LMFDB - Embedded newform 1050.3.h.c.349.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(349,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.349");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.h (of order $2$, degree $1$, not 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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.8
Character	$\chi$	$=$	1050.349
Dual form			1050.3.h.c.349.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -2.44949i q^{6} +(6.69738 - 2.03595i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -2.44949i q^{6} +(6.69738 - 2.03595i) q^{7} -2.82843i q^{8} +3.00000 q^{9} -5.30397 q^{11} +3.46410 q^{12} -15.0546 q^{13} +(2.87926 + 9.47153i) q^{14} +4.00000 q^{16} -1.80427 q^{17} +4.24264i q^{18} -7.35835i q^{19} +(-11.6002 + 3.52636i) q^{21} -7.50095i q^{22} +15.8246i q^{23} +4.89898i q^{24} -21.2904i q^{26} -5.19615 q^{27} +(-13.3948 + 4.07189i) q^{28} +44.3922 q^{29} +6.10279i q^{31} +5.65685i q^{32} +9.18674 q^{33} -2.55162i q^{34} -6.00000 q^{36} +36.0606i q^{37} +10.4063 q^{38} +26.0753 q^{39} -18.8619i q^{41} +(-4.98703 - 16.4052i) q^{42} +36.0186i q^{43} +10.6079 q^{44} -22.3793 q^{46} +26.7314 q^{47} -6.92820 q^{48} +(40.7099 - 27.2710i) q^{49} +3.12509 q^{51} +30.1092 q^{52} +80.7350i q^{53} -7.34847i q^{54} +(-5.75852 - 18.9431i) q^{56} +12.7450i q^{57} +62.7801i q^{58} +38.7017i q^{59} -25.5365i q^{61} -8.63065 q^{62} +(20.0921 - 6.10784i) q^{63} -8.00000 q^{64} +12.9920i q^{66} +90.4318i q^{67} +3.60854 q^{68} -27.4089i q^{69} -41.4375 q^{71} -8.48528i q^{72} -106.712 q^{73} -50.9974 q^{74} +14.7167i q^{76} +(-35.5227 + 10.7986i) q^{77} +36.8761i q^{78} +16.1960 q^{79} +9.00000 q^{81} +26.6748 q^{82} +34.7857 q^{83} +(23.2004 - 7.05272i) q^{84} -50.9379 q^{86} -76.8896 q^{87} +15.0019i q^{88} +58.7705i q^{89} +(-100.826 + 30.6503i) q^{91} -31.6491i q^{92} -10.5703i q^{93} +37.8039i q^{94} -9.79796i q^{96} -140.734 q^{97} +(38.5670 + 57.5724i) q^{98} -15.9119 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 48 q^{4} + 72 q^{9}+O(q^{10}) $ 24 * q - 48 * q^4 + 72 * q^9	$ 24 q - 48 q^{4} + 72 q^{9} - 32 q^{11} - 16 q^{14} + 96 q^{16} - 12 q^{21} - 96 q^{29} - 144 q^{36} + 24 q^{39} + 64 q^{44} + 160 q^{46} - 236 q^{49} + 144 q^{51} + 32 q^{56} - 192 q^{64} + 496 q^{71} + 128 q^{74} + 416 q^{79} + 216 q^{81} + 24 q^{84} + 256 q^{86} - 316 q^{91} - 96 q^{99}+O(q^{100}) $ 24 * q - 48 * q^4 + 72 * q^9 - 32 * q^11 - 16 * q^14 + 96 * q^16 - 12 * q^21 - 96 * q^29 - 144 * q^36 + 24 * q^39 + 64 * q^44 + 160 * q^46 - 236 * q^49 + 144 * q^51 + 32 * q^56 - 192 * q^64 + 496 * q^71 + 128 * q^74 + 416 * q^79 + 216 * q^81 + 24 * q^84 + 256 * q^86 - 316 * q^91 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	6.69738	−	2.03595i	0.956769	−	0.290849i
$7$	6.69738	−	2.03595i	0.956769	−	0.290849i
$8$		−	2.82843i		−	0.353553i
$9$	3.00000			0.333333
$10$		0			0
$11$	−5.30397			−0.482179			−0.241090	−	0.970503i	$-0.577505\pi$
$11$	−5.30397			−0.482179			−0.241090	+	0.970503i	$0.577505\pi$
$12$	3.46410			0.288675
$13$	−15.0546			−1.15805			−0.579023	−	0.815311i	$-0.696566\pi$
$13$	−15.0546			−1.15805			−0.579023	+	0.815311i	$0.696566\pi$
$14$	2.87926	+	9.47153i	0.205662	+	0.676538i
$15$		0			0
$16$	4.00000			0.250000
$17$	−1.80427			−0.106133			−0.0530667	−	0.998591i	$-0.516900\pi$
$17$	−1.80427			−0.106133			−0.0530667	+	0.998591i	$0.516900\pi$
$18$			4.24264i			0.235702i
$19$		−	7.35835i		−	0.387282i	−0.981073	−	0.193641i	$-0.937970\pi$
$19$		−	7.35835i		−	0.387282i	0.981073	−	0.193641i	$-0.0620296\pi$
$20$		0			0
$21$	−11.6002	+	3.52636i	−0.552391	+	0.167922i
$22$		−	7.50095i		−	0.340952i
$23$			15.8246i			0.688024i	0.938965	+	0.344012i	$0.111786\pi$
$23$			15.8246i			0.688024i	−0.938965	+	0.344012i	$0.888214\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$		−	21.2904i		−	0.818862i
$27$	−5.19615			−0.192450
$28$	−13.3948	+	4.07189i	−0.478384	+	0.145425i
$29$	44.3922			1.53077			0.765384	−	0.643574i	$-0.222549\pi$
$29$	44.3922			1.53077			0.765384	+	0.643574i	$0.222549\pi$
$30$		0			0
$31$			6.10279i			0.196864i	0.995144	+	0.0984322i	$0.0313827\pi$
$31$			6.10279i			0.196864i	−0.995144	+	0.0984322i	$0.968617\pi$
$32$			5.65685i			0.176777i
$33$	9.18674			0.278386
$34$		−	2.55162i		−	0.0750477i
$35$		0			0
$36$	−6.00000			−0.166667
$37$			36.0606i			0.974611i	0.873232	+	0.487305i	$0.162020\pi$
$37$			36.0606i			0.974611i	−0.873232	+	0.487305i	$0.837980\pi$
$38$	10.4063			0.273849
$39$	26.0753			0.668598
$40$		0			0
$41$		−	18.8619i		−	0.460047i	−0.973185	−	0.230024i	$-0.926120\pi$
$41$		−	18.8619i		−	0.460047i	0.973185	−	0.230024i	$-0.0738803\pi$
$42$	−4.98703	−	16.4052i	−0.118739	−	0.390599i
$43$			36.0186i			0.837641i	0.908069	+	0.418820i	$0.137556\pi$
$43$			36.0186i			0.837641i	−0.908069	+	0.418820i	$0.862444\pi$
$44$	10.6079			0.241090
$45$		0			0
$46$	−22.3793			−0.486506
$47$	26.7314			0.568753			0.284376	−	0.958713i	$-0.408213\pi$
$47$	26.7314			0.568753			0.284376	+	0.958713i	$0.408213\pi$
$48$	−6.92820			−0.144338
$49$	40.7099	−	27.2710i	0.830813	−	0.556551i
$50$		0			0
$51$	3.12509			0.0612762
$52$	30.1092			0.579023
$53$			80.7350i			1.52330i	0.647987	+	0.761651i	$0.275611\pi$
$53$			80.7350i			1.52330i	−0.647987	+	0.761651i	$0.724389\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	−5.75852	−	18.9431i	−0.102831	−	0.338269i
$57$			12.7450i			0.223597i
$58$			62.7801i			1.08242i
$59$			38.7017i			0.655961i	0.944684	+	0.327981i	$0.106368\pi$
$59$			38.7017i			0.655961i	−0.944684	+	0.327981i	$0.893632\pi$
$60$		0			0
$61$		−	25.5365i		−	0.418630i	−0.977848	−	0.209315i	$-0.932877\pi$
$61$		−	25.5365i		−	0.418630i	0.977848	−	0.209315i	$-0.0671235\pi$
$62$	−8.63065			−0.139204
$63$	20.0921	−	6.10784i	0.318923	−	0.0969498i
$64$	−8.00000			−0.125000
$65$		0			0
$66$			12.9920i			0.196849i
$67$			90.4318i			1.34973i	0.737942	+	0.674864i	$0.235798\pi$
$67$			90.4318i			1.34973i	−0.737942	+	0.674864i	$0.764202\pi$
$68$	3.60854			0.0530667
$69$		−	27.4089i		−	0.397231i
$70$		0			0
$71$	−41.4375			−0.583626			−0.291813	−	0.956475i	$-0.594259\pi$
$71$	−41.4375			−0.583626			−0.291813	+	0.956475i	$0.594259\pi$
$72$		−	8.48528i		−	0.117851i
$73$	−106.712			−1.46181			−0.730903	−	0.682481i	$-0.760901\pi$
$73$	−106.712			−1.46181			−0.730903	+	0.682481i	$0.760901\pi$
$74$	−50.9974			−0.689154
$75$		0			0
$76$			14.7167i			0.193641i
$77$	−35.5227	+	10.7986i	−0.461334	+	0.140241i
$78$			36.8761i			0.472770i
$79$	16.1960			0.205013			0.102507	−	0.994732i	$-0.467314\pi$
$79$	16.1960			0.205013			0.102507	+	0.994732i	$0.467314\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	26.6748			0.325302
$83$	34.7857			0.419105			0.209552	−	0.977797i	$-0.432799\pi$
$83$	34.7857			0.419105			0.209552	+	0.977797i	$0.432799\pi$
$84$	23.2004	−	7.05272i	0.276195	−	0.0839610i
$85$		0			0
$86$	−50.9379			−0.592302
$87$	−76.8896			−0.883789
$88$			15.0019i			0.170476i
$89$			58.7705i			0.660342i	0.943921	+	0.330171i	$0.107106\pi$
$89$			58.7705i			0.660342i	−0.943921	+	0.330171i	$0.892894\pi$
$90$		0			0
$91$	−100.826	+	30.6503i	−1.10798	+	0.336817i
$92$		−	31.6491i		−	0.344012i
$93$		−	10.5703i		−	0.113660i
$94$			37.8039i			0.402169i
$95$		0			0
$96$		−	9.79796i		−	0.102062i
$97$	−140.734			−1.45087			−0.725433	−	0.688293i	$-0.758360\pi$
$97$	−140.734			−1.45087			−0.725433	+	0.688293i	$0.758360\pi$
$98$	38.5670	+	57.5724i	0.393541	+	0.587474i
$99$	−15.9119			−0.160726
$100$		0			0
$101$			96.7964i			0.958380i	0.877711	+	0.479190i	$0.159070\pi$
$101$			96.7964i			0.958380i	−0.877711	+	0.479190i	$0.840930\pi$
$102$			4.41954i			0.0433288i
$103$	−102.523			−0.995374			−0.497687	−	0.867357i	$-0.665817\pi$
$103$	−102.523			−0.995374			−0.497687	+	0.867357i	$0.665817\pi$
$104$			42.5808i			0.409431i
$105$		0			0
$106$	−114.177			−1.07714
$107$			139.632i			1.30497i	0.757800	+	0.652487i	$0.226274\pi$
$107$			139.632i			1.30497i	−0.757800	+	0.652487i	$0.773726\pi$
$108$	10.3923			0.0962250
$109$	27.3238			0.250677			0.125338	−	0.992114i	$-0.459998\pi$
$109$	27.3238			0.250677			0.125338	+	0.992114i	$0.459998\pi$
$110$		0			0
$111$		−	62.4588i		−	0.562692i
$112$	26.7895	−	8.14378i	0.239192	−	0.0727123i
$113$			46.4392i			0.410966i	0.978661	+	0.205483i	$0.0658765\pi$
$113$			46.4392i			0.410966i	−0.978661	+	0.205483i	$0.934123\pi$
$114$	−18.0242			−0.158107
$115$		0			0
$116$	−88.7845			−0.765384
$117$	−45.1638			−0.386015
$118$	−54.7325			−0.463835
$119$	−12.0839	+	3.67339i	−0.101545	+	0.0308688i
$120$		0			0
$121$	−92.8679			−0.767503
$122$	36.1140			0.296016
$123$			32.6698i			0.265608i
$124$		−	12.2056i		−	0.0984322i
$125$		0			0
$126$	8.63779	+	28.4146i	0.0685538	+	0.225513i
$127$			60.7189i			0.478101i	0.971007	+	0.239051i	$0.0768362\pi$
$127$			60.7189i			0.478101i	−0.971007	+	0.239051i	$0.923164\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		−	62.3860i		−	0.483612i
$130$		0			0
$131$		−	202.250i		−	1.54389i	−0.635688	−	0.771946i	$-0.719283\pi$
$131$		−	202.250i		−	1.54389i	0.635688	−	0.771946i	$-0.280717\pi$
$132$	−18.3735			−0.139193
$133$	−14.9812	−	49.2817i	−0.112641	−	0.370539i
$134$	−127.890			−0.954402
$135$		0			0
$136$			5.10324i			0.0375238i
$137$			118.169i			0.862548i	0.902221	+	0.431274i	$0.141936\pi$
$137$			118.169i			0.862548i	−0.902221	+	0.431274i	$0.858064\pi$
$138$	38.7621			0.280885
$139$			256.027i			1.84192i	0.389658	+	0.920959i	$0.372593\pi$
$139$			256.027i			1.84192i	−0.389658	+	0.920959i	$0.627407\pi$
$140$		0			0
$141$	−46.3001			−0.328370
$142$		−	58.6014i		−	0.412686i
$143$	79.8491			0.558385
$144$	12.0000			0.0833333
$145$		0			0
$146$		−	150.913i		−	1.03365i
$147$	−70.5115	+	47.2348i	−0.479670	+	0.321325i
$148$		−	72.1212i		−	0.487305i
$149$	264.538			1.77543			0.887713	−	0.460398i	$-0.152293\pi$
$149$	264.538			1.77543			0.887713	+	0.460398i	$0.152293\pi$
$150$		0			0
$151$	12.8709			0.0852377			0.0426188	−	0.999091i	$-0.486430\pi$
$151$	12.8709			0.0852377			0.0426188	+	0.999091i	$0.486430\pi$
$152$	−20.8126			−0.136925
$153$	−5.41281			−0.0353778
$154$	−15.2715	−	50.2367i	−0.0991657	−	0.326212i
$155$		0			0
$156$	−52.1507			−0.334299
$157$	203.635			1.29704			0.648518	−	0.761200i	$-0.275389\pi$
$157$	203.635			1.29704			0.648518	+	0.761200i	$0.275389\pi$
$158$			22.9047i			0.144966i
$159$		−	139.837i		−	0.879479i
$160$		0			0
$161$	32.2179	+	105.983i	0.200111	+	0.658280i
$162$			12.7279i			0.0785674i
$163$		−	261.841i		−	1.60639i	−0.595718	−	0.803194i	$-0.703132\pi$
$163$		−	261.841i		−	1.60639i	0.595718	−	0.803194i	$-0.296868\pi$
$164$			37.7239i			0.230024i
$165$		0			0
$166$			49.1944i			0.296352i
$167$	−90.7037			−0.543136			−0.271568	−	0.962419i	$-0.587542\pi$
$167$	−90.7037			−0.543136			−0.271568	+	0.962419i	$0.587542\pi$
$168$	9.97405	+	32.8103i	0.0593694	+	0.195300i
$169$	57.6409			0.341070
$170$		0			0
$171$		−	22.0750i		−	0.129094i
$172$		−	72.0371i		−	0.418820i
$173$	248.626			1.43714			0.718572	−	0.695452i	$-0.244796\pi$
$173$	248.626			1.43714			0.718572	+	0.695452i	$0.244796\pi$
$174$		−	108.738i		−	0.624933i
$175$		0			0
$176$	−21.2159			−0.120545
$177$		−	67.0333i		−	0.378719i
$178$	−83.1140			−0.466933
$179$	−138.861			−0.775761			−0.387880	−	0.921710i	$-0.626793\pi$
$179$	−138.861			−0.775761			−0.387880	+	0.921710i	$0.626793\pi$
$180$		0			0
$181$			148.488i			0.820375i	0.912001	+	0.410187i	$0.134537\pi$
$181$			148.488i			0.820375i	−0.912001	+	0.410187i	$0.865463\pi$
$182$	−43.3461	−	142.590i	−0.238166	−	0.783462i
$183$			44.2304i			0.241696i
$184$	44.7586			0.243253
$185$		0			0
$186$	14.9487			0.0803695
$187$	9.56979			0.0511753
$188$	−53.4628			−0.284376
$189$	−34.8006	+	10.5791i	−0.184130	+	0.0559740i
$190$		0			0
$191$	−46.0781			−0.241247			−0.120623	−	0.992698i	$-0.538489\pi$
$191$	−46.0781			−0.241247			−0.120623	+	0.992698i	$0.538489\pi$
$192$	13.8564			0.0721688
$193$		−	26.4406i		−	0.136998i	−0.997651	−	0.0684991i	$-0.978179\pi$
$193$		−	26.4406i		−	0.136998i	0.997651	−	0.0684991i	$-0.0218210\pi$
$194$		−	199.028i		−	1.02592i
$195$		0			0
$196$	−81.4197	+	54.5420i	−0.415407	+	0.278276i
$197$			286.547i			1.45455i	0.686345	+	0.727277i	$0.259214\pi$
$197$			286.547i			1.45455i	−0.686345	+	0.727277i	$0.740786\pi$
$198$		−	22.5028i		−	0.113651i
$199$		−	34.4563i		−	0.173147i	−0.996245	−	0.0865737i	$-0.972408\pi$
$199$		−	34.4563i		−	0.173147i	0.996245	−	0.0865737i	$-0.0275918\pi$
$200$		0			0
$201$		−	156.632i		−	0.779266i
$202$	−136.891			−0.677677
$203$	297.312	−	90.3802i	1.46459	−	0.445223i
$204$	−6.25017			−0.0306381
$205$		0			0
$206$		−	144.990i		−	0.703835i
$207$			47.4737i			0.229341i
$208$	−60.2184			−0.289511
$209$			39.0285i			0.186739i
$210$		0			0
$211$	121.627			0.576432			0.288216	−	0.957565i	$-0.406938\pi$
$211$	121.627			0.576432			0.288216	+	0.957565i	$0.406938\pi$
$212$		−	161.470i		−	0.761651i
$213$	71.7718			0.336957
$214$	−197.470			−0.922756
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	12.4250	+	40.8727i	0.0572579	+	0.188354i
$218$			38.6416i			0.177255i
$219$	184.830			0.843974
$220$		0			0
$221$	27.1625			0.122907
$222$	88.3301			0.397883
$223$	−302.025			−1.35437			−0.677187	−	0.735811i	$-0.736801\pi$
$223$	−302.025			−1.35437			−0.677187	+	0.735811i	$0.736801\pi$
$224$	11.5170	+	37.8861i	0.0514154	+	0.169134i
$225$		0			0
$226$	−65.6749			−0.290597
$227$	159.784			0.703892			0.351946	−	0.936020i	$-0.385520\pi$
$227$	159.784			0.703892			0.351946	+	0.936020i	$0.385520\pi$
$228$		−	25.4901i		−	0.111799i
$229$			46.0123i			0.200927i	0.994941	+	0.100463i	$0.0320325\pi$
$229$			46.0123i			0.200927i	−0.994941	+	0.100463i	$0.967967\pi$
$230$		0			0
$231$	61.5271	−	18.7037i	0.266351	−	0.0809684i
$232$		−	125.560i		−	0.541208i
$233$			97.3113i			0.417645i	0.977954	+	0.208822i	$0.0669631\pi$
$233$			97.3113i			0.417645i	−0.977954	+	0.208822i	$0.933037\pi$
$234$		−	63.8712i		−	0.272954i
$235$		0			0
$236$		−	77.4034i		−	0.327981i
$237$	−28.0524			−0.118364
$238$	−5.19496	−	17.0892i	−0.0218276	−	0.0718033i
$239$	−124.280			−0.520000			−0.260000	−	0.965609i	$-0.583722\pi$
$239$	−124.280			−0.520000			−0.260000	+	0.965609i	$0.583722\pi$
$240$		0			0
$241$			332.949i			1.38153i	0.723078	+	0.690766i	$0.242727\pi$
$241$			332.949i			1.38153i	−0.723078	+	0.690766i	$0.757273\pi$
$242$		−	131.335i		−	0.542707i
$243$	−15.5885			−0.0641500
$244$			51.0729i			0.209315i
$245$		0			0
$246$	−46.2021			−0.187813
$247$			110.777i			0.448490i
$248$	17.2613			0.0696020
$249$	−60.2506			−0.241970
$250$		0			0
$251$		−	154.118i		−	0.614018i	−0.951707	−	0.307009i	$-0.900672\pi$
$251$		−	154.118i		−	0.614018i	0.951707	−	0.307009i	$-0.0993281\pi$
$252$	−40.1843	+	12.2157i	−0.159461	+	0.0484749i
$253$		−	83.9329i		−	0.331751i
$254$	−85.8695			−0.338069
$255$		0			0
$256$	16.0000			0.0625000
$257$	410.364			1.59675			0.798373	−	0.602164i	$-0.205694\pi$
$257$	410.364			1.59675			0.798373	+	0.602164i	$0.205694\pi$
$258$	88.2271			0.341965
$259$	73.4174	+	241.512i	0.283465	+	0.932477i
$260$		0			0
$261$	133.177			0.510256
$262$	286.025			1.09170
$263$		−	342.998i		−	1.30418i	−0.758143	−	0.652088i	$-0.773893\pi$
$263$		−	342.998i		−	1.30418i	0.758143	−	0.652088i	$-0.226107\pi$
$264$		−	25.9840i		−	0.0984244i
$265$		0			0
$266$	69.6948	−	21.1866i	0.262011	−	0.0796489i
$267$		−	101.793i		−	0.381249i
$268$		−	180.864i		−	0.674864i
$269$		−	238.076i		−	0.885042i	−0.896758	−	0.442521i	$-0.854084\pi$
$269$		−	238.076i		−	0.885042i	0.896758	−	0.442521i	$-0.145916\pi$
$270$		0			0
$271$		−	32.6454i		−	0.120463i	−0.998184	−	0.0602313i	$-0.980816\pi$
$271$		−	32.6454i		−	0.120463i	0.998184	−	0.0602313i	$-0.0191838\pi$
$272$	−7.21707			−0.0265334
$273$	174.636	−	53.0879i	0.639694	−	0.194461i
$274$	−167.116			−0.609914
$275$		0			0
$276$			54.8179i			0.198615i
$277$			230.271i			0.831301i	0.909524	+	0.415651i	$0.136446\pi$
$277$			230.271i			0.831301i	−0.909524	+	0.415651i	$0.863554\pi$
$278$	−362.076			−1.30243
$279$			18.3084i			0.0656214i
$280$		0			0
$281$	486.859			1.73260			0.866298	−	0.499528i	$-0.166493\pi$
$281$	486.859			1.73260			0.866298	+	0.499528i	$0.166493\pi$
$282$		−	65.4783i		−	0.232192i
$283$	−324.645			−1.14716			−0.573578	−	0.819151i	$-0.694445\pi$
$283$	−324.645			−1.14716			−0.573578	+	0.819151i	$0.694445\pi$
$284$	82.8749			0.291813
$285$		0			0
$286$			112.924i			0.394838i
$287$	−38.4019	−	126.326i	−0.133804	−	0.440159i
$288$			16.9706i			0.0589256i
$289$	−285.745			−0.988736
$290$		0			0
$291$	243.758			0.837658
$292$	213.424			0.730903
$293$	128.334			0.438000			0.219000	−	0.975725i	$-0.429721\pi$
$293$	128.334			0.438000			0.219000	+	0.975725i	$0.429721\pi$
$294$	−66.8001	−	99.7184i	−0.227211	−	0.339178i
$295$		0			0
$296$	101.995			0.344577
$297$	27.5602			0.0927954
$298$			374.114i			1.25542i
$299$		−	238.232i		−	0.796763i
$300$		0			0
$301$	73.3318	+	241.230i	0.243627	+	0.801429i
$302$			18.2022i			0.0602721i
$303$		−	167.656i		−	0.553321i
$304$		−	29.4334i		−	0.0968204i
$305$		0			0
$306$		−	7.65486i		−	0.0250159i
$307$	−290.110			−0.944983			−0.472492	−	0.881335i	$-0.656645\pi$
$307$	−290.110			−0.944983			−0.472492	+	0.881335i	$0.656645\pi$
$308$	71.0454	−	21.5972i	0.230667	−	0.0701207i
$309$	177.576			0.574679
$310$		0			0
$311$			76.1670i			0.244910i	0.992474	+	0.122455i	$0.0390767\pi$
$311$			76.1670i			0.244910i	−0.992474	+	0.122455i	$0.960923\pi$
$312$		−	73.7522i		−	0.236385i
$313$	−527.145			−1.68417			−0.842085	−	0.539344i	$-0.818672\pi$
$313$	−527.145			−1.68417			−0.842085	+	0.539344i	$0.818672\pi$
$314$			287.983i			0.917142i
$315$		0			0
$316$	−32.3921			−0.102507
$317$		−	488.328i		−	1.54047i	−0.637763	−	0.770233i	$-0.720140\pi$
$317$		−	488.328i		−	1.54047i	0.637763	−	0.770233i	$-0.279860\pi$
$318$	197.760			0.621886
$319$	−235.455			−0.738104
$320$		0			0
$321$		−	241.850i		−	0.753427i
$322$	−149.883	+	45.5630i	−0.465474	+	0.141500i
$323$			13.2764i			0.0411035i
$324$	−18.0000			−0.0555556
$325$		0			0
$326$	370.299			1.13589
$327$	−47.3261			−0.144728
$328$	−53.3496			−0.162651
$329$	179.030	−	54.4236i	0.544165	−	0.165421i
$330$		0			0
$331$	519.849			1.57054			0.785271	−	0.619152i	$-0.212524\pi$
$331$	519.849			1.57054			0.785271	+	0.619152i	$0.212524\pi$
$332$	−69.5714			−0.209552
$333$			108.182i			0.324870i
$334$		−	128.274i		−	0.384055i
$335$		0			0
$336$	−46.4008	+	14.1054i	−0.138098	+	0.0419805i
$337$		−	460.233i		−	1.36568i	−0.730570	−	0.682838i	$-0.760745\pi$
$337$		−	460.233i		−	1.36568i	0.730570	−	0.682838i	$-0.239255\pi$
$338$			81.5165i			0.241173i
$339$		−	80.4350i		−	0.237271i
$340$		0			0
$341$		−	32.3690i		−	0.0949238i
$342$	31.2188			0.0912831
$343$	217.127	−	265.527i	0.633024	−	0.774132i
$344$	101.876			0.296151
$345$		0			0
$346$			351.610i			1.01621i
$347$			5.51518i			0.0158939i	0.999968	+	0.00794695i	$0.00252962\pi$
$347$			5.51518i			0.0158939i	−0.999968	+	0.00794695i	$0.997470\pi$
$348$	153.779			0.441894
$349$			563.892i			1.61574i	0.589364	+	0.807868i	$0.299378\pi$
$349$			563.892i			1.61574i	−0.589364	+	0.807868i	$0.700622\pi$
$350$		0			0
$351$	78.2260			0.222866
$352$		−	30.0038i		−	0.0852380i
$353$	274.152			0.776633			0.388317	−	0.921526i	$-0.373057\pi$
$353$	274.152			0.776633			0.388317	+	0.921526i	$0.373057\pi$
$354$	94.7994			0.267795
$355$		0			0
$356$		−	117.541i		−	0.330171i
$357$	20.9299	−	6.36250i	0.0586271	−	0.0178221i
$358$		−	196.379i		−	0.548546i
$359$	65.4883			0.182419			0.0912093	−	0.995832i	$-0.470927\pi$
$359$	65.4883			0.182419			0.0912093	+	0.995832i	$0.470927\pi$
$360$		0			0
$361$	306.855			0.850013
$362$	−209.993			−0.580092
$363$	160.852			0.443118
$364$	201.653	−	61.3007i	0.553991	−	0.168408i
$365$		0			0
$366$	−62.5513			−0.170905
$367$	−159.838			−0.435526			−0.217763	−	0.976002i	$-0.569876\pi$
$367$	−159.838			−0.435526			−0.217763	+	0.976002i	$0.569876\pi$
$368$			63.2982i			0.172006i
$369$		−	56.5858i		−	0.153349i
$370$		0			0
$371$	164.372	+	540.713i	0.443051	+	1.45745i
$372$			21.1407i			0.0568298i
$373$			470.755i			1.26208i	0.775751	+	0.631039i	$0.217371\pi$
$373$			470.755i			1.26208i	−0.775751	+	0.631039i	$0.782629\pi$
$374$			13.5337i			0.0361864i
$375$		0			0
$376$		−	75.6078i		−	0.201085i
$377$	−668.307			−1.77270
$378$	−14.9611	−	49.2155i	−0.0395796	−	0.130200i
$379$	−61.4701			−0.162190			−0.0810951	−	0.996706i	$-0.525842\pi$
$379$	−61.4701			−0.162190			−0.0810951	+	0.996706i	$0.525842\pi$
$380$		0			0
$381$		−	105.168i		−	0.276032i
$382$		−	65.1643i		−	0.170587i
$383$	120.113			0.313611			0.156806	−	0.987629i	$-0.449880\pi$
$383$	120.113			0.313611			0.156806	+	0.987629i	$0.449880\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	37.3927			0.0968723
$387$			108.056i			0.279214i
$388$	281.468			0.725433
$389$	−309.597			−0.795879			−0.397939	−	0.917412i	$-0.630275\pi$
$389$	−309.597			−0.795879			−0.397939	+	0.917412i	$0.630275\pi$
$390$		0			0
$391$		−	28.5517i		−	0.0730224i
$392$	−77.1341	−	115.145i	−0.196771	−	0.293737i
$393$			350.307i			0.891367i
$394$	−405.239			−1.02852
$395$		0			0
$396$	31.8238			0.0803632
$397$	754.188			1.89972			0.949858	−	0.312680i	$-0.101227\pi$
$397$	754.188			1.89972			0.949858	+	0.312680i	$0.101227\pi$
$398$	48.7286			0.122434
$399$	25.9482	+	85.3584i	0.0650331	+	0.213931i
$400$		0			0
$401$	235.697			0.587774			0.293887	−	0.955840i	$-0.405051\pi$
$401$	235.697			0.587774			0.293887	+	0.955840i	$0.405051\pi$
$402$	221.512			0.551024
$403$		−	91.8751i		−	0.227978i
$404$		−	193.593i		−	0.479190i
$405$		0			0
$406$	127.817	+	420.462i	0.314820	+	1.03562i
$407$		−	191.264i		−	0.469937i
$408$		−	8.83908i		−	0.0216644i
$409$		−	81.3407i		−	0.198877i	−0.995044	−	0.0994385i	$-0.968295\pi$
$409$		−	81.3407i		−	0.198877i	0.995044	−	0.0994385i	$-0.0317047\pi$
$410$		0			0
$411$		−	204.675i		−	0.497993i
$412$	205.047			0.497687
$413$	78.7946	+	259.200i	0.190786	+	0.627603i
$414$	−67.1379			−0.162169
$415$		0			0
$416$		−	85.1617i		−	0.204716i
$417$		−	443.451i		−	1.06343i
$418$	−55.1946			−0.132044
$419$		−	213.030i		−	0.508424i	−0.967149	−	0.254212i	$-0.918184\pi$
$419$		−	213.030i		−	0.508424i	0.967149	−	0.254212i	$-0.0818161\pi$
$420$		0			0
$421$	416.836			0.990108			0.495054	−	0.868862i	$-0.335148\pi$
$421$	416.836			0.990108			0.495054	+	0.868862i	$0.335148\pi$
$422$			172.007i			0.407599i
$423$	80.1942			0.189584
$424$	228.353			0.538569
$425$		0			0
$426$			101.501i			0.238264i
$427$	−51.9908	−	171.027i	−0.121758	−	0.400533i
$428$		−	279.265i		−	0.652487i
$429$	−138.303			−0.322384
$430$		0			0
$431$	−331.912			−0.770096			−0.385048	−	0.922896i	$-0.625815\pi$
$431$	−331.912			−0.770096			−0.385048	+	0.922896i	$0.625815\pi$
$432$	−20.7846			−0.0481125
$433$	−304.120			−0.702356			−0.351178	−	0.936309i	$-0.614219\pi$
$433$	−304.120			−0.702356			−0.351178	+	0.936309i	$0.614219\pi$
$434$	−57.8028	+	17.5715i	−0.133186	+	0.0404874i
$435$		0			0
$436$	−54.6475			−0.125338
$437$	116.443			0.266459
$438$			261.390i			0.596780i
$439$		−	24.3758i		−	0.0555258i	−0.999615	−	0.0277629i	$-0.991162\pi$
$439$		−	24.3758i		−	0.0555258i	0.999615	−	0.0277629i	$-0.00883834\pi$
$440$		0			0
$441$	122.130	−	81.8130i	0.276938	−	0.185517i
$442$			38.4136i			0.0869087i
$443$			30.3119i			0.0684241i	0.999415	+	0.0342121i	$0.0108922\pi$
$443$			30.3119i			0.0684241i	−0.999415	+	0.0342121i	$0.989108\pi$
$444$			124.918i			0.281346i
$445$		0			0
$446$		−	427.128i		−	0.957687i
$447$	−458.194			−1.02504
$448$	−53.5791	+	16.2876i	−0.119596	+	0.0363562i
$449$	550.099			1.22517			0.612583	−	0.790407i	$-0.290131\pi$
$449$	550.099			1.22517			0.612583	+	0.790407i	$0.290131\pi$
$450$		0			0
$451$			100.043i			0.221825i
$452$		−	92.8783i		−	0.205483i
$453$	−22.2930			−0.0492120
$454$			225.968i			0.497727i
$455$		0			0
$456$	36.0484			0.0790535
$457$		−	477.234i		−	1.04428i	−0.852861	−	0.522138i	$-0.825135\pi$
$457$		−	477.234i		−	1.04428i	0.852861	−	0.522138i	$-0.174865\pi$
$458$	−65.0712			−0.142077
$459$	9.37526			0.0204254
$460$		0			0
$461$			860.755i			1.86715i	0.358386	+	0.933574i	$0.383327\pi$
$461$			860.755i			1.86715i	−0.358386	+	0.933574i	$0.616673\pi$
$462$	26.4510	+	87.0125i	0.0572533	+	0.188339i
$463$		−	774.505i		−	1.67280i	−0.548122	−	0.836398i	$-0.684657\pi$
$463$		−	774.505i		−	1.67280i	0.548122	−	0.836398i	$-0.315343\pi$
$464$	177.569			0.382692
$465$		0			0
$466$	−137.619			−0.295320
$467$	769.862			1.64853			0.824263	−	0.566207i	$-0.191590\pi$
$467$	769.862			1.64853			0.824263	+	0.566207i	$0.191590\pi$
$468$	90.3276			0.193008
$469$	184.114	+	605.656i	0.392568	+	1.29138i
$470$		0			0
$471$	−352.705			−0.748844
$472$	109.465			0.231917
$473$		−	191.041i		−	0.403893i
$474$		−	39.6720i		−	0.0836962i
$475$		0			0
$476$	24.1678	−	7.34679i	0.0507726	−	0.0154344i
$477$			242.205i			0.507767i
$478$		−	175.758i		−	0.367695i
$479$		−	724.734i		−	1.51302i	−0.653985	−	0.756508i	$-0.726904\pi$
$479$		−	724.734i		−	1.51302i	0.653985	−	0.756508i	$-0.273096\pi$
$480$		0			0
$481$		−	542.878i		−	1.12864i
$482$	−470.861			−0.976891
$483$	−55.8031	−	183.568i	−0.115534	−	0.380058i
$484$	185.736			0.383752
$485$		0			0
$486$		−	22.0454i		−	0.0453609i
$487$			58.9904i			0.121130i	0.998164	+	0.0605651i	$0.0192903\pi$
$487$			58.9904i			0.121130i	−0.998164	+	0.0605651i	$0.980710\pi$
$488$	−72.2280			−0.148008
$489$			453.522i			0.927448i
$490$		0			0
$491$	−574.652			−1.17037			−0.585185	−	0.810900i	$-0.698978\pi$
$491$	−574.652			−1.17037			−0.585185	+	0.810900i	$0.698978\pi$
$492$		−	65.3396i		−	0.132804i
$493$	−80.0955			−0.162466
$494$	−156.662			−0.317130
$495$		0			0
$496$			24.4112i			0.0492161i
$497$	−277.523	+	84.3644i	−0.558396	+	0.169747i
$498$		−	85.2072i		−	0.171099i
$499$	−282.439			−0.566010			−0.283005	−	0.959118i	$-0.591331\pi$
$499$	−282.439			−0.566010			−0.283005	+	0.959118i	$0.591331\pi$
$500$		0			0
$501$	157.103			0.313580
$502$	217.956			0.434176
$503$	87.4043			0.173766			0.0868830	−	0.996219i	$-0.472309\pi$
$503$	87.4043			0.173766			0.0868830	+	0.996219i	$0.472309\pi$
$504$	−17.2756	−	56.8292i	−0.0342769	−	0.112756i
$505$		0			0
$506$	118.699			0.234583
$507$	−99.8370			−0.196917
$508$		−	121.438i		−	0.239051i
$509$		−	632.350i		−	1.24234i	−0.783677	−	0.621169i	$-0.786658\pi$
$509$		−	632.350i		−	1.24234i	0.783677	−	0.621169i	$-0.213342\pi$
$510$		0			0
$511$	−714.690	+	217.260i	−1.39861	+	0.425165i
$512$			22.6274i			0.0441942i
$513$			38.2351i			0.0745324i
$514$			580.342i			1.12907i
$515$		0			0
$516$			124.772i			0.241806i
$517$	−141.782			−0.274241
$518$	−341.549	+	103.828i	−0.659361	+	0.200440i
$519$	−430.633			−0.829736
$520$		0			0
$521$			637.695i			1.22398i	0.790864	+	0.611992i	$0.209631\pi$
$521$			637.695i			1.22398i	−0.790864	+	0.611992i	$0.790369\pi$
$522$			188.340i			0.360805i
$523$	−315.243			−0.602759			−0.301380	−	0.953504i	$-0.597447\pi$
$523$	−315.243			−0.602759			−0.301380	+	0.953504i	$0.597447\pi$
$524$			404.500i			0.771946i
$525$		0			0
$526$	485.073			0.922192
$527$		−	11.0111i		−	0.0208939i
$528$	36.7470			0.0695965
$529$	278.584			0.526623
$530$		0			0
$531$			116.105i			0.218654i
$532$	29.9624	+	98.5634i	0.0563203	+	0.185269i
$533$			283.959i			0.532756i
$534$	143.958			0.269584
$535$		0			0
$536$	255.780			0.477201
$537$	240.515			0.447886
$538$	336.691			0.625819
$539$	−215.924	+	144.645i	−0.400601	+	0.268357i
$540$		0			0
$541$	−273.034			−0.504684			−0.252342	−	0.967638i	$-0.581201\pi$
$541$	−273.034			−0.504684			−0.252342	+	0.967638i	$0.581201\pi$
$542$	46.1675			0.0851800
$543$		−	257.188i		−	0.473644i
$544$		−	10.2065i		−	0.0187619i
$545$		0			0
$546$	75.0777	+	246.973i	0.137505	+	0.452332i
$547$		−	31.9994i		−	0.0584998i	−0.999572	−	0.0292499i	$-0.990688\pi$
$547$		−	31.9994i		−	0.0584998i	0.999572	−	0.0292499i	$-0.00931186\pi$
$548$		−	236.338i		−	0.431274i
$549$		−	76.6094i		−	0.139543i
$550$		0			0
$551$		−	326.654i		−	0.592838i
$552$	−77.5242			−0.140442
$553$	108.471	−	32.9742i	0.196150	−	0.0596279i
$554$	−325.652			−0.587819
$555$		0			0
$556$		−	512.053i		−	0.920959i
$557$		−	134.429i		−	0.241344i	−0.992692	−	0.120672i	$-0.961495\pi$
$557$		−	134.429i		−	0.241344i	0.992692	−	0.120672i	$-0.0385049\pi$
$558$	−25.8920			−0.0464014
$559$		−	542.245i		−	0.970027i
$560$		0			0
$561$	−16.5754			−0.0295461
$562$			688.523i			1.22513i
$563$	138.895			0.246706			0.123353	−	0.992363i	$-0.460635\pi$
$563$	138.895			0.246706			0.123353	+	0.992363i	$0.460635\pi$
$564$	92.6002			0.164185
$565$		0			0
$566$		−	459.118i		−	0.811162i
$567$	60.2764	−	18.3235i	0.106308	−	0.0323166i
$568$			117.203i			0.206343i
$569$	247.938			0.435744			0.217872	−	0.975977i	$-0.430088\pi$
$569$	247.938			0.435744			0.217872	+	0.975977i	$0.430088\pi$
$570$		0			0
$571$	−1085.67			−1.90134			−0.950672	−	0.310197i	$-0.899605\pi$
$571$	−1085.67			−1.90134			−0.950672	+	0.310197i	$0.899605\pi$
$572$	−159.698			−0.279193
$573$	79.8096			0.139284
$574$	178.651	−	54.3084i	0.311239	−	0.0946140i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	155.146			0.268884			0.134442	−	0.990921i	$-0.457076\pi$
$577$	155.146			0.268884			0.134442	+	0.990921i	$0.457076\pi$
$578$		−	404.104i		−	0.699142i
$579$			45.7965i			0.0790959i
$580$		0			0
$581$	232.973	−	70.8217i	0.400986	−	0.121896i
$582$			344.726i			0.592313i
$583$		−	428.216i		−	0.734504i
$584$			301.827i			0.516827i
$585$		0			0
$586$			181.492i			0.309713i
$587$	−938.218			−1.59833			−0.799164	−	0.601113i	$-0.794724\pi$
$587$	−938.218			−1.59833			−0.799164	+	0.601113i	$0.794724\pi$
$588$	141.023	−	94.4695i	0.239835	−	0.160662i
$589$	44.9065			0.0762419
$590$		0			0
$591$		−	496.314i		−	0.839787i
$592$			144.242i			0.243653i
$593$	−736.439			−1.24189			−0.620943	−	0.783856i	$-0.713250\pi$
$593$	−736.439			−1.24189			−0.620943	+	0.783856i	$0.713250\pi$
$594$			38.9761i			0.0656163i
$595$		0			0
$596$	−529.077			−0.887713
$597$			59.6801i			0.0999667i
$598$	336.911			0.563397
$599$	−385.386			−0.643383			−0.321692	−	0.946845i	$-0.604251\pi$
$599$	−385.386			−0.643383			−0.321692	+	0.946845i	$0.604251\pi$
$600$		0			0
$601$		−	965.914i		−	1.60718i	−0.595184	−	0.803589i	$-0.702921\pi$
$601$		−	965.914i		−	1.60718i	0.595184	−	0.803589i	$-0.297079\pi$
$602$	−341.151	+	103.707i	−0.566696	+	0.172271i
$603$			271.295i			0.449909i
$604$	−25.7418			−0.0426188
$605$		0			0
$606$	237.102			0.391257
$607$	1162.16			1.91460			0.957298	−	0.289103i	$-0.0933571\pi$
$607$	1162.16			1.91460			0.957298	+	0.289103i	$0.0933571\pi$
$608$	41.6251			0.0684623
$609$	−514.959	+	156.543i	−0.845582	+	0.257049i
$610$		0			0
$611$	−402.430			−0.658642
$612$	10.8256			0.0176889
$613$			709.805i			1.15792i	0.815356	+	0.578960i	$0.196541\pi$
$613$			709.805i			1.15792i	−0.815356	+	0.578960i	$0.803459\pi$
$614$		−	410.277i		−	0.668204i
$615$		0			0
$616$	30.5430	+	100.473i	0.0495828	+	0.163106i
$617$			326.387i			0.528990i	0.964387	+	0.264495i	$0.0852053\pi$
$617$			326.387i			0.528990i	−0.964387	+	0.264495i	$0.914795\pi$
$618$			251.130i			0.406360i
$619$		−	340.928i		−	0.550772i	−0.961334	−	0.275386i	$-0.911194\pi$
$619$		−	340.928i		−	0.550772i	0.961334	−	0.275386i	$-0.0888056\pi$
$620$		0			0
$621$		−	82.2268i		−	0.132410i
$622$	−107.716			−0.173177
$623$	119.653	+	393.608i	0.192060	+	0.631795i
$624$	104.301			0.167150
$625$		0			0
$626$		−	745.496i		−	1.19089i
$627$		−	67.5993i		−	0.107814i
$628$	−407.269			−0.648518
$629$		−	65.0630i		−	0.103439i
$630$		0			0
$631$	−64.3589			−0.101995			−0.0509975	−	0.998699i	$-0.516240\pi$
$631$	−64.3589			−0.101995			−0.0509975	+	0.998699i	$0.516240\pi$
$632$		−	45.8093i		−	0.0724831i
$633$	−210.664			−0.332803
$634$	690.600			1.08927
$635$		0			0
$636$			279.674i			0.439739i
$637$	−612.870	+	410.554i	−0.962120	+	0.644512i
$638$		−	332.984i		−	0.521918i
$639$	−124.312			−0.194542
$640$		0			0
$641$	−621.739			−0.969952			−0.484976	−	0.874527i	$-0.661172\pi$
$641$	−621.739			−0.969952			−0.484976	+	0.874527i	$0.661172\pi$
$642$	342.028			0.532754
$643$	396.767			0.617056			0.308528	−	0.951215i	$-0.400164\pi$
$643$	396.767			0.617056			0.308528	+	0.951215i	$0.400164\pi$
$644$	−64.4358	−	211.966i	−0.100056	−	0.329140i
$645$		0			0
$646$	−18.7757			−0.0290646
$647$	564.262			0.872121			0.436060	−	0.899917i	$-0.356373\pi$
$647$	564.262			0.872121			0.436060	+	0.899917i	$0.356373\pi$
$648$		−	25.4558i		−	0.0392837i
$649$		−	205.273i		−	0.316291i
$650$		0			0
$651$	−21.5207	−	70.7937i	−0.0330578	−	0.108746i
$652$			523.682i			0.803194i
$653$			804.359i			1.23179i	0.787828	+	0.615895i	$0.211206\pi$
$653$			804.359i			1.23179i	−0.787828	+	0.615895i	$0.788794\pi$
$654$		−	66.9293i		−	0.102338i
$655$		0			0
$656$		−	75.4477i		−	0.115012i
$657$	−320.136			−0.487269
$658$	76.9667	+	253.187i	0.116971	+	0.384783i
$659$	−229.717			−0.348584			−0.174292	−	0.984694i	$-0.555764\pi$
$659$	−229.717			−0.348584			−0.174292	+	0.984694i	$0.555764\pi$
$660$		0			0
$661$		−	411.750i		−	0.622920i	−0.950259	−	0.311460i	$-0.899182\pi$
$661$		−	411.750i		−	0.622920i	0.950259	−	0.311460i	$-0.100818\pi$
$662$			735.178i			1.11054i
$663$	−47.0469			−0.0709606
$664$		−	98.3888i		−	0.148176i
$665$		0			0
$666$	−152.992			−0.229718
$667$			702.487i			1.05320i
$668$	181.407			0.271568
$669$	523.123			0.781948
$670$		0			0
$671$			135.445i			0.201855i
$672$	−19.9481	−	65.6207i	−0.0296847	−	0.0976498i
$673$			905.399i			1.34532i	0.739952	+	0.672659i	$0.234848\pi$
$673$			905.399i			1.34532i	−0.739952	+	0.672659i	$0.765152\pi$
$674$	650.868			0.965679
$675$		0			0
$676$	−115.282			−0.170535
$677$	632.507			0.934279			0.467139	−	0.884184i	$-0.345285\pi$
$677$	632.507			0.934279			0.467139	+	0.884184i	$0.345285\pi$
$678$	113.752			0.167776
$679$	−942.549	+	286.527i	−1.38814	+	0.421983i
$680$		0			0
$681$	−276.753			−0.406392
$682$	45.7767			0.0671213
$683$		−	1050.88i		−	1.53862i	−0.638876	−	0.769310i	$-0.720600\pi$
$683$		−	1050.88i		−	1.53862i	0.638876	−	0.769310i	$-0.279400\pi$
$684$			44.1501i			0.0645469i
$685$		0			0
$686$	375.512	+	307.064i	0.547394	+	0.447615i
$687$		−	79.6956i		−	0.116005i
$688$			144.074i			0.209410i
$689$		−	1215.43i		−	1.76405i
$690$		0			0
$691$		−	1353.15i		−	1.95825i	−0.203270	−	0.979123i	$-0.565157\pi$
$691$		−	1353.15i		−	1.95825i	0.203270	−	0.979123i	$-0.434843\pi$
$692$	−497.252			−0.718572
$693$	−106.568	+	32.3958i	−0.153778	+	0.0467472i
$694$	−7.79965			−0.0112387
$695$		0			0
$696$			217.477i			0.312467i
$697$			34.0320i			0.0488264i
$698$	−797.463			−1.14250
$699$		−	168.548i		−	0.241127i
$700$		0			0
$701$	−1124.26			−1.60379			−0.801897	−	0.597462i	$-0.796176\pi$
$701$	−1124.26			−1.60379			−0.801897	+	0.597462i	$0.796176\pi$
$702$			110.628i			0.157590i
$703$	265.347			0.377449
$704$	42.4318			0.0602724
$705$		0			0
$706$			387.709i			0.549163i
$707$	197.072	+	648.283i	0.278744	+	0.916949i
$708$			134.067i			0.189360i
$709$	−270.618			−0.381689			−0.190845	−	0.981620i	$-0.561123\pi$
$709$	−270.618			−0.381689			−0.190845	+	0.981620i	$0.561123\pi$
$710$		0			0
$711$	48.5881			0.0683377
$712$	166.228			0.233466
$713$	−96.5740			−0.135447
$714$	8.99794	+	29.5993i	0.0126022	+	0.0414556i
$715$		0			0
$716$	277.722			0.387880
$717$	215.259			0.300222
$718$			92.6144i			0.128989i
$719$			865.721i			1.20406i	0.798473	+	0.602031i	$0.205642\pi$
$719$			865.721i			1.20406i	−0.798473	+	0.602031i	$0.794358\pi$
$720$		0			0
$721$	−686.639	+	208.732i	−0.952342	+	0.289504i
$722$			433.958i			0.601050i
$723$		−	576.685i		−	0.797628i
$724$		−	296.976i		−	0.410187i
$725$		0			0
$726$			227.479i			0.313332i
$727$	−747.526			−1.02823			−0.514117	−	0.857720i	$-0.671880\pi$
$727$	−747.526			−1.02823			−0.514117	+	0.857720i	$0.671880\pi$
$728$	86.6922	+	285.180i	0.119083	+	0.391731i
$729$	27.0000			0.0370370
$730$		0			0
$731$		−	64.9872i		−	0.0889017i
$732$		−	88.4609i		−	0.120848i
$733$	506.845			0.691467			0.345733	−	0.938333i	$-0.387630\pi$
$733$	506.845			0.691467			0.345733	+	0.938333i	$0.387630\pi$
$734$		−	226.045i		−	0.307963i
$735$		0			0
$736$	−89.5172			−0.121627
$737$		−	479.647i		−	0.650811i
$738$	80.0244			0.108434
$739$	350.632			0.474468			0.237234	−	0.971453i	$-0.423759\pi$
$739$	350.632			0.474468			0.237234	+	0.971453i	$0.423759\pi$
$740$		0			0
$741$		−	191.871i		−	0.258936i
$742$	−764.684	+	232.457i	−1.03057	+	0.313285i
$743$			958.163i			1.28959i	0.764357	+	0.644793i	$0.223056\pi$
$743$			958.163i			1.28959i	−0.764357	+	0.644793i	$0.776944\pi$
$744$	−29.8975			−0.0401848
$745$		0			0
$746$	−665.749			−0.892424
$747$	104.357			0.139702
$748$	−19.1396			−0.0255877
$749$	284.284	+	935.171i	0.379551	+	1.24856i
$750$		0			0
$751$	−457.638			−0.609371			−0.304686	−	0.952453i	$-0.598551\pi$
$751$	−457.638			−0.609371			−0.304686	+	0.952453i	$0.598551\pi$
$752$	106.926			0.142188
$753$			266.941i			0.354503i
$754$		−	945.129i		−	1.25349i
$755$		0			0
$756$	69.6012	−	21.1582i	0.0920651	−	0.0279870i
$757$		−	1273.11i		−	1.68179i	−0.541201	−	0.840893i	$-0.682030\pi$
$757$		−	1273.11i		−	1.68179i	0.541201	−	0.840893i	$-0.317970\pi$
$758$		−	86.9319i		−	0.114686i
$759$			145.376i			0.191536i
$760$		0			0
$761$		−	103.915i		−	0.136551i	−0.997667	−	0.0682754i	$-0.978250\pi$
$761$		−	103.915i		−	0.136551i	0.997667	−	0.0682754i	$-0.0217496\pi$
$762$	148.730			0.195184
$763$	182.998	−	55.6297i	0.239840	−	0.0729091i
$764$	92.1562			0.120623
$765$		0			0
$766$			169.866i			0.221757i
$767$		−	582.639i		−	0.759633i
$768$	−27.7128			−0.0360844
$769$			433.921i			0.564266i	0.959375	+	0.282133i	$0.0910420\pi$
$769$			433.921i			0.564266i	−0.959375	+	0.282133i	$0.908958\pi$
$770$		0			0
$771$	−710.771			−0.921881
$772$			52.8813i			0.0684991i
$773$	−1220.86			−1.57937			−0.789687	−	0.613510i	$-0.789757\pi$
$773$	−1220.86			−1.57937			−0.789687	+	0.613510i	$0.789757\pi$
$774$	−152.814			−0.197434
$775$		0			0
$776$			398.056i			0.512958i
$777$	−127.163	−	418.310i	−0.163659	−	0.538366i
$778$		−	437.836i		−	0.562771i
$779$	−138.793			−0.178168
$780$		0			0
$781$	219.783			0.281412
$782$	40.3783			0.0516346
$783$	−230.669			−0.294596
$784$	162.839	−	109.084i	0.207703	−	0.139138i
$785$		0			0
$786$	−495.409			−0.630292
$787$	−866.849			−1.10146			−0.550730	−	0.834683i	$-0.685651\pi$
$787$	−866.849			−1.10146			−0.550730	+	0.834683i	$0.685651\pi$
$788$		−	573.094i		−	0.727277i
$789$			594.091i			0.752967i
$790$		0			0
$791$	94.5476	+	311.021i	0.119529	+	0.393199i
$792$			45.0057i			0.0568253i
$793$			384.441i			0.484793i
$794$			1066.58i			1.34330i
$795$		0			0
$796$			68.9127i			0.0865737i
$797$	915.806			1.14907			0.574533	−	0.818481i	$-0.305184\pi$
$797$	915.806			1.14907			0.574533	+	0.818481i	$0.305184\pi$
$798$	−120.715	+	36.6963i	−0.151272	+	0.0459853i
$799$	−48.2306			−0.0603637
$800$		0			0
$801$			176.311i			0.220114i
$802$			333.326i			0.415619i
$803$	565.996			0.704852
$804$			313.265i			0.389633i
$805$		0			0
$806$	129.931			0.161205
$807$			412.360i			0.510979i
$808$	273.782			0.338839
$809$	693.212			0.856875			0.428437	−	0.903571i	$-0.359064\pi$
$809$	693.212			0.856875			0.428437	+	0.903571i	$0.359064\pi$
$810$		0			0
$811$			1165.31i			1.43688i	0.695591	+	0.718438i	$0.255143\pi$
$811$			1165.31i			1.43688i	−0.695591	+	0.718438i	$0.744857\pi$
$812$	−594.624	+	180.760i	−0.732295	+	0.222611i
$813$			56.5435i			0.0695492i
$814$	270.489			0.332296
$815$		0			0
$816$	12.5003			0.0153190
$817$	265.037			0.324403
$818$	115.033			0.140627
$819$	−302.479	+	91.9510i	−0.369327	+	0.112272i
$820$		0			0
$821$	−392.977			−0.478657			−0.239329	−	0.970939i	$-0.576927\pi$
$821$	−392.977			−0.478657			−0.239329	+	0.970939i	$0.576927\pi$
$822$	289.454			0.352134
$823$			1430.26i			1.73786i	0.494931	+	0.868932i	$0.335193\pi$
$823$			1430.26i			1.73786i	−0.494931	+	0.868932i	$0.664807\pi$
$824$			289.980i			0.351918i
$825$		0			0
$826$	−366.564	+	111.432i	−0.443782	+	0.134906i
$827$			667.082i			0.806629i	0.915062	+	0.403314i	$0.132142\pi$
$827$			667.082i			0.806629i	−0.915062	+	0.403314i	$0.867858\pi$
$828$		−	94.9473i		−	0.114671i
$829$		−	851.079i		−	1.02663i	−0.858199	−	0.513317i	$-0.828417\pi$
$829$		−	851.079i		−	1.02663i	0.858199	−	0.513317i	$-0.171583\pi$
$830$		0			0
$831$		−	398.840i		−	0.479952i
$832$	120.437			0.144756
$833$	−73.4515	+	49.2042i	−0.0881771	+	0.0590687i
$834$	627.135			0.751960
$835$		0			0
$836$		−	78.0569i		−	0.0933695i
$837$		−	31.7110i		−	0.0378866i
$838$	301.269			0.359510
$839$			1401.61i			1.67057i	0.549815	+	0.835287i	$0.314698\pi$
$839$			1401.61i			1.67057i	−0.549815	+	0.835287i	$0.685302\pi$
$840$		0			0
$841$	1129.67			1.34325
$842$			589.494i			0.700112i
$843$	−843.265			−1.00031
$844$	−243.254			−0.288216
$845$		0			0
$846$			113.412i			0.134056i
$847$	−621.972	+	189.074i	−0.734323	+	0.223228i
$848$			322.940i			0.380826i
$849$	562.302			0.662311
$850$		0			0
$851$	−570.643			−0.670556
$852$	−143.544			−0.168478
$853$	390.367			0.457640			0.228820	−	0.973469i	$-0.426513\pi$
$853$	390.367			0.457640			0.228820	+	0.973469i	$0.426513\pi$
$854$	241.869	−	73.5261i	0.283219	−	0.0860962i
$855$		0			0
$856$	394.940			0.461378
$857$	−1123.67			−1.31117			−0.655583	−	0.755124i	$-0.727577\pi$
$857$	−1123.67			−1.31117			−0.655583	+	0.755124i	$0.727577\pi$
$858$		−	195.590i		−	0.227960i
$859$		−	774.660i		−	0.901816i	−0.892571	−	0.450908i	$-0.851100\pi$
$859$		−	774.660i		−	0.901816i	0.892571	−	0.450908i	$-0.148900\pi$
$860$		0			0
$861$	66.5140	+	218.802i	0.0772520	+	0.254126i
$862$		−	469.394i		−	0.544540i
$863$			596.376i			0.691050i	0.938409	+	0.345525i	$0.112299\pi$
$863$			596.376i			0.691050i	−0.938409	+	0.345525i	$0.887701\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$		−	430.091i		−	0.496641i
$867$	494.924			0.570847
$868$	−24.8499	−	81.7455i	−0.0286289	−	0.0941768i
$869$	−85.9033			−0.0988530
$870$		0			0
$871$		−	1361.41i		−	1.56305i
$872$		−	77.2832i		−	0.0886276i
$873$	−422.202			−0.483622
$874$			164.675i			0.188415i
$875$		0			0
$876$	−369.661			−0.421987
$877$			481.187i			0.548674i	0.961634	+	0.274337i	$0.0884584\pi$
$877$			481.187i			0.548674i	−0.961634	+	0.274337i	$0.911542\pi$
$878$	34.4726			0.0392627
$879$	−222.281			−0.252879
$880$		0			0
$881$			1098.21i			1.24655i	0.782004	+	0.623273i	$0.214197\pi$
$881$			1098.21i			1.24655i	−0.782004	+	0.623273i	$0.785803\pi$
$882$	115.701	+	172.717i	0.131180	+	0.195825i
$883$		−	930.631i		−	1.05394i	−0.849883	−	0.526971i	$-0.823328\pi$
$883$		−	930.631i		−	1.05394i	0.849883	−	0.526971i	$-0.176672\pi$
$884$	−54.3251			−0.0614537
$885$		0			0
$886$	−42.8675			−0.0483832
$887$	1762.36			1.98688			0.993441	−	0.114343i	$-0.0364764\pi$
$887$	1762.36			1.98688			0.993441	+	0.114343i	$0.0364764\pi$
$888$	−176.660			−0.198942
$889$	123.620	+	406.657i	0.139055	+	0.457432i
$890$		0			0
$891$	−47.7357			−0.0535754
$892$	604.051			0.677187
$893$		−	196.699i		−	0.220268i
$894$		−	647.984i		−	0.724814i
$895$		0			0
$896$	−23.0341	−	75.7722i	−0.0257077	−	0.0845672i
$897$			412.630i			0.460012i
$898$			777.958i			0.866323i
$899$			270.917i			0.301353i
$900$		0			0
$901$		−	145.668i		−	0.161673i
$902$	−141.482			−0.156854
$903$	−127.014	−	417.823i	−0.140658	−	0.462705i
$904$	131.350			0.145298
$905$		0			0
$906$		−	31.5271i		−	0.0347981i
$907$		−	135.202i		−	0.149065i	−0.997219	−	0.0745327i	$-0.976253\pi$
$907$		−	135.202i		−	0.149065i	0.997219	−	0.0745327i	$-0.0237465\pi$
$908$	−319.567			−0.351946
$909$			290.389i			0.319460i
$910$		0			0
$911$	−995.115			−1.09233			−0.546166	−	0.837677i	$-0.683913\pi$
$911$	−995.115			−1.09233			−0.546166	+	0.837677i	$0.683913\pi$
$912$			50.9801i			0.0558993i
$913$	−184.502			−0.202083
$914$	674.911			0.738414
$915$		0			0
$916$		−	92.0245i		−	0.100463i
$917$	−411.770	−	1354.55i	−0.449040	−	1.47715i
$918$			13.2586i			0.0144429i
$919$	−514.989			−0.560380			−0.280190	−	0.959945i	$-0.590397\pi$
$919$	−514.989			−0.560380			−0.280190	+	0.959945i	$0.590397\pi$
$920$		0			0
$921$	502.485			0.545586
$922$	−1217.29			−1.32027
$923$	623.824			0.675866
$924$	−123.054	+	37.4074i	−0.133176	+	0.0404842i
$925$		0			0
$926$	1095.32			1.18285
$927$	−307.570			−0.331791
$928$			251.120i			0.270604i
$929$		−	865.807i		−	0.931977i	−0.884791	−	0.465989i	$-0.845699\pi$
$929$		−	865.807i		−	0.931977i	0.884791	−	0.465989i	$-0.154301\pi$
$930$		0			0
$931$	−200.670	−	299.557i	−0.215542	−	0.321759i
$932$		−	194.623i		−	0.208822i
$933$		−	131.925i		−	0.141399i
$934$			1088.75i			1.16568i
$935$		0			0
$936$			127.742i			0.136477i
$937$	−1000.06			−1.06730			−0.533649	−	0.845706i	$-0.679180\pi$
$937$	−1000.06			−1.06730			−0.533649	+	0.845706i	$0.679180\pi$
$938$	−856.527	+	260.377i	−0.913142	+	0.277587i
$939$	913.043			0.972356
$940$		0			0
$941$		−	776.370i		−	0.825048i	−0.910947	−	0.412524i	$-0.864647\pi$
$941$		−	776.370i		−	0.825048i	0.910947	−	0.412524i	$-0.135353\pi$
$942$		−	498.801i		−	0.529512i
$943$	298.482			0.316523
$944$			154.807i			0.163990i
$945$		0			0
$946$	270.173			0.285595
$947$			472.690i			0.499144i	0.968356	+	0.249572i	$0.0802900\pi$
$947$			472.690i			0.499144i	−0.968356	+	0.249572i	$0.919710\pi$
$948$	56.1047			0.0591822
$949$	1606.50			1.69284
$950$		0			0
$951$			845.808i			0.889388i
$952$	10.3899	+	34.1784i	0.0109138	+	0.0359016i
$953$			104.665i			0.109827i	0.998491	+	0.0549133i	$0.0174882\pi$
$953$			104.665i			0.109827i	−0.998491	+	0.0549133i	$0.982512\pi$
$954$	−342.530			−0.359046
$955$		0			0
$956$	248.560			0.260000
$957$	407.820			0.426144
$958$	1024.93			1.06986
$959$	240.586	+	791.424i	0.250872	+	0.825259i
$960$		0			0
$961$	923.756			0.961244
$962$	767.745			0.798072
$963$			418.897i			0.434992i
$964$		−	665.899i		−	0.690766i
$965$		0			0
$966$	259.604	−	78.9175i	0.268742	−	0.0816951i
$967$		−	1463.91i		−	1.51386i	−0.653495	−	0.756931i	$-0.726698\pi$
$967$		−	1463.91i		−	1.51386i	0.653495	−	0.756931i	$-0.273302\pi$
$968$			262.670i			0.271353i
$969$		−	22.9955i		−	0.0237311i
$970$		0			0
$971$			101.826i			0.104867i	0.998624	+	0.0524333i	$0.0166977\pi$
$971$			101.826i			0.104867i	−0.998624	+	0.0524333i	$0.983302\pi$
$972$	31.1769			0.0320750
$973$	521.256	+	1714.71i	0.535721	+	1.76229i
$974$	−83.4250			−0.0856520
$975$		0			0
$976$		−	102.146i		−	0.104658i
$977$		−	69.4893i		−	0.0711252i	−0.999367	−	0.0355626i	$-0.988678\pi$
$977$		−	69.4893i		−	0.0711252i	0.999367	−	0.0355626i	$-0.0113223\pi$
$978$	−641.377			−0.655805
$979$		−	311.717i		−	0.318403i
$980$		0			0
$981$	81.9713			0.0835589
$982$		−	812.681i		−	0.827577i
$983$	166.731			0.169614			0.0848070	−	0.996397i	$-0.472973\pi$
$983$	166.731			0.169614			0.0848070	+	0.996397i	$0.472973\pi$
$984$	92.4042			0.0939067
$985$		0			0
$986$		−	113.272i		−	0.114881i
$987$	−310.090	+	94.2645i	−0.314174	+	0.0955061i
$988$		−	221.554i		−	0.224245i
$989$	−569.978			−0.576317
$990$		0			0
$991$	−990.392			−0.999387			−0.499693	−	0.866202i	$-0.666554\pi$
$991$	−990.392			−0.999387			−0.499693	+	0.866202i	$0.666554\pi$
$992$	−34.5226			−0.0348010
$993$	−900.405			−0.906753
$994$	−119.309	−	392.476i	−0.120030	−	0.394845i
$995$		0			0
$996$	120.501			0.120985
$997$	−567.448			−0.569156			−0.284578	−	0.958653i	$-0.591853\pi$
$997$	−567.448			−0.569156			−0.284578	+	0.958653i	$0.591853\pi$
$998$		−	399.429i		−	0.400230i
$999$		−	187.376i		−	0.187564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.h.c.349.8		24
5.2	odd	4		1050.3.f.d.601.5	yes	12
5.3	odd	4		1050.3.f.c.601.8	✓	12
5.4	even	2	inner	1050.3.h.c.349.19		24
7.6	odd	2	inner	1050.3.h.c.349.20		24
35.13	even	4		1050.3.f.c.601.11	yes	12
35.27	even	4		1050.3.f.d.601.2	yes	12
35.34	odd	2	inner	1050.3.h.c.349.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.f.c.601.8	✓	12	5.3	odd	4
1050.3.f.c.601.11	yes	12	35.13	even	4
1050.3.f.d.601.2	yes	12	35.27	even	4
1050.3.f.d.601.5	yes	12	5.2	odd	4
1050.3.h.c.349.7		24	35.34	odd	2	inner
1050.3.h.c.349.8		24	1.1	even	1	trivial
1050.3.h.c.349.19		24	5.4	even	2	inner
1050.3.h.c.349.20		24	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -2.44949i q^{6} +(6.69738 - 2.03595i) q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} -2.44949i q^{6} +(6.69738 - 2.03595i) q^{7} -2.82843i q^{8} +3.00000 q^{9} -5.30397 q^{11} +3.46410 q^{12} -15.0546 q^{13} +(2.87926 + 9.47153i) q^{14} +4.00000 q^{16} -1.80427 q^{17} +4.24264i q^{18} -7.35835i q^{19} +(-11.6002 + 3.52636i) q^{21} -7.50095i q^{22} +15.8246i q^{23} +4.89898i q^{24} -21.2904i q^{26} -5.19615 q^{27} +(-13.3948 + 4.07189i) q^{28} +44.3922 q^{29} +6.10279i q^{31} +5.65685i q^{32} +9.18674 q^{33} -2.55162i q^{34} -6.00000 q^{36} +36.0606i q^{37} +10.4063 q^{38} +26.0753 q^{39} -18.8619i q^{41} +(-4.98703 - 16.4052i) q^{42} +36.0186i q^{43} +10.6079 q^{44} -22.3793 q^{46} +26.7314 q^{47} -6.92820 q^{48} +(40.7099 - 27.2710i) q^{49} +3.12509 q^{51} +30.1092 q^{52} +80.7350i q^{53} -7.34847i q^{54} +(-5.75852 - 18.9431i) q^{56} +12.7450i q^{57} +62.7801i q^{58} +38.7017i q^{59} -25.5365i q^{61} -8.63065 q^{62} +(20.0921 - 6.10784i) q^{63} -8.00000 q^{64} +12.9920i q^{66} +90.4318i q^{67} +3.60854 q^{68} -27.4089i q^{69} -41.4375 q^{71} -8.48528i q^{72} -106.712 q^{73} -50.9974 q^{74} +14.7167i q^{76} +(-35.5227 + 10.7986i) q^{77} +36.8761i q^{78} +16.1960 q^{79} +9.00000 q^{81} +26.6748 q^{82} +34.7857 q^{83} +(23.2004 - 7.05272i) q^{84} -50.9379 q^{86} -76.8896 q^{87} +15.0019i q^{88} +58.7705i q^{89} +(-100.826 + 30.6503i) q^{91} -31.6491i q^{92} -10.5703i q^{93} +37.8039i q^{94} -9.79796i q^{96} -140.734 q^{97} +(38.5670 + 57.5724i) q^{98} -15.9119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 48 q^{4} + 72 q^{9}+O(q^{10}) \) 24 * q - 48 * q^4 + 72 * q^9	\( 24 q - 48 q^{4} + 72 q^{9} - 32 q^{11} - 16 q^{14} + 96 q^{16} - 12 q^{21} - 96 q^{29} - 144 q^{36} + 24 q^{39} + 64 q^{44} + 160 q^{46} - 236 q^{49} + 144 q^{51} + 32 q^{56} - 192 q^{64} + 496 q^{71} + 128 q^{74} + 416 q^{79} + 216 q^{81} + 24 q^{84} + 256 q^{86} - 316 q^{91} - 96 q^{99}+O(q^{100}) \) 24 * q - 48 * q^4 + 72 * q^9 - 32 * q^11 - 16 * q^14 + 96 * q^16 - 12 * q^21 - 96 * q^29 - 144 * q^36 + 24 * q^39 + 64 * q^44 + 160 * q^46 - 236 * q^49 + 144 * q^51 + 32 * q^56 - 192 * q^64 + 496 * q^71 + 128 * q^74 + 416 * q^79 + 216 * q^81 + 24 * q^84 + 256 * q^86 - 316 * q^91 - 96 * q^99

Introduction

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