LMFDB - Embedded newform 310.2.q.d.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(41,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("310.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.q (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:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			51.1
Root			$-0.104528 - 0.994522i$ of defining polynomial
Character	$\chi$	$=$	310.51
Dual form			310.2.q.d.231.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-0.755585 - 0.839162i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.564602 + 0.977920i) q^{6} +(-0.186415 - 1.77362i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.180301 - 1.71545i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.755585 - 0.839162i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.564602 + 0.977920i) q^{6} +(-0.186415 - 1.77362i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.180301 - 1.71545i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-4.95485 - 2.20604i) q^{11} +(1.10453 + 0.234775i) q^{12} +(-0.935398 + 0.198825i) q^{13} +(-1.62920 + 0.725368i) q^{14} +(0.348943 - 1.07394i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.21188 - 1.87525i) q^{17} +(-1.68720 + 0.358626i) q^{18} +(-7.94417 - 1.68859i) q^{19} +(-0.913545 - 0.406737i) q^{20} +(-1.34750 + 1.49655i) q^{21} +(-0.566937 + 5.39405i) q^{22} +(1.16535 + 0.846678i) q^{23} +(-0.118034 - 1.12302i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.478148 + 0.828176i) q^{26} +(-4.31641 + 3.13605i) q^{27} +(1.19332 + 1.32531i) q^{28} +(-2.44279 - 7.51813i) q^{29} -1.12920 q^{30} +(2.22335 + 5.10458i) q^{31} -1.00000 q^{32} +(1.89259 + 5.82478i) q^{33} +(-3.08501 - 3.42625i) q^{34} +(1.44279 - 1.04825i) q^{35} +(0.862449 + 1.49381i) q^{36} +(0.755585 - 1.30871i) q^{37} +(0.848943 + 8.07716i) q^{38} +(0.873619 + 0.634721i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-4.67274 + 5.18961i) q^{41} +(1.83970 + 0.819089i) q^{42} +(9.38850 + 1.99559i) q^{43} +(5.30524 - 1.12766i) q^{44} +(1.57577 - 0.701579i) q^{45} +(0.445125 - 1.36995i) q^{46} +(3.47262 - 10.6876i) q^{47} +(-1.03158 + 0.459289i) q^{48} +(3.73607 - 0.794126i) q^{49} +(0.978148 + 0.207912i) q^{50} +(-4.75607 - 2.11754i) q^{51} +(0.639886 - 0.710666i) q^{52} +(0.731988 - 6.96440i) q^{53} +(4.31641 + 3.13605i) q^{54} +(-0.566937 - 5.39405i) q^{55} +(0.891693 - 1.54446i) q^{56} +(4.58550 + 7.94232i) q^{57} +(-6.39531 + 4.64646i) q^{58} +(-6.05626 - 6.72615i) q^{59} +(0.348943 + 1.07394i) q^{60} +9.32912 q^{61} +(4.16769 - 3.69193i) q^{62} -3.07616 q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.639886 - 0.710666i) q^{65} +(4.95485 - 3.59991i) q^{66} +(-1.20810 - 2.09249i) q^{67} +(-2.30524 + 3.99279i) q^{68} +(-0.170023 - 1.61766i) q^{69} +(-1.44279 - 1.04825i) q^{70} +(-0.673699 + 6.40982i) q^{71} +(1.15418 - 1.28185i) q^{72} +(9.85111 + 4.38600i) q^{73} +(-1.47815 - 0.314190i) q^{74} +(1.10453 - 0.234775i) q^{75} +(7.41949 - 3.30337i) q^{76} +(-2.98902 + 9.19925i) q^{77} +(0.333693 - 1.02700i) q^{78} +(11.3060 - 5.03377i) q^{79} +(0.978148 - 0.207912i) q^{80} +(0.831460 + 0.176732i) q^{81} +(6.37957 + 2.84037i) q^{82} +(-0.642222 + 0.713259i) q^{83} +(0.210500 - 2.00278i) q^{84} +(3.72995 + 2.70997i) q^{85} +(-1.00329 - 9.54567i) q^{86} +(-4.46320 + 7.73049i) q^{87} +(-2.71188 - 4.69711i) q^{88} +(5.70054 - 4.14169i) q^{89} +(-1.15418 - 1.28185i) q^{90} +(0.527011 + 1.62197i) q^{91} -1.44045 q^{92} +(2.60364 - 5.72270i) q^{93} -11.2376 q^{94} +(-2.50973 - 7.72415i) q^{95} +(0.755585 + 0.839162i) q^{96} +(-12.4997 + 9.08154i) q^{97} +(-1.90977 - 3.30781i) q^{98} +(-4.67772 + 8.10204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 8 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 7 q^{7} + 2 q^{8} + q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 8 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 7 * q^7 + 2 * q^8 + q^9	\( 8 q + 2 q^{2} - 8 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 7 q^{7} + 2 q^{8} + q^{9} + q^{10} + 6 q^{11} + 7 q^{12} - 10 q^{13} - 8 q^{14} - q^{15} - 2 q^{16} + 18 q^{17} - q^{18} - 13 q^{19} - q^{20} + 21 q^{21} + 9 q^{22} - 12 q^{23} + 8 q^{24} - 4 q^{25} - 5 q^{26} - 17 q^{27} + 3 q^{28} - 9 q^{29} - 4 q^{30} - 11 q^{31} - 8 q^{32} - 39 q^{33} - 3 q^{34} + q^{35} - 4 q^{36} + 8 q^{37} + 3 q^{38} + q^{40} - 3 q^{41} + 34 q^{42} + 21 q^{43} + 21 q^{44} + 14 q^{45} - 18 q^{46} - 9 q^{47} + 7 q^{48} + 12 q^{49} - q^{50} - 39 q^{51} + 5 q^{52} - 12 q^{53} + 17 q^{54} + 9 q^{55} - 8 q^{56} + 14 q^{57} - 6 q^{58} - 30 q^{59} - q^{60} + 68 q^{61} + q^{62} - 46 q^{63} - 2 q^{64} - 5 q^{65} - 6 q^{66} + 23 q^{67} + 3 q^{68} + 42 q^{69} - q^{70} - 16 q^{72} + 17 q^{73} - 3 q^{74} + 7 q^{75} + 12 q^{76} - 36 q^{77} - 5 q^{78} + 51 q^{79} - q^{80} - 11 q^{81} + 3 q^{82} + 6 q^{83} + 26 q^{84} + 6 q^{85} - 26 q^{86} - 6 q^{87} - 6 q^{88} - 21 q^{89} + 16 q^{90} - 10 q^{91} - 12 q^{92} + 58 q^{93} - 36 q^{94} + 4 q^{95} + 8 q^{96} - 6 q^{97} + 8 q^{98} + 36 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 8 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 7 * q^7 + 2 * q^8 + q^9 + q^10 + 6 * q^11 + 7 * q^12 - 10 * q^13 - 8 * q^14 - q^15 - 2 * q^16 + 18 * q^17 - q^18 - 13 * q^19 - q^20 + 21 * q^21 + 9 * q^22 - 12 * q^23 + 8 * q^24 - 4 * q^25 - 5 * q^26 - 17 * q^27 + 3 * q^28 - 9 * q^29 - 4 * q^30 - 11 * q^31 - 8 * q^32 - 39 * q^33 - 3 * q^34 + q^35 - 4 * q^36 + 8 * q^37 + 3 * q^38 + q^40 - 3 * q^41 + 34 * q^42 + 21 * q^43 + 21 * q^44 + 14 * q^45 - 18 * q^46 - 9 * q^47 + 7 * q^48 + 12 * q^49 - q^50 - 39 * q^51 + 5 * q^52 - 12 * q^53 + 17 * q^54 + 9 * q^55 - 8 * q^56 + 14 * q^57 - 6 * q^58 - 30 * q^59 - q^60 + 68 * q^61 + q^62 - 46 * q^63 - 2 * q^64 - 5 * q^65 - 6 * q^66 + 23 * q^67 + 3 * q^68 + 42 * q^69 - q^70 - 16 * q^72 + 17 * q^73 - 3 * q^74 + 7 * q^75 + 12 * q^76 - 36 * q^77 - 5 * q^78 + 51 * q^79 - q^80 - 11 * q^81 + 3 * q^82 + 6 * q^83 + 26 * q^84 + 6 * q^85 - 26 * q^86 - 6 * q^87 - 6 * q^88 - 21 * q^89 + 16 * q^90 - 10 * q^91 - 12 * q^92 + 58 * q^93 - 36 * q^94 + 4 * q^95 + 8 * q^96 - 6 * q^97 + 8 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$1$	$e\left(\frac{4}{15}\right)$

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
$3$	−0.755585	−	0.839162i	−0.436237	−	0.484491i	0.484435	−	0.874827i	$-0.339025\pi$
$3$	−0.755585	−	0.839162i	−0.436237	−	0.484491i	−0.920672	+	0.390337i	$0.872359\pi$
$4$	−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
$6$	−0.564602	+	0.977920i	−0.230498	+	0.399234i
$7$	−0.186415	−	1.77362i	−0.0704581	−	0.670364i	−0.971566	−	0.236769i	$-0.923912\pi$
$7$	−0.186415	−	1.77362i	−0.0704581	−	0.670364i	0.901108	−	0.433595i	$-0.142755\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	0.180301	−	1.71545i	0.0601003	−	0.571816i
$10$	0.669131	−	0.743145i	0.211598	−	0.235003i
$11$	−4.95485	−	2.20604i	−1.49394	−	0.665147i	−0.512815	−	0.858499i	$-0.671397\pi$
$11$	−4.95485	−	2.20604i	−1.49394	−	0.665147i	−0.981129	+	0.193353i	$0.938064\pi$
$12$	1.10453	+	0.234775i	0.318850	+	0.0677736i
$13$	−0.935398	+	0.198825i	−0.259433	+	0.0551441i	−0.335792	−	0.941936i	$-0.609004\pi$
$13$	−0.935398	+	0.198825i	−0.259433	+	0.0551441i	0.0763590	+	0.997080i	$0.475670\pi$
$14$	−1.62920	+	0.725368i	−0.435423	+	0.193863i
$15$	0.348943	−	1.07394i	0.0900968	−	0.277289i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	4.21188	−	1.87525i	1.02153	−	0.454815i	0.173541	−	0.984827i	$-0.444479\pi$
$17$	4.21188	−	1.87525i	1.02153	−	0.454815i	0.847990	+	0.530012i	$0.177813\pi$
$18$	−1.68720	+	0.358626i	−0.397678	+	0.0845291i
$19$	−7.94417	−	1.68859i	−1.82252	−	0.387388i	−0.835695	−	0.549194i	$-0.814935\pi$
$19$	−7.94417	−	1.68859i	−1.82252	−	0.387388i	−0.986823	+	0.161806i	$0.948268\pi$
$20$	−0.913545	−	0.406737i	−0.204275	−	0.0909491i
$21$	−1.34750	+	1.49655i	−0.294049	+	0.326574i
$22$	−0.566937	+	5.39405i	−0.120871	+	1.15002i
$23$	1.16535	+	0.846678i	0.242993	+	0.176545i	0.702616	−	0.711570i	$-0.252015\pi$
$23$	1.16535	+	0.846678i	0.242993	+	0.176545i	−0.459623	+	0.888114i	$0.652015\pi$
$24$	−0.118034	−	1.12302i	−0.0240936	−	0.229235i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.478148	+	0.828176i	0.0937725	+	0.162419i
$27$	−4.31641	+	3.13605i	−0.830693	+	0.603534i
$28$	1.19332	+	1.32531i	0.225516	+	0.250461i
$29$	−2.44279	−	7.51813i	−0.453615	−	1.39608i	−0.872754	−	0.488160i	$-0.837668\pi$
$29$	−2.44279	−	7.51813i	−0.453615	−	1.39608i	0.419139	−	0.907922i	$-0.362332\pi$
$30$	−1.12920			−0.206164
$31$	2.22335	+	5.10458i	0.399326	+	0.916809i
$31$	2.22335	+	5.10458i	0.399326	+	0.916809i
$32$	−1.00000			−0.176777
$33$	1.89259	+	5.82478i	0.329457	+	1.01396i
$34$	−3.08501	−	3.42625i	−0.529075	−	0.587597i
$35$	1.44279	−	1.04825i	0.243876	−	0.177186i
$36$	0.862449	+	1.49381i	0.143741	+	0.248968i
$37$	0.755585	−	1.30871i	0.124217	−	0.215151i	−0.797209	−	0.603703i	$-0.793691\pi$
$37$	0.755585	−	1.30871i	0.124217	−	0.215151i	0.921427	+	0.388552i	$0.127025\pi$
$38$	0.848943	+	8.07716i	0.137717	+	1.31029i
$39$	0.873619	+	0.634721i	0.139891	+	0.101637i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	−4.67274	+	5.18961i	−0.729760	+	0.810481i	−0.987812	−	0.155650i	$-0.950253\pi$
$41$	−4.67274	+	5.18961i	−0.729760	+	0.810481i	0.258052	+	0.966131i	$0.416919\pi$
$42$	1.83970	+	0.819089i	0.283873	+	0.126388i
$43$	9.38850	+	1.99559i	1.43173	+	0.304324i	0.857549	−	0.514402i	$-0.171986\pi$
$43$	9.38850	+	1.99559i	1.43173	+	0.304324i	0.574184	+	0.818726i	$0.305319\pi$
$44$	5.30524	−	1.12766i	0.799795	−	0.170002i
$45$	1.57577	−	0.701579i	0.234902	−	0.104585i
$46$	0.445125	−	1.36995i	0.0656301	−	0.201989i
$47$	3.47262	−	10.6876i	0.506534	−	1.55895i	−0.291642	−	0.956528i	$-0.594201\pi$
$47$	3.47262	−	10.6876i	0.506534	−	1.55895i	0.798176	−	0.602425i	$-0.205799\pi$
$48$	−1.03158	+	0.459289i	−0.148896	+	0.0662926i
$49$	3.73607	−	0.794126i	0.533724	−	0.113447i
$50$	0.978148	+	0.207912i	0.138331	+	0.0294032i
$51$	−4.75607	−	2.11754i	−0.665983	−	0.296515i
$52$	0.639886	−	0.710666i	0.0887363	−	0.0985516i
$53$	0.731988	−	6.96440i	0.100546	−	0.956634i	−0.821671	−	0.569962i	$-0.806958\pi$
$53$	0.731988	−	6.96440i	0.100546	−	0.956634i	0.922217	−	0.386672i	$-0.126375\pi$
$54$	4.31641	+	3.13605i	0.587389	+	0.426763i
$55$	−0.566937	−	5.39405i	−0.0764458	−	0.727333i
$56$	0.891693	−	1.54446i	0.119157	−	0.206387i
$57$	4.58550	+	7.94232i	0.607364	+	1.05199i
$58$	−6.39531	+	4.64646i	−0.839745	+	0.610110i
$59$	−6.05626	−	6.72615i	−0.788457	−	0.875671i	0.206242	−	0.978501i	$-0.433877\pi$
$59$	−6.05626	−	6.72615i	−0.788457	−	0.875671i	−0.994699	+	0.102831i	$0.967210\pi$
$60$	0.348943	+	1.07394i	0.0450484	+	0.138645i
$61$	9.32912			1.19447			0.597236	−	0.802066i	$-0.296266\pi$
$61$	9.32912			1.19447			0.597236	+	0.802066i	$0.296266\pi$
$62$	4.16769	−	3.69193i	0.529297	−	0.468876i
$63$	−3.07616			−0.387560
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−0.639886	−	0.710666i	−0.0793681	−	0.0881472i
$66$	4.95485	−	3.59991i	0.609900	−	0.443118i
$67$	−1.20810	−	2.09249i	−0.147593	−	0.255639i	0.782744	−	0.622343i	$-0.213819\pi$
$67$	−1.20810	−	2.09249i	−0.147593	−	0.255639i	−0.930337	+	0.366705i	$0.880486\pi$
$68$	−2.30524	+	3.99279i	−0.279551	+	0.484197i
$69$	−0.170023	−	1.61766i	−0.0204683	−	0.194743i
$70$	−1.44279	−	1.04825i	−0.172446	−	0.125290i
$71$	−0.673699	+	6.40982i	−0.0799534	+	0.760705i	0.878939	+	0.476935i	$0.158252\pi$
$71$	−0.673699	+	6.40982i	−0.0799534	+	0.760705i	−0.958892	+	0.283771i	$0.908415\pi$
$72$	1.15418	−	1.28185i	0.136022	−	0.151067i
$73$	9.85111	+	4.38600i	1.15299	+	0.513342i	0.892016	−	0.452005i	$-0.149291\pi$
$73$	9.85111	+	4.38600i	1.15299	+	0.513342i	0.260970	+	0.965347i	$0.415958\pi$
$74$	−1.47815	−	0.314190i	−0.171831	−	0.0365238i
$75$	1.10453	−	0.234775i	0.127540	−	0.0271095i
$76$	7.41949	−	3.30337i	0.851074	−	0.378923i
$77$	−2.98902	+	9.19925i	−0.340630	+	1.04835i
$78$	0.333693	−	1.02700i	0.0377833	−	0.116285i
$79$	11.3060	−	5.03377i	1.27203	−	0.566343i	0.344040	−	0.938955i	$-0.388204\pi$
$79$	11.3060	−	5.03377i	1.27203	−	0.566343i	0.927987	+	0.372612i	$0.121538\pi$
$80$	0.978148	−	0.207912i	0.109360	−	0.0232452i
$81$	0.831460	+	0.176732i	0.0923844	+	0.0196369i
$82$	6.37957	+	2.84037i	0.704505	+	0.313666i
$83$	−0.642222	+	0.713259i	−0.0704930	+	0.0782904i	−0.777360	−	0.629056i	$-0.783441\pi$
$83$	−0.642222	+	0.713259i	−0.0704930	+	0.0782904i	0.706867	+	0.707347i	$0.250108\pi$
$84$	0.210500	−	2.00278i	0.0229675	−	0.218521i
$85$	3.72995	+	2.70997i	0.404570	+	0.293938i
$86$	−1.00329	−	9.54567i	−0.108188	−	1.02934i
$87$	−4.46320	+	7.73049i	−0.478505	+	0.828795i
$88$	−2.71188	−	4.69711i	−0.289087	−	0.500714i
$89$	5.70054	−	4.14169i	0.604257	−	0.439018i	−0.243131	−	0.969994i	$-0.578174\pi$
$89$	5.70054	−	4.14169i	0.604257	−	0.439018i	0.847387	+	0.530975i	$0.178174\pi$
$90$	−1.15418	−	1.28185i	−0.121661	−	0.135119i
$91$	0.527011	+	1.62197i	0.0552458	+	0.170029i
$92$	−1.44045			−0.150178
$93$	2.60364	−	5.72270i	0.269985	−	0.593416i
$94$	−11.2376			−1.15907
$95$	−2.50973	−	7.72415i	−0.257493	−	0.792481i
$96$	0.755585	+	0.839162i	0.0771166	+	0.0856466i
$97$	−12.4997	+	9.08154i	−1.26915	+	0.922091i	−0.999168	−	0.0407749i	$-0.987017\pi$
$97$	−12.4997	+	9.08154i	−1.26915	+	0.922091i	−0.269981	+	0.962866i	$0.587017\pi$
$98$	−1.90977	−	3.30781i	−0.192916	−	0.334140i
$99$	−4.67772	+	8.10204i	−0.470128	+	0.814286i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	3.47059	+	2.52153i	0.345337	+	0.250902i	0.746910	−	0.664925i	$-0.231537\pi$
$101$	3.47059	+	2.52153i	0.345337	+	0.250902i	−0.401573	+	0.915827i	$0.631537\pi$
$102$	−0.544193	+	5.17765i	−0.0538831	+	0.512664i
$103$	−7.92416	+	8.80068i	−0.780791	+	0.867156i	−0.993947	−	0.109862i	$-0.964959\pi$
$103$	−7.92416	+	8.80068i	−0.780791	+	0.867156i	0.213156	+	0.977018i	$0.431626\pi$
$104$	−0.873619	−	0.388960i	−0.0856654	−	0.0381407i
$105$	−1.96980	−	0.418694i	−0.192233	−	0.0408604i
$106$	−6.84973	+	1.45596i	−0.665305	+	0.141415i
$107$	18.8311	−	8.38416i	1.82047	−	0.810527i	0.875652	−	0.482942i	$-0.160432\pi$
$107$	18.8311	−	8.38416i	1.82047	−	0.810527i	0.944822	−	0.327585i	$-0.106235\pi$
$108$	1.64872	−	5.07424i	0.158648	−	0.488269i
$109$	−3.06838	+	9.44350i	−0.293898	+	0.904524i	0.689692	+	0.724103i	$0.257746\pi$
$109$	−3.06838	+	9.44350i	−0.293898	+	0.904524i	−0.983590	+	0.180421i	$0.942254\pi$
$110$	−4.95485	+	2.20604i	−0.472427	+	0.210338i
$111$	−1.66913	+	0.354785i	−0.158427	+	0.0336747i
$112$	−1.74441	−	0.370787i	−0.164832	−	0.0350361i
$113$	−2.23800	−	0.996422i	−0.210533	−	0.0937355i	0.298761	−	0.954328i	$-0.403427\pi$
$113$	−2.23800	−	0.996422i	−0.210533	−	0.0937355i	−0.509294	+	0.860593i	$0.670093\pi$
$114$	6.13660	−	6.81538i	0.574745	−	0.638319i
$115$	−0.150568	+	1.43256i	−0.0140406	+	0.133587i
$116$	6.39531	+	4.64646i	0.593789	+	0.431413i
$117$	0.172421	+	1.64048i	0.0159403	+	0.151662i
$118$	−4.52547	+	7.83834i	−0.416603	+	0.721577i
$119$	−4.11113	−	7.12069i	−0.376867	−	0.652752i
$120$	0.913545	−	0.663730i	0.0833949	−	0.0605899i
$121$	12.3235	+	13.6866i	1.12032	+	1.24424i
$122$	−2.88286	−	8.87252i	−0.261002	−	0.803281i
$123$	7.88558			0.711019
$124$	−4.79912	−	2.82284i	−0.430974	−	0.253498i
$125$	−1.00000			−0.0894427
$126$	0.950585	+	2.92560i	0.0846849	+	0.260633i
$127$	−5.89829	−	6.55072i	−0.523389	−	0.581282i	0.422259	−	0.906475i	$-0.361237\pi$
$127$	−5.89829	−	6.55072i	−0.523389	−	0.581282i	−0.945648	+	0.325193i	$0.894571\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−5.41919	−	9.38632i	−0.477133	−	0.826419i
$130$	−0.478148	+	0.828176i	−0.0419363	+	0.0726358i
$131$	−0.813284	−	7.73788i	−0.0710569	−	0.676061i	−0.970841	−	0.239725i	$-0.922943\pi$
$131$	−0.813284	−	7.73788i	−0.0710569	−	0.676061i	0.899784	−	0.436336i	$-0.143724\pi$
$132$	−4.95485	−	3.59991i	−0.431265	−	0.313332i
$133$	−1.51399	+	14.4047i	−0.131280	+	1.24904i
$134$	−1.61676	+	1.79559i	−0.139666	+	0.155115i
$135$	−4.87411	−	2.17009i	−0.419496	−	0.186772i
$136$	4.50973	+	0.958572i	0.386706	+	0.0821969i
$137$	−3.02547	+	0.643083i	−0.258483	+	0.0549423i	−0.335330	−	0.942101i	$-0.608848\pi$
$137$	−3.02547	+	0.643083i	−0.258483	+	0.0549423i	0.0768473	+	0.997043i	$0.475515\pi$
$138$	−1.48594	+	0.661585i	−0.126492	+	0.0563178i
$139$	−0.848579	+	2.61166i	−0.0719755	+	0.221518i	−0.980573	−	0.196155i	$-0.937154\pi$
$139$	−0.848579	+	2.61166i	−0.0719755	+	0.221518i	0.908597	+	0.417673i	$0.137154\pi$
$140$	−0.551097	+	1.69610i	−0.0465762	+	0.143347i
$141$	−11.5925	+	5.16133i	−0.976267	+	0.434662i
$142$	6.30428	−	1.34002i	0.529044	−	0.112452i
$143$	5.07337	+	1.07838i	0.424257	+	0.0901786i
$144$	−1.57577	−	0.701579i	−0.131314	−	0.0584649i
$145$	5.28950	−	5.87458i	0.439269	−	0.487858i
$146$	1.12717	−	10.7243i	0.0932853	−	0.887551i
$147$	−3.48932	−	2.53514i	−0.287794	−	0.209095i
$148$	0.157960	+	1.50289i	0.0129843	+	0.123537i
$149$	−0.512716	+	0.888049i	−0.0420033	+	0.0727518i	−0.886263	−	0.463183i	$-0.846707\pi$
$149$	−0.512716	+	0.888049i	−0.0420033	+	0.0727518i	0.844259	+	0.535935i	$0.180041\pi$
$150$	−0.564602	−	0.977920i	−0.0460996	−	0.0798468i
$151$	−8.68274	+	6.30838i	−0.706591	+	0.513369i	−0.882072	−	0.471114i	$-0.843852\pi$
$151$	−8.68274	+	6.30838i	−0.706591	+	0.513369i	0.175481	+	0.984483i	$0.443852\pi$
$152$	−5.43444	−	6.03556i	−0.440792	−	0.489549i
$153$	−2.45749	−	7.56337i	−0.198676	−	0.611462i
$154$	9.67266			0.779445
$155$	−3.30902	+	4.47777i	−0.265787	+	0.359663i
$156$	−1.07985			−0.0864574
$157$	2.04683	+	6.29949i	0.163355	+	0.502754i	0.998911	−	0.0466501i	$-0.0148546\pi$
$157$	2.04683	+	6.29949i	0.163355	+	0.502754i	−0.835556	+	0.549405i	$0.814855\pi$
$158$	−8.28115	−	9.19715i	−0.658813	−	0.731686i
$159$	−6.39734	+	4.64794i	−0.507342	+	0.368606i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	1.28444	−	2.22472i	0.101228	−	0.175333i
$162$	−0.0888528	−	0.845378i	−0.00698094	−	0.0664192i
$163$	10.1484	+	7.37324i	0.794883	+	0.577517i	0.909409	−	0.415904i	$-0.136535\pi$
$163$	10.1484	+	7.37324i	0.794883	+	0.577517i	−0.114525	+	0.993420i	$0.536535\pi$
$164$	0.729954	−	6.94505i	0.0569999	−	0.542317i
$165$	−4.09811	+	4.55142i	−0.319038	+	0.354327i
$166$	0.876807	+	0.390380i	0.0680534	+	0.0302993i
$167$	9.71135	+	2.06421i	0.751487	+	0.159733i	0.567703	−	0.823233i	$-0.307832\pi$
$167$	9.71135	+	2.06421i	0.751487	+	0.159733i	0.183784	+	0.982967i	$0.441165\pi$
$168$	−1.96980	+	0.418694i	−0.151973	+	0.0323029i
$169$	−11.0407	+	4.91562i	−0.849281	+	0.378124i
$170$	1.42472	−	4.38482i	0.109271	−	0.336301i
$171$	−4.32902	+	13.3234i	−0.331049	+	1.01886i
$172$	−8.76844	+	3.90396i	−0.668587	+	0.297674i
$173$	2.43747	−	0.518099i	0.185317	−	0.0393904i	−0.114318	−	0.993444i	$-0.536468\pi$
$173$	2.43747	−	0.518099i	0.185317	−	0.0393904i	0.299635	+	0.954054i	$0.403135\pi$
$174$	8.73133	+	1.85590i	0.661921	+	0.140696i
$175$	1.62920	+	0.725368i	0.123156	+	0.0548327i
$176$	−3.62920	+	4.03064i	−0.273562	+	0.303821i
$177$	−1.06832	+	10.1644i	−0.0802997	+	0.764000i
$178$	−5.70054	−	4.14169i	−0.427274	−	0.310433i
$179$	−1.01604	−	9.66698i	−0.0759424	−	0.722544i	−0.964554	−	0.263884i	$-0.914996\pi$
$179$	−1.01604	−	9.66698i	−0.0759424	−	0.722544i	0.888612	−	0.458660i	$-0.151670\pi$
$180$	−0.862449	+	1.49381i	−0.0642831	+	0.111342i
$181$	−10.2150	−	17.6929i	−0.759275	−	1.31510i	−0.943221	−	0.332167i	$-0.892220\pi$
$181$	−10.2150	−	17.6929i	−0.759275	−	1.31510i	0.183945	−	0.982937i	$-0.441113\pi$
$182$	1.37973	−	1.00243i	0.102273	−	0.0743054i
$183$	−7.04895	−	7.82865i	−0.521073	−	0.578710i
$184$	0.445125	+	1.36995i	0.0328150	+	0.100994i
$185$	1.51117			0.111103
$186$	−6.24718	−	0.707795i	−0.458065	−	0.0518981i
$187$	−25.0061			−1.82863
$188$	3.47262	+	10.6876i	0.253267	+	0.779476i
$189$	6.36680	+	7.07105i	0.463117	+	0.514343i
$190$	−6.57055	+	4.77378i	−0.476678	+	0.346327i
$191$	−9.77487	−	16.9306i	−0.707285	−	1.22505i	−0.965861	−	0.259063i	$-0.916586\pi$
$191$	−9.77487	−	16.9306i	−0.707285	−	1.22505i	0.258575	−	0.965991i	$-0.416747\pi$
$192$	0.564602	−	0.977920i	0.0407466	−	0.0705753i
$193$	−2.14017	−	20.3624i	−0.154053	−	1.46572i	−0.749330	−	0.662197i	$-0.769624\pi$
$193$	−2.14017	−	20.3624i	−0.154053	−	1.46572i	0.595277	−	0.803521i	$-0.297042\pi$
$194$	12.4997	+	9.08154i	0.897424	+	0.652017i
$195$	−0.112875	+	1.07394i	−0.00808317	+	0.0769062i
$196$	−2.55577	+	2.83847i	−0.182555	+	0.202748i
$197$	−22.0279	−	9.80744i	−1.56942	−	0.698751i	−0.576453	−	0.817131i	$-0.695563\pi$
$197$	−22.0279	−	9.80744i	−1.56942	−	0.698751i	−0.992968	+	0.118379i	$0.962230\pi$
$198$	9.15099	+	1.94510i	0.650333	+	0.138233i
$199$	6.74727	−	1.43418i	0.478301	−	0.101666i	0.0375490	−	0.999295i	$-0.488045\pi$
$199$	6.74727	−	1.43418i	0.478301	−	0.101666i	0.440753	+	0.897629i	$0.354712\pi$
$200$	−0.913545	+	0.406737i	−0.0645974	+	0.0287606i
$201$	−0.843118	+	2.59485i	−0.0594690	+	0.183027i
$202$	1.32565	−	4.07992i	0.0932722	−	0.287062i
$203$	−12.8789	+	5.73406i	−0.903923	+	0.402452i
$204$	5.09240	−	1.08242i	0.356540	−	0.0757848i
$205$	−6.83070	−	1.45191i	−0.477077	−	0.101406i
$206$	10.8186	+	4.81677i	0.753771	+	0.335600i
$207$	1.66255	−	1.84644i	0.115555	−	0.128337i
$208$	−0.0999601	+	0.951057i	−0.00693098	+	0.0659439i
$209$	35.6371	+	25.8919i	2.46507	+	1.79098i
$210$	0.210500	+	2.00278i	0.0145259	+	0.138205i
$211$	3.44969	−	5.97504i	0.237487	−	0.411339i	−0.722506	−	0.691365i	$-0.757010\pi$
$211$	3.44969	−	5.97504i	0.237487	−	0.411339i	0.959992	+	0.280026i	$0.0903431\pi$
$212$	3.50138	+	6.06457i	0.240476	+	0.416516i
$213$	5.88791	−	4.27782i	0.403433	−	0.293111i
$214$	−13.7929	−	15.3186i	−0.942867	−	1.04716i
$215$	2.96602	+	9.12848i	0.202281	+	0.622557i
$216$	−5.33537			−0.363026
$217$	8.63910	−	4.89494i	0.586460	−	0.332290i
$218$	9.92949			0.672510
$219$	−3.76279	−	11.5807i	−0.254266	−	0.782550i
$220$	3.62920	+	4.03064i	0.244681	+	0.271746i
$221$	−3.56694	+	2.59153i	−0.239938	+	0.174325i
$222$	0.853210	+	1.47780i	0.0572637	+	0.0991836i
$223$	11.5235	−	19.9593i	0.771673	−	1.33658i	−0.164973	−	0.986298i	$-0.552754\pi$
$223$	11.5235	−	19.9593i	0.771673	−	1.33658i	0.936646	−	0.350279i	$-0.113913\pi$
$224$	0.186415	+	1.77362i	0.0124554	+	0.118505i
$225$	1.39547	+	1.01387i	0.0930314	+	0.0675913i
$226$	−0.256073	+	2.43638i	−0.0170337	+	0.162065i
$227$	−6.54848	+	7.27282i	−0.434638	+	0.482714i	−0.920178	−	0.391500i	$-0.871956\pi$
$227$	−6.54848	+	7.27282i	−0.434638	+	0.482714i	0.485540	+	0.874214i	$0.338623\pi$
$228$	−8.37812	−	3.73018i	−0.554855	−	0.247037i
$229$	9.43034	+	2.00448i	0.623174	+	0.132460i	0.508668	−	0.860963i	$-0.330138\pi$
$229$	9.43034	+	2.00448i	0.623174	+	0.132460i	0.114506	+	0.993423i	$0.463471\pi$
$230$	1.40898	−	0.299487i	0.0929052	−	0.0197476i
$231$	9.97812	−	4.44254i	0.656512	−	0.292298i
$232$	2.44279	−	7.51813i	0.160377	−	0.493590i
$233$	3.68588	−	11.3440i	0.241470	−	0.743169i	−0.754727	−	0.656039i	$-0.772230\pi$
$233$	3.68588	−	11.3440i	0.241470	−	0.743169i	0.996197	−	0.0871299i	$-0.0277695\pi$
$234$	1.50690	−	0.670917i	0.0985094	−	0.0438592i
$235$	10.9921	−	2.33644i	0.717044	−	0.152412i
$236$	8.85315	+	1.88179i	0.576291	+	0.122494i
$237$	−12.7668	−	5.68415i	−0.829294	−	0.369225i
$238$	−5.50177	+	6.11033i	−0.356627	+	0.396074i
$239$	−1.56710	+	14.9099i	−0.101367	+	0.964442i	0.819108	+	0.573640i	$0.194469\pi$
$239$	−1.56710	+	14.9099i	−0.101367	+	0.964442i	−0.920475	+	0.390802i	$0.872198\pi$
$240$	−0.913545	−	0.663730i	−0.0589691	−	0.0428436i
$241$	0.219073	+	2.08434i	0.0141117	+	0.134264i	0.999309	−	0.0371581i	$-0.0118305\pi$
$241$	0.219073	+	2.08434i	0.0141117	+	0.134264i	−0.985198	+	0.171422i	$0.945164\pi$
$242$	9.20859	−	15.9497i	0.591951	−	1.02529i
$243$	7.52313	+	13.0304i	0.482609	+	0.835903i
$244$	−7.54742	+	5.48352i	−0.483174	+	0.351047i
$245$	2.55577	+	2.83847i	0.163282	+	0.181343i
$246$	−2.43678	−	7.49963i	−0.155363	−	0.478159i
$247$	7.76669			0.494183
$248$	−1.20167	+	5.43654i	−0.0763058	+	0.345221i
$249$	1.08379			0.0686826
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	2.11235	+	2.34601i	0.133331	+	0.148079i	0.806113	−	0.591762i	$-0.201568\pi$
$251$	2.11235	+	2.34601i	0.133331	+	0.148079i	−0.672782	+	0.739841i	$0.734901\pi$
$252$	2.48866	−	1.80812i	0.156771	−	0.113901i
$253$	−3.90634	−	6.76598i	−0.245589	−	0.425373i
$254$	−4.40743	+	7.63390i	−0.276547	+	0.478993i
$255$	−0.544193	−	5.17765i	−0.0340787	−	0.324237i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−0.557547	+	5.30470i	−0.0347788	+	0.330898i	0.963274	+	0.268521i	$0.0865349\pi$
$257$	−0.557547	+	5.30470i	−0.0347788	+	0.330898i	−0.998053	+	0.0623772i	$0.980132\pi$
$258$	−7.25229	+	8.05449i	−0.451508	+	0.501451i
$259$	−2.46201	−	1.09616i	−0.152982	−	0.0681118i
$260$	0.935398	+	0.198825i	0.0580109	+	0.0123306i
$261$	−13.3374	+	2.83495i	−0.825565	+	0.175479i
$262$	−7.10784	+	3.16461i	−0.439124	+	0.195511i
$263$	−1.55380	+	4.78209i	−0.0958112	+	0.294877i	−0.987464	−	0.157843i	$-0.949546\pi$
$263$	−1.55380	+	4.78209i	−0.0958112	+	0.294877i	0.891653	+	0.452719i	$0.149546\pi$
$264$	−1.89259	+	5.82478i	−0.116481	+	0.358490i
$265$	6.39734	−	2.84828i	0.392985	−	0.174968i
$266$	14.1675	−	3.01140i	0.868667	−	0.184641i
$267$	−7.78280	−	1.65428i	−0.476299	−	0.101241i
$268$	2.20731	+	0.982759i	0.134833	+	0.0600315i
$269$	0.289802	−	0.321857i	0.0176695	−	0.0196240i	−0.734245	−	0.678884i	$-0.762464\pi$
$269$	0.289802	−	0.321857i	0.0176695	−	0.0196240i	0.751915	+	0.659260i	$0.229130\pi$
$270$	−0.557699	+	5.30615i	−0.0339405	+	0.322922i
$271$	8.94512	+	6.49901i	0.543378	+	0.394787i	0.825338	−	0.564639i	$-0.190985\pi$
$271$	8.94512	+	6.49901i	0.543378	+	0.394787i	−0.281960	+	0.959426i	$0.590985\pi$
$272$	−0.481926	−	4.58522i	−0.0292211	−	0.278020i
$273$	0.962897	−	1.66779i	0.0582772	−	0.100939i
$274$	1.54653	+	2.67867i	0.0934292	+	0.161824i
$275$	4.38791	−	3.18801i	0.264601	−	0.192244i
$276$	1.08839	+	1.20878i	0.0655131	+	0.0727597i
$277$	−0.229755	−	0.707112i	−0.0138046	−	0.0424862i	0.943917	−	0.330183i	$-0.107110\pi$
$277$	−0.229755	−	0.707112i	−0.0138046	−	0.0424862i	−0.957722	+	0.287697i	$0.907110\pi$
$278$	2.74606			0.164698
$279$	9.15751	−	2.89369i	0.548246	−	0.173240i
$280$	1.78339			0.106578
$281$	−1.89566	−	5.83424i	−0.113085	−	0.348041i	0.878457	−	0.477821i	$-0.158573\pi$
$281$	−1.89566	−	5.83424i	−0.113085	−	0.348041i	−0.991543	+	0.129779i	$0.958573\pi$
$282$	8.49100	+	9.43021i	0.505632	+	0.561561i
$283$	18.2441	−	13.2551i	1.08450	−	0.787934i	0.106036	−	0.994362i	$-0.466184\pi$
$283$	18.2441	−	13.2551i	1.08450	−	0.787934i	0.978462	+	0.206428i	$0.0661840\pi$
$284$	−3.22256	−	5.58164i	−0.191224	−	0.331210i
$285$	−4.58550	+	7.94232i	−0.271622	+	0.470462i
$286$	−0.542159	−	5.15830i	−0.0320586	−	0.305017i
$287$	10.0754	+	7.32024i	0.594735	+	0.432100i
$288$	−0.180301	+	1.71545i	−0.0106243	+	0.101084i
$289$	2.84815	−	3.16319i	0.167538	−	0.186070i
$290$	−7.22161	−	3.21527i	−0.424067	−	0.188807i
$291$	17.0655	+	3.62737i	1.00039	+	0.212640i
$292$	−10.5477	+	2.24199i	−0.617260	+	0.131203i
$293$	10.5457	−	4.69525i	0.616086	−	0.274299i	−0.0748729	−	0.997193i	$-0.523855\pi$
$293$	10.5457	−	4.69525i	0.616086	−	0.274299i	0.690959	+	0.722894i	$0.257188\pi$
$294$	−1.33280	+	4.10194i	−0.0777305	+	0.239230i
$295$	2.79689	−	8.60795i	0.162841	−	0.501174i
$296$	1.38052	−	0.614648i	0.0802413	−	0.0357257i
$297$	28.3054	−	6.01651i	1.64245	−	0.349113i
$298$	1.00302	+	0.213199i	0.0581036	+	0.0123503i
$299$	−1.25841	−	0.560280i	−0.0727756	−	0.0324018i
$300$	−0.755585	+	0.839162i	−0.0436237	+	0.0484491i
$301$	1.78925	−	17.0236i	0.103131	−	0.981225i
$302$	8.68274	+	6.30838i	0.499635	+	0.363006i
$303$	−0.506352	−	4.81762i	−0.0290892	−	0.276765i
$304$	−4.06082	+	7.03355i	−0.232904	+	0.403402i
$305$	4.66456	+	8.07926i	0.267092	+	0.462617i
$306$	−6.43379	+	4.67442i	−0.367795	+	0.267219i
$307$	8.00073	+	8.88571i	0.456626	+	0.507134i	0.926860	−	0.375408i	$-0.122497\pi$
$307$	8.00073	+	8.88571i	0.456626	+	0.507134i	−0.470234	+	0.882542i	$0.655831\pi$
$308$	−2.98902	−	9.19925i	−0.170315	−	0.524176i
$309$	13.3726			0.760739
$310$	5.28115	+	1.76336i	0.299949	+	0.100152i
$311$	−14.9943			−0.850247			−0.425124	−	0.905135i	$-0.639769\pi$
$311$	−14.9943			−0.850247			−0.425124	+	0.905135i	$0.639769\pi$
$312$	0.333693	+	1.02700i	0.0188916	+	0.0581425i
$313$	6.29434	+	6.99057i	0.355777	+	0.395130i	0.894291	−	0.447486i	$-0.147681\pi$
$313$	6.29434	+	6.99057i	0.355777	+	0.395130i	−0.538514	+	0.842617i	$0.681014\pi$
$314$	5.35867	−	3.89330i	0.302407	−	0.219712i
$315$	−1.53808	−	2.66403i	−0.0866610	−	0.150101i
$316$	−6.18799	+	10.7179i	−0.348102	+	0.602930i
$317$	0.333990	+	3.17770i	0.0187588	+	0.178478i	0.999889	−	0.0148680i	$-0.00473281\pi$
$317$	0.333990	+	3.17770i	0.0187588	+	0.178478i	−0.981131	+	0.193346i	$0.938066\pi$
$318$	6.39734	+	4.64794i	0.358745	+	0.260644i
$319$	−4.48166	+	42.6401i	−0.250925	+	2.38739i
$320$	−0.669131	+	0.743145i	−0.0374055	+	0.0415431i
$321$	−21.2642	−	9.46743i	−1.18685	−	0.528420i
$322$	−2.51275	−	0.534102i	−0.140030	−	0.0297643i
$323$	−36.6264	+	7.78518i	−2.03795	+	0.433179i
$324$	−0.776546	+	0.345740i	−0.0431414	+	0.0192078i
$325$	0.295511	−	0.909491i	0.0163920	−	0.0504495i
$326$	3.87634	−	11.9301i	0.214691	−	0.660750i
$327$	10.2431	−	4.56050i	0.566442	−	0.252196i
$328$	−6.83070	+	1.45191i	−0.377163	+	0.0801684i
$329$	−19.6031	−	4.16677i	−1.08075	−	0.229722i
$330$	5.59504	+	2.49107i	0.307997	+	0.137129i
$331$	−4.40938	+	4.89711i	−0.242361	+	0.269170i	−0.852037	−	0.523481i	$-0.824633\pi$
$331$	−4.40938	+	4.89711i	−0.242361	+	0.269170i	0.609676	+	0.792651i	$0.291300\pi$
$332$	0.100325	−	0.954527i	0.00550604	−	0.0523865i
$333$	−2.10880	−	1.53213i	−0.115561	−	0.0839602i
$334$	−1.03779	−	9.87392i	−0.0567854	−	0.540277i
$335$	1.20810	−	2.09249i	0.0660057	−	0.114325i
$336$	1.00690	+	1.74401i	0.0549311	+	0.0951434i
$337$	−1.48527	+	1.07911i	−0.0809079	+	0.0587831i	−0.627504	−	0.778613i	$-0.715923\pi$
$337$	−1.48527	+	1.07911i	−0.0809079	+	0.0587831i	0.546596	+	0.837396i	$0.315923\pi$
$338$	8.08678	+	8.98128i	0.439863	+	0.488517i
$339$	0.854840	+	2.63093i	0.0464285	+	0.142892i
$340$	−4.61048			−0.250038
$341$	0.244530	−	30.1972i	0.0132420	−	1.63527i
$342$	14.0090			0.757521
$343$	−5.96261	−	18.3510i	−0.321951	−	0.990862i
$344$	6.42248	+	7.13289i	0.346277	+	0.384580i
$345$	1.31592	−	0.956072i	0.0708468	−	0.0514732i
$346$	−1.24596	−	2.15807i	−0.0669832	−	0.116018i
$347$	9.06927	−	15.7084i	0.486864	−	0.843273i	−0.513022	−	0.858376i	$-0.671474\pi$
$347$	9.06927	−	15.7084i	0.486864	−	0.843273i	0.999886	+	0.0151022i	$0.00480737\pi$
$348$	−0.933063	−	8.87750i	−0.0500174	−	0.475884i
$349$	−24.4268	−	17.7471i	−1.30754	−	0.949982i	−0.307539	−	0.951535i	$-0.599505\pi$
$349$	−24.4268	−	17.7471i	−1.30754	−	0.949982i	−0.999999	+	0.00155361i	$0.999505\pi$
$350$	0.186415	−	1.77362i	0.00996428	−	0.0948038i
$351$	3.41403	−	3.79167i	0.182228	−	0.202384i
$352$	4.95485	+	2.20604i	0.264094	+	0.117582i
$353$	32.9029	+	6.99373i	1.75124	+	0.372238i	0.968288	−	0.249838i	$-0.0803773\pi$
$353$	32.9029	+	6.99373i	1.75124	+	0.372238i	0.782957	+	0.622076i	$0.213711\pi$
$354$	9.99701	−	2.12493i	0.531335	−	0.112939i
$355$	−5.88791	+	2.62147i	−0.312498	+	0.139133i
$356$	−2.17741	+	6.70139i	−0.115403	+	0.355173i
$357$	−2.86910	+	8.83019i	−0.151849	+	0.467343i
$358$	−8.87987	+	3.95357i	−0.469316	+	0.208953i
$359$	−12.8161	+	2.72414i	−0.676407	+	0.143775i	−0.533292	−	0.845931i	$-0.679045\pi$
$359$	−12.8161	+	2.72414i	−0.676407	+	0.143775i	−0.143115	+	0.989706i	$0.545712\pi$
$360$	1.68720	+	0.358626i	0.0889235	+	0.0189013i
$361$	42.9012	+	19.1008i	2.25796	+	1.00531i
$362$	−13.6703	+	15.1825i	−0.718497	+	0.797972i
$363$	2.17385	−	20.6828i	0.114098	−	1.08557i
$364$	−1.37973	−	1.00243i	−0.0723177	−	0.0525418i
$365$	1.12717	+	10.7243i	0.0589988	+	0.561336i
$366$	−5.26724	+	9.12313i	−0.275323	+	0.476874i
$367$	−6.80333	−	11.7837i	−0.355131	−	0.615105i	0.632009	−	0.774961i	$-0.282230\pi$
$367$	−6.80333	−	11.7837i	−0.355131	−	0.615105i	−0.987140	+	0.159856i	$0.948897\pi$
$368$	1.16535	−	0.846678i	0.0607482	−	0.0441361i
$369$	8.06001	+	8.95154i	0.419587	+	0.465999i
$370$	−0.466977	−	1.43721i	−0.0242770	−	0.0747169i
$371$	−12.4886			−0.648377
$372$	1.25733	+	6.16014i	0.0651895	+	0.319388i
$373$	−23.7593			−1.23021			−0.615106	−	0.788444i	$-0.710887\pi$
$373$	−23.7593			−1.23021			−0.615106	+	0.788444i	$0.710887\pi$
$374$	7.72732	+	23.7822i	0.399570	+	1.22975i
$375$	0.755585	+	0.839162i	0.0390182	+	0.0433342i
$376$	9.09145	−	6.60532i	0.468856	−	0.340644i
$377$	3.77977	+	6.54676i	0.194668	+	0.337175i
$378$	4.75752	−	8.24026i	0.244700	−	0.423833i
$379$	2.64998	+	25.2129i	0.136120	+	1.29510i	0.822881	+	0.568214i	$0.192365\pi$
$379$	2.64998	+	25.2129i	0.136120	+	1.29510i	−0.686761	+	0.726884i	$0.740968\pi$
$380$	6.57055	+	4.77378i	0.337062	+	0.244890i
$381$	−1.04045	+	9.89925i	−0.0533040	+	0.507154i
$382$	−13.0813	+	14.5283i	−0.669299	+	0.743332i
$383$	1.72486	+	0.767957i	0.0881362	+	0.0392407i	0.450331	−	0.892862i	$-0.351306\pi$
$383$	1.72486	+	0.767957i	0.0881362	+	0.0392407i	−0.362195	+	0.932102i	$0.617973\pi$
$384$	−1.10453	−	0.234775i	−0.0563652	−	0.0119808i
$385$	−9.46129	+	2.01106i	−0.482192	+	0.102493i
$386$	−18.7044	+	8.32776i	−0.952031	+	0.423872i
$387$	5.11608	−	15.7457i	0.260065	−	0.800398i
$388$	4.77445	−	14.6942i	0.242386	−	0.745987i
$389$	−10.1168	+	4.50429i	−0.512942	+	0.228376i	−0.646850	−	0.762617i	$-0.723914\pi$
$389$	−10.1168	+	4.50429i	−0.512942	+	0.228376i	0.133908	+	0.990994i	$0.457247\pi$
$390$	1.05626	−	0.224514i	0.0534856	−	0.0113687i
$391$	6.49606	+	1.38078i	0.328520	+	0.0698290i
$392$	3.48932	+	1.55354i	0.176237	+	0.0784658i
$393$	−5.87883	+	6.52910i	−0.296548	+	0.329350i
$394$	−2.52044	+	23.9804i	−0.126978	+	1.20812i
$395$	10.0124	+	7.27442i	0.503778	+	0.366016i
$396$	−0.977909	−	9.30418i	−0.0491418	−	0.467553i
$397$	3.50256	−	6.06661i	0.175788	−	0.304474i	−0.764646	−	0.644451i	$-0.777086\pi$
$397$	3.50256	−	6.06661i	0.175788	−	0.304474i	0.940434	+	0.339977i	$0.110419\pi$
$398$	−3.44901	−	5.97385i	−0.172883	−	0.299442i
$399$	13.2318	−	9.61348i	0.662420	−	0.481276i
$400$	0.669131	+	0.743145i	0.0334565	+	0.0371572i
$401$	−11.4335	−	35.1887i	−0.570961	−	1.75724i	−0.649537	−	0.760330i	$-0.725037\pi$
$401$	−11.4335	−	35.1887i	−0.570961	−	1.75724i	0.0785763	−	0.996908i	$-0.474963\pi$
$402$	2.72839			0.136080
$403$	−3.09464	−	4.33275i	−0.154155	−	0.215830i
$404$	−4.28989			−0.213430
$405$	0.262675	+	0.808431i	0.0130524	+	0.0401713i
$406$	9.43322	+	10.4767i	0.468163	+	0.519948i
$407$	−6.63089	+	4.81762i	−0.328681	+	0.238801i
$408$	−2.60309	−	4.50868i	−0.128872	−	0.223213i
$409$	−5.40526	+	9.36219i	−0.267273	+	0.462930i	−0.968157	−	0.250345i	$-0.919456\pi$
$409$	−5.40526	+	9.36219i	−0.267273	+	0.462930i	0.700884	+	0.713276i	$0.252789\pi$
$410$	0.729954	+	6.94505i	0.0360499	+	0.342992i
$411$	2.82565	+	2.05295i	0.139379	+	0.101265i
$412$	1.23788	−	11.7776i	0.0609858	−	0.580241i
$413$	−10.8006	+	11.9953i	−0.531465	+	0.590251i
$414$	−2.26983	−	1.01059i	−0.111556	−	0.0496679i
$415$	−0.938812	−	0.199551i	−0.0460844	−	0.00979555i
$416$	0.935398	−	0.198825i	0.0458617	−	0.00974820i
$417$	2.83278	−	1.26123i	0.138722	−	0.0617629i
$418$	13.6122	−	41.8939i	0.665792	−	2.04910i
$419$	−8.71763	+	26.8301i	−0.425884	+	1.31074i	0.476261	+	0.879304i	$0.341992\pi$
$419$	−8.71763	+	26.8301i	−0.425884	+	1.31074i	−0.902145	+	0.431432i	$0.858008\pi$
$420$	1.83970	−	0.819089i	0.0897684	−	0.0399675i
$421$	−21.5034	+	4.57069i	−1.04801	+	0.222762i	−0.699567	−	0.714567i	$-0.746624\pi$
$421$	−21.5034	+	4.57069i	−1.04801	+	0.222762i	−0.348446	+	0.937329i	$0.613290\pi$
$422$	−6.74862	−	1.43446i	−0.328518	−	0.0698286i
$423$	−17.7080	−	7.88410i	−0.860991	−	0.383338i
$424$	4.68576	−	5.20407i	0.227561	−	0.252732i
$425$	−0.481926	+	4.58522i	−0.0233768	+	0.222416i
$426$	−5.88791	−	4.27782i	−0.285270	−	0.207261i
$427$	−1.73909	−	16.5463i	−0.0841602	−	0.800731i
$428$	−10.3066	+	17.8516i	−0.498189	+	0.862889i
$429$	−2.92843	−	5.07219i	−0.141386	−	0.244888i
$430$	7.76515	−	5.64171i	0.374469	−	0.272067i
$431$	−2.84139	−	3.15568i	−0.136865	−	0.152004i	0.670816	−	0.741624i	$-0.265944\pi$
$431$	−2.84139	−	3.15568i	−0.136865	−	0.152004i	−0.807681	+	0.589620i	$0.799277\pi$
$432$	1.64872	+	5.07424i	0.0793241	+	0.244135i
$433$	−28.1373			−1.35219			−0.676096	−	0.736814i	$-0.736329\pi$
$433$	−28.1373			−1.35219			−0.676096	+	0.736814i	$0.736329\pi$
$434$	−7.32499	−	6.70365i	−0.351611	−	0.321785i
$435$	−8.92640			−0.427988
$436$	−3.06838	−	9.44350i	−0.146949	−	0.452262i
$437$	−7.82807	−	8.69395i	−0.374467	−	0.415888i
$438$	−9.85111	+	7.15725i	−0.470704	+	0.341987i
$439$	−4.53732	−	7.85888i	−0.216555	−	0.375084i	0.737198	−	0.675677i	$-0.236149\pi$
$439$	−4.53732	−	7.85888i	−0.216555	−	0.375084i	−0.953752	+	0.300593i	$0.902815\pi$
$440$	2.71188	−	4.69711i	0.129284	−	0.223926i
$441$	−0.688665	−	6.55221i	−0.0327936	−	0.312010i
$442$	3.56694	+	2.59153i	0.169662	+	0.123267i
$443$	−2.52494	+	24.0232i	−0.119963	+	1.14137i	0.754506	+	0.656293i	$0.227877\pi$
$443$	−2.52494	+	24.0232i	−0.119963	+	1.14137i	−0.874469	+	0.485081i	$0.838790\pi$
$444$	1.14182	−	1.26812i	0.0541883	−	0.0601822i
$445$	6.43708	+	2.86597i	0.305147	+	0.135860i
$446$	−22.5434	−	4.79175i	−1.06746	−	0.226896i
$447$	1.13262	−	0.240745i	0.0535710	−	0.0113869i
$448$	1.62920	−	0.725368i	0.0769727	−	0.0342704i
$449$	9.93552	−	30.5784i	0.468886	−	1.44308i	−0.385142	−	0.922857i	$-0.625848\pi$
$449$	9.93552	−	30.5784i	0.468886	−	1.44308i	0.854028	−	0.520226i	$-0.174152\pi$
$450$	0.533023	−	1.64048i	0.0251269	−	0.0773327i
$451$	34.6012	−	15.4055i	1.62931	−	0.725415i
$452$	2.39626	−	0.509341i	0.112711	−	0.0239574i
$453$	11.8543	+	2.51971i	0.556964	+	0.118386i
$454$	8.94045	+	3.98055i	0.419596	+	0.186816i
$455$	−1.14116	+	1.26739i	−0.0534986	+	0.0594162i
$456$	−0.958630	+	9.12076i	−0.0448920	+	0.427119i
$457$	17.2840	+	12.5575i	0.808510	+	0.587417i	0.913398	−	0.407067i	$-0.133448\pi$
$457$	17.2840	+	12.5575i	0.808510	+	0.587417i	−0.104888	+	0.994484i	$0.533448\pi$
$458$	−1.00776	−	9.58821i	−0.0470896	−	0.448027i
$459$	−12.2993	+	21.3030i	−0.574083	+	0.994340i
$460$	−0.720227	−	1.24747i	−0.0335808	−	0.0581636i
$461$	−9.53986	+	6.93112i	−0.444316	+	0.322814i	−0.787347	−	0.616510i	$-0.788546\pi$
$461$	−9.53986	+	6.93112i	−0.444316	+	0.322814i	0.343032	+	0.939324i	$0.388546\pi$
$462$	−7.30852	−	8.11693i	−0.340023	−	0.377634i
$463$	−2.18619	−	6.72839i	−0.101601	−	0.312695i	0.887317	−	0.461160i	$-0.152567\pi$
$463$	−2.18619	−	6.72839i	−0.101601	−	0.312695i	−0.988918	+	0.148465i	$0.952567\pi$
$464$	−7.90503			−0.366982
$465$	6.25782	−	0.606533i	0.290199	−	0.0281273i
$466$	−11.9278			−0.552543
$467$	−2.42250	−	7.45570i	−0.112100	−	0.345009i	0.879231	−	0.476396i	$-0.158057\pi$
$467$	−2.42250	−	7.45570i	−0.112100	−	0.345009i	−0.991331	+	0.131387i	$0.958057\pi$
$468$	−1.10374	−	1.22583i	−0.0510203	−	0.0566638i
$469$	−3.48607	+	2.53278i	−0.160972	+	0.116953i
$470$	−5.61882	−	9.73209i	−0.259177	−	0.448908i
$471$	3.73974	−	6.47743i	0.172318	−	0.298464i
$472$	−0.946080	−	9.00135i	−0.0435469	−	0.414321i
$473$	−42.1163	−	30.5993i	−1.93651	−	1.40696i
$474$	−1.46079	+	13.8985i	−0.0670962	+	0.638378i
$475$	5.43444	−	6.03556i	0.249349	−	0.276930i
$476$	7.51141	+	3.34429i	0.344285	+	0.153285i
$477$	−11.8151	−	2.51137i	−0.540976	−	0.114988i
$478$	14.6644	−	3.11702i	0.670735	−	0.142569i
$479$	24.7143	−	11.0035i	1.12922	−	0.502763i	0.244859	−	0.969559i	$-0.421258\pi$
$479$	24.7143	−	11.0035i	1.12922	−	0.502763i	0.884365	+	0.466795i	$0.154592\pi$
$480$	−0.348943	+	1.07394i	−0.0159270	+	0.0490183i
$481$	−0.446568	+	1.37440i	−0.0203618	+	0.0626670i
$482$	1.91462	−	0.852445i	0.0872087	−	0.0388278i
$483$	−2.83741	+	0.603110i	−0.129107	+	0.0274424i
$484$	−18.0147	−	3.82915i	−0.818851	−	0.174052i
$485$	−14.1147	−	6.28426i	−0.640915	−	0.285354i
$486$	10.0679	−	11.1816i	0.456690	−	0.507205i
$487$	1.21961	−	11.6038i	0.0552657	−	0.525818i	−0.931509	−	0.363719i	$-0.881507\pi$
$487$	1.21961	−	11.6038i	0.0552657	−	0.525818i	0.986774	−	0.162099i	$-0.0518265\pi$
$488$	7.54742	+	5.48352i	0.341656	+	0.248227i
$489$	−1.48063	−	14.0873i	−0.0669564	−	0.637048i
$490$	1.90977	−	3.30781i	0.0862745	−	0.149432i
$491$	7.81631	+	13.5382i	0.352745	+	0.610972i	0.986729	−	0.162374i	$-0.0519150\pi$
$491$	7.81631	+	13.5382i	0.352745	+	0.610972i	−0.633984	+	0.773346i	$0.718582\pi$
$492$	−6.37957	+	4.63503i	−0.287613	+	0.208963i
$493$	−24.3871	−	27.0846i	−1.09834	−	1.21983i
$494$	−2.40004	−	7.38656i	−0.107983	−	0.332337i
$495$	−9.35543			−0.420495
$496$	5.54179	−	0.537133i	0.248834	−	0.0241180i
$497$	11.4941			0.515583
$498$	−0.334911	−	1.03075i	−0.0150077	−	0.0461890i
$499$	1.68070	+	1.86661i	0.0752387	+	0.0835610i	0.779589	−	0.626292i	$-0.215428\pi$
$499$	1.68070	+	1.86661i	0.0752387	+	0.0835610i	−0.704350	+	0.709853i	$0.748761\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$	−5.60554	−	9.70909i	−0.250437	−	0.433770i
$502$	1.57843	−	2.73392i	0.0704488	−	0.122021i
$503$	3.43176	+	32.6510i	0.153014	+	1.45584i	0.754157	+	0.656694i	$0.228046\pi$
$503$	3.43176	+	32.6510i	0.153014	+	1.45584i	−0.601143	+	0.799141i	$0.705288\pi$
$504$	−2.48866	−	1.80812i	−0.110854	−	0.0805401i
$505$	−0.448415	+	4.26639i	−0.0199542	+	0.189852i
$506$	−5.22770	+	5.80595i	−0.232400	+	0.258106i
$507$	12.4672	+	5.55073i	0.553686	+	0.246517i
$508$	8.62224	+	1.83271i	0.382550	+	0.0813135i
$509$	32.3368	−	6.87340i	1.43330	−	0.304658i	0.575148	−	0.818049i	$-0.304944\pi$
$509$	32.3368	−	6.87340i	1.43330	−	0.304658i	0.858155	+	0.513391i	$0.171611\pi$
$510$	−4.75607	+	2.11754i	−0.210602	+	0.0937663i
$511$	5.94269	−	18.2897i	0.262889	−	0.809089i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	39.5858	−	17.6247i	1.74775	−	0.778151i
$514$	5.21736	−	1.10898i	0.230128	−	0.0489152i
$515$	−11.5837	−	2.46219i	−0.510438	−	0.108497i
$516$	9.90136	+	4.40837i	0.435883	+	0.194068i
$517$	−40.7837	+	45.2949i	−1.79367	+	1.99207i
$518$	−0.281704	+	2.68024i	−0.0123774	+	0.117763i
$519$	−2.27648	−	1.65396i	−0.0999265	−	0.0726008i
$520$	−0.0999601	−	0.951057i	−0.00438354	−	0.0417066i
$521$	−3.59172	+	6.22103i	−0.157356	+	0.272548i	−0.933914	−	0.357497i	$-0.883630\pi$
$521$	−3.59172	+	6.22103i	−0.157356	+	0.272548i	0.776558	+	0.630045i	$0.216964\pi$
$522$	6.81769	+	11.8086i	0.298402	+	0.516848i
$523$	1.29785	−	0.942941i	0.0567509	−	0.0412319i	−0.559048	−	0.829135i	$-0.688833\pi$
$523$	1.29785	−	0.942941i	0.0567509	−	0.0412319i	0.615799	+	0.787903i	$0.288833\pi$
$524$	5.20617	+	5.78204i	0.227433	+	0.252590i
$525$	−0.622301	−	1.91524i	−0.0271594	−	0.0835881i
$526$	5.02819			0.219240
$527$	18.9369	+	17.3305i	0.824902	+	0.754930i
$528$	6.12453			0.266536
$529$	−6.46621	−	19.9009i	−0.281140	−	0.865258i
$530$	−4.68576	−	5.20407i	−0.203536	−	0.226050i
$531$	−12.6303	+	9.17646i	−0.548109	+	0.398225i
$532$	−7.24202	−	12.5435i	−0.313981	−	0.543831i
$533$	3.33905	−	5.78341i	0.144630	−	0.250507i
$534$	0.831698	+	7.91308i	0.0359911	+	0.342432i
$535$	16.6765	+	12.1162i	0.720986	+	0.523827i
$536$	0.252562	−	2.40297i	0.0109090	−	0.103792i
$537$	−7.34446	+	8.15685i	−0.316937	+	0.351994i
$538$	−0.395658	−	0.176158i	−0.0170580	−	0.00759472i
$539$	−20.2635	−	4.30715i	−0.872812	−	0.185522i
$540$	5.21878	−	1.10929i	0.224581	−	0.0477361i
$541$	5.73541	−	2.55357i	0.246585	−	0.109787i	−0.279723	−	0.960081i	$-0.590243\pi$
$541$	5.73541	−	2.55357i	0.246585	−	0.109787i	0.526308	+	0.850294i	$0.323576\pi$
$542$	3.41673	−	10.5156i	0.146761	−	0.451685i
$543$	−7.12892	+	21.9405i	−0.305931	+	0.941559i
$544$	−4.21188	+	1.87525i	−0.180583	+	0.0804007i
$545$	−9.71251	+	2.06446i	−0.416038	+	0.0884316i
$546$	−1.88371	−	0.400395i	−0.0806154	−	0.0171353i
$547$	−2.86131	−	1.27394i	−0.122341	−	0.0544696i	0.344653	−	0.938730i	$-0.387996\pi$
$547$	−2.86131	−	1.27394i	−0.122341	−	0.0544696i	−0.466994	+	0.884260i	$0.654663\pi$
$548$	2.06966	−	2.29859i	0.0884114	−	0.0981909i
$549$	1.68205	−	16.0036i	0.0717881	−	0.683018i
$550$	−4.38791	−	3.18801i	−0.187101	−	0.135937i
$551$	6.71093	+	63.8502i	0.285895	+	2.72011i
$552$	0.813284	−	1.40865i	0.0346157	−	0.0599561i
$553$	−11.0356	−	19.1142i	−0.469281	−	0.812818i
$554$	−0.601505	+	0.437019i	−0.0255555	+	0.0185672i
$555$	−1.14182	−	1.26812i	−0.0484675	−	0.0538286i
$556$	−0.848579	−	2.61166i	−0.0359877	−	0.110759i
$557$	22.7920			0.965728			0.482864	−	0.875695i	$-0.339597\pi$
$557$	22.7920			0.965728			0.482864	+	0.875695i	$0.339597\pi$
$558$	−5.58189	−	7.81511i	−0.236300	−	0.330840i
$559$	−9.17876			−0.388220
$560$	−0.551097	−	1.69610i	−0.0232881	−	0.0716733i
$561$	18.8943	+	20.9842i	0.797716	+	0.885954i
$562$	−4.96290	+	3.60576i	−0.209347	+	0.152100i
$563$	19.2686	+	33.3741i	0.812073	+	1.40655i	0.911411	+	0.411498i	$0.134994\pi$
$563$	19.2686	+	33.3741i	0.812073	+	1.40655i	−0.0993377	+	0.995054i	$0.531672\pi$
$564$	6.34480	−	10.9895i	0.267164	−	0.462742i
$565$	−0.256073	−	2.43638i	−0.0107731	−	0.102499i
$566$	−18.2441	−	13.2551i	−0.766856	−	0.557154i
$567$	0.158459	−	1.50764i	0.00665465	−	0.0633148i
$568$	−4.31263	+	4.78966i	−0.180954	+	0.200970i
$569$	−2.74358	−	1.22152i	−0.115017	−	0.0512087i	0.348422	−	0.937338i	$-0.386718\pi$
$569$	−2.74358	−	1.22152i	−0.115017	−	0.0512087i	−0.463438	+	0.886129i	$0.653384\pi$
$570$	8.97059	+	1.90676i	0.375737	+	0.0798653i
$571$	17.1772	−	3.65112i	0.718842	−	0.152795i	0.166054	−	0.986117i	$-0.446897\pi$
$571$	17.1772	−	3.65112i	0.718842	−	0.152795i	0.552788	+	0.833322i	$0.313564\pi$
$572$	−4.73830	+	2.10963i	−0.198118	+	0.0882080i
$573$	−6.82175	+	20.9952i	−0.284983	+	0.877087i
$574$	3.84848	−	11.8444i	0.160632	−	0.494375i
$575$	−1.31592	+	0.585886i	−0.0548777	+	0.0244331i
$576$	1.68720	−	0.358626i	0.0703002	−	0.0149428i
$577$	−19.9265	−	4.23550i	−0.829550	−	0.176326i	−0.226481	−	0.974015i	$-0.572722\pi$
$577$	−19.9265	−	4.23550i	−0.829550	−	0.176326i	−0.603069	+	0.797689i	$0.706056\pi$
$578$	−3.88850	−	1.73127i	−0.161740	−	0.0720115i
$579$	−15.4703	+	17.1815i	−0.642923	+	0.714038i
$580$	−0.826301	+	7.86173i	−0.0343103	+	0.326441i
$581$	1.38477	+	1.00609i	0.0574499	+	0.0417398i
$582$	−1.82368	−	17.3511i	−0.0755939	−	0.719227i
$583$	−18.9906	+	32.8928i	−0.786512	+	1.36228i
$584$	5.39169	+	9.33869i	0.223110	+	0.386438i
$585$	−1.33448	+	0.969558i	−0.0551741	+	0.0400863i
$586$	−7.72424	−	8.57864i	−0.319086	−	0.354380i
$587$	−4.59971	−	14.1565i	−0.189850	−	0.584299i	0.810148	−	0.586226i	$-0.199387\pi$
$587$	−4.59971	−	14.1565i	−0.189850	−	0.584299i	−0.999998	+	0.00192635i	$0.999387\pi$
$588$	4.31303			0.177867
$589$	−9.04317	−	44.3059i	−0.372618	−	1.82559i
$590$	−9.05093			−0.372621
$591$	8.41390	+	25.8953i	0.346102	+	1.06519i
$592$	−1.01117	−	1.12302i	−0.0415588	−	0.0461558i
$593$	9.32331	−	6.77378i	0.382863	−	0.278166i	−0.379662	−	0.925125i	$-0.623960\pi$
$593$	9.32331	−	6.77378i	0.382863	−	0.278166i	0.762524	+	0.646959i	$0.223960\pi$
$594$	−14.4689	−	25.0609i	−0.593666	−	1.02826i
$595$	4.11113	−	7.12069i	0.168540	−	0.291920i
$596$	−0.107187	−	1.01981i	−0.00439054	−	0.0417732i
$597$	−6.30165	−	4.57841i	−0.257909	−	0.187382i
$598$	−0.143988	+	1.36995i	−0.00588810	+	0.0560216i
$599$	−14.9918	+	16.6501i	−0.612549	+	0.680304i	−0.967002	−	0.254769i	$-0.918000\pi$
$599$	−14.9918	+	16.6501i	−0.612549	+	0.680304i	0.354453	+	0.935074i	$0.384667\pi$
$600$	1.03158	+	0.459289i	0.0421141	+	0.0187504i
$601$	35.1675	+	7.47508i	1.43451	+	0.304915i	0.858621	−	0.512612i	$-0.171322\pi$
$601$	35.1675	+	7.47508i	1.43451	+	0.304915i	0.575891	+	0.817526i	$0.304655\pi$
$602$	−16.7433	+	3.55890i	−0.682407	+	0.145050i
$603$	−3.80739	+	1.69516i	−0.155049	+	0.0690322i
$604$	3.31651	−	10.2072i	0.134947	−	0.415324i
$605$	−5.69122	+	17.5158i	−0.231381	+	0.712118i
$606$	−4.42536	+	1.97030i	−0.179768	+	0.0800378i
$607$	30.2928	−	6.43894i	1.22955	−	0.261348i	0.453059	−	0.891480i	$-0.350333\pi$
$607$	30.2928	−	6.43894i	1.22955	−	0.261348i	0.776488	+	0.630132i	$0.216999\pi$
$608$	7.94417	+	1.68859i	0.322179	+	0.0684812i
$609$	14.5429	+	6.47493i	0.589309	+	0.262377i
$610$	6.24240	−	6.93289i	0.252747	−	0.280705i
$611$	−1.12332	+	10.6876i	−0.0454445	+	0.432376i
$612$	6.43379	+	4.67442i	0.260071	+	0.188952i
$613$	3.31775	+	31.5663i	0.134003	+	1.27495i	0.830348	+	0.557245i	$0.188142\pi$
$613$	3.31775	+	31.5663i	0.134003	+	1.27495i	−0.696345	+	0.717707i	$0.745192\pi$
$614$	5.97845	−	10.3550i	0.241271	−	0.417893i
$615$	3.94279	+	6.82911i	0.158989	+	0.275376i
$616$	−7.82535	+	5.68545i	−0.315292	+	0.229073i
$617$	18.7326	+	20.8047i	0.754147	+	0.837565i	0.990983	−	0.133984i	$-0.0427771\pi$
$617$	18.7326	+	20.8047i	0.754147	+	0.837565i	−0.236836	+	0.971550i	$0.576110\pi$
$618$	−4.13235	−	12.7181i	−0.166228	−	0.511596i
$619$	39.9653			1.60634			0.803170	−	0.595750i	$-0.203145\pi$
$619$	39.9653			1.60634			0.803170	+	0.595750i	$0.203145\pi$
$620$	0.0450850	−	5.56758i	0.00181066	−	0.223599i
$621$	−7.68536			−0.308403
$622$	4.63348	+	14.2604i	0.185786	+	0.571790i
$623$	−8.40843	−	9.33851i	−0.336877	−	0.374139i
$624$	0.873619	−	0.634721i	0.0349728	−	0.0254092i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	4.70337	−	8.14647i	0.187984	−	0.325599i
$627$	−5.19938	−	49.4688i	−0.207643	−	1.97559i
$628$	−5.35867	−	3.89330i	−0.213834	−	0.155360i
$629$	0.728272	−	6.92905i	0.0290381	−	0.276279i
$630$	−2.05835	+	2.28603i	−0.0820067	+	0.0910777i
$631$	−15.1790	−	6.75814i	−0.604268	−	0.269037i	0.0817143	−	0.996656i	$-0.473960\pi$
$631$	−15.1790	−	6.75814i	−0.604268	−	0.269037i	−0.685982	+	0.727618i	$0.740627\pi$
$632$	12.1055	+	2.57311i	0.481533	+	0.102353i
$633$	−7.62057	+	1.61980i	−0.302890	+	0.0643813i
$634$	2.91897	−	1.29961i	0.115927	−	0.0516140i
$635$	2.72394	−	8.38343i	0.108096	−	0.332686i
$636$	2.44357	−	7.52052i	0.0968937	−	0.298208i
$637$	−3.33682	+	1.48565i	−0.132210	+	0.0588635i
$638$	41.9381	−	8.91422i	1.66034	−	0.352917i
$639$	10.8742	+	2.31139i	0.430178	+	0.0914373i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	−18.1970	+	20.2098i	−0.718736	+	0.798238i	−0.986240	−	0.165319i	$-0.947135\pi$
$641$	−18.1970	+	20.2098i	−0.718736	+	0.798238i	0.267504	+	0.963557i	$0.413801\pi$
$642$	−2.43306	+	23.1490i	−0.0960253	+	0.913620i
$643$	31.3484	+	22.7759i	1.23626	+	0.898194i	0.997343	−	0.0728463i	$-0.0232082\pi$
$643$	31.3484	+	22.7759i	1.23626	+	0.898194i	0.238915	+	0.971040i	$0.423208\pi$
$644$	0.268522	+	2.55481i	0.0105812	+	0.100674i
$645$	5.41919	−	9.38632i	0.213380	−	0.369586i
$646$	18.7223	+	32.4280i	0.736620	+	1.27586i
$647$	9.49935	−	6.90168i	0.373458	−	0.271333i	−0.385185	−	0.922839i	$-0.625863\pi$
$647$	9.49935	−	6.90168i	0.373458	−	0.271333i	0.758643	+	0.651506i	$0.225863\pi$
$648$	0.568784	+	0.631699i	0.0223440	+	0.0248155i
$649$	15.1697	+	46.6874i	0.595462	+	1.83264i
$650$	−0.956295			−0.0375090
$651$	−10.6352	−	3.55106i	−0.416827	−	0.139177i
$652$	−12.5441			−0.491265
$653$	−6.83028	−	21.0214i	−0.267289	−	0.822632i	−0.991157	−	0.132694i	$-0.957637\pi$
$653$	−6.83028	−	21.0214i	−0.267289	−	0.822632i	0.723868	−	0.689939i	$-0.242363\pi$
$654$	−7.50257	−	8.33245i	−0.293374	−	0.325825i
$655$	6.29456	−	4.57326i	0.245949	−	0.178692i
$656$	3.49165	+	6.04772i	0.136326	+	0.236124i
$657$	9.30012	−	16.1083i	0.362832	−	0.628444i
$658$	2.09486	+	19.9313i	0.0816662	+	0.777002i
$659$	2.55748	+	1.85812i	0.0996252	+	0.0723819i	0.636483	−	0.771291i	$-0.280389\pi$
$659$	2.55748	+	1.85812i	0.0996252	+	0.0723819i	−0.536857	+	0.843673i	$0.680389\pi$
$660$	0.640188	−	6.09098i	0.0249193	−	0.237091i
$661$	−0.328313	+	0.364629i	−0.0127699	+	0.0141824i	−0.749496	−	0.662009i	$-0.769704\pi$
$661$	−0.328313	+	0.364629i	−0.0127699	+	0.0141824i	0.736726	+	0.676191i	$0.236371\pi$
$662$	6.02001	+	2.68028i	0.233974	+	0.104172i
$663$	4.86984	+	1.03512i	0.189129	+	0.0402006i
$664$	−0.938812	+	0.199551i	−0.0364330	+	0.00774406i
$665$	−13.2318	+	5.89119i	−0.513108	+	0.228450i
$666$	−0.805488	+	2.47904i	−0.0312120	+	0.0960607i
$667$	3.51873	−	10.8295i	0.136246	−	0.419321i
$668$	−9.06996	+	4.03821i	−0.350927	+	0.156243i
$669$	−25.4561	+	5.41087i	−0.984191	+	0.209196i
$670$	−2.36340	−	0.502357i	−0.0913063	−	0.0194077i
$671$	−46.2244	−	20.5804i	−1.78447	−	0.794499i
$672$	1.34750	−	1.49655i	0.0519809	−	0.0577307i
$673$	−0.465639	+	4.43026i	−0.0179491	+	0.170774i	−0.999824	−	0.0187555i	$-0.994030\pi$
$673$	−0.465639	+	4.43026i	−0.0179491	+	0.170774i	0.981875	+	0.189529i	$0.0606962\pi$
$674$	1.48527	+	1.07911i	0.0572105	+	0.0415659i
$675$	−0.557699	−	5.30615i	−0.0214658	−	0.204234i
$676$	6.04275	−	10.4663i	0.232413	−	0.402552i
$677$	8.11290	+	14.0519i	0.311804	+	0.540060i	0.978753	−	0.205043i	$-0.0657335\pi$
$677$	8.11290	+	14.0519i	0.311804	+	0.540060i	−0.666949	+	0.745103i	$0.732400\pi$
$678$	2.23800	−	1.62600i	0.0859499	−	0.0624462i
$679$	18.4373	+	20.4767i	0.707558	+	0.785823i
$680$	1.42472	+	4.38482i	0.0546354	+	0.168150i
$681$	11.0510			0.423476
$682$	−28.7948	+	9.09890i	−1.10261	+	0.348415i
$683$	−3.25536			−0.124563			−0.0622815	−	0.998059i	$-0.519838\pi$
$683$	−3.25536			−0.124563			−0.0622815	+	0.998059i	$0.519838\pi$
$684$	−4.32902	−	13.3234i	−0.165524	−	0.509431i
$685$	−2.06966	−	2.29859i	−0.0790776	−	0.0878246i
$686$	−15.6103	+	11.3416i	−0.596004	+	0.433023i
$687$	−5.44334	−	9.42814i	−0.207676	−	0.359706i
$688$	4.79912	−	8.31233i	0.182965	−	0.316905i
$689$	0.699996	+	6.66002i	0.0266677	+	0.253727i
$690$	−1.31592	−	0.956072i	−0.0500962	−	0.0363971i
$691$	1.57567	−	14.9915i	0.0599412	−	0.570303i	−0.922795	−	0.385291i	$-0.874101\pi$
$691$	1.57567	−	14.9915i	0.0599412	−	0.570303i	0.982736	−	0.185012i	$-0.0592323\pi$
$692$	−1.66742	+	1.85186i	−0.0633858	+	0.0703971i
$693$	15.2419	+	6.78614i	0.578992	+	0.257784i
$694$	−17.7422	−	3.77122i	−0.673484	−	0.143153i
$695$	−2.68605	+	0.570938i	−0.101888	+	0.0216569i
$696$	−8.15467	+	3.63069i	−0.309102	+	0.137621i
$697$	−9.94923	+	30.6206i	−0.376854	+	1.15984i
$698$	−9.33022	+	28.7155i	−0.353154	+	1.08690i
$699$	−12.3044	+	5.47829i	−0.465397	+	0.207208i
$700$	−1.74441	+	0.370787i	−0.0659327	+	0.0140144i
$701$	17.9756	+	3.82082i	0.678927	+	0.144310i	0.534453	−	0.845198i	$-0.320518\pi$
$701$	17.9756	+	3.82082i	0.678927	+	0.144310i	0.144474	+	0.989509i	$0.453851\pi$
$702$	−4.66109	−	2.07525i	−0.175921	−	0.0783252i
$703$	−8.21237	+	9.12076i	−0.309735	+	0.343996i
$704$	0.566937	−	5.39405i	0.0213673	−	0.203296i
$705$	−10.2661	−	7.45876i	−0.386644	−	0.280913i
$706$	−3.51612	−	33.4537i	−0.132331	−	1.25905i
$707$	3.82526	−	6.62555i	0.143864	−	0.249179i
$708$	−5.11018	−	8.85108i	−0.192052	−	0.332644i
$709$	33.5195	−	24.3533i	1.25885	−	0.914608i	0.260150	−	0.965568i	$-0.416228\pi$
$709$	33.5195	−	24.3533i	1.25885	−	0.914608i	0.998701	+	0.0509598i	$0.0162280\pi$
$710$	4.31263	+	4.78966i	0.161850	+	0.179753i
$711$	−6.59668	−	20.3025i	−0.247395	−	0.761403i
$712$	7.04626			0.264070
$713$	−1.73094	+	7.83109i	−0.0648244	+	0.293277i
$714$	9.28461			0.347468
$715$	1.60278	+	4.93286i	0.0599407	+	0.184479i
$716$	6.50410	+	7.22354i	0.243070	+	0.269956i
$717$	13.6959	−	9.95066i	0.511483	−	0.371614i
$718$	6.55120	+	11.3470i	0.244489	+	0.423467i
$719$	−5.89665	+	10.2133i	−0.219908	+	0.380892i	−0.954780	−	0.297315i	$-0.903909\pi$
$719$	−5.89665	+	10.2133i	−0.219908	+	0.380892i	0.734872	+	0.678206i	$0.237242\pi$
$720$	−0.180301	−	1.71545i	−0.00671942	−	0.0639310i
$721$	17.0862	+	12.4139i	0.636324	+	0.462316i
$722$	4.90878	−	46.7039i	0.182686	−	1.73814i
$723$	1.58357	−	1.75873i	0.0588935	−	0.0654079i
$724$	18.6637	+	8.30963i	0.693633	+	0.308825i
$725$	7.73229	+	1.64355i	0.287170	+	0.0610399i
$726$	−20.3423	+	4.32389i	−0.754974	+	0.160475i
$727$	−26.6182	+	11.8512i	−0.987214	+	0.439536i	−0.835859	−	0.548943i	$-0.815030\pi$
$727$	−26.6182	+	11.8512i	−0.987214	+	0.439536i	−0.151355	+	0.988480i	$0.548364\pi$
$728$	−0.527011	+	1.62197i	−0.0195323	+	0.0601143i
$729$	6.03832	−	18.5840i	0.223641	−	0.688297i
$730$	9.85111	−	4.38600i	0.364606	−	0.162333i
$731$	43.2855	−	9.20061i	1.60097	−	0.340297i
$732$	10.3043	+	2.19024i	0.380857	+	0.0809537i
$733$	19.9775	+	8.89456i	0.737886	+	0.328528i	0.741035	−	0.671467i	$-0.234335\pi$
$733$	19.9775	+	8.89456i	0.737886	+	0.328528i	−0.00314821	+	0.999995i	$0.501002\pi$
$734$	−9.10463	+	10.1117i	−0.336058	+	0.373230i
$735$	0.450835	−	4.28941i	0.0166293	−	0.158217i
$736$	−1.16535	−	0.846678i	−0.0429554	−	0.0312090i
$737$	1.36984	+	13.0331i	0.0504586	+	0.480081i
$738$	6.02274	−	10.4317i	0.221700	−	0.383996i
$739$	12.8334	+	22.2282i	0.472086	+	0.817677i	0.999490	−	0.0319380i	$-0.0101679\pi$
$739$	12.8334	+	22.2282i	0.472086	+	0.817677i	−0.527404	+	0.849615i	$0.676835\pi$
$740$	−1.22256	+	0.888244i	−0.0449423	+	0.0326525i
$741$	−5.86840	−	6.51752i	−0.215581	−	0.239427i
$742$	3.85920	+	11.8774i	0.141676	+	0.436033i
$743$	19.5530			0.717329			0.358664	−	0.933467i	$-0.383232\pi$
$743$	19.5530			0.717329			0.358664	+	0.933467i	$0.383232\pi$
$744$	5.47010	−	3.09938i	0.200544	−	0.113629i
$745$	−1.02543			−0.0375689
$746$	7.34204	+	22.5965i	0.268811	+	0.827316i
$747$	1.10777	+	1.23030i	0.0405311	+	0.0450143i
$748$	20.2304	−	14.6982i	0.739696	−	0.537421i
$749$	−18.3807	−	31.8363i	−0.671615	−	1.16327i
$750$	0.564602	−	0.977920i	0.0206164	−	0.0357086i
$751$	−3.33554	−	31.7355i	−0.121715	−	1.15804i	−0.869441	−	0.494037i	$-0.835521\pi$
$751$	−3.33554	−	31.7355i	−0.121715	−	1.15804i	0.747726	−	0.664008i	$-0.231146\pi$
$752$	−9.09145	−	6.60532i	−0.331531	−	0.240871i
$753$	0.372617	−	3.54521i	0.0135789	−	0.129195i
$754$	5.05832	−	5.61784i	0.184213	−	0.204590i
$755$	−9.80459	−	4.36528i	−0.356825	−	0.158869i
$756$	−9.30711	−	1.97829i	−0.338496	−	0.0719496i
$757$	−24.4262	+	5.19194i	−0.887784	+	0.188704i	−0.629162	−	0.777274i	$-0.716602\pi$
$757$	−24.4262	+	5.19194i	−0.887784	+	0.188704i	−0.258622	+	0.965979i	$0.583268\pi$
$758$	23.1600	−	10.3115i	0.841208	−	0.374530i
$759$	−2.72618	+	8.39033i	−0.0989542	+	0.304550i
$760$	2.50973	−	7.72415i	0.0910374	−	0.280184i
$761$	15.4580	−	6.88232i	0.560350	−	0.249484i	−0.106961	−	0.994263i	$-0.534112\pi$
$761$	15.4580	−	6.88232i	0.560350	−	0.249484i	0.667311	+	0.744779i	$0.267445\pi$
$762$	9.73627	−	2.06951i	0.352708	−	0.0749703i
$763$	17.3211	+	3.68172i	0.627068	+	0.133287i
$764$	17.8596	+	7.95160i	0.646137	+	0.287679i
$765$	5.32133	−	5.90993i	0.192393	−	0.213674i
$766$	0.197359	−	1.87775i	0.00713089	−	0.0678459i
$767$	7.00234	+	5.08749i	0.252840	+	0.183699i
$768$	0.118034	+	1.12302i	0.00425918	+	0.0405234i
$769$	20.0333	−	34.6987i	0.722419	−	1.25127i	−0.237608	−	0.971361i	$-0.576363\pi$
$769$	20.0333	−	34.6987i	0.722419	−	1.25127i	0.960027	−	0.279906i	$-0.0903033\pi$
$770$	4.83633	+	8.37677i	0.174289	+	0.301878i
$771$	4.87278	−	3.54028i	0.175489	−	0.127500i
$772$	13.7002	+	15.2156i	0.493080	+	0.547620i
$773$	6.16401	+	18.9709i	0.221704	+	0.682335i	0.998609	+	0.0527176i	$0.0167883\pi$
$773$	6.16401	+	18.9709i	0.221704	+	0.682335i	−0.776905	+	0.629617i	$0.783212\pi$
$774$	−16.5560			−0.595093
$775$	−5.53237	−	0.626809i	−0.198729	−	0.0225156i
$776$	−15.4504			−0.554639
$777$	0.940402	+	2.89426i	0.0337367	+	0.103831i
$778$	7.41009	+	8.22974i	0.265665	+	0.295050i
$779$	45.8842	−	33.3368i	1.64397	−	1.19441i
$780$	−0.539926	−	0.935180i	−0.0193325	−	0.0334848i
$781$	17.4784	−	30.2735i	0.625427	−	1.08327i
$782$	−0.694193	−	6.60480i	−0.0248243	−	0.236187i
$783$	34.1214	+	24.7906i	1.21940	+	0.885944i
$784$	0.399250	−	3.79861i	0.0142589	−	0.135665i
$785$	−4.43211	+	4.92235i	−0.158189	+	0.175686i
$786$	8.02620	+	3.57350i	0.286285	+	0.127462i
$787$	18.4076	+	3.91265i	0.656159	+	0.139471i	0.523947	−	0.851751i	$-0.324459\pi$
$787$	18.4076	+	3.91265i	0.656159	+	0.139471i	0.132212	+	0.991222i	$0.457792\pi$
$788$	23.5856	−	5.01327i	0.840202	−	0.178590i
$789$	5.18698	−	2.30939i	0.184661	−	0.0822165i
$790$	3.82439	−	11.7703i	0.136066	−	0.418767i
$791$	−1.35007	+	4.15510i	−0.0480031	+	0.147738i
$792$	−8.54661	+	3.80520i	−0.303691	+	0.135212i
$793$	−8.72644	+	1.85486i	−0.309885	+	0.0658681i
$794$	−6.85203	−	1.45644i	−0.243170	−	0.0516873i
$795$	−7.22390	−	3.21629i	−0.256205	−	0.114070i
$796$	−4.61567	+	5.12622i	−0.163598	+	0.181694i
$797$	−3.94231	+	37.5086i	−0.139644	+	1.32862i	0.670290	+	0.742100i	$0.266170\pi$
$797$	−3.94231	+	37.5086i	−0.139644	+	1.32862i	−0.809933	+	0.586522i	$0.800497\pi$
$798$	−13.2318	−	9.61348i	−0.468401	−	0.340314i
$799$	−5.41572	−	51.5271i	−0.191594	−	1.82290i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−6.07704	−	10.5257i	−0.214722	−	0.371909i
$802$	−29.9333	+	21.7478i	−1.05698	+	0.767941i
$803$	−39.1351	−	43.4639i	−1.38105	−	1.53381i
$804$	−0.843118	−	2.59485i	−0.0297345	−	0.0915133i
$805$	2.56889			0.0905414
$806$	−3.16440	+	4.28207i	−0.111461	+	0.150829i
$807$	−0.489060			−0.0172157
$808$	1.32565	+	4.07992i	0.0466361	+	0.143531i
$809$	−31.0695	−	34.5062i	−1.09235	−	1.21317i	−0.975495	−	0.220023i	$-0.929387\pi$
$809$	−31.0695	−	34.5062i	−1.09235	−	1.21317i	−0.116851	−	0.993149i	$-0.537280\pi$
$810$	0.687693	−	0.499638i	0.0241631	−	0.0175555i
$811$	19.6835	+	34.0929i	0.691183	+	1.19716i	0.971451	+	0.237242i	$0.0762434\pi$
$811$	19.6835	+	34.0929i	0.691183	+	1.19716i	−0.280268	+	0.959922i	$0.590423\pi$
$812$	7.04886	−	12.2090i	0.247367	−	0.428452i
$813$	−1.30508	−	12.4170i	−0.0457710	−	0.435482i
$814$	6.63089	+	4.81762i	0.232412	+	0.168858i
$815$	−1.31122	+	12.4754i	−0.0459299	+	0.436994i
$816$	−3.48361	+	3.86894i	−0.121951	+	0.135440i
$817$	−71.2142	−	31.7066i	−2.49147	−	1.10927i
$818$	10.5743	+	2.24763i	0.369721	+	0.0785867i
$819$	2.87743	−	0.611617i	0.100546	−	0.0213716i
$820$	6.37957	−	2.84037i	0.222784	−	0.0991899i
$821$	0.543199	−	1.67179i	0.0189578	−	0.0583460i	−0.941130	−	0.338045i	$-0.890235\pi$
$821$	0.543199	−	1.67179i	0.0189578	−	0.0583460i	0.960088	+	0.279699i	$0.0902345\pi$
$822$	1.07930	−	3.32175i	0.0376450	−	0.115859i
$823$	−2.65095	+	1.18028i	−0.0924065	+	0.0411420i	−0.452419	−	0.891805i	$-0.649439\pi$
$823$	−2.65095	+	1.18028i	−0.0924065	+	0.0411420i	0.360013	+	0.932947i	$0.382772\pi$
$824$	−11.5837	+	2.46219i	−0.403537	+	0.0857744i
$825$	−5.99070	−	1.27336i	−0.208569	−	0.0443328i
$826$	14.7458	+	6.56526i	0.513073	+	0.228435i
$827$	−10.7366	+	11.9242i	−0.373347	+	0.414644i	−0.900313	−	0.435242i	$-0.856663\pi$
$827$	−10.7366	+	11.9242i	−0.373347	+	0.414644i	0.526966	+	0.849886i	$0.323329\pi$
$828$	−0.259715	+	2.47103i	−0.00902573	+	0.0858741i
$829$	−38.6470	−	28.0787i	−1.34226	−	0.975212i	−0.999357	−	0.0358425i	$-0.988589\pi$
$829$	−38.6470	−	28.0787i	−1.34226	−	0.975212i	−0.342907	−	0.939369i	$-0.611411\pi$
$830$	0.100325	+	0.954527i	0.00348233	+	0.0331321i
$831$	−0.419783	+	0.727085i	−0.0145621	+	0.0252223i
$832$	−0.478148	−	0.828176i	−0.0165768	−	0.0287118i
$833$	14.2467	−	10.3508i	0.493618	−	0.358635i
$834$	−2.07488	−	2.30439i	−0.0718472	−	0.0797944i
$835$	3.06802	+	9.44238i	0.106173	+	0.326767i
$836$	−44.0499			−1.52350
$837$	−25.6051	−	15.0609i	−0.885043	−	0.520580i
$838$	28.2108			0.974527
$839$	5.32708	+	16.3951i	0.183911	+	0.566020i	0.999928	−	0.0120079i	$-0.00382234\pi$
$839$	5.32708	+	16.3951i	0.183911	+	0.566020i	−0.816017	+	0.578028i	$0.803822\pi$
$840$	−1.34750	−	1.49655i	−0.0464932	−	0.0516359i
$841$	−27.0936	+	19.6847i	−0.934263	+	0.678782i
$842$	10.9919	+	19.0386i	0.378806	+	0.656112i
$843$	−3.46354	+	5.99903i	−0.119291	+	0.206617i
$844$	0.721182	+	6.86159i	0.0248241	+	0.236186i
$845$	−9.77737	−	7.10368i	−0.336352	−	0.244374i
$846$	−2.02616	+	19.2776i	−0.0696607	+	0.662778i
$847$	21.9776	−	24.4085i	0.755158	−	0.838688i
$848$	−6.39734	−	2.84828i	−0.219686	−	0.0978103i
$849$	−24.9081	−	5.29439i	−0.854845	−	0.181703i
$850$	4.50973	−	0.958572i	0.154682	−	0.0328788i
$851$	1.98858	−	0.885373i	0.0681676	−	0.0303502i
$852$	−2.24898	+	6.92166i	−0.0770489	+	0.237132i
$853$	−12.7249	+	39.1634i	−0.435694	+	1.34093i	0.456680	+	0.889631i	$0.349038\pi$
$853$	−12.7249	+	39.1634i	−0.435694	+	1.34093i	−0.892374	+	0.451297i	$0.850962\pi$
$854$	−15.1990	+	6.76705i	−0.520101	+	0.231564i
$855$	−13.7029	+	2.91264i	−0.468629	+	0.0996101i
$856$	20.1628	+	4.28573i	0.689150	+	0.146483i
$857$	9.67167	+	4.30610i	0.330378	+	0.147094i	0.565221	−	0.824940i	$-0.308791\pi$
$857$	9.67167	+	4.30610i	0.330378	+	0.147094i	−0.234843	+	0.972033i	$0.575458\pi$
$858$	−3.91901	+	4.35250i	−0.133793	+	0.148592i
$859$	−1.54126	+	14.6641i	−0.0525871	+	0.500333i	0.936250	+	0.351334i	$0.114272\pi$
$859$	−1.54126	+	14.6641i	−0.0525871	+	0.500333i	−0.988837	+	0.148999i	$0.952395\pi$
$860$	−7.76515	−	5.64171i	−0.264789	−	0.192381i
$861$	−1.46999	−	13.9860i	−0.0500970	−	0.476641i
$862$	−2.12319	+	3.67748i	−0.0723162	+	0.125255i
$863$	21.4582	+	37.1667i	0.730446	+	1.26517i	0.956693	+	0.291100i	$0.0940212\pi$
$863$	21.4582	+	37.1667i	0.730446	+	1.26517i	−0.226247	+	0.974070i	$0.572645\pi$
$864$	4.31641	−	3.13605i	0.146847	−	0.106691i
$865$	1.66742	+	1.85186i	0.0566940	+	0.0629651i
$866$	8.69490	+	26.7601i	0.295465	+	0.909347i
$867$	−4.80646			−0.163236
$868$	−4.11200	+	9.03802i	−0.139570	+	0.306771i
$869$	−67.1244			−2.27704
$870$	2.75841	+	8.48951i	0.0935188	+	0.287821i
$871$	1.54610	+	1.71711i	0.0523875	+	0.0581822i
$872$	−8.03312	+	5.83641i	−0.272036	+	0.197646i
$873$	13.3252	+	23.0799i	0.450990	+	0.781138i
$874$	−5.84943	+	10.1315i	−0.197860	+	0.342704i
$875$	0.186415	+	1.77362i	0.00630196	+	0.0599592i
$876$	9.85111	+	7.15725i	0.332838	+	0.241821i
$877$	3.84684	−	36.6003i	0.129899	−	1.23590i	−0.714287	−	0.699853i	$-0.753249\pi$
$877$	3.84684	−	36.6003i	0.129899	−	1.23590i	0.844186	−	0.536050i	$-0.180084\pi$
$878$	−6.07212	+	6.74378i	−0.204924	+	0.227591i
$879$	−11.9082	−	5.30189i	−0.401655	−	0.178828i
$880$	−5.30524	−	1.12766i	−0.178840	−	0.0380135i
$881$	35.3004	−	7.50332i	1.18930	−	0.252793i	0.429570	−	0.903033i	$-0.358665\pi$
$881$	35.3004	−	7.50332i	1.18930	−	0.252793i	0.759729	+	0.650240i	$0.225332\pi$
$882$	−6.01872	+	2.67971i	−0.202661	+	0.0902304i
$883$	0.208755	−	0.642482i	0.00702517	−	0.0216213i	−0.947482	−	0.319808i	$-0.896382\pi$
$883$	0.208755	−	0.642482i	0.00702517	−	0.0216213i	0.954508	+	0.298186i	$0.0963817\pi$
$884$	1.36245	−	4.19319i	0.0458241	−	0.141032i
$885$	−9.33675	+	4.15699i	−0.313852	+	0.139736i
$886$	23.6276	−	5.02221i	0.793786	−	0.168724i
$887$	−24.0247	−	5.10661i	−0.806670	−	0.171463i	−0.213922	−	0.976851i	$-0.568624\pi$
$887$	−24.0247	−	5.10661i	−0.806670	−	0.171463i	−0.592748	+	0.805388i	$0.701957\pi$
$888$	−1.55889	−	0.694064i	−0.0523130	−	0.0232912i
$889$	−10.5189	+	11.6825i	−0.352794	+	0.391817i
$890$	0.736535	−	7.00766i	0.0246887	−	0.234897i
$891$	−3.72988	−	2.70992i	−0.124956	−	0.0907856i
$892$	2.40907	+	22.9208i	0.0806618	+	0.767446i
$893$	−45.6341	+	79.0406i	−1.52709	+	2.64499i
$894$	−0.578961	−	1.00279i	−0.0193633	−	0.0335383i
$895$	7.86383	−	5.71341i	0.262859	−	0.190978i
$896$	−1.19332	−	1.32531i	−0.0398660	−	0.0442756i
$897$	0.480669	+	1.47935i	0.0160491	+	0.0493940i
$898$	−32.1520			−1.07293
$899$	32.9457	−	29.1849i	1.09880	−	0.973370i
$900$	−1.72490			−0.0574966
$901$	−9.97694	−	30.7059i	−0.332380	−	1.02296i
$902$	−25.3438	−	28.1472i	−0.843858	−	0.937199i
$903$	−15.6375	+	11.3613i	−0.520384	+	0.378081i
$904$	−1.22490	−	2.12159i	−0.0407395	−	0.0705629i
$905$	10.2150	−	17.6929i	0.339558	−	0.588132i
$906$	−1.26679	−	12.0527i	−0.0420864	−	0.400426i
$907$	−7.84470	−	5.69951i	−0.260479	−	0.189249i	0.449879	−	0.893089i	$-0.351467\pi$
$907$	−7.84470	−	5.69951i	−0.260479	−	0.189249i	−0.710358	+	0.703840i	$0.751467\pi$
$908$	1.02297	−	9.73293i	0.0339485	−	0.322999i
$909$	4.95131	−	5.49899i	0.164225	−	0.182390i
$910$	1.55800	+	0.693666i	0.0516472	+	0.0229948i
$911$	−33.3688	−	7.09276i	−1.10556	−	0.234994i	−0.381251	−	0.924472i	$-0.624507\pi$
$911$	−33.3688	−	7.09276i	−1.10556	−	0.234994i	−0.724307	+	0.689478i	$0.757840\pi$
$912$	8.97059	−	1.90676i	0.297046	−	0.0631391i
$913$	4.75559	−	2.11733i	0.157387	−	0.0700733i
$914$	6.60189	−	20.3185i	0.218371	−	0.672077i
$915$	3.25534	−	10.0189i	0.107618	−	0.331214i
$916$	−8.80751	+	3.92136i	−0.291008	+	0.129565i
$917$	−13.5724	+	2.88491i	−0.448201	+	0.0952680i
$918$	24.0611	+	5.11434i	0.794134	+	0.168798i
$919$	−31.0383	−	13.8191i	−1.02386	−	0.455851i	−0.175054	−	0.984559i	$-0.556010\pi$
$919$	−31.0383	−	13.8191i	−1.02386	−	0.455851i	−0.848804	+	0.528708i	$0.822677\pi$
$920$	−0.963852	+	1.07047i	−0.0317773	+	0.0352922i
$921$	1.41132	−	13.4278i	0.0465046	−	0.442462i
$922$	9.53986	+	6.93112i	0.314179	+	0.228264i
$923$	−0.644255	−	6.12968i	−0.0212059	−	0.201761i
$924$	−5.46120	+	9.45908i	−0.179660	+	0.311181i
$925$	0.755585	+	1.30871i	0.0248435	+	0.0430302i
$926$	−5.72351	+	4.15837i	−0.188086	+	0.136653i
$927$	13.6684	+	15.1803i	0.448928	+	0.498585i
$928$	2.44279	+	7.51813i	0.0801885	+	0.246795i
$929$	42.0239			1.37876			0.689380	−	0.724400i	$-0.257883\pi$
$929$	42.0239			1.37876			0.689380	+	0.724400i	$0.257883\pi$
$930$	−2.51062	−	5.76411i	−0.0823264	−	0.189013i
$931$	−31.0209			−1.01667
$932$	3.68588	+	11.3440i	0.120735	+	0.371585i
$933$	11.3294	+	12.5826i	0.370909	+	0.411937i
$934$	−6.34220	+	4.60788i	−0.207523	+	0.150774i
$935$	−12.5031	−	21.6559i	−0.408894	−	0.708225i
$936$	−0.824756	+	1.42852i	−0.0269580	+	0.0466926i
$937$	5.47004	+	52.0440i	0.178698	+	1.70020i	0.605490	+	0.795853i	$0.292977\pi$
$937$	5.47004	+	52.0440i	0.178698	+	1.70020i	−0.426792	+	0.904350i	$0.640356\pi$
$938$	3.48607	+	2.53278i	0.113824	+	0.0826982i
$939$	1.11031	−	10.5639i	0.0362337	−	0.344741i
$940$	−7.51945	+	8.35120i	−0.245258	+	0.272386i
$941$	0.934482	+	0.416058i	0.0304632	+	0.0135631i	0.421912	−	0.906637i	$-0.361359\pi$
$941$	0.934482	+	0.416058i	0.0304632	+	0.0135631i	−0.391448	+	0.920200i	$0.628026\pi$
$942$	−7.31604	−	1.55507i	−0.238370	−	0.0506670i
$943$	−9.83932	+	2.09141i	−0.320412	+	0.0681057i
$944$	−8.26844	+	3.68135i	−0.269115	+	0.119818i
$945$	−2.94031	+	9.04933i	−0.0956482	+	0.294375i
$946$	−16.0870	+	49.5107i	−0.523033	+	1.60973i
$947$	−44.2741	+	19.7121i	−1.43872	+	0.640557i	−0.970069	−	0.242829i	$-0.921925\pi$
$947$	−44.2741	+	19.7121i	−1.43872	+	0.640557i	−0.468646	+	0.883386i	$0.655258\pi$
$948$	13.6696	−	2.90557i	0.443969	−	0.0943685i
$949$	−10.0868	−	2.14401i	−0.327430	−	0.0695974i
$950$	−7.41949	−	3.30337i	−0.240720	−	0.107176i
$951$	2.41425	−	2.68130i	0.0782875	−	0.0869470i
$952$	0.859460	−	8.17722i	0.0278553	−	0.265025i
$953$	−28.2741	−	20.5423i	−0.915887	−	0.665431i	0.0266097	−	0.999646i	$-0.491529\pi$
$953$	−28.2741	−	20.5423i	−0.915887	−	0.665431i	−0.942497	+	0.334215i	$0.891529\pi$
$954$	1.26260	+	12.0129i	0.0408783	+	0.388931i
$955$	9.77487	−	16.9306i	0.316307	−	0.547861i
$956$	−7.49602	−	12.9835i	−0.242439	−	0.419916i
$957$	39.1683	−	28.4574i	1.26613	−	0.919898i
$958$	−18.1021	−	20.1044i	−0.584852	−	0.649544i
$959$	1.70457	+	5.24614i	0.0550435	+	0.169407i
$960$	1.12920			0.0364449
$961$	−21.1134	+	22.6985i	−0.681078	+	0.732211i
$962$	1.44512			0.0465927
$963$	−10.9873	−	33.8155i	−0.354062	−	1.08969i
$964$	−1.40238	−	1.55750i	−0.0451675	−	0.0501635i
$965$	16.5643	−	12.0346i	0.533223	−	0.387409i
$966$	1.45040	+	2.51216i	0.0466658	+	0.0808276i
$967$	12.7622	−	22.1048i	0.410406	−	0.710844i	−0.584528	−	0.811373i	$-0.698720\pi$
$967$	12.7622	−	22.1048i	0.410406	−	0.710844i	0.994934	+	0.100529i	$0.0320537\pi$
$968$	1.92512	+	18.3163i	0.0618757	+	0.588708i
$969$	34.2074	+	24.8531i	1.09890	+	0.798398i
$970$	−1.61501	+	15.3658i	−0.0518549	+	0.493366i
$971$	18.2028	−	20.2163i	0.584157	−	0.648772i	−0.376530	−	0.926404i	$-0.622883\pi$
$971$	18.2028	−	20.2163i	0.584157	−	0.648772i	0.960687	+	0.277632i	$0.0895496\pi$
$972$	−13.7454	−	6.11987i	−0.440885	−	0.196295i
$973$	4.79026	+	1.01820i	0.153569	+	0.0326421i
$974$	−11.4127	+	2.42585i	−0.365688	+	0.0777294i
$975$	−0.986494	+	0.439216i	−0.0315931	+	0.0140662i
$976$	2.88286	−	8.87252i	0.0922780	−	0.284003i
$977$	3.79767	−	11.6880i	0.121498	−	0.373933i	−0.871749	−	0.489954i	$-0.837014\pi$
$977$	3.79767	−	11.6880i	0.121498	−	0.373933i	0.993247	+	0.116020i	$0.0370137\pi$
$978$	−12.9402	+	5.76136i	−0.413783	+	0.184228i
$979$	−37.3821	+	7.94581i	−1.19474	+	0.253949i
$980$	−3.73607	−	0.794126i	−0.119344	−	0.0253674i
$981$	15.6466	+	6.96632i	0.499558	+	0.222418i
$982$	10.4603	−	11.6173i	0.333800	−	0.370723i
$983$	4.53136	−	43.1130i	0.144528	−	1.37509i	−0.646314	−	0.763071i	$-0.723691\pi$
$983$	4.53136	−	43.1130i	0.144528	−	1.37509i	0.790842	−	0.612020i	$-0.209643\pi$
$984$	6.37957	+	4.63503i	0.203373	+	0.147759i
$985$	−2.52044	−	23.9804i	−0.0803080	−	0.764080i
$986$	−18.2230	+	31.5631i	−0.580338	+	1.00518i
$987$	11.3152	+	19.5986i	0.360168	+	0.623829i
$988$	−6.28339	+	4.56515i	−0.199901	+	0.145237i
$989$	9.25129	+	10.2746i	0.294174	+	0.326713i
$990$	2.89099	+	8.89754i	0.0918816	+	0.282783i
$991$	28.2275			0.896675			0.448338	−	0.893864i	$-0.352016\pi$
$991$	28.2275			0.896675			0.448338	+	0.893864i	$0.352016\pi$
$992$	−2.22335	−	5.10458i	−0.0705915	−	0.162070i
$993$	7.44114			0.236137
$994$	−3.55189	−	10.9316i	−0.112659	−	0.346729i
$995$	4.61567	+	5.12622i	0.146327	+	0.162512i
$996$	−0.876807	+	0.637038i	−0.0277827	+	0.0201853i
$997$	−13.2790	−	22.9998i	−0.420549	−	0.728412i	0.575444	−	0.817841i	$-0.304829\pi$
$997$	−13.2790	−	22.9998i	−0.420549	−	0.728412i	−0.995993	+	0.0894291i	$0.971496\pi$
$998$	1.25589	−	2.17526i	0.0397544	−	0.0688566i
$999$	0.842777	+	8.01849i	0.0266643	+	0.253694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.q.d.51.1	✓	8
31.13	odd	30		9610.2.a.bg.1.3		4
31.14	even	15	inner	310.2.q.d.231.1	yes	8
31.18	even	15		9610.2.a.bc.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.q.d.51.1	✓	8	1.1	even	1	trivial
310.2.q.d.231.1	yes	8	31.14	even	15	inner
9610.2.a.bc.1.2		4	31.18	even	15
9610.2.a.bg.1.3		4	31.13	odd	30

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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.755585 - 0.839162i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.564602 + 0.977920i) q^{6} +(-0.186415 - 1.77362i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.180301 - 1.71545i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.755585 - 0.839162i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.564602 + 0.977920i) q^{6} +(-0.186415 - 1.77362i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.180301 - 1.71545i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-4.95485 - 2.20604i) q^{11} +(1.10453 + 0.234775i) q^{12} +(-0.935398 + 0.198825i) q^{13} +(-1.62920 + 0.725368i) q^{14} +(0.348943 - 1.07394i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.21188 - 1.87525i) q^{17} +(-1.68720 + 0.358626i) q^{18} +(-7.94417 - 1.68859i) q^{19} +(-0.913545 - 0.406737i) q^{20} +(-1.34750 + 1.49655i) q^{21} +(-0.566937 + 5.39405i) q^{22} +(1.16535 + 0.846678i) q^{23} +(-0.118034 - 1.12302i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.478148 + 0.828176i) q^{26} +(-4.31641 + 3.13605i) q^{27} +(1.19332 + 1.32531i) q^{28} +(-2.44279 - 7.51813i) q^{29} -1.12920 q^{30} +(2.22335 + 5.10458i) q^{31} -1.00000 q^{32} +(1.89259 + 5.82478i) q^{33} +(-3.08501 - 3.42625i) q^{34} +(1.44279 - 1.04825i) q^{35} +(0.862449 + 1.49381i) q^{36} +(0.755585 - 1.30871i) q^{37} +(0.848943 + 8.07716i) q^{38} +(0.873619 + 0.634721i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-4.67274 + 5.18961i) q^{41} +(1.83970 + 0.819089i) q^{42} +(9.38850 + 1.99559i) q^{43} +(5.30524 - 1.12766i) q^{44} +(1.57577 - 0.701579i) q^{45} +(0.445125 - 1.36995i) q^{46} +(3.47262 - 10.6876i) q^{47} +(-1.03158 + 0.459289i) q^{48} +(3.73607 - 0.794126i) q^{49} +(0.978148 + 0.207912i) q^{50} +(-4.75607 - 2.11754i) q^{51} +(0.639886 - 0.710666i) q^{52} +(0.731988 - 6.96440i) q^{53} +(4.31641 + 3.13605i) q^{54} +(-0.566937 - 5.39405i) q^{55} +(0.891693 - 1.54446i) q^{56} +(4.58550 + 7.94232i) q^{57} +(-6.39531 + 4.64646i) q^{58} +(-6.05626 - 6.72615i) q^{59} +(0.348943 + 1.07394i) q^{60} +9.32912 q^{61} +(4.16769 - 3.69193i) q^{62} -3.07616 q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.639886 - 0.710666i) q^{65} +(4.95485 - 3.59991i) q^{66} +(-1.20810 - 2.09249i) q^{67} +(-2.30524 + 3.99279i) q^{68} +(-0.170023 - 1.61766i) q^{69} +(-1.44279 - 1.04825i) q^{70} +(-0.673699 + 6.40982i) q^{71} +(1.15418 - 1.28185i) q^{72} +(9.85111 + 4.38600i) q^{73} +(-1.47815 - 0.314190i) q^{74} +(1.10453 - 0.234775i) q^{75} +(7.41949 - 3.30337i) q^{76} +(-2.98902 + 9.19925i) q^{77} +(0.333693 - 1.02700i) q^{78} +(11.3060 - 5.03377i) q^{79} +(0.978148 - 0.207912i) q^{80} +(0.831460 + 0.176732i) q^{81} +(6.37957 + 2.84037i) q^{82} +(-0.642222 + 0.713259i) q^{83} +(0.210500 - 2.00278i) q^{84} +(3.72995 + 2.70997i) q^{85} +(-1.00329 - 9.54567i) q^{86} +(-4.46320 + 7.73049i) q^{87} +(-2.71188 - 4.69711i) q^{88} +(5.70054 - 4.14169i) q^{89} +(-1.15418 - 1.28185i) q^{90} +(0.527011 + 1.62197i) q^{91} -1.44045 q^{92} +(2.60364 - 5.72270i) q^{93} -11.2376 q^{94} +(-2.50973 - 7.72415i) q^{95} +(0.755585 + 0.839162i) q^{96} +(-12.4997 + 9.08154i) q^{97} +(-1.90977 - 3.30781i) q^{98} +(-4.67772 + 8.10204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 8 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 7 q^{7} + 2 q^{8} + q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 8 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 7 * q^7 + 2 * q^8 + q^9	\( 8 q + 2 q^{2} - 8 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 7 q^{7} + 2 q^{8} + q^{9} + q^{10} + 6 q^{11} + 7 q^{12} - 10 q^{13} - 8 q^{14} - q^{15} - 2 q^{16} + 18 q^{17} - q^{18} - 13 q^{19} - q^{20} + 21 q^{21} + 9 q^{22} - 12 q^{23} + 8 q^{24} - 4 q^{25} - 5 q^{26} - 17 q^{27} + 3 q^{28} - 9 q^{29} - 4 q^{30} - 11 q^{31} - 8 q^{32} - 39 q^{33} - 3 q^{34} + q^{35} - 4 q^{36} + 8 q^{37} + 3 q^{38} + q^{40} - 3 q^{41} + 34 q^{42} + 21 q^{43} + 21 q^{44} + 14 q^{45} - 18 q^{46} - 9 q^{47} + 7 q^{48} + 12 q^{49} - q^{50} - 39 q^{51} + 5 q^{52} - 12 q^{53} + 17 q^{54} + 9 q^{55} - 8 q^{56} + 14 q^{57} - 6 q^{58} - 30 q^{59} - q^{60} + 68 q^{61} + q^{62} - 46 q^{63} - 2 q^{64} - 5 q^{65} - 6 q^{66} + 23 q^{67} + 3 q^{68} + 42 q^{69} - q^{70} - 16 q^{72} + 17 q^{73} - 3 q^{74} + 7 q^{75} + 12 q^{76} - 36 q^{77} - 5 q^{78} + 51 q^{79} - q^{80} - 11 q^{81} + 3 q^{82} + 6 q^{83} + 26 q^{84} + 6 q^{85} - 26 q^{86} - 6 q^{87} - 6 q^{88} - 21 q^{89} + 16 q^{90} - 10 q^{91} - 12 q^{92} + 58 q^{93} - 36 q^{94} + 4 q^{95} + 8 q^{96} - 6 q^{97} + 8 q^{98} + 36 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 8 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 7 * q^7 + 2 * q^8 + q^9 + q^10 + 6 * q^11 + 7 * q^12 - 10 * q^13 - 8 * q^14 - q^15 - 2 * q^16 + 18 * q^17 - q^18 - 13 * q^19 - q^20 + 21 * q^21 + 9 * q^22 - 12 * q^23 + 8 * q^24 - 4 * q^25 - 5 * q^26 - 17 * q^27 + 3 * q^28 - 9 * q^29 - 4 * q^30 - 11 * q^31 - 8 * q^32 - 39 * q^33 - 3 * q^34 + q^35 - 4 * q^36 + 8 * q^37 + 3 * q^38 + q^40 - 3 * q^41 + 34 * q^42 + 21 * q^43 + 21 * q^44 + 14 * q^45 - 18 * q^46 - 9 * q^47 + 7 * q^48 + 12 * q^49 - q^50 - 39 * q^51 + 5 * q^52 - 12 * q^53 + 17 * q^54 + 9 * q^55 - 8 * q^56 + 14 * q^57 - 6 * q^58 - 30 * q^59 - q^60 + 68 * q^61 + q^62 - 46 * q^63 - 2 * q^64 - 5 * q^65 - 6 * q^66 + 23 * q^67 + 3 * q^68 + 42 * q^69 - q^70 - 16 * q^72 + 17 * q^73 - 3 * q^74 + 7 * q^75 + 12 * q^76 - 36 * q^77 - 5 * q^78 + 51 * q^79 - q^80 - 11 * q^81 + 3 * q^82 + 6 * q^83 + 26 * q^84 + 6 * q^85 - 26 * q^86 - 6 * q^87 - 6 * q^88 - 21 * q^89 + 16 * q^90 - 10 * q^91 - 12 * q^92 + 58 * q^93 - 36 * q^94 + 4 * q^95 + 8 * q^96 - 6 * q^97 + 8 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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