LMFDB - Embedded newform 825.2.cv.a.422.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(38,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 19, 8]))

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

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

chi := DirichletCharacter("825.38");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.cv (of order $20$, degree $8$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$928$
Relative dimension:	$116$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			422.8
Character	$\chi$	$=$	825.422
Dual form			825.2.cv.a.608.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.395170 + 2.49501i) q^{2} +(-1.66780 - 0.467371i) q^{3} +(-4.16679 - 1.35387i) q^{4} +(-0.105290 - 2.23359i) q^{5} +(1.82516 - 3.97649i) q^{6} +(0.988634 - 1.94030i) q^{7} +(2.73085 - 5.35960i) q^{8} +(2.56313 + 1.55896i) q^{9} +O(q^{10})$	\(q+(-0.395170 + 2.49501i) q^{2} +(-1.66780 - 0.467371i) q^{3} +(-4.16679 - 1.35387i) q^{4} +(-0.105290 - 2.23359i) q^{5} +(1.82516 - 3.97649i) q^{6} +(0.988634 - 1.94030i) q^{7} +(2.73085 - 5.35960i) q^{8} +(2.56313 + 1.55896i) q^{9} +(5.61442 + 0.619949i) q^{10} +(-3.23766 - 0.719398i) q^{11} +(6.31662 + 4.20542i) q^{12} +(-1.07948 - 2.11860i) q^{13} +(4.45039 + 3.23340i) q^{14} +(-0.868311 + 3.77439i) q^{15} +(5.20412 + 3.78102i) q^{16} +(2.22285 + 4.36258i) q^{17} +(-4.90250 + 5.77897i) q^{18} +(-1.10263 + 0.358267i) q^{19} +(-2.58527 + 9.44943i) q^{20} +(-2.55569 + 2.77398i) q^{21} +(3.07433 - 7.79371i) q^{22} +(-4.95313 + 2.52374i) q^{23} +(-7.05944 + 7.66243i) q^{24} +(-4.97783 + 0.470347i) q^{25} +(5.71251 - 1.85611i) q^{26} +(-3.54618 - 3.79798i) q^{27} +(-6.74635 + 6.74635i) q^{28} +(-2.17558 + 6.69574i) q^{29} +(-9.07400 - 3.65797i) q^{30} +9.76449 q^{31} +(-2.98337 + 2.98337i) q^{32} +(5.06356 + 2.71300i) q^{33} +(-11.7631 + 3.82206i) q^{34} +(-4.43793 - 2.00391i) q^{35} +(-8.56938 - 9.96602i) q^{36} +(-3.96161 - 0.627457i) q^{37} +(-0.458151 - 2.89265i) q^{38} +(0.810189 + 4.03793i) q^{39} +(-12.2587 - 5.53529i) q^{40} +7.61370i q^{41} +(-5.91118 - 7.47266i) q^{42} +(-8.42050 + 8.42050i) q^{43} +(12.5167 + 7.38096i) q^{44} +(3.21221 - 5.88912i) q^{45} +(-4.33943 - 13.3554i) q^{46} +(1.82458 - 11.5199i) q^{47} +(-6.91231 - 8.73824i) q^{48} +(1.32712 + 1.82662i) q^{49} +(0.793571 - 12.6056i) q^{50} +(-1.66833 - 8.31482i) q^{51} +(1.62966 + 10.2892i) q^{52} +(3.28243 - 6.44214i) q^{53} +(10.8773 - 7.34689i) q^{54} +(-1.26595 + 7.30735i) q^{55} +(-7.69944 - 10.5974i) q^{56} +(2.00641 - 0.0821803i) q^{57} +(-15.8462 - 8.07404i) q^{58} +(-1.40880 + 1.02355i) q^{59} +(8.72811 - 14.5515i) q^{60} +(1.41589 + 4.35765i) q^{61} +(-3.85864 + 24.3625i) q^{62} +(5.55886 - 3.43200i) q^{63} +(1.29743 + 1.78577i) q^{64} +(-4.61843 + 2.63418i) q^{65} +(-8.76993 + 11.5615i) q^{66} +(2.80979 + 0.445027i) q^{67} +(-3.35576 - 21.1874i) q^{68} +(9.44036 - 1.89416i) q^{69} +(6.75350 - 10.2808i) q^{70} +0.232686i q^{71} +(15.3549 - 9.48004i) q^{72} +(-7.21050 + 7.21050i) q^{73} +(3.13102 - 9.63629i) q^{74} +(8.52186 + 1.54205i) q^{75} +5.07948 q^{76} +(-4.59672 + 5.57083i) q^{77} +(-10.3948 + 0.425759i) q^{78} +(-6.64089 + 2.15776i) q^{79} +(7.89729 - 12.0220i) q^{80} +(4.13926 + 7.99165i) q^{81} +(-18.9962 - 3.00871i) q^{82} +(-4.68065 + 2.38491i) q^{83} +(14.4046 - 8.09853i) q^{84} +(9.51017 - 5.42426i) q^{85} +(-17.6817 - 24.3367i) q^{86} +(6.75782 - 10.1504i) q^{87} +(-12.6973 + 15.3880i) q^{88} +(-0.0432300 + 0.133048i) q^{89} +(13.4240 + 10.3417i) q^{90} -5.17794 q^{91} +(24.0555 - 3.81001i) q^{92} +(-16.2852 - 4.56364i) q^{93} +(28.0213 + 9.10466i) q^{94} +(0.916316 + 2.42510i) q^{95} +(6.37002 - 3.58134i) q^{96} +(-7.21489 + 14.1600i) q^{97} +(-5.08186 + 2.58934i) q^{98} +(-7.17703 - 6.89131i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) $ 928 * q - 8 * q^3 - 20 * q^4 - 2 * q^6 - 20 * q^7 - 10 * q^9	$ 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 20 q^{7} - 10 q^{9} - 8 q^{12} - 24 q^{13} + 26 q^{15} + 204 q^{16} + 2 q^{18} - 40 q^{19} - 12 q^{21} - 40 q^{22} + 40 q^{24} - 8 q^{25} - 14 q^{27} + 8 q^{28} - 26 q^{30} - 24 q^{31} - 12 q^{33} - 40 q^{34} - 34 q^{36} + 16 q^{37} - 60 q^{39} - 28 q^{40} - 26 q^{42} - 40 q^{43} - 28 q^{45} - 4 q^{46} - 36 q^{48} + 60 q^{49} - 12 q^{51} - 68 q^{52} - 80 q^{54} - 32 q^{55} + 30 q^{57} + 112 q^{58} - 80 q^{60} - 4 q^{61} - 14 q^{63} + 100 q^{64} - 30 q^{66} - 12 q^{67} - 110 q^{69} + 60 q^{70} - 138 q^{72} + 140 q^{73} - 86 q^{75} - 128 q^{76} + 20 q^{78} - 20 q^{79} + 18 q^{81} + 52 q^{82} - 10 q^{84} + 28 q^{85} + 44 q^{87} - 36 q^{88} - 184 q^{90} - 24 q^{91} - 98 q^{93} - 300 q^{94} + 14 q^{96} + 4 q^{97}+O(q^{100}) $ 928 * q - 8 * q^3 - 20 * q^4 - 2 * q^6 - 20 * q^7 - 10 * q^9 - 8 * q^12 - 24 * q^13 + 26 * q^15 + 204 * q^16 + 2 * q^18 - 40 * q^19 - 12 * q^21 - 40 * q^22 + 40 * q^24 - 8 * q^25 - 14 * q^27 + 8 * q^28 - 26 * q^30 - 24 * q^31 - 12 * q^33 - 40 * q^34 - 34 * q^36 + 16 * q^37 - 60 * q^39 - 28 * q^40 - 26 * q^42 - 40 * q^43 - 28 * q^45 - 4 * q^46 - 36 * q^48 + 60 * q^49 - 12 * q^51 - 68 * q^52 - 80 * q^54 - 32 * q^55 + 30 * q^57 + 112 * q^58 - 80 * q^60 - 4 * q^61 - 14 * q^63 + 100 * q^64 - 30 * q^66 - 12 * q^67 - 110 * q^69 + 60 * q^70 - 138 * q^72 + 140 * q^73 - 86 * q^75 - 128 * q^76 + 20 * q^78 - 20 * q^79 + 18 * q^81 + 52 * q^82 - 10 * q^84 + 28 * q^85 + 44 * q^87 - 36 * q^88 - 184 * q^90 - 24 * q^91 - 98 * q^93 - 300 * q^94 + 14 * q^96 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{17}{20}\right)$

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 $

$2$	−0.395170	+	2.49501i	−0.279428	+	1.76424i	0.304579	+	0.952487i	$0.401484\pi$
$2$	−0.395170	+	2.49501i	−0.279428	+	1.76424i	−0.584006	+	0.811749i	$0.698516\pi$
$3$	−1.66780	−	0.467371i	−0.962906	−	0.269837i
$3$	−1.66780	−	0.467371i	−0.962906	−	0.269837i
$4$	−4.16679	−	1.35387i	−2.08339	−	0.676936i
$5$	−0.105290	−	2.23359i	−0.0470869	−	0.998891i
$5$	−0.105290	−	2.23359i	−0.0470869	−	0.998891i
$6$	1.82516	−	3.97649i	0.745118	−	1.62339i
$7$	0.988634	−	1.94030i	0.373669	−	0.733366i	−0.625222	−	0.780447i	$-0.714992\pi$
$7$	0.988634	−	1.94030i	0.373669	−	0.733366i	0.998891	+	0.0470806i	$0.0149918\pi$
$8$	2.73085	−	5.35960i	0.965502	−	1.89490i
$9$	2.56313	+	1.55896i	0.854376	+	0.519655i
$10$	5.61442	+	0.619949i	1.77544	+	0.196045i
$11$	−3.23766	−	0.719398i	−0.976192	−	0.216907i
$11$	−3.23766	−	0.719398i	−0.976192	−	0.216907i
$12$	6.31662	+	4.20542i	1.82345	+	1.21400i
$13$	−1.07948	−	2.11860i	−0.299394	−	0.587595i	0.691478	−	0.722397i	$-0.256960\pi$
$13$	−1.07948	−	2.11860i	−0.299394	−	0.587595i	−0.990872	+	0.134803i	$0.956960\pi$
$14$	4.45039	+	3.23340i	1.18942	+	0.864162i
$15$	−0.868311	+	3.77439i	−0.224197	+	0.974544i
$16$	5.20412	+	3.78102i	1.30103	+	0.945254i
$17$	2.22285	+	4.36258i	0.539120	+	1.05808i	0.986504	+	0.163740i	$0.0523557\pi$
$17$	2.22285	+	4.36258i	0.539120	+	1.05808i	−0.447384	+	0.894342i	$0.647644\pi$
$18$	−4.90250	+	5.77897i	−1.15553	+	1.36212i
$19$	−1.10263	+	0.358267i	−0.252961	+	0.0821920i	−0.432753	−	0.901513i	$-0.642458\pi$
$19$	−1.10263	+	0.358267i	−0.252961	+	0.0821920i	0.179792	+	0.983705i	$0.442458\pi$
$20$	−2.58527	+	9.44943i	−0.578084	+	2.11296i
$21$	−2.55569	+	2.77398i	−0.557697	+	0.605333i
$22$	3.07433	−	7.79371i	0.655450	−	1.66162i
$23$	−4.95313	+	2.52374i	−1.03280	+	0.526237i	−0.886367	−	0.462984i	$-0.846779\pi$
$23$	−4.95313	+	2.52374i	−1.03280	+	0.526237i	−0.146432	+	0.989221i	$0.546779\pi$
$24$	−7.05944	+	7.66243i	−1.44100	+	1.56409i
$25$	−4.97783	+	0.470347i	−0.995566	+	0.0940694i
$26$	5.71251	−	1.85611i	1.12031	−	0.364012i
$27$	−3.54618	−	3.79798i	−0.682462	−	0.730921i
$28$	−6.74635	+	6.74635i	−1.27494	+	1.27494i
$29$	−2.17558	+	6.69574i	−0.403995	+	1.24337i	0.517737	+	0.855540i	$0.326774\pi$
$29$	−2.17558	+	6.69574i	−0.403995	+	1.24337i	−0.921732	+	0.387828i	$0.873226\pi$
$30$	−9.07400	−	3.65797i	−1.65668	−	0.667851i
$31$	9.76449			1.75375			0.876877	−	0.480714i	$-0.159623\pi$
$31$	9.76449			1.75375			0.876877	+	0.480714i	$0.159623\pi$
$32$	−2.98337	+	2.98337i	−0.527391	+	0.527391i
$33$	5.06356	+	2.71300i	0.881452	+	0.472273i
$34$	−11.7631	+	3.82206i	−2.01735	+	0.655477i
$35$	−4.43793	−	2.00391i	−0.750147	−	0.338722i
$36$	−8.56938	−	9.96602i	−1.42823	−	1.66100i
$37$	−3.96161	−	0.627457i	−0.651285	−	0.103153i	−0.177955	−	0.984039i	$-0.556948\pi$
$37$	−3.96161	−	0.627457i	−0.651285	−	0.103153i	−0.473330	+	0.880885i	$0.656948\pi$
$38$	−0.458151	−	2.89265i	−0.0743219	−	0.469250i
$39$	0.810189	+	4.03793i	0.129734	+	0.646586i
$40$	−12.2587	−	5.53529i	−1.93826	−	0.875206i
$41$			7.61370i			1.18906i	0.804074	+	0.594530i	$0.202662\pi$
$41$			7.61370i			1.18906i	−0.804074	+	0.594530i	$0.797338\pi$
$42$	−5.91118	−	7.47266i	−0.912115	−	1.15306i
$43$	−8.42050	+	8.42050i	−1.28411	+	1.28411i	−0.345809	+	0.938305i	$0.612396\pi$
$43$	−8.42050	+	8.42050i	−1.28411	+	1.28411i	−0.938305	+	0.345809i	$0.887604\pi$
$44$	12.5167	+	7.38096i	1.88696	+	1.11272i
$45$	3.21221	−	5.88912i	0.478848	−	0.877898i
$46$	−4.33943	−	13.3554i	−0.639814	−	1.96915i
$47$	1.82458	−	11.5199i	0.266142	−	1.68035i	−0.386190	−	0.922419i	$-0.626209\pi$
$47$	1.82458	−	11.5199i	0.266142	−	1.68035i	0.652331	−	0.757934i	$-0.273791\pi$
$48$	−6.91231	−	8.73824i	−0.997706	−	1.26126i
$49$	1.32712	+	1.82662i	0.189588	+	0.260945i
$50$	0.793571	−	12.6056i	0.112228	−	1.78270i
$51$	−1.66833	−	8.31482i	−0.233612	−	1.16431i
$52$	1.62966	+	10.2892i	0.225993	+	1.42686i
$53$	3.28243	−	6.44214i	0.450877	−	0.884895i	−0.547952	−	0.836510i	$-0.684592\pi$
$53$	3.28243	−	6.44214i	0.450877	−	0.884895i	0.998829	−	0.0483856i	$-0.0154076\pi$
$54$	10.8773	−	7.34689i	1.48022	−	0.999786i
$55$	−1.26595	+	7.30735i	−0.170700	+	0.985323i
$56$	−7.69944	−	10.5974i	−1.02888	−	1.41613i
$57$	2.00641	−	0.0821803i	0.265756	−	0.0108850i
$58$	−15.8462	−	8.07404i	−2.08071	−	1.06017i
$59$	−1.40880	+	1.02355i	−0.183410	+	0.133255i	−0.675702	−	0.737175i	$-0.736159\pi$
$59$	−1.40880	+	1.02355i	−0.183410	+	0.133255i	0.492292	+	0.870430i	$0.336159\pi$
$60$	8.72811	−	14.5515i	1.12679	−	1.87859i
$61$	1.41589	+	4.35765i	0.181286	+	0.557940i	0.999865	−	0.0164541i	$-0.00523775\pi$
$61$	1.41589	+	4.35765i	0.181286	+	0.557940i	−0.818579	+	0.574394i	$0.805238\pi$
$62$	−3.85864	+	24.3625i	−0.490047	+	3.09404i
$63$	5.55886	−	3.43200i	0.700351	−	0.432392i
$64$	1.29743	+	1.78577i	0.162179	+	0.223221i
$65$	−4.61843	+	2.63418i	−0.572845	+	0.326730i
$66$	−8.76993	+	11.5615i	−1.07950	+	1.42312i
$67$	2.80979	+	0.445027i	0.343271	+	0.0543687i	0.325690	−	0.945477i	$-0.394404\pi$
$67$	2.80979	+	0.445027i	0.343271	+	0.0543687i	0.0175809	+	0.999845i	$0.494404\pi$
$68$	−3.35576	−	21.1874i	−0.406945	−	2.56935i
$69$	9.44036	−	1.89416i	1.13649	−	0.228030i
$70$	6.75350	−	10.2808i	0.807198	−	1.22879i
$71$			0.232686i			0.0276147i	0.999905	+	0.0138073i	$0.00439515\pi$
$71$			0.232686i			0.0276147i	−0.999905	+	0.0138073i	$0.995605\pi$
$72$	15.3549	−	9.48004i	1.80960	−	1.11723i
$73$	−7.21050	+	7.21050i	−0.843925	+	0.843925i	−0.989367	−	0.145442i	$-0.953540\pi$
$73$	−7.21050	+	7.21050i	−0.843925	+	0.843925i	0.145442	+	0.989367i	$0.453540\pi$
$74$	3.13102	−	9.63629i	0.363974	−	1.12020i
$75$	8.52186	+	1.54205i	0.984020	+	0.178060i
$76$	5.07948			0.582656
$77$	−4.59672	+	5.57083i	−0.523844	+	0.634855i
$78$	−10.3948	+	0.425759i	−1.17698	+	0.0482077i
$79$	−6.64089	+	2.15776i	−0.747159	+	0.242767i	−0.657758	−	0.753229i	$-0.728495\pi$
$79$	−6.64089	+	2.15776i	−0.747159	+	0.242767i	−0.0894006	+	0.995996i	$0.528495\pi$
$80$	7.89729	−	12.0220i	0.882944	−	1.34410i
$81$	4.13926	+	7.99165i	0.459918	+	0.887961i
$82$	−18.9962	−	3.00871i	−2.09778	−	0.332256i
$83$	−4.68065	+	2.38491i	−0.513769	+	0.261778i	−0.691597	−	0.722283i	$-0.743093\pi$
$83$	−4.68065	+	2.38491i	−0.513769	+	0.261778i	0.177829	+	0.984061i	$0.443093\pi$
$84$	14.4046	−	8.09853i	1.57167	−	0.883622i
$85$	9.51017	−	5.42426i	1.03152	−	0.588343i
$86$	−17.6817	−	24.3367i	−1.90666	−	2.62430i
$87$	6.75782	−	10.1504i	0.724515	−	1.08823i
$88$	−12.6973	+	15.3880i	−1.35353	+	1.64037i
$89$	−0.0432300	+	0.133048i	−0.00458237	+	0.0141031i	−0.953322	−	0.301957i	$-0.902360\pi$
$89$	−0.0432300	+	0.133048i	−0.00458237	+	0.0141031i	0.948739	+	0.316060i	$0.102360\pi$
$90$	13.4240	+	10.3417i	1.41502	+	1.09011i
$91$	−5.17794			−0.542796
$92$	24.0555	−	3.81001i	2.50796	−	0.397221i
$93$	−16.2852	−	4.56364i	−1.68870	−	0.473227i
$94$	28.0213	+	9.10466i	2.89017	+	0.939074i
$95$	0.916316	+	2.42510i	0.0940120	+	0.248810i
$96$	6.37002	−	3.58134i	0.650137	−	0.365519i
$97$	−7.21489	+	14.1600i	−0.732561	+	1.43773i	0.160145	+	0.987093i	$0.448804\pi$
$97$	−7.21489	+	14.1600i	−0.732561	+	1.43773i	−0.892706	+	0.450639i	$0.851196\pi$
$98$	−5.08186	+	2.58934i	−0.513345	+	0.261563i
$99$	−7.17703	−	6.89131i	−0.721319	−	0.692603i
$100$	21.3783	+	4.77950i	2.13783	+	0.477950i
$101$	−1.40541	+	1.93438i	−0.139844	+	0.192478i	−0.873194	−	0.487372i	$-0.837955\pi$
$101$	−1.40541	+	1.93438i	−0.139844	+	0.192478i	0.733351	+	0.679851i	$0.237955\pi$
$102$	21.4048	−	0.876715i	2.11939	−	0.0868077i
$103$	−3.59235	−	7.05038i	−0.353965	−	0.694694i	0.643531	−	0.765420i	$-0.277469\pi$
$103$	−3.59235	−	7.05038i	−0.353965	−	0.694694i	−0.997496	+	0.0707253i	$0.977469\pi$
$104$	−14.3028			−1.40250
$105$	6.46503	+	5.41628i	0.630922	+	0.528575i
$106$	14.7761	+	10.7354i	1.43518	+	1.04272i
$107$	−0.315401	−	0.619009i	−0.0304909	−	0.0598418i	0.875259	−	0.483655i	$-0.160691\pi$
$107$	−0.315401	−	0.619009i	−0.0304909	−	0.0598418i	−0.905749	+	0.423814i	$0.860691\pi$
$108$	9.63420	+	20.6264i	0.927052	+	1.98478i
$109$	3.56169	−	1.15726i	0.341148	−	0.110846i	−0.133432	−	0.991058i	$-0.542600\pi$
$109$	3.56169	−	1.15726i	0.341148	−	0.110846i	0.474580	+	0.880212i	$0.342600\pi$
$110$	−17.7316	−	6.04619i	−1.69064	−	0.576482i
$111$	6.31393	+	2.89802i	0.599291	+	0.275067i
$112$	12.4813	−	6.35954i	1.17937	−	0.600920i
$113$	−0.854684	−	0.854684i	−0.0804019	−	0.0804019i	0.665762	−	0.746164i	$-0.268107\pi$
$113$	−0.854684	−	0.854684i	−0.0804019	−	0.0804019i	−0.746164	+	0.665762i	$0.768107\pi$
$114$	−0.587835	+	5.03849i	−0.0550558	+	0.471898i
$115$	6.15852	+	10.7975i	0.574285	+	1.00687i
$116$	18.1303	−	24.9543i	1.68336	−	2.31695i
$117$	0.535974	−	7.11312i	0.0495508	−	0.657609i
$118$	−1.99706	−	3.91945i	−0.183844	−	0.360814i
$119$	10.6623			0.977413
$120$	17.8580	+	14.9611i	1.63020	+	1.36576i
$121$	9.96493	+	4.65834i	0.905903	+	0.423485i
$122$	−11.4319	+	1.81063i	−1.03499	+	0.163927i
$123$	3.55842	−	12.6981i	0.320852	−	1.14495i
$124$	−40.6866	−	13.2199i	−3.65376	−	1.18718i
$125$	1.57467	+	11.0689i	0.140843	+	0.990032i
$126$	6.36618	+	15.2256i	0.567144	+	1.35641i
$127$	−8.09611	+	15.8895i	−0.718413	+	1.40997i	0.185671	+	0.982612i	$0.440554\pi$
$127$	−8.09611	+	15.8895i	−0.718413	+	1.40997i	−0.904085	+	0.427354i	$0.859446\pi$
$128$	−12.4867	+	6.36231i	−1.10368	+	0.562354i
$129$	17.9792	−	10.1082i	1.58298	−	0.889980i
$130$	−4.74724	−	12.5640i	−0.416361	−	1.10193i
$131$	1.87821	+	2.58514i	0.164100	+	0.225865i	0.883146	−	0.469098i	$-0.155421\pi$
$131$	1.87821	+	2.58514i	0.164100	+	0.225865i	−0.719046	+	0.694963i	$0.755421\pi$
$132$	−17.4257	−	18.1599i	−1.51671	−	1.58062i
$133$	−0.394953	+	2.49364i	−0.0342468	+	0.216226i
$134$	−2.22069	+	6.83459i	−0.191839	+	0.590418i
$135$	−8.10974	+	8.32059i	−0.697975	+	0.716122i
$136$	29.4520			2.52548
$137$	−9.24642	+	1.46449i	−0.789975	+	0.125120i	−0.538368	−	0.842710i	$-0.680959\pi$
$137$	−9.24642	+	1.46449i	−0.789975	+	0.125120i	−0.251607	+	0.967830i	$0.580959\pi$
$138$	0.995392	+	24.3023i	0.0847334	+	2.06875i
$139$		−	14.1197i		−	1.19762i	−0.800891	−	0.598810i	$-0.795640\pi$
$139$		−	14.1197i		−	1.19762i	0.800891	−	0.598810i	$-0.204360\pi$
$140$	15.7789	+	14.3582i	1.33356	+	1.21349i
$141$	−8.42711	+	18.3602i	−0.709690	+	1.54621i
$142$	−0.580552	−	0.0919504i	−0.0487188	−	0.00771631i
$143$	1.97088	+	7.63590i	0.164813	+	0.638546i
$144$	7.44437	+	17.8043i	0.620364	+	1.48369i
$145$	15.1846	+	4.15435i	1.26101	+	0.345000i
$146$	−15.1409	−	20.8396i	−1.25307	−	1.72470i
$147$	−1.35966	−	3.66669i	−0.112143	−	0.302424i
$148$	15.6577	+	7.97799i	1.28705	+	0.655787i
$149$	−0.445257	+	0.323498i	−0.0364769	+	0.0265020i	−0.605874	−	0.795560i	$-0.707177\pi$
$149$	−0.445257	+	0.323498i	−0.0364769	+	0.0265020i	0.569397	+	0.822062i	$0.307177\pi$
$150$	−7.21500	+	20.6527i	−0.589102	+	1.68629i
$151$	−0.857726	+	2.63981i	−0.0698007	+	0.214825i	−0.979872	−	0.199628i	$-0.936027\pi$
$151$	−0.857726	+	2.63981i	−0.0698007	+	0.214825i	0.910071	+	0.414452i	$0.136027\pi$
$152$	−1.09096	+	6.88804i	−0.0884884	+	0.558694i
$153$	−1.10367	+	14.6472i	−0.0892261	+	1.18416i
$154$	−12.0828	−	13.6703i	−0.973658	−	1.10158i
$155$	−1.02810	−	21.8098i	−0.0825789	−	1.75181i
$156$	2.09095	−	17.9221i	0.167410	−	1.43491i
$157$	−20.5382	+	10.4648i	−1.63913	+	0.835179i	−0.641446	+	0.767168i	$0.721665\pi$
$157$	−20.5382	+	10.4648i	−1.63913	+	0.835179i	−0.997685	+	0.0680108i	$0.978335\pi$
$158$	−2.75934	−	17.4218i	−0.219521	−	1.38600i
$159$	−8.48531	+	9.21010i	−0.672929	+	0.730408i
$160$	6.97774	+	6.34951i	0.551639	+	0.501973i
$161$			12.1056i			0.954058i
$162$	−21.5749	+	7.16942i	−1.69509	+	0.563283i
$163$	−5.08055	−	9.97114i	−0.397939	−	0.781000i	0.601906	−	0.798567i	$-0.294408\pi$
$163$	−5.08055	−	9.97114i	−0.397939	−	0.781000i	−0.999846	+	0.0175666i	$0.994408\pi$
$164$	10.3080	−	31.7247i	0.804917	−	2.47728i
$165$	5.52659	−	11.5956i	0.430244	−	0.902712i
$166$	−4.10072	−	12.6207i	−0.318277	−	0.979557i
$167$	14.0411	−	14.0411i	1.08653	−	1.08653i	0.0906497	−	0.995883i	$-0.471106\pi$
$167$	14.0411	−	14.0411i	1.08653	−	1.08653i	0.995883	−	0.0906497i	$-0.0288944\pi$
$168$	7.88824	+	21.2728i	0.608591	+	1.64123i
$169$	4.31801	−	5.94324i	0.332155	−	0.457172i
$170$	9.77543	+	25.8714i	0.749741	+	1.98425i
$171$	−3.38471	−	0.800679i	−0.258835	−	0.0612295i
$172$	46.4867	−	23.6862i	3.54458	−	1.80605i
$173$	−2.50470	−	15.8141i	−0.190429	−	1.20232i	−0.878881	−	0.477041i	$-0.841709\pi$
$173$	−2.50470	−	15.8141i	−0.190429	−	1.20232i	0.688452	−	0.725282i	$-0.258291\pi$
$174$	22.6547	+	20.8719i	1.71745	+	1.58230i
$175$	−4.00864	+	10.1235i	−0.303024	+	0.765265i
$176$	−14.1291	−	15.9855i	−1.06502	−	1.20495i
$177$	2.82798	−	1.04865i	0.212564	−	0.0788216i
$178$	−0.314873	−	0.160436i	−0.0236007	−	0.0120252i
$179$	−10.6937	+	7.76945i	−0.799287	+	0.580716i	−0.910705	−	0.413058i	$-0.864461\pi$
$179$	−10.6937	+	7.76945i	−0.799287	+	0.580716i	0.111418	+	0.993774i	$0.464461\pi$
$180$	−21.3577	+	20.1898i	−1.59191	+	1.50486i
$181$	−1.70358	+	5.24308i	−0.126626	+	0.389715i	−0.994194	−	0.107604i	$-0.965682\pi$
$181$	−1.70358	+	5.24308i	−0.126626	+	0.389715i	0.867568	+	0.497319i	$0.165682\pi$
$182$	2.04617	−	12.9190i	0.151672	−	0.957621i
$183$	−0.324780	−	7.92944i	−0.0240084	−	0.586161i
$184$			33.4388i			2.46514i
$185$	−0.984365	+	8.91467i	−0.0723720	+	0.655420i
$186$	17.8218	−	38.8284i	1.30675	−	2.84703i
$187$	−4.05840	−	15.7237i	−0.296779	−	1.14983i
$188$	−23.1991	+	45.5308i	−1.69197	+	3.32068i
$189$	−10.8751	+	3.12586i	−0.791047	+	0.227372i
$190$	−6.41275	+	1.32789i	−0.465230	+	0.0963350i
$191$	5.85179	+	8.05429i	0.423420	+	0.582788i	0.966427	−	0.256940i	$-0.0827143\pi$
$191$	5.85179	+	8.05429i	0.423420	+	0.582788i	−0.543007	+	0.839728i	$0.682714\pi$
$192$	−1.32925	−	3.58469i	−0.0959303	−	0.258702i
$193$	1.70784	−	10.7829i	0.122933	−	0.776168i	−0.846784	−	0.531937i	$-0.821464\pi$
$193$	1.70784	−	10.7829i	0.122933	−	0.776168i	0.969717	−	0.244231i	$-0.0785356\pi$
$194$	−32.4782	−	23.5968i	−2.33180	−	1.69415i
$195$	8.93376	−	2.23478i	0.639760	−	0.160036i
$196$	−3.05680	−	9.40787i	−0.218343	−	0.671991i
$197$	−4.18677	+	0.663119i	−0.298295	+	0.0472453i	−0.303788	−	0.952740i	$-0.598251\pi$
$197$	−4.18677	+	0.663119i	−0.298295	+	0.0472453i	0.00549311	+	0.999985i	$0.498251\pi$
$198$	20.0300	−	15.1835i	1.42347	−	1.07905i
$199$			3.36286i			0.238387i	0.992871	+	0.119193i	$0.0380308\pi$
$199$			3.36286i			0.238387i	−0.992871	+	0.119193i	$0.961969\pi$
$200$	−11.0728	+	27.9636i	−0.782968	+	1.97733i
$201$	−4.47818	−	2.05543i	−0.315867	−	0.144979i
$202$	−4.27092	−	4.27092i	−0.300501	−	0.300501i
$203$	10.8409	+	10.8409i	0.760883	+	0.760883i
$204$	−4.30564	+	36.9048i	−0.301455	+	2.58385i
$205$	17.0059	−	0.801643i	1.18774	−	0.0559892i
$206$	19.0103	−	6.17683i	1.32451	−	0.430360i
$207$	−16.6299	−	1.25307i	−1.15586	−	0.0870940i
$208$	2.39271	−	15.1070i	0.165905	−	1.04748i
$209$	3.82769	−	0.366716i	0.264767	−	0.0253663i
$210$	−16.0684	+	13.9899i	−1.10883	+	0.965397i
$211$	−8.53803	+	6.20324i	−0.587782	+	0.427049i	−0.841521	−	0.540224i	$-0.818340\pi$
$211$	−8.53803	+	6.20324i	−0.587782	+	0.427049i	0.253739	+	0.967273i	$0.418340\pi$
$212$	−22.3990	+	22.3990i	−1.53837	+	1.53837i
$213$	0.108750	−	0.388073i	0.00745146	−	0.0265904i
$214$	1.66907	−	0.542313i	0.114095	−	0.0370718i
$215$	19.6945	+	17.9213i	1.34315	+	1.22222i
$216$	−30.0397	+	8.63438i	−2.04394	+	0.587495i
$217$	9.65351	−	18.9461i	0.655323	−	1.28614i
$218$	1.47990	+	9.34375i	0.100232	+	0.632838i
$219$	15.3957	−	8.65571i	1.04034	−	0.584899i
$220$	15.1681	−	28.7343i	1.02264	−	1.93726i
$221$	6.84305	−	9.41866i	0.460314	−	0.633567i
$222$	−9.72565	+	14.6081i	−0.652743	+	0.980430i
$223$	12.8324	−	2.03245i	0.859321	−	0.136103i	0.288803	−	0.957388i	$-0.406743\pi$
$223$	12.8324	−	2.03245i	0.859321	−	0.136103i	0.570518	+	0.821285i	$0.306743\pi$
$224$	2.83919	+	8.73812i	0.189701	+	0.583840i
$225$	−13.4921	−	6.55470i	−0.899471	−	0.436980i
$226$	2.47019	−	1.79470i	0.164315	−	0.119382i
$227$	−7.85035	+	7.85035i	−0.521046	+	0.521046i	−0.917887	−	0.396841i	$-0.870106\pi$
$227$	−7.85035	+	7.85035i	−0.521046	+	0.521046i	0.396841	+	0.917887i	$0.370106\pi$
$228$	−8.47157	−	2.37400i	−0.561043	−	0.157222i
$229$	−5.34549	+	1.73686i	−0.353240	+	0.114775i	−0.480262	−	0.877125i	$-0.659458\pi$
$229$	−5.34549	+	1.73686i	−0.353240	+	0.114775i	0.127022	+	0.991900i	$0.459458\pi$
$230$	−29.3736	+	11.0987i	−1.93684	+	0.731826i
$231$	10.2701	−	7.14267i	0.675720	−	0.469953i
$232$	29.9453	+	29.9453i	1.96600	+	1.96600i
$233$	8.14550	+	8.14550i	0.533630	+	0.533630i	0.921651	−	0.388021i	$-0.126841\pi$
$233$	8.14550	+	8.14550i	0.533630	+	0.533630i	−0.388021	+	0.921651i	$0.626841\pi$
$234$	17.5355	+	4.14815i	1.14633	+	0.271173i
$235$	−25.9229	−	2.86242i	−1.69102	−	0.186724i
$236$	7.25594	−	2.35760i	0.472321	−	0.153467i
$237$	12.0842	−	0.494953i	0.784951	−	0.0321506i
$238$	−4.21343	+	26.6026i	−0.273116	+	1.72439i
$239$	−10.5369	−	7.65552i	−0.681577	−	0.495195i	0.192304	−	0.981335i	$-0.438404\pi$
$239$	−10.5369	−	7.65552i	−0.681577	−	0.495195i	−0.873880	+	0.486141i	$0.838404\pi$
$240$	−18.7898	+	16.3593i	−1.21288	+	1.05599i
$241$	1.73938	+	5.35325i	0.112043	+	0.344833i	0.991319	−	0.131480i	$-0.0419729\pi$
$241$	1.73938	+	5.35325i	0.112043	+	0.344833i	−0.879276	+	0.476313i	$0.841973\pi$
$242$	−15.5604	+	23.0217i	−1.00026	+	1.47989i
$243$	−3.16841	−	15.2631i	−0.203253	−	0.979126i
$244$		−	20.0743i		−	1.28513i
$245$	3.94018	−	3.15655i	0.251729	−	0.201665i
$246$	30.2758	+	13.8962i	1.93031	+	0.885990i
$247$	1.94930	+	1.94930i	0.124031	+	0.124031i
$248$	26.6654	−	52.3338i	1.69325	−	3.32320i
$249$	8.92104	−	1.78996i	0.565348	−	0.113434i
$250$	−28.2392	−	0.445274i	−1.78601	−	0.0281616i
$251$	−5.44865	+	7.49943i	−0.343916	+	0.473360i	−0.945580	−	0.325390i	$-0.894505\pi$
$251$	−5.44865	+	7.49943i	−0.343916	+	0.473360i	0.601664	+	0.798749i	$0.294505\pi$
$252$	−27.8091	+	6.77445i	−1.75181	+	0.426750i
$253$	17.8521	−	4.60777i	1.12235	−	0.289688i
$254$	−36.4451	−	26.4789i	−2.28677	−	1.66143i
$255$	−18.3962	+	4.60182i	−1.15202	+	0.288177i
$256$	−9.57543	−	29.4701i	−0.598464	−	1.84188i
$257$	17.1335	+	8.72996i	1.06876	+	0.544560i	0.897658	−	0.440693i	$-0.145267\pi$
$257$	17.1335	+	8.72996i	1.06876	+	0.544560i	0.171101	+	0.985253i	$0.445267\pi$
$258$	18.1153	+	48.8528i	1.12781	+	3.04144i
$259$	−5.13404	+	7.06640i	−0.319014	+	0.439085i
$260$	22.8103	−	4.72333i	1.41464	−	0.292929i
$261$	−16.0147	+	13.7704i	−0.991285	+	0.852366i
$262$	−7.19215	+	3.66459i	−0.444333	+	0.226399i
$263$	3.89423	−	7.64286i	0.240129	−	0.471279i	−0.739218	−	0.673466i	$-0.764805\pi$
$263$	3.89423	−	7.64286i	0.240129	−	0.471279i	0.979347	+	0.202187i	$0.0648048\pi$
$264$	28.3684	−	19.7298i	1.74596	−	1.21429i
$265$	−14.7347	−	6.65331i	−0.905144	−	0.408710i
$266$	−6.06556	−	1.97082i	−0.371904	−	0.120839i
$267$	0.134282	−	0.201694i	0.00821792	−	0.0123434i
$268$	−11.1053	−	5.65843i	−0.678364	−	0.345644i
$269$	−0.789516	+	2.42988i	−0.0481377	+	0.148153i	−0.972236	−	0.234002i	$-0.924818\pi$
$269$	−0.789516	+	2.42988i	−0.0481377	+	0.148153i	0.924098	+	0.382154i	$0.124818\pi$
$270$	−17.5552	−	23.5219i	−1.06838	−	1.43150i
$271$	−7.30064	+	22.4691i	−0.443482	+	1.36490i	0.440657	+	0.897675i	$0.354745\pi$
$271$	−7.30064	+	22.4691i	−0.443482	+	1.36490i	−0.884140	+	0.467223i	$0.845255\pi$
$272$	−4.92703	+	31.1080i	−0.298745	+	1.88620i
$273$	8.63579	+	2.42002i	0.522662	+	0.146466i
$274$		−	23.6486i		−	1.42866i
$275$	16.4549	+	2.05821i	0.992268	+	0.124115i
$276$	−41.9004	−	4.88847i	−2.52211	−	0.294252i
$277$	25.1855	+	3.98900i	1.51325	+	0.239676i	0.857178	−	0.515021i	$-0.172216\pi$
$277$	25.1855	+	3.98900i	1.51325	+	0.239676i	0.656074	+	0.754696i	$0.272216\pi$
$278$	35.2288	+	5.57970i	2.11288	+	0.334648i
$279$	25.0277	+	15.2225i	1.49837	+	0.911347i
$280$	−22.8595	+	18.3132i	−1.36611	+	1.09442i
$281$	3.58411	+	1.16455i	0.213810	+	0.0694711i	0.413964	−	0.910293i	$-0.364144\pi$
$281$	3.58411	+	1.16455i	0.213810	+	0.0694711i	−0.200154	+	0.979765i	$0.564144\pi$
$282$	−42.4787	−	28.2811i	−2.52957	−	1.68411i
$283$	−2.74863	−	1.40050i	−0.163389	−	0.0832510i	0.370384	−	0.928879i	$-0.379226\pi$
$283$	−2.74863	−	1.40050i	−0.163389	−	0.0832510i	−0.533773	+	0.845628i	$0.679226\pi$
$284$	0.315026	−	0.969551i	0.0186934	−	0.0575323i
$285$	−0.394811	−	4.47285i	−0.0233866	−	0.264949i
$286$	−19.8305	+	1.89988i	−1.17260	+	0.112342i
$287$	14.7729	+	7.52716i	0.872016	+	0.444314i
$288$	−12.2977	+	2.99580i	−0.724652	+	0.176529i
$289$	−4.09873	+	5.64142i	−0.241102	+	0.331848i
$290$	−16.3656	+	36.2440i	−0.961023	+	2.12832i
$291$	18.6510	−	20.2441i	1.09334	−	1.18673i
$292$	39.8067	−	20.2825i	2.32951	−	1.18695i
$293$	5.87904	−	11.5383i	0.343457	−	0.674073i	−0.653074	−	0.757294i	$-0.726521\pi$
$293$	5.87904	−	11.5383i	0.343457	−	0.674073i	0.996531	+	0.0832213i	$0.0265208\pi$
$294$	9.68572	−	1.94339i	0.564883	−	0.113341i
$295$	2.43453	+	3.03891i	0.141744	+	0.176932i
$296$	−14.1815	+	19.5191i	−0.824282	+	1.13453i
$297$	8.74908	+	14.8477i	0.507673	+	0.861550i
$298$	−0.631178	−	1.23876i	−0.0365631	−	0.0717592i
$299$	10.6936	+	7.76937i	0.618428	+	0.449314i
$300$	−33.4211	−	17.9629i	−1.92957	−	1.03709i
$301$	8.01353	+	24.6631i	0.461892	+	1.42156i
$302$	−6.24739	−	3.18321i	−0.359497	−	0.183173i
$303$	3.24802	−	2.56932i	0.186594	−	0.147603i
$304$	−7.09284	−	2.30460i	−0.406802	−	0.132178i
$305$	9.58411	−	3.62132i	0.548785	−	0.207356i
$306$	−36.1087	−	8.54179i	−2.06420	−	0.488302i
$307$	14.6574	+	14.6574i	0.836544	+	0.836544i	0.988402	−	0.151859i	$-0.0485258\pi$
$307$	14.6574	+	14.6574i	0.836544	+	0.836544i	−0.151859	+	0.988402i	$0.548526\pi$
$308$	26.6957	−	16.9891i	1.52113	−	0.968044i
$309$	2.69618	+	13.4376i	0.153381	+	0.764438i
$310$	54.8220	+	6.05349i	3.11368	+	0.343815i
$311$	11.4926	−	15.8182i	0.651687	−	0.896970i	−0.347484	−	0.937686i	$-0.612964\pi$
$311$	11.4926	−	15.8182i	0.651687	−	0.896970i	0.999171	+	0.0407162i	$0.0129639\pi$
$312$	23.8542	+	6.68469i	1.35048	+	0.378446i
$313$	10.4367	−	1.65300i	0.589915	−	0.0934333i	0.145661	−	0.989335i	$-0.453469\pi$
$313$	10.4367	−	1.65300i	0.589915	−	0.0934333i	0.444253	+	0.895901i	$0.353469\pi$
$314$	−17.9935	−	55.3784i	−1.01543	−	3.12519i
$315$	−8.25097	−	12.0548i	−0.464890	−	0.679214i
$316$	30.5925			1.72096
$317$	13.9809	−	13.9809i	0.785245	−	0.785245i	−0.195466	−	0.980711i	$-0.562622\pi$
$317$	13.9809	−	13.9809i	0.785245	−	0.785245i	0.980711	+	0.195466i	$0.0626218\pi$
$318$	−19.6261	−	24.8105i	−1.10058	−	1.39130i
$319$	11.8607	−	20.1134i	0.664071	−	1.12614i
$320$	3.85206	−	3.08596i	0.215337	−	0.172510i
$321$	0.236719	+	1.17979i	0.0132124	+	0.0658496i
$322$	−30.2036	−	4.78379i	−1.68318	−	0.266590i
$323$	−4.01395	−	4.01395i	−0.223342	−	0.223342i
$324$	−6.42776	−	38.9035i	−0.357098	−	2.16131i
$325$	6.36995	+	10.0383i	0.353341	+	0.556825i
$326$	26.8858	−	8.73571i	1.48906	−	0.483826i
$327$	−6.48106	+	0.265456i	−0.358403	+	0.0146798i
$328$	40.8064	+	20.7919i	2.25315	+	1.14804i
$329$	−20.5483	−	14.9292i	−1.13286	−	0.823075i
$330$	26.7470	+	18.3711i	1.47238	+	1.01130i
$331$	−3.99322	+	2.90124i	−0.219487	+	0.159467i	−0.692096	−	0.721806i	$-0.743312\pi$
$331$	−3.99322	+	2.90124i	−0.219487	+	0.159467i	0.472609	+	0.881272i	$0.343312\pi$
$332$	22.7322	−	3.60042i	1.24759	−	0.197599i
$333$	−9.17594	−	7.78426i	−0.502838	−	0.426575i
$334$	29.4840	+	40.5813i	1.61329	+	2.22051i
$335$	0.698166	−	6.32277i	0.0381449	−	0.345450i
$336$	−23.7886	+	4.77306i	−1.29777	+	0.260392i
$337$	−26.5191	−	4.20021i	−1.44459	−	0.228800i	−0.615596	−	0.788062i	$-0.711085\pi$
$337$	−26.5191	−	4.20021i	−1.44459	−	0.228800i	−0.828991	+	0.559262i	$0.811085\pi$
$338$	13.1221	+	13.1221i	0.713746	+	0.713746i
$339$	1.02599	+	1.82490i	0.0557241	+	0.0991149i
$340$	−46.9706	+	9.72619i	−2.54734	+	0.527477i
$341$	−31.6141	−	7.02456i	−1.71200	−	0.380401i
$342$	3.33524	−	8.12848i	0.180349	−	0.439538i
$343$	19.9121	−	3.15377i	1.07515	−	0.170288i
$344$	22.1354	+	68.1256i	1.19346	+	3.67309i
$345$	−5.22474	−	20.8864i	−0.281291	−	1.12449i
$346$	40.4460			2.17439
$347$	−12.1640	+	12.1640i	−0.652998	+	0.652998i	−0.953714	−	0.300716i	$-0.902774\pi$
$347$	−12.1640	+	12.1640i	−0.652998	+	0.652998i	0.300716	+	0.953714i	$0.402774\pi$
$348$	−41.9007	+	33.1452i	−2.24611	+	1.77677i
$349$	14.6432	+	4.75787i	0.783834	+	0.254683i	0.673476	−	0.739209i	$-0.264800\pi$
$349$	14.6432	+	4.75787i	0.783834	+	0.254683i	0.110358	+	0.993892i	$0.464800\pi$
$350$	−23.6741	−	14.0021i	−1.26543	−	0.748443i
$351$	−4.21836	+	11.6128i	−0.225160	+	0.619845i
$352$	11.8054	−	7.51293i	0.629230	−	0.400440i
$353$	4.25674	+	26.8760i	0.226563	+	1.43047i	0.794436	+	0.607348i	$0.207767\pi$
$353$	4.25674	+	26.8760i	0.226563	+	1.43047i	−0.567872	+	0.823117i	$0.692233\pi$
$354$	1.49886	+	7.47023i	0.0796637	+	0.397038i
$355$	0.519724	−	0.0244994i	0.0275841	−	0.00130029i
$356$	0.360260	−	0.495856i	0.0190937	−	0.0262803i
$357$	−17.7826	−	4.98326i	−0.941157	−	0.263742i
$358$	−15.1590	−	29.7512i	−0.801177	−	1.57240i
$359$	13.1392	−	9.54618i	0.693460	−	0.503828i	−0.184336	−	0.982863i	$-0.559013\pi$
$359$	13.1392	−	9.54618i	0.693460	−	0.503828i	0.877796	+	0.479035i	$0.159013\pi$
$360$	−22.7912	−	33.2985i	−1.20120	−	1.75498i
$361$	−14.2839	+	10.3778i	−0.751783	+	0.546202i
$362$	−12.4083	−	6.32236i	−0.652167	−	0.332296i
$363$	−14.4424	−	12.4265i	−0.758028	−	0.652222i
$364$	21.5754	+	7.01027i	1.13086	+	0.367438i
$365$	16.8645	+	15.3461i	0.882727	+	0.803251i
$366$	19.9124	+	2.32315i	1.04084	+	0.121433i
$367$	−4.30623	−	27.1885i	−0.224783	−	1.41923i	−0.799398	−	0.600802i	$-0.794848\pi$
$367$	−4.30623	−	27.1885i	−0.224783	−	1.41923i	0.574614	−	0.818424i	$-0.305152\pi$
$368$	−35.3190	−	5.59398i	−1.84113	−	0.291606i
$369$	−11.8695	+	19.5149i	−0.617900	+	1.01590i
$370$	−21.8532	−	5.97881i	−1.13609	−	0.310824i
$371$	−9.25458	−	12.7378i	−0.480474	−	0.661315i
$372$	61.6786	+	41.0638i	3.19788	+	2.12906i
$373$	−2.92230	−	5.73533i	−0.151311	−	0.296964i	0.802892	−	0.596124i	$-0.203294\pi$
$373$	−2.92230	−	5.73533i	−0.151311	−	0.296964i	−0.954203	+	0.299160i	$0.903294\pi$
$374$	40.8345	−	3.91220i	2.11150	−	0.202295i
$375$	2.54703	−	19.1967i	0.131528	−	0.991312i
$376$	−56.7595	−	41.2382i	−2.92715	−	2.12670i
$377$	16.5341	−	2.61874i	0.851549	−	0.134872i
$378$	−3.50151	−	28.3687i	−0.180098	−	1.45913i
$379$		−	25.7060i		−	1.32043i	−0.751078	−	0.660213i	$-0.770466\pi$
$379$		−	25.7060i		−	1.32043i	0.751078	−	0.660213i	$-0.229534\pi$
$380$	−0.534816	−	11.3455i	−0.0274355	−	0.582010i
$381$	20.9290	−	22.7167i	1.07223	−	1.16381i
$382$	−22.4080	+	11.4174i	−1.14649	+	0.584167i
$383$	−18.6767	−	18.6767i	−0.954337	−	0.954337i	0.0446648	−	0.999002i	$-0.485778\pi$
$383$	−18.6767	−	18.6767i	−0.954337	−	0.954337i	−0.999002	+	0.0446648i	$0.985778\pi$
$384$	23.7990	−	4.77514i	1.21449	−	0.243681i
$385$	12.9269	+	9.68062i	0.658817	+	0.493370i
$386$	26.2285	+	8.52214i	1.33499	+	0.433766i
$387$	−34.7101	+	8.45557i	−1.76441	+	0.429821i
$388$	49.2338	−	49.2338i	2.49947	−	2.49947i
$389$	18.5131			0.938653			0.469326	−	0.883025i	$-0.344497\pi$
$389$	18.5131			0.938653			0.469326	+	0.883025i	$0.344497\pi$
$390$	2.04544	+	23.1729i	0.103575	+	1.17341i
$391$	−22.0201	−	15.9985i	−1.11360	−	0.809081i
$392$	13.4141	−	2.12458i	0.677514	−	0.107308i
$393$	−1.92427	−	5.18932i	−0.0970666	−	0.261767i
$394$		−	10.7081i		−	0.539464i
$395$	5.51876	+	14.6058i	0.277679	+	0.734899i
$396$	20.5752	+	38.4314i	1.03394	+	1.93125i
$397$	0.180600	+	1.14026i	0.00906405	+	0.0572282i	0.991806	−	0.127755i	$-0.0407770\pi$
$397$	0.180600	+	1.14026i	0.00906405	+	0.0572282i	−0.982742	+	0.184983i	$0.940777\pi$
$398$	−8.39035	−	1.32890i	−0.420570	−	0.0666118i
$399$	1.82416	−	3.97430i	0.0913220	−	0.198964i
$400$	−27.6836	−	16.3735i	−1.38418	−	0.818675i
$401$	−10.8529	−	14.9377i	−0.541968	−	0.745955i	0.446927	−	0.894570i	$-0.352518\pi$
$401$	−10.8529	−	14.9377i	−0.541968	−	0.745955i	−0.988895	+	0.148615i	$0.952518\pi$
$402$	6.89796	−	10.3609i	0.344039	−	0.516752i
$403$	−10.5406	−	20.6871i	−0.525064	−	1.03050i
$404$	8.47495	−	6.15741i	0.421645	−	0.306343i
$405$	17.4142	−	10.0868i	0.865320	−	0.501219i
$406$	−31.3322	+	22.7642i	−1.55499	+	1.12977i
$407$	12.3750	+	4.88147i	0.613405	+	0.241966i
$408$	−49.1200	−	13.7650i	−2.43180	−	0.681468i
$409$	−24.5250	−	7.96866i	−1.21268	−	0.394025i	−0.368271	−	0.929719i	$-0.620050\pi$
$409$	−24.5250	−	7.96866i	−1.21268	−	0.394025i	−0.844412	+	0.535694i	$0.820050\pi$
$410$	−4.72011	+	42.7465i	−0.233109	+	2.11110i
$411$	16.1057	+	1.87903i	0.794434	+	0.0926856i
$412$	5.42324	+	34.2410i	0.267184	+	1.68693i
$413$	0.593217	+	3.74542i	0.0291903	+	0.184300i
$414$	9.69806	−	40.9966i	0.476634	−	2.01487i
$415$	5.81974	+	10.2035i	0.285680	+	0.500872i
$416$	9.54108	+	3.10008i	0.467790	+	0.151994i
$417$	−6.59915	+	23.5489i	−0.323162	+	1.15320i
$418$	−0.597628	+	9.69502i	−0.0292310	+	0.474199i
$419$	−22.4786	+	16.3317i	−1.09815	+	0.797853i	−0.980757	−	0.195232i	$-0.937454\pi$
$419$	−22.4786	+	16.3317i	−1.09815	+	0.797853i	−0.117394	+	0.993085i	$0.537454\pi$
$420$	−19.6054	−	31.3213i	−0.956647	−	1.52832i
$421$	−8.99888	+	6.53807i	−0.438579	+	0.318646i	−0.785070	−	0.619407i	$-0.787373\pi$
$421$	−8.99888	+	6.53807i	−0.438579	+	0.318646i	0.346491	+	0.938053i	$0.387373\pi$
$422$	−12.1032	−	23.7538i	−0.589173	−	1.15632i
$423$	22.6358	−	26.6826i	1.10059	−	1.29735i
$424$	−25.5634	−	35.1850i	−1.24147	−	1.70874i
$425$	−13.1169	−	20.6707i	−0.636262	−	1.00268i
$426$	0.925271	+	0.424688i	0.0448295	+	0.0205762i
$427$	9.85496	+	1.56087i	0.476915	+	0.0755359i
$428$	0.476149	+	3.00629i	0.0230156	+	0.145314i
$429$	0.281756	−	13.6563i	0.0136033	−	0.659332i
$430$	−52.4965	+	42.0560i	−2.53161	+	2.02812i
$431$		−	16.6908i		−	0.803968i	−0.915647	−	0.401984i	$-0.868321\pi$
$431$		−	16.6908i		−	0.803968i	0.915647	−	0.401984i	$-0.131679\pi$
$432$	−4.09454	−	33.1733i	−0.196999	−	1.59605i
$433$	−23.2958	+	3.68969i	−1.11953	+	0.177315i	−0.688649	−	0.725095i	$-0.741796\pi$
$433$	−23.2958	+	3.68969i	−1.11953	+	0.177315i	−0.430877	+	0.902411i	$0.641796\pi$
$434$	43.4558	+	31.5725i	2.08595	+	1.51553i
$435$	−23.3833	−	14.0255i	−1.12114	−	0.672470i
$436$	−16.4076			−0.785780
$437$	4.55730	−	4.55730i	0.218005	−	0.218005i
$438$	15.5121	+	41.8328i	0.741199	+	1.99885i
$439$	−19.1220	−	6.21310i	−0.912642	−	0.296535i	−0.185197	−	0.982701i	$-0.559292\pi$
$439$	−19.1220	−	6.21310i	−0.912642	−	0.296535i	−0.727445	+	0.686166i	$0.759292\pi$
$440$	35.7074	+	26.7403i	1.70228	+	1.27479i
$441$	0.553937	+	6.75078i	0.0263779	+	0.321466i
$442$	20.7954	+	20.7954i	0.989138	+	0.989138i
$443$	−33.5044	+	17.0713i	−1.59184	+	0.811084i	−0.591855	+	0.806044i	$0.701604\pi$
$443$	−33.5044	+	17.0713i	−1.59184	+	0.811084i	−0.999987	+	0.00503973i	$0.998396\pi$
$444$	−22.3853	−	20.6237i	−1.06236	−	0.978756i
$445$	0.301726	+	0.0825493i	0.0143032	+	0.00391321i
$446$			32.8201i			1.55408i
$447$	0.893794	−	0.331431i	0.0422750	−	0.0156761i
$448$	4.74762	−	0.751949i	0.224304	−	0.0355262i
$449$	−2.46005	−	1.78733i	−0.116097	−	0.0843492i	0.528222	−	0.849106i	$-0.322859\pi$
$449$	−2.46005	−	1.78733i	−0.116097	−	0.0843492i	−0.644319	+	0.764757i	$0.722859\pi$
$450$	21.6857	−	31.0726i	1.02227	−	1.46478i
$451$	5.47728	−	24.6506i	0.257915	−	1.16075i
$452$	2.40416	+	4.71842i	0.113082	+	0.221936i
$453$	2.66429	−	4.00180i	0.125179	−	0.188021i
$454$	−16.4844	−	22.6889i	−0.773653	−	1.06484i
$455$	0.545184	+	11.5654i	0.0255586	+	0.542194i
$456$	5.03877	−	10.9780i	0.235962	−	0.514092i
$457$	12.1525	+	1.92476i	0.568468	+	0.0900365i	0.434051	−	0.900888i	$-0.357084\pi$
$457$	12.1525	+	1.92476i	0.568468	+	0.0900365i	0.134417	+	0.990925i	$0.457084\pi$
$458$	−2.22109	−	14.0234i	−0.103785	−	0.655270i
$459$	8.68637	−	23.9128i	0.405445	−	1.11615i
$460$	−11.0428	−	53.3288i	−0.514872	−	2.48647i
$461$	−26.1581	−	8.49927i	−1.21830	−	0.395850i	−0.371839	−	0.928297i	$-0.621273\pi$
$461$	−26.1581	−	8.49927i	−1.21830	−	0.395850i	−0.846463	+	0.532447i	$0.821273\pi$
$462$	13.7626	+	28.4464i	0.640294	+	1.32345i
$463$	−31.9034	−	16.2556i	−1.48268	−	0.755462i	−0.489492	−	0.872008i	$-0.662818\pi$
$463$	−31.9034	−	16.2556i	−1.48268	−	0.755462i	−0.993185	+	0.116546i	$0.962818\pi$
$464$	−36.6387	+	26.6195i	−1.70091	+	1.23578i
$465$	−8.47862	+	36.8550i	−0.393187	+	1.70911i
$466$	−23.5420	+	17.1042i	−1.09056	+	0.792338i
$467$	−0.0428370	−	0.0840724i	−0.00198226	−	0.00389041i	0.890013	−	0.455935i	$-0.150695\pi$
$467$	−0.0428370	−	0.0840724i	−0.00198226	−	0.00389041i	−0.891996	+	0.452044i	$0.850695\pi$
$468$	−11.8635	+	28.9132i	−0.548393	+	1.33652i
$469$	3.64134	−	5.01188i	0.168142	−	0.231427i
$470$	17.3857	−	63.5466i	0.801943	−	2.93119i
$471$	39.1447	−	7.85417i	1.80369	−	0.361901i
$472$	1.63861	+	10.3458i	0.0754232	+	0.476203i
$473$	33.3204	−	21.2051i	1.53208	−	0.975009i
$474$	−3.54039	+	30.3457i	−0.162616	+	1.39382i
$475$	5.32020	−	2.30201i	0.244108	−	0.105623i
$476$	−44.4276	−	14.4354i	−2.03634	−	0.661646i
$477$	18.4564	−	11.3948i	0.845058	−	0.521733i
$478$	23.2645	−	23.2645i	1.06409	−	1.06409i
$479$	23.0811			1.05460			0.527301	−	0.849679i	$-0.323204\pi$
$479$	23.0811			1.05460			0.527301	+	0.849679i	$0.323204\pi$
$480$	−8.66992	−	13.8509i	−0.395726	−	0.632205i
$481$	2.94715	+	9.07041i	0.134379	+	0.413575i
$482$	−14.0437	+	2.22431i	−0.639675	+	0.101315i
$483$	5.65782	−	20.1898i	0.257440	−	0.918668i
$484$	−35.2150	−	32.9015i	−1.60068	−	1.49552i
$485$	32.3873	+	14.6242i	1.47063	+	0.664050i
$486$	39.3335	−	1.87368i	1.78420	−	0.0849920i
$487$	−24.9130	−	24.9130i	−1.12892	−	1.12892i	−0.990353	−	0.138564i	$-0.955751\pi$
$487$	−24.9130	−	24.9130i	−1.12892	−	1.12892i	−0.138564	−	0.990353i	$-0.544249\pi$
$488$	27.2218	+	4.31151i	1.23227	+	0.195173i
$489$	3.81313	+	19.0044i	0.172436	+	0.859409i
$490$	6.31858	+	11.0782i	0.285444	+	0.500460i
$491$	−1.85733	−	2.55639i	−0.0838199	−	0.115368i	0.765048	−	0.643973i	$-0.222715\pi$
$491$	−1.85733	−	2.55639i	−0.0838199	−	0.115368i	−0.848868	+	0.528605i	$0.822715\pi$
$492$	−32.0188	+	48.0928i	−1.44352	+	2.16819i
$493$	−34.0467	+	5.39246i	−1.53339	+	0.242864i
$494$	−5.63381	+	4.09320i	−0.253477	+	0.184162i
$495$	−14.6367	+	16.7561i	−0.657870	+	0.753132i
$496$	50.8156	+	36.9197i	2.28169	+	1.65774i
$497$	0.451481	+	0.230041i	0.0202517	+	0.0103187i
$498$	0.940635	+	22.9654i	0.0421509	+	1.02910i
$499$	40.2224	−	13.0690i	1.80060	−	0.585050i	0.800698	−	0.599068i	$-0.204462\pi$
$499$	40.2224	−	13.0690i	1.80060	−	0.585050i	0.999902	+	0.0140173i	$0.00446200\pi$
$500$	8.42452	−	48.2536i	0.376756	−	2.15797i
$501$	−29.9802	+	16.8554i	−1.33942	+	0.753043i
$502$	−16.5580	−	16.5580i	−0.739019	−	0.739019i
$503$	−34.6409	−	5.48658i	−1.54456	−	0.244635i	−0.674761	−	0.738036i	$-0.735753\pi$
$503$	−34.6409	−	5.48658i	−1.54456	−	0.244635i	−0.869802	+	0.493402i	$0.835753\pi$
$504$	−3.21374	−	39.1656i	−0.143151	−	1.74457i
$505$	4.46859	+	2.93544i	0.198849	+	0.130625i
$506$	4.44178	+	46.3621i	0.197461	+	2.06105i
$507$	−9.97929	+	7.89403i	−0.443196	+	0.350586i
$508$	55.2471	−	55.2471i	2.45119	−	2.45119i
$509$	−45.0741			−1.99787			−0.998937	−	0.0460914i	$-0.985323\pi$
$509$	−45.0741			−1.99787			−0.998937	+	0.0460914i	$0.985323\pi$
$510$	−4.21192	−	47.7172i	−0.186507	−	2.11295i
$511$	6.86201	+	21.1191i	0.303558	+	0.934254i
$512$	49.6288	−	7.86043i	2.19330	−	0.347385i
$513$	5.27082	+	2.91729i	0.232712	+	0.128802i
$514$	−28.5520	+	39.2984i	−1.25937	+	1.73338i
$515$	−15.3694	+	8.76615i	−0.677257	+	0.386283i
$516$	−88.6009	+	17.7773i	−3.90043	+	0.782602i
$517$	−14.1948	+	35.9850i	−0.624285	+	1.58262i
$518$	−15.6019	−	15.6019i	−0.685508	−	0.685508i
$519$	−3.21369	+	27.5454i	−0.141065	+	1.20911i
$520$	1.50593	+	31.9465i	0.0660395	+	1.40095i
$521$	−4.20552	−	1.36646i	−0.184247	−	0.0598655i	0.215440	−	0.976517i	$-0.430881\pi$
$521$	−4.20552	−	1.36646i	−0.184247	−	0.0598655i	−0.399687	+	0.916652i	$0.630881\pi$
$522$	−28.0287	−	45.3984i	−1.22678	−	1.98704i
$523$	−9.31279	−	4.74511i	−0.407220	−	0.207489i	0.238368	−	0.971175i	$-0.423388\pi$
$523$	−9.31279	−	4.74511i	−0.407220	−	0.207489i	−0.645588	+	0.763686i	$0.723388\pi$
$524$	−4.32617	−	13.3146i	−0.188990	−	0.581650i
$525$	11.4170	−	15.0105i	0.498280	−	0.655111i
$526$	17.5301	+	12.7364i	0.764349	+	0.555332i
$527$	21.7050	+	42.5984i	0.945483	+	1.85562i
$528$	16.0935	+	33.2642i	0.700378	+	1.44764i
$529$	4.64513	−	6.39347i	0.201962	−	0.277977i
$530$	22.4228	−	34.1339i	0.973983	−	1.48268i
$531$	−5.20662	+	0.427231i	−0.225948	+	0.0185402i
$532$	5.02175	−	9.85573i	0.217720	−	0.427300i
$533$	16.1304	−	8.21885i	0.698685	−	0.355998i
$534$	0.450163	+	0.414737i	0.0194804	+	0.0179474i
$535$	−1.34940	+	0.769650i	−0.0583397	+	0.0332749i
$536$	10.0583	−	13.8440i	0.434452	−	0.597972i
$537$	21.4662	−	7.95997i	0.926336	−	0.343498i
$538$	−5.75058	−	2.93007i	−0.247925	−	0.126324i
$539$	−2.98269	−	6.86870i	−0.128473	−	0.295856i
$540$	45.0566	−	23.6906i	1.93893	−	1.01948i
$541$	−3.47834	+	10.7052i	−0.149546	+	0.460254i	−0.997567	−	0.0697072i	$-0.977794\pi$
$541$	−3.47834	+	10.7052i	−0.149546	+	0.460254i	0.848022	+	0.529961i	$0.177794\pi$
$542$	−53.1755	−	27.0942i	−2.28408	−	1.16380i
$543$	5.29170	−	7.94822i	0.227089	−	0.341091i
$544$	−19.6468	−	6.38363i	−0.842349	−	0.273696i
$545$	−2.95985	−	7.83349i	−0.126786	−	0.335550i
$546$	−9.45057	+	20.5900i	−0.404447	+	0.881172i
$547$	29.3632	+	4.65067i	1.25548	+	0.198848i	0.748514	−	0.663119i	$-0.230768\pi$
$547$	29.3632	+	4.65067i	1.25548	+	0.198848i	0.506964	+	0.861967i	$0.330768\pi$
$548$	40.5106	+	6.41625i	1.73053	+	0.274089i
$549$	−3.16432	+	13.3765i	−0.135050	+	0.570897i
$550$	−11.6377	+	40.2417i	−0.496235	+	1.71591i
$551$		−	8.16237i		−	0.347729i
$552$	15.6283	−	55.7692i	0.665184	−	2.37370i
$553$	−2.37871	+	15.0186i	−0.101153	+	0.638655i
$554$	−19.9052	+	61.2618i	−0.845689	+	2.60276i
$555$	5.80818	−	14.4078i	0.246544	−	0.611579i
$556$	−19.1163	+	58.8339i	−0.810712	+	2.49511i
$557$	35.9787	+	18.3321i	1.52447	+	0.776755i	0.997330	−	0.0730240i	$-0.0232650\pi$
$557$	35.9787	+	18.3321i	1.52447	+	0.776755i	0.527138	+	0.849780i	$0.323265\pi$
$558$	−47.8704	+	56.4287i	−2.02652	+	2.38882i
$559$	26.9295	+	8.74991i	1.13899	+	0.370082i
$560$	−15.5187	−	27.2085i	−0.655786	−	1.14977i
$561$	−0.580186	+	28.1208i	−0.0244955	+	1.18726i
$562$	−4.32189	+	8.48218i	−0.182308	+	0.357799i
$563$	−7.27962	+	3.70915i	−0.306800	+	0.156322i	−0.600611	−	0.799541i	$-0.705076\pi$
$563$	−7.27962	+	3.70915i	−0.306800	+	0.156322i	0.293812	+	0.955863i	$0.405076\pi$
$564$	59.9713	−	65.0938i	2.52525	−	2.74094i
$565$	−1.81902	+	1.99900i	−0.0765269	+	0.0840986i
$566$	4.58043	−	6.30442i	0.192530	−	0.264995i
$567$	19.5985	−	0.130604i	0.823058	−	0.00548487i
$568$	1.24710	+	0.635430i	0.0523272	+	0.0266620i
$569$	8.81124	+	27.1182i	0.369386	+	1.13685i	0.947189	+	0.320677i	$0.103910\pi$
$569$	8.81124	+	27.1182i	0.369386	+	1.13685i	−0.577802	+	0.816177i	$0.696090\pi$
$570$	11.3158	+	0.782481i	0.473967	+	0.0327745i
$571$	−11.1297	−	8.08617i	−0.465762	−	0.338396i	0.330025	−	0.943972i	$-0.392943\pi$
$571$	−11.1297	−	8.08617i	−0.465762	−	0.338396i	−0.795787	+	0.605576i	$0.792943\pi$
$572$	2.12578	−	34.4855i	0.0888834	−	1.44191i
$573$	−5.99528	−	16.1679i	−0.250456	−	0.675425i
$574$	−24.6181	+	33.8839i	−1.02754	+	1.41429i
$575$	23.4688	−	14.8925i	0.978716	−	0.621058i
$576$	0.541548	+	6.59980i	0.0225645	+	0.274992i
$577$	9.32467	−	18.3007i	0.388191	−	0.761868i	−0.611375	−	0.791341i	$-0.709383\pi$
$577$	9.32467	−	18.3007i	0.388191	−	0.761868i	0.999566	+	0.0294736i	$0.00938311\pi$
$578$	−12.4557	−	12.4557i	−0.518088	−	0.518088i
$579$	−7.88794	+	17.1855i	−0.327812	+	0.714205i
$580$	−57.6465	−	37.8683i	−2.39364	−	1.57239i
$581$			11.4397i			0.474599i
$582$	43.1388	+	54.5342i	1.78816	+	2.26052i
$583$	−15.2619	+	18.4961i	−0.632082	+	0.766030i
$584$	18.9546	+	58.3362i	0.784346	+	2.41397i
$585$	−15.9442	−	0.448207i	−0.659212	−	0.0185311i
$586$	26.4648	+	19.2278i	1.09325	+	0.794295i
$587$	3.30237	−	20.8503i	0.136303	−	0.860586i	−0.820879	−	0.571101i	$-0.806516\pi$
$587$	3.30237	−	20.8503i	0.136303	−	0.860586i	0.957183	−	0.289484i	$-0.0934837\pi$
$588$	0.701178	+	17.1191i	0.0289161	+	0.705981i
$589$	−10.7666	+	3.49829i	−0.443632	+	0.144145i
$590$	−8.54416	+	4.87328i	−0.351758	+	0.200630i
$591$	7.29263	+	0.850822i	0.299979	+	0.0349981i
$592$	−18.2443	−	18.2443i	−0.749835	−	0.749835i
$593$	−12.4175	−	12.4175i	−0.509925	−	0.509925i	0.404578	−	0.914503i	$-0.367418\pi$
$593$	−12.4175	−	12.4175i	−0.509925	−	0.509925i	−0.914503	+	0.404578i	$0.867418\pi$
$594$	−40.5024	+	15.9616i	−1.66184	+	0.654914i
$595$	−1.12263	−	23.8152i	−0.0460234	−	0.976329i
$596$	2.29327	−	0.745127i	0.0939358	−	0.0305216i
$597$	1.57170	−	5.60858i	0.0643254	−	0.229544i
$598$	−23.6104	+	23.6104i	−0.965503	+	0.965503i
$599$	−12.6465	+	9.18819i	−0.516720	+	0.375419i	−0.815367	−	0.578944i	$-0.803465\pi$
$599$	−12.6465	+	9.18819i	−0.516720	+	0.375419i	0.298647	+	0.954364i	$0.403465\pi$
$600$	31.5367	−	41.4627i	1.28748	−	1.69271i
$601$	9.18091	+	28.2559i	0.374497	+	1.15258i	0.943817	+	0.330467i	$0.107206\pi$
$601$	9.18091	+	28.2559i	0.374497	+	1.15258i	−0.569320	+	0.822116i	$0.692794\pi$
$602$	−64.7014	+	10.2477i	−2.63703	+	0.417665i
$603$	6.50808	+	5.52103i	0.265029	+	0.224834i
$604$	7.14792	−	9.83827i	0.290845	−	0.400314i
$605$	9.35560	−	22.7480i	0.380359	−	0.924839i
$606$	5.12695	+	9.11915i	0.208268	+	0.370440i
$607$	1.81170	+	11.4386i	0.0735347	+	0.464280i	0.996788	+	0.0800875i	$0.0255200\pi$
$607$	1.81170	+	11.4386i	0.0735347	+	0.464280i	−0.923253	+	0.384192i	$0.874480\pi$
$608$	2.22072	−	4.35841i	0.0900620	−	0.176757i
$609$	−13.0138	−	23.1472i	−0.527345	−	0.937973i
$610$	5.24786	+	25.3435i	0.212480	+	1.02613i
$611$	−26.3757	+	8.56999i	−1.06705	+	0.346705i
$612$	24.4292	−	59.5376i	0.987491	−	2.40666i
$613$	26.4084	−	26.4084i	1.06662	−	1.06662i	0.0690075	−	0.997616i	$-0.478017\pi$
$613$	26.4084	−	26.4084i	1.06662	−	1.06662i	0.997616	−	0.0690075i	$-0.0219832\pi$
$614$	−42.3626	+	30.7782i	−1.70961	+	1.24211i
$615$	−28.7371	−	6.61106i	−1.15879	−	0.266584i
$616$	17.3045	+	39.8497i	0.697217	+	1.60559i
$617$	1.29447	−	8.17298i	0.0521135	−	0.329032i	−0.947834	−	0.318765i	$-0.896732\pi$
$617$	1.29447	−	8.17298i	0.0521135	−	0.329032i	0.999947	−	0.0102667i	$-0.00326805\pi$
$618$	−34.5924	+	1.41686i	−1.39151	+	0.0569945i
$619$	−29.2330	+	9.49836i	−1.17497	+	0.381771i	−0.830496	−	0.557024i	$-0.811943\pi$
$619$	−29.2330	+	9.49836i	−1.17497	+	0.381771i	−0.344475	+	0.938795i	$0.611943\pi$
$620$	−25.2439	+	92.2689i	−1.01382	+	3.70561i
$621$	27.1498	+	9.86221i	1.08948	+	0.395757i
$622$	34.9251	+	34.9251i	1.40037	+	1.40037i
$623$	0.215415	+	0.215415i	0.00863043	+	0.00863043i
$624$	−11.0511	+	24.0772i	−0.442400	+	0.963860i
$625$	24.5575	−	4.68261i	0.982302	−	0.187305i
$626$			26.6927i			1.06686i
$627$	−6.55522	−	1.17734i	−0.261790	−	0.0470184i
$628$	99.7465	−	15.7983i	3.98032	−	0.630420i
$629$	−6.06872	−	18.6776i	−0.241976	−	0.744724i
$630$	33.3375	−	15.8225i	1.32820	−	0.630384i
$631$	−31.4208	−	22.8285i	−1.25084	−	0.908789i	−0.252571	−	0.967578i	$-0.581276\pi$
$631$	−31.4208	−	22.8285i	−1.25084	−	0.908789i	−0.998270	+	0.0587889i	$0.981276\pi$
$632$	−6.57058	+	41.4850i	−0.261364	+	1.65019i
$633$	17.1390	−	6.35536i	0.681213	−	0.252603i
$634$	29.3576	+	40.4072i	1.16594	+	1.60478i
$635$	36.3430	+	16.4104i	1.44223	+	0.651226i
$636$	47.8258	−	26.8885i	1.89642	−	1.06620i
$637$	2.43728	−	4.78343i	0.0965685	−	0.189526i
$638$	45.4962	+	37.5407i	1.80121	+	1.48625i
$639$	−0.362748	+	0.596403i	−0.0143501	+	0.0235933i
$640$	15.5255	+	27.2204i	0.613700	+	1.07598i
$641$			20.5476i			0.811582i	0.913966	+	0.405791i	$0.133004\pi$
$641$			20.5476i			0.811582i	−0.913966	+	0.405791i	$0.866996\pi$
$642$	−3.03714	+	0.124397i	−0.119866	+	0.00490957i
$643$	−3.44335	+	21.7405i	−0.135792	+	0.857360i	0.821914	+	0.569612i	$0.192906\pi$
$643$	−3.44335	+	21.7405i	−0.135792	+	0.857360i	−0.957706	+	0.287748i	$0.907094\pi$
$644$	16.3895	−	50.4416i	0.645836	−	1.98768i
$645$	−24.4706	−	39.0939i	−0.963531	−	1.53932i
$646$	11.6010	−	8.42864i	0.456436	−	0.331620i
$647$	2.71103	+	1.38134i	0.106582	+	0.0543060i	0.506469	−	0.862258i	$-0.330951\pi$
$647$	2.71103	+	1.38134i	0.106582	+	0.0543060i	−0.399887	+	0.916564i	$0.630951\pi$
$648$	54.1358	−	0.360762i	2.12665	−	0.0141721i
$649$	5.29757	−	2.30044i	0.207948	−	0.0903000i
$650$	−27.5629	+	11.9262i	−1.08110	+	0.467785i
$651$	−24.9550	+	27.0865i	−0.978063	+	1.06161i
$652$	7.66993	+	48.4261i	0.300378	+	1.89651i
$653$	5.27767	−	2.68911i	0.206531	−	0.105233i	−0.347665	−	0.937619i	$-0.613026\pi$
$653$	5.27767	−	2.68911i	0.206531	−	0.105233i	0.554197	+	0.832386i	$0.313026\pi$
$654$	1.89881	−	16.2752i	0.0742492	−	0.636410i
$655$	5.57638	−	4.46734i	0.217887	−	0.174554i
$656$	−28.7875	+	39.6226i	−1.12396	+	1.54700i
$657$	−29.7223	+	7.24053i	−1.15958	+	0.282480i
$658$	45.3686	−	45.3686i	1.76865	−	1.76865i
$659$	−4.23443	−	13.0322i	−0.164950	−	0.507664i	0.834083	−	0.551639i	$-0.185998\pi$
$659$	−4.23443	−	13.0322i	−0.164950	−	0.507664i	−0.999033	+	0.0439759i	$0.985998\pi$
$660$	−38.7270	+	40.8339i	−1.50745	+	1.58946i
$661$	11.1752	−	34.3938i	0.434665	−	1.33776i	−0.458764	−	0.888558i	$-0.651708\pi$
$661$	11.1752	−	34.3938i	0.434665	−	1.33776i	0.893429	−	0.449204i	$-0.148292\pi$
$662$	−5.66062	−	11.1096i	−0.220006	−	0.431787i
$663$	−15.8149	+	12.5102i	−0.614199	+	0.485856i
$664$			31.5993i			1.22629i
$665$	5.61134	+	0.619608i	0.217598	+	0.0240274i
$666$	23.0478	−	19.8179i	0.893086	−	0.767929i
$667$	−6.12242	−	38.6554i	−0.237061	−	1.49674i
$668$	−77.5161	+	39.4964i	−2.99919	+	1.52816i
$669$	−22.3518	−	2.60776i	−0.864171	−	0.100822i
$670$	15.4995	+	4.24050i	0.598797	+	0.163825i
$671$	−1.44928	−	15.1272i	−0.0559488	−	0.583979i
$672$	−0.651261	−	15.9004i	−0.0251229	−	0.613371i
$673$	−3.38276	+	21.3579i	−0.130396	+	0.823288i	0.832620	+	0.553844i	$0.186840\pi$
$673$	−3.38276	+	21.3579i	−0.130396	+	0.823288i	−0.963016	+	0.269444i	$0.913160\pi$
$674$	20.9591	−	64.5055i	0.807315	−	2.48466i
$675$	19.4386	+	17.2377i	0.748193	+	0.663481i
$676$	−26.0386	+	18.9182i	−1.00149	+	0.727622i
$677$	−7.87312	−	4.01156i	−0.302589	−	0.154177i	0.296103	−	0.955156i	$-0.404313\pi$
$677$	−7.87312	−	4.01156i	−0.302589	−	0.154177i	−0.598692	+	0.800979i	$0.704313\pi$
$678$	−4.95858	+	1.83871i	−0.190433	+	0.0706151i
$679$	20.3419	+	27.9982i	0.780649	+	1.07447i
$680$	−3.10098	−	65.7835i	−0.118917	−	2.52268i
$681$	16.7618	−	9.42380i	0.642315	−	0.361121i
$682$	30.0193	−	76.1016i	1.14950	−	2.91408i
$683$	0.866555	+	0.137249i	0.0331578	+	0.00525168i	0.172991	−	0.984923i	$-0.444657\pi$
$683$	0.866555	+	0.137249i	0.0331578	+	0.00525168i	−0.139834	+	0.990175i	$0.544657\pi$
$684$	13.0194	+	7.91873i	0.497808	+	0.302780i
$685$	4.24462	+	20.4985i	0.162178	+	0.783207i
$686$			50.9272i			1.94441i
$687$	9.72698	−	0.398405i	0.371107	−	0.0152001i
$688$	−75.6593	+	11.9833i	−2.88449	+	0.456858i
$689$	−17.1916			−0.654950
$690$	54.1765	−	4.78207i	2.06246	−	0.182050i
$691$	−0.302581	+	0.931249i	−0.0115107	+	0.0354264i	−0.956647	−	0.291250i	$-0.905929\pi$
$691$	−0.302581	+	0.931249i	−0.0115107	+	0.0354264i	0.945136	+	0.326677i	$0.105929\pi$
$692$	−10.9737	+	69.2850i	−0.417156	+	2.63382i
$693$	−20.4667	+	7.11264i	−0.777466	+	0.270187i
$694$	−25.5424	−	35.1561i	−0.969577	−	1.33451i
$695$	−31.5377	+	1.48666i	−1.19629	+	0.0563922i
$696$	−35.9473	−	63.9384i	−1.36258	−	2.42358i
$697$	−33.2154	+	16.9241i	−1.25812	+	0.641045i
$698$	−17.6575	+	34.6548i	−0.668346	+	1.31170i
$699$	−9.77812	−	17.3921i	−0.369842	−	0.657828i
$700$	30.4091	−	36.7553i	1.14935	−	1.38922i
$701$	−34.0135	−	11.0517i	−1.28467	−	0.417416i	−0.414449	−	0.910072i	$-0.636026\pi$
$701$	−34.0135	−	11.0517i	−1.28467	−	0.417416i	−0.870224	+	0.492657i	$0.836026\pi$
$702$	−27.3070	−	15.1139i	−1.03064	−	0.570437i
$703$	4.59299	−	0.727459i	0.173228	−	0.0274366i
$704$	−2.91598	−	6.71508i	−0.109900	−	0.253084i
$705$	41.8964	+	16.8895i	1.57791	+	0.636097i
$706$	−68.7380			−2.58699
$707$	2.36385	+	4.63932i	0.0889018	+	0.174480i
$708$	−13.2033	+	0.540793i	−0.496212	+	0.0203242i
$709$	21.6292	−	29.7700i	0.812301	−	1.11804i	−0.178664	−	0.983910i	$-0.557177\pi$
$709$	21.6292	−	29.7700i	0.812301	−	1.11804i	0.990964	−	0.134126i	$-0.0428226\pi$
$710$	−0.144253	+	1.30640i	−0.00541373	+	0.0490281i
$711$	−20.3853	−	4.82230i	−0.764510	−	0.180851i
$712$	0.595030	+	0.595030i	0.0222997	+	0.0222997i
$713$	−48.3648	+	24.6431i	−1.81128	+	0.922891i
$714$	19.4604	−	42.3986i	0.728288	−	1.58673i
$715$	16.8479	−	5.20612i	0.630077	−	0.194698i
$716$	55.0773	−	17.8957i	2.05834	−	0.668794i
$717$	13.9955	+	17.6925i	0.522673	+	0.660740i
$718$	18.6256	+	36.5547i	0.695100	+	1.36421i
$719$	8.36713	+	6.07908i	0.312041	+	0.226711i	0.732772	−	0.680474i	$-0.238226\pi$
$719$	8.36713	+	6.07908i	0.312041	+	0.226711i	−0.420731	+	0.907186i	$0.638226\pi$
$720$	38.9836	−	18.5023i	1.45283	−	0.689538i
$721$	−17.2314			−0.641731
$722$	−20.2482	−	39.7394i	−0.753561	−	1.47895i
$723$	−0.398983	−	9.74110i	−0.0148384	−	0.362275i
$724$	14.1969	−	19.5404i	0.527625	−	0.726213i
$725$	7.68033	−	34.3535i	0.285240	−	1.27586i
$726$	36.7114	−	31.1232i	1.36249	−	1.15509i
$727$	−44.7923	+	22.8228i	−1.66125	+	0.846451i	−0.666347	+	0.745641i	$0.732143\pi$
$727$	−44.7923	+	22.8228i	−1.66125	+	0.846451i	−0.994906	+	0.100809i	$0.967857\pi$
$728$	−14.1402	+	27.7517i	−0.524071	+	1.02855i
$729$	−1.84924	+	26.9366i	−0.0684903	+	0.997652i
$730$	−44.9529	+	36.0127i	−1.66378	+	1.33289i
$731$	−55.4526	−	18.0176i	−2.05099	−	0.666407i
$732$	−9.38216	+	33.4800i	−0.346774	+	1.23746i
$733$	41.0910	−	6.50818i	1.51773	−	0.240385i	0.658738	−	0.752372i	$-0.271091\pi$
$733$	41.0910	−	6.50818i	1.51773	−	0.240385i	0.858993	+	0.511987i	$0.171091\pi$
$734$	69.5371			2.56666
$735$	−8.04672	+	3.42298i	−0.296808	+	0.126259i
$736$	7.24776	−	22.3063i	0.267156	−	0.822221i
$737$	−8.77701	−	3.46221i	−0.323305	−	0.127532i
$738$	−43.9993	−	37.3261i	−1.61964	−	1.37399i
$739$	6.32395	+	8.70417i	0.232630	+	0.320188i	0.909334	−	0.416068i	$-0.136592\pi$
$739$	6.32395	+	8.70417i	0.232630	+	0.320188i	−0.676703	+	0.736256i	$0.736592\pi$
$740$	16.1710	−	35.8128i	0.594456	−	1.31651i
$741$	−2.34000	−	4.16208i	−0.0859619	−	0.152898i
$742$	35.4381	−	18.0566i	1.30097	−	0.662879i
$743$	14.6881	+	2.32636i	0.538853	+	0.0853459i	0.419928	−	0.907557i	$-0.362055\pi$
$743$	14.6881	+	2.32636i	0.538853	+	0.0853459i	0.118925	+	0.992903i	$0.462055\pi$
$744$	−68.9319	+	74.8197i	−2.52716	+	2.74302i
$745$	0.769442	+	0.960460i	0.0281902	+	0.0351885i
$746$	15.4645	−	5.02472i	0.566196	−	0.183968i
$747$	−15.7151	−	1.18413i	−0.574986	−	0.0433252i
$748$	−4.37737	+	71.0118i	−0.160052	+	2.59645i
$749$	−1.51288			−0.0552795
$750$	46.8893	+	13.9408i	1.71216	+	0.509047i
$751$	1.13212	−	3.48430i	0.0413116	−	0.127144i	−0.928274	−	0.371898i	$-0.878707\pi$
$751$	1.13212	−	3.48430i	0.0413116	−	0.127144i	0.969585	+	0.244754i	$0.0787072\pi$
$752$	53.0523	−	53.0523i	1.93462	−	1.93462i
$753$	12.5923	−	9.96102i	0.458889	−	0.363000i
$754$			42.2875i			1.54002i
$755$	5.98655	+	1.63786i	0.217873	+	0.0596079i
$756$	49.5462	+	1.69871i	1.80198	+	0.0617816i
$757$	6.45398	+	40.7488i	0.234574	+	1.48104i	0.770860	+	0.637004i	$0.219827\pi$
$757$	6.45398	+	40.7488i	0.234574	+	1.48104i	−0.536287	+	0.844036i	$0.680173\pi$
$758$	64.1365	+	10.1582i	2.32954	+	0.368964i
$759$	−31.9274	−	0.658724i	−1.15889	−	0.0239102i
$760$	15.4999	+	1.71151i	0.562240	+	0.0620830i
$761$	1.88723	+	2.59755i	0.0684120	+	0.0941610i	0.841852	−	0.539709i	$-0.181466\pi$
$761$	1.88723	+	2.59755i	0.0684120	+	0.0941610i	−0.773440	+	0.633870i	$0.781466\pi$
$762$	48.4077	+	61.1950i	1.75363	+	2.21686i
$763$	1.27576	−	8.05486i	0.0461858	−	0.291606i
$764$	−13.4787	−	41.4831i	−0.487641	−	1.50081i
$765$	32.8320	+	0.922938i	1.18704	+	0.0333689i
$766$	53.9791	−	39.2181i	1.95034	−	1.41701i
$767$	3.68928	+	1.87978i	0.133212	+	0.0678750i
$768$	2.19644	+	53.6256i	0.0792572	+	1.93505i
$769$	1.33418	+	1.83634i	0.0481118	+	0.0662202i	0.832395	−	0.554183i	$-0.186969\pi$
$769$	1.33418	+	1.83634i	0.0481118	+	0.0662202i	−0.784283	+	0.620403i	$0.786969\pi$
$770$	−29.2615	+	28.4273i	−1.05451	+	1.02445i
$771$	−24.4952	−	22.5676i	−0.882172	−	0.812751i
$772$	−21.7148	+	42.6178i	−0.781534	+	1.53385i
$773$	−2.53768	−	16.0223i	−0.0912739	−	0.576281i	−0.990361	−	0.138511i	$-0.955768\pi$
$773$	−2.53768	−	16.0223i	−0.0912739	−	0.576281i	0.899087	−	0.437770i	$-0.144232\pi$
$774$	−7.38031	−	89.9433i	−0.265280	−	3.23294i
$775$	−48.6060	+	4.59270i	−1.74598	+	0.164975i
$776$	56.1892	+	77.3378i	2.01708	+	2.77627i
$777$	11.8652	−	9.38586i	0.425662	−	0.336716i
$778$	−7.31584	+	46.1904i	−0.262286	+	1.65601i
$779$	−2.72773	−	8.39510i	−0.0977312	−	0.300786i
$780$	−40.2507	−	2.78331i	−1.44121	−	0.0996584i
$781$	0.167393	−	0.753357i	0.00598981	−	0.0269572i
$782$	48.6181	−	48.6181i	1.73858	−	1.73858i
$783$	33.1452	−	15.4815i	1.18451	−	0.553263i
$784$			14.5238i			0.518707i
$785$	25.5364	+	44.7722i	0.911434	+	1.59799i
$786$	13.7078	−	2.75040i	0.488941	−	0.0981036i
$787$	−3.11864	−	19.6903i	−0.111167	−	0.701884i	−0.978822	−	0.204715i	$-0.934373\pi$
$787$	−3.11864	−	19.6903i	−0.111167	−	0.701884i	0.867654	−	0.497168i	$-0.165627\pi$
$788$	18.3432	+	2.90527i	0.653448	+	0.103496i
$789$	−10.0669	+	10.9267i	−0.358390	+	0.389002i
$790$	−38.6225	+	7.99755i	−1.37413	+	0.284540i
$791$	−2.50332	+	0.813377i	−0.0890077	+	0.0289204i
$792$	−56.5341	+	19.6469i	−2.00885	+	0.698121i
$793$	7.70370	−	7.70370i	0.273567	−	0.273567i
$794$	−2.91633			−0.103497
$795$	21.4650	+	17.9830i	0.761284	+	0.637790i
$796$	4.55288	−	14.0123i	0.161372	−	0.496653i
$797$	−21.5397	+	21.5397i	−0.762975	+	0.762975i	−0.976859	−	0.213884i	$-0.931388\pi$
$797$	−21.5397	+	21.5397i	−0.762975	+	0.762975i	0.213884	+	0.976859i	$0.431388\pi$
$798$	9.19506	+	6.12181i	0.325501	+	0.216710i
$799$	54.3124	−	17.6472i	1.92143	−	0.624312i
$800$	13.4475	−	16.2539i	0.475441	−	0.574664i
$801$	−0.318221	+	0.273626i	−0.0112438	+	0.00966809i
$802$	41.5585	−	21.1751i	1.46748	−	0.747719i
$803$	28.5324	−	18.1580i	1.00689	−	0.640780i
$804$	15.8768	+	14.6274i	0.559933	+	0.515870i
$805$	27.0390	−	1.27460i	0.952999	−	0.0449236i
$806$	55.7797	−	18.1239i	1.96476	−	0.638388i
$807$	2.45241	−	3.68357i	0.0863290	−	0.129668i
$808$	6.52954	+	12.8149i	0.229708	+	0.450828i
$809$	−13.9841	−	10.1600i	−0.491653	−	0.357207i	0.314166	−	0.949368i	$-0.398275\pi$
$809$	−13.9841	−	10.1600i	−0.491653	−	0.357207i	−0.805820	+	0.592161i	$0.798275\pi$
$810$	18.2852	+	47.4347i	0.642475	+	1.66668i
$811$	−9.26839	−	6.73388i	−0.325457	−	0.236459i	0.413043	−	0.910711i	$-0.364466\pi$
$811$	−9.26839	−	6.73388i	−0.325457	−	0.236459i	−0.738501	+	0.674253i	$0.764466\pi$
$812$	−30.4946	−	59.8490i	−1.07015	−	2.10029i
$813$	22.6774	−	34.0618i	0.795331	−	1.19460i
$814$	−17.0695	+	28.9466i	−0.598287	+	1.01458i
$815$	−21.7365	+	12.3977i	−0.761396	+	0.434273i
$816$	22.7563	−	49.5793i	0.796630	−	1.73562i
$817$	6.26792	−	12.3015i	0.219287	−	0.430375i
$818$	29.5734	−	58.0411i	1.03401	−	2.02936i
$819$	−13.2717	−	8.07223i	−0.463752	−	0.282067i
$820$	−71.9451	−	19.6835i	−2.51243	−	0.687377i
$821$	28.1857	+	9.15809i	0.983688	+	0.319620i	0.756329	−	0.654191i	$-0.226991\pi$
$821$	28.1857	+	9.15809i	0.983688	+	0.319620i	0.227359	+	0.973811i	$0.426991\pi$
$822$	−11.0527	+	39.4412i	−0.385506	+	1.37567i
$823$	3.41608	−	21.5683i	0.119077	−	0.751823i	−0.853817	−	0.520573i	$-0.825718\pi$
$823$	3.41608	−	21.5683i	0.119077	−	0.751823i	0.972894	−	0.231250i	$-0.0742816\pi$
$824$	−47.5974			−1.65813
$825$	−26.4816	−	11.1232i	−0.921970	−	0.387261i
$826$	−9.57928			−0.333306
$827$	−5.65712	+	35.7177i	−0.196717	+	1.24202i	0.669672	+	0.742657i	$0.266435\pi$
$827$	−5.65712	+	35.7177i	−0.196717	+	1.24202i	−0.866390	+	0.499368i	$0.833565\pi$
$828$	67.5969	+	27.7361i	2.34916	+	0.963894i
$829$	−29.8342	−	9.69371i	−1.03618	−	0.336676i	−0.258951	−	0.965890i	$-0.583377\pi$
$829$	−29.8342	−	9.69371i	−1.03618	−	0.336676i	−0.777232	+	0.629214i	$0.783377\pi$
$830$	−27.7577	+	10.4881i	−0.963484	+	0.364049i
$831$	−40.1402	−	18.4238i	−1.39245	−	0.639116i
$832$	2.38277	−	4.67645i	0.0826077	−	0.162127i
$833$	−5.01880	+	9.84994i	−0.173891	+	0.341280i
$834$	−56.1469	−	25.7708i	−1.94421	−	0.892368i
$835$	−32.8404	−	29.8836i	−1.13649	−	1.03417i
$836$	−16.4456	−	3.65417i	−0.568785	−	0.126382i
$837$	−34.6266	−	37.0853i	−1.19687	−	1.28186i
$838$	−31.8647	−	62.5380i	−1.10075	−	2.16034i
$839$	40.0073	+	29.0670i	1.38120	+	1.00350i	0.996766	+	0.0803532i	$0.0256048\pi$
$839$	40.0073	+	29.0670i	1.38120	+	1.00350i	0.384438	+	0.923151i	$0.374395\pi$
$840$	46.6841	−	19.8589i	1.61076	−	0.685196i
$841$	−16.6383	−	12.0884i	−0.573734	−	0.416842i
$842$	−12.7564	−	25.0359i	−0.439616	−	0.862795i
$843$	−5.43331	−	3.61734i	−0.187133	−	0.124588i
$844$	43.9746	−	14.2882i	1.51367	−	0.491820i
$845$	−13.7294	−	9.01890i	−0.472305	−	0.310260i
$846$	57.6283	+	67.0206i	1.98130	+	2.30421i
$847$	18.8903	−	14.7296i	0.649077	−	0.506115i
$848$	41.4400	−	21.1147i	1.42306	−	0.725083i
$849$	3.92962	+	3.62038i	0.134864	+	0.124251i
$850$	56.7569	−	24.5583i	1.94675	−	0.842342i
$851$	21.2059	−	6.89022i	0.726929	−	0.236194i
$852$	−0.978541	+	1.46979i	−0.0335243	+	0.0503540i
$853$	−24.1729	+	24.1729i	−0.827664	+	0.827664i	−0.987193	−	0.159529i	$-0.949002\pi$
$853$	−24.1729	+	24.1729i	−0.827664	+	0.827664i	0.159529	+	0.987193i	$0.449002\pi$
$854$	−7.78877	+	23.9714i	−0.266526	+	0.820284i
$855$	−1.43201	+	7.64435i	−0.0489738	+	0.261431i
$856$	−4.17895			−0.142834
$857$	13.6178	−	13.6178i	0.465176	−	0.465176i	−0.435171	−	0.900348i	$-0.643312\pi$
$857$	13.6178	−	13.6178i	0.465176	−	0.465176i	0.900348	+	0.435171i	$0.143312\pi$
$858$	33.9612	+	6.09955i	1.15942	+	0.208235i
$859$	−2.37775	+	0.772578i	−0.0811278	+	0.0263600i	−0.349300	−	0.937011i	$-0.613580\pi$
$859$	−2.37775	+	0.772578i	−0.0811278	+	0.0263600i	0.268172	+	0.963371i	$0.413580\pi$
$860$	−57.7997	−	101.338i	−1.97095	−	3.45560i
$861$	−21.1203	−	19.4582i	−0.719777	−	0.663135i
$862$	41.6437	+	6.59572i	1.41839	+	0.224651i
$863$	7.14691	+	45.1238i	0.243284	+	1.53603i	0.742673	+	0.669655i	$0.233558\pi$
$863$	7.14691	+	45.1238i	0.243284	+	1.53603i	−0.499389	+	0.866378i	$0.666442\pi$
$864$	21.9104	+	0.751205i	0.745405	+	0.0255565i
$865$	−35.0584	+	7.25954i	−1.19202	+	0.246832i
$866$		−	59.5813i		−	2.02465i
$867$	9.47251	−	7.49314i	0.321703	−	0.254480i
$868$	−65.8747	+	65.8747i	−2.23593	+	2.23593i
$869$	23.0533	−	2.20865i	0.782028	−	0.0749232i
$870$	44.2340	−	52.7990i	1.49967	−	1.79005i
$871$	−2.09028	−	6.43323i	−0.0708265	−	0.217982i
$872$	3.52398	−	22.2495i	0.119337	−	0.753464i
$873$	−40.5677	+	25.0462i	−1.37301	+	0.847686i
$874$	9.56959	+	13.1714i	0.323696	+	0.445530i
$875$	23.0338	+	7.88774i	0.778684	+	0.266654i
$876$	−75.8692	+	15.2228i	−2.56338	+	0.514329i
$877$	−3.22470	−	20.3600i	−0.108890	−	0.687507i	−0.980384	−	0.197099i	$-0.936848\pi$
$877$	−3.22470	−	20.3600i	−0.108890	−	0.687507i	0.871493	−	0.490408i	$-0.163152\pi$
$878$	23.0582	−	45.2542i	0.778176	−	1.52726i
$879$	−15.1977	+	16.4959i	−0.512607	+	0.556392i
$880$	−34.2174	+	33.2418i	−1.15347	+	1.12058i
$881$	9.77534	+	13.4546i	0.329339	+	0.453297i	0.941290	−	0.337599i	$-0.109615\pi$
$881$	9.77534	+	13.4546i	0.329339	+	0.453297i	−0.611950	+	0.790896i	$0.709615\pi$
$882$	−17.0621	−	1.28563i	−0.574512	−	0.0432895i
$883$	27.2171	+	13.8678i	0.915927	+	0.466688i	0.847396	−	0.530961i	$-0.178169\pi$
$883$	27.2171	+	13.8678i	0.915927	+	0.466688i	0.0685308	+	0.997649i	$0.478169\pi$
$884$	−41.2652	+	29.9809i	−1.38790	+	1.00837i
$885$	−2.64002	−	6.20613i	−0.0887432	−	0.208617i
$886$	−29.3532	−	90.3398i	−0.986140	−	3.03503i
$887$	−7.32389	+	46.2412i	−0.245912	+	1.55263i	0.487670	+	0.873028i	$0.337847\pi$
$887$	−7.32389	+	46.2412i	−0.245912	+	1.55263i	−0.733583	+	0.679600i	$0.762153\pi$
$888$	32.7746	−	25.9261i	1.09984	−	0.870022i
$889$	22.8264	+	31.4178i	0.765572	+	1.05372i
$890$	−0.325194	+	0.720188i	−0.0109005	+	0.0241408i
$891$	−7.65236	−	28.8521i	−0.256364	−	0.966580i
$892$	−56.2215	−	8.90462i	−1.88244	−	0.298149i
$893$	2.11537	+	13.3559i	0.0707881	+	0.446939i
$894$	0.473721	+	2.36099i	0.0158436	+	0.0789635i
$895$	18.4797	+	23.0673i	0.617707	+	0.771056i
$896$			30.5181i			1.01954i
$897$	−14.2037	−	17.9557i	−0.474247	−	0.599522i
$898$	5.43153	−	5.43153i	0.181253	−	0.181253i
$899$	−21.2434	+	65.3805i	−0.708507	+	2.18056i
$900$	47.3444	+	45.5786i	1.57815	+	1.51929i
$901$	35.4007			1.17937
$902$	59.3389	+	23.4070i	1.97577	+	0.779369i
$903$	−1.83817	−	44.8785i	−0.0611704	−	1.49346i
$904$	−6.91478	+	2.24675i	−0.229982	+	0.0747257i
$905$	11.8903	+	3.25306i	0.395246	+	0.108135i
$906$	8.93168	+	8.22881i	0.296735	+	0.273384i
$907$	−51.0772	−	8.08984i	−1.69599	−	0.268619i	−0.767791	−	0.640700i	$-0.778644\pi$
$907$	−51.0772	−	8.08984i	−1.69599	−	0.268619i	−0.928200	+	0.372082i	$0.878644\pi$
$908$	43.3391	−	22.0824i	1.43826	−	0.732829i
$909$	−6.61788	+	2.76709i	−0.219501	+	0.0917784i
$910$	−29.0712	−	3.21006i	−0.963700	−	0.106413i
$911$	21.4190	+	29.4807i	0.709643	+	0.976739i	0.999805	+	0.0197618i	$0.00629079\pi$
$911$	21.4190	+	29.4807i	0.709643	+	0.976739i	−0.290162	+	0.956978i	$0.593709\pi$
$912$	10.7524	+	7.15861i	0.356046	+	0.237045i
$913$	16.8701	−	4.35429i	0.558318	−	0.144106i
$914$	−9.60458	+	29.5599i	−0.317691	+	0.977754i
$915$	−17.6769	+	1.56031i	−0.584381	+	0.0515823i
$916$	24.6250			0.813633
$917$	6.87282	−	1.08855i	0.226961	−	0.0359470i
$918$	56.2300	+	31.1222i	1.85587	+	1.02719i
$919$	−38.0829	−	12.3739i	−1.25624	−	0.408177i	−0.396087	−	0.918213i	$-0.629632\pi$
$919$	−38.0829	−	12.3739i	−1.25624	−	0.408177i	−0.860153	+	0.510036i	$0.829632\pi$
$920$	74.6884	−	3.52075i	2.46240	−	0.116076i
$921$	−17.5952	−	31.2962i	−0.579783	−	1.03124i
$922$	31.5426	−	61.9059i	1.03880	−	2.03876i
$923$	0.492968	−	0.251180i	0.0162262	−	0.00826768i
$924$	−52.4634	+	15.8577i	−1.72592	+	0.521679i
$925$	20.0153	+	1.26004i	0.658100	+	0.0414300i
$926$	53.1651	−	73.1755i	1.74711	−	2.40470i
$927$	1.78364	−	23.6714i	0.0585823	−	0.777470i
$928$	−13.4853	−	26.4664i	−0.442678	−	0.868804i
$929$	1.60841			0.0527701			0.0263851	−	0.999652i	$-0.491600\pi$
$929$	1.60841			0.0527701			0.0263851	+	0.999652i	$0.491600\pi$
$930$	−88.6030	−	35.7182i	−2.90541	−	1.17125i
$931$	−2.11774	−	1.53862i	−0.0694060	−	0.0504264i
$932$	−22.9126	−	44.9686i	−0.750528	−	1.47299i
$933$	−26.5604	+	21.0104i	−0.869548	+	0.687849i
$934$	0.226689	−	0.0736558i	0.00741750	−	0.00241009i
$935$	−34.6929	+	10.7203i	−1.13458	+	0.350592i
$936$	−36.6598	−	22.2975i	−1.19826	−	0.728816i
$937$	−4.70200	+	2.39579i	−0.153608	+	0.0782670i	−0.529105	−	0.848557i	$-0.677472\pi$
$937$	−4.70200	+	2.39579i	−0.153608	+	0.0782670i	0.375497	+	0.926824i	$0.377472\pi$
$938$	11.0657	+	11.0657i	0.361309	+	0.361309i
$939$	−18.1788	−	2.12090i	−0.593244	−	0.0692131i
$940$	104.140	+	47.0233i	3.39666	+	1.53373i
$941$	−12.1185	+	16.6797i	−0.395053	+	0.543743i	−0.959494	−	0.281730i	$-0.909092\pi$
$941$	−12.1185	+	16.6797i	−0.395053	+	0.543743i	0.564441	+	0.825473i	$0.309092\pi$
$942$	4.12741	+	100.770i	0.134478	+	3.28326i
$943$	−19.2150	−	37.7116i	−0.625727	−	1.22806i
$944$	−11.2017			−0.364583
$945$	8.12691	+	23.9614i	0.264368	+	0.779463i
$946$	39.7395	+	91.5143i	1.29204	+	2.97539i
$947$	−25.0775	+	3.97188i	−0.814908	+	0.129069i	−0.549957	−	0.835193i	$-0.685356\pi$
$947$	−25.0775	+	3.97188i	−0.814908	+	0.129069i	−0.264951	+	0.964262i	$0.585356\pi$
$948$	−51.0223	−	14.2980i	−1.65713	−	0.464379i
$949$	23.0598	+	7.49258i	0.748552	+	0.243219i
$950$	3.64114	+	14.1836i	0.118134	+	0.460178i
$951$	−29.8516	+	16.7831i	−0.968005	+	0.544229i
$952$	29.1172	−	57.1457i	0.943694	−	1.85210i
$953$	−17.5393	+	8.93671i	−0.568153	+	0.289488i	−0.714375	−	0.699763i	$-0.753289\pi$
$953$	−17.5393	+	8.93671i	−0.568153	+	0.289488i	0.146222	+	0.989252i	$0.453289\pi$
$954$	21.1368	+	50.5516i	0.684329	+	1.63667i
$955$	17.3738	−	13.9185i	0.562204	−	0.450392i
$956$	33.5405	+	46.1646i	1.08478	+	1.49307i
$957$	−29.1817	+	28.0019i	−0.943311	+	0.905173i
$958$	−9.12096	+	57.5875i	−0.294685	+	1.86057i
$959$	−6.29977	+	19.3887i	−0.203430	+	0.626094i
$960$	−7.86676	+	3.34643i	−0.253898	+	0.108005i
$961$	64.3453			2.07565
$962$	−23.7954	+	3.76881i	−0.767193	+	0.121511i
$963$	0.156600	−	2.07830i	0.00504635	−	0.0669722i
$964$		−	24.6608i		−	0.794269i
$965$	−24.2643	−	2.67929i	−0.781096	−	0.0862492i
$966$	48.1379	+	22.0947i	1.54881	+	0.710886i
$967$	−33.2067	−	5.25942i	−1.06785	−	0.169131i	−0.402320	−	0.915499i	$-0.631796\pi$
$967$	−33.2067	−	5.25942i	−1.06785	−	0.169131i	−0.665534	+	0.746368i	$0.731796\pi$
$968$	52.1796	−	40.6868i	1.67712	−	1.30772i
$969$	4.81847	+	8.57048i	0.154792	+	0.275323i
$970$	−49.2860	+	75.0275i	−1.58248	+	2.40899i
$971$	1.14100	+	1.57045i	0.0366164	+	0.0503981i	0.826933	−	0.562301i	$-0.190084\pi$
$971$	1.14100	+	1.57045i	0.0366164	+	0.0503981i	−0.790316	+	0.612699i	$0.790084\pi$
$972$	−7.46216	+	67.8876i	−0.239349	+	2.17749i
$973$	−27.3966	−	13.9592i	−0.878294	−	0.447513i
$974$	72.0031	−	52.3133i	2.30713	−	1.67623i
$975$	−5.93221	−	19.7190i	−0.189983	−	0.631515i
$976$	−9.10790	+	28.0312i	−0.291537	+	0.897258i
$977$	−5.95651	+	37.6079i	−0.190566	+	1.20318i	0.688053	+	0.725661i	$0.258466\pi$
$977$	−5.95651	+	37.6079i	−0.190566	+	1.20318i	−0.878619	+	0.477524i	$0.841534\pi$
$978$	−48.9229	+	2.00382i	−1.56438	+	0.0640752i
$979$	0.235679	−	0.399666i	0.00753232	−	0.0127734i
$980$	−20.6915	+	7.81819i	−0.660964	+	0.249743i
$981$	10.9332	+	2.58633i	0.349070	+	0.0825751i
$982$	7.11217	−	3.62383i	0.226958	−	0.115641i
$983$	−1.93745	−	12.2326i	−0.0617949	−	0.390158i	−0.999129	−	0.0417261i	$-0.986714\pi$
$983$	−1.93745	−	12.2326i	−0.0617949	−	0.390158i	0.937334	−	0.348432i	$-0.113286\pi$
$984$	−58.3394	−	53.7484i	−1.85979	−	1.71344i
$985$	1.92196	+	9.28170i	0.0612387	+	0.295739i
$986$		−	87.0777i		−	2.77312i
$987$	27.2930	+	34.5027i	0.868747	+	1.09823i
$988$	−5.48320	−	10.7614i	−0.174444	−	0.342366i
$989$	20.4566	−	62.9590i	0.650483	−	2.00198i
$990$	−36.0227	−	43.1401i	−1.14488	−	1.37108i
$991$	−1.72999	−	5.32436i	−0.0549550	−	0.169134i	0.919812	−	0.392360i	$-0.128341\pi$
$991$	−1.72999	−	5.32436i	−0.0549550	−	0.169134i	−0.974767	+	0.223226i	$0.928341\pi$
$992$	−29.1311	+	29.1311i	−0.924914	+	0.924914i
$993$	8.01585	−	2.97239i	0.254375	−	0.0943258i
$994$	−0.752365	+	1.03554i	−0.0238636	+	0.0328454i
$995$	7.51124	−	0.354074i	0.238122	−	0.0112249i
$996$	−39.5955	−	4.61956i	−1.25463	−	0.146376i
$997$	41.3707	−	21.0794i	1.31022	−	0.667592i	0.347398	−	0.937718i	$-0.387065\pi$
$997$	41.3707	−	21.0794i	1.31022	−	0.667592i	0.962825	+	0.270125i	$0.0870652\pi$
$998$	16.7127	+	105.520i	0.529030	+	3.34016i
$999$	11.6655	+	17.2712i	0.369080	+	0.546436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.cv.a.422.8	✓	928
3.2	odd	2	inner	825.2.cv.a.422.109	yes	928
11.3	even	5		825.2.df.a.47.109	yes	928
25.8	odd	20		825.2.df.a.158.8	yes	928
33.14	odd	10		825.2.df.a.47.8	yes	928
75.8	even	20		825.2.df.a.158.109	yes	928
275.58	odd	20	inner	825.2.cv.a.608.109	yes	928
825.608	even	20	inner	825.2.cv.a.608.8	yes	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.cv.a.422.8	✓	928	1.1	even	1	trivial
825.2.cv.a.422.109	yes	928	3.2	odd	2	inner
825.2.cv.a.608.8	yes	928	825.608	even	20	inner
825.2.cv.a.608.109	yes	928	275.58	odd	20	inner
825.2.df.a.47.8	yes	928	33.14	odd	10
825.2.df.a.47.109	yes	928	11.3	even	5
825.2.df.a.158.8	yes	928	25.8	odd	20
825.2.df.a.158.109	yes	928	75.8	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.cv (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.395170 + 2.49501i) q^{2} +(-1.66780 - 0.467371i) q^{3} +(-4.16679 - 1.35387i) q^{4} +(-0.105290 - 2.23359i) q^{5} +(1.82516 - 3.97649i) q^{6} +(0.988634 - 1.94030i) q^{7} +(2.73085 - 5.35960i) q^{8} +(2.56313 + 1.55896i) q^{9} +O(q^{10})\)	\(q+(-0.395170 + 2.49501i) q^{2} +(-1.66780 - 0.467371i) q^{3} +(-4.16679 - 1.35387i) q^{4} +(-0.105290 - 2.23359i) q^{5} +(1.82516 - 3.97649i) q^{6} +(0.988634 - 1.94030i) q^{7} +(2.73085 - 5.35960i) q^{8} +(2.56313 + 1.55896i) q^{9} +(5.61442 + 0.619949i) q^{10} +(-3.23766 - 0.719398i) q^{11} +(6.31662 + 4.20542i) q^{12} +(-1.07948 - 2.11860i) q^{13} +(4.45039 + 3.23340i) q^{14} +(-0.868311 + 3.77439i) q^{15} +(5.20412 + 3.78102i) q^{16} +(2.22285 + 4.36258i) q^{17} +(-4.90250 + 5.77897i) q^{18} +(-1.10263 + 0.358267i) q^{19} +(-2.58527 + 9.44943i) q^{20} +(-2.55569 + 2.77398i) q^{21} +(3.07433 - 7.79371i) q^{22} +(-4.95313 + 2.52374i) q^{23} +(-7.05944 + 7.66243i) q^{24} +(-4.97783 + 0.470347i) q^{25} +(5.71251 - 1.85611i) q^{26} +(-3.54618 - 3.79798i) q^{27} +(-6.74635 + 6.74635i) q^{28} +(-2.17558 + 6.69574i) q^{29} +(-9.07400 - 3.65797i) q^{30} +9.76449 q^{31} +(-2.98337 + 2.98337i) q^{32} +(5.06356 + 2.71300i) q^{33} +(-11.7631 + 3.82206i) q^{34} +(-4.43793 - 2.00391i) q^{35} +(-8.56938 - 9.96602i) q^{36} +(-3.96161 - 0.627457i) q^{37} +(-0.458151 - 2.89265i) q^{38} +(0.810189 + 4.03793i) q^{39} +(-12.2587 - 5.53529i) q^{40} +7.61370i q^{41} +(-5.91118 - 7.47266i) q^{42} +(-8.42050 + 8.42050i) q^{43} +(12.5167 + 7.38096i) q^{44} +(3.21221 - 5.88912i) q^{45} +(-4.33943 - 13.3554i) q^{46} +(1.82458 - 11.5199i) q^{47} +(-6.91231 - 8.73824i) q^{48} +(1.32712 + 1.82662i) q^{49} +(0.793571 - 12.6056i) q^{50} +(-1.66833 - 8.31482i) q^{51} +(1.62966 + 10.2892i) q^{52} +(3.28243 - 6.44214i) q^{53} +(10.8773 - 7.34689i) q^{54} +(-1.26595 + 7.30735i) q^{55} +(-7.69944 - 10.5974i) q^{56} +(2.00641 - 0.0821803i) q^{57} +(-15.8462 - 8.07404i) q^{58} +(-1.40880 + 1.02355i) q^{59} +(8.72811 - 14.5515i) q^{60} +(1.41589 + 4.35765i) q^{61} +(-3.85864 + 24.3625i) q^{62} +(5.55886 - 3.43200i) q^{63} +(1.29743 + 1.78577i) q^{64} +(-4.61843 + 2.63418i) q^{65} +(-8.76993 + 11.5615i) q^{66} +(2.80979 + 0.445027i) q^{67} +(-3.35576 - 21.1874i) q^{68} +(9.44036 - 1.89416i) q^{69} +(6.75350 - 10.2808i) q^{70} +0.232686i q^{71} +(15.3549 - 9.48004i) q^{72} +(-7.21050 + 7.21050i) q^{73} +(3.13102 - 9.63629i) q^{74} +(8.52186 + 1.54205i) q^{75} +5.07948 q^{76} +(-4.59672 + 5.57083i) q^{77} +(-10.3948 + 0.425759i) q^{78} +(-6.64089 + 2.15776i) q^{79} +(7.89729 - 12.0220i) q^{80} +(4.13926 + 7.99165i) q^{81} +(-18.9962 - 3.00871i) q^{82} +(-4.68065 + 2.38491i) q^{83} +(14.4046 - 8.09853i) q^{84} +(9.51017 - 5.42426i) q^{85} +(-17.6817 - 24.3367i) q^{86} +(6.75782 - 10.1504i) q^{87} +(-12.6973 + 15.3880i) q^{88} +(-0.0432300 + 0.133048i) q^{89} +(13.4240 + 10.3417i) q^{90} -5.17794 q^{91} +(24.0555 - 3.81001i) q^{92} +(-16.2852 - 4.56364i) q^{93} +(28.0213 + 9.10466i) q^{94} +(0.916316 + 2.42510i) q^{95} +(6.37002 - 3.58134i) q^{96} +(-7.21489 + 14.1600i) q^{97} +(-5.08186 + 2.58934i) q^{98} +(-7.17703 - 6.89131i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) \) 928 * q - 8 * q^3 - 20 * q^4 - 2 * q^6 - 20 * q^7 - 10 * q^9	\( 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 20 q^{7} - 10 q^{9} - 8 q^{12} - 24 q^{13} + 26 q^{15} + 204 q^{16} + 2 q^{18} - 40 q^{19} - 12 q^{21} - 40 q^{22} + 40 q^{24} - 8 q^{25} - 14 q^{27} + 8 q^{28} - 26 q^{30} - 24 q^{31} - 12 q^{33} - 40 q^{34} - 34 q^{36} + 16 q^{37} - 60 q^{39} - 28 q^{40} - 26 q^{42} - 40 q^{43} - 28 q^{45} - 4 q^{46} - 36 q^{48} + 60 q^{49} - 12 q^{51} - 68 q^{52} - 80 q^{54} - 32 q^{55} + 30 q^{57} + 112 q^{58} - 80 q^{60} - 4 q^{61} - 14 q^{63} + 100 q^{64} - 30 q^{66} - 12 q^{67} - 110 q^{69} + 60 q^{70} - 138 q^{72} + 140 q^{73} - 86 q^{75} - 128 q^{76} + 20 q^{78} - 20 q^{79} + 18 q^{81} + 52 q^{82} - 10 q^{84} + 28 q^{85} + 44 q^{87} - 36 q^{88} - 184 q^{90} - 24 q^{91} - 98 q^{93} - 300 q^{94} + 14 q^{96} + 4 q^{97}+O(q^{100}) \) 928 * q - 8 * q^3 - 20 * q^4 - 2 * q^6 - 20 * q^7 - 10 * q^9 - 8 * q^12 - 24 * q^13 + 26 * q^15 + 204 * q^16 + 2 * q^18 - 40 * q^19 - 12 * q^21 - 40 * q^22 + 40 * q^24 - 8 * q^25 - 14 * q^27 + 8 * q^28 - 26 * q^30 - 24 * q^31 - 12 * q^33 - 40 * q^34 - 34 * q^36 + 16 * q^37 - 60 * q^39 - 28 * q^40 - 26 * q^42 - 40 * q^43 - 28 * q^45 - 4 * q^46 - 36 * q^48 + 60 * q^49 - 12 * q^51 - 68 * q^52 - 80 * q^54 - 32 * q^55 + 30 * q^57 + 112 * q^58 - 80 * q^60 - 4 * q^61 - 14 * q^63 + 100 * q^64 - 30 * q^66 - 12 * q^67 - 110 * q^69 + 60 * q^70 - 138 * q^72 + 140 * q^73 - 86 * q^75 - 128 * q^76 + 20 * q^78 - 20 * q^79 + 18 * q^81 + 52 * q^82 - 10 * q^84 + 28 * q^85 + 44 * q^87 - 36 * q^88 - 184 * q^90 - 24 * q^91 - 98 * q^93 - 300 * q^94 + 14 * q^96 + 4 * q^97

Introduction

L-functions

Modular forms

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