LMFDB - Embedded newform 312.4.m.a.181.68

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			181.68
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.67

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.30493 + 1.63930i) q^{2} -3.00000i q^{3} +(2.62541 + 7.55693i) q^{4} +3.15976 q^{5} +(4.91789 - 6.91479i) q^{6} +31.8225i q^{7} +(-6.33669 + 21.7220i) q^{8} -9.00000 q^{9} +(7.28302 + 5.17979i) q^{10} -30.3274 q^{11} +(22.6708 - 7.87622i) q^{12} +(-42.8769 - 18.9360i) q^{13} +(-52.1666 + 73.3487i) q^{14} -9.47928i q^{15} +(-50.2145 + 39.6800i) q^{16} +33.4761 q^{17} +(-20.7444 - 14.7537i) q^{18} -32.4678 q^{19} +(8.29565 + 23.8781i) q^{20} +95.4676 q^{21} +(-69.9025 - 49.7156i) q^{22} +92.1829 q^{23} +(65.1661 + 19.0101i) q^{24} -115.016 q^{25} +(-67.7866 - 113.934i) q^{26} +27.0000i q^{27} +(-240.481 + 83.5470i) q^{28} -11.6863i q^{29} +(15.5394 - 21.8491i) q^{30} +328.498i q^{31} +(-180.788 + 9.14316i) q^{32} +90.9822i q^{33} +(77.1601 + 54.8773i) q^{34} +100.551i q^{35} +(-23.6286 - 68.0124i) q^{36} +271.273 q^{37} +(-74.8359 - 53.2243i) q^{38} +(-56.8079 + 128.631i) q^{39} +(-20.0224 + 68.6364i) q^{40} +153.109i q^{41} +(220.046 + 156.500i) q^{42} -26.1234i q^{43} +(-79.6217 - 229.182i) q^{44} -28.4378 q^{45} +(212.475 + 151.115i) q^{46} -72.2968i q^{47} +(119.040 + 150.643i) q^{48} -669.673 q^{49} +(-265.104 - 188.545i) q^{50} -100.428i q^{51} +(30.5285 - 373.733i) q^{52} +666.675i q^{53} +(-44.2610 + 62.2331i) q^{54} -95.8272 q^{55} +(-691.250 - 201.649i) q^{56} +97.4033i q^{57} +(19.1574 - 26.9362i) q^{58} +512.543 q^{59} +(71.6343 - 24.8869i) q^{60} -527.725i q^{61} +(-538.505 + 757.164i) q^{62} -286.403i q^{63} +(-431.693 - 275.291i) q^{64} +(-135.481 - 59.8331i) q^{65} +(-149.147 + 209.708i) q^{66} +863.838 q^{67} +(87.8884 + 252.977i) q^{68} -276.549i q^{69} +(-164.834 + 231.764i) q^{70} -810.528i q^{71} +(57.0302 - 195.498i) q^{72} +157.904i q^{73} +(625.266 + 444.697i) q^{74} +345.048i q^{75} +(-85.2410 - 245.357i) q^{76} -965.094i q^{77} +(-341.802 + 203.360i) q^{78} +796.996 q^{79} +(-158.666 + 125.379i) q^{80} +81.0000 q^{81} +(-250.991 + 352.905i) q^{82} +69.5892 q^{83} +(250.641 + 721.442i) q^{84} +105.776 q^{85} +(42.8240 - 60.2126i) q^{86} -35.0590 q^{87} +(192.175 - 658.772i) q^{88} +1637.05i q^{89} +(-65.5472 - 46.6181i) q^{90} +(602.590 - 1364.45i) q^{91} +(242.017 + 696.620i) q^{92} +985.493 q^{93} +(118.516 - 166.639i) q^{94} -102.590 q^{95} +(27.4295 + 542.365i) q^{96} -904.235i q^{97} +(-1543.55 - 1097.79i) q^{98} +272.946 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 $

$2$	2.30493	+	1.63930i	0.814916	+	0.579579i
$2$	2.30493	+	1.63930i	0.814916	+	0.579579i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	2.62541	+	7.55693i	0.328176	+	0.944617i
$5$	3.15976			0.282617			0.141309	−	0.989966i	$-0.454869\pi$
$5$	3.15976			0.282617			0.141309	+	0.989966i	$0.454869\pi$
$6$	4.91789	−	6.91479i	0.334620	−	0.470492i
$7$			31.8225i			1.71825i	0.511762	+	0.859127i	$0.328993\pi$
$7$			31.8225i			1.71825i	−0.511762	+	0.859127i	$0.671007\pi$
$8$	−6.33669	+	21.7220i	−0.280045	+	0.959987i
$9$	−9.00000			−0.333333
$10$	7.28302	+	5.17979i	0.230309	+	0.163799i
$11$	−30.3274			−0.831277			−0.415639	−	0.909530i	$-0.636442\pi$
$11$	−30.3274			−0.831277			−0.415639	+	0.909530i	$0.636442\pi$
$12$	22.6708	−	7.87622i	0.545375	−	0.189472i
$13$	−42.8769	−	18.9360i	−0.914763	−	0.403991i
$13$	−42.8769	−	18.9360i	−0.914763	−	0.403991i
$14$	−52.1666	+	73.3487i	−0.995865	+	1.40023i
$15$		−	9.47928i		−	0.163169i
$16$	−50.2145	+	39.6800i	−0.784602	+	0.620000i
$17$	33.4761			0.477597			0.238799	−	0.971069i	$-0.423246\pi$
$17$	33.4761			0.477597			0.238799	+	0.971069i	$0.423246\pi$
$18$	−20.7444	−	14.7537i	−0.271639	−	0.193193i
$19$	−32.4678			−0.392032			−0.196016	−	0.980601i	$-0.562800\pi$
$19$	−32.4678			−0.392032			−0.196016	+	0.980601i	$0.562800\pi$
$20$	8.29565	+	23.8781i	0.0927482	+	0.266965i
$21$	95.4676			0.992035
$22$	−69.9025	−	49.7156i	−0.677421	−	0.481791i
$23$	92.1829			0.835716			0.417858	−	0.908512i	$-0.362781\pi$
$23$	92.1829			0.835716			0.417858	+	0.908512i	$0.362781\pi$
$24$	65.1661	+	19.0101i	0.554249	+	0.161684i
$25$	−115.016			−0.920127
$26$	−67.7866	−	113.934i	−0.511310	−	0.859397i
$27$			27.0000i			0.192450i
$28$	−240.481	+	83.5470i	−1.62309	+	0.563889i
$29$		−	11.6863i		−	0.0748309i	−0.999300	−	0.0374155i	$-0.988088\pi$
$29$		−	11.6863i		−	0.0748309i	0.999300	−	0.0374155i	$-0.0119125\pi$
$30$	15.5394	−	21.8491i	0.0945695	−	0.132969i
$31$			328.498i			1.90322i	0.307304	+	0.951611i	$0.400573\pi$
$31$			328.498i			1.90322i	−0.307304	+	0.951611i	$0.599427\pi$
$32$	−180.788	+	9.14316i	−0.998724	+	0.0505093i
$33$			90.9822i			0.479938i
$34$	77.1601	+	54.8773i	0.389202	+	0.276805i
$35$			100.551i			0.485609i
$36$	−23.6286	−	68.0124i	−0.109392	−	0.314872i
$37$	271.273			1.20532			0.602662	−	0.797996i	$-0.294107\pi$
$37$	271.273			1.20532			0.602662	+	0.797996i	$0.294107\pi$
$38$	−74.8359	−	53.2243i	−0.319473	−	0.227214i
$39$	−56.8079	+	128.631i	−0.233245	+	0.528139i
$40$	−20.0224	+	68.6364i	−0.0791455	+	0.271309i
$41$			153.109i			0.583209i	0.956539	+	0.291605i	$0.0941892\pi$
$41$			153.109i			0.583209i	−0.956539	+	0.291605i	$0.905811\pi$
$42$	220.046	+	156.500i	0.808425	+	0.574963i
$43$		−	26.1234i		−	0.0926461i	−0.998927	−	0.0463230i	$-0.985250\pi$
$43$		−	26.1234i		−	0.0926461i	0.998927	−	0.0463230i	$-0.0147504\pi$
$44$	−79.6217	−	229.182i	−0.272805	−	0.785239i
$45$	−28.4378			−0.0942058
$46$	212.475	+	151.115i	0.681038	+	0.484364i
$47$		−	72.2968i		−	0.224374i	−0.993687	−	0.112187i	$-0.964214\pi$
$47$		−	72.2968i		−	0.224374i	0.993687	−	0.112187i	$-0.0357855\pi$
$48$	119.040	+	150.643i	0.357957	+	0.452990i
$49$	−669.673			−1.95240
$50$	−265.104	−	188.545i	−0.749826	−	0.533287i
$51$		−	100.428i		−	0.275741i
$52$	30.5285	−	373.733i	0.0814142	−	0.996680i
$53$			666.675i			1.72783i	0.503641	+	0.863913i	$0.331993\pi$
$53$			666.675i			1.72783i	−0.503641	+	0.863913i	$0.668007\pi$
$54$	−44.2610	+	62.2331i	−0.111540	+	0.156831i
$55$	−95.8272			−0.234933
$56$	−691.250	−	201.649i	−1.64950	−	0.481188i
$57$			97.4033i			0.226340i
$58$	19.1574	−	26.9362i	0.0433704	−	0.0609809i
$59$	512.543			1.13097			0.565487	−	0.824757i	$-0.308688\pi$
$59$	512.543			1.13097			0.565487	+	0.824757i	$0.308688\pi$
$60$	71.6343	−	24.8869i	0.154132	−	0.0535482i
$61$		−	527.725i		−	1.10768i	−0.832624	−	0.553838i	$-0.813163\pi$
$61$		−	527.725i		−	1.10768i	0.832624	−	0.553838i	$-0.186837\pi$
$62$	−538.505	+	757.164i	−1.10307	+	1.55097i
$63$		−	286.403i		−	0.572752i
$64$	−431.693	−	275.291i	−0.843150	−	0.537679i
$65$	−135.481	−	59.8331i	−0.258528	−	0.114175i
$66$	−149.147	+	209.708i	−0.278162	+	0.391109i
$67$	863.838			1.57514			0.787572	−	0.616223i	$-0.211338\pi$
$67$	863.838			1.57514			0.787572	+	0.616223i	$0.211338\pi$
$68$	87.8884	+	252.977i	0.156736	+	0.451146i
$69$		−	276.549i		−	0.482501i
$70$	−164.834	+	231.764i	−0.281449	+	0.395730i
$71$		−	810.528i		−	1.35482i	−0.735608	−	0.677408i	$-0.763103\pi$
$71$		−	810.528i		−	1.35482i	0.735608	−	0.677408i	$-0.236897\pi$
$72$	57.0302	−	195.498i	0.0933483	−	0.319996i
$73$			157.904i			0.253167i	0.991956	+	0.126584i	$0.0404012\pi$
$73$			157.904i			0.253167i	−0.991956	+	0.126584i	$0.959599\pi$
$74$	625.266	+	444.697i	0.982238	+	0.698581i
$75$			345.048i			0.531236i
$76$	−85.2410	−	245.357i	−0.128655	−	0.370320i
$77$		−	965.094i		−	1.42835i
$78$	−341.802	+	203.360i	−0.496173	+	0.295205i
$79$	796.996			1.13505			0.567526	−	0.823356i	$-0.307901\pi$
$79$	796.996			1.13505			0.567526	+	0.823356i	$0.307901\pi$
$80$	−158.666	+	125.379i	−0.221742	+	0.175223i
$81$	81.0000			0.111111
$82$	−250.991	+	352.905i	−0.338016	+	0.475267i
$83$	69.5892			0.0920290			0.0460145	−	0.998941i	$-0.485348\pi$
$83$	69.5892			0.0920290			0.0460145	+	0.998941i	$0.485348\pi$
$84$	250.641	+	721.442i	0.325562	+	0.937093i
$85$	105.776			0.134977
$86$	42.8240	−	60.2126i	0.0536958	−	0.0754988i
$87$	−35.0590			−0.0432036
$88$	192.175	−	658.772i	0.232795	−	0.798015i
$89$			1637.05i			1.94975i	0.222761	+	0.974873i	$0.428493\pi$
$89$			1637.05i			1.94975i	−0.222761	+	0.974873i	$0.571507\pi$
$90$	−65.5472	−	46.6181i	−0.0767698	−	0.0545997i
$91$	602.590	−	1364.45i	0.694160	−	1.57180i
$92$	242.017	+	696.620i	0.274262	+	0.789431i
$93$	985.493			1.09883
$94$	118.516	−	166.639i	0.130042	−	0.182846i
$95$	−102.590			−0.110795
$96$	27.4295	+	542.365i	0.0291616	+	0.576613i
$97$		−	904.235i		−	0.946507i	−0.880926	−	0.473253i	$-0.843080\pi$
$97$		−	904.235i		−	0.946507i	0.880926	−	0.473253i	$-0.156920\pi$
$98$	−1543.55	−	1097.79i	−1.59104	−	1.13157i
$99$	272.946			0.277092
$100$	−301.963	−	869.168i	−0.301963	−	0.869168i
$101$		−	571.027i		−	0.562567i	−0.959625	−	0.281283i	$-0.909240\pi$
$101$		−	571.027i		−	0.562567i	0.959625	−	0.281283i	$-0.0907601\pi$
$102$	164.632	−	231.480i	0.159814	−	0.224706i
$103$	−348.693			−0.333570			−0.166785	−	0.985993i	$-0.553339\pi$
$103$	−348.693			−0.333570			−0.166785	+	0.985993i	$0.553339\pi$
$104$	683.025	−	811.382i	0.644001	−	0.765025i
$105$	301.654			0.280366
$106$	−1092.88	+	1536.64i	−1.00141	+	1.40803i
$107$			224.543i			0.202873i	0.994842	+	0.101436i	$0.0323439\pi$
$107$			224.543i			0.202873i	−0.994842	+	0.101436i	$0.967656\pi$
$108$	−204.037	+	70.8859i	−0.181792	+	0.0631574i
$109$	−933.844			−0.820606			−0.410303	−	0.911949i	$-0.634577\pi$
$109$	−933.844			−0.820606			−0.410303	+	0.911949i	$0.634577\pi$
$110$	−220.875	−	157.089i	−0.191451	−	0.136163i
$111$		−	813.819i		−	0.695895i
$112$	−1262.72	−	1597.95i	−1.06532	−	1.34815i
$113$	−39.1345			−0.0325793			−0.0162897	−	0.999867i	$-0.505185\pi$
$113$	−39.1345			−0.0325793			−0.0162897	+	0.999867i	$0.505185\pi$
$114$	−159.673	+	224.508i	−0.131182	+	0.184448i
$115$	291.276			0.236188
$116$	88.3128	−	30.6813i	0.0706865	−	0.0245577i
$117$	385.892	+	170.424i	0.304921	+	0.134664i
$118$	1181.38	+	840.211i	0.921648	+	0.655489i
$119$			1065.29i			0.820634i
$120$	205.909	+	60.0672i	0.156640	+	0.0456947i
$121$	−411.250			−0.308978
$122$	865.098	−	1216.37i	0.641986	−	0.902663i
$123$	459.327			0.336716
$124$	−2482.43	+	862.439i	−1.79782	+	0.624591i
$125$	−758.392			−0.542661
$126$	469.499	−	660.138i	0.331955	−	0.466744i
$127$	2654.51			1.85472			0.927360	−	0.374170i	$-0.122072\pi$
$127$	2654.51			1.85472			0.927360	+	0.374170i	$0.122072\pi$
$128$	−543.737	−	1342.20i	−0.375469	−	0.926835i
$129$	−78.3702			−0.0534892
$130$	−214.189	−	360.004i	−0.144505	−	0.242880i
$131$			1492.43i			0.995378i	0.867356	+	0.497689i	$0.165818\pi$
$131$			1492.43i			0.995378i	−0.867356	+	0.497689i	$0.834182\pi$
$132$	−687.546	+	238.865i	−0.453358	+	0.157504i
$133$		−	1033.21i		−	0.673611i
$134$	1991.09	+	1416.09i	1.28361	+	0.912920i
$135$			85.3135i			0.0543897i
$136$	−212.128	+	727.169i	−0.133749	+	0.458487i
$137$		−	1648.95i		−	1.02832i	−0.857695	−	0.514158i	$-0.828104\pi$
$137$		−	1648.95i		−	1.02832i	0.857695	−	0.514158i	$-0.171896\pi$
$138$	453.346	−	637.426i	0.279648	−	0.393198i
$139$			733.234i			0.447425i	0.974655	+	0.223713i	$0.0718177\pi$
$139$			733.234i			0.447425i	−0.974655	+	0.223713i	$0.928182\pi$
$140$	−759.861	+	263.988i	−0.458714	+	0.159365i
$141$	−216.890			−0.129542
$142$	1328.70	−	1868.21i	0.785223	−	1.10406i
$143$	1300.34	+	574.278i	0.760422	+	0.335829i
$144$	451.930	−	357.120i	0.261534	−	0.206667i
$145$		−	36.9260i		−	0.0211485i
$146$	−258.851	+	363.957i	−0.146731	+	0.206310i
$147$			2009.02i			1.12722i
$148$	712.202	+	2049.99i	0.395558	+	1.13857i
$149$	2501.73			1.37550			0.687750	−	0.725948i	$-0.258598\pi$
$149$	2501.73			1.37550			0.687750	+	0.725948i	$0.258598\pi$
$150$	−565.636	+	795.311i	−0.307893	+	0.432912i
$151$			398.863i			0.214961i	0.994207	+	0.107480i	$0.0342782\pi$
$151$			398.863i			0.214961i	−0.994207	+	0.107480i	$0.965722\pi$
$152$	205.738	−	705.265i	0.109787	−	0.376346i
$153$	−301.285			−0.159199
$154$	1582.08	−	2224.47i	0.827840	−	1.16398i
$155$			1037.97i			0.537884i
$156$	−1121.20	−	91.5855i	−0.575434	−	0.0470045i
$157$		−	1705.02i		−	0.866720i	−0.901221	−	0.433360i	$-0.857328\pi$
$157$		−	1705.02i		−	0.866720i	0.901221	−	0.433360i	$-0.142672\pi$
$158$	1837.02	+	1306.51i	0.924971	+	0.657852i
$159$	2000.02			0.997561
$160$	−571.247	+	28.8902i	−0.282257	+	0.0142748i
$161$			2933.49i			1.43597i
$162$	186.699	+	132.783i	0.0905462	+	0.0643977i
$163$	−1303.86			−0.626542			−0.313271	−	0.949664i	$-0.601425\pi$
$163$	−1303.86			−0.626542			−0.313271	+	0.949664i	$0.601425\pi$
$164$	−1157.03	+	401.973i	−0.550909	+	0.191395i
$165$			287.482i			0.135639i
$166$	160.398	+	114.077i	0.0749959	+	0.0533381i
$167$			2448.11i			1.13437i	0.823590	+	0.567186i	$0.191968\pi$
$167$			2448.11i			1.13437i	−0.823590	+	0.567186i	$0.808032\pi$
$168$	−604.948	+	2073.75i	−0.277814	+	0.952340i
$169$	1479.86	+	1623.83i	0.673582	+	0.739113i
$170$	243.807	+	173.399i	0.109995	+	0.0782301i
$171$	292.210			0.130677
$172$	197.413	−	68.5845i	0.0875151	−	0.0304042i
$173$		−	2513.15i		−	1.10446i	−0.833692	−	0.552229i	$-0.813777\pi$
$173$		−	2513.15i		−	1.10446i	0.833692	−	0.552229i	$-0.186223\pi$
$174$	−80.8085	−	57.4721i	−0.0352073	−	0.0250399i
$175$		−	3660.10i		−	1.58101i
$176$	1522.87	−	1203.39i	0.652222	−	0.515392i
$177$		−	1537.63i		−	0.652968i
$178$	−2683.62	+	3773.30i	−1.13003	+	1.58888i
$179$			2275.36i			0.950104i	0.879958	+	0.475052i	$0.157571\pi$
$179$			2275.36i			0.950104i	−0.879958	+	0.475052i	$0.842429\pi$
$180$	−74.6608	−	214.903i	−0.0309161	−	0.0889884i
$181$		−	3625.71i		−	1.48893i	−0.667661	−	0.744466i	$-0.732704\pi$
$181$		−	3625.71i		−	1.48893i	0.667661	−	0.744466i	$-0.267296\pi$
$182$	3625.67	−	2157.14i	1.47666	−	0.878560i
$183$	−1583.17			−0.639517
$184$	−584.135	+	2002.40i	−0.234038	+	0.802276i
$185$	857.158			0.340646
$186$	2271.49	+	1615.52i	0.895451	+	0.636857i
$187$	−1015.24			−0.397016
$188$	546.342	−	189.808i	0.211947	−	0.0736340i
$189$	−859.208			−0.330678
$190$	−236.463	−	168.176i	−0.0902887	−	0.0642146i
$191$	3729.40			1.41283			0.706414	−	0.707799i	$-0.250312\pi$
$191$	3729.40			1.41283			0.706414	+	0.707799i	$0.250312\pi$
$192$	−825.874	+	1295.08i	−0.310429	+	0.486793i
$193$			767.818i			0.286366i	0.989696	+	0.143183i	$0.0457338\pi$
$193$			767.818i			0.286366i	−0.989696	+	0.143183i	$0.954266\pi$
$194$	1482.31	−	2084.20i	0.548576	−	0.771323i
$195$	−179.499	+	406.442i	−0.0659190	+	0.149261i
$196$	−1758.16	−	5060.67i	−0.640730	−	1.84427i
$197$	−3005.02			−1.08680			−0.543398	−	0.839475i	$-0.682863\pi$
$197$	−3005.02			−1.08680			−0.543398	+	0.839475i	$0.682863\pi$
$198$	629.123	+	447.441i	0.225807	+	0.160597i
$199$	−3534.47			−1.25906			−0.629528	−	0.776978i	$-0.716752\pi$
$199$	−3534.47			−1.25906			−0.629528	+	0.776978i	$0.716752\pi$
$200$	728.820	−	2498.38i	0.257677	−	0.883310i
$201$		−	2591.51i		−	0.909409i
$202$	936.083	−	1316.18i	0.326052	−	0.458445i
$203$	371.888			0.128579
$204$	758.931	−	263.665i	0.260469	−	0.0904914i
$205$			483.787i			0.164825i
$206$	−803.712	−	571.611i	−0.271831	−	0.193330i
$207$	−829.646			−0.278572
$208$	2904.42	−	750.497i	0.968199	−	0.250181i
$209$	984.662			0.325888
$210$	695.292	+	494.502i	0.228475	+	0.162495i
$211$		−	2159.43i		−	0.704556i	−0.935895	−	0.352278i	$-0.885407\pi$
$211$		−	2159.43i		−	0.704556i	0.935895	−	0.352278i	$-0.114593\pi$
$212$	−5038.02	+	1750.29i	−1.63213	+	0.567030i
$213$	−2431.58			−0.782203
$214$	−368.093	+	517.556i	−0.117581	+	0.165324i
$215$		−	82.5437i		−	0.0261834i
$216$	−586.495	−	171.091i	−0.184750	−	0.0538946i
$217$	−10453.6			−3.27022
$218$	−2152.44	−	1530.85i	−0.668725	−	0.475606i
$219$	473.711			0.146166
$220$	−251.585	−	724.160i	−0.0770994	−	0.221922i
$221$	−1435.35	−	633.902i	−0.436888	−	0.192945i
$222$	1334.09	−	1875.80i	0.403326	−	0.567096i
$223$		−	3677.94i		−	1.10445i	−0.833694	−	0.552227i	$-0.813778\pi$
$223$		−	3677.94i		−	1.10445i	0.833694	−	0.552227i	$-0.186222\pi$
$224$	−290.958	−	5753.14i	−0.0867878	−	1.71606i
$225$	1035.14			0.306709
$226$	−90.2023	−	64.1531i	−0.0265494	−	0.0188823i
$227$	2985.71			0.872990			0.436495	−	0.899707i	$-0.356220\pi$
$227$	2985.71			0.872990			0.436495	+	0.899707i	$0.356220\pi$
$228$	−736.070	+	255.723i	−0.213804	+	0.0742792i
$229$	−111.331			−0.0321264			−0.0160632	−	0.999871i	$-0.505113\pi$
$229$	−111.331			−0.0321264			−0.0160632	+	0.999871i	$0.505113\pi$
$230$	671.370	+	477.488i	0.192473	+	0.136890i
$231$	−2895.28			−0.824656
$232$	253.851	+	74.0526i	0.0718367	+	0.0209560i
$233$	4372.15			1.22931			0.614654	−	0.788797i	$-0.289296\pi$
$233$	4372.15			1.22931			0.614654	+	0.788797i	$0.289296\pi$
$234$	610.080	+	1025.41i	0.170437	+	0.286466i
$235$		−	228.440i		−	0.0634120i
$236$	1345.63	+	3873.25i	0.371158	+	1.06834i
$237$		−	2390.99i		−	0.655322i
$238$	−1746.34	+	2455.43i	−0.475622	+	0.668747i
$239$			3323.79i			0.899573i	0.893136	+	0.449787i	$0.148500\pi$
$239$			3323.79i			0.899573i	−0.893136	+	0.449787i	$0.851500\pi$
$240$	376.138	+	475.997i	0.101165	+	0.128023i
$241$		−	1479.10i		−	0.395342i	−0.980268	−	0.197671i	$-0.936662\pi$
$241$		−	1479.10i		−	0.395342i	0.980268	−	0.197671i	$-0.0633377\pi$
$242$	−947.901	−	674.160i	−0.251791	−	0.179077i
$243$		−	243.000i		−	0.0641500i
$244$	3987.98	−	1385.49i	1.04633	−	0.363512i
$245$	−2116.00			−0.551782
$246$	1058.72	+	752.973i	0.274395	+	0.195154i
$247$	1392.12	+	614.808i	0.358617	+	0.158378i
$248$	−7135.63	−	2081.59i	−1.82707	−	0.532988i
$249$		−	208.768i		−	0.0531330i
$250$	−1748.04	−	1243.23i	−0.442223	−	0.314515i
$251$			3963.27i			0.996651i	0.866990	+	0.498325i	$0.166052\pi$
$251$			3963.27i			0.996651i	−0.866990	+	0.498325i	$0.833948\pi$
$252$	2164.33	−	751.923i	0.541031	−	0.187963i
$253$	−2795.67			−0.694712
$254$	6118.46	+	4351.53i	1.51144	+	1.07496i
$255$		−	317.329i		−	0.0779292i
$256$	946.991	−	3985.02i	0.231199	−	0.972906i
$257$	−4738.68			−1.15016			−0.575080	−	0.818097i	$-0.695029\pi$
$257$	−4738.68			−1.15016			−0.575080	+	0.818097i	$0.695029\pi$
$258$	−180.638	−	128.472i	−0.0435892	−	0.0310013i
$259$			8632.59i			2.07106i
$260$	96.4627	−	1180.90i	0.0230091	−	0.281679i
$261$			105.177i			0.0249436i
$262$	−2446.54	+	3439.95i	−0.576900	+	0.811149i
$263$	4228.54			0.991417			0.495709	−	0.868489i	$-0.334908\pi$
$263$	4228.54			0.991417			0.495709	+	0.868489i	$0.334908\pi$
$264$	−1976.32	−	576.526i	−0.460734	−	0.134404i
$265$			2106.53i			0.488314i
$266$	1693.73	−	2381.47i	0.390411	−	0.548936i
$267$	4911.16			1.12569
$268$	2267.92	+	6527.97i	0.516924	+	1.48791i
$269$			6051.15i			1.37154i	0.727817	+	0.685771i	$0.240535\pi$
$269$			6051.15i			1.37154i	−0.727817	+	0.685771i	$0.759465\pi$
$270$	−139.854	+	196.642i	−0.0315232	+	0.0443231i
$271$		−	3361.97i		−	0.753598i	−0.926295	−	0.376799i	$-0.877025\pi$
$271$		−	3361.97i		−	0.753598i	0.926295	−	0.376799i	$-0.122975\pi$
$272$	−1680.99	+	1328.33i	−0.374724	+	0.296110i
$273$	−4093.35	−	1807.77i	−0.907476	−	0.400774i
$274$	2703.12	−	3800.71i	0.595991	−	0.837991i
$275$	3488.13			0.764881
$276$	2089.86	−	726.052i	0.455778	−	0.158345i
$277$			5266.13i			1.14228i	0.820853	+	0.571139i	$0.193498\pi$
$277$			5266.13i			1.14228i	−0.820853	+	0.571139i	$0.806502\pi$
$278$	−1201.99	+	1690.05i	−0.259319	+	0.364614i
$279$		−	2956.48i		−	0.634408i
$280$	−2184.18	−	637.164i	−0.466178	−	0.135992i
$281$			5935.42i			1.26006i	0.776570	+	0.630031i	$0.216958\pi$
$281$			5935.42i			1.26006i	−0.776570	+	0.630031i	$0.783042\pi$
$282$	−499.917	−	355.548i	−0.105566	−	0.0750800i
$283$			173.311i			0.0364038i	0.999834	+	0.0182019i	$0.00579417\pi$
$283$			173.311i			0.0364038i	−0.999834	+	0.0182019i	$0.994206\pi$
$284$	6125.10	−	2127.96i	1.27978	−	0.444618i
$285$			307.771i			0.0639676i
$286$	2055.79	+	3455.32i	0.425040	+	0.714397i
$287$	−4872.31			−1.00210
$288$	1627.09	−	82.2884i	0.332908	−	0.0168364i
$289$	−3792.35			−0.771901
$290$	60.5327	−	85.1118i	0.0122572	−	0.0172343i
$291$	−2712.70			−0.546466
$292$	−1193.27	+	414.561i	−0.239146	+	0.0830834i
$293$	−8551.32			−1.70503			−0.852515	−	0.522703i	$-0.824923\pi$
$293$	−8551.32			−1.70503			−0.852515	+	0.522703i	$0.824923\pi$
$294$	−3293.38	+	4630.65i	−0.653312	+	0.918588i
$295$	1619.51			0.319633
$296$	−1718.97	+	5892.60i	−0.337545	+	1.15710i
$297$		−	818.839i		−	0.159979i
$298$	5766.31	+	4101.08i	1.12092	+	0.797211i
$299$	−3952.52	−	1745.57i	−0.764482	−	0.337622i
$300$	−2607.50	+	905.890i	−0.501814	+	0.174339i
$301$	831.313			0.159190
$302$	−653.856	+	919.352i	−0.124587	+	0.175175i
$303$	−1713.08			−0.324798
$304$	1630.35	−	1288.32i	0.307589	−	0.243060i
$305$		−	1667.48i		−	0.313049i
$306$	−694.441	−	493.896i	−0.129734	−	0.0922685i
$307$	−8547.36			−1.58900			−0.794501	−	0.607263i	$-0.792267\pi$
$307$	−8547.36			−1.58900			−0.794501	+	0.607263i	$0.792267\pi$
$308$	7293.15	−	2533.76i	1.34924	−	0.468748i
$309$			1046.08i			0.192587i
$310$	−1701.55	+	2392.46i	−0.311746	+	0.438330i
$311$	−5897.36			−1.07527			−0.537634	−	0.843178i	$-0.680682\pi$
$311$	−5897.36			−1.07527			−0.537634	+	0.843178i	$0.680682\pi$
$312$	−2434.15	−	2049.08i	−0.441687	−	0.371814i
$313$	2734.59			0.493829			0.246914	−	0.969037i	$-0.420583\pi$
$313$	2734.59			0.493829			0.246914	+	0.969037i	$0.420583\pi$
$314$	2795.03	−	3929.94i	0.502333	−	0.706304i
$315$		−	904.963i		−	0.161870i
$316$	2092.44	+	6022.84i	0.372496	+	1.07219i
$317$	571.593			0.101274			0.0506370	−	0.998717i	$-0.483875\pi$
$317$	571.593			0.101274			0.0506370	+	0.998717i	$0.483875\pi$
$318$	4609.91	+	3278.63i	0.812928	+	0.578166i
$319$			354.416i			0.0622052i
$320$	−1364.04	−	869.855i	−0.238289	−	0.151957i
$321$	673.629			0.117129
$322$	−4808.87	+	6761.50i	−0.832260	+	1.17020i
$323$	−1086.89			−0.187234
$324$	212.658	+	612.112i	0.0364640	+	0.104957i
$325$	4931.53	+	2177.94i	0.841698	+	0.371724i
$326$	−3005.31	−	2137.42i	−0.510579	−	0.363131i
$327$			2801.53i			0.473777i
$328$	−3325.83	−	970.203i	−0.559873	−	0.163325i
$329$	2300.67			0.385531
$330$	−471.268	+	662.625i	−0.0786135	+	0.110534i
$331$	−606.517			−0.100717			−0.0503583	−	0.998731i	$-0.516036\pi$
$331$	−606.517			−0.100717			−0.0503583	+	0.998731i	$0.516036\pi$
$332$	182.700	+	525.881i	0.0302017	+	0.0869322i
$333$	−2441.46			−0.401775
$334$	−4013.17	+	5642.71i	−0.657458	+	0.924417i
$335$	2729.52			0.445163
$336$	−4793.86	+	3788.16i	−0.778352	+	0.615062i
$337$	−2.45017			−0.000396051			−0.000198026	−	1.00000i	$-0.500063\pi$
$337$	−2.45017			−0.000396051			−0.000198026		1.00000i	$0.500063\pi$
$338$	749.030	+	6168.75i	0.120538	+	0.992709i
$339$			117.404i			0.0188097i
$340$	277.706	+	799.346i	0.0442963	+	0.127502i
$341$		−	9962.47i		−	1.58211i
$342$	673.523	+	479.019i	0.106491	+	0.0757379i
$343$		−	10395.6i		−	1.63646i
$344$	567.453	+	165.536i	0.0889390	+	0.0259451i
$345$		−	873.827i		−	0.136363i
$346$	4119.80	−	5792.64i	0.640121	−	0.900041i
$347$			902.500i			0.139622i	0.997560	+	0.0698109i	$0.0222396\pi$
$347$			902.500i			0.139622i	−0.997560	+	0.0698109i	$0.977760\pi$
$348$	−92.0440	−	264.938i	−0.0141784	−	0.0408109i
$349$	4953.37			0.759735			0.379868	−	0.925041i	$-0.375970\pi$
$349$	4953.37			0.759735			0.379868	+	0.925041i	$0.375970\pi$
$350$	5999.99	−	8436.27i	0.916323	−	1.28839i
$351$	511.271	−	1157.68i	0.0777482	−	0.176046i
$352$	5482.84	−	277.288i	0.830216	−	0.0419872i
$353$			4514.62i			0.680705i	0.940298	+	0.340352i	$0.110546\pi$
$353$			4514.62i			0.680705i	−0.940298	+	0.340352i	$0.889454\pi$
$354$	2520.63	−	3544.13i	0.378447	−	0.532114i
$355$		−	2561.07i		−	0.382895i
$356$	−12371.1	+	4297.93i	−1.84176	+	0.639859i
$357$	3195.88			0.473793
$358$	−3730.00	+	5244.55i	−0.550661	+	0.774255i
$359$			3303.93i			0.485724i	0.970061	+	0.242862i	$0.0780863\pi$
$359$			3303.93i			0.485724i	−0.970061	+	0.242862i	$0.921914\pi$
$360$	180.202	−	617.727i	0.0263818	−	0.0904363i
$361$	−5804.85			−0.846311
$362$	5943.61	−	8357.00i	0.862954	−	1.21335i
$363$			1233.75i			0.178388i
$364$	11893.1	+	971.494i	1.71255	+	0.139890i
$365$			498.937i			0.0715495i
$366$	−3649.11	−	2595.30i	−0.521153	−	0.370651i
$367$	12769.7			1.81627			0.908134	−	0.418679i	$-0.137507\pi$
$367$	12769.7			1.81627			0.908134	+	0.418679i	$0.137507\pi$
$368$	−4628.92	+	3657.82i	−0.655704	+	0.518144i
$369$		−	1377.98i		−	0.194403i
$370$	1975.69	+	1405.14i	0.277598	+	0.197431i
$371$	−21215.3			−2.96885
$372$	2587.32	+	7447.30i	0.360608	+	1.03797i
$373$			8952.31i			1.24272i	0.783527	+	0.621358i	$0.213419\pi$
$373$			8952.31i			1.24272i	−0.783527	+	0.621358i	$0.786581\pi$
$374$	−2340.07	−	1664.29i	−0.323534	−	0.230102i
$375$			2275.18i			0.313306i
$376$	1570.43	+	458.122i	0.215396	+	0.0628347i
$377$	−221.292	+	501.074i	−0.0302310	+	0.0684525i
$378$	−1980.41	−	1408.50i	−0.269475	−	0.191654i
$379$	−2688.52			−0.364380			−0.182190	−	0.983263i	$-0.558319\pi$
$379$	−2688.52			−0.364380			−0.182190	+	0.983263i	$0.558319\pi$
$380$	−269.341	−	775.268i	−0.0363603	−	0.104659i
$381$		−	7963.52i		−	1.07082i
$382$	8596.01	+	6113.60i	1.15134	+	0.818846i
$383$			12013.3i			1.60274i	0.598168	+	0.801371i	$0.295896\pi$
$383$			12013.3i			1.60274i	−0.598168	+	0.801371i	$0.704104\pi$
$384$	−4026.60	+	1631.21i	−0.535108	+	0.216777i
$385$		−	3049.46i		−	0.403676i
$386$	−1258.68	+	1769.77i	−0.165972	+	0.233365i
$387$			235.111i			0.0308820i
$388$	6833.24	−	2373.98i	0.894086	−	0.310620i
$389$		−	11974.3i		−	1.56073i	−0.625325	−	0.780364i	$-0.715034\pi$
$389$		−	11974.3i		−	1.56073i	0.625325	−	0.780364i	$-0.284966\pi$
$390$	−1080.01	+	642.568i	−0.140227	+	0.0834300i
$391$	3085.93			0.399136
$392$	4243.51	−	14546.6i	0.546759	−	1.87428i
$393$	4477.30			0.574681
$394$	−6926.37	−	4926.13i	−0.885648	−	0.629885i
$395$	2518.31			0.320785
$396$	716.595	+	2062.64i	0.0909350	+	0.261746i
$397$	−3566.63			−0.450891			−0.225446	−	0.974256i	$-0.572384\pi$
$397$	−3566.63			−0.450891			−0.225446	+	0.974256i	$0.572384\pi$
$398$	−8146.72	−	5794.06i	−1.02603	−	0.729723i
$399$	−3099.62			−0.388910
$400$	5775.47	−	4563.83i	0.721933	−	0.570479i
$401$		−	7221.88i		−	0.899361i	−0.893190	−	0.449680i	$-0.851538\pi$
$401$		−	7221.88i		−	0.899361i	0.893190	−	0.449680i	$-0.148462\pi$
$402$	4248.26	−	5973.26i	0.527075	−	0.741092i
$403$	6220.42	−	14085.0i	0.768886	−	1.74100i
$404$	4315.21	−	1499.18i	0.531410	−	0.184621i
$405$	255.940			0.0314019
$406$	857.177	+	609.636i	0.104781	+	0.0745215i
$407$	−8227.00			−1.00196
$408$	2181.51	+	636.384i	0.264708	+	0.0772198i
$409$			4995.74i			0.603969i	0.953313	+	0.301984i	$0.0976491\pi$
$409$			4995.74i			0.603969i	−0.953313	+	0.301984i	$0.902351\pi$
$410$	−793.071	+	1115.10i	−0.0955292	+	0.134319i
$411$	−4946.85			−0.593699
$412$	−915.459	−	2635.05i	−0.109469	−	0.315096i
$413$			16310.4i			1.94330i
$414$	−1912.28	−	1360.04i	−0.227013	−	0.161455i
$415$	219.885			0.0260090
$416$	7924.78	+	3031.37i	0.934000	+	0.357272i
$417$	2199.70			0.258321
$418$	2269.58	+	1614.15i	0.265571	+	0.188878i
$419$			4651.46i			0.542336i	0.962532	+	0.271168i	$0.0874099\pi$
$419$			4651.46i			0.542336i	−0.962532	+	0.271168i	$0.912590\pi$
$420$	791.965	+	2279.58i	0.0920094	+	0.264839i
$421$	4982.78			0.576831			0.288416	−	0.957505i	$-0.406871\pi$
$421$	4982.78			0.576831			0.288416	+	0.957505i	$0.406871\pi$
$422$	3539.95	−	4977.33i	0.408346	−	0.574154i
$423$			650.671i			0.0747913i
$424$	−14481.5	−	4224.51i	−1.65869	−	0.483869i
$425$	−3850.29			−0.439450
$426$	−5604.63	−	3986.09i	−0.637430	−	0.453349i
$427$	16793.5			1.90327
$428$	−1696.86	+	589.517i	−0.191637	+	0.0665779i
$429$	1722.83	−	3901.03i	0.193891	−	0.439030i
$430$	135.314	−	190.257i	0.0151754	−	0.0213373i
$431$		−	1566.50i		−	0.175071i	−0.996161	−	0.0875354i	$-0.972101\pi$
$431$		−	1566.50i		−	0.175071i	0.996161	−	0.0875354i	$-0.0278991\pi$
$432$	−1071.36	−	1355.79i	−0.119319	−	0.150997i
$433$	6832.62			0.758325			0.379163	−	0.925330i	$-0.376212\pi$
$433$	6832.62			0.758325			0.379163	+	0.925330i	$0.376212\pi$
$434$	−24094.9	−	17136.6i	−2.66496	−	1.89535i
$435$	−110.778			−0.0122101
$436$	−2451.72	−	7057.00i	−0.269303	−	0.775158i
$437$	−2992.97			−0.327628
$438$	1091.87	+	776.553i	0.119113	+	0.0847150i
$439$	11087.7			1.20543			0.602717	−	0.797955i	$-0.294085\pi$
$439$	11087.7			1.20543			0.602717	+	0.797955i	$0.294085\pi$
$440$	607.228	−	2081.56i	0.0657919	−	0.225533i
$441$	6027.06			0.650800
$442$	−2269.23	−	3814.07i	−0.244200	−	0.410445i
$443$			6400.66i			0.686467i	0.939250	+	0.343233i	$0.111522\pi$
$443$			6400.66i			0.686467i	−0.939250	+	0.343233i	$0.888478\pi$
$444$	6149.98	−	2136.61i	0.657354	−	0.228376i
$445$			5172.70i			0.551032i
$446$	6029.25	−	8477.40i	0.640119	−	0.900037i
$447$		−	7505.18i		−	0.794145i
$448$	8760.47	−	13737.5i	0.923869	−	1.44875i
$449$			1185.40i			0.124593i	0.998058	+	0.0622965i	$0.0198424\pi$
$449$			1185.40i			0.124593i	−0.998058	+	0.0622965i	$0.980158\pi$
$450$	2385.93	+	1696.91i	0.249942	+	0.177762i
$451$		−	4643.39i		−	0.484809i
$452$	−102.744	−	295.737i	−0.0106917	−	0.0307750i
$453$	1196.59			0.124108
$454$	6881.86	+	4894.47i	0.711414	+	0.505967i
$455$	1904.04	−	4311.34i	0.196182	−	0.444217i
$456$	−2115.80	−	617.214i	−0.217283	−	0.0633853i
$457$		−	10739.6i		−	1.09930i	−0.835396	−	0.549648i	$-0.814762\pi$
$457$		−	10739.6i		−	1.09930i	0.835396	−	0.549648i	$-0.185238\pi$
$458$	−256.610	−	182.504i	−0.0261803	−	0.0186198i
$459$			903.855i			0.0919136i
$460$	764.717	+	2201.15i	0.0775111	+	0.223107i
$461$	18672.2			1.88645			0.943223	−	0.332159i	$-0.107777\pi$
$461$	18672.2			1.88645			0.943223	+	0.332159i	$0.107777\pi$
$462$	−6673.42	−	4746.23i	−0.672025	−	0.477954i
$463$			6961.59i			0.698775i	0.936978	+	0.349387i	$0.113610\pi$
$463$			6961.59i			0.698775i	−0.936978	+	0.349387i	$0.886390\pi$
$464$	463.714	+	586.823i	0.0463952	+	0.0587124i
$465$	3113.92			0.310547
$466$	10077.5	+	7167.25i	1.00178	+	0.712482i
$467$		−	8319.54i		−	0.824374i	−0.911099	−	0.412187i	$-0.864765\pi$
$467$		−	8319.54i		−	0.824374i	0.911099	−	0.412187i	$-0.135235\pi$
$468$	−274.756	+	3363.59i	−0.0271381	+	0.332227i
$469$			27489.5i			2.70650i
$470$	374.482	−	526.539i	0.0367523	−	0.0516754i
$471$	−5115.05			−0.500401
$472$	−3247.83	+	11133.5i	−0.316723	+	1.08572i
$473$			792.255i			0.0770146i
$474$	3919.54	−	5511.06i	0.379811	−	0.534032i
$475$	3734.31			0.360720
$476$	−8050.36	+	2796.83i	−0.775184	+	0.269312i
$477$		−	6000.07i		−	0.575942i
$478$	−5448.68	+	7661.10i	−0.521374	+	0.733077i
$479$		−	10801.1i		−	1.03030i	−0.857100	−	0.515151i	$-0.827736\pi$
$479$		−	10801.1i		−	1.03030i	0.857100	−	0.515151i	$-0.172264\pi$
$480$	86.6705	+	1713.74i	0.00824156	+	0.162961i
$481$	−11631.4	−	5136.82i	−1.10259	−	0.486941i
$482$	2424.69	−	3409.23i	0.229132	−	0.322170i
$483$	8800.48			0.829059
$484$	−1079.70	−	3107.79i	−0.101399	−	0.291866i
$485$		−	2857.16i		−	0.267499i
$486$	398.349	−	560.098i	0.0371800	−	0.0522769i
$487$			11483.4i			1.06851i	0.845324	+	0.534255i	$0.179408\pi$
$487$			11483.4i			1.06851i	−0.845324	+	0.534255i	$0.820592\pi$
$488$	11463.3	+	3344.03i	1.06335	+	0.310199i
$489$			3911.59i			0.361734i
$490$	−4877.24	−	3468.76i	−0.449656	−	0.319801i
$491$		−	18363.8i		−	1.68787i	−0.536443	−	0.843936i	$-0.680232\pi$
$491$		−	18363.8i		−	1.68787i	0.536443	−	0.843936i	$-0.319768\pi$
$492$	1205.92	+	3471.10i	0.110502	+	0.318068i
$493$		−	391.213i		−	0.0357390i
$494$	2200.88	+	3699.18i	0.200450	+	0.336911i
$495$	862.445			0.0783112
$496$	−13034.8	−	16495.3i	−1.18000	−	1.49327i
$497$	25793.0			2.32792
$498$	342.232	−	481.195i	0.0307948	−	0.0432989i
$499$	−76.2986			−0.00684488			−0.00342244	−	0.999994i	$-0.501089\pi$
$499$	−76.2986			−0.00684488			−0.00342244	+	0.999994i	$0.501089\pi$
$500$	−1991.09	−	5731.12i	−0.178088	−	0.512607i
$501$	7344.32			0.654930
$502$	−6496.98	+	9135.06i	−0.577638	+	0.812187i
$503$	2934.86			0.260157			0.130079	−	0.991504i	$-0.458477\pi$
$503$	2934.86			0.260157			0.130079	+	0.991504i	$0.458477\pi$
$504$	6221.25	+	1814.85i	0.549834	+	0.160396i
$505$		−	1804.31i		−	0.158991i
$506$	−6443.82	−	4582.93i	−0.566132	−	0.402641i
$507$	4871.49	−	4439.58i	0.426727	−	0.388893i
$508$	6969.16	+	20059.9i	0.608674	+	1.75200i
$509$	−13001.0			−1.13214			−0.566069	−	0.824358i	$-0.691537\pi$
$509$	−13001.0			−1.13214			−0.566069	+	0.824358i	$0.691537\pi$
$510$	520.197	−	731.422i	0.0451661	−	0.0635057i
$511$	−5024.89			−0.435006
$512$	8715.39	−	7632.80i	0.752284	−	0.658839i
$513$		−	876.629i		−	0.0754466i
$514$	−10922.3	−	7768.11i	−0.937283	−	0.666609i
$515$	−1101.78			−0.0942727
$516$	−205.754	−	592.239i	−0.0175539	−	0.0505268i
$517$			2192.57i			0.186517i
$518$	−14151.4	+	19897.5i	−1.20034	+	1.68774i
$519$	−7539.45			−0.637659
$520$	2158.19	−	2563.77i	0.182006	−	0.216209i
$521$	11843.0			0.995878			0.497939	−	0.867212i	$-0.334090\pi$
$521$	11843.0			0.995878			0.497939	+	0.867212i	$0.334090\pi$
$522$	−172.416	+	242.425i	−0.0144568	+	0.0203270i
$523$		−	5094.18i		−	0.425914i	−0.977062	−	0.212957i	$-0.931691\pi$
$523$		−	5094.18i		−	0.425914i	0.977062	−	0.212957i	$-0.0683094\pi$
$524$	−11278.2	+	3918.24i	−0.940250	+	0.326659i
$525$	−10980.3			−0.912798
$526$	9746.48	+	6931.83i	0.807921	+	0.574605i
$527$			10996.8i			0.908974i
$528$	−3610.17	−	4568.62i	−0.297562	−	0.376560i
$529$	−3669.31			−0.301579
$530$	−3453.23	+	4855.41i	−0.283017	+	0.397935i
$531$	−4612.89			−0.376991
$532$	7807.87	−	2712.58i	0.636304	−	0.221063i
$533$	2899.26	−	6564.83i	0.235612	−	0.533498i
$534$	11319.9	+	8050.86i	0.917340	+	0.652425i
$535$			709.502i			0.0573354i
$536$	−5473.87	+	18764.3i	−0.441111	+	1.51212i
$537$	6826.09			0.548543
$538$	−9919.63	+	13947.5i	−0.794918	+	1.11769i
$539$	20309.4			1.62299
$540$	−644.708	+	223.982i	−0.0513775	+	0.0178494i
$541$	4124.52			0.327776			0.163888	−	0.986479i	$-0.447596\pi$
$541$	4124.52			0.327776			0.163888	+	0.986479i	$0.447596\pi$
$542$	5511.27	−	7749.10i	0.436770	−	0.614119i
$543$	−10877.1			−0.859635
$544$	−6052.09	+	306.078i	−0.476988	+	0.0241231i
$545$	−2950.72			−0.231917
$546$	−6471.42	−	10877.0i	−0.507237	−	0.852551i
$547$		−	6416.94i		−	0.501588i	−0.968040	−	0.250794i	$-0.919308\pi$
$547$		−	6416.94i		−	0.501588i	0.968040	−	0.250794i	$-0.0806917\pi$
$548$	12461.0	−	4329.16i	0.971365	−	0.337468i
$549$			4749.52i			0.369225i
$550$	8039.90	+	5718.09i	0.623314	+	0.443309i
$551$			379.429i			0.0293361i
$552$	6007.20	+	1752.40i	0.463194	+	0.135122i
$553$			25362.4i			1.95031i
$554$	−8632.75	+	12138.1i	−0.662041	+	0.930860i
$555$		−	2571.47i		−	0.196672i
$556$	−5541.00	+	1925.04i	−0.422646	+	0.146834i
$557$	14142.7			1.07585			0.537924	−	0.842994i	$-0.319209\pi$
$557$	14142.7			1.07585			0.537924	+	0.842994i	$0.319209\pi$
$558$	4846.55	−	6814.48i	0.367690	−	0.516989i
$559$	−494.672	+	1120.09i	−0.0374282	+	0.0847492i
$560$	−3989.89	−	5049.14i	−0.301078	−	0.381009i
$561$			3045.73i			0.229217i
$562$	−9729.92	+	13680.7i	−0.730306	+	1.02684i
$563$		−	3830.12i		−	0.286714i	−0.989671	−	0.143357i	$-0.954210\pi$
$563$		−	3830.12i		−	0.286714i	0.989671	−	0.143357i	$-0.0457898\pi$
$564$	−569.425	−	1639.03i	−0.0425126	−	0.122368i
$565$	−123.656			−0.00920749
$566$	−284.109	+	399.470i	−0.0210989	+	0.0296660i
$567$			2577.62i			0.190917i
$568$	17606.3	+	5136.06i	1.30061	+	0.379409i
$569$	22320.1			1.64448			0.822238	−	0.569144i	$-0.192725\pi$
$569$	22320.1			1.64448			0.822238	+	0.569144i	$0.192725\pi$
$570$	−504.528	+	709.390i	−0.0370743	+	0.0521282i
$571$		−	19368.3i		−	1.41951i	−0.704449	−	0.709754i	$-0.748806\pi$
$571$		−	19368.3i		−	1.41951i	0.704449	−	0.709754i	$-0.251194\pi$
$572$	−925.850	+	11334.3i	−0.0676778	+	0.828518i
$573$		−	11188.2i		−	0.815696i
$574$	−11230.3	−	7987.17i	−0.816629	−	0.580798i
$575$	−10602.5			−0.768965
$576$	3885.23	+	2477.62i	0.281050	+	0.179226i
$577$		−	3965.92i		−	0.286141i	−0.989712	−	0.143071i	$-0.954302\pi$
$577$		−	3965.92i		−	0.286141i	0.989712	−	0.143071i	$-0.0456976\pi$
$578$	−8741.10	−	6216.79i	−0.629034	−	0.447378i
$579$	2303.45			0.165334
$580$	279.047	−	96.9456i	0.0199772	−	0.00694043i
$581$			2214.50i			0.158129i
$582$	−6252.59	−	4446.93i	−0.445324	−	0.316720i
$583$		−	20218.5i		−	1.43630i
$584$	−3429.99	−	1000.59i	−0.243037	−	0.0708982i
$585$	1219.33	+	538.497i	0.0861760	+	0.0380583i
$586$	−19710.2	−	14018.2i	−1.38946	−	0.988200i
$587$	−1149.02			−0.0807926			−0.0403963	−	0.999184i	$-0.512862\pi$
$587$	−1149.02			−0.0807926			−0.0403963	+	0.999184i	$0.512862\pi$
$588$	−15182.0	+	5274.49i	−1.06479	+	0.369925i
$589$		−	10665.6i		−	0.746125i
$590$	3732.86	+	2654.86i	0.260474	+	0.185253i
$591$			9015.07i			0.627463i
$592$	−13621.8	+	10764.1i	−0.945700	+	0.747302i
$593$		−	6509.04i		−	0.450749i	−0.974272	−	0.225374i	$-0.927639\pi$
$593$		−	6509.04i		−	0.450749i	0.974272	−	0.225374i	$-0.0723606\pi$
$594$	1342.32	−	1887.37i	0.0927208	−	0.130370i
$595$			3366.07i			0.231925i
$596$	6568.05	+	18905.4i	0.451406	+	1.29932i
$597$			10603.4i			0.726917i
$598$	−6248.77	−	10502.8i	−0.427310	−	0.718211i
$599$	11194.9			0.763622			0.381811	−	0.924240i	$-0.375301\pi$
$599$	11194.9			0.763622			0.381811	+	0.924240i	$0.375301\pi$
$600$	−7495.14	−	2186.46i	−0.509979	−	0.148770i
$601$	−2151.98			−0.146058			−0.0730292	−	0.997330i	$-0.523267\pi$
$601$	−2151.98			−0.146058			−0.0730292	+	0.997330i	$0.523267\pi$
$602$	1916.12	+	1362.77i	0.129726	+	0.0922630i
$603$	−7774.54			−0.525048
$604$	−3014.18	+	1047.18i	−0.203055	+	0.0705448i
$605$	−1299.45			−0.0873225
$606$	−3948.53	−	2808.25i	−0.264683	−	0.188246i
$607$	−7666.01			−0.512609			−0.256305	−	0.966596i	$-0.582505\pi$
$607$	−7666.01			−0.512609			−0.256305	+	0.966596i	$0.582505\pi$
$608$	5869.79	−	296.858i	0.391532	−	0.0198013i
$609$		−	1115.67i		−	0.0742349i
$610$	2733.50	−	3843.43i	0.181437	−	0.255108i
$611$	−1369.01	+	3099.86i	−0.0906451	+	0.205249i
$612$	−790.995	−	2276.79i	−0.0522453	−	0.150382i
$613$	−3102.78			−0.204437			−0.102219	−	0.994762i	$-0.532594\pi$
$613$	−3102.78			−0.204437			−0.102219	+	0.994762i	$0.532594\pi$
$614$	−19701.1	−	14011.7i	−1.29490	−	0.920952i
$615$	1451.36			0.0951618
$616$	20963.8	+	6115.50i	1.37119	+	0.400001i
$617$		−	3290.36i		−	0.214692i	−0.994222	−	0.107346i	$-0.965765\pi$
$617$		−	3290.36i		−	0.214692i	0.994222	−	0.107346i	$-0.0342353\pi$
$618$	−1714.83	+	2411.14i	−0.111619	+	0.156942i
$619$	−28037.4			−1.82054			−0.910272	−	0.414011i	$-0.864127\pi$
$619$	−28037.4			−1.82054			−0.910272	+	0.414011i	$0.864127\pi$
$620$	−7843.89	+	2725.10i	−0.508094	+	0.176520i
$621$			2488.94i			0.160834i
$622$	−13593.0	−	9667.53i	−0.876254	−	0.623204i
$623$	−52095.2			−3.35016
$624$	−2251.49	−	8713.27i	−0.144442	−	0.558990i
$625$	11980.7			0.766762
$626$	6303.05	+	4482.81i	0.402429	+	0.286213i
$627$		−	2953.99i		−	0.188151i
$628$	12884.7	−	4476.36i	0.818719	−	0.284437i
$629$	9081.17			0.575660
$630$	1483.50	−	2085.88i	0.0938163	−	0.131910i
$631$			19986.5i			1.26094i	0.776216	+	0.630468i	$0.217137\pi$
$631$			19986.5i			1.26094i	−0.776216	+	0.630468i	$0.782863\pi$
$632$	−5050.32	+	17312.4i	−0.317865	+	1.08963i
$633$	−6478.29			−0.406775
$634$	1317.48	+	937.011i	0.0825298	+	0.0586963i
$635$	8387.61			0.524176
$636$	5250.87	+	15114.0i	0.327375	+	0.942313i
$637$	28713.5	+	12680.9i	1.78598	+	0.788752i
$638$	−580.993	+	816.904i	−0.0360529	+	0.0506920i
$639$			7294.75i			0.451605i
$640$	−1718.08	−	4241.03i	−0.106114	−	0.261940i
$641$	−20297.4			−1.25070			−0.625350	−	0.780344i	$-0.715044\pi$
$641$	−20297.4			−1.25070			−0.625350	+	0.780344i	$0.715044\pi$
$642$	1552.67	+	1104.28i	0.0954500	+	0.0678854i
$643$	−9815.56			−0.602003			−0.301002	−	0.953624i	$-0.597321\pi$
$643$	−9815.56			−0.602003			−0.301002	+	0.953624i	$0.597321\pi$
$644$	−22168.2	+	7701.61i	−1.35644	+	0.471251i
$645$	−247.631			−0.0151170
$646$	−2505.22	−	1781.74i	−0.152580	−	0.108517i
$647$	−4770.57			−0.289877			−0.144938	−	0.989441i	$-0.546298\pi$
$647$	−4770.57			−0.289877			−0.144938	+	0.989441i	$0.546298\pi$
$648$	−513.272	+	1759.48i	−0.0311161	+	0.106665i
$649$	−15544.1			−0.940152
$650$	7796.54	+	13104.2i	0.470470	+	0.790754i
$651$			31360.9i			1.88806i
$652$	−3423.16	−	9853.20i	−0.205616	−	0.591842i
$653$			23058.8i			1.38187i	0.722918	+	0.690933i	$0.242800\pi$
$653$			23058.8i			1.38187i	−0.722918	+	0.690933i	$0.757200\pi$
$654$	−4592.54	+	6457.33i	−0.274591	+	0.386088i
$655$			4715.73i			0.281311i
$656$	−6075.36	−	7688.28i	−0.361590	−	0.457587i
$657$		−	1421.13i		−	0.0843891i
$658$	5302.87	+	3771.48i	0.314176	+	0.223446i
$659$			8574.94i			0.506878i	0.967351	+	0.253439i	$0.0815616\pi$
$659$			8574.94i			0.506878i	−0.967351	+	0.253439i	$0.918438\pi$
$660$	−2172.48	+	754.756i	−0.128127	+	0.0445134i
$661$	23616.3			1.38967			0.694833	−	0.719171i	$-0.255478\pi$
$661$	23616.3			1.38967			0.694833	+	0.719171i	$0.255478\pi$
$662$	−1397.98	−	994.263i	−0.0820756	−	0.0583733i
$663$	−1901.71	+	4306.06i	−0.111397	+	0.252237i
$664$	−440.965	+	1511.62i	−0.0257722	+	0.0883467i
$665$		−	3264.68i		−	0.190374i
$666$	−5627.39	−	4002.28i	−0.327413	−	0.232860i
$667$		−	1077.28i		−	0.0625374i
$668$	−18500.2	+	6427.27i	−1.07155	+	0.372273i
$669$	−11033.8			−0.637657
$670$	6291.35	+	4474.50i	0.362770	+	0.258007i
$671$			16004.5i			0.920786i
$672$	−17259.4	+	872.875i	−0.990769	+	0.0501070i
$673$	−14768.2			−0.845874			−0.422937	−	0.906159i	$-0.639001\pi$
$673$	−14768.2			−0.845874			−0.422937	+	0.906159i	$0.639001\pi$
$674$	−5.64747	−	4.01656i	−0.000322749	−	0.000229543i
$675$		−	3105.43i		−	0.177079i
$676$	−8385.95	+	15446.4i	−0.477125	+	0.878835i
$677$		−	23267.6i		−	1.32089i	−0.750872	−	0.660447i	$-0.770367\pi$
$677$		−	23267.6i		−	1.32089i	0.750872	−	0.660447i	$-0.229633\pi$
$678$	−192.459	+	270.607i	−0.0109017	+	0.0153283i
$679$	28775.0			1.62634
$680$	−670.273	+	2297.68i	−0.0377997	+	0.129576i
$681$		−	8957.14i		−	0.504021i
$682$	16331.5	−	22962.8i	0.916956	−	1.28928i
$683$	13908.6			0.779206			0.389603	−	0.920983i	$-0.372612\pi$
$683$	13908.6			0.779206			0.389603	+	0.920983i	$0.372612\pi$
$684$	767.169	+	2208.21i	0.0428851	+	0.123440i
$685$		−	5210.28i		−	0.290620i
$686$	17041.4	−	23961.0i	0.948461	−	1.33358i
$687$			333.993i			0.0185482i
$688$	1036.58	+	1311.77i	0.0574406	+	0.0726903i
$689$	12624.1	−	28584.9i	0.698027	−	1.58055i
$690$	1432.46	−	2014.11i	0.0790333	−	0.111124i
$691$	13598.7			0.748651			0.374326	−	0.927297i	$-0.377874\pi$
$691$	13598.7			0.748651			0.374326	+	0.927297i	$0.377874\pi$
$692$	18991.7	−	6598.04i	1.04329	−	0.362456i
$693$			8685.85i			0.476115i
$694$	−1479.47	+	2080.20i	−0.0809219	+	0.113780i
$695$			2316.84i			0.126450i
$696$	222.158	−	761.552i	0.0120990	−	0.0414749i
$697$			5125.49i			0.278539i
$698$	11417.2	+	8120.04i	0.619120	+	0.440327i
$699$		−	13116.4i		−	0.709741i
$700$	27659.1	−	9609.24i	1.49345	−	0.518850i
$701$			12703.4i			0.684453i	0.939617	+	0.342227i	$0.111181\pi$
$701$			12703.4i			0.684453i	−0.939617	+	0.342227i	$0.888819\pi$
$702$	3076.22	−	1830.24i	0.165391	−	0.0984016i
$703$	−8807.63			−0.472526
$704$	13092.1	+	8348.87i	0.700891	+	0.446960i
$705$	−685.321			−0.0366109
$706$	−7400.80	+	10405.9i	−0.394522	+	0.554717i
$707$	18171.5			0.966633
$708$	11619.8	−	4036.90i	0.616804	−	0.214288i
$709$	3667.61			0.194273			0.0971367	−	0.995271i	$-0.469032\pi$
$709$	3667.61			0.194273			0.0971367	+	0.995271i	$0.469032\pi$
$710$	4198.36	−	5903.09i	0.221918	−	0.312027i
$711$	−7172.96			−0.378350
$712$	−35560.1	−	10373.5i	−1.87173	−	0.546016i
$713$			30281.9i			1.59055i
$714$	7366.29	+	5239.01i	0.386101	+	0.274601i
$715$	4108.78	+	1814.58i	0.214908	+	0.0949111i
$716$	−17194.8	+	5973.75i	−0.897484	+	0.311801i
$717$	9971.37			0.519369
$718$	−5416.13	+	7615.34i	−0.281516	+	0.395824i
$719$	13537.6			0.702181			0.351090	−	0.936342i	$-0.385811\pi$
$719$	13537.6			0.702181			0.351090	+	0.936342i	$0.385811\pi$
$720$	1427.99	−	1128.41i	0.0739140	−	0.0584076i
$721$		−	11096.3i		−	0.573158i
$722$	−13379.8	−	9515.87i	−0.689672	−	0.490504i
$723$	−4437.31			−0.228251
$724$	27399.2	−	9518.95i	1.40647	−	0.488631i
$725$			1344.11i			0.0688540i
$726$	−2022.48	+	2843.70i	−0.103390	+	0.145372i
$727$	11439.0			0.583561			0.291780	−	0.956485i	$-0.405752\pi$
$727$	11439.0			0.583561			0.291780	+	0.956485i	$0.405752\pi$
$728$	25820.2	+	21735.6i	1.31451	+	1.10656i
$729$	−729.000			−0.0370370
$730$	−817.907	+	1150.02i	−0.0414686	+	0.0583068i
$731$		−	874.510i		−	0.0442475i
$732$	−4156.47	−	11963.9i	−0.209874	−	0.604099i
$733$	−29164.6			−1.46960			−0.734802	−	0.678281i	$-0.762725\pi$
$733$	−29164.6			−1.46960			−0.734802	+	0.678281i	$0.762725\pi$
$734$	29433.2	+	20933.3i	1.48011	+	1.05267i
$735$			6348.01i			0.318571i
$736$	−16665.6	+	842.843i	−0.834649	+	0.0422114i
$737$	−26197.9			−1.30938
$738$	2258.92	−	3176.15i	0.112672	−	0.158422i
$739$	−31446.7			−1.56534			−0.782671	−	0.622436i	$-0.786143\pi$
$739$	−31446.7			−1.56534			−0.782671	+	0.622436i	$0.786143\pi$
$740$	2250.39	+	6477.48i	0.111792	+	0.321780i
$741$	1844.42	−	4176.35i	0.0914394	−	0.207047i
$742$	−48899.7	−	34778.1i	−2.41936	−	1.72068i
$743$		−	574.677i		−	0.0283753i	−0.999899	−	0.0141876i	$-0.995484\pi$
$743$		−	574.677i		−	0.0283753i	0.999899	−	0.0141876i	$-0.00451622\pi$
$744$	−6244.76	+	21406.9i	−0.307721	+	1.05486i
$745$	7904.86			0.388740
$746$	−14675.5	+	20634.4i	−0.720252	+	1.01271i
$747$	−626.303			−0.0306763
$748$	−2665.43	−	7672.13i	−0.130291	−	0.375028i
$749$	−7145.53			−0.348587
$750$	−3729.69	+	5244.12i	−0.181586	+	0.255318i
$751$	−10250.8			−0.498080			−0.249040	−	0.968493i	$-0.580115\pi$
$751$	−10250.8			−0.498080			−0.249040	+	0.968493i	$0.580115\pi$
$752$	2868.74	+	3630.35i	0.139112	+	0.176044i
$753$	11889.8			0.575417
$754$	−1331.47	+	792.177i	−0.0643094	+	0.0382618i
$755$			1260.31i			0.0607516i
$756$	−2255.77	−	6492.98i	−0.108521	−	0.312364i
$757$			873.168i			0.0419232i	0.999780	+	0.0209616i	$0.00667277\pi$
$757$			873.168i			0.0419232i	−0.999780	+	0.0209616i	$0.993327\pi$
$758$	−6196.86	−	4407.29i	−0.296939	−	0.211187i
$759$			8387.00i			0.401092i
$760$	650.083	−	2228.47i	0.0310276	−	0.106362i
$761$		−	25191.5i		−	1.19999i	−0.800004	−	0.599995i	$-0.795169\pi$
$761$		−	25191.5i		−	1.19999i	0.800004	−	0.599995i	$-0.204831\pi$
$762$	13054.6	−	18355.4i	0.620627	−	0.872631i
$763$		−	29717.3i		−	1.41001i
$764$	9791.19	+	28182.8i	0.463656	+	1.33458i
$765$	−951.988			−0.0449924
$766$	−19693.3	+	27689.8i	−0.928916	+	1.30610i
$767$	−21976.3	−	9705.49i	−1.03457	−	0.456903i
$768$	−11955.1	−	2840.97i	−0.561708	−	0.133483i
$769$			21012.5i			0.985347i	0.870214	+	0.492673i	$0.163980\pi$
$769$			21012.5i			0.985347i	−0.870214	+	0.492673i	$0.836020\pi$
$770$	4998.98	−	7028.80i	0.233962	−	0.328962i
$771$			14216.1i			0.664045i
$772$	−5802.35	+	2015.83i	−0.270507	+	0.0939785i
$773$	12118.6			0.563874			0.281937	−	0.959433i	$-0.409023\pi$
$773$	12118.6			0.563874			0.281937	+	0.959433i	$0.409023\pi$
$774$	−385.416	+	541.914i	−0.0178986	+

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+(2.30493 + 1.63930i) q^{2} -3.00000i q^{3} +(2.62541 + 7.55693i) q^{4} +3.15976 q^{5} +(4.91789 - 6.91479i) q^{6} +31.8225i q^{7} +(-6.33669 + 21.7220i) q^{8} -9.00000 q^{9} +(7.28302 + 5.17979i) q^{10} -30.3274 q^{11} +(22.6708 - 7.87622i) q^{12} +(-42.8769 - 18.9360i) q^{13} +(-52.1666 + 73.3487i) q^{14} -9.47928i q^{15} +(-50.2145 + 39.6800i) q^{16} +33.4761 q^{17} +(-20.7444 - 14.7537i) q^{18} -32.4678 q^{19} +(8.29565 + 23.8781i) q^{20} +95.4676 q^{21} +(-69.9025 - 49.7156i) q^{22} +92.1829 q^{23} +(65.1661 + 19.0101i) q^{24} -115.016 q^{25} +(-67.7866 - 113.934i) q^{26} +27.0000i q^{27} +(-240.481 + 83.5470i) q^{28} -11.6863i q^{29} +(15.5394 - 21.8491i) q^{30} +328.498i q^{31} +(-180.788 + 9.14316i) q^{32} +90.9822i q^{33} +(77.1601 + 54.8773i) q^{34} +100.551i q^{35} +(-23.6286 - 68.0124i) q^{36} +271.273 q^{37} +(-74.8359 - 53.2243i) q^{38} +(-56.8079 + 128.631i) q^{39} +(-20.0224 + 68.6364i) q^{40} +153.109i q^{41} +(220.046 + 156.500i) q^{42} -26.1234i q^{43} +(-79.6217 - 229.182i) q^{44} -28.4378 q^{45} +(212.475 + 151.115i) q^{46} -72.2968i q^{47} +(119.040 + 150.643i) q^{48} -669.673 q^{49} +(-265.104 - 188.545i) q^{50} -100.428i q^{51} +(30.5285 - 373.733i) q^{52} +666.675i q^{53} +(-44.2610 + 62.2331i) q^{54} -95.8272 q^{55} +(-691.250 - 201.649i) q^{56} +97.4033i q^{57} +(19.1574 - 26.9362i) q^{58} +512.543 q^{59} +(71.6343 - 24.8869i) q^{60} -527.725i q^{61} +(-538.505 + 757.164i) q^{62} -286.403i q^{63} +(-431.693 - 275.291i) q^{64} +(-135.481 - 59.8331i) q^{65} +(-149.147 + 209.708i) q^{66} +863.838 q^{67} +(87.8884 + 252.977i) q^{68} -276.549i q^{69} +(-164.834 + 231.764i) q^{70} -810.528i q^{71} +(57.0302 - 195.498i) q^{72} +157.904i q^{73} +(625.266 + 444.697i) q^{74} +345.048i q^{75} +(-85.2410 - 245.357i) q^{76} -965.094i q^{77} +(-341.802 + 203.360i) q^{78} +796.996 q^{79} +(-158.666 + 125.379i) q^{80} +81.0000 q^{81} +(-250.991 + 352.905i) q^{82} +69.5892 q^{83} +(250.641 + 721.442i) q^{84} +105.776 q^{85} +(42.8240 - 60.2126i) q^{86} -35.0590 q^{87} +(192.175 - 658.772i) q^{88} +1637.05i q^{89} +(-65.5472 - 46.6181i) q^{90} +(602.590 - 1364.45i) q^{91} +(242.017 + 696.620i) q^{92} +985.493 q^{93} +(118.516 - 166.639i) q^{94} -102.590 q^{95} +(27.4295 + 542.365i) q^{96} -904.235i q^{97} +(-1543.55 - 1097.79i) q^{98} +272.946 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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