LMFDB - Embedded newform 165.2.p.b.41.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(41,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("165.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.p (of order $10$, degree $4$, 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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.8
Character	$\chi$	$=$	165.41
Dual form			165.2.p.b.161.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.860692 - 0.625329i) q^{2} +(1.72070 + 0.197973i) q^{3} +(-0.268280 + 0.825682i) q^{4} +(0.587785 - 0.809017i) q^{5} +(1.60479 - 0.905610i) q^{6} +(-2.18340 - 0.709430i) q^{7} +(0.942926 + 2.90203i) q^{8} +(2.92161 + 0.681304i) q^{9} +O(q^{10})$	\(q+(0.860692 - 0.625329i) q^{2} +(1.72070 + 0.197973i) q^{3} +(-0.268280 + 0.825682i) q^{4} +(0.587785 - 0.809017i) q^{5} +(1.60479 - 0.905610i) q^{6} +(-2.18340 - 0.709430i) q^{7} +(0.942926 + 2.90203i) q^{8} +(2.92161 + 0.681304i) q^{9} -1.06387i q^{10} +(-2.26806 - 2.41990i) q^{11} +(-0.625093 + 1.36764i) q^{12} +(-1.13108 - 1.55680i) q^{13} +(-2.32286 + 0.754744i) q^{14} +(1.17157 - 1.27571i) q^{15} +(1.22156 + 0.887513i) q^{16} +(3.01987 + 2.19406i) q^{17} +(2.94065 - 1.24058i) q^{18} +(-8.13782 + 2.64414i) q^{19} +(0.510300 + 0.702367i) q^{20} +(-3.61653 - 1.65297i) q^{21} +(-3.46533 - 0.664507i) q^{22} -4.81565i q^{23} +(1.04797 + 5.18019i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(-1.94703 - 0.632628i) q^{26} +(4.89234 + 1.75072i) q^{27} +(1.17153 - 1.61247i) q^{28} +(1.01807 - 3.13331i) q^{29} +(0.210618 - 1.83061i) q^{30} +(3.98742 - 2.89703i) q^{31} -4.49638 q^{32} +(-3.42357 - 4.61294i) q^{33} +3.97119 q^{34} +(-1.85731 + 1.34942i) q^{35} +(-1.34635 + 2.22954i) q^{36} +(-3.59329 + 11.0590i) q^{37} +(-5.35070 + 7.36461i) q^{38} +(-1.63805 - 2.90271i) q^{39} +(2.90203 + 0.942926i) q^{40} +(0.619630 + 1.90703i) q^{41} +(-4.14637 + 0.838824i) q^{42} +6.20394i q^{43} +(2.60654 - 1.22348i) q^{44} +(2.26847 - 1.96317i) q^{45} +(-3.01137 - 4.14479i) q^{46} +(3.15533 - 1.02523i) q^{47} +(1.92623 + 1.76898i) q^{48} +(-1.39916 - 1.01655i) q^{49} +(-0.860692 - 0.625329i) q^{50} +(4.76192 + 4.37317i) q^{51} +(1.58887 - 0.516256i) q^{52} +(3.55103 + 4.88758i) q^{53} +(5.30557 - 1.55249i) q^{54} +(-3.29087 + 0.412514i) q^{55} -7.00524i q^{56} +(-14.5262 + 2.93870i) q^{57} +(-1.08310 - 3.33345i) q^{58} +(-0.0820820 - 0.0266700i) q^{59} +(0.739023 + 1.30959i) q^{60} +(4.79602 - 6.60115i) q^{61} +(1.62034 - 4.98690i) q^{62} +(-5.89572 - 3.56024i) q^{63} +(-6.31311 + 4.58674i) q^{64} -1.92431 q^{65} +(-5.83124 - 1.82946i) q^{66} +3.92216 q^{67} +(-2.62177 + 1.90483i) q^{68} +(0.953369 - 8.28629i) q^{69} +(-0.754744 + 2.32286i) q^{70} +(8.64598 - 11.9002i) q^{71} +(0.777703 + 9.12102i) q^{72} +(5.23264 + 1.70019i) q^{73} +(3.82280 + 11.7654i) q^{74} +(-0.343442 - 1.69766i) q^{75} -7.42863i q^{76} +(3.23533 + 6.89265i) q^{77} +(-3.22501 - 1.47402i) q^{78} +(0.0325499 + 0.0448010i) q^{79} +(1.43603 - 0.466593i) q^{80} +(8.07165 + 3.98101i) q^{81} +(1.72583 + 1.25389i) q^{82} +(-1.22085 - 0.886997i) q^{83} +(2.33507 - 2.54265i) q^{84} +(3.55007 - 1.15349i) q^{85} +(3.87950 + 5.33968i) q^{86} +(2.37211 - 5.18994i) q^{87} +(4.88401 - 8.86375i) q^{88} +1.65507i q^{89} +(0.724821 - 3.10823i) q^{90} +(1.36517 + 4.20155i) q^{91} +(3.97620 + 1.29195i) q^{92} +(7.43469 - 4.19552i) q^{93} +(2.07466 - 2.85552i) q^{94} +(-2.64414 + 8.13782i) q^{95} +(-7.73691 - 0.890160i) q^{96} +(6.60805 - 4.80103i) q^{97} -1.83993 q^{98} +(-4.97770 - 8.61525i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) $ 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9	$ 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9} + 8 q^{12} + 6 q^{15} + 32 q^{16} - 30 q^{18} - 100 q^{19} - 82 q^{22} + 100 q^{24} + 12 q^{25} + 14 q^{27} + 30 q^{28} + 10 q^{30} + 10 q^{31} - 46 q^{33} - 28 q^{34} + 14 q^{36} + 6 q^{37} - 50 q^{40} - 52 q^{42} + 32 q^{45} + 20 q^{46} - 80 q^{48} - 26 q^{49} - 30 q^{51} + 40 q^{52} + 6 q^{55} - 70 q^{57} + 92 q^{58} + 44 q^{60} + 70 q^{61} - 20 q^{63} + 18 q^{64} + 76 q^{66} + 20 q^{67} + 42 q^{69} - 4 q^{70} - 80 q^{72} + 90 q^{73} - 6 q^{75} - 108 q^{78} - 100 q^{79} + 38 q^{81} - 34 q^{82} + 70 q^{84} + 20 q^{85} + 74 q^{88} + 20 q^{90} - 86 q^{91} + 76 q^{93} + 10 q^{94} - 30 q^{96} + 6 q^{97} - 28 q^{99}+O(q^{100}) $ 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9 + 8 * q^12 + 6 * q^15 + 32 * q^16 - 30 * q^18 - 100 * q^19 - 82 * q^22 + 100 * q^24 + 12 * q^25 + 14 * q^27 + 30 * q^28 + 10 * q^30 + 10 * q^31 - 46 * q^33 - 28 * q^34 + 14 * q^36 + 6 * q^37 - 50 * q^40 - 52 * q^42 + 32 * q^45 + 20 * q^46 - 80 * q^48 - 26 * q^49 - 30 * q^51 + 40 * q^52 + 6 * q^55 - 70 * q^57 + 92 * q^58 + 44 * q^60 + 70 * q^61 - 20 * q^63 + 18 * q^64 + 76 * q^66 + 20 * q^67 + 42 * q^69 - 4 * q^70 - 80 * q^72 + 90 * q^73 - 6 * q^75 - 108 * q^78 - 100 * q^79 + 38 * q^81 - 34 * q^82 + 70 * q^84 + 20 * q^85 + 74 * q^88 + 20 * q^90 - 86 * q^91 + 76 * q^93 + 10 * q^94 - 30 * q^96 + 6 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

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 $

$2$	0.860692	−	0.625329i	0.608601	−	0.442174i	−0.240321	−	0.970694i	$-0.577253\pi$
$2$	0.860692	−	0.625329i	0.608601	−	0.442174i	0.848921	+	0.528519i	$0.177253\pi$
$3$	1.72070	+	0.197973i	0.993446	+	0.114300i
$3$	1.72070	+	0.197973i	0.993446	+	0.114300i
$4$	−0.268280	+	0.825682i	−0.134140	+	0.412841i
$5$	0.587785	−	0.809017i	0.262866	−	0.361803i
$5$	0.587785	−	0.809017i	0.262866	−	0.361803i
$6$	1.60479	−	0.905610i	0.655153	−	0.369714i
$7$	−2.18340	−	0.709430i	−0.825249	−	0.268139i	−0.134206	−	0.990953i	$-0.542848\pi$
$7$	−2.18340	−	0.709430i	−0.825249	−	0.268139i	−0.691043	+	0.722814i	$0.742848\pi$
$8$	0.942926	+	2.90203i	0.333375	+	1.02602i
$9$	2.92161	+	0.681304i	0.973871	+	0.227101i
$10$		−	1.06387i		−	0.336426i
$11$	−2.26806	−	2.41990i	−0.683845	−	0.729628i
$11$	−2.26806	−	2.41990i	−0.683845	−	0.729628i
$12$	−0.625093	+	1.36764i	−0.180449	+	0.394803i
$13$	−1.13108	−	1.55680i	−0.313706	−	0.431780i	0.622826	−	0.782360i	$-0.285984\pi$
$13$	−1.13108	−	1.55680i	−0.313706	−	0.431780i	−0.936533	+	0.350581i	$0.885984\pi$
$14$	−2.32286	+	0.754744i	−0.620811	+	0.201714i
$15$	1.17157	−	1.27571i	0.302497	−	0.329387i
$16$	1.22156	+	0.887513i	0.305389	+	0.221878i
$17$	3.01987	+	2.19406i	0.732426	+	0.532138i	0.890330	−	0.455316i	$-0.150474\pi$
$17$	3.01987	+	2.19406i	0.732426	+	0.532138i	−0.157904	+	0.987454i	$0.550474\pi$
$18$	2.94065	−	1.24058i	0.693117	−	0.292407i
$19$	−8.13782	+	2.64414i	−1.86695	+	0.606607i	−0.874325	+	0.485341i	$0.838696\pi$
$19$	−8.13782	+	2.64414i	−1.86695	+	0.606607i	−0.992620	+	0.121266i	$0.961304\pi$
$20$	0.510300	+	0.702367i	0.114106	+	0.157054i
$21$	−3.61653	−	1.65297i	−0.789192	−	0.360708i
$22$	−3.46533	−	0.664507i	−0.738811	−	0.141673i
$23$		−	4.81565i		−	1.00413i	−0.864829	−	0.502067i	$-0.832573\pi$
$23$		−	4.81565i		−	1.00413i	0.864829	−	0.502067i	$-0.167427\pi$
$24$	1.04797	+	5.18019i	0.213916	+	1.05740i
$25$	−0.309017	−	0.951057i	−0.0618034	−	0.190211i
$26$	−1.94703	−	0.632628i	−0.381844	−	0.124069i
$27$	4.89234	+	1.75072i	0.941531	+	0.336926i
$28$	1.17153	−	1.61247i	0.221398	−	0.304728i
$29$	1.01807	−	3.13331i	0.189052	−	0.581842i	−0.810943	−	0.585125i	$-0.801045\pi$
$29$	1.01807	−	3.13331i	0.189052	−	0.581842i	0.999995	+	0.00328386i	$0.00104529\pi$
$30$	0.210618	−	1.83061i	0.0384534	−	0.334221i
$31$	3.98742	−	2.89703i	0.716162	−	0.520322i	−0.168994	−	0.985617i	$-0.554052\pi$
$31$	3.98742	−	2.89703i	0.716162	−	0.520322i	0.885156	+	0.465295i	$0.154052\pi$
$32$	−4.49638			−0.794854
$33$	−3.42357	−	4.61294i	−0.595967	−	0.803009i
$34$	3.97119			0.681053
$35$	−1.85731	+	1.34942i	−0.313943	+	0.228093i
$36$	−1.34635	+	2.22954i	−0.224392	+	0.371591i
$37$	−3.59329	+	11.0590i	−0.590733	+	1.81809i	−0.0158175	+	0.999875i	$0.505035\pi$
$37$	−3.59329	+	11.0590i	−0.590733	+	1.81809i	−0.574915	+	0.818213i	$0.694965\pi$
$38$	−5.35070	+	7.36461i	−0.867998	+	1.19470i
$39$	−1.63805	−	2.90271i	−0.262298	−	0.464806i
$40$	2.90203	+	0.942926i	0.458851	+	0.149090i
$41$	0.619630	+	1.90703i	0.0967700	+	0.297827i	0.987711	−	0.156292i	$-0.0499540\pi$
$41$	0.619630	+	1.90703i	0.0967700	+	0.297827i	−0.890941	+	0.454119i	$0.849954\pi$
$42$	−4.14637	+	0.838824i	−0.639799	+	0.129433i
$43$			6.20394i			0.946092i	0.881038	+	0.473046i	$0.156846\pi$
$43$			6.20394i			0.946092i	−0.881038	+	0.473046i	$0.843154\pi$
$44$	2.60654	−	1.22348i	0.392951	−	0.184447i
$45$	2.26847	−	1.96317i	0.338163	−	0.292653i
$46$	−3.01137	−	4.14479i	−0.444002	−	0.611116i
$47$	3.15533	−	1.02523i	0.460252	−	0.149545i	−0.0697083	−	0.997567i	$-0.522207\pi$
$47$	3.15533	−	1.02523i	0.460252	−	0.149545i	0.529960	+	0.848023i	$0.322207\pi$
$48$	1.92623	+	1.76898i	0.278027	+	0.255330i
$49$	−1.39916	−	1.01655i	−0.199881	−	0.145222i
$50$	−0.860692	−	0.625329i	−0.121720	−	0.0884349i
$51$	4.76192	+	4.37317i	0.666802	+	0.612367i
$52$	1.58887	−	0.516256i	0.220337	−	0.0715918i
$53$	3.55103	+	4.88758i	0.487772	+	0.671361i	0.979975	−	0.199120i	$-0.0638083\pi$
$53$	3.55103	+	4.88758i	0.487772	+	0.671361i	−0.492203	+	0.870480i	$0.663808\pi$
$54$	5.30557	−	1.55249i	0.721997	−	0.211267i
$55$	−3.29087	+	0.412514i	−0.443741	+	0.0556233i
$56$		−	7.00524i		−	0.936114i
$57$	−14.5262	+	2.93870i	−1.92404	+	0.389240i
$58$	−1.08310	−	3.33345i	−0.142218	−	0.437703i
$59$	−0.0820820	−	0.0266700i	−0.0106862	−	0.00347214i	0.303669	−	0.952778i	$-0.401788\pi$
$59$	−0.0820820	−	0.0266700i	−0.0106862	−	0.00347214i	−0.314355	+	0.949305i	$0.601788\pi$
$60$	0.739023	+	1.30959i	0.0954074	+	0.169067i
$61$	4.79602	−	6.60115i	0.614067	−	0.845191i	−0.382837	−	0.923816i	$-0.625053\pi$
$61$	4.79602	−	6.60115i	0.614067	−	0.845191i	0.996904	+	0.0786250i	$0.0250530\pi$
$62$	1.62034	−	4.98690i	0.205784	−	0.633337i
$63$	−5.89572	−	3.56024i	−0.742791	−	0.448548i
$64$	−6.31311	+	4.58674i	−0.789138	+	0.573342i
$65$	−1.92431			−0.238682
$66$	−5.83124	−	1.82946i	−0.717776	−	0.225191i
$67$	3.92216			0.479169			0.239584	−	0.970876i	$-0.422989\pi$
$67$	3.92216			0.479169			0.239584	+	0.970876i	$0.422989\pi$
$68$	−2.62177	+	1.90483i	−0.317936	+	0.230994i
$69$	0.953369	−	8.28629i	0.114772	−	0.997552i
$70$	−0.754744	+	2.32286i	−0.0902092	+	0.277635i
$71$	8.64598	−	11.9002i	1.02609	−	1.41229i	0.118243	−	0.992985i	$-0.462274\pi$
$71$	8.64598	−	11.9002i	1.02609	−	1.41229i	0.907845	−	0.419305i	$-0.137726\pi$
$72$	0.777703	+	9.12102i	0.0916532	+	1.07492i
$73$	5.23264	+	1.70019i	0.612434	+	0.198992i	0.598778	−	0.800915i	$-0.295653\pi$
$73$	5.23264	+	1.70019i	0.612434	+	0.198992i	0.0136559	+	0.999907i	$0.495653\pi$
$74$	3.82280	+	11.7654i	0.444392	+	1.36770i
$75$	−0.343442	−	1.69766i	−0.0396573	−	0.196029i
$76$		−	7.42863i		−	0.852122i
$77$	3.23533	+	6.89265i	0.368700	+	0.785490i
$78$	−3.22501	−	1.47402i	−0.365160	−	0.166900i
$79$	0.0325499	+	0.0448010i	0.00366215	+	0.00504051i	0.810844	−	0.585262i	$-0.199008\pi$
$79$	0.0325499	+	0.0448010i	0.00366215	+	0.00504051i	−0.807182	+	0.590303i	$0.799008\pi$
$80$	1.43603	−	0.466593i	0.160553	−	0.0521667i
$81$	8.07165	+	3.98101i	0.896850	+	0.442335i
$82$	1.72583	+	1.25389i	0.190586	+	0.138469i
$83$	−1.22085	−	0.886997i	−0.134005	−	0.0973605i	0.518763	−	0.854918i	$-0.326393\pi$
$83$	−1.22085	−	0.886997i	−0.134005	−	0.0973605i	−0.652769	+	0.757557i	$0.726393\pi$
$84$	2.33507	−	2.54265i	0.254777	−	0.277425i
$85$	3.55007	−	1.15349i	0.385059	−	0.125113i
$86$	3.87950	+	5.33968i	0.418338	+	0.575792i
$87$	2.37211	−	5.18994i	0.254317	−	0.556420i
$88$	4.88401	−	8.86375i	0.520637	−	0.944879i
$89$			1.65507i			0.175437i	0.996145	+	0.0877187i	$0.0279577\pi$
$89$			1.65507i			0.175437i	−0.996145	+	0.0877187i	$0.972042\pi$
$90$	0.724821	−	3.10823i	0.0764028	−	0.327636i
$91$	1.36517	+	4.20155i	0.143108	+	0.440442i
$92$	3.97620	+	1.29195i	0.414548	+	0.134695i
$93$	7.43469	−	4.19552i	0.770941	−	0.435055i
$94$	2.07466	−	2.85552i	0.213985	−	0.294525i
$95$	−2.64414	+	8.13782i	−0.271283	+	0.834923i
$96$	−7.73691	−	0.890160i	−0.789645	−	0.0908516i
$97$	6.60805	−	4.80103i	0.670946	−	0.487471i	−0.199396	−	0.979919i	$-0.563898\pi$
$97$	6.60805	−	4.80103i	0.670946	−	0.487471i	0.870342	+	0.492448i	$0.163898\pi$
$98$	−1.83993			−0.185861
$99$	−4.97770	−	8.61525i	−0.500277	−	0.865865i
$100$	0.868174			0.0868174
$101$	8.64372	−	6.28003i	0.860083	−	0.624887i	−0.0678248	−	0.997697i	$-0.521606\pi$
$101$	8.64372	−	6.28003i	0.860083	−	0.624887i	0.927907	+	0.372811i	$0.121606\pi$
$102$	6.83322	+	0.786187i	0.676589	+	0.0778441i
$103$	−1.97224	+	6.06993i	−0.194331	+	0.598088i	0.805653	+	0.592388i	$0.201815\pi$
$103$	−1.97224	+	6.06993i	−0.194331	+	0.598088i	−0.999984	+	0.00570051i	$0.998185\pi$
$104$	3.45136	−	4.75039i	0.338434	−	0.465814i
$105$	−3.46303	+	1.95424i	−0.337957	+	0.190715i
$106$	6.11269	+	1.98613i	0.593717	+	0.192910i
$107$	−1.22154	−	3.75952i	−0.118091	−	0.363447i	0.874488	−	0.485047i	$-0.161197\pi$
$107$	−1.22154	−	3.75952i	−0.118091	−	0.363447i	−0.992579	+	0.121600i	$0.961197\pi$
$108$	−2.75806	+	3.56983i	−0.265394	+	0.343507i
$109$		−	6.02866i		−	0.577441i	−0.957413	−	0.288720i	$-0.906770\pi$
$109$		−	6.02866i		−	0.577441i	0.957413	−	0.288720i	$-0.0932298\pi$
$110$	−2.57447	+	2.41292i	−0.245466	+	0.230063i
$111$	−8.37235	+	18.3178i	−0.794668	+	1.73865i
$112$	−2.03752	−	2.80441i	−0.192528	−	0.264992i
$113$	−14.7344	+	4.78748i	−1.38609	+	0.450369i	−0.904667	−	0.426119i	$-0.859881\pi$
$113$	−14.7344	+	4.78748i	−1.38609	+	0.450369i	−0.481425	+	0.876487i	$0.659881\pi$
$114$	−10.6649	+	11.6130i	−0.998863	+	1.08766i
$115$	−3.89595	−	2.83057i	−0.363299	−	0.263952i
$116$	2.31399	+	1.68121i	0.214849	+	0.156097i
$117$	−2.24393	−	5.31899i	−0.207452	−	0.491741i
$118$	−0.0873248	+	0.0283735i	−0.00803890	+	0.00261200i
$119$	−5.03705	−	6.93291i	−0.461746	−	0.635539i
$120$	4.80685	+	2.19702i	0.438803	+	0.200559i
$121$	−0.711843	+	10.9769i	−0.0647130	+	0.997904i
$122$		−	8.68064i		−	0.785909i
$123$	0.688658	+	3.40409i	0.0620942	+	0.306936i
$124$	1.32228	+	4.06956i	0.118744	+	0.365457i
$125$	−0.951057	−	0.309017i	−0.0850651	−	0.0276393i
$126$	−7.30072	+	0.622495i	−0.650400	+	0.0554563i
$127$	4.57069	−	6.29102i	0.405583	−	0.558237i	−0.556551	−	0.830813i	$-0.687876\pi$
$127$	4.57069	−	6.29102i	0.405583	−	0.558237i	0.962134	+	0.272576i	$0.0878756\pi$
$128$	0.213498	−	0.657080i	0.0188707	−	0.0580782i
$129$	−1.22821	+	10.6751i	−0.108138	+	0.939891i
$130$	−1.65624	+	1.20333i	−0.145262	+	0.105539i
$131$	−10.5252			−0.919591			−0.459796	−	0.888025i	$-0.652077\pi$
$131$	−10.5252			−0.919591			−0.459796	+	0.888025i	$0.652077\pi$
$132$	4.72730	−	1.58922i	0.411458	−	0.138324i
$133$	19.6440			1.70335
$134$	3.37577	−	2.45264i	0.291622	−	0.211876i
$135$	4.29201	−	2.92894i	0.369397	−	0.252083i
$136$	−3.51972	+	10.8326i	−0.301813	+	0.928886i
$137$	−2.04595	+	2.81600i	−0.174797	+	0.240587i	−0.887422	−	0.460958i	$-0.847506\pi$
$137$	−2.04595	+	2.81600i	−0.174797	+	0.240587i	0.712625	+	0.701545i	$0.247506\pi$
$138$	−4.36110	−	7.72811i	−0.371242	−	0.657861i
$139$	9.11024	+	2.96010i	0.772721	+	0.251072i	0.668729	−	0.743506i	$-0.266839\pi$
$139$	9.11024	+	2.96010i	0.772721	+	0.251072i	0.103991	+	0.994578i	$0.466839\pi$
$140$	−0.615909	−	1.89557i	−0.0520538	−	0.160205i
$141$	5.63234	−	1.13944i	0.474328	−	0.0959582i
$142$		−	15.6490i		−	1.31323i
$143$	−1.20195	+	6.26803i	−0.100512	+	0.524159i
$144$	2.96425	+	3.42522i	0.247021	+	0.285435i
$145$	−1.93649	−	2.66535i	−0.160817	−	0.221346i
$146$	5.56687	−	1.80878i	0.460717	−	0.149696i
$147$	−2.20629	−	2.02618i	−0.181972	−	0.167116i
$148$	−8.16721	−	5.93383i	−0.671341	−	0.487757i
$149$	−7.71489	−	5.60520i	−0.632029	−	0.459196i	0.225074	−	0.974342i	$-0.427738\pi$
$149$	−7.71489	−	5.60520i	−0.632029	−	0.459196i	−0.857102	+	0.515146i	$0.827738\pi$
$150$	−1.35719	−	1.24640i	−0.110814	−	0.101768i
$151$	−17.5178	+	5.69187i	−1.42558	+	0.463198i	−0.917369	−	0.398037i	$-0.869692\pi$
$151$	−17.5178	+	5.69187i	−1.42558	+	0.463198i	−0.508207	+	0.861235i	$0.669692\pi$
$152$	−15.3467	−	21.1230i	−1.24478	−	1.71330i
$153$	7.32806	+	8.46765i	0.592439	+	0.684569i
$154$	7.09479	+	3.90930i	0.571714	+	0.315020i
$155$		−	4.92872i		−	0.395885i
$156$	2.83618	−	0.573768i	0.227076	−	0.0459382i
$157$	5.14284	+	15.8280i	0.410444	+	1.26322i	0.916263	+	0.400576i	$0.131190\pi$
$157$	5.14284	+	15.8280i	0.410444	+	1.26322i	−0.505820	+	0.862639i	$0.668810\pi$
$158$	0.0560308	+	0.0182055i	0.00445757	+	0.00144835i
$159$	5.14266	+	9.11306i	0.407839	+	0.722713i
$160$	−2.64290	+	3.63764i	−0.208940	+	0.287581i
$161$	−3.41637	+	10.5145i	−0.269248	+	0.828659i
$162$	9.43664	−	1.62101i	0.741413	−	0.127359i
$163$	−14.3103	+	10.3970i	−1.12087	+	0.814358i	−0.984340	−	0.176278i	$-0.943594\pi$
$163$	−14.3103	+	10.3970i	−1.12087	+	0.814358i	−0.136528	+	0.990636i	$0.543594\pi$
$164$	−1.74083			−0.135936
$165$	−5.74427	+	0.0583089i	−0.447191	+	0.00453934i
$166$	−1.60544			−0.124606
$167$	−2.07029	+	1.50415i	−0.160204	+	0.116395i	−0.664999	−	0.746844i	$-0.731568\pi$
$167$	−2.07029	+	1.50415i	−0.160204	+	0.116395i	0.504795	+	0.863239i	$0.331568\pi$
$168$	1.38685	−	12.0539i	0.106998	−	0.929979i
$169$	2.87294	−	8.84198i	0.220995	−	0.680153i
$170$	2.33420	−	3.21276i	0.179025	−	0.246407i
$171$	−25.5770	+	2.18082i	−1.95593	+	0.166772i
$172$	−5.12248	−	1.66440i	−0.390586	−	0.126909i
$173$	3.92775	+	12.0884i	0.298621	+	0.919062i	0.981981	+	0.188980i	$0.0605182\pi$
$173$	3.92775	+	12.0884i	0.298621	+	0.919062i	−0.683360	+	0.730082i	$0.739482\pi$
$174$	−1.20376	−	5.95029i	−0.0912570	−	0.451090i
$175$			2.29577i			0.173544i
$176$	−0.622865	−	4.96897i	−0.0469502	−	0.374551i
$177$	−0.135958	−	0.0621411i	−0.0102193	−	0.00467081i
$178$	1.03496	+	1.42451i	0.0775739	+	0.106771i
$179$	−19.7630	+	6.42140i	−1.47716	+	0.479958i	−0.933263	−	0.359194i	$-0.883052\pi$
$179$	−19.7630	+	6.42140i	−1.47716	+	0.479958i	−0.543897	+	0.839152i	$0.683052\pi$
$180$	1.01237	+	2.39971i	0.0754578	+	0.178864i
$181$	4.00813	+	2.91208i	0.297922	+	0.216453i	0.726697	−	0.686958i	$-0.241055\pi$
$181$	4.00813	+	2.91208i	0.297922	+	0.216453i	−0.428775	+	0.903411i	$0.641055\pi$
$182$	3.80234	+	2.76256i	0.281848	+	0.204775i
$183$	9.55935	−	10.4091i	0.706648	−	0.769464i
$184$	13.9752	−	4.54081i	1.03026	−	0.334753i
$185$	6.83484	+	9.40735i	0.502507	+	0.691642i
$186$	3.77539	−	8.26017i	0.276825	−	0.605665i
$187$	−1.53982	−	12.2840i	−0.112602	−	0.898298i
$188$			2.88035i			0.210071i
$189$	−9.43993	−	7.29330i	−0.686654	−	0.530509i
$190$	2.81303	+	8.65761i	0.204079	+	0.628089i
$191$	−2.12592	−	0.690754i	−0.153826	−	0.0499812i	0.231092	−	0.972932i	$-0.425770\pi$
$191$	−2.12592	−	0.690754i	−0.153826	−	0.0499812i	−0.384918	+	0.922951i	$0.625770\pi$
$192$	−11.7710	+	6.64258i	−0.849499	+	0.479387i
$193$	−1.97994	+	2.72516i	−0.142519	+	0.196161i	−0.874309	−	0.485369i	$-0.838685\pi$
$193$	−1.97994	+	2.72516i	−0.142519	+	0.196161i	0.731790	+	0.681530i	$0.238685\pi$
$194$	2.68527	−	8.26442i	0.192791	−	0.593351i
$195$	−3.31117	−	0.380962i	−0.237118	−	0.0272813i
$196$	1.21472	−	0.882544i	0.0867656	−	0.0630389i
$197$	5.54825			0.395296			0.197648	−	0.980273i	$-0.436670\pi$
$197$	5.54825			0.395296			0.197648	+	0.980273i	$0.436670\pi$
$198$	−9.67163	−	4.30238i	−0.687333	−	0.305757i
$199$	−18.2058			−1.29058			−0.645288	−	0.763940i	$-0.723262\pi$
$199$	−18.2058			−1.29058			−0.645288	+	0.763940i	$0.723262\pi$
$200$	2.46861	−	1.79355i	0.174557	−	0.126823i
$201$	6.74886	+	0.776482i	0.476028	+	0.0547688i
$202$	3.51249	−	10.8103i	0.247138	−	0.760613i
$203$	−4.44573	+	6.11903i	−0.312029	+	0.429472i
$204$	−4.88838	+	2.75860i	−0.342255	+	0.193140i
$205$	1.90703	+	0.619630i	0.133192	+	0.0432768i
$206$	2.09821	+	6.45764i	0.146189	+	0.449925i
$207$	3.28092	−	14.0695i	0.228040	−	0.977896i
$208$		−	2.90557i		−	0.201465i
$209$	24.8556	+	13.6957i	1.71930	+	0.947350i
$210$	−1.75855	+	3.84753i	−0.121352	+	0.265505i
$211$	−5.49233	−	7.55955i	−0.378108	−	0.520421i	0.576974	−	0.816762i	$-0.304233\pi$
$211$	−5.49233	−	7.55955i	−0.378108	−	0.520421i	−0.955082	+	0.296342i	$0.904233\pi$
$212$	−4.98826	+	1.62078i	−0.342595	+	0.111316i
$213$	17.2330	−	18.7649i	1.18079	−	1.28575i
$214$	−3.40231	−	2.47192i	−0.232577	−	0.168977i
$215$	5.01909	+	3.64658i	0.342299	+	0.248695i
$216$	−0.467521	+	15.8485i	−0.0318108	+	1.07835i
$217$	−10.7614	+	3.49659i	−0.730530	+	0.237364i
$218$	−3.76989	−	5.18881i	−0.255329	−	0.351431i
$219$	8.66721	+	3.96143i	0.585676	+	0.267689i
$220$	0.542271	−	2.82788i	0.0365599	−	0.190656i
$221$		−	7.18301i		−	0.483181i
$222$	4.24867	+	21.0015i	0.285152	+	1.40953i
$223$	−4.95786	−	15.2587i	−0.332003	−	1.02180i	−0.968179	−	0.250257i	$-0.919485\pi$
$223$	−4.95786	−	15.2587i	−0.332003	−	1.02180i	0.636176	−	0.771544i	$-0.280515\pi$
$224$	9.81740	+	3.18987i	0.655952	+	0.213132i
$225$	−0.254870	−	2.98915i	−0.0169913	−	0.199277i
$226$	−9.68799	+	13.3344i	−0.644435	+	0.886989i
$227$	−0.470272	+	1.44735i	−0.0312131	+	0.0960639i	−0.965449	−	0.260591i	$-0.916083\pi$
$227$	−0.470272	+	1.44735i	−0.0312131	+	0.0960639i	0.934236	+	0.356655i	$0.116083\pi$
$228$	1.47067	−	12.7824i	0.0973973	−	0.846538i
$229$	−2.13096	+	1.54823i	−0.140817	+	0.102310i	−0.655964	−	0.754792i	$-0.727738\pi$
$229$	−2.13096	+	1.54823i	−0.140817	+	0.102310i	0.515146	+	0.857102i	$0.327738\pi$
$230$	−5.12325			−0.337817
$231$	4.20247	+	12.5007i	0.276502	+	0.822484i
$232$	10.0529			0.660007
$233$	21.1262	−	15.3491i	1.38402	−	1.00555i	0.387529	−	0.921857i	$-0.373329\pi$
$233$	21.1262	−	15.3491i	1.38402	−	1.00555i	0.996492	−	0.0836927i	$-0.0266714\pi$
$234$	−5.25745	−	3.17481i	−0.343690	−	0.207544i
$235$	1.02523	−	3.15533i	0.0668785	−	0.205831i
$236$	0.0440420	−	0.0606186i	0.00286689	−	0.00394593i
$237$	0.0471391	+	0.0835331i	0.00306202	+	0.00542606i
$238$	−8.67070	−	2.81728i	−0.562038	−	0.182617i
$239$	−7.24254	−	22.2903i	−0.468481	−	1.44184i	−0.854551	−	0.519367i	$-0.826168\pi$
$239$	−7.24254	−	22.2903i	−0.468481	−	1.44184i	0.386070	−	0.922469i	$-0.373832\pi$
$240$	2.56334	−	0.518572i	0.165463	−	0.0334737i
$241$			20.2637i			1.30530i	0.757661	+	0.652648i	$0.226342\pi$
$241$			20.2637i			1.30530i	−0.757661	+	0.652648i	$0.773658\pi$
$242$	6.25152	+	9.89290i	0.401863	+	0.635940i
$243$	13.1008	+	8.44809i	0.840414	+	0.541945i
$244$	4.16378	+	5.73095i	0.266558	+	0.366886i
$245$	−1.64482	+	0.534433i	−0.105083	+	0.0341437i
$246$	2.72140	+	2.49923i	0.173510	+	0.159345i
$247$	13.3210	+	9.67825i	0.847593	+	0.615812i
$248$	12.1671	+	8.83992i	0.772612	+	0.561336i
$249$	−1.92511	−	1.76795i	−0.121999	−	0.112039i
$250$	−1.01180	+	0.328755i	−0.0639921	+	0.0207923i
$251$	16.0938	+	22.1512i	1.01583	+	1.39817i	0.915087	+	0.403256i	$0.132122\pi$
$251$	16.0938	+	22.1512i	1.01583	+	1.39817i	0.100742	+	0.994913i	$0.467878\pi$
$252$	4.52133	−	3.91285i	0.284817	−	0.246486i
$253$	−11.6534	+	10.9222i	−0.732643	+	0.686671i
$254$		−	8.27281i		−	0.519082i
$255$	6.33696	−	1.28199i	0.396836	−	0.0802812i
$256$	−5.04992	−	15.5421i	−0.315620	−	0.971378i
$257$	1.58146	+	0.513846i	0.0986485	+	0.0320528i	0.357925	−	0.933750i	$-0.383484\pi$
$257$	1.58146	+	0.513846i	0.0986485	+	0.0320528i	−0.259277	+	0.965803i	$0.583484\pi$
$258$	5.61835	+	9.95602i	0.349783	+	0.619835i
$259$	15.6912	−	21.5971i	0.975002	−	1.34198i
$260$	0.516256	−	1.58887i	0.0320168	−	0.0985377i
$261$	5.10916	−	8.46071i	0.316249	−	0.523705i
$262$	−9.05895	+	6.58171i	−0.559664	+	0.406620i
$263$	5.20475			0.320939			0.160469	−	0.987041i	$-0.448699\pi$
$263$	5.20475			0.320939			0.160469	+	0.987041i	$0.448699\pi$
$264$	10.1587	−	14.2850i	0.625225	−	0.879178i
$265$	6.04138			0.371119
$266$	16.9074	−	12.2839i	1.03666	−	0.753177i
$267$	−0.327659	+	2.84788i	−0.0200524	+	0.174288i
$268$	−1.05224	+	3.23846i	−0.0642758	+	0.197821i
$269$	−0.441362	+	0.607483i	−0.0269103	+	0.0370389i	−0.822260	−	0.569112i	$-0.807287\pi$
$269$	−0.441362	+	0.607483i	−0.0269103	+	0.0370389i	0.795350	+	0.606151i	$0.207287\pi$
$270$	1.86254	−	5.20483i	0.113351	−	0.316756i
$271$	−26.1825	−	8.50721i	−1.59047	−	0.516776i	−0.625746	−	0.780027i	$-0.715205\pi$
$271$	−26.1825	−	8.50721i	−1.59047	−	0.516776i	−0.964727	+	0.263251i	$0.915205\pi$
$272$	1.74168	+	5.36034i	0.105605	+	0.325018i
$273$	1.51725	+	7.49988i	0.0918281	+	0.453913i
$274$			3.70310i			0.223712i
$275$	−1.60059	+	2.90484i	−0.0965195	+	0.175168i
$276$	6.58608	+	3.01023i	0.396435	+	0.181195i
$277$	1.99461	+	2.74535i	0.119845	+	0.164952i	0.864724	−	0.502247i	$-0.167493\pi$
$277$	1.99461	+	2.74535i	0.119845	+	0.164952i	−0.744880	+	0.667199i	$0.767493\pi$
$278$	9.69214	−	3.14917i	0.581296	−	0.188875i
$279$	13.6235	−	5.74736i	0.815615	−	0.344085i
$280$	−5.66736	−	4.11757i	−0.338689	−	0.246072i
$281$	−9.96332	−	7.23877i	−0.594362	−	0.431829i	0.249511	−	0.968372i	$-0.419730\pi$
$281$	−9.96332	−	7.23877i	−0.594362	−	0.431829i	−0.843873	+	0.536543i	$0.819730\pi$
$282$	4.13518	−	4.50277i	0.246246	−	0.268136i
$283$	22.3804	−	7.27184i	1.33038	−	0.432266i	0.444332	−	0.895862i	$-0.353441\pi$
$283$	22.3804	−	7.27184i	1.33038	−	0.432266i	0.886047	+	0.463596i	$0.153441\pi$
$284$	7.50621	+	10.3314i	0.445412	+	0.613057i
$285$	−6.16084	+	13.4793i	−0.364937	+	0.798444i
$286$	2.88507	+	6.14645i	0.170598	+	0.363447i
$287$		−	4.60339i		−	0.271729i
$288$	−13.1367	−	3.06340i	−0.774086	−	0.180512i
$289$	−0.947596	−	2.91640i	−0.0557410	−	0.171553i
$290$	−3.33345	−	1.08310i	−0.195747	−	0.0636020i
$291$	12.3210	−	6.95292i	0.722267	−	0.407587i
$292$	−2.80763	+	3.86437i	−0.164304	+	0.226145i
$293$	0.200874	−	0.618227i	0.0117352	−	0.0361172i	−0.945017	−	0.327020i	$-0.893956\pi$
$293$	0.200874	−	0.618227i	0.0117352	−	0.0361172i	0.956753	+	0.290903i	$0.0939556\pi$
$294$	−3.16596	−	0.364256i	−0.184643	−	0.0212438i
$295$	−0.0698231	+	0.0507294i	−0.00406526	+	0.00295358i
$296$	−35.4817			−2.06233
$297$	−6.85953	−	15.8097i	−0.398030	−	0.917372i
$298$	−10.1452			−0.587698
$299$	−7.49703	+	5.44691i	−0.433564	+	0.315003i
$300$	1.49387	+	0.171875i	0.0862484	+	0.00992320i
$301$	4.40126	−	13.5457i	0.253685	−	0.780761i
$302$	−11.5181	+	15.8533i	−0.662793	+	0.912256i
$303$	16.1165	−	9.09483i	0.925870	−	0.522484i
$304$	−12.2875	−	3.99246i	−0.704738	−	0.228983i
$305$	−2.52142	−	7.76012i	−0.144376	−	0.444343i
$306$	11.6023	+	2.70558i	0.663258	+	0.154668i
$307$			9.98155i			0.569677i	0.958575	+	0.284839i	$0.0919400\pi$
$307$			9.98155i			0.569677i	−0.958575	+	0.284839i	$0.908060\pi$
$308$	−6.55911	+	0.822190i	−0.373740	+	0.0468487i
$309$	−4.59531	+	10.0541i	−0.261418	+	0.571956i
$310$	−3.08207	−	4.24211i	−0.175050	−	0.240936i
$311$	20.2539	−	6.58090i	1.14849	−	0.373168i	0.327918	−	0.944706i	$-0.393653\pi$
$311$	20.2539	−	6.58090i	1.14849	−	0.373168i	0.820576	+	0.571538i	$0.193653\pi$
$312$	6.87920	−	7.49071i	0.389458	−	0.424078i
$313$	−13.6038	−	9.88377i	−0.768934	−	0.558664i	0.132703	−	0.991156i	$-0.457634\pi$
$313$	−13.6038	−	9.88377i	−0.768934	−	0.558664i	−0.901638	+	0.432492i	$0.857634\pi$
$314$	14.3241	+	10.4071i	0.808358	+	0.587306i
$315$	−6.34571	+	2.67708i	−0.357540	+	0.150836i
$316$	−0.0457239	+	0.0148566i	−0.00257217	+	0.000835749i
$317$	−18.3668	−	25.2798i	−1.03158	−	1.41985i	−0.903751	−	0.428058i	$-0.859198\pi$
$317$	−18.3668	−	25.2798i	−1.03158	−	1.41985i	−0.127833	−	0.991796i	$-0.540802\pi$
$318$	10.1249	+	4.62769i	0.567776	+	0.259508i
$319$	−9.89136	+	4.64289i	−0.553810	+	0.259952i
$320$			7.80343i			0.436225i
$321$	−1.35762	−	6.71084i	−0.0757752	−	0.374563i
$322$	3.63459	+	11.1861i	0.202548	+	0.623377i
$323$	−30.3766	−	9.86994i	−1.69020	−	0.549178i
$324$	−5.45252	+	5.59659i	−0.302918	+	0.310922i
$325$	−1.13108	+	1.55680i	−0.0627412	+	0.0863559i
$326$	−5.81518	+	17.8973i	−0.322073	+	0.991238i
$327$	1.19351	−	10.3735i	0.0660013	−	0.573656i
$328$	−4.94998	+	3.59637i	−0.273317	+	0.198576i
$329$	−7.61668			−0.419921
$330$	−4.90758	+	3.64224i	−0.270153	+	0.200499i
$331$	−16.4306			−0.903108			−0.451554	−	0.892244i	$-0.649130\pi$
$331$	−16.4306			−0.903108			−0.451554	+	0.892244i	$0.649130\pi$
$332$	1.05991	−	0.770067i	0.0581699	−	0.0422629i
$333$	−18.0327	+	29.8620i	−0.988187	+	1.63643i
$334$	−0.841290	+	2.58922i	−0.0460333	+	0.141676i
$335$	2.30539	−	3.17310i	0.125957	−	0.173365i
$336$	−2.95076	−	5.22891i	−0.160977	−	0.285261i
$337$	−21.6852	−	7.04596i	−1.18127	−	0.383818i	−0.348431	−	0.937334i	$-0.613286\pi$
$337$	−21.6852	−	7.04596i	−1.18127	−	0.383818i	−0.832838	+	0.553517i	$0.813286\pi$
$338$	−3.05644	−	9.40675i	−0.166248	−	0.511660i
$339$	−26.3012	+	5.32082i	−1.42848	+	0.288987i
$340$			3.24069i			0.175751i
$341$	−16.0542	−	3.07854i	−0.869385	−	0.166712i
$342$	−20.6502	+	17.8711i	−1.11664	+	0.966357i
$343$	11.7797	+	16.2133i	0.636043	+	0.875438i
$344$	−18.0040	+	5.84986i	−0.970711	+	0.315403i
$345$	−6.14338	−	5.64185i	−0.330748	−	0.303747i
$346$	10.9398	+	7.94822i	0.588127	+	0.427299i
$347$	24.8429	+	18.0494i	1.33364	+	0.968944i	0.999652	+	0.0263657i	$0.00839344\pi$
$347$	24.8429	+	18.0494i	1.33364	+	0.968944i	0.333985	+	0.942578i	$0.391607\pi$
$348$	3.64885	+	3.35097i	0.195599	+	0.179631i
$349$	6.77469	−	2.20123i	0.362641	−	0.117829i	−0.122028	−	0.992527i	$-0.538940\pi$
$349$	6.77469	−	2.20123i	0.362641	−	0.117829i	0.484669	+	0.874697i	$0.338940\pi$
$350$	1.43561	+	1.97595i	0.0767365	+	0.105619i
$351$	−2.80812	−	9.59662i	−0.149886	−	0.512230i
$352$	10.1980	+	10.8808i	0.543557	+	0.579948i
$353$		−	12.1379i		−	0.646034i	−0.946393	−	0.323017i	$-0.895303\pi$
$353$		−	12.1379i		−	0.646034i	0.946393	−	0.323017i	$-0.104697\pi$
$354$	−0.155877	+	0.0315344i	−0.00828477	+	0.00167603i
$355$	−4.54546	−	13.9895i	−0.241248	−	0.742485i
$356$	−1.36656	−	0.444024i	−0.0724278	−	0.0235332i
$357$	−7.29473	−	12.9267i	−0.386078	−	0.684151i
$358$	−12.9944	+	17.8853i	−0.686775	+	0.945265i
$359$	−3.61159	+	11.1153i	−0.190613	+	0.586645i	−1.00000		0.000629983i	$-0.999799\pi$
$359$	−3.61159	+	11.1153i	−0.190613	+	0.586645i	0.809387	+	0.587275i	$0.199799\pi$
$360$	7.83619	+	4.73203i	0.413003	+	0.249400i
$361$	43.8614	−	31.8672i	2.30849	−	1.67722i
$362$	5.27077			0.277026
$363$	−3.39801	+	18.7471i	−0.178349	+	0.983967i
$364$	−3.83540			−0.201029
$365$	4.45115	−	3.23395i	0.232984	−	0.169273i
$366$	1.71853	−	14.9368i	0.0898291	−	0.780758i
$367$	5.02699	−	15.4715i	0.262407	−	0.807605i	−0.729873	−	0.683583i	$-0.760421\pi$
$367$	5.02699	−	15.4715i	0.262407	−	0.807605i	0.992280	−	0.124022i	$-0.0395793\pi$
$368$	4.27395	−	5.88259i	0.222795	−	0.306651i
$369$	0.511056	+	5.99375i	0.0266045	+	0.312022i
$370$	11.7654	+	3.82280i	0.611653	+	0.198738i
$371$	−4.28594	−	13.1908i	−0.222515	−	0.684830i
$372$	1.46958	+	7.26426i	0.0761944	+	0.376635i
$373$			7.79759i			0.403744i	0.979412	+	0.201872i	$0.0647025\pi$
$373$			7.79759i			0.403744i	−0.979412	+	0.201872i	$0.935297\pi$
$374$	−9.00687	−	9.60988i	−0.465734	−	0.496915i
$375$	−1.57531	−	0.720009i	−0.0813484	−	0.0371811i
$376$	5.95048	+	8.19014i	0.306873	+	0.422374i
$377$	−6.02948	+	1.95910i	−0.310534	+	0.100899i
$378$	−12.6856	−	0.374217i	−0.652476	−	0.0192476i
$379$	17.4264	+	12.6610i	0.895134	+	0.650353i	0.937212	−	0.348761i	$-0.113398\pi$
$379$	17.4264	+	12.6610i	0.895134	+	0.650353i	−0.0420772	+	0.999114i	$0.513398\pi$
$380$	−6.00989	−	4.36644i	−0.308301	−	0.223994i
$381$	9.11024	−	9.92008i	0.466732	−	0.508221i
$382$	−2.26171	+	0.734875i	−0.115719	+	0.0375995i
$383$	−8.26426	−	11.3748i	−0.422284	−	0.581224i	0.543877	−	0.839165i	$-0.316956\pi$
$383$	−8.26426	−	11.3748i	−0.422284	−	0.581224i	−0.966161	+	0.257941i	$0.916956\pi$
$384$	0.497450	−	1.08837i	0.0253854	−	0.0555406i
$385$	7.47795	+	1.43396i	0.381111	+	0.0730814i
$386$			3.58363i			0.182402i
$387$	−4.22677	+	18.1255i	−0.214859	+	0.921372i
$388$	2.19132	+	6.74418i	0.111247	+	0.342384i
$389$	−13.1324	−	4.26698i	−0.665839	−	0.216344i	−0.0434542	−	0.999055i	$-0.513836\pi$
$389$	−13.1324	−	4.26698i	−0.665839	−	0.216344i	−0.622385	+	0.782711i	$0.713836\pi$
$390$	−3.08812	+	1.74268i	−0.156373	+	0.0882439i
$391$	10.5658	−	14.5426i	0.534338	−	0.735453i
$392$	1.63076	−	5.01895i	0.0823656	−	0.253495i
$393$	−18.1107	−	2.08370i	−0.913564	−	0.105109i
$394$	4.77533	−	3.46948i	0.240578	−	0.174790i
$395$	0.0553771			0.00278633
$396$	8.44888	−	1.79869i	0.424572	−	0.0903877i
$397$	−25.0721			−1.25833			−0.629167	−	0.777270i	$-0.716604\pi$
$397$	−25.0721			−1.25833			−0.629167	+	0.777270i	$0.716604\pi$
$398$	−15.6696	+	11.3846i	−0.785445	+	0.570659i
$399$	33.8014	+	3.88897i	1.69219	+	0.194692i
$400$	0.466593	−	1.43603i	0.0233297	−	0.0718013i
$401$	−1.57644	+	2.16979i	−0.0787239	+	0.108354i	−0.846563	−	0.532289i	$-0.821332\pi$
$401$	−1.57644	+	2.16979i	−0.0787239	+	0.108354i	0.767839	+	0.640643i	$0.221332\pi$
$402$	6.29425	−	3.55195i	0.313929	−	0.177155i
$403$	−9.02021	−	2.93084i	−0.449329	−	0.145996i
$404$	2.86637	+	8.82178i	0.142607	+	0.438900i
$405$	7.96510	−	4.19012i	0.395789	−	0.208209i
$406$			8.04664i			0.399348i
$407$	34.9115	−	16.3870i	1.73050	−	0.812275i
$408$	−8.20094	+	17.9428i	−0.406007	+	0.888301i
$409$	10.8586	+	14.9456i	0.536925	+	0.739013i	0.988166	−	0.153389i	$-0.0490186\pi$
$409$	10.8586	+	14.9456i	0.536925	+	0.739013i	−0.451241	+	0.892402i	$0.649019\pi$
$410$	2.02883	−	0.659208i	0.100197	−	0.0325560i
$411$	−4.07795	+	4.44045i	−0.201150	+	0.219031i
$412$	−4.48272	−	3.25689i	−0.220848	−	0.160455i
$413$	0.160297	+	0.116463i	0.00788772	+	0.00573076i
$414$	−5.97419	−	14.1611i	−0.293615	−	0.695982i
$415$	−1.43519	+	0.466322i	−0.0704508	+	0.0228908i
$416$	5.08578	+	6.99997i	0.249351	+	0.343202i
$417$	15.0900	+	6.89702i	0.738959	+	0.337748i
$418$	29.9573	−	3.75518i	1.46526	−	0.183672i
$419$		−	9.74244i		−	0.475949i	−0.971271	−	0.237975i	$-0.923516\pi$
$419$		−	9.74244i		−	0.475949i	0.971271	−	0.237975i	$-0.0764835\pi$
$420$	−0.684522	−	3.38364i	−0.0334013	−	0.165105i
$421$	4.24632	+	13.0688i	0.206953	+	0.636936i	0.999628	+	0.0272907i	$0.00868799\pi$
$421$	4.24632	+	13.0688i	0.206953	+	0.636936i	−0.792675	+	0.609645i	$0.791312\pi$
$422$	−9.45441	−	3.07192i	−0.460233	−	0.149539i
$423$	9.91714	−	0.845584i	0.482188	−	0.0411137i
$424$	−10.8355	+	14.9138i	−0.526220	+	0.724280i
$425$	1.15349	−	3.55007i	0.0559523	−	0.172204i
$426$	3.09807	−	26.9271i	0.150102	−	1.30462i
$427$	−15.1547	+	11.0105i	−0.733387	+	0.532837i
$428$	3.43189			0.165887
$429$	−3.30909	+	10.5474i	−0.159764	+	0.509235i
$430$	6.60020			0.318290
$431$	9.18622	−	6.67418i	0.442485	−	0.321484i	−0.344137	−	0.938920i	$-0.611828\pi$
$431$	9.18622	−	6.67418i	0.442485	−	0.321484i	0.786621	+	0.617436i	$0.211828\pi$
$432$	4.42248	+	6.48061i	0.212777	+	0.311799i
$433$	3.58521	−	11.0342i	0.172294	−	0.530268i	−0.827205	−	0.561900i	$-0.810071\pi$
$433$	3.58521	−	11.0342i	0.172294	−	0.530268i	0.999500	+	0.0316324i	$0.0100706\pi$
$434$	−7.07572	+	9.73889i	−0.339645	+	0.467482i
$435$	−2.80446	−	4.96965i	−0.134463	−	0.238276i
$436$	4.97776	+	1.61737i	0.238391	+	0.0774580i
$437$	12.7333	+	39.1889i	0.609114	+	1.87466i
$438$	9.93699	−	2.01029i	0.474808	−	0.0960552i
$439$			8.90504i			0.425015i	0.977159	+	0.212507i	$0.0681629\pi$
$439$			8.90504i			0.425015i	−0.977159	+	0.212507i	$0.931837\pi$
$440$	−4.30017	−	9.16123i	−0.205003	−	0.436745i
$441$	−3.39524	−	3.92323i	−0.161678	−	0.186820i
$442$	−4.49174	−	6.18235i	−0.213650	−	0.294065i
$443$	3.68935	−	1.19874i	0.175286	−	0.0569540i	−0.220059	−	0.975487i	$-0.570625\pi$
$443$	3.68935	−	1.19874i	0.175286	−	0.0569540i	0.395345	+	0.918533i	$0.370625\pi$
$444$	−12.8786	−	11.8272i	−0.611190	−	0.561295i
$445$	1.33898	+	0.972827i	0.0634738	+	0.0461164i
$446$	−13.8089	−	10.0328i	−0.653871	−	0.475065i
$447$	−12.1653	−	11.1722i	−0.575401	−	0.528427i
$448$	17.0380	−	5.53599i	0.804971	−	0.261551i
$449$	−6.57956	−	9.05599i	−0.310509	−	0.427379i	0.625031	−	0.780600i	$-0.285086\pi$
$449$	−6.57956	−	9.05599i	−0.310509	−	0.427379i	−0.935540	+	0.353221i	$0.885086\pi$
$450$	−2.08857	−	2.41336i	−0.0984561	−	0.113767i
$451$	3.20946	−	5.82468i	0.151127	−	0.274274i
$452$		−	13.4503i		−	0.632648i
$453$	−31.2697	+	6.32596i	−1.46918	+	0.297219i
$454$	0.500310	+	1.53980i	0.0234807	+	0.0722662i
$455$	4.20155	+	1.36517i	0.196972	+	0.0640000i
$456$	−22.2253	−	39.3845i	−1.04080	−	1.84435i
$457$	2.24245	−	3.08647i	0.104897	−	0.144379i	−0.753341	−	0.657630i	$-0.771559\pi$
$457$	2.24245	−	3.08647i	0.104897	−	0.144379i	0.858238	+	0.513251i	$0.171559\pi$
$458$	−0.865942	+	2.66510i	−0.0404628	+	0.124532i
$459$	10.9330	+	16.0210i	0.510310	+	0.747798i
$460$	3.38236	−	2.45743i	0.157703	−	0.114578i
$461$	15.1781			0.706915			0.353457	−	0.935451i	$-0.385006\pi$
$461$	15.1781			0.706915			0.353457	+	0.935451i	$0.385006\pi$
$462$	11.4341	+	8.13130i	0.531961	+	0.378302i
$463$	−6.65471			−0.309271			−0.154635	−	0.987972i	$-0.549420\pi$
$463$	−6.65471			−0.309271			−0.154635	+	0.987972i	$0.549420\pi$
$464$	4.02449	−	2.92396i	0.186832	−	0.135742i
$465$	0.975753	−	8.48085i	0.0452495	−	0.393290i
$466$	8.58490	−	26.4216i	0.397688	−	1.22396i
$467$	−3.39202	+	4.66871i	−0.156964	+	0.216042i	−0.880255	−	0.474501i	$-0.842629\pi$
$467$	−3.39202	+	4.66871i	−0.156964	+	0.216042i	0.723291	+	0.690543i	$0.242629\pi$
$468$	4.99380	−	0.425796i	0.230838	−	0.0196824i
$469$	−8.56366	−	2.78250i	−0.395433	−	0.128484i
$470$	−1.09071	−	3.35687i	−0.0503108	−	0.154841i
$471$	5.71576	+	28.2534i	0.263368	+	1.30185i
$472$		−	0.263352i		−	0.0121218i
$473$	15.0129	−	14.0709i	0.690295	−	0.646980i
$474$	0.0928079	+	0.0424188i	0.00426281	+	0.00194836i
$475$	5.02945	+	6.92245i	0.230767	+	0.317624i
$476$	7.07572	−	2.29904i	0.324315	−	0.105376i
$477$	7.04482	+	16.6990i	0.322560	+	0.764592i
$478$	−20.1723	−	14.6561i	−0.922661	−	0.670353i
$479$	26.2909	+	19.1015i	1.20126	+	0.872769i	0.994408	−	0.105602i	$-0.0336771\pi$
$479$	26.2909	+	19.1015i	1.20126	+	0.872769i	0.206855	+	0.978372i	$0.433677\pi$
$480$	−5.26780	+	5.73607i	−0.240441	+	0.261815i
$481$	21.2810	−	6.91461i	0.970330	−	0.315279i
$482$	12.6714	+	17.4408i	0.577169	+	0.794405i
$483$	−7.96014	+	17.4160i	−0.362199	+	0.792454i
$484$	−8.87249	−	3.53266i	−0.403295	−	0.160575i
$485$		−	8.16800i		−	0.370890i
$486$	16.5585	−	0.921079i	0.751111	−	0.0417810i
$487$	−7.94102	−	24.4399i	−0.359842	−	1.10748i	−0.953148	−	0.302503i	$-0.902178\pi$
$487$	−7.94102	−	24.4399i	−0.359842	−	1.10748i	0.593306	−	0.804977i	$-0.297822\pi$
$488$	23.6790	+	7.69378i	1.07190	+	0.348281i
$489$	−26.6820	+	15.0571i	−1.20660	+	0.680907i
$490$	−1.08148	+	1.48853i	−0.0488564	+	0.0672451i
$491$	−12.8968	+	39.6924i	−0.582027	+	1.79129i	0.0288703	+	0.999583i	$0.490809\pi$
$491$	−12.8968	+	39.6924i	−0.582027	+	1.79129i	−0.610897	+	0.791710i	$0.709191\pi$
$492$	−2.99545	−	0.344637i	−0.135045	−	0.0155375i
$493$	9.94914	−	7.22847i	0.448087	−	0.325554i
$494$	17.5173			0.788142
$495$	−9.89570	−	1.03688i	−0.444779	−	0.0466041i
$496$	7.44201			0.334156
$497$	−27.3200	+	19.8491i	−1.22547	+	0.890355i
$498$	−2.76247	−	0.317833i	−0.123789	−	0.0142424i
$499$	6.48866	−	19.9700i	0.290472	−	0.893981i	−0.694233	−	0.719751i	$-0.744256\pi$
$499$	6.48866	−	19.9700i	0.290472	−	0.893981i	0.984705	−	0.174231i	$-0.0557438\pi$
$500$	0.510300	−	0.702367i	0.0228213	−	0.0314108i
$501$	−3.86013	+	2.17834i	−0.172458	+	0.0973208i
$502$	27.7035	+	9.00142i	1.23647	+	0.401753i
$503$	8.32580	+	25.6242i	0.371229	+	1.14253i	0.945988	+	0.324202i	$0.105096\pi$
$503$	8.32580	+	25.6242i	0.371229	+	1.14253i	−0.574759	+	0.818323i	$0.694904\pi$
$504$	4.77269	−	20.4666i	0.212593	−	0.911654i
$505$		−	10.6842i		−	0.475442i
$506$	−3.20004	+	16.6878i	−0.142259	+	0.741865i
$507$	6.69393	−	14.6456i	0.297288	−	0.650436i
$508$	3.96815	+	5.46170i	0.176058	+	0.242324i
$509$	27.1750	−	8.82971i	1.20451	−	0.391370i	0.363094	−	0.931753i	$-0.381721\pi$
$509$	27.1750	−	8.82971i	1.20451	−	0.391370i	0.841419	+	0.540383i	$0.181721\pi$
$510$	4.65250	−	5.06608i	0.206016	−	0.224330i
$511$	−10.2188	−	7.42439i	−0.452053	−	0.328436i
$512$	−12.9474	−	9.40686i	−0.572201	−	0.415728i
$513$	−44.4421	−	1.31102i	−1.96217	−	0.0578828i
$514$	1.68247	−	0.546667i	0.0742105	−	0.0241125i
$515$	3.75142	+	5.16339i	0.165307	+	0.227526i
$516$	−8.48475	−	3.87804i	−0.373520	−	0.170721i
$517$	−9.63741	−	5.31031i	−0.423853	−	0.233547i
$518$		−	28.4005i		−	1.24785i
$519$	4.36531	+	21.5780i	0.191616	+	0.947171i
$520$	−1.81449	−	5.58442i	−0.0795705	−	0.244893i
$521$	−36.4491	−	11.8430i	−1.59686	−	0.518852i	−0.630534	−	0.776162i	$-0.717164\pi$
$521$	−36.4491	−	11.8430i	−1.59686	−	0.518852i	−0.966329	+	0.257309i	$0.917164\pi$
$522$	−0.893318	−	10.4770i	−0.0390995	−	0.458564i
$523$	−7.01145	+	9.65043i	−0.306589	+	0.421984i	−0.934314	−	0.356452i	$-0.883986\pi$
$523$	−7.01145	+	9.65043i	−0.306589	+	0.421984i	0.627725	+	0.778436i	$0.283986\pi$
$524$	2.82371	−	8.69047i	0.123354	−	0.379645i
$525$	−0.454499	+	3.95032i	−0.0198360	+	0.172406i
$526$	4.47968	−	3.25468i	0.195324	−	0.141911i
$527$	18.3977			0.801419
$528$	−0.0880421	−	8.67342i	−0.00383154	−	0.377462i
$529$	−0.190521			−0.00828354
$530$	5.19977	−	3.77785i	0.225863	−	0.164099i
$531$	−0.221641	−	0.133842i	−0.00961842	−	0.00580826i
$532$	−5.27010	+	16.2197i	−0.228488	+	0.703213i
$533$	2.26801	−	3.12165i	0.0982384	−	0.135214i
$534$	1.49885	+	2.65604i	0.0648616	+	0.114938i
$535$	−3.75952	−	1.22154i	−0.162538	−	0.0528119i
$536$	3.69831	+	11.3822i	0.159743	+	0.491637i
$537$	−35.2775	+	7.13676i	−1.52234	+	0.307974i
$538$			0.798852i			0.0344410i
$539$	0.713427	+	5.69144i	0.0307295	+	0.245148i
$540$	1.26691	+	4.32961i	0.0545192	+	0.186317i
$541$	−12.9079	−	17.7662i	−0.554955	−	0.763830i	0.435719	−	0.900083i	$-0.356494\pi$
$541$	−12.9079	−	17.7662i	−0.554955	−	0.763830i	−0.990674	+	0.136253i	$0.956494\pi$
$542$	−27.8549	+	9.05059i	−1.19647	+	0.388756i
$543$	6.32028	+	5.80431i	0.271229	+	0.249087i
$544$	−13.5785	−	9.86533i	−0.582172	−	0.422973i
$545$	−4.87729	−	3.54356i	−0.208920	−	0.151789i
$546$	5.99577	+	5.50630i	0.256595	+	0.235648i
$547$	21.6597	−	7.03767i	0.926102	−	0.300909i	0.193135	−	0.981172i	$-0.438135\pi$
$547$	21.6597	−	7.03767i	0.926102	−	0.300909i	0.732968	+	0.680263i	$0.238135\pi$
$548$	−1.77624	−	2.44478i	−0.0758771	−	0.104436i
$549$	18.5095	−	16.0185i	0.789966	−	0.683652i
$550$	0.438862	+	3.50107i	0.0187131	+	0.149286i
$551$			28.1903i			1.20095i
$552$	24.9460	−	5.04666i	1.06177	−	0.214800i
$553$	−0.0392862	−	0.120911i	−0.00167062	−	0.00514164i
$554$	3.43349	+	1.11561i	0.145875	+	0.0473976i
$555$	9.89830	+	17.5403i	0.420159	+	0.744545i
$556$	−4.88820	+	6.72803i	−0.207306	+	0.285332i
$557$	6.27152	−	19.3018i	0.265733	−	0.817842i	−0.725791	−	0.687916i	$-0.758526\pi$
$557$	6.27152	−	19.3018i	0.265733	−	0.817842i	0.991524	−	0.129926i	$-0.0414741\pi$
$558$	8.13160	−	13.4658i	0.344238	−	0.570055i
$559$	9.65831	−	7.01717i	0.408503	−	0.296795i
$560$	−3.46644			−0.146484
$561$	−0.217653	−	21.4420i	−0.00918933	−	0.905281i
$562$	−13.1020			−0.552673
$563$	30.2324	−	21.9652i	1.27415	−	0.925721i	0.274786	−	0.961505i	$-0.411393\pi$
$563$	30.2324	−	21.9652i	1.27415	−	0.925721i	0.999360	+	0.0357842i	$0.0113929\pi$
$564$	−0.570231	+	4.95621i	−0.0240110	+	0.208694i
$565$	−4.78748	+	14.7344i	−0.201411	+	0.619879i
$566$	14.7154	−	20.2539i	0.618532	−	0.851337i
$567$	−14.7994	−	14.4184i	−0.621517	−	0.605517i
$568$	42.6871	+	13.8699i	1.79111	+	0.581968i
$569$	−9.41935	−	28.9898i	−0.394880	−	1.21532i	−0.929055	−	0.369941i	$-0.879378\pi$
$569$	−9.41935	−	28.9898i	−0.394880	−	1.21532i	0.534175	−	0.845374i	$-0.320622\pi$
$570$	3.12641	+	15.4541i	0.130951	+	0.647299i
$571$			15.1236i			0.632905i	0.948608	+	0.316452i	$0.102492\pi$
$571$			15.1236i			0.632905i	−0.948608	+	0.316452i	$0.897508\pi$
$572$	−4.85294	−	2.67402i	−0.202912	−	0.111806i
$573$	−3.52132	−	1.60945i	−0.147105	−	0.0672359i
$574$	−2.87863	−	3.96210i	−0.120152	−	0.165375i
$575$	−4.57996	+	1.48812i	−0.190997	+	0.0620588i
$576$	−21.5694	+	9.09954i	−0.898726	+	0.379147i
$577$	34.8383	+	25.3115i	1.45034	+	1.05373i	0.985752	+	0.168203i	$0.0537963\pi$
$577$	34.8383	+	25.3115i	1.45034	+	1.05373i	0.464584	+	0.885529i	$0.346204\pi$
$578$	−2.63930	−	1.91756i	−0.109780	−	0.0797601i
$579$	−3.94639	+	4.29720i	−0.164006	+	0.178586i
$580$	2.72026	−	0.883866i	0.112953	−	0.0367005i
$581$	2.03634	+	2.80278i	0.0844815	+	0.116279i
$582$	6.25668	−	13.6890i	0.259348	−	0.567426i
$583$	3.77351	−	19.6785i	0.156283	−	0.814998i
$584$			16.7884i			0.694710i
$585$	−5.62210	−	1.31104i	−0.232445	−	0.0542049i
$586$	−0.213705	−	0.657715i	−0.00882806	−	0.0271700i
$587$	−20.3038	−	6.59710i	−0.838027	−	0.272292i	−0.141604	−	0.989923i	$-0.545226\pi$
$587$	−20.3038	−	6.59710i	−0.838027	−	0.272292i	−0.696423	+	0.717632i	$0.745226\pi$
$588$	2.26488	−	1.27811i	0.0934023	−	0.0527085i
$589$	−24.7888	+	34.1188i	−1.02140	+	1.40584i
$590$	−0.0283735	+	0.0873248i	−0.00116812	+	0.00359511i
$591$	9.54686	+	1.09840i	0.392706	+	0.0451822i
$592$	−14.2044	+	10.3201i	−0.583797	+	0.424154i
$593$	7.99783			0.328432			0.164216	−	0.986424i	$-0.447491\pi$
$593$	7.99783			0.328432			0.164216	+	0.986424i	$0.447491\pi$
$594$	−15.7902	−	9.31782i	−0.647880	−	0.382315i
$595$	−8.56955			−0.351317
$596$	6.69787	−	4.86629i	0.274355	−	0.199331i
$597$	−31.3267	−	3.60426i	−1.28212	−	0.147512i
$598$	−3.04652	+	9.37621i	−0.124581	+	0.383422i
$599$	12.8548	−	17.6932i	0.525235	−	0.722923i	−0.461160	−	0.887317i	$-0.652567\pi$
$599$	12.8548	−	17.6932i	0.525235	−	0.722923i	0.986395	+	0.164393i	$0.0525667\pi$
$600$	4.60282	−	2.59745i	0.187909	−	0.106040i
$601$	35.1056	+	11.4065i	1.43199	+	0.465281i	0.919390	−	0.393348i	$-0.128683\pi$
$601$	35.1056	+	11.4065i	1.43199	+	0.465281i	0.512598	+	0.858629i	$0.328683\pi$
$602$	−4.68239	−	14.4109i	−0.190840	−	0.587345i
$603$	11.4590	+	2.67218i	0.466648	+	0.108820i
$604$		−	15.9911i		−	0.650670i
$605$	8.46212	+	7.02798i	0.344034	+	0.285728i
$606$	8.18410	−	17.9060i	0.332456	−	0.727380i
$607$	22.4457	+	30.8938i	0.911041	+	1.25394i	0.966810	+	0.255496i	$0.0822389\pi$
$607$	22.4457	+	30.8938i	0.911041	+	1.25394i	−0.0557691	+	0.998444i	$0.517761\pi$
$608$	36.5907	−	11.8890i	1.48395	−	0.482164i
$609$	−8.86117	+	9.64887i	−0.359073	+	0.390992i
$610$	−7.02279	−	5.10235i	−0.284344	−	0.206588i
$611$	−5.16502	−	3.75261i	−0.208954	−	0.151814i
$612$	−8.95757	+	3.77895i	−0.362088	+	0.152755i
$613$	−0.572067	+	0.185876i	−0.0231056	+	0.00750745i	−0.320547	−	0.947233i	$-0.603867\pi$
$613$	−0.572067	+	0.185876i	−0.0231056	+	0.00750745i	0.297441	+	0.954740i	$0.403867\pi$
$614$	6.24175	+	8.59104i	0.251897	+	0.346706i
$615$	3.15875	+	1.44374i	0.127373	+	0.0582171i
$616$	−16.9520	+	15.8883i	−0.683015	+	0.640157i
$617$			46.3358i			1.86541i	0.360643	+	0.932704i	$0.382557\pi$
$617$			46.3358i			1.86541i	−0.360643	+	0.932704i	$0.617443\pi$
$618$	2.33196	+	11.5270i	0.0938051	+	0.463686i
$619$	4.93861	+	15.1995i	0.198499	+	0.610918i	0.999918	+	0.0128143i	$0.00407904\pi$
$619$	4.93861	+	15.1995i	0.198499	+	0.610918i	−0.801418	+	0.598104i	$0.795921\pi$
$620$	4.06956	+	1.32228i	0.163437	+	0.0531040i
$621$	8.43086	−	23.5598i	0.338319	−	0.945423i
$622$	13.3171	−	18.3295i	0.533969	−	0.734945i
$623$	1.17416	−	3.61369i	0.0470417	−	0.144779i
$624$	0.575225	−	4.99962i	0.0230274	−	0.200145i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−17.8893			−0.715001
$627$	40.0576	+	28.4869i	1.59975	+	1.13766i
$628$	−14.4487			−0.576564
$629$	−35.1154	+	25.5128i	−1.40014	+	1.01726i
$630$	−3.78765	+	6.27230i	−0.150903	+	0.249894i
$631$	−1.53008	+	4.70911i	−0.0609116	+	0.187467i	−0.976882	−	0.213779i	$-0.931423\pi$
$631$	−1.53008	+	4.70911i	−0.0609116	+	0.187467i	0.915970	+	0.401246i	$0.131423\pi$
$632$	−0.0993218	+	0.136705i	−0.00395081	+	0.00543782i
$633$	−7.95407	−	14.0950i	−0.316146	−	0.560228i
$634$	−31.6164	−	10.2728i	−1.25565	−	0.407984i
$635$	−2.40295	−	7.39553i	−0.0953583	−	0.293483i
$636$	−8.90417	+	1.80134i	−0.353073	+	0.0714279i
$637$			3.32803i			0.131861i
$638$	−5.61008	+	10.1814i	−0.222105	+	0.403087i
$639$	33.3678	−	28.8772i	1.32001	−	1.14236i
$640$	−0.406098	−	0.558945i	−0.0160524	−	0.0220943i
$641$	−28.9141	+	9.39474i	−1.14204	+	0.371070i	−0.818138	−	0.575022i	$-0.804994\pi$
$641$	−28.9141	+	9.39474i	−1.14204	+	0.371070i	−0.323898	+	0.946092i	$0.604994\pi$
$642$	−5.36498	−	4.92700i	−0.211739	−	0.194453i
$643$	−7.11815	−	5.17164i	−0.280712	−	0.203949i	0.438516	−	0.898724i	$-0.355504\pi$
$643$	−7.11815	−	5.17164i	−0.280712	−	0.203949i	−0.719228	+	0.694774i	$0.755504\pi$
$644$	−7.76510	−	5.64167i	−0.305988	−	0.222313i
$645$	7.91442	+	7.26832i	0.311630	+	0.286190i
$646$	−32.3168	+	10.5004i	−1.27149	+	0.413132i
$647$	3.23801	+	4.45673i	0.127299	+	0.175212i	0.867909	−	0.496723i	$-0.165463\pi$
$647$	3.23801	+	4.45673i	0.127299	+	0.175212i	−0.740610	+	0.671935i	$0.765463\pi$
$648$	−3.94204	+	27.1780i	−0.154858	+	1.06765i
$649$	0.121628	+	0.259119i	0.00477430	+	0.0101713i
$650$			2.04723i			0.0802988i
$651$	−19.2093	+	3.88611i	−0.752873	+	0.152309i
$652$	−4.74548	−	14.6051i	−0.185847	−	0.571979i
$653$	−22.6057	−	7.34505i	−0.884631	−	0.287434i	−0.168752	−	0.985659i	$-0.553974\pi$
$653$	−22.6057	−	7.34505i	−0.884631	−	0.287434i	−0.715879	+	0.698225i	$0.753974\pi$
$654$	−5.45961	−	9.67473i	−0.213488	−	0.378312i
$655$	−6.18656	+	8.51507i	−0.241729	+	0.332711i
$656$	−0.935596	+	2.87947i	−0.0365289	+	0.112424i
$657$	14.1294	+	8.53231i	0.551241	+	0.332877i
$658$	−6.55561	+	4.76293i	−0.255564	+	0.185678i
$659$	−34.2726			−1.33507			−0.667536	−	0.744577i	$-0.732651\pi$
$659$	−34.2726			−1.33507			−0.667536	+	0.744577i	$0.732651\pi$
$660$	1.49293	−	4.75858i	0.0581122	−	0.185228i
$661$	2.60406			0.101286			0.0506431	−	0.998717i	$-0.483873\pi$
$661$	2.60406			0.101286			0.0506431	+	0.998717i	$0.483873\pi$
$662$	−14.1417	+	10.2745i	−0.549632	+	0.399331i
$663$	1.42204	−	12.3598i	0.0552275	−	0.480015i
$664$	1.42292	−	4.37930i	0.0552201	−	0.169950i
$665$	11.5464	−	15.8923i	0.447752	−	0.616277i
$666$	3.15296	+	36.9784i	0.122175	+	1.43288i
$667$	−15.0889	−	4.90270i	−0.584246	−	0.189833i
$668$	−0.686535	−	2.11294i	−0.0265628	−	0.0817520i
$669$	−5.51018	−	27.2372i	−0.213036	−	1.05305i
$670$		−	4.17268i		−	0.161205i
$671$	−26.8518	+	3.36589i	−1.03660	+	0.129939i
$672$	16.2613	+	7.43238i	0.627293	+	0.286710i
$673$	−3.78493	−	5.20951i	−0.145898	−	0.200812i	0.729813	−	0.683647i	$-0.239607\pi$
$673$	−3.78493	−	5.20951i	−0.145898	−	0.200812i	−0.875711	+	0.482835i	$0.839607\pi$
$674$	−23.0703	+	7.49600i	−0.888636	+	0.288735i
$675$	0.153217	−	5.19389i	0.00589731	−	0.199913i
$676$	6.52992	+	4.74426i	0.251151	+	0.182472i
$677$	−2.13640	−	1.55218i	−0.0821084	−	0.0596553i	0.545974	−	0.837802i	$-0.316160\pi$
$677$	−2.13640	−	1.55218i	−0.0821084	−	0.0596553i	−0.628082	+	0.778147i	$0.716160\pi$
$678$	−19.3100	+	21.0265i	−0.741594	+	0.807517i
$679$	−17.8340	+	5.79463i	−0.684408	+	0.222378i
$680$	6.69490	+	9.21474i	0.256738	+	0.353369i
$681$	−1.09573	+	2.39735i	−0.0419886	+	0.0918667i
$682$	−15.7428	+	7.38950i	−0.602824	+	0.282959i
$683$			1.32020i			0.0505162i	0.999681	+	0.0252581i	$0.00804076\pi$
$683$			1.32020i			0.0505162i	−0.999681	+	0.0252581i	$0.991959\pi$
$684$	5.06115	−	21.7036i	0.193518	−	0.829857i
$685$	1.07562	+	3.31041i	0.0410972	+	0.126484i
$686$	20.2773	+	6.58851i	0.774193	+	0.251550i
$687$	−3.97324	+	2.24217i	−0.151589	+	0.0855440i
$688$	−5.50607	+	7.57846i	−0.209917	+	0.288926i
$689$	3.59248	−	11.0565i	0.136863	−	0.421220i
$690$	−8.81557	−	1.01426i	−0.335603	−	0.0386124i
$691$	−33.6567	+	24.4531i	−1.28036	+	0.930238i	−0.999564	−	0.0295288i	$-0.990599\pi$
$691$	−33.6567	+	24.4531i	−1.28036	+	0.930238i	−0.280799	+	0.959767i	$0.590599\pi$
$692$	−11.0349			−0.419484
$693$	4.75639	+	22.3419i	0.180680	+	0.848698i
$694$	32.6689			1.24009
$695$	7.74963	−	5.63044i	0.293960	−	0.213575i
$696$	17.2981	+	1.99021i	0.655682	+	0.0754386i
$697$	−2.31293	+	7.11847i	−0.0876085	+	0.269631i
$698$	4.45443	−	6.13099i	0.168603	−	0.232061i
$699$	39.3905	−	22.2287i	1.48988	−	0.840767i
$700$	−1.89557	−	0.615909i	−0.0716459	−	0.0232792i
$701$	3.58594	+	11.0364i	0.135439	+	0.416839i	0.995658	−	0.0930862i	$-0.0296732\pi$
$701$	3.58594	+	11.0364i	0.135439	+	0.416839i	−0.860219	+	0.509925i	$0.829673\pi$
$702$	−8.41797	−	6.50373i	−0.317716	−	0.245467i
$703$		−	99.4973i		−	3.75261i
$704$	25.4179	+	4.87411i	0.957974	+	0.183700i
$705$	2.38878	−	5.22640i	0.0899666	−	0.196838i
$706$	−7.59017	−	10.4470i	−0.285660	−	0.393177i
$707$	−23.3280	+	7.57972i	−0.877339	+	0.285065i
$708$	0.0877838	−	0.0955872i	0.00329912	−	0.00359239i
$709$	−1.91218	−	1.38928i	−0.0718136	−	0.0521756i	0.551299	−	0.834308i	$-0.314132\pi$
$709$	−1.91218	−	1.38928i	−0.0718136	−	0.0521756i	−0.623113	+	0.782132i	$0.714132\pi$
$710$	−12.6603	−	9.19822i	−0.475131	−	0.345203i
$711$	0.0645750	+	0.153068i	0.00242175	+	0.00574049i
$712$	−4.80307	+	1.56061i	−0.180003	+	0.0584864i
$713$	−13.9511	−	19.2020i	−0.522473	−	0.719122i
$714$	−14.3619	−	6.56425i	−0.537481	−	0.245661i
$715$	4.36445	+	4.65665i	0.163221	+	0.174149i
$716$		−	18.0407i		−	0.674214i
$717$	−8.04937	−	39.7887i	−0.300609	−	1.48593i
$718$	3.84228	+	11.8253i	0.143393	+	0.441317i
$719$	31.8881	+	10.3611i	1.18922	+	0.386402i	0.835786	−	0.549056i	$-0.185012\pi$
$719$	31.8881	+	10.3611i	1.18922	+	0.386402i	0.353438	+	0.935458i	$0.385012\pi$
$720$	4.51340	−	0.384835i	0.168205	−	0.0143420i
$721$	8.61239	−	11.8539i	0.320742	−	0.441464i
$722$	17.8237	−	54.8556i	0.663328	−	2.04151i
$723$	−4.01165	+	34.8677i	−0.149195	+	1.29674i
$724$	−3.47976	+	2.52819i	−0.129324	+	0.0939595i
$725$	−3.29456			−0.122357
$726$	8.79847	+	18.2603i	0.326542	+	0.677705i
$727$	7.65405			0.283873			0.141936	−	0.989876i	$-0.454667\pi$
$727$	7.65405			0.283873			0.141936	+	0.989876i	$0.454667\pi$
$728$	−10.9058	+	7.92351i	−0.404195	+	0.293665i
$729$	20.8700	+	17.1302i	0.772962	+	0.634453i
$730$	1.80878	−	5.56687i	0.0669461	−	0.206039i
$731$	−13.6118	+	18.7351i	−0.503452	+	0.692942i
$732$	6.03004	+	10.6856i	0.222877	+	0.394949i
$733$	22.5520	+	7.32760i	0.832978	+	0.270651i	0.694299	−	0.719686i	$-0.255714\pi$
$733$	22.5520	+	7.32760i	0.832978	+	0.270651i	0.138679	+	0.990337i	$0.455714\pi$
$734$	−5.34808	−	16.4597i	−0.197401	−	0.607538i
$735$	−2.93604	+	0.593970i	−0.108297	+	0.0219089i
$736$			21.6530i			0.798140i
$737$	−8.89569	−	9.49125i	−0.327677	−	0.349615i
$738$	4.18793	+	4.83919i	0.154160	+	0.178133i
$739$	−6.03119	−	8.30121i	−0.221861	−	0.305365i	0.683548	−	0.729905i	$-0.260436\pi$
$739$	−6.03119	−	8.30121i	−0.221861	−	0.305365i	−0.905409	+	0.424540i	$0.860436\pi$
$740$	−9.60113	+	3.11960i	−0.352945	+	0.114679i
$741$	21.0054	+	19.2905i	0.771651	+	0.708656i
$742$	−11.9374	−	8.67306i	−0.438237	−	0.318398i
$743$	−22.3105	−	16.2096i	−0.818495	−	0.594671i	0.0977862	−	0.995207i	$-0.468824\pi$
$743$	−22.3105	−	16.2096i	−0.818495	−	0.594671i	−0.916281	+	0.400536i	$0.868824\pi$
$744$	19.1859	+	17.6196i	0.703388	+	0.645966i
$745$	−9.06940	+	2.94683i	−0.332277	+	0.107963i
$746$	4.87606	+	6.71132i	0.178525	+	0.245719i
$747$	−2.96253	−	3.42323i	−0.108393	−	0.125249i
$748$	10.5558	+	2.02417i	0.385959	+	0.0740110i
$749$			9.07515i			0.331599i
$750$	−1.80609	+	0.365379i	−0.0659492	+	0.0133417i
$751$	−0.307278	−	0.945704i	−0.0112127	−	0.0345092i	0.945294	−	0.326221i	$-0.105775\pi$
$751$	−0.307278	−	0.945704i	−0.0112127	−	0.0345092i	−0.956506	+	0.291712i	$0.905775\pi$
$752$	4.76431	+	1.54802i	0.173737	+	0.0564505i
$753$	23.3072	+	41.3016i	0.849362	+	1.50511i
$754$	−3.96444	+	5.45659i	−0.144376	+	0.198717i
$755$	−5.69187	+	17.5178i	−0.207148	+	0.637537i
$756$	8.55450	−	5.83774i	0.311124	−	0.212316i
$757$	29.7895	−	21.6434i	1.08272	−	0.786641i	0.104564	−	0.994518i	$-0.466655\pi$
$757$	29.7895	−	21.6434i	1.08272	−	0.786641i	0.978155	+	0.207877i	$0.0666554\pi$
$758$	22.9161			0.832349
$759$	−22.2143	+	16.4867i	−0.806328	+	0.598430i
$760$	−26.1094			−0.947088
$761$	26.1077	−	18.9684i	0.946404	−	0.687603i	−0.00354971	−	0.999994i	$-0.501130\pi$
$761$	26.1077	−	18.9684i	0.946404	−	0.687603i	0.949954	+	0.312391i	$0.101130\pi$
$762$	1.63779	−	14.2350i	0.0593309	−	0.515680i
$763$	−4.27691	+	13.1630i	−0.154835	+	0.476532i
$764$	1.14069	−	1.57002i	0.0412686	−	0.0568013i
$765$	11.1578	−	0.951369i	0.403411	−	0.0343968i
$766$	−14.2260	−	4.62229i	−0.514005	−	0.167010i
$767$	0.0513216	+	0.157952i	0.00185311	+	0.00570330i
$768$	−5.61249	−	27.7429i	−0.202523	−	1.00109i
$769$			31.0262i			1.11883i	0.828887	+	0.559416i	$0.188975\pi$
$769$			31.0262i			1.11883i	−0.828887	+	0.559416i	$0.811025\pi$
$770$	7.33290	−	3.44198i	0.264259	−	0.124040i
$771$	2.61948	+	1.19726i	0.0943383	+	0.0431183i
$772$	−1.71893	−	2.36591i	−0.0618658	−	0.0851509i
$773$	16.7282	−	5.43531i	0.601671	−	0.195495i	0.00768523	−	0.999970i	$-0.497554\pi$
$773$	16.7282	−	5.43531i	0.601671	−	0.195495i	0.593985	+	0.804476i	$0.297554\pi$
$774$	7.69647	+	18.2436i	0.276644	+	0.655752i
$775$	−3.98742	−	2.89703i	−0.143232	−	0.104064i
$776$	20.1636	+	14.6497i	0.723833	+	0.525895i
$777$	31.2754	−	34.0556i	1.12200	−	1.22174i
$778$	−13.9712	+	4.53952i	−0.500892	+	0.162750i
$779$	−10.0849	−	13.8807i	−0.361328	−	0.497326i
$780$	1.20288	−	2.63177i	0.0430698	−	0.0942324i
$781$	−48.4068	+	6.06783i	−1.73213	+	0.217124i
$782$		−	19.1239i		−	0.683868i
$783$	10.4663	−	13.5469i	0.374036	−	0.484125i
$784$	−0.806955	−	2.48355i	−0.0288198	−	0.0886983i
$785$	15.8280	+	5.14284i	0.564927	+	0.183556i
$786$	−16.8907	+	9.53172i	−0.602473	+	0.339985i
$787$	17.5914	−	24.2125i	0.627066	−	0.863083i	−0.370777	−	0.928722i	$-0.620909\pi$
$787$	17.5914	−	24.2125i	0.627066	−	0.863083i	0.997843	+	0.0656393i	$0.0209087\pi$
$788$	−1.48849	+	4.58109i	−0.0530251	+	0.163195i
$789$	8.95581	+	1.03040i	0.318835	+	0.0366832i
$790$	0.0476626	−	0.0346289i	0.00169576	−	0.00123204i
$791$	35.5674			1.26463
$792$	20.3081	−	22.5690i	0.721617	−	0.801953i
$793$	−15.7014			−0.557573
$794$	−21.5794	+	15.6783i	−0.765823	+	0.556403i
$795$	10.3954	+	1.19603i	0.368687	+	0.0424188i
$796$	4.88426	−	15.0322i	0.173118	−	0.532803i
$797$	−6.68168	+	9.19655i	−0.236677	+	0.325758i	−0.910790	−	0.412870i	$-0.864526\pi$
$797$	−6.68168	+	9.19655i	−0.236677	+	0.325758i	0.674113	+	0.738629i	$0.264526\pi$
$798$	31.5245	−	17.7898i	1.11595	−	0.629751i
$799$	11.7781	+	3.82693i	0.416679	+	0.135387i
$800$	1.38946	+	4.27631i	0.0491247	+	0.151190i
$801$	−1.12761	+	4.83548i	−0.0398420	+	0.170853i
$802$			2.85332i			0.100754i
$803$	−7.75363	−	16.5186i	−0.273620	−	0.582929i
$804$	−2.45172	+	5.36410i	−0.0864654	+	0.189177i
$805$	6.49832	+	8.94418i	0.229036	+	0.315241i
$806$	−9.59636	+	3.11805i	−0.338017	+	0.109829i
$807$	−0.879717	+	0.957918i	−0.0309675	+	0.0337203i
$808$	26.3752	+	19.1627i	0.927877	+	0.674142i
$809$	2.59123	+	1.88264i	0.0911028	+	0.0661901i	0.632404	−	0.774639i	$-0.282068\pi$
$809$	2.59123	+	1.88264i	0.0911028	+	0.0661901i	−0.541301	+	0.840829i	$0.682068\pi$
$810$	4.23529	−	8.58721i	0.148813	−	0.301724i
$811$	−35.2471	+	11.4525i	−1.23769	+	0.402151i	−0.853496	−	0.521100i	$-0.825522\pi$
$811$	−35.2471	+	11.4525i	−1.23769	+	0.402151i	−0.384197	+	0.923251i	$0.625522\pi$
$812$	−3.85967	−	5.31238i	−0.135448	−	0.186428i
$813$	−43.3680	−	19.8218i	−1.52098	−	0.695180i
$814$	19.8007	−	35.9353i	0.694014	−	1.25953i
$815$			17.6885i			0.619601i
$816$	1.93571	+	9.56834i	0.0677633	+	0.334959i
$817$	−16.4041	−	50.4866i	−0.573906	−	1.76630i
$818$	18.6919	+	6.07335i	0.653546	+	0.212350i
$819$	1.12596	+	13.2054i	0.0393442	+	0.461434i
$820$	−1.02324	+	1.40836i	−0.0357329	+	0.0491822i
$821$	3.75058	−	11.5431i	0.130896	−	0.402857i	−0.864033	−	0.503435i	$-0.832069\pi$
$821$	3.75058	−	11.5431i	0.130896	−	0.402857i	0.994929	+	0.100578i	$0.0320693\pi$
$822$	−0.733113	+	6.37192i	−0.0255703	+	0.222246i
$823$	0.799265	−	0.580700i	0.0278606	−	0.0202419i	−0.573768	−	0.819018i	$-0.694519\pi$
$823$	0.799265	−	0.580700i	0.0278606	−	0.0202419i	0.601628	+	0.798776i	$0.294519\pi$
$824$	−19.4748			−0.678436
$825$	−3.32922	+	4.68148i	−0.115909	+	0.162988i
$826$	0.210794			0.00733447
$827$	25.0529	−	18.2020i	0.871175	−	0.632945i	−0.0597272	−	0.998215i	$-0.519023\pi$
$827$	25.0529	−	18.2020i	0.871175	−	0.632945i	0.930902	+	0.365269i	$0.119023\pi$
$828$	10.7367	+	6.48357i	0.373127	+	0.225319i
$829$	−3.18552	+	9.80403i	−0.110638	+	0.340508i	−0.991012	−	0.133771i	$-0.957291\pi$
$829$	−3.18552	+	9.80403i	−0.110638	+	0.340508i	0.880375	+	0.474279i	$0.157291\pi$
$830$	−0.943652	+	1.29883i	−0.0327546	+	0.0450829i
$831$	2.88862	+	5.11879i	0.100205	+	0.177569i
$832$	14.2813	+	4.64028i	0.495115	+	0.160873i
$833$	−1.99491	−	6.13971i	−0.0691196	−	0.212728i
$834$	17.3007	−	3.49999i	0.599075	−	0.121195i
$835$			2.55902i			0.0885585i
$836$	−17.9765	+	16.8485i	−0.621732	+	0.582719i
$837$	24.5797	−	7.19240i	0.849599	−	0.248606i
$838$	−6.09223	−	8.38523i	−0.210453	−	0.289663i
$839$	32.9397	−	10.7028i	1.13721	−	0.369500i	0.320895	−	0.947115i	$-0.396016\pi$
$839$	32.9397	−	10.7028i	1.13721	−	0.369500i	0.816310	+	0.577614i	$0.196016\pi$
$840$	−8.93665	−	8.20709i	−0.308344	−	0.283172i
$841$	14.6803	+	10.6659i	0.506218	+	0.367789i
$842$	11.8271	+	8.59288i	0.407588	+	0.296130i
$843$	−15.7108	−	14.4282i	−0.541109	−	0.496934i
$844$	7.71527	−	2.50684i	0.265571	−	0.0862891i
$845$	−5.46465	−	7.52144i	−0.187990	−	0.258745i
$846$	8.00683	−	6.92926i	0.275280	−	0.238233i
$847$	9.34162	−	23.4621i	0.320982	−	0.806167i
$848$			9.12204i			0.313252i
$849$	39.9496	−	8.08194i	1.37107	−	0.277371i
$850$	−1.22716	−	3.77682i	−0.0420914	−	0.129544i
$851$	53.2563	+	17.3040i	1.82560	+	0.593174i
$852$	10.8706	+	19.2633i	0.372420	+	0.659949i
$853$	−26.1958	+	36.0555i	−0.896928	+	1.23452i	0.0745091	+	0.997220i	$0.476261\pi$
$853$	−26.1958	+	36.0555i	−0.896928	+	1.23452i	−0.971437	+	0.237296i	$0.923739\pi$
$854$	−6.15831	+	18.9533i	−0.210733	+	0.648570i
$855$	−13.2695	+	21.9741i	−0.453807	+	0.751499i
$856$	9.75842	−	7.08990i	0.333536	−	0.242328i
$857$	31.9868			1.09265			0.546324	−	0.837574i	$-0.316027\pi$
$857$	31.9868			1.09265			0.546324	+	0.837574i	$0.316027\pi$
$858$	3.74751	+	11.1474i	0.127938	+	0.380565i
$859$	−8.24402			−0.281282			−0.140641	−	0.990061i	$-0.544916\pi$
$859$	−8.24402			−0.281282			−0.140641	+	0.990061i	$0.544916\pi$
$860$	−4.35744	+	3.16587i	−0.148588	+	0.107955i
$861$	0.911346	−	7.92105i	0.0310586	−	0.269949i
$862$	3.73294	−	11.4888i	0.127145	−	0.391311i
$863$	−27.9532	+	38.4743i	−0.951539	+	1.30968i	−0.000698318		1.00000i	$0.500222\pi$
$863$	−27.9532	+	38.4743i	−0.951539	+	1.30968i	−0.950840	+	0.309681i	$0.899778\pi$
$864$	−21.9978	−	7.87189i	−0.748380	−	0.267807i
$865$	12.0884	+	3.92775i	0.411017	+	0.133548i
$866$	−3.81421	−	11.7389i	−0.129612	−	0.398905i
$867$	−1.05316	−	5.20585i	−0.0357672	−	0.176800i
$868$		−	9.82355i		−	0.333433i
$869$	0.0345892	−	0.180379i	0.00117336	−	0.00611893i
$870$	−5.52144	−	2.52363i	−0.187194	−	0.0855589i
$871$	−4.43630	−	6.10604i	−0.150318	−	0.206895i
$872$	17.4953	−	5.68458i	0.592467	−	0.192504i
$873$	22.5771	−	9.52467i	0.764121	−	0.322361i
$874$	35.4654	+	25.7671i	1.19963	+	0.871586i
$875$	1.85731	+	1.34942i	0.0627886	+	0.0456186i
$876$	−5.59613	+	6.09359i	−0.189076	+	0.205883i
$877$	−39.3171	+	12.7749i	−1.32764	+	0.431378i	−0.885113	−	0.465376i	$-0.845919\pi$
$877$	−39.3171	+	12.7749i	−1.32764	+	0.431378i	−0.442530	+	0.896754i	$0.645919\pi$
$878$	5.56858	+	7.66450i	0.187931	+	0.258664i
$879$	0.468036	−	1.02402i	0.0157865	−	0.0345392i
$880$	−4.38610	−	2.41678i	−0.147855	−	0.0814697i
$881$			14.9910i			0.505059i	0.967589	+	0.252529i	$0.0812625\pi$
$881$			14.9910i			0.505059i	−0.967589	+	0.252529i	$0.918738\pi$
$882$	−5.37556	−	1.25355i	−0.181005	−	0.0422092i
$883$	16.4547	+	50.6424i	0.553745	+	1.70425i	0.699234	+	0.714893i	$0.253525\pi$
$883$	16.4547	+	50.6424i	0.553745	+	1.70425i	−0.145488	+	0.989360i	$0.546475\pi$
$884$	5.93088	+	1.92706i	0.199477	+	0.0648141i
$885$	−0.130188	+	0.0734670i	−0.00437621	+	0.00246957i
$886$	2.42579	−	3.33881i	0.0814959	−	0.112169i
$887$	−10.2206	+	31.4557i	−0.343174	+	1.05618i	0.619380	+	0.785091i	$0.287384\pi$
$887$	−10.2206	+	31.4557i	−0.343174	+	1.05618i	−0.962554	+	0.271089i	$0.912616\pi$
$888$	−61.0534	−	7.02442i	−2.04882	−	0.235724i
$889$	−14.4427	+	10.4932i	−0.484393	+	0.351932i
$890$	1.76079			0.0590217
$891$	−8.67330	−	28.5618i	−0.290567	−	0.956855i
$892$	13.9290			0.466376
$893$	−22.9667	+	16.6863i	−0.768550	+	0.558384i
$894$	−17.4569	−	2.00848i	−0.583846	−	0.0671737i
$895$	−6.42140	+	19.7630i	−0.214644	+	0.660606i
$896$	−0.932305	+	1.28321i	−0.0311461	+	0.0428690i
$897$	−13.9785	+	7.88828i	−0.466727	+	0.263382i
$898$	−11.3259	−	3.68002i	−0.377952	−	0.122804i
$899$	−5.01781	−	15.4432i	−0.167353	−	0.515061i
$900$	2.53647	+	0.591490i	0.0845489	+	0.0197163i
$901$			22.5510i			0.751284i
$902$	−0.879991	−	7.02022i	−0.0293005	−	0.233748i
$903$	10.2549	−	22.4367i	0.341263	−	0.746648i
$904$	−27.7868	−	38.2453i	−0.924176	−	1.27202i
$905$	4.71184	−	1.53097i	0.156627	−	0.0508912i
$906$	−22.9577	+	24.9985i	−0.762720	+	0.830520i
$907$	6.80404	+	4.94342i	0.225924	+	0.164144i	0.694989	−	0.719020i	$-0.255409\pi$
$907$	6.80404	+	4.94342i	0.225924	+	0.164144i	−0.469065	+	0.883164i	$0.655409\pi$
$908$	−1.06889	−	0.776591i	−0.0354722	−	0.0257721i
$909$	29.5322	−	12.4588i	0.979522	−	0.413233i
$910$	4.46992	−	1.45236i	0.148176	−	0.0481454i
$911$	−12.6734	−	17.4435i	−0.419890	−	0.577928i	0.545706	−	0.837977i	$-0.316262\pi$
$911$	−12.6734	−	17.4435i	−0.419890	−	0.577928i	−0.965596	+	0.260048i	$0.916262\pi$
$912$	−20.3527	−	9.30241i	−0.673946	−	0.308034i
$913$	0.622503	+	4.96609i	0.0206019	+	0.164353i
$914$		−	4.05877i		−	0.134252i
$915$	−2.80231	−	13.8520i	−0.0926414	−	0.457933i
$916$	−0.706652	−	2.17485i	−0.0233484	−	0.0718591i
$917$	22.9807	+	7.46690i	0.758891	+	0.246579i
$918$	19.4284	+	6.95243i	0.641232	+	0.229464i
$919$	17.5369	−	24.1374i	0.578487	−	0.796220i	−0.415041	−	0.909803i	$-0.636233\pi$
$919$	17.5369	−	24.1374i	0.578487	−	0.796220i	0.993529	+	0.113583i	$0.0362328\pi$
$920$	4.54081	−	13.9752i	0.149706	−	0.460748i
$921$	−1.97608	+	17.1753i	−0.0651139	+	0.565944i
$922$	13.0637	−	9.49131i	0.430229	−	0.312580i
$923$	−28.3055			−0.931688
$924$	−11.4490	+	0.116217i	−0.376645	+	0.00382325i
$925$	11.6281			0.382330
$926$	−5.72765	+	4.16138i	−0.188222	+	0.136752i
$927$	−9.89759	+	16.3903i	−0.325079	+	0.538328i
$928$	−4.57765	+	14.0886i	−0.150269	+	0.462479i
$929$	−4.79988	+	6.60647i	−0.157479	+	0.216751i	−0.880465	−	0.474112i	$-0.842769\pi$
$929$	−4.79988	+	6.60647i	−0.157479	+	0.216751i	0.722986	+	0.690863i	$0.242769\pi$
$930$	−4.46350	−	7.90956i	−0.146364	−	0.259365i
$931$	14.0741	+	4.57294i	0.461259	+	0.149872i
$932$	7.00571	+	21.5614i	0.229480	+	0.706266i
$933$	36.1537	−	7.31402i	1.18362	−	0.239450i
$934$			6.13945i			0.200889i
$935$	−10.8431	−	5.97464i	−0.354607	−	0.195392i
$936$	13.3200	−	11.5274i	0.435378	−	0.376784i
$937$	−13.8586	−	19.0748i	−0.452742	−	0.623146i	0.520242	−	0.854019i	$-0.325842\pi$
$937$	−13.8586	−	19.0748i	−0.452742	−	0.623146i	−0.972984	+	0.230873i	$0.925842\pi$
$938$	−9.11065	+	2.96023i	−0.297473	+	0.0966549i
$939$	−21.4514	−	19.7002i	−0.700040	−	0.642891i
$940$	2.33025	+	1.69303i	0.0760044	+	0.0552204i
$941$	−34.1063	−	24.7796i	−1.11183	−	0.807793i	−0.128881	−	0.991660i	$-0.541138\pi$
$941$	−34.1063	−	24.7796i	−1.11183	−	0.807793i	−0.982951	+	0.183867i	$0.941138\pi$
$942$	22.5872	+	20.7433i	0.735931	+	0.675852i
$943$	9.18357	−	2.98392i	0.299058	−	0.0971699i
$944$	−0.0765977	−	0.105428i	−0.00249304	−	0.00343138i
$945$	−11.4491	+	3.35017i	−0.372438	+	0.108981i
$946$	4.12256	−	21.4987i	0.134036	−	0.698983i
$947$		−	12.5815i		−	0.408844i	−0.978883	−	0.204422i	$-0.934468\pi$
$947$		−	12.5815i		−	0.408844i	0.978883	−	0.204422i	$-0.0655315\pi$
$948$	−0.0816183	+	0.0165117i	−0.00265084	+	0.000536274i
$949$	−3.27170	−	10.0692i	−0.106204	−	0.326862i
$950$	8.65761	+	2.81303i	0.280890	+	0.0912667i
$951$	−26.5991	−	47.1350i	−0.862535	−	1.52846i
$952$	15.3699	−	21.1549i	0.498142	−	0.685634i
$953$	6.94003	−	21.3592i	0.224810	−	0.691893i	−0.773501	−	0.633795i	$-0.781496\pi$
$953$	6.94003	−	21.3592i	0.224810	−	0.691893i	0.998311	−	0.0580979i	$-0.0185036\pi$
$954$	16.5058	+	9.96731i	0.534394	+	0.322704i
$955$	−1.80842	+	1.31389i	−0.0585190	+	0.0425165i
$956$	20.3477			0.658092
$957$	−17.9392	+	6.03079i	−0.579893	+	0.194948i
$958$	34.5731			1.11701
$959$	6.46488	−	4.69701i	0.208762	−	0.151674i
$960$	−1.54487	+	13.4274i	−0.0498604	+	0.433366i
$961$	−2.07279	+	6.37939i	−0.0668642	+	0.205787i
$962$	13.9925	−	19.2590i	0.451135	−	0.620934i
$963$	−1.00750	−	11.8161i	−0.0324662	−	0.380769i
$964$	−16.7313	−	5.43634i	−0.538880	−	0.175093i
$965$	1.04092	+	3.20361i	0.0335083	+	0.103128i
$966$	4.03948	+	19.9675i	0.129968	+	0.642443i
$967$			35.9453i			1.15592i	0.816065	+	0.577961i	$0.196151\pi$
$967$			35.9453i			1.15592i	−0.816065	+	0.577961i	$0.803849\pi$
$968$	−32.5266	+	8.28466i	−1.04545	+	0.266279i
$969$	−50.3150	−	22.9969i	−1.61635	−	0.738768i
$970$	−5.10769	−	7.03013i	−0.163998	−	0.225724i
$971$	25.1567	−	8.17390i	0.807317	−	0.262313i	0.123856	−	0.992300i	$-0.460474\pi$
$971$	25.1567	−	8.17390i	0.807317	−	0.262313i	0.683461	+	0.729987i	$0.260474\pi$
$972$	−10.4901	+	8.55060i	−0.336471	+	0.274261i
$973$	−17.7913	−	12.9262i	−0.570364	−	0.414394i
$974$	−22.1178	−	16.0695i	−0.708699	−	0.514900i
$975$	−2.25446	+	2.45487i	−0.0722005	+	0.0786187i
$976$	11.7172	−	3.80715i	0.375059	−	0.121864i
$977$	15.2223	+	20.9517i	0.487004	+	0.670304i	0.979832	−	0.199823i	$-0.0640367\pi$
$977$	15.2223	+	20.9517i	0.487004	+	0.670304i	−0.492828	+	0.870127i	$0.664037\pi$
$978$	−13.5493	+	29.6446i	−0.433260	+	0.947929i
$979$	4.00511	−	3.75380i	0.128004	−	0.119972i
$980$		−	1.50147i		−	0.0479628i
$981$	4.10735	−	17.6134i	0.131137	−	0.562353i
$982$	13.7206	+	42.2277i	0.437842	+	1.34754i
$983$	12.6670	+	4.11577i	0.404016	+	0.131273i	0.503974	−	0.863719i	$-0.331871\pi$
$983$	12.6670	+	4.11577i	0.404016	+	0.131273i	−0.0999578	+	0.994992i	$0.531871\pi$
$984$	−9.22941	+	5.20831i	−0.294223	+	0.166035i
$985$	3.26118	−	4.48863i	0.103910	−	0.143019i
$986$	4.04296	−	12.4430i	0.128754	−	0.396265i
$987$	−13.1060	−	1.50790i	−0.417169	−	0.0479968i
$988$	−11.5649	+	8.40240i	−0.367929	+	0.267316i
$989$	29.8760			0.950002
$990$	−9.16553	+	5.29564i	−0.291300	+	0.168306i
$991$	36.3428			1.15447			0.577233	−	0.816580i	$-0.304133\pi$
$991$	36.3428			1.15447			0.577233	+	0.816580i	$0.304133\pi$
$992$	−17.9289	+	13.0261i	−0.569244	+	0.413580i
$993$	−28.2721	−	3.25281i	−0.897189	−	0.103225i
$994$	−11.1018	+	34.1680i	−0.352129	+	1.08374i
$995$	−10.7011	+	14.7288i	−0.339248	+	0.466934i
$996$	1.97623	−	1.11522i	0.0626194	−	0.0353372i
$997$	−16.2176	−	5.26942i	−0.513617	−	0.166884i	0.0407295	−	0.999170i	$-0.487032\pi$
$997$	−16.2176	−	5.26942i	−0.513617	−	0.166884i	−0.554347	+	0.832286i	$0.687032\pi$
$998$	−6.90311	−	21.2456i	−0.218514	−	0.672517i
$999$	−36.9408	+	47.8135i	−1.16875	+	1.51275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.p.b.41.8	yes	48
3.2	odd	2	inner	165.2.p.b.41.5	✓	48
5.2	odd	4		825.2.bs.g.74.8		48
5.3	odd	4		825.2.bs.h.74.5		48
5.4	even	2		825.2.bi.e.701.5		48
11.7	odd	10	inner	165.2.p.b.161.5	yes	48
15.2	even	4		825.2.bs.h.74.6		48
15.8	even	4		825.2.bs.g.74.7		48
15.14	odd	2		825.2.bi.e.701.8		48
33.29	even	10	inner	165.2.p.b.161.8	yes	48
55.7	even	20		825.2.bs.g.524.7		48
55.18	even	20		825.2.bs.h.524.6		48
55.29	odd	10		825.2.bi.e.326.8		48
165.29	even	10		825.2.bi.e.326.5		48
165.62	odd	20		825.2.bs.h.524.5		48
165.128	odd	20		825.2.bs.g.524.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.p.b.41.5	✓	48	3.2	odd	2	inner
165.2.p.b.41.8	yes	48	1.1	even	1	trivial
165.2.p.b.161.5	yes	48	11.7	odd	10	inner
165.2.p.b.161.8	yes	48	33.29	even	10	inner
825.2.bi.e.326.5		48	165.29	even	10
825.2.bi.e.326.8		48	55.29	odd	10
825.2.bi.e.701.5		48	5.4	even	2
825.2.bi.e.701.8		48	15.14	odd	2
825.2.bs.g.74.7		48	15.8	even	4
825.2.bs.g.74.8		48	5.2	odd	4
825.2.bs.g.524.7		48	55.7	even	20
825.2.bs.g.524.8		48	165.128	odd	20
825.2.bs.h.74.5		48	5.3	odd	4
825.2.bs.h.74.6		48	15.2	even	4
825.2.bs.h.524.5		48	165.62	odd	20
825.2.bs.h.524.6		48	55.18	even	20

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.860692 - 0.625329i) q^{2} +(1.72070 + 0.197973i) q^{3} +(-0.268280 + 0.825682i) q^{4} +(0.587785 - 0.809017i) q^{5} +(1.60479 - 0.905610i) q^{6} +(-2.18340 - 0.709430i) q^{7} +(0.942926 + 2.90203i) q^{8} +(2.92161 + 0.681304i) q^{9} +O(q^{10})\)	\(q+(0.860692 - 0.625329i) q^{2} +(1.72070 + 0.197973i) q^{3} +(-0.268280 + 0.825682i) q^{4} +(0.587785 - 0.809017i) q^{5} +(1.60479 - 0.905610i) q^{6} +(-2.18340 - 0.709430i) q^{7} +(0.942926 + 2.90203i) q^{8} +(2.92161 + 0.681304i) q^{9} -1.06387i q^{10} +(-2.26806 - 2.41990i) q^{11} +(-0.625093 + 1.36764i) q^{12} +(-1.13108 - 1.55680i) q^{13} +(-2.32286 + 0.754744i) q^{14} +(1.17157 - 1.27571i) q^{15} +(1.22156 + 0.887513i) q^{16} +(3.01987 + 2.19406i) q^{17} +(2.94065 - 1.24058i) q^{18} +(-8.13782 + 2.64414i) q^{19} +(0.510300 + 0.702367i) q^{20} +(-3.61653 - 1.65297i) q^{21} +(-3.46533 - 0.664507i) q^{22} -4.81565i q^{23} +(1.04797 + 5.18019i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(-1.94703 - 0.632628i) q^{26} +(4.89234 + 1.75072i) q^{27} +(1.17153 - 1.61247i) q^{28} +(1.01807 - 3.13331i) q^{29} +(0.210618 - 1.83061i) q^{30} +(3.98742 - 2.89703i) q^{31} -4.49638 q^{32} +(-3.42357 - 4.61294i) q^{33} +3.97119 q^{34} +(-1.85731 + 1.34942i) q^{35} +(-1.34635 + 2.22954i) q^{36} +(-3.59329 + 11.0590i) q^{37} +(-5.35070 + 7.36461i) q^{38} +(-1.63805 - 2.90271i) q^{39} +(2.90203 + 0.942926i) q^{40} +(0.619630 + 1.90703i) q^{41} +(-4.14637 + 0.838824i) q^{42} +6.20394i q^{43} +(2.60654 - 1.22348i) q^{44} +(2.26847 - 1.96317i) q^{45} +(-3.01137 - 4.14479i) q^{46} +(3.15533 - 1.02523i) q^{47} +(1.92623 + 1.76898i) q^{48} +(-1.39916 - 1.01655i) q^{49} +(-0.860692 - 0.625329i) q^{50} +(4.76192 + 4.37317i) q^{51} +(1.58887 - 0.516256i) q^{52} +(3.55103 + 4.88758i) q^{53} +(5.30557 - 1.55249i) q^{54} +(-3.29087 + 0.412514i) q^{55} -7.00524i q^{56} +(-14.5262 + 2.93870i) q^{57} +(-1.08310 - 3.33345i) q^{58} +(-0.0820820 - 0.0266700i) q^{59} +(0.739023 + 1.30959i) q^{60} +(4.79602 - 6.60115i) q^{61} +(1.62034 - 4.98690i) q^{62} +(-5.89572 - 3.56024i) q^{63} +(-6.31311 + 4.58674i) q^{64} -1.92431 q^{65} +(-5.83124 - 1.82946i) q^{66} +3.92216 q^{67} +(-2.62177 + 1.90483i) q^{68} +(0.953369 - 8.28629i) q^{69} +(-0.754744 + 2.32286i) q^{70} +(8.64598 - 11.9002i) q^{71} +(0.777703 + 9.12102i) q^{72} +(5.23264 + 1.70019i) q^{73} +(3.82280 + 11.7654i) q^{74} +(-0.343442 - 1.69766i) q^{75} -7.42863i q^{76} +(3.23533 + 6.89265i) q^{77} +(-3.22501 - 1.47402i) q^{78} +(0.0325499 + 0.0448010i) q^{79} +(1.43603 - 0.466593i) q^{80} +(8.07165 + 3.98101i) q^{81} +(1.72583 + 1.25389i) q^{82} +(-1.22085 - 0.886997i) q^{83} +(2.33507 - 2.54265i) q^{84} +(3.55007 - 1.15349i) q^{85} +(3.87950 + 5.33968i) q^{86} +(2.37211 - 5.18994i) q^{87} +(4.88401 - 8.86375i) q^{88} +1.65507i q^{89} +(0.724821 - 3.10823i) q^{90} +(1.36517 + 4.20155i) q^{91} +(3.97620 + 1.29195i) q^{92} +(7.43469 - 4.19552i) q^{93} +(2.07466 - 2.85552i) q^{94} +(-2.64414 + 8.13782i) q^{95} +(-7.73691 - 0.890160i) q^{96} +(6.60805 - 4.80103i) q^{97} -1.83993 q^{98} +(-4.97770 - 8.61525i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9	\( 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9} + 8 q^{12} + 6 q^{15} + 32 q^{16} - 30 q^{18} - 100 q^{19} - 82 q^{22} + 100 q^{24} + 12 q^{25} + 14 q^{27} + 30 q^{28} + 10 q^{30} + 10 q^{31} - 46 q^{33} - 28 q^{34} + 14 q^{36} + 6 q^{37} - 50 q^{40} - 52 q^{42} + 32 q^{45} + 20 q^{46} - 80 q^{48} - 26 q^{49} - 30 q^{51} + 40 q^{52} + 6 q^{55} - 70 q^{57} + 92 q^{58} + 44 q^{60} + 70 q^{61} - 20 q^{63} + 18 q^{64} + 76 q^{66} + 20 q^{67} + 42 q^{69} - 4 q^{70} - 80 q^{72} + 90 q^{73} - 6 q^{75} - 108 q^{78} - 100 q^{79} + 38 q^{81} - 34 q^{82} + 70 q^{84} + 20 q^{85} + 74 q^{88} + 20 q^{90} - 86 q^{91} + 76 q^{93} + 10 q^{94} - 30 q^{96} + 6 q^{97} - 28 q^{99}+O(q^{100}) \) 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9 + 8 * q^12 + 6 * q^15 + 32 * q^16 - 30 * q^18 - 100 * q^19 - 82 * q^22 + 100 * q^24 + 12 * q^25 + 14 * q^27 + 30 * q^28 + 10 * q^30 + 10 * q^31 - 46 * q^33 - 28 * q^34 + 14 * q^36 + 6 * q^37 - 50 * q^40 - 52 * q^42 + 32 * q^45 + 20 * q^46 - 80 * q^48 - 26 * q^49 - 30 * q^51 + 40 * q^52 + 6 * q^55 - 70 * q^57 + 92 * q^58 + 44 * q^60 + 70 * q^61 - 20 * q^63 + 18 * q^64 + 76 * q^66 + 20 * q^67 + 42 * q^69 - 4 * q^70 - 80 * q^72 + 90 * q^73 - 6 * q^75 - 108 * q^78 - 100 * q^79 + 38 * q^81 - 34 * q^82 + 70 * q^84 + 20 * q^85 + 74 * q^88 + 20 * q^90 - 86 * q^91 + 76 * q^93 + 10 * q^94 - 30 * q^96 + 6 * q^97 - 28 * q^99

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