LMFDB - Embedded newform 975.2.c.i.274.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(274,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("975.274");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.3
Root			$1.40680 + 0.144584i$ of defining polynomial
Character	$\chi$	$=$	975.274
Dual form			975.2.c.i.274.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.289169i q^{2} +1.00000i q^{3} +1.91638 q^{4} +0.289169 q^{6} +4.91638i q^{7} -1.13249i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.289169i q^{2} +1.00000i q^{3} +1.91638 q^{4} +0.289169 q^{6} +4.91638i q^{7} -1.13249i q^{8} -1.00000 q^{9} +4.91638 q^{11} +1.91638i q^{12} -1.00000i q^{13} +1.42166 q^{14} +3.50528 q^{16} -4.33804i q^{17} +0.289169i q^{18} -2.57834 q^{19} -4.91638 q^{21} -1.42166i q^{22} +6.33804i q^{23} +1.13249 q^{24} -0.289169 q^{26} -1.00000i q^{27} +9.42166i q^{28} -6.00000 q^{29} +1.42166 q^{31} -3.27861i q^{32} +4.91638i q^{33} -1.25443 q^{34} -1.91638 q^{36} +9.49472i q^{37} +0.745574i q^{38} +1.00000 q^{39} +4.33804 q^{41} +1.42166i q^{42} +1.15667i q^{43} +9.42166 q^{44} +1.83276 q^{46} -5.42166i q^{47} +3.50528i q^{48} -17.1708 q^{49} +4.33804 q^{51} -1.91638i q^{52} +0.338044i q^{53} -0.289169 q^{54} +5.56777 q^{56} -2.57834i q^{57} +1.73501i q^{58} +11.2544 q^{59} -10.1708 q^{61} -0.411100i q^{62} -4.91638i q^{63} +6.06249 q^{64} +1.42166 q^{66} -7.25443i q^{67} -8.31335i q^{68} -6.33804 q^{69} +0.916382 q^{71} +1.13249i q^{72} +3.15667i q^{73} +2.74557 q^{74} -4.94108 q^{76} +24.1708i q^{77} -0.289169i q^{78} +3.49472 q^{79} +1.00000 q^{81} -1.25443i q^{82} -11.2544i q^{83} -9.42166 q^{84} +0.334474 q^{86} -6.00000i q^{87} -5.56777i q^{88} +0.338044 q^{89} +4.91638 q^{91} +12.1461i q^{92} +1.42166i q^{93} -1.56777 q^{94} +3.27861 q^{96} -12.3380i q^{97} +4.96526i q^{98} -4.91638 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 16 q^{4} - 6 q^{9}+O(q^{10}) $ 6 * q - 16 * q^4 - 6 * q^9	$ 6 q - 16 q^{4} - 6 q^{9} + 2 q^{11} + 12 q^{14} + 52 q^{16} - 12 q^{19} - 2 q^{21} + 12 q^{24} - 36 q^{29} + 12 q^{31} + 44 q^{34} + 16 q^{36} + 6 q^{39} + 2 q^{41} + 60 q^{44} - 44 q^{46} - 24 q^{49} + 2 q^{51} - 32 q^{56} + 16 q^{59} + 18 q^{61} - 60 q^{64} + 12 q^{66} - 14 q^{69} - 22 q^{71} + 68 q^{74} + 8 q^{76} - 10 q^{79} + 6 q^{81} - 60 q^{84} + 112 q^{86} - 22 q^{89} + 2 q^{91} + 56 q^{94} - 44 q^{96} - 2 q^{99}+O(q^{100}) $ 6 * q - 16 * q^4 - 6 * q^9 + 2 * q^11 + 12 * q^14 + 52 * q^16 - 12 * q^19 - 2 * q^21 + 12 * q^24 - 36 * q^29 + 12 * q^31 + 44 * q^34 + 16 * q^36 + 6 * q^39 + 2 * q^41 + 60 * q^44 - 44 * q^46 - 24 * q^49 + 2 * q^51 - 32 * q^56 + 16 * q^59 + 18 * q^61 - 60 * q^64 + 12 * q^66 - 14 * q^69 - 22 * q^71 + 68 * q^74 + 8 * q^76 - 10 * q^79 + 6 * q^81 - 60 * q^84 + 112 * q^86 - 22 * q^89 + 2 * q^91 + 56 * q^94 - 44 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	− 0.289169i	− 0.204473i	−0.994760	−	0.102237i	$-0.967400\pi$
$2$	− 0.289169i	− 0.204473i	0.994760	−	0.102237i	$-0.0325999\pi$
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	1.91638	0.958191
$5$	0	0
$5$	0	0
$6$	0.289169	0.118053
$7$	4.91638i	1.85822i	0.369807	+	0.929109i	$0.379424\pi$
$7$	4.91638i	1.85822i	−0.369807	+	0.929109i	$0.620576\pi$
$8$	− 1.13249i	− 0.400397i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	4.91638	1.48234	0.741172	−	0.671315i	$-0.234270\pi$
$11$	4.91638	1.48234	0.741172	+	0.671315i	$0.234270\pi$
$12$	1.91638i	0.553212i
$13$	− 1.00000i	− 0.277350i
$13$	− 1.00000i	− 0.277350i
$14$	1.42166	0.379955
$15$	0	0
$16$	3.50528	0.876320
$17$	− 4.33804i	− 1.05213i	−0.850444	−	0.526065i	$-0.823667\pi$
$17$	− 4.33804i	− 1.05213i	0.850444	−	0.526065i	$-0.176333\pi$
$18$	0.289169i	0.0681577i
$19$	−2.57834	−0.591511	−0.295756	−	0.955264i	$-0.595571\pi$
$19$	−2.57834	−0.591511	−0.295756	+	0.955264i	$0.595571\pi$
$20$	0	0
$21$	−4.91638	−1.07284
$22$	− 1.42166i	− 0.303100i
$23$	6.33804i	1.32157i	0.750574	+	0.660787i	$0.229777\pi$
$23$	6.33804i	1.32157i	−0.750574	+	0.660787i	$0.770223\pi$
$24$	1.13249	0.231169
$25$	0	0
$26$	−0.289169	−0.0567106
$27$	− 1.00000i	− 0.192450i
$28$	9.42166i	1.78053i
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	1.42166	0.255338	0.127669	−	0.991817i	$-0.459250\pi$
$31$	1.42166	0.255338	0.127669	+	0.991817i	$0.459250\pi$
$32$	− 3.27861i	− 0.579581i
$33$	4.91638i	0.855832i
$34$	−1.25443	−0.215132
$35$	0	0
$36$	−1.91638	−0.319397
$37$	9.49472i	1.56092i	0.625204	+	0.780461i	$0.285016\pi$
$37$	9.49472i	1.56092i	−0.625204	+	0.780461i	$0.714984\pi$
$38$	0.745574i	0.120948i
$39$	1.00000	0.160128
$40$	0	0
$41$	4.33804	0.677489	0.338744	−	0.940878i	$-0.389998\pi$
$41$	4.33804	0.677489	0.338744	+	0.940878i	$0.389998\pi$
$42$	1.42166i	0.219367i
$43$	1.15667i	0.176391i	0.996103	+	0.0881956i	$0.0281100\pi$
$43$	1.15667i	0.176391i	−0.996103	+	0.0881956i	$0.971890\pi$
$44$	9.42166	1.42037
$45$	0	0
$46$	1.83276	0.270226
$47$	− 5.42166i	− 0.790831i	−0.918502	−	0.395415i	$-0.870601\pi$
$47$	− 5.42166i	− 0.790831i	0.918502	−	0.395415i	$-0.129399\pi$
$48$	3.50528i	0.505944i
$49$	−17.1708	−2.45297
$50$	0	0
$51$	4.33804	0.607448
$52$	− 1.91638i	− 0.265754i
$53$	0.338044i	0.0464340i	0.999730	+	0.0232170i	$0.00739086\pi$
$53$	0.338044i	0.0464340i	−0.999730	+	0.0232170i	$0.992609\pi$
$54$	−0.289169	−0.0393509
$55$	0	0
$56$	5.56777	0.744025
$57$	− 2.57834i	− 0.341509i
$58$	1.73501i	0.227818i
$59$	11.2544	1.46520	0.732601	−	0.680659i	$-0.238306\pi$
$59$	11.2544	1.46520	0.732601	+	0.680659i	$0.238306\pi$
$60$	0	0
$61$	−10.1708	−1.30224	−0.651119	−	0.758975i	$-0.725700\pi$
$61$	−10.1708	−1.30224	−0.651119	+	0.758975i	$0.725700\pi$
$62$	− 0.411100i	− 0.0522098i
$63$	− 4.91638i	− 0.619406i
$64$	6.06249	0.757812
$65$	0	0
$66$	1.42166	0.174995
$67$	− 7.25443i	− 0.886269i	−0.896455	−	0.443135i	$-0.853866\pi$
$67$	− 7.25443i	− 0.886269i	0.896455	−	0.443135i	$-0.146134\pi$
$68$	− 8.31335i	− 1.00814i
$69$	−6.33804	−0.763011
$70$	0	0
$71$	0.916382	0.108754	0.0543772	−	0.998520i	$-0.482683\pi$
$71$	0.916382	0.108754	0.0543772	+	0.998520i	$0.482683\pi$
$72$	1.13249i	0.133466i
$73$	3.15667i	0.369461i	0.982789	+	0.184730i	$0.0591412\pi$
$73$	3.15667i	0.369461i	−0.982789	+	0.184730i	$0.940859\pi$
$74$	2.74557	0.319166
$75$	0	0
$76$	−4.94108	−0.566780
$77$	24.1708i	2.75452i
$78$	− 0.289169i	− 0.0327419i
$79$	3.49472	0.393187	0.196593	−	0.980485i	$-0.437012\pi$
$79$	3.49472	0.393187	0.196593	+	0.980485i	$0.437012\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 1.25443i	− 0.138528i
$83$	− 11.2544i	− 1.23533i	−0.786440	−	0.617667i	$-0.788078\pi$
$83$	− 11.2544i	− 1.23533i	0.786440	−	0.617667i	$-0.211922\pi$
$84$	−9.42166	−1.02799
$85$	0	0
$86$	0.334474	0.0360672
$87$	− 6.00000i	− 0.643268i
$88$	− 5.56777i	− 0.593527i
$89$	0.338044	0.0358326	0.0179163	−	0.999839i	$-0.494297\pi$
$89$	0.338044	0.0358326	0.0179163	+	0.999839i	$0.494297\pi$
$90$	0	0
$91$	4.91638	0.515377
$92$	12.1461i	1.26632i
$93$	1.42166i	0.147420i
$94$	−1.56777	−0.161704
$95$	0	0
$96$	3.27861	0.334621
$97$	− 12.3380i	− 1.25274i	−0.779526	−	0.626369i	$-0.784540\pi$
$97$	− 12.3380i	− 1.25274i	0.779526	−	0.626369i	$-0.215460\pi$
$98$	4.96526i	0.501567i
$99$	−4.91638	−0.494115
$100$	0	0
$101$	10.6761	1.06231	0.531155	−	0.847274i	$-0.321758\pi$
$101$	10.6761	1.06231	0.531155	+	0.847274i	$0.321758\pi$
$102$	− 1.25443i	− 0.124207i
$103$	14.5089i	1.42960i	0.699329	+	0.714800i	$0.253482\pi$
$103$	14.5089i	1.42960i	−0.699329	+	0.714800i	$0.746518\pi$
$104$	−1.13249	−0.111050
$105$	0	0
$106$	0.0977518	0.00949450
$107$	4.17081i	0.403207i	0.979467	+	0.201604i	$0.0646153\pi$
$107$	4.17081i	0.403207i	−0.979467	+	0.201604i	$0.935385\pi$
$108$	− 1.91638i	− 0.184404i
$109$	3.83276	0.367112	0.183556	−	0.983009i	$-0.441239\pi$
$109$	3.83276	0.367112	0.183556	+	0.983009i	$0.441239\pi$
$110$	0	0
$111$	−9.49472	−0.901199
$112$	17.2333i	1.62839i
$113$	0.843326i	0.0793334i	0.999213	+	0.0396667i	$0.0126296\pi$
$113$	0.843326i	0.0793334i	−0.999213	+	0.0396667i	$0.987370\pi$
$114$	−0.745574	−0.0698294
$115$	0	0
$116$	−11.4983	−1.06759
$117$	1.00000i	0.0924500i
$118$	− 3.25443i	− 0.299594i
$119$	21.3275	1.95509
$120$	0	0
$121$	13.1708	1.19735
$122$	2.94108i	0.266273i
$123$	4.33804i	0.391148i
$124$	2.72445	0.244663
$125$	0	0
$126$	−1.42166	−0.126652
$127$	1.83276i	0.162631i	0.996688	+	0.0813157i	$0.0259122\pi$
$127$	1.83276i	0.162631i	−0.996688	+	0.0813157i	$0.974088\pi$
$128$	− 8.31029i	− 0.734533i
$129$	−1.15667	−0.101839
$130$	0	0
$131$	5.83276	0.509611	0.254805	−	0.966992i	$-0.417989\pi$
$131$	5.83276	0.509611	0.254805	+	0.966992i	$0.417989\pi$
$132$	9.42166i	0.820050i
$133$	− 12.6761i	− 1.09916i
$134$	−2.09775	−0.181218
$135$	0	0
$136$	−4.91281	−0.421270
$137$	− 16.5089i	− 1.41045i	−0.708985	−	0.705223i	$-0.750847\pi$
$137$	− 16.5089i	− 1.41045i	0.708985	−	0.705223i	$-0.249153\pi$
$138$	1.83276i	0.156015i
$139$	−7.49472	−0.635694	−0.317847	−	0.948142i	$-0.602960\pi$
$139$	−7.49472	−0.635694	−0.317847	+	0.948142i	$0.602960\pi$
$140$	0	0
$141$	5.42166	0.456586
$142$	− 0.264989i	− 0.0222374i
$143$	− 4.91638i	− 0.411128i
$144$	−3.50528	−0.292107
$145$	0	0
$146$	0.912811	0.0755448
$147$	− 17.1708i	− 1.41622i
$148$	18.1955i	1.49566i
$149$	−20.4842	−1.67813	−0.839064	−	0.544033i	$-0.816897\pi$
$149$	−20.4842	−1.67813	−0.839064	+	0.544033i	$0.816897\pi$
$150$	0	0
$151$	−16.4111	−1.33552	−0.667758	−	0.744378i	$-0.732746\pi$
$151$	−16.4111	−1.33552	−0.667758	+	0.744378i	$0.732746\pi$
$152$	2.91995i	0.236839i
$153$	4.33804i	0.350710i
$154$	6.98944	0.563225
$155$	0	0
$156$	1.91638	0.153433
$157$	− 21.6655i	− 1.72910i	−0.502549	−	0.864549i	$-0.667604\pi$
$157$	− 21.6655i	− 1.72910i	0.502549	−	0.864549i	$-0.332396\pi$
$158$	− 1.01056i	− 0.0803961i
$159$	−0.338044	−0.0268087
$160$	0	0
$161$	−31.1602	−2.45577
$162$	− 0.289169i	− 0.0227192i
$163$	− 6.07306i	− 0.475678i	−0.971305	−	0.237839i	$-0.923561\pi$
$163$	− 6.07306i	− 0.475678i	0.971305	−	0.237839i	$-0.0764391\pi$
$164$	8.31335	0.649163
$165$	0	0
$166$	−3.25443	−0.252592
$167$	− 0.745574i	− 0.0576942i	−0.999584	−	0.0288471i	$-0.990816\pi$
$167$	− 0.745574i	− 0.0576942i	0.999584	−	0.0288471i	$-0.00918360\pi$
$168$	5.56777i	0.429563i
$169$	−1.00000	−0.0769231
$170$	0	0
$171$	2.57834	0.197170
$172$	2.21663i	0.169016i
$173$	− 0.843326i	− 0.0641169i	−0.999486	−	0.0320584i	$-0.989794\pi$
$173$	− 0.843326i	− 0.0641169i	0.999486	−	0.0320584i	$-0.0102063\pi$
$174$	−1.73501	−0.131531
$175$	0	0
$176$	17.2333	1.29901
$177$	11.2544i	0.845934i
$178$	− 0.0977518i	− 0.00732681i
$179$	18.9894	1.41934	0.709669	−	0.704536i	$-0.248845\pi$
$179$	18.9894	1.41934	0.709669	+	0.704536i	$0.248845\pi$
$180$	0	0
$181$	17.4947	1.30037	0.650186	−	0.759775i	$-0.274691\pi$
$181$	17.4947	1.30037	0.650186	+	0.759775i	$0.274691\pi$
$182$	− 1.42166i	− 0.105381i
$183$	− 10.1708i	− 0.751848i
$184$	7.17780	0.529154
$185$	0	0
$186$	0.411100	0.0301433
$187$	− 21.3275i	− 1.55962i
$188$	− 10.3900i	− 0.757767i
$189$	4.91638	0.357614
$190$	0	0
$191$	−22.5089	−1.62868	−0.814342	−	0.580386i	$-0.802902\pi$
$191$	−22.5089	−1.62868	−0.814342	+	0.580386i	$0.802902\pi$
$192$	6.06249i	0.437523i
$193$	− 2.65139i	− 0.190851i	−0.995437	−	0.0954257i	$-0.969579\pi$
$193$	− 2.65139i	− 0.190851i	0.995437	−	0.0954257i	$-0.0304212\pi$
$194$	−3.56777	−0.256151
$195$	0	0
$196$	−32.9058	−2.35042
$197$	− 12.9894i	− 0.925459i	−0.886500	−	0.462730i	$-0.846870\pi$
$197$	− 12.9894i	− 0.925459i	0.886500	−	0.462730i	$-0.153130\pi$
$198$	1.42166i	0.101033i
$199$	2.84333	0.201558	0.100779	−	0.994909i	$-0.467866\pi$
$199$	2.84333	0.201558	0.100779	+	0.994909i	$0.467866\pi$
$200$	0	0
$201$	7.25443	0.511688
$202$	− 3.08719i	− 0.217214i
$203$	− 29.4983i	− 2.07037i
$204$	8.31335	0.582051
$205$	0	0
$206$	4.19550	0.292315
$207$	− 6.33804i	− 0.440525i
$208$	− 3.50528i	− 0.243048i
$209$	−12.6761	−0.876823
$210$	0	0
$211$	6.31335	0.434629	0.217314	−	0.976102i	$-0.430270\pi$
$211$	6.31335	0.434629	0.217314	+	0.976102i	$0.430270\pi$
$212$	0.647822i	0.0444926i
$213$	0.916382i	0.0627894i
$214$	1.20607	0.0824450
$215$	0	0
$216$	−1.13249	−0.0770565
$217$	6.98944i	0.474474i
$218$	− 1.10831i	− 0.0750645i
$219$	−3.15667	−0.213308
$220$	0	0
$221$	−4.33804	−0.291808
$222$	2.74557i	0.184271i
$223$	− 19.2544i	− 1.28937i	−0.764448	−	0.644686i	$-0.776988\pi$
$223$	− 19.2544i	− 1.28937i	0.764448	−	0.644686i	$-0.223012\pi$
$224$	16.1189	1.07699
$225$	0	0
$226$	0.243863	0.0162215
$227$	− 13.0872i	− 0.868627i	−0.900762	−	0.434314i	$-0.856991\pi$
$227$	− 13.0872i	− 0.868627i	0.900762	−	0.434314i	$-0.143009\pi$
$228$	− 4.94108i	− 0.327231i
$229$	24.5089	1.61959	0.809795	−	0.586713i	$-0.199578\pi$
$229$	24.5089	1.61959	0.809795	+	0.586713i	$0.199578\pi$
$230$	0	0
$231$	−24.1708	−1.59032
$232$	6.79497i	0.446111i
$233$	− 8.33804i	− 0.546243i	−0.961979	−	0.273122i	$-0.911944\pi$
$233$	− 8.33804i	− 0.546243i	0.961979	−	0.273122i	$-0.0880562\pi$
$234$	0.289169	0.0189035
$235$	0	0
$236$	21.5678	1.40394
$237$	3.49472i	0.227006i
$238$	− 6.16724i	− 0.399763i
$239$	−8.91638	−0.576753	−0.288376	−	0.957517i	$-0.593115\pi$
$239$	−8.91638	−0.576753	−0.288376	+	0.957517i	$0.593115\pi$
$240$	0	0
$241$	−6.00000	−0.386494	−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000	−0.386494	−0.193247	+	0.981150i	$0.561902\pi$
$242$	− 3.80858i	− 0.244825i
$243$	1.00000i	0.0641500i
$244$	−19.4911	−1.24779
$245$	0	0
$246$	1.25443	0.0799793
$247$	2.57834i	0.164056i
$248$	− 1.61003i	− 0.102237i
$249$	11.2544	0.713220
$250$	0	0
$251$	−6.31335	−0.398495	−0.199248	−	0.979949i	$-0.563850\pi$
$251$	−6.31335	−0.398495	−0.199248	+	0.979949i	$0.563850\pi$
$252$	− 9.42166i	− 0.593509i
$253$	31.1602i	1.95903i
$254$	0.529977	0.0332537
$255$	0	0
$256$	9.72191	0.607619
$257$	− 11.1567i	− 0.695934i	−0.937507	−	0.347967i	$-0.886872\pi$
$257$	− 11.1567i	− 0.695934i	0.937507	−	0.347967i	$-0.113128\pi$
$258$	0.334474i	0.0208234i
$259$	−46.6797	−2.90053
$260$	0	0
$261$	6.00000	0.371391
$262$	− 1.68665i	− 0.104202i
$263$	− 8.00000i	− 0.493301i	−0.969104	−	0.246651i	$-0.920670\pi$
$263$	− 8.00000i	− 0.493301i	0.969104	−	0.246651i	$-0.0793300\pi$
$264$	5.56777	0.342673
$265$	0	0
$266$	−3.66553	−0.224748
$267$	0.338044i	0.0206880i
$268$	− 13.9022i	− 0.849215i
$269$	−18.6761	−1.13870	−0.569351	−	0.822095i	$-0.692805\pi$
$269$	−18.6761	−1.13870	−0.569351	+	0.822095i	$0.692805\pi$
$270$	0	0
$271$	6.57834	0.399606	0.199803	−	0.979836i	$-0.435970\pi$
$271$	6.57834	0.399606	0.199803	+	0.979836i	$0.435970\pi$
$272$	− 15.2061i	− 0.922003i
$273$	4.91638i	0.297553i
$274$	−4.77384	−0.288398
$275$	0	0
$276$	−12.1461	−0.731110
$277$	25.6655i	1.54209i	0.636779	+	0.771046i	$0.280266\pi$
$277$	25.6655i	1.54209i	−0.636779	+	0.771046i	$0.719734\pi$
$278$	2.16724i	0.129982i
$279$	−1.42166	−0.0851127
$280$	0	0
$281$	3.15667	0.188311	0.0941557	−	0.995557i	$-0.469985\pi$
$281$	3.15667	0.188311	0.0941557	+	0.995557i	$0.469985\pi$
$282$	− 1.56777i	− 0.0933596i
$283$	3.47002i	0.206271i	0.994667	+	0.103136i	$0.0328876\pi$
$283$	3.47002i	0.206271i	−0.994667	+	0.103136i	$0.967112\pi$
$284$	1.75614	0.104208
$285$	0	0
$286$	−1.42166	−0.0840647
$287$	21.3275i	1.25892i
$288$	3.27861i	0.193194i
$289$	−1.81863	−0.106978
$290$	0	0
$291$	12.3380	0.723269
$292$	6.04939i	0.354014i
$293$	− 28.6550i	− 1.67404i	−0.547172	−	0.837020i	$-0.684296\pi$
$293$	− 28.6550i	− 1.67404i	0.547172	−	0.837020i	$-0.315704\pi$
$294$	−4.96526	−0.289580
$295$	0	0
$296$	10.7527	0.624989
$297$	− 4.91638i	− 0.285277i
$298$	5.92337i	0.343132i
$299$	6.33804	0.366539
$300$	0	0
$301$	−5.68665	−0.327773
$302$	4.74557i	0.273077i
$303$	10.6761i	0.613325i
$304$	−9.03780	−0.518353
$305$	0	0
$306$	1.25443	0.0717108
$307$	− 1.92694i	− 0.109977i	−0.998487	−	0.0549883i	$-0.982488\pi$
$307$	− 1.92694i	− 0.109977i	0.998487	−	0.0549883i	$-0.0175121\pi$
$308$	46.3205i	2.63935i
$309$	−14.5089	−0.825380
$310$	0	0
$311$	−29.9789	−1.69995	−0.849973	−	0.526826i	$-0.823382\pi$
$311$	−29.9789	−1.69995	−0.849973	+	0.526826i	$0.823382\pi$
$312$	− 1.13249i	− 0.0641149i
$313$	16.3133i	0.922085i	0.887378	+	0.461042i	$0.152524\pi$
$313$	16.3133i	0.922085i	−0.887378	+	0.461042i	$0.847476\pi$
$314$	−6.26499	−0.353554
$315$	0	0
$316$	6.69721	0.376748
$317$	30.6761i	1.72294i	0.507808	+	0.861470i	$0.330456\pi$
$317$	30.6761i	1.72294i	−0.507808	+	0.861470i	$0.669544\pi$
$318$	0.0977518i	0.00548165i
$319$	−29.4983	−1.65159
$320$	0	0
$321$	−4.17081	−0.232792
$322$	9.01056i	0.502139i
$323$	11.1849i	0.622347i
$324$	1.91638	0.106466
$325$	0	0
$326$	−1.75614	−0.0972634
$327$	3.83276i	0.211952i
$328$	− 4.91281i	− 0.271265i
$329$	26.6550	1.46954
$330$	0	0
$331$	−10.0978	−0.555023	−0.277511	−	0.960722i	$-0.589510\pi$
$331$	−10.0978	−0.555023	−0.277511	+	0.960722i	$0.589510\pi$
$332$	− 21.5678i	− 1.18369i
$333$	− 9.49472i	− 0.520307i
$334$	−0.215597	−0.0117969
$335$	0	0
$336$	−17.2333	−0.940154
$337$	− 1.32391i	− 0.0721180i	−0.999350	−	0.0360590i	$-0.988520\pi$
$337$	− 1.32391i	− 0.0721180i	0.999350	−	0.0360590i	$-0.0114804\pi$
$338$	0.289169i	0.0157287i
$339$	−0.843326	−0.0458032
$340$	0	0
$341$	6.98944	0.378499
$342$	− 0.745574i	− 0.0403160i
$343$	− 50.0036i	− 2.69994i
$344$	1.30993	0.0706265
$345$	0	0
$346$	−0.243863	−0.0131102
$347$	− 7.49472i	− 0.402338i	−0.979557	−	0.201169i	$-0.935526\pi$
$347$	− 7.49472i	− 0.402338i	0.979557	−	0.201169i	$-0.0644740\pi$
$348$	− 11.4983i	− 0.616373i
$349$	22.1461	1.18545	0.592727	−	0.805403i	$-0.298051\pi$
$349$	22.1461	1.18545	0.592727	+	0.805403i	$0.298051\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	− 16.1189i	− 0.859139i
$353$	− 4.50885i	− 0.239982i	−0.992775	−	0.119991i	$-0.961713\pi$
$353$	− 4.50885i	− 0.239982i	0.992775	−	0.119991i	$-0.0382866\pi$
$354$	3.25443	0.172971
$355$	0	0
$356$	0.647822	0.0343345
$357$	21.3275i	1.12877i
$358$	− 5.49115i	− 0.290216i
$359$	20.4111	1.07726	0.538628	−	0.842543i	$-0.318943\pi$
$359$	20.4111	1.07726	0.538628	+	0.842543i	$0.318943\pi$
$360$	0	0
$361$	−12.3522	−0.650115
$362$	− 5.05892i	− 0.265891i
$363$	13.1708i	0.691288i
$364$	9.42166	0.493829
$365$	0	0
$366$	−2.94108	−0.153733
$367$	− 10.3133i	− 0.538352i	−0.963091	−	0.269176i	$-0.913249\pi$
$367$	− 10.3133i	− 0.538352i	0.963091	−	0.269176i	$-0.0867514\pi$
$368$	22.2166i	1.15812i
$369$	−4.33804	−0.225830
$370$	0	0
$371$	−1.66196	−0.0862844
$372$	2.72445i	0.141256i
$373$	− 18.6761i	− 0.967011i	−0.875341	−	0.483506i	$-0.839363\pi$
$373$	− 18.6761i	− 0.967011i	0.875341	−	0.483506i	$-0.160637\pi$
$374$	−6.16724	−0.318900
$375$	0	0
$376$	−6.14000	−0.316646
$377$	6.00000i	0.309016i
$378$	− 1.42166i	− 0.0731224i
$379$	28.7527	1.47693	0.738464	−	0.674293i	$-0.235552\pi$
$379$	28.7527	1.47693	0.738464	+	0.674293i	$0.235552\pi$
$380$	0	0
$381$	−1.83276	−0.0938953
$382$	6.50885i	0.333022i
$383$	14.2439i	0.727827i	0.931433	+	0.363914i	$0.118560\pi$
$383$	14.2439i	0.727827i	−0.931433	+	0.363914i	$0.881440\pi$
$384$	8.31029	0.424083
$385$	0	0
$386$	−0.766699	−0.0390240
$387$	− 1.15667i	− 0.0587971i
$388$	− 23.6444i	− 1.20036i
$389$	−34.6761	−1.75815	−0.879074	−	0.476686i	$-0.841838\pi$
$389$	−34.6761	−1.75815	−0.879074	+	0.476686i	$0.841838\pi$
$390$	0	0
$391$	27.4947	1.39047
$392$	19.4458i	0.982163i
$393$	5.83276i	0.294224i
$394$	−3.75614	−0.189231
$395$	0	0
$396$	−9.42166	−0.473456
$397$	7.18137i	0.360423i	0.983628	+	0.180211i	$0.0576782\pi$
$397$	7.18137i	0.360423i	−0.983628	+	0.180211i	$0.942322\pi$
$398$	− 0.822200i	− 0.0412132i
$399$	12.6761	0.634598
$400$	0	0
$401$	37.8610	1.89069	0.945345	−	0.326072i	$-0.105725\pi$
$401$	37.8610	1.89069	0.945345	+	0.326072i	$0.105725\pi$
$402$	− 2.09775i	− 0.104626i
$403$	− 1.42166i	− 0.0708181i
$404$	20.4595	1.01790
$405$	0	0
$406$	−8.52998	−0.423336
$407$	46.6797i	2.31382i
$408$	− 4.91281i	− 0.243220i
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	0	0
$411$	16.5089	0.814322
$412$	27.8045i	1.36983i
$413$	55.3311i	2.72266i
$414$	−1.83276	−0.0900754
$415$	0	0
$416$	−3.27861	−0.160747
$417$	− 7.49472i	− 0.367018i
$418$	3.66553i	0.179287i
$419$	33.4983	1.63650	0.818249	−	0.574864i	$-0.194945\pi$
$419$	33.4983	1.63650	0.818249	+	0.574864i	$0.194945\pi$
$420$	0	0
$421$	13.5194	0.658896	0.329448	−	0.944174i	$-0.393137\pi$
$421$	13.5194	0.658896	0.329448	+	0.944174i	$0.393137\pi$
$422$	− 1.82562i	− 0.0888699i
$423$	5.42166i	0.263610i
$424$	0.382833	0.0185920
$425$	0	0
$426$	0.264989	0.0128387
$427$	− 50.0036i	− 2.41984i
$428$	7.99286i	0.386349i
$429$	4.91638	0.237365
$430$	0	0
$431$	12.4111	0.597822	0.298911	−	0.954281i	$-0.403377\pi$
$431$	12.4111	0.597822	0.298911	+	0.954281i	$0.403377\pi$
$432$	− 3.50528i	− 0.168648i
$433$	17.3239i	0.832534i	0.909242	+	0.416267i	$0.136662\pi$
$433$	17.3239i	0.832534i	−0.909242	+	0.416267i	$0.863338\pi$
$434$	2.02113	0.0970171
$435$	0	0
$436$	7.34504	0.351763
$437$	− 16.3416i	− 0.781725i
$438$	0.912811i	0.0436158i
$439$	−0.651393	−0.0310893	−0.0155446	−	0.999879i	$-0.504948\pi$
$439$	−0.651393	−0.0310893	−0.0155446	+	0.999879i	$0.504948\pi$
$440$	0	0
$441$	17.1708	0.817658
$442$	1.25443i	0.0596670i
$443$	8.84690i	0.420329i	0.977666	+	0.210164i	$0.0673999\pi$
$443$	8.84690i	0.420329i	−0.977666	+	0.210164i	$0.932600\pi$
$444$	−18.1955	−0.863520
$445$	0	0
$446$	−5.56777	−0.263642
$447$	− 20.4842i	− 0.968867i
$448$	29.8055i	1.40818i
$449$	−4.33804	−0.204725	−0.102362	−	0.994747i	$-0.532640\pi$
$449$	−4.33804	−0.204725	−0.102362	+	0.994747i	$0.532640\pi$
$450$	0	0
$451$	21.3275	1.00427
$452$	1.61613i	0.0760166i
$453$	− 16.4111i	− 0.771061i
$454$	−3.78440	−0.177611
$455$	0	0
$456$	−2.91995	−0.136739
$457$	15.3275i	0.716989i	0.933532	+	0.358495i	$0.116710\pi$
$457$	15.3275i	0.716989i	−0.933532	+	0.358495i	$0.883290\pi$
$458$	− 7.08719i	− 0.331163i
$459$	−4.33804	−0.202483
$460$	0	0
$461$	−11.8575	−0.552257	−0.276128	−	0.961121i	$-0.589052\pi$
$461$	−11.8575	−0.552257	−0.276128	+	0.961121i	$0.589052\pi$
$462$	6.98944i	0.325178i
$463$	26.4147i	1.22759i	0.789464	+	0.613797i	$0.210359\pi$
$463$	26.4147i	1.22759i	−0.789464	+	0.613797i	$0.789641\pi$
$464$	−21.0317	−0.976372
$465$	0	0
$466$	−2.41110	−0.111692
$467$	− 33.6691i	− 1.55802i	−0.627012	−	0.779010i	$-0.715722\pi$
$467$	− 33.6691i	− 1.55802i	0.627012	−	0.779010i	$-0.284278\pi$
$468$	1.91638i	0.0885848i
$469$	35.6655	1.64688
$470$	0	0
$471$	21.6655	0.998295
$472$	− 12.7456i	− 0.586663i
$473$	5.68665i	0.261473i
$474$	1.01056	0.0464167
$475$	0	0
$476$	40.8716	1.87335
$477$	− 0.338044i	− 0.0154780i
$478$	2.57834i	0.117930i
$479$	−10.7491	−0.491141	−0.245570	−	0.969379i	$-0.578975\pi$
$479$	−10.7491	−0.491141	−0.245570	+	0.969379i	$0.578975\pi$
$480$	0	0
$481$	9.49472	0.432922
$482$	1.73501i	0.0790276i
$483$	− 31.1602i	− 1.41784i
$484$	25.2403	1.14729
$485$	0	0
$486$	0.289169	0.0131170
$487$	22.7491i	1.03086i	0.856931	+	0.515431i	$0.172368\pi$
$487$	22.7491i	1.03086i	−0.856931	+	0.515431i	$0.827632\pi$
$488$	11.5184i	0.521413i
$489$	6.07306	0.274633
$490$	0	0
$491$	−17.6867	−0.798187	−0.399094	−	0.916910i	$-0.630675\pi$
$491$	−17.6867	−0.798187	−0.399094	+	0.916910i	$0.630675\pi$
$492$	8.31335i	0.374795i
$493$	26.0283i	1.17225i
$494$	0.745574	0.0335450
$495$	0	0
$496$	4.98333	0.223758
$497$	4.50528i	0.202089i
$498$	− 3.25443i	− 0.145834i
$499$	−19.9305	−0.892212	−0.446106	−	0.894980i	$-0.647190\pi$
$499$	−19.9305	−0.892212	−0.446106	+	0.894980i	$0.647190\pi$
$500$	0	0
$501$	0.745574	0.0333098
$502$	1.82562i	0.0814815i
$503$	− 33.3522i	− 1.48710i	−0.668680	−	0.743550i	$-0.733140\pi$
$503$	− 33.3522i	− 1.48710i	0.668680	−	0.743550i	$-0.266860\pi$
$504$	−5.56777	−0.248008
$505$	0	0
$506$	9.01056	0.400568
$507$	− 1.00000i	− 0.0444116i
$508$	3.51227i	0.155832i
$509$	−13.8363	−0.613285	−0.306642	−	0.951825i	$-0.599206\pi$
$509$	−13.8363	−0.613285	−0.306642	+	0.951825i	$0.599206\pi$
$510$	0	0
$511$	−15.5194	−0.686538
$512$	− 19.4319i	− 0.858775i
$513$	2.57834i	0.113836i
$514$	−3.22616	−0.142300
$515$	0	0
$516$	−2.21663	−0.0975817
$517$	− 26.6550i	− 1.17228i
$518$	13.4983i	0.593081i
$519$	0.843326	0.0370179
$520$	0	0
$521$	−23.3522	−1.02308	−0.511539	−	0.859260i	$-0.670924\pi$
$521$	−23.3522	−1.02308	−0.511539	+	0.859260i	$0.670924\pi$
$522$	− 1.73501i	− 0.0759394i
$523$	4.00000i	0.174908i	0.996169	+	0.0874539i	$0.0278730\pi$
$523$	4.00000i	0.174908i	−0.996169	+	0.0874539i	$0.972127\pi$
$524$	11.1778	0.488304
$525$	0	0
$526$	−2.31335	−0.100867
$527$	− 6.16724i	− 0.268649i
$528$	17.2333i	0.749983i
$529$	−17.1708	−0.746557
$530$	0	0
$531$	−11.2544	−0.488400
$532$	− 24.2922i	− 1.05320i
$533$	− 4.33804i	− 0.187902i
$534$	0.0977518	0.00423014
$535$	0	0
$536$	−8.21560	−0.354860
$537$	18.9894i	0.819455i
$538$	5.40054i	0.232834i
$539$	−84.4182	−3.63615
$540$	0	0
$541$	16.1744	0.695391	0.347695	−	0.937608i	$-0.386964\pi$
$541$	16.1744	0.695391	0.347695	+	0.937608i	$0.386964\pi$
$542$	− 1.90225i	− 0.0817086i
$543$	17.4947i	0.750770i
$544$	−14.2227	−0.609795
$545$	0	0
$546$	1.42166	0.0608416
$547$	9.68665i	0.414171i	0.978323	+	0.207086i	$0.0663979\pi$
$547$	9.68665i	0.414171i	−0.978323	+	0.207086i	$0.933602\pi$
$548$	− 31.6373i	− 1.35148i
$549$	10.1708	0.434079
$550$	0	0
$551$	15.4700	0.659045
$552$	7.17780i	0.305507i
$553$	17.1814i	0.730626i
$554$	7.42166	0.315316
$555$	0	0
$556$	−14.3627	−0.609116
$557$	0.647822i	0.0274491i	0.999906	+	0.0137246i	$0.00436880\pi$
$557$	0.647822i	0.0274491i	−0.999906	+	0.0137246i	$0.995631\pi$
$558$	0.411100i	0.0174033i
$559$	1.15667	0.0489221
$560$	0	0
$561$	21.3275	0.900447
$562$	− 0.912811i	− 0.0385046i
$563$	16.3169i	0.687676i	0.939029	+	0.343838i	$0.111727\pi$
$563$	16.3169i	0.687676i	−0.939029	+	0.343838i	$0.888273\pi$
$564$	10.3900	0.437497
$565$	0	0
$566$	1.00342	0.0421769
$567$	4.91638i	0.206469i
$568$	− 1.03780i	− 0.0435450i
$569$	−44.6550	−1.87203	−0.936017	−	0.351956i	$-0.885517\pi$
$569$	−44.6550	−1.87203	−0.936017	+	0.351956i	$0.885517\pi$
$570$	0	0
$571$	−6.67252	−0.279236	−0.139618	−	0.990205i	$-0.544587\pi$
$571$	−6.67252	−0.279236	−0.139618	+	0.990205i	$0.544587\pi$
$572$	− 9.42166i	− 0.393940i
$573$	− 22.5089i	− 0.940321i
$574$	6.16724	0.257415
$575$	0	0
$576$	−6.06249	−0.252604
$577$	15.3275i	0.638091i	0.947739	+	0.319046i	$0.103362\pi$
$577$	15.3275i	0.638091i	−0.947739	+	0.319046i	$0.896638\pi$
$578$	0.525891i	0.0218742i
$579$	2.65139	0.110188
$580$	0	0
$581$	55.3311	2.29552
$582$	− 3.56777i	− 0.147889i
$583$	1.66196i	0.0688312i
$584$	3.57492	0.147931
$585$	0	0
$586$	−8.28611	−0.342296
$587$	12.2650i	0.506230i	0.967436	+	0.253115i	$0.0814551\pi$
$587$	12.2650i	0.506230i	−0.967436	+	0.253115i	$0.918545\pi$
$588$	− 32.9058i	− 1.35701i
$589$	−3.66553	−0.151035
$590$	0	0
$591$	12.9894	0.534314
$592$	33.2817i	1.36787i
$593$	5.85389i	0.240390i	0.992750	+	0.120195i	$0.0383520\pi$
$593$	5.85389i	0.240390i	−0.992750	+	0.120195i	$0.961648\pi$
$594$	−1.42166	−0.0583315
$595$	0	0
$596$	−39.2555	−1.60797
$597$	2.84333i	0.116370i
$598$	− 1.83276i	− 0.0749473i
$599$	−27.1355	−1.10873	−0.554364	−	0.832274i	$-0.687039\pi$
$599$	−27.1355	−1.10873	−0.554364	+	0.832274i	$0.687039\pi$
$600$	0	0
$601$	34.1708	1.39386	0.696928	−	0.717141i	$-0.254550\pi$
$601$	34.1708	1.39386	0.696928	+	0.717141i	$0.254550\pi$
$602$	1.64440i	0.0670208i
$603$	7.25443i	0.295423i
$604$	−31.4499	−1.27968
$605$	0	0
$606$	3.08719	0.125408
$607$	10.3133i	0.418606i	0.977851	+	0.209303i	$0.0671195\pi$
$607$	10.3133i	0.418606i	−0.977851	+	0.209303i	$0.932881\pi$
$608$	8.45335i	0.342829i
$609$	29.4983	1.19533
$610$	0	0
$611$	−5.42166	−0.219337
$612$	8.31335i	0.336047i
$613$	− 0.484156i	− 0.0195549i	−0.999952	−	0.00977744i	$-0.996888\pi$
$613$	− 0.484156i	− 0.0195549i	0.999952	−	0.00977744i	$-0.00311230\pi$
$614$	−0.557212	−0.0224872
$615$	0	0
$616$	27.3733	1.10290
$617$	− 7.15667i	− 0.288117i	−0.989569	−	0.144058i	$-0.953985\pi$
$617$	− 7.15667i	− 0.288117i	0.989569	−	0.144058i	$-0.0460153\pi$
$618$	4.19550i	0.168768i
$619$	−5.42166	−0.217915	−0.108958	−	0.994046i	$-0.534751\pi$
$619$	−5.42166	−0.217915	−0.108958	+	0.994046i	$0.534751\pi$
$620$	0	0
$621$	6.33804	0.254337
$622$	8.66895i	0.347593i
$623$	1.66196i	0.0665848i
$624$	3.50528	0.140324
$625$	0	0
$626$	4.71731	0.188542
$627$	− 12.6761i	− 0.506234i
$628$	− 41.5194i	− 1.65681i
$629$	41.1885	1.64229
$630$	0	0
$631$	−10.7244	−0.426934	−0.213467	−	0.976950i	$-0.568476\pi$
$631$	−10.7244	−0.426934	−0.213467	+	0.976950i	$0.568476\pi$
$632$	− 3.95775i	− 0.157431i
$633$	6.31335i	0.250933i
$634$	8.87056	0.352295
$635$	0	0
$636$	−0.647822	−0.0256878
$637$	17.1708i	0.680332i
$638$	8.52998i	0.337705i
$639$	−0.916382	−0.0362515
$640$	0	0
$641$	−0.362741	−0.0143274	−0.00716370	−	0.999974i	$-0.502280\pi$
$641$	−0.362741	−0.0143274	−0.00716370	+	0.999974i	$0.502280\pi$
$642$	1.20607i	0.0475996i
$643$	9.39697i	0.370580i	0.982684	+	0.185290i	$0.0593225\pi$
$643$	9.39697i	0.370580i	−0.982684	+	0.185290i	$0.940678\pi$
$644$	−59.7149	−2.35310
$645$	0	0
$646$	3.23433	0.127253
$647$	18.0036i	0.707793i	0.935285	+	0.353897i	$0.115144\pi$
$647$	18.0036i	0.707793i	−0.935285	+	0.353897i	$0.884856\pi$
$648$	− 1.13249i	− 0.0444886i
$649$	55.3311	2.17193
$650$	0	0
$651$	−6.98944	−0.273938
$652$	− 11.6383i	− 0.455791i
$653$	34.8222i	1.36270i	0.731959	+	0.681349i	$0.238606\pi$
$653$	34.8222i	1.36270i	−0.731959	+	0.681349i	$0.761394\pi$
$654$	1.10831	0.0433385
$655$	0	0
$656$	15.2061	0.593697
$657$	− 3.15667i	− 0.123154i
$658$	− 7.70778i	− 0.300480i
$659$	−11.4700	−0.446809	−0.223404	−	0.974726i	$-0.571717\pi$
$659$	−11.4700	−0.446809	−0.223404	+	0.974726i	$0.571717\pi$
$660$	0	0
$661$	12.1672	0.473251	0.236625	−	0.971601i	$-0.423959\pi$
$661$	12.1672	0.473251	0.236625	+	0.971601i	$0.423959\pi$
$662$	2.91995i	0.113487i
$663$	− 4.33804i	− 0.168476i
$664$	−12.7456	−0.494624
$665$	0	0
$666$	−2.74557	−0.106389
$667$	− 38.0283i	− 1.47246i
$668$	− 1.42880i	− 0.0552821i
$669$	19.2544	0.744419
$670$	0	0
$671$	−50.0036	−1.93037
$672$	16.1189i	0.621799i
$673$	27.9789i	1.07851i	0.842144	+	0.539253i	$0.181293\pi$
$673$	27.9789i	1.07851i	−0.842144	+	0.539253i	$0.818707\pi$
$674$	−0.382833	−0.0147462
$675$	0	0
$676$	−1.91638	−0.0737070
$677$	22.9930i	0.883693i	0.897091	+	0.441847i	$0.145676\pi$
$677$	22.9930i	0.883693i	−0.897091	+	0.441847i	$0.854324\pi$
$678$	0.243863i	0.00936551i
$679$	60.6585	2.32786
$680$	0	0
$681$	13.0872	0.501502
$682$	− 2.02113i	− 0.0773929i
$683$	28.6066i	1.09460i	0.836936	+	0.547301i	$0.184345\pi$
$683$	28.6066i	1.09460i	−0.836936	+	0.547301i	$0.815655\pi$
$684$	4.94108	0.188927
$685$	0	0
$686$	−14.4595	−0.552065
$687$	24.5089i	0.935071i
$688$	4.05447i	0.154575i
$689$	0.338044	0.0128785
$690$	0	0
$691$	−19.4005	−0.738031	−0.369016	−	0.929423i	$-0.620305\pi$
$691$	−19.4005	−0.738031	−0.369016	+	0.929423i	$0.620305\pi$
$692$	− 1.61613i	− 0.0614362i
$693$	− 24.1708i	− 0.918173i
$694$	−2.16724	−0.0822672
$695$	0	0
$696$	−6.79497	−0.257563
$697$	− 18.8186i	− 0.712806i
$698$	− 6.40396i	− 0.242393i
$699$	8.33804	0.315374
$700$	0	0
$701$	−38.9683	−1.47181	−0.735906	−	0.677083i	$-0.763244\pi$
$701$	−38.9683	−1.47181	−0.735906	+	0.677083i	$0.763244\pi$
$702$	0.289169i	0.0109140i
$703$	− 24.4806i	− 0.923303i
$704$	29.8055	1.12334
$705$	0	0
$706$	−1.30382	−0.0490698
$707$	52.4877i	1.97400i
$708$	21.5678i	0.810567i
$709$	17.5194	0.657955	0.328978	−	0.944338i	$-0.393296\pi$
$709$	17.5194	0.657955	0.328978	+	0.944338i	$0.393296\pi$
$710$	0	0
$711$	−3.49472	−0.131062
$712$	− 0.382833i	− 0.0143473i
$713$	9.01056i	0.337448i
$714$	6.16724	0.230803
$715$	0	0
$716$	36.3910	1.36000
$717$	− 8.91638i	− 0.332988i
$718$	− 5.90225i	− 0.220270i
$719$	4.33447	0.161649	0.0808243	−	0.996728i	$-0.474245\pi$
$719$	4.33447	0.161649	0.0808243	+	0.996728i	$0.474245\pi$
$720$	0	0
$721$	−71.3311	−2.65651
$722$	3.57186i	0.132931i
$723$	− 6.00000i	− 0.223142i
$724$	33.5266	1.24600
$725$	0	0
$726$	3.80858	0.141350
$727$	22.1672i	0.822137i	0.911604	+	0.411069i	$0.134844\pi$
$727$	22.1672i	0.822137i	−0.911604	+	0.411069i	$0.865156\pi$
$728$	− 5.56777i	− 0.206355i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	5.01770	0.185586
$732$	− 19.4911i	− 0.720414i
$733$	2.83976i	0.104889i	0.998624	+	0.0524444i	$0.0167012\pi$
$733$	2.83976i	0.104889i	−0.998624	+	0.0524444i	$0.983299\pi$
$734$	−2.98230	−0.110079
$735$	0	0
$736$	20.7799	0.765959
$737$	− 35.6655i	− 1.31376i
$738$	1.25443i	0.0461761i
$739$	43.9305	1.61601	0.808005	−	0.589176i	$-0.200547\pi$
$739$	43.9305	1.61601	0.808005	+	0.589176i	$0.200547\pi$
$740$	0	0
$741$	−2.57834	−0.0947176
$742$	0.480585i	0.0176428i
$743$	− 41.0872i	− 1.50734i	−0.657251	−	0.753671i	$-0.728281\pi$
$743$	− 41.0872i	− 1.50734i	0.657251	−	0.753671i	$-0.271719\pi$
$744$	1.61003	0.0590264
$745$	0	0
$746$	−5.40054	−0.197728
$747$	11.2544i	0.411778i
$748$	− 40.8716i	− 1.49441i
$749$	−20.5053	−0.749247
$750$	0	0
$751$	23.6902	0.864468	0.432234	−	0.901761i	$-0.357725\pi$
$751$	23.6902	0.864468	0.432234	+	0.901761i	$0.357725\pi$
$752$	− 19.0045i	− 0.693021i
$753$	− 6.31335i	− 0.230071i
$754$	1.73501	0.0631854
$755$	0	0
$756$	9.42166	0.342663
$757$	9.32391i	0.338883i	0.985540	+	0.169442i	$0.0541964\pi$
$757$	9.32391i	0.338883i	−0.985540	+	0.169442i	$0.945804\pi$
$758$	− 8.31438i	− 0.301992i
$759$	−31.1602	−1.13105
$760$	0	0
$761$	−42.8222	−1.55230	−0.776152	−	0.630546i	$-0.782831\pi$
$761$	−42.8222	−1.55230	−0.776152	+	0.630546i	$0.782831\pi$
$762$	0.529977i	0.0191991i
$763$	18.8433i	0.682174i
$764$	−43.1355	−1.56059
$765$	0	0
$766$	4.11888	0.148821
$767$	− 11.2544i	− 0.406374i
$768$	9.72191i	0.350809i
$769$	17.3239	0.624716	0.312358	−	0.949964i	$-0.398881\pi$
$769$	17.3239	0.624716	0.312358	+	0.949964i	$0.398881\pi$
$770$	0	0
$771$	11.1567	0.401798
$772$	− 5.08108i	− 0.182872i
$773$	11.6373i	0.418563i	0.977855	+	0.209282i	$0.0671125\pi$
$773$	11.6373i	0.418563i	−0.977855	+	0.209282i	$0.932887\pi$
$774$	−0.334474	−0.0120224
$775$	0	0
$776$	−13.9728	−0.501593
$777$	− 46.6797i	− 1.67462i
$778$	10.0272i	0.359494i
$779$	−11.1849	−0.400742
$780$	0	0
$781$	4.50528	0.161212
$782$	− 7.95061i	− 0.284313i
$783$	6.00000i	0.214423i
$784$	−60.1885	−2.14959
$785$	0	0
$786$	1.68665	0.0601609
$787$	20.9411i	0.746469i	0.927737	+	0.373234i	$0.121751\pi$
$787$	20.9411i	0.746469i	−0.927737	+	0.373234i	$0.878249\pi$
$788$	− 24.8927i	− 0.886766i
$789$	8.00000	0.284808
$790$	0	0
$791$	−4.14611	−0.147419
$792$	5.56777i	0.197842i
$793$	10.1708i	0.361176i
$794$	2.07663	0.0736967
$795$	0	0
$796$	5.44890	0.193131
$797$	20.3380i	0.720410i	0.932873	+	0.360205i	$0.117293\pi$
$797$	20.3380i	0.720410i	−0.932873	+	0.360205i	$0.882707\pi$
$798$	− 3.66553i	− 0.129758i
$799$	−23.5194	−0.832057
$800$	0	0
$801$	−0.338044	−0.0119442
$802$	− 10.9482i	− 0.386595i
$803$	15.5194i	0.547668i
$804$	13.9022	0.490294
$805$	0	0
$806$	−0.411100	−0.0144804
$807$	− 18.6761i	− 0.657429i
$808$	− 12.0906i	− 0.425346i
$809$	−7.68665	−0.270248	−0.135124	−	0.990829i	$-0.543143\pi$
$809$	−7.68665	−0.270248	−0.135124	+	0.990829i	$0.543143\pi$
$810$	0	0
$811$	−44.4111	−1.55948	−0.779742	−	0.626101i	$-0.784650\pi$
$811$	−44.4111	−1.55948	−0.779742	+	0.626101i	$0.784650\pi$
$812$	− 56.5300i	− 1.98381i
$813$	6.57834i	0.230712i
$814$	13.4983	0.473115
$815$	0	0
$816$	15.2061	0.532319
$817$	− 2.98230i	− 0.104337i
$818$	− 4.04836i	− 0.141548i
$819$	−4.91638	−0.171792
$820$	0	0
$821$	−46.4630	−1.62157	−0.810785	−	0.585343i	$-0.800960\pi$
$821$	−46.4630	−1.62157	−0.810785	+	0.585343i	$0.800960\pi$
$822$	− 4.77384i	− 0.166507i
$823$	− 46.5089i	− 1.62120i	−0.585603	−	0.810598i	$-0.699142\pi$
$823$	− 46.5089i	− 1.62120i	0.585603	−	0.810598i	$-0.300858\pi$
$824$	16.4312	0.572408
$825$	0	0
$826$	16.0000	0.556711
$827$	39.4005i	1.37009i	0.728500	+	0.685045i	$0.240218\pi$
$827$	39.4005i	1.37009i	−0.728500	+	0.685045i	$0.759782\pi$
$828$	− 12.1461i	− 0.422107i
$829$	−47.6444	−1.65476	−0.827379	−	0.561644i	$-0.810169\pi$
$829$	−47.6444	−1.65476	−0.827379	+	0.561644i	$0.810169\pi$
$830$	0	0
$831$	−25.6655	−0.890327
$832$	− 6.06249i	− 0.210179i
$833$	74.4877i	2.58085i
$834$	−2.16724	−0.0750453
$835$	0	0
$836$	−24.2922	−0.840164
$837$	− 1.42166i	− 0.0491399i
$838$	− 9.68665i	− 0.334620i
$839$	39.9058	1.37770	0.688851	−	0.724903i	$-0.258115\pi$
$839$	39.9058	1.37770	0.688851	+	0.724903i	$0.258115\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	− 3.90939i	− 0.134726i
$843$	3.15667i	0.108722i
$844$	12.0988	0.416457
$845$	0	0
$846$	1.56777	0.0539012
$847$	64.7527i	2.22493i
$848$	1.18494i	0.0406910i
$849$	−3.47002	−0.119091
$850$	0	0
$851$	−60.1779	−2.06287
$852$	1.75614i	0.0601643i
$853$	− 29.5019i	− 1.01012i	−0.863083	−	0.505062i	$-0.831470\pi$
$853$	− 29.5019i	− 1.01012i	0.863083	−	0.505062i	$-0.168530\pi$
$854$	−14.4595	−0.494793
$855$	0	0
$856$	4.72342	0.161443
$857$	8.33804i	0.284822i	0.989808	+	0.142411i	$0.0454855\pi$
$857$	8.33804i	0.284822i	−0.989808	+	0.142411i	$0.954515\pi$
$858$	− 1.42166i	− 0.0485348i
$859$	4.17081	0.142306	0.0711531	−	0.997465i	$-0.477332\pi$
$859$	4.17081	0.142306	0.0711531	+	0.997465i	$0.477332\pi$
$860$	0	0
$861$	−21.3275	−0.726839
$862$	− 3.58890i	− 0.122238i
$863$	3.93051i	0.133796i	0.997760	+	0.0668981i	$0.0213103\pi$
$863$	3.93051i	0.133796i	−0.997760	+	0.0668981i	$0.978690\pi$
$864$	−3.27861	−0.111540
$865$	0	0
$866$	5.00953	0.170231
$867$	− 1.81863i	− 0.0617639i
$868$	13.3944i	0.454637i
$869$	17.1814	0.582838
$870$	0	0
$871$	−7.25443	−0.245807
$872$	− 4.34058i	− 0.146991i
$873$	12.3380i	0.417580i
$874$	−4.72548	−0.159842
$875$	0	0
$876$	−6.04939	−0.204390
$877$	− 23.0177i	− 0.777253i	−0.921395	−	0.388626i	$-0.872950\pi$
$877$	− 23.0177i	− 0.777253i	0.921395	−	0.388626i	$-0.127050\pi$
$878$	0.188362i	0.00635692i
$879$	28.6550	0.966508
$880$	0	0
$881$	−15.3522	−0.517228	−0.258614	−	0.965981i	$-0.583266\pi$
$881$	−15.3522	−0.517228	−0.258614	+	0.965981i	$0.583266\pi$
$882$	− 4.96526i	− 0.167189i
$883$	− 42.8011i	− 1.44037i	−0.693782	−	0.720185i	$-0.744057\pi$
$883$	− 42.8011i	− 1.44037i	0.693782	−	0.720185i	$-0.255943\pi$
$884$	−8.31335	−0.279608
$885$	0	0
$886$	2.55824	0.0859459
$887$	− 53.1885i	− 1.78590i	−0.450160	−	0.892948i	$-0.648633\pi$
$887$	− 53.1885i	− 1.78590i	0.450160	−	0.892948i	$-0.351367\pi$
$888$	10.7527i	0.360837i
$889$	−9.01056	−0.302205
$890$	0	0
$891$	4.91638	0.164705
$892$	− 36.8988i	− 1.23546i
$893$	13.9789i	0.467785i
$894$	−5.92337	−0.198107
$895$	0	0
$896$	40.8566	1.36492
$897$	6.33804i	0.211621i
$898$	1.25443i	0.0418607i
$899$	−8.52998	−0.284491
$900$	0	0
$901$	1.46645	0.0488546
$902$	− 6.16724i	− 0.205347i
$903$	− 5.68665i	− 0.189240i
$904$	0.955062	0.0317649
$905$	0	0
$906$	−4.74557	−0.157661
$907$	11.8116i	0.392199i	0.980584	+	0.196099i	$0.0628276\pi$
$907$	11.8116i	0.392199i	−0.980584	+	0.196099i	$0.937172\pi$
$908$	− 25.0800i	− 0.832311i
$909$	−10.6761	−0.354104
$910$	0	0
$911$	44.1955	1.46426	0.732131	−	0.681164i	$-0.238526\pi$
$911$	44.1955	1.46426	0.732131	+	0.681164i	$0.238526\pi$
$912$	− 9.03780i	− 0.299271i
$913$	− 55.3311i	− 1.83119i
$914$	4.43223	0.146605
$915$	0	0
$916$	46.9683	1.55188
$917$	28.6761i	0.946968i
$918$	1.25443i	0.0414022i
$919$	−55.2096	−1.82120	−0.910599	−	0.413291i	$-0.864379\pi$
$919$	−55.2096	−1.82120	−0.910599	+	0.413291i	$0.864379\pi$
$920$	0	0
$921$	1.92694	0.0634950
$922$	3.42880i	0.112922i
$923$	− 0.916382i	− 0.0301631i
$924$	−46.3205	−1.52383
$925$	0	0
$926$	7.63829	0.251010
$927$	− 14.5089i	− 0.476533i
$928$	19.6716i	0.645753i
$929$	−22.9930	−0.754376	−0.377188	−	0.926137i	$-0.623109\pi$
$929$	−22.9930	−0.754376	−0.377188	+	0.926137i	$0.623109\pi$
$930$	0	0
$931$	44.2721	1.45096
$932$	− 15.9789i	− 0.523405i
$933$	− 29.9789i	− 0.981464i
$934$	−9.73604	−0.318573
$935$	0	0
$936$	1.13249	0.0370167
$937$	7.97887i	0.260658i	0.991471	+	0.130329i	$0.0416034\pi$
$937$	7.97887i	0.260658i	−0.991471	+	0.130329i	$0.958397\pi$
$938$	− 10.3133i	− 0.336743i
$939$	−16.3133	−0.532366
$940$	0	0
$941$	41.5019	1.35292	0.676461	−	0.736478i	$-0.263513\pi$
$941$	41.5019	1.35292	0.676461	+	0.736478i	$0.263513\pi$
$942$	− 6.26499i	− 0.204124i
$943$	27.4947i	0.895351i
$944$	39.4499	1.28399
$945$	0	0
$946$	1.64440	0.0534641
$947$	47.4499i	1.54192i	0.636886	+	0.770958i	$0.280222\pi$
$947$	47.4499i	1.54192i	−0.636886	+	0.770958i	$0.719778\pi$
$948$	6.69721i	0.217515i
$949$	3.15667	0.102470
$950$	0	0
$951$	−30.6761	−0.994740
$952$	− 24.1533i	− 0.782811i
$953$	− 30.3663i	− 0.983661i	−0.870691	−	0.491831i	$-0.836328\pi$
$953$	− 30.3663i	− 0.983661i	0.870691	−	0.491831i	$-0.163672\pi$
$954$	−0.0977518	−0.00316483
$955$	0	0
$956$	−17.0872	−0.552639
$957$	− 29.4983i	− 0.953544i
$958$	3.10831i	0.100425i
$959$	81.1638	2.62092
$960$	0	0
$961$	−28.9789	−0.934802
$962$	− 2.74557i	− 0.0885209i
$963$	− 4.17081i	− 0.134402i
$964$	−11.4983	−0.370335
$965$	0	0
$966$	−9.01056	−0.289910
$967$	− 41.0943i	− 1.32150i	−0.750604	−	0.660752i	$-0.770237\pi$
$967$	− 41.0943i	− 1.32150i	0.750604	−	0.660752i	$-0.229763\pi$
$968$	− 14.9159i	− 0.479414i
$969$	−11.1849	−0.359312
$970$	0	0
$971$	38.1744	1.22507	0.612537	−	0.790442i	$-0.290149\pi$
$971$	38.1744	1.22507	0.612537	+	0.790442i	$0.290149\pi$
$972$	1.91638i	0.0614680i
$973$	− 36.8469i	− 1.18126i
$974$	6.57834	0.210784
$975$	0	0
$976$	−35.6515	−1.14118
$977$	− 10.4806i	− 0.335304i	−0.985846	−	0.167652i	$-0.946382\pi$
$977$	− 10.4806i	− 0.335304i	0.985846	−	0.167652i	$-0.0536184\pi$
$978$	− 1.75614i	− 0.0561551i
$979$	1.66196	0.0531163
$980$	0	0
$981$	−3.83276	−0.122371
$982$	5.11442i	0.163208i
$983$	0.0766264i	0.00244400i	0.999999	+	0.00122200i	$0.000388975\pi$
$983$	0.0766264i	0.00244400i	−0.999999	+	0.00122200i	$0.999611\pi$
$984$	4.91281	0.156615
$985$	0	0
$986$	7.52656	0.239694
$987$	26.6550i	0.848437i
$988$	4.94108i	0.157197i
$989$	−7.33105	−0.233114
$990$	0	0
$991$	−13.8575	−0.440197	−0.220098	−	0.975478i	$-0.570638\pi$
$991$	−13.8575	−0.440197	−0.220098	+	0.975478i	$0.570638\pi$
$992$	− 4.66107i	− 0.147989i
$993$	− 10.0978i	− 0.320442i
$994$	1.30279	0.0413219
$995$	0	0
$996$	21.5678	0.683401
$997$	− 10.3416i	− 0.327522i	−0.986500	−	0.163761i	$-0.947637\pi$
$997$	− 10.3416i	− 0.327522i	0.986500	−	0.163761i	$-0.0523626\pi$
$998$	5.76328i	0.182433i
$999$	9.49472	0.300400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.c.i.274.3		6
3.2	odd	2		2925.2.c.w.2224.4		6
5.2	odd	4		975.2.a.o.1.2		3
5.3	odd	4		195.2.a.e.1.2	✓	3
5.4	even	2	inner	975.2.c.i.274.4		6
15.2	even	4		2925.2.a.bh.1.2		3
15.8	even	4		585.2.a.n.1.2		3
15.14	odd	2		2925.2.c.w.2224.3		6
20.3	even	4		3120.2.a.bj.1.1		3
35.13	even	4		9555.2.a.bq.1.2		3
60.23	odd	4		9360.2.a.dd.1.1		3
65.38	odd	4		2535.2.a.bc.1.2		3
195.38	even	4		7605.2.a.bx.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.a.e.1.2	✓	3	5.3	odd	4
585.2.a.n.1.2		3	15.8	even	4
975.2.a.o.1.2		3	5.2	odd	4
975.2.c.i.274.3		6	1.1	even	1	trivial
975.2.c.i.274.4		6	5.4	even	2	inner
2535.2.a.bc.1.2		3	65.38	odd	4
2925.2.a.bh.1.2		3	15.2	even	4
2925.2.c.w.2224.3		6	15.14	odd	2
2925.2.c.w.2224.4		6	3.2	odd	2
3120.2.a.bj.1.1		3	20.3	even	4
7605.2.a.bx.1.2		3	195.38	even	4
9360.2.a.dd.1.1		3	60.23	odd	4
9555.2.a.bq.1.2		3	35.13	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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.289169i q^{2} +1.00000i q^{3} +1.91638 q^{4} +0.289169 q^{6} +4.91638i q^{7} -1.13249i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.289169i q^{2} +1.00000i q^{3} +1.91638 q^{4} +0.289169 q^{6} +4.91638i q^{7} -1.13249i q^{8} -1.00000 q^{9} +4.91638 q^{11} +1.91638i q^{12} -1.00000i q^{13} +1.42166 q^{14} +3.50528 q^{16} -4.33804i q^{17} +0.289169i q^{18} -2.57834 q^{19} -4.91638 q^{21} -1.42166i q^{22} +6.33804i q^{23} +1.13249 q^{24} -0.289169 q^{26} -1.00000i q^{27} +9.42166i q^{28} -6.00000 q^{29} +1.42166 q^{31} -3.27861i q^{32} +4.91638i q^{33} -1.25443 q^{34} -1.91638 q^{36} +9.49472i q^{37} +0.745574i q^{38} +1.00000 q^{39} +4.33804 q^{41} +1.42166i q^{42} +1.15667i q^{43} +9.42166 q^{44} +1.83276 q^{46} -5.42166i q^{47} +3.50528i q^{48} -17.1708 q^{49} +4.33804 q^{51} -1.91638i q^{52} +0.338044i q^{53} -0.289169 q^{54} +5.56777 q^{56} -2.57834i q^{57} +1.73501i q^{58} +11.2544 q^{59} -10.1708 q^{61} -0.411100i q^{62} -4.91638i q^{63} +6.06249 q^{64} +1.42166 q^{66} -7.25443i q^{67} -8.31335i q^{68} -6.33804 q^{69} +0.916382 q^{71} +1.13249i q^{72} +3.15667i q^{73} +2.74557 q^{74} -4.94108 q^{76} +24.1708i q^{77} -0.289169i q^{78} +3.49472 q^{79} +1.00000 q^{81} -1.25443i q^{82} -11.2544i q^{83} -9.42166 q^{84} +0.334474 q^{86} -6.00000i q^{87} -5.56777i q^{88} +0.338044 q^{89} +4.91638 q^{91} +12.1461i q^{92} +1.42166i q^{93} -1.56777 q^{94} +3.27861 q^{96} -12.3380i q^{97} +4.96526i q^{98} -4.91638 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 16 q^{4} - 6 q^{9}+O(q^{10}) \) 6 * q - 16 * q^4 - 6 * q^9	\( 6 q - 16 q^{4} - 6 q^{9} + 2 q^{11} + 12 q^{14} + 52 q^{16} - 12 q^{19} - 2 q^{21} + 12 q^{24} - 36 q^{29} + 12 q^{31} + 44 q^{34} + 16 q^{36} + 6 q^{39} + 2 q^{41} + 60 q^{44} - 44 q^{46} - 24 q^{49} + 2 q^{51} - 32 q^{56} + 16 q^{59} + 18 q^{61} - 60 q^{64} + 12 q^{66} - 14 q^{69} - 22 q^{71} + 68 q^{74} + 8 q^{76} - 10 q^{79} + 6 q^{81} - 60 q^{84} + 112 q^{86} - 22 q^{89} + 2 q^{91} + 56 q^{94} - 44 q^{96} - 2 q^{99}+O(q^{100}) \) 6 * q - 16 * q^4 - 6 * q^9 + 2 * q^11 + 12 * q^14 + 52 * q^16 - 12 * q^19 - 2 * q^21 + 12 * q^24 - 36 * q^29 + 12 * q^31 + 44 * q^34 + 16 * q^36 + 6 * q^39 + 2 * q^41 + 60 * q^44 - 44 * q^46 - 24 * q^49 + 2 * q^51 - 32 * q^56 + 16 * q^59 + 18 * q^61 - 60 * q^64 + 12 * q^66 - 14 * q^69 - 22 * q^71 + 68 * q^74 + 8 * q^76 - 10 * q^79 + 6 * q^81 - 60 * q^84 + 112 * q^86 - 22 * q^89 + 2 * q^91 + 56 * q^94 - 44 * q^96 - 2 * q^99

Introduction

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