LMFDB - Embedded newform 150.2.h.b.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(19,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("150.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.h (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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 $ x^16 - 4x^15 - 24x^14 + 94x^13 + 262x^12 - 936x^11 - 1584x^10 + 4642x^9 + 6259x^8 - 11958x^7 - 15752x^6 + 14670x^5 + 18271x^4 - 10440x^3 + 1135x^2 + 21080*x + 11105
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.1
Root			$2.17199 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	150.109
Dual form			150.2.h.b.139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.53938 - 1.62182i) q^{5} +(0.309017 - 0.951057i) q^{6} -4.63137i q^{7} +(0.951057 + 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.53938 - 1.62182i) q^{5} +(0.309017 - 0.951057i) q^{6} -4.63137i q^{7} +(0.951057 + 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(2.21691 - 0.292102i) q^{10} +(2.05464 + 1.49278i) q^{11} +(0.587785 + 0.809017i) q^{12} +(0.0846260 + 0.116478i) q^{13} +(3.74686 + 2.72225i) q^{14} +(1.96521 + 1.06675i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-7.12436 - 2.31485i) q^{17} +1.00000i q^{18} +(2.08298 - 6.41074i) q^{19} +(-1.06675 + 1.96521i) q^{20} +(1.43117 + 4.40469i) q^{21} +(-2.41537 + 0.784803i) q^{22} +(0.985910 - 1.35699i) q^{23} -1.00000 q^{24} +(-0.260613 + 4.99320i) q^{25} -0.143974 q^{26} +(-0.587785 + 0.809017i) q^{27} +(-4.40469 + 1.43117i) q^{28} +(0.696812 + 2.14457i) q^{29} +(-2.01814 + 0.962868i) q^{30} +(0.310207 - 0.954718i) q^{31} -1.00000i q^{32} +(-2.41537 - 0.784803i) q^{33} +(6.06035 - 4.40310i) q^{34} +(-7.51126 + 7.12944i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-0.0523017 - 0.0719871i) q^{37} +(3.96205 + 5.45330i) q^{38} +(-0.116478 - 0.0846260i) q^{39} +(-0.962868 - 2.01814i) q^{40} +(-2.48680 + 1.80677i) q^{41} +(-4.40469 - 1.43117i) q^{42} +9.02860i q^{43} +(0.784803 - 2.41537i) q^{44} +(-2.19867 - 0.407256i) q^{45} +(0.518324 + 1.59524i) q^{46} +(10.3526 - 3.36376i) q^{47} +(0.587785 - 0.809017i) q^{48} -14.4496 q^{49} +(-3.88640 - 3.14577i) q^{50} +7.49100 q^{51} +(0.0846260 - 0.116478i) q^{52} +(4.72205 - 1.53429i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-0.741845 - 5.63022i) q^{55} +(1.43117 - 4.40469i) q^{56} +6.74065i q^{57} +(-2.14457 - 0.696812i) q^{58} +(4.25029 - 3.08802i) q^{59} +(0.407256 - 2.19867i) q^{60} +(11.0841 + 8.05305i) q^{61} +(0.590048 + 0.812131i) q^{62} +(-2.72225 - 3.74686i) q^{63} +(0.809017 + 0.587785i) q^{64} +(0.0586344 - 0.316552i) q^{65} +(2.05464 - 1.49278i) q^{66} +(7.27491 + 2.36376i) q^{67} +7.49100i q^{68} +(-0.518324 + 1.59524i) q^{69} +(-1.35283 - 10.2673i) q^{70} +(-3.17196 - 9.76228i) q^{71} +(0.951057 - 0.309017i) q^{72} +(1.15547 - 1.59036i) q^{73} +0.0889810 q^{74} +(-1.29513 - 4.82935i) q^{75} -6.74065 q^{76} +(6.91363 - 9.51580i) q^{77} +(0.136928 - 0.0444905i) q^{78} +(-0.230908 - 0.710661i) q^{79} +(2.19867 + 0.407256i) q^{80} +(0.309017 - 0.951057i) q^{81} -3.07386i q^{82} +(-2.95072 - 0.958745i) q^{83} +(3.74686 - 2.72225i) q^{84} +(7.21284 + 15.1179i) q^{85} +(-7.30429 - 5.30688i) q^{86} +(-1.32542 - 1.82428i) q^{87} +(1.49278 + 2.05464i) q^{88} +(0.593709 + 0.431355i) q^{89} +(1.62182 - 1.53938i) q^{90} +(0.539451 - 0.391934i) q^{91} +(-1.59524 - 0.518324i) q^{92} +1.00385i q^{93} +(-3.36376 + 10.3526i) q^{94} +(-13.6036 + 6.49035i) q^{95} +(0.309017 + 0.951057i) q^{96} +(-8.67406 + 2.81837i) q^{97} +(8.49326 - 11.6900i) q^{98} +2.53967 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^9	$ 16 q + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{9} + 2 q^{10} + 2 q^{11} + 20 q^{13} + 2 q^{14} - 2 q^{15} - 4 q^{16} - 30 q^{17} - 4 q^{20} - 2 q^{21} - 20 q^{22} - 10 q^{23} - 16 q^{24} + 24 q^{25} + 4 q^{26} - 10 q^{29} - 6 q^{30} - 18 q^{31} - 20 q^{33} + 12 q^{34} - 34 q^{35} - 4 q^{36} + 20 q^{37} + 10 q^{38} - 4 q^{39} - 2 q^{40} + 22 q^{41} + 8 q^{44} - 4 q^{45} - 6 q^{46} - 50 q^{47} - 52 q^{49} + 12 q^{50} + 28 q^{51} + 20 q^{52} + 30 q^{53} + 4 q^{54} + 18 q^{55} - 2 q^{56} - 30 q^{58} + 20 q^{59} + 2 q^{60} + 12 q^{61} + 50 q^{62} + 10 q^{63} + 4 q^{64} - 8 q^{65} + 2 q^{66} - 50 q^{67} + 6 q^{69} - 12 q^{70} - 28 q^{71} + 20 q^{73} + 12 q^{74} + 28 q^{75} + 20 q^{76} + 100 q^{77} - 20 q^{79} + 4 q^{80} - 4 q^{81} - 30 q^{83} + 2 q^{84} - 4 q^{85} - 6 q^{86} + 10 q^{87} + 70 q^{89} + 8 q^{90} + 12 q^{91} - 30 q^{92} + 2 q^{94} - 30 q^{95} - 4 q^{96} - 10 q^{97} + 60 q^{98} - 12 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^9 + 2 * q^10 + 2 * q^11 + 20 * q^13 + 2 * q^14 - 2 * q^15 - 4 * q^16 - 30 * q^17 - 4 * q^20 - 2 * q^21 - 20 * q^22 - 10 * q^23 - 16 * q^24 + 24 * q^25 + 4 * q^26 - 10 * q^29 - 6 * q^30 - 18 * q^31 - 20 * q^33 + 12 * q^34 - 34 * q^35 - 4 * q^36 + 20 * q^37 + 10 * q^38 - 4 * q^39 - 2 * q^40 + 22 * q^41 + 8 * q^44 - 4 * q^45 - 6 * q^46 - 50 * q^47 - 52 * q^49 + 12 * q^50 + 28 * q^51 + 20 * q^52 + 30 * q^53 + 4 * q^54 + 18 * q^55 - 2 * q^56 - 30 * q^58 + 20 * q^59 + 2 * q^60 + 12 * q^61 + 50 * q^62 + 10 * q^63 + 4 * q^64 - 8 * q^65 + 2 * q^66 - 50 * q^67 + 6 * q^69 - 12 * q^70 - 28 * q^71 + 20 * q^73 + 12 * q^74 + 28 * q^75 + 20 * q^76 + 100 * q^77 - 20 * q^79 + 4 * q^80 - 4 * q^81 - 30 * q^83 + 2 * q^84 - 4 * q^85 - 6 * q^86 + 10 * q^87 + 70 * q^89 + 8 * q^90 + 12 * q^91 - 30 * q^92 + 2 * q^94 - 30 * q^95 - 4 * q^96 - 10 * q^97 + 60 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−1.53938	−	1.62182i	−0.688432	−	0.725301i
$5$	−1.53938	−	1.62182i	−0.688432	−	0.725301i
$6$	0.309017	−	0.951057i	0.126156	−	0.388267i
$7$		−	4.63137i		−	1.75049i	−0.483677	−	0.875247i	$-0.660699\pi$
$7$		−	4.63137i		−	1.75049i	0.483677	−	0.875247i	$-0.339301\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	2.21691	−	0.292102i	0.701048	−	0.0923709i
$11$	2.05464	+	1.49278i	0.619497	+	0.450091i	0.852746	−	0.522326i	$-0.174936\pi$
$11$	2.05464	+	1.49278i	0.619497	+	0.450091i	−0.233249	+	0.972417i	$0.574936\pi$
$12$	0.587785	+	0.809017i	0.169679	+	0.233543i
$13$	0.0846260	+	0.116478i	0.0234710	+	0.0323051i	0.820591	−	0.571516i	$-0.193644\pi$
$13$	0.0846260	+	0.116478i	0.0234710	+	0.0323051i	−0.797120	+	0.603821i	$0.793644\pi$
$14$	3.74686	+	2.72225i	1.00139	+	0.727552i
$15$	1.96521	+	1.06675i	0.507415	+	0.275434i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−7.12436	−	2.31485i	−1.72791	−	0.561433i	−0.734767	−	0.678320i	$-0.762708\pi$
$17$	−7.12436	−	2.31485i	−1.72791	−	0.561433i	−0.993145	+	0.116887i	$0.962708\pi$
$18$			1.00000i			0.235702i
$19$	2.08298	−	6.41074i	0.477867	−	1.47072i	−0.364184	−	0.931327i	$-0.618652\pi$
$19$	2.08298	−	6.41074i	0.477867	−	1.47072i	0.842051	−	0.539397i	$-0.181348\pi$
$20$	−1.06675	+	1.96521i	−0.238532	+	0.439434i
$21$	1.43117	+	4.40469i	0.312307	+	0.961183i
$22$	−2.41537	+	0.784803i	−0.514959	+	0.167320i
$23$	0.985910	−	1.35699i	0.205576	−	0.282952i	−0.693763	−	0.720204i	$-0.744048\pi$
$23$	0.985910	−	1.35699i	0.205576	−	0.282952i	0.899339	+	0.437252i	$0.144048\pi$
$24$	−1.00000			−0.204124
$25$	−0.260613	+	4.99320i	−0.0521225	+	0.998641i
$26$	−0.143974			−0.0282357
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	−4.40469	+	1.43117i	−0.832409	+	0.270466i
$29$	0.696812	+	2.14457i	0.129395	+	0.398236i	0.994676	−	0.103050i	$-0.0328603\pi$
$29$	0.696812	+	2.14457i	0.129395	+	0.398236i	−0.865281	+	0.501287i	$0.832860\pi$
$30$	−2.01814	+	0.962868i	−0.368460	+	0.175795i
$31$	0.310207	−	0.954718i	0.0557148	−	0.171472i	−0.919327	−	0.393495i	$-0.871266\pi$
$31$	0.310207	−	0.954718i	0.0557148	−	0.171472i	0.975042	+	0.222023i	$0.0712659\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−2.41537	−	0.784803i	−0.420463	−	0.136617i
$34$	6.06035	−	4.40310i	1.03934	−	0.755125i
$35$	−7.51126	+	7.12944i	−1.26963	+	1.20510i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	−0.0523017	−	0.0719871i	−0.00859835	−	0.0118346i	0.804696	−	0.593687i	$-0.202328\pi$
$37$	−0.0523017	−	0.0719871i	−0.00859835	−	0.0118346i	−0.813295	+	0.581852i	$0.802328\pi$
$38$	3.96205	+	5.45330i	0.642730	+	0.884642i
$39$	−0.116478	−	0.0846260i	−0.0186514	−	0.0135510i
$40$	−0.962868	−	2.01814i	−0.152243	−	0.319096i
$41$	−2.48680	+	1.80677i	−0.388373	+	0.282170i	−0.764789	−	0.644281i	$-0.777157\pi$
$41$	−2.48680	+	1.80677i	−0.388373	+	0.282170i	0.376415	+	0.926451i	$0.377157\pi$
$42$	−4.40469	−	1.43117i	−0.679659	−	0.220835i
$43$			9.02860i			1.37685i	0.725308	+	0.688424i	$0.241697\pi$
$43$			9.02860i			1.37685i	−0.725308	+	0.688424i	$0.758303\pi$
$44$	0.784803	−	2.41537i	0.118313	−	0.364131i
$45$	−2.19867	−	0.407256i	−0.327758	−	0.0607102i
$46$	0.518324	+	1.59524i	0.0764226	+	0.235205i
$47$	10.3526	−	3.36376i	1.51008	−	0.490655i	0.567141	−	0.823620i	$-0.308049\pi$
$47$	10.3526	−	3.36376i	1.51008	−	0.490655i	0.942939	+	0.332965i	$0.108049\pi$
$48$	0.587785	−	0.809017i	0.0848395	−	0.116772i
$49$	−14.4496			−2.06423
$50$	−3.88640	−	3.14577i	−0.549620	−	0.444879i
$51$	7.49100			1.04895
$52$	0.0846260	−	0.116478i	0.0117355	−	0.0161525i
$53$	4.72205	−	1.53429i	0.648624	−	0.210751i	0.0338165	−	0.999428i	$-0.489234\pi$
$53$	4.72205	−	1.53429i	0.648624	−	0.210751i	0.614807	+	0.788677i	$0.289234\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	−0.741845	−	5.63022i	−0.100030	−	0.759179i
$56$	1.43117	−	4.40469i	0.191248	−	0.588602i
$57$			6.74065i			0.892821i
$58$	−2.14457	−	0.696812i	−0.281596	−	0.0914959i
$59$	4.25029	−	3.08802i	0.553341	−	0.402026i	−0.275675	−	0.961251i	$-0.588901\pi$
$59$	4.25029	−	3.08802i	0.553341	−	0.402026i	0.829016	+	0.559225i	$0.188901\pi$
$60$	0.407256	−	2.19867i	0.0525765	−	0.283847i
$61$	11.0841	+	8.05305i	1.41917	+	1.03109i	0.991908	+	0.126960i	$0.0405221\pi$
$61$	11.0841	+	8.05305i	1.41917	+	1.03109i	0.427263	+	0.904127i	$0.359478\pi$
$62$	0.590048	+	0.812131i	0.0749362	+	0.103141i
$63$	−2.72225	−	3.74686i	−0.342971	−	0.472060i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	0.0586344	−	0.316552i	0.00727270	−	0.0392634i
$66$	2.05464	−	1.49278i	0.252909	−	0.183749i
$67$	7.27491	+	2.36376i	0.888771	+	0.288779i	0.717595	−	0.696461i	$-0.245243\pi$
$67$	7.27491	+	2.36376i	0.888771	+	0.288779i	0.171177	+	0.985240i	$0.445243\pi$
$68$			7.49100i			0.908417i
$69$	−0.518324	+	1.59524i	−0.0623988	+	0.192044i
$70$	−1.35283	−	10.2673i	−0.161695	−	1.22718i
$71$	−3.17196	−	9.76228i	−0.376442	−	1.15857i	−0.942501	−	0.334204i	$-0.891532\pi$
$71$	−3.17196	−	9.76228i	−0.376442	−	1.15857i	0.566059	−	0.824365i	$-0.308468\pi$
$72$	0.951057	−	0.309017i	0.112083	−	0.0364180i
$73$	1.15547	−	1.59036i	0.135237	−	0.186138i	−0.736027	−	0.676952i	$-0.763301\pi$
$73$	1.15547	−	1.59036i	0.135237	−	0.186138i	0.871264	+	0.490814i	$0.163301\pi$
$74$	0.0889810			0.0103438
$75$	−1.29513	−	4.82935i	−0.149548	−	0.557646i
$76$	−6.74065			−0.773206
$77$	6.91363	−	9.51580i	0.787881	−	1.08443i
$78$	0.136928	−	0.0444905i	0.0155040	−	0.00503756i
$79$	−0.230908	−	0.710661i	−0.0259792	−	0.0799556i	0.937226	−	0.348722i	$-0.113384\pi$
$79$	−0.230908	−	0.710661i	−0.0259792	−	0.0799556i	−0.963205	+	0.268766i	$0.913384\pi$
$80$	2.19867	+	0.407256i	0.245819	+	0.0455326i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		−	3.07386i		−	0.339451i
$83$	−2.95072	−	0.958745i	−0.323883	−	0.105236i	0.142563	−	0.989786i	$-0.454466\pi$
$83$	−2.95072	−	0.958745i	−0.323883	−	0.105236i	−0.466446	+	0.884550i	$0.654466\pi$
$84$	3.74686	−	2.72225i	0.408816	−	0.297022i
$85$	7.21284	+	15.1179i	0.782343	+	1.63976i
$86$	−7.30429	−	5.30688i	−0.787642	−	0.572255i
$87$	−1.32542	−	1.82428i	−0.142099	−	0.195583i
$88$	1.49278	+	2.05464i	0.159131	+	0.219025i
$89$	0.593709	+	0.431355i	0.0629331	+	0.0457236i	0.618807	−	0.785543i	$-0.287616\pi$
$89$	0.593709	+	0.431355i	0.0629331	+	0.0457236i	−0.555874	+	0.831267i	$0.687616\pi$
$90$	1.62182	−	1.53938i	0.170955	−	0.162265i
$91$	0.539451	−	0.391934i	0.0565498	−	0.0410859i
$92$	−1.59524	−	0.518324i	−0.166315	−	0.0540390i
$93$			1.00385i			0.104094i
$94$	−3.36376	+	10.3526i	−0.346945	+	1.06779i
$95$	−13.6036	+	6.49035i	−1.39570	+	0.665896i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	−8.67406	+	2.81837i	−0.880717	+	0.286162i	−0.714255	−	0.699886i	$-0.753234\pi$
$97$	−8.67406	+	2.81837i	−0.880717	+	0.286162i	−0.166462	+	0.986048i	$0.553234\pi$
$98$	8.49326	−	11.6900i	0.857948	−	1.18086i
$99$	2.53967			0.255247
$100$	4.82935	−	1.29513i	0.482935	−	0.129513i
$101$	−2.88013			−0.286583			−0.143292	−	0.989680i	$-0.545769\pi$
$101$	−2.88013			−0.286583			−0.143292	+	0.989680i	$0.545769\pi$
$102$	−4.40310	+	6.06035i	−0.435972	+	0.600064i
$103$	10.6246	−	3.45214i	1.04687	−	0.340149i	0.265432	−	0.964130i	$-0.414486\pi$
$103$	10.6246	−	3.45214i	1.04687	−	0.340149i	0.781440	+	0.623981i	$0.214486\pi$
$104$	0.0444905	+	0.136928i	0.00436265	+	0.0134269i
$105$	4.94051	−	9.10161i	0.482145	−	0.888226i
$106$	−1.53429	+	4.72205i	−0.149023	+	0.458646i
$107$		−	14.0538i		−	1.35863i	−0.733846	−	0.679316i	$-0.762277\pi$
$107$		−	14.0538i		−	1.35863i	0.733846	−	0.679316i	$-0.237723\pi$
$108$	0.951057	+	0.309017i	0.0915155	+	0.0297352i
$109$	5.43552	−	3.94914i	0.520628	−	0.378259i	−0.296212	−	0.955122i	$-0.595724\pi$
$109$	5.43552	−	3.94914i	0.520628	−	0.378259i	0.816841	+	0.576863i	$0.195724\pi$
$110$	4.99099	+	2.70920i	0.475872	+	0.258312i
$111$	0.0719871	+	0.0523017i	0.00683272	+	0.00496426i
$112$	2.72225	+	3.74686i	0.257229	+	0.354045i
$113$	−0.586387	−	0.807092i	−0.0551626	−	0.0759248i	0.780545	−	0.625100i	$-0.214942\pi$
$113$	−0.586387	−	0.807092i	−0.0551626	−	0.0759248i	−0.835707	+	0.549175i	$0.814942\pi$
$114$	−5.45330	−	3.96205i	−0.510748	−	0.371080i
$115$	−3.71849	+	0.489952i	−0.346751	+	0.0456883i
$116$	1.82428	−	1.32542i	0.169380	−	0.123062i
$117$	0.136928	+	0.0444905i	0.0126590	+	0.00411315i
$118$			5.25365i			0.483638i
$119$	−10.7209	+	32.9956i	−0.982784	+	3.02470i
$120$	1.53938	+	1.62182i	0.140526	+	0.148051i
$121$	−1.40604	−	4.32736i	−0.127822	−	0.393396i
$122$	−13.0301	+	4.23374i	−1.17969	+	0.383305i
$123$	1.80677	−	2.48680i	0.162911	−	0.224227i
$124$	−1.00385			−0.0901484
$125$	8.49927	−	7.26377i	0.760198	−	0.649692i
$126$	4.63137			0.412595
$127$	−6.77227	+	9.32123i	−0.600942	+	0.827125i	−0.995794	−	0.0916192i	$-0.970796\pi$
$127$	−6.77227	+	9.32123i	−0.600942	+	0.827125i	0.394852	+	0.918745i	$0.370796\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	−2.78999	−	8.58671i	−0.245645	−	0.756017i
$130$	0.221631	+	0.233501i	0.0194383	+	0.0204794i
$131$	−0.551316	+	1.69677i	−0.0481687	+	0.148248i	−0.972248	−	0.233953i	$-0.924834\pi$
$131$	−0.551316	+	1.69677i	−0.0481687	+	0.148248i	0.924079	+	0.382201i	$0.124834\pi$
$132$			2.53967i			0.221050i
$133$	−29.6905	−	9.64703i	−2.57449	−	0.836504i
$134$	−6.18841	+	4.49614i	−0.534597	+	0.388407i
$135$	2.21691	−	0.292102i	0.190801	−	0.0251402i
$136$	−6.06035	−	4.40310i	−0.519670	−	0.377563i
$137$	9.41828	+	12.9632i	0.804658	+	1.10752i	0.992126	+	0.125246i	$0.0399721\pi$
$137$	9.41828	+	12.9632i	0.804658	+	1.10752i	−0.187467	+	0.982271i	$0.560028\pi$
$138$	−0.985910	−	1.35699i	−0.0839262	−	0.115515i
$139$	−2.99660	−	2.17716i	−0.254168	−	0.184664i	0.453404	−	0.891305i	$-0.350210\pi$
$139$	−2.99660	−	2.17716i	−0.254168	−	0.184664i	−0.707572	+	0.706641i	$0.750210\pi$
$140$	9.10161	+	4.94051i	0.769226	+	0.417549i
$141$	−8.80644	+	6.39825i	−0.741636	+	0.538830i
$142$	9.76228	+	3.17196i	0.819232	+	0.266185i
$143$			0.365648i			0.0305770i
$144$	−0.309017	+	0.951057i	−0.0257514	+	0.0792547i
$145$	2.40545	−	4.43141i	0.199762	−	0.368009i
$146$	0.607465	+	1.86958i	0.0502741	+	0.154728i
$147$	13.7424	−	4.46517i	1.13345	−	0.368281i
$148$	−0.0523017	+	0.0719871i	−0.00429918	+	0.00591731i
$149$	−1.88534			−0.154453			−0.0772267	−	0.997014i	$-0.524607\pi$
$149$	−1.88534			−0.154453			−0.0772267	+	0.997014i	$0.524607\pi$
$150$	4.66828	+	1.79084i	0.381164	+	0.146222i
$151$	−6.15090			−0.500553			−0.250276	−	0.968174i	$-0.580522\pi$
$151$	−6.15090			−0.500553			−0.250276	+	0.968174i	$0.580522\pi$
$152$	3.96205	−	5.45330i	0.321365	−	0.442321i
$153$	−7.12436	+	2.31485i	−0.575971	+	0.187144i
$154$	3.63471	+	11.1865i	0.292893	+	0.901433i
$155$	−2.02591	+	0.966575i	−0.162725	+	0.0776371i
$156$	−0.0444905	+	0.136928i	−0.00356209	+	0.0109630i
$157$			23.4830i			1.87414i	0.349137	+	0.937072i	$0.386475\pi$
$157$			23.4830i			1.87414i	−0.349137	+	0.937072i	$0.613525\pi$
$158$	0.710661	+	0.230908i	0.0565372	+	0.0183700i
$159$	−4.01682	+	2.91839i	−0.318554	+	0.231443i
$160$	−1.62182	+	1.53938i	−0.128216	+	0.121699i
$161$	−6.28472	−	4.56611i	−0.495305	−	0.359860i
$162$	0.587785	+	0.809017i	0.0461808	+	0.0635624i
$163$	9.27366	+	12.7641i	0.726369	+	0.999762i	0.999288	+	0.0377245i	$0.0120109\pi$
$163$	9.27366	+	12.7641i	0.726369	+	0.999762i	−0.272919	+	0.962037i	$0.587989\pi$
$164$	2.48680	+	1.80677i	0.194187	+	0.141085i
$165$	2.44537	+	5.12542i	0.190372	+	0.399013i
$166$	2.51003	−	1.82364i	0.194816	−	0.141542i
$167$	3.84208	+	1.24837i	0.297309	+	0.0966016i	0.453873	−	0.891066i	$-0.350042\pi$
$167$	3.84208	+	1.24837i	0.297309	+	0.0966016i	−0.156564	+	0.987668i	$0.550042\pi$
$168$			4.63137i			0.357318i
$169$	4.01082	−	12.3440i	0.308524	−	0.949540i
$170$	−16.4702	−	3.05076i	−1.26321	−	0.233982i
$171$	−2.08298	−	6.41074i	−0.159289	−	0.490241i
$172$	8.58671	−	2.78999i	0.654730	−	0.212735i
$173$	11.8495	−	16.3094i	0.900899	−	1.23998i	−0.0692809	−	0.997597i	$-0.522070\pi$
$173$	11.8495	−	16.3094i	0.900899	−	1.23998i	0.970180	−	0.242384i	$-0.0779295\pi$
$174$	2.25493			0.170946
$175$	23.1254	+	1.20699i	1.74811	+	0.0912402i
$176$	−2.53967			−0.191435
$177$	−3.08802	+	4.25029i	−0.232110	+	0.319472i
$178$	−0.697947	+	0.226777i	−0.0523134	+	0.0169976i
$179$	2.39818	+	7.38084i	0.179248	+	0.551670i	0.999802	−	0.0198998i	$-0.00633471\pi$
$179$	2.39818	+	7.38084i	0.179248	+	0.551670i	−0.820554	+	0.571570i	$0.806335\pi$
$180$	0.292102	+	2.21691i	0.0217720	+	0.165238i
$181$	3.64358	−	11.2138i	0.270825	−	0.833515i	−0.719469	−	0.694525i	$-0.755615\pi$
$181$	3.64358	−	11.2138i	0.270825	−	0.833515i	0.990294	−	0.138990i	$-0.0443855\pi$
$182$			0.666798i			0.0494264i
$183$	−13.0301	−	4.23374i	−0.963214	−	0.312967i
$184$	1.35699	−	0.985910i	0.100039	−	0.0726822i
$185$	−0.0362381	+	0.195640i	−0.00266427	+	0.0143837i
$186$	−0.812131	−	0.590048i	−0.0595484	−	0.0432644i
$187$	−11.1824	−	15.3913i	−0.817741	−	1.12552i
$188$	−6.39825	−	8.80644i	−0.466641	−	0.642276i
$189$	3.74686	+	2.72225i	0.272544	+	0.198015i
$190$	2.74517	−	14.8205i	0.199156	−	1.07519i
$191$	−3.95155	+	2.87097i	−0.285924	+	0.207736i	−0.721497	−	0.692417i	$-0.756546\pi$
$191$	−3.95155	+	2.87097i	−0.285924	+	0.207736i	0.435573	+	0.900153i	$0.356546\pi$
$192$	−0.951057	−	0.309017i	−0.0686366	−	0.0223014i
$193$		−	18.7342i		−	1.34852i	−0.738496	−	0.674258i	$-0.764464\pi$
$193$		−	18.7342i		−	1.34852i	0.738496	−	0.674258i	$-0.235536\pi$
$194$	2.81837	−	8.67406i	0.202347	−	0.622761i
$195$	0.0420552	+	0.319178i	0.00301164	+	0.0228568i
$196$	4.46517	+	13.7424i	0.318941	+	0.981598i
$197$	−1.19314	+	0.387674i	−0.0850075	+	0.0276206i	−0.351212	−	0.936296i	$-0.614230\pi$
$197$	−1.19314	+	0.387674i	−0.0850075	+	0.0276206i	0.266204	+	0.963917i	$0.414230\pi$
$198$	−1.49278	+	2.05464i	−0.106087	+	0.146017i
$199$	−19.3703			−1.37312			−0.686562	−	0.727071i	$-0.740881\pi$
$199$	−19.3703			−1.37312			−0.686562	+	0.727071i	$0.740881\pi$
$200$	−1.79084	+	4.66828i	−0.126632	+	0.330098i
$201$	−7.64929			−0.539539
$202$	1.69290	−	2.33007i	0.119112	−	0.163943i
$203$	9.93229	−	3.22720i	0.697110	−	0.226505i
$204$	−2.31485	−	7.12436i	−0.162072	−	0.498805i
$205$	6.75839	+	1.25185i	0.472027	+	0.0874328i
$206$	−3.45214	+	10.6246i	−0.240522	+	0.740250i
$207$		−	1.67733i		−	0.116583i
$208$	−0.136928	−	0.0444905i	−0.00949423	−	0.00308486i
$209$	13.8496	−	10.0623i	0.957997	−	0.696026i
$210$	4.45940	+	9.34675i	0.307728	+	0.644987i
$211$	1.01062	+	0.734260i	0.0695741	+	0.0505485i	0.622029	−	0.782994i	$-0.286309\pi$
$211$	1.01062	+	0.734260i	0.0695741	+	0.0505485i	−0.552455	+	0.833543i	$0.686309\pi$
$212$	−2.91839	−	4.01682i	−0.200436	−	0.275876i
$213$	6.03342	+	8.30429i	0.413403	+	0.569001i
$214$	11.3698	+	8.26061i	0.777221	+	0.564684i
$215$	14.6428	−	13.8985i	0.998629	−	0.947867i
$216$	−0.809017	+	0.587785i	−0.0550466	+	0.0399937i
$217$	−4.42165	−	1.43668i	−0.300161	−	0.0975283i
$218$			6.71867i			0.455046i
$219$	−0.607465	+	1.86958i	−0.0410487	+	0.126335i
$220$	−5.12542	+	2.44537i	−0.345556	+	0.164867i
$221$	−0.333278	−	1.02573i	−0.0224187	−	0.0689978i
$222$	−0.0846260	+	0.0274966i	−0.00567972	+	0.00184545i
$223$	12.8640	−	17.7058i	0.861437	−	1.18567i	−0.119788	−	0.992800i	$-0.538221\pi$
$223$	12.8640	−	17.7058i	0.861437	−	1.18567i	0.981225	−	0.192867i	$-0.0617787\pi$
$224$	−4.63137			−0.309446
$225$	2.72409	+	4.19277i	0.181606	+	0.279518i
$226$	0.997621			0.0663607
$227$	−8.52486	+	11.7335i	−0.565815	+	0.778777i	−0.992051	−	0.125835i	$-0.959839\pi$
$227$	−8.52486	+	11.7335i	−0.565815	+	0.778777i	0.426237	+	0.904612i	$0.359839\pi$
$228$	6.41074	−	2.08298i	0.424562	−	0.137948i
$229$	−1.45262	−	4.47071i	−0.0959920	−	0.295433i	0.891519	−	0.452983i	$-0.149640\pi$
$229$	−1.45262	−	4.47071i	−0.0959920	−	0.295433i	−0.987511	+	0.157550i	$0.949640\pi$
$230$	1.78929	−	3.29630i	0.117982	−	0.217352i
$231$	−3.63471	+	11.1865i	−0.239146	+	0.736017i
$232$			2.25493i			0.148044i
$233$	−11.2403	−	3.65218i	−0.736374	−	0.239262i	−0.0832661	−	0.996527i	$-0.526535\pi$
$233$	−11.2403	−	3.65218i	−0.736374	−	0.239262i	−0.653108	+	0.757265i	$0.726535\pi$
$234$	−0.116478	+	0.0846260i	−0.00761438	+	0.00553217i
$235$	−21.3920	−	11.6119i	−1.39546	−	0.757480i
$236$	−4.25029	−	3.08802i	−0.276671	−	0.201013i
$237$	0.439213	+	0.604525i	0.0285299	+	0.0392681i
$238$	−20.3924	−	28.0677i	−1.32184	−	1.81936i
$239$	7.85849	+	5.70953i	0.508324	+	0.369319i	0.812187	−	0.583397i	$-0.198277\pi$
$239$	7.85849	+	5.70953i	0.508324	+	0.369319i	−0.303864	+	0.952716i	$0.598277\pi$
$240$	−2.21691	+	0.292102i	−0.143101	+	0.0188551i
$241$	−5.40451	+	3.92661i	−0.348135	+	0.252935i	−0.748086	−	0.663601i	$-0.769027\pi$
$241$	−5.40451	+	3.92661i	−0.348135	+	0.252935i	0.399951	+	0.916537i	$0.369027\pi$
$242$	4.32736	+	1.40604i	0.278173	+	0.0903839i
$243$			1.00000i			0.0641500i
$244$	4.23374	−	13.0301i	0.271037	−	0.834168i
$245$	22.2434	+	23.4347i	1.42108	+	1.49719i
$246$	0.949874	+	2.92341i	0.0605618	+	0.186390i
$247$	0.922982	−	0.299895i	0.0587279	−	0.0190819i
$248$	0.590048	−	0.812131i	0.0374681	−	0.0515704i
$249$	3.10257			0.196617
$250$	0.880772	+	11.1456i	0.0557049	+	0.704909i
$251$	−19.6023			−1.23729			−0.618644	−	0.785672i	$-0.712317\pi$
$251$	−19.6023			−1.23729			−0.618644	+	0.785672i	$0.712317\pi$
$252$	−2.72225	+	3.74686i	−0.171486	+	0.236030i
$253$	4.05138	−	1.31637i	0.254708	−	0.0827597i
$254$	−3.56039	−	10.9578i	−0.223399	−	0.687551i
$255$	−11.5315	−	12.1491i	−0.722131	−	0.760804i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$		−	9.46931i		−	0.590679i	−0.955392	−	0.295340i	$-0.904567\pi$
$257$		−	9.46931i		−	0.590679i	0.955392	−	0.295340i	$-0.0954328\pi$
$258$	8.58671	+	2.78999i	0.534585	+	0.173697i
$259$	−0.333399	+	0.242229i	−0.0207164	+	0.0150514i
$260$	−0.319178	+	0.0420552i	−0.0197946	+	0.00260815i
$261$	1.82428	+	1.32542i	0.112920	+	0.0820412i
$262$	−1.04866	−	1.44336i	−0.0647867	−	0.0891713i
$263$	12.4296	+	17.1079i	0.766441	+	1.05492i	0.996651	+	0.0817747i	$0.0260588\pi$
$263$	12.4296	+	17.1079i	0.766441	+	1.05492i	−0.230210	+	0.973141i	$0.573941\pi$
$264$	−2.05464	−	1.49278i	−0.126454	−	0.0918745i
$265$	−9.75738	−	5.29647i	−0.599391	−	0.325360i
$266$	25.2563	−	18.3497i	1.54856	−	1.12509i
$267$	−0.697947	−	0.226777i	−0.0427137	−	0.0138785i
$268$		−	7.64929i		−	0.467255i
$269$	0.603355	−	1.85694i	0.0367872	−	0.113219i	−0.930977	−	0.365079i	$-0.881042\pi$
$269$	0.603355	−	1.85694i	0.0367872	−	0.113219i	0.967764	+	0.251859i	$0.0810420\pi$
$270$	−1.06675	+	1.96521i	−0.0649203	+	0.119599i
$271$	−4.91521	−	15.1274i	−0.298577	−	0.918927i	−0.981996	−	0.188900i	$-0.939508\pi$
$271$	−4.91521	−	15.1274i	−0.298577	−	0.918927i	0.683419	−	0.730027i	$-0.260492\pi$
$272$	7.12436	−	2.31485i	0.431978	−	0.140358i
$273$	−0.391934	+	0.539451i	−0.0237209	+	0.0326491i
$274$	−16.0233			−0.968006
$275$	−7.98924	+	9.87020i	−0.481769	+	0.595195i
$276$	1.67733			0.100963
$277$	1.16998	−	1.61033i	0.0702970	−	0.0967555i	−0.772421	−	0.635111i	$-0.780954\pi$
$277$	1.16998	−	1.61033i	0.0702970	−	0.0967555i	0.842718	+	0.538356i	$0.180954\pi$
$278$	3.52272	−	1.14460i	0.211278	−	0.0686485i
$279$	−0.310207	−	0.954718i	−0.0185716	−	0.0571575i
$280$	−9.34675	+	4.45940i	−0.558575	+	0.266500i
$281$	−7.78302	+	23.9537i	−0.464296	+	1.42896i	0.395569	+	0.918436i	$0.370547\pi$
$281$	−7.78302	+	23.9537i	−0.464296	+	1.42896i	−0.859866	+	0.510521i	$0.829453\pi$
$282$		−	10.8854i		−	0.648214i
$283$	10.7090	+	3.47958i	0.636586	+	0.206839i	0.609490	−	0.792794i	$-0.291374\pi$
$283$	10.7090	+	3.47958i	0.636586	+	0.206839i	0.0270957	+	0.999633i	$0.491374\pi$
$284$	−8.30429	+	6.03342i	−0.492769	+	0.358018i
$285$	10.9321	−	10.3764i	0.647564	−	0.614647i
$286$	−0.295815	−	0.214922i	−0.0174919	−	0.0127086i
$287$	8.36781	+	11.5173i	0.493936	+	0.679845i
$288$	−0.587785	−	0.809017i	−0.0346356	−	0.0476718i
$289$	31.6448	+	22.9913i	1.86146	+	1.35243i
$290$	2.17120	+	4.55077i	0.127497	+	0.267230i
$291$	7.37859	−	5.36086i	0.432541	−	0.314259i
$292$	−1.86958	−	0.607465i	−0.109409	−	0.0355492i
$293$			20.0482i			1.17123i	0.810591	+	0.585613i	$0.199146\pi$
$293$			20.0482i			1.17123i	−0.810591	+	0.585613i	$0.800854\pi$
$294$	−4.46517	+	13.7424i	−0.260414	+	0.801472i
$295$	−11.5510	−	2.13958i	−0.672527	−	0.124571i
$296$	−0.0274966	−	0.0846260i	−0.00159821	−	0.00491878i
$297$	−2.41537	+	0.784803i	−0.140154	+	0.0455389i
$298$	1.10818	−	1.52528i	0.0641950	−	0.0883569i
$299$	0.241492			0.0139659
$300$	−4.19277	+	2.72409i	−0.242070	+	0.157275i
$301$	41.8148			2.41016
$302$	3.61541	−	4.97618i	0.208043	−	0.286347i
$303$	2.73916	−	0.890008i	0.157361	−	0.0511296i
$304$	2.08298	+	6.41074i	0.119467	+	0.367681i
$305$	−4.00200	−	30.3731i	−0.229154	−	1.73916i
$306$	2.31485	−	7.12436i	0.132331	−	0.407273i
$307$			14.4493i			0.824668i	0.911033	+	0.412334i	$0.135286\pi$
$307$			14.4493i			0.824668i	−0.911033	+	0.412334i	$0.864714\pi$
$308$	−11.1865	−	3.63471i	−0.637410	−	0.207107i
$309$	−9.03781	+	6.56635i	−0.514143	+	0.373547i
$310$	0.408824	−	2.20713i	0.0232196	−	0.125357i
$311$	19.0778	+	13.8608i	1.08180	+	0.785977i	0.977997	−	0.208621i	$-0.0668975\pi$
$311$	19.0778	+	13.8608i	1.08180	+	0.785977i	0.103807	+	0.994597i	$0.466897\pi$
$312$	−0.0846260	−	0.116478i	−0.00479100	−	0.00659425i
$313$	16.1598	+	22.2420i	0.913405	+	1.25719i	0.965991	+	0.258577i	$0.0832537\pi$
$313$	16.1598	+	22.2420i	0.913405	+	1.25719i	−0.0525858	+	0.998616i	$0.516746\pi$
$314$	−18.9981	−	13.8029i	−1.07213	−	0.778945i
$315$	−1.88615	+	10.1828i	−0.106273	+	0.573738i
$316$	−0.604525	+	0.439213i	−0.0340072	+	0.0247077i
$317$	−5.74985	−	1.86824i	−0.322944	−	0.104931i	0.143059	−	0.989714i	$-0.454306\pi$
$317$	−5.74985	−	1.86824i	−0.322944	−	0.104931i	−0.466002	+	0.884783i	$0.654306\pi$
$318$		−	4.96506i		−	0.278427i
$319$	−1.76968	+	5.44650i	−0.0990829	+	0.304946i
$320$	−0.292102	−	2.21691i	−0.0163290	−	0.123929i
$321$	4.34286	+	13.3660i	0.242395	+	0.746015i
$322$	7.38813	−	2.40055i	0.411724	−	0.133777i
$323$	−29.6798	+	40.8507i	−1.65143	+	2.27299i
$324$	−1.00000			−0.0555556
$325$	−0.603651	+	0.392199i	−0.0334845	+	0.0217553i
$326$	−15.7773			−0.873824
$327$	−3.94914	+	5.43552i	−0.218388	+	0.300585i
$328$	−2.92341	+	0.949874i	−0.161418	+	0.0524480i
$329$	−15.5788	−	47.9467i	−0.858888	−	2.64339i
$330$	−5.58390	−	1.03430i	−0.307384	−	0.0569362i
$331$	5.23211	−	16.1028i	0.287583	−	0.885089i	−0.698030	−	0.716069i	$-0.745940\pi$
$331$	5.23211	−	16.1028i	0.287583	−	0.885089i	0.985613	−	0.169020i	$-0.0540603\pi$
$332$			3.10257i			0.170275i
$333$	−0.0846260	−	0.0274966i	−0.00463747	−	0.00150681i
$334$	−3.26827	+	2.37454i	−0.178832	+	0.129929i
$335$	−7.36525	−	15.4373i	−0.402407	−	0.843432i
$336$	−3.74686	−	2.72225i	−0.204408	−	0.148511i
$337$	−13.3205	−	18.3341i	−0.725616	−	0.998724i	−0.999319	−	0.0369100i	$-0.988249\pi$
$337$	−13.3205	−	18.3341i	−0.725616	−	0.998724i	0.273703	−	0.961814i	$-0.411751\pi$
$338$	7.62902	+	10.5005i	0.414964	+	0.571149i
$339$	0.807092	+	0.586387i	0.0438352	+	0.0318482i
$340$	12.1491	−	11.5315i	0.658876	−	0.625384i
$341$	2.06255	−	1.49853i	0.111693	−	0.0811500i
$342$	6.41074	+	2.08298i	0.346653	+	0.112634i
$343$			34.5018i			1.86292i
$344$	−2.78999	+	8.58671i	−0.150426	+	0.462964i
$345$	3.38509	−	1.61505i	0.182247	−	0.0869512i
$346$	6.22964	+	19.1729i	0.334908	+	1.03074i
$347$	−9.75025	+	3.16805i	−0.523421	+	0.170070i	−0.558797	−	0.829304i	$-0.688737\pi$
$347$	−9.75025	+	3.16805i	−0.523421	+	0.170070i	0.0353763	+	0.999374i	$0.488737\pi$
$348$	−1.32542	+	1.82428i	−0.0710497	+	0.0977916i
$349$	−1.38746			−0.0742691			−0.0371346	−	0.999310i	$-0.511823\pi$
$349$	−1.38746			−0.0742691			−0.0371346	+	0.999310i	$0.511823\pi$
$350$	−14.5692	+	17.9994i	−0.778758	+	0.962107i
$351$	−0.143974			−0.00768478
$352$	1.49278	−	2.05464i	0.0795656	−	0.109513i
$353$	−12.2858	+	3.99189i	−0.653906	+	0.212467i	−0.617136	−	0.786857i	$-0.711707\pi$
$353$	−12.2858	+	3.99189i	−0.653906	+	0.212467i	−0.0367706	+	0.999324i	$0.511707\pi$
$354$	−1.62347	−	4.99652i	−0.0862863	−	0.265562i
$355$	−10.9498	+	20.1722i	−0.581156	+	1.07063i
$356$	0.226777	−	0.697947i	0.0120191	−	0.0369911i
$357$		−	34.6936i		−	1.83618i
$358$	−7.38084	−	2.39818i	−0.390089	−	0.126748i
$359$	7.98876	−	5.80417i	0.421630	−	0.306332i	−0.356663	−	0.934233i	$-0.616086\pi$
$359$	7.98876	−	5.80417i	0.421630	−	0.306332i	0.778294	+	0.627901i	$0.216086\pi$
$360$	−1.96521	−	1.06675i	−0.103576	−	0.0562226i
$361$	−21.3875	−	15.5389i	−1.12566	−	0.817837i
$362$	6.93051	+	9.53902i	0.364259	+	0.501360i
$363$	2.67445	+	3.68107i	0.140372	+	0.193206i
$364$	−0.539451	−	0.391934i	−0.0282749	−	0.0205429i
$365$	−4.35799	+	0.574214i	−0.228108	+	0.0300557i
$366$	11.0841	−	8.05305i	0.579374	−	0.420940i
$367$	−5.05886	−	1.64372i	−0.264070	−	0.0858016i	0.173989	−	0.984748i	$-0.444334\pi$
$367$	−5.05886	−	1.64372i	−0.264070	−	0.0858016i	−0.438060	+	0.898946i	$0.644334\pi$
$368$			1.67733i			0.0874369i
$369$	−0.949874	+	2.92341i	−0.0494485	+	0.152187i
$370$	−0.136976	−	0.144311i	−0.00712103	−	0.00750239i
$371$	−7.10585	−	21.8696i	−0.368918	−	1.13541i
$372$	0.954718	−	0.310207i	0.0494998	−	0.0160835i
$373$	−5.69246	+	7.83499i	−0.294744	+	0.405681i	−0.930548	−	0.366170i	$-0.880669\pi$
$373$	−5.69246	+	7.83499i	−0.294744	+	0.405681i	0.635804	+	0.771851i	$0.280669\pi$
$374$	19.0247			0.983744
$375$	−5.83866	+	9.53468i	−0.301507	+	0.492369i
$376$	10.8854			0.561369
$377$	−0.190826	+	0.262649i	−0.00982803	+	0.0135271i
$378$	−4.40469	+	1.43117i	−0.226553	+	0.0736116i
$379$	6.95968	+	21.4197i	0.357495	+	1.10026i	0.954549	+	0.298055i	$0.0963379\pi$
$379$	6.95968	+	21.4197i	0.357495	+	1.10026i	−0.597054	+	0.802201i	$0.703662\pi$
$380$	10.3764	+	10.9321i	0.532300	+	0.560807i
$381$	3.56039	−	10.9578i	0.182404	−	0.561383i
$382$		−	4.88438i		−	0.249907i
$383$	−6.85864	−	2.22851i	−0.350460	−	0.113871i	0.128497	−	0.991710i	$-0.458985\pi$
$383$	−6.85864	−	2.22851i	−0.350460	−	0.113871i	−0.478957	+	0.877839i	$0.658985\pi$
$384$	0.809017	−	0.587785i	0.0412850	−	0.0299953i
$385$	−26.0756	+	3.43576i	−1.32894	+	0.175102i
$386$	15.1563	+	11.0117i	0.771434	+	0.560479i
$387$	5.30688	+	7.30429i	0.269764	+	0.371298i
$388$	5.36086	+	7.37859i	0.272157	+	0.374591i
$389$	10.7139	+	7.78411i	0.543217	+	0.394670i	0.825278	−	0.564726i	$-0.191018\pi$
$389$	10.7139	+	7.78411i	0.543217	+	0.394670i	−0.282062	+	0.959396i	$0.591018\pi$
$390$	−0.282940	−	0.153584i	−0.0143272	−	0.00777705i
$391$	−10.1652	+	7.38545i	−0.514076	+	0.373498i
$392$	−13.7424	−	4.46517i	−0.694095	−	0.225525i
$393$		−	1.78409i		−	0.0899957i
$394$	0.387674	−	1.19314i	0.0195307	−	0.0601094i
$395$	−0.797111	+	1.46847i	−0.0401070	+	0.0738867i
$396$	−0.784803	−	2.41537i	−0.0394378	−	0.121377i
$397$	−27.8304	+	9.04265i	−1.39677	+	0.453838i	−0.908144	−	0.418657i	$-0.862501\pi$
$397$	−27.8304	+	9.04265i	−1.39677	+	0.453838i	−0.488624	+	0.872494i	$0.662501\pi$
$398$	11.3856	−	15.6709i	0.570707	−	0.785511i
$399$	31.2184			1.56288
$400$	−2.72409	−	4.19277i	−0.136205	−	0.209639i
$401$	27.4005			1.36832			0.684158	−	0.729334i	$-0.260170\pi$
$401$	27.4005			1.36832			0.684158	+	0.729334i	$0.260170\pi$
$402$	4.49614	−	6.18841i	0.224247	−	0.308650i
$403$	0.137455	−	0.0446618i	0.00684711	−	0.00222476i
$404$	0.890008	+	2.73916i	0.0442796	+	0.136279i
$405$	−2.01814	+	0.962868i	−0.100282	+	0.0478453i
$406$	−3.22720	+	9.93229i	−0.160163	+	0.492931i
$407$		−	0.225983i		−	0.0112016i
$408$	7.12436	+	2.31485i	0.352709	+	0.114602i
$409$	8.09226	−	5.87937i	0.400137	−	0.290716i	−0.369460	−	0.929247i	$-0.620457\pi$
$409$	8.09226	−	5.87937i	0.400137	−	0.290716i	0.769597	+	0.638530i	$0.220457\pi$
$410$	−4.98525	+	4.73184i	−0.246204	+	0.233689i
$411$	−12.9632	−	9.41828i	−0.639425	−	0.464570i
$412$	−6.56635	−	9.03781i	−0.323501	−	0.445261i
$413$	−14.3018	−	19.6847i	−0.703744	−	0.968620i
$414$	1.35699	+	0.985910i	0.0666924	+	0.0484548i
$415$	2.98736	+	6.26141i	0.146644	+	0.307360i
$416$	0.116478	−	0.0846260i	0.00571079	−	0.00414913i
$417$	3.52272	+	1.14460i	0.172508	+	0.0560513i
$418$			17.1191i			0.837320i
$419$	2.48795	−	7.65713i	0.121544	−	0.374075i	−0.871711	−	0.490020i	$-0.836990\pi$
$419$	2.48795	−	7.65713i	0.121544	−	0.374075i	0.993256	+	0.115945i	$0.0369895\pi$
$420$	−10.1828	−	1.88615i	−0.496872	−	0.0920349i
$421$	3.10662	+	9.56120i	0.151408	+	0.465984i	0.997779	−	0.0666083i	$-0.0212178\pi$
$421$	3.10662	+	9.56120i	0.151408	+	0.465984i	−0.846372	+	0.532593i	$0.821218\pi$
$422$	−1.18806	+	0.386023i	−0.0578337	+	0.0187913i
$423$	6.39825	−	8.80644i	0.311094	−	0.428184i
$424$	4.96506			0.241125
$425$	13.4152	−	34.9701i	0.650733	−	1.69630i
$426$	−10.2647			−0.497325
$427$	37.2967	−	51.3345i	1.80491	−	2.48425i
$428$	−13.3660	+	4.34286i	−0.646068	+	0.209920i
$429$	−0.112991	−	0.347752i	−0.00545528	−	0.0167896i
$430$	2.63727	+	20.0156i	0.127181	+	0.965236i
$431$	7.09793	−	21.8452i	0.341895	−	1.05225i	−0.621329	−	0.783549i	$-0.713407\pi$
$431$	7.09793	−	21.8452i	0.341895	−	1.05225i	0.963225	−	0.268697i	$-0.0865929\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	17.1156	+	5.56121i	0.822525	+	0.267254i	0.689893	−	0.723911i	$-0.257657\pi$
$433$	17.1156	+	5.56121i	0.822525	+	0.267254i	0.132631	+	0.991165i	$0.457657\pi$
$434$	3.76128	−	2.73273i	0.180547	−	0.131175i
$435$	−0.918335	+	4.95785i	−0.0440308	+	0.237711i
$436$	−5.43552	−	3.94914i	−0.260314	−	0.189129i
$437$	−6.64567	−	9.14699i	−0.317906	−	0.437560i
$438$	−1.15547	−	1.59036i	−0.0552103	−	0.0759905i
$439$	−21.1610	−	15.3743i	−1.00996	−	0.733777i	−0.0457572	−	0.998953i	$-0.514570\pi$
$439$	−21.1610	−	15.3743i	−1.00996	−	0.733777i	−0.964200	+	0.265176i	$0.914570\pi$
$440$	1.03430	−	5.58390i	0.0493082	−	0.266202i
$441$	−11.6900	+	8.49326i	−0.556665	+	0.404441i
$442$	1.02573	+	0.333278i	0.0487888	+	0.0158524i
$443$		−	40.5689i		−	1.92749i	−0.266833	−	0.963743i	$-0.585977\pi$
$443$		−	40.5689i		−	1.92749i	0.266833	−	0.963743i	$-0.414023\pi$
$444$	0.0274966	−	0.0846260i	0.00130493	−	0.00401617i
$445$	−0.214364	−	1.62691i	−0.0101618	−	0.0771230i
$446$	6.76301	+	20.8144i	0.320238	+	0.985590i
$447$	1.79307	−	0.582604i	0.0848093	−	0.0275562i
$448$	2.72225	−	3.74686i	0.128614	−	0.177022i
$449$	23.1589			1.09294			0.546468	−	0.837480i	$-0.315972\pi$
$449$	23.1589			1.09294			0.546468	+	0.837480i	$0.315972\pi$
$450$	−4.99320	−	0.260613i	−0.235382	−	0.0122854i
$451$	−7.80660			−0.367598
$452$	−0.586387	+	0.807092i	−0.0275813	+	0.0379624i
$453$	5.84985	−	1.90073i	0.274850	−	0.0893042i
$454$	−4.48178	−	13.7935i	−0.210340	−	0.647361i
$455$	−1.46607	−	0.271558i	−0.0687303	−	0.0127308i
$456$	−2.08298	+	6.41074i	−0.0975443	+	0.300210i
$457$			38.3997i			1.79626i	0.439728	+	0.898131i	$0.355075\pi$
$457$			38.3997i			1.79626i	−0.439728	+	0.898131i	$0.644925\pi$
$458$	4.47071	+	1.45262i	0.208903	+	0.0678766i
$459$	6.06035	−	4.40310i	0.282873	−	0.205519i
$460$	1.61505	+	3.38509i	0.0753020	+	0.157830i
$461$	26.3670	+	19.1567i	1.22803	+	0.892217i	0.996741	−	0.0806677i	$-0.0257053\pi$
$461$	26.3670	+	19.1567i	1.22803	+	0.892217i	0.231290	+	0.972885i	$0.425705\pi$
$462$	−6.91363	−	9.51580i	−0.321651	−	0.442715i
$463$	1.49167	+	2.05311i	0.0693238	+	0.0954160i	0.842271	−	0.539054i	$-0.181218\pi$
$463$	1.49167	+	2.05311i	0.0693238	+	0.0954160i	−0.772947	+	0.634470i	$0.781218\pi$
$464$	−1.82428	−	1.32542i	−0.0846900	−	0.0615309i
$465$	1.62807	−	1.54531i	0.0754997	−	0.0716619i
$466$	9.56154	−	6.94686i	0.442930	−	0.321807i
$467$	−1.42329	−	0.462456i	−0.0658622	−	0.0213999i	0.275901	−	0.961186i	$-0.411024\pi$
$467$	−1.42329	−	0.462456i	−0.0658622	−	0.0213999i	−0.341763	+	0.939786i	$0.611024\pi$
$468$		−	0.143974i		−	0.00665521i
$469$	10.9475	−	33.6928i	0.505506	−	1.55579i
$470$	21.9682	−	10.4812i	1.01332	−	0.483460i
$471$	−7.25663	−	22.3336i	−0.334368	−	1.02908i
$472$	4.99652	−	1.62347i	0.229983	−	0.0747262i
$473$	−13.4777	+	18.5505i	−0.619707	+	0.852954i
$474$	−0.747233			−0.0343216
$475$	31.4673	+	12.0714i	1.44382	+	0.553876i
$476$	34.6936			1.59018
$477$	2.91839	−	4.01682i	0.133624	−	0.183917i
$478$	−9.23821	+	3.00168i	−0.422546	+	0.137294i
$479$	−7.50880	−	23.1097i	−0.343086	−	1.05591i	−0.962600	−	0.270925i	$-0.912670\pi$
$479$	−7.50880	−	23.1097i	−0.343086	−	1.05591i	0.619514	−	0.784985i	$-0.287330\pi$
$480$	1.06675	−	1.96521i	0.0486902	−	0.0896991i
$481$	0.00395881	−	0.0121840i	0.000180506	−	0.000555541i
$482$		−	6.68035i		−	0.304281i
$483$	7.38813	+	2.40055i	0.336171	+	0.109229i
$484$	−3.68107	+	2.67445i	−0.167321	+	0.121566i
$485$	17.9236	+	9.72923i	0.813868	+	0.441782i
$486$	−0.809017	−	0.587785i	−0.0366978	−	0.0266625i
$487$	−5.87877	−	8.09143i	−0.266392	−	0.366658i	0.654775	−	0.755824i	$-0.272763\pi$
$487$	−5.87877	−	8.09143i	−0.266392	−	0.366658i	−0.921168	+	0.389166i	$0.872763\pi$
$488$	8.05305	+	11.0841i	0.364545	+	0.501753i
$489$	−12.7641	−	9.27366i	−0.577213	−	0.419370i
$490$	−32.0334	+	4.22076i	−1.44712	+	0.190674i
$491$	−3.38163	+	2.45690i	−0.152611	+	0.110878i	−0.661470	−	0.749971i	$-0.730067\pi$
$491$	−3.38163	+	2.45690i	−0.152611	+	0.110878i	0.508860	+	0.860850i	$0.330067\pi$
$492$	−2.92341	−	0.949874i	−0.131798	−	0.0428236i
$493$		−	16.8917i		−	0.760764i
$494$	−0.299895	+	0.922982i	−0.0134929	+	0.0415269i
$495$	−3.90953	−	4.11890i	−0.175720	−	0.185131i
$496$	0.310207	+	0.954718i	0.0139287	+	0.0428681i
$497$	−45.2127	+	14.6905i	−2.02807	+	0.658959i
$498$	−1.82364	+	2.51003i	−0.0817194	+	0.112477i
$499$	−1.70548			−0.0763476			−0.0381738	−	0.999271i	$-0.512154\pi$
$499$	−1.70548			−0.0763476			−0.0381738	+	0.999271i	$0.512154\pi$
$500$	−9.53468	−	5.83866i	−0.426404	−	0.261113i
$501$	−4.03980			−0.180485
$502$	11.5220	−	15.8586i	0.514250	−	0.707804i
$503$	29.4265	−	9.56125i	1.31206	−	0.426315i	0.432301	−	0.901729i	$-0.357702\pi$
$503$	29.4265	−	9.56125i	1.31206	−	0.426315i	0.879762	+	0.475414i	$0.157702\pi$
$504$	−1.43117	−	4.40469i	−0.0637495	−	0.196201i
$505$	4.43361	+	4.67105i	0.197293	+	0.207859i
$506$	−1.31637	+	4.05138i	−0.0585199	+	0.180106i
$507$			12.9793i			0.576430i
$508$	10.9578	+	3.56039i	0.486172	+	0.157967i
$509$	−29.2182	+	21.2283i	−1.29507	+	0.940926i	−0.999895	−	0.0145162i	$-0.995379\pi$
$509$	−29.2182	+	21.2283i	−1.29507	+	0.940926i	−0.295179	+	0.955442i	$0.595379\pi$
$510$	16.6068	−	2.18814i	0.735364	−	0.0968924i
$511$	−7.36556	−	5.35139i	−0.325833	−	0.236732i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	3.96205	+	5.45330i	0.174929	+	0.240769i
$514$	7.66083	+	5.56592i	0.337905	+	0.245502i
$515$	−21.9540	−	11.9170i	−0.967410	−	0.525127i
$516$	−7.30429	+	5.30688i	−0.321553	+	0.233622i
$517$	26.2922	+	8.54286i	1.15633	+	0.375714i
$518$		−	0.412104i		−	0.0181068i
$519$	−6.22964	+	19.1729i	−0.273451	+	0.841595i
$520$	0.153584	−	0.282940i	0.00673513	−	0.0124077i
$521$	1.38131	+	4.25122i	0.0605161	+	0.186249i	0.976744	−	0.214407i	$-0.0687820\pi$
$521$	1.38131	+	4.25122i	0.0605161	+	0.186249i	−0.916228	+	0.400657i	$0.868782\pi$
$522$	−2.14457	+	0.696812i	−0.0938652	+	0.0304986i
$523$	−18.0150	+	24.7955i	−0.787741	+	1.08423i	0.206644	+	0.978416i	$0.433746\pi$
$523$	−18.0150	+	24.7955i	−0.787741	+	1.08423i	−0.994386	+	0.105817i	$0.966254\pi$
$524$	1.78409			0.0779385
$525$	−22.3665	+	5.99821i	−0.976155	+	0.261784i
$526$	−21.1465			−0.922030
$527$	−4.42005	+	6.08368i	−0.192540	+	0.265009i
$528$	2.41537	−	0.784803i	0.105116	−	0.0341541i
$529$	6.23799	+	19.1986i	0.271217	+	0.834720i
$530$	10.0202	−	4.78070i	0.435249	−	0.207660i
$531$	1.62347	−	4.99652i	0.0704525	−	0.216830i
$532$			31.2184i			1.35349i
$533$	−0.420896	−	0.136757i	−0.0182310	−	0.00592362i
$534$	0.593709	−	0.431355i	0.0256923	−	0.0186666i
$535$	−22.7928	+	21.6341i	−0.985417	+	0.935326i
$536$	6.18841	+	4.49614i	0.267298	+	0.194204i
$537$	−4.56161	−	6.27852i	−0.196848	−	0.270938i
$538$	1.14765	+	1.57960i	0.0494787	+	0.0681016i
$539$	−29.6887	−	21.5701i	−1.27878	−	0.929090i
$540$	−0.962868	−	2.01814i	−0.0414352	−	0.0868469i
$541$	−11.9065	+	8.65055i	−0.511899	+	0.371916i	−0.813543	−	0.581504i	$-0.802464\pi$
$541$	−11.9065	+	8.65055i	−0.511899	+	0.371916i	0.301645	+	0.953420i	$0.402464\pi$
$542$	15.1274	+	4.91521i	0.649780	+	0.211126i
$543$			11.7909i			0.505995i
$544$	−2.31485	+	7.12436i	−0.0992482	+	0.305455i
$545$	−14.7721	−	2.73622i	−0.632769	−	0.117207i
$546$	−0.206052	−	0.634163i	−0.00881821	−	0.0271397i
$547$	10.1457	−	3.29653i	0.433798	−	0.140950i	−0.0839742	−	0.996468i	$-0.526761\pi$
$547$	10.1457	−	3.29653i	0.433798	−	0.140950i	0.517773	+	0.855518i	$0.326761\pi$
$548$	9.41828	−	12.9632i	0.402329	−	0.553759i
$549$	13.7007			0.584730
$550$	−3.28920	−	12.2650i	−0.140252	−	0.522981i
$551$	15.1997			0.647529
$552$	−0.985910	+	1.35699i	−0.0419631	+	0.0577573i
$553$	−3.29134	+	1.06942i	−0.139962	+	0.0454764i
$554$	0.615092	+	1.89306i	0.0261328	+	0.0804284i
$555$	−0.0259916	−	0.197263i	−0.00110328	−	0.00837333i
$556$	−1.14460	+	3.52272i	−0.0485418	+	0.149396i
$557$			16.1652i			0.684942i	0.939528	+	0.342471i	$0.111264\pi$
$557$			16.1652i			0.684942i	−0.939528	+	0.342471i	$0.888736\pi$
$558$	0.954718	+	0.310207i	0.0404164	+	0.0131321i
$559$	−1.05163	+	0.764054i	−0.0444792	+	0.0323160i
$560$	1.88615	−	10.1828i	0.0797045	−	0.430304i
$561$	15.3913	+	11.1824i	0.649821	+	0.472123i
$562$	−14.8042	−	20.3762i	−0.624477	−	0.859519i
$563$	−25.5559	−	35.1746i	−1.07705	−	1.48243i	−0.862726	−	0.505672i	$-0.831245\pi$
$563$	−25.5559	−	35.1746i	−1.07705	−	1.48243i	−0.214326	−	0.976762i	$-0.568755\pi$
$564$	8.80644	+	6.39825i	0.370818	+	0.269415i
$565$	−0.406287	+	2.19344i	−0.0170926	+	0.0922786i
$566$	−9.10965	+	6.61855i	−0.382907	+	0.278198i
$567$	−4.40469	−	1.43117i	−0.184980	−	0.0601036i
$568$		−	10.2647i		−	0.430696i
$569$	−3.71683	+	11.4392i	−0.155818	+	0.479558i	−0.998243	−	0.0592558i	$-0.981127\pi$
$569$	−3.71683	+	11.4392i	−0.155818	+	0.479558i	0.842425	+	0.538813i	$0.181127\pi$
$570$	1.96896	+	14.9434i	0.0824706	+	0.625910i
$571$	5.80332	+	17.8608i	0.242861	+	0.747450i	0.995981	+	0.0895664i	$0.0285481\pi$
$571$	5.80332	+	17.8608i	0.242861	+	0.747450i	−0.753120	+	0.657884i	$0.771452\pi$
$572$	0.347752	−	0.112991i	0.0145402	−	0.00472441i
$573$	2.87097	−	3.95155i	0.119936	−	0.165078i
$574$	−14.2362			−0.594206
$575$	6.51878	+	5.27650i	0.271852	+	0.220045i
$576$	1.00000			0.0416667
$577$	−12.4817	+	17.1796i	−0.519619	+	0.715195i	−0.985504	−	0.169651i	$-0.945736\pi$
$577$	−12.4817	+	17.1796i	−0.519619	+	0.715195i	0.465885	+	0.884845i	$0.345736\pi$
$578$	−37.2007	+	12.0872i	−1.54734	+	0.502762i
$579$	5.78918	+	17.8173i	0.240590	+	0.740460i
$580$	−4.95785	−	0.918335i	−0.205863	−	0.0381318i
$581$	−4.44031	+	13.6659i	−0.184215	+	0.566955i
$582$			9.12044i			0.378055i
$583$	11.9925	+	3.89659i	0.496678	+	0.161380i
$584$	1.59036	−	1.15547i	0.0658097	−	0.0478135i
$585$	−0.138628	−	0.290560i	−0.00573157	−	0.0120132i
$586$	−16.2193	−	11.7840i	−0.670013	−	0.486793i
$587$	19.1781	+	26.3964i	0.791566	+	1.08950i	0.993911	+	0.110183i	$0.0351438\pi$
$587$	19.1781	+	26.3964i	0.791566	+	1.08950i	−0.202345	+	0.979314i	$0.564856\pi$
$588$	−8.49326	−	11.6900i	−0.350256	−	0.482086i
$589$	−5.47429	−	3.97731i	−0.225564	−	0.163882i
$590$	8.52049	−	8.08737i	0.350783	−	0.332952i
$591$	1.01494	−	0.737399i	0.0417492	−	0.0303326i
$592$	0.0846260	+	0.0274966i	0.00347811	+	0.00113011i
$593$			0.911868i			0.0374460i	0.999825	+	0.0187230i	$0.00596006\pi$
$593$			0.911868i			0.0374460i	−0.999825	+	0.0187230i	$0.994040\pi$
$594$	0.784803	−	2.41537i	0.0322008	−	0.0991040i
$595$	70.0165	−	33.4053i	2.87040	−	1.36949i
$596$	0.582604	+	1.79307i	0.0238644	+	0.0734470i
$597$	18.4222	−	5.98575i	0.753972	−	0.244980i
$598$	−0.141946	+	0.195371i	−0.00580459	+	0.00798933i
$599$	35.5516			1.45260			0.726300	−	0.687378i	$-0.241238\pi$
$599$	35.5516			1.45260			0.726300	+	0.687378i	$0.241238\pi$
$600$	0.260613	−	4.99320i	0.0106395	−	0.203847i
$601$	−42.8608			−1.74833			−0.874164	−	0.485630i	$-0.838590\pi$
$601$	−42.8608			−1.74833			−0.874164	+	0.485630i	$0.838590\pi$
$602$	−24.5781	+	33.8289i	−1.00173	+	1.37876i
$603$	7.27491	−	2.36376i	0.296257	−	0.0962598i
$604$	1.90073	+	5.84985i	0.0773397	+	0.238027i
$605$	−4.85377	+	8.94180i	−0.197334	+	0.363536i
$606$	−0.890008	+	2.73916i	−0.0361541	+	0.111271i
$607$		−	47.7389i		−	1.93766i	−0.247724	−	0.968831i	$-0.579683\pi$
$607$		−	47.7389i		−	1.93766i	0.247724	−	0.968831i	$-0.420317\pi$
$608$	−6.41074	−	2.08298i	−0.259990	−	0.0844758i
$609$	−8.44891	+	6.13849i	−0.342367	+	0.248744i
$610$	26.9247	+	14.6152i	1.09015	+	0.591752i
$611$	1.26790	+	0.921184i	0.0512938	+	0.0372671i
$612$	4.40310	+	6.06035i	0.177985	+	0.244975i
$613$	−14.4025	−	19.8234i	−0.581713	−	0.800660i	0.412169	−	0.911108i	$-0.364771\pi$
$613$	−14.4025	−	19.8234i	−0.581713	−	0.800660i	−0.993882	+	0.110448i	$0.964771\pi$
$614$	−11.6898	−	8.49311i	−0.471761	−	0.342754i
$615$	−6.81446	+	0.897881i	−0.274785	+	0.0362061i
$616$	9.51580	−	6.91363i	0.383402	−	0.278558i
$617$	−2.49230	−	0.809796i	−0.100336	−	0.0326012i	0.258419	−	0.966033i	$-0.416799\pi$
$617$	−2.49230	−	0.809796i	−0.100336	−	0.0326012i	−0.358755	+	0.933432i	$0.616799\pi$
$618$		−	11.1713i		−	0.449378i
$619$	2.08751	−	6.42470i	0.0839041	−	0.258230i	−0.900299	−	0.435271i	$-0.856652\pi$
$619$	2.08751	−	6.42470i	0.0839041	−	0.258230i	0.984204	+	0.177041i	$0.0566525\pi$
$620$	1.54531	+	1.62807i	0.0620610	+	0.0653847i
$621$	0.518324	+	1.59524i	0.0207996	+	0.0640146i
$622$	−22.4273	+	7.28708i	−0.899254	+	0.292185i
$623$	1.99777	−	2.74969i	0.0800388	−	0.110164i
$624$	0.143974			0.00576358
$625$	−24.8642	−	2.60258i	−0.994566	−	0.104103i
$626$	−27.4927			−1.09883
$627$	−10.0623	+	13.8496i	−0.401851	+	0.553100i
$628$	22.3336	−	7.25663i	0.891208	−	0.289571i
$629$	0.205977	+	0.633933i	0.00821285	+	0.0252766i
$630$	−7.12944	−	7.51126i	−0.284044	−	0.299256i
$631$	−9.31855	+	28.6796i	−0.370966	+	1.14172i	0.575194	+	0.818017i	$0.304926\pi$
$631$	−9.31855	+	28.6796i	−0.370966	+	1.14172i	−0.946160	+	0.323699i	$0.895074\pi$
$632$		−	0.747233i		−	0.0297234i
$633$	−1.18806	−	0.386023i	−0.0472210	−	0.0153430i
$634$	4.89111	−	3.55360i	0.194251	−	0.141132i
$635$	25.5425	−	3.36551i	1.01362	−	0.133556i
$636$	4.01682	+	2.91839i	0.159277	+	0.115722i
$637$	−1.22281	−	1.68305i	−0.0484495	−	0.0666850i
$638$	−3.36612	−	4.63307i	−0.133266	−	0.183425i
$639$	−8.30429	−	6.03342i	−0.328513	−	0.238678i
$640$	1.96521	+	1.06675i	0.0776817	+	0.0421670i
$641$	−16.6059	+	12.0649i	−0.655892	+	0.476534i	−0.865273	−	0.501301i	$-0.832855\pi$
$641$	−16.6059	+	12.0649i	−0.655892	+	0.476534i	0.209381	+	0.977834i	$0.432855\pi$
$642$	−13.3660	−	4.34286i	−0.527512	−	0.171399i
$643$		−	33.4413i		−	1.31880i	−0.751793	−	0.659399i	$-0.770811\pi$
$643$		−	33.4413i		−	1.31880i	0.751793	−	0.659399i	$-0.229189\pi$
$644$	−2.40055	+	7.38813i	−0.0945949	+	0.291133i
$645$	−9.63125	+	17.7431i	−0.379230	+	0.698633i
$646$	−15.6036	−	48.0228i	−0.613914	−	1.88943i
$647$	17.2006	−	5.58881i	0.676224	−	0.219719i	0.0492828	−	0.998785i	$-0.484306\pi$
$647$	17.2006	−	5.58881i	0.676224	−	0.219719i	0.626942	+	0.779066i	$0.284306\pi$
$648$	0.587785	−	0.809017i	0.0230904	−	0.0317812i
$649$	13.3426			0.523742
$650$	0.0375215	−	0.718893i	0.00147172	−	0.0281973i
$651$	4.64920			0.182217
$652$	9.27366	−	12.7641i	0.363185	−	0.499881i
$653$	−29.4770	+	9.57766i	−1.15352	+	0.374803i	−0.822470	−	0.568809i	$-0.807404\pi$
$653$	−29.4770	+	9.57766i	−1.15352	+	0.374803i	−0.331055	+	0.943612i	$0.607404\pi$
$654$	−2.07618	−	6.38984i	−0.0811852	−	0.249862i
$655$	3.60055	−	1.71785i	0.140685	−	0.0671218i
$656$	0.949874	−	2.92341i	0.0370864	−	0.114140i
$657$		−	1.96580i		−	0.0766930i
$658$	47.9467	+	15.5788i	1.86916	+	0.607326i
$659$	−17.4953	+	12.7110i	−0.681519	+	0.495152i	−0.873861	−	0.486176i	$-0.838392\pi$
$659$	−17.4953	+	12.7110i	−0.681519	+	0.495152i	0.192343	+	0.981328i	$0.438392\pi$
$660$	4.11890	−	3.90953i	0.160328	−	0.152178i
$661$	29.7396	+	21.6071i	1.15674	+	0.840418i	0.989362	−	0.145476i	$-0.0464713\pi$
$661$	29.7396	+	21.6071i	1.15674	+	0.840418i	0.167374	+	0.985893i	$0.446471\pi$
$662$	9.95207	+	13.6978i	0.386798	+	0.532382i
$663$	0.633933	+	0.872534i	0.0246199	+	0.0338864i
$664$	−2.51003	−	1.82364i	−0.0974080	−	0.0707710i
$665$	30.0592	+	63.0032i	1.16565	+	2.44316i
$666$	0.0719871	−	0.0523017i	0.00278945	−	0.00202665i
$667$	3.59715	+	1.16878i	0.139282	+	0.0452555i
$668$		−	4.03980i		−	0.156305i
$669$	−6.76301	+	20.8144i	−0.261473	+	0.804731i
$670$	16.8183	+	3.11522i	0.649746	+	0.120351i
$671$	10.7523	+	33.0923i	0.415089	+	1.27751i
$672$	4.40469	−	1.43117i	0.169915	−	0.0552087i
$673$	18.1235	−	24.9448i	0.698608	−	0.961552i	−0.301360	−	0.953511i	$-0.597440\pi$
$673$	18.1235	−	24.9448i	0.698608	−	0.961552i	0.999968	−	0.00804101i	$-0.00255956\pi$
$674$	22.6622			0.872917
$675$	−3.88640	−	3.14577i	−0.149588	−	0.121081i
$676$	−12.9793			−0.499203
$677$	15.1708	−	20.8808i	0.583061	−	0.802515i	−0.410966	−	0.911651i	$-0.634808\pi$
$677$	15.1708	−	20.8808i	0.583061	−	0.802515i	0.994027	+	0.109136i	$0.0348085\pi$
$678$	−0.948794	+	0.308282i	−0.0364382	+	0.0118395i
$679$	13.0529	+	40.1728i	0.500925	+	1.54169i
$680$	2.18814	+	16.6068i	0.0839113	+	0.636844i
$681$	4.48178	−	13.7935i	0.171742	−	0.528568i
$682$			2.54945i			0.0976235i
$683$	19.8582	+	6.45234i	0.759855	+	0.246892i	0.663216	−	0.748428i	$-0.269191\pi$
$683$	19.8582	+	6.45234i	0.759855	+	0.246892i	0.0966385	+	0.995320i	$0.469191\pi$
$684$	−5.45330	+	3.96205i	−0.208512	+	0.151493i
$685$	6.52560	−	35.2300i	0.249331	−	1.34607i
$686$	−27.9126	−	20.2797i	−1.06571	−	0.774281i
$687$	2.76305	+	3.80302i	0.105417	+	0.145094i
$688$	−5.30688	−	7.30429i	−0.202323	−	0.278473i
$689$	0.578318	+	0.420173i	0.0220322	+	0.0160073i
$690$	−0.683103	+	3.68789i	−0.0260053	+	0.140396i
$691$	−16.7033	+	12.1357i	−0.635424	+	0.461662i	−0.858275	−	0.513190i	$-0.828464\pi$
$691$	−16.7033	+	12.1357i	−0.635424	+	0.461662i	0.222851	+	0.974852i	$0.428464\pi$
$692$	−19.1729	−	6.22964i	−0.728843	−	0.236815i
$693$		−	11.7622i		−	0.446808i
$694$	3.16805	−	9.75025i	0.120258	−	0.370115i
$695$	1.08195	+	8.21143i	0.0410406	+	0.311477i
$696$	−0.696812	−	2.14457i	−0.0264126	−	0.0812896i
$697$	21.8993	−	7.11551i	0.829494	−	0.269519i
$698$	0.815529	−	1.12248i	0.0308682	−	0.0424865i
$699$	11.8187			0.447025
$700$	−5.99821	−	22.3665i	−0.226711	−	0.845375i
$701$	−12.3050			−0.464752			−0.232376	−	0.972626i	$-0.574650\pi$
$701$	−12.3050			−0.464752			−0.232376	+	0.972626i	$0.574650\pi$
$702$	0.0846260	−	0.116478i	0.00319400	−	0.00439617i
$703$	−0.570434	+	0.185345i	−0.0215143	+	0.00699043i
$704$	0.784803	+	2.41537i	0.0295784	+	0.0910328i
$705$	23.9333	+	4.43313i	0.901380	+	0.166961i
$706$	3.99189	−	12.2858i	0.150237	−	0.462382i
$707$			13.3389i			0.501662i
$708$	4.99652	+	1.62347i	0.187781	+	0.0610137i
$709$	−19.9814	+	14.5173i	−0.750417	+	0.545210i	−0.895956	−	0.444143i	$-0.853508\pi$
$709$	−19.9814	+	14.5173i	−0.750417	+	0.545210i	0.145539	+	0.989353i	$0.453508\pi$
$710$	−9.88352	−	20.7155i	−0.370922	−	0.777440i
$711$	−0.604525	−	0.439213i	−0.0226714	−	0.0164718i
$712$	0.431355	+	0.593709i	0.0161657	+	0.0222502i
$713$	−0.989705	−	1.36221i	−0.0370648	−	0.0510153i
$714$	28.0677	+	20.3924i	1.05041	+	0.763166i
$715$	0.593016	−	0.562871i	0.0221775	−	0.0210502i
$716$	6.27852	−	4.56161i	0.234639	−	0.170475i
$717$	−9.23821	−	3.00168i	−0.345007	−	0.112100i
$718$			9.87465i			0.368519i
$719$	6.49650	−	19.9942i	0.242279	−	0.745657i	−0.753793	−	0.657111i	$-0.771778\pi$
$719$	6.49650	−	19.9942i	0.242279	−	0.745657i	0.996072	−	0.0885457i	$-0.0282219\pi$
$720$	2.01814	−	0.962868i	0.0752116	−	0.0358840i
$721$	−15.9881	−	49.2064i	−0.595429	−	1.83254i
$722$	25.1425	−	8.16929i	0.935706	−	0.304029i
$723$	3.92661	−	5.40451i	0.146032	−	0.200996i
$724$	−11.7909			−0.438205
$725$	−10.8899	+	2.92042i	−0.404439	+	0.108462i
$726$	−4.55005			−0.168868
$727$	−5.09683	+	7.01519i	−0.189031	+	0.260179i	−0.893005	−	0.450047i	$-0.851407\pi$
$727$	−5.09683	+	7.01519i	−0.189031	+	0.260179i	0.703974	+	0.710226i	$0.251407\pi$
$728$	0.634163	−	0.206052i	0.0235036	−	0.00763680i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	2.09701	−	3.86320i	0.0776139	−	0.142983i
$731$	20.8998	−	64.3230i	0.773008	−	2.37907i
$732$			13.7007i			0.506391i
$733$	−32.2766	−	10.4873i	−1.19216	−	0.387357i	−0.355291	−	0.934756i	$-0.615618\pi$
$733$	−32.2766	−	10.4873i	−1.19216	−	0.387357i	−0.836872	+	0.547398i	$0.815618\pi$
$734$	4.30332	−	3.12654i	0.158838	−	0.115403i
$735$	−28.3965	−	15.4141i	−1.04742	−	0.568557i
$736$	−1.35699	−	0.985910i	−0.0500193	−	0.0363411i
$737$	11.4187	+	15.7165i	0.420614	+	0.578926i
$738$	−1.80677	−	2.48680i	−0.0665080	−	0.0915405i
$739$	−13.2781	−	9.64708i	−0.488442	−	0.354874i	0.316143	−	0.948712i	$-0.397612\pi$
$739$	−13.2781	−	9.64708i	−0.488442	−	0.354874i	−0.804585	+	0.593838i	$0.797612\pi$
$740$	0.197263	−	0.0259916i	0.00725152	−	0.000955469i
$741$	−0.785135	+	0.570434i	−0.0288427	+	0.0209554i
$742$	21.8696	+	7.10585i	0.802857	+	0.260864i
$743$		−	3.98742i		−	0.146284i	−0.997322	−	0.0731422i	$-0.976697\pi$
$743$		−	3.98742i		−	0.146284i	0.997322	−	0.0731422i	$-0.0233027\pi$
$744$	−0.310207	+	0.954718i	−0.0113727	+	0.0350017i
$745$	2.90226	+	3.05769i	0.106331	+	0.112025i
$746$	−2.99270	−	9.21059i	−0.109571	−	0.337224i
$747$	−2.95072	+	0.958745i	−0.107961	+	0.0350787i
$748$	−11.1824	+	15.3913i	−0.408870	+	0.562762i
$749$	−65.0883			−2.37828
$750$	−4.28184	−	10.3279i	−0.156351	−	0.377122i
$751$	37.5827			1.37141			0.685706	−	0.727879i	$-0.259494\pi$
$751$	37.5827			1.37141			0.685706	+	0.727879i	$0.259494\pi$
$752$	−6.39825	+	8.80644i	−0.233320	+	0.321138i
$753$	18.6429	−	6.05745i	0.679385	−	0.220746i
$754$	−0.100323	−	0.308763i	−0.00365355	−	0.0112445i
$755$	9.46858	+	9.97566i	0.344597	+	0.363051i
$756$	1.43117	−	4.40469i	0.0520512	−	0.160197i
$757$		−	31.2749i		−	1.13671i	−0.822785	−	0.568353i	$-0.807581\pi$
$757$		−	31.2749i		−	1.13671i	0.822785	−	0.568353i	$-0.192419\pi$
$758$	−21.4197	−	6.95968i	−0.777999	−	0.252787i
$759$	−3.44631	+	2.50389i	−0.125093	+	0.0908855i
$760$	−14.9434	+	1.96896i	−0.542054	+	0.0714217i
$761$	−24.2292	−	17.6035i	−0.878306	−	0.638127i	0.0544967	−	0.998514i	$-0.482645\pi$
$761$	−24.2292	−	17.6035i	−0.878306	−	0.638127i	−0.932803	+	0.360387i	$0.882645\pi$
$762$	6.77227	+	9.32123i	0.245333	+	0.337673i
$763$	−18.2899	−	25.1739i	−0.662139	−	0.911357i
$764$	3.95155	+	2.87097i	0.142962	+	0.103868i
$765$	14.7214	+	7.99102i	0.532253	+	0.288916i
$766$	5.83431	−	4.23887i	0.210802	−	0.153157i
$767$	0.719370	+	0.233738i	0.0259750	+	0.00843978i
$768$			1.00000i			0.0360844i
$769$	11.4039	−	35.0975i	0.411234	−	1.26565i	−0.504342	−	0.863504i	$-0.668265\pi$
$769$	11.4039	−	35.0975i	0.411234	−	1.26565i	0.915576	−	0.402145i	$-0.131735\pi$
$770$	12.5473	−	23.1151i	0.452173	−	0.833011i
$771$	2.92618	+	9.00585i	0.105384	+	0.324338i
$772$	−17.8173	+	5.78918i	−0.641257	+	0.208357i
$773$	−26.0028	+	35.7898i	−0.935256	+	1.28727i	0.0225174	+	0.999746i	$0.492832\pi$
$773$	−26.0028	+	35.7898i	−0.935256	+	1.28727i	−0.957774	+	0.287523i	$0.907168\pi$
$774$	−9.02860			−0.324526
$775$	4.68626	+	1.79774i	0.168335	+	0.0645766i
$776$	−9.12044			−0.327405
$777$	0.242229	−	0.333399i	0.00868990	−	0.0119606i
$778$	−12.5950	+	4.09235i	−0.451551	+	0.146718i
$779$	6.40277	+	19.7057i	0.229403	+	0.706030i
$780$	0.290560	−	0.138628i	0.0104037	−	0.00496369i
$781$	8.05574	−	24.7930i	0.288257	−	0.887164i
$782$		−	12.5649i		−	0.449319i
$783$	−2.14457	−	0.696812i	−0.0766406	−	0.0249020i
$784$	11.6900	−	8.49326i	0.417499	−	0.303331i
$785$	38.0852	−	36.1492i	1.35932	−	1.29022i
$786$	1.44336	+	1.04866i	0.0514830	+	0.0374046i
$787$	23.5408	+	32.4011i	0.839138	+	1.15497i	0.986153	+	0.165840i	$0.0530336\pi$
$787$	23.5408	+	32.4011i	0.839138	+	1.15497i	−0.147015	+	0.989134i	$0.546966\pi$
$788$	0.737399	+	1.01494i	0.0262688	+	0.0361559i
$789$	−17.1079	−	12.4296i	−0.609056	−	0.442505i
$790$	−0.719487	−	1.50802i	−0.0255982	−	0.0536530i
$791$	−3.73794	+	2.71577i	−0.132906	+	0.0965618i
$792$	2.41537	+	0.784803i	0.0858266	+	0.0278867i
$793$			1.97254i			0.0700471i
$794$	9.04265	−	27.8304i	0.320912	−	0.987664i
$795$	10.9165	+	2.02205i	0.387169	+	0.0717147i
$796$	5.98575	+	18.4222i	0.212159	+	0.652959i
$797$	42.3012	−	13.7445i	1.49838	−	0.486854i	0.558838	−	0.829277i	$-0.311247\pi$
$797$	42.3012	−	13.7445i	1.49838	−	0.486854i	0.939546	+	0.342423i	$0.111247\pi$
$798$	−18.3497	+	25.2563i	−0.649574	+	0.894062i
$799$	−81.5422			−2.88476
$800$	4.99320	+	0.260613i	0.176536	+	0.00921405i
$801$	0.733865			0.0259299
$802$	−16.1056	+	22.1675i	−0.568709	+	0.782761i
$803$	4.74813	−	1.54276i	0.167558	−	0.0544429i
$804$	2.36376	+	7.27491i	0.0833634	+	0.256566i
$805$	2.26915	+	17.2217i	0.0799770	+	0.606985i
$806$	−0.0446618	+	0.137455i	−0.00157314	+	0.00484164i
$807$			1.95250i			0.0687312i
$808$	−2.73916	−	0.890008i	−0.0963635	−	0.0313104i
$809$	−27.7120	+	20.1339i	−0.974301	+	0.707871i	−0.956428	−	0.291969i	$-0.905689\pi$
$809$	−27.7120	+	20.1339i	−0.974301	+	0.707871i	−0.0178730	+	0.999840i	$0.505689\pi$
$810$	0.407256	−	2.19867i	0.0143095	−	0.0772533i
$811$	−8.61506	−	6.25921i	−0.302516	−	0.219790i	0.426163	−	0.904646i	$-0.359865\pi$
$811$	−8.61506	−	6.25921i	−0.302516	−	0.219790i	−0.728678	+	0.684856i	$0.759865\pi$
$812$	−6.13849	−	8.44891i	−0.215419	−	0.296499i
$813$	9.34928	+	12.8682i	0.327893	+	0.451307i
$814$	0.182824	+	0.132829i	0.00640798	+	0.00465567i
$815$	6.42540	−	34.6890i	0.225072	−	1.21510i
$816$	−6.06035	+	4.40310i	−0.212155	+	0.154139i
$817$	57.8800	+	18.8063i	2.02496	+	0.657951i
$818$			10.0026i			0.349732i
$819$	0.206052	−	0.634163i	0.00720004	−	0.0221594i
$820$	−0.897881	−	6.81446i	−0.0313554	−	0.237971i
$821$	−4.55450	−	14.0173i	−0.158953	−	0.489208i	0.839587	−	0.543226i	$-0.182797\pi$
$821$	−4.55450	−	14.0173i	−0.158953	−	0.489208i	−0.998540	+	0.0540178i	$0.982797\pi$
$822$	15.2391	−	4.95149i	0.531525	−	0.172703i
$823$	1.66495	−	2.29161i	0.0580365	−	0.0798805i	−0.779012	−	0.627009i	$-0.784279\pi$
$823$	1.66495	−	2.29161i	0.0580365	−	0.0798805i	0.837049	+	0.547128i	$0.184279\pi$
$824$	11.1713			0.389172
$825$	4.54816	−	11.8559i	0.158346	−	0.412770i
$826$	24.3316			0.846605
$827$	−12.8205	+	17.6459i	−0.445813	+	0.613609i	−0.971492	−	0.237074i	$-0.923812\pi$
$827$	−12.8205	+	17.6459i	−0.445813	+	0.613609i	0.525678	+	0.850683i	$0.323812\pi$
$828$	−1.59524	+	0.518324i	−0.0554383	+	0.0180130i
$829$	12.5472	+	38.6164i	0.435784	+	1.34120i	0.892281	+	0.451480i	$0.149104\pi$
$829$	12.5472	+	38.6164i	0.435784	+	1.34120i	−0.456497	+	0.889725i	$0.650896\pi$
$830$	−6.82151	−	1.26354i	−0.236778	−	0.0438581i
$831$	−0.615092	+	1.89306i	−0.0213373	+	0.0656695i
$832$			0.143974i			0.00499141i
$833$	102.944	+	33.4486i	3.56680	+	1.15892i
$834$	−2.99660	+	2.17716i	−0.103764	+	0.0753888i
$835$	−3.88979	−	8.15288i	−0.134612	−	0.282142i
$836$	−13.8496	−	10.0623i	−0.478999	−	0.348013i
$837$	0.590048	+	0.812131i	0.0203950	+	0.0280714i
$838$	4.73236	+	6.51354i	0.163477	+	0.225007i
$839$	23.3715	+	16.9804i	0.806875	+	0.586229i	0.912923	−	0.408132i	$-0.133820\pi$
$839$	23.3715	+	16.9804i	0.806875	+	0.586229i	−0.106048	+	0.994361i	$0.533820\pi$
$840$	7.51126	−	7.12944i	0.259163	−	0.245989i
$841$	19.3479	−	14.0571i	0.667168	−	0.484726i
$842$	−9.56120	−	3.10662i	−0.329501	−	0.107061i
$843$		−	25.1864i		−	0.867465i
$844$	0.386023	−	1.18806i	0.0132875	−	0.0408946i
$845$	−26.1940	+	12.4973i	−0.901100	+	0.429921i
$846$	3.36376	+	10.3526i	0.115648	+	0.355929i
$847$	−20.0416	+	6.51191i	−0.688637	+	0.223752i
$848$	−2.91839	+	4.01682i	−0.100218	+	0.137938i
$849$	−11.2601			−0.386447
$850$	20.4062	+	31.4080i	0.699926	+	1.07729i
$851$	−0.149251			−0.00511624
$852$	6.03342	−	8.30429i	0.206702	−	0.284500i
$853$	−23.5949	+	7.66646i	−0.807875	+	0.262495i	−0.683698	−	0.729765i	$-0.739629\pi$
$853$	−23.5949	+	7.66646i	−0.807875	+	0.262495i	−0.124178	+	0.992260i	$0.539629\pi$
$854$	19.6080	+	60.3473i	0.670973	+	2.06504i
$855$	−7.19058	+	13.2468i	−0.245913	+	0.453030i
$856$	4.34286	−	13.3660i	0.148436	−	0.456839i
$857$			20.0312i			0.684251i	0.939654	+	0.342126i	$0.111147\pi$
$857$			20.0312i			0.684251i	−0.939654	+	0.342126i	$0.888853\pi$
$858$	0.347752	+	0.112991i	0.0118720	+	0.00385746i
$859$	−25.7151	+	18.6831i	−0.877387	+	0.637459i	−0.932559	−	0.361018i	$-0.882429\pi$
$859$	−25.7151	+	18.6831i	−0.877387	+	0.637459i	0.0551721	+	0.998477i	$0.482429\pi$
$860$	−17.7431	−	9.63125i	−0.605034	−	0.328423i
$861$	−11.5173	−	8.36781i	−0.392509	−	0.285174i
$862$	13.5011	+	18.5826i	0.459848	+	0.632927i
$863$	−14.0480	−	19.3354i	−0.478199	−	0.658184i	0.499959	−	0.866049i	$-0.333348\pi$
$863$	−14.0480	−	19.3354i	−0.478199	−	0.658184i	−0.978157	+	0.207865i	$0.933348\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	−44.6918	+	5.88865i	−1.51957	+	0.200220i
$866$	−14.5594	+	10.5780i	−0.494749	+	0.359456i
$867$	−37.2007	−	12.0872i	−1.26340	−	0.410504i
$868$			4.64920i			0.157804i
$869$	0.586431	−	1.80485i	0.0198933	−	0.0612253i
$870$	−3.47120	−	3.65710i	−0.117685	−	0.123987i
$871$	0.340321	+	1.04740i	0.0115313	+	0.0354898i
$872$	6.38984	−	2.07618i	0.216387	−	0.0703085i
$873$	−5.36086	+	7.37859i	−0.181438	+	0.249728i
$874$	11.3063			0.382441
$875$	−33.6412	−	39.3633i	−1.13728	−	1.33072i
$876$	1.96580			0.0664181
$877$	2.76512	−	3.80586i	0.0933715	−	0.128515i	−0.759775	−	0.650186i	$-0.774691\pi$
$877$	2.76512	−	3.80586i	0.0933715	−	0.128515i	0.853147	+	0.521671i	$0.174691\pi$
$878$	24.8762	−	8.08277i	0.839531	−	0.272780i
$879$	−6.19522	−	19.0669i	−0.208960	−	0.643112i
$880$	3.90953	+	4.11890i	0.131790	+	0.138848i
$881$	−13.7902	+	42.4420i	−0.464605	+	1.42991i	0.394873	+	0.918736i	$0.370789\pi$
$881$	−13.7902	+	42.4420i	−0.464605	+	1.42991i	−0.859478	+	0.511172i	$0.829211\pi$
$882$		−	14.4496i		−	0.486543i
$883$	30.6286	+	9.95182i	1.03073	+	0.334905i	0.775080	−	0.631863i	$-0.217710\pi$
$883$	30.6286	+	9.95182i	1.03073	+	0.334905i	0.255653	+	0.966769i	$0.417710\pi$
$884$	−0.872534	+	0.633933i	−0.0293465	+	0.0213215i
$885$	11.6469	−	1.53460i	0.391505	−	0.0515851i
$886$	32.8209	+	23.8458i	1.10264	+	0.801115i
$887$	−25.2895	−	34.8080i	−0.849137	−	1.16874i	−0.984052	−	0.177880i	$-0.943076\pi$
$887$	−25.2895	−	34.8080i	−0.849137	−	1.16874i	0.134915	−	0.990857i	$-0.456924\pi$
$888$	0.0523017	+	0.0719871i	0.00175513	+	0.00241573i
$889$	43.1701	+	31.3649i	1.44788	+	1.05194i
$890$	1.44220	+	0.782850i	0.0483426	+	0.0262412i
$891$	2.05464	−	1.49278i	0.0688330	−	0.0500101i
$892$	−20.8144	−	6.76301i	−0.696917	−	0.226442i
$893$		−	73.3744i		−	2.45538i
$894$	−0.582604	+	1.79307i	−0.0194852	+	0.0599692i
$895$	8.27869	−	15.2513i	0.276726	−	0.509796i
$896$	1.43117	+	4.40469i	0.0478121	+	0.147151i
$897$	−0.229673	+	0.0746253i	−0.00766856	+	0.00249167i
$898$	−13.6125	+	18.7360i	−0.454254	+	0.625227i
$899$	2.26361			0.0754957
$900$	3.14577	−	3.88640i	0.104859	−	0.129547i
$901$	−37.1933			−1.23909
$902$	4.58860	−	6.31567i	0.152784	−	0.210289i
$903$	−39.7682	+	12.9215i	−1.32340	+	0.430000i
$904$	−0.308282	−	0.948794i	−0.0102533	−	0.0315564i
$905$	−23.7956	+	11.3531i	−0.790994	+	0.377388i
$906$	−1.90073	+	5.84985i	−0.0631476	+	0.194348i
$907$		−	39.3398i		−	1.30626i	−0.757247	−	0.653129i	$-0.773456\pi$
$907$		−	39.3398i		−	1.30626i	0.757247	−	0.653129i	$-0.226544\pi$
$908$	13.7935	+	4.48178i	0.457754	+	0.148733i
$909$	−2.33007	+	1.69290i	−0.0772836	+	0.0561498i
$910$	1.08143	−	1.02646i	0.0358490	−	0.0340267i
$911$	11.0045	+	7.99523i	0.364595	+	0.264894i	0.754966	−	0.655764i	$-0.227653\pi$
$911$	11.0045	+	7.99523i	0.364595	+	0.264894i	−0.390371	+	0.920658i	$0.627653\pi$
$912$	−3.96205	−	5.45330i	−0.131197	−	0.180577i
$913$	−4.63146	−	6.37465i	−0.153279	−	0.210970i
$914$	−31.0660	−	22.5708i	−1.02757	−	0.746575i
$915$	13.1919	+	27.6499i	0.436112	+	0.914076i
$916$	−3.80302	+	2.76305i	−0.125655	+	0.0912938i
$917$	7.85839	+	2.55335i	0.259507	+	0.0843189i
$918$			7.49100i			0.247240i
$919$	4.38951	−	13.5095i	0.144797	−	0.445638i	−0.852188	−	0.523235i	$-0.824725\pi$
$919$	4.38951	−	13.5095i	0.144797	−	0.445638i	0.996985	+	0.0775974i	$0.0247249\pi$
$920$	−3.68789	−	0.683103i	−0.121586	−	0.0225212i
$921$	−4.46509	−	13.7421i	−0.147130	−	0.452819i
$922$	−30.9962	+	10.0713i	−1.02081	+	0.331680i
$923$	0.868657	−	1.19560i	0.0285922	−	0.0393538i
$924$	11.7622			0.386947
$925$	0.373077	−	0.242392i	0.0122667	−	0.00796981i
$926$	−2.53778			−0.0833966
$927$	6.56635	−	9.03781i	0.215667	−	0.296841i
$928$	2.14457	−	0.696812i	0.0703989	−	0.0228740i
$929$	−2.50600	−	7.71269i	−0.0822193	−	0.253045i	0.901493	−	0.432793i	$-0.142472\pi$
$929$	−2.50600	−	7.71269i	−0.0822193	−	0.253045i	−0.983713	+	0.179748i	$0.942472\pi$
$930$	0.293227	+	2.22544i	0.00961529	+	0.0729751i
$931$	−30.0981	+	92.6326i	−0.986427	+	3.03591i
$932$			11.8187i			0.387135i
$933$	−22.4273	−	7.28708i	−0.734238	−	0.238568i
$934$	1.21073	−	0.879644i	0.0396161	−	0.0287828i
$935$	−7.74793	+	41.8290i	−0.253384	+	1.36795i
$936$	0.116478	+	0.0846260i	0.00380719	+	0.00276609i
$937$	6.18675	+	8.51533i	0.202112	+	0.278184i	0.898027	−	0.439941i	$-0.145001\pi$
$937$	6.18675	+	8.51533i	0.202112	+	0.278184i	−0.695914	+	0.718125i	$0.745001\pi$
$938$	20.8233	+	28.6608i	0.679904	+	0.935808i
$939$	−22.2420	−	16.1598i	−0.725841	−	0.527354i
$940$	−4.43313	+	23.9333i	−0.144593	+	0.780618i
$941$	40.0792	−	29.1193i	1.30655	−	0.949261i	0.306549	−	0.951855i	$-0.400826\pi$
$941$	40.0792	−	29.1193i	1.30655	−	0.949261i	0.999997	+	0.00259412i	$0.000825736\pi$
$942$	22.3336	+	7.25663i	0.727668	+	0.236434i
$943$			5.15587i			0.167898i
$944$	−1.62347	+	4.99652i	−0.0528394	+	0.162623i
$945$	−1.35283	−	10.2673i	−0.0440077	−	0.333996i
$946$	−7.08567	−	21.8074i	−0.230375	−	0.709021i
$947$	10.0635	−	3.26983i	0.327020	−	0.106255i	−0.140906	−	0.990023i	$-0.545001\pi$
$947$	10.0635	−	3.26983i	0.327020	−	0.106255i	0.467926	+	0.883768i	$0.345001\pi$
$948$	0.439213	−	0.604525i	0.0142650	−	0.0196340i
$949$	0.283024			0.00918735
$950$	−28.2620	+	18.3621i	−0.916940	+	0.595747i
$951$	6.04575			0.196047
$952$	−20.3924	+	28.0677i	−0.660921	+	0.909680i
$953$	24.7411	−	8.03886i	0.801442	−	0.260404i	0.120473	−	0.992717i	$-0.461559\pi$
$953$	24.7411	−	8.03886i	0.801442	−	0.260404i	0.680969	+	0.732312i	$0.261559\pi$
$954$	1.53429	+	4.72205i	0.0496744	+	0.152882i
$955$	10.7391	+	1.98919i	0.347510	+	0.0643688i
$956$	3.00168	−	9.23821i	0.0970812	−	0.298785i
$957$		−	5.72679i		−	0.185121i
$958$	23.1097	+	7.50880i	0.746641	+	0.242598i
$959$	60.0372	−	43.6196i	1.93870	−	1.40855i
$960$	0.962868	+	2.01814i	0.0310764	+	0.0651352i
$961$	24.2643	+	17.6290i	0.782718	+	0.568678i
$962$	0.00753010	+	0.0103643i	0.000242780	+	0.000334158i
$963$	−8.26061	−	11.3698i	−0.266195	−	0.366385i
$964$	5.40451	+	3.92661i	0.174068	+	0.126468i
$965$	−30.3835	+	28.8390i	−0.978079	+	0.928361i
$966$	−6.28472	+	4.56611i	−0.202207	+	0.146912i
$967$	−28.1049	−	9.13183i	−0.903793	−	0.293660i	−0.179991	−	0.983668i	$-0.557607\pi$
$967$	−28.1049	−	9.13183i	−0.903793	−	0.293660i	−0.723802	+	0.690008i	$0.757607\pi$
$968$		−	4.55005i		−	0.146244i
$969$	15.6036	−	48.0228i	0.501259	−	1.54272i
$970$	−18.4063	+	8.78178i	−0.590991	+	0.281966i
$971$	11.0850	+	34.1161i	0.355734	+	1.09484i	0.955583	+	0.294723i	$0.0952275\pi$
$971$	11.0850	+	34.1161i	0.355734	+	1.09484i	−0.599849	+	0.800114i	$0.704773\pi$
$972$	0.951057	−	0.309017i	0.0305052	−	0.00991172i
$973$	−10.0832	+	13.8784i	−0.323253	+	0.444920i
$974$	10.0016			0.320470
$975$	0.452910	−	0.559542i	0.0145047	−	0.0179197i
$976$	−13.7007			−0.438548
$977$	−12.7115	+	17.4959i	−0.406677	+	0.559743i	−0.962404	−	0.271622i	$-0.912440\pi$
$977$	−12.7115	+	17.4959i	−0.406677	+	0.559743i	0.555727	+	0.831365i	$0.312440\pi$
$978$	15.0051	−	4.87545i	0.479810	−	0.155900i
$979$	0.575939	+	1.77256i	0.0184071	+	0.0566512i
$980$	15.4141	−	28.3965i	0.492385	−	0.907092i
$981$	2.07618	−	6.38984i	0.0662875	−	0.204012i
$982$		−	4.17992i		−	0.133387i
$983$	−13.9026	−	4.51722i	−0.443424	−	0.144077i	0.0787911	−	0.996891i	$-0.474894\pi$
$983$	−13.9026	−	4.51722i	−0.443424	−	0.144077i	−0.522215	+	0.852814i	$0.674894\pi$
$984$	2.48680	−	1.80677i	0.0792764	−	0.0575977i
$985$	2.46543	+	1.33828i	0.0785552	+	0.0426411i
$986$	13.6657	+	9.92869i	0.435204	+	0.316194i
$987$	29.6327	+	40.7859i	0.943219	+	1.29823i
$988$	−0.570434	−	0.785135i	−0.0181479	−	0.0249785i
$989$	12.2517	+	8.90139i	0.389582	+	0.283048i
$990$	5.63022	−	0.741845i	0.178940	−	0.0235774i
$991$	10.5772	−	7.68477i	0.335995	−	0.244115i	−0.406975	−	0.913439i	$-0.633416\pi$
$991$	10.5772	−	7.68477i	0.335995	−	0.244115i	0.742970	+	0.669325i	$0.233416\pi$
$992$	−0.954718	−	0.310207i	−0.0303123	−	0.00984907i
$993$			16.9315i			0.537304i
$994$	14.6905	−	45.2127i	0.465955	−	1.43406i
$995$	29.8183	+	31.4152i	0.945302	+	0.995928i
$996$	−0.958745	−	2.95072i	−0.0303790	−	0.0934970i
$997$	−11.5998	+	3.76901i	−0.367370	+	0.119366i	−0.486884	−	0.873467i	$-0.661866\pi$
$997$	−11.5998	+	3.76901i	−0.367370	+	0.119366i	0.119514	+	0.992833i	$0.461866\pi$
$998$	1.00245	−	1.37976i	0.0317321	−	0.0436755i
$999$	0.0889810			0.00281523

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.h.b.109.1	✓	16
3.2	odd	2		450.2.l.c.109.4		16
5.2	odd	4		750.2.g.f.451.4		16
5.3	odd	4		750.2.g.g.451.1		16
5.4	even	2		750.2.h.d.49.4		16
25.2	odd	20		750.2.g.f.301.4		16
25.6	even	5		3750.2.c.k.1249.1		16
25.8	odd	20		3750.2.a.u.1.1		8
25.11	even	5		750.2.h.d.199.3		16
25.14	even	10	inner	150.2.h.b.139.1	yes	16
25.17	odd	20		3750.2.a.v.1.8		8
25.19	even	10		3750.2.c.k.1249.16		16
25.23	odd	20		750.2.g.g.301.1		16
75.14	odd	10		450.2.l.c.289.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.109.1	✓	16	1.1	even	1	trivial
150.2.h.b.139.1	yes	16	25.14	even	10	inner
450.2.l.c.109.4		16	3.2	odd	2
450.2.l.c.289.4		16	75.14	odd	10
750.2.g.f.301.4		16	25.2	odd	20
750.2.g.f.451.4		16	5.2	odd	4
750.2.g.g.301.1		16	25.23	odd	20
750.2.g.g.451.1		16	5.3	odd	4
750.2.h.d.49.4		16	5.4	even	2
750.2.h.d.199.3		16	25.11	even	5
3750.2.a.u.1.1		8	25.8	odd	20
3750.2.a.v.1.8		8	25.17	odd	20
3750.2.c.k.1249.1		16	25.6	even	5
3750.2.c.k.1249.16		16	25.19	even	10

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.53938 - 1.62182i) q^{5} +(0.309017 - 0.951057i) q^{6} -4.63137i q^{7} +(0.951057 + 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.53938 - 1.62182i) q^{5} +(0.309017 - 0.951057i) q^{6} -4.63137i q^{7} +(0.951057 + 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(2.21691 - 0.292102i) q^{10} +(2.05464 + 1.49278i) q^{11} +(0.587785 + 0.809017i) q^{12} +(0.0846260 + 0.116478i) q^{13} +(3.74686 + 2.72225i) q^{14} +(1.96521 + 1.06675i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-7.12436 - 2.31485i) q^{17} +1.00000i q^{18} +(2.08298 - 6.41074i) q^{19} +(-1.06675 + 1.96521i) q^{20} +(1.43117 + 4.40469i) q^{21} +(-2.41537 + 0.784803i) q^{22} +(0.985910 - 1.35699i) q^{23} -1.00000 q^{24} +(-0.260613 + 4.99320i) q^{25} -0.143974 q^{26} +(-0.587785 + 0.809017i) q^{27} +(-4.40469 + 1.43117i) q^{28} +(0.696812 + 2.14457i) q^{29} +(-2.01814 + 0.962868i) q^{30} +(0.310207 - 0.954718i) q^{31} -1.00000i q^{32} +(-2.41537 - 0.784803i) q^{33} +(6.06035 - 4.40310i) q^{34} +(-7.51126 + 7.12944i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-0.0523017 - 0.0719871i) q^{37} +(3.96205 + 5.45330i) q^{38} +(-0.116478 - 0.0846260i) q^{39} +(-0.962868 - 2.01814i) q^{40} +(-2.48680 + 1.80677i) q^{41} +(-4.40469 - 1.43117i) q^{42} +9.02860i q^{43} +(0.784803 - 2.41537i) q^{44} +(-2.19867 - 0.407256i) q^{45} +(0.518324 + 1.59524i) q^{46} +(10.3526 - 3.36376i) q^{47} +(0.587785 - 0.809017i) q^{48} -14.4496 q^{49} +(-3.88640 - 3.14577i) q^{50} +7.49100 q^{51} +(0.0846260 - 0.116478i) q^{52} +(4.72205 - 1.53429i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-0.741845 - 5.63022i) q^{55} +(1.43117 - 4.40469i) q^{56} +6.74065i q^{57} +(-2.14457 - 0.696812i) q^{58} +(4.25029 - 3.08802i) q^{59} +(0.407256 - 2.19867i) q^{60} +(11.0841 + 8.05305i) q^{61} +(0.590048 + 0.812131i) q^{62} +(-2.72225 - 3.74686i) q^{63} +(0.809017 + 0.587785i) q^{64} +(0.0586344 - 0.316552i) q^{65} +(2.05464 - 1.49278i) q^{66} +(7.27491 + 2.36376i) q^{67} +7.49100i q^{68} +(-0.518324 + 1.59524i) q^{69} +(-1.35283 - 10.2673i) q^{70} +(-3.17196 - 9.76228i) q^{71} +(0.951057 - 0.309017i) q^{72} +(1.15547 - 1.59036i) q^{73} +0.0889810 q^{74} +(-1.29513 - 4.82935i) q^{75} -6.74065 q^{76} +(6.91363 - 9.51580i) q^{77} +(0.136928 - 0.0444905i) q^{78} +(-0.230908 - 0.710661i) q^{79} +(2.19867 + 0.407256i) q^{80} +(0.309017 - 0.951057i) q^{81} -3.07386i q^{82} +(-2.95072 - 0.958745i) q^{83} +(3.74686 - 2.72225i) q^{84} +(7.21284 + 15.1179i) q^{85} +(-7.30429 - 5.30688i) q^{86} +(-1.32542 - 1.82428i) q^{87} +(1.49278 + 2.05464i) q^{88} +(0.593709 + 0.431355i) q^{89} +(1.62182 - 1.53938i) q^{90} +(0.539451 - 0.391934i) q^{91} +(-1.59524 - 0.518324i) q^{92} +1.00385i q^{93} +(-3.36376 + 10.3526i) q^{94} +(-13.6036 + 6.49035i) q^{95} +(0.309017 + 0.951057i) q^{96} +(-8.67406 + 2.81837i) q^{97} +(8.49326 - 11.6900i) q^{98} +2.53967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^9	\( 16 q + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{9} + 2 q^{10} + 2 q^{11} + 20 q^{13} + 2 q^{14} - 2 q^{15} - 4 q^{16} - 30 q^{17} - 4 q^{20} - 2 q^{21} - 20 q^{22} - 10 q^{23} - 16 q^{24} + 24 q^{25} + 4 q^{26} - 10 q^{29} - 6 q^{30} - 18 q^{31} - 20 q^{33} + 12 q^{34} - 34 q^{35} - 4 q^{36} + 20 q^{37} + 10 q^{38} - 4 q^{39} - 2 q^{40} + 22 q^{41} + 8 q^{44} - 4 q^{45} - 6 q^{46} - 50 q^{47} - 52 q^{49} + 12 q^{50} + 28 q^{51} + 20 q^{52} + 30 q^{53} + 4 q^{54} + 18 q^{55} - 2 q^{56} - 30 q^{58} + 20 q^{59} + 2 q^{60} + 12 q^{61} + 50 q^{62} + 10 q^{63} + 4 q^{64} - 8 q^{65} + 2 q^{66} - 50 q^{67} + 6 q^{69} - 12 q^{70} - 28 q^{71} + 20 q^{73} + 12 q^{74} + 28 q^{75} + 20 q^{76} + 100 q^{77} - 20 q^{79} + 4 q^{80} - 4 q^{81} - 30 q^{83} + 2 q^{84} - 4 q^{85} - 6 q^{86} + 10 q^{87} + 70 q^{89} + 8 q^{90} + 12 q^{91} - 30 q^{92} + 2 q^{94} - 30 q^{95} - 4 q^{96} - 10 q^{97} + 60 q^{98} - 12 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^9 + 2 * q^10 + 2 * q^11 + 20 * q^13 + 2 * q^14 - 2 * q^15 - 4 * q^16 - 30 * q^17 - 4 * q^20 - 2 * q^21 - 20 * q^22 - 10 * q^23 - 16 * q^24 + 24 * q^25 + 4 * q^26 - 10 * q^29 - 6 * q^30 - 18 * q^31 - 20 * q^33 + 12 * q^34 - 34 * q^35 - 4 * q^36 + 20 * q^37 + 10 * q^38 - 4 * q^39 - 2 * q^40 + 22 * q^41 + 8 * q^44 - 4 * q^45 - 6 * q^46 - 50 * q^47 - 52 * q^49 + 12 * q^50 + 28 * q^51 + 20 * q^52 + 30 * q^53 + 4 * q^54 + 18 * q^55 - 2 * q^56 - 30 * q^58 + 20 * q^59 + 2 * q^60 + 12 * q^61 + 50 * q^62 + 10 * q^63 + 4 * q^64 - 8 * q^65 + 2 * q^66 - 50 * q^67 + 6 * q^69 - 12 * q^70 - 28 * q^71 + 20 * q^73 + 12 * q^74 + 28 * q^75 + 20 * q^76 + 100 * q^77 - 20 * q^79 + 4 * q^80 - 4 * q^81 - 30 * q^83 + 2 * q^84 - 4 * q^85 - 6 * q^86 + 10 * q^87 + 70 * q^89 + 8 * q^90 + 12 * q^91 - 30 * q^92 + 2 * q^94 - 30 * q^95 - 4 * q^96 - 10 * q^97 + 60 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more