LMFDB - Embedded newform 230.3.f.b.47.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,3,Mod(47,230)] 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("230.47"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.26704608029$
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			47.2
Character	$\chi$	$=$	230.47
Dual form			230.3.f.b.93.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} +(-3.54993 + 3.54993i) q^{3} +2.00000i q^{4} +(3.53474 + 3.53633i) q^{5} -7.09985 q^{6} +(9.46554 + 9.46554i) q^{7} +(-2.00000 + 2.00000i) q^{8} -16.2040i q^{9} +(-0.00158807 + 7.07107i) q^{10} +7.06989 q^{11} +(-7.09985 - 7.09985i) q^{12} +(-6.95822 + 6.95822i) q^{13} +18.9311i q^{14} +(-25.1018 - 0.00563754i) q^{15} -4.00000 q^{16} +(-5.69985 - 5.69985i) q^{17} +(16.2040 - 16.2040i) q^{18} -34.4850i q^{19} +(-7.07266 + 7.06948i) q^{20} -67.2040 q^{21} +(7.06989 + 7.06989i) q^{22} +(3.39116 - 3.39116i) q^{23} -14.1997i q^{24} +(-0.0112294 + 25.0000i) q^{25} -13.9164 q^{26} +(25.5736 + 25.5736i) q^{27} +(-18.9311 + 18.9311i) q^{28} -17.8745i q^{29} +(-25.0961 - 25.1074i) q^{30} +44.2437 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-25.0976 + 25.0976i) q^{33} -11.3997i q^{34} +(-0.0150320 + 66.9315i) q^{35} +32.4079 q^{36} +(-0.847681 - 0.847681i) q^{37} +(34.4850 - 34.4850i) q^{38} -49.4023i q^{39} +(-14.1421 - 0.00317614i) q^{40} -38.8737 q^{41} +(-67.2040 - 67.2040i) q^{42} +(20.7171 - 20.7171i) q^{43} +14.1398i q^{44} +(57.3025 - 57.2768i) q^{45} +6.78233 q^{46} +(16.1802 + 16.1802i) q^{47} +(14.1997 - 14.1997i) q^{48} +130.193i q^{49} +(-25.0112 + 24.9888i) q^{50} +40.4681 q^{51} +(-13.9164 - 13.9164i) q^{52} +(67.0136 - 67.0136i) q^{53} +51.1471i q^{54} +(24.9902 + 25.0014i) q^{55} -37.8622 q^{56} +(122.419 + 122.419i) q^{57} +(17.8745 - 17.8745i) q^{58} +39.2085i q^{59} +(0.0112751 - 50.2036i) q^{60} -10.2316 q^{61} +(44.2437 + 44.2437i) q^{62} +(153.379 - 153.379i) q^{63} -8.00000i q^{64} +(-49.2020 - 0.0110501i) q^{65} -50.1952 q^{66} +(-32.8500 - 32.8500i) q^{67} +(11.3997 - 11.3997i) q^{68} +24.0768i q^{69} +(-66.9465 + 66.9165i) q^{70} -50.4379 q^{71} +(32.4079 + 32.4079i) q^{72} +(-66.5292 + 66.5292i) q^{73} -1.69536i q^{74} +(-88.7083 - 88.7880i) q^{75} +68.9700 q^{76} +(66.9203 + 66.9203i) q^{77} +(49.4023 - 49.4023i) q^{78} -10.1138i q^{79} +(-14.1390 - 14.1453i) q^{80} -35.7329 q^{81} +(-38.8737 - 38.8737i) q^{82} +(69.4699 - 69.4699i) q^{83} -134.408i q^{84} +(0.00905177 - 40.3040i) q^{85} +41.4342 q^{86} +(63.4532 + 63.4532i) q^{87} +(-14.1398 + 14.1398i) q^{88} +54.6197i q^{89} +(114.579 + 0.0257331i) q^{90} -131.727 q^{91} +(6.78233 + 6.78233i) q^{92} +(-157.062 + 157.062i) q^{93} +32.3604i q^{94} +(121.950 - 121.896i) q^{95} +28.3994 q^{96} +(-29.8681 - 29.8681i) q^{97} +(-130.193 + 130.193i) q^{98} -114.560i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28}+ \cdots - 484 q^{98}+O(q^{100}) $ 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8 + 16 * q^10 - 8 * q^11 - 24 * q^13 - 24 * q^15 - 96 * q^16 - 12 * q^17 + 88 * q^18 + 24 * q^20 - 24 * q^21 - 8 * q^22 - 48 * q^25 - 48 * q^26 + 60 * q^27 - 16 * q^28 + 12 * q^30 + 12 * q^31 - 96 * q^32 + 92 * q^33 + 48 * q^35 + 176 * q^36 - 100 * q^37 + 56 * q^38 + 16 * q^40 + 116 * q^41 - 24 * q^42 - 120 * q^43 - 204 * q^45 + 56 * q^47 - 104 * q^50 + 176 * q^51 - 48 * q^52 - 192 * q^53 + 180 * q^55 - 32 * q^56 + 28 * q^58 + 72 * q^60 - 152 * q^61 + 12 * q^62 + 364 * q^63 + 40 * q^65 + 184 * q^66 + 72 * q^67 + 24 * q^68 - 100 * q^70 - 28 * q^71 + 176 * q^72 - 364 * q^73 + 276 * q^75 + 112 * q^76 - 92 * q^77 - 32 * q^78 - 16 * q^80 - 440 * q^81 + 116 * q^82 + 360 * q^83 + 232 * q^85 - 240 * q^86 + 176 * q^87 + 16 * q^88 - 84 * q^90 - 432 * q^91 + 192 * q^93 + 144 * q^95 - 432 * q^97 - 484 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	−3.54993	+	3.54993i	−1.18331	+	1.18331i	−0.204427	+	0.978882i	$0.565533\pi$
$3$	−3.54993	+	3.54993i	−1.18331	+	1.18331i	−0.978882	+	0.204427i	$0.934467\pi$
$4$			2.00000i			0.500000i
$5$	3.53474	+	3.53633i	0.706948	+	0.707266i
$5$	3.53474	+	3.53633i	0.706948	+	0.707266i
$6$	−7.09985			−1.18331
$7$	9.46554	+	9.46554i	1.35222	+	1.35222i	0.883173	+	0.469047i	$0.155403\pi$
$7$	9.46554	+	9.46554i	1.35222	+	1.35222i	0.469047	+	0.883173i	$0.344597\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	16.2040i		−	1.80044i
$10$	−0.00158807	+	7.07107i	−0.000158807	+	0.707107i
$11$	7.06989			0.642717			0.321359	−	0.946958i	$-0.395861\pi$
$11$	7.06989			0.642717			0.321359	+	0.946958i	$0.395861\pi$
$12$	−7.09985	−	7.09985i	−0.591655	−	0.591655i
$13$	−6.95822	+	6.95822i	−0.535247	+	0.535247i	−0.922129	−	0.386882i	$-0.873552\pi$
$13$	−6.95822	+	6.95822i	−0.535247	+	0.535247i	0.386882	+	0.922129i	$0.373552\pi$
$14$			18.9311i			1.35222i
$15$	−25.1018	−	0.00563754i	−1.67345	−	0.000375836i
$16$	−4.00000			−0.250000
$17$	−5.69985	−	5.69985i	−0.335285	−	0.335285i	0.519304	−	0.854590i	$-0.326191\pi$
$17$	−5.69985	−	5.69985i	−0.335285	−	0.335285i	−0.854590	+	0.519304i	$0.826191\pi$
$18$	16.2040	−	16.2040i	0.900221	−	0.900221i
$19$		−	34.4850i		−	1.81500i	−0.420052	−	0.907500i	$-0.637988\pi$
$19$		−	34.4850i		−	1.81500i	0.420052	−	0.907500i	$-0.362012\pi$
$20$	−7.07266	+	7.06948i	−0.353633	+	0.353474i
$21$	−67.2040			−3.20019
$22$	7.06989	+	7.06989i	0.321359	+	0.321359i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$24$		−	14.1997i		−	0.591655i
$25$	−0.0112294	+	25.0000i	−0.000449175	+	1.00000i
$26$	−13.9164			−0.535247
$27$	25.5736	+	25.5736i	0.947169	+	0.947169i
$28$	−18.9311	+	18.9311i	−0.676110	+	0.676110i
$29$		−	17.8745i		−	0.616362i	−0.951328	−	0.308181i	$-0.900280\pi$
$29$		−	17.8745i		−	0.616362i	0.951328	−	0.308181i	$-0.0997203\pi$
$30$	−25.0961	−	25.1074i	−0.836538	−	0.836914i
$31$	44.2437			1.42722			0.713608	−	0.700545i	$-0.247060\pi$
$31$	44.2437			1.42722			0.713608	+	0.700545i	$0.247060\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−25.0976	+	25.0976i	−0.760533	+	0.760533i
$34$		−	11.3997i		−	0.335285i
$35$	−0.0150320	+	66.9315i	−0.000429485	+	1.91233i
$36$	32.4079			0.900221
$37$	−0.847681	−	0.847681i	−0.0229103	−	0.0229103i	0.695559	−	0.718469i	$-0.255157\pi$
$37$	−0.847681	−	0.847681i	−0.0229103	−	0.0229103i	−0.718469	+	0.695559i	$0.755157\pi$
$38$	34.4850	−	34.4850i	0.907500	−	0.907500i
$39$		−	49.4023i		−	1.26673i
$40$	−14.1421	−	0.00317614i	−0.353553	−	7.94036e-5i
$41$	−38.8737			−0.948139			−0.474069	−	0.880488i	$-0.657215\pi$
$41$	−38.8737			−0.948139			−0.474069	+	0.880488i	$0.657215\pi$
$42$	−67.2040	−	67.2040i	−1.60009	−	1.60009i
$43$	20.7171	−	20.7171i	0.481793	−	0.481793i	−0.423911	−	0.905704i	$-0.639343\pi$
$43$	20.7171	−	20.7171i	0.481793	−	0.481793i	0.905704	+	0.423911i	$0.139343\pi$
$44$			14.1398i			0.321359i
$45$	57.3025	−	57.2768i	1.27339	−	1.27282i
$46$	6.78233			0.147442
$47$	16.1802	+	16.1802i	0.344260	+	0.344260i	0.857966	−	0.513706i	$-0.171728\pi$
$47$	16.1802	+	16.1802i	0.344260	+	0.344260i	−0.513706	+	0.857966i	$0.671728\pi$
$48$	14.1997	−	14.1997i	0.295827	−	0.295827i
$49$			130.193i			2.65700i
$50$	−25.0112	+	24.9888i	−0.500225	+	0.499775i
$51$	40.4681			0.793493
$52$	−13.9164	−	13.9164i	−0.267624	−	0.267624i
$53$	67.0136	−	67.0136i	1.26441	−	1.26441i	0.315474	−	0.948934i	$-0.397836\pi$
$53$	67.0136	−	67.0136i	1.26441	−	1.26441i	0.948934	−	0.315474i	$-0.102164\pi$
$54$			51.1471i			0.947169i
$55$	24.9902	+	25.0014i	0.454368	+	0.454572i
$56$	−37.8622			−0.676110
$57$	122.419	+	122.419i	2.14771	+	2.14771i
$58$	17.8745	−	17.8745i	0.308181	−	0.308181i
$59$			39.2085i			0.664552i	0.943182	+	0.332276i	$0.107816\pi$
$59$			39.2085i			0.664552i	−0.943182	+	0.332276i	$0.892184\pi$
$60$	0.0112751	−	50.2036i	0.000187918	−	0.836726i
$61$	−10.2316			−0.167730			−0.0838652	−	0.996477i	$-0.526727\pi$
$61$	−10.2316			−0.167730			−0.0838652	+	0.996477i	$0.526727\pi$
$62$	44.2437	+	44.2437i	0.713608	+	0.713608i
$63$	153.379	−	153.379i	2.43459	−	2.43459i
$64$		−	8.00000i		−	0.125000i
$65$	−49.2020	−	0.0110501i	−0.756954	−	0.000170002i
$66$	−50.1952			−0.760533
$67$	−32.8500	−	32.8500i	−0.490299	−	0.490299i	0.418101	−	0.908400i	$-0.362696\pi$
$67$	−32.8500	−	32.8500i	−0.490299	−	0.490299i	−0.908400	+	0.418101i	$0.862696\pi$
$68$	11.3997	−	11.3997i	0.167643	−	0.167643i
$69$			24.0768i			0.348939i
$70$	−66.9465	+	66.9165i	−0.956379	+	0.955949i
$71$	−50.4379			−0.710394			−0.355197	−	0.934792i	$-0.615586\pi$
$71$	−50.4379			−0.710394			−0.355197	+	0.934792i	$0.615586\pi$
$72$	32.4079	+	32.4079i	0.450110	+	0.450110i
$73$	−66.5292	+	66.5292i	−0.911359	+	0.911359i	−0.996379	−	0.0850203i	$-0.972904\pi$
$73$	−66.5292	+	66.5292i	−0.911359	+	0.911359i	0.0850203	+	0.996379i	$0.472904\pi$
$74$		−	1.69536i		−	0.0229103i
$75$	−88.7083	−	88.7880i	−1.18278	−	1.18384i
$76$	68.9700			0.907500
$77$	66.9203	+	66.9203i	0.869095	+	0.869095i
$78$	49.4023	−	49.4023i	0.633363	−	0.633363i
$79$		−	10.1138i		−	0.128023i	−0.997949	−	0.0640114i	$-0.979611\pi$
$79$		−	10.1138i		−	0.128023i	0.997949	−	0.0640114i	$-0.0203894\pi$
$80$	−14.1390	−	14.1453i	−0.176737	−	0.176816i
$81$	−35.7329			−0.441147
$82$	−38.8737	−	38.8737i	−0.474069	−	0.474069i
$83$	69.4699	−	69.4699i	0.836987	−	0.836987i	−0.151474	−	0.988461i	$-0.548402\pi$
$83$	69.4699	−	69.4699i	0.836987	−	0.836987i	0.988461	+	0.151474i	$0.0484021\pi$
$84$		−	134.408i		−	1.60009i
$85$	0.00905177	−	40.3040i	0.000106491	−	0.474165i
$86$	41.4342			0.481793
$87$	63.4532	+	63.4532i	0.729347	+	0.729347i
$88$	−14.1398	+	14.1398i	−0.160679	+	0.160679i
$89$			54.6197i			0.613705i	0.951757	+	0.306852i	$0.0992758\pi$
$89$			54.6197i			0.613705i	−0.951757	+	0.306852i	$0.900724\pi$
$90$	114.579	+	0.0257331i	1.27310	+	0.000285923i
$91$	−131.727			−1.44754
$92$	6.78233	+	6.78233i	0.0737210	+	0.0737210i
$93$	−157.062	+	157.062i	−1.68884	+	1.68884i
$94$			32.3604i			0.344260i
$95$	121.950	−	121.896i	1.28369	−	1.28311i
$96$	28.3994			0.295827
$97$	−29.8681	−	29.8681i	−0.307919	−	0.307919i	0.536183	−	0.844102i	$-0.319866\pi$
$97$	−29.8681	−	29.8681i	−0.307919	−	0.307919i	−0.844102	+	0.536183i	$0.819866\pi$
$98$	−130.193	+	130.193i	−1.32850	+	1.32850i
$99$		−	114.560i		−	1.15717i
$100$	−50.0000	−	0.0224587i	−0.500000	−	0.000224587i
$101$	35.8530			0.354980			0.177490	−	0.984123i	$-0.443202\pi$
$101$	35.8530			0.354980			0.177490	+	0.984123i	$0.443202\pi$
$102$	40.4681	+	40.4681i	0.396746	+	0.396746i
$103$	−118.711	+	118.711i	−1.15253	+	1.15253i	−0.166489	+	0.986043i	$0.553243\pi$
$103$	−118.711	+	118.711i	−1.15253	+	1.15253i	−0.986043	+	0.166489i	$0.946757\pi$
$104$		−	27.8329i		−	0.267624i
$105$	−237.549	−	237.655i	−2.26237	−	2.26338i
$106$	134.027			1.26441
$107$	22.0133	+	22.0133i	0.205732	+	0.205732i	0.802451	−	0.596719i	$-0.203529\pi$
$107$	22.0133	+	22.0133i	0.205732	+	0.205732i	−0.596719	+	0.802451i	$0.703529\pi$
$108$	−51.1471	+	51.1471i	−0.473585	+	0.473585i
$109$		−	84.6803i		−	0.776884i	−0.921473	−	0.388442i	$-0.873013\pi$
$109$		−	84.6803i		−	0.776884i	0.921473	−	0.388442i	$-0.126987\pi$
$110$	−0.0112275	+	49.9917i	−0.000102068	+	0.454470i
$111$	6.01842			0.0542200
$112$	−37.8622	−	37.8622i	−0.338055	−	0.338055i
$113$	28.4423	−	28.4423i	0.251702	−	0.251702i	−0.569966	−	0.821668i	$-0.693044\pi$
$113$	28.4423	−	28.4423i	0.251702	−	0.251702i	0.821668	+	0.569966i	$0.193044\pi$
$114$			244.839i			2.14771i
$115$	23.9792	+	0.00538541i	0.208514	+	4.68297e-5i
$116$	35.7490			0.308181
$117$	112.751	+	112.751i	0.963682	+	0.963682i
$118$	−39.2085	+	39.2085i	−0.332276	+	0.332276i
$119$		−	107.904i		−	0.906759i
$120$	50.2148	−	50.1923i	0.418457	−	0.418269i
$121$	−71.0167			−0.586915
$122$	−10.2316	−	10.2316i	−0.0838652	−	0.0838652i
$123$	137.999	−	137.999i	1.12194	−	1.12194i
$124$			88.4874i			0.713608i
$125$	−88.4479	+	88.3288i	−0.707583	+	0.706630i
$126$	306.759			2.43459
$127$	136.506	+	136.506i	1.07485	+	1.07485i	0.996962	+	0.0778848i	$0.0248166\pi$
$127$	136.506	+	136.506i	1.07485	+	1.07485i	0.0778848	+	0.996962i	$0.475183\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$			147.088i			1.14022i
$130$	−49.1910	−	49.2131i	−0.378392	−	0.378562i
$131$	75.5156			0.576455			0.288228	−	0.957562i	$-0.406934\pi$
$131$	75.5156			0.576455			0.288228	+	0.957562i	$0.406934\pi$
$132$	−50.1952	−	50.1952i	−0.380266	−	0.380266i
$133$	326.419	−	326.419i	2.45428	−	2.45428i
$134$		−	65.7001i		−	0.490299i
$135$	−0.0406127	+	180.832i	−0.000300835	+	1.33950i
$136$	22.7994			0.167643
$137$	−130.794	−	130.794i	−0.954701	−	0.954701i	0.0443162	−	0.999018i	$-0.485889\pi$
$137$	−130.794	−	130.794i	−0.954701	−	0.954701i	−0.999018	+	0.0443162i	$0.985889\pi$
$138$	−24.0768	+	24.0768i	−0.174469	+	0.174469i
$139$			48.2637i			0.347221i	0.984814	+	0.173611i	$0.0555434\pi$
$139$			48.2637i			0.347221i	−0.984814	+	0.173611i	$0.944457\pi$
$140$	−133.863	−	0.0300639i	−0.956164	−	0.000214742i
$141$	−114.877			−0.814732
$142$	−50.4379	−	50.4379i	−0.355197	−	0.355197i
$143$	−49.1938	+	49.1938i	−0.344013	+	0.344013i
$144$			64.8159i			0.450110i
$145$	63.2101	−	63.1817i	0.435932	−	0.435736i
$146$	−133.058			−0.911359
$147$	−462.176	−	462.176i	−3.14405	−	3.14405i
$148$	1.69536	−	1.69536i	0.0114552	−	0.0114552i
$149$		−	265.549i		−	1.78221i	−0.453799	−	0.891104i	$-0.649932\pi$
$149$		−	265.549i		−	1.78221i	0.453799	−	0.891104i	$-0.350068\pi$
$150$	0.0797269	−	177.496i	0.000531512	−	1.18331i
$151$	195.152			1.29240			0.646198	−	0.763170i	$-0.276358\pi$
$151$	195.152			1.29240			0.646198	+	0.763170i	$0.276358\pi$
$152$	68.9700	+	68.9700i	0.453750	+	0.453750i
$153$	−92.3602	+	92.3602i	−0.603662	+	0.603662i
$154$			133.841i			0.869095i
$155$	156.390	+	156.460i	1.00897	+	1.00942i
$156$	98.8047			0.633363
$157$	194.421	+	194.421i	1.23835	+	1.23835i	0.960676	+	0.277672i	$0.0895629\pi$
$157$	194.421	+	194.421i	1.23835	+	1.23835i	0.277672	+	0.960676i	$0.410437\pi$
$158$	10.1138	−	10.1138i	0.0640114	−	0.0640114i
$159$			475.787i			2.99237i
$160$	0.00635229	−	28.2843i	3.97018e−5	−	0.176777i
$161$	64.1984			0.398748
$162$	−35.7329	−	35.7329i	−0.220573	−	0.220573i
$163$	−105.269	+	105.269i	−0.645821	+	0.645821i	−0.951980	−	0.306159i	$-0.900956\pi$
$163$	−105.269	+	105.269i	−0.645821	+	0.645821i	0.306159	+	0.951980i	$0.400956\pi$
$164$		−	77.7474i		−	0.474069i
$165$	−177.467	−	0.0398568i	−1.07556	−	0.000241556i
$166$	138.940			0.836987
$167$	−95.5218	−	95.5218i	−0.571987	−	0.571987i	0.360696	−	0.932683i	$-0.382539\pi$
$167$	−95.5218	−	95.5218i	−0.571987	−	0.571987i	−0.932683	+	0.360696i	$0.882539\pi$
$168$	134.408	−	134.408i	0.800047	−	0.800047i
$169$			72.1664i			0.427020i
$170$	40.3131	−	40.2950i	0.237136	−	0.237029i
$171$	−558.794			−3.26780
$172$	41.4342	+	41.4342i	0.240896	+	0.240896i
$173$	−98.5609	+	98.5609i	−0.569716	+	0.569716i	−0.932049	−	0.362333i	$-0.881980\pi$
$173$	−98.5609	+	98.5609i	−0.569716	+	0.569716i	0.362333	+	0.932049i	$0.381980\pi$
$174$			126.906i			0.729347i
$175$	−236.745	+	236.532i	−1.35283	+	1.35161i
$176$	−28.2796			−0.160679
$177$	−139.188	−	139.188i	−0.786370	−	0.786370i
$178$	−54.6197	+	54.6197i	−0.306852	+	0.306852i
$179$		−	25.4849i		−	0.142374i	−0.997463	−	0.0711869i	$-0.977321\pi$
$179$		−	25.4849i		−	0.142374i	0.997463	−	0.0711869i	$-0.0226787\pi$
$180$	114.554	+	114.605i	0.636409	+	0.636695i
$181$	−326.572			−1.80427			−0.902133	−	0.431457i	$-0.858000\pi$
$181$	−326.572			−1.80427			−0.902133	+	0.431457i	$0.858000\pi$
$182$	−131.727	−	131.727i	−0.723772	−	0.723772i
$183$	36.3213	−	36.3213i	0.198477	−	0.198477i
$184$			13.5647i			0.0737210i
$185$	0.00134618	−	5.99401i	7.27664e−6	−	0.0324001i
$186$	−314.124			−1.68884
$187$	−40.2973	−	40.2973i	−0.215494	−	0.215494i
$188$	−32.3604	+	32.3604i	−0.172130	+	0.172130i
$189$			484.135i			2.56156i
$190$	243.846	+	0.0547647i	1.28340	+	0.000288235i
$191$	188.733			0.988129			0.494065	−	0.869425i	$-0.335511\pi$
$191$	188.733			0.988129			0.494065	+	0.869425i	$0.335511\pi$
$192$	28.3994	+	28.3994i	0.147914	+	0.147914i
$193$	−146.791	+	146.791i	−0.760575	+	0.760575i	−0.976426	−	0.215851i	$-0.930748\pi$
$193$	−146.791	+	146.791i	−0.760575	+	0.760575i	0.215851	+	0.976426i	$0.430748\pi$
$194$		−	59.7362i		−	0.307919i
$195$	174.703	−	174.624i	0.895912	−	0.895510i
$196$	−260.386			−1.32850
$197$	−117.074	−	117.074i	−0.594286	−	0.594286i	0.344500	−	0.938786i	$-0.388048\pi$
$197$	−117.074	−	117.074i	−0.594286	−	0.594286i	−0.938786	+	0.344500i	$0.888048\pi$
$198$	114.560	−	114.560i	0.578587	−	0.578587i
$199$			71.0996i			0.357285i	0.983914	+	0.178642i	$0.0571705\pi$
$199$			71.0996i			0.357285i	−0.983914	+	0.178642i	$0.942830\pi$
$200$	−49.9775	−	50.0225i	−0.249888	−	0.250112i
$201$	233.230			1.16035
$202$	35.8530	+	35.8530i	0.177490	+	0.177490i
$203$	169.192	−	169.192i	0.833458	−	0.833458i
$204$			80.9362i			0.396746i
$205$	−137.408	−	137.470i	−0.670285	−	0.670586i
$206$	−237.422			−1.15253
$207$	−54.9503	−	54.9503i	−0.265461	−	0.265461i
$208$	27.8329	−	27.8329i	0.133812	−	0.133812i
$209$		−	243.805i		−	1.16653i
$210$	0.106725	−	475.204i	0.000508213	−	2.26288i
$211$	62.6847			0.297084			0.148542	−	0.988906i	$-0.452542\pi$
$211$	62.6847			0.297084			0.148542	+	0.988906i	$0.452542\pi$
$212$	134.027	+	134.027i	0.632204	+	0.632204i
$213$	179.051	−	179.051i	0.840615	−	0.840615i
$214$			44.0266i			0.205732i
$215$	146.492	+	0.0329002i	0.681358	+	0.000153024i
$216$	−102.294			−0.473585
$217$	418.790	+	418.790i	1.92991	+	1.92991i
$218$	84.6803	−	84.6803i	0.388442	−	0.388442i
$219$		−	472.348i		−	2.15684i
$220$	−50.0029	+	49.9804i	−0.227286	+	0.227184i
$221$	79.3216			0.358921
$222$	6.01842	+	6.01842i	0.0271100	+	0.0271100i
$223$	117.343	−	117.343i	0.526201	−	0.526201i	−0.393236	−	0.919437i	$-0.628645\pi$
$223$	117.343	−	117.343i	0.526201	−	0.526201i	0.919437	+	0.393236i	$0.128645\pi$
$224$		−	75.7243i		−	0.338055i
$225$	405.099	+	0.181960i	1.80044	+	0.000808712i
$226$	56.8846			0.251702
$227$	−119.753	−	119.753i	−0.527548	−	0.527548i	0.392292	−	0.919841i	$-0.371682\pi$
$227$	−119.753	−	119.753i	−0.527548	−	0.527548i	−0.919841	+	0.392292i	$0.871682\pi$
$228$	−244.839	+	244.839i	−1.07385	+	1.07385i
$229$		−	29.6939i		−	0.129668i	−0.997896	−	0.0648338i	$-0.979348\pi$
$229$		−	29.6939i		−	0.129668i	0.997896	−	0.0648338i	$-0.0206517\pi$
$230$	23.9738	+	23.9845i	0.104234	+	0.104281i
$231$	−475.125			−2.05682
$232$	35.7490	+	35.7490i	0.154091	+	0.154091i
$233$	74.9049	−	74.9049i	0.321480	−	0.321480i	−0.527855	−	0.849335i	$-0.677003\pi$
$233$	74.9049	−	74.9049i	0.321480	−	0.321480i	0.849335	+	0.527855i	$0.177003\pi$
$234$			225.501i			0.963682i
$235$	−0.0256954	+	114.411i	−0.000109342	+	0.486857i
$236$	−78.4171			−0.332276
$237$	35.9032	+	35.9032i	0.151490	+	0.151490i
$238$	107.904	−	107.904i	0.453380	−	0.453380i
$239$		−	213.990i		−	0.895354i	−0.894195	−	0.447677i	$-0.852251\pi$
$239$		−	213.990i		−	0.895354i	0.894195	−	0.447677i	$-0.147749\pi$
$240$	100.407	+	0.0225502i	0.418363	+	9.39590e-5i
$241$	12.1580			0.0504483			0.0252241	−	0.999682i	$-0.491970\pi$
$241$	12.1580			0.0504483			0.0252241	+	0.999682i	$0.491970\pi$
$242$	−71.0167	−	71.0167i	−0.293457	−	0.293457i
$243$	−103.313	+	103.313i	−0.425156	+	0.425156i
$244$		−	20.4631i		−	0.0838652i
$245$	−460.405	+	460.198i	−1.87920	+	1.87836i
$246$	275.998			1.12194
$247$	239.954	+	239.954i	0.971474	+	0.971474i
$248$	−88.4874	+	88.4874i	−0.356804	+	0.356804i
$249$			493.226i			1.98083i
$250$	−176.777	−	0.119105i	−0.707107	−	0.000476422i
$251$	246.854			0.983484			0.491742	−	0.870741i	$-0.336360\pi$
$251$	246.854			0.983484			0.491742	+	0.870741i	$0.336360\pi$
$252$	306.759	+	306.759i	1.21730	+	1.21730i
$253$	23.9752	−	23.9752i	0.0947635	−	0.0947635i
$254$			273.011i			1.07485i
$255$	143.044	+	143.109i	0.560958	+	0.561210i
$256$	16.0000			0.0625000
$257$	98.2482	+	98.2482i	0.382289	+	0.382289i	0.871926	−	0.489637i	$-0.162871\pi$
$257$	98.2482	+	98.2482i	0.382289	+	0.382289i	−0.489637	+	0.871926i	$0.662871\pi$
$258$	−147.088	+	147.088i	−0.570110	+	0.570110i
$259$		−	16.0475i		−	0.0619596i
$260$	0.0221003	−	98.4040i	8.50011e−5	−	0.378477i
$261$	−289.638			−1.10972
$262$	75.5156	+	75.5156i	0.288228	+	0.288228i
$263$	141.958	−	141.958i	0.539762	−	0.539762i	−0.383697	−	0.923459i	$-0.625349\pi$
$263$	141.958	−	141.958i	0.539762	−	0.539762i	0.923459	+	0.383697i	$0.125349\pi$
$264$		−	100.390i		−	0.380266i
$265$	473.858	+	0.106422i	1.78814	+	0.000401594i
$266$	652.839			2.45428
$267$	−193.896	−	193.896i	−0.726203	−	0.726203i
$268$	65.7001	−	65.7001i	0.245150	−	0.245150i
$269$		−	128.672i		−	0.478334i	−0.970978	−	0.239167i	$-0.923126\pi$
$269$		−	128.672i		−	0.478334i	0.970978	−	0.239167i	$-0.0768743\pi$
$270$	−180.873	+	180.792i	−0.669900	+	0.669599i
$271$	−1.78031			−0.00656941			−0.00328470	−	0.999995i	$-0.501046\pi$
$271$	−1.78031			−0.00656941			−0.00328470	+	0.999995i	$0.501046\pi$
$272$	22.7994	+	22.7994i	0.0838213	+	0.0838213i
$273$	467.620	−	467.620i	1.71289	−	1.71289i
$274$		−	261.588i		−	0.954701i
$275$	−0.0793903	+	176.747i	−0.000288692	+	0.642717i
$276$	−48.1536			−0.174469
$277$	117.201	+	117.201i	0.423110	+	0.423110i	0.886273	−	0.463163i	$-0.153286\pi$
$277$	117.201	+	117.201i	0.423110	+	0.423110i	−0.463163	+	0.886273i	$0.653286\pi$
$278$	−48.2637	+	48.2637i	−0.173611	+	0.173611i
$279$		−	716.923i		−	2.56962i
$280$	−133.833	−	133.893i	−0.477975	−	0.478189i
$281$	17.3126			0.0616106			0.0308053	−	0.999525i	$-0.490193\pi$
$281$	17.3126			0.0616106			0.0308053	+	0.999525i	$0.490193\pi$
$282$	−114.877	−	114.877i	−0.407366	−	0.407366i
$283$	−135.928	+	135.928i	−0.480312	+	0.480312i	−0.905231	−	0.424919i	$-0.860302\pi$
$283$	−135.928	+	135.928i	−0.480312	+	0.480312i	0.424919	+	0.905231i	$0.360302\pi$
$284$		−	100.876i		−	0.355197i
$285$	−0.194411	+	865.635i	−0.000682142	+	3.03732i
$286$	−98.3876			−0.344013
$287$	−367.961	−	367.961i	−1.28209	−	1.28209i
$288$	−64.8159	+	64.8159i	−0.225055	+	0.225055i
$289$		−	224.023i		−	0.775167i
$290$	126.392	+	0.0283860i	0.435834	+	9.78828e-5i
$291$	212.059			0.728726
$292$	−133.058	−	133.058i	−0.455679	−	0.455679i
$293$	270.859	−	270.859i	0.924434	−	0.924434i	−0.0729054	−	0.997339i	$-0.523227\pi$
$293$	270.859	−	270.859i	0.924434	−	0.924434i	0.997339	+	0.0729054i	$0.0232271\pi$
$294$		−	924.351i		−	3.14405i
$295$	−138.654	+	138.592i	−0.470015	+	0.469803i
$296$	3.39073			0.0114552
$297$	180.802	+	180.802i	0.608762	+	0.608762i
$298$	265.549	−	265.549i	0.891104	−	0.891104i
$299$			47.1929i			0.157836i
$300$	177.576	−	177.417i	0.591920	−	0.591389i
$301$	392.197			1.30298
$302$	195.152	+	195.152i	0.646198	+	0.646198i
$303$	−127.275	+	127.275i	−0.420051	+	0.420051i
$304$			137.940i			0.453750i
$305$	−36.1659	−	36.1821i	−0.118577	−	0.118630i
$306$	−184.720			−0.603662
$307$	−239.476	−	239.476i	−0.780052	−	0.780052i	0.199787	−	0.979839i	$-0.435975\pi$
$307$	−239.476	−	239.476i	−0.780052	−	0.780052i	−0.979839	+	0.199787i	$0.935975\pi$
$308$	−133.841	+	133.841i	−0.434548	+	0.434548i
$309$		−	842.829i		−	2.72760i
$310$	−0.0702622	+	312.850i	−0.000226652	+	1.00919i
$311$	222.369			0.715014			0.357507	−	0.933911i	$-0.383627\pi$
$311$	222.369			0.715014			0.357507	+	0.933911i	$0.383627\pi$
$312$	98.8047	+	98.8047i	0.316682	+	0.316682i
$313$	244.143	−	244.143i	0.780011	−	0.780011i	−0.199822	−	0.979832i	$-0.564036\pi$
$313$	244.143	−	244.143i	0.780011	−	0.780011i	0.979832	+	0.199822i	$0.0640362\pi$
$314$			388.841i			1.23835i
$315$	1084.56	+	0.243577i	3.44303	+	0.000773262i
$316$	20.2276			0.0640114
$317$	−156.030	−	156.030i	−0.492209	−	0.492209i	0.416792	−	0.909002i	$-0.363154\pi$
$317$	−156.030	−	156.030i	−0.492209	−	0.492209i	−0.909002	+	0.416792i	$0.863154\pi$
$318$	−475.787	+	475.787i	−1.49619	+	1.49619i
$319$		−	126.371i		−	0.396147i
$320$	28.2906	−	28.2779i	0.0884082	−	0.0883685i
$321$	−156.291			−0.486889
$322$	64.1984	+	64.1984i	0.199374	+	0.199374i
$323$	−196.559	+	196.559i	−0.608543	+	0.608543i
$324$		−	71.4658i		−	0.220573i
$325$	−173.877	−	174.034i	−0.535007	−	0.535488i
$326$	−210.538			−0.645821
$327$	300.609	+	300.609i	0.919293	+	0.919293i
$328$	77.7474	−	77.7474i	0.237035	−	0.237035i
$329$			306.309i			0.931031i
$330$	−177.427	−	177.507i	−0.537657	−	0.537899i
$331$	335.345			1.01313			0.506563	−	0.862203i	$-0.330916\pi$
$331$	335.345			1.01313			0.506563	+	0.862203i	$0.330916\pi$
$332$	138.940	+	138.940i	0.418493	+	0.418493i
$333$	−13.7358	+	13.7358i	−0.0412487	+	0.0412487i
$334$		−	191.044i		−	0.571987i
$335$	0.0521682	−	232.285i	0.000155726	−	0.693388i
$336$	268.816			0.800047
$337$	−288.096	−	288.096i	−0.854883	−	0.854883i	0.135847	−	0.990730i	$-0.456624\pi$
$337$	−288.096	−	288.096i	−0.854883	−	0.854883i	−0.990730	+	0.135847i	$0.956624\pi$
$338$	−72.1664	+	72.1664i	−0.213510	+	0.213510i
$339$			201.936i			0.595682i
$340$	80.6081	+	0.0181035i	0.237083	+	5.32457e-5i
$341$	312.798			0.917296
$342$	−558.794	−	558.794i	−1.63390	−	1.63390i
$343$	−768.535	+	768.535i	−2.24063	+	2.24063i
$344$			82.8683i			0.240896i
$345$	−85.1434	+	85.1051i	−0.246792	+	0.246682i
$346$	−197.122			−0.569716
$347$	−104.868	−	104.868i	−0.302212	−	0.302212i	0.539666	−	0.841879i	$-0.318550\pi$
$347$	−104.868	−	104.868i	−0.302212	−	0.302212i	−0.841879	+	0.539666i	$0.818550\pi$
$348$	−126.906	+	126.906i	−0.364674	+	0.364674i
$349$			287.151i			0.822783i	0.911459	+	0.411391i	$0.134957\pi$
$349$			287.151i			0.822783i	−0.911459	+	0.411391i	$0.865043\pi$
$350$	−473.277	−	0.212584i	−1.35222	−	0.000607383i
$351$	−355.893			−1.01394
$352$	−28.2796	−	28.2796i	−0.0803396	−	0.0803396i
$353$	−193.073	+	193.073i	−0.546950	+	0.546950i	−0.925557	−	0.378608i	$-0.876403\pi$
$353$	−193.073	+	193.073i	−0.546950	+	0.546950i	0.378608	+	0.925557i	$0.376403\pi$
$354$		−	278.375i		−	0.786370i
$355$	−178.285	−	178.365i	−0.502211	−	0.502437i
$356$	−109.239			−0.306852
$357$	383.053	+	383.053i	1.07298	+	1.07298i
$358$	25.4849	−	25.4849i	0.0711869	−	0.0711869i
$359$		−	269.618i		−	0.751024i	−0.926817	−	0.375512i	$-0.877467\pi$
$359$		−	269.618i		−	0.751024i	0.926817	−	0.375512i	$-0.122533\pi$
$360$	−0.0514661	+	229.159i	−0.000142961	+	0.636552i
$361$	−828.216			−2.29423
$362$	−326.572	−	326.572i	−0.902133	−	0.902133i
$363$	252.104	−	252.104i	0.694502	−	0.694502i
$364$		−	263.453i		−	0.723772i
$365$	−470.432	−	0.105653i	−1.28886	−	0.000289461i
$366$	72.6425			0.198477
$367$	434.802	+	434.802i	1.18475	+	1.18475i	0.978500	+	0.206246i	$0.0661248\pi$
$367$	434.802	+	434.802i	1.18475	+	1.18475i	0.206246	+	0.978500i	$0.433875\pi$
$368$	−13.5647	+	13.5647i	−0.0368605	+	0.0368605i
$369$			629.908i			1.70707i
$370$	5.99536	−	5.99267i	0.0162037	−	0.0161964i
$371$	1268.64			3.41952
$372$	−314.124	−	314.124i	−0.844419	−	0.844419i
$373$	−131.607	+	131.607i	−0.352835	+	0.352835i	−0.861163	−	0.508328i	$-0.830264\pi$
$373$	−131.607	+	131.607i	−0.352835	+	0.352835i	0.508328	+	0.861163i	$0.330264\pi$
$374$		−	80.5946i		−	0.215494i
$375$	0.422815	−	627.544i	0.00112751	−	1.67345i
$376$	−64.7209			−0.172130
$377$	124.375	+	124.375i	0.329906	+	0.329906i
$378$	−484.135	+	484.135i	−1.28078	+	1.28078i
$379$		−	204.936i		−	0.540727i	−0.962758	−	0.270364i	$-0.912856\pi$
$379$		−	204.936i		−	0.540727i	0.962758	−	0.270364i	$-0.0871439\pi$
$380$	243.791	+	243.901i	0.641555	+	0.641844i
$381$	−969.170			−2.54375
$382$	188.733	+	188.733i	0.494065	+	0.494065i
$383$	−196.483	+	196.483i	−0.513011	+	0.513011i	−0.915448	−	0.402437i	$-0.868163\pi$
$383$	−196.483	+	196.483i	−0.513011	+	0.513011i	0.402437	+	0.915448i	$0.368163\pi$
$384$			56.7988i			0.147914i
$385$	−0.106274	+	473.198i	−0.000276037	+	1.22909i
$386$	−293.582			−0.760575
$387$	−335.699	−	335.699i	−0.867439	−	0.867439i
$388$	59.7362	−	59.7362i	0.153959	−	0.153959i
$389$		−	542.460i		−	1.39450i	−0.716828	−	0.697250i	$-0.754407\pi$
$389$		−	542.460i		−	1.39450i	0.716828	−	0.697250i	$-0.245593\pi$
$390$	349.327	+	0.0784545i	0.895711	+	0.000201165i
$391$	−38.6583			−0.0988703
$392$	−260.386	−	260.386i	−0.664250	−	0.664250i
$393$	−268.075	+	268.075i	−0.682125	+	0.682125i
$394$		−	234.149i		−	0.594286i
$395$	35.7657	−	35.7496i	0.0905461	−	0.0905054i
$396$	229.120			0.578587
$397$	−176.892	−	176.892i	−0.445572	−	0.445572i	0.448307	−	0.893879i	$-0.352027\pi$
$397$	−176.892	−	176.892i	−0.445572	−	0.445572i	−0.893879	+	0.448307i	$0.852027\pi$
$398$	−71.0996	+	71.0996i	−0.178642	+	0.178642i
$399$			2317.53i			5.80834i
$400$	0.0449175	−	100.000i	0.000112294	−	0.250000i
$401$	−734.716			−1.83221			−0.916105	−	0.400939i	$-0.868684\pi$
$401$	−734.716			−1.83221			−0.916105	+	0.400939i	$0.868684\pi$
$402$	233.230	+	233.230i	0.580175	+	0.580175i
$403$	−307.857	+	307.857i	−0.763914	+	0.763914i
$404$			71.7059i			0.177490i
$405$	−126.306	−	126.363i	−0.311868	−	0.312008i
$406$	338.384			0.833458
$407$	−5.99301	−	5.99301i	−0.0147248	−	0.0147248i
$408$	−80.9362	+	80.9362i	−0.198373	+	0.198373i
$409$		−	153.786i		−	0.376005i	−0.982169	−	0.188003i	$-0.939799\pi$
$409$		−	153.786i		−	0.376005i	0.982169	−	0.188003i	$-0.0602014\pi$
$410$	0.0617342	−	274.878i	0.000150571	−	0.670435i
$411$	928.619			2.25941
$412$	−237.422	−	237.422i	−0.576266	−	0.576266i
$413$	−371.130	+	371.130i	−0.898620	+	0.898620i
$414$		−	109.901i		−	0.265461i
$415$	491.226	+	0.110323i	1.18368	+	0.000265839i
$416$	55.6657			0.133812
$417$	−171.333	−	171.333i	−0.410870	−	0.410870i
$418$	243.805	−	243.805i	0.583266	−	0.583266i
$419$		−	259.536i		−	0.619418i	−0.950831	−	0.309709i	$-0.899768\pi$
$419$		−	259.536i		−	0.619418i	0.950831	−	0.309709i	$-0.100232\pi$
$420$	475.311	−	475.097i	1.13169	−	1.13118i
$421$	113.209			0.268906			0.134453	−	0.990920i	$-0.457072\pi$
$421$	113.209			0.268906			0.134453	+	0.990920i	$0.457072\pi$
$422$	62.6847	+	62.6847i	0.148542	+	0.148542i
$423$	262.184	−	262.184i	0.619820	−	0.619820i
$424$			268.055i			0.632204i
$425$	142.560	−	142.432i	0.335436	−	0.335135i
$426$	358.102			0.840615
$427$	−96.8472	−	96.8472i	−0.226808	−	0.226808i
$428$	−44.0266	+	44.0266i	−0.102866	+	0.102866i
$429$		−	349.269i		−	0.814147i
$430$	146.459	+	146.525i	0.340602	+	0.340755i
$431$	−450.882			−1.04613			−0.523065	−	0.852293i	$-0.675212\pi$
$431$	−450.882			−1.04613			−0.523065	+	0.852293i	$0.675212\pi$
$432$	−102.294	−	102.294i	−0.236792	−	0.236792i
$433$	177.577	−	177.577i	0.410108	−	0.410108i	−0.471668	−	0.881776i	$-0.656348\pi$
$433$	177.577	−	177.577i	0.410108	−	0.410108i	0.881776	+	0.471668i	$0.156348\pi$
$434$			837.581i			1.92991i
$435$	−0.100768	+	448.682i	−0.000231651	+	1.03145i
$436$	169.361			0.388442
$437$	−116.944	−	116.944i	−0.267607	−	0.267607i
$438$	472.348	−	472.348i	1.07842	−	1.07842i
$439$		−	713.713i		−	1.62577i	−0.582425	−	0.812884i	$-0.697896\pi$
$439$		−	713.713i		−	1.62577i	0.582425	−	0.812884i	$-0.302104\pi$
$440$	−99.9833	−	0.0224550i	−0.227235	−	5.10340e-5i
$441$	2109.64			4.78377
$442$	79.3216	+	79.3216i	0.179461	+	0.179461i
$443$	−279.293	+	279.293i	−0.630457	+	0.630457i	−0.948183	−	0.317725i	$-0.897081\pi$
$443$	−279.293	+	279.293i	−0.630457	+	0.630457i	0.317725	+	0.948183i	$0.397081\pi$
$444$			12.0368i			0.0271100i
$445$	−193.153	+	193.067i	−0.434052	+	0.433857i
$446$	234.686			0.526201
$447$	942.679	+	942.679i	2.10890	+	2.10890i
$448$	75.7243	−	75.7243i	0.169028	−	0.169028i
$449$		−	541.558i		−	1.20614i	−0.797687	−	0.603071i	$-0.793943\pi$
$449$		−	541.558i		−	1.20614i	0.797687	−	0.603071i	$-0.206057\pi$
$450$	404.917	+	405.281i	0.899816	+	0.900625i
$451$	−274.833			−0.609385
$452$	56.8846	+	56.8846i	0.125851	+	0.125851i
$453$	−692.775	+	692.775i	−1.52930	+	1.52930i
$454$		−	239.507i		−	0.527548i
$455$	−465.619	−	465.828i	−1.02334	−	1.02380i
$456$	−489.677			−1.07385
$457$	408.672	+	408.672i	0.894249	+	0.894249i	0.994920	−	0.100670i	$-0.0320988\pi$
$457$	408.672	+	408.672i	0.894249	+	0.894249i	−0.100670	+	0.994920i	$0.532099\pi$
$458$	29.6939	−	29.6939i	0.0648338	−	0.0648338i
$459$		−	291.531i		−	0.635144i
$460$	−0.0107708	+	47.9583i	−2.34148e−5	+	0.104257i
$461$	130.430			0.282928			0.141464	−	0.989943i	$-0.454819\pi$
$461$	130.430			0.282928			0.141464	+	0.989943i	$0.454819\pi$
$462$	−475.125	−	475.125i	−1.02841	−	1.02841i
$463$	−415.078	+	415.078i	−0.896496	+	0.896496i	−0.995124	−	0.0986285i	$-0.968554\pi$
$463$	−415.078	+	415.078i	−0.896496	+	0.896496i	0.0986285	+	0.995124i	$0.468554\pi$
$464$			71.4980i			0.154091i
$465$	−1110.60	−	0.249426i	−2.38838	−	0.000536399i
$466$	149.810			0.321480
$467$	116.835	+	116.835i	0.250183	+	0.250183i	0.821046	−	0.570863i	$-0.193391\pi$
$467$	116.835	+	116.835i	0.250183	+	0.250183i	−0.570863	+	0.821046i	$0.693391\pi$
$468$	−225.501	+	225.501i	−0.481841	+	0.481841i
$469$		−	621.887i		−	1.32598i
$470$	−114.437	+	114.386i	−0.243483	+	0.243374i
$471$	−1380.36			−2.93070
$472$	−78.4171	−	78.4171i	−0.166138	−	0.166138i
$473$	146.467	−	146.467i	0.309656	−	0.309656i
$474$			71.8065i			0.151490i
$475$	862.125	+	0.387245i	1.81500	+	0.000815252i
$476$	215.809			0.453380
$477$	−1085.89	−	1085.89i	−2.27649	−	2.27649i
$478$	213.990	−	213.990i	0.447677	−	0.447677i
$479$			426.572i			0.890546i	0.895395	+	0.445273i	$0.146893\pi$
$479$			426.572i			0.890546i	−0.895395	+	0.445273i	$0.853107\pi$
$480$	100.385	+	100.430i	0.209134	+	0.209228i
$481$	11.7967			0.0245254
$482$	12.1580	+	12.1580i	0.0252241	+	0.0252241i
$483$	−227.900	+	227.900i	−0.471842	+	0.471842i
$484$		−	142.033i		−	0.293457i
$485$	0.0474327	−	211.199i	9.77994e−5	−	0.435463i
$486$	−206.626			−0.425156
$487$	129.475	+	129.475i	0.265863	+	0.265863i	0.827431	−	0.561568i	$-0.189802\pi$
$487$	129.475	+	129.475i	0.265863	+	0.265863i	−0.561568	+	0.827431i	$0.689802\pi$
$488$	20.4631	−	20.4631i	0.0419326	−	0.0419326i
$489$		−	747.394i		−	1.52841i
$490$	−920.603	−	0.206756i	−1.87878	−	0.000421951i
$491$	−280.807			−0.571908			−0.285954	−	0.958243i	$-0.592310\pi$
$491$	−280.807			−0.571908			−0.285954	+	0.958243i	$0.592310\pi$
$492$	275.998	+	275.998i	0.560971	+	0.560971i
$493$	−101.882	+	101.882i	−0.206657	+	0.206657i
$494$			479.908i			0.971474i
$495$	405.123	−	404.941i	0.818429	−	0.818062i
$496$	−176.975			−0.356804
$497$	−477.422	−	477.422i	−0.960609	−	0.960609i
$498$	−493.226	+	493.226i	−0.990414	+	0.990414i
$499$			525.230i			1.05256i	0.850310	+	0.526282i	$0.176414\pi$
$499$			525.230i			1.05256i	−0.850310	+	0.526282i	$0.823586\pi$
$500$	−176.658	−	176.896i	−0.353315	−	0.353792i
$501$	678.191			1.35367
$502$	246.854	+	246.854i	0.491742	+	0.491742i
$503$	546.330	−	546.330i	1.08614	−	1.08614i	0.0902219	−	0.995922i	$-0.471242\pi$
$503$	546.330	−	546.330i	1.08614	−	1.08614i	0.995922	−	0.0902219i	$-0.0287576\pi$
$504$			613.517i			1.21730i
$505$	126.731	+	126.788i	0.250952	+	0.251065i
$506$	47.9503			0.0947635
$507$	−256.186	−	256.186i	−0.505297	−	0.505297i
$508$	−273.011	+	273.011i	−0.537424	+	0.537424i
$509$			382.232i			0.750946i	0.926833	+	0.375473i	$0.122520\pi$
$509$			382.232i			0.750946i	−0.926833	+	0.375473i	$0.877480\pi$
$510$	−0.0642663	+	286.153i	−0.000126012	+	0.561084i
$511$	−1259.47			−2.46472
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	881.905	−	881.905i	1.71911	−	1.71911i
$514$			196.496i			0.382289i
$515$	−839.412	−	0.188521i	−1.62993	−	0.000366061i
$516$	−294.177			−0.570110
$517$	114.392	+	114.392i	0.221262	+	0.221262i
$518$	16.0475	−	16.0475i	0.0309798	−	0.0309798i
$519$		−	699.768i		−	1.34830i
$520$	98.4262	−	98.3819i	0.189281	−	0.189196i
$521$	890.745			1.70968			0.854842	−	0.518889i	$-0.173654\pi$
$521$	890.745			1.70968			0.854842	+	0.518889i	$0.173654\pi$
$522$	−289.638	−	289.638i	−0.554862	−	0.554862i
$523$	−454.620	+	454.620i	−0.869254	+	0.869254i	−0.992390	−	0.123136i	$-0.960705\pi$
$523$	−454.620	+	454.620i	−0.869254	+	0.869254i	0.123136	+	0.992390i	$0.460705\pi$
$524$			151.031i			0.288228i
$525$	0.754658	−	1680.10i	0.00143744	−	3.20019i
$526$	283.915			0.539762
$527$	−252.182	−	252.182i	−0.478525	−	0.478525i
$528$	100.390	−	100.390i	0.190133	−	0.190133i
$529$		−	23.0000i		−	0.0434783i
$530$	473.752	+	473.964i	0.893871	+	0.894272i
$531$	635.334			1.19649
$532$	652.839	+	652.839i	1.22714	+	1.22714i
$533$	270.492	−	270.492i	0.507489	−	0.507489i
$534$		−	387.792i		−	0.726203i
$535$	−0.0349587	+	155.658i	−6.53434e−5	+	0.290949i
$536$	131.400			0.245150
$537$	90.4695	+	90.4695i	0.168472	+	0.168472i
$538$	128.672	−	128.672i	0.239167	−	0.239167i
$539$			920.450i			1.70770i
$540$	−361.665	−	0.0812253i	−0.669750	−	0.000150417i
$541$	−31.2712			−0.0578025			−0.0289013	−	0.999582i	$-0.509201\pi$
$541$	−31.2712			−0.0578025			−0.0289013	+	0.999582i	$0.509201\pi$
$542$	−1.78031	−	1.78031i	−0.00328470	−	0.00328470i
$543$	1159.31	−	1159.31i	2.13501	−	2.13501i
$544$			45.5988i			0.0838213i
$545$	299.457	−	299.323i	0.549463	−	0.549216i
$546$	935.240			1.71289
$547$	−128.742	−	128.742i	−0.235360	−	0.235360i	0.579566	−	0.814925i	$-0.303222\pi$
$547$	−128.742	−	128.742i	−0.235360	−	0.235360i	−0.814925	+	0.579566i	$0.803222\pi$
$548$	261.588	−	261.588i	0.477351	−	0.477351i
$549$			165.792i			0.301989i
$550$	−176.827	+	176.668i	−0.321503	+	0.321214i
$551$	−616.403			−1.11870
$552$	−48.1536	−	48.1536i	−0.0872347	−	0.0872347i
$553$	95.7326	−	95.7326i	0.173115	−	0.173115i
$554$			234.403i			0.423110i
$555$	21.2735	+	21.2831i	0.0383307	+	0.0383479i
$556$	−96.5274			−0.173611
$557$	332.522	+	332.522i	0.596987	+	0.596987i	0.939510	−	0.342523i	$-0.111281\pi$
$557$	332.522	+	332.522i	0.596987	+	0.596987i	−0.342523	+	0.939510i	$0.611281\pi$
$558$	716.923	−	716.923i	1.28481	−	1.28481i
$559$			288.308i			0.515756i
$560$	0.0601278	−	267.726i	0.000107371	−	0.478082i
$561$	286.105			0.509991
$562$	17.3126	+	17.3126i	0.0308053	+	0.0308053i
$563$	−673.400	+	673.400i	−1.19609	+	1.19609i	−0.220765	+	0.975327i	$0.570855\pi$
$563$	−673.400	+	673.400i	−1.19609	+	1.19609i	−0.975327	+	0.220765i	$0.929145\pi$
$564$		−	229.754i		−	0.407366i
$565$	201.117	+	0.0451684i	0.355960	+	7.99441e-5i
$566$	−271.856			−0.480312
$567$	−338.231	−	338.231i	−0.596528	−	0.596528i
$568$	100.876	−	100.876i	0.177598	−	0.177598i
$569$			39.7127i			0.0697939i	0.999391	+	0.0348969i	$0.0111103\pi$
$569$			39.7127i			0.0697939i	−0.999391	+	0.0348969i	$0.988890\pi$
$570$	−865.829	+	865.441i	−1.51900	+	1.51832i
$571$	212.890			0.372837			0.186419	−	0.982470i	$-0.440312\pi$
$571$	212.890			0.372837			0.186419	+	0.982470i	$0.440312\pi$
$572$	−98.3876	−	98.3876i	−0.172006	−	0.172006i
$573$	−669.987	+	669.987i	−1.16926	+	1.16926i
$574$		−	735.921i		−	1.28209i
$575$	84.7410	+	84.8172i	0.147376	+	0.147508i
$576$	−129.632			−0.225055
$577$	503.393	+	503.393i	0.872431	+	0.872431i	0.992737	−	0.120306i	$-0.0383875\pi$
$577$	503.393	+	503.393i	0.872431	+	0.872431i	−0.120306	+	0.992737i	$0.538388\pi$
$578$	224.023	−	224.023i	0.387584	−	0.387584i
$579$		−	1042.20i		−	1.79999i
$580$	126.363	+	126.420i	0.217868	+	0.217966i
$581$	1315.14			2.26358
$582$	212.059	+	212.059i	0.364363	+	0.364363i
$583$	473.779	−	473.779i	0.812657	−	0.812657i
$584$		−	266.117i		−	0.455679i
$585$	−0.179056	+	797.268i	−0.000306079	+	1.36285i
$586$	541.718			0.924434
$587$	−201.749	−	201.749i	−0.343695	−	0.343695i	0.514060	−	0.857755i	$-0.328141\pi$
$587$	−201.749	−	201.749i	−0.343695	−	0.343695i	−0.857755	+	0.514060i	$0.828141\pi$
$588$	924.351	−	924.351i	1.57203	−	1.57203i
$589$		−	1525.74i		−	2.59040i
$590$	−277.246	−	0.0622660i	−0.469909	−	0.000105536i
$591$	831.211			1.40645
$592$	3.39073	+	3.39073i	0.00572758	+	0.00572758i
$593$	−493.576	+	493.576i	−0.832337	+	0.832337i	−0.987836	−	0.155499i	$-0.950302\pi$
$593$	−493.576	+	493.576i	−0.832337	+	0.832337i	0.155499	+	0.987836i	$0.450302\pi$
$594$			361.605i			0.608762i
$595$	381.585	−	381.414i	0.641320	−	0.641032i
$596$	531.098			0.891104
$597$	−252.399	−	252.399i	−0.422778	−	0.422778i
$598$	−47.1929	+	47.1929i	−0.0789179	+	0.0789179i
$599$			378.431i			0.631771i	0.948797	+	0.315886i	$0.102302\pi$
$599$			378.431i			0.631771i	−0.948797	+	0.315886i	$0.897698\pi$
$600$	354.993	+	0.159454i	0.591655	+	0.000265756i
$601$	−1015.33			−1.68941			−0.844703	−	0.535235i	$-0.820223\pi$
$601$	−1015.33			−1.68941			−0.844703	+	0.535235i	$0.820223\pi$
$602$	392.197	+	392.197i	0.651490	+	0.651490i
$603$	−532.301	+	532.301i	−0.882755	+	0.882755i
$604$			390.304i			0.646198i
$605$	−251.026	−	251.138i	−0.414918	−	0.415105i
$606$	−254.551			−0.420051
$607$	−557.733	−	557.733i	−0.918835	−	0.918835i	0.0781094	−	0.996945i	$-0.475112\pi$
$607$	−557.733	−	557.733i	−0.918835	−	0.918835i	−0.996945	+	0.0781094i	$0.975112\pi$
$608$	−137.940	+	137.940i	−0.226875	+	0.226875i
$609$			1201.24i			1.97248i
$610$	0.0162484	−	72.3480i	2.66368e−5	−	0.118603i
$611$	−225.171			−0.368529
$612$	−184.720	−	184.720i	−0.301831	−	0.301831i
$613$	−162.839	+	162.839i	−0.265643	+	0.265643i	−0.827342	−	0.561699i	$-0.810148\pi$
$613$	−162.839	+	162.839i	−0.265643	+	0.265643i	0.561699	+	0.827342i	$0.310148\pi$
$614$		−	478.952i		−	0.780052i
$615$	975.799	+	0.219152i	1.58666	+	0.000356345i
$616$	−267.681			−0.434548
$617$	605.990	+	605.990i	0.982155	+	0.982155i	0.999844	−	0.0176884i	$-0.00563069\pi$
$617$	605.990	+	605.990i	0.982155	+	0.982155i	−0.0176884	+	0.999844i	$0.505631\pi$
$618$	842.829	−	842.829i	1.36380	−	1.36380i
$619$		−	422.816i		−	0.683064i	−0.939870	−	0.341532i	$-0.889054\pi$
$619$		−	422.816i		−	0.683064i	0.939870	−	0.341532i	$-0.110946\pi$
$620$	−312.920	+	312.780i	−0.504710	+	0.504484i
$621$	173.448			0.279305
$622$	222.369	+	222.369i	0.357507	+	0.357507i
$623$	−517.005	+	517.005i	−0.829864	+	0.829864i
$624$			197.609i			0.316682i
$625$	−625.000	−	0.561468i	−1.00000	−	0.000898349i
$626$	488.287			0.780011
$627$	865.490	+	865.490i	1.38037	+	1.38037i
$628$	−388.841	+	388.841i	−0.619174	+	0.619174i
$629$			9.66332i			0.0153630i
$630$	1084.31	+	1084.80i	1.72113	+	1.72190i
$631$	761.602			1.20698			0.603488	−	0.797372i	$-0.293777\pi$
$631$	761.602			1.20698			0.603488	+	0.797372i	$0.293777\pi$
$632$	20.2276	+	20.2276i	0.0320057	+	0.0320057i
$633$	−222.526	+	222.526i	−0.351542	+	0.351542i
$634$		−	312.061i		−	0.492209i
$635$	−0.216781	+	965.240i	−0.000341387	+	1.52006i
$636$	−951.574			−1.49619
$637$	−905.911	−	905.911i	−1.42215	−	1.42215i
$638$	126.371	−	126.371i	0.198073	−	0.198073i
$639$			817.295i			1.27902i
$640$	56.5685	+	0.0127046i	0.0883883	+	1.98509e-5i
$641$	713.025			1.11236			0.556182	−	0.831061i	$-0.312266\pi$
$641$	713.025			1.11236			0.556182	+	0.831061i	$0.312266\pi$
$642$	−156.291	−	156.291i	−0.243444	−	0.243444i
$643$	687.034	−	687.034i	1.06848	−	1.06848i	0.0710061	−	0.997476i	$-0.477379\pi$
$643$	687.034	−	687.034i	1.06848	−	1.06848i	0.997476	−	0.0710061i	$-0.0226210\pi$
$644$			128.397i			0.199374i
$645$	−520.152	+	519.919i	−0.806438	+	0.806076i
$646$	−393.119			−0.608543
$647$	60.0315	+	60.0315i	0.0927845	+	0.0927845i	0.751976	−	0.659191i	$-0.229101\pi$
$647$	60.0315	+	60.0315i	0.0927845	+	0.0927845i	−0.659191	+	0.751976i	$0.729101\pi$
$648$	71.4658	−	71.4658i	0.110287	−	0.110287i
$649$			277.200i			0.427119i
$650$	0.156273	−	347.911i	0.000240420	−	0.535247i
$651$	−2973.35			−4.56736
$652$	−210.538	−	210.538i	−0.322911	−	0.322911i
$653$	−562.028	+	562.028i	−0.860686	+	0.860686i	−0.991418	−	0.130732i	$-0.958267\pi$
$653$	−562.028	+	562.028i	−0.860686	+	0.860686i	0.130732	+	0.991418i	$0.458267\pi$
$654$			601.218i			0.919293i
$655$	266.928	+	267.048i	0.407524	+	0.407707i
$656$	155.495			0.237035
$657$	1078.04	+	1078.04i	1.64085	+	1.64085i
$658$	−306.309	+	306.309i	−0.465515	+	0.465515i
$659$		−	152.978i		−	0.232137i	−0.993241	−	0.116069i	$-0.962971\pi$
$659$		−	152.978i		−	0.232137i	0.993241	−	0.116069i	$-0.0370292\pi$
$660$	0.0797135	−	354.933i	0.000120778	−	0.537778i
$661$	−283.007			−0.428149			−0.214075	−	0.976817i	$-0.568674\pi$
$661$	−283.007			−0.428149			−0.214075	+	0.976817i	$0.568674\pi$
$662$	335.345	+	335.345i	0.506563	+	0.506563i
$663$	−281.586	+	281.586i	−0.424715	+	0.424715i
$664$			277.880i			0.418493i
$665$	2308.13	+	0.518377i	3.47088	+	0.000779515i
$666$	−27.4716			−0.0412487
$667$	−60.6154	−	60.6154i	−0.0908777	−	0.0908777i
$668$	191.044	−	191.044i	0.285994	−	0.285994i
$669$			833.117i			1.24532i
$670$	232.337	−	232.233i	0.346772	−	0.346616i
$671$	−72.3359			−0.107803
$672$	268.816	+	268.816i	0.400024	+	0.400024i
$673$	380.707	−	380.707i	0.565687	−	0.565687i	−0.365230	−	0.930917i	$-0.619010\pi$
$673$	380.707	−	380.707i	0.565687	−	0.565687i	0.930917	+	0.365230i	$0.119010\pi$
$674$		−	576.191i		−	0.854883i
$675$	−639.626	+	639.052i	−0.947595	+	0.946744i
$676$	−144.333			−0.213510
$677$	−425.366	−	425.366i	−0.628311	−	0.628311i	0.319332	−	0.947643i	$-0.396541\pi$
$677$	−425.366	−	425.366i	−0.628311	−	0.628311i	−0.947643	+	0.319332i	$0.896541\pi$
$678$	−201.936	+	201.936i	−0.297841	+	0.297841i
$679$		−	565.436i		−	0.832748i
$680$	80.5900	+	80.6262i	0.118515	+	0.118568i
$681$	850.232			1.24851
$682$	312.798	+	312.798i	0.458648	+	0.458648i
$683$	375.760	−	375.760i	0.550161	−	0.550161i	−0.376326	−	0.926487i	$-0.622813\pi$
$683$	375.760	−	375.760i	0.550161	−	0.550161i	0.926487	+	0.376326i	$0.122813\pi$
$684$		−	1117.59i		−	1.63390i
$685$	0.207710	−	924.854i	0.000303227	−	1.35015i
$686$	−1537.07			−2.24063
$687$	105.411	+	105.411i	0.153437	+	0.153437i
$688$	−82.8683	+	82.8683i	−0.120448	+	0.120448i
$689$			932.591i			1.35354i
$690$	−170.249	−	0.0382357i	−0.246737	−	5.54140e-5i
$691$	−669.698			−0.969172			−0.484586	−	0.874744i	$-0.661030\pi$
$691$	−669.698			−0.969172			−0.484586	+	0.874744i	$0.661030\pi$
$692$	−197.122	−	197.122i	−0.284858	−	0.284858i
$693$	1084.37	−	1084.37i	1.56475	−	1.56475i
$694$		−	209.735i		−	0.302212i
$695$	−170.676	+	170.600i	−0.245577	+	0.245467i
$696$	−253.813			−0.364674
$697$	221.574	+	221.574i	0.317897	+	0.317897i
$698$	−287.151	+	287.151i	−0.411391	+	0.411391i
$699$			531.814i			0.760821i
$700$	−473.064	−	473.490i	−0.675806	−	0.676414i
$701$	120.988			0.172594			0.0862971	−	0.996269i	$-0.472497\pi$
$701$	120.988			0.172594			0.0862971	+	0.996269i	$0.472497\pi$
$702$	−355.893	−	355.893i	−0.506970	−	0.506970i
$703$	−29.2323	+	29.2323i	−0.0415822	+	0.0415822i
$704$		−	56.5591i		−	0.0803396i
$705$	−406.061	−	406.243i	−0.575973	−	0.576232i
$706$	−386.147			−0.546950
$707$	339.368	+	339.368i	0.480011	+	0.480011i
$708$	278.375	−	278.375i	0.393185	−	0.393185i
$709$		−	601.912i		−	0.848960i	−0.905437	−	0.424480i	$-0.860457\pi$
$709$		−	601.912i		−	0.848960i	0.905437	−	0.424480i	$-0.139543\pi$
$710$	0.0800991	−	356.650i	0.000112816	−	0.502324i
$711$	−163.884			−0.230497
$712$	−109.239	−	109.239i	−0.153426	−	0.153426i
$713$	150.038	−	150.038i	0.210431	−	0.210431i
$714$			766.105i			1.07298i
$715$	−347.853	−	0.0781233i	−0.486507	−	0.000109263i
$716$	50.9698			0.0711869
$717$	759.648	+	759.648i	1.05948	+	1.05948i
$718$	269.618	−	269.618i	0.375512	−	0.375512i
$719$			713.517i			0.992374i	0.868216	+	0.496187i	$0.165267\pi$
$719$			713.517i			0.992374i	−0.868216	+	0.496187i	$0.834733\pi$
$720$	−229.210	+	229.107i	−0.318347	+	0.318205i
$721$	−2247.32			−3.11695
$722$	−828.216	−	828.216i	−1.14711	−	1.14711i
$723$	−43.1601	+	43.1601i	−0.0596959	+	0.0596959i
$724$		−	653.145i		−	0.902133i
$725$	446.863	+	0.200719i	0.616362	+	0.000276854i
$726$	504.208			0.694502
$727$	−168.465	−	168.465i	−0.231726	−	0.231726i	0.581687	−	0.813413i	$-0.302393\pi$
$727$	−168.465	−	168.465i	−0.231726	−	0.231726i	−0.813413	+	0.581687i	$0.802393\pi$
$728$	263.453	−	263.453i	0.361886	−	0.361886i
$729$		−	1055.10i		−	1.44733i
$730$	−470.327	−	470.538i	−0.644283	−	0.644573i
$731$	−236.169			−0.323076
$732$	72.6425	+	72.6425i	0.0992384	+	0.0992384i
$733$	445.823	−	445.823i	0.608216	−	0.608216i	−0.334263	−	0.942480i	$-0.608487\pi$
$733$	445.823	−	445.823i	0.608216	−	0.608216i	0.942480	+	0.334263i	$0.108487\pi$
$734$			869.604i			1.18475i
$735$	0.733968	−	3268.07i	0.000998596	−	4.44636i
$736$	−27.1293			−0.0368605
$737$	−232.246	−	232.246i	−0.315124	−	0.315124i
$738$	−629.908	+	629.908i	−0.853534	+	0.853534i
$739$			1089.24i			1.47393i	0.675930	+	0.736966i	$0.263742\pi$
$739$			1089.24i			1.47393i	−0.675930	+	0.736966i	$0.736258\pi$
$740$	11.9880	+	0.00269236i	0.0162000	+	3.63832e-6i
$741$	−1703.64			−2.29911
$742$	1268.64	+	1268.64i	1.70976	+	1.70976i
$743$	898.533	−	898.533i	1.20933	−	1.20933i	0.238087	−	0.971244i	$-0.423480\pi$
$743$	898.533	−	898.533i	1.20933	−	1.20933i	0.971244	−	0.238087i	$-0.0765203\pi$
$744$		−	628.248i		−	0.844419i
$745$	939.068	−	938.646i	1.26049	−	1.25993i
$746$	−263.215			−0.352835
$747$	−1125.69	−	1125.69i	−1.50695	−	1.50695i
$748$	80.5946	−	80.5946i	0.107747	−	0.107747i
$749$			416.736i			0.556390i
$750$	627.967	−	627.121i	0.837289	−	0.836162i
$751$	−706.083			−0.940190			−0.470095	−	0.882616i	$-0.655780\pi$
$751$	−706.083			−0.940190			−0.470095	+	0.882616i	$0.655780\pi$
$752$	−64.7209	−	64.7209i	−0.0860650	−	0.0860650i
$753$	−876.315	+	876.315i	−1.16377	+	1.16377i
$754$			248.749i			0.329906i
$755$	689.811	+	690.121i	0.913657	+	0.914067i
$756$	−968.271			−1.28078
$757$	−51.7068	−	51.7068i	−0.0683049	−	0.0683049i	0.672129	−	0.740434i	$-0.265380\pi$
$757$	−51.7068	−	51.7068i	−0.0683049	−	0.0683049i	−0.740434	+	0.672129i	$0.765380\pi$
$758$	204.936	−	204.936i	0.270364	−	0.270364i
$759$			170.220i			0.224269i
$760$	−0.109529	+	487.692i	−0.000144118	+	0.641700i
$761$	890.543			1.17023			0.585114	−	0.810951i	$-0.301050\pi$
$761$	890.543			1.17023			0.585114	+	0.810951i	$0.301050\pi$
$762$	−969.170	−	969.170i	−1.27188	−	1.27188i
$763$	801.545	−	801.545i	1.05052	−	1.05052i
$764$			377.465i			0.494065i
$765$	−653.085	−	0.146675i	−0.853706	−	0.000191732i
$766$	−392.967			−0.513011
$767$	−272.822	−	272.822i	−0.355700	−	0.355700i
$768$	−56.7988	+	56.7988i	−0.0739568	+	0.0739568i
$769$		−	488.299i		−	0.634979i	−0.948262	−	0.317489i	$-0.897160\pi$
$769$		−	488.299i		−	0.634979i	0.948262	−	0.317489i	$-0.102840\pi$
$770$	−473.304	+	473.092i	−0.614681	+	0.614405i
$771$	−697.548			−0.904732
$772$	−293.582	−	293.582i	−0.380288	−	0.380288i
$773$	606.134	−	606.134i	0.784132	−	0.784132i	−0.196393	−	0.980525i	$-0.562923\pi$
$773$	606.134	−	606.134i	0.784132	−	0.784132i	0.980525	+	0.196393i	$0.0629228\pi$
$774$		−	671.398i		−	0.867439i
$775$	−0.496828	+	1106.09i	−0.000641069	+	1.42722i
$776$	119.472			0.153959
$777$	56.9676	+	56.9676i	0.0733173	+	0.0733173i
$778$	542.460	−	542.460i	0.697250	−	0.697250i
$779$			1340.56i			1.72087i
$780$	349.249	+	349.406i	0.447755	+	0.447956i
$781$	−356.591			−0.456582
$782$	−38.6583	−	38.6583i	−0.0494351	−	0.0494351i
$783$	457.115	−	457.115i	0.583799	−	0.583799i
$784$		−	520.772i		−	0.664250i
$785$	−0.308754	+	1374.76i	−0.000393317	+	1.75129i
$786$	−536.150			−0.682125
$787$	−9.33333	−	9.33333i	−0.0118594	−	0.0118594i	0.701152	−	0.713012i	$-0.252669\pi$
$787$	−9.33333	−	9.33333i	−0.0118594	−	0.0118594i	−0.713012	+	0.701152i	$0.752669\pi$
$788$	234.149	−	234.149i	0.297143	−	0.297143i
$789$			1007.88i			1.27741i
$790$	71.5153	+	0.0160614i	0.0905257	+	2.03309e-5i
$791$	538.443			0.680712
$792$	229.120	+	229.120i	0.289294	+	0.289294i
$793$	71.1934	−	71.1934i	0.0897773	−	0.0897773i
$794$		−	353.784i		−	0.445572i
$795$	−1682.54	+	1681.78i	−2.11640	+	2.11545i
$796$	−142.199			−0.178642
$797$	584.178	+	584.178i	0.732971	+	0.732971i	0.971207	−	0.238236i	$-0.0765692\pi$
$797$	584.178	+	584.178i	0.732971	+	0.732971i	−0.238236	+	0.971207i	$0.576569\pi$
$798$	−2317.53	+	2317.53i	−2.90417	+	2.90417i
$799$		−	184.450i		−	0.230851i
$800$	100.045	−	99.9551i	0.125056	−	0.124944i
$801$	885.056			1.10494
$802$	−734.716	−	734.716i	−0.916105	−	0.916105i
$803$	−470.354	+	470.354i	−0.585746	+	0.585746i
$804$			466.461i			0.580175i
$805$	226.925	+	227.027i	0.281894	+	0.282021i
$806$	−615.714			−0.763914
$807$	456.775	+	456.775i	0.566017	+	0.566017i
$808$	−71.7059	+	71.7059i	−0.0887450	+	0.0887450i
$809$		−	1601.21i		−	1.97924i	−0.143703	−	0.989621i	$-0.545901\pi$
$809$		−	1601.21i		−	1.97924i	0.143703	−	0.989621i	$-0.454099\pi$
$810$	0.0567464	−	252.670i	7.00573e−5	−	0.311938i
$811$	698.505			0.861289			0.430644	−	0.902522i	$-0.358286\pi$
$811$	698.505			0.861289			0.430644	+	0.902522i	$0.358286\pi$
$812$	338.384	+	338.384i	0.416729	+	0.416729i
$813$	6.31997	−	6.31997i	0.00777364	−	0.00777364i
$814$		−	11.9860i		−	0.0147248i
$815$	−744.363	−	0.167175i	−0.913329	−	0.000205122i
$816$	−161.872			−0.198373
$817$	−714.429	−	714.429i	−0.874454	−	0.874454i
$818$	153.786	−	153.786i	0.188003	−	0.188003i
$819$			2134.49i			2.60622i
$820$	274.940	−	274.817i	0.335293	−	0.335142i
$821$	770.534			0.938531			0.469266	−	0.883057i	$-0.344519\pi$
$821$	770.534			0.938531			0.469266	+	0.883057i	$0.344519\pi$
$822$	928.619	+	928.619i	1.12971	+	1.12971i
$823$	539.421	−	539.421i	0.655432	−	0.655432i	−0.298864	−	0.954296i	$-0.596608\pi$
$823$	539.421	−	539.421i	0.655432	−	0.655432i	0.954296	+	0.298864i	$0.0966076\pi$
$824$		−	474.843i		−	0.576266i
$825$	−627.158	−	627.721i	−0.760191	−	0.760875i
$826$	−742.260			−0.898620
$827$	334.622	+	334.622i	0.404622	+	0.404622i	0.879858	−	0.475236i	$-0.157637\pi$
$827$	334.622	+	334.622i	0.404622	+	0.404622i	−0.475236	+	0.879858i	$0.657637\pi$
$828$	109.901	−	109.901i	0.132730	−	0.132730i
$829$			11.0088i			0.0132796i	0.999978	+	0.00663979i	$0.00211353\pi$
$829$			11.0088i			0.0132796i	−0.999978	+	0.00663979i	$0.997886\pi$
$830$	491.116	+	491.337i	0.591706	+	0.591972i
$831$	−832.113			−1.00134
$832$	55.6657	+	55.6657i	0.0669059	+	0.0669059i
$833$	742.081	−	742.081i	0.890853	−	0.890853i
$834$		−	342.665i		−	0.410870i
$835$	0.151696	−	675.441i	0.000181671	−	0.808912i
$836$	487.610			0.583266
$837$	1131.47	+	1131.47i	1.35181	+	1.35181i
$838$	259.536	−	259.536i	0.309709	−	0.309709i
$839$		−	34.9755i		−	0.0416871i	−0.999783	−	0.0208436i	$-0.993365\pi$
$839$		−	34.9755i		−	0.0416871i	0.999783	−	0.0208436i	$-0.00663519\pi$
$840$	950.408	+	0.213449i	1.13144	+	0.000254107i
$841$	521.502			0.620097
$842$	113.209	+	113.209i	0.134453	+	0.134453i
$843$	−61.4584	+	61.4584i	−0.0729044	+	0.0729044i
$844$			125.369i			0.148542i
$845$	−255.204	+	255.090i	−0.302017	+	0.301881i
$846$	524.368			0.619820
$847$	−672.211	−	672.211i	−0.793638	−	0.793638i
$848$	−268.055	+	268.055i	−0.316102	+	0.316102i
$849$		−	965.071i		−	1.13671i
$850$	284.993	+	0.128011i	0.335285	+	0.000150602i
$851$	−5.74926			−0.00675588
$852$	358.102	+	358.102i	0.420308	+	0.420308i
$853$	−574.177	+	574.177i	−0.673127	+	0.673127i	−0.958436	−	0.285309i	$-0.907904\pi$
$853$	−574.177	+	574.177i	−0.673127	+	0.673127i	0.285309	+	0.958436i	$0.407904\pi$
$854$		−	193.694i		−	0.226808i
$855$	−1975.19	−	1976.08i	−2.31017	−	2.31120i
$856$	−88.0533			−0.102866
$857$	−698.376	−	698.376i	−0.814907	−	0.814907i	0.170458	−	0.985365i	$-0.445475\pi$
$857$	−698.376	−	698.376i	−0.814907	−	0.814907i	−0.985365	+	0.170458i	$0.945475\pi$
$858$	349.269	−	349.269i	0.407073	−	0.407073i
$859$		−	211.633i		−	0.246371i	−0.992384	−	0.123186i	$-0.960689\pi$
$859$		−	211.633i		−	0.246371i	0.992384	−	0.123186i	$-0.0393111\pi$
$860$	−0.0658004	+	292.984i	−7.65121e−5	+	0.340679i
$861$	2612.47			3.03422
$862$	−450.882	−	450.882i	−0.523065	−	0.523065i
$863$	1113.78	−	1113.78i	1.29060	−	1.29060i	0.356176	−	0.934419i	$-0.384080\pi$
$863$	1113.78	−	1113.78i	1.29060	−	1.29060i	0.934419	−	0.356176i	$-0.115920\pi$
$864$		−	204.589i		−	0.236792i
$865$	−696.931	−	0.156522i	−0.805700	−	0.000180950i
$866$	355.153			0.410108
$867$	795.267	+	795.267i	0.917263	+	0.917263i
$868$	−837.581	+	837.581i	−0.964955	+	0.964955i
$869$		−	71.5034i		−	0.0822824i
$870$	−448.783	+	448.581i	−0.515842	+	0.515611i
$871$	457.155			0.524863
$872$	169.361	+	169.361i	0.194221	+	0.194221i
$873$	−483.982	+	483.982i	−0.554389	+	0.554389i
$874$		−	233.889i		−	0.267607i
$875$	−1673.29	−	1.12740i	−1.91233	−	0.00128845i
$876$	944.695			1.07842
$877$	−910.352	−	910.352i	−1.03803	−	1.03803i	−0.999248	−	0.0387817i	$-0.987652\pi$
$877$	−910.352	−	910.352i	−1.03803	−	1.03803i	−0.0387817	−	0.999248i	$-0.512348\pi$
$878$	713.713	−	713.713i	0.812884	−	0.812884i
$879$			1923.06i			2.18778i
$880$	−99.9609	−	100.006i	−0.113592	−	0.113643i
$881$	1332.24			1.51219			0.756093	−	0.654465i	$-0.227106\pi$
$881$	1332.24			1.51219			0.756093	+	0.654465i	$0.227106\pi$
$882$	2109.64	+	2109.64i	2.39189	+	2.39189i
$883$	−63.8806	+	63.8806i	−0.0723450	+	0.0723450i	−0.742353	−	0.670008i	$-0.766290\pi$
$883$	−63.8806	+	63.8806i	−0.0723450	+	0.0723450i	0.670008	+	0.742353i	$0.266290\pi$
$884$			158.643i			0.179461i
$885$	0.221040	−	984.204i	0.000249762	−	1.11210i
$886$	−558.585			−0.630457
$887$	174.929	+	174.929i	0.197214	+	0.197214i	0.798805	−	0.601591i	$-0.205466\pi$
$887$	174.929	+	174.929i	0.197214	+	0.197214i	−0.601591	+	0.798805i	$0.705466\pi$
$888$	−12.0368	+	12.0368i	−0.0135550	+	0.0135550i
$889$			2584.20i			2.90686i
$890$	−386.220	−	0.0867401i	−0.433955	−	9.74607e-5i
$891$	−252.628			−0.283533
$892$	234.686	+	234.686i	0.263101	+	0.263101i
$893$	557.975	−	557.975i	0.624832	−	0.624832i
$894$			1885.36i			2.10890i
$895$	90.1230	−	90.0825i	0.100696	−	0.100651i
$896$	151.449			0.169028
$897$	−167.531	−	167.531i	−0.186769	−	0.186769i
$898$	541.558	−	541.558i	0.603071	−	0.603071i
$899$		−	790.834i		−	0.879682i
$900$	−0.363921	+	810.198i	−0.000404356	+	0.900220i
$901$	−763.936			−0.847875
$902$	−274.833	−	274.833i	−0.304692	−	0.304692i
$903$	−1392.27	+	1392.27i	−1.54183	+	1.54183i
$904$			113.769i			0.125851i
$905$	−1154.35	−	1154.87i	−1.27552	−	1.27610i
$906$	−1385.55			−1.52930
$907$	−642.379	−	642.379i	−0.708246	−	0.708246i	0.257920	−	0.966166i	$-0.416963\pi$
$907$	−642.379	−	642.379i	−0.708246	−	0.708246i	−0.966166	+	0.257920i	$0.916963\pi$
$908$	239.507	−	239.507i	0.263774	−	0.263774i
$909$		−	580.960i		−	0.639120i
$910$	0.209191	−	931.448i	0.000229881	−	1.02357i
$911$	−597.269			−0.655619			−0.327809	−	0.944744i	$-0.606310\pi$
$911$	−597.269			−0.655619			−0.327809	+	0.944744i	$0.606310\pi$
$912$	−489.677	−	489.677i	−0.536927	−	0.536927i
$913$	491.144	−	491.144i	0.537946	−	0.537946i
$914$			817.344i			0.894249i
$915$	256.830	+	0.0576808i	0.280689	+	6.30391e-5i
$916$	59.3878			0.0648338
$917$	714.797	+	714.797i	0.779495	+	0.779495i
$918$	291.531	−	291.531i	0.317572	−	0.317572i
$919$			854.011i			0.929283i	0.885499	+	0.464642i	$0.153817\pi$
$919$			854.011i			0.929283i	−0.885499	+	0.464642i	$0.846183\pi$
$920$	−47.9691	+	47.9475i	−0.0521403	+	0.0521169i
$921$	1700.25			1.84609
$922$	130.430	+	130.430i	0.141464	+	0.141464i
$923$	350.958	−	350.958i	0.380236	−	0.380236i
$924$		−	950.249i		−	1.02841i
$925$	21.2016	−	21.1825i	0.0229206	−	0.0229000i
$926$	−830.155			−0.896496
$927$	1923.59	+	1923.59i	2.07507	+	2.07507i
$928$	−71.4980	+	71.4980i	−0.0770453	+	0.0770453i
$929$			722.278i			0.777479i	0.921348	+	0.388740i	$0.127089\pi$
$929$			722.278i			0.777479i	−0.921348	+	0.388740i	$0.872911\pi$
$930$	−1110.35	−	1110.84i	−1.19392	−	1.19446i
$931$	4489.71			4.82245
$932$	149.810	+	149.810i	0.160740	+	0.160740i
$933$	−789.395	+	789.395i	−0.846082	+	0.846082i
$934$			233.671i			0.250183i
$935$	0.0639950	−	284.945i	6.84439e−5	−	0.304754i
$936$	−451.003			−0.481841
$937$	−329.995	−	329.995i	−0.352183	−	0.352183i	0.508738	−	0.860921i	$-0.330112\pi$
$937$	−329.995	−	329.995i	−0.352183	−	0.352183i	−0.860921	+	0.508738i	$0.830112\pi$
$938$	621.887	−	621.887i	0.662992	−	0.662992i
$939$			1733.38i			1.84599i
$940$	−228.823	−	0.0513907i	−0.243429	−	5.46710e-5i
$941$	−1606.78			−1.70752			−0.853761	−	0.520665i	$-0.825684\pi$
$941$	−1606.78			−1.70752			−0.853761	+	0.520665i	$0.825684\pi$
$942$	−1380.36	−	1380.36i	−1.46535	−	1.46535i
$943$	−131.827	+	131.827i	−0.139795	+	0.139795i
$944$		−	156.834i		−	0.166138i
$945$	−1712.06	+	1711.29i	−1.81171	+	1.81089i
$946$	292.935			0.309656
$947$	−151.840	−	151.840i	−0.160338	−	0.160338i	0.622379	−	0.782716i	$-0.286166\pi$
$947$	−151.840	−	151.840i	−0.160338	−	0.160338i	−0.782716	+	0.622379i	$0.786166\pi$
$948$	−71.8065	+	71.8065i	−0.0757452	+	0.0757452i
$949$		−	925.849i		−	0.975605i
$950$	861.738	+	862.512i	0.907092	+	0.907908i
$951$	1107.79			1.16487
$952$	215.809	+	215.809i	0.226690	+	0.226690i
$953$	−82.6477	+	82.6477i	−0.0867237	+	0.0867237i	−0.749138	−	0.662414i	$-0.769532\pi$
$953$	−82.6477	+	82.6477i	−0.0867237	+	0.0867237i	0.662414	+	0.749138i	$0.269532\pi$
$954$		−	2171.77i		−	2.27649i
$955$	667.121	+	667.421i	0.698556	+	0.698870i
$956$	427.979			0.447677
$957$	448.607	+	448.607i	0.468764	+	0.468764i
$958$	−426.572	+	426.572i	−0.445273	+	0.445273i
$959$		−	2476.07i		−	2.58193i
$960$	−0.0451003	+	200.814i	−4.69795e−5	+	0.209181i
$961$	996.504			1.03694
$962$	11.7967	+	11.7967i	0.0122627	+	0.0122627i
$963$	356.703	−	356.703i	0.370408	−	0.370408i
$964$			24.3161i			0.0252241i
$965$	−1037.97	−	0.233115i	−1.07562	−	0.000241570i
$966$	−455.800			−0.471842
$967$	824.740	+	824.740i	0.852885	+	0.852885i	0.990488	−	0.137602i	$-0.0439396\pi$
$967$	824.740	+	824.740i	0.852885	+	0.852885i	−0.137602	+	0.990488i	$0.543940\pi$
$968$	142.033	−	142.033i	0.146729	−	0.146729i
$969$		−	1395.54i		−	1.44019i
$970$	211.247	−	211.152i	0.217780	−	0.217682i
$971$	977.693			1.00689			0.503446	−	0.864026i	$-0.332065\pi$
$971$	977.693			1.00689			0.503446	+	0.864026i	$0.332065\pi$
$972$	−206.626	−	206.626i	−0.212578	−	0.212578i
$973$	−456.842	+	456.842i	−0.469519	+	0.469519i
$974$			258.950i			0.265863i
$975$	1235.06	+	0.554757i	1.26673	+	0.000568981i
$976$	40.9262			0.0419326
$977$	−459.402	−	459.402i	−0.470217	−	0.470217i	0.431768	−	0.901985i	$-0.357890\pi$
$977$	−459.402	−	459.402i	−0.470217	−	0.470217i	−0.901985	+	0.431768i	$0.857890\pi$
$978$	747.394	−	747.394i	0.764206	−	0.764206i
$979$			386.155i			0.394439i
$980$	−920.397	−	920.810i	−0.939180	−	0.939602i
$981$	−1372.16			−1.39873
$982$	−280.807	−	280.807i	−0.285954	−	0.285954i
$983$	−1286.10	+	1286.10i	−1.30834	+	1.30834i	−0.385723	+	0.922615i	$0.626048\pi$
$983$	−1286.10	+	1286.10i	−1.30834	+	1.30834i	−0.922615	+	0.385723i	$0.873952\pi$
$984$			551.995i			0.560971i
$985$	0.185922	−	827.840i	0.000188754	−	0.840447i
$986$	−203.764			−0.206657
$987$	−1087.38	−	1087.38i	−1.10170	−	1.10170i
$988$	−479.908	+	479.908i	−0.485737	+	0.485737i
$989$		−	140.510i		−	0.142073i
$990$	810.063	+	0.181930i	0.818246	+	0.000183768i
$991$	1070.39			1.08011			0.540054	−	0.841630i	$-0.318404\pi$
$991$	1070.39			1.08011			0.540054	+	0.841630i	$0.318404\pi$
$992$	−176.975	−	176.975i	−0.178402	−	0.178402i
$993$	−1190.45	+	1190.45i	−1.19884	+	1.19884i
$994$		−	954.845i		−	0.960609i
$995$	−251.432	+	251.319i	−0.252695	+	0.252582i
$996$	−986.452			−0.990414
$997$	348.585	+	348.585i	0.349634	+	0.349634i	0.859973	−	0.510339i	$-0.170480\pi$
$997$	348.585	+	348.585i	0.349634	+	0.349634i	−0.510339	+	0.859973i	$0.670480\pi$
$998$	−525.230	+	525.230i	−0.526282	+	0.526282i
$999$		−	43.3565i		−	0.0433999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.b.47.2	✓	24
5.3	odd	4	inner	230.3.f.b.93.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.b.47.2	✓	24	1.1	even	1	trivial
230.3.f.b.93.2	yes	24	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-3.54993 + 3.54993i) q^{3} +2.00000i q^{4} +(3.53474 + 3.53633i) q^{5} -7.09985 q^{6} +(9.46554 + 9.46554i) q^{7} +(-2.00000 + 2.00000i) q^{8} -16.2040i q^{9} +(-0.00158807 + 7.07107i) q^{10} +7.06989 q^{11} +(-7.09985 - 7.09985i) q^{12} +(-6.95822 + 6.95822i) q^{13} +18.9311i q^{14} +(-25.1018 - 0.00563754i) q^{15} -4.00000 q^{16} +(-5.69985 - 5.69985i) q^{17} +(16.2040 - 16.2040i) q^{18} -34.4850i q^{19} +(-7.07266 + 7.06948i) q^{20} -67.2040 q^{21} +(7.06989 + 7.06989i) q^{22} +(3.39116 - 3.39116i) q^{23} -14.1997i q^{24} +(-0.0112294 + 25.0000i) q^{25} -13.9164 q^{26} +(25.5736 + 25.5736i) q^{27} +(-18.9311 + 18.9311i) q^{28} -17.8745i q^{29} +(-25.0961 - 25.1074i) q^{30} +44.2437 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-25.0976 + 25.0976i) q^{33} -11.3997i q^{34} +(-0.0150320 + 66.9315i) q^{35} +32.4079 q^{36} +(-0.847681 - 0.847681i) q^{37} +(34.4850 - 34.4850i) q^{38} -49.4023i q^{39} +(-14.1421 - 0.00317614i) q^{40} -38.8737 q^{41} +(-67.2040 - 67.2040i) q^{42} +(20.7171 - 20.7171i) q^{43} +14.1398i q^{44} +(57.3025 - 57.2768i) q^{45} +6.78233 q^{46} +(16.1802 + 16.1802i) q^{47} +(14.1997 - 14.1997i) q^{48} +130.193i q^{49} +(-25.0112 + 24.9888i) q^{50} +40.4681 q^{51} +(-13.9164 - 13.9164i) q^{52} +(67.0136 - 67.0136i) q^{53} +51.1471i q^{54} +(24.9902 + 25.0014i) q^{55} -37.8622 q^{56} +(122.419 + 122.419i) q^{57} +(17.8745 - 17.8745i) q^{58} +39.2085i q^{59} +(0.0112751 - 50.2036i) q^{60} -10.2316 q^{61} +(44.2437 + 44.2437i) q^{62} +(153.379 - 153.379i) q^{63} -8.00000i q^{64} +(-49.2020 - 0.0110501i) q^{65} -50.1952 q^{66} +(-32.8500 - 32.8500i) q^{67} +(11.3997 - 11.3997i) q^{68} +24.0768i q^{69} +(-66.9465 + 66.9165i) q^{70} -50.4379 q^{71} +(32.4079 + 32.4079i) q^{72} +(-66.5292 + 66.5292i) q^{73} -1.69536i q^{74} +(-88.7083 - 88.7880i) q^{75} +68.9700 q^{76} +(66.9203 + 66.9203i) q^{77} +(49.4023 - 49.4023i) q^{78} -10.1138i q^{79} +(-14.1390 - 14.1453i) q^{80} -35.7329 q^{81} +(-38.8737 - 38.8737i) q^{82} +(69.4699 - 69.4699i) q^{83} -134.408i q^{84} +(0.00905177 - 40.3040i) q^{85} +41.4342 q^{86} +(63.4532 + 63.4532i) q^{87} +(-14.1398 + 14.1398i) q^{88} +54.6197i q^{89} +(114.579 + 0.0257331i) q^{90} -131.727 q^{91} +(6.78233 + 6.78233i) q^{92} +(-157.062 + 157.062i) q^{93} +32.3604i q^{94} +(121.950 - 121.896i) q^{95} +28.3994 q^{96} +(-29.8681 - 29.8681i) q^{97} +(-130.193 + 130.193i) q^{98} -114.560i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28}+ \cdots - 484 q^{98}+O(q^{100}) \) 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8 + 16 * q^10 - 8 * q^11 - 24 * q^13 - 24 * q^15 - 96 * q^16 - 12 * q^17 + 88 * q^18 + 24 * q^20 - 24 * q^21 - 8 * q^22 - 48 * q^25 - 48 * q^26 + 60 * q^27 - 16 * q^28 + 12 * q^30 + 12 * q^31 - 96 * q^32 + 92 * q^33 + 48 * q^35 + 176 * q^36 - 100 * q^37 + 56 * q^38 + 16 * q^40 + 116 * q^41 - 24 * q^42 - 120 * q^43 - 204 * q^45 + 56 * q^47 - 104 * q^50 + 176 * q^51 - 48 * q^52 - 192 * q^53 + 180 * q^55 - 32 * q^56 + 28 * q^58 + 72 * q^60 - 152 * q^61 + 12 * q^62 + 364 * q^63 + 40 * q^65 + 184 * q^66 + 72 * q^67 + 24 * q^68 - 100 * q^70 - 28 * q^71 + 176 * q^72 - 364 * q^73 + 276 * q^75 + 112 * q^76 - 92 * q^77 - 32 * q^78 - 16 * q^80 - 440 * q^81 + 116 * q^82 + 360 * q^83 + 232 * q^85 - 240 * q^86 + 176 * q^87 + 16 * q^88 - 84 * q^90 - 432 * q^91 + 192 * q^93 + 144 * q^95 - 432 * q^97 - 484 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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