LMFDB - Embedded newform 9075.2.a.x.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9075,2,Mod(1,9075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9075, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("9075.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9075 = 3 \cdot 5^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9075.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:	$72.4642398343$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	9075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} +1.61803 q^{6} -3.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} +1.61803 q^{6} -3.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} -0.618034 q^{12} -6.23607 q^{13} +4.85410 q^{14} -4.85410 q^{16} +0.618034 q^{17} -1.61803 q^{18} -0.854102 q^{19} +3.00000 q^{21} +5.47214 q^{23} -2.23607 q^{24} +10.0902 q^{26} -1.00000 q^{27} -1.85410 q^{28} -4.47214 q^{29} -3.85410 q^{31} +3.38197 q^{32} -1.00000 q^{34} +0.618034 q^{36} +4.23607 q^{37} +1.38197 q^{38} +6.23607 q^{39} +5.94427 q^{41} -4.85410 q^{42} -1.76393 q^{43} -8.85410 q^{46} +0.618034 q^{47} +4.85410 q^{48} +2.00000 q^{49} -0.618034 q^{51} -3.85410 q^{52} +7.38197 q^{53} +1.61803 q^{54} -6.70820 q^{56} +0.854102 q^{57} +7.23607 q^{58} -5.32624 q^{59} +1.14590 q^{61} +6.23607 q^{62} -3.00000 q^{63} +4.23607 q^{64} -10.5623 q^{67} +0.381966 q^{68} -5.47214 q^{69} +14.5623 q^{71} +2.23607 q^{72} -1.23607 q^{73} -6.85410 q^{74} -0.527864 q^{76} -10.0902 q^{78} +0.527864 q^{79} +1.00000 q^{81} -9.61803 q^{82} +12.7082 q^{83} +1.85410 q^{84} +2.85410 q^{86} +4.47214 q^{87} +9.47214 q^{89} +18.7082 q^{91} +3.38197 q^{92} +3.85410 q^{93} -1.00000 q^{94} -3.38197 q^{96} -15.0344 q^{97} -3.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} - q^{4} + q^{6} - 6 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 - 2 * q^3 - q^4 + q^6 - 6 * q^7 + 2 * q^9	$ 2 q - q^{2} - 2 q^{3} - q^{4} + q^{6} - 6 q^{7} + 2 q^{9} + q^{12} - 8 q^{13} + 3 q^{14} - 3 q^{16} - q^{17} - q^{18} + 5 q^{19} + 6 q^{21} + 2 q^{23} + 9 q^{26} - 2 q^{27} + 3 q^{28} - q^{31} + 9 q^{32} - 2 q^{34} - q^{36} + 4 q^{37} + 5 q^{38} + 8 q^{39} - 6 q^{41} - 3 q^{42} - 8 q^{43} - 11 q^{46} - q^{47} + 3 q^{48} + 4 q^{49} + q^{51} - q^{52} + 17 q^{53} + q^{54} - 5 q^{57} + 10 q^{58} + 5 q^{59} + 9 q^{61} + 8 q^{62} - 6 q^{63} + 4 q^{64} - q^{67} + 3 q^{68} - 2 q^{69} + 9 q^{71} + 2 q^{73} - 7 q^{74} - 10 q^{76} - 9 q^{78} + 10 q^{79} + 2 q^{81} - 17 q^{82} + 12 q^{83} - 3 q^{84} - q^{86} + 10 q^{89} + 24 q^{91} + 9 q^{92} + q^{93} - 2 q^{94} - 9 q^{96} - q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q - q^2 - 2 * q^3 - q^4 + q^6 - 6 * q^7 + 2 * q^9 + q^12 - 8 * q^13 + 3 * q^14 - 3 * q^16 - q^17 - q^18 + 5 * q^19 + 6 * q^21 + 2 * q^23 + 9 * q^26 - 2 * q^27 + 3 * q^28 - q^31 + 9 * q^32 - 2 * q^34 - q^36 + 4 * q^37 + 5 * q^38 + 8 * q^39 - 6 * q^41 - 3 * q^42 - 8 * q^43 - 11 * q^46 - q^47 + 3 * q^48 + 4 * q^49 + q^51 - q^52 + 17 * q^53 + q^54 - 5 * q^57 + 10 * q^58 + 5 * q^59 + 9 * q^61 + 8 * q^62 - 6 * q^63 + 4 * q^64 - q^67 + 3 * q^68 - 2 * q^69 + 9 * q^71 + 2 * q^73 - 7 * q^74 - 10 * q^76 - 9 * q^78 + 10 * q^79 + 2 * q^81 - 17 * q^82 + 12 * q^83 - 3 * q^84 - q^86 + 10 * q^89 + 24 * q^91 + 9 * q^92 + q^93 - 2 * q^94 - 9 * q^96 - q^97 - 2 * q^98

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 $

$2$	−1.61803	−1.14412	−0.572061	−	0.820211i	$-0.693856\pi$
$2$	−1.61803	−1.14412	−0.572061	+	0.820211i	$0.693856\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.618034	0.309017
$5$	0	0
$5$	0	0
$6$	1.61803	0.660560
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	2.23607	0.790569
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0
$11$	0	0
$12$	−0.618034	−0.178411
$13$	−6.23607	−1.72957	−0.864787	−	0.502139i	$-0.832547\pi$
$13$	−6.23607	−1.72957	−0.864787	+	0.502139i	$0.832547\pi$
$14$	4.85410	1.29731
$15$	0	0
$16$	−4.85410	−1.21353
$17$	0.618034	0.149895	0.0749476	−	0.997187i	$-0.476121\pi$
$17$	0.618034	0.149895	0.0749476	+	0.997187i	$0.476121\pi$
$18$	−1.61803	−0.381374
$19$	−0.854102	−0.195944	−0.0979722	−	0.995189i	$-0.531236\pi$
$19$	−0.854102	−0.195944	−0.0979722	+	0.995189i	$0.531236\pi$
$20$	0	0
$21$	3.00000	0.654654
$22$	0	0
$23$	5.47214	1.14102	0.570510	−	0.821291i	$-0.306746\pi$
$23$	5.47214	1.14102	0.570510	+	0.821291i	$0.306746\pi$
$24$	−2.23607	−0.456435
$25$	0	0
$26$	10.0902	1.97885
$27$	−1.00000	−0.192450
$28$	−1.85410	−0.350392
$29$	−4.47214	−0.830455	−0.415227	−	0.909718i	$-0.636298\pi$
$29$	−4.47214	−0.830455	−0.415227	+	0.909718i	$0.636298\pi$
$30$	0	0
$31$	−3.85410	−0.692217	−0.346109	−	0.938194i	$-0.612497\pi$
$31$	−3.85410	−0.692217	−0.346109	+	0.938194i	$0.612497\pi$
$32$	3.38197	0.597853
$33$	0	0
$34$	−1.00000	−0.171499
$35$	0	0
$36$	0.618034	0.103006
$37$	4.23607	0.696405	0.348203	−	0.937419i	$-0.386792\pi$
$37$	4.23607	0.696405	0.348203	+	0.937419i	$0.386792\pi$
$38$	1.38197	0.224184
$39$	6.23607	0.998570
$40$	0	0
$41$	5.94427	0.928339	0.464170	−	0.885746i	$-0.346353\pi$
$41$	5.94427	0.928339	0.464170	+	0.885746i	$0.346353\pi$
$42$	−4.85410	−0.749004
$43$	−1.76393	−0.268997	−0.134499	−	0.990914i	$-0.542942\pi$
$43$	−1.76393	−0.268997	−0.134499	+	0.990914i	$0.542942\pi$
$44$	0	0
$45$	0	0
$46$	−8.85410	−1.30547
$47$	0.618034	0.0901495	0.0450748	−	0.998984i	$-0.485647\pi$
$47$	0.618034	0.0901495	0.0450748	+	0.998984i	$0.485647\pi$
$48$	4.85410	0.700629
$49$	2.00000	0.285714
$50$	0	0
$51$	−0.618034	−0.0865421
$52$	−3.85410	−0.534468
$53$	7.38197	1.01399	0.506996	−	0.861949i	$-0.330756\pi$
$53$	7.38197	1.01399	0.506996	+	0.861949i	$0.330756\pi$
$54$	1.61803	0.220187
$55$	0	0
$56$	−6.70820	−0.896421
$57$	0.854102	0.113129
$58$	7.23607	0.950142
$59$	−5.32624	−0.693417	−0.346709	−	0.937973i	$-0.612701\pi$
$59$	−5.32624	−0.693417	−0.346709	+	0.937973i	$0.612701\pi$
$60$	0	0
$61$	1.14590	0.146717	0.0733586	−	0.997306i	$-0.476628\pi$
$61$	1.14590	0.146717	0.0733586	+	0.997306i	$0.476628\pi$
$62$	6.23607	0.791981
$63$	−3.00000	−0.377964
$64$	4.23607	0.529508
$65$	0	0
$66$	0	0
$67$	−10.5623	−1.29039	−0.645196	−	0.764017i	$-0.723224\pi$
$67$	−10.5623	−1.29039	−0.645196	+	0.764017i	$0.723224\pi$
$68$	0.381966	0.0463202
$69$	−5.47214	−0.658768
$70$	0	0
$71$	14.5623	1.72823	0.864114	−	0.503296i	$-0.167880\pi$
$71$	14.5623	1.72823	0.864114	+	0.503296i	$0.167880\pi$
$72$	2.23607	0.263523
$73$	−1.23607	−0.144671	−0.0723354	−	0.997380i	$-0.523045\pi$
$73$	−1.23607	−0.144671	−0.0723354	+	0.997380i	$0.523045\pi$
$74$	−6.85410	−0.796773
$75$	0	0
$76$	−0.527864	−0.0605502
$77$	0	0
$78$	−10.0902	−1.14249
$79$	0.527864	0.0593893	0.0296947	−	0.999559i	$-0.490547\pi$
$79$	0.527864	0.0593893	0.0296947	+	0.999559i	$0.490547\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−9.61803	−1.06213
$83$	12.7082	1.39491	0.697453	−	0.716630i	$-0.254316\pi$
$83$	12.7082	1.39491	0.697453	+	0.716630i	$0.254316\pi$
$84$	1.85410	0.202299
$85$	0	0
$86$	2.85410	0.307766
$87$	4.47214	0.479463
$88$	0	0
$89$	9.47214	1.00404	0.502022	−	0.864855i	$-0.332590\pi$
$89$	9.47214	1.00404	0.502022	+	0.864855i	$0.332590\pi$
$90$	0	0
$91$	18.7082	1.96115
$92$	3.38197	0.352594
$93$	3.85410	0.399652
$94$	−1.00000	−0.103142
$95$	0	0
$96$	−3.38197	−0.345170
$97$	−15.0344	−1.52652	−0.763258	−	0.646094i	$-0.776402\pi$
$97$	−15.0344	−1.52652	−0.763258	+	0.646094i	$0.776402\pi$
$98$	−3.23607	−0.326892
$99$	0	0
$100$	0	0
$101$	−3.00000	−0.298511	−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000	−0.298511	−0.149256	+	0.988799i	$0.547688\pi$
$102$	1.00000	0.0990148
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	−13.9443	−1.36735
$105$	0	0
$106$	−11.9443	−1.16013
$107$	−0.236068	−0.0228216	−0.0114108	−	0.999935i	$-0.503632\pi$
$107$	−0.236068	−0.0228216	−0.0114108	+	0.999935i	$0.503632\pi$
$108$	−0.618034	−0.0594703
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	−4.23607	−0.402070
$112$	14.5623	1.37601
$113$	12.7082	1.19549	0.597744	−	0.801687i	$-0.296064\pi$
$113$	12.7082	1.19549	0.597744	+	0.801687i	$0.296064\pi$
$114$	−1.38197	−0.129433
$115$	0	0
$116$	−2.76393	−0.256625
$117$	−6.23607	−0.576525
$118$	8.61803	0.793354
$119$	−1.85410	−0.169965
$120$	0	0
$121$	0	0
$122$	−1.85410	−0.167863
$123$	−5.94427	−0.535977
$124$	−2.38197	−0.213907
$125$	0	0
$126$	4.85410	0.432438
$127$	−9.70820	−0.861464	−0.430732	−	0.902480i	$-0.641745\pi$
$127$	−9.70820	−0.861464	−0.430732	+	0.902480i	$0.641745\pi$
$128$	−13.6180	−1.20368
$129$	1.76393	0.155306
$130$	0	0
$131$	−13.8541	−1.21044	−0.605219	−	0.796059i	$-0.706915\pi$
$131$	−13.8541	−1.21044	−0.605219	+	0.796059i	$0.706915\pi$
$132$	0	0
$133$	2.56231	0.222180
$134$	17.0902	1.47637
$135$	0	0
$136$	1.38197	0.118503
$137$	1.47214	0.125773	0.0628865	−	0.998021i	$-0.479969\pi$
$137$	1.47214	0.125773	0.0628865	+	0.998021i	$0.479969\pi$
$138$	8.85410	0.753711
$139$	5.85410	0.496538	0.248269	−	0.968691i	$-0.420138\pi$
$139$	5.85410	0.496538	0.248269	+	0.968691i	$0.420138\pi$
$140$	0	0
$141$	−0.618034	−0.0520479
$142$	−23.5623	−1.97730
$143$	0	0
$144$	−4.85410	−0.404508
$145$	0	0
$146$	2.00000	0.165521
$147$	−2.00000	−0.164957
$148$	2.61803	0.215201
$149$	15.0000	1.22885	0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000	1.22885	0.614424	+	0.788976i	$0.289388\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	−1.90983	−0.154908
$153$	0.618034	0.0499651
$154$	0	0
$155$	0	0
$156$	3.85410	0.308575
$157$	−9.70820	−0.774799	−0.387400	−	0.921912i	$-0.626627\pi$
$157$	−9.70820	−0.774799	−0.387400	+	0.921912i	$0.626627\pi$
$158$	−0.854102	−0.0679487
$159$	−7.38197	−0.585428
$160$	0	0
$161$	−16.4164	−1.29379
$162$	−1.61803	−0.127125
$163$	15.2705	1.19608	0.598039	−	0.801467i	$-0.295947\pi$
$163$	15.2705	1.19608	0.598039	+	0.801467i	$0.295947\pi$
$164$	3.67376	0.286873
$165$	0	0
$166$	−20.5623	−1.59594
$167$	19.0344	1.47293	0.736465	−	0.676476i	$-0.236494\pi$
$167$	19.0344	1.47293	0.736465	+	0.676476i	$0.236494\pi$
$168$	6.70820	0.517549
$169$	25.8885	1.99143
$170$	0	0
$171$	−0.854102	−0.0653148
$172$	−1.09017	−0.0831247
$173$	−17.6180	−1.33947	−0.669737	−	0.742598i	$-0.733593\pi$
$173$	−17.6180	−1.33947	−0.669737	+	0.742598i	$0.733593\pi$
$174$	−7.23607	−0.548565
$175$	0	0
$176$	0	0
$177$	5.32624	0.400345
$178$	−15.3262	−1.14875
$179$	2.23607	0.167132	0.0835658	−	0.996502i	$-0.473369\pi$
$179$	2.23607	0.167132	0.0835658	+	0.996502i	$0.473369\pi$
$180$	0	0
$181$	−8.52786	−0.633871	−0.316936	−	0.948447i	$-0.602654\pi$
$181$	−8.52786	−0.633871	−0.316936	+	0.948447i	$0.602654\pi$
$182$	−30.2705	−2.24380
$183$	−1.14590	−0.0847072
$184$	12.2361	0.902055
$185$	0	0
$186$	−6.23607	−0.457251
$187$	0	0
$188$	0.381966	0.0278577
$189$	3.00000	0.218218
$190$	0	0
$191$	1.47214	0.106520	0.0532600	−	0.998581i	$-0.483039\pi$
$191$	1.47214	0.106520	0.0532600	+	0.998581i	$0.483039\pi$
$192$	−4.23607	−0.305712
$193$	−1.56231	−0.112457	−0.0562286	−	0.998418i	$-0.517908\pi$
$193$	−1.56231	−0.112457	−0.0562286	+	0.998418i	$0.517908\pi$
$194$	24.3262	1.74652
$195$	0	0
$196$	1.23607	0.0882906
$197$	−26.6180	−1.89646	−0.948228	−	0.317590i	$-0.897127\pi$
$197$	−26.6180	−1.89646	−0.948228	+	0.317590i	$0.897127\pi$
$198$	0	0
$199$	−3.29180	−0.233349	−0.116675	−	0.993170i	$-0.537223\pi$
$199$	−3.29180	−0.233349	−0.116675	+	0.993170i	$0.537223\pi$
$200$	0	0
$201$	10.5623	0.745008
$202$	4.85410	0.341533
$203$	13.4164	0.941647
$204$	−0.381966	−0.0267430
$205$	0	0
$206$	−9.70820	−0.676403
$207$	5.47214	0.380340
$208$	30.2705	2.09888
$209$	0	0
$210$	0	0
$211$	11.2705	0.775894	0.387947	−	0.921682i	$-0.373184\pi$
$211$	11.2705	0.775894	0.387947	+	0.921682i	$0.373184\pi$
$212$	4.56231	0.313340
$213$	−14.5623	−0.997793
$214$	0.381966	0.0261107
$215$	0	0
$216$	−2.23607	−0.152145
$217$	11.5623	0.784900
$218$	0	0
$219$	1.23607	0.0835257
$220$	0	0
$221$	−3.85410	−0.259255
$222$	6.85410	0.460017
$223$	12.7082	0.851004	0.425502	−	0.904957i	$-0.360097\pi$
$223$	12.7082	0.851004	0.425502	+	0.904957i	$0.360097\pi$
$224$	−10.1459	−0.677901
$225$	0	0
$226$	−20.5623	−1.36778
$227$	−10.8885	−0.722698	−0.361349	−	0.932431i	$-0.617684\pi$
$227$	−10.8885	−0.722698	−0.361349	+	0.932431i	$0.617684\pi$
$228$	0.527864	0.0349587
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	0	0
$231$	0	0
$232$	−10.0000	−0.656532
$233$	−8.67376	−0.568237	−0.284119	−	0.958789i	$-0.591701\pi$
$233$	−8.67376	−0.568237	−0.284119	+	0.958789i	$0.591701\pi$
$234$	10.0902	0.659615
$235$	0	0
$236$	−3.29180	−0.214278
$237$	−0.527864	−0.0342885
$238$	3.00000	0.194461
$239$	−17.5623	−1.13601	−0.568006	−	0.823025i	$-0.692285\pi$
$239$	−17.5623	−1.13601	−0.568006	+	0.823025i	$0.692285\pi$
$240$	0	0
$241$	17.1246	1.10309	0.551547	−	0.834144i	$-0.314038\pi$
$241$	17.1246	1.10309	0.551547	+	0.834144i	$0.314038\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	0.708204	0.0453381
$245$	0	0
$246$	9.61803	0.613223
$247$	5.32624	0.338900
$248$	−8.61803	−0.547246
$249$	−12.7082	−0.805350
$250$	0	0
$251$	16.7984	1.06030	0.530152	−	0.847903i	$-0.322135\pi$
$251$	16.7984	1.06030	0.530152	+	0.847903i	$0.322135\pi$
$252$	−1.85410	−0.116797
$253$	0	0
$254$	15.7082	0.985620
$255$	0	0
$256$	13.5623	0.847644
$257$	27.3262	1.70456	0.852282	−	0.523083i	$-0.175218\pi$
$257$	27.3262	1.70456	0.852282	+	0.523083i	$0.175218\pi$
$258$	−2.85410	−0.177689
$259$	−12.7082	−0.789649
$260$	0	0
$261$	−4.47214	−0.276818
$262$	22.4164	1.38489
$263$	0.673762	0.0415459	0.0207730	−	0.999784i	$-0.493387\pi$
$263$	0.673762	0.0415459	0.0207730	+	0.999784i	$0.493387\pi$
$264$	0	0
$265$	0	0
$266$	−4.14590	−0.254201
$267$	−9.47214	−0.579685
$268$	−6.52786	−0.398753
$269$	24.4721	1.49209	0.746046	−	0.665894i	$-0.231950\pi$
$269$	24.4721	1.49209	0.746046	+	0.665894i	$0.231950\pi$
$270$	0	0
$271$	6.27051	0.380906	0.190453	−	0.981696i	$-0.439004\pi$
$271$	6.27051	0.380906	0.190453	+	0.981696i	$0.439004\pi$
$272$	−3.00000	−0.181902
$273$	−18.7082	−1.13227
$274$	−2.38197	−0.143900
$275$	0	0
$276$	−3.38197	−0.203570
$277$	−10.4377	−0.627140	−0.313570	−	0.949565i	$-0.601525\pi$
$277$	−10.4377	−0.627140	−0.313570	+	0.949565i	$0.601525\pi$
$278$	−9.47214	−0.568101
$279$	−3.85410	−0.230739
$280$	0	0
$281$	−5.23607	−0.312358	−0.156179	−	0.987729i	$-0.549918\pi$
$281$	−5.23607	−0.312358	−0.156179	+	0.987729i	$0.549918\pi$
$282$	1.00000	0.0595491
$283$	22.1803	1.31848	0.659242	−	0.751931i	$-0.270877\pi$
$283$	22.1803	1.31848	0.659242	+	0.751931i	$0.270877\pi$
$284$	9.00000	0.534052
$285$	0	0
$286$	0	0
$287$	−17.8328	−1.05264
$288$	3.38197	0.199284
$289$	−16.6180	−0.977531
$290$	0	0
$291$	15.0344	0.881335
$292$	−0.763932	−0.0447057
$293$	−17.9443	−1.04832	−0.524158	−	0.851621i	$-0.675620\pi$
$293$	−17.9443	−1.04832	−0.524158	+	0.851621i	$0.675620\pi$
$294$	3.23607	0.188731
$295$	0	0
$296$	9.47214	0.550557
$297$	0	0
$298$	−24.2705	−1.40595
$299$	−34.1246	−1.97348
$300$	0	0
$301$	5.29180	0.305014
$302$	−3.23607	−0.186215
$303$	3.00000	0.172345
$304$	4.14590	0.237784
$305$	0	0
$306$	−1.00000	−0.0571662
$307$	19.5623	1.11648	0.558240	−	0.829680i	$-0.311477\pi$
$307$	19.5623	1.11648	0.558240	+	0.829680i	$0.311477\pi$
$308$	0	0
$309$	−6.00000	−0.341328
$310$	0	0
$311$	11.4721	0.650525	0.325263	−	0.945624i	$-0.394547\pi$
$311$	11.4721	0.650525	0.325263	+	0.945624i	$0.394547\pi$
$312$	13.9443	0.789439
$313$	27.8328	1.57320	0.786602	−	0.617461i	$-0.211838\pi$
$313$	27.8328	1.57320	0.786602	+	0.617461i	$0.211838\pi$
$314$	15.7082	0.886465
$315$	0	0
$316$	0.326238	0.0183523
$317$	−25.3607	−1.42440	−0.712199	−	0.701978i	$-0.752301\pi$
$317$	−25.3607	−1.42440	−0.712199	+	0.701978i	$0.752301\pi$
$318$	11.9443	0.669802
$319$	0	0
$320$	0	0
$321$	0.236068	0.0131760
$322$	26.5623	1.48026
$323$	−0.527864	−0.0293711
$324$	0.618034	0.0343352
$325$	0	0
$326$	−24.7082	−1.36846
$327$	0	0
$328$	13.2918	0.733917
$329$	−1.85410	−0.102220
$330$	0	0
$331$	−22.5967	−1.24203	−0.621015	−	0.783799i	$-0.713279\pi$
$331$	−22.5967	−1.24203	−0.621015	+	0.783799i	$0.713279\pi$
$332$	7.85410	0.431050
$333$	4.23607	0.232135
$334$	−30.7984	−1.68521
$335$	0	0
$336$	−14.5623	−0.794439
$337$	13.7082	0.746733	0.373367	−	0.927684i	$-0.378203\pi$
$337$	13.7082	0.746733	0.373367	+	0.927684i	$0.378203\pi$
$338$	−41.8885	−2.27844
$339$	−12.7082	−0.690215
$340$	0	0
$341$	0	0
$342$	1.38197	0.0747282
$343$	15.0000	0.809924
$344$	−3.94427	−0.212661
$345$	0	0
$346$	28.5066	1.53252
$347$	3.05573	0.164040	0.0820200	−	0.996631i	$-0.473863\pi$
$347$	3.05573	0.164040	0.0820200	+	0.996631i	$0.473863\pi$
$348$	2.76393	0.148162
$349$	30.1246	1.61253	0.806267	−	0.591552i	$-0.201485\pi$
$349$	30.1246	1.61253	0.806267	+	0.591552i	$0.201485\pi$
$350$	0	0
$351$	6.23607	0.332857
$352$	0	0
$353$	1.52786	0.0813200	0.0406600	−	0.999173i	$-0.487054\pi$
$353$	1.52786	0.0813200	0.0406600	+	0.999173i	$0.487054\pi$
$354$	−8.61803	−0.458043
$355$	0	0
$356$	5.85410	0.310267
$357$	1.85410	0.0981295
$358$	−3.61803	−0.191219
$359$	−17.2361	−0.909685	−0.454842	−	0.890572i	$-0.650304\pi$
$359$	−17.2361	−0.909685	−0.454842	+	0.890572i	$0.650304\pi$
$360$	0	0
$361$	−18.2705	−0.961606
$362$	13.7984	0.725226
$363$	0	0
$364$	11.5623	0.606029
$365$	0	0
$366$	1.85410	0.0969155
$367$	14.5623	0.760146	0.380073	−	0.924956i	$-0.375899\pi$
$367$	14.5623	0.760146	0.380073	+	0.924956i	$0.375899\pi$
$368$	−26.5623	−1.38466
$369$	5.94427	0.309446
$370$	0	0
$371$	−22.1459	−1.14976
$372$	2.38197	0.123499
$373$	−22.4164	−1.16068	−0.580339	−	0.814375i	$-0.697080\pi$
$373$	−22.4164	−1.16068	−0.580339	+	0.814375i	$0.697080\pi$
$374$	0	0
$375$	0	0
$376$	1.38197	0.0712695
$377$	27.8885	1.43633
$378$	−4.85410	−0.249668
$379$	28.4164	1.45965	0.729826	−	0.683633i	$-0.239601\pi$
$379$	28.4164	1.45965	0.729826	+	0.683633i	$0.239601\pi$
$380$	0	0
$381$	9.70820	0.497366
$382$	−2.38197	−0.121872
$383$	8.88854	0.454183	0.227092	−	0.973873i	$-0.427078\pi$
$383$	8.88854	0.454183	0.227092	+	0.973873i	$0.427078\pi$
$384$	13.6180	0.694942
$385$	0	0
$386$	2.52786	0.128665
$387$	−1.76393	−0.0896657
$388$	−9.29180	−0.471719
$389$	−9.27051	−0.470034	−0.235017	−	0.971991i	$-0.575515\pi$
$389$	−9.27051	−0.470034	−0.235017	+	0.971991i	$0.575515\pi$
$390$	0	0
$391$	3.38197	0.171033
$392$	4.47214	0.225877
$393$	13.8541	0.698847
$394$	43.0689	2.16978
$395$	0	0
$396$	0	0
$397$	25.2918	1.26936	0.634679	−	0.772776i	$-0.281132\pi$
$397$	25.2918	1.26936	0.634679	+	0.772776i	$0.281132\pi$
$398$	5.32624	0.266980
$399$	−2.56231	−0.128276
$400$	0	0
$401$	−14.9098	−0.744561	−0.372281	−	0.928120i	$-0.621424\pi$
$401$	−14.9098	−0.744561	−0.372281	+	0.928120i	$0.621424\pi$
$402$	−17.0902	−0.852380
$403$	24.0344	1.19724
$404$	−1.85410	−0.0922450
$405$	0	0
$406$	−21.7082	−1.07736
$407$	0	0
$408$	−1.38197	−0.0684175
$409$	−28.9443	−1.43120	−0.715601	−	0.698509i	$-0.753847\pi$
$409$	−28.9443	−1.43120	−0.715601	+	0.698509i	$0.753847\pi$
$410$	0	0
$411$	−1.47214	−0.0726151
$412$	3.70820	0.182690
$413$	15.9787	0.786261
$414$	−8.85410	−0.435155
$415$	0	0
$416$	−21.0902	−1.03403
$417$	−5.85410	−0.286677
$418$	0	0
$419$	−21.5066	−1.05067	−0.525333	−	0.850897i	$-0.676059\pi$
$419$	−21.5066	−1.05067	−0.525333	+	0.850897i	$0.676059\pi$
$420$	0	0
$421$	−3.72949	−0.181764	−0.0908821	−	0.995862i	$-0.528969\pi$
$421$	−3.72949	−0.181764	−0.0908821	+	0.995862i	$0.528969\pi$
$422$	−18.2361	−0.887718
$423$	0.618034	0.0300498
$424$	16.5066	0.801630
$425$	0	0
$426$	23.5623	1.14160
$427$	−3.43769	−0.166362
$428$	−0.145898	−0.00705225
$429$	0	0
$430$	0	0
$431$	−1.49342	−0.0719356	−0.0359678	−	0.999353i	$-0.511451\pi$
$431$	−1.49342	−0.0719356	−0.0359678	+	0.999353i	$0.511451\pi$
$432$	4.85410	0.233543
$433$	6.00000	0.288342	0.144171	−	0.989553i	$-0.453949\pi$
$433$	6.00000	0.288342	0.144171	+	0.989553i	$0.453949\pi$
$434$	−18.7082	−0.898023
$435$	0	0
$436$	0	0
$437$	−4.67376	−0.223576
$438$	−2.00000	−0.0955637
$439$	16.7082	0.797439	0.398720	−	0.917073i	$-0.369455\pi$
$439$	16.7082	0.797439	0.398720	+	0.917073i	$0.369455\pi$
$440$	0	0
$441$	2.00000	0.0952381
$442$	6.23607	0.296620
$443$	0.875388	0.0415909	0.0207955	−	0.999784i	$-0.493380\pi$
$443$	0.875388	0.0415909	0.0207955	+	0.999784i	$0.493380\pi$
$444$	−2.61803	−0.124246
$445$	0	0
$446$	−20.5623	−0.973653
$447$	−15.0000	−0.709476
$448$	−12.7082	−0.600406
$449$	−15.5279	−0.732805	−0.366403	−	0.930456i	$-0.619411\pi$
$449$	−15.5279	−0.732805	−0.366403	+	0.930456i	$0.619411\pi$
$450$	0	0
$451$	0	0
$452$	7.85410	0.369426
$453$	−2.00000	−0.0939682
$454$	17.6180	0.826855
$455$	0	0
$456$	1.90983	0.0894360
$457$	−32.7984	−1.53424	−0.767122	−	0.641502i	$-0.778312\pi$
$457$	−32.7984	−1.53424	−0.767122	+	0.641502i	$0.778312\pi$
$458$	−16.1803	−0.756058
$459$	−0.618034	−0.0288474
$460$	0	0
$461$	−9.90983	−0.461547	−0.230773	−	0.973008i	$-0.574126\pi$
$461$	−9.90983	−0.461547	−0.230773	+	0.973008i	$0.574126\pi$
$462$	0	0
$463$	−8.79837	−0.408895	−0.204448	−	0.978878i	$-0.565540\pi$
$463$	−8.79837	−0.408895	−0.204448	+	0.978878i	$0.565540\pi$
$464$	21.7082	1.00778
$465$	0	0
$466$	14.0344	0.650133
$467$	14.2361	0.658767	0.329383	−	0.944196i	$-0.393159\pi$
$467$	14.2361	0.658767	0.329383	+	0.944196i	$0.393159\pi$
$468$	−3.85410	−0.178156
$469$	31.6869	1.46317
$470$	0	0
$471$	9.70820	0.447330
$472$	−11.9098	−0.548194
$473$	0	0
$474$	0.854102	0.0392302
$475$	0	0
$476$	−1.14590	−0.0525222
$477$	7.38197	0.337997
$478$	28.4164	1.29974
$479$	−16.9098	−0.772630	−0.386315	−	0.922367i	$-0.626252\pi$
$479$	−16.9098	−0.772630	−0.386315	+	0.922367i	$0.626252\pi$
$480$	0	0
$481$	−26.4164	−1.20448
$482$	−27.7082	−1.26207
$483$	16.4164	0.746972
$484$	0	0
$485$	0	0
$486$	1.61803	0.0733955
$487$	−39.1803	−1.77543	−0.887715	−	0.460393i	$-0.847709\pi$
$487$	−39.1803	−1.77543	−0.887715	+	0.460393i	$0.847709\pi$
$488$	2.56231	0.115990
$489$	−15.2705	−0.690556
$490$	0	0
$491$	−26.2148	−1.18306	−0.591528	−	0.806284i	$-0.701475\pi$
$491$	−26.2148	−1.18306	−0.591528	+	0.806284i	$0.701475\pi$
$492$	−3.67376	−0.165626
$493$	−2.76393	−0.124481
$494$	−8.61803	−0.387744
$495$	0	0
$496$	18.7082	0.840023
$497$	−43.6869	−1.95963
$498$	20.5623	0.921419
$499$	2.56231	0.114705	0.0573523	−	0.998354i	$-0.481734\pi$
$499$	2.56231	0.114705	0.0573523	+	0.998354i	$0.481734\pi$
$500$	0	0
$501$	−19.0344	−0.850396
$502$	−27.1803	−1.21312
$503$	30.0689	1.34071	0.670353	−	0.742043i	$-0.266143\pi$
$503$	30.0689	1.34071	0.670353	+	0.742043i	$0.266143\pi$
$504$	−6.70820	−0.298807
$505$	0	0
$506$	0	0
$507$	−25.8885	−1.14975
$508$	−6.00000	−0.266207
$509$	21.3820	0.947739	0.473869	−	0.880595i	$-0.342857\pi$
$509$	21.3820	0.947739	0.473869	+	0.880595i	$0.342857\pi$
$510$	0	0
$511$	3.70820	0.164041
$512$	5.29180	0.233867
$513$	0.854102	0.0377095
$514$	−44.2148	−1.95023
$515$	0	0
$516$	1.09017	0.0479921
$517$	0	0
$518$	20.5623	0.903456
$519$	17.6180	0.773346
$520$	0	0
$521$	38.8328	1.70130	0.850648	−	0.525735i	$-0.176210\pi$
$521$	38.8328	1.70130	0.850648	+	0.525735i	$0.176210\pi$
$522$	7.23607	0.316714
$523$	−34.9787	−1.52951	−0.764756	−	0.644320i	$-0.777141\pi$
$523$	−34.9787	−1.52951	−0.764756	+	0.644320i	$0.777141\pi$
$524$	−8.56231	−0.374046
$525$	0	0
$526$	−1.09017	−0.0475337
$527$	−2.38197	−0.103760
$528$	0	0
$529$	6.94427	0.301925
$530$	0	0
$531$	−5.32624	−0.231139
$532$	1.58359	0.0686574
$533$	−37.0689	−1.60563
$534$	15.3262	0.663231
$535$	0	0
$536$	−23.6180	−1.02014
$537$	−2.23607	−0.0964935
$538$	−39.5967	−1.70714
$539$	0	0
$540$	0	0
$541$	−0.562306	−0.0241754	−0.0120877	−	0.999927i	$-0.503848\pi$
$541$	−0.562306	−0.0241754	−0.0120877	+	0.999927i	$0.503848\pi$
$542$	−10.1459	−0.435804
$543$	8.52786	0.365966
$544$	2.09017	0.0896153
$545$	0	0
$546$	30.2705	1.29546
$547$	−19.3820	−0.828713	−0.414357	−	0.910115i	$-0.635993\pi$
$547$	−19.3820	−0.828713	−0.414357	+	0.910115i	$0.635993\pi$
$548$	0.909830	0.0388660
$549$	1.14590	0.0489057
$550$	0	0
$551$	3.81966	0.162723
$552$	−12.2361	−0.520802
$553$	−1.58359	−0.0673412
$554$	16.8885	0.717525
$555$	0	0
$556$	3.61803	0.153439
$557$	−26.0902	−1.10548	−0.552738	−	0.833355i	$-0.686417\pi$
$557$	−26.0902	−1.10548	−0.552738	+	0.833355i	$0.686417\pi$
$558$	6.23607	0.263994
$559$	11.0000	0.465250
$560$	0	0
$561$	0	0
$562$	8.47214	0.357375
$563$	−26.8885	−1.13322	−0.566609	−	0.823987i	$-0.691745\pi$
$563$	−26.8885	−1.13322	−0.566609	+	0.823987i	$0.691745\pi$
$564$	−0.381966	−0.0160837
$565$	0	0
$566$	−35.8885	−1.50851
$567$	−3.00000	−0.125988
$568$	32.5623	1.36628
$569$	34.0689	1.42824	0.714121	−	0.700022i	$-0.246827\pi$
$569$	34.0689	1.42824	0.714121	+	0.700022i	$0.246827\pi$
$570$	0	0
$571$	−25.6869	−1.07496	−0.537482	−	0.843275i	$-0.680624\pi$
$571$	−25.6869	−1.07496	−0.537482	+	0.843275i	$0.680624\pi$
$572$	0	0
$573$	−1.47214	−0.0614994
$574$	28.8541	1.20435
$575$	0	0
$576$	4.23607	0.176503
$577$	−15.2361	−0.634286	−0.317143	−	0.948378i	$-0.602723\pi$
$577$	−15.2361	−0.634286	−0.317143	+	0.948378i	$0.602723\pi$
$578$	26.8885	1.11842
$579$	1.56231	0.0649272
$580$	0	0
$581$	−38.1246	−1.58168
$582$	−24.3262	−1.00836
$583$	0	0
$584$	−2.76393	−0.114372
$585$	0	0
$586$	29.0344	1.19940
$587$	−24.3050	−1.00317	−0.501586	−	0.865108i	$-0.667250\pi$
$587$	−24.3050	−1.00317	−0.501586	+	0.865108i	$0.667250\pi$
$588$	−1.23607	−0.0509746
$589$	3.29180	0.135636
$590$	0	0
$591$	26.6180	1.09492
$592$	−20.5623	−0.845106
$593$	29.2148	1.19971	0.599854	−	0.800110i	$-0.295225\pi$
$593$	29.2148	1.19971	0.599854	+	0.800110i	$0.295225\pi$
$594$	0	0
$595$	0	0
$596$	9.27051	0.379735
$597$	3.29180	0.134724
$598$	55.2148	2.25790
$599$	−21.7082	−0.886973	−0.443487	−	0.896281i	$-0.646259\pi$
$599$	−21.7082	−0.886973	−0.443487	+	0.896281i	$0.646259\pi$
$600$	0	0
$601$	−19.8328	−0.808997	−0.404499	−	0.914539i	$-0.632554\pi$
$601$	−19.8328	−0.808997	−0.404499	+	0.914539i	$0.632554\pi$
$602$	−8.56231	−0.348974
$603$	−10.5623	−0.430130
$604$	1.23607	0.0502949
$605$	0	0
$606$	−4.85410	−0.197184
$607$	2.32624	0.0944191	0.0472095	−	0.998885i	$-0.484967\pi$
$607$	2.32624	0.0944191	0.0472095	+	0.998885i	$0.484967\pi$
$608$	−2.88854	−0.117146
$609$	−13.4164	−0.543660
$610$	0	0
$611$	−3.85410	−0.155920
$612$	0.381966	0.0154401
$613$	−3.34752	−0.135205	−0.0676026	−	0.997712i	$-0.521535\pi$
$613$	−3.34752	−0.135205	−0.0676026	+	0.997712i	$0.521535\pi$
$614$	−31.6525	−1.27739
$615$	0	0
$616$	0	0
$617$	−46.4164	−1.86865	−0.934327	−	0.356417i	$-0.883998\pi$
$617$	−46.4164	−1.86865	−0.934327	+	0.356417i	$0.883998\pi$
$618$	9.70820	0.390521
$619$	−31.1803	−1.25324	−0.626622	−	0.779323i	$-0.715563\pi$
$619$	−31.1803	−1.25324	−0.626622	+	0.779323i	$0.715563\pi$
$620$	0	0
$621$	−5.47214	−0.219589
$622$	−18.5623	−0.744281
$623$	−28.4164	−1.13848
$624$	−30.2705	−1.21179
$625$	0	0
$626$	−45.0344	−1.79994
$627$	0	0
$628$	−6.00000	−0.239426
$629$	2.61803	0.104388
$630$	0	0
$631$	12.7295	0.506753	0.253377	−	0.967368i	$-0.418459\pi$
$631$	12.7295	0.506753	0.253377	+	0.967368i	$0.418459\pi$
$632$	1.18034	0.0469514
$633$	−11.2705	−0.447963
$634$	41.0344	1.62969
$635$	0	0
$636$	−4.56231	−0.180907
$637$	−12.4721	−0.494164
$638$	0	0
$639$	14.5623	0.576076
$640$	0	0
$641$	−6.74265	−0.266318	−0.133159	−	0.991095i	$-0.542512\pi$
$641$	−6.74265	−0.266318	−0.133159	+	0.991095i	$0.542512\pi$
$642$	−0.381966	−0.0150750
$643$	18.4377	0.727112	0.363556	−	0.931572i	$-0.381563\pi$
$643$	18.4377	0.727112	0.363556	+	0.931572i	$0.381563\pi$
$644$	−10.1459	−0.399804
$645$	0	0
$646$	0.854102	0.0336042
$647$	−3.20163	−0.125869	−0.0629345	−	0.998018i	$-0.520046\pi$
$647$	−3.20163	−0.125869	−0.0629345	+	0.998018i	$0.520046\pi$
$648$	2.23607	0.0878410
$649$	0	0
$650$	0	0
$651$	−11.5623	−0.453162
$652$	9.43769	0.369609
$653$	−21.9656	−0.859579	−0.429789	−	0.902929i	$-0.641412\pi$
$653$	−21.9656	−0.859579	−0.429789	+	0.902929i	$0.641412\pi$
$654$	0	0
$655$	0	0
$656$	−28.8541	−1.12656
$657$	−1.23607	−0.0482236
$658$	3.00000	0.116952
$659$	20.6525	0.804506	0.402253	−	0.915528i	$-0.368227\pi$
$659$	20.6525	0.804506	0.402253	+	0.915528i	$0.368227\pi$
$660$	0	0
$661$	−21.0902	−0.820313	−0.410156	−	0.912015i	$-0.634526\pi$
$661$	−21.0902	−0.820313	−0.410156	+	0.912015i	$0.634526\pi$
$662$	36.5623	1.42103
$663$	3.85410	0.149681
$664$	28.4164	1.10277
$665$	0	0
$666$	−6.85410	−0.265591
$667$	−24.4721	−0.947565
$668$	11.7639	0.455160
$669$	−12.7082	−0.491328
$670$	0	0
$671$	0	0
$672$	10.1459	0.391387
$673$	14.4164	0.555712	0.277856	−	0.960623i	$-0.410376\pi$
$673$	14.4164	0.555712	0.277856	+	0.960623i	$0.410376\pi$
$674$	−22.1803	−0.854355
$675$	0	0
$676$	16.0000	0.615385
$677$	−22.4721	−0.863674	−0.431837	−	0.901952i	$-0.642134\pi$
$677$	−22.4721	−0.863674	−0.431837	+	0.901952i	$0.642134\pi$
$678$	20.5623	0.789691
$679$	45.1033	1.73091
$680$	0	0
$681$	10.8885	0.417250
$682$	0	0
$683$	38.8885	1.48803	0.744014	−	0.668164i	$-0.232919\pi$
$683$	38.8885	1.48803	0.744014	+	0.668164i	$0.232919\pi$
$684$	−0.527864	−0.0201834
$685$	0	0
$686$	−24.2705	−0.926652
$687$	−10.0000	−0.381524
$688$	8.56231	0.326435
$689$	−46.0344	−1.75377
$690$	0	0
$691$	−39.7082	−1.51057	−0.755286	−	0.655396i	$-0.772502\pi$
$691$	−39.7082	−1.51057	−0.755286	+	0.655396i	$0.772502\pi$
$692$	−10.8885	−0.413920
$693$	0	0
$694$	−4.94427	−0.187682
$695$	0	0
$696$	10.0000	0.379049
$697$	3.67376	0.139154
$698$	−48.7426	−1.84494
$699$	8.67376	0.328072
$700$	0	0
$701$	49.6869	1.87665	0.938324	−	0.345756i	$-0.112377\pi$
$701$	49.6869	1.87665	0.938324	+	0.345756i	$0.112377\pi$
$702$	−10.0902	−0.380829
$703$	−3.61803	−0.136457
$704$	0	0
$705$	0	0
$706$	−2.47214	−0.0930401
$707$	9.00000	0.338480
$708$	3.29180	0.123713
$709$	6.25735	0.235000	0.117500	−	0.993073i	$-0.462512\pi$
$709$	6.25735	0.235000	0.117500	+	0.993073i	$0.462512\pi$
$710$	0	0
$711$	0.527864	0.0197964
$712$	21.1803	0.793767
$713$	−21.0902	−0.789833
$714$	−3.00000	−0.112272
$715$	0	0
$716$	1.38197	0.0516465
$717$	17.5623	0.655876
$718$	27.8885	1.04079
$719$	−28.4164	−1.05975	−0.529877	−	0.848075i	$-0.677762\pi$
$719$	−28.4164	−1.05975	−0.529877	+	0.848075i	$0.677762\pi$
$720$	0	0
$721$	−18.0000	−0.670355
$722$	29.5623	1.10020
$723$	−17.1246	−0.636871
$724$	−5.27051	−0.195877
$725$	0	0
$726$	0	0
$727$	−32.1459	−1.19223	−0.596113	−	0.802901i	$-0.703289\pi$
$727$	−32.1459	−1.19223	−0.596113	+	0.802901i	$0.703289\pi$
$728$	41.8328	1.55043
$729$	1.00000	0.0370370
$730$	0	0
$731$	−1.09017	−0.0403214
$732$	−0.708204	−0.0261760
$733$	24.2918	0.897238	0.448619	−	0.893723i	$-0.351916\pi$
$733$	24.2918	0.897238	0.448619	+	0.893723i	$0.351916\pi$
$734$	−23.5623	−0.869701
$735$	0	0
$736$	18.5066	0.682162
$737$	0	0
$738$	−9.61803	−0.354045
$739$	−25.0000	−0.919640	−0.459820	−	0.888012i	$-0.652086\pi$
$739$	−25.0000	−0.919640	−0.459820	+	0.888012i	$0.652086\pi$
$740$	0	0
$741$	−5.32624	−0.195664
$742$	35.8328	1.31546
$743$	−12.8197	−0.470308	−0.235154	−	0.971958i	$-0.575559\pi$
$743$	−12.8197	−0.470308	−0.235154	+	0.971958i	$0.575559\pi$
$744$	8.61803	0.315952
$745$	0	0
$746$	36.2705	1.32796
$747$	12.7082	0.464969
$748$	0	0
$749$	0.708204	0.0258772
$750$	0	0
$751$	−52.9230	−1.93119	−0.965594	−	0.260056i	$-0.916259\pi$
$751$	−52.9230	−1.93119	−0.965594	+	0.260056i	$0.916259\pi$
$752$	−3.00000	−0.109399
$753$	−16.7984	−0.612167
$754$	−45.1246	−1.64334
$755$	0	0
$756$	1.85410	0.0674330
$757$	15.9443	0.579504	0.289752	−	0.957102i	$-0.406427\pi$
$757$	15.9443	0.579504	0.289752	+	0.957102i	$0.406427\pi$
$758$	−45.9787	−1.67002
$759$	0	0
$760$	0	0
$761$	4.88854	0.177210	0.0886048	−	0.996067i	$-0.471759\pi$
$761$	4.88854	0.177210	0.0886048	+	0.996067i	$0.471759\pi$
$762$	−15.7082	−0.569048
$763$	0	0
$764$	0.909830	0.0329165
$765$	0	0
$766$	−14.3820	−0.519642
$767$	33.2148	1.19932
$768$	−13.5623	−0.489388
$769$	−47.6869	−1.71963	−0.859817	−	0.510602i	$-0.829423\pi$
$769$	−47.6869	−1.71963	−0.859817	+	0.510602i	$0.829423\pi$
$770$	0	0
$771$	−27.3262	−0.984130
$772$	−0.965558	−0.0347512
$773$	−49.2492	−1.77137	−0.885686	−	0.464285i	$-0.846311\pi$
$773$	−49.2492	−1.77137	−0.885686	+	0.464285i	$0.846311\pi$
$774$	2.85410	0.102589
$775$	0	0
$776$	−33.6180	−1.20682
$777$	12.7082	0.455904
$778$	15.0000	0.537776
$779$	−5.07701	−0.181903
$780$	0	0
$781$	0	0
$782$	−5.47214	−0.195683
$783$	4.47214	0.159821
$784$	−9.70820	−0.346722
$785$	0	0
$786$	−22.4164	−0.799567
$787$	23.7082	0.845106	0.422553	−	0.906338i	$-0.361134\pi$
$787$	23.7082	0.845106	0.422553	+	0.906338i	$0.361134\pi$
$788$	−16.4508	−0.586037
$789$	−0.673762	−0.0239866
$790$	0	0
$791$	−38.1246	−1.35556
$792$	0	0
$793$	−7.14590	−0.253758
$794$	−40.9230	−1.45230
$795$	0	0
$796$	−2.03444	−0.0721089
$797$	−15.2361	−0.539689	−0.269845	−	0.962904i	$-0.586972\pi$
$797$	−15.2361	−0.539689	−0.269845	+	0.962904i	$0.586972\pi$
$798$	4.14590	0.146763
$799$	0.381966	0.0135130
$800$	0	0
$801$	9.47214	0.334681
$802$	24.1246	0.851870
$803$	0	0
$804$	6.52786	0.230220
$805$	0	0
$806$	−38.8885	−1.36979
$807$	−24.4721	−0.861460
$808$	−6.70820	−0.235994
$809$	25.3262	0.890423	0.445212	−	0.895425i	$-0.353128\pi$
$809$	25.3262	0.890423	0.445212	+	0.895425i	$0.353128\pi$
$810$	0	0
$811$	45.7426	1.60624	0.803121	−	0.595816i	$-0.203171\pi$
$811$	45.7426	1.60624	0.803121	+	0.595816i	$0.203171\pi$
$812$	8.29180	0.290985
$813$	−6.27051	−0.219916
$814$	0	0
$815$	0	0
$816$	3.00000	0.105021
$817$	1.50658	0.0527085
$818$	46.8328	1.63747
$819$	18.7082	0.653718
$820$	0	0
$821$	13.5836	0.474071	0.237035	−	0.971501i	$-0.423824\pi$
$821$	13.5836	0.474071	0.237035	+	0.971501i	$0.423824\pi$
$822$	2.38197	0.0830806
$823$	26.5279	0.924703	0.462352	−	0.886697i	$-0.347006\pi$
$823$	26.5279	0.924703	0.462352	+	0.886697i	$0.347006\pi$
$824$	13.4164	0.467383
$825$	0	0
$826$	−25.8541	−0.899579
$827$	−12.8754	−0.447721	−0.223861	−	0.974621i	$-0.571866\pi$
$827$	−12.8754	−0.447721	−0.223861	+	0.974621i	$0.571866\pi$
$828$	3.38197	0.117531
$829$	−42.6869	−1.48258	−0.741289	−	0.671186i	$-0.765785\pi$
$829$	−42.6869	−1.48258	−0.741289	+	0.671186i	$0.765785\pi$
$830$	0	0
$831$	10.4377	0.362080
$832$	−26.4164	−0.915824
$833$	1.23607	0.0428272
$834$	9.47214	0.327993
$835$	0	0
$836$	0	0
$837$	3.85410	0.133217
$838$	34.7984	1.20209
$839$	−23.2918	−0.804122	−0.402061	−	0.915613i	$-0.631706\pi$
$839$	−23.2918	−0.804122	−0.402061	+	0.915613i	$0.631706\pi$
$840$	0	0
$841$	−9.00000	−0.310345
$842$	6.03444	0.207961
$843$	5.23607	0.180340
$844$	6.96556	0.239764
$845$	0	0
$846$	−1.00000	−0.0343807
$847$	0	0
$848$	−35.8328	−1.23050
$849$	−22.1803	−0.761227
$850$	0	0
$851$	23.1803	0.794612
$852$	−9.00000	−0.308335
$853$	−7.94427	−0.272007	−0.136003	−	0.990708i	$-0.543426\pi$
$853$	−7.94427	−0.272007	−0.136003	+	0.990708i	$0.543426\pi$
$854$	5.56231	0.190338
$855$	0	0
$856$	−0.527864	−0.0180420
$857$	41.7214	1.42517	0.712587	−	0.701584i	$-0.247523\pi$
$857$	41.7214	1.42517	0.712587	+	0.701584i	$0.247523\pi$
$858$	0	0
$859$	42.8885	1.46334	0.731669	−	0.681660i	$-0.238742\pi$
$859$	42.8885	1.46334	0.731669	+	0.681660i	$0.238742\pi$
$860$	0	0
$861$	17.8328	0.607741
$862$	2.41641	0.0823032
$863$	23.8885	0.813175	0.406588	−	0.913612i	$-0.366719\pi$
$863$	23.8885	0.813175	0.406588	+	0.913612i	$0.366719\pi$
$864$	−3.38197	−0.115057
$865$	0	0
$866$	−9.70820	−0.329898
$867$	16.6180	0.564378
$868$	7.14590	0.242548
$869$	0	0
$870$	0	0
$871$	65.8673	2.23183
$872$	0	0
$873$	−15.0344	−0.508839
$874$	7.56231	0.255799
$875$	0	0
$876$	0.763932	0.0258109
$877$	20.4164	0.689413	0.344707	−	0.938710i	$-0.387978\pi$
$877$	20.4164	0.689413	0.344707	+	0.938710i	$0.387978\pi$
$878$	−27.0344	−0.912368
$879$	17.9443	0.605245
$880$	0	0
$881$	25.0902	0.845309	0.422655	−	0.906291i	$-0.361098\pi$
$881$	25.0902	0.845309	0.422655	+	0.906291i	$0.361098\pi$
$882$	−3.23607	−0.108964
$883$	−37.4164	−1.25916	−0.629581	−	0.776935i	$-0.716774\pi$
$883$	−37.4164	−1.25916	−0.629581	+	0.776935i	$0.716774\pi$
$884$	−2.38197	−0.0801142
$885$	0	0
$886$	−1.41641	−0.0475852
$887$	−3.00000	−0.100730	−0.0503651	−	0.998731i	$-0.516038\pi$
$887$	−3.00000	−0.100730	−0.0503651	+	0.998731i	$0.516038\pi$
$888$	−9.47214	−0.317864
$889$	29.1246	0.976808
$890$	0	0
$891$	0	0
$892$	7.85410	0.262975
$893$	−0.527864	−0.0176643
$894$	24.2705	0.811727
$895$	0	0
$896$	40.8541	1.36484
$897$	34.1246	1.13939
$898$	25.1246	0.838419
$899$	17.2361	0.574855
$900$	0	0
$901$	4.56231	0.151992
$902$	0	0
$903$	−5.29180	−0.176100
$904$	28.4164	0.945116
$905$	0	0
$906$	3.23607	0.107511
$907$	−3.97871	−0.132111	−0.0660555	−	0.997816i	$-0.521041\pi$
$907$	−3.97871	−0.132111	−0.0660555	+	0.997816i	$0.521041\pi$
$908$	−6.72949	−0.223326
$909$	−3.00000	−0.0995037
$910$	0	0
$911$	35.9443	1.19089	0.595443	−	0.803397i	$-0.296976\pi$
$911$	35.9443	1.19089	0.595443	+	0.803397i	$0.296976\pi$
$912$	−4.14590	−0.137284
$913$	0	0
$914$	53.0689	1.75536
$915$	0	0
$916$	6.18034	0.204204
$917$	41.5623	1.37251
$918$	1.00000	0.0330049
$919$	−46.9574	−1.54898	−0.774491	−	0.632585i	$-0.781994\pi$
$919$	−46.9574	−1.54898	−0.774491	+	0.632585i	$0.781994\pi$
$920$	0	0
$921$	−19.5623	−0.644600
$922$	16.0344	0.528066
$923$	−90.8115	−2.98910
$924$	0	0
$925$	0	0
$926$	14.2361	0.467826
$927$	6.00000	0.197066
$928$	−15.1246	−0.496490
$929$	2.88854	0.0947700	0.0473850	−	0.998877i	$-0.484911\pi$
$929$	2.88854	0.0947700	0.0473850	+	0.998877i	$0.484911\pi$
$930$	0	0
$931$	−1.70820	−0.0559841
$932$	−5.36068	−0.175595
$933$	−11.4721	−0.375581
$934$	−23.0344	−0.753710
$935$	0	0
$936$	−13.9443	−0.455783
$937$	−32.5967	−1.06489	−0.532445	−	0.846465i	$-0.678727\pi$
$937$	−32.5967	−1.06489	−0.532445	+	0.846465i	$0.678727\pi$
$938$	−51.2705	−1.67404
$939$	−27.8328	−0.908290
$940$	0	0
$941$	33.6312	1.09635	0.548173	−	0.836365i	$-0.315324\pi$
$941$	33.6312	1.09635	0.548173	+	0.836365i	$0.315324\pi$
$942$	−15.7082	−0.511801
$943$	32.5279	1.05925
$944$	25.8541	0.841479
$945$	0	0
$946$	0	0
$947$	−2.67376	−0.0868856	−0.0434428	−	0.999056i	$-0.513833\pi$
$947$	−2.67376	−0.0868856	−0.0434428	+	0.999056i	$0.513833\pi$
$948$	−0.326238	−0.0105957
$949$	7.70820	0.250219
$950$	0	0
$951$	25.3607	0.822376
$952$	−4.14590	−0.134369
$953$	−60.1803	−1.94943	−0.974716	−	0.223446i	$-0.928269\pi$
$953$	−60.1803	−1.94943	−0.974716	+	0.223446i	$0.928269\pi$
$954$	−11.9443	−0.386710
$955$	0	0
$956$	−10.8541	−0.351047
$957$	0	0
$958$	27.3607	0.883983
$959$	−4.41641	−0.142613
$960$	0	0
$961$	−16.1459	−0.520835
$962$	42.7426	1.37808
$963$	−0.236068	−0.00760718
$964$	10.5836	0.340875
$965$	0	0
$966$	−26.5623	−0.854628
$967$	−25.6869	−0.826036	−0.413018	−	0.910723i	$-0.635525\pi$
$967$	−25.6869	−0.826036	−0.413018	+	0.910723i	$0.635525\pi$
$968$	0	0
$969$	0.527864	0.0169574
$970$	0	0
$971$	−33.7771	−1.08396	−0.541979	−	0.840392i	$-0.682325\pi$
$971$	−33.7771	−1.08396	−0.541979	+	0.840392i	$0.682325\pi$
$972$	−0.618034	−0.0198234
$973$	−17.5623	−0.563022
$974$	63.3951	2.03131
$975$	0	0
$976$	−5.56231	−0.178045
$977$	49.3607	1.57919	0.789594	−	0.613630i	$-0.210291\pi$
$977$	49.3607	1.57919	0.789594	+	0.613630i	$0.210291\pi$
$978$	24.7082	0.790081
$979$	0	0
$980$	0	0
$981$	0	0
$982$	42.4164	1.35356
$983$	−35.3050	−1.12605	−0.563027	−	0.826439i	$-0.690363\pi$
$983$	−35.3050	−1.12605	−0.563027	+	0.826439i	$0.690363\pi$
$984$	−13.2918	−0.423727
$985$	0	0
$986$	4.47214	0.142422
$987$	1.85410	0.0590167
$988$	3.29180	0.104726
$989$	−9.65248	−0.306931
$990$	0	0
$991$	−12.2705	−0.389786	−0.194893	−	0.980825i	$-0.562436\pi$
$991$	−12.2705	−0.389786	−0.194893	+	0.980825i	$0.562436\pi$
$992$	−13.0344	−0.413844
$993$	22.5967	0.717086
$994$	70.6869	2.24205
$995$	0	0
$996$	−7.85410	−0.248867
$997$	−33.9787	−1.07612	−0.538058	−	0.842908i	$-0.680842\pi$
$997$	−33.9787	−1.07612	−0.538058	+	0.842908i	$0.680842\pi$
$998$	−4.14590	−0.131236
$999$	−4.23607	−0.134023

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9075.2.a.x.1.1		2
5.4	even	2		363.2.a.h.1.2		2
11.5	even	5		825.2.n.f.751.1		4
11.9	even	5		825.2.n.f.301.1		4
11.10	odd	2		9075.2.a.bv.1.2		2
15.14	odd	2		1089.2.a.m.1.1		2
20.19	odd	2		5808.2.a.bl.1.2		2
55.4	even	10		363.2.e.h.148.1		4
55.9	even	10		33.2.e.a.4.1	✓	4
55.14	even	10		363.2.e.h.130.1		4
55.19	odd	10		363.2.e.c.130.1		4
55.24	odd	10		363.2.e.j.202.1		4
55.27	odd	20		825.2.bx.b.124.2		8
55.29	odd	10		363.2.e.c.148.1		4
55.38	odd	20		825.2.bx.b.124.1		8
55.39	odd	10		363.2.e.j.124.1		4
55.42	odd	20		825.2.bx.b.499.1		8
55.49	even	10		33.2.e.a.25.1	yes	4
55.53	odd	20		825.2.bx.b.499.2		8
55.54	odd	2		363.2.a.e.1.1		2
165.104	odd	10		99.2.f.b.91.1		4
165.119	odd	10		99.2.f.b.37.1		4
165.164	even	2		1089.2.a.s.1.2		2
220.119	odd	10		528.2.y.f.433.1		4
220.159	odd	10		528.2.y.f.289.1		4
220.219	even	2		5808.2.a.bm.1.2		2
495.49	even	30		891.2.n.d.784.1		8
495.104	odd	30		891.2.n.a.784.1		8
495.119	odd	30		891.2.n.a.433.1		8
495.214	even	30		891.2.n.d.190.1		8
495.229	even	30		891.2.n.d.136.1		8
495.284	odd	30		891.2.n.a.136.1		8
495.394	even	30		891.2.n.d.433.1		8
495.434	odd	30		891.2.n.a.190.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.4.1	✓	4	55.9	even	10
33.2.e.a.25.1	yes	4	55.49	even	10
99.2.f.b.37.1		4	165.119	odd	10
99.2.f.b.91.1		4	165.104	odd	10
363.2.a.e.1.1		2	55.54	odd	2
363.2.a.h.1.2		2	5.4	even	2
363.2.e.c.130.1		4	55.19	odd	10
363.2.e.c.148.1		4	55.29	odd	10
363.2.e.h.130.1		4	55.14	even	10
363.2.e.h.148.1		4	55.4	even	10
363.2.e.j.124.1		4	55.39	odd	10
363.2.e.j.202.1		4	55.24	odd	10
528.2.y.f.289.1		4	220.159	odd	10
528.2.y.f.433.1		4	220.119	odd	10
825.2.n.f.301.1		4	11.9	even	5
825.2.n.f.751.1		4	11.5	even	5
825.2.bx.b.124.1		8	55.38	odd	20
825.2.bx.b.124.2		8	55.27	odd	20
825.2.bx.b.499.1		8	55.42	odd	20
825.2.bx.b.499.2		8	55.53	odd	20
891.2.n.a.136.1		8	495.284	odd	30
891.2.n.a.190.1		8	495.434	odd	30
891.2.n.a.433.1		8	495.119	odd	30
891.2.n.a.784.1		8	495.104	odd	30
891.2.n.d.136.1		8	495.229	even	30
891.2.n.d.190.1		8	495.214	even	30
891.2.n.d.433.1		8	495.394	even	30
891.2.n.d.784.1		8	495.49	even	30
1089.2.a.m.1.1		2	15.14	odd	2
1089.2.a.s.1.2		2	165.164	even	2
5808.2.a.bl.1.2		2	20.19	odd	2
5808.2.a.bm.1.2		2	220.219	even	2
9075.2.a.x.1.1		2	1.1	even	1	trivial
9075.2.a.bv.1.2		2	11.10	odd	2

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:	\( N \)	\(=\)	\( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9075.a (trivial)

\(f(q)\)	\(=\)	\(q-1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} +1.61803 q^{6} -3.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} +1.61803 q^{6} -3.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} -0.618034 q^{12} -6.23607 q^{13} +4.85410 q^{14} -4.85410 q^{16} +0.618034 q^{17} -1.61803 q^{18} -0.854102 q^{19} +3.00000 q^{21} +5.47214 q^{23} -2.23607 q^{24} +10.0902 q^{26} -1.00000 q^{27} -1.85410 q^{28} -4.47214 q^{29} -3.85410 q^{31} +3.38197 q^{32} -1.00000 q^{34} +0.618034 q^{36} +4.23607 q^{37} +1.38197 q^{38} +6.23607 q^{39} +5.94427 q^{41} -4.85410 q^{42} -1.76393 q^{43} -8.85410 q^{46} +0.618034 q^{47} +4.85410 q^{48} +2.00000 q^{49} -0.618034 q^{51} -3.85410 q^{52} +7.38197 q^{53} +1.61803 q^{54} -6.70820 q^{56} +0.854102 q^{57} +7.23607 q^{58} -5.32624 q^{59} +1.14590 q^{61} +6.23607 q^{62} -3.00000 q^{63} +4.23607 q^{64} -10.5623 q^{67} +0.381966 q^{68} -5.47214 q^{69} +14.5623 q^{71} +2.23607 q^{72} -1.23607 q^{73} -6.85410 q^{74} -0.527864 q^{76} -10.0902 q^{78} +0.527864 q^{79} +1.00000 q^{81} -9.61803 q^{82} +12.7082 q^{83} +1.85410 q^{84} +2.85410 q^{86} +4.47214 q^{87} +9.47214 q^{89} +18.7082 q^{91} +3.38197 q^{92} +3.85410 q^{93} -1.00000 q^{94} -3.38197 q^{96} -15.0344 q^{97} -3.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} - q^{4} + q^{6} - 6 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 - 2 * q^3 - q^4 + q^6 - 6 * q^7 + 2 * q^9	\( 2 q - q^{2} - 2 q^{3} - q^{4} + q^{6} - 6 q^{7} + 2 q^{9} + q^{12} - 8 q^{13} + 3 q^{14} - 3 q^{16} - q^{17} - q^{18} + 5 q^{19} + 6 q^{21} + 2 q^{23} + 9 q^{26} - 2 q^{27} + 3 q^{28} - q^{31} + 9 q^{32} - 2 q^{34} - q^{36} + 4 q^{37} + 5 q^{38} + 8 q^{39} - 6 q^{41} - 3 q^{42} - 8 q^{43} - 11 q^{46} - q^{47} + 3 q^{48} + 4 q^{49} + q^{51} - q^{52} + 17 q^{53} + q^{54} - 5 q^{57} + 10 q^{58} + 5 q^{59} + 9 q^{61} + 8 q^{62} - 6 q^{63} + 4 q^{64} - q^{67} + 3 q^{68} - 2 q^{69} + 9 q^{71} + 2 q^{73} - 7 q^{74} - 10 q^{76} - 9 q^{78} + 10 q^{79} + 2 q^{81} - 17 q^{82} + 12 q^{83} - 3 q^{84} - q^{86} + 10 q^{89} + 24 q^{91} + 9 q^{92} + q^{93} - 2 q^{94} - 9 q^{96} - q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 + q^6 - 6 * q^7 + 2 * q^9 + q^12 - 8 * q^13 + 3 * q^14 - 3 * q^16 - q^17 - q^18 + 5 * q^19 + 6 * q^21 + 2 * q^23 + 9 * q^26 - 2 * q^27 + 3 * q^28 - q^31 + 9 * q^32 - 2 * q^34 - q^36 + 4 * q^37 + 5 * q^38 + 8 * q^39 - 6 * q^41 - 3 * q^42 - 8 * q^43 - 11 * q^46 - q^47 + 3 * q^48 + 4 * q^49 + q^51 - q^52 + 17 * q^53 + q^54 - 5 * q^57 + 10 * q^58 + 5 * q^59 + 9 * q^61 + 8 * q^62 - 6 * q^63 + 4 * q^64 - q^67 + 3 * q^68 - 2 * q^69 + 9 * q^71 + 2 * q^73 - 7 * q^74 - 10 * q^76 - 9 * q^78 + 10 * q^79 + 2 * q^81 - 17 * q^82 + 12 * q^83 - 3 * q^84 - q^86 + 10 * q^89 + 24 * q^91 + 9 * q^92 + q^93 - 2 * q^94 - 9 * q^96 - q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more