LMFDB - Embedded newform 867.2.e.k.829.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(616,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("867.616"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.e (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,-36,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			829.9
Character	$\chi$	$=$	867.829
Dual form			867.2.e.k.616.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.43915i q^{2} +(-0.707107 - 0.707107i) q^{3} -0.0711653 q^{4} +(-1.63621 - 1.63621i) q^{5} +(1.01764 - 1.01764i) q^{6} +(-3.14078 + 3.14078i) q^{7} +2.77589i q^{8} +1.00000i q^{9} +(2.35475 - 2.35475i) q^{10} +(3.19932 - 3.19932i) q^{11} +(0.0503215 + 0.0503215i) q^{12} -1.17466 q^{13} +(-4.52006 - 4.52006i) q^{14} +2.31394i q^{15} -4.13727 q^{16} -1.43915 q^{18} -4.86615i q^{19} +(0.116441 + 0.116441i) q^{20} +4.44173 q^{21} +(4.60432 + 4.60432i) q^{22} +(0.442223 - 0.442223i) q^{23} +(1.96285 - 1.96285i) q^{24} +0.354337i q^{25} -1.69052i q^{26} +(0.707107 - 0.707107i) q^{27} +(0.223514 - 0.223514i) q^{28} +(-1.06796 - 1.06796i) q^{29} -3.33012 q^{30} +(-6.17723 - 6.17723i) q^{31} -0.402383i q^{32} -4.52453 q^{33} +10.2779 q^{35} -0.0711653i q^{36} +(-6.21727 - 6.21727i) q^{37} +7.00315 q^{38} +(0.830610 + 0.830610i) q^{39} +(4.54193 - 4.54193i) q^{40} +(-0.328780 + 0.328780i) q^{41} +6.39233i q^{42} -1.51327i q^{43} +(-0.227681 + 0.227681i) q^{44} +(1.63621 - 1.63621i) q^{45} +(0.636427 + 0.636427i) q^{46} -6.01904 q^{47} +(2.92549 + 2.92549i) q^{48} -12.7289i q^{49} -0.509946 q^{50} +0.0835951 q^{52} -7.12324i q^{53} +(1.01764 + 1.01764i) q^{54} -10.4695 q^{55} +(-8.71845 - 8.71845i) q^{56} +(-3.44089 + 3.44089i) q^{57} +(1.53696 - 1.53696i) q^{58} -10.4025i q^{59} -0.164673i q^{60} +(1.80936 - 1.80936i) q^{61} +(8.88999 - 8.88999i) q^{62} +(-3.14078 - 3.14078i) q^{63} -7.69544 q^{64} +(1.92198 + 1.92198i) q^{65} -6.51150i q^{66} -3.71801 q^{67} -0.625397 q^{69} +14.7915i q^{70} +(10.7784 + 10.7784i) q^{71} -2.77589 q^{72} +(1.91050 + 1.91050i) q^{73} +(8.94761 - 8.94761i) q^{74} +(0.250554 - 0.250554i) q^{75} +0.346301i q^{76} +20.0967i q^{77} +(-1.19538 + 1.19538i) q^{78} +(-11.8067 + 11.8067i) q^{79} +(6.76942 + 6.76942i) q^{80} -1.00000 q^{81} +(-0.473165 - 0.473165i) q^{82} +4.45459i q^{83} -0.316097 q^{84} +2.17782 q^{86} +1.51032i q^{87} +(8.88098 + 8.88098i) q^{88} -1.54030 q^{89} +(2.35475 + 2.35475i) q^{90} +(3.68934 - 3.68934i) q^{91} +(-0.0314709 + 0.0314709i) q^{92} +8.73592i q^{93} -8.66233i q^{94} +(-7.96203 + 7.96203i) q^{95} +(-0.284528 + 0.284528i) q^{96} +(-2.71449 - 2.71449i) q^{97} +18.3189 q^{98} +(3.19932 + 3.19932i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 36 q^{4} - 36 q^{13} + 60 q^{16} + 12 q^{18} - 12 q^{21} - 48 q^{30} - 36 q^{33} + 24 q^{38} - 96 q^{47} + 48 q^{50} - 72 q^{52} + 96 q^{55} - 96 q^{64} - 24 q^{67} - 36 q^{69} - 48 q^{72} - 24 q^{81}+ \cdots + 228 q^{98}+O(q^{100}) $ 24 * q - 36 * q^4 - 36 * q^13 + 60 * q^16 + 12 * q^18 - 12 * q^21 - 48 * q^30 - 36 * q^33 + 24 * q^38 - 96 * q^47 + 48 * q^50 - 72 * q^52 + 96 * q^55 - 96 * q^64 - 24 * q^67 - 36 * q^69 - 48 * q^72 - 24 * q^81 - 60 * q^84 + 24 * q^86 + 228 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$			1.43915i			1.01764i	0.860874	+	0.508818i	$0.169917\pi$
$2$			1.43915i			1.01764i	−0.860874	+	0.508818i	$0.830083\pi$
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−0.0711653			−0.0355827
$5$	−1.63621	−	1.63621i	−0.731733	−	0.731733i	0.239230	−	0.970963i	$-0.423105\pi$
$5$	−1.63621	−	1.63621i	−0.731733	−	0.731733i	−0.970963	+	0.239230i	$0.923105\pi$
$6$	1.01764	−	1.01764i	0.415448	−	0.415448i
$7$	−3.14078	+	3.14078i	−1.18710	+	1.18710i	−0.209236	+	0.977865i	$0.567098\pi$
$7$	−3.14078	+	3.14078i	−1.18710	+	1.18710i	−0.977865	+	0.209236i	$0.932902\pi$
$8$			2.77589i			0.981426i
$9$			1.00000i			0.333333i
$10$	2.35475	−	2.35475i	0.744638	−	0.744638i
$11$	3.19932	−	3.19932i	0.964633	−	0.964633i	−0.0347629	−	0.999396i	$-0.511068\pi$
$11$	3.19932	−	3.19932i	0.964633	−	0.964633i	0.999396	+	0.0347629i	$0.0110676\pi$
$12$	0.0503215	+	0.0503215i	0.0145266	+	0.0145266i
$13$	−1.17466			−0.325792			−0.162896	−	0.986643i	$-0.552084\pi$
$13$	−1.17466			−0.325792			−0.162896	+	0.986643i	$0.552084\pi$
$14$	−4.52006	−	4.52006i	−1.20804	−	1.20804i
$15$			2.31394i			0.597458i
$16$	−4.13727			−1.03432
$17$		0			0
$17$		0			0
$18$	−1.43915			−0.339212
$19$		−	4.86615i		−	1.11637i	−0.829716	−	0.558186i	$-0.811498\pi$
$19$		−	4.86615i		−	1.11637i	0.829716	−	0.558186i	$-0.188502\pi$
$20$	0.116441	+	0.116441i	0.0260370	+	0.0260370i
$21$	4.44173			0.969264
$22$	4.60432	+	4.60432i	0.981645	+	0.981645i
$23$	0.442223	−	0.442223i	0.0922098	−	0.0922098i	−0.659497	−	0.751707i	$-0.729231\pi$
$23$	0.442223	−	0.442223i	0.0922098	−	0.0922098i	0.751707	+	0.659497i	$0.229231\pi$
$24$	1.96285	−	1.96285i	0.400665	−	0.400665i
$25$			0.354337i			0.0708674i
$26$		−	1.69052i		−	0.331538i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	0.223514	−	0.223514i	0.0422402	−	0.0422402i
$29$	−1.06796	−	1.06796i	−0.198315	−	0.198315i	0.600963	−	0.799277i	$-0.294784\pi$
$29$	−1.06796	−	1.06796i	−0.198315	−	0.198315i	−0.799277	+	0.600963i	$0.794784\pi$
$30$	−3.33012			−0.607994
$31$	−6.17723	−	6.17723i	−1.10946	−	1.10946i	−0.993221	−	0.116243i	$-0.962915\pi$
$31$	−6.17723	−	6.17723i	−1.10946	−	1.10946i	−0.116243	−	0.993221i	$-0.537085\pi$
$32$		−	0.402383i		−	0.0711319i
$33$	−4.52453			−0.787619
$34$		0			0
$35$	10.2779			1.73728
$36$		−	0.0711653i		−	0.0118609i
$37$	−6.21727	−	6.21727i	−1.02211	−	1.02211i	−0.999750	−	0.0223623i	$-0.992881\pi$
$37$	−6.21727	−	6.21727i	−1.02211	−	1.02211i	−0.0223623	−	0.999750i	$-0.507119\pi$
$38$	7.00315			1.13606
$39$	0.830610	+	0.830610i	0.133004	+	0.133004i
$40$	4.54193	−	4.54193i	0.718142	−	0.718142i
$41$	−0.328780	+	0.328780i	−0.0513468	+	0.0513468i	−0.732314	−	0.680967i	$-0.761560\pi$
$41$	−0.328780	+	0.328780i	−0.0513468	+	0.0513468i	0.680967	+	0.732314i	$0.261560\pi$
$42$			6.39233i			0.986358i
$43$		−	1.51327i		−	0.230771i	−0.993321	−	0.115385i	$-0.963190\pi$
$43$		−	1.51327i		−	0.230771i	0.993321	−	0.115385i	$-0.0368103\pi$
$44$	−0.227681	+	0.227681i	−0.0343242	+	0.0343242i
$45$	1.63621	−	1.63621i	0.243911	−	0.243911i
$46$	0.636427	+	0.636427i	0.0938360	+	0.0938360i
$47$	−6.01904			−0.877968			−0.438984	−	0.898495i	$-0.644661\pi$
$47$	−6.01904			−0.877968			−0.438984	+	0.898495i	$0.644661\pi$
$48$	2.92549	+	2.92549i	0.422258	+	0.422258i
$49$		−	12.7289i		−	1.81842i
$50$	−0.509946			−0.0721172
$51$		0			0
$52$	0.0835951			0.0115925
$53$		−	7.12324i		−	0.978452i	−0.872157	−	0.489226i	$-0.837279\pi$
$53$		−	7.12324i		−	0.978452i	0.872157	−	0.489226i	$-0.162721\pi$
$54$	1.01764	+	1.01764i	0.138483	+	0.138483i
$55$	−10.4695			−1.41171
$56$	−8.71845	−	8.71845i	−1.16505	−	1.16505i
$57$	−3.44089	+	3.44089i	−0.455757	+	0.455757i
$58$	1.53696	−	1.53696i	0.201812	−	0.201812i
$59$		−	10.4025i		−	1.35429i	−0.735852	−	0.677143i	$-0.763218\pi$
$59$		−	10.4025i		−	1.35429i	0.735852	−	0.677143i	$-0.236782\pi$
$60$		−	0.164673i		−	0.0212591i
$61$	1.80936	−	1.80936i	0.231665	−	0.231665i	−0.581722	−	0.813387i	$-0.697621\pi$
$61$	1.80936	−	1.80936i	0.231665	−	0.231665i	0.813387	+	0.581722i	$0.197621\pi$
$62$	8.88999	−	8.88999i	1.12903	−	1.12903i
$63$	−3.14078	−	3.14078i	−0.395700	−	0.395700i
$64$	−7.69544			−0.961930
$65$	1.92198	+	1.92198i	0.238393	+	0.238393i
$66$		−	6.51150i		−	0.801510i
$67$	−3.71801			−0.454227			−0.227114	−	0.973868i	$-0.572929\pi$
$67$	−3.71801			−0.454227			−0.227114	+	0.973868i	$0.572929\pi$
$68$		0			0
$69$	−0.625397			−0.0752890
$70$			14.7915i			1.76792i
$71$	10.7784	+	10.7784i	1.27916	+	1.27916i	0.941140	+	0.338016i	$0.109756\pi$
$71$	10.7784	+	10.7784i	1.27916	+	1.27916i	0.338016	+	0.941140i	$0.390244\pi$
$72$	−2.77589			−0.327142
$73$	1.91050	+	1.91050i	0.223608	+	0.223608i	0.810016	−	0.586408i	$-0.199459\pi$
$73$	1.91050	+	1.91050i	0.223608	+	0.223608i	−0.586408	+	0.810016i	$0.699459\pi$
$74$	8.94761	−	8.94761i	1.04014	−	1.04014i
$75$	0.250554	−	0.250554i	0.0289315	−	0.0289315i
$76$			0.346301i			0.0397235i
$77$			20.0967i			2.29023i
$78$	−1.19538	+	1.19538i	−0.135350	+	0.135350i
$79$	−11.8067	+	11.8067i	−1.32836	+	1.32836i	−0.421557	+	0.906802i	$0.638516\pi$
$79$	−11.8067	+	11.8067i	−1.32836	+	1.32836i	−0.906802	+	0.421557i	$0.861484\pi$
$80$	6.76942	+	6.76942i	0.756844	+	0.756844i
$81$	−1.00000			−0.111111
$82$	−0.473165	−	0.473165i	−0.0522523	−	0.0522523i
$83$			4.45459i			0.488954i	0.969655	+	0.244477i	$0.0786163\pi$
$83$			4.45459i			0.488954i	−0.969655	+	0.244477i	$0.921384\pi$
$84$	−0.316097			−0.0344890
$85$		0			0
$86$	2.17782			0.234841
$87$			1.51032i			0.161923i
$88$	8.88098	+	8.88098i	0.946715	+	0.946715i
$89$	−1.54030			−0.163272			−0.0816359	−	0.996662i	$-0.526014\pi$
$89$	−1.54030			−0.163272			−0.0816359	+	0.996662i	$0.526014\pi$
$90$	2.35475	+	2.35475i	0.248213	+	0.248213i
$91$	3.68934	−	3.68934i	0.386748	−	0.386748i
$92$	−0.0314709	+	0.0314709i	−0.00328107	+	0.00328107i
$93$			8.73592i			0.905873i
$94$		−	8.66233i		−	0.893451i
$95$	−7.96203	+	7.96203i	−0.816887	+	0.816887i
$96$	−0.284528	+	0.284528i	−0.0290395	+	0.0290395i
$97$	−2.71449	−	2.71449i	−0.275614	−	0.275614i	0.555741	−	0.831355i	$-0.312435\pi$
$97$	−2.71449	−	2.71449i	−0.275614	−	0.275614i	−0.831355	+	0.555741i	$0.812435\pi$
$98$	18.3189			1.85049
$99$	3.19932	+	3.19932i	0.321544	+	0.321544i
$100$		−	0.0252165i		−	0.00252165i
$101$	11.9158			1.18567			0.592833	−	0.805325i	$-0.298009\pi$
$101$	11.9158			1.18567			0.592833	+	0.805325i	$0.298009\pi$
$102$		0			0
$103$	−1.41240			−0.139168			−0.0695838	−	0.997576i	$-0.522167\pi$
$103$	−1.41240			−0.139168			−0.0695838	+	0.997576i	$0.522167\pi$
$104$		−	3.26073i		−	0.319741i
$105$	−7.26758	−	7.26758i	−0.709243	−	0.709243i
$106$	10.2514			0.995708
$107$	11.0690	+	11.0690i	1.07009	+	1.07009i	0.997351	+	0.0727340i	$0.0231724\pi$
$107$	11.0690	+	11.0690i	1.07009	+	1.07009i	0.0727340	+	0.997351i	$0.476828\pi$
$108$	−0.0503215	+	0.0503215i	−0.00484219	+	0.00484219i
$109$	7.17270	−	7.17270i	0.687020	−	0.687020i	−0.274552	−	0.961572i	$-0.588530\pi$
$109$	7.17270	−	7.17270i	0.687020	−	0.687020i	0.961572	+	0.274552i	$0.0885296\pi$
$110$		−	15.0672i		−	1.43660i
$111$			8.79254i			0.834551i
$112$	12.9942	−	12.9942i	1.22784	−	1.22784i
$113$	0.564809	−	0.564809i	0.0531327	−	0.0531327i	−0.680041	−	0.733174i	$-0.738038\pi$
$113$	0.564809	−	0.564809i	0.0531327	−	0.0531327i	0.733174	+	0.680041i	$0.238038\pi$
$114$	−4.95197	−	4.95197i	−0.463795	−	0.463795i
$115$	−1.44713			−0.134946
$116$	0.0760015	+	0.0760015i	0.00705657	+	0.00705657i
$117$		−	1.17466i		−	0.108597i
$118$	14.9708			1.37817
$119$		0			0
$120$	−6.42326			−0.586360
$121$		−	9.47136i		−	0.861033i
$122$	2.60395	+	2.60395i	0.235751	+	0.235751i
$123$	0.464965			0.0419245
$124$	0.439605	+	0.439605i	0.0394777	+	0.0394777i
$125$	−7.60126	+	7.60126i	−0.679877	+	0.679877i
$126$	4.52006	−	4.52006i	0.402679	−	0.402679i
$127$			3.36696i			0.298769i	0.988779	+	0.149385i	$0.0477293\pi$
$127$			3.36696i			0.298769i	−0.988779	+	0.149385i	$0.952271\pi$
$128$		−	11.8797i		−	1.05003i
$129$	−1.07004	+	1.07004i	−0.0942118	+	0.0942118i
$130$	−2.76603	+	2.76603i	−0.242597	+	0.242597i
$131$	−1.01799	−	1.01799i	−0.0889422	−	0.0889422i	0.661236	−	0.750178i	$-0.270032\pi$
$131$	−1.01799	−	1.01799i	−0.0889422	−	0.0889422i	−0.750178	+	0.661236i	$0.770032\pi$
$132$	0.321990			0.0280256
$133$	15.2835	+	15.2835i	1.32525	+	1.32525i
$134$		−	5.35079i		−	0.462238i
$135$	−2.31394			−0.199153
$136$		0			0
$137$	7.86924			0.672315			0.336157	−	0.941806i	$-0.390873\pi$
$137$	7.86924			0.672315			0.336157	+	0.941806i	$0.390873\pi$
$138$		−	0.900043i		−	0.0766168i
$139$	−6.94933	−	6.94933i	−0.589434	−	0.589434i	0.348044	−	0.937478i	$-0.386846\pi$
$139$	−6.94933	−	6.94933i	−0.589434	−	0.589434i	−0.937478	+	0.348044i	$0.886846\pi$
$140$	−0.731431			−0.0618172
$141$	4.25611	+	4.25611i	0.358429	+	0.358429i
$142$	−15.5117	+	15.5117i	−1.30172	+	1.30172i
$143$	−3.75812	+	3.75812i	−0.314270	+	0.314270i
$144$		−	4.13727i		−	0.344772i
$145$			3.49480i			0.290227i
$146$	−2.74951	+	2.74951i	−0.227551	+	0.227551i
$147$	−9.00072	+	9.00072i	−0.742367	+	0.742367i
$148$	0.442454	+	0.442454i	0.0363695	+	0.0363695i
$149$	6.30050			0.516157			0.258078	−	0.966124i	$-0.416911\pi$
$149$	6.30050			0.516157			0.258078	+	0.966124i	$0.416911\pi$
$150$	0.360586	+	0.360586i	0.0294417	+	0.0294417i
$151$			10.8279i			0.881159i	0.897714	+	0.440580i	$0.145227\pi$
$151$			10.8279i			0.881159i	−0.897714	+	0.440580i	$0.854773\pi$
$152$	13.5079			1.09564
$153$		0			0
$154$	−28.9223			−2.33062
$155$			20.2144i			1.62366i
$156$	−0.0591106	−	0.0591106i	−0.00473264	−	0.00473264i
$157$	−10.8250			−0.863933			−0.431966	−	0.901890i	$-0.642180\pi$
$157$	−10.8250			−0.863933			−0.431966	+	0.901890i	$0.642180\pi$
$158$	−16.9917	−	16.9917i	−1.35179	−	1.35179i
$159$	−5.03689	+	5.03689i	−0.399451	+	0.399451i
$160$	−0.658381	+	0.658381i	−0.0520496	+	0.0520496i
$161$			2.77784i			0.218925i
$162$		−	1.43915i		−	0.113071i
$163$	−7.97484	+	7.97484i	−0.624638	+	0.624638i	−0.946714	−	0.322076i	$-0.895619\pi$
$163$	−7.97484	+	7.97484i	−0.624638	+	0.624638i	0.322076	+	0.946714i	$0.395619\pi$
$164$	0.0233977	−	0.0233977i	0.00182706	−	0.00182706i
$165$	7.40306	+	7.40306i	0.576327	+	0.576327i
$166$	−6.41084			−0.497577
$167$	−8.74472	−	8.74472i	−0.676687	−	0.676687i	0.282562	−	0.959249i	$-0.408816\pi$
$167$	−8.74472	−	8.74472i	−0.676687	−	0.676687i	−0.959249	+	0.282562i	$0.908816\pi$
$168$			12.3297i			0.951261i
$169$	−11.6202			−0.893860
$170$		0			0
$171$	4.86615			0.372124
$172$			0.107692i			0.00821145i
$173$	−2.26090	−	2.26090i	−0.171893	−	0.171893i	0.615917	−	0.787811i	$-0.288785\pi$
$173$	−2.26090	−	2.26090i	−0.171893	−	0.171893i	−0.787811	+	0.615917i	$0.788785\pi$
$174$	−2.17358			−0.164779
$175$	−1.11289	−	1.11289i	−0.0841268	−	0.0841268i
$176$	−13.2365	+	13.2365i	−0.997736	+	0.997736i
$177$	−7.35565	+	7.35565i	−0.552885	+	0.552885i
$178$		−	2.21673i		−	0.166151i
$179$		−	19.0135i		−	1.42113i	−0.703629	−	0.710567i	$-0.748438\pi$
$179$		−	19.0135i		−	1.42113i	0.703629	−	0.710567i	$-0.251562\pi$
$180$	−0.116441	+	0.116441i	−0.00867901	+	0.00867901i
$181$	8.49913	−	8.49913i	0.631736	−	0.631736i	−0.316768	−	0.948503i	$-0.602598\pi$
$181$	8.49913	−	8.49913i	0.631736	−	0.631736i	0.948503	+	0.316768i	$0.102598\pi$
$182$	5.30953	+	5.30953i	0.393569	+	0.393569i
$183$	−2.55882			−0.189154
$184$	1.22756	+	1.22756i	0.0904971	+	0.0904971i
$185$			20.3455i			1.49583i
$186$	−12.5723			−0.921849
$187$		0			0
$188$	0.428347			0.0312404
$189$			4.44173i			0.323088i
$190$	−11.4586	−	11.4586i	−0.831293	−	0.831293i
$191$	−22.3102			−1.61431			−0.807154	−	0.590341i	$-0.798993\pi$
$191$	−22.3102			−1.61431			−0.807154	+	0.590341i	$0.798993\pi$
$192$	5.44150	+	5.44150i	0.392706	+	0.392706i
$193$	2.47198	−	2.47198i	0.177937	−	0.177937i	−0.612519	−	0.790456i	$-0.709844\pi$
$193$	2.47198	−	2.47198i	0.177937	−	0.177937i	0.790456	+	0.612519i	$0.209844\pi$
$194$	3.90657	−	3.90657i	0.280475	−	0.280475i
$195$		−	2.71810i		−	0.194647i
$196$			0.905859i			0.0647042i
$197$	−8.48335	+	8.48335i	−0.604413	+	0.604413i	−0.941481	−	0.337067i	$-0.890565\pi$
$197$	−8.48335	+	8.48335i	−0.604413	+	0.604413i	0.337067	+	0.941481i	$0.390565\pi$
$198$	−4.60432	+	4.60432i	−0.327215	+	0.327215i
$199$	2.84435	+	2.84435i	0.201630	+	0.201630i	0.800698	−	0.599068i	$-0.204462\pi$
$199$	2.84435	+	2.84435i	0.201630	+	0.201630i	−0.599068	+	0.800698i	$0.704462\pi$
$200$	−0.983601			−0.0695511
$201$	2.62903	+	2.62903i	0.185438	+	0.185438i
$202$			17.1487i			1.20658i
$203$	6.70843			0.470839
$204$		0			0
$205$	1.07590			0.0751443
$206$		−	2.03266i		−	0.141622i
$207$	0.442223	+	0.442223i	0.0307366	+	0.0307366i
$208$	4.85988			0.336972
$209$	−15.5684	−	15.5684i	−1.07689	−	1.07689i
$210$	10.4592	−	10.4592i	0.721751	−	0.721751i
$211$	−11.2855	+	11.2855i	−0.776929	+	0.776929i	−0.979307	−	0.202378i	$-0.935133\pi$
$211$	−11.2855	+	11.2855i	−0.776929	+	0.776929i	0.202378	+	0.979307i	$0.435133\pi$
$212$			0.506928i			0.0348159i
$213$		−	15.2429i		−	1.04443i
$214$	−15.9301	+	15.9301i	−1.08896	+	1.08896i
$215$	−2.47601	+	2.47601i	−0.168863	+	0.168863i
$216$	1.96285	+	1.96285i	0.133555	+	0.133555i
$217$	38.8026			2.63409
$218$	10.3226	+	10.3226i	0.699136	+	0.699136i
$219$		−	2.70186i		−	0.182575i
$220$	0.745066			0.0502323
$221$		0			0
$222$	−12.6538			−0.849269
$223$		−	5.35573i		−	0.358646i	−0.983790	−	0.179323i	$-0.942609\pi$
$223$		−	5.35573i		−	0.358646i	0.983790	−	0.179323i	$-0.0573908\pi$
$224$	1.26379	+	1.26379i	0.0844408	+	0.0844408i
$225$	−0.354337			−0.0236225
$226$	0.812847	+	0.812847i	0.0540698	+	0.0540698i
$227$	−1.21109	+	1.21109i	−0.0803829	+	0.0803829i	−0.746155	−	0.665772i	$-0.768102\pi$
$227$	−1.21109	+	1.21109i	−0.0803829	+	0.0803829i	0.665772	+	0.746155i	$0.268102\pi$
$228$	0.244872	−	0.244872i	0.0162171	−	0.0162171i
$229$		−	0.380619i		−	0.0251520i	−0.999921	−	0.0125760i	$-0.995997\pi$
$229$		−	0.380619i		−	0.0251520i	0.999921	−	0.0125760i	$-0.00400317\pi$
$230$		−	2.08265i		−	0.137326i
$231$	14.2105	−	14.2105i	0.934984	−	0.934984i
$232$	2.96453	−	2.96453i	0.194631	−	0.194631i
$233$	−6.33766	−	6.33766i	−0.415194	−	0.415194i	0.468349	−	0.883543i	$-0.344849\pi$
$233$	−6.33766	−	6.33766i	−0.415194	−	0.415194i	−0.883543	+	0.468349i	$0.844849\pi$
$234$	1.69052			0.110513
$235$	9.84839	+	9.84839i	0.642438	+	0.642438i
$236$			0.740295i			0.0481891i
$237$	16.6972			1.08460
$238$		0			0
$239$	−6.70928			−0.433987			−0.216994	−	0.976173i	$-0.569625\pi$
$239$	−6.70928			−0.433987			−0.216994	+	0.976173i	$0.569625\pi$
$240$		−	9.57340i		−	0.617960i
$241$	6.25076	+	6.25076i	0.402647	+	0.402647i	0.879165	−	0.476518i	$-0.158101\pi$
$241$	6.25076	+	6.25076i	0.402647	+	0.402647i	−0.476518	+	0.879165i	$0.658101\pi$
$242$	13.6307			0.876218
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−0.128764	+	0.128764i	−0.00824326	+	0.00824326i
$245$	−20.8272	+	20.8272i	−1.33060	+	1.33060i
$246$			0.669156i			0.0426638i
$247$			5.71607i			0.363705i
$248$	17.1473	−	17.1473i	1.08886	−	1.08886i
$249$	3.14987	−	3.14987i	0.199615	−	0.199615i
$250$	−10.9394	−	10.9394i	−0.691867	−	0.691867i
$251$	24.4193			1.54133			0.770667	−	0.637238i	$-0.219923\pi$
$251$	24.4193			1.54133			0.770667	+	0.637238i	$0.219923\pi$
$252$	0.223514	+	0.223514i	0.0140801	+	0.0140801i
$253$		−	2.82963i		−	0.177897i
$254$	−4.84557			−0.304038
$255$		0			0
$256$	1.70583			0.106614
$257$		−	25.9327i		−	1.61764i	−0.588057	−	0.808819i	$-0.700107\pi$
$257$		−	25.9327i		−	1.61764i	0.588057	−	0.808819i	$-0.299893\pi$
$258$	−1.53995	−	1.53995i	−0.0958733	−	0.0958733i
$259$	39.0541			2.42670
$260$	−0.136779	−	0.136779i	−0.00848266	−	0.00848266i
$261$	1.06796	−	1.06796i	0.0661049	−	0.0661049i
$262$	1.46504	−	1.46504i	0.0905108	−	0.0905108i
$263$			1.74151i			0.107386i	0.998557	+	0.0536932i	$0.0170993\pi$
$263$			1.74151i			0.107386i	−0.998557	+	0.0536932i	$0.982901\pi$
$264$		−	12.5596i		−	0.772990i
$265$	−11.6551	+	11.6551i	−0.715966	+	0.715966i
$266$	−21.9953	+	21.9953i	−1.34862	+	1.34862i
$267$	1.08916	+	1.08916i	0.0666555	+	0.0666555i
$268$	0.264594			0.0161626
$269$	−22.2585	−	22.2585i	−1.35712	−	1.35712i	−0.877445	−	0.479678i	$-0.840754\pi$
$269$	−22.2585	−	22.2585i	−1.35712	−	1.35712i	−0.479678	−	0.877445i	$-0.659246\pi$
$270$		−	3.33012i		−	0.202665i
$271$	−19.8066			−1.20316			−0.601582	−	0.798811i	$-0.705463\pi$
$271$	−19.8066			−1.20316			−0.601582	+	0.798811i	$0.705463\pi$
$272$		0			0
$273$	−5.21752			−0.315779
$274$			11.3251i			0.684172i
$275$	1.13364	+	1.13364i	0.0683610	+	0.0683610i
$276$	0.0445066			0.00267898
$277$	−1.64808	−	1.64808i	−0.0990234	−	0.0990234i	0.655860	−	0.754883i	$-0.272306\pi$
$277$	−1.64808	−	1.64808i	−0.0990234	−	0.0990234i	−0.754883	+	0.655860i	$0.772306\pi$
$278$	10.0012	−	10.0012i	0.599830	−	0.599830i
$279$	6.17723	−	6.17723i	0.369821	−	0.369821i
$280$			28.5303i			1.70501i
$281$			0.306147i			0.0182632i	0.999958	+	0.00913161i	$0.00290672\pi$
$281$			0.306147i			0.0182632i	−0.999958	+	0.00913161i	$0.997093\pi$
$282$	−6.12519	+	6.12519i	−0.364750	+	0.364750i
$283$	−12.9501	+	12.9501i	−0.769803	+	0.769803i	−0.978072	−	0.208268i	$-0.933217\pi$
$283$	−12.9501	+	12.9501i	−0.769803	+	0.769803i	0.208268	+	0.978072i	$0.433217\pi$
$284$	−0.767046	−	0.767046i	−0.0455158	−	0.0455158i
$285$	11.2600			0.666985
$286$	−5.40851	−	5.40851i	−0.319812	−	0.319812i
$287$		−	2.06525i		−	0.121908i
$288$	0.402383			0.0237106
$289$		0			0
$290$	−5.02955			−0.295345
$291$			3.83886i			0.225038i
$292$	−0.135962	−	0.135962i	−0.00795656	−	0.00795656i
$293$	−15.2652			−0.891801			−0.445900	−	0.895083i	$-0.647116\pi$
$293$	−15.2652			−0.891801			−0.445900	+	0.895083i	$0.647116\pi$
$294$	−12.9534	−	12.9534i	−0.755459	−	0.755459i
$295$	−17.0206	+	17.0206i	−0.990976	+	0.990976i
$296$	17.2585	−	17.2585i	1.00313	−	1.00313i
$297$		−	4.52453i		−	0.262540i
$298$			9.06739i			0.525260i
$299$	−0.519461	+	0.519461i	−0.0300412	+	0.0300412i
$300$	−0.0178308	+	0.0178308i	−0.00102946	+	0.00102946i
$301$	4.75283	+	4.75283i	0.273948	+	0.273948i
$302$	−15.5830			−0.896699
$303$	−8.42574	−	8.42574i	−0.484046	−	0.484046i
$304$			20.1326i			1.15468i
$305$	−5.92097			−0.339034
$306$		0			0
$307$	29.9884			1.71153			0.855765	−	0.517365i	$-0.173087\pi$
$307$	29.9884			1.71153			0.855765	+	0.517365i	$0.173087\pi$
$308$		−	1.43019i		−	0.0814926i
$309$	0.998716	+	0.998716i	0.0568150	+	0.0568150i
$310$	−29.0917			−1.65230
$311$	16.4930	+	16.4930i	0.935229	+	0.935229i	0.998026	−	0.0627969i	$-0.0200020\pi$
$311$	16.4930	+	16.4930i	0.935229	+	0.935229i	−0.0627969	+	0.998026i	$0.520002\pi$
$312$	−2.30568	+	2.30568i	−0.130534	+	0.130534i
$313$	16.9400	−	16.9400i	0.957506	−	0.957506i	−0.0416273	−	0.999133i	$-0.513254\pi$
$313$	16.9400	−	16.9400i	0.957506	−	0.957506i	0.999133	+	0.0416273i	$0.0132542\pi$
$314$		−	15.5789i		−	0.879169i
$315$			10.2779i			0.579094i
$316$	0.840229	−	0.840229i	0.0472666	−	0.0472666i
$317$	13.2826	−	13.2826i	0.746024	−	0.746024i	−0.227706	−	0.973730i	$-0.573122\pi$
$317$	13.2826	−	13.2826i	0.746024	−	0.746024i	0.973730	+	0.227706i	$0.0731224\pi$
$318$	−7.24886	−	7.24886i	−0.406496	−	0.406496i
$319$	−6.83348			−0.382602
$320$	12.5913	+	12.5913i	0.703876	+	0.703876i
$321$		−	15.6540i		−	0.873721i
$322$	−3.99775			−0.222786
$323$		0			0
$324$	0.0711653			0.00395363
$325$		−	0.416226i		−	0.0230880i
$326$	−11.4770	−	11.4770i	−0.635654	−	0.635654i
$327$	−10.1437			−0.560949
$328$	−0.912657	−	0.912657i	−0.0503930	−	0.0503930i
$329$	18.9045	−	18.9045i	1.04224	−	1.04224i
$330$	−10.6541	+	10.6541i	−0.586491	+	0.586491i
$331$			23.6869i			1.30195i	0.759099	+	0.650975i	$0.225640\pi$
$331$			23.6869i			1.30195i	−0.759099	+	0.650975i	$0.774360\pi$
$332$		−	0.317012i		−	0.0173983i
$333$	6.21727	−	6.21727i	0.340704	−	0.340704i
$334$	12.5850	−	12.5850i	0.688621	−	0.688621i
$335$	6.08343	+	6.08343i	0.332373	+	0.332373i
$336$	−18.3766			−1.00253
$337$	4.29265	+	4.29265i	0.233835	+	0.233835i	0.814292	−	0.580456i	$-0.197126\pi$
$337$	4.29265	+	4.29265i	0.233835	+	0.233835i	−0.580456	+	0.814292i	$0.697126\pi$
$338$		−	16.7232i		−	0.909624i
$339$	−0.798760			−0.0433827
$340$		0			0
$341$	−39.5259			−2.14045
$342$			7.00315i			0.378687i
$343$	17.9933	+	17.9933i	0.971547	+	0.971547i
$344$	4.20066			0.226484
$345$	1.02328	+	1.02328i	0.0550915	+	0.0550915i
$346$	3.25379	−	3.25379i	0.174925	−	0.174925i
$347$	−5.04525	+	5.04525i	−0.270843	+	0.270843i	−0.829440	−	0.558596i	$-0.811340\pi$
$347$	−5.04525	+	5.04525i	−0.270843	+	0.270843i	0.558596	+	0.829440i	$0.311340\pi$
$348$		−	0.107482i		−	0.00576166i
$349$			15.7825i			0.844819i	0.906405	+	0.422410i	$0.138816\pi$
$349$			15.7825i			0.844819i	−0.906405	+	0.422410i	$0.861184\pi$
$350$	1.60163	−	1.60163i	0.0856105	−	0.0856105i
$351$	−0.830610	+	0.830610i	−0.0443347	+	0.0443347i
$352$	−1.28735	−	1.28735i	−0.0686162	−	0.0686162i
$353$	−35.2308			−1.87515			−0.937573	−	0.347788i	$-0.886933\pi$
$353$	−35.2308			−1.87515			−0.937573	+	0.347788i	$0.886933\pi$
$354$	−10.5859	−	10.5859i	−0.562635	−	0.562635i
$355$		−	35.2712i		−	1.87200i
$356$	0.109616			0.00580965
$357$		0			0
$358$	27.3633			1.44620
$359$			25.7316i			1.35806i	0.734110	+	0.679030i	$0.237600\pi$
$359$			25.7316i			1.35806i	−0.734110	+	0.679030i	$0.762400\pi$
$360$	4.54193	+	4.54193i	0.239381	+	0.239381i
$361$	−4.67944			−0.246287
$362$	12.2316	+	12.2316i	0.642877	+	0.642877i
$363$	−6.69726	+	6.69726i	−0.351515	+	0.351515i
$364$	−0.262553	+	0.262553i	−0.0137615	+	0.0137615i
$365$		−	6.25195i		−	0.327242i
$366$		−	3.68254i		−	0.192489i
$367$	−5.84137	+	5.84137i	−0.304917	+	0.304917i	−0.842934	−	0.538017i	$-0.819174\pi$
$367$	−5.84137	+	5.84137i	−0.304917	+	0.304917i	0.538017	+	0.842934i	$0.319174\pi$
$368$	−1.82959	+	1.82959i	−0.0953741	+	0.0953741i
$369$	−0.328780	−	0.328780i	−0.0171156	−	0.0171156i
$370$	−29.2802			−1.52221
$371$	22.3725	+	22.3725i	1.16152	+	1.16152i
$372$		−	0.621695i		−	0.0322334i
$373$	23.4360			1.21347			0.606734	−	0.794905i	$-0.292479\pi$
$373$	23.4360			1.21347			0.606734	+	0.794905i	$0.292479\pi$
$374$		0			0
$375$	10.7498			0.555117
$376$		−	16.7082i		−	0.861660i
$377$	1.25449	+	1.25449i	0.0646093	+	0.0646093i
$378$	−6.39233			−0.328786
$379$	−10.6505	−	10.6505i	−0.547079	−	0.547079i	0.378516	−	0.925595i	$-0.376435\pi$
$379$	−10.6505	−	10.6505i	−0.547079	−	0.547079i	−0.925595	+	0.378516i	$0.876435\pi$
$380$	0.566620	−	0.566620i	0.0290670	−	0.0290670i
$381$	2.38080	−	2.38080i	0.121972	−	0.121972i
$382$		−	32.1078i		−	1.64278i
$383$		−	15.9980i		−	0.817459i	−0.912656	−	0.408729i	$-0.865972\pi$
$383$		−	15.9980i		−	0.817459i	0.912656	−	0.408729i	$-0.134028\pi$
$384$	−8.40021	+	8.40021i	−0.428672	+	0.428672i
$385$	32.8824	−	32.8824i	1.67584	−	1.67584i
$386$	3.55757	+	3.55757i	0.181075	+	0.181075i
$387$	1.51327			0.0769236
$388$	0.193177	+	0.193177i	0.00980710	+	0.00980710i
$389$		−	2.98991i		−	0.151595i	−0.997123	−	0.0757973i	$-0.975850\pi$
$389$		−	2.98991i		−	0.151595i	0.997123	−	0.0757973i	$-0.0241502\pi$
$390$	3.91176			0.198080
$391$		0			0
$392$	35.3341			1.78464
$393$			1.43966i			0.0726210i
$394$	−12.2088	−	12.2088i	−0.615073	−	0.615073i
$395$	38.6364			1.94401
$396$	−0.227681	−	0.227681i	−0.0114414	−	0.0114414i
$397$	8.94678	−	8.94678i	0.449026	−	0.449026i	−0.446004	−	0.895031i	$-0.647153\pi$
$397$	8.94678	−	8.94678i	0.449026	−	0.449026i	0.895031	+	0.446004i	$0.147153\pi$
$398$	−4.09345	+	4.09345i	−0.205186	+	0.205186i
$399$		−	21.6141i		−	1.08206i
$400$		−	1.46599i		−	0.0732994i
$401$	10.3724	−	10.3724i	0.517975	−	0.517975i	−0.398983	−	0.916958i	$-0.630637\pi$
$401$	10.3724	−	10.3724i	0.517975	−	0.517975i	0.916958	+	0.398983i	$0.130637\pi$
$402$	−3.78358	+	3.78358i	−0.188708	+	0.188708i
$403$	7.25615	+	7.25615i	0.361454	+	0.361454i
$404$	−0.847992			−0.0421892
$405$	1.63621	+	1.63621i	0.0813037	+	0.0813037i
$406$			9.65446i			0.479143i
$407$	−39.7821			−1.97193
$408$		0			0
$409$	−16.3219			−0.807067			−0.403534	−	0.914965i	$-0.632218\pi$
$409$	−16.3219			−0.807067			−0.403534	+	0.914965i	$0.632218\pi$
$410$			1.54839i			0.0764695i
$411$	−5.56440	−	5.56440i	−0.274471	−	0.274471i
$412$	0.100514			0.00495196
$413$	32.6718	+	32.6718i	1.60767	+	1.60767i
$414$	−0.636427	+	0.636427i	−0.0312787	+	0.0312787i
$415$	7.28862	−	7.28862i	0.357784	−	0.357784i
$416$			0.472663i			0.0231742i
$417$			9.82784i			0.481271i
$418$	22.4053	−	22.4053i	1.09588	−	1.09588i
$419$	11.1085	−	11.1085i	0.542685	−	0.542685i	−0.381630	−	0.924315i	$-0.624637\pi$
$419$	11.1085	−	11.1085i	0.542685	−	0.542685i	0.924315	+	0.381630i	$0.124637\pi$
$420$	0.517200	+	0.517200i	0.0252368	+	0.0252368i
$421$	−22.1035			−1.07726			−0.538630	−	0.842542i	$-0.681058\pi$
$421$	−22.1035			−1.07726			−0.538630	+	0.842542i	$0.681058\pi$
$422$	−16.2416	−	16.2416i	−0.790631	−	0.790631i
$423$		−	6.01904i		−	0.292656i
$424$	19.7733			0.960278
$425$		0			0
$426$	21.9369			1.06285
$427$			11.3656i			0.550019i
$428$	−0.787733	−	0.787733i	−0.0380765	−	0.0380765i
$429$	5.31478			0.256600
$430$	−3.56337	−	3.56337i	−0.171841	−	0.171841i
$431$	−2.93823	+	2.93823i	−0.141529	+	0.141529i	−0.774322	−	0.632792i	$-0.781909\pi$
$431$	−2.93823	+	2.93823i	−0.141529	+	0.141529i	0.632792	+	0.774322i	$0.281909\pi$
$432$	−2.92549	+	2.92549i	−0.140753	+	0.140753i
$433$		−	13.0766i		−	0.628420i	−0.949354	−	0.314210i	$-0.898260\pi$
$433$		−	13.0766i		−	0.628420i	0.949354	−	0.314210i	$-0.101740\pi$
$434$			55.8429i			2.68055i
$435$	2.47119	−	2.47119i	0.118485	−	0.118485i
$436$	−0.510448	+	0.510448i	−0.0244460	+	0.0244460i
$437$	−2.15192	−	2.15192i	−0.102940	−	0.102940i
$438$	3.88839			0.185795
$439$	−8.19806	−	8.19806i	−0.391272	−	0.391272i	0.483869	−	0.875141i	$-0.339231\pi$
$439$	−8.19806	−	8.19806i	−0.391272	−	0.391272i	−0.875141	+	0.483869i	$0.839231\pi$
$440$		−	29.0622i		−	1.38549i
$441$	12.7289			0.606140
$442$		0			0
$443$	17.6619			0.839144			0.419572	−	0.907722i	$-0.362180\pi$
$443$	17.6619			0.839144			0.419572	+	0.907722i	$0.362180\pi$
$444$		−	0.625724i		−	0.0296956i
$445$	2.52025	+	2.52025i	0.119471	+	0.119471i
$446$	7.70773			0.364971
$447$	−4.45512	−	4.45512i	−0.210720	−	0.210720i
$448$	24.1697	−	24.1697i	1.14191	−	1.14191i
$449$	24.8487	−	24.8487i	1.17268	−	1.17268i	0.191118	−	0.981567i	$-0.438789\pi$
$449$	24.8487	−	24.8487i	1.17268	−	1.17268i	0.981567	−	0.191118i	$-0.0612112\pi$
$450$		−	0.509946i		−	0.0240391i
$451$			2.10375i			0.0990616i
$452$	−0.0401948	+	0.0401948i	−0.00189060	+	0.00189060i
$453$	7.65646	−	7.65646i	0.359732	−	0.359732i
$454$	−1.74295	−	1.74295i	−0.0818005	−	0.0818005i
$455$	−12.0730			−0.565993
$456$	−9.55153	−	9.55153i	−0.447292	−	0.447292i
$457$		−	24.6306i		−	1.15217i	−0.817389	−	0.576086i	$-0.804580\pi$
$457$		−	24.6306i		−	1.15217i	0.817389	−	0.576086i	$-0.195420\pi$
$458$	0.547769			0.0255956
$459$		0			0
$460$	0.102986			0.00480174
$461$			1.00413i			0.0467668i	0.999727	+	0.0233834i	$0.00744385\pi$
$461$			1.00413i			0.0467668i	−0.999727	+	0.0233834i	$0.992556\pi$
$462$	20.4511	+	20.4511i	0.951473	+	0.951473i
$463$	20.4600			0.950856			0.475428	−	0.879755i	$-0.342293\pi$
$463$	20.4600			0.950856			0.475428	+	0.879755i	$0.342293\pi$
$464$	4.41842	+	4.41842i	0.205120	+	0.205120i
$465$	14.2938	−	14.2938i	0.662858	−	0.662858i
$466$	9.12087	−	9.12087i	0.422516	−	0.422516i
$467$			35.1659i			1.62728i	0.581366	+	0.813642i	$0.302519\pi$
$467$			35.1659i			1.62728i	−0.581366	+	0.813642i	$0.697481\pi$
$468$			0.0835951i			0.00386418i
$469$	11.6774	−	11.6774i	0.539214	−	0.539214i
$470$	−14.1734	+	14.1734i	−0.653768	+	0.653768i
$471$	7.65446	+	7.65446i	0.352699	+	0.352699i
$472$	28.8761			1.32913
$473$	−4.84143	−	4.84143i	−0.222609	−	0.222609i
$474$			24.0299i			1.10373i
$475$	1.72426			0.0791144
$476$		0			0
$477$	7.12324			0.326151
$478$		−	9.65570i		−	0.441641i
$479$	2.72746	+	2.72746i	0.124621	+	0.124621i	0.766666	−	0.642046i	$-0.221914\pi$
$479$	2.72746	+	2.72746i	0.124621	+	0.124621i	−0.642046	+	0.766666i	$0.721914\pi$
$480$	0.931092			0.0424983
$481$	7.30317	+	7.30317i	0.332996	+	0.332996i
$482$	−8.99580	+	8.99580i	−0.409748	+	0.409748i
$483$	1.96423	−	1.96423i	0.0893757	−	0.0893757i
$484$			0.674032i			0.0306378i
$485$			8.88292i			0.403353i
$486$	−1.01764	+	1.01764i	−0.0461609	+	0.0461609i
$487$	−14.4030	+	14.4030i	−0.652662	+	0.652662i	−0.953633	−	0.300971i	$-0.902689\pi$
$487$	−14.4030	+	14.4030i	−0.652662	+	0.652662i	0.300971	+	0.953633i	$0.402689\pi$
$488$	5.02259	+	5.02259i	0.227362	+	0.227362i
$489$	11.2781			0.510015
$490$	−29.9735	−	29.9735i	−1.35406	−	1.35406i
$491$			6.38676i			0.288231i	0.989561	+	0.144115i	$0.0460336\pi$
$491$			6.38676i			0.288231i	−0.989561	+	0.144115i	$0.953966\pi$
$492$	−0.0330894			−0.00149178
$493$		0			0
$494$	−8.22631			−0.370119
$495$		−	10.4695i		−	0.470569i
$496$	25.5569	+	25.5569i	1.14754	+	1.14754i
$497$	−67.7048			−3.03698
$498$	4.53315	+	4.53315i	0.203135	+	0.203135i
$499$	−1.16238	+	1.16238i	−0.0520351	+	0.0520351i	−0.732646	−	0.680610i	$-0.761715\pi$
$499$	−1.16238	+	1.16238i	−0.0520351	+	0.0520351i	0.680610	+	0.732646i	$0.261715\pi$
$500$	0.540946	−	0.540946i	0.0241919	−	0.0241919i
$501$			12.3669i			0.552513i
$502$			35.1432i			1.56852i
$503$	18.8175	−	18.8175i	0.839031	−	0.839031i	−0.149700	−	0.988731i	$-0.547831\pi$
$503$	18.8175	−	18.8175i	0.839031	−	0.839031i	0.988731	+	0.149700i	$0.0478308\pi$
$504$	8.71845	−	8.71845i	0.388351	−	0.388351i
$505$	−19.4967	−	19.4967i	−0.867592	−	0.867592i
$506$	4.07227			0.181035
$507$	8.21670	+	8.21670i	0.364917	+	0.364917i
$508$		−	0.239611i		−	0.0106310i
$509$	14.0065			0.620827			0.310413	−	0.950602i	$-0.399533\pi$
$509$	14.0065			0.620827			0.310413	+	0.950602i	$0.399533\pi$
$510$		0			0
$511$	−12.0009			−0.530890
$512$		−	21.3044i		−	0.941532i
$513$	−3.44089	−	3.44089i	−0.151919	−	0.151919i
$514$	37.3212			1.64617
$515$	2.31097	+	2.31097i	0.101834	+	0.101834i
$516$	0.0761498	−	0.0761498i	0.00335231	−	0.00335231i
$517$	−19.2569	+	19.2569i	−0.846916	+	0.846916i
$518$			56.2048i			2.46950i
$519$			3.19740i			0.140350i
$520$	−5.33522	+	5.33522i	−0.233965	+	0.233965i
$521$	−13.4078	+	13.4078i	−0.587405	+	0.587405i	−0.936928	−	0.349523i	$-0.886344\pi$
$521$	−13.4078	+	13.4078i	−0.587405	+	0.587405i	0.349523	+	0.936928i	$0.386344\pi$
$522$	1.53696	+	1.53696i	0.0672707	+	0.0672707i
$523$	−20.3838			−0.891320			−0.445660	−	0.895202i	$-0.647031\pi$
$523$	−20.3838			−0.891320			−0.445660	+	0.895202i	$0.647031\pi$
$524$	0.0724456	+	0.0724456i	0.00316480	+	0.00316480i
$525$			1.57387i			0.0686893i
$526$	−2.50631			−0.109280
$527$		0			0
$528$	18.7192			0.814648
$529$			22.6089i			0.982995i
$530$	−16.7735	−	16.7735i	−0.728593	−	0.728593i
$531$	10.4025			0.451428
$532$	−1.08765	−	1.08765i	−0.0471558	−	0.0471558i
$533$	0.386204	−	0.386204i	0.0167284	−	0.0167284i
$534$	−1.56747	+	1.56747i	−0.0678310	+	0.0678310i
$535$		−	36.2225i		−	1.56603i
$536$		−	10.3208i		−	0.445790i
$537$	−13.4446	+	13.4446i	−0.580176	+	0.580176i
$538$	32.0334	−	32.0334i	1.38106	−	1.38106i
$539$	−40.7240	−	40.7240i	−1.75411	−	1.75411i
$540$	0.164673			0.00708638
$541$	−15.9391	−	15.9391i	−0.685276	−	0.685276i	0.275908	−	0.961184i	$-0.411021\pi$
$541$	−15.9391	−	15.9391i	−0.685276	−	0.685276i	−0.961184	+	0.275908i	$0.911021\pi$
$542$		−	28.5047i		−	1.22438i
$543$	−12.0196			−0.515810
$544$		0			0
$545$	−23.4720			−1.00543
$546$		−	7.50881i		−	0.321348i
$547$	2.33861	+	2.33861i	0.0999919	+	0.0999919i	0.755333	−	0.655341i	$-0.227475\pi$
$547$	2.33861	+	2.33861i	0.0999919	+	0.0999919i	−0.655341	+	0.755333i	$0.727475\pi$
$548$	−0.560018			−0.0239228
$549$	1.80936	+	1.80936i	0.0772216	+	0.0772216i
$550$	−1.63148	+	1.63148i	−0.0695666	+	0.0695666i
$551$	−5.19684	+	5.19684i	−0.221393	+	0.221393i
$552$		−	1.73603i		−	0.0738905i
$553$		−	74.1644i		−	3.15379i
$554$	2.37184	−	2.37184i	0.100770	−	0.100770i
$555$	14.3864	−	14.3864i	0.610669	−	0.610669i
$556$	0.494551	+	0.494551i	0.0209737	+	0.0209737i
$557$	−34.4355			−1.45908			−0.729540	−	0.683938i	$-0.760266\pi$
$557$	−34.4355			−1.45908			−0.729540	+	0.683938i	$0.760266\pi$
$558$	8.88999	+	8.88999i	0.376343	+	0.376343i
$559$			1.77757i			0.0751833i
$560$	−42.5224			−1.79690
$561$		0			0
$562$	−0.440593			−0.0185853
$563$			4.70471i			0.198280i	0.995074	+	0.0991399i	$0.0316091\pi$
$563$			4.70471i			0.198280i	−0.995074	+	0.0991399i	$0.968391\pi$
$564$	−0.302887	−	0.302887i	−0.0127539	−	0.0127539i
$565$	−1.84829			−0.0777580
$566$	−18.6372	−	18.6372i	−0.783380	−	0.783380i
$567$	3.14078	−	3.14078i	0.131900	−	0.131900i
$568$	−29.9196	+	29.9196i	−1.25540	+	1.25540i
$569$			37.2742i			1.56262i	0.624145	+	0.781308i	$0.285447\pi$
$569$			37.2742i			1.56262i	−0.624145	+	0.781308i	$0.714553\pi$
$570$			16.2049i			0.678748i
$571$	14.3630	−	14.3630i	0.601071	−	0.601071i	−0.339526	−	0.940597i	$-0.610267\pi$
$571$	14.3630	−	14.3630i	0.601071	−	0.601071i	0.940597	+	0.339526i	$0.110267\pi$
$572$	0.267448	−	0.267448i	0.0111826	−	0.0111826i
$573$	15.7757	+	15.7757i	0.659039	+	0.659039i
$574$	2.97221			0.124058
$575$	0.156696	+	0.156696i	0.00653467	+	0.00653467i
$576$		−	7.69544i		−	0.320643i
$577$	−33.5408			−1.39632			−0.698161	−	0.715941i	$-0.745998\pi$
$577$	−33.5408			−1.39632			−0.698161	+	0.715941i	$0.745998\pi$
$578$		0			0
$579$	−3.49591			−0.145285
$580$		−	0.248708i		−	0.0103271i
$581$	−13.9909	−	13.9909i	−0.580438	−	0.580438i
$582$	−5.52472			−0.229007
$583$	−22.7896	−	22.7896i	−0.943847	−	0.943847i
$584$	−5.30335	+	5.30335i	−0.219454	+	0.219454i
$585$	−1.92198	+	1.92198i	−0.0794643	+	0.0794643i
$586$		−	21.9689i		−	0.907528i
$587$		−	21.8364i		−	0.901285i	−0.892705	−	0.450642i	$-0.851195\pi$
$587$		−	21.8364i		−	0.901285i	0.892705	−	0.450642i	$-0.148805\pi$
$588$	0.640539	−	0.640539i	0.0264154	−	0.0264154i
$589$	−30.0594	+	30.0594i	−1.23857	+	1.23857i
$590$	−24.4952	−	24.4952i	−1.00845	−	1.00845i
$591$	11.9973			0.493501
$592$	25.7225	+	25.7225i	1.05719	+	1.05719i
$593$			24.6066i			1.01047i	0.862981	+	0.505236i	$0.168594\pi$
$593$			24.6066i			1.01047i	−0.862981	+	0.505236i	$0.831406\pi$
$594$	6.51150			0.267170
$595$		0			0
$596$	−0.448377			−0.0183662
$597$		−	4.02251i		−	0.164630i
$598$	−0.747585	−	0.747585i	−0.0305710	−	0.0305710i
$599$	40.9057			1.67136			0.835681	−	0.549215i	$-0.185073\pi$
$599$	40.9057			1.67136			0.835681	+	0.549215i	$0.185073\pi$
$600$	0.695511	+	0.695511i	0.0283941	+	0.0283941i
$601$	26.0607	−	26.0607i	1.06304	−	1.06304i	0.0651648	−	0.997875i	$-0.479243\pi$
$601$	26.0607	−	26.0607i	1.06304	−	1.06304i	0.997875	−	0.0651648i	$-0.0207573\pi$
$602$	−6.84005	+	6.84005i	−0.278780	+	0.278780i
$603$		−	3.71801i		−	0.151409i
$604$		−	0.770569i		−	0.0313540i
$605$	−15.4971	+	15.4971i	−0.630046	+	0.630046i
$606$	12.1259	−	12.1259i	0.492583	−	0.492583i
$607$	34.1097	+	34.1097i	1.38447	+	1.38447i	0.836495	+	0.547975i	$0.184601\pi$
$607$	34.1097	+	34.1097i	1.38447	+	1.38447i	0.547975	+	0.836495i	$0.315399\pi$
$608$	−1.95806			−0.0794097
$609$	−4.74357	−	4.74357i	−0.192219	−	0.192219i
$610$		−	8.52119i		−	0.345013i
$611$	7.07033			0.286035
$612$		0			0
$613$	26.2900			1.06184			0.530922	−	0.847421i	$-0.321846\pi$
$613$	26.2900			1.06184			0.530922	+	0.847421i	$0.321846\pi$
$614$			43.1580i			1.74171i
$615$	−0.760778	−	0.760778i	−0.0306775	−	0.0306775i
$616$	−55.7863			−2.24769
$617$	−2.76674	−	2.76674i	−0.111385	−	0.111385i	0.649218	−	0.760603i	$-0.275096\pi$
$617$	−2.76674	−	2.76674i	−0.111385	−	0.111385i	−0.760603	+	0.649218i	$0.775096\pi$
$618$	−1.43731	+	1.43731i	−0.0578169	+	0.0578169i
$619$	6.01489	−	6.01489i	0.241759	−	0.241759i	−0.575819	−	0.817578i	$-0.695317\pi$
$619$	6.01489	−	6.01489i	0.241759	−	0.241759i	0.817578	+	0.575819i	$0.195317\pi$
$620$		−	1.43857i		−	0.0577743i
$621$		−	0.625397i		−	0.0250963i
$622$	−23.7359	+	23.7359i	−0.951723	+	0.951723i
$623$	4.83775	−	4.83775i	0.193820	−	0.193820i
$624$	−3.43645	−	3.43645i	−0.137568	−	0.137568i
$625$	26.6461			1.06585
$626$	24.3793	+	24.3793i	0.974392	+	0.974392i
$627$			22.0170i			0.879276i
$628$	0.770368			0.0307410
$629$		0			0
$630$	−14.7915			−0.589307
$631$			7.26384i			0.289169i	0.989492	+	0.144584i	$0.0461845\pi$
$631$			7.26384i			0.289169i	−0.989492	+	0.144584i	$0.953815\pi$
$632$	−32.7741	−	32.7741i	−1.30369	−	1.30369i
$633$	15.9602			0.634360
$634$	19.1157	+	19.1157i	0.759181	+	0.759181i
$635$	5.50904	−	5.50904i	0.218619	−	0.218619i
$636$	0.358452	−	0.358452i	0.0142136	−	0.0142136i
$637$			14.9522i			0.592427i
$638$		−	9.83444i		−	0.389349i
$639$	−10.7784	+	10.7784i	−0.426385	+	0.426385i
$640$	−19.4376	+	19.4376i	−0.768339	+	0.768339i
$641$	27.3089	+	27.3089i	1.07864	+	1.07864i	0.996632	+	0.0820060i	$0.0261327\pi$
$641$	27.3089	+	27.3089i	1.07864	+	1.07864i	0.0820060	+	0.996632i	$0.473867\pi$
$642$	22.5285			0.889130
$643$	−22.3713	−	22.3713i	−0.882238	−	0.882238i	0.111524	−	0.993762i	$-0.464427\pi$
$643$	−22.3713	−	22.3713i	−0.882238	−	0.882238i	−0.993762	+	0.111524i	$0.964427\pi$
$644$		−	0.197686i		−	0.00778993i
$645$	3.50161			0.137876
$646$		0			0
$647$	2.64576			0.104016			0.0520078	−	0.998647i	$-0.483438\pi$
$647$	2.64576			0.104016			0.0520078	+	0.998647i	$0.483438\pi$
$648$		−	2.77589i		−	0.109047i
$649$	−33.2809	−	33.2809i	−1.30639	−	1.30639i
$650$	0.599013			0.0234952
$651$	−27.4376	−	27.4376i	−1.07536	−	1.07536i
$652$	0.567532	−	0.567532i	0.0222263	−	0.0222263i
$653$	24.8454	−	24.8454i	0.972274	−	0.972274i	−0.0273518	−	0.999626i	$-0.508707\pi$
$653$	24.8454	−	24.8454i	0.972274	−	0.972274i	0.999626	+	0.0273518i	$0.00870743\pi$
$654$		−	14.5984i		−	0.570842i
$655$			3.33128i			0.130164i
$656$	1.36025	−	1.36025i	0.0531088	−	0.0531088i
$657$	−1.91050	+	1.91050i	−0.0745359	+	0.0745359i
$658$	27.2064	+	27.2064i	1.06062	+	1.06062i
$659$	−23.7941			−0.926888			−0.463444	−	0.886126i	$-0.653387\pi$
$659$	−23.7941			−0.926888			−0.463444	+	0.886126i	$0.653387\pi$
$660$	−0.526841	−	0.526841i	−0.0205073	−	0.0205073i
$661$			35.3068i			1.37328i	0.726999	+	0.686639i	$0.240914\pi$
$661$			35.3068i			1.37328i	−0.726999	+	0.686639i	$0.759086\pi$
$662$	−34.0891			−1.32491
$663$		0			0
$664$	−12.3654			−0.479872
$665$		−	50.0139i		−	1.93945i
$666$	8.94761	+	8.94761i	0.346713	+	0.346713i
$667$	−0.944550			−0.0365731
$668$	0.622321	+	0.622321i	0.0240783	+	0.0240783i
$669$	−3.78708	+	3.78708i	−0.146417	+	0.146417i
$670$	−8.75500	+	8.75500i	−0.338235	+	0.338235i
$671$		−	11.5775i		−	0.446943i
$672$		−	1.78728i		−	0.0689457i
$673$	16.4791	−	16.4791i	0.635223	−	0.635223i	−0.314150	−	0.949373i	$-0.601720\pi$
$673$	16.4791	−	16.4791i	0.635223	−	0.635223i	0.949373	+	0.314150i	$0.101720\pi$
$674$	−6.17778	+	6.17778i	−0.237959	+	0.237959i
$675$	0.250554	+	0.250554i	0.00964384	+	0.00964384i
$676$	0.826954			0.0318059
$677$	7.28515	+	7.28515i	0.279991	+	0.279991i	0.833105	−	0.553114i	$-0.186561\pi$
$677$	7.28515	+	7.28515i	0.279991	+	0.279991i	−0.553114	+	0.833105i	$0.686561\pi$
$678$		−	1.14954i		−	0.0441478i
$679$	17.0512			0.654365
$680$		0			0
$681$	1.71274			0.0656324
$682$		−	56.8839i		−	2.17820i
$683$	19.5096	+	19.5096i	0.746514	+	0.746514i	0.973823	−	0.227309i	$-0.0729926\pi$
$683$	19.5096	+	19.5096i	0.746514	+	0.746514i	−0.227309	+	0.973823i	$0.572993\pi$
$684$	−0.346301			−0.0132412
$685$	−12.8757	−	12.8757i	−0.491955	−	0.491955i
$686$	−25.8951	+	25.8951i	−0.988681	+	0.988681i
$687$	−0.269138	+	0.269138i	−0.0102683	+	0.0102683i
$688$			6.26078i			0.238690i
$689$			8.36738i			0.318772i
$690$	−1.47266	+	1.47266i	−0.0560630	+	0.0560630i
$691$	18.0483	−	18.0483i	0.686590	−	0.686590i	−0.274886	−	0.961477i	$-0.588640\pi$
$691$	18.0483	−	18.0483i	0.686590	−	0.686590i	0.961477	+	0.274886i	$0.0886403\pi$
$692$	0.160898	+	0.160898i	0.00611642	+	0.00611642i
$693$	−20.0967			−0.763411
$694$	−7.26090	−	7.26090i	−0.275620	−	0.275620i
$695$			22.7411i			0.862618i
$696$	−4.19248			−0.158916
$697$		0			0
$698$	−22.7135			−0.859718
$699$			8.96281i			0.339005i
$700$	0.0791994	+	0.0791994i	0.00299346	+	0.00299346i
$701$	14.8327			0.560225			0.280113	−	0.959967i	$-0.409628\pi$
$701$	14.8327			0.560225			0.280113	+	0.959967i	$0.409628\pi$
$702$	−1.19538	−	1.19538i	−0.0451166	−	0.0451166i
$703$	−30.2542	+	30.2542i	−1.14106	+	1.14106i
$704$	−24.6202	+	24.6202i	−0.927909	+	0.927909i
$705$		−	13.9277i		−	0.524549i
$706$		−	50.7026i		−	1.90822i
$707$	−37.4249	+	37.4249i	−1.40751	+	1.40751i
$708$	0.523468	−	0.523468i	0.0196731	−	0.0196731i
$709$	3.31985	+	3.31985i	0.124680	+	0.124680i	0.766693	−	0.642014i	$-0.221901\pi$
$709$	3.31985	+	3.31985i	0.124680	+	0.124680i	−0.642014	+	0.766693i	$0.721901\pi$
$710$	50.7607			1.90502
$711$	−11.8067	−	11.8067i	−0.442786	−	0.442786i
$712$		−	4.27571i		−	0.160239i
$713$	−5.46342			−0.204607
$714$		0			0
$715$	12.2981			0.459923
$716$			1.35310i			0.0505678i
$717$	4.74418	+	4.74418i	0.177175	+	0.177175i
$718$	−37.0317			−1.38201
$719$	0.291916	+	0.291916i	0.0108866	+	0.0108866i	0.712529	−	0.701643i	$-0.247550\pi$
$719$	0.291916	+	0.291916i	0.0108866	+	0.0108866i	−0.701643	+	0.712529i	$0.747550\pi$
$720$	−6.76942	+	6.76942i	−0.252281	+	0.252281i
$721$	4.43602	−	4.43602i	0.165206	−	0.165206i
$722$		−	6.73444i		−	0.250630i
$723$		−	8.83991i		−	0.328760i
$724$	−0.604844	+	0.604844i	−0.0224788	+	0.0224788i
$725$	0.378417	−	0.378417i	0.0140541	−	0.0140541i
$726$	−9.63839	−	9.63839i	−0.357714	−	0.357714i
$727$	32.9236			1.22107			0.610534	−	0.791990i	$-0.290955\pi$
$727$	32.9236			1.22107			0.610534	+	0.791990i	$0.290955\pi$
$728$	10.2412	+	10.2412i	0.379565	+	0.379565i
$729$		−	1.00000i		−	0.0370370i
$730$	8.99753			0.333013
$731$		0			0
$732$	0.182099			0.00673059
$733$		−	36.5965i		−	1.35172i	−0.737029	−	0.675861i	$-0.763772\pi$
$733$		−	36.5965i		−	1.35172i	0.737029	−	0.675861i	$-0.236228\pi$
$734$	−8.40664	−	8.40664i	−0.310295	−	0.310295i
$735$	29.4540			1.08643
$736$	−0.177943	−	0.177943i	−0.00655906	−	0.00655906i
$737$	−11.8951	+	11.8951i	−0.438163	+	0.438163i
$738$	0.473165	−	0.473165i	0.0174174	−	0.0174174i
$739$		−	45.0262i		−	1.65632i	−0.560494	−	0.828158i	$-0.689389\pi$
$739$		−	45.0262i		−	1.65632i	0.560494	−	0.828158i	$-0.310611\pi$
$740$		−	1.44789i		−	0.0532255i
$741$	4.04187	−	4.04187i	0.148482	−	0.148482i
$742$	−32.1975	+	32.1975i	−1.18201	+	1.18201i
$743$	−13.9598	−	13.9598i	−0.512137	−	0.512137i	0.403044	−	0.915181i	$-0.367952\pi$
$743$	−13.9598	−	13.9598i	−0.512137	−	0.512137i	−0.915181	+	0.403044i	$0.867952\pi$
$744$	−24.2500			−0.889047
$745$	−10.3089	−	10.3089i	−0.377689	−	0.377689i
$746$			33.7280i			1.23487i
$747$	−4.45459			−0.162985
$748$		0			0
$749$	−69.5308			−2.54060
$750$			15.4706i			0.564907i
$751$	16.4501	+	16.4501i	0.600272	+	0.600272i	0.940385	−	0.340112i	$-0.110465\pi$
$751$	16.4501	+	16.4501i	0.600272	+	0.600272i	−0.340112	+	0.940385i	$0.610465\pi$
$752$	24.9024			0.908097
$753$	−17.2671	−	17.2671i	−0.629247	−	0.629247i
$754$	−1.80540	+	1.80540i	−0.0657488	+	0.0657488i
$755$	17.7166	−	17.7166i	0.644774	−	0.644774i
$756$		−	0.316097i		−	0.0114963i
$757$		−	9.82437i		−	0.357073i	−0.983933	−	0.178536i	$-0.942864\pi$
$757$		−	9.82437i		−	0.357073i	0.983933	−	0.178536i	$-0.0571362\pi$
$758$	15.3277	−	15.3277i	0.556728	−	0.556728i
$759$	−2.00085	+	2.00085i	−0.0726262	+	0.0726262i
$760$	−22.1017	−	22.1017i	−0.801714	−	0.801714i
$761$	38.2412			1.38624			0.693121	−	0.720822i	$-0.256235\pi$
$761$	38.2412			1.38624			0.693121	+	0.720822i	$0.256235\pi$
$762$	3.42634	+	3.42634i	0.124123	+	0.124123i
$763$			45.0557i			1.63112i
$764$	1.58771			0.0574414
$765$		0			0
$766$	23.0236			0.831876
$767$			12.2194i			0.441215i
$768$	−1.20620	−	1.20620i	−0.0435252	−	0.0435252i
$769$	−44.2020			−1.59396			−0.796982	−	0.604002i	$-0.793572\pi$
$769$	−44.2020			−1.59396			−0.796982	+	0.604002i	$0.793572\pi$
$770$	47.3228	+	47.3228i	1.70540	+	1.70540i
$771$	−18.3372	+	18.3372i	−0.660398	+	0.660398i
$772$	−0.175920	+	0.175920i	−0.00633148	+	0.00633148i
$773$			5.09149i			0.183128i	0.995799	+	0.0915641i	$0.0291866\pi$
$773$			5.09149i			0.183128i	−0.995799	+	0.0915641i	$0.970813\pi$
$774$			2.17782i			0.0782802i
$775$	2.18882	−	2.18882i	0.0786248	−	0.0786248i
$776$	7.53512	−	7.53512i	0.270495	−	0.270495i
$777$	−27.6154	−	27.6154i	−0.990697	−	0.990697i
$778$	4.30295			0.154268
$779$	1.59989	+	1.59989i	0.0573221	+	0.0573221i
$780$			0.193434i			0.00692606i
$781$	68.9670			2.46783
$782$		0			0
$783$	−1.51032			−0.0539744
$784$			52.6630i			1.88082i
$785$	17.7120	+	17.7120i	0.632169	+	0.632169i
$786$	−2.07189			−0.0739017
$787$	6.55852	+	6.55852i	0.233786	+	0.233786i	0.814271	−	0.580485i	$-0.197137\pi$
$787$	6.55852	+	6.55852i	0.233786	+	0.233786i	−0.580485	+	0.814271i	$0.697137\pi$
$788$	0.603720	−	0.603720i	0.0215066	−	0.0215066i
$789$	1.23144	−	1.23144i	0.0438403	−	0.0438403i
$790$			55.6038i			1.97829i
$791$			3.54787i			0.126148i
$792$	−8.88098	+	8.88098i	−0.315572	+	0.315572i
$793$	−2.12538	+	2.12538i	−0.0754746	+	0.0754746i
$794$	12.8758	+	12.8758i	0.456945	+	0.456945i
$795$	16.4828			0.584584
$796$	−0.202419	−	0.202419i	−0.00717454	−	0.00717454i
$797$		−	24.7276i		−	0.875897i	−0.899000	−	0.437949i	$-0.855705\pi$
$797$		−	24.7276i		−	0.875897i	0.899000	−	0.437949i	$-0.144295\pi$
$798$	31.1061			1.10114
$799$		0			0
$800$	0.142579			0.00504094
$801$		−	1.54030i		−	0.0544240i
$802$	14.9276	+	14.9276i	0.527110	+	0.527110i
$803$	12.2246			0.431398
$804$	−0.187096	−	0.187096i	−0.00659836	−	0.00659836i
$805$	4.54512	−	4.54512i	0.160195	−	0.160195i
$806$	−10.4427	+	10.4427i	−0.367829	+	0.367829i
$807$			31.4782i			1.10809i
$808$			33.0770i			1.16364i
$809$	21.0019	−	21.0019i	0.738388	−	0.738388i	−0.233878	−	0.972266i	$-0.575142\pi$
$809$	21.0019	−	21.0019i	0.738388	−	0.738388i	0.972266	+	0.233878i	$0.0751417\pi$
$810$	−2.35475	+	2.35475i	−0.0827376	+	0.0827376i
$811$	−19.9949	−	19.9949i	−0.702115	−	0.702115i	0.262749	−	0.964864i	$-0.415371\pi$
$811$	−19.9949	−	19.9949i	−0.702115	−	0.702115i	−0.964864	+	0.262749i	$0.915371\pi$
$812$	−0.477408			−0.0167537
$813$	14.0054	+	14.0054i	0.491190	+	0.491190i
$814$		−	57.2526i		−	2.00670i
$815$	26.0970			0.914137
$816$		0			0
$817$	−7.36378			−0.257626
$818$		−	23.4898i		−	0.821301i
$819$	3.68934	+	3.68934i	0.128916	+	0.128916i
$820$	−0.0765670			−0.00267383
$821$	−30.3203	−	30.3203i	−1.05819	−	1.05819i	−0.998199	−	0.0599883i	$-0.980894\pi$
$821$	−30.3203	−	30.3203i	−1.05819	−	1.05819i	−0.0599883	−	0.998199i	$-0.519106\pi$
$822$	8.00803	−	8.00803i	0.279312	−	0.279312i
$823$	−20.6449	+	20.6449i	−0.719635	+	0.719635i	−0.968530	−	0.248895i	$-0.919932\pi$
$823$	−20.6449	+	20.6449i	−0.719635	+	0.719635i	0.248895	+	0.968530i	$0.419932\pi$
$824$		−	3.92066i		−	0.136583i
$825$		−	1.60321i		−	0.0558166i
$826$	−47.0198	+	47.0198i	−1.63603	+	1.63603i
$827$	−36.0839	+	36.0839i	−1.25476	+	1.25476i	−0.301198	+	0.953562i	$0.597387\pi$
$827$	−36.0839	+	36.0839i	−1.25476	+	1.25476i	−0.953562	+	0.301198i	$0.902613\pi$
$828$	−0.0314709	−	0.0314709i	−0.00109369	−	0.00109369i
$829$	16.2122			0.563072			0.281536	−	0.959551i	$-0.409156\pi$
$829$	16.2122			0.563072			0.281536	+	0.959551i	$0.409156\pi$
$830$	10.4894	+	10.4894i	0.364094	+	0.364094i
$831$			2.33073i			0.0808522i
$832$	9.03952			0.313389
$833$		0			0
$834$	−14.1438			−0.489759
$835$			28.6163i			0.990309i
$836$	1.10793	+	1.10793i	0.0383186	+	0.0383186i
$837$	−8.73592			−0.301958
$838$	15.9868	+	15.9868i	0.552256	+	0.552256i
$839$	25.2983	−	25.2983i	0.873394	−	0.873394i	−0.119446	−	0.992841i	$-0.538112\pi$
$839$	25.2983	−	25.2983i	0.873394	−	0.873394i	0.992841	+	0.119446i	$0.0381120\pi$
$840$	20.1740	−	20.1740i	0.696069	−	0.696069i
$841$		−	26.7189i		−	0.921343i
$842$		−	31.8104i		−	1.09626i
$843$	0.216479	−	0.216479i	0.00745593	−	0.00745593i
$844$	0.803140	−	0.803140i	0.0276452	−	0.0276452i
$845$	19.0130	+	19.0130i	0.654067	+	0.654067i
$846$	8.66233			0.297817
$847$	29.7474	+	29.7474i	1.02213	+	1.02213i
$848$			29.4707i			1.01203i
$849$	18.3142			0.628542
$850$		0			0
$851$	−5.49883			−0.188498
$852$			1.08477i			0.0371635i
$853$	−36.7210	−	36.7210i	−1.25730	−	1.25730i	−0.952376	−	0.304927i	$-0.901368\pi$
$853$	−36.7210	−	36.7210i	−1.25730	−	1.25730i	−0.304927	−	0.952376i	$-0.598632\pi$
$854$	−16.3568			−0.559720
$855$	−7.96203	−	7.96203i	−0.272296	−	0.272296i
$856$	−30.7265	+	30.7265i	−1.05021	+	1.05021i
$857$	25.8044	−	25.8044i	0.881460	−	0.881460i	−0.112223	−	0.993683i	$-0.535797\pi$
$857$	25.8044	−	25.8044i	0.881460	−	0.881460i	0.993683	+	0.112223i	$0.0357970\pi$
$858$			7.64879i			0.261125i
$859$			26.0367i			0.888361i	0.895937	+	0.444181i	$0.146505\pi$
$859$			26.0367i			0.888361i	−0.895937	+	0.444181i	$0.853495\pi$
$860$	0.176206	−	0.176206i	0.00600859	−	0.00600859i
$861$	−1.46035	+	1.46035i	−0.0497686	+	0.0497686i
$862$	−4.22856	−	4.22856i	−0.144025	−	0.144025i
$863$	−37.5428			−1.27797			−0.638986	−	0.769218i	$-0.720646\pi$
$863$	−37.5428			−1.27797			−0.638986	+	0.769218i	$0.720646\pi$
$864$	−0.284528	−	0.284528i	−0.00967983	−	0.00967983i
$865$			7.39860i			0.251560i
$866$	18.8192			0.639502
$867$		0			0
$868$	−2.76140			−0.0937280
$869$			75.5470i			2.56276i
$870$	3.55643	+	3.55643i	0.120574	+	0.120574i
$871$	4.36740			0.147984
$872$	19.9106	+	19.9106i	0.674259	+	0.674259i
$873$	2.71449	−	2.71449i	0.0918715	−	0.0918715i
$874$	3.09695	−	3.09695i	0.104756	−	0.104756i
$875$		−	47.7477i		−	1.61417i
$876$			0.192279i			0.00649650i
$877$	27.6293	−	27.6293i	0.932976	−	0.932976i	−0.0649145	−	0.997891i	$-0.520677\pi$
$877$	27.6293	−	27.6293i	0.932976	−	0.932976i	0.997891	+	0.0649145i	$0.0206775\pi$
$878$	11.7983	−	11.7983i	0.398173	−	0.398173i
$879$	10.7941	+	10.7941i	0.364076	+	0.364076i
$880$	43.3151			1.46015
$881$	31.2782	+	31.2782i	1.05379	+	1.05379i	0.998469	+	0.0553191i	$0.0176176\pi$
$881$	31.2782	+	31.2782i	1.05379	+	1.05379i	0.0553191	+	0.998469i	$0.482382\pi$
$882$			18.3189i			0.616830i
$883$	−21.8625			−0.735733			−0.367866	−	0.929879i	$-0.619912\pi$
$883$	−21.8625			−0.735733			−0.367866	+	0.929879i	$0.619912\pi$
$884$		0			0
$885$	24.0707			0.809128
$886$			25.4182i			0.853943i
$887$	−0.309008	−	0.309008i	−0.0103755	−	0.0103755i	0.701900	−	0.712275i	$-0.252335\pi$
$887$	−0.309008	−	0.309008i	−0.0103755	−	0.0103755i	−0.712275	+	0.701900i	$0.752335\pi$
$888$	−24.4071			−0.819050
$889$	−10.5749	−	10.5749i	−0.354670	−	0.354670i
$890$	−3.62703	+	3.62703i	−0.121578	+	0.121578i
$891$	−3.19932	+	3.19932i	−0.107181	+	0.107181i
$892$			0.381143i			0.0127616i
$893$			29.2896i			0.980139i
$894$	6.41161	−	6.41161i	0.214436	−	0.214436i
$895$	−31.1100	+	31.1100i	−1.03989	+	1.03989i
$896$	37.3114	+	37.3114i	1.24649	+	1.24649i
$897$	0.734629			0.0245285
$898$	35.7612	+	35.7612i	1.19337	+	1.19337i
$899$			13.1940i			0.440046i
$900$	0.0252165			0.000840551
$901$		0			0
$902$	−3.02762			−0.100809
$903$		−	6.72151i		−	0.223678i
$904$	1.56785	+	1.56785i	0.0521458	+	0.0521458i
$905$	−27.8127			−0.924524
$906$	11.0188	+	11.0188i	0.366076	+	0.366076i
$907$	−12.0258	+	12.0258i	−0.399310	+	0.399310i	−0.877990	−	0.478680i	$-0.841116\pi$
$907$	−12.0258	+	12.0258i	−0.399310	+	0.399310i	0.478680	+	0.877990i	$0.341116\pi$
$908$	0.0861877	−	0.0861877i	0.00286024	−	0.00286024i
$909$			11.9158i			0.395222i
$910$		−	17.3750i		−	0.575975i
$911$	13.5337	−	13.5337i	0.448392	−	0.448392i	−0.446428	−	0.894820i	$-0.647304\pi$
$911$	13.5337	−	13.5337i	0.448392	−	0.448392i	0.894820	+	0.446428i	$0.147304\pi$
$912$	14.2359	−	14.2359i	0.471397	−	0.471397i
$913$	14.2517	+	14.2517i	0.471661	+	0.471661i
$914$	35.4472			1.17249
$915$	4.18676	+	4.18676i	0.138410	+	0.138410i
$916$			0.0270869i			0.000894975i
$917$	6.39456			0.211167
$918$		0			0
$919$	−48.0934			−1.58645			−0.793227	−	0.608926i	$-0.791601\pi$
$919$	−48.0934			−1.58645			−0.793227	+	0.608926i	$0.791601\pi$
$920$		−	4.01709i		−	0.132439i
$921$	−21.2050	−	21.2050i	−0.698729	−	0.698729i
$922$	−1.44509			−0.0475916
$923$	−12.6609	−	12.6609i	−0.416739	−	0.416739i
$924$	−1.01130	+	1.01130i	−0.0332692	+	0.0332692i
$925$	2.20301	−	2.20301i	0.0724345	−	0.0724345i
$926$			29.4451i			0.967625i
$927$		−	1.41240i		−	0.0463892i
$928$	−0.429728	+	0.429728i	−0.0141065	+	0.0141065i
$929$	−3.69272	+	3.69272i	−0.121154	+	0.121154i	−0.765084	−	0.643930i	$-0.777303\pi$
$929$	−3.69272	+	3.69272i	−0.121154	+	0.121154i	0.643930	+	0.765084i	$0.277303\pi$
$930$	20.5709	+	20.5709i	0.674548	+	0.674548i
$931$	−61.9410			−2.03003
$932$	0.451022	+	0.451022i	0.0147737	+	0.0147737i
$933$		−	23.3246i		−	0.763612i
$934$	−50.6092			−1.65598
$935$		0			0
$936$	3.26073			0.106580
$937$			6.53593i			0.213520i	0.994285	+	0.106760i	$0.0340476\pi$
$937$			6.53593i			0.213520i	−0.994285	+	0.106760i	$0.965952\pi$
$938$	16.8056	+	16.8056i	0.548723	+	0.548723i
$939$	−23.9568			−0.781800
$940$	−0.700864	−	0.700864i	−0.0228597	−	0.0228597i
$941$	5.97644	−	5.97644i	0.194826	−	0.194826i	−0.602951	−	0.797778i	$-0.706009\pi$
$941$	5.97644	−	5.97644i	0.194826	−	0.194826i	0.797778	+	0.602951i	$0.206009\pi$
$942$	−11.0160	+	11.0160i	−0.358919	+	0.358919i
$943$			0.290788i			0.00946935i
$944$			43.0378i			1.40076i
$945$	7.26758	−	7.26758i	0.236414	−	0.236414i
$946$	6.96756	−	6.96756i	0.226535	−	0.226535i
$947$	−32.7585	−	32.7585i	−1.06451	−	1.06451i	−0.997770	−	0.0667393i	$-0.978740\pi$
$947$	−32.7585	−	32.7585i	−1.06451	−	1.06451i	−0.0667393	−	0.997770i	$-0.521260\pi$
$948$	−1.18826			−0.0385930
$949$	−2.24419	−	2.24419i	−0.0728496	−	0.0728496i
$950$			2.48147i			0.0805097i
$951$	−18.7844			−0.609126
$952$		0			0
$953$	34.8809			1.12990			0.564951	−	0.825124i	$-0.308895\pi$
$953$	34.8809			1.12990			0.564951	+	0.825124i	$0.308895\pi$
$954$			10.2514i			0.331903i
$955$	36.5040	+	36.5040i	1.18124	+	1.18124i
$956$	0.477468			0.0154424
$957$	4.83200	+	4.83200i	0.156196	+	0.156196i
$958$	−3.92523	+	3.92523i	−0.126818	+	0.126818i
$959$	−24.7155	+	24.7155i	−0.798106	+	0.798106i
$960$		−	17.8068i		−	0.574713i
$961$			45.3164i			1.46182i
$962$	−10.5104	+	10.5104i	−0.338869	+	0.338869i
$963$	−11.0690	+	11.0690i	−0.356695	+	0.356695i
$964$	−0.444837	−	0.444837i	−0.0143272	−	0.0143272i
$965$	−8.08934			−0.260405
$966$	2.82683	+	2.82683i	0.0909519	+	0.0909519i
$967$		−	45.1412i		−	1.45164i	−0.687884	−	0.725821i	$-0.741460\pi$
$967$		−	45.1412i		−	1.45164i	0.687884	−	0.725821i	$-0.258540\pi$
$968$	26.2915			0.845039
$969$		0			0
$970$	−12.7839			−0.410466
$971$		−	42.2005i		−	1.35428i	−0.735855	−	0.677139i	$-0.763220\pi$
$971$		−	42.2005i		−	1.35428i	0.735855	−	0.677139i	$-0.236780\pi$
$972$	−0.0503215	−	0.0503215i	−0.00161406	−	0.00161406i
$973$	43.6526			1.39944
$974$	−20.7281	−	20.7281i	−0.664172	−	0.664172i
$975$	−0.294316	+	0.294316i	−0.00942565	+	0.00942565i
$976$	−7.48581	+	7.48581i	−0.239615	+	0.239615i
$977$		−	38.0075i		−	1.21597i	−0.793950	−	0.607983i	$-0.791979\pi$
$977$		−	38.0075i		−	1.21597i	0.793950	−	0.607983i	$-0.208021\pi$
$978$			16.2310i			0.519009i
$979$	−4.92793	+	4.92793i	−0.157497	+	0.157497i
$980$	1.48217	−	1.48217i	0.0473462	−	0.0473462i
$981$	7.17270	+	7.17270i	0.229007	+	0.229007i
$982$	−9.19154			−0.293314
$983$	30.6728	+	30.6728i	0.978310	+	0.978310i	0.999770	−	0.0214593i	$-0.00683124\pi$
$983$	30.6728	+	30.6728i	0.978310	+	0.978310i	−0.0214593	+	0.999770i	$0.506831\pi$
$984$			1.29069i			0.0411457i
$985$	27.7610			0.884539
$986$		0			0
$987$	−26.7349			−0.850983
$988$		−	0.406786i		−	0.0129416i
$989$	−0.669200	−	0.669200i	−0.0212793	−	0.0212793i
$990$	15.0672			0.478868
$991$	28.4673	+	28.4673i	0.904292	+	0.904292i	0.995804	−	0.0915120i	$-0.0291700\pi$
$991$	28.4673	+	28.4673i	0.904292	+	0.904292i	−0.0915120	+	0.995804i	$0.529170\pi$
$992$	−2.48561	+	2.48561i	−0.0789183	+	0.0789183i
$993$	16.7492	−	16.7492i	0.531519	−	0.531519i
$994$		−	97.4377i		−	3.09054i
$995$		−	9.30787i		−	0.295079i
$996$	−0.224161	+	0.224161i	−0.00710283	+	0.00710283i
$997$	22.5059	−	22.5059i	0.712770	−	0.712770i	−0.254343	−	0.967114i	$-0.581859\pi$
$997$	22.5059	−	22.5059i	0.712770	−	0.712770i	0.967114	+	0.254343i	$0.0818594\pi$
$998$	−1.67284	−	1.67284i	−0.0529528	−	0.0529528i
$999$	−8.79254			−0.278184

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.e.k.829.9		24
17.2	even	8		867.2.a.o.1.2	✓	6
17.3	odd	16		867.2.h.m.712.9		48
17.4	even	4	inner	867.2.e.k.616.3		24
17.5	odd	16		867.2.h.m.733.4		48
17.6	odd	16		867.2.h.m.757.3		48
17.7	odd	16		867.2.h.m.688.9		48
17.8	even	8		867.2.d.g.577.10		12
17.9	even	8		867.2.d.g.577.9		12
17.10	odd	16		867.2.h.m.688.10		48
17.11	odd	16		867.2.h.m.757.4		48
17.12	odd	16		867.2.h.m.733.3		48
17.13	even	4	inner	867.2.e.k.616.4		24
17.14	odd	16		867.2.h.m.712.10		48
17.15	even	8		867.2.a.p.1.2	yes	6
17.16	even	2	inner	867.2.e.k.829.10		24
51.2	odd	8		2601.2.a.bh.1.5		6
51.32	odd	8		2601.2.a.bi.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.o.1.2	✓	6	17.2	even	8
867.2.a.p.1.2	yes	6	17.15	even	8
867.2.d.g.577.9		12	17.9	even	8
867.2.d.g.577.10		12	17.8	even	8
867.2.e.k.616.3		24	17.4	even	4	inner
867.2.e.k.616.4		24	17.13	even	4	inner
867.2.e.k.829.9		24	1.1	even	1	trivial
867.2.e.k.829.10		24	17.16	even	2	inner
867.2.h.m.688.9		48	17.7	odd	16
867.2.h.m.688.10		48	17.10	odd	16
867.2.h.m.712.9		48	17.3	odd	16
867.2.h.m.712.10		48	17.14	odd	16
867.2.h.m.733.3		48	17.12	odd	16
867.2.h.m.733.4		48	17.5	odd	16
867.2.h.m.757.3		48	17.6	odd	16
867.2.h.m.757.4		48	17.11	odd	16
2601.2.a.bh.1.5		6	51.2	odd	8
2601.2.a.bi.1.5		6	51.32	odd	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.43915i q^{2} +(-0.707107 - 0.707107i) q^{3} -0.0711653 q^{4} +(-1.63621 - 1.63621i) q^{5} +(1.01764 - 1.01764i) q^{6} +(-3.14078 + 3.14078i) q^{7} +2.77589i q^{8} +1.00000i q^{9} +(2.35475 - 2.35475i) q^{10} +(3.19932 - 3.19932i) q^{11} +(0.0503215 + 0.0503215i) q^{12} -1.17466 q^{13} +(-4.52006 - 4.52006i) q^{14} +2.31394i q^{15} -4.13727 q^{16} -1.43915 q^{18} -4.86615i q^{19} +(0.116441 + 0.116441i) q^{20} +4.44173 q^{21} +(4.60432 + 4.60432i) q^{22} +(0.442223 - 0.442223i) q^{23} +(1.96285 - 1.96285i) q^{24} +0.354337i q^{25} -1.69052i q^{26} +(0.707107 - 0.707107i) q^{27} +(0.223514 - 0.223514i) q^{28} +(-1.06796 - 1.06796i) q^{29} -3.33012 q^{30} +(-6.17723 - 6.17723i) q^{31} -0.402383i q^{32} -4.52453 q^{33} +10.2779 q^{35} -0.0711653i q^{36} +(-6.21727 - 6.21727i) q^{37} +7.00315 q^{38} +(0.830610 + 0.830610i) q^{39} +(4.54193 - 4.54193i) q^{40} +(-0.328780 + 0.328780i) q^{41} +6.39233i q^{42} -1.51327i q^{43} +(-0.227681 + 0.227681i) q^{44} +(1.63621 - 1.63621i) q^{45} +(0.636427 + 0.636427i) q^{46} -6.01904 q^{47} +(2.92549 + 2.92549i) q^{48} -12.7289i q^{49} -0.509946 q^{50} +0.0835951 q^{52} -7.12324i q^{53} +(1.01764 + 1.01764i) q^{54} -10.4695 q^{55} +(-8.71845 - 8.71845i) q^{56} +(-3.44089 + 3.44089i) q^{57} +(1.53696 - 1.53696i) q^{58} -10.4025i q^{59} -0.164673i q^{60} +(1.80936 - 1.80936i) q^{61} +(8.88999 - 8.88999i) q^{62} +(-3.14078 - 3.14078i) q^{63} -7.69544 q^{64} +(1.92198 + 1.92198i) q^{65} -6.51150i q^{66} -3.71801 q^{67} -0.625397 q^{69} +14.7915i q^{70} +(10.7784 + 10.7784i) q^{71} -2.77589 q^{72} +(1.91050 + 1.91050i) q^{73} +(8.94761 - 8.94761i) q^{74} +(0.250554 - 0.250554i) q^{75} +0.346301i q^{76} +20.0967i q^{77} +(-1.19538 + 1.19538i) q^{78} +(-11.8067 + 11.8067i) q^{79} +(6.76942 + 6.76942i) q^{80} -1.00000 q^{81} +(-0.473165 - 0.473165i) q^{82} +4.45459i q^{83} -0.316097 q^{84} +2.17782 q^{86} +1.51032i q^{87} +(8.88098 + 8.88098i) q^{88} -1.54030 q^{89} +(2.35475 + 2.35475i) q^{90} +(3.68934 - 3.68934i) q^{91} +(-0.0314709 + 0.0314709i) q^{92} +8.73592i q^{93} -8.66233i q^{94} +(-7.96203 + 7.96203i) q^{95} +(-0.284528 + 0.284528i) q^{96} +(-2.71449 - 2.71449i) q^{97} +18.3189 q^{98} +(3.19932 + 3.19932i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 36 q^{4} - 36 q^{13} + 60 q^{16} + 12 q^{18} - 12 q^{21} - 48 q^{30} - 36 q^{33} + 24 q^{38} - 96 q^{47} + 48 q^{50} - 72 q^{52} + 96 q^{55} - 96 q^{64} - 24 q^{67} - 36 q^{69} - 48 q^{72} - 24 q^{81}+ \cdots + 228 q^{98}+O(q^{100}) \) 24 * q - 36 * q^4 - 36 * q^13 + 60 * q^16 + 12 * q^18 - 12 * q^21 - 48 * q^30 - 36 * q^33 + 24 * q^38 - 96 * q^47 + 48 * q^50 - 72 * q^52 + 96 * q^55 - 96 * q^64 - 24 * q^67 - 36 * q^69 - 48 * q^72 - 24 * q^81 - 60 * q^84 + 24 * q^86 + 228 * q^98

Introduction

L-functions

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