LMFDB - Embedded newform 930.2.bg.f.361.1

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:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	16.0.1669788916259765625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 16x^{14} + 90x^{12} + 239x^{10} + 329x^{8} + 239x^{6} + 90x^{4} + 16x^{2} + 1 $ x^16 + 16x^14 + 90x^12 + 239x^10 + 329x^8 + 239x^6 + 90x^4 + 16*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			361.1
Root			$-0.361487i$ of defining polynomial
Character	$\chi$	$=$	930.361
Dual form			930.2.bg.f.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.0662721 - 0.630537i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(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} +(-0.0662721 - 0.630537i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(4.10593 + 1.82808i) q^{11} +(-0.978148 - 0.207912i) q^{12} +(-0.188862 + 0.0401438i) q^{13} +(-0.579197 + 0.257875i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.34897 + 1.49106i) q^{17} +(0.978148 - 0.207912i) q^{18} +(4.11030 + 0.873672i) q^{19} +(0.913545 + 0.406737i) q^{20} +(0.424235 - 0.471161i) q^{21} +(0.469803 - 4.46988i) q^{22} +(3.42283 + 2.48683i) q^{23} +(0.104528 + 0.994522i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.0965405 + 0.167213i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.424235 + 0.471161i) q^{28} +(-0.643213 - 1.97961i) q^{29} -1.00000 q^{30} +(4.61162 - 3.11977i) q^{31} -1.00000 q^{32} +(1.38888 + 4.27453i) q^{33} +(2.45297 + 2.72430i) q^{34} +(-0.512925 + 0.372662i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.86215 - 3.22535i) q^{37} +(-0.439242 - 4.17911i) q^{38} +(-0.156206 - 0.113490i) q^{39} +(0.104528 - 0.994522i) q^{40} +(0.000998901 - 0.00110939i) q^{41} +(-0.579197 - 0.257875i) q^{42} +(6.41595 + 1.36375i) q^{43} +(-4.39629 + 0.934460i) q^{44} +(0.913545 - 0.406737i) q^{45} +(1.30740 - 4.02377i) q^{46} +(0.500395 - 1.54006i) q^{47} +(0.913545 - 0.406737i) q^{48} +(6.45385 - 1.37181i) q^{49} +(0.978148 + 0.207912i) q^{50} +(-3.34897 - 1.49106i) q^{51} +(0.129196 - 0.143487i) q^{52} +(-0.161026 + 1.53206i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-0.469803 - 4.46988i) q^{55} +(0.317005 - 0.549069i) q^{56} +(2.10107 + 3.63915i) q^{57} +(-1.68395 + 1.22346i) q^{58} +(1.32764 + 1.47450i) q^{59} +(0.309017 + 0.951057i) q^{60} +9.00433 q^{61} +(-4.39215 - 3.42185i) q^{62} +0.634010 q^{63} +(0.309017 + 0.951057i) q^{64} +(0.129196 + 0.143487i) q^{65} +(3.63613 - 2.64180i) q^{66} +(1.19645 + 2.07232i) q^{67} +(1.83295 - 3.17476i) q^{68} +(0.442244 + 4.20767i) q^{69} +(0.512925 + 0.372662i) q^{70} +(0.115531 - 1.09920i) q^{71} +(-0.669131 + 0.743145i) q^{72} +(10.0086 + 4.45610i) q^{73} +(-3.64292 - 0.774327i) q^{74} +(-0.978148 + 0.207912i) q^{75} +(-3.83884 + 1.70916i) q^{76} +(0.880562 - 2.71009i) q^{77} +(-0.0596653 + 0.183631i) q^{78} +(-3.81812 + 1.69994i) q^{79} +(-0.978148 + 0.207912i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-0.00136377 - 0.000607190i) q^{82} +(-4.18090 + 4.64336i) q^{83} +(-0.0662721 + 0.630537i) q^{84} +(2.96578 + 2.15476i) q^{85} +(-0.685632 - 6.52335i) q^{86} +(1.04074 - 1.80261i) q^{87} +(2.24725 + 3.89235i) q^{88} +(-6.23989 + 4.53354i) q^{89} +(-0.669131 - 0.743145i) q^{90} +(0.0378284 + 0.116424i) q^{91} -4.23085 q^{92} +(5.40422 + 1.33957i) q^{93} -1.61931 q^{94} +(-1.29853 - 3.99646i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(-4.10581 + 2.98305i) q^{97} +(-3.29902 - 5.71406i) q^{98} +(-2.24725 + 3.89235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} - 13 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 - 13 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} - 13 q^{7} + 4 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{14} - 4 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{18} + 9 q^{19} + 2 q^{20} + 2 q^{21} - 13 q^{22} - 3 q^{23} - 2 q^{24} - 8 q^{25} + q^{26} - 4 q^{27} + 2 q^{28} - q^{29} - 16 q^{30} - 19 q^{31} - 16 q^{32} + 14 q^{33} + 4 q^{34} + 11 q^{35} - 8 q^{36} - 3 q^{37} + 6 q^{38} - 13 q^{39} - 2 q^{40} - 2 q^{42} + 2 q^{43} - 7 q^{44} + 2 q^{45} - 7 q^{46} - q^{47} + 2 q^{48} + 3 q^{49} - 2 q^{50} + 6 q^{51} - 6 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} - 7 q^{56} - 6 q^{57} - 4 q^{58} + 16 q^{59} - 4 q^{60} - 28 q^{61} - 21 q^{62} - 14 q^{63} - 4 q^{64} - 6 q^{65} + 11 q^{66} + 47 q^{67} - 4 q^{68} + 9 q^{69} - 11 q^{70} + 3 q^{71} - 2 q^{72} - 27 q^{73} + 8 q^{74} + 2 q^{75} - 6 q^{76} + 14 q^{77} - 12 q^{78} + 4 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} + 66 q^{83} - 13 q^{84} + 18 q^{85} + 13 q^{86} + 3 q^{87} - 3 q^{88} - 45 q^{89} - 2 q^{90} + 12 q^{91} - 8 q^{92} - 26 q^{93} + 36 q^{94} - 18 q^{95} - 2 q^{96} + 5 q^{97} - 13 q^{98} + 3 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 - 13 * q^7 + 4 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 6 * q^13 - 2 * q^14 - 4 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^18 + 9 * q^19 + 2 * q^20 + 2 * q^21 - 13 * q^22 - 3 * q^23 - 2 * q^24 - 8 * q^25 + q^26 - 4 * q^27 + 2 * q^28 - q^29 - 16 * q^30 - 19 * q^31 - 16 * q^32 + 14 * q^33 + 4 * q^34 + 11 * q^35 - 8 * q^36 - 3 * q^37 + 6 * q^38 - 13 * q^39 - 2 * q^40 - 2 * q^42 + 2 * q^43 - 7 * q^44 + 2 * q^45 - 7 * q^46 - q^47 + 2 * q^48 + 3 * q^49 - 2 * q^50 + 6 * q^51 - 6 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 - 7 * q^56 - 6 * q^57 - 4 * q^58 + 16 * q^59 - 4 * q^60 - 28 * q^61 - 21 * q^62 - 14 * q^63 - 4 * q^64 - 6 * q^65 + 11 * q^66 + 47 * q^67 - 4 * q^68 + 9 * q^69 - 11 * q^70 + 3 * q^71 - 2 * q^72 - 27 * q^73 + 8 * q^74 + 2 * q^75 - 6 * q^76 + 14 * q^77 - 12 * q^78 + 4 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 + 66 * q^83 - 13 * q^84 + 18 * q^85 + 13 * q^86 + 3 * q^87 - 3 * q^88 - 45 * q^89 - 2 * q^90 + 12 * q^91 - 8 * q^92 - 26 * q^93 + 36 * q^94 - 18 * q^95 - 2 * q^96 + 5 * q^97 - 13 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{15}\right)$

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
$7$	−0.0662721	−	0.630537i	−0.0250485	−	0.238321i	−0.999882	−	0.0153848i	$-0.995103\pi$
$7$	−0.0662721	−	0.630537i	−0.0250485	−	0.238321i	0.974833	−	0.222936i	$-0.0715640\pi$
$8$	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
$11$	4.10593	+	1.82808i	1.23799	+	0.551186i	0.918130	−	0.396280i	$-0.129699\pi$
$11$	4.10593	+	1.82808i	1.23799	+	0.551186i	0.319855	+	0.947466i	$0.396366\pi$
$12$	−0.978148	−	0.207912i	−0.282367	−	0.0600189i
$13$	−0.188862	+	0.0401438i	−0.0523808	+	0.0111339i	−0.234028	−	0.972230i	$-0.575191\pi$
$13$	−0.188862	+	0.0401438i	−0.0523808	+	0.0111339i	0.181647	+	0.983364i	$0.441857\pi$
$14$	−0.579197	+	0.257875i	−0.154797	+	0.0689200i
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−3.34897	+	1.49106i	−0.812244	+	0.361634i	−0.770457	−	0.637492i	$-0.779972\pi$
$17$	−3.34897	+	1.49106i	−0.812244	+	0.361634i	−0.0417872	+	0.999127i	$0.513305\pi$
$18$	0.978148	−	0.207912i	0.230552	−	0.0490053i
$19$	4.11030	+	0.873672i	0.942969	+	0.200434i	0.653649	−	0.756798i	$-0.273237\pi$
$19$	4.11030	+	0.873672i	0.942969	+	0.200434i	0.289320	+	0.957232i	$0.406571\pi$
$20$	0.913545	+	0.406737i	0.204275	+	0.0909491i
$21$	0.424235	−	0.471161i	0.0925758	−	0.102816i
$22$	0.469803	−	4.46988i	0.100162	−	0.952982i
$23$	3.42283	+	2.48683i	0.713709	+	0.518540i	0.884368	−	0.466790i	$-0.154590\pi$
$23$	3.42283	+	2.48683i	0.713709	+	0.518540i	−0.170659	+	0.985330i	$0.554590\pi$
$24$	0.104528	+	0.994522i	0.0213368	+	0.203006i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.0965405	+	0.167213i	0.0189331	+	0.0327932i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	0.424235	+	0.471161i	0.0801730	+	0.0890411i
$29$	−0.643213	−	1.97961i	−0.119442	−	0.367604i	0.873406	−	0.486993i	$-0.161906\pi$
$29$	−0.643213	−	1.97961i	−0.119442	−	0.367604i	−0.992847	+	0.119389i	$0.961906\pi$
$30$	−1.00000			−0.182574
$31$	4.61162	−	3.11977i	0.828271	−	0.560327i
$31$	4.61162	−	3.11977i	0.828271	−	0.560327i
$32$	−1.00000			−0.176777
$33$	1.38888	+	4.27453i	0.241773	+	0.744099i
$34$	2.45297	+	2.72430i	0.420680	+	0.467213i
$35$	−0.512925	+	0.372662i	−0.0867001	+	0.0629913i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	1.86215	−	3.22535i	0.306136	−	0.530243i	−0.671377	−	0.741116i	$-0.734297\pi$
$37$	1.86215	−	3.22535i	0.306136	−	0.530243i	0.977514	+	0.210872i	$0.0676304\pi$
$38$	−0.439242	−	4.17911i	−0.0712545	−	0.677941i
$39$	−0.156206	−	0.113490i	−0.0250129	−	0.0181730i
$40$	0.104528	−	0.994522i	0.0165274	−	0.157248i
$41$	0.000998901	−	0.00110939i	0.000156002	−	0.000173258i	−0.743067	−	0.669217i	$-0.766630\pi$
$41$	0.000998901	−	0.00110939i	0.000156002	−	0.000173258i	0.743223	+	0.669044i	$0.233296\pi$
$42$	−0.579197	−	0.257875i	−0.0893720	−	0.0397910i
$43$	6.41595	+	1.36375i	0.978423	+	0.207970i	0.669251	−	0.743036i	$-0.266615\pi$
$43$	6.41595	+	1.36375i	0.978423	+	0.207970i	0.309171	+	0.951006i	$0.399948\pi$
$44$	−4.39629	+	0.934460i	−0.662765	+	0.140875i
$45$	0.913545	−	0.406737i	0.136183	−	0.0606327i
$46$	1.30740	−	4.02377i	0.192766	−	0.593273i
$47$	0.500395	−	1.54006i	0.0729901	−	0.224640i	−0.907906	−	0.419175i	$-0.862320\pi$
$47$	0.500395	−	1.54006i	0.0729901	−	0.224640i	0.980896	+	0.194534i	$0.0623195\pi$
$48$	0.913545	−	0.406737i	0.131859	−	0.0587074i
$49$	6.45385	−	1.37181i	0.921978	−	0.195973i
$50$	0.978148	+	0.207912i	0.138331	+	0.0294032i
$51$	−3.34897	−	1.49106i	−0.468949	−	0.208790i
$52$	0.129196	−	0.143487i	0.0179163	−	0.0198981i
$53$	−0.161026	+	1.53206i	−0.0221186	+	0.210444i	0.977881	+	0.209164i	$0.0670742\pi$
$53$	−0.161026	+	1.53206i	−0.0221186	+	0.210444i	−0.999999	+	0.00128025i	$0.999592\pi$
$54$	0.809017	+	0.587785i	0.110093	+	0.0799874i
$55$	−0.469803	−	4.46988i	−0.0633483	−	0.602719i
$56$	0.317005	−	0.549069i	0.0423616	−	0.0733724i
$57$	2.10107	+	3.63915i	0.278293	+	0.482018i
$58$	−1.68395	+	1.22346i	−0.221114	+	0.160649i
$59$	1.32764	+	1.47450i	0.172844	+	0.191963i	0.823343	−	0.567545i	$-0.192107\pi$
$59$	1.32764	+	1.47450i	0.172844	+	0.191963i	−0.650498	+	0.759508i	$0.725440\pi$
$60$	0.309017	+	0.951057i	0.0398939	+	0.122781i
$61$	9.00433			1.15289			0.576443	−	0.817137i	$-0.304440\pi$
$61$	9.00433			1.15289			0.576443	+	0.817137i	$0.304440\pi$
$62$	−4.39215	−	3.42185i	−0.557803	−	0.434575i
$63$	0.634010			0.0798777
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	0.129196	+	0.143487i	0.0160248	+	0.0177974i
$66$	3.63613	−	2.64180i	0.447576	−	0.325183i
$67$	1.19645	+	2.07232i	0.146170	+	0.253174i	0.929809	−	0.368043i	$-0.119972\pi$
$67$	1.19645	+	2.07232i	0.146170	+	0.253174i	−0.783639	+	0.621217i	$0.786639\pi$
$68$	1.83295	−	3.17476i	0.222278	−	0.384997i
$69$	0.442244	+	4.20767i	0.0532399	+	0.506544i
$70$	0.512925	+	0.372662i	0.0613062	+	0.0445416i
$71$	0.115531	−	1.09920i	0.0137110	−	0.130452i	−0.985525	−	0.169529i	$-0.945775\pi$
$71$	0.115531	−	1.09920i	0.0137110	−	0.130452i	0.999236	+	0.0390776i	$0.0124420\pi$
$72$	−0.669131	+	0.743145i	−0.0788578	+	0.0875805i
$73$	10.0086	+	4.45610i	1.17141	+	0.521547i	0.897848	−	0.440306i	$-0.145130\pi$
$73$	10.0086	+	4.45610i	1.17141	+	0.521547i	0.273566	+	0.961853i	$0.411797\pi$
$74$	−3.64292	−	0.774327i	−0.423481	−	0.0900137i
$75$	−0.978148	+	0.207912i	−0.112947	+	0.0240076i
$76$	−3.83884	+	1.70916i	−0.440345	+	0.196054i
$77$	0.880562	−	2.71009i	0.100349	−	0.308844i
$78$	−0.0596653	+	0.183631i	−0.00675576	+	0.0207921i
$79$	−3.81812	+	1.69994i	−0.429572	+	0.191258i	−0.610121	−	0.792308i	$-0.708879\pi$
$79$	−3.81812	+	1.69994i	−0.429572	+	0.191258i	0.180549	+	0.983566i	$0.442213\pi$
$80$	−0.978148	+	0.207912i	−0.109360	+	0.0232452i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−0.00136377		0.000607190i	−0.000150603		6.70530e-5i
$83$	−4.18090	+	4.64336i	−0.458914	+	0.509675i	−0.927541	−	0.373720i	$-0.878082\pi$
$83$	−4.18090	+	4.64336i	−0.458914	+	0.509675i	0.468628	+	0.883396i	$0.344749\pi$
$84$	−0.0662721	+	0.630537i	−0.00723088	+	0.0687972i
$85$	2.96578	+	2.15476i	0.321684	+	0.233717i
$86$	−0.685632	−	6.52335i	−0.0739336	−	0.703431i
$87$	1.04074	−	1.80261i	0.111579	−	0.193261i
$88$	2.24725	+	3.89235i	0.239558	+	0.414926i
$89$	−6.23989	+	4.53354i	−0.661427	+	0.480555i	−0.867144	−	0.498057i	$-0.834047\pi$
$89$	−6.23989	+	4.53354i	−0.661427	+	0.480555i	0.205718	+	0.978611i	$0.434047\pi$
$90$	−0.669131	−	0.743145i	−0.0705326	−	0.0783343i
$91$	0.0378284	+	0.116424i	0.00396549	+	0.0122045i
$92$	−4.23085			−0.441096
$93$	5.40422	+	1.33957i	0.560391	+	0.138907i
$94$	−1.61931			−0.167019
$95$	−1.29853	−	3.99646i	−0.133226	−	0.410029i
$96$	−0.669131	−	0.743145i	−0.0682929	−	0.0758469i
$97$	−4.10581	+	2.98305i	−0.416882	+	0.302883i	−0.776382	−	0.630262i	$-0.782947\pi$
$97$	−4.10581	+	2.98305i	−0.416882	+	0.302883i	0.359500	+	0.933145i	$0.382947\pi$
$98$	−3.29902	−	5.71406i	−0.333251	−	0.577208i
$99$	−2.24725	+	3.89235i	−0.225857	+	0.391196i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	5.16933	+	3.75574i	0.514368	+	0.373710i	0.814478	−	0.580195i	$-0.197024\pi$
$101$	5.16933	+	3.75574i	0.514368	+	0.373710i	−0.300110	+	0.953904i	$0.597024\pi$
$102$	−0.383191	+	3.64582i	−0.0379416	+	0.360990i
$103$	0.763915	−	0.848413i	0.0752707	−	0.0835966i	−0.704333	−	0.709870i	$-0.748754\pi$
$103$	0.763915	−	0.848413i	0.0752707	−	0.0835966i	0.779604	+	0.626273i	$0.215420\pi$
$104$	−0.176388	−	0.0785331i	−0.0172963	−	0.00770080i
$105$	−0.620155	−	0.131818i	−0.0605210	−	0.0128641i
$106$	1.50683	−	0.320287i	0.146356	−	0.0311090i
$107$	−4.95915	+	2.20796i	−0.479420	+	0.213451i	−0.632195	−	0.774810i	$-0.717846\pi$
$107$	−4.95915	+	2.20796i	−0.479420	+	0.213451i	0.152775	+	0.988261i	$0.451179\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	1.36645	−	4.20552i	0.130883	−	0.402815i	−0.864044	−	0.503416i	$-0.832076\pi$
$109$	1.36645	−	4.20552i	0.130883	−	0.402815i	0.994927	+	0.100601i	$0.0320764\pi$
$110$	−4.10593	+	1.82808i	−0.391485	+	0.174300i
$111$	3.64292	−	0.774327i	0.345771	−	0.0734959i
$112$	−0.620155	−	0.131818i	−0.0585992	−	0.0124556i
$113$	−15.2795	−	6.80286i	−1.43737	−	0.639960i	−0.467594	−	0.883944i	$-0.654879\pi$
$113$	−15.2795	−	6.80286i	−1.43737	−	0.639960i	−0.969779	+	0.243984i	$0.921546\pi$
$114$	2.81177	−	3.12279i	0.263347	−	0.292476i
$115$	0.442244	−	4.20767i	0.0412395	−	0.392367i
$116$	1.68395	+	1.22346i	0.156351	+	0.113596i
$117$	−0.0201825	−	0.192023i	−0.00186587	−	0.0177526i
$118$	0.992066	−	1.71831i	0.0913271	−	0.158183i
$119$	1.16211	+	2.01283i	0.106530	+	0.184516i
$120$	0.809017	−	0.587785i	0.0738528	−	0.0536572i
$121$	6.15637	+	6.83734i	0.559670	+	0.621576i
$122$	−2.78249	−	8.56363i	−0.251915	−	0.775314i
$123$	0.00149283			0.000134604
$124$	−1.89712	+	5.23459i	−0.170367	+	0.470080i
$125$	1.00000			0.0894427
$126$	−0.195920	−	0.602979i	−0.0174539	−	0.0537177i
$127$	−12.4772	−	13.8574i	−1.10718	−	1.22964i	−0.971031	−	0.238955i	$-0.923195\pi$
$127$	−12.4772	−	13.8574i	−1.10718	−	1.22964i	−0.136146	−	0.990689i	$-0.543472\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	3.27964	+	5.68050i	0.288756	+	0.500141i
$130$	0.0965405	−	0.167213i	0.00846716	−	0.0146655i
$131$	−0.373275	−	3.55148i	−0.0326132	−	0.310294i	−0.998652	−	0.0518983i	$-0.983473\pi$
$131$	−0.373275	−	3.55148i	−0.0326132	−	0.310294i	0.966039	−	0.258396i	$-0.0831938\pi$
$132$	−3.63613	−	2.64180i	−0.316484	−	0.229939i
$133$	0.278484	−	2.64960i	0.0241476	−	0.229749i
$134$	1.60117	−	1.77828i	0.138320	−	0.153620i
$135$	0.913545	+	0.406737i	0.0786255	+	0.0350063i
$136$	−3.58579	−	0.762184i	−0.307479	−	0.0653567i
$137$	0.492445	−	0.104672i	0.0420724	−	0.00894277i	−0.186827	−	0.982393i	$-0.559821\pi$
$137$	0.492445	−	0.104672i	0.0420724	−	0.00894277i	0.228900	+	0.973450i	$0.426487\pi$
$138$	3.86507	−	1.72084i	0.329017	−	0.146488i
$139$	5.57942	−	17.1717i	0.473240	−	1.45648i	−0.375076	−	0.926994i	$-0.622383\pi$
$139$	5.57942	−	17.1717i	0.473240	−	1.45648i	0.848316	−	0.529490i	$-0.177617\pi$
$140$	0.195920	−	0.602979i	0.0165583	−	0.0509611i
$141$	1.47932	−	0.658634i	0.124581	−	0.0554670i
$142$	−1.08111	+	0.229796i	−0.0907245	+	0.0192841i
$143$	−0.848839	−	0.180426i	−0.0709835	−	0.0150880i
$144$	0.913545	+	0.406737i	0.0761288	+	0.0338947i
$145$	−1.39278	+	1.54684i	−0.115664	+	0.128458i
$146$	1.14519	−	10.8957i	0.0947763	−	0.901737i
$147$	5.33792	+	3.87823i	0.440264	+	0.319871i
$148$	0.389296	+	3.70391i	0.0319999	+	0.304459i
$149$	1.27456	−	2.20761i	0.104416	−	0.180855i	−0.809083	−	0.587694i	$-0.800036\pi$
$149$	1.27456	−	2.20761i	0.104416	−	0.180855i	0.913500	+	0.406840i	$0.133369\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	−15.7807	+	11.4654i	−1.28422	+	0.933038i	−0.999672	−	0.0256248i	$-0.991842\pi$
$151$	−15.7807	+	11.4654i	−1.28422	+	0.933038i	−0.284545	+	0.958663i	$0.591842\pi$
$152$	2.81177	+	3.12279i	0.228065	+	0.253292i
$153$	−1.13283	−	3.48648i	−0.0915835	−	0.281865i
$154$	−2.84956			−0.229624
$155$	−5.00761	−	2.43390i	−0.402221	−	0.195495i
$156$	0.193081			0.0154588
$157$	−1.37501	−	4.23184i	−0.109738	−	0.337738i	0.881075	−	0.472976i	$-0.156820\pi$
$157$	−1.37501	−	4.23184i	−0.109738	−	0.337738i	−0.990813	+	0.135238i	$0.956820\pi$
$158$	2.79660	+	3.10594i	0.222486	+	0.247095i
$159$	−1.24629	+	0.905480i	−0.0988369	+	0.0718092i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	1.34120	−	2.32303i	0.105701	−	0.183080i
$162$	0.104528	+	0.994522i	0.00821253	+	0.0781370i
$163$	−13.5280	−	9.82867i	−1.05959	−	0.769841i	−0.0855814	−	0.996331i	$-0.527275\pi$
$163$	−13.5280	−	9.82867i	−1.05959	−	0.769841i	−0.974013	+	0.226491i	$0.927275\pi$
$164$	−0.000156044		0.00148466i	−1.21850e−5		0.000115932i
$165$	3.00741	−	3.34007i	0.234126	−	0.260024i
$166$	5.70807	+	2.54140i	0.443032	+	0.197251i
$167$	−16.4878	−	3.50458i	−1.27586	−	0.271193i	−0.480320	−	0.877093i	$-0.659480\pi$
$167$	−16.4878	−	3.50458i	−1.27586	−	0.271193i	−0.795540	+	0.605901i	$0.792813\pi$
$168$	0.620155	−	0.131818i	0.0478460	−	0.0101700i
$169$	−11.8420	+	5.27241i	−0.910926	+	0.405570i
$170$	1.13283	−	3.48648i	0.0868838	−	0.267401i
$171$	−1.29853	+	3.99646i	−0.0993011	+	0.305617i
$172$	−5.99220	+	2.66790i	−0.456901	+	0.203425i
$173$	−8.94652	+	1.90164i	−0.680192	+	0.144579i	−0.535035	−	0.844830i	$-0.679702\pi$
$173$	−8.94652	+	1.90164i	−0.680192	+	0.144579i	−0.145156	+	0.989409i	$0.546368\pi$
$174$	−2.03600	−	0.432764i	−0.154348	−	0.0328078i
$175$	0.579197	+	0.257875i	0.0437832	+	0.0194935i
$176$	3.00741	−	3.34007i	0.226692	−	0.251767i
$177$	−0.207398	+	1.97326i	−0.0155890	+	0.148320i
$178$	6.23989	+	4.53354i	0.467699	+	0.339803i
$179$	0.811490	+	7.72081i	0.0606536	+	0.577080i	0.982072	+	0.188508i	$0.0603651\pi$
$179$	0.811490	+	7.72081i	0.0606536	+	0.577080i	−0.921418	+	0.388573i	$0.872968\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	2.62248	+	4.54227i	0.194928	+	0.337625i	0.946877	−	0.321597i	$-0.104219\pi$
$181$	2.62248	+	4.54227i	0.194928	+	0.337625i	−0.751949	+	0.659221i	$0.770886\pi$
$182$	0.0990360	−	0.0719539i	0.00734104	−	0.00533358i
$183$	6.02507	+	6.69152i	0.445386	+	0.494652i
$184$	1.30740	+	4.02377i	0.0963831	+	0.296637i
$185$	−3.72431			−0.273817
$186$	−0.395989	−	5.55366i	−0.0290353	−	0.407214i
$187$	−16.4764			−1.20487
$188$	0.500395	+	1.54006i	0.0364951	+	0.112320i
$189$	0.424235	+	0.471161i	0.0308586	+	0.0342719i
$190$	−3.39960	+	2.46995i	−0.246633	+	0.179189i
$191$	−0.302866	−	0.524579i	−0.0219146	−	0.0379572i	0.854860	−	0.518859i	$-0.173643\pi$
$191$	−0.302866	−	0.524579i	−0.0219146	−	0.0379572i	−0.876775	+	0.480901i	$0.840310\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	1.60988	+	15.3169i	0.115881	+	1.10254i	0.885695	+	0.464268i	$0.153683\pi$
$193$	1.60988	+	15.3169i	0.115881	+	1.10254i	−0.769813	+	0.638269i	$0.779651\pi$
$194$	4.10581	+	2.98305i	0.294780	+	0.214170i
$195$	−0.0201825	+	0.192023i	−0.00144530	+	0.0137511i
$196$	−4.41494	+	4.90329i	−0.315353	+	0.350235i
$197$	−17.9194	−	7.97825i	−1.27671	−	0.568427i	−0.347394	−	0.937719i	$-0.612933\pi$
$197$	−17.9194	−	7.97825i	−1.27671	−	0.568427i	−0.929313	+	0.369293i	$0.879600\pi$
$198$	4.39629	+	0.934460i	0.312430	+	0.0664091i
$199$	21.4332	−	4.55576i	1.51936	−	0.322950i	0.628709	−	0.777641i	$-0.283584\pi$
$199$	21.4332	−	4.55576i	1.51936	−	0.322950i	0.890649	+	0.454691i	$0.150250\pi$
$200$	−0.913545	+	0.406737i	−0.0645974	+	0.0287606i
$201$	−0.739449	+	2.27579i	−0.0521567	+	0.160522i
$202$	1.97451	−	6.07691i	0.138926	−	0.427570i
$203$	−1.20559	+	0.536762i	−0.0846156	+	0.0376733i
$204$	3.58579	−	0.762184i	0.251056	−	0.0533635i
$205$	−0.00146021		0.000310378i	−0.000101986		2.16777e-5i
$206$	−1.04295	−	0.464352i	−0.0726659	−	0.0323529i
$207$	−2.83099	+	3.14413i	−0.196767	+	0.218532i
$208$	−0.0201825	+	0.192023i	−0.00139940	+	0.0133144i
$209$	15.2795	+	11.1012i	1.05690	+	0.767886i
$210$	0.0662721	+	0.630537i	0.00457321	+	0.0435112i
$211$	−4.65072	+	8.05529i	−0.320169	+	0.554549i	−0.980523	−	0.196406i	$-0.937073\pi$
$211$	−4.65072	+	8.05529i	−0.320169	+	0.554549i	0.660354	+	0.750955i	$0.270406\pi$
$212$	−0.770247	−	1.33411i	−0.0529008	−	0.0916269i
$213$	0.894174	−	0.649655i	0.0612678	−	0.0445136i
$214$	3.63236	+	4.03414i	0.248303	+	0.275768i
$215$	−2.02693	−	6.23825i	−0.138235	−	0.425445i
$216$	−1.00000			−0.0680414
$217$	−2.27275	−	2.70104i	−0.154284	−	0.183359i
$218$	−4.42194			−0.299492
$219$	3.38551	+	10.4195i	0.228772	+	0.704086i
$220$	3.00741	+	3.34007i	0.202759	+	0.225187i
$221$	0.572635	−	0.416044i	0.0385196	−	0.0279861i
$222$	−1.86215	−	3.22535i	−0.124980	−	0.216471i
$223$	0.782618	−	1.35553i	0.0524080	−	0.0907733i	−0.838631	−	0.544700i	$-0.816644\pi$
$223$	0.782618	−	1.35553i	0.0524080	−	0.0907733i	0.891039	+	0.453926i	$0.149977\pi$
$224$	0.0662721	+	0.630537i	0.00442799	+	0.0421295i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	−1.74829	+	16.6339i	−0.116294	+	1.10647i
$227$	−7.69845	+	8.55000i	−0.510964	+	0.567483i	−0.942326	−	0.334696i	$-0.891367\pi$
$227$	−7.69845	+	8.55000i	−0.510964	+	0.567483i	0.431362	+	0.902179i	$0.358033\pi$
$228$	−3.83884	−	1.70916i	−0.254233	−	0.113192i
$229$	23.6519	+	5.02736i	1.56296	+	0.332218i	0.906521	−	0.422161i	$-0.138728\pi$
$229$	23.6519	+	5.02736i	1.56296	+	0.332218i	0.656440	+	0.754379i	$0.272062\pi$
$230$	−4.13839	+	0.879642i	−0.272878	+	0.0580019i
$231$	2.60320	−	1.15902i	0.171278	−	0.0762579i
$232$	0.643213	−	1.97961i	0.0422290	−	0.129967i
$233$	−0.507898	+	1.56315i	−0.0332735	+	0.102405i	−0.966314	−	0.257366i	$-0.917145\pi$
$233$	−0.507898	+	1.56315i	−0.0332735	+	0.102405i	0.933040	+	0.359772i	$0.117145\pi$
$234$	−0.176388	+	0.0785331i	−0.0115309	+	0.00513387i
$235$	−1.58393	+	0.336674i	−0.103324	+	0.0219622i
$236$	−1.94077	−	0.412524i	−0.126334	−	0.0268530i
$237$	−3.81812	−	1.69994i	−0.248014	−	0.110423i
$238$	1.55521	−	1.72723i	0.100809	−	0.111960i
$239$	−0.168605	+	1.60417i	−0.0109062	+	0.103765i	−0.998621	−	0.0525035i	$-0.983280\pi$
$239$	−0.168605	+	1.60417i	−0.0109062	+	0.103765i	0.987715	+	0.156269i	$0.0499466\pi$
$240$	−0.809017	−	0.587785i	−0.0522218	−	0.0379414i
$241$	1.12961	+	10.7475i	0.0727644	+	0.692307i	0.968719	+	0.248161i	$0.0798262\pi$
$241$	1.12961	+	10.7475i	0.0727644	+	0.692307i	−0.895954	+	0.444146i	$0.853507\pi$
$242$	4.60027	−	7.96791i	0.295717	−	0.512197i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−7.28466	+	5.29261i	−0.466352	+	0.338825i
$245$	−4.41494	−	4.90329i	−0.282060	−	0.313260i
$246$	−0.000461311	−	0.00141977i	−2.94121e−5	−	9.05212e-5i
$247$	−0.811351			−0.0516251
$248$	5.56463	+	0.186696i	0.353355	+	0.0118552i
$249$	−6.24826			−0.395968
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−5.84669	−	6.49340i	−0.369040	−	0.409860i	0.529811	−	0.848116i	$-0.322263\pi$
$251$	−5.84669	−	6.49340i	−0.369040	−	0.409860i	−0.898850	+	0.438256i	$0.855596\pi$
$252$	−0.512925	+	0.372662i	−0.0323112	+	0.0234755i
$253$	9.50777	+	16.4679i	0.597749	+	1.03533i
$254$	−9.32348	+	16.1487i	−0.585007	+	1.01326i
$255$	0.383191	+	3.64582i	0.0239964	+	0.228310i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.62829	+	15.4922i	−0.101570	+	0.966376i	0.818469	+	0.574550i	$0.194823\pi$
$257$	−1.62829	+	15.4922i	−0.101570	+	0.966376i	−0.920039	+	0.391826i	$0.871844\pi$
$258$	4.38902	−	4.87450i	0.273248	−	0.303473i
$259$	−2.15711	−	0.960406i	−0.134036	−	0.0596767i
$260$	−0.188862	−	0.0401438i	−0.0117127	−	0.00248961i
$261$	2.03600	−	0.432764i	0.126025	−	0.0267874i
$262$	−3.26231	+	1.45247i	−0.201546	+	0.0897341i
$263$	1.40570	−	4.32629i	0.0866791	−	0.266771i	−0.898317	−	0.439348i	$-0.855209\pi$
$263$	1.40570	−	4.32629i	0.0866791	−	0.266771i	0.984996	+	0.172577i	$0.0552095\pi$
$264$	−1.38888	+	4.27453i	−0.0854795	+	0.263079i
$265$	1.40731	−	0.626576i	0.0864505	−	0.0384902i
$266$	−2.60597	+	0.553917i	−0.159783	+	0.0339628i
$267$	−7.54438	−	1.60361i	−0.461709	−	0.0981392i
$268$	−2.18603	−	0.973283i	−0.133533	−	0.0594527i
$269$	1.12910	−	1.25400i	0.0688427	−	0.0764575i	−0.707740	−	0.706473i	$-0.750285\pi$
$269$	1.12910	−	1.25400i	0.0688427	−	0.0764575i	0.776582	+	0.630016i	$0.216952\pi$
$270$	0.104528	−	0.994522i	0.00636140	−	0.0605247i
$271$	10.6335	+	7.72570i	0.645940	+	0.469303i	0.861886	−	0.507102i	$-0.169283\pi$
$271$	10.6335	+	7.72570i	0.645940	+	0.469303i	−0.215946	+	0.976405i	$0.569283\pi$
$272$	0.383191	+	3.64582i	0.0232344	+	0.221060i
$273$	−0.0612076	+	0.106015i	−0.00370445	+	0.00641630i
$274$	−0.251723	−	0.435997i	−0.0152072	−	0.0263396i
$275$	−3.63613	+	2.64180i	−0.219267	+	0.159307i
$276$	−2.83099	−	3.14413i	−0.170406	−	0.189254i
$277$	−3.72938	−	11.4779i	−0.224077	−	0.689638i	−0.998384	−	0.0568278i	$-0.981901\pi$
$277$	−3.72938	−	11.4779i	−0.224077	−	0.689638i	0.774307	−	0.632810i	$-0.218099\pi$
$278$	−18.0554			−1.08289
$279$	2.62063	+	4.91246i	0.156893	+	0.294101i
$280$	−0.634010			−0.0378893
$281$	−4.75038	−	14.6202i	−0.283384	−	0.872166i	−0.986878	−	0.161465i	$-0.948378\pi$
$281$	−4.75038	−	14.6202i	−0.283384	−	0.872166i	0.703495	−	0.710701i	$-0.251622\pi$
$282$	−1.08353	−	1.20338i	−0.0645234	−	0.0716604i
$283$	−7.97728	+	5.79583i	−0.474200	+	0.344527i	−0.799076	−	0.601230i	$-0.794677\pi$
$283$	−7.97728	+	5.79583i	−0.474200	+	0.344527i	0.324876	+	0.945757i	$0.394677\pi$
$284$	0.552630	+	0.957183i	0.0327925	+	0.0567984i
$285$	2.10107	−	3.63915i	0.124456	−	0.215565i
$286$	0.0907101	+	0.863049i	0.00536380	+	0.0510331i
$287$	−0.000765712	0	0.000556322i	−4.51985e−5	0	3.28387e-5i
$288$	0.104528	−	0.994522i	0.00615940	−	0.0586028i
$289$	−2.38289	+	2.64646i	−0.140170	+	0.155674i
$290$	1.90153	+	0.846614i	0.111662	+	0.0497149i
$291$	−4.96416	−	1.05517i	−0.291004	−	0.0618549i
$292$	−10.7163	+	2.27783i	−0.627126	+	0.133300i
$293$	9.63366	−	4.28918i	0.562805	−	0.250577i	−0.105557	−	0.994413i	$-0.533663\pi$
$293$	9.63366	−	4.28918i	0.562805	−	0.250577i	0.668362	+	0.743836i	$0.266996\pi$
$294$	2.03890	−	6.27510i	0.118911	−	0.365971i
$295$	0.613130	−	1.88702i	0.0356978	−	0.109867i
$296$	3.40232	−	1.51481i	0.197756	−	0.0880467i
$297$	−4.39629	+	0.934460i	−0.255098	+	0.0542228i
$298$	−2.49343	−	0.529994i	−0.144440	−	0.0307017i
$299$	−0.746271	−	0.332261i	−0.0431580	−	0.0192152i
$300$	0.669131	−	0.743145i	0.0386323	−	0.0429055i
$301$	0.434697	−	4.13587i	0.0250555	−	0.238387i
$302$	15.7807	+	11.4654i	0.908078	+	0.659757i
$303$	0.667900	+	6.35464i	0.0383698	+	0.365065i
$304$	2.10107	−	3.63915i	0.120504	−	0.208720i
$305$	−4.50217	−	7.79798i	−0.257793	−	0.446511i
$306$	−2.96578	+	2.15476i	−0.169542	+	0.123180i
$307$	−5.32669	−	5.91589i	−0.304010	−	0.337638i	0.571711	−	0.820455i	$-0.306280\pi$
$307$	−5.32669	−	5.91589i	−0.304010	−	0.337638i	−0.875721	+	0.482818i	$0.839613\pi$
$308$	0.880562	+	2.71009i	0.0501747	+	0.154422i
$309$	1.14165			0.0649463
$310$	−0.767336	+	5.51463i	−0.0435818	+	0.313210i
$311$	−3.25508			−0.184579			−0.0922893	−	0.995732i	$-0.529418\pi$
$311$	−3.25508			−0.184579			−0.0922893	+	0.995732i	$0.529418\pi$
$312$	−0.0596653	−	0.183631i	−0.00337788	−	0.0103961i
$313$	−0.810733	−	0.900411i	−0.0458254	−	0.0508942i	0.719796	−	0.694185i	$-0.244235\pi$
$313$	−0.810733	−	0.900411i	−0.0458254	−	0.0508942i	−0.765622	+	0.643291i	$0.777569\pi$
$314$	−3.59982	+	2.61542i	−0.203150	+	0.147597i
$315$	−0.317005	−	0.549069i	−0.0178612	−	0.0309365i
$316$	2.08973	−	3.61951i	0.117556	−	0.203614i
$317$	3.69028	+	35.1107i	0.207267	+	1.97201i	0.233500	+	0.972357i	$0.424982\pi$
$317$	3.69028	+	35.1107i	0.207267	+	1.97201i	−0.0262333	+	0.999656i	$0.508351\pi$
$318$	1.24629	+	0.905480i	0.0698883	+	0.0507768i
$319$	0.977887	−	9.30397i	0.0547511	−	0.520922i
$320$	0.669131	−	0.743145i	0.0374055	−	0.0415431i
$321$	−4.95915	−	2.20796i	−0.276793	−	0.123236i
$322$	−2.62378	−	0.557702i	−0.146218	−	0.0310795i
$323$	−15.0680	+	3.20280i	−0.838404	+	0.178208i
$324$	0.913545	−	0.406737i	0.0507525	−	0.0225965i
$325$	0.0596653	−	0.183631i	0.00330963	−	0.0101860i
$326$	−5.16724	+	15.9031i	−0.286187	+	0.880792i
$327$	4.03964	−	1.79857i	0.223393	−	0.0994609i
$328$	0.00146021		0.000310378i	8.06267e−5		1.71377e-5i
$329$	−1.00423	−	0.213455i	−0.0553647	−	0.0117681i
$330$	−4.10593	−	1.82808i	−0.226024	−	0.100632i
$331$	−21.1664	+	23.5077i	−1.16341	+	1.29210i	−0.214438	+	0.976738i	$0.568792\pi$
$331$	−21.1664	+	23.5077i	−1.16341	+	1.29210i	−0.948972	+	0.315360i	$0.897875\pi$
$332$	0.653121	−	6.21403i	0.0358447	−	0.341039i
$333$	3.01303	+	2.18909i	0.165113	+	0.119962i
$334$	1.76194	+	16.7638i	0.0964092	+	0.917272i
$335$	1.19645	−	2.07232i	0.0653692	−	0.113223i
$336$	−0.317005	−	0.549069i	−0.0172940	−	0.0299542i
$337$	16.0556	−	11.6651i	0.874605	−	0.635438i	−0.0572136	−	0.998362i	$-0.518222\pi$
$337$	16.0556	−	11.6651i	0.874605	−	0.635438i	0.931819	+	0.362924i	$0.118222\pi$
$338$	8.67375	+	9.63318i	0.471790	+	0.523976i
$339$	−5.16846	−	15.9069i	−0.280712	−	0.863943i
$340$	−3.66590			−0.198811
$341$	24.6382	−	4.37915i	1.33423	−	0.237145i
$342$	4.20213			0.227225
$343$	−2.66412	−	8.19933i	−0.143849	−	0.442722i
$344$	4.38902	+	4.87450i	0.236640	+	0.262815i
$345$	3.42283	−	2.48683i	0.184279	−	0.133886i
$346$	4.57320	+	7.92101i	0.245857	+	0.425836i
$347$	6.86293	−	11.8869i	0.368421	−	0.638124i	−0.620898	−	0.783892i	$-0.713232\pi$
$347$	6.86293	−	11.8869i	0.368421	−	0.638124i	0.989319	+	0.145767i	$0.0465651\pi$
$348$	0.217574	+	2.07008i	0.0116632	+	0.110968i
$349$	−16.1909	−	11.7634i	−0.866679	−	0.629679i	0.0630145	−	0.998013i	$-0.479929\pi$
$349$	−16.1909	−	11.7634i	−0.866679	−	0.629679i	−0.929694	+	0.368333i	$0.879929\pi$
$350$	0.0662721	−	0.630537i	0.00354239	−	0.0337036i
$351$	0.129196	−	0.143487i	0.00689599	−	0.00765877i
$352$	−4.10593	−	1.82808i	−0.218847	−	0.0974369i
$353$	4.35714	+	0.926139i	0.231907	+	0.0492934i	0.322399	−	0.946604i	$-0.395511\pi$
$353$	4.35714	+	0.926139i	0.231907	+	0.0492934i	−0.0904920	+	0.995897i	$0.528844\pi$
$354$	1.94077	−	0.412524i	0.103151	−	0.0219254i
$355$	−1.00970	+	0.449550i	−0.0535896	+	0.0238596i
$356$	2.38343	−	7.33543i	0.126321	−	0.388777i
$357$	−0.718223	+	2.21046i	−0.0380124	+	0.116990i
$358$	7.09216	−	3.15763i	0.374832	−	0.166886i
$359$	12.3412	−	2.62321i	0.651345	−	0.138448i	0.129623	−	0.991563i	$-0.458623\pi$
$359$	12.3412	−	2.62321i	0.651345	−	0.138448i	0.521722	+	0.853116i	$0.325290\pi$
$360$	0.978148	+	0.207912i	0.0515529	+	0.0109579i
$361$	−1.22606	−	0.545878i	−0.0645295	−	0.0287304i
$362$	3.50957	−	3.89777i	0.184459	−	0.204862i
$363$	−0.961719	+	9.15015i	−0.0504772	+	0.480258i
$364$	−0.0990360	−	0.0719539i	−0.00519090	−	0.00377141i
$365$	−1.14519	−	10.8957i	−0.0599418	−	0.570308i
$366$	4.50217	−	7.79798i	0.235332	−	0.407607i
$367$	−16.6589	−	28.8541i	−0.869588	−	1.50617i	−0.862418	−	0.506197i	$-0.831051\pi$
$367$	−16.6589	−	28.8541i	−0.869588	−	1.50617i	−0.00717038	−	0.999974i	$-0.502282\pi$
$368$	3.42283	−	2.48683i	0.178427	−	0.129635i
$369$	0.000998901		0.00110939i	5.20007e−5		5.77526e-5i
$370$	1.15087	+	3.54203i	0.0598311	+	0.184141i
$371$	0.976689			0.0507072
$372$	−5.15948	+	2.09278i	−0.267507	+	0.108506i
$373$	−34.0930			−1.76527			−0.882633	−	0.470063i	$-0.844231\pi$
$373$	−34.0930			−1.76527			−0.882633	+	0.470063i	$0.844231\pi$
$374$	5.09149	+	15.6700i	0.263275	+	0.810276i
$375$	0.669131	+	0.743145i	0.0345538	+	0.0383758i
$376$	1.31005	−	0.951808i	0.0675607	−	0.0490857i
$377$	0.200947	+	0.348051i	0.0103493	+	0.0179255i
$378$	0.317005	−	0.549069i	0.0163050	−	0.0282410i
$379$	−2.35636	−	22.4193i	−0.121038	−	1.15160i	−0.871400	−	0.490574i	$-0.836787\pi$
$379$	−2.35636	−	22.4193i	−0.121038	−	1.15160i	0.750362	−	0.661028i	$-0.229879\pi$
$380$	3.39960	+	2.46995i	0.174396	+	0.126706i
$381$	1.94914	−	18.5448i	0.0998573	−	0.950079i
$382$	−0.405314	+	0.450146i	−0.0207376	+	0.0230315i
$383$	−9.67002	−	4.30537i	−0.494115	−	0.219994i	0.144523	−	0.989501i	$-0.453835\pi$
$383$	−9.67002	−	4.30537i	−0.494115	−	0.219994i	−0.638638	+	0.769507i	$0.720502\pi$
$384$	0.978148	+	0.207912i	0.0499159	+	0.0106099i
$385$	−2.78729	+	0.592457i	−0.142053	+	0.0301944i
$386$	14.0698	−	6.26428i	0.716134	−	0.318843i
$387$	−2.02693	+	6.23825i	−0.103035	+	0.317108i
$388$	1.56828	−	4.82667i	0.0796174	−	0.245037i
$389$	34.3199	−	15.2802i	1.74009	−	0.774738i	0.746030	−	0.665913i	$-0.231958\pi$
$389$	34.3199	−	15.2802i	1.74009	−	0.774738i	0.994061	−	0.108825i	$-0.0347089\pi$
$390$	0.188862	−	0.0401438i	0.00956338	−	0.00203276i
$391$	−15.1709	−	3.22468i	−0.767227	−	0.163079i
$392$	6.02760	+	2.68366i	0.304440	+	0.135545i
$393$	2.38949	−	2.65380i	0.120534	−	0.133866i
$394$	−2.05035	+	19.5078i	−0.103295	+	0.982789i
$395$	3.38125	+	2.45662i	0.170129	+	0.123606i
$396$	−0.469803	−	4.46988i	−0.0236085	−	0.224620i
$397$	18.8090	−	32.5782i	0.943999	−	1.63505i	0.186255	−	0.982501i	$-0.440365\pi$
$397$	18.8090	−	32.5782i	0.943999	−	1.63505i	0.757744	−	0.652552i	$-0.226302\pi$
$398$	−10.9560	−	18.9764i	−0.549175	−	0.951199i
$399$	2.15538	−	1.56597i	0.107904	−	0.0783967i
$400$	0.669131	+	0.743145i	0.0334565	+	0.0371572i
$401$	4.57739	+	14.0877i	0.228584	+	0.703508i	0.997908	+	0.0646500i	$0.0205931\pi$
$401$	4.57739	+	14.0877i	0.228584	+	0.703508i	−0.769324	+	0.638859i	$0.779407\pi$
$402$	2.39291			0.119347
$403$	−0.745719	+	0.774333i	−0.0371469	+	0.0385723i
$404$	−6.38964			−0.317897
$405$	0.309017	+	0.951057i	0.0153552	+	0.0472584i
$406$	0.883038	+	0.980713i	0.0438244	+	0.0486720i
$407$	13.5421	−	9.83888i	0.671255	−	0.487695i
$408$	−1.83295	−	3.17476i	−0.0907446	−	0.157174i
$409$	8.92636	−	15.4609i	0.441380	−	0.764493i	−0.556412	−	0.830907i	$-0.687822\pi$
$409$	8.92636	−	15.4609i	0.441380	−	0.764493i	0.997792	+	0.0664136i	$0.0211557\pi$
$410$	0.000156044		0.00148466i	7.70645e−6		7.33219e-5i
$411$	0.407297	+	0.295918i	0.0200905	+	0.0145966i
$412$	−0.119335	+	1.13540i	−0.00587922	+	0.0559371i
$413$	0.841739	−	0.934846i	0.0414193	−	0.0460008i
$414$	3.86507	+	1.72084i	0.189958	+	0.0845747i
$415$	6.11172	+	1.29909i	0.300013	+	0.0637697i
$416$	0.188862	−	0.0401438i	0.00925970	−	0.00196821i
$417$	16.4944	−	7.34379i	0.807735	−	0.359627i
$418$	5.83625	−	17.9621i	0.285460	−	0.878556i
$419$	−4.96653	+	15.2854i	−0.242631	+	0.746742i	0.753386	+	0.657579i	$0.228419\pi$
$419$	−4.96653	+	15.2854i	−0.242631	+	0.746742i	−0.996017	+	0.0891631i	$0.971581\pi$
$420$	0.579197	−	0.257875i	0.0282619	−	0.0125830i
$421$	−9.26482	+	1.96930i	−0.451540	+	0.0959777i	−0.428068	−	0.903747i	$-0.640805\pi$
$421$	−9.26482	+	1.96930i	−0.451540	+	0.0959777i	−0.0234722	+	0.999724i	$0.507472\pi$
$422$	9.09819	+	1.93388i	0.442893	+	0.0941398i
$423$	1.47932	+	0.658634i	0.0719268	+	0.0320239i
$424$	−1.03079	+	1.14481i	−0.0500597	+	0.0555969i
$425$	0.383191	−	3.64582i	0.0185875	−	0.176848i
$426$	−0.894174	−	0.649655i	−0.0433229	−	0.0314759i
$427$	−0.596736	−	5.67756i	−0.0288781	−	0.274757i
$428$	2.71424	−	4.70119i	0.131198	−	0.227241i
$429$	−0.433901	−	0.751539i	−0.0209490	−	0.0362847i
$430$	−5.30657	+	3.85545i	−0.255906	+	0.185926i
$431$	0.345869	+	0.384126i	0.0166599	+	0.0185027i	0.751417	−	0.659827i	$-0.229371\pi$
$431$	0.345869	+	0.384126i	0.0166599	+	0.0185027i	−0.734757	+	0.678330i	$0.762704\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	30.0956			1.44630			0.723150	−	0.690691i	$-0.242693\pi$
$433$	30.0956			1.44630			0.723150	+	0.690691i	$0.242693\pi$
$434$	−1.86653	+	2.99618i	−0.0895961	+	0.143821i
$435$	−2.08148			−0.0997993
$436$	1.36645	+	4.20552i	0.0654413	+	0.201408i
$437$	11.8962	+	13.2121i	0.569072	+	0.632018i
$438$	8.86338	−	6.43962i	0.423509	−	0.307697i
$439$	11.1712	+	19.3491i	0.533171	+	0.923480i	0.999249	+	0.0387365i	$0.0123333\pi$
$439$	11.1712	+	19.3491i	0.533171	+	0.923480i	−0.466078	+	0.884744i	$0.654333\pi$
$440$	2.24725	−	3.89235i	0.107133	−	0.185561i
$441$	0.689682	+	6.56189i	0.0328420	+	0.312471i
$442$	−0.572635	−	0.416044i	−0.0272375	−	0.0197892i
$443$	−1.72416	+	16.4043i	−0.0819172	+	0.779390i	0.874034	+	0.485865i	$0.161495\pi$
$443$	−1.72416	+	16.4043i	−0.0819172	+	0.779390i	−0.955951	+	0.293526i	$0.905171\pi$
$444$	−2.49205	+	2.76770i	−0.118267	+	0.131349i
$445$	7.04611	+	3.13713i	0.334018	+	0.148714i
$446$	−1.53103	−	0.325431i	−0.0724965	−	0.0154096i
$447$	2.49343	−	0.529994i	0.117935	−	0.0250679i
$448$	0.579197	−	0.257875i	0.0273645	−	0.0121835i
$449$	9.62968	−	29.6371i	0.454453	−	1.39866i	−0.417324	−	0.908758i	$-0.637032\pi$
$449$	9.62968	−	29.6371i	0.454453	−	1.39866i	0.871777	−	0.489904i	$-0.162968\pi$
$450$	−0.309017	+	0.951057i	−0.0145672	+	0.0448332i
$451$	0.00612948	−	0.00272902i	0.000288626	−	0.000128504i
$452$	16.3600	−	3.47742i	0.769509	−	0.163564i
$453$	−19.0798	−	4.05553i	−0.896446	−	0.190546i
$454$	10.5105	+	4.67957i	0.493282	+	0.219623i
$455$	0.0819118	−	0.0909723i	0.00384008	−	0.00426484i
$456$	−0.439242	+	4.17911i	−0.0205694	+	0.195705i
$457$	29.1503	+	21.1789i	1.36359	+	0.990709i	0.998207	+	0.0598536i	$0.0190634\pi$
$457$	29.1503	+	21.1789i	1.36359	+	0.990709i	0.365387	+	0.930856i	$0.380937\pi$
$458$	−2.52753	−	24.0478i	−0.118104	−	1.12368i
$459$	1.83295	−	3.17476i	0.0855548	−	0.148185i
$460$	2.11542	+	3.66402i	0.0986321	+	0.170836i
$461$	−32.2835	+	23.4554i	−1.50359	+	1.09242i	−0.534671	+	0.845060i	$0.679565\pi$
$461$	−32.2835	+	23.4554i	−1.50359	+	1.09242i	−0.968922	+	0.247365i	$0.920435\pi$
$462$	−1.90673	−	2.11764i	−0.0887090	−	0.0985213i
$463$	−4.87898	−	15.0160i	−0.226745	−	0.697851i	−0.998110	−	0.0614570i	$-0.980425\pi$
$463$	−4.87898	−	15.0160i	−0.226745	−	0.697851i	0.771364	−	0.636394i	$-0.219575\pi$
$464$	−2.08148			−0.0966303
$465$	−1.54201	−	5.34997i	−0.0715089	−	0.248099i
$466$	1.64359			0.0761380
$467$	−13.1075	−	40.3407i	−0.606543	−	1.86675i	−0.485815	−	0.874062i	$-0.661477\pi$
$467$	−13.1075	−	40.3407i	−0.606543	−	1.86675i	−0.120728	−	0.992686i	$-0.538523\pi$
$468$	0.129196	+	0.143487i	0.00597210	+	0.00663269i
$469$	1.22738	−	0.891745i	0.0566752	−	0.0411770i
$470$	0.809656	+	1.40237i	0.0373467	+	0.0646863i
$471$	2.22481	−	3.85349i	0.102514	−	0.177559i
$472$	0.207398	+	1.97326i	0.00954628	+	0.0908268i
$473$	23.8504	+	17.3283i	1.09664	+	0.796757i
$474$	−0.436872	+	4.15656i	−0.0200662	+	0.190917i
$475$	−2.81177	+	3.12279i	−0.129013	+	0.143284i
$476$	−2.12328	−	0.945345i	−0.0973203	−	0.0433298i
$477$	−1.50683	−	0.320287i	−0.0689931	−	0.0146649i
$478$	1.57776	−	0.335363i	0.0721650	−	0.0153391i
$479$	17.2192	−	7.66648i	0.786766	−	0.350291i	0.0262877	−	0.999654i	$-0.491631\pi$
$479$	17.2192	−	7.66648i	0.786766	−	0.350291i	0.760478	+	0.649364i	$0.224965\pi$
$480$	−0.309017	+	0.951057i	−0.0141046	+	0.0434096i
$481$	−0.222212	+	0.683898i	−0.0101320	+	0.0311831i
$482$	9.87241	−	4.39548i	0.449676	−	0.200209i
$483$	2.62378	−	0.557702i	0.119386	−	0.0253763i
$484$	−8.99950	−	1.91290i	−0.409068	−	0.0869501i
$485$	4.63630	+	2.06421i	0.210524	+	0.0937312i
$486$	−0.669131	+	0.743145i	−0.0303524	+	0.0337097i
$487$	4.42733	−	42.1232i	0.200621	−	1.90878i	−0.179349	−	0.983785i	$-0.557399\pi$
$487$	4.42733	−	42.1232i	0.200621	−	1.90878i	0.379971	−	0.924999i	$-0.375934\pi$
$488$	7.28466	+	5.29261i	0.329761	+	0.239585i
$489$	−1.74788	−	16.6299i	−0.0790417	−	0.752031i
$490$	−3.29902	+	5.71406i	−0.149034	+	0.258135i
$491$	10.8799	+	18.8445i	0.491002	+	0.850440i	0.999946	−	0.0103596i	$-0.00329761\pi$
$491$	10.8799	+	18.8445i	0.491002	+	0.850440i	−0.508945	+	0.860799i	$0.669964\pi$
$492$	−0.00120773		0.000877466i	−5.44486e−5		3.95592e-5i
$493$	5.10580	+	5.67057i	0.229954	+	0.255390i
$494$	0.250721	+	0.771641i	0.0112805	+	0.0347178i
$495$	4.49450			0.202013
$496$	−1.54201	−	5.34997i	−0.0692382	−	0.240221i
$497$	−0.700746			−0.0314327
$498$	1.93082	+	5.94245i	0.0865221	+	0.266288i
$499$	−23.3746	−	25.9601i	−1.04639	−	1.16213i	−0.986472	−	0.163932i	$-0.947582\pi$
$499$	−23.3746	−	25.9601i	−1.04639	−	1.16213i	−0.0599192	−	0.998203i	$-0.519084\pi$
$500$	−0.809017	+	0.587785i	−0.0361803	+	0.0262866i
$501$	−8.42805	−	14.5978i	−0.376537	−	0.652182i
$502$	−4.36887	+	7.56710i	−0.194992	+	0.337736i
$503$	1.63822	+	15.5867i	0.0730448	+	0.694975i	0.968363	+	0.249547i	$0.0802817\pi$
$503$	1.63822	+	15.5867i	0.0730448	+	0.694975i	−0.895318	+	0.445428i	$0.853052\pi$
$504$	0.512925	+	0.372662i	0.0228475	+	0.0165997i
$505$	0.667900	−	6.35464i	0.0297211	−	0.282778i
$506$	12.7239	−	14.1313i	0.565646	−	0.628213i
$507$	−11.8420	−	5.27241i	−0.525923	−	0.234156i
$508$	18.2395	+	3.87692i	0.809246	+	0.172010i
$509$	6.94320	−	1.47582i	0.307752	−	0.0654147i	−0.0514469	−	0.998676i	$-0.516383\pi$
$509$	6.94320	−	1.47582i	0.307752	−	0.0654147i	0.359199	+	0.933261i	$0.383050\pi$
$510$	3.34897	−	1.49106i	0.148295	−	0.0660251i
$511$	2.14645	−	6.60608i	0.0949532	−	0.292236i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−3.83884	+	1.70916i	−0.169489	+	0.0754613i
$514$	15.2371	−	3.23875i	0.672080	−	0.142855i
$515$	−1.11670	−	0.237363i	−0.0492079	−	0.0104595i
$516$	−5.99220	−	2.66790i	−0.263792	−	0.117448i
$517$	4.86993	−	5.40861i	0.214179	−	0.237870i
$518$	−0.246818	+	2.34831i	−0.0108445	+	0.103179i
$519$	−7.39959	−	5.37612i	−0.324806	−	0.235985i
$520$	0.0201825	+	0.192023i	0.000885059	+	0.00842078i
$521$	9.23239	−	15.9910i	0.404478	−	0.700577i	−0.589782	−	0.807562i	$-0.700786\pi$
$521$	9.23239	−	15.9910i	0.404478	−	0.700577i	0.994261	+	0.106985i	$0.0341198\pi$
$522$	−1.04074	−	1.80261i	−0.0455520	−	0.0788983i
$523$	7.92382	−	5.75699i	0.346485	−	0.251736i	−0.400908	−	0.916118i	$-0.631305\pi$
$523$	7.92382	−	5.75699i	0.346485	−	0.251736i	0.747393	+	0.664382i	$0.231305\pi$
$524$	2.38949	+	2.65380i	0.104385	+	0.115932i
$525$	0.195920	+	0.602979i	0.00855064	+	0.0263162i
$526$	−4.54893			−0.198343
$527$	−10.7924	+	17.3242i	−0.470125	+	0.754654i
$528$	4.49450			0.195598
$529$	−1.57597	−	4.85033i	−0.0685203	−	0.210884i
$530$	−1.03079	−	1.14481i	−0.0447748	−	0.0497274i
$531$	−1.60520	+	1.16624i	−0.0696596	+	0.0506107i
$532$	1.33210	+	2.30726i	0.0577537	+	0.100032i
$533$	−0.000144119	0	0.000249621i	−6.24248e−6	0	1.08123e-5i
$534$	0.806220	+	7.67067i	0.0348886	+	0.331942i
$535$	4.39173	+	3.19078i	0.189871	+	0.137949i
$536$	−0.250127	+	2.37980i	−0.0108038	+	0.102792i
$537$	−5.19469	+	5.76928i	−0.224167	+	0.248963i
$538$	−1.54153	−	0.686335i	−0.0664603	−	0.0295900i
$539$	29.0068	+	6.16559i	1.24941	+	0.265571i
$540$	−0.978148	+	0.207912i	−0.0420928	+	0.00894709i
$541$	−8.76732	+	3.90346i	−0.376937	+	0.167823i	−0.586455	−	0.809982i	$-0.699477\pi$
$541$	−8.76732	+	3.90346i	−0.376937	+	0.167823i	0.209519	+	0.977805i	$0.432810\pi$
$542$	4.06164	−	12.5004i	0.174462	−	0.536940i
$543$	−1.62078	+	4.98826i	−0.0695545	+	0.214067i
$544$	3.34897	−	1.49106i	0.143586	−	0.0639285i
$545$	−4.32531	+	0.919373i	−0.185276	+	0.0393816i
$546$	0.119740	+	0.0254516i	0.00512441	+	0.00108923i
$547$	14.5320	+	6.47008i	0.621345	+	0.276640i	0.693167	−	0.720777i	$-0.256215\pi$
$547$	14.5320	+	6.47008i	0.621345	+	0.276640i	−0.0718224	+	0.997417i	$0.522881\pi$
$548$	−0.336871	+	0.374134i	−0.0143904	+	0.0159822i
$549$	−0.941209	+	8.95501i	−0.0401698	+	0.382190i
$550$	3.63613	+	2.64180i	0.155045	+	0.112647i
$551$	−0.914274	−	8.69874i	−0.0389494	−	0.370579i
$552$	−2.11542	+	3.66402i	−0.0900384	+	0.155951i
$553$	1.32491	+	2.29481i	0.0563408	+	0.0975852i
$554$	−9.76365	+	7.09371i	−0.414818	+	0.301383i
$555$	−2.49205	−	2.76770i	−0.105782	−	0.117482i
$556$	5.57942	+	17.1717i	0.236620	+	0.728242i
$557$	5.75477			0.243837			0.121919	−	0.992540i	$-0.461095\pi$
$557$	5.75477			0.243837			0.121919	+	0.992540i	$0.461095\pi$
$558$	3.86221	−	4.01040i	0.163500	−	0.169774i
$559$	−1.26647			−0.0535661
$560$	0.195920	+	0.602979i	0.00827913	+	0.0254805i
$561$	−11.0249	−	12.2444i	−0.465470	−	0.516957i
$562$	−12.4367	+	9.03576i	−0.524608	+	0.381150i
$563$	9.88188	+	17.1159i	0.416472	+	0.721350i	0.995582	−	0.0938994i	$-0.0299332\pi$
$563$	9.88188	+	17.1159i	0.416472	+	0.721350i	−0.579110	+	0.815249i	$0.696600\pi$
$564$	−0.809656	+	1.40237i	−0.0340927	+	0.0590502i
$565$	1.74829	+	16.6339i	0.0735510	+	0.699791i
$566$	7.97728	+	5.79583i	0.335310	+	0.243617i
$567$	−0.0662721	+	0.630537i	−0.00278317	+	0.0264801i
$568$	0.739563	−	0.821368i	0.0310314	−	0.0344638i
$569$	2.63499	+	1.17317i	0.110465	+	0.0491821i	0.461225	−	0.887283i	$-0.347410\pi$
$569$	2.63499	+	1.17317i	0.110465	+	0.0491821i	−0.350760	+	0.936465i	$0.614077\pi$
$570$	−4.11030	−	0.873672i	−0.172162	−	0.0365941i
$571$	−28.6873	+	6.09767i	−1.20052	+	0.255179i	−0.764421	−	0.644717i	$-0.776975\pi$
$571$	−28.6873	+	6.09767i	−1.20052	+	0.255179i	−0.436104	+	0.899897i	$0.643642\pi$
$572$	0.792777	−	0.352967i	0.0331477	−	0.0147583i
$573$	0.187181	−	0.576085i	0.00781961	−	0.0240663i
$574$	−0.000292476	0	0.000900148i	−1.22077e−5	0	3.75715e-5i
$575$	−3.86507	+	1.72084i	−0.161185	+	0.0717640i
$576$	−0.978148	+	0.207912i	−0.0407562	+	0.00866299i
$577$	−4.21286	−	0.895472i	−0.175384	−	0.0372790i	0.119383	−	0.992848i	$-0.461908\pi$
$577$	−4.21286	−	0.895472i	−0.175384	−	0.0372790i	−0.294766	+	0.955569i	$0.595242\pi$
$578$	3.25329	+	1.44846i	0.135319	+	0.0602479i
$579$	−10.3055	+	11.4454i	−0.428282	+	0.475655i
$580$	0.217574	−	2.07008i	0.00903427	−	0.0859553i
$581$	3.20489	+	2.32849i	0.132961	+	0.0966020i
$582$	0.530489	+	5.04726i	0.0219895	+	0.209216i
$583$	−3.46188	+	5.99615i	−0.143376	+	0.248335i
$584$	5.47787	+	9.48795i	0.226676	+	0.392614i
$585$	−0.156206	+	0.113490i	−0.00645831	+	0.00469224i
$586$	−7.05622	−	7.83673i	−0.291490	−	0.323732i
$587$	1.22650	+	3.77477i	0.0506229	+	0.155801i	0.973172	−	0.230078i	$-0.0738981\pi$
$587$	1.22650	+	3.77477i	0.0506229	+	0.155801i	−0.922549	+	0.385879i	$0.873898\pi$
$588$	−6.59803			−0.272098
$589$	21.6808	−	8.79416i	0.893343	−	0.362357i
$590$	−1.98413			−0.0816854
$591$	−6.06145	−	18.6552i	−0.249335	−	0.767374i
$592$	−2.49205	−	2.76770i	−0.102423	−	0.113752i
$593$	16.3647	−	11.8897i	0.672018	−	0.488250i	−0.198682	−	0.980064i	$-0.563666\pi$
$593$	16.3647	−	11.8897i	0.672018	−	0.488250i	0.870700	+	0.491814i	$0.163666\pi$
$594$	2.24725	+	3.89235i	0.0922058	+	0.159705i
$595$	1.16211	−	2.01283i	0.0476418	−	0.0825181i
$596$	0.266457	+	2.53517i	0.0109145	+	0.103844i
$597$	17.7272	+	12.8796i	0.725526	+	0.527125i
$598$	−0.0853889	+	0.812421i	−0.00349181	+	0.0332224i
$599$	14.4076	−	16.0012i	0.588678	−	0.653793i	−0.373046	−	0.927813i	$-0.621687\pi$
$599$	14.4076	−	16.0012i	0.588678	−	0.653793i	0.961724	+	0.274020i	$0.0883534\pi$
$600$	−0.913545	−	0.406737i	−0.0372953	−	0.0166050i
$601$	−14.3887	−	3.05841i	−0.586927	−	0.124755i	−0.0951296	−	0.995465i	$-0.530327\pi$
$601$	−14.3887	−	3.05841i	−0.586927	−	0.124755i	−0.491797	+	0.870710i	$0.663660\pi$
$602$	−4.06777	+	0.864632i	−0.165790	+	0.0352398i
$603$	−2.18603	+	0.973283i	−0.0890220	+	0.0396352i
$604$	6.02770	−	18.5513i	0.245264	−	0.754844i
$605$	2.84313	−	8.75024i	0.115590	−	0.355748i
$606$	5.83723	−	2.59890i	0.237121	−	0.105573i
$607$	−1.45773	+	0.309851i	−0.0591675	+	0.0125764i	−0.237400	−	0.971412i	$-0.576295\pi$
$607$	−1.45773	+	0.309851i	−0.0591675	+	0.0125764i	0.178233	+	0.983988i	$0.442962\pi$
$608$	−4.11030	−	0.873672i	−0.166695	−	0.0354321i
$609$	−1.20559	−	0.536762i	−0.0488529	−	0.0217507i
$610$	−6.02507	+	6.69152i	−0.243948	+	0.270932i
$611$	−0.0326817	+	0.310946i	−0.00132216	+	0.0125795i
$612$	2.96578	+	2.15476i	0.119884	+	0.0871011i
$613$	−0.361546	−	3.43988i	−0.0146027	−	0.138935i	0.984791	−	0.173741i	$-0.0555855\pi$
$613$	−0.361546	−	3.43988i	−0.0146027	−	0.138935i	−0.999394	+	0.0348055i	$0.988919\pi$
$614$	−3.98031	+	6.89409i	−0.160632	+	0.278223i
$615$	−0.000746417	−	0.00129283i	−3.00984e−5	−	5.21320e-5i
$616$	2.30534	−	1.67493i	0.0928849	−	0.0674848i
$617$	1.83683	+	2.04000i	0.0739478	+	0.0821274i	0.778983	−	0.627045i	$-0.215736\pi$
$617$	1.83683	+	2.04000i	0.0739478	+	0.0821274i	−0.705036	+	0.709172i	$0.749069\pi$
$618$	−0.352790	−	1.08578i	−0.0141913	−	0.0436763i
$619$	−46.5423			−1.87069			−0.935347	−	0.353731i	$-0.884913\pi$
$619$	−46.5423			−1.87069			−0.935347	+	0.353731i	$0.884913\pi$
$620$	5.48185	−	0.974336i	0.220156	−	0.0391303i
$621$	−4.23085			−0.169778
$622$	1.00587	+	3.09576i	0.0403319	+	0.124129i
$623$	3.27210	+	3.63403i	0.131094	+	0.145594i
$624$	−0.156206	+	0.113490i	−0.00625323	+	0.00454324i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.605811	+	1.04930i	−0.0242131	+	0.0419383i
$627$	1.97418	+	18.7830i	0.0788410	+	0.750122i
$628$	3.59982	+	2.61542i	0.143648	+	0.104367i
$629$	−1.42712	+	13.5782i	−0.0569031	+	0.541396i
$630$	−0.424235	+	0.471161i	−0.0169019	+	0.0187715i
$631$	12.9969	+	5.78658i	0.517397	+	0.230360i	0.648786	−	0.760971i	$-0.275277\pi$
$631$	12.9969	+	5.78658i	0.517397	+	0.230360i	−0.131389	+	0.991331i	$0.541944\pi$
$632$	−4.08812	−	0.868958i	−0.162617	−	0.0345653i
$633$	−9.09819	+	1.93388i	−0.361621	+	0.0768648i
$634$	32.2519	−	14.3595i	1.28089	−	0.570287i
$635$	−5.76222	+	17.7343i	−0.228667	+	0.703764i
$636$	0.476039	−	1.46510i	0.0188762	−	0.0580949i
$637$	−1.16381	+	0.518164i	−0.0461120	+	0.0205304i
$638$	−9.15078	+	1.94506i	−0.362283	+	0.0770056i
$639$	1.08111	+	0.229796i	0.0427679	+	0.00909061i
$640$	−0.913545	−	0.406737i	−0.0361111	−	0.0160777i
$641$	24.5363	−	27.2504i	0.969127	−	1.07632i	−0.0279258	−	0.999610i	$-0.508890\pi$
$641$	24.5363	−	27.2504i	0.969127	−	1.07632i	0.997053	−	0.0767149i	$-0.0244431\pi$
$642$	−0.567430	+	5.39873i	−0.0223947	+	0.213071i
$643$	1.49162	+	1.08372i	0.0588237	+	0.0427379i	0.616809	−	0.787113i	$-0.288425\pi$
$643$	1.49162	+	1.08372i	0.0588237	+	0.0427379i	−0.557985	+	0.829851i	$0.688425\pi$
$644$	0.280387	+	2.66770i	0.0110488	+	0.105122i
$645$	3.27964	−	5.68050i	0.129136	−	0.223670i
$646$	7.70230	+	13.3408i	0.303043	+	0.524886i
$647$	−33.0798	+	24.0339i	−1.30050	+	0.944870i	−0.999960	−	0.00889927i	$-0.997167\pi$
$647$	−33.0798	+	24.0339i	−1.30050	+	0.944870i	−0.300541	+	0.953769i	$0.597167\pi$
$648$	−0.669131	−	0.743145i	−0.0262859	−	0.0291935i
$649$	2.75572	+	8.48122i	0.108171	+	0.332917i
$650$	−0.193081			−0.00757326
$651$	0.486499	−	3.49633i	0.0190674	−	0.137032i
$652$	16.7215			0.654866
$653$	−7.29129	−	22.4403i	−0.285330	−	0.878156i	−0.986299	−	0.164965i	$-0.947249\pi$
$653$	−7.29129	−	22.4403i	−0.285330	−	0.878156i	0.700969	−	0.713192i	$-0.252751\pi$
$654$	−2.95886	−	3.28614i	−0.115700	−	0.128498i
$655$	−2.88903	+	2.09900i	−0.112884	+	0.0820149i
$656$	−0.000746417	−	0.00129283i	−2.91427e−5	−	5.04766e-5i
$657$	−5.47787	+	9.48795i	−0.213712	+	0.370160i
$658$	0.107315	+	1.02104i	0.00418358	+	0.0398041i
$659$	−18.1395	−	13.1791i	−0.706613	−	0.513385i	0.175466	−	0.984485i	$-0.443857\pi$
$659$	−18.1395	−	13.1791i	−0.706613	−	0.513385i	−0.882079	+	0.471101i	$0.843857\pi$
$660$	−0.469803	+	4.46988i	−0.0182871	+	0.173990i
$661$	−7.06067	+	7.84166i	−0.274628	+	0.305005i	−0.864643	−	0.502387i	$-0.832455\pi$
$661$	−7.06067	+	7.84166i	−0.274628	+	0.305005i	0.590015	+	0.807392i	$0.299122\pi$
$662$	28.8979	+	12.8662i	1.12315	+	0.500058i
$663$	0.692348	+	0.147163i	0.0268886	+	0.00571534i
$664$	−6.11172	+	1.29909i	−0.237181	+	0.0504144i
$665$	−2.43386	+	1.08363i	−0.0943811	+	0.0420212i
$666$	1.15087	−	3.54203i	0.0445955	−	0.137251i
$667$	2.72133	−	8.37541i	0.105370	−	0.324297i
$668$	15.3988	−	6.85599i	0.595798	−	0.265266i
$669$	1.53103	−	0.325431i	0.0591931	−	0.0125819i
$670$	−2.34062	−	0.497513i	−0.0904259	−	0.0192206i
$671$	36.9712	+	16.4606i	1.42726	+	0.635455i
$672$	−0.424235	+	0.471161i	−0.0163652	+	0.0181754i
$673$	−3.21403	+	30.5795i	−0.123892	+	1.17875i	0.739122	+	0.673571i	$0.235241\pi$
$673$	−3.21403	+	30.5795i	−0.123892	+	1.17875i	−0.863014	+	0.505180i	$0.831426\pi$
$674$	−16.0556	−	11.6651i	−0.618439	−	0.449322i
$675$	−0.104528	−	0.994522i	−0.00402330	−	0.0382792i
$676$	6.48136	−	11.2260i	0.249283	−	0.431771i
$677$	10.6144	+	18.3848i	0.407946	+	0.706584i	0.994659	−	0.103211i	$-0.0329117\pi$
$677$	10.6144	+	18.3848i	0.407946	+	0.706584i	−0.586713	+	0.809795i	$0.699578\pi$
$678$	−13.5312	+	9.83099i	−0.519662	+	0.377557i
$679$	2.15302	+	2.39117i	0.0826254	+	0.0917648i
$680$	1.13283	+	3.48648i	0.0434419	+	0.133700i
$681$	−11.5052			−0.440879
$682$	−11.7784	−	22.0791i	−0.451020	−	0.845451i
$683$	−25.6450			−0.981277			−0.490639	−	0.871363i	$-0.663236\pi$
$683$	−25.6450			−0.981277			−0.490639	+	0.871363i	$0.663236\pi$
$684$	−1.29853	−	3.99646i	−0.0496505	−	0.152809i
$685$	−0.336871	−	0.374134i	−0.0128712	−	0.0142949i
$686$	−6.97477	+	5.06747i	−0.266298	+	0.193477i
$687$	12.0901	+	20.9407i	0.461268	+	0.798939i
$688$	3.27964	−	5.68050i	0.125035	−	0.216567i
$689$	−0.0310910	−	0.295811i	−0.00118447	−	0.0112695i
$690$	−3.42283	−	2.48683i	−0.130305	−	0.0946720i
$691$	−2.41853	+	23.0107i	−0.0920050	+	0.875369i	0.847029	+	0.531546i	$0.178389\pi$
$691$	−2.41853	+	23.0107i	−0.0920050	+	0.875369i	−0.939034	+	0.343823i	$0.888278\pi$
$692$	6.12013	−	6.79710i	0.232653	−	0.258387i
$693$	2.60320	+	1.15902i	0.0988875	+	0.0440275i
$694$	−13.4259	−	2.85377i	−0.509641	−	0.108327i
$695$	−17.6608	+	3.75393i	−0.669914	+	0.142395i
$696$	1.90153	−	0.846614i	0.0720772	−	0.0320908i
$697$	−0.00169112	+	0.00520474i	−6.40558e−5	+	0.000197143i
$698$	−6.18438	+	19.0336i	−0.234082	+	0.720431i
$699$	−1.50150	+	0.668510i	−0.0567919	+	0.0252854i
$700$	−0.620155	+	0.131818i	−0.0234397	+	0.00498226i
$701$	−22.3982	−	4.76089i	−0.845969	−	0.179816i	−0.235518	−	0.971870i	$-0.575679\pi$
$701$	−22.3982	−	4.76089i	−0.845969	−	0.179816i	−0.610451	+	0.792054i	$0.709012\pi$
$702$	−0.176388	−	0.0785331i	−0.00665734	−	0.00296404i
$703$	10.4719	−	11.6302i	0.394956	−	0.438643i
$704$	−0.469803	+	4.46988i	−0.0177064	+	0.168465i
$705$	−1.31005	−	0.951808i	−0.0493394	−	0.0358472i
$706$	−0.465620	−	4.43008i	−0.0175239	−	0.166728i
$707$	2.02555	−	3.50835i	0.0761786	−	0.131945i
$708$	−0.992066	−	1.71831i	−0.0372841	−	0.0645780i
$709$	−30.5475	+	22.1941i	−1.14724	+	0.833515i	−0.988111	−	0.153743i	$-0.950867\pi$
$709$	−30.5475	+	22.1941i	−1.14724	+	0.833515i	−0.159125	+	0.987259i	$0.550867\pi$
$710$	0.739563	+	0.821368i	0.0277553	+	0.0308254i
$711$	−1.29152	−	3.97490i	−0.0484359	−	0.149070i
$712$	−7.71293			−0.289054
$713$	23.5431	+	0.789883i	0.881696	+	0.0295813i
$714$	2.32422			0.0869817
$715$	0.268166	+	0.825329i	0.0100288	+	0.0308656i
$716$	−5.19469	−	5.76928i	−0.194135	−	0.215608i
$717$	−1.30495	+	0.948102i	−0.0487342	+	0.0354075i
$718$	−6.30846	−	10.9266i	−0.235430	−	0.407776i
$719$	3.97056	−	6.87720i	0.148077	−	0.256476i	−0.782440	−	0.622726i	$-0.786025\pi$
$719$	3.97056	−	6.87720i	0.148077	−	0.256476i	0.930517	+	0.366250i	$0.119358\pi$
$720$	−0.104528	−	0.994522i	−0.00389555	−	0.0370636i
$721$	−0.585582	−	0.425450i	−0.0218082	−	0.0158446i
$722$	−0.140287	+	1.33474i	−0.00522093	+	0.0496738i
$723$	−7.23109	+	8.03094i	−0.268927	+	0.298674i
$724$	−4.79151	−	2.13332i	−0.178075	−	0.0792842i
$725$	2.03600	+	0.432764i	0.0756150	+	0.0160725i
$726$	8.99950	−	1.91290i	0.334003	−	0.0709944i
$727$	22.2561	−	9.90905i	0.825432	−	0.367506i	0.0498533	−	0.998757i	$-0.484125\pi$
$727$	22.2561	−	9.90905i	0.825432	−	0.367506i	0.775579	+	0.631250i	$0.217458\pi$
$728$	−0.0378284	+	0.116424i	−0.00140201	+	0.00431495i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−10.0086	+	4.45610i	−0.370434	+	0.164928i
$731$	−23.5202	+	4.99938i	−0.869927	+	0.184909i
$732$	−8.80757	−	1.87211i	−0.325537	−	0.0691950i
$733$	−1.79632	−	0.799775i	−0.0663488	−	0.0295404i	0.373294	−	0.927713i	$-0.378228\pi$
$733$	−1.79632	−	0.799775i	−0.0663488	−	0.0295404i	−0.439643	+	0.898173i	$0.644895\pi$
$734$	−22.2940	+	24.7600i	−0.822886	+	0.913907i
$735$	0.689682	−	6.56189i	0.0254393	−	0.242039i
$736$	−3.42283	−	2.48683i	−0.126167	−	0.0916657i
$737$	1.12420	+	10.6960i	0.0414103	+	0.393993i
$738$	0.000746417	−	0.00129283i	2.74760e−5	−	4.75898e-5i
$739$	−15.4132	−	26.6964i	−0.566983	−	0.982044i	−0.996862	−	0.0791571i	$-0.974777\pi$
$739$	−15.4132	−	26.6964i	−0.566983	−	0.982044i	0.429879	−	0.902887i	$-0.358556\pi$
$740$	3.01303	−	2.18909i	0.110761	−	0.0804727i
$741$	−0.542900	−	0.602952i	−0.0199439	−	0.0221500i
$742$	−0.301814	−	0.928887i	−0.0110799	−	0.0341005i
$743$	−44.5730			−1.63522			−0.817612	−	0.575769i	$-0.804703\pi$
$743$	−44.5730			−1.63522			−0.817612	+	0.575769i	$0.804703\pi$
$744$	3.58472	+	4.26025i	0.131422	+	0.156188i
$745$	−2.54913			−0.0933929
$746$	10.5353	+	32.4243i	0.385725	+	1.18714i
$747$	−4.18090	−	4.64336i	−0.152971	−	0.169892i
$748$	13.3297	−	9.68459i	0.487382	−	0.354104i
$749$	1.72085	+	2.98060i	0.0628786	+	0.108909i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	2.12765	+	20.2433i	0.0776392	+	0.738688i	0.962215	+	0.272291i	$0.0877814\pi$
$751$	2.12765	+	20.2433i	0.0776392	+	0.738688i	−0.884576	+	0.466397i	$0.845552\pi$
$752$	−1.31005	−	0.951808i	−0.0477726	−	0.0347089i
$753$	0.913342	−	8.68987i	0.0332840	−	0.316677i
$754$	0.268920	−	0.298666i	0.00979348	−	0.0108768i
$755$	17.8197	+	7.93382i	0.648524	+	0.288741i
$756$	−0.620155	−	0.131818i	−0.0225548	−	0.00479418i
$757$	3.94647	−	0.838848i	0.143437	−	0.0304885i	−0.135634	−	0.990759i	$-0.543307\pi$
$757$	3.94647	−	0.838848i	0.143437	−	0.0304885i	0.279071	+	0.960271i	$0.409974\pi$
$758$	−20.5939	+	9.16897i	−0.748002	+	0.333032i
$759$	−5.87613	+	18.0849i	−0.213290	+	0.656439i
$760$	1.29853	−	3.99646i	0.0471026	−	0.144967i
$761$	4.60087	−	2.04844i	0.166781	−	0.0742559i	−0.321648	−	0.946859i	$-0.604237\pi$
$761$	4.60087	−	2.04844i	0.166781	−	0.0742559i	0.488429	+	0.872604i	$0.337570\pi$
$762$	−18.2395	+	3.87692i	−0.660746	+	0.140446i
$763$	−2.74229	−	0.582892i	−0.0992776	−	0.0211021i
$764$	0.553363	+	0.246373i	0.0200200	+	0.00891347i
$765$	−2.45297	+	2.72430i	−0.0886872	+	0.0984971i
$766$	−1.10645	+	10.5272i	−0.0399777	+	0.380362i
$767$	−0.309933	−	0.225179i	−0.0111910	−	0.00813076i
$768$	−0.104528	−	0.994522i	−0.00377185	−	0.0358867i
$769$	−10.5142	+	18.2112i	−0.379153	+	0.656712i	−0.990939	−	0.134311i	$-0.957118\pi$
$769$	−10.5142	+	18.2112i	−0.379153	+	0.656712i	0.611786	+	0.791023i	$0.290451\pi$
$770$	1.42478	+	2.46779i	0.0513455	+	0.0889330i
$771$	−12.6025	+	9.15624i	−0.453867	+	0.329754i
$772$	−10.3055	−	11.4454i	−0.370903	−	0.411929i
$773$	1.30413	+	4.01369i	0.0469062	+	0.144363i	0.971767	−	0.235944i	$-0.0758183\pi$
$773$	1.30413	+	4.01369i	0.0469062	+	0.144363i	−0.924860	+	0.380307i	$0.875818\pi$
$774$	6.55928			0.235769
$775$	0.395989	+	5.55366i	0.0142243	+	0.199494i
$776$	−5.07506			−0.182184
$777$	−0.729666	−	2.24568i	−0.0261766	−	0.0805633i
$778$	−25.1378	−	27.9184i	−0.901234	−	1.00092i
$779$	0.00507503	−	0.00368723i	0.000181832	−	0.000132109i
$780$	−0.0965405	−	0.167213i	−0.00345670	−	0.00598719i
$781$	2.48380	−	4.30206i	0.0888772	−	0.153940i
$782$	1.62122	+	15.4249i	0.0579748	+	0.551593i
$783$	1.68395	+	1.22346i	0.0601796	+	0.0437230i
$784$	0.689682	−	6.56189i	0.0246315	−	0.234353i
$785$	−2.97738	+	3.30671i	−0.106267	+	0.118022i
$786$	−3.26231	−	1.45247i	−0.116363	−	0.0518080i
$787$	−19.9797	−	4.24682i	−0.712199	−	0.151383i	−0.162455	−	0.986716i	$-0.551941\pi$
$787$	−19.9797	−	4.24682i	−0.712199	−	0.151383i	−0.549744	+	0.835333i	$0.685275\pi$
$788$	19.1866	−	4.07824i	0.683495	−	0.145281i
$789$	4.15566	−	1.85022i	0.147945	−	0.0658695i
$790$	1.29152	−	3.97490i	0.0459503	−	0.141421i
$791$	−3.27685	+	10.0851i	−0.116511	+	0.358585i
$792$	−4.10593	+	1.82808i	−0.145898	+	0.0649579i
$793$	−1.70057	+	0.361468i	−0.0603891	+	0.0128361i
$794$	−36.7960	−	7.82124i	−1.30584	−	0.277565i
$795$	1.40731	+	0.626576i	0.0499122	+	0.0222223i
$796$	−14.6620	+	16.2838i	−0.519681	+	0.577164i
$797$	−1.66016	+	15.7954i	−0.0588059	+	0.559501i	0.924962	+	0.380058i	$0.124096\pi$
$797$	−1.66016	+	15.7954i	−0.0588059	+	0.559501i	−0.983768	+	0.179443i	$0.942571\pi$
$798$	−2.15538	−	1.56597i	−0.0762995	−	0.0554349i
$799$	0.620506	+	5.90372i	0.0219519	+	0.208859i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−3.85646	−	6.67959i	−0.136261	−	0.236012i
$802$	11.9838	−	8.70671i	0.423161	−	0.307444i
$803$	32.9484	+	36.5929i	1.16272	+	1.29134i
$804$	−0.739449	−	2.27579i	−0.0260784	−	0.0802609i
$805$	−2.68240			−0.0945421
$806$	0.966874	+	0.469939i	0.0340567	+	0.0165529i
$807$	1.68742			0.0594000
$808$	1.97451	+	6.07691i	0.0694630	+	0.213785i
$809$	−15.9417	−	17.7051i	−0.560481	−	0.622478i	0.394589	−	0.918858i	$-0.370887\pi$
$809$	−15.9417	−	17.7051i	−0.560481	−	0.622478i	−0.955070	+	0.296380i	$0.904220\pi$
$810$	0.809017	−	0.587785i	0.0284260	−	0.0206527i
$811$	15.6090	+	27.0356i	0.548106	+	0.949347i	0.998404	+	0.0564687i	$0.0179841\pi$
$811$	15.6090	+	27.0356i	0.548106	+	0.949347i	−0.450299	+	0.892878i	$0.648683\pi$
$812$	0.659840	−	1.14288i	0.0231558	−	0.0401071i
$813$	1.37390	+	13.0717i	0.0481846	+	0.458446i
$814$	−13.5421	−	9.83888i	−0.474649	−	0.344853i
$815$	−1.74788	+	16.6299i	−0.0612254	+	0.582521i
$816$	−2.45297	+	2.72430i	−0.0858710	+	0.0953694i
$817$	25.1800	+	11.2109i	0.880937	+	0.392219i
$818$	−17.4626	−	3.71179i	−0.610566	−	0.129780i
$819$	−0.119740	+	0.0254516i	−0.00418406	+	0.000889349i
$820$	0.00136377		0.000607190i	4.76250e−5		2.12040e-5i
$821$	9.07803	−	27.9393i	0.316825	−	0.975089i	−0.658171	−	0.752868i	$-0.728670\pi$
$821$	9.07803	−	27.9393i	0.316825	−	0.975089i	0.974997	−	0.222220i	$-0.0713304\pi$
$822$	0.155574	−	0.478806i	0.00542625	−	0.0167003i
$823$	11.3703	−	5.06238i	0.396343	−	0.176463i	−0.198880	−	0.980024i	$-0.563730\pi$
$823$	11.3703	−	5.06238i	0.396343	−	0.176463i	0.595223	+	0.803560i	$0.297064\pi$
$824$	1.11670	−	0.237363i	0.0389022	−	0.00826893i
$825$	−4.39629	−	0.934460i	−0.153059	−	0.0325337i
$826$	−1.14920	−	0.511658i	−0.0399859	−	0.0178029i
$827$	5.13241	−	5.70012i	0.178471	−	0.198213i	−0.647271	−	0.762260i	$-0.724090\pi$
$827$	5.13241	−	5.70012i	0.178471	−	0.198213i	0.825742	+	0.564047i	$0.190756\pi$
$828$	0.442244	−	4.20767i	0.0153690	−	0.146227i
$829$	4.34158	+	3.15434i	0.150789	+	0.109555i	0.660622	−	0.750719i	$-0.270293\pi$
$829$	4.34158	+	3.15434i	0.150789	+	0.109555i	−0.509833	+	0.860274i	$0.670293\pi$
$830$	−0.653121	−	6.21403i	−0.0226702	−	0.215692i
$831$	6.03427	−	10.4517i	0.209326	−	0.362564i
$832$	−0.0965405	−	0.167213i	−0.00334694	−	0.00579707i
$833$	−19.5683	+	14.2172i	−0.678001	+	0.492597i
$834$	−12.0814	−	13.4178i	−0.418345	−	0.464619i
$835$	5.20882	+	16.0311i	0.180259	+	0.554779i
$836$	−18.8865			−0.653203
$837$	−1.89712	+	5.23459i	−0.0655742	+	0.180934i
$838$	16.0720			0.555200
$839$	−7.70257	−	23.7061i	−0.265922	−	0.818424i	−0.991480	−	0.130263i	$-0.958418\pi$
$839$	−7.70257	−	23.7061i	−0.265922	−	0.818424i	0.725557	−	0.688162i	$-0.241582\pi$
$840$	−0.424235	−	0.471161i	−0.0146375	−	0.0162566i
$841$	19.9564	−	14.4992i	0.688151	−	0.499971i
$842$	4.73590	+	8.20282i	0.163210	+	0.282688i
$843$	7.68627	−	13.3130i	0.264729	−	0.458525i
$844$	−0.972266	−	9.25049i	−0.0334668	−	0.318415i
$845$	10.4871	+	7.61930i	0.360766	+	0.262112i
$846$	0.169264	−	1.61044i	0.00581942	−	0.0553681i
$847$	3.90320	−	4.33494i	0.134116	−	0.148950i
$848$	1.40731	+	0.626576i	0.0483273	+	0.0215167i
$849$	−9.64499	−	2.05011i	−0.331015	−	0.0703594i
$850$	−3.58579	+	0.762184i	−0.122992	+	0.0261427i
$851$	14.3947	−	6.40894i	0.493444	−	0.219696i
$852$	−0.341544	+	1.05116i	−0.0117011	+	0.0360123i
$853$	−2.36278	+	7.27190i	−0.0809002	+	0.248985i	−0.983323	−	0.181866i	$-0.941786\pi$
$853$	−2.36278	+	7.27190i	−0.0809002	+	0.248985i	0.902423	+	0.430851i	$0.141786\pi$
$854$	−5.21528	+	2.32199i	−0.178463	+	0.0794570i
$855$	4.11030	−	0.873672i	0.140569	−	0.0298790i
$856$	−5.30985	−	1.12864i	−0.181487	−	0.0385762i
$857$	50.2710	+	22.3821i	1.71722	+	0.764557i	0.997528	+	0.0702678i	$0.0223854\pi$
$857$	50.2710	+	22.3821i	1.71722	+	0.764557i	0.719696	+	0.694290i	$0.244281\pi$
$858$	−0.580673	+	0.644903i	−0.0198239	+	0.0220166i
$859$	4.42966	−	42.1454i	0.151138	−	1.43798i	−0.611544	−	0.791210i	$-0.709451\pi$
$859$	4.42966	−	42.1454i	0.151138	−	1.43798i	0.762682	−	0.646773i	$-0.223882\pi$
$860$	5.30657	+	3.85545i	0.180953	+	0.131470i
$861$	−9.89332e−5	0	0.000941287i	−3.37164e−6	0	3.20790e-5i
$862$	0.258447	−	0.447643i	0.00880273	−	0.0152468i
$863$	2.45117	+	4.24555i	0.0834389	+	0.144520i	0.904725	−	0.425996i	$-0.140076\pi$
$863$	2.45117	+	4.24555i	0.0834389	+	0.144520i	−0.821286	+	0.570517i	$0.806743\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	6.12013	+	6.79710i	0.208091	+	0.231108i
$866$	−9.30004	−	28.6226i	−0.316028	−	0.972635i
$867$	−3.56117			−0.120944
$868$	3.42633	+	0.849300i	0.116297	+	0.0288271i
$869$	−18.7846			−0.637223
$870$	0.643213	+	1.97961i	0.0218070	+	0.0671149i
$871$	−0.309155	−	0.343351i	−0.0104753	−	0.0116340i
$872$	3.57742	−	2.59915i	0.121147	−	0.0880184i
$873$	−2.53753	−	4.39513i	−0.0858825	−	0.148753i
$874$	8.88929	−	15.3967i	0.300685	−	0.520801i
$875$	−0.0662721	−	0.630537i	−0.00224041	−	0.0213160i
$876$	−8.86338	−	6.43962i	−0.299466	−	0.217575i
$877$	−3.14638	+	29.9358i	−0.106246	+	1.01086i	0.803390	+	0.595454i	$0.203028\pi$
$877$	−3.14638	+	29.9358i	−0.106246	+	1.01086i	−0.909635	+	0.415408i	$0.863639\pi$
$878$	14.9500	−	16.6036i	0.504537	−	0.560345i
$879$	9.63366	+	4.28918i	0.324935	+	0.144671i
$880$	−4.39629	−	0.934460i	−0.148199	−	0.0315006i
$881$	−47.4901	+	10.0943i	−1.59998	+	0.340087i	−0.919626	−	0.392796i	$-0.871508\pi$
$881$	−47.4901	+	10.0943i	−1.59998	+	0.340087i	−0.680356	+	0.732882i	$0.738175\pi$
$882$	6.02760	−	2.68366i	0.202960	−	0.0903636i
$883$	15.4611	−	47.5844i	0.520308	−	1.60134i	−0.253104	−	0.967439i	$-0.581452\pi$
$883$	15.4611	−	47.5844i	0.520308	−	1.60134i	0.773412	−	0.633904i	$-0.218548\pi$
$884$	−0.218727	+	0.673173i	−0.00735659	+	0.0226412i
$885$	1.81259	−	0.807019i	0.0609297	−	0.0271277i
$886$	16.1342	−	3.42943i	0.542038	−	0.115214i
$887$	26.2505	+	5.57972i	0.881406	+	0.187349i	0.626317	−	0.779569i	$-0.284562\pi$
$887$	26.2505	+	5.57972i	0.881406	+	0.187349i	0.255090	+	0.966917i	$0.417895\pi$
$888$	3.40232	+	1.51481i	0.114175	+	0.0508338i
$889$	−7.91070	+	8.78572i	−0.265316	+	0.294664i
$890$	0.806220	−	7.67067i	0.0270246	−	0.257122i
$891$	−3.63613	−	2.64180i	−0.121815	−	0.0885037i
$892$	0.163612	+	1.55666i	0.00547813	+	0.0521209i
$893$	3.40228	−	5.89292i	0.113853	−	0.197199i
$894$	−1.27456	−	2.20761i	−0.0426278	−	0.0738336i
$895$	6.28067	−	4.56318i	0.209940	−	0.152530i
$896$	−0.424235	−	0.471161i	−0.0141727	−	0.0157404i
$897$	−0.252435	−	0.776914i	−0.00842855	−	0.0259404i
$898$	−31.1623			−1.03990
$899$	−9.14217	−	7.12251i	−0.304908	−	0.237549i
$900$	1.00000			0.0333333
$901$	−1.74511	−	5.37090i	−0.0581381	−	0.178931i
$902$	−0.00448956	−	0.00498616i	−0.000149486	−	0.000166021i
$903$	3.36442	−	2.44439i	0.111961	−	0.0813443i
$904$	−8.36274	−	14.4847i	−0.278141	−	0.481754i
$905$	2.62248	−	4.54227i	0.0871743	−	0.150990i
$906$	2.03894	+	19.3992i	0.0677391	+	0.644495i
$907$	−11.5984	−	8.42675i	−0.385119	−	0.279806i	0.378333	−	0.925669i	$-0.376497\pi$
$907$	−11.5984	−	8.42675i	−0.385119	−	0.279806i	−0.763453	+	0.645864i	$0.776497\pi$
$908$	1.20262	−	11.4421i	0.0399102	−	0.379721i
$909$	−4.27551	+	4.74843i	−0.141810	+	0.157495i
$910$	−0.111832	−	0.0497908i	−0.00370719	−	0.00165055i
$911$	54.5387	+	11.5926i	1.80695	+	0.384078i	0.983149	−	0.182806i	$-0.0585179\pi$
$911$	54.5387	+	11.5926i	1.80695	+	0.384078i	0.823798	+	0.566884i	$0.191851\pi$
$912$	4.11030	−	0.873672i	0.136106	−	0.0289302i
$913$	−25.6549	+	11.4223i	−0.849055	+	0.378024i
$914$	11.1344	−	34.2683i	0.368294	−	1.13349i
$915$	2.78249	−	8.56363i	0.0919863	−	0.283105i
$916$	−22.0898	+	9.83501i	−0.729867	+	0.324958i
$917$	−2.21460	+	0.470728i	−0.0731325	+	0.0155448i
$918$	−3.58579	−	0.762184i	−0.118349	−	0.0251558i
$919$	−11.1514	−	4.96492i	−0.367851	−	0.163778i	0.214483	−	0.976728i	$-0.431193\pi$
$919$	−11.1514	−	4.96492i	−0.367851	−	0.163778i	−0.582333	+	0.812950i	$0.697860\pi$
$920$	2.83099	−	3.14413i	0.0933349	−	0.103659i
$921$	0.832111	−	7.91700i	0.0274190	−	0.260874i
$922$	32.2835	+	23.4554i	1.06320	+	0.772461i
$923$	0.0223069	+	0.212236i	0.000734239	+	0.00698582i
$924$	−1.42478	+	2.46779i	−0.0468718	+	0.0811844i
$925$	1.86215	+	3.22535i	0.0612272	+	0.106049i
$926$	−12.7733	+	9.28037i	−0.419758	+	0.304972i
$927$	0.763915	+	0.848413i	0.0250902	+	0.0278655i
$928$	0.643213	+	1.97961i	0.0211145	+	0.0649837i
$929$	−31.0404			−1.01840			−0.509202	−	0.860647i	$-0.670059\pi$
$929$	−31.0404			−1.01840			−0.509202	+	0.860647i	$0.670059\pi$
$930$	−4.61162	+	3.11977i	−0.151221	+	0.102301i
$931$	27.7258			0.908676
$932$	−0.507898	−	1.56315i	−0.0166368	−	0.0512027i
$933$	−2.17807	−	2.41900i	−0.0713069	−	0.0791944i
$934$	−34.3159	+	24.9320i	−1.12285	+	0.815798i
$935$	8.23820	+	14.2690i	0.269418	+	0.466646i
$936$	0.0965405	−	0.167213i	0.00315552	−	0.00546553i
$937$	3.55907	+	33.8623i	0.116270	+	1.10623i	0.884655	+	0.466245i	$0.154394\pi$
$937$	3.55907	+	33.8623i	0.116270	+	1.10623i	−0.768386	+	0.639987i	$0.778940\pi$
$938$	−1.22738	−	0.891745i	−0.0400754	−	0.0291165i
$939$	0.126649	−	1.20498i	0.00413303	−	0.0393232i
$940$	1.08353	−	1.20338i	0.0353409	−	0.0392500i
$941$	−29.8184	−	13.2760i	−0.972052	−	0.432786i	−0.141630	−	0.989920i	$-0.545234\pi$
$941$	−29.8184	−	13.2760i	−0.972052	−	0.432786i	−0.830422	+	0.557134i	$0.811901\pi$
$942$	−4.35239	−	0.925129i	−0.141808	−	0.0301423i
$943$	0.00617793	−	0.00131316i	0.000201181	−	4.27624e-5i
$944$	1.81259	−	0.807019i	0.0589949	−	0.0262662i
$945$	0.195920	−	0.602979i	0.00637327	−	0.0196149i
$946$	9.11004	−	28.0378i	0.296193	−	0.911588i
$947$	−1.66142	+	0.739711i	−0.0539889	+	0.0240374i	−0.433553	−	0.901128i	$-0.642740\pi$
$947$	−1.66142	+	0.739711i	−0.0539889	+	0.0240374i	0.379565	+	0.925165i	$0.376074\pi$
$948$	4.08812	−	0.868958i	0.132776	−	0.0282224i
$949$	−2.06912	−	0.439805i	−0.0671665	−	0.0142767i
$950$	3.83884	+	1.70916i	0.124548	+	0.0554525i
$951$	−23.6230	+	26.2360i	−0.766030	+	0.850762i
$952$	−0.242947	+	2.31149i	−0.00787396	+	0.0749157i
$953$	−13.9771	−	10.1550i	−0.452763	−	0.328952i	0.337923	−	0.941174i	$-0.390276\pi$
$953$	−13.9771	−	10.1550i	−0.452763	−	0.328952i	−0.790686	+	0.612222i	$0.790276\pi$
$954$	0.161026	+	1.53206i	0.00521339	+	0.0496021i
$955$	−0.302866	+	0.524579i	−0.00980051	+	0.0169750i
$956$	−0.806503	−	1.39690i	−0.0260842	−	0.0451791i
$957$	7.56853	−	5.49886i	0.244656	−	0.177753i
$958$	−12.6123	−	14.0074i	−0.407484	−	0.452557i
$959$	−0.0986352	−	0.303568i	−0.00318510	−	0.00980272i
$960$	1.00000			0.0322749
$961$	11.5341	−	28.7744i	0.372067	−	0.928206i
$962$	0.719093			0.0231845
$963$	−1.67749	−	5.16278i	−0.0540564	−	0.166368i
$964$	−7.23109	−	8.03094i	−0.232898	−	0.258659i
$965$	12.4599	−	9.05267i	0.401099	−	0.291416i
$966$	−1.34120	−	2.32303i	−0.0431524	−	0.0747421i
$967$	9.91914	−	17.1805i	0.318978	−	0.552486i	−0.661297	−	0.750124i	$-0.729994\pi$
$967$	9.91914	−	17.1805i	0.318978	−	0.552486i	0.980275	+	0.197638i	$0.0633270\pi$
$968$	0.961719	+	9.15015i	0.0309108	+	0.294097i
$969$	−12.4626	−	9.05460i	−0.400356	−	0.290876i
$970$	0.530489	−	5.04726i	0.0170330	−	0.162058i
$971$	12.8675	−	14.2908i	0.412938	−	0.458614i	−0.500413	−	0.865787i	$-0.666818\pi$
$971$	12.8675	−	14.2908i	0.412938	−	0.458614i	0.913351	+	0.407172i	$0.133485\pi$
$972$	0.913545	+	0.406737i	0.0293020	+	0.0130461i
$973$	−11.1971	−	2.38003i	−0.358964	−	0.0763002i
$974$	−41.4297	+	8.80615i	−1.32749	+	0.282167i
$975$	0.176388	−	0.0785331i	0.00564894	−	0.00251507i
$976$	2.78249	−	8.56363i	0.0890654	−	0.274115i
$977$	−16.9170	+	52.0652i	−0.541223	+	1.66571i	0.188581	+	0.982058i	$0.439611\pi$
$977$	−16.9170	+	52.0652i	−0.541223	+	1.66571i	−0.729804	+	0.683656i	$0.760389\pi$
$978$	−15.2759	+	6.80126i	−0.488469	+	0.217480i
$979$	−33.9082	+	7.20742i	−1.08371	+	0.230350i
$980$	6.45385	+	1.37181i	0.206161	+	0.0438208i
$981$	4.03964	+	1.79857i	0.128976	+	0.0574238i
$982$	14.5601	−	16.1706i	0.464632	−	0.516026i
$983$	−0.281455	+	2.67787i	−0.00897703	+	0.0854107i	−0.998093	−	0.0617267i	$-0.980339\pi$
$983$	−0.281455	+	2.67787i	−0.00897703	+	0.0854107i	0.989116	+	0.147137i	$0.0470060\pi$
$984$	0.00120773		0.000877466i	3.85010e−5		2.79726e-5i
$985$	2.05035	+	19.5078i	0.0653297	+	0.621571i
$986$	3.81525	−	6.60821i	0.121502	−	0.210448i
$987$	−0.513330	−	0.889114i	−0.0163395	−	0.0283008i
$988$	0.656397	−	0.476900i	0.0208828	−	0.0151722i
$989$	18.5693	+	20.6232i	0.590468	+	0.655781i
$990$	−1.38888	−	4.27453i	−0.0441414	−	0.135853i
$991$	−11.9870			−0.380779			−0.190390	−	0.981709i	$-0.560975\pi$
$991$	−11.9870			−0.380779			−0.190390	+	0.981709i	$0.560975\pi$
$992$	−4.61162	+	3.11977i	−0.146419	+	0.0990528i
$993$	−31.6327			−1.00383
$994$	0.216542	+	0.666449i	0.00686831	+	0.0211385i
$995$	−14.6620	−	16.2838i	−0.464817	−	0.516231i
$996$	5.05495	−	3.67264i	0.160172	−	0.116372i
$997$	25.9367	+	44.9236i	0.821423	+	1.42275i	0.904623	+	0.426213i	$0.140153\pi$
$997$	25.9367	+	44.9236i	0.821423	+	1.42275i	−0.0832004	+	0.996533i	$0.526514\pi$
$998$	−17.4664	+	30.2527i	−0.552889	+	0.957632i
$999$	0.389296	+	3.70391i	0.0123168	+	0.117186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.f.361.1	✓	16
31.14	even	15	inner	930.2.bg.f.541.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.f.361.1	✓	16	1.1	even	1	trivial
930.2.bg.f.541.1	yes	16	31.14	even	15	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.0662721 - 0.630537i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(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} +(-0.0662721 - 0.630537i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(4.10593 + 1.82808i) q^{11} +(-0.978148 - 0.207912i) q^{12} +(-0.188862 + 0.0401438i) q^{13} +(-0.579197 + 0.257875i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.34897 + 1.49106i) q^{17} +(0.978148 - 0.207912i) q^{18} +(4.11030 + 0.873672i) q^{19} +(0.913545 + 0.406737i) q^{20} +(0.424235 - 0.471161i) q^{21} +(0.469803 - 4.46988i) q^{22} +(3.42283 + 2.48683i) q^{23} +(0.104528 + 0.994522i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.0965405 + 0.167213i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.424235 + 0.471161i) q^{28} +(-0.643213 - 1.97961i) q^{29} -1.00000 q^{30} +(4.61162 - 3.11977i) q^{31} -1.00000 q^{32} +(1.38888 + 4.27453i) q^{33} +(2.45297 + 2.72430i) q^{34} +(-0.512925 + 0.372662i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.86215 - 3.22535i) q^{37} +(-0.439242 - 4.17911i) q^{38} +(-0.156206 - 0.113490i) q^{39} +(0.104528 - 0.994522i) q^{40} +(0.000998901 - 0.00110939i) q^{41} +(-0.579197 - 0.257875i) q^{42} +(6.41595 + 1.36375i) q^{43} +(-4.39629 + 0.934460i) q^{44} +(0.913545 - 0.406737i) q^{45} +(1.30740 - 4.02377i) q^{46} +(0.500395 - 1.54006i) q^{47} +(0.913545 - 0.406737i) q^{48} +(6.45385 - 1.37181i) q^{49} +(0.978148 + 0.207912i) q^{50} +(-3.34897 - 1.49106i) q^{51} +(0.129196 - 0.143487i) q^{52} +(-0.161026 + 1.53206i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-0.469803 - 4.46988i) q^{55} +(0.317005 - 0.549069i) q^{56} +(2.10107 + 3.63915i) q^{57} +(-1.68395 + 1.22346i) q^{58} +(1.32764 + 1.47450i) q^{59} +(0.309017 + 0.951057i) q^{60} +9.00433 q^{61} +(-4.39215 - 3.42185i) q^{62} +0.634010 q^{63} +(0.309017 + 0.951057i) q^{64} +(0.129196 + 0.143487i) q^{65} +(3.63613 - 2.64180i) q^{66} +(1.19645 + 2.07232i) q^{67} +(1.83295 - 3.17476i) q^{68} +(0.442244 + 4.20767i) q^{69} +(0.512925 + 0.372662i) q^{70} +(0.115531 - 1.09920i) q^{71} +(-0.669131 + 0.743145i) q^{72} +(10.0086 + 4.45610i) q^{73} +(-3.64292 - 0.774327i) q^{74} +(-0.978148 + 0.207912i) q^{75} +(-3.83884 + 1.70916i) q^{76} +(0.880562 - 2.71009i) q^{77} +(-0.0596653 + 0.183631i) q^{78} +(-3.81812 + 1.69994i) q^{79} +(-0.978148 + 0.207912i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-0.00136377 - 0.000607190i) q^{82} +(-4.18090 + 4.64336i) q^{83} +(-0.0662721 + 0.630537i) q^{84} +(2.96578 + 2.15476i) q^{85} +(-0.685632 - 6.52335i) q^{86} +(1.04074 - 1.80261i) q^{87} +(2.24725 + 3.89235i) q^{88} +(-6.23989 + 4.53354i) q^{89} +(-0.669131 - 0.743145i) q^{90} +(0.0378284 + 0.116424i) q^{91} -4.23085 q^{92} +(5.40422 + 1.33957i) q^{93} -1.61931 q^{94} +(-1.29853 - 3.99646i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(-4.10581 + 2.98305i) q^{97} +(-3.29902 - 5.71406i) q^{98} +(-2.24725 + 3.89235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} - 13 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 - 13 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} - 13 q^{7} + 4 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{14} - 4 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{18} + 9 q^{19} + 2 q^{20} + 2 q^{21} - 13 q^{22} - 3 q^{23} - 2 q^{24} - 8 q^{25} + q^{26} - 4 q^{27} + 2 q^{28} - q^{29} - 16 q^{30} - 19 q^{31} - 16 q^{32} + 14 q^{33} + 4 q^{34} + 11 q^{35} - 8 q^{36} - 3 q^{37} + 6 q^{38} - 13 q^{39} - 2 q^{40} - 2 q^{42} + 2 q^{43} - 7 q^{44} + 2 q^{45} - 7 q^{46} - q^{47} + 2 q^{48} + 3 q^{49} - 2 q^{50} + 6 q^{51} - 6 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} - 7 q^{56} - 6 q^{57} - 4 q^{58} + 16 q^{59} - 4 q^{60} - 28 q^{61} - 21 q^{62} - 14 q^{63} - 4 q^{64} - 6 q^{65} + 11 q^{66} + 47 q^{67} - 4 q^{68} + 9 q^{69} - 11 q^{70} + 3 q^{71} - 2 q^{72} - 27 q^{73} + 8 q^{74} + 2 q^{75} - 6 q^{76} + 14 q^{77} - 12 q^{78} + 4 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} + 66 q^{83} - 13 q^{84} + 18 q^{85} + 13 q^{86} + 3 q^{87} - 3 q^{88} - 45 q^{89} - 2 q^{90} + 12 q^{91} - 8 q^{92} - 26 q^{93} + 36 q^{94} - 18 q^{95} - 2 q^{96} + 5 q^{97} - 13 q^{98} + 3 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 - 13 * q^7 + 4 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 6 * q^13 - 2 * q^14 - 4 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^18 + 9 * q^19 + 2 * q^20 + 2 * q^21 - 13 * q^22 - 3 * q^23 - 2 * q^24 - 8 * q^25 + q^26 - 4 * q^27 + 2 * q^28 - q^29 - 16 * q^30 - 19 * q^31 - 16 * q^32 + 14 * q^33 + 4 * q^34 + 11 * q^35 - 8 * q^36 - 3 * q^37 + 6 * q^38 - 13 * q^39 - 2 * q^40 - 2 * q^42 + 2 * q^43 - 7 * q^44 + 2 * q^45 - 7 * q^46 - q^47 + 2 * q^48 + 3 * q^49 - 2 * q^50 + 6 * q^51 - 6 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 - 7 * q^56 - 6 * q^57 - 4 * q^58 + 16 * q^59 - 4 * q^60 - 28 * q^61 - 21 * q^62 - 14 * q^63 - 4 * q^64 - 6 * q^65 + 11 * q^66 + 47 * q^67 - 4 * q^68 + 9 * q^69 - 11 * q^70 + 3 * q^71 - 2 * q^72 - 27 * q^73 + 8 * q^74 + 2 * q^75 - 6 * q^76 + 14 * q^77 - 12 * q^78 + 4 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 + 66 * q^83 - 13 * q^84 + 18 * q^85 + 13 * q^86 + 3 * q^87 - 3 * q^88 - 45 * q^89 - 2 * q^90 + 12 * q^91 - 8 * q^92 - 26 * q^93 + 36 * q^94 - 18 * q^95 - 2 * q^96 + 5 * q^97 - 13 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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