LMFDB - Embedded newform 930.2.bg.g.691.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			691.2
Character	$\chi$	$=$	930.691
Dual form			930.2.bg.g.751.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.302260 - 0.134575i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.302260 - 0.134575i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-0.978148 + 0.207912i) q^{10} +(-0.175142 + 1.66636i) q^{11} +(0.669131 + 0.743145i) q^{12} +(1.96411 - 2.18137i) q^{13} +(-0.0345848 - 0.329052i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.731213 - 6.95703i) q^{17} +(0.669131 - 0.743145i) q^{18} +(-4.68670 - 5.20511i) q^{19} +(-0.104528 + 0.994522i) q^{20} +(-0.323634 + 0.0687906i) q^{21} +(1.53068 + 0.681505i) q^{22} +(-5.63255 + 4.09229i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.46766 - 2.54206i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.323634 - 0.0687906i) q^{28} +(-1.98646 + 6.11369i) q^{29} +1.00000 q^{30} +(-5.06680 - 2.30816i) q^{31} +1.00000 q^{32} +(0.517771 - 1.59354i) q^{33} +(-6.84249 - 1.45442i) q^{34} +(-0.267675 - 0.194477i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(0.0433172 - 0.0750276i) q^{37} +(-6.39862 + 2.84885i) q^{38} +(-2.37472 + 1.72534i) q^{39} +(0.913545 + 0.406737i) q^{40} +(-1.36333 + 0.289785i) q^{41} +(-0.0345848 + 0.329052i) q^{42} +(0.874215 + 0.970914i) q^{43} +(1.12116 - 1.24517i) q^{44} +(-0.104528 - 0.994522i) q^{45} +(2.15144 + 6.62146i) q^{46} +(1.89273 + 5.82521i) q^{47} +(-0.104528 - 0.994522i) q^{48} +(-4.61066 + 5.12066i) q^{49} +(0.669131 + 0.743145i) q^{50} +(-0.731213 + 6.95703i) q^{51} +(-2.87118 + 0.610287i) q^{52} +(0.0609445 + 0.0271343i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(1.53068 - 0.681505i) q^{55} +(-0.165432 + 0.286537i) q^{56} +(3.50208 + 6.06578i) q^{57} +(5.20062 + 3.77847i) q^{58} +(-6.89909 - 1.46645i) q^{59} +(0.309017 - 0.951057i) q^{60} +0.495615 q^{61} +(-3.76091 + 4.10555i) q^{62} +0.330865 q^{63} +(0.309017 - 0.951057i) q^{64} +(-2.87118 - 0.610287i) q^{65} +(-1.35554 - 0.984860i) q^{66} +(-1.14806 - 1.98849i) q^{67} +(-3.49768 + 6.05815i) q^{68} +(6.36030 - 2.83179i) q^{69} +(-0.267675 + 0.194477i) q^{70} +(5.01908 + 2.23464i) q^{71} +(-0.978148 + 0.207912i) q^{72} +(1.56707 - 14.9097i) q^{73} +(-0.0579697 - 0.0643819i) q^{74} +(0.669131 - 0.743145i) q^{75} +(0.732134 + 6.96579i) q^{76} +(0.171312 + 0.527245i) q^{77} +(0.907064 + 2.79166i) q^{78} +(-1.59505 - 15.1759i) q^{79} +(0.669131 - 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.145691 + 1.38615i) q^{82} +(-3.96617 + 0.843035i) q^{83} +(0.302260 + 0.134575i) q^{84} +(-5.65936 + 4.11176i) q^{85} +(1.19354 - 0.531399i) q^{86} +(3.21416 - 5.56709i) q^{87} +(-0.837772 - 1.45106i) q^{88} +(-12.0272 - 8.73825i) q^{89} +(-0.978148 - 0.207912i) q^{90} +(0.300115 - 0.923660i) q^{91} +6.96221 q^{92} +(4.47618 + 3.31116i) q^{93} +6.12499 q^{94} +(-2.16441 + 6.66135i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(1.15972 + 0.842583i) q^{97} +(3.44526 + 5.96737i) q^{98} +(-0.837772 + 1.45106i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{20} + 4 q^{21} + 3 q^{22} + 5 q^{23} + 3 q^{24} - 12 q^{25} - 3 q^{26} - 6 q^{27} + 4 q^{28} - 15 q^{29} + 24 q^{30} + 15 q^{31} + 24 q^{32} + 4 q^{33} - 9 q^{34} - 3 q^{35} - 12 q^{36} + 6 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} - 6 q^{42} - 13 q^{43} - 2 q^{44} + 3 q^{45} - 10 q^{46} + 4 q^{47} + 3 q^{48} + 3 q^{50} - 9 q^{51} - 3 q^{52} - 6 q^{54} + 3 q^{55} - 11 q^{56} - 14 q^{57} + 22 q^{59} - 6 q^{60} + 16 q^{61} - 5 q^{62} + 22 q^{63} - 6 q^{64} - 3 q^{65} - 6 q^{66} - 19 q^{67} - 9 q^{68} - 10 q^{69} - 3 q^{70} - 45 q^{71} + 3 q^{72} + 11 q^{73} - 35 q^{74} + 3 q^{75} + 6 q^{76} - 50 q^{77} + 6 q^{78} + 36 q^{79} + 3 q^{80} + 3 q^{81} - 20 q^{82} - 4 q^{83} + 9 q^{84} - 12 q^{85} + 22 q^{86} - 15 q^{87} - 2 q^{88} - 7 q^{89} + 3 q^{90} - 32 q^{91} + 10 q^{92} + 7 q^{93} + 54 q^{94} - 2 q^{95} + 3 q^{96} + 11 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 6 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^18 + q^19 + 3 * q^20 + 4 * q^21 + 3 * q^22 + 5 * q^23 + 3 * q^24 - 12 * q^25 - 3 * q^26 - 6 * q^27 + 4 * q^28 - 15 * q^29 + 24 * q^30 + 15 * q^31 + 24 * q^32 + 4 * q^33 - 9 * q^34 - 3 * q^35 - 12 * q^36 + 6 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 - 6 * q^42 - 13 * q^43 - 2 * q^44 + 3 * q^45 - 10 * q^46 + 4 * q^47 + 3 * q^48 + 3 * q^50 - 9 * q^51 - 3 * q^52 - 6 * q^54 + 3 * q^55 - 11 * q^56 - 14 * q^57 + 22 * q^59 - 6 * q^60 + 16 * q^61 - 5 * q^62 + 22 * q^63 - 6 * q^64 - 3 * q^65 - 6 * q^66 - 19 * q^67 - 9 * q^68 - 10 * q^69 - 3 * q^70 - 45 * q^71 + 3 * q^72 + 11 * q^73 - 35 * q^74 + 3 * q^75 + 6 * q^76 - 50 * q^77 + 6 * q^78 + 36 * q^79 + 3 * q^80 + 3 * q^81 - 20 * q^82 - 4 * q^83 + 9 * q^84 - 12 * q^85 + 22 * q^86 - 15 * q^87 - 2 * q^88 - 7 * q^89 + 3 * q^90 - 32 * q^91 + 10 * q^92 + 7 * q^93 + 54 * q^94 - 2 * q^95 + 3 * q^96 + 11 * q^97 - 15 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i
$4$	−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
$7$	0.302260	−	0.134575i	0.114243	−	0.0508645i	−0.348819	−	0.937190i	$-0.613417\pi$
$7$	0.302260	−	0.134575i	0.114243	−	0.0508645i	0.463062	+	0.886326i	$0.346751\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	−0.978148	+	0.207912i	−0.309317	+	0.0657474i
$11$	−0.175142	+	1.66636i	−0.0528073	+	0.502428i	0.935867	+	0.352353i	$0.114618\pi$
$11$	−0.175142	+	1.66636i	−0.0528073	+	0.502428i	−0.988675	+	0.150075i	$0.952048\pi$
$12$	0.669131	+	0.743145i	0.193161	+	0.214527i
$13$	1.96411	−	2.18137i	0.544747	−	0.605003i	−0.406418	−	0.913687i	$-0.633222\pi$
$13$	1.96411	−	2.18137i	0.544747	−	0.605003i	0.951164	+	0.308685i	$0.0998888\pi$
$14$	−0.0345848	−	0.329052i	−0.00924317	−	0.0879429i
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.731213	−	6.95703i	−0.177345	−	1.68733i	−0.615271	−	0.788316i	$-0.710953\pi$
$17$	−0.731213	−	6.95703i	−0.177345	−	1.68733i	0.437925	−	0.899011i	$-0.355713\pi$
$18$	0.669131	−	0.743145i	0.157716	−	0.175161i
$19$	−4.68670	−	5.20511i	−1.07520	−	1.19413i	−0.980067	−	0.198669i	$-0.936338\pi$
$19$	−4.68670	−	5.20511i	−1.07520	−	1.19413i	−0.0951360	−	0.995464i	$-0.530329\pi$
$20$	−0.104528	+	0.994522i	−0.0233733	+	0.222382i
$21$	−0.323634	+	0.0687906i	−0.0706228	+	0.0150113i
$22$	1.53068	+	0.681505i	0.326343	+	0.145297i
$23$	−5.63255	+	4.09229i	−1.17447	+	0.853301i	−0.991537	−	0.129825i	$-0.958558\pi$
$23$	−5.63255	+	4.09229i	−1.17447	+	0.853301i	−0.182931	+	0.983126i	$0.558558\pi$
$24$	0.913545	−	0.406737i	0.186477	−	0.0830248i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.46766	−	2.54206i	−0.287832	−	0.498539i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−0.323634	−	0.0687906i	−0.0611611	−	0.0130002i
$29$	−1.98646	+	6.11369i	−0.368876	+	1.13528i	0.578642	+	0.815582i	$0.303583\pi$
$29$	−1.98646	+	6.11369i	−0.368876	+	1.13528i	−0.947518	+	0.319703i	$0.896417\pi$
$30$	1.00000			0.182574
$31$	−5.06680	−	2.30816i	−0.910023	−	0.414557i
$31$	−5.06680	−	2.30816i	−0.910023	−	0.414557i
$32$	1.00000			0.176777
$33$	0.517771	−	1.59354i	0.0901324	−	0.277399i
$34$	−6.84249	−	1.45442i	−1.17348	−	0.249430i
$35$	−0.267675	−	0.194477i	−0.0452453	−	0.0328727i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	0.0433172	−	0.0750276i	0.00712130	−	0.0123345i	−0.862443	−	0.506155i	$-0.831067\pi$
$37$	0.0433172	−	0.0750276i	0.00712130	−	0.0123345i	0.869564	+	0.493820i	$0.164400\pi$
$38$	−6.39862	+	2.84885i	−1.03799	+	0.462144i
$39$	−2.37472	+	1.72534i	−0.380260	+	0.276275i
$40$	0.913545	+	0.406737i	0.144444	+	0.0643107i
$41$	−1.36333	+	0.289785i	−0.212917	+	0.0452568i	−0.313135	−	0.949709i	$-0.601379\pi$
$41$	−1.36333	+	0.289785i	−0.212917	+	0.0452568i	0.100218	+	0.994965i	$0.468046\pi$
$42$	−0.0345848	+	0.329052i	−0.00533655	+	0.0507738i
$43$	0.874215	+	0.970914i	0.133317	+	0.148063i	0.806106	−	0.591771i	$-0.201571\pi$
$43$	0.874215	+	0.970914i	0.133317	+	0.148063i	−0.672790	+	0.739834i	$0.734904\pi$
$44$	1.12116	−	1.24517i	0.169021	−	0.187717i
$45$	−0.104528	−	0.994522i	−0.0155822	−	0.148255i
$46$	2.15144	+	6.62146i	0.317213	+	0.976281i
$47$	1.89273	+	5.82521i	0.276082	+	0.849695i	0.988931	+	0.148376i	$0.0474047\pi$
$47$	1.89273	+	5.82521i	0.276082	+	0.849695i	−0.712848	+	0.701318i	$0.752595\pi$
$48$	−0.104528	−	0.994522i	−0.0150874	−	0.143547i
$49$	−4.61066	+	5.12066i	−0.658666	+	0.731523i
$50$	0.669131	+	0.743145i	0.0946294	+	0.105097i
$51$	−0.731213	+	6.95703i	−0.102390	+	0.974179i
$52$	−2.87118	+	0.610287i	−0.398161	+	0.0846316i
$53$	0.0609445	+	0.0271343i	0.00837138	+	0.00372718i	0.410918	−	0.911672i	$-0.365208\pi$
$53$	0.0609445	+	0.0271343i	0.00837138	+	0.00372718i	−0.402547	+	0.915399i	$0.631875\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	1.53068	−	0.681505i	0.206397	−	0.0918941i
$56$	−0.165432	+	0.286537i	−0.0221068	+	0.0382901i
$57$	3.50208	+	6.06578i	0.463862	+	0.803433i
$58$	5.20062	+	3.77847i	0.682875	+	0.496137i
$59$	−6.89909	−	1.46645i	−0.898185	−	0.190915i	−0.264390	−	0.964416i	$-0.585171\pi$
$59$	−6.89909	−	1.46645i	−0.898185	−	0.190915i	−0.633795	+	0.773501i	$0.718504\pi$
$60$	0.309017	−	0.951057i	0.0398939	−	0.122781i
$61$	0.495615			0.0634571			0.0317285	−	0.999497i	$-0.489899\pi$
$61$	0.495615			0.0634571			0.0317285	+	0.999497i	$0.489899\pi$
$62$	−3.76091	+	4.10555i	−0.477636	+	0.521405i
$63$	0.330865			0.0416850
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−2.87118	−	0.610287i	−0.356126	−	0.0756968i
$66$	−1.35554	−	0.984860i	−0.166856	−	0.121228i
$67$	−1.14806	−	1.98849i	−0.140258	−	0.242933i	0.787336	−	0.616524i	$-0.211460\pi$
$67$	−1.14806	−	1.98849i	−0.140258	−	0.242933i	−0.927594	+	0.373591i	$0.878126\pi$
$68$	−3.49768	+	6.05815i	−0.424155	+	0.734659i
$69$	6.36030	−	2.83179i	0.765690	−	0.340907i
$70$	−0.267675	+	0.194477i	−0.0319933	+	0.0232445i
$71$	5.01908	+	2.23464i	0.595655	+	0.265203i	0.682342	−	0.731033i	$-0.260961\pi$
$71$	5.01908	+	2.23464i	0.595655	+	0.265203i	−0.0866871	+	0.996236i	$0.527628\pi$
$72$	−0.978148	+	0.207912i	−0.115276	+	0.0245026i
$73$	1.56707	−	14.9097i	0.183412	−	1.74505i	−0.385553	−	0.922686i	$-0.625989\pi$
$73$	1.56707	−	14.9097i	0.183412	−	1.74505i	0.568965	−	0.822362i	$-0.307344\pi$
$74$	−0.0579697	−	0.0643819i	−0.00673884	−	0.00748424i
$75$	0.669131	−	0.743145i	0.0772645	−	0.0858110i
$76$	0.732134	+	6.96579i	0.0839816	+	0.799031i
$77$	0.171312	+	0.527245i	0.0195228	+	0.0600851i
$78$	0.907064	+	2.79166i	0.102705	+	0.316093i
$79$	−1.59505	−	15.1759i	−0.179458	−	1.70742i	−0.599875	−	0.800093i	$-0.704783\pi$
$79$	−1.59505	−	15.1759i	−0.179458	−	1.70742i	0.420418	−	0.907331i	$-0.361883\pi$
$80$	0.669131	−	0.743145i	0.0748111	−	0.0830861i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	−0.145691	+	1.38615i	−0.0160888	+	0.153075i
$83$	−3.96617	+	0.843035i	−0.435343	+	0.0925351i	−0.420370	−	0.907353i	$-0.638100\pi$
$83$	−3.96617	+	0.843035i	−0.435343	+	0.0925351i	−0.0149735	+	0.999888i	$0.504766\pi$
$84$	0.302260	+	0.134575i	0.0329793	+	0.0146833i
$85$	−5.65936	+	4.11176i	−0.613843	+	0.445983i
$86$	1.19354	−	0.531399i	0.128703	−	0.0573022i
$87$	3.21416	−	5.56709i	0.344594	−	0.596854i
$88$	−0.837772	−	1.45106i	−0.0893067	−	0.154684i
$89$	−12.0272	−	8.73825i	−1.27488	−	0.926252i	−0.275491	−	0.961304i	$-0.588841\pi$
$89$	−12.0272	−	8.73825i	−1.27488	−	0.926252i	−0.999386	+	0.0350513i	$0.988841\pi$
$90$	−0.978148	−	0.207912i	−0.103106	−	0.0219158i
$91$	0.300115	−	0.923660i	0.0314606	−	0.0968259i
$92$	6.96221			0.725861
$93$	4.47618	+	3.31116i	0.464158	+	0.343352i
$94$	6.12499			0.631745
$95$	−2.16441	+	6.66135i	−0.222063	+	0.683441i
$96$	−0.978148	−	0.207912i	−0.0998318	−	0.0212199i
$97$	1.15972	+	0.842583i	0.117751	+	0.0855513i	0.645102	−	0.764096i	$-0.276815\pi$
$97$	1.15972	+	0.842583i	0.117751	+	0.0855513i	−0.527351	+	0.849648i	$0.676815\pi$
$98$	3.44526	+	5.96737i	0.348024	+	0.602796i
$99$	−0.837772	+	1.45106i	−0.0841992	+	0.145837i
$100$	0.913545	−	0.406737i	0.0913545	−	0.0406737i
$101$	−8.47746	+	6.15923i	−0.843538	+	0.612867i	−0.923357	−	0.383943i	$-0.874566\pi$
$101$	−8.47746	+	6.15923i	−0.843538	+	0.612867i	0.0798184	+	0.996809i	$0.474566\pi$
$102$	6.39057	+	2.84527i	0.632761	+	0.281723i
$103$	−6.27598	+	1.33400i	−0.618391	+	0.131443i	−0.506446	−	0.862272i	$-0.669041\pi$
$103$	−6.27598	+	1.33400i	−0.618391	+	0.131443i	−0.111944	+	0.993714i	$0.535708\pi$
$104$	−0.306825	+	2.91924i	−0.0300866	+	0.286255i
$105$	0.221392	+	0.245880i	0.0216056	+	0.0239955i
$106$	0.0446391	−	0.0495768i	0.00433573	−	0.00481532i
$107$	0.933174	+	8.87856i	0.0902134	+	0.858323i	0.942266	+	0.334866i	$0.108691\pi$
$107$	0.933174	+	8.87856i	0.0902134	+	0.858323i	−0.852052	+	0.523457i	$0.824642\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	−2.47542	−	7.61856i	−0.237102	−	0.729726i	−0.996836	−	0.0794910i	$-0.974670\pi$
$109$	−2.47542	−	7.61856i	−0.237102	−	0.729726i	0.759733	−	0.650235i	$-0.225330\pi$
$110$	−0.175142	−	1.66636i	−0.0166991	−	0.158882i
$111$	−0.0579697	+	0.0643819i	−0.00550224	+	0.00611086i
$112$	0.221392	+	0.245880i	0.0209195	+	0.0232335i
$113$	1.44762	−	13.7732i	0.136180	−	1.29567i	−0.686485	−	0.727144i	$-0.740847\pi$
$113$	1.44762	−	13.7732i	0.136180	−	1.29567i	0.822665	−	0.568526i	$-0.192486\pi$
$114$	6.85110	−	1.45625i	0.641665	−	0.136390i
$115$	6.36030	+	2.83179i	0.593101	+	0.264065i
$116$	5.20062	−	3.77847i	0.482865	−	0.350822i
$117$	2.68155	−	1.19390i	0.247909	−	0.110376i
$118$	−3.52661	+	6.10827i	−0.324651	+	0.562312i
$119$	−1.15726	−	2.00443i	−0.106086	−	0.183746i
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	8.01353	+	1.70333i	0.728503	+	0.154848i
$122$	0.153154	−	0.471358i	0.0138659	−	0.0426748i
$123$	1.39379			0.125674
$124$	2.74242	+	4.84553i	0.246277	+	0.435141i
$125$	1.00000			0.0894427
$126$	0.102243	−	0.314671i	0.00910851	−	0.0280331i
$127$	18.7063	+	3.97614i	1.65991	+	0.352825i	0.939983	−	0.341222i	$-0.110841\pi$
$127$	18.7063	+	3.97614i	1.65991	+	0.352825i	0.719930	+	0.694047i	$0.244174\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−0.653247	−	1.13146i	−0.0575152	−	0.0996192i
$130$	−1.46766	+	2.54206i	−0.128722	+	0.222954i
$131$	−0.500751	+	0.222949i	−0.0437508	+	0.0194791i	−0.428495	−	0.903544i	$-0.640956\pi$
$131$	−0.500751	+	0.222949i	−0.0437508	+	0.0194791i	0.384745	+	0.923023i	$0.374290\pi$
$132$	−1.35554	+	0.984860i	−0.117985	+	0.0857210i
$133$	−2.11708	−	0.942583i	−0.183574	−	0.0817323i
$134$	−2.24594	+	0.477389i	−0.194020	+	0.0412402i
$135$	−0.104528	+	0.994522i	−0.00899638	+	0.0855948i
$136$	4.68080	+	5.19856i	0.401376	+	0.445773i
$137$	5.64612	−	6.27065i	0.482381	−	0.535738i	−0.451998	−	0.892019i	$-0.649289\pi$
$137$	5.64612	−	6.27065i	0.482381	−	0.535738i	0.934379	+	0.356281i	$0.115955\pi$
$138$	−0.727749	−	6.92407i	−0.0619501	−	0.589416i
$139$	−2.81228	−	8.65530i	−0.238534	−	0.734133i	−0.996633	−	0.0819932i	$-0.973871\pi$
$139$	−2.81228	−	8.65530i	−0.238534	−	0.734133i	0.758099	−	0.652140i	$-0.226129\pi$
$140$	0.102243	+	0.314671i	0.00864109	+	0.0265945i
$141$	−0.640236	−	6.09144i	−0.0539176	−	0.512992i
$142$	3.67625	−	4.08289i	0.308504	−	0.342628i
$143$	3.29096	+	3.65498i	0.275204	+	0.305644i
$144$	−0.104528	+	0.994522i	−0.00871071	+	0.0828768i
$145$	6.28784	−	1.33652i	0.522177	−	0.110992i
$146$	−13.6957	−	6.09772i	−1.13346	−	0.504651i
$147$	5.57455	−	4.05015i	0.459782	−	0.334051i
$148$	−0.0791444	+	0.0352374i	−0.00650563	+	0.00289649i
$149$	2.89890	−	5.02105i	0.237488	−	0.411340i	−0.722505	−	0.691366i	$-0.757009\pi$
$149$	2.89890	−	5.02105i	0.237488	−	0.411340i	0.959993	+	0.280025i	$0.0903428\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	11.2572	+	8.17886i	0.916101	+	0.665586i	0.942550	−	0.334064i	$-0.108420\pi$
$151$	11.2572	+	8.17886i	0.916101	+	0.665586i	−0.0264498	+	0.999650i	$0.508420\pi$
$152$	6.85110	+	1.45625i	0.555698	+	0.118117i
$153$	2.16168	−	6.65297i	0.174762	−	0.537861i
$154$	0.554378			0.0446730
$155$	0.534476	+	5.54205i	0.0429301	+	0.445148i
$156$	2.93532			0.235014
$157$	6.08638	−	18.7320i	0.485746	−	1.49497i	−0.345151	−	0.938547i	$-0.612172\pi$
$157$	6.08638	−	18.7320i	0.485746	−	1.49497i	0.830897	−	0.556426i	$-0.187828\pi$
$158$	−14.9261	−	3.17263i	−1.18745	−	0.252401i
$159$	−0.0539712	−	0.0392124i	−0.00428020	−	0.00310975i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−1.15177	+	1.99493i	−0.0907726	+	0.157223i
$162$	0.913545	−	0.406737i	0.0717749	−	0.0319562i
$163$	−0.0355692	+	0.0258425i	−0.00278599	+	0.00202414i	−0.589177	−	0.808004i	$-0.700548\pi$
$163$	−0.0355692	+	0.0258425i	−0.00278599	+	0.00202414i	0.586391	+	0.810028i	$0.300548\pi$
$164$	1.27329	+	0.566905i	0.0994273	+	0.0442679i
$165$	−1.63893	+	0.348365i	−0.127590	+	0.0271202i
$166$	−0.423839	+	4.03256i	−0.0328963	+	0.312987i
$167$	5.22666	+	5.80480i	0.404451	+	0.449189i	0.910619	−	0.413246i	$-0.135605\pi$
$167$	5.22666	+	5.80480i	0.404451	+	0.449189i	−0.506168	+	0.862435i	$0.668938\pi$
$168$	0.221392	−	0.245880i	0.0170807	−	0.0189701i
$169$	0.458242	+	4.35988i	0.0352494	+	0.335375i
$170$	2.16168	+	6.65297i	0.165793	+	0.510260i
$171$	−2.16441	−	6.66135i	−0.165516	−	0.509406i
$172$	−0.136566	−	1.29934i	−0.0104130	−	0.0990735i
$173$	11.6695	−	12.9603i	0.887218	−	0.985355i	−0.112748	−	0.993624i	$-0.535965\pi$
$173$	11.6695	−	12.9603i	0.887218	−	0.985355i	0.999966	+	0.00826832i	$0.00263192\pi$
$174$	−4.30138	−	4.77717i	−0.326087	−	0.362156i
$175$	−0.0345848	+	0.329052i	−0.00261436	+	0.0248740i
$176$	−1.63893	+	0.348365i	−0.123539	+	0.0262590i
$177$	6.44344	+	2.86880i	0.484318	+	0.215632i
$178$	−12.0272	+	8.73825i	−0.901474	+	0.654959i
$179$	−14.2850	+	6.36009i	−1.06771	+	0.475375i	−0.863915	−	0.503638i	$-0.831994\pi$
$179$	−14.2850	+	6.36009i	−1.06771	+	0.475375i	−0.203795	+	0.979014i	$0.565328\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−2.53068	−	4.38327i	−0.188104	−	0.325806i	0.756514	−	0.653977i	$-0.226901\pi$
$181$	−2.53068	−	4.38327i	−0.188104	−	0.325806i	−0.944618	+	0.328172i	$0.893568\pi$
$182$	−0.785712	−	0.570853i	−0.0582408	−	0.0423145i
$183$	−0.484785	−	0.103044i	−0.0358363	−	0.00761725i
$184$	2.15144	−	6.62146i	0.158606	−	0.488140i
$185$	−0.0866344			−0.00636949
$186$	4.53232	−	3.23390i	0.332326	−	0.237121i
$187$	11.7210			0.857125
$188$	1.89273	−	5.82521i	0.138041	−	0.424847i
$189$	−0.323634	−	0.0687906i	−0.0235409	−	0.00500378i
$190$	5.66649	+	4.11694i	0.411090	+	0.298674i
$191$	−6.27904	−	10.8756i	−0.454336	−	0.786932i	0.544314	−	0.838882i	$-0.316790\pi$
$191$	−6.27904	−	10.8756i	−0.454336	−	0.786932i	−0.998650	+	0.0519490i	$0.983457\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	20.6229	−	9.18189i	1.48447	−	0.660927i	0.505107	−	0.863057i	$-0.331453\pi$
$193$	20.6229	−	9.18189i	1.48447	−	0.660927i	0.979359	+	0.202130i	$0.0647864\pi$
$194$	1.15972	−	0.842583i	0.0832628	−	0.0604939i
$195$	2.68155	+	1.19390i	0.192030	+	0.0854971i
$196$	6.73995	−	1.43262i	0.481425	−	0.102330i
$197$	−1.27971	+	12.1756i	−0.0911755	+	0.867477i	0.849367	+	0.527802i	$0.176984\pi$
$197$	−1.27971	+	12.1756i	−0.0911755	+	0.867477i	−0.940543	+	0.339675i	$0.889683\pi$
$198$	1.12116	+	1.24517i	0.0796772	+	0.0884905i
$199$	−8.12548	+	9.02426i	−0.576000	+	0.639713i	−0.958788	−	0.284124i	$-0.908297\pi$
$199$	−8.12548	+	9.02426i	−0.576000	+	0.639713i	0.382788	+	0.923836i	$0.374964\pi$
$200$	−0.104528	−	0.994522i	−0.00739128	−	0.0703233i
$201$	0.709539	+	2.18374i	0.0500470	+	0.154029i
$202$	3.23810	+	9.96585i	0.227832	+	0.701195i
$203$	0.222322	+	2.11525i	0.0156039	+	0.148462i
$204$	4.68080	−	5.19856i	0.327722	−	0.363972i
$205$	0.932627	+	1.03579i	0.0651375	+	0.0723425i
$206$	−0.670674	+	6.38104i	−0.0467281	+	0.444588i
$207$	−6.81007	+	1.44753i	−0.473333	+	0.100610i
$208$	2.68155	+	1.19390i	0.185932	+	0.0827822i
$209$	9.49444	−	6.89812i	0.656744	−	0.477153i
$210$	0.302260	−	0.134575i	0.0208579	−	0.00928654i
$211$	−8.12424	+	14.0716i	−0.559296	+	0.968729i	0.438259	+	0.898849i	$0.355595\pi$
$211$	−8.12424	+	14.0716i	−0.559296	+	0.968729i	−0.997555	+	0.0698806i	$0.977738\pi$
$212$	−0.0333561	−	0.0577744i	−0.00229090	−	0.00396796i
$213$	−4.44479	−	3.22933i	−0.304552	−	0.221270i
$214$	8.73238	+	1.85612i	0.596933	+	0.126882i
$215$	0.403729	−	1.24255i	0.0275341	−	0.0847412i
$216$	1.00000			0.0680414
$217$	−1.84211	−	0.0158002i	−0.125050	−	0.00107259i
$218$	−8.01063			−0.542548
$219$	−4.63273	+	14.2581i	−0.313051	+	0.963471i
$220$	−1.63893	−	0.348365i	−0.110497	−	0.0234868i
$221$	−16.6120	−	12.0693i	−1.11745	−	0.811872i
$222$	0.0433172	+	0.0750276i	0.00290726	+	0.00503552i
$223$	13.2059	−	22.8733i	0.884334	−	1.53171i	0.0378584	−	0.999283i	$-0.487946\pi$
$223$	13.2059	−	22.8733i	0.884334	−	1.53171i	0.846475	−	0.532428i	$-0.178720\pi$
$224$	0.302260	−	0.134575i	0.0201956	−	0.00899165i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	−12.6517	−	5.63291i	−0.841580	−	0.374696i
$227$	−13.0447	+	2.77273i	−0.865804	+	0.184032i	−0.619343	−	0.785120i	$-0.712601\pi$
$227$	−13.0447	+	2.77273i	−0.865804	+	0.184032i	−0.246461	+	0.969153i	$0.579268\pi$
$228$	0.732134	−	6.96579i	0.0484868	−	0.461321i
$229$	−4.87919	−	5.41889i	−0.322426	−	0.358090i	0.560041	−	0.828465i	$-0.310785\pi$
$229$	−4.87919	−	5.41889i	−0.322426	−	0.358090i	−0.882467	+	0.470375i	$0.844119\pi$
$230$	4.65863	−	5.17393i	0.307181	−	0.341159i
$231$	−0.0579483	−	0.551341i	−0.00381272	−	0.0362756i
$232$	−1.98646	−	6.11369i	−0.130417	−	0.401384i
$233$	6.70706	+	20.6422i	0.439394	+	1.35232i	0.888516	+	0.458845i	$0.151737\pi$
$233$	6.70706	+	20.6422i	0.439394	+	1.35232i	−0.449122	+	0.893470i	$0.648263\pi$
$234$	−0.306825	−	2.91924i	−0.0200577	−	0.190837i
$235$	4.09842	−	4.55175i	0.267351	−	0.296924i
$236$	4.71953	+	5.24156i	0.307215	+	0.341197i
$237$	−1.59505	+	15.1759i	−0.103610	+	0.985782i
$238$	−2.26394	+	0.481214i	−0.146749	+	0.0311925i
$239$	−0.811436	−	0.361274i	−0.0524874	−	0.0233689i	0.380325	−	0.924853i	$-0.375812\pi$
$239$	−0.811436	−	0.361274i	−0.0524874	−	0.0233689i	−0.432812	+	0.901484i	$0.642479\pi$
$240$	−0.809017	+	0.587785i	−0.0522218	+	0.0379414i
$241$	22.4685	−	10.0036i	1.44732	−	0.644390i	0.475417	−	0.879760i	$-0.342297\pi$
$241$	22.4685	−	10.0036i	1.44732	−	0.644390i	0.971906	+	0.235371i	$0.0756304\pi$
$242$	4.09628	−	7.09496i	0.263319	−	0.456081i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−0.400961	−	0.291315i	−0.0256689	−	0.0186496i
$245$	6.73995	+	1.43262i	0.430600	+	0.0915268i
$246$	0.430705	−	1.32557i	0.0274607	−	0.0845154i
$247$	−20.5595			−1.30817
$248$	5.45582	−	1.11085i	0.346445	−	0.0705390i
$249$	4.05477			0.256961
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	−0.751738	−	0.159787i	−0.0474493	−	0.0100857i	0.184126	−	0.982903i	$-0.441055\pi$
$251$	−0.751738	−	0.159787i	−0.0474493	−	0.0100857i	−0.231575	+	0.972817i	$0.574388\pi$
$252$	−0.267675	−	0.194477i	−0.0168619	−	0.0122509i
$253$	−5.83274	−	10.1026i	−0.366701	−	0.635145i
$254$	9.56209	−	16.5620i	0.599979	−	1.03919i
$255$	6.39057	−	2.84527i	0.400193	−	0.178177i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	6.55034	+	2.91640i	0.408599	+	0.181920i	0.600735	−	0.799448i	$-0.294875\pi$
$257$	6.55034	+	2.91640i	0.408599	+	0.181920i	−0.192136	+	0.981368i	$0.561541\pi$
$258$	−1.27794	+	0.271635i	−0.0795613	+	0.0169113i
$259$	0.00299623	−	0.0285072i	0.000186177	−	0.00177135i
$260$	1.96411	+	2.18137i	0.121809	+	0.135283i
$261$	−4.30138	+	4.77717i	−0.266249	+	0.295699i
$262$	0.0572963	+	0.545138i	0.00353978	+	0.0336787i
$263$	−6.09832	−	18.7687i	−0.376039	−	1.15733i	−0.942775	−	0.333429i	$-0.891794\pi$
$263$	−6.09832	−	18.7687i	−0.376039	−	1.15733i	0.566737	−	0.823899i	$-0.308206\pi$
$264$	0.517771	+	1.59354i	0.0318666	+	0.0980754i
$265$	−0.00697331	−	0.0663467i	−0.000428367	−	0.00407564i
$266$	−1.55066	+	1.72219i	−0.0950772	+	0.105594i
$267$	9.94756	+	11.0479i	0.608781	+	0.676119i
$268$	−0.240009	+	2.28354i	−0.0146609	+	0.139489i
$269$	0.142760	−	0.0303445i	0.00870422	−	0.00185014i	−0.203558	−	0.979063i	$-0.565250\pi$
$269$	0.142760	−	0.0303445i	0.00870422	−	0.00185014i	0.212262	+	0.977213i	$0.431917\pi$
$270$	0.913545	+	0.406737i	0.0555966	+	0.0247532i
$271$	−5.65499	+	4.10859i	−0.343516	+	0.249579i	−0.746144	−	0.665785i	$-0.768097\pi$
$271$	−5.65499	+	4.10859i	−0.343516	+	0.249579i	0.402628	+	0.915364i	$0.368097\pi$
$272$	6.39057	−	2.84527i	0.387485	−	0.172520i
$273$	−0.485597	+	0.841078i	−0.0293897	+	0.0509044i
$274$	−4.21900	−	7.30752i	−0.254879	−	0.441463i
$275$	−1.35554	−	0.984860i	−0.0817423	−	0.0593893i
$276$	−6.81007	−	1.44753i	−0.409918	−	0.0871308i
$277$	0.164690	−	0.506864i	0.00989527	−	0.0304545i	−0.945987	−	0.324205i	$-0.894903\pi$
$277$	0.164690	−	0.506864i	0.00989527	−	0.0304545i	0.955882	+	0.293750i	$0.0949034\pi$
$278$	−9.10072			−0.545825
$279$	−3.68994	−	4.16946i	−0.220911	−	0.249619i
$280$	0.330865			0.0197729
$281$	7.09356	−	21.8317i	0.423166	−	1.30237i	−0.481573	−	0.876406i	$-0.659934\pi$
$281$	7.09356	−	21.8317i	0.423166	−	1.30237i	0.904739	−	0.425966i	$-0.140066\pi$
$282$	−5.99114	−	1.27346i	−0.356767	−	0.0758333i
$283$	8.26668	+	6.00610i	0.491403	+	0.357025i	0.805724	−	0.592292i	$-0.201777\pi$
$283$	8.26668	+	6.00610i	0.491403	+	0.357025i	−0.314320	+	0.949317i	$0.601777\pi$
$284$	−2.74703	−	4.75800i	−0.163006	−	0.282335i
$285$	3.50208	−	6.06578i	0.207445	−	0.359306i
$286$	4.49305	−	2.00043i	0.265680	−	0.118288i
$287$	−0.373083	+	0.271060i	−0.0220224	+	0.0160002i
$288$	0.913545	+	0.406737i	0.0538312	+	0.0239672i
$289$	−31.2371	+	6.63964i	−1.83747	+	0.390567i
$290$	0.671942	−	6.39310i	0.0394578	−	0.375416i
$291$	−0.959191	−	1.06529i	−0.0562287	−	0.0624483i
$292$	−10.0315	+	11.1411i	−0.587048	+	0.651983i
$293$	2.97720	+	28.3262i	0.173930	+	1.65483i	0.638739	+	0.769423i	$0.279456\pi$
$293$	2.97720	+	28.3262i	0.173930	+	1.65483i	−0.464809	+	0.885411i	$0.653877\pi$
$294$	−2.12929	−	6.55328i	−0.124183	−	0.382195i
$295$	2.17956	+	6.70801i	0.126899	+	0.390555i
$296$	0.00905576	+	0.0861598i	0.000526355	+	0.00500794i
$297$	1.12116	−	1.24517i	0.0650561	−	0.0722522i
$298$	−3.87949	−	4.30861i	−0.224733	−	0.249591i
$299$	−2.13618	+	20.3244i	−0.123538	+	1.17539i
$300$	−0.978148	+	0.207912i	−0.0564734	+	0.0120038i
$301$	0.394901	+	0.175821i	0.0227617	+	0.0101342i
$302$	11.2572	−	8.17886i	0.647781	−	0.470640i
$303$	9.57278	−	4.26208i	0.549942	−	0.244850i
$304$	3.50208	−	6.06578i	0.200858	−	0.347896i
$305$	−0.247808	−	0.429216i	−0.0141894	−	0.0245768i
$306$	−5.65936	−	4.11176i	−0.323524	−	0.235054i
$307$	9.41285	+	2.00076i	0.537219	+	0.114190i	0.468528	−	0.883448i	$-0.344784\pi$
$307$	9.41285	+	2.00076i	0.537219	+	0.114190i	0.0686911	+	0.997638i	$0.478118\pi$
$308$	0.171312	−	0.527245i	0.00976142	−	0.0300426i
$309$	6.41619			0.365004
$310$	5.43597	+	1.20427i	0.308742	+	0.0683980i
$311$	−15.3820			−0.872233			−0.436117	−	0.899890i	$-0.643647\pi$
$311$	−15.3820			−0.872233			−0.436117	+	0.899890i	$0.643647\pi$
$312$	0.907064	−	2.79166i	0.0513524	−	0.158046i
$313$	29.6784	+	6.30833i	1.67752	+	0.356568i	0.945728	−	0.324960i	$-0.105351\pi$
$313$	29.6784	+	6.30833i	1.67752	+	0.356568i	0.731792	+	0.681528i	$0.238684\pi$
$314$	−15.9344	−	11.5770i	−0.899227	−	0.653327i
$315$	−0.165432	−	0.286537i	−0.00932105	−	0.0161445i
$316$	−7.62976	+	13.2151i	−0.429207	+	0.743409i
$317$	5.82573	−	2.59378i	0.327206	−	0.145681i	−0.236558	−	0.971617i	$-0.576019\pi$
$317$	5.82573	−	2.59378i	0.327206	−	0.145681i	0.563764	+	0.825936i	$0.309353\pi$
$318$	−0.0539712	+	0.0392124i	−0.00302656	+	0.00219892i
$319$	−9.83973	−	4.38093i	−0.550919	−	0.245285i
$320$	−0.978148	+	0.207912i	−0.0546801	+	0.0116226i
$321$	0.933174	−	8.87856i	0.0520847	−	0.495553i
$322$	1.54138	+	1.71187i	0.0858975	+	0.0953988i
$323$	−32.7851	+	36.4115i	−1.82421	+	2.02599i
$324$	−0.104528	−	0.994522i	−0.00580714	−	0.0552512i
$325$	0.907064	+	2.79166i	0.0503148	+	0.154853i
$326$	0.0135862	+	0.0418141i	0.000752471	+	0.00231587i
$327$	0.837339	+	7.96675i	0.0463049	+	0.440562i
$328$	0.932627	−	1.03579i	0.0514957	−	0.0571918i
$329$	1.35602	+	1.50601i	0.0747599	+	0.0830293i
$330$	−0.175142	+	1.66636i	−0.00964125	+	0.0917303i
$331$	20.8323	−	4.42805i	1.14505	−	0.243388i	0.403948	−	0.914782i	$-0.367638\pi$
$331$	20.8323	−	4.42805i	1.14505	−	0.243388i	0.741100	+	0.671394i	$0.234304\pi$
$332$	3.70422	+	1.64923i	0.203296	+	0.0905130i
$333$	0.0700887	−	0.0509224i	0.00384084	−	0.00279053i
$334$	7.13582	−	3.17707i	0.390455	−	0.173842i
$335$	−1.14806	+	1.98849i	−0.0627251	+	0.108643i
$336$	−0.165432	−	0.286537i	−0.00902507	−	0.0156319i
$337$	0.625757	+	0.454639i	0.0340871	+	0.0247658i	0.604698	−	0.796455i	$-0.293294\pi$
$337$	0.625757	+	0.454639i	0.0340871	+	0.0247658i	−0.570611	+	0.821220i	$0.693294\pi$
$338$	4.28810	+	0.911463i	0.233242	+	0.0495771i
$339$	−4.27959	+	13.1712i	−0.232435	+	0.715362i
$340$	6.99535			0.379376
$341$	4.73364	−	8.03887i	0.256341	−	0.435329i
$342$	−7.00416			−0.378742
$343$	−1.42021	+	4.37095i	−0.0766839	+	0.236009i
$344$	−1.27794	−	0.271635i	−0.0689021	−	0.0146456i
$345$	−5.63255	−	4.09229i	−0.303246	−	0.220321i
$346$	−8.71992	−	15.1033i	−0.468786	−	0.811961i
$347$	−1.33898	+	2.31919i	−0.0718804	+	0.124501i	−0.899725	−	0.436456i	$-0.856233\pi$
$347$	−1.33898	+	2.31919i	−0.0718804	+	0.124501i	0.827845	+	0.560957i	$0.189567\pi$
$348$	−5.87256	+	2.61463i	−0.314802	+	0.140159i
$349$	11.9737	−	8.69940i	0.640937	−	0.465668i	−0.219235	−	0.975672i	$-0.570356\pi$
$349$	11.9737	−	8.69940i	0.640937	−	0.465668i	0.860172	+	0.510004i	$0.170356\pi$
$350$	0.302260	+	0.134575i	0.0161565	+	0.00719332i
$351$	−2.87118	+	0.610287i	−0.153252	+	0.0325747i
$352$	−0.175142	+	1.66636i	−0.00933510	+	0.0888175i
$353$	−17.5761	−	19.5202i	−0.935480	−	1.03896i	−0.999160	−	0.0409853i	$-0.986950\pi$
$353$	−17.5761	−	19.5202i	−0.935480	−	1.03896i	0.0636799	−	0.997970i	$-0.479716\pi$
$354$	4.71953	−	5.24156i	0.250840	−	0.278586i
$355$	−0.574286	−	5.46397i	−0.0304800	−	0.289997i
$356$	4.59397	+	14.1388i	0.243480	+	0.749354i
$357$	0.715224	+	2.20123i	0.0378537	+	0.116502i
$358$	1.63450	+	15.5512i	0.0863859	+	0.821907i
$359$	20.8013	−	23.1022i	1.09785	−	1.21929i	0.123954	−	0.992288i	$-0.460442\pi$
$359$	20.8013	−	23.1022i	1.09785	−	1.21929i	0.973895	−	0.226997i	$-0.0728909\pi$
$360$	0.669131	+	0.743145i	0.0352663	+	0.0391672i
$361$	−3.14195	+	29.8936i	−0.165366	+	1.57335i
$362$	−4.95076	+	1.05232i	−0.260206	+	0.0553085i
$363$	−7.48427	−	3.33221i	−0.392822	−	0.174896i
$364$	−0.785712	+	0.570853i	−0.0411825	+	0.0299208i
$365$	−13.6957	+	6.09772i	−0.716866	+	0.319169i
$366$	−0.247808	+	0.429216i	−0.0129531	+	0.0224355i
$367$	−2.96660	−	5.13830i	−0.154855	−	0.268217i	0.778151	−	0.628077i	$-0.216158\pi$
$367$	−2.96660	−	5.13830i	−0.154855	−	0.268217i	−0.933006	+	0.359860i	$0.882824\pi$
$368$	−5.63255	−	4.09229i	−0.293617	−	0.213325i
$369$	−1.36333	−	0.289785i	−0.0709722	−	0.0150856i
$370$	−0.0267715	+	0.0823942i	−0.00139178	+	0.00428347i
$371$	0.0220727			0.00114596
$372$	−1.67505	−	5.30982i	−0.0868475	−	0.275301i
$373$	−26.5576			−1.37510			−0.687550	−	0.726137i	$-0.741314\pi$
$373$	−26.5576			−1.37510			−0.687550	+	0.726137i	$0.741314\pi$
$374$	3.62199	−	11.1473i	0.187289	−	0.576415i
$375$	−0.978148	−	0.207912i	−0.0505113	−	0.0107365i
$376$	−4.95522	−	3.60018i	−0.255546	−	0.185665i
$377$	9.43459	+	16.3412i	0.485906	+	0.841614i
$378$	−0.165432	+	0.286537i	−0.00850892	+	0.0147379i
$379$	−24.8239	+	11.0523i	−1.27512	+	0.567720i	−0.928864	−	0.370420i	$-0.879214\pi$
$379$	−24.8239	+	11.0523i	−1.27512	+	0.567720i	−0.346256	+	0.938140i	$0.612547\pi$
$380$	5.66649	−	4.11694i	0.290685	−	0.211195i
$381$	−17.4708	−	7.77850i	−0.895056	−	0.398505i
$382$	−12.2837	+	2.61097i	−0.628487	+	0.133589i
$383$	2.16754	−	20.6228i	0.110756	−	1.05378i	−0.788104	−	0.615542i	$-0.788937\pi$
$383$	2.16754	−	20.6228i	0.110756	−	1.05378i	0.898861	−	0.438235i	$-0.144396\pi$
$384$	0.669131	+	0.743145i	0.0341464	+	0.0379235i
$385$	0.370951	−	0.411983i	0.0189054	−	0.0209966i
$386$	−2.35968	−	22.4509i	−0.120105	−	1.14272i
$387$	0.403729	+	1.24255i	0.0205227	+	0.0631623i
$388$	−0.442972	−	1.36333i	−0.0224885	−	0.0692125i
$389$	−1.68071	−	15.9909i	−0.0852153	−	0.810769i	−0.950758	−	0.309934i	$-0.899693\pi$
$389$	−1.68071	−	15.9909i	−0.0852153	−	0.810769i	0.865543	−	0.500835i	$-0.166974\pi$
$390$	1.96411	−	2.18137i	0.0994567	−	0.110458i
$391$	32.5887	+	36.1935i	1.64808	+	1.83038i
$392$	0.720256	−	6.85278i	0.0363784	−	0.346118i
$393$	0.536162	−	0.113965i	0.0270458	−	0.00574876i
$394$	11.1843	+	4.97955i	0.563454	+	0.250866i
$395$	−12.3452	+	8.96932i	−0.621155	+	0.451295i
$396$	1.53068	−	0.681505i	0.0769198	−	0.0342469i
$397$	12.2468	−	21.2121i	0.614649	−	1.06460i	−0.375797	−	0.926702i	$-0.622631\pi$
$397$	12.2468	−	21.2121i	0.614649	−	1.06460i	0.990446	−	0.137901i	$-0.0440356\pi$
$398$	6.07167	+	10.5164i	0.304345	+	0.527141i
$399$	1.87484	+	1.36215i	0.0938594	+	0.0681928i
$400$	−0.978148	−	0.207912i	−0.0489074	−	0.0103956i
$401$	8.97601	−	27.6253i	0.448240	−	1.37954i	−0.430650	−	0.902519i	$-0.641716\pi$
$401$	8.97601	−	27.6253i	0.448240	−	1.37954i	0.878891	−	0.477023i	$-0.158284\pi$
$402$	2.29612			0.114520
$403$	−14.9867	+	6.51907i	−0.746540	+	0.324738i
$404$	10.4787			0.521335
$405$	0.309017	−	0.951057i	0.0153552	−	0.0472584i
$406$	2.08042	+	0.442208i	0.103250	+	0.0219464i
$407$	0.117437	+	0.0853227i	0.00582112	+	0.00422929i
$408$	−3.49768	−	6.05815i	−0.173161	−	0.299923i
$409$	−6.70760	+	11.6179i	−0.331670	+	0.574469i	−0.982839	−	0.184464i	$-0.940945\pi$
$409$	−6.70760	+	11.6179i	−0.331670	+	0.574469i	0.651170	+	0.758932i	$0.274279\pi$
$410$	1.27329	−	0.566905i	0.0628833	−	0.0279975i
$411$	−6.82648	+	4.95973i	−0.336725	+	0.244645i
$412$	5.86148	+	2.60970i	0.288774	+	0.128571i
$413$	−2.28266	+	0.485195i	−0.112323	+	0.0238749i
$414$	−0.727749	+	6.92407i	−0.0357669	+	0.340300i
$415$	2.71317	+	3.01328i	0.133184	+	0.147916i
$416$	1.96411	−	2.18137i	0.0962985	−	0.106950i
$417$	0.951285	+	9.05087i	0.0465846	+	0.443223i
$418$	−3.62655	−	11.1614i	−0.177381	−	0.545921i
$419$	11.4871	+	35.3538i	0.561183	+	1.72715i	0.679027	+	0.734113i	$0.262402\pi$
$419$	11.4871	+	35.3538i	0.561183	+	1.72715i	−0.117844	+	0.993032i	$0.537598\pi$
$420$	−0.0345848	−	0.329052i	−0.00168756	−	0.0160561i
$421$	−17.1236	+	19.0176i	−0.834551	+	0.926863i	−0.998219	−	0.0596526i	$-0.981001\pi$
$421$	−17.1236	+	19.0176i	−0.834551	+	0.926863i	0.163668	+	0.986515i	$0.447667\pi$
$422$	10.8724	+	12.0750i	0.529258	+	0.587801i
$423$	−0.640236	+	6.09144i	−0.0311293	+	0.296176i
$424$	−0.0652543	+	0.0138702i	−0.00316903	+	0.000673598i
$425$	6.39057	+	2.84527i	0.309988	+	0.138016i
$426$	−4.44479	+	3.22933i	−0.215351	+	0.156462i
$427$	0.149805	−	0.0666973i	0.00724956	−	0.00322771i
$428$	4.46373	−	7.73141i	0.215763	−	0.373712i
$429$	−2.45913	−	4.25933i	−0.118728	−	0.205643i
$430$	−1.05698	−	0.767938i	−0.0509719	−	0.0370332i
$431$	35.9195	+	7.63492i	1.73018	+	0.367761i	0.962122	−	0.272619i	$-0.0878898\pi$
$431$	35.9195	+	7.63492i	1.73018	+	0.367761i	0.768058	+	0.640380i	$0.221223\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	−37.3039			−1.79271			−0.896356	−	0.443335i	$-0.853795\pi$
$433$	−37.3039			−1.79271			−0.896356	+	0.443335i	$0.853795\pi$
$434$	−0.584270	+	1.74707i	−0.0280458	+	0.0838619i
$435$	−6.42832			−0.308214
$436$	−2.47542	+	7.61856i	−0.118551	+	0.364863i
$437$	47.6988	+	10.1387i	2.28175	+	0.485000i
$438$	12.1286	+	8.81197i	0.579529	+	0.421052i
$439$	10.3517	+	17.9296i	0.494057	+	0.855733i	0.999977	−	0.00684828i	$-0.00217989\pi$
$439$	10.3517	+	17.9296i	0.494057	+	0.855733i	−0.505919	+	0.862581i	$0.668847\pi$
$440$	−0.837772	+	1.45106i	−0.0399392	+	0.0691767i
$441$	−6.29481	+	2.80263i	−0.299753	+	0.133459i
$442$	−16.6120	+	12.0693i	−0.790153	+	0.574080i
$443$	24.7043	+	10.9991i	1.17374	+	0.522581i	0.898576	−	0.438818i	$-0.144603\pi$
$443$	24.7043	+	10.9991i	1.17374	+	0.522581i	0.275159	+	0.961399i	$0.411269\pi$
$444$	0.0847412	−	0.0180123i	0.00402164	−	0.000854826i
$445$	−1.55396	+	14.7850i	−0.0736648	+	0.700874i
$446$	−17.6730	−	19.6278i	−0.836839	−	0.929404i
$447$	−3.87949	+	4.30861i	−0.183494	+	0.203790i
$448$	−0.0345848	−	0.329052i	−0.00163398	−	0.0155462i
$449$	8.58320	+	26.4164i	0.405066	+	1.24667i	0.920840	+	0.389941i	$0.127505\pi$
$449$	8.58320	+	26.4164i	0.405066	+	1.24667i	−0.515773	+	0.856725i	$0.672495\pi$
$450$	0.309017	+	0.951057i	0.0145672	+	0.0448332i
$451$	−0.244111	−	2.32256i	−0.0114947	−	0.109365i
$452$	−9.26681	+	10.2918i	−0.435874	+	0.484087i
$453$	−9.31075	−	10.3406i	−0.437457	−	0.485846i
$454$	−1.39400	+	13.2630i	−0.0654237	+	0.622464i
$455$	−0.949971	+	0.201922i	−0.0445353	+	0.00946627i
$456$	−6.39862	−	2.84885i	−0.299643	−	0.133410i
$457$	−30.5984	+	22.2310i	−1.43133	+	1.03992i	−0.441565	+	0.897229i	$0.645577\pi$
$457$	−30.5984	+	22.2310i	−1.43133	+	1.03992i	−0.989767	+	0.142695i	$0.954423\pi$
$458$	−6.66142	+	2.96586i	−0.311268	+	0.138585i
$459$	−3.49768	+	6.05815i	−0.163257	+	0.282770i
$460$	−3.48111	−	6.02945i	−0.162307	−	0.281125i
$461$	5.46162	+	3.96810i	0.254373	+	0.184813i	0.707663	−	0.706551i	$-0.249750\pi$
$461$	5.46162	+	3.96810i	0.254373	+	0.184813i	−0.453290	+	0.891363i	$0.649750\pi$
$462$	−0.542263	−	0.115262i	−0.0252284	−	0.00536246i
$463$	8.98323	−	27.6476i	0.417486	−	1.28489i	−0.492522	−	0.870300i	$-0.663925\pi$
$463$	8.98323	−	27.6476i	0.417486	−	1.28489i	0.910008	−	0.414591i	$-0.136075\pi$
$464$	−6.42832			−0.298427
$465$	0.629461	−	5.53207i	0.0291906	−	0.256544i
$466$	21.7045			1.00544
$467$	6.11887	−	18.8319i	0.283147	−	0.871438i	−0.703801	−	0.710398i	$-0.748515\pi$
$467$	6.11887	−	18.8319i	0.283147	−	0.871438i	0.986948	−	0.161040i	$-0.0514849\pi$
$468$	−2.87118	−	0.610287i	−0.132720	−	0.0282105i
$469$	−0.614613	−	0.446542i	−0.0283802	−	0.0206194i
$470$	−3.06250	−	5.30440i	−0.141262	−	0.244674i
$471$	−9.84797	+	17.0572i	−0.453771	+	0.785954i
$472$	6.44344	−	2.86880i	0.296583	−	0.132047i
$473$	−1.77101	+	1.28671i	−0.0814310	+	0.0591631i
$474$	13.9403	+	6.20660i	0.640297	+	0.285079i
$475$	6.85110	−	1.45625i	0.314350	−	0.0668172i
$476$	−0.241933	+	2.30183i	−0.0110890	+	0.105504i
$477$	0.0446391	+	0.0495768i	0.00204388	+	0.00226996i
$478$	−0.594340	+	0.660081i	−0.0271845	+	0.0301914i
$479$	3.49826	+	33.2837i	0.159839	+	1.52077i	0.720925	+	0.693013i	$0.243717\pi$
$479$	3.49826	+	33.2837i	0.159839	+	1.52077i	−0.561086	+	0.827758i	$0.689616\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	−0.0785829	−	0.241853i	−0.00358307	−	0.0110276i
$482$	−2.57086	−	24.4601i	−0.117099	−	1.11413i
$483$	1.54138	−	1.71187i	0.0701350	−	0.0778928i
$484$	−5.48189	−	6.08826i	−0.249177	−	0.276739i
$485$	0.149840	−	1.42563i	0.00680390	−	0.0647347i
$486$	−0.978148	+	0.207912i	−0.0443697	+	0.00943107i
$487$	−28.7308	−	12.7918i	−1.30192	−	0.579651i	−0.365590	−	0.930776i	$-0.619133\pi$
$487$	−28.7308	−	12.7918i	−1.30192	−	0.579651i	−0.936329	+	0.351125i	$0.885799\pi$
$488$	−0.400961	+	0.291315i	−0.0181507	+	0.0131872i
$489$	0.0401648	−	0.0178825i	0.00181632	−	0.000808676i
$490$	3.44526	−	5.96737i	0.155641	−	0.269578i
$491$	−18.4617	−	31.9766i	−0.833166	−	1.44309i	−0.895515	−	0.445031i	$-0.853192\pi$
$491$	−18.4617	−	31.9766i	−0.833166	−	1.44309i	0.0623489	−	0.998054i	$-0.480141\pi$
$492$	−1.12760	−	0.819249i	−0.0508361	−	0.0369346i
$493$	43.9857	+	9.34944i	1.98101	+	0.421078i
$494$	−6.35322	+	19.5532i	−0.285845	+	0.879740i
$495$	1.67554			0.0753101
$496$	0.629461	−	5.53207i	0.0282636	−	0.248397i
$497$	1.81779			0.0815391
$498$	1.25299	−	3.85632i	0.0561480	−	0.172806i
$499$	−35.2206	−	7.48638i	−1.57669	−	0.335136i	−0.665268	−	0.746605i	$-0.731683\pi$
$499$	−35.2206	−	7.48638i	−1.57669	−	0.335136i	−0.911424	+	0.411468i	$0.865016\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	−3.90556	−	6.76464i	−0.174488	−	0.302222i
$502$	−0.384266	+	0.665569i	−0.0171506	+	0.0297058i
$503$	−2.86293	+	1.27466i	−0.127652	+	0.0568343i	−0.469569	−	0.882896i	$-0.655591\pi$
$503$	−2.86293	+	1.27466i	−0.127652	+	0.0568343i	0.341917	+	0.939730i	$0.388924\pi$
$504$	−0.267675	+	0.194477i	−0.0119232	+	0.00866271i
$505$	9.57278	+	4.26208i	0.425983	+	0.189660i
$506$	−11.4106	+	2.42539i	−0.507262	+	0.107822i
$507$	0.458242	−	4.35988i	0.0203512	−	0.193629i
$508$	−12.7966	−	14.2120i	−0.567756	−	0.630557i
$509$	6.88017	−	7.64121i	0.304958	−	0.338691i	−0.571114	−	0.820871i	$-0.693488\pi$
$509$	6.88017	−	7.64121i	0.304958	−	0.338691i	0.876072	+	0.482181i	$0.160155\pi$
$510$	−0.731213	−	6.95703i	−0.0323787	−	0.308062i
$511$	−1.53280	−	4.71749i	−0.0678073	−	0.208689i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	0.732134	+	6.96579i	0.0323245	+	0.307547i
$514$	4.79783	−	5.32853i	0.211623	−	0.235031i
$515$	4.29327	+	4.76816i	0.189184	+	0.210110i
$516$	−0.136566	+	1.29934i	−0.00601197	+	0.0572001i
$517$	−10.0384	+	2.13373i	−0.441489	+	0.0938414i
$518$	−0.0261861	−	0.0116588i	−0.00115055	−	0.000512258i
$519$	−14.1091	+	10.2509i	−0.619322	+	0.449964i
$520$	2.68155	−	1.19390i	0.117594	−	0.0523561i
$521$	−5.58058	+	9.66586i	−0.244490	+	0.423469i	−0.961988	−	0.273092i	$-0.911954\pi$
$521$	−5.58058	+	9.66586i	−0.244490	+	0.423469i	0.717498	+	0.696560i	$0.245287\pi$
$522$	3.21416	+	5.56709i	0.140680	+	0.243665i
$523$	−6.57776	−	4.77903i	−0.287626	−	0.208972i	0.434611	−	0.900618i	$-0.356886\pi$
$523$	−6.57776	−	4.77903i	−0.287626	−	0.208972i	−0.722237	+	0.691646i	$0.756886\pi$
$524$	0.536162	+	0.113965i	0.0234224	+	0.00497858i
$525$	0.102243	−	0.314671i	0.00446224	−	0.0137334i
$526$	−19.7346			−0.860469
$527$	−12.3530	+	36.9376i	−0.538105	+	1.60903i
$528$	1.67554			0.0729187
$529$	7.87140	−	24.2257i	0.342235	−	1.05329i
$530$	−0.0652543	−	0.0138702i	−0.00283447	−	0.000602484i
$531$	−5.70617	−	4.14578i	−0.247627	−	0.179911i
$532$	1.15871	+	2.00695i	0.0502366	+	0.0870124i
$533$	−2.04561	+	3.54310i	−0.0886052	+	0.153469i
$534$	13.5811	−	6.04671i	0.587713	−	0.261667i
$535$	7.22247	−	5.24743i	0.312255	−	0.226866i
$536$	2.09761	+	0.933915i	0.0906028	+	0.0403390i
$537$	15.2952	−	3.25109i	0.660035	−	0.140295i
$538$	0.0152558	−	0.145150i	0.000657726	−	0.00625785i
$539$	−7.72537	−	8.57989i	−0.332755	−	0.369562i
$540$	0.669131	−	0.743145i	0.0287948	−	0.0319799i
$541$	−1.21544	−	11.5641i	−0.0522557	−	0.497179i	−0.989080	−	0.147379i	$-0.952916\pi$
$541$	−1.21544	−	11.5641i	−0.0522557	−	0.497179i	0.936824	−	0.349800i	$-0.113750\pi$
$542$	2.16001	+	6.64784i	0.0927805	+	0.285549i
$543$	1.56405	+	4.81364i	0.0671197	+	0.206573i
$544$	−0.731213	−	6.95703i	−0.0313505	−	0.298280i
$545$	−5.36016	+	5.95306i	−0.229604	+	0.255001i
$546$	0.649855	+	0.721737i	0.0278112	+	0.0308875i
$547$	−2.39521	+	22.7889i	−0.102412	+	0.974385i	0.815810	+	0.578319i	$0.196291\pi$
$547$	−2.39521	+	22.7889i	−0.102412	+	0.974385i	−0.918222	+	0.396065i	$0.870375\pi$
$548$	−8.25360	+	1.75436i	−0.352576	+	0.0749424i
$549$	0.452767	+	0.201585i	0.0193236	+	0.00860344i
$550$	−1.35554	+	0.984860i	−0.0578005	+	0.0419946i
$551$	41.1324	−	18.3133i	1.75230	−	0.780173i
$552$	−3.48111	+	6.02945i	−0.148166	+	0.256631i
$553$	−2.52442	−	4.37242i	−0.107349	−	0.185934i
$554$	−0.431164	−	0.313259i	−0.0183184	−	0.0133091i
$555$	0.0847412	+	0.0180123i	0.00359706	+	0.000764579i
$556$	−2.81228	+	8.65530i	−0.119267	+	0.367067i
$557$	−31.1193			−1.31857			−0.659284	−	0.751894i	$-0.729141\pi$
$557$	−31.1193			−1.31857			−0.659284	+	0.751894i	$0.729141\pi$
$558$	−5.10564	+	2.22090i	−0.216139	+	0.0940184i
$559$	3.83498			0.162202
$560$	0.102243	−	0.314671i	0.00432055	−	0.0132973i
$561$	−11.4649	−	2.43694i	−0.484048	−	0.102887i
$562$	−18.5712	−	13.4928i	−0.783378	−	0.569157i
$563$	−5.75293	−	9.96436i	−0.242457	−	0.419948i	0.718957	−	0.695055i	$-0.244620\pi$
$563$	−5.75293	−	9.96436i	−0.242457	−	0.419948i	−0.961414	+	0.275107i	$0.911287\pi$
$564$	−3.06250	+	5.30440i	−0.128954	+	0.223355i
$565$	−12.6517	+	5.63291i	−0.532262	+	0.236978i
$566$	8.26668	−	6.00610i	0.347475	−	0.252455i
$567$	0.302260	+	0.134575i	0.0126937	+	0.00565161i
$568$	−5.37401	+	1.14228i	−0.225488	+	0.0479290i
$569$	2.50352	−	23.8194i	0.104953	−	0.998563i	−0.807635	−	0.589683i	$-0.799253\pi$
$569$	2.50352	−	23.8194i	0.104953	−	0.998563i	0.912588	−	0.408880i	$-0.134081\pi$
$570$	−4.68670	−	5.20511i	−0.196304	−	0.218018i
$571$	5.92324	−	6.57842i	0.247880	−	0.275298i	−0.606346	−	0.795201i	$-0.707365\pi$
$571$	5.92324	−	6.57842i	0.247880	−	0.275298i	0.854225	+	0.519903i	$0.174032\pi$
$572$	−0.514098	−	4.89131i	−0.0214955	−	0.204516i
$573$	3.88066	+	11.9435i	0.162117	+	0.498945i
$574$	0.142505	+	0.438585i	0.00594804	+	0.0183062i
$575$	−0.727749	−	6.92407i	−0.0303492	−	0.288754i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	−14.4379	−	16.0349i	−0.601056	−	0.667541i	0.363446	−	0.931615i	$-0.381600\pi$
$577$	−14.4379	−	16.0349i	−0.601056	−	0.667541i	−0.964502	+	0.264075i	$0.914934\pi$
$578$	−3.33811	+	31.7600i	−0.138847	+	1.32104i
$579$	−22.0812	+	4.69351i	−0.917664	+	0.195056i
$580$	−5.87256	−	2.61463i	−0.243845	−	0.108567i
$581$	−1.08536	+	0.788562i	−0.0450284	+	0.0327150i
$582$	−1.30956	+	0.583052i	−0.0542829	+	0.0241683i
$583$	−0.0558895	+	0.0968035i	−0.00231471	+	0.00400919i
$584$	7.49591	+	12.9833i	0.310183	+	0.537253i
$585$	−2.37472	−	1.72534i	−0.0981828	−	0.0713339i
$586$	27.8598	+	5.92179i	1.15088	+	0.244627i
$587$	−8.21580	+	25.2856i	−0.339102	+	1.04365i	0.625564	+	0.780173i	$0.284869\pi$
$587$	−8.21580	+	25.2856i	−0.339102	+	1.04365i	−0.964666	+	0.263476i	$0.915131\pi$
$588$	−6.89053			−0.284161
$589$	11.7323	+	37.1908i	0.483423	+	1.53242i
$590$	7.05322			0.290376
$591$	3.78320	−	11.6435i	0.155620	−	0.478949i
$592$	0.0847412	+	0.0180123i	0.00348284	+	0.000740301i
$593$	17.8774	+	12.9887i	0.734136	+	0.533381i	0.890869	−	0.454260i	$-0.150096\pi$
$593$	17.8774	+	12.9887i	0.734136	+	0.533381i	−0.156733	+	0.987641i	$0.550096\pi$
$594$	−0.837772	−	1.45106i	−0.0343742	−	0.0595378i
$595$	−1.15726	+	2.00443i	−0.0474429	+	0.0821735i
$596$	−5.29656	+	2.35818i	−0.216956	+	0.0965949i
$597$	9.82417	−	7.13767i	0.402076	−	0.292126i
$598$	18.6695	+	8.31220i	0.763453	+	0.339911i
$599$	−19.2231	+	4.08600i	−0.785435	+	0.166949i	−0.583136	−	0.812374i	$-0.698175\pi$
$599$	−19.2231	+	4.08600i	−0.785435	+	0.166949i	−0.202299	+	0.979324i	$0.564841\pi$
$600$	−0.104528	+	0.994522i	−0.00426736	+	0.0406012i
$601$	−13.0205	−	14.4607i	−0.531117	−	0.589866i	0.416555	−	0.909111i	$-0.363237\pi$
$601$	−13.0205	−	14.4607i	−0.531117	−	0.589866i	−0.947672	+	0.319245i	$0.896571\pi$
$602$	0.289247	−	0.321241i	0.0117888	−	0.0130928i
$603$	−0.240009	−	2.28354i	−0.00977394	−	0.0929928i
$604$	−4.29988	−	13.2337i	−0.174960	−	0.538470i
$605$	−2.53164	−	7.79158i	−0.102926	−	0.316773i
$606$	−1.09532	−	10.4213i	−0.0444945	−	0.423337i
$607$	10.3798	−	11.5279i	0.421302	−	0.467903i	−0.494708	−	0.869060i	$-0.664725\pi$
$607$	10.3798	−	11.5279i	0.421302	−	0.467903i	0.916010	+	0.401156i	$0.131391\pi$
$608$	−4.68670	−	5.20511i	−0.190071	−	0.211095i
$609$	0.222322	−	2.11525i	0.00900894	−	0.0857143i
$610$	−0.484785	+	0.103044i	−0.0196284	+	0.00417214i
$611$	16.4245	+	7.31264i	0.664462	+	0.295838i
$612$	−5.65936	+	4.11176i	−0.228766	+	0.166208i
$613$	−31.8802	+	14.1940i	−1.28763	+	0.573290i	−0.932379	−	0.361481i	$-0.882271\pi$
$613$	−31.8802	+	14.1940i	−1.28763	+	0.573290i	−0.355251	+	0.934771i	$0.615605\pi$
$614$	4.81157	−	8.33388i	0.194179	−	0.336328i
$615$	−0.696895	−	1.20706i	−0.0281015	−	0.0486732i
$616$	−0.448501	−	0.325855i	−0.0180706	−	0.0131291i
$617$	−13.6057	−	2.89199i	−0.547746	−	0.116427i	−0.0742772	−	0.997238i	$-0.523665\pi$
$617$	−13.6057	−	2.89199i	−0.547746	−	0.116427i	−0.473469	+	0.880811i	$0.656998\pi$
$618$	1.98271	−	6.10216i	0.0797563	−	0.245465i
$619$	−12.3376			−0.495889			−0.247944	−	0.968774i	$-0.579755\pi$
$619$	−12.3376			−0.495889			−0.247944	+	0.968774i	$0.579755\pi$
$620$	2.82514	−	4.79777i	0.113460	−	0.192683i
$621$	6.96221			0.279384
$622$	−4.75330	+	14.6292i	−0.190590	+	0.586576i
$623$	−4.81128	−	1.02267i	−0.192760	−	0.0409723i
$624$	−2.37472	−	1.72534i	−0.0950650	−	0.0690688i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	15.1707	−	26.2764i	0.606343	−	1.05022i
$627$	−10.7212	+	4.77337i	−0.428162	+	0.190630i
$628$	−15.9344	+	11.5770i	−0.635850	+	0.461972i
$629$	−0.553643	−	0.246498i	−0.0220752	−	0.00982851i
$630$	−0.323634	+	0.0687906i	−0.0128939	+	0.00274068i
$631$	1.97922	−	18.8310i	0.0787916	−	0.749652i	−0.881788	−	0.471646i	$-0.843660\pi$
$631$	1.97922	−	18.8310i	0.0787916	−	0.749652i	0.960579	−	0.278005i	$-0.0896733\pi$
$632$	10.2106	+	11.3400i	0.406156	+	0.451082i
$633$	10.8724	−	12.0750i	0.432138	−	0.479937i
$634$	−0.666584	−	6.34212i	−0.0264734	−	0.251878i
$635$	−5.90969	−	18.1882i	−0.234519	−	0.721776i
$636$	0.0206152	+	0.0634470i	0.000817445	+	0.00251584i
$637$	2.11418	+	20.1151i	0.0837670	+	0.796990i
$638$	−7.20715	+	8.00436i	−0.285334	+	0.316895i
$639$	3.67625	+	4.08289i	0.145430	+	0.161517i
$640$	−0.104528	+	0.994522i	−0.00413185	+	0.0393119i
$641$	−6.29139	+	1.33728i	−0.248495	+	0.0528193i	−0.330475	−	0.943815i	$-0.607209\pi$
$641$	−6.29139	+	1.33728i	−0.248495	+	0.0528193i	0.0819800	+	0.996634i	$0.473876\pi$
$642$	−8.15565	−	3.63113i	−0.321878	−	0.143309i
$643$	−5.52821	+	4.01648i	−0.218011	+	0.158394i	−0.691431	−	0.722443i	$-0.743019\pi$
$643$	−5.52821	+	4.01648i	−0.218011	+	0.158394i	0.473420	+	0.880837i	$0.343019\pi$
$644$	2.10440	−	0.936938i	0.0829249	−	0.0369205i
$645$	−0.653247	+	1.13146i	−0.0257216	+	0.0445511i
$646$	24.4983	+	42.4323i	0.963872	+	1.66948i
$647$	20.7398	+	15.0683i	0.815364	+	0.592397i	0.915381	−	0.402589i	$-0.131890\pi$
$647$	20.7398	+	15.0683i	0.815364	+	0.592397i	−0.100017	+	0.994986i	$0.531890\pi$
$648$	−0.978148	−	0.207912i	−0.0384253	−	0.00816754i
$649$	3.65195	−	11.2396i	0.143352	−	0.441191i
$650$	2.93532			0.115133
$651$	1.79857	+	0.398451i	0.0704915	+	0.0156165i
$652$	0.0439659			0.00172184
$653$	3.02131	−	9.29865i	0.118233	−	0.363884i	−0.874375	−	0.485252i	$-0.838728\pi$
$653$	3.02131	−	9.29865i	0.118233	−	0.363884i	0.992608	+	0.121368i	$0.0387280\pi$
$654$	7.83558	+	1.66550i	0.306395	+	0.0651263i
$655$	0.443455	+	0.322189i	0.0173272	+	0.0125890i
$656$	−0.696895	−	1.20706i	−0.0272092	−	0.0471277i
$657$	7.49591	−	12.9833i	0.292443	−	0.506527i
$658$	1.85134	−	0.824269i	0.0721727	−	0.0321334i
$659$	−16.3325	+	11.8662i	−0.636223	+	0.462243i	−0.858550	−	0.512729i	$-0.828635\pi$
$659$	−16.3325	+	11.8662i	−0.636223	+	0.462243i	0.222328	+	0.974972i	$0.428635\pi$
$660$	1.53068	+	0.681505i	0.0595818	+	0.0265275i
$661$	10.7757	−	2.29045i	0.419127	−	0.0890881i	0.00647932	−	0.999979i	$-0.497938\pi$
$661$	10.7757	−	2.29045i	0.419127	−	0.0890881i	0.412647	+	0.910891i	$0.364604\pi$
$662$	2.22622	−	21.1811i	0.0865245	−	0.823226i
$663$	13.7397	+	15.2594i	0.533604	+	0.592627i
$664$	2.71317	−	3.01328i	0.105292	−	0.116938i
$665$	0.242237	+	2.30473i	0.00939356	+	0.0893738i
$666$	−0.0267715	−	0.0823942i	−0.00103737	−	0.00319271i
$667$	−13.8302	−	42.5648i	−0.535506	−	1.64812i
$668$	−0.816485	−	7.76834i	−0.0315908	−	0.300566i
$669$	−17.6730	+	19.6278i	−0.683276	+	0.758855i
$670$	1.53640	+	1.70635i	0.0593564	+	0.0659219i
$671$	−0.0868031	+	0.825876i	−0.00335099	+	0.0318826i
$672$	−0.323634	+	0.0687906i	−0.0124845	+	0.00265366i
$673$	−26.9369	−	11.9931i	−1.03834	−	0.462300i	−0.184501	−	0.982832i	$-0.559067\pi$
$673$	−26.9369	−	11.9931i	−1.03834	−	0.462300i	−0.853842	+	0.520532i	$0.825734\pi$
$674$	0.625757	−	0.454639i	0.0241033	−	0.0175120i
$675$	0.913545	−	0.406737i	0.0351624	−	0.0156553i
$676$	2.19195	−	3.79656i	0.0843057	−	0.146022i
$677$	−17.6478	−	30.5670i	−0.678262	−	1.17478i	−0.975504	−	0.219982i	$-0.929400\pi$
$677$	−17.6478	−	30.5670i	−0.678262	−	1.17478i	0.297242	−	0.954802i	$-0.403933\pi$
$678$	11.2041	+	8.14026i	0.430291	+	0.312625i
$679$	0.463926	+	0.0986105i	0.0178038	+	0.00378432i
$680$	2.16168	−	6.65297i	0.0828967	−	0.255130i
$681$	13.3361			0.511040
$682$	−6.18265	−	6.98610i	−0.236746	−	0.267512i
$683$	35.1169			1.34371			0.671855	−	0.740683i	$-0.265498\pi$
$683$	35.1169			1.34371			0.671855	+	0.740683i	$0.265498\pi$
$684$	−2.16441	+	6.66135i	−0.0827581	+	0.254703i
$685$	−8.25360	−	1.75436i	−0.315354	−	0.0670306i
$686$	3.71815	+	2.70139i	0.141960	+	0.103140i
$687$	3.64592	+	6.31492i	0.139100	+	0.240929i
$688$	−0.653247	+	1.13146i	−0.0249048	+	0.0431364i
$689$	0.178892	−	0.0796477i	0.00681523	−	0.00303434i
$690$	−5.63255	+	4.09229i	−0.214427	+	0.155791i
$691$	−5.67740	−	2.52774i	−0.215979	−	0.0961599i	0.295896	−	0.955220i	$-0.404382\pi$
$691$	−5.67740	−	2.52774i	−0.215979	−	0.0961599i	−0.511874	+	0.859060i	$0.671049\pi$
$692$	−17.0587	+	3.62595i	−0.648476	+	0.137838i
$693$	−0.0579483	+	0.551341i	−0.00220127	+	0.0209437i
$694$	1.79191	+	1.99012i	0.0680200	+	0.0755439i
$695$	−6.08957	+	6.76316i	−0.230991	+	0.256541i
$696$	0.671942	+	6.39310i	0.0254699	+	0.242330i
$697$	3.01293	+	9.27285i	0.114123	+	0.351234i
$698$	−4.57355	−	14.0759i	−0.173111	−	0.532782i
$699$	−2.26874	−	21.5856i	−0.0858115	−	0.816442i
$700$	0.221392	−	0.245880i	0.00836782	−	0.00929340i
$701$	−14.9410	−	16.5936i	−0.564312	−	0.626732i	0.391688	−	0.920098i	$-0.371891\pi$
$701$	−14.9410	−	16.5936i	−0.564312	−	0.626732i	−0.956000	+	0.293366i	$0.905225\pi$
$702$	−0.306825	+	2.91924i	−0.0115803	+	0.110180i
$703$	−0.593541	+	0.126161i	−0.0223858	+	0.00475825i
$704$	1.53068	+	0.681505i	0.0576899	+	0.0256852i
$705$	−4.95522	+	3.60018i	−0.186624	+	0.135591i
$706$	−23.9961	+	10.6838i	−0.903106	+	0.402089i
$707$	−1.73352	+	3.00254i	−0.0651956	+	0.112922i
$708$	−3.52661	−	6.10827i	−0.132538	−	0.229563i
$709$	24.8515	+	18.0557i	0.933318	+	0.678095i	0.946803	−	0.321814i	$-0.104293\pi$
$709$	24.8515	+	18.0557i	0.933318	+	0.678095i	−0.0134849	+	0.999909i	$0.504293\pi$
$710$	−5.37401	−	1.14228i	−0.201683	−	0.0428690i
$711$	4.71545	−	14.5127i	0.176843	−	0.544267i
$712$	14.8664			0.557142
$713$	37.9846	−	7.73397i	1.42253	−	0.289640i
$714$	2.31451			0.0866185
$715$	1.51982	−	4.67754i	0.0568382	−	0.174930i
$716$	15.2952	+	3.25109i	0.571607	+	0.121499i
$717$	0.718591	+	0.522087i	0.0268363	+	0.0194977i
$718$	−15.5435	−	26.9222i	−0.580079	−	1.00473i
$719$	17.2555	−	29.8874i	0.643521	−	1.11461i	−0.341120	−	0.940020i	$-0.610806\pi$
$719$	17.2555	−	29.8874i	0.643521	−	1.11461i	0.984641	−	0.174591i	$-0.0558603\pi$
$720$	0.913545	−	0.406737i	0.0340458	−	0.0151582i
$721$	−1.71745	+	1.24780i	−0.0639613	+	0.0464706i
$722$	27.4596	+	12.2258i	1.02194	+	0.454997i
$723$	−24.0574	+	5.11355i	−0.894703	+	0.190175i
$724$	−0.529056	+	5.03363i	−0.0196622	+	0.187074i
$725$	−4.30138	−	4.77717i	−0.159749	−	0.177420i
$726$	−5.48189	+	6.08826i	−0.203452	+	0.225956i
$727$	−2.79155	−	26.5599i	−0.103533	−	0.985051i	−0.915765	−	0.401715i	$-0.868414\pi$
$727$	−2.79155	−	26.5599i	−0.103533	−	0.985051i	0.812232	−	0.583335i	$-0.198253\pi$
$728$	0.300115	+	0.923660i	0.0111230	+	0.0342331i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	1.56707	+	14.9097i	0.0579999	+	0.551832i
$731$	6.11544	−	6.79188i	0.226188	−	0.251207i
$732$	0.331631	+	0.368314i	0.0122575	+	0.0136133i
$733$	−2.26071	+	21.5092i	−0.0835011	+	0.794460i	0.869996	+	0.493058i	$0.164121\pi$
$733$	−2.26071	+	21.5092i	−0.0835011	+	0.794460i	−0.953497	+	0.301402i	$0.902546\pi$
$734$	−5.80355	+	1.23358i	−0.214213	+	0.0455323i
$735$	−6.29481	−	2.80263i	−0.232188	−	0.103377i
$736$	−5.63255	+	4.09229i	−0.207618	+	0.150844i
$737$	3.51463	−	1.56481i	0.129463	−	0.0576407i
$738$	−0.696895	+	1.20706i	−0.0256531	+	0.0444324i
$739$	−10.9810	−	19.0197i	−0.403943	−	0.699649i	0.590255	−	0.807217i	$-0.299027\pi$
$739$	−10.9810	−	19.0197i	−0.403943	−	0.699649i	−0.994198	+	0.107567i	$0.965694\pi$
$740$	0.0700887	+	0.0509224i	0.00257651	+	0.00187194i
$741$	20.1102	+	4.27455i	0.738766	+	0.157030i
$742$	0.00682083	−	0.0209924i	0.000250401	−	0.000770654i
$743$	0.805584			0.0295540			0.0147770	−	0.999891i	$-0.495296\pi$
$743$	0.805584			0.0295540			0.0147770	+	0.999891i	$0.495296\pi$
$744$	−5.56756	−	0.0477542i	−0.204117	−	0.00175076i
$745$	−5.79781			−0.212415
$746$	−8.20675	+	25.2578i	−0.300471	+	0.924753i
$747$	−3.96617	−	0.843035i	−0.145114	−	0.0308450i
$748$	−9.48250	−	6.88944i	−0.346714	−	0.251903i
$749$	1.47689	+	2.55805i	0.0539644	+	0.0934691i
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	14.7264	−	6.55663i	0.537375	−	0.239255i	−0.120059	−	0.992767i	$-0.538308\pi$
$751$	14.7264	−	6.55663i	0.537375	−	0.239255i	0.657434	+	0.753512i	$0.271642\pi$
$752$	−4.95522	+	3.60018i	−0.180698	+	0.131285i
$753$	0.702090	+	0.312590i	0.0255856	+	0.0113914i
$754$	18.4568	−	3.92312i	0.672158	−	0.142872i
$755$	1.45448	−	13.8385i	0.0529340	−	0.503634i
$756$	0.221392	+	0.245880i	0.00805193	+	0.00894258i
$757$	12.7855	−	14.1998i	0.464698	−	0.516099i	−0.464555	−	0.885544i	$-0.653786\pi$
$757$	12.7855	−	14.1998i	0.464698	−	0.516099i	0.929252	+	0.369445i	$0.120452\pi$
$758$	2.84037	+	27.0243i	0.103167	+	0.981568i
$759$	3.60483	+	11.0945i	0.130847	+	0.402706i
$760$	−2.16441	−	6.66135i	−0.0785112	−	0.241633i
$761$	−2.18244	−	20.7646i	−0.0791135	−	0.752715i	−0.960116	−	0.279603i	$-0.909797\pi$
$761$	−2.18244	−	20.7646i	−0.0791135	−	0.752715i	0.881002	−	0.473112i	$-0.156869\pi$
$762$	−12.7966	+	14.2120i	−0.463571	+	0.514848i
$763$	−1.77349	−	1.96966i	−0.0642045	−	0.0713063i
$764$	−1.31268	+	12.4893i	−0.0474910	+	0.451847i
$765$	−6.84249	+	1.45442i	−0.247391	+	0.0525845i
$766$	−18.9436	−	8.43426i	−0.684462	−	0.304742i
$767$	−16.7495	+	12.1692i	−0.604788	+	0.439404i
$768$	0.913545	−	0.406737i	0.0329647	−	0.0146768i
$769$	1.07236	−	1.85738i	0.0386702	−	0.0669787i	−0.846043	−	0.533115i	$-0.821021\pi$
$769$	1.07236	−	1.85738i	0.0386702	−	0.0669787i	0.884713	+	0.466137i	$0.154354\pi$
$770$	−0.277189	−	0.480105i	−0.00998920	−	0.0173018i
$771$	−5.80084	−	4.21456i	−0.208912	−	0.151784i
$772$	−22.0812	−	4.69351i	−0.794720	−	0.168923i
$773$	2.96592	−	9.12817i	0.106677	−	0.328317i	−0.883444	−	0.468538i	$-0.844781\pi$
$773$	2.96592	−	9.12817i	0.106677	−	0.328317i	0.990120	+	0.140220i	$0.0447811\pi$
$774$	1.30649			0.0469609
$775$	4.53232	−	3.23390i	0.162806	−	0.116165i
$776$	−1.43349			−0.0514592
$777$	−0.00885774	+	0.0272613i	−0.000317770	+	0.000977994i
$778$	−15.7276	−	3.34300i	−0.563861	−	0.119852i
$779$	7.89789	+	5.73815i	0.282971	+	0.205591i
$780$	−1.46766	−	2.54206i	−0.0525507	−	0.0910204i
$781$	−4.60277	+	7.97224i	−0.164700	+	0.285269i
$782$	44.4925	−	19.8093i	1.59105	−	0.708381i
$783$	5.20062	−	3.77847i	0.185855	−	0.135032i
$784$	−6.29481	−	2.80263i	−0.224815	−	0.100094i
$785$	−19.2655	+	4.09502i	−0.687617	+	0.146157i
$786$	0.0572963	−	0.545138i	0.00204369	−	0.0194444i
$787$	−24.5094	−	27.2205i	−0.873667	−	0.970306i	0.126097	−	0.992018i	$-0.459755\pi$
$787$	−24.5094	−	27.2205i	−0.873667	−	0.970306i	−0.999764	+	0.0217123i	$0.993088\pi$
$788$	8.19196	−	9.09809i	0.291826	−	0.324106i
$789$	2.06283	+	19.6265i	0.0734385	+	0.698721i
$790$	4.71545	+	14.5127i	0.167768	+	0.516337i
$791$	−1.41596	−	4.35789i	−0.0503459	−	0.154949i
$792$	−0.175142	−	1.66636i	−0.00622340	−	0.0592117i
$793$	0.973445	−	1.08112i	0.0345680	−	0.0383917i
$794$	−16.3894	−	18.2023i	−0.581638	−	0.645975i
$795$	−0.00697331	+	0.0663467i	−0.000247318	+	0.00235307i
$796$	11.8780	−	2.52474i	0.421004	−	0.0894871i
$797$	6.18295	+	2.75282i	0.219011	+	0.0975101i	0.513310	−	0.858204i	$-0.328419\pi$
$797$	6.18295	+	2.75282i	0.219011	+	0.0975101i	−0.294298	+	0.955714i	$0.595086\pi$
$798$	1.87484	−	1.36215i	0.0663686	−	0.0482196i
$799$	39.1422	−	17.4272i	1.38475	−	0.616531i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−7.43320	−	12.8747i	−0.262639	−	0.454904i
$802$	−23.4995	−	17.0734i	−0.829796	−	0.602882i
$803$	24.5705	+	5.22262i	0.867075	+	0.184302i
$804$	0.709539	−	2.18374i	0.0250235	−	0.0770144i
$805$	2.30355			0.0811894
$806$	1.56886	+	16.2677i	0.0552607	+	0.573005i
$807$	−0.145949			−0.00513765
$808$	3.23810	−	9.96585i	0.113916	−	0.350597i
$809$	36.8977	+	7.84286i	1.29726	+	0.275740i	0.804253	−	0.594287i	$-0.202566\pi$
$809$	36.8977	+	7.84286i	1.29726	+	0.275740i	0.493003	+	0.870028i	$0.335899\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	13.1458	+	22.7691i	0.461610	+	0.799532i	0.999041	−	0.0437753i	$-0.0139386\pi$
$811$	13.1458	+	22.7691i	0.461610	+	0.799532i	−0.537431	+	0.843308i	$0.680605\pi$
$812$	1.06345	−	1.84195i	0.0373198	−	0.0646398i
$813$	6.38563	−	2.84307i	0.223954	−	0.0997107i
$814$	0.117437	−	0.0853227i	0.00411615	−	0.00299056i
$815$	0.0401648	+	0.0178825i	0.00140691	+	0.000626398i
$816$	−6.84249	+	1.45442i	−0.239535	+	0.0509147i
$817$	0.956529	−	9.10076i	0.0334647	−	0.318395i
$818$	8.97652	+	9.96944i	0.313857	+	0.348573i
$819$	0.649855	−	0.721737i	0.0227078	−	0.0252195i
$820$	−0.145691	−	1.38615i	−0.00508774	−	0.0484066i
$821$	13.4077	+	41.2646i	0.467931	+	1.44014i	0.855259	+	0.518201i	$0.173398\pi$
$821$	13.4077	+	41.2646i	0.467931	+	1.44014i	−0.387328	+	0.921942i	$0.626602\pi$
$822$	2.60748	+	8.02501i	0.0909464	+	0.279904i
$823$	−3.63066	−	34.5434i	−0.126557	−	1.20411i	−0.854863	−	0.518854i	$-0.826359\pi$
$823$	−3.63066	−	34.5434i	−0.126557	−	1.20411i	0.728306	−	0.685252i	$-0.240308\pi$
$824$	4.29327	−	4.76816i	0.149563	−	0.166107i
$825$	1.12116	+	1.24517i	0.0390337	+	0.0433513i
$826$	−0.243934	+	2.32088i	−0.00848755	+	0.0807536i
$827$	−18.8122	+	3.99865i	−0.654163	+	0.139047i	−0.523025	−	0.852318i	$-0.675196\pi$
$827$	−18.8122	+	3.99865i	−0.654163	+	0.139047i	−0.131138	+	0.991364i	$0.541863\pi$
$828$	6.36030	+	2.83179i	0.221036	+	0.0984114i
$829$	−18.0503	+	13.1143i	−0.626913	+	0.455479i	−0.855329	−	0.518085i	$-0.826645\pi$
$829$	−18.0503	+	13.1143i	−0.626913	+	0.455479i	0.228416	+	0.973564i	$0.426645\pi$
$830$	3.70422	−	1.64923i	0.128575	−	0.0572454i
$831$	−0.266474	+	0.461547i	−0.00924389	+	0.0160109i
$832$	−1.46766	−	2.54206i	−0.0508820	−	0.0881301i
$833$	38.9960	+	28.3322i	1.35113	+	0.981653i
$834$	8.90185	+	1.89215i	0.308246	+	0.0655197i
$835$	2.41377	−	7.42882i	0.0835320	−	0.257085i
$836$	−11.7358			−0.405890
$837$	2.74242	+	4.84553i	0.0947920	+	0.167486i
$838$	37.1732			1.28413
$839$	−1.45077	+	4.46501i	−0.0500861	+	0.154149i	−0.972971	−	0.230926i	$-0.925824\pi$
$839$	−1.45077	+	4.46501i	−0.0500861	+	0.154149i	0.922885	+	0.385075i	$0.125824\pi$
$840$	−0.323634	−	0.0687906i	−0.0111664	−	0.00237350i
$841$	−9.96974	−	7.24344i	−0.343784	−	0.249774i
$842$	12.7954	+	22.1622i	0.440958	+	0.763761i
$843$	−11.4776	+	19.8798i	−0.395310	+	0.684697i
$844$	14.8437	−	6.60886i	0.510942	−	0.227486i
$845$	3.54665	−	2.57679i	0.122008	−	0.0886442i
$846$	5.59546	+	2.49126i	0.192376	+	0.0856512i
$847$	2.65139	−	0.563571i	0.0911029	−	0.0193645i
$848$	−0.00697331	+	0.0663467i	−0.000239465	+	0.00227835i
$849$	−6.83730	−	7.59359i	−0.234655	−	0.260611i
$850$	4.68080	−	5.19856i	0.160550	−	0.178309i
$851$	0.0630481	+	0.599863i	0.00216126	+	0.0205630i
$852$	1.69776	+	5.22517i	0.0581643	+	0.179011i
$853$	9.03518	+	27.8074i	0.309359	+	0.952108i	0.978015	+	0.208536i	$0.0668699\pi$
$853$	9.03518	+	27.8074i	0.309359	+	0.952108i	−0.668656	+	0.743572i	$0.733130\pi$
$854$	−0.0171407	−	0.163083i	−0.000586544	−	0.00558060i
$855$	−4.68670	+	5.20511i	−0.160282	+	0.178011i
$856$	−5.97364	−	6.63440i	−0.204175	−	0.226759i
$857$	1.28949	−	12.2687i	0.0440483	−	0.419091i	−0.950172	−	0.311728i	$-0.899092\pi$
$857$	1.28949	−	12.2687i	0.0440483	−	0.419091i	0.994220	−	0.107364i	$-0.0342409\pi$
$858$	−4.81078	+	1.02256i	−0.164237	+	0.0349097i
$859$	−0.785406	−	0.349686i	−0.0267977	−	0.0119311i	0.393294	−	0.919413i	$-0.371335\pi$
$859$	−0.785406	−	0.349686i	−0.0267977	−	0.0119311i	−0.420092	+	0.907482i	$0.638002\pi$
$860$	−1.05698	+	0.767938i	−0.0360426	+	0.0261865i
$861$	0.421287	−	0.187569i	0.0143574	−	0.00639233i
$862$	18.3610	−	31.8021i	0.625377	−	1.08318i
$863$	−0.952051	−	1.64900i	−0.0324082	−	0.0561326i	0.849366	−	0.527804i	$-0.176984\pi$
$863$	−0.952051	−	1.64900i	−0.0324082	−	0.0561326i	−0.881775	+	0.471671i	$0.843651\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	−17.0587	−	3.62595i	−0.580014	−	0.123286i
$866$	−11.5275	+	35.4781i	−0.391722	+	1.20560i
$867$	31.9349			1.08457
$868$	1.48101	+	1.09555i	0.0502687	+	0.0371853i
$869$	25.5680			0.867334
$870$	−1.98646	+	6.11369i	−0.0673473	+	0.207274i
$871$	−6.59255	−	1.40129i	−0.223380	−	0.0474809i
$872$	6.48074	+	4.70853i	0.219465	+	0.159451i
$873$	0.716744	+	1.24144i	0.0242581	+	0.0420163i
$874$	24.3822	−	42.2313i	0.824741	−	1.42849i
$875$	0.302260	−	0.134575i	0.0102182	−	0.00454946i
$876$	12.1286	−	8.81197i	0.409789	−	0.297729i
$877$	7.51042	+	3.34385i	0.253609	+	0.112914i	0.529604	−	0.848245i	$-0.322341\pi$
$877$	7.51042	+	3.34385i	0.253609	+	0.112914i	−0.275995	+	0.961159i	$0.589007\pi$
$878$	20.2509	−	4.30446i	0.683434	−	0.145268i
$879$	2.97720	−	28.3262i	0.100419	−	0.955419i
$880$	1.12116	+	1.24517i	0.0377942	+	0.0419747i
$881$	−11.0006	+	12.2175i	−0.370621	+	0.411616i	−0.899388	−	0.437150i	$-0.855988\pi$
$881$	−11.0006	+	12.2175i	−0.370621	+	0.411616i	0.528767	+	0.848767i	$0.322654\pi$
$882$	0.720256	+	6.85278i	0.0242523	+	0.230745i
$883$	7.36404	+	22.6642i	0.247820	+	0.762711i	0.995160	+	0.0982691i	$0.0313306\pi$
$883$	7.36404	+	22.6642i	0.247820	+	0.762711i	−0.747340	+	0.664442i	$0.768669\pi$
$884$	6.34523	+	19.5286i	0.213413	+	0.656818i
$885$	−0.737262	−	7.01458i	−0.0247828	−	0.235793i
$886$	18.0948	−	20.0963i	0.607905	−	0.675147i
$887$	−18.6071	−	20.6653i	−0.624765	−	0.693871i	0.344809	−	0.938673i	$-0.387944\pi$
$887$	−18.6071	−	20.6653i	−0.624765	−	0.693871i	−0.969573	+	0.244802i	$0.921277\pi$
$888$	0.00905576	−	0.0861598i	0.000303891	−	0.00289133i
$889$	6.18924	−	1.31556i	0.207580	−	0.0441226i
$890$	13.5811	+	6.04671i	0.455240	+	0.202686i
$891$	−1.35554	+	0.984860i	−0.0454124	+	0.0329940i
$892$	−24.1284	+	10.7427i	−0.807879	+	0.359691i
$893$	21.4502	−	37.1529i	0.717804	−	1.24327i
$894$	2.89890	+	5.02105i	0.0969539	+	0.167929i
$895$	12.6505	+	9.19112i	0.422859	+	0.307225i
$896$	−0.323634	−	0.0687906i	−0.0108119	−	0.00229813i
$897$	6.31517	−	19.4361i	0.210857	−	0.648952i
$898$	27.7758			0.926891
$899$	24.1763	−	26.3918i	0.806326	−	0.880215i
$900$	1.00000			0.0333333
$901$	0.144210	−	0.443834i	0.00480434	−	0.0147863i
$902$	−2.28432	−	0.485548i	−0.0760596	−	0.0161670i
$903$	−0.349716	−	0.254083i	−0.0116378	−	0.00845536i
$904$	6.92452	+	11.9936i	0.230306	+	0.398902i
$905$	−2.53068	+	4.38327i	−0.0841227	+	0.145705i
$906$	−12.7117	+	5.65962i	−0.422318	+	0.188028i
$907$	6.41295	−	4.65928i	0.212939	−	0.154709i	−0.476204	−	0.879335i	$-0.657988\pi$
$907$	6.41295	−	4.65928i	0.212939	−	0.154709i	0.689142	+	0.724626i	$0.257988\pi$
$908$	12.1831	+	5.42427i	0.404311	+	0.180011i
$909$	−10.2497	+	2.17865i	−0.339962	+	0.0722612i
$910$	−0.101517	+	0.965873i	−0.00336527	+	0.0320184i
$911$	8.01089	+	8.89699i	0.265412	+	0.294770i	0.861089	−	0.508454i	$-0.169783\pi$
$911$	8.01089	+	8.89699i	0.265412	+	0.294770i	−0.595677	+	0.803224i	$0.703116\pi$
$912$	−4.68670	+	5.20511i	−0.155192	+	0.172358i
$913$	−0.710161	−	6.75673i	−0.0235029	−	0.223615i
$914$	11.6875	+	35.9706i	0.386590	+	1.18980i
$915$	0.153154	+	0.471358i	0.00506310	+	0.0155826i
$916$	0.762204	+	7.25189i	0.0251839	+	0.239609i
$917$	−0.121354	+	0.134777i	−0.00400745	+	0.00445073i
$918$	4.68080	+	5.19856i	0.154490	+	0.171578i
$919$	−2.28041	+	21.6967i	−0.0752238	+	0.715707i	0.890297	+	0.455381i	$0.150497\pi$
$919$	−2.28041	+	21.6967i	−0.0752238	+	0.715707i	−0.965521	+	0.260326i	$0.916170\pi$
$920$	−6.81007	+	1.44753i	−0.224521	+	0.0477235i
$921$	−8.79117	−	3.91408i	−0.289679	−	0.128973i
$922$	5.46162	−	3.96810i	0.179869	−	0.130682i
$923$	14.7326	−	6.55938i	0.484930	−	0.215905i
$924$	−0.277189	+	0.480105i	−0.00911885	+	0.0157943i
$925$	0.0433172	+	0.0750276i	0.00142426	+	0.00246689i
$926$	−23.5184	−	17.0871i	−0.772863	−	0.561518i
$927$	−6.27598	−	1.33400i	−0.206130	−	0.0438143i
$928$	−1.98646	+	6.11369i	−0.0652087	+	0.200692i
$929$	18.2019			0.597184			0.298592	−	0.954381i	$-0.403483\pi$
$929$	18.2019			0.597184			0.298592	+	0.954381i	$0.403483\pi$
$930$	−5.06680	−	2.30816i	−0.166147	−	0.0756874i
$931$	48.2624			1.58174
$932$	6.70706	−	20.6422i	0.219697	−	0.676158i
$933$	15.0459	+	3.19810i	0.492580	+	0.104701i
$934$	−16.0194	−	11.6388i	−0.524171	−	0.380832i
$935$	−5.86051	−	10.1507i	−0.191659	−	0.331963i
$936$	−1.46766	+	2.54206i	−0.0479720	+	0.0830899i
$937$	−18.7777	+	8.36036i	−0.613440	+	0.273121i	−0.689846	−	0.723956i	$-0.742322\pi$
$937$	−18.7777	+	8.36036i	−0.613440	+	0.273121i	0.0764065	+	0.997077i	$0.475655\pi$
$938$	−0.614613	+	0.446542i	−0.0200678	+	0.0145801i
$939$	−27.7182	−	12.3410i	−0.904551	−	0.402732i
$940$	−5.99114	+	1.27346i	−0.195410	+	0.0415356i
$941$	−0.105242	+	1.00131i	−0.00343080	+	0.0326419i	−0.996103	−	0.0881935i	$-0.971891\pi$
$941$	−0.105242	+	1.00131i	−0.00343080	+	0.0326419i	0.992673	+	0.120835i	$0.0385573\pi$
$942$	13.1792	+	14.6369i	0.429400	+	0.476897i
$943$	6.49315	−	7.21137i	0.211446	−	0.234835i
$944$	−0.737262	−	7.01458i	−0.0239958	−	0.228305i
$945$	0.102243	+	0.314671i	0.00332596	+	0.0102362i
$946$	0.676465	+	2.08194i	0.0219938	+	0.0676899i
$947$	−1.58588	−	15.0886i	−0.0515341	−	0.490314i	−0.989599	−	0.143854i	$-0.954050\pi$
$947$	−1.58588	−	15.0886i	−0.0515341	−	0.490314i	0.938065	−	0.346460i	$-0.112616\pi$
$948$	10.2106	−	11.3400i	0.331625	−	0.368307i
$949$	−29.4456	−	32.7027i	−0.955845	−	1.06157i
$950$	0.732134	−	6.96579i	0.0237536	−	0.226000i
$951$	−6.23770	+	1.32586i	−0.202271	+	0.0429941i
$952$	2.11441	+	0.941397i	0.0685285	+	0.0305109i
$953$	33.9280	−	24.6501i	1.09904	−	0.798496i	0.118133	−	0.992998i	$-0.462309\pi$
$953$	33.9280	−	24.6501i	1.09904	−	0.798496i	0.980902	+	0.194502i	$0.0623090\pi$
$954$	0.0609445	−	0.0271343i	0.00197315	−	0.000878504i
$955$	−6.27904	+	10.8756i	−0.203185	+	0.351927i
$956$	0.444114	+	0.769227i	0.0143637	+	0.0248786i
$957$	8.71386	+	6.33099i	0.281679	+	0.204652i
$958$	32.7357	+	6.95819i	1.05764	+	0.224809i
$959$	0.862724	−	2.65519i	0.0278588	−	0.0857406i
$960$	1.00000			0.0322749
$961$	20.3448	+	23.3899i	0.656285	+	0.754513i
$962$	−0.254300			−0.00819895
$963$	−2.75874	+	8.49053i	−0.0888991	+	0.273603i
$964$	−24.0574	−	5.11355i	−0.774836	−	0.164696i
$965$	−18.2632	−	13.2690i	−0.587912	−	0.427143i
$966$	−1.15177	−	1.99493i	−0.0370577	−	0.0641859i
$967$	7.54117	−	13.0617i	0.242508	−	0.420036i	−0.718920	−	0.695093i	$-0.755363\pi$
$967$	7.54117	−	13.0617i	0.242508	−	0.420036i	0.961428	+	0.275057i	$0.0886967\pi$
$968$	−7.48427	+	3.33221i	−0.240554	+	0.107101i
$969$	39.6391	−	28.7995i	1.27339	−	0.925172i
$970$	−1.30956	−	0.583052i	−0.0420473	−	0.0187207i
$971$	−55.6477	+	11.8283i	−1.78582	+	0.379588i	−0.977796	−	0.209561i	$-0.932797\pi$
$971$	−55.6477	+	11.8283i	−1.78582	+	0.379588i	−0.808025	+	0.589149i	$0.799463\pi$
$972$	−0.104528	+	0.994522i	−0.00335275	+	0.0318993i
$973$	−2.01482	−	2.23769i	−0.0645923	−	0.0717370i
$974$	−21.0440	+	23.3718i	−0.674294	+	0.748880i
$975$	−0.306825	−	2.91924i	−0.00982625	−	0.0934905i
$976$	0.153154	+	0.471358i	0.00490233	+	0.0150878i
$977$	−14.4232	−	44.3899i	−0.461438	−	1.42016i	−0.863408	−	0.504507i	$-0.831674\pi$
$977$	−14.4232	−	44.3899i	−0.461438	−	1.42016i	0.401970	−	0.915653i	$-0.368326\pi$
$978$	−0.00459569	−	0.0437250i	−0.000146954	−	0.00139817i
$979$	16.6676	−	18.5112i	0.532698	−	0.591621i
$980$	−4.61066	−	5.12066i	−0.147282	−	0.163574i
$981$	0.837339	−	7.96675i	0.0267342	−	0.254359i
$982$	−36.1166	+	7.67682i	−1.15253	+	0.244977i
$983$	−15.5813	−	6.93724i	−0.496966	−	0.221264i	0.142919	−	0.989734i	$-0.454351\pi$
$983$	−15.5813	−	6.93724i	−0.496966	−	0.221264i	−0.639885	+	0.768471i	$0.721018\pi$
$984$	−1.12760	+	0.819249i	−0.0359466	+	0.0261167i
$985$	11.1843	−	4.97955i	0.356360	−	0.158662i
$986$	22.4842	−	38.9437i	0.716042	−	1.24022i
$987$	−1.01327	−	1.75504i	−0.0322528	−	0.0558634i
$988$	16.6330	+	12.0845i	0.529165	+	0.384461i
$989$	−8.89731	−	1.89118i	−0.282918	−	0.0601361i
$990$	0.517771	−	1.59354i	0.0164559	−	0.0506459i
$991$	36.2040			1.15006			0.575028	−	0.818134i	$-0.304991\pi$
$991$	36.2040			1.15006			0.575028	+	0.818134i	$0.304991\pi$
$992$	−5.06680	−	2.30816i	−0.160871	−	0.0732840i
$993$	−21.2977			−0.675863
$994$	0.561729	−	1.72882i	0.0178170	−	0.0548349i
$995$	11.8780	+	2.52474i	0.376557	+	0.0800397i
$996$	−3.28038	−	2.38334i	−0.103943	−	0.0755189i
$997$	−8.00304	−	13.8617i	−0.253459	−	0.439003i	0.711017	−	0.703175i	$-0.248235\pi$
$997$	−8.00304	−	13.8617i	−0.253459	−	0.439003i	−0.964476	+	0.264171i	$0.914902\pi$
$998$	−18.0037	+	31.1834i	−0.569898	+	0.987093i
$999$	−0.0791444	+	0.0352374i	−0.00250402	+	0.00111486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.g.691.2	✓	24
31.7	even	15	inner	930.2.bg.g.751.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.g.691.2	✓	24	1.1	even	1	trivial
930.2.bg.g.751.2	yes	24	31.7	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)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.302260 - 0.134575i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.302260 - 0.134575i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-0.978148 + 0.207912i) q^{10} +(-0.175142 + 1.66636i) q^{11} +(0.669131 + 0.743145i) q^{12} +(1.96411 - 2.18137i) q^{13} +(-0.0345848 - 0.329052i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.731213 - 6.95703i) q^{17} +(0.669131 - 0.743145i) q^{18} +(-4.68670 - 5.20511i) q^{19} +(-0.104528 + 0.994522i) q^{20} +(-0.323634 + 0.0687906i) q^{21} +(1.53068 + 0.681505i) q^{22} +(-5.63255 + 4.09229i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.46766 - 2.54206i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.323634 - 0.0687906i) q^{28} +(-1.98646 + 6.11369i) q^{29} +1.00000 q^{30} +(-5.06680 - 2.30816i) q^{31} +1.00000 q^{32} +(0.517771 - 1.59354i) q^{33} +(-6.84249 - 1.45442i) q^{34} +(-0.267675 - 0.194477i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(0.0433172 - 0.0750276i) q^{37} +(-6.39862 + 2.84885i) q^{38} +(-2.37472 + 1.72534i) q^{39} +(0.913545 + 0.406737i) q^{40} +(-1.36333 + 0.289785i) q^{41} +(-0.0345848 + 0.329052i) q^{42} +(0.874215 + 0.970914i) q^{43} +(1.12116 - 1.24517i) q^{44} +(-0.104528 - 0.994522i) q^{45} +(2.15144 + 6.62146i) q^{46} +(1.89273 + 5.82521i) q^{47} +(-0.104528 - 0.994522i) q^{48} +(-4.61066 + 5.12066i) q^{49} +(0.669131 + 0.743145i) q^{50} +(-0.731213 + 6.95703i) q^{51} +(-2.87118 + 0.610287i) q^{52} +(0.0609445 + 0.0271343i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(1.53068 - 0.681505i) q^{55} +(-0.165432 + 0.286537i) q^{56} +(3.50208 + 6.06578i) q^{57} +(5.20062 + 3.77847i) q^{58} +(-6.89909 - 1.46645i) q^{59} +(0.309017 - 0.951057i) q^{60} +0.495615 q^{61} +(-3.76091 + 4.10555i) q^{62} +0.330865 q^{63} +(0.309017 - 0.951057i) q^{64} +(-2.87118 - 0.610287i) q^{65} +(-1.35554 - 0.984860i) q^{66} +(-1.14806 - 1.98849i) q^{67} +(-3.49768 + 6.05815i) q^{68} +(6.36030 - 2.83179i) q^{69} +(-0.267675 + 0.194477i) q^{70} +(5.01908 + 2.23464i) q^{71} +(-0.978148 + 0.207912i) q^{72} +(1.56707 - 14.9097i) q^{73} +(-0.0579697 - 0.0643819i) q^{74} +(0.669131 - 0.743145i) q^{75} +(0.732134 + 6.96579i) q^{76} +(0.171312 + 0.527245i) q^{77} +(0.907064 + 2.79166i) q^{78} +(-1.59505 - 15.1759i) q^{79} +(0.669131 - 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.145691 + 1.38615i) q^{82} +(-3.96617 + 0.843035i) q^{83} +(0.302260 + 0.134575i) q^{84} +(-5.65936 + 4.11176i) q^{85} +(1.19354 - 0.531399i) q^{86} +(3.21416 - 5.56709i) q^{87} +(-0.837772 - 1.45106i) q^{88} +(-12.0272 - 8.73825i) q^{89} +(-0.978148 - 0.207912i) q^{90} +(0.300115 - 0.923660i) q^{91} +6.96221 q^{92} +(4.47618 + 3.31116i) q^{93} +6.12499 q^{94} +(-2.16441 + 6.66135i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(1.15972 + 0.842583i) q^{97} +(3.44526 + 5.96737i) q^{98} +(-0.837772 + 1.45106i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{20} + 4 q^{21} + 3 q^{22} + 5 q^{23} + 3 q^{24} - 12 q^{25} - 3 q^{26} - 6 q^{27} + 4 q^{28} - 15 q^{29} + 24 q^{30} + 15 q^{31} + 24 q^{32} + 4 q^{33} - 9 q^{34} - 3 q^{35} - 12 q^{36} + 6 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} - 6 q^{42} - 13 q^{43} - 2 q^{44} + 3 q^{45} - 10 q^{46} + 4 q^{47} + 3 q^{48} + 3 q^{50} - 9 q^{51} - 3 q^{52} - 6 q^{54} + 3 q^{55} - 11 q^{56} - 14 q^{57} + 22 q^{59} - 6 q^{60} + 16 q^{61} - 5 q^{62} + 22 q^{63} - 6 q^{64} - 3 q^{65} - 6 q^{66} - 19 q^{67} - 9 q^{68} - 10 q^{69} - 3 q^{70} - 45 q^{71} + 3 q^{72} + 11 q^{73} - 35 q^{74} + 3 q^{75} + 6 q^{76} - 50 q^{77} + 6 q^{78} + 36 q^{79} + 3 q^{80} + 3 q^{81} - 20 q^{82} - 4 q^{83} + 9 q^{84} - 12 q^{85} + 22 q^{86} - 15 q^{87} - 2 q^{88} - 7 q^{89} + 3 q^{90} - 32 q^{91} + 10 q^{92} + 7 q^{93} + 54 q^{94} - 2 q^{95} + 3 q^{96} + 11 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 6 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^18 + q^19 + 3 * q^20 + 4 * q^21 + 3 * q^22 + 5 * q^23 + 3 * q^24 - 12 * q^25 - 3 * q^26 - 6 * q^27 + 4 * q^28 - 15 * q^29 + 24 * q^30 + 15 * q^31 + 24 * q^32 + 4 * q^33 - 9 * q^34 - 3 * q^35 - 12 * q^36 + 6 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 - 6 * q^42 - 13 * q^43 - 2 * q^44 + 3 * q^45 - 10 * q^46 + 4 * q^47 + 3 * q^48 + 3 * q^50 - 9 * q^51 - 3 * q^52 - 6 * q^54 + 3 * q^55 - 11 * q^56 - 14 * q^57 + 22 * q^59 - 6 * q^60 + 16 * q^61 - 5 * q^62 + 22 * q^63 - 6 * q^64 - 3 * q^65 - 6 * q^66 - 19 * q^67 - 9 * q^68 - 10 * q^69 - 3 * q^70 - 45 * q^71 + 3 * q^72 + 11 * q^73 - 35 * q^74 + 3 * q^75 + 6 * q^76 - 50 * q^77 + 6 * q^78 + 36 * q^79 + 3 * q^80 + 3 * q^81 - 20 * q^82 - 4 * q^83 + 9 * q^84 - 12 * q^85 + 22 * q^86 - 15 * q^87 - 2 * q^88 - 7 * q^89 + 3 * q^90 - 32 * q^91 + 10 * q^92 + 7 * q^93 + 54 * q^94 - 2 * q^95 + 3 * q^96 + 11 * q^97 - 15 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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