LMFDB - Embedded newform 930.2.bg.i.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			541.1
Character	$\chi$	$=$	930.541
Dual form			930.2.bg.i.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.540069 + 5.13841i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.540069 + 5.13841i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(0.669131 + 0.743145i) q^{10} +(-1.96701 + 0.875770i) q^{11} +(-0.978148 + 0.207912i) q^{12} +(-5.94445 - 1.26353i) q^{13} +(-4.72003 - 2.10149i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-5.35985 - 2.38636i) q^{17} +(0.978148 + 0.207912i) q^{18} +(-1.35896 + 0.288855i) q^{19} +(-0.913545 + 0.406737i) q^{20} +(3.45721 + 3.83962i) q^{21} +(-0.225067 - 2.14137i) q^{22} +(-0.725036 + 0.526770i) q^{23} +(0.104528 - 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(3.03863 - 5.26305i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(3.45721 - 3.83962i) q^{28} +(-0.410947 + 1.26476i) q^{29} +1.00000 q^{30} +(3.79321 + 4.07573i) q^{31} -1.00000 q^{32} +(-0.665363 + 2.04778i) q^{33} +(3.92585 - 4.36010i) q^{34} +(4.17996 + 3.03692i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.21179 - 3.83093i) q^{37} +(0.145223 - 1.38171i) q^{38} +(-4.91660 + 3.57212i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(7.43013 + 8.25200i) q^{41} +(-4.72003 + 2.10149i) q^{42} +(-3.44085 + 0.731376i) q^{43} +(2.10611 + 0.447667i) q^{44} +(-0.913545 - 0.406737i) q^{45} +(-0.276939 - 0.852331i) q^{46} +(-1.54690 - 4.76088i) q^{47} +(0.913545 + 0.406737i) q^{48} +(-19.2646 - 4.09481i) q^{49} +(0.978148 - 0.207912i) q^{50} +(-5.35985 + 2.38636i) q^{51} +(4.06647 + 4.51628i) q^{52} +(-0.922602 - 8.77797i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-0.225067 + 2.14137i) q^{55} +(2.58336 + 4.47451i) q^{56} +(-0.694658 + 1.20318i) q^{57} +(-1.07587 - 0.781668i) q^{58} +(-0.484470 + 0.538059i) q^{59} +(-0.309017 + 0.951057i) q^{60} -2.66579 q^{61} +(-5.04842 + 2.34809i) q^{62} +5.16672 q^{63} +(0.309017 - 0.951057i) q^{64} +(-4.06647 + 4.51628i) q^{65} +(-1.74194 - 1.26560i) q^{66} +(-7.33942 + 12.7123i) q^{67} +(2.93354 + 5.08105i) q^{68} +(-0.0936778 + 0.891284i) q^{69} +(-4.17996 + 3.03692i) q^{70} +(0.0601060 + 0.571870i) q^{71} +(-0.669131 - 0.743145i) q^{72} +(-8.43237 + 3.75433i) q^{73} +(4.32691 - 0.919714i) q^{74} +(-0.978148 - 0.207912i) q^{75} +(1.26920 + 0.565086i) q^{76} +(-3.43774 - 10.5803i) q^{77} +(-1.87797 - 5.77981i) q^{78} +(1.31508 + 0.585510i) q^{79} +(0.978148 + 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-10.1442 + 4.51647i) q^{82} +(9.27134 + 10.2969i) q^{83} +(-0.540069 - 5.13841i) q^{84} +(-4.74657 + 3.44859i) q^{85} +(0.367702 - 3.49845i) q^{86} +(0.664926 + 1.15169i) q^{87} +(-1.07658 + 1.86469i) q^{88} +(8.39785 + 6.10139i) q^{89} +(0.669131 - 0.743145i) q^{90} +(9.70296 - 29.8626i) q^{91} +0.896194 q^{92} +(5.56701 - 0.0917075i) q^{93} +5.00588 q^{94} +(-0.429322 + 1.32132i) q^{95} +(-0.669131 + 0.743145i) q^{96} +(2.37706 + 1.72703i) q^{97} +(9.84748 - 17.0563i) q^{98} +(1.07658 + 1.86469i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 13 * q^11 + 3 * q^12 + 11 * q^13 - 8 * q^14 + 6 * q^15 - 6 * q^16 - 29 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^20 - 2 * q^21 - 17 * q^22 - 5 * q^23 - 3 * q^24 - 12 * q^25 + 9 * q^26 - 6 * q^27 - 2 * q^28 + 13 * q^29 + 24 * q^30 + 57 * q^31 - 24 * q^32 + 16 * q^33 + 29 * q^34 + q^35 - 12 * q^36 - 24 * q^37 + 6 * q^38 - 17 * q^39 + 3 * q^40 + 32 * q^41 - 8 * q^42 + 49 * q^43 - 8 * q^44 - 3 * q^45 + 28 * q^47 + 3 * q^48 + 12 * q^49 - 3 * q^50 - 29 * q^51 - 19 * q^52 - 36 * q^53 + 6 * q^54 - 17 * q^55 - 3 * q^56 - 6 * q^57 + 2 * q^58 + 6 * q^60 + 33 * q^62 - 6 * q^63 - 6 * q^64 + 19 * q^65 + 4 * q^66 - 5 * q^67 + 11 * q^68 + 10 * q^69 - q^70 - 11 * q^71 - 3 * q^72 - 13 * q^73 + 9 * q^74 + 3 * q^75 - 6 * q^76 + 4 * q^77 - 8 * q^78 - 68 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 + 10 * q^83 - 7 * q^84 + 2 * q^85 - 34 * q^86 + 11 * q^87 - 12 * q^88 + 55 * q^89 + 3 * q^90 + 38 * q^91 + 10 * q^92 + 19 * q^93 + 42 * q^94 + 18 * q^95 - 3 * q^96 - q^97 + 63 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{15}\right)$

Coefficient data

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

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

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

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−0.540069	+	5.13841i	−0.204127	+	1.94214i	0.112643	+	0.993635i	$0.464068\pi$
$7$	−0.540069	+	5.13841i	−0.204127	+	1.94214i	−0.316770	+	0.948502i	$0.602598\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	0.669131	+	0.743145i	0.211598	+	0.235003i
$11$	−1.96701	+	0.875770i	−0.593076	+	0.264054i	−0.681250	−	0.732051i	$-0.738563\pi$
$11$	−1.96701	+	0.875770i	−0.593076	+	0.264054i	0.0881742	+	0.996105i	$0.471897\pi$
$12$	−0.978148	+	0.207912i	−0.282367	+	0.0600189i
$13$	−5.94445	−	1.26353i	−1.64869	−	0.350441i	−0.712431	−	0.701742i	$-0.752406\pi$
$13$	−5.94445	−	1.26353i	−1.64869	−	0.350441i	−0.936262	+	0.351301i	$0.885739\pi$
$14$	−4.72003	−	2.10149i	−1.26148	−	0.561648i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−5.35985	−	2.38636i	−1.29996	−	0.578777i	−0.364165	−	0.931335i	$-0.618646\pi$
$17$	−5.35985	−	2.38636i	−1.29996	−	0.578777i	−0.935790	+	0.352557i	$0.885312\pi$
$18$	0.978148	+	0.207912i	0.230552	+	0.0490053i
$19$	−1.35896	+	0.288855i	−0.311766	+	0.0662679i	−0.361137	−	0.932513i	$-0.617611\pi$
$19$	−1.35896	+	0.288855i	−0.311766	+	0.0662679i	0.0493716	+	0.998780i	$0.484278\pi$
$20$	−0.913545	+	0.406737i	−0.204275	+	0.0909491i
$21$	3.45721	+	3.83962i	0.754425	+	0.837874i
$22$	−0.225067	−	2.14137i	−0.0479844	−	0.456541i
$23$	−0.725036	+	0.526770i	−0.151180	+	0.109839i	−0.660804	−	0.750558i	$-0.729785\pi$
$23$	−0.725036	+	0.526770i	−0.151180	+	0.109839i	0.509624	+	0.860397i	$0.329785\pi$
$24$	0.104528	−	0.994522i	0.0213368	−	0.203006i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	3.03863	−	5.26305i	0.595924	−	1.03217i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	3.45721	−	3.83962i	0.653351	−	0.725620i
$29$	−0.410947	+	1.26476i	−0.0763109	+	0.234861i	−0.981934	−	0.189222i	$-0.939403\pi$
$29$	−0.410947	+	1.26476i	−0.0763109	+	0.234861i	0.905623	+	0.424083i	$0.139403\pi$
$30$	1.00000			0.182574
$31$	3.79321	+	4.07573i	0.681280	+	0.732023i
$31$	3.79321	+	4.07573i	0.681280	+	0.732023i
$32$	−1.00000			−0.176777
$33$	−0.665363	+	2.04778i	−0.115825	+	0.356472i
$34$	3.92585	−	4.36010i	0.673277	−	0.747750i
$35$	4.17996	+	3.03692i	0.706543	+	0.513333i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−2.21179	−	3.83093i	−0.363616	−	0.629801i	0.624937	−	0.780675i	$-0.285125\pi$
$37$	−2.21179	−	3.83093i	−0.363616	−	0.629801i	−0.988553	+	0.150874i	$0.951791\pi$
$38$	0.145223	−	1.38171i	0.0235583	−	0.224142i
$39$	−4.91660	+	3.57212i	−0.787286	+	0.571997i
$40$	−0.104528	−	0.994522i	−0.0165274	−	0.157248i
$41$	7.43013	+	8.25200i	1.16039	+	1.28875i	0.950396	+	0.311044i	$0.100679\pi$
$41$	7.43013	+	8.25200i	1.16039	+	1.28875i	0.209997	+	0.977702i	$0.432655\pi$
$42$	−4.72003	+	2.10149i	−0.728317	+	0.324267i
$43$	−3.44085	+	0.731376i	−0.524725	+	0.111534i	−0.462656	−	0.886538i	$-0.653103\pi$
$43$	−3.44085	+	0.731376i	−0.524725	+	0.111534i	−0.0620694	+	0.998072i	$0.519770\pi$
$44$	2.10611	+	0.447667i	0.317508	+	0.0674884i
$45$	−0.913545	−	0.406737i	−0.136183	−	0.0606327i
$46$	−0.276939	−	0.852331i	−0.0408324	−	0.125669i
$47$	−1.54690	−	4.76088i	−0.225639	−	0.694445i	−0.998226	−	0.0595366i	$-0.981038\pi$
$47$	−1.54690	−	4.76088i	−0.225639	−	0.694445i	0.772587	−	0.634909i	$-0.218962\pi$
$48$	0.913545	+	0.406737i	0.131859	+	0.0587074i
$49$	−19.2646	−	4.09481i	−2.75208	−	0.584973i
$50$	0.978148	−	0.207912i	0.138331	−	0.0294032i
$51$	−5.35985	+	2.38636i	−0.750529	+	0.334157i
$52$	4.06647	+	4.51628i	0.563919	+	0.626295i
$53$	−0.922602	−	8.77797i	−0.126729	−	1.20575i	−0.854324	−	0.519740i	$-0.826029\pi$
$53$	−0.922602	−	8.77797i	−0.126729	−	1.20575i	0.727595	−	0.686007i	$-0.240638\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	−0.225067	+	2.14137i	−0.0303480	+	0.288742i
$56$	2.58336	+	4.47451i	0.345216	+	0.597931i
$57$	−0.694658	+	1.20318i	−0.0920097	+	0.159365i
$58$	−1.07587	−	0.781668i	−0.141269	−	0.102638i
$59$	−0.484470	+	0.538059i	−0.0630727	+	0.0700493i	−0.773855	−	0.633362i	$-0.781674\pi$
$59$	−0.484470	+	0.538059i	−0.0630727	+	0.0700493i	0.710783	+	0.703412i	$0.248341\pi$
$60$	−0.309017	+	0.951057i	−0.0398939	+	0.122781i
$61$	−2.66579			−0.341319			−0.170659	−	0.985330i	$-0.554590\pi$
$61$	−2.66579			−0.341319			−0.170659	+	0.985330i	$0.554590\pi$
$62$	−5.04842	+	2.34809i	−0.641149	+	0.298207i
$63$	5.16672			0.650945
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−4.06647	+	4.51628i	−0.504384	+	0.560175i
$66$	−1.74194	−	1.26560i	−0.214418	−	0.155784i
$67$	−7.33942	+	12.7123i	−0.896653	+	1.55305i	−0.0649085	+	0.997891i	$0.520676\pi$
$67$	−7.33942	+	12.7123i	−0.896653	+	1.55305i	−0.831745	+	0.555158i	$0.812658\pi$
$68$	2.93354	+	5.08105i	0.355745	+	0.616168i
$69$	−0.0936778	+	0.891284i	−0.0112775	+	0.107298i
$70$	−4.17996	+	3.03692i	−0.499601	+	0.362981i
$71$	0.0601060	+	0.571870i	0.00713327	+	0.0678685i	0.997509	−	0.0705334i	$-0.0224701\pi$
$71$	0.0601060	+	0.571870i	0.00713327	+	0.0678685i	−0.990376	+	0.138402i	$0.955803\pi$
$72$	−0.669131	−	0.743145i	−0.0788578	−	0.0875805i
$73$	−8.43237	+	3.75433i	−0.986934	+	0.439411i	−0.835759	−	0.549096i	$-0.814972\pi$
$73$	−8.43237	+	3.75433i	−0.986934	+	0.439411i	−0.151174	+	0.988507i	$0.548306\pi$
$74$	4.32691	−	0.919714i	0.502994	−	0.106915i
$75$	−0.978148	−	0.207912i	−0.112947	−	0.0240076i
$76$	1.26920	+	0.565086i	0.145588	+	0.0648198i
$77$	−3.43774	−	10.5803i	−0.391767	−	1.20574i
$78$	−1.87797	−	5.77981i	−0.212639	−	0.654435i
$79$	1.31508	+	0.585510i	0.147958	+	0.0658751i	0.479380	−	0.877608i	$-0.340862\pi$
$79$	1.31508	+	0.585510i	0.147958	+	0.0658751i	−0.331422	+	0.943483i	$0.607528\pi$
$80$	0.978148	+	0.207912i	0.109360	+	0.0232452i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−10.1442	+	4.51647i	−1.12023	+	0.498761i
$83$	9.27134	+	10.2969i	1.01766	+	1.13023i	0.991439	+	0.130572i	$0.0416814\pi$
$83$	9.27134	+	10.2969i	1.01766	+	1.13023i	0.0262232	+	0.999656i	$0.491652\pi$
$84$	−0.540069	−	5.13841i	−0.0589264	−	0.560647i
$85$	−4.74657	+	3.44859i	−0.514838	+	0.374052i
$86$	0.367702	−	3.49845i	0.0396503	−	0.377248i
$87$	0.664926	+	1.15169i	0.0712876	+	0.123474i
$88$	−1.07658	+	1.86469i	−0.114764	+	0.198777i
$89$	8.39785	+	6.10139i	0.890170	+	0.646747i	0.935922	−	0.352206i	$-0.114568\pi$
$89$	8.39785	+	6.10139i	0.890170	+	0.646747i	−0.0457522	+	0.998953i	$0.514568\pi$
$90$	0.669131	−	0.743145i	0.0705326	−	0.0783343i
$91$	9.70296	−	29.8626i	1.01715	−	3.13046i
$92$	0.896194			0.0934347
$93$	5.56701	−	0.0917075i	0.577272	−	0.00950962i
$94$	5.00588			0.516317
$95$	−0.429322	+	1.32132i	−0.0440475	+	0.135564i
$96$	−0.669131	+	0.743145i	−0.0682929	+	0.0758469i
$97$	2.37706	+	1.72703i	0.241353	+	0.175353i	0.701886	−	0.712289i	$-0.252342\pi$
$97$	2.37706	+	1.72703i	0.241353	+	0.175353i	−0.460533	+	0.887643i	$0.652342\pi$
$98$	9.84748	−	17.0563i	0.994746	−	1.72295i
$99$	1.07658	+	1.86469i	0.108200	+	0.187409i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	0.429346	−	0.311938i	0.0427215	−	0.0310390i	−0.566220	−	0.824254i	$-0.691595\pi$
$101$	0.429346	−	0.311938i	0.0427215	−	0.0310390i	0.608941	+	0.793215i	$0.291595\pi$
$102$	−0.613278	−	5.83495i	−0.0607235	−	0.577746i
$103$	−9.72528	−	10.8010i	−0.958261	−	1.06426i	−0.997883	−	0.0650416i	$-0.979282\pi$
$103$	−9.72528	−	10.8010i	−0.958261	−	1.06426i	0.0396218	−	0.999215i	$-0.487385\pi$
$104$	−5.55185	+	2.47184i	−0.544403	+	0.242384i
$105$	5.05381	−	1.07422i	0.493202	−	0.104833i
$106$	8.63345	+	1.83510i	0.838555	+	0.178240i
$107$	10.7194	+	4.77259i	1.03628	+	0.461384i	0.853129	−	0.521700i	$-0.174702\pi$
$107$	10.7194	+	4.77259i	1.03628	+	0.461384i	0.183156	+	0.983084i	$0.441369\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	−0.224042	−	0.689530i	−0.0214593	−	0.0660450i	0.939753	−	0.341853i	$-0.111055\pi$
$109$	−0.224042	−	0.689530i	−0.0214593	−	0.0660450i	−0.961213	+	0.275808i	$0.911055\pi$
$110$	−1.96701	−	0.875770i	−0.187547	−	0.0835014i
$111$	−4.32691	−	0.919714i	−0.410693	−	0.0872954i
$112$	−5.05381	+	1.07422i	−0.477540	+	0.101504i
$113$	1.58018	−	0.703540i	0.148651	−	0.0661835i	−0.331063	−	0.943609i	$-0.607407\pi$
$113$	1.58018	−	0.703540i	0.148651	−	0.0661835i	0.479714	+	0.877425i	$0.340741\pi$
$114$	−0.929634	−	1.03246i	−0.0870682	−	0.0966990i
$115$	0.0936778	+	0.891284i	0.00873550	+	0.0831127i
$116$	1.07587	−	0.781668i	0.0998923	−	0.0725760i
$117$	−0.635246	+	6.04396i	−0.0587285	+	0.558764i
$118$	−0.362015	−	0.627028i	−0.0333262	−	0.0577226i
$119$	15.1568	−	26.2523i	1.38942	−	2.40655i
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	−4.25828	+	4.72930i	−0.387116	+	0.429936i
$122$	0.823773	−	2.53531i	0.0745809	−	0.229536i
$123$	11.1042			1.00123
$124$	−0.673116	−	5.52693i	−0.0604476	−	0.496333i
$125$	−1.00000			−0.0894427
$126$	−1.59660	+	4.91384i	−0.142237	+	0.437760i
$127$	−2.38046	+	2.64377i	−0.211232	+	0.234597i	−0.839445	−	0.543445i	$-0.817120\pi$
$127$	−2.38046	+	2.64377i	−0.211232	+	0.234597i	0.628213	+	0.778041i	$0.283786\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−1.75886	+	3.04644i	−0.154859	+	0.268224i
$130$	−3.03863	−	5.26305i	−0.266505	−	0.461600i
$131$	−0.133722	+	1.27228i	−0.0116833	+	0.111159i	−0.998809	−	0.0487854i	$-0.984465\pi$
$131$	−0.133722	+	1.27228i	−0.0116833	+	0.111159i	0.987126	+	0.159945i	$0.0511316\pi$
$132$	1.74194	−	1.26560i	0.151617	−	0.110156i
$133$	−0.750326	−	7.13888i	−0.0650616	−	0.619019i
$134$	−9.82207	−	10.9085i	−0.848497	−	0.942352i
$135$	−0.913545	+	0.406737i	−0.0786255	+	0.0350063i
$136$	−5.73888	+	1.21984i	−0.492105	+	0.104600i
$137$	11.8496	+	2.51871i	1.01238	+	0.215188i	0.684096	−	0.729392i	$-0.260197\pi$
$137$	11.8496	+	2.51871i	1.01238	+	0.215188i	0.328282	+	0.944580i	$0.393530\pi$
$138$	−0.818714	−	0.364515i	−0.0696935	−	0.0310296i
$139$	2.48376	+	7.64423i	0.210670	+	0.648375i	0.999433	+	0.0336774i	$0.0107219\pi$
$139$	2.48376	+	7.64423i	0.210670	+	0.648375i	−0.788763	+	0.614697i	$0.789278\pi$
$140$	−1.59660	−	4.91384i	−0.134938	−	0.415295i
$141$	−4.57310	−	2.03608i	−0.385125	−	0.171469i
$142$	−0.562455	−	0.119553i	−0.0472001	−	0.0100327i
$143$	12.7994	−	2.72059i	1.07034	−	0.227507i
$144$	0.913545	−	0.406737i	0.0761288	−	0.0338947i
$145$	0.889845	+	0.988273i	0.0738976	+	0.0820716i
$146$	−0.964837	−	9.17981i	−0.0798505	−	0.759726i
$147$	−15.9336	+	11.5764i	−1.31418	+	0.954806i
$148$	−0.462390	+	4.39935i	−0.0380082	+	0.361624i
$149$	7.38767	+	12.7958i	0.605221	+	1.04827i	0.992016	+	0.126108i	$0.0402487\pi$
$149$	7.38767	+	12.7958i	0.605221	+	1.04827i	−0.386795	+	0.922166i	$0.626418\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−7.69221	−	5.58872i	−0.625983	−	0.454803i	0.229023	−	0.973421i	$-0.426447\pi$
$151$	−7.69221	−	5.58872i	−0.625983	−	0.454803i	−0.855006	+	0.518618i	$0.826447\pi$
$152$	−0.929634	+	1.03246i	−0.0754033	+	0.0837438i
$153$	−1.81303	+	5.57993i	−0.146575	+	0.451111i
$154$	11.1248			0.896460
$155$	5.42629	−	1.24715i	0.435850	−	0.100173i
$156$	6.07725			0.486570
$157$	−3.02984	+	9.32490i	−0.241808	+	0.744208i	0.754337	+	0.656487i	$0.227958\pi$
$157$	−3.02984	+	9.32490i	−0.241808	+	0.744208i	−0.996145	+	0.0877208i	$0.972042\pi$
$158$	−0.963235	+	1.06978i	−0.0766309	+	0.0851072i
$159$	−7.14065	−	5.18798i	−0.566290	−	0.411434i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−2.31519	−	4.01003i	−0.182463	−	0.316034i
$162$	0.104528	−	0.994522i	0.00821253	−	0.0781370i
$163$	14.2533	−	10.3556i	1.11640	−	0.811115i	0.132744	−	0.991150i	$-0.457621\pi$
$163$	14.2533	−	10.3556i	1.11640	−	0.811115i	0.983660	+	0.180035i	$0.0576211\pi$
$164$	−1.16070	−	11.0433i	−0.0906355	−	0.862339i
$165$	1.44075	+	1.60011i	0.112162	+	0.124568i
$166$	−12.6579	+	5.63566i	−0.982444	+	0.437412i
$167$	−14.6000	+	3.10332i	−1.12978	+	0.240142i	−0.734626	−	0.678472i	$-0.762643\pi$
$167$	−14.6000	+	3.10332i	−1.12978	+	0.240142i	−0.395155	+	0.918614i	$0.629309\pi$
$168$	5.05381	+	1.07422i	0.389910	+	0.0828779i
$169$	21.8639	+	9.73442i	1.68184	+	0.748802i
$170$	−1.81303	−	5.57993i	−0.139053	−	0.427961i
$171$	0.429322	+	1.32132i	0.0328311	+	0.101044i
$172$	3.21360	+	1.43079i	0.245035	+	0.109096i
$173$	−21.9095	−	4.65701i	−1.66575	−	0.354066i	−0.723848	−	0.689960i	$-0.757628\pi$
$173$	−21.9095	−	4.65701i	−1.66575	−	0.354066i	−0.941900	+	0.335894i	$0.890962\pi$
$174$	−1.30079	+	0.276492i	−0.0986128	+	0.0209608i
$175$	4.72003	−	2.10149i	0.356801	−	0.158858i
$176$	−1.44075	−	1.60011i	−0.108600	−	0.120613i
$177$	0.0756817	+	0.720063i	0.00568859	+	0.0541233i
$178$	−8.39785	+	6.10139i	−0.629445	+	0.457319i
$179$	1.85134	−	17.6143i	0.138376	−	1.31656i	−0.676294	−	0.736632i	$-0.736415\pi$
$179$	1.85134	−	17.6143i	0.138376	−	1.31656i	0.814669	−	0.579926i	$-0.196918\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	12.0826	−	20.9277i	0.898093	−	1.55554i	0.0681627	−	0.997674i	$-0.478286\pi$
$181$	12.0826	−	20.9277i	0.898093	−	1.55554i	0.829930	−	0.557868i	$-0.188380\pi$
$182$	25.4027	+	18.4561i	1.88297	+	1.36806i
$183$	−1.78376	+	1.98106i	−0.131859	+	0.146444i
$184$	−0.276939	+	0.852331i	−0.0204162	+	0.0628347i
$185$	−4.42358			−0.325228
$186$	−1.63308	+	5.32288i	−0.119743	+	0.390292i
$187$	12.6328			0.923801
$188$	−1.54690	+	4.76088i	−0.112819	+	0.347223i
$189$	3.45721	−	3.83962i	0.251475	−	0.279291i
$190$	−1.12398	−	0.816619i	−0.0815421	−	0.0592438i
$191$	−3.59028	+	6.21855i	−0.259784	+	0.449959i	−0.966184	−	0.257854i	$-0.916985\pi$
$191$	−3.59028	+	6.21855i	−0.259784	+	0.449959i	0.706400	+	0.707813i	$0.250318\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−1.64560	+	15.6569i	−0.118453	+	1.12701i	0.760248	+	0.649633i	$0.225078\pi$
$193$	−1.64560	+	15.6569i	−0.118453	+	1.12701i	−0.878701	+	0.477373i	$0.841589\pi$
$194$	−2.37706	+	1.72703i	−0.170663	+	0.123994i
$195$	0.635246	+	6.04396i	0.0454909	+	0.432817i
$196$	13.1785	+	14.6362i	0.941322	+	1.04544i
$197$	6.90578	−	3.07465i	0.492016	−	0.219060i	−0.145703	−	0.989328i	$-0.546544\pi$
$197$	6.90578	−	3.07465i	0.492016	−	0.219060i	0.637720	+	0.770269i	$0.279878\pi$
$198$	−2.10611	+	0.447667i	−0.149675	+	0.0318143i
$199$	19.2006	+	4.08122i	1.36110	+	0.289310i	0.829888	−	0.557930i	$-0.188404\pi$
$199$	19.2006	+	4.08122i	1.36110	+	0.289310i	0.531210	+	0.847240i	$0.321738\pi$
$200$	−0.913545	−	0.406737i	−0.0645974	−	0.0287606i
$201$	4.53601	+	13.9604i	0.319946	+	0.984692i
$202$	0.163996	+	0.504727i	0.0115387	+	0.0355124i
$203$	−6.27695	−	2.79468i	−0.440555	−	0.196148i
$204$	5.73888	+	1.21984i	0.401802	+	0.0854056i
$205$	10.8615	−	2.30869i	0.758601	−	0.161246i
$206$	13.2777	−	5.91160i	0.925098	−	0.411880i
$207$	0.599671	+	0.666002i	0.0416800	+	0.0462903i
$208$	−0.635246	−	6.04396i	−0.0440464	−	0.419073i
$209$	2.42011	−	1.75831i	0.167403	−	0.121625i
$210$	−0.540069	+	5.13841i	−0.0372683	+	0.354584i
$211$	−10.5161	−	18.2144i	−0.723958	−	1.25393i	−0.959401	−	0.282045i	$-0.908987\pi$
$211$	−10.5161	−	18.2144i	−0.723958	−	1.25393i	0.235443	−	0.971888i	$-0.424346\pi$
$212$	−4.41316	+	7.64382i	−0.303097	+	0.524980i
$213$	0.465201	+	0.337988i	0.0318750	+	0.0231586i
$214$	−7.85148	+	8.71995i	−0.536716	+	0.596084i
$215$	−1.08704	+	3.34555i	−0.0741352	+	0.228165i
$216$	−1.00000			−0.0680414
$217$	−22.9914	+	17.2899i	−1.56076	+	1.17371i
$218$	0.725014			0.0491042
$219$	−2.85234	+	8.77861i	−0.192743	+	0.593203i
$220$	1.44075	−	1.60011i	0.0971351	−	0.107879i
$221$	28.8461	+	20.9579i	1.94040	+	1.40978i
$222$	2.21179	−	3.83093i	0.148446	−	0.257115i
$223$	11.4919	+	19.9046i	0.769556	+	1.33291i	0.937804	+	0.347166i	$0.112856\pi$
$223$	11.4919	+	19.9046i	0.769556	+	1.33291i	−0.168248	+	0.985745i	$0.553811\pi$
$224$	0.540069	−	5.13841i	0.0360849	−	0.343325i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	0.180805	+	1.72024i	0.0120270	+	0.114429i
$227$	−11.7272	−	13.0244i	−0.778363	−	0.864460i	0.215336	−	0.976540i	$-0.430915\pi$
$227$	−11.7272	−	13.0244i	−0.778363	−	0.864460i	−0.993699	+	0.112080i	$0.964249\pi$
$228$	1.26920	−	0.565086i	0.0840550	−	0.0374237i
$229$	−7.86894	+	1.67259i	−0.519994	+	0.110528i	−0.460429	−	0.887696i	$-0.652305\pi$
$229$	−7.86894	+	1.67259i	−0.519994	+	0.110528i	−0.0595646	+	0.998224i	$0.518971\pi$
$230$	−0.876610	−	0.186329i	−0.0578019	−	0.0122862i
$231$	−10.1630	−	4.52485i	−0.668676	−	0.297714i
$232$	0.410947	+	1.26476i	0.0269800	+	0.0830359i
$233$	6.43518	+	19.8055i	0.421583	+	1.29750i	0.906229	+	0.422788i	$0.138949\pi$
$233$	6.43518	+	19.8055i	0.421583	+	1.29750i	−0.484646	+	0.874711i	$0.661051\pi$
$234$	−5.55185	−	2.47184i	−0.362935	−	0.161589i
$235$	−4.89649	−	1.04078i	−0.319412	−	0.0678931i
$236$	0.708208	−	0.150534i	0.0461004	−	0.00979895i
$237$	1.31508	−	0.585510i	0.0854235	−	0.0380330i
$238$	20.2838	+	22.5274i	1.31480	+	1.46023i
$239$	−0.235516	−	2.24079i	−0.0152343	−	0.144944i	0.984261	−	0.176723i	$-0.0565496\pi$
$239$	−0.235516	−	2.24079i	−0.0152343	−	0.144944i	−0.999495	+	0.0317783i	$0.989883\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	−2.54591	+	24.2227i	−0.163997	+	1.56032i	0.534785	+	0.844988i	$0.320393\pi$
$241$	−2.54591	+	24.2227i	−0.163997	+	1.56032i	−0.698782	+	0.715335i	$0.746274\pi$
$242$	−3.18195	−	5.51130i	−0.204543	−	0.354280i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	2.15667	+	1.56691i	0.138066	+	0.100311i
$245$	−13.1785	+	14.6362i	−0.841944	+	0.935073i
$246$	−3.43137	+	10.5607i	−0.218776	+	0.673325i
$247$	8.44322			0.537229
$248$	5.46442	+	1.06774i	0.346991	+	0.0678017i
$249$	13.8558			0.878076
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	6.64081	−	7.37537i	0.419164	−	0.465529i	−0.496169	−	0.868226i	$-0.665260\pi$
$251$	6.64081	−	7.37537i	0.419164	−	0.465529i	0.915333	+	0.402697i	$0.131927\pi$
$252$	−4.17996	−	3.03692i	−0.263313	−	0.191308i
$253$	0.964825	−	1.67113i	0.0606580	−	0.105063i
$254$	−1.77877	−	3.08092i	−0.111610	−	0.193314i
$255$	−0.613278	+	5.83495i	−0.0384049	+	0.365399i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−1.52818	−	14.5397i	−0.0953253	−	0.906960i	−0.932778	−	0.360450i	$-0.882623\pi$
$257$	−1.52818	−	14.5397i	−0.0953253	−	0.906960i	0.837453	−	0.546509i	$-0.184044\pi$
$258$	−2.35382	−	2.61418i	−0.146542	−	0.162752i
$259$	20.8794	−	9.29612i	1.29739	−	0.577633i
$260$	5.94445	−	1.26353i	0.368659	−	0.0783609i
$261$	1.30079	+	0.276492i	0.0805170	+	0.0171144i
$262$	−1.16869	−	0.520332i	−0.0722016	−	0.0321462i
$263$	−9.20138	−	28.3189i	−0.567382	−	1.74622i	−0.660767	−	0.750591i	$-0.729769\pi$
$263$	−9.20138	−	28.3189i	−0.567382	−	1.74622i	0.0933856	−	0.995630i	$-0.470231\pi$
$264$	0.665363	+	2.04778i	0.0409503	+	0.126032i
$265$	−8.06325	−	3.58999i	−0.495321	−	0.220531i
$266$	7.02134	+	1.49243i	0.430506	+	0.0915069i
$267$	10.1535	−	2.15819i	0.621383	−	0.132079i
$268$	13.4098	−	5.97043i	0.819134	−	0.364702i
$269$	−4.92925	−	5.47448i	−0.300542	−	0.333785i	0.573892	−	0.818931i	$-0.305433\pi$
$269$	−4.92925	−	5.47448i	−0.300542	−	0.333785i	−0.874433	+	0.485146i	$0.838766\pi$
$270$	−0.104528	−	0.994522i	−0.00636140	−	0.0605247i
$271$	−3.73187	+	2.71136i	−0.226695	+	0.164704i	−0.695335	−	0.718686i	$-0.744744\pi$
$271$	−3.73187	+	2.71136i	−0.226695	+	0.164704i	0.468640	+	0.883389i	$0.344744\pi$
$272$	0.613278	−	5.83495i	0.0371854	−	0.353796i
$273$	−15.6997	−	27.1927i	−0.950190	−	1.64578i
$274$	−6.05715	+	10.4913i	−0.365926	+	0.633802i
$275$	1.74194	+	1.26560i	0.105043	+	0.0763183i
$276$	0.599671	−	0.666002i	0.0360959	−	0.0400886i
$277$	6.63229	−	20.4121i	0.398496	−	1.22644i	−0.527710	−	0.849425i	$-0.676949\pi$
$277$	6.63229	−	20.4121i	0.398496	−	1.22644i	0.926206	−	0.377019i	$-0.123051\pi$
$278$	−8.03761			−0.482064
$279$	3.65690	−	4.19846i	0.218933	−	0.251355i
$280$	5.16672			0.308770
$281$	5.72870	−	17.6311i	0.341746	−	1.05178i	−0.621557	−	0.783369i	$-0.713500\pi$
$281$	5.72870	−	17.6311i	0.341746	−	1.05178i	0.963303	−	0.268416i	$-0.0865003\pi$
$282$	3.34959	−	3.72010i	0.199465	−	0.221528i
$283$	1.07077	+	0.777957i	0.0636504	+	0.0462447i	0.619155	−	0.785268i	$-0.287475\pi$
$283$	1.07077	+	0.777957i	0.0636504	+	0.0462447i	−0.555505	+	0.831513i	$0.687475\pi$
$284$	0.287510	−	0.497982i	0.0170606	−	0.0295498i
$285$	0.694658	+	1.20318i	0.0411480	+	0.0712704i
$286$	−1.36779	+	13.0136i	−0.0808789	+	0.769511i
$287$	−46.4150	+	33.7225i	−2.73979	+	1.99057i
$288$	0.104528	+	0.994522i	0.00615940	+	0.0586028i
$289$	11.6581	+	12.9476i	0.685770	+	0.761624i
$290$	−1.21488	+	0.540900i	−0.0713403	+	0.0317627i
$291$	2.87399	−	0.610886i	0.168477	−	0.0358108i
$292$	9.02867	+	1.91910i	0.528363	+	0.112307i
$293$	7.74210	+	3.44701i	0.452299	+	0.201376i	0.620226	−	0.784423i	$-0.287041\pi$
$293$	7.74210	+	3.44701i	0.452299	+	0.201376i	−0.167928	+	0.985799i	$0.553707\pi$
$294$	−6.08608	−	18.7310i	−0.354947	−	1.09242i
$295$	0.223738	+	0.688593i	0.0130265	+	0.0400914i
$296$	−4.04114	−	1.79923i	−0.234887	−	0.104578i
$297$	2.10611	+	0.447667i	0.122209	+	0.0259763i
$298$	−14.4525	+	3.07196i	−0.837208	+	0.177954i
$299$	4.97553	−	2.21525i	0.287742	−	0.128111i
$300$	0.669131	+	0.743145i	0.0386323	+	0.0429055i
$301$	−1.89981	−	18.0755i	−0.109503	−	1.04186i
$302$	7.69221	−	5.58872i	0.442637	−	0.321594i
$303$	0.0554733	−	0.527794i	0.00318686	−	0.0303210i
$304$	−0.694658	−	1.20318i	−0.0398414	−	0.0690073i
$305$	−1.33289	+	2.30864i	−0.0763212	+	0.132192i
$306$	−4.74657	−	3.44859i	−0.271344	−	0.197143i
$307$	−4.25223	+	4.72258i	−0.242688	+	0.269532i	−0.852167	−	0.523270i	$-0.824712\pi$
$307$	−4.25223	+	4.72258i	−0.242688	+	0.269532i	0.609479	+	0.792802i	$0.291379\pi$
$308$	−3.43774	+	10.5803i	−0.195884	+	0.602868i
$309$	−14.5342			−0.826822
$310$	−0.490706	+	5.54610i	−0.0278702	+	0.314997i
$311$	13.2896			0.753586			0.376793	−	0.926298i	$-0.377027\pi$
$311$	13.2896			0.753586			0.376793	+	0.926298i	$0.377027\pi$
$312$	−1.87797	+	5.77981i	−0.106319	+	0.327217i
$313$	−1.92670	+	2.13981i	−0.108903	+	0.120949i	−0.795132	−	0.606437i	$-0.792598\pi$
$313$	−1.92670	+	2.13981i	−0.108903	+	0.120949i	0.686228	+	0.727386i	$0.259265\pi$
$314$	−7.93223	−	5.76310i	−0.447642	−	0.325231i
$315$	2.58336	−	4.47451i	0.145556	−	0.252110i
$316$	−0.719766	−	1.24667i	−0.0404900	−	0.0701307i
$317$	−2.42371	+	23.0600i	−0.136129	+	1.29518i	0.686721	+	0.726921i	$0.259050\pi$
$317$	−2.42371	+	23.0600i	−0.136129	+	1.29518i	−0.822850	+	0.568259i	$0.807617\pi$
$318$	7.14065	−	5.18798i	0.400428	−	0.290928i
$319$	−0.299305	−	2.84770i	−0.0167579	−	0.159441i
$320$	−0.669131	−	0.743145i	−0.0374055	−	0.0415431i
$321$	10.7194	−	4.77259i	0.598299	−	0.266380i
$322$	4.52920	−	0.962710i	0.252402	−	0.0536497i
$323$	7.97312	+	1.69474i	0.443636	+	0.0942977i
$324$	0.913545	+	0.406737i	0.0507525	+	0.0225965i
$325$	1.87797	+	5.77981i	0.104171	+	0.320606i
$326$	5.44428	+	16.7558i	0.301531	+	0.928016i
$327$	−0.662334	−	0.294890i	−0.0366271	−	0.0163075i
$328$	10.8615	+	2.30869i	0.599727	+	0.127476i
$329$	25.2988	−	5.37742i	1.39477	−	0.296467i
$330$	−1.96701	+	0.875770i	−0.108280	+	0.0482095i
$331$	−16.4143	−	18.2300i	−0.902213	−	1.00201i	−0.999977	−	0.00679914i	$-0.997836\pi$
$331$	−16.4143	−	18.2300i	−0.902213	−	1.00201i	0.0977641	−	0.995210i	$-0.468831\pi$
$332$	−1.44833	−	13.7799i	−0.0794872	−	0.756270i
$333$	−3.57875	+	2.60012i	−0.196114	+	0.142485i
$334$	1.56021	−	14.8444i	0.0853709	−	0.812249i
$335$	7.33942	+	12.7123i	0.400996	+	0.694545i
$336$	−2.58336	+	4.47451i	−0.140934	+	0.244104i
$337$	−5.49842	−	3.99484i	−0.299518	−	0.217613i	0.427868	−	0.903841i	$-0.359265\pi$
$337$	−5.49842	−	3.99484i	−0.299518	−	0.217613i	−0.727386	+	0.686229i	$0.759265\pi$
$338$	−16.0143	+	17.7857i	−0.871063	+	0.967413i
$339$	0.534513	−	1.64506i	0.0290307	−	0.0893474i
$340$	5.86709			0.318188
$341$	−11.0307	−	4.69503i	−0.597345	−	0.254250i
$342$	−1.38932			−0.0751256
$343$	20.2688	−	62.3811i	1.09441	−	3.36826i
$344$	−2.35382	+	2.61418i	−0.126909	+	0.140947i
$345$	0.725036	+	0.526770i	0.0390346	+	0.0283603i
$346$	11.1995	−	19.3981i	0.602088	−	1.04285i
$347$	0.787324	+	1.36369i	0.0422658	+	0.0732065i	0.886384	−	0.462950i	$-0.153209\pi$
$347$	0.787324	+	1.36369i	0.0422658	+	0.0732065i	−0.844119	+	0.536156i	$0.819876\pi$
$348$	0.139007	−	1.32257i	0.00745158	−	0.0708971i
$349$	11.8950	−	8.64219i	0.636723	−	0.462606i	−0.222000	−	0.975047i	$-0.571259\pi$
$349$	11.8950	−	8.64219i	0.636723	−	0.462606i	0.858723	+	0.512441i	$0.171259\pi$
$350$	0.540069	+	5.13841i	0.0288679	+	0.274660i
$351$	4.06647	+	4.51628i	0.217052	+	0.241061i
$352$	1.96701	−	0.875770i	0.104842	−	0.0466787i
$353$	−20.8765	+	4.43744i	−1.11114	+	0.236181i	−0.726692	−	0.686964i	$-0.758943\pi$
$353$	−20.8765	+	4.43744i	−1.11114	+	0.236181i	−0.384453	+	0.923145i	$0.625610\pi$
$354$	−0.708208	−	0.150534i	−0.0376408	−	0.00800081i
$355$	0.525307	+	0.233882i	0.0278804	+	0.0124132i
$356$	−3.20769	−	9.87226i	−0.170007	−	0.523229i
$357$	−9.36741	−	28.8299i	−0.495776	−	1.52584i
$358$	16.1801	+	7.20386i	0.855147	+	0.380736i
$359$	15.5973	+	3.31530i	0.823192	+	0.174975i	0.600205	−	0.799846i	$-0.295086\pi$
$359$	15.5973	+	3.31530i	0.823192	+	0.174975i	0.222988	+	0.974821i	$0.428419\pi$
$360$	−0.978148	+	0.207912i	−0.0515529	+	0.0109579i
$361$	−15.5940	+	6.94291i	−0.820739	+	0.365417i
$362$	16.1697	+	17.9582i	0.849859	+	0.943864i
$363$	0.665208	+	6.32903i	0.0349144	+	0.332188i
$364$	−25.4027	+	18.4561i	−1.33146	+	0.967364i
$365$	−0.964837	+	9.17981i	−0.0505019	+	0.480493i
$366$	−1.33289	−	2.30864i	−0.0696714	−	0.120674i
$367$	−17.8953	+	30.9956i	−0.934129	+	1.61796i	−0.157949	+	0.987447i	$0.550488\pi$
$367$	−17.8953	+	30.9956i	−0.934129	+	1.61796i	−0.776180	+	0.630511i	$0.782845\pi$
$368$	−0.725036	−	0.526770i	−0.0377951	−	0.0274598i
$369$	7.43013	−	8.25200i	0.386797	−	0.429582i
$370$	1.36696	−	4.20707i	0.0710649	−	0.218715i
$371$	45.6031			2.36760
$372$	−4.55771	−	3.19801i	−0.236306	−	0.165809i
$373$	4.40876			0.228277			0.114138	−	0.993465i	$-0.463589\pi$
$373$	4.40876			0.228277			0.114138	+	0.993465i	$0.463589\pi$
$374$	−3.90375	+	12.0145i	−0.201858	+	0.621255i
$375$	−0.669131	+	0.743145i	−0.0345538	+	0.0383758i
$376$	−4.04984	−	2.94238i	−0.208855	−	0.151742i
$377$	4.04092	−	6.99909i	0.208118	−	0.360471i
$378$	2.58336	+	4.47451i	0.132874	+	0.230144i
$379$	0.454737	−	4.32654i	0.0233583	−	0.222239i	−0.976615	−	0.214994i	$-0.931027\pi$
$379$	0.454737	−	4.32654i	0.0233583	−	0.222239i	0.999974	−	0.00724569i	$-0.00230639\pi$
$380$	1.12398	−	0.816619i	0.0576590	−	0.0418917i
$381$	0.371864	+	3.53805i	0.0190512	+	0.181260i
$382$	−4.80474	−	5.33620i	−0.245832	−	0.273024i
$383$	−12.1894	+	5.42707i	−0.622849	+	0.277310i	−0.693798	−	0.720170i	$-0.744064\pi$
$383$	−12.1894	+	5.42707i	−0.622849	+	0.277310i	0.0709487	+	0.997480i	$0.477397\pi$
$384$	0.978148	−	0.207912i	0.0499159	−	0.0106099i
$385$	−10.8817	−	2.31297i	−0.554581	−	0.117880i
$386$	−14.3820	−	6.40330i	−0.732027	−	0.325919i
$387$	1.08704	+	3.34555i	0.0552572	+	0.170064i
$388$	−0.907954	−	2.79440i	−0.0460944	−	0.141864i
$389$	−29.6965	−	13.2217i	−1.50567	−	0.670368i	−0.522432	−	0.852681i	$-0.674975\pi$
$389$	−29.6965	−	13.2217i	−1.50567	−	0.670368i	−0.983241	+	0.182313i	$0.941642\pi$
$390$	−5.94445	−	1.26353i	−0.301009	−	0.0639814i
$391$	5.14315	−	1.09321i	0.260100	−	0.0552860i
$392$	−17.9922	+	8.01067i	−0.908746	+	0.404600i
$393$	0.856009	+	0.950694i	0.0431799	+	0.0479562i
$394$	0.790164	+	7.51791i	0.0398079	+	0.378747i
$395$	1.16461	−	0.846136i	0.0585977	−	0.0425737i
$396$	0.225067	−	2.14137i	0.0113100	−	0.107608i
$397$	8.46604	+	14.6636i	0.424898	+	0.735945i	0.996411	−	0.0846479i	$-0.0269765\pi$
$397$	8.46604	+	14.6636i	0.424898	+	0.735945i	−0.571513	+	0.820593i	$0.693643\pi$
$398$	−9.81480	+	16.9997i	−0.491971	+	0.852120i
$399$	−5.80729	−	4.21924i	−0.290728	−	0.211226i
$400$	0.669131	−	0.743145i	0.0334565	−	0.0371572i
$401$	0.133984	−	0.412360i	0.00669083	−	0.0205923i	−0.947655	−	0.319295i	$-0.896554\pi$
$401$	0.133984	−	0.412360i	0.00669083	−	0.0205923i	0.954346	+	0.298703i	$0.0965539\pi$
$402$	−14.6788			−0.732114
$403$	−17.3987	−	29.0208i	−0.866692	−	1.44563i
$404$	−0.530701			−0.0264034
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	4.59758	−	5.10613i	0.228174	−	0.253413i
$407$	7.70563	+	5.59847i	0.381954	+	0.277506i
$408$	−2.93354	+	5.08105i	−0.145232	+	0.251549i
$409$	10.8320	+	18.7616i	0.535608	+	0.927701i	0.999134	+	0.0416171i	$0.0132510\pi$
$409$	10.8320	+	18.7616i	0.535608	+	0.927701i	−0.463525	+	0.886084i	$0.653416\pi$
$410$	−1.16070	+	11.0433i	−0.0573229	+	0.545391i
$411$	9.80068	−	7.12061i	0.483432	−	0.351234i
$412$	1.51924	+	14.4546i	0.0748475	+	0.712127i
$413$	−2.50312	−	2.78000i	−0.123171	−	0.136795i
$414$	−0.818714	+	0.364515i	−0.0402376	+	0.0179149i
$415$	13.5530	−	2.88078i	0.665292	−	0.141412i
$416$	5.94445	+	1.26353i	0.291451	+	0.0619497i
$417$	7.34273	+	3.26919i	0.359575	+	0.160093i
$418$	0.924400	+	2.84501i	0.0452139	+	0.139154i
$419$	11.7780	+	36.2488i	0.575391	+	1.77087i	0.634846	+	0.772639i	$0.281064\pi$
$419$	11.7780	+	36.2488i	0.575391	+	1.77087i	−0.0594550	+	0.998231i	$0.518936\pi$
$420$	−4.72003	−	2.10149i	−0.230314	−	0.102542i
$421$	−11.0668	−	2.35233i	−0.539365	−	0.114646i	−0.0698291	−	0.997559i	$-0.522245\pi$
$421$	−11.0668	−	2.35233i	−0.539365	−	0.114646i	−0.469536	+	0.882913i	$0.655579\pi$
$422$	20.5726	−	4.37284i	1.00146	−	0.212867i
$423$	−4.57310	+	2.03608i	−0.222352	+	0.0989974i
$424$	−5.90596	−	6.55924i	−0.286819	−	0.318545i
$425$	0.613278	+	5.83495i	0.0297483	+	0.283037i
$426$	−0.465201	+	0.337988i	−0.0225391	+	0.0163756i
$427$	1.43971	−	13.6979i	0.0696724	−	0.662888i
$428$	−5.86693	−	10.1618i	−0.283589	−	0.491190i
$429$	6.54265	−	11.3322i	0.315882	−	0.547124i
$430$	−2.84590	−	2.06767i	−0.137241	−	0.0997117i
$431$	−24.6276	+	27.3518i	−1.18627	+	1.31749i	−0.249158	+	0.968463i	$0.580154\pi$
$431$	−24.6276	+	27.3518i	−1.18627	+	1.31749i	−0.937113	+	0.349025i	$0.886513\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	−15.0629			−0.723878			−0.361939	−	0.932202i	$-0.617885\pi$
$433$	−15.0629			−0.723878			−0.361939	+	0.932202i	$0.617885\pi$
$434$	−9.33894	−	27.2090i	−0.448284	−	1.30607i
$435$	1.32985			0.0637615
$436$	−0.224042	+	0.689530i	−0.0107297	+	0.0330225i
$437$	0.833132	−	0.925287i	0.0398541	−	0.0442625i
$438$	−7.46753	−	5.42548i	−0.356812	−	0.259239i
$439$	−9.10527	+	15.7708i	−0.434571	+	0.752699i	−0.997261	−	0.0739693i	$-0.976433\pi$
$439$	−9.10527	+	15.7708i	−0.434571	+	0.752699i	0.562690	+	0.826668i	$0.309767\pi$
$440$	1.07658	+	1.86469i	0.0513240	+	0.0888957i
$441$	−2.05868	+	19.5871i	−0.0980326	+	0.932718i
$442$	−28.8461	+	20.9579i	−1.37207	+	0.996867i
$443$	2.04314	+	19.4392i	0.0970724	+	0.923582i	0.929344	+	0.369215i	$0.120373\pi$
$443$	2.04314	+	19.4392i	0.0970724	+	0.923582i	−0.832272	+	0.554368i	$0.812960\pi$
$444$	2.95995	+	3.28736i	0.140473	+	0.156011i
$445$	9.48289	−	4.22205i	0.449532	−	0.200145i
$446$	−22.4816	+	4.77861i	−1.06453	+	0.226274i
$447$	14.4525	+	3.07196i	0.683578	+	0.145299i
$448$	4.72003	+	2.10149i	0.223001	+	0.0992862i
$449$	−3.43910	−	10.5845i	−0.162301	−	0.499511i	0.836526	−	0.547927i	$-0.184583\pi$
$449$	−3.43910	−	10.5845i	−0.162301	−	0.499511i	−0.998827	+	0.0484156i	$0.984583\pi$
$450$	−0.309017	−	0.951057i	−0.0145672	−	0.0448332i
$451$	−21.8420	−	9.72469i	−1.02850	−	0.457918i
$452$	−1.69192	−	0.359629i	−0.0795813	−	0.0169155i
$453$	−9.30032	+	1.97684i	−0.436967	+	0.0928802i
$454$	16.0109	−	7.12849i	0.751427	−	0.334557i
$455$	−21.0103	−	23.3343i	−0.984979	−	1.09393i
$456$	0.145223	+	1.38171i	0.00680069	+	0.0647043i
$457$	−24.4125	+	17.7367i	−1.14197	+	0.829688i	−0.987392	−	0.158293i	$-0.949401\pi$
$457$	−24.4125	+	17.7367i	−1.14197	+	0.829688i	−0.154575	+	0.987981i	$0.549401\pi$
$458$	0.840904	−	8.00067i	0.0392929	−	0.373847i
$459$	2.93354	+	5.08105i	0.136926	+	0.237163i
$460$	0.448097	−	0.776127i	0.0208926	−	0.0361871i
$461$	−25.8566	−	18.7859i	−1.20426	−	0.874947i	−0.209564	−	0.977795i	$-0.567204\pi$
$461$	−25.8566	−	18.7859i	−1.20426	−	0.874947i	−0.994697	+	0.102848i	$0.967204\pi$
$462$	7.44393	−	8.26732i	0.346323	−	0.384631i
$463$	10.4418	−	32.1365i	0.485270	−	1.49351i	−0.346319	−	0.938117i	$-0.612568\pi$
$463$	10.4418	−	32.1365i	0.485270	−	1.49351i	0.831589	−	0.555391i	$-0.187432\pi$
$464$	−1.32985			−0.0617369
$465$	2.70408	−	4.86702i	0.125399	−	0.225703i
$466$	−20.8247			−0.964685
$467$	12.5875	−	38.7402i	0.582478	−	1.79268i	−0.0266921	−	0.999644i	$-0.508497\pi$
$467$	12.5875	−	38.7402i	0.582478	−	1.79268i	0.609170	−	0.793040i	$-0.291503\pi$
$468$	4.06647	−	4.51628i	0.187973	−	0.208765i
$469$	−61.3570	−	44.5785i	−2.83320	−	2.05844i
$470$	2.50294	−	4.33522i	0.115452	−	0.199969i
$471$	4.90239	+	8.49119i	0.225890	+	0.391253i
$472$	−0.0756817	+	0.720063i	−0.00348353	+	0.0331436i
$473$	6.12768	−	4.45202i	0.281751	−	0.204704i
$474$	0.150472	+	1.43165i	0.00691141	+	0.0657577i
$475$	0.929634	+	1.03246i	0.0426545	+	0.0473726i
$476$	−27.6928	+	12.3296i	−1.26930	+	0.565128i
$477$	−8.63345	+	1.83510i	−0.395298	+	0.0840233i
$478$	2.20389	+	0.468452i	0.100804	+	0.0214265i
$479$	10.0324	+	4.46672i	0.458393	+	0.204090i	0.622924	−	0.782282i	$-0.285944\pi$
$479$	10.0324	+	4.46672i	0.458393	+	0.204090i	−0.164531	+	0.986372i	$0.552611\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	8.30737	+	25.5674i	0.378783	+	1.16578i
$482$	−22.2505	−	9.90654i	−1.01348	−	0.451231i
$483$	−4.52920	−	0.962710i	−0.206086	−	0.0438048i
$484$	6.22483	−	1.32313i	0.282947	−	0.0601422i
$485$	2.68418	−	1.19507i	0.121882	−	0.0542655i
$486$	−0.669131	−	0.743145i	−0.0303524	−	0.0337097i
$487$	1.61049	+	15.3228i	0.0729784	+	0.694343i	0.968447	+	0.249219i	$0.0801739\pi$
$487$	1.61049	+	15.3228i	0.0729784	+	0.694343i	−0.895469	+	0.445124i	$0.853159\pi$
$488$	−2.15667	+	1.56691i	−0.0976277	+	0.0709306i
$489$	1.84159	−	17.5215i	0.0832795	−	0.792351i
$490$	−9.84748	−	17.0563i	−0.444864	−	0.770527i
$491$	8.36244	−	14.4842i	0.377392	−	0.653662i	−0.613290	−	0.789858i	$-0.710154\pi$
$491$	8.36244	−	14.4842i	0.377392	−	0.653662i	0.990682	+	0.136196i	$0.0434877\pi$
$492$	−8.98346	−	6.52686i	−0.405005	−	0.294254i
$493$	5.22080	−	5.79829i	0.235133	−	0.261142i
$494$	−2.60910	+	8.02998i	−0.117389	+	0.361286i
$495$	2.15316			0.0967774
$496$	−2.70408	+	4.86702i	−0.121417	+	0.218536i
$497$	−2.97097			−0.133266
$498$	−4.28168	+	13.1777i	−0.191867	+	0.590505i
$499$	18.9597	−	21.0569i	0.848753	−	0.942635i	−0.150188	−	0.988658i	$-0.547988\pi$
$499$	18.9597	−	21.0569i	0.848753	−	0.942635i	0.998940	+	0.0460221i	$0.0146545\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	−7.46308	+	12.9264i	−0.333426	+	0.577511i
$502$	4.96227	+	8.59490i	0.221477	+	0.383609i
$503$	0.257068	−	2.44584i	0.0114621	−	0.109054i	−0.987295	−	0.158898i	$-0.949206\pi$
$503$	0.257068	−	2.44584i	0.0114621	−	0.109054i	0.998757	+	0.0498440i	$0.0158724\pi$
$504$	4.17996	−	3.03692i	0.186190	−	0.135275i
$505$	−0.0554733	−	0.527794i	−0.00246853	−	0.0234865i
$506$	1.29119	+	1.43401i	0.0574003	+	0.0637495i
$507$	21.8639	−	9.73442i	0.971008	−	0.432321i
$508$	3.47980	−	0.739655i	0.154391	−	0.0328169i
$509$	−8.60095	−	1.82819i	−0.381230	−	0.0810330i	0.0133105	−	0.999911i	$-0.495763\pi$
$509$	−8.60095	−	1.82819i	−0.381230	−	0.0810330i	−0.394541	+	0.918878i	$0.629096\pi$
$510$	−5.35985	−	2.38636i	−0.237338	−	0.105670i
$511$	−14.7372	−	45.3566i	−0.651937	−	2.00646i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	1.26920	+	0.565086i	0.0560367	+	0.0249491i
$514$	14.3003	+	3.03962i	0.630758	+	0.134072i
$515$	−14.2166	+	3.02183i	−0.626458	+	0.133158i
$516$	3.21360	−	1.43079i	0.141471	−	0.0629869i
$517$	7.21221	+	8.00997i	0.317192	+	0.352278i
$518$	2.38904	+	22.7302i	0.104968	+	0.998707i
$519$	−18.1211	+	13.1658i	−0.795430	+	0.577914i
$520$	−0.635246	+	6.04396i	−0.0278574	+	0.265045i
$521$	−7.25205	−	12.5609i	−0.317718	−	0.550304i	0.662294	−	0.749244i	$-0.269583\pi$
$521$	−7.25205	−	12.5609i	−0.317718	−	0.550304i	−0.980012	+	0.198941i	$0.936250\pi$
$522$	−0.664926	+	1.15169i	−0.0291030	+	0.0504079i
$523$	21.0949	+	15.3264i	0.922418	+	0.670176i	0.944125	−	0.329589i	$-0.106910\pi$
$523$	21.0949	+	15.3264i	0.922418	+	0.670176i	−0.0217070	+	0.999764i	$0.506910\pi$
$524$	0.856009	−	0.950694i	0.0373949	−	0.0415313i
$525$	1.59660	−	4.91384i	0.0696815	−	0.214458i
$526$	29.7763			1.29831
$527$	−10.6049	−	30.8973i	−0.461956	−	1.34591i
$528$	−2.15316			−0.0937043
$529$	−6.85920	+	21.1104i	−0.298226	+	0.917845i
$530$	5.90596	−	6.55924i	0.256539	−	0.284915i
$531$	0.585752	+	0.425574i	0.0254195	+	0.0184683i
$532$	−3.58910	+	6.21651i	−0.155607	+	0.269520i
$533$	−33.7414	−	58.4418i	−1.46150	−	2.53140i
$534$	−1.08504	+	10.3234i	−0.0469542	+	0.446739i
$535$	9.49289	−	6.89699i	0.410413	−	0.298183i
$536$	1.53436	+	14.5984i	0.0662741	+	0.630556i
$537$	−11.8512	−	13.1621i	−0.511418	−	0.567987i
$538$	6.72977	−	2.99628i	0.290141	−	0.129179i
$539$	41.4798	−	8.81680i	1.78666	−	0.379766i
$540$	0.978148	+	0.207912i	0.0420928	+	0.00894709i
$541$	−41.0328	−	18.2690i	−1.76414	−	0.785445i	−0.987917	−	0.154983i	$-0.950468\pi$
$541$	−41.0328	−	18.2690i	−1.76414	−	0.785445i	−0.776220	−	0.630462i	$-0.782866\pi$
$542$	−1.42545	−	4.38708i	−0.0612282	−	0.188441i
$543$	−7.46746	−	22.9825i	−0.320459	−	0.986272i
$544$	5.35985	+	2.38636i	0.229802	+	0.102314i
$545$	−0.709171	−	0.150739i	−0.0303776	−	0.00645695i
$546$	30.7133	−	6.52831i	1.31441	−	0.279386i
$547$	23.2799	−	10.3649i	0.995376	−	0.443170i	0.156609	−	0.987661i	$-0.449944\pi$
$547$	23.2799	−	10.3649i	0.995376	−	0.443170i	0.838767	+	0.544491i	$0.183277\pi$
$548$	−8.10605	−	9.00268i	−0.346273	−	0.384576i
$549$	0.278650	+	2.65118i	0.0118925	+	0.113150i
$550$	−1.74194	+	1.26560i	−0.0742767	+	0.0539652i
$551$	0.193125	−	1.83746i	0.00822741	−	0.0782786i
$552$	0.448097	+	0.776127i	0.0190723	+	0.0330341i
$553$	−3.71883	+	6.44120i	−0.158141	+	0.273908i
$554$	17.3636	+	12.6154i	0.737707	+	0.535975i
$555$	−2.95995	+	3.28736i	−0.125643	+	0.139541i
$556$	2.48376	−	7.64423i	0.105335	−	0.324187i
$557$	−11.4140			−0.483628			−0.241814	−	0.970323i	$-0.577742\pi$
$557$	−11.4140			−0.483628			−0.241814	+	0.970323i	$0.577742\pi$
$558$	2.86293	+	4.77532i	0.121197	+	0.202155i
$559$	21.3781			0.904197
$560$	−1.59660	+	4.91384i	−0.0674688	+	0.207648i
$561$	8.45299	−	9.38799i	0.356885	−	0.396361i
$562$	14.9979	+	10.8966i	0.632650	+	0.459647i
$563$	−10.6442	+	18.4363i	−0.448600	+	0.776999i	−0.998295	−	0.0583669i	$-0.981411\pi$
$563$	−10.6442	+	18.4363i	−0.448600	+	0.776999i	0.549695	+	0.835366i	$0.314744\pi$
$564$	2.50294	+	4.33522i	0.105393	+	0.182546i
$565$	0.180805	−	1.72024i	0.00760652	−	0.0723712i
$566$	−1.07077	+	0.777957i	−0.0450077	+	0.0327000i
$567$	−0.540069	−	5.13841i	−0.0226808	−	0.215793i
$568$	0.384764	+	0.427323i	0.0161443	+	0.0179301i
$569$	−6.12142	+	2.72543i	−0.256623	+	0.114256i	−0.531016	−	0.847362i	$-0.678190\pi$
$569$	−6.12142	+	2.72543i	−0.256623	+	0.114256i	0.274393	+	0.961618i	$0.411523\pi$
$570$	−1.35896	+	0.288855i	−0.0569204	+	0.0120988i
$571$	−24.9370	−	5.30053i	−1.04358	−	0.221820i	−0.345932	−	0.938259i	$-0.612437\pi$
$571$	−24.9370	−	5.30053i	−1.04358	−	0.221820i	−0.697649	+	0.716439i	$0.745771\pi$
$572$	−11.9540	−	5.32227i	−0.499823	−	0.222535i
$573$	2.21892	+	6.82912i	0.0926966	+	0.285291i
$574$	−17.7289	−	54.5641i	−0.739992	−	2.27746i
$575$	0.818714	+	0.364515i	0.0341427	+	0.0152013i
$576$	−0.978148	−	0.207912i	−0.0407562	−	0.00866299i
$577$	−12.3644	+	2.62813i	−0.514735	+	0.109410i	−0.457953	−	0.888976i	$-0.651417\pi$
$577$	−12.3644	+	2.62813i	−0.514735	+	0.109410i	−0.0567818	+	0.998387i	$0.518084\pi$
$578$	−15.9165	+	7.08646i	−0.662037	+	0.294758i
$579$	10.5342	+	11.6994i	0.437786	+	0.486211i
$580$	−0.139007	−	1.32257i	−0.00577197	−	0.0549166i
$581$	−57.9167	+	42.0790i	−2.40279	+	1.74573i
$582$	−0.307126	+	2.92211i	−0.0127308	+	0.121125i
$583$	9.50225	+	16.4584i	0.393543	+	0.681636i
$584$	−4.61519	+	7.99374i	−0.190978	+	0.330783i
$585$	4.91660	+	3.57212i	0.203276	+	0.147689i
$586$	−5.67074	+	6.29799i	−0.234256	+	0.260168i
$587$	−8.25336	+	25.4012i	−0.340653	+	1.04842i	0.623218	+	0.782049i	$0.285825\pi$
$587$	−8.25336	+	25.4012i	−0.340653	+	1.04842i	−0.963870	+	0.266372i	$0.914175\pi$
$588$	19.6950			0.812207
$589$	−6.33210	−	4.44305i	−0.260910	−	0.183073i
$590$	−0.724030			−0.0298078
$591$	2.33596	−	7.18934i	0.0960884	−	0.295730i
$592$	2.95995	−	3.28736i	0.121653	−	0.135110i
$593$	−1.38713	−	1.00781i	−0.0569624	−	0.0413856i	0.558940	−	0.829208i	$-0.311208\pi$
$593$	−1.38713	−	1.00781i	−0.0569624	−	0.0413856i	−0.615902	+	0.787823i	$0.711208\pi$
$594$	−1.07658	+	1.86469i	−0.0441726	+	0.0765093i
$595$	−15.1568	−	26.2523i	−0.621368	−	1.07624i
$596$	1.54444	−	14.6944i	0.0632628	−	0.601906i
$597$	15.8807	−	11.5380i	0.649953	−	0.472218i
$598$	0.569303	+	5.41656i	0.0232805	+	0.221500i
$599$	−3.79987	−	4.22019i	−0.155259	−	0.172432i	0.660497	−	0.750828i	$-0.270345\pi$
$599$	−3.79987	−	4.22019i	−0.155259	−	0.172432i	−0.815756	+	0.578396i	$0.803679\pi$
$600$	−0.913545	+	0.406737i	−0.0372953	+	0.0166050i
$601$	0.0374571	−	0.00796175i	0.00152791	−	0.000324766i	−0.207148	−	0.978310i	$-0.566418\pi$
$601$	0.0374571	−	0.00796175i	0.00152791	−	0.000324766i	0.208676	+	0.977985i	$0.433085\pi$
$602$	17.7779	+	3.77881i	0.724574	+	0.154013i
$603$	13.4098	+	5.97043i	0.546089	+	0.243135i
$604$	2.93816	+	9.04273i	0.119552	+	0.367944i
$605$	1.96655	+	6.05243i	0.0799517	+	0.246066i
$606$	0.484819	+	0.215855i	0.0196944	+	0.00876853i
$607$	28.1453	+	5.98248i	1.14238	+	0.242821i	0.739972	−	0.672637i	$-0.234839\pi$
$607$	28.1453	+	5.98248i	1.14238	+	0.242821i	0.402412	+	0.915459i	$0.368172\pi$
$608$	1.35896	−	0.288855i	0.0551129	−	0.0117146i
$609$	−6.27695	+	2.79468i	−0.254355	+	0.113246i
$610$	−1.78376	−	1.98106i	−0.0722223	−	0.0802110i
$611$	3.17997	+	30.2554i	0.128648	+	1.22400i
$612$	4.74657	−	3.44859i	0.191869	−	0.139401i
$613$	−4.39380	+	41.8042i	−0.177464	+	1.68846i	0.436961	+	0.899480i	$0.356055\pi$
$613$	−4.39380	+	41.8042i	−0.177464	+	1.68846i	−0.614425	+	0.788975i	$0.710612\pi$
$614$	−3.17743	−	5.50347i	−0.128231	−	0.222102i
$615$	5.55208	−	9.61649i	0.223882	−	0.387774i
$616$	−9.00013	−	6.53898i	−0.362626	−	0.263463i
$617$	9.51406	−	10.5664i	0.383022	−	0.425389i	−0.520546	−	0.853833i	$-0.674272\pi$
$617$	9.51406	−	10.5664i	0.383022	−	0.425389i	0.903568	+	0.428445i	$0.140938\pi$
$618$	4.49132	−	13.8229i	0.180667	−	0.556037i
$619$	−12.4871			−0.501901			−0.250950	−	0.968000i	$-0.580743\pi$
$619$	−12.4871			−0.501901			−0.250950	+	0.968000i	$0.580743\pi$
$620$	−5.12302	−	2.18053i	−0.205745	−	0.0875721i
$621$	0.896194			0.0359630
$622$	−4.10672	+	12.6392i	−0.164665	+	0.506785i
$623$	−35.8869	+	39.8564i	−1.43778	+	1.59681i
$624$	−4.91660	−	3.57212i	−0.196822	−	0.142999i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−1.43970	−	2.49364i	−0.0575421	−	0.0996658i
$627$	0.312689	−	2.97503i	0.0124876	−	0.118811i
$628$	7.93223	−	5.76310i	0.316530	−	0.229973i
$629$	2.71288	+	25.8114i	0.108170	+	1.02917i
$630$	3.45721	+	3.83962i	0.137738	+	0.152974i
$631$	−32.3901	+	14.4210i	−1.28943	+	0.574091i	−0.932880	−	0.360186i	$-0.882713\pi$
$631$	−32.3901	+	14.4210i	−1.28943	+	0.574091i	−0.356548	+	0.934277i	$0.616047\pi$
$632$	1.40807	−	0.299296i	0.0560102	−	0.0119053i
$633$	−20.5726	−	4.37284i	−0.817688	−	0.173805i
$634$	−21.1824	−	9.43103i	−0.841262	−	0.374554i
$635$	1.09934	+	3.38342i	0.0436260	+	0.134267i
$636$	2.72748	+	8.39433i	0.108152	+	0.332857i
$637$	109.343	+	48.6828i	4.33234	+	1.92888i
$638$	2.80082	+	0.595332i	0.110885	+	0.0235694i
$639$	0.562455	−	0.119553i	0.0222504	−	0.00472946i
$640$	0.913545	−	0.406737i	0.0361111	−	0.0160777i
$641$	−24.7031	−	27.4356i	−0.975714	−	1.08364i	−0.996478	−	0.0838558i	$-0.973277\pi$
$641$	−24.7031	−	27.4356i	−0.975714	−	1.08364i	0.0207639	−	0.999784i	$-0.493390\pi$
$642$	1.22652	+	11.6696i	0.0484070	+	0.460561i
$643$	−5.62174	+	4.08443i	−0.221700	+	0.161074i	−0.693092	−	0.720850i	$-0.743752\pi$
$643$	−5.62174	+	4.08443i	−0.221700	+	0.161074i	0.471392	+	0.881924i	$0.343752\pi$
$644$	−0.484007	+	4.60501i	−0.0190725	+	0.181463i
$645$	1.75886	+	3.04644i	0.0692551	+	0.119953i
$646$	−4.07562	+	7.05918i	−0.160353	+	0.277740i
$647$	20.6139	+	14.9769i	0.810415	+	0.588801i	0.913951	−	0.405825i	$-0.133016\pi$
$647$	20.6139	+	14.9769i	0.810415	+	0.588801i	−0.103536	+	0.994626i	$0.533016\pi$
$648$	−0.669131	+	0.743145i	−0.0262859	+	0.0291935i
$649$	0.481743	−	1.48265i	0.0189101	−	0.0581992i
$650$	−6.07725			−0.238369
$651$	−2.53534	+	28.6551i	−0.0993677	+	1.12308i
$652$	−17.6180			−0.689976
$653$	9.63072	−	29.6403i	0.376879	−	1.15991i	−0.565323	−	0.824870i	$-0.691248\pi$
$653$	9.63072	−	29.6403i	0.376879	−	1.15991i	0.942202	−	0.335045i	$-0.108752\pi$
$654$	0.485129	−	0.538791i	0.0189701	−	0.0210684i
$655$	1.03496	+	0.751945i	0.0404394	+	0.0293809i
$656$	−5.55208	+	9.61649i	−0.216772	+	0.375461i
$657$	4.61519	+	7.99374i	0.180056	+	0.311865i
$658$	−2.70352	+	25.7223i	−0.105394	+	1.00276i
$659$	−32.6813	+	23.7444i	−1.27308	+	0.924949i	−0.999321	−	0.0368487i	$-0.988268\pi$
$659$	−32.6813	+	23.7444i	−1.27308	+	0.924949i	−0.273762	+	0.961797i	$0.588268\pi$
$660$	−0.225067	−	2.14137i	−0.00876071	−	0.0833526i
$661$	−4.06076	−	4.50993i	−0.157945	−	0.175416i	0.658978	−	0.752162i	$-0.270989\pi$
$661$	−4.06076	−	4.50993i	−0.157945	−	0.175416i	−0.816924	+	0.576746i	$0.804322\pi$
$662$	22.4100	−	9.97758i	0.870990	−	0.387790i
$663$	34.8766	−	7.41325i	1.35450	−	0.287907i
$664$	13.5530	+	2.88078i	0.525959	+	0.111796i
$665$	−6.55761	−	2.91964i	−0.254293	−	0.113219i
$666$	−1.36696	−	4.20707i	−0.0529687	−	0.163021i
$667$	−0.368288	−	1.13347i	−0.0142602	−	0.0438883i
$668$	13.6357	+	6.07102i	0.527582	+	0.234895i
$669$	22.4816	+	4.77861i	0.869189	+	0.184752i
$670$	−14.3581	+	3.05190i	−0.554701	+	0.117905i
$671$	5.24363	−	2.33461i	0.202428	−	0.0901268i
$672$	−3.45721	−	3.83962i	−0.133365	−	0.148117i
$673$	−1.09494	−	10.4177i	−0.0422069	−	0.401572i	−0.995146	−	0.0984098i	$-0.968624\pi$
$673$	−1.09494	−	10.4177i	−0.0422069	−	0.401572i	0.952939	−	0.303162i	$-0.0980423\pi$
$674$	5.49842	−	3.99484i	0.211791	−	0.153875i
$675$	−0.104528	+	0.994522i	−0.00402330	+	0.0382792i
$676$	−11.9665	−	20.7266i	−0.460250	−	0.797176i
$677$	10.5540	−	18.2801i	0.405624	−	0.702561i	−0.588770	−	0.808301i	$-0.700388\pi$
$677$	10.5540	−	18.2801i	0.405624	−	0.702561i	0.994394	+	0.105739i	$0.0337209\pi$
$678$	1.39937	+	1.01670i	0.0537426	+	0.0390463i
$679$	−10.1580	+	11.2816i	−0.389827	+	0.432947i
$680$	−1.81303	+	5.57993i	−0.0695265	+	0.213981i
$681$	−17.5261			−0.671600
$682$	7.87390	−	9.03996i	0.301507	−	0.346158i
$683$	−11.5099			−0.440413			−0.220206	−	0.975453i	$-0.570673\pi$
$683$	−11.5099			−0.440413			−0.220206	+	0.975453i	$0.570673\pi$
$684$	0.429322	−	1.32132i	0.0164155	−	0.0505219i
$685$	8.10605	−	9.00268i	0.309716	−	0.343975i
$686$	53.0645	+	38.5536i	2.02601	+	1.47198i
$687$	−4.02237	+	6.96694i	−0.153463	+	0.265806i
$688$	−1.75886	−	3.04644i	−0.0670560	−	0.116144i
$689$	−5.60688	+	53.3459i	−0.213605	+	2.03232i
$690$	−0.725036	+	0.526770i	−0.0276017	+	0.0200538i
$691$	3.83119	+	36.4513i	0.145745	+	1.38667i	0.785865	+	0.618398i	$0.212218\pi$
$691$	3.83119	+	36.4513i	0.145745	+	1.38667i	−0.640120	+	0.768275i	$0.721115\pi$
$692$	14.9878	+	16.6457i	0.569752	+	0.632773i
$693$	−10.1630	+	4.52485i	−0.386060	+	0.171885i
$694$	−1.54024	+	0.327388i	−0.0584667	+	0.0124275i
$695$	7.86197	+	1.67111i	0.298222	+	0.0633890i
$696$	1.21488	+	0.540900i	0.0460499	+	0.0205028i
$697$	−20.1322	−	61.9605i	−0.762561	−	2.34692i
$698$	4.54347	+	13.9834i	0.171973	+	0.529278i
$699$	19.0243	+	8.47017i	0.719565	+	0.320371i
$700$	−5.05381	−	1.07422i	−0.191016	−	0.0406017i
$701$	31.4654	−	6.68817i	1.18843	−	0.252609i	0.429066	−	0.903273i	$-0.358843\pi$
$701$	31.4654	−	6.68817i	1.18843	−	0.252609i	0.759365	+	0.650664i	$0.225510\pi$
$702$	−5.55185	+	2.47184i	−0.209541	+	0.0932936i
$703$	4.11231	+	4.56718i	0.155099	+	0.172255i
$704$	0.225067	+	2.14137i	0.00848252	+	0.0807058i
$705$	−4.04984	+	2.94238i	−0.152526	+	0.110817i
$706$	2.23094	−	21.2260i	0.0839626	−	0.798850i
$707$	1.37099	+	2.37463i	0.0515614	+	0.0893070i
$708$	0.362015	−	0.627028i	0.0136054	−	0.0235652i
$709$	36.3070	+	26.3786i	1.36354	+	0.990669i	0.998211	+	0.0597909i	$0.0190434\pi$
$709$	36.3070	+	26.3786i	1.36354	+	0.990669i	0.365329	+	0.930879i	$0.380957\pi$
$710$	−0.384764	+	0.427323i	−0.0144399	+	0.0160372i
$711$	0.444840	−	1.36908i	0.0166828	−	0.0513444i
$712$	10.3803			0.389019
$713$	−4.89718	−	0.956905i	−0.183401	−	0.0358364i
$714$	30.3136			1.13446
$715$	4.04358	−	12.4449i	0.151221	−	0.465411i
$716$	−11.8512	+	13.1621i	−0.442901	+	0.491891i
$717$	−1.82282	−	1.32436i	−0.0680745	−	0.0494590i
$718$	−7.97286	+	13.8094i	−0.297544	+	0.515362i
$719$	15.0784	+	26.1166i	0.562331	+	0.973986i	0.997293	+	0.0735366i	$0.0234286\pi$
$719$	15.0784	+	26.1166i	0.562331	+	0.973986i	−0.434962	+	0.900449i	$0.643238\pi$
$720$	0.104528	−	0.994522i	0.00389555	−	0.0370636i
$721$	60.7524	−	44.1392i	2.26254	−	1.64383i
$722$	−1.78428	−	16.9763i	−0.0664040	−	0.631792i
$723$	16.2975	+	18.1002i	0.606109	+	0.673152i
$724$	−22.0760	+	9.82887i	−0.820448	+	0.365287i
$725$	1.30079	−	0.276492i	0.0483102	−	0.0102687i
$726$	−6.22483	−	1.32313i	−0.231025	−	0.0491059i
$727$	12.6400	+	5.62771i	0.468793	+	0.208720i	0.627517	−	0.778603i	$-0.284071\pi$
$727$	12.6400	+	5.62771i	0.468793	+	0.208720i	−0.158724	+	0.987323i	$0.550738\pi$
$728$	−9.70296	−	29.8626i	−0.359616	−	1.10678i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−8.43237	−	3.75433i	−0.312096	−	0.138954i
$731$	20.1878	+	4.29105i	0.746672	+	0.158710i
$732$	2.60753	−	0.554248i	0.0963771	−	0.0204856i
$733$	7.39858	−	3.29406i	0.273273	−	0.121669i	−0.265525	−	0.964104i	$-0.585545\pi$
$733$	7.39858	−	3.29406i	0.273273	−	0.121669i	0.538798	+	0.842435i	$0.318879\pi$
$734$	−23.9486	−	26.5976i	−0.883960	−	0.981737i
$735$	2.05868	+	19.5871i	0.0759357	+	0.722480i
$736$	0.725036	−	0.526770i	0.0267252	−	0.0194170i
$737$	3.30372	−	31.4328i	0.121694	−	1.15784i
$738$	5.55208	+	9.61649i	0.204375	+	0.353988i
$739$	−19.5802	+	33.9138i	−0.720268	+	1.24754i	0.240624	+	0.970618i	$0.422648\pi$
$739$	−19.5802	+	33.9138i	−0.720268	+	1.24754i	−0.960892	+	0.276922i	$0.910685\pi$
$740$	3.57875	+	2.60012i	0.131558	+	0.0955821i
$741$	5.64962	−	6.27454i	0.207544	−	0.230501i
$742$	−14.0921	+	43.3711i	−0.517339	+	1.59220i
$743$	35.2641			1.29372			0.646858	−	0.762610i	$-0.276083\pi$
$743$	35.2641			1.29372			0.646858	+	0.762610i	$0.276083\pi$
$744$	4.44990	−	3.34640i	0.163141	−	0.122685i
$745$	14.7753			0.541326
$746$	−1.36238	+	4.19298i	−0.0498803	+	0.153516i
$747$	9.27134	−	10.2969i	0.339221	−	0.376743i
$748$	−10.2201	−	7.42537i	−0.373685	−	0.271498i
$749$	−30.3128	+	52.5032i	−1.10760	+	1.91843i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	1.69547	−	16.1313i	0.0618685	−	0.588640i	−0.919039	−	0.394166i	$-0.871033\pi$
$751$	1.69547	−	16.1313i	0.0618685	−	0.588640i	0.980908	−	0.194474i	$-0.0622999\pi$
$752$	4.04984	−	2.94238i	0.147683	−	0.107298i
$753$	−1.03740	−	9.87017i	−0.0378048	−	0.359689i
$754$	5.40781	+	6.00598i	0.196941	+	0.218725i
$755$	−8.68607	+	3.86729i	−0.316119	+	0.140745i
$756$	−5.05381	+	1.07422i	−0.183805	+	0.0390690i
$757$	12.5037	+	2.65774i	0.454454	+	0.0965971i	0.429451	−	0.903090i	$-0.358707\pi$
$757$	12.5037	+	2.65774i	0.454454	+	0.0965971i	0.0250030	+	0.999687i	$0.492040\pi$
$758$	3.97426	+	1.76945i	0.144352	+	0.0642695i
$759$	−0.596295	−	1.83521i	−0.0216441	−	0.0666138i
$760$	0.429322	+	1.32132i	0.0155732	+	0.0479292i
$761$	−11.7221	−	5.21902i	−0.424926	−	0.189189i	0.183121	−	0.983090i	$-0.441380\pi$
$761$	−11.7221	−	5.21902i	−0.424926	−	0.189189i	−0.608047	+	0.793901i	$0.708047\pi$
$762$	−3.47980	−	0.739655i	−0.126060	−	0.0267949i
$763$	3.66409	−	0.778826i	0.132649	−	0.0281954i
$764$	6.55977	−	2.92060i	0.237324	−	0.105664i
$765$	3.92585	+	4.36010i	0.141939	+	0.157640i
$766$	−1.39472	−	13.2699i	−0.0503933	−	0.479460i
$767$	3.55976	−	2.58632i	0.128536	−	0.0933866i
$768$	−0.104528	+	0.994522i	−0.00377185	+	0.0358867i
$769$	7.46854	+	12.9359i	0.269322	+	0.466480i	0.968687	−	0.248285i	$-0.0798670\pi$
$769$	7.46854	+	12.9359i	0.269322	+	0.466480i	−0.699365	+	0.714765i	$0.746534\pi$
$770$	5.56239	−	9.63434i	0.200455	−	0.347197i
$771$	−11.8276	−	8.59328i	−0.425962	−	0.309479i
$772$	10.5342	−	11.6994i	0.379134	−	0.421071i
$773$	9.05372	−	27.8645i	0.325640	−	1.00222i	−0.645511	−	0.763751i	$-0.723356\pi$
$773$	9.05372	−	27.8645i	0.325640	−	1.00222i	0.971151	−	0.238465i	$-0.0766443\pi$
$774$	−3.51772			−0.126442
$775$	1.63308	−	5.32288i	0.0586620	−	0.191203i
$776$	2.93820			0.105475
$777$	7.06270	−	21.7368i	0.253373	−	0.779802i
$778$	21.7513	−	24.1573i	0.779823	−	0.866081i
$779$	−12.4809	−	9.06787i	−0.447173	−	0.324890i
$780$	3.03863	−	5.26305i	0.108800	−	0.188448i
$781$	−0.619056	−	1.07224i	−0.0221515	−	0.0383676i
$782$	−0.549616	+	5.22924i	−0.0196542	+	0.186997i
$783$	1.07587	−	0.781668i	0.0384486	−	0.0279345i
$784$	−2.05868	−	19.5871i	−0.0735245	−	0.699539i
$785$	6.56068	+	7.28637i	0.234161	+	0.260062i
$786$	−1.16869	+	0.520332i	−0.0416856	+	0.0185596i
$787$	−6.61200	+	1.40542i	−0.235692	+	0.0500980i	−0.324243	−	0.945974i	$-0.605110\pi$
$787$	−6.61200	+	1.40542i	−0.235692	+	0.0500980i	0.0885511	+	0.996072i	$0.471776\pi$
$788$	−7.39413	−	1.57167i	−0.263405	−	0.0559884i
$789$	−27.2020	−	12.1111i	−0.968417	−	0.431167i
$790$	0.444840	+	1.36908i	0.0158267	+	0.0487096i
$791$	2.76168	+	8.49957i	0.0981939	+	0.302210i
$792$	1.96701	+	0.875770i	0.0698947	+	0.0311191i
$793$	15.8466	+	3.36830i	0.562730	+	0.119612i
$794$	−16.5621	+	3.52038i	−0.587766	+	0.124933i
$795$	−8.06325	+	3.58999i	−0.285974	+	0.127324i
$796$	−13.1348	−	14.5876i	−0.465549	−	0.517045i
$797$	1.88075	+	17.8941i	0.0666196	+	0.633843i	0.975984	+	0.217842i	$0.0699019\pi$
$797$	1.88075	+	17.8941i	0.0666196	+	0.633843i	−0.909364	+	0.416000i	$0.863431\pi$
$798$	5.80729	−	4.21924i	0.205576	−	0.149360i
$799$	−3.07000	+	29.2091i	−0.108609	+	1.03334i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	5.19016	−	8.98961i	0.183385	−	0.317632i
$802$	0.350774	+	0.254852i	0.0123863	+	0.00899915i
$803$	13.2986	−	14.7696i	0.469298	−	0.521209i
$804$	4.53601	−	13.9604i	0.159973	−	0.492346i
$805$	−4.63038			−0.163199
$806$	32.9769	−	7.57924i	1.16156	−	0.266967i
$807$	−7.36665			−0.259318
$808$	0.163996	−	0.504727i	0.00576934	−	0.0177562i
$809$	16.5476	−	18.3780i	0.581782	−	0.646134i	−0.378356	−	0.925660i	$-0.623511\pi$
$809$	16.5476	−	18.3780i	0.581782	−	0.646134i	0.960138	+	0.279526i	$0.0901772\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	13.8014	−	23.9047i	0.484632	−	0.839408i	−0.515212	−	0.857063i	$-0.672287\pi$
$811$	13.8014	−	23.9047i	0.484632	−	0.839408i	0.999844	+	0.0176550i	$0.00562005\pi$
$812$	3.43549	+	5.95044i	0.120562	+	0.208819i
$813$	−0.482174	+	4.58758i	−0.0169106	+	0.160893i
$814$	−7.70563	+	5.59847i	−0.270082	+	0.196226i
$815$	−1.84159	−	17.5215i	−0.0645080	−	0.613753i
$816$	−3.92585	−	4.36010i	−0.137432	−	0.152634i
$817$	4.46470	−	1.98781i	0.156200	−	0.0695448i
$818$	−21.1906	+	4.50420i	−0.740912	+	0.157486i
$819$	−30.7133	−	6.52831i	−1.07321	−	0.228118i
$820$	−10.1442	−	4.51647i	−0.354249	−	0.157722i
$821$	5.48164	+	16.8708i	0.191311	+	0.588794i	1.00000		0.000557470i	$0.000177448\pi$
$821$	5.48164	+	16.8708i	0.191311	+	0.588794i	−0.808689	+	0.588236i	$0.799823\pi$
$822$	3.74353	+	11.5214i	0.130570	+	0.401855i
$823$	−32.1392	−	14.3093i	−1.12030	−	0.498790i	−0.238846	−	0.971058i	$-0.576769\pi$
$823$	−32.1392	−	14.3093i	−1.12030	−	0.498790i	−0.881455	+	0.472267i	$0.843436\pi$
$824$	−14.2166	−	3.02183i	−0.495259	−	0.105271i
$825$	2.10611	−	0.447667i	0.0733253	−	0.0155858i
$826$	3.41744	−	1.52154i	0.118908	−	0.0529413i
$827$	2.75868	+	3.06382i	0.0959286	+	0.106539i	0.789197	−	0.614140i	$-0.210497\pi$
$827$	2.75868	+	3.06382i	0.0959286	+	0.106539i	−0.693269	+	0.720679i	$0.743830\pi$
$828$	−0.0936778	−	0.891284i	−0.00325553	−	0.0309743i
$829$	−35.9292	+	26.1041i	−1.24787	+	0.906632i	−0.998096	−	0.0616724i	$-0.980357\pi$
$829$	−35.9292	+	26.1041i	−1.24787	+	0.906632i	−0.249775	+	0.968304i	$0.580357\pi$
$830$	−1.44833	+	13.7799i	−0.0502721	+	0.478307i
$831$	−10.7313	−	18.5871i	−0.372264	−	0.644780i
$832$	−3.03863	+	5.26305i	−0.105345	+	0.182464i
$833$	93.4836	+	67.9198i	3.23902	+	2.35328i
$834$	−5.37821	+	5.97311i	−0.186232	+	0.206832i
$835$	−4.61244	+	14.1956i	−0.159620	+	0.491260i
$836$	−2.99142			−0.103460
$837$	−0.673116	−	5.52693i	−0.0232663	−	0.191039i
$838$	−38.1143			−1.31663
$839$	14.5787	−	44.8687i	0.503314	−	1.54904i	−0.300273	−	0.953853i	$-0.597078\pi$
$839$	14.5787	−	44.8687i	0.503314	−	1.54904i	0.803587	−	0.595187i	$-0.202922\pi$
$840$	3.45721	−	3.83962i	0.119285	−	0.132479i
$841$	22.0307	+	16.0063i	0.759681	+	0.551940i
$842$	5.65704	−	9.79828i	0.194955	−	0.337671i
$843$	−9.26923	−	16.0548i	−0.319249	−	0.552956i
$844$	−2.19846	+	20.9170i	−0.0756743	+	0.719993i
$845$	19.3622	−	14.0675i	0.666080	−	0.483935i
$846$	−0.523257	−	4.97846i	−0.0179900	−	0.171163i
$847$	−22.0013	−	24.4349i	−0.755974	−	0.839594i
$848$	8.06325	−	3.58999i	0.276893	−	0.123281i
$849$	1.29462	−	0.275179i	0.0444311	−	0.00944413i
$850$	−5.73888	−	1.21984i	−0.196842	−	0.0418400i
$851$	3.62165	+	1.61246i	0.124148	+	0.0552744i
$852$	−0.177691	−	0.546877i	−0.00608759	−	0.0187357i
$853$	4.21607	+	12.9757i	0.144355	+	0.444280i	0.996928	−	0.0783293i	$-0.0249585\pi$
$853$	4.21607	+	12.9757i	0.144355	+	0.444280i	−0.852572	+	0.522610i	$0.824959\pi$
$854$	12.5826	+	5.60213i	0.430567	+	0.191701i
$855$	1.35896	+	0.288855i	0.0464753	+	0.00987863i
$856$	11.4774	−	2.43961i	0.392291	−	0.0833840i
$857$	−26.3334	+	11.7244i	−0.899533	+	0.400498i	−0.803793	−	0.594908i	$-0.797188\pi$
$857$	−26.3334	+	11.7244i	−0.899533	+	0.400498i	−0.0957397	+	0.995406i	$0.530522\pi$
$858$	8.75578	+	9.72427i	0.298917	+	0.331981i
$859$	1.82933	+	17.4049i	0.0624158	+	0.593847i	0.980371	+	0.197162i	$0.0631726\pi$
$859$	1.82933	+	17.4049i	0.0624158	+	0.593847i	−0.917955	+	0.396684i	$0.870161\pi$
$860$	2.84590	−	2.06767i	0.0970443	−	0.0705068i
$861$	−5.99701	+	57.0578i	−0.204378	+	1.94452i
$862$	−18.4027	−	31.8744i	−0.626799	−	1.08565i
$863$	−12.3471	+	21.3858i	−0.420300	+	0.727980i	−0.995969	−	0.0897026i	$-0.971408\pi$
$863$	−12.3471	+	21.3858i	−0.420300	+	0.727980i	0.575669	+	0.817683i	$0.304742\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	−14.9878	+	16.6457i	−0.509601	+	0.565970i
$866$	4.65470	−	14.3257i	0.158173	−	0.486807i
$867$	17.4227			0.591707
$868$	28.7632	−	0.473827i	0.976285	−	0.0160827i
$869$	−3.09955			−0.105145
$870$	−0.410947	+	1.26476i	−0.0139324	+	0.0428795i
$871$	59.6912	−	66.2938i	2.02256	−	2.24628i
$872$	−0.586549	−	0.426153i	−0.0198631	−	0.0144314i
$873$	1.46910	−	2.54456i	0.0497215	−	0.0861202i
$874$	0.622548	+	1.07829i	0.0210580	+	0.0364735i
$875$	0.540069	−	5.13841i	0.0182577	−	0.173710i
$876$	7.46753	−	5.42548i	0.252304	−	0.183310i
$877$	−3.73464	−	35.5327i	−0.126110	−	1.19985i	−0.856252	−	0.516558i	$-0.827213\pi$
$877$	−3.73464	−	35.5327i	−0.126110	−	1.19985i	0.730142	−	0.683295i	$-0.239454\pi$
$878$	−12.1852	−	13.5331i	−0.411232	−	0.456719i
$879$	7.74210	−	3.44701i	0.261135	−	0.116265i
$880$	−2.10611	+	0.447667i	−0.0709969	+	0.0150909i
$881$	5.15801	+	1.09637i	0.173778	+	0.0369376i	0.293979	−	0.955812i	$-0.405021\pi$
$881$	5.15801	+	1.09637i	0.173778	+	0.0369376i	−0.120201	+	0.992750i	$0.538354\pi$
$882$	−17.9922	−	8.01067i	−0.605831	−	0.269733i
$883$	6.03298	+	18.5676i	0.203026	+	0.624850i	0.999789	+	0.0205573i	$0.00654406\pi$
$883$	6.03298	+	18.5676i	0.203026	+	0.624850i	−0.796763	+	0.604292i	$0.793456\pi$
$884$	−11.0182	−	33.9107i	−0.370584	−	1.14054i
$885$	0.661434	+	0.294489i	0.0222339	+	0.00989915i
$886$	−19.1191	−	4.06389i	−0.642319	−	0.136529i
$887$	−32.7804	+	6.96770i	−1.10066	+	0.233952i	−0.722213	−	0.691671i	$-0.756875\pi$
$887$	−32.7804	+	6.96770i	−1.10066	+	0.233952i	−0.378447	+	0.925623i	$0.623542\pi$
$888$	−4.04114	+	1.79923i	−0.135612	+	0.0603783i
$889$	−12.2992	−	13.6596i	−0.412501	−	0.458129i
$890$	1.08504	+	10.3234i	0.0363706	+	0.346043i
$891$	1.74194	−	1.26560i	0.0583573	−	0.0423991i
$892$	2.40247	−	22.8579i	0.0804405	−	0.765340i
$893$	3.47738	+	6.02299i	0.116366	+	0.201552i
$894$	−7.38767	+	12.7958i	−0.247081	+	0.427956i
$895$	−14.3288	−	10.4105i	−0.478959	−	0.347984i
$896$	−3.45721	+	3.83962i	−0.115497	+	0.128273i
$897$	1.68303	−	5.17983i	0.0561947	−	0.172949i
$898$	11.1292			0.371385
$899$	−6.71365	+	3.12261i	−0.223913	+	0.104145i
$900$	1.00000			0.0333333
$901$	−16.0024	+	49.2503i	−0.533117	+	1.64077i
$902$	15.9983	−	17.7679i	0.532684	−	0.591606i
$903$	−14.7039	−	10.6830i	−0.489317	−	0.355509i
$904$	0.864860	−	1.49798i	0.0287648	−	0.0498221i
$905$	−12.0826	−	20.9277i	−0.401639	−	0.695660i
$906$	0.993866	−	9.45600i	0.0330190	−	0.314155i
$907$	13.1959	−	9.58738i	0.438163	−	0.318344i	−0.346742	−	0.937961i	$-0.612712\pi$
$907$	13.1959	−	9.58738i	0.438163	−	0.318344i	0.784904	+	0.619617i	$0.212712\pi$
$908$	1.83197	+	17.4301i	0.0607961	+	0.578437i
$909$	−0.355108	−	0.394388i	−0.0117782	−	0.0130810i
$910$	28.6848	−	12.7713i	0.950892	−	0.423365i
$911$	−22.0956	+	4.69657i	−0.732060	+	0.155604i	−0.558836	−	0.829278i	$-0.688752\pi$
$911$	−22.0956	+	4.69657i	−0.732060	+	0.155604i	−0.173224	+	0.984882i	$0.555419\pi$
$912$	−1.35896	−	0.288855i	−0.0449995	−	0.00956495i
$913$	−27.2545	−	12.1345i	−0.901993	−	0.401593i
$914$	−9.32474	−	28.6986i	−0.308435	−	0.949265i
$915$	0.823773	+	2.53531i	0.0272331	+	0.0838148i
$916$	7.34923	+	3.27209i	0.242825	+	0.108113i
$917$	−6.46527	−	1.37424i	−0.213502	−	0.0453812i
$918$	−5.73888	+	1.21984i	−0.189411	+	0.0402606i
$919$	−42.4154	+	18.8846i	−1.39916	+	0.622945i	−0.961150	−	0.276027i	$-0.910982\pi$
$919$	−42.4154	+	18.8846i	−1.39916	+	0.622945i	−0.438007	+	0.898972i	$0.644315\pi$
$920$	0.599671	+	0.666002i	0.0197706	+	0.0219574i
$921$	0.664264	+	6.32005i	0.0218882	+	0.208253i
$922$	25.8566	−	18.7859i	0.851541	−	0.618681i
$923$	0.365279	−	3.47540i	0.0120233	−	0.114394i
$924$	5.56239	+	9.63434i	0.182989	+	0.316946i
$925$	−2.21179	+	3.83093i	−0.0727232	+	0.125960i
$926$	27.3369	+	19.8614i	0.898347	+	0.652687i
$927$	−9.72528	+	10.8010i	−0.319420	+	0.354752i
$928$	0.410947	−	1.26476i	0.0134900	−	0.0415179i
$929$	11.9159			0.390946			0.195473	−	0.980709i	$-0.437376\pi$
$929$	11.9159			0.390946			0.195473	+	0.980709i	$0.437376\pi$
$930$	3.79321	+	4.07573i	0.124384	+	0.133648i
$931$	27.3625			0.896771
$932$	6.43518	−	19.8055i	0.210791	−	0.648749i
$933$	8.89250	−	9.87612i	0.291127	−	0.323330i
$934$	32.9544	+	23.9428i	1.07830	+	0.783431i
$935$	6.31639	−	10.9403i	0.206568	−	0.357787i
$936$	3.03863	+	5.26305i	0.0993206	+	0.172028i
$937$	−1.14531	+	10.8969i	−0.0374158	+	0.355987i	0.959756	+	0.280834i	$0.0906111\pi$
$937$	−1.14531	+	10.8969i	−0.0374158	+	0.355987i	−0.997172	+	0.0751528i	$0.976056\pi$
$938$	61.3570	−	44.5785i	2.00338	−	1.45554i
$939$	0.300980	+	2.86363i	0.00982210	+	0.0934510i
$940$	3.34959	+	3.72010i	0.109252	+	0.121336i
$941$	−11.3522	+	5.05431i	−0.370070	+	0.164766i	−0.583341	−	0.812227i	$-0.698255\pi$
$941$	−11.3522	+	5.05431i	−0.370070	+	0.164766i	0.213271	+	0.976993i	$0.431588\pi$
$942$	−9.59052	+	2.03853i	−0.312476	+	0.0664188i
$943$	−9.73402	−	2.06903i	−0.316983	−	0.0673769i
$944$	−0.661434	−	0.294489i	−0.0215278	−	0.00958482i
$945$	−1.59660	−	4.91384i	−0.0519375	−	0.159847i
$946$	2.34056	+	7.20352i	0.0760983	+	0.234206i
$947$	6.72439	+	2.99389i	0.218513	+	0.0972884i	0.513074	−	0.858344i	$-0.328507\pi$
$947$	6.72439	+	2.99389i	0.218513	+	0.0972884i	−0.294561	+	0.955633i	$0.595173\pi$
$948$	−1.40807	−	0.299296i	−0.0457321	−	0.00972067i
$949$	54.8695	−	11.6629i	1.78114	−	0.378593i
$950$	−1.26920	+	0.565086i	−0.0411784	+	0.0183338i
$951$	15.5152	+	17.2313i	0.503114	+	0.558765i
$952$	−3.16863	−	30.1475i	−0.102696	−	0.977087i
$953$	13.9550	−	10.1389i	0.452048	−	0.328432i	−0.338356	−	0.941018i	$-0.609871\pi$
$953$	13.9550	−	10.1389i	0.452048	−	0.328432i	0.790404	+	0.612586i	$0.209871\pi$
$954$	0.922602	−	8.77797i	0.0298703	−	0.284197i
$955$	3.59028	+	6.21855i	0.116179	+	0.201228i
$956$	−1.12657	+	1.95127i	−0.0364357	+	0.0631085i
$957$	−2.31653	−	1.68306i	−0.0748827	−	0.0544055i
$958$	−7.34830	+	8.16111i	−0.237413	+	0.263673i
$959$	−19.3417	+	59.5278i	−0.624578	+	1.92225i
$960$	−1.00000			−0.0322749
$961$	−2.22315	+	30.9202i	−0.0717144	+	0.997425i
$962$	−26.8832			−0.866749
$963$	3.62596	−	11.1596i	0.116845	−	0.359612i
$964$	16.2975	−	18.1002i	0.524906	−	0.582967i
$965$	12.7364	+	9.25357i	0.410001	+	0.297883i
$966$	2.31519	−	4.01003i	0.0744900	−	0.129021i
$967$	−16.4036	−	28.4119i	−0.527505	−	0.913666i	−0.999486	−	0.0320569i	$-0.989794\pi$
$967$	−16.4036	−	28.4119i	−0.527505	−	0.913666i	0.471981	−	0.881609i	$-0.343539\pi$
$968$	−0.665208	+	6.32903i	−0.0213806	+	0.203423i
$969$	6.59449	−	4.79118i	0.211846	−	0.153915i
$970$	0.307126	+	2.92211i	0.00986121	+	0.0938232i
$971$	29.7246	+	33.0125i	0.953907	+	1.05942i	0.998174	+	0.0604017i	$0.0192382\pi$
$971$	29.7246	+	33.0125i	0.953907	+	1.05942i	−0.0442668	+	0.999020i	$0.514095\pi$
$972$	0.913545	−	0.406737i	0.0293020	−	0.0130461i
$973$	−40.6206	+	8.63417i	−1.30224	+	0.276799i
$974$	−15.0705	−	3.20334i	−0.482891	−	0.102642i
$975$	5.55185	+	2.47184i	0.177801	+	0.0791623i
$976$	−0.823773	−	2.53531i	−0.0263683	−	0.0811534i
$977$	−15.4623	−	47.5881i	−0.494683	−	1.52248i	−0.817450	−	0.575999i	$-0.804613\pi$
$977$	−15.4623	−	47.5881i	−0.494683	−	1.52248i	0.322768	−	0.946478i	$-0.395387\pi$
$978$	16.0949	+	7.16591i	0.514658	+	0.229140i
$979$	−21.8621	−	4.64693i	−0.698715	−	0.148516i
$980$	19.2646	−	4.09481i	0.615385	−	0.130804i
$981$	−0.662334	+	0.294890i	−0.0211467	+	0.00941511i
$982$	11.1911	+	12.4290i	0.357123	+	0.396626i
$983$	−3.67447	−	34.9603i	−0.117197	−	1.11506i	−0.882149	−	0.470971i	$-0.843904\pi$
$983$	−3.67447	−	34.9603i	−0.117197	−	1.11506i	0.764951	−	0.644088i	$-0.222763\pi$
$984$	8.98346	−	6.52686i	0.286382	−	0.208069i
$985$	0.790164	−	7.51791i	0.0251767	−	0.239540i
$986$	3.90118	+	6.75704i	0.124239	+	0.215188i
$987$	12.9320	−	22.3989i	0.411630	−	0.712964i
$988$	−6.83071	−	4.96280i	−0.217314	−	0.157888i
$989$	2.10948	−	2.34281i	0.0670774	−	0.0744970i
$990$	−0.665363	+	2.04778i	−0.0211466	+	0.0650827i
$991$	49.6210			1.57626			0.788132	−	0.615506i	$-0.211048\pi$
$991$	49.6210			1.57626			0.788132	+	0.615506i	$0.211048\pi$
$992$	−3.79321	−	4.07573i	−0.120434	−	0.129405i
$993$	−24.5308			−0.778462
$994$	0.918079	−	2.82556i	0.0291197	−	0.0896212i
$995$	13.1348	−	14.5876i	0.416400	−	0.462459i
$996$	−11.2096	−	8.14424i	−0.355189	−	0.258060i
$997$	−30.5717	+	52.9518i	−0.968217	+	1.67700i	−0.267505	+	0.963556i	$0.586199\pi$
$997$	−30.5717	+	52.9518i	−0.968217	+	1.67700i	−0.700712	+	0.713445i	$0.747134\pi$
$998$	14.1674	+	24.5387i	0.448462	+	0.776758i
$999$	−0.462390	+	4.39935i	−0.0146294	+	0.139189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.i.541.1	yes	24
31.20	even	15	inner	930.2.bg.i.361.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.i.361.1	✓	24	31.20	even	15	inner
930.2.bg.i.541.1	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.540069 + 5.13841i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.540069 + 5.13841i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(0.669131 + 0.743145i) q^{10} +(-1.96701 + 0.875770i) q^{11} +(-0.978148 + 0.207912i) q^{12} +(-5.94445 - 1.26353i) q^{13} +(-4.72003 - 2.10149i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-5.35985 - 2.38636i) q^{17} +(0.978148 + 0.207912i) q^{18} +(-1.35896 + 0.288855i) q^{19} +(-0.913545 + 0.406737i) q^{20} +(3.45721 + 3.83962i) q^{21} +(-0.225067 - 2.14137i) q^{22} +(-0.725036 + 0.526770i) q^{23} +(0.104528 - 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(3.03863 - 5.26305i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(3.45721 - 3.83962i) q^{28} +(-0.410947 + 1.26476i) q^{29} +1.00000 q^{30} +(3.79321 + 4.07573i) q^{31} -1.00000 q^{32} +(-0.665363 + 2.04778i) q^{33} +(3.92585 - 4.36010i) q^{34} +(4.17996 + 3.03692i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.21179 - 3.83093i) q^{37} +(0.145223 - 1.38171i) q^{38} +(-4.91660 + 3.57212i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(7.43013 + 8.25200i) q^{41} +(-4.72003 + 2.10149i) q^{42} +(-3.44085 + 0.731376i) q^{43} +(2.10611 + 0.447667i) q^{44} +(-0.913545 - 0.406737i) q^{45} +(-0.276939 - 0.852331i) q^{46} +(-1.54690 - 4.76088i) q^{47} +(0.913545 + 0.406737i) q^{48} +(-19.2646 - 4.09481i) q^{49} +(0.978148 - 0.207912i) q^{50} +(-5.35985 + 2.38636i) q^{51} +(4.06647 + 4.51628i) q^{52} +(-0.922602 - 8.77797i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-0.225067 + 2.14137i) q^{55} +(2.58336 + 4.47451i) q^{56} +(-0.694658 + 1.20318i) q^{57} +(-1.07587 - 0.781668i) q^{58} +(-0.484470 + 0.538059i) q^{59} +(-0.309017 + 0.951057i) q^{60} -2.66579 q^{61} +(-5.04842 + 2.34809i) q^{62} +5.16672 q^{63} +(0.309017 - 0.951057i) q^{64} +(-4.06647 + 4.51628i) q^{65} +(-1.74194 - 1.26560i) q^{66} +(-7.33942 + 12.7123i) q^{67} +(2.93354 + 5.08105i) q^{68} +(-0.0936778 + 0.891284i) q^{69} +(-4.17996 + 3.03692i) q^{70} +(0.0601060 + 0.571870i) q^{71} +(-0.669131 - 0.743145i) q^{72} +(-8.43237 + 3.75433i) q^{73} +(4.32691 - 0.919714i) q^{74} +(-0.978148 - 0.207912i) q^{75} +(1.26920 + 0.565086i) q^{76} +(-3.43774 - 10.5803i) q^{77} +(-1.87797 - 5.77981i) q^{78} +(1.31508 + 0.585510i) q^{79} +(0.978148 + 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-10.1442 + 4.51647i) q^{82} +(9.27134 + 10.2969i) q^{83} +(-0.540069 - 5.13841i) q^{84} +(-4.74657 + 3.44859i) q^{85} +(0.367702 - 3.49845i) q^{86} +(0.664926 + 1.15169i) q^{87} +(-1.07658 + 1.86469i) q^{88} +(8.39785 + 6.10139i) q^{89} +(0.669131 - 0.743145i) q^{90} +(9.70296 - 29.8626i) q^{91} +0.896194 q^{92} +(5.56701 - 0.0917075i) q^{93} +5.00588 q^{94} +(-0.429322 + 1.32132i) q^{95} +(-0.669131 + 0.743145i) q^{96} +(2.37706 + 1.72703i) q^{97} +(9.84748 - 17.0563i) q^{98} +(1.07658 + 1.86469i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 13 * q^11 + 3 * q^12 + 11 * q^13 - 8 * q^14 + 6 * q^15 - 6 * q^16 - 29 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^20 - 2 * q^21 - 17 * q^22 - 5 * q^23 - 3 * q^24 - 12 * q^25 + 9 * q^26 - 6 * q^27 - 2 * q^28 + 13 * q^29 + 24 * q^30 + 57 * q^31 - 24 * q^32 + 16 * q^33 + 29 * q^34 + q^35 - 12 * q^36 - 24 * q^37 + 6 * q^38 - 17 * q^39 + 3 * q^40 + 32 * q^41 - 8 * q^42 + 49 * q^43 - 8 * q^44 - 3 * q^45 + 28 * q^47 + 3 * q^48 + 12 * q^49 - 3 * q^50 - 29 * q^51 - 19 * q^52 - 36 * q^53 + 6 * q^54 - 17 * q^55 - 3 * q^56 - 6 * q^57 + 2 * q^58 + 6 * q^60 + 33 * q^62 - 6 * q^63 - 6 * q^64 + 19 * q^65 + 4 * q^66 - 5 * q^67 + 11 * q^68 + 10 * q^69 - q^70 - 11 * q^71 - 3 * q^72 - 13 * q^73 + 9 * q^74 + 3 * q^75 - 6 * q^76 + 4 * q^77 - 8 * q^78 - 68 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 + 10 * q^83 - 7 * q^84 + 2 * q^85 - 34 * q^86 + 11 * q^87 - 12 * q^88 + 55 * q^89 + 3 * q^90 + 38 * q^91 + 10 * q^92 + 19 * q^93 + 42 * q^94 + 18 * q^95 - 3 * q^96 - q^97 + 63 * q^98 + 12 * q^99

Introduction

L-functions

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