LMFDB - Embedded newform 1380.2.p.a.91.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(91,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))

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

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

chi := DirichletCharacter("1380.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.p (of order $2$, degree $1$, 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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.6
Character	$\chi$	$=$	1380.91
Dual form			1380.2.p.a.91.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32949 + 0.482147i) q^{2} -1.00000i q^{3} +(1.53507 - 1.28202i) q^{4} -1.00000i q^{5} +(0.482147 + 1.32949i) q^{6} -4.27008 q^{7} +(-1.42273 + 2.44455i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.32949 + 0.482147i) q^{2} -1.00000i q^{3} +(1.53507 - 1.28202i) q^{4} -1.00000i q^{5} +(0.482147 + 1.32949i) q^{6} -4.27008 q^{7} +(-1.42273 + 2.44455i) q^{8} -1.00000 q^{9} +(0.482147 + 1.32949i) q^{10} -6.33992 q^{11} +(-1.28202 - 1.53507i) q^{12} +5.06818 q^{13} +(5.67701 - 2.05880i) q^{14} -1.00000 q^{15} +(0.712870 - 3.93596i) q^{16} -2.28607i q^{17} +(1.32949 - 0.482147i) q^{18} -2.14696 q^{19} +(-1.28202 - 1.53507i) q^{20} +4.27008i q^{21} +(8.42884 - 3.05678i) q^{22} +(4.21933 - 2.27976i) q^{23} +(2.44455 + 1.42273i) q^{24} -1.00000 q^{25} +(-6.73807 + 2.44361i) q^{26} +1.00000i q^{27} +(-6.55486 + 5.47430i) q^{28} -0.184440 q^{29} +(1.32949 - 0.482147i) q^{30} +6.08631i q^{31} +(0.949963 + 5.57652i) q^{32} +6.33992i q^{33} +(1.10222 + 3.03930i) q^{34} +4.27008i q^{35} +(-1.53507 + 1.28202i) q^{36} -0.639401i q^{37} +(2.85435 - 1.03515i) q^{38} -5.06818i q^{39} +(2.44455 + 1.42273i) q^{40} -9.20080 q^{41} +(-2.05880 - 5.67701i) q^{42} +5.56828 q^{43} +(-9.73221 + 8.12788i) q^{44} +1.00000i q^{45} +(-4.51036 + 5.06524i) q^{46} +13.4174i q^{47} +(-3.93596 - 0.712870i) q^{48} +11.2335 q^{49} +(1.32949 - 0.482147i) q^{50} -2.28607 q^{51} +(7.78000 - 6.49748i) q^{52} -1.68353i q^{53} +(-0.482147 - 1.32949i) q^{54} +6.33992i q^{55} +(6.07517 - 10.4384i) q^{56} +2.14696i q^{57} +(0.245211 - 0.0889274i) q^{58} +6.99605i q^{59} +(-1.53507 + 1.28202i) q^{60} +10.7249i q^{61} +(-2.93450 - 8.09167i) q^{62} +4.27008 q^{63} +(-3.95167 - 6.95589i) q^{64} -5.06818i q^{65} +(-3.05678 - 8.42884i) q^{66} +11.6198 q^{67} +(-2.93078 - 3.50928i) q^{68} +(-2.27976 - 4.21933i) q^{69} +(-2.05880 - 5.67701i) q^{70} -14.8246i q^{71} +(1.42273 - 2.44455i) q^{72} +4.06642 q^{73} +(0.308285 + 0.850075i) q^{74} +1.00000i q^{75} +(-3.29573 + 2.75244i) q^{76} +27.0719 q^{77} +(2.44361 + 6.73807i) q^{78} +3.65467 q^{79} +(-3.93596 - 0.712870i) q^{80} +1.00000 q^{81} +(12.2323 - 4.43614i) q^{82} +1.98859 q^{83} +(5.47430 + 6.55486i) q^{84} -2.28607 q^{85} +(-7.40296 + 2.68473i) q^{86} +0.184440i q^{87} +(9.02001 - 15.4983i) q^{88} +13.1874i q^{89} +(-0.482147 - 1.32949i) q^{90} -21.6415 q^{91} +(3.55427 - 8.90883i) q^{92} +6.08631 q^{93} +(-6.46916 - 17.8382i) q^{94} +2.14696i q^{95} +(5.57652 - 0.949963i) q^{96} -8.73755i q^{97} +(-14.9348 + 5.41622i) q^{98} +6.33992 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} - 2 q^{10} + 20 q^{14} - 48 q^{15} - 6 q^{16} + 4 q^{18} + 16 q^{19} + 28 q^{22} + 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} + 4 q^{30} + 16 q^{32} - 28 q^{34} + 2 q^{36} + 2 q^{40} - 8 q^{41} + 14 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} + 16 q^{51} - 16 q^{52} + 2 q^{54} + 40 q^{56} - 8 q^{58} + 2 q^{60} + 24 q^{62} - 26 q^{64} - 48 q^{67} - 44 q^{68} - 8 q^{69} + 4 q^{72} + 20 q^{74} - 64 q^{76} + 32 q^{77} - 64 q^{79} + 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} - 40 q^{86} + 2 q^{90} - 4 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 - 2 * q^10 + 20 * q^14 - 48 * q^15 - 6 * q^16 + 4 * q^18 + 16 * q^19 + 28 * q^22 + 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 + 4 * q^30 + 16 * q^32 - 28 * q^34 + 2 * q^36 + 2 * q^40 - 8 * q^41 + 14 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 + 16 * q^51 - 16 * q^52 + 2 * q^54 + 40 * q^56 - 8 * q^58 + 2 * q^60 + 24 * q^62 - 26 * q^64 - 48 * q^67 - 44 * q^68 - 8 * q^69 + 4 * q^72 + 20 * q^74 - 64 * q^76 + 32 * q^77 - 64 * q^79 + 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 - 40 * q^86 + 2 * q^90 - 4 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.32949	+	0.482147i	−0.940089	+	0.340929i
$2$	−1.32949	+	0.482147i	−0.940089	+	0.340929i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.53507	−	1.28202i	0.767534	−	0.641008i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.482147	+	1.32949i	0.196836	+	0.542761i
$7$	−4.27008			−1.61394			−0.806968	−	0.590595i	$-0.798893\pi$
$7$	−4.27008			−1.61394			−0.806968	+	0.590595i	$0.798893\pi$
$8$	−1.42273	+	2.44455i	−0.503012	+	0.864280i
$9$	−1.00000			−0.333333
$10$	0.482147	+	1.32949i	0.152468	+	0.420421i
$11$	−6.33992			−1.91156			−0.955779	−	0.294085i	$-0.904985\pi$
$11$	−6.33992			−1.91156			−0.955779	+	0.294085i	$0.904985\pi$
$12$	−1.28202	−	1.53507i	−0.370086	−	0.443136i
$13$	5.06818			1.40566			0.702829	−	0.711358i	$-0.251920\pi$
$13$	5.06818			1.40566			0.702829	+	0.711358i	$0.251920\pi$
$14$	5.67701	−	2.05880i	1.51724	−	0.550239i
$15$	−1.00000			−0.258199
$16$	0.712870	−	3.93596i	0.178217	−	0.983991i
$17$		−	2.28607i		−	0.554454i	−0.960804	−	0.277227i	$-0.910585\pi$
$17$		−	2.28607i		−	0.554454i	0.960804	−	0.277227i	$-0.0894153\pi$
$18$	1.32949	−	0.482147i	0.313363	−	0.113643i
$19$	−2.14696			−0.492546			−0.246273	−	0.969200i	$-0.579206\pi$
$19$	−2.14696			−0.492546			−0.246273	+	0.969200i	$0.579206\pi$
$20$	−1.28202	−	1.53507i	−0.286667	−	0.343252i
$21$			4.27008i			0.931807i
$22$	8.42884	−	3.05678i	1.79704	−	0.651707i
$23$	4.21933	−	2.27976i	0.879790	−	0.475362i
$23$	4.21933	−	2.27976i	0.879790	−	0.475362i
$24$	2.44455	+	1.42273i	0.498992	+	0.290414i
$25$	−1.00000			−0.200000
$26$	−6.73807	+	2.44361i	−1.32144	+	0.479231i
$27$			1.00000i			0.192450i
$28$	−6.55486	+	5.47430i	−1.23875	+	1.03455i
$29$	−0.184440			−0.0342497			−0.0171249	−	0.999853i	$-0.505451\pi$
$29$	−0.184440			−0.0342497			−0.0171249	+	0.999853i	$0.505451\pi$
$30$	1.32949	−	0.482147i	0.242730	−	0.0880276i
$31$			6.08631i			1.09313i	0.837415	+	0.546567i	$0.184066\pi$
$31$			6.08631i			1.09313i	−0.837415	+	0.546567i	$0.815934\pi$
$32$	0.949963	+	5.57652i	0.167931	+	0.985799i
$33$			6.33992i			1.10364i
$34$	1.10222	+	3.03930i	0.189030	+	0.521236i
$35$			4.27008i			0.721774i
$36$	−1.53507	+	1.28202i	−0.255845	+	0.213669i
$37$		−	0.639401i		−	0.105117i	−0.998618	−	0.0525584i	$-0.983262\pi$
$37$		−	0.639401i		−	0.105117i	0.998618	−	0.0525584i	$-0.0167376\pi$
$38$	2.85435	−	1.03515i	0.463037	−	0.167924i
$39$		−	5.06818i		−	0.811558i
$40$	2.44455	+	1.42273i	0.386518	+	0.224954i
$41$	−9.20080			−1.43692			−0.718462	−	0.695566i	$-0.755154\pi$
$41$	−9.20080			−1.43692			−0.718462	+	0.695566i	$0.755154\pi$
$42$	−2.05880	−	5.67701i	−0.317680	−	0.875981i
$43$	5.56828			0.849155			0.424578	−	0.905392i	$-0.360423\pi$
$43$	5.56828			0.849155			0.424578	+	0.905392i	$0.360423\pi$
$44$	−9.73221	+	8.12788i	−1.46719	+	1.22532i
$45$			1.00000i			0.149071i
$46$	−4.51036	+	5.06524i	−0.665016	+	0.746829i
$47$			13.4174i			1.95713i	0.205942	+	0.978564i	$0.433974\pi$
$47$			13.4174i			1.95713i	−0.205942	+	0.978564i	$0.566026\pi$
$48$	−3.93596	−	0.712870i	−0.568108	−	0.102894i
$49$	11.2335			1.60479
$50$	1.32949	−	0.482147i	0.188018	−	0.0681859i
$51$	−2.28607			−0.320114
$52$	7.78000	−	6.49748i	1.07889	−	0.901039i
$53$		−	1.68353i		−	0.231251i	−0.993293	−	0.115626i	$-0.963113\pi$
$53$		−	1.68353i		−	0.231251i	0.993293	−	0.115626i	$-0.0368873\pi$
$54$	−0.482147	−	1.32949i	−0.0656119	−	0.180920i
$55$			6.33992i			0.854875i
$56$	6.07517	−	10.4384i	0.811829	−	1.39489i
$57$			2.14696i			0.284372i
$58$	0.245211	−	0.0889274i	0.0321978	−	0.0116767i
$59$			6.99605i			0.910808i	0.890285	+	0.455404i	$0.150505\pi$
$59$			6.99605i			0.910808i	−0.890285	+	0.455404i	$0.849495\pi$
$60$	−1.53507	+	1.28202i	−0.198176	+	0.165508i
$61$			10.7249i			1.37319i	0.727041	+	0.686594i	$0.240895\pi$
$61$			10.7249i			1.37319i	−0.727041	+	0.686594i	$0.759105\pi$
$62$	−2.93450	−	8.09167i	−0.372682	−	1.02764i
$63$	4.27008			0.537979
$64$	−3.95167	−	6.95589i	−0.493958	−	0.869486i
$65$		−	5.06818i		−	0.628630i
$66$	−3.05678	−	8.42884i	−0.376263	−	1.03752i
$67$	11.6198			1.41959			0.709795	−	0.704409i	$-0.248788\pi$
$67$	11.6198			1.41959			0.709795	+	0.704409i	$0.248788\pi$
$68$	−2.93078	−	3.50928i	−0.355409	−	0.425562i
$69$	−2.27976	−	4.21933i	−0.274450	−	0.507947i
$70$	−2.05880	−	5.67701i	−0.246074	−	0.678532i
$71$		−	14.8246i		−	1.75936i	−0.475569	−	0.879678i	$-0.657758\pi$
$71$		−	14.8246i		−	1.75936i	0.475569	−	0.879678i	$-0.342242\pi$
$72$	1.42273	−	2.44455i	0.167671	−	0.288093i
$73$	4.06642			0.475938			0.237969	−	0.971273i	$-0.423518\pi$
$73$	4.06642			0.475938			0.237969	+	0.971273i	$0.423518\pi$
$74$	0.308285	+	0.850075i	0.0358374	+	0.0988192i
$75$			1.00000i			0.115470i
$76$	−3.29573	+	2.75244i	−0.378046	+	0.315726i
$77$	27.0719			3.08513
$78$	2.44361	+	6.73807i	0.276684	+	0.762936i
$79$	3.65467			0.411182			0.205591	−	0.978638i	$-0.434088\pi$
$79$	3.65467			0.411182			0.205591	+	0.978638i	$0.434088\pi$
$80$	−3.93596	−	0.712870i	−0.440054	−	0.0797013i
$81$	1.00000			0.111111
$82$	12.2323	−	4.43614i	1.35084	−	0.489890i
$83$	1.98859			0.218276			0.109138	−	0.994027i	$-0.465191\pi$
$83$	1.98859			0.218276			0.109138	+	0.994027i	$0.465191\pi$
$84$	5.47430	+	6.55486i	0.597296	+	0.715194i
$85$	−2.28607			−0.247959
$86$	−7.40296	+	2.68473i	−0.798281	+	0.289502i
$87$			0.184440i			0.0197741i
$88$	9.02001	−	15.4983i	0.961537	−	1.65212i
$89$			13.1874i			1.39786i	0.715191	+	0.698930i	$0.246340\pi$
$89$			13.1874i			1.39786i	−0.715191	+	0.698930i	$0.753660\pi$
$90$	−0.482147	−	1.32949i	−0.0508228	−	0.140140i
$91$	−21.6415			−2.26864
$92$	3.55427	−	8.90883i	0.370558	−	0.928809i
$93$	6.08631			0.631121
$94$	−6.46916	−	17.8382i	−0.667243	−	1.83987i
$95$			2.14696i			0.220273i
$96$	5.57652	−	0.949963i	0.569151	−	0.0969552i
$97$		−	8.73755i		−	0.887164i	−0.896234	−	0.443582i	$-0.853707\pi$
$97$		−	8.73755i		−	0.887164i	0.896234	−	0.443582i	$-0.146293\pi$
$98$	−14.9348	+	5.41622i	−1.50865	+	0.547121i
$99$	6.33992			0.637186
$100$	−1.53507	+	1.28202i	−0.153507	+	0.128202i
$101$	−1.23440			−0.122827			−0.0614135	−	0.998112i	$-0.519561\pi$
$101$	−1.23440			−0.122827			−0.0614135	+	0.998112i	$0.519561\pi$
$102$	3.03930	−	1.10222i	0.300936	−	0.109136i
$103$	5.53812			0.545687			0.272844	−	0.962058i	$-0.412036\pi$
$103$	5.53812			0.545687			0.272844	+	0.962058i	$0.412036\pi$
$104$	−7.21066	+	12.3894i	−0.707063	+	1.21488i
$105$	4.27008			0.416717
$106$	0.811711	+	2.23824i	0.0788403	+	0.217397i
$107$	−8.82985			−0.853614			−0.426807	−	0.904343i	$-0.640362\pi$
$107$	−8.82985			−0.853614			−0.426807	+	0.904343i	$0.640362\pi$
$108$	1.28202	+	1.53507i	0.123362	+	0.147712i
$109$			13.7436i			1.31640i	0.752843	+	0.658200i	$0.228682\pi$
$109$			13.7436i			1.31640i	−0.752843	+	0.658200i	$0.771318\pi$
$110$	−3.05678	−	8.42884i	−0.291452	−	0.803658i
$111$	−0.639401			−0.0606892
$112$	−3.04401	+	16.8069i	−0.287632	+	1.58810i
$113$			9.28660i			0.873610i	0.899556	+	0.436805i	$0.143890\pi$
$113$			9.28660i			0.873610i	−0.899556	+	0.436805i	$0.856110\pi$
$114$	−1.03515	−	2.85435i	−0.0969507	−	0.267335i
$115$	−2.27976	−	4.21933i	−0.212588	−	0.393454i
$116$	−0.283129	+	0.236456i	−0.0262878	+	0.0219543i
$117$	−5.06818			−0.468553
$118$	−3.37312	−	9.30115i	−0.310521	−	0.856240i
$119$			9.76170i			0.894853i
$120$	1.42273	−	2.44455i	0.129877	−	0.223156i
$121$	29.1946			2.65406
$122$	−5.17100	−	14.2587i	−0.468161	−	1.29092i
$123$			9.20080i			0.829609i
$124$	7.80275	+	9.34291i	0.700708	+	0.839018i
$125$			1.00000i			0.0894427i
$126$	−5.67701	+	2.05880i	−0.505748	+	0.183413i
$127$			1.34406i			0.119266i	0.998220	+	0.0596328i	$0.0189930\pi$
$127$			1.34406i			0.119266i	−0.998220	+	0.0596328i	$0.981007\pi$
$128$	8.60745	+	7.34247i	0.760798	+	0.648989i
$129$		−	5.56828i		−	0.490260i
$130$	2.44361	+	6.73807i	0.214318	+	0.590968i
$131$		−	4.08505i		−	0.356913i	−0.983948	−	0.178456i	$-0.942890\pi$
$131$		−	4.08505i		−	0.356913i	0.983948	−	0.178456i	$-0.0571103\pi$
$132$	8.12788	+	9.73221i	0.707441	+	0.847081i
$133$	9.16768			0.794939
$134$	−15.4484	+	5.60247i	−1.33454	+	0.483980i
$135$	1.00000			0.0860663
$136$	5.58842	+	3.25247i	0.479203	+	0.278897i
$137$			4.20683i			0.359413i	0.983720	+	0.179707i	$0.0575149\pi$
$137$			4.20683i			0.359413i	−0.983720	+	0.179707i	$0.942485\pi$
$138$	5.06524	+	4.51036i	0.431182	+	0.383947i
$139$			3.26694i			0.277098i	0.990356	+	0.138549i	$0.0442439\pi$
$139$			3.26694i			0.277098i	−0.990356	+	0.138549i	$0.955756\pi$
$140$	5.47430	+	6.55486i	0.462663	+	0.553987i
$141$	13.4174			1.12995
$142$	7.14764	+	19.7091i	0.599817	+	1.65395i
$143$	−32.1318			−2.68700
$144$	−0.712870	+	3.93596i	−0.0594058	+	0.327997i
$145$			0.184440i			0.0153169i
$146$	−5.40625	+	1.96061i	−0.447424	+	0.162261i
$147$		−	11.2335i		−	0.926527i
$148$	−0.819722	−	0.981524i	−0.0673807	−	0.0806808i
$149$		−	4.04197i		−	0.331131i	−0.986199	−	0.165566i	$-0.947055\pi$
$149$		−	4.04197i		−	0.331131i	0.986199	−	0.165566i	$-0.0529450\pi$
$150$	−0.482147	−	1.32949i	−0.0393671	−	0.108552i
$151$		−	13.1086i		−	1.06676i	−0.845874	−	0.533382i	$-0.820921\pi$
$151$		−	13.1086i		−	1.06676i	0.845874	−	0.533382i	$-0.179079\pi$
$152$	3.05455	−	5.24835i	0.247757	−	0.425698i
$153$			2.28607i			0.184818i
$154$	−35.9918	+	13.0527i	−2.90030	+	1.05181i
$155$	6.08631			0.488864
$156$	−6.49748	−	7.78000i	−0.520215	−	0.622898i
$157$		−	5.45303i		−	0.435200i	−0.976038	−	0.217600i	$-0.930177\pi$
$157$		−	5.45303i		−	0.435200i	0.976038	−	0.217600i	$-0.0698228\pi$
$158$	−4.85883	+	1.76209i	−0.386548	+	0.140184i
$159$	−1.68353			−0.133513
$160$	5.57652	−	0.949963i	0.440863	−	0.0751012i
$161$	−18.0168	+	9.73473i	−1.41993	+	0.767204i
$162$	−1.32949	+	0.482147i	−0.104454	+	0.0378811i
$163$			11.4235i			0.894754i	0.894345	+	0.447377i	$0.147642\pi$
$163$			11.4235i			0.894754i	−0.894345	+	0.447377i	$0.852358\pi$
$164$	−14.1239	+	11.7956i	−1.10289	+	0.921080i
$165$	6.33992			0.493562
$166$	−2.64380	+	0.958792i	−0.205199	+	0.0744167i
$167$			20.6429i			1.59739i	0.601734	+	0.798697i	$0.294477\pi$
$167$			20.6429i			1.59739i	−0.601734	+	0.798697i	$0.705523\pi$
$168$	−10.4384	−	6.07517i	−0.805342	−	0.468710i
$169$	12.6864			0.975877
$170$	3.03930	−	1.10222i	0.233104	−	0.0845366i
$171$	2.14696			0.164182
$172$	8.54769	−	7.13863i	0.651756	−	0.544315i
$173$	−5.69694			−0.433131			−0.216565	−	0.976268i	$-0.569485\pi$
$173$	−5.69694			−0.433131			−0.216565	+	0.976268i	$0.569485\pi$
$174$	−0.0889274	−	0.245211i	−0.00674157	−	0.0185894i
$175$	4.27008			0.322787
$176$	−4.51954	+	24.9537i	−0.340673	+	1.88096i
$177$	6.99605			0.525855
$178$	−6.35825	−	17.5324i	−0.476571	−	1.31411i
$179$			4.11047i			0.307231i	0.988131	+	0.153615i	$0.0490917\pi$
$179$			4.11047i			0.307231i	−0.988131	+	0.153615i	$0.950908\pi$
$180$	1.28202	+	1.53507i	0.0955558	+	0.114417i
$181$			11.3771i			0.845655i	0.906210	+	0.422827i	$0.138962\pi$
$181$			11.3771i			0.845655i	−0.906210	+	0.422827i	$0.861038\pi$
$182$	28.7721	−	10.4344i	2.13273	−	0.773448i
$183$	10.7249			0.792811
$184$	−0.429988	+	13.5578i	−0.0316991	+	0.999497i
$185$	−0.639401			−0.0470097
$186$	−8.09167	+	2.93450i	−0.593310	+	0.215168i
$187$			14.4935i			1.05987i
$188$	17.2013	+	20.5966i	1.25454	+	1.50216i
$189$		−	4.27008i		−	0.310602i
$190$	−1.03515	−	2.85435i	−0.0750977	−	0.207077i
$191$	−6.76632			−0.489593			−0.244797	−	0.969574i	$-0.578721\pi$
$191$	−6.76632			−0.489593			−0.244797	+	0.969574i	$0.578721\pi$
$192$	−6.95589	+	3.95167i	−0.501998	+	0.285187i
$193$	−22.6747			−1.63216			−0.816079	−	0.577941i	$-0.803857\pi$
$193$	−22.6747			−1.63216			−0.816079	+	0.577941i	$0.803857\pi$
$194$	4.21279	+	11.6165i	0.302460	+	0.834013i
$195$	−5.06818			−0.362940
$196$	17.2443	−	14.4016i	1.23173	−	1.02868i
$197$	−18.6303			−1.32735			−0.663677	−	0.748019i	$-0.731005\pi$
$197$	−18.6303			−1.32735			−0.663677	+	0.748019i	$0.731005\pi$
$198$	−8.42884	+	3.05678i	−0.599012	+	0.217236i
$199$	−8.02404			−0.568809			−0.284405	−	0.958704i	$-0.591796\pi$
$199$	−8.02404			−0.568809			−0.284405	+	0.958704i	$0.591796\pi$
$200$	1.42273	−	2.44455i	0.100602	−	0.172856i
$201$		−	11.6198i		−	0.819600i
$202$	1.64111	−	0.595160i	0.115468	−	0.0418753i
$203$	0.787574			0.0552769
$204$	−3.50928	+	2.93078i	−0.245698	+	0.205196i
$205$			9.20080i			0.642612i
$206$	−7.36286	+	2.67019i	−0.512994	+	0.186041i
$207$	−4.21933	+	2.27976i	−0.293263	+	0.158454i
$208$	3.61295	−	19.9482i	0.250513	−	1.38316i
$209$	13.6116			0.941531
$210$	−5.67701	+	2.05880i	−0.391751	+	0.142071i
$211$			19.6771i			1.35463i	0.735694	+	0.677314i	$0.236856\pi$
$211$			19.6771i			1.35463i	−0.735694	+	0.677314i	$0.763144\pi$
$212$	−2.15832	−	2.58434i	−0.148234	−	0.177493i
$213$	−14.8246			−1.01577
$214$	11.7392	−	4.25729i	0.802473	−	0.291022i
$215$		−	5.56828i		−	0.379754i
$216$	−2.44455	−	1.42273i	−0.166331	−	0.0968047i
$217$		−	25.9890i		−	1.76425i
$218$	−6.62644	−	18.2719i	−0.448799	−	1.23753i
$219$		−	4.06642i		−	0.274783i
$220$	8.12788	+	9.73221i	0.547982	+	0.656146i
$221$		−	11.5862i		−	0.779373i
$222$	0.850075	−	0.308285i	0.0570533	−	0.0206908i
$223$		−	21.7302i		−	1.45516i	−0.686022	−	0.727581i	$-0.740644\pi$
$223$		−	21.7302i		−	1.45516i	0.686022	−	0.727581i	$-0.259356\pi$
$224$	−4.05641	−	23.8122i	−0.271031	−	1.59102i
$225$	1.00000			0.0666667
$226$	−4.47751	−	12.3464i	−0.297839	−	0.821271i
$227$	19.5294			1.29621			0.648106	−	0.761550i	$-0.275562\pi$
$227$	19.5294			1.29621			0.648106	+	0.761550i	$0.275562\pi$
$228$	2.75244	+	3.29573i	0.182285	+	0.218265i
$229$		−	6.03097i		−	0.398538i	−0.979945	−	0.199269i	$-0.936143\pi$
$229$		−	6.03097i		−	0.398538i	0.979945	−	0.199269i	$-0.0638567\pi$
$230$	5.06524	+	4.51036i	0.333992	+	0.297404i
$231$		−	27.0719i		−	1.78120i
$232$	0.262409	−	0.450874i	0.0172280	−	0.0296013i
$233$	15.5780			1.02055			0.510275	−	0.860011i	$-0.329544\pi$
$233$	15.5780			1.02055			0.510275	+	0.860011i	$0.329544\pi$
$234$	6.73807	−	2.44361i	0.440481	−	0.159744i
$235$	13.4174			0.875254
$236$	8.96904	+	10.7394i	0.583835	+	0.699076i
$237$		−	3.65467i		−	0.237396i
$238$	−4.70657	−	12.9780i	−0.305082	−	0.841241i
$239$		−	29.6232i		−	1.91616i	−0.286496	−	0.958081i	$-0.592491\pi$
$239$		−	29.6232i		−	1.91616i	0.286496	−	0.958081i	$-0.407509\pi$
$240$	−0.712870	+	3.93596i	−0.0460155	+	0.254065i
$241$			1.02822i			0.0662336i	0.999451	+	0.0331168i	$0.0105433\pi$
$241$			1.02822i			0.0662336i	−0.999451	+	0.0331168i	$0.989457\pi$
$242$	−38.8139	+	14.0761i	−2.49505	+	0.904846i
$243$		−	1.00000i		−	0.0641500i
$244$	13.7496	+	16.4635i	0.880225	+	1.05397i
$245$		−	11.2335i		−	0.717685i
$246$	−4.43614	−	12.2323i	−0.282838	−	0.779906i
$247$	−10.8812			−0.692352
$248$	−14.8783	−	8.65919i	−0.944773	−	0.549859i
$249$		−	1.98859i		−	0.126022i
$250$	−0.482147	−	1.32949i	−0.0304937	−	0.0840841i
$251$	−7.72202			−0.487410			−0.243705	−	0.969849i	$-0.578363\pi$
$251$	−7.72202			−0.487410			−0.243705	+	0.969849i	$0.578363\pi$
$252$	6.55486	−	5.47430i	0.412917	−	0.344849i
$253$	−26.7502	+	14.4535i	−1.68177	+	0.908683i
$254$	−0.648033	−	1.78690i	−0.0406612	−	0.112120i
$255$			2.28607i			0.143159i
$256$	−14.9836	−	5.61166i	−0.936477	−	0.350729i
$257$	15.8364			0.987846			0.493923	−	0.869506i	$-0.335563\pi$
$257$	15.8364			0.987846			0.493923	+	0.869506i	$0.335563\pi$
$258$	2.68473	+	7.40296i	0.167144	+	0.460888i
$259$			2.73029i			0.169652i
$260$	−6.49748	−	7.78000i	−0.402957	−	0.482495i
$261$	0.184440			0.0114166
$262$	1.96960	+	5.43102i	0.121682	+	0.335530i
$263$	−18.7282			−1.15483			−0.577414	−	0.816452i	$-0.695938\pi$
$263$	−18.7282			−1.15483			−0.577414	+	0.816452i	$0.695938\pi$
$264$	−15.4983	−	9.02001i	−0.953853	−	0.555143i
$265$	−1.68353			−0.103419
$266$	−12.1883	+	4.42017i	−0.747313	+	0.271018i
$267$	13.1874			0.807054
$268$	17.8372	−	14.8968i	1.08958	−	0.909968i
$269$	−7.39847			−0.451093			−0.225546	−	0.974232i	$-0.572417\pi$
$269$	−7.39847			−0.451093			−0.225546	+	0.974232i	$0.572417\pi$
$270$	−1.32949	+	0.482147i	−0.0809100	+	0.0293425i
$271$			6.22206i			0.377963i	0.981981	+	0.188982i	$0.0605186\pi$
$271$			6.22206i			0.377963i	−0.981981	+	0.188982i	$0.939481\pi$
$272$	−8.99789	−	1.62967i	−0.545577	−	0.0988133i
$273$			21.6415i			1.30980i
$274$	−2.02831	−	5.59292i	−0.122535	−	0.337880i
$275$	6.33992			0.382312
$276$	−8.90883	−	3.55427i	−0.536248	−	0.213942i
$277$	−11.9387			−0.717326			−0.358663	−	0.933467i	$-0.616767\pi$
$277$	−11.9387			−0.717326			−0.358663	+	0.933467i	$0.616767\pi$
$278$	−1.57514	−	4.34335i	−0.0944709	−	0.260497i
$279$		−	6.08631i		−	0.364378i
$280$	−10.4384	−	6.07517i	−0.623815	−	0.363061i
$281$			28.3633i			1.69201i	0.533174	+	0.846006i	$0.320999\pi$
$281$			28.3633i			1.69201i	−0.533174	+	0.846006i	$0.679001\pi$
$282$	−17.8382	+	6.46916i	−1.06225	+	0.385233i
$283$	−11.4358			−0.679788			−0.339894	−	0.940464i	$-0.610391\pi$
$283$	−11.4358			−0.679788			−0.339894	+	0.940464i	$0.610391\pi$
$284$	−19.0054	−	22.7568i	−1.12776	−	1.35037i
$285$	2.14696			0.127175
$286$	42.7188	−	15.4923i	2.52602	−	0.916077i
$287$	39.2881			2.31910
$288$	−0.949963	−	5.57652i	−0.0559771	−	0.328600i
$289$	11.7739			0.692581
$290$	−0.0889274	−	0.245211i	−0.00522200	−	0.0143993i
$291$	−8.73755			−0.512205
$292$	6.24223	−	5.21322i	0.365299	−	0.305080i
$293$			21.5790i			1.26066i	0.776327	+	0.630330i	$0.217080\pi$
$293$			21.5790i			1.26066i	−0.776327	+	0.630330i	$0.782920\pi$
$294$	5.41622	+	14.9348i	0.315880	+	0.871018i
$295$	6.99605			0.407326
$296$	1.56305	+	0.909696i	0.0908504	+	0.0528750i
$297$		−	6.33992i		−	0.367880i
$298$	1.94882	+	5.37375i	0.112892	+	0.311293i
$299$	21.3843	−	11.5542i	1.23668	−	0.668197i
$300$	1.28202	+	1.53507i	0.0740172	+	0.0886272i
$301$	−23.7770			−1.37048
$302$	6.32029	+	17.4277i	0.363692	+	1.00285i
$303$			1.23440i			0.0709142i
$304$	−1.53050	+	8.45036i	−0.0877804	+	0.484661i
$305$	10.7249			0.614109
$306$	−1.10222	−	3.03930i	−0.0630099	−	0.173745i
$307$		−	5.89225i		−	0.336289i	−0.985762	−	0.168144i	$-0.946223\pi$
$307$		−	5.89225i		−	0.336289i	0.985762	−	0.168144i	$-0.0537775\pi$
$308$	41.5573	−	34.7067i	2.36795	−	1.97760i
$309$		−	5.53812i		−	0.315053i
$310$	−8.09167	+	2.93450i	−0.459576	+	0.166668i
$311$		−	10.5498i		−	0.598224i	−0.954218	−	0.299112i	$-0.903310\pi$
$311$		−	10.5498i		−	0.598224i	0.954218	−	0.299112i	$-0.0966905\pi$
$312$	12.3894	+	7.21066i	0.701413	+	0.408223i
$313$			22.2836i			1.25954i	0.776781	+	0.629771i	$0.216851\pi$
$313$			22.2836i			1.25954i	−0.776781	+	0.629771i	$0.783149\pi$
$314$	2.62916	+	7.24974i	0.148372	+	0.409126i
$315$		−	4.27008i		−	0.240591i
$316$	5.61017	−	4.68534i	0.315597	−	0.263571i
$317$	4.20644			0.236257			0.118129	−	0.992998i	$-0.462310\pi$
$317$	4.20644			0.236257			0.118129	+	0.992998i	$0.462310\pi$
$318$	2.23824	−	0.811711i	0.125514	−	0.0455185i
$319$	1.16934			0.0654703
$320$	−6.95589	+	3.95167i	−0.388846	+	0.220905i
$321$			8.82985i			0.492834i
$322$	19.2596	−	21.6290i	1.07329	−	1.20533i
$323$			4.90810i			0.273094i
$324$	1.53507	−	1.28202i	0.0852816	−	0.0712231i
$325$	−5.06818			−0.281132
$326$	−5.50779	−	15.1873i	−0.305048	−	0.841149i
$327$	13.7436			0.760023
$328$	13.0903	−	22.4918i	0.722790	−	1.24190i
$329$		−	57.2933i		−	3.15868i
$330$	−8.42884	+	3.05678i	−0.463992	+	0.168270i
$331$			16.0620i			0.882847i	0.897299	+	0.441423i	$0.145526\pi$
$331$			16.0620i			0.882847i	−0.897299	+	0.441423i	$0.854474\pi$
$332$	3.05262	−	2.54940i	0.167534	−	0.139917i
$333$			0.639401i			0.0350390i
$334$	−9.95290	−	27.4444i	−0.544598	−	1.50169i
$335$		−	11.6198i		−	0.634860i
$336$	16.8069	+	3.04401i	0.916890	+	0.166064i
$337$		−	3.96429i		−	0.215948i	−0.994154	−	0.107974i	$-0.965564\pi$
$337$		−	3.96429i		−	0.215948i	0.994154	−	0.107974i	$-0.0344364\pi$
$338$	−16.8664	+	6.11671i	−0.917411	+	0.332705i
$339$	9.28660			0.504379
$340$	−3.50928	+	2.93078i	−0.190317	+	0.158944i
$341$		−	38.5868i		−	2.08959i
$342$	−2.85435	+	1.03515i	−0.154346	+	0.0559745i
$343$	−18.0775			−0.976096
$344$	−7.92217	+	13.6120i	−0.427135	+	0.733907i
$345$	−4.21933	+	2.27976i	−0.227161	+	0.122738i
$346$	7.57401	−	2.74677i	0.407181	−	0.147667i
$347$		−	7.81164i		−	0.419351i	−0.977771	−	0.209675i	$-0.932759\pi$
$347$		−	7.81164i		−	0.419351i	0.977771	−	0.209675i	$-0.0672408\pi$
$348$	0.236456	+	0.283129i	0.0126753	+	0.0151773i
$349$	−33.4169			−1.78876			−0.894382	−	0.447305i	$-0.852384\pi$
$349$	−33.4169			−1.78876			−0.894382	+	0.447305i	$0.852384\pi$
$350$	−5.67701	+	2.05880i	−0.303449	+	0.110048i
$351$			5.06818i			0.270519i
$352$	−6.02269	−	35.3547i	−0.321011	−	1.88441i
$353$	−0.0557663			−0.00296814			−0.00148407	−	0.999999i	$-0.500472\pi$
$353$	−0.0557663			−0.00296814			−0.00148407	+	0.999999i	$0.500472\pi$
$354$	−9.30115	+	3.37312i	−0.494350	+	0.179279i
$355$	−14.8246			−0.786808
$356$	16.9064	+	20.2435i	0.896039	+	1.07290i
$357$	9.76170			0.516644
$358$	−1.98185	−	5.46481i	−0.104744	−	0.288824i
$359$	10.1353			0.534923			0.267462	−	0.963569i	$-0.413815\pi$
$359$	10.1353			0.534923			0.267462	+	0.963569i	$0.413815\pi$
$360$	−2.44455	−	1.42273i	−0.128839	−	0.0749846i
$361$	−14.3906			−0.757398
$362$	−5.48545	−	15.1257i	−0.288309	−	0.794991i
$363$		−	29.1946i		−	1.53232i
$364$	−33.2212	+	27.7447i	−1.74126	+	1.45422i
$365$		−	4.06642i		−	0.212846i
$366$	−14.2587	+	5.17100i	−0.745313	+	0.270293i
$367$	−26.4828			−1.38239			−0.691195	−	0.722668i	$-0.742915\pi$
$367$	−26.4828			−1.38239			−0.691195	+	0.722668i	$0.742915\pi$
$368$	−5.96521	−	18.2323i	−0.310958	−	0.950424i
$369$	9.20080			0.478975
$370$	0.850075	−	0.308285i	0.0441933	−	0.0160270i
$371$			7.18881i			0.373225i
$372$	9.34291	−	7.80275i	0.484407	−	0.404554i
$373$			22.9313i			1.18734i	0.804710	+	0.593668i	$0.202321\pi$
$373$			22.9313i			1.18734i	−0.804710	+	0.593668i	$0.797679\pi$
$374$	−6.98801	−	19.2689i	−0.361341	−	0.996373i
$375$	1.00000			0.0516398
$376$	−32.7995	−	19.0894i	−1.69151	−	0.984459i
$377$	−0.934776			−0.0481434
$378$	2.05880	+	5.67701i	0.105893	+	0.291994i
$379$	−17.6902			−0.908686			−0.454343	−	0.890827i	$-0.650126\pi$
$379$	−17.6902			−0.908686			−0.454343	+	0.890827i	$0.650126\pi$
$380$	2.75244	+	3.29573i	0.141197	+	0.169067i
$381$	1.34406			0.0688581
$382$	8.99572	−	3.26236i	0.460261	−	0.166917i
$383$	34.2904			1.75216			0.876079	−	0.482167i	$-0.160150\pi$
$383$	34.2904			1.75216			0.876079	+	0.482167i	$0.160150\pi$
$384$	7.34247	−	8.60745i	0.374694	−	0.439247i
$385$		−	27.0719i		−	1.37971i
$386$	30.1457	−	10.9325i	1.53437	−	0.556451i
$387$	−5.56828			−0.283052
$388$	−11.2017	−	13.4127i	−0.568679	−	0.680929i
$389$		−	0.380521i		−	0.0192932i	−0.999953	−	0.00964660i	$-0.996929\pi$
$389$		−	0.380521i		−	0.0192932i	0.999953	−	0.00964660i	$-0.00307066\pi$
$390$	6.73807	−	2.44361i	0.341195	−	0.123737i
$391$	−5.21169	−	9.64568i	−0.263566	−	0.487803i
$392$	−15.9823	+	27.4610i	−0.807229	+	1.38699i
$393$	−4.08505			−0.206064
$394$	24.7687	−	8.98254i	1.24783	−	0.452534i
$395$		−	3.65467i		−	0.183886i
$396$	9.73221	−	8.12788i	0.489062	−	0.408441i
$397$	−13.1522			−0.660089			−0.330045	−	0.943965i	$-0.607064\pi$
$397$	−13.1522			−0.660089			−0.330045	+	0.943965i	$0.607064\pi$
$398$	10.6679	−	3.86877i	0.534731	−	0.193924i
$399$		−	9.16768i		−	0.458958i
$400$	−0.712870	+	3.93596i	−0.0356435	+	0.196798i
$401$		−	7.17569i		−	0.358337i	−0.983818	−	0.179169i	$-0.942659\pi$
$401$		−	7.17569i		−	0.358337i	0.983818	−	0.179169i	$-0.0573407\pi$
$402$	5.60247	+	15.4484i	0.279426	+	0.770497i
$403$			30.8465i			1.53657i
$404$	−1.89488	+	1.58252i	−0.0942739	+	0.0787331i
$405$		−	1.00000i		−	0.0496904i
$406$	−1.04707	+	0.379727i	−0.0519652	+	0.0188455i
$407$			4.05375i			0.200937i
$408$	3.25247	−	5.58842i	0.161021	−	0.276668i
$409$	0.900619			0.0445327			0.0222664	−	0.999752i	$-0.492912\pi$
$409$	0.900619			0.0445327			0.0222664	+	0.999752i	$0.492912\pi$
$410$	−4.43614	−	12.2323i	−0.219085	−	0.604112i
$411$	4.20683			0.207507
$412$	8.50139	−	7.09996i	0.418834	−	0.349790i
$413$		−	29.8736i		−	1.46999i
$414$	4.51036	−	5.06524i	0.221672	−	0.248943i
$415$		−	1.98859i		−	0.0976160i
$416$	4.81458	+	28.2628i	0.236054	+	1.38570i
$417$	3.26694			0.159983
$418$	−18.0964	+	6.56277i	−0.885123	+	0.320996i
$419$	3.26664			0.159586			0.0797929	−	0.996811i	$-0.474574\pi$
$419$	3.26664			0.159586			0.0797929	+	0.996811i	$0.474574\pi$
$420$	6.55486	−	5.47430i	0.319844	−	0.267119i
$421$		−	4.17945i		−	0.203694i	−0.994800	−	0.101847i	$-0.967525\pi$
$421$		−	4.17945i		−	0.203694i	0.994800	−	0.101847i	$-0.0324752\pi$
$422$	−9.48726	−	26.1604i	−0.461833	−	1.27347i
$423$		−	13.4174i		−	0.652376i
$424$	4.11548	+	2.39522i	0.199866	+	0.116322i
$425$			2.28607i			0.110891i
$426$	19.7091	−	7.14764i	0.954909	−	0.346304i
$427$		−	45.7963i		−	2.21624i
$428$	−13.5544	+	11.3200i	−0.655178	+	0.547173i
$429$			32.1318i			1.55134i
$430$	2.68473	+	7.40296i	0.129469	+	0.357002i
$431$	17.2005			0.828520			0.414260	−	0.910159i	$-0.364040\pi$
$431$	17.2005			0.828520			0.414260	+	0.910159i	$0.364040\pi$
$432$	3.93596	+	0.712870i	0.189369	+	0.0342980i
$433$		−	16.2997i		−	0.783313i	−0.920111	−	0.391657i	$-0.871902\pi$
$433$		−	16.2997i		−	0.783313i	0.920111	−	0.391657i	$-0.128098\pi$
$434$	12.5305	+	34.5520i	0.601485	+	1.65855i
$435$	0.184440			0.00884324
$436$	17.6195	+	21.0974i	0.843822	+	1.01038i
$437$	−9.05872	+	4.89455i	−0.433337	+	0.234138i
$438$	1.96061	+	5.40625i	0.0936817	+	0.258321i
$439$			6.44669i			0.307684i	0.988095	+	0.153842i	$0.0491647\pi$
$439$			6.44669i			0.307684i	−0.988095	+	0.153842i	$0.950835\pi$
$440$	−15.4983	−	9.02001i	−0.738851	−	0.430012i
$441$	−11.2335			−0.534931
$442$	5.58626	+	15.4037i	0.265711	+	0.732680i
$443$		−	21.1812i		−	1.00635i	−0.864185	−	0.503175i	$-0.832165\pi$
$443$		−	21.1812i		−	1.00635i	0.864185	−	0.503175i	$-0.167835\pi$
$444$	−0.981524	+	0.819722i	−0.0465811	+	0.0389023i
$445$	13.1874			0.625142
$446$	10.4772	+	28.8900i	0.496108	+	1.36798i
$447$	−4.04197			−0.191179
$448$	16.8739	+	29.7022i	0.797217	+	1.40329i
$449$	−10.8884			−0.513855			−0.256927	−	0.966431i	$-0.582710\pi$
$449$	−10.8884			−0.513855			−0.256927	+	0.966431i	$0.582710\pi$
$450$	−1.32949	+	0.482147i	−0.0626726	+	0.0227286i
$451$	58.3324			2.74676
$452$	11.9056	+	14.2556i	0.559991	+	0.670526i
$453$	−13.1086			−0.615897
$454$	−25.9641	+	9.41604i	−1.21855	+	0.441917i
$455$			21.6415i			1.01457i
$456$	−5.24835	−	3.05455i	−0.245777	−	0.143042i
$457$			19.9654i			0.933942i	0.884273	+	0.466971i	$0.154655\pi$
$457$			19.9654i			0.933942i	−0.884273	+	0.466971i	$0.845345\pi$
$458$	2.90782	+	8.01810i	0.135873	+	0.374661i
$459$	2.28607			0.106705
$460$	−8.90883	−	3.55427i	−0.415376	−	0.165719i
$461$	−23.0529			−1.07368			−0.536840	−	0.843684i	$-0.680382\pi$
$461$	−23.0529			−1.07368			−0.536840	+	0.843684i	$0.680382\pi$
$462$	13.0527	+	35.9918i	0.607265	+	1.67449i
$463$			31.1058i			1.44561i	0.691053	+	0.722804i	$0.257147\pi$
$463$			31.1058i			1.44561i	−0.691053	+	0.722804i	$0.742853\pi$
$464$	−0.131482	+	0.725951i	−0.00610390	+	0.0337014i
$465$		−	6.08631i		−	0.282246i
$466$	−20.7108	+	7.51090i	−0.959408	+	0.347936i
$467$	35.4360			1.63978			0.819891	−	0.572520i	$-0.194034\pi$
$467$	35.4360			1.63978			0.819891	+	0.572520i	$0.194034\pi$
$468$	−7.78000	+	6.49748i	−0.359630	+	0.300346i
$469$	−49.6176			−2.29113
$470$	−17.8382	+	6.46916i	−0.822817	+	0.298400i
$471$	−5.45303			−0.251263
$472$	−17.1022	−	9.95350i	−0.787192	−	0.458147i
$473$	−35.3025			−1.62321
$474$	1.76209	+	4.85883i	0.0809354	+	0.223174i
$475$	2.14696			0.0985093
$476$	12.5146	+	14.9849i	0.573608	+	0.686830i
$477$			1.68353i			0.0770837i
$478$	14.2827	+	39.3836i	0.653276	+	1.80136i
$479$	−29.2482			−1.33638			−0.668192	−	0.743989i	$-0.732932\pi$
$479$	−29.2482			−1.33638			−0.668192	+	0.743989i	$0.732932\pi$
$480$	−0.949963	−	5.57652i	−0.0433597	−	0.254532i
$481$		−	3.24060i		−	0.147758i
$482$	−0.495754	−	1.36701i	−0.0225810	−	0.0622655i
$483$	9.73473	+	18.0168i	0.442946	+	0.819795i
$484$	44.8157	−	37.4280i	2.03708	−	1.70127i
$485$	−8.73755			−0.396752
$486$	0.482147	+	1.32949i	0.0218706	+	0.0603067i
$487$		−	13.0759i		−	0.592526i	−0.955106	−	0.296263i	$-0.904260\pi$
$487$		−	13.0759i		−	0.592526i	0.955106	−	0.296263i	$-0.0957405\pi$
$488$	−26.2177	−	15.2587i	−1.18682	−	0.690730i
$489$	11.4235			0.516587
$490$	5.41622	+	14.9348i	0.244680	+	0.674687i
$491$			16.4461i			0.742203i	0.928592	+	0.371102i	$0.121020\pi$
$491$			16.4461i			0.742203i	−0.928592	+	0.371102i	$0.878980\pi$
$492$	11.7956	+	14.1239i	0.531786	+	0.636753i
$493$			0.421644i			0.0189899i
$494$	14.4664	−	5.24632i	0.650873	−	0.236043i
$495$		−	6.33992i		−	0.284958i
$496$	23.9555	+	4.33875i	1.07563	+	0.194816i
$497$			63.3022i			2.83949i
$498$	0.958792	+	2.64380i	0.0429645	+	0.118472i
$499$			33.1788i			1.48529i	0.669686	+	0.742644i	$0.266429\pi$
$499$			33.1788i			1.48529i	−0.669686	+	0.742644i	$0.733571\pi$
$500$	1.28202	+	1.53507i	0.0573335	+	0.0686503i
$501$	20.6429			0.922255
$502$	10.2663	−	3.72315i	0.458209	−	0.166172i
$503$	−5.75291			−0.256510			−0.128255	−	0.991741i	$-0.540938\pi$
$503$	−5.75291			−0.256510			−0.128255	+	0.991741i	$0.540938\pi$
$504$	−6.07517	+	10.4384i	−0.270610	+	0.464964i
$505$			1.23440i			0.0549299i
$506$	28.5953	−	32.1132i	1.27122	−	1.42761i
$507$		−	12.6864i		−	0.563423i
$508$	1.72310	+	2.06322i	0.0764503	+	0.0915405i
$509$	33.4402			1.48221			0.741105	−	0.671389i	$-0.234302\pi$
$509$	33.4402			1.48221			0.741105	+	0.671389i	$0.234302\pi$
$510$	−1.10222	−	3.03930i	−0.0488072	−	0.134582i
$511$	−17.3639			−0.768134
$512$	22.6262	+	0.236311i	0.999945	+	0.0104436i
$513$		−	2.14696i		−	0.0947906i
$514$	−21.0542	+	7.63546i	−0.928663	+	0.336786i
$515$		−	5.53812i		−	0.244039i
$516$	−7.13863	−	8.54769i	−0.314261	−	0.376291i
$517$		−	85.0653i		−	3.74117i
$518$	−1.31640	−	3.62988i	−0.0578394	−	0.159488i
$519$			5.69694i			0.250068i
$520$	12.3894	+	7.21066i	0.543312	+	0.316208i
$521$			42.6418i			1.86817i	0.357050	+	0.934085i	$0.383783\pi$
$521$			42.6418i			1.86817i	−0.357050	+	0.934085i	$0.616217\pi$
$522$	−0.245211	+	0.0889274i	−0.0107326	+	0.00389225i
$523$	−23.8459			−1.04271			−0.521353	−	0.853341i	$-0.674573\pi$
$523$	−23.8459			−1.04271			−0.521353	+	0.853341i	$0.674573\pi$
$524$	−5.23710	−	6.27083i	−0.228784	−	0.273943i
$525$		−	4.27008i		−	0.186361i
$526$	24.8988	−	9.02972i	1.08564	−	0.393715i
$527$	13.9137			0.606092
$528$	24.9537	+	4.51954i	1.08597	+	0.196688i
$529$	12.6054	−	19.2381i	0.548062	−	0.836438i
$530$	2.23824	−	0.811711i	0.0972227	−	0.0352585i
$531$		−	6.99605i		−	0.303603i
$532$	14.0730	−	11.7531i	0.610143	−	0.509562i
$533$	−46.6313			−2.01983
$534$	−17.5324	+	6.35825i	−0.758703	+	0.275149i
$535$			8.82985i			0.381748i
$536$	−16.5319	+	28.4053i	−0.714070	+	1.22692i
$537$	4.11047			0.177380
$538$	9.83617	−	3.56715i	0.424067	−	0.153791i
$539$	−71.2198			−3.06765
$540$	1.53507	−	1.28202i	0.0660588	−	0.0551692i
$541$	−21.7135			−0.933535			−0.466768	−	0.884380i	$-0.654582\pi$
$541$	−21.7135			−0.933535			−0.466768	+	0.884380i	$0.654582\pi$
$542$	−2.99995	−	8.27214i	−0.128859	−	0.355319i
$543$	11.3771			0.488239
$544$	12.7483	−	2.17168i	0.546580	−	0.0931101i
$545$	13.7436			0.588712
$546$	−10.4344	−	28.7721i	−0.446550	−	1.23133i
$547$		−	0.483696i		−	0.0206813i	−0.999947	−	0.0103407i	$-0.996708\pi$
$547$		−	0.483696i		−	0.0206813i	0.999947	−	0.0103407i	$-0.00329159\pi$
$548$	5.39322	+	6.45776i	0.230387	+	0.275862i
$549$		−	10.7249i		−	0.457730i
$550$	−8.42884	+	3.05678i	−0.359407	+	0.130341i
$551$	0.395986			0.0168696
$552$	13.5578	+	0.429988i	0.577060	+	0.0183015i
$553$	−15.6057			−0.663622
$554$	15.8723	−	5.75620i	0.674350	−	0.244557i
$555$			0.639401i			0.0271411i
$556$	4.18827	+	5.01497i	0.177622	+	0.212682i
$557$		−	44.9485i		−	1.90453i	−0.305272	−	0.952265i	$-0.598748\pi$
$557$		−	44.9485i		−	1.90453i	0.305272	−	0.952265i	$-0.401252\pi$
$558$	2.93450	+	8.09167i	0.124227	+	0.342548i
$559$	28.2210			1.19362
$560$	16.8069	+	3.04401i	0.710220	+	0.128633i
$561$	14.4935			0.611917
$562$	−13.6753	−	37.7086i	−0.576857	−	1.59064i
$563$	−33.9938			−1.43267			−0.716334	−	0.697757i	$-0.754181\pi$
$563$	−33.9938			−1.43267			−0.716334	+	0.697757i	$0.754181\pi$
$564$	20.5966	−	17.2013i	0.867274	−	0.724306i
$565$	9.28660			0.390690
$566$	15.2038	−	5.51374i	0.639061	−	0.231760i
$567$	−4.27008			−0.179326
$568$	36.2395	+	21.0914i	1.52058	+	0.884977i
$569$			11.3973i			0.477801i	0.971044	+	0.238900i	$0.0767870\pi$
$569$			11.3973i			0.477801i	−0.971044	+	0.238900i	$0.923213\pi$
$570$	−2.85435	+	1.03515i	−0.119556	+	0.0433577i
$571$	−21.2400			−0.888866			−0.444433	−	0.895812i	$-0.646595\pi$
$571$	−21.2400			−0.888866			−0.444433	+	0.895812i	$0.646595\pi$
$572$	−49.3246	+	41.1935i	−2.06236	+	1.72239i
$573$			6.76632i			0.282667i
$574$	−52.2330	+	18.9427i	−2.18016	+	0.790651i
$575$	−4.21933	+	2.27976i	−0.175958	+	0.0950724i
$576$	3.95167	+	6.95589i	0.164653	+	0.289829i
$577$	31.9987			1.33212			0.666062	−	0.745896i	$-0.267978\pi$
$577$	31.9987			1.33212			0.666062	+	0.745896i	$0.267978\pi$
$578$	−15.6532	+	5.67674i	−0.651088	+	0.236121i
$579$			22.6747i			0.942327i
$580$	0.236456	+	0.283129i	0.00981828	+	0.0117563i
$581$	−8.49142			−0.352284
$582$	11.6165	−	4.21279i	0.481518	−	0.174626i
$583$			10.6735i			0.442050i
$584$	−5.78543	+	9.94057i	−0.239403	+	0.411344i
$585$			5.06818i			0.209543i
$586$	−10.4043	−	28.6890i	−0.429796	−	1.18513i
$587$		−	41.5654i		−	1.71559i	−0.513994	−	0.857794i	$-0.671835\pi$
$587$		−	41.5654i		−	1.71559i	0.513994	−	0.857794i	$-0.328165\pi$
$588$	−14.4016	−	17.2443i	−0.593911	−	0.711141i
$589$		−	13.0671i		−	0.538419i
$590$	−9.30115	+	3.37312i	−0.382922	+	0.138869i
$591$			18.6303i			0.766348i
$592$	−2.51666	−	0.455810i	−0.103434	−	0.0187337i
$593$	40.3723			1.65789			0.828945	−	0.559330i	$-0.188942\pi$
$593$	40.3723			1.65789			0.828945	+	0.559330i	$0.188942\pi$
$594$	3.05678	+	8.42884i	0.125421	+	0.345840i
$595$	9.76170			0.400190
$596$	−5.18187	−	6.20470i	−0.212258	−	0.254155i
$597$			8.02404i			0.328402i
$598$	−22.8593	+	25.6715i	−0.934786	+	1.04979i
$599$		−	2.25262i		−	0.0920395i	−0.998941	−	0.0460198i	$-0.985346\pi$
$599$		−	2.25262i		−	0.0920395i	0.998941	−	0.0460198i	$-0.0146537\pi$
$600$	−2.44455	−	1.42273i	−0.0997984	−	0.0580828i
$601$	−0.510957			−0.0208424			−0.0104212	−	0.999946i	$-0.503317\pi$
$601$	−0.510957			−0.0208424			−0.0104212	+	0.999946i	$0.503317\pi$
$602$	31.6112	−	11.4640i	1.28838	−	0.467238i
$603$	−11.6198			−0.473196
$604$	−16.8055	−	20.1226i	−0.683805	−	0.818779i
$605$		−	29.1946i		−	1.18693i
$606$	−0.595160	−	1.64111i	−0.0241767	−	0.0666656i
$607$			47.9293i			1.94539i	0.232083	+	0.972696i	$0.425446\pi$
$607$			47.9293i			1.94539i	−0.232083	+	0.972696i	$0.574554\pi$
$608$	−2.03953	−	11.9726i	−0.0827140	−	0.485552i
$609$		−	0.787574i		−	0.0319141i
$610$	−14.2587	+	5.17100i	−0.577317	+	0.209368i
$611$			68.0017i			2.75106i
$612$	2.93078	+	3.50928i	0.118470	+	0.141854i
$613$		−	13.6334i		−	0.550649i	−0.961351	−	0.275325i	$-0.911215\pi$
$613$		−	13.6334i		−	0.550649i	0.961351	−	0.275325i	$-0.0887854\pi$
$614$	2.84093	+	7.83367i	0.114651	+	0.316141i
$615$	9.20080			0.371012
$616$	−38.5161	+	66.1788i	−1.55186	+	2.66642i
$617$			44.3044i			1.78363i	0.452402	+	0.891814i	$0.350567\pi$
$617$			44.3044i			1.78363i	−0.452402	+	0.891814i	$0.649433\pi$
$618$	2.67019	+	7.36286i	0.107411	+	0.296177i
$619$	−26.7059			−1.07340			−0.536700	−	0.843773i	$-0.680329\pi$
$619$	−26.7059			−1.07340			−0.536700	+	0.843773i	$0.680329\pi$
$620$	9.34291	−	7.80275i	0.375220	−	0.313366i
$621$	2.27976	+	4.21933i	0.0914835	+	0.169316i
$622$	5.08656	+	14.0258i	0.203952	+	0.562384i
$623$		−	56.3111i		−	2.25606i
$624$	−19.9482	−	3.61295i	−0.798565	−	0.144634i
$625$	1.00000			0.0400000
$626$	−10.7440	−	29.6257i	−0.429415	−	1.18408i
$627$		−	13.6116i		−	0.543593i
$628$	−6.99088	−	8.37078i	−0.278966	−	0.334031i
$629$	−1.46172			−0.0582824
$630$	2.05880	+	5.67701i	0.0820247	+	0.226177i
$631$	29.7923			1.18601			0.593006	−	0.805198i	$-0.297941\pi$
$631$	29.7923			1.18601			0.593006	+	0.805198i	$0.297941\pi$
$632$	−5.19962	+	8.93403i	−0.206830	+	0.355377i
$633$	19.6771			0.782095
$634$	−5.59241	+	2.02812i	−0.222103	+	0.0805471i
$635$	1.34406			0.0533372
$636$	−2.58434	+	2.15832i	−0.102476	+	0.0855828i
$637$	56.9336			2.25579
$638$	−1.55462	+	0.563793i	−0.0615479	+	0.0223208i
$639$			14.8246i			0.586452i
$640$	7.34247	−	8.60745i	0.290237	−	0.340239i
$641$			16.6470i			0.657517i	0.944414	+	0.328758i	$0.106630\pi$
$641$			16.6470i			0.657517i	−0.944414	+	0.328758i	$0.893370\pi$
$642$	−4.25729	−	11.7392i	−0.168022	−	0.463308i
$643$	19.8644			0.783375			0.391687	−	0.920098i	$-0.371891\pi$
$643$	19.8644			0.783375			0.391687	+	0.920098i	$0.371891\pi$
$644$	−15.1770	+	38.0414i	−0.598057	+	1.49904i
$645$	−5.56828			−0.219251
$646$	−2.36643	−	6.52526i	−0.0931058	−	0.256733i
$647$		−	3.09993i		−	0.121871i	−0.998142	−	0.0609354i	$-0.980592\pi$
$647$		−	3.09993i		−	0.121871i	0.998142	−	0.0609354i	$-0.0194083\pi$
$648$	−1.42273	+	2.44455i	−0.0558902	+	0.0960311i
$649$		−	44.3544i		−	1.74106i
$650$	6.73807	−	2.44361i	0.264289	−	0.0958461i
$651$	−25.9890			−1.01859
$652$	14.6451	+	17.5358i	0.573545	+	0.686755i
$653$	10.1831			0.398497			0.199249	−	0.979949i	$-0.436150\pi$
$653$	10.1831			0.398497			0.199249	+	0.979949i	$0.436150\pi$
$654$	−18.2719	+	6.62644i	−0.714490	+	0.259114i
$655$	−4.08505			−0.159616
$656$	−6.55898	+	36.2140i	−0.256085	+	1.41392i
$657$	−4.06642			−0.158646
$658$	27.6238	+	76.1707i	1.07689	+	2.96944i
$659$	−34.4249			−1.34100			−0.670501	−	0.741908i	$-0.733921\pi$
$659$	−34.4249			−1.34100			−0.670501	+	0.741908i	$0.733921\pi$
$660$	9.73221	−	8.12788i	0.378826	−	0.316377i
$661$		−	36.0651i		−	1.40277i	−0.712783	−	0.701385i	$-0.752565\pi$
$661$		−	36.0651i		−	1.40277i	0.712783	−	0.701385i	$-0.247435\pi$
$662$	−7.74424	−	21.3542i	−0.300989	−	0.829955i
$663$	−11.5862			−0.449971
$664$	−2.82923	+	4.86121i	−0.109795	+	0.188651i
$665$		−	9.16768i		−	0.355507i
$666$	−0.308285	−	0.850075i	−0.0119458	−	0.0329397i
$667$	−0.778214	+	0.420479i	−0.0301326	+	0.0162810i
$668$	26.4645	+	31.6882i	1.02394	+	1.22605i
$669$	−21.7302			−0.840138
$670$	5.60247	+	15.4484i	0.216442	+	0.596824i
$671$		−	67.9953i		−	2.62493i
$672$	−23.8122	+	4.05641i	−0.918574	+	0.156480i
$673$	17.8360			0.687527			0.343764	−	0.939056i	$-0.388298\pi$
$673$	17.8360			0.687527			0.343764	+	0.939056i	$0.388298\pi$
$674$	1.91137	+	5.27047i	0.0736232	+	0.203011i
$675$		−	1.00000i		−	0.0384900i
$676$	19.4745	−	16.2642i	0.749019	−	0.625545i
$677$			31.3870i			1.20630i	0.797627	+	0.603151i	$0.206088\pi$
$677$			31.3870i			1.20630i	−0.797627	+	0.603151i	$0.793912\pi$
$678$	−12.3464	+	4.47751i	−0.474161	+	0.171958i
$679$			37.3100i			1.43183i
$680$	3.25247	−	5.58842i	0.124726	−	0.214306i
$681$		−	19.5294i		−	0.748368i
$682$	18.6045	+	51.3006i	0.712403	+	1.96440i
$683$			27.7435i			1.06157i	0.847505	+	0.530787i	$0.178104\pi$
$683$			27.7435i			1.06157i	−0.847505	+	0.530787i	$0.821896\pi$
$684$	3.29573	−	2.75244i	0.126015	−	0.105242i
$685$	4.20683			0.160735
$686$	24.0338	−	8.71603i	0.917617	−	0.332780i
$687$	−6.03097			−0.230096
$688$	3.96946	−	21.9166i	0.151334	−	0.835561i
$689$		−	8.53244i		−	0.325060i
$690$	4.51036	−	5.06524i	0.171706	−	0.192830i
$691$			0.927373i			0.0352789i	0.999844	+	0.0176395i	$0.00561511\pi$
$691$			0.927373i			0.0352789i	−0.999844	+	0.0176395i	$0.994385\pi$
$692$	−8.74520	+	7.30357i	−0.332443	+	0.277640i
$693$	−27.0719			−1.02838
$694$	3.76636	+	10.3855i	0.142969	+	0.394227i
$695$	3.26694			0.123922
$696$	−0.450874	−	0.262409i	−0.0170903	−	0.00994660i
$697$			21.0337i			0.796708i
$698$	44.4273	−	16.1118i	1.68160	−	0.609842i
$699$		−	15.5780i		−	0.589215i
$700$	6.55486	−	5.47430i	0.247750	−	0.206909i
$701$			11.5413i			0.435910i	0.975959	+	0.217955i	$0.0699385\pi$
$701$			11.5413i			0.435910i	−0.975959	+	0.217955i	$0.930061\pi$
$702$	−2.44361	−	6.73807i	−0.0922280	−	0.254312i
$703$			1.37277i			0.0517749i
$704$	25.0533	+	44.0998i	0.944230	+	1.66207i
$705$		−	13.4174i		−	0.505328i
$706$	0.0741406	−	0.0268876i	0.00279032	−	0.00101193i
$707$	5.27096			0.198235
$708$	10.7394	−	8.96904i	0.403612	−	0.337077i
$709$		−	46.1072i		−	1.73159i	−0.500398	−	0.865796i	$-0.666813\pi$
$709$		−	46.1072i		−	1.73159i	0.500398	−	0.865796i	$-0.333187\pi$
$710$	19.7091	−	7.14764i	0.739670	−	0.268246i
$711$	−3.65467			−0.137061
$712$	−32.2372	−	18.7621i	−1.20814	−	0.703140i
$713$	13.8753	+	25.6801i	0.519635	+	0.961729i
$714$	−12.9780	+	4.70657i	−0.485691	+	0.176139i
$715$			32.1318i			1.20166i
$716$	5.26969	+	6.30985i	0.196938	+	0.235810i
$717$	−29.6232			−1.10630
$718$	−13.4748	+	4.88673i	−0.502875	+	0.182371i
$719$			11.3976i			0.425058i	0.977155	+	0.212529i	$0.0681700\pi$
$719$			11.3976i			0.425058i	−0.977155	+	0.212529i	$0.931830\pi$
$720$	3.93596	+	0.712870i	0.146685	+	0.0265671i
$721$	−23.6482			−0.880705
$722$	19.1321	−	6.93837i	0.712021	−	0.258219i
$723$	1.02822			0.0382400
$724$	14.5857	+	17.4647i	0.542072	+	0.649069i
$725$	0.184440			0.00684994
$726$	14.0761	+	38.8139i	0.522413	+	1.44052i
$727$	−20.4020			−0.756668			−0.378334	−	0.925669i	$-0.623503\pi$
$727$	−20.4020			−0.756668			−0.378334	+	0.925669i	$0.623503\pi$
$728$	30.7900	−	52.9037i	1.14115	−	1.96074i
$729$	−1.00000			−0.0370370
$730$	1.96061	+	5.40625i	0.0725655	+	0.200094i
$731$		−	12.7295i		−	0.470817i
$732$	16.4635	−	13.7496i	0.608509	−	0.508198i
$733$			14.1545i			0.522807i	0.965230	+	0.261403i	$0.0841853\pi$
$733$			14.1545i			0.522807i	−0.965230	+	0.261403i	$0.915815\pi$
$734$	35.2085	−	12.7686i	1.29957	−	0.471297i
$735$	−11.2335			−0.414355
$736$	16.7213	+	21.3635i	0.616356	+	0.787468i
$737$	−73.6689			−2.71363
$738$	−12.2323	+	4.43614i	−0.450279	+	0.163297i
$739$		−	20.9145i		−	0.769354i	−0.923051	−	0.384677i	$-0.874313\pi$
$739$		−	20.9145i		−	0.769354i	0.923051	−	0.384677i	$-0.125687\pi$
$740$	−0.981524	+	0.819722i	−0.0360815	+	0.0301336i
$741$			10.8812i			0.399730i
$742$	−3.46607	−	9.55743i	−0.127243	−	0.350864i
$743$	42.2593			1.55034			0.775171	−	0.631752i	$-0.217664\pi$
$743$	42.2593			1.55034			0.775171	+	0.631752i	$0.217664\pi$
$744$	−8.65919	+	14.8783i	−0.317461	+	0.545465i
$745$	−4.04197			−0.148086
$746$	−11.0563	−	30.4868i	−0.404798	−	1.11620i
$747$	−1.98859			−0.0727587
$748$	18.5809	+	22.2485i	0.679386	+	0.813487i
$749$	37.7041			1.37768
$750$	−1.32949	+	0.482147i	−0.0485460	+	0.0176055i
$751$	2.04064			0.0744641			0.0372320	−	0.999307i	$-0.488146\pi$
$751$	2.04064			0.0744641			0.0372320	+	0.999307i	$0.488146\pi$
$752$	52.8104	+	9.56486i	1.92580	+	0.348794i
$753$			7.72202i			0.281406i
$754$	1.24277	−	0.450700i	0.0452591	−	0.0164135i
$755$	−13.1086			−0.477072
$756$	−5.47430	−	6.55486i	−0.199099	−	0.238398i
$757$			16.9083i			0.614544i	0.951622	+	0.307272i	$0.0994161\pi$
$757$			16.9083i			0.614544i	−0.951622	+	0.307272i	$0.900584\pi$
$758$	23.5189	−	8.52930i	0.854246	−	0.309798i
$759$	14.4535	+	26.7502i	0.524628	+	0.970971i
$760$	−5.24835	−	3.05455i	−0.190378	−	0.110800i
$761$	15.7867			0.572269			0.286134	−	0.958189i	$-0.407630\pi$
$761$	15.7867			0.572269			0.286134	+	0.958189i	$0.407630\pi$
$762$	−1.78690	+	0.648033i	−0.0647327	+	0.0234757i
$763$		−	58.6863i		−	2.12459i
$764$	−10.3868	+	8.67452i	−0.375780	+	0.313833i
$765$	2.28607			0.0826531
$766$	−45.5886	+	16.5330i	−1.64718	+	0.597362i
$767$			35.4572i			1.28028i
$768$	−5.61166	+	14.9836i	−0.202493	+	0.540675i
$769$			2.35009i			0.0847464i	0.999102	+	0.0423732i	$0.0134919\pi$
$769$			2.35009i			0.0847464i	−0.999102	+	0.0423732i	$0.986508\pi$
$770$	13.0527	+	35.9918i	0.470385	+	1.29705i
$771$		−	15.8364i		−	0.570333i
$772$	−34.8072	+	29.0693i	−1.25274	+	1.04623i
$773$			37.8489i			1.36133i	0.732595	+	0.680665i	$0.238309\pi$
$773$			37.8489i			1.36133i	−0.732595	+	0.680665i	$0.761691\pi$
$774$	7.40296	−	2.68473i	0.266094	−	0.0965007i
$775$		−	6.08631i		−	0.218627i
$776$	21.3594	+	12.4312i	0.766758	+	0.446254i
$777$	2.73029			0.0979486
$778$	0.183467	+	0.505898i	0.00657762	+	0.0181373i
$779$	19.7538			0.707752
$780$	−7.78000	+	6.49748i	−0.278569	+	0.232647i
$781$			93.9868i			3.36311i
$782$	11.5795	+	10.3110i	0.414082	+	0.368721i
$783$		−	0.184440i		−	0.00659136i
$784$	8.00805	−	44.2148i	0.286002	−	1.57910i
$785$	−5.45303			−0.194627
$786$	5.43102	−	1.96960i	0.193718	−	0.0702532i
$787$	−7.72930			−0.275520			−0.137760	−	0.990466i	$-0.543990\pi$
$787$	−7.72930			−0.275520			−0.137760	+	0.990466i	$0.543990\pi$
$788$	−28.5988	+	23.8843i	−1.01879	+	0.850844i
$789$			18.7282i			0.666740i
$790$	1.76209	+	4.85883i	0.0626923	+	0.172870i
$791$		−	39.6545i		−	1.40995i
$792$	−9.02001	+	15.4983i	−0.320512	+	0.550707i
$793$			54.3559i			1.93023i
$794$	17.4857	−	6.34129i	0.620543	−	0.225044i
$795$			1.68353i			0.0597088i
$796$	−12.3175	+	10.2870i	−0.436581	+	0.364611i
$797$		−	42.3887i		−	1.50149i	−0.660594	−	0.750743i	$-0.729696\pi$
$797$		−	42.3887i		−	1.50149i	0.660594	−	0.750743i	$-0.270304\pi$
$798$	4.42017	+	12.1883i	0.156472	+	0.431461i
$799$	30.6731			1.08514
$800$	−0.949963	−	5.57652i	−0.0335863	−	0.197160i
$801$		−	13.1874i		−	0.465953i
$802$	3.45974	+	9.53999i	0.122168	+	0.336869i
$803$	−25.7808			−0.909784
$804$	−14.8968	−	17.8372i	−0.525370	−	0.629071i
$805$	9.73473	+	18.0168i	0.343104	+	0.635010i
$806$	−14.8725	−	41.0100i	−0.523863	−	1.44452i
$807$			7.39847i			0.260439i
$808$	1.75621	−	3.01754i	0.0617834	−	0.106157i
$809$	20.6701			0.726720			0.363360	−	0.931649i	$-0.381629\pi$
$809$	20.6701			0.726720			0.363360	+	0.931649i	$0.381629\pi$
$810$	0.482147	+	1.32949i	0.0169409	+	0.0467134i
$811$			30.9310i			1.08613i	0.839689	+	0.543067i	$0.182737\pi$
$811$			30.9310i			1.08613i	−0.839689	+	0.543067i	$0.817263\pi$
$812$	1.20898	−	1.00968i	0.0424269	−	0.0354329i
$813$	6.22206			0.218217
$814$	−1.95450	−	5.38941i	−0.0685054	−	0.188899i
$815$	11.4235			0.400146
$816$	−1.62967	+	8.99789i	−0.0570499	+	0.314989i
$817$	−11.9549			−0.418248
$818$	−1.19736	+	0.434231i	−0.0418647	+	0.0151825i
$819$	21.6415			0.756215
$820$	11.7956	+	14.1239i	0.411919	+	0.493227i
$821$	2.34307			0.0817735			0.0408868	−	0.999164i	$-0.486982\pi$
$821$	2.34307			0.0817735			0.0408868	+	0.999164i	$0.486982\pi$
$822$	−5.59292	+	2.02831i	−0.195075	+	0.0707454i
$823$		−	38.8494i		−	1.35420i	−0.735889	−	0.677102i	$-0.763236\pi$
$823$		−	38.8494i		−	1.35420i	0.735889	−	0.677102i	$-0.236764\pi$
$824$	−7.87926	+	13.5382i	−0.274487	+	0.471626i
$825$		−	6.33992i		−	0.220728i
$826$	14.4035	+	39.7166i	0.501161	+	1.38192i
$827$	−0.484323			−0.0168415			−0.00842077	−	0.999965i	$-0.502680\pi$
$827$	−0.484323			−0.0168415			−0.00842077	+	0.999965i	$0.502680\pi$
$828$	−3.55427	+	8.90883i	−0.123519	+	0.309603i
$829$	21.9471			0.762255			0.381128	−	0.924522i	$-0.375536\pi$
$829$	21.9471			0.762255			0.381128	+	0.924522i	$0.375536\pi$
$830$	0.958792	+	2.64380i	0.0332802	+	0.0917677i
$831$			11.9387i			0.414148i
$832$	−20.0277	−	35.2536i	−0.694337	−	1.22220i
$833$		−	25.6807i		−	0.889783i
$834$	−4.34335	+	1.57514i	−0.150398	+	0.0545428i
$835$	20.6429			0.714376
$836$	20.8947	−	17.4502i	0.722657	−	0.603529i
$837$	−6.08631			−0.210374
$838$	−4.34295	+	1.57500i	−0.150025	+	0.0544075i
$839$	41.6416			1.43763			0.718813	−	0.695203i	$-0.244686\pi$
$839$	41.6416			1.43763			0.718813	+	0.695203i	$0.244686\pi$
$840$	−6.07517	+	10.4384i	−0.209613	+	0.360160i
$841$	−28.9660			−0.998827
$842$	2.01511	+	5.55652i	0.0694452	+	0.191490i
$843$	28.3633			0.976883
$844$	25.2264	+	30.2057i	0.868327	+	1.03972i
$845$		−	12.6864i		−	0.436425i
$846$	6.46916	+	17.8382i	0.222414	+	0.613292i
$847$	−124.663			−4.28348
$848$	−6.62633	−	1.20014i	−0.227549	−	0.0412130i
$849$			11.4358i			0.392476i
$850$	−1.10222	−	3.03930i	−0.0378059	−	0.104247i
$851$	−1.45768	−	2.69784i	−0.0499686	−	0.0924808i
$852$	−22.7568	+	19.0054i	−0.779634	+	0.651114i
$853$	−25.8101			−0.883721			−0.441860	−	0.897084i	$-0.645681\pi$
$853$	−25.8101			−0.883721			−0.441860	+	0.897084i	$0.645681\pi$
$854$	22.0806	+	60.8856i	0.755581	+	2.08346i
$855$		−	2.14696i		−	0.0734245i
$856$	12.5625	−	21.5850i	0.429378	−	0.737761i
$857$	−0.817165			−0.0279138			−0.0139569	−	0.999903i	$-0.504443\pi$
$857$	−0.817165			−0.0279138			−0.0139569	+	0.999903i	$0.504443\pi$
$858$	−15.4923	−	42.7188i	−0.528897	−	1.45840i
$859$		−	5.27081i		−	0.179838i	−0.995949	−	0.0899189i	$-0.971339\pi$
$859$		−	5.27081i		−	0.179838i	0.995949	−	0.0899189i	$-0.0286608\pi$
$860$	−7.13863	−	8.54769i	−0.243425	−	0.291474i
$861$		−	39.2881i		−	1.33894i
$862$	−22.8679	+	8.29318i	−0.778882	+	0.282467i
$863$		−	3.58063i		−	0.121886i	−0.998141	−	0.0609430i	$-0.980589\pi$
$863$		−	3.58063i		−	0.121886i	0.998141	−	0.0609430i	$-0.0194108\pi$
$864$	−5.57652	+	0.949963i	−0.189717	+	0.0323184i
$865$			5.69694i			0.193702i
$866$	7.85885	+	21.6702i	0.267055	+	0.736384i
$867$		−	11.7739i		−	0.399862i
$868$	−33.3183	−	39.8949i	−1.13090	−	1.35412i
$869$	−23.1703			−0.785999
$870$	−0.245211	+	0.0889274i	−0.00831343	+	0.00301492i
$871$	58.8914			1.99546
$872$	−33.5970	−	19.5535i	−1.13774	−	0.662164i
$873$			8.73755i			0.295721i
$874$	9.68356	−	10.8749i	0.327551	−	0.367848i
$875$		−	4.27008i		−	0.144355i
$876$	−5.21322	−	6.24223i	−0.176138	−	0.210905i
$877$	−43.6993			−1.47562			−0.737810	−	0.675008i	$-0.764140\pi$
$877$	−43.6993			−1.47562			−0.737810	+	0.675008i	$0.764140\pi$
$878$	−3.10825	−	8.57079i	−0.104899	−	0.289250i
$879$	21.5790			0.727842
$880$	24.9537	+	4.51954i	0.841189	+	0.152354i
$881$		−	21.6563i		−	0.729620i	−0.931082	−	0.364810i	$-0.881134\pi$
$881$		−	21.6563i		−	0.729620i	0.931082	−	0.364810i	$-0.118866\pi$
$882$	14.9348	−	5.41622i	0.502882	−	0.182374i
$883$			37.3040i			1.25538i	0.778464	+	0.627689i	$0.215999\pi$
$883$			37.3040i			1.25538i	−0.778464	+	0.627689i	$0.784001\pi$
$884$	−14.8537	−	17.7856i	−0.499584	−	0.598195i
$885$		−	6.99605i		−	0.235170i
$886$	10.2125	+	28.1601i	0.343094	+	0.946058i
$887$			6.79994i			0.228320i	0.993462	+	0.114160i	$0.0364176\pi$
$887$			6.79994i			0.228320i	−0.993462	+	0.114160i	$0.963582\pi$
$888$	0.909696	−	1.56305i	0.0305274	−	0.0524525i
$889$		−	5.73922i		−	0.192487i
$890$	−17.5324	+	6.35825i	−0.587689	+	0.213129i
$891$	−6.33992			−0.212395
$892$	−27.8585	−	33.3574i	−0.932771	−	1.11689i
$893$		−	28.8066i		−	0.963977i
$894$	5.37375	−	1.94882i	0.179725	−	0.0651784i
$895$	4.11047			0.137398
$896$	−36.7544	−	31.3529i	−1.22788	−	1.04743i
$897$	−11.5542	−	21.3843i	−0.385784	−	0.714000i
$898$	14.4760	−	5.24980i	0.483069	−	0.175188i
$899$		−	1.12256i		−	0.0374395i
$900$	1.53507	−	1.28202i	0.0511689	−	0.0427339i
$901$	−3.84868			−0.128218
$902$	−77.5521	+	28.1248i	−2.58220	+	0.936453i
$903$			23.7770i			0.791248i
$904$	−22.7016	−	13.2124i	−0.755043	−	0.439436i
$905$	11.3771			0.378188
$906$	17.4277	−	6.32029i	0.578998	−	0.209977i
$907$	29.6090			0.983151			0.491575	−	0.870835i	$-0.336421\pi$
$907$	29.6090			0.983151			0.491575	+	0.870835i	$0.336421\pi$
$908$	29.9789	−	25.0370i	0.994886	−	0.830882i
$909$	1.23440			0.0409423
$910$	−10.4344	−	28.7721i	−0.345896	−	0.953785i
$911$	44.4726			1.47344			0.736721	−	0.676196i	$-0.236373\pi$
$911$	44.4726			1.47344			0.736721	+	0.676196i	$0.236373\pi$
$912$	8.45036	+	1.53050i	0.279819	+	0.0506800i
$913$	−12.6075			−0.417247
$914$	−9.62626	−	26.5437i	−0.318408	−	0.877989i
$915$		−	10.7249i		−	0.354556i
$916$	−7.73180	−	9.25795i	−0.255466	−	0.305891i
$917$			17.4435i			0.576035i
$918$	−3.03930	+	1.10222i	−0.100312	+	0.0363788i
$919$	25.2267			0.832153			0.416076	−	0.909330i	$-0.363405\pi$
$919$	25.2267			0.832153			0.416076	+	0.909330i	$0.363405\pi$
$920$	13.5578	+	0.429988i	0.446989	+	0.0141763i
$921$	−5.89225			−0.194156
$922$	30.6485	−	11.1149i	1.00935	−	0.366049i
$923$		−	75.1337i		−	2.47306i
$924$	−34.7067	−	41.5573i	−1.14177	−	1.36713i
$925$			0.639401i			0.0210234i
$926$	−14.9976	−	41.3547i	−0.492850	−	1.35900i
$927$	−5.53812			−0.181896
$928$	−0.175212	−	1.02854i	−0.00575160	−	0.0337633i
$929$	−7.22571			−0.237068			−0.118534	−	0.992950i	$-0.537819\pi$
$929$	−7.22571			−0.237068			−0.118534	+	0.992950i	$0.537819\pi$
$930$	2.93450	+	8.09167i	0.0962260	+	0.265336i
$931$	−24.1180			−0.790434
$932$	23.9133	−	19.9713i	0.783307	−	0.654181i
$933$	−10.5498			−0.345385
$934$	−47.1116	+	17.0853i	−1.54154	+	0.559050i
$935$	14.4935			0.473989
$936$	7.21066	−	12.3894i	0.235688	−	0.404961i
$937$		−	5.18714i		−	0.169457i	−0.996404	−	0.0847283i	$-0.972998\pi$
$937$		−	5.18714i		−	0.169457i	0.996404	−	0.0847283i	$-0.0270022\pi$
$938$	65.9659	−	23.9230i	2.15386	−	0.781113i
$939$	22.2836			0.727197
$940$	20.5966	−	17.2013i	0.671788	−	0.561045i
$941$			5.57594i			0.181770i	0.995861	+	0.0908852i	$0.0289696\pi$
$941$			5.57594i			0.181770i	−0.995861	+	0.0908852i	$0.971030\pi$
$942$	7.24974	−	2.62916i	0.236209	−	0.0856628i
$943$	−38.8212	+	20.9756i	−1.26419	+	0.683059i
$944$	27.5362	+	4.98727i	0.896227	+	0.162322i
$945$	−4.27008			−0.138906
$946$	46.9342	−	17.0210i	1.52596	−	0.553400i
$947$			16.3670i			0.531856i	0.963993	+	0.265928i	$0.0856783\pi$
$947$			16.3670i			0.531856i	−0.963993	+	0.265928i	$0.914322\pi$
$948$	−4.68534	−	5.61017i	−0.152173	−	0.182210i
$949$	20.6093			0.669007
$950$	−2.85435	+	1.03515i	−0.0926075	+	0.0335847i
$951$		−	4.20644i		−	0.136403i
$952$	−23.8630	−	13.8883i	−0.773403	−	0.450122i
$953$			28.4543i			0.921727i	0.887471	+	0.460863i	$0.152460\pi$
$953$			28.4543i			0.921727i	−0.887471	+	0.460863i	$0.847540\pi$
$954$	−0.811711	−	2.23824i	−0.0262801	−	0.0724655i
$955$			6.76632i			0.218953i
$956$	−37.9774	−	45.4736i	−1.22828	−	1.47072i
$957$		−	1.16934i		−	0.0377993i
$958$	38.8851	−	14.1019i	1.25632	−	0.455613i
$959$		−	17.9635i		−	0.580070i
$960$	3.95167	+	6.95589i	0.127539	+	0.224500i
$961$	−6.04320			−0.194942
$962$	1.56244	+	4.30833i	0.0503752	+	0.138906i
$963$	8.82985			0.284538
$964$	1.31820	+	1.57839i	0.0424563	+	0.0508366i
$965$			22.6747i			0.729923i
$966$	−21.6290	−	19.2596i	−0.695900	−	0.619666i
$967$			29.3267i			0.943085i	0.881843	+	0.471542i	$0.156303\pi$
$967$			29.3267i			0.943085i	−0.881843	+	0.471542i	$0.843697\pi$
$968$	−41.5361	+	71.3678i	−1.33502	+	2.29385i
$969$	4.90810			0.157671
$970$	11.6165	−	4.21279i	0.372982	−	0.135264i
$971$	23.4011			0.750977			0.375488	−	0.926827i	$-0.377475\pi$
$971$	23.4011			0.750977			0.375488	+	0.926827i	$0.377475\pi$
$972$	−1.28202	−	1.53507i	−0.0411207	−	0.0492373i
$973$		−	13.9501i		−	0.447219i
$974$	6.30451	+	17.3842i	0.202010	+	0.557027i
$975$			5.06818i			0.162312i
$976$	42.2130	+	7.64549i	1.35121	+	0.244726i
$977$		−	53.5732i		−	1.71396i	−0.515351	−	0.856979i	$-0.672338\pi$
$977$		−	53.5732i		−	1.71396i	0.515351	−	0.856979i	$-0.327662\pi$
$978$	−15.1873	+	5.50779i	−0.485637	+	0.176120i
$979$		−	83.6069i		−	2.67209i
$980$	−14.4016	−	17.2443i	−0.460042	−	0.550848i
$981$		−	13.7436i		−	0.438800i
$982$	−7.92945	−	21.8649i	−0.253039	−	0.697737i
$983$	−31.8612			−1.01622			−0.508108	−	0.861294i	$-0.669655\pi$
$983$	−31.8612			−1.01622			−0.508108	+	0.861294i	$0.669655\pi$
$984$	−22.4918	−	13.0903i	−0.717014	−	0.417303i
$985$			18.6303i			0.593611i
$986$	−0.203294	−	0.560570i	−0.00647421	−	0.0178522i
$987$	−57.2933			−1.82367
$988$	−16.7033	+	13.9498i	−0.531404	+	0.443803i
$989$	23.4944	−	12.6943i	0.747078	−	0.403656i
$990$	3.05678	+	8.42884i	0.0971507	+	0.267886i
$991$			20.7723i			0.659855i	0.944006	+	0.329928i	$0.107024\pi$
$991$			20.7723i			0.659855i	−0.944006	+	0.329928i	$0.892976\pi$
$992$	−33.9404	+	5.78177i	−1.07761	+	0.183571i
$993$	16.0620			0.509712
$994$	−30.5210	−	84.1594i	−0.968066	−	2.66937i
$995$			8.02404i			0.254379i
$996$	−2.54940	−	3.05262i	−0.0807809	−	0.0967259i
$997$	−23.2860			−0.737475			−0.368737	−	0.929534i	$-0.620210\pi$
$997$	−23.2860			−0.737475			−0.368737	+	0.929534i	$0.620210\pi$
$998$	−15.9971	−	44.1108i	−0.506379	−	1.39630i
$999$	0.639401			0.0202297

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.p.a.91.6	yes	48
4.3	odd	2		1380.2.p.b.91.5	yes	48
23.22	odd	2		1380.2.p.b.91.6	yes	48
92.91	even	2	inner	1380.2.p.a.91.5	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.p.a.91.5	✓	48	92.91	even	2	inner
1380.2.p.a.91.6	yes	48	1.1	even	1	trivial
1380.2.p.b.91.5	yes	48	4.3	odd	2
1380.2.p.b.91.6	yes	48	23.22	odd	2

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:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32949 + 0.482147i) q^{2} -1.00000i q^{3} +(1.53507 - 1.28202i) q^{4} -1.00000i q^{5} +(0.482147 + 1.32949i) q^{6} -4.27008 q^{7} +(-1.42273 + 2.44455i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.32949 + 0.482147i) q^{2} -1.00000i q^{3} +(1.53507 - 1.28202i) q^{4} -1.00000i q^{5} +(0.482147 + 1.32949i) q^{6} -4.27008 q^{7} +(-1.42273 + 2.44455i) q^{8} -1.00000 q^{9} +(0.482147 + 1.32949i) q^{10} -6.33992 q^{11} +(-1.28202 - 1.53507i) q^{12} +5.06818 q^{13} +(5.67701 - 2.05880i) q^{14} -1.00000 q^{15} +(0.712870 - 3.93596i) q^{16} -2.28607i q^{17} +(1.32949 - 0.482147i) q^{18} -2.14696 q^{19} +(-1.28202 - 1.53507i) q^{20} +4.27008i q^{21} +(8.42884 - 3.05678i) q^{22} +(4.21933 - 2.27976i) q^{23} +(2.44455 + 1.42273i) q^{24} -1.00000 q^{25} +(-6.73807 + 2.44361i) q^{26} +1.00000i q^{27} +(-6.55486 + 5.47430i) q^{28} -0.184440 q^{29} +(1.32949 - 0.482147i) q^{30} +6.08631i q^{31} +(0.949963 + 5.57652i) q^{32} +6.33992i q^{33} +(1.10222 + 3.03930i) q^{34} +4.27008i q^{35} +(-1.53507 + 1.28202i) q^{36} -0.639401i q^{37} +(2.85435 - 1.03515i) q^{38} -5.06818i q^{39} +(2.44455 + 1.42273i) q^{40} -9.20080 q^{41} +(-2.05880 - 5.67701i) q^{42} +5.56828 q^{43} +(-9.73221 + 8.12788i) q^{44} +1.00000i q^{45} +(-4.51036 + 5.06524i) q^{46} +13.4174i q^{47} +(-3.93596 - 0.712870i) q^{48} +11.2335 q^{49} +(1.32949 - 0.482147i) q^{50} -2.28607 q^{51} +(7.78000 - 6.49748i) q^{52} -1.68353i q^{53} +(-0.482147 - 1.32949i) q^{54} +6.33992i q^{55} +(6.07517 - 10.4384i) q^{56} +2.14696i q^{57} +(0.245211 - 0.0889274i) q^{58} +6.99605i q^{59} +(-1.53507 + 1.28202i) q^{60} +10.7249i q^{61} +(-2.93450 - 8.09167i) q^{62} +4.27008 q^{63} +(-3.95167 - 6.95589i) q^{64} -5.06818i q^{65} +(-3.05678 - 8.42884i) q^{66} +11.6198 q^{67} +(-2.93078 - 3.50928i) q^{68} +(-2.27976 - 4.21933i) q^{69} +(-2.05880 - 5.67701i) q^{70} -14.8246i q^{71} +(1.42273 - 2.44455i) q^{72} +4.06642 q^{73} +(0.308285 + 0.850075i) q^{74} +1.00000i q^{75} +(-3.29573 + 2.75244i) q^{76} +27.0719 q^{77} +(2.44361 + 6.73807i) q^{78} +3.65467 q^{79} +(-3.93596 - 0.712870i) q^{80} +1.00000 q^{81} +(12.2323 - 4.43614i) q^{82} +1.98859 q^{83} +(5.47430 + 6.55486i) q^{84} -2.28607 q^{85} +(-7.40296 + 2.68473i) q^{86} +0.184440i q^{87} +(9.02001 - 15.4983i) q^{88} +13.1874i q^{89} +(-0.482147 - 1.32949i) q^{90} -21.6415 q^{91} +(3.55427 - 8.90883i) q^{92} +6.08631 q^{93} +(-6.46916 - 17.8382i) q^{94} +2.14696i q^{95} +(5.57652 - 0.949963i) q^{96} -8.73755i q^{97} +(-14.9348 + 5.41622i) q^{98} +6.33992 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} - 2 q^{10} + 20 q^{14} - 48 q^{15} - 6 q^{16} + 4 q^{18} + 16 q^{19} + 28 q^{22} + 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} + 4 q^{30} + 16 q^{32} - 28 q^{34} + 2 q^{36} + 2 q^{40} - 8 q^{41} + 14 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} + 16 q^{51} - 16 q^{52} + 2 q^{54} + 40 q^{56} - 8 q^{58} + 2 q^{60} + 24 q^{62} - 26 q^{64} - 48 q^{67} - 44 q^{68} - 8 q^{69} + 4 q^{72} + 20 q^{74} - 64 q^{76} + 32 q^{77} - 64 q^{79} + 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} - 40 q^{86} + 2 q^{90} - 4 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 - 2 * q^10 + 20 * q^14 - 48 * q^15 - 6 * q^16 + 4 * q^18 + 16 * q^19 + 28 * q^22 + 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 + 4 * q^30 + 16 * q^32 - 28 * q^34 + 2 * q^36 + 2 * q^40 - 8 * q^41 + 14 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 + 16 * q^51 - 16 * q^52 + 2 * q^54 + 40 * q^56 - 8 * q^58 + 2 * q^60 + 24 * q^62 - 26 * q^64 - 48 * q^67 - 44 * q^68 - 8 * q^69 + 4 * q^72 + 20 * q^74 - 64 * q^76 + 32 * q^77 - 64 * q^79 + 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 - 40 * q^86 + 2 * q^90 - 4 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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