LMFDB - Embedded newform 825.2.df.a.47.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(47,825)]

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, 17, 16]))

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

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

chi := DirichletCharacter("825.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.df (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			47.8
Character	$\chi$	$=$	825.47
Dual form			825.2.df.a.158.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.25078 - 1.14683i) q^{2} +(-1.44175 + 0.959875i) q^{3} +(2.57522 + 3.54448i) q^{4} +(-2.09173 + 0.790353i) q^{5} +(4.34587 - 0.507027i) q^{6} +(-1.94030 + 0.988634i) q^{7} +(-0.940987 - 5.94116i) q^{8} +(1.15728 - 2.76780i) q^{9} +O(q^{10})$	\(q+(-2.25078 - 1.14683i) q^{2} +(-1.44175 + 0.959875i) q^{3} +(2.57522 + 3.54448i) q^{4} +(-2.09173 + 0.790353i) q^{5} +(4.34587 - 0.507027i) q^{6} +(-1.94030 + 0.988634i) q^{7} +(-0.940987 - 5.94116i) q^{8} +(1.15728 - 2.76780i) q^{9} +(5.61442 + 0.619949i) q^{10} +(3.04218 + 1.32105i) q^{11} +(-7.11508 - 2.63837i) q^{12} +(-2.34849 + 0.371964i) q^{13} +5.50099 q^{14} +(2.25711 - 3.14729i) q^{15} +(-1.98780 + 6.11781i) q^{16} +(3.46217 - 3.46217i) q^{17} +(-5.77897 + 4.90250i) q^{18} +(0.681464 - 0.937954i) q^{19} +(-8.18805 - 5.37878i) q^{20} +(1.84847 - 3.28781i) q^{21} +(-5.33225 - 6.46224i) q^{22} +(4.95313 - 2.52374i) q^{23} +(7.05944 + 7.66243i) q^{24} +(3.75068 - 3.30641i) q^{25} +(5.71251 + 1.85611i) q^{26} +(0.988235 + 5.10131i) q^{27} +(-8.50090 - 4.33142i) q^{28} +(-5.69573 + 4.13819i) q^{29} +(-8.68966 + 4.49534i) q^{30} +(3.01739 - 9.28658i) q^{31} +(2.98337 - 2.98337i) q^{32} +(-5.65409 + 1.01549i) q^{33} +(-11.7631 + 3.82206i) q^{34} +(3.27723 - 3.60148i) q^{35} +(12.7907 - 3.02573i) q^{36} +(2.83620 + 2.83620i) q^{37} +(-2.60950 + 1.32961i) q^{38} +(3.02889 - 2.79053i) q^{39} +(6.66391 + 11.6836i) q^{40} +(4.47522 + 6.15961i) q^{41} +(-7.93104 + 5.28026i) q^{42} +(-8.42050 + 8.42050i) q^{43} +(3.15184 + 14.1849i) q^{44} +(-0.233180 + 6.70415i) q^{45} -14.0427 q^{46} +(-5.29513 - 10.3923i) q^{47} +(-3.00643 - 10.7284i) q^{48} +(-1.32712 + 1.82662i) q^{49} +(-12.2338 + 3.14061i) q^{50} +(-1.66833 + 8.31482i) q^{51} +(-7.36629 - 7.36629i) q^{52} +(5.11251 + 5.11251i) q^{53} +(3.62603 - 12.6153i) q^{54} +(-7.40751 - 0.358881i) q^{55} +(7.69944 + 10.5974i) q^{56} +(-0.0821803 + 2.00641i) q^{57} +(17.5656 - 2.78212i) q^{58} -1.74137 q^{59} +(16.9681 - 0.104668i) q^{60} +(-3.70684 + 2.69318i) q^{61} +(-17.4416 + 17.4416i) q^{62} +(0.490867 + 6.51449i) q^{63} +(2.09929 - 0.682102i) q^{64} +(4.61843 - 2.63418i) q^{65} +(13.8907 + 4.19863i) q^{66} +(2.80979 + 0.445027i) q^{67} +(21.1874 + 3.35576i) q^{68} +(-4.71869 + 8.39299i) q^{69} +(-11.5066 + 4.34772i) q^{70} +(0.221297 - 0.0719038i) q^{71} +(-17.5329 - 4.27112i) q^{72} +(10.0716 - 1.59519i) q^{73} +(-3.13102 - 9.63629i) q^{74} +(-2.23380 + 8.36721i) q^{75} +5.07948 q^{76} +(-7.20878 + 0.444369i) q^{77} +(-10.0176 + 2.80726i) q^{78} +6.98265i q^{79} +(-0.677291 - 14.3679i) q^{80} +(-6.32141 - 6.40623i) q^{81} +(-3.00871 - 18.9962i) q^{82} +(3.71459 + 3.71459i) q^{83} +(16.4138 - 1.91498i) q^{84} +(-4.50559 + 9.97825i) q^{85} +(28.6095 - 9.29581i) q^{86} +(4.23967 - 11.4334i) q^{87} +(4.98590 - 19.3171i) q^{88} +(0.0432300 - 0.133048i) q^{89} +(8.21335 - 14.8221i) q^{90} +(4.18905 - 3.04352i) q^{91} +(21.7007 + 11.0571i) q^{92} +(4.56364 + 16.2852i) q^{93} +29.4633i q^{94} +(-0.684125 + 2.50055i) q^{95} +(-1.43761 + 7.16494i) q^{96} +(11.2375 + 11.2375i) 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} - 12 q^{6}+O(q^{10}) $ 928 * q - 8 * q^3 - 20 * q^4 - 12 * q^6	$ 928 q - 8 q^{3} - 20 q^{4} - 12 q^{6} - 8 q^{12} - 4 q^{13} - 14 q^{15} + 204 q^{16} + 2 q^{18} - 20 q^{19} - 12 q^{21} - 20 q^{22} - 40 q^{24} - 8 q^{25} - 14 q^{27} - 32 q^{28} + 74 q^{30} - 4 q^{31} - 42 q^{33} - 40 q^{34} + 36 q^{36} - 84 q^{37} + 40 q^{39} - 108 q^{40} - 46 q^{42} - 40 q^{43} - 28 q^{45} - 24 q^{46} + 54 q^{48} - 60 q^{49} - 12 q^{51} - 28 q^{52} - 80 q^{54} - 112 q^{55} + 30 q^{57} - 188 q^{58} + 10 q^{60} - 4 q^{61} + 56 q^{63} - 180 q^{64} + 30 q^{66} - 12 q^{67} - 10 q^{69} - 80 q^{70} + 112 q^{72} - 20 q^{73} - 46 q^{75} - 128 q^{76} + 20 q^{78} - 32 q^{81} + 12 q^{82} - 12 q^{85} + 44 q^{87} + 164 q^{88} - 74 q^{90} - 4 q^{91} + 172 q^{93} - 66 q^{96} - 96 q^{97}+O(q^{100}) $ 928 * q - 8 * q^3 - 20 * q^4 - 12 * q^6 - 8 * q^12 - 4 * q^13 - 14 * q^15 + 204 * q^16 + 2 * q^18 - 20 * q^19 - 12 * q^21 - 20 * q^22 - 40 * q^24 - 8 * q^25 - 14 * q^27 - 32 * q^28 + 74 * q^30 - 4 * q^31 - 42 * q^33 - 40 * q^34 + 36 * q^36 - 84 * q^37 + 40 * q^39 - 108 * q^40 - 46 * q^42 - 40 * q^43 - 28 * q^45 - 24 * q^46 + 54 * q^48 - 60 * q^49 - 12 * q^51 - 28 * q^52 - 80 * q^54 - 112 * q^55 + 30 * q^57 - 188 * q^58 + 10 * q^60 - 4 * q^61 + 56 * q^63 - 180 * q^64 + 30 * q^66 - 12 * q^67 - 10 * q^69 - 80 * q^70 + 112 * q^72 - 20 * q^73 - 46 * q^75 - 128 * q^76 + 20 * q^78 - 32 * q^81 + 12 * q^82 - 12 * q^85 + 44 * q^87 + 164 * q^88 - 74 * q^90 - 4 * q^91 + 172 * q^93 - 66 * q^96 - 96 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{17}{20}\right)$

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 $

$2$	−2.25078	−	1.14683i	−1.59154	−	0.810930i	−0.999989	−	0.00466332i	$-0.998516\pi$
$2$	−2.25078	−	1.14683i	−1.59154	−	0.810930i	−0.591552	−	0.806267i	$-0.701484\pi$
$3$	−1.44175	+	0.959875i	−0.832394	+	0.554184i
$3$	−1.44175	+	0.959875i	−0.832394	+	0.554184i
$4$	2.57522	+	3.54448i	1.28761	+	1.77224i
$5$	−2.09173	+	0.790353i	−0.935451	+	0.353457i
$5$	−2.09173	+	0.790353i	−0.935451	+	0.353457i
$6$	4.34587	−	0.507027i	1.77419	−	0.206993i
$7$	−1.94030	+	0.988634i	−0.733366	+	0.373669i	−0.780447	−	0.625222i	$-0.785008\pi$
$7$	−1.94030	+	0.988634i	−0.733366	+	0.373669i	0.0470806	+	0.998891i	$0.485008\pi$
$8$	−0.940987	−	5.94116i	−0.332689	−	2.10052i
$9$	1.15728	−	2.76780i	0.385760	−	0.922599i
$10$	5.61442	+	0.619949i	1.77544	+	0.196045i
$11$	3.04218	+	1.32105i	0.917251	+	0.398310i
$11$	3.04218	+	1.32105i	0.917251	+	0.398310i
$12$	−7.11508	−	2.63837i	−2.05395	−	0.761630i
$13$	−2.34849	+	0.371964i	−0.651354	+	0.103164i	−0.473362	−	0.880868i	$-0.656960\pi$
$13$	−2.34849	+	0.371964i	−0.651354	+	0.103164i	−0.177991	+	0.984032i	$0.556960\pi$
$14$	5.50099			1.47020
$15$	2.25711	−	3.14729i	0.582784	−	0.812627i
$16$	−1.98780	+	6.11781i	−0.496949	+	1.52945i
$17$	3.46217	−	3.46217i	0.839698	−	0.839698i	−0.149121	−	0.988819i	$-0.547644\pi$
$17$	3.46217	−	3.46217i	0.839698	−	0.839698i	0.988819	+	0.149121i	$0.0476443\pi$
$18$	−5.77897	+	4.90250i	−1.36212	+	1.15553i
$19$	0.681464	−	0.937954i	0.156339	−	0.215182i	−0.723662	−	0.690155i	$-0.757542\pi$
$19$	0.681464	−	0.937954i	0.156339	−	0.215182i	0.880000	+	0.474973i	$0.157542\pi$
$20$	−8.18805	−	5.37878i	−1.83090	−	1.20273i
$21$	1.84847	−	3.28781i	0.403368	−	0.717459i
$22$	−5.33225	−	6.46224i	−1.13684	−	1.37775i
$23$	4.95313	−	2.52374i	1.03280	−	0.526237i	0.146432	−	0.989221i	$-0.453221\pi$
$23$	4.95313	−	2.52374i	1.03280	−	0.526237i	0.886367	+	0.462984i	$0.153221\pi$
$24$	7.05944	+	7.66243i	1.44100	+	1.56409i
$25$	3.75068	−	3.30641i	0.750137	−	0.661283i
$26$	5.71251	+	1.85611i	1.12031	+	0.364012i
$27$	0.988235	+	5.10131i	0.190186	+	0.981748i
$28$	−8.50090	−	4.33142i	−1.60652	−	0.818562i
$29$	−5.69573	+	4.13819i	−1.05767	+	0.768443i	−0.973656	−	0.228021i	$-0.926774\pi$
$29$	−5.69573	+	4.13819i	−1.05767	+	0.768443i	−0.0840152	+	0.996464i	$0.526774\pi$
$30$	−8.68966	+	4.49534i	−1.58651	+	0.820732i
$31$	3.01739	−	9.28658i	0.541940	−	1.66792i	−0.186217	−	0.982509i	$-0.559623\pi$
$31$	3.01739	−	9.28658i	0.541940	−	1.66792i	0.728156	−	0.685411i	$-0.240377\pi$
$32$	2.98337	−	2.98337i	0.527391	−	0.527391i
$33$	−5.65409	+	1.01549i	−0.984251	+	0.176775i
$34$	−11.7631	+	3.82206i	−2.01735	+	0.655477i
$35$	3.27723	−	3.60148i	0.553952	−	0.608762i
$36$	12.7907	−	3.02573i	2.13178	−	0.504288i
$37$	2.83620	+	2.83620i	0.466268	+	0.466268i	0.900703	−	0.434435i	$-0.143052\pi$
$37$	2.83620	+	2.83620i	0.466268	+	0.466268i	−0.434435	+	0.900703i	$0.643052\pi$
$38$	−2.60950	+	1.32961i	−0.423316	+	0.215690i
$39$	3.02889	−	2.79053i	0.485011	−	0.446843i
$40$	6.66391	+	11.6836i	1.05366	+	1.84734i
$41$	4.47522	+	6.15961i	0.698912	+	0.961969i	0.999965	+	0.00836214i	$0.00266178\pi$
$41$	4.47522	+	6.15961i	0.698912	+	0.961969i	−0.301053	+	0.953607i	$0.597338\pi$
$42$	−7.93104	+	5.28026i	−1.22379	+	0.814762i
$43$	−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	$0.887604\pi$
$44$	3.15184	+	14.1849i	0.475158	+	2.13846i
$45$	−0.233180	+	6.70415i	−0.0347604	+	0.999396i
$46$	−14.0427			−2.07048
$47$	−5.29513	−	10.3923i	−0.772374	−	1.51587i	−0.854618	−	0.519256i	$-0.826209\pi$
$47$	−5.29513	−	10.3923i	−0.772374	−	1.51587i	0.0822449	−	0.996612i	$-0.473791\pi$
$48$	−3.00643	−	10.7284i	−0.433941	−	1.54851i
$49$	−1.32712	+	1.82662i	−0.189588	+	0.260945i
$50$	−12.2338	+	3.14061i	−1.73013	+	0.444149i
$51$	−1.66833	+	8.31482i	−0.233612	+	1.16431i
$52$	−7.36629	−	7.36629i	−1.02152	−	1.02152i
$53$	5.11251	+	5.11251i	0.702257	+	0.702257i	0.964895	−	0.262638i	$-0.0845924\pi$
$53$	5.11251	+	5.11251i	0.702257	+	0.702257i	−0.262638	+	0.964895i	$0.584592\pi$
$54$	3.62603	−	12.6153i	0.493441	−	1.71672i
$55$	−7.40751	−	0.358881i	−0.998828	−	0.0483915i
$56$	7.69944	+	10.5974i	1.02888	+	1.41613i
$57$	−0.0821803	+	2.00641i	−0.0108850	+	0.265756i
$58$	17.5656	−	2.78212i	2.30648	−	0.365311i
$59$	−1.74137			−0.226708			−0.113354	−	0.993555i	$-0.536159\pi$
$59$	−1.74137			−0.226708			−0.113354	+	0.993555i	$0.536159\pi$
$60$	16.9681	−	0.104668i	2.19057	−	0.0135126i
$61$	−3.70684	+	2.69318i	−0.474612	+	0.344826i	−0.799236	−	0.601017i	$-0.794762\pi$
$61$	−3.70684	+	2.69318i	−0.474612	+	0.344826i	0.324624	+	0.945843i	$0.394762\pi$
$62$	−17.4416	+	17.4416i	−2.21509	+	2.21509i
$63$	0.490867	+	6.51449i	0.0618434	+	0.820749i
$64$	2.09929	−	0.682102i	0.262412	−	0.0852627i
$65$	4.61843	−	2.63418i	0.572845	−	0.326730i
$66$	13.8907	+	4.19863i	1.70983	+	0.516815i
$67$	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	$0.494404\pi$
$68$	21.1874	+	3.35576i	2.56935	+	0.406945i
$69$	−4.71869	+	8.39299i	−0.568063	+	1.01040i
$70$	−11.5066	+	4.34772i	−1.37530	+	0.519652i
$71$	0.221297	−	0.0719038i	0.0262631	−	0.00853341i	−0.295856	−	0.955233i	$-0.595605\pi$
$71$	0.221297	−	0.0719038i	0.0262631	−	0.00853341i	0.322119	+	0.946699i	$0.395605\pi$
$72$	−17.5329	−	4.27112i	−2.06627	−	0.503356i
$73$	10.0716	−	1.59519i	1.17880	−	0.186703i	0.463870	−	0.885903i	$-0.346460\pi$
$73$	10.0716	−	1.59519i	1.17880	−	0.186703i	0.714926	+	0.699200i	$0.246460\pi$
$74$	−3.13102	−	9.63629i	−0.363974	−	1.12020i
$75$	−2.23380	+	8.36721i	−0.257937	+	0.966162i
$76$	5.07948			0.582656
$77$	−7.20878	+	0.444369i	−0.821516	+	0.0506406i
$78$	−10.0176	+	2.80726i	−1.13427	+	0.317859i
$79$			6.98265i			0.785609i	0.919622	+	0.392805i	$0.128495\pi$
$79$			6.98265i			0.785609i	−0.919622	+	0.392805i	$0.871505\pi$
$80$	−0.677291	−	14.3679i	−0.0757234	−	1.60638i
$81$	−6.32141	−	6.40623i	−0.702379	−	0.711803i
$82$	−3.00871	−	18.9962i	−0.332256	−	2.09778i
$83$	3.71459	+	3.71459i	0.407729	+	0.407729i	0.880946	−	0.473217i	$-0.156907\pi$
$83$	3.71459	+	3.71459i	0.407729	+	0.407729i	−0.473217	+	0.880946i	$0.656907\pi$
$84$	16.4138	−	1.91498i	1.79089	−	0.208941i
$85$	−4.50559	+	9.97825i	−0.488700	+	1.08229i
$86$	28.6095	−	9.29581i	3.08505	−	1.00239i
$87$	4.23967	−	11.4334i	0.454540	−	1.22579i
$88$	4.98590	−	19.3171i	0.531498	−	2.05921i
$89$	0.0432300	−	0.133048i	0.00458237	−	0.0141031i	−0.948739	−	0.316060i	$-0.897640\pi$
$89$	0.0432300	−	0.133048i	0.00458237	−	0.0141031i	0.953322	+	0.301957i	$0.0976399\pi$
$90$	8.21335	−	14.8221i	0.865763	−	1.56239i
$91$	4.18905	−	3.04352i	0.439131	−	0.319048i
$92$	21.7007	+	11.0571i	2.26246	+	1.15278i
$93$	4.56364	+	16.2852i	0.473227	+	1.68870i
$94$			29.4633i			3.03891i
$95$	−0.684125	+	2.50055i	−0.0701897	+	0.256551i
$96$	−1.43761	+	7.16494i	−0.146725	+	0.731269i
$97$	11.2375	+	11.2375i	1.14099	+	1.14099i	0.988269	+	0.152721i	$0.0488037\pi$
$97$	11.2375	+	11.2375i	1.14099	+	1.14099i	0.152721	+	0.988269i	$0.451196\pi$
$98$	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	0.733351	−	0.679851i	$-0.237955\pi$
$101$	−1.40541	−	1.93438i	−0.139844	−	0.192478i	−0.873194	+	0.487372i	$0.837955\pi$
$102$	13.2907	−	16.8015i	1.31598	−	1.66360i
$103$	−1.23784	+	7.81541i	−0.121968	+	0.770075i	0.848562	+	0.529095i	$0.177469\pi$
$103$	−1.23784	+	7.81541i	−0.121968	+	0.770075i	−0.970530	+	0.240979i	$0.922531\pi$
$104$	4.41980	+	13.6027i	0.433397	+	1.33386i
$105$	−1.26796	+	8.33816i	−0.123740	+	0.813721i
$106$	−5.64395	−	17.3703i	−0.548189	−	1.68715i
$107$	−0.619009	−	0.315401i	−0.0598418	−	0.0304909i	0.423814	−	0.905749i	$-0.360691\pi$
$107$	−0.619009	−	0.315401i	−0.0598418	−	0.0304909i	−0.483655	+	0.875259i	$0.660691\pi$
$108$	−15.5366	+	16.6398i	−1.49501	+	1.60116i
$109$	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	$0.342600\pi$
$110$	16.2611	+	9.30291i	1.55043	+	0.886997i
$111$	−6.81149	−	1.36669i	−0.646518	−	0.129720i
$112$	−2.19135	−	13.8356i	−0.207063	−	1.30734i
$113$	−1.19382	−	0.189083i	−0.112306	−	0.0177875i	0.100029	−	0.994985i	$-0.468107\pi$
$113$	−1.19382	−	0.189083i	−0.112306	−	0.0177875i	−0.212334	+	0.977197i	$0.568107\pi$
$114$	2.48598	−	4.42175i	0.232834	−	0.414135i
$115$	−8.36597	+	9.19372i	−0.780130	+	0.857319i
$116$	−29.3355	−	9.53168i	−2.72373	−	0.884994i
$117$	−1.68833	+	6.93061i	−0.156087	+	0.640735i
$118$	3.91945	+	1.99706i	0.360814	+	0.183844i
$119$	−3.29484	+	10.1405i	−0.302037	+	0.929575i
$120$	−20.8225	−	10.4483i	−1.90082	−	0.953795i
$121$	7.50968	+	8.03771i	0.682698	+	0.730701i
$122$	11.4319	−	1.81063i	1.03499	−	0.163927i
$123$	−12.3646	−	4.58496i	−1.11488	−	0.413412i
$124$	40.6866	−	13.2199i	3.65376	−	1.18718i
$125$	−5.23219	+	9.88049i	−0.467982	+	0.883738i
$126$	6.36618	−	15.2256i	0.567144	−	1.35641i
$127$	−17.6137	−	2.78973i	−1.56296	−	0.247548i	−0.685815	−	0.727776i	$-0.740554\pi$
$127$	−17.6137	−	2.78973i	−1.56296	−	0.247548i	−0.877144	+	0.480228i	$0.840554\pi$
$128$	−13.8417	−	2.19230i	−1.22344	−	0.193774i
$129$	4.05761	−	20.2229i	0.357253	−	1.78052i
$130$	−13.4160	+	0.632420i	−1.17666	+	0.0554669i
$131$	−1.87821	−	2.58514i	−0.164100	−	0.225865i	0.719046	−	0.694963i	$-0.244579\pi$
$131$	−1.87821	−	2.58514i	−0.164100	−	0.225865i	−0.883146	+	0.469098i	$0.844579\pi$
$132$	−18.1599	−	17.4257i	−1.58062	−	1.51671i
$133$	−0.394953	+	2.49364i	−0.0342468	+	0.216226i
$134$	−5.81385	−	4.22401i	−0.502240	−	0.364899i
$135$	−6.09896	−	9.88952i	−0.524915	−	0.851155i
$136$	−23.8271	−	17.3114i	−2.04316	−	1.48444i
$137$	4.25011	+	8.34132i	0.363112	+	0.712647i	0.998211	−	0.0597834i	$-0.0190410\pi$
$137$	4.25011	+	8.34132i	0.363112	+	0.712647i	−0.635100	+	0.772430i	$0.719041\pi$
$138$	20.2460	−	13.4792i	1.72346	−	1.14743i
$139$	−8.29937	+	11.4231i	−0.703943	+	0.968895i	0.295963	+	0.955199i	$0.404360\pi$
$139$	−8.29937	+	11.4231i	−0.703943	+	0.968895i	−0.999906	+	0.0136954i	$0.995640\pi$
$140$	21.2050	+	2.34147i	1.79215	+	0.197890i
$141$	17.6095	+	9.90038i	1.48299	+	0.833763i
$142$	−0.580552	−	0.0919504i	−0.0487188	−	0.00771631i
$143$	−7.63590	−	1.97088i	−0.638546	−	0.164813i
$144$	14.6324	+	12.5818i	1.21937	+	1.04849i
$145$	8.64332	−	13.1576i	0.717788	−	1.09268i
$146$	−24.4984	−	7.96003i	−2.02751	−	0.658776i
$147$	0.160042	−	3.90739i	0.0132000	−	0.322276i
$148$	−2.74903	+	17.3567i	−0.225969	+	1.42671i
$149$	0.445257	+	0.323498i	0.0364769	+	0.0265020i	0.605874	−	0.795560i	$-0.292823\pi$
$149$	0.445257	+	0.323498i	0.0364769	+	0.0265020i	−0.569397	+	0.822062i	$0.692823\pi$
$150$	14.6235	−	16.2709i	1.19401	−	1.32852i
$151$	−0.857726	−	2.63981i	−0.0698007	−	0.214825i	0.910071	−	0.414452i	$-0.136027\pi$
$151$	−0.857726	−	2.63981i	−0.0698007	−	0.214825i	−0.979872	+	0.199628i	$0.936027\pi$
$152$	−6.21379	−	3.16608i	−0.504005	−	0.256803i
$153$	−5.57588	−	13.5893i	−0.450783	−	1.09863i
$154$	16.7350	+	7.26706i	1.34854	+	0.585596i
$155$	1.02810	+	21.8098i	0.0825789	+	1.75181i
$156$	17.6911	+	3.54962i	1.41642	+	0.284197i
$157$	10.4648	−	20.5382i	0.835179	−	1.63913i	0.0680108	−	0.997685i	$-0.478335\pi$
$157$	10.4648	−	20.5382i	0.835179	−	1.63913i	0.767168	−	0.641446i	$-0.221665\pi$
$158$	8.00790	−	15.7164i	0.637075	−	1.25033i
$159$	−12.2783	−	2.46358i	−0.973734	−	0.195375i
$160$	−3.88250	+	8.59834i	−0.306939	+	0.679758i
$161$	−7.11551	+	9.79366i	−0.560781	+	0.771849i
$162$	6.88125	+	21.6686i	0.540642	+	1.70244i
$163$	−11.0531	+	1.75064i	−0.865745	+	0.137121i	−0.573483	−	0.819218i	$-0.694408\pi$
$163$	−11.0531	+	1.75064i	−0.865745	+	0.137121i	−0.292263	+	0.956338i	$0.594408\pi$
$164$	−10.3080	+	31.7247i	−0.804917	+	2.47728i
$165$	11.0242	−	6.59287i	0.858237	−	0.513254i
$166$	−4.10072	−	12.6207i	−0.318277	−	0.979557i
$167$	9.01494	+	17.6928i	0.697597	+	1.36911i	0.919129	+	0.393958i	$0.128894\pi$
$167$	9.01494	+	17.6928i	0.697597	+	1.36911i	−0.221532	+	0.975153i	$0.571106\pi$
$168$	−21.2728	−	7.88824i	−1.64123	−	0.608591i
$169$	−6.98669	+	2.27011i	−0.537438	+	0.174624i
$170$	21.5844	−	17.2917i	1.65545	−	1.32621i
$171$	−1.80742	−	2.97163i	−0.138217	−	0.227246i
$172$	−51.5309	−	8.16169i	−3.92919	−	0.622323i
$173$	−11.3216	−	11.3216i	−0.860768	−	0.860768i	0.130659	−	0.991427i	$-0.458291\pi$
$173$	−11.3216	−	11.3216i	−0.860768	−	0.860768i	−0.991427	+	0.130659i	$0.958291\pi$
$174$	−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
$177$	2.51062	−	1.67150i	0.188710	−	0.125638i
$178$	−0.249885	+	0.249885i	−0.0187296	+	0.0187296i
$179$	−4.08464	+	12.5712i	−0.305300	+	0.939618i	0.674265	+	0.738490i	$0.264461\pi$
$179$	−4.08464	+	12.5712i	−0.305300	+	0.939618i	−0.979565	+	0.201128i	$0.935539\pi$
$180$	−24.3632	+	16.4381i	−1.81593	+	1.22523i
$181$	−5.51291			−0.409771			−0.204886	−	0.978786i	$-0.565682\pi$
$181$	−5.51291			−0.409771			−0.204886	+	0.978786i	$0.565682\pi$
$182$	−12.9190	+	2.04617i	−0.957621	+	0.151672i
$183$	2.75922	−	7.44099i	0.203967	−	0.550053i
$184$	−19.6548	−	27.0525i	−1.44897	−	1.99434i
$185$	−8.17417	−	3.69097i	−0.600977	−	0.271366i
$186$	8.40465	−	41.8882i	0.616259	−	3.07139i
$187$	15.1062	−	5.95884i	1.10467	−	0.435753i
$188$	23.1991	−	45.5308i	1.69197	−	3.32068i
$189$	−6.96081	−	8.92109i	−0.506324	−	0.648914i
$190$	4.40751	−	4.84360i	0.319754	−	0.351392i
$191$			9.95565i			0.720366i	0.932882	+	0.360183i	$0.117286\pi$
$191$			9.95565i			0.720366i	−0.932882	+	0.360183i	$0.882714\pi$
$192$	−2.37192	+	2.99848i	−0.171179	+	0.216397i
$193$	10.7829	−	1.70784i	0.776168	−	0.122933i	0.244231	−	0.969717i	$-0.421464\pi$
$193$	10.7829	−	1.70784i	0.776168	−	0.122933i	0.531937	+	0.846784i	$0.321464\pi$
$194$	−12.4056	−	38.1805i	−0.890669	−	2.74120i
$195$	−4.13012	+	8.23094i	−0.295764	+	0.589430i
$196$	−9.89202			−0.706573
$197$	4.18677	−	0.663119i	0.298295	−	0.0472453i	−0.00549311	−	0.999985i	$-0.501749\pi$
$197$	4.18677	−	0.663119i	0.298295	−	0.0472453i	0.303788	+	0.952740i	$0.401749\pi$
$198$	−24.0571	+	7.27998i	−1.70966	+	0.517366i
$199$			3.36286i			0.238387i	0.992871	+	0.119193i	$0.0380308\pi$
$199$			3.36286i			0.238387i	−0.992871	+	0.119193i	$0.961969\pi$
$200$	−23.1733	−	19.1721i	−1.63860	−	1.35567i
$201$	−4.47818	+	2.05543i	−0.315867	+	0.144979i
$202$	0.944863	+	5.96563i	0.0664803	+	0.419740i
$203$	6.96030	−	13.6604i	0.488517	−	0.958769i
$204$	−33.7680	+	15.4991i	−2.36423	+	1.08515i
$205$	−14.2292	−	9.34725i	−0.993812	−	0.652840i
$206$	11.7490	−	16.1712i	0.818594	−	1.12670i
$207$	−1.25307	−	16.6299i	−0.0870940	−	1.15586i
$208$	2.39271	−	15.1070i	0.165905	−	1.04748i
$209$	3.31221	−	1.95318i	0.229111	−	0.135104i
$210$	12.4163	−	17.3132i	0.856809	−	1.19473i
$211$	3.26124	+	10.0371i	0.224513	+	0.690980i	0.998341	+	0.0575836i	$0.0183396\pi$
$211$	3.26124	+	10.0371i	0.224513	+	0.690980i	−0.773828	+	0.633396i	$0.781660\pi$
$212$	−4.95537	+	31.2870i	−0.340336	+	2.14880i
$213$	−0.250036	+	0.316085i	−0.0171322	+	0.0216578i
$214$	1.03154	+	1.41979i	0.0705147	+	0.0970551i
$215$	10.9583	−	24.2686i	0.747347	−	1.65510i
$216$	29.3778	−	10.6715i	1.99891	−	0.726106i
$217$	3.32637	+	21.0019i	0.225809	+	1.42570i
$218$	−9.34375	−	1.47990i	−0.632838	−	0.100232i
$219$	−12.9896	+	11.9674i	−0.877755	+	0.808681i
$220$	−17.8039	−	27.1800i	−1.20034	−	1.83247i
$221$	−6.84305	+	9.41866i	−0.460314	+	0.633567i
$222$	13.7638	+	10.8877i	0.923765	+	0.730736i
$223$	−9.18698	+	9.18698i	−0.615206	+	0.615206i	−0.944298	−	0.329092i	$-0.893257\pi$
$223$	−9.18698	+	9.18698i	−0.615206	+	0.615206i	0.329092	+	0.944298i	$0.393257\pi$
$224$	−2.83919	+	8.73812i	−0.189701	+	0.583840i
$225$	−4.81089	−	14.2076i	−0.320726	−	0.947172i
$226$	2.47019	+	1.79470i	0.164315	+	0.119382i
$227$	−10.9654	+	1.73675i	−0.727798	+	0.115272i	−0.509329	−	0.860572i	$-0.670106\pi$
$227$	−10.9654	+	1.73675i	−0.727798	+	0.115272i	−0.218469	+	0.975844i	$0.570106\pi$
$228$	−7.32333	+	4.87567i	−0.485000	+	0.322899i
$229$			5.62058i			0.371419i	0.982605	+	0.185709i	$0.0594583\pi$
$229$			5.62058i			0.371419i	−0.982605	+	0.185709i	$0.940542\pi$
$230$	29.3736	−	11.0987i	1.93684	−	0.731826i
$231$	9.96671	−	7.56020i	0.655761	−	0.497424i
$232$	29.9453	+	29.9453i	1.96600	+	1.96600i
$233$	−10.2639	+	5.22974i	−0.672413	+	0.342611i	−0.756637	−	0.653835i	$-0.773159\pi$
$233$	−10.2639	+	5.22974i	−0.672413	+	0.342611i	0.0842241	+	0.996447i	$0.473159\pi$
$234$	11.7483	−	13.6630i	0.768010	−	0.893180i
$235$	19.2895	+	17.5528i	1.25831	+	1.14502i
$236$	−4.48442	−	6.17227i	−0.291911	−	0.401781i
$237$	−6.70247	−	10.0672i	−0.435372	−	0.653936i
$238$	19.0453	−	19.0453i	1.23453	−	1.23453i
$239$	−13.0244			−0.842475			−0.421238	−	0.906950i	$-0.638404\pi$
$239$	−13.0244			−0.842475			−0.421238	+	0.906950i	$0.638404\pi$
$240$	14.7679	+	20.0648i	0.953261	+	1.29518i
$241$	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	$0.841973\pi$
$242$	−7.68474	−	26.7034i	−0.493994	−	1.71656i
$243$	15.2631	+	3.16841i	0.979126	+	0.203253i
$244$	−19.0918	−	6.20331i	−1.22223	−	0.397126i
$245$	1.33230	−	4.86968i	0.0851173	−	0.311113i
$246$	22.5718	+	24.4998i	1.43913	+	1.56205i
$247$	−1.25152	+	2.45626i	−0.0796326	+	0.156288i
$248$	−58.0124	−	9.18826i	−3.68379	−	0.583455i
$249$	−8.92104	−	1.78996i	−0.565348	−	0.113434i
$250$	23.1077	−	16.2384i	1.46146	−	1.02700i
$251$	−5.44865	−	7.49943i	−0.343916	−	0.473360i	0.601664	−	0.798749i	$-0.294505\pi$
$251$	−5.44865	−	7.49943i	−0.343916	−	0.473360i	−0.945580	+	0.325390i	$0.894505\pi$
$252$	−21.8264	+	18.5161i	−1.37493	+	1.16640i
$253$	18.4023	−	1.13437i	1.15694	−	0.0713171i
$254$	36.4451	+	26.4789i	2.28677	+	1.66143i
$255$	−3.08195	−	18.7109i	−0.192999	−	1.17172i
$256$	25.0688	+	18.2135i	1.56680	+	1.13835i
$257$	8.72996	+	17.1335i	0.544560	+	1.06876i	0.985253	+	0.171101i	$0.0547326\pi$
$257$	8.72996	+	17.1335i	0.544560	+	1.06876i	−0.440693	+	0.897658i	$0.645267\pi$
$258$	−32.3250	+	40.8638i	−2.01246	+	2.54407i
$259$	−8.30705	−	2.69913i	−0.516175	−	0.167715i
$260$	21.2303	+	9.58633i	1.31664	+	0.594519i
$261$	4.86213	+	20.5537i	0.300958	+	1.27224i
$262$	1.26273	+	7.97256i	0.0780117	+	0.492547i
$263$	−3.89423	+	7.64286i	−0.240129	+	0.471279i	−0.979347	−	0.202187i	$-0.935195\pi$
$263$	−3.89423	+	7.64286i	−0.240129	+	0.471279i	0.739218	+	0.673466i	$0.235195\pi$
$264$	11.3536	+	32.6363i	0.698768	+	2.00863i
$265$	−14.7347	−	6.65331i	−0.905144	−	0.408710i
$266$	3.74872	−	5.15968i	0.229849	−	0.316360i
$267$	0.0653829	+	0.233317i	0.00400137	+	0.0142788i
$268$	5.65843	+	11.1053i	0.345644	+	0.678364i
$269$	2.55493			0.155777			0.0778884	−	0.996962i	$-0.475182\pi$
$269$	2.55493			0.155777			0.0778884	+	0.996962i	$0.475182\pi$
$270$	2.38582	+	29.2536i	0.145196	+	1.78032i
$271$	19.1133	−	13.8866i	1.16105	−	0.843553i	0.171141	−	0.985247i	$-0.445255\pi$
$271$	19.1133	−	13.8866i	1.16105	−	0.843553i	0.989911	+	0.141693i	$0.0452547\pi$
$272$	14.2988	+	28.0630i	0.866992	+	1.70157i
$273$	−3.11815	+	8.40895i	−0.188719	+	0.508933i
$274$		−	23.6486i		−	1.42866i
$275$	15.7782	−	5.10386i	0.951459	−	0.307775i
$276$	−41.9004	+	4.88847i	−2.52211	+	0.294252i
$277$	11.5765	−	22.7202i	0.695566	−	1.36512i	−0.224931	−	0.974375i	$-0.572216\pi$
$277$	11.5765	−	22.7202i	0.695566	−	1.36512i	0.920497	−	0.390750i	$-0.127784\pi$
$278$	31.7804	−	16.1929i	1.90606	−	0.971186i
$279$	−22.2114	−	19.0987i	−1.32976	−	1.14341i
$280$	−24.4808	−	16.0816i	−1.46301	−	0.961058i
$281$		−	3.76855i		−	0.224813i	−0.993662	−	0.112407i	$-0.964144\pi$
$281$		−	3.76855i		−	0.224813i	0.993662	−	0.112407i	$-0.0358559\pi$
$282$	−28.2811	−	42.4787i	−1.68411	−	2.52957i
$283$	3.04688	−	0.482579i	0.181118	−	0.0286863i	−0.0652164	−	0.997871i	$-0.520774\pi$
$283$	3.04688	−	0.482579i	0.181118	−	0.0286863i	0.246335	+	0.969185i	$0.420774\pi$
$284$	0.824749	+	0.599216i	0.0489399	+	0.0355569i
$285$	−1.41388	−	4.26183i	−0.0837508	−	0.252449i
$286$	14.9265	+	13.1931i	0.882620	+	0.780123i
$287$	−14.7729	−	7.52716i	−0.872016	−	0.444314i
$288$	−4.80478	−	11.7100i	−0.283124	−	0.690017i
$289$		−	6.97318i		−	0.410187i
$290$	−34.5437	+	19.7025i	−2.02848	+	1.15697i
$291$	−26.9881	−	5.41503i	−1.58207	−	0.317435i
$292$	31.5908	+	31.5908i	1.84871	+	1.84871i
$293$	11.5383	−	5.87904i	0.674073	−	0.343457i	−0.0832213	−	0.996531i	$-0.526521\pi$
$293$	11.5383	−	5.87904i	0.674073	−	0.343457i	0.757294	+	0.653074i	$0.226521\pi$
$294$	−4.84132	+	8.61113i	−0.282352	+	0.502211i
$295$	3.64249	−	1.37630i	0.212074	−	0.0801313i
$296$	14.1815	−	19.5191i	0.824282	−	1.13453i
$297$	−3.73268	+	16.8246i	−0.216592	+	0.976262i
$298$	−0.631178	−	1.23876i	−0.0365631	−	0.0717592i
$299$	−10.6936	+	7.76937i	−0.618428	+	0.449314i
$300$	−35.4099	+	13.6297i	−2.04439	+	0.786911i
$301$	8.01353	−	24.6631i	0.461892	−	1.42156i
$302$	−1.09686	+	6.92529i	−0.0631171	+	0.398506i
$303$	3.88301	+	1.43987i	0.223073	+	0.0827186i
$304$	4.38362	+	6.03353i	0.251418	+	0.346047i
$305$	5.62515	−	8.56311i	0.322095	−	0.490322i
$306$	−3.03448	+	36.9810i	−0.173470	+	2.11406i
$307$	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	$0.548526\pi$
$308$	−20.1392	−	24.4070i	−1.14754	−	1.39072i
$309$	−5.71716	−	12.4560i	−0.325238	−	0.708598i
$310$	22.6981	−	50.2682i	1.28917	−	2.85504i
$311$		−	19.5524i		−	1.10872i	−0.832278	−	0.554358i	$-0.812964\pi$
$311$		−	19.5524i		−	1.10872i	0.832278	−	0.554358i	$-0.187036\pi$
$312$	−19.4292	−	15.3693i	−1.09996	−	0.870114i
$313$	4.79720	+	9.41504i	0.271154	+	0.532170i	0.985925	−	0.167189i	$-0.0534690\pi$
$313$	4.79720	+	9.41504i	0.271154	+	0.532170i	−0.714771	+	0.699359i	$0.753469\pi$
$314$	−47.1077	+	34.2258i	−2.65844	+	1.93147i
$315$	−6.17551	−	13.2386i	−0.347951	−	0.745912i
$316$	−24.7499	+	17.9818i	−1.39229	+	1.01156i
$317$	8.97628	+	17.6169i	0.504158	+	0.989466i	0.993113	+	0.117157i	$0.0373782\pi$
$317$	8.97628	+	17.6169i	0.504158	+	0.989466i	−0.488955	+	0.872309i	$0.662622\pi$
$318$	24.8105	+	19.6261i	1.39130	+	1.10058i
$319$	−22.7942	+	5.06479i	−1.27623	+	0.283574i
$320$	−3.85206	+	3.08596i	−0.215337	+	0.172510i
$321$	1.19520	−	0.139443i	0.0667096	−	0.00778293i
$322$	27.2471	−	13.8831i	1.51842	−	0.773674i
$323$	−0.888013	−	5.60669i	−0.0494104	−	0.311965i
$324$	6.42776	−	38.9035i	0.357098	−	2.16131i
$325$	−7.57857	+	9.16019i	−0.420384	+	0.508116i
$326$	26.8858	+	8.73571i	1.48906	+	0.483826i
$327$	−4.02423	+	5.08725i	−0.222540	+	0.281326i
$328$	32.3841	−	32.3841i	1.78811	−	1.78811i
$329$	20.5483	+	14.9292i	1.13286	+	0.823075i
$330$	−32.3740	+	2.19616i	−1.78213	+	0.120895i
$331$	−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	$0.343312\pi$
$332$	−3.60042	+	22.7322i	−0.197599	+	1.24759i
$333$	11.1323	−	4.56775i	0.610046	−	0.250311i
$334$		−	50.1612i		−	2.74470i
$335$	−6.22906	+	1.28985i	−0.340330	+	0.0704720i
$336$	16.4398	+	17.8441i	0.896867	+	0.973474i
$337$	18.9856	+	18.9856i	1.03421	+	1.03421i	0.999394	+	0.0348163i	$0.0110846\pi$
$337$	18.9856	+	18.9856i	1.03421	+	1.03421i	0.0348163	+	0.999394i	$0.488915\pi$
$338$	18.3289	+	2.90302i	0.996962	+	0.157903i
$339$	1.90269	−	0.873312i	0.103340	−	0.0474318i
$340$	−46.9706	+	9.72619i	−2.54734	+	0.527477i
$341$	21.4474	−	24.2653i	1.16144	−	1.31404i
$342$	0.660163	+	8.76129i	0.0356975	+	0.473756i
$343$	3.15377	−	19.9121i	0.170288	−	1.07515i
$344$	57.9511	+	42.1040i	3.12452	+	2.27009i
$345$	3.23680	−	21.2853i	0.174264	−	1.14596i
$346$	12.4985	+	38.4665i	0.671924	+	2.06797i
$347$	15.3275	+	7.80977i	0.822826	+	0.419251i	0.814110	−	0.580711i	$-0.197226\pi$
$347$	15.3275	+	7.80977i	0.822826	+	0.419251i	0.00871619	+	0.999962i	$0.497226\pi$
$348$	51.4436	−	14.4161i	2.75767	−	0.772786i
$349$	−14.6432	+	4.75787i	−0.783834	+	0.254683i	−0.673476	−	0.739209i	$-0.735200\pi$
$349$	−14.6432	+	4.75787i	−0.783834	+	0.254683i	−0.110358	+	0.993892i	$0.535200\pi$
$350$	20.6325	−	18.1885i	1.10285	−	0.972218i
$351$	−4.21836	−	11.6128i	−0.225160	−	0.619845i
$352$	13.0171	−	5.13478i	0.693815	−	0.273684i
$353$	−4.25674	−	26.8760i	−0.226563	−	1.43047i	−0.794436	−	0.607348i	$-0.792233\pi$
$353$	−4.25674	−	26.8760i	−0.226563	−	1.43047i	0.567872	−	0.823117i	$-0.307767\pi$
$354$	−7.56779	+	0.882925i	−0.402223	+	0.0469269i
$355$	−0.406065	+	0.325306i	−0.0215517	+	0.0172655i
$356$	0.582913	−	0.189400i	0.0308943	−	0.0100382i
$357$	−4.98326	−	17.7826i	−0.263742	−	0.941157i
$358$	23.6107	−	23.6107i	1.24786	−	1.24786i
$359$	16.2409			0.857164			0.428582	−	0.903503i	$-0.359013\pi$
$359$	16.2409			0.857164			0.428582	+	0.903503i	$0.359013\pi$
$360$	40.0499	−	4.92316i	2.11081	−	0.259473i
$361$	5.45596	+	16.7917i	0.287156	+	0.883774i
$362$	12.4083	+	6.32236i	0.652167	+	0.332296i
$363$	−18.5423	−	4.38001i	−0.973216	−	0.229891i
$364$	21.5754	+	7.01027i	1.13086	+	0.367438i
$365$	−19.8064	+	11.2969i	−1.03671	+	0.591305i
$366$	−14.7439	+	13.5837i	−0.770677	+	0.710029i
$367$	−12.4972	+	24.5271i	−0.652347	+	1.28030i	0.293584	+	0.955933i	$0.405152\pi$
$367$	−12.4972	+	24.5271i	−0.652347	+	1.28030i	−0.945931	+	0.324369i	$0.894848\pi$
$368$	5.59398	+	35.3190i	0.291606	+	1.84113i
$369$	22.2276	−	5.25811i	1.15712	−	0.273726i
$370$	14.1653	+	17.6819i	0.736420	+	0.919240i
$371$	−14.9742	−	4.86542i	−0.777423	−	0.252600i
$372$	−45.9704	+	58.1138i	−2.38345	+	3.01306i
$373$	−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
$375$	−1.94053	−	19.2674i	−0.100209	−	0.994966i
$376$	−56.7595	+	41.2382i	−2.92715	+	2.12670i
$377$	11.8371	−	11.8371i	0.609642	−	0.609642i
$378$	5.43627	+	28.0623i	0.279612	+	1.44337i
$379$	24.4478	−	7.94358i	1.25580	−	0.408034i	0.395804	−	0.918335i	$-0.370466\pi$
$379$	24.4478	−	7.94358i	1.25580	−	0.408034i	0.859996	+	0.510301i	$0.170466\pi$
$380$	−10.6249	+	4.01458i	−0.545046	+	0.205944i
$381$	28.0723	−	12.8848i	1.43819	−	0.660109i
$382$	11.4174	−	22.4080i	0.584167	−	1.14649i
$383$	23.5341	−	11.9912i	1.20254	−	0.612722i	0.266230	−	0.963910i	$-0.414222\pi$
$383$	23.5341	−	11.9912i	1.20254	−	0.612722i	0.936305	+	0.351187i	$0.114222\pi$
$384$	22.0605	−	10.1255i	1.12577	−	0.516716i
$385$	14.7276	−	6.62698i	0.750589	−	0.337742i
$386$	−26.2285	−	8.52214i	−1.33499	−	0.433766i
$387$	13.5614	+	33.0511i	0.689363	+	1.68008i
$388$	−10.8921	+	68.7698i	−0.552961	+	3.49126i
$389$	14.9774	+	10.8817i	0.759386	+	0.551726i	0.898722	−	0.438519i	$-0.144497\pi$
$389$	14.9774	+	10.8817i	0.759386	+	0.551726i	−0.139336	+	0.990245i	$0.544497\pi$
$390$	18.7355	−	13.7895i	0.948708	−	0.698258i
$391$	8.41093	−	25.8862i	0.425359	−	1.30912i
$392$	12.1010	+	6.16578i	0.611194	+	0.311419i
$393$	5.18932	+	1.92427i	0.261767	+	0.0970666i
$394$	−10.1840	−	3.30897i	−0.513061	−	0.166704i
$395$	−5.51876	−	14.6058i	−0.277679	−	0.734899i
$396$	42.9085	+	7.69225i	2.15624	+	0.386550i
$397$	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	$0.940777\pi$
$398$	3.85662	−	7.56905i	0.193315	−	0.379402i
$399$	−1.82416	−	3.97430i	−0.0913220	−	0.198964i
$400$	12.7724	+	29.5185i	0.638621	+	1.47592i
$401$	−10.8529	+	14.9377i	−0.541968	+	0.745955i	−0.988895	−	0.148615i	$-0.952518\pi$
$401$	−10.8529	+	14.9377i	−0.541968	+	0.745955i	0.446927	+	0.894570i	$0.352518\pi$
$402$	12.4366	+	0.509389i	0.620283	+	0.0254060i
$403$	−3.63204	+	22.9318i	−0.180925	+	1.14231i
$404$	3.23714	−	9.96290i	0.161054	−	0.495673i
$405$	18.2859	+	8.40397i	0.908633	+	0.417596i
$406$	−31.3322	+	22.7642i	−1.55499	+	1.12977i
$407$	4.88147	+	12.3750i	0.241966	+	0.613405i
$408$	50.9696	+	2.08765i	2.52337	+	0.103354i
$409$	−15.1573	+	20.8622i	−0.749479	+	1.03157i	0.248537	+	0.968622i	$0.420050\pi$
$409$	−15.1573	+	20.8622i	−0.749479	+	1.03157i	−0.998017	+	0.0629476i	$0.979950\pi$
$410$	21.3071	+	37.3571i	1.05228	+	1.84493i
$411$	−14.1342	−	7.94650i	−0.697190	−	0.391972i
$412$	−30.8893	+	15.7389i	−1.52180	+	0.775398i
$413$	3.37880	−	1.72158i	0.166260	−	0.0847135i
$414$	−16.2513	+	38.8673i	−0.798709	+	1.91023i
$415$	−10.7058	−	4.83409i	−0.525525	−	0.237296i
$416$	−5.89671	+	8.11613i	−0.289110	+	0.397926i
$417$	1.00085	−	24.4356i	0.0490119	−	1.19662i
$418$	−9.69502	+	0.597628i	−0.474199	+	0.0292310i
$419$	22.4786	−	16.3317i	1.09815	−	0.797853i	0.117394	−	0.993085i	$-0.462546\pi$
$419$	22.4786	−	16.3317i	1.09815	−	0.797853i	0.980757	+	0.195232i	$0.0625460\pi$
$420$	−32.8197	+	16.9783i	−1.60144	+	0.828456i
$421$	3.43727	−	10.5788i	0.167522	−	0.515580i	−0.831691	−	0.555239i	$-0.812627\pi$
$421$	3.43727	−	10.5788i	0.167522	−	0.515580i	0.999213	+	0.0396584i	$0.0126270\pi$
$422$	4.17046	−	26.3313i	0.203015	−	1.28179i
$423$	−34.8916	+	2.62908i	−1.69649	+	0.127830i
$424$	25.5634	−	35.1850i	1.24147	−	1.70874i
$425$	1.53814	−	24.4328i	0.0746109	−	1.18517i
$426$	0.925271	−	0.424688i	0.0448295	−	0.0205762i
$427$	4.52983	−	8.89029i	0.219214	−	0.430231i
$428$	−0.476149	−	3.00629i	−0.0230156	−	0.145314i
$429$	12.9008	−	4.48800i	0.622859	−	0.216682i
$430$	−52.4965	+	42.0560i	−2.53161	+	2.02812i
$431$	15.8739	+	5.15775i	0.764619	+	0.248440i	0.665260	−	0.746612i	$-0.268321\pi$
$431$	15.8739	+	5.15775i	0.764619	+	0.248440i	0.0993593	+	0.995052i	$0.468321\pi$
$432$	−33.1733	−	4.09454i	−1.59605	−	0.196999i
$433$	21.0155	+	10.7079i	1.00994	+	0.514589i	0.879010	−	0.476803i	$-0.158204\pi$
$433$	21.0155	+	10.7079i	1.00994	+	0.514589i	0.130928	+	0.991392i	$0.458204\pi$
$434$	16.5986	−	51.0854i	0.796761	−	2.45218i
$435$	0.168194	+	27.2665i	0.00806430	+	1.30733i
$436$	13.2740	+	9.64413i	0.635709	+	0.461870i
$437$	1.00822	−	6.36565i	0.0482297	−	0.304510i
$438$	42.9612	−	12.0391i	2.05277	−	0.575250i
$439$	−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	$0.759292\pi$
$440$	4.83821	+	44.3469i	0.230652	+	2.11416i
$441$	3.51987	+	5.78709i	0.167613	+	0.275576i
$442$	26.2038	−	13.3515i	1.24639	−	0.635066i
$443$	−17.0713	+	33.5044i	−0.811084	+	1.59184i	−0.00503973	+	0.999987i	$0.501604\pi$
$443$	−17.0713	+	33.5044i	−0.811084	+	1.59184i	−0.806044	+	0.591855i	$0.798396\pi$
$444$	−12.6968	−	27.6627i	−0.602566	−	1.31281i
$445$	0.0147295	+	0.312468i	0.000698245	+	0.0148124i
$446$	31.2138	−	10.1420i	1.47801	−	0.480236i
$447$	−0.952467	−	0.0390119i	−0.0450501	−	0.00184520i
$448$	−3.39892	+	3.39892i	−0.160584	+	0.160584i
$449$	2.46005	−	1.78733i	0.116097	−	0.0843492i	−0.528222	−	0.849106i	$-0.677141\pi$
$449$	2.46005	−	1.78733i	0.116097	−	0.0843492i	0.644319	+	0.764757i	$0.277141\pi$
$450$	−5.46541	+	37.4954i	−0.257642	+	1.76755i
$451$	5.47728	+	24.6506i	0.257915	+	1.16075i
$452$	−2.40416	−	4.71842i	−0.113082	−	0.221936i
$453$	3.77051	+	2.98263i	0.177154	+	0.140136i
$454$	26.6724	+	8.66639i	1.25180	+	0.406734i
$455$	−6.35690	+	9.67705i	−0.298016	+	0.453667i
$456$	11.9978	−	1.39976i	0.561847	−	0.0655500i
$457$	1.92476	+	12.1525i	0.0900365	+	0.568468i	0.990925	+	0.134417i	$0.0429162\pi$
$457$	1.92476	+	12.1525i	0.0900365	+	0.568468i	−0.900888	+	0.434051i	$0.857084\pi$
$458$	6.44585	−	12.6507i	0.301195	−	0.591128i
$459$	21.0830	+	14.2402i	0.984071	+	0.664673i
$460$	−54.1311	−	5.97720i	−2.52388	−	0.278689i
$461$	26.1581	+	8.49927i	1.21830	+	0.395850i	0.846463	−	0.532447i	$-0.178727\pi$
$461$	26.1581	+	8.49927i	1.21830	+	0.395850i	0.371839	+	0.928297i	$0.378727\pi$
$462$	−31.1031	+	5.58622i	−1.44705	+	0.259894i
$463$	−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	$0.962818\pi$
$464$	−13.9947	−	43.0713i	−0.649689	−	1.99954i
$465$	−22.4170	−	30.4575i	−1.03956	−	1.41243i
$466$	29.0995			1.34801
$467$	−0.0667202	+	0.0667202i	−0.00308744	+	0.00308744i	−0.708649	−	0.705561i	$-0.750695\pi$
$467$	−0.0667202	+	0.0667202i	−0.00308744	+	0.00308744i	0.705561	+	0.708649i	$0.250695\pi$
$468$	−28.9132	+	11.8635i	−1.33652	+	0.548393i
$469$	−5.89182	+	1.91437i	−0.272059	+	0.0883973i
$470$	−23.2864	−	61.6293i	−1.07412	−	2.84275i
$471$	4.62660	+	39.6559i	0.213183	+	1.82725i
$472$	1.63861	+	10.3458i	0.0754232	+	0.476203i
$473$	−36.7405	+	14.4928i	−1.68933	+	0.666379i
$474$	3.54039	+	30.3457i	0.162616	+	1.39382i
$475$	−0.545309	−	5.77117i	−0.0250205	−	0.264800i
$476$	−44.4276	+	14.4354i	−2.03634	+	0.661646i
$477$	20.0670	−	8.23379i	0.918804	−	0.376999i
$478$	29.3149	+	14.9367i	1.34083	+	0.683189i
$479$	−7.13245	−	21.9514i	−0.325890	−	1.00299i	−0.971037	−	0.238928i	$-0.923204\pi$
$479$	−7.13245	−	21.9514i	−0.325890	−	1.00299i	0.645147	−	0.764058i	$-0.276796\pi$
$480$	−2.65574	−	16.1234i	−0.121217	−	0.735927i
$481$	−7.71575	−	5.60582i	−0.351808	−	0.255603i
$482$	2.22431	−	14.0437i	0.101315	−	0.639675i
$483$	0.858087	−	20.9500i	0.0390443	−	0.953258i
$484$	−9.15047	+	47.3167i	−0.415931	+	2.15076i
$485$	−32.3873	−	14.6242i	−1.47063	−	0.664050i
$486$	−30.7202	−	24.6355i	−1.39349	−	1.11749i
$487$	34.7986	+	5.51155i	1.57687	+	0.249752i	0.882659	−	0.470015i	$-0.155751\pi$
$487$	34.7986	+	5.51155i	1.57687	+	0.249752i	0.694216	+	0.719767i	$0.255751\pi$
$488$	19.4887	+	19.4887i	0.882211	+	0.882211i
$489$	14.2554	−	13.1336i	0.644651	−	0.593921i
$490$	−8.58340	+	9.43266i	−0.387758	+	0.426124i
$491$		−	3.15987i		−	0.142603i	−0.997455	−	0.0713015i	$-0.977285\pi$
$491$		−	3.15987i		−	0.142603i	0.997455	−	0.0713015i	$-0.0227152\pi$
$492$	−15.5902	−	55.6333i	−0.702861	−	2.50815i
$493$	−5.39246	+	34.0467i	−0.242864	+	1.53339i
$494$	5.63381	−	4.09320i	0.253477	−	0.184162i
$495$	−9.56586	+	20.0872i	−0.429954	+	0.902851i
$496$	50.8156	+	36.9197i	2.28169	+	1.65774i
$497$	−0.358297	+	0.358297i	−0.0160718	+	0.0160718i
$498$	18.0265	+	14.2597i	0.807787	+	0.638993i
$499$	−40.2224	−	13.0690i	−1.80060	−	0.585050i	−0.800698	−	0.599068i	$-0.795538\pi$
$499$	−40.2224	−	13.0690i	−1.80060	−	0.585050i	−0.999902	+	0.0140173i	$0.995538\pi$
$500$	−48.4953	+	6.89900i	−2.16877	+	0.308532i
$501$	−29.9802	−	16.8554i	−1.33942	−	0.753043i
$502$	3.66315	+	23.1282i	0.163494	+	1.03226i
$503$	−31.2500	+	15.9227i	−1.39337	+	0.709957i	−0.979700	−	0.200469i	$-0.935753\pi$
$503$	−31.2500	+	15.9227i	−1.39337	+	0.709957i	−0.413670	+	0.910427i	$0.635753\pi$
$504$	38.2418	−	9.04638i	1.70342	−	0.402958i
$505$	4.46859	+	2.93544i	0.198849	+	0.130625i
$506$	−42.7204	−	18.5510i	−1.89915	−	0.824695i
$507$	7.89403	−	9.97929i	0.350586	−	0.443196i
$508$	−35.4708	−	69.6154i	−1.57376	−	3.08868i
$509$	−36.4657	+	26.4939i	−1.61631	+	1.17432i	−0.781065	+	0.624449i	$0.785323\pi$
$509$	−36.4657	+	26.4939i	−1.61631	+	1.17432i	−0.835249	+	0.549872i	$0.814677\pi$
$510$	−14.5215	+	45.6486i	−0.643021	+	2.02136i
$511$	−17.9650	+	13.0523i	−0.794724	+	0.577401i
$512$	−22.8118	−	44.7708i	−1.00815	−	1.97861i
$513$	5.45825	+	2.54944i	0.240987	+	0.112561i
$514$		−	48.5755i		−	2.14257i
$515$	−3.58770	−	17.3261i	−0.158093	−	0.763477i
$516$	82.1288	−	37.6961i	3.61552	−	1.65948i
$517$	−2.38004	−	38.6102i	−0.104674	−	1.69808i
$518$	15.6019	+	15.6019i	0.685508	+	0.685508i
$519$	27.1903	+	5.45559i	1.19352	+	0.239474i
$520$	−19.9960	−	24.9601i	−0.876882	−	1.09457i
$521$	−2.59915	−	3.57743i	−0.113871	−	0.156730i	0.748277	−	0.663386i	$-0.230881\pi$
$521$	−2.59915	−	3.57743i	−0.113871	−	0.156730i	−0.862148	+	0.506656i	$0.830881\pi$
$522$	12.6280	−	51.8378i	0.552712	−	2.26888i
$523$	1.63505	−	10.3233i	0.0714958	−	0.451407i	−0.925806	−	0.377999i	$-0.876612\pi$
$523$	1.63505	−	10.3233i	0.0714958	−	0.451407i	0.997302	−	0.0734082i	$-0.0233876\pi$
$524$	4.32617	−	13.3146i	0.188990	−	0.581650i
$525$	−3.93785	−	18.4433i	−0.171862	−	0.804933i
$526$	17.5301	−	12.7364i	0.764349	−	0.555332i
$527$	−21.7050	−	42.5984i	−0.945483	−	1.85562i
$528$	5.02659	−	36.6093i	0.218754	−	1.59321i
$529$	4.64513	−	6.39347i	0.201962	−	0.277977i
$530$	25.5343	+	31.8733i	1.10914	+	1.38449i
$531$	−2.01526	+	4.81977i	−0.0874547	+	0.209160i
$532$	−9.85573	+	5.02175i	−0.427300	+	0.217720i
$533$	−12.8012	−	12.8012i	−0.554479	−	0.554479i
$534$	0.120413	−	0.600129i	0.00521077	−	0.0259701i
$535$	1.54408	+	0.170498i	0.0667563	+	0.00737129i
$536$		−	17.1122i		−	0.739134i
$537$	−6.17779	−	22.0453i	−0.266591	−	0.951325i
$538$	−5.75058	−	2.93007i	−0.247925	−	0.126324i
$539$	−6.45036	+	3.80371i	−0.277837	+	0.163838i
$540$	19.3471	−	47.0853i	0.832566	−	2.02623i
$541$	9.10642	+	6.61620i	0.391515	+	0.284453i	0.766076	−	0.642750i	$-0.222206\pi$
$541$	9.10642	+	6.61620i	0.391515	+	0.284453i	−0.374561	+	0.927202i	$0.622206\pi$
$542$	−58.9454	+	9.33604i	−2.53192	+	0.401017i
$543$	7.94822	−	5.29170i	0.341091	−	0.227089i
$544$		−	20.6579i		−	0.885699i
$545$	−6.53545	+	5.23567i	−0.279948	+	0.224271i
$546$	16.6619	−	15.3507i	0.713063	−	0.656949i
$547$	−26.4889	+	13.4968i	−1.13258	+	0.577080i	−0.916794	−	0.399360i	$-0.869232\pi$
$547$	−26.4889	+	13.4968i	−1.13258	+	0.577080i	−0.215789	+	0.976440i	$0.569232\pi$
$548$	−18.6207	+	36.5451i	−0.795436	+	1.56113i
$549$	3.16432	+	13.3765i	0.135050	+	0.570897i
$550$	−41.3664	−	6.60719i	−1.76387	−	0.281732i
$551$			8.16237i			0.347729i
$552$	54.3043	+	20.1368i	2.31135	+	0.857078i
$553$	−6.90328	−	13.5485i	−0.293558	−	0.576139i
$554$	−52.1124	+	37.8618i	−2.21404	+	1.60860i
$555$	15.3280	−	2.52473i	0.650636	−	0.107169i
$556$	−61.8616			−2.62352
$557$	18.3321	+	35.9787i	0.776755	+	1.52447i	0.849780	+	0.527138i	$0.176735\pi$
$557$	18.3321	+	35.9787i	0.776755	+	1.52447i	−0.0730240	+	0.997330i	$0.523265\pi$
$558$	28.0900	+	68.4597i	1.18915	+	2.89813i
$559$	16.6433	−	22.9076i	0.703938	−	0.968887i
$560$	15.5187	+	27.2085i	0.655786	+	1.14977i
$561$	−16.0596	+	23.0912i	−0.678037	+	0.974912i
$562$	−4.32189	+	8.48218i	−0.182308	+	0.357799i
$563$	−1.27809	−	8.06952i	−0.0538649	−	0.340090i	−0.999873	−	0.0159463i	$-0.994924\pi$
$563$	−1.27809	−	8.06952i	−0.0538649	−	0.340090i	0.946008	−	0.324144i	$-0.105076\pi$
$564$	10.2566	+	87.9123i	0.431882	+	3.70177i
$565$	2.64660	−	0.548031i	0.111343	−	0.0230559i
$566$	−7.41129	−	2.40807i	−0.311520	−	0.101219i
$567$	18.5989	+	6.18047i	0.781079	+	0.259555i
$568$	−0.635430	−	1.24710i	−0.0266620	−	0.0523272i
$569$	23.0681	+	16.7600i	0.967066	+	0.702614i	0.954781	−	0.297310i	$-0.0960895\pi$
$569$	23.0681	+	16.7600i	0.967066	+	0.702614i	0.0122849	+	0.999925i	$0.496090\pi$
$570$	−1.70527	+	11.2139i	−0.0714259	+	0.469699i
$571$	−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	$0.792943\pi$
$572$	−12.6783	−	32.1407i	−0.530108	−	1.34387i
$573$	−9.55618	−	14.3535i	−0.399215	−	0.599628i
$574$	24.6181	+	33.8839i	1.02754	+	1.41429i
$575$	10.2331	−	25.8429i	0.426749	−	1.07772i
$576$	0.541548	−	6.59980i	0.0225645	−	0.274992i
$577$	20.2865	+	3.21306i	0.844537	+	0.133762i	0.563685	−	0.825990i	$-0.309383\pi$
$577$	20.2865	+	3.21306i	0.844537	+	0.133762i	0.280852	+	0.959751i	$0.409383\pi$
$578$	−7.99704	+	15.6951i	−0.332633	+	0.652829i
$579$	−13.9069	+	12.8125i	−0.577950	+	0.532469i
$580$	68.8954	−	3.24767i	2.86073	−	0.134852i
$581$	−10.8798	−	3.53506i	−0.451370	−	0.146659i
$582$	54.5342	+	43.1388i	2.26052	+	1.78816i
$583$	8.79929	+	22.3070i	0.364429	+	0.923862i
$584$	−18.9546	−	58.3362i	−0.784346	−	2.41397i
$585$	−1.94608	−	15.8314i	−0.0804606	−	0.654546i
$586$	−32.7123			−1.35133
$587$	14.9272	−	14.9272i	0.616111	−	0.616111i	−0.328420	−	0.944532i	$-0.606516\pi$
$587$	14.9272	−	14.9272i	0.616111	−	0.616111i	0.944532	+	0.328420i	$0.106516\pi$
$588$	14.2618	−	9.49511i	0.588147	−	0.391572i
$589$	−6.65415	−	9.15865i	−0.274179	−	0.377376i
$590$	−9.77682	−	1.07956i	−0.402505	−	0.0444449i
$591$	−5.39976	+	4.97483i	−0.222116	+	0.204637i
$592$	−22.9891	+	11.7135i	−0.944847	+	0.481424i
$593$	12.4175	+	12.4175i	0.509925	+	0.509925i	0.914503	−	0.404578i	$-0.132582\pi$
$593$	12.4175	+	12.4175i	0.509925	+	0.509925i	−0.404578	+	0.914503i	$0.632582\pi$
$594$	27.6964	−	33.5877i	1.13640	−	1.37812i
$595$	−1.12263	−	23.8152i	−0.0460234	−	0.976329i
$596$			2.41128i			0.0987700i
$597$	−3.22792	−	4.84839i	−0.132110	−	0.198432i
$598$	32.9791	−	5.22338i	1.34862	−	0.213600i
$599$	12.6465	+	9.18819i	0.516720	+	0.375419i	0.815367	−	0.578944i	$-0.196535\pi$
$599$	12.6465	+	9.18819i	0.516720	+	0.375419i	−0.298647	+	0.954364i	$0.596535\pi$
$600$	51.8129	+	5.39794i	2.11525	+	0.220370i
$601$	9.18091	−	28.2559i	0.374497	−	1.15258i	−0.569320	−	0.822116i	$-0.692794\pi$
$601$	9.18091	−	28.2559i	0.374497	−	1.15258i	0.943817	−	0.330467i	$-0.107206\pi$
$602$	−46.3211	+	46.3211i	−1.88791	+	1.88791i
$603$	4.48346	−	7.26191i	0.182580	−	0.295728i
$604$	7.14792	−	9.83827i	0.290845	−	0.400314i
$605$	−22.0609	−	10.8774i	−0.896901	−	0.442231i
$606$	−7.08852	−	7.69399i	−0.287951	−	0.312547i
$607$	11.4386	+	1.81170i	0.464280	+	0.0735347i	0.384192	−	0.923253i	$-0.374480\pi$
$607$	11.4386	+	1.81170i	0.464280	+	0.0735347i	0.0800875	+	0.996788i	$0.474480\pi$
$608$	−0.765207	−	4.83133i	−0.0310333	−	0.195936i
$609$	3.07723	+	26.3758i	0.124696	+	1.06880i
$610$	−22.4814	+	12.8226i	−0.910245	+	0.519171i
$611$	16.3011	+	22.4365i	0.659472	+	0.907685i
$612$	33.8078	−	54.7589i	1.36660	−	2.21350i
$613$	−5.84237	+	36.8873i	−0.235971	+	1.48986i	0.530556	+	0.847650i	$0.321983\pi$
$613$	−5.84237	+	36.8873i	−0.235971	+	1.48986i	−0.766527	+	0.642212i	$0.778017\pi$
$614$	−16.1811	−	49.8002i	−0.653015	−	2.00977i
$615$	29.4872	−	0.181893i	1.18904	−	0.00733461i
$616$	9.42344	+	42.4104i	0.379681	+	1.70876i
$617$	−1.29447	+	8.17298i	−0.0521135	+	0.329032i	0.947834	+	0.318765i	$0.103268\pi$
$617$	−1.29447	+	8.17298i	−0.0521135	+	0.329032i	−0.999947	+	0.0102667i	$0.996732\pi$
$618$	−1.41686	+	34.5924i	−0.0569945	+	1.39151i
$619$	18.0670	−	24.8670i	0.726172	−	0.999491i	−0.273124	−	0.961979i	$-0.588057\pi$
$619$	18.0670	−	24.8670i	0.726172	−	0.999491i	0.999296	−	0.0375117i	$-0.0119431\pi$
$620$	−74.6570	+	59.8092i	−2.99830	+	2.40199i
$621$	17.7693	+	22.7734i	0.713056	+	0.913865i
$622$	−22.4233	+	44.0081i	−0.899091	+	1.76457i
$623$	0.0476567	+	0.300892i	0.00190932	+	0.0120550i
$624$	11.0511	+	24.0772i	0.442400	+	0.963860i
$625$	3.13527	−	24.8026i	0.125411	−	0.992105i
$626$		−	26.6927i		−	1.06686i
$627$	−2.90057	+	5.99530i	−0.115838	+	0.239429i
$628$	99.7465	−	15.7983i	3.98032	−	0.630420i
$629$	19.6388			0.783050
$630$	−1.28272	+	36.8795i	−0.0511048	+	1.46931i
$631$	12.0017	+	36.9373i	0.477779	+	1.47045i	0.842173	+	0.539207i	$0.181276\pi$
$631$	12.0017	+	36.9373i	0.477779	+	1.47045i	−0.364394	+	0.931245i	$0.618724\pi$
$632$	41.4850	−	6.57058i	1.65019	−	0.261364i
$633$	−14.3362	−	11.3405i	−0.569813	−	0.450746i
$634$		−	49.9461i		−	1.98361i
$635$	39.0479	−	8.08564i	1.54957	−	0.320869i
$636$	−22.8872	−	49.8645i	−0.907537	−	1.97726i
$637$	2.43728	−	4.78343i	0.0965685	−	0.189526i
$638$	57.1131	+	14.7413i	2.26113	+	0.583614i
$639$	0.0570873	−	0.695718i	0.00225834	−	0.0275222i
$640$	30.6857	−	6.35409i	1.21296	−	0.251167i
$641$	12.0776	+	16.6234i	0.477036	+	0.656583i	0.977932	−	0.208924i	$-0.0669962\pi$
$641$	12.0776	+	16.6234i	0.477036	+	0.656583i	−0.500896	+	0.865507i	$0.666996\pi$
$642$	−2.85005	−	1.05684i	−0.112482	−	0.0417100i
$643$	−21.7405	+	3.44335i	−0.857360	+	0.135792i	−0.569612	−	0.821914i	$-0.692906\pi$
$643$	−21.7405	+	3.44335i	−0.857360	+	0.135792i	−0.287748	+	0.957706i	$0.592906\pi$
$644$	−53.0374			−2.08997
$645$	7.49576	+	45.5078i	0.295145	+	1.79187i
$646$	−4.43120	+	13.6378i	−0.174343	+	0.536573i
$647$	−2.15148	+	2.15148i	−0.0845836	+	0.0845836i	−0.748133	−	0.663549i	$-0.769049\pi$
$647$	−2.15148	+	2.15148i	−0.0845836	+	0.0845836i	0.663549	+	0.748133i	$0.269049\pi$
$648$	−32.1121	+	43.5847i	−1.26148	+	1.71217i
$649$	−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
$652$	−34.6692	−	34.6692i	−1.35775	−	1.35775i
$653$	5.85034	+	0.926604i	0.228942	+	0.0362608i	0.269851	−	0.962902i	$-0.413026\pi$
$653$	5.85034	+	0.926604i	0.228942	+	0.0362608i	−0.0409094	+	0.999163i	$0.513026\pi$
$654$	14.8919	−	6.83518i	0.582318	−	0.267277i
$655$	5.97189	+	3.92297i	0.233341	+	0.153283i
$656$	−46.5792	+	15.1345i	−1.81861	+	0.590903i
$657$	7.24053	−	29.7223i	0.282480	−	1.15958i
$658$	−29.1284	−	57.1678i	−1.13554	−	2.22863i
$659$	4.23443	+	13.0322i	0.164950	+	0.507664i	0.999033	−	0.0439759i	$-0.0140025\pi$
$659$	4.23443	+	13.0322i	0.164950	+	0.507664i	−0.834083	+	0.551639i	$0.814002\pi$
$660$	51.7581	+	22.0972i	2.01468	+	0.860132i
$661$	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	$-0.148292\pi$
$662$	12.3151	−	1.95052i	0.478639	−	0.0758090i
$663$	0.825230	−	20.1478i	0.0320493	−	0.782476i
$664$	18.5736	−	25.5643i	0.720795	−	0.992089i
$665$	−1.14472	−	5.52817i	−0.0443902	−	0.214373i
$666$	−30.2948	−	2.48584i	−1.17390	−	0.0963245i
$667$	−17.7680	+	34.8716i	−0.687978	+	1.35023i
$668$	−39.4964	+	77.5161i	−1.52816	+	2.99919i
$669$	4.42696	−	22.0637i	0.171156	−	0.853031i
$670$	15.4995	+	4.24050i	0.598797	+	0.163825i
$671$	−14.8347	+	3.29621i	−0.572686	+	0.127249i
$672$	−4.29411	−	15.3234i	−0.165649	−	0.591114i
$673$	19.2673	+	9.81717i	0.742699	+	0.378424i	0.784031	−	0.620722i	$-0.213160\pi$
$673$	19.2673	+	9.81717i	0.742699	+	0.378424i	−0.0413323	+	0.999145i	$0.513160\pi$
$674$	−20.9591	−	64.5055i	−0.807315	−	2.48466i
$675$	20.5736	+	15.8659i	0.791878	+	0.610679i
$676$	−26.0386	−	18.9182i	−1.00149	−	0.727622i
$677$	−1.38229	+	8.72742i	−0.0531256	+	0.335422i	0.946783	+	0.321874i	$0.104313\pi$
$677$	−1.38229	+	8.72742i	−0.0531256	+	0.335422i	−0.999908	+	0.0135483i	$0.995687\pi$
$678$	−5.28408	−	0.216429i	−0.202934	−	0.00831192i
$679$	−32.9138	−	10.6943i	−1.26312	−	0.410411i
$680$	63.5221	+	17.3790i	2.43596	+	0.666455i
$681$	14.1423	−	13.0293i	0.541933	−	0.499286i
$682$	−76.1016	+	30.0193i	−2.91408	+	1.14950i
$683$	−0.866555	−	0.137249i	−0.0331578	−	0.00525168i	0.139834	−	0.990175i	$-0.455343\pi$
$683$	−0.866555	−	0.137249i	−0.0331578	−	0.00525168i	−0.172991	+	0.984923i	$0.555343\pi$
$684$	5.87837	−	14.0590i	0.224765	−	0.537558i
$685$	−15.4827	−	14.0887i	−0.591563	−	0.538302i
$686$	−29.9342	+	41.2010i	−1.14289	+	1.57306i
$687$	−5.39506	−	8.10347i	−0.205834	−	0.309167i
$688$	−34.7768	−	68.2533i	−1.32585	−	2.60213i
$689$	−13.9083	−	10.1050i	−0.529865	−	0.384970i
$690$	−31.6959	+	44.1965i	−1.20664	+	1.68253i
$691$	0.792167	+	0.575543i	0.0301355	+	0.0218947i	0.602751	−	0.797929i	$-0.294071\pi$
$691$	0.792167	+	0.575543i	0.0301355	+	0.0218947i	−0.572616	+	0.819824i	$0.694071\pi$
$692$	10.9737	−	69.2850i	0.417156	−	2.63382i
$693$	−7.11264	+	20.4667i	−0.270187	+	0.777466i
$694$	−25.5424	−	35.1561i	−0.969577	−	1.33451i
$695$	8.33177	−	30.4535i	0.316042	−	1.15517i
$696$	−71.9173	−	14.4298i	−2.72602	−	0.546962i
$697$	36.8195	+	5.83164i	1.39464	+	0.220889i
$698$	38.4151	+	6.08436i	1.45403	+	0.230296i
$699$	9.77812	−	17.3921i	0.369842	−	0.657828i
$700$	−46.2057	+	11.8617i	−1.74641	+	0.448329i
$701$	−34.0135	+	11.0517i	−1.28467	+	0.417416i	−0.870224	−	0.492657i	$-0.836026\pi$
$701$	−34.0135	+	11.0517i	−1.28467	+	0.417416i	−0.414449	+	0.910072i	$0.636026\pi$
$702$	−3.82328	+	30.9756i	−0.144300	+	1.16910i
$703$	4.59299	−	0.727459i	0.173228	−	0.0274366i
$704$	7.28751	+	0.698189i	0.274658	+	0.0263140i
$705$	−44.6592	−	6.79121i	−1.68196	−	0.255772i
$706$	−21.2412	+	65.3737i	−0.799423	+	2.46037i
$707$	4.63932	+	2.36385i	0.174480	+	0.0889018i
$708$	12.3900	+	4.59438i	0.465645	+	0.172667i
$709$	34.9967	+	11.3711i	1.31433	+	0.427052i	0.880544	−	0.473964i	$-0.157177\pi$
$709$	34.9967	+	11.3711i	1.31433	+	0.427052i	0.433786	+	0.901016i	$0.357177\pi$
$710$	1.28703	−	0.266505i	0.0483015	−	0.0100018i
$711$	19.3266	+	8.08087i	0.724803	+	0.303056i
$712$	−0.831139	−	0.131640i	−0.0311483	−	0.00493340i
$713$	−8.49143	−	53.6128i	−0.318007	−	2.00781i
$714$	−9.17744	+	45.7397i	−0.343457	+	1.71177i
$715$	17.5299	−	1.91250i	0.655583	−	0.0715234i
$716$	−55.0773	+	17.8957i	−2.05834	+	0.668794i
$717$	18.7778	−	12.5018i	0.701271	−	0.466887i
$718$	−36.5547	−	18.6256i	−1.36421	−	0.695100i
$719$	3.19596	+	9.83615i	0.119189	+	0.366827i	0.992798	−	0.119803i	$-0.0382262\pi$
$719$	3.19596	+	9.83615i	0.119189	+	0.366827i	−0.873609	+	0.486629i	$0.838226\pi$
$720$	−40.5512	−	14.7530i	−1.51125	−	0.549814i
$721$	−5.32479	−	16.3880i	−0.198306	−	0.610322i
$722$	6.97707	−	44.0515i	0.259660	−	1.63943i
$723$	−7.64620	−	6.04846i	−0.284365	−	0.224945i
$724$	−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	$0.967857\pi$
$728$	−22.0239	−	22.0239i	−0.816259	−	0.816259i
$729$	−25.0468	+	10.0826i	−0.927659	+	0.373429i
$730$	57.5354	−	2.71217i	2.12948	−	0.100382i
$731$			58.3063i			2.15654i
$732$	33.4800	−	9.38216i	1.23746	−	0.346774i
$733$	−37.0687	−	18.8875i	−1.36916	−	0.697624i	−0.394001	−	0.919110i	$-0.628909\pi$
$733$	−37.0687	−	18.8875i	−1.36916	−	0.697624i	−0.975164	+	0.221486i	$0.928909\pi$
$734$	56.2567	−	40.8729i	2.07647	−	1.50865i
$735$	2.75345	+	8.29970i	0.101563	+	0.306139i
$736$	7.24776	−	22.3063i	0.267156	−	0.822221i
$737$	7.95998	+	5.06571i	0.293210	+	0.186598i
$738$	−56.0596	−	13.6564i	−2.06358	−	0.502701i
$739$	10.2324	−	3.32470i	0.376404	−	0.122301i	−0.114704	−	0.993400i	$-0.536592\pi$
$739$	10.2324	−	3.32470i	0.376404	−	0.122301i	0.491108	+	0.871099i	$0.336592\pi$
$740$	−7.96768	−	38.4782i	−0.292898	−	1.41449i
$741$	−0.553315	−	4.74261i	−0.0203265	−	0.174224i
$742$	28.1238	+	28.1238i	1.03246	+	1.03246i
$743$	−2.32636	−	14.6881i	−0.0853459	−	0.538853i	−0.992903	−	0.118925i	$-0.962055\pi$
$743$	−2.32636	−	14.6881i	−0.0853459	−	0.538853i	0.907557	−	0.419928i	$-0.137945\pi$
$744$	92.4589	−	42.4375i	3.38971	−	1.55583i
$745$	−1.18704	−	0.324761i	−0.0434896	−	0.0118983i
$746$			16.2603i			0.595333i
$747$	14.5800	−	5.98242i	0.533456	−	0.218885i
$748$	60.0227	+	38.1983i	2.19465	+	1.39667i
$749$	1.51288			0.0552795
$750$	−17.7288	+	45.5922i	−0.647362	+	1.66479i
$751$	1.13212	+	3.48430i	0.0413116	+	0.127144i	0.969585	−	0.244754i	$-0.0787072\pi$
$751$	1.13212	+	3.48430i	0.0413116	+	0.127144i	−0.928274	+	0.371898i	$0.878707\pi$
$752$	74.1036	−	11.7369i	2.70228	−	0.427999i
$753$	15.0541	+	5.58226i	0.548602	+	0.203429i
$754$	−40.2178	+	13.0676i	−1.46465	+	0.475893i
$755$	3.88051	+	4.84387i	0.141226	+	0.176286i
$756$	13.6951	−	47.6462i	0.498084	−	1.73288i
$757$	40.7488	+	6.45398i	1.48104	+	0.234574i	0.844036	−	0.536287i	$-0.180173\pi$
$757$	40.7488	+	6.45398i	1.48104	+	0.234574i	0.637004	+	0.770860i	$0.280173\pi$
$758$	−64.1365	−	10.1582i	−2.32954	−	0.368964i
$759$	−25.4426	+	19.2994i	−0.923508	+	0.700522i
$760$	15.4999	+	1.71151i	0.562240	+	0.0620830i
$761$	−3.05360	+	0.992174i	−0.110693	+	0.0359663i	−0.363840	−	0.931462i	$-0.618534\pi$
$761$	−3.05360	+	0.992174i	−0.110693	+	0.0359663i	0.253147	+	0.967428i	$0.418534\pi$
$762$	−77.9611	−	3.19319i	−2.82423	−	0.115677i
$763$	−5.76664	+	5.76664i	−0.208767	+	0.208767i
$764$	−35.2876	+	25.6380i	−1.27666	+	0.927549i
$765$	22.4036	+	24.0182i	0.810003	+	0.868379i
$766$	−66.7219			−2.41076
$767$	4.08960	−	0.647729i	0.147667	−	0.0233881i
$768$	−53.6256	−	2.19644i	−1.93505	−	0.0792572i
$769$	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	$0.786969\pi$
$770$	−40.7486	−	1.97420i	−1.46848	−	0.0711452i
$771$	−29.0324	−	16.3225i	−1.04558	−	0.587842i
$772$	33.8216	+	33.8216i	1.21727	+	1.21727i
$773$	−11.4707	−	11.4707i	−0.412572	−	0.412572i	0.470062	−	0.882633i	$-0.344232\pi$
$773$	−11.4707	−	11.4707i	−0.412572	−	0.412572i	−0.882633	+	0.470062i	$0.844232\pi$
$774$	7.38031	−	89.9433i	0.265280	−	3.23294i
$775$	−19.3880	−	44.8078i	−0.696437	−	1.60954i
$776$	56.1892	−	77.3378i	2.01708	−	2.77627i
$777$	14.5675	−	4.08227i	0.522606	−	0.146451i
$778$	−21.2314	−	41.6689i	−0.761182	−	1.49390i
$779$	8.82713			0.316265
$780$	−39.8104	+	6.55732i	−1.42544	+	0.234790i
$781$	0.768213	+	0.0735996i	0.0274888	+	0.00263360i
$782$	−48.6181	+	48.6181i	−1.73858	+	1.73858i
$783$	−26.7389	−	24.9662i	−0.955572	−	0.892220i
$784$	−8.53687	−	11.7500i	−0.304888	−	0.419642i
$785$	−5.65701	+	51.2314i	−0.201907	+	1.82853i
$786$	−9.47321	−	10.2824i	−0.337898	−	0.366760i
$787$	17.7629	−	9.05064i	0.633179	−	0.322621i	−0.107776	−	0.994175i	$-0.534373\pi$
$787$	17.7629	−	9.05064i	0.633179	−	0.322621i	0.740955	+	0.671555i	$0.234373\pi$
$788$	13.1323	+	13.1323i	0.467817	+	0.467817i
$789$	−1.72169	−	14.7571i	−0.0612938	−	0.525366i
$790$	−4.32889	+	39.2036i	−0.154015	+	1.39480i
$791$	2.50332	−	0.813377i	0.0890077	−	0.0289204i
$792$	−47.6959	−	36.1553i	−1.69480	−	1.28472i
$793$	7.70370	−	7.70370i	0.273567	−	0.273567i
$794$	0.901196	−	2.77360i	0.0319823	−	0.0984313i
$795$	27.6301	−	4.55105i	0.979937	−	0.161409i
$796$	−11.9196	+	8.66008i	−0.422478	+	0.306949i
$797$	27.1416	+	13.8293i	0.961404	+	0.489860i	0.862954	−	0.505282i	$-0.168612\pi$
$797$	27.1416	+	13.8293i	0.961404	+	0.489860i	0.0984501	+	0.995142i	$0.468612\pi$
$798$	−0.452073	+	11.0373i	−0.0160032	+	0.390715i
$799$	−54.3124	−	17.6472i	−1.92143	−	0.624312i
$800$	1.32543	−	21.0540i	0.0468610	−	0.744370i
$801$	−0.318221	−	0.273626i	−0.0112438	−	0.00966809i
$802$	41.5585	−	21.1751i	1.46748	−	0.747719i
$803$	32.7470	+	8.45225i	1.15562	+	0.298273i
$804$	−18.8177	−	10.5797i	−0.663650	−	0.373116i
$805$	7.14330	−	26.1095i	0.251768	−	0.920238i
$806$	34.4738	−	47.4491i	1.21429	−	1.67132i
$807$	−3.68357	+	2.45241i	−0.129668	+	0.0863290i
$808$	−10.1700	+	10.1700i	−0.357779	+	0.357779i
$809$	−5.34144	+	16.4392i	−0.187795	+	0.577973i	−0.999985	−	0.00541921i	$-0.998275\pi$
$809$	−5.34144	+	16.4392i	−0.187795	+	0.577973i	0.812190	+	0.583392i	$0.198275\pi$
$810$	−31.5195	−	39.8862i	−1.10748	−	1.40146i
$811$	11.4564			0.402287			0.201144	−	0.979562i	$-0.435534\pi$
$811$	11.4564			0.402287			0.201144	+	0.979562i	$0.435534\pi$
$812$	66.3431	−	10.5077i	2.32819	−	0.368749i
$813$	−14.2272	+	38.3674i	−0.498968	+	1.34561i
$814$	3.20487	−	33.4515i	0.112330	−	1.17248i
$815$	21.7365	−	12.3977i	0.761396	−	0.434273i
$816$	−47.5522	−	26.7347i	−1.66466	−	0.935901i
$817$	2.15978	+	13.6363i	0.0755611	+	0.477074i
$818$	58.0411	−	29.5734i	2.02936	−	1.03401i
$819$	−3.57595	−	15.1166i	−0.124954	−	0.528218i
$820$	−3.51217	−	74.5064i	−0.122650	−	2.60188i
$821$	17.4197	+	23.9762i	0.607953	+	0.836775i	0.996407	−	0.0846928i	$-0.0269909\pi$
$821$	17.4197	+	23.9762i	0.607953	+	0.836775i	−0.388454	+	0.921468i	$0.626991\pi$
$822$	22.6997	+	34.0954i	0.791744	+	1.18921i
$823$	−19.4570	−	9.91385i	−0.678229	−	0.345575i	0.0807089	−	0.996738i	$-0.474282\pi$
$823$	−19.4570	−	9.91385i	−0.678229	−	0.345575i	−0.758938	+	0.651163i	$0.774282\pi$
$824$	47.5974			1.65813
$825$	−17.8491	+	22.5036i	−0.621425	+	0.783474i
$826$	−9.57928			−0.333306
$827$	−32.2214	−	16.4176i	−1.12045	−	0.570896i	−0.207198	−	0.978299i	$-0.566435\pi$
$827$	−32.2214	−	16.4176i	−1.12045	−	0.570896i	−0.913249	+	0.407403i	$0.866435\pi$
$828$	55.7176	−	47.2671i	1.93632	−	1.64265i
$829$	18.4385	+	25.3785i	0.640396	+	0.881430i	0.998637	−	0.0521994i	$-0.0166231\pi$
$829$	18.4385	+	25.3785i	0.640396	+	0.881430i	−0.358240	+	0.933629i	$0.616623\pi$
$830$	18.5524	+	23.1581i	0.643964	+	0.803831i
$831$	5.11812	+	43.8688i	0.177546	+	1.52179i
$832$	−4.67645	+	2.38277i	−0.162127	+	0.0826077i
$833$	1.72936	+	10.9187i	0.0599187	+	0.378312i
$834$	−30.2762	+	53.8513i	−1.04838	+	1.86472i
$835$	−32.8404	−	29.8836i	−1.13649	−	1.03417i
$836$	15.4527	+	6.71022i	0.534442	+	0.232078i
$837$	50.3557	+	6.21534i	1.74055	+	0.214834i
$838$	−69.3239	+	10.9798i	−2.39476	+	0.379292i
$839$	49.4517			1.70726			0.853631	−	0.520878i	$-0.174395\pi$
$839$	49.4517			1.70726			0.853631	+	0.520878i	$0.174395\pi$
$840$	50.7315	−	0.312939i	1.75040	−	0.0107974i
$841$	6.35525	−	19.5595i	0.219147	−	0.674464i
$842$	−19.8686	+	19.8686i	−0.684718	+	0.684718i
$843$	3.61734	+	5.43331i	0.124588	+	0.187133i
$844$	−27.1778	+	37.4070i	−0.935498	+	1.28760i
$845$	12.8201	−	10.2704i	0.441025	−	0.353313i
$846$	81.5485	+	34.0973i	2.80369	+	1.17229i
$847$	−22.5174	−	8.17128i	−0.773707	−	0.280768i
$848$	−41.4400	+	21.1147i	−1.42306	+	0.725083i
$849$	−3.92962	+	3.62038i	−0.134864	+	0.124251i
$850$	−31.4823	+	53.2289i	−1.07983	+	1.82574i
$851$	21.2059	+	6.89022i	0.726929	+	0.236194i
$852$	−1.76425	−	0.0722617i	−0.0604423	−	0.00247564i
$853$	−30.4596	−	15.5200i	−1.04292	−	0.531393i	−0.153338	−	0.988174i	$-0.549002\pi$
$853$	−30.4596	−	15.5200i	−1.04292	−	0.531393i	−0.889579	+	0.456781i	$0.849002\pi$
$854$	−20.3913	+	14.8151i	−0.697775	+	0.506963i
$855$	6.12928	+	4.78735i	0.209617	+	0.163724i
$856$	−1.29137	+	3.97442i	−0.0441380	+	0.135843i
$857$	−13.6178	+	13.6178i	−0.465176	+	0.465176i	−0.900348	−	0.435171i	$-0.856688\pi$
$857$	−13.6178	+	13.6178i	−0.465176	+	0.465176i	0.435171	+	0.900348i	$0.356688\pi$
$858$	−34.1839	−	4.69358i	−1.16702	−	0.160236i
$859$	−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	$0.413580\pi$
$860$	114.239	−	23.6555i	3.89553	−	0.806647i
$861$	28.5239	−	3.32785i	0.972093	−	0.113413i
$862$	−29.8136	−	29.8136i	−1.01546	−	1.01546i
$863$	40.7068	−	20.7411i	1.38567	−	0.706037i	0.407381	−	0.913258i	$-0.366442\pi$
$863$	40.7068	−	20.7411i	1.38567	−	0.706037i	0.978294	+	0.207222i	$0.0664422\pi$
$864$	18.1674	+	12.2708i	0.618067	+	0.417463i
$865$	32.6299	+	14.7337i	1.10945	+	0.500962i
$866$	−35.0210	−	48.2023i	−1.19006	−	1.63798i
$867$	6.69338	+	10.0536i	0.227319	+	0.341437i
$868$	−65.8747	+	65.8747i	−2.23593	+	2.23593i
$869$	−9.22440	+	21.2424i	−0.312916	+	0.720601i
$870$	30.8914	−	61.5637i	1.04732	−	2.08721i
$871$	−6.76430			−0.229199
$872$	−10.2270	−	20.0716i	−0.346329	−	0.679709i
$873$	44.1079	−	18.0981i	1.49283	−	0.612529i
$874$	−9.56959	+	13.1714i	−0.323696	+	0.445530i
$875$	0.383852	−	24.3439i	0.0129766	−	0.822974i
$876$	−75.8692	−	15.2228i	−2.56338	−	0.514329i
$877$	14.5761	+	14.5761i	0.492201	+	0.492201i	0.908999	−	0.416798i	$-0.136848\pi$
$877$	14.5761	+	14.5761i	0.492201	+	0.492201i	−0.416798	+	0.908999i	$0.636848\pi$
$878$	35.9139	+	35.9139i	1.21204	+	1.21204i
$879$	−10.9921	+	19.5514i	−0.370756	+	0.659452i
$880$	16.9202	−	44.6044i	0.570380	−	1.50361i
$881$	−9.77534	−	13.4546i	−0.329339	−	0.453297i	0.611950	−	0.790896i	$-0.290385\pi$
$881$	−9.77534	−	13.4546i	−0.329339	−	0.453297i	−0.941290	+	0.337599i	$0.890385\pi$
$882$	−1.28563	−	17.0621i	−0.0432895	−	0.574512i
$883$	−30.1703	+	4.77851i	−1.01531	+	0.160810i	−0.641846	−	0.766834i	$-0.721831\pi$
$883$	−30.1703	+	4.77851i	−1.01531	+	0.160810i	−0.373467	+	0.927643i	$0.621831\pi$
$884$	−51.0066			−1.71554
$885$	−3.93048	+	5.48061i	−0.132122	+	0.184229i
$886$	76.8476	−	55.8331i	2.58175	−	1.87575i
$887$	−33.1051	+	33.1051i	−1.11156	+	1.11156i	−0.118619	+	0.992940i	$0.537847\pi$
$887$	−33.1051	+	33.1051i	−1.11156	+	1.11156i	−0.992940	+	0.118619i	$0.962153\pi$
$888$	−1.71020	+	41.7542i	−0.0573905	+	1.40118i
$889$	36.9339	−	12.0005i	1.23872	−	0.402485i
$890$	0.325194	−	0.720188i	0.0109005	−	0.0241408i
$891$	−10.7679	−	27.8398i	−0.360739	−	0.932667i
$892$	−56.2215	−	8.90462i	−1.88244	−	0.298149i
$893$	−13.3559	−	2.11537i	−0.446939	−	0.0707881i
$894$	2.09905	+	1.18012i	0.0702028	+	0.0394692i
$895$	−1.39174	−	29.5239i	−0.0465206	−	0.986877i
$896$	29.0244	−	9.43061i	0.969638	−	0.315054i
$897$	7.95989	−	21.4660i	0.265773	−	0.716730i
$898$	−7.58678	+	1.20163i	−0.253174	+	0.0400988i
$899$	21.2434	+	65.3805i	0.708507	+	2.18056i
$900$	37.9694	−	53.6397i	1.26565	−	1.78799i
$901$	35.4007			1.17937
$902$	15.9419	−	61.7645i	0.530806	−	2.05653i
$903$	12.1200	+	43.2500i	0.403329	+	1.43927i
$904$			7.27063i			0.241818i
$905$	11.5315	−	4.35714i	0.383321	−	0.144836i
$906$	−5.06602	−	11.0374i	−0.168307	−	0.366692i
$907$	−8.08984	−	51.0772i	−0.268619	−	1.69599i	−0.640700	−	0.767791i	$-0.721356\pi$
$907$	−8.08984	−	51.0772i	−0.268619	−	1.69599i	0.372082	−	0.928200i	$-0.378644\pi$
$908$	−34.3941	−	34.3941i	−1.14141	−	1.14141i
$909$	−6.98043	+	1.65127i	−0.231526	+	0.0547693i
$910$	25.4059	−	14.4906i	0.842198	−	0.480359i
$911$	−34.6566	+	11.2606i	−1.14823	+	0.373081i	−0.820475	−	0.571683i	$-0.806291\pi$
$911$	−34.6566	+	11.2606i	−1.14823	+	0.373081i	−0.327751	+	0.944764i	$0.606291\pi$
$912$	−12.1115	−	4.49111i	−0.401052	−	0.148716i
$913$	6.39329	+	16.2076i	0.211587	+	0.536392i
$914$	9.60458	−	29.5599i	0.317691	−	0.977754i
$915$	0.109462	+	17.7453i	0.00361872	+	0.586642i
$916$	−19.9221	+	14.4742i	−0.658243	+	0.478242i
$917$	6.20006	+	3.15909i	0.204744	+	0.104322i
$918$	−31.1222	−	56.2300i	−1.02719	−	1.85587i
$919$		−	40.0428i		−	1.32089i	−0.750875	−	0.660444i	$-0.770368\pi$
$919$		−	40.0428i		−	1.32089i	0.750875	−	0.660444i	$-0.229632\pi$
$920$	62.4936	+	41.0524i	2.06035	+	1.35346i
$921$	−35.2016	−	7.06303i	−1.15993	−	0.232735i
$922$	−49.1288	−	49.1288i	−1.61797	−	1.61797i
$923$	−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
$927$	20.1989	+	12.4707i	0.663420	+	0.409591i
$928$	−4.64673	+	29.3383i	−0.152536	+	0.963076i
$929$	−0.497025	−	1.52969i	−0.0163069	−	0.0501874i	0.942572	−	0.334003i	$-0.108400\pi$
$929$	−0.497025	−	1.52969i	−0.0163069	−	0.0501874i	−0.958879	+	0.283816i	$0.908400\pi$
$930$	15.5262	+	94.2615i	0.509123	+	3.09096i
$931$	0.808903	+	2.48955i	0.0265107	+	0.0815916i
$932$	−44.9686	−	22.9126i	−1.47299	−	0.750528i
$933$	18.7679	+	28.1897i	0.614433	+	0.922888i
$934$	0.226689	−	0.0736558i	0.00741750	−	0.00241009i
$935$	−26.8885	+	24.4035i	−0.879349	+	0.798080i
$936$	42.7646	+	3.50905i	1.39780	+	0.114697i
$937$	0.825533	+	5.21221i	0.0269690	+	0.170275i	0.997497	−	0.0707145i	$-0.0225279\pi$
$937$	0.825533	+	5.21221i	0.0269690	+	0.170275i	−0.970528	+	0.240990i	$0.922528\pi$
$938$	15.4566	+	2.44809i	0.504677	+	0.0799330i
$939$	−15.9536	−	8.96941i	−0.520627	−	0.292706i
$940$	−12.5409	+	113.574i	−0.409039	+	3.70437i
$941$	19.6082	+	6.37109i	0.639209	+	0.207691i	0.610650	−	0.791901i	$-0.290908\pi$
$941$	19.6082	+	6.37109i	0.639209	+	0.207691i	0.0285586	+	0.999592i	$0.490908\pi$
$942$	35.0650	−	94.5625i	1.14248	−	3.08101i
$943$	37.7116	+	19.2150i	1.22806	+	0.625727i
$944$	3.46150	−	10.6534i	0.112662	−	0.346739i
$945$	21.6110	+	13.1590i	0.703005	+	0.428064i
$946$	99.3155	+	9.51504i	3.22902	+	0.309361i
$947$	25.0775	−	3.97188i	0.814908	−	0.129069i	0.264951	−	0.964262i	$-0.414644\pi$
$947$	25.0775	−	3.97188i	0.814908	−	0.129069i	0.549957	+	0.835193i	$0.314644\pi$
$948$	18.4228	−	49.6821i	0.598344	−	1.61360i
$949$	−23.0598	+	7.49258i	−0.748552	+	0.243219i
$950$	−5.39118	+	13.6150i	−0.174913	+	0.441729i
$951$	−29.8516	−	16.7831i	−0.968005	−	0.544229i
$952$	63.3465	+	10.0331i	2.05307	+	0.325175i
$953$	−19.4424	−	3.07938i	−0.629802	−	0.0997509i	−0.166631	−	0.986019i	$-0.553289\pi$
$953$	−19.4424	−	3.07938i	−0.629802	−	0.0997509i	−0.463172	+	0.886268i	$0.653289\pi$
$954$	−54.6091	−	4.48096i	−1.76803	−	0.145076i
$955$	−7.86848	−	20.8246i	−0.254618	−	0.673867i
$956$	−33.5405	−	46.1646i	−1.08478	−	1.49307i
$957$	28.0019	−	29.1817i	0.905173	−	0.943311i
$958$	−9.12096	+	57.5875i	−0.294685	+	1.86057i
$959$	−16.4930	−	11.9829i	−0.532587	−	0.386947i
$960$	2.59157	−	8.14667i	0.0836424	−	0.262933i
$961$	−52.0564	−	37.8212i	−1.67924	−	1.22004i
$962$	10.9375	+	21.4661i	0.352640	+	0.692095i
$963$	−1.58933	+	1.34828i	−0.0512155	+	0.0434479i
$964$	−14.4952	+	19.9510i	−0.466860	+	0.642577i
$965$	−21.2051	+	12.0946i	−0.682616	+	0.389340i
$966$	−25.9574	+	46.1697i	−0.835167	+	1.48549i
$967$	−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	$0.731796\pi$
$968$	40.6868	−	52.1796i	1.30772	−	1.67712i
$969$	6.66202	+	7.23106i	0.214015	+	0.232295i
$970$	56.1252	+	70.0585i	1.80207	+	2.24944i
$971$	1.84617	+	0.599858i	0.0592465	+	0.0192504i	0.338490	−	0.940970i	$-0.390084\pi$
$971$	1.84617	+	0.599858i	0.0592465	+	0.0192504i	−0.279244	+	0.960220i	$0.590084\pi$
$972$	28.0753	+	62.2590i	0.900517	+	1.99696i
$973$	4.81003	−	30.3693i	0.154202	−	0.973596i
$974$	−72.0031	−	52.3133i	−2.30713	−	1.67623i
$975$	2.13376	−	20.4812i	0.0683349	−	0.655923i
$976$	−9.10790	−	28.0312i	−0.291537	−	0.897258i
$977$	−33.9266	−	17.2865i	−1.08541	−	0.553043i	−0.182644	−	0.983179i	$-0.558466\pi$
$977$	−33.9266	−	17.2865i	−1.08541	−	0.553043i	−0.902764	+	0.430136i	$0.858466\pi$
$978$	−47.1477	+	13.2123i	−1.50762	+	0.422482i
$979$	0.307276	−	0.347647i	0.00982058	−	0.0111109i
$980$	20.6915	−	7.81819i	0.660964	−	0.249743i
$981$	0.918797	−	11.1973i	0.0293349	−	0.357502i
$982$	−3.62383	+	7.11217i	−0.115641	+	0.226958i
$983$	5.62269	−	11.0351i	0.179336	−	0.351966i	−0.783786	−	0.621030i	$-0.786714\pi$
$983$	5.62269	−	11.0351i	0.179336	−	0.351966i	0.963122	+	0.269064i	$0.0867143\pi$
$984$	−15.6050	+	77.7745i	−0.497471	+	2.47936i
$985$	−8.23350	+	4.69609i	−0.262341	+	0.149630i
$986$	51.1830	−	70.4473i	1.63000	−	2.24350i
$987$	−43.9557	−	1.80037i	−1.39913	−	0.0573064i
$988$	−11.9291	+	1.88938i	−0.379515	+	0.0601093i
$989$	−20.4566	+	62.9590i	−0.650483	+	2.00198i
$990$	44.5672	−	34.2413i	1.41644	−	1.08826i
$991$	−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	$0.928341\pi$
$992$	−18.7033	−	36.7074i	−0.593831	−	1.16546i
$993$	2.97239	−	8.01585i	0.0943258	−	0.254375i
$994$	1.21735	−	0.395542i	0.0386121	−	0.0125458i
$995$	−2.65784	−	7.03419i	−0.0842593	−	0.222999i
$996$	−16.6291	−	36.2300i	−0.526914	−	1.14799i
$997$	−45.8598	−	7.26348i	−1.45239	−	0.230037i	−0.620166	−	0.784470i	$-0.712935\pi$
$997$	−45.8598	−	7.26348i	−1.45239	−	0.230037i	−0.832228	+	0.554434i	$0.812935\pi$
$998$	75.5437	+	75.5437i	2.39129	+	2.39129i
$999$	−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.df.a.47.8	yes	928
3.2	odd	2	inner	825.2.df.a.47.109	yes	928
11.4	even	5		825.2.cv.a.422.109	yes	928
25.8	odd	20		825.2.cv.a.608.8	yes	928
33.26	odd	10		825.2.cv.a.422.8	✓	928
75.8	even	20		825.2.cv.a.608.109	yes	928
275.158	odd	20	inner	825.2.df.a.158.109	yes	928
825.158	even	20	inner	825.2.df.a.158.8	yes	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.cv.a.422.8	✓	928	33.26	odd	10
825.2.cv.a.422.109	yes	928	11.4	even	5
825.2.cv.a.608.8	yes	928	25.8	odd	20
825.2.cv.a.608.109	yes	928	75.8	even	20
825.2.df.a.47.8	yes	928	1.1	even	1	trivial
825.2.df.a.47.109	yes	928	3.2	odd	2	inner
825.2.df.a.158.8	yes	928	825.158	even	20	inner
825.2.df.a.158.109	yes	928	275.158	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.df (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.25078 - 1.14683i) q^{2} +(-1.44175 + 0.959875i) q^{3} +(2.57522 + 3.54448i) q^{4} +(-2.09173 + 0.790353i) q^{5} +(4.34587 - 0.507027i) q^{6} +(-1.94030 + 0.988634i) q^{7} +(-0.940987 - 5.94116i) q^{8} +(1.15728 - 2.76780i) q^{9} +O(q^{10})\)	\(q+(-2.25078 - 1.14683i) q^{2} +(-1.44175 + 0.959875i) q^{3} +(2.57522 + 3.54448i) q^{4} +(-2.09173 + 0.790353i) q^{5} +(4.34587 - 0.507027i) q^{6} +(-1.94030 + 0.988634i) q^{7} +(-0.940987 - 5.94116i) q^{8} +(1.15728 - 2.76780i) q^{9} +(5.61442 + 0.619949i) q^{10} +(3.04218 + 1.32105i) q^{11} +(-7.11508 - 2.63837i) q^{12} +(-2.34849 + 0.371964i) q^{13} +5.50099 q^{14} +(2.25711 - 3.14729i) q^{15} +(-1.98780 + 6.11781i) q^{16} +(3.46217 - 3.46217i) q^{17} +(-5.77897 + 4.90250i) q^{18} +(0.681464 - 0.937954i) q^{19} +(-8.18805 - 5.37878i) q^{20} +(1.84847 - 3.28781i) q^{21} +(-5.33225 - 6.46224i) q^{22} +(4.95313 - 2.52374i) q^{23} +(7.05944 + 7.66243i) q^{24} +(3.75068 - 3.30641i) q^{25} +(5.71251 + 1.85611i) q^{26} +(0.988235 + 5.10131i) q^{27} +(-8.50090 - 4.33142i) q^{28} +(-5.69573 + 4.13819i) q^{29} +(-8.68966 + 4.49534i) q^{30} +(3.01739 - 9.28658i) q^{31} +(2.98337 - 2.98337i) q^{32} +(-5.65409 + 1.01549i) q^{33} +(-11.7631 + 3.82206i) q^{34} +(3.27723 - 3.60148i) q^{35} +(12.7907 - 3.02573i) q^{36} +(2.83620 + 2.83620i) q^{37} +(-2.60950 + 1.32961i) q^{38} +(3.02889 - 2.79053i) q^{39} +(6.66391 + 11.6836i) q^{40} +(4.47522 + 6.15961i) q^{41} +(-7.93104 + 5.28026i) q^{42} +(-8.42050 + 8.42050i) q^{43} +(3.15184 + 14.1849i) q^{44} +(-0.233180 + 6.70415i) q^{45} -14.0427 q^{46} +(-5.29513 - 10.3923i) q^{47} +(-3.00643 - 10.7284i) q^{48} +(-1.32712 + 1.82662i) q^{49} +(-12.2338 + 3.14061i) q^{50} +(-1.66833 + 8.31482i) q^{51} +(-7.36629 - 7.36629i) q^{52} +(5.11251 + 5.11251i) q^{53} +(3.62603 - 12.6153i) q^{54} +(-7.40751 - 0.358881i) q^{55} +(7.69944 + 10.5974i) q^{56} +(-0.0821803 + 2.00641i) q^{57} +(17.5656 - 2.78212i) q^{58} -1.74137 q^{59} +(16.9681 - 0.104668i) q^{60} +(-3.70684 + 2.69318i) q^{61} +(-17.4416 + 17.4416i) q^{62} +(0.490867 + 6.51449i) q^{63} +(2.09929 - 0.682102i) q^{64} +(4.61843 - 2.63418i) q^{65} +(13.8907 + 4.19863i) q^{66} +(2.80979 + 0.445027i) q^{67} +(21.1874 + 3.35576i) q^{68} +(-4.71869 + 8.39299i) q^{69} +(-11.5066 + 4.34772i) q^{70} +(0.221297 - 0.0719038i) q^{71} +(-17.5329 - 4.27112i) q^{72} +(10.0716 - 1.59519i) q^{73} +(-3.13102 - 9.63629i) q^{74} +(-2.23380 + 8.36721i) q^{75} +5.07948 q^{76} +(-7.20878 + 0.444369i) q^{77} +(-10.0176 + 2.80726i) q^{78} +6.98265i q^{79} +(-0.677291 - 14.3679i) q^{80} +(-6.32141 - 6.40623i) q^{81} +(-3.00871 - 18.9962i) q^{82} +(3.71459 + 3.71459i) q^{83} +(16.4138 - 1.91498i) q^{84} +(-4.50559 + 9.97825i) q^{85} +(28.6095 - 9.29581i) q^{86} +(4.23967 - 11.4334i) q^{87} +(4.98590 - 19.3171i) q^{88} +(0.0432300 - 0.133048i) q^{89} +(8.21335 - 14.8221i) q^{90} +(4.18905 - 3.04352i) q^{91} +(21.7007 + 11.0571i) q^{92} +(4.56364 + 16.2852i) q^{93} +29.4633i q^{94} +(-0.684125 + 2.50055i) q^{95} +(-1.43761 + 7.16494i) q^{96} +(11.2375 + 11.2375i) q^{97} +(5.08186 - 2.58934i) q^{98} +(7.17703 - 6.89131i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{3} - 20 q^{4} - 12 q^{6}+O(q^{10}) \) 928 * q - 8 * q^3 - 20 * q^4 - 12 * q^6	\( 928 q - 8 q^{3} - 20 q^{4} - 12 q^{6} - 8 q^{12} - 4 q^{13} - 14 q^{15} + 204 q^{16} + 2 q^{18} - 20 q^{19} - 12 q^{21} - 20 q^{22} - 40 q^{24} - 8 q^{25} - 14 q^{27} - 32 q^{28} + 74 q^{30} - 4 q^{31} - 42 q^{33} - 40 q^{34} + 36 q^{36} - 84 q^{37} + 40 q^{39} - 108 q^{40} - 46 q^{42} - 40 q^{43} - 28 q^{45} - 24 q^{46} + 54 q^{48} - 60 q^{49} - 12 q^{51} - 28 q^{52} - 80 q^{54} - 112 q^{55} + 30 q^{57} - 188 q^{58} + 10 q^{60} - 4 q^{61} + 56 q^{63} - 180 q^{64} + 30 q^{66} - 12 q^{67} - 10 q^{69} - 80 q^{70} + 112 q^{72} - 20 q^{73} - 46 q^{75} - 128 q^{76} + 20 q^{78} - 32 q^{81} + 12 q^{82} - 12 q^{85} + 44 q^{87} + 164 q^{88} - 74 q^{90} - 4 q^{91} + 172 q^{93} - 66 q^{96} - 96 q^{97}+O(q^{100}) \) 928 * q - 8 * q^3 - 20 * q^4 - 12 * q^6 - 8 * q^12 - 4 * q^13 - 14 * q^15 + 204 * q^16 + 2 * q^18 - 20 * q^19 - 12 * q^21 - 20 * q^22 - 40 * q^24 - 8 * q^25 - 14 * q^27 - 32 * q^28 + 74 * q^30 - 4 * q^31 - 42 * q^33 - 40 * q^34 + 36 * q^36 - 84 * q^37 + 40 * q^39 - 108 * q^40 - 46 * q^42 - 40 * q^43 - 28 * q^45 - 24 * q^46 + 54 * q^48 - 60 * q^49 - 12 * q^51 - 28 * q^52 - 80 * q^54 - 112 * q^55 + 30 * q^57 - 188 * q^58 + 10 * q^60 - 4 * q^61 + 56 * q^63 - 180 * q^64 + 30 * q^66 - 12 * q^67 - 10 * q^69 - 80 * q^70 + 112 * q^72 - 20 * q^73 - 46 * q^75 - 128 * q^76 + 20 * q^78 - 32 * q^81 + 12 * q^82 - 12 * q^85 + 44 * q^87 + 164 * q^88 - 74 * q^90 - 4 * q^91 + 172 * q^93 - 66 * q^96 - 96 * q^97

Introduction

L-functions

Modular forms

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