LMFDB - Embedded newform 460.2.g.c.459.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(459,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("460.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.g (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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			459.19
Character	$\chi$	$=$	460.459
Dual form			460.2.g.c.459.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.627129 + 1.26756i) q^{2} -3.03928 q^{3} +(-1.21342 - 1.58985i) q^{4} +(-0.951754 - 2.02340i) q^{5} +(1.90602 - 3.85247i) q^{6} -1.96560i q^{7} +(2.77620 - 0.541043i) q^{8} +6.23720 q^{9} +O(q^{10})$	\(q+(-0.627129 + 1.26756i) q^{2} -3.03928 q^{3} +(-1.21342 - 1.58985i) q^{4} +(-0.951754 - 2.02340i) q^{5} +(1.90602 - 3.85247i) q^{6} -1.96560i q^{7} +(2.77620 - 0.541043i) q^{8} +6.23720 q^{9} +(3.16166 + 0.0625285i) q^{10} -5.30588 q^{11} +(3.68792 + 4.83198i) q^{12} -0.315328i q^{13} +(2.49151 + 1.23268i) q^{14} +(2.89264 + 6.14968i) q^{15} +(-1.05523 + 3.85830i) q^{16} -1.43205 q^{17} +(-3.91152 + 7.90602i) q^{18} +4.48278 q^{19} +(-2.06203 + 3.96838i) q^{20} +5.97399i q^{21} +(3.32747 - 6.72552i) q^{22} +(0.916686 - 4.70741i) q^{23} +(-8.43763 + 1.64438i) q^{24} +(-3.18833 + 3.85157i) q^{25} +(0.399697 + 0.197751i) q^{26} -9.83873 q^{27} +(-3.12500 + 2.38509i) q^{28} -6.11341 q^{29} +(-9.60915 - 0.190041i) q^{30} +7.40223i q^{31} +(-4.22887 - 3.75722i) q^{32} +16.1260 q^{33} +(0.898081 - 1.81521i) q^{34} +(-3.97720 + 1.87077i) q^{35} +(-7.56833 - 9.91619i) q^{36} -6.56660 q^{37} +(-2.81128 + 5.68219i) q^{38} +0.958368i q^{39} +(-3.73701 - 5.10243i) q^{40} -0.152099 q^{41} +(-7.57239 - 3.74646i) q^{42} +8.98786i q^{43} +(6.43825 + 8.43553i) q^{44} +(-5.93628 - 12.6204i) q^{45} +(5.39204 + 4.11411i) q^{46} +1.31095 q^{47} +(3.20713 - 11.7264i) q^{48} +3.13643 q^{49} +(-2.88260 - 6.45683i) q^{50} +4.35240 q^{51} +(-0.501323 + 0.382625i) q^{52} +10.8030 q^{53} +(6.17015 - 12.4712i) q^{54} +(5.04989 + 10.7359i) q^{55} +(-1.06347 - 5.45689i) q^{56} -13.6244 q^{57} +(3.83389 - 7.74911i) q^{58} +7.22568i q^{59} +(6.26707 - 12.0610i) q^{60} -4.20106i q^{61} +(-9.38278 - 4.64215i) q^{62} -12.2598i q^{63} +(7.41454 - 3.00409i) q^{64} +(-0.638035 + 0.300115i) q^{65} +(-10.1131 + 20.4407i) q^{66} +3.99252i q^{67} +(1.73768 + 2.27674i) q^{68} +(-2.78606 + 14.3071i) q^{69} +(0.122906 - 6.21455i) q^{70} +0.608318i q^{71} +(17.3157 - 3.37459i) q^{72} +14.2324i q^{73} +(4.11810 - 8.32356i) q^{74} +(9.69021 - 11.7060i) q^{75} +(-5.43949 - 7.12693i) q^{76} +10.4292i q^{77} +(-1.21479 - 0.601020i) q^{78} +4.74332 q^{79} +(8.81122 - 1.53700i) q^{80} +11.1910 q^{81} +(0.0953854 - 0.192794i) q^{82} +5.33199i q^{83} +(9.49773 - 7.24895i) q^{84} +(1.36296 + 2.89762i) q^{85} +(-11.3927 - 5.63654i) q^{86} +18.5803 q^{87} +(-14.7302 + 2.87071i) q^{88} +10.5110i q^{89} +(19.7199 + 0.390003i) q^{90} -0.619807 q^{91} +(-8.59638 + 4.25467i) q^{92} -22.4974i q^{93} +(-0.822133 + 1.66170i) q^{94} +(-4.26650 - 9.07047i) q^{95} +(12.8527 + 11.4192i) q^{96} +6.27182 q^{97} +(-1.96694 + 3.97561i) q^{98} -33.0938 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) $ 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9	$ 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9} - 8 q^{16} - 100 q^{24} - 24 q^{25} - 24 q^{26} - 16 q^{29} + 104 q^{41} - 8 q^{46} + 32 q^{49} - 32 q^{50} + 52 q^{54} - 92 q^{64} + 32 q^{69} - 44 q^{70} + 24 q^{81} + 56 q^{85} + 28 q^{94} + 88 q^{96}+O(q^{100}) $ 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9 - 8 * q^16 - 100 * q^24 - 24 * q^25 - 24 * q^26 - 16 * q^29 + 104 * q^41 - 8 * q^46 + 32 * q^49 - 32 * q^50 + 52 * q^54 - 92 * q^64 + 32 * q^69 - 44 * q^70 + 24 * q^81 + 56 * q^85 + 28 * q^94 + 88 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−0.627129	+	1.26756i	−0.443447	+	0.896301i
$2$	−0.627129	+	1.26756i	−0.443447	+	0.896301i
$3$	−3.03928			−1.75473			−0.877363	−	0.479827i	$-0.840700\pi$
$3$	−3.03928			−1.75473			−0.877363	+	0.479827i	$0.840700\pi$
$4$	−1.21342	−	1.58985i	−0.606710	−	0.794924i
$5$	−0.951754	−	2.02340i	−0.425637	−	0.904894i
$5$	−0.951754	−	2.02340i	−0.425637	−	0.904894i
$6$	1.90602	−	3.85247i	0.778128	−	1.57276i
$7$		−	1.96560i		−	0.742926i	−0.928448	−	0.371463i	$-0.878856\pi$
$7$		−	1.96560i		−	0.742926i	0.928448	−	0.371463i	$-0.121144\pi$
$8$	2.77620	−	0.541043i	0.981534	−	0.191288i
$9$	6.23720			2.07907
$10$	3.16166	+	0.0625285i	0.999804	+	0.0197733i
$11$	−5.30588			−1.59978			−0.799891	−	0.600145i	$-0.795109\pi$
$11$	−5.30588			−1.59978			−0.799891	+	0.600145i	$0.795109\pi$
$12$	3.68792	+	4.83198i	1.06461	+	1.39487i
$13$		−	0.315328i		−	0.0874562i	−0.999043	−	0.0437281i	$-0.986076\pi$
$13$		−	0.315328i		−	0.0874562i	0.999043	−	0.0437281i	$-0.0139235\pi$
$14$	2.49151	+	1.23268i	0.665885	+	0.329448i
$15$	2.89264	+	6.14968i	0.746877	+	1.58784i
$16$	−1.05523	+	3.85830i	−0.263807	+	0.964575i
$17$	−1.43205			−0.347323			−0.173662	−	0.984805i	$-0.555560\pi$
$17$	−1.43205			−0.347323			−0.173662	+	0.984805i	$0.555560\pi$
$18$	−3.91152	+	7.90602i	−0.921955	+	1.86347i
$19$	4.48278			1.02842			0.514210	−	0.857664i	$-0.328085\pi$
$19$	4.48278			1.02842			0.514210	+	0.857664i	$0.328085\pi$
$20$	−2.06203	+	3.96838i	−0.461083	+	0.887357i
$21$			5.97399i			1.30363i
$22$	3.32747	−	6.72552i	0.709419	−	1.43389i
$23$	0.916686	−	4.70741i	0.191142	−	0.981562i
$23$	0.916686	−	4.70741i	0.191142	−	0.981562i
$24$	−8.43763	+	1.64438i	−1.72232	+	0.335658i
$25$	−3.18833	+	3.85157i	−0.637665	+	0.770313i
$26$	0.399697	+	0.197751i	0.0783870	+	0.0387822i
$27$	−9.83873			−1.89346
$28$	−3.12500	+	2.38509i	−0.590569	+	0.450740i
$29$	−6.11341			−1.13523			−0.567616	−	0.823294i	$-0.692134\pi$
$29$	−6.11341			−1.13523			−0.567616	+	0.823294i	$0.692134\pi$
$30$	−9.60915	−	0.190041i	−1.75438	−	0.0346967i
$31$			7.40223i			1.32948i	0.747075	+	0.664740i	$0.231458\pi$
$31$			7.40223i			1.32948i	−0.747075	+	0.664740i	$0.768542\pi$
$32$	−4.22887	−	3.75722i	−0.747565	−	0.664188i
$33$	16.1260			2.80718
$34$	0.898081	−	1.81521i	0.154020	−	0.311306i
$35$	−3.97720	+	1.87077i	−0.672269	+	0.316217i
$36$	−7.56833	−	9.91619i	−1.26139	−	1.65270i
$37$	−6.56660			−1.07954			−0.539771	−	0.841812i	$-0.681489\pi$
$37$	−6.56660			−1.07954			−0.539771	+	0.841812i	$0.681489\pi$
$38$	−2.81128	+	5.68219i	−0.456050	+	0.921774i
$39$			0.958368i			0.153462i
$40$	−3.73701	−	5.10243i	−0.590873	−	0.806765i
$41$	−0.152099			−0.0237538			−0.0118769	−	0.999929i	$-0.503781\pi$
$41$	−0.152099			−0.0237538			−0.0118769	+	0.999929i	$0.503781\pi$
$42$	−7.57239	−	3.74646i	−1.16845	−	0.578092i
$43$			8.98786i			1.37064i	0.728244	+	0.685318i	$0.240337\pi$
$43$			8.98786i			1.37064i	−0.728244	+	0.685318i	$0.759663\pi$
$44$	6.43825	+	8.43553i	0.970603	+	1.27170i
$45$	−5.93628	−	12.6204i	−0.884928	−	1.88133i
$46$	5.39204	+	4.11411i	0.795013	+	0.606592i
$47$	1.31095			0.191221			0.0956107	−	0.995419i	$-0.469520\pi$
$47$	1.31095			0.191221			0.0956107	+	0.995419i	$0.469520\pi$
$48$	3.20713	−	11.7264i	0.462909	−	1.69257i
$49$	3.13643			0.448061
$50$	−2.88260	−	6.45683i	−0.407662	−	0.913133i
$51$	4.35240			0.609458
$52$	−0.501323	+	0.382625i	−0.0695210	+	0.0530605i
$53$	10.8030			1.48390			0.741952	−	0.670453i	$-0.233900\pi$
$53$	10.8030			1.48390			0.741952	+	0.670453i	$0.233900\pi$
$54$	6.17015	−	12.4712i	0.839651	−	1.69711i
$55$	5.04989	+	10.7359i	0.680927	+	1.44763i
$56$	−1.06347	−	5.45689i	−0.142113	−	0.729207i
$57$	−13.6244			−1.80460
$58$	3.83389	−	7.74911i	0.503415	−	1.01751i
$59$			7.22568i			0.940703i	0.882479	+	0.470352i	$0.155873\pi$
$59$			7.22568i			0.940703i	−0.882479	+	0.470352i	$0.844127\pi$
$60$	6.26707	−	12.0610i	0.809075	−	1.55707i
$61$		−	4.20106i		−	0.537891i	−0.963155	−	0.268945i	$-0.913325\pi$
$61$		−	4.20106i		−	0.537891i	0.963155	−	0.268945i	$-0.0866751\pi$
$62$	−9.38278	−	4.64215i	−1.19161	−	0.589554i
$63$		−	12.2598i		−	1.54459i
$64$	7.41454	−	3.00409i	0.926818	−	0.375511i
$65$	−0.638035	+	0.300115i	−0.0791385	+	0.0372246i
$66$	−10.1131	+	20.4407i	−1.24484	+	2.51608i
$67$			3.99252i			0.487764i	0.969805	+	0.243882i	$0.0784210\pi$
$67$			3.99252i			0.487764i	−0.969805	+	0.243882i	$0.921579\pi$
$68$	1.73768	+	2.27674i	0.210724	+	0.276096i
$69$	−2.78606	+	14.3071i	−0.335402	+	1.72237i
$70$	0.122906	−	6.21455i	0.0146901	−	0.742781i
$71$			0.608318i			0.0721940i	0.999348	+	0.0360970i	$0.0114925\pi$
$71$			0.608318i			0.0721940i	−0.999348	+	0.0360970i	$0.988507\pi$
$72$	17.3157	−	3.37459i	2.04067	−	0.397700i
$73$			14.2324i			1.66577i	0.553443	+	0.832887i	$0.313314\pi$
$73$			14.2324i			1.66577i	−0.553443	+	0.832887i	$0.686686\pi$
$74$	4.11810	−	8.32356i	0.478720	−	0.967595i
$75$	9.69021	−	11.7060i	1.11893	−	1.35169i
$76$	−5.43949	−	7.12693i	−0.623952	−	0.817515i
$77$			10.4292i			1.18852i
$78$	−1.21479	−	0.601020i	−0.137548	−	0.0680521i
$79$	4.74332			0.533666			0.266833	−	0.963743i	$-0.414023\pi$
$79$	4.74332			0.533666			0.266833	+	0.963743i	$0.414023\pi$
$80$	8.81122	−	1.53700i	0.985124	−	0.171842i
$81$	11.1910			1.24345
$82$	0.0953854	−	0.192794i	0.0105336	−	0.0212906i
$83$			5.33199i			0.585262i	0.956225	+	0.292631i	$0.0945307\pi$
$83$			5.33199i			0.585262i	−0.956225	+	0.292631i	$0.905469\pi$
$84$	9.49773	−	7.24895i	1.03629	−	0.790926i
$85$	1.36296	+	2.89762i	0.147834	+	0.314291i
$86$	−11.3927	−	5.63654i	−1.22850	−	0.607804i
$87$	18.5803			1.99202
$88$	−14.7302	+	2.87071i	−1.57024	+	0.306019i
$89$			10.5110i			1.11416i	0.830459	+	0.557080i	$0.188078\pi$
$89$			10.5110i			1.11416i	−0.830459	+	0.557080i	$0.811922\pi$
$90$	19.7199	+	0.390003i	2.07866	+	0.0411099i
$91$	−0.619807			−0.0649734
$92$	−8.59638	+	4.25467i	−0.896235	+	0.443580i
$93$		−	22.4974i		−	2.33287i
$94$	−0.822133	+	1.66170i	−0.0847965	+	0.171392i
$95$	−4.26650	−	9.07047i	−0.437734	−	0.930611i
$96$	12.8527	+	11.4192i	1.31177	+	1.16547i
$97$	6.27182			0.636806			0.318403	−	0.947955i	$-0.396853\pi$
$97$	6.27182			0.636806			0.318403	+	0.947955i	$0.396853\pi$
$98$	−1.96694	+	3.97561i	−0.198691	+	0.401598i
$99$	−33.0938			−3.32605
$100$	9.99218	+	0.395388i	0.999218	+	0.0395388i
$101$	−17.2761			−1.71904			−0.859519	−	0.511103i	$-0.829237\pi$
$101$	−17.2761			−1.71904			−0.859519	+	0.511103i	$0.829237\pi$
$102$	−2.72951	+	5.51693i	−0.270262	+	0.546257i
$103$		−	10.8970i		−	1.07372i	−0.843673	−	0.536858i	$-0.819611\pi$
$103$		−	10.8970i		−	1.07372i	0.843673	−	0.536858i	$-0.180389\pi$
$104$	−0.170606	−	0.875412i	−0.0167293	−	0.0858412i
$105$	12.0878	−	5.68577i	1.17965	−	0.554875i
$106$	−6.77486	+	13.6934i	−0.658033	+	1.33002i
$107$		−	10.6102i		−	1.02573i	−0.858470	−	0.512863i	$-0.828585\pi$
$107$		−	10.6102i		−	1.02573i	0.858470	−	0.512863i	$-0.171415\pi$
$108$	11.9385	+	15.6421i	1.14878	+	1.50516i
$109$		−	11.5772i		−	1.10889i	−0.832219	−	0.554447i	$-0.812930\pi$
$109$		−	11.5772i		−	1.10889i	0.832219	−	0.554447i	$-0.187070\pi$
$110$	−16.7754	−	0.331769i	−1.59947	−	0.0316329i
$111$	19.9577			1.89430
$112$	7.58387	+	2.07415i	0.716608	+	0.195989i
$113$	−3.56369			−0.335244			−0.167622	−	0.985851i	$-0.553609\pi$
$113$	−3.56369			−0.335244			−0.167622	+	0.985851i	$0.553609\pi$
$114$	8.54425	−	17.2698i	0.800243	−	1.61746i
$115$	−10.3974	+	2.62547i	−0.969567	+	0.244826i
$116$	7.41813	+	9.71938i	0.688756	+	0.902422i
$117$		−	1.96676i		−	0.181827i
$118$	−9.15898	−	4.53143i	−0.843153	−	0.417152i
$119$			2.81484i			0.258036i
$120$	11.3578	+	15.5077i	1.03682	+	1.41565i
$121$	17.1523			1.55930
$122$	5.32510	+	2.63461i	0.482112	+	0.238526i
$123$	0.462270			0.0416815
$124$	11.7684	−	8.98201i	1.05684	−	0.806608i
$125$	10.8278	+	2.78553i	0.968466	+	0.249145i
$126$	15.5401	+	7.68848i	1.38442	+	0.684944i
$127$	−1.35452			−0.120194			−0.0600971	−	0.998193i	$-0.519141\pi$
$127$	−1.35452			−0.120194			−0.0600971	+	0.998193i	$0.519141\pi$
$128$	−0.842013	+	11.2823i	−0.0744242	+	0.997227i
$129$		−	27.3166i		−	2.40509i
$130$	0.0197170	−	0.996959i	0.00172929	−	0.0874391i
$131$		−	8.96892i		−	0.783618i	−0.920047	−	0.391809i	$-0.871849\pi$
$131$		−	8.96892i		−	0.783618i	0.920047	−	0.391809i	$-0.128151\pi$
$132$	−19.5676	−	25.6379i	−1.70314	−	2.23149i
$133$		−	8.81134i		−	0.764040i
$134$	−5.06076	−	2.50382i	−0.437183	−	0.216298i
$135$	9.36406	+	19.9077i	0.805930	+	1.71338i
$136$	−3.97566	+	0.774802i	−0.340910	+	0.0664387i
$137$	−20.3624			−1.73968			−0.869839	−	0.493336i	$-0.835777\pi$
$137$	−20.3624			−1.73968			−0.869839	+	0.493336i	$0.835777\pi$
$138$	−16.3879	−	12.5039i	−1.39503	−	1.06440i
$139$			16.2845i			1.38123i	0.723222	+	0.690616i	$0.242660\pi$
$139$			16.2845i			1.38123i	−0.723222	+	0.690616i	$0.757340\pi$
$140$	7.80024	+	4.05311i	0.659240	+	0.342551i
$141$	−3.98433			−0.335541
$142$	−0.771080	−	0.381494i	−0.0647076	−	0.0320142i
$143$			1.67309i			0.139911i
$144$	−6.58166	+	24.0650i	−0.548472	+	2.00542i
$145$	5.81846	+	12.3699i	0.483197	+	1.02726i
$146$	−18.0404	−	8.92554i	−1.49303	−	0.738683i
$147$	−9.53247			−0.786225
$148$	7.96804	+	10.4399i	0.654969	+	0.858154i
$149$			12.8748i			1.05475i	0.849634	+	0.527373i	$0.176823\pi$
$149$			12.8748i			1.05475i	−0.849634	+	0.527373i	$0.823177\pi$
$150$	8.76102	+	19.6241i	0.715335	+	1.60230i
$151$		−	7.83400i		−	0.637522i	−0.947835	−	0.318761i	$-0.896733\pi$
$151$		−	7.83400i		−	0.637522i	0.947835	−	0.318761i	$-0.103267\pi$
$152$	12.4451	−	2.42538i	1.00943	−	0.196724i
$153$	−8.93199			−0.722108
$154$	−13.2197	−	6.54046i	−1.06527	−	0.527045i
$155$	14.9777	−	7.04511i	1.20304	−	0.565877i
$156$	1.52366	−	1.16290i	0.121990	−	0.0931067i
$157$	5.46720			0.436330			0.218165	−	0.975912i	$-0.429993\pi$
$157$	5.46720			0.436330			0.218165	+	0.975912i	$0.429993\pi$
$158$	−2.97467	+	6.01245i	−0.236652	+	0.478325i
$159$	−32.8333			−2.60385
$160$	−3.57753	+	12.1327i	−0.282828	+	0.959171i
$161$	−9.25287	−	1.80184i	−0.729228	−	0.142005i
$162$	−7.01821	+	14.1853i	−0.551403	+	1.11450i
$163$	5.70232			0.446641			0.223320	−	0.974745i	$-0.428310\pi$
$163$	5.70232			0.446641			0.223320	+	0.974745i	$0.428310\pi$
$164$	0.184559	+	0.241814i	0.0144117	+	0.0188825i
$165$	−15.3480	−	32.6295i	−1.19484	−	2.54020i
$166$	−6.75862	−	3.34384i	−0.524571	−	0.259533i
$167$	−10.1090			−0.782257			−0.391129	−	0.920336i	$-0.627915\pi$
$167$	−10.1090			−0.782257			−0.391129	+	0.920336i	$0.627915\pi$
$168$	3.23219	+	16.5850i	0.249369	+	1.27956i
$169$	12.9006			0.992351
$170$	−4.52766	−	0.0895441i	−0.347256	−	0.00686772i
$171$	27.9600			2.13815
$172$	14.2893	−	10.9060i	1.08955	−	0.831578i
$173$			6.64716i			0.505375i	0.967548	+	0.252687i	$0.0813144\pi$
$173$			6.64716i			0.505375i	−0.967548	+	0.252687i	$0.918686\pi$
$174$	−11.6523	+	23.5517i	−0.883356	+	1.78545i
$175$	7.57063	+	6.26697i	0.572286	+	0.473738i
$176$	5.59891	−	20.4717i	0.422034	−	1.54311i
$177$		−	21.9608i		−	1.65068i
$178$	−13.3233	−	6.59173i	−0.998622	−	0.494071i
$179$		−	18.0713i		−	1.35071i	−0.737491	−	0.675357i	$-0.763989\pi$
$179$		−	18.0713i		−	1.35071i	0.737491	−	0.675357i	$-0.236011\pi$
$180$	−12.8613	+	24.7516i	−0.958622	+	1.84487i
$181$		−	8.00130i		−	0.594732i	−0.954764	−	0.297366i	$-0.903892\pi$
$181$		−	8.00130i		−	0.594732i	0.954764	−	0.297366i	$-0.0961081\pi$
$182$	0.388699	−	0.785643i	0.0288123	−	0.0582357i
$183$			12.7682i			0.943851i
$184$	−0.00200930	−	13.5647i	−0.000148128	−	1.00000i
$185$	6.24979	+	13.2869i	0.459494	+	0.976871i
$186$	28.5168	+	14.1088i	2.09096	+	1.03451i
$187$	7.59829			0.555642
$188$	−1.59073	−	2.08421i	−0.116016	−	0.152006i
$189$			19.3390i			1.40670i
$190$	14.1730	+	0.280302i	1.02822	+	0.0203352i
$191$	−11.2451			−0.813670			−0.406835	−	0.913502i	$-0.633368\pi$
$191$	−11.2451			−0.813670			−0.406835	+	0.913502i	$0.633368\pi$
$192$	−22.5348	+	9.13024i	−1.62631	+	0.658919i
$193$		−	12.0682i		−	0.868689i	−0.900747	−	0.434344i	$-0.856980\pi$
$193$		−	12.0682i		−	0.868689i	0.900747	−	0.434344i	$-0.143020\pi$
$194$	−3.93324	+	7.94990i	−0.282390	+	0.570770i
$195$	1.93917	−	0.912131i	0.138867	−	0.0653190i
$196$	−3.80580	−	4.98644i	−0.271843	−	0.356174i
$197$			6.58115i			0.468888i	0.972130	+	0.234444i	$0.0753269\pi$
$197$			6.58115i			0.468888i	−0.972130	+	0.234444i	$0.924673\pi$
$198$	20.7541	−	41.9484i	1.47493	−	2.98114i
$199$	−22.8257			−1.61807			−0.809037	−	0.587758i	$-0.800011\pi$
$199$	−22.8257			−1.61807			−0.809037	+	0.587758i	$0.800011\pi$
$200$	−6.76756	+	12.4177i	−0.478539	+	0.878066i
$201$		−	12.1344i		−	0.855893i
$202$	10.8344	−	21.8985i	0.762302	−	1.54078i
$203$			12.0165i			0.843393i
$204$	−5.28128	−	6.91965i	−0.369764	−	0.484472i
$205$	0.144761	+	0.307757i	0.0101105	+	0.0214947i
$206$	13.8126	+	6.83384i	0.962372	+	0.476136i
$207$	5.71755	−	29.3610i	0.397397	−	2.04073i
$208$	1.21663	+	0.332743i	0.0843581	+	0.0230716i
$209$	−23.7851			−1.64525
$210$	−0.373545	+	18.8877i	−0.0257771	+	1.30338i
$211$		−	9.60875i		−	0.661494i	−0.943720	−	0.330747i	$-0.892699\pi$
$211$		−	9.60875i		−	0.661494i	0.943720	−	0.330747i	$-0.107301\pi$
$212$	−13.1086	−	17.1751i	−0.900299	−	1.17959i
$213$		−	1.84885i		−	0.126681i
$214$	13.4491	+	6.65396i	0.919359	+	0.454855i
$215$	18.1861	−	8.55423i	1.24028	−	0.583394i
$216$	−27.3143	+	5.32318i	−1.85850	+	0.362196i
$217$	14.5498			0.987705
$218$	14.6748	+	7.26039i	0.993902	+	0.491735i
$219$		−	43.2561i		−	2.92298i
$220$	10.9409	−	21.0557i	0.737633	−	1.41958i
$221$			0.451565i			0.0303756i
$222$	−12.5161	+	25.2976i	−0.840022	+	1.69786i
$223$	−6.16459			−0.412812			−0.206406	−	0.978466i	$-0.566177\pi$
$223$	−6.16459			−0.412812			−0.206406	+	0.978466i	$0.566177\pi$
$224$	−7.38518	+	8.31225i	−0.493443	+	0.555385i
$225$	−19.8862	+	24.0230i	−1.32575	+	1.60153i
$226$	2.23489	−	4.51720i	0.148663	−	0.300479i
$227$			21.9012i			1.45364i	0.686830	+	0.726818i	$0.259002\pi$
$227$			21.9012i			1.45364i	−0.686830	+	0.726818i	$0.740998\pi$
$228$	16.5321	+	21.6607i	1.09487	+	1.43452i
$229$			13.8844i			0.917510i	0.888563	+	0.458755i	$0.151704\pi$
$229$			13.8844i			0.917510i	−0.888563	+	0.458755i	$0.848296\pi$
$230$	3.19260	−	14.8259i	0.210514	−	0.977591i
$231$		−	31.6973i		−	2.08553i
$232$	−16.9720	+	3.30762i	−1.11427	+	0.217156i
$233$			17.3917i			1.13937i	0.821864	+	0.569684i	$0.192935\pi$
$233$			17.3917i			1.13937i	−0.821864	+	0.569684i	$0.807065\pi$
$234$	2.49299	+	1.23341i	0.162972	+	0.0806307i
$235$	−1.24770	−	2.65258i	−0.0813910	−	0.173035i
$236$	11.4877	−	8.76778i	0.747787	−	0.570734i
$237$	−14.4163			−0.936437
$238$	−3.56797	−	1.76526i	−0.231277	−	0.114425i
$239$		−	18.0859i		−	1.16988i	−0.811076	−	0.584941i	$-0.801118\pi$
$239$		−	18.0859i		−	1.16988i	0.811076	−	0.584941i	$-0.198882\pi$
$240$	−26.7797	+	4.67138i	−1.72862	+	0.301536i
$241$			6.55414i			0.422189i	0.977466	+	0.211095i	$0.0677028\pi$
$241$			6.55414i			0.422189i	−0.977466	+	0.211095i	$0.932297\pi$
$242$	−10.7567	+	21.7416i	−0.691468	+	1.39760i
$243$	−4.49642			−0.288446
$244$	−6.67904	+	5.09765i	−0.427582	+	0.326343i
$245$	−2.98511	−	6.34626i	−0.190712	−	0.405448i
$246$	−0.289903	+	0.585955i	−0.0184835	+	0.0373591i
$247$		−	1.41354i		−	0.0899417i
$248$	4.00493	+	20.5501i	0.254313	+	1.30493i
$249$		−	16.2054i		−	1.02697i
$250$	−10.3212	+	11.9780i	−0.652772	+	0.757554i
$251$	−23.1792			−1.46306			−0.731530	−	0.681809i	$-0.761193\pi$
$251$	−23.1792			−1.46306			−0.731530	+	0.681809i	$0.761193\pi$
$252$	−19.4912	+	14.8763i	−1.22783	+	0.937118i
$253$	−4.86382	+	24.9769i	−0.305786	+	1.57029i
$254$	0.849459	−	1.71694i	0.0532998	−	0.107730i
$255$	−4.14241	−	8.80666i	−0.259408	−	0.551495i
$256$	−13.7730	−	8.14278i	−0.860812	−	0.508924i
$257$			17.8689i			1.11463i	0.830300	+	0.557317i	$0.188169\pi$
$257$			17.8689i			1.11463i	−0.830300	+	0.557317i	$0.811831\pi$
$258$	34.6254	+	17.1310i	2.15568	+	1.06653i
$259$			12.9073i			0.802020i
$260$	1.25134	+	0.650214i	0.0776048	+	0.0403246i
$261$	−38.1305			−2.36022
$262$	11.3686	+	5.62467i	0.702357	+	0.347493i
$263$			2.81172i			0.173378i	0.996235	+	0.0866891i	$0.0276287\pi$
$263$			2.81172i			0.173378i	−0.996235	+	0.0866891i	$0.972371\pi$
$264$	44.7690	−	8.72488i	2.75534	−	0.536979i
$265$	−10.2818	−	21.8588i	−0.631605	−	1.34278i
$266$	11.1689	+	5.52584i	0.684809	+	0.338811i
$267$		−	31.9457i		−	1.95505i
$268$	6.34750	−	4.84460i	0.387735	−	0.295931i
$269$	21.7129			1.32386			0.661930	−	0.749566i	$-0.269738\pi$
$269$	21.7129			1.32386			0.661930	+	0.749566i	$0.269738\pi$
$270$	−31.1067	−	0.615202i	−1.89309	−	0.0374400i
$271$			26.6902i			1.62131i	0.585521	+	0.810657i	$0.300890\pi$
$271$			26.6902i			1.62131i	−0.585521	+	0.810657i	$0.699110\pi$
$272$	1.51114	−	5.52529i	0.0916264	−	0.335020i
$273$	1.88376			0.114011
$274$	12.7699	−	25.8106i	0.771455	−	1.55927i
$275$	16.9169	−	20.4359i	1.02013	−	1.23233i
$276$	26.1268	−	12.9311i	1.57265	−	0.778361i
$277$			14.3237i			0.860628i	0.902679	+	0.430314i	$0.141597\pi$
$277$			14.3237i			0.860628i	−0.902679	+	0.430314i	$0.858403\pi$
$278$	−20.6416	−	10.2125i	−1.23800	−	0.612503i
$279$			46.1692i			2.76408i
$280$	−10.0293	+	7.34545i	−0.599366	+	0.438975i
$281$		−	7.07446i		−	0.422027i	−0.977483	−	0.211013i	$-0.932324\pi$
$281$		−	7.07446i		−	0.422027i	0.977483	−	0.211013i	$-0.0676763\pi$
$282$	2.49869	−	5.05038i	0.148795	−	0.300746i
$283$			7.08249i			0.421010i	0.977593	+	0.210505i	$0.0675108\pi$
$283$			7.08249i			0.421010i	−0.977593	+	0.210505i	$0.932489\pi$
$284$	0.967132	−	0.738144i	0.0573887	−	0.0438008i
$285$	12.9671	+	27.5677i	0.768104	+	1.63297i
$286$	−2.12074	−	1.04924i	−0.125402	−	0.0620430i
$287$			0.298965i			0.0176473i
$288$	−26.3763	−	23.4345i	−1.55424	−	1.38089i
$289$	−14.9492			−0.879366
$290$	−19.3285	−	0.382263i	−1.13501	−	0.0224472i
$291$	−19.0618			−1.11742
$292$	22.6273	−	17.2698i	1.32416	−	1.01064i
$293$	4.07886			0.238289			0.119145	−	0.992877i	$-0.461985\pi$
$293$	4.07886			0.238289			0.119145	+	0.992877i	$0.461985\pi$
$294$	5.97809	−	12.0830i	0.348649	−	0.704694i
$295$	14.6205	−	6.87707i	0.851236	−	0.400399i
$296$	−18.2302	+	3.55281i	−1.05961	+	0.206503i
$297$	52.2031			3.02913
$298$	−16.3196	−	8.07417i	−0.945370	−	0.467724i
$299$	−1.48438	−	0.289057i	−0.0858437	−	0.0167166i
$300$	−30.3690	−	1.20169i	−1.75335	−	0.0693798i
$301$	17.6665			1.01828
$302$	9.93006	+	4.91292i	0.571411	+	0.282707i
$303$	52.5069			3.01644
$304$	−4.73036	+	17.2959i	−0.271304	+	0.991989i
$305$	−8.50044	+	3.99838i	−0.486734	+	0.228946i
$306$	5.60150	−	11.3218i	0.320217	−	0.647226i
$307$	−12.1381			−0.692758			−0.346379	−	0.938095i	$-0.612589\pi$
$307$	−12.1381			−0.692758			−0.346379	+	0.938095i	$0.612589\pi$
$308$	16.5809	−	12.6550i	0.944782	−	0.721086i
$309$			33.1191i			1.88408i
$310$	−0.462851	+	23.4033i	−0.0262882	+	1.32922i
$311$			23.4935i			1.33219i	0.745865	+	0.666097i	$0.232036\pi$
$311$			23.4935i			1.33219i	−0.745865	+	0.666097i	$0.767964\pi$
$312$	0.518518	+	2.66062i	0.0293553	+	0.150628i
$313$	−1.95042			−0.110244			−0.0551220	−	0.998480i	$-0.517555\pi$
$313$	−1.95042			−0.110244			−0.0551220	+	0.998480i	$0.517555\pi$
$314$	−3.42864	+	6.93001i	−0.193489	+	0.391083i
$315$	−24.8066	+	11.6683i	−1.39769	+	0.657436i
$316$	−5.75564	−	7.54116i	−0.323780	−	0.424223i
$317$			0.290018i			0.0162890i	0.999967	+	0.00814452i	$0.00259251\pi$
$317$			0.290018i			0.0162890i	−0.999967	+	0.00814452i	$0.997407\pi$
$318$	20.5907	−	41.6181i	1.15467	−	2.33383i
$319$	32.4370			1.81612
$320$	−13.1353	−	12.1435i	−0.734286	−	0.678840i
$321$			32.2473i			1.79987i
$322$	8.08667	−	10.5986i	0.450653	−	0.590636i
$323$	−6.41957			−0.357194
$324$	−13.5794	−	17.7920i	−0.754411	−	0.988446i
$325$	1.21451	+	1.00537i	0.0673687	+	0.0557678i
$326$	−3.57609	+	7.22804i	−0.198061	+	0.400324i
$327$			35.1863i			1.94580i
$328$	−0.422256	+	0.0822919i	−0.0233152	+	0.00454381i
$329$		−	2.57679i		−	0.142063i
$330$	50.9850	+	1.00834i	2.80663	+	0.0555071i
$331$			11.4185i			0.627619i	0.949486	+	0.313810i	$0.101605\pi$
$331$			11.4185i			0.627619i	−0.949486	+	0.313810i	$0.898395\pi$
$332$	8.47705	−	6.46994i	0.465239	−	0.355084i
$333$	−40.9572			−2.24444
$334$	6.33964	−	12.8138i	0.346890	−	0.701138i
$335$	8.07848	−	3.79990i	0.441375	−	0.207611i
$336$	−23.0495	−	6.30392i	−1.25745	−	0.343907i
$337$	−17.7990			−0.969572			−0.484786	−	0.874633i	$-0.661102\pi$
$337$	−17.7990			−0.969572			−0.484786	+	0.874633i	$0.661102\pi$
$338$	−8.09032	+	16.3523i	−0.440055	+	0.889445i
$339$	10.8310			0.588262
$340$	2.95293	−	5.68293i	0.160145	−	0.308200i
$341$		−	39.2753i		−	2.12688i
$342$	−17.5345	+	35.4410i	−0.948157	+	1.91643i
$343$		−	19.9241i		−	1.07580i
$344$	4.86282	+	24.9521i	0.262186	+	1.34533i
$345$	31.6007	−	7.97952i	1.70132	−	0.429603i
$346$	−8.42568	−	4.16863i	−0.452968	−	0.224107i
$347$	6.82029			0.366132			0.183066	−	0.983101i	$-0.441398\pi$
$347$	6.82029			0.366132			0.183066	+	0.983101i	$0.441398\pi$
$348$	−22.5457	−	29.5399i	−1.20858	−	1.58350i
$349$	11.8293			0.633208			0.316604	−	0.948558i	$-0.397457\pi$
$349$	11.8293			0.633208			0.316604	+	0.948558i	$0.397457\pi$
$350$	−12.6915	+	5.66604i	−0.678390	+	0.302862i
$351$			3.10242i			0.165595i
$352$	22.4379	+	19.9353i	1.19594	+	1.06256i
$353$		−	21.7201i		−	1.15604i	−0.816022	−	0.578021i	$-0.803825\pi$
$353$		−	21.7201i		−	1.15604i	0.816022	−	0.578021i	$-0.196175\pi$
$354$	27.8367	+	13.7723i	1.47950	+	0.731988i
$355$	1.23087	−	0.578969i	0.0653279	−	0.0307285i
$356$	16.7108	−	12.7542i	0.885672	−	0.675972i
$357$		−	8.55506i		−	0.452782i
$358$	22.9065	+	11.3331i	1.21065	+	0.598970i
$359$	−4.50420			−0.237723			−0.118861	−	0.992911i	$-0.537924\pi$
$359$	−4.50420			−0.237723			−0.118861	+	0.992911i	$0.537924\pi$
$360$	−23.3084	−	31.8248i	−1.22846	−	1.67732i
$361$	1.09531			0.0576480
$362$	10.1421	+	5.01784i	0.533058	+	0.263732i
$363$	−52.1307			−2.73615
$364$	0.752086	+	0.985399i	0.0394200	+	0.0516489i
$365$	28.7979	−	13.5457i	1.50735	−	0.709016i
$366$	−16.1844	−	8.00729i	−0.845974	−	0.418548i
$367$			11.8186i			0.616927i	0.951236	+	0.308464i	$0.0998148\pi$
$367$			11.8186i			0.616927i	−0.951236	+	0.308464i	$0.900185\pi$
$368$	17.1953	+	8.50424i	0.896366	+	0.443314i
$369$	−0.948669			−0.0493857
$370$	−20.7614	−	0.410600i	−1.07933	−	0.0213461i
$371$		−	21.2343i		−	1.10243i
$372$	−35.7675	+	27.2988i	−1.85446	+	1.41538i
$373$	−28.6637			−1.48415			−0.742075	−	0.670317i	$-0.766158\pi$
$373$	−28.6637			−1.48415			−0.742075	+	0.670317i	$0.766158\pi$
$374$	−4.76511	+	9.63129i	−0.246398	+	0.498022i
$375$	−32.9086	−	8.46599i	−1.69939	−	0.437182i
$376$	3.63945	−	0.709279i	0.187690	−	0.0365783i
$377$			1.92773i			0.0992830i
$378$	−24.5133	−	12.1280i	−1.26083	−	0.623799i
$379$	−30.0386			−1.54298			−0.771489	−	0.636243i	$-0.780488\pi$
$379$	−30.0386			−1.54298			−0.771489	+	0.636243i	$0.780488\pi$
$380$	−9.24361	+	17.7894i	−0.474187	+	0.912576i
$381$	4.11676			0.210908
$382$	7.05215	−	14.2539i	0.360819	−	0.729293i
$383$			5.76649i			0.294654i	0.989088	+	0.147327i	$0.0470669\pi$
$383$			5.76649i			0.294654i	−0.989088	+	0.147327i	$0.952933\pi$
$384$	2.55911	−	34.2901i	0.130594	−	1.74986i
$385$	21.1025	−	9.92605i	1.07548	−	0.505878i
$386$	15.2972	+	7.56832i	0.778606	+	0.385217i
$387$			56.0590i			2.84964i
$388$	−7.61034	−	9.97123i	−0.386356	−	0.506212i
$389$			23.6265i			1.19791i	0.800782	+	0.598956i	$0.204418\pi$
$389$			23.6265i			1.19791i	−0.800782	+	0.598956i	$0.795582\pi$
$390$	−0.0599253	+	3.03003i	−0.00303444	+	0.153432i
$391$	−1.31274	+	6.74125i	−0.0663882	+	0.340920i
$392$	8.70734	−	1.69694i	0.439787	−	0.0857086i
$393$			27.2590i			1.37504i
$394$	−8.34201	−	4.12723i	−0.420264	−	0.207927i
$395$	−4.51448	−	9.59766i	−0.227148	−	0.482911i
$396$	40.1566	+	52.6141i	2.01795	+	2.64396i
$397$		−	12.8794i		−	0.646400i	−0.946331	−	0.323200i	$-0.895241\pi$
$397$		−	12.8794i		−	0.646400i	0.946331	−	0.323200i	$-0.104759\pi$
$398$	14.3147	−	28.9330i	0.717530	−	1.45028i
$399$			26.7801i			1.34068i
$400$	−11.4961	−	16.3658i	−0.574805	−	0.818291i
$401$		−	0.810438i		−	0.0404713i	−0.999795	−	0.0202357i	$-0.993558\pi$
$401$		−	0.810438i		−	0.0404713i	0.999795	−	0.0202357i	$-0.00644165\pi$
$402$	15.3811	+	7.60981i	0.767137	+	0.379543i
$403$	2.33413			0.116271
$404$	20.9632	+	27.4664i	1.04296	+	1.36650i
$405$	−10.6511	−	22.6440i	−0.529258	−	1.12519i
$406$	−15.2316	−	7.53589i	−0.755933	−	0.374000i
$407$	34.8416			1.72703
$408$	12.0831	−	2.35484i	0.598204	−	0.116582i
$409$	−2.68630			−0.132829			−0.0664145	−	0.997792i	$-0.521156\pi$
$409$	−2.68630			−0.132829			−0.0664145	+	0.997792i	$0.521156\pi$
$410$	−0.480884	−	0.00951051i	−0.0237492	−	0.000469690i
$411$	61.8870			3.05266
$412$	−17.3246	+	13.2227i	−0.853522	+	0.651433i
$413$	14.2028			0.698873
$414$	33.6312	+	25.6605i	1.65288	+	1.26114i
$415$	10.7888	−	5.07474i	0.529600	−	0.249109i
$416$	−1.18475	+	1.33348i	−0.0580874	+	0.0653792i
$417$		−	49.4930i		−	2.42368i
$418$	14.9163	−	30.1490i	0.729580	−	1.47464i
$419$	15.3053			0.747715			0.373857	−	0.927486i	$-0.378035\pi$
$419$	15.3053			0.747715			0.373857	+	0.927486i	$0.378035\pi$
$420$	−23.7071	−	12.3185i	−1.15679	−	0.601083i
$421$		−	34.1894i		−	1.66629i	−0.553056	−	0.833144i	$-0.686539\pi$
$421$		−	34.1894i		−	1.66629i	0.553056	−	0.833144i	$-0.313461\pi$
$422$	12.1797	+	6.02592i	0.592897	+	0.293337i
$423$	8.17663			0.397562
$424$	29.9912	−	5.84488i	1.45650	−	0.283853i
$425$	4.56585	−	5.51564i	0.221476	−	0.267548i
$426$	2.34352	+	1.15946i	0.113544	+	0.0561762i
$427$	−8.25759			−0.399613
$428$	−16.8686	+	12.8746i	−0.815374	+	0.622318i
$429$		−	5.08498i		−	0.245505i
$430$	−0.561998	+	28.4165i	−0.0271019	+	1.37037i
$431$	7.29598			0.351435			0.175718	−	0.984441i	$-0.443775\pi$
$431$	7.29598			0.351435			0.175718	+	0.984441i	$0.443775\pi$
$432$	10.3821	−	37.9608i	0.499509	−	1.82639i
$433$	−28.2265			−1.35648			−0.678239	−	0.734841i	$-0.737257\pi$
$433$	−28.2265			−1.35648			−0.678239	+	0.734841i	$0.737257\pi$
$434$	−9.12460	+	18.4428i	−0.437995	+	0.885281i
$435$	−17.6839	−	37.5955i	−0.847879	−	1.80257i
$436$	−18.4060	+	14.0480i	−0.881485	+	0.672776i
$437$	4.10930	−	21.1023i	0.196575	−	1.00946i
$438$	54.8298	+	27.1272i	2.61987	+	1.29619i
$439$		−	5.24795i		−	0.250471i	−0.992127	−	0.125235i	$-0.960031\pi$
$439$		−	5.24795i		−	0.250471i	0.992127	−	0.125235i	$-0.0399686\pi$
$440$	19.8281	+	27.0729i	0.945268	+	1.29065i
$441$	19.5625			0.931549
$442$	−0.572387	−	0.283190i	−0.0272257	−	0.0134700i
$443$	−23.6676			−1.12448			−0.562242	−	0.826973i	$-0.690061\pi$
$443$	−23.6676			−1.12448			−0.562242	+	0.826973i	$0.690061\pi$
$444$	−24.2171	−	31.7297i	−1.14929	−	1.50583i
$445$	21.2679	−	10.0039i	1.00820	−	0.474228i
$446$	3.86599	−	7.81400i	0.183060	−	0.370003i
$447$		−	39.1301i		−	1.85079i
$448$	−5.90482	−	14.5740i	−0.278977	−	0.688557i
$449$	7.63135			0.360146			0.180073	−	0.983653i	$-0.442367\pi$
$449$	7.63135			0.360146			0.180073	+	0.983653i	$0.442367\pi$
$450$	−17.9794	−	40.2725i	−0.847555	−	1.89846i
$451$	0.807017			0.0380009
$452$	4.32425	+	5.66573i	0.203396	+	0.266493i
$453$			23.8097i			1.11868i
$454$	−27.7611	−	13.7349i	−1.30289	−	0.644610i
$455$	0.589904	+	1.25412i	0.0276551	+	0.0587941i
$456$	−37.8240	+	7.37139i	−1.77127	+	0.345197i
$457$	4.49342			0.210193			0.105097	−	0.994462i	$-0.466485\pi$
$457$	4.49342			0.210193			0.105097	+	0.994462i	$0.466485\pi$
$458$	−17.5994	−	8.70734i	−0.822365	−	0.406867i
$459$	14.0896			0.657645
$460$	16.7906	+	13.3446i	0.782864	+	0.622193i
$461$	18.8701			0.878867			0.439433	−	0.898275i	$-0.355179\pi$
$461$	18.8701			0.878867			0.439433	+	0.898275i	$0.355179\pi$
$462$	40.1782	+	19.8783i	1.86926	+	0.924821i
$463$	17.9468			0.834057			0.417028	−	0.908893i	$-0.363072\pi$
$463$	17.9468			0.834057			0.417028	+	0.908893i	$0.363072\pi$
$464$	6.45104	−	23.5874i	0.299482	−	1.09502i
$465$	−45.5214	+	21.4120i	−2.11100	+	0.992959i
$466$	−22.0450	−	10.9068i	−1.02122	−	0.505250i
$467$			8.94489i			0.413920i	0.978349	+	0.206960i	$0.0663571\pi$
$467$			8.94489i			0.413920i	−0.978349	+	0.206960i	$0.933643\pi$
$468$	−3.12685	+	2.38651i	−0.144539	+	0.110316i
$469$	7.84769			0.362373
$470$	4.14477	+	0.0819716i	0.191184	+	0.00378107i
$471$	−16.6163			−0.765640
$472$	3.90940	+	20.0599i	0.179945	+	0.923332i
$473$		−	47.6885i		−	2.19272i
$474$	9.04086	−	18.2735i	0.415260	−	0.839329i
$475$	−14.2926	+	17.2657i	−0.655788	+	0.792206i
$476$	4.47516	−	3.41558i	0.205119	−	0.156553i
$477$	67.3803			3.08513
$478$	22.9250	+	11.3422i	1.04857	+	0.518780i
$479$	2.65650			0.121379			0.0606894	−	0.998157i	$-0.480670\pi$
$479$	2.65650			0.121379			0.0606894	+	0.998157i	$0.480670\pi$
$480$	10.8731	−	36.8745i	0.496286	−	1.68308i
$481$			2.07063i			0.0944126i
$482$	−8.30777	−	4.11029i	−0.378408	−	0.187218i
$483$	28.1220	+	5.47627i	1.27960	+	0.249179i
$484$	−20.8130	−	27.2696i	−0.946044	−	1.23953i
$485$	−5.96923	−	12.6904i	−0.271049	−	0.576242i
$486$	2.81983	−	5.69949i	0.127910	−	0.258534i
$487$	−31.3103			−1.41880			−0.709402	−	0.704804i	$-0.751035\pi$
$487$	−31.3103			−1.41880			−0.709402	+	0.704804i	$0.751035\pi$
$488$	−2.27296	−	11.6630i	−0.102892	−	0.527958i
$489$	−17.3309			−0.783732
$490$	9.91632	+	0.196116i	0.447974	+	0.00885963i
$491$		−	15.8572i		−	0.715626i	−0.933793	−	0.357813i	$-0.883523\pi$
$491$		−	15.8572i		−	0.715626i	0.933793	−	0.357813i	$-0.116477\pi$
$492$	−0.560927	−	0.734938i	−0.0252885	−	0.0331336i
$493$	8.75471			0.394292
$494$	1.79175	+	0.886474i	0.0806148	+	0.0398844i
$495$	31.4972	+	66.9621i	1.41569	+	3.00972i
$496$	−28.5601	−	7.81105i	−1.28238	−	0.350726i
$497$	1.19571			0.0536348
$498$	20.5413	+	10.1629i	0.920478	+	0.455409i
$499$			11.1197i			0.497786i	0.968531	+	0.248893i	$0.0800667\pi$
$499$			11.1197i			0.497786i	−0.968531	+	0.248893i	$0.919933\pi$
$500$	−8.71007	−	20.5945i	−0.389526	−	0.921015i
$501$	30.7240			1.37265
$502$	14.5364	−	29.3811i	0.648790	−	1.31134i
$503$			22.9162i			1.02178i	0.859646	+	0.510891i	$0.170684\pi$
$503$			22.9162i			1.02178i	−0.859646	+	0.510891i	$0.829316\pi$
$504$	−6.63309	−	34.0357i	−0.295461	−	1.51607i
$505$	16.4426	+	34.9566i	0.731687	+	1.55555i
$506$	−28.6095	−	21.8289i	−1.27185	−	0.970415i
$507$	−39.2084			−1.74131
$508$	1.64360	+	2.15348i	0.0729230	+	0.0955452i
$509$	33.8034			1.49831			0.749154	−	0.662396i	$-0.230460\pi$
$509$	33.8034			1.49831			0.749154	+	0.662396i	$0.230460\pi$
$510$	13.7608	+	0.272149i	0.609339	+	0.0120510i
$511$	27.9751			1.23755
$512$	18.9589	−	12.3515i	0.837873	−	0.545865i
$513$	−44.1049			−1.94728
$514$	−22.6499	−	11.2061i	−0.999046	−	0.494281i
$515$	−22.0491	+	10.3713i	−0.971598	+	0.457014i
$516$	−43.4292	+	33.1465i	−1.91186	+	1.45919i
$517$	−6.95573			−0.305912
$518$	−16.3608	−	8.09453i	−0.718851	−	0.355653i
$519$		−	20.2026i		−	0.886794i
$520$	−1.60894	+	1.17838i	−0.0705566	+	0.0516755i
$521$			37.4724i			1.64170i	0.571147	+	0.820848i	$0.306499\pi$
$521$			37.4724i			1.64170i	−0.571147	+	0.820848i	$0.693501\pi$
$522$	23.9127	−	48.3327i	1.04663	−	2.11547i
$523$		−	25.5681i		−	1.11802i	−0.829162	−	0.559008i	$-0.811182\pi$
$523$		−	25.5681i		−	1.11802i	0.829162	−	0.559008i	$-0.188818\pi$
$524$	−14.2592	+	10.8831i	−0.622917	+	0.475429i
$525$	−23.0092	−	19.0470i	−1.00420	−	0.831281i
$526$	−3.56403	−	1.76331i	−0.155399	−	0.0768840i
$527$		−	10.6004i		−	0.461760i
$528$	−17.0166	+	62.2191i	−0.740554	+	2.70774i
$529$	−21.3194	−	8.63043i	−0.926929	−	0.375236i
$530$	34.1554	+	0.675495i	1.48361	+	0.0293416i
$531$			45.0680i			1.95578i
$532$	−14.0087	+	10.6918i	−0.607353	+	0.463550i
$533$			0.0479609i			0.00207742i
$534$	40.4931	+	20.0341i	1.75231	+	0.866959i
$535$	−21.4687	+	10.0983i	−0.928173	+	0.436588i
$536$	2.16013	+	11.0840i	0.0933033	+	0.478757i
$537$			54.9238i			2.37014i
$538$	−13.6168	+	27.5224i	−0.587062	+	1.18658i
$539$	−16.6415			−0.716800
$540$	20.2877	−	39.0438i	0.873044	−	1.68018i
$541$	6.58911			0.283288			0.141644	−	0.989918i	$-0.454761\pi$
$541$	6.58911			0.283288			0.141644	+	0.989918i	$0.454761\pi$
$542$	−33.8314	−	16.7382i	−1.45318	−	0.718967i
$543$			24.3181i			1.04359i
$544$	6.05596	+	5.38053i	0.259647	+	0.230688i
$545$	−23.4253	+	11.0186i	−1.00343	+	0.471987i
$546$	−1.18136	+	2.38779i	−0.0505577	+	0.102188i
$547$	12.3733			0.529043			0.264522	−	0.964380i	$-0.414786\pi$
$547$	12.3733			0.529043			0.264522	+	0.964380i	$0.414786\pi$
$548$	24.7081	+	32.3731i	1.05548	+	1.38291i
$549$		−	26.2028i		−	1.11831i
$550$	15.2947	+	34.2591i	0.652170	+	1.46081i
$551$	−27.4051			−1.16749
$552$	0.00610683	+	41.2267i	0.000259924	+	1.75473i
$553$		−	9.32346i		−	0.396474i
$554$	−18.1562	−	8.98281i	−0.771381	−	0.381643i
$555$	−18.9948	−	40.3825i	−0.806286	−	1.71414i
$556$	25.8898	−	19.7599i	1.09797	−	0.838006i
$557$	−36.0239			−1.52638			−0.763190	−	0.646174i	$-0.776368\pi$
$557$	−36.0239			−1.52638			−0.763190	+	0.646174i	$0.776368\pi$
$558$	−58.5222	−	28.9540i	−2.47744	−	1.22572i
$559$	2.83412			0.119871
$560$	−3.02113	−	17.3193i	−0.127666	−	0.731874i
$561$	−23.0933			−0.975000
$562$	8.96730	+	4.43659i	0.378263	+	0.187146i
$563$		−	20.0892i		−	0.846660i	−0.905976	−	0.423330i	$-0.860861\pi$
$563$		−	20.0892i		−	0.846660i	0.905976	−	0.423330i	$-0.139139\pi$
$564$	4.83466	+	6.33448i	0.203576	+	0.266730i
$565$	3.39176	+	7.21079i	0.142692	+	0.303360i
$566$	−8.97748	−	4.44163i	−0.377352	−	0.186696i
$567$		−	21.9970i		−	0.923789i
$568$	0.329126	+	1.68881i	0.0138098	+	0.0708609i
$569$			1.67886i			0.0703814i	0.999381	+	0.0351907i	$0.0112039\pi$
$569$			1.67886i			0.0703814i	−0.999381	+	0.0351907i	$0.988796\pi$
$570$	−43.0757	−	0.851914i	−1.80424	−	0.0356828i
$571$	−22.8810			−0.957541			−0.478771	−	0.877940i	$-0.658917\pi$
$571$	−22.8810			−0.957541			−0.478771	+	0.877940i	$0.658917\pi$
$572$	2.65996	−	2.03016i	0.111218	−	0.0848852i
$573$	34.1771			1.42777
$574$	−0.378956	−	0.187489i	−0.0158173	−	0.00782565i
$575$	15.2082	+	18.5394i	0.634226	+	0.773148i
$576$	46.2460	−	18.7371i	1.92692	−	0.780711i
$577$		−	19.2083i		−	0.799651i	−0.916591	−	0.399826i	$-0.869071\pi$
$577$		−	19.2083i		−	0.799651i	0.916591	−	0.399826i	$-0.130929\pi$
$578$	9.37509	−	18.9491i	0.389952	−	0.788177i
$579$			36.6786i			1.52431i
$580$	12.6060	−	24.2603i	0.523436	−	1.00736i
$581$	10.4805			0.434806
$582$	11.9542	−	24.1620i	0.495517	−	1.00155i
$583$	−57.3193			−2.37392
$584$	7.70034	+	39.5119i	0.318642	+	1.63501i
$585$	−3.97955	+	1.87187i	−0.164534	+	0.0773924i
$586$	−2.55797	+	5.17020i	−0.105669	+	0.213579i
$587$	−31.4892			−1.29970			−0.649849	−	0.760064i	$-0.725168\pi$
$587$	−31.4892			−1.29970			−0.649849	+	0.760064i	$0.725168\pi$
$588$	11.5669	+	15.1552i	0.477010	+	0.624989i
$589$			33.1826i			1.36726i
$590$	−0.451811	+	22.8451i	−0.0186008	+	0.940519i
$591$		−	20.0019i		−	0.822770i
$592$	6.92926	−	25.3359i	0.284791	−	1.04130i
$593$		−	35.6962i		−	1.46587i	−0.680301	−	0.732933i	$-0.738151\pi$
$593$		−	35.6962i		−	1.46587i	0.680301	−	0.732933i	$-0.261849\pi$
$594$	−32.7381	+	66.1706i	−1.34326	+	2.71501i
$595$	5.69555	−	2.67903i	0.233495	−	0.109830i
$596$	20.4690	−	15.6226i	0.838443	−	0.639925i
$597$	69.3737			2.83928
$598$	1.29729	−	1.70026i	0.0530502	−	0.0695288i
$599$			1.31702i			0.0538120i	0.999638	+	0.0269060i	$0.00856549\pi$
$599$			1.31702i			0.0538120i	−0.999638	+	0.0269060i	$0.991435\pi$
$600$	20.5685	−	37.7409i	0.839705	−	1.54077i
$601$	−45.1682			−1.84245			−0.921225	−	0.389030i	$-0.872810\pi$
$601$	−45.1682			−1.84245			−0.921225	+	0.389030i	$0.872810\pi$
$602$	−11.0792	+	22.3934i	−0.451553	+	0.912686i
$603$			24.9021i			1.01409i
$604$	−12.4549	+	9.50592i	−0.506781	+	0.386790i
$605$	−16.3248	−	34.7061i	−0.663698	−	1.41100i
$606$	−32.9286	+	66.5557i	−1.33763	+	2.70364i
$607$	29.5404			1.19901			0.599505	−	0.800371i	$-0.295364\pi$
$607$	29.5404			1.19901			0.599505	+	0.800371i	$0.295364\pi$
$608$	−18.9571	−	16.8428i	−0.768811	−	0.683065i
$609$		−	36.5214i		−	1.47992i
$610$	0.262686	−	13.2823i	0.0106359	−	0.537786i
$611$		−	0.413378i		−	0.0167235i
$612$	10.8382	+	14.2005i	0.438110	+	0.574021i
$613$	21.6214			0.873280			0.436640	−	0.899636i	$-0.356168\pi$
$613$	21.6214			0.873280			0.436640	+	0.899636i	$0.356168\pi$
$614$	7.61215	−	15.3858i	0.307201	−	0.620919i
$615$	−0.439967	−	0.935358i	−0.0177412	−	0.0377173i
$616$	5.64266	+	28.9536i	0.227349	+	1.16657i
$617$	−17.0808			−0.687645			−0.343823	−	0.939035i	$-0.611722\pi$
$617$	−17.0808			−0.687645			−0.343823	+	0.939035i	$0.611722\pi$
$618$	−41.9804	−	20.7699i	−1.68870	−	0.835488i
$619$	25.0506			1.00687			0.503434	−	0.864034i	$-0.332070\pi$
$619$	25.0506			1.00687			0.503434	+	0.864034i	$0.332070\pi$
$620$	−29.3749	−	15.2636i	−1.17972	−	0.613001i
$621$	−9.01903	+	46.3149i	−0.361921	+	1.85855i
$622$	−29.7794	−	14.7335i	−1.19405	−	0.590758i
$623$	20.6603			0.827738
$624$	−3.69767	−	1.01130i	−0.148025	−	0.0404843i
$625$	−4.66914	−	24.5601i	−0.186766	−	0.982405i
$626$	1.22316	−	2.47227i	0.0488874	−	0.0988119i
$627$	72.2894			2.88696
$628$	−6.63401	−	8.69202i	−0.264726	−	0.346849i
$629$	9.40371			0.374950
$630$	0.766588	−	38.7614i	0.0305416	−	1.54429i
$631$	15.7315			0.626261			0.313131	−	0.949710i	$-0.398622\pi$
$631$	15.7315			0.626261			0.313131	+	0.949710i	$0.398622\pi$
$632$	13.1684	−	2.56634i	0.523811	−	0.102084i
$633$			29.2036i			1.16074i
$634$	−0.367616	−	0.181879i	−0.0145999	−	0.00722333i
$635$	1.28917	+	2.74074i	0.0511592	+	0.108763i
$636$	39.8405	+	52.1999i	1.57978	+	2.06986i
$637$		−	0.989003i		−	0.0391857i
$638$	−20.3422	+	41.1159i	−0.805354	+	1.62779i
$639$			3.79420i			0.150096i
$640$	23.6301	−	9.03428i	0.934062	−	0.357111i
$641$			30.3401i			1.19836i	0.800614	+	0.599181i	$0.204507\pi$
$641$			30.3401i			1.19836i	−0.800614	+	0.599181i	$0.795493\pi$
$642$	−40.8754	−	20.2232i	−1.61322	−	0.798147i
$643$		−	25.1755i		−	0.992823i	−0.868087	−	0.496411i	$-0.834651\pi$
$643$		−	25.1755i		−	0.992823i	0.868087	−	0.496411i	$-0.165349\pi$
$644$	8.36296	+	16.8970i	0.329547	+	0.665836i
$645$	−55.2725	+	25.9987i	−2.17635	+	1.02370i
$646$	4.02590	−	8.13719i	0.158397	−	0.320154i
$647$	0.617495			0.0242762			0.0121381	−	0.999926i	$-0.496136\pi$
$647$	0.617495			0.0242762			0.0121381	+	0.999926i	$0.496136\pi$
$648$	31.0685	−	6.05483i	1.22049	−	0.237856i
$649$		−	38.3386i		−	1.50492i
$650$	−2.03602	+	0.908964i	−0.0798591	+	0.0356525i
$651$	−44.2209			−1.73315
$652$	−6.91931	−	9.06582i	−0.270981	−	0.355045i
$653$			9.46066i			0.370224i	0.982717	+	0.185112i	$0.0592648\pi$
$653$			9.46066i			0.370224i	−0.982717	+	0.185112i	$0.940735\pi$
$654$	−44.6007	−	22.0663i	−1.74403	−	0.862861i
$655$	−18.1477	+	8.53621i	−0.709091	+	0.333537i
$656$	0.160499	−	0.586842i	0.00626642	−	0.0229123i
$657$			88.7702i			3.46325i
$658$	3.26624	+	1.61598i	0.127331	+	0.0629975i
$659$	5.61344			0.218668			0.109334	−	0.994005i	$-0.465128\pi$
$659$	5.61344			0.218668			0.109334	+	0.994005i	$0.465128\pi$
$660$	−33.2523	+	63.9942i	−1.29434	+	2.49097i
$661$			18.4372i			0.717124i	0.933506	+	0.358562i	$0.116733\pi$
$661$			18.4372i			0.717124i	−0.933506	+	0.358562i	$0.883267\pi$
$662$	−14.4737	−	7.16089i	−0.562535	−	0.278316i
$663$		−	1.37243i		−	0.0533008i
$664$	2.88484	+	14.8027i	0.111953	+	0.574454i
$665$	−17.8289	+	8.38623i	−0.691375	+	0.325204i
$666$	25.6854	−	51.9157i	0.995290	−	2.01169i
$667$	−5.60408	+	28.7783i	−0.216991	+	1.11430i
$668$	12.2664	+	16.0718i	0.474603	+	0.621835i
$669$	18.7359			0.724372
$670$	−0.249647	+	12.6230i	−0.00964469	+	0.487669i
$671$			22.2903i			0.860508i
$672$	22.4456	−	25.2632i	0.865857	−	0.974550i
$673$			16.1011i			0.620652i	0.950630	+	0.310326i	$0.100438\pi$
$673$			16.1011i			0.620652i	−0.950630	+	0.310326i	$0.899562\pi$
$674$	11.1622	−	22.5613i	0.429954	−	0.869028i
$675$	31.3691	−	37.8945i	1.20740	−	1.45856i
$676$	−15.6538	−	20.5099i	−0.602069	−	0.788844i
$677$	−24.6759			−0.948371			−0.474186	−	0.880425i	$-0.657257\pi$
$677$	−24.6759			−0.948371			−0.474186	+	0.880425i	$0.657257\pi$
$678$	−6.79246	+	13.7290i	−0.260863	+	0.527259i
$679$		−	12.3279i		−	0.473100i
$680$	5.35159	+	7.30694i	0.205224	+	0.280208i
$681$		−	66.5639i		−	2.55073i
$682$	49.7839	+	24.6307i	1.90632	+	0.943158i
$683$	9.43088			0.360862			0.180431	−	0.983588i	$-0.442251\pi$
$683$	9.43088			0.360862			0.180431	+	0.983588i	$0.442251\pi$
$684$	−33.9272	−	44.4521i	−1.29724	−	1.69967i
$685$	19.3800	+	41.2014i	0.740472	+	1.57422i
$686$	25.2550	+	12.4950i	0.964242	+	0.477061i
$687$		−	42.1987i		−	1.60998i
$688$	−34.6779	−	9.48424i	−1.32208	−	0.361583i
$689$		−	3.40648i		−	0.129777i
$690$	−9.70318	+	45.0600i	−0.369394	+	1.71540i
$691$			37.5697i			1.42922i	0.699524	+	0.714610i	$0.253396\pi$
$691$			37.5697i			1.42922i	−0.699524	+	0.714610i	$0.746604\pi$
$692$	10.5680	−	8.06580i	0.401734	−	0.306616i
$693$			65.0491i			2.47101i
$694$	−4.27720	+	8.64513i	−0.162360	+	0.328165i
$695$	32.9501	−	15.4988i	1.24987	−	0.587904i
$696$	51.5827	−	10.0528i	1.95524	−	0.381049i
$697$	0.217813			0.00825026
$698$	−7.41850	+	14.9944i	−0.280794	+	0.567545i
$699$		−	52.8582i		−	1.99928i
$700$	0.777173	−	19.6406i	0.0293744	−	0.742345i
$701$			31.0741i			1.17365i	0.809713	+	0.586826i	$0.199623\pi$
$701$			31.0741i			1.17365i	−0.809713	+	0.586826i	$0.800377\pi$
$702$	−3.93251	−	1.94562i	−0.148423	−	0.0734327i
$703$	−29.4366			−1.11022
$704$	−39.3407	+	15.9393i	−1.48271	+	0.600735i
$705$	3.79210	+	8.06191i	0.142819	+	0.303629i
$706$	27.5315	+	13.6213i	1.03616	+	0.512643i
$707$			33.9579i			1.27712i
$708$	−34.9144	+	26.6477i	−1.31216	+	1.00148i
$709$		−	2.26915i		−	0.0852196i	−0.999092	−	0.0426098i	$-0.986433\pi$
$709$		−	2.26915i		−	0.0852196i	0.999092	−	0.0426098i	$-0.0135672\pi$
$710$	−0.0380372	+	1.92329i	−0.00142751	+	0.0721799i
$711$	29.5850			1.10953
$712$	5.68689	+	29.1805i	0.213125	+	1.09359i
$713$	34.8453	+	6.78553i	1.30497	+	0.254120i
$714$	10.8441	+	5.36513i	0.405829	+	0.200785i
$715$	3.38534	−	1.59237i	0.126604	−	0.0595513i
$716$	−28.7307	+	21.9281i	−1.07372	+	0.819492i
$717$			54.9681i			2.05282i
$718$	2.82471	−	5.70935i	0.105417	−	0.213071i
$719$			1.64576i			0.0613764i	0.999529	+	0.0306882i	$0.00976989\pi$
$719$			1.64576i			0.0613764i	−0.999529	+	0.0306882i	$0.990230\pi$
$720$	54.9573	−	9.58659i	2.04814	−	0.357271i
$721$	−21.4192			−0.797691
$722$	−0.686901	+	1.38837i	−0.0255638	+	0.0516699i
$723$		−	19.9198i		−	0.740826i
$724$	−12.7208	+	9.70893i	−0.472766	+	0.360829i
$725$	19.4915	−	23.5462i	0.723898	−	0.874484i
$726$	32.6926	−	66.0788i	1.21334	−	2.45241i
$727$			35.3467i			1.31094i	0.755222	+	0.655469i	$0.227529\pi$
$727$			35.3467i			1.31094i	−0.755222	+	0.655469i	$0.772471\pi$
$728$	−1.72071	+	0.335342i	−0.0637736	+	0.0124286i
$729$	−19.9072			−0.737304
$730$	−0.889930	+	44.9979i	−0.0329378	+	1.66545i
$731$		−	12.8711i		−	0.476054i
$732$	20.2995	−	15.4932i	0.750290	−	0.572643i
$733$	−3.58076			−0.132258			−0.0661292	−	0.997811i	$-0.521065\pi$
$733$	−3.58076			−0.132258			−0.0661292	+	0.997811i	$0.521065\pi$
$734$	−14.9808	−	7.41180i	−0.552952	−	0.273575i
$735$	9.07257	+	19.2880i	0.334647	+	0.711450i
$736$	−21.5633	+	16.4628i	−0.794834	+	0.606827i
$737$		−	21.1838i		−	0.780316i
$738$	0.594938	−	1.20250i	0.0219000	−	0.0442645i
$739$			42.9433i			1.57969i	0.613303	+	0.789847i	$0.289840\pi$
$739$			42.9433i			1.57969i	−0.613303	+	0.789847i	$0.710160\pi$
$740$	13.5405	−	26.0588i	0.497759	−	0.957940i
$741$			4.29615i			0.157823i
$742$	26.9158	+	13.3167i	0.988109	+	0.488870i
$743$		−	24.4266i		−	0.896125i	−0.894002	−	0.448062i	$-0.852114\pi$
$743$		−	24.4266i		−	0.896125i	0.894002	−	0.448062i	$-0.147886\pi$
$744$	−12.1721	−	62.4573i	−0.446250	−	2.28980i
$745$	26.0510	−	12.2537i	0.954434	−	0.448940i
$746$	17.9758	−	36.3329i	0.658141	−	1.33024i
$747$			33.2567i			1.21680i
$748$	−9.21991	−	12.0801i	−0.337113	−	0.441693i
$749$	−20.8554			−0.762039
$750$	31.3691	−	36.4044i	1.14544	−	1.32930i
$751$	−31.2187			−1.13919			−0.569594	−	0.821927i	$-0.692899\pi$
$751$	−31.2187			−1.13919			−0.569594	+	0.821927i	$0.692899\pi$
$752$	−1.38335	+	5.05803i	−0.0504455	+	0.184447i
$753$	70.4481			2.56727
$754$	−2.44351	−	1.20893i	−0.0889874	−	0.0440267i
$755$	−15.8513	+	7.45604i	−0.576889	+	0.271353i
$756$	30.7460	−	23.4663i	1.11822	−	0.853461i
$757$	−50.3322			−1.82935			−0.914677	−	0.404185i	$-0.867555\pi$
$757$	−50.3322			−1.82935			−0.914677	+	0.404185i	$0.867555\pi$
$758$	18.8380	−	38.0757i	0.684229	−	1.38297i
$759$	14.7825	−	75.9118i	0.536571	−	2.75542i
$760$	−16.7522	−	22.8731i	−0.607665	−	0.829693i
$761$	18.0523			0.654396			0.327198	−	0.944956i	$-0.393896\pi$
$761$	18.0523			0.654396			0.327198	+	0.944956i	$0.393896\pi$
$762$	−2.58174	+	5.21824i	−0.0935265	+	0.189037i
$763$	−22.7561			−0.823825
$764$	13.6451	+	17.8781i	0.493661	+	0.646805i
$765$	8.50106	+	18.0730i	0.307356	+	0.653431i
$766$	−7.30937	−	3.61633i	−0.264098	−	0.130663i
$767$	2.27846			0.0822703
$768$	41.8599	+	24.7481i	1.51049	+	0.893022i
$769$		−	52.1627i		−	1.88103i	−0.339746	−	0.940517i	$-0.610341\pi$
$769$		−	52.1627i		−	1.88103i	0.339746	−	0.940517i	$-0.389659\pi$
$770$	−0.652124	+	32.9736i	−0.0235009	+	1.18829i
$771$		−	54.3086i		−	1.95588i
$772$	−19.1866	+	14.6438i	−0.690541	+	0.527042i
$773$	3.28678			0.118217			0.0591086	−	0.998252i	$-0.481174\pi$
$773$	3.28678			0.118217			0.0591086	+	0.998252i	$0.481174\pi$
$774$	−71.0582	−	35.1562i	−2.55414	−	1.26366i
$775$	−28.5102	−	23.6007i	−1.02412	−	0.847764i
$776$	17.4118	−	3.39332i	0.625047	−	0.121813i
$777$		−	39.2288i		−	1.40733i
$778$	−29.9481	−	14.8169i	−1.07369	−	0.531211i
$779$	−0.681825			−0.0244289
$780$	−3.80317	−	1.97618i	−0.136175	−	0.0707586i
$781$		−	3.22766i		−	0.115495i
$782$	−7.72168	−	5.89161i	−0.276127	−	0.210684i
$783$	60.1482			2.14952
$784$	−3.30965	+	12.1013i	−0.118202	+	0.432189i
$785$	−5.20343	−	11.0624i	−0.185718	−	0.394832i
$786$	−34.5525	−	17.0949i	−1.23245	−	0.609755i
$787$			36.8898i			1.31498i	0.753463	+	0.657490i	$0.228382\pi$
$787$			36.8898i			1.31498i	−0.753463	+	0.657490i	$0.771618\pi$
$788$	10.4630	−	7.98570i	0.372730	−	0.284479i
$789$		−	8.54559i		−	0.304231i
$790$	14.9968	+	0.296593i	0.533561	+	0.0105523i
$791$			7.00478i			0.249061i
$792$	−91.8749	+	17.9052i	−3.26463	+	0.636233i
$793$	−1.32471			−0.0470419
$794$	16.3255	+	8.07706i	0.579369	+	0.286644i
$795$	31.2492	+	66.4349i	1.10829	+	2.35620i
$796$	27.6972	+	36.2894i	0.981700	+	1.28624i
$797$	25.1170			0.889689			0.444844	−	0.895608i	$-0.353259\pi$
$797$	25.1170			0.889689			0.444844	+	0.895608i	$0.353259\pi$
$798$	−33.9454	−	16.7946i	−1.20165	−	0.594521i
$799$	−1.87734			−0.0664156
$800$	27.9542	−	4.30853i	0.988330	−	0.152329i
$801$			65.5590i			2.31641i
$802$	1.02728	+	0.508249i	0.0362745	+	0.0179469i
$803$		−	75.5153i		−	2.66488i
$804$	−19.2918	+	14.7241i	−0.680369	+	0.519278i
$805$	5.16061	+	20.4372i	0.181888	+	0.720316i
$806$	−1.46380	+	2.95865i	−0.0515601	+	0.104214i
$807$	−65.9915			−2.32301
$808$	−47.9619	+	9.34713i	−1.68729	+	0.328831i
$809$	8.04409			0.282815			0.141408	−	0.989951i	$-0.454837\pi$
$809$	8.04409			0.282815			0.141408	+	0.989951i	$0.454837\pi$
$810$	35.3822	+	0.699759i	1.24320	+	0.0245870i
$811$		−	28.5641i		−	1.00302i	−0.865152	−	0.501510i	$-0.832778\pi$
$811$		−	28.5641i		−	1.00302i	0.865152	−	0.501510i	$-0.167222\pi$
$812$	19.1044	−	14.5810i	0.670433	−	0.511694i
$813$		−	81.1189i		−	2.84496i
$814$	−21.8502	+	44.1638i	−0.765848	+	1.54794i
$815$	−5.42721	−	11.5381i	−0.190107	−	0.404162i
$816$	−4.59277	+	16.7929i	−0.160779	+	0.587868i
$817$			40.2906i			1.40959i
$818$	1.68466	−	3.40505i	0.0589027	−	0.119055i
$819$	−3.86586			−0.135084
$820$	0.313631	−	0.603585i	0.0109525	−	0.0210781i
$821$	0.711372			0.0248271			0.0124135	−	0.999923i	$-0.496049\pi$
$821$	0.711372			0.0248271			0.0124135	+	0.999923i	$0.496049\pi$
$822$	−38.8111	+	78.4455i	−1.35369	+	2.73610i
$823$	4.70445			0.163987			0.0819934	−	0.996633i	$-0.473871\pi$
$823$	4.70445			0.163987			0.0819934	+	0.996633i	$0.473871\pi$
$824$	−5.89576	−	30.2523i	−0.205389	−	1.05389i
$825$	−51.4150	+	62.1105i	−1.79004	+	2.16241i
$826$	−8.90697	+	18.0029i	−0.309913	+	0.626400i
$827$		−	12.4128i		−	0.431637i	−0.976433	−	0.215819i	$-0.930758\pi$
$827$		−	12.4128i		−	0.431637i	0.976433	−	0.215819i	$-0.0692420\pi$
$828$	−53.6173	+	26.5372i	−1.86333	+	0.922231i
$829$	12.0648			0.419029			0.209514	−	0.977806i	$-0.432812\pi$
$829$	12.0648			0.419029			0.209514	+	0.977806i	$0.432812\pi$
$830$	−0.333402	+	16.8579i	−0.0115725	+	0.585148i
$831$		−	43.5337i		−	1.51017i
$832$	−0.947271	−	2.33801i	−0.0328407	−	0.0810560i
$833$	−4.49153			−0.155622
$834$	62.7354	+	31.0385i	2.17235	+	1.07478i
$835$	9.62128	+	20.4546i	0.332958	+	0.707860i
$836$	28.8613	+	37.8146i	0.998188	+	1.30785i
$837$		−	72.8286i		−	2.51732i
$838$	−9.59842	+	19.4004i	−0.331572	+	0.670177i
$839$	13.2758			0.458331			0.229165	−	0.973388i	$-0.426400\pi$
$839$	13.2758			0.458331			0.229165	+	0.973388i	$0.426400\pi$
$840$	30.4819	−	22.3248i	1.05172	−	0.770280i
$841$	8.37376			0.288750
$842$	43.3371	+	21.4411i	1.49349	+	0.738910i
$843$			21.5012i			0.740541i
$844$	−15.2764	+	11.6594i	−0.525837	+	0.401335i
$845$	−12.2782	−	26.1031i	−0.422382	−	0.897973i
$846$	−5.12780	+	10.3644i	−0.176297	+	0.356335i
$847$		−	33.7146i		−	1.15845i
$848$	−11.3996	+	41.6812i	−0.391464	+	1.43134i
$849$		−	21.5256i		−	0.738758i
$850$	4.12804	+	9.24651i	0.141590	+	0.317153i
$851$	−6.01951	+	30.9117i	−0.206346	+	1.05964i
$852$	−2.93938	+	2.24342i	−0.100702	+	0.0768584i
$853$		−	5.60642i		−	0.191960i	−0.995383	−	0.0959801i	$-0.969401\pi$
$853$		−	5.60642i		−	0.191960i	0.995383	−	0.0959801i	$-0.0305985\pi$
$854$	5.17857	−	10.4670i	0.177207	−	0.358173i
$855$	−26.6110	−	56.5743i	−0.910078	−	1.93480i
$856$	−5.74058	−	29.4560i	−0.196209	−	1.00679i
$857$		−	48.7034i		−	1.66368i	−0.555017	−	0.831839i	$-0.687288\pi$
$857$		−	48.7034i		−	1.66368i	0.555017	−	0.831839i	$-0.312712\pi$
$858$	6.44552	+	3.18894i	0.220047	+	0.108869i
$859$			18.4565i			0.629729i	0.949137	+	0.314865i	$0.101959\pi$
$859$			18.4565i			0.629729i	−0.949137	+	0.314865i	$0.898041\pi$
$860$	−35.6673	−	18.5332i	−1.21624	−	0.631977i
$861$		−	0.908636i		−	0.0309662i
$862$	−4.57552	+	9.24810i	−0.155843	+	0.314992i
$863$	10.6497			0.362520			0.181260	−	0.983435i	$-0.441982\pi$
$863$	10.6497			0.362520			0.181260	+	0.983435i	$0.441982\pi$
$864$	41.6067	+	36.9663i	1.41549	+	1.25762i
$865$	13.4499	−	6.32647i	0.457310	−	0.215106i
$866$	17.7016	−	35.7788i	0.601526	−	1.21581i
$867$	45.4348			1.54305
$868$	−17.6550	−	23.1320i	−0.599250	−	0.785150i
$869$	−25.1675			−0.853749
$870$	58.7447	+	1.16180i	1.99163	+	0.0393887i
$871$	1.25895			0.0426580
$872$	−6.26376	−	32.1406i	−0.212118	−	1.08842i
$873$	39.1185			1.32396
$874$	24.1713	+	18.4426i	0.817608	+	0.623831i
$875$	5.47523	−	21.2831i	0.185096	−	0.719499i
$876$	−68.7706	+	52.4878i	−2.32354	+	1.77340i
$877$		−	42.0887i		−	1.42123i	−0.703579	−	0.710617i	$-0.748416\pi$
$877$		−	42.0887i		−	1.42123i	0.703579	−	0.710617i	$-0.251584\pi$
$878$	6.65209	+	3.29114i	0.224497	+	0.111071i
$879$	−12.3968			−0.418133
$880$	−46.7513	+	8.15515i	−1.57598	+	0.274910i
$881$		−	8.00319i		−	0.269634i	−0.990870	−	0.134817i	$-0.956955\pi$
$881$		−	8.00319i		−	0.269634i	0.990870	−	0.134817i	$-0.0430447\pi$
$882$	−12.2682	+	24.7967i	−0.413092	+	0.834948i
$883$	25.1885			0.847660			0.423830	−	0.905742i	$-0.360685\pi$
$883$	25.1885			0.847660			0.423830	+	0.905742i	$0.360685\pi$
$884$	0.717920	−	0.547938i	0.0241463	−	0.0184292i
$885$	−44.4356	+	20.9013i	−1.49369	+	0.702590i
$886$	14.8427	−	30.0002i	0.498649	−	1.00788i
$887$	0.951905			0.0319618			0.0159809	−	0.999872i	$-0.494913\pi$
$887$	0.951905			0.0319618			0.0159809	+	0.999872i	$0.494913\pi$
$888$	55.4065	−	10.7980i	1.85932	−	0.362357i
$889$			2.66244i			0.0892954i
$890$	−0.657235	+	33.2321i	−0.0220306	+	1.11394i
$891$	−59.3782			−1.98925
$892$	7.48024	+	9.80076i	0.250457	+	0.328154i
$893$	5.87669			0.196656
$894$	49.5998	+	24.5396i	1.65887	+	0.820728i
$895$	−36.5656	+	17.1995i	−1.22225	+	0.574915i
$896$	22.1765	+	1.65506i	0.740865	+	0.0552916i
$897$	4.51143	+	0.878522i	0.150632	+	0.0293330i
$898$	−4.78584	+	9.67320i	−0.159705	+	0.322799i
$899$		−	45.2529i		−	1.50927i
$900$	62.3232	+	2.46611i	2.07744	+	0.0822037i
$901$	−15.4704			−0.515395
$902$	−0.506103	+	1.02294i	−0.0168514	+	0.0340603i
$903$	−53.6934			−1.78680
$904$	−9.89352	+	1.92811i	−0.329053	+	0.0641281i
$905$	−16.1899	+	7.61527i	−0.538169	+	0.253140i
$906$	−30.1802	−	14.9317i	−1.00267	−	0.496073i
$907$			22.9903i			0.763381i	0.924290	+	0.381690i	$0.124658\pi$
$907$			22.9903i			0.763381i	−0.924290	+	0.381690i	$0.875342\pi$
$908$	34.8196	−	26.5754i	1.15553	−	0.881935i
$909$	−107.755			−3.57399
$910$	−1.95962	−	0.0387556i	−0.0649607	−	0.00128474i
$911$	−35.5666			−1.17838			−0.589188	−	0.807996i	$-0.700552\pi$
$911$	−35.5666			−1.17838			−0.589188	+	0.807996i	$0.700552\pi$
$912$	14.3769	−	52.5671i	0.476065	−	1.74067i
$913$		−	28.2909i		−	0.936292i
$914$	−2.81795	+	5.69568i	−0.0932095	+	0.188396i
$915$	25.8352	−	12.1522i	0.854085	−	0.401738i
$916$	22.0742	−	16.8477i	0.729351	−	0.556662i
$917$	−17.6293			−0.582170
$918$	−8.83597	+	17.8594i	−0.291631	+	0.589447i
$919$	20.0233			0.660507			0.330253	−	0.943892i	$-0.392866\pi$
$919$	20.0233			0.660507			0.330253	+	0.943892i	$0.392866\pi$
$920$	−27.4449	+	12.9143i	−0.904831	+	0.425772i
$921$	36.8910			1.21560
$922$	−11.8340	+	23.9190i	−0.389731	+	0.787729i
$923$	0.191819			0.00631381
$924$	−50.3938	+	38.4621i	−1.65783	+	1.26531i
$925$	20.9365	−	25.2917i	0.688387	−	0.831586i
$926$	−11.2549	+	22.7486i	−0.369860	+	0.747566i
$927$		−	67.9669i		−	2.23232i
$928$	25.8528	+	22.9694i	0.848659	+	0.754008i
$929$	−48.4534			−1.58970			−0.794852	−	0.606803i	$-0.792452\pi$
$929$	−48.4534			−1.58970			−0.794852	+	0.606803i	$0.792452\pi$
$930$	1.40673	−	71.1292i	0.0461285	−	2.33242i
$931$	14.0599			0.460795
$932$	27.6502	−	21.1034i	0.905711	−	0.691266i
$933$		−	71.4032i		−	2.33764i
$934$	−11.3382	−	5.60960i	−0.370997	−	0.183552i
$935$	−7.23171	−	15.3744i	−0.236502	−	0.502797i
$936$	−1.06410	−	5.46012i	−0.0347813	−	0.178469i
$937$	−5.53983			−0.180978			−0.0904892	−	0.995897i	$-0.528843\pi$
$937$	−5.53983			−0.180978			−0.0904892	+	0.995897i	$0.528843\pi$
$938$	−4.92151	+	9.94742i	−0.160693	+	0.324795i
$939$	5.92786			0.193448
$940$	−2.70321	+	5.20234i	−0.0881689	+	0.169682i
$941$		−	21.9834i		−	0.716640i	−0.933599	−	0.358320i	$-0.883350\pi$
$941$		−	21.9834i		−	0.716640i	0.933599	−	0.358320i	$-0.116650\pi$
$942$	10.4206	−	21.0622i	0.339521	−	0.686244i
$943$	−0.139427	+	0.715990i	−0.00454036	+	0.0233159i
$944$	−27.8788	−	7.62474i	−0.907379	−	0.248164i
$945$	39.1306	−	18.4060i	1.27292	−	0.598746i
$946$	60.4480	+	29.9068i	1.96534	+	0.972354i
$947$	2.09657			0.0681295			0.0340647	−	0.999420i	$-0.489155\pi$
$947$	2.09657			0.0681295			0.0340647	+	0.999420i	$0.489155\pi$
$948$	17.4930	+	22.9197i	0.568145	+	0.744396i
$949$	4.48786			0.145682
$950$	−12.9221	−	28.9445i	−0.419247	−	0.939084i
$951$		−	0.881445i		−	0.0285828i
$952$	1.52295	+	7.81454i	0.0493590	+	0.253271i
$953$	14.5951			0.472781			0.236391	−	0.971658i	$-0.424036\pi$
$953$	14.5951			0.472781			0.236391	+	0.971658i	$0.424036\pi$
$954$	−42.2562	+	85.4087i	−1.36809	+	2.76521i
$955$	10.7026	+	22.7535i	0.346328	+	0.736285i
$956$	−28.7539	+	21.9458i	−0.929966	+	0.709778i
$957$	−98.5850			−3.18680
$958$	−1.66597	+	3.36728i	−0.0538250	+	0.108792i
$959$			40.0243i			1.29245i
$960$	39.9218	+	36.9073i	1.28847	+	1.19118i
$961$	−23.7931			−0.767518
$962$	−2.62465	−	1.29855i	−0.0846221	−	0.0418670i
$963$		−	66.1779i		−	2.13255i
$964$	10.4201	−	7.95292i	0.335608	−	0.256146i
$965$	−24.4189	+	11.4860i	−0.786071	+	0.369747i
$966$	−24.5776	+	32.2120i	−0.790772	+	1.03640i
$967$	7.59575			0.244263			0.122131	−	0.992514i	$-0.461027\pi$
$967$	7.59575			0.244263			0.122131	+	0.992514i	$0.461027\pi$
$968$	47.6183	−	9.28016i	1.53051	−	0.298275i
$969$	19.5108			0.626779
$970$	19.8293	+	0.392167i	0.636682	+	0.0125917i
$971$	5.38902			0.172942			0.0864710	−	0.996254i	$-0.472441\pi$
$971$	5.38902			0.172942			0.0864710	+	0.996254i	$0.472441\pi$
$972$	5.45604	+	7.14862i	0.175003	+	0.229292i
$973$	32.0087			1.02615
$974$	19.6356	−	39.6877i	0.629165	−	1.27168i
$975$	−3.69122	−	3.05559i	−0.118214	−	0.0978572i
$976$	16.2090	+	4.43308i	0.518836	+	0.141899i
$977$	−36.9313			−1.18154			−0.590768	−	0.806841i	$-0.701175\pi$
$977$	−36.9313			−1.18154			−0.590768	+	0.806841i	$0.701175\pi$
$978$	10.8687	−	21.9680i	0.347544	−	0.702459i
$979$		−	55.7699i		−	1.78241i
$980$	−6.46740	+	12.4465i	−0.206593	+	0.397590i
$981$		−	72.2092i		−	2.30546i
$982$	20.1000	+	9.94451i	0.641416	+	0.317342i
$983$			39.8734i			1.27176i	0.771786	+	0.635882i	$0.219363\pi$
$983$			39.8734i			1.27176i	−0.771786	+	0.635882i	$0.780637\pi$
$984$	1.28335	−	0.250108i	0.0409118	−	0.00797315i
$985$	13.3163	−	6.26364i	0.424294	−	0.199576i
$986$	−5.49033	+	11.0971i	−0.174848	+	0.353405i
$987$			7.83159i			0.249282i
$988$	−2.24732	+	1.71522i	−0.0714968	+	0.0545685i
$989$	42.3095	+	8.23905i	1.34536	+	0.261986i
$990$	−104.631	−	2.06931i	−3.32540	−	0.0657669i
$991$		−	2.38830i		−	0.0758667i	−0.999280	−	0.0379334i	$-0.987923\pi$
$991$		−	2.38830i		−	0.0758667i	0.999280	−	0.0379334i	$-0.0120775\pi$
$992$	27.8118	−	31.3031i	0.883026	−	0.993873i
$993$		−	34.7041i		−	1.10130i
$994$	−0.749863	+	1.51563i	−0.0237842	+	0.0480729i
$995$	21.7245	+	46.1857i	0.688713	+	1.46418i
$996$	−25.7641	+	19.6639i	−0.816366	+	0.623075i
$997$			3.56721i			0.112975i	0.998403	+	0.0564873i	$0.0179900\pi$
$997$			3.56721i			0.112975i	−0.998403	+	0.0564873i	$0.982010\pi$
$998$	−14.0949	−	6.97348i	−0.446166	−	0.220742i
$999$	64.6070			2.04408

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.g.c.459.19	yes	56
4.3	odd	2	inner	460.2.g.c.459.39	yes	56
5.4	even	2	inner	460.2.g.c.459.38	yes	56
20.19	odd	2	inner	460.2.g.c.459.18	yes	56
23.22	odd	2	inner	460.2.g.c.459.20	yes	56
92.91	even	2	inner	460.2.g.c.459.40	yes	56
115.114	odd	2	inner	460.2.g.c.459.37	yes	56
460.459	even	2	inner	460.2.g.c.459.17	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.g.c.459.17	✓	56	460.459	even	2	inner
460.2.g.c.459.18	yes	56	20.19	odd	2	inner
460.2.g.c.459.19	yes	56	1.1	even	1	trivial
460.2.g.c.459.20	yes	56	23.22	odd	2	inner
460.2.g.c.459.37	yes	56	115.114	odd	2	inner
460.2.g.c.459.38	yes	56	5.4	even	2	inner
460.2.g.c.459.39	yes	56	4.3	odd	2	inner
460.2.g.c.459.40	yes	56	92.91	even	2	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.627129 + 1.26756i) q^{2} -3.03928 q^{3} +(-1.21342 - 1.58985i) q^{4} +(-0.951754 - 2.02340i) q^{5} +(1.90602 - 3.85247i) q^{6} -1.96560i q^{7} +(2.77620 - 0.541043i) q^{8} +6.23720 q^{9} +O(q^{10})\)	\(q+(-0.627129 + 1.26756i) q^{2} -3.03928 q^{3} +(-1.21342 - 1.58985i) q^{4} +(-0.951754 - 2.02340i) q^{5} +(1.90602 - 3.85247i) q^{6} -1.96560i q^{7} +(2.77620 - 0.541043i) q^{8} +6.23720 q^{9} +(3.16166 + 0.0625285i) q^{10} -5.30588 q^{11} +(3.68792 + 4.83198i) q^{12} -0.315328i q^{13} +(2.49151 + 1.23268i) q^{14} +(2.89264 + 6.14968i) q^{15} +(-1.05523 + 3.85830i) q^{16} -1.43205 q^{17} +(-3.91152 + 7.90602i) q^{18} +4.48278 q^{19} +(-2.06203 + 3.96838i) q^{20} +5.97399i q^{21} +(3.32747 - 6.72552i) q^{22} +(0.916686 - 4.70741i) q^{23} +(-8.43763 + 1.64438i) q^{24} +(-3.18833 + 3.85157i) q^{25} +(0.399697 + 0.197751i) q^{26} -9.83873 q^{27} +(-3.12500 + 2.38509i) q^{28} -6.11341 q^{29} +(-9.60915 - 0.190041i) q^{30} +7.40223i q^{31} +(-4.22887 - 3.75722i) q^{32} +16.1260 q^{33} +(0.898081 - 1.81521i) q^{34} +(-3.97720 + 1.87077i) q^{35} +(-7.56833 - 9.91619i) q^{36} -6.56660 q^{37} +(-2.81128 + 5.68219i) q^{38} +0.958368i q^{39} +(-3.73701 - 5.10243i) q^{40} -0.152099 q^{41} +(-7.57239 - 3.74646i) q^{42} +8.98786i q^{43} +(6.43825 + 8.43553i) q^{44} +(-5.93628 - 12.6204i) q^{45} +(5.39204 + 4.11411i) q^{46} +1.31095 q^{47} +(3.20713 - 11.7264i) q^{48} +3.13643 q^{49} +(-2.88260 - 6.45683i) q^{50} +4.35240 q^{51} +(-0.501323 + 0.382625i) q^{52} +10.8030 q^{53} +(6.17015 - 12.4712i) q^{54} +(5.04989 + 10.7359i) q^{55} +(-1.06347 - 5.45689i) q^{56} -13.6244 q^{57} +(3.83389 - 7.74911i) q^{58} +7.22568i q^{59} +(6.26707 - 12.0610i) q^{60} -4.20106i q^{61} +(-9.38278 - 4.64215i) q^{62} -12.2598i q^{63} +(7.41454 - 3.00409i) q^{64} +(-0.638035 + 0.300115i) q^{65} +(-10.1131 + 20.4407i) q^{66} +3.99252i q^{67} +(1.73768 + 2.27674i) q^{68} +(-2.78606 + 14.3071i) q^{69} +(0.122906 - 6.21455i) q^{70} +0.608318i q^{71} +(17.3157 - 3.37459i) q^{72} +14.2324i q^{73} +(4.11810 - 8.32356i) q^{74} +(9.69021 - 11.7060i) q^{75} +(-5.43949 - 7.12693i) q^{76} +10.4292i q^{77} +(-1.21479 - 0.601020i) q^{78} +4.74332 q^{79} +(8.81122 - 1.53700i) q^{80} +11.1910 q^{81} +(0.0953854 - 0.192794i) q^{82} +5.33199i q^{83} +(9.49773 - 7.24895i) q^{84} +(1.36296 + 2.89762i) q^{85} +(-11.3927 - 5.63654i) q^{86} +18.5803 q^{87} +(-14.7302 + 2.87071i) q^{88} +10.5110i q^{89} +(19.7199 + 0.390003i) q^{90} -0.619807 q^{91} +(-8.59638 + 4.25467i) q^{92} -22.4974i q^{93} +(-0.822133 + 1.66170i) q^{94} +(-4.26650 - 9.07047i) q^{95} +(12.8527 + 11.4192i) q^{96} +6.27182 q^{97} +(-1.96694 + 3.97561i) q^{98} -33.0938 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) \) 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9	\( 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9} - 8 q^{16} - 100 q^{24} - 24 q^{25} - 24 q^{26} - 16 q^{29} + 104 q^{41} - 8 q^{46} + 32 q^{49} - 32 q^{50} + 52 q^{54} - 92 q^{64} + 32 q^{69} - 44 q^{70} + 24 q^{81} + 56 q^{85} + 28 q^{94} + 88 q^{96}+O(q^{100}) \) 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9 - 8 * q^16 - 100 * q^24 - 24 * q^25 - 24 * q^26 - 16 * q^29 + 104 * q^41 - 8 * q^46 + 32 * q^49 - 32 * q^50 + 52 * q^54 - 92 * q^64 + 32 * q^69 - 44 * q^70 + 24 * q^81 + 56 * q^85 + 28 * q^94 + 88 * q^96

Introduction

L-functions

Modular forms

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