LMFDB - Embedded newform 8025.2.a.ba.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8025,2,Mod(1,8025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8025, 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("8025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8025 = 3 \cdot 5^{2} \cdot 107 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8025.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:	$64.0799476221$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.13231312.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 9x^{3} + 8x^{2} - 9x + 1 $ x^6 - x^5 - 8x^4 + 9x^3 + 8x^2 - 9x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 321)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.42204$ of defining polynomial
Character	$\chi$	$=$	8025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.11100 q^{2} -1.00000 q^{3} -0.765670 q^{4} -1.11100 q^{6} +0.814220 q^{7} -3.07267 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.11100 q^{2} -1.00000 q^{3} -0.765670 q^{4} -1.11100 q^{6} +0.814220 q^{7} -3.07267 q^{8} +1.00000 q^{9} +1.47853 q^{11} +0.765670 q^{12} -1.41630 q^{13} +0.904602 q^{14} -1.88241 q^{16} -7.97920 q^{17} +1.11100 q^{18} -0.789564 q^{19} -0.814220 q^{21} +1.64265 q^{22} -7.47081 q^{23} +3.07267 q^{24} -1.57352 q^{26} -1.00000 q^{27} -0.623424 q^{28} -6.33103 q^{29} +10.4906 q^{31} +4.05398 q^{32} -1.47853 q^{33} -8.86492 q^{34} -0.765670 q^{36} +1.40473 q^{37} -0.877209 q^{38} +1.41630 q^{39} +10.2259 q^{41} -0.904602 q^{42} +7.23371 q^{43} -1.13207 q^{44} -8.30010 q^{46} -10.4316 q^{47} +1.88241 q^{48} -6.33705 q^{49} +7.97920 q^{51} +1.08442 q^{52} +1.85852 q^{53} -1.11100 q^{54} -2.50183 q^{56} +0.789564 q^{57} -7.03380 q^{58} -6.27365 q^{59} +8.00449 q^{61} +11.6551 q^{62} +0.814220 q^{63} +8.26880 q^{64} -1.64265 q^{66} +7.68475 q^{67} +6.10943 q^{68} +7.47081 q^{69} -11.4845 q^{71} -3.07267 q^{72} +11.0580 q^{73} +1.56066 q^{74} +0.604546 q^{76} +1.20385 q^{77} +1.57352 q^{78} -1.00637 q^{79} +1.00000 q^{81} +11.3610 q^{82} +8.35121 q^{83} +0.623424 q^{84} +8.03668 q^{86} +6.33103 q^{87} -4.54304 q^{88} -7.78967 q^{89} -1.15318 q^{91} +5.72018 q^{92} -10.4906 q^{93} -11.5896 q^{94} -4.05398 q^{96} +6.58550 q^{97} -7.04048 q^{98} +1.47853 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 - 6 * q^8 + 6 * q^9	$ 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} - 6 q^{8} + 6 q^{9} + 6 q^{11} - 7 q^{12} + 8 q^{13} - 2 q^{14} + q^{16} - 4 q^{17} - 3 q^{18} - 4 q^{19} + 22 q^{22} - 14 q^{23} + 6 q^{24} - 7 q^{26} - 6 q^{27} + 16 q^{28} + 10 q^{29} + 12 q^{31} - 5 q^{32} - 6 q^{33} - q^{34} + 7 q^{36} + 12 q^{37} + q^{38} - 8 q^{39} - 6 q^{41} + 2 q^{42} + 12 q^{43} + 4 q^{44} + 18 q^{46} - 16 q^{47} - q^{48} - 12 q^{49} + 4 q^{51} + 25 q^{52} - 12 q^{53} + 3 q^{54} - 32 q^{56} + 4 q^{57} - 12 q^{58} + 8 q^{59} - 24 q^{61} + 8 q^{62} - 12 q^{64} - 22 q^{66} + 4 q^{67} + 15 q^{68} + 14 q^{69} + 36 q^{71} - 6 q^{72} + 26 q^{73} - 39 q^{74} - 17 q^{76} - 14 q^{77} + 7 q^{78} + 8 q^{79} + 6 q^{81} + 38 q^{82} + 8 q^{83} - 16 q^{84} + 16 q^{86} - 10 q^{87} + 8 q^{88} - 8 q^{89} - 18 q^{91} - 2 q^{92} - 12 q^{93} + 24 q^{94} + 5 q^{96} + 24 q^{97} - 43 q^{98} + 6 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 - 6 * q^8 + 6 * q^9 + 6 * q^11 - 7 * q^12 + 8 * q^13 - 2 * q^14 + q^16 - 4 * q^17 - 3 * q^18 - 4 * q^19 + 22 * q^22 - 14 * q^23 + 6 * q^24 - 7 * q^26 - 6 * q^27 + 16 * q^28 + 10 * q^29 + 12 * q^31 - 5 * q^32 - 6 * q^33 - q^34 + 7 * q^36 + 12 * q^37 + q^38 - 8 * q^39 - 6 * q^41 + 2 * q^42 + 12 * q^43 + 4 * q^44 + 18 * q^46 - 16 * q^47 - q^48 - 12 * q^49 + 4 * q^51 + 25 * q^52 - 12 * q^53 + 3 * q^54 - 32 * q^56 + 4 * q^57 - 12 * q^58 + 8 * q^59 - 24 * q^61 + 8 * q^62 - 12 * q^64 - 22 * q^66 + 4 * q^67 + 15 * q^68 + 14 * q^69 + 36 * q^71 - 6 * q^72 + 26 * q^73 - 39 * q^74 - 17 * q^76 - 14 * q^77 + 7 * q^78 + 8 * q^79 + 6 * q^81 + 38 * q^82 + 8 * q^83 - 16 * q^84 + 16 * q^86 - 10 * q^87 + 8 * q^88 - 8 * q^89 - 18 * q^91 - 2 * q^92 - 12 * q^93 + 24 * q^94 + 5 * q^96 + 24 * q^97 - 43 * q^98 + 6 * 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 $

$2$	1.11100	0.785599	0.392799	−	0.919624i	$-0.371507\pi$
$2$	1.11100	0.785599	0.392799	+	0.919624i	$0.371507\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.765670	−0.382835
$5$	0	0
$5$	0	0
$6$	−1.11100	−0.453566
$7$	0.814220	0.307746	0.153873	−	0.988091i	$-0.450825\pi$
$7$	0.814220	0.307746	0.153873	+	0.988091i	$0.450825\pi$
$8$	−3.07267	−1.08635
$9$	1.00000	0.333333
$10$	0	0
$11$	1.47853	0.445794	0.222897	−	0.974842i	$-0.428449\pi$
$11$	1.47853	0.445794	0.222897	+	0.974842i	$0.428449\pi$
$12$	0.765670	0.221030
$13$	−1.41630	−0.392812	−0.196406	−	0.980523i	$-0.562927\pi$
$13$	−1.41630	−0.392812	−0.196406	+	0.980523i	$0.562927\pi$
$14$	0.904602	0.241765
$15$	0	0
$16$	−1.88241	−0.470602
$17$	−7.97920	−1.93524	−0.967620	−	0.252411i	$-0.918777\pi$
$17$	−7.97920	−1.93524	−0.967620	+	0.252411i	$0.918777\pi$
$18$	1.11100	0.261866
$19$	−0.789564	−0.181139	−0.0905693	−	0.995890i	$-0.528869\pi$
$19$	−0.789564	−0.181139	−0.0905693	+	0.995890i	$0.528869\pi$
$20$	0	0
$21$	−0.814220	−0.177677
$22$	1.64265	0.350215
$23$	−7.47081	−1.55777	−0.778886	−	0.627165i	$-0.784215\pi$
$23$	−7.47081	−1.55777	−0.778886	+	0.627165i	$0.784215\pi$
$24$	3.07267	0.627206
$25$	0	0
$26$	−1.57352	−0.308592
$27$	−1.00000	−0.192450
$28$	−0.623424	−0.117816
$29$	−6.33103	−1.17564	−0.587822	−	0.808991i	$-0.700014\pi$
$29$	−6.33103	−1.17564	−0.587822	+	0.808991i	$0.700014\pi$
$30$	0	0
$31$	10.4906	1.88416	0.942082	−	0.335381i	$-0.108865\pi$
$31$	10.4906	1.88416	0.942082	+	0.335381i	$0.108865\pi$
$32$	4.05398	0.716649
$33$	−1.47853	−0.257379
$34$	−8.86492	−1.52032
$35$	0	0
$36$	−0.765670	−0.127612
$37$	1.40473	0.230936	0.115468	−	0.993311i	$-0.463163\pi$
$37$	1.40473	0.230936	0.115468	+	0.993311i	$0.463163\pi$
$38$	−0.877209	−0.142302
$39$	1.41630	0.226790
$40$	0	0
$41$	10.2259	1.59701	0.798506	−	0.601987i	$-0.205624\pi$
$41$	10.2259	1.59701	0.798506	+	0.601987i	$0.205624\pi$
$42$	−0.904602	−0.139583
$43$	7.23371	1.10313	0.551565	−	0.834132i	$-0.314031\pi$
$43$	7.23371	1.10313	0.551565	+	0.834132i	$0.314031\pi$
$44$	−1.13207	−0.170665
$45$	0	0
$46$	−8.30010	−1.22378
$47$	−10.4316	−1.52161	−0.760805	−	0.648981i	$-0.775196\pi$
$47$	−10.4316	−1.52161	−0.760805	+	0.648981i	$0.775196\pi$
$48$	1.88241	0.271702
$49$	−6.33705	−0.905292
$50$	0	0
$51$	7.97920	1.11731
$52$	1.08442	0.150382
$53$	1.85852	0.255287	0.127643	−	0.991820i	$-0.459259\pi$
$53$	1.85852	0.255287	0.127643	+	0.991820i	$0.459259\pi$
$54$	−1.11100	−0.151189
$55$	0	0
$56$	−2.50183	−0.334321
$57$	0.789564	0.104580
$58$	−7.03380	−0.923583
$59$	−6.27365	−0.816760	−0.408380	−	0.912812i	$-0.633906\pi$
$59$	−6.27365	−0.816760	−0.408380	+	0.912812i	$0.633906\pi$
$60$	0	0
$61$	8.00449	1.02487	0.512435	−	0.858726i	$-0.328744\pi$
$61$	8.00449	1.02487	0.512435	+	0.858726i	$0.328744\pi$
$62$	11.6551	1.48020
$63$	0.814220	0.102582
$64$	8.26880	1.03360
$65$	0	0
$66$	−1.64265	−0.202197
$67$	7.68475	0.938841	0.469421	−	0.882975i	$-0.344463\pi$
$67$	7.68475	0.938841	0.469421	+	0.882975i	$0.344463\pi$
$68$	6.10943	0.740878
$69$	7.47081	0.899380
$70$	0	0
$71$	−11.4845	−1.36296	−0.681482	−	0.731835i	$-0.738664\pi$
$71$	−11.4845	−1.36296	−0.681482	+	0.731835i	$0.738664\pi$
$72$	−3.07267	−0.362118
$73$	11.0580	1.29424	0.647122	−	0.762387i	$-0.275973\pi$
$73$	11.0580	1.29424	0.647122	+	0.762387i	$0.275973\pi$
$74$	1.56066	0.181423
$75$	0	0
$76$	0.604546	0.0693462
$77$	1.20385	0.137191
$78$	1.57352	0.178166
$79$	−1.00637	−0.113226	−0.0566129	−	0.998396i	$-0.518030\pi$
$79$	−1.00637	−0.113226	−0.0566129	+	0.998396i	$0.518030\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	11.3610	1.25461
$83$	8.35121	0.916664	0.458332	−	0.888781i	$-0.348447\pi$
$83$	8.35121	0.916664	0.458332	+	0.888781i	$0.348447\pi$
$84$	0.623424	0.0680211
$85$	0	0
$86$	8.03668	0.866617
$87$	6.33103	0.678758
$88$	−4.54304	−0.484289
$89$	−7.78967	−0.825703	−0.412851	−	0.910798i	$-0.635467\pi$
$89$	−7.78967	−0.825703	−0.412851	+	0.910798i	$0.635467\pi$
$90$	0	0
$91$	−1.15318	−0.120886
$92$	5.72018	0.596370
$93$	−10.4906	−1.08782
$94$	−11.5896	−1.19537
$95$	0	0
$96$	−4.05398	−0.413757
$97$	6.58550	0.668656	0.334328	−	0.942457i	$-0.391491\pi$
$97$	6.58550	0.668656	0.334328	+	0.942457i	$0.391491\pi$
$98$	−7.04048	−0.711196
$99$	1.47853	0.148598
$100$	0	0
$101$	−7.95454	−0.791507	−0.395753	−	0.918357i	$-0.629517\pi$
$101$	−7.95454	−0.791507	−0.395753	+	0.918357i	$0.629517\pi$
$102$	8.86492	0.877758
$103$	−11.6094	−1.14391	−0.571956	−	0.820284i	$-0.693815\pi$
$103$	−11.6094	−1.14391	−0.571956	+	0.820284i	$0.693815\pi$
$104$	4.35183	0.426732
$105$	0	0
$106$	2.06482	0.200553
$107$	1.00000	0.0966736
$107$	1.00000	0.0966736
$108$	0.765670	0.0736766
$109$	9.60720	0.920203	0.460101	−	0.887866i	$-0.347813\pi$
$109$	9.60720	0.920203	0.460101	+	0.887866i	$0.347813\pi$
$110$	0	0
$111$	−1.40473	−0.133331
$112$	−1.53270	−0.144826
$113$	−8.36779	−0.787175	−0.393588	−	0.919287i	$-0.628766\pi$
$113$	−8.36779	−0.787175	−0.393588	+	0.919287i	$0.628766\pi$
$114$	0.877209	0.0821582
$115$	0	0
$116$	4.84748	0.450077
$117$	−1.41630	−0.130937
$118$	−6.97005	−0.641646
$119$	−6.49683	−0.595563
$120$	0	0
$121$	−8.81395	−0.801268
$122$	8.89302	0.805136
$123$	−10.2259	−0.922035
$124$	−8.03233	−0.721324
$125$	0	0
$126$	0.904602	0.0805883
$127$	−1.42572	−0.126512	−0.0632561	−	0.997997i	$-0.520149\pi$
$127$	−1.42572	−0.126512	−0.0632561	+	0.997997i	$0.520149\pi$
$128$	1.07872	0.0953464
$129$	−7.23371	−0.636892
$130$	0	0
$131$	3.51655	0.307242	0.153621	−	0.988130i	$-0.450906\pi$
$131$	3.51655	0.307242	0.153621	+	0.988130i	$0.450906\pi$
$132$	1.13207	0.0985337
$133$	−0.642879	−0.0557447
$134$	8.53779	0.737552
$135$	0	0
$136$	24.5175	2.10235
$137$	8.77119	0.749373	0.374687	−	0.927151i	$-0.377750\pi$
$137$	8.77119	0.749373	0.374687	+	0.927151i	$0.377750\pi$
$138$	8.30010	0.706552
$139$	21.9935	1.86546	0.932732	−	0.360570i	$-0.117418\pi$
$139$	21.9935	1.86546	0.932732	+	0.360570i	$0.117418\pi$
$140$	0	0
$141$	10.4316	0.878502
$142$	−12.7594	−1.07074
$143$	−2.09405	−0.175113
$144$	−1.88241	−0.156867
$145$	0	0
$146$	12.2855	1.01676
$147$	6.33705	0.522671
$148$	−1.07556	−0.0884104
$149$	9.15638	0.750120	0.375060	−	0.927001i	$-0.377622\pi$
$149$	9.15638	0.750120	0.375060	+	0.927001i	$0.377622\pi$
$150$	0	0
$151$	−1.38806	−0.112959	−0.0564793	−	0.998404i	$-0.517988\pi$
$151$	−1.38806	−0.112959	−0.0564793	+	0.998404i	$0.517988\pi$
$152$	2.42607	0.196780
$153$	−7.97920	−0.645080
$154$	1.33748	0.107777
$155$	0	0
$156$	−1.08442	−0.0868231
$157$	21.8123	1.74081	0.870404	−	0.492339i	$-0.163858\pi$
$157$	21.8123	1.74081	0.870404	+	0.492339i	$0.163858\pi$
$158$	−1.11808	−0.0889500
$159$	−1.85852	−0.147390
$160$	0	0
$161$	−6.08289	−0.479399
$162$	1.11100	0.0872887
$163$	−11.6805	−0.914885	−0.457442	−	0.889239i	$-0.651234\pi$
$163$	−11.6805	−0.914885	−0.457442	+	0.889239i	$0.651234\pi$
$164$	−7.82964	−0.611392
$165$	0	0
$166$	9.27823	0.720130
$167$	−9.47728	−0.733374	−0.366687	−	0.930344i	$-0.619508\pi$
$167$	−9.47728	−0.733374	−0.366687	+	0.930344i	$0.619508\pi$
$168$	2.50183	0.193020
$169$	−10.9941	−0.845699
$170$	0	0
$171$	−0.789564	−0.0603795
$172$	−5.53863	−0.422317
$173$	3.41990	0.260010	0.130005	−	0.991513i	$-0.458501\pi$
$173$	3.41990	0.260010	0.130005	+	0.991513i	$0.458501\pi$
$174$	7.03380	0.533231
$175$	0	0
$176$	−2.78320	−0.209792
$177$	6.27365	0.471557
$178$	−8.65435	−0.648671
$179$	9.38806	0.701696	0.350848	−	0.936432i	$-0.385893\pi$
$179$	9.38806	0.701696	0.350848	+	0.936432i	$0.385893\pi$
$180$	0	0
$181$	19.6691	1.46199	0.730995	−	0.682383i	$-0.239056\pi$
$181$	19.6691	1.46199	0.730995	+	0.682383i	$0.239056\pi$
$182$	−1.28119	−0.0949681
$183$	−8.00449	−0.591709
$184$	22.9554	1.69229
$185$	0	0
$186$	−11.6551	−0.854592
$187$	−11.7975	−0.862718
$188$	7.98719	0.582525
$189$	−0.814220	−0.0592258
$190$	0	0
$191$	14.4307	1.04417	0.522086	−	0.852893i	$-0.325154\pi$
$191$	14.4307	1.04417	0.522086	+	0.852893i	$0.325154\pi$
$192$	−8.26880	−0.596749
$193$	7.53941	0.542699	0.271349	−	0.962481i	$-0.412530\pi$
$193$	7.53941	0.542699	0.271349	+	0.962481i	$0.412530\pi$
$194$	7.31652	0.525295
$195$	0	0
$196$	4.85209	0.346578
$197$	8.26792	0.589065	0.294532	−	0.955642i	$-0.404836\pi$
$197$	8.26792	0.589065	0.294532	+	0.955642i	$0.404836\pi$
$198$	1.64265	0.116738
$199$	7.92853	0.562039	0.281019	−	0.959702i	$-0.409327\pi$
$199$	7.92853	0.562039	0.281019	+	0.959702i	$0.409327\pi$
$200$	0	0
$201$	−7.68475	−0.542040
$202$	−8.83753	−0.621807
$203$	−5.15485	−0.361800
$204$	−6.10943	−0.427746
$205$	0	0
$206$	−12.8981	−0.898655
$207$	−7.47081	−0.519257
$208$	2.66606	0.184858
$209$	−1.16740	−0.0807504
$210$	0	0
$211$	−4.90371	−0.337585	−0.168793	−	0.985652i	$-0.553987\pi$
$211$	−4.90371	−0.337585	−0.168793	+	0.985652i	$0.553987\pi$
$212$	−1.42301	−0.0977327
$213$	11.4845	0.786908
$214$	1.11100	0.0759467
$215$	0	0
$216$	3.07267	0.209069
$217$	8.54165	0.579845
$218$	10.6736	0.722910
$219$	−11.0580	−0.747232
$220$	0	0
$221$	11.3010	0.760185
$222$	−1.56066	−0.104745
$223$	5.30243	0.355077	0.177538	−	0.984114i	$-0.443187\pi$
$223$	5.30243	0.355077	0.177538	+	0.984114i	$0.443187\pi$
$224$	3.30083	0.220546
$225$	0	0
$226$	−9.29665	−0.618404
$227$	−1.14301	−0.0758641	−0.0379321	−	0.999280i	$-0.512077\pi$
$227$	−1.14301	−0.0758641	−0.0379321	+	0.999280i	$0.512077\pi$
$228$	−0.604546	−0.0400370
$229$	−26.5636	−1.75537	−0.877687	−	0.479233i	$-0.840915\pi$
$229$	−26.5636	−1.75537	−0.877687	+	0.479233i	$0.840915\pi$
$230$	0	0
$231$	−1.20385	−0.0792075
$232$	19.4532	1.27716
$233$	11.3737	0.745117	0.372559	−	0.928009i	$-0.378481\pi$
$233$	11.3737	0.745117	0.372559	+	0.928009i	$0.378481\pi$
$234$	−1.57352	−0.102864
$235$	0	0
$236$	4.80355	0.312684
$237$	1.00637	0.0653709
$238$	−7.21800	−0.467873
$239$	−3.61842	−0.234056	−0.117028	−	0.993129i	$-0.537337\pi$
$239$	−3.61842	−0.234056	−0.117028	+	0.993129i	$0.537337\pi$
$240$	0	0
$241$	−13.8280	−0.890742	−0.445371	−	0.895346i	$-0.646928\pi$
$241$	−13.8280	−0.890742	−0.445371	+	0.895346i	$0.646928\pi$
$242$	−9.79233	−0.629475
$243$	−1.00000	−0.0641500
$244$	−6.12880	−0.392356
$245$	0	0
$246$	−11.3610	−0.724349
$247$	1.11826	0.0711533
$248$	−32.2341	−2.04687
$249$	−8.35121	−0.529236
$250$	0	0
$251$	−22.7156	−1.43380	−0.716898	−	0.697178i	$-0.754439\pi$
$251$	−22.7156	−1.43380	−0.716898	+	0.697178i	$0.754439\pi$
$252$	−0.623424	−0.0392720
$253$	−11.0458	−0.694445
$254$	−1.58398	−0.0993879
$255$	0	0
$256$	−15.3391	−0.958696
$257$	2.76289	0.172344	0.0861722	−	0.996280i	$-0.472536\pi$
$257$	2.76289	0.172344	0.0861722	+	0.996280i	$0.472536\pi$
$258$	−8.03668	−0.500342
$259$	1.14376	0.0710697
$260$	0	0
$261$	−6.33103	−0.391881
$262$	3.90690	0.241369
$263$	17.6436	1.08795	0.543976	−	0.839101i	$-0.316918\pi$
$263$	17.6436	1.08795	0.543976	+	0.839101i	$0.316918\pi$
$264$	4.54304	0.279605
$265$	0	0
$266$	−0.714241	−0.0437930
$267$	7.78967	0.476720
$268$	−5.88398	−0.359421
$269$	19.4817	1.18782	0.593911	−	0.804531i	$-0.297583\pi$
$269$	19.4817	1.18782	0.593911	+	0.804531i	$0.297583\pi$
$270$	0	0
$271$	1.79253	0.108889	0.0544443	−	0.998517i	$-0.482661\pi$
$271$	1.79253	0.108889	0.0544443	+	0.998517i	$0.482661\pi$
$272$	15.0201	0.910729
$273$	1.15318	0.0697937
$274$	9.74483	0.588707
$275$	0	0
$276$	−5.72018	−0.344314
$277$	10.7146	0.643779	0.321890	−	0.946777i	$-0.395682\pi$
$277$	10.7146	0.643779	0.321890	+	0.946777i	$0.395682\pi$
$278$	24.4349	1.46551
$279$	10.4906	0.628055
$280$	0	0
$281$	19.3179	1.15241	0.576205	−	0.817305i	$-0.304533\pi$
$281$	19.3179	1.15241	0.576205	+	0.817305i	$0.304533\pi$
$282$	11.5896	0.690150
$283$	13.9517	0.829341	0.414671	−	0.909972i	$-0.363897\pi$
$283$	13.9517	0.829341	0.414671	+	0.909972i	$0.363897\pi$
$284$	8.79337	0.521790
$285$	0	0
$286$	−2.32649	−0.137568
$287$	8.32610	0.491474
$288$	4.05398	0.238883
$289$	46.6676	2.74516
$290$	0	0
$291$	−6.58550	−0.386049
$292$	−8.46679	−0.495482
$293$	32.7891	1.91556	0.957781	−	0.287500i	$-0.0928241\pi$
$293$	32.7891	1.91556	0.957781	+	0.287500i	$0.0928241\pi$
$294$	7.04048	0.410609
$295$	0	0
$296$	−4.31627	−0.250878
$297$	−1.47853	−0.0857930
$298$	10.1728	0.589293
$299$	10.5809	0.611911
$300$	0	0
$301$	5.88983	0.339484
$302$	−1.54214	−0.0887402
$303$	7.95454	0.456977
$304$	1.48628	0.0852442
$305$	0	0
$306$	−8.86492	−0.506774
$307$	25.6693	1.46503	0.732513	−	0.680753i	$-0.238348\pi$
$307$	25.6693	1.46503	0.732513	+	0.680753i	$0.238348\pi$
$308$	−0.921751	−0.0525216
$309$	11.6094	0.660438
$310$	0	0
$311$	21.2833	1.20687	0.603434	−	0.797413i	$-0.293799\pi$
$311$	21.2833	1.20687	0.603434	+	0.797413i	$0.293799\pi$
$312$	−4.35183	−0.246374
$313$	−12.3159	−0.696136	−0.348068	−	0.937469i	$-0.613162\pi$
$313$	−12.3159	−0.696136	−0.348068	+	0.937469i	$0.613162\pi$
$314$	24.2335	1.36758
$315$	0	0
$316$	0.770549	0.0433468
$317$	−3.54158	−0.198915	−0.0994576	−	0.995042i	$-0.531711\pi$
$317$	−3.54158	−0.198915	−0.0994576	+	0.995042i	$0.531711\pi$
$318$	−2.06482	−0.115789
$319$	−9.36062	−0.524094
$320$	0	0
$321$	−1.00000	−0.0558146
$322$	−6.75811	−0.376615
$323$	6.30009	0.350547
$324$	−0.765670	−0.0425372
$325$	0	0
$326$	−12.9770	−0.718732
$327$	−9.60720	−0.531279
$328$	−31.4207	−1.73492
$329$	−8.49364	−0.468270
$330$	0	0
$331$	5.25634	0.288915	0.144457	−	0.989511i	$-0.453856\pi$
$331$	5.25634	0.288915	0.144457	+	0.989511i	$0.453856\pi$
$332$	−6.39427	−0.350931
$333$	1.40473	0.0769787
$334$	−10.5293	−0.576137
$335$	0	0
$336$	1.53270	0.0836154
$337$	25.8253	1.40679	0.703396	−	0.710798i	$-0.251666\pi$
$337$	25.8253	1.40679	0.703396	+	0.710798i	$0.251666\pi$
$338$	−12.2145	−0.664380
$339$	8.36779	0.454476
$340$	0	0
$341$	15.5107	0.839949
$342$	−0.877209	−0.0474340
$343$	−10.8593	−0.586347
$344$	−22.2268	−1.19839
$345$	0	0
$346$	3.79952	0.204264
$347$	−11.0144	−0.591282	−0.295641	−	0.955299i	$-0.595533\pi$
$347$	−11.0144	−0.591282	−0.295641	+	0.955299i	$0.595533\pi$
$348$	−4.84748	−0.259852
$349$	−31.5624	−1.68950	−0.844750	−	0.535162i	$-0.820251\pi$
$349$	−31.5624	−1.68950	−0.844750	+	0.535162i	$0.820251\pi$
$350$	0	0
$351$	1.41630	0.0755966
$352$	5.99393	0.319477
$353$	−8.69467	−0.462771	−0.231385	−	0.972862i	$-0.574326\pi$
$353$	−8.69467	−0.462771	−0.231385	+	0.972862i	$0.574326\pi$
$354$	6.97005	0.370454
$355$	0	0
$356$	5.96431	0.316108
$357$	6.49683	0.343848
$358$	10.4302	0.551252
$359$	26.3598	1.39122	0.695609	−	0.718420i	$-0.255135\pi$
$359$	26.3598	1.39122	0.695609	+	0.718420i	$0.255135\pi$
$360$	0	0
$361$	−18.3766	−0.967189
$362$	21.8524	1.14854
$363$	8.81395	0.462612
$364$	0.882957	0.0462795
$365$	0	0
$366$	−8.89302	−0.464846
$367$	10.8637	0.567079	0.283539	−	0.958961i	$-0.408491\pi$
$367$	10.8637	0.567079	0.283539	+	0.958961i	$0.408491\pi$
$368$	14.0631	0.733091
$369$	10.2259	0.532337
$370$	0	0
$371$	1.51324	0.0785635
$372$	8.03233	0.416457
$373$	9.77674	0.506220	0.253110	−	0.967437i	$-0.418546\pi$
$373$	9.77674	0.506220	0.253110	+	0.967437i	$0.418546\pi$
$374$	−13.1071	−0.677750
$375$	0	0
$376$	32.0530	1.65301
$377$	8.96666	0.461806
$378$	−0.904602	−0.0465277
$379$	22.3643	1.14878	0.574388	−	0.818583i	$-0.305240\pi$
$379$	22.3643	1.14878	0.574388	+	0.818583i	$0.305240\pi$
$380$	0	0
$381$	1.42572	0.0730419
$382$	16.0326	0.820300
$383$	2.97536	0.152034	0.0760168	−	0.997107i	$-0.475780\pi$
$383$	2.97536	0.152034	0.0760168	+	0.997107i	$0.475780\pi$
$384$	−1.07872	−0.0550483
$385$	0	0
$386$	8.37632	0.426343
$387$	7.23371	0.367710
$388$	−5.04232	−0.255985
$389$	−18.4262	−0.934243	−0.467122	−	0.884193i	$-0.654709\pi$
$389$	−18.4262	−0.934243	−0.467122	+	0.884193i	$0.654709\pi$
$390$	0	0
$391$	59.6111	3.01466
$392$	19.4717	0.983467
$393$	−3.51655	−0.177387
$394$	9.18569	0.462768
$395$	0	0
$396$	−1.13207	−0.0568885
$397$	29.4128	1.47619	0.738093	−	0.674698i	$-0.235726\pi$
$397$	29.4128	1.47619	0.738093	+	0.674698i	$0.235726\pi$
$398$	8.80863	0.441537
$399$	0.642879	0.0321842
$400$	0	0
$401$	14.7737	0.737763	0.368881	−	0.929476i	$-0.379741\pi$
$401$	14.7737	0.737763	0.368881	+	0.929476i	$0.379741\pi$
$402$	−8.53779	−0.425826
$403$	−14.8578	−0.740122
$404$	6.09056	0.303016
$405$	0	0
$406$	−5.72706	−0.284229
$407$	2.07694	0.102950
$408$	−24.5175	−1.21379
$409$	−26.6440	−1.31746	−0.658730	−	0.752380i	$-0.728906\pi$
$409$	−26.6440	−1.31746	−0.658730	+	0.752380i	$0.728906\pi$
$410$	0	0
$411$	−8.77119	−0.432651
$412$	8.88900	0.437929
$413$	−5.10813	−0.251355
$414$	−8.30010	−0.407928
$415$	0	0
$416$	−5.74166	−0.281508
$417$	−21.9935	−1.07703
$418$	−1.29698	−0.0634374
$419$	25.6330	1.25226	0.626128	−	0.779721i	$-0.284639\pi$
$419$	25.6330	1.25226	0.626128	+	0.779721i	$0.284639\pi$
$420$	0	0
$421$	10.9489	0.533617	0.266809	−	0.963750i	$-0.414031\pi$
$421$	10.9489	0.533617	0.266809	+	0.963750i	$0.414031\pi$
$422$	−5.44804	−0.265206
$423$	−10.4316	−0.507203
$424$	−5.71060	−0.277331
$425$	0	0
$426$	12.7594	0.618194
$427$	6.51742	0.315400
$428$	−0.765670	−0.0370101
$429$	2.09405	0.101102
$430$	0	0
$431$	−13.2195	−0.636761	−0.318380	−	0.947963i	$-0.603139\pi$
$431$	−13.2195	−0.636761	−0.318380	+	0.947963i	$0.603139\pi$
$432$	1.88241	0.0905675
$433$	−18.9799	−0.912113	−0.456057	−	0.889951i	$-0.650739\pi$
$433$	−18.9799	−0.912113	−0.456057	+	0.889951i	$0.650739\pi$
$434$	9.48980	0.455525
$435$	0	0
$436$	−7.35595	−0.352286
$437$	5.89869	0.282173
$438$	−12.2855	−0.587024
$439$	−12.2128	−0.582884	−0.291442	−	0.956589i	$-0.594135\pi$
$439$	−12.2128	−0.582884	−0.291442	+	0.956589i	$0.594135\pi$
$440$	0	0
$441$	−6.33705	−0.301764
$442$	12.5554	0.597200
$443$	−3.19168	−0.151642	−0.0758208	−	0.997121i	$-0.524158\pi$
$443$	−3.19168	−0.151642	−0.0758208	+	0.997121i	$0.524158\pi$
$444$	1.07556	0.0510438
$445$	0	0
$446$	5.89102	0.278948
$447$	−9.15638	−0.433082
$448$	6.73263	0.318087
$449$	−20.7466	−0.979091	−0.489546	−	0.871978i	$-0.662837\pi$
$449$	−20.7466	−0.979091	−0.489546	+	0.871978i	$0.662837\pi$
$450$	0	0
$451$	15.1193	0.711938
$452$	6.40696	0.301358
$453$	1.38806	0.0652167
$454$	−1.26989	−0.0595987
$455$	0	0
$456$	−2.42607	−0.113611
$457$	23.5355	1.10094	0.550472	−	0.834854i	$-0.314448\pi$
$457$	23.5355	1.10094	0.550472	+	0.834854i	$0.314448\pi$
$458$	−29.5123	−1.37902
$459$	7.97920	0.372437
$460$	0	0
$461$	8.69970	0.405185	0.202593	−	0.979263i	$-0.435063\pi$
$461$	8.69970	0.405185	0.202593	+	0.979263i	$0.435063\pi$
$462$	−1.33748	−0.0622253
$463$	−7.13960	−0.331805	−0.165903	−	0.986142i	$-0.553054\pi$
$463$	−7.13960	−0.331805	−0.165903	+	0.986142i	$0.553054\pi$
$464$	11.9176	0.553260
$465$	0	0
$466$	12.6363	0.585363
$467$	−13.9286	−0.644537	−0.322268	−	0.946648i	$-0.604445\pi$
$467$	−13.9286	−0.644537	−0.322268	+	0.946648i	$0.604445\pi$
$468$	1.08442	0.0501273
$469$	6.25708	0.288925
$470$	0	0
$471$	−21.8123	−1.00506
$472$	19.2769	0.887290
$473$	10.6953	0.491768
$474$	1.11808	0.0513553
$475$	0	0
$476$	4.97442	0.228002
$477$	1.85852	0.0850956
$478$	−4.02007	−0.183874
$479$	3.09915	0.141604	0.0708019	−	0.997490i	$-0.477444\pi$
$479$	3.09915	0.141604	0.0708019	+	0.997490i	$0.477444\pi$
$480$	0	0
$481$	−1.98952	−0.0907144
$482$	−15.3630	−0.699766
$483$	6.08289	0.276781
$484$	6.74857	0.306753
$485$	0	0
$486$	−1.11100	−0.0503962
$487$	24.9469	1.13045	0.565227	−	0.824936i	$-0.308789\pi$
$487$	24.9469	1.13045	0.565227	+	0.824936i	$0.308789\pi$
$488$	−24.5952	−1.11337
$489$	11.6805	0.528209
$490$	0	0
$491$	−31.0189	−1.39986	−0.699932	−	0.714209i	$-0.746787\pi$
$491$	−31.0189	−1.39986	−0.699932	+	0.714209i	$0.746787\pi$
$492$	7.82964	0.352987
$493$	50.5166	2.27515
$494$	1.24239	0.0558979
$495$	0	0
$496$	−19.7476	−0.886692
$497$	−9.35094	−0.419447
$498$	−9.27823	−0.415767
$499$	−20.3081	−0.909115	−0.454557	−	0.890717i	$-0.650203\pi$
$499$	−20.3081	−0.909115	−0.454557	+	0.890717i	$0.650203\pi$
$500$	0	0
$501$	9.47728	0.423414
$502$	−25.2371	−1.12639
$503$	28.6698	1.27832	0.639161	−	0.769073i	$-0.279282\pi$
$503$	28.6698	1.27832	0.639161	+	0.769073i	$0.279282\pi$
$504$	−2.50183	−0.111440
$505$	0	0
$506$	−12.2720	−0.545555
$507$	10.9941	0.488265
$508$	1.09163	0.0484333
$509$	34.5760	1.53255	0.766277	−	0.642510i	$-0.222107\pi$
$509$	34.5760	1.53255	0.766277	+	0.642510i	$0.222107\pi$
$510$	0	0
$511$	9.00366	0.398298
$512$	−19.1993	−0.848497
$513$	0.789564	0.0348601
$514$	3.06958	0.135393
$515$	0	0
$516$	5.53863	0.243825
$517$	−15.4235	−0.678324
$518$	1.27072	0.0558323
$519$	−3.41990	−0.150117
$520$	0	0
$521$	36.3260	1.59147	0.795736	−	0.605644i	$-0.207084\pi$
$521$	36.3260	1.59147	0.795736	+	0.605644i	$0.207084\pi$
$522$	−7.03380	−0.307861
$523$	−18.7896	−0.821614	−0.410807	−	0.911722i	$-0.634753\pi$
$523$	−18.7896	−0.821614	−0.410807	+	0.911722i	$0.634753\pi$
$524$	−2.69252	−0.117623
$525$	0	0
$526$	19.6021	0.854693
$527$	−83.7065	−3.64631
$528$	2.78320	0.121123
$529$	32.8131	1.42665
$530$	0	0
$531$	−6.27365	−0.272253
$532$	0.492233	0.0213410
$533$	−14.4829	−0.627325
$534$	8.65435	0.374510
$535$	0	0
$536$	−23.6127	−1.01991
$537$	−9.38806	−0.405125
$538$	21.6443	0.933151
$539$	−9.36951	−0.403574
$540$	0	0
$541$	9.44589	0.406111	0.203055	−	0.979167i	$-0.434913\pi$
$541$	9.44589	0.406111	0.203055	+	0.979167i	$0.434913\pi$
$542$	1.99151	0.0855427
$543$	−19.6691	−0.844080
$544$	−32.3475	−1.38689
$545$	0	0
$546$	1.28119	0.0548299
$547$	−1.20226	−0.0514051	−0.0257025	−	0.999670i	$-0.508182\pi$
$547$	−1.20226	−0.0514051	−0.0257025	+	0.999670i	$0.508182\pi$
$548$	−6.71584	−0.286886
$549$	8.00449	0.341623
$550$	0	0
$551$	4.99876	0.212954
$552$	−22.9554	−0.977045
$553$	−0.819409	−0.0348448
$554$	11.9040	0.505752
$555$	0	0
$556$	−16.8398	−0.714165
$557$	21.7932	0.923409	0.461704	−	0.887034i	$-0.347238\pi$
$557$	21.7932	0.923409	0.461704	+	0.887034i	$0.347238\pi$
$558$	11.6551	0.493399
$559$	−10.2451	−0.433322
$560$	0	0
$561$	11.7975	0.498090
$562$	21.4623	0.905331
$563$	33.2610	1.40179	0.700893	−	0.713267i	$-0.252785\pi$
$563$	33.2610	1.40179	0.700893	+	0.713267i	$0.252785\pi$
$564$	−7.98719	−0.336321
$565$	0	0
$566$	15.5004	0.651529
$567$	0.814220	0.0341940
$568$	35.2882	1.48066
$569$	2.88481	0.120937	0.0604687	−	0.998170i	$-0.480740\pi$
$569$	2.88481	0.120937	0.0604687	+	0.998170i	$0.480740\pi$
$570$	0	0
$571$	−24.0445	−1.00623	−0.503115	−	0.864220i	$-0.667813\pi$
$571$	−24.0445	−1.00623	−0.503115	+	0.864220i	$0.667813\pi$
$572$	1.60335	0.0670394
$573$	−14.4307	−0.602853
$574$	9.25034	0.386102
$575$	0	0
$576$	8.26880	0.344533
$577$	−12.0695	−0.502458	−0.251229	−	0.967928i	$-0.580835\pi$
$577$	−12.0695	−0.502458	−0.251229	+	0.967928i	$0.580835\pi$
$578$	51.8479	2.15659
$579$	−7.53941	−0.313327
$580$	0	0
$581$	6.79972	0.282100
$582$	−7.31652	−0.303279
$583$	2.74787	0.113805
$584$	−33.9776	−1.40600
$585$	0	0
$586$	36.4289	1.50486
$587$	−35.5089	−1.46561	−0.732805	−	0.680438i	$-0.761789\pi$
$587$	−35.5089	−1.46561	−0.732805	+	0.680438i	$0.761789\pi$
$588$	−4.85209	−0.200097
$589$	−8.28299	−0.341295
$590$	0	0
$591$	−8.26792	−0.340097
$592$	−2.64428	−0.108679
$593$	−3.98563	−0.163670	−0.0818352	−	0.996646i	$-0.526078\pi$
$593$	−3.98563	−0.163670	−0.0818352	+	0.996646i	$0.526078\pi$
$594$	−1.64265	−0.0673989
$595$	0	0
$596$	−7.01076	−0.287172
$597$	−7.92853	−0.324493
$598$	11.7555	0.480716
$599$	35.2412	1.43992	0.719958	−	0.694018i	$-0.244161\pi$
$599$	35.2412	1.43992	0.719958	+	0.694018i	$0.244161\pi$
$600$	0	0
$601$	−14.9691	−0.610602	−0.305301	−	0.952256i	$-0.598757\pi$
$601$	−14.9691	−0.610602	−0.305301	+	0.952256i	$0.598757\pi$
$602$	6.54362	0.266698
$603$	7.68475	0.312947
$604$	1.06280	0.0432445
$605$	0	0
$606$	8.83753	0.359000
$607$	−31.5921	−1.28228	−0.641142	−	0.767422i	$-0.721539\pi$
$607$	−31.5921	−1.28228	−0.641142	+	0.767422i	$0.721539\pi$
$608$	−3.20088	−0.129813
$609$	5.15485	0.208885
$610$	0	0
$611$	14.7743	0.597706
$612$	6.10943	0.246959
$613$	8.90251	0.359569	0.179785	−	0.983706i	$-0.442460\pi$
$613$	8.90251	0.359569	0.179785	+	0.983706i	$0.442460\pi$
$614$	28.5187	1.15092
$615$	0	0
$616$	−3.69903	−0.149038
$617$	27.0331	1.08831	0.544156	−	0.838984i	$-0.316850\pi$
$617$	27.0331	1.08831	0.544156	+	0.838984i	$0.316850\pi$
$618$	12.8981	0.518839
$619$	47.9971	1.92916	0.964582	−	0.263782i	$-0.0849698\pi$
$619$	47.9971	1.92916	0.964582	+	0.263782i	$0.0849698\pi$
$620$	0	0
$621$	7.47081	0.299793
$622$	23.6459	0.948113
$623$	−6.34250	−0.254107
$624$	−2.66606	−0.106728
$625$	0	0
$626$	−13.6830	−0.546884
$627$	1.16740	0.0466213
$628$	−16.7010	−0.666442
$629$	−11.2086	−0.446917
$630$	0	0
$631$	−0.230699	−0.00918397	−0.00459199	−	0.999989i	$-0.501462\pi$
$631$	−0.230699	−0.00918397	−0.00459199	+	0.999989i	$0.501462\pi$
$632$	3.09225	0.123003
$633$	4.90371	0.194905
$634$	−3.93471	−0.156267
$635$	0	0
$636$	1.42301	0.0564260
$637$	8.97517	0.355609
$638$	−10.3997	−0.411728
$639$	−11.4845	−0.454321
$640$	0	0
$641$	−39.2103	−1.54871	−0.774357	−	0.632749i	$-0.781926\pi$
$641$	−39.2103	−1.54871	−0.774357	+	0.632749i	$0.781926\pi$
$642$	−1.11100	−0.0438478
$643$	4.11144	0.162139	0.0810696	−	0.996708i	$-0.474166\pi$
$643$	4.11144	0.162139	0.0810696	+	0.996708i	$0.474166\pi$
$644$	4.65748	0.183531
$645$	0	0
$646$	6.99943	0.275389
$647$	9.57257	0.376337	0.188168	−	0.982137i	$-0.439745\pi$
$647$	9.57257	0.376337	0.188168	+	0.982137i	$0.439745\pi$
$648$	−3.07267	−0.120706
$649$	−9.27579	−0.364107
$650$	0	0
$651$	−8.54165	−0.334774
$652$	8.94338	0.350250
$653$	−45.8792	−1.79539	−0.897695	−	0.440617i	$-0.854760\pi$
$653$	−45.8792	−1.79539	−0.897695	+	0.440617i	$0.854760\pi$
$654$	−10.6736	−0.417372
$655$	0	0
$656$	−19.2493	−0.751558
$657$	11.0580	0.431414
$658$	−9.43647	−0.367872
$659$	−50.3908	−1.96295	−0.981473	−	0.191599i	$-0.938633\pi$
$659$	−50.3908	−1.96295	−0.981473	+	0.191599i	$0.938633\pi$
$660$	0	0
$661$	−21.9351	−0.853177	−0.426588	−	0.904446i	$-0.640285\pi$
$661$	−21.9351	−0.853177	−0.426588	+	0.904446i	$0.640285\pi$
$662$	5.83982	0.226971
$663$	−11.3010	−0.438893
$664$	−25.6605	−0.995821
$665$	0	0
$666$	1.56066	0.0604744
$667$	47.2980	1.83138
$668$	7.25647	0.280761
$669$	−5.30243	−0.205004
$670$	0	0
$671$	11.8349	0.456880
$672$	−3.30083	−0.127332
$673$	−10.7726	−0.415255	−0.207627	−	0.978208i	$-0.566574\pi$
$673$	−10.7726	−0.415255	−0.207627	+	0.978208i	$0.566574\pi$
$674$	28.6920	1.10517
$675$	0	0
$676$	8.41784	0.323763
$677$	6.99290	0.268759	0.134379	−	0.990930i	$-0.457096\pi$
$677$	6.99290	0.268759	0.134379	+	0.990930i	$0.457096\pi$
$678$	9.29665	0.357036
$679$	5.36205	0.205777
$680$	0	0
$681$	1.14301	0.0438002
$682$	17.2324	0.659863
$683$	9.14049	0.349751	0.174876	−	0.984591i	$-0.444048\pi$
$683$	9.14049	0.349751	0.174876	+	0.984591i	$0.444048\pi$
$684$	0.604546	0.0231154
$685$	0	0
$686$	−12.0647	−0.460633
$687$	26.5636	1.01347
$688$	−13.6168	−0.519135
$689$	−2.63222	−0.100280
$690$	0	0
$691$	−40.4731	−1.53967	−0.769834	−	0.638244i	$-0.779661\pi$
$691$	−40.4731	−1.53967	−0.769834	+	0.638244i	$0.779661\pi$
$692$	−2.61852	−0.0995410
$693$	1.20385	0.0457305
$694$	−12.2370	−0.464510
$695$	0	0
$696$	−19.4532	−0.737371
$697$	−81.5942	−3.09060
$698$	−35.0660	−1.32727
$699$	−11.3737	−0.430194
$700$	0	0
$701$	14.3576	0.542278	0.271139	−	0.962540i	$-0.412600\pi$
$701$	14.3576	0.542278	0.271139	+	0.962540i	$0.412600\pi$
$702$	1.57352	0.0593886
$703$	−1.10912	−0.0418314
$704$	12.2257	0.460773
$705$	0	0
$706$	−9.65982	−0.363552
$707$	−6.47675	−0.243583
$708$	−4.80355	−0.180528
$709$	−7.06205	−0.265221	−0.132610	−	0.991168i	$-0.542336\pi$
$709$	−7.06205	−0.265221	−0.132610	+	0.991168i	$0.542336\pi$
$710$	0	0
$711$	−1.00637	−0.0377419
$712$	23.9351	0.897005
$713$	−78.3732	−2.93510
$714$	7.21800	0.270127
$715$	0	0
$716$	−7.18815	−0.268634
$717$	3.61842	0.135132
$718$	29.2859	1.09294
$719$	13.5328	0.504687	0.252344	−	0.967638i	$-0.418799\pi$
$719$	13.5328	0.504687	0.252344	+	0.967638i	$0.418799\pi$
$720$	0	0
$721$	−9.45264	−0.352035
$722$	−20.4165	−0.759822
$723$	13.8280	0.514270
$724$	−15.0600	−0.559701
$725$	0	0
$726$	9.79233	0.363428
$727$	−35.0382	−1.29950	−0.649748	−	0.760150i	$-0.725126\pi$
$727$	−35.0382	−1.29950	−0.649748	+	0.760150i	$0.725126\pi$
$728$	3.54335	0.131325
$729$	1.00000	0.0370370
$730$	0	0
$731$	−57.7192	−2.13482
$732$	6.12880	0.226527
$733$	−18.4562	−0.681695	−0.340848	−	0.940119i	$-0.610714\pi$
$733$	−18.4562	−0.681695	−0.340848	+	0.940119i	$0.610714\pi$
$734$	12.0696	0.445496
$735$	0	0
$736$	−30.2865	−1.11638
$737$	11.3621	0.418530
$738$	11.3610	0.418203
$739$	4.64846	0.170996	0.0854981	−	0.996338i	$-0.472752\pi$
$739$	4.64846	0.170996	0.0854981	+	0.996338i	$0.472752\pi$
$740$	0	0
$741$	−1.11826	−0.0410804
$742$	1.68122	0.0617194
$743$	38.9947	1.43058	0.715289	−	0.698829i	$-0.246295\pi$
$743$	38.9947	1.43058	0.715289	+	0.698829i	$0.246295\pi$
$744$	32.2341	1.18176
$745$	0	0
$746$	10.8620	0.397686
$747$	8.35121	0.305555
$748$	9.03298	0.330279
$749$	0.814220	0.0297510
$750$	0	0
$751$	32.0594	1.16987	0.584933	−	0.811082i	$-0.301121\pi$
$751$	32.0594	1.16987	0.584933	+	0.811082i	$0.301121\pi$
$752$	19.6366	0.716073
$753$	22.7156	0.827802
$754$	9.96199	0.362794
$755$	0	0
$756$	0.623424	0.0226737
$757$	−54.6416	−1.98598	−0.992990	−	0.118194i	$-0.962289\pi$
$757$	−54.6416	−1.98598	−0.992990	+	0.118194i	$0.962289\pi$
$758$	24.8468	0.902477
$759$	11.0458	0.400938
$760$	0	0
$761$	−41.0534	−1.48818	−0.744092	−	0.668078i	$-0.767117\pi$
$761$	−41.0534	−1.48818	−0.744092	+	0.668078i	$0.767117\pi$
$762$	1.58398	0.0573816
$763$	7.82238	0.283189
$764$	−11.0492	−0.399746
$765$	0	0
$766$	3.30563	0.119437
$767$	8.88539	0.320833
$768$	15.3391	0.553504
$769$	−30.2469	−1.09073	−0.545365	−	0.838199i	$-0.683609\pi$
$769$	−30.2469	−1.09073	−0.545365	+	0.838199i	$0.683609\pi$
$770$	0	0
$771$	−2.76289	−0.0995031
$772$	−5.77270	−0.207764
$773$	−4.25365	−0.152993	−0.0764965	−	0.997070i	$-0.524373\pi$
$773$	−4.25365	−0.152993	−0.0764965	+	0.997070i	$0.524373\pi$
$774$	8.03668	0.288872
$775$	0	0
$776$	−20.2351	−0.726397
$777$	−1.14376	−0.0410321
$778$	−20.4715	−0.733940
$779$	−8.07398	−0.289280
$780$	0	0
$781$	−16.9802	−0.607601
$782$	66.2282	2.36832
$783$	6.33103	0.226253
$784$	11.9289	0.426033
$785$	0	0
$786$	−3.90690	−0.139355
$787$	−19.3734	−0.690589	−0.345294	−	0.938494i	$-0.612221\pi$
$787$	−19.3734	−0.690589	−0.345294	+	0.938494i	$0.612221\pi$
$788$	−6.33049	−0.225515
$789$	−17.6436	−0.628129
$790$	0	0
$791$	−6.81322	−0.242250
$792$	−4.54304	−0.161430
$793$	−11.3368	−0.402581
$794$	32.6778	1.15969
$795$	0	0
$796$	−6.07064	−0.215168
$797$	−2.77325	−0.0982335	−0.0491167	−	0.998793i	$-0.515641\pi$
$797$	−2.77325	−0.0982335	−0.0491167	+	0.998793i	$0.515641\pi$
$798$	0.714241	0.0252839
$799$	83.2361	2.94468
$800$	0	0
$801$	−7.78967	−0.275234
$802$	16.4136	0.579585
$803$	16.3496	0.576965
$804$	5.88398	0.207512
$805$	0	0
$806$	−16.5071	−0.581439
$807$	−19.4817	−0.685789
$808$	24.4417	0.859856
$809$	43.2120	1.51925	0.759626	−	0.650361i	$-0.225382\pi$
$809$	43.2120	1.51925	0.759626	+	0.650361i	$0.225382\pi$
$810$	0	0
$811$	−23.0182	−0.808278	−0.404139	−	0.914698i	$-0.632429\pi$
$811$	−23.0182	−0.808278	−0.404139	+	0.914698i	$0.632429\pi$
$812$	3.94692	0.138510
$813$	−1.79253	−0.0628669
$814$	2.30748	0.0808773
$815$	0	0
$816$	−15.0201	−0.525810
$817$	−5.71148	−0.199819
$818$	−29.6016	−1.03499
$819$	−1.15318	−0.0402954
$820$	0	0
$821$	25.9076	0.904183	0.452092	−	0.891972i	$-0.350678\pi$
$821$	25.9076	0.904183	0.452092	+	0.891972i	$0.350678\pi$
$822$	−9.74483	−0.339890
$823$	17.1504	0.597824	0.298912	−	0.954281i	$-0.403376\pi$
$823$	17.1504	0.597824	0.298912	+	0.954281i	$0.403376\pi$
$824$	35.6720	1.24269
$825$	0	0
$826$	−5.67516	−0.197464
$827$	−22.3748	−0.778047	−0.389024	−	0.921228i	$-0.627188\pi$
$827$	−22.3748	−0.778047	−0.389024	+	0.921228i	$0.627188\pi$
$828$	5.72018	0.198790
$829$	−30.8850	−1.07268	−0.536340	−	0.844002i	$-0.680193\pi$
$829$	−30.8850	−1.07268	−0.536340	+	0.844002i	$0.680193\pi$
$830$	0	0
$831$	−10.7146	−0.371686
$832$	−11.7111	−0.406010
$833$	50.5646	1.75196
$834$	−24.4349	−0.846110
$835$	0	0
$836$	0.893839	0.0309141
$837$	−10.4906	−0.362608
$838$	28.4784	0.983770
$839$	−29.6038	−1.02204	−0.511019	−	0.859570i	$-0.670732\pi$
$839$	−29.6038	−1.02204	−0.511019	+	0.859570i	$0.670732\pi$
$840$	0	0
$841$	11.0820	0.382137
$842$	12.1643	0.419209
$843$	−19.3179	−0.665344
$844$	3.75462	0.129239
$845$	0	0
$846$	−11.5896	−0.398458
$847$	−7.17649	−0.246587
$848$	−3.49849	−0.120139
$849$	−13.9517	−0.478820
$850$	0	0
$851$	−10.4945	−0.359746
$852$	−8.79337	−0.301256
$853$	−15.0570	−0.515540	−0.257770	−	0.966206i	$-0.582988\pi$
$853$	−15.0570	−0.515540	−0.257770	+	0.966206i	$0.582988\pi$
$854$	7.24087	0.247778
$855$	0	0
$856$	−3.07267	−0.105022
$857$	−38.6468	−1.32015	−0.660075	−	0.751200i	$-0.729476\pi$
$857$	−38.6468	−1.32015	−0.660075	+	0.751200i	$0.729476\pi$
$858$	2.32649	0.0794252
$859$	4.00237	0.136559	0.0682795	−	0.997666i	$-0.478249\pi$
$859$	4.00237	0.136559	0.0682795	+	0.997666i	$0.478249\pi$
$860$	0	0
$861$	−8.32610	−0.283753
$862$	−14.6869	−0.500238
$863$	−7.47406	−0.254420	−0.127210	−	0.991876i	$-0.540602\pi$
$863$	−7.47406	−0.254420	−0.127210	+	0.991876i	$0.540602\pi$
$864$	−4.05398	−0.137919
$865$	0	0
$866$	−21.0867	−0.716555
$867$	−46.6676	−1.58492
$868$	−6.54008	−0.221985
$869$	−1.48795	−0.0504753
$870$	0	0
$871$	−10.8839	−0.368788
$872$	−29.5198	−0.999665
$873$	6.58550	0.222885
$874$	6.55347	0.221674
$875$	0	0
$876$	8.46679	0.286066
$877$	−12.7653	−0.431052	−0.215526	−	0.976498i	$-0.569147\pi$
$877$	−12.7653	−0.431052	−0.215526	+	0.976498i	$0.569147\pi$
$878$	−13.5684	−0.457912
$879$	−32.7891	−1.10595
$880$	0	0
$881$	19.3525	0.652003	0.326002	−	0.945369i	$-0.394299\pi$
$881$	19.3525	0.652003	0.326002	+	0.945369i	$0.394299\pi$
$882$	−7.04048	−0.237065
$883$	−36.4648	−1.22714	−0.613569	−	0.789641i	$-0.710267\pi$
$883$	−36.4648	−1.22714	−0.613569	+	0.789641i	$0.710267\pi$
$884$	−8.65281	−0.291025
$885$	0	0
$886$	−3.54597	−0.119129
$887$	31.9737	1.07357	0.536786	−	0.843718i	$-0.319638\pi$
$887$	31.9737	1.07357	0.536786	+	0.843718i	$0.319638\pi$
$888$	4.31627	0.144845
$889$	−1.16085	−0.0389337
$890$	0	0
$891$	1.47853	0.0495326
$892$	−4.05991	−0.135936
$893$	8.23644	0.275622
$894$	−10.1728	−0.340228
$895$	0	0
$896$	0.878317	0.0293425
$897$	−10.5809	−0.353287
$898$	−23.0495	−0.769172
$899$	−66.4162	−2.21511
$900$	0	0
$901$	−14.8295	−0.494041
$902$	16.7976	0.559297
$903$	−5.88983	−0.196001
$904$	25.7115	0.855150
$905$	0	0
$906$	1.54214	0.0512342
$907$	−12.9626	−0.430416	−0.215208	−	0.976568i	$-0.569043\pi$
$907$	−12.9626	−0.430416	−0.215208	+	0.976568i	$0.569043\pi$
$908$	0.875167	0.0290434
$909$	−7.95454	−0.263836
$910$	0	0
$911$	40.0408	1.32661	0.663306	−	0.748348i	$-0.269153\pi$
$911$	40.0408	1.32661	0.663306	+	0.748348i	$0.269153\pi$
$912$	−1.48628	−0.0492158
$913$	12.3475	0.408643
$914$	26.1480	0.864899
$915$	0	0
$916$	20.3390	0.672019
$917$	2.86325	0.0945527
$918$	8.86492	0.292586
$919$	54.0728	1.78370	0.891848	−	0.452335i	$-0.149409\pi$
$919$	54.0728	1.78370	0.891848	+	0.452335i	$0.149409\pi$
$920$	0	0
$921$	−25.6693	−0.845833
$922$	9.66540	0.318313
$923$	16.2656	0.535388
$924$	0.921751	0.0303234
$925$	0	0
$926$	−7.93212	−0.260666
$927$	−11.6094	−0.381304
$928$	−25.6659	−0.842523
$929$	4.69919	0.154175	0.0770877	−	0.997024i	$-0.475438\pi$
$929$	4.69919	0.154175	0.0770877	+	0.997024i	$0.475438\pi$
$930$	0	0
$931$	5.00351	0.163983
$932$	−8.70852	−0.285257
$933$	−21.2833	−0.696785
$934$	−15.4747	−0.506347
$935$	0	0
$936$	4.35183	0.142244
$937$	42.1288	1.37629	0.688144	−	0.725575i	$-0.258426\pi$
$937$	42.1288	1.37629	0.688144	+	0.725575i	$0.258426\pi$
$938$	6.95164	0.226979
$939$	12.3159	0.401914
$940$	0	0
$941$	12.3583	0.402869	0.201435	−	0.979502i	$-0.435440\pi$
$941$	12.3583	0.402869	0.201435	+	0.979502i	$0.435440\pi$
$942$	−24.2335	−0.789570
$943$	−76.3955	−2.48778
$944$	11.8096	0.384369
$945$	0	0
$946$	11.8825	0.386332
$947$	27.2018	0.883941	0.441970	−	0.897030i	$-0.354280\pi$
$947$	27.2018	0.883941	0.441970	+	0.897030i	$0.354280\pi$
$948$	−0.770549	−0.0250263
$949$	−15.6615	−0.508394
$950$	0	0
$951$	3.54158	0.114844
$952$	19.9626	0.646992
$953$	17.8082	0.576863	0.288432	−	0.957500i	$-0.406866\pi$
$953$	17.8082	0.576863	0.288432	+	0.957500i	$0.406866\pi$
$954$	2.06482	0.0668509
$955$	0	0
$956$	2.77051	0.0896048
$957$	9.36062	0.302586
$958$	3.44317	0.111244
$959$	7.14168	0.230617
$960$	0	0
$961$	79.0524	2.55008
$962$	−2.21037	−0.0712651
$963$	1.00000	0.0322245
$964$	10.5877	0.341007
$965$	0	0
$966$	6.75811	0.217439
$967$	12.0649	0.387982	0.193991	−	0.981003i	$-0.437857\pi$
$967$	12.0649	0.387982	0.193991	+	0.981003i	$0.437857\pi$
$968$	27.0824	0.870460
$969$	−6.30009	−0.202388
$970$	0	0
$971$	3.97980	0.127718	0.0638589	−	0.997959i	$-0.479659\pi$
$971$	3.97980	0.127718	0.0638589	+	0.997959i	$0.479659\pi$
$972$	0.765670	0.0245589
$973$	17.9075	0.574090
$974$	27.7162	0.888083
$975$	0	0
$976$	−15.0677	−0.482306
$977$	−39.4504	−1.26213	−0.631065	−	0.775730i	$-0.717382\pi$
$977$	−39.4504	−1.26213	−0.631065	+	0.775730i	$0.717382\pi$
$978$	12.9770	0.414960
$979$	−11.5173	−0.368093
$980$	0	0
$981$	9.60720	0.306734
$982$	−34.4622	−1.09973
$983$	6.11895	0.195164	0.0975821	−	0.995227i	$-0.468889\pi$
$983$	6.11895	0.195164	0.0975821	+	0.995227i	$0.468889\pi$
$984$	31.4207	1.00166
$985$	0	0
$986$	56.1241	1.78736
$987$	8.49364	0.270356
$988$	−0.856220	−0.0272400
$989$	−54.0417	−1.71843
$990$	0	0
$991$	39.8066	1.26450	0.632249	−	0.774765i	$-0.282132\pi$
$991$	39.8066	1.26450	0.632249	+	0.774765i	$0.282132\pi$
$992$	42.5286	1.35028
$993$	−5.25634	−0.166805
$994$	−10.3889	−0.329517
$995$	0	0
$996$	6.39427	0.202610
$997$	−41.0386	−1.29971	−0.649853	−	0.760060i	$-0.725169\pi$
$997$	−41.0386	−1.29971	−0.649853	+	0.760060i	$0.725169\pi$
$998$	−22.5624	−0.714199
$999$	−1.40473	−0.0444437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8025.2.a.ba.1.5		6
5.4	even	2		321.2.a.c.1.2	✓	6
15.14	odd	2		963.2.a.d.1.5		6
20.19	odd	2		5136.2.a.bg.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
321.2.a.c.1.2	✓	6	5.4	even	2
963.2.a.d.1.5		6	15.14	odd	2
5136.2.a.bg.1.3		6	20.19	odd	2
8025.2.a.ba.1.5		6	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:	\( N \)	\(=\)	\( 8025 = 3 \cdot 5^{2} \cdot 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8025.a (trivial)

\(f(q)\)	\(=\)	\(q+1.11100 q^{2} -1.00000 q^{3} -0.765670 q^{4} -1.11100 q^{6} +0.814220 q^{7} -3.07267 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.11100 q^{2} -1.00000 q^{3} -0.765670 q^{4} -1.11100 q^{6} +0.814220 q^{7} -3.07267 q^{8} +1.00000 q^{9} +1.47853 q^{11} +0.765670 q^{12} -1.41630 q^{13} +0.904602 q^{14} -1.88241 q^{16} -7.97920 q^{17} +1.11100 q^{18} -0.789564 q^{19} -0.814220 q^{21} +1.64265 q^{22} -7.47081 q^{23} +3.07267 q^{24} -1.57352 q^{26} -1.00000 q^{27} -0.623424 q^{28} -6.33103 q^{29} +10.4906 q^{31} +4.05398 q^{32} -1.47853 q^{33} -8.86492 q^{34} -0.765670 q^{36} +1.40473 q^{37} -0.877209 q^{38} +1.41630 q^{39} +10.2259 q^{41} -0.904602 q^{42} +7.23371 q^{43} -1.13207 q^{44} -8.30010 q^{46} -10.4316 q^{47} +1.88241 q^{48} -6.33705 q^{49} +7.97920 q^{51} +1.08442 q^{52} +1.85852 q^{53} -1.11100 q^{54} -2.50183 q^{56} +0.789564 q^{57} -7.03380 q^{58} -6.27365 q^{59} +8.00449 q^{61} +11.6551 q^{62} +0.814220 q^{63} +8.26880 q^{64} -1.64265 q^{66} +7.68475 q^{67} +6.10943 q^{68} +7.47081 q^{69} -11.4845 q^{71} -3.07267 q^{72} +11.0580 q^{73} +1.56066 q^{74} +0.604546 q^{76} +1.20385 q^{77} +1.57352 q^{78} -1.00637 q^{79} +1.00000 q^{81} +11.3610 q^{82} +8.35121 q^{83} +0.623424 q^{84} +8.03668 q^{86} +6.33103 q^{87} -4.54304 q^{88} -7.78967 q^{89} -1.15318 q^{91} +5.72018 q^{92} -10.4906 q^{93} -11.5896 q^{94} -4.05398 q^{96} +6.58550 q^{97} -7.04048 q^{98} +1.47853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 - 6 * q^8 + 6 * q^9	\( 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 3 q^{6} - 6 q^{8} + 6 q^{9} + 6 q^{11} - 7 q^{12} + 8 q^{13} - 2 q^{14} + q^{16} - 4 q^{17} - 3 q^{18} - 4 q^{19} + 22 q^{22} - 14 q^{23} + 6 q^{24} - 7 q^{26} - 6 q^{27} + 16 q^{28} + 10 q^{29} + 12 q^{31} - 5 q^{32} - 6 q^{33} - q^{34} + 7 q^{36} + 12 q^{37} + q^{38} - 8 q^{39} - 6 q^{41} + 2 q^{42} + 12 q^{43} + 4 q^{44} + 18 q^{46} - 16 q^{47} - q^{48} - 12 q^{49} + 4 q^{51} + 25 q^{52} - 12 q^{53} + 3 q^{54} - 32 q^{56} + 4 q^{57} - 12 q^{58} + 8 q^{59} - 24 q^{61} + 8 q^{62} - 12 q^{64} - 22 q^{66} + 4 q^{67} + 15 q^{68} + 14 q^{69} + 36 q^{71} - 6 q^{72} + 26 q^{73} - 39 q^{74} - 17 q^{76} - 14 q^{77} + 7 q^{78} + 8 q^{79} + 6 q^{81} + 38 q^{82} + 8 q^{83} - 16 q^{84} + 16 q^{86} - 10 q^{87} + 8 q^{88} - 8 q^{89} - 18 q^{91} - 2 q^{92} - 12 q^{93} + 24 q^{94} + 5 q^{96} + 24 q^{97} - 43 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 3 * q^6 - 6 * q^8 + 6 * q^9 + 6 * q^11 - 7 * q^12 + 8 * q^13 - 2 * q^14 + q^16 - 4 * q^17 - 3 * q^18 - 4 * q^19 + 22 * q^22 - 14 * q^23 + 6 * q^24 - 7 * q^26 - 6 * q^27 + 16 * q^28 + 10 * q^29 + 12 * q^31 - 5 * q^32 - 6 * q^33 - q^34 + 7 * q^36 + 12 * q^37 + q^38 - 8 * q^39 - 6 * q^41 + 2 * q^42 + 12 * q^43 + 4 * q^44 + 18 * q^46 - 16 * q^47 - q^48 - 12 * q^49 + 4 * q^51 + 25 * q^52 - 12 * q^53 + 3 * q^54 - 32 * q^56 + 4 * q^57 - 12 * q^58 + 8 * q^59 - 24 * q^61 + 8 * q^62 - 12 * q^64 - 22 * q^66 + 4 * q^67 + 15 * q^68 + 14 * q^69 + 36 * q^71 - 6 * q^72 + 26 * q^73 - 39 * q^74 - 17 * q^76 - 14 * q^77 + 7 * q^78 + 8 * q^79 + 6 * q^81 + 38 * q^82 + 8 * q^83 - 16 * q^84 + 16 * q^86 - 10 * q^87 + 8 * q^88 - 8 * q^89 - 18 * q^91 - 2 * q^92 - 12 * q^93 + 24 * q^94 + 5 * q^96 + 24 * q^97 - 43 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more