LMFDB - Embedded newform 950.2.b.c.799.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(799,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("950.799");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.b (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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	950.799
Dual form			950.2.b.c.799.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +3.00000i q^{7} -1.00000i q^{8} +2.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +3.00000i q^{7} -1.00000i q^{8} +2.00000 q^{9} +2.00000 q^{11} -1.00000i q^{12} +1.00000i q^{13} -3.00000 q^{14} +1.00000 q^{16} +3.00000i q^{17} +2.00000i q^{18} +1.00000 q^{19} -3.00000 q^{21} +2.00000i q^{22} +1.00000i q^{23} +1.00000 q^{24} -1.00000 q^{26} +5.00000i q^{27} -3.00000i q^{28} +5.00000 q^{29} -8.00000 q^{31} +1.00000i q^{32} +2.00000i q^{33} -3.00000 q^{34} -2.00000 q^{36} -2.00000i q^{37} +1.00000i q^{38} -1.00000 q^{39} -8.00000 q^{41} -3.00000i q^{42} -4.00000i q^{43} -2.00000 q^{44} -1.00000 q^{46} +8.00000i q^{47} +1.00000i q^{48} -2.00000 q^{49} -3.00000 q^{51} -1.00000i q^{52} +1.00000i q^{53} -5.00000 q^{54} +3.00000 q^{56} +1.00000i q^{57} +5.00000i q^{58} -15.0000 q^{59} +2.00000 q^{61} -8.00000i q^{62} +6.00000i q^{63} -1.00000 q^{64} -2.00000 q^{66} +3.00000i q^{67} -3.00000i q^{68} -1.00000 q^{69} +2.00000 q^{71} -2.00000i q^{72} -9.00000i q^{73} +2.00000 q^{74} -1.00000 q^{76} +6.00000i q^{77} -1.00000i q^{78} +10.0000 q^{79} +1.00000 q^{81} -8.00000i q^{82} +6.00000i q^{83} +3.00000 q^{84} +4.00000 q^{86} +5.00000i q^{87} -2.00000i q^{88} -3.00000 q^{91} -1.00000i q^{92} -8.00000i q^{93} -8.00000 q^{94} -1.00000 q^{96} -2.00000i q^{97} -2.00000i q^{98} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 - 2 * q^6 + 4 * q^9	$ 2 q - 2 q^{4} - 2 q^{6} + 4 q^{9} + 4 q^{11} - 6 q^{14} + 2 q^{16} + 2 q^{19} - 6 q^{21} + 2 q^{24} - 2 q^{26} + 10 q^{29} - 16 q^{31} - 6 q^{34} - 4 q^{36} - 2 q^{39} - 16 q^{41} - 4 q^{44} - 2 q^{46} - 4 q^{49} - 6 q^{51} - 10 q^{54} + 6 q^{56} - 30 q^{59} + 4 q^{61} - 2 q^{64} - 4 q^{66} - 2 q^{69} + 4 q^{71} + 4 q^{74} - 2 q^{76} + 20 q^{79} + 2 q^{81} + 6 q^{84} + 8 q^{86} - 6 q^{91} - 16 q^{94} - 2 q^{96} + 8 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 - 2 * q^6 + 4 * q^9 + 4 * q^11 - 6 * q^14 + 2 * q^16 + 2 * q^19 - 6 * q^21 + 2 * q^24 - 2 * q^26 + 10 * q^29 - 16 * q^31 - 6 * q^34 - 4 * q^36 - 2 * q^39 - 16 * q^41 - 4 * q^44 - 2 * q^46 - 4 * q^49 - 6 * q^51 - 10 * q^54 + 6 * q^56 - 30 * q^59 + 4 * q^61 - 2 * q^64 - 4 * q^66 - 2 * q^69 + 4 * q^71 + 4 * q^74 - 2 * q^76 + 20 * q^79 + 2 * q^81 + 6 * q^84 + 8 * q^86 - 6 * q^91 - 16 * q^94 - 2 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$1$

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	0.957427	+	0.288675i	$0.0932147\pi$
$3$	1.00000i	0.577350i	−0.957427	+	0.288675i	$0.906785\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	3.00000i	1.13389i	0.823754	+	0.566947i	$0.191875\pi$
$7$	3.00000i	1.13389i	−0.823754	+	0.566947i	$0.808125\pi$
$8$	− 1.00000i	− 0.353553i
$9$	2.00000	0.666667
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	− 1.00000i	− 0.288675i
$13$	1.00000i	0.277350i	0.990338	+	0.138675i	$0.0442844\pi$
$13$	1.00000i	0.277350i	−0.990338	+	0.138675i	$0.955716\pi$
$14$	−3.00000	−0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	3.00000i	0.727607i	0.931476	+	0.363803i	$0.118522\pi$
$17$	3.00000i	0.727607i	−0.931476	+	0.363803i	$0.881478\pi$
$18$	2.00000i	0.471405i
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	−3.00000	−0.654654
$22$	2.00000i	0.426401i
$23$	1.00000i	0.208514i	0.994550	+	0.104257i	$0.0332465\pi$
$23$	1.00000i	0.208514i	−0.994550	+	0.104257i	$0.966753\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−1.00000	−0.196116
$27$	5.00000i	0.962250i
$28$	− 3.00000i	− 0.566947i
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	0	0
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	1.00000i	0.176777i
$33$	2.00000i	0.348155i
$34$	−3.00000	−0.514496
$35$	0	0
$36$	−2.00000	−0.333333
$37$	− 2.00000i	− 0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$	− 2.00000i	− 0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$	1.00000i	0.162221i
$39$	−1.00000	−0.160128
$40$	0	0
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	− 3.00000i	− 0.462910i
$43$	− 4.00000i	− 0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$	− 4.00000i	− 0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	−1.00000	−0.147442
$47$	8.00000i	1.16692i	0.812142	+	0.583460i	$0.198301\pi$
$47$	8.00000i	1.16692i	−0.812142	+	0.583460i	$0.801699\pi$
$48$	1.00000i	0.144338i
$49$	−2.00000	−0.285714
$50$	0	0
$51$	−3.00000	−0.420084
$52$	− 1.00000i	− 0.138675i
$53$	1.00000i	0.137361i	0.997639	+	0.0686803i	$0.0218788\pi$
$53$	1.00000i	0.137361i	−0.997639	+	0.0686803i	$0.978121\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	3.00000	0.400892
$57$	1.00000i	0.132453i
$58$	5.00000i	0.656532i
$59$	−15.0000	−1.95283	−0.976417	−	0.215894i	$-0.930733\pi$
$59$	−15.0000	−1.95283	−0.976417	+	0.215894i	$0.930733\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	− 8.00000i	− 1.01600i
$63$	6.00000i	0.755929i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−2.00000	−0.246183
$67$	3.00000i	0.366508i	0.983066	+	0.183254i	$0.0586631\pi$
$67$	3.00000i	0.366508i	−0.983066	+	0.183254i	$0.941337\pi$
$68$	− 3.00000i	− 0.363803i
$69$	−1.00000	−0.120386
$70$	0	0
$71$	2.00000	0.237356	0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000	0.237356	0.118678	+	0.992933i	$0.462134\pi$
$72$	− 2.00000i	− 0.235702i
$73$	− 9.00000i	− 1.05337i	−0.850060	−	0.526685i	$-0.823435\pi$
$73$	− 9.00000i	− 1.05337i	0.850060	−	0.526685i	$-0.176565\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	−1.00000	−0.114708
$77$	6.00000i	0.683763i
$78$	− 1.00000i	− 0.113228i
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 8.00000i	− 0.883452i
$83$	6.00000i	0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$	6.00000i	0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$	3.00000	0.327327
$85$	0	0
$86$	4.00000	0.431331
$87$	5.00000i	0.536056i
$88$	− 2.00000i	− 0.213201i
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	−3.00000	−0.314485
$92$	− 1.00000i	− 0.104257i
$93$	− 8.00000i	− 0.829561i
$94$	−8.00000	−0.825137
$95$	0	0
$96$	−1.00000	−0.102062
$97$	− 2.00000i	− 0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$	− 2.00000i	− 0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$	− 2.00000i	− 0.202031i
$99$	4.00000	0.402015
$100$	0	0
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	− 3.00000i	− 0.297044i
$103$	6.00000i	0.591198i	0.955312	+	0.295599i	$0.0955191\pi$
$103$	6.00000i	0.591198i	−0.955312	+	0.295599i	$0.904481\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	−1.00000	−0.0971286
$107$	− 7.00000i	− 0.676716i	−0.941018	−	0.338358i	$-0.890129\pi$
$107$	− 7.00000i	− 0.676716i	0.941018	−	0.338358i	$-0.109871\pi$
$108$	− 5.00000i	− 0.481125i
$109$	15.0000	1.43674	0.718370	−	0.695662i	$-0.244889\pi$
$109$	15.0000	1.43674	0.718370	+	0.695662i	$0.244889\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	3.00000i	0.283473i
$113$	− 14.0000i	− 1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$	− 14.0000i	− 1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$	−1.00000	−0.0936586
$115$	0	0
$116$	−5.00000	−0.464238
$117$	2.00000i	0.184900i
$118$	− 15.0000i	− 1.38086i
$119$	−9.00000	−0.825029
$120$	0	0
$121$	−7.00000	−0.636364
$122$	2.00000i	0.181071i
$123$	− 8.00000i	− 0.721336i
$124$	8.00000	0.718421
$125$	0	0
$126$	−6.00000	−0.534522
$127$	18.0000i	1.59724i	0.601834	+	0.798621i	$0.294437\pi$
$127$	18.0000i	1.59724i	−0.601834	+	0.798621i	$0.705563\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	4.00000	0.352180
$130$	0	0
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	− 2.00000i	− 0.174078i
$133$	3.00000i	0.260133i
$134$	−3.00000	−0.259161
$135$	0	0
$136$	3.00000	0.257248
$137$	− 17.0000i	− 1.45241i	−0.687479	−	0.726204i	$-0.741283\pi$
$137$	− 17.0000i	− 1.45241i	0.687479	−	0.726204i	$-0.258717\pi$
$138$	− 1.00000i	− 0.0851257i
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	2.00000i	0.167836i
$143$	2.00000i	0.167248i
$144$	2.00000	0.166667
$145$	0	0
$146$	9.00000	0.744845
$147$	− 2.00000i	− 0.164957i
$148$	2.00000i	0.164399i
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	− 1.00000i	− 0.0811107i
$153$	6.00000i	0.485071i
$154$	−6.00000	−0.483494
$155$	0	0
$156$	1.00000	0.0800641
$157$	− 2.00000i	− 0.159617i	−0.996810	−	0.0798087i	$-0.974569\pi$
$157$	− 2.00000i	− 0.159617i	0.996810	−	0.0798087i	$-0.0254309\pi$
$158$	10.0000i	0.795557i
$159$	−1.00000	−0.0793052
$160$	0	0
$161$	−3.00000	−0.236433
$162$	1.00000i	0.0785674i
$163$	16.0000i	1.25322i	0.779334	+	0.626608i	$0.215557\pi$
$163$	16.0000i	1.25322i	−0.779334	+	0.626608i	$0.784443\pi$
$164$	8.00000	0.624695
$165$	0	0
$166$	−6.00000	−0.465690
$167$	− 12.0000i	− 0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$	− 12.0000i	− 0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$	3.00000i	0.231455i
$169$	12.0000	0.923077
$170$	0	0
$171$	2.00000	0.152944
$172$	4.00000i	0.304997i
$173$	6.00000i	0.456172i	0.973641	+	0.228086i	$0.0732467\pi$
$173$	6.00000i	0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$174$	−5.00000	−0.379049
$175$	0	0
$176$	2.00000	0.150756
$177$	− 15.0000i	− 1.12747i
$178$	0	0
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	22.0000	1.63525	0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000	1.63525	0.817624	+	0.575753i	$0.195291\pi$
$182$	− 3.00000i	− 0.222375i
$183$	2.00000i	0.147844i
$184$	1.00000	0.0737210
$185$	0	0
$186$	8.00000	0.586588
$187$	6.00000i	0.438763i
$188$	− 8.00000i	− 0.583460i
$189$	−15.0000	−1.09109
$190$	0	0
$191$	7.00000	0.506502	0.253251	−	0.967401i	$-0.418500\pi$
$191$	7.00000	0.506502	0.253251	+	0.967401i	$0.418500\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	6.00000i	0.431889i	0.976406	+	0.215945i	$0.0692831\pi$
$193$	6.00000i	0.431889i	−0.976406	+	0.215945i	$0.930717\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	2.00000	0.142857
$197$	8.00000i	0.569976i	0.958531	+	0.284988i	$0.0919897\pi$
$197$	8.00000i	0.569976i	−0.958531	+	0.284988i	$0.908010\pi$
$198$	4.00000i	0.284268i
$199$	25.0000	1.77220	0.886102	−	0.463491i	$-0.153403\pi$
$199$	25.0000	1.77220	0.886102	+	0.463491i	$0.153403\pi$
$200$	0	0
$201$	−3.00000	−0.211604
$202$	2.00000i	0.140720i
$203$	15.0000i	1.05279i
$204$	3.00000	0.210042
$205$	0	0
$206$	−6.00000	−0.418040
$207$	2.00000i	0.139010i
$208$	1.00000i	0.0693375i
$209$	2.00000	0.138343
$210$	0	0
$211$	27.0000	1.85876	0.929378	−	0.369129i	$-0.120344\pi$
$211$	27.0000	1.85876	0.929378	+	0.369129i	$0.120344\pi$
$212$	− 1.00000i	− 0.0686803i
$213$	2.00000i	0.137038i
$214$	7.00000	0.478510
$215$	0	0
$216$	5.00000	0.340207
$217$	− 24.0000i	− 1.62923i
$218$	15.0000i	1.01593i
$219$	9.00000	0.608164
$220$	0	0
$221$	−3.00000	−0.201802
$222$	2.00000i	0.134231i
$223$	− 14.0000i	− 0.937509i	−0.883328	−	0.468755i	$-0.844703\pi$
$223$	− 14.0000i	− 0.937509i	0.883328	−	0.468755i	$-0.155297\pi$
$224$	−3.00000	−0.200446
$225$	0	0
$226$	14.0000	0.931266
$227$	− 17.0000i	− 1.12833i	−0.825662	−	0.564165i	$-0.809198\pi$
$227$	− 17.0000i	− 1.12833i	0.825662	−	0.564165i	$-0.190802\pi$
$228$	− 1.00000i	− 0.0662266i
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	0	0
$231$	−6.00000	−0.394771
$232$	− 5.00000i	− 0.328266i
$233$	6.00000i	0.393073i	0.980497	+	0.196537i	$0.0629694\pi$
$233$	6.00000i	0.393073i	−0.980497	+	0.196537i	$0.937031\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	15.0000	0.976417
$237$	10.0000i	0.649570i
$238$	− 9.00000i	− 0.583383i
$239$	−15.0000	−0.970269	−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000	−0.970269	−0.485135	+	0.874439i	$0.661229\pi$
$240$	0	0
$241$	−8.00000	−0.515325	−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000	−0.515325	−0.257663	+	0.966235i	$0.582952\pi$
$242$	− 7.00000i	− 0.449977i
$243$	16.0000i	1.02640i
$244$	−2.00000	−0.128037
$245$	0	0
$246$	8.00000	0.510061
$247$	1.00000i	0.0636285i
$248$	8.00000i	0.508001i
$249$	−6.00000	−0.380235
$250$	0	0
$251$	2.00000	0.126239	0.0631194	−	0.998006i	$-0.479895\pi$
$251$	2.00000	0.126239	0.0631194	+	0.998006i	$0.479895\pi$
$252$	− 6.00000i	− 0.377964i
$253$	2.00000i	0.125739i
$254$	−18.0000	−1.12942
$255$	0	0
$256$	1.00000	0.0625000
$257$	8.00000i	0.499026i	0.968371	+	0.249513i	$0.0802706\pi$
$257$	8.00000i	0.499026i	−0.968371	+	0.249513i	$0.919729\pi$
$258$	4.00000i	0.249029i
$259$	6.00000	0.372822
$260$	0	0
$261$	10.0000	0.618984
$262$	12.0000i	0.741362i
$263$	− 24.0000i	− 1.47990i	−0.672660	−	0.739952i	$-0.734848\pi$
$263$	− 24.0000i	− 1.47990i	0.672660	−	0.739952i	$-0.265152\pi$
$264$	2.00000	0.123091
$265$	0	0
$266$	−3.00000	−0.183942
$267$	0	0
$268$	− 3.00000i	− 0.183254i
$269$	−30.0000	−1.82913	−0.914566	−	0.404436i	$-0.867468\pi$
$269$	−30.0000	−1.82913	−0.914566	+	0.404436i	$0.867468\pi$
$270$	0	0
$271$	7.00000	0.425220	0.212610	−	0.977137i	$-0.431804\pi$
$271$	7.00000	0.425220	0.212610	+	0.977137i	$0.431804\pi$
$272$	3.00000i	0.181902i
$273$	− 3.00000i	− 0.181568i
$274$	17.0000	1.02701
$275$	0	0
$276$	1.00000	0.0601929
$277$	28.0000i	1.68236i	0.540758	+	0.841178i	$0.318138\pi$
$277$	28.0000i	1.68236i	−0.540758	+	0.841178i	$0.681862\pi$
$278$	0	0
$279$	−16.0000	−0.957895
$280$	0	0
$281$	−8.00000	−0.477240	−0.238620	−	0.971113i	$-0.576695\pi$
$281$	−8.00000	−0.477240	−0.238620	+	0.971113i	$0.576695\pi$
$282$	− 8.00000i	− 0.476393i
$283$	6.00000i	0.356663i	0.983970	+	0.178331i	$0.0570699\pi$
$283$	6.00000i	0.356663i	−0.983970	+	0.178331i	$0.942930\pi$
$284$	−2.00000	−0.118678
$285$	0	0
$286$	−2.00000	−0.118262
$287$	− 24.0000i	− 1.41668i
$288$	2.00000i	0.117851i
$289$	8.00000	0.470588
$290$	0	0
$291$	2.00000	0.117242
$292$	9.00000i	0.526685i
$293$	− 9.00000i	− 0.525786i	−0.964825	−	0.262893i	$-0.915323\pi$
$293$	− 9.00000i	− 0.525786i	0.964825	−	0.262893i	$-0.0846766\pi$
$294$	2.00000	0.116642
$295$	0	0
$296$	−2.00000	−0.116248
$297$	10.0000i	0.580259i
$298$	0	0
$299$	−1.00000	−0.0578315
$300$	0	0
$301$	12.0000	0.691669
$302$	2.00000i	0.115087i
$303$	2.00000i	0.114897i
$304$	1.00000	0.0573539
$305$	0	0
$306$	−6.00000	−0.342997
$307$	− 12.0000i	− 0.684876i	−0.939540	−	0.342438i	$-0.888747\pi$
$307$	− 12.0000i	− 0.684876i	0.939540	−	0.342438i	$-0.111253\pi$
$308$	− 6.00000i	− 0.341882i
$309$	−6.00000	−0.341328
$310$	0	0
$311$	7.00000	0.396934	0.198467	−	0.980108i	$-0.436404\pi$
$311$	7.00000	0.396934	0.198467	+	0.980108i	$0.436404\pi$
$312$	1.00000i	0.0566139i
$313$	− 29.0000i	− 1.63918i	−0.572953	−	0.819588i	$-0.694202\pi$
$313$	− 29.0000i	− 1.63918i	0.572953	−	0.819588i	$-0.305798\pi$
$314$	2.00000	0.112867
$315$	0	0
$316$	−10.0000	−0.562544
$317$	− 27.0000i	− 1.51647i	−0.651981	−	0.758236i	$-0.726062\pi$
$317$	− 27.0000i	− 1.51647i	0.651981	−	0.758236i	$-0.273938\pi$
$318$	− 1.00000i	− 0.0560772i
$319$	10.0000	0.559893
$320$	0	0
$321$	7.00000	0.390702
$322$	− 3.00000i	− 0.167183i
$323$	3.00000i	0.166924i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−16.0000	−0.886158
$327$	15.0000i	0.829502i
$328$	8.00000i	0.441726i
$329$	−24.0000	−1.32316
$330$	0	0
$331$	17.0000	0.934405	0.467202	−	0.884150i	$-0.345262\pi$
$331$	17.0000	0.934405	0.467202	+	0.884150i	$0.345262\pi$
$332$	− 6.00000i	− 0.329293i
$333$	− 4.00000i	− 0.219199i
$334$	12.0000	0.656611
$335$	0	0
$336$	−3.00000	−0.163663
$337$	− 32.0000i	− 1.74315i	−0.490261	−	0.871576i	$-0.663099\pi$
$337$	− 32.0000i	− 1.74315i	0.490261	−	0.871576i	$-0.336901\pi$
$338$	12.0000i	0.652714i
$339$	14.0000	0.760376
$340$	0	0
$341$	−16.0000	−0.866449
$342$	2.00000i	0.108148i
$343$	15.0000i	0.809924i
$344$	−4.00000	−0.215666
$345$	0	0
$346$	−6.00000	−0.322562
$347$	− 2.00000i	− 0.107366i	−0.998558	−	0.0536828i	$-0.982904\pi$
$347$	− 2.00000i	− 0.107366i	0.998558	−	0.0536828i	$-0.0170960\pi$
$348$	− 5.00000i	− 0.268028i
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	0	0
$351$	−5.00000	−0.266880
$352$	2.00000i	0.106600i
$353$	− 9.00000i	− 0.479022i	−0.970894	−	0.239511i	$-0.923013\pi$
$353$	− 9.00000i	− 0.479022i	0.970894	−	0.239511i	$-0.0769871\pi$
$354$	15.0000	0.797241
$355$	0	0
$356$	0	0
$357$	− 9.00000i	− 0.476331i
$358$	0	0
$359$	15.0000	0.791670	0.395835	−	0.918322i	$-0.370455\pi$
$359$	15.0000	0.791670	0.395835	+	0.918322i	$0.370455\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	22.0000i	1.15629i
$363$	− 7.00000i	− 0.367405i
$364$	3.00000	0.157243
$365$	0	0
$366$	−2.00000	−0.104542
$367$	28.0000i	1.46159i	0.682598	+	0.730794i	$0.260850\pi$
$367$	28.0000i	1.46159i	−0.682598	+	0.730794i	$0.739150\pi$
$368$	1.00000i	0.0521286i
$369$	−16.0000	−0.832927
$370$	0	0
$371$	−3.00000	−0.155752
$372$	8.00000i	0.414781i
$373$	− 29.0000i	− 1.50156i	−0.660551	−	0.750782i	$-0.729677\pi$
$373$	− 29.0000i	− 1.50156i	0.660551	−	0.750782i	$-0.270323\pi$
$374$	−6.00000	−0.310253
$375$	0	0
$376$	8.00000	0.412568
$377$	5.00000i	0.257513i
$378$	− 15.0000i	− 0.771517i
$379$	−15.0000	−0.770498	−0.385249	−	0.922813i	$-0.625884\pi$
$379$	−15.0000	−0.770498	−0.385249	+	0.922813i	$0.625884\pi$
$380$	0	0
$381$	−18.0000	−0.922168
$382$	7.00000i	0.358151i
$383$	26.0000i	1.32854i	0.747494	+	0.664269i	$0.231257\pi$
$383$	26.0000i	1.32854i	−0.747494	+	0.664269i	$0.768743\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−6.00000	−0.305392
$387$	− 8.00000i	− 0.406663i
$388$	2.00000i	0.101535i
$389$	30.0000	1.52106	0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000	1.52106	0.760530	+	0.649303i	$0.224939\pi$
$390$	0	0
$391$	−3.00000	−0.151717
$392$	2.00000i	0.101015i
$393$	12.0000i	0.605320i
$394$	−8.00000	−0.403034
$395$	0	0
$396$	−4.00000	−0.201008
$397$	8.00000i	0.401508i	0.979642	+	0.200754i	$0.0643393\pi$
$397$	8.00000i	0.401508i	−0.979642	+	0.200754i	$0.935661\pi$
$398$	25.0000i	1.25314i
$399$	−3.00000	−0.150188
$400$	0	0
$401$	−8.00000	−0.399501	−0.199750	−	0.979847i	$-0.564013\pi$
$401$	−8.00000	−0.399501	−0.199750	+	0.979847i	$0.564013\pi$
$402$	− 3.00000i	− 0.149626i
$403$	− 8.00000i	− 0.398508i
$404$	−2.00000	−0.0995037
$405$	0	0
$406$	−15.0000	−0.744438
$407$	− 4.00000i	− 0.198273i
$408$	3.00000i	0.148522i
$409$	20.0000	0.988936	0.494468	−	0.869196i	$-0.335363\pi$
$409$	20.0000	0.988936	0.494468	+	0.869196i	$0.335363\pi$
$410$	0	0
$411$	17.0000	0.838548
$412$	− 6.00000i	− 0.295599i
$413$	− 45.0000i	− 2.21431i
$414$	−2.00000	−0.0982946
$415$	0	0
$416$	−1.00000	−0.0490290
$417$	0	0
$418$	2.00000i	0.0978232i
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	−13.0000	−0.633581	−0.316791	−	0.948495i	$-0.602605\pi$
$421$	−13.0000	−0.633581	−0.316791	+	0.948495i	$0.602605\pi$
$422$	27.0000i	1.31434i
$423$	16.0000i	0.777947i
$424$	1.00000	0.0485643
$425$	0	0
$426$	−2.00000	−0.0969003
$427$	6.00000i	0.290360i
$428$	7.00000i	0.338358i
$429$	−2.00000	−0.0965609
$430$	0	0
$431$	−18.0000	−0.867029	−0.433515	−	0.901146i	$-0.642727\pi$
$431$	−18.0000	−0.867029	−0.433515	+	0.901146i	$0.642727\pi$
$432$	5.00000i	0.240563i
$433$	− 14.0000i	− 0.672797i	−0.941720	−	0.336399i	$-0.890791\pi$
$433$	− 14.0000i	− 0.672797i	0.941720	−	0.336399i	$-0.109209\pi$
$434$	24.0000	1.15204
$435$	0	0
$436$	−15.0000	−0.718370
$437$	1.00000i	0.0478365i
$438$	9.00000i	0.430037i
$439$	−20.0000	−0.954548	−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000	−0.954548	−0.477274	+	0.878755i	$0.658375\pi$
$440$	0	0
$441$	−4.00000	−0.190476
$442$	− 3.00000i	− 0.142695i
$443$	26.0000i	1.23530i	0.786454	+	0.617649i	$0.211915\pi$
$443$	26.0000i	1.23530i	−0.786454	+	0.617649i	$0.788085\pi$
$444$	−2.00000	−0.0949158
$445$	0	0
$446$	14.0000	0.662919
$447$	0	0
$448$	− 3.00000i	− 0.141737i
$449$	−10.0000	−0.471929	−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000	−0.471929	−0.235965	+	0.971762i	$0.575825\pi$
$450$	0	0
$451$	−16.0000	−0.753411
$452$	14.0000i	0.658505i
$453$	2.00000i	0.0939682i
$454$	17.0000	0.797850
$455$	0	0
$456$	1.00000	0.0468293
$457$	− 7.00000i	− 0.327446i	−0.986506	−	0.163723i	$-0.947650\pi$
$457$	− 7.00000i	− 0.327446i	0.986506	−	0.163723i	$-0.0523504\pi$
$458$	10.0000i	0.467269i
$459$	−15.0000	−0.700140
$460$	0	0
$461$	−28.0000	−1.30409	−0.652045	−	0.758180i	$-0.726089\pi$
$461$	−28.0000	−1.30409	−0.652045	+	0.758180i	$0.726089\pi$
$462$	− 6.00000i	− 0.279145i
$463$	− 4.00000i	− 0.185896i	−0.995671	−	0.0929479i	$-0.970371\pi$
$463$	− 4.00000i	− 0.185896i	0.995671	−	0.0929479i	$-0.0296290\pi$
$464$	5.00000	0.232119
$465$	0	0
$466$	−6.00000	−0.277945
$467$	− 2.00000i	− 0.0925490i	−0.998929	−	0.0462745i	$-0.985265\pi$
$467$	− 2.00000i	− 0.0925490i	0.998929	−	0.0462745i	$-0.0147349\pi$
$468$	− 2.00000i	− 0.0924500i
$469$	−9.00000	−0.415581
$470$	0	0
$471$	2.00000	0.0921551
$472$	15.0000i	0.690431i
$473$	− 8.00000i	− 0.367840i
$474$	−10.0000	−0.459315
$475$	0	0
$476$	9.00000	0.412514
$477$	2.00000i	0.0915737i
$478$	− 15.0000i	− 0.686084i
$479$	20.0000	0.913823	0.456912	−	0.889512i	$-0.348956\pi$
$479$	20.0000	0.913823	0.456912	+	0.889512i	$0.348956\pi$
$480$	0	0
$481$	2.00000	0.0911922
$482$	− 8.00000i	− 0.364390i
$483$	− 3.00000i	− 0.136505i
$484$	7.00000	0.318182
$485$	0	0
$486$	−16.0000	−0.725775
$487$	− 2.00000i	− 0.0906287i	−0.998973	−	0.0453143i	$-0.985571\pi$
$487$	− 2.00000i	− 0.0906287i	0.998973	−	0.0453143i	$-0.0144289\pi$
$488$	− 2.00000i	− 0.0905357i
$489$	−16.0000	−0.723545
$490$	0	0
$491$	−28.0000	−1.26362	−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000	−1.26362	−0.631811	+	0.775122i	$0.717688\pi$
$492$	8.00000i	0.360668i
$493$	15.0000i	0.675566i
$494$	−1.00000	−0.0449921
$495$	0	0
$496$	−8.00000	−0.359211
$497$	6.00000i	0.269137i
$498$	− 6.00000i	− 0.268866i
$499$	−40.0000	−1.79065	−0.895323	−	0.445418i	$-0.853055\pi$
$499$	−40.0000	−1.79065	−0.895323	+	0.445418i	$0.853055\pi$
$500$	0	0
$501$	12.0000	0.536120
$502$	2.00000i	0.0892644i
$503$	− 39.0000i	− 1.73892i	−0.494000	−	0.869462i	$-0.664466\pi$
$503$	− 39.0000i	− 1.73892i	0.494000	−	0.869462i	$-0.335534\pi$
$504$	6.00000	0.267261
$505$	0	0
$506$	−2.00000	−0.0889108
$507$	12.0000i	0.532939i
$508$	− 18.0000i	− 0.798621i
$509$	30.0000	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$510$	0	0
$511$	27.0000	1.19441
$512$	1.00000i	0.0441942i
$513$	5.00000i	0.220755i
$514$	−8.00000	−0.352865
$515$	0	0
$516$	−4.00000	−0.176090
$517$	16.0000i	0.703679i
$518$	6.00000i	0.263625i
$519$	−6.00000	−0.263371
$520$	0	0
$521$	−28.0000	−1.22670	−0.613351	−	0.789810i	$-0.710179\pi$
$521$	−28.0000	−1.22670	−0.613351	+	0.789810i	$0.710179\pi$
$522$	10.0000i	0.437688i
$523$	− 29.0000i	− 1.26808i	−0.773300	−	0.634041i	$-0.781395\pi$
$523$	− 29.0000i	− 1.26808i	0.773300	−	0.634041i	$-0.218605\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	24.0000	1.04645
$527$	− 24.0000i	− 1.04546i
$528$	2.00000i	0.0870388i
$529$	22.0000	0.956522
$530$	0	0
$531$	−30.0000	−1.30189
$532$	− 3.00000i	− 0.130066i
$533$	− 8.00000i	− 0.346518i
$534$	0	0
$535$	0	0
$536$	3.00000	0.129580
$537$	0	0
$538$	− 30.0000i	− 1.29339i
$539$	−4.00000	−0.172292
$540$	0	0
$541$	2.00000	0.0859867	0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000	0.0859867	0.0429934	+	0.999075i	$0.486311\pi$
$542$	7.00000i	0.300676i
$543$	22.0000i	0.944110i
$544$	−3.00000	−0.128624
$545$	0	0
$546$	3.00000	0.128388
$547$	28.0000i	1.19719i	0.801050	+	0.598597i	$0.204275\pi$
$547$	28.0000i	1.19719i	−0.801050	+	0.598597i	$0.795725\pi$
$548$	17.0000i	0.726204i
$549$	4.00000	0.170716
$550$	0	0
$551$	5.00000	0.213007
$552$	1.00000i	0.0425628i
$553$	30.0000i	1.27573i
$554$	−28.0000	−1.18961
$555$	0	0
$556$	0	0
$557$	28.0000i	1.18640i	0.805056	+	0.593199i	$0.202135\pi$
$557$	28.0000i	1.18640i	−0.805056	+	0.593199i	$0.797865\pi$
$558$	− 16.0000i	− 0.677334i
$559$	4.00000	0.169182
$560$	0	0
$561$	−6.00000	−0.253320
$562$	− 8.00000i	− 0.337460i
$563$	36.0000i	1.51722i	0.651546	+	0.758610i	$0.274121\pi$
$563$	36.0000i	1.51722i	−0.651546	+	0.758610i	$0.725879\pi$
$564$	8.00000	0.336861
$565$	0	0
$566$	−6.00000	−0.252199
$567$	3.00000i	0.125988i
$568$	− 2.00000i	− 0.0839181i
$569$	−40.0000	−1.67689	−0.838444	−	0.544988i	$-0.816534\pi$
$569$	−40.0000	−1.67689	−0.838444	+	0.544988i	$0.816534\pi$
$570$	0	0
$571$	−28.0000	−1.17176	−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000	−1.17176	−0.585882	+	0.810397i	$0.699252\pi$
$572$	− 2.00000i	− 0.0836242i
$573$	7.00000i	0.292429i
$574$	24.0000	1.00174
$575$	0	0
$576$	−2.00000	−0.0833333
$577$	− 37.0000i	− 1.54033i	−0.637845	−	0.770165i	$-0.720174\pi$
$577$	− 37.0000i	− 1.54033i	0.637845	−	0.770165i	$-0.279826\pi$
$578$	8.00000i	0.332756i
$579$	−6.00000	−0.249351
$580$	0	0
$581$	−18.0000	−0.746766
$582$	2.00000i	0.0829027i
$583$	2.00000i	0.0828315i
$584$	−9.00000	−0.372423
$585$	0	0
$586$	9.00000	0.371787
$587$	− 12.0000i	− 0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$	− 12.0000i	− 0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$	2.00000i	0.0824786i
$589$	−8.00000	−0.329634
$590$	0	0
$591$	−8.00000	−0.329076
$592$	− 2.00000i	− 0.0821995i
$593$	− 34.0000i	− 1.39621i	−0.715994	−	0.698106i	$-0.754026\pi$
$593$	− 34.0000i	− 1.39621i	0.715994	−	0.698106i	$-0.245974\pi$
$594$	−10.0000	−0.410305
$595$	0	0
$596$	0	0
$597$	25.0000i	1.02318i
$598$	− 1.00000i	− 0.0408930i
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	−8.00000	−0.326327	−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000	−0.326327	−0.163163	+	0.986599i	$0.552170\pi$
$602$	12.0000i	0.489083i
$603$	6.00000i	0.244339i
$604$	−2.00000	−0.0813788
$605$	0	0
$606$	−2.00000	−0.0812444
$607$	− 22.0000i	− 0.892952i	−0.894795	−	0.446476i	$-0.852679\pi$
$607$	− 22.0000i	− 0.892952i	0.894795	−	0.446476i	$-0.147321\pi$
$608$	1.00000i	0.0405554i
$609$	−15.0000	−0.607831
$610$	0	0
$611$	−8.00000	−0.323645
$612$	− 6.00000i	− 0.242536i
$613$	− 34.0000i	− 1.37325i	−0.727013	−	0.686624i	$-0.759092\pi$
$613$	− 34.0000i	− 1.37325i	0.727013	−	0.686624i	$-0.240908\pi$
$614$	12.0000	0.484281
$615$	0	0
$616$	6.00000	0.241747
$617$	18.0000i	0.724653i	0.932051	+	0.362326i	$0.118017\pi$
$617$	18.0000i	0.724653i	−0.932051	+	0.362326i	$0.881983\pi$
$618$	− 6.00000i	− 0.241355i
$619$	−10.0000	−0.401934	−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000	−0.401934	−0.200967	+	0.979598i	$0.564408\pi$
$620$	0	0
$621$	−5.00000	−0.200643
$622$	7.00000i	0.280674i
$623$	0	0
$624$	−1.00000	−0.0400320
$625$	0	0
$626$	29.0000	1.15907
$627$	2.00000i	0.0798723i
$628$	2.00000i	0.0798087i
$629$	6.00000	0.239236
$630$	0	0
$631$	32.0000	1.27390	0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000	1.27390	0.636950	+	0.770905i	$0.280196\pi$
$632$	− 10.0000i	− 0.397779i
$633$	27.0000i	1.07315i
$634$	27.0000	1.07231
$635$	0	0
$636$	1.00000	0.0396526
$637$	− 2.00000i	− 0.0792429i
$638$	10.0000i	0.395904i
$639$	4.00000	0.158238
$640$	0	0
$641$	42.0000	1.65890	0.829450	−	0.558581i	$-0.188654\pi$
$641$	42.0000	1.65890	0.829450	+	0.558581i	$0.188654\pi$
$642$	7.00000i	0.276268i
$643$	26.0000i	1.02534i	0.858586	+	0.512670i	$0.171344\pi$
$643$	26.0000i	1.02534i	−0.858586	+	0.512670i	$0.828656\pi$
$644$	3.00000	0.118217
$645$	0	0
$646$	−3.00000	−0.118033
$647$	23.0000i	0.904223i	0.891961	+	0.452112i	$0.149329\pi$
$647$	23.0000i	0.904223i	−0.891961	+	0.452112i	$0.850671\pi$
$648$	− 1.00000i	− 0.0392837i
$649$	−30.0000	−1.17760
$650$	0	0
$651$	24.0000	0.940634
$652$	− 16.0000i	− 0.626608i
$653$	36.0000i	1.40879i	0.709809	+	0.704394i	$0.248781\pi$
$653$	36.0000i	1.40879i	−0.709809	+	0.704394i	$0.751219\pi$
$654$	−15.0000	−0.586546
$655$	0	0
$656$	−8.00000	−0.312348
$657$	− 18.0000i	− 0.702247i
$658$	− 24.0000i	− 0.935617i
$659$	−5.00000	−0.194772	−0.0973862	−	0.995247i	$-0.531048\pi$
$659$	−5.00000	−0.194772	−0.0973862	+	0.995247i	$0.531048\pi$
$660$	0	0
$661$	−23.0000	−0.894596	−0.447298	−	0.894385i	$-0.647614\pi$
$661$	−23.0000	−0.894596	−0.447298	+	0.894385i	$0.647614\pi$
$662$	17.0000i	0.660724i
$663$	− 3.00000i	− 0.116510i
$664$	6.00000	0.232845
$665$	0	0
$666$	4.00000	0.154997
$667$	5.00000i	0.193601i
$668$	12.0000i	0.464294i
$669$	14.0000	0.541271
$670$	0	0
$671$	4.00000	0.154418
$672$	− 3.00000i	− 0.115728i
$673$	− 44.0000i	− 1.69608i	−0.529936	−	0.848038i	$-0.677784\pi$
$673$	− 44.0000i	− 1.69608i	0.529936	−	0.848038i	$-0.322216\pi$
$674$	32.0000	1.23259
$675$	0	0
$676$	−12.0000	−0.461538
$677$	13.0000i	0.499631i	0.968294	+	0.249815i	$0.0803699\pi$
$677$	13.0000i	0.499631i	−0.968294	+	0.249815i	$0.919630\pi$
$678$	14.0000i	0.537667i
$679$	6.00000	0.230259
$680$	0	0
$681$	17.0000	0.651441
$682$	− 16.0000i	− 0.612672i
$683$	− 4.00000i	− 0.153056i	−0.997067	−	0.0765279i	$-0.975617\pi$
$683$	− 4.00000i	− 0.153056i	0.997067	−	0.0765279i	$-0.0243834\pi$
$684$	−2.00000	−0.0764719
$685$	0	0
$686$	−15.0000	−0.572703
$687$	10.0000i	0.381524i
$688$	− 4.00000i	− 0.152499i
$689$	−1.00000	−0.0380970
$690$	0	0
$691$	42.0000	1.59776	0.798878	−	0.601494i	$-0.205427\pi$
$691$	42.0000	1.59776	0.798878	+	0.601494i	$0.205427\pi$
$692$	− 6.00000i	− 0.228086i
$693$	12.0000i	0.455842i
$694$	2.00000	0.0759190
$695$	0	0
$696$	5.00000	0.189525
$697$	− 24.0000i	− 0.909065i
$698$	− 10.0000i	− 0.378506i
$699$	−6.00000	−0.226941
$700$	0	0
$701$	−28.0000	−1.05755	−0.528773	−	0.848763i	$-0.677348\pi$
$701$	−28.0000	−1.05755	−0.528773	+	0.848763i	$0.677348\pi$
$702$	− 5.00000i	− 0.188713i
$703$	− 2.00000i	− 0.0754314i
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	9.00000	0.338719
$707$	6.00000i	0.225653i
$708$	15.0000i	0.563735i
$709$	30.0000	1.12667	0.563337	−	0.826227i	$-0.309517\pi$
$709$	30.0000	1.12667	0.563337	+	0.826227i	$0.309517\pi$
$710$	0	0
$711$	20.0000	0.750059
$712$	0	0
$713$	− 8.00000i	− 0.299602i
$714$	9.00000	0.336817
$715$	0	0
$716$	0	0
$717$	− 15.0000i	− 0.560185i
$718$	15.0000i	0.559795i
$719$	5.00000	0.186469	0.0932343	−	0.995644i	$-0.470279\pi$
$719$	5.00000	0.186469	0.0932343	+	0.995644i	$0.470279\pi$
$720$	0	0
$721$	−18.0000	−0.670355
$722$	1.00000i	0.0372161i
$723$	− 8.00000i	− 0.297523i
$724$	−22.0000	−0.817624
$725$	0	0
$726$	7.00000	0.259794
$727$	− 17.0000i	− 0.630495i	−0.949009	−	0.315248i	$-0.897912\pi$
$727$	− 17.0000i	− 0.630495i	0.949009	−	0.315248i	$-0.102088\pi$
$728$	3.00000i	0.111187i
$729$	−13.0000	−0.481481
$730$	0	0
$731$	12.0000	0.443836
$732$	− 2.00000i	− 0.0739221i
$733$	36.0000i	1.32969i	0.746981	+	0.664845i	$0.231502\pi$
$733$	36.0000i	1.32969i	−0.746981	+	0.664845i	$0.768498\pi$
$734$	−28.0000	−1.03350
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	6.00000i	0.221013i
$738$	− 16.0000i	− 0.588968i
$739$	40.0000	1.47142	0.735712	−	0.677295i	$-0.236848\pi$
$739$	40.0000	1.47142	0.735712	+	0.677295i	$0.236848\pi$
$740$	0	0
$741$	−1.00000	−0.0367359
$742$	− 3.00000i	− 0.110133i
$743$	16.0000i	0.586983i	0.955962	+	0.293492i	$0.0948173\pi$
$743$	16.0000i	0.586983i	−0.955962	+	0.293492i	$0.905183\pi$
$744$	−8.00000	−0.293294
$745$	0	0
$746$	29.0000	1.06177
$747$	12.0000i	0.439057i
$748$	− 6.00000i	− 0.219382i
$749$	21.0000	0.767323
$750$	0	0
$751$	32.0000	1.16770	0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000	1.16770	0.583848	+	0.811863i	$0.301546\pi$
$752$	8.00000i	0.291730i
$753$	2.00000i	0.0728841i
$754$	−5.00000	−0.182089
$755$	0	0
$756$	15.0000	0.545545
$757$	− 2.00000i	− 0.0726912i	−0.999339	−	0.0363456i	$-0.988428\pi$
$757$	− 2.00000i	− 0.0726912i	0.999339	−	0.0363456i	$-0.0115717\pi$
$758$	− 15.0000i	− 0.544825i
$759$	−2.00000	−0.0725954
$760$	0	0
$761$	27.0000	0.978749	0.489375	−	0.872074i	$-0.337225\pi$
$761$	27.0000	0.978749	0.489375	+	0.872074i	$0.337225\pi$
$762$	− 18.0000i	− 0.652071i
$763$	45.0000i	1.62911i
$764$	−7.00000	−0.253251
$765$	0	0
$766$	−26.0000	−0.939418
$767$	− 15.0000i	− 0.541619i
$768$	1.00000i	0.0360844i
$769$	35.0000	1.26213	0.631066	−	0.775729i	$-0.282618\pi$
$769$	35.0000	1.26213	0.631066	+	0.775729i	$0.282618\pi$
$770$	0	0
$771$	−8.00000	−0.288113
$772$	− 6.00000i	− 0.215945i
$773$	− 9.00000i	− 0.323708i	−0.986815	−	0.161854i	$-0.948253\pi$
$773$	− 9.00000i	− 0.323708i	0.986815	−	0.161854i	$-0.0517473\pi$
$774$	8.00000	0.287554
$775$	0	0
$776$	−2.00000	−0.0717958
$777$	6.00000i	0.215249i
$778$	30.0000i	1.07555i
$779$	−8.00000	−0.286630
$780$	0	0
$781$	4.00000	0.143131
$782$	− 3.00000i	− 0.107280i
$783$	25.0000i	0.893427i
$784$	−2.00000	−0.0714286
$785$	0	0
$786$	−12.0000	−0.428026
$787$	− 17.0000i	− 0.605985i	−0.952993	−	0.302992i	$-0.902014\pi$
$787$	− 17.0000i	− 0.605985i	0.952993	−	0.302992i	$-0.0979856\pi$
$788$	− 8.00000i	− 0.284988i
$789$	24.0000	0.854423
$790$	0	0
$791$	42.0000	1.49335
$792$	− 4.00000i	− 0.142134i
$793$	2.00000i	0.0710221i
$794$	−8.00000	−0.283909
$795$	0	0
$796$	−25.0000	−0.886102
$797$	3.00000i	0.106265i	0.998587	+	0.0531327i	$0.0169206\pi$
$797$	3.00000i	0.106265i	−0.998587	+	0.0531327i	$0.983079\pi$
$798$	− 3.00000i	− 0.106199i
$799$	−24.0000	−0.849059
$800$	0	0
$801$	0	0
$802$	− 8.00000i	− 0.282490i
$803$	− 18.0000i	− 0.635206i
$804$	3.00000	0.105802
$805$	0	0
$806$	8.00000	0.281788
$807$	− 30.0000i	− 1.05605i
$808$	− 2.00000i	− 0.0703598i
$809$	15.0000	0.527372	0.263686	−	0.964609i	$-0.415062\pi$
$809$	15.0000	0.527372	0.263686	+	0.964609i	$0.415062\pi$
$810$	0	0
$811$	−3.00000	−0.105344	−0.0526721	−	0.998612i	$-0.516774\pi$
$811$	−3.00000	−0.105344	−0.0526721	+	0.998612i	$0.516774\pi$
$812$	− 15.0000i	− 0.526397i
$813$	7.00000i	0.245501i
$814$	4.00000	0.140200
$815$	0	0
$816$	−3.00000	−0.105021
$817$	− 4.00000i	− 0.139942i
$818$	20.0000i	0.699284i
$819$	−6.00000	−0.209657
$820$	0	0
$821$	12.0000	0.418803	0.209401	−	0.977830i	$-0.432848\pi$
$821$	12.0000	0.418803	0.209401	+	0.977830i	$0.432848\pi$
$822$	17.0000i	0.592943i
$823$	− 29.0000i	− 1.01088i	−0.862863	−	0.505438i	$-0.831331\pi$
$823$	− 29.0000i	− 1.01088i	0.862863	−	0.505438i	$-0.168669\pi$
$824$	6.00000	0.209020
$825$	0	0
$826$	45.0000	1.56575
$827$	23.0000i	0.799788i	0.916561	+	0.399894i	$0.130953\pi$
$827$	23.0000i	0.799788i	−0.916561	+	0.399894i	$0.869047\pi$
$828$	− 2.00000i	− 0.0695048i
$829$	15.0000	0.520972	0.260486	−	0.965478i	$-0.416117\pi$
$829$	15.0000	0.520972	0.260486	+	0.965478i	$0.416117\pi$
$830$	0	0
$831$	−28.0000	−0.971309
$832$	− 1.00000i	− 0.0346688i
$833$	− 6.00000i	− 0.207888i
$834$	0	0
$835$	0	0
$836$	−2.00000	−0.0691714
$837$	− 40.0000i	− 1.38260i
$838$	0	0
$839$	−20.0000	−0.690477	−0.345238	−	0.938515i	$-0.612202\pi$
$839$	−20.0000	−0.690477	−0.345238	+	0.938515i	$0.612202\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	− 13.0000i	− 0.448010i
$843$	− 8.00000i	− 0.275535i
$844$	−27.0000	−0.929378
$845$	0	0
$846$	−16.0000	−0.550091
$847$	− 21.0000i	− 0.721569i
$848$	1.00000i	0.0343401i
$849$	−6.00000	−0.205919
$850$	0	0
$851$	2.00000	0.0685591
$852$	− 2.00000i	− 0.0685189i
$853$	6.00000i	0.205436i	0.994711	+	0.102718i	$0.0327539\pi$
$853$	6.00000i	0.205436i	−0.994711	+	0.102718i	$0.967246\pi$
$854$	−6.00000	−0.205316
$855$	0	0
$856$	−7.00000	−0.239255
$857$	− 12.0000i	− 0.409912i	−0.978771	−	0.204956i	$-0.934295\pi$
$857$	− 12.0000i	− 0.409912i	0.978771	−	0.204956i	$-0.0657052\pi$
$858$	− 2.00000i	− 0.0682789i
$859$	50.0000	1.70598	0.852989	−	0.521929i	$-0.174787\pi$
$859$	50.0000	1.70598	0.852989	+	0.521929i	$0.174787\pi$
$860$	0	0
$861$	24.0000	0.817918
$862$	− 18.0000i	− 0.613082i
$863$	− 54.0000i	− 1.83818i	−0.394046	−	0.919091i	$-0.628925\pi$
$863$	− 54.0000i	− 1.83818i	0.394046	−	0.919091i	$-0.371075\pi$
$864$	−5.00000	−0.170103
$865$	0	0
$866$	14.0000	0.475739
$867$	8.00000i	0.271694i
$868$	24.0000i	0.814613i
$869$	20.0000	0.678454
$870$	0	0
$871$	−3.00000	−0.101651
$872$	− 15.0000i	− 0.507964i
$873$	− 4.00000i	− 0.135379i
$874$	−1.00000	−0.0338255
$875$	0	0
$876$	−9.00000	−0.304082
$877$	13.0000i	0.438979i	0.975615	+	0.219489i	$0.0704391\pi$
$877$	13.0000i	0.438979i	−0.975615	+	0.219489i	$0.929561\pi$
$878$	− 20.0000i	− 0.674967i
$879$	9.00000	0.303562
$880$	0	0
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	− 4.00000i	− 0.134687i
$883$	− 34.0000i	− 1.14419i	−0.820187	−	0.572096i	$-0.806131\pi$
$883$	− 34.0000i	− 1.14419i	0.820187	−	0.572096i	$-0.193869\pi$
$884$	3.00000	0.100901
$885$	0	0
$886$	−26.0000	−0.873487
$887$	− 2.00000i	− 0.0671534i	−0.999436	−	0.0335767i	$-0.989310\pi$
$887$	− 2.00000i	− 0.0671534i	0.999436	−	0.0335767i	$-0.0106898\pi$
$888$	− 2.00000i	− 0.0671156i
$889$	−54.0000	−1.81110
$890$	0	0
$891$	2.00000	0.0670025
$892$	14.0000i	0.468755i
$893$	8.00000i	0.267710i
$894$	0	0
$895$	0	0
$896$	3.00000	0.100223
$897$	− 1.00000i	− 0.0333890i
$898$	− 10.0000i	− 0.333704i
$899$	−40.0000	−1.33407
$900$	0	0
$901$	−3.00000	−0.0999445
$902$	− 16.0000i	− 0.532742i
$903$	12.0000i	0.399335i
$904$	−14.0000	−0.465633
$905$	0	0
$906$	−2.00000	−0.0664455
$907$	53.0000i	1.75984i	0.475125	+	0.879918i	$0.342403\pi$
$907$	53.0000i	1.75984i	−0.475125	+	0.879918i	$0.657597\pi$
$908$	17.0000i	0.564165i
$909$	4.00000	0.132672
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	1.00000i	0.0331133i
$913$	12.0000i	0.397142i
$914$	7.00000	0.231539
$915$	0	0
$916$	−10.0000	−0.330409
$917$	36.0000i	1.18882i
$918$	− 15.0000i	− 0.495074i
$919$	−5.00000	−0.164935	−0.0824674	−	0.996594i	$-0.526280\pi$
$919$	−5.00000	−0.164935	−0.0824674	+	0.996594i	$0.526280\pi$
$920$	0	0
$921$	12.0000	0.395413
$922$	− 28.0000i	− 0.922131i
$923$	2.00000i	0.0658308i
$924$	6.00000	0.197386
$925$	0	0
$926$	4.00000	0.131448
$927$	12.0000i	0.394132i
$928$	5.00000i	0.164133i
$929$	55.0000	1.80449	0.902246	−	0.431222i	$-0.141918\pi$
$929$	55.0000	1.80449	0.902246	+	0.431222i	$0.141918\pi$
$930$	0	0
$931$	−2.00000	−0.0655474
$932$	− 6.00000i	− 0.196537i
$933$	7.00000i	0.229170i
$934$	2.00000	0.0654420
$935$	0	0
$936$	2.00000	0.0653720
$937$	− 7.00000i	− 0.228680i	−0.993442	−	0.114340i	$-0.963525\pi$
$937$	− 7.00000i	− 0.228680i	0.993442	−	0.114340i	$-0.0364753\pi$
$938$	− 9.00000i	− 0.293860i
$939$	29.0000	0.946379
$940$	0	0
$941$	7.00000	0.228193	0.114097	−	0.993470i	$-0.463603\pi$
$941$	7.00000	0.228193	0.114097	+	0.993470i	$0.463603\pi$
$942$	2.00000i	0.0651635i
$943$	− 8.00000i	− 0.260516i
$944$	−15.0000	−0.488208
$945$	0	0
$946$	8.00000	0.260102
$947$	− 12.0000i	− 0.389948i	−0.980808	−	0.194974i	$-0.937538\pi$
$947$	− 12.0000i	− 0.389948i	0.980808	−	0.194974i	$-0.0624622\pi$
$948$	− 10.0000i	− 0.324785i
$949$	9.00000	0.292152
$950$	0	0
$951$	27.0000	0.875535
$952$	9.00000i	0.291692i
$953$	46.0000i	1.49009i	0.667016	+	0.745043i	$0.267571\pi$
$953$	46.0000i	1.49009i	−0.667016	+	0.745043i	$0.732429\pi$
$954$	−2.00000	−0.0647524
$955$	0	0
$956$	15.0000	0.485135
$957$	10.0000i	0.323254i
$958$	20.0000i	0.646171i
$959$	51.0000	1.64688
$960$	0	0
$961$	33.0000	1.06452
$962$	2.00000i	0.0644826i
$963$	− 14.0000i	− 0.451144i
$964$	8.00000	0.257663
$965$	0	0
$966$	3.00000	0.0965234
$967$	48.0000i	1.54358i	0.635880	+	0.771788i	$0.280637\pi$
$967$	48.0000i	1.54358i	−0.635880	+	0.771788i	$0.719363\pi$
$968$	7.00000i	0.224989i
$969$	−3.00000	−0.0963739
$970$	0	0
$971$	−28.0000	−0.898563	−0.449281	−	0.893390i	$-0.648320\pi$
$971$	−28.0000	−0.898563	−0.449281	+	0.893390i	$0.648320\pi$
$972$	− 16.0000i	− 0.513200i
$973$	0	0
$974$	2.00000	0.0640841
$975$	0	0
$976$	2.00000	0.0640184
$977$	8.00000i	0.255943i	0.991778	+	0.127971i	$0.0408466\pi$
$977$	8.00000i	0.255943i	−0.991778	+	0.127971i	$0.959153\pi$
$978$	− 16.0000i	− 0.511624i
$979$	0	0
$980$	0	0
$981$	30.0000	0.957826
$982$	− 28.0000i	− 0.893516i
$983$	6.00000i	0.191370i	0.995412	+	0.0956851i	$0.0305042\pi$
$983$	6.00000i	0.191370i	−0.995412	+	0.0956851i	$0.969496\pi$
$984$	−8.00000	−0.255031
$985$	0	0
$986$	−15.0000	−0.477697
$987$	− 24.0000i	− 0.763928i
$988$	− 1.00000i	− 0.0318142i
$989$	4.00000	0.127193
$990$	0	0
$991$	−8.00000	−0.254128	−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000	−0.254128	−0.127064	+	0.991894i	$0.540555\pi$
$992$	− 8.00000i	− 0.254000i
$993$	17.0000i	0.539479i
$994$	−6.00000	−0.190308
$995$	0	0
$996$	6.00000	0.190117
$997$	28.0000i	0.886769i	0.896332	+	0.443384i	$0.146222\pi$
$997$	28.0000i	0.886769i	−0.896332	+	0.443384i	$0.853778\pi$
$998$	− 40.0000i	− 1.26618i
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.b.c.799.2		2
5.2	odd	4		950.2.a.b.1.1		1
5.3	odd	4		38.2.a.b.1.1	✓	1
5.4	even	2	inner	950.2.b.c.799.1		2
15.2	even	4		8550.2.a.u.1.1		1
15.8	even	4		342.2.a.d.1.1		1
20.3	even	4		304.2.a.d.1.1		1
20.7	even	4		7600.2.a.h.1.1		1
35.13	even	4		1862.2.a.f.1.1		1
40.3	even	4		1216.2.a.g.1.1		1
40.13	odd	4		1216.2.a.n.1.1		1
55.43	even	4		4598.2.a.a.1.1		1
60.23	odd	4		2736.2.a.w.1.1		1
65.38	odd	4		6422.2.a.b.1.1		1
95.3	even	36		722.2.e.d.389.1		6
95.8	even	12		722.2.c.f.653.1		2
95.13	even	36		722.2.e.d.245.1		6
95.18	even	4		722.2.a.b.1.1		1
95.23	odd	36		722.2.e.c.415.1		6
95.28	odd	36		722.2.e.c.423.1		6
95.33	even	36		722.2.e.d.595.1		6
95.43	odd	36		722.2.e.c.595.1		6
95.48	even	36		722.2.e.d.423.1		6
95.53	even	36		722.2.e.d.415.1		6
95.63	odd	36		722.2.e.c.245.1		6
95.68	odd	12		722.2.c.d.653.1		2
95.73	odd	36		722.2.e.c.389.1		6
95.78	even	36		722.2.e.d.99.1		6
95.83	odd	12		722.2.c.d.429.1		2
95.88	even	12		722.2.c.f.429.1		2
95.93	odd	36		722.2.e.c.99.1		6
285.113	odd	4		6498.2.a.y.1.1		1
380.303	odd	4		5776.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.a.b.1.1	✓	1	5.3	odd	4
304.2.a.d.1.1		1	20.3	even	4
342.2.a.d.1.1		1	15.8	even	4
722.2.a.b.1.1		1	95.18	even	4
722.2.c.d.429.1		2	95.83	odd	12
722.2.c.d.653.1		2	95.68	odd	12
722.2.c.f.429.1		2	95.88	even	12
722.2.c.f.653.1		2	95.8	even	12
722.2.e.c.99.1		6	95.93	odd	36
722.2.e.c.245.1		6	95.63	odd	36
722.2.e.c.389.1		6	95.73	odd	36
722.2.e.c.415.1		6	95.23	odd	36
722.2.e.c.423.1		6	95.28	odd	36
722.2.e.c.595.1		6	95.43	odd	36
722.2.e.d.99.1		6	95.78	even	36
722.2.e.d.245.1		6	95.13	even	36
722.2.e.d.389.1		6	95.3	even	36
722.2.e.d.415.1		6	95.53	even	36
722.2.e.d.423.1		6	95.48	even	36
722.2.e.d.595.1		6	95.33	even	36
950.2.a.b.1.1		1	5.2	odd	4
950.2.b.c.799.1		2	5.4	even	2	inner
950.2.b.c.799.2		2	1.1	even	1	trivial
1216.2.a.g.1.1		1	40.3	even	4
1216.2.a.n.1.1		1	40.13	odd	4
1862.2.a.f.1.1		1	35.13	even	4
2736.2.a.w.1.1		1	60.23	odd	4
4598.2.a.a.1.1		1	55.43	even	4
5776.2.a.d.1.1		1	380.303	odd	4
6422.2.a.b.1.1		1	65.38	odd	4
6498.2.a.y.1.1		1	285.113	odd	4
7600.2.a.h.1.1		1	20.7	even	4
8550.2.a.u.1.1		1	15.2	even	4

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +3.00000i q^{7} -1.00000i q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +3.00000i q^{7} -1.00000i q^{8} +2.00000 q^{9} +2.00000 q^{11} -1.00000i q^{12} +1.00000i q^{13} -3.00000 q^{14} +1.00000 q^{16} +3.00000i q^{17} +2.00000i q^{18} +1.00000 q^{19} -3.00000 q^{21} +2.00000i q^{22} +1.00000i q^{23} +1.00000 q^{24} -1.00000 q^{26} +5.00000i q^{27} -3.00000i q^{28} +5.00000 q^{29} -8.00000 q^{31} +1.00000i q^{32} +2.00000i q^{33} -3.00000 q^{34} -2.00000 q^{36} -2.00000i q^{37} +1.00000i q^{38} -1.00000 q^{39} -8.00000 q^{41} -3.00000i q^{42} -4.00000i q^{43} -2.00000 q^{44} -1.00000 q^{46} +8.00000i q^{47} +1.00000i q^{48} -2.00000 q^{49} -3.00000 q^{51} -1.00000i q^{52} +1.00000i q^{53} -5.00000 q^{54} +3.00000 q^{56} +1.00000i q^{57} +5.00000i q^{58} -15.0000 q^{59} +2.00000 q^{61} -8.00000i q^{62} +6.00000i q^{63} -1.00000 q^{64} -2.00000 q^{66} +3.00000i q^{67} -3.00000i q^{68} -1.00000 q^{69} +2.00000 q^{71} -2.00000i q^{72} -9.00000i q^{73} +2.00000 q^{74} -1.00000 q^{76} +6.00000i q^{77} -1.00000i q^{78} +10.0000 q^{79} +1.00000 q^{81} -8.00000i q^{82} +6.00000i q^{83} +3.00000 q^{84} +4.00000 q^{86} +5.00000i q^{87} -2.00000i q^{88} -3.00000 q^{91} -1.00000i q^{92} -8.00000i q^{93} -8.00000 q^{94} -1.00000 q^{96} -2.00000i q^{97} -2.00000i q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 - 2 * q^6 + 4 * q^9	\( 2 q - 2 q^{4} - 2 q^{6} + 4 q^{9} + 4 q^{11} - 6 q^{14} + 2 q^{16} + 2 q^{19} - 6 q^{21} + 2 q^{24} - 2 q^{26} + 10 q^{29} - 16 q^{31} - 6 q^{34} - 4 q^{36} - 2 q^{39} - 16 q^{41} - 4 q^{44} - 2 q^{46} - 4 q^{49} - 6 q^{51} - 10 q^{54} + 6 q^{56} - 30 q^{59} + 4 q^{61} - 2 q^{64} - 4 q^{66} - 2 q^{69} + 4 q^{71} + 4 q^{74} - 2 q^{76} + 20 q^{79} + 2 q^{81} + 6 q^{84} + 8 q^{86} - 6 q^{91} - 16 q^{94} - 2 q^{96} + 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 - 2 * q^6 + 4 * q^9 + 4 * q^11 - 6 * q^14 + 2 * q^16 + 2 * q^19 - 6 * q^21 + 2 * q^24 - 2 * q^26 + 10 * q^29 - 16 * q^31 - 6 * q^34 - 4 * q^36 - 2 * q^39 - 16 * q^41 - 4 * q^44 - 2 * q^46 - 4 * q^49 - 6 * q^51 - 10 * q^54 + 6 * q^56 - 30 * q^59 + 4 * q^61 - 2 * q^64 - 4 * q^66 - 2 * q^69 + 4 * q^71 + 4 * q^74 - 2 * q^76 + 20 * q^79 + 2 * q^81 + 6 * q^84 + 8 * q^86 - 6 * q^91 - 16 * q^94 - 2 * q^96 + 8 * q^99

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