LMFDB - Embedded newform 1849.2.a.m.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{44})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 11x^{8} + 44x^{6} - 77x^{4} + 55x^{2} - 11 $ x^10 - 11x^8 + 44x^6 - 77x^4 + 55x^2 - 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.563465$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.563465 q^{2} -2.07496 q^{3} -1.68251 q^{4} -1.25580 q^{5} +1.16917 q^{6} +1.91459 q^{7} +2.07496 q^{8} +1.30548 q^{9} +O(q^{10})$	\(q-0.563465 q^{2} -2.07496 q^{3} -1.68251 q^{4} -1.25580 q^{5} +1.16917 q^{6} +1.91459 q^{7} +2.07496 q^{8} +1.30548 q^{9} +0.707599 q^{10} +0.634356 q^{11} +3.49114 q^{12} -5.68965 q^{13} -1.07880 q^{14} +2.60574 q^{15} +2.19584 q^{16} -5.78084 q^{17} -0.735591 q^{18} +3.28109 q^{19} +2.11289 q^{20} -3.97270 q^{21} -0.357438 q^{22} +9.50494 q^{23} -4.30548 q^{24} -3.42297 q^{25} +3.20592 q^{26} +3.51608 q^{27} -3.22130 q^{28} +4.12807 q^{29} -1.46824 q^{30} +3.12343 q^{31} -5.38721 q^{32} -1.31627 q^{33} +3.25730 q^{34} -2.40433 q^{35} -2.19647 q^{36} +10.6751 q^{37} -1.84878 q^{38} +11.8058 q^{39} -2.60574 q^{40} -2.15325 q^{41} +2.23848 q^{42} -1.06731 q^{44} -1.63942 q^{45} -5.35570 q^{46} +1.01308 q^{47} -4.55630 q^{48} -3.33436 q^{49} +1.92872 q^{50} +11.9950 q^{51} +9.57287 q^{52} +2.43788 q^{53} -1.98119 q^{54} -0.796624 q^{55} +3.97270 q^{56} -6.80815 q^{57} -2.32602 q^{58} +1.54924 q^{59} -4.38417 q^{60} -3.56631 q^{61} -1.75994 q^{62} +2.49945 q^{63} -1.35618 q^{64} +7.14505 q^{65} +0.741670 q^{66} -5.63797 q^{67} +9.72631 q^{68} -19.7224 q^{69} +1.35476 q^{70} -12.9142 q^{71} +2.70882 q^{72} +5.02757 q^{73} -6.01503 q^{74} +7.10254 q^{75} -5.52046 q^{76} +1.21453 q^{77} -6.65217 q^{78} +8.13626 q^{79} -2.75754 q^{80} -11.2122 q^{81} +1.21328 q^{82} +3.15484 q^{83} +6.68409 q^{84} +7.25957 q^{85} -8.56559 q^{87} +1.31627 q^{88} -0.861116 q^{89} +0.923754 q^{90} -10.8933 q^{91} -15.9921 q^{92} -6.48100 q^{93} -0.570833 q^{94} -4.12039 q^{95} +11.1783 q^{96} -15.6367 q^{97} +1.87880 q^{98} +0.828137 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9}+O(q^{10}) $ 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9	$ 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9} - 22 q^{10} - 10 q^{11} - 14 q^{13} - 22 q^{14} - 22 q^{15} - 26 q^{16} - 16 q^{17} - 44 q^{21} - 18 q^{23} - 44 q^{24} - 6 q^{25} - 2 q^{31} - 28 q^{36} - 22 q^{38} + 22 q^{40} - 2 q^{44} - 18 q^{47} + 18 q^{49} + 28 q^{52} + 2 q^{53} + 44 q^{56} - 22 q^{57} - 22 q^{58} + 14 q^{59} + 8 q^{64} - 22 q^{66} + 26 q^{67} + 32 q^{68} + 44 q^{74} - 44 q^{78} - 56 q^{79} + 2 q^{81} - 38 q^{83} - 22 q^{87} - 22 q^{90} - 74 q^{92} + 22 q^{96} + 34 q^{97} - 36 q^{99}+O(q^{100}) $ 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9 - 22 * q^10 - 10 * q^11 - 14 * q^13 - 22 * q^14 - 22 * q^15 - 26 * q^16 - 16 * q^17 - 44 * q^21 - 18 * q^23 - 44 * q^24 - 6 * q^25 - 2 * q^31 - 28 * q^36 - 22 * q^38 + 22 * q^40 - 2 * q^44 - 18 * q^47 + 18 * q^49 + 28 * q^52 + 2 * q^53 + 44 * q^56 - 22 * q^57 - 22 * q^58 + 14 * q^59 + 8 * q^64 - 22 * q^66 + 26 * q^67 + 32 * q^68 + 44 * q^74 - 44 * q^78 - 56 * q^79 + 2 * q^81 - 38 * q^83 - 22 * q^87 - 22 * q^90 - 74 * q^92 + 22 * q^96 + 34 * q^97 - 36 * 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 $

$2$	−0.563465	−0.398430	−0.199215	−	0.979956i	$-0.563839\pi$
$2$	−0.563465	−0.398430	−0.199215	+	0.979956i	$0.563839\pi$
$3$	−2.07496	−1.19798	−0.598991	−	0.800756i	$-0.704431\pi$
$3$	−2.07496	−1.19798	−0.598991	+	0.800756i	$0.704431\pi$
$4$	−1.68251	−0.841254
$5$	−1.25580	−0.561610	−0.280805	−	0.959765i	$-0.590601\pi$
$5$	−1.25580	−0.561610	−0.280805	+	0.959765i	$0.590601\pi$
$6$	1.16917	0.477312
$7$	1.91459	0.723645	0.361823	−	0.932247i	$-0.382155\pi$
$7$	1.91459	0.723645	0.361823	+	0.932247i	$0.382155\pi$
$8$	2.07496	0.733611
$9$	1.30548	0.435159
$10$	0.707599	0.223762
$11$	0.634356	0.191266	0.0956328	−	0.995417i	$-0.469513\pi$
$11$	0.634356	0.191266	0.0956328	+	0.995417i	$0.469513\pi$
$12$	3.49114	1.00781
$13$	−5.68965	−1.57802	−0.789012	−	0.614377i	$-0.789407\pi$
$13$	−5.68965	−1.57802	−0.789012	+	0.614377i	$0.789407\pi$
$14$	−1.07880	−0.288322
$15$	2.60574	0.672799
$16$	2.19584	0.548961
$17$	−5.78084	−1.40206	−0.701030	−	0.713132i	$-0.747276\pi$
$17$	−5.78084	−1.40206	−0.701030	+	0.713132i	$0.747276\pi$
$18$	−0.735591	−0.173380
$19$	3.28109	0.752734	0.376367	−	0.926471i	$-0.377173\pi$
$19$	3.28109	0.752734	0.376367	+	0.926471i	$0.377173\pi$
$20$	2.11289	0.472457
$21$	−3.97270	−0.866913
$22$	−0.357438	−0.0762060
$23$	9.50494	1.98192	0.990958	−	0.134172i	$-0.0428374\pi$
$23$	9.50494	1.98192	0.990958	+	0.134172i	$0.0428374\pi$
$24$	−4.30548	−0.878852
$25$	−3.42297	−0.684594
$26$	3.20592	0.628732
$27$	3.51608	0.676669
$28$	−3.22130	−0.608769
$29$	4.12807	0.766563	0.383281	−	0.923632i	$-0.374794\pi$
$29$	4.12807	0.766563	0.383281	+	0.923632i	$0.374794\pi$
$30$	−1.46824	−0.268063
$31$	3.12343	0.560984	0.280492	−	0.959856i	$-0.409502\pi$
$31$	3.12343	0.560984	0.280492	+	0.959856i	$0.409502\pi$
$32$	−5.38721	−0.952333
$33$	−1.31627	−0.229133
$34$	3.25730	0.558623
$35$	−2.40433	−0.406407
$36$	−2.19647	−0.366079
$37$	10.6751	1.75497	0.877486	−	0.479603i	$-0.159219\pi$
$37$	10.6751	1.75497	0.877486	+	0.479603i	$0.159219\pi$
$38$	−1.84878	−0.299912
$39$	11.8058	1.89044
$40$	−2.60574	−0.412003
$41$	−2.15325	−0.336282	−0.168141	−	0.985763i	$-0.553776\pi$
$41$	−2.15325	−0.336282	−0.168141	+	0.985763i	$0.553776\pi$
$42$	2.23848	0.345404
$43$	0	0
$43$	0	0
$44$	−1.06731	−0.160903
$45$	−1.63942	−0.244390
$46$	−5.35570	−0.789655
$47$	1.01308	0.147772	0.0738861	−	0.997267i	$-0.476460\pi$
$47$	1.01308	0.147772	0.0738861	+	0.997267i	$0.476460\pi$
$48$	−4.55630	−0.657645
$49$	−3.33436	−0.476338
$50$	1.92872	0.272763
$51$	11.9950	1.67964
$52$	9.57287	1.32752
$53$	2.43788	0.334869	0.167434	−	0.985883i	$-0.446452\pi$
$53$	2.43788	0.334869	0.167434	+	0.985883i	$0.446452\pi$
$54$	−1.98119	−0.269605
$55$	−0.796624	−0.107417
$56$	3.97270	0.530874
$57$	−6.80815	−0.901761
$58$	−2.32602	−0.305422
$59$	1.54924	0.201693	0.100847	−	0.994902i	$-0.467845\pi$
$59$	1.54924	0.201693	0.100847	+	0.994902i	$0.467845\pi$
$60$	−4.38417	−0.565994
$61$	−3.56631	−0.456620	−0.228310	−	0.973589i	$-0.573320\pi$
$61$	−3.56631	−0.456620	−0.228310	+	0.973589i	$0.573320\pi$
$62$	−1.75994	−0.223513
$63$	2.49945	0.314901
$64$	−1.35618	−0.169523
$65$	7.14505	0.886235
$66$	0.741670	0.0912933
$67$	−5.63797	−0.688788	−0.344394	−	0.938825i	$-0.611916\pi$
$67$	−5.63797	−0.688788	−0.344394	+	0.938825i	$0.611916\pi$
$68$	9.72631	1.17949
$69$	−19.7224	−2.37430
$70$	1.35476	0.161925
$71$	−12.9142	−1.53264	−0.766319	−	0.642461i	$-0.777914\pi$
$71$	−12.9142	−1.53264	−0.766319	+	0.642461i	$0.777914\pi$
$72$	2.70882	0.319237
$73$	5.02757	0.588433	0.294217	−	0.955739i	$-0.404941\pi$
$73$	5.02757	0.588433	0.294217	+	0.955739i	$0.404941\pi$
$74$	−6.01503	−0.699233
$75$	7.10254	0.820131
$76$	−5.52046	−0.633240
$77$	1.21453	0.138408
$78$	−6.65217	−0.753210
$79$	8.13626	0.915400	0.457700	−	0.889107i	$-0.348673\pi$
$79$	8.13626	0.915400	0.457700	+	0.889107i	$0.348673\pi$
$80$	−2.75754	−0.308302
$81$	−11.2122	−1.24580
$82$	1.21328	0.133985
$83$	3.15484	0.346288	0.173144	−	0.984897i	$-0.444607\pi$
$83$	3.15484	0.346288	0.173144	+	0.984897i	$0.444607\pi$
$84$	6.68409	0.729294
$85$	7.25957	0.787411
$86$	0	0
$87$	−8.56559	−0.918328
$88$	1.31627	0.140314
$89$	−0.861116	−0.0912781	−0.0456390	−	0.998958i	$-0.514532\pi$
$89$	−0.861116	−0.0912781	−0.0456390	+	0.998958i	$0.514532\pi$
$90$	0.923754	0.0973722
$91$	−10.8933	−1.14193
$92$	−15.9921	−1.66729
$93$	−6.48100	−0.672048
$94$	−0.570833	−0.0588769
$95$	−4.12039	−0.422743
$96$	11.1783	1.14088
$97$	−15.6367	−1.58767	−0.793834	−	0.608135i	$-0.791918\pi$
$97$	−15.6367	−1.58767	−0.793834	+	0.608135i	$0.791918\pi$
$98$	1.87880	0.189787
$99$	0.828137	0.0832309
$100$	5.75917	0.575917
$101$	−11.4425	−1.13857	−0.569286	−	0.822140i	$-0.692780\pi$
$101$	−11.4425	−1.13857	−0.569286	+	0.822140i	$0.692780\pi$
$102$	−6.75879	−0.669220
$103$	−0.697420	−0.0687189	−0.0343594	−	0.999410i	$-0.510939\pi$
$103$	−0.697420	−0.0687189	−0.0343594	+	0.999410i	$0.510939\pi$
$104$	−11.8058	−1.15766
$105$	4.98891	0.486868
$106$	−1.37366	−0.133422
$107$	7.07010	0.683492	0.341746	−	0.939792i	$-0.388982\pi$
$107$	7.07010	0.683492	0.341746	+	0.939792i	$0.388982\pi$
$108$	−5.91582	−0.569250
$109$	−1.79842	−0.172257	−0.0861286	−	0.996284i	$-0.527450\pi$
$109$	−1.79842	−0.172257	−0.0861286	+	0.996284i	$0.527450\pi$
$110$	0.448870	0.0427981
$111$	−22.1504	−2.10242
$112$	4.20413	0.397253
$113$	−11.9556	−1.12469	−0.562344	−	0.826903i	$-0.690100\pi$
$113$	−11.9556	−1.12469	−0.562344	+	0.826903i	$0.690100\pi$
$114$	3.83615	0.359289
$115$	−11.9363	−1.11306
$116$	−6.94550	−0.644874
$117$	−7.42770	−0.686691
$118$	−0.872941	−0.0803607
$119$	−11.0679	−1.01459
$120$	5.40681	0.493572
$121$	−10.5976	−0.963417
$122$	2.00949	0.181931
$123$	4.46792	0.402859
$124$	−5.25519	−0.471930
$125$	10.5776	0.946085
$126$	−1.40835	−0.125466
$127$	9.81007	0.870503	0.435252	−	0.900309i	$-0.356659\pi$
$127$	9.81007	0.870503	0.435252	+	0.900309i	$0.356659\pi$
$128$	11.5386	1.01988
$129$	0	0
$130$	−4.02599	−0.353103
$131$	−16.3144	−1.42540	−0.712699	−	0.701470i	$-0.752528\pi$
$131$	−16.3144	−1.42540	−0.712699	+	0.701470i	$0.752528\pi$
$132$	2.21463	0.192759
$133$	6.28193	0.544712
$134$	3.17680	0.274434
$135$	−4.41548	−0.380024
$136$	−11.9950	−1.02857
$137$	−15.3101	−1.30803	−0.654017	−	0.756480i	$-0.726918\pi$
$137$	−15.3101	−1.30803	−0.654017	+	0.756480i	$0.726918\pi$
$138$	11.1129	0.945992
$139$	−13.0189	−1.10425	−0.552124	−	0.833762i	$-0.686183\pi$
$139$	−13.0189	−1.10425	−0.552124	+	0.833762i	$0.686183\pi$
$140$	4.04531	0.341891
$141$	−2.10210	−0.177028
$142$	7.27672	0.610649
$143$	−3.60926	−0.301822
$144$	2.86662	0.238885
$145$	−5.18402	−0.430510
$146$	−2.83286	−0.234449
$147$	6.91868	0.570643
$148$	−17.9609	−1.47638
$149$	−6.87119	−0.562910	−0.281455	−	0.959574i	$-0.590817\pi$
$149$	−6.87119	−0.562910	−0.281455	+	0.959574i	$0.590817\pi$
$150$	−4.00203	−0.326765
$151$	12.5372	1.02026	0.510132	−	0.860096i	$-0.329596\pi$
$151$	12.5372	1.02026	0.510132	+	0.860096i	$0.329596\pi$
$152$	6.80815	0.552213
$153$	−7.54675	−0.610119
$154$	−0.684345	−0.0551461
$155$	−3.92240	−0.315054
$156$	−19.8634	−1.59034
$157$	4.64464	0.370682	0.185341	−	0.982674i	$-0.440661\pi$
$157$	4.64464	0.370682	0.185341	+	0.982674i	$0.440661\pi$
$158$	−4.58450	−0.364723
$159$	−5.05852	−0.401167
$160$	6.76525	0.534840
$161$	18.1980	1.43420
$162$	6.31766	0.496362
$163$	−5.69669	−0.446199	−0.223099	−	0.974796i	$-0.571617\pi$
$163$	−5.69669	−0.446199	−0.223099	+	0.974796i	$0.571617\pi$
$164$	3.62286	0.282898
$165$	1.65297	0.128683
$166$	−1.77764	−0.137972
$167$	−5.50814	−0.426233	−0.213116	−	0.977027i	$-0.568361\pi$
$167$	−5.50814	−0.426233	−0.213116	+	0.977027i	$0.568361\pi$
$168$	−8.24320	−0.635977
$169$	19.3721	1.49016
$170$	−4.09052	−0.313728
$171$	4.28339	0.327559
$172$	0	0
$173$	−12.0002	−0.912355	−0.456178	−	0.889889i	$-0.650782\pi$
$173$	−12.0002	−0.912355	−0.456178	+	0.889889i	$0.650782\pi$
$174$	4.82641	0.365889
$175$	−6.55357	−0.495403
$176$	1.39295	0.104997
$177$	−3.21461	−0.241625
$178$	0.485209	0.0363679
$179$	14.1631	1.05860	0.529299	−	0.848436i	$-0.322455\pi$
$179$	14.1631	1.05860	0.529299	+	0.848436i	$0.322455\pi$
$180$	2.75833	0.205594
$181$	−8.35239	−0.620828	−0.310414	−	0.950601i	$-0.600468\pi$
$181$	−8.35239	−0.620828	−0.310414	+	0.950601i	$0.600468\pi$
$182$	6.13801	0.454979
$183$	7.39997	0.547022
$184$	19.7224	1.45395
$185$	−13.4057	−0.985610
$186$	3.65182	0.267764
$187$	−3.66711	−0.268166
$188$	−1.70451	−0.124314
$189$	6.73183	0.489668
$190$	2.32170	0.168434
$191$	−4.69247	−0.339535	−0.169768	−	0.985484i	$-0.554302\pi$
$191$	−4.69247	−0.339535	−0.169768	+	0.985484i	$0.554302\pi$
$192$	2.81403	0.203085
$193$	5.59833	0.402976	0.201488	−	0.979491i	$-0.435422\pi$
$193$	5.59833	0.402976	0.201488	+	0.979491i	$0.435422\pi$
$194$	8.81074	0.632574
$195$	−14.8257	−1.06169
$196$	5.61009	0.400721
$197$	13.3380	0.950296	0.475148	−	0.879906i	$-0.342395\pi$
$197$	13.3380	0.950296	0.475148	+	0.879906i	$0.342395\pi$
$198$	−0.466626	−0.0331617
$199$	21.6651	1.53580	0.767898	−	0.640572i	$-0.221303\pi$
$199$	21.6651	1.53580	0.767898	+	0.640572i	$0.221303\pi$
$200$	−7.10254	−0.502225
$201$	11.6986	0.825155
$202$	6.44745	0.453641
$203$	7.90354	0.554720
$204$	−20.1817	−1.41300
$205$	2.70405	0.188859
$206$	0.392972	0.0273797
$207$	12.4085	0.862448
$208$	−12.4936	−0.866274
$209$	2.08138	0.143972
$210$	−2.81108	−0.193983
$211$	−10.1882	−0.701385	−0.350692	−	0.936491i	$-0.614054\pi$
$211$	−10.1882	−0.701385	−0.350692	+	0.936491i	$0.614054\pi$
$212$	−4.10175	−0.281710
$213$	26.7966	1.83607
$214$	−3.98375	−0.272324
$215$	0	0
$216$	7.29573	0.496412
$217$	5.98007	0.405953
$218$	1.01335	0.0686324
$219$	−10.4320	−0.704932
$220$	1.34033	0.0903647
$221$	32.8910	2.21249
$222$	12.4810	0.837668
$223$	9.65168	0.646324	0.323162	−	0.946344i	$-0.395254\pi$
$223$	9.65168	0.646324	0.323162	+	0.946344i	$0.395254\pi$
$224$	−10.3143	−0.689151
$225$	−4.46861	−0.297907
$226$	6.73656	0.448109
$227$	−28.1295	−1.86702	−0.933510	−	0.358553i	$-0.883270\pi$
$227$	−28.1295	−1.86702	−0.933510	+	0.358553i	$0.883270\pi$
$228$	11.4548	0.758610
$229$	6.24141	0.412444	0.206222	−	0.978505i	$-0.433883\pi$
$229$	6.24141	0.412444	0.206222	+	0.978505i	$0.433883\pi$
$230$	6.72568	0.443478
$231$	−2.52010	−0.165811
$232$	8.56559	0.562359
$233$	−17.5410	−1.14915	−0.574574	−	0.818452i	$-0.694832\pi$
$233$	−17.5410	−1.14915	−0.574574	+	0.818452i	$0.694832\pi$
$234$	4.18525	0.273598
$235$	−1.27222	−0.0829904
$236$	−2.60660	−0.169675
$237$	−16.8824	−1.09663
$238$	6.23638	0.404245
$239$	−12.5969	−0.814826	−0.407413	−	0.913244i	$-0.633569\pi$
$239$	−12.5969	−0.814826	−0.407413	+	0.913244i	$0.633569\pi$
$240$	5.72179	0.369340
$241$	13.0691	0.841853	0.420926	−	0.907095i	$-0.361705\pi$
$241$	13.0691	0.841853	0.420926	+	0.907095i	$0.361705\pi$
$242$	5.97137	0.383854
$243$	12.7166	0.815771
$244$	6.00035	0.384133
$245$	4.18729	0.267516
$246$	−2.51752	−0.160511
$247$	−18.6683	−1.18783
$248$	6.48100	0.411544
$249$	−6.54617	−0.414847
$250$	−5.96008	−0.376949
$251$	11.1178	0.701747	0.350873	−	0.936423i	$-0.385885\pi$
$251$	11.1178	0.701747	0.350873	+	0.936423i	$0.385885\pi$
$252$	−4.20534	−0.264911
$253$	6.02952	0.379072
$254$	−5.52763	−0.346835
$255$	−15.0634	−0.943304
$256$	−3.78922	−0.236826
$257$	−19.6332	−1.22469	−0.612344	−	0.790592i	$-0.709773\pi$
$257$	−19.6332	−1.22469	−0.612344	+	0.790592i	$0.709773\pi$
$258$	0	0
$259$	20.4383	1.26998
$260$	−12.0216	−0.745548
$261$	5.38910	0.333577
$262$	9.19261	0.567922
$263$	20.0090	1.23381	0.616905	−	0.787037i	$-0.288386\pi$
$263$	20.0090	1.23381	0.616905	+	0.787037i	$0.288386\pi$
$264$	−2.73121	−0.168094
$265$	−3.06149	−0.188066
$266$	−3.53965	−0.217030
$267$	1.78678	0.109349
$268$	9.48593	0.579445
$269$	−12.7559	−0.777743	−0.388871	−	0.921292i	$-0.627135\pi$
$269$	−12.7559	−0.777743	−0.388871	+	0.921292i	$0.627135\pi$
$270$	2.48797	0.151413
$271$	−23.2586	−1.41286	−0.706430	−	0.707783i	$-0.749696\pi$
$271$	−23.2586	−1.41286	−0.706430	+	0.707783i	$0.749696\pi$
$272$	−12.6938	−0.769676
$273$	22.6032	1.36801
$274$	8.62673	0.521160
$275$	−2.17138	−0.130939
$276$	33.1831	1.99739
$277$	13.8873	0.834404	0.417202	−	0.908814i	$-0.363011\pi$
$277$	13.8873	0.834404	0.417202	+	0.908814i	$0.363011\pi$
$278$	7.33570	0.439966
$279$	4.07756	0.244117
$280$	−4.98891	−0.298144
$281$	−11.6035	−0.692208	−0.346104	−	0.938196i	$-0.612496\pi$
$281$	−11.6035	−0.692208	−0.346104	+	0.938196i	$0.612496\pi$
$282$	1.18446	0.0705334
$283$	2.67279	0.158881	0.0794403	−	0.996840i	$-0.474687\pi$
$283$	2.67279	0.158881	0.0794403	+	0.996840i	$0.474687\pi$
$284$	21.7283	1.28934
$285$	8.54966	0.506438
$286$	2.03369	0.120255
$287$	−4.12259	−0.243349
$288$	−7.03288	−0.414416
$289$	16.4181	0.965772
$290$	2.92102	0.171528
$291$	32.4456	1.90200
$292$	−8.45893	−0.495021
$293$	23.8266	1.39196	0.695982	−	0.718059i	$-0.254969\pi$
$293$	23.8266	1.39196	0.695982	+	0.718059i	$0.254969\pi$
$294$	−3.89844	−0.227361
$295$	−1.94553	−0.113273
$296$	22.1504	1.28747
$297$	2.23044	0.129424
$298$	3.87168	0.224280
$299$	−54.0797	−3.12751
$300$	−11.9501	−0.689938
$301$	0	0
$302$	−7.06429	−0.406504
$303$	23.7428	1.36399
$304$	7.20476	0.413222
$305$	4.47857	0.256442
$306$	4.25233	0.243090
$307$	−5.33565	−0.304521	−0.152261	−	0.988340i	$-0.548655\pi$
$307$	−5.33565	−0.304521	−0.152261	+	0.988340i	$0.548655\pi$
$308$	−2.04345	−0.116437
$309$	1.44712	0.0823239
$310$	2.21013	0.125527
$311$	−23.0284	−1.30582	−0.652911	−	0.757435i	$-0.726452\pi$
$311$	−23.0284	−1.30582	−0.652911	+	0.757435i	$0.726452\pi$
$312$	24.4967	1.38685
$313$	−1.74238	−0.0984852	−0.0492426	−	0.998787i	$-0.515681\pi$
$313$	−1.74238	−0.0984852	−0.0492426	+	0.998787i	$0.515681\pi$
$314$	−2.61709	−0.147691
$315$	−3.13880	−0.176851
$316$	−13.6893	−0.770084
$317$	32.5720	1.82942	0.914712	−	0.404106i	$-0.132417\pi$
$317$	32.5720	1.82942	0.914712	+	0.404106i	$0.132417\pi$
$318$	2.85030	0.159837
$319$	2.61867	0.146617
$320$	1.70309	0.0952058
$321$	−14.6702	−0.818811
$322$	−10.2539	−0.571430
$323$	−18.9675	−1.05538
$324$	18.8645	1.04803
$325$	19.4755	1.08031
$326$	3.20988	0.177779
$327$	3.73165	0.206361
$328$	−4.46792	−0.246700
$329$	1.93962	0.106935
$330$	−0.931389	−0.0512713
$331$	−14.0839	−0.774120	−0.387060	−	0.922055i	$-0.626509\pi$
$331$	−14.0839	−0.774120	−0.387060	+	0.922055i	$0.626509\pi$
$332$	−5.30803	−0.291316
$333$	13.9361	0.763691
$334$	3.10364	0.169824
$335$	7.08016	0.386830
$336$	−8.72342	−0.475902
$337$	−20.3596	−1.10906	−0.554530	−	0.832163i	$-0.687102\pi$
$337$	−20.3596	−1.10906	−0.554530	+	0.832163i	$0.687102\pi$
$338$	−10.9155	−0.593725
$339$	24.8074	1.34735
$340$	−12.2143	−0.662413
$341$	1.98136	0.107297
$342$	−2.41354	−0.130509
$343$	−19.7860	−1.06834
$344$	0	0
$345$	24.7674	1.33343
$346$	6.76167	0.363510
$347$	−13.6840	−0.734597	−0.367299	−	0.930103i	$-0.619717\pi$
$347$	−13.6840	−0.734597	−0.367299	+	0.930103i	$0.619717\pi$
$348$	14.4117	0.772547
$349$	14.7755	0.790917	0.395458	−	0.918484i	$-0.370586\pi$
$349$	14.7755	0.790917	0.395458	+	0.918484i	$0.370586\pi$
$350$	3.69271	0.197383
$351$	−20.0052	−1.06780
$352$	−3.41741	−0.182149
$353$	−26.9956	−1.43683	−0.718414	−	0.695616i	$-0.755132\pi$
$353$	−26.9956	−1.43683	−0.718414	+	0.695616i	$0.755132\pi$
$354$	1.81132	0.0962706
$355$	16.2177	0.860745
$356$	1.44883	0.0767880
$357$	22.9655	1.21546
$358$	−7.98039	−0.421777
$359$	11.7883	0.622165	0.311082	−	0.950383i	$-0.399308\pi$
$359$	11.7883	0.622165	0.311082	+	0.950383i	$0.399308\pi$
$360$	−3.40173	−0.179287
$361$	−8.23445	−0.433392
$362$	4.70628	0.247357
$363$	21.9896	1.15416
$364$	18.3281	0.960653
$365$	−6.31362	−0.330470
$366$	−4.16963	−0.217950
$367$	−25.1670	−1.31371	−0.656853	−	0.754019i	$-0.728113\pi$
$367$	−25.1670	−1.31371	−0.656853	+	0.754019i	$0.728113\pi$
$368$	20.8714	1.08799
$369$	−2.81102	−0.146336
$370$	7.55367	0.392697
$371$	4.66753	0.242326
$372$	10.9043	0.565363
$373$	−14.2790	−0.739337	−0.369668	−	0.929164i	$-0.620529\pi$
$373$	−14.2790	−0.739337	−0.369668	+	0.929164i	$0.620529\pi$
$374$	2.06629	0.106845
$375$	−21.9480	−1.13339
$376$	2.10210	0.108407
$377$	−23.4873	−1.20966
$378$	−3.79315	−0.195099
$379$	9.38475	0.482062	0.241031	−	0.970517i	$-0.422514\pi$
$379$	9.38475	0.482062	0.241031	+	0.970517i	$0.422514\pi$
$380$	6.93258	0.355634
$381$	−20.3555	−1.04285
$382$	2.64404	0.135281
$383$	−7.68512	−0.392691	−0.196346	−	0.980535i	$-0.562907\pi$
$383$	−7.68512	−0.392691	−0.196346	+	0.980535i	$0.562907\pi$
$384$	−23.9421	−1.22179
$385$	−1.52520	−0.0777316
$386$	−3.15446	−0.160558
$387$	0	0
$388$	26.3089	1.33563
$389$	21.1580	1.07275	0.536376	−	0.843979i	$-0.319793\pi$
$389$	21.1580	1.07275	0.536376	+	0.843979i	$0.319793\pi$
$390$	8.35378	0.423010
$391$	−54.9465	−2.77877
$392$	−6.91868	−0.349446
$393$	33.8519	1.70760
$394$	−7.51552	−0.378626
$395$	−10.2175	−0.514098
$396$	−1.39335	−0.0700183
$397$	15.0722	0.756454	0.378227	−	0.925713i	$-0.376534\pi$
$397$	15.0722	0.756454	0.378227	+	0.925713i	$0.376534\pi$
$398$	−12.2075	−0.611907
$399$	−13.0348	−0.652555
$400$	−7.51631	−0.375815
$401$	2.77241	0.138447	0.0692237	−	0.997601i	$-0.477948\pi$
$401$	2.77241	0.138447	0.0692237	+	0.997601i	$0.477948\pi$
$402$	−6.59175	−0.328766
$403$	−17.7712	−0.885246
$404$	19.2521	0.957827
$405$	14.0802	0.699652
$406$	−4.45337	−0.221017
$407$	6.77180	0.335666
$408$	24.8893	1.23220
$409$	−19.1827	−0.948523	−0.474261	−	0.880384i	$-0.657285\pi$
$409$	−19.1827	−0.948523	−0.474261	+	0.880384i	$0.657285\pi$
$410$	−1.52364	−0.0752472
$411$	31.7680	1.56700
$412$	1.17341	0.0578100
$413$	2.96615	0.145955
$414$	−6.99174	−0.343625
$415$	−3.96184	−0.194479
$416$	30.6513	1.50281
$417$	27.0138	1.32287
$418$	−1.17279	−0.0573628
$419$	0.575111	0.0280960	0.0140480	−	0.999901i	$-0.495528\pi$
$419$	0.575111	0.0280960	0.0140480	+	0.999901i	$0.495528\pi$
$420$	−8.39387	−0.409579
$421$	7.75469	0.377940	0.188970	−	0.981983i	$-0.439485\pi$
$421$	7.75469	0.377940	0.188970	+	0.981983i	$0.439485\pi$
$422$	5.74070	0.279453
$423$	1.32255	0.0643044
$424$	5.05852	0.245663
$425$	19.7876	0.959842
$426$	−15.0989	−0.731546
$427$	−6.82801	−0.330431
$428$	−11.8955	−0.574990
$429$	7.48909	0.361577
$430$	0	0
$431$	−30.8493	−1.48596	−0.742980	−	0.669314i	$-0.766588\pi$
$431$	−30.8493	−1.48596	−0.742980	+	0.669314i	$0.766588\pi$
$432$	7.72075	0.371465
$433$	19.4062	0.932602	0.466301	−	0.884626i	$-0.345586\pi$
$433$	19.4062	0.932602	0.466301	+	0.884626i	$0.345586\pi$
$434$	−3.36956	−0.161744
$435$	10.7567	0.515742
$436$	3.02585	0.144912
$437$	31.1866	1.49186
$438$	5.87809	0.280866
$439$	12.8683	0.614170	0.307085	−	0.951682i	$-0.400646\pi$
$439$	12.8683	0.614170	0.307085	+	0.951682i	$0.400646\pi$
$440$	−1.65297	−0.0788021
$441$	−4.35293	−0.207283
$442$	−18.5329	−0.881521
$443$	2.87049	0.136381	0.0681906	−	0.997672i	$-0.478277\pi$
$443$	2.87049	0.136381	0.0681906	+	0.997672i	$0.478277\pi$
$444$	37.2682	1.76867
$445$	1.08139	0.0512627
$446$	−5.43838	−0.257515
$447$	14.2575	0.674356
$448$	−2.59653	−0.122674
$449$	−18.3534	−0.866150	−0.433075	−	0.901358i	$-0.642572\pi$
$449$	−18.3534	−0.866150	−0.433075	+	0.901358i	$0.642572\pi$
$450$	2.51790	0.118695
$451$	−1.36593	−0.0643191
$452$	20.1154	0.946148
$453$	−26.0143	−1.22226
$454$	15.8500	0.743876
$455$	13.6798	0.641320
$456$	−14.1267	−0.661541
$457$	30.4630	1.42500	0.712500	−	0.701672i	$-0.247563\pi$
$457$	30.4630	1.42500	0.712500	+	0.701672i	$0.247563\pi$
$458$	−3.51682	−0.164330
$459$	−20.3259	−0.948731
$460$	20.0829	0.936370
$461$	−13.6332	−0.634961	−0.317480	−	0.948265i	$-0.602837\pi$
$461$	−13.6332	−0.634961	−0.317480	+	0.948265i	$0.602837\pi$
$462$	1.41999	0.0660640
$463$	4.57394	0.212569	0.106285	−	0.994336i	$-0.466105\pi$
$463$	4.57394	0.212569	0.106285	+	0.994336i	$0.466105\pi$
$464$	9.06459	0.420813
$465$	8.13883	0.377429
$466$	9.88374	0.457855
$467$	−32.0492	−1.48306	−0.741530	−	0.670920i	$-0.765900\pi$
$467$	−32.0492	−1.48306	−0.741530	+	0.670920i	$0.765900\pi$
$468$	12.4972	0.577682
$469$	−10.7944	−0.498438
$470$	0.716851	0.0330659
$471$	−9.63746	−0.444071
$472$	3.21461	0.147964
$473$	0	0
$474$	9.51267	0.436931
$475$	−11.2311	−0.515317
$476$	18.6218	0.853531
$477$	3.18260	0.145721
$478$	7.09792	0.324651
$479$	−30.6305	−1.39954	−0.699771	−	0.714367i	$-0.746715\pi$
$479$	−30.6305	−1.39954	−0.699771	+	0.714367i	$0.746715\pi$
$480$	−14.0377	−0.640728
$481$	−60.7374	−2.76939
$482$	−7.36396	−0.335419
$483$	−37.7602	−1.71815
$484$	17.8305	0.810478
$485$	19.6366	0.891651
$486$	−7.16536	−0.325028
$487$	13.6789	0.619852	0.309926	−	0.950761i	$-0.399696\pi$
$487$	13.6789	0.619852	0.309926	+	0.950761i	$0.399696\pi$
$488$	−7.39997	−0.334981
$489$	11.8204	0.534538
$490$	−2.35939	−0.106586
$491$	−4.72280	−0.213137	−0.106569	−	0.994305i	$-0.533986\pi$
$491$	−4.72280	−0.213137	−0.106569	+	0.994305i	$0.533986\pi$
$492$	−7.51731	−0.338907
$493$	−23.8637	−1.07477
$494$	10.5189	0.473268
$495$	−1.03997	−0.0467434
$496$	6.85856	0.307958
$497$	−24.7254	−1.10909
$498$	3.68854	0.165287
$499$	−22.2197	−0.994691	−0.497345	−	0.867553i	$-0.665692\pi$
$499$	−22.2197	−0.994691	−0.497345	+	0.867553i	$0.665692\pi$
$500$	−17.7968	−0.795898
$501$	11.4292	0.510619
$502$	−6.26447	−0.279597
$503$	−5.99796	−0.267436	−0.133718	−	0.991019i	$-0.542692\pi$
$503$	−5.99796	−0.267436	−0.133718	+	0.991019i	$0.542692\pi$
$504$	5.18626	0.231014
$505$	14.3695	0.639433
$506$	−3.39742	−0.151034
$507$	−40.1964	−1.78519
$508$	−16.5055	−0.732314
$509$	−7.51237	−0.332980	−0.166490	−	0.986043i	$-0.553243\pi$
$509$	−7.51237	−0.332980	−0.166490	+	0.986043i	$0.553243\pi$
$510$	8.48768	0.375841
$511$	9.62572	0.425817
$512$	−20.9421	−0.925517
$513$	11.5366	0.509352
$514$	11.0626	0.487952
$515$	0.875820	0.0385932
$516$	0	0
$517$	0.642651	0.0282638
$518$	−11.5163	−0.505997
$519$	24.8999	1.09298
$520$	14.8257	0.650151
$521$	−10.2926	−0.450925	−0.225462	−	0.974252i	$-0.572389\pi$
$521$	−10.2926	−0.450925	−0.225462	+	0.974252i	$0.572389\pi$
$522$	−3.03657	−0.132907
$523$	11.3478	0.496206	0.248103	−	0.968734i	$-0.420193\pi$
$523$	11.3478	0.496206	0.248103	+	0.968734i	$0.420193\pi$
$524$	27.4491	1.19912
$525$	13.5984	0.593484
$526$	−11.2744	−0.491587
$527$	−18.0560	−0.786533
$528$	−2.89032	−0.125785
$529$	67.3438	2.92799
$530$	1.72504	0.0749311
$531$	2.02249	0.0877687
$532$	−10.5694	−0.458241
$533$	12.2513	0.530661
$534$	−1.00679	−0.0435681
$535$	−8.87862	−0.383856
$536$	−11.6986	−0.505302
$537$	−29.3879	−1.26818
$538$	7.18752	0.309876
$539$	−2.11517	−0.0911070
$540$	7.42908	0.319697
$541$	−26.7275	−1.14911	−0.574553	−	0.818467i	$-0.694824\pi$
$541$	−26.7275	−1.14911	−0.574553	+	0.818467i	$0.694824\pi$
$542$	13.1054	0.562926
$543$	17.3309	0.743740
$544$	31.1426	1.33523
$545$	2.25845	0.0967414
$546$	−12.7361	−0.545057
$547$	30.6376	1.30997	0.654984	−	0.755643i	$-0.272676\pi$
$547$	30.6376	1.30997	0.654984	+	0.755643i	$0.272676\pi$
$548$	25.7594	1.10039
$549$	−4.65574	−0.198702
$550$	1.22350	0.0521701
$551$	13.5446	0.577018
$552$	−40.9233	−1.74181
$553$	15.5776	0.662425
$554$	−7.82499	−0.332452
$555$	27.8164	1.18074
$556$	21.9044	0.928953
$557$	−14.3011	−0.605955	−0.302978	−	0.952998i	$-0.597981\pi$
$557$	−14.3011	−0.605955	−0.302978	+	0.952998i	$0.597981\pi$
$558$	−2.29756	−0.0972636
$559$	0	0
$560$	−5.27954	−0.223101
$561$	7.60913	0.321258
$562$	6.53818	0.275797
$563$	24.6057	1.03701	0.518503	−	0.855076i	$-0.326490\pi$
$563$	24.6057	1.03701	0.518503	+	0.855076i	$0.326490\pi$
$564$	3.53679	0.148926
$565$	15.0138	0.631636
$566$	−1.50602	−0.0633028
$567$	−21.4666	−0.901514
$568$	−26.7966	−1.12436
$569$	0.00221871	9.30130e−5 0	4.65065e−5	−	1.00000i	$-0.499985\pi$
$569$	0.00221871	9.30130e−5 0	4.65065e−5		1.00000i	$0.499985\pi$
$570$	−4.81744	−0.201780
$571$	17.1054	0.715837	0.357919	−	0.933753i	$-0.383487\pi$
$571$	17.1054	0.715837	0.357919	+	0.933753i	$0.383487\pi$
$572$	6.07261	0.253909
$573$	9.73670	0.406757
$574$	2.32293	0.0969574
$575$	−32.5351	−1.35681
$576$	−1.77047	−0.0737694
$577$	7.99163	0.332696	0.166348	−	0.986067i	$-0.446803\pi$
$577$	7.99163	0.332696	0.166348	+	0.986067i	$0.446803\pi$
$578$	−9.25104	−0.384793
$579$	−11.6163	−0.482758
$580$	8.72216	0.362168
$581$	6.04020	0.250590
$582$	−18.2820	−0.757812
$583$	1.54649	0.0640489
$584$	10.4320	0.431681
$585$	9.32770	0.385653
$586$	−13.4254	−0.554600
$587$	39.0328	1.61106	0.805529	−	0.592557i	$-0.201881\pi$
$587$	39.0328	1.61106	0.805529	+	0.592557i	$0.201881\pi$
$588$	−11.6407	−0.480056
$589$	10.2482	0.422272
$590$	1.09624	0.0451314
$591$	−27.6759	−1.13844
$592$	23.4408	0.963411
$593$	22.5910	0.927700	0.463850	−	0.885914i	$-0.346468\pi$
$593$	22.5910	0.927700	0.463850	+	0.885914i	$0.346468\pi$
$594$	−1.25678	−0.0515662
$595$	13.8991	0.569807
$596$	11.5608	0.473550
$597$	−44.9542	−1.83985
$598$	30.4721	1.24609
$599$	−28.3674	−1.15906	−0.579529	−	0.814951i	$-0.696764\pi$
$599$	−28.3674	−1.15906	−0.579529	+	0.814951i	$0.696764\pi$
$600$	14.7375	0.601656
$601$	12.7606	0.520517	0.260259	−	0.965539i	$-0.416192\pi$
$601$	12.7606	0.520517	0.260259	+	0.965539i	$0.416192\pi$
$602$	0	0
$603$	−7.36024	−0.299732
$604$	−21.0940	−0.858301
$605$	13.3084	0.541065
$606$	−13.3782	−0.543453
$607$	20.7954	0.844058	0.422029	−	0.906582i	$-0.361318\pi$
$607$	20.7954	0.844058	0.422029	+	0.906582i	$0.361318\pi$
$608$	−17.6759	−0.716853
$609$	−16.3996	−0.664544
$610$	−2.52352	−0.102174
$611$	−5.76404	−0.233188
$612$	12.6975	0.513265
$613$	−22.2261	−0.897704	−0.448852	−	0.893606i	$-0.648167\pi$
$613$	−22.2261	−0.897704	−0.448852	+	0.893606i	$0.648167\pi$
$614$	3.00645	0.121330
$615$	−5.61081	−0.226250
$616$	2.52010	0.101538
$617$	−18.1174	−0.729379	−0.364689	−	0.931129i	$-0.618825\pi$
$617$	−18.1174	−0.729379	−0.364689	+	0.931129i	$0.618825\pi$
$618$	−0.815403	−0.0328003
$619$	1.85051	0.0743785	0.0371892	−	0.999308i	$-0.488160\pi$
$619$	1.85051	0.0743785	0.0371892	+	0.999308i	$0.488160\pi$
$620$	6.59946	0.265041
$621$	33.4201	1.34110
$622$	12.9757	0.520279
$623$	−1.64868	−0.0660530
$624$	25.9237	1.03778
$625$	3.83156	0.153263
$626$	0.981771	0.0392395
$627$	−4.31879	−0.172476
$628$	−7.81464	−0.311838
$629$	−61.7109	−2.46058
$630$	1.76861	0.0704629
$631$	−19.4877	−0.775793	−0.387896	−	0.921703i	$-0.626798\pi$
$631$	−19.4877	−0.775793	−0.387896	+	0.921703i	$0.626798\pi$
$632$	16.8824	0.671547
$633$	21.1402	0.840246
$634$	−18.3532	−0.728897
$635$	−12.3195	−0.488884
$636$	8.51099	0.337483
$637$	18.9714	0.751672
$638$	−1.47553	−0.0584167
$639$	−16.8592	−0.666941
$640$	−14.4901	−0.572773
$641$	−41.1921	−1.62699	−0.813496	−	0.581571i	$-0.802438\pi$
$641$	−41.1921	−1.62699	−0.813496	+	0.581571i	$0.802438\pi$
$642$	8.26615	0.326239
$643$	39.7276	1.56670	0.783352	−	0.621578i	$-0.213508\pi$
$643$	39.7276	1.56670	0.783352	+	0.621578i	$0.213508\pi$
$644$	−30.6183	−1.20653
$645$	0	0
$646$	10.6875	0.420494
$647$	−15.7885	−0.620711	−0.310356	−	0.950621i	$-0.600448\pi$
$647$	−15.7885	−0.620711	−0.310356	+	0.950621i	$0.600448\pi$
$648$	−23.2648	−0.913929
$649$	0.982768	0.0385770
$650$	−10.9738	−0.430426
$651$	−12.4084	−0.486324
$652$	9.58471	0.375366
$653$	4.71375	0.184463	0.0922316	−	0.995738i	$-0.470600\pi$
$653$	4.71375	0.184463	0.0922316	+	0.995738i	$0.470600\pi$
$654$	−2.10266	−0.0822203
$655$	20.4876	0.800518
$656$	−4.72821	−0.184605
$657$	6.56338	0.256062
$658$	−1.09291	−0.0426060
$659$	−21.6336	−0.842724	−0.421362	−	0.906893i	$-0.638448\pi$
$659$	−21.6336	−0.842724	−0.421362	+	0.906893i	$0.638448\pi$
$660$	−2.78113	−0.108255
$661$	12.2966	0.478283	0.239142	−	0.970985i	$-0.423134\pi$
$661$	12.2966	0.478283	0.239142	+	0.970985i	$0.423134\pi$
$662$	7.93577	0.308432
$663$	−68.2476	−2.65052
$664$	6.54617	0.254041
$665$	−7.88884	−0.305916
$666$	−7.85248	−0.304278
$667$	39.2370	1.51926
$668$	9.26748	0.358570
$669$	−20.0269	−0.774284
$670$	−3.98942	−0.154125
$671$	−2.26231	−0.0873356
$672$	21.4017	0.825590
$673$	−36.4097	−1.40349	−0.701745	−	0.712428i	$-0.747596\pi$
$673$	−36.4097	−1.40349	−0.701745	+	0.712428i	$0.747596\pi$
$674$	11.4720	0.441883
$675$	−12.0354	−0.463243
$676$	−32.5937	−1.25360
$677$	8.71539	0.334960	0.167480	−	0.985876i	$-0.446437\pi$
$677$	8.71539	0.334960	0.167480	+	0.985876i	$0.446437\pi$
$678$	−13.9781	−0.536827
$679$	−29.9378	−1.14891
$680$	15.0634	0.577653
$681$	58.3677	2.23665
$682$	−1.11643	−0.0427503
$683$	17.6293	0.674565	0.337282	−	0.941403i	$-0.390492\pi$
$683$	17.6293	0.674565	0.337282	+	0.941403i	$0.390492\pi$
$684$	−7.20683	−0.275560
$685$	19.2265	0.734605
$686$	11.1487	0.425661
$687$	−12.9507	−0.494100
$688$	0	0
$689$	−13.8707	−0.528431
$690$	−13.9555	−0.531279
$691$	−31.9988	−1.21729	−0.608645	−	0.793443i	$-0.708287\pi$
$691$	−31.9988	−1.21729	−0.608645	+	0.793443i	$0.708287\pi$
$692$	20.1904	0.767522
$693$	1.58554	0.0602297
$694$	7.71047	0.292686
$695$	16.3491	0.620158
$696$	−17.7733	−0.673695
$697$	12.4476	0.471487
$698$	−8.32550	−0.315125
$699$	36.3969	1.37666
$700$	11.0264	0.416760
$701$	−38.1378	−1.44045	−0.720223	−	0.693743i	$-0.755961\pi$
$701$	−38.1378	−1.44045	−0.720223	+	0.693743i	$0.755961\pi$
$702$	11.2723	0.425444
$703$	35.0259	1.32103
$704$	−0.860303	−0.0324239
$705$	2.63981	0.0994210
$706$	15.2111	0.572476
$707$	−21.9076	−0.823922
$708$	5.40861	0.203268
$709$	15.0765	0.566212	0.283106	−	0.959089i	$-0.408635\pi$
$709$	15.0765	0.566212	0.283106	+	0.959089i	$0.408635\pi$
$710$	−9.13810	−0.342947
$711$	10.6217	0.398345
$712$	−1.78678	−0.0669626
$713$	29.6880	1.11182
$714$	−12.9403	−0.484278
$715$	4.53251	0.169506
$716$	−23.8295	−0.890549
$717$	26.1381	0.976146
$718$	−6.64232	−0.247889
$719$	6.43610	0.240026	0.120013	−	0.992772i	$-0.461706\pi$
$719$	6.43610	0.240026	0.120013	+	0.992772i	$0.461706\pi$
$720$	−3.59990	−0.134160
$721$	−1.33527	−0.0497281
$722$	4.63982	0.172676
$723$	−27.1179	−1.00852
$724$	14.0530	0.522274
$725$	−14.1302	−0.524784
$726$	−12.3904	−0.459850
$727$	23.3433	0.865754	0.432877	−	0.901453i	$-0.357498\pi$
$727$	23.3433	0.865754	0.432877	+	0.901453i	$0.357498\pi$
$728$	−22.6032	−0.837732
$729$	7.24998	0.268518
$730$	3.55751	0.131669
$731$	0	0
$732$	−12.4505	−0.460184
$733$	34.2172	1.26384	0.631921	−	0.775033i	$-0.282267\pi$
$733$	34.2172	1.26384	0.631921	+	0.775033i	$0.282267\pi$
$734$	14.1807	0.523420
$735$	−8.68848	−0.320479
$736$	−51.2051	−1.88744
$737$	−3.57648	−0.131741
$738$	1.58391	0.0583046
$739$	47.8055	1.75855	0.879277	−	0.476310i	$-0.158026\pi$
$739$	47.8055	1.75855	0.879277	+	0.476310i	$0.158026\pi$
$740$	22.5553	0.829148
$741$	38.7360	1.42300
$742$	−2.62999	−0.0965501
$743$	11.1786	0.410102	0.205051	−	0.978751i	$-0.434264\pi$
$743$	11.1786	0.410102	0.205051	+	0.978751i	$0.434264\pi$
$744$	−13.4478	−0.493022
$745$	8.62884	0.316136
$746$	8.04570	0.294574
$747$	4.11856	0.150690
$748$	6.16994	0.225595
$749$	13.5363	0.494606
$750$	12.3670	0.451578
$751$	−18.6023	−0.678808	−0.339404	−	0.940641i	$-0.610225\pi$
$751$	−18.6023	−0.678808	−0.339404	+	0.940641i	$0.610225\pi$
$752$	2.22456	0.0811212
$753$	−23.0690	−0.840679
$754$	13.2342	0.481963
$755$	−15.7442	−0.572991
$756$	−11.3263	−0.411935
$757$	−12.9317	−0.470011	−0.235006	−	0.971994i	$-0.575511\pi$
$757$	−12.9317	−0.470011	−0.235006	+	0.971994i	$0.575511\pi$
$758$	−5.28798	−0.192068
$759$	−12.5110	−0.454122
$760$	−8.54966	−0.310129
$761$	−31.3101	−1.13499	−0.567495	−	0.823377i	$-0.692087\pi$
$761$	−31.3101	−1.13499	−0.567495	+	0.823377i	$0.692087\pi$
$762$	11.4696	0.415501
$763$	−3.44322	−0.124653
$764$	7.89511	0.285635
$765$	9.47720	0.342649
$766$	4.33030	0.156460
$767$	−8.81461	−0.318277
$768$	7.86250	0.283714
$769$	−33.2208	−1.19797	−0.598987	−	0.800759i	$-0.704430\pi$
$769$	−33.2208	−1.19797	−0.598987	+	0.800759i	$0.704430\pi$
$770$	0.859399	0.0309706
$771$	40.7383	1.46715
$772$	−9.41923	−0.339005
$773$	15.9707	0.574425	0.287212	−	0.957867i	$-0.407271\pi$
$773$	15.9707	0.574425	0.287212	+	0.957867i	$0.407271\pi$
$774$	0	0
$775$	−10.6914	−0.384046
$776$	−32.4456	−1.16473
$777$	−42.4088	−1.52141
$778$	−11.9218	−0.427416
$779$	−7.06502	−0.253131
$780$	24.9444	0.893153
$781$	−8.19222	−0.293141
$782$	30.9605	1.10714
$783$	14.5146	0.518709
$784$	−7.32174	−0.261491
$785$	−5.83273	−0.208179
$786$	−19.0743	−0.680359
$787$	−10.8741	−0.387620	−0.193810	−	0.981039i	$-0.562084\pi$
$787$	−10.8741	−0.387620	−0.193810	+	0.981039i	$0.562084\pi$
$788$	−22.4413	−0.799439
$789$	−41.5181	−1.47808
$790$	5.75721	0.204832
$791$	−22.8900	−0.813875
$792$	1.71836	0.0610591
$793$	20.2911	0.720557
$794$	−8.49269	−0.301394
$795$	6.35248	0.225299
$796$	−36.4516	−1.29199
$797$	16.2345	0.575056	0.287528	−	0.957772i	$-0.407167\pi$
$797$	16.2345	0.575056	0.287528	+	0.957772i	$0.407167\pi$
$798$	7.34464	0.259997
$799$	−5.85643	−0.207186
$800$	18.4403	0.651961
$801$	−1.12417	−0.0397205
$802$	−1.56215	−0.0551616
$803$	3.18927	0.112547
$804$	−19.6830	−0.694164
$805$	−22.8530	−0.805464
$806$	10.0135	0.352709
$807$	26.4681	0.931721
$808$	−23.7428	−0.835268
$809$	−28.3771	−0.997687	−0.498843	−	0.866692i	$-0.666242\pi$
$809$	−28.3771	−0.997687	−0.498843	+	0.866692i	$0.666242\pi$
$810$	−7.93371	−0.278762
$811$	10.5723	0.371242	0.185621	−	0.982621i	$-0.440570\pi$
$811$	10.5723	0.371242	0.185621	+	0.982621i	$0.440570\pi$
$812$	−13.2978	−0.466660
$813$	48.2608	1.69258
$814$	−3.81567	−0.133739
$815$	7.15389	0.250590
$816$	26.3392	0.922058
$817$	0	0
$818$	10.8088	0.377920
$819$	−14.2210	−0.496921
$820$	−4.54959	−0.158878
$821$	−0.785288	−0.0274067	−0.0137034	−	0.999906i	$-0.504362\pi$
$821$	−0.785288	−0.0274067	−0.0137034	+	0.999906i	$0.504362\pi$
$822$	−17.9002	−0.624340
$823$	11.3968	0.397267	0.198634	−	0.980074i	$-0.436350\pi$
$823$	11.3968	0.397267	0.198634	+	0.980074i	$0.436350\pi$
$824$	−1.44712	−0.0504129
$825$	4.50554	0.156863
$826$	−1.67132	−0.0581527
$827$	−17.9989	−0.625885	−0.312942	−	0.949772i	$-0.601315\pi$
$827$	−17.9989	−0.625885	−0.312942	+	0.949772i	$0.601315\pi$
$828$	−20.8773	−0.725538
$829$	−17.4920	−0.607523	−0.303762	−	0.952748i	$-0.598243\pi$
$829$	−17.4920	−0.607523	−0.303762	+	0.952748i	$0.598243\pi$
$830$	2.23236	0.0774863
$831$	−28.8156	−0.999601
$832$	7.71621	0.267511
$833$	19.2754	0.667854
$834$	−15.2213	−0.527071
$835$	6.91712	0.239377
$836$	−3.50194	−0.121117
$837$	10.9822	0.379600
$838$	−0.324055	−0.0111943
$839$	5.28064	0.182308	0.0911539	−	0.995837i	$-0.470944\pi$
$839$	5.28064	0.182308	0.0911539	+	0.995837i	$0.470944\pi$
$840$	10.3518	0.357171
$841$	−11.9591	−0.412381
$842$	−4.36950	−0.150583
$843$	24.0769	0.829253
$844$	17.1417	0.590042
$845$	−24.3275	−0.836890
$846$	−0.745209	−0.0256208
$847$	−20.2900	−0.697172
$848$	5.35321	0.183830
$849$	−5.54594	−0.190336
$850$	−11.1496	−0.382430
$851$	101.466	3.47821
$852$	−45.0854	−1.54460
$853$	−44.8997	−1.53734	−0.768668	−	0.639648i	$-0.779080\pi$
$853$	−44.8997	−1.53734	−0.768668	+	0.639648i	$0.779080\pi$
$854$	3.84735	0.131653
$855$	−5.37907	−0.183960
$856$	14.6702	0.501417
$857$	−27.8117	−0.950028	−0.475014	−	0.879978i	$-0.657557\pi$
$857$	−27.8117	−0.950028	−0.475014	+	0.879978i	$0.657557\pi$
$858$	−4.21984	−0.144063
$859$	30.8667	1.05316	0.526579	−	0.850126i	$-0.323474\pi$
$859$	30.8667	1.05316	0.526579	+	0.850126i	$0.323474\pi$
$860$	0	0
$861$	8.55422	0.291527
$862$	17.3825	0.592051
$863$	−31.3545	−1.06732	−0.533661	−	0.845699i	$-0.679184\pi$
$863$	−31.3545	−1.06732	−0.533661	+	0.845699i	$0.679184\pi$
$864$	−18.9418	−0.644414
$865$	15.0698	0.512388
$866$	−10.9347	−0.371577
$867$	−34.0670	−1.15698
$868$	−10.0615	−0.341510
$869$	5.16128	0.175085
$870$	−6.06100	−0.205487
$871$	32.0781	1.08692
$872$	−3.73165	−0.126370
$873$	−20.4134	−0.690888
$874$	−17.5725	−0.594400
$875$	20.2516	0.684630
$876$	17.5520	0.593026
$877$	−54.2804	−1.83292	−0.916460	−	0.400127i	$-0.868966\pi$
$877$	−54.2804	−1.83292	−0.916460	+	0.400127i	$0.868966\pi$
$878$	−7.25083	−0.244704
$879$	−49.4393	−1.66755
$880$	−1.74926	−0.0589676
$881$	−38.8494	−1.30887	−0.654435	−	0.756118i	$-0.727093\pi$
$881$	−38.8494	−1.30887	−0.654435	+	0.756118i	$0.727093\pi$
$882$	2.45273	0.0825876
$883$	18.1383	0.610402	0.305201	−	0.952288i	$-0.401276\pi$
$883$	18.1383	0.610402	0.305201	+	0.952288i	$0.401276\pi$
$884$	−55.3393	−1.86126
$885$	4.03691	0.135699
$886$	−1.61742	−0.0543383
$887$	15.1762	0.509567	0.254783	−	0.966998i	$-0.417996\pi$
$887$	15.1762	0.509567	0.254783	+	0.966998i	$0.417996\pi$
$888$	−45.9613	−1.54236
$889$	18.7822	0.629935
$890$	−0.609325	−0.0204246
$891$	−7.11250	−0.238278
$892$	−16.2390	−0.543722
$893$	3.32399	0.111233
$894$	−8.03359	−0.268683
$895$	−17.7860	−0.594519
$896$	22.0916	0.738029
$897$	112.214	3.74670
$898$	10.3415	0.345100
$899$	12.8937	0.430029
$900$	7.51846	0.250615
$901$	−14.0930	−0.469506
$902$	0.769654	0.0256267
$903$	0	0
$904$	−24.8074	−0.825083
$905$	10.4889	0.348664
$906$	14.6581	0.486984
$907$	30.5772	1.01530	0.507650	−	0.861563i	$-0.330514\pi$
$907$	30.5772	1.01530	0.507650	+	0.861563i	$0.330514\pi$
$908$	47.3280	1.57064
$909$	−14.9379	−0.495459
$910$	−7.70810	−0.255521
$911$	28.9994	0.960792	0.480396	−	0.877052i	$-0.340493\pi$
$911$	28.9994	0.960792	0.480396	+	0.877052i	$0.340493\pi$
$912$	−14.9496	−0.495032
$913$	2.00129	0.0662330
$914$	−17.1648	−0.567762
$915$	−9.29288	−0.307213
$916$	−10.5012	−0.346970
$917$	−31.2354	−1.03148
$918$	11.4529	0.378003
$919$	−19.1384	−0.631317	−0.315658	−	0.948873i	$-0.602225\pi$
$919$	−19.1384	−0.631317	−0.315658	+	0.948873i	$0.602225\pi$
$920$	−24.7674	−0.816556
$921$	11.0713	0.364811
$922$	7.68183	0.252987
$923$	73.4774	2.41854
$924$	4.24009	0.139489
$925$	−36.5405	−1.20144
$926$	−2.57726	−0.0846939
$927$	−0.910466	−0.0299036
$928$	−22.2388	−0.730023
$929$	−13.2547	−0.434873	−0.217437	−	0.976074i	$-0.569770\pi$
$929$	−13.2547	−0.434873	−0.217437	+	0.976074i	$0.569770\pi$
$930$	−4.58595	−0.150379
$931$	−10.9403	−0.358555
$932$	29.5128	0.966726
$933$	47.7831	1.56435
$934$	18.0586	0.590896
$935$	4.60516	0.150605
$936$	−15.4122	−0.503764
$937$	−34.7757	−1.13607	−0.568037	−	0.823003i	$-0.692297\pi$
$937$	−34.7757	−1.13607	−0.568037	+	0.823003i	$0.692297\pi$
$938$	6.08226	0.198593
$939$	3.61538	0.117983
$940$	2.14052	0.0698160
$941$	35.2449	1.14895	0.574475	−	0.818522i	$-0.305206\pi$
$941$	35.2449	1.14895	0.574475	+	0.818522i	$0.305206\pi$
$942$	5.43037	0.176931
$943$	−20.4665	−0.666482
$944$	3.40188	0.110722
$945$	−8.45382	−0.275003
$946$	0	0
$947$	−49.1252	−1.59635	−0.798177	−	0.602424i	$-0.794202\pi$
$947$	−49.1252	−1.59635	−0.798177	+	0.602424i	$0.794202\pi$
$948$	28.4048	0.922546
$949$	−28.6051	−0.928562
$950$	6.32832	0.205318
$951$	−67.5857	−2.19162
$952$	−22.9655	−0.744317
$953$	34.1506	1.10625	0.553123	−	0.833099i	$-0.313436\pi$
$953$	34.1506	1.10625	0.553123	+	0.833099i	$0.313436\pi$
$954$	−1.79328	−0.0580597
$955$	5.89280	0.190686
$956$	21.1944	0.685475
$957$	−5.43364	−0.175645
$958$	17.2592	0.557620
$959$	−29.3126	−0.946553
$960$	−3.53386	−0.114055
$961$	−21.2442	−0.685297
$962$	34.2234	1.10341
$963$	9.22985	0.297428
$964$	−21.9888	−0.708212
$965$	−7.03037	−0.226316
$966$	21.2766	0.684562
$967$	−8.62632	−0.277404	−0.138702	−	0.990334i	$-0.544293\pi$
$967$	−8.62632	−0.277404	−0.138702	+	0.990334i	$0.544293\pi$
$968$	−21.9896	−0.706773
$969$	39.3568	1.26432
$970$	−11.0645	−0.355260
$971$	−49.0762	−1.57493	−0.787465	−	0.616359i	$-0.788607\pi$
$971$	−49.0762	−1.57493	−0.787465	+	0.616359i	$0.788607\pi$
$972$	−21.3958	−0.686270
$973$	−24.9258	−0.799084
$974$	−7.70761	−0.246968
$975$	−40.4110	−1.29419
$976$	−7.83107	−0.250666
$977$	−46.6369	−1.49205	−0.746023	−	0.665921i	$-0.768039\pi$
$977$	−46.6369	−1.49205	−0.746023	+	0.665921i	$0.768039\pi$
$978$	−6.66039	−0.212976
$979$	−0.546254	−0.0174584
$980$	−7.04514	−0.225049
$981$	−2.34779	−0.0749592
$982$	2.66114	0.0849202
$983$	−30.4945	−0.972624	−0.486312	−	0.873785i	$-0.661658\pi$
$983$	−30.4945	−0.972624	−0.486312	+	0.873785i	$0.661658\pi$
$984$	9.27078	0.295542
$985$	−16.7499	−0.533696
$986$	13.4464	0.428220
$987$	−4.02464	−0.128106
$988$	31.4095	0.999268
$989$	0	0
$990$	0.585989	0.0186240
$991$	19.3735	0.615420	0.307710	−	0.951480i	$-0.400437\pi$
$991$	19.3735	0.615420	0.307710	+	0.951480i	$0.400437\pi$
$992$	−16.8266	−0.534244
$993$	29.2235	0.927381
$994$	13.9319	0.441893
$995$	−27.2070	−0.862519
$996$	11.0140	0.348991
$997$	53.7576	1.70252	0.851261	−	0.524743i	$-0.175839\pi$
$997$	53.7576	1.70252	0.851261	+	0.524743i	$0.175839\pi$
$998$	12.5200	0.396315
$999$	37.5344	1.18753

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.m.1.5	✓	10
43.42	odd	2	inner	1849.2.a.m.1.6	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.m.1.5	✓	10	1.1	even	1	trivial
1849.2.a.m.1.6	yes	10	43.42	odd	2	inner

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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-0.563465 q^{2} -2.07496 q^{3} -1.68251 q^{4} -1.25580 q^{5} +1.16917 q^{6} +1.91459 q^{7} +2.07496 q^{8} +1.30548 q^{9} +O(q^{10})\)	\(q-0.563465 q^{2} -2.07496 q^{3} -1.68251 q^{4} -1.25580 q^{5} +1.16917 q^{6} +1.91459 q^{7} +2.07496 q^{8} +1.30548 q^{9} +0.707599 q^{10} +0.634356 q^{11} +3.49114 q^{12} -5.68965 q^{13} -1.07880 q^{14} +2.60574 q^{15} +2.19584 q^{16} -5.78084 q^{17} -0.735591 q^{18} +3.28109 q^{19} +2.11289 q^{20} -3.97270 q^{21} -0.357438 q^{22} +9.50494 q^{23} -4.30548 q^{24} -3.42297 q^{25} +3.20592 q^{26} +3.51608 q^{27} -3.22130 q^{28} +4.12807 q^{29} -1.46824 q^{30} +3.12343 q^{31} -5.38721 q^{32} -1.31627 q^{33} +3.25730 q^{34} -2.40433 q^{35} -2.19647 q^{36} +10.6751 q^{37} -1.84878 q^{38} +11.8058 q^{39} -2.60574 q^{40} -2.15325 q^{41} +2.23848 q^{42} -1.06731 q^{44} -1.63942 q^{45} -5.35570 q^{46} +1.01308 q^{47} -4.55630 q^{48} -3.33436 q^{49} +1.92872 q^{50} +11.9950 q^{51} +9.57287 q^{52} +2.43788 q^{53} -1.98119 q^{54} -0.796624 q^{55} +3.97270 q^{56} -6.80815 q^{57} -2.32602 q^{58} +1.54924 q^{59} -4.38417 q^{60} -3.56631 q^{61} -1.75994 q^{62} +2.49945 q^{63} -1.35618 q^{64} +7.14505 q^{65} +0.741670 q^{66} -5.63797 q^{67} +9.72631 q^{68} -19.7224 q^{69} +1.35476 q^{70} -12.9142 q^{71} +2.70882 q^{72} +5.02757 q^{73} -6.01503 q^{74} +7.10254 q^{75} -5.52046 q^{76} +1.21453 q^{77} -6.65217 q^{78} +8.13626 q^{79} -2.75754 q^{80} -11.2122 q^{81} +1.21328 q^{82} +3.15484 q^{83} +6.68409 q^{84} +7.25957 q^{85} -8.56559 q^{87} +1.31627 q^{88} -0.861116 q^{89} +0.923754 q^{90} -10.8933 q^{91} -15.9921 q^{92} -6.48100 q^{93} -0.570833 q^{94} -4.12039 q^{95} +11.1783 q^{96} -15.6367 q^{97} +1.87880 q^{98} +0.828137 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9}+O(q^{10}) \) 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9	\( 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9} - 22 q^{10} - 10 q^{11} - 14 q^{13} - 22 q^{14} - 22 q^{15} - 26 q^{16} - 16 q^{17} - 44 q^{21} - 18 q^{23} - 44 q^{24} - 6 q^{25} - 2 q^{31} - 28 q^{36} - 22 q^{38} + 22 q^{40} - 2 q^{44} - 18 q^{47} + 18 q^{49} + 28 q^{52} + 2 q^{53} + 44 q^{56} - 22 q^{57} - 22 q^{58} + 14 q^{59} + 8 q^{64} - 22 q^{66} + 26 q^{67} + 32 q^{68} + 44 q^{74} - 44 q^{78} - 56 q^{79} + 2 q^{81} - 38 q^{83} - 22 q^{87} - 22 q^{90} - 74 q^{92} + 22 q^{96} + 34 q^{97} - 36 q^{99}+O(q^{100}) \) 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9 - 22 * q^10 - 10 * q^11 - 14 * q^13 - 22 * q^14 - 22 * q^15 - 26 * q^16 - 16 * q^17 - 44 * q^21 - 18 * q^23 - 44 * q^24 - 6 * q^25 - 2 * q^31 - 28 * q^36 - 22 * q^38 + 22 * q^40 - 2 * q^44 - 18 * q^47 + 18 * q^49 + 28 * q^52 + 2 * q^53 + 44 * q^56 - 22 * q^57 - 22 * q^58 + 14 * q^59 + 8 * q^64 - 22 * q^66 + 26 * q^67 + 32 * q^68 + 44 * q^74 - 44 * q^78 - 56 * q^79 + 2 * q^81 - 38 * q^83 - 22 * q^87 - 22 * q^90 - 74 * q^92 + 22 * q^96 + 34 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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