LMFDB - Embedded newform 312.4.m.a.181.40

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			181.40
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.39

$q$-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} +(-132.099 - 11.2158i) 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} +(91.7235 - 363.586i) 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} +(33.6475 - 396.298i) 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	$-0.434494\pi$
$5$	4.56929			0.408690			0.204345	+	0.978899i	$0.434494\pi$
$6$	−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	$-0.539485\pi$
$11$	−9.02801			−0.247459			−0.123729	+	0.992316i	$0.539485\pi$
$12$	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	$-0.552131\pi$
$19$	−27.0061			−0.326085			−0.163043	+	0.986619i	$0.552131\pi$
$20$	−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
$26$	−132.099	−	11.2158i	−0.996415	−	0.0846003i
$27$		−	27.0000i		−	0.192450i
$28$	58.7243	−	174.379i	0.396351	−	1.17695i
$29$			142.184i			0.910442i	0.890378	+	0.455221i	$0.150440\pi$
$29$			142.184i			0.910442i	−0.890378	+	0.455221i	$0.849560\pi$
$30$	−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	$-0.680093\pi$
$37$	−241.300			−1.07215			−0.536074	+	0.844171i	$0.680093\pi$
$38$	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	$0.114355\pi$
$43$			198.269i			0.703156i	−0.936159	+	0.351578i	$0.885645\pi$
$44$	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
$52$	91.7235	−	363.586i	0.244611	−	0.969621i
$53$			531.123i			1.37652i	0.725466	+	0.688258i	$0.241624\pi$
$53$			531.123i			1.37652i	−0.725466	+	0.688258i	$0.758376\pi$
$54$	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	$-0.363021\pi$
$59$	378.115			0.834345			0.417172	+	0.908827i	$0.363021\pi$
$60$	34.9991	−	103.928i	0.0753060	−	0.223618i
$61$		−	878.946i		−	1.84488i	−0.386145	−	0.922438i	$-0.626193\pi$
$61$		−	878.946i		−	1.84488i	0.386145	−	0.922438i	$-0.373807\pi$
$62$	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	$-0.427520\pi$
$67$	247.600			0.451480			0.225740	+	0.974188i	$0.427520\pi$
$68$	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
$78$	33.6475	−	396.298i	0.0488440	−	0.575280i
$79$	−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	$-0.552138\pi$
$83$	−246.607			−0.326128			−0.163064	+	0.986616i	$0.552138\pi$
$84$	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	$0.142205\pi$
$101$			877.066i			0.864073i	−0.901856	+	0.432036i	$0.857795\pi$
$102$	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	$0.690422\pi$
$104$	972.891	+	422.311i	0.917306	+	0.398183i
$105$	−315.284			−0.293034
$106$	−1482.47	−	242.918i	−1.35840	−	0.222587i
$107$			1125.19i			1.01660i	0.861179	+	0.508301i	$0.169726\pi$
$107$			1125.19i			1.01660i	−0.861179	+	0.508301i	$0.830274\pi$
$108$	−68.9366	+	204.704i	−0.0614206	+	0.182386i
$109$	−788.108			−0.692542			−0.346271	−	0.938135i	$-0.612552\pi$
$109$	−788.108			−0.692542			−0.346271	+	0.938135i	$0.612552\pi$
$110$	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
$130$	−603.600	−	51.2485i	−0.407225	−	0.0345753i
$131$			142.564i			0.0950833i	0.998869	+	0.0475417i	$0.0151387\pi$
$131$			142.564i			0.0950833i	−0.998869	+	0.0475417i	$0.984861\pi$
$132$	−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	$0.0811946\pi$
$139$			827.007i			0.504646i	−0.967643	+	0.252323i	$0.918805\pi$
$140$	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	$-0.166359\pi$
$149$	3151.97			1.73302			0.866509	+	0.499162i	$0.166359\pi$
$150$	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
$156$	1090.76	+	275.171i	0.559811	+	0.141226i
$157$			307.214i			0.156168i	0.996947	+	0.0780840i	$0.0248802\pi$
$157$			307.214i			0.156168i	−0.996947	+	0.0780840i	$0.975120\pi$
$158$	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	$-0.528235\pi$
$163$	−368.699			−0.177170			−0.0885851	+	0.996069i	$0.528235\pi$
$164$	−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	$0.283838\pi$
$173$			3541.26i			1.55629i	−0.628088	+	0.778143i	$0.716162\pi$
$174$	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	$0.286873\pi$
$179$			3755.60i			1.56819i	−0.620640	+	0.784096i	$0.713127\pi$
$180$	311.784	+	104.997i	0.129106	+	0.0434779i
$181$			1146.21i			0.470701i	0.971911	+	0.235350i	$0.0756238\pi$
$181$			1146.21i			0.470701i	−0.971911	+	0.235350i	$0.924376\pi$
$182$	257.967	−	3038.31i	0.105065	−	1.23744i
$183$	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	$-0.259771\pi$
$197$	3788.49			1.37014			0.685072	+	0.728475i	$0.259771\pi$
$198$	−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
$208$	−1623.72	+	2522.39i	−0.541274	+	0.840846i
$209$	243.811			0.0806927
$210$	144.200	−	880.021i	0.0473846	−	0.289177i
$211$		−	5166.95i		−	1.68582i	−0.538055	−	0.842909i	$-0.680841\pi$
$211$		−	5166.95i		−	1.68582i	0.538055	−	0.842909i	$-0.319159\pi$
$212$	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	$-0.527254\pi$
$227$	−584.946			−0.171032			−0.0855159	+	0.996337i	$0.527254\pi$
$228$	−206.856	+	614.250i	−0.0600851	+	0.178420i
$229$	−4584.28			−1.32287			−0.661436	−	0.750001i	$-0.730053\pi$
$229$	−4584.28			−1.32287			−0.661436	+	0.750001i	$0.730053\pi$
$230$	−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	$0.293247\pi$
$234$	1188.89	+	100.943i	0.332138	+	0.0282001i
$235$		−	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	$0.00393588\pi$
$251$			98.3380i			0.0247292i	−0.999924	+	0.0123646i	$0.996064\pi$
$252$	−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
$260$	419.112	−	1661.33i	0.0999700	−	0.396275i
$261$		−	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	$0.0179086\pi$
$269$			496.183i			0.112464i	−0.998418	+	0.0562320i	$0.982091\pi$
$270$	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	$0.125504\pi$
$277$			3541.96i			0.768289i	−0.923273	+	0.384144i	$0.874496\pi$
$278$	−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	$0.155607\pi$
$283$			4471.46i			0.939226i	−0.882872	+	0.469613i	$0.844393\pi$
$284$	−465.081	+	1381.04i	−0.0971743	+	0.288555i
$285$		−	370.196i		−	0.0769422i
$286$	1192.59	+	101.257i	0.246572	+	0.0209351i
$287$	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	$-0.393527\pi$
$293$	3292.99			0.656582			0.328291	+	0.944577i	$0.393527\pi$
$294$	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	$-0.401563\pi$
$307$	3274.18			0.608688			0.304344	+	0.952562i	$0.401563\pi$
$308$	−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	$0.406033\pi$
$312$	−1266.93	+	2918.67i	−0.229891	+	0.529607i
$313$	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	$-0.694480\pi$
$317$	−6475.59			−1.14734			−0.573668	+	0.819088i	$0.694480\pi$
$318$	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	$-0.187404\pi$
$331$	10016.3			1.66327			0.831637	+	0.555319i	$0.187404\pi$
$332$	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	$0.679179\pi$
$338$	43.4135	−	6213.90i	0.00698634	−	0.999976i
$339$		−	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	$0.219542\pi$
$347$			8226.15i			1.27263i	−0.771429	+	0.636315i	$0.780458\pi$
$348$	3233.95	+	1089.07i	0.498155	+	0.167760i
$349$	5987.66			0.918373			0.459187	−	0.888340i	$-0.348141\pi$
$349$	5987.66			0.918373			0.459187	+	0.888340i	$0.348141\pi$
$350$	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
$364$	8362.55	+	2109.66i	1.20417	+	0.303781i
$365$			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	$-0.587448\pi$
$373$		−	13867.4i		−	1.92500i	0.271282	−	0.962500i	$-0.412552\pi$
$374$	−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	$-0.597411\pi$
$379$	−4445.76			−0.602542			−0.301271	+	0.953539i	$0.597411\pi$
$380$	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	$0.0945266\pi$
$389$			4490.10i			0.585237i	−0.956229	+	0.292619i	$0.905473\pi$
$390$	153.745	−	1810.80i	0.0199621	−	0.235111i
$391$	−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	$-0.705172\pi$
$397$	−9505.67			−1.20170			−0.600852	+	0.799361i	$0.705172\pi$
$398$	−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
$416$	−6297.85	−	5685.80i	−0.742254	−	0.670118i
$417$	−2481.02			−0.291358
$418$	−111.511	+	680.526i	−0.0130483	+	0.0796307i
$419$			12868.1i			1.50035i	0.661241	+	0.750174i	$0.270030\pi$
$419$			12868.1i			1.50035i	−0.661241	+	0.750174i	$0.729970\pi$
$420$	2390.37	+	804.985i	0.277709	+	0.0935220i
$421$	−4414.39			−0.511031			−0.255516	−	0.966805i	$-0.582245\pi$
$421$	−4414.39			−0.511031			−0.255516	+	0.966805i	$0.582245\pi$
$422$	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
$442$	7849.93	+	666.496i	0.844758	+	0.0717239i
$443$		−	3110.29i		−	0.333576i	−0.985993	−	0.166788i	$-0.946660\pi$
$443$		−	3110.29i		−	0.333576i	0.985993	−	0.166788i	$-0.0533395\pi$
$444$	−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	$-0.479464\pi$
$461$	1276.30			0.128944			0.0644722	+	0.997920i	$0.479464\pi$
$462$	−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	$-0.625148\pi$
$467$		−	18643.9i		−	1.84740i	0.383112	−	0.923702i	$-0.374852\pi$
$468$	−825.512	+	3272.27i	−0.0815369	+	0.323207i
$469$			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	$0.147068\pi$
$491$			9699.68i			0.891528i	−0.895150	+	0.445764i	$0.852932\pi$
$492$	−6379.12	−	2148.25i	−0.584539	−	0.196851i
$493$		−	8449.19i		−	0.771871i
$494$	3567.48	+	302.896i	0.324916	+	0.0275869i
$495$	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	$-0.346302\pi$
$499$	10351.2			0.928620			0.464310	+	0.885673i	$0.346302\pi$
$500$	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	$-0.415436\pi$
$509$	6030.07			0.525104			0.262552	+	0.964918i	$0.415436\pi$
$510$	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
$520$	4445.43	+	1929.66i	0.374894	+	0.162733i
$521$	−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	$0.346362\pi$
$523$			21188.4i			1.77152i	−0.464144	+	0.885760i	$0.653638\pi$
$524$	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	$-0.565010\pi$
$541$	−5104.29			−0.405639			−0.202819	+	0.979216i	$0.565010\pi$
$542$	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
$546$	9114.92	+	773.900i	0.714437	+	0.0606591i
$547$			10142.1i			0.792770i	0.918084	+	0.396385i	$0.129735\pi$
$547$			10142.1i			0.792770i	−0.918084	+	0.396385i	$0.870265\pi$
$548$	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	$-0.483778\pi$
$557$	1339.31			0.101882			0.0509409	+	0.998702i	$0.483778\pi$
$558$	−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	$-0.904523\pi$
$563$		−	7894.26i		−	0.590947i	0.955351	−	0.295474i	$-0.0954775\pi$
$564$	−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	$-0.884911\pi$
$571$		−	9653.04i		−	0.707473i	0.935345	−	0.353737i	$-0.115089\pi$
$572$	−828.080	+	3282.46i	−0.0605311	+	0.239941i
$573$			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	$-0.728680\pi$
$587$	−18721.5			−1.31639			−0.658195	+	0.752847i	$0.728680\pi$
$588$	−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
$598$	−4724.82	−	401.159i	−0.323097	−	0.0274325i
$599$	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	$-0.659614\pi$
$613$	−14591.0			−0.961382			−0.480691	+	0.876890i	$0.659614\pi$
$614$	−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	$-0.557580\pi$
$619$	−5541.38			−0.359817			−0.179909	+	0.983683i	$0.557580\pi$
$620$	−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
$624$	−7567.16	−	4871.17i	−0.485463	−	0.312505i
$625$	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	$-0.608728\pi$
$643$	−10923.5			−0.669952			−0.334976	+	0.942227i	$0.608728\pi$
$644$	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
$650$	13754.4	+	1167.81i	0.829986	+	0.0704697i
$651$			20965.1i			1.26219i
$652$	2795.34	+	941.365i	0.167905	+	0.0565440i
$653$		−	3560.37i		−	0.213366i	−0.994293	−	0.106683i	$-0.965977\pi$
$653$		−	3560.37i		−	0.213366i	0.994293	−	0.106683i	$-0.0340230\pi$
$654$	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	$-0.810394\pi$
$659$		−	18983.0i		−	1.12212i	0.827776	−	0.561058i	$-0.189606\pi$
$660$	−315.972	+	938.264i	−0.0186351	+	0.0553362i
$661$	−6588.80			−0.387707			−0.193854	−	0.981030i	$-0.562099\pi$
$661$	−6588.80			−0.387707			−0.193854	+	0.981030i	$0.562099\pi$
$662$	−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
$676$	17324.4	+	2963.21i	0.985686	+	0.168594i
$677$			7932.48i			0.450325i	0.974321	+	0.225162i	$0.0722913\pi$
$677$			7932.48i			0.450325i	−0.974321	+	0.225162i	$0.927709\pi$
$678$	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	$-0.467398\pi$
$683$	3650.03			0.204487			0.102244	+	0.994759i	$0.467398\pi$
$684$	−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	$-0.430908\pi$
$691$	7823.65			0.430717			0.215359	+	0.976535i	$0.430908\pi$
$692$	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	$-0.694806\pi$
$701$		−	30382.7i		−	1.63700i	0.574507	−	0.818500i	$-0.305194\pi$
$702$	−302.828	+	3566.68i	−0.0162813	+	0.191760i
$703$	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	$-0.677307\pi$
$709$	−19960.9			−1.05733			−0.528665	+	0.848830i	$0.677307\pi$
$710$	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	$0.325247\pi$
$728$	−9713.24	+	22376.7i	−0.494501	+	1.13920i
$729$	−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	$-0.794218\pi$
$733$	−31681.2			−1.59642			−0.798208	+	0.602382i	$0.794218\pi$
$734$	−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	$-0.185057\pi$
$739$	33577.7			1.67142			0.835709	+	0.549173i	$0.185057\pi$
$740$	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
$754$	1594.71	−	18782.3i	0.0770237	−	0.907179i
$755$			4269.28i			0.205795i
$756$	−4708.23	−	1585.55i	−0.226504	−	0.0762779i
$757$			35511.1i			1.70498i	0.522741	+	0.852492i	$0.324910\pi$
$757$			35511.1i			1.70498i	−0.522741	+	0.852492i	$0.675090\pi$
$758$	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	$-0.255136\pi$
$773$	29899.4			1.39121			0.695605	+	0.718424i	$0.255136\pi$
$774$	4980.68	+	816.134i	0.231301	+

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} +(-132.099 - 11.2158i) 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} +(91.7235 - 363.586i) 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} +(33.6475 - 396.298i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more