LMFDB - Embedded newform 150.4.c.c.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,4,Mod(49,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("150.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	150.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:	$8.85028650086$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	150.49
Dual form			150.4.c.c.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +6.00000 q^{6} +4.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +6.00000 q^{6} +4.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} -48.0000 q^{11} -12.0000i q^{12} +2.00000i q^{13} +8.00000 q^{14} +16.0000 q^{16} +114.000i q^{17} +18.0000i q^{18} -140.000 q^{19} -12.0000 q^{21} +96.0000i q^{22} +72.0000i q^{23} -24.0000 q^{24} +4.00000 q^{26} -27.0000i q^{27} -16.0000i q^{28} -210.000 q^{29} +272.000 q^{31} -32.0000i q^{32} -144.000i q^{33} +228.000 q^{34} +36.0000 q^{36} +334.000i q^{37} +280.000i q^{38} -6.00000 q^{39} -198.000 q^{41} +24.0000i q^{42} -268.000i q^{43} +192.000 q^{44} +144.000 q^{46} -216.000i q^{47} +48.0000i q^{48} +327.000 q^{49} -342.000 q^{51} -8.00000i q^{52} -78.0000i q^{53} -54.0000 q^{54} -32.0000 q^{56} -420.000i q^{57} +420.000i q^{58} -240.000 q^{59} +302.000 q^{61} -544.000i q^{62} -36.0000i q^{63} -64.0000 q^{64} -288.000 q^{66} -596.000i q^{67} -456.000i q^{68} -216.000 q^{69} -768.000 q^{71} -72.0000i q^{72} -478.000i q^{73} +668.000 q^{74} +560.000 q^{76} -192.000i q^{77} +12.0000i q^{78} +640.000 q^{79} +81.0000 q^{81} +396.000i q^{82} -348.000i q^{83} +48.0000 q^{84} -536.000 q^{86} -630.000i q^{87} -384.000i q^{88} -210.000 q^{89} -8.00000 q^{91} -288.000i q^{92} +816.000i q^{93} -432.000 q^{94} +96.0000 q^{96} +1534.00i q^{97} -654.000i q^{98} +432.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{4} + 12 q^{6} - 18 q^{9}+O(q^{10}) $ 2 * q - 8 * q^4 + 12 * q^6 - 18 * q^9	$ 2 q - 8 q^{4} + 12 q^{6} - 18 q^{9} - 96 q^{11} + 16 q^{14} + 32 q^{16} - 280 q^{19} - 24 q^{21} - 48 q^{24} + 8 q^{26} - 420 q^{29} + 544 q^{31} + 456 q^{34} + 72 q^{36} - 12 q^{39} - 396 q^{41} + 384 q^{44} + 288 q^{46} + 654 q^{49} - 684 q^{51} - 108 q^{54} - 64 q^{56} - 480 q^{59} + 604 q^{61} - 128 q^{64} - 576 q^{66} - 432 q^{69} - 1536 q^{71} + 1336 q^{74} + 1120 q^{76} + 1280 q^{79} + 162 q^{81} + 96 q^{84} - 1072 q^{86} - 420 q^{89} - 16 q^{91} - 864 q^{94} + 192 q^{96} + 864 q^{99}+O(q^{100}) $ 2 * q - 8 * q^4 + 12 * q^6 - 18 * q^9 - 96 * q^11 + 16 * q^14 + 32 * q^16 - 280 * q^19 - 24 * q^21 - 48 * q^24 + 8 * q^26 - 420 * q^29 + 544 * q^31 + 456 * q^34 + 72 * q^36 - 12 * q^39 - 396 * q^41 + 384 * q^44 + 288 * q^46 + 654 * q^49 - 684 * q^51 - 108 * q^54 - 64 * q^56 - 480 * q^59 + 604 * q^61 - 128 * q^64 - 576 * q^66 - 432 * q^69 - 1536 * q^71 + 1336 * q^74 + 1120 * q^76 + 1280 * q^79 + 162 * q^81 + 96 * q^84 - 1072 * q^86 - 420 * q^89 - 16 * q^91 - 864 * q^94 + 192 * q^96 + 864 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 2.00000i	− 0.707107i
$2$	− 2.00000i	− 0.707107i
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	6.00000	0.408248
$7$	4.00000i	0.215980i	0.994152	+	0.107990i	$0.0344414\pi$
$7$	4.00000i	0.215980i	−0.994152	+	0.107990i	$0.965559\pi$
$8$	8.00000i	0.353553i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−48.0000	−1.31569	−0.657843	−	0.753155i	$-0.728531\pi$
$11$	−48.0000	−1.31569	−0.657843	+	0.753155i	$0.728531\pi$
$12$	− 12.0000i	− 0.288675i
$13$	2.00000i	0.0426692i	0.999772	+	0.0213346i	$0.00679154\pi$
$13$	2.00000i	0.0426692i	−0.999772	+	0.0213346i	$0.993208\pi$
$14$	8.00000	0.152721
$15$	0	0
$16$	16.0000	0.250000
$17$	114.000i	1.62642i	0.581974	+	0.813208i	$0.302281\pi$
$17$	114.000i	1.62642i	−0.581974	+	0.813208i	$0.697719\pi$
$18$	18.0000i	0.235702i
$19$	−140.000	−1.69043	−0.845216	−	0.534425i	$-0.820528\pi$
$19$	−140.000	−1.69043	−0.845216	+	0.534425i	$0.820528\pi$
$20$	0	0
$21$	−12.0000	−0.124696
$22$	96.0000i	0.930330i
$23$	72.0000i	0.652741i	0.945242	+	0.326370i	$0.105826\pi$
$23$	72.0000i	0.652741i	−0.945242	+	0.326370i	$0.894174\pi$
$24$	−24.0000	−0.204124
$25$	0	0
$26$	4.00000	0.0301717
$27$	− 27.0000i	− 0.192450i
$28$	− 16.0000i	− 0.107990i
$29$	−210.000	−1.34469	−0.672345	−	0.740238i	$-0.734713\pi$
$29$	−210.000	−1.34469	−0.672345	+	0.740238i	$0.734713\pi$
$30$	0	0
$31$	272.000	1.57589	0.787946	−	0.615745i	$-0.211145\pi$
$31$	272.000	1.57589	0.787946	+	0.615745i	$0.211145\pi$
$32$	− 32.0000i	− 0.176777i
$33$	− 144.000i	− 0.759612i
$34$	228.000	1.15005
$35$	0	0
$36$	36.0000	0.166667
$37$	334.000i	1.48403i	0.670381	+	0.742017i	$0.266131\pi$
$37$	334.000i	1.48403i	−0.670381	+	0.742017i	$0.733869\pi$
$38$	280.000i	1.19532i
$39$	−6.00000	−0.0246351
$40$	0	0
$41$	−198.000	−0.754205	−0.377102	−	0.926172i	$-0.623080\pi$
$41$	−198.000	−0.754205	−0.377102	+	0.926172i	$0.623080\pi$
$42$	24.0000i	0.0881733i
$43$	− 268.000i	− 0.950456i	−0.879863	−	0.475228i	$-0.842366\pi$
$43$	− 268.000i	− 0.950456i	0.879863	−	0.475228i	$-0.157634\pi$
$44$	192.000	0.657843
$45$	0	0
$46$	144.000	0.461557
$47$	− 216.000i	− 0.670358i	−0.942154	−	0.335179i	$-0.891203\pi$
$47$	− 216.000i	− 0.670358i	0.942154	−	0.335179i	$-0.108797\pi$
$48$	48.0000i	0.144338i
$49$	327.000	0.953353
$50$	0	0
$51$	−342.000	−0.939011
$52$	− 8.00000i	− 0.0213346i
$53$	− 78.0000i	− 0.202153i	−0.994879	−	0.101077i	$-0.967771\pi$
$53$	− 78.0000i	− 0.202153i	0.994879	−	0.101077i	$-0.0322287\pi$
$54$	−54.0000	−0.136083
$55$	0	0
$56$	−32.0000	−0.0763604
$57$	− 420.000i	− 0.975971i
$58$	420.000i	0.950840i
$59$	−240.000	−0.529582	−0.264791	−	0.964306i	$-0.585303\pi$
$59$	−240.000	−0.529582	−0.264791	+	0.964306i	$0.585303\pi$
$60$	0	0
$61$	302.000	0.633888	0.316944	−	0.948444i	$-0.397343\pi$
$61$	302.000	0.633888	0.316944	+	0.948444i	$0.397343\pi$
$62$	− 544.000i	− 1.11432i
$63$	− 36.0000i	− 0.0719932i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	−288.000	−0.537127
$67$	− 596.000i	− 1.08676i	−0.839487	−	0.543381i	$-0.817144\pi$
$67$	− 596.000i	− 1.08676i	0.839487	−	0.543381i	$-0.182856\pi$
$68$	− 456.000i	− 0.813208i
$69$	−216.000	−0.376860
$70$	0	0
$71$	−768.000	−1.28373	−0.641865	−	0.766818i	$-0.721839\pi$
$71$	−768.000	−1.28373	−0.641865	+	0.766818i	$0.721839\pi$
$72$	− 72.0000i	− 0.117851i
$73$	− 478.000i	− 0.766379i	−0.923670	−	0.383190i	$-0.874826\pi$
$73$	− 478.000i	− 0.766379i	0.923670	−	0.383190i	$-0.125174\pi$
$74$	668.000	1.04937
$75$	0	0
$76$	560.000	0.845216
$77$	− 192.000i	− 0.284161i
$78$	12.0000i	0.0174196i
$79$	640.000	0.911464	0.455732	−	0.890117i	$-0.349378\pi$
$79$	640.000	0.911464	0.455732	+	0.890117i	$0.349378\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	396.000i	0.533303i
$83$	− 348.000i	− 0.460216i	−0.973165	−	0.230108i	$-0.926092\pi$
$83$	− 348.000i	− 0.460216i	0.973165	−	0.230108i	$-0.0739080\pi$
$84$	48.0000	0.0623480
$85$	0	0
$86$	−536.000	−0.672074
$87$	− 630.000i	− 0.776357i
$88$	− 384.000i	− 0.465165i
$89$	−210.000	−0.250112	−0.125056	−	0.992150i	$-0.539911\pi$
$89$	−210.000	−0.250112	−0.125056	+	0.992150i	$0.539911\pi$
$90$	0	0
$91$	−8.00000	−0.00921569
$92$	− 288.000i	− 0.326370i
$93$	816.000i	0.909841i
$94$	−432.000	−0.474015
$95$	0	0
$96$	96.0000	0.102062
$97$	1534.00i	1.60571i	0.596173	+	0.802856i	$0.296687\pi$
$97$	1534.00i	1.60571i	−0.596173	+	0.802856i	$0.703313\pi$
$98$	− 654.000i	− 0.674122i
$99$	432.000	0.438562
$100$	0	0
$101$	1722.00	1.69649	0.848245	−	0.529605i	$-0.177660\pi$
$101$	1722.00	1.69649	0.848245	+	0.529605i	$0.177660\pi$
$102$	684.000i	0.663981i
$103$	1052.00i	1.00638i	0.864177	+	0.503188i	$0.167840\pi$
$103$	1052.00i	1.00638i	−0.864177	+	0.503188i	$0.832160\pi$
$104$	−16.0000	−0.0150859
$105$	0	0
$106$	−156.000	−0.142944
$107$	564.000i	0.509570i	0.966998	+	0.254785i	$0.0820046\pi$
$107$	564.000i	0.509570i	−0.966998	+	0.254785i	$0.917995\pi$
$108$	108.000i	0.0962250i
$109$	610.000	0.536031	0.268016	−	0.963415i	$-0.413632\pi$
$109$	610.000	0.536031	0.268016	+	0.963415i	$0.413632\pi$
$110$	0	0
$111$	−1002.00	−0.856807
$112$	64.0000i	0.0539949i
$113$	1302.00i	1.08391i	0.840407	+	0.541955i	$0.182316\pi$
$113$	1302.00i	1.08391i	−0.840407	+	0.541955i	$0.817684\pi$
$114$	−840.000	−0.690116
$115$	0	0
$116$	840.000	0.672345
$117$	− 18.0000i	− 0.0142231i
$118$	480.000i	0.374471i
$119$	−456.000	−0.351273
$120$	0	0
$121$	973.000	0.731029
$122$	− 604.000i	− 0.448226i
$123$	− 594.000i	− 0.435440i
$124$	−1088.00	−0.787946
$125$	0	0
$126$	−72.0000	−0.0509069
$127$	124.000i	0.0866395i	0.999061	+	0.0433198i	$0.0137934\pi$
$127$	124.000i	0.0866395i	−0.999061	+	0.0433198i	$0.986207\pi$
$128$	128.000i	0.0883883i
$129$	804.000	0.548746
$130$	0	0
$131$	192.000	0.128054	0.0640272	−	0.997948i	$-0.479606\pi$
$131$	192.000	0.128054	0.0640272	+	0.997948i	$0.479606\pi$
$132$	576.000i	0.379806i
$133$	− 560.000i	− 0.365099i
$134$	−1192.00	−0.768456
$135$	0	0
$136$	−912.000	−0.575025
$137$	2514.00i	1.56778i	0.620901	+	0.783889i	$0.286767\pi$
$137$	2514.00i	1.56778i	−0.620901	+	0.783889i	$0.713233\pi$
$138$	432.000i	0.266480i
$139$	−1340.00	−0.817679	−0.408839	−	0.912606i	$-0.634066\pi$
$139$	−1340.00	−0.817679	−0.408839	+	0.912606i	$0.634066\pi$
$140$	0	0
$141$	648.000	0.387032
$142$	1536.00i	0.907734i
$143$	− 96.0000i	− 0.0561393i
$144$	−144.000	−0.0833333
$145$	0	0
$146$	−956.000	−0.541912
$147$	981.000i	0.550418i
$148$	− 1336.00i	− 0.742017i
$149$	−1410.00	−0.775246	−0.387623	−	0.921818i	$-0.626704\pi$
$149$	−1410.00	−0.775246	−0.387623	+	0.921818i	$0.626704\pi$
$150$	0	0
$151$	−2128.00	−1.14685	−0.573424	−	0.819258i	$-0.694385\pi$
$151$	−2128.00	−1.14685	−0.573424	+	0.819258i	$0.694385\pi$
$152$	− 1120.00i	− 0.597658i
$153$	− 1026.00i	− 0.542138i
$154$	−384.000	−0.200932
$155$	0	0
$156$	24.0000	0.0123176
$157$	− 3026.00i	− 1.53822i	−0.639114	−	0.769112i	$-0.720699\pi$
$157$	− 3026.00i	− 1.53822i	0.639114	−	0.769112i	$-0.279301\pi$
$158$	− 1280.00i	− 0.644502i
$159$	234.000	0.116713
$160$	0	0
$161$	−288.000	−0.140979
$162$	− 162.000i	− 0.0785674i
$163$	2612.00i	1.25514i	0.778561	+	0.627569i	$0.215950\pi$
$163$	2612.00i	1.25514i	−0.778561	+	0.627569i	$0.784050\pi$
$164$	792.000	0.377102
$165$	0	0
$166$	−696.000	−0.325422
$167$	24.0000i	0.0111208i	0.999985	+	0.00556041i	$0.00176994\pi$
$167$	24.0000i	0.0111208i	−0.999985	+	0.00556041i	$0.998230\pi$
$168$	− 96.0000i	− 0.0440867i
$169$	2193.00	0.998179
$170$	0	0
$171$	1260.00	0.563477
$172$	1072.00i	0.475228i
$173$	1962.00i	0.862243i	0.902294	+	0.431122i	$0.141882\pi$
$173$	1962.00i	0.862243i	−0.902294	+	0.431122i	$0.858118\pi$
$174$	−1260.00	−0.548968
$175$	0	0
$176$	−768.000	−0.328921
$177$	− 720.000i	− 0.305754i
$178$	420.000i	0.176856i
$179$	120.000	0.0501074	0.0250537	−	0.999686i	$-0.492024\pi$
$179$	120.000	0.0501074	0.0250537	+	0.999686i	$0.492024\pi$
$180$	0	0
$181$	902.000	0.370415	0.185208	−	0.982699i	$-0.440704\pi$
$181$	902.000	0.370415	0.185208	+	0.982699i	$0.440704\pi$
$182$	16.0000i	0.00651648i
$183$	906.000i	0.365975i
$184$	−576.000	−0.230779
$185$	0	0
$186$	1632.00	0.643355
$187$	− 5472.00i	− 2.13985i
$188$	864.000i	0.335179i
$189$	108.000	0.0415653
$190$	0	0
$191$	−168.000	−0.0636443	−0.0318221	−	0.999494i	$-0.510131\pi$
$191$	−168.000	−0.0636443	−0.0318221	+	0.999494i	$0.510131\pi$
$192$	− 192.000i	− 0.0721688i
$193$	− 1318.00i	− 0.491563i	−0.969325	−	0.245782i	$-0.920955\pi$
$193$	− 1318.00i	− 0.491563i	0.969325	−	0.245782i	$-0.0790446\pi$
$194$	3068.00	1.13541
$195$	0	0
$196$	−1308.00	−0.476676
$197$	4014.00i	1.45170i	0.687851	+	0.725852i	$0.258554\pi$
$197$	4014.00i	1.45170i	−0.687851	+	0.725852i	$0.741446\pi$
$198$	− 864.000i	− 0.310110i
$199$	−2000.00	−0.712443	−0.356222	−	0.934401i	$-0.615935\pi$
$199$	−2000.00	−0.712443	−0.356222	+	0.934401i	$0.615935\pi$
$200$	0	0
$201$	1788.00	0.627442
$202$	− 3444.00i	− 1.19960i
$203$	− 840.000i	− 0.290426i
$204$	1368.00	0.469506
$205$	0	0
$206$	2104.00	0.711615
$207$	− 648.000i	− 0.217580i
$208$	32.0000i	0.0106673i
$209$	6720.00	2.22408
$210$	0	0
$211$	−3868.00	−1.26201	−0.631005	−	0.775779i	$-0.717357\pi$
$211$	−3868.00	−1.26201	−0.631005	+	0.775779i	$0.717357\pi$
$212$	312.000i	0.101077i
$213$	− 2304.00i	− 0.741162i
$214$	1128.00	0.360320
$215$	0	0
$216$	216.000	0.0680414
$217$	1088.00i	0.340361i
$218$	− 1220.00i	− 0.379031i
$219$	1434.00	0.442469
$220$	0	0
$221$	−228.000	−0.0693979
$222$	2004.00i	0.605854i
$223$	− 3148.00i	− 0.945317i	−0.881246	−	0.472658i	$-0.843294\pi$
$223$	− 3148.00i	− 0.945317i	0.881246	−	0.472658i	$-0.156706\pi$
$224$	128.000	0.0381802
$225$	0	0
$226$	2604.00	0.766440
$227$	− 2556.00i	− 0.747347i	−0.927560	−	0.373673i	$-0.878098\pi$
$227$	− 2556.00i	− 0.747347i	0.927560	−	0.373673i	$-0.121902\pi$
$228$	1680.00i	0.487986i
$229$	610.000	0.176026	0.0880130	−	0.996119i	$-0.471948\pi$
$229$	610.000	0.176026	0.0880130	+	0.996119i	$0.471948\pi$
$230$	0	0
$231$	576.000	0.164061
$232$	− 1680.00i	− 0.475420i
$233$	− 2058.00i	− 0.578644i	−0.957232	−	0.289322i	$-0.906570\pi$
$233$	− 2058.00i	− 0.578644i	0.957232	−	0.289322i	$-0.0934298\pi$
$234$	−36.0000	−0.0100572
$235$	0	0
$236$	960.000	0.264791
$237$	1920.00i	0.526234i
$238$	912.000i	0.248387i
$239$	−4920.00	−1.33158	−0.665792	−	0.746138i	$-0.731906\pi$
$239$	−4920.00	−1.33158	−0.665792	+	0.746138i	$0.731906\pi$
$240$	0	0
$241$	−1438.00	−0.384356	−0.192178	−	0.981360i	$-0.561555\pi$
$241$	−1438.00	−0.384356	−0.192178	+	0.981360i	$0.561555\pi$
$242$	− 1946.00i	− 0.516916i
$243$	243.000i	0.0641500i
$244$	−1208.00	−0.316944
$245$	0	0
$246$	−1188.00	−0.307903
$247$	− 280.000i	− 0.0721294i
$248$	2176.00i	0.557162i
$249$	1044.00	0.265706
$250$	0	0
$251$	792.000	0.199166	0.0995829	−	0.995029i	$-0.468249\pi$
$251$	792.000	0.199166	0.0995829	+	0.995029i	$0.468249\pi$
$252$	144.000i	0.0359966i
$253$	− 3456.00i	− 0.858802i
$254$	248.000	0.0612634
$255$	0	0
$256$	256.000	0.0625000
$257$	− 2166.00i	− 0.525725i	−0.964833	−	0.262863i	$-0.915333\pi$
$257$	− 2166.00i	− 0.525725i	0.964833	−	0.262863i	$-0.0846666\pi$
$258$	− 1608.00i	− 0.388022i
$259$	−1336.00	−0.320521
$260$	0	0
$261$	1890.00	0.448230
$262$	− 384.000i	− 0.0905481i
$263$	3192.00i	0.748392i	0.927350	+	0.374196i	$0.122081\pi$
$263$	3192.00i	0.748392i	−0.927350	+	0.374196i	$0.877919\pi$
$264$	1152.00	0.268563
$265$	0	0
$266$	−1120.00	−0.258164
$267$	− 630.000i	− 0.144402i
$268$	2384.00i	0.543381i
$269$	−5490.00	−1.24435	−0.622177	−	0.782877i	$-0.713752\pi$
$269$	−5490.00	−1.24435	−0.622177	+	0.782877i	$0.713752\pi$
$270$	0	0
$271$	−6328.00	−1.41845	−0.709223	−	0.704985i	$-0.750954\pi$
$271$	−6328.00	−1.41845	−0.709223	+	0.704985i	$0.750954\pi$
$272$	1824.00i	0.406604i
$273$	− 24.0000i	− 0.00532068i
$274$	5028.00	1.10859
$275$	0	0
$276$	864.000	0.188430
$277$	574.000i	0.124507i	0.998060	+	0.0622533i	$0.0198287\pi$
$277$	574.000i	0.124507i	−0.998060	+	0.0622533i	$0.980171\pi$
$278$	2680.00i	0.578186i
$279$	−2448.00	−0.525297
$280$	0	0
$281$	4242.00	0.900557	0.450278	−	0.892888i	$-0.351325\pi$
$281$	4242.00	0.900557	0.450278	+	0.892888i	$0.351325\pi$
$282$	− 1296.00i	− 0.273673i
$283$	− 628.000i	− 0.131911i	−0.997823	−	0.0659553i	$-0.978991\pi$
$283$	− 628.000i	− 0.131911i	0.997823	−	0.0659553i	$-0.0210095\pi$
$284$	3072.00	0.641865
$285$	0	0
$286$	−192.000	−0.0396965
$287$	− 792.000i	− 0.162893i
$288$	288.000i	0.0589256i
$289$	−8083.00	−1.64523
$290$	0	0
$291$	−4602.00	−0.927058
$292$	1912.00i	0.383190i
$293$	− 558.000i	− 0.111258i	−0.998451	−	0.0556292i	$-0.982284\pi$
$293$	− 558.000i	− 0.111258i	0.998451	−	0.0556292i	$-0.0177165\pi$
$294$	1962.00	0.389205
$295$	0	0
$296$	−2672.00	−0.524685
$297$	1296.00i	0.253204i
$298$	2820.00i	0.548182i
$299$	−144.000	−0.0278520
$300$	0	0
$301$	1072.00	0.205279
$302$	4256.00i	0.810945i
$303$	5166.00i	0.979468i
$304$	−2240.00	−0.422608
$305$	0	0
$306$	−2052.00	−0.383350
$307$	6964.00i	1.29465i	0.762216	+	0.647323i	$0.224112\pi$
$307$	6964.00i	1.29465i	−0.762216	+	0.647323i	$0.775888\pi$
$308$	768.000i	0.142081i
$309$	−3156.00	−0.581031
$310$	0	0
$311$	2832.00	0.516360	0.258180	−	0.966097i	$-0.416877\pi$
$311$	2832.00	0.516360	0.258180	+	0.966097i	$0.416877\pi$
$312$	− 48.0000i	− 0.00870982i
$313$	8642.00i	1.56062i	0.625392	+	0.780311i	$0.284939\pi$
$313$	8642.00i	1.56062i	−0.625392	+	0.780311i	$0.715061\pi$
$314$	−6052.00	−1.08769
$315$	0	0
$316$	−2560.00	−0.455732
$317$	2214.00i	0.392273i	0.980577	+	0.196137i	$0.0628396\pi$
$317$	2214.00i	0.392273i	−0.980577	+	0.196137i	$0.937160\pi$
$318$	− 468.000i	− 0.0825287i
$319$	10080.0	1.76919
$320$	0	0
$321$	−1692.00	−0.294200
$322$	576.000i	0.0996870i
$323$	− 15960.0i	− 2.74934i
$324$	−324.000	−0.0555556
$325$	0	0
$326$	5224.00	0.887517
$327$	1830.00i	0.309478i
$328$	− 1584.00i	− 0.266652i
$329$	864.000	0.144784
$330$	0	0
$331$	10772.0	1.78877	0.894385	−	0.447299i	$-0.147614\pi$
$331$	10772.0	1.78877	0.894385	+	0.447299i	$0.147614\pi$
$332$	1392.00i	0.230108i
$333$	− 3006.00i	− 0.494678i
$334$	48.0000	0.00786360
$335$	0	0
$336$	−192.000	−0.0311740
$337$	1654.00i	0.267356i	0.991025	+	0.133678i	$0.0426789\pi$
$337$	1654.00i	0.267356i	−0.991025	+	0.133678i	$0.957321\pi$
$338$	− 4386.00i	− 0.705819i
$339$	−3906.00	−0.625796
$340$	0	0
$341$	−13056.0	−2.07338
$342$	− 2520.00i	− 0.398439i
$343$	2680.00i	0.421885i
$344$	2144.00	0.336037
$345$	0	0
$346$	3924.00	0.609698
$347$	− 2196.00i	− 0.339733i	−0.985467	−	0.169867i	$-0.945666\pi$
$347$	− 2196.00i	− 0.339733i	0.985467	−	0.169867i	$-0.0543337\pi$
$348$	2520.00i	0.388179i
$349$	−8270.00	−1.26843	−0.634216	−	0.773156i	$-0.718677\pi$
$349$	−8270.00	−1.26843	−0.634216	+	0.773156i	$0.718677\pi$
$350$	0	0
$351$	54.0000	0.00821170
$352$	1536.00i	0.232583i
$353$	10302.0i	1.55331i	0.629923	+	0.776657i	$0.283086\pi$
$353$	10302.0i	1.55331i	−0.629923	+	0.776657i	$0.716914\pi$
$354$	−1440.00	−0.216201
$355$	0	0
$356$	840.000	0.125056
$357$	− 1368.00i	− 0.202807i
$358$	− 240.000i	− 0.0354313i
$359$	2280.00	0.335192	0.167596	−	0.985856i	$-0.446400\pi$
$359$	2280.00	0.335192	0.167596	+	0.985856i	$0.446400\pi$
$360$	0	0
$361$	12741.0	1.85756
$362$	− 1804.00i	− 0.261923i
$363$	2919.00i	0.422060i
$364$	32.0000	0.00460785
$365$	0	0
$366$	1812.00	0.258783
$367$	8764.00i	1.24653i	0.782010	+	0.623266i	$0.214195\pi$
$367$	8764.00i	1.24653i	−0.782010	+	0.623266i	$0.785805\pi$
$368$	1152.00i	0.163185i
$369$	1782.00	0.251402
$370$	0	0
$371$	312.000	0.0436610
$372$	− 3264.00i	− 0.454921i
$373$	− 1318.00i	− 0.182958i	−0.995807	−	0.0914792i	$-0.970841\pi$
$373$	− 1318.00i	− 0.182958i	0.995807	−	0.0914792i	$-0.0291595\pi$
$374$	−10944.0	−1.51310
$375$	0	0
$376$	1728.00	0.237007
$377$	− 420.000i	− 0.0573769i
$378$	− 216.000i	− 0.0293911i
$379$	−1100.00	−0.149085	−0.0745425	−	0.997218i	$-0.523750\pi$
$379$	−1100.00	−0.149085	−0.0745425	+	0.997218i	$0.523750\pi$
$380$	0	0
$381$	−372.000	−0.0500214
$382$	336.000i	0.0450033i
$383$	− 3528.00i	− 0.470685i	−0.971912	−	0.235343i	$-0.924379\pi$
$383$	− 3528.00i	− 0.470685i	0.971912	−	0.235343i	$-0.0756212\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	−2636.00	−0.347588
$387$	2412.00i	0.316819i
$388$	− 6136.00i	− 0.802856i
$389$	9630.00	1.25517	0.627584	−	0.778549i	$-0.284044\pi$
$389$	9630.00	1.25517	0.627584	+	0.778549i	$0.284044\pi$
$390$	0	0
$391$	−8208.00	−1.06163
$392$	2616.00i	0.337061i
$393$	576.000i	0.0739322i
$394$	8028.00	1.02651
$395$	0	0
$396$	−1728.00	−0.219281
$397$	3094.00i	0.391142i	0.980690	+	0.195571i	$0.0626560\pi$
$397$	3094.00i	0.391142i	−0.980690	+	0.195571i	$0.937344\pi$
$398$	4000.00i	0.503774i
$399$	1680.00	0.210790
$400$	0	0
$401$	−1638.00	−0.203985	−0.101992	−	0.994785i	$-0.532522\pi$
$401$	−1638.00	−0.203985	−0.101992	+	0.994785i	$0.532522\pi$
$402$	− 3576.00i	− 0.443668i
$403$	544.000i	0.0672421i
$404$	−6888.00	−0.848245
$405$	0	0
$406$	−1680.00	−0.205362
$407$	− 16032.0i	− 1.95252i
$408$	− 2736.00i	− 0.331991i
$409$	13750.0	1.66233	0.831166	−	0.556024i	$-0.187674\pi$
$409$	13750.0	1.66233	0.831166	+	0.556024i	$0.187674\pi$
$410$	0	0
$411$	−7542.00	−0.905157
$412$	− 4208.00i	− 0.503188i
$413$	− 960.000i	− 0.114379i
$414$	−1296.00	−0.153852
$415$	0	0
$416$	64.0000	0.00754293
$417$	− 4020.00i	− 0.472087i
$418$	− 13440.0i	− 1.57266i
$419$	12480.0	1.45510	0.727551	−	0.686053i	$-0.240658\pi$
$419$	12480.0	1.45510	0.727551	+	0.686053i	$0.240658\pi$
$420$	0	0
$421$	7262.00	0.840685	0.420342	−	0.907366i	$-0.361910\pi$
$421$	7262.00	0.840685	0.420342	+	0.907366i	$0.361910\pi$
$422$	7736.00i	0.892376i
$423$	1944.00i	0.223453i
$424$	624.000	0.0714720
$425$	0	0
$426$	−4608.00	−0.524081
$427$	1208.00i	0.136907i
$428$	− 2256.00i	− 0.254785i
$429$	288.000	0.0324121
$430$	0	0
$431$	9792.00	1.09435	0.547174	−	0.837019i	$-0.315704\pi$
$431$	9792.00	1.09435	0.547174	+	0.837019i	$0.315704\pi$
$432$	− 432.000i	− 0.0481125i
$433$	1802.00i	0.199997i	0.994988	+	0.0999984i	$0.0318838\pi$
$433$	1802.00i	0.199997i	−0.994988	+	0.0999984i	$0.968116\pi$
$434$	2176.00	0.240671
$435$	0	0
$436$	−2440.00	−0.268016
$437$	− 10080.0i	− 1.10341i
$438$	− 2868.00i	− 0.312873i
$439$	2320.00	0.252227	0.126113	−	0.992016i	$-0.459750\pi$
$439$	2320.00	0.252227	0.126113	+	0.992016i	$0.459750\pi$
$440$	0	0
$441$	−2943.00	−0.317784
$442$	456.000i	0.0490717i
$443$	11172.0i	1.19819i	0.800678	+	0.599095i	$0.204473\pi$
$443$	11172.0i	1.19819i	−0.800678	+	0.599095i	$0.795527\pi$
$444$	4008.00	0.428404
$445$	0	0
$446$	−6296.00	−0.668440
$447$	− 4230.00i	− 0.447589i
$448$	− 256.000i	− 0.0269975i
$449$	−6810.00	−0.715777	−0.357888	−	0.933764i	$-0.616503\pi$
$449$	−6810.00	−0.715777	−0.357888	+	0.933764i	$0.616503\pi$
$450$	0	0
$451$	9504.00	0.992297
$452$	− 5208.00i	− 0.541955i
$453$	− 6384.00i	− 0.662134i
$454$	−5112.00	−0.528454
$455$	0	0
$456$	3360.00	0.345058
$457$	− 17066.0i	− 1.74686i	−0.486952	−	0.873429i	$-0.661891\pi$
$457$	− 17066.0i	− 1.74686i	0.486952	−	0.873429i	$-0.338109\pi$
$458$	− 1220.00i	− 0.124469i
$459$	3078.00	0.313004
$460$	0	0
$461$	−18918.0	−1.91128	−0.955639	−	0.294541i	$-0.904833\pi$
$461$	−18918.0	−1.91128	−0.955639	+	0.294541i	$0.904833\pi$
$462$	− 1152.00i	− 0.116008i
$463$	1052.00i	0.105595i	0.998605	+	0.0527976i	$0.0168138\pi$
$463$	1052.00i	0.105595i	−0.998605	+	0.0527976i	$0.983186\pi$
$464$	−3360.00	−0.336173
$465$	0	0
$466$	−4116.00	−0.409163
$467$	− 11076.0i	− 1.09751i	−0.835984	−	0.548754i	$-0.815102\pi$
$467$	− 11076.0i	− 1.09751i	0.835984	−	0.548754i	$-0.184898\pi$
$468$	72.0000i	0.00711154i
$469$	2384.00	0.234718
$470$	0	0
$471$	9078.00	0.888094
$472$	− 1920.00i	− 0.187236i
$473$	12864.0i	1.25050i
$474$	3840.00	0.372103
$475$	0	0
$476$	1824.00	0.175636
$477$	702.000i	0.0673844i
$478$	9840.00i	0.941571i
$479$	9000.00	0.858498	0.429249	−	0.903186i	$-0.358778\pi$
$479$	9000.00	0.858498	0.429249	+	0.903186i	$0.358778\pi$
$480$	0	0
$481$	−668.000	−0.0633226
$482$	2876.00i	0.271781i
$483$	− 864.000i	− 0.0813941i
$484$	−3892.00	−0.365515
$485$	0	0
$486$	486.000	0.0453609
$487$	8764.00i	0.815472i	0.913100	+	0.407736i	$0.133682\pi$
$487$	8764.00i	0.815472i	−0.913100	+	0.407736i	$0.866318\pi$
$488$	2416.00i	0.224113i
$489$	−7836.00	−0.724655
$490$	0	0
$491$	5592.00	0.513978	0.256989	−	0.966414i	$-0.417270\pi$
$491$	5592.00	0.513978	0.256989	+	0.966414i	$0.417270\pi$
$492$	2376.00i	0.217720i
$493$	− 23940.0i	− 2.18703i
$494$	−560.000	−0.0510032
$495$	0	0
$496$	4352.00	0.393973
$497$	− 3072.00i	− 0.277260i
$498$	− 2088.00i	− 0.187883i
$499$	−4700.00	−0.421645	−0.210823	−	0.977524i	$-0.567614\pi$
$499$	−4700.00	−0.421645	−0.210823	+	0.977524i	$0.567614\pi$
$500$	0	0
$501$	−72.0000	−0.00642060
$502$	− 1584.00i	− 0.140831i
$503$	− 11808.0i	− 1.04671i	−0.852116	−	0.523353i	$-0.824681\pi$
$503$	− 11808.0i	− 1.04671i	0.852116	−	0.523353i	$-0.175319\pi$
$504$	288.000	0.0254535
$505$	0	0
$506$	−6912.00	−0.607265
$507$	6579.00i	0.576299i
$508$	− 496.000i	− 0.0433198i
$509$	−1170.00	−0.101885	−0.0509424	−	0.998702i	$-0.516222\pi$
$509$	−1170.00	−0.101885	−0.0509424	+	0.998702i	$0.516222\pi$
$510$	0	0
$511$	1912.00	0.165522
$512$	− 512.000i	− 0.0441942i
$513$	3780.00i	0.325324i
$514$	−4332.00	−0.371744
$515$	0	0
$516$	−3216.00	−0.274373
$517$	10368.0i	0.881981i
$518$	2672.00i	0.226643i
$519$	−5886.00	−0.497816
$520$	0	0
$521$	−16638.0	−1.39909	−0.699543	−	0.714590i	$-0.746613\pi$
$521$	−16638.0	−1.39909	−0.699543	+	0.714590i	$0.746613\pi$
$522$	− 3780.00i	− 0.316947i
$523$	15692.0i	1.31198i	0.754771	+	0.655988i	$0.227748\pi$
$523$	15692.0i	1.31198i	−0.754771	+	0.655988i	$0.772252\pi$
$524$	−768.000	−0.0640272
$525$	0	0
$526$	6384.00	0.529193
$527$	31008.0i	2.56305i
$528$	− 2304.00i	− 0.189903i
$529$	6983.00	0.573929
$530$	0	0
$531$	2160.00	0.176527
$532$	2240.00i	0.182549i
$533$	− 396.000i	− 0.0321814i
$534$	−1260.00	−0.102108
$535$	0	0
$536$	4768.00	0.384228
$537$	360.000i	0.0289295i
$538$	10980.0i	0.879891i
$539$	−15696.0	−1.25431
$540$	0	0
$541$	−22018.0	−1.74977	−0.874887	−	0.484327i	$-0.839064\pi$
$541$	−22018.0	−1.74977	−0.874887	+	0.484327i	$0.839064\pi$
$542$	12656.0i	1.00299i
$543$	2706.00i	0.213859i
$544$	3648.00	0.287512
$545$	0	0
$546$	−48.0000	−0.00376229
$547$	4564.00i	0.356751i	0.983963	+	0.178375i	$0.0570841\pi$
$547$	4564.00i	0.356751i	−0.983963	+	0.178375i	$0.942916\pi$
$548$	− 10056.0i	− 0.783889i
$549$	−2718.00	−0.211296
$550$	0	0
$551$	29400.0	2.27311
$552$	− 1728.00i	− 0.133240i
$553$	2560.00i	0.196858i
$554$	1148.00	0.0880394
$555$	0	0
$556$	5360.00	0.408839
$557$	7734.00i	0.588331i	0.955755	+	0.294165i	$0.0950416\pi$
$557$	7734.00i	0.588331i	−0.955755	+	0.294165i	$0.904958\pi$
$558$	4896.00i	0.371441i
$559$	536.000	0.0405552
$560$	0	0
$561$	16416.0	1.23544
$562$	− 8484.00i	− 0.636790i
$563$	− 20148.0i	− 1.50824i	−0.656739	−	0.754118i	$-0.728065\pi$
$563$	− 20148.0i	− 1.50824i	0.656739	−	0.754118i	$-0.271935\pi$
$564$	−2592.00	−0.193516
$565$	0	0
$566$	−1256.00	−0.0932749
$567$	324.000i	0.0239977i
$568$	− 6144.00i	− 0.453867i
$569$	24030.0	1.77046	0.885228	−	0.465156i	$-0.154002\pi$
$569$	24030.0	1.77046	0.885228	+	0.465156i	$0.154002\pi$
$570$	0	0
$571$	2372.00	0.173844	0.0869222	−	0.996215i	$-0.472297\pi$
$571$	2372.00	0.173844	0.0869222	+	0.996215i	$0.472297\pi$
$572$	384.000i	0.0280697i
$573$	− 504.000i	− 0.0367450i
$574$	−1584.00	−0.115183
$575$	0	0
$576$	576.000	0.0416667
$577$	− 8546.00i	− 0.616594i	−0.951290	−	0.308297i	$-0.900241\pi$
$577$	− 8546.00i	− 0.616594i	0.951290	−	0.308297i	$-0.0997590\pi$
$578$	16166.0i	1.16335i
$579$	3954.00	0.283804
$580$	0	0
$581$	1392.00	0.0993974
$582$	9204.00i	0.655529i
$583$	3744.00i	0.265970i
$584$	3824.00	0.270956
$585$	0	0
$586$	−1116.00	−0.0786716
$587$	15444.0i	1.08593i	0.839755	+	0.542966i	$0.182699\pi$
$587$	15444.0i	1.08593i	−0.839755	+	0.542966i	$0.817301\pi$
$588$	− 3924.00i	− 0.275209i
$589$	−38080.0	−2.66394
$590$	0	0
$591$	−12042.0	−0.838142
$592$	5344.00i	0.371009i
$593$	18342.0i	1.27018i	0.772439	+	0.635089i	$0.219037\pi$
$593$	18342.0i	1.27018i	−0.772439	+	0.635089i	$0.780963\pi$
$594$	2592.00	0.179042
$595$	0	0
$596$	5640.00	0.387623
$597$	− 6000.00i	− 0.411329i
$598$	288.000i	0.0196943i
$599$	−24600.0	−1.67801	−0.839006	−	0.544123i	$-0.816863\pi$
$599$	−24600.0	−1.67801	−0.839006	+	0.544123i	$0.816863\pi$
$600$	0	0
$601$	−8998.00	−0.610709	−0.305354	−	0.952239i	$-0.598775\pi$
$601$	−8998.00	−0.610709	−0.305354	+	0.952239i	$0.598775\pi$
$602$	− 2144.00i	− 0.145154i
$603$	5364.00i	0.362254i
$604$	8512.00	0.573424
$605$	0	0
$606$	10332.0	0.692589
$607$	− 4076.00i	− 0.272553i	−0.990671	−	0.136277i	$-0.956486\pi$
$607$	− 4076.00i	− 0.272553i	0.990671	−	0.136277i	$-0.0435136\pi$
$608$	4480.00i	0.298829i
$609$	2520.00	0.167677
$610$	0	0
$611$	432.000	0.0286037
$612$	4104.00i	0.271069i
$613$	− 4078.00i	− 0.268693i	−0.990934	−	0.134347i	$-0.957106\pi$
$613$	− 4078.00i	− 0.268693i	0.990934	−	0.134347i	$-0.0428935\pi$
$614$	13928.0	0.915453
$615$	0	0
$616$	1536.00	0.100466
$617$	− 10086.0i	− 0.658099i	−0.944313	−	0.329049i	$-0.893272\pi$
$617$	− 10086.0i	− 0.658099i	0.944313	−	0.329049i	$-0.106728\pi$
$618$	6312.00i	0.410851i
$619$	−8780.00	−0.570110	−0.285055	−	0.958511i	$-0.592012\pi$
$619$	−8780.00	−0.570110	−0.285055	+	0.958511i	$0.592012\pi$
$620$	0	0
$621$	1944.00	0.125620
$622$	− 5664.00i	− 0.365122i
$623$	− 840.000i	− 0.0540191i
$624$	−96.0000	−0.00615878
$625$	0	0
$626$	17284.0	1.10353
$627$	20160.0i	1.28407i
$628$	12104.0i	0.769112i
$629$	−38076.0	−2.41366
$630$	0	0
$631$	2792.00	0.176145	0.0880727	−	0.996114i	$-0.471929\pi$
$631$	2792.00	0.176145	0.0880727	+	0.996114i	$0.471929\pi$
$632$	5120.00i	0.322251i
$633$	− 11604.0i	− 0.728622i
$634$	4428.00	0.277379
$635$	0	0
$636$	−936.000	−0.0583566
$637$	654.000i	0.0406788i
$638$	− 20160.0i	− 1.25101i
$639$	6912.00	0.427910
$640$	0	0
$641$	7602.00	0.468426	0.234213	−	0.972185i	$-0.424749\pi$
$641$	7602.00	0.468426	0.234213	+	0.972185i	$0.424749\pi$
$642$	3384.00i	0.208031i
$643$	24212.0i	1.48496i	0.669869	+	0.742479i	$0.266350\pi$
$643$	24212.0i	1.48496i	−0.669869	+	0.742479i	$0.733650\pi$
$644$	1152.00	0.0704894
$645$	0	0
$646$	−31920.0	−1.94408
$647$	− 9456.00i	− 0.574581i	−0.957844	−	0.287290i	$-0.907246\pi$
$647$	− 9456.00i	− 0.574581i	0.957844	−	0.287290i	$-0.0927545\pi$
$648$	648.000i	0.0392837i
$649$	11520.0	0.696764
$650$	0	0
$651$	−3264.00	−0.196507
$652$	− 10448.0i	− 0.627569i
$653$	− 9558.00i	− 0.572792i	−0.958111	−	0.286396i	$-0.907543\pi$
$653$	− 9558.00i	− 0.572792i	0.958111	−	0.286396i	$-0.0924574\pi$
$654$	3660.00	0.218834
$655$	0	0
$656$	−3168.00	−0.188551
$657$	4302.00i	0.255460i
$658$	− 1728.00i	− 0.102378i
$659$	29280.0	1.73078	0.865392	−	0.501095i	$-0.167069\pi$
$659$	29280.0	1.73078	0.865392	+	0.501095i	$0.167069\pi$
$660$	0	0
$661$	−29098.0	−1.71223	−0.856113	−	0.516789i	$-0.827127\pi$
$661$	−29098.0	−1.71223	−0.856113	+	0.516789i	$0.827127\pi$
$662$	− 21544.0i	− 1.26485i
$663$	− 684.000i	− 0.0400669i
$664$	2784.00	0.162711
$665$	0	0
$666$	−6012.00	−0.349790
$667$	− 15120.0i	− 0.877734i
$668$	− 96.0000i	− 0.00556041i
$669$	9444.00	0.545779
$670$	0	0
$671$	−14496.0	−0.833997
$672$	384.000i	0.0220433i
$673$	− 11638.0i	− 0.666585i	−0.942823	−	0.333293i	$-0.891840\pi$
$673$	− 11638.0i	− 0.666585i	0.942823	−	0.333293i	$-0.108160\pi$
$674$	3308.00	0.189050
$675$	0	0
$676$	−8772.00	−0.499090
$677$	− 3426.00i	− 0.194493i	−0.995260	−	0.0972466i	$-0.968996\pi$
$677$	− 3426.00i	− 0.194493i	0.995260	−	0.0972466i	$-0.0310035\pi$
$678$	7812.00i	0.442505i
$679$	−6136.00	−0.346801
$680$	0	0
$681$	7668.00	0.431481
$682$	26112.0i	1.46610i
$683$	− 20148.0i	− 1.12876i	−0.825516	−	0.564379i	$-0.809116\pi$
$683$	− 20148.0i	− 1.12876i	0.825516	−	0.564379i	$-0.190884\pi$
$684$	−5040.00	−0.281739
$685$	0	0
$686$	5360.00	0.298317
$687$	1830.00i	0.101629i
$688$	− 4288.00i	− 0.237614i
$689$	156.000	0.00862573
$690$	0	0
$691$	−29428.0	−1.62011	−0.810053	−	0.586356i	$-0.800562\pi$
$691$	−29428.0	−1.62011	−0.810053	+	0.586356i	$0.800562\pi$
$692$	− 7848.00i	− 0.431122i
$693$	1728.00i	0.0947205i
$694$	−4392.00	−0.240228
$695$	0	0
$696$	5040.00	0.274484
$697$	− 22572.0i	− 1.22665i
$698$	16540.0i	0.896917i
$699$	6174.00	0.334080
$700$	0	0
$701$	16242.0	0.875110	0.437555	−	0.899192i	$-0.355845\pi$
$701$	16242.0	0.875110	0.437555	+	0.899192i	$0.355845\pi$
$702$	− 108.000i	− 0.00580655i
$703$	− 46760.0i	− 2.50866i
$704$	3072.00	0.164461
$705$	0	0
$706$	20604.0	1.09836
$707$	6888.00i	0.366407i
$708$	2880.00i	0.152877i
$709$	−2030.00	−0.107529	−0.0537646	−	0.998554i	$-0.517122\pi$
$709$	−2030.00	−0.107529	−0.0537646	+	0.998554i	$0.517122\pi$
$710$	0	0
$711$	−5760.00	−0.303821
$712$	− 1680.00i	− 0.0884279i
$713$	19584.0i	1.02865i
$714$	−2736.00	−0.143406
$715$	0	0
$716$	−480.000	−0.0250537
$717$	− 14760.0i	− 0.768790i
$718$	− 4560.00i	− 0.237016i
$719$	−6960.00	−0.361007	−0.180504	−	0.983574i	$-0.557773\pi$
$719$	−6960.00	−0.361007	−0.180504	+	0.983574i	$0.557773\pi$
$720$	0	0
$721$	−4208.00	−0.217357
$722$	− 25482.0i	− 1.31349i
$723$	− 4314.00i	− 0.221908i
$724$	−3608.00	−0.185208
$725$	0	0
$726$	5838.00	0.298441
$727$	− 18596.0i	− 0.948676i	−0.880343	−	0.474338i	$-0.842687\pi$
$727$	− 18596.0i	− 0.948676i	0.880343	−	0.474338i	$-0.157313\pi$
$728$	− 64.0000i	− 0.00325824i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	30552.0	1.54584
$732$	− 3624.00i	− 0.182988i
$733$	21242.0i	1.07038i	0.844731	+	0.535192i	$0.179761\pi$
$733$	21242.0i	1.07038i	−0.844731	+	0.535192i	$0.820239\pi$
$734$	17528.0	0.881431
$735$	0	0
$736$	2304.00	0.115389
$737$	28608.0i	1.42984i
$738$	− 3564.00i	− 0.177768i
$739$	340.000	0.0169244	0.00846218	−	0.999964i	$-0.497306\pi$
$739$	340.000	0.0169244	0.00846218	+	0.999964i	$0.497306\pi$
$740$	0	0
$741$	840.000	0.0416440
$742$	− 624.000i	− 0.0308730i
$743$	− 21888.0i	− 1.08074i	−0.841426	−	0.540372i	$-0.818284\pi$
$743$	− 21888.0i	− 1.08074i	0.841426	−	0.540372i	$-0.181716\pi$
$744$	−6528.00	−0.321678
$745$	0	0
$746$	−2636.00	−0.129371
$747$	3132.00i	0.153405i
$748$	21888.0i	1.06993i
$749$	−2256.00	−0.110057
$750$	0	0
$751$	17792.0	0.864500	0.432250	−	0.901754i	$-0.357720\pi$
$751$	17792.0	0.864500	0.432250	+	0.901754i	$0.357720\pi$
$752$	− 3456.00i	− 0.167590i
$753$	2376.00i	0.114988i
$754$	−840.000	−0.0405716
$755$	0	0
$756$	−432.000	−0.0207827
$757$	− 37346.0i	− 1.79308i	−0.442960	−	0.896541i	$-0.646072\pi$
$757$	− 37346.0i	− 1.79308i	0.442960	−	0.896541i	$-0.353928\pi$
$758$	2200.00i	0.105419i
$759$	10368.0	0.495829
$760$	0	0
$761$	−11358.0	−0.541034	−0.270517	−	0.962715i	$-0.587195\pi$
$761$	−11358.0	−0.541034	−0.270517	+	0.962715i	$0.587195\pi$
$762$	744.000i	0.0353704i
$763$	2440.00i	0.115772i
$764$	672.000	0.0318221
$765$	0	0
$766$	−7056.00	−0.332825
$767$	− 480.000i	− 0.0225969i
$768$	768.000i	0.0360844i
$769$	34270.0	1.60703	0.803516	−	0.595283i	$-0.202960\pi$
$769$	34270.0	1.60703	0.803516	+	0.595283i	$0.202960\pi$
$770$	0	0
$771$	6498.00	0.303528
$772$	5272.00i	0.245782i
$773$	− 13278.0i	− 0.617822i	−0.951091	−	0.308911i	$-0.900035\pi$
$773$	− 13278.0i	− 0.617822i	0.951091	−	0.308911i	$-0.0999645\pi$
$774$	4824.00	0.224025
$775$	0	0
$776$	−12272.0	−0.567705
$777$	− 4008.00i	− 0.185053i
$778$	− 19260.0i	− 0.887538i
$779$	27720.0	1.27493
$780$	0	0
$781$	36864.0	1.68899
$782$	16416.0i	0.750684i
$783$	5670.00i	0.258786i
$784$	5232.00	0.238338
$785$	0	0
$786$	1152.00	0.0522780
$787$	11164.0i	0.505659i	0.967511	+	0.252829i	$0.0813612\pi$
$787$	11164.0i	0.505659i	−0.967511	+	0.252829i	$0.918639\pi$
$788$	− 16056.0i	− 0.725852i
$789$	−9576.00	−0.432084
$790$	0	0
$791$	−5208.00	−0.234103
$792$	3456.00i	0.155055i
$793$	604.000i	0.0270475i
$794$	6188.00	0.276579
$795$	0	0
$796$	8000.00	0.356222
$797$	5094.00i	0.226397i	0.993572	+	0.113199i	$0.0361097\pi$
$797$	5094.00i	0.226397i	−0.993572	+	0.113199i	$0.963890\pi$
$798$	− 3360.00i	− 0.149051i
$799$	24624.0	1.09028
$800$	0	0
$801$	1890.00	0.0833706
$802$	3276.00i	0.144239i
$803$	22944.0i	1.00831i
$804$	−7152.00	−0.313721
$805$	0	0
$806$	1088.00	0.0475474
$807$	− 16470.0i	− 0.718428i
$808$	13776.0i	0.599799i
$809$	8790.00	0.382002	0.191001	−	0.981590i	$-0.438827\pi$
$809$	8790.00	0.382002	0.191001	+	0.981590i	$0.438827\pi$
$810$	0	0
$811$	5852.00	0.253380	0.126690	−	0.991942i	$-0.459565\pi$
$811$	5852.00	0.253380	0.126690	+	0.991942i	$0.459565\pi$
$812$	3360.00i	0.145213i
$813$	− 18984.0i	− 0.818940i
$814$	−32064.0	−1.38064
$815$	0	0
$816$	−5472.00	−0.234753
$817$	37520.0i	1.60668i
$818$	− 27500.0i	− 1.17545i
$819$	72.0000	0.00307190
$820$	0	0
$821$	−29478.0	−1.25309	−0.626546	−	0.779384i	$-0.715532\pi$
$821$	−29478.0	−1.25309	−0.626546	+	0.779384i	$0.715532\pi$
$822$	15084.0i	0.640042i
$823$	39332.0i	1.66589i	0.553356	+	0.832945i	$0.313347\pi$
$823$	39332.0i	1.66589i	−0.553356	+	0.832945i	$0.686653\pi$
$824$	−8416.00	−0.355807
$825$	0	0
$826$	−1920.00	−0.0808781
$827$	− 6756.00i	− 0.284074i	−0.989861	−	0.142037i	$-0.954635\pi$
$827$	− 6756.00i	− 0.284074i	0.989861	−	0.142037i	$-0.0453652\pi$
$828$	2592.00i	0.108790i
$829$	−3950.00	−0.165488	−0.0827438	−	0.996571i	$-0.526368\pi$
$829$	−3950.00	−0.165488	−0.0827438	+	0.996571i	$0.526368\pi$
$830$	0	0
$831$	−1722.00	−0.0718839
$832$	− 128.000i	− 0.00533366i
$833$	37278.0i	1.55055i
$834$	−8040.00	−0.333816
$835$	0	0
$836$	−26880.0	−1.11204
$837$	− 7344.00i	− 0.303280i
$838$	− 24960.0i	− 1.02891i
$839$	−12360.0	−0.508599	−0.254300	−	0.967126i	$-0.581845\pi$
$839$	−12360.0	−0.508599	−0.254300	+	0.967126i	$0.581845\pi$
$840$	0	0
$841$	19711.0	0.808192
$842$	− 14524.0i	− 0.594454i
$843$	12726.0i	0.519937i
$844$	15472.0	0.631005
$845$	0	0
$846$	3888.00	0.158005
$847$	3892.00i	0.157887i
$848$	− 1248.00i	− 0.0505383i
$849$	1884.00	0.0761587
$850$	0	0
$851$	−24048.0	−0.968690
$852$	9216.00i	0.370581i
$853$	− 35998.0i	− 1.44496i	−0.691394	−	0.722478i	$-0.743003\pi$
$853$	− 35998.0i	− 1.44496i	0.691394	−	0.722478i	$-0.256997\pi$
$854$	2416.00	0.0968077
$855$	0	0
$856$	−4512.00	−0.180160
$857$	21594.0i	0.860720i	0.902657	+	0.430360i	$0.141613\pi$
$857$	21594.0i	0.860720i	−0.902657	+	0.430360i	$0.858387\pi$
$858$	− 576.000i	− 0.0229188i
$859$	−9260.00	−0.367808	−0.183904	−	0.982944i	$-0.558874\pi$
$859$	−9260.00	−0.367808	−0.183904	+	0.982944i	$0.558874\pi$
$860$	0	0
$861$	2376.00	0.0940463
$862$	− 19584.0i	− 0.773821i
$863$	31632.0i	1.24770i	0.781544	+	0.623850i	$0.214433\pi$
$863$	31632.0i	1.24770i	−0.781544	+	0.623850i	$0.785567\pi$
$864$	−864.000	−0.0340207
$865$	0	0
$866$	3604.00	0.141419
$867$	− 24249.0i	− 0.949872i
$868$	− 4352.00i	− 0.170180i
$869$	−30720.0	−1.19920
$870$	0	0
$871$	1192.00	0.0463713
$872$	4880.00i	0.189516i
$873$	− 13806.0i	− 0.535237i
$874$	−20160.0	−0.780231
$875$	0	0
$876$	−5736.00	−0.221235
$877$	39694.0i	1.52836i	0.645003	+	0.764180i	$0.276856\pi$
$877$	39694.0i	1.52836i	−0.645003	+	0.764180i	$0.723144\pi$
$878$	− 4640.00i	− 0.178351i
$879$	1674.00	0.0642351
$880$	0	0
$881$	1242.00	0.0474961	0.0237480	−	0.999718i	$-0.492440\pi$
$881$	1242.00	0.0474961	0.0237480	+	0.999718i	$0.492440\pi$
$882$	5886.00i	0.224707i
$883$	− 2668.00i	− 0.101682i	−0.998707	−	0.0508411i	$-0.983810\pi$
$883$	− 2668.00i	− 0.101682i	0.998707	−	0.0508411i	$-0.0161902\pi$
$884$	912.000	0.0346990
$885$	0	0
$886$	22344.0	0.847248
$887$	4344.00i	0.164439i	0.996614	+	0.0822194i	$0.0262008\pi$
$887$	4344.00i	0.164439i	−0.996614	+	0.0822194i	$0.973799\pi$
$888$	− 8016.00i	− 0.302927i
$889$	−496.000	−0.0187124
$890$	0	0
$891$	−3888.00	−0.146187
$892$	12592.0i	0.472658i
$893$	30240.0i	1.13319i
$894$	−8460.00	−0.316493
$895$	0	0
$896$	−512.000	−0.0190901
$897$	− 432.000i	− 0.0160803i
$898$	13620.0i	0.506131i
$899$	−57120.0	−2.11909
$900$	0	0
$901$	8892.00	0.328785
$902$	− 19008.0i	− 0.701660i
$903$	3216.00i	0.118518i
$904$	−10416.0	−0.383220
$905$	0	0
$906$	−12768.0	−0.468199
$907$	− 4436.00i	− 0.162398i	−0.996698	−	0.0811990i	$-0.974125\pi$
$907$	− 4436.00i	− 0.162398i	0.996698	−	0.0811990i	$-0.0258749\pi$
$908$	10224.0i	0.373673i
$909$	−15498.0	−0.565496
$910$	0	0
$911$	22752.0	0.827450	0.413725	−	0.910402i	$-0.364227\pi$
$911$	22752.0	0.827450	0.413725	+	0.910402i	$0.364227\pi$
$912$	− 6720.00i	− 0.243993i
$913$	16704.0i	0.605500i
$914$	−34132.0	−1.23521
$915$	0	0
$916$	−2440.00	−0.0880130
$917$	768.000i	0.0276571i
$918$	− 6156.00i	− 0.221327i
$919$	27160.0	0.974892	0.487446	−	0.873153i	$-0.337929\pi$
$919$	27160.0	0.974892	0.487446	+	0.873153i	$0.337929\pi$
$920$	0	0
$921$	−20892.0	−0.747465
$922$	37836.0i	1.35148i
$923$	− 1536.00i	− 0.0547758i
$924$	−2304.00	−0.0820303
$925$	0	0
$926$	2104.00	0.0746671
$927$	− 9468.00i	− 0.335458i
$928$	6720.00i	0.237710i
$929$	33030.0	1.16650	0.583250	−	0.812292i	$-0.301781\pi$
$929$	33030.0	1.16650	0.583250	+	0.812292i	$0.301781\pi$
$930$	0	0
$931$	−45780.0	−1.61158
$932$	8232.00i	0.289322i
$933$	8496.00i	0.298121i
$934$	−22152.0	−0.776055
$935$	0	0
$936$	144.000	0.00502862
$937$	29974.0i	1.04505i	0.852625	+	0.522523i	$0.175009\pi$
$937$	29974.0i	1.04505i	−0.852625	+	0.522523i	$0.824991\pi$
$938$	− 4768.00i	− 0.165971i
$939$	−25926.0	−0.901026
$940$	0	0
$941$	13962.0	0.483686	0.241843	−	0.970315i	$-0.422248\pi$
$941$	13962.0	0.483686	0.241843	+	0.970315i	$0.422248\pi$
$942$	− 18156.0i	− 0.627977i
$943$	− 14256.0i	− 0.492300i
$944$	−3840.00	−0.132396
$945$	0	0
$946$	25728.0	0.884238
$947$	− 35196.0i	− 1.20773i	−0.797088	−	0.603863i	$-0.793627\pi$
$947$	− 35196.0i	− 1.20773i	0.797088	−	0.603863i	$-0.206373\pi$
$948$	− 7680.00i	− 0.263117i
$949$	956.000	0.0327008
$950$	0	0
$951$	−6642.00	−0.226479
$952$	− 3648.00i	− 0.124194i
$953$	− 28338.0i	− 0.963230i	−0.876383	−	0.481615i	$-0.840050\pi$
$953$	− 28338.0i	− 0.963230i	0.876383	−	0.481615i	$-0.159950\pi$
$954$	1404.00	0.0476480
$955$	0	0
$956$	19680.0	0.665792
$957$	30240.0i	1.02144i
$958$	− 18000.0i	− 0.607050i
$959$	−10056.0	−0.338608
$960$	0	0
$961$	44193.0	1.48343
$962$	1336.00i	0.0447759i
$963$	− 5076.00i	− 0.169857i
$964$	5752.00	0.192178
$965$	0	0
$966$	−1728.00	−0.0575543
$967$	17524.0i	0.582765i	0.956607	+	0.291383i	$0.0941153\pi$
$967$	17524.0i	0.582765i	−0.956607	+	0.291383i	$0.905885\pi$
$968$	7784.00i	0.258458i
$969$	47880.0	1.58733
$970$	0	0
$971$	−26808.0	−0.886004	−0.443002	−	0.896521i	$-0.646087\pi$
$971$	−26808.0	−0.886004	−0.443002	+	0.896521i	$0.646087\pi$
$972$	− 972.000i	− 0.0320750i
$973$	− 5360.00i	− 0.176602i
$974$	17528.0	0.576626
$975$	0	0
$976$	4832.00	0.158472
$977$	10914.0i	0.357390i	0.983905	+	0.178695i	$0.0571875\pi$
$977$	10914.0i	0.357390i	−0.983905	+	0.178695i	$0.942813\pi$
$978$	15672.0i	0.512408i
$979$	10080.0	0.329069
$980$	0	0
$981$	−5490.00	−0.178677
$982$	− 11184.0i	− 0.363438i
$983$	22272.0i	0.722652i	0.932440	+	0.361326i	$0.117676\pi$
$983$	22272.0i	0.722652i	−0.932440	+	0.361326i	$0.882324\pi$
$984$	4752.00	0.153951
$985$	0	0
$986$	−47880.0	−1.54646
$987$	2592.00i	0.0835910i
$988$	1120.00i	0.0360647i
$989$	19296.0	0.620402
$990$	0	0
$991$	14072.0	0.451071	0.225536	−	0.974235i	$-0.427587\pi$
$991$	14072.0	0.451071	0.225536	+	0.974235i	$0.427587\pi$
$992$	− 8704.00i	− 0.278581i
$993$	32316.0i	1.03275i
$994$	−6144.00	−0.196052
$995$	0	0
$996$	−4176.00	−0.132853
$997$	− 4826.00i	− 0.153301i	−0.997058	−	0.0766504i	$-0.975577\pi$
$997$	− 4826.00i	− 0.153301i	0.997058	−	0.0766504i	$-0.0244225\pi$
$998$	9400.00i	0.298148i
$999$	9018.00	0.285602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.4.c.c.49.1		2
3.2	odd	2		450.4.c.j.199.2		2
4.3	odd	2		1200.4.f.r.49.1		2
5.2	odd	4		30.4.a.b.1.1	✓	1
5.3	odd	4		150.4.a.b.1.1		1
5.4	even	2	inner	150.4.c.c.49.2		2
15.2	even	4		90.4.a.c.1.1		1
15.8	even	4		450.4.a.r.1.1		1
15.14	odd	2		450.4.c.j.199.1		2
20.3	even	4		1200.4.a.ba.1.1		1
20.7	even	4		240.4.a.b.1.1		1
20.19	odd	2		1200.4.f.r.49.2		2
35.27	even	4		1470.4.a.r.1.1		1
40.27	even	4		960.4.a.bg.1.1		1
40.37	odd	4		960.4.a.n.1.1		1
45.2	even	12		810.4.e.p.271.1		2
45.7	odd	12		810.4.e.i.271.1		2
45.22	odd	12		810.4.e.i.541.1		2
45.32	even	12		810.4.e.p.541.1		2
60.47	odd	4		720.4.a.y.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.4.a.b.1.1	✓	1	5.2	odd	4
90.4.a.c.1.1		1	15.2	even	4
150.4.a.b.1.1		1	5.3	odd	4
150.4.c.c.49.1		2	1.1	even	1	trivial
150.4.c.c.49.2		2	5.4	even	2	inner
240.4.a.b.1.1		1	20.7	even	4
450.4.a.r.1.1		1	15.8	even	4
450.4.c.j.199.1		2	15.14	odd	2
450.4.c.j.199.2		2	3.2	odd	2
720.4.a.y.1.1		1	60.47	odd	4
810.4.e.i.271.1		2	45.7	odd	12
810.4.e.i.541.1		2	45.22	odd	12
810.4.e.p.271.1		2	45.2	even	12
810.4.e.p.541.1		2	45.32	even	12
960.4.a.n.1.1		1	40.37	odd	4
960.4.a.bg.1.1		1	40.27	even	4
1200.4.a.ba.1.1		1	20.3	even	4
1200.4.f.r.49.1		2	4.3	odd	2
1200.4.f.r.49.2		2	20.19	odd	2
1470.4.a.r.1.1		1	35.27	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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	150.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +6.00000 q^{6} +4.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +6.00000 q^{6} +4.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} -48.0000 q^{11} -12.0000i q^{12} +2.00000i q^{13} +8.00000 q^{14} +16.0000 q^{16} +114.000i q^{17} +18.0000i q^{18} -140.000 q^{19} -12.0000 q^{21} +96.0000i q^{22} +72.0000i q^{23} -24.0000 q^{24} +4.00000 q^{26} -27.0000i q^{27} -16.0000i q^{28} -210.000 q^{29} +272.000 q^{31} -32.0000i q^{32} -144.000i q^{33} +228.000 q^{34} +36.0000 q^{36} +334.000i q^{37} +280.000i q^{38} -6.00000 q^{39} -198.000 q^{41} +24.0000i q^{42} -268.000i q^{43} +192.000 q^{44} +144.000 q^{46} -216.000i q^{47} +48.0000i q^{48} +327.000 q^{49} -342.000 q^{51} -8.00000i q^{52} -78.0000i q^{53} -54.0000 q^{54} -32.0000 q^{56} -420.000i q^{57} +420.000i q^{58} -240.000 q^{59} +302.000 q^{61} -544.000i q^{62} -36.0000i q^{63} -64.0000 q^{64} -288.000 q^{66} -596.000i q^{67} -456.000i q^{68} -216.000 q^{69} -768.000 q^{71} -72.0000i q^{72} -478.000i q^{73} +668.000 q^{74} +560.000 q^{76} -192.000i q^{77} +12.0000i q^{78} +640.000 q^{79} +81.0000 q^{81} +396.000i q^{82} -348.000i q^{83} +48.0000 q^{84} -536.000 q^{86} -630.000i q^{87} -384.000i q^{88} -210.000 q^{89} -8.00000 q^{91} -288.000i q^{92} +816.000i q^{93} -432.000 q^{94} +96.0000 q^{96} +1534.00i q^{97} -654.000i q^{98} +432.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{4} + 12 q^{6} - 18 q^{9}+O(q^{10}) \) 2 * q - 8 * q^4 + 12 * q^6 - 18 * q^9	\( 2 q - 8 q^{4} + 12 q^{6} - 18 q^{9} - 96 q^{11} + 16 q^{14} + 32 q^{16} - 280 q^{19} - 24 q^{21} - 48 q^{24} + 8 q^{26} - 420 q^{29} + 544 q^{31} + 456 q^{34} + 72 q^{36} - 12 q^{39} - 396 q^{41} + 384 q^{44} + 288 q^{46} + 654 q^{49} - 684 q^{51} - 108 q^{54} - 64 q^{56} - 480 q^{59} + 604 q^{61} - 128 q^{64} - 576 q^{66} - 432 q^{69} - 1536 q^{71} + 1336 q^{74} + 1120 q^{76} + 1280 q^{79} + 162 q^{81} + 96 q^{84} - 1072 q^{86} - 420 q^{89} - 16 q^{91} - 864 q^{94} + 192 q^{96} + 864 q^{99}+O(q^{100}) \) 2 * q - 8 * q^4 + 12 * q^6 - 18 * q^9 - 96 * q^11 + 16 * q^14 + 32 * q^16 - 280 * q^19 - 24 * q^21 - 48 * q^24 + 8 * q^26 - 420 * q^29 + 544 * q^31 + 456 * q^34 + 72 * q^36 - 12 * q^39 - 396 * q^41 + 384 * q^44 + 288 * q^46 + 654 * q^49 - 684 * q^51 - 108 * q^54 - 64 * q^56 - 480 * q^59 + 604 * q^61 - 128 * q^64 - 576 * q^66 - 432 * q^69 - 1536 * q^71 + 1336 * q^74 + 1120 * q^76 + 1280 * q^79 + 162 * q^81 + 96 * q^84 - 1072 * q^86 - 420 * q^89 - 16 * q^91 - 864 * q^94 + 192 * q^96 + 864 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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