1.23346i) q^{38} +(0.935038 - 3.22504i) q^{39} +(-0.626684 - 0.946762i) q^{40} +(0.737616 + 2.51209i) q^{41} +(-0.322305 - 0.366068i) q^{42} +(0.603362 - 4.19647i) q^{43} +(-5.48778 + 0.839551i) q^{44} +(-0.492792 + 1.09881i) q^{45} +(-0.303356 + 6.77554i) q^{46} +10.3020 q^{47} +(6.60422 - 2.09385i) q^{48} +(-0.990561 + 6.88951i) q^{49} +(6.76908 - 1.00439i) q^{50} +(7.88606 + 6.78642i) q^{51} +(0.0349291 + 3.87715i) q^{52} +(3.98112 + 4.59445i) q^{53} +(-5.62384 - 4.72995i) q^{54} +(-0.313924 + 1.06913i) q^{55} +(0.477856 + 0.298053i) q^{56} +(2.29493 - 0.00781571i) q^{57} +(-0.0348122 - 7.72851i) q^{58} +(2.26806 + 1.96528i) q^{59} +(0.180794 - 1.37875i) q^{60} +(12.8744 - 1.85106i) q^{61} +(10.5631 + 3.04998i) q^{62} +(-0.00406868 - 0.597338i) q^{63} +(-6.61069 + 4.50541i) q^{64} +(0.707886 + 0.323281i) q^{65} +(-5.74886 - 3.63064i) q^{66} +(-6.04275 + 3.88344i) q^{67} +(-10.9725 - 4.89199i) q^{68} +(-5.72164 + 6.02186i) q^{69} +(0.0948166 - 0.0615401i) q^{70} +(-0.954427 + 0.613373i) q^{71} +(7.78853 + 3.36732i) q^{72} +(-2.19756 + 4.81199i) q^{73} +(3.38806 - 3.94580i) q^{74} +(7.06607 + 4.50716i) q^{75} +(-2.53581 + 0.769460i) q^{76} +(-0.0786593 - 0.547087i) q^{77} +(-3.08126 + 3.61333i) q^{78} +(-6.79900 - 5.89137i) q^{79} +(0.257108 + 1.58495i) q^{80} +(-1.40207 - 8.89012i) q^{81} +(0.510424 - 3.66726i) q^{82} +(0.477157 - 1.62505i) q^{83} +(0.202529 + 0.659359i) q^{84} +(-1.82230 + 1.57903i) q^{85} +(-3.21879 + 5.05848i) q^{86} +(6.17422 - 7.17466i) q^{87} +(7.56237 + 2.10994i) q^{88} +(-7.02729 - 1.01037i) q^{89} +(1.27439 - 1.12977i) q^{90} -0.386020 q^{91} +(4.33227 - 8.55754i) q^{92} +(7.31856 + 11.3031i) q^{93} +(-13.2798 - 5.99254i) q^{94} +(-0.0756936 + 0.526461i) q^{95} +(-9.73112 - 1.14250i) q^{96} +(-11.3768 + 3.34052i) q^{97} +(5.28440 - 8.30470i) q^{98} +(-2.40048 - 7.97396i) 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

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