LMFDB - Embedded newform 1875.2.b.b.1249.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1249,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1875.1249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.9719503790$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1249.2
Root			$-0.618034i$ of defining polynomial
Character	$\chi$	$=$	1875.1249
Dual form			1875.2.b.b.1249.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.47214i q^{7} -3.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.47214i q^{7} -3.00000i q^{8} -1.00000 q^{9} -1.23607 q^{11} +1.00000i q^{12} +5.61803i q^{13} +4.47214 q^{14} -1.00000 q^{16} -3.85410i q^{17} +1.00000i q^{18} -1.23607 q^{19} -4.47214 q^{21} +1.23607i q^{22} +4.47214i q^{23} +3.00000 q^{24} +5.61803 q^{26} -1.00000i q^{27} +4.47214i q^{28} -6.61803 q^{29} +2.76393 q^{31} -5.00000i q^{32} -1.23607i q^{33} -3.85410 q^{34} -1.00000 q^{36} +3.09017i q^{37} +1.23607i q^{38} -5.61803 q^{39} -3.61803 q^{41} +4.47214i q^{42} +7.70820i q^{43} -1.23607 q^{44} +4.47214 q^{46} +0.763932i q^{47} -1.00000i q^{48} -13.0000 q^{49} +3.85410 q^{51} +5.61803i q^{52} +3.61803i q^{53} -1.00000 q^{54} +13.4164 q^{56} -1.23607i q^{57} +6.61803i q^{58} +4.00000 q^{59} +1.61803 q^{61} -2.76393i q^{62} -4.47214i q^{63} -7.00000 q^{64} -1.23607 q^{66} -0.763932i q^{67} -3.85410i q^{68} -4.47214 q^{69} -5.23607 q^{71} +3.00000i q^{72} -8.09017i q^{73} +3.09017 q^{74} -1.23607 q^{76} -5.52786i q^{77} +5.61803i q^{78} +1.00000 q^{81} +3.61803i q^{82} +12.4721i q^{83} -4.47214 q^{84} +7.70820 q^{86} -6.61803i q^{87} +3.70820i q^{88} -5.38197 q^{89} -25.1246 q^{91} +4.47214i q^{92} +2.76393i q^{93} +0.763932 q^{94} +5.00000 q^{96} -2.14590i q^{97} +13.0000i q^{98} +1.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^4 + 4 * q^6 - 4 * q^9	$ 4 q + 4 q^{4} + 4 q^{6} - 4 q^{9} + 4 q^{11} - 4 q^{16} + 4 q^{19} + 12 q^{24} + 18 q^{26} - 22 q^{29} + 20 q^{31} - 2 q^{34} - 4 q^{36} - 18 q^{39} - 10 q^{41} + 4 q^{44} - 52 q^{49} + 2 q^{51} - 4 q^{54} + 16 q^{59} + 2 q^{61} - 28 q^{64} + 4 q^{66} - 12 q^{71} - 10 q^{74} + 4 q^{76} + 4 q^{81} + 4 q^{86} - 26 q^{89} - 20 q^{91} + 12 q^{94} + 20 q^{96} - 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^4 + 4 * q^6 - 4 * q^9 + 4 * q^11 - 4 * q^16 + 4 * q^19 + 12 * q^24 + 18 * q^26 - 22 * q^29 + 20 * q^31 - 2 * q^34 - 4 * q^36 - 18 * q^39 - 10 * q^41 + 4 * q^44 - 52 * q^49 + 2 * q^51 - 4 * q^54 + 16 * q^59 + 2 * q^61 - 28 * q^64 + 4 * q^66 - 12 * q^71 - 10 * q^74 + 4 * q^76 + 4 * q^81 + 4 * q^86 - 26 * q^89 - 20 * q^91 + 12 * q^94 + 20 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times$.

$n$	$626$	$1252$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	− 1.00000i	− 0.707107i	−0.935414	−	0.353553i	$-0.884973\pi$
$2$	− 1.00000i	− 0.707107i	0.935414	−	0.353553i	$-0.115027\pi$
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	4.47214i	1.69031i	0.534522	+	0.845154i	$0.320491\pi$
$7$	4.47214i	1.69031i	−0.534522	+	0.845154i	$0.679509\pi$
$8$	− 3.00000i	− 1.06066i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−1.23607	−0.372689	−0.186344	−	0.982485i	$-0.559664\pi$
$11$	−1.23607	−0.372689	−0.186344	+	0.982485i	$0.559664\pi$
$12$	1.00000i	0.288675i
$13$	5.61803i	1.55816i	0.626923	+	0.779081i	$0.284314\pi$
$13$	5.61803i	1.55816i	−0.626923	+	0.779081i	$0.715686\pi$
$14$	4.47214	1.19523
$15$	0	0
$16$	−1.00000	−0.250000
$17$	− 3.85410i	− 0.934757i	−0.884057	−	0.467379i	$-0.845199\pi$
$17$	− 3.85410i	− 0.934757i	0.884057	−	0.467379i	$-0.154801\pi$
$18$	1.00000i	0.235702i
$19$	−1.23607	−0.283573	−0.141787	−	0.989897i	$-0.545285\pi$
$19$	−1.23607	−0.283573	−0.141787	+	0.989897i	$0.545285\pi$
$20$	0	0
$21$	−4.47214	−0.975900
$22$	1.23607i	0.263531i
$23$	4.47214i	0.932505i	0.884652	+	0.466252i	$0.154396\pi$
$23$	4.47214i	0.932505i	−0.884652	+	0.466252i	$0.845604\pi$
$24$	3.00000	0.612372
$25$	0	0
$26$	5.61803	1.10179
$27$	− 1.00000i	− 0.192450i
$28$	4.47214i	0.845154i
$29$	−6.61803	−1.22894	−0.614469	−	0.788941i	$-0.710630\pi$
$29$	−6.61803	−1.22894	−0.614469	+	0.788941i	$0.710630\pi$
$30$	0	0
$31$	2.76393	0.496417	0.248208	−	0.968707i	$-0.420158\pi$
$31$	2.76393	0.496417	0.248208	+	0.968707i	$0.420158\pi$
$32$	− 5.00000i	− 0.883883i
$33$	− 1.23607i	− 0.215172i
$34$	−3.85410	−0.660973
$35$	0	0
$36$	−1.00000	−0.166667
$37$	3.09017i	0.508021i	0.967201	+	0.254010i	$0.0817497\pi$
$37$	3.09017i	0.508021i	−0.967201	+	0.254010i	$0.918250\pi$
$38$	1.23607i	0.200517i
$39$	−5.61803	−0.899605
$40$	0	0
$41$	−3.61803	−0.565042	−0.282521	−	0.959261i	$-0.591171\pi$
$41$	−3.61803	−0.565042	−0.282521	+	0.959261i	$0.591171\pi$
$42$	4.47214i	0.690066i
$43$	7.70820i	1.17549i	0.809046	+	0.587745i	$0.199984\pi$
$43$	7.70820i	1.17549i	−0.809046	+	0.587745i	$0.800016\pi$
$44$	−1.23607	−0.186344
$45$	0	0
$46$	4.47214	0.659380
$47$	0.763932i	0.111431i	0.998447	+	0.0557155i	$0.0177440\pi$
$47$	0.763932i	0.111431i	−0.998447	+	0.0557155i	$0.982256\pi$
$48$	− 1.00000i	− 0.144338i
$49$	−13.0000	−1.85714
$50$	0	0
$51$	3.85410	0.539682
$52$	5.61803i	0.779081i
$53$	3.61803i	0.496975i	0.968635	+	0.248488i	$0.0799335\pi$
$53$	3.61803i	0.496975i	−0.968635	+	0.248488i	$0.920066\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	13.4164	1.79284
$57$	− 1.23607i	− 0.163721i
$58$	6.61803i	0.868990i
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	0	0
$61$	1.61803	0.207168	0.103584	−	0.994621i	$-0.466969\pi$
$61$	1.61803	0.207168	0.103584	+	0.994621i	$0.466969\pi$
$62$	− 2.76393i	− 0.351020i
$63$	− 4.47214i	− 0.563436i
$64$	−7.00000	−0.875000
$65$	0	0
$66$	−1.23607	−0.152149
$67$	− 0.763932i	− 0.0933292i	−0.998911	−	0.0466646i	$-0.985141\pi$
$67$	− 0.763932i	− 0.0933292i	0.998911	−	0.0466646i	$-0.0148592\pi$
$68$	− 3.85410i	− 0.467379i
$69$	−4.47214	−0.538382
$70$	0	0
$71$	−5.23607	−0.621407	−0.310703	−	0.950507i	$-0.600565\pi$
$71$	−5.23607	−0.621407	−0.310703	+	0.950507i	$0.600565\pi$
$72$	3.00000i	0.353553i
$73$	− 8.09017i	− 0.946883i	−0.880825	−	0.473441i	$-0.843012\pi$
$73$	− 8.09017i	− 0.946883i	0.880825	−	0.473441i	$-0.156988\pi$
$74$	3.09017	0.359225
$75$	0	0
$76$	−1.23607	−0.141787
$77$	− 5.52786i	− 0.629959i
$78$	5.61803i	0.636117i
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	3.61803i	0.399545i
$83$	12.4721i	1.36899i	0.729015	+	0.684497i	$0.239978\pi$
$83$	12.4721i	1.36899i	−0.729015	+	0.684497i	$0.760022\pi$
$84$	−4.47214	−0.487950
$85$	0	0
$86$	7.70820	0.831197
$87$	− 6.61803i	− 0.709528i
$88$	3.70820i	0.395296i
$89$	−5.38197	−0.570487	−0.285244	−	0.958455i	$-0.592075\pi$
$89$	−5.38197	−0.570487	−0.285244	+	0.958455i	$0.592075\pi$
$90$	0	0
$91$	−25.1246	−2.63377
$92$	4.47214i	0.466252i
$93$	2.76393i	0.286606i
$94$	0.763932	0.0787936
$95$	0	0
$96$	5.00000	0.510310
$97$	− 2.14590i	− 0.217883i	−0.994048	−	0.108941i	$-0.965254\pi$
$97$	− 2.14590i	− 0.217883i	0.994048	−	0.108941i	$-0.0347461\pi$
$98$	13.0000i	1.31320i
$99$	1.23607	0.124230
$100$	0	0
$101$	3.56231	0.354463	0.177231	−	0.984169i	$-0.443286\pi$
$101$	3.56231	0.354463	0.177231	+	0.984169i	$0.443286\pi$
$102$	− 3.85410i	− 0.381613i
$103$	3.23607i	0.318859i	0.987209	+	0.159430i	$0.0509655\pi$
$103$	3.23607i	0.318859i	−0.987209	+	0.159430i	$0.949034\pi$
$104$	16.8541	1.65268
$105$	0	0
$106$	3.61803	0.351415
$107$	− 7.52786i	− 0.727746i	−0.931449	−	0.363873i	$-0.881454\pi$
$107$	− 7.52786i	− 0.727746i	0.931449	−	0.363873i	$-0.118546\pi$
$108$	− 1.00000i	− 0.0962250i
$109$	7.90983	0.757624	0.378812	−	0.925474i	$-0.376333\pi$
$109$	7.90983	0.757624	0.378812	+	0.925474i	$0.376333\pi$
$110$	0	0
$111$	−3.09017	−0.293306
$112$	− 4.47214i	− 0.422577i
$113$	18.3262i	1.72399i	0.506919	+	0.861994i	$0.330784\pi$
$113$	18.3262i	1.72399i	−0.506919	+	0.861994i	$0.669216\pi$
$114$	−1.23607	−0.115768
$115$	0	0
$116$	−6.61803	−0.614469
$117$	− 5.61803i	− 0.519387i
$118$	− 4.00000i	− 0.368230i
$119$	17.2361	1.58003
$120$	0	0
$121$	−9.47214	−0.861103
$122$	− 1.61803i	− 0.146490i
$123$	− 3.61803i	− 0.326227i
$124$	2.76393	0.248208
$125$	0	0
$126$	−4.47214	−0.398410
$127$	3.70820i	0.329050i	0.986373	+	0.164525i	$0.0526091\pi$
$127$	3.70820i	0.329050i	−0.986373	+	0.164525i	$0.947391\pi$
$128$	− 3.00000i	− 0.265165i
$129$	−7.70820	−0.678670
$130$	0	0
$131$	−8.18034	−0.714720	−0.357360	−	0.933967i	$-0.616323\pi$
$131$	−8.18034	−0.714720	−0.357360	+	0.933967i	$0.616323\pi$
$132$	− 1.23607i	− 0.107586i
$133$	− 5.52786i	− 0.479327i
$134$	−0.763932	−0.0659937
$135$	0	0
$136$	−11.5623	−0.991460
$137$	7.61803i	0.650853i	0.945567	+	0.325426i	$0.105508\pi$
$137$	7.61803i	0.650853i	−0.945567	+	0.325426i	$0.894492\pi$
$138$	4.47214i	0.380693i
$139$	22.9443	1.94611	0.973054	−	0.230578i	$-0.0740616\pi$
$139$	22.9443	1.94611	0.973054	+	0.230578i	$0.0740616\pi$
$140$	0	0
$141$	−0.763932	−0.0643347
$142$	5.23607i	0.439401i
$143$	− 6.94427i	− 0.580709i
$144$	1.00000	0.0833333
$145$	0	0
$146$	−8.09017	−0.669547
$147$	− 13.0000i	− 1.07222i
$148$	3.09017i	0.254010i
$149$	18.8541	1.54459	0.772294	−	0.635265i	$-0.219109\pi$
$149$	18.8541	1.54459	0.772294	+	0.635265i	$0.219109\pi$
$150$	0	0
$151$	7.52786	0.612609	0.306304	−	0.951934i	$-0.400907\pi$
$151$	7.52786	0.612609	0.306304	+	0.951934i	$0.400907\pi$
$152$	3.70820i	0.300775i
$153$	3.85410i	0.311586i
$154$	−5.52786	−0.445448
$155$	0	0
$156$	−5.61803	−0.449803
$157$	− 10.7984i	− 0.861804i	−0.902399	−	0.430902i	$-0.858195\pi$
$157$	− 10.7984i	− 0.861804i	0.902399	−	0.430902i	$-0.141805\pi$
$158$	0	0
$159$	−3.61803	−0.286929
$160$	0	0
$161$	−20.0000	−1.57622
$162$	− 1.00000i	− 0.0785674i
$163$	− 14.9443i	− 1.17053i	−0.810844	−	0.585263i	$-0.800991\pi$
$163$	− 14.9443i	− 1.17053i	0.810844	−	0.585263i	$-0.199009\pi$
$164$	−3.61803	−0.282521
$165$	0	0
$166$	12.4721	0.968025
$167$	− 3.41641i	− 0.264370i	−0.991225	−	0.132185i	$-0.957801\pi$
$167$	− 3.41641i	− 0.264370i	0.991225	−	0.132185i	$-0.0421992\pi$
$168$	13.4164i	1.03510i
$169$	−18.5623	−1.42787
$170$	0	0
$171$	1.23607	0.0945245
$172$	7.70820i	0.587745i
$173$	21.0902i	1.60346i	0.597689	+	0.801728i	$0.296086\pi$
$173$	21.0902i	1.60346i	−0.597689	+	0.801728i	$0.703914\pi$
$174$	−6.61803	−0.501712
$175$	0	0
$176$	1.23607	0.0931721
$177$	4.00000i	0.300658i
$178$	5.38197i	0.403395i
$179$	16.1803	1.20938	0.604688	−	0.796463i	$-0.293298\pi$
$179$	16.1803	1.20938	0.604688	+	0.796463i	$0.293298\pi$
$180$	0	0
$181$	14.7984	1.09995	0.549977	−	0.835180i	$-0.314636\pi$
$181$	14.7984	1.09995	0.549977	+	0.835180i	$0.314636\pi$
$182$	25.1246i	1.86236i
$183$	1.61803i	0.119609i
$184$	13.4164	0.989071
$185$	0	0
$186$	2.76393	0.202661
$187$	4.76393i	0.348373i
$188$	0.763932i	0.0557155i
$189$	4.47214	0.325300
$190$	0	0
$191$	6.65248	0.481356	0.240678	−	0.970605i	$-0.422630\pi$
$191$	6.65248	0.481356	0.240678	+	0.970605i	$0.422630\pi$
$192$	− 7.00000i	− 0.505181i
$193$	23.3262i	1.67906i	0.543314	+	0.839530i	$0.317169\pi$
$193$	23.3262i	1.67906i	−0.543314	+	0.839530i	$0.682831\pi$
$194$	−2.14590	−0.154067
$195$	0	0
$196$	−13.0000	−0.928571
$197$	− 7.61803i	− 0.542762i	−0.962472	−	0.271381i	$-0.912520\pi$
$197$	− 7.61803i	− 0.542762i	0.962472	−	0.271381i	$-0.0874804\pi$
$198$	− 1.23607i	− 0.0878435i
$199$	−12.6525	−0.896910	−0.448455	−	0.893805i	$-0.648026\pi$
$199$	−12.6525	−0.896910	−0.448455	+	0.893805i	$0.648026\pi$
$200$	0	0
$201$	0.763932	0.0538836
$202$	− 3.56231i	− 0.250643i
$203$	− 29.5967i	− 2.07728i
$204$	3.85410	0.269841
$205$	0	0
$206$	3.23607	0.225468
$207$	− 4.47214i	− 0.310835i
$208$	− 5.61803i	− 0.389541i
$209$	1.52786	0.105685
$210$	0	0
$211$	17.8885	1.23150	0.615749	−	0.787942i	$-0.288854\pi$
$211$	17.8885	1.23150	0.615749	+	0.787942i	$0.288854\pi$
$212$	3.61803i	0.248488i
$213$	− 5.23607i	− 0.358769i
$214$	−7.52786	−0.514594
$215$	0	0
$216$	−3.00000	−0.204124
$217$	12.3607i	0.839098i
$218$	− 7.90983i	− 0.535721i
$219$	8.09017	0.546683
$220$	0	0
$221$	21.6525	1.45650
$222$	3.09017i	0.207399i
$223$	8.18034i	0.547796i	0.961759	+	0.273898i	$0.0883131\pi$
$223$	8.18034i	0.547796i	−0.961759	+	0.273898i	$0.911687\pi$
$224$	22.3607	1.49404
$225$	0	0
$226$	18.3262	1.21904
$227$	20.0000i	1.32745i	0.747978	+	0.663723i	$0.231025\pi$
$227$	20.0000i	1.32745i	−0.747978	+	0.663723i	$0.768975\pi$
$228$	− 1.23607i	− 0.0818606i
$229$	−21.9787	−1.45239	−0.726197	−	0.687487i	$-0.758714\pi$
$229$	−21.9787	−1.45239	−0.726197	+	0.687487i	$0.758714\pi$
$230$	0	0
$231$	5.52786	0.363707
$232$	19.8541i	1.30349i
$233$	12.3820i	0.811170i	0.914057	+	0.405585i	$0.132932\pi$
$233$	12.3820i	0.811170i	−0.914057	+	0.405585i	$0.867068\pi$
$234$	−5.61803	−0.367262
$235$	0	0
$236$	4.00000	0.260378
$237$	0	0
$238$	− 17.2361i	− 1.11725i
$239$	24.9443	1.61351	0.806755	−	0.590886i	$-0.201222\pi$
$239$	24.9443	1.61351	0.806755	+	0.590886i	$0.201222\pi$
$240$	0	0
$241$	28.0344	1.80586	0.902929	−	0.429791i	$-0.141413\pi$
$241$	28.0344	1.80586	0.902929	+	0.429791i	$0.141413\pi$
$242$	9.47214i	0.608892i
$243$	1.00000i	0.0641500i
$244$	1.61803	0.103584
$245$	0	0
$246$	−3.61803	−0.230677
$247$	− 6.94427i	− 0.441853i
$248$	− 8.29180i	− 0.526530i
$249$	−12.4721	−0.790390
$250$	0	0
$251$	−9.05573	−0.571592	−0.285796	−	0.958290i	$-0.592258\pi$
$251$	−9.05573	−0.571592	−0.285796	+	0.958290i	$0.592258\pi$
$252$	− 4.47214i	− 0.281718i
$253$	− 5.52786i	− 0.347534i
$254$	3.70820	0.232673
$255$	0	0
$256$	−17.0000	−1.06250
$257$	− 11.7984i	− 0.735962i	−0.929833	−	0.367981i	$-0.880049\pi$
$257$	− 11.7984i	− 0.735962i	0.929833	−	0.367981i	$-0.119951\pi$
$258$	7.70820i	0.479892i
$259$	−13.8197	−0.858712
$260$	0	0
$261$	6.61803	0.409646
$262$	8.18034i	0.505383i
$263$	− 23.8885i	− 1.47303i	−0.676421	−	0.736515i	$-0.736470\pi$
$263$	− 23.8885i	− 1.47303i	0.676421	−	0.736515i	$-0.263530\pi$
$264$	−3.70820	−0.228224
$265$	0	0
$266$	−5.52786	−0.338935
$267$	− 5.38197i	− 0.329371i
$268$	− 0.763932i	− 0.0466646i
$269$	6.85410	0.417902	0.208951	−	0.977926i	$-0.432995\pi$
$269$	6.85410	0.417902	0.208951	+	0.977926i	$0.432995\pi$
$270$	0	0
$271$	−0.180340	−0.0109549	−0.00547743	−	0.999985i	$-0.501744\pi$
$271$	−0.180340	−0.0109549	−0.00547743	+	0.999985i	$0.501744\pi$
$272$	3.85410i	0.233689i
$273$	− 25.1246i	− 1.52061i
$274$	7.61803	0.460222
$275$	0	0
$276$	−4.47214	−0.269191
$277$	− 18.7984i	− 1.12948i	−0.825267	−	0.564742i	$-0.808976\pi$
$277$	− 18.7984i	− 1.12948i	0.825267	−	0.564742i	$-0.191024\pi$
$278$	− 22.9443i	− 1.37611i
$279$	−2.76393	−0.165472
$280$	0	0
$281$	−19.6180	−1.17031	−0.585157	−	0.810920i	$-0.698967\pi$
$281$	−19.6180	−1.17031	−0.585157	+	0.810920i	$0.698967\pi$
$282$	0.763932i	0.0454915i
$283$	13.7082i	0.814868i	0.913235	+	0.407434i	$0.133576\pi$
$283$	13.7082i	0.814868i	−0.913235	+	0.407434i	$0.866424\pi$
$284$	−5.23607	−0.310703
$285$	0	0
$286$	−6.94427	−0.410623
$287$	− 16.1803i	− 0.955095i
$288$	5.00000i	0.294628i
$289$	2.14590	0.126229
$290$	0	0
$291$	2.14590	0.125795
$292$	− 8.09017i	− 0.473441i
$293$	− 20.7984i	− 1.21505i	−0.794299	−	0.607527i	$-0.792162\pi$
$293$	− 20.7984i	− 1.21505i	0.794299	−	0.607527i	$-0.207838\pi$
$294$	−13.0000	−0.758175
$295$	0	0
$296$	9.27051	0.538837
$297$	1.23607i	0.0717239i
$298$	− 18.8541i	− 1.09219i
$299$	−25.1246	−1.45299
$300$	0	0
$301$	−34.4721	−1.98694
$302$	− 7.52786i	− 0.433180i
$303$	3.56231i	0.204649i
$304$	1.23607	0.0708934
$305$	0	0
$306$	3.85410	0.220324
$307$	− 32.6525i	− 1.86358i	−0.363004	−	0.931788i	$-0.618249\pi$
$307$	− 32.6525i	− 1.86358i	0.363004	−	0.931788i	$-0.381751\pi$
$308$	− 5.52786i	− 0.314979i
$309$	−3.23607	−0.184093
$310$	0	0
$311$	17.7082	1.00414	0.502070	−	0.864827i	$-0.332572\pi$
$311$	17.7082	1.00414	0.502070	+	0.864827i	$0.332572\pi$
$312$	16.8541i	0.954176i
$313$	− 0.472136i	− 0.0266867i	−0.999911	−	0.0133434i	$-0.995753\pi$
$313$	− 0.472136i	− 0.0266867i	0.999911	−	0.0133434i	$-0.00424745\pi$
$314$	−10.7984	−0.609387
$315$	0	0
$316$	0	0
$317$	− 28.8328i	− 1.61941i	−0.586836	−	0.809706i	$-0.699627\pi$
$317$	− 28.8328i	− 1.61941i	0.586836	−	0.809706i	$-0.300373\pi$
$318$	3.61803i	0.202889i
$319$	8.18034	0.458011
$320$	0	0
$321$	7.52786	0.420164
$322$	20.0000i	1.11456i
$323$	4.76393i	0.265072i
$324$	1.00000	0.0555556
$325$	0	0
$326$	−14.9443	−0.827687
$327$	7.90983i	0.437415i
$328$	10.8541i	0.599318i
$329$	−3.41641	−0.188353
$330$	0	0
$331$	−6.94427	−0.381692	−0.190846	−	0.981620i	$-0.561123\pi$
$331$	−6.94427	−0.381692	−0.190846	+	0.981620i	$0.561123\pi$
$332$	12.4721i	0.684497i
$333$	− 3.09017i	− 0.169340i
$334$	−3.41641	−0.186938
$335$	0	0
$336$	4.47214	0.243975
$337$	− 2.94427i	− 0.160385i	−0.996779	−	0.0801924i	$-0.974447\pi$
$337$	− 2.94427i	− 0.160385i	0.996779	−	0.0801924i	$-0.0255535\pi$
$338$	18.5623i	1.00966i
$339$	−18.3262	−0.995345
$340$	0	0
$341$	−3.41641	−0.185009
$342$	− 1.23607i	− 0.0668389i
$343$	− 26.8328i	− 1.44884i
$344$	23.1246	1.24680
$345$	0	0
$346$	21.0902	1.13381
$347$	20.2918i	1.08932i	0.838657	+	0.544660i	$0.183341\pi$
$347$	20.2918i	1.08932i	−0.838657	+	0.544660i	$0.816659\pi$
$348$	− 6.61803i	− 0.354764i
$349$	4.03444	0.215959	0.107979	−	0.994153i	$-0.465562\pi$
$349$	4.03444	0.215959	0.107979	+	0.994153i	$0.465562\pi$
$350$	0	0
$351$	5.61803	0.299868
$352$	6.18034i	0.329413i
$353$	14.3607i	0.764342i	0.924092	+	0.382171i	$0.124823\pi$
$353$	14.3607i	0.764342i	−0.924092	+	0.382171i	$0.875177\pi$
$354$	4.00000	0.212598
$355$	0	0
$356$	−5.38197	−0.285244
$357$	17.2361i	0.912229i
$358$	− 16.1803i	− 0.855158i
$359$	37.4164	1.97476	0.987381	−	0.158361i	$-0.0506211\pi$
$359$	37.4164	1.97476	0.987381	+	0.158361i	$0.0506211\pi$
$360$	0	0
$361$	−17.4721	−0.919586
$362$	− 14.7984i	− 0.777785i
$363$	− 9.47214i	− 0.497158i
$364$	−25.1246	−1.31689
$365$	0	0
$366$	1.61803	0.0845760
$367$	6.00000i	0.313197i	0.987662	+	0.156599i	$0.0500529\pi$
$367$	6.00000i	0.313197i	−0.987662	+	0.156599i	$0.949947\pi$
$368$	− 4.47214i	− 0.233126i
$369$	3.61803	0.188347
$370$	0	0
$371$	−16.1803	−0.840041
$372$	2.76393i	0.143303i
$373$	2.58359i	0.133773i	0.997761	+	0.0668867i	$0.0213066\pi$
$373$	2.58359i	0.133773i	−0.997761	+	0.0668867i	$0.978693\pi$
$374$	4.76393	0.246337
$375$	0	0
$376$	2.29180	0.118190
$377$	− 37.1803i	− 1.91488i
$378$	− 4.47214i	− 0.230022i
$379$	3.41641	0.175489	0.0877445	−	0.996143i	$-0.472034\pi$
$379$	3.41641	0.175489	0.0877445	+	0.996143i	$0.472034\pi$
$380$	0	0
$381$	−3.70820	−0.189977
$382$	− 6.65248i	− 0.340370i
$383$	− 32.8328i	− 1.67768i	−0.544379	−	0.838839i	$-0.683235\pi$
$383$	− 32.8328i	− 1.67768i	0.544379	−	0.838839i	$-0.316765\pi$
$384$	3.00000	0.153093
$385$	0	0
$386$	23.3262	1.18727
$387$	− 7.70820i	− 0.391830i
$388$	− 2.14590i	− 0.108941i
$389$	25.9098	1.31368	0.656840	−	0.754030i	$-0.271893\pi$
$389$	25.9098	1.31368	0.656840	+	0.754030i	$0.271893\pi$
$390$	0	0
$391$	17.2361	0.871665
$392$	39.0000i	1.96980i
$393$	− 8.18034i	− 0.412644i
$394$	−7.61803	−0.383791
$395$	0	0
$396$	1.23607	0.0621148
$397$	6.94427i	0.348523i	0.984699	+	0.174262i	$0.0557538\pi$
$397$	6.94427i	0.348523i	−0.984699	+	0.174262i	$0.944246\pi$
$398$	12.6525i	0.634211i
$399$	5.52786	0.276739
$400$	0	0
$401$	−22.4508	−1.12114	−0.560571	−	0.828106i	$-0.689418\pi$
$401$	−22.4508	−1.12114	−0.560571	+	0.828106i	$0.689418\pi$
$402$	− 0.763932i	− 0.0381015i
$403$	15.5279i	0.773498i
$404$	3.56231	0.177231
$405$	0	0
$406$	−29.5967	−1.46886
$407$	− 3.81966i	− 0.189334i
$408$	− 11.5623i	− 0.572419i
$409$	−1.20163	−0.0594166	−0.0297083	−	0.999559i	$-0.509458\pi$
$409$	−1.20163	−0.0594166	−0.0297083	+	0.999559i	$0.509458\pi$
$410$	0	0
$411$	−7.61803	−0.375770
$412$	3.23607i	0.159430i
$413$	17.8885i	0.880238i
$414$	−4.47214	−0.219793
$415$	0	0
$416$	28.0902	1.37723
$417$	22.9443i	1.12359i
$418$	− 1.52786i	− 0.0747303i
$419$	−15.0557	−0.735520	−0.367760	−	0.929921i	$-0.619875\pi$
$419$	−15.0557	−0.735520	−0.367760	+	0.929921i	$0.619875\pi$
$420$	0	0
$421$	29.8541	1.45500	0.727500	−	0.686108i	$-0.240682\pi$
$421$	29.8541	1.45500	0.727500	+	0.686108i	$0.240682\pi$
$422$	− 17.8885i	− 0.870801i
$423$	− 0.763932i	− 0.0371436i
$424$	10.8541	0.527122
$425$	0	0
$426$	−5.23607	−0.253688
$427$	7.23607i	0.350178i
$428$	− 7.52786i	− 0.363873i
$429$	6.94427	0.335273
$430$	0	0
$431$	20.6525	0.994795	0.497397	−	0.867523i	$-0.334289\pi$
$431$	20.6525	0.994795	0.497397	+	0.867523i	$0.334289\pi$
$432$	1.00000i	0.0481125i
$433$	− 21.9787i	− 1.05623i	−0.849173	−	0.528115i	$-0.822899\pi$
$433$	− 21.9787i	− 1.05623i	0.849173	−	0.528115i	$-0.177101\pi$
$434$	12.3607	0.593332
$435$	0	0
$436$	7.90983	0.378812
$437$	− 5.52786i	− 0.264434i
$438$	− 8.09017i	− 0.386563i
$439$	−16.1803	−0.772245	−0.386123	−	0.922447i	$-0.626186\pi$
$439$	−16.1803	−0.772245	−0.386123	+	0.922447i	$0.626186\pi$
$440$	0	0
$441$	13.0000	0.619048
$442$	− 21.6525i	− 1.02990i
$443$	− 35.2361i	− 1.67412i	−0.547114	−	0.837058i	$-0.684274\pi$
$443$	− 35.2361i	− 1.67412i	0.547114	−	0.837058i	$-0.315726\pi$
$444$	−3.09017	−0.146653
$445$	0	0
$446$	8.18034	0.387350
$447$	18.8541i	0.891768i
$448$	− 31.3050i	− 1.47902i
$449$	−16.7984	−0.792764	−0.396382	−	0.918086i	$-0.629734\pi$
$449$	−16.7984	−0.792764	−0.396382	+	0.918086i	$0.629734\pi$
$450$	0	0
$451$	4.47214	0.210585
$452$	18.3262i	0.861994i
$453$	7.52786i	0.353690i
$454$	20.0000	0.938647
$455$	0	0
$456$	−3.70820	−0.173653
$457$	22.3607i	1.04599i	0.852336	+	0.522994i	$0.175185\pi$
$457$	22.3607i	1.04599i	−0.852336	+	0.522994i	$0.824815\pi$
$458$	21.9787i	1.02700i
$459$	−3.85410	−0.179894
$460$	0	0
$461$	−32.7984	−1.52757	−0.763786	−	0.645469i	$-0.776662\pi$
$461$	−32.7984	−1.52757	−0.763786	+	0.645469i	$0.776662\pi$
$462$	− 5.52786i	− 0.257180i
$463$	18.7639i	0.872034i	0.899938	+	0.436017i	$0.143611\pi$
$463$	18.7639i	0.872034i	−0.899938	+	0.436017i	$0.856389\pi$
$464$	6.61803	0.307235
$465$	0	0
$466$	12.3820	0.573583
$467$	− 28.1803i	− 1.30403i	−0.758206	−	0.652015i	$-0.773924\pi$
$467$	− 28.1803i	− 1.30403i	0.758206	−	0.652015i	$-0.226076\pi$
$468$	− 5.61803i	− 0.259694i
$469$	3.41641	0.157755
$470$	0	0
$471$	10.7984	0.497563
$472$	− 12.0000i	− 0.552345i
$473$	− 9.52786i	− 0.438092i
$474$	0	0
$475$	0	0
$476$	17.2361	0.790014
$477$	− 3.61803i	− 0.165658i
$478$	− 24.9443i	− 1.14092i
$479$	−18.9443	−0.865586	−0.432793	−	0.901493i	$-0.642472\pi$
$479$	−18.9443	−0.865586	−0.432793	+	0.901493i	$0.642472\pi$
$480$	0	0
$481$	−17.3607	−0.791579
$482$	− 28.0344i	− 1.27693i
$483$	− 20.0000i	− 0.910032i
$484$	−9.47214	−0.430552
$485$	0	0
$486$	1.00000	0.0453609
$487$	− 9.70820i	− 0.439921i	−0.975509	−	0.219960i	$-0.929407\pi$
$487$	− 9.70820i	− 0.439921i	0.975509	−	0.219960i	$-0.0705928\pi$
$488$	− 4.85410i	− 0.219735i
$489$	14.9443	0.675803
$490$	0	0
$491$	5.88854	0.265746	0.132873	−	0.991133i	$-0.457580\pi$
$491$	5.88854	0.265746	0.132873	+	0.991133i	$0.457580\pi$
$492$	− 3.61803i	− 0.163114i
$493$	25.5066i	1.14876i
$494$	−6.94427	−0.312438
$495$	0	0
$496$	−2.76393	−0.124104
$497$	− 23.4164i	− 1.05037i
$498$	12.4721i	0.558890i
$499$	6.00000	0.268597	0.134298	−	0.990941i	$-0.457122\pi$
$499$	6.00000	0.268597	0.134298	+	0.990941i	$0.457122\pi$
$500$	0	0
$501$	3.41641	0.152634
$502$	9.05573i	0.404177i
$503$	8.58359i	0.382723i	0.981520	+	0.191362i	$0.0612904\pi$
$503$	8.58359i	0.382723i	−0.981520	+	0.191362i	$0.938710\pi$
$504$	−13.4164	−0.597614
$505$	0	0
$506$	−5.52786	−0.245744
$507$	− 18.5623i	− 0.824381i
$508$	3.70820i	0.164525i
$509$	−20.1459	−0.892951	−0.446476	−	0.894796i	$-0.647321\pi$
$509$	−20.1459	−0.892951	−0.446476	+	0.894796i	$0.647321\pi$
$510$	0	0
$511$	36.1803	1.60052
$512$	11.0000i	0.486136i
$513$	1.23607i	0.0545737i
$514$	−11.7984	−0.520404
$515$	0	0
$516$	−7.70820	−0.339335
$517$	− 0.944272i	− 0.0415290i
$518$	13.8197i	0.607201i
$519$	−21.0902	−0.925756
$520$	0	0
$521$	−27.0344	−1.18440	−0.592200	−	0.805791i	$-0.701741\pi$
$521$	−27.0344	−1.18440	−0.592200	+	0.805791i	$0.701741\pi$
$522$	− 6.61803i	− 0.289663i
$523$	− 25.7082i	− 1.12414i	−0.827089	−	0.562071i	$-0.810005\pi$
$523$	− 25.7082i	− 1.12414i	0.827089	−	0.562071i	$-0.189995\pi$
$524$	−8.18034	−0.357360
$525$	0	0
$526$	−23.8885	−1.04159
$527$	− 10.6525i	− 0.464029i
$528$	1.23607i	0.0537930i
$529$	3.00000	0.130435
$530$	0	0
$531$	−4.00000	−0.173585
$532$	− 5.52786i	− 0.239663i
$533$	− 20.3262i	− 0.880427i
$534$	−5.38197	−0.232900
$535$	0	0
$536$	−2.29180	−0.0989905
$537$	16.1803i	0.698233i
$538$	− 6.85410i	− 0.295501i
$539$	16.0689	0.692136
$540$	0	0
$541$	−19.6738	−0.845841	−0.422921	−	0.906167i	$-0.638995\pi$
$541$	−19.6738	−0.845841	−0.422921	+	0.906167i	$0.638995\pi$
$542$	0.180340i	0.00774626i
$543$	14.7984i	0.635059i
$544$	−19.2705	−0.826216
$545$	0	0
$546$	−25.1246	−1.07523
$547$	− 42.3607i	− 1.81121i	−0.424120	−	0.905606i	$-0.639417\pi$
$547$	− 42.3607i	− 1.81121i	0.424120	−	0.905606i	$-0.360583\pi$
$548$	7.61803i	0.325426i
$549$	−1.61803	−0.0690560
$550$	0	0
$551$	8.18034	0.348494
$552$	13.4164i	0.571040i
$553$	0	0
$554$	−18.7984	−0.798666
$555$	0	0
$556$	22.9443	0.973054
$557$	11.2705i	0.477547i	0.971075	+	0.238773i	$0.0767453\pi$
$557$	11.2705i	0.477547i	−0.971075	+	0.238773i	$0.923255\pi$
$558$	2.76393i	0.117007i
$559$	−43.3050	−1.83160
$560$	0	0
$561$	−4.76393	−0.201133
$562$	19.6180i	0.827537i
$563$	− 26.4721i	− 1.11567i	−0.829953	−	0.557834i	$-0.811633\pi$
$563$	− 26.4721i	− 1.11567i	0.829953	−	0.557834i	$-0.188367\pi$
$564$	−0.763932	−0.0321673
$565$	0	0
$566$	13.7082	0.576199
$567$	4.47214i	0.187812i
$568$	15.7082i	0.659102i
$569$	−3.27051	−0.137107	−0.0685535	−	0.997647i	$-0.521838\pi$
$569$	−3.27051	−0.137107	−0.0685535	+	0.997647i	$0.521838\pi$
$570$	0	0
$571$	−16.7639	−0.701549	−0.350774	−	0.936460i	$-0.614082\pi$
$571$	−16.7639	−0.701549	−0.350774	+	0.936460i	$0.614082\pi$
$572$	− 6.94427i	− 0.290355i
$573$	6.65248i	0.277911i
$574$	−16.1803	−0.675354
$575$	0	0
$576$	7.00000	0.291667
$577$	13.0557i	0.543517i	0.962365	+	0.271759i	$0.0876052\pi$
$577$	13.0557i	0.543517i	−0.962365	+	0.271759i	$0.912395\pi$
$578$	− 2.14590i	− 0.0892576i
$579$	−23.3262	−0.969405
$580$	0	0
$581$	−55.7771	−2.31402
$582$	− 2.14590i	− 0.0889503i
$583$	− 4.47214i	− 0.185217i
$584$	−24.2705	−1.00432
$585$	0	0
$586$	−20.7984	−0.859173
$587$	41.4164i	1.70944i	0.519091	+	0.854719i	$0.326271\pi$
$587$	41.4164i	1.70944i	−0.519091	+	0.854719i	$0.673729\pi$
$588$	− 13.0000i	− 0.536111i
$589$	−3.41641	−0.140771
$590$	0	0
$591$	7.61803	0.313364
$592$	− 3.09017i	− 0.127005i
$593$	9.74265i	0.400083i	0.979787	+	0.200041i	$0.0641076\pi$
$593$	9.74265i	0.400083i	−0.979787	+	0.200041i	$0.935892\pi$
$594$	1.23607	0.0507165
$595$	0	0
$596$	18.8541	0.772294
$597$	− 12.6525i	− 0.517831i
$598$	25.1246i	1.02742i
$599$	3.52786	0.144145	0.0720723	−	0.997399i	$-0.477039\pi$
$599$	3.52786	0.144145	0.0720723	+	0.997399i	$0.477039\pi$
$600$	0	0
$601$	−8.67376	−0.353810	−0.176905	−	0.984228i	$-0.556609\pi$
$601$	−8.67376	−0.353810	−0.176905	+	0.984228i	$0.556609\pi$
$602$	34.4721i	1.40498i
$603$	0.763932i	0.0311097i
$604$	7.52786	0.306304
$605$	0	0
$606$	3.56231	0.144709
$607$	34.7639i	1.41102i	0.708698	+	0.705512i	$0.249283\pi$
$607$	34.7639i	1.41102i	−0.708698	+	0.705512i	$0.750717\pi$
$608$	6.18034i	0.250646i
$609$	29.5967	1.19932
$610$	0	0
$611$	−4.29180	−0.173627
$612$	3.85410i	0.155793i
$613$	1.49342i	0.0603188i	0.999545	+	0.0301594i	$0.00960148\pi$
$613$	1.49342i	0.0603188i	−0.999545	+	0.0301594i	$0.990399\pi$
$614$	−32.6525	−1.31775
$615$	0	0
$616$	−16.5836	−0.668172
$617$	19.9787i	0.804313i	0.915571	+	0.402156i	$0.131739\pi$
$617$	19.9787i	0.804313i	−0.915571	+	0.402156i	$0.868261\pi$
$618$	3.23607i	0.130174i
$619$	16.3607	0.657591	0.328796	−	0.944401i	$-0.393357\pi$
$619$	16.3607	0.657591	0.328796	+	0.944401i	$0.393357\pi$
$620$	0	0
$621$	4.47214	0.179461
$622$	− 17.7082i	− 0.710034i
$623$	− 24.0689i	− 0.964299i
$624$	5.61803	0.224901
$625$	0	0
$626$	−0.472136	−0.0188703
$627$	1.52786i	0.0610170i
$628$	− 10.7984i	− 0.430902i
$629$	11.9098	0.474876
$630$	0	0
$631$	23.7082	0.943809	0.471904	−	0.881650i	$-0.343567\pi$
$631$	23.7082	0.943809	0.471904	+	0.881650i	$0.343567\pi$
$632$	0	0
$633$	17.8885i	0.711006i
$634$	−28.8328	−1.14510
$635$	0	0
$636$	−3.61803	−0.143464
$637$	− 73.0344i	− 2.89373i
$638$	− 8.18034i	− 0.323863i
$639$	5.23607	0.207136
$640$	0	0
$641$	21.0557	0.831651	0.415826	−	0.909444i	$-0.363493\pi$
$641$	21.0557	0.831651	0.415826	+	0.909444i	$0.363493\pi$
$642$	− 7.52786i	− 0.297101i
$643$	− 21.8885i	− 0.863200i	−0.902065	−	0.431600i	$-0.857949\pi$
$643$	− 21.8885i	− 0.863200i	0.902065	−	0.431600i	$-0.142051\pi$
$644$	−20.0000	−0.788110
$645$	0	0
$646$	4.76393	0.187434
$647$	34.3607i	1.35086i	0.737425	+	0.675429i	$0.236041\pi$
$647$	34.3607i	1.35086i	−0.737425	+	0.675429i	$0.763959\pi$
$648$	− 3.00000i	− 0.117851i
$649$	−4.94427	−0.194080
$650$	0	0
$651$	−12.3607	−0.484453
$652$	− 14.9443i	− 0.585263i
$653$	− 42.1033i	− 1.64763i	−0.566858	−	0.823815i	$-0.691841\pi$
$653$	− 42.1033i	− 1.64763i	0.566858	−	0.823815i	$-0.308159\pi$
$654$	7.90983	0.309299
$655$	0	0
$656$	3.61803	0.141260
$657$	8.09017i	0.315628i
$658$	3.41641i	0.133185i
$659$	33.4164	1.30172	0.650859	−	0.759198i	$-0.274409\pi$
$659$	33.4164	1.30172	0.650859	+	0.759198i	$0.274409\pi$
$660$	0	0
$661$	−1.41641	−0.0550919	−0.0275459	−	0.999621i	$-0.508769\pi$
$661$	−1.41641	−0.0550919	−0.0275459	+	0.999621i	$0.508769\pi$
$662$	6.94427i	0.269897i
$663$	21.6525i	0.840912i
$664$	37.4164	1.45204
$665$	0	0
$666$	−3.09017	−0.119742
$667$	− 29.5967i	− 1.14599i
$668$	− 3.41641i	− 0.132185i
$669$	−8.18034	−0.316270
$670$	0	0
$671$	−2.00000	−0.0772091
$672$	22.3607i	0.862582i
$673$	5.20163i	0.200508i	0.994962	+	0.100254i	$0.0319655\pi$
$673$	5.20163i	0.200508i	−0.994962	+	0.100254i	$0.968034\pi$
$674$	−2.94427	−0.113409
$675$	0	0
$676$	−18.5623	−0.713935
$677$	− 10.5836i	− 0.406760i	−0.979100	−	0.203380i	$-0.934807\pi$
$677$	− 10.5836i	− 0.406760i	0.979100	−	0.203380i	$-0.0651928\pi$
$678$	18.3262i	0.703815i
$679$	9.59675	0.368289
$680$	0	0
$681$	−20.0000	−0.766402
$682$	3.41641i	0.130821i
$683$	− 19.4164i	− 0.742948i	−0.928443	−	0.371474i	$-0.878852\pi$
$683$	− 19.4164i	− 0.742948i	0.928443	−	0.371474i	$-0.121148\pi$
$684$	1.23607	0.0472622
$685$	0	0
$686$	−26.8328	−1.02448
$687$	− 21.9787i	− 0.838540i
$688$	− 7.70820i	− 0.293873i
$689$	−20.3262	−0.774368
$690$	0	0
$691$	−16.7639	−0.637730	−0.318865	−	0.947800i	$-0.603302\pi$
$691$	−16.7639	−0.637730	−0.318865	+	0.947800i	$0.603302\pi$
$692$	21.0902i	0.801728i
$693$	5.52786i	0.209986i
$694$	20.2918	0.770266
$695$	0	0
$696$	−19.8541	−0.752568
$697$	13.9443i	0.528177i
$698$	− 4.03444i	− 0.152706i
$699$	−12.3820	−0.468329
$700$	0	0
$701$	20.5623	0.776628	0.388314	−	0.921527i	$-0.373058\pi$
$701$	20.5623	0.776628	0.388314	+	0.921527i	$0.373058\pi$
$702$	− 5.61803i	− 0.212039i
$703$	− 3.81966i	− 0.144061i
$704$	8.65248	0.326102
$705$	0	0
$706$	14.3607	0.540471
$707$	15.9311i	0.599151i
$708$	4.00000i	0.150329i
$709$	40.2705	1.51239	0.756195	−	0.654346i	$-0.227056\pi$
$709$	40.2705	1.51239	0.756195	+	0.654346i	$0.227056\pi$
$710$	0	0
$711$	0	0
$712$	16.1459i	0.605093i
$713$	12.3607i	0.462911i
$714$	17.2361	0.645044
$715$	0	0
$716$	16.1803	0.604688
$717$	24.9443i	0.931561i
$718$	− 37.4164i	− 1.39637i
$719$	0.111456	0.00415661	0.00207831	−	0.999998i	$-0.499338\pi$
$719$	0.111456	0.00415661	0.00207831	+	0.999998i	$0.499338\pi$
$720$	0	0
$721$	−14.4721	−0.538971
$722$	17.4721i	0.650246i
$723$	28.0344i	1.04261i
$724$	14.7984	0.549977
$725$	0	0
$726$	−9.47214	−0.351544
$727$	− 46.6525i	− 1.73024i	−0.501561	−	0.865122i	$-0.667241\pi$
$727$	− 46.6525i	− 1.73024i	0.501561	−	0.865122i	$-0.332759\pi$
$728$	75.3738i	2.79354i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	29.7082	1.09880
$732$	1.61803i	0.0598043i
$733$	29.4164i	1.08652i	0.839565	+	0.543260i	$0.182810\pi$
$733$	29.4164i	1.08652i	−0.839565	+	0.543260i	$0.817190\pi$
$734$	6.00000	0.221464
$735$	0	0
$736$	22.3607	0.824226
$737$	0.944272i	0.0347827i
$738$	− 3.61803i	− 0.133182i
$739$	−4.29180	−0.157876	−0.0789381	−	0.996880i	$-0.525153\pi$
$739$	−4.29180	−0.157876	−0.0789381	+	0.996880i	$0.525153\pi$
$740$	0	0
$741$	6.94427	0.255104
$742$	16.1803i	0.593999i
$743$	41.1246i	1.50872i	0.656463	+	0.754358i	$0.272052\pi$
$743$	41.1246i	1.50872i	−0.656463	+	0.754358i	$0.727948\pi$
$744$	8.29180	0.303992
$745$	0	0
$746$	2.58359	0.0945920
$747$	− 12.4721i	− 0.456332i
$748$	4.76393i	0.174187i
$749$	33.6656	1.23012
$750$	0	0
$751$	36.6525	1.33747	0.668734	−	0.743502i	$-0.266837\pi$
$751$	36.6525	1.33747	0.668734	+	0.743502i	$0.266837\pi$
$752$	− 0.763932i	− 0.0278577i
$753$	− 9.05573i	− 0.330009i
$754$	−37.1803	−1.35403
$755$	0	0
$756$	4.47214	0.162650
$757$	− 29.6180i	− 1.07649i	−0.842790	−	0.538243i	$-0.819088\pi$
$757$	− 29.6180i	− 1.07649i	0.842790	−	0.538243i	$-0.180912\pi$
$758$	− 3.41641i	− 0.124090i
$759$	5.52786	0.200649
$760$	0	0
$761$	32.7426	1.18692	0.593460	−	0.804863i	$-0.297762\pi$
$761$	32.7426	1.18692	0.593460	+	0.804863i	$0.297762\pi$
$762$	3.70820i	0.134334i
$763$	35.3738i	1.28062i
$764$	6.65248	0.240678
$765$	0	0
$766$	−32.8328	−1.18630
$767$	22.4721i	0.811422i
$768$	− 17.0000i	− 0.613435i
$769$	50.3607	1.81605	0.908026	−	0.418913i	$-0.137589\pi$
$769$	50.3607	1.81605	0.908026	+	0.418913i	$0.137589\pi$
$770$	0	0
$771$	11.7984	0.424908
$772$	23.3262i	0.839530i
$773$	28.9230i	1.04029i	0.854079	+	0.520144i	$0.174122\pi$
$773$	28.9230i	1.04029i	−0.854079	+	0.520144i	$0.825878\pi$
$774$	−7.70820	−0.277066
$775$	0	0
$776$	−6.43769	−0.231100
$777$	− 13.8197i	− 0.495778i
$778$	− 25.9098i	− 0.928912i
$779$	4.47214	0.160231
$780$	0	0
$781$	6.47214	0.231591
$782$	− 17.2361i	− 0.616361i
$783$	6.61803i	0.236509i
$784$	13.0000	0.464286
$785$	0	0
$786$	−8.18034	−0.291783
$787$	14.1803i	0.505475i	0.967535	+	0.252737i	$0.0813308\pi$
$787$	14.1803i	0.505475i	−0.967535	+	0.252737i	$0.918669\pi$
$788$	− 7.61803i	− 0.271381i
$789$	23.8885	0.850455
$790$	0	0
$791$	−81.9574	−2.91407
$792$	− 3.70820i	− 0.131765i
$793$	9.09017i	0.322801i
$794$	6.94427	0.246443
$795$	0	0
$796$	−12.6525	−0.448455
$797$	49.1033i	1.73933i	0.493643	+	0.869665i	$0.335665\pi$
$797$	49.1033i	1.73933i	−0.493643	+	0.869665i	$0.664335\pi$
$798$	− 5.52786i	− 0.195684i
$799$	2.94427	0.104161
$800$	0	0
$801$	5.38197	0.190162
$802$	22.4508i	0.792767i
$803$	10.0000i	0.352892i
$804$	0.763932	0.0269418
$805$	0	0
$806$	15.5279	0.546946
$807$	6.85410i	0.241276i
$808$	− 10.6869i	− 0.375964i
$809$	−28.2148	−0.991979	−0.495989	−	0.868329i	$-0.665195\pi$
$809$	−28.2148	−0.991979	−0.495989	+	0.868329i	$0.665195\pi$
$810$	0	0
$811$	4.76393	0.167284	0.0836421	−	0.996496i	$-0.473345\pi$
$811$	4.76393	0.167284	0.0836421	+	0.996496i	$0.473345\pi$
$812$	− 29.5967i	− 1.03864i
$813$	− 0.180340i	− 0.00632480i
$814$	−3.81966	−0.133879
$815$	0	0
$816$	−3.85410	−0.134921
$817$	− 9.52786i	− 0.333338i
$818$	1.20163i	0.0420139i
$819$	25.1246	0.877925
$820$	0	0
$821$	22.9443	0.800761	0.400380	−	0.916349i	$-0.368878\pi$
$821$	22.9443	0.800761	0.400380	+	0.916349i	$0.368878\pi$
$822$	7.61803i	0.265709i
$823$	− 19.2361i	− 0.670527i	−0.942124	−	0.335264i	$-0.891175\pi$
$823$	− 19.2361i	− 0.670527i	0.942124	−	0.335264i	$-0.108825\pi$
$824$	9.70820	0.338201
$825$	0	0
$826$	17.8885	0.622422
$827$	36.0689i	1.25424i	0.778923	+	0.627119i	$0.215766\pi$
$827$	36.0689i	1.25424i	−0.778923	+	0.627119i	$0.784234\pi$
$828$	− 4.47214i	− 0.155417i
$829$	−11.5066	−0.399640	−0.199820	−	0.979833i	$-0.564036\pi$
$829$	−11.5066	−0.399640	−0.199820	+	0.979833i	$0.564036\pi$
$830$	0	0
$831$	18.7984	0.652108
$832$	− 39.3262i	− 1.36339i
$833$	50.1033i	1.73598i
$834$	22.9443	0.794495
$835$	0	0
$836$	1.52786	0.0528423
$837$	− 2.76393i	− 0.0955355i
$838$	15.0557i	0.520091i
$839$	−14.0689	−0.485712	−0.242856	−	0.970062i	$-0.578084\pi$
$839$	−14.0689	−0.485712	−0.242856	+	0.970062i	$0.578084\pi$
$840$	0	0
$841$	14.7984	0.510289
$842$	− 29.8541i	− 1.02884i
$843$	− 19.6180i	− 0.675681i
$844$	17.8885	0.615749
$845$	0	0
$846$	−0.763932	−0.0262645
$847$	− 42.3607i	− 1.45553i
$848$	− 3.61803i	− 0.124244i
$849$	−13.7082	−0.470464
$850$	0	0
$851$	−13.8197	−0.473732
$852$	− 5.23607i	− 0.179385i
$853$	23.1459i	0.792500i	0.918143	+	0.396250i	$0.129689\pi$
$853$	23.1459i	0.792500i	−0.918143	+	0.396250i	$0.870311\pi$
$854$	7.23607	0.247613
$855$	0	0
$856$	−22.5836	−0.771891
$857$	12.4721i	0.426040i	0.977048	+	0.213020i	$0.0683300\pi$
$857$	12.4721i	0.426040i	−0.977048	+	0.213020i	$0.931670\pi$
$858$	− 6.94427i	− 0.237074i
$859$	23.4164	0.798958	0.399479	−	0.916742i	$-0.369191\pi$
$859$	23.4164	0.798958	0.399479	+	0.916742i	$0.369191\pi$
$860$	0	0
$861$	16.1803	0.551425
$862$	− 20.6525i	− 0.703426i
$863$	10.8754i	0.370203i	0.982719	+	0.185101i	$0.0592613\pi$
$863$	10.8754i	0.370203i	−0.982719	+	0.185101i	$0.940739\pi$
$864$	−5.00000	−0.170103
$865$	0	0
$866$	−21.9787	−0.746867
$867$	2.14590i	0.0728785i
$868$	12.3607i	0.419549i
$869$	0	0
$870$	0	0
$871$	4.29180	0.145422
$872$	− 23.7295i	− 0.803582i
$873$	2.14590i	0.0726276i
$874$	−5.52786	−0.186983
$875$	0	0
$876$	8.09017	0.273342
$877$	33.2148i	1.12158i	0.827957	+	0.560792i	$0.189503\pi$
$877$	33.2148i	1.12158i	−0.827957	+	0.560792i	$0.810497\pi$
$878$	16.1803i	0.546060i
$879$	20.7984	0.701512
$880$	0	0
$881$	42.9443	1.44683	0.723415	−	0.690414i	$-0.242572\pi$
$881$	42.9443	1.44683	0.723415	+	0.690414i	$0.242572\pi$
$882$	− 13.0000i	− 0.437733i
$883$	22.1803i	0.746428i	0.927745	+	0.373214i	$0.121744\pi$
$883$	22.1803i	0.746428i	−0.927745	+	0.373214i	$0.878256\pi$
$884$	21.6525	0.728252
$885$	0	0
$886$	−35.2361	−1.18378
$887$	23.1246i	0.776448i	0.921565	+	0.388224i	$0.126911\pi$
$887$	23.1246i	0.776448i	−0.921565	+	0.388224i	$0.873089\pi$
$888$	9.27051i	0.311098i
$889$	−16.5836	−0.556196
$890$	0	0
$891$	−1.23607	−0.0414098
$892$	8.18034i	0.273898i
$893$	− 0.944272i	− 0.0315989i
$894$	18.8541	0.630575
$895$	0	0
$896$	13.4164	0.448211
$897$	− 25.1246i	− 0.838886i
$898$	16.7984i	0.560569i
$899$	−18.2918	−0.610066
$900$	0	0
$901$	13.9443	0.464551
$902$	− 4.47214i	− 0.148906i
$903$	− 34.4721i	− 1.14716i
$904$	54.9787	1.82856
$905$	0	0
$906$	7.52786	0.250097
$907$	− 7.12461i	− 0.236569i	−0.992980	−	0.118284i	$-0.962261\pi$
$907$	− 7.12461i	− 0.236569i	0.992980	−	0.118284i	$-0.0377395\pi$
$908$	20.0000i	0.663723i
$909$	−3.56231	−0.118154
$910$	0	0
$911$	18.1803	0.602342	0.301171	−	0.953570i	$-0.402623\pi$
$911$	18.1803	0.602342	0.301171	+	0.953570i	$0.402623\pi$
$912$	1.23607i	0.0409303i
$913$	− 15.4164i	− 0.510209i
$914$	22.3607	0.739626
$915$	0	0
$916$	−21.9787	−0.726197
$917$	− 36.5836i	− 1.20810i
$918$	3.85410i	0.127204i
$919$	−49.1935	−1.62274	−0.811372	−	0.584530i	$-0.801279\pi$
$919$	−49.1935	−1.62274	−0.811372	+	0.584530i	$0.801279\pi$
$920$	0	0
$921$	32.6525	1.07594
$922$	32.7984i	1.08016i
$923$	− 29.4164i	− 0.968253i
$924$	5.52786	0.181853
$925$	0	0
$926$	18.7639	0.616621
$927$	− 3.23607i	− 0.106286i
$928$	33.0902i	1.08624i
$929$	9.09017	0.298239	0.149119	−	0.988819i	$-0.452356\pi$
$929$	9.09017	0.298239	0.149119	+	0.988819i	$0.452356\pi$
$930$	0	0
$931$	16.0689	0.526636
$932$	12.3820i	0.405585i
$933$	17.7082i	0.579741i
$934$	−28.1803	−0.922089
$935$	0	0
$936$	−16.8541	−0.550894
$937$	48.6869i	1.59053i	0.606260	+	0.795266i	$0.292669\pi$
$937$	48.6869i	1.59053i	−0.606260	+	0.795266i	$0.707331\pi$
$938$	− 3.41641i	− 0.111550i
$939$	0.472136	0.0154076
$940$	0	0
$941$	−10.3262	−0.336626	−0.168313	−	0.985734i	$-0.553832\pi$
$941$	−10.3262	−0.336626	−0.168313	+	0.985734i	$0.553832\pi$
$942$	− 10.7984i	− 0.351830i
$943$	− 16.1803i	− 0.526904i
$944$	−4.00000	−0.130189
$945$	0	0
$946$	−9.52786	−0.309778
$947$	− 2.58359i	− 0.0839555i	−0.999119	−	0.0419777i	$-0.986634\pi$
$947$	− 2.58359i	− 0.0839555i	0.999119	−	0.0419777i	$-0.0133659\pi$
$948$	0	0
$949$	45.4508	1.47540
$950$	0	0
$951$	28.8328	0.934968
$952$	− 51.7082i	− 1.67587i
$953$	− 1.09017i	− 0.0353141i	−0.999844	−	0.0176570i	$-0.994379\pi$
$953$	− 1.09017i	− 0.0353141i	0.999844	−	0.0176570i	$-0.00562070\pi$
$954$	−3.61803	−0.117138
$955$	0	0
$956$	24.9443	0.806755
$957$	8.18034i	0.264433i
$958$	18.9443i	0.612062i
$959$	−34.0689	−1.10014
$960$	0	0
$961$	−23.3607	−0.753570
$962$	17.3607i	0.559731i
$963$	7.52786i	0.242582i
$964$	28.0344	0.902929
$965$	0	0
$966$	−20.0000	−0.643489
$967$	18.8328i	0.605623i	0.953051	+	0.302811i	$0.0979252\pi$
$967$	18.8328i	0.605623i	−0.953051	+	0.302811i	$0.902075\pi$
$968$	28.4164i	0.913338i
$969$	−4.76393	−0.153040
$970$	0	0
$971$	−33.4164	−1.07238	−0.536192	−	0.844096i	$-0.680138\pi$
$971$	−33.4164	−1.07238	−0.536192	+	0.844096i	$0.680138\pi$
$972$	1.00000i	0.0320750i
$973$	102.610i	3.28952i
$974$	−9.70820	−0.311071
$975$	0	0
$976$	−1.61803	−0.0517920
$977$	3.25735i	0.104212i	0.998642	+	0.0521060i	$0.0165934\pi$
$977$	3.25735i	0.104212i	−0.998642	+	0.0521060i	$0.983407\pi$
$978$	− 14.9443i	− 0.477865i
$979$	6.65248	0.212614
$980$	0	0
$981$	−7.90983	−0.252541
$982$	− 5.88854i	− 0.187911i
$983$	8.29180i	0.264467i	0.991219	+	0.132234i	$0.0422149\pi$
$983$	8.29180i	0.264467i	−0.991219	+	0.132234i	$0.957785\pi$
$984$	−10.8541	−0.346016
$985$	0	0
$986$	25.5066	0.812295
$987$	− 3.41641i	− 0.108745i
$988$	− 6.94427i	− 0.220927i
$989$	−34.4721	−1.09615
$990$	0	0
$991$	37.1246	1.17930	0.589651	−	0.807658i	$-0.299265\pi$
$991$	37.1246	1.17930	0.589651	+	0.807658i	$0.299265\pi$
$992$	− 13.8197i	− 0.438775i
$993$	− 6.94427i	− 0.220370i
$994$	−23.4164	−0.742723
$995$	0	0
$996$	−12.4721	−0.395195
$997$	17.4164i	0.551583i	0.961217	+	0.275792i	$0.0889400\pi$
$997$	17.4164i	0.551583i	−0.961217	+	0.275792i	$0.911060\pi$
$998$	− 6.00000i	− 0.189927i
$999$	3.09017	0.0977687

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.b.b.1249.2		4
5.2	odd	4		1875.2.a.d.1.1		2
5.3	odd	4		1875.2.a.a.1.2		2
5.4	even	2	inner	1875.2.b.b.1249.3		4
15.2	even	4		5625.2.a.a.1.1		2
15.8	even	4		5625.2.a.h.1.2		2
25.2	odd	20		75.2.g.a.46.1	yes	4
25.9	even	10		375.2.i.a.349.1		8
25.11	even	5		375.2.i.a.274.1		8
25.12	odd	20		75.2.g.a.31.1	✓	4
25.13	odd	20		375.2.g.a.151.1		4
25.14	even	10		375.2.i.a.274.2		8
25.16	even	5		375.2.i.a.349.2		8
25.23	odd	20		375.2.g.a.226.1		4
75.2	even	20		225.2.h.a.46.1		4
75.62	even	20		225.2.h.a.181.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.a.31.1	✓	4	25.12	odd	20
75.2.g.a.46.1	yes	4	25.2	odd	20
225.2.h.a.46.1		4	75.2	even	20
225.2.h.a.181.1		4	75.62	even	20
375.2.g.a.151.1		4	25.13	odd	20
375.2.g.a.226.1		4	25.23	odd	20
375.2.i.a.274.1		8	25.11	even	5
375.2.i.a.274.2		8	25.14	even	10
375.2.i.a.349.1		8	25.9	even	10
375.2.i.a.349.2		8	25.16	even	5
1875.2.a.a.1.2		2	5.3	odd	4
1875.2.a.d.1.1		2	5.2	odd	4
1875.2.b.b.1249.2		4	1.1	even	1	trivial
1875.2.b.b.1249.3		4	5.4	even	2	inner
5625.2.a.a.1.1		2	15.2	even	4
5625.2.a.h.1.2		2	15.8	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.47214i q^{7} -3.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.47214i q^{7} -3.00000i q^{8} -1.00000 q^{9} -1.23607 q^{11} +1.00000i q^{12} +5.61803i q^{13} +4.47214 q^{14} -1.00000 q^{16} -3.85410i q^{17} +1.00000i q^{18} -1.23607 q^{19} -4.47214 q^{21} +1.23607i q^{22} +4.47214i q^{23} +3.00000 q^{24} +5.61803 q^{26} -1.00000i q^{27} +4.47214i q^{28} -6.61803 q^{29} +2.76393 q^{31} -5.00000i q^{32} -1.23607i q^{33} -3.85410 q^{34} -1.00000 q^{36} +3.09017i q^{37} +1.23607i q^{38} -5.61803 q^{39} -3.61803 q^{41} +4.47214i q^{42} +7.70820i q^{43} -1.23607 q^{44} +4.47214 q^{46} +0.763932i q^{47} -1.00000i q^{48} -13.0000 q^{49} +3.85410 q^{51} +5.61803i q^{52} +3.61803i q^{53} -1.00000 q^{54} +13.4164 q^{56} -1.23607i q^{57} +6.61803i q^{58} +4.00000 q^{59} +1.61803 q^{61} -2.76393i q^{62} -4.47214i q^{63} -7.00000 q^{64} -1.23607 q^{66} -0.763932i q^{67} -3.85410i q^{68} -4.47214 q^{69} -5.23607 q^{71} +3.00000i q^{72} -8.09017i q^{73} +3.09017 q^{74} -1.23607 q^{76} -5.52786i q^{77} +5.61803i q^{78} +1.00000 q^{81} +3.61803i q^{82} +12.4721i q^{83} -4.47214 q^{84} +7.70820 q^{86} -6.61803i q^{87} +3.70820i q^{88} -5.38197 q^{89} -25.1246 q^{91} +4.47214i q^{92} +2.76393i q^{93} +0.763932 q^{94} +5.00000 q^{96} -2.14590i q^{97} +13.0000i q^{98} +1.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^4 + 4 * q^6 - 4 * q^9	\( 4 q + 4 q^{4} + 4 q^{6} - 4 q^{9} + 4 q^{11} - 4 q^{16} + 4 q^{19} + 12 q^{24} + 18 q^{26} - 22 q^{29} + 20 q^{31} - 2 q^{34} - 4 q^{36} - 18 q^{39} - 10 q^{41} + 4 q^{44} - 52 q^{49} + 2 q^{51} - 4 q^{54} + 16 q^{59} + 2 q^{61} - 28 q^{64} + 4 q^{66} - 12 q^{71} - 10 q^{74} + 4 q^{76} + 4 q^{81} + 4 q^{86} - 26 q^{89} - 20 q^{91} + 12 q^{94} + 20 q^{96} - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^4 + 4 * q^6 - 4 * q^9 + 4 * q^11 - 4 * q^16 + 4 * q^19 + 12 * q^24 + 18 * q^26 - 22 * q^29 + 20 * q^31 - 2 * q^34 - 4 * q^36 - 18 * q^39 - 10 * q^41 + 4 * q^44 - 52 * q^49 + 2 * q^51 - 4 * q^54 + 16 * q^59 + 2 * q^61 - 28 * q^64 + 4 * q^66 - 12 * q^71 - 10 * q^74 + 4 * q^76 + 4 * q^81 + 4 * q^86 - 26 * q^89 - 20 * q^91 + 12 * q^94 + 20 * q^96 - 4 * q^99

Introduction

L-functions

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Database

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