LMFDB - Embedded newform 312.4.m.a.181.46

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			181.46
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.45

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.457367 + 2.79120i) q^{2} -3.00000i q^{3} +(-7.58163 + 2.55321i) q^{4} -4.56929 q^{5} +(8.37361 - 1.37210i) q^{6} +23.0002i q^{7} +(-10.5941 - 19.9941i) q^{8} -9.00000 q^{9} +(-2.08984 - 12.7538i) q^{10} +9.02801 q^{11} +(7.65962 + 22.7449i) q^{12} +(-3.63901 - 46.7307i) q^{13} +(-64.1982 + 10.5195i) q^{14} +13.7079i q^{15} +(50.9623 - 38.7150i) q^{16} -59.4245 q^{17} +(-4.11630 - 25.1208i) q^{18} +27.0061 q^{19} +(34.6427 - 11.6664i) q^{20} +69.0006 q^{21} +(4.12911 + 25.1990i) q^{22} +35.7672 q^{23} +(-59.9824 + 31.7823i) q^{24} -104.122 q^{25} +(128.770 - 31.5303i) q^{26} +27.0000i q^{27} +(-58.7243 - 174.379i) q^{28} -142.184i q^{29} +(-38.2615 + 6.26953i) q^{30} -303.839i q^{31} +(131.370 + 124.539i) q^{32} -27.0840i q^{33} +(-27.1788 - 165.866i) q^{34} -105.095i q^{35} +(68.2347 - 22.9789i) q^{36} +241.300 q^{37} +(12.3517 + 75.3795i) q^{38} +(-140.192 + 10.9170i) q^{39} +(48.4076 + 91.3590i) q^{40} -280.464i q^{41} +(31.5586 + 192.595i) q^{42} -198.269i q^{43} +(-68.4470 + 23.0504i) q^{44} +41.1236 q^{45} +(16.3587 + 99.8335i) q^{46} -319.409i q^{47} +(-116.145 - 152.887i) q^{48} -186.009 q^{49} +(-47.6217 - 290.624i) q^{50} +178.273i q^{51} +(146.903 + 345.004i) q^{52} -531.123i q^{53} +(-75.3625 + 12.3489i) q^{54} -41.2516 q^{55} +(459.869 - 243.666i) q^{56} -81.0182i q^{57} +(396.863 - 65.0301i) q^{58} -378.115 q^{59} +(-34.9991 - 103.928i) q^{60} +878.946i q^{61} +(848.076 - 138.966i) q^{62} -207.002i q^{63} +(-287.530 + 423.640i) q^{64} +(16.6277 + 213.526i) q^{65} +(75.5970 - 12.3873i) q^{66} -247.600 q^{67} +(450.534 - 151.723i) q^{68} -107.302i q^{69} +(293.340 - 48.0668i) q^{70} -182.156i q^{71} +(95.3470 + 179.947i) q^{72} +815.886i q^{73} +(110.363 + 673.517i) q^{74} +312.365i q^{75} +(-204.750 + 68.9521i) q^{76} +207.646i q^{77} +(-94.5909 - 386.311i) q^{78} -817.462 q^{79} +(-232.862 + 176.900i) q^{80} +81.0000 q^{81} +(782.832 - 128.275i) q^{82} +246.607 q^{83} +(-523.137 + 176.173i) q^{84} +271.528 q^{85} +(553.408 - 90.6816i) q^{86} -426.551 q^{87} +(-95.6437 - 180.507i) q^{88} +355.903i q^{89} +(18.8086 + 114.784i) q^{90} +(1074.81 - 83.6980i) q^{91} +(-271.174 + 91.3211i) q^{92} -911.517 q^{93} +(891.534 - 146.087i) q^{94} -123.399 q^{95} +(373.617 - 394.109i) q^{96} +506.709i q^{97} +(-85.0742 - 519.188i) q^{98} -81.2521 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 $

$2$	0.457367	+	2.79120i	0.161704	+	0.986839i
$2$	0.457367	+	2.79120i	0.161704	+	0.986839i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−7.58163	+	2.55321i	−0.947704	+	0.319151i
$5$	−4.56929			−0.408690			−0.204345	−	0.978899i	$-0.565506\pi$
$5$	−4.56929			−0.408690			−0.204345	+	0.978899i	$0.565506\pi$
$6$	8.37361	−	1.37210i	0.569752	−	0.0933596i
$7$			23.0002i			1.24189i	0.783853	+	0.620947i	$0.213252\pi$
$7$			23.0002i			1.24189i	−0.783853	+	0.620947i	$0.786748\pi$
$8$	−10.5941	−	19.9941i	−0.468198	−	0.883624i
$9$	−9.00000			−0.333333
$10$	−2.08984	−	12.7538i	−0.0660866	−	0.403311i
$11$	9.02801			0.247459			0.123729	−	0.992316i	$-0.460515\pi$
$11$	9.02801			0.247459			0.123729	+	0.992316i	$0.460515\pi$
$12$	7.65962	+	22.7449i	0.184262	+	0.547157i
$13$	−3.63901	−	46.7307i	−0.0776370	−	0.996982i
$13$	−3.63901	−	46.7307i	−0.0776370	−	0.996982i
$14$	−64.1982	+	10.5195i	−1.22555	+	0.200819i
$15$			13.7079i			0.235957i
$16$	50.9623	−	38.7150i	0.796285	−	0.604921i
$17$	−59.4245			−0.847797			−0.423899	−	0.905710i	$-0.639339\pi$
$17$	−59.4245			−0.847797			−0.423899	+	0.905710i	$0.639339\pi$
$18$	−4.11630	−	25.1208i	−0.0539012	−	0.328946i
$19$	27.0061			0.326085			0.163043	−	0.986619i	$-0.447869\pi$
$19$	27.0061			0.326085			0.163043	+	0.986619i	$0.447869\pi$
$20$	34.6427	−	11.6664i	0.387317	−	0.130434i
$21$	69.0006			0.717008
$22$	4.12911	+	25.1990i	0.0400150	+	0.244202i
$23$	35.7672			0.324260			0.162130	−	0.986769i	$-0.448164\pi$
$23$	35.7672			0.324260			0.162130	+	0.986769i	$0.448164\pi$
$24$	−59.9824	+	31.7823i	−0.510160	+	0.270314i
$25$	−104.122			−0.832972
$26$	128.770	−	31.5303i	0.971307	−	0.237831i
$27$			27.0000i			0.192450i
$28$	−58.7243	−	174.379i	−0.396351	−	1.17695i
$29$		−	142.184i		−	0.910442i	−0.890378	−	0.455221i	$-0.849560\pi$
$29$		−	142.184i		−	0.910442i	0.890378	−	0.455221i	$-0.150440\pi$
$30$	−38.2615	+	6.26953i	−0.232852	+	0.0381551i
$31$		−	303.839i		−	1.76036i	−0.474643	−	0.880179i	$-0.657423\pi$
$31$		−	303.839i		−	1.76036i	0.474643	−	0.880179i	$-0.342577\pi$
$32$	131.370	+	124.539i	0.725722	+	0.687988i
$33$		−	27.0840i		−	0.142870i
$34$	−27.1788	−	165.866i	−0.137092	−	0.836640i
$35$		−	105.095i		−	0.507550i
$36$	68.2347	−	22.9789i	0.315901	−	0.106384i
$37$	241.300			1.07215			0.536074	−	0.844171i	$-0.319907\pi$
$37$	241.300			1.07215			0.536074	+	0.844171i	$0.319907\pi$
$38$	12.3517	+	75.3795i	0.0527292	+	0.321794i
$39$	−140.192	+	10.9170i	−0.575608	+	0.0448237i
$40$	48.4076	+	91.3590i	0.191348	+	0.361128i
$41$		−	280.464i		−	1.06832i	−0.845383	−	0.534160i	$-0.820628\pi$
$41$		−	280.464i		−	1.06832i	0.845383	−	0.534160i	$-0.179372\pi$
$42$	31.5586	+	192.595i	0.115943	+	0.707571i
$43$		−	198.269i		−	0.703156i	−0.936159	−	0.351578i	$-0.885645\pi$
$43$		−	198.269i		−	0.703156i	0.936159	−	0.351578i	$-0.114355\pi$
$44$	−68.4470	+	23.0504i	−0.234518	+	0.0789767i
$45$	41.1236			0.136230
$46$	16.3587	+	99.8335i	0.0524340	+	0.319992i
$47$		−	319.409i		−	0.991288i	−0.868526	−	0.495644i	$-0.834932\pi$
$47$		−	319.409i		−	0.991288i	0.868526	−	0.495644i	$-0.165068\pi$
$48$	−116.145	−	152.887i	−0.349251	−	0.459736i
$49$	−186.009			−0.542300
$50$	−47.6217	−	290.624i	−0.134695	−	0.822010i
$51$			178.273i			0.489476i
$52$	146.903	+	345.004i	0.391764	+	0.920066i
$53$		−	531.123i		−	1.37652i	−0.725466	−	0.688258i	$-0.758376\pi$
$53$		−	531.123i		−	1.37652i	0.725466	−	0.688258i	$-0.241624\pi$
$54$	−75.3625	+	12.3489i	−0.189917	+	0.0311199i
$55$	−41.2516			−0.101134
$56$	459.869	−	243.666i	1.09737	−	0.581452i
$57$		−	81.0182i		−	0.188265i
$58$	396.863	−	65.0301i	0.898460	−	0.147222i
$59$	−378.115			−0.834345			−0.417172	−	0.908827i	$-0.636979\pi$
$59$	−378.115			−0.834345			−0.417172	+	0.908827i	$0.636979\pi$
$60$	−34.9991	−	103.928i	−0.0753060	−	0.223618i
$61$			878.946i			1.84488i	0.386145	+	0.922438i	$0.373807\pi$
$61$			878.946i			1.84488i	−0.386145	+	0.922438i	$0.626193\pi$
$62$	848.076	−	138.966i	1.73719	−	0.284656i
$63$		−	207.002i		−	0.413965i
$64$	−287.530	+	423.640i	−0.561582	+	0.827421i
$65$	16.6277	+	213.526i	0.0317295	+	0.407457i
$66$	75.5970	−	12.3873i	0.140990	−	0.0231027i
$67$	−247.600			−0.451480			−0.225740	−	0.974188i	$-0.572480\pi$
$67$	−247.600			−0.451480			−0.225740	+	0.974188i	$0.572480\pi$
$68$	450.534	−	151.723i	0.803461	−	0.270575i
$69$		−	107.302i		−	0.187211i
$70$	293.340	−	48.0668i	0.500870	−	0.0820726i
$71$		−	182.156i		−	0.304478i	−0.988344	−	0.152239i	$-0.951352\pi$
$71$		−	182.156i		−	0.304478i	0.988344	−	0.152239i	$-0.0486483\pi$
$72$	95.3470	+	179.947i	0.156066	+	0.294541i
$73$			815.886i			1.30811i	0.756446	+	0.654057i	$0.226934\pi$
$73$			815.886i			1.30811i	−0.756446	+	0.654057i	$0.773066\pi$
$74$	110.363	+	673.517i	0.173370	+	1.05804i
$75$			312.365i			0.480917i
$76$	−204.750	+	68.9521i	−0.309032	+	0.104070i
$77$			207.646i			0.307317i
$78$	−94.5909	−	386.311i	−0.137312	−	0.560784i
$79$	−817.462			−1.16420			−0.582099	−	0.813118i	$-0.697769\pi$
$79$	−817.462			−1.16420			−0.582099	+	0.813118i	$0.697769\pi$
$80$	−232.862	+	176.900i	−0.325434	+	0.247225i
$81$	81.0000			0.111111
$82$	782.832	−	128.275i	1.05426	−	0.172751i
$83$	246.607			0.326128			0.163064	−	0.986616i	$-0.447862\pi$
$83$	246.607			0.326128			0.163064	+	0.986616i	$0.447862\pi$
$84$	−523.137	+	176.173i	−0.679511	+	0.228834i
$85$	271.528			0.346486
$86$	553.408	−	90.6816i	0.693902	−	0.113703i
$87$	−426.551			−0.525644
$88$	−95.6437	−	180.507i	−0.115860	−	0.218660i
$89$			355.903i			0.423883i	0.977282	+	0.211942i	$0.0679787\pi$
$89$			355.903i			0.423883i	−0.977282	+	0.211942i	$0.932021\pi$
$90$	18.8086	+	114.784i	0.0220289	+	0.134437i
$91$	1074.81	−	83.6980i	1.23815	−	0.0964168i
$92$	−271.174	+	91.3211i	−0.307302	+	0.103488i
$93$	−911.517			−1.01634
$94$	891.534	−	146.087i	0.978242	−	0.160295i
$95$	−123.399			−0.133268
$96$	373.617	−	394.109i	0.397210	−	0.418996i
$97$			506.709i			0.530397i	0.964194	+	0.265199i	$0.0854375\pi$
$97$			506.709i			0.530397i	−0.964194	+	0.265199i	$0.914563\pi$
$98$	−85.0742	−	519.188i	−0.0876918	−	0.535163i
$99$	−81.2521			−0.0824863
$100$	789.411	−	265.844i	0.789411	−	0.265844i
$101$		−	877.066i		−	0.864073i	−0.901856	−	0.432036i	$-0.857795\pi$
$101$		−	877.066i		−	0.864073i	0.901856	−	0.432036i	$-0.142205\pi$
$102$	−497.597	+	81.5363i	−0.483034	+	0.0791500i
$103$	−1177.42			−1.12636			−0.563179	−	0.826335i	$-0.690422\pi$
$103$	−1177.42			−1.12636			−0.563179	+	0.826335i	$0.690422\pi$
$104$	−895.787	+	567.829i	−0.844607	+	0.535387i
$105$	−315.284			−0.293034
$106$	1482.47	−	242.918i	1.35840	−	0.222587i
$107$		−	1125.19i		−	1.01660i	−0.861179	−	0.508301i	$-0.830274\pi$
$107$		−	1125.19i		−	1.01660i	0.861179	−	0.508301i	$-0.169726\pi$
$108$	−68.9366	−	204.704i	−0.0614206	−	0.182386i
$109$	788.108			0.692542			0.346271	−	0.938135i	$-0.387448\pi$
$109$	788.108			0.692542			0.346271	+	0.938135i	$0.387448\pi$
$110$	−18.8671	−	115.142i	−0.0163537	−	0.0998029i
$111$		−	723.900i		−	0.619005i
$112$	890.451	+	1172.14i	0.751248	+	0.988902i
$113$	−1182.33			−0.984284			−0.492142	−	0.870515i	$-0.663786\pi$
$113$	−1182.33			−0.984284			−0.492142	+	0.870515i	$0.663786\pi$
$114$	226.138	−	37.0551i	0.185788	−	0.0304432i
$115$	−163.431			−0.132522
$116$	363.024	+	1077.98i	0.290569	+	0.862830i
$117$	32.7511	+	420.576i	0.0258790	+	0.332327i
$118$	−172.937	−	1055.39i	−0.134917	−	0.823364i
$119$		−	1366.77i		−	1.05287i
$120$	274.077	−	145.223i	0.208497	−	0.110475i
$121$	−1249.50			−0.938764
$122$	−2453.32	+	402.001i	−1.82060	+	0.298323i
$123$	−841.392			−0.616795
$124$	775.764	+	2303.59i	0.561820	+	1.66830i
$125$	1046.92			0.749118
$126$	577.784	−	94.6757i	0.408516	−	0.0669395i
$127$	1038.87			0.725864			0.362932	−	0.931816i	$-0.381776\pi$
$127$	1038.87			0.725864			0.362932	+	0.931816i	$0.381776\pi$
$128$	−1313.97	−	608.795i	−0.907342	−	0.420394i
$129$	−594.806			−0.405967
$130$	−588.390	+	144.071i	−0.396963	+	0.0971991i
$131$		−	142.564i		−	0.0950833i	−0.998869	−	0.0475417i	$-0.984861\pi$
$131$		−	142.564i		−	0.0950833i	0.998869	−	0.0475417i	$-0.0151387\pi$
$132$	69.1511	+	205.341i	0.0455972	+	0.135399i
$133$			621.145i			0.404963i
$134$	−113.244	−	691.102i	−0.0730059	−	0.445538i
$135$		−	123.371i		−	0.0786524i
$136$	629.549	+	1188.14i	0.396937	+	0.749134i
$137$			2413.02i			1.50481i	0.658703	+	0.752403i	$0.271105\pi$
$137$			2413.02i			1.50481i	−0.658703	+	0.752403i	$0.728895\pi$
$138$	299.500	−	49.0762i	0.184748	−	0.0302728i
$139$		−	827.007i		−	0.504646i	−0.967643	−	0.252323i	$-0.918805\pi$
$139$		−	827.007i		−	0.504646i	0.967643	−	0.252323i	$-0.0811946\pi$
$140$	268.328	+	796.789i	0.161985	+	0.481007i
$141$	−958.226			−0.572320
$142$	508.434	−	83.3120i	0.300471	−	0.0492351i
$143$	−32.8530	−	421.885i	−0.0192119	−	0.246712i
$144$	−458.660	+	348.435i	−0.265428	+	0.201640i
$145$			649.679i			0.372089i
$146$	−2277.30	+	373.159i	−1.29090	+	0.211527i
$147$			558.026i			0.313097i
$148$	−1829.45	+	616.089i	−1.01608	+	0.342177i
$149$	−3151.97			−1.73302			−0.866509	−	0.499162i	$-0.833641\pi$
$149$	−3151.97			−1.73302			−0.866509	+	0.499162i	$0.833641\pi$
$150$	−871.873	+	142.865i	−0.474588	+	0.0777660i
$151$			934.341i			0.503547i	0.967786	+	0.251774i	$0.0810138\pi$
$151$			934.341i			0.503547i	−0.967786	+	0.251774i	$0.918986\pi$
$152$	−286.105	−	539.963i	−0.152672	−	0.288137i
$153$	534.820			0.282599
$154$	−579.582	+	94.9703i	−0.303273	+	0.0496943i
$155$			1388.33i			0.719441i
$156$	1035.01	−	440.708i	0.531200	−	0.226185i
$157$		−	307.214i		−	0.156168i	−0.996947	−	0.0780840i	$-0.975120\pi$
$157$		−	307.214i		−	0.156168i	0.996947	−	0.0780840i	$-0.0248802\pi$
$158$	−373.880	−	2281.70i	−0.188255	−	1.14888i
$159$	−1593.37			−0.794732
$160$	−600.267	−	569.056i	−0.296595	−	0.281174i
$161$			822.652i			0.402696i
$162$	37.0467	+	226.087i	0.0179671	+	0.109649i
$163$	368.699			0.177170			0.0885851	−	0.996069i	$-0.471765\pi$
$163$	368.699			0.177170			0.0885851	+	0.996069i	$0.471765\pi$
$164$	716.083	+	2126.37i	0.340955	+	1.01245i
$165$			123.755i			0.0583897i
$166$	112.790	+	688.329i	0.0527360	+	0.321836i
$167$			402.412i			0.186464i	0.995644	+	0.0932322i	$0.0297199\pi$
$167$			402.412i			0.186464i	−0.995644	+	0.0932322i	$0.970280\pi$
$168$	−730.999	−	1379.61i	−0.335701	−	0.633565i
$169$	−2170.52	+	340.107i	−0.987945	+	0.154805i
$170$	124.188	+	757.890i	0.0560281	+	0.341926i
$171$	−243.055			−0.108695
$172$	506.221	+	1503.20i	0.224413	+	0.666384i
$173$		−	3541.26i		−	1.55629i	−0.628088	−	0.778143i	$-0.716162\pi$
$173$		−	3541.26i		−	1.55629i	0.628088	−	0.778143i	$-0.283838\pi$
$174$	−195.090	−	1190.59i	−0.0849986	−	0.518726i
$175$		−	2394.82i		−	1.03446i
$176$	460.088	−	349.519i	0.197048	−	0.149693i
$177$			1134.34i			0.481709i
$178$	−993.397	+	162.778i	−0.418305	+	0.0685434i
$179$		−	3755.60i		−	1.56819i	−0.620640	−	0.784096i	$-0.713127\pi$
$179$		−	3755.60i		−	1.56819i	0.620640	−	0.784096i	$-0.286873\pi$
$180$	−311.784	+	104.997i	−0.129106	+	0.0434779i
$181$		−	1146.21i		−	0.470701i	−0.971911	−	0.235350i	$-0.924376\pi$
$181$		−	1146.21i		−	0.470701i	0.971911	−	0.235350i	$-0.0756238\pi$
$182$	725.203	+	2961.75i	0.295360	+	1.20626i
$183$	2636.84			1.06514
$184$	−378.921	−	715.134i	−0.151818	−	0.286524i
$185$	−1102.57			−0.438176
$186$	−416.897	−	2544.23i	−0.164346	−	1.00297i
$187$	−536.485			−0.209795
$188$	815.517	+	2421.64i	0.316371	+	0.939448i
$189$	−621.005			−0.239003
$190$	−56.4385	−	344.431i	−0.0215499	−	0.131514i
$191$	2181.45			0.826410			0.413205	−	0.910638i	$-0.364409\pi$
$191$	2181.45			0.826410			0.413205	+	0.910638i	$0.364409\pi$
$192$	1270.92	+	862.589i	0.477712	+	0.324229i
$193$			4438.58i			1.65542i	0.561158	+	0.827709i	$0.310356\pi$
$193$			4438.58i			1.65542i	−0.561158	+	0.827709i	$0.689644\pi$
$194$	−1414.33	+	231.752i	−0.523417	+	0.0857671i
$195$	640.579	−	49.8831i	0.235245	−	0.0183190i
$196$	1410.25	−	474.919i	0.513939	−	0.173075i
$197$	−3788.49			−1.37014			−0.685072	−	0.728475i	$-0.740229\pi$
$197$	−3788.49			−1.37014			−0.685072	+	0.728475i	$0.740229\pi$
$198$	−37.1620	−	226.791i	−0.0133383	−	0.0814007i
$199$	1535.85			0.547102			0.273551	−	0.961858i	$-0.411802\pi$
$199$	1535.85			0.547102			0.273551	+	0.961858i	$0.411802\pi$
$200$	1103.07	+	2081.82i	0.389996	+	0.736034i
$201$			742.800i			0.260662i
$202$	2448.07	−	401.141i	0.852701	−	0.139724i
$203$	3270.25			1.13067
$204$	−455.169	−	1351.60i	−0.156217	−	0.463878i
$205$			1281.52i			0.436612i
$206$	−538.514	−	3286.42i	−0.182136	−	1.11153i
$207$	−321.905			−0.108087
$208$	−1994.63	−	2240.62i	−0.664916	−	0.746918i
$209$	243.811			0.0806927
$210$	−144.200	−	880.021i	−0.0473846	−	0.289177i
$211$			5166.95i			1.68582i	0.538055	+	0.842909i	$0.319159\pi$
$211$			5166.95i			1.68582i	−0.538055	+	0.842909i	$0.680841\pi$
$212$	1356.07	+	4026.78i	0.439316	+	1.30453i
$213$	−546.467			−0.175790
$214$	3140.64	−	514.626i	1.00322	−	0.164388i
$215$			905.948i			0.287373i
$216$	539.841	−	286.041i	0.170053	−	0.0901047i
$217$	6988.35			2.18618
$218$	360.454	+	2199.77i	0.111986	+	0.683428i
$219$	2447.66			0.755240
$220$	312.755	−	105.324i	0.0958450	−	0.0322770i
$221$	216.246	+	2776.95i	0.0658204	+	0.845238i
$222$	2020.55	−	331.088i	0.610858	−	0.100095i
$223$		−	4812.46i		−	1.44514i	−0.691297	−	0.722570i	$-0.742961\pi$
$223$		−	4812.46i		−	1.44514i	0.691297	−	0.722570i	$-0.257039\pi$
$224$	−2864.42	+	3021.53i	−0.854408	+	0.901270i
$225$	937.094			0.277657
$226$	−540.758	−	3300.12i	−0.159162	−	0.971330i
$227$	584.946			0.171032			0.0855159	−	0.996337i	$-0.472746\pi$
$227$	584.946			0.171032			0.0855159	+	0.996337i	$0.472746\pi$
$228$	206.856	+	614.250i	0.0600851	+	0.178420i
$229$	4584.28			1.32287			0.661436	−	0.750001i	$-0.269947\pi$
$229$	4584.28			1.32287			0.661436	+	0.750001i	$0.269947\pi$
$230$	−74.7478	−	456.169i	−0.0214292	−	0.130778i
$231$	622.938			0.177430
$232$	−2842.84	+	1506.31i	−0.804489	+	0.426267i
$233$	4302.16			1.20963			0.604815	−	0.796366i	$-0.293247\pi$
$233$	4302.16			1.20963			0.604815	+	0.796366i	$0.293247\pi$
$234$	−1158.93	+	283.773i	−0.323769	+	0.0792769i
$235$			1459.47i			0.405130i
$236$	2866.73	−	965.405i	0.790712	−	0.266282i
$237$			2452.39i			0.672150i
$238$	3814.94	−	625.117i	1.03902	−	0.170253i
$239$		−	7132.42i		−	1.93037i	−0.261573	−	0.965184i	$-0.584241\pi$
$239$		−	7132.42i		−	1.93037i	0.261573	−	0.965184i	$-0.415759\pi$
$240$	530.700	+	698.585i	0.142736	+	0.187889i
$241$		−	813.188i		−	0.217353i	−0.994077	−	0.108676i	$-0.965339\pi$
$241$		−	813.188i		−	0.217353i	0.994077	−	0.108676i	$-0.0346612\pi$
$242$	−571.478	−	3487.59i	−0.151802	−	0.926409i
$243$		−	243.000i		−	0.0641500i
$244$	−2244.13	−	6663.84i	−0.588794	−	1.74840i
$245$	849.929			0.221632
$246$	−384.825	−	2348.50i	−0.0997379	−	0.608677i
$247$	−98.2755	−	1262.01i	−0.0253163	−	0.325101i
$248$	−6074.99	+	3218.90i	−1.55549	+	0.824195i
$249$		−	739.820i		−	0.188290i
$250$	478.828	+	2922.18i	0.121135	+	0.739259i
$251$		−	98.3380i		−	0.0247292i	−0.999924	−	0.0123646i	$-0.996064\pi$
$251$		−	98.3380i		−	0.0247292i	0.999924	−	0.0123646i	$-0.00393588\pi$
$252$	528.518	+	1569.41i	0.132117	+	0.392316i
$253$	322.906			0.0802409
$254$	475.144	+	2899.69i	0.117375	+	0.716311i
$255$		−	814.584i		−	0.200044i
$256$	1098.30	−	3946.00i	0.268141	−	0.963380i
$257$	2348.27			0.569966			0.284983	−	0.958533i	$-0.408012\pi$
$257$	2348.27			0.569966			0.284983	+	0.958533i	$0.408012\pi$
$258$	−272.045	−	1660.23i	−0.0656464	−	0.400624i
$259$			5549.94i			1.33149i
$260$	−671.242	−	1576.42i	−0.160110	−	0.376022i
$261$			1279.65i			0.303481i
$262$	397.926	−	65.2043i	0.0938320	−	0.0153753i
$263$	−3653.13			−0.856507			−0.428254	−	0.903659i	$-0.640871\pi$
$263$	−3653.13			−0.856507			−0.428254	+	0.903659i	$0.640871\pi$
$264$	−541.521	+	286.931i	−0.126244	+	0.0668916i
$265$			2426.86i			0.562568i
$266$	−1733.74	+	284.091i	−0.399634	+	0.0654840i
$267$	1067.71			0.244729
$268$	1877.21	−	632.174i	0.427869	−	0.144090i
$269$		−	496.183i		−	0.112464i	−0.998418	−	0.0562320i	$-0.982091\pi$
$269$		−	496.183i		−	0.112464i	0.998418	−	0.0562320i	$-0.0179086\pi$
$270$	344.353	−	56.4258i	0.0776173	−	0.0127184i
$271$		−	1164.70i		−	0.261072i	−0.991444	−	0.130536i	$-0.958330\pi$
$271$		−	1164.70i		−	0.261072i	0.991444	−	0.130536i	$-0.0416698\pi$
$272$	−3028.41	+	2300.62i	−0.675089	+	0.512850i
$273$	−251.094	−	3224.44i	−0.0556663	−	0.714843i
$274$	−6735.23	+	1103.64i	−1.48500	+	0.243332i
$275$	−940.010			−0.206126
$276$	273.963	+	813.521i	0.0597487	+	0.177421i
$277$		−	3541.96i		−	0.768289i	−0.923273	−	0.384144i	$-0.874496\pi$
$277$		−	3541.96i		−	0.768289i	0.923273	−	0.384144i	$-0.125504\pi$
$278$	2308.35	−	378.246i	0.498005	−	0.0816031i
$279$			2734.55i			0.586786i
$280$	−2101.27	+	1113.38i	−0.448483	+	0.237634i
$281$			1001.92i			0.212703i	0.994329	+	0.106352i	$0.0339169\pi$
$281$			1001.92i			0.212703i	−0.994329	+	0.106352i	$0.966083\pi$
$282$	−438.261	−	2674.60i	−0.0925463	−	0.564788i
$283$		−	4471.46i		−	0.939226i	−0.882872	−	0.469613i	$-0.844393\pi$
$283$		−	4471.46i		−	0.939226i	0.882872	−	0.469613i	$-0.155607\pi$
$284$	465.081	+	1381.04i	0.0971743	+	0.288555i
$285$			370.196i			0.0769422i
$286$	1162.54	−	284.656i	0.240358	−	0.0588533i
$287$	6450.73			1.32674
$288$	−1182.33	−	1120.85i	−0.241907	−	0.229329i
$289$	−1381.73			−0.281240
$290$	−1813.39	+	297.141i	−0.367192	+	0.0601681i
$291$	1520.13			0.306225
$292$	−2083.13	−	6185.75i	−0.417486	−	1.23970i
$293$	−3292.99			−0.656582			−0.328291	−	0.944577i	$-0.606473\pi$
$293$	−3292.99			−0.656582			−0.328291	+	0.944577i	$0.606473\pi$
$294$	−1557.56	+	255.223i	−0.308976	+	0.0506289i
$295$	1727.72			0.340988
$296$	−2556.36	−	4824.58i	−0.501977	−	0.947375i
$297$			243.756i			0.0476235i
$298$	−1441.61	−	8797.79i	−0.280235	−	1.71021i
$299$	−130.157	−	1671.43i	−0.0251745	−	0.323281i
$300$	−797.532	−	2368.23i	−0.153485	−	0.455767i
$301$	4560.22			0.873245
$302$	−2607.94	+	427.337i	−0.496920	+	0.0814254i
$303$	−2631.20			−0.498873
$304$	1376.29	−	1045.54i	0.259657	−	0.197256i
$305$		−	4016.16i		−	0.753983i
$306$	244.609	+	1492.79i	0.0456973	+	0.278880i
$307$	−3274.18			−0.608688			−0.304344	−	0.952562i	$-0.598437\pi$
$307$	−3274.18			−0.608688			−0.304344	+	0.952562i	$0.598437\pi$
$308$	−530.163	−	1574.29i	−0.0980806	−	0.291246i
$309$			3532.27i			0.650303i
$310$	−3875.11	+	634.976i	−0.709972	+	0.116336i
$311$	3191.33			0.581876			0.290938	−	0.956742i	$-0.406033\pi$
$311$	3191.33			0.581876			0.290938	+	0.956742i	$0.406033\pi$
$312$	1703.49	+	2687.36i	0.309106	+	0.487634i
$313$	5529.90			0.998621			0.499311	−	0.866423i	$-0.333587\pi$
$313$	5529.90			0.998621			0.499311	+	0.866423i	$0.333587\pi$
$314$	857.498	−	140.510i	0.154113	−	0.0252529i
$315$			945.852i			0.169183i
$316$	6197.70	−	2087.15i	1.10332	−	0.371555i
$317$	6475.59			1.14734			0.573668	−	0.819088i	$-0.305520\pi$
$317$	6475.59			1.14734			0.573668	+	0.819088i	$0.305520\pi$
$318$	−728.754	−	4447.41i	−0.128511	−	0.784272i
$319$		−	1283.63i		−	0.225297i
$320$	1313.81	−	1935.73i	0.229513	−	0.338159i
$321$	−3375.58			−0.586936
$322$	−2296.19	+	376.254i	−0.397396	+	0.0651174i
$323$	−1604.82			−0.276454
$324$	−614.112	+	206.810i	−0.105300	+	0.0354612i
$325$	378.900	+	4865.67i	0.0646694	+	0.830458i
$326$	168.631	+	1029.11i	0.0286491	+	0.174839i
$327$		−	2364.32i		−	0.399839i
$328$	−5607.63	+	2971.27i	−0.943993	+	0.500185i
$329$	7346.46			1.23107
$330$	−345.425	+	56.6014i	−0.0576213	+	0.00944182i
$331$	−10016.3			−1.66327			−0.831637	−	0.555319i	$-0.812596\pi$
$331$	−10016.3			−1.66327			−0.831637	+	0.555319i	$0.812596\pi$
$332$	−1869.68	+	629.638i	−0.309072	+	0.104084i
$333$	−2171.70			−0.357382
$334$	−1123.21	+	184.050i	−0.184010	+	0.0301519i
$335$	1131.36			0.184515
$336$	3516.43	−	2671.35i	0.570943	−	0.433733i
$337$	−6602.82			−1.06730			−0.533648	−	0.845707i	$-0.679179\pi$
$337$	−6602.82			−1.06730			−0.533648	+	0.845707i	$0.679179\pi$
$338$	−1942.03	−	5902.80i	−0.312522	−	0.949910i
$339$			3546.99i			0.568277i
$340$	−2058.62	+	693.267i	−0.328366	+	0.110581i
$341$		−	2743.06i		−	0.435616i
$342$	−111.165	−	678.415i	−0.0175764	−	0.107265i
$343$			3610.83i			0.568415i
$344$	−3964.21	+	2100.48i	−0.621325	+	0.329216i
$345$			490.292i			0.0765115i
$346$	9884.39	−	1619.66i	1.53580	−	0.251657i
$347$		−	8226.15i		−	1.27263i	−0.771429	−	0.636315i	$-0.780458\pi$
$347$		−	8226.15i		−	1.27263i	0.771429	−	0.636315i	$-0.219542\pi$
$348$	3233.95	−	1089.07i	0.498155	−	0.167760i
$349$	−5987.66			−0.918373			−0.459187	−	0.888340i	$-0.651859\pi$
$349$	−5987.66			−0.918373			−0.459187	+	0.888340i	$0.651859\pi$
$350$	6684.42	−	1095.31i	1.02085	−	0.167276i
$351$	1261.73	−	98.2533i	0.191869	−	0.0149412i
$352$	1186.01	+	1124.34i	0.179586	+	0.170249i
$353$			8372.28i			1.26236i	0.775638	+	0.631178i	$0.217428\pi$
$353$			8372.28i			1.26236i	−0.775638	+	0.631178i	$0.782572\pi$
$354$	−3166.18	+	518.811i	−0.475369	+	0.0778941i
$355$			832.323i			0.124437i
$356$	−908.693	−	2698.32i	−0.135283	−	0.401716i
$357$	−4100.32			−0.607877
$358$	10482.6	−	1717.68i	1.54755	−	0.253582i
$359$			5365.50i			0.788803i	0.918938	+	0.394401i	$0.129048\pi$
$359$			5365.50i			0.788803i	−0.918938	+	0.394401i	$0.870952\pi$
$360$	−435.668	−	822.231i	−0.0637826	−	0.120376i
$361$	−6129.67			−0.893668
$362$	3199.29	−	524.237i	0.464506	−	0.0761140i
$363$			3748.49i			0.541996i
$364$	−7935.15	+	3378.79i	−1.14262	+	0.486530i
$365$		−	3728.02i		−	0.534613i
$366$	1206.00	+	7359.95i	0.172237	+	1.05112i
$367$	2032.50			0.289089			0.144545	−	0.989498i	$-0.453828\pi$
$367$	2032.50			0.289089			0.144545	+	0.989498i	$0.453828\pi$
$368$	1822.78	−	1384.73i	0.258203	−	0.196152i
$369$			2524.18i			0.356107i
$370$	−504.279	−	3077.50i	−0.0708546	−	0.432409i
$371$	12215.9			1.70949
$372$	6910.78	−	2327.29i	0.963192	−	0.324367i
$373$			13867.4i			1.92500i	0.271282	+	0.962500i	$0.412552\pi$
$373$			13867.4i			1.92500i	−0.271282	+	0.962500i	$0.587448\pi$
$374$	−245.370	−	1497.44i	−0.0339246	−	0.207034i
$375$		−	3140.77i		−	0.432503i
$376$	−6386.30	+	3383.85i	−0.875926	+	0.464119i
$377$	−6644.34	+	517.408i	−0.907694	+	0.0706840i
$378$	−284.027	−	1733.35i	−0.0386476	−	0.235857i
$379$	4445.76			0.602542			0.301271	−	0.953539i	$-0.402589\pi$
$379$	4445.76			0.602542			0.301271	+	0.953539i	$0.402589\pi$
$380$	935.564	−	315.063i	0.126298	−	0.0425325i
$381$		−	3116.61i		−	0.419078i
$382$	997.724	+	6088.87i	0.133633	+	0.815534i
$383$		−	1882.41i		−	0.251141i	−0.992085	−	0.125570i	$-0.959924\pi$
$383$		−	1882.41i		−	0.251141i	0.992085	−	0.125570i	$-0.0400761\pi$
$384$	−1826.39	+	3941.91i	−0.242714	+	0.523854i
$385$		−	948.795i		−	0.125598i
$386$	−12389.0	+	2030.06i	−1.63363	+	0.267687i
$387$			1784.42i			0.234385i
$388$	−1293.73	−	3841.68i	−0.169277	−	0.502659i
$389$		−	4490.10i		−	0.585237i	−0.956229	−	0.292619i	$-0.905473\pi$
$389$		−	4490.10i		−	0.585237i	0.956229	−	0.292619i	$-0.0945266\pi$
$390$	432.213	+	1765.17i	0.0561179	+	0.229187i
$391$	−2125.45			−0.274907
$392$	1970.60	+	3719.08i	0.253903	+	0.479189i
$393$	−427.693			−0.0548964
$394$	−1732.73	−	10574.4i	−0.221557	−	1.35211i
$395$	3735.23			0.475796
$396$	616.023	−	207.453i	0.0781725	−	0.0263256i
$397$	9505.67			1.20170			0.600852	−	0.799361i	$-0.294828\pi$
$397$	9505.67			1.20170			0.600852	+	0.799361i	$0.294828\pi$
$398$	702.445	+	4286.86i	0.0884683	+	0.539902i
$399$	1863.44			0.233806
$400$	−5306.27	+	4031.06i	−0.663284	+	0.503883i
$401$		−	9181.79i		−	1.14343i	−0.820451	−	0.571716i	$-0.806278\pi$
$401$		−	9181.79i		−	1.14343i	0.820451	−	0.571716i	$-0.193722\pi$
$402$	−2073.31	+	339.732i	−0.257232	+	0.0421500i
$403$	−14198.6	+	1105.67i	−1.75504	+	0.136669i
$404$	2239.33	+	6649.59i	0.275770	+	0.818885i
$405$	−370.113			−0.0454100
$406$	1495.70	+	9127.93i	0.182834	+	1.11579i
$407$	2178.46			0.265312
$408$	3564.42	−	1888.65i	0.432513	−	0.229172i
$409$		−	3469.65i		−	0.419470i	−0.977758	−	0.209735i	$-0.932740\pi$
$409$		−	3469.65i		−	0.419470i	0.977758	−	0.209735i	$-0.0672601\pi$
$410$	−3576.99	+	586.126i	−0.430866	+	0.0706017i
$411$	7239.07			0.868800
$412$	8926.78	−	3006.20i	1.06745	−	0.359478i
$413$		−	8696.71i		−	1.03617i
$414$	−147.229	−	898.501i	−0.0174780	−	0.106664i
$415$	−1126.82			−0.133285
$416$	5341.74	−	6592.20i	0.629568	−	0.776945i
$417$	−2481.02			−0.291358
$418$	111.511	+	680.526i	0.0130483	+	0.0796307i
$419$		−	12868.1i		−	1.50035i	−0.661241	−	0.750174i	$-0.729970\pi$
$419$		−	12868.1i		−	1.50035i	0.661241	−	0.750174i	$-0.270030\pi$
$420$	2390.37	−	804.985i	0.277709	−	0.0935220i
$421$	4414.39			0.511031			0.255516	−	0.966805i	$-0.417755\pi$
$421$	4414.39			0.511031			0.255516	+	0.966805i	$0.417755\pi$
$422$	−14422.0	+	2363.19i	−1.66363	+	0.272603i
$423$			2874.68i			0.330429i
$424$	−10619.3	+	5626.77i	−1.21632	+	0.644482i
$425$	6187.37			0.706192
$426$	−249.936	−	1525.30i	−0.0284259	−	0.173477i
$427$	−20215.9			−2.29114
$428$	2872.85	+	8530.79i	0.324450	+	0.963438i
$429$	−1265.65	+	98.5591i	−0.142439	+	0.0110920i
$430$	−2528.69	+	414.351i	−0.283591	+	0.0464692i
$431$			11981.4i			1.33903i	0.742797	+	0.669517i	$0.233499\pi$
$431$			11981.4i			1.33903i	−0.742797	+	0.669517i	$0.766501\pi$
$432$	1045.30	+	1375.98i	0.116417	+	0.153245i
$433$	4268.40			0.473733			0.236866	−	0.971542i	$-0.423880\pi$
$433$	4268.40			0.473733			0.236866	+	0.971542i	$0.423880\pi$
$434$	3196.24	+	19505.9i	0.353513	+	2.15740i
$435$	1949.04			0.214826
$436$	−5975.14	+	2012.20i	−0.656325	+	0.221025i
$437$	965.932			0.105736
$438$	1119.48	+	6831.91i	0.122125	+	0.745300i
$439$	7424.25			0.807152			0.403576	−	0.914946i	$-0.367767\pi$
$439$	7424.25			0.807152			0.403576	+	0.914946i	$0.367767\pi$
$440$	437.024	+	824.790i	0.0473507	+	0.0893643i
$441$	1674.08			0.180767
$442$	−7652.12	+	1873.67i	−0.823471	+	0.201632i
$443$			3110.29i			0.333576i	0.985993	+	0.166788i	$0.0533395\pi$
$443$			3110.29i			0.333576i	−0.985993	+	0.166788i	$0.946660\pi$
$444$	1848.27	+	5488.34i	0.197556	+	0.586633i
$445$		−	1626.22i		−	0.173237i
$446$	13432.6	−	2201.06i	1.42612	−	0.233684i
$447$			9455.91i			1.00056i
$448$	−9743.79	−	6613.24i	−1.02757	−	0.697425i
$449$			5412.37i			0.568876i	0.958694	+	0.284438i	$0.0918071\pi$
$449$			5412.37i			0.568876i	−0.958694	+	0.284438i	$0.908193\pi$
$450$	428.596	+	2615.62i	0.0448982	+	0.274003i
$451$		−	2532.03i		−	0.264365i
$452$	8963.98	−	3018.73i	0.932810	−	0.314135i
$453$	2803.02			0.290723
$454$	267.535	+	1632.70i	0.0276565	+	0.168781i
$455$	−4911.14	+	382.441i	−0.506018	+	0.0394046i
$456$	−1619.89	+	858.316i	−0.166356	+	0.0881455i
$457$		−	3771.11i		−	0.386007i	−0.981198	−	0.193003i	$-0.938177\pi$
$457$		−	3771.11i		−	0.386007i	0.981198	−	0.193003i	$-0.0618228\pi$
$458$	2096.70	+	12795.7i	0.213913	+	1.30546i
$459$		−	1604.46i		−	0.163159i
$460$	1239.07	−	417.273i	0.125591	−	0.0422944i
$461$	−1276.30			−0.128944			−0.0644722	−	0.997920i	$-0.520536\pi$
$461$	−1276.30			−0.128944			−0.0644722	+	0.997920i	$0.520536\pi$
$462$	284.911	+	1738.75i	0.0286910	+	0.175095i
$463$			10359.5i			1.03984i	0.854216	+	0.519919i	$0.174038\pi$
$463$			10359.5i			1.03984i	−0.854216	+	0.519919i	$0.825962\pi$
$464$	−5504.63	−	7246.00i	−0.550746	−	0.724972i
$465$	4164.99			0.415369
$466$	1967.66	+	12008.2i	0.195602	+	1.19371i
$467$			18643.9i			1.84740i	0.383112	+	0.923702i	$0.374852\pi$
$467$			18643.9i			1.84740i	−0.383112	+	0.923702i	$0.625148\pi$
$468$	−1322.13	−	3105.03i	−0.130588	−	0.306689i
$469$		−	5694.85i		−	0.560690i
$470$	−4073.68	+	667.514i	−0.399798	+	0.0655109i
$471$	−921.643			−0.0901636
$472$	4005.79	+	7560.07i	0.390638	+	0.737247i
$473$		−	1789.97i		−	0.174002i
$474$	−6845.11	+	1121.64i	−0.663304	+	0.108689i
$475$	−2811.92			−0.271620
$476$	3489.66	+	10362.4i	0.336026	+	0.997813i
$477$			4780.10i			0.458838i
$478$	19908.0	−	3262.13i	1.90496	−	0.312147i
$479$			4124.15i			0.393397i	0.980464	+	0.196699i	$0.0630221\pi$
$479$			4124.15i			0.393397i	−0.980464	+	0.196699i	$0.936978\pi$
$480$	−1707.17	+	1800.80i	−0.162336	+	0.171239i
$481$	−878.093	−	11276.1i	−0.0832383	−	1.06891i
$482$	2269.77	−	371.925i	0.214492	−	0.0351467i
$483$	2467.96			0.232497
$484$	9473.21	−	3190.22i	0.889670	−	0.299607i
$485$		−	2315.30i		−	0.216768i
$486$	678.262	−	111.140i	0.0633058	−	0.0103733i
$487$		−	3948.63i		−	0.367412i	−0.982981	−	0.183706i	$-0.941191\pi$
$487$		−	3948.63i		−	0.367412i	0.982981	−	0.183706i	$-0.0588095\pi$
$488$	17573.7	−	9311.65i	1.63018	−	0.863767i
$489$		−	1106.10i		−	0.102289i
$490$	388.729	+	2372.32i	0.0358388	+	0.218716i
$491$		−	9699.68i		−	0.891528i	−0.895150	−	0.445764i	$-0.852932\pi$
$491$		−	9699.68i		−	0.891528i	0.895150	−	0.445764i	$-0.147068\pi$
$492$	6379.12	−	2148.25i	0.584539	−	0.196851i
$493$			8449.19i			0.771871i
$494$	3477.59	−	851.510i	0.316729	−	0.0775531i
$495$	371.265			0.0337113
$496$	−11763.1	−	15484.3i	−1.06488	−	1.40175i
$497$	4189.62			0.378129
$498$	2064.99	−	338.369i	0.185812	−	0.0304472i
$499$	−10351.2			−0.928620			−0.464310	−	0.885673i	$-0.653698\pi$
$499$	−10351.2			−0.928620			−0.464310	+	0.885673i	$0.653698\pi$
$500$	−7937.39	+	2673.01i	−0.709942	+	0.239082i
$501$	1207.23			0.107655
$502$	274.481	−	44.9765i	0.0244038	−	0.00399881i
$503$	−14291.2			−1.26682			−0.633412	−	0.773815i	$-0.718346\pi$
$503$	−14291.2			−1.26682			−0.633412	+	0.773815i	$0.718346\pi$
$504$	−4138.82	+	2193.00i	−0.365789	+	0.193817i
$505$			4007.57i			0.353138i
$506$	147.687	+	901.297i	0.0129752	+	0.0791849i
$507$	1020.32	+	6511.55i	0.0893769	+	0.570390i
$508$	−7876.32	+	2652.45i	−0.687904	+	0.231660i
$509$	−6030.07			−0.525104			−0.262552	−	0.964918i	$-0.584564\pi$
$509$	−6030.07			−0.525104			−0.262552	+	0.964918i	$0.584564\pi$
$510$	2273.67	−	372.564i	0.197411	−	0.0323478i
$511$	−18765.5			−1.62454
$512$	11516.4	+	1260.82i	0.994060	+	0.108830i
$513$			729.164i			0.0627551i
$514$	1074.02	+	6554.51i	0.0921655	+	0.562465i
$515$	5379.99			0.460331
$516$	4509.60	−	1518.66i	0.384737	−	0.129565i
$517$		−	2883.62i		−	0.245303i
$518$	−15491.0	+	2538.36i	−1.31397	+	0.215307i
$519$	−10623.8			−0.898522
$520$	4093.11	−	2594.58i	0.345183	−	0.218807i
$521$	−2617.24			−0.220083			−0.110042	−	0.993927i	$-0.535098\pi$
$521$	−2617.24			−0.220083			−0.110042	+	0.993927i	$0.535098\pi$
$522$	−3571.77	+	585.271i	−0.299487	+	0.0490739i
$523$		−	21188.4i		−	1.77152i	−0.464144	−	0.885760i	$-0.653638\pi$
$523$		−	21188.4i		−	1.77152i	0.464144	−	0.885760i	$-0.346362\pi$
$524$	363.997	+	1080.87i	0.0303459	+	0.0901108i
$525$	−7184.45			−0.597248
$526$	−1670.82	−	10196.6i	−0.138500	−	0.845235i
$527$			18055.5i			1.49243i
$528$	−1048.56	−	1380.26i	−0.0864253	−	0.113766i
$529$	−10887.7			−0.894856
$530$	−6773.85	+	1109.96i	−0.555164	+	0.0909693i
$531$	3403.03			0.278115
$532$	−1585.91	−	4709.29i	−0.129244	−	0.383785i
$533$	−13106.3	+	1020.61i	−1.06510	+	0.0829411i
$534$	488.334	+	2980.19i	0.0395736	+	0.241508i
$535$			5141.33i			0.415475i
$536$	2623.10	+	4950.54i	0.211382	+	0.398938i
$537$	−11266.8			−0.905396
$538$	1384.95	−	226.938i	0.110984	−	0.0181858i
$539$	−1679.29			−0.134197
$540$	314.992	+	935.353i	0.0251020	+	0.0745392i
$541$	5104.29			0.405639			0.202819	−	0.979216i	$-0.434990\pi$
$541$	5104.29			0.405639			0.202819	+	0.979216i	$0.434990\pi$
$542$	3250.92	−	532.695i	0.257636	−	0.0422163i
$543$	−3438.62			−0.271759
$544$	−7806.58	−	7400.67i	−0.615265	−	0.583274i
$545$	−3601.10			−0.283035
$546$	8885.24	−	2175.61i	0.696434	−	0.170526i
$547$		−	10142.1i		−	0.792770i	−0.918084	−	0.396385i	$-0.870265\pi$
$547$		−	10142.1i		−	0.792770i	0.918084	−	0.396385i	$-0.129735\pi$
$548$	−6160.95	−	18294.6i	−0.480260	−	1.42611i
$549$		−	7910.51i		−	0.614959i
$550$	−429.929	−	2623.76i	−0.0333314	−	0.203414i
$551$		−	3839.82i		−	0.296882i
$552$	−2145.40	+	1136.76i	−0.165424	+	0.0876520i
$553$		−	18801.8i		−	1.44581i
$554$	9886.34	−	1619.98i	0.758178	−	0.124235i
$555$			3307.71i			0.252981i
$556$	2111.52	+	6270.07i	0.161058	+	0.478255i
$557$	−1339.31			−0.101882			−0.0509409	−	0.998702i	$-0.516222\pi$
$557$	−1339.31			−0.101882			−0.0509409	+	0.998702i	$0.516222\pi$
$558$	−7632.68	+	1250.69i	−0.579063	+	0.0948854i
$559$	−9265.24	+	721.503i	−0.701034	+	0.0545909i
$560$	−4068.73	−	5355.86i	−0.307027	−	0.404154i
$561$			1609.45i			0.121125i
$562$	−2796.57	+	458.245i	−0.209904	+	0.0343949i
$563$			7894.26i			0.590947i	0.955351	+	0.295474i	$0.0954775\pi$
$563$			7894.26i			0.590947i	−0.955351	+	0.295474i	$0.904523\pi$
$564$	7264.92	−	2446.55i	0.542390	−	0.182657i
$565$	5402.41			0.402267
$566$	12480.8	−	2045.10i	0.926865	−	0.151876i
$567$			1863.02i			0.137988i
$568$	−3642.04	+	1929.78i	−0.269044	+	0.142556i
$569$	−5150.43			−0.379468			−0.189734	−	0.981836i	$-0.560763\pi$
$569$	−5150.43			−0.379468			−0.189734	+	0.981836i	$0.560763\pi$
$570$	−1033.29	+	169.315i	−0.0759296	+	0.0124418i
$571$			9653.04i			0.707473i	0.935345	+	0.353737i	$0.115089\pi$
$571$			9653.04i			0.707473i	−0.935345	+	0.353737i	$0.884911\pi$
$572$	1326.24	+	3114.70i	0.0969456	+	0.227678i
$573$		−	6544.35i		−	0.477128i
$574$	2950.35	+	18005.3i	0.214539	+	1.30928i
$575$	−3724.14			−0.270099
$576$	2587.77	−	3812.76i	0.187194	−	0.275807i
$577$			6097.68i			0.439948i	0.975506	+	0.219974i	$0.0705972\pi$
$577$			6097.68i			0.439948i	−0.975506	+	0.219974i	$0.929403\pi$
$578$	−631.958	−	3856.69i	−0.0454775	−	0.277539i
$579$	13315.7			0.955756
$580$	−1658.76	−	4925.62i	−0.118752	−	0.352630i
$581$			5672.00i			0.405016i
$582$	695.256	+	4242.98i	0.0495177	+	0.302195i
$583$		−	4794.98i		−	0.340631i
$584$	16312.9	−	8643.59i	1.15588	−	0.612456i
$585$	−149.649	−	1921.74i	−0.0105765	−	0.135819i
$586$	−1506.10	−	9191.41i	−0.106172	−	0.647941i
$587$	18721.5			1.31639			0.658195	−	0.752847i	$-0.271320\pi$
$587$	18721.5			1.31639			0.658195	+	0.752847i	$0.271320\pi$
$588$	−1424.76	−	4230.75i	−0.0999251	−	0.296723i
$589$		−	8205.50i		−	0.574027i
$590$	790.200	+	4822.41i	0.0551390	+	0.336501i
$591$			11365.5i			0.791053i
$592$	12297.2	−	9341.91i	0.853735	−	0.648565i
$593$		−	27503.7i		−	1.90462i	−0.305127	−	0.952312i	$-0.598699\pi$
$593$		−	27503.7i		−	1.90462i	0.305127	−	0.952312i	$-0.401301\pi$
$594$	−680.373	+	111.486i	−0.0469967	+	0.00770088i
$595$			6245.19i			0.430299i
$596$	23897.1	−	8047.64i	1.64239	−	0.553094i
$597$		−	4607.54i		−	0.315869i
$598$	4605.76	−	1127.75i	0.314956	−	0.0771189i
$599$	6924.86			0.472357			0.236179	−	0.971710i	$-0.424105\pi$
$599$	6924.86			0.472357			0.236179	+	0.971710i	$0.424105\pi$
$600$	6245.46	−	3309.22i	0.424950	−	0.225164i
$601$	−438.105			−0.0297349			−0.0148674	−	0.999889i	$-0.504733\pi$
$601$	−438.105			−0.0297349			−0.0148674	+	0.999889i	$0.504733\pi$
$602$	2085.69	+	12728.5i	0.141207	+	0.861752i
$603$	2228.40			0.150493
$604$	−2385.57	−	7083.83i	−0.160708	−	0.477214i
$605$	5709.31			0.383664
$606$	−1203.42	−	7344.21i	−0.0806695	−	0.492307i
$607$	−130.867			−0.00875076			−0.00437538	−	0.999990i	$-0.501393\pi$
$607$	−130.867			−0.00875076			−0.00437538	+	0.999990i	$0.501393\pi$
$608$	3547.78	+	3363.31i	0.236647	+	0.224343i
$609$		−	9810.75i		−	0.652794i
$610$	11209.9	−	1836.86i	0.744060	−	0.121922i
$611$	−14926.2	+	1162.33i	−0.988296	+	0.0769606i
$612$	−4054.81	+	1365.51i	−0.267820	+	0.0901918i
$613$	14591.0			0.961382			0.480691	−	0.876890i	$-0.340386\pi$
$613$	14591.0			0.961382			0.480691	+	0.876890i	$0.340386\pi$
$614$	−1497.50	−	9138.89i	−0.0984270	−	0.600677i
$615$	3844.57			0.252078
$616$	4151.70	−	2199.82i	0.271553	−	0.143885i
$617$		−	26154.6i		−	1.70656i	−0.521457	−	0.853278i	$-0.674611\pi$
$617$		−	26154.6i		−	1.70656i	0.521457	−	0.853278i	$-0.325389\pi$
$618$	−9859.27	+	1615.54i	−0.641745	+	0.105156i
$619$	5541.38			0.359817			0.179909	−	0.983683i	$-0.442420\pi$
$619$	5541.38			0.359817			0.179909	+	0.983683i	$0.442420\pi$
$620$	−3544.69	−	10525.8i	−0.229610	−	0.681817i
$621$			965.714i			0.0624038i
$622$	1459.61	+	8907.64i	0.0940915	+	0.574218i
$623$	−8185.83			−0.526418
$624$	−6721.85	+	5983.89i	−0.431233	+	0.383890i
$625$	8231.49			0.526815
$626$	2529.19	+	15435.1i	0.161481	+	0.985479i
$627$		−	731.433i		−	0.0465879i
$628$	784.382	+	2329.19i	0.0498412	+	0.148001i
$629$	−14339.1			−0.908963
$630$	−2640.06	+	432.601i	−0.166957	+	0.0273575i
$631$		−	3022.53i		−	0.190689i	−0.995444	−	0.0953447i	$-0.969605\pi$
$631$		−	3022.53i		−	0.190689i	0.995444	−	0.0953447i	$-0.0303953\pi$
$632$	8660.28	+	16344.4i	0.545075	+	1.02871i
$633$	15500.9			0.973308
$634$	2961.72	+	18074.7i	0.185528	+	1.13224i
$635$	−4746.90			−0.296653
$636$	12080.3	−	4068.20i	0.753170	−	0.253639i
$637$	676.888	+	8692.32i	0.0421025	+	0.540663i
$638$	3582.88	−	587.092i	0.222332	−	0.0364313i
$639$			1639.40i			0.101493i
$640$	6003.92	+	2781.76i	0.370822	+	0.171811i
$641$	−24068.8			−1.48309			−0.741545	−	0.670904i	$-0.765906\pi$
$641$	−24068.8			−1.48309			−0.741545	+	0.670904i	$0.765906\pi$
$642$	−1543.88	−	9421.92i	−0.0949096	−	0.579211i
$643$	10923.5			0.669952			0.334976	−	0.942227i	$-0.391272\pi$
$643$	10923.5			0.669952			0.334976	+	0.942227i	$0.391272\pi$
$644$	−2100.40	−	6237.05i	−0.128521	−	0.381637i
$645$	2717.84			0.165915
$646$	−733.992	−	4479.39i	−0.0447036	−	0.272816i
$647$	−6403.53			−0.389102			−0.194551	−	0.980892i	$-0.562325\pi$
$647$	−6403.53			−0.389102			−0.194551	+	0.980892i	$0.562325\pi$
$648$	−858.123	−	1619.52i	−0.0520220	−	0.0981804i
$649$	−3413.62			−0.206466
$650$	−13407.8	+	3282.98i	−0.809072	+	0.198106i
$651$		−	20965.1i		−	1.26219i
$652$	−2795.34	+	941.365i	−0.167905	+	0.0565440i
$653$			3560.37i			0.213366i	0.994293	+	0.106683i	$0.0340230\pi$
$653$			3560.37i			0.213366i	−0.994293	+	0.106683i	$0.965977\pi$
$654$	6599.31	−	1081.36i	0.394577	−	0.0646554i
$655$			651.419i			0.0388596i
$656$	−10858.2	−	14293.1i	−0.646249	−	0.850688i
$657$		−	7342.98i		−	0.436038i
$658$	3360.03	+	20505.5i	0.199069	+	1.21487i
$659$			18983.0i			1.12212i	0.827776	+	0.561058i	$0.189606\pi$
$659$			18983.0i			1.12212i	−0.827776	+	0.561058i	$0.810394\pi$
$660$	−315.972	−	938.264i	−0.0186351	−	0.0553362i
$661$	6588.80			0.387707			0.193854	−	0.981030i	$-0.437901\pi$
$661$	6588.80			0.387707			0.193854	+	0.981030i	$0.437901\pi$
$662$	−4581.11	−	27957.4i	−0.268957	−	1.64138i
$663$	8330.84	−	648.739i	0.487999	−	0.0380014i
$664$	−2612.58	−	4930.68i	−0.152692	−	0.288174i
$665$		−	2838.19i		−	0.165504i
$666$	−993.263	−	6061.65i	−0.0577900	−	0.352679i
$667$		−	5085.51i		−	0.295220i
$668$	−1027.44	−	3050.94i	−0.0595103	−	0.176713i
$669$	−14437.4			−0.834352
$670$	517.445	+	3157.85i	0.0298368	+	0.182087i
$671$			7935.13i			0.456531i
$672$	9064.59	+	8593.27i	0.520348	+	0.493292i
$673$	−11113.6			−0.636547			−0.318273	−	0.947999i	$-0.603103\pi$
$673$	−11113.6			−0.636547			−0.318273	+	0.947999i	$0.603103\pi$
$674$	−3019.91	−	18429.8i	−0.172586	−	1.05325i
$675$		−	2811.28i		−	0.160306i
$676$	15587.7	−	8120.34i	0.886873	−	0.462013i
$677$		−	7932.48i		−	0.450325i	−0.974321	−	0.225162i	$-0.927709\pi$
$677$		−	7932.48i		−	0.450325i	0.974321	−	0.225162i	$-0.0722913\pi$
$678$	−9900.36	+	1622.27i	−0.560798	+	0.0918924i
$679$	−11654.4			−0.658697
$680$	−2876.60	−	5428.96i	−0.162224	−	0.306163i
$681$		−	1754.84i		−	0.0987453i
$682$	7656.44	−	1254.58i	0.429883	−	0.0704406i
$683$	−3650.03			−0.204487			−0.102244	−	0.994759i	$-0.532602\pi$
$683$	−3650.03			−0.204487			−0.102244	+	0.994759i	$0.532602\pi$
$684$	1842.75	−	620.569i	0.103011	−	0.0346901i
$685$		−	11025.8i		−	0.614999i
$686$	−10078.6	+	1651.47i	−0.560934	+	0.0919148i
$687$		−	13752.8i		−	0.763761i
$688$	−7675.97	−	10104.2i	−0.425354	−	0.559913i
$689$	−24819.7	+	1932.76i	−1.37236	+	0.106868i
$690$	−1368.51	+	224.243i	−0.0755045	+	0.0123722i
$691$	−7823.65			−0.430717			−0.215359	−	0.976535i	$-0.569092\pi$
$691$	−7823.65			−0.430717			−0.215359	+	0.976535i	$0.569092\pi$
$692$	9041.58	+	26848.6i	0.496690	+	1.47490i
$693$		−	1868.81i		−	0.102439i
$694$	22960.9	−	3762.37i	1.25588	−	0.205789i
$695$			3778.84i			0.206244i
$696$	4518.93	+	8528.51i	0.246105	+	0.464472i
$697$			16666.4i			0.905719i
$698$	−2738.56	−	16712.8i	−0.148504	−	0.906287i
$699$		−	12906.5i		−	0.698380i
$700$	6114.46	+	18156.6i	0.330150	+	0.980365i
$701$			30382.7i			1.63700i	0.574507	+	0.818500i	$0.305194\pi$
$701$			30382.7i			1.63700i	−0.574507	+	0.818500i	$0.694806\pi$
$702$	851.318	+	3476.80i	0.0457705	+	0.186928i
$703$	6516.56			0.349611
$704$	−2595.82	+	3824.62i	−0.138968	+	0.204753i
$705$	4378.42			0.233902
$706$	−23368.7	+	3829.20i	−1.24574	+	0.204127i
$707$	20172.7			1.07309
$708$	−2896.21	−	8600.18i	−0.153738	−	0.456518i
$709$	19960.9			1.05733			0.528665	−	0.848830i	$-0.322693\pi$
$709$	19960.9			1.05733			0.528665	+	0.848830i	$0.322693\pi$
$710$	−2323.18	+	380.677i	−0.122799	+	0.0201219i
$711$	7357.16			0.388066
$712$	7115.96	−	3770.47i	0.374553	−	0.198461i
$713$		−	10867.5i		−	0.570813i
$714$	−1875.35	−	11444.8i	−0.0982959	−	0.599877i
$715$	150.115	+	1927.72i	0.00785173	+	0.100829i
$716$	9588.81	+	28473.5i	0.500490	+	1.48618i
$717$	−21397.3			−1.11450
$718$	−14976.2	+	2454.00i	−0.778422	+	0.127552i
$719$	10658.4			0.552838			0.276419	−	0.961037i	$-0.410852\pi$
$719$	10658.4			0.552838			0.276419	+	0.961037i	$0.410852\pi$
$720$	2095.75	−	1592.10i	0.108478	−	0.0824084i
$721$		−	27080.9i		−	1.39882i
$722$	−2803.51	−	17109.2i	−0.144509	−	0.881907i
$723$	−2439.56			−0.125489
$724$	2926.50	+	8690.11i	0.150225	+	0.446085i
$725$			14804.4i			0.758373i
$726$	−10462.8	+	1714.43i	−0.534863	+	0.0876427i
$727$	20458.2			1.04368			0.521838	−	0.853045i	$-0.325247\pi$
$727$	20458.2			1.04368			0.521838	+	0.853045i	$0.325247\pi$
$728$	−13060.2	−	20603.3i	−0.664893	−	1.04891i
$729$	−729.000			−0.0370370
$730$	10405.7	−	1705.07i	0.527577	−	0.0864488i
$731$			11782.0i			0.596134i
$732$	−19991.5	+	6732.39i	−1.00944	+	0.339940i
$733$	31681.2			1.59642			0.798208	−	0.602382i	$-0.205782\pi$
$733$	31681.2			1.59642			0.798208	+	0.602382i	$0.205782\pi$
$734$	929.598	+	5673.12i	0.0467467	+	0.285284i
$735$		−	2549.79i		−	0.127960i
$736$	4698.73	+	4454.41i	0.235323	+	0.223087i
$737$	−2235.33			−0.111723
$738$	−7045.49	+	1154.47i	−0.351420	+	0.0575837i
$739$	−33577.7			−1.67142			−0.835709	−	0.549173i	$-0.814943\pi$
$739$	−33577.7			−1.67142			−0.835709	+	0.549173i	$0.814943\pi$
$740$	8359.28	−	2815.09i	0.415261	−	0.139844i
$741$	−3786.04	+	294.826i	−0.187697	+	0.0146164i
$742$	5587.16	+	34097.1i	0.276430	+	1.68699i
$743$		−	19963.9i		−	0.985740i	−0.870103	−	0.492870i	$-0.835948\pi$
$743$		−	19963.9i		−	0.985740i	0.870103	−	0.492870i	$-0.164052\pi$
$744$	9656.70	+	18225.0i	0.475849	+	0.898064i
$745$	14402.3			0.708267
$746$	−38706.6	+	6342.47i	−1.89967	+	0.311279i
$747$	−2219.46			−0.108709
$748$	4067.43	−	1369.76i	0.198823	−	0.0669562i
$749$	25879.6			1.26251
$750$	8766.53	−	1436.48i	0.426811	−	0.0699373i
$751$	34167.4			1.66017			0.830083	−	0.557640i	$-0.188293\pi$
$751$	34167.4			1.66017			0.830083	+	0.557640i	$0.188293\pi$
$752$	−12365.9	−	16277.8i	−0.599651	−	0.789348i
$753$	−295.014			−0.0142774
$754$	−4483.09	−	18309.1i	−0.216531	−	0.884319i
$755$		−	4269.28i		−	0.205795i
$756$	4708.23	−	1585.55i	0.226504	−	0.0762779i
$757$		−	35511.1i		−	1.70498i	−0.522741	−	0.852492i	$-0.675090\pi$
$757$		−	35511.1i		−	1.70498i	0.522741	−	0.852492i	$-0.324910\pi$
$758$	2033.34	+	12409.0i	0.0974332	+	0.594612i
$759$		−	968.719i		−	0.0463271i
$760$	1307.30	+	2467.25i	0.0623957	+	0.117759i
$761$			29278.7i			1.39468i	0.716741	+	0.697340i	$0.245633\pi$
$761$			29278.7i			1.39468i	−0.716741	+	0.697340i	$0.754367\pi$
$762$	8699.08	−	1425.43i	0.413562	−	0.0677663i
$763$			18126.6i			0.860063i
$764$	−16539.0	+	5569.70i	−0.783192	+	0.263749i
$765$	−2443.75			−0.115495
$766$	5254.20	−	860.954i	0.247835	−	0.0406103i
$767$	1375.96	+	17669.6i	0.0647760	+	0.831826i
$768$	−11838.0	−	3294.91i	−0.556208	−	0.154811i
$769$			26102.0i			1.22401i	0.790855	+	0.612003i	$0.209636\pi$
$769$			26102.0i			1.22401i	−0.790855	+	0.612003i	$0.790364\pi$
$770$	2648.28	−	433.947i	0.123945	−	0.0203096i
$771$		−	7044.82i		−	0.329070i
$772$	−11332.6	−	33651.6i	−0.528328	−	1.56885i
$773$	−29899.4			−1.39121			−0.695605	−	0.718424i	$-0.744864\pi$
$773$	−29899.4			−1.39121			−0.695605	+	0.718424i	$0.744864\pi$
$774$	−4980.68	+	816.134i

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+(0.457367 + 2.79120i) q^{2} -3.00000i q^{3} +(-7.58163 + 2.55321i) q^{4} -4.56929 q^{5} +(8.37361 - 1.37210i) q^{6} +23.0002i q^{7} +(-10.5941 - 19.9941i) q^{8} -9.00000 q^{9} +(-2.08984 - 12.7538i) q^{10} +9.02801 q^{11} +(7.65962 + 22.7449i) q^{12} +(-3.63901 - 46.7307i) q^{13} +(-64.1982 + 10.5195i) q^{14} +13.7079i q^{15} +(50.9623 - 38.7150i) q^{16} -59.4245 q^{17} +(-4.11630 - 25.1208i) q^{18} +27.0061 q^{19} +(34.6427 - 11.6664i) q^{20} +69.0006 q^{21} +(4.12911 + 25.1990i) q^{22} +35.7672 q^{23} +(-59.9824 + 31.7823i) q^{24} -104.122 q^{25} +(128.770 - 31.5303i) q^{26} +27.0000i q^{27} +(-58.7243 - 174.379i) q^{28} -142.184i q^{29} +(-38.2615 + 6.26953i) q^{30} -303.839i q^{31} +(131.370 + 124.539i) q^{32} -27.0840i q^{33} +(-27.1788 - 165.866i) q^{34} -105.095i q^{35} +(68.2347 - 22.9789i) q^{36} +241.300 q^{37} +(12.3517 + 75.3795i) q^{38} +(-140.192 + 10.9170i) q^{39} +(48.4076 + 91.3590i) q^{40} -280.464i q^{41} +(31.5586 + 192.595i) q^{42} -198.269i q^{43} +(-68.4470 + 23.0504i) q^{44} +41.1236 q^{45} +(16.3587 + 99.8335i) q^{46} -319.409i q^{47} +(-116.145 - 152.887i) q^{48} -186.009 q^{49} +(-47.6217 - 290.624i) q^{50} +178.273i q^{51} +(146.903 + 345.004i) q^{52} -531.123i q^{53} +(-75.3625 + 12.3489i) q^{54} -41.2516 q^{55} +(459.869 - 243.666i) q^{56} -81.0182i q^{57} +(396.863 - 65.0301i) q^{58} -378.115 q^{59} +(-34.9991 - 103.928i) q^{60} +878.946i q^{61} +(848.076 - 138.966i) q^{62} -207.002i q^{63} +(-287.530 + 423.640i) q^{64} +(16.6277 + 213.526i) q^{65} +(75.5970 - 12.3873i) q^{66} -247.600 q^{67} +(450.534 - 151.723i) q^{68} -107.302i q^{69} +(293.340 - 48.0668i) q^{70} -182.156i q^{71} +(95.3470 + 179.947i) q^{72} +815.886i q^{73} +(110.363 + 673.517i) q^{74} +312.365i q^{75} +(-204.750 + 68.9521i) q^{76} +207.646i q^{77} +(-94.5909 - 386.311i) q^{78} -817.462 q^{79} +(-232.862 + 176.900i) q^{80} +81.0000 q^{81} +(782.832 - 128.275i) q^{82} +246.607 q^{83} +(-523.137 + 176.173i) q^{84} +271.528 q^{85} +(553.408 - 90.6816i) q^{86} -426.551 q^{87} +(-95.6437 - 180.507i) q^{88} +355.903i q^{89} +(18.8086 + 114.784i) q^{90} +(1074.81 - 83.6980i) q^{91} +(-271.174 + 91.3211i) q^{92} -911.517 q^{93} +(891.534 - 146.087i) q^{94} -123.399 q^{95} +(373.617 - 394.109i) q^{96} +506.709i q^{97} +(-85.0742 - 519.188i) q^{98} -81.2521 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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