LMFDB - Embedded newform 312.4.m.a.181.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,4,Mod(181,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.m (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.29
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33907 - 2.49136i) q^{2} +3.00000i q^{3} +(-4.41379 + 6.67222i) q^{4} +12.3731 q^{5} +(7.47409 - 4.01721i) q^{6} -26.6265i q^{7} +(22.5333 + 2.06180i) q^{8} -9.00000 q^{9} +(-16.5684 - 30.8259i) q^{10} -33.2518 q^{11} +(-20.0166 - 13.2414i) q^{12} +(46.5141 + 5.78242i) q^{13} +(-66.3362 + 35.6547i) q^{14} +37.1193i q^{15} +(-25.0369 - 58.8995i) q^{16} +16.3112 q^{17} +(12.0516 + 22.4223i) q^{18} -43.9139 q^{19} +(-54.6122 + 82.5560i) q^{20} +79.8794 q^{21} +(44.5265 + 82.8424i) q^{22} +60.7638 q^{23} +(-6.18539 + 67.5999i) q^{24} +28.0936 q^{25} +(-47.8795 - 123.627i) q^{26} -27.0000i q^{27} +(177.657 + 117.524i) q^{28} -218.423i q^{29} +(92.4777 - 49.7053i) q^{30} -12.9421i q^{31} +(-113.214 + 141.247i) q^{32} -99.7554i q^{33} +(-21.8418 - 40.6372i) q^{34} -329.452i q^{35} +(39.7241 - 60.0499i) q^{36} +295.814 q^{37} +(58.8037 + 109.405i) q^{38} +(-17.3473 + 139.542i) q^{39} +(278.807 + 25.5108i) q^{40} -241.804i q^{41} +(-106.964 - 199.009i) q^{42} -290.617i q^{43} +(146.766 - 221.863i) q^{44} -111.358 q^{45} +(-81.3669 - 151.385i) q^{46} -385.921i q^{47} +(176.699 - 75.1108i) q^{48} -365.968 q^{49} +(-37.6192 - 69.9913i) q^{50} +48.9337i q^{51} +(-243.885 + 284.830i) q^{52} +220.063i q^{53} +(-67.2668 + 36.1549i) q^{54} -411.428 q^{55} +(54.8983 - 599.981i) q^{56} -131.742i q^{57} +(-544.171 + 292.484i) q^{58} +310.241 q^{59} +(-247.668 - 163.837i) q^{60} -156.672i q^{61} +(-32.2434 + 17.3303i) q^{62} +239.638i q^{63} +(503.498 + 92.9181i) q^{64} +(575.524 + 71.5465i) q^{65} +(-248.527 + 133.579i) q^{66} -586.837 q^{67} +(-71.9943 + 108.832i) q^{68} +182.291i q^{69} +(-820.784 + 441.159i) q^{70} -1144.05i q^{71} +(-202.800 - 18.5562i) q^{72} +792.744i q^{73} +(-396.115 - 736.981i) q^{74} +84.2808i q^{75} +(193.827 - 293.003i) q^{76} +885.378i q^{77} +(370.880 - 143.639i) q^{78} -1067.92 q^{79} +(-309.785 - 728.769i) q^{80} +81.0000 q^{81} +(-602.423 + 323.793i) q^{82} +1488.87 q^{83} +(-352.571 + 532.972i) q^{84} +201.820 q^{85} +(-724.033 + 389.156i) q^{86} +655.269 q^{87} +(-749.273 - 68.5585i) q^{88} -216.421i q^{89} +(149.116 + 277.433i) q^{90} +(153.965 - 1238.51i) q^{91} +(-268.199 + 405.429i) q^{92} +38.8262 q^{93} +(-961.469 + 516.774i) q^{94} -543.351 q^{95} +(-423.740 - 339.642i) q^{96} -789.333i q^{97} +(490.056 + 911.759i) q^{98} +299.266 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.33907	−	2.49136i	−0.473432	−	0.880830i
$2$	−1.33907	−	2.49136i	−0.473432	−	0.880830i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−4.41379	+	6.67222i	−0.551724	+	0.834027i
$5$	12.3731			1.10668			0.553342	−	0.832954i	$-0.313352\pi$
$5$	12.3731			1.10668			0.553342	+	0.832954i	$0.313352\pi$
$6$	7.47409	−	4.01721i	0.508548	−	0.273336i
$7$		−	26.6265i		−	1.43769i	−0.695169	−	0.718847i	$-0.744670\pi$
$7$		−	26.6265i		−	1.43769i	0.695169	−	0.718847i	$-0.255330\pi$
$8$	22.5333	+	2.06180i	0.995840	+	0.0911194i
$9$	−9.00000			−0.333333
$10$	−16.5684	−	30.8259i	−0.523940	−	0.974800i
$11$	−33.2518			−0.911436			−0.455718	−	0.890124i	$-0.650617\pi$
$11$	−33.2518			−0.911436			−0.455718	+	0.890124i	$0.650617\pi$
$12$	−20.0166	−	13.2414i	−0.481526	−	0.318538i
$13$	46.5141	+	5.78242i	0.992361	+	0.123366i
$13$	46.5141	+	5.78242i	0.992361	+	0.123366i
$14$	−66.3362	+	35.6547i	−1.26636	+	0.680651i
$15$			37.1193i			0.638944i
$16$	−25.0369	−	58.8995i	−0.391202	−	0.920305i
$17$	16.3112			0.232709			0.116354	−	0.993208i	$-0.462879\pi$
$17$	16.3112			0.232709			0.116354	+	0.993208i	$0.462879\pi$
$18$	12.0516	+	22.4223i	0.157811	+	0.293610i
$19$	−43.9139			−0.530239			−0.265119	−	0.964216i	$-0.585411\pi$
$19$	−43.9139			−0.530239			−0.265119	+	0.964216i	$0.585411\pi$
$20$	−54.6122	+	82.5560i	−0.610583	+	0.923004i
$21$	79.8794			0.830053
$22$	44.5265	+	82.8424i	0.431503	+	0.802821i
$23$	60.7638			0.550875			0.275438	−	0.961319i	$-0.411177\pi$
$23$	60.7638			0.550875			0.275438	+	0.961319i	$0.411177\pi$
$24$	−6.18539	+	67.5999i	−0.0526078	+	0.574948i
$25$	28.0936			0.224749
$26$	−47.8795	−	123.627i	−0.361152	−	0.932507i
$27$		−	27.0000i		−	0.192450i
$28$	177.657	+	117.524i	1.19908	+	0.793209i
$29$		−	218.423i		−	1.39863i	−0.714816	−	0.699313i	$-0.753489\pi$
$29$		−	218.423i		−	1.39863i	0.714816	−	0.699313i	$-0.246511\pi$
$30$	92.4777	−	49.7053i	0.562801	−	0.302497i
$31$		−	12.9421i		−	0.0749827i	−0.999297	−	0.0374914i	$-0.988063\pi$
$31$		−	12.9421i		−	0.0749827i	0.999297	−	0.0374914i	$-0.0119367\pi$
$32$	−113.214	+	141.247i	−0.625424	+	0.780285i
$33$		−	99.7554i		−	0.526218i
$34$	−21.8418	−	40.6372i	−0.110172	−	0.204977i
$35$		−	329.452i		−	1.59107i
$36$	39.7241	−	60.0499i	0.183908	−	0.278009i
$37$	295.814			1.31437			0.657183	−	0.753731i	$-0.271748\pi$
$37$	295.814			1.31437			0.657183	+	0.753731i	$0.271748\pi$
$38$	58.8037	+	109.405i	0.251032	+	0.467050i
$39$	−17.3473	+	139.542i	−0.0712252	+	0.572940i
$40$	278.807	+	25.5108i	1.10208	+	0.100840i
$41$		−	241.804i		−	0.921061i	−0.887644	−	0.460530i	$-0.847659\pi$
$41$		−	241.804i		−	0.921061i	0.887644	−	0.460530i	$-0.152341\pi$
$42$	−106.964	−	199.009i	−0.392974	−	0.731135i
$43$		−	290.617i		−	1.03067i	−0.856990	−	0.515333i	$-0.827668\pi$
$43$		−	290.617i		−	1.03067i	0.856990	−	0.515333i	$-0.172332\pi$
$44$	146.766	−	221.863i	0.502861	−	0.760162i
$45$	−111.358			−0.368895
$46$	−81.3669	−	151.385i	−0.260802	−	0.485227i
$47$		−	385.921i		−	1.19771i	−0.800858	−	0.598854i	$-0.795623\pi$
$47$		−	385.921i		−	1.19771i	0.800858	−	0.598854i	$-0.204377\pi$
$48$	176.699	−	75.1108i	0.531338	−	0.225861i
$49$	−365.968			−1.06696
$50$	−37.6192	−	69.9913i	−0.106403	−	0.197965i
$51$			48.9337i			0.134355i
$52$	−243.885	+	284.830i	−0.650399	+	0.759592i
$53$			220.063i			0.570338i	0.958477	+	0.285169i	$0.0920498\pi$
$53$			220.063i			0.570338i	−0.958477	+	0.285169i	$0.907950\pi$
$54$	−67.2668	+	36.1549i	−0.169516	+	0.0911121i
$55$	−411.428			−1.00867
$56$	54.8983	−	599.981i	0.131002	−	1.43171i
$57$		−	131.742i		−	0.306133i
$58$	−544.171	+	292.484i	−1.23195	+	0.662155i
$59$	310.241			0.684575			0.342288	−	0.939595i	$-0.388798\pi$
$59$	310.241			0.684575			0.342288	+	0.939595i	$0.388798\pi$
$60$	−247.668	−	163.837i	−0.532897	−	0.352521i
$61$		−	156.672i		−	0.328848i	−0.986390	−	0.164424i	$-0.947423\pi$
$61$		−	156.672i		−	0.328848i	0.986390	−	0.164424i	$-0.0525766\pi$
$62$	−32.2434	+	17.3303i	−0.0660470	+	0.0354992i
$63$			239.638i			0.479231i
$64$	503.498	+	92.9181i	0.983395	+	0.181481i
$65$	575.524	+	71.5465i	1.09823	+	0.136527i
$66$	−248.527	+	133.579i	−0.463509	+	0.249129i
$67$	−586.837			−1.07005			−0.535027	−	0.844835i	$-0.679699\pi$
$67$	−586.837			−1.07005			−0.535027	+	0.844835i	$0.679699\pi$
$68$	−71.9943	+	108.832i	−0.128391	+	0.194086i
$69$			182.291i			0.318048i
$70$	−820.784	+	441.159i	−1.40146	+	0.753265i
$71$		−	1144.05i		−	1.91231i	−0.292857	−	0.956156i	$-0.594606\pi$
$71$		−	1144.05i		−	1.91231i	0.292857	−	0.956156i	$-0.405394\pi$
$72$	−202.800	−	18.5562i	−0.331947	−	0.0303731i
$73$			792.744i			1.27101i	0.772097	+	0.635505i	$0.219208\pi$
$73$			792.744i			1.27101i	−0.772097	+	0.635505i	$0.780792\pi$
$74$	−396.115	−	736.981i	−0.622263	−	1.15773i
$75$			84.2808i			0.129759i
$76$	193.827	−	293.003i	0.292545	−	0.442233i
$77$			885.378i			1.31037i
$78$	370.880	−	143.639i	0.538383	−	0.208511i
$79$	−1067.92			−1.52090			−0.760449	−	0.649398i	$-0.775021\pi$
$79$	−1067.92			−1.52090			−0.760449	+	0.649398i	$0.775021\pi$
$80$	−309.785	−	728.769i	−0.432937	−	1.01849i
$81$	81.0000			0.111111
$82$	−602.423	+	323.793i	−0.811298	+	0.436060i
$83$	1488.87			1.96897			0.984484	−	0.175474i	$-0.0561457\pi$
$83$	1488.87			1.96897			0.984484	+	0.175474i	$0.0561457\pi$
$84$	−352.571	+	532.972i	−0.457960	+	0.692286i
$85$	201.820			0.257535
$86$	−724.033	+	389.156i	−0.907842	+	0.487951i
$87$	655.269			0.807497
$88$	−749.273	−	68.5585i	−0.907645	−	0.0830495i
$89$		−	216.421i		−	0.257759i	−0.991660	−	0.128879i	$-0.958862\pi$
$89$		−	216.421i		−	0.257759i	0.991660	−	0.128879i	$-0.0411380\pi$
$90$	149.116	+	277.433i	0.174647	+	0.324933i
$91$	153.965	−	1238.51i	0.177362	−	1.42671i
$92$	−268.199	+	405.429i	−0.303931	+	0.459445i
$93$	38.8262			0.0432913
$94$	−961.469	+	516.774i	−1.05498	+	0.567034i
$95$	−543.351			−0.586806
$96$	−423.740	−	339.642i	−0.450498	−	0.361089i
$97$		−	789.333i		−	0.826233i	−0.910678	−	0.413116i	$-0.864440\pi$
$97$		−	789.333i		−	0.826233i	0.910678	−	0.413116i	$-0.135560\pi$
$98$	490.056	+	911.759i	0.505134	+	0.939812i
$99$	299.266			0.303812
$100$	−123.999	+	187.446i	−0.123999	+	0.187446i
$101$		−	330.153i		−	0.325262i	−0.986687	−	0.162631i	$-0.948002\pi$
$101$		−	330.153i		−	0.325262i	0.986687	−	0.162631i	$-0.0519980\pi$
$102$	121.912	−	65.5255i	0.118344	−	0.0636078i
$103$	1253.95			1.19957			0.599786	−	0.800161i	$-0.295253\pi$
$103$	1253.95			1.19957			0.599786	+	0.800161i	$0.295253\pi$
$104$	1036.19	+	226.200i	0.976992	+	0.213276i
$105$	988.355			0.918606
$106$	548.256	−	294.679i	0.502371	−	0.270017i
$107$		−	338.058i		−	0.305433i	−0.988270	−	0.152716i	$-0.951198\pi$
$107$		−	338.058i		−	0.305433i	0.988270	−	0.152716i	$-0.0488021\pi$
$108$	180.150	+	119.172i	0.160509	+	0.106179i
$109$	2042.84			1.79512			0.897560	−	0.440892i	$-0.145338\pi$
$109$	2042.84			1.79512			0.897560	+	0.440892i	$0.145338\pi$
$110$	550.930	+	1025.02i	0.477538	+	0.888468i
$111$			887.442i			0.758849i
$112$	−1568.28	+	666.645i	−1.32312	+	0.562429i
$113$	698.175			0.581228			0.290614	−	0.956840i	$-0.406140\pi$
$113$	698.175			0.581228			0.290614	+	0.956840i	$0.406140\pi$
$114$	−328.216	+	176.411i	−0.269652	+	0.144933i
$115$	751.836			0.609644
$116$	1457.37	+	964.073i	1.16649	+	0.771655i
$117$	−418.627	−	52.0418i	−0.330787	−	0.0411219i
$118$	−415.434	−	772.923i	−0.324100	−	0.602994i
$119$		−	434.310i		−	0.334564i
$120$	−76.5324	+	836.420i	−0.0582202	+	0.636286i
$121$	−225.317			−0.169284
$122$	−390.326	+	209.794i	−0.289660	+	0.155687i
$123$	725.413			0.531775
$124$	86.3523	+	57.1236i	0.0625376	+	0.0413697i
$125$	−1199.03			−0.857958
$126$	597.026	−	320.892i	0.422121	−	0.226884i
$127$	−2143.64			−1.49777			−0.748887	−	0.662698i	$-0.769411\pi$
$127$	−2143.64			−1.49777			−0.748887	+	0.662698i	$0.769411\pi$
$128$	−442.726	−	1378.82i	−0.305717	−	0.952122i
$129$	871.851			0.595056
$130$	−592.418	−	1529.65i	−0.399681	−	1.03199i
$131$			737.484i			0.491865i	0.969287	+	0.245932i	$0.0790941\pi$
$131$			737.484i			0.491865i	−0.969287	+	0.245932i	$0.920906\pi$
$132$	665.590	+	440.299i	0.438880	+	0.290327i
$133$			1169.27i			0.762321i
$134$	785.816	+	1462.03i	0.506598	+	0.942536i
$135$		−	334.074i		−	0.212981i
$136$	367.545	+	33.6304i	0.231741	+	0.0212043i
$137$		−	675.377i		−	0.421178i	−0.977575	−	0.210589i	$-0.932462\pi$
$137$		−	675.377i		−	0.421178i	0.977575	−	0.210589i	$-0.0675381\pi$
$138$	454.154	−	244.101i	0.280146	−	0.150574i
$139$			1169.92i			0.713894i	0.934125	+	0.356947i	$0.116182\pi$
$139$			1169.92i			0.713894i	−0.934125	+	0.356947i	$0.883818\pi$
$140$	2198.17	+	1454.13i	1.32700	+	0.877832i
$141$	1157.76			0.691497
$142$	−2850.25	+	1531.97i	−1.68442	+	0.905351i
$143$	−1546.68	−	192.276i	−0.904474	−	0.112440i
$144$	225.332	+	530.096i	0.130401	+	0.306768i
$145$		−	2702.57i		−	1.54784i
$146$	1975.01	−	1061.54i	1.11954	−	0.601737i
$147$		−	1097.90i		−	0.616011i
$148$	−1305.66	+	1973.74i	−0.725167	+	1.09622i
$149$	345.352			0.189881			0.0949407	−	0.995483i	$-0.469734\pi$
$149$	345.352			0.189881			0.0949407	+	0.995483i	$0.469734\pi$
$150$	209.974	−	112.858i	0.114295	−	0.0614320i
$151$			3320.28i			1.78941i	0.446659	+	0.894704i	$0.352614\pi$
$151$			3320.28i			1.78941i	−0.446659	+	0.894704i	$0.647386\pi$
$152$	−989.524	−	90.5415i	−0.528033	−	0.0483150i
$153$	−146.801			−0.0775696
$154$	2205.80	−	1185.58i	1.15421	−	0.620370i
$155$		−	160.134i		−	0.0829821i
$156$	−854.490	−	731.655i	−0.438551	−	0.375508i
$157$			1992.84i			1.01303i	0.862231	+	0.506515i	$0.169066\pi$
$157$			1992.84i			1.01303i	−0.862231	+	0.506515i	$0.830934\pi$
$158$	1430.03	+	2660.59i	0.720042	+	1.33965i
$159$	−660.188			−0.329285
$160$	−1400.81	+	1747.66i	−0.692147	+	0.863528i
$161$		−	1617.92i		−	0.791989i
$162$	−108.465	−	201.800i	−0.0526036	−	0.0978700i
$163$	1280.70			0.615411			0.307706	−	0.951482i	$-0.400439\pi$
$163$	1280.70			0.615411			0.307706	+	0.951482i	$0.400439\pi$
$164$	1613.37	+	1067.27i	0.768190	+	0.508171i
$165$		−	1234.28i		−	0.582357i
$166$	−1993.70	−	3709.31i	−0.932173	−	1.73433i
$167$			607.816i			0.281642i	0.990035	+	0.140821i	$0.0449742\pi$
$167$			607.816i			0.281642i	−0.990035	+	0.140821i	$0.955026\pi$
$168$	1799.94	+	164.695i	0.826600	+	0.0756339i
$169$	2130.13	+	537.928i	0.969562	+	0.244847i
$170$	−270.251	−	502.808i	−0.121925	−	0.226845i
$171$	395.225			0.176746
$172$	1939.06	+	1282.72i	0.859604	+	0.568643i
$173$			880.682i			0.387035i	0.981097	+	0.193517i	$0.0619896\pi$
$173$			880.682i			0.387035i	−0.981097	+	0.193517i	$0.938010\pi$
$174$	−877.451	−	1632.51i	−0.382295	−	0.711268i
$175$		−	748.032i		−	0.323120i
$176$	832.524	+	1958.52i	0.356556	+	0.838799i
$177$			930.723i			0.395240i
$178$	−539.182	+	289.802i	−0.227042	+	0.122031i
$179$			592.328i			0.247333i	0.992324	+	0.123667i	$0.0394654\pi$
$179$			592.328i			0.247333i	−0.992324	+	0.123667i	$0.960535\pi$
$180$	491.510	−	743.004i	0.203528	−	0.307668i
$181$			4237.05i			1.73999i	0.493062	+	0.869994i	$0.335877\pi$
$181$			4237.05i			1.73999i	−0.493062	+	0.869994i	$0.664123\pi$
$182$	−3291.74	+	1274.86i	−1.34066	+	0.519225i
$183$	470.015			0.189861
$184$	1369.21	+	125.283i	0.548583	+	0.0501954i
$185$	3660.14			1.45459
$186$	−51.9910	−	96.7302i	−0.0204955	−	0.0381323i
$187$	−542.378			−0.212099
$188$	2574.95	+	1703.37i	0.998921	+	0.660804i
$189$	−718.914			−0.276684
$190$	727.584	+	1353.68i	0.277813	+	0.516877i
$191$	−3247.76			−1.23037			−0.615183	−	0.788385i	$-0.710918\pi$
$191$	−3247.76			−1.23037			−0.615183	+	0.788385i	$0.710918\pi$
$192$	−278.754	+	1510.49i	−0.104778	+	0.567763i
$193$			3309.31i			1.23424i	0.786868	+	0.617122i	$0.211701\pi$
$193$			3309.31i			1.23424i	−0.786868	+	0.617122i	$0.788299\pi$
$194$	−1966.52	+	1056.97i	−0.727771	+	0.391165i
$195$	−214.639	+	1726.57i	−0.0788238	+	0.634063i
$196$	1615.31	−	2441.82i	0.588668	−	0.889875i
$197$	−927.123			−0.335304			−0.167652	−	0.985846i	$-0.553618\pi$
$197$	−927.123			−0.335304			−0.167652	+	0.985846i	$0.553618\pi$
$198$	−400.738	−	745.581i	−0.143834	−	0.267607i
$199$	−2866.60			−1.02114			−0.510572	−	0.859835i	$-0.670566\pi$
$199$	−2866.60			−1.02114			−0.510572	+	0.859835i	$0.670566\pi$
$200$	633.041	+	57.9233i	0.223814	+	0.0204790i
$201$		−	1760.51i		−	0.617796i
$202$	−822.532	+	442.098i	−0.286501	+	0.153990i
$203$	−5815.83			−2.01079
$204$	−326.496	−	215.983i	−0.112055	−	0.0741266i
$205$		−	2991.87i		−	1.01932i
$206$	−1679.13	−	3124.06i	−0.567916	−	1.05662i
$207$	−546.874			−0.183625
$208$	−823.990	−	2884.43i	−0.274680	−	0.961536i
$209$	1460.22			0.483279
$210$	−1323.48	−	2462.35i	−0.434898	−	0.809136i
$211$			2889.60i			0.942788i	0.881923	+	0.471394i	$0.156249\pi$
$211$			2889.60i			0.942788i	−0.881923	+	0.471394i	$0.843751\pi$
$212$	−1468.31	−	971.310i	−0.475678	−	0.314669i
$213$	3432.16			1.10407
$214$	−842.226	+	452.683i	−0.269035	+	0.144602i
$215$		−	3595.83i		−	1.14062i
$216$	55.6685	−	608.399i	0.0175359	−	0.191649i
$217$	−344.601			−0.107802
$218$	−2735.50	−	5089.45i	−0.849868	−	1.58120i
$219$	−2378.23			−0.733818
$220$	1815.96	−	2745.14i	0.556508	−	0.841259i
$221$	758.702	+	94.3183i	0.230931	+	0.0287083i
$222$	2210.94	−	1188.35i	0.668417	−	0.359264i
$223$		−	2734.42i		−	0.821122i	−0.911833	−	0.410561i	$-0.865333\pi$
$223$		−	2734.42i		−	0.821122i	0.911833	−	0.410561i	$-0.134667\pi$
$224$	3760.90	+	3014.48i	1.12181	+	0.899168i
$225$	−252.842			−0.0749162
$226$	−934.904	−	1739.41i	−0.275172	−	0.511963i
$227$	−5723.82			−1.67358			−0.836792	−	0.547522i	$-0.815571\pi$
$227$	−5723.82			−1.67358			−0.836792	+	0.547522i	$0.815571\pi$
$228$	879.009	+	581.480i	0.255324	+	0.168901i
$229$	−1732.49			−0.499940			−0.249970	−	0.968254i	$-0.580421\pi$
$229$	−1732.49			−0.499940			−0.249970	+	0.968254i	$0.580421\pi$
$230$	−1006.76	−	1873.10i	−0.288625	−	0.536993i
$231$	−2656.13			−0.756540
$232$	450.344	−	4921.79i	0.127442	−	1.39281i
$233$	−215.288			−0.0605321			−0.0302661	−	0.999542i	$-0.509635\pi$
$233$	−215.288			−0.0605321			−0.0302661	+	0.999542i	$0.509635\pi$
$234$	430.916	+	1112.64i	0.120384	+	0.310836i
$235$		−	4775.03i		−	1.32548i
$236$	−1369.34	+	2069.99i	−0.377696	+	0.570954i
$237$		−	3203.77i		−	0.878091i
$238$	−1082.02	+	581.571i	−0.294694	+	0.158393i
$239$			1089.11i			0.294765i	0.989080	+	0.147382i	$0.0470848\pi$
$239$			1089.11i			0.294765i	−0.989080	+	0.147382i	$0.952915\pi$
$240$	2186.31	−	929.354i	0.588023	−	0.249956i
$241$			662.017i			0.176947i	0.996079	+	0.0884736i	$0.0281989\pi$
$241$			662.017i			0.176947i	−0.996079	+	0.0884736i	$0.971801\pi$
$242$	301.715	+	561.347i	0.0801445	+	0.149110i
$243$			243.000i			0.0641500i
$244$	1045.35	+	691.516i	0.274268	+	0.181433i
$245$	−4528.16			−1.18079
$246$	−971.378	−	1807.27i	−0.251759	−	0.468403i
$247$	−2042.62	−	253.928i	−0.526188	−	0.0654133i
$248$	26.6839	−	291.627i	0.00683238	−	0.0746708i
$249$			4466.60i			1.13678i
$250$	1605.59	+	2987.23i	0.406185	+	0.755715i
$251$		−	3890.75i		−	0.978414i	−0.872168	−	0.489207i	$-0.837286\pi$
$251$		−	3890.75i		−	0.978414i	0.872168	−	0.489207i	$-0.162714\pi$
$252$	−1598.92	−	1057.71i	−0.399692	−	0.264403i
$253$	−2020.51			−0.502088
$254$	2870.48	+	5340.59i	0.709095	+	1.31928i
$255$			605.461i			0.148688i
$256$	−2842.30	+	2949.33i	−0.693922	+	0.720050i
$257$	5412.97			1.31382			0.656910	−	0.753969i	$-0.271863\pi$
$257$	5412.97			1.31382			0.656910	+	0.753969i	$0.271863\pi$
$258$	−1167.47	−	2172.10i	−0.281719	−	0.524143i
$259$		−	7876.48i		−	1.88965i
$260$	−3017.61	+	3524.23i	−0.719786	+	0.840628i
$261$			1965.81i			0.466209i
$262$	1837.34	−	987.542i	0.433249	−	0.232865i
$263$	4583.78			1.07471			0.537354	−	0.843357i	$-0.319424\pi$
$263$	4583.78			1.07471			0.537354	+	0.843357i	$0.319424\pi$
$264$	205.675	−	2247.82i	0.0479487	−	0.524029i
$265$			2722.86i			0.631184i
$266$	2913.08	−	1565.73i	0.671475	−	0.360907i
$267$	649.262			0.148817
$268$	2590.18	−	3915.51i	0.590374	−	0.892454i
$269$		−	7190.74i		−	1.62984i	−0.579574	−	0.814920i	$-0.696781\pi$
$269$		−	7190.74i		−	1.62984i	0.579574	−	0.814920i	$-0.303219\pi$
$270$	−832.299	+	447.348i	−0.187600	+	0.100832i
$271$			4023.60i			0.901906i	0.892548	+	0.450953i	$0.148916\pi$
$271$			4023.60i			0.901906i	−0.892548	+	0.450953i	$0.851084\pi$
$272$	−408.383	−	960.723i	−0.0910362	−	0.214163i
$273$	3715.52	+	461.896i	0.823712	+	0.102400i
$274$	−1682.61	+	904.376i	−0.370986	+	0.199399i
$275$	−934.163			−0.204844
$276$	−1216.29	−	804.596i	−0.265261	−	0.175475i
$277$			4021.05i			0.872208i	0.899896	+	0.436104i	$0.143642\pi$
$277$			4021.05i			0.872208i	−0.899896	+	0.436104i	$0.856358\pi$
$278$	2914.69	−	1566.60i	0.628819	−	0.337980i
$279$			116.479i			0.0249942i
$280$	679.262	−	7423.63i	0.144977	−	1.58445i
$281$			3305.74i			0.701794i	0.936414	+	0.350897i	$0.114123\pi$
$281$			3305.74i			0.701794i	−0.936414	+	0.350897i	$0.885877\pi$
$282$	−1550.32	−	2884.41i	−0.327377	−	0.609092i
$283$		−	1829.42i		−	0.384268i	−0.981369	−	0.192134i	$-0.938459\pi$
$283$		−	1829.42i		−	0.384268i	0.981369	−	0.192134i	$-0.0615409\pi$
$284$	7633.37	+	5049.61i	1.59492	+	1.05507i
$285$		−	1630.05i		−	0.338793i
$286$	1592.08	+	4110.81i	0.329167	+	0.849921i
$287$	−6438.39			−1.32420
$288$	1018.93	−	1271.22i	0.208475	−	0.260095i
$289$	−4646.94			−0.945847
$290$	−6733.09	+	3618.93i	−1.36338	+	0.732796i
$291$	2368.00			0.477026
$292$	−5289.36	−	3499.00i	−1.06006	−	0.701246i
$293$	2987.24			0.595620			0.297810	−	0.954625i	$-0.403744\pi$
$293$	2987.24			0.595620			0.297810	+	0.954625i	$0.403744\pi$
$294$	−2735.28	+	1470.17i	−0.542601	+	0.291639i
$295$	3838.64			0.757608
$296$	6665.66	+	609.908i	1.30890	+	0.119764i
$297$			897.799i			0.175406i
$298$	−462.450	−	860.398i	−0.0898960	−	0.167253i
$299$	2826.37	+	351.362i	0.546667	+	0.0679591i
$300$	−562.339	−	371.997i	−0.108222	−	0.0715909i
$301$	−7738.10			−1.48178
$302$	8272.03	−	4446.09i	1.57617	−	0.847164i
$303$	990.460			0.187790
$304$	1099.47	+	2586.51i	0.207431	+	0.487981i
$305$		−	1938.51i		−	0.363931i
$306$	196.577	+	365.735i	0.0367240	+	0.0683257i
$307$	2216.84			0.412123			0.206061	−	0.978539i	$-0.433935\pi$
$307$	2216.84			0.412123			0.206061	+	0.978539i	$0.433935\pi$
$308$	−5907.43	−	3907.87i	−1.09288	−	0.722960i
$309$			3761.86i			0.692573i
$310$	−398.951	+	214.430i	−0.0730932	+	0.0392864i
$311$	5640.21			1.02838			0.514191	−	0.857676i	$-0.328092\pi$
$311$	5640.21			1.02838			0.514191	+	0.857676i	$0.328092\pi$
$312$	−678.599	+	3108.58i	−0.123135	+	0.564067i
$313$	9322.22			1.68346			0.841730	−	0.539899i	$-0.181537\pi$
$313$	9322.22			1.68346			0.841730	+	0.539899i	$0.181537\pi$
$314$	4964.88	−	2668.54i	0.892307	−	0.479601i
$315$			2965.07i			0.530357i
$316$	4713.59	−	7125.43i	0.839115	−	1.26847i
$317$	−5397.79			−0.956372			−0.478186	−	0.878259i	$-0.658705\pi$
$317$	−5397.79			−0.956372			−0.478186	+	0.878259i	$0.658705\pi$
$318$	884.037	+	1644.77i	0.155894	+	0.290044i
$319$			7262.96i			1.27476i
$320$	6229.83	+	1149.68i	1.08831	+	0.200842i
$321$	1014.17			0.176342
$322$	−4030.84	+	2166.51i	−0.697608	+	0.374953i
$323$	−716.289			−0.123391
$324$	−357.517	+	540.450i	−0.0613026	+	0.0926697i
$325$	1306.75	+	162.449i	0.223032	+	0.0277263i
$326$	−1714.94	−	3190.69i	−0.291356	−	0.542073i
$327$			6128.51i			1.03641i
$328$	498.551	−	5448.65i	0.0839265	−	0.917229i
$329$	−10275.7			−1.72194
$330$	−3075.05	+	1652.79i	−0.512957	+	0.275707i
$331$	3179.90			0.528046			0.264023	−	0.964516i	$-0.414951\pi$
$331$	3179.90			0.528046			0.264023	+	0.964516i	$0.414951\pi$
$332$	−6571.54	+	9934.04i	−1.08633	+	1.64217i
$333$	−2662.33			−0.438122
$334$	1514.29	−	813.908i	0.248079	−	0.133339i
$335$	−7261.00			−1.18421
$336$	−1999.93	−	4704.85i	−0.324718	−	0.763901i
$337$	−3425.43			−0.553694			−0.276847	−	0.960914i	$-0.589290\pi$
$337$	−3425.43			−0.553694			−0.276847	+	0.960914i	$0.589290\pi$
$338$	−1512.21	−	6027.25i	−0.243353	−	0.969938i
$339$			2094.52i			0.335572i
$340$	−890.792	+	1346.59i	−0.142088	+	0.214791i
$341$			430.347i			0.0683420i
$342$	−529.233	−	984.649i	−0.0836774	−	0.155683i
$343$			611.554i			0.0962706i
$344$	599.193	−	6548.55i	0.0939137	−	1.02638i
$345$			2255.51i			0.351978i
$346$	2194.10	−	1179.29i	0.340912	−	0.183235i
$347$			12219.0i			1.89035i	0.326558	+	0.945177i	$0.394111\pi$
$347$			12219.0i			1.89035i	−0.326558	+	0.945177i	$0.605889\pi$
$348$	−2892.22	+	4372.10i	−0.445515	+	0.673474i
$349$	5703.61			0.874805			0.437403	−	0.899266i	$-0.355898\pi$
$349$	5703.61			0.874805			0.437403	+	0.899266i	$0.355898\pi$
$350$	−1863.62	+	1001.67i	−0.284614	+	0.152975i
$351$	156.125	−	1255.88i	0.0237417	−	0.190980i
$352$	3764.57	−	4696.71i	0.570035	−	0.711180i
$353$		−	6902.30i		−	1.04071i	−0.853949	−	0.520357i	$-0.825799\pi$
$353$		−	6902.30i		−	1.04071i	0.853949	−	0.520357i	$-0.174201\pi$
$354$	2318.77	−	1246.30i	0.348139	−	0.187119i
$355$		−	14155.5i		−	2.11632i
$356$	1444.01	+	955.235i	0.214978	+	0.142212i
$357$	1302.93			0.193161
$358$	1475.70	−	793.168i	0.217859	−	0.117096i
$359$			5910.58i			0.868937i	0.900687	+	0.434468i	$0.143064\pi$
$359$			5910.58i			0.868937i	−0.900687	+	0.434468i	$0.856936\pi$
$360$	−2509.26	−	229.597i	−0.367360	−	0.0336134i
$361$	−4930.57			−0.718847
$362$	10556.0	−	5673.71i	1.53263	−	0.823767i
$363$		−	675.951i		−	0.0977362i
$364$	7584.01	+	6493.79i	1.09206	+	0.935075i
$365$			9808.70i			1.40661i
$366$	−629.383	−	1170.98i	−0.0898862	−	0.167235i
$367$	8817.17			1.25409			0.627047	−	0.778982i	$-0.284263\pi$
$367$	8817.17			1.25409			0.627047	+	0.778982i	$0.284263\pi$
$368$	−1521.34	−	3578.96i	−0.215504	−	0.506973i
$369$			2176.24i			0.307020i
$370$	−4901.18	−	9118.73i	−0.688649	−	1.28124i
$371$	5859.49			0.819972
$372$	−171.371	+	259.057i	−0.0238848	+	0.0361061i
$373$			7090.83i			0.984314i	0.870506	+	0.492157i	$0.163791\pi$
$373$			7090.83i			0.984314i	−0.870506	+	0.492157i	$0.836209\pi$
$374$	726.281	+	1351.26i	0.100415	+	0.186823i
$375$		−	3597.10i		−	0.495342i
$376$	795.690	−	8696.06i	0.109134	−	1.19273i
$377$	1263.01	−	10159.8i	0.172543	−	1.38794i
$378$	962.676	+	1791.08i	0.130991	+	0.243712i
$379$	−7150.31			−0.969094			−0.484547	−	0.874765i	$-0.661016\pi$
$379$	−7150.31			−0.969094			−0.484547	+	0.874765i	$0.661016\pi$
$380$	2398.24	−	3625.35i	0.323755	−	0.489412i
$381$		−	6430.92i		−	0.864740i
$382$	4348.98	+	8091.36i	0.582495	+	1.08374i
$383$		−	6280.67i		−	0.837930i	−0.908002	−	0.418965i	$-0.862393\pi$
$383$		−	6280.67i		−	0.837930i	0.908002	−	0.418965i	$-0.137607\pi$
$384$	4136.46	−	1328.18i	0.549708	−	0.176506i
$385$			10954.9i			1.45016i
$386$	8244.69	−	4431.39i	1.08716	−	0.584331i
$387$			2615.55i			0.343556i
$388$	5266.60	+	3483.95i	0.689101	+	0.455852i
$389$			5719.43i			0.745467i	0.927938	+	0.372734i	$0.121579\pi$
$389$			5719.43i			0.745467i	−0.927938	+	0.372734i	$0.878421\pi$
$390$	4588.94	−	1777.25i	0.595820	−	0.230756i
$391$	991.132			0.128194
$392$	−8246.46	−	754.551i	−1.06252	−	0.0972209i
$393$	−2212.45			−0.283978
$394$	1241.48	+	2309.80i	0.158744	+	0.295345i
$395$	−13213.5			−1.68315
$396$	−1320.90	+	1996.77i	−0.167620	+	0.253387i
$397$	2754.07			0.348168			0.174084	−	0.984731i	$-0.444304\pi$
$397$	2754.07			0.348168			0.174084	+	0.984731i	$0.444304\pi$
$398$	3838.57	+	7141.73i	0.483442	+	0.899454i
$399$	−3507.81			−0.440126
$400$	−703.377	−	1654.70i	−0.0879222	−	0.206837i
$401$		−	12405.6i		−	1.54490i	−0.635073	−	0.772452i	$-0.719030\pi$
$401$		−	12405.6i		−	1.54490i	0.635073	−	0.772452i	$-0.280970\pi$
$402$	−4386.08	+	2357.45i	−0.544173	+	0.292485i
$403$	74.8365	−	601.989i	0.00925030	−	0.0744099i
$404$	2202.85	+	1457.23i	0.271277	+	0.179455i
$405$	1002.22			0.122965
$406$	7787.80	+	14489.4i	0.951975	+	1.77117i
$407$	−9836.35			−1.19796
$408$	−100.891	+	1102.64i	−0.0122423	+	0.133796i
$409$		−	2163.40i		−	0.261549i	−0.991412	−	0.130774i	$-0.958254\pi$
$409$		−	2163.40i		−	0.261549i	0.991412	−	0.130774i	$-0.0417463\pi$
$410$	−7453.84	+	4006.32i	−0.897851	+	0.482581i
$411$	2026.13			0.243167
$412$	−5534.69	+	8366.66i	−0.661832	+	1.00047i
$413$		−	8260.61i		−	0.984209i
$414$	732.302	+	1362.46i	0.0869340	+	0.161742i
$415$	18421.9			2.17902
$416$	−6082.79	+	5915.31i	−0.716907	+	0.697168i
$417$	−3509.76			−0.412167
$418$	−1955.33	−	3637.93i	−0.228800	−	0.425687i
$419$			1787.02i			0.208357i	0.994559	+	0.104178i	$0.0332213\pi$
$419$			1787.02i			0.208357i	−0.994559	+	0.104178i	$0.966779\pi$
$420$	−4362.39	+	6594.52i	−0.506816	+	0.766142i
$421$	6432.75			0.744686			0.372343	−	0.928095i	$-0.378554\pi$
$421$	6432.75			0.744686			0.372343	+	0.928095i	$0.378554\pi$
$422$	7199.05	−	3869.37i	0.830436	−	0.446346i
$423$			3473.29i			0.399236i
$424$	−453.724	+	4958.73i	−0.0519689	+	0.567966i
$425$	458.241			0.0523010
$426$	−4595.90	−	8550.76i	−0.522704	−	0.972502i
$427$	−4171.61			−0.472783
$428$	2255.60	+	1492.12i	0.254739	+	0.168515i
$429$	576.828	−	4640.04i	0.0649173	−	0.522198i
$430$	−8958.53	+	4815.07i	−1.00469	+	0.540007i
$431$			13495.7i			1.50828i	0.656716	+	0.754138i	$0.271945\pi$
$431$			13495.7i			1.50828i	−0.656716	+	0.754138i	$0.728055\pi$
$432$	−1590.29	+	675.997i	−0.177113	+	0.0752869i
$433$	−8248.31			−0.915447			−0.457724	−	0.889095i	$-0.651335\pi$
$433$	−8248.31			−0.915447			−0.457724	+	0.889095i	$0.651335\pi$
$434$	461.445	+	858.527i	0.0510370	+	0.0949554i
$435$	8107.71			0.893644
$436$	−9016.64	+	13630.2i	−0.990410	+	1.49718i
$437$	−2668.37			−0.292095
$438$	3184.62	+	5925.04i	0.347413	+	0.646369i
$439$	−1721.73			−0.187184			−0.0935918	−	0.995611i	$-0.529835\pi$
$439$	−1721.73			−0.187184			−0.0935918	+	0.995611i	$0.529835\pi$
$440$	−9270.82	−	848.281i	−1.00448	−	0.0919095i
$441$	3293.71			0.355654
$442$	−780.973	−	2016.50i	−0.0840432	−	0.217003i
$443$			6001.77i			0.643686i	0.946793	+	0.321843i	$0.104302\pi$
$443$			6001.77i			0.643686i	−0.946793	+	0.321843i	$0.895698\pi$
$444$	−5921.21	−	3916.98i	−0.632901	−	0.418675i
$445$		−	2677.79i		−	0.285258i
$446$	−6812.44	+	3661.58i	−0.723269	+	0.388746i
$447$			1036.06i			0.109628i
$448$	2474.08	−	13406.4i	0.260914	−	1.41382i
$449$		−	2201.06i		−	0.231346i	−0.993287	−	0.115673i	$-0.963098\pi$
$449$		−	2201.06i		−	0.231346i	0.993287	−	0.115673i	$-0.0369025\pi$
$450$	338.573	+	629.922i	0.0354678	+	0.0659885i
$451$			8040.43i			0.839488i
$452$	−3081.60	+	4658.37i	−0.320677	+	0.484760i
$453$	−9960.85			−1.03312
$454$	7664.59	+	14260.1i	0.792328	+	1.47414i
$455$	1905.03	−	15324.2i	0.196284	−	1.57892i
$456$	271.624	−	2968.57i	0.0278947	−	0.304860i
$457$		−	3684.35i		−	0.377126i	−0.982061	−	0.188563i	$-0.939617\pi$
$457$		−	3684.35i		−	0.377126i	0.982061	−	0.188563i	$-0.0603830\pi$
$458$	2319.93	+	4316.27i	0.236688	+	0.440363i
$459$		−	440.403i		−	0.0447848i
$460$	−3318.45	+	5016.42i	−0.336355	+	0.508460i
$461$	−9222.51			−0.931746			−0.465873	−	0.884851i	$-0.654260\pi$
$461$	−9222.51			−0.931746			−0.465873	+	0.884851i	$0.654260\pi$
$462$	3556.75	+	6617.39i	0.358171	+	0.666383i
$463$		−	8406.97i		−	0.843856i	−0.906629	−	0.421928i	$-0.861354\pi$
$463$		−	8406.97i		−	0.843856i	0.906629	−	0.421928i	$-0.138646\pi$
$464$	−12865.0	+	5468.64i	−1.28716	+	0.547145i
$465$	480.401			0.0479098
$466$	288.285	+	536.361i	0.0286579	+	0.0533185i
$467$		−	2355.31i		−	0.233385i	−0.993168	−	0.116692i	$-0.962771\pi$
$467$		−	2355.31i		−	0.233385i	0.993168	−	0.116692i	$-0.0372291\pi$
$468$	2194.97	−	2563.47i	0.216800	−	0.253197i
$469$			15625.4i			1.53841i
$470$	−11896.3	+	6394.10i	−1.16753	+	0.627527i
$471$	−5978.51			−0.584873
$472$	6990.75	+	639.654i	0.681727	+	0.0623781i
$473$			9663.54i			0.939387i
$474$	−7981.77	+	4290.08i	−0.773449	+	0.415717i
$475$	−1233.70			−0.119170
$476$	2897.81	+	1916.95i	0.279035	+	0.184587i
$477$		−	1980.56i		−	0.190113i
$478$	2713.37	−	1458.40i	0.259638	−	0.139551i
$479$		−	15585.6i		−	1.48669i	−0.668909	−	0.743345i	$-0.733238\pi$
$479$		−	15585.6i		−	1.48669i	0.668909	−	0.743345i	$-0.266762\pi$
$480$	−5242.98	−	4202.42i	−0.498558	−	0.399611i
$481$	13759.5	+	1710.52i	1.30433	+	0.162148i
$482$	1649.33	−	886.487i	0.155860	−	0.0837726i
$483$	4853.77			0.457255
$484$	994.502	−	1503.36i	0.0933980	−	0.141187i
$485$		−	9766.49i		−	0.914379i
$486$	605.401	−	325.394i	0.0565053	−	0.0303707i
$487$		−	12945.1i		−	1.20452i	−0.798302	−	0.602258i	$-0.794268\pi$
$487$		−	12945.1i		−	1.20452i	0.798302	−	0.602258i	$-0.205732\pi$
$488$	323.025	−	3530.33i	0.0299645	−	0.327480i
$489$			3842.09i			0.355308i
$490$	6063.52	+	11281.3i	0.559024	+	1.04007i
$491$			2831.65i			0.260266i	0.991497	+	0.130133i	$0.0415404\pi$
$491$			2831.65i			0.260266i	−0.991497	+	0.130133i	$0.958460\pi$
$492$	−3201.82	+	4840.11i	−0.293393	+	0.443515i
$493$		−	3562.75i		−	0.325473i
$494$	2102.57	+	5428.93i	0.191497	+	0.494451i
$495$	3702.85			0.336224
$496$	−762.281	+	324.030i	−0.0690070	+	0.0293334i
$497$	−30462.1			−2.74932
$498$	11127.9	−	5981.09i	1.00131	−	0.538190i
$499$	−617.209			−0.0553708			−0.0276854	−	0.999617i	$-0.508814\pi$
$499$	−617.209			−0.0553708			−0.0276854	+	0.999617i	$0.508814\pi$
$500$	5292.28	−	8000.21i	0.473356	−	0.715560i
$501$	−1823.45			−0.162606
$502$	−9693.27	+	5209.98i	−0.861817	+	0.463213i
$503$	21442.2			1.90071			0.950356	−	0.311164i	$-0.100719\pi$
$503$	21442.2			1.90071			0.950356	+	0.311164i	$0.100719\pi$
$504$	−494.085	+	5399.83i	−0.0436672	+	0.477237i
$505$		−	4085.02i		−	0.359962i
$506$	2705.60	+	5033.82i	0.237704	+	0.442254i
$507$	−1613.79	+	6390.38i	−0.141362	+	0.559777i
$508$	9461.57	−	14302.8i	0.826357	−	1.24918i
$509$	21026.3			1.83099			0.915497	−	0.402324i	$-0.131797\pi$
$509$	21026.3			1.83099			0.915497	+	0.402324i	$0.131797\pi$
$510$	1508.42	−	810.754i	0.130969	−	0.0703937i
$511$	21108.0			1.82732
$512$	11153.9	+	3131.86i	0.962767	+	0.270332i
$513$			1185.67i			0.102044i
$514$	−7248.33	−	13485.7i	−0.622004	−	1.15725i
$515$	15515.3			1.32755
$516$	−3848.16	+	5817.18i	−0.328306	+	0.496292i
$517$			12832.6i			1.09163i
$518$	−19623.2	+	10547.1i	−1.66446	+	0.894624i
$519$	−2642.05			−0.223455
$520$	12820.9	+	2798.79i	1.08122	+	0.236029i
$521$	−13521.4			−1.13702			−0.568508	−	0.822678i	$-0.692479\pi$
$521$	−13521.4			−1.13702			−0.568508	+	0.822678i	$0.692479\pi$
$522$	4897.54	−	2632.35i	0.410651	−	0.220718i
$523$			7317.92i			0.611836i	0.952058	+	0.305918i	$0.0989634\pi$
$523$			7317.92i			0.611836i	−0.952058	+	0.305918i	$0.901037\pi$
$524$	−4920.65	−	3255.10i	−0.410229	−	0.271373i
$525$	2244.10			0.186553
$526$	−6138.00	−	11419.9i	−0.508801	−	0.946635i
$527$		−	211.101i		−	0.0174491i
$528$	−5875.55	+	2497.57i	−0.484281	+	0.205858i
$529$	−8474.76			−0.696537
$530$	6783.63	−	3646.09i	0.555966	−	0.298823i
$531$	−2792.17			−0.228192
$532$	−7801.63	−	5160.91i	−0.635796	−	0.420590i
$533$	1398.21	−	11247.3i	0.113627	−	0.914025i
$534$	−869.406	−	1617.55i	−0.0704549	−	0.131083i
$535$		−	4182.83i		−	0.338018i
$536$	−13223.4	−	1209.94i	−1.06560	−	0.0975026i
$537$	−1776.98			−0.142798
$538$	−17914.7	+	9628.89i	−1.43561	+	0.771619i
$539$	12169.1			0.972468
$540$	2229.01	+	1474.53i	0.177632	+	0.117507i
$541$	19861.4			1.57839			0.789196	−	0.614141i	$-0.210498\pi$
$541$	19861.4			1.57839			0.789196	+	0.614141i	$0.210498\pi$
$542$	10024.3	−	5387.88i	0.794426	−	0.426991i
$543$	−12711.2			−1.00458
$544$	−1846.66	+	2303.90i	−0.145542	+	0.181579i
$545$	25276.2			1.98663
$546$	−3824.58	−	9875.22i	−0.299775	−	0.774030i
$547$		−	5823.75i		−	0.455221i	−0.973752	−	0.227610i	$-0.926909\pi$
$547$		−	5823.75i		−	0.455221i	0.973752	−	0.227610i	$-0.0730912\pi$
$548$	4506.26	+	2980.97i	0.351273	+	0.232374i
$549$			1410.05i			0.109616i
$550$	1250.91	+	2327.34i	0.0969798	+	0.180433i
$551$			9591.80i			0.741605i
$552$	−375.848	+	4107.62i	−0.0289803	+	0.316725i
$553$			28435.1i			2.18658i
$554$	10017.9	−	5384.47i	0.768267	−	0.412932i
$555$			10980.4i			0.839806i
$556$	−7805.95	−	5163.77i	−0.595407	−	0.393872i
$557$	900.989			0.0685388			0.0342694	−	0.999413i	$-0.489090\pi$
$557$	900.989			0.0685388			0.0342694	+	0.999413i	$0.489090\pi$
$558$	290.191	−	155.973i	0.0220157	−	0.0118331i
$559$	1680.47	−	13517.8i	0.127149	−	1.02279i
$560$	−19404.5	+	8248.46i	−1.46427	+	0.622431i
$561$		−	1627.13i		−	0.122456i
$562$	8235.81	−	4426.62i	0.618161	−	0.332252i
$563$			21415.2i			1.60310i	0.597930	+	0.801548i	$0.295990\pi$
$563$			21415.2i			1.60310i	−0.597930	+	0.801548i	$0.704010\pi$
$564$	−5110.12	+	7724.84i	−0.381515	+	0.576727i
$565$	8638.58			0.643235
$566$	−4557.76	+	2449.72i	−0.338475	+	0.181925i
$567$		−	2156.74i		−	0.159744i
$568$	2358.81	−	25779.3i	0.174249	−	1.90436i
$569$	18554.5			1.36704			0.683519	−	0.729933i	$-0.260449\pi$
$569$	18554.5			1.36704			0.683519	+	0.729933i	$0.260449\pi$
$570$	−4061.05	+	2182.75i	−0.298419	+	0.160396i
$571$		−	3256.22i		−	0.238649i	−0.992855	−	0.119325i	$-0.961927\pi$
$571$		−	3256.22i		−	0.238649i	0.992855	−	0.119325i	$-0.0380729\pi$
$572$	8109.62	−	9471.11i	0.592798	−	0.692320i
$573$		−	9743.29i		−	0.710352i
$574$	8621.45	+	16040.4i	0.626921	+	1.16640i
$575$	1707.07			0.123808
$576$	−4531.48	−	836.263i	−0.327798	−	0.0604936i
$577$		−	25127.4i		−	1.81294i	−0.422271	−	0.906469i	$-0.638767\pi$
$577$		−	25127.4i		−	1.81294i	0.422271	−	0.906469i	$-0.361233\pi$
$578$	6222.58	+	11577.2i	0.447794	+	0.833130i
$579$	−9927.92			−0.712591
$580$	18032.1	+	11928.6i	1.29094	+	0.853978i
$581$		−	39643.2i		−	2.83077i
$582$	−3170.91	−	5899.55i	−0.225839	−	0.420179i
$583$		−	7317.48i		−	0.519827i
$584$	−1634.48	+	17863.1i	−0.115814	+	1.26572i
$585$	−5179.71	−	643.918i	−0.366077	−	0.0455090i
$586$	−4000.13	−	7442.31i	−0.281986	−	0.524640i
$587$	20095.7			1.41301			0.706506	−	0.707707i	$-0.250271\pi$
$587$	20095.7			1.41301			0.706506	+	0.707707i	$0.250271\pi$
$588$	7325.45	+	4845.92i	0.513770	+	0.339868i
$589$			568.336i			0.0397587i
$590$	−5140.21	−	9563.45i	−0.358676	−	0.667324i
$591$		−	2781.37i		−	0.193588i
$592$	−7406.28	−	17423.3i	−0.514183	−	1.20962i
$593$			13639.0i			0.944498i	0.881465	+	0.472249i	$0.156558\pi$
$593$			13639.0i			0.944498i	−0.881465	+	0.472249i	$0.843442\pi$
$594$	2236.74	−	1202.21i	0.154503	−	0.0830429i
$595$		−	5373.76i		−	0.370257i
$596$	−1524.31	+	2304.26i	−0.104762	+	0.158366i
$597$		−	8599.79i		−	0.589557i
$598$	−2909.34	−	7512.03i	−0.198949	−	0.513695i
$599$	185.240			0.0126356			0.00631779	−	0.999980i	$-0.497989\pi$
$599$	185.240			0.0126356			0.00631779	+	0.999980i	$0.497989\pi$
$600$	−173.770	+	1899.12i	−0.0118235	+	0.129219i
$601$	−14787.9			−1.00368			−0.501841	−	0.864960i	$-0.667344\pi$
$601$	−14787.9			−1.00368			−0.501841	+	0.864960i	$0.667344\pi$
$602$	10361.8	+	19278.4i	0.701524	+	1.30520i
$603$	5281.54			0.356685
$604$	−22153.6	−	14655.0i	−1.49242	−	0.987259i
$605$	−2787.87			−0.187344
$606$	−1326.29	−	2467.60i	−0.0889060	−	0.165411i
$607$	17628.9			1.17880			0.589402	−	0.807840i	$-0.299363\pi$
$607$	17628.9			1.17880			0.589402	+	0.807840i	$0.299363\pi$
$608$	4971.66	−	6202.69i	0.331624	−	0.413737i
$609$		−	17447.5i		−	1.16093i
$610$	−4829.54	+	2595.80i	−0.320562	+	0.172297i
$611$	2231.55	−	17950.8i	0.147756	−	1.18856i
$612$	647.948	−	979.488i	0.0427970	−	0.0646952i
$613$	−952.713			−0.0627728			−0.0313864	−	0.999507i	$-0.509992\pi$
$613$	−952.713			−0.0627728			−0.0313864	+	0.999507i	$0.509992\pi$
$614$	−2968.50	−	5522.96i	−0.195112	−	0.363010i
$615$	8975.61			0.588506
$616$	−1825.47	+	19950.5i	−0.119400	+	1.30491i
$617$			5438.09i			0.354828i	0.984136	+	0.177414i	$0.0567732\pi$
$617$			5438.09i			0.354828i	−0.984136	+	0.177414i	$0.943227\pi$
$618$	9372.17	−	5037.40i	0.610039	−	0.327886i
$619$	6308.80			0.409648			0.204824	−	0.978799i	$-0.434338\pi$
$619$	6308.80			0.409648			0.204824	+	0.978799i	$0.434338\pi$
$620$	1068.45	+	706.795i	0.0692094	+	0.0457832i
$621$		−	1640.62i		−	0.106016i
$622$	−7552.62	−	14051.8i	−0.486869	−	0.905830i
$623$	−5762.51			−0.370578
$624$	8653.30	−	2471.97i	0.555143	−	0.158586i
$625$	−18347.4			−1.17424
$626$	−12483.1	−	23225.0i	−0.797004	−	1.48284i
$627$			4380.65i			0.279021i
$628$	−13296.6	−	8795.95i	−0.844894	−	0.558912i
$629$	4825.09			0.305865
$630$	7387.06	−	3970.43i	0.467155	−	0.251088i
$631$			27401.6i			1.72875i	0.502847	+	0.864376i	$0.332286\pi$
$631$			27401.6i			1.72875i	−0.502847	+	0.864376i	$0.667714\pi$
$632$	−24063.9	−	2201.84i	−1.51457	−	0.138583i
$633$	−8668.80			−0.544319
$634$	7228.01	+	13447.9i	0.452777	+	0.842401i
$635$	−26523.5			−1.65756
$636$	2913.93	−	4404.92i	0.181674	−	0.274633i
$637$	−17022.7	−	2116.18i	−1.05881	−	0.131627i
$638$	18094.7	−	9725.61i	1.12285	−	0.603512i
$639$			10296.5i			0.637437i
$640$	−5477.89	−	17060.3i	−0.338332	−	1.05370i
$641$	−12116.7			−0.746613			−0.373306	−	0.927708i	$-0.621776\pi$
$641$	−12116.7			−0.746613			−0.373306	+	0.927708i	$0.621776\pi$
$642$	−1358.05	−	2526.68i	−0.0834859	−	0.155327i
$643$	13041.8			0.799875			0.399938	−	0.916542i	$-0.369032\pi$
$643$	13041.8			0.799875			0.399938	+	0.916542i	$0.369032\pi$
$644$	10795.1	+	7141.18i	0.660541	+	0.436959i
$645$	10787.5			0.658538
$646$	959.160	+	1784.54i	0.0584174	+	0.108687i
$647$	−22126.1			−1.34446			−0.672232	−	0.740341i	$-0.734664\pi$
$647$	−22126.1			−1.34446			−0.672232	+	0.740341i	$0.734664\pi$
$648$	1825.20	+	167.006i	0.110649	+	0.0101244i
$649$	−10316.1			−0.623946
$650$	−1345.11	−	3473.12i	−0.0811684	−	0.209580i
$651$		−	1033.80i		−	0.0622396i
$652$	−5652.73	+	8545.10i	−0.339537	+	0.513270i
$653$			20990.8i			1.25794i	0.777431	+	0.628969i	$0.216523\pi$
$653$			20990.8i			1.25794i	−0.777431	+	0.628969i	$0.783477\pi$
$654$	15268.3	−	8206.49i	0.912904	−	0.490672i
$655$			9124.96i			0.544339i
$656$	−14242.2	+	6054.04i	−0.847657	+	0.360321i
$657$		−	7134.70i		−	0.423670i
$658$	13759.9	+	25600.5i	0.815221	+	1.51673i
$659$			8421.74i			0.497822i	0.968526	+	0.248911i	$0.0800726\pi$
$659$			8421.74i			0.497822i	−0.968526	+	0.248911i	$0.919927\pi$
$660$	8235.41	+	5447.87i	0.485701	+	0.321300i
$661$	23890.2			1.40578			0.702891	−	0.711298i	$-0.251892\pi$
$661$	23890.2			1.40578			0.702891	+	0.711298i	$0.251892\pi$
$662$	−4258.11	−	7922.29i	−0.249994	−	0.465119i
$663$	−282.955	+	2276.11i	−0.0165747	+	0.133328i
$664$	33549.1	+	3069.74i	1.96078	+	0.179411i
$665$			14467.5i			0.843648i
$666$	3565.04	+	6632.82i	0.207421	+	0.385911i
$667$		−	13272.2i		−	0.770468i
$668$	−4055.48	−	2682.77i	−0.234897	−	0.155389i
$669$	8203.26			0.474075
$670$	9722.98	+	18089.8i	0.560644	+	1.04309i
$671$			5209.62i			0.299724i
$672$	−9043.45	+	11282.7i	−0.519135	+	0.647677i
$673$	−22344.0			−1.27979			−0.639894	−	0.768463i	$-0.721022\pi$
$673$	−22344.0			−1.27979			−0.639894	+	0.768463i	$0.721022\pi$
$674$	4586.89	+	8533.99i	0.262137	+	0.487711i
$675$		−	758.527i		−	0.0432529i
$676$	−12991.1	+	11838.4i	−0.739139	+	0.673553i
$677$		−	28460.2i		−	1.61568i	−0.589404	−	0.807838i	$-0.700637\pi$
$677$		−	28460.2i		−	1.61568i	0.589404	−	0.807838i	$-0.299363\pi$
$678$	5218.22	−	2804.71i	0.295582	−	0.158871i
$679$	−21017.1			−1.18787
$680$	4547.67	+	416.112i	0.256464	+	0.0234664i
$681$		−	17171.5i		−	0.966244i
$682$	1072.15	−	576.265i	0.0601977	−	0.0323553i
$683$	18506.1			1.03677			0.518387	−	0.855146i	$-0.326533\pi$
$683$	18506.1			1.03677			0.518387	+	0.855146i	$0.326533\pi$
$684$	−1744.44	+	2637.03i	−0.0975151	+	0.147411i
$685$		−	8356.50i		−	0.466110i
$686$	1523.60	−	818.913i	0.0847981	−	0.0455776i
$687$		−	5197.48i		−	0.288641i
$688$	−17117.2	+	7276.16i	−0.948527	+	0.403199i
$689$	−1272.49	+	10236.0i	−0.0703602	+	0.565982i
$690$	5619.30	−	3020.28i	0.310033	−	0.166638i
$691$	827.958			0.0455818			0.0227909	−	0.999740i	$-0.492745\pi$
$691$	827.958			0.0455818			0.0227909	+	0.999740i	$0.492745\pi$
$692$	−5876.10	−	3887.14i	−0.322797	−	0.213536i
$693$		−	7968.40i		−	0.436789i
$694$	30442.1	−	16362.1i	1.66508	−	0.894955i
$695$			14475.5i			0.790054i
$696$	14765.4	+	1351.03i	0.804138	+	0.0735786i
$697$		−	3944.12i		−	0.214339i
$698$	−7637.52	−	14209.8i	−0.414161	−	0.770555i
$699$		−	645.864i		−	0.0349482i
$700$	4991.03	+	3301.66i	0.269491	+	0.178273i
$701$			14181.4i			0.764085i	0.924145	+	0.382043i	$0.124779\pi$
$701$			14181.4i			0.764085i	−0.924145	+	0.382043i	$0.875221\pi$
$702$	−3337.92	+	1292.75i	−0.179461	+	0.0695037i
$703$	−12990.3			−0.696928
$704$	−16742.2	−	3089.70i	−0.896301	−	0.165408i
$705$	14325.1			0.765269
$706$	−17196.1	+	9242.66i	−0.916693	+	0.492708i
$707$	−8790.81			−0.467627
$708$	−6209.98	−	4108.01i	−0.329640	−	0.218063i
$709$	−31124.9			−1.64869			−0.824343	−	0.566090i	$-0.808455\pi$
$709$	−31124.9			−1.64869			−0.824343	+	0.566090i	$0.808455\pi$
$710$	−35266.5	+	18955.2i	−1.86412	+	1.00194i
$711$	9611.32			0.506966
$712$	446.215	−	4876.67i	0.0234868	−	0.256687i
$713$		−	786.409i		−	0.0413061i
$714$	−1744.71	−	3246.07i	−0.0914485	−	0.170142i
$715$	−19137.2	−	2379.05i	−1.00097	−	0.124436i
$716$	−3952.14	−	2614.41i	−0.206283	−	0.136460i
$717$	−3267.33			−0.170182
$718$	14725.4	−	7914.67i	0.765386	−	0.411383i
$719$	32557.2			1.68871			0.844353	−	0.535787i	$-0.179985\pi$
$719$	32557.2			1.68871			0.844353	+	0.535787i	$0.179985\pi$
$720$	2788.06	+	6558.92i	0.144312	+	0.339495i
$721$		−	33388.4i		−	1.72462i
$722$	6602.37	+	12283.8i	0.340325	+	0.633182i
$723$	−1986.05			−0.102161
$724$	−28270.5	−	18701.5i	−1.45120	−	0.959992i
$725$		−	6136.29i		−	0.314339i
$726$	−1684.04	+	905.145i	−0.0860890	+	0.0462715i
$727$	7446.98			0.379908			0.189954	−	0.981793i	$-0.439166\pi$
$727$	7446.98			0.379908			0.189954	+	0.981793i	$0.439166\pi$
$728$	6022.89	−	27590.2i	0.306625	−	1.40461i
$729$	−729.000			−0.0370370
$730$	24437.0	−	13134.5i	1.23898	−	0.665932i
$731$		−	4740.32i		−	0.239845i
$732$	−2074.55	+	3136.04i	−0.104751	+	0.158349i
$733$	−20527.0			−1.03435			−0.517177	−	0.855878i	$-0.673017\pi$
$733$	−20527.0			−1.03435			−0.517177	+	0.855878i	$0.673017\pi$
$734$	−11806.8	−	21966.8i	−0.593728	−	1.10464i
$735$		−	13584.5i		−	0.681729i
$736$	−6879.31	+	8582.68i	−0.344531	+	0.429839i
$737$	19513.4			0.975286
$738$	5421.80	−	2914.13i	0.270433	−	0.145353i
$739$	29880.4			1.48737			0.743686	−	0.668529i	$-0.233076\pi$
$739$	29880.4			1.48737			0.743686	+	0.668529i	$0.233076\pi$
$740$	−16155.1	+	24421.2i	−0.802530	+	1.21316i
$741$	761.785	−	6127.85i	0.0377664	−	0.303795i
$742$	−7846.26	−	14598.1i	−0.388201	−	0.722256i
$743$		−	7500.75i		−	0.370358i	−0.982705	−	0.185179i	$-0.940714\pi$
$743$		−	7500.75i		−	0.370358i	0.982705	−	0.185179i	$-0.0592865\pi$
$744$	874.882	+	80.0517i	0.0431112	+	0.00394468i
$745$	4273.08			0.210139
$746$	17665.8	−	9495.11i	0.867014	−	0.466006i
$747$	−13399.8			−0.656323
$748$	2393.94	−	3618.86i	0.117020	−	0.176897i
$749$	−9001.29			−0.439119
$750$	−8961.68	+	4816.76i	−0.436312	+	0.234511i
$751$	27102.8			1.31691			0.658453	−	0.752622i	$-0.271211\pi$
$751$	27102.8			1.31691			0.658453	+	0.752622i	$0.271211\pi$
$752$	−22730.5	+	9662.27i	−1.10226	+	0.468546i
$753$	11672.3			0.564888
$754$	−27002.9	+	10458.0i	−1.30423	+	0.505116i
$755$			41082.2i			1.98031i
$756$	3173.14	−	4796.75i	0.152653	−	0.230762i
$757$		−	18795.2i		−	0.902409i	−0.892421	−	0.451205i	$-0.850994\pi$
$757$		−	18795.2i		−	0.902409i	0.892421	−	0.451205i	$-0.149006\pi$
$758$	9574.76	+	17814.0i	0.458801	+	0.853608i
$759$		−	6061.52i		−	0.289880i
$760$	−12243.5	−	1120.28i	−0.584365	−	0.0534694i
$761$			19585.4i			0.932942i	0.884537	+	0.466471i	$0.154475\pi$
$761$			19585.4i			0.932942i	−0.884537	+	0.466471i	$0.845525\pi$
$762$	−16021.8	+	8611.45i	−0.761689	+	0.409396i
$763$		−	54393.5i		−	2.58083i
$764$	14334.9	−	21669.8i	0.678822	−	1.02616i
$765$	−1816.38			−0.0858450
$766$	−15647.4	+	8410.25i	−0.738074	+	0.396703i
$767$	14430.6	+	1793.94i	0.679346	+	0.0844531i
$768$	−8847.98	−	8526.91i	−0.415721	−	0.400636i
$769$		−	39015.6i		−	1.82957i	−0.403940	−	0.914785i	$-0.632360\pi$
$769$		−	39015.6i		−	1.82957i	0.403940	−	0.914785i	$-0.367640\pi$
$770$	27292.6	−	14669.3i	1.27734	−	0.686553i
$771$			16238.9i			0.758534i
$772$	−22080.4	−	14606.6i	−1.02939	−	0.680961i
$773$	−38584.9			−1.79535			−0.897673	−	0.440663i	$-0.854743\pi$
$773$	−38584.9			−1.79535			−0.897673	+	0.440663i	$0.854743\pi$
$774$	6516.29	−	3502.40i	0.302614	−	0.162650i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33907 - 2.49136i) q^{2} +3.00000i q^{3} +(-4.41379 + 6.67222i) q^{4} +12.3731 q^{5} +(7.47409 - 4.01721i) q^{6} -26.6265i q^{7} +(22.5333 + 2.06180i) q^{8} -9.00000 q^{9} +(-16.5684 - 30.8259i) q^{10} -33.2518 q^{11} +(-20.0166 - 13.2414i) q^{12} +(46.5141 + 5.78242i) q^{13} +(-66.3362 + 35.6547i) q^{14} +37.1193i q^{15} +(-25.0369 - 58.8995i) q^{16} +16.3112 q^{17} +(12.0516 + 22.4223i) q^{18} -43.9139 q^{19} +(-54.6122 + 82.5560i) q^{20} +79.8794 q^{21} +(44.5265 + 82.8424i) q^{22} +60.7638 q^{23} +(-6.18539 + 67.5999i) q^{24} +28.0936 q^{25} +(-47.8795 - 123.627i) q^{26} -27.0000i q^{27} +(177.657 + 117.524i) q^{28} -218.423i q^{29} +(92.4777 - 49.7053i) q^{30} -12.9421i q^{31} +(-113.214 + 141.247i) q^{32} -99.7554i q^{33} +(-21.8418 - 40.6372i) q^{34} -329.452i q^{35} +(39.7241 - 60.0499i) q^{36} +295.814 q^{37} +(58.8037 + 109.405i) q^{38} +(-17.3473 + 139.542i) q^{39} +(278.807 + 25.5108i) q^{40} -241.804i q^{41} +(-106.964 - 199.009i) q^{42} -290.617i q^{43} +(146.766 - 221.863i) q^{44} -111.358 q^{45} +(-81.3669 - 151.385i) q^{46} -385.921i q^{47} +(176.699 - 75.1108i) q^{48} -365.968 q^{49} +(-37.6192 - 69.9913i) q^{50} +48.9337i q^{51} +(-243.885 + 284.830i) q^{52} +220.063i q^{53} +(-67.2668 + 36.1549i) q^{54} -411.428 q^{55} +(54.8983 - 599.981i) q^{56} -131.742i q^{57} +(-544.171 + 292.484i) q^{58} +310.241 q^{59} +(-247.668 - 163.837i) q^{60} -156.672i q^{61} +(-32.2434 + 17.3303i) q^{62} +239.638i q^{63} +(503.498 + 92.9181i) q^{64} +(575.524 + 71.5465i) q^{65} +(-248.527 + 133.579i) q^{66} -586.837 q^{67} +(-71.9943 + 108.832i) q^{68} +182.291i q^{69} +(-820.784 + 441.159i) q^{70} -1144.05i q^{71} +(-202.800 - 18.5562i) q^{72} +792.744i q^{73} +(-396.115 - 736.981i) q^{74} +84.2808i q^{75} +(193.827 - 293.003i) q^{76} +885.378i q^{77} +(370.880 - 143.639i) q^{78} -1067.92 q^{79} +(-309.785 - 728.769i) q^{80} +81.0000 q^{81} +(-602.423 + 323.793i) q^{82} +1488.87 q^{83} +(-352.571 + 532.972i) q^{84} +201.820 q^{85} +(-724.033 + 389.156i) q^{86} +655.269 q^{87} +(-749.273 - 68.5585i) q^{88} -216.421i q^{89} +(149.116 + 277.433i) q^{90} +(153.965 - 1238.51i) q^{91} +(-268.199 + 405.429i) q^{92} +38.8262 q^{93} +(-961.469 + 516.774i) q^{94} -543.351 q^{95} +(-423.740 - 339.642i) q^{96} -789.333i q^{97} +(490.056 + 911.759i) q^{98} +299.266 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

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