LMFDB - Embedded newform 9025.2.a.bd.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9025 = 5^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9025.a (trivial)

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:	yes
Analytic conductor:	$72.0649878242$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.347296$ of defining polynomial
Character	$\chi$	$=$	9025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.34730 q^{2} +2.87939 q^{3} -0.184793 q^{4} +3.87939 q^{6} -0.347296 q^{7} -2.94356 q^{8} +5.29086 q^{9} +O(q^{10})$	\(q+1.34730 q^{2} +2.87939 q^{3} -0.184793 q^{4} +3.87939 q^{6} -0.347296 q^{7} -2.94356 q^{8} +5.29086 q^{9} -2.22668 q^{11} -0.532089 q^{12} -2.57398 q^{13} -0.467911 q^{14} -3.59627 q^{16} -0.467911 q^{17} +7.12836 q^{18} -1.00000 q^{21} -3.00000 q^{22} +2.69459 q^{23} -8.47565 q^{24} -3.46791 q^{26} +6.59627 q^{27} +0.0641778 q^{28} -6.87939 q^{29} -7.10607 q^{31} +1.04189 q^{32} -6.41147 q^{33} -0.630415 q^{34} -0.977711 q^{36} -4.94356 q^{37} -7.41147 q^{39} +2.47565 q^{41} -1.34730 q^{42} -3.90167 q^{43} +0.411474 q^{44} +3.63041 q^{46} +7.29086 q^{47} -10.3550 q^{48} -6.87939 q^{49} -1.34730 q^{51} +0.475652 q^{52} +2.83750 q^{53} +8.88713 q^{54} +1.02229 q^{56} -9.26857 q^{58} -6.30541 q^{59} +9.12836 q^{61} -9.57398 q^{62} -1.83750 q^{63} +8.59627 q^{64} -8.63816 q^{66} -7.67499 q^{67} +0.0864665 q^{68} +7.75877 q^{69} -9.30541 q^{71} -15.5740 q^{72} -1.38919 q^{73} -6.66044 q^{74} +0.773318 q^{77} -9.98545 q^{78} -11.8452 q^{79} +3.12061 q^{81} +3.33544 q^{82} +14.8307 q^{83} +0.184793 q^{84} -5.25671 q^{86} -19.8084 q^{87} +6.55438 q^{88} -10.2909 q^{89} +0.893933 q^{91} -0.497941 q^{92} -20.4611 q^{93} +9.82295 q^{94} +3.00000 q^{96} -9.45336 q^{97} -9.26857 q^{98} -11.7811 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{6} + 6 q^{8}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 6 * q^6 + 6 * q^8	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{6} + 6 q^{8} + 3 q^{12} - 6 q^{14} + 3 q^{16} - 6 q^{17} + 3 q^{18} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 6 q^{24} - 15 q^{26} + 6 q^{27} - 9 q^{28} - 15 q^{29} - 9 q^{31} - 9 q^{33} - 9 q^{34} - 9 q^{36} - 12 q^{39} - 12 q^{41} - 3 q^{42} - 9 q^{44} + 18 q^{46} + 6 q^{47} - 6 q^{48} - 15 q^{49} - 3 q^{51} - 18 q^{52} + 6 q^{53} - 3 q^{54} - 3 q^{56} - 18 q^{58} - 21 q^{59} + 9 q^{61} - 21 q^{62} - 3 q^{63} + 12 q^{64} - 9 q^{66} - 18 q^{67} - 15 q^{68} + 12 q^{69} - 30 q^{71} - 39 q^{72} + 3 q^{74} + 9 q^{77} - 12 q^{78} - 9 q^{79} + 15 q^{81} - 18 q^{82} - 3 q^{84} + 21 q^{86} - 21 q^{87} + 9 q^{88} - 15 q^{89} + 15 q^{91} + 24 q^{92} - 24 q^{93} + 9 q^{94} + 9 q^{96} - 15 q^{97} - 18 q^{98} - 18 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 6 * q^6 + 6 * q^8 + 3 * q^12 - 6 * q^14 + 3 * q^16 - 6 * q^17 + 3 * q^18 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 6 * q^24 - 15 * q^26 + 6 * q^27 - 9 * q^28 - 15 * q^29 - 9 * q^31 - 9 * q^33 - 9 * q^34 - 9 * q^36 - 12 * q^39 - 12 * q^41 - 3 * q^42 - 9 * q^44 + 18 * q^46 + 6 * q^47 - 6 * q^48 - 15 * q^49 - 3 * q^51 - 18 * q^52 + 6 * q^53 - 3 * q^54 - 3 * q^56 - 18 * q^58 - 21 * q^59 + 9 * q^61 - 21 * q^62 - 3 * q^63 + 12 * q^64 - 9 * q^66 - 18 * q^67 - 15 * q^68 + 12 * q^69 - 30 * q^71 - 39 * q^72 + 3 * q^74 + 9 * q^77 - 12 * q^78 - 9 * q^79 + 15 * q^81 - 18 * q^82 - 3 * q^84 + 21 * q^86 - 21 * q^87 + 9 * q^88 - 15 * q^89 + 15 * q^91 + 24 * q^92 - 24 * q^93 + 9 * q^94 + 9 * q^96 - 15 * q^97 - 18 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.34730	0.952682	0.476341	−	0.879261i	$-0.341963\pi$
$2$	1.34730	0.952682	0.476341	+	0.879261i	$0.341963\pi$
$3$	2.87939	1.66241	0.831207	−	0.555963i	$-0.187650\pi$
$3$	2.87939	1.66241	0.831207	+	0.555963i	$0.187650\pi$
$4$	−0.184793	−0.0923963
$5$	0	0
$5$	0	0
$6$	3.87939	1.58375
$7$	−0.347296	−0.131266	−0.0656328	−	0.997844i	$-0.520907\pi$
$7$	−0.347296	−0.131266	−0.0656328	+	0.997844i	$0.520907\pi$
$8$	−2.94356	−1.04071
$9$	5.29086	1.76362
$10$	0	0
$11$	−2.22668	−0.671370	−0.335685	−	0.941974i	$-0.608968\pi$
$11$	−2.22668	−0.671370	−0.335685	+	0.941974i	$0.608968\pi$
$12$	−0.532089	−0.153601
$13$	−2.57398	−0.713893	−0.356947	−	0.934125i	$-0.616182\pi$
$13$	−2.57398	−0.713893	−0.356947	+	0.934125i	$0.616182\pi$
$14$	−0.467911	−0.125055
$15$	0	0
$16$	−3.59627	−0.899067
$17$	−0.467911	−0.113485	−0.0567426	−	0.998389i	$-0.518071\pi$
$17$	−0.467911	−0.113485	−0.0567426	+	0.998389i	$0.518071\pi$
$18$	7.12836	1.68017
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−1.00000	−0.218218
$22$	−3.00000	−0.639602
$23$	2.69459	0.561861	0.280931	−	0.959728i	$-0.409357\pi$
$23$	2.69459	0.561861	0.280931	+	0.959728i	$0.409357\pi$
$24$	−8.47565	−1.73009
$25$	0	0
$26$	−3.46791	−0.680113
$27$	6.59627	1.26945
$28$	0.0641778	0.0121285
$29$	−6.87939	−1.27747	−0.638735	−	0.769427i	$-0.720542\pi$
$29$	−6.87939	−1.27747	−0.638735	+	0.769427i	$0.720542\pi$
$30$	0	0
$31$	−7.10607	−1.27629	−0.638144	−	0.769917i	$-0.720297\pi$
$31$	−7.10607	−1.27629	−0.638144	+	0.769917i	$0.720297\pi$
$32$	1.04189	0.184182
$33$	−6.41147	−1.11609
$34$	−0.630415	−0.108115
$35$	0	0
$36$	−0.977711	−0.162952
$37$	−4.94356	−0.812717	−0.406358	−	0.913714i	$-0.633202\pi$
$37$	−4.94356	−0.812717	−0.406358	+	0.913714i	$0.633202\pi$
$38$	0	0
$39$	−7.41147	−1.18679
$40$	0	0
$41$	2.47565	0.386632	0.193316	−	0.981137i	$-0.438076\pi$
$41$	2.47565	0.386632	0.193316	+	0.981137i	$0.438076\pi$
$42$	−1.34730	−0.207892
$43$	−3.90167	−0.595000	−0.297500	−	0.954722i	$-0.596153\pi$
$43$	−3.90167	−0.595000	−0.297500	+	0.954722i	$0.596153\pi$
$44$	0.411474	0.0620321
$45$	0	0
$46$	3.63041	0.535275
$47$	7.29086	1.06348	0.531741	−	0.846907i	$-0.321538\pi$
$47$	7.29086	1.06348	0.531741	+	0.846907i	$0.321538\pi$
$48$	−10.3550	−1.49462
$49$	−6.87939	−0.982769
$50$	0	0
$51$	−1.34730	−0.188659
$52$	0.475652	0.0659611
$53$	2.83750	0.389760	0.194880	−	0.980827i	$-0.437568\pi$
$53$	2.83750	0.389760	0.194880	+	0.980827i	$0.437568\pi$
$54$	8.88713	1.20938
$55$	0	0
$56$	1.02229	0.136609
$57$	0	0
$58$	−9.26857	−1.21702
$59$	−6.30541	−0.820894	−0.410447	−	0.911884i	$-0.634627\pi$
$59$	−6.30541	−0.820894	−0.410447	+	0.911884i	$0.634627\pi$
$60$	0	0
$61$	9.12836	1.16877	0.584383	−	0.811478i	$-0.301337\pi$
$61$	9.12836	1.16877	0.584383	+	0.811478i	$0.301337\pi$
$62$	−9.57398	−1.21590
$63$	−1.83750	−0.231503
$64$	8.59627	1.07453
$65$	0	0
$66$	−8.63816	−1.06328
$67$	−7.67499	−0.937650	−0.468825	−	0.883291i	$-0.655322\pi$
$67$	−7.67499	−0.937650	−0.468825	+	0.883291i	$0.655322\pi$
$68$	0.0864665	0.0104856
$69$	7.75877	0.934046
$70$	0	0
$71$	−9.30541	−1.10435	−0.552174	−	0.833729i	$-0.686202\pi$
$71$	−9.30541	−1.10435	−0.552174	+	0.833729i	$0.686202\pi$
$72$	−15.5740	−1.83541
$73$	−1.38919	−0.162592	−0.0812959	−	0.996690i	$-0.525906\pi$
$73$	−1.38919	−0.162592	−0.0812959	+	0.996690i	$0.525906\pi$
$74$	−6.66044	−0.774261
$75$	0	0
$76$	0	0
$77$	0.773318	0.0881278
$78$	−9.98545	−1.13063
$79$	−11.8452	−1.33269	−0.666347	−	0.745642i	$-0.732143\pi$
$79$	−11.8452	−1.33269	−0.666347	+	0.745642i	$0.732143\pi$
$80$	0	0
$81$	3.12061	0.346735
$82$	3.33544	0.368337
$83$	14.8307	1.62788	0.813940	−	0.580949i	$-0.197319\pi$
$83$	14.8307	1.62788	0.813940	+	0.580949i	$0.197319\pi$
$84$	0.184793	0.0201625
$85$	0	0
$86$	−5.25671	−0.566846
$87$	−19.8084	−2.12368
$88$	6.55438	0.698699
$89$	−10.2909	−1.09083	−0.545414	−	0.838166i	$-0.683628\pi$
$89$	−10.2909	−1.09083	−0.545414	+	0.838166i	$0.683628\pi$
$90$	0	0
$91$	0.893933	0.0937097
$92$	−0.497941	−0.0519139
$93$	−20.4611	−2.12172
$94$	9.82295	1.01316
$95$	0	0
$96$	3.00000	0.306186
$97$	−9.45336	−0.959844	−0.479922	−	0.877311i	$-0.659335\pi$
$97$	−9.45336	−0.959844	−0.479922	+	0.877311i	$0.659335\pi$
$98$	−9.26857	−0.936267
$99$	−11.7811	−1.18404
$100$	0	0
$101$	−9.24897	−0.920307	−0.460153	−	0.887839i	$-0.652206\pi$
$101$	−9.24897	−0.920307	−0.460153	+	0.887839i	$0.652206\pi$
$102$	−1.81521	−0.179732
$103$	5.50980	0.542897	0.271448	−	0.962453i	$-0.412497\pi$
$103$	5.50980	0.542897	0.271448	+	0.962453i	$0.412497\pi$
$104$	7.57667	0.742953
$105$	0	0
$106$	3.82295	0.371318
$107$	−10.2344	−0.989399	−0.494699	−	0.869064i	$-0.664722\pi$
$107$	−10.2344	−0.989399	−0.494699	+	0.869064i	$0.664722\pi$
$108$	−1.21894	−0.117293
$109$	−1.82295	−0.174607	−0.0873034	−	0.996182i	$-0.527825\pi$
$109$	−1.82295	−0.174607	−0.0873034	+	0.996182i	$0.527825\pi$
$110$	0	0
$111$	−14.2344	−1.35107
$112$	1.24897	0.118017
$113$	17.6878	1.66393	0.831963	−	0.554830i	$-0.187217\pi$
$113$	17.6878	1.66393	0.831963	+	0.554830i	$0.187217\pi$
$114$	0	0
$115$	0	0
$116$	1.27126	0.118033
$117$	−13.6186	−1.25904
$118$	−8.49525	−0.782051
$119$	0.162504	0.0148967
$120$	0	0
$121$	−6.04189	−0.549263
$122$	12.2986	1.11346
$123$	7.12836	0.642742
$124$	1.31315	0.117924
$125$	0	0
$126$	−2.47565	−0.220549
$127$	−11.6040	−1.02969	−0.514845	−	0.857284i	$-0.672150\pi$
$127$	−11.6040	−1.02969	−0.514845	+	0.857284i	$0.672150\pi$
$128$	9.49794	0.839507
$129$	−11.2344	−0.989136
$130$	0	0
$131$	1.84524	0.161219	0.0806096	−	0.996746i	$-0.474313\pi$
$131$	1.84524	0.161219	0.0806096	+	0.996746i	$0.474313\pi$
$132$	1.18479	0.103123
$133$	0	0
$134$	−10.3405	−0.893282
$135$	0	0
$136$	1.37733	0.118105
$137$	−0.255777	−0.0218525	−0.0109263	−	0.999940i	$-0.503478\pi$
$137$	−0.255777	−0.0218525	−0.0109263	+	0.999940i	$0.503478\pi$
$138$	10.4534	0.889849
$139$	4.26352	0.361627	0.180813	−	0.983517i	$-0.442127\pi$
$139$	4.26352	0.361627	0.180813	+	0.983517i	$0.442127\pi$
$140$	0	0
$141$	20.9932	1.76795
$142$	−12.5371	−1.05209
$143$	5.73143	0.479286
$144$	−19.0273	−1.58561
$145$	0	0
$146$	−1.87164	−0.154898
$147$	−19.8084	−1.63377
$148$	0.913534	0.0750920
$149$	16.5594	1.35660	0.678301	−	0.734784i	$-0.262717\pi$
$149$	16.5594	1.35660	0.678301	+	0.734784i	$0.262717\pi$
$150$	0	0
$151$	−4.36184	−0.354962	−0.177481	−	0.984124i	$-0.556795\pi$
$151$	−4.36184	−0.354962	−0.177481	+	0.984124i	$0.556795\pi$
$152$	0	0
$153$	−2.47565	−0.200145
$154$	1.04189	0.0839578
$155$	0	0
$156$	1.36959	0.109655
$157$	9.61856	0.767644	0.383822	−	0.923407i	$-0.374608\pi$
$157$	9.61856	0.767644	0.383822	+	0.923407i	$0.374608\pi$
$158$	−15.9590	−1.26963
$159$	8.17024	0.647943
$160$	0	0
$161$	−0.935822	−0.0737531
$162$	4.20439	0.330328
$163$	−8.35504	−0.654417	−0.327209	−	0.944952i	$-0.606108\pi$
$163$	−8.35504	−0.654417	−0.327209	+	0.944952i	$0.606108\pi$
$164$	−0.457482	−0.0357233
$165$	0	0
$166$	19.9813	1.55085
$167$	−4.03508	−0.312244	−0.156122	−	0.987738i	$-0.549899\pi$
$167$	−4.03508	−0.312244	−0.156122	+	0.987738i	$0.549899\pi$
$168$	2.94356	0.227101
$169$	−6.37464	−0.490357
$170$	0	0
$171$	0	0
$172$	0.721000	0.0549758
$173$	20.1438	1.53151	0.765754	−	0.643134i	$-0.222366\pi$
$173$	20.1438	1.53151	0.765754	+	0.643134i	$0.222366\pi$
$174$	−26.6878	−2.02320
$175$	0	0
$176$	8.00774	0.603606
$177$	−18.1557	−1.36467
$178$	−13.8648	−1.03921
$179$	−11.5125	−0.860484	−0.430242	−	0.902714i	$-0.641572\pi$
$179$	−11.5125	−0.860484	−0.430242	+	0.902714i	$0.641572\pi$
$180$	0	0
$181$	8.53714	0.634561	0.317280	−	0.948332i	$-0.397230\pi$
$181$	8.53714	0.634561	0.317280	+	0.948332i	$0.397230\pi$
$182$	1.20439	0.0892755
$183$	26.2841	1.94297
$184$	−7.93170	−0.584733
$185$	0	0
$186$	−27.5672	−2.02132
$187$	1.04189	0.0761905
$188$	−1.34730	−0.0982617
$189$	−2.29086	−0.166635
$190$	0	0
$191$	18.3354	1.32671	0.663353	−	0.748307i	$-0.269133\pi$
$191$	18.3354	1.32671	0.663353	+	0.748307i	$0.269133\pi$
$192$	24.7520	1.78632
$193$	−0.297667	−0.0214265	−0.0107133	−	0.999943i	$-0.503410\pi$
$193$	−0.297667	−0.0214265	−0.0107133	+	0.999943i	$0.503410\pi$
$194$	−12.7365	−0.914426
$195$	0	0
$196$	1.27126	0.0908042
$197$	−13.1411	−0.936268	−0.468134	−	0.883657i	$-0.655074\pi$
$197$	−13.1411	−0.936268	−0.468134	+	0.883657i	$0.655074\pi$
$198$	−15.8726	−1.12802
$199$	−0.256711	−0.0181978	−0.00909888	−	0.999959i	$-0.502896\pi$
$199$	−0.256711	−0.0181978	−0.00909888	+	0.999959i	$0.502896\pi$
$200$	0	0
$201$	−22.0993	−1.55876
$202$	−12.4611	−0.876760
$203$	2.38919	0.167688
$204$	0.248970	0.0174314
$205$	0	0
$206$	7.42333	0.517208
$207$	14.2567	0.990910
$208$	9.25671	0.641837
$209$	0	0
$210$	0	0
$211$	2.44831	0.168549	0.0842743	−	0.996443i	$-0.473143\pi$
$211$	2.44831	0.168549	0.0842743	+	0.996443i	$0.473143\pi$
$212$	−0.524348	−0.0360124
$213$	−26.7939	−1.83588
$214$	−13.7888	−0.942583
$215$	0	0
$216$	−19.4165	−1.32113
$217$	2.46791	0.167533
$218$	−2.45605	−0.166345
$219$	−4.00000	−0.270295
$220$	0	0
$221$	1.20439	0.0810162
$222$	−19.1780	−1.28714
$223$	8.50980	0.569858	0.284929	−	0.958549i	$-0.408030\pi$
$223$	8.50980	0.569858	0.284929	+	0.958549i	$0.408030\pi$
$224$	−0.361844	−0.0241767
$225$	0	0
$226$	23.8307	1.58519
$227$	14.1506	0.939211	0.469606	−	0.882876i	$-0.344396\pi$
$227$	14.1506	0.939211	0.469606	+	0.882876i	$0.344396\pi$
$228$	0	0
$229$	−20.5330	−1.35686	−0.678430	−	0.734665i	$-0.737339\pi$
$229$	−20.5330	−1.35686	−0.678430	+	0.734665i	$0.737339\pi$
$230$	0	0
$231$	2.22668	0.146505
$232$	20.2499	1.32947
$233$	−17.6509	−1.15635	−0.578176	−	0.815912i	$-0.696235\pi$
$233$	−17.6509	−1.15635	−0.578176	+	0.815912i	$0.696235\pi$
$234$	−18.3482	−1.19946
$235$	0	0
$236$	1.16519	0.0758475
$237$	−34.1070	−2.21549
$238$	0.218941	0.0141918
$239$	2.35235	0.152161	0.0760804	−	0.997102i	$-0.475759\pi$
$239$	2.35235	0.152161	0.0760804	+	0.997102i	$0.475759\pi$
$240$	0	0
$241$	13.8007	0.888979	0.444489	−	0.895784i	$-0.353385\pi$
$241$	13.8007	0.888979	0.444489	+	0.895784i	$0.353385\pi$
$242$	−8.14022	−0.523273
$243$	−10.8033	−0.693035
$244$	−1.68685	−0.107990
$245$	0	0
$246$	9.60401	0.612329
$247$	0	0
$248$	20.9172	1.32824
$249$	42.7033	2.70621
$250$	0	0
$251$	−4.16519	−0.262905	−0.131452	−	0.991322i	$-0.541964\pi$
$251$	−4.16519	−0.262905	−0.131452	+	0.991322i	$0.541964\pi$
$252$	0.339556	0.0213900
$253$	−6.00000	−0.377217
$254$	−15.6340	−0.980967
$255$	0	0
$256$	−4.39599	−0.274750
$257$	−0.667252	−0.0416220	−0.0208110	−	0.999783i	$-0.506625\pi$
$257$	−0.667252	−0.0416220	−0.0208110	+	0.999783i	$0.506625\pi$
$258$	−15.1361	−0.942332
$259$	1.71688	0.106682
$260$	0	0
$261$	−36.3979	−2.25297
$262$	2.48608	0.153591
$263$	−11.3996	−0.702930	−0.351465	−	0.936201i	$-0.614316\pi$
$263$	−11.3996	−0.702930	−0.351465	+	0.936201i	$0.614316\pi$
$264$	18.8726	1.16153
$265$	0	0
$266$	0	0
$267$	−29.6313	−1.81341
$268$	1.41828	0.0866353
$269$	19.3901	1.18224	0.591118	−	0.806585i	$-0.298687\pi$
$269$	19.3901	1.18224	0.591118	+	0.806585i	$0.298687\pi$
$270$	0	0
$271$	−13.3942	−0.813642	−0.406821	−	0.913508i	$-0.633363\pi$
$271$	−13.3942	−0.813642	−0.406821	+	0.913508i	$0.633363\pi$
$272$	1.68273	0.102031
$273$	2.57398	0.155784
$274$	−0.344608	−0.0208185
$275$	0	0
$276$	−1.43376	−0.0863024
$277$	−17.7469	−1.06631	−0.533154	−	0.846018i	$-0.678993\pi$
$277$	−17.7469	−1.06631	−0.533154	+	0.846018i	$0.678993\pi$
$278$	5.74422	0.344516
$279$	−37.5972	−2.25089
$280$	0	0
$281$	18.2790	1.09043	0.545217	−	0.838295i	$-0.316447\pi$
$281$	18.2790	1.09043	0.545217	+	0.838295i	$0.316447\pi$
$282$	28.2841	1.68429
$283$	−7.68779	−0.456991	−0.228496	−	0.973545i	$-0.573381\pi$
$283$	−7.68779	−0.456991	−0.228496	+	0.973545i	$0.573381\pi$
$284$	1.71957	0.102038
$285$	0	0
$286$	7.72193	0.456608
$287$	−0.859785	−0.0507515
$288$	5.51249	0.324827
$289$	−16.7811	−0.987121
$290$	0	0
$291$	−27.2199	−1.59566
$292$	0.256711	0.0150229
$293$	10.5030	0.613591	0.306796	−	0.951775i	$-0.400743\pi$
$293$	10.5030	0.613591	0.306796	+	0.951775i	$0.400743\pi$
$294$	−26.6878	−1.55646
$295$	0	0
$296$	14.5517	0.845800
$297$	−14.6878	−0.852272
$298$	22.3105	1.29241
$299$	−6.93582	−0.401109
$300$	0	0
$301$	1.35504	0.0781030
$302$	−5.87670	−0.338166
$303$	−26.6313	−1.52993
$304$	0	0
$305$	0	0
$306$	−3.33544	−0.190674
$307$	11.6955	0.667499	0.333749	−	0.942662i	$-0.391686\pi$
$307$	11.6955	0.667499	0.333749	+	0.942662i	$0.391686\pi$
$308$	−0.142903	−0.00814268
$309$	15.8648	0.902519
$310$	0	0
$311$	15.9659	0.905340	0.452670	−	0.891678i	$-0.350471\pi$
$311$	15.9659	0.905340	0.452670	+	0.891678i	$0.350471\pi$
$312$	21.8161	1.23510
$313$	26.6287	1.50514	0.752570	−	0.658512i	$-0.228814\pi$
$313$	26.6287	1.50514	0.752570	+	0.658512i	$0.228814\pi$
$314$	12.9590	0.731321
$315$	0	0
$316$	2.18891	0.123136
$317$	−29.5321	−1.65869	−0.829344	−	0.558739i	$-0.811285\pi$
$317$	−29.5321	−1.65869	−0.829344	+	0.558739i	$0.811285\pi$
$318$	11.0077	0.617283
$319$	15.3182	0.857655
$320$	0	0
$321$	−29.4688	−1.64479
$322$	−1.26083	−0.0702633
$323$	0	0
$324$	−0.576666	−0.0320370
$325$	0	0
$326$	−11.2567	−0.623452
$327$	−5.24897	−0.290269
$328$	−7.28724	−0.402370
$329$	−2.53209	−0.139599
$330$	0	0
$331$	27.6655	1.52063	0.760317	−	0.649553i	$-0.225044\pi$
$331$	27.6655	1.52063	0.760317	+	0.649553i	$0.225044\pi$
$332$	−2.74060	−0.150410
$333$	−26.1557	−1.43332
$334$	−5.43645	−0.297469
$335$	0	0
$336$	3.59627	0.196192
$337$	−17.8598	−0.972884	−0.486442	−	0.873713i	$-0.661706\pi$
$337$	−17.8598	−0.972884	−0.486442	+	0.873713i	$0.661706\pi$
$338$	−8.58853	−0.467154
$339$	50.9299	2.76614
$340$	0	0
$341$	15.8229	0.856861
$342$	0	0
$343$	4.82026	0.260270
$344$	11.4848	0.619220
$345$	0	0
$346$	27.1397	1.45904
$347$	5.80066	0.311396	0.155698	−	0.987805i	$-0.450237\pi$
$347$	5.80066	0.311396	0.155698	+	0.987805i	$0.450237\pi$
$348$	3.66044	0.196220
$349$	5.37227	0.287571	0.143786	−	0.989609i	$-0.454072\pi$
$349$	5.37227	0.287571	0.143786	+	0.989609i	$0.454072\pi$
$350$	0	0
$351$	−16.9786	−0.906253
$352$	−2.31996	−0.123654
$353$	25.2344	1.34309	0.671546	−	0.740963i	$-0.265630\pi$
$353$	25.2344	1.34309	0.671546	+	0.740963i	$0.265630\pi$
$354$	−24.4611	−1.30009
$355$	0	0
$356$	1.90167	0.100789
$357$	0.467911	0.0247645
$358$	−15.5107	−0.819768
$359$	6.68685	0.352919	0.176459	−	0.984308i	$-0.443536\pi$
$359$	6.68685	0.352919	0.176459	+	0.984308i	$0.443536\pi$
$360$	0	0
$361$	0	0
$362$	11.5021	0.604535
$363$	−17.3969	−0.913102
$364$	−0.165192	−0.00865842
$365$	0	0
$366$	35.4124	1.85104
$367$	−8.11886	−0.423801	−0.211901	−	0.977291i	$-0.567965\pi$
$367$	−8.11886	−0.423801	−0.211901	+	0.977291i	$0.567965\pi$
$368$	−9.69047	−0.505151
$369$	13.0983	0.681872
$370$	0	0
$371$	−0.985452	−0.0511621
$372$	3.78106	0.196039
$373$	−34.8976	−1.80693	−0.903463	−	0.428665i	$-0.858984\pi$
$373$	−34.8976	−1.80693	−0.903463	+	0.428665i	$0.858984\pi$
$374$	1.40373	0.0725853
$375$	0	0
$376$	−21.4611	−1.10677
$377$	17.7074	0.911977
$378$	−3.08647	−0.158751
$379$	1.70140	0.0873950	0.0436975	−	0.999045i	$-0.486086\pi$
$379$	1.70140	0.0873950	0.0436975	+	0.999045i	$0.486086\pi$
$380$	0	0
$381$	−33.4124	−1.71177
$382$	24.7033	1.26393
$383$	−2.93676	−0.150061	−0.0750306	−	0.997181i	$-0.523905\pi$
$383$	−2.93676	−0.150061	−0.0750306	+	0.997181i	$0.523905\pi$
$384$	27.3482	1.39561
$385$	0	0
$386$	−0.401045	−0.0204127
$387$	−20.6432	−1.04935
$388$	1.74691	0.0886860
$389$	−24.5672	−1.24561	−0.622803	−	0.782379i	$-0.714006\pi$
$389$	−24.5672	−1.24561	−0.622803	+	0.782379i	$0.714006\pi$
$390$	0	0
$391$	−1.26083	−0.0637629
$392$	20.2499	1.02277
$393$	5.31315	0.268013
$394$	−17.7050	−0.891966
$395$	0	0
$396$	2.17705	0.109401
$397$	31.8357	1.59779	0.798895	−	0.601470i	$-0.205418\pi$
$397$	31.8357	1.59779	0.798895	+	0.601470i	$0.205418\pi$
$398$	−0.345866	−0.0173367
$399$	0	0
$400$	0	0
$401$	−0.0864665	−0.00431793	−0.00215896	−	0.999998i	$-0.500687\pi$
$401$	−0.0864665	−0.00431793	−0.00215896	+	0.999998i	$0.500687\pi$
$402$	−29.7743	−1.48500
$403$	18.2909	0.911133
$404$	1.70914	0.0850329
$405$	0	0
$406$	3.21894	0.159753
$407$	11.0077	0.545633
$408$	3.96585	0.196339
$409$	20.0060	0.989232	0.494616	−	0.869112i	$-0.335309\pi$
$409$	20.0060	0.989232	0.494616	+	0.869112i	$0.335309\pi$
$410$	0	0
$411$	−0.736482	−0.0363280
$412$	−1.01817	−0.0501616
$413$	2.18984	0.107755
$414$	19.2080	0.944022
$415$	0	0
$416$	−2.68180	−0.131486
$417$	12.2763	0.601174
$418$	0	0
$419$	25.4097	1.24135	0.620673	−	0.784070i	$-0.286859\pi$
$419$	25.4097	1.24135	0.620673	+	0.784070i	$0.286859\pi$
$420$	0	0
$421$	4.36959	0.212961	0.106480	−	0.994315i	$-0.466042\pi$
$421$	4.36959	0.212961	0.106480	+	0.994315i	$0.466042\pi$
$422$	3.29860	0.160573
$423$	38.5749	1.87558
$424$	−8.35235	−0.405626
$425$	0	0
$426$	−36.0993	−1.74901
$427$	−3.17024	−0.153419
$428$	1.89124	0.0914168
$429$	16.5030	0.796772
$430$	0	0
$431$	−38.3063	−1.84515	−0.922576	−	0.385816i	$-0.873920\pi$
$431$	−38.3063	−1.84515	−0.922576	+	0.385816i	$0.873920\pi$
$432$	−23.7219	−1.14132
$433$	18.1310	0.871322	0.435661	−	0.900111i	$-0.356515\pi$
$433$	18.1310	0.871322	0.435661	+	0.900111i	$0.356515\pi$
$434$	3.32501	0.159605
$435$	0	0
$436$	0.336867	0.0161330
$437$	0	0
$438$	−5.38919	−0.257505
$439$	−6.09059	−0.290688	−0.145344	−	0.989381i	$-0.546429\pi$
$439$	−6.09059	−0.290688	−0.145344	+	0.989381i	$0.546429\pi$
$440$	0	0
$441$	−36.3979	−1.73323
$442$	1.62267	0.0771827
$443$	29.8931	1.42026	0.710132	−	0.704068i	$-0.248635\pi$
$443$	29.8931	1.42026	0.710132	+	0.704068i	$0.248635\pi$
$444$	2.63041	0.124834
$445$	0	0
$446$	11.4652	0.542894
$447$	47.6810	2.25523
$448$	−2.98545	−0.141049
$449$	−11.2499	−0.530916	−0.265458	−	0.964122i	$-0.585523\pi$
$449$	−11.2499	−0.530916	−0.265458	+	0.964122i	$0.585523\pi$
$450$	0	0
$451$	−5.51249	−0.259573
$452$	−3.26857	−0.153741
$453$	−12.5594	−0.590093
$454$	19.0651	0.894770
$455$	0	0
$456$	0	0
$457$	23.3901	1.09414	0.547072	−	0.837086i	$-0.315742\pi$
$457$	23.3901	1.09414	0.547072	+	0.837086i	$0.315742\pi$
$458$	−27.6641	−1.29266
$459$	−3.08647	−0.144064
$460$	0	0
$461$	−36.6236	−1.70573	−0.852866	−	0.522130i	$-0.825137\pi$
$461$	−36.6236	−1.70573	−0.852866	+	0.522130i	$0.825137\pi$
$462$	3.00000	0.139573
$463$	42.9864	1.99775	0.998873	−	0.0474549i	$-0.0151110\pi$
$463$	42.9864	1.99775	0.998873	+	0.0474549i	$0.0151110\pi$
$464$	24.7401	1.14853
$465$	0	0
$466$	−23.7811	−1.10164
$467$	−25.5963	−1.18445	−0.592227	−	0.805771i	$-0.701751\pi$
$467$	−25.5963	−1.18445	−0.592227	+	0.805771i	$0.701751\pi$
$468$	2.51661	0.116330
$469$	2.66550	0.123081
$470$	0	0
$471$	27.6955	1.27614
$472$	18.5604	0.854310
$473$	8.68779	0.399465
$474$	−45.9522	−2.11066
$475$	0	0
$476$	−0.0300295	−0.00137640
$477$	15.0128	0.687389
$478$	3.16931	0.144961
$479$	38.1762	1.74432	0.872158	−	0.489224i	$-0.162720\pi$
$479$	38.1762	1.74432	0.872158	+	0.489224i	$0.162720\pi$
$480$	0	0
$481$	12.7246	0.580193
$482$	18.5936	0.846914
$483$	−2.69459	−0.122608
$484$	1.11650	0.0507498
$485$	0	0
$486$	−14.5553	−0.660242
$487$	−7.76382	−0.351812	−0.175906	−	0.984407i	$-0.556286\pi$
$487$	−7.76382	−0.351812	−0.175906	+	0.984407i	$0.556286\pi$
$488$	−26.8699	−1.21634
$489$	−24.0574	−1.08791
$490$	0	0
$491$	−36.7229	−1.65728	−0.828640	−	0.559782i	$-0.810885\pi$
$491$	−36.7229	−1.65728	−0.828640	+	0.559782i	$0.810885\pi$
$492$	−1.31727	−0.0593870
$493$	3.21894	0.144974
$494$	0	0
$495$	0	0
$496$	25.5553	1.14747
$497$	3.23173	0.144963
$498$	57.5340	2.57816
$499$	4.92633	0.220533	0.110266	−	0.993902i	$-0.464830\pi$
$499$	4.92633	0.220533	0.110266	+	0.993902i	$0.464830\pi$
$500$	0	0
$501$	−11.6186	−0.519079
$502$	−5.61175	−0.250465
$503$	−32.9495	−1.46915	−0.734574	−	0.678529i	$-0.762618\pi$
$503$	−32.9495	−1.46915	−0.734574	+	0.678529i	$0.762618\pi$
$504$	5.40879	0.240926
$505$	0	0
$506$	−8.08378	−0.359368
$507$	−18.3550	−0.815176
$508$	2.14433	0.0951394
$509$	−36.9350	−1.63712	−0.818558	−	0.574424i	$-0.805226\pi$
$509$	−36.9350	−1.63712	−0.818558	+	0.574424i	$0.805226\pi$
$510$	0	0
$511$	0.482459	0.0213427
$512$	−24.9186	−1.10126
$513$	0	0
$514$	−0.898986	−0.0396526
$515$	0	0
$516$	2.07604	0.0913924
$517$	−16.2344	−0.713989
$518$	2.31315	0.101634
$519$	58.0019	2.54600
$520$	0	0
$521$	9.29179	0.407081	0.203540	−	0.979067i	$-0.434755\pi$
$521$	9.29179	0.407081	0.203540	+	0.979067i	$0.434755\pi$
$522$	−49.0387	−2.14637
$523$	28.4151	1.24251	0.621253	−	0.783610i	$-0.286624\pi$
$523$	28.4151	1.24251	0.621253	+	0.783610i	$0.286624\pi$
$524$	−0.340986	−0.0148960
$525$	0	0
$526$	−15.3587	−0.669669
$527$	3.32501	0.144840
$528$	23.0574	1.00344
$529$	−15.7392	−0.684312
$530$	0	0
$531$	−33.3610	−1.44775
$532$	0	0
$533$	−6.37227	−0.276014
$534$	−39.9222	−1.72760
$535$	0	0
$536$	22.5918	0.975818
$537$	−33.1489	−1.43048
$538$	26.1242	1.12630
$539$	15.3182	0.659802
$540$	0	0
$541$	14.9855	0.644275	0.322137	−	0.946693i	$-0.395599\pi$
$541$	14.9855	0.644275	0.322137	+	0.946693i	$0.395599\pi$
$542$	−18.0460	−0.775142
$543$	24.5817	1.05490
$544$	−0.487511	−0.0209019
$545$	0	0
$546$	3.46791	0.148413
$547$	3.88713	0.166202	0.0831008	−	0.996541i	$-0.473518\pi$
$547$	3.88713	0.166202	0.0831008	+	0.996541i	$0.473518\pi$
$548$	0.0472658	0.00201909
$549$	48.2968	2.06126
$550$	0	0
$551$	0	0
$552$	−22.8384	−0.972068
$553$	4.11381	0.174937
$554$	−23.9103	−1.01585
$555$	0	0
$556$	−0.787866	−0.0334130
$557$	−13.2044	−0.559488	−0.279744	−	0.960075i	$-0.590250\pi$
$557$	−13.2044	−0.559488	−0.279744	+	0.960075i	$0.590250\pi$
$558$	−50.6546	−2.14438
$559$	10.0428	0.424766
$560$	0	0
$561$	3.00000	0.126660
$562$	24.6272	1.03884
$563$	−10.7128	−0.451489	−0.225745	−	0.974187i	$-0.572481\pi$
$563$	−10.7128	−0.451489	−0.225745	+	0.974187i	$0.572481\pi$
$564$	−3.87939	−0.163352
$565$	0	0
$566$	−10.3577	−0.435368
$567$	−1.08378	−0.0455144
$568$	27.3911	1.14930
$569$	−13.4706	−0.564717	−0.282358	−	0.959309i	$-0.591117\pi$
$569$	−13.4706	−0.564717	−0.282358	+	0.959309i	$0.591117\pi$
$570$	0	0
$571$	12.6655	0.530035	0.265017	−	0.964244i	$-0.414622\pi$
$571$	12.6655	0.530035	0.265017	+	0.964244i	$0.414622\pi$
$572$	−1.05913	−0.0442843
$573$	52.7948	2.20553
$574$	−1.15839	−0.0483501
$575$	0	0
$576$	45.4816	1.89507
$577$	10.5544	0.439384	0.219692	−	0.975569i	$-0.429495\pi$
$577$	10.5544	0.439384	0.219692	+	0.975569i	$0.429495\pi$
$578$	−22.6091	−0.940413
$579$	−0.857097	−0.0356197
$580$	0	0
$581$	−5.15064	−0.213685
$582$	−36.6732	−1.52015
$583$	−6.31820	−0.261673
$584$	4.08915	0.169210
$585$	0	0
$586$	14.1506	0.584558
$587$	19.1548	0.790602	0.395301	−	0.918552i	$-0.370640\pi$
$587$	19.1548	0.790602	0.395301	+	0.918552i	$0.370640\pi$
$588$	3.66044	0.150954
$589$	0	0
$590$	0	0
$591$	−37.8384	−1.55647
$592$	17.7784	0.730687
$593$	8.69459	0.357044	0.178522	−	0.983936i	$-0.442868\pi$
$593$	8.69459	0.357044	0.178522	+	0.983936i	$0.442868\pi$
$594$	−19.7888	−0.811944
$595$	0	0
$596$	−3.06006	−0.125345
$597$	−0.739170	−0.0302522
$598$	−9.34461	−0.382129
$599$	19.8316	0.810298	0.405149	−	0.914251i	$-0.367220\pi$
$599$	19.8316	0.810298	0.405149	+	0.914251i	$0.367220\pi$
$600$	0	0
$601$	−33.7615	−1.37716	−0.688579	−	0.725161i	$-0.741765\pi$
$601$	−33.7615	−1.37716	−0.688579	+	0.725161i	$0.741765\pi$
$602$	1.82564	0.0744074
$603$	−40.6073	−1.65366
$604$	0.806036	0.0327971
$605$	0	0
$606$	−35.8803	−1.45754
$607$	−35.2850	−1.43217	−0.716087	−	0.698011i	$-0.754068\pi$
$607$	−35.2850	−1.43217	−0.716087	+	0.698011i	$0.754068\pi$
$608$	0	0
$609$	6.87939	0.278767
$610$	0	0
$611$	−18.7665	−0.759212
$612$	0.457482	0.0184926
$613$	−18.4534	−0.745324	−0.372662	−	0.927967i	$-0.621555\pi$
$613$	−18.4534	−0.745324	−0.372662	+	0.927967i	$0.621555\pi$
$614$	15.7573	0.635914
$615$	0	0
$616$	−2.27631	−0.0917152
$617$	35.6854	1.43664	0.718320	−	0.695712i	$-0.244911\pi$
$617$	35.6854	1.43664	0.718320	+	0.695712i	$0.244911\pi$
$618$	21.3746	0.859814
$619$	3.65951	0.147088	0.0735441	−	0.997292i	$-0.476569\pi$
$619$	3.65951	0.147088	0.0735441	+	0.997292i	$0.476569\pi$
$620$	0	0
$621$	17.7743	0.713256
$622$	21.5107	0.862502
$623$	3.57398	0.143188
$624$	26.6536	1.06700
$625$	0	0
$626$	35.8767	1.43392
$627$	0	0
$628$	−1.77744	−0.0709275
$629$	2.31315	0.0922313
$630$	0	0
$631$	−0.793852	−0.0316028	−0.0158014	−	0.999875i	$-0.505030\pi$
$631$	−0.793852	−0.0316028	−0.0158014	+	0.999875i	$0.505030\pi$
$632$	34.8672	1.38694
$633$	7.04963	0.280198
$634$	−39.7885	−1.58020
$635$	0	0
$636$	−1.50980	−0.0598675
$637$	17.7074	0.701592
$638$	20.6382	0.817072
$639$	−49.2336	−1.94765
$640$	0	0
$641$	29.3824	1.16053	0.580267	−	0.814426i	$-0.302948\pi$
$641$	29.3824	1.16053	0.580267	+	0.814426i	$0.302948\pi$
$642$	−39.7033	−1.56696
$643$	−22.2139	−0.876030	−0.438015	−	0.898968i	$-0.644318\pi$
$643$	−22.2139	−0.876030	−0.438015	+	0.898968i	$0.644318\pi$
$644$	0.172933	0.00681451
$645$	0	0
$646$	0	0
$647$	−11.2591	−0.442640	−0.221320	−	0.975201i	$-0.571037\pi$
$647$	−11.2591	−0.442640	−0.221320	+	0.975201i	$0.571037\pi$
$648$	−9.18573	−0.360849
$649$	14.0401	0.551123
$650$	0	0
$651$	7.10607	0.278509
$652$	1.54395	0.0604657
$653$	−27.0000	−1.05659	−0.528296	−	0.849060i	$-0.677169\pi$
$653$	−27.0000	−1.05659	−0.528296	+	0.849060i	$0.677169\pi$
$654$	−7.07192	−0.276534
$655$	0	0
$656$	−8.90310	−0.347608
$657$	−7.34998	−0.286750
$658$	−3.41147	−0.132993
$659$	28.0259	1.09173	0.545867	−	0.837872i	$-0.316200\pi$
$659$	28.0259	1.09173	0.545867	+	0.837872i	$0.316200\pi$
$660$	0	0
$661$	11.3678	0.442157	0.221079	−	0.975256i	$-0.429042\pi$
$661$	11.3678	0.442157	0.221079	+	0.975256i	$0.429042\pi$
$662$	37.2736	1.44868
$663$	3.46791	0.134683
$664$	−43.6551	−1.69415
$665$	0	0
$666$	−35.2395	−1.36550
$667$	−18.5371	−0.717761
$668$	0.745653	0.0288502
$669$	24.5030	0.947340
$670$	0	0
$671$	−20.3259	−0.784674
$672$	−1.04189	−0.0401917
$673$	16.5672	0.638618	0.319309	−	0.947651i	$-0.396549\pi$
$673$	16.5672	0.638618	0.319309	+	0.947651i	$0.396549\pi$
$674$	−24.0624	−0.926850
$675$	0	0
$676$	1.17799	0.0453071
$677$	9.04963	0.347806	0.173903	−	0.984763i	$-0.444362\pi$
$677$	9.04963	0.347806	0.173903	+	0.984763i	$0.444362\pi$
$678$	68.6177	2.63525
$679$	3.28312	0.125995
$680$	0	0
$681$	40.7452	1.56136
$682$	21.3182	0.816316
$683$	−8.73143	−0.334099	−0.167049	−	0.985949i	$-0.553424\pi$
$683$	−8.73143	−0.334099	−0.167049	+	0.985949i	$0.553424\pi$
$684$	0	0
$685$	0	0
$686$	6.49432	0.247954
$687$	−59.1225	−2.25566
$688$	14.0315	0.534944
$689$	−7.30365	−0.278247
$690$	0	0
$691$	34.7202	1.32082	0.660409	−	0.750906i	$-0.270383\pi$
$691$	34.7202	1.32082	0.660409	+	0.750906i	$0.270383\pi$
$692$	−3.72243	−0.141506
$693$	4.09152	0.155424
$694$	7.81521	0.296661
$695$	0	0
$696$	58.3073	2.21013
$697$	−1.15839	−0.0438770
$698$	7.23804	0.273964
$699$	−50.8239	−1.92234
$700$	0	0
$701$	39.4151	1.48869	0.744344	−	0.667797i	$-0.232762\pi$
$701$	39.4151	1.48869	0.744344	+	0.667797i	$0.232762\pi$
$702$	−22.8753	−0.863371
$703$	0	0
$704$	−19.1411	−0.721409
$705$	0	0
$706$	33.9982	1.27954
$707$	3.21213	0.120805
$708$	3.35504	0.126090
$709$	−41.1215	−1.54435	−0.772176	−	0.635409i	$-0.780832\pi$
$709$	−41.1215	−1.54435	−0.772176	+	0.635409i	$0.780832\pi$
$710$	0	0
$711$	−62.6715	−2.35036
$712$	30.2918	1.13523
$713$	−19.1480	−0.717097
$714$	0.630415	0.0235927
$715$	0	0
$716$	2.12742	0.0795055
$717$	6.77332	0.252954
$718$	9.00917	0.336219
$719$	−42.3955	−1.58109	−0.790543	−	0.612407i	$-0.790201\pi$
$719$	−42.3955	−1.58109	−0.790543	+	0.612407i	$0.790201\pi$
$720$	0	0
$721$	−1.91353	−0.0712637
$722$	0	0
$723$	39.7374	1.47785
$724$	−1.57760	−0.0586310
$725$	0	0
$726$	−23.4388	−0.869896
$727$	−51.6563	−1.91583	−0.957914	−	0.287057i	$-0.907323\pi$
$727$	−51.6563	−1.91583	−0.957914	+	0.287057i	$0.907323\pi$
$728$	−2.63135	−0.0975243
$729$	−40.4688	−1.49885
$730$	0	0
$731$	1.82564	0.0675236
$732$	−4.85710	−0.179523
$733$	22.9162	0.846430	0.423215	−	0.906029i	$-0.360902\pi$
$733$	22.9162	0.846430	0.423215	+	0.906029i	$0.360902\pi$
$734$	−10.9385	−0.403748
$735$	0	0
$736$	2.80747	0.103485
$737$	17.0898	0.629510
$738$	17.6473	0.649607
$739$	28.1266	1.03465	0.517327	−	0.855788i	$-0.326927\pi$
$739$	28.1266	1.03465	0.517327	+	0.855788i	$0.326927\pi$
$740$	0	0
$741$	0	0
$742$	−1.32770	−0.0487413
$743$	−6.13247	−0.224979	−0.112489	−	0.993653i	$-0.535882\pi$
$743$	−6.13247	−0.224979	−0.112489	+	0.993653i	$0.535882\pi$
$744$	60.2285	2.20809
$745$	0	0
$746$	−47.0173	−1.72143
$747$	78.4671	2.87096
$748$	−0.192533	−0.00703972
$749$	3.55438	0.129874
$750$	0	0
$751$	5.64084	0.205837	0.102919	−	0.994690i	$-0.467182\pi$
$751$	5.64084	0.205837	0.102919	+	0.994690i	$0.467182\pi$
$752$	−26.2199	−0.956140
$753$	−11.9932	−0.437056
$754$	23.8571	0.868824
$755$	0	0
$756$	0.423334	0.0153965
$757$	−15.6919	−0.570332	−0.285166	−	0.958478i	$-0.592049\pi$
$757$	−15.6919	−0.570332	−0.285166	+	0.958478i	$0.592049\pi$
$758$	2.29229	0.0832597
$759$	−17.2763	−0.627090
$760$	0	0
$761$	4.86484	0.176350	0.0881751	−	0.996105i	$-0.471896\pi$
$761$	4.86484	0.176350	0.0881751	+	0.996105i	$0.471896\pi$
$762$	−45.0164	−1.63077
$763$	0.633103	0.0229199
$764$	−3.38825	−0.122583
$765$	0	0
$766$	−3.95668	−0.142961
$767$	16.2300	0.586031
$768$	−12.6578	−0.456747
$769$	22.5321	0.812528	0.406264	−	0.913756i	$-0.366831\pi$
$769$	22.5321	0.812528	0.406264	+	0.913756i	$0.366831\pi$
$770$	0	0
$771$	−1.92127	−0.0691930
$772$	0.0550065	0.00197973
$773$	26.4320	0.950693	0.475347	−	0.879799i	$-0.342323\pi$
$773$	26.4320	0.950693	0.475347	+	0.879799i	$0.342323\pi$
$774$	−27.8125	−0.999700
$775$	0	0
$776$	27.8266	0.998916
$777$	4.94356	0.177349
$778$	−33.0993	−1.18667
$779$	0	0
$780$	0	0
$781$	20.7202	0.741426
$782$	−1.69871	−0.0607458
$783$	−45.3783	−1.62169
$784$	24.7401	0.883575
$785$	0	0
$786$	7.15839	0.255331
$787$	15.5577	0.554571	0.277286	−	0.960788i	$-0.410565\pi$
$787$	15.5577	0.554571	0.277286	+	0.960788i	$0.410565\pi$
$788$	2.42839	0.0865077
$789$	−32.8239	−1.16856
$790$	0	0
$791$	−6.14290	−0.218417
$792$	34.6783	1.23224
$793$	−23.4962	−0.834374
$794$	42.8922	1.52219
$795$	0	0
$796$	0.0474383	0.00168141
$797$	−33.4935	−1.18640	−0.593200	−	0.805055i	$-0.702136\pi$
$797$	−33.4935	−1.18640	−0.593200	+	0.805055i	$0.702136\pi$
$798$	0	0
$799$	−3.41147	−0.120689
$800$	0	0
$801$	−54.4475	−1.92381
$802$	−0.116496	−0.00411362
$803$	3.09327	0.109159
$804$	4.08378	0.144024
$805$	0	0
$806$	24.6432	0.868020
$807$	55.8316	1.96537
$808$	27.2249	0.957770
$809$	41.1162	1.44557	0.722784	−	0.691074i	$-0.242862\pi$
$809$	41.1162	1.44557	0.722784	+	0.691074i	$0.242862\pi$
$810$	0	0
$811$	16.6878	0.585987	0.292994	−	0.956114i	$-0.405349\pi$
$811$	16.6878	0.585987	0.292994	+	0.956114i	$0.405349\pi$
$812$	−0.441504	−0.0154937
$813$	−38.5672	−1.35261
$814$	14.8307	0.519815
$815$	0	0
$816$	4.84524	0.169617
$817$	0	0
$818$	26.9540	0.942424
$819$	4.72967	0.165268
$820$	0	0
$821$	−31.3901	−1.09552	−0.547761	−	0.836635i	$-0.684520\pi$
$821$	−31.3901	−1.09552	−0.547761	+	0.836635i	$0.684520\pi$
$822$	−0.992259	−0.0346090
$823$	−46.3259	−1.61482	−0.807410	−	0.589990i	$-0.799132\pi$
$823$	−46.3259	−1.61482	−0.807410	+	0.589990i	$0.799132\pi$
$824$	−16.2184	−0.564996
$825$	0	0
$826$	2.95037	0.102657
$827$	−40.7588	−1.41732	−0.708661	−	0.705549i	$-0.750700\pi$
$827$	−40.7588	−1.41732	−0.708661	+	0.705549i	$0.750700\pi$
$828$	−2.63453	−0.0915564
$829$	−35.4834	−1.23239	−0.616195	−	0.787594i	$-0.711327\pi$
$829$	−35.4834	−1.23239	−0.616195	+	0.787594i	$0.711327\pi$
$830$	0	0
$831$	−51.1002	−1.77265
$832$	−22.1266	−0.767102
$833$	3.21894	0.111530
$834$	16.5398	0.572727
$835$	0	0
$836$	0	0
$837$	−46.8735	−1.62019
$838$	34.2344	1.18261
$839$	−38.2026	−1.31890	−0.659451	−	0.751748i	$-0.729211\pi$
$839$	−38.2026	−1.31890	−0.659451	+	0.751748i	$0.729211\pi$
$840$	0	0
$841$	18.3259	0.631929
$842$	5.88713	0.202884
$843$	52.6323	1.81275
$844$	−0.452430	−0.0155733
$845$	0	0
$846$	51.9718	1.78683
$847$	2.09833	0.0720993
$848$	−10.2044	−0.350420
$849$	−22.1361	−0.759709
$850$	0	0
$851$	−13.3209	−0.456634
$852$	4.95130	0.169629
$853$	25.6016	0.876584	0.438292	−	0.898833i	$-0.355584\pi$
$853$	25.6016	0.876584	0.438292	+	0.898833i	$0.355584\pi$
$854$	−4.27126	−0.146159
$855$	0	0
$856$	30.1257	1.02967
$857$	21.0865	0.720300	0.360150	−	0.932894i	$-0.382726\pi$
$857$	21.0865	0.720300	0.360150	+	0.932894i	$0.382726\pi$
$858$	22.2344	0.759071
$859$	−19.5672	−0.667623	−0.333812	−	0.942640i	$-0.608335\pi$
$859$	−19.5672	−0.667623	−0.333812	+	0.942640i	$0.608335\pi$
$860$	0	0
$861$	−2.47565	−0.0843700
$862$	−51.6100	−1.75784
$863$	−4.94894	−0.168464	−0.0842319	−	0.996446i	$-0.526844\pi$
$863$	−4.94894	−0.168464	−0.0842319	+	0.996446i	$0.526844\pi$
$864$	6.87258	0.233810
$865$	0	0
$866$	24.4279	0.830093
$867$	−48.3191	−1.64100
$868$	−0.456052	−0.0154794
$869$	26.3756	0.894730
$870$	0	0
$871$	19.7553	0.669381
$872$	5.36596	0.181714
$873$	−50.0164	−1.69280
$874$	0	0
$875$	0	0
$876$	0.739170	0.0249742
$877$	−1.21987	−0.0411922	−0.0205961	−	0.999788i	$-0.506556\pi$
$877$	−1.21987	−0.0411922	−0.0205961	+	0.999788i	$0.506556\pi$
$878$	−8.20582	−0.276933
$879$	30.2422	1.02004
$880$	0	0
$881$	46.5030	1.56673	0.783363	−	0.621565i	$-0.213503\pi$
$881$	46.5030	1.56673	0.783363	+	0.621565i	$0.213503\pi$
$882$	−49.0387	−1.65122
$883$	−12.9249	−0.434957	−0.217479	−	0.976065i	$-0.569783\pi$
$883$	−12.9249	−0.434957	−0.217479	+	0.976065i	$0.569783\pi$
$884$	−0.222563	−0.00748560
$885$	0	0
$886$	40.2749	1.35306
$887$	23.2243	0.779796	0.389898	−	0.920858i	$-0.372510\pi$
$887$	23.2243	0.779796	0.389898	+	0.920858i	$0.372510\pi$
$888$	41.8999	1.40607
$889$	4.03003	0.135163
$890$	0	0
$891$	−6.94862	−0.232787
$892$	−1.57255	−0.0526528
$893$	0	0
$894$	64.2404	2.14852
$895$	0	0
$896$	−3.29860	−0.110198
$897$	−19.9709	−0.666809
$898$	−15.1570	−0.505794
$899$	48.8854	1.63042
$900$	0	0
$901$	−1.32770	−0.0442320
$902$	−7.42696	−0.247291
$903$	3.90167	0.129840
$904$	−52.0651	−1.73166
$905$	0	0
$906$	−16.9213	−0.562172
$907$	39.9968	1.32807	0.664036	−	0.747700i	$-0.268842\pi$
$907$	39.9968	1.32807	0.664036	+	0.747700i	$0.268842\pi$
$908$	−2.61493	−0.0867796
$909$	−48.9350	−1.62307
$910$	0	0
$911$	−18.7997	−0.622863	−0.311431	−	0.950269i	$-0.600808\pi$
$911$	−18.7997	−0.622863	−0.311431	+	0.950269i	$0.600808\pi$
$912$	0	0
$913$	−33.0232	−1.09291
$914$	31.5134	1.04237
$915$	0	0
$916$	3.79435	0.125369
$917$	−0.640844	−0.0211625
$918$	−4.15839	−0.137247
$919$	39.8316	1.31392	0.656962	−	0.753924i	$-0.271841\pi$
$919$	39.8316	1.31392	0.656962	+	0.753924i	$0.271841\pi$
$920$	0	0
$921$	33.6759	1.10966
$922$	−49.3429	−1.62502
$923$	23.9519	0.788387
$924$	−0.411474	−0.0135365
$925$	0	0
$926$	57.9154	1.90322
$927$	29.1516	0.957463
$928$	−7.16756	−0.235287
$929$	26.9540	0.884332	0.442166	−	0.896933i	$-0.354210\pi$
$929$	26.9540	0.884332	0.442166	+	0.896933i	$0.354210\pi$
$930$	0	0
$931$	0	0
$932$	3.26176	0.106843
$933$	45.9718	1.50505
$934$	−34.4858	−1.12841
$935$	0	0
$936$	40.0871	1.31029
$937$	−2.62361	−0.0857095	−0.0428548	−	0.999081i	$-0.513645\pi$
$937$	−2.62361	−0.0857095	−0.0428548	+	0.999081i	$0.513645\pi$
$938$	3.59121	0.117257
$939$	76.6742	2.50217
$940$	0	0
$941$	−18.6696	−0.608612	−0.304306	−	0.952574i	$-0.598425\pi$
$941$	−18.6696	−0.608612	−0.304306	+	0.952574i	$0.598425\pi$
$942$	37.3141	1.21576
$943$	6.67087	0.217234
$944$	22.6759	0.738039
$945$	0	0
$946$	11.7050	0.380563
$947$	−8.39961	−0.272951	−0.136475	−	0.990643i	$-0.543577\pi$
$947$	−8.39961	−0.272951	−0.136475	+	0.990643i	$0.543577\pi$
$948$	6.30272	0.204703
$949$	3.57573	0.116073
$950$	0	0
$951$	−85.0343	−2.75742
$952$	−0.478340	−0.0155031
$953$	−33.6928	−1.09142	−0.545709	−	0.837975i	$-0.683740\pi$
$953$	−33.6928	−1.09142	−0.545709	+	0.837975i	$0.683740\pi$
$954$	20.2267	0.654863
$955$	0	0
$956$	−0.434696	−0.0140591
$957$	44.1070	1.42578
$958$	51.4347	1.66178
$959$	0.0888306	0.00286849
$960$	0	0
$961$	19.4962	0.628909
$962$	17.1438	0.552739
$963$	−54.1489	−1.74492
$964$	−2.55026	−0.0821383
$965$	0	0
$966$	−3.63041	−0.116807
$967$	−11.7433	−0.377639	−0.188819	−	0.982012i	$-0.560466\pi$
$967$	−11.7433	−0.377639	−0.188819	+	0.982012i	$0.560466\pi$
$968$	17.7847	0.571621
$969$	0	0
$970$	0	0
$971$	12.8093	0.411071	0.205536	−	0.978650i	$-0.434106\pi$
$971$	12.8093	0.411071	0.205536	+	0.978650i	$0.434106\pi$
$972$	1.99638	0.0640339
$973$	−1.48070	−0.0474692
$974$	−10.4602	−0.335165
$975$	0	0
$976$	−32.8280	−1.05080
$977$	−14.5276	−0.464781	−0.232390	−	0.972623i	$-0.574655\pi$
$977$	−14.5276	−0.464781	−0.232390	+	0.972623i	$0.574655\pi$
$978$	−32.4124	−1.03643
$979$	22.9145	0.732350
$980$	0	0
$981$	−9.64496	−0.307940
$982$	−49.4766	−1.57886
$983$	37.0502	1.18172	0.590860	−	0.806774i	$-0.298789\pi$
$983$	37.0502	1.18172	0.590860	+	0.806774i	$0.298789\pi$
$984$	−20.9828	−0.668906
$985$	0	0
$986$	4.33687	0.138114
$987$	−7.29086	−0.232071
$988$	0	0
$989$	−10.5134	−0.334307
$990$	0	0
$991$	3.43140	0.109002	0.0545010	−	0.998514i	$-0.482643\pi$
$991$	3.43140	0.109002	0.0545010	+	0.998514i	$0.482643\pi$
$992$	−7.40373	−0.235069
$993$	79.6596	2.52792
$994$	4.35410	0.138104
$995$	0	0
$996$	−7.89124	−0.250044
$997$	−12.7760	−0.404620	−0.202310	−	0.979322i	$-0.564845\pi$
$997$	−12.7760	−0.404620	−0.202310	+	0.979322i	$0.564845\pi$
$998$	6.63722	0.210098
$999$	−32.6091	−1.03170

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.bd.1.2		3
5.4	even	2		361.2.a.g.1.2		3
15.14	odd	2		3249.2.a.z.1.2		3
19.6	even	9		475.2.l.a.226.1		6
19.16	even	9		475.2.l.a.351.1		6
19.18	odd	2		9025.2.a.x.1.2		3
20.19	odd	2		5776.2.a.br.1.3		3
95.4	even	18		361.2.e.g.54.1		6
95.9	even	18		361.2.e.f.62.1		6
95.14	odd	18		361.2.e.a.234.1		6
95.24	even	18		361.2.e.g.234.1		6
95.29	odd	18		361.2.e.b.62.1		6
95.34	odd	18		361.2.e.a.54.1		6
95.44	even	18		19.2.e.a.17.1	yes	6
95.49	even	6		361.2.c.i.292.2		6
95.54	even	18		19.2.e.a.9.1	✓	6
95.59	odd	18		361.2.e.b.99.1		6
95.63	odd	36		475.2.u.a.74.1		12
95.64	even	6		361.2.c.i.68.2		6
95.69	odd	6		361.2.c.h.68.2		6
95.73	odd	36		475.2.u.a.199.2		12
95.74	even	18		361.2.e.f.99.1		6
95.79	odd	18		361.2.e.h.28.1		6
95.82	odd	36		475.2.u.a.74.2		12
95.84	odd	6		361.2.c.h.292.2		6
95.89	odd	18		361.2.e.h.245.1		6
95.92	odd	36		475.2.u.a.199.1		12
95.94	odd	2		361.2.a.h.1.2		3
285.44	odd	18		171.2.u.c.55.1		6
285.149	odd	18		171.2.u.c.28.1		6
285.284	even	2		3249.2.a.s.1.2		3
380.139	odd	18		304.2.u.b.17.1		6
380.339	odd	18		304.2.u.b.161.1		6
380.379	even	2		5776.2.a.bi.1.1		3
665.44	even	18		931.2.v.b.606.1		6
665.54	odd	18		931.2.x.b.655.1		6
665.139	odd	18		931.2.w.a.834.1		6
665.149	even	18		931.2.x.a.655.1		6
665.234	odd	18		931.2.x.b.226.1		6
665.244	odd	18		931.2.w.a.883.1		6
665.339	odd	18		931.2.v.a.275.1		6
665.424	even	18		931.2.x.a.226.1		6
665.529	even	18		931.2.v.b.275.1		6
665.614	odd	18		931.2.v.a.606.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	95.54	even	18
19.2.e.a.17.1	yes	6	95.44	even	18
171.2.u.c.28.1		6	285.149	odd	18
171.2.u.c.55.1		6	285.44	odd	18
304.2.u.b.17.1		6	380.139	odd	18
304.2.u.b.161.1		6	380.339	odd	18
361.2.a.g.1.2		3	5.4	even	2
361.2.a.h.1.2		3	95.94	odd	2
361.2.c.h.68.2		6	95.69	odd	6
361.2.c.h.292.2		6	95.84	odd	6
361.2.c.i.68.2		6	95.64	even	6
361.2.c.i.292.2		6	95.49	even	6
361.2.e.a.54.1		6	95.34	odd	18
361.2.e.a.234.1		6	95.14	odd	18
361.2.e.b.62.1		6	95.29	odd	18
361.2.e.b.99.1		6	95.59	odd	18
361.2.e.f.62.1		6	95.9	even	18
361.2.e.f.99.1		6	95.74	even	18
361.2.e.g.54.1		6	95.4	even	18
361.2.e.g.234.1		6	95.24	even	18
361.2.e.h.28.1		6	95.79	odd	18
361.2.e.h.245.1		6	95.89	odd	18
475.2.l.a.226.1		6	19.6	even	9
475.2.l.a.351.1		6	19.16	even	9
475.2.u.a.74.1		12	95.63	odd	36
475.2.u.a.74.2		12	95.82	odd	36
475.2.u.a.199.1		12	95.92	odd	36
475.2.u.a.199.2		12	95.73	odd	36
931.2.v.a.275.1		6	665.339	odd	18
931.2.v.a.606.1		6	665.614	odd	18
931.2.v.b.275.1		6	665.529	even	18
931.2.v.b.606.1		6	665.44	even	18
931.2.w.a.834.1		6	665.139	odd	18
931.2.w.a.883.1		6	665.244	odd	18
931.2.x.a.226.1		6	665.424	even	18
931.2.x.a.655.1		6	665.149	even	18
931.2.x.b.226.1		6	665.234	odd	18
931.2.x.b.655.1		6	665.54	odd	18
3249.2.a.s.1.2		3	285.284	even	2
3249.2.a.z.1.2		3	15.14	odd	2
5776.2.a.bi.1.1		3	380.379	even	2
5776.2.a.br.1.3		3	20.19	odd	2
9025.2.a.x.1.2		3	19.18	odd	2
9025.2.a.bd.1.2		3	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q+1.34730 q^{2} +2.87939 q^{3} -0.184793 q^{4} +3.87939 q^{6} -0.347296 q^{7} -2.94356 q^{8} +5.29086 q^{9} +O(q^{10})\)	\(q+1.34730 q^{2} +2.87939 q^{3} -0.184793 q^{4} +3.87939 q^{6} -0.347296 q^{7} -2.94356 q^{8} +5.29086 q^{9} -2.22668 q^{11} -0.532089 q^{12} -2.57398 q^{13} -0.467911 q^{14} -3.59627 q^{16} -0.467911 q^{17} +7.12836 q^{18} -1.00000 q^{21} -3.00000 q^{22} +2.69459 q^{23} -8.47565 q^{24} -3.46791 q^{26} +6.59627 q^{27} +0.0641778 q^{28} -6.87939 q^{29} -7.10607 q^{31} +1.04189 q^{32} -6.41147 q^{33} -0.630415 q^{34} -0.977711 q^{36} -4.94356 q^{37} -7.41147 q^{39} +2.47565 q^{41} -1.34730 q^{42} -3.90167 q^{43} +0.411474 q^{44} +3.63041 q^{46} +7.29086 q^{47} -10.3550 q^{48} -6.87939 q^{49} -1.34730 q^{51} +0.475652 q^{52} +2.83750 q^{53} +8.88713 q^{54} +1.02229 q^{56} -9.26857 q^{58} -6.30541 q^{59} +9.12836 q^{61} -9.57398 q^{62} -1.83750 q^{63} +8.59627 q^{64} -8.63816 q^{66} -7.67499 q^{67} +0.0864665 q^{68} +7.75877 q^{69} -9.30541 q^{71} -15.5740 q^{72} -1.38919 q^{73} -6.66044 q^{74} +0.773318 q^{77} -9.98545 q^{78} -11.8452 q^{79} +3.12061 q^{81} +3.33544 q^{82} +14.8307 q^{83} +0.184793 q^{84} -5.25671 q^{86} -19.8084 q^{87} +6.55438 q^{88} -10.2909 q^{89} +0.893933 q^{91} -0.497941 q^{92} -20.4611 q^{93} +9.82295 q^{94} +3.00000 q^{96} -9.45336 q^{97} -9.26857 q^{98} -11.7811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{6} + 6 q^{8}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 6 * q^6 + 6 * q^8	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{6} + 6 q^{8} + 3 q^{12} - 6 q^{14} + 3 q^{16} - 6 q^{17} + 3 q^{18} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 6 q^{24} - 15 q^{26} + 6 q^{27} - 9 q^{28} - 15 q^{29} - 9 q^{31} - 9 q^{33} - 9 q^{34} - 9 q^{36} - 12 q^{39} - 12 q^{41} - 3 q^{42} - 9 q^{44} + 18 q^{46} + 6 q^{47} - 6 q^{48} - 15 q^{49} - 3 q^{51} - 18 q^{52} + 6 q^{53} - 3 q^{54} - 3 q^{56} - 18 q^{58} - 21 q^{59} + 9 q^{61} - 21 q^{62} - 3 q^{63} + 12 q^{64} - 9 q^{66} - 18 q^{67} - 15 q^{68} + 12 q^{69} - 30 q^{71} - 39 q^{72} + 3 q^{74} + 9 q^{77} - 12 q^{78} - 9 q^{79} + 15 q^{81} - 18 q^{82} - 3 q^{84} + 21 q^{86} - 21 q^{87} + 9 q^{88} - 15 q^{89} + 15 q^{91} + 24 q^{92} - 24 q^{93} + 9 q^{94} + 9 q^{96} - 15 q^{97} - 18 q^{98} - 18 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 6 * q^6 + 6 * q^8 + 3 * q^12 - 6 * q^14 + 3 * q^16 - 6 * q^17 + 3 * q^18 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 6 * q^24 - 15 * q^26 + 6 * q^27 - 9 * q^28 - 15 * q^29 - 9 * q^31 - 9 * q^33 - 9 * q^34 - 9 * q^36 - 12 * q^39 - 12 * q^41 - 3 * q^42 - 9 * q^44 + 18 * q^46 + 6 * q^47 - 6 * q^48 - 15 * q^49 - 3 * q^51 - 18 * q^52 + 6 * q^53 - 3 * q^54 - 3 * q^56 - 18 * q^58 - 21 * q^59 + 9 * q^61 - 21 * q^62 - 3 * q^63 + 12 * q^64 - 9 * q^66 - 18 * q^67 - 15 * q^68 + 12 * q^69 - 30 * q^71 - 39 * q^72 + 3 * q^74 + 9 * q^77 - 12 * q^78 - 9 * q^79 + 15 * q^81 - 18 * q^82 - 3 * q^84 + 21 * q^86 - 21 * q^87 + 9 * q^88 - 15 * q^89 + 15 * q^91 + 24 * q^92 - 24 * q^93 + 9 * q^94 + 9 * q^96 - 15 * q^97 - 18 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

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