LMFDB - Embedded newform 920.2.bo.a.333.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(37,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 22, 11, 42]))

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

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

chi := DirichletCharacter("920.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bo (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$2800$
Relative dimension:	$140$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			333.16
Character	$\chi$	$=$	920.333
Dual form			920.2.bo.a.757.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33461 + 0.467781i) q^{2} +(-0.360129 - 0.481075i) q^{3} +(1.56236 - 1.24861i) q^{4} +(-2.13955 - 0.649856i) q^{5} +(0.705669 + 0.473586i) q^{6} +(-0.369805 + 5.17055i) q^{7} +(-1.50107 + 2.39725i) q^{8} +(0.743457 - 2.53198i) q^{9} +O(q^{10})$	\(q+(-1.33461 + 0.467781i) q^{2} +(-0.360129 - 0.481075i) q^{3} +(1.56236 - 1.24861i) q^{4} +(-2.13955 - 0.649856i) q^{5} +(0.705669 + 0.473586i) q^{6} +(-0.369805 + 5.17055i) q^{7} +(-1.50107 + 2.39725i) q^{8} +(0.743457 - 2.53198i) q^{9} +(3.15946 - 0.133538i) q^{10} +(-3.41839 - 2.19687i) q^{11} +(-1.16333 - 0.301955i) q^{12} +(0.206244 + 2.88367i) q^{13} +(-1.92514 - 7.07365i) q^{14} +(0.457885 + 1.26332i) q^{15} +(0.881952 - 3.90156i) q^{16} +(1.79289 - 4.80692i) q^{17} +(0.192188 + 3.72698i) q^{18} +(1.27966 + 0.584400i) q^{19} +(-4.15417 + 1.65615i) q^{20} +(2.62060 - 1.68416i) q^{21} +(5.58987 + 1.33290i) q^{22} +(-4.73448 - 0.764630i) q^{23} +(1.69383 - 0.141190i) q^{24} +(4.15538 + 2.78080i) q^{25} +(-1.62418 - 3.75210i) q^{26} +(-3.17496 + 1.18420i) q^{27} +(5.87822 + 8.54001i) q^{28} +(3.06869 + 6.71949i) q^{29} +(-1.20205 - 1.47185i) q^{30} +(-0.369395 - 2.56920i) q^{31} +(0.648012 + 5.61962i) q^{32} +(0.174202 + 2.43566i) q^{33} +(-0.144221 + 7.25404i) q^{34} +(4.15133 - 10.8223i) q^{35} +(-1.99990 - 4.88416i) q^{36} +(4.79026 - 2.61568i) q^{37} +(-1.98121 - 0.181346i) q^{38} +(1.31299 - 1.13771i) q^{39} +(4.76948 - 4.15356i) q^{40} +(10.1071 - 2.96771i) q^{41} +(-2.70966 + 3.47356i) q^{42} +(1.87922 - 1.40677i) q^{43} +(-8.08380 + 0.835932i) q^{44} +(-3.23609 + 4.93417i) q^{45} +(6.67636 - 1.19422i) q^{46} +(3.03668 - 3.03668i) q^{47} +(-2.19456 + 0.980777i) q^{48} +(-19.6691 - 2.82799i) q^{49} +(-6.84661 - 1.76748i) q^{50} +(-2.95816 + 0.868596i) q^{51} +(3.92281 + 4.24782i) q^{52} +(0.912112 - 12.7530i) q^{53} +(3.68338 - 3.06563i) q^{54} +(5.88618 + 6.92178i) q^{55} +(-11.8400 - 8.64786i) q^{56} +(-0.179701 - 0.826071i) q^{57} +(-7.23875 - 7.53242i) q^{58} +(-2.66782 + 3.07883i) q^{59} +(2.29277 + 1.40204i) q^{60} +(-1.54622 - 10.7542i) q^{61} +(1.69482 + 3.25608i) q^{62} +(12.8168 + 4.78042i) q^{63} +(-3.49359 - 7.19686i) q^{64} +(1.43270 - 6.30380i) q^{65} +(-1.37185 - 3.16916i) q^{66} +(1.67825 - 7.71481i) q^{67} +(-3.20082 - 9.74878i) q^{68} +(1.33718 + 2.55301i) q^{69} +(-0.477916 + 16.3855i) q^{70} +(4.50022 - 2.89212i) q^{71} +(4.95381 + 5.58292i) q^{72} +(3.93686 - 1.46837i) q^{73} +(-5.16956 + 5.73170i) q^{74} +(-0.158694 - 3.00050i) q^{75} +(2.72897 - 0.684747i) q^{76} +(12.6232 - 16.8626i) q^{77} +(-1.22013 + 2.13259i) q^{78} +(7.10492 - 8.19952i) q^{79} +(-4.42243 + 7.77445i) q^{80} +(-4.94680 - 3.17912i) q^{81} +(-12.1008 + 8.68863i) q^{82} +(5.45672 + 9.99323i) q^{83} +(1.99147 - 5.90337i) q^{84} +(-6.95979 + 9.11955i) q^{85} +(-1.84997 + 2.75655i) q^{86} +(2.12746 - 3.89615i) q^{87} +(10.3977 - 4.89709i) q^{88} +(0.322025 - 2.23973i) q^{89} +(2.01080 - 8.09896i) q^{90} -14.9864 q^{91} +(-8.35170 + 4.71689i) q^{92} +(-1.10295 + 1.10295i) q^{93} +(-2.63228 + 5.47327i) q^{94} +(-2.35812 - 2.08195i) q^{95} +(2.47009 - 2.33553i) q^{96} +(6.87214 + 3.75247i) q^{97} +(27.5734 - 5.42656i) q^{98} +(-8.10385 + 7.02203i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2800 q - 18 q^{2} - 28 q^{6} - 44 q^{7} - 18 q^{8}+O(q^{10}) $ 2800 * q - 18 * q^2 - 28 * q^6 - 44 * q^7 - 18 * q^8	$ 2800 q - 18 q^{2} - 28 q^{6} - 44 q^{7} - 18 q^{8} - 22 q^{10} - 6 q^{12} - 44 q^{15} - 44 q^{16} - 44 q^{17} - 38 q^{18} - 22 q^{20} - 40 q^{23} - 36 q^{25} - 36 q^{26} - 22 q^{28} - 22 q^{30} - 104 q^{31} - 38 q^{32} - 44 q^{33} - 36 q^{36} - 22 q^{38} - 22 q^{40} - 72 q^{41} + 198 q^{42} - 28 q^{46} - 80 q^{47} - 10 q^{48} - 2 q^{50} - 146 q^{52} + 4 q^{55} - 44 q^{56} - 44 q^{57} - 42 q^{58} - 22 q^{60} + 46 q^{62} - 44 q^{63} - 44 q^{65} - 44 q^{66} - 64 q^{70} - 72 q^{71} - 104 q^{72} - 36 q^{73} - 44 q^{76} - 114 q^{78} - 220 q^{80} + 176 q^{81} - 10 q^{82} - 44 q^{86} - 12 q^{87} - 22 q^{88} - 440 q^{90} - 2 q^{92} - 76 q^{95} - 124 q^{96} - 44 q^{97} + 30 q^{98}+O(q^{100}) $ 2800 * q - 18 * q^2 - 28 * q^6 - 44 * q^7 - 18 * q^8 - 22 * q^10 - 6 * q^12 - 44 * q^15 - 44 * q^16 - 44 * q^17 - 38 * q^18 - 22 * q^20 - 40 * q^23 - 36 * q^25 - 36 * q^26 - 22 * q^28 - 22 * q^30 - 104 * q^31 - 38 * q^32 - 44 * q^33 - 36 * q^36 - 22 * q^38 - 22 * q^40 - 72 * q^41 + 198 * q^42 - 28 * q^46 - 80 * q^47 - 10 * q^48 - 2 * q^50 - 146 * q^52 + 4 * q^55 - 44 * q^56 - 44 * q^57 - 42 * q^58 - 22 * q^60 + 46 * q^62 - 44 * q^63 - 44 * q^65 - 44 * q^66 - 64 * q^70 - 72 * q^71 - 104 * q^72 - 36 * q^73 - 44 * q^76 - 114 * q^78 - 220 * q^80 + 176 * q^81 - 10 * q^82 - 44 * q^86 - 12 * q^87 - 22 * q^88 - 440 * q^90 - 2 * q^92 - 76 * q^95 - 124 * q^96 - 44 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{9}{22}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.33461	+	0.467781i	−0.943711	+	0.330771i
$2$	−1.33461	+	0.467781i	−0.943711	+	0.330771i
$3$	−0.360129	−	0.481075i	−0.207920	−	0.277749i	0.684443	−	0.729066i	$-0.260045\pi$
$3$	−0.360129	−	0.481075i	−0.207920	−	0.277749i	−0.892364	+	0.451317i	$0.850954\pi$
$4$	1.56236	−	1.24861i	0.781181	−	0.624304i
$5$	−2.13955	−	0.649856i	−0.956837	−	0.290624i
$5$	−2.13955	−	0.649856i	−0.956837	−	0.290624i
$6$	0.705669	+	0.473586i	0.288088	+	0.193341i
$7$	−0.369805	+	5.17055i	−0.139773	+	1.95428i	0.130373	+	0.991465i	$0.458382\pi$
$7$	−0.369805	+	5.17055i	−0.139773	+	1.95428i	−0.270146	+	0.962819i	$0.587072\pi$
$8$	−1.50107	+	2.39725i	−0.530708	+	0.847555i
$9$	0.743457	−	2.53198i	0.247819	−	0.843994i
$10$	3.15946	−	0.133538i	0.999108	−	0.0422285i
$11$	−3.41839	−	2.19687i	−1.03068	−	0.662380i	−0.0880183	−	0.996119i	$-0.528053\pi$
$11$	−3.41839	−	2.19687i	−1.03068	−	0.662380i	−0.942666	+	0.333738i	$0.891690\pi$
$12$	−1.16333	−	0.301955i	−0.335823	−	0.0871668i
$13$	0.206244	+	2.88367i	0.0572019	+	0.799787i	0.942382	+	0.334539i	$0.108580\pi$
$13$	0.206244	+	2.88367i	0.0572019	+	0.799787i	−0.885180	+	0.465248i	$0.845965\pi$
$14$	−1.92514	−	7.07365i	−0.514515	−	1.89051i
$15$	0.457885	+	1.26332i	0.118225	+	0.326187i
$16$	0.881952	−	3.90156i	0.220488	−	0.975390i
$17$	1.79289	−	4.80692i	0.434840	−	1.16585i	−0.516115	−	0.856519i	$-0.672622\pi$
$17$	1.79289	−	4.80692i	0.434840	−	1.16585i	0.950954	−	0.309331i	$-0.100105\pi$
$18$	0.192188	+	3.72698i	0.0452991	+	0.878457i
$19$	1.27966	+	0.584400i	0.293573	+	0.134070i	0.556757	−	0.830675i	$-0.312045\pi$
$19$	1.27966	+	0.584400i	0.293573	+	0.134070i	−0.263184	+	0.964746i	$0.584773\pi$
$20$	−4.15417	+	1.65615i	−0.928901	+	0.370327i
$21$	2.62060	−	1.68416i	0.571862	−	0.367514i
$22$	5.58987	+	1.33290i	1.19176	+	0.284175i
$23$	−4.73448	−	0.764630i	−0.987208	−	0.159436i
$23$	−4.73448	−	0.764630i	−0.987208	−	0.159436i
$24$	1.69383	−	0.141190i	0.345753	−	0.0288204i
$25$	4.15538	+	2.78080i	0.831075	+	0.556160i
$26$	−1.62418	−	3.75210i	−0.318528	−	0.735847i
$27$	−3.17496	+	1.18420i	−0.611021	+	0.227899i
$28$	5.87822	+	8.54001i	1.11088	+	1.61391i
$29$	3.06869	+	6.71949i	0.569841	+	1.24778i	0.946882	+	0.321582i	$0.104214\pi$
$29$	3.06869	+	6.71949i	0.569841	+	1.24778i	−0.377041	+	0.926197i	$0.623058\pi$
$30$	−1.20205	−	1.47185i	−0.219464	−	0.268721i
$31$	−0.369395	−	2.56920i	−0.0663453	−	0.461442i	−0.995729	−	0.0923262i	$-0.970570\pi$
$31$	−0.369395	−	2.56920i	−0.0663453	−	0.461442i	0.929384	−	0.369116i	$-0.120339\pi$
$32$	0.648012	+	5.61962i	0.114553	+	0.993417i
$33$	0.174202	+	2.43566i	0.0303246	+	0.423994i
$34$	−0.144221	+	7.25404i	−0.0247336	+	1.24406i
$35$	4.15133	−	10.8223i	0.701703	−	1.82931i
$36$	−1.99990	−	4.88416i	−0.333317	−	0.814026i
$37$	4.79026	−	2.61568i	0.787514	−	0.430015i	−0.0345553	−	0.999403i	$-0.511001\pi$
$37$	4.79026	−	2.61568i	0.787514	−	0.430015i	0.822069	+	0.569388i	$0.192820\pi$
$38$	−1.98121	−	0.181346i	−0.321395	−	0.0294183i
$39$	1.31299	−	1.13771i	0.210247	−	0.182180i
$40$	4.76948	−	4.15356i	0.754121	−	0.656736i
$41$	10.1071	−	2.96771i	1.57846	−	0.463478i	0.629011	−	0.777396i	$-0.283460\pi$
$41$	10.1071	−	2.96771i	1.57846	−	0.463478i	0.949450	+	0.313918i	$0.101642\pi$
$42$	−2.70966	+	3.47356i	−0.418110	+	0.535982i
$43$	1.87922	−	1.40677i	0.286579	−	0.214530i	−0.446310	−	0.894878i	$-0.647262\pi$
$43$	1.87922	−	1.40677i	0.286579	−	0.214530i	0.732889	+	0.680348i	$0.238171\pi$
$44$	−8.08380	+	0.835932i	−1.21868	+	0.126021i
$45$	−3.23609	+	4.93417i	−0.482407	+	0.735542i
$46$	6.67636	−	1.19422i	0.984376	−	0.176078i
$47$	3.03668	−	3.03668i	0.442945	−	0.442945i	−0.450056	−	0.893000i	$-0.648596\pi$
$47$	3.03668	−	3.03668i	0.442945	−	0.442945i	0.893000	+	0.450056i	$0.148596\pi$
$48$	−2.19456	+	0.980777i	−0.316758	+	0.141563i
$49$	−19.6691	−	2.82799i	−2.80987	−	0.403998i
$50$	−6.84661	−	1.76748i	−0.968256	−	0.249959i
$51$	−2.95816	+	0.868596i	−0.414226	+	0.121628i
$52$	3.92281	+	4.24782i	0.543996	+	0.589067i
$53$	0.912112	−	12.7530i	0.125288	−	1.75176i	−0.414583	−	0.910011i	$-0.636073\pi$
$53$	0.912112	−	12.7530i	0.125288	−	1.75176i	0.539871	−	0.841747i	$-0.318473\pi$
$54$	3.68338	−	3.06563i	0.501245	−	0.417179i
$55$	5.88618	+	6.92178i	0.793693	+	0.933332i
$56$	−11.8400	−	8.64786i	−1.58218	−	1.15562i
$57$	−0.179701	−	0.826071i	−0.0238019	−	0.109416i
$58$	−7.23875	−	7.53242i	−0.950494	−	0.989055i
$59$	−2.66782	+	3.07883i	−0.347321	+	0.400830i	−0.902352	−	0.431000i	$-0.858161\pi$
$59$	−2.66782	+	3.07883i	−0.347321	+	0.400830i	0.555031	+	0.831830i	$0.312706\pi$
$60$	2.29277	+	1.40204i	0.295996	+	0.181003i
$61$	−1.54622	−	10.7542i	−0.197973	−	1.37693i	−0.810155	−	0.586216i	$-0.800617\pi$
$61$	−1.54622	−	10.7542i	−0.197973	−	1.37693i	0.612182	−	0.790717i	$-0.290292\pi$
$62$	1.69482	+	3.25608i	0.215242	+	0.413523i
$63$	12.8168	+	4.78042i	1.61476	+	0.602276i
$64$	−3.49359	−	7.19686i	−0.436699	−	0.899608i
$65$	1.43270	−	6.30380i	0.177705	−	0.781890i
$66$	−1.37185	−	3.16916i	−0.168863	−	0.390097i
$67$	1.67825	−	7.71481i	0.205031	−	0.942514i	−0.753482	−	0.657468i	$-0.771627\pi$
$67$	1.67825	−	7.71481i	0.205031	−	0.942514i	0.958514	−	0.285046i	$-0.0920090\pi$
$68$	−3.20082	−	9.74878i	−0.388157	−	1.18221i
$69$	1.33718	+	2.55301i	0.160977	+	0.307346i
$70$	−0.477916	+	16.3855i	−0.0571219	+	1.95844i
$71$	4.50022	−	2.89212i	0.534078	−	0.343231i	−0.245641	−	0.969361i	$-0.578998\pi$
$71$	4.50022	−	2.89212i	0.534078	−	0.343231i	0.779719	+	0.626130i	$0.215362\pi$
$72$	4.95381	+	5.58292i	0.583812	+	0.657954i
$73$	3.93686	−	1.46837i	0.460774	−	0.171860i	−0.108348	−	0.994113i	$-0.534556\pi$
$73$	3.93686	−	1.46837i	0.460774	−	0.171860i	0.569122	+	0.822253i	$0.307283\pi$
$74$	−5.16956	+	5.73170i	−0.600949	+	0.666297i
$75$	−0.158694	−	3.00050i	−0.0183244	−	0.346467i
$76$	2.72897	−	0.684747i	0.313035	−	0.0785458i
$77$	12.6232	−	16.8626i	1.43854	−	1.92167i
$78$	−1.22013	+	2.13259i	−0.138152	+	0.241469i
$79$	7.10492	−	8.19952i	0.799366	−	0.922518i	−0.198980	−	0.980004i	$-0.563763\pi$
$79$	7.10492	−	8.19952i	0.799366	−	0.922518i	0.998346	+	0.0574859i	$0.0183084\pi$
$80$	−4.42243	+	7.77445i	−0.494443	+	0.869210i
$81$	−4.94680	−	3.17912i	−0.549645	−	0.353235i
$82$	−12.1008	+	8.68863i	−1.33631	+	0.959498i
$83$	5.45672	+	9.99323i	0.598953	+	1.09690i	0.984694	+	0.174293i	$0.0557639\pi$
$83$	5.45672	+	9.99323i	0.598953	+	1.09690i	−0.385741	+	0.922607i	$0.626054\pi$
$84$	1.99147	−	5.90337i	0.217288	−	0.644111i
$85$	−6.95979	+	9.11955i	−0.754895	+	0.989154i
$86$	−1.84997	+	2.75655i	−0.199487	+	0.297247i
$87$	2.12746	−	3.89615i	0.228088	−	0.417711i
$88$	10.3977	−	4.89709i	1.10840	−	0.522031i
$89$	0.322025	−	2.23973i	0.0341346	−	0.237411i	−0.965610	−	0.259993i	$-0.916280\pi$
$89$	0.322025	−	2.23973i	0.0341346	−	0.237411i	0.999745	+	0.0225821i	$0.00718872\pi$
$90$	2.01080	−	8.09896i	0.211957	−	0.853706i
$91$	−14.9864			−1.57101
$92$	−8.35170	+	4.71689i	−0.870725	+	0.491770i
$93$	−1.10295	+	1.10295i	−0.114370	+	0.114370i
$94$	−2.63228	+	5.47327i	−0.271499	+	0.564525i
$95$	−2.35812	−	2.08195i	−0.241938	−	0.213603i
$96$	2.47009	−	2.33553i	0.252103	−	0.238369i
$97$	6.87214	+	3.75247i	0.697761	+	0.381006i	0.788640	−	0.614856i	$-0.210786\pi$
$97$	6.87214	+	3.75247i	0.697761	+	0.381006i	−0.0908790	+	0.995862i	$0.528968\pi$
$98$	27.5734	−	5.42656i	2.78534	−	0.548165i
$99$	−8.10385	+	7.02203i	−0.814468	+	0.705740i
$100$	9.96434	−	0.843817i	0.996434	−	0.0843817i
$101$	0.852079	−	2.90192i	0.0847850	−	0.288751i	−0.906176	−	0.422901i	$-0.861012\pi$
$101$	0.852079	−	2.90192i	0.0847850	−	0.288751i	0.990961	+	0.134149i	$0.0428301\pi$
$102$	3.54168	−	2.54301i	0.350679	−	0.251795i
$103$	−9.97536	+	2.17001i	−0.982901	+	0.213817i	−0.675175	−	0.737658i	$-0.735932\pi$
$103$	−9.97536	+	2.17001i	−0.982901	+	0.213817i	−0.307726	+	0.951475i	$0.599568\pi$
$104$	−7.22247	−	3.83417i	−0.708221	−	0.375971i
$105$	−6.70138	+	1.90033i	−0.653988	+	0.185454i
$106$	4.74829	+	17.4469i	0.461195	+	1.69460i
$107$	3.22741	+	2.41601i	0.312005	+	0.233564i	0.743791	−	0.668412i	$-0.233026\pi$
$107$	3.22741	+	2.41601i	0.312005	+	0.233564i	−0.431786	+	0.901976i	$0.642117\pi$
$108$	−3.48184	+	5.81443i	−0.335040	+	0.559494i
$109$	5.93685	−	2.71127i	0.568647	−	0.259692i	−0.110277	−	0.993901i	$-0.535174\pi$
$109$	5.93685	−	2.71127i	0.568647	−	0.259692i	0.678924	+	0.734209i	$0.262447\pi$
$110$	−11.0936	−	6.48442i	−1.05774	−	0.618265i
$111$	−2.98345	−	1.36250i	−0.283176	−	0.129322i
$112$	19.8471	+	6.00300i	1.87537	+	0.567230i
$113$	1.77679	−	8.16777i	0.167146	−	0.768360i	−0.814882	−	0.579627i	$-0.803198\pi$
$113$	1.77679	−	8.16777i	0.167146	−	0.768360i	0.982028	−	0.188733i	$-0.0604380\pi$
$114$	0.626250	+	1.01842i	0.0586537	+	0.0953838i
$115$	9.63278	+	4.71270i	0.898261	+	0.439461i
$116$	13.1844	+	6.66669i	1.22414	+	0.618987i
$117$	7.45474	+	1.62168i	0.689191	+	0.149924i
$118$	2.12028	−	5.35700i	0.195188	−	0.493151i
$119$	24.1914	+	11.0479i	2.21762	+	1.01276i
$120$	−3.71580	−	0.798664i	−0.339205	−	0.0729077i
$121$	2.28961	+	5.01356i	0.208147	+	0.455778i
$122$	7.09420	+	13.6293i	0.642279	+	1.23394i
$123$	−5.06754	−	3.79351i	−0.456925	−	0.342050i
$124$	−3.78505	−	3.55279i	−0.339908	−	0.319050i
$125$	−7.08353	−	8.65007i	−0.633570	−	0.773686i
$126$	−19.3416	−	0.384539i	−1.72309	−	0.0342574i
$127$	−7.17258	+	1.56030i	−0.636464	+	0.138454i	−0.519208	−	0.854648i	$-0.673773\pi$
$127$	−7.17258	+	1.56030i	−0.636464	+	0.138454i	−0.117255	+	0.993102i	$0.537410\pi$
$128$	8.02913	+	7.97076i	0.709682	+	0.704523i
$129$	−1.35352	−	0.397431i	−0.119171	−	0.0349918i
$130$	1.03670	+	9.08330i	0.0909247	+	0.796658i
$131$	6.50169	−	5.63374i	0.568055	−	0.492222i	−0.322827	−	0.946458i	$-0.604633\pi$
$131$	6.50169	−	5.63374i	0.568055	−	0.492222i	0.890882	+	0.454236i	$0.150088\pi$
$132$	3.31335	+	3.58787i	0.288390	+	0.312284i
$133$	−3.49489	+	6.40042i	−0.303046	+	0.554986i
$134$	1.36903	+	11.0813i	0.118266	+	0.957280i
$135$	7.56255	−	0.470390i	0.650881	−	0.0404847i
$136$	8.83214	+	11.5135i	0.757350	+	0.987276i
$137$	−3.73100	−	3.73100i	−0.318761	−	0.318761i	0.529530	−	0.848291i	$-0.322368\pi$
$137$	−3.73100	−	3.73100i	−0.318761	−	0.318761i	−0.848291	+	0.529530i	$0.822368\pi$
$138$	−2.97886	−	2.78176i	−0.253577	−	0.236799i
$139$	9.39747			0.797083			0.398542	−	0.917150i	$-0.369516\pi$
$139$	9.39747			0.797083			0.398542	+	0.917150i	$0.369516\pi$
$140$	−7.02700	−	22.0918i	−0.593890	−	1.86710i
$141$	−2.55446	−	0.367276i	−0.215125	−	0.0309303i
$142$	−4.65316	+	5.96496i	−0.390484	+	0.500568i
$143$	5.63002	−	10.3106i	0.470806	−	0.862217i
$144$	−9.22298	−	5.13373i	−0.768582	−	0.427811i
$145$	−2.19892	−	16.3709i	−0.182611	−	1.35953i
$146$	−4.56729	+	3.80129i	−0.377992	+	0.314597i
$147$	5.72292	+	10.4808i	0.472019	+	0.864438i
$148$	4.21816	−	10.0678i	0.346731	−	0.827568i
$149$	−8.13516	+	12.6586i	−0.666458	+	1.03703i	0.329228	+	0.944250i	$0.393211\pi$
$149$	−8.13516	+	12.6586i	−0.666458	+	1.03703i	−0.995687	+	0.0927792i	$0.970425\pi$
$150$	1.61537	+	3.93025i	0.131894	+	0.320904i
$151$	−0.906765	+	1.04646i	−0.0737915	+	0.0851599i	−0.791445	−	0.611241i	$-0.790671\pi$
$151$	−0.906765	+	1.04646i	−0.0737915	+	0.0851599i	0.717653	+	0.696400i	$0.245216\pi$
$152$	−3.32180	+	2.19043i	−0.269434	+	0.177667i
$153$	−10.8381	−	8.11330i	−0.876209	−	0.655922i
$154$	−8.95899	+	28.4098i	−0.721936	+	2.28933i
$155$	−0.879268	+	5.73699i	−0.0706245	+	0.460806i
$156$	0.630809	−	3.41693i	0.0505051	−	0.273573i
$157$	−3.67092	−	9.84212i	−0.292971	−	0.785487i	−0.997149	−	0.0754624i	$-0.975957\pi$
$157$	−3.67092	−	9.84212i	−0.292971	−	0.785487i	0.704177	−	0.710024i	$-0.251316\pi$
$158$	−5.64672	+	14.2667i	−0.449229	+	1.13500i
$159$	−6.46363	+	4.15392i	−0.512599	+	0.329428i
$160$	2.26548	−	12.4446i	0.179102	−	0.983830i
$161$	5.70440	−	24.1971i	0.449569	−	1.90700i
$162$	8.08918	+	1.92886i	0.635546	+	0.151546i
$163$	−0.724482	+	3.33039i	−0.0567458	+	0.260856i	−0.996776	−	0.0802350i	$-0.974433\pi$
$163$	−0.724482	+	3.33039i	−0.0567458	+	0.260856i	0.940030	+	0.341091i	$0.110797\pi$
$164$	12.0854	−	17.2564i	0.943713	−	1.34750i
$165$	1.21011	−	5.32443i	0.0942072	−	0.414506i
$166$	−11.9572	−	10.7845i	−0.928061	−	0.837040i
$167$	5.20829	+	1.94259i	0.403030	+	0.150322i	0.542801	−	0.839861i	$-0.317364\pi$
$167$	5.20829	+	1.94259i	0.403030	+	0.150322i	−0.139771	+	0.990184i	$0.544637\pi$
$168$	0.103644	+	8.81027i	0.00799629	+	0.679727i
$169$	4.59464	−	0.660610i	0.353434	−	0.0508161i
$170$	5.02265	−	15.4267i	0.385220	−	1.18317i
$171$	2.43106	−	2.80559i	0.185908	−	0.214549i
$172$	1.17952	−	4.54430i	0.0899378	−	0.346499i
$173$	−0.883958	+	0.192293i	−0.0672061	+	0.0146198i	−0.246043	−	0.969259i	$-0.579130\pi$
$173$	−0.883958	+	0.192293i	−0.0672061	+	0.0146198i	0.178837	+	0.983879i	$0.442767\pi$
$174$	−1.01678	+	6.19503i	−0.0770821	+	0.469644i
$175$	−15.9150	+	20.4572i	−1.20306	+	1.54642i
$176$	−11.5861	+	11.3995i	−0.873333	+	0.859272i
$177$	2.44191	+	0.174649i	0.183545	+	0.0131274i
$178$	0.617926	+	3.13980i	0.0463155	+	0.235338i
$179$	1.63760	−	0.480842i	0.122400	−	0.0359398i	−0.219959	−	0.975509i	$-0.570592\pi$
$179$	1.63760	−	0.480842i	0.122400	−	0.0359398i	0.342359	+	0.939569i	$0.388774\pi$
$180$	1.10490	+	11.7496i	0.0823547	+	0.875761i
$181$	−1.97467	+	13.7341i	−0.146776	+	1.02085i	0.774677	+	0.632357i	$0.217912\pi$
$181$	−1.97467	+	13.7341i	−0.146776	+	1.02085i	−0.921453	+	0.388490i	$0.872997\pi$
$182$	20.0010	−	7.01037i	1.48258	−	0.519643i
$183$	−4.61674	+	4.61674i	−0.341279	+	0.341279i
$184$	8.93979	−	10.2020i	0.659050	−	0.752099i
$185$	−11.9488	+	2.48341i	−0.878495	+	0.182584i
$186$	0.956067	−	1.98794i	0.0701023	−	0.145763i
$187$	−16.6890	+	12.4932i	−1.22042	+	0.913594i
$188$	0.952768	−	8.53601i	0.0694878	−	0.622552i
$189$	−4.94884	−	16.8542i	−0.359975	−	1.22596i
$190$	4.12106	+	1.67550i	0.298973	+	0.121554i
$191$	11.7781	−	10.2057i	0.852230	−	0.738462i	−0.114728	−	0.993397i	$-0.536600\pi$
$191$	11.7781	−	10.2057i	0.852230	−	0.738462i	0.966958	+	0.254935i	$0.0820542\pi$
$192$	−2.20409	+	4.27248i	−0.159067	+	0.308339i
$193$	8.70997	+	15.9511i	0.626957	+	1.14819i	0.977359	+	0.211587i	$0.0678633\pi$
$193$	8.70997	+	15.9511i	0.626957	+	1.14819i	−0.350402	+	0.936600i	$0.613955\pi$
$194$	−10.9270	−	1.79343i	−0.784510	−	0.128761i
$195$	−3.54856	+	1.58094i	−0.254118	+	0.113214i
$196$	−34.2613	+	20.1406i	−2.44723	+	1.43862i
$197$	−23.5357	+	1.68331i	−1.67685	+	0.119931i	−0.877071	−	0.480361i	$-0.840506\pi$
$197$	−23.5357	+	1.68331i	−1.67685	+	0.119931i	−0.799781	+	0.600291i	$0.795051\pi$
$198$	7.53071	−	13.1625i	0.535184	−	0.935417i
$199$	0.781260	+	5.43378i	0.0553820	+	0.385191i	0.998594	+	0.0530005i	$0.0168785\pi$
$199$	0.781260	+	5.43378i	0.0553820	+	0.385191i	−0.943212	+	0.332190i	$0.892212\pi$
$200$	−12.9038	+	5.78729i	−0.912434	+	0.409223i
$201$	−4.31579	+	1.97096i	−0.304413	+	0.139021i
$202$	0.220267	+	4.27151i	0.0154980	+	0.300542i
$203$	−35.8783	+	13.3819i	−2.51816	+	0.939226i
$204$	−3.53719	+	5.05065i	−0.247653	+	0.353616i
$205$	−23.5532	−	0.218579i	−1.64503	−	0.0152662i
$206$	12.2981	−	7.56239i	0.856850	−	0.526897i
$207$	−5.45591	+	11.4192i	−0.379212	+	0.793686i
$208$	11.4327	+	1.73859i	0.792716	+	0.120549i
$209$	−3.09052	−	4.80894i	−0.213776	−	0.332642i
$210$	8.05478	−	5.67098i	0.555833	−	0.391335i
$211$	−0.489868	−	0.223715i	−0.0337239	−	0.0154012i	0.398482	−	0.917176i	$-0.369537\pi$
$211$	−0.489868	−	0.223715i	−0.0337239	−	0.0154012i	−0.432206	+	0.901775i	$0.642265\pi$
$212$	−14.4985	−	21.0637i	−0.995758	−	1.44666i
$213$	−3.01198	−	1.12341i	−0.206378	−	0.0769749i
$214$	−5.43749	−	1.71470i	−0.371699	−	0.117215i
$215$	−4.93490	+	1.78863i	−0.336557	+	0.121984i
$216$	1.92701	−	9.38873i	0.131117	−	0.638822i
$217$	13.4208	−	0.959873i	0.911062	−	0.0651604i
$218$	−6.65509	+	6.39562i	−0.450740	+	0.433166i
$219$	−2.12417	−	1.36512i	−0.143538	−	0.0922465i
$220$	17.8389	+	3.46478i	1.20270	+	0.233595i
$221$	14.2314	+	4.17871i	0.957306	+	0.281090i
$222$	4.61909	+	0.422799i	0.310013	+	0.0283764i
$223$	1.03033	−	14.4059i	0.0689958	−	0.964688i	−0.838574	−	0.544787i	$-0.816610\pi$
$223$	1.03033	−	14.4059i	0.0689958	−	0.964688i	0.907570	−	0.419900i	$-0.137935\pi$
$224$	−29.2961	+	1.27242i	−1.95743	+	0.0850170i
$225$	10.1303	−	8.45392i	0.675352	−	0.563595i
$226$	1.44941	+	11.7319i	0.0964131	+	0.780397i
$227$	−11.0297	−	14.7339i	−0.732064	−	0.977924i	−0.999895	−	0.0144577i	$-0.995398\pi$
$227$	−11.0297	−	14.7339i	−0.732064	−	0.977924i	0.267831	−	0.963466i	$-0.413693\pi$
$228$	−1.31220	−	1.06625i	−0.0869023	−	0.0706138i
$229$		−	11.7779i		−	0.778305i	−0.921173	−	0.389152i	$-0.872768\pi$
$229$		−	11.7779i		−	0.778305i	0.921173	−	0.389152i	$-0.127232\pi$
$230$	−15.0605	−	1.78358i	−0.993060	−	0.117606i
$231$	−12.6581			−0.832843
$232$	−20.7146	−	2.73001i	−1.35998	−	0.179234i
$233$	−23.7644	+	17.7898i	−1.55686	+	1.16545i	−0.638546	+	0.769584i	$0.720464\pi$
$233$	−23.7644	+	17.7898i	−1.55686	+	1.16545i	−0.918310	+	0.395863i	$0.870445\pi$
$234$	−10.7078	+	1.32288i	−0.699988	+	0.0864791i
$235$	−8.47053	+	4.52373i	−0.552556	+	0.295095i
$236$	−0.323850	+	8.14132i	−0.0210808	+	0.529955i
$237$	−6.50327	−	0.465123i	−0.422433	−	0.0302130i
$238$	−37.4541	−	3.42828i	−2.42779	−	0.222223i
$239$	−6.69850	+	22.8130i	−0.433290	+	1.47565i	0.396740	+	0.917931i	$0.370141\pi$
$239$	−6.69850	+	22.8130i	−0.433290	+	1.47565i	−0.830030	+	0.557719i	$0.811677\pi$
$240$	5.33274	−	0.672277i	0.344227	−	0.0433953i
$241$	6.62795	−	10.3133i	0.426944	−	0.664338i	−0.559426	−	0.828880i	$-0.688978\pi$
$241$	6.62795	−	10.3133i	0.426944	−	0.664338i	0.986370	+	0.164543i	$0.0526148\pi$
$242$	−5.40099	−	5.62010i	−0.347188	−	0.361274i
$243$	0.977312	+	13.6646i	0.0626946	+	0.876585i
$244$	−15.8435	−	14.8713i	−1.01428	−	0.952038i
$245$	40.2453	+	18.8327i	2.57118	+	1.20318i
$246$	8.53772	+	2.69236i	0.544345	+	0.171659i
$247$	−1.42130	+	3.81064i	−0.0904349	+	0.242465i
$248$	6.71349	+	2.97101i	0.426307	+	0.188659i
$249$	2.84238	−	6.22394i	0.180128	−	0.394426i
$250$	13.5001	+	8.23092i	0.853820	+	0.520569i
$251$	11.5221	−	7.40482i	0.727270	−	0.467388i	−0.123889	−	0.992296i	$-0.539537\pi$
$251$	11.5221	−	7.40482i	0.727270	−	0.467388i	0.851159	+	0.524908i	$0.175900\pi$
$252$	25.9934	−	8.53442i	1.63743	−	0.537618i
$253$	14.5045	+	13.0148i	0.911892	+	0.818236i
$254$	8.84271	−	5.43759i	0.554841	−	0.341184i
$255$	6.89361	+	0.0639741i	0.431695	+	0.00400621i
$256$	−14.4443	−	6.88198i	−0.902770	−	0.430124i
$257$	−0.863080	−	2.31401i	−0.0538374	−	0.144344i	0.907247	−	0.420598i	$-0.138180\pi$
$257$	−0.863080	−	2.31401i	−0.0538374	−	0.144344i	−0.961085	+	0.276254i	$0.910907\pi$
$258$	1.99234	−	0.102738i	0.124037	−	0.00639620i
$259$	11.7530	+	25.7356i	0.730298	+	1.59913i
$260$	−5.63258	−	11.6377i	−0.349318	−	0.721740i
$261$	19.2951	−	2.77421i	1.19433	−	0.171719i
$262$	−6.04185	+	10.5602i	−0.373267	+	0.652412i
$263$	1.55329	+	21.7179i	0.0957801	+	1.33918i	0.787187	+	0.616715i	$0.211537\pi$
$263$	1.55329	+	21.7179i	0.0957801	+	1.33918i	−0.691407	+	0.722466i	$0.743009\pi$
$264$	−6.10037	−	3.23849i	−0.375452	−	0.199315i
$265$	−10.2391	+	26.6930i	−0.628984	+	1.63974i
$266$	1.67032	−	10.1769i	0.102414	−	0.623985i
$267$	−1.19345	+	0.651674i	−0.0730380	+	0.0398818i
$268$	−7.01074	−	14.1488i	−0.428249	−	0.864277i
$269$	11.7449	+	13.5544i	0.716101	+	0.826425i	0.990832	−	0.135096i	$-0.0431344\pi$
$269$	11.7449	+	13.5544i	0.716101	+	0.826425i	−0.274731	+	0.961521i	$0.588589\pi$
$270$	−9.87301	+	4.16540i	−0.600852	+	0.253498i
$271$	−9.82950	+	2.88620i	−0.597099	+	0.175324i	−0.566297	−	0.824201i	$-0.691624\pi$
$271$	−9.82950	+	2.88620i	−0.597099	+	0.175324i	−0.0308024	+	0.999525i	$0.509806\pi$
$272$	−17.1733	−	11.2345i	−1.04128	−	0.681194i
$273$	5.39705	+	7.20961i	0.326644	+	0.436346i
$274$	6.72472	+	3.23414i	0.406255	+	0.195381i
$275$	−8.09565	−	18.6347i	−0.488186	−	1.12371i
$276$	5.27687	+	2.31911i	0.317630	+	0.139594i
$277$	14.5333	+	14.5333i	0.873218	+	0.873218i	0.992822	−	0.119603i	$-0.0381623\pi$
$277$	14.5333	+	14.5333i	0.873218	+	0.873218i	−0.119603	+	0.992822i	$0.538162\pi$
$278$	−12.5420	+	4.39596i	−0.752216	+	0.263652i
$279$	−6.77979	−	0.974787i	−0.405896	−	0.0583590i
$280$	19.7124	+	26.1968i	1.17804	+	1.56556i
$281$	−3.64476	−	12.4129i	−0.217428	−	0.740492i	−0.993895	−	0.110334i	$-0.964808\pi$
$281$	−3.64476	−	12.4129i	−0.217428	−	0.740492i	0.776466	−	0.630159i	$-0.217010\pi$
$282$	3.58102	−	0.704759i	0.213246	−	0.0419678i
$283$	0.402409	−	5.62641i	0.0239207	−	0.334456i	−0.971374	−	0.237557i	$-0.923653\pi$
$283$	0.402409	−	5.62641i	0.0239207	−	0.334456i	0.995294	−	0.0968983i	$-0.0308922\pi$
$284$	3.41985	−	10.1375i	0.202931	−	0.601553i
$285$	−0.152348	+	1.88420i	−0.00902429	+	0.111610i
$286$	−2.69077	+	16.3943i	−0.159109	+	0.969413i
$287$	11.6070	+	53.3566i	0.685141	+	3.14954i
$288$	14.7105	+	2.53719i	0.866826	+	0.149505i
$289$	−7.04433	−	6.10394i	−0.414372	−	0.359056i
$290$	10.5927	+	20.8202i	0.622025	+	1.22260i
$291$	−0.669632	−	4.65739i	−0.0392545	−	0.273021i
$292$	4.31738	−	7.20973i	0.252655	−	0.421917i
$293$	7.91955	−	21.2331i	0.462665	−	1.24045i	−0.470945	−	0.882163i	$-0.656087\pi$
$293$	7.91955	−	21.2331i	0.462665	−	1.24045i	0.933610	−	0.358291i	$-0.116640\pi$
$294$	−12.5406	−	11.3106i	−0.731380	−	0.659649i
$295$	7.70875	−	4.85363i	0.448821	−	0.282589i
$296$	−0.920073	+	15.4097i	−0.0534782	+	0.895673i
$297$	13.4548	+	2.92691i	0.780726	+	0.169836i
$298$	4.93583	−	20.6997i	0.285925	−	1.19910i
$299$	1.22848	−	13.8104i	0.0710450	−	0.798677i
$300$	−3.99438	−	4.48971i	−0.230616	−	0.259214i
$301$	6.57882	+	10.2368i	0.379197	+	0.590042i
$302$	0.720662	−	1.82079i	0.0414694	−	0.104774i
$303$	−1.70290	+	0.635148i	−0.0978290	+	0.0364883i
$304$	3.40867	−	4.47724i	0.195500	−	0.256788i
$305$	−3.68045	+	24.0140i	−0.210742	+	1.37504i
$306$	18.2599	+	5.75823i	1.04385	+	0.329176i
$307$	−4.14060	+	5.53120i	−0.236317	+	0.315682i	−0.902985	−	0.429673i	$-0.858629\pi$
$307$	−4.14060	+	5.53120i	−0.236317	+	0.315682i	0.666668	+	0.745355i	$0.267720\pi$
$308$	−1.33280	−	42.1068i	−0.0759432	−	2.39926i
$309$	4.63635	+	4.01742i	0.263753	+	0.228543i
$310$	−1.51017	−	8.06795i	−0.0857721	−	0.458229i
$311$	−8.46657	−	5.44114i	−0.480095	−	0.308539i	0.278116	−	0.960548i	$-0.410290\pi$
$311$	−8.46657	−	5.44114i	−0.480095	−	0.308539i	−0.758211	+	0.652009i	$0.773926\pi$
$312$	0.756491	+	4.85535i	0.0428279	+	0.274880i
$313$	27.5313	−	15.0332i	1.55616	−	0.849729i	0.556339	−	0.830956i	$-0.312206\pi$
$313$	27.5313	−	15.0332i	1.55616	−	0.849729i	0.999824	−	0.0187736i	$-0.00597616\pi$
$314$	9.50320	+	11.4182i	0.536296	+	0.644366i
$315$	−24.3156	−	18.5570i	−1.37003	−	1.04557i
$316$	0.862474	−	21.6819i	0.0485180	−	1.21970i
$317$	10.5089	+	5.73831i	0.590240	+	0.322295i	0.746464	−	0.665426i	$-0.231750\pi$
$317$	10.5089	+	5.73831i	0.590240	+	0.322295i	−0.156224	+	0.987722i	$0.549932\pi$
$318$	6.68330	−	8.56743i	0.374781	−	0.480437i
$319$	4.27185	−	29.7114i	0.239178	−	1.66352i
$320$	2.79780	+	17.6684i	0.156402	+	0.987694i
$321$		−	2.42270i		−	0.135222i
$322$	3.70581	+	34.9621i	0.206517	+	1.94836i
$323$	5.10345	−	5.10345i	0.283964	−	0.283964i
$324$	−11.6982	+	1.20969i	−0.649898	+	0.0672049i
$325$	−7.16190	+	12.5563i	−0.397271	+	0.696497i
$326$	−0.590992	−	4.78367i	−0.0327320	−	0.264943i
$327$	−3.44235	−	1.87967i	−0.190362	−	0.103946i
$328$	−8.05709	+	28.6839i	−0.444878	+	1.58380i
$329$	14.5783	+	16.8243i	0.803728	+	0.927552i
$330$	0.875637	+	7.67210i	0.0482022	+	0.422335i
$331$	1.83490	−	6.24911i	0.100855	−	0.343482i	−0.893570	−	0.448924i	$-0.851807\pi$
$331$	1.83490	−	6.24911i	0.100855	−	0.343482i	0.994425	+	0.105442i	$0.0336256\pi$
$332$	21.0030	+	8.79974i	1.15269	+	0.482949i
$333$	−3.06150	−	14.0735i	−0.167769	−	0.771222i
$334$	−7.85974	−	0.156263i	−0.430066	−	0.00855032i
$335$	−8.60423	+	15.4156i	−0.470099	+	0.842246i
$336$	−4.25960	−	11.7098i	−0.232380	−	0.638821i
$337$	−3.53189	+	4.71805i	−0.192394	+	0.257009i	−0.886357	−	0.463002i	$-0.846772\pi$
$337$	−3.53189	+	4.71805i	−0.192394	+	0.257009i	0.693963	+	0.720011i	$0.255863\pi$
$338$	−5.82303	+	3.03094i	−0.316731	+	0.164861i
$339$	−4.56919	+	2.08668i	−0.248164	+	0.113333i
$340$	0.513034	+	22.9381i	0.0278232	+	1.24399i
$341$	−4.38145	+	9.59404i	−0.237269	+	0.519547i
$342$	−1.93211	+	4.88157i	−0.104477	+	0.263965i
$343$	14.1828	−	65.1971i	0.765797	−	3.52031i
$344$	0.551532	+	6.61662i	0.0297366	+	0.356744i
$345$	−1.20188	−	6.33127i	−0.0647068	−	0.340864i
$346$	1.08979	−	0.670135i	0.0585874	−	0.0360267i
$347$	−16.8409	−	3.66351i	−0.904065	−	0.196667i	−0.263580	−	0.964638i	$-0.584903\pi$
$347$	−16.8409	−	3.66351i	−0.904065	−	0.196667i	−0.640485	+	0.767970i	$0.721267\pi$
$348$	−1.54091	−	8.74357i	−0.0826012	−	0.468704i
$349$	−4.06694	+	8.90536i	−0.217698	+	0.476693i	−0.986700	−	0.162554i	$-0.948027\pi$
$349$	−4.06694	+	8.90536i	−0.217698	+	0.476693i	0.769001	+	0.639247i	$0.220754\pi$
$350$	11.6707	−	34.7471i	0.623828	−	1.85731i
$351$	−4.06966	−	8.91131i	−0.217222	−	0.475651i
$352$	10.1304	−	20.6336i	0.539952	−	1.09978i
$353$	−12.1554	+	16.2377i	−0.646968	+	0.864248i	−0.997379	−	0.0723478i	$-0.976951\pi$
$353$	−12.1554	+	16.2377i	−0.646968	+	0.864248i	0.350412	+	0.936596i	$0.386042\pi$
$354$	−3.34069	+	0.909191i	−0.177556	+	0.0483229i
$355$	−11.5079	+	3.26334i	−0.610777	+	0.173200i
$356$	−2.29343	−	3.90136i	−0.121552	−	0.206772i
$357$	−3.39717	−	15.6165i	−0.179797	−	0.826515i
$358$	−1.96062	+	1.40777i	−0.103622	+	0.0744031i
$359$	−18.9628	−	5.56798i	−1.00082	−	0.293867i	−0.260026	−	0.965602i	$-0.583731\pi$
$359$	−18.9628	−	5.56798i	−1.00082	−	0.293867i	−0.740791	+	0.671735i	$0.765549\pi$
$360$	−6.97084	−	15.1642i	−0.367395	−	0.799225i
$361$	−11.1464	−	12.8636i	−0.586650	−	0.677031i
$362$	−3.78914	−	19.2534i	−0.199153	−	1.01193i
$363$	1.58734	−	2.90700i	0.0833139	−	0.152578i
$364$	−23.4143	+	18.7122i	−1.22724	+	0.980786i
$365$	−9.37735	+	0.583270i	−0.490833	+	0.0305298i
$366$	4.00192	−	8.32116i	0.209184	−	0.434954i
$367$	−5.33255	−	5.33255i	−0.278357	−	0.278357i	0.554096	−	0.832453i	$-0.313064\pi$
$367$	−5.33255	−	5.33255i	−0.278357	−	0.278357i	−0.832453	+	0.554096i	$0.813064\pi$
$368$	−7.15884	+	17.7975i	−0.373180	+	0.927759i
$369$		−	27.7973i		−	1.44707i
$370$	14.7853	−	8.90381i	0.768652	−	0.462887i
$371$	65.6027	+	9.43225i	3.40592	+	0.489698i
$372$	−0.346054	+	3.10036i	−0.0179421	+	0.160746i
$373$	3.76548	+	2.05611i	0.194969	+	0.106461i	0.573768	−	0.819018i	$-0.305481\pi$
$373$	3.76548	+	2.05611i	0.194969	+	0.106461i	−0.378799	+	0.925479i	$0.623663\pi$
$374$	16.4292	−	24.4803i	0.849532	−	1.26585i
$375$	−1.61036	+	6.52285i	−0.0831584	+	0.336838i
$376$	2.72141	+	11.8379i	0.140346	+	0.610494i
$377$	−18.7439	+	10.2350i	−0.965361	+	0.527127i
$378$	14.4888	+	20.1788i	0.745226	+	1.03789i
$379$	12.5718	−	19.5621i	0.645771	−	1.00484i	−0.351860	−	0.936053i	$-0.614451\pi$
$379$	12.5718	−	19.5621i	0.645771	−	1.00484i	0.997631	−	0.0687870i	$-0.0219129\pi$
$380$	−6.28377	−	0.308388i	−0.322351	−	0.0158200i
$381$	3.33367	+	2.88864i	0.170789	+	0.147990i
$382$	−10.9450	+	19.1302i	−0.559997	+	0.978787i
$383$	16.9752	+	12.7074i	0.867390	+	0.649320i	0.937411	−	0.348225i	$-0.113216\pi$
$383$	16.9752	+	12.7074i	0.867390	+	0.649320i	−0.0700206	+	0.997546i	$0.522306\pi$
$384$	0.943019	−	6.73312i	0.0481232	−	0.343598i
$385$	−37.9661	+	27.8751i	−1.93493	+	1.42065i
$386$	−19.0860	−	17.2142i	−0.971454	−	0.876177i
$387$	−2.16479	−	5.80403i	−0.110043	−	0.295035i
$388$	15.4222	−	2.71789i	0.782941	−	0.137980i
$389$	−2.17279	−	3.38092i	−0.110165	−	0.171420i	0.781794	−	0.623537i	$-0.214305\pi$
$389$	−2.17279	−	3.38092i	−0.110165	−	0.171420i	−0.891958	+	0.452118i	$0.850669\pi$
$390$	3.99641	−	3.76989i	0.202366	−	0.190896i
$391$	−12.1639	+	21.3874i	−0.615156	+	1.08161i
$392$	36.3040	−	42.9067i	1.83363	−	2.16711i
$393$	−5.05170	−	1.09893i	−0.254824	−	0.0554337i
$394$	30.6236	−	13.2561i	1.54279	−	0.667834i
$395$	−20.5299	+	12.9261i	−1.03297	+	0.650384i
$396$	−3.89339	+	21.0895i	−0.195650	+	1.05979i
$397$	1.69724	−	4.55049i	0.0851823	−	0.228383i	−0.887374	−	0.461050i	$-0.847473\pi$
$397$	1.69724	−	4.55049i	0.0851823	−	0.228383i	0.972556	+	0.232668i	$0.0747455\pi$
$398$	−3.58450	−	6.88652i	−0.179675	−	0.345190i
$399$	4.33769	−	0.623666i	0.217156	−	0.0312224i
$400$	14.5143	−	13.7599i	0.725715	−	0.687995i
$401$	−20.1755	−	17.4822i	−1.00752	−	0.873019i	−0.0155973	−	0.999878i	$-0.504965\pi$
$401$	−20.1755	−	17.4822i	−1.00752	−	0.873019i	−0.991921	+	0.126859i	$0.959510\pi$
$402$	4.83792	−	4.64930i	0.241294	−	0.231886i
$403$	7.33255	−	1.59510i	0.365260	−	0.0794575i
$404$	−2.29210	−	5.59776i	−0.114036	−	0.278499i
$405$	8.51798	+	10.0166i	0.423262	+	0.497729i
$406$	41.6237	−	34.6428i	2.06575	−	1.71929i
$407$	−22.1213	−	1.58215i	−1.09651	−	0.0784240i
$408$	2.35817	−	8.39527i	0.116747	−	0.415628i
$409$	−1.81420	−	6.17861i	−0.0897067	−	0.305513i	0.902402	−	0.430896i	$-0.141802\pi$
$409$	−1.81420	−	6.17861i	−0.0897067	−	0.305513i	−0.992108	+	0.125383i	$0.959984\pi$
$410$	31.5366	−	10.7260i	1.55748	−	0.529721i
$411$	−0.451253	+	3.13853i	−0.0222587	+	0.154812i
$412$	−12.8756	+	15.8457i	−0.634337	+	0.780659i
$413$	−14.9327	−	14.9327i	−0.734789	−	0.734789i
$414$	1.93985	−	17.7923i	0.0953385	−	0.874443i
$415$	−5.18078	−	24.9271i	−0.254314	−	1.22362i
$416$	−16.0715	+	3.02767i	−0.787970	+	0.148444i
$417$	−3.38430	−	4.52089i	−0.165730	−	0.221389i
$418$	6.37417	+	4.97237i	0.311771	+	0.243207i
$419$	1.60567	+	5.46841i	0.0784422	+	0.267150i	0.989371	−	0.145414i	$-0.0464515\pi$
$419$	1.60567	+	5.46841i	0.0784422	+	0.267150i	−0.910929	+	0.412564i	$0.864633\pi$
$420$	−8.09721	+	11.3364i	−0.395103	+	0.553160i
$421$	8.15392	+	9.41012i	0.397398	+	0.458621i	0.918820	−	0.394678i	$-0.129144\pi$
$421$	8.15392	+	9.41012i	0.397398	+	0.458621i	−0.521422	+	0.853299i	$0.674598\pi$
$422$	0.758432	+	0.0694216i	0.0369199	+	0.00337939i
$423$	−5.43117	−	9.94644i	−0.264072	−	0.483613i
$424$	29.2029	+	21.3297i	1.41822	+	1.03586i
$425$	20.8172	−	14.9889i	1.00978	−	0.727069i
$426$	4.54533	+	0.0903676i	0.220222	+	0.00437833i
$427$	56.1769	−	4.01785i	2.71859	−	0.194437i
$428$	8.05902	−	0.255091i	0.389548	−	0.0123303i
$429$	−6.98772	+	1.00468i	−0.337370	+	0.0485065i
$430$	5.74947	−	4.69557i	0.277264	−	0.226441i
$431$	29.8882	−	13.6495i	1.43966	−	0.657473i	0.465860	−	0.884859i	$-0.345745\pi$
$431$	29.8882	−	13.6495i	1.43966	−	0.657473i	0.973805	+	0.227386i	$0.0730178\pi$
$432$	1.82006	+	13.4317i	0.0875675	+	0.646233i
$433$	−9.49776	−	25.4645i	−0.456433	−	1.22375i	−0.937785	−	0.347217i	$-0.887127\pi$
$433$	−9.49776	−	25.4645i	−0.456433	−	1.22375i	0.481351	−	0.876528i	$-0.340146\pi$
$434$	−17.4625	+	7.55904i	−0.838226	+	0.362845i
$435$	−7.08375	+	6.95348i	−0.339640	+	0.333394i
$436$	5.89019	−	11.6488i	0.282089	−	0.557875i
$437$	−5.61167	−	3.74530i	−0.268442	−	0.179162i
$438$	3.47352	+	0.828258i	0.165971	+	0.0395757i
$439$	5.55858	+	8.64932i	0.265297	+	0.412810i	0.948188	−	0.317711i	$-0.102914\pi$
$439$	5.55858	+	8.64932i	0.265297	+	0.412810i	−0.682891	+	0.730520i	$0.739278\pi$
$440$	−25.4288	+	3.72059i	−1.21227	+	0.177372i
$441$	−21.7835	+	47.6993i	−1.03731	+	2.27139i
$442$	−20.9480	+	1.08022i	−0.996397	+	0.0513809i
$443$	−4.23541	−	1.57973i	−0.201231	−	0.0750551i	0.246828	−	0.969059i	$-0.420612\pi$
$443$	−4.23541	−	1.57973i	−0.201231	−	0.0750551i	−0.448059	+	0.894004i	$0.647884\pi$
$444$	−6.36245	+	1.59645i	−0.301949	+	0.0757641i
$445$	−2.14449	+	4.58276i	−0.101659	+	0.217244i
$446$	5.36370	+	19.7082i	0.253978	+	0.933208i
$447$	9.01943	−	0.645082i	0.426604	−	0.0305113i
$448$	38.5037	−	15.4024i	1.81913	−	0.727693i
$449$	3.27879	−	5.10189i	0.154736	−	0.240773i	−0.755227	−	0.655463i	$-0.772474\pi$
$449$	3.27879	−	5.10189i	0.154736	−	0.240773i	0.909963	+	0.414690i	$0.136110\pi$
$450$	−9.56538	+	16.0214i	−0.450916	+	0.755258i
$451$	−41.0696	−	12.0591i	−1.93389	−	0.567842i
$452$	−7.42236	−	14.9795i	−0.349119	−	0.704578i
$453$	0.829980	+	0.0593613i	0.0389958	+	0.00278904i
$454$	21.6125	+	14.5045i	1.01433	+	0.680732i
$455$	32.0643	+	9.73903i	1.50320	+	0.456573i
$456$	2.25004	+	0.809201i	0.105368	+	0.0378943i
$457$	−7.87413	+	5.89450i	−0.368336	+	0.275733i	−0.767372	−	0.641202i	$-0.778436\pi$
$457$	−7.87413	+	5.89450i	−0.368336	+	0.275733i	0.399036	+	0.916935i	$0.369345\pi$
$458$	5.50947	+	15.7189i	0.257441	+	0.734495i
$459$			17.3849i			0.811459i
$460$	20.9342	−	4.66463i	0.976063	−	0.217490i
$461$		−	35.7780i		−	1.66635i	−0.553012	−	0.833173i	$-0.686522\pi$
$461$		−	35.7780i		−	1.66635i	0.553012	−	0.833173i	$-0.313478\pi$
$462$	16.8936	−	5.92122i	0.785963	−	0.275480i
$463$	−4.46276	+	3.34078i	−0.207402	+	0.155259i	−0.697929	−	0.716167i	$-0.745895\pi$
$463$	−4.46276	+	3.34078i	−0.207402	+	0.155259i	0.490527	+	0.871426i	$0.336804\pi$
$464$	28.9229	−	6.04640i	1.34271	−	0.280697i
$465$	3.07658	−	1.64306i	0.142673	−	0.0761951i
$466$	23.3944	−	34.8589i	1.08373	−	1.61481i
$467$	25.9784	+	1.85801i	1.20214	+	0.0859785i	0.658000	−	0.753018i	$-0.271403\pi$
$467$	25.9784	+	1.85801i	1.20214	+	0.0859785i	0.544137	+	0.838997i	$0.316857\pi$
$468$	13.6718	−	6.77440i	0.631981	−	0.313147i
$469$	39.2692	+	11.5305i	1.81328	+	0.532428i
$470$	9.18873	−	9.99976i	0.423845	−	0.461254i
$471$	−3.41280	+	5.31042i	−0.157253	+	0.244691i
$472$	−3.37614	−	11.0170i	−0.155399	−	0.507097i
$473$	−9.51441	+	0.680484i	−0.437473	+	0.0312887i
$474$	8.89690	−	2.42135i	0.408648	−	0.111216i
$475$	3.69235	+	5.98687i	0.169417	+	0.274697i
$476$	51.5902	−	12.9449i	2.36463	−	0.593327i
$477$	−31.6122	−	11.7908i	−1.44742	−	0.539861i
$478$	−1.73160	−	33.5798i	−0.0792016	−	1.53591i
$479$	−12.0929	+	26.4798i	−0.552540	+	1.20989i	0.403046	+	0.915180i	$0.367951\pi$
$479$	−12.0929	+	26.4798i	−0.552540	+	1.20989i	−0.955586	+	0.294713i	$0.904776\pi$
$480$	−6.80265	+	3.39178i	−0.310497	+	0.154813i
$481$	8.53073	+	13.2741i	0.388968	+	0.605246i
$482$	−4.02136	+	16.8646i	−0.183168	+	0.768163i
$483$	−13.6950	+	5.96983i	−0.623142	+	0.271637i
$484$	9.83718	+	4.97416i	0.447144	+	0.226098i
$485$	−12.2648	−	12.4945i	−0.556914	−	0.567347i
$486$	−7.69637	−	17.7797i	−0.349115	−	0.806506i
$487$	−9.34892	−	25.0654i	−0.423640	−	1.13582i	−0.957039	−	0.289959i	$-0.906358\pi$
$487$	−9.34892	−	25.0654i	−0.423640	−	1.13582i	0.533399	−	0.845864i	$-0.320914\pi$
$488$	28.1014	+	12.4361i	1.27209	+	0.562956i
$489$	1.86308	−	0.850838i	0.0842512	−	0.0384762i
$490$	−62.5213	−	6.30833i	−2.82442	−	0.284981i
$491$	−1.54691	+	0.222412i	−0.0698111	+	0.0100373i	−0.177132	−	0.984187i	$-0.556682\pi$
$491$	−1.54691	+	0.222412i	−0.0698111	+	0.0100373i	0.107321	+	0.994224i	$0.465773\pi$
$492$	−12.6539	+	0.400533i	−0.570484	+	0.0180574i
$493$	37.8019	−	2.70365i	1.70251	−	0.121766i
$494$	0.114330	−	5.75057i	0.00514393	−	0.258730i
$495$	21.9019	−	9.75767i	0.984418	−	0.438575i
$496$	−10.3497	−	0.824695i	−0.464714	−	0.0370299i
$497$	13.2896	+	24.3381i	0.596121	+	1.09171i
$498$	−0.882025	+	9.63614i	−0.0395245	+	0.431806i
$499$	15.9218	+	18.3747i	0.712756	+	0.822564i	0.990416	−	0.138115i	$-0.0441044\pi$
$499$	15.9218	+	18.3747i	0.712756	+	0.822564i	−0.277660	+	0.960679i	$0.589559\pi$
$500$	−21.8676	−	4.66999i	−0.977948	−	0.208848i
$501$	−0.941122	−	3.20517i	−0.0420462	−	0.143196i
$502$	−11.9137	+	15.2724i	−0.531734	+	0.681639i
$503$	−8.44345	−	11.2791i	−0.376475	−	0.502911i	0.571787	−	0.820402i	$-0.306251\pi$
$503$	−8.44345	−	11.2791i	−0.376475	−	0.502911i	−0.948261	+	0.317491i	$0.897160\pi$
$504$	−30.6987	+	23.5493i	−1.36743	+	1.04897i
$505$	−3.70890	+	5.65507i	−0.165044	+	0.251647i
$506$	−25.4460	−	10.5848i	−1.13121	−	0.470551i
$507$	−1.97247	−	1.97247i	−0.0876003	−	0.0876003i
$508$	−9.25797	+	11.3935i	−0.410756	+	0.505505i
$509$	1.30092	−	9.04812i	0.0576624	−	0.401051i	−0.940465	−	0.339889i	$-0.889610\pi$
$509$	1.30092	−	9.04812i	0.0576624	−	0.401051i	0.998128	−	0.0611617i	$-0.0194805\pi$
$510$	−9.23020	+	3.13932i	−0.408720	+	0.139011i
$511$	6.13642	+	20.8987i	0.271459	+	0.924506i
$512$	22.4968	+	2.42798i	0.994226	+	0.107302i
$513$	−4.75490	−	0.340077i	−0.209934	−	0.0150148i
$514$	2.23432	+	2.68456i	0.0985517	+	0.118411i
$515$	22.7530	+	1.83970i	1.00262	+	0.0810669i
$516$	−2.61093	+	1.06909i	−0.114940	+	0.0470641i
$517$	−17.0517	+	3.70938i	−0.749934	+	0.163138i
$518$	−27.7243	−	28.8491i	−1.21814	−	1.26756i
$519$	0.410846	+	0.356000i	0.0180342	+	0.0156267i
$520$	12.9612	+	12.8970i	0.568386	+	0.565570i
$521$	−39.0799	+	5.61883i	−1.71212	+	0.246166i	−0.927503	−	0.373816i	$-0.878049\pi$
$521$	−39.0799	+	5.61883i	−1.71212	+	0.246166i	−0.784617	+	0.619981i	$0.787140\pi$
$522$	−24.4536	+	12.7283i	−1.07031	+	0.557105i
$523$	−7.71805	+	20.6929i	−0.337487	+	0.904837i	0.651740	+	0.758443i	$0.274039\pi$
$523$	−7.71805	+	20.6929i	−0.337487	+	0.904837i	−0.989226	+	0.146394i	$0.953233\pi$
$524$	3.12365	−	16.9200i	0.136457	−	0.739154i
$525$	15.5729	+	0.289064i	0.679657	+	0.0126158i
$526$	−12.2322	−	28.2582i	−0.533351	−	1.23212i
$527$	−13.0122	−	2.83064i	−0.566822	−	0.123305i
$528$	9.65651	+	1.46848i	0.420245	+	0.0639073i
$529$	21.8307	+	7.24026i	0.949160	+	0.314794i
$530$	1.17877	−	40.4143i	0.0512023	−	1.75549i
$531$	5.81214	+	9.04386i	0.252225	+	0.392470i
$532$	2.53133	+	14.3635i	0.109747	+	0.622738i
$533$	10.6424	+	28.5335i	0.460975	+	1.23592i
$534$	1.28795	−	1.42800i	0.0557351	−	0.0617957i
$535$	−5.33515	−	7.26652i	−0.230659	−	0.314159i
$536$	15.9751	+	15.6037i	0.690021	+	0.673975i
$537$	−0.821067	−	0.614643i	−0.0354317	−	0.0265238i
$538$	−22.0154	−	12.5957i	−0.949150	−	0.543041i
$539$	61.0239	+	52.8775i	2.62849	+	2.27760i
$540$	11.2281	−	10.1776i	0.483181	−	0.437974i
$541$	−1.25569	+	1.95390i	−0.0539865	+	0.0840046i	−0.867198	−	0.497964i	$-0.834081\pi$
$541$	−1.25569	+	1.95390i	−0.0539865	+	0.0840046i	0.813211	+	0.581969i	$0.197717\pi$
$542$	11.7684	−	8.45000i	0.505497	−	0.362958i
$543$	7.31827	−	3.99608i	0.314057	−	0.171488i
$544$	28.1749	+	6.96041i	1.20799	+	0.298425i
$545$	−14.4641	+	1.94281i	−0.619575	+	0.0832206i
$546$	−10.5755	−	7.09738i	−0.452588	−	0.303740i
$547$	22.7614	+	12.4287i	0.973207	+	0.531411i	0.885452	−	0.464731i	$-0.153849\pi$
$547$	22.7614	+	12.4287i	0.973207	+	0.531411i	0.0877547	+	0.996142i	$0.472031\pi$
$548$	−10.4877	−	1.17062i	−0.448014	−	0.0500062i
$549$	−28.3789	−	4.08028i	−1.21118	−	0.174142i
$550$	19.5215	+	21.0830i	0.832398	+	0.898983i
$551$			10.3920i			0.442713i
$552$	−8.12739	−	0.626693i	−0.345925	−	0.0266738i
$553$	39.7686	+	39.7686i	1.69113	+	1.69113i
$554$	−26.1946	−	12.5978i	−1.11290	−	0.535231i
$555$	5.49782	+	4.85394i	0.233370	+	0.206038i
$556$	14.6823	−	11.7338i	0.622666	−	0.497623i
$557$	1.20476	−	2.20635i	0.0510473	−	0.0934862i	−0.850910	−	0.525312i	$-0.823949\pi$
$557$	1.20476	−	2.20635i	0.0510473	−	0.0934862i	0.901957	+	0.431826i	$0.142130\pi$
$558$	9.50436	−	1.87050i	0.402352	−	0.0791844i
$559$	4.44424	+	5.12893i	0.187971	+	0.216931i
$560$	−38.5627	−	25.7414i	−1.62957	−	1.08777i
$561$	12.0204	+	3.52949i	0.507500	+	0.149015i
$562$	10.6709	+	14.8614i	0.450123	+	0.626892i
$563$	−9.61288	−	44.1897i	−0.405135	−	1.86237i	−0.498720	−	0.866763i	$-0.666196\pi$
$563$	−9.61288	−	44.1897i	−0.405135	−	1.86237i	0.0935854	−	0.995611i	$-0.470167\pi$
$564$	−4.44958	+	2.61571i	−0.187361	+	0.110141i
$565$	−9.10941	+	16.3207i	−0.383236	+	0.686618i
$566$	2.09487	+	7.69730i	0.0880539	+	0.323542i
$567$	18.2671	−	24.4020i	0.767148	−	1.02479i
$568$	0.177982	+	15.1294i	0.00746795	+	0.634816i
$569$	4.87094	+	10.6659i	0.204201	+	0.447137i	0.983830	−	0.179104i	$-0.0573199\pi$
$569$	4.87094	+	10.6659i	0.204201	+	0.447137i	−0.779630	+	0.626241i	$0.784593\pi$
$570$	−0.678069	−	2.58594i	−0.0284012	−	0.108313i
$571$	18.6423	−	40.8209i	0.780154	−	1.70830i	0.0772542	−	0.997011i	$-0.475385\pi$
$571$	18.6423	−	40.8209i	0.780154	−	1.70830i	0.702900	−	0.711288i	$-0.251888\pi$
$572$	−4.07779	−	23.1386i	−0.170501	−	0.967474i
$573$	−9.15135	−	1.99075i	−0.382303	−	0.0831649i
$574$	−40.4501	−	65.7807i	−1.68835	−	2.74563i
$575$	−17.5473	−	16.3430i	−0.731772	−	0.681550i
$576$	−20.8197	+	3.49515i	−0.867485	+	0.145631i
$577$	3.91091	−	17.9782i	0.162813	−	0.748440i	−0.821242	−	0.570579i	$-0.806719\pi$
$577$	3.91091	−	17.9782i	0.162813	−	0.748440i	0.984056	−	0.177861i	$-0.0569177\pi$
$578$	12.2567	+	4.85118i	0.509813	+	0.201782i
$579$	4.53698	−	9.93461i	0.188551	−	0.412868i
$580$	−23.8764	−	22.8317i	−0.991413	−	0.948035i
$581$	−53.6884	+	24.5187i	−2.22737	+	1.01721i
$582$	3.07234	+	5.90256i	0.127352	+	0.244669i
$583$	−31.1346	+	41.5910i	−1.28946	+	1.72252i
$584$	−2.38944	+	11.6418i	−0.0988757	+	0.481739i
$585$	−14.8960	−	8.31418i	−0.615872	−	0.343749i
$586$	−0.637052	+	32.0426i	−0.0263164	+	1.32367i
$587$	−2.74295	−	12.6092i	−0.113214	−	0.520436i	−0.998468	−	0.0553284i	$-0.982379\pi$
$587$	−2.74295	−	12.6092i	−0.113214	−	0.520436i	0.885254	−	0.465107i	$-0.153984\pi$
$588$	22.0276	+	9.22904i	0.908405	+	0.380599i
$589$	1.02874	−	3.50357i	0.0423885	−	0.144362i
$590$	−8.01773	+	10.0837i	−0.330085	+	0.415139i
$591$	9.28569	+	10.7163i	0.381962	+	0.440808i
$592$	−5.98045	−	20.9964i	−0.245795	−	0.862946i
$593$	23.1439	+	12.6375i	0.950408	+	0.518962i	0.878130	−	0.478423i	$-0.158791\pi$
$593$	23.1439	+	12.6375i	0.950408	+	0.518962i	0.0722781	+	0.997385i	$0.476973\pi$
$594$	−19.3260	+	2.38761i	−0.792956	+	0.0979648i
$595$	−44.5793	−	39.3584i	−1.82757	−	1.61354i
$596$	3.09552	+	29.9349i	0.126797	+	1.22618i
$597$	2.33271	−	2.33271i	0.0954713	−	0.0954713i
$598$	4.82070	+	19.0062i	0.197133	+	0.777219i
$599$		−	11.1423i		−	0.455262i	−0.973747	−	0.227631i	$-0.926902\pi$
$599$		−	11.1423i		−	0.455262i	0.973747	−	0.227631i	$-0.0730980\pi$
$600$	7.43114	+	4.12352i	0.303375	+	0.168342i
$601$	−0.673594	+	4.68495i	−0.0274765	+	0.191103i	−0.998937	−	0.0460986i	$-0.985321\pi$
$601$	−0.673594	+	4.68495i	−0.0274765	+	0.191103i	0.971460	+	0.237202i	$0.0762302\pi$
$602$	−13.5688	−	10.5847i	−0.553021	−	0.431402i
$603$	−18.2860	−	9.98494i	−0.744666	−	0.406618i
$604$	−0.110073	+	2.76715i	−0.00447881	+	0.112594i
$605$	−1.64066	−	12.2147i	−0.0667024	−	0.496598i
$606$	1.97559	−	1.64426i	0.0802530	−	0.0667934i
$607$	−6.39336	+	3.49104i	−0.259499	+	0.141697i	−0.603733	−	0.797187i	$-0.706320\pi$
$607$	−6.39336	+	3.49104i	−0.259499	+	0.141697i	0.344234	+	0.938884i	$0.388139\pi$
$608$	−2.45487	+	7.56988i	−0.0995581	+	0.306999i
$609$	19.3585	+	12.4410i	0.784446	+	0.504133i
$610$	−6.32131	−	33.7709i	−0.255942	−	1.36734i
$611$	9.38308	+	8.13048i	0.379599	+	0.328924i
$612$	−27.0634	+	0.856632i	−1.09397	+	0.0346273i
$613$	−15.8321	+	21.1492i	−0.639452	+	0.854208i	−0.996814	−	0.0797578i	$-0.974585\pi$
$613$	−15.8321	+	21.1492i	−0.639452	+	0.854208i	0.357362	+	0.933966i	$0.383676\pi$
$614$	2.93870	−	9.31888i	0.118596	−	0.376079i
$615$	8.37704	+	11.4096i	0.337795	+	0.460079i
$616$	21.4755	+	55.5727i	0.865273	+	2.23909i
$617$	−13.5612	+	5.05808i	−0.545955	+	0.203631i	−0.607281	−	0.794487i	$-0.707740\pi$
$617$	−13.5612	+	5.05808i	−0.545955	+	0.203631i	0.0613260	+	0.998118i	$0.480467\pi$
$618$	−8.06698	−	3.19289i	−0.324502	−	0.128437i
$619$	11.6005	+	18.0507i	0.466263	+	0.725520i	0.992153	−	0.125033i	$-0.0399037\pi$
$619$	11.6005	+	18.0507i	0.466263	+	0.725520i	−0.525889	+	0.850553i	$0.676267\pi$
$620$	5.78952	+	10.0611i	0.232513	+	0.404064i
$621$	15.9373	−	3.17890i	0.639541	−	0.127565i
$622$	13.8448	+	3.30129i	0.555127	+	0.132370i
$623$	11.4616	+	2.49331i	0.459198	+	0.0998924i
$624$	−3.28086	−	6.12612i	−0.131339	−	0.245241i
$625$	9.53428	+	23.1105i	0.381371	+	0.924422i
$626$	−29.7113	+	32.9421i	−1.18750	+	1.31663i
$627$	−1.20048	+	3.21861i	−0.0479426	+	0.128539i
$628$	−18.0243	−	10.7934i	−0.719246	−	0.430704i
$629$	−3.98497	−	27.7160i	−0.158891	−	1.10511i
$630$	41.1325	+	13.3920i	1.63876	+	0.533550i
$631$	−0.334551	−	0.289890i	−0.0133183	−	0.0115404i	0.648176	−	0.761490i	$-0.275532\pi$
$631$	−0.334551	−	0.289890i	−0.0133183	−	0.0115404i	−0.661494	+	0.749950i	$0.730077\pi$
$632$	8.99130	+	29.3403i	0.357655	+	1.16709i
$633$	0.0687916	+	0.316230i	0.00273422	+	0.0125690i
$634$	−16.7096	−	2.74252i	−0.663622	−	0.108920i
$635$	16.3601	+	1.32280i	0.649230	+	0.0524937i
$636$	−4.91191	+	14.5605i	−0.194770	+	0.577361i
$637$	4.09835	−	57.3025i	0.162383	−	2.27041i
$638$	8.19716	+	41.6513i	0.324528	+	1.64899i
$639$	−3.97706	−	13.5446i	−0.157330	−	0.535817i
$640$	−11.9989	−	22.2716i	−0.474298	−	0.880364i
$641$	13.6757	+	1.96627i	0.540157	+	0.0776629i	0.406993	−	0.913431i	$-0.366577\pi$
$641$	13.6757	+	1.96627i	0.540157	+	0.0776629i	0.133164	+	0.991094i	$0.457486\pi$
$642$	1.13329	+	3.23336i	0.0447275	+	0.127610i
$643$	−15.2973	−	15.2973i	−0.603265	−	0.603265i	0.337913	−	0.941177i	$-0.390279\pi$
$643$	−15.2973	−	15.2973i	−0.603265	−	0.603265i	−0.941177	+	0.337913i	$0.890279\pi$
$644$	−21.3004	−	44.9272i	−0.839354	−	1.77038i
$645$	2.63766	+	1.72992i	0.103858	+	0.0681155i
$646$	−4.42381	+	9.19840i	−0.174053	+	0.361906i
$647$	−9.00180	−	12.0250i	−0.353897	−	0.472751i	0.587900	−	0.808934i	$-0.299955\pi$
$647$	−9.00180	−	12.0250i	−0.353897	−	0.472751i	−0.941797	+	0.336183i	$0.890864\pi$
$648$	15.0466	−	7.08664i	0.591087	−	0.278390i
$649$	15.8835	−	4.66380i	0.623480	−	0.183070i
$650$	3.68476	−	20.1079i	0.144528	−	0.788697i
$651$	−5.29498	−	6.11073i	−0.207527	−	0.239498i
$652$	3.02645	+	6.10787i	0.118525	+	0.239203i
$653$	26.3519	−	14.3892i	1.03123	−	0.563094i	0.127787	−	0.991802i	$-0.459213\pi$
$653$	26.3519	−	14.3892i	1.03123	−	0.563094i	0.903443	+	0.428707i	$0.141031\pi$
$654$	5.47347	+	0.898354i	0.214029	+	0.0351284i
$655$	−17.5718	+	7.82853i	−0.686588	+	0.305886i
$656$	−2.66472	−	42.0508i	−0.104040	−	1.64181i
$657$	−0.791007	−	11.0597i	−0.0308601	−	0.431481i
$658$	−27.3264	−	15.6344i	−1.06529	−	0.609491i
$659$	−24.9662	+	3.58960i	−0.972545	+	0.139831i	−0.610230	−	0.792225i	$-0.708923\pi$
$659$	−24.9662	+	3.58960i	−0.972545	+	0.139831i	−0.362315	+	0.932056i	$0.618014\pi$
$660$	−4.75749	−	9.82965i	−0.185185	−	0.382618i
$661$	15.9718	+	34.9733i	0.621229	+	1.36030i	0.914622	+	0.404310i	$0.132488\pi$
$661$	15.9718	+	34.9733i	0.621229	+	1.36030i	−0.293392	+	0.955992i	$0.594784\pi$
$662$	0.474334	+	9.19845i	0.0184355	+	0.357508i
$663$	−3.11485	−	8.35124i	−0.120971	−	0.324335i
$664$	−32.1472	−	1.91942i	−1.24755	−	0.0744878i
$665$	11.6369	−	11.4229i	0.451258	−	0.442959i
$666$	10.6692	+	17.3505i	0.413424	+	0.672318i
$667$	−9.39073	−	34.1597i	−0.363611	−	1.32267i
$668$	10.5628	−	3.46809i	0.408686	−	0.134184i
$669$	−7.30136	+	4.69230i	−0.282287	+	0.181415i
$670$	4.27215	−	24.5987i	0.165048	−	0.950332i
$671$	−18.3399	+	40.1589i	−0.708006	+	1.55032i
$672$	11.1625	+	13.6354i	0.430603	+	0.525998i
$673$	0.00606846	−	0.0162702i	0.000233922	−	0.000627169i	−0.936833	−	0.349778i	$-0.886257\pi$
$673$	0.00606846	−	0.0162702i	0.000233922	−	0.000627169i	0.937067	+	0.349151i	$0.113530\pi$
$674$	2.50668	−	7.94890i	0.0965536	−	0.306180i
$675$	−16.4862	−	3.90814i	−0.634553	−	0.150425i
$676$	6.35365	−	6.76902i	0.244371	−	0.260347i
$677$	−1.09959	−	15.3743i	−0.0422606	−	0.590881i	−0.973824	−	0.227303i	$-0.927009\pi$
$677$	−1.09959	−	15.3743i	−0.0422606	−	0.590881i	0.931564	−	0.363579i	$-0.118445\pi$
$678$	5.12197	−	4.92228i	0.196708	−	0.189039i
$679$	−21.9437	+	34.1451i	−0.842122	+	1.31037i
$680$	−11.4147	−	30.3734i	−0.437734	−	1.16477i
$681$	−3.11602	+	10.6122i	−0.119406	+	0.406660i
$682$	1.35962	−	14.8539i	0.0520625	−	0.568783i
$683$	−17.9818	−	1.28608i	−0.688054	−	0.0492106i	−0.277065	−	0.960851i	$-0.589362\pi$
$683$	−17.9818	−	1.28608i	−0.688054	−	0.0492106i	−0.410989	+	0.911641i	$0.634816\pi$
$684$	0.295109	−	7.41879i	0.0112838	−	0.283665i
$685$	5.55806	+	10.4073i	0.212363	+	0.397642i
$686$	11.5695	+	93.6471i	0.441726	+	3.57546i
$687$	−5.66605	+	4.24155i	−0.216173	+	0.161825i
$688$	−3.83121	−	8.57260i	−0.146063	−	0.326827i
$689$	36.9636			1.40820
$690$	4.56568	+	7.88756i	0.173813	+	0.300274i
$691$			8.79514i			0.334583i	0.985907	+	0.167292i	$0.0535021\pi$
$691$			8.79514i			0.334583i	−0.985907	+	0.167292i	$0.946498\pi$
$692$	−1.14096	+	1.40415i	−0.0433729	+	0.0533778i
$693$	−33.3109	−	44.4982i	−1.26538	−	1.69035i
$694$	24.1897	−	2.98848i	0.918228	−	0.113441i
$695$	−20.1064	−	6.10700i	−0.762679	−	0.231652i
$696$	6.14658	+	10.9484i	0.232986	+	0.414999i
$697$	3.85534	−	53.9048i	0.146032	−	2.04179i
$698$	1.26202	−	13.7876i	0.0477682	−	0.521868i
$699$	17.1165	+	5.02584i	0.647404	+	0.190095i
$700$	0.678139	+	51.8331i	0.0256312	+	1.95911i
$701$	3.77652	+	2.42702i	0.142637	+	0.0916674i	0.610013	−	0.792391i	$-0.291164\pi$
$701$	3.77652	+	2.42702i	0.142637	+	0.0916674i	−0.467376	+	0.884059i	$0.654801\pi$
$702$	9.59994	+	9.98941i	0.362327	+	0.377026i
$703$	7.65849	−	0.547746i	0.288845	−	0.0206586i
$704$	−3.86809	+	32.2767i	−0.145784	+	1.21647i
$705$	5.22673	+	2.44584i	0.196850	+	0.0921157i
$706$	8.62703	−	27.3571i	0.324683	−	1.02960i
$707$	14.6894	+	5.47886i	0.552452	+	0.206054i
$708$	4.03322	−	2.77613i	0.151578	−	0.104333i
$709$	−32.3330	−	14.7660i	−1.21429	−	0.554549i	−0.297811	−	0.954625i	$-0.596256\pi$
$709$	−32.3330	−	14.7660i	−1.21429	−	0.554549i	−0.916482	+	0.400076i	$0.868984\pi$
$710$	13.8320	−	9.73847i	0.519107	−	0.365478i
$711$	−15.4788	−	24.0855i	−0.580501	−	0.903277i
$712$	4.88581	+	4.13396i	0.183104	+	0.154927i
$713$	−0.215592	+	12.4463i	−0.00807400	+	0.466117i
$714$	11.8390	+	19.2529i	0.443064	+	0.720520i
$715$	−18.7462	+	18.4014i	−0.701066	+	0.688174i
$716$	1.95814	−	2.79597i	0.0731790	−	0.104490i
$717$	13.3871	−	4.99313i	0.499950	−	0.186472i
$718$	27.9125	−	1.43935i	1.04168	−	0.0537162i
$719$	30.2609	−	13.8197i	1.12854	−	0.515387i	0.238443	−	0.971156i	$-0.423363\pi$
$719$	30.2609	−	13.8197i	1.12854	−	0.515387i	0.890098	+	0.455769i	$0.150636\pi$
$720$	16.3969	+	16.9775i	0.611075	+	0.632714i
$721$	−7.53119	−	52.3806i	−0.280476	−	1.95075i
$722$	20.8934	+	11.9538i	0.777570	+	0.444874i
$723$	−7.34839	+	0.525567i	−0.273289	+	0.0195460i
$724$	14.0634	+	23.9232i	0.522661	+	0.889100i
$725$	−5.93402	+	36.4554i	−0.220384	+	1.35392i
$726$	−0.758643	+	4.62224i	−0.0281559	+	0.171547i
$727$	−23.7655	−	43.5233i	−0.881415	−	1.61419i	−0.785551	−	0.618797i	$-0.787620\pi$
$727$	−23.7655	−	43.5233i	−0.881415	−	1.61419i	−0.0958641	−	0.995394i	$-0.530561\pi$
$728$	22.4957	−	35.9262i	0.833745	−	1.33151i
$729$	−7.11030	+	6.16111i	−0.263344	+	0.228189i
$730$	12.2423	−	5.16498i	0.453106	−	0.191165i
$731$	−3.39299	−	11.5555i	−0.125494	−	0.427394i
$732$	−1.44852	+	12.9775i	−0.0535388	+	0.479663i
$733$	9.40676	−	7.04181i	0.347447	−	0.260095i	−0.411274	−	0.911512i	$-0.634916\pi$
$733$	9.40676	−	7.04181i	0.347447	−	0.260095i	0.758720	+	0.651417i	$0.225825\pi$
$734$	9.61134	+	4.62241i	0.354761	+	0.170616i
$735$	−5.43352	−	26.1432i	−0.200418	−	0.964306i
$736$	1.22892	−	27.1015i	0.0452988	−	0.998973i
$737$	−22.6854	+	22.6854i	−0.835626	+	0.835626i
$738$	13.0030	+	37.0985i	0.478649	+	1.36562i
$739$	5.94612	−	41.3561i	0.218731	−	1.52131i	−0.523998	−	0.851719i	$-0.675560\pi$
$739$	5.94612	−	41.3561i	0.218731	−	1.52131i	0.742730	−	0.669591i	$-0.233531\pi$
$740$	−15.5676	+	18.7994i	−0.572276	+	0.691079i
$741$	2.34506	−	0.688570i	0.0861478	−	0.0252953i
$742$	−91.9662	+	18.0993i	−3.37618	+	0.664447i
$743$	−1.23388	−	0.0882487i	−0.0452666	−	0.00323753i	0.0486875	−	0.998814i	$-0.484496\pi$
$743$	−1.23388	−	0.0882487i	−0.0452666	−	0.00323753i	−0.0939541	+	0.995577i	$0.529951\pi$
$744$	−0.988440	−	4.29964i	−0.0362380	−	0.157633i
$745$	25.6318	−	21.7970i	0.939078	−	0.798579i
$746$	−5.98726	−	0.982682i	−0.219209	−	0.0359785i
$747$	29.3595	−	6.38677i	1.07421	−	0.233680i
$748$	−10.4751	+	40.3569i	−0.383007	+	1.47560i
$749$	−13.6856	+	15.7940i	−0.500061	+	0.577101i
$750$	−0.902067	−	9.45874i	−0.0329388	−	0.345384i
$751$	−4.04170	+	0.581108i	−0.147484	+	0.0212049i	−0.215661	−	0.976468i	$-0.569191\pi$
$751$	−4.04170	+	0.581108i	−0.147484	+	0.0212049i	0.0681776	+	0.997673i	$0.478282\pi$
$752$	−9.16957	−	14.5260i	−0.334380	−	0.529708i
$753$	−7.71172	−	2.87632i	−0.281031	−	0.104819i
$754$	20.2281	−	22.4277i	0.736664	−	0.816769i
$755$	2.62012	−	1.64970i	0.0953560	−	0.0600386i
$756$	−28.7762	−	20.1532i	−1.04658	−	0.732965i
$757$	−6.92324	+	31.8256i	−0.251629	+	1.15672i	0.661786	+	0.749693i	$0.269799\pi$
$757$	−6.92324	+	31.8256i	−0.251629	+	1.15672i	−0.913415	+	0.407029i	$0.866565\pi$
$758$	−7.62768	+	31.9887i	−0.277050	+	1.16188i
$759$	1.03762	−	11.6648i	0.0376633	−	0.423405i
$760$	8.53064	−	2.52785i	0.309439	−	0.0916948i
$761$	8.74987	−	5.62320i	0.317182	−	0.203841i	−0.372356	−	0.928090i	$-0.621450\pi$
$761$	8.74987	−	5.62320i	0.317182	−	0.203841i	0.689538	+	0.724249i	$0.257814\pi$
$762$	−5.80040	−	2.29578i	−0.210126	−	0.0831674i
$763$	11.8233	+	31.6994i	0.428031	+	1.14760i
$764$	5.65861	−	30.6513i	0.204721	−	1.10892i
$765$	17.9162	+	24.4020i	0.647762	+	0.882258i
$766$	−28.5995	−	9.01882i	−1.03334	−	0.325863i
$767$	−9.42857	−	7.05814i	−0.340446	−	0.254855i
$768$	1.89106	+	9.42721i	0.0682378	+	0.340175i
$769$	14.8900	−	17.1840i	0.536948	−	0.619671i	−0.420844	−	0.907133i	$-0.638266\pi$
$769$	14.8900	−	17.1840i	0.536948	−	0.619671i	0.957792	+	0.287462i	$0.0928114\pi$
$770$	37.6305	−	54.9622i	1.35611	−	1.98070i
$771$	−0.802392	+	1.24855i	−0.0288974	+	0.0449653i
$772$	33.5248	+	14.0461i	1.20659	+	0.505530i
$773$	10.0392	+	18.3854i	0.361084	+	0.661276i	0.993560	−	0.113304i	$-0.0361434\pi$
$773$	10.0392	+	18.3854i	0.361084	+	0.661276i	−0.632477	+	0.774579i	$0.717962\pi$
$774$	5.60416	+	6.73346i	0.201437	+	0.242029i
$775$	5.60946	−	11.7032i	0.201498	−	0.420391i
$776$	−19.3112	+	10.8415i	−0.693230	+	0.389188i
$777$	8.14814	−	14.9222i	0.292313	−	0.535331i
$778$	4.48135	+	3.49582i	0.160664	+	0.125331i
$779$	14.6679	+	2.10893i	0.525533	+	0.0755602i
$780$	−3.57016	+	6.90077i	−0.127832	+	0.247087i
$781$	−21.7371			−0.777815
$782$	6.22947	−	34.2339i	0.222765	−	1.22420i
$783$	−17.7002	−	17.7002i	−0.632553	−	0.632553i
$784$	−28.3808	+	74.2459i	−1.01360	+	2.65164i
$785$	1.45817	+	23.4433i	0.0520444	+	0.836727i
$786$	7.25610	−	0.896446i	0.258817	−	0.0319752i
$787$	2.20113	−	4.03107i	0.0784618	−	0.143692i	−0.835502	−	0.549487i	$-0.814823\pi$
$787$	2.20113	−	4.03107i	0.0784618	−	0.143692i	0.913964	+	0.405795i	$0.133005\pi$
$788$	−34.6696	+	32.0169i	−1.23505	+	1.14055i
$789$	9.88854	−	8.56847i	0.352041	−	0.305046i
$790$	21.3527	−	26.8548i	0.759696	−	0.955451i
$791$	41.5748	+	12.2075i	1.47823	+	0.434048i
$792$	−4.66911	−	29.9675i	−0.165909	−	1.06485i
$793$	30.6927	−	6.67678i	1.08993	−	0.237099i
$794$	−0.136527	+	6.86706i	−0.00484516	+	0.243703i
$795$	16.5287	−	4.68711i	0.586214	−	0.166235i
$796$	8.00528	+	7.51405i	0.283740	+	0.266328i
$797$	−10.8111	−	8.09310i	−0.382950	−	0.286672i	0.390409	−	0.920642i	$-0.372334\pi$
$797$	−10.8111	−	8.09310i	−0.382950	−	0.286672i	−0.773358	+	0.633969i	$0.781425\pi$
$798$	−5.49739	+	2.86144i	−0.194605	+	0.101294i
$799$	−9.15265	−	20.0415i	−0.323797	−	0.709017i
$800$	−12.9343	+	25.1536i	−0.457297	+	0.889314i
$801$	−5.43155	−	2.48051i	−0.191914	−	0.0876443i
$802$	35.1043	+	13.8942i	1.23958	+	0.490620i
$803$	−16.6835	−	3.62928i	−0.588750	−	0.128075i
$804$	−4.28188	+	8.46809i	−0.151010	+	0.298646i
$805$	−27.9295	+	48.0640i	−0.984385	+	1.69403i
$806$	−9.03993	+	5.55886i	−0.318418	+	0.195802i
$807$	2.29099	−	10.5315i	0.0806467	−	0.370727i
$808$	5.67758	+	6.39862i	0.199737	+	0.225103i
$809$	−4.30966	−	1.96815i	−0.151519	−	0.0691966i	0.338212	−	0.941070i	$-0.390178\pi$
$809$	−4.30966	−	1.96815i	−0.151519	−	0.0691966i	−0.489731	+	0.871873i	$0.662905\pi$
$810$	−16.0537	−	9.38370i	−0.564071	−	0.329709i
$811$	36.4212	−	16.6330i	1.27892	−	0.584064i	0.344017	−	0.938963i	$-0.388212\pi$
$811$	36.4212	−	16.6330i	1.27892	−	0.584064i	0.934904	+	0.354899i	$0.115485\pi$
$812$	−39.3461	+	65.7053i	−1.38078	+	2.30581i
$813$	4.92836	+	3.68933i	0.172845	+	0.129390i
$814$	30.2634	−	8.23637i	1.06073	−	0.288684i
$815$	3.71434	−	6.65474i	0.130108	−	0.233105i
$816$	0.779916	+	12.3075i	0.0273025	+	0.430849i
$817$	3.22688	−	0.701964i	0.112894	−	0.0245586i
$818$	5.31149	+	7.39738i	0.185712	+	0.258643i
$819$	−11.1418	+	37.9454i	−0.389325	+	1.32592i
$820$	−37.0716	+	29.0673i	−1.29460	+	1.01507i
$821$	−40.5305	+	35.1199i	−1.41452	+	1.22569i	−0.476474	+	0.879188i	$0.658085\pi$
$821$	−40.5305	+	35.1199i	−1.41452	+	1.22569i	−0.938049	+	0.346503i	$0.887369\pi$
$822$	−0.865899	−	4.39980i	−0.0302017	−	0.153461i
$823$	−1.59187	−	0.869227i	−0.0554891	−	0.0302993i	0.451265	−	0.892390i	$-0.350973\pi$
$823$	−1.59187	−	0.869227i	−0.0554891	−	0.0302993i	−0.506754	+	0.862091i	$0.669155\pi$
$824$	9.77164	−	27.1707i	0.340411	−	0.946537i
$825$	−6.04921	+	10.6055i	−0.210607	+	0.369236i
$826$	26.9145	+	12.9441i	0.936476	+	0.450382i
$827$	−35.2248	+	35.2248i	−1.22489	+	1.22489i	−0.259014	+	0.965873i	$0.583398\pi$
$827$	−35.2248	+	35.2248i	−1.22489	+	1.22489i	−0.965873	+	0.259014i	$0.916602\pi$
$828$	5.73394	+	24.6532i	0.199268	+	0.856756i
$829$	−19.5813			−0.680085			−0.340043	−	0.940410i	$-0.610441\pi$
$829$	−19.5813			−0.680085			−0.340043	+	0.940410i	$0.610441\pi$
$830$	18.5747	+	30.8445i	0.644739	+	1.07063i
$831$	1.75775	−	12.2254i	0.0609757	−	0.424095i
$832$	20.0329	−	11.5587i	0.694515	−	0.400725i
$833$	−48.8584	+	89.4775i	−1.69284	+	3.10021i
$834$	6.63150	+	4.45052i	0.229630	+	0.154109i
$835$	−9.88102	−	7.54092i	−0.341947	−	0.260964i
$836$	−10.8330	−	3.65446i	−0.374667	−	0.126392i
$837$	4.21526	+	7.71967i	0.145701	+	0.266831i
$838$	−4.70096	−	6.54709i	−0.162392	−	0.226166i
$839$	−10.5972	−	6.81038i	−0.365855	−	0.235120i	0.344777	−	0.938685i	$-0.387954\pi$
$839$	−10.5972	−	6.81038i	−0.365855	−	0.235120i	−0.710632	+	0.703564i	$0.751591\pi$
$840$	5.50365	−	18.9174i	0.189894	−	0.652712i
$841$	−16.7438	+	19.3233i	−0.577371	+	0.666322i
$842$	−15.2842	−	8.74459i	−0.526727	−	0.301358i
$843$	−4.65897	+	6.22365i	−0.160463	+	0.214354i
$844$	−1.04468	+	0.262129i	−0.0359595	+	0.00902286i
$845$	−10.2598	−	1.57244i	−0.352947	−	0.0540937i
$846$	11.9012	+	10.7340i	0.409173	+	0.369043i
$847$	−26.7696	+	9.98453i	−0.919813	+	0.343072i
$848$	−48.9521	−	14.8062i	−1.68102	−	0.508447i
$849$	−2.85165	+	1.83264i	−0.0978683	+	0.0628961i
$850$	−20.7714	+	29.7422i	−0.712451	+	1.02015i
$851$	−24.6794	+	8.72112i	−0.846000	+	0.298956i
$852$	−6.10851	+	2.00561i	−0.209274	+	0.0687112i
$853$	3.25257	−	14.9518i	0.111366	−	0.511940i	−0.887342	−	0.461113i	$-0.847450\pi$
$853$	3.25257	−	14.9518i	0.111366	−	0.511940i	0.998707	−	0.0508278i	$-0.0161860\pi$
$854$	−73.0947	+	31.6407i	−2.50125	+	1.08272i
$855$	−7.02461	+	4.42287i	−0.240236	+	0.151259i
$856$	−10.6363	+	4.11030i	−0.363542	+	0.140487i
$857$	30.3221	+	11.3095i	1.03578	+	0.386327i	0.809118	−	0.587646i	$-0.199945\pi$
$857$	30.3221	+	11.3095i	1.03578	+	0.386327i	0.226664	+	0.973973i	$0.427218\pi$
$858$	8.85590	−	4.60958i	0.302335	−	0.157368i
$859$	−1.55166	−	10.7920i	−0.0529418	−	0.368219i	−0.999019	−	0.0442779i	$-0.985901\pi$
$859$	−1.55166	−	10.7920i	−0.0529418	−	0.368219i	0.946077	−	0.323941i	$-0.105008\pi$
$860$	−5.47679	+	8.95625i	−0.186757	+	0.305405i
$861$	21.4886	−	24.7991i	0.732328	−	0.845151i
$862$	−33.5041	+	32.1979i	−1.14115	+	1.09666i
$863$	6.74794	+	31.0198i	0.229703	+	1.05593i	0.937087	+	0.349097i	$0.113512\pi$
$863$	6.74794	+	31.0198i	0.229703	+	1.05593i	−0.707384	+	0.706829i	$0.750125\pi$
$864$	−8.71215	−	17.0747i	−0.296393	−	0.580892i
$865$	2.01624	+	0.163024i	0.0685542	+	0.00554297i
$866$	24.5876	+	29.5423i	0.835521	+	1.00389i
$867$	−0.399594	+	5.58706i	−0.0135709	+	0.189746i
$868$	19.7696	−	18.2570i	0.671024	−	0.619682i
$869$	−42.3007	+	12.4206i	−1.43495	+	0.421340i
$870$	6.20133	−	12.5938i	0.210245	−	0.426971i
$871$	22.5931	+	3.24840i	0.765539	+	0.110068i
$872$	−2.41203	+	18.3019i	−0.0816817	+	0.619780i
$873$	14.6103	−	14.6103i	0.494485	−	0.494485i
$874$	9.24136	+	2.37348i	0.312594	+	0.0802840i
$875$	47.3451	−	33.4269i	1.60056	−	1.13003i
$876$	−5.02323	+	0.519444i	−0.169719	+	0.0175504i
$877$	22.2124	−	16.6280i	0.750059	−	0.561487i	−0.154420	−	0.988005i	$-0.549351\pi$
$877$	22.2124	−	16.6280i	0.750059	−	0.561487i	0.904479	+	0.426518i	$0.140260\pi$
$878$	−11.4645	−	8.94326i	−0.386909	−	0.301821i
$879$	−13.0668	+	3.83676i	−0.440732	+	0.129411i
$880$	32.1971	−	16.8606i	1.08536	−	0.568371i
$881$	−4.86505	+	4.21559i	−0.163908	+	0.142027i	−0.732953	−	0.680279i	$-0.761858\pi$
$881$	−4.86505	+	4.21559i	−0.163908	+	0.142027i	0.569045	+	0.822306i	$0.307313\pi$
$882$	6.75969	−	73.8498i	0.227611	−	2.48665i
$883$	−33.1270	+	18.0887i	−1.11481	+	0.608734i	−0.927596	−	0.373584i	$-0.878129\pi$
$883$	−33.1270	+	18.0887i	−1.11481	+	0.608734i	−0.187217	+	0.982319i	$0.559947\pi$
$884$	27.4521	−	11.2408i	0.923315	−	0.378068i
$885$	−5.11110	−	1.96056i	−0.171808	−	0.0659035i
$886$	6.39159	+	0.127074i	0.214730	+	0.00426913i
$887$	−2.54461	−	35.5782i	−0.0854395	−	1.19460i	−0.841559	−	0.540166i	$-0.818361\pi$
$887$	−2.54461	−	35.5782i	−0.0854395	−	1.19460i	0.756119	−	0.654434i	$-0.227093\pi$
$888$	7.74460	−	5.10687i	0.259892	−	0.171375i
$889$	−5.41515	−	37.6632i	−0.181618	−	1.26318i
$890$	0.718334	−	7.11934i	0.0240786	−	0.238641i
$891$	9.92601	+	21.7349i	0.332534	+	0.728148i
$892$	−16.3775	−	23.7936i	−0.548360	−	0.796670i
$893$	5.66054	−	2.11127i	0.189423	−	0.0706510i
$894$	−11.7357	+	5.08005i	−0.392499	+	0.169902i
$895$	−3.81620	−	0.0354151i	−0.127562	−	0.00118380i
$896$	−44.1824	+	38.5674i	−1.47603	+	1.28845i
$897$	−7.08626	+	4.38253i	−0.236603	+	0.146328i
$898$	−1.98933	+	8.34278i	−0.0663849	+	0.278402i
$899$	16.1302	−	10.3662i	0.537971	−	0.345733i
$900$	5.27152	−	25.8568i	0.175717	−	0.861895i
$901$	−59.6674	−	27.2492i	−1.98781	−	0.907802i
$902$	60.4529	−	3.11736i	2.01286	−	0.103797i
$903$	2.55547	−	6.85149i	0.0850409	−	0.228003i
$904$	16.9131	+	16.5198i	0.562521	+	0.549440i
$905$	13.1501	−	28.1016i	0.437124	−	0.934128i
$906$	−1.13547	+	0.309024i	−0.0377233	+	0.0102666i
$907$	1.36379	+	19.0683i	0.0452840	+	0.633152i	0.968523	+	0.248925i	$0.0800774\pi$
$907$	1.36379	+	19.0683i	0.0452840	+	0.633152i	−0.923239	+	0.384227i	$0.874468\pi$
$908$	−35.6292	−	9.24797i	−1.18240	−	0.306905i
$909$	−6.71411	−	4.31490i	−0.222693	−	0.143116i
$910$	−47.3490	+	2.00127i	−1.56961	+	0.0663413i
$911$	3.12607	−	10.6464i	0.103571	−	0.352731i	−0.891359	−	0.453298i	$-0.850247\pi$
$911$	3.12607	−	10.6464i	0.103571	−	0.352731i	0.994930	+	0.100567i	$0.0320656\pi$
$912$	−3.38145	−	0.0274423i	−0.111971	−	0.000908707i
$913$	3.30060	−	46.1485i	0.109234	−	1.52729i
$914$	7.75155	−	11.5502i	0.256399	−	0.382047i
$915$	12.8780	−	6.87754i	0.425733	−	0.227365i
$916$	−14.7060	−	18.4013i	−0.485899	−	0.607997i
$917$	26.7252	+	35.7007i	0.882544	+	1.17894i
$918$	−8.13233	−	23.2021i	−0.268407	−	0.765783i
$919$	40.4730			1.33508			0.667540	−	0.744574i	$-0.267347\pi$
$919$	40.4730			1.33508			0.667540	+	0.744574i	$0.267347\pi$
$920$	−25.7570	+	16.0181i	−0.849182	+	0.528100i
$921$	4.15207			0.136815
$922$	16.7362	+	47.7496i	0.551179	+	1.57255i
$923$	9.26806	+	12.3807i	0.305062	+	0.407515i
$924$	−19.7766	+	15.8050i	−0.650601	+	0.519948i
$925$	27.1790	+	2.45163i	0.893640	+	0.0806092i
$926$	4.39328	−	6.54622i	0.144372	−	0.215122i
$927$	−1.92183	+	26.8707i	−0.0631212	+	0.882550i
$928$	−35.7724	+	21.5992i	−1.17429	+	0.709027i
$929$	5.58865	−	19.0332i	0.183358	−	0.624459i	−0.815592	−	0.578628i	$-0.803588\pi$
$929$	5.58865	−	19.0332i	0.183358	−	0.624459i	0.998949	−	0.0458308i	$-0.0145935\pi$
$930$	−3.33743	+	3.63201i	−0.109439	+	0.119098i
$931$	−23.5170	−	15.1135i	−0.770739	−	0.495324i
$932$	−14.9161	+	57.4665i	−0.488592	+	1.88238i
$933$	0.431458	+	6.03257i	0.0141253	+	0.197497i
$934$	−35.5401	+	9.67247i	−1.16291	+	0.316493i
$935$	43.8257	−	15.8845i	1.43325	−	0.519477i
$936$	−15.0776	+	15.4366i	−0.492828	+	0.504561i
$937$	−8.26943	+	22.1712i	−0.270150	+	0.724301i	0.729055	+	0.684455i	$0.239960\pi$
$937$	−8.26943	+	22.1712i	−0.270150	+	0.724301i	−0.999206	+	0.0398467i	$0.987313\pi$
$938$	−57.8028	+	2.98070i	−1.88733	+	0.0973232i
$939$	−17.1469	−	7.83075i	−0.559569	−	0.255547i
$940$	−7.58567	+	17.6441i	−0.247417	+	0.575486i
$941$	−3.01233	+	1.93590i	−0.0981990	+	0.0631087i	−0.588819	−	0.808265i	$-0.700407\pi$
$941$	−3.01233	+	1.93590i	−0.0981990	+	0.0631087i	0.490620	+	0.871374i	$0.336770\pi$
$942$	2.07064	−	8.68377i	0.0674651	−	0.282933i
$943$	−50.1210	+	6.32238i	−1.63217	+	0.205885i
$944$	9.65935	+	13.1241i	0.314385	+	0.427152i
$945$	−0.364494	+	39.2765i	−0.0118570	+	1.27766i
$946$	12.3797	−	5.35884i	0.402499	−	0.174231i
$947$	2.04099	−	0.761248i	0.0663231	−	0.0247372i	−0.316084	−	0.948731i	$-0.602368\pi$
$947$	2.04099	−	0.761248i	0.0663231	−	0.0247372i	0.382407	+	0.923994i	$0.375095\pi$
$948$	−10.7412	+	7.39335i	−0.348859	+	0.240125i
$949$	5.04626	+	11.0498i	0.163809	+	0.358691i
$950$	−7.72839	−	6.26292i	−0.250742	−	0.203196i
$951$	−1.02401	−	7.12211i	−0.0332057	−	0.230950i
$952$	−62.7974	+	41.4093i	−2.03528	+	1.34208i
$953$	−0.689204	−	9.63634i	−0.0223255	−	0.312152i	−0.996328	−	0.0856153i	$-0.972714\pi$
$953$	−0.689204	−	9.63634i	−0.0223255	−	0.312152i	0.974003	−	0.226536i	$-0.0727402\pi$
$954$	47.7055	+	0.948452i	1.54452	+	0.0307073i
$955$	−31.8320	+	14.1817i	−1.03006	+	0.458909i
$956$	18.0190	+	44.0060i	0.582777	+	1.42325i
$957$	−15.8318	+	8.64483i	−0.511770	+	0.279448i
$958$	3.75258	−	40.9970i	0.121240	−	1.32455i
$959$	20.6711	−	17.9116i	0.667504	−	0.578395i
$960$	7.49227	−	7.70885i	0.241812	−	0.248802i
$961$	23.2800	−	6.83561i	0.750966	−	0.220504i
$962$	−17.5945	−	13.7252i	−0.567271	−	0.442518i
$963$	8.51672	−	6.37553i	0.274447	−	0.205449i
$964$	−2.52201	−	24.3888i	−0.0812284	−	0.785511i
$965$	−8.26952	−	39.7885i	−0.266205	−	1.28084i
$966$	15.4848	−	14.3736i	0.498217	−	0.462464i
$967$	8.01200	−	8.01200i	0.257648	−	0.257648i	−0.566449	−	0.824097i	$-0.691683\pi$
$967$	8.01200	−	8.01200i	0.257648	−	0.257648i	0.824097	+	0.566449i	$0.191683\pi$
$968$	−15.4556	−	2.03692i	−0.496762	−	0.0654689i
$969$	−4.29304	−	0.617246i	−0.137912	−	0.0198288i
$970$	22.2133	+	10.9381i	0.713227	+	0.351201i
$971$	41.8493	−	12.2881i	1.34301	−	0.394342i	0.470266	−	0.882525i	$-0.344158\pi$
$971$	41.8493	−	12.2881i	1.34301	−	0.394342i	0.872742	+	0.488182i	$0.162340\pi$
$972$	18.5887	+	20.1288i	0.596232	+	0.645631i
$973$	−3.47523	+	48.5901i	−0.111411	+	1.55773i
$974$	24.2023	+	29.0793i	0.775491	+	0.931760i
$975$	8.61972	−	1.07646i	0.276052	−	0.0344742i
$976$	−43.3218	−	3.45202i	−1.38670	−	0.110496i
$977$	−4.52677	−	20.8092i	−0.144824	−	0.665746i	−0.991113	−	0.133022i	$-0.957532\pi$
$977$	−4.52677	−	20.8092i	−0.144824	−	0.665746i	0.846289	−	0.532724i	$-0.178832\pi$
$978$	−2.08847	+	2.00705i	−0.0667820	+	0.0641783i
$979$	−6.02120	+	6.94884i	−0.192439	+	0.222086i
$980$	86.3924	−	20.8271i	2.75970	−	0.665297i
$981$	−2.45109	−	17.0477i	−0.0782572	−	0.544291i
$982$	1.96048	−	1.02045i	0.0625615	−	0.0325638i
$983$	−28.9055	−	10.7812i	−0.921941	−	0.343866i	−0.156727	−	0.987642i	$-0.550094\pi$
$983$	−28.9055	−	10.7812i	−0.921941	−	0.343866i	−0.765214	+	0.643776i	$0.777367\pi$
$984$	16.7007	−	6.45383i	0.532399	−	0.205741i
$985$	51.4499	+	11.6933i	1.63933	+	0.372580i
$986$	−49.1861	+	21.2913i	−1.56640	+	0.678054i
$987$	2.84368	−	13.0722i	0.0905152	−	0.416092i
$988$	2.53742	+	7.72825i	0.0807261	+	0.245868i
$989$	−9.97281	+	5.22341i	−0.317117	+	0.166095i
$990$	−24.6661	+	23.2680i	−0.783939	+	0.739505i
$991$	34.6305	−	22.2557i	1.10007	−	0.706975i	0.140966	−	0.990014i	$-0.454979\pi$
$991$	34.6305	−	22.2557i	1.10007	−	0.706975i	0.959108	+	0.283039i	$0.0913427\pi$
$992$	14.1985	−	3.74073i	0.450804	−	0.118768i
$993$	−3.66710	+	1.36776i	−0.116372	+	0.0434044i
$994$	−29.1214	−	26.2653i	−0.923674	−	0.833083i
$995$	1.85963	−	12.1336i	0.0589542	−	0.384660i
$996$	−3.33044	−	13.2731i	−0.105529	−	0.420573i
$997$	−1.41022	+	1.88383i	−0.0446620	+	0.0596615i	−0.822316	−	0.569031i	$-0.807319\pi$
$997$	−1.41022	+	1.88383i	−0.0446620	+	0.0596615i	0.777654	+	0.628692i	$0.216409\pi$
$998$	−29.8447	−	17.0751i	−0.944716	−	0.540504i
$999$	−12.1114	+	13.9773i	−0.383188	+	0.442222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bo.a.333.16	✓	2800
5.2	odd	4	inner	920.2.bo.a.517.56	yes	2800
8.5	even	2	inner	920.2.bo.a.333.105	yes	2800
23.21	odd	22	inner	920.2.bo.a.573.36	yes	2800
40.37	odd	4	inner	920.2.bo.a.517.36	yes	2800
115.67	even	44	inner	920.2.bo.a.757.105	yes	2800
184.21	odd	22	inner	920.2.bo.a.573.56	yes	2800
920.757	even	44	inner	920.2.bo.a.757.16	yes	2800

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bo.a.333.16	✓	2800	1.1	even	1	trivial
920.2.bo.a.333.105	yes	2800	8.5	even	2	inner
920.2.bo.a.517.36	yes	2800	40.37	odd	4	inner
920.2.bo.a.517.56	yes	2800	5.2	odd	4	inner
920.2.bo.a.573.36	yes	2800	23.21	odd	22	inner
920.2.bo.a.573.56	yes	2800	184.21	odd	22	inner
920.2.bo.a.757.16	yes	2800	920.757	even	44	inner
920.2.bo.a.757.105	yes	2800	115.67	even	44	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bo (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33461 + 0.467781i) q^{2} +(-0.360129 - 0.481075i) q^{3} +(1.56236 - 1.24861i) q^{4} +(-2.13955 - 0.649856i) q^{5} +(0.705669 + 0.473586i) q^{6} +(-0.369805 + 5.17055i) q^{7} +(-1.50107 + 2.39725i) q^{8} +(0.743457 - 2.53198i) q^{9} +O(q^{10})\)	\(q+(-1.33461 + 0.467781i) q^{2} +(-0.360129 - 0.481075i) q^{3} +(1.56236 - 1.24861i) q^{4} +(-2.13955 - 0.649856i) q^{5} +(0.705669 + 0.473586i) q^{6} +(-0.369805 + 5.17055i) q^{7} +(-1.50107 + 2.39725i) q^{8} +(0.743457 - 2.53198i) q^{9} +(3.15946 - 0.133538i) q^{10} +(-3.41839 - 2.19687i) q^{11} +(-1.16333 - 0.301955i) q^{12} +(0.206244 + 2.88367i) q^{13} +(-1.92514 - 7.07365i) q^{14} +(0.457885 + 1.26332i) q^{15} +(0.881952 - 3.90156i) q^{16} +(1.79289 - 4.80692i) q^{17} +(0.192188 + 3.72698i) q^{18} +(1.27966 + 0.584400i) q^{19} +(-4.15417 + 1.65615i) q^{20} +(2.62060 - 1.68416i) q^{21} +(5.58987 + 1.33290i) q^{22} +(-4.73448 - 0.764630i) q^{23} +(1.69383 - 0.141190i) q^{24} +(4.15538 + 2.78080i) q^{25} +(-1.62418 - 3.75210i) q^{26} +(-3.17496 + 1.18420i) q^{27} +(5.87822 + 8.54001i) q^{28} +(3.06869 + 6.71949i) q^{29} +(-1.20205 - 1.47185i) q^{30} +(-0.369395 - 2.56920i) q^{31} +(0.648012 + 5.61962i) q^{32} +(0.174202 + 2.43566i) q^{33} +(-0.144221 + 7.25404i) q^{34} +(4.15133 - 10.8223i) q^{35} +(-1.99990 - 4.88416i) q^{36} +(4.79026 - 2.61568i) q^{37} +(-1.98121 - 0.181346i) q^{38} +(1.31299 - 1.13771i) q^{39} +(4.76948 - 4.15356i) q^{40} +(10.1071 - 2.96771i) q^{41} +(-2.70966 + 3.47356i) q^{42} +(1.87922 - 1.40677i) q^{43} +(-8.08380 + 0.835932i) q^{44} +(-3.23609 + 4.93417i) q^{45} +(6.67636 - 1.19422i) q^{46} +(3.03668 - 3.03668i) q^{47} +(-2.19456 + 0.980777i) q^{48} +(-19.6691 - 2.82799i) q^{49} +(-6.84661 - 1.76748i) q^{50} +(-2.95816 + 0.868596i) q^{51} +(3.92281 + 4.24782i) q^{52} +(0.912112 - 12.7530i) q^{53} +(3.68338 - 3.06563i) q^{54} +(5.88618 + 6.92178i) q^{55} +(-11.8400 - 8.64786i) q^{56} +(-0.179701 - 0.826071i) q^{57} +(-7.23875 - 7.53242i) q^{58} +(-2.66782 + 3.07883i) q^{59} +(2.29277 + 1.40204i) q^{60} +(-1.54622 - 10.7542i) q^{61} +(1.69482 + 3.25608i) q^{62} +(12.8168 + 4.78042i) q^{63} +(-3.49359 - 7.19686i) q^{64} +(1.43270 - 6.30380i) q^{65} +(-1.37185 - 3.16916i) q^{66} +(1.67825 - 7.71481i) q^{67} +(-3.20082 - 9.74878i) q^{68} +(1.33718 + 2.55301i) q^{69} +(-0.477916 + 16.3855i) q^{70} +(4.50022 - 2.89212i) q^{71} +(4.95381 + 5.58292i) q^{72} +(3.93686 - 1.46837i) q^{73} +(-5.16956 + 5.73170i) q^{74} +(-0.158694 - 3.00050i) q^{75} +(2.72897 - 0.684747i) q^{76} +(12.6232 - 16.8626i) q^{77} +(-1.22013 + 2.13259i) q^{78} +(7.10492 - 8.19952i) q^{79} +(-4.42243 + 7.77445i) q^{80} +(-4.94680 - 3.17912i) q^{81} +(-12.1008 + 8.68863i) q^{82} +(5.45672 + 9.99323i) q^{83} +(1.99147 - 5.90337i) q^{84} +(-6.95979 + 9.11955i) q^{85} +(-1.84997 + 2.75655i) q^{86} +(2.12746 - 3.89615i) q^{87} +(10.3977 - 4.89709i) q^{88} +(0.322025 - 2.23973i) q^{89} +(2.01080 - 8.09896i) q^{90} -14.9864 q^{91} +(-8.35170 + 4.71689i) q^{92} +(-1.10295 + 1.10295i) q^{93} +(-2.63228 + 5.47327i) q^{94} +(-2.35812 - 2.08195i) q^{95} +(2.47009 - 2.33553i) q^{96} +(6.87214 + 3.75247i) q^{97} +(27.5734 - 5.42656i) q^{98} +(-8.10385 + 7.02203i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2800 q - 18 q^{2} - 28 q^{6} - 44 q^{7} - 18 q^{8}+O(q^{10}) \) 2800 * q - 18 * q^2 - 28 * q^6 - 44 * q^7 - 18 * q^8	\( 2800 q - 18 q^{2} - 28 q^{6} - 44 q^{7} - 18 q^{8} - 22 q^{10} - 6 q^{12} - 44 q^{15} - 44 q^{16} - 44 q^{17} - 38 q^{18} - 22 q^{20} - 40 q^{23} - 36 q^{25} - 36 q^{26} - 22 q^{28} - 22 q^{30} - 104 q^{31} - 38 q^{32} - 44 q^{33} - 36 q^{36} - 22 q^{38} - 22 q^{40} - 72 q^{41} + 198 q^{42} - 28 q^{46} - 80 q^{47} - 10 q^{48} - 2 q^{50} - 146 q^{52} + 4 q^{55} - 44 q^{56} - 44 q^{57} - 42 q^{58} - 22 q^{60} + 46 q^{62} - 44 q^{63} - 44 q^{65} - 44 q^{66} - 64 q^{70} - 72 q^{71} - 104 q^{72} - 36 q^{73} - 44 q^{76} - 114 q^{78} - 220 q^{80} + 176 q^{81} - 10 q^{82} - 44 q^{86} - 12 q^{87} - 22 q^{88} - 440 q^{90} - 2 q^{92} - 76 q^{95} - 124 q^{96} - 44 q^{97} + 30 q^{98}+O(q^{100}) \) 2800 * q - 18 * q^2 - 28 * q^6 - 44 * q^7 - 18 * q^8 - 22 * q^10 - 6 * q^12 - 44 * q^15 - 44 * q^16 - 44 * q^17 - 38 * q^18 - 22 * q^20 - 40 * q^23 - 36 * q^25 - 36 * q^26 - 22 * q^28 - 22 * q^30 - 104 * q^31 - 38 * q^32 - 44 * q^33 - 36 * q^36 - 22 * q^38 - 22 * q^40 - 72 * q^41 + 198 * q^42 - 28 * q^46 - 80 * q^47 - 10 * q^48 - 2 * q^50 - 146 * q^52 + 4 * q^55 - 44 * q^56 - 44 * q^57 - 42 * q^58 - 22 * q^60 + 46 * q^62 - 44 * q^63 - 44 * q^65 - 44 * q^66 - 64 * q^70 - 72 * q^71 - 104 * q^72 - 36 * q^73 - 44 * q^76 - 114 * q^78 - 220 * q^80 + 176 * q^81 - 10 * q^82 - 44 * q^86 - 12 * q^87 - 22 * q^88 - 440 * q^90 - 2 * q^92 - 76 * q^95 - 124 * q^96 - 44 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

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