LMFDB - Embedded newform 750.2.c.b.499.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(499,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("750.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.c (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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			499.4
Root			$0.618034i$ of defining polynomial
Character	$\chi$	$=$	750.499
Dual form			750.2.c.b.499.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +1.23607i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +1.23607i q^{7} -1.00000i q^{8} -1.00000 q^{9} +1.38197 q^{11} -1.00000i q^{12} +2.85410i q^{13} -1.23607 q^{14} +1.00000 q^{16} +4.85410i q^{17} -1.00000i q^{18} -6.00000 q^{19} -1.23607 q^{21} +1.38197i q^{22} +3.09017i q^{23} +1.00000 q^{24} -2.85410 q^{26} -1.00000i q^{27} -1.23607i q^{28} -9.32624 q^{29} +2.14590 q^{31} +1.00000i q^{32} +1.38197i q^{33} -4.85410 q^{34} +1.00000 q^{36} -7.85410i q^{37} -6.00000i q^{38} -2.85410 q^{39} -3.23607 q^{41} -1.23607i q^{42} +0.145898i q^{43} -1.38197 q^{44} -3.09017 q^{46} +10.8541i q^{47} +1.00000i q^{48} +5.47214 q^{49} -4.85410 q^{51} -2.85410i q^{52} -3.23607i q^{53} +1.00000 q^{54} +1.23607 q^{56} -6.00000i q^{57} -9.32624i q^{58} -6.38197 q^{59} +13.4164 q^{61} +2.14590i q^{62} -1.23607i q^{63} -1.00000 q^{64} -1.38197 q^{66} -2.38197i q^{67} -4.85410i q^{68} -3.09017 q^{69} -8.94427 q^{71} +1.00000i q^{72} +12.0000i q^{73} +7.85410 q^{74} +6.00000 q^{76} +1.70820i q^{77} -2.85410i q^{78} +1.14590 q^{79} +1.00000 q^{81} -3.23607i q^{82} +8.18034i q^{83} +1.23607 q^{84} -0.145898 q^{86} -9.32624i q^{87} -1.38197i q^{88} +9.23607 q^{89} -3.52786 q^{91} -3.09017i q^{92} +2.14590i q^{93} -10.8541 q^{94} -1.00000 q^{96} -18.1803i q^{97} +5.47214i q^{98} -1.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 10 q^{11} + 4 q^{14} + 4 q^{16} - 24 q^{19} + 4 q^{21} + 4 q^{24} + 2 q^{26} - 6 q^{29} + 22 q^{31} - 6 q^{34} + 4 q^{36} + 2 q^{39} - 4 q^{41} - 10 q^{44} + 10 q^{46} + 4 q^{49} - 6 q^{51} + 4 q^{54} - 4 q^{56} - 30 q^{59} - 4 q^{64} - 10 q^{66} + 10 q^{69} + 18 q^{74} + 24 q^{76} + 18 q^{79} + 4 q^{81} - 4 q^{84} - 14 q^{86} + 28 q^{89} - 32 q^{91} - 30 q^{94} - 4 q^{96} - 10 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 10 * q^11 + 4 * q^14 + 4 * q^16 - 24 * q^19 + 4 * q^21 + 4 * q^24 + 2 * q^26 - 6 * q^29 + 22 * q^31 - 6 * q^34 + 4 * q^36 + 2 * q^39 - 4 * q^41 - 10 * q^44 + 10 * q^46 + 4 * q^49 - 6 * q^51 + 4 * q^54 - 4 * q^56 - 30 * q^59 - 4 * q^64 - 10 * q^66 + 10 * q^69 + 18 * q^74 + 24 * q^76 + 18 * q^79 + 4 * q^81 - 4 * q^84 - 14 * q^86 + 28 * q^89 - 32 * q^91 - 30 * q^94 - 4 * q^96 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$-1$	$1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	1.23607i	0.467190i	0.972334	+	0.233595i	$0.0750489\pi$
$7$	1.23607i	0.467190i	−0.972334	+	0.233595i	$0.924951\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	1.38197	0.416678	0.208339	−	0.978057i	$-0.433194\pi$
$11$	1.38197	0.416678	0.208339	+	0.978057i	$0.433194\pi$
$12$	− 1.00000i	− 0.288675i
$13$	2.85410i	0.791585i	0.918340	+	0.395793i	$0.129530\pi$
$13$	2.85410i	0.791585i	−0.918340	+	0.395793i	$0.870470\pi$
$14$	−1.23607	−0.330353
$15$	0	0
$16$	1.00000	0.250000
$17$	4.85410i	1.17729i	0.808391	+	0.588646i	$0.200339\pi$
$17$	4.85410i	1.17729i	−0.808391	+	0.588646i	$0.799661\pi$
$18$	− 1.00000i	− 0.235702i
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	0	0
$21$	−1.23607	−0.269732
$22$	1.38197i	0.294636i
$23$	3.09017i	0.644345i	0.946681	+	0.322172i	$0.104413\pi$
$23$	3.09017i	0.644345i	−0.946681	+	0.322172i	$0.895587\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−2.85410	−0.559735
$27$	− 1.00000i	− 0.192450i
$28$	− 1.23607i	− 0.233595i
$29$	−9.32624	−1.73184	−0.865919	−	0.500183i	$-0.833266\pi$
$29$	−9.32624	−1.73184	−0.865919	+	0.500183i	$0.833266\pi$
$30$	0	0
$31$	2.14590	0.385415	0.192707	−	0.981256i	$-0.438273\pi$
$31$	2.14590	0.385415	0.192707	+	0.981256i	$0.438273\pi$
$32$	1.00000i	0.176777i
$33$	1.38197i	0.240569i
$34$	−4.85410	−0.832472
$35$	0	0
$36$	1.00000	0.166667
$37$	− 7.85410i	− 1.29121i	−0.763673	−	0.645603i	$-0.776606\pi$
$37$	− 7.85410i	− 1.29121i	0.763673	−	0.645603i	$-0.223394\pi$
$38$	− 6.00000i	− 0.973329i
$39$	−2.85410	−0.457022
$40$	0	0
$41$	−3.23607	−0.505389	−0.252694	−	0.967546i	$-0.581317\pi$
$41$	−3.23607	−0.505389	−0.252694	+	0.967546i	$0.581317\pi$
$42$	− 1.23607i	− 0.190729i
$43$	0.145898i	0.0222492i	0.999938	+	0.0111246i	$0.00354115\pi$
$43$	0.145898i	0.0222492i	−0.999938	+	0.0111246i	$0.996459\pi$
$44$	−1.38197	−0.208339
$45$	0	0
$46$	−3.09017	−0.455621
$47$	10.8541i	1.58323i	0.611018	+	0.791617i	$0.290760\pi$
$47$	10.8541i	1.58323i	−0.611018	+	0.791617i	$0.709240\pi$
$48$	1.00000i	0.144338i
$49$	5.47214	0.781734
$50$	0	0
$51$	−4.85410	−0.679710
$52$	− 2.85410i	− 0.395793i
$53$	− 3.23607i	− 0.444508i	−0.974989	−	0.222254i	$-0.928659\pi$
$53$	− 3.23607i	− 0.444508i	0.974989	−	0.222254i	$-0.0713414\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	1.23607	0.165177
$57$	− 6.00000i	− 0.794719i
$58$	− 9.32624i	− 1.22460i
$59$	−6.38197	−0.830861	−0.415431	−	0.909625i	$-0.636369\pi$
$59$	−6.38197	−0.830861	−0.415431	+	0.909625i	$0.636369\pi$
$60$	0	0
$61$	13.4164	1.71780	0.858898	−	0.512148i	$-0.171150\pi$
$61$	13.4164	1.71780	0.858898	+	0.512148i	$0.171150\pi$
$62$	2.14590i	0.272529i
$63$	− 1.23607i	− 0.155730i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−1.38197	−0.170108
$67$	− 2.38197i	− 0.291003i	−0.989358	−	0.145502i	$-0.953520\pi$
$67$	− 2.38197i	− 0.291003i	0.989358	−	0.145502i	$-0.0464796\pi$
$68$	− 4.85410i	− 0.588646i
$69$	−3.09017	−0.372013
$70$	0	0
$71$	−8.94427	−1.06149	−0.530745	−	0.847532i	$-0.678088\pi$
$71$	−8.94427	−1.06149	−0.530745	+	0.847532i	$0.678088\pi$
$72$	1.00000i	0.117851i
$73$	12.0000i	1.40449i	0.711934	+	0.702247i	$0.247820\pi$
$73$	12.0000i	1.40449i	−0.711934	+	0.702247i	$0.752180\pi$
$74$	7.85410	0.913021
$75$	0	0
$76$	6.00000	0.688247
$77$	1.70820i	0.194668i
$78$	− 2.85410i	− 0.323163i
$79$	1.14590	0.128924	0.0644618	−	0.997920i	$-0.479467\pi$
$79$	1.14590	0.128924	0.0644618	+	0.997920i	$0.479467\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 3.23607i	− 0.357364i
$83$	8.18034i	0.897909i	0.893555	+	0.448954i	$0.148203\pi$
$83$	8.18034i	0.897909i	−0.893555	+	0.448954i	$0.851797\pi$
$84$	1.23607	0.134866
$85$	0	0
$86$	−0.145898	−0.0157326
$87$	− 9.32624i	− 0.999878i
$88$	− 1.38197i	− 0.147318i
$89$	9.23607	0.979021	0.489511	−	0.871997i	$-0.337175\pi$
$89$	9.23607	0.979021	0.489511	+	0.871997i	$0.337175\pi$
$90$	0	0
$91$	−3.52786	−0.369821
$92$	− 3.09017i	− 0.322172i
$93$	2.14590i	0.222519i
$94$	−10.8541	−1.11952
$95$	0	0
$96$	−1.00000	−0.102062
$97$	− 18.1803i	− 1.84593i	−0.384879	−	0.922967i	$-0.625757\pi$
$97$	− 18.1803i	− 1.84593i	0.384879	−	0.922967i	$-0.374243\pi$
$98$	5.47214i	0.552769i
$99$	−1.38197	−0.138893
$100$	0	0
$101$	−2.32624	−0.231469	−0.115735	−	0.993280i	$-0.536922\pi$
$101$	−2.32624	−0.231469	−0.115735	+	0.993280i	$0.536922\pi$
$102$	− 4.85410i	− 0.480628i
$103$	− 4.00000i	− 0.394132i	−0.980390	−	0.197066i	$-0.936859\pi$
$103$	− 4.00000i	− 0.394132i	0.980390	−	0.197066i	$-0.0631413\pi$
$104$	2.85410	0.279868
$105$	0	0
$106$	3.23607	0.314315
$107$	8.18034i	0.790823i	0.918504	+	0.395412i	$0.129398\pi$
$107$	8.18034i	0.790823i	−0.918504	+	0.395412i	$0.870602\pi$
$108$	1.00000i	0.0962250i
$109$	13.4164	1.28506	0.642529	−	0.766261i	$-0.277885\pi$
$109$	13.4164	1.28506	0.642529	+	0.766261i	$0.277885\pi$
$110$	0	0
$111$	7.85410	0.745478
$112$	1.23607i	0.116797i
$113$	12.3262i	1.15955i	0.814775	+	0.579777i	$0.196861\pi$
$113$	12.3262i	1.15955i	−0.814775	+	0.579777i	$0.803139\pi$
$114$	6.00000	0.561951
$115$	0	0
$116$	9.32624	0.865919
$117$	− 2.85410i	− 0.263862i
$118$	− 6.38197i	− 0.587508i
$119$	−6.00000	−0.550019
$120$	0	0
$121$	−9.09017	−0.826379
$122$	13.4164i	1.21466i
$123$	− 3.23607i	− 0.291786i
$124$	−2.14590	−0.192707
$125$	0	0
$126$	1.23607	0.110118
$127$	13.4164i	1.19051i	0.803535	+	0.595257i	$0.202950\pi$
$127$	13.4164i	1.19051i	−0.803535	+	0.595257i	$0.797050\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−0.145898	−0.0128456
$130$	0	0
$131$	17.8885	1.56293	0.781465	−	0.623949i	$-0.214473\pi$
$131$	17.8885	1.56293	0.781465	+	0.623949i	$0.214473\pi$
$132$	− 1.38197i	− 0.120285i
$133$	− 7.41641i	− 0.643084i
$134$	2.38197	0.205771
$135$	0	0
$136$	4.85410	0.416236
$137$	− 4.61803i	− 0.394545i	−0.980349	−	0.197273i	$-0.936792\pi$
$137$	− 4.61803i	− 0.394545i	0.980349	−	0.197273i	$-0.0632084\pi$
$138$	− 3.09017i	− 0.263053i
$139$	21.2361	1.80122	0.900610	−	0.434628i	$-0.143120\pi$
$139$	21.2361	1.80122	0.900610	+	0.434628i	$0.143120\pi$
$140$	0	0
$141$	−10.8541	−0.914080
$142$	− 8.94427i	− 0.750587i
$143$	3.94427i	0.329837i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−12.0000	−0.993127
$147$	5.47214i	0.451334i
$148$	7.85410i	0.645603i
$149$	20.4721	1.67714	0.838571	−	0.544792i	$-0.183391\pi$
$149$	20.4721	1.67714	0.838571	+	0.544792i	$0.183391\pi$
$150$	0	0
$151$	−17.8541	−1.45295	−0.726473	−	0.687195i	$-0.758842\pi$
$151$	−17.8541	−1.45295	−0.726473	+	0.687195i	$0.758842\pi$
$152$	6.00000i	0.486664i
$153$	− 4.85410i	− 0.392431i
$154$	−1.70820	−0.137651
$155$	0	0
$156$	2.85410	0.228511
$157$	0.437694i	0.0349318i	0.999847	+	0.0174659i	$0.00555985\pi$
$157$	0.437694i	0.0349318i	−0.999847	+	0.0174659i	$0.994440\pi$
$158$	1.14590i	0.0911628i
$159$	3.23607	0.256637
$160$	0	0
$161$	−3.81966	−0.301031
$162$	1.00000i	0.0785674i
$163$	20.2705i	1.58771i	0.608108	+	0.793854i	$0.291929\pi$
$163$	20.2705i	1.58771i	−0.608108	+	0.793854i	$0.708071\pi$
$164$	3.23607	0.252694
$165$	0	0
$166$	−8.18034	−0.634918
$167$	23.0902i	1.78677i	0.449291	+	0.893385i	$0.351677\pi$
$167$	23.0902i	1.78677i	−0.449291	+	0.893385i	$0.648323\pi$
$168$	1.23607i	0.0953647i
$169$	4.85410	0.373392
$170$	0	0
$171$	6.00000	0.458831
$172$	− 0.145898i	− 0.0111246i
$173$	− 9.23607i	− 0.702205i	−0.936337	−	0.351103i	$-0.885807\pi$
$173$	− 9.23607i	− 0.702205i	0.936337	−	0.351103i	$-0.114193\pi$
$174$	9.32624	0.707020
$175$	0	0
$176$	1.38197	0.104170
$177$	− 6.38197i	− 0.479698i
$178$	9.23607i	0.692273i
$179$	−7.41641	−0.554328	−0.277164	−	0.960823i	$-0.589395\pi$
$179$	−7.41641	−0.554328	−0.277164	+	0.960823i	$0.589395\pi$
$180$	0	0
$181$	7.41641	0.551257	0.275629	−	0.961264i	$-0.411114\pi$
$181$	7.41641	0.551257	0.275629	+	0.961264i	$0.411114\pi$
$182$	− 3.52786i	− 0.261503i
$183$	13.4164i	0.991769i
$184$	3.09017	0.227810
$185$	0	0
$186$	−2.14590	−0.157345
$187$	6.70820i	0.490552i
$188$	− 10.8541i	− 0.791617i
$189$	1.23607	0.0899107
$190$	0	0
$191$	6.00000	0.434145	0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000	0.434145	0.217072	+	0.976156i	$0.430349\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	− 17.1246i	− 1.23266i	−0.787489	−	0.616328i	$-0.788619\pi$
$193$	− 17.1246i	− 1.23266i	0.787489	−	0.616328i	$-0.211381\pi$
$194$	18.1803	1.30527
$195$	0	0
$196$	−5.47214	−0.390867
$197$	1.52786i	0.108856i	0.998518	+	0.0544279i	$0.0173335\pi$
$197$	1.52786i	0.108856i	−0.998518	+	0.0544279i	$0.982666\pi$
$198$	− 1.38197i	− 0.0982120i
$199$	15.6180	1.10713	0.553567	−	0.832805i	$-0.313266\pi$
$199$	15.6180	1.10713	0.553567	+	0.832805i	$0.313266\pi$
$200$	0	0
$201$	2.38197	0.168011
$202$	− 2.32624i	− 0.163674i
$203$	− 11.5279i	− 0.809097i
$204$	4.85410	0.339855
$205$	0	0
$206$	4.00000	0.278693
$207$	− 3.09017i	− 0.214782i
$208$	2.85410i	0.197896i
$209$	−8.29180	−0.573556
$210$	0	0
$211$	3.41641	0.235195	0.117598	−	0.993061i	$-0.462481\pi$
$211$	3.41641	0.235195	0.117598	+	0.993061i	$0.462481\pi$
$212$	3.23607i	0.222254i
$213$	− 8.94427i	− 0.612851i
$214$	−8.18034	−0.559197
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	2.65248i	0.180062i
$218$	13.4164i	0.908674i
$219$	−12.0000	−0.810885
$220$	0	0
$221$	−13.8541	−0.931928
$222$	7.85410i	0.527133i
$223$	− 21.7082i	− 1.45369i	−0.686802	−	0.726844i	$-0.740986\pi$
$223$	− 21.7082i	− 1.45369i	0.686802	−	0.726844i	$-0.259014\pi$
$224$	−1.23607	−0.0825883
$225$	0	0
$226$	−12.3262	−0.819929
$227$	16.4721i	1.09329i	0.837363	+	0.546647i	$0.184096\pi$
$227$	16.4721i	1.09329i	−0.837363	+	0.546647i	$0.815904\pi$
$228$	6.00000i	0.397360i
$229$	1.70820	0.112881	0.0564406	−	0.998406i	$-0.482025\pi$
$229$	1.70820	0.112881	0.0564406	+	0.998406i	$0.482025\pi$
$230$	0	0
$231$	−1.70820	−0.112392
$232$	9.32624i	0.612298i
$233$	7.32624i	0.479958i	0.970778	+	0.239979i	$0.0771405\pi$
$233$	7.32624i	0.479958i	−0.970778	+	0.239979i	$0.922859\pi$
$234$	2.85410	0.186578
$235$	0	0
$236$	6.38197	0.415431
$237$	1.14590i	0.0744341i
$238$	− 6.00000i	− 0.388922i
$239$	26.6525	1.72401	0.862003	−	0.506904i	$-0.169210\pi$
$239$	26.6525	1.72401	0.862003	+	0.506904i	$0.169210\pi$
$240$	0	0
$241$	0.0901699	0.00580836	0.00290418	−	0.999996i	$-0.499076\pi$
$241$	0.0901699	0.00580836	0.00290418	+	0.999996i	$0.499076\pi$
$242$	− 9.09017i	− 0.584338i
$243$	1.00000i	0.0641500i
$244$	−13.4164	−0.858898
$245$	0	0
$246$	3.23607	0.206324
$247$	− 17.1246i	− 1.08961i
$248$	− 2.14590i	− 0.136265i
$249$	−8.18034	−0.518408
$250$	0	0
$251$	7.90983	0.499264	0.249632	−	0.968341i	$-0.419690\pi$
$251$	7.90983	0.499264	0.249632	+	0.968341i	$0.419690\pi$
$252$	1.23607i	0.0778650i
$253$	4.27051i	0.268485i
$254$	−13.4164	−0.841820
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 23.5066i	− 1.46630i	−0.680067	−	0.733150i	$-0.738049\pi$
$257$	− 23.5066i	− 1.46630i	0.680067	−	0.733150i	$-0.261951\pi$
$258$	− 0.145898i	− 0.00908321i
$259$	9.70820	0.603238
$260$	0	0
$261$	9.32624	0.577280
$262$	17.8885i	1.10516i
$263$	− 15.9787i	− 0.985290i	−0.870230	−	0.492645i	$-0.836030\pi$
$263$	− 15.9787i	− 0.985290i	0.870230	−	0.492645i	$-0.163970\pi$
$264$	1.38197	0.0850541
$265$	0	0
$266$	7.41641	0.454729
$267$	9.23607i	0.565238i
$268$	2.38197i	0.145502i
$269$	−22.6180	−1.37905	−0.689523	−	0.724264i	$-0.742180\pi$
$269$	−22.6180	−1.37905	−0.689523	+	0.724264i	$0.742180\pi$
$270$	0	0
$271$	−8.56231	−0.520123	−0.260062	−	0.965592i	$-0.583743\pi$
$271$	−8.56231	−0.520123	−0.260062	+	0.965592i	$0.583743\pi$
$272$	4.85410i	0.294323i
$273$	− 3.52786i	− 0.213516i
$274$	4.61803	0.278986
$275$	0	0
$276$	3.09017	0.186006
$277$	− 14.3607i	− 0.862850i	−0.902149	−	0.431425i	$-0.858011\pi$
$277$	− 14.3607i	− 0.862850i	0.902149	−	0.431425i	$-0.141989\pi$
$278$	21.2361i	1.27365i
$279$	−2.14590	−0.128472
$280$	0	0
$281$	22.4721	1.34058	0.670288	−	0.742101i	$-0.266171\pi$
$281$	22.4721	1.34058	0.670288	+	0.742101i	$0.266171\pi$
$282$	− 10.8541i	− 0.646352i
$283$	− 21.0902i	− 1.25368i	−0.779148	−	0.626840i	$-0.784348\pi$
$283$	− 21.0902i	− 1.25368i	0.779148	−	0.626840i	$-0.215652\pi$
$284$	8.94427	0.530745
$285$	0	0
$286$	−3.94427	−0.233230
$287$	− 4.00000i	− 0.236113i
$288$	− 1.00000i	− 0.0589256i
$289$	−6.56231	−0.386018
$290$	0	0
$291$	18.1803	1.06575
$292$	− 12.0000i	− 0.702247i
$293$	− 15.5967i	− 0.911172i	−0.890192	−	0.455586i	$-0.849430\pi$
$293$	− 15.5967i	− 0.911172i	0.890192	−	0.455586i	$-0.150570\pi$
$294$	−5.47214	−0.319141
$295$	0	0
$296$	−7.85410	−0.456510
$297$	− 1.38197i	− 0.0801898i
$298$	20.4721i	1.18592i
$299$	−8.81966	−0.510054
$300$	0	0
$301$	−0.180340	−0.0103946
$302$	− 17.8541i	− 1.02739i
$303$	− 2.32624i	− 0.133639i
$304$	−6.00000	−0.344124
$305$	0	0
$306$	4.85410	0.277491
$307$	33.0902i	1.88856i	0.329149	+	0.944278i	$0.393238\pi$
$307$	33.0902i	1.88856i	−0.329149	+	0.944278i	$0.606762\pi$
$308$	− 1.70820i	− 0.0973340i
$309$	4.00000	0.227552
$310$	0	0
$311$	−4.47214	−0.253592	−0.126796	−	0.991929i	$-0.540469\pi$
$311$	−4.47214	−0.253592	−0.126796	+	0.991929i	$0.540469\pi$
$312$	2.85410i	0.161582i
$313$	30.9443i	1.74907i	0.484959	+	0.874537i	$0.338834\pi$
$313$	30.9443i	1.74907i	−0.484959	+	0.874537i	$0.661166\pi$
$314$	−0.437694	−0.0247005
$315$	0	0
$316$	−1.14590	−0.0644618
$317$	− 9.70820i	− 0.545267i	−0.962118	−	0.272634i	$-0.912105\pi$
$317$	− 9.70820i	− 0.545267i	0.962118	−	0.272634i	$-0.0878947\pi$
$318$	3.23607i	0.181470i
$319$	−12.8885	−0.721620
$320$	0	0
$321$	−8.18034	−0.456582
$322$	− 3.81966i	− 0.212861i
$323$	− 29.1246i	− 1.62054i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−20.2705	−1.12268
$327$	13.4164i	0.741929i
$328$	3.23607i	0.178682i
$329$	−13.4164	−0.739671
$330$	0	0
$331$	−21.4164	−1.17715	−0.588576	−	0.808442i	$-0.700311\pi$
$331$	−21.4164	−1.17715	−0.588576	+	0.808442i	$0.700311\pi$
$332$	− 8.18034i	− 0.448954i
$333$	7.85410i	0.430402i
$334$	−23.0902	−1.26344
$335$	0	0
$336$	−1.23607	−0.0674330
$337$	12.9443i	0.705119i	0.935789	+	0.352560i	$0.114689\pi$
$337$	12.9443i	0.705119i	−0.935789	+	0.352560i	$0.885311\pi$
$338$	4.85410i	0.264028i
$339$	−12.3262	−0.669469
$340$	0	0
$341$	2.96556	0.160594
$342$	6.00000i	0.324443i
$343$	15.4164i	0.832408i
$344$	0.145898	0.00786629
$345$	0	0
$346$	9.23607	0.496534
$347$	− 24.3607i	− 1.30775i	−0.756603	−	0.653875i	$-0.773142\pi$
$347$	− 24.3607i	− 1.30775i	0.756603	−	0.653875i	$-0.226858\pi$
$348$	9.32624i	0.499939i
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	2.85410	0.152341
$352$	1.38197i	0.0736590i
$353$	1.20163i	0.0639561i	0.999489	+	0.0319781i	$0.0101807\pi$
$353$	1.20163i	0.0639561i	−0.999489	+	0.0319781i	$0.989819\pi$
$354$	6.38197	0.339198
$355$	0	0
$356$	−9.23607	−0.489511
$357$	− 6.00000i	− 0.317554i
$358$	− 7.41641i	− 0.391969i
$359$	−23.8885	−1.26079	−0.630395	−	0.776275i	$-0.717107\pi$
$359$	−23.8885	−1.26079	−0.630395	+	0.776275i	$0.717107\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	7.41641i	0.389798i
$363$	− 9.09017i	− 0.477110i
$364$	3.52786	0.184910
$365$	0	0
$366$	−13.4164	−0.701287
$367$	− 10.2918i	− 0.537227i	−0.963248	−	0.268614i	$-0.913434\pi$
$367$	− 10.2918i	− 0.537227i	0.963248	−	0.268614i	$-0.0865655\pi$
$368$	3.09017i	0.161086i
$369$	3.23607	0.168463
$370$	0	0
$371$	4.00000	0.207670
$372$	− 2.14590i	− 0.111260i
$373$	− 32.7426i	− 1.69535i	−0.530516	−	0.847675i	$-0.678002\pi$
$373$	− 32.7426i	− 1.69535i	0.530516	−	0.847675i	$-0.321998\pi$
$374$	−6.70820	−0.346873
$375$	0	0
$376$	10.8541	0.559758
$377$	− 26.6180i	− 1.37090i
$378$	1.23607i	0.0635765i
$379$	1.23607	0.0634925	0.0317463	−	0.999496i	$-0.489893\pi$
$379$	1.23607	0.0634925	0.0317463	+	0.999496i	$0.489893\pi$
$380$	0	0
$381$	−13.4164	−0.687343
$382$	6.00000i	0.306987i
$383$	17.8885i	0.914062i	0.889451	+	0.457031i	$0.151087\pi$
$383$	17.8885i	0.914062i	−0.889451	+	0.457031i	$0.848913\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	17.1246	0.871620
$387$	− 0.145898i	− 0.00741641i
$388$	18.1803i	0.922967i
$389$	−18.2705	−0.926352	−0.463176	−	0.886266i	$-0.653290\pi$
$389$	−18.2705	−0.926352	−0.463176	+	0.886266i	$0.653290\pi$
$390$	0	0
$391$	−15.0000	−0.758583
$392$	− 5.47214i	− 0.276385i
$393$	17.8885i	0.902358i
$394$	−1.52786	−0.0769727
$395$	0	0
$396$	1.38197	0.0694464
$397$	− 32.4721i	− 1.62973i	−0.579651	−	0.814865i	$-0.696811\pi$
$397$	− 32.4721i	− 1.62973i	0.579651	−	0.814865i	$-0.303189\pi$
$398$	15.6180i	0.782861i
$399$	7.41641	0.371285
$400$	0	0
$401$	−10.4721	−0.522954	−0.261477	−	0.965210i	$-0.584209\pi$
$401$	−10.4721	−0.522954	−0.261477	+	0.965210i	$0.584209\pi$
$402$	2.38197i	0.118802i
$403$	6.12461i	0.305089i
$404$	2.32624	0.115735
$405$	0	0
$406$	11.5279	0.572118
$407$	− 10.8541i	− 0.538018i
$408$	4.85410i	0.240314i
$409$	−13.5623	−0.670613	−0.335306	−	0.942109i	$-0.608840\pi$
$409$	−13.5623	−0.670613	−0.335306	+	0.942109i	$0.608840\pi$
$410$	0	0
$411$	4.61803	0.227791
$412$	4.00000i	0.197066i
$413$	− 7.88854i	− 0.388170i
$414$	3.09017	0.151874
$415$	0	0
$416$	−2.85410	−0.139934
$417$	21.2361i	1.03993i
$418$	− 8.29180i	− 0.405565i
$419$	8.94427	0.436956	0.218478	−	0.975842i	$-0.429891\pi$
$419$	8.94427	0.436956	0.218478	+	0.975842i	$0.429891\pi$
$420$	0	0
$421$	14.4721	0.705329	0.352664	−	0.935750i	$-0.385276\pi$
$421$	14.4721	0.705329	0.352664	+	0.935750i	$0.385276\pi$
$422$	3.41641i	0.166308i
$423$	− 10.8541i	− 0.527744i
$424$	−3.23607	−0.157157
$425$	0	0
$426$	8.94427	0.433351
$427$	16.5836i	0.802536i
$428$	− 8.18034i	− 0.395412i
$429$	−3.94427	−0.190431
$430$	0	0
$431$	−21.7082	−1.04565	−0.522824	−	0.852441i	$-0.675121\pi$
$431$	−21.7082	−1.04565	−0.522824	+	0.852441i	$0.675121\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	− 0.180340i	− 0.00866658i	−0.999991	−	0.00433329i	$-0.998621\pi$
$433$	− 0.180340i	− 0.00866658i	0.999991	−	0.00433329i	$-0.00137933\pi$
$434$	−2.65248	−0.127323
$435$	0	0
$436$	−13.4164	−0.642529
$437$	− 18.5410i	− 0.886937i
$438$	− 12.0000i	− 0.573382i
$439$	−28.3262	−1.35194	−0.675969	−	0.736930i	$-0.736275\pi$
$439$	−28.3262	−1.35194	−0.675969	+	0.736930i	$0.736275\pi$
$440$	0	0
$441$	−5.47214	−0.260578
$442$	− 13.8541i	− 0.658972i
$443$	32.6525i	1.55137i	0.631123	+	0.775683i	$0.282594\pi$
$443$	32.6525i	1.55137i	−0.631123	+	0.775683i	$0.717406\pi$
$444$	−7.85410	−0.372739
$445$	0	0
$446$	21.7082	1.02791
$447$	20.4721i	0.968299i
$448$	− 1.23607i	− 0.0583987i
$449$	−2.94427	−0.138949	−0.0694744	−	0.997584i	$-0.522132\pi$
$449$	−2.94427	−0.138949	−0.0694744	+	0.997584i	$0.522132\pi$
$450$	0	0
$451$	−4.47214	−0.210585
$452$	− 12.3262i	− 0.579777i
$453$	− 17.8541i	− 0.838859i
$454$	−16.4721	−0.773076
$455$	0	0
$456$	−6.00000	−0.280976
$457$	22.9443i	1.07329i	0.843809	+	0.536644i	$0.180308\pi$
$457$	22.9443i	1.07329i	−0.843809	+	0.536644i	$0.819692\pi$
$458$	1.70820i	0.0798191i
$459$	4.85410	0.226570
$460$	0	0
$461$	−15.9787	−0.744203	−0.372101	−	0.928192i	$-0.621363\pi$
$461$	−15.9787	−0.744203	−0.372101	+	0.928192i	$0.621363\pi$
$462$	− 1.70820i	− 0.0794728i
$463$	− 2.29180i	− 0.106509i	−0.998581	−	0.0532544i	$-0.983041\pi$
$463$	− 2.29180i	− 0.106509i	0.998581	−	0.0532544i	$-0.0169594\pi$
$464$	−9.32624	−0.432960
$465$	0	0
$466$	−7.32624	−0.339381
$467$	− 2.29180i	− 0.106052i	−0.998593	−	0.0530258i	$-0.983113\pi$
$467$	− 2.29180i	− 0.106052i	0.998593	−	0.0530258i	$-0.0168866\pi$
$468$	2.85410i	0.131931i
$469$	2.94427	0.135954
$470$	0	0
$471$	−0.437694	−0.0201679
$472$	6.38197i	0.293754i
$473$	0.201626i	0.00927078i
$474$	−1.14590	−0.0526328
$475$	0	0
$476$	6.00000	0.275010
$477$	3.23607i	0.148169i
$478$	26.6525i	1.21906i
$479$	−6.65248	−0.303959	−0.151980	−	0.988384i	$-0.548565\pi$
$479$	−6.65248	−0.303959	−0.151980	+	0.988384i	$0.548565\pi$
$480$	0	0
$481$	22.4164	1.02210
$482$	0.0901699i	0.00410713i
$483$	− 3.81966i	− 0.173801i
$484$	9.09017	0.413190
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	17.5967i	0.797385i	0.917085	+	0.398692i	$0.130536\pi$
$487$	17.5967i	0.797385i	−0.917085	+	0.398692i	$0.869464\pi$
$488$	− 13.4164i	− 0.607332i
$489$	−20.2705	−0.916664
$490$	0	0
$491$	2.61803	0.118150	0.0590751	−	0.998254i	$-0.481185\pi$
$491$	2.61803	0.118150	0.0590751	+	0.998254i	$0.481185\pi$
$492$	3.23607i	0.145893i
$493$	− 45.2705i	− 2.03888i
$494$	17.1246	0.770473
$495$	0	0
$496$	2.14590	0.0963537
$497$	− 11.0557i	− 0.495917i
$498$	− 8.18034i	− 0.366570i
$499$	−13.2361	−0.592528	−0.296264	−	0.955106i	$-0.595741\pi$
$499$	−13.2361	−0.592528	−0.296264	+	0.955106i	$0.595741\pi$
$500$	0	0
$501$	−23.0902	−1.03159
$502$	7.90983i	0.353033i
$503$	− 10.4721i	− 0.466929i	−0.972365	−	0.233465i	$-0.924994\pi$
$503$	− 10.4721i	− 0.466929i	0.972365	−	0.233465i	$-0.0750063\pi$
$504$	−1.23607	−0.0550588
$505$	0	0
$506$	−4.27051	−0.189847
$507$	4.85410i	0.215578i
$508$	− 13.4164i	− 0.595257i
$509$	−2.94427	−0.130503	−0.0652513	−	0.997869i	$-0.520785\pi$
$509$	−2.94427	−0.130503	−0.0652513	+	0.997869i	$0.520785\pi$
$510$	0	0
$511$	−14.8328	−0.656165
$512$	1.00000i	0.0441942i
$513$	6.00000i	0.264906i
$514$	23.5066	1.03683
$515$	0	0
$516$	0.145898	0.00642280
$517$	15.0000i	0.659699i
$518$	9.70820i	0.426554i
$519$	9.23607	0.405418
$520$	0	0
$521$	−8.18034	−0.358387	−0.179194	−	0.983814i	$-0.557349\pi$
$521$	−8.18034	−0.358387	−0.179194	+	0.983814i	$0.557349\pi$
$522$	9.32624i	0.408198i
$523$	11.9098i	0.520781i	0.965503	+	0.260390i	$0.0838512\pi$
$523$	11.9098i	0.520781i	−0.965503	+	0.260390i	$0.916149\pi$
$524$	−17.8885	−0.781465
$525$	0	0
$526$	15.9787	0.696705
$527$	10.4164i	0.453746i
$528$	1.38197i	0.0601424i
$529$	13.4508	0.584820
$530$	0	0
$531$	6.38197	0.276954
$532$	7.41641i	0.321542i
$533$	− 9.23607i	− 0.400059i
$534$	−9.23607	−0.399684
$535$	0	0
$536$	−2.38197	−0.102885
$537$	− 7.41641i	− 0.320042i
$538$	− 22.6180i	− 0.975133i
$539$	7.56231	0.325732
$540$	0	0
$541$	11.7082	0.503375	0.251688	−	0.967809i	$-0.419014\pi$
$541$	11.7082	0.503375	0.251688	+	0.967809i	$0.419014\pi$
$542$	− 8.56231i	− 0.367783i
$543$	7.41641i	0.318269i
$544$	−4.85410	−0.208118
$545$	0	0
$546$	3.52786	0.150979
$547$	5.43769i	0.232499i	0.993220	+	0.116250i	$0.0370872\pi$
$547$	5.43769i	0.232499i	−0.993220	+	0.116250i	$0.962913\pi$
$548$	4.61803i	0.197273i
$549$	−13.4164	−0.572598
$550$	0	0
$551$	55.9574	2.38387
$552$	3.09017i	0.131526i
$553$	1.41641i	0.0602318i
$554$	14.3607	0.610127
$555$	0	0
$556$	−21.2361	−0.900610
$557$	− 10.3607i	− 0.438996i	−0.975613	−	0.219498i	$-0.929558\pi$
$557$	− 10.3607i	− 0.438996i	0.975613	−	0.219498i	$-0.0704420\pi$
$558$	− 2.14590i	− 0.0908431i
$559$	−0.416408	−0.0176122
$560$	0	0
$561$	−6.70820	−0.283221
$562$	22.4721i	0.947930i
$563$	− 12.6525i	− 0.533238i	−0.963802	−	0.266619i	$-0.914093\pi$
$563$	− 12.6525i	− 0.533238i	0.963802	−	0.266619i	$-0.0859066\pi$
$564$	10.8541	0.457040
$565$	0	0
$566$	21.0902	0.886486
$567$	1.23607i	0.0519100i
$568$	8.94427i	0.375293i
$569$	13.0557	0.547325	0.273662	−	0.961826i	$-0.411765\pi$
$569$	13.0557	0.547325	0.273662	+	0.961826i	$0.411765\pi$
$570$	0	0
$571$	12.3607	0.517278	0.258639	−	0.965974i	$-0.416726\pi$
$571$	12.3607	0.517278	0.258639	+	0.965974i	$0.416726\pi$
$572$	− 3.94427i	− 0.164918i
$573$	6.00000i	0.250654i
$574$	4.00000	0.166957
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 4.11146i	− 0.171162i	−0.996331	−	0.0855811i	$-0.972725\pi$
$577$	− 4.11146i	− 0.171162i	0.996331	−	0.0855811i	$-0.0272747\pi$
$578$	− 6.56231i	− 0.272956i
$579$	17.1246	0.711675
$580$	0	0
$581$	−10.1115	−0.419494
$582$	18.1803i	0.753599i
$583$	− 4.47214i	− 0.185217i
$584$	12.0000	0.496564
$585$	0	0
$586$	15.5967	0.644296
$587$	− 18.6525i	− 0.769870i	−0.922944	−	0.384935i	$-0.874224\pi$
$587$	− 18.6525i	− 0.769870i	0.922944	−	0.384935i	$-0.125776\pi$
$588$	− 5.47214i	− 0.225667i
$589$	−12.8754	−0.530521
$590$	0	0
$591$	−1.52786	−0.0628479
$592$	− 7.85410i	− 0.322802i
$593$	34.7984i	1.42900i	0.699636	+	0.714499i	$0.253345\pi$
$593$	34.7984i	1.42900i	−0.699636	+	0.714499i	$0.746655\pi$
$594$	1.38197	0.0567028
$595$	0	0
$596$	−20.4721	−0.838571
$597$	15.6180i	0.639204i
$598$	− 8.81966i	− 0.360663i
$599$	31.8885	1.30293	0.651465	−	0.758678i	$-0.274155\pi$
$599$	31.8885	1.30293	0.651465	+	0.758678i	$0.274155\pi$
$600$	0	0
$601$	40.6869	1.65965	0.829827	−	0.558021i	$-0.188439\pi$
$601$	40.6869	1.65965	0.829827	+	0.558021i	$0.188439\pi$
$602$	− 0.180340i	− 0.00735011i
$603$	2.38197i	0.0970012i
$604$	17.8541	0.726473
$605$	0	0
$606$	2.32624	0.0944970
$607$	47.4164i	1.92457i	0.272039	+	0.962286i	$0.412302\pi$
$607$	47.4164i	1.92457i	−0.272039	+	0.962286i	$0.587698\pi$
$608$	− 6.00000i	− 0.243332i
$609$	11.5279	0.467133
$610$	0	0
$611$	−30.9787	−1.25326
$612$	4.85410i	0.196215i
$613$	37.7771i	1.52580i	0.646515	+	0.762901i	$0.276226\pi$
$613$	37.7771i	1.52580i	−0.646515	+	0.762901i	$0.723774\pi$
$614$	−33.0902	−1.33541
$615$	0	0
$616$	1.70820	0.0688255
$617$	31.3050i	1.26029i	0.776478	+	0.630145i	$0.217005\pi$
$617$	31.3050i	1.26029i	−0.776478	+	0.630145i	$0.782995\pi$
$618$	4.00000i	0.160904i
$619$	47.7082	1.91755	0.958777	−	0.284159i	$-0.0917142\pi$
$619$	47.7082	1.91755	0.958777	+	0.284159i	$0.0917142\pi$
$620$	0	0
$621$	3.09017	0.124004
$622$	− 4.47214i	− 0.179316i
$623$	11.4164i	0.457389i
$624$	−2.85410	−0.114256
$625$	0	0
$626$	−30.9443	−1.23678
$627$	− 8.29180i	− 0.331142i
$628$	− 0.437694i	− 0.0174659i
$629$	38.1246	1.52013
$630$	0	0
$631$	−15.0344	−0.598512	−0.299256	−	0.954173i	$-0.596738\pi$
$631$	−15.0344	−0.598512	−0.299256	+	0.954173i	$0.596738\pi$
$632$	− 1.14590i	− 0.0455814i
$633$	3.41641i	0.135790i
$634$	9.70820	0.385562
$635$	0	0
$636$	−3.23607	−0.128318
$637$	15.6180i	0.618809i
$638$	− 12.8885i	− 0.510262i
$639$	8.94427	0.353830
$640$	0	0
$641$	−30.6525	−1.21070	−0.605350	−	0.795959i	$-0.706967\pi$
$641$	−30.6525	−1.21070	−0.605350	+	0.795959i	$0.706967\pi$
$642$	− 8.18034i	− 0.322852i
$643$	− 31.5623i	− 1.24470i	−0.782741	−	0.622348i	$-0.786179\pi$
$643$	− 31.5623i	− 1.24470i	0.782741	−	0.622348i	$-0.213821\pi$
$644$	3.81966	0.150516
$645$	0	0
$646$	29.1246	1.14589
$647$	− 12.6180i	− 0.496066i	−0.968752	−	0.248033i	$-0.920216\pi$
$647$	− 12.6180i	− 0.496066i	0.968752	−	0.248033i	$-0.0797842\pi$
$648$	− 1.00000i	− 0.0392837i
$649$	−8.81966	−0.346202
$650$	0	0
$651$	−2.65248	−0.103959
$652$	− 20.2705i	− 0.793854i
$653$	− 9.88854i	− 0.386969i	−0.981103	−	0.193484i	$-0.938021\pi$
$653$	− 9.88854i	− 0.386969i	0.981103	−	0.193484i	$-0.0619789\pi$
$654$	−13.4164	−0.524623
$655$	0	0
$656$	−3.23607	−0.126347
$657$	− 12.0000i	− 0.468165i
$658$	− 13.4164i	− 0.523026i
$659$	−2.02129	−0.0787381	−0.0393691	−	0.999225i	$-0.512535\pi$
$659$	−2.02129	−0.0787381	−0.0393691	+	0.999225i	$0.512535\pi$
$660$	0	0
$661$	5.70820	0.222023	0.111012	−	0.993819i	$-0.464591\pi$
$661$	5.70820	0.222023	0.111012	+	0.993819i	$0.464591\pi$
$662$	− 21.4164i	− 0.832372i
$663$	− 13.8541i	− 0.538049i
$664$	8.18034	0.317459
$665$	0	0
$666$	−7.85410	−0.304340
$667$	− 28.8197i	− 1.11590i
$668$	− 23.0902i	− 0.893385i
$669$	21.7082	0.839288
$670$	0	0
$671$	18.5410	0.715768
$672$	− 1.23607i	− 0.0476824i
$673$	47.3050i	1.82347i	0.410777	+	0.911736i	$0.365258\pi$
$673$	47.3050i	1.82347i	−0.410777	+	0.911736i	$0.634742\pi$
$674$	−12.9443	−0.498595
$675$	0	0
$676$	−4.85410	−0.186696
$677$	− 31.2361i	− 1.20050i	−0.799813	−	0.600250i	$-0.795068\pi$
$677$	− 31.2361i	− 1.20050i	0.799813	−	0.600250i	$-0.204932\pi$
$678$	− 12.3262i	− 0.473386i
$679$	22.4721	0.862401
$680$	0	0
$681$	−16.4721	−0.631214
$682$	2.96556i	0.113557i
$683$	10.7639i	0.411870i	0.978566	+	0.205935i	$0.0660236\pi$
$683$	10.7639i	0.411870i	−0.978566	+	0.205935i	$0.933976\pi$
$684$	−6.00000	−0.229416
$685$	0	0
$686$	−15.4164	−0.588601
$687$	1.70820i	0.0651720i
$688$	0.145898i	0.00556231i
$689$	9.23607	0.351866
$690$	0	0
$691$	26.7639	1.01815	0.509074	−	0.860723i	$-0.329988\pi$
$691$	26.7639	1.01815	0.509074	+	0.860723i	$0.329988\pi$
$692$	9.23607i	0.351103i
$693$	− 1.70820i	− 0.0648893i
$694$	24.3607	0.924719
$695$	0	0
$696$	−9.32624	−0.353510
$697$	− 15.7082i	− 0.594991i
$698$	0	0
$699$	−7.32624	−0.277104
$700$	0	0
$701$	12.2148	0.461346	0.230673	−	0.973031i	$-0.425907\pi$
$701$	12.2148	0.461346	0.230673	+	0.973031i	$0.425907\pi$
$702$	2.85410i	0.107721i
$703$	47.1246i	1.77734i
$704$	−1.38197	−0.0520848
$705$	0	0
$706$	−1.20163	−0.0452238
$707$	− 2.87539i	− 0.108140i
$708$	6.38197i	0.239849i
$709$	6.87539	0.258211	0.129105	−	0.991631i	$-0.458789\pi$
$709$	6.87539	0.258211	0.129105	+	0.991631i	$0.458789\pi$
$710$	0	0
$711$	−1.14590	−0.0429745
$712$	− 9.23607i	− 0.346136i
$713$	6.63119i	0.248340i
$714$	6.00000	0.224544
$715$	0	0
$716$	7.41641	0.277164
$717$	26.6525i	0.995355i
$718$	− 23.8885i	− 0.891513i
$719$	7.23607	0.269860	0.134930	−	0.990855i	$-0.456919\pi$
$719$	7.23607	0.269860	0.134930	+	0.990855i	$0.456919\pi$
$720$	0	0
$721$	4.94427	0.184134
$722$	17.0000i	0.632674i
$723$	0.0901699i	0.00335346i
$724$	−7.41641	−0.275629
$725$	0	0
$726$	9.09017	0.337368
$727$	7.34752i	0.272505i	0.990674	+	0.136252i	$0.0435058\pi$
$727$	7.34752i	0.272505i	−0.990674	+	0.136252i	$0.956494\pi$
$728$	3.52786i	0.130751i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−0.708204	−0.0261939
$732$	− 13.4164i	− 0.495885i
$733$	− 34.6869i	− 1.28119i	−0.767879	−	0.640595i	$-0.778688\pi$
$733$	− 34.6869i	− 1.28119i	0.767879	−	0.640595i	$-0.221312\pi$
$734$	10.2918	0.379877
$735$	0	0
$736$	−3.09017	−0.113905
$737$	− 3.29180i	− 0.121255i
$738$	3.23607i	0.119121i
$739$	−8.65248	−0.318286	−0.159143	−	0.987256i	$-0.550873\pi$
$739$	−8.65248	−0.318286	−0.159143	+	0.987256i	$0.550873\pi$
$740$	0	0
$741$	17.1246	0.629088
$742$	4.00000i	0.146845i
$743$	19.6180i	0.719716i	0.933007	+	0.359858i	$0.117175\pi$
$743$	19.6180i	0.719716i	−0.933007	+	0.359858i	$0.882825\pi$
$744$	2.14590	0.0786724
$745$	0	0
$746$	32.7426	1.19879
$747$	− 8.18034i	− 0.299303i
$748$	− 6.70820i	− 0.245276i
$749$	−10.1115	−0.369465
$750$	0	0
$751$	−43.4164	−1.58429	−0.792144	−	0.610335i	$-0.791035\pi$
$751$	−43.4164	−1.58429	−0.792144	+	0.610335i	$0.791035\pi$
$752$	10.8541i	0.395808i
$753$	7.90983i	0.288250i
$754$	26.6180	0.969372
$755$	0	0
$756$	−1.23607	−0.0449554
$757$	4.83282i	0.175652i	0.996136	+	0.0878258i	$0.0279919\pi$
$757$	4.83282i	0.175652i	−0.996136	+	0.0878258i	$0.972008\pi$
$758$	1.23607i	0.0448960i
$759$	−4.27051	−0.155010
$760$	0	0
$761$	−32.6525	−1.18365	−0.591826	−	0.806066i	$-0.701593\pi$
$761$	−32.6525	−1.18365	−0.591826	+	0.806066i	$0.701593\pi$
$762$	− 13.4164i	− 0.486025i
$763$	16.5836i	0.600366i
$764$	−6.00000	−0.217072
$765$	0	0
$766$	−17.8885	−0.646339
$767$	− 18.2148i	− 0.657698i
$768$	1.00000i	0.0360844i
$769$	22.9230	0.826624	0.413312	−	0.910589i	$-0.364372\pi$
$769$	22.9230	0.826624	0.413312	+	0.910589i	$0.364372\pi$
$770$	0	0
$771$	23.5066	0.846569
$772$	17.1246i	0.616328i
$773$	6.47214i	0.232787i	0.993203	+	0.116393i	$0.0371333\pi$
$773$	6.47214i	0.232787i	−0.993203	+	0.116393i	$0.962867\pi$
$774$	0.145898	0.00524420
$775$	0	0
$776$	−18.1803	−0.652636
$777$	9.70820i	0.348280i
$778$	− 18.2705i	− 0.655030i
$779$	19.4164	0.695665
$780$	0	0
$781$	−12.3607	−0.442300
$782$	− 15.0000i	− 0.536399i
$783$	9.32624i	0.333293i
$784$	5.47214	0.195433
$785$	0	0
$786$	−17.8885	−0.638063
$787$	− 38.5623i	− 1.37460i	−0.726375	−	0.687299i	$-0.758796\pi$
$787$	− 38.5623i	− 1.37460i	0.726375	−	0.687299i	$-0.241204\pi$
$788$	− 1.52786i	− 0.0544279i
$789$	15.9787	0.568857
$790$	0	0
$791$	−15.2361	−0.541732
$792$	1.38197i	0.0491060i
$793$	38.2918i	1.35978i
$794$	32.4721	1.15239
$795$	0	0
$796$	−15.6180	−0.553567
$797$	34.4721i	1.22107i	0.791991	+	0.610533i	$0.209045\pi$
$797$	34.4721i	1.22107i	−0.791991	+	0.610533i	$0.790955\pi$
$798$	7.41641i	0.262538i
$799$	−52.6869	−1.86393
$800$	0	0
$801$	−9.23607	−0.326340
$802$	− 10.4721i	− 0.369784i
$803$	16.5836i	0.585222i
$804$	−2.38197	−0.0840055
$805$	0	0
$806$	−6.12461	−0.215730
$807$	− 22.6180i	− 0.796193i
$808$	2.32624i	0.0818368i
$809$	29.5279	1.03814	0.519072	−	0.854730i	$-0.326278\pi$
$809$	29.5279	1.03814	0.519072	+	0.854730i	$0.326278\pi$
$810$	0	0
$811$	−34.0000	−1.19390	−0.596951	−	0.802278i	$-0.703621\pi$
$811$	−34.0000	−1.19390	−0.596951	+	0.802278i	$0.703621\pi$
$812$	11.5279i	0.404549i
$813$	− 8.56231i	− 0.300293i
$814$	10.8541	0.380436
$815$	0	0
$816$	−4.85410	−0.169928
$817$	− 0.875388i	− 0.0306260i
$818$	− 13.5623i	− 0.474195i
$819$	3.52786	0.123274
$820$	0	0
$821$	36.2148	1.26390	0.631952	−	0.775007i	$-0.282254\pi$
$821$	36.2148	1.26390	0.631952	+	0.775007i	$0.282254\pi$
$822$	4.61803i	0.161072i
$823$	− 15.1246i	− 0.527211i	−0.964631	−	0.263605i	$-0.915088\pi$
$823$	− 15.1246i	− 0.527211i	0.964631	−	0.263605i	$-0.0849117\pi$
$824$	−4.00000	−0.139347
$825$	0	0
$826$	7.88854	0.274478
$827$	18.0000i	0.625921i	0.949766	+	0.312961i	$0.101321\pi$
$827$	18.0000i	0.625921i	−0.949766	+	0.312961i	$0.898679\pi$
$828$	3.09017i	0.107391i
$829$	−34.1803	−1.18713	−0.593566	−	0.804785i	$-0.702280\pi$
$829$	−34.1803	−1.18713	−0.593566	+	0.804785i	$0.702280\pi$
$830$	0	0
$831$	14.3607	0.498166
$832$	− 2.85410i	− 0.0989482i
$833$	26.5623i	0.920329i
$834$	−21.2361	−0.735345
$835$	0	0
$836$	8.29180	0.286778
$837$	− 2.14590i	− 0.0741731i
$838$	8.94427i	0.308975i
$839$	11.1246	0.384064	0.192032	−	0.981389i	$-0.438492\pi$
$839$	11.1246	0.384064	0.192032	+	0.981389i	$0.438492\pi$
$840$	0	0
$841$	57.9787	1.99927
$842$	14.4721i	0.498743i
$843$	22.4721i	0.773981i
$844$	−3.41641	−0.117598
$845$	0	0
$846$	10.8541	0.373172
$847$	− 11.2361i	− 0.386076i
$848$	− 3.23607i	− 0.111127i
$849$	21.0902	0.723813
$850$	0	0
$851$	24.2705	0.831982
$852$	8.94427i	0.306426i
$853$	− 29.0902i	− 0.996028i	−0.867169	−	0.498014i	$-0.834063\pi$
$853$	− 29.0902i	− 0.996028i	0.867169	−	0.498014i	$-0.165937\pi$
$854$	−16.5836	−0.567479
$855$	0	0
$856$	8.18034	0.279598
$857$	− 12.3262i	− 0.421056i	−0.977588	−	0.210528i	$-0.932482\pi$
$857$	− 12.3262i	− 0.421056i	0.977588	−	0.210528i	$-0.0675184\pi$
$858$	− 3.94427i	− 0.134655i
$859$	15.7082	0.535957	0.267979	−	0.963425i	$-0.413644\pi$
$859$	15.7082	0.535957	0.267979	+	0.963425i	$0.413644\pi$
$860$	0	0
$861$	4.00000	0.136320
$862$	− 21.7082i	− 0.739384i
$863$	− 8.56231i	− 0.291464i	−0.989324	−	0.145732i	$-0.953446\pi$
$863$	− 8.56231i	− 0.291464i	0.989324	−	0.145732i	$-0.0465538\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	0.180340	0.00612820
$867$	− 6.56231i	− 0.222868i
$868$	− 2.65248i	− 0.0900309i
$869$	1.58359	0.0537197
$870$	0	0
$871$	6.79837	0.230354
$872$	− 13.4164i	− 0.454337i
$873$	18.1803i	0.615311i
$874$	18.5410	0.627159
$875$	0	0
$876$	12.0000	0.405442
$877$	− 26.3951i	− 0.891300i	−0.895207	−	0.445650i	$-0.852973\pi$
$877$	− 26.3951i	− 0.891300i	0.895207	−	0.445650i	$-0.147027\pi$
$878$	− 28.3262i	− 0.955964i
$879$	15.5967	0.526065
$880$	0	0
$881$	−5.05573	−0.170332	−0.0851659	−	0.996367i	$-0.527142\pi$
$881$	−5.05573	−0.170332	−0.0851659	+	0.996367i	$0.527142\pi$
$882$	− 5.47214i	− 0.184256i
$883$	46.9787i	1.58096i	0.612488	+	0.790480i	$0.290169\pi$
$883$	46.9787i	1.58096i	−0.612488	+	0.790480i	$0.709831\pi$
$884$	13.8541	0.465964
$885$	0	0
$886$	−32.6525	−1.09698
$887$	− 54.4721i	− 1.82900i	−0.404591	−	0.914498i	$-0.632586\pi$
$887$	− 54.4721i	− 1.82900i	0.404591	−	0.914498i	$-0.367414\pi$
$888$	− 7.85410i	− 0.263566i
$889$	−16.5836	−0.556196
$890$	0	0
$891$	1.38197	0.0462976
$892$	21.7082i	0.726844i
$893$	− 65.1246i	− 2.17931i
$894$	−20.4721	−0.684691
$895$	0	0
$896$	1.23607	0.0412941
$897$	− 8.81966i	− 0.294480i
$898$	− 2.94427i	− 0.0982516i
$899$	−20.0132	−0.667476
$900$	0	0
$901$	15.7082	0.523316
$902$	− 4.47214i	− 0.148906i
$903$	− 0.180340i	− 0.00600134i
$904$	12.3262	0.409965
$905$	0	0
$906$	17.8541	0.593163
$907$	− 23.1459i	− 0.768547i	−0.923219	−	0.384273i	$-0.874452\pi$
$907$	− 23.1459i	− 0.768547i	0.923219	−	0.384273i	$-0.125548\pi$
$908$	− 16.4721i	− 0.546647i
$909$	2.32624	0.0771564
$910$	0	0
$911$	37.5279	1.24335	0.621677	−	0.783274i	$-0.286452\pi$
$911$	37.5279	1.24335	0.621677	+	0.783274i	$0.286452\pi$
$912$	− 6.00000i	− 0.198680i
$913$	11.3050i	0.374139i
$914$	−22.9443	−0.758929
$915$	0	0
$916$	−1.70820	−0.0564406
$917$	22.1115i	0.730185i
$918$	4.85410i	0.160209i
$919$	−21.8885	−0.722036	−0.361018	−	0.932559i	$-0.617571\pi$
$919$	−21.8885	−0.722036	−0.361018	+	0.932559i	$0.617571\pi$
$920$	0	0
$921$	−33.0902	−1.09036
$922$	− 15.9787i	− 0.526231i
$923$	− 25.5279i	− 0.840260i
$924$	1.70820	0.0561958
$925$	0	0
$926$	2.29180	0.0753131
$927$	4.00000i	0.131377i
$928$	− 9.32624i	− 0.306149i
$929$	24.5410	0.805165	0.402582	−	0.915384i	$-0.368113\pi$
$929$	24.5410	0.805165	0.402582	+	0.915384i	$0.368113\pi$
$930$	0	0
$931$	−32.8328	−1.07605
$932$	− 7.32624i	− 0.239979i
$933$	− 4.47214i	− 0.146411i
$934$	2.29180	0.0749899
$935$	0	0
$936$	−2.85410	−0.0932892
$937$	27.4164i	0.895655i	0.894120	+	0.447828i	$0.147802\pi$
$937$	27.4164i	0.895655i	−0.894120	+	0.447828i	$0.852198\pi$
$938$	2.94427i	0.0961339i
$939$	−30.9443	−1.00983
$940$	0	0
$941$	−22.4508	−0.731877	−0.365938	−	0.930639i	$-0.619252\pi$
$941$	−22.4508	−0.731877	−0.365938	+	0.930639i	$0.619252\pi$
$942$	− 0.437694i	− 0.0142608i
$943$	− 10.0000i	− 0.325645i
$944$	−6.38197	−0.207715
$945$	0	0
$946$	−0.201626	−0.00655543
$947$	55.3050i	1.79717i	0.438800	+	0.898585i	$0.355404\pi$
$947$	55.3050i	1.79717i	−0.438800	+	0.898585i	$0.644596\pi$
$948$	− 1.14590i	− 0.0372170i
$949$	−34.2492	−1.11178
$950$	0	0
$951$	9.70820	0.314810
$952$	6.00000i	0.194461i
$953$	− 1.63932i	− 0.0531028i	−0.999647	−	0.0265514i	$-0.991547\pi$
$953$	− 1.63932i	− 0.0531028i	0.999647	−	0.0265514i	$-0.00845257\pi$
$954$	−3.23607	−0.104772
$955$	0	0
$956$	−26.6525	−0.862003
$957$	− 12.8885i	− 0.416627i
$958$	− 6.65248i	− 0.214932i
$959$	5.70820	0.184328
$960$	0	0
$961$	−26.3951	−0.851456
$962$	22.4164i	0.722734i
$963$	− 8.18034i	− 0.263608i
$964$	−0.0901699	−0.00290418
$965$	0	0
$966$	3.81966	0.122896
$967$	− 39.0132i	− 1.25458i	−0.778786	−	0.627289i	$-0.784164\pi$
$967$	− 39.0132i	− 1.25458i	0.778786	−	0.627289i	$-0.215836\pi$
$968$	9.09017i	0.292169i
$969$	29.1246	0.935617
$970$	0	0
$971$	52.0902	1.67165	0.835827	−	0.548994i	$-0.184989\pi$
$971$	52.0902	1.67165	0.835827	+	0.548994i	$0.184989\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	26.2492i	0.841511i
$974$	−17.5967	−0.563836
$975$	0	0
$976$	13.4164	0.429449
$977$	54.2837i	1.73669i	0.495962	+	0.868344i	$0.334815\pi$
$977$	54.2837i	1.73669i	−0.495962	+	0.868344i	$0.665185\pi$
$978$	− 20.2705i	− 0.648179i
$979$	12.7639	0.407937
$980$	0	0
$981$	−13.4164	−0.428353
$982$	2.61803i	0.0835448i
$983$	− 24.9787i	− 0.796697i	−0.917234	−	0.398349i	$-0.869583\pi$
$983$	− 24.9787i	− 0.796697i	0.917234	−	0.398349i	$-0.130417\pi$
$984$	−3.23607	−0.103162
$985$	0	0
$986$	45.2705	1.44171
$987$	− 13.4164i	− 0.427049i
$988$	17.1246i	0.544806i
$989$	−0.450850	−0.0143362
$990$	0	0
$991$	−8.68692	−0.275949	−0.137975	−	0.990436i	$-0.544059\pi$
$991$	−8.68692	−0.275949	−0.137975	+	0.990436i	$0.544059\pi$
$992$	2.14590i	0.0681323i
$993$	− 21.4164i	− 0.679629i
$994$	11.0557	0.350666
$995$	0	0
$996$	8.18034	0.259204
$997$	38.2705i	1.21204i	0.795450	+	0.606020i	$0.207235\pi$
$997$	38.2705i	1.21204i	−0.795450	+	0.606020i	$0.792765\pi$
$998$	− 13.2361i	− 0.418980i
$999$	−7.85410	−0.248493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.c.b.499.4		4
3.2	odd	2		2250.2.c.b.1999.2		4
4.3	odd	2		6000.2.f.a.1249.1		4
5.2	odd	4		750.2.a.c.1.1	✓	2
5.3	odd	4		750.2.a.f.1.2	yes	2
5.4	even	2	inner	750.2.c.b.499.1		4
15.2	even	4		2250.2.a.n.1.1		2
15.8	even	4		2250.2.a.c.1.2		2
15.14	odd	2		2250.2.c.b.1999.3		4
20.3	even	4		6000.2.a.y.1.1		2
20.7	even	4		6000.2.a.d.1.2		2
20.19	odd	2		6000.2.f.a.1249.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.a.c.1.1	✓	2	5.2	odd	4
750.2.a.f.1.2	yes	2	5.3	odd	4
750.2.c.b.499.1		4	5.4	even	2	inner
750.2.c.b.499.4		4	1.1	even	1	trivial
2250.2.a.c.1.2		2	15.8	even	4
2250.2.a.n.1.1		2	15.2	even	4
2250.2.c.b.1999.2		4	3.2	odd	2
2250.2.c.b.1999.3		4	15.14	odd	2
6000.2.a.d.1.2		2	20.7	even	4
6000.2.a.y.1.1		2	20.3	even	4
6000.2.f.a.1249.1		4	4.3	odd	2
6000.2.f.a.1249.4		4	20.19	odd	2

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +1.23607i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +1.23607i q^{7} -1.00000i q^{8} -1.00000 q^{9} +1.38197 q^{11} -1.00000i q^{12} +2.85410i q^{13} -1.23607 q^{14} +1.00000 q^{16} +4.85410i q^{17} -1.00000i q^{18} -6.00000 q^{19} -1.23607 q^{21} +1.38197i q^{22} +3.09017i q^{23} +1.00000 q^{24} -2.85410 q^{26} -1.00000i q^{27} -1.23607i q^{28} -9.32624 q^{29} +2.14590 q^{31} +1.00000i q^{32} +1.38197i q^{33} -4.85410 q^{34} +1.00000 q^{36} -7.85410i q^{37} -6.00000i q^{38} -2.85410 q^{39} -3.23607 q^{41} -1.23607i q^{42} +0.145898i q^{43} -1.38197 q^{44} -3.09017 q^{46} +10.8541i q^{47} +1.00000i q^{48} +5.47214 q^{49} -4.85410 q^{51} -2.85410i q^{52} -3.23607i q^{53} +1.00000 q^{54} +1.23607 q^{56} -6.00000i q^{57} -9.32624i q^{58} -6.38197 q^{59} +13.4164 q^{61} +2.14590i q^{62} -1.23607i q^{63} -1.00000 q^{64} -1.38197 q^{66} -2.38197i q^{67} -4.85410i q^{68} -3.09017 q^{69} -8.94427 q^{71} +1.00000i q^{72} +12.0000i q^{73} +7.85410 q^{74} +6.00000 q^{76} +1.70820i q^{77} -2.85410i q^{78} +1.14590 q^{79} +1.00000 q^{81} -3.23607i q^{82} +8.18034i q^{83} +1.23607 q^{84} -0.145898 q^{86} -9.32624i q^{87} -1.38197i q^{88} +9.23607 q^{89} -3.52786 q^{91} -3.09017i q^{92} +2.14590i q^{93} -10.8541 q^{94} -1.00000 q^{96} -18.1803i q^{97} +5.47214i q^{98} -1.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 10 q^{11} + 4 q^{14} + 4 q^{16} - 24 q^{19} + 4 q^{21} + 4 q^{24} + 2 q^{26} - 6 q^{29} + 22 q^{31} - 6 q^{34} + 4 q^{36} + 2 q^{39} - 4 q^{41} - 10 q^{44} + 10 q^{46} + 4 q^{49} - 6 q^{51} + 4 q^{54} - 4 q^{56} - 30 q^{59} - 4 q^{64} - 10 q^{66} + 10 q^{69} + 18 q^{74} + 24 q^{76} + 18 q^{79} + 4 q^{81} - 4 q^{84} - 14 q^{86} + 28 q^{89} - 32 q^{91} - 30 q^{94} - 4 q^{96} - 10 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 10 * q^11 + 4 * q^14 + 4 * q^16 - 24 * q^19 + 4 * q^21 + 4 * q^24 + 2 * q^26 - 6 * q^29 + 22 * q^31 - 6 * q^34 + 4 * q^36 + 2 * q^39 - 4 * q^41 - 10 * q^44 + 10 * q^46 + 4 * q^49 - 6 * q^51 + 4 * q^54 - 4 * q^56 - 30 * q^59 - 4 * q^64 - 10 * q^66 + 10 * q^69 + 18 * q^74 + 24 * q^76 + 18 * q^79 + 4 * q^81 - 4 * q^84 - 14 * q^86 + 28 * q^89 - 32 * q^91 - 30 * q^94 - 4 * q^96 - 10 * q^99

Introduction

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