LMFDB - Embedded newform 276.2.e.a.91.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(91,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("276.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.e (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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.13
Character	$\chi$	$=$	276.91
Dual form			276.2.e.a.91.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.714279 - 1.22058i) q^{2} +1.00000i q^{3} +(-0.979610 - 1.74366i) q^{4} -3.78153i q^{5} +(1.22058 + 0.714279i) q^{6} -1.02234 q^{7} +(-2.82799 - 0.0497743i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.714279 - 1.22058i) q^{2} +1.00000i q^{3} +(-0.979610 - 1.74366i) q^{4} -3.78153i q^{5} +(1.22058 + 0.714279i) q^{6} -1.02234 q^{7} +(-2.82799 - 0.0497743i) q^{8} -1.00000 q^{9} +(-4.61564 - 2.70107i) q^{10} -4.16390 q^{11} +(1.74366 - 0.979610i) q^{12} +5.75925 q^{13} +(-0.730233 + 1.24784i) q^{14} +3.78153 q^{15} +(-2.08073 + 3.41622i) q^{16} -2.80681i q^{17} +(-0.714279 + 1.22058i) q^{18} +4.00376 q^{19} +(-6.59371 + 3.70442i) q^{20} -1.02234i q^{21} +(-2.97419 + 5.08236i) q^{22} +(4.42742 - 1.84336i) q^{23} +(0.0497743 - 2.82799i) q^{24} -9.29995 q^{25} +(4.11371 - 7.02960i) q^{26} -1.00000i q^{27} +(1.00149 + 1.78261i) q^{28} +0.341603 q^{29} +(2.70107 - 4.61564i) q^{30} -5.39782i q^{31} +(2.68354 + 4.97982i) q^{32} -4.16390i q^{33} +(-3.42593 - 2.00485i) q^{34} +3.86599i q^{35} +(0.979610 + 1.74366i) q^{36} +10.6917i q^{37} +(2.85981 - 4.88690i) q^{38} +5.75925i q^{39} +(-0.188223 + 10.6941i) q^{40} +8.31977 q^{41} +(-1.24784 - 0.730233i) q^{42} +8.92015 q^{43} +(4.07900 + 7.26045i) q^{44} +3.78153i q^{45} +(0.912452 - 6.72067i) q^{46} +2.69990i q^{47} +(-3.41622 - 2.08073i) q^{48} -5.95483 q^{49} +(-6.64276 + 11.3513i) q^{50} +2.80681 q^{51} +(-5.64182 - 10.0422i) q^{52} -0.814576i q^{53} +(-1.22058 - 0.714279i) q^{54} +15.7459i q^{55} +(2.89115 + 0.0508860i) q^{56} +4.00376i q^{57} +(0.244000 - 0.416952i) q^{58} -2.67041i q^{59} +(-3.70442 - 6.59371i) q^{60} +7.77081i q^{61} +(-6.58844 - 3.85555i) q^{62} +1.02234 q^{63} +(7.99505 + 0.281522i) q^{64} -21.7787i q^{65} +(-5.08236 - 2.97419i) q^{66} -14.8080 q^{67} +(-4.89414 + 2.74958i) q^{68} +(1.84336 + 4.42742i) q^{69} +(4.71873 + 2.76140i) q^{70} -2.36679i q^{71} +(2.82799 + 0.0497743i) q^{72} +5.19128 q^{73} +(13.0501 + 7.63689i) q^{74} -9.29995i q^{75} +(-3.92213 - 6.98122i) q^{76} +4.25691 q^{77} +(7.02960 + 4.11371i) q^{78} +6.91022 q^{79} +(12.9185 + 7.86833i) q^{80} +1.00000 q^{81} +(5.94264 - 10.1549i) q^{82} +1.12198 q^{83} +(-1.78261 + 1.00149i) q^{84} -10.6140 q^{85} +(6.37147 - 10.8877i) q^{86} +0.341603i q^{87} +(11.7755 + 0.207255i) q^{88} +9.76786i q^{89} +(4.61564 + 2.70107i) q^{90} -5.88788 q^{91} +(-7.55134 - 5.91415i) q^{92} +5.39782 q^{93} +(3.29543 + 1.92848i) q^{94} -15.1403i q^{95} +(-4.97982 + 2.68354i) q^{96} -10.8995i q^{97} +(-4.25341 + 7.26832i) q^{98} +4.16390 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 4 q^{6} + 4 q^{8} - 24 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 4 * q^6 + 4 * q^8 - 24 * q^9	$ 24 q + 4 q^{2} + 4 q^{6} + 4 q^{8} - 24 q^{9} + 8 q^{16} - 4 q^{18} - 4 q^{24} - 24 q^{25} + 40 q^{26} - 32 q^{29} - 36 q^{32} + 16 q^{41} - 32 q^{48} + 40 q^{49} - 12 q^{50} - 40 q^{52} - 4 q^{54} + 24 q^{58} - 40 q^{62} + 48 q^{64} + 16 q^{69} + 72 q^{70} - 4 q^{72} + 16 q^{77} + 24 q^{81} - 40 q^{82} - 64 q^{85} + 44 q^{92} + 16 q^{93} + 72 q^{94} + 44 q^{96} - 52 q^{98}+O(q^{100}) $ 24 * q + 4 * q^2 + 4 * q^6 + 4 * q^8 - 24 * q^9 + 8 * q^16 - 4 * q^18 - 4 * q^24 - 24 * q^25 + 40 * q^26 - 32 * q^29 - 36 * q^32 + 16 * q^41 - 32 * q^48 + 40 * q^49 - 12 * q^50 - 40 * q^52 - 4 * q^54 + 24 * q^58 - 40 * q^62 + 48 * q^64 + 16 * q^69 + 72 * q^70 - 4 * q^72 + 16 * q^77 + 24 * q^81 - 40 * q^82 - 64 * q^85 + 44 * q^92 + 16 * q^93 + 72 * q^94 + 44 * q^96 - 52 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	0.714279	−	1.22058i	0.505072	−	0.863077i
$2$	0.714279	−	1.22058i	0.505072	−	0.863077i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.979610	−	1.74366i	−0.489805	−	0.871832i
$5$		−	3.78153i		−	1.69115i	−0.533856	−	0.845575i	$-0.679258\pi$
$5$		−	3.78153i		−	1.69115i	0.533856	−	0.845575i	$-0.320742\pi$
$6$	1.22058	+	0.714279i	0.498298	+	0.291603i
$7$	−1.02234			−0.386407			−0.193203	−	0.981159i	$-0.561888\pi$
$7$	−1.02234			−0.386407			−0.193203	+	0.981159i	$0.561888\pi$
$8$	−2.82799	−	0.0497743i	−0.999845	−	0.0175979i
$9$	−1.00000			−0.333333
$10$	−4.61564	−	2.70107i	−1.45959	−	0.854152i
$11$	−4.16390			−1.25546			−0.627732	−	0.778430i	$-0.716017\pi$
$11$	−4.16390			−1.25546			−0.627732	+	0.778430i	$0.716017\pi$
$12$	1.74366	−	0.979610i	0.503352	−	0.282789i
$13$	5.75925			1.59733			0.798664	−	0.601778i	$-0.205541\pi$
$13$	5.75925			1.59733			0.798664	+	0.601778i	$0.205541\pi$
$14$	−0.730233	+	1.24784i	−0.195163	+	0.333499i
$15$	3.78153			0.976386
$16$	−2.08073	+	3.41622i	−0.520182	+	0.854056i
$17$		−	2.80681i		−	0.680752i	−0.940289	−	0.340376i	$-0.889446\pi$
$17$		−	2.80681i		−	0.680752i	0.940289	−	0.340376i	$-0.110554\pi$
$18$	−0.714279	+	1.22058i	−0.168357	+	0.287692i
$19$	4.00376			0.918527			0.459263	−	0.888300i	$-0.348113\pi$
$19$	4.00376			0.918527			0.459263	+	0.888300i	$0.348113\pi$
$20$	−6.59371	+	3.70442i	−1.47440	+	0.828334i
$21$		−	1.02234i		−	0.223092i
$22$	−2.97419	+	5.08236i	−0.634099	+	1.08356i
$23$	4.42742	−	1.84336i	0.923180	−	0.384367i
$23$	4.42742	−	1.84336i	0.923180	−	0.384367i
$24$	0.0497743	−	2.82799i	0.0101601	−	0.577261i
$25$	−9.29995			−1.85999
$26$	4.11371	−	7.02960i	0.806765	−	1.37862i
$27$		−	1.00000i		−	0.192450i
$28$	1.00149	+	1.78261i	0.189264	+	0.336882i
$29$	0.341603			0.0634341			0.0317170	−	0.999497i	$-0.489902\pi$
$29$	0.341603			0.0634341			0.0317170	+	0.999497i	$0.489902\pi$
$30$	2.70107	−	4.61564i	0.493145	−	0.842697i
$31$		−	5.39782i		−	0.969477i	−0.874659	−	0.484738i	$-0.838915\pi$
$31$		−	5.39782i		−	0.969477i	0.874659	−	0.484738i	$-0.161085\pi$
$32$	2.68354	+	4.97982i	0.474387	+	0.880316i
$33$		−	4.16390i		−	0.724842i
$34$	−3.42593	−	2.00485i	−0.587542	−	0.343829i
$35$			3.86599i			0.653472i
$36$	0.979610	+	1.74366i	0.163268	+	0.290611i
$37$			10.6917i			1.75771i	0.477087	+	0.878856i	$0.341693\pi$
$37$			10.6917i			1.75771i	−0.477087	+	0.878856i	$0.658307\pi$
$38$	2.85981	−	4.88690i	0.463922	−	0.792759i
$39$			5.75925i			0.922217i
$40$	−0.188223	+	10.6941i	−0.0297606	+	1.69089i
$41$	8.31977			1.29933			0.649665	−	0.760221i	$-0.274909\pi$
$41$	8.31977			1.29933			0.649665	+	0.760221i	$0.274909\pi$
$42$	−1.24784	−	0.730233i	−0.192546	−	0.112677i
$43$	8.92015			1.36031			0.680155	−	0.733069i	$-0.261913\pi$
$43$	8.92015			1.36031			0.680155	+	0.733069i	$0.261913\pi$
$44$	4.07900	+	7.26045i	0.614933	+	1.09455i
$45$			3.78153i			0.563717i
$46$	0.912452	−	6.72067i	0.134534	−	0.990909i
$47$			2.69990i			0.393820i	0.980422	+	0.196910i	$0.0630907\pi$
$47$			2.69990i			0.393820i	−0.980422	+	0.196910i	$0.936909\pi$
$48$	−3.41622	−	2.08073i	−0.493089	−	0.300327i
$49$	−5.95483			−0.850690
$50$	−6.64276	+	11.3513i	−0.939428	+	1.60531i
$51$	2.80681			0.393032
$52$	−5.64182	−	10.0422i	−0.782379	−	1.39260i
$53$		−	0.814576i		−	0.111891i	−0.998434	−	0.0559453i	$-0.982183\pi$
$53$		−	0.814576i		−	0.111891i	0.998434	−	0.0559453i	$-0.0178173\pi$
$54$	−1.22058	−	0.714279i	−0.166099	−	0.0972011i
$55$			15.7459i			2.12318i
$56$	2.89115	+	0.0508860i	0.386347	+	0.00679993i
$57$			4.00376i			0.530312i
$58$	0.244000	−	0.416952i	0.0320388	−	0.0547485i
$59$		−	2.67041i		−	0.347657i	−0.984776	−	0.173829i	$-0.944386\pi$
$59$		−	2.67041i		−	0.347657i	0.984776	−	0.173829i	$-0.0556139\pi$
$60$	−3.70442	−	6.59371i	−0.478239	−	0.851245i
$61$			7.77081i			0.994951i	0.867478	+	0.497475i	$0.165740\pi$
$61$			7.77081i			0.994951i	−0.867478	+	0.497475i	$0.834260\pi$
$62$	−6.58844	−	3.85555i	−0.836733	−	0.489655i
$63$	1.02234			0.128802
$64$	7.99505	+	0.281522i	0.999381	+	0.0351903i
$65$		−	21.7787i		−	2.70132i
$66$	−5.08236	−	2.97419i	−0.625595	−	0.366097i
$67$	−14.8080			−1.80909			−0.904544	−	0.426380i	$-0.859789\pi$
$67$	−14.8080			−1.80909			−0.904544	+	0.426380i	$0.859789\pi$
$68$	−4.89414	+	2.74958i	−0.593501	+	0.333436i
$69$	1.84336	+	4.42742i	0.221914	+	0.532998i
$70$	4.71873	+	2.76140i	0.563997	+	0.330050i
$71$		−	2.36679i		−	0.280886i	−0.990089	−	0.140443i	$-0.955147\pi$
$71$		−	2.36679i		−	0.280886i	0.990089	−	0.140443i	$-0.0448527\pi$
$72$	2.82799	+	0.0497743i	0.333282	+	0.00586595i
$73$	5.19128			0.607594			0.303797	−	0.952737i	$-0.401746\pi$
$73$	5.19128			0.607594			0.303797	+	0.952737i	$0.401746\pi$
$74$	13.0501	+	7.63689i	1.51704	+	0.887771i
$75$		−	9.29995i		−	1.07387i
$76$	−3.92213	−	6.98122i	−0.449899	−	0.800801i
$77$	4.25691			0.485120
$78$	7.02960	+	4.11371i	0.795945	+	0.465786i
$79$	6.91022			0.777460			0.388730	−	0.921352i	$-0.372914\pi$
$79$	6.91022			0.777460			0.388730	+	0.921352i	$0.372914\pi$
$80$	12.9185	+	7.86833i	1.44434	+	0.879706i
$81$	1.00000			0.111111
$82$	5.94264	−	10.1549i	0.656255	−	1.12142i
$83$	1.12198			0.123153			0.0615766	−	0.998102i	$-0.480387\pi$
$83$	1.12198			0.123153			0.0615766	+	0.998102i	$0.480387\pi$
$84$	−1.78261	+	1.00149i	−0.194499	+	0.109272i
$85$	−10.6140			−1.15125
$86$	6.37147	−	10.8877i	0.687054	−	1.17405i
$87$			0.341603i			0.0366237i
$88$	11.7755	+	0.207255i	1.25527	+	0.0220935i
$89$			9.76786i			1.03539i	0.855565	+	0.517696i	$0.173210\pi$
$89$			9.76786i			1.03539i	−0.855565	+	0.517696i	$0.826790\pi$
$90$	4.61564	+	2.70107i	0.486531	+	0.284717i
$91$	−5.88788			−0.617218
$92$	−7.55134	−	5.91415i	−0.787282	−	0.616593i
$93$	5.39782			0.559728
$94$	3.29543	+	1.92848i	0.339897	+	0.198907i
$95$		−	15.1403i		−	1.55337i
$96$	−4.97982	+	2.68354i	−0.508251	+	0.273887i
$97$		−	10.8995i		−	1.10668i	−0.832956	−	0.553339i	$-0.813354\pi$
$97$		−	10.8995i		−	1.10668i	0.832956	−	0.553339i	$-0.186646\pi$
$98$	−4.25341	+	7.26832i	−0.429659	+	0.734211i
$99$	4.16390			0.418488
$100$	9.11032	+	16.2160i	0.911032	+	1.62160i
$101$	−7.92158			−0.788226			−0.394113	−	0.919062i	$-0.628948\pi$
$101$	−7.92158			−0.788226			−0.394113	+	0.919062i	$0.628948\pi$
$102$	2.00485	−	3.42593i	0.198509	−	0.339217i
$103$	−3.57377			−0.352134			−0.176067	−	0.984378i	$-0.556337\pi$
$103$	−3.57377			−0.352134			−0.176067	+	0.984378i	$0.556337\pi$
$104$	−16.2871	−	0.286662i	−1.59708	−	0.0281095i
$105$	−3.86599			−0.377282
$106$	−0.994252	−	0.581835i	−0.0965703	−	0.0565128i
$107$	−3.49439			−0.337816			−0.168908	−	0.985632i	$-0.554024\pi$
$107$	−3.49439			−0.337816			−0.168908	+	0.985632i	$0.554024\pi$
$108$	−1.74366	+	0.979610i	−0.167784	+	0.0942630i
$109$		−	2.15719i		−	0.206621i	−0.994649	−	0.103311i	$-0.967056\pi$
$109$		−	2.15719i		−	0.206621i	0.994649	−	0.103311i	$-0.0329436\pi$
$110$	19.2191	+	11.2470i	1.83247	+	1.07236i
$111$	−10.6917			−1.01482
$112$	2.12720	−	3.49253i	0.201002	−	0.330013i
$113$		−	0.687167i		−	0.0646433i	−0.999478	−	0.0323216i	$-0.989710\pi$
$113$		−	0.687167i		−	0.0646433i	0.999478	−	0.0323216i	$-0.0102901\pi$
$114$	4.88690	+	2.85981i	0.457700	+	0.267845i
$115$	−6.97072	−	16.7424i	−0.650023	−	1.56124i
$116$	−0.334638	−	0.595641i	−0.0310703	−	0.0553039i
$117$	−5.75925			−0.532442
$118$	−3.25943	−	1.90742i	−0.300055	−	0.175592i
$119$			2.86950i			0.263047i
$120$	−10.6941	−	0.188223i	−0.976235	−	0.0171823i
$121$	6.33809			0.576190
$122$	9.48487	+	5.55053i	0.858719	+	0.502521i
$123$			8.31977i			0.750169i
$124$	−9.41198	+	5.28776i	−0.845221	+	0.474855i
$125$			16.2604i			1.45437i
$126$	0.730233	−	1.24784i	0.0650544	−	0.111166i
$127$		−	4.32407i		−	0.383700i	−0.981424	−	0.191850i	$-0.938551\pi$
$127$		−	4.32407i		−	0.383700i	0.981424	−	0.191850i	$-0.0614486\pi$
$128$	6.05431	−	9.55747i	0.535131	−	0.844769i
$129$			8.92015i			0.785375i
$130$	−26.5826	−	15.5561i	−2.33145	−	1.36436i
$131$			10.2833i			0.898452i	0.893418	+	0.449226i	$0.148300\pi$
$131$			10.2833i			0.898452i	−0.893418	+	0.449226i	$0.851700\pi$
$132$	−7.26045	+	4.07900i	−0.631941	+	0.355032i
$133$	−4.09319			−0.354925
$134$	−10.5771	+	18.0743i	−0.913719	+	1.56138i
$135$	−3.78153			−0.325462
$136$	−0.139707	+	7.93763i	−0.0119798	+	0.680646i
$137$		−	7.32794i		−	0.626068i	−0.949742	−	0.313034i	$-0.898655\pi$
$137$		−	7.32794i		−	0.626068i	0.949742	−	0.313034i	$-0.101345\pi$
$138$	6.72067	+	0.912452i	0.572102	+	0.0776731i
$139$		−	0.706954i		−	0.0599631i	−0.999550	−	0.0299815i	$-0.990455\pi$
$139$		−	0.706954i		−	0.0599631i	0.999550	−	0.0299815i	$-0.00954485\pi$
$140$	6.74099	−	3.78716i	0.569717	−	0.320074i
$141$	−2.69990			−0.227372
$142$	−2.88885	−	1.69055i	−0.242427	−	0.141868i
$143$	−23.9809			−2.00539
$144$	2.08073	−	3.41622i	0.173394	−	0.284685i
$145$		−	1.29178i		−	0.107277i
$146$	3.70802	−	6.33635i	0.306878	−	0.524400i
$147$		−	5.95483i		−	0.491146i
$148$	18.6428	−	10.4737i	1.53243	−	0.860937i
$149$		−	0.382789i		−	0.0313593i	−0.999877	−	0.0156797i	$-0.995009\pi$
$149$		−	0.382789i		−	0.0313593i	0.999877	−	0.0156797i	$-0.00499120\pi$
$150$	−11.3513	−	6.64276i	−0.926829	−	0.542379i
$151$			6.34904i			0.516678i	0.966054	+	0.258339i	$0.0831751\pi$
$151$			6.34904i			0.516678i	−0.966054	+	0.258339i	$0.916825\pi$
$152$	−11.3226	−	0.199284i	−0.918384	−	0.0161641i
$153$			2.80681i			0.226917i
$154$	3.04062	−	5.19588i	0.245020	−	0.418696i
$155$	−20.4120			−1.63953
$156$	10.0422	−	5.64182i	0.804019	−	0.451707i
$157$			14.4032i			1.14950i	0.818329	+	0.574749i	$0.194901\pi$
$157$			14.4032i			1.14950i	−0.818329	+	0.574749i	$0.805099\pi$
$158$	4.93583	−	8.43445i	0.392673	−	0.671009i
$159$	0.814576			0.0646001
$160$	18.8313	−	10.1479i	1.48875	−	0.802260i
$161$	−4.52631	+	1.88453i	−0.356723	+	0.148522i
$162$	0.714279	−	1.22058i	0.0561191	−	0.0958975i
$163$		−	13.7153i		−	1.07426i	−0.843499	−	0.537131i	$-0.819508\pi$
$163$		−	13.7153i		−	1.07426i	0.843499	−	0.537131i	$-0.180492\pi$
$164$	−8.15013	−	14.5069i	−0.636419	−	1.13280i
$165$	−15.7459			−1.22582
$166$	0.801407	−	1.36946i	0.0622012	−	0.106291i
$167$		−	13.6811i		−	1.05867i	−0.848412	−	0.529337i	$-0.822441\pi$
$167$		−	13.6811i		−	1.05867i	0.848412	−	0.529337i	$-0.177559\pi$
$168$	−0.0508860	+	2.89115i	−0.00392594	+	0.223057i
$169$	20.1689			1.55145
$170$	−7.58138	+	12.9552i	−0.581466	+	0.993621i
$171$	−4.00376			−0.306176
$172$	−8.73827	−	15.5537i	−0.666287	−	1.18596i
$173$	−3.49528			−0.265741			−0.132871	−	0.991133i	$-0.542419\pi$
$173$	−3.49528			−0.265741			−0.132871	+	0.991133i	$0.542419\pi$
$174$	0.416952	+	0.244000i	0.0316091	+	0.0184976i
$175$	9.50767			0.718712
$176$	8.66395	−	14.2248i	0.653070	−	1.07224i
$177$	2.67041			0.200720
$178$	11.9224	+	6.97698i	0.893623	+	0.522947i
$179$			26.0258i			1.94526i	0.232363	+	0.972629i	$0.425354\pi$
$179$			26.0258i			1.94526i	−0.232363	+	0.972629i	$0.574646\pi$
$180$	6.59371	−	3.70442i	0.491466	−	0.276111i
$181$			6.69764i			0.497832i	0.968525	+	0.248916i	$0.0800743\pi$
$181$			6.69764i			0.497832i	−0.968525	+	0.248916i	$0.919926\pi$
$182$	−4.20559	+	7.18661i	−0.311739	+	0.532707i
$183$	−7.77081			−0.574435
$184$	−12.6124	+	4.99263i	−0.929801	+	0.368062i
$185$	40.4311			2.97256
$186$	3.85555	−	6.58844i	0.282703	−	0.483088i
$187$			11.6873i			0.854659i
$188$	4.70771	−	2.64485i	0.343345	−	0.192895i
$189$			1.02234i			0.0743640i
$190$	−18.4799	−	10.8144i	−1.34068	−	0.784561i
$191$	17.1708			1.24243			0.621217	−	0.783639i	$-0.286639\pi$
$191$	17.1708			1.24243			0.621217	+	0.783639i	$0.286639\pi$
$192$	−0.281522	+	7.99505i	−0.0203171	+	0.576993i
$193$	8.99448			0.647437			0.323718	−	0.946153i	$-0.395067\pi$
$193$	8.99448			0.647437			0.323718	+	0.946153i	$0.395067\pi$
$194$	−13.3037	−	7.78529i	−0.955148	−	0.558951i
$195$	21.7787			1.55961
$196$	5.83341	+	10.3832i	0.416672	+	0.741659i
$197$	−15.7039			−1.11886			−0.559429	−	0.828878i	$-0.688980\pi$
$197$	−15.7039			−1.11886			−0.559429	+	0.828878i	$0.688980\pi$
$198$	2.97419	−	5.08236i	0.211366	−	0.361188i
$199$	17.4402			1.23630			0.618152	−	0.786058i	$-0.287881\pi$
$199$	17.4402			1.23630			0.618152	+	0.786058i	$0.287881\pi$
$200$	26.3001	+	0.462898i	1.85970	+	0.0327318i
$201$		−	14.8080i		−	1.04448i
$202$	−5.65822	+	9.66889i	−0.398111	+	0.680300i
$203$	−0.349233			−0.0245113
$204$	−2.74958	−	4.89414i	−0.192509	−	0.342658i
$205$		−	31.4614i		−	2.19736i
$206$	−2.55267	+	4.36205i	−0.177853	+	0.303919i
$207$	−4.42742	+	1.84336i	−0.307727	+	0.128122i
$208$	−11.9834	+	19.6749i	−0.830901	+	1.36421i
$209$	−16.6713			−1.15318
$210$	−2.76140	+	4.71873i	−0.190554	+	0.325624i
$211$			2.65058i			0.182474i	0.995829	+	0.0912368i	$0.0290820\pi$
$211$			2.65058i			0.182474i	−0.995829	+	0.0912368i	$0.970918\pi$
$212$	−1.42035	+	0.797967i	−0.0975498	+	0.0548046i
$213$	2.36679			0.162170
$214$	−2.49597	+	4.26517i	−0.170621	+	0.291561i
$215$		−	33.7318i		−	2.30049i
$216$	−0.0497743	+	2.82799i	−0.00338671	+	0.192420i
$217$			5.51838i			0.374612i
$218$	−2.63301	−	1.54084i	−0.178330	−	0.104359i
$219$			5.19128i			0.350794i
$220$	27.4556	−	15.4249i	1.85105	−	1.03994i
$221$		−	16.1651i		−	1.08738i
$222$	−7.63689	+	13.0501i	−0.512555	+	0.875864i
$223$			24.2438i			1.62349i	0.584014	+	0.811743i	$0.301481\pi$
$223$			24.2438i			1.62349i	−0.584014	+	0.811743i	$0.698519\pi$
$224$	−2.74348	−	5.09105i	−0.183306	−	0.340160i
$225$	9.29995			0.619996
$226$	−0.838740	−	0.490829i	−0.0557921	−	0.0326495i
$227$	−6.20857			−0.412078			−0.206039	−	0.978544i	$-0.566057\pi$
$227$	−6.20857			−0.412078			−0.206039	+	0.978544i	$0.566057\pi$
$228$	6.98122	−	3.92213i	0.462343	−	0.259749i
$229$		−	11.1620i		−	0.737604i	−0.929508	−	0.368802i	$-0.879768\pi$
$229$		−	11.1620i		−	0.737604i	0.929508	−	0.368802i	$-0.120232\pi$
$230$	−25.4144	−	3.45046i	−1.67578	−	0.227517i
$231$			4.25691i			0.280084i
$232$	−0.966049	−	0.0170030i	−0.0634243	−	0.00111630i
$233$	−23.6813			−1.55141			−0.775707	−	0.631094i	$-0.782606\pi$
$233$	−23.6813			−1.55141			−0.775707	+	0.631094i	$0.782606\pi$
$234$	−4.11371	+	7.02960i	−0.268922	+	0.459539i
$235$	10.2097			0.666009
$236$	−4.65629	+	2.61596i	−0.303099	+	0.170284i
$237$			6.91022i			0.448867i
$238$	3.50245	+	2.04963i	0.227030	+	0.132858i
$239$			5.75021i			0.371950i	0.982554	+	0.185975i	$0.0595444\pi$
$239$			5.75021i			0.371950i	−0.982554	+	0.185975i	$0.940456\pi$
$240$	−7.86833	+	12.9185i	−0.507898	+	0.833888i
$241$		−	12.3285i		−	0.794151i	−0.917786	−	0.397076i	$-0.870025\pi$
$241$		−	12.3285i		−	0.794151i	0.917786	−	0.397076i	$-0.129975\pi$
$242$	4.52717	−	7.73612i	0.291017	−	0.497296i
$243$			1.00000i			0.0641500i
$244$	13.5497	−	7.61237i	0.867430	−	0.487332i
$245$			22.5183i			1.43864i
$246$	10.1549	+	5.94264i	0.647454	+	0.378889i
$247$	23.0587			1.46719
$248$	−0.268672	+	15.2650i	−0.0170607	+	0.969326i
$249$			1.12198i			0.0711026i
$250$	19.8470	+	11.6144i	1.25523	+	0.734562i
$251$	21.0263			1.32717			0.663583	−	0.748103i	$-0.269035\pi$
$251$	21.0263			1.32717			0.663583	+	0.748103i	$0.269035\pi$
$252$	−1.00149	−	1.78261i	−0.0630880	−	0.112294i
$253$	−18.4353	+	7.67557i	−1.15902	+	0.482559i
$254$	−5.27786	−	3.08860i	−0.331162	−	0.193796i
$255$		−	10.6140i		−	0.664677i
$256$	−7.34115	−	14.2165i	−0.458822	−	0.888528i
$257$	−19.1154			−1.19239			−0.596193	−	0.802841i	$-0.703321\pi$
$257$	−19.1154			−1.19239			−0.596193	+	0.802841i	$0.703321\pi$
$258$	10.8877	+	6.37147i	0.677839	+	0.396671i
$259$		−	10.9306i		−	0.679192i
$260$	−37.9748	+	21.3347i	−2.35510	+	1.32312i
$261$	−0.341603			−0.0211447
$262$	12.5515	+	7.34512i	0.775434	+	0.453783i
$263$	−4.96561			−0.306192			−0.153096	−	0.988211i	$-0.548924\pi$
$263$	−4.96561			−0.306192			−0.153096	+	0.988211i	$0.548924\pi$
$264$	−0.207255	+	11.7755i	−0.0127557	+	0.724730i
$265$	−3.08034			−0.189224
$266$	−2.92368	+	4.99605i	−0.179262	+	0.306328i
$267$	−9.76786			−0.597784
$268$	14.5061	+	25.8202i	0.886101	+	1.57722i
$269$	9.04263			0.551339			0.275669	−	0.961252i	$-0.411100\pi$
$269$	9.04263			0.551339			0.275669	+	0.961252i	$0.411100\pi$
$270$	−2.70107	+	4.61564i	−0.164382	+	0.280899i
$271$		−	6.06709i		−	0.368550i	−0.982875	−	0.184275i	$-0.941006\pi$
$271$		−	6.06709i		−	0.368550i	0.982875	−	0.184275i	$-0.0589936\pi$
$272$	9.58869	+	5.84021i	0.581400	+	0.354115i
$273$		−	5.88788i		−	0.356351i
$274$	−8.94431	−	5.23420i	−0.540345	−	0.316209i
$275$	38.7241			2.33515
$276$	5.91415	−	7.55134i	0.355990	−	0.454537i
$277$	31.4785			1.89136			0.945681	−	0.325097i	$-0.105397\pi$
$277$	31.4785			1.89136			0.945681	+	0.325097i	$0.105397\pi$
$278$	−0.862891	−	0.504963i	−0.0517528	−	0.0302856i
$279$			5.39782i			0.323159i
$280$	0.192427	−	10.9330i	0.0114997	−	0.653371i
$281$			3.23860i			0.193199i	0.995323	+	0.0965993i	$0.0307965\pi$
$281$			3.23860i			0.193199i	−0.995323	+	0.0965993i	$0.969203\pi$
$282$	−1.92848	+	3.29543i	−0.114839	+	0.196240i
$283$	−23.0191			−1.36834			−0.684172	−	0.729321i	$-0.739836\pi$
$283$	−23.0191			−1.36834			−0.684172	+	0.729321i	$0.739836\pi$
$284$	−4.12688	+	2.31853i	−0.244886	+	0.137580i
$285$	15.1403			0.896836
$286$	−17.1291	+	29.2706i	−1.01286	+	1.73080i
$287$	−8.50560			−0.502070
$288$	−2.68354	−	4.97982i	−0.158129	−	0.293439i
$289$	9.12181			0.536577
$290$	−1.57672	−	0.922692i	−0.0925880	−	0.0541824i
$291$	10.8995			0.638940
$292$	−5.08543	−	9.05185i	−0.297602	−	0.529719i
$293$			30.4767i			1.78047i	0.455506	+	0.890233i	$0.349458\pi$
$293$			30.4767i			1.78047i	−0.455506	+	0.890233i	$0.650542\pi$
$294$	−7.26832	−	4.25341i	−0.423897	−	0.248064i
$295$	−10.0982			−0.587941
$296$	0.532174	−	30.2361i	0.0309320	−	1.75744i
$297$			4.16390i			0.241614i
$298$	−0.467224	−	0.273419i	−0.0270655	−	0.0158387i
$299$	25.4986	−	10.6164i	1.47462	−	0.613960i
$300$	−16.2160	+	9.11032i	−0.936230	+	0.525985i
$301$	−9.11938			−0.525633
$302$	7.74949	+	4.53499i	0.445933	+	0.260959i
$303$		−	7.92158i		−	0.455083i
$304$	−8.33074	+	13.6777i	−0.477801	+	0.784473i
$305$	29.3855			1.68261
$306$	3.42593	+	2.00485i	0.195847	+	0.114610i
$307$			28.6158i			1.63319i	0.577211	+	0.816595i	$0.304141\pi$
$307$			28.6158i			1.63319i	−0.577211	+	0.816595i	$0.695859\pi$
$308$	−4.17011	−	7.42262i	−0.237614	−	0.422943i
$309$		−	3.57377i		−	0.203305i
$310$	−14.5799	+	24.9144i	−0.828080	+	1.41504i
$311$			27.4154i			1.55458i	0.629141	+	0.777291i	$0.283407\pi$
$311$			27.4154i			1.55458i	−0.629141	+	0.777291i	$0.716593\pi$
$312$	0.286662	−	16.2871i	0.0162291	−	0.922075i
$313$		−	9.19221i		−	0.519574i	−0.965666	−	0.259787i	$-0.916348\pi$
$313$		−	9.19221i		−	0.519574i	0.965666	−	0.259787i	$-0.0836524\pi$
$314$	17.5802	+	10.2879i	0.992107	+	0.580579i
$315$		−	3.86599i		−	0.217824i
$316$	−6.76932	−	12.0491i	−0.380804	−	0.677815i
$317$	4.89112			0.274713			0.137356	−	0.990522i	$-0.456139\pi$
$317$	4.89112			0.274713			0.137356	+	0.990522i	$0.456139\pi$
$318$	0.581835	−	0.994252i	0.0326277	−	0.0557549i
$319$	−1.42240			−0.0796392
$320$	1.06458	−	30.2335i	0.0595120	−	1.69010i
$321$		−	3.49439i		−	0.195038i
$322$	−0.932832	+	6.87078i	−0.0519847	+	0.382894i
$323$		−	11.2378i		−	0.625289i
$324$	−0.979610	−	1.74366i	−0.0544228	−	0.0968702i
$325$	−53.5607			−2.97101
$326$	−16.7405	−	9.79653i	−0.927171	−	0.542579i
$327$	2.15719			0.119293
$328$	−23.5282	−	0.414111i	−1.29913	−	0.0228654i
$329$		−	2.76020i		−	0.152175i
$330$	−11.2470	+	19.2191i	−0.619126	+	1.05798i
$331$		−	9.27238i		−	0.509656i	−0.966986	−	0.254828i	$-0.917981\pi$
$331$		−	9.27238i		−	0.509656i	0.966986	−	0.254828i	$-0.0820189\pi$
$332$	−1.09910	−	1.95636i	−0.0603211	−	0.107369i
$333$		−	10.6917i		−	0.585904i
$334$	−16.6988	−	9.77211i	−0.913717	−	0.534706i
$335$			55.9970i			3.05944i
$336$	3.49253	+	2.12720i	0.190533	+	0.116048i
$337$		−	31.9595i		−	1.74095i	−0.492216	−	0.870473i	$-0.663813\pi$
$337$		−	31.9595i		−	1.74095i	0.492216	−	0.870473i	$-0.336187\pi$
$338$	14.4062	−	24.6177i	0.783596	−	1.33903i
$339$	0.687167			0.0373218
$340$	10.3976	+	18.5073i	0.563890	+	1.00370i
$341$			22.4760i			1.21714i
$342$	−2.85981	+	4.88690i	−0.154641	+	0.264253i
$343$	13.2442			0.715119
$344$	−25.2261	−	0.443994i	−1.36010	−	0.0239385i
$345$	16.7424	−	6.97072i	0.901380	−	0.375291i
$346$	−2.49661	+	4.26625i	−0.134218	+	0.229355i
$347$			17.4157i			0.934922i	0.884014	+	0.467461i	$0.154831\pi$
$347$			17.4157i			0.934922i	−0.884014	+	0.467461i	$0.845169\pi$
$348$	0.595641	−	0.334638i	0.0319297	−	0.0179385i
$349$	14.0294			0.750976			0.375488	−	0.926827i	$-0.377475\pi$
$349$	14.0294			0.750976			0.375488	+	0.926827i	$0.377475\pi$
$350$	6.79113	−	11.6048i	0.363001	−	0.620304i
$351$		−	5.75925i		−	0.307406i
$352$	−11.1740	−	20.7355i	−0.595576	−	1.10521i
$353$	10.5138			0.559594			0.279797	−	0.960059i	$-0.409733\pi$
$353$	10.5138			0.559594			0.279797	+	0.960059i	$0.409733\pi$
$354$	1.90742	−	3.25943i	0.101378	−	0.173237i
$355$	−8.95008			−0.475021
$356$	17.0319	−	9.56870i	0.902687	−	0.507140i
$357$	−2.86950			−0.151870
$358$	31.7664	+	18.5897i	1.67891	+	0.982495i
$359$	26.7026			1.40931			0.704654	−	0.709551i	$-0.251102\pi$
$359$	26.7026			1.40931			0.704654	+	0.709551i	$0.251102\pi$
$360$	0.188223	−	10.6941i	0.00992021	−	0.563629i
$361$	−2.96987			−0.156309
$362$	8.17498	+	4.78399i	0.429668	+	0.251441i
$363$			6.33809i			0.332663i
$364$	5.76783	+	10.2665i	0.302317	+	0.538110i
$365$		−	19.6310i		−	1.02753i
$366$	−5.55053	+	9.48487i	−0.290131	+	0.495782i
$367$	−22.7892			−1.18959			−0.594794	−	0.803878i	$-0.702766\pi$
$367$	−22.7892			−1.18959			−0.594794	+	0.803878i	$0.702766\pi$
$368$	−2.91492	+	18.9606i	−0.151951	+	0.988388i
$369$	−8.31977			−0.433110
$370$	28.8791	−	49.3493i	1.50135	−	2.56555i
$371$			0.832771i			0.0432353i
$372$	−5.28776	−	9.41198i	−0.274157	−	0.487988i
$373$			29.4873i			1.52679i	0.645930	+	0.763397i	$0.276470\pi$
$373$			29.4873i			1.52679i	−0.645930	+	0.763397i	$0.723530\pi$
$374$	14.2652	+	8.34799i	0.737637	+	0.431664i
$375$	−16.2604			−0.839681
$376$	0.134385	−	7.63527i	0.00693039	−	0.393759i
$377$	1.96738			0.101325
$378$	1.24784	+	0.730233i	0.0641819	+	0.0375591i
$379$	2.86951			0.147397			0.0736984	−	0.997281i	$-0.476520\pi$
$379$	2.86951			0.147397			0.0736984	+	0.997281i	$0.476520\pi$
$380$	−26.3997	+	14.8316i	−1.35427	+	0.760847i
$381$	4.32407			0.221529
$382$	12.2647	−	20.9582i	0.627518	−	1.07232i
$383$	−27.8917			−1.42520			−0.712599	−	0.701572i	$-0.752482\pi$
$383$	−27.8917			−1.42520			−0.712599	+	0.701572i	$0.752482\pi$
$384$	9.55747	+	6.05431i	0.487728	+	0.308958i
$385$		−	16.0976i		−	0.820410i
$386$	6.42457	−	10.9784i	0.327002	−	0.558788i
$387$	−8.92015			−0.453436
$388$	−19.0051	+	10.6773i	−0.964837	+	0.542056i
$389$			2.26388i			0.114783i	0.998352	+	0.0573917i	$0.0182784\pi$
$389$			2.26388i			0.114783i	−0.998352	+	0.0573917i	$0.981722\pi$
$390$	15.5561	−	26.5826i	0.787714	−	1.34606i
$391$	−5.17396	−	12.4269i	−0.261659	−	0.628457i
$392$	16.8402	+	0.296397i	0.850558	+	0.0149703i
$393$	−10.2833			−0.518722
$394$	−11.2170	+	19.1678i	−0.565104	+	0.965662i
$395$		−	26.1312i		−	1.31480i
$396$	−4.07900	−	7.26045i	−0.204978	−	0.364851i
$397$	14.1054			0.707930			0.353965	−	0.935259i	$-0.384833\pi$
$397$	14.1054			0.707930			0.353965	+	0.935259i	$0.384833\pi$
$398$	12.4572	−	21.2871i	0.624423	−	1.06703i
$399$		−	4.09319i		−	0.204916i
$400$	19.3507	−	31.7707i	0.967533	−	1.58853i
$401$		−	27.7645i		−	1.38649i	−0.720701	−	0.693246i	$-0.756180\pi$
$401$		−	27.7645i		−	1.38649i	0.720701	−	0.693246i	$-0.243820\pi$
$402$	−18.0743	−	10.5771i	−0.901465	−	0.527536i
$403$		−	31.0874i		−	1.54857i
$404$	7.76006	+	13.8126i	0.386077	+	0.687201i
$405$		−	3.78153i		−	0.187906i
$406$	−0.249450	+	0.426265i	−0.0123800	+	0.0211552i
$407$		−	44.5194i		−	2.20674i
$408$	−7.93763	−	0.139707i	−0.392971	−	0.00691653i
$409$	−30.1790			−1.49225			−0.746127	−	0.665804i	$-0.768089\pi$
$409$	−30.1790			−1.49225			−0.746127	+	0.665804i	$0.768089\pi$
$410$	−38.4011	−	22.4723i	−1.89649	−	1.10983i
$411$	7.32794			0.361461
$412$	3.50090	+	6.23145i	0.172477	+	0.307001i
$413$			2.73005i			0.134337i
$414$	−0.912452	+	6.72067i	−0.0448446	+	0.330303i
$415$		−	4.24280i		−	0.208271i
$416$	15.4552	+	28.6800i	0.757751	+	1.40615i
$417$	0.706954			0.0346197
$418$	−11.9080	+	20.3486i	−0.582437	+	0.995281i
$419$	24.3639			1.19026			0.595128	−	0.803631i	$-0.297101\pi$
$419$	24.3639			1.19026			0.595128	+	0.803631i	$0.297101\pi$
$420$	3.78716	+	6.74099i	0.184795	+	0.328927i
$421$			20.0093i			0.975196i	0.873068	+	0.487598i	$0.162127\pi$
$421$			20.0093i			0.975196i	−0.873068	+	0.487598i	$0.837873\pi$
$422$	3.23524	+	1.89326i	0.157489	+	0.0921622i
$423$		−	2.69990i		−	0.131273i
$424$	−0.0405449	+	2.30361i	−0.00196904	+	0.111873i
$425$			26.1032i			1.26619i
$426$	1.69055	−	2.88885i	0.0819073	−	0.139965i
$427$		−	7.94438i		−	0.384456i
$428$	3.42314	+	6.09305i	0.165464	+	0.294518i
$429$		−	23.9809i		−	1.15781i
$430$	−41.1722	−	24.0939i	−1.98550	−	1.16191i
$431$	−11.9663			−0.576394			−0.288197	−	0.957571i	$-0.593056\pi$
$431$	−11.9663			−0.576394			−0.288197	+	0.957571i	$0.593056\pi$
$432$	3.41622	+	2.08073i	0.164363	+	0.100109i
$433$			8.07822i			0.388215i	0.980980	+	0.194107i	$0.0621810\pi$
$433$			8.07822i			0.388215i	−0.980980	+	0.194107i	$0.937819\pi$
$434$	6.73560	+	3.94167i	0.323319	+	0.189206i
$435$	1.29178			0.0619361
$436$	−3.76141	+	2.11321i	−0.180139	+	0.101204i
$437$	17.7263	−	7.38038i	0.847966	−	0.353051i
$438$	6.33635	+	3.70802i	0.302763	+	0.177176i
$439$			21.9504i			1.04764i	0.851830	+	0.523818i	$0.175493\pi$
$439$			21.9504i			1.04764i	−0.851830	+	0.523818i	$0.824507\pi$
$440$	0.783741	−	44.5293i	0.0373634	−	2.12285i
$441$	5.95483			0.283563
$442$	−19.7308	−	11.5464i	−0.938496	−	0.549207i
$443$			2.92531i			0.138986i	0.997582	+	0.0694928i	$0.0221381\pi$
$443$			2.92531i			0.138986i	−0.997582	+	0.0694928i	$0.977862\pi$
$444$	10.4737	+	18.6428i	0.497062	+	0.884749i
$445$	36.9374			1.75100
$446$	29.5914	+	17.3169i	1.40119	+	0.819977i
$447$	0.382789			0.0181053
$448$	−8.17362	−	0.287810i	−0.386167	−	0.0135978i
$449$	−31.0423			−1.46498			−0.732489	−	0.680779i	$-0.761641\pi$
$449$	−31.0423			−1.46498			−0.732489	+	0.680779i	$0.761641\pi$
$450$	6.64276	−	11.3513i	0.313143	−	0.535105i
$451$	−34.6427			−1.63126
$452$	−1.19819	+	0.673156i	−0.0563581	+	0.0316626i
$453$	−6.34904			−0.298304
$454$	−4.43466	+	7.57804i	−0.208129	+	0.355655i
$455$			22.2652i			1.04381i
$456$	0.199284	−	11.3226i	0.00933235	−	0.530229i
$457$		−	7.04266i		−	0.329442i	−0.986340	−	0.164721i	$-0.947328\pi$
$457$		−	7.04266i		−	0.329442i	0.986340	−	0.164721i	$-0.0526723\pi$
$458$	−13.6240	−	7.97276i	−0.636609	−	0.372543i
$459$	−2.80681			−0.131011
$460$	−22.3645	+	28.5556i	−1.04275	+	1.33141i
$461$	−4.88736			−0.227627			−0.113813	−	0.993502i	$-0.536307\pi$
$461$	−4.88736			−0.227627			−0.113813	+	0.993502i	$0.536307\pi$
$462$	5.19588	+	3.04062i	0.241734	+	0.141462i
$463$		−	17.4728i		−	0.812032i	−0.913866	−	0.406016i	$-0.866918\pi$
$463$		−	17.4728i		−	0.812032i	0.913866	−	0.406016i	$-0.133082\pi$
$464$	−0.710783	+	1.16699i	−0.0329973	+	0.0541762i
$465$		−	20.4120i		−	0.946583i
$466$	−16.9151	+	28.9048i	−0.783575	+	1.33899i
$467$	−21.6721			−1.00286			−0.501432	−	0.865197i	$-0.667193\pi$
$467$	−21.6721			−1.00286			−0.501432	+	0.865197i	$0.667193\pi$
$468$	5.64182	+	10.0422i	0.260793	+	0.464200i
$469$	15.1388			0.699044
$470$	7.29260	−	12.4617i	0.336382	−	0.574817i
$471$	−14.4032			−0.663664
$472$	−0.132918	+	7.55188i	−0.00611803	+	0.347604i
$473$	−37.1426			−1.70782
$474$	8.43445	+	4.93583i	0.387407	+	0.226710i
$475$	−37.2348			−1.70845
$476$	5.00345	−	2.81100i	0.229333	−	0.128842i
$477$			0.814576i			0.0372969i
$478$	7.01857	+	4.10726i	0.321022	+	0.187862i
$479$	38.7920			1.77245			0.886226	−	0.463254i	$-0.153318\pi$
$479$	38.7920			1.77245			0.886226	+	0.463254i	$0.153318\pi$
$480$	10.1479	+	18.8313i	0.463185	+	0.859529i
$481$			61.5764i			2.80764i
$482$	−15.0479	−	8.80602i	−0.685414	−	0.401103i
$483$	−1.88453	−	4.52631i	−0.0857492	−	0.205954i
$484$	−6.20886	−	11.0515i	−0.282221	−	0.502341i
$485$	−41.2168			−1.87156
$486$	1.22058	+	0.714279i	0.0553664	+	0.0324004i
$487$		−	29.5419i		−	1.33867i	−0.742960	−	0.669336i	$-0.766579\pi$
$487$		−	29.5419i		−	1.33867i	0.742960	−	0.669336i	$-0.233421\pi$
$488$	0.386787	−	21.9758i	0.0175090	−	0.994797i
$489$	13.7153			0.620226
$490$	27.4853	+	16.0844i	1.24166	+	0.726619i
$491$		−	15.6437i		−	0.705991i	−0.935625	−	0.352996i	$-0.885163\pi$
$491$		−	15.6437i		−	0.705991i	0.935625	−	0.352996i	$-0.114837\pi$
$492$	14.5069	−	8.15013i	0.654021	−	0.367436i
$493$		−	0.958815i		−	0.0431829i
$494$	16.4703	−	28.1448i	0.741035	−	1.26630i
$495$		−	15.7459i		−	0.707726i
$496$	18.4401	+	11.2314i	0.827987	+	0.504304i
$497$			2.41965i			0.108536i
$498$	1.36946	+	0.801407i	0.0613670	+	0.0359119i
$499$			35.1984i			1.57570i	0.615868	+	0.787849i	$0.288805\pi$
$499$			35.1984i			1.57570i	−0.615868	+	0.787849i	$0.711195\pi$
$500$	28.3526	−	15.9288i	1.26797	−	0.712358i
$501$	13.6811			0.611225
$502$	15.0186	−	25.6642i	0.670314	−	1.14545i
$503$	−26.6899			−1.19004			−0.595022	−	0.803709i	$-0.702857\pi$
$503$	−26.6899			−1.19004			−0.595022	+	0.803709i	$0.702857\pi$
$504$	−2.89115	−	0.0508860i	−0.128782	−	0.00226664i
$505$			29.9557i			1.33301i
$506$	−3.79936	+	27.9842i	−0.168902	+	1.24405i
$507$			20.1689i			0.895733i
$508$	−7.53973	+	4.23591i	−0.334521	+	0.187938i
$509$	−4.70015			−0.208330			−0.104165	−	0.994560i	$-0.533217\pi$
$509$	−4.70015			−0.208330			−0.104165	+	0.994560i	$0.533217\pi$
$510$	−12.9552	−	7.58138i	−0.573667	−	0.335709i
$511$	−5.30723			−0.234778
$512$	−22.5959	−	1.19409i	−0.998607	−	0.0527718i
$513$		−	4.00376i		−	0.176771i
$514$	−13.6537	+	23.3318i	−0.602241	+	1.02912i
$515$			13.5143i			0.595511i
$516$	15.5537	−	8.73827i	0.684715	−	0.384681i
$517$		−	11.2421i		−	0.494427i
$518$	−13.3416	−	7.80747i	−0.586195	−	0.343041i
$519$		−	3.49528i		−	0.153426i
$520$	−1.08402	+	61.5901i	−0.0475375	+	2.70090i
$521$			1.58918i			0.0696231i	0.999394	+	0.0348116i	$0.0110831\pi$
$521$			1.58918i			0.0696231i	−0.999394	+	0.0348116i	$0.988917\pi$
$522$	−0.244000	+	0.416952i	−0.0106796	+	0.0182495i
$523$	−2.47426			−0.108192			−0.0540959	−	0.998536i	$-0.517228\pi$
$523$	−2.47426			−0.108192			−0.0540959	+	0.998536i	$0.517228\pi$
$524$	17.9305	−	10.0736i	0.783299	−	0.440067i
$525$			9.50767i			0.414949i
$526$	−3.54683	+	6.06090i	−0.154649	+	0.264268i
$527$	−15.1507			−0.659973
$528$	14.2248	+	8.66395i	0.619056	+	0.377050i
$529$	16.2040	−	16.3226i	0.704524	−	0.709680i
$530$	−2.20022	+	3.75979i	−0.0955716	+	0.163315i
$531$			2.67041i			0.115886i
$532$	4.00973	+	7.13715i	0.173844	+	0.309435i
$533$	47.9156			2.07546
$534$	−6.97698	+	11.9224i	−0.301924	+	0.515934i
$535$			13.2141i			0.571297i
$536$	41.8769	+	0.737059i	1.80881	+	0.0318361i
$537$	−26.0258			−1.12310
$538$	6.45896	−	11.0372i	0.278466	−	0.475848i
$539$	24.7953			1.06801
$540$	3.70442	+	6.59371i	0.159413	+	0.283748i
$541$	9.66457			0.415512			0.207756	−	0.978181i	$-0.433384\pi$
$541$	9.66457			0.415512			0.207756	+	0.978181i	$0.433384\pi$
$542$	−7.40535	−	4.33360i	−0.318087	−	0.186144i
$543$	−6.69764			−0.287423
$544$	13.9774	−	7.53219i	0.599277	−	0.322940i
$545$	−8.15747			−0.349428
$546$	−7.18661	−	4.20559i	−0.307558	−	0.179983i
$547$		−	10.7576i		−	0.459962i	−0.973195	−	0.229981i	$-0.926134\pi$
$547$		−	10.7576i		−	0.459962i	0.973195	−	0.229981i	$-0.0738664\pi$
$548$	−12.7775	+	7.17853i	−0.545826	+	0.306652i
$549$		−	7.77081i		−	0.331650i
$550$	27.6598	−	47.2657i	1.17942	−	2.01541i
$551$	1.36770			0.0582659
$552$	−4.99263	−	12.6124i	−0.212500	−	0.536821i
$553$	−7.06457			−0.300416
$554$	22.4845	−	38.4219i	0.955273	−	1.63239i
$555$			40.4311i			1.71621i
$556$	−1.23269	+	0.692539i	−0.0522777	+	0.0293702i
$557$			19.7483i			0.836762i	0.908272	+	0.418381i	$0.137402\pi$
$557$			19.7483i			0.836762i	−0.908272	+	0.418381i	$0.862598\pi$
$558$	6.58844	+	3.85555i	0.278911	+	0.163218i
$559$	51.3733			2.17286
$560$	−13.2071	−	8.04407i	−0.558101	−	0.339924i
$561$	−11.6873			−0.493438
$562$	3.95296	+	2.31326i	0.166745	+	0.0975791i
$563$	−13.5629			−0.571606			−0.285803	−	0.958288i	$-0.592260\pi$
$563$	−13.5629			−0.571606			−0.285803	+	0.958288i	$0.592260\pi$
$564$	2.64485	+	4.70771i	0.111368	+	0.198230i
$565$	−2.59854			−0.109321
$566$	−16.4421	+	28.0966i	−0.691112	+	1.18099i
$567$	−1.02234			−0.0429341
$568$	−0.117805	+	6.69325i	−0.00494300	+	0.280843i
$569$			22.1659i			0.929243i	0.885509	+	0.464621i	$0.153810\pi$
$569$			22.1659i			0.929243i	−0.885509	+	0.464621i	$0.846190\pi$
$570$	10.8144	−	18.4799i	0.452967	−	0.774039i
$571$	0.830063			0.0347370			0.0173685	−	0.999849i	$-0.494471\pi$
$571$	0.830063			0.0347370			0.0173685	+	0.999849i	$0.494471\pi$
$572$	23.4920	+	41.8147i	0.982249	+	1.74836i
$573$			17.1708i			0.717320i
$574$	−6.07537	+	10.3817i	−0.253581	+	0.433325i
$575$	−41.1747	+	17.1431i	−1.71711	+	0.714919i
$576$	−7.99505	−	0.281522i	−0.333127	−	0.0117301i
$577$	−3.58731			−0.149342			−0.0746708	−	0.997208i	$-0.523791\pi$
$577$	−3.58731			−0.149342			−0.0746708	+	0.997208i	$0.523791\pi$
$578$	6.51552	−	11.1339i	0.271010	−	0.463107i
$579$			8.99448i			0.373798i
$580$	−2.25243	+	1.26544i	−0.0935271	+	0.0525446i
$581$	−1.14704			−0.0475872
$582$	7.78529	−	13.3037i	0.322711	−	0.551455i
$583$			3.39182i			0.140475i
$584$	−14.6809	−	0.258392i	−0.607499	−	0.0106923i
$585$			21.7787i			0.900440i
$586$	37.1991	+	21.7688i	1.53668	+	0.899262i
$587$		−	27.3709i		−	1.12972i	−0.825187	−	0.564860i	$-0.808930\pi$
$587$		−	27.3709i		−	1.12972i	0.825187	−	0.564860i	$-0.191070\pi$
$588$	−10.3832	+	5.83341i	−0.428197	+	0.240566i
$589$		−	21.6116i		−	0.890490i
$590$	−7.21295	+	12.3256i	−0.296952	+	0.507439i
$591$		−	15.7039i		−	0.645973i
$592$	−36.5254	−	22.2466i	−1.50118	−	0.914330i
$593$	29.7156			1.22027			0.610137	−	0.792296i	$-0.291114\pi$
$593$	29.7156			1.22027			0.610137	+	0.792296i	$0.291114\pi$
$594$	5.08236	+	2.97419i	0.208532	+	0.122032i
$595$	10.8511			0.444852
$596$	−0.667456	+	0.374984i	−0.0273401	+	0.0153600i
$597$			17.4402i			0.713781i
$598$	5.25504	−	38.7060i	0.214894	−	1.58281i
$599$		−	2.73087i		−	0.111580i	−0.998443	−	0.0557902i	$-0.982232\pi$
$599$		−	2.73087i		−	0.111580i	0.998443	−	0.0557902i	$-0.0177678\pi$
$600$	−0.462898	+	26.3001i	−0.0188977	+	1.07370i
$601$	−33.8681			−1.38151			−0.690753	−	0.723090i	$-0.742721\pi$
$601$	−33.8681			−1.38151			−0.690753	+	0.723090i	$0.742721\pi$
$602$	−6.51379	+	11.1309i	−0.265482	+	0.453662i
$603$	14.8080			0.603030
$604$	11.0706	−	6.21959i	0.450456	−	0.253071i
$605$		−	23.9677i		−	0.974424i
$606$	−9.66889	−	5.65822i	−0.392772	−	0.229849i
$607$		−	28.8726i		−	1.17190i	−0.810346	−	0.585952i	$-0.800721\pi$
$607$		−	28.8726i		−	1.17190i	0.810346	−	0.585952i	$-0.199279\pi$
$608$	10.7443	+	19.9380i	0.435737	+	0.808594i
$609$		−	0.349233i		−	0.0141516i
$610$	20.9895	−	35.8673i	0.849839	−	1.45222i
$611$			15.5494i			0.629060i
$612$	4.89414	−	2.74958i	0.197834	−	0.111145i
$613$		−	1.07656i		−	0.0434818i	−0.999764	−	0.0217409i	$-0.993079\pi$
$613$		−	1.07656i		−	0.0434818i	0.999764	−	0.0217409i	$-0.00692088\pi$
$614$	34.9277	+	20.4397i	1.40957	+	0.824878i
$615$	31.4614			1.26865
$616$	−12.0385	−	0.211884i	−0.485045	−	0.00853707i
$617$		−	8.83195i		−	0.355561i	−0.984070	−	0.177781i	$-0.943108\pi$
$617$		−	8.83195i		−	0.355561i	0.984070	−	0.177781i	$-0.0568917\pi$
$618$	−4.36205	−	2.55267i	−0.175468	−	0.102683i
$619$	−20.3851			−0.819347			−0.409674	−	0.912232i	$-0.634357\pi$
$619$	−20.3851			−0.819347			−0.409674	+	0.912232i	$0.634357\pi$
$620$	19.9958	+	35.5916i	0.803051	+	1.42940i
$621$	−1.84336	−	4.42742i	−0.0739715	−	0.177666i
$622$	33.4625	+	19.5822i	1.34172	+	0.785175i
$623$		−	9.98604i		−	0.400082i
$624$	−19.6749	−	11.9834i	−0.787625	−	0.479721i
$625$	14.9893			0.599571
$626$	−11.2198	−	6.56580i	−0.448433	−	0.262422i
$627$		−	16.6713i		−	0.665787i
$628$	25.1143	−	14.1095i	1.00217	−	0.563031i
$629$	30.0097			1.19657
$630$	−4.71873	−	2.76140i	−0.187999	−	0.110017i
$631$	−6.21298			−0.247335			−0.123667	−	0.992324i	$-0.539466\pi$
$631$	−6.21298			−0.247335			−0.123667	+	0.992324i	$0.539466\pi$
$632$	−19.5420	−	0.343951i	−0.777340	−	0.0136816i
$633$	−2.65058			−0.105351
$634$	3.49363	−	5.96999i	0.138750	−	0.237098i
$635$	−16.3516			−0.648894
$636$	−0.797967	−	1.42035i	−0.0316415	−	0.0563204i
$637$	−34.2953			−1.35883
$638$	−1.01599	+	1.73615i	−0.0402235	+	0.0687348i
$639$			2.36679i			0.0936287i
$640$	−36.1418	−	22.8946i	−1.42863	−	0.904987i
$641$			16.1002i			0.635921i	0.948104	+	0.317960i	$0.102998\pi$
$641$			16.1002i			0.635921i	−0.948104	+	0.317960i	$0.897002\pi$
$642$	−4.26517	−	2.49597i	−0.168333	−	0.0985082i
$643$	8.14353			0.321150			0.160575	−	0.987024i	$-0.448665\pi$
$643$	8.14353			0.321150			0.160575	+	0.987024i	$0.448665\pi$
$644$	7.72001	+	6.04625i	0.304211	+	0.238256i
$645$	33.7318			1.32819
$646$	−13.7166	−	8.02694i	−0.539673	−	0.315816i
$647$			25.7912i			1.01396i	0.861959	+	0.506978i	$0.169238\pi$
$647$			25.7912i			1.01396i	−0.861959	+	0.506978i	$0.830762\pi$
$648$	−2.82799	−	0.0497743i	−0.111094	−	0.00195532i
$649$			11.1193i			0.436471i
$650$	−38.2573	+	65.3749i	−1.50057	+	2.56421i
$651$	−5.51838			−0.216282
$652$	−23.9148	+	13.4356i	−0.936576	+	0.526179i
$653$	−36.8619			−1.44252			−0.721260	−	0.692665i	$-0.756437\pi$
$653$	−36.8619			−1.44252			−0.721260	+	0.692665i	$0.756437\pi$
$654$	1.54084	−	2.63301i	0.0602515	−	0.102959i
$655$	38.8864			1.51942
$656$	−17.3112	+	28.4222i	−0.675888	+	1.10970i
$657$	−5.19128			−0.202531
$658$	−3.36903	−	1.97155i	−0.131339	−	0.0768592i
$659$	−23.0516			−0.897963			−0.448982	−	0.893541i	$-0.648213\pi$
$659$	−23.0516			−0.897963			−0.448982	+	0.893541i	$0.648213\pi$
$660$	15.4249	+	27.4556i	0.600412	+	1.06871i
$661$			15.4291i			0.600123i	0.953920	+	0.300061i	$0.0970072\pi$
$661$			15.4291i			0.600123i	−0.953920	+	0.300061i	$0.902993\pi$
$662$	−11.3176	−	6.62307i	−0.439873	−	0.257413i
$663$	16.1651			0.627801
$664$	−3.17295	−	0.0558457i	−0.123134	−	0.00216723i
$665$			15.4785i			0.600231i
$666$	−13.0501	−	7.63689i	−0.505681	−	0.295924i
$667$	1.51242	−	0.629697i	0.0585611	−	0.0243820i
$668$	−23.8552	+	13.4021i	−0.922985	+	0.518544i
$669$	−24.2438			−0.937320
$670$	68.3485	+	39.9975i	2.64053	+	1.54524i
$671$		−	32.3569i		−	1.24912i
$672$	5.09105	−	2.74348i	0.196392	−	0.105832i
$673$	11.2843			0.434978			0.217489	−	0.976063i	$-0.430213\pi$
$673$	11.2843			0.434978			0.217489	+	0.976063i	$0.430213\pi$
$674$	−39.0090	−	22.8280i	−1.50257	−	0.879302i
$675$			9.29995i			0.357955i
$676$	−19.7577	−	35.1678i	−0.759911	−	1.35261i
$677$		−	28.5070i		−	1.09561i	−0.836606	−	0.547806i	$-0.815463\pi$
$677$		−	28.5070i		−	1.09561i	0.836606	−	0.547806i	$-0.184537\pi$
$678$	0.490829	−	0.838740i	0.0188502	−	0.0322116i
$679$			11.1430i			0.427627i
$680$	30.0164	+	0.528306i	1.15108	+	0.0202596i
$681$		−	6.20857i		−	0.237913i
$682$	27.4336	+	16.0541i	1.05049	+	0.614744i
$683$		−	26.1642i		−	1.00115i	−0.865694	−	0.500573i	$-0.833123\pi$
$683$		−	26.1642i		−	1.00115i	0.865694	−	0.500573i	$-0.166877\pi$
$684$	3.92213	+	6.98122i	0.149966	+	0.266934i
$685$	−27.7108			−1.05878
$686$	9.46005	−	16.1655i	0.361186	−	0.617203i
$687$	11.1620			0.425856
$688$	−18.5604	+	30.4732i	−0.707608	+	1.16178i
$689$		−	4.69134i		−	0.178726i
$690$	3.45046	−	25.4144i	0.131357	−	0.967510i
$691$		−	42.6495i		−	1.62246i	−0.584725	−	0.811232i	$-0.698797\pi$
$691$		−	42.6495i		−	1.62246i	0.584725	−	0.811232i	$-0.301203\pi$
$692$	3.42401	+	6.09459i	0.130161	+	0.231682i
$693$	−4.25691			−0.161707
$694$	21.2571	+	12.4397i	0.806910	+	0.472203i
$695$	−2.67337			−0.101407
$696$	0.0170030	−	0.966049i	0.000644499	−	0.0366180i
$697$		−	23.3520i		−	0.884521i
$698$	10.0209	−	17.1239i	0.379296	−	0.648150i
$699$		−	23.6813i		−	0.895709i
$700$	−9.31381	−	16.5782i	−0.352029	−	0.626596i
$701$			8.56934i			0.323659i	0.986819	+	0.161830i	$0.0517395\pi$
$701$			8.56934i			0.323659i	−0.986819	+	0.161830i	$0.948260\pi$
$702$	−7.02960	−	4.11371i	−0.265315	−	0.155262i
$703$			42.8072i			1.61451i
$704$	−33.2906	−	1.17223i	−1.25469	−	0.0441801i
$705$			10.2097i			0.384521i
$706$	7.50980	−	12.8329i	0.282635	−	0.482973i
$707$	8.09851			0.304576
$708$	−2.61596	−	4.65629i	−0.0983138	−	0.174994i
$709$		−	50.0440i		−	1.87944i	−0.341943	−	0.939721i	$-0.611085\pi$
$709$		−	50.0440i		−	1.87944i	0.341943	−	0.939721i	$-0.388915\pi$
$710$	−6.39285	+	10.9242i	−0.239920	+	0.409980i
$711$	−6.91022			−0.259153
$712$	0.486188	−	27.6234i	0.0182207	−	1.03523i
$713$	−9.95012	−	23.8984i	−0.372635	−	0.895002i
$714$	−2.04963	+	3.50245i	−0.0767054	+	0.131076i
$715$			90.6846i			3.39141i
$716$	45.3802	−	25.4951i	1.69594	−	0.952798i
$717$	−5.75021			−0.214746
$718$	19.0731	−	32.5925i	0.711802	−	1.21634i
$719$			32.9114i			1.22739i	0.789543	+	0.613695i	$0.210317\pi$
$719$			32.9114i			1.22739i	−0.789543	+	0.613695i	$0.789683\pi$
$720$	−12.9185	−	7.86833i	−0.481445	−	0.293235i
$721$	3.65359			0.136067
$722$	−2.12132	+	3.62495i	−0.0789473	+	0.134907i
$723$	12.3285			0.458504
$724$	11.6784	−	6.56108i	0.434026	−	0.243841i
$725$	−3.17689			−0.117987
$726$	7.73612	+	4.52717i	0.287114	+	0.168019i
$727$	0.793020			0.0294115			0.0147057	−	0.999892i	$-0.495319\pi$
$727$	0.793020			0.0294115			0.0147057	+	0.999892i	$0.495319\pi$
$728$	16.6509	+	0.293065i	0.617122	+	0.0108617i
$729$	−1.00000			−0.0370370
$730$	−23.9611	−	14.0220i	−0.886840	−	0.518977i
$731$		−	25.0372i		−	0.926033i
$732$	7.61237	+	13.5497i	0.281361	+	0.500811i
$733$		−	28.1816i		−	1.04091i	−0.853889	−	0.520456i	$-0.825762\pi$
$733$		−	28.1816i		−	1.04091i	0.853889	−	0.520456i	$-0.174238\pi$
$734$	−16.2779	+	27.8160i	−0.600827	+	1.02671i
$735$	−22.5183			−0.830602
$736$	21.0607	+	17.1010i	0.776309	+	0.630352i
$737$	61.6592			2.27125
$738$	−5.94264	+	10.1549i	−0.218752	+	0.373807i
$739$		−	28.9097i		−	1.06346i	−0.846914	−	0.531730i	$-0.821542\pi$
$739$		−	28.9097i		−	1.06346i	0.846914	−	0.531730i	$-0.178458\pi$
$740$	−39.6068	−	70.4983i	−1.45597	−	2.59157i
$741$			23.0587i			0.847081i
$742$	1.01646	+	0.594831i	0.0373154	+	0.0218369i
$743$	34.6908			1.27268			0.636341	−	0.771408i	$-0.280447\pi$
$743$	34.6908			1.27268			0.636341	+	0.771408i	$0.280447\pi$
$744$	−15.2650	−	0.268672i	−0.559641	−	0.00985001i
$745$	−1.44753			−0.0530333
$746$	35.9915	+	21.0621i	1.31774	+	0.771140i
$747$	−1.12198			−0.0410511
$748$	20.3787	−	11.4490i	0.745119	−	0.418617i
$749$	3.57244			0.130534
$750$	−11.6144	+	19.8470i	−0.424099	+	0.724710i
$751$	41.9033			1.52907			0.764536	−	0.644581i	$-0.222968\pi$
$751$	41.9033			1.52907			0.764536	+	0.644581i	$0.222968\pi$
$752$	−9.22344	−	5.61775i	−0.336344	−	0.204858i
$753$			21.0263i			0.766240i
$754$	1.40526	−	2.40133i	0.0511764	−	0.0874513i
$755$	24.0091			0.873780
$756$	1.78261	−	1.00149i	0.0648329	−	0.0364239i
$757$			5.44668i			0.197963i	0.995089	+	0.0989815i	$0.0315585\pi$
$757$			5.44668i			0.197963i	−0.995089	+	0.0989815i	$0.968442\pi$
$758$	2.04963	−	3.50245i	0.0744460	−	0.127215i
$759$	−7.67557	−	18.4353i	−0.278606	−	0.669160i
$760$	−0.753600	+	42.8167i	−0.0273359	+	1.55313i
$761$	−2.39310			−0.0867498			−0.0433749	−	0.999059i	$-0.513811\pi$
$761$	−2.39310			−0.0867498			−0.0433749	+	0.999059i	$0.513811\pi$
$762$	3.08860	−	5.27786i	0.111888	−	0.191197i
$763$			2.20537i			0.0798398i
$764$	−16.8207	−	29.9401i	−0.608551	−	1.08319i
$765$	10.6140			0.383751
$766$	−19.9224	+	34.0439i	−0.719827	+	1.23006i
$767$		−	15.3795i		−	0.555323i
$768$	14.2165	−	7.34115i	0.512992	−	0.264901i
$769$		−	40.1929i		−	1.44939i	−0.689068	−	0.724697i	$-0.741980\pi$
$769$		−	40.1929i		−	1.44939i	0.689068	−	0.724697i	$-0.258020\pi$
$770$	−19.6484	−	11.4982i	−0.708078	−	0.414366i
$771$		−	19.1154i		−	0.688425i
$772$	−8.81109	−	15.6834i	−0.317118	−	0.564456i
$773$			1.02655i			0.0369225i	0.999830	+	0.0184612i	$0.00587673\pi$
$773$			1.02655i			0.0369225i	−0.999830	+	0.0184612i	$0.994123\pi$
$774$	−6.37147	+	10.8877i	−0.229018	+	0.391351i
$775$			50.1994i			1.80322i
$776$	−0.542515	+	30.8237i	−0.0194752	+	1.10651i
$777$	10.9306			0.392132
$778$	2.76324	+	1.61705i	0.0990670	+	0.0579739i
$779$	33.3104			1.19347
$780$	−21.3347	−	37.9748i	−0.763904	−	1.35972i
$781$			9.85508i			0.352642i
$782$	−18.8637	−	2.56108i	−0.674563	−	0.0915841i
$783$		−	0.341603i		−	0.0122079i
$784$	12.3904	−	20.3430i	0.442513	−	0.726536i
$785$	54.4660			1.94398
$786$	−7.34512	+	12.5515i	−0.261992	+	0.447697i
$787$	29.7905			1.06192			0.530958	−	0.847398i	$-0.321832\pi$
$787$	29.7905			1.06192			0.530958	+	0.847398i	$0.321832\pi$
$788$	15.3837	+	27.3824i	0.548023	+	0.975457i
$789$		−	4.96561i		−	0.176780i
$790$	−31.8951	−	18.6650i	−1.13478	−	0.664070i
$791$			0.702516i			0.0249786i
$792$	−11.7755	−	0.207255i	−0.418423	−	0.00736449i
$793$			44.7540i			1.58926i
$794$	10.0752	−	17.2167i	0.357555	−	0.610998i
$795$		−	3.08034i		−	0.109248i
$796$	−17.0846	−	30.4099i	−0.605548	−	1.07785i
$797$		−	42.4174i		−	1.50250i	−0.660017	−	0.751251i	$-0.729451\pi$
$797$		−	42.4174i		−	1.50250i	0.660017	−	0.751251i	$-0.270549\pi$
$798$	−4.99605	−	2.92368i	−0.176858	−	0.103497i
$799$	7.57810			0.268094
$800$	−24.9568	−	46.3121i	−0.882355	−	1.63738i
$801$		−	9.76786i		−	0.345131i
$802$	−33.8887	−	19.8316i	−1.19665	−	0.700278i
$803$	−21.6160			−0.762812
$804$	−25.8202	+	14.5061i	−0.910609	+	0.511591i
$805$	7.12641	+	17.1164i	0.251173	+	0.603272i
$806$	−37.9445	−	22.2051i	−1.33654	−	0.782140i
$807$			9.04263i			0.318316i
$808$	22.4021	+	0.394291i	0.788104	+	0.0138711i
$809$	−29.6442			−1.04224			−0.521118	−	0.853485i	$-0.674485\pi$
$809$	−29.6442			−1.04224			−0.521118	+	0.853485i	$0.674485\pi$
$810$	−4.61564	−	2.70107i	−0.162177	−	0.0949058i
$811$			2.07439i			0.0728418i	0.999337	+	0.0364209i	$0.0115957\pi$
$811$			2.07439i			0.0728418i	−0.999337	+	0.0364209i	$0.988404\pi$
$812$	0.342112	+	0.608945i	0.0120058	+	0.0213698i
$813$	6.06709			0.212782
$814$	−54.3393	−	31.7993i	−1.90459	−	1.11456i
$815$	−51.8646			−1.81674
$816$	−5.84021	+	9.58869i	−0.204448	+	0.335671i
$817$	35.7142			1.24948
$818$	−21.5562	+	36.8357i	−0.753695	+	1.28793i
$819$	5.88788			0.205739
$820$	−54.8582	+	30.8200i	−1.91573	+	1.07628i
$821$	−14.6390			−0.510904			−0.255452	−	0.966822i	$-0.582224\pi$
$821$	−14.6390			−0.510904			−0.255452	+	0.966822i	$0.582224\pi$
$822$	5.23420	−	8.94431i	0.182564	−	0.311969i
$823$		−	36.8036i		−	1.28289i	−0.767168	−	0.641446i	$-0.778335\pi$
$823$		−	36.8036i		−	1.28289i	0.767168	−	0.641446i	$-0.221665\pi$
$824$	10.1066	+	0.177882i	0.352079	+	0.00619680i
$825$			38.7241i			1.34820i
$826$	3.33224	+	1.95002i	0.115943	+	0.0678499i
$827$	−20.8771			−0.725970			−0.362985	−	0.931795i	$-0.618242\pi$
$827$	−20.8771			−0.725970			−0.362985	+	0.931795i	$0.618242\pi$
$828$	7.55134	+	5.91415i	0.262427	+	0.205531i
$829$	17.8407			0.619632			0.309816	−	0.950797i	$-0.399733\pi$
$829$	17.8407			0.619632			0.309816	+	0.950797i	$0.399733\pi$
$830$	−5.17865	−	3.03054i	−0.179754	−	0.105192i
$831$			31.4785i			1.09198i
$832$	46.0454	+	1.62136i	1.59634	+	0.0562104i
$833$			16.7141i			0.579109i
$834$	0.504963	−	0.862891i	0.0174854	−	0.0298795i
$835$	−51.7353			−1.79038
$836$	16.3314	+	29.0691i	0.564832	+	1.00538i
$837$	−5.39782			−0.186576
$838$	17.4026	−	29.7380i	0.601164	−	1.02728i
$839$	−30.5659			−1.05525			−0.527625	−	0.849477i	$-0.676917\pi$
$839$	−30.5659			−1.05525			−0.527625	+	0.849477i	$0.676917\pi$
$840$	10.9330	+	0.192427i	0.377224	+	0.00663936i
$841$	−28.8833			−0.995976
$842$	24.4229	+	14.2923i	0.841669	+	0.492544i
$843$	−3.23860			−0.111543
$844$	4.62172	−	2.59654i	0.159086	−	0.0893765i
$845$		−	76.2693i		−	2.62374i
$846$	−3.29543	−	1.92848i	−0.113299	−	0.0663025i
$847$	−6.47966			−0.222644
$848$	2.78277	+	1.69491i	0.0955608	+	0.0582035i
$849$		−	23.0191i		−	0.790014i
$850$	31.8609	+	18.6450i	1.09282	+	0.639517i
$851$	19.7087	+	47.3368i	0.675607	+	1.62269i
$852$	−2.31853	−	4.12688i	−0.0794316	−	0.141385i
$853$	24.6193			0.842948			0.421474	−	0.906840i	$-0.361513\pi$
$853$	24.6193			0.842948			0.421474	+	0.906840i	$0.361513\pi$
$854$	−9.69672	−	5.67451i	−0.331815	−	0.194178i
$855$			15.1403i			0.517789i
$856$	9.88210	+	0.173931i	0.337763	+	0.00594483i
$857$	−29.1797			−0.996760			−0.498380	−	0.866959i	$-0.666072\pi$
$857$	−29.1797			−0.996760			−0.498380	+	0.866959i	$0.666072\pi$
$858$	−29.2706	−	17.1291i	−0.999280	−	0.584777i
$859$		−	4.44412i		−	0.151631i	−0.997122	−	0.0758157i	$-0.975844\pi$
$859$		−	4.44412i		−	0.151631i	0.997122	−	0.0758157i	$-0.0241561\pi$
$860$	−58.8169	+	33.0440i	−2.00564	+	1.12679i
$861$		−	8.50560i		−	0.289870i
$862$	−8.54724	+	14.6057i	−0.291120	+	0.497473i
$863$		−	11.8945i		−	0.404895i	−0.979293	−	0.202447i	$-0.935111\pi$
$863$		−	11.8945i		−	0.404895i	0.979293	−	0.202447i	$-0.0648895\pi$
$864$	4.97982	−	2.68354i	0.169417	−	0.0912958i
$865$			13.2175i			0.449408i
$866$	9.86008	+	5.77011i	0.335059	+	0.196076i
$867$			9.12181i			0.309793i
$868$	9.62220	−	5.40586i	0.326599	−	0.183487i
$869$	−28.7735			−0.976074
$870$	0.922692	−	1.57672i	0.0312822	−	0.0534557i
$871$	−85.2831			−2.88971
$872$	−0.107373	+	6.10051i	−0.00363609	+	0.206589i
$873$			10.8995i			0.368892i
$874$	3.65324	−	26.9080i	0.123573	−	0.910176i
$875$		−	16.6236i		−	0.561979i
$876$	9.05185	−	5.08543i	0.305834	−	0.171821i
$877$	−18.3997			−0.621314			−0.310657	−	0.950522i	$-0.600549\pi$
$877$	−18.3997			−0.621314			−0.310657	+	0.950522i	$0.600549\pi$
$878$	26.7921	+	15.6787i	0.904190	+	0.529131i
$879$	−30.4767			−1.02795
$880$	−53.7915	−	32.7629i	−1.81331	−	1.10444i
$881$		−	2.28963i		−	0.0771395i	−0.999256	−	0.0385697i	$-0.987720\pi$
$881$		−	2.28963i		−	0.0771395i	0.999256	−	0.0385697i	$-0.0122802\pi$
$882$	4.25341	−	7.26832i	0.143220	−	0.244737i
$883$			33.2434i			1.11873i	0.828921	+	0.559366i	$0.188955\pi$
$883$			33.2434i			1.11873i	−0.828921	+	0.559366i	$0.811045\pi$
$884$	−28.1865	+	15.8355i	−0.948016	+	0.532606i
$885$		−	10.0982i		−	0.339448i
$886$	3.57056	+	2.08949i	0.119955	+	0.0701977i
$887$			7.21083i			0.242116i	0.992645	+	0.121058i	$0.0386287\pi$
$887$			7.21083i			0.242116i	−0.992645	+	0.121058i	$0.961371\pi$
$888$	30.2361	+	0.532174i	1.01466	+	0.0178586i
$889$			4.42066i			0.148264i
$890$	26.3836	−	45.0849i	0.884382	−	1.51125i
$891$	−4.16390			−0.139496
$892$	42.2731	−	23.7495i	1.41541	−	0.795192i
$893$			10.8097i			0.361734i
$894$	0.273419	−	0.467224i	0.00914448	−	0.0156263i
$895$	98.4172			3.28972
$896$	−6.18954	+	9.77095i	−0.206778	+	0.326424i
$897$	10.6164	+	25.4986i	0.354470	+	0.851373i
$898$	−22.1729	+	37.8895i	−0.739919	+	1.26439i
$899$		−	1.84391i		−	0.0614979i
$900$	−9.11032	−	16.2160i	−0.303677	−	0.540533i
$901$	−2.28636			−0.0761698
$902$	−24.7446	+	42.2841i	−0.823904	+	1.40791i
$903$		−	9.11938i		−	0.303474i
$904$	−0.0342033	+	1.94330i	−0.00113758	+	0.0646333i
$905$	25.3273			0.841909
$906$	−4.53499	+	7.74949i	−0.150665	+	0.257459i
$907$	19.2080			0.637792			0.318896	−	0.947790i	$-0.396688\pi$
$907$	19.2080			0.637792			0.318896	+	0.947790i	$0.396688\pi$
$908$	6.08198	+	10.8257i	0.201838	+	0.359262i
$909$	7.92158			0.262742
$910$	27.1764	+	15.9036i	0.900887	+	0.527198i
$911$	24.6794			0.817665			0.408833	−	0.912609i	$-0.365936\pi$
$911$	24.6794			0.817665			0.408833	+	0.912609i	$0.365936\pi$
$912$	−13.6777	−	8.33074i	−0.452916	−	0.275858i
$913$	−4.67181			−0.154614
$914$	−8.59610	−	5.03043i	−0.284334	−	0.166392i
$915$			29.3855i			0.971456i
$916$	−19.4627	+	10.9344i	−0.643066	+	0.361282i
$917$		−	10.5129i		−	0.347168i
$918$	−2.00485	+	3.42593i	−0.0661698	+	0.113072i
$919$	36.1695			1.19312			0.596560	−	0.802568i	$-0.296534\pi$
$919$	36.1695			1.19312			0.596560	+	0.802568i	$0.296534\pi$
$920$	18.8798	+	47.6943i	0.622447	+	1.57243i
$921$	−28.6158			−0.942923
$922$	−3.49094	+	5.96539i	−0.114968	+	0.196460i
$923$		−	13.6309i		−	0.448667i
$924$	7.42262	−	4.17011i	0.244186	−	0.137187i
$925$		−	99.4327i		−	3.26933i
$926$	−21.3269	−	12.4805i	−0.700846	−	0.410134i
$927$	3.57377			0.117378
$928$	0.916704	+	1.70112i	0.0300923	+	0.0558421i
$929$	19.8450			0.651095			0.325547	−	0.945526i	$-0.394451\pi$
$929$	19.8450			0.651095			0.325547	+	0.945526i	$0.394451\pi$
$930$	−24.9144	−	14.5799i	−0.816975	−	0.478092i
$931$	−23.8417			−0.781381
$932$	23.1984	+	41.2922i	0.759890	+	1.35257i
$933$	−27.4154			−0.897538
$934$	−15.4799	+	26.4524i	−0.506518	+	0.865548i
$935$	44.1958			1.44536
$936$	16.2871	+	0.286662i	0.532360	+	0.00936985i
$937$			33.2780i			1.08715i	0.839362	+	0.543573i	$0.182929\pi$
$937$			33.2780i			1.08715i	−0.839362	+	0.543573i	$0.817071\pi$
$938$	10.8133	−	18.4780i	0.353067	−	0.603329i
$939$	9.19221			0.299976
$940$	−10.0016	−	17.8023i	−0.326215	−	0.580648i
$941$		−	17.6138i		−	0.574194i	−0.957901	−	0.287097i	$-0.907310\pi$
$941$		−	17.6138i		−	0.574194i	0.957901	−	0.287097i	$-0.0926903\pi$
$942$	−10.2879	+	17.5802i	−0.335198	+	0.572793i
$943$	36.8351	−	15.3363i	1.19952	−	0.499420i
$944$	9.12271	+	5.55639i	0.296919	+	0.180845i
$945$	3.86599			0.125761
$946$	−26.5302	+	45.3354i	−0.862571	+	1.47398i
$947$			45.0168i			1.46285i	0.681921	+	0.731425i	$0.261145\pi$
$947$			45.0168i			1.46285i	−0.681921	+	0.731425i	$0.738855\pi$
$948$	12.0491	−	6.76932i	0.391337	−	0.219857i
$949$	29.8979			0.970526
$950$	−26.5960	+	45.4479i	−0.862889	+	1.47452i
$951$			4.89112i			0.158606i
$952$	0.142827	−	8.11493i	0.00462907	−	0.263006i
$953$			39.4151i			1.27678i	0.769713	+	0.638390i	$0.220399\pi$
$953$			39.4151i			1.27678i	−0.769713	+	0.638390i	$0.779601\pi$
$954$	0.994252	+	0.581835i	0.0321901	+	0.0188376i
$955$		−	64.9318i		−	2.10114i
$956$	10.0264	−	5.63297i	0.324278	−	0.182183i
$957$		−	1.42240i		−	0.0459797i
$958$	27.7083	−	47.3486i	0.895215	−	1.52976i
$959$			7.49162i			0.241917i
$960$	30.2335	+	1.06458i	0.975781	+	0.0343593i
$961$	1.86357			0.0601152
$962$	75.1587	+	43.9827i	2.42321	+	1.41806i
$963$	3.49439			0.112605
$964$	−21.4968	+	12.0772i	−0.692367	+	0.388979i
$965$		−	34.0129i		−	1.09491i
$966$	−6.87078	−	0.932832i	−0.221064	−	0.0300134i
$967$		−	24.3005i		−	0.781450i	−0.920507	−	0.390725i	$-0.872224\pi$
$967$		−	24.3005i		−	0.781450i	0.920507	−	0.390725i	$-0.127776\pi$
$968$	−17.9240	−	0.315474i	−0.576101	−	0.0101397i
$969$	11.2378			0.361011
$970$	−29.4403	+	50.3082i	−0.945271	+	1.61530i
$971$	−15.5499			−0.499020			−0.249510	−	0.968372i	$-0.580270\pi$
$971$	−15.5499			−0.499020			−0.249510	+	0.968372i	$0.580270\pi$
$972$	1.74366	−	0.979610i	0.0559280	−	0.0314210i
$973$			0.722745i			0.0231701i
$974$	−36.0582	−	21.1012i	−1.15538	−	0.676125i
$975$		−	53.5607i		−	1.71531i
$976$	−26.5468	−	16.1689i	−0.849743	−	0.517555i
$977$		−	37.7336i		−	1.20720i	−0.797286	−	0.603602i	$-0.793732\pi$
$977$		−	37.7336i		−	1.20720i	0.797286	−	0.603602i	$-0.206268\pi$
$978$	9.79653	−	16.7405i	0.313258	−	0.535303i
$979$		−	40.6724i		−	1.29990i
$980$	39.2644	−	22.0592i	1.25426	−	0.704655i
$981$			2.15719i			0.0688738i
$982$	−19.0943	−	11.1740i	−0.609325	−	0.356576i
$983$	19.1931			0.612166			0.306083	−	0.952005i	$-0.400982\pi$
$983$	19.1931			0.612166			0.306083	+	0.952005i	$0.400982\pi$
$984$	0.414111	−	23.5282i	0.0132014	−	0.750052i
$985$			59.3848i			1.89216i
$986$	−1.17031	−	0.684862i	−0.0372702	−	0.0218104i
$987$	2.76020			0.0878581
$988$	−22.5885	−	40.2066i	−0.718636	−	1.27914i
$989$	39.4932	−	16.4430i	1.25581	−	0.522858i
$990$	−19.2191	−	11.2470i	−0.610822	−	0.357452i
$991$			24.2887i			0.771555i	0.922592	+	0.385778i	$0.126067\pi$
$991$			24.2887i			0.771555i	−0.922592	+	0.385778i	$0.873933\pi$
$992$	26.8802	−	14.4852i	0.853446	−	0.459907i
$993$	9.27238			0.294250
$994$	2.95337	+	1.72831i	0.0936752	+	0.0548186i
$995$		−	65.9507i		−	2.09078i
$996$	1.95636	−	1.09910i	0.0619895	−	0.0348264i
$997$	4.39684			0.139249			0.0696247	−	0.997573i	$-0.477820\pi$
$997$	4.39684			0.139249			0.0696247	+	0.997573i	$0.477820\pi$
$998$	42.9624	+	25.1415i	1.35995	+	0.795841i
$999$	10.6917			0.338272

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.e.a.91.13	✓	24
3.2	odd	2		828.2.e.f.91.12		24
4.3	odd	2	inner	276.2.e.a.91.15	yes	24
8.3	odd	2		4416.2.i.d.1471.23		24
8.5	even	2		4416.2.i.d.1471.22		24
12.11	even	2		828.2.e.f.91.10		24
23.22	odd	2	inner	276.2.e.a.91.14	yes	24
69.68	even	2		828.2.e.f.91.11		24
92.91	even	2	inner	276.2.e.a.91.16	yes	24
184.45	odd	2		4416.2.i.d.1471.21		24
184.91	even	2		4416.2.i.d.1471.24		24
276.275	odd	2		828.2.e.f.91.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.e.a.91.13	✓	24	1.1	even	1	trivial
276.2.e.a.91.14	yes	24	23.22	odd	2	inner
276.2.e.a.91.15	yes	24	4.3	odd	2	inner
276.2.e.a.91.16	yes	24	92.91	even	2	inner
828.2.e.f.91.9		24	276.275	odd	2
828.2.e.f.91.10		24	12.11	even	2
828.2.e.f.91.11		24	69.68	even	2
828.2.e.f.91.12		24	3.2	odd	2
4416.2.i.d.1471.21		24	184.45	odd	2
4416.2.i.d.1471.22		24	8.5	even	2
4416.2.i.d.1471.23		24	8.3	odd	2
4416.2.i.d.1471.24		24	184.91	even	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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.714279 - 1.22058i) q^{2} +1.00000i q^{3} +(-0.979610 - 1.74366i) q^{4} -3.78153i q^{5} +(1.22058 + 0.714279i) q^{6} -1.02234 q^{7} +(-2.82799 - 0.0497743i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.714279 - 1.22058i) q^{2} +1.00000i q^{3} +(-0.979610 - 1.74366i) q^{4} -3.78153i q^{5} +(1.22058 + 0.714279i) q^{6} -1.02234 q^{7} +(-2.82799 - 0.0497743i) q^{8} -1.00000 q^{9} +(-4.61564 - 2.70107i) q^{10} -4.16390 q^{11} +(1.74366 - 0.979610i) q^{12} +5.75925 q^{13} +(-0.730233 + 1.24784i) q^{14} +3.78153 q^{15} +(-2.08073 + 3.41622i) q^{16} -2.80681i q^{17} +(-0.714279 + 1.22058i) q^{18} +4.00376 q^{19} +(-6.59371 + 3.70442i) q^{20} -1.02234i q^{21} +(-2.97419 + 5.08236i) q^{22} +(4.42742 - 1.84336i) q^{23} +(0.0497743 - 2.82799i) q^{24} -9.29995 q^{25} +(4.11371 - 7.02960i) q^{26} -1.00000i q^{27} +(1.00149 + 1.78261i) q^{28} +0.341603 q^{29} +(2.70107 - 4.61564i) q^{30} -5.39782i q^{31} +(2.68354 + 4.97982i) q^{32} -4.16390i q^{33} +(-3.42593 - 2.00485i) q^{34} +3.86599i q^{35} +(0.979610 + 1.74366i) q^{36} +10.6917i q^{37} +(2.85981 - 4.88690i) q^{38} +5.75925i q^{39} +(-0.188223 + 10.6941i) q^{40} +8.31977 q^{41} +(-1.24784 - 0.730233i) q^{42} +8.92015 q^{43} +(4.07900 + 7.26045i) q^{44} +3.78153i q^{45} +(0.912452 - 6.72067i) q^{46} +2.69990i q^{47} +(-3.41622 - 2.08073i) q^{48} -5.95483 q^{49} +(-6.64276 + 11.3513i) q^{50} +2.80681 q^{51} +(-5.64182 - 10.0422i) q^{52} -0.814576i q^{53} +(-1.22058 - 0.714279i) q^{54} +15.7459i q^{55} +(2.89115 + 0.0508860i) q^{56} +4.00376i q^{57} +(0.244000 - 0.416952i) q^{58} -2.67041i q^{59} +(-3.70442 - 6.59371i) q^{60} +7.77081i q^{61} +(-6.58844 - 3.85555i) q^{62} +1.02234 q^{63} +(7.99505 + 0.281522i) q^{64} -21.7787i q^{65} +(-5.08236 - 2.97419i) q^{66} -14.8080 q^{67} +(-4.89414 + 2.74958i) q^{68} +(1.84336 + 4.42742i) q^{69} +(4.71873 + 2.76140i) q^{70} -2.36679i q^{71} +(2.82799 + 0.0497743i) q^{72} +5.19128 q^{73} +(13.0501 + 7.63689i) q^{74} -9.29995i q^{75} +(-3.92213 - 6.98122i) q^{76} +4.25691 q^{77} +(7.02960 + 4.11371i) q^{78} +6.91022 q^{79} +(12.9185 + 7.86833i) q^{80} +1.00000 q^{81} +(5.94264 - 10.1549i) q^{82} +1.12198 q^{83} +(-1.78261 + 1.00149i) q^{84} -10.6140 q^{85} +(6.37147 - 10.8877i) q^{86} +0.341603i q^{87} +(11.7755 + 0.207255i) q^{88} +9.76786i q^{89} +(4.61564 + 2.70107i) q^{90} -5.88788 q^{91} +(-7.55134 - 5.91415i) q^{92} +5.39782 q^{93} +(3.29543 + 1.92848i) q^{94} -15.1403i q^{95} +(-4.97982 + 2.68354i) q^{96} -10.8995i q^{97} +(-4.25341 + 7.26832i) q^{98} +4.16390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 4 q^{6} + 4 q^{8} - 24 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 4 * q^6 + 4 * q^8 - 24 * q^9	\( 24 q + 4 q^{2} + 4 q^{6} + 4 q^{8} - 24 q^{9} + 8 q^{16} - 4 q^{18} - 4 q^{24} - 24 q^{25} + 40 q^{26} - 32 q^{29} - 36 q^{32} + 16 q^{41} - 32 q^{48} + 40 q^{49} - 12 q^{50} - 40 q^{52} - 4 q^{54} + 24 q^{58} - 40 q^{62} + 48 q^{64} + 16 q^{69} + 72 q^{70} - 4 q^{72} + 16 q^{77} + 24 q^{81} - 40 q^{82} - 64 q^{85} + 44 q^{92} + 16 q^{93} + 72 q^{94} + 44 q^{96} - 52 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 4 * q^6 + 4 * q^8 - 24 * q^9 + 8 * q^16 - 4 * q^18 - 4 * q^24 - 24 * q^25 + 40 * q^26 - 32 * q^29 - 36 * q^32 + 16 * q^41 - 32 * q^48 + 40 * q^49 - 12 * q^50 - 40 * q^52 - 4 * q^54 + 24 * q^58 - 40 * q^62 + 48 * q^64 + 16 * q^69 + 72 * q^70 - 4 * q^72 + 16 * q^77 + 24 * q^81 - 40 * q^82 - 64 * q^85 + 44 * q^92 + 16 * q^93 + 72 * q^94 + 44 * q^96 - 52 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more