LMFDB - Embedded newform 121.8.a.d.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [121,8,Mod(1,121)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("121.1"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(121, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	121.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$37.7985880836$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 395x^{3} + 660x^{2} + 21600x - 76032 $ x^5 - 2x^4 - 395x^3 + 660x^2 + 21600x - 76032
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$4.59754$ of defining polynomial
Character	$\chi$	$=$	121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.59754 q^{2} +60.4351 q^{3} -121.253 q^{4} -21.1080 q^{5} +156.982 q^{6} +295.244 q^{7} -647.443 q^{8} +1465.40 q^{9} -54.8289 q^{10} -7327.92 q^{12} -10072.4 q^{13} +766.908 q^{14} -1275.67 q^{15} +13838.6 q^{16} +32418.4 q^{17} +3806.42 q^{18} -31592.8 q^{19} +2559.41 q^{20} +17843.1 q^{21} -105343. q^{23} -39128.3 q^{24} -77679.5 q^{25} -26163.5 q^{26} -43610.2 q^{27} -35799.2 q^{28} -15267.4 q^{29} -3313.59 q^{30} -116447. q^{31} +118819. q^{32} +84207.9 q^{34} -6232.03 q^{35} -177683. q^{36} +147308. q^{37} -82063.6 q^{38} -608729. q^{39} +13666.3 q^{40} +633548. q^{41} +46348.2 q^{42} -707573. q^{43} -30931.6 q^{45} -273631. q^{46} -808891. q^{47} +836337. q^{48} -736374. q^{49} -201775. q^{50} +1.95921e6 q^{51} +1.22131e6 q^{52} +522483. q^{53} -113279. q^{54} -191154. q^{56} -1.90932e6 q^{57} -39657.6 q^{58} +47939.4 q^{59} +154678. q^{60} +127585. q^{61} -302474. q^{62} +432650. q^{63} -1.46270e6 q^{64} +212609. q^{65} -3.94947e6 q^{67} -3.93082e6 q^{68} -6.36639e6 q^{69} -16187.9 q^{70} -1.39647e6 q^{71} -948761. q^{72} +4.84150e6 q^{73} +382639. q^{74} -4.69456e6 q^{75} +3.83072e6 q^{76} -1.58119e6 q^{78} +280171. q^{79} -292106. q^{80} -5.84040e6 q^{81} +1.64566e6 q^{82} -1.40096e6 q^{83} -2.16353e6 q^{84} -684288. q^{85} -1.83795e6 q^{86} -922684. q^{87} -1.20164e6 q^{89} -80346.0 q^{90} -2.97383e6 q^{91} +1.27731e7 q^{92} -7.03746e6 q^{93} -2.10113e6 q^{94} +666863. q^{95} +7.18083e6 q^{96} +1.06983e7 q^{97} -1.91276e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 8 q^{2} - 14 q^{3} + 166 q^{4} - 515 q^{5} - 692 q^{6} + 1286 q^{7} - 2334 q^{8} + 1133 q^{9} + 6836 q^{10} + 10496 q^{12} + 6533 q^{13} - 18668 q^{14} + 2074 q^{15} + 15010 q^{16} - 32705 q^{17}+ \cdots - 9136104 q^{98}+O(q^{100}) $ 5 * q - 8 * q^2 - 14 * q^3 + 166 * q^4 - 515 * q^5 - 692 * q^6 + 1286 * q^7 - 2334 * q^8 + 1133 * q^9 + 6836 * q^10 + 10496 * q^12 + 6533 * q^13 - 18668 * q^14 + 2074 * q^15 + 15010 * q^16 - 32705 * q^17 + 21848 * q^18 + 29910 * q^19 - 79078 * q^20 - 23132 * q^21 - 45214 * q^23 - 94992 * q^24 + 11764 * q^25 - 58196 * q^26 - 230348 * q^27 + 21856 * q^28 + 242061 * q^29 + 477220 * q^30 + 55310 * q^31 - 40750 * q^32 - 194608 * q^34 - 1092602 * q^35 - 1250618 * q^36 + 586689 * q^37 - 166692 * q^38 - 283790 * q^39 + 1951374 * q^40 + 565735 * q^41 - 1120208 * q^42 - 287040 * q^43 - 1566547 * q^45 - 1904780 * q^46 - 3182566 * q^47 + 949544 * q^48 - 765183 * q^49 - 4244056 * q^50 + 3141694 * q^51 + 4918498 * q^52 - 1220883 * q^53 + 913528 * q^54 - 5142192 * q^56 - 7377636 * q^57 - 10076868 * q^58 + 1304864 * q^59 - 7345528 * q^60 - 3437754 * q^61 + 4156516 * q^62 + 7075454 * q^63 - 4731286 * q^64 - 3342779 * q^65 - 5199446 * q^67 - 10501510 * q^68 - 11265124 * q^69 + 9858572 * q^70 - 3440220 * q^71 - 5576286 * q^72 + 9963974 * q^73 + 7512132 * q^74 - 241456 * q^75 - 7011480 * q^76 - 8493404 * q^78 - 7834562 * q^79 - 17690746 * q^80 + 4373321 * q^81 - 898480 * q^82 - 6230682 * q^83 + 19063160 * q^84 + 11708303 * q^85 + 6786552 * q^86 + 13109106 * q^87 - 13960869 * q^89 - 12112156 * q^90 + 573182 * q^91 - 3324824 * q^92 + 7120948 * q^93 - 9234428 * q^94 - 8171634 * q^95 - 4167472 * q^96 - 15733241 * q^97 - 9136104 * q^98

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 $

$2$	2.59754	0.229592	0.114796	−	0.993389i	$-0.463379\pi$
$2$	2.59754	0.229592	0.114796	+	0.993389i	$0.463379\pi$
$3$	60.4351	1.29230	0.646152	−	0.763209i	$-0.276377\pi$
$3$	60.4351	1.29230	0.646152	+	0.763209i	$0.276377\pi$
$4$	−121.253	−0.947288
$5$	−21.1080	−0.0755184	−0.0377592	−	0.999287i	$-0.512022\pi$
$5$	−21.1080	−0.0755184	−0.0377592	+	0.999287i	$0.512022\pi$
$6$	156.982	0.296703
$7$	295.244	0.325341	0.162670	−	0.986680i	$-0.447989\pi$
$7$	295.244	0.325341	0.162670	+	0.986680i	$0.447989\pi$
$8$	−647.443	−0.447082
$9$	1465.40	0.670048
$10$	−54.8289	−0.0173384
$11$	0	0
$11$	0	0
$12$	−7327.92	−1.22418
$13$	−10072.4	−1.27155	−0.635774	−	0.771875i	$-0.719319\pi$
$13$	−10072.4	−1.27155	−0.635774	+	0.771875i	$0.719319\pi$
$14$	766.908	0.0746957
$15$	−1275.67	−0.0975927
$16$	13838.6	0.844641
$17$	32418.4	1.60037	0.800184	−	0.599754i	$-0.204735\pi$
$17$	32418.4	1.60037	0.800184	+	0.599754i	$0.204735\pi$
$18$	3806.42	0.153838
$19$	−31592.8	−1.05670	−0.528349	−	0.849027i	$-0.677189\pi$
$19$	−31592.8	−1.05670	−0.528349	+	0.849027i	$0.677189\pi$
$20$	2559.41	0.0715376
$21$	17843.1	0.420439
$22$	0	0
$23$	−105343.	−1.80533	−0.902665	−	0.430344i	$-0.858392\pi$
$23$	−105343.	−1.80533	−0.902665	+	0.430344i	$0.858392\pi$
$24$	−39128.3	−0.577765
$25$	−77679.5	−0.994297
$26$	−26163.5	−0.291937
$27$	−43610.2	−0.426398
$28$	−35799.2	−0.308191
$29$	−15267.4	−0.116244	−0.0581221	−	0.998309i	$-0.518511\pi$
$29$	−15267.4	−0.116244	−0.0581221	+	0.998309i	$0.518511\pi$
$30$	−3313.59	−0.0224065
$31$	−116447.	−0.702039	−0.351019	−	0.936368i	$-0.614165\pi$
$31$	−116447.	−0.702039	−0.351019	+	0.936368i	$0.614165\pi$
$32$	118819.	0.641004
$33$	0	0
$34$	84207.9	0.367432
$35$	−6232.03	−0.0245692
$36$	−177683.	−0.634729
$37$	147308.	0.478103	0.239051	−	0.971007i	$-0.423164\pi$
$37$	147308.	0.478103	0.239051	+	0.971007i	$0.423164\pi$
$38$	−82063.6	−0.242610
$39$	−608729.	−1.64323
$40$	13666.3	0.0337629
$41$	633548.	1.43561	0.717804	−	0.696245i	$-0.245147\pi$
$41$	633548.	1.43561	0.717804	+	0.696245i	$0.245147\pi$
$42$	46348.2	0.0965295
$43$	−707573.	−1.35716	−0.678581	−	0.734526i	$-0.737405\pi$
$43$	−707573.	−1.35716	−0.678581	+	0.734526i	$0.737405\pi$
$44$	0	0
$45$	−30931.6	−0.0506010
$46$	−273631.	−0.414489
$47$	−808891.	−1.13644	−0.568222	−	0.822876i	$-0.692368\pi$
$47$	−808891.	−1.13644	−0.568222	+	0.822876i	$0.692368\pi$
$48$	836337.	1.09153
$49$	−736374.	−0.894153
$50$	−201775.	−0.228283
$51$	1.95921e6	2.06816
$52$	1.22131e6	1.20452
$53$	522483.	0.482066	0.241033	−	0.970517i	$-0.422514\pi$
$53$	522483.	0.482066	0.241033	+	0.970517i	$0.422514\pi$
$54$	−113279.	−0.0978975
$55$	0	0
$56$	−191154.	−0.145454
$57$	−1.90932e6	−1.36558
$58$	−39657.6	−0.0266887
$59$	47939.4	0.0303886	0.0151943	−	0.999885i	$-0.495163\pi$
$59$	47939.4	0.0303886	0.0151943	+	0.999885i	$0.495163\pi$
$60$	154678.	0.0924483
$61$	127585.	0.0719689	0.0359844	−	0.999352i	$-0.488543\pi$
$61$	127585.	0.0719689	0.0359844	+	0.999352i	$0.488543\pi$
$62$	−302474.	−0.161182
$63$	432650.	0.217994
$64$	−1.46270e6	−0.697472
$65$	212609.	0.0960253
$66$	0	0
$67$	−3.94947e6	−1.60427	−0.802134	−	0.597144i	$-0.796302\pi$
$67$	−3.94947e6	−1.60427	−0.802134	+	0.597144i	$0.796302\pi$
$68$	−3.93082e6	−1.51601
$69$	−6.36639e6	−2.33303
$70$	−16187.9	−0.00564090
$71$	−1.39647e6	−0.463050	−0.231525	−	0.972829i	$-0.574371\pi$
$71$	−1.39647e6	−0.463050	−0.231525	+	0.972829i	$0.574371\pi$
$72$	−948761.	−0.299566
$73$	4.84150e6	1.45663	0.728315	−	0.685242i	$-0.240304\pi$
$73$	4.84150e6	1.45663	0.728315	+	0.685242i	$0.240304\pi$
$74$	382639.	0.109769
$75$	−4.69456e6	−1.28493
$76$	3.83072e6	1.00100
$77$	0	0
$78$	−1.58119e6	−0.377272
$79$	280171.	0.0639334	0.0319667	−	0.999489i	$-0.489823\pi$
$79$	280171.	0.0639334	0.0319667	+	0.999489i	$0.489823\pi$
$80$	−292106.	−0.0637859
$81$	−5.84040e6	−1.22108
$82$	1.64566e6	0.329604
$83$	−1.40096e6	−0.268938	−0.134469	−	0.990918i	$-0.542933\pi$
$83$	−1.40096e6	−0.268938	−0.134469	+	0.990918i	$0.542933\pi$
$84$	−2.16353e6	−0.398277
$85$	−684288.	−0.120857
$86$	−1.83795e6	−0.311593
$87$	−922684.	−0.150223
$88$	0	0
$89$	−1.20164e6	−0.180680	−0.0903398	−	0.995911i	$-0.528795\pi$
$89$	−1.20164e6	−0.180680	−0.0903398	+	0.995911i	$0.528795\pi$
$90$	−80346.0	−0.0116176
$91$	−2.97383e6	−0.413687
$92$	1.27731e7	1.71017
$93$	−7.03746e6	−0.907247
$94$	−2.10113e6	−0.260918
$95$	666863.	0.0798002
$96$	7.18083e6	0.828372
$97$	1.06983e7	1.19018	0.595090	−	0.803659i	$-0.297116\pi$
$97$	1.06983e7	1.19018	0.595090	+	0.803659i	$0.297116\pi$
$98$	−1.91276e6	−0.205290
$99$	0	0
$100$	9.41885e6	0.941885
$101$	377690.	0.0364763	0.0182381	−	0.999834i	$-0.494194\pi$
$101$	377690.	0.0364763	0.0182381	+	0.999834i	$0.494194\pi$
$102$	5.08911e6	0.474834
$103$	−344214.	−0.0310383	−0.0155192	−	0.999880i	$-0.504940\pi$
$103$	−344214.	−0.0310383	−0.0155192	+	0.999880i	$0.504940\pi$
$104$	6.52133e6	0.568486
$105$	−376633.	−0.0317509
$106$	1.35717e6	0.110679
$107$	−1.00553e6	−0.0793508	−0.0396754	−	0.999213i	$-0.512632\pi$
$107$	−1.00553e6	−0.0793508	−0.0396754	+	0.999213i	$0.512632\pi$
$108$	5.28786e6	0.403921
$109$	−2.08924e7	−1.54524	−0.772618	−	0.634871i	$-0.781053\pi$
$109$	−2.08924e7	−1.54524	−0.772618	+	0.634871i	$0.781053\pi$
$110$	0	0
$111$	8.90259e6	0.617854
$112$	4.08577e6	0.274796
$113$	1.91290e7	1.24715	0.623574	−	0.781765i	$-0.285680\pi$
$113$	1.91290e7	1.24715	0.623574	+	0.781765i	$0.285680\pi$
$114$	−4.95952e6	−0.313525
$115$	2.22358e6	0.136336
$116$	1.85121e6	0.110117
$117$	−1.47601e7	−0.851999
$118$	124524.	0.00697698
$119$	9.57135e6	0.520665
$120$	825921.	0.0436319
$121$	0	0
$122$	331406.	0.0165235
$123$	3.82885e7	1.85524
$124$	1.41195e7	0.665032
$125$	3.28873e6	0.150606
$126$	1.12382e6	0.0500497
$127$	2.01921e7	0.874717	0.437359	−	0.899287i	$-0.355914\pi$
$127$	2.01921e7	0.874717	0.437359	+	0.899287i	$0.355914\pi$
$128$	−1.90083e7	−0.801138
$129$	−4.27622e7	−1.75386
$130$	552261.	0.0220466
$131$	4.56469e7	1.77403	0.887017	−	0.461737i	$-0.152774\pi$
$131$	4.56469e7	1.77403	0.887017	+	0.461737i	$0.152774\pi$
$132$	0	0
$133$	−9.32761e6	−0.343787
$134$	−1.02589e7	−0.368327
$135$	920525.	0.0322009
$136$	−2.09891e7	−0.715496
$137$	2.95397e7	0.981485	0.490742	−	0.871305i	$-0.336726\pi$
$137$	2.95397e7	0.981485	0.490742	+	0.871305i	$0.336726\pi$
$138$	−1.65369e7	−0.535646
$139$	−1.34228e7	−0.423927	−0.211964	−	0.977278i	$-0.567986\pi$
$139$	−1.34228e7	−0.423927	−0.211964	+	0.977278i	$0.567986\pi$
$140$	755651.	0.0232741
$141$	−4.88854e7	−1.46863
$142$	−3.62739e6	−0.106313
$143$	0	0
$144$	2.02790e7	0.565950
$145$	322264.	0.00877858
$146$	1.25760e7	0.334431
$147$	−4.45028e7	−1.15552
$148$	−1.78615e7	−0.452901
$149$	7.61769e7	1.88656	0.943282	−	0.331994i	$-0.107721\pi$
$149$	7.61769e7	1.88656	0.943282	+	0.331994i	$0.107721\pi$
$150$	−1.21943e7	−0.295010
$151$	−6.44790e7	−1.52405	−0.762025	−	0.647548i	$-0.775795\pi$
$151$	−6.44790e7	−1.52405	−0.762025	+	0.647548i	$0.775795\pi$
$152$	2.04546e7	0.472430
$153$	4.75058e7	1.07232
$154$	0	0
$155$	2.45796e6	0.0530168
$156$	7.38100e7	1.55661
$157$	3.94569e7	0.813719	0.406860	−	0.913491i	$-0.366624\pi$
$157$	3.94569e7	0.813719	0.406860	+	0.913491i	$0.366624\pi$
$158$	727753.	0.0146786
$159$	3.15763e7	0.622976
$160$	−2.50804e6	−0.0484076
$161$	−3.11018e7	−0.587348
$162$	−1.51707e7	−0.280351
$163$	4.22974e7	0.764992	0.382496	−	0.923957i	$-0.375065\pi$
$163$	4.22974e7	0.764992	0.382496	+	0.923957i	$0.375065\pi$
$164$	−7.68194e7	−1.35993
$165$	0	0
$166$	−3.63904e6	−0.0617459
$167$	−7.40788e7	−1.23080	−0.615398	−	0.788217i	$-0.711005\pi$
$167$	−7.40788e7	−1.23080	−0.615398	+	0.788217i	$0.711005\pi$
$168$	−1.15524e7	−0.187971
$169$	3.87055e7	0.616836
$170$	−1.77746e6	−0.0277479
$171$	−4.62960e7	−0.708039
$172$	8.57952e7	1.28562
$173$	1.16085e8	1.70457	0.852284	−	0.523080i	$-0.175217\pi$
$173$	1.16085e8	1.70457	0.852284	+	0.523080i	$0.175217\pi$
$174$	−2.39671e6	−0.0344899
$175$	−2.29344e7	−0.323485
$176$	0	0
$177$	2.89722e6	0.0392713
$178$	−3.12130e6	−0.0414826
$179$	4.91110e7	0.640019	0.320009	−	0.947414i	$-0.396314\pi$
$179$	4.91110e7	0.640019	0.320009	+	0.947414i	$0.396314\pi$
$180$	3.75055e6	0.0479337
$181$	−7.70573e6	−0.0965914	−0.0482957	−	0.998833i	$-0.515379\pi$
$181$	−7.70573e6	−0.0965914	−0.0482957	+	0.998833i	$0.515379\pi$
$182$	−7.72464e6	−0.0949792
$183$	7.71060e6	0.0930057
$184$	6.82034e7	0.807130
$185$	−3.10939e6	−0.0361056
$186$	−1.82801e7	−0.208297
$187$	0	0
$188$	9.80803e7	1.07654
$189$	−1.28757e7	−0.138725
$190$	1.73220e6	0.0183215
$191$	1.08230e8	1.12391	0.561955	−	0.827168i	$-0.310049\pi$
$191$	1.08230e8	1.12391	0.561955	+	0.827168i	$0.310049\pi$
$192$	−8.83986e7	−0.901345
$193$	1.87441e7	0.187678	0.0938391	−	0.995587i	$-0.470086\pi$
$193$	1.87441e7	0.187678	0.0938391	+	0.995587i	$0.470086\pi$
$194$	2.77892e7	0.273256
$195$	1.28491e7	0.124094
$196$	8.92874e7	0.847020
$197$	1.10380e7	0.102863	0.0514314	−	0.998677i	$-0.483622\pi$
$197$	1.10380e7	0.102863	0.0514314	+	0.998677i	$0.483622\pi$
$198$	0	0
$199$	−6.27029e7	−0.564030	−0.282015	−	0.959410i	$-0.591003\pi$
$199$	−6.27029e7	−0.564030	−0.282015	+	0.959410i	$0.591003\pi$
$200$	5.02930e7	0.444532
$201$	−2.38686e8	−2.07320
$202$	981064.	0.00837466
$203$	−4.50761e6	−0.0378190
$204$	−2.37559e8	−1.95914
$205$	−1.33729e7	−0.108415
$206$	−894108.	−0.00712615
$207$	−1.54369e8	−1.20966
$208$	−1.39388e8	−1.07400
$209$	0	0
$210$	−978318.	−0.00728975
$211$	−1.78374e8	−1.30720	−0.653602	−	0.756839i	$-0.726743\pi$
$211$	−1.78374e8	−1.30720	−0.653602	+	0.756839i	$0.726743\pi$
$212$	−6.33526e7	−0.456655
$213$	−8.43958e7	−0.598401
$214$	−2.61190e6	−0.0182183
$215$	1.49355e7	0.102491
$216$	2.82351e7	0.190635
$217$	−3.43802e7	−0.228402
$218$	−5.42687e7	−0.354774
$219$	2.92596e8	1.88241
$220$	0	0
$221$	−3.26532e8	−2.03495
$222$	2.31248e7	0.141854
$223$	−2.08265e8	−1.25762	−0.628811	−	0.777558i	$-0.716458\pi$
$223$	−2.08265e8	−1.25762	−0.628811	+	0.777558i	$0.716458\pi$
$224$	3.50807e7	0.208545
$225$	−1.13831e8	−0.666227
$226$	4.96883e7	0.286335
$227$	1.60033e8	0.908071	0.454035	−	0.890984i	$-0.349984\pi$
$227$	1.60033e8	0.908071	0.454035	+	0.890984i	$0.349984\pi$
$228$	2.31510e8	1.29359
$229$	−1.51850e8	−0.835587	−0.417794	−	0.908542i	$-0.637196\pi$
$229$	−1.51850e8	−0.835587	−0.417794	+	0.908542i	$0.637196\pi$
$230$	5.77582e6	0.0313016
$231$	0	0
$232$	9.88476e6	0.0519706
$233$	−2.90404e8	−1.50403	−0.752015	−	0.659146i	$-0.770918\pi$
$233$	−2.90404e8	−1.50403	−0.752015	+	0.659146i	$0.770918\pi$
$234$	−3.83399e7	−0.195612
$235$	1.70741e7	0.0858224
$236$	−5.81279e6	−0.0287867
$237$	1.69321e7	0.0826213
$238$	2.48619e7	0.119541
$239$	−2.30380e8	−1.09157	−0.545786	−	0.837924i	$-0.683769\pi$
$239$	−2.30380e8	−1.09157	−0.545786	+	0.837924i	$0.683769\pi$
$240$	−1.76534e7	−0.0824308
$241$	2.33650e7	0.107524	0.0537620	−	0.998554i	$-0.482879\pi$
$241$	2.33650e7	0.107524	0.0537620	+	0.998554i	$0.482879\pi$
$242$	0	0
$243$	−2.57590e8	−1.15161
$244$	−1.54700e7	−0.0681752
$245$	1.55434e7	0.0675250
$246$	9.94558e7	0.425949
$247$	3.18217e8	1.34364
$248$	7.53926e7	0.313869
$249$	−8.46669e7	−0.347549
$250$	8.54259e6	0.0345780
$251$	2.47481e8	0.987834	0.493917	−	0.869509i	$-0.335565\pi$
$251$	2.47481e8	0.987834	0.493917	+	0.869509i	$0.335565\pi$
$252$	−5.24600e7	−0.206503
$253$	0	0
$254$	5.24496e7	0.200828
$255$	−4.13550e7	−0.156184
$256$	1.37851e8	0.513537
$257$	−3.46056e8	−1.27169	−0.635844	−	0.771818i	$-0.719348\pi$
$257$	−3.46056e8	−1.27169	−0.635844	+	0.771818i	$0.719348\pi$
$258$	−1.11076e8	−0.402673
$259$	4.34920e7	0.155546
$260$	−2.57795e7	−0.0909636
$261$	−2.23727e7	−0.0778892
$262$	1.18570e8	0.407304
$263$	−3.54188e8	−1.20057	−0.600287	−	0.799785i	$-0.704947\pi$
$263$	−3.54188e8	−1.20057	−0.600287	+	0.799785i	$0.704947\pi$
$264$	0	0
$265$	−1.10286e7	−0.0364049
$266$	−2.42288e7	−0.0789308
$267$	−7.26211e7	−0.233493
$268$	4.78884e8	1.51970
$269$	−3.65883e8	−1.14606	−0.573032	−	0.819533i	$-0.694233\pi$
$269$	−3.65883e8	−1.14606	−0.573032	+	0.819533i	$0.694233\pi$
$270$	2.39110e6	0.00739306
$271$	4.87162e8	1.48690	0.743449	−	0.668793i	$-0.233189\pi$
$271$	4.87162e8	1.48690	0.743449	+	0.668793i	$0.233189\pi$
$272$	4.48625e8	1.35174
$273$	−1.79724e8	−0.534609
$274$	7.67304e7	0.225341
$275$	0	0
$276$	7.71942e8	2.21005
$277$	1.76195e8	0.498099	0.249049	−	0.968491i	$-0.419882\pi$
$277$	1.76195e8	0.498099	0.249049	+	0.968491i	$0.419882\pi$
$278$	−3.48662e7	−0.0973303
$279$	−1.70640e8	−0.470400
$280$	4.03489e6	0.0109844
$281$	1.90439e8	0.512015	0.256008	−	0.966675i	$-0.417593\pi$
$281$	1.90439e8	0.512015	0.256008	+	0.966675i	$0.417593\pi$
$282$	−1.26982e8	−0.337186
$283$	−2.35805e8	−0.618444	−0.309222	−	0.950990i	$-0.600069\pi$
$283$	−2.35805e8	−0.618444	−0.309222	+	0.950990i	$0.600069\pi$
$284$	1.69326e8	0.438641
$285$	4.03019e7	0.103126
$286$	0	0
$287$	1.87051e8	0.467062
$288$	1.74117e8	0.429504
$289$	6.40613e8	1.56118
$290$	837093.	0.00201549
$291$	6.46551e8	1.53807
$292$	−5.87045e8	−1.37985
$293$	−6.40112e8	−1.48669	−0.743343	−	0.668910i	$-0.766761\pi$
$293$	−6.40112e8	−1.48669	−0.743343	+	0.668910i	$0.766761\pi$
$294$	−1.15598e8	−0.265298
$295$	−1.01191e6	−0.00229490
$296$	−9.53738e7	−0.213751
$297$	0	0
$298$	1.97872e8	0.433140
$299$	1.06106e9	2.29557
$300$	5.69229e8	1.21720
$301$	−2.08907e8	−0.441540
$302$	−1.67487e8	−0.349910
$303$	2.28257e7	0.0471384
$304$	−4.37201e8	−0.892531
$305$	−2.69307e6	−0.00543498
$306$	1.23398e8	0.246197
$307$	4.17417e8	0.823352	0.411676	−	0.911330i	$-0.364944\pi$
$307$	4.17417e8	0.823352	0.411676	+	0.911330i	$0.364944\pi$
$308$	0	0
$309$	−2.08026e7	−0.0401109
$310$	6.38464e6	0.0121722
$311$	−1.06418e8	−0.200611	−0.100305	−	0.994957i	$-0.531982\pi$
$311$	−1.06418e8	−0.200611	−0.100305	+	0.994957i	$0.531982\pi$
$312$	3.94117e8	0.734657
$313$	−4.49441e8	−0.828452	−0.414226	−	0.910174i	$-0.635948\pi$
$313$	−4.49441e8	−0.828452	−0.414226	+	0.910174i	$0.635948\pi$
$314$	1.02491e8	0.186823
$315$	−9.13239e6	−0.0164626
$316$	−3.39715e7	−0.0605633
$317$	−3.35109e8	−0.590852	−0.295426	−	0.955366i	$-0.595462\pi$
$317$	−3.35109e8	−0.590852	−0.295426	+	0.955366i	$0.595462\pi$
$318$	8.20206e7	0.143030
$319$	0	0
$320$	3.08748e7	0.0526719
$321$	−6.07692e7	−0.102545
$322$	−8.07881e7	−0.134850
$323$	−1.02419e9	−1.69111
$324$	7.08165e8	1.15672
$325$	7.82422e8	1.26430
$326$	1.09869e8	0.175636
$327$	−1.26263e9	−1.99691
$328$	−4.10186e8	−0.641834
$329$	−2.38821e8	−0.369731
$330$	0	0
$331$	−4.88718e7	−0.0740730	−0.0370365	−	0.999314i	$-0.511792\pi$
$331$	−4.88718e7	−0.0740730	−0.0370365	+	0.999314i	$0.511792\pi$
$332$	1.69870e8	0.254761
$333$	2.15865e8	0.320352
$334$	−1.92422e8	−0.282581
$335$	8.33655e7	0.121152
$336$	2.46924e8	0.355120
$337$	−5.99212e8	−0.852856	−0.426428	−	0.904522i	$-0.640228\pi$
$337$	−5.99212e8	−0.852856	−0.426428	+	0.904522i	$0.640228\pi$
$338$	1.00539e8	0.141621
$339$	1.15606e9	1.61169
$340$	8.29719e7	0.114487
$341$	0	0
$342$	−1.20256e8	−0.162560
$343$	−4.60557e8	−0.616246
$344$	4.58113e8	0.606762
$345$	1.34382e8	0.176187
$346$	3.01535e8	0.391355
$347$	3.94938e8	0.507430	0.253715	−	0.967279i	$-0.418347\pi$
$347$	3.94938e8	0.507430	0.253715	+	0.967279i	$0.418347\pi$
$348$	1.11878e8	0.142304
$349$	−7.96196e8	−1.00261	−0.501304	−	0.865271i	$-0.667146\pi$
$349$	−7.96196e8	−1.00261	−0.501304	+	0.865271i	$0.667146\pi$
$350$	−5.95730e7	−0.0742697
$351$	4.39261e8	0.542185
$352$	0	0
$353$	−1.33540e9	−1.61584	−0.807921	−	0.589290i	$-0.799407\pi$
$353$	−1.33540e9	−1.61584	−0.807921	+	0.589290i	$0.799407\pi$
$354$	7.52564e6	0.00901638
$355$	2.94768e7	0.0349688
$356$	1.45702e8	0.171155
$357$	5.78445e8	0.672858
$358$	1.27568e8	0.146943
$359$	−5.81785e8	−0.663639	−0.331820	−	0.943343i	$-0.607662\pi$
$359$	−5.81785e8	−0.663639	−0.331820	+	0.943343i	$0.607662\pi$
$360$	2.00265e7	0.0226228
$361$	1.04236e8	0.116612
$362$	−2.00159e7	−0.0221766
$363$	0	0
$364$	3.60586e8	0.391880
$365$	−1.02194e8	−0.110002
$366$	2.00286e7	0.0213534
$367$	7.79336e8	0.822988	0.411494	−	0.911413i	$-0.365007\pi$
$367$	7.79336e8	0.822988	0.411494	+	0.911413i	$0.365007\pi$
$368$	−1.45779e9	−1.52486
$369$	9.28398e8	0.961927
$370$	−8.07675e6	−0.00828955
$371$	1.54260e8	0.156836
$372$	8.53311e8	0.859424
$373$	2.20836e8	0.220338	0.110169	−	0.993913i	$-0.464861\pi$
$373$	2.20836e8	0.220338	0.110169	+	0.993913i	$0.464861\pi$
$374$	0	0
$375$	1.98754e8	0.194629
$376$	5.23711e8	0.508083
$377$	1.53780e8	0.147810
$378$	−3.34450e7	−0.0318501
$379$	9.68504e8	0.913827	0.456914	−	0.889511i	$-0.348955\pi$
$379$	9.68504e8	0.913827	0.456914	+	0.889511i	$0.348955\pi$
$380$	−8.08590e7	−0.0755937
$381$	1.22031e9	1.13040
$382$	2.81132e8	0.258041
$383$	−1.53664e9	−1.39758	−0.698790	−	0.715326i	$-0.746278\pi$
$383$	−1.53664e9	−1.39758	−0.698790	+	0.715326i	$0.746278\pi$
$384$	−1.14877e9	−1.03531
$385$	0	0
$386$	4.86885e7	0.0430894
$387$	−1.03687e9	−0.909364
$388$	−1.29720e9	−1.12744
$389$	5.52254e7	0.0475680	0.0237840	−	0.999717i	$-0.492429\pi$
$389$	5.52254e7	0.0475680	0.0237840	+	0.999717i	$0.492429\pi$
$390$	3.33759e7	0.0284910
$391$	−3.41504e9	−2.88919
$392$	4.76760e8	0.399760
$393$	2.75867e9	2.29259
$394$	2.86716e7	0.0236165
$395$	−5.91385e6	−0.00482815
$396$	0	0
$397$	1.17675e9	0.943883	0.471941	−	0.881630i	$-0.343553\pi$
$397$	1.17675e9	0.943883	0.471941	+	0.881630i	$0.343553\pi$
$398$	−1.62873e8	−0.129497
$399$	−5.63715e8	−0.444277
$400$	−1.07497e9	−0.839824
$401$	−1.61271e9	−1.24897	−0.624484	−	0.781038i	$-0.714691\pi$
$401$	−1.61271e9	−1.24897	−0.624484	+	0.781038i	$0.714691\pi$
$402$	−6.19997e8	−0.475990
$403$	1.17290e9	0.892676
$404$	−4.57960e7	−0.0345535
$405$	1.23279e8	0.0922143
$406$	−1.17087e7	−0.00868294
$407$	0	0
$408$	−1.26848e9	−0.924637
$409$	7.75445e8	0.560428	0.280214	−	0.959938i	$-0.409595\pi$
$409$	7.75445e8	0.560428	0.280214	+	0.959938i	$0.409595\pi$
$410$	−3.47367e7	−0.0248912
$411$	1.78523e9	1.26838
$412$	4.17369e7	0.0294022
$413$	1.41538e7	0.00988666
$414$	−4.00978e8	−0.277728
$415$	2.95714e7	0.0203097
$416$	−1.19680e9	−0.815068
$417$	−8.11208e8	−0.547843
$418$	0	0
$419$	2.03873e9	1.35397	0.676987	−	0.735995i	$-0.263285\pi$
$419$	2.03873e9	1.35397	0.676987	+	0.735995i	$0.263285\pi$
$420$	4.56678e7	0.0300772
$421$	−1.32883e9	−0.867927	−0.433963	−	0.900930i	$-0.642885\pi$
$421$	−1.32883e9	−0.867927	−0.433963	+	0.900930i	$0.642885\pi$
$422$	−4.63333e8	−0.300123
$423$	−1.18535e9	−0.761472
$424$	−3.38278e8	−0.215523
$425$	−2.51824e9	−1.59124
$426$	−2.19221e8	−0.137388
$427$	3.76687e7	0.0234144
$428$	1.21923e8	0.0751681
$429$	0	0
$430$	3.87954e7	0.0235310
$431$	−1.36032e9	−0.818410	−0.409205	−	0.912442i	$-0.634194\pi$
$431$	−1.36032e9	−0.818410	−0.409205	+	0.912442i	$0.634194\pi$
$432$	−6.03504e8	−0.360153
$433$	1.68711e9	0.998702	0.499351	−	0.866400i	$-0.333572\pi$
$433$	1.68711e9	0.998702	0.499351	+	0.866400i	$0.333572\pi$
$434$	−8.93039e7	−0.0524392
$435$	1.94761e7	0.0113446
$436$	2.53326e9	1.46378
$437$	3.32807e9	1.90769
$438$	7.60029e8	0.432186
$439$	1.54155e9	0.869626	0.434813	−	0.900521i	$-0.356814\pi$
$439$	1.54155e9	0.869626	0.434813	+	0.900521i	$0.356814\pi$
$440$	0	0
$441$	−1.07908e9	−0.599126
$442$	−8.48180e8	−0.467208
$443$	−1.33969e9	−0.732137	−0.366069	−	0.930588i	$-0.619296\pi$
$443$	−1.33969e9	−0.732137	−0.366069	+	0.930588i	$0.619296\pi$
$444$	−1.07946e9	−0.585285
$445$	2.53642e7	0.0136446
$446$	−5.40977e8	−0.288740
$447$	4.60376e9	2.43801
$448$	−4.31855e8	−0.226916
$449$	−1.95067e9	−1.01700	−0.508502	−	0.861061i	$-0.669800\pi$
$449$	−1.95067e9	−1.01700	−0.508502	+	0.861061i	$0.669800\pi$
$450$	−2.95681e8	−0.152960
$451$	0	0
$452$	−2.31945e9	−1.18141
$453$	−3.89679e9	−1.96953
$454$	4.15692e8	0.208486
$455$	6.27718e7	0.0312410
$456$	1.23617e9	0.610524
$457$	7.91764e8	0.388051	0.194026	−	0.980996i	$-0.437846\pi$
$457$	7.91764e8	0.388051	0.194026	+	0.980996i	$0.437846\pi$
$458$	−3.94437e8	−0.191844
$459$	−1.41377e9	−0.682393
$460$	−2.69615e8	−0.129149
$461$	3.78622e8	0.179992	0.0899960	−	0.995942i	$-0.471315\pi$
$461$	3.78622e8	0.179992	0.0899960	+	0.995942i	$0.471315\pi$
$462$	0	0
$463$	−2.62457e9	−1.22892	−0.614461	−	0.788947i	$-0.710627\pi$
$463$	−2.62457e9	−1.22892	−0.614461	+	0.788947i	$0.710627\pi$
$464$	−2.11279e8	−0.0981846
$465$	1.48547e8	0.0685138
$466$	−7.54334e8	−0.345313
$467$	−4.73636e8	−0.215197	−0.107598	−	0.994194i	$-0.534316\pi$
$467$	−4.73636e8	−0.215197	−0.107598	+	0.994194i	$0.534316\pi$
$468$	1.78971e9	0.807088
$469$	−1.16606e9	−0.521934
$470$	4.43506e7	0.0197041
$471$	2.38458e9	1.05157
$472$	−3.10381e7	−0.0135862
$473$	0	0
$474$	4.39818e7	0.0189692
$475$	2.45411e9	1.05067
$476$	−1.16055e9	−0.493220
$477$	7.65645e8	0.323008
$478$	−5.98421e8	−0.250616
$479$	2.96021e9	1.23069	0.615344	−	0.788259i	$-0.289017\pi$
$479$	2.96021e9	1.23069	0.615344	+	0.788259i	$0.289017\pi$
$480$	−1.51573e8	−0.0625574
$481$	−1.48375e9	−0.607931
$482$	6.06913e7	0.0246866
$483$	−1.87964e9	−0.759032
$484$	0	0
$485$	−2.25819e8	−0.0898805
$486$	−6.69099e8	−0.264401
$487$	−6.18664e8	−0.242719	−0.121359	−	0.992609i	$-0.538725\pi$
$487$	−6.18664e8	−0.242719	−0.121359	+	0.992609i	$0.538725\pi$
$488$	−8.26040e7	−0.0321760
$489$	2.55624e9	0.988602
$490$	4.03746e7	0.0155032
$491$	−3.06639e9	−1.16908	−0.584538	−	0.811366i	$-0.698724\pi$
$491$	−3.06639e9	−1.16908	−0.584538	+	0.811366i	$0.698724\pi$
$492$	−4.64259e9	−1.75745
$493$	−4.94943e8	−0.186034
$494$	8.26580e8	0.308490
$495$	0	0
$496$	−1.61146e9	−0.592971
$497$	−4.12300e8	−0.150649
$498$	−2.19925e8	−0.0797945
$499$	−2.46711e9	−0.888867	−0.444433	−	0.895812i	$-0.646595\pi$
$499$	−2.46711e9	−0.888867	−0.444433	+	0.895812i	$0.646595\pi$
$500$	−3.98767e8	−0.142667
$501$	−4.47695e9	−1.59056
$502$	6.42841e8	0.226799
$503$	4.46072e9	1.56285	0.781424	−	0.624000i	$-0.214493\pi$
$503$	4.46072e9	1.56285	0.781424	+	0.624000i	$0.214493\pi$
$504$	−2.80116e8	−0.0974612
$505$	−7.97229e6	−0.00275463
$506$	0	0
$507$	2.33917e9	0.797139
$508$	−2.44834e9	−0.828609
$509$	5.04416e9	1.69542	0.847708	−	0.530463i	$-0.177982\pi$
$509$	5.04416e9	1.69542	0.847708	+	0.530463i	$0.177982\pi$
$510$	−1.07421e8	−0.0358587
$511$	1.42942e9	0.473902
$512$	2.79113e9	0.919042
$513$	1.37777e9	0.450574
$514$	−8.98893e8	−0.291969
$515$	7.26568e6	0.00234396
$516$	5.18504e9	1.66141
$517$	0	0
$518$	1.12972e8	0.0357122
$519$	7.01560e9	2.20282
$520$	−1.37653e8	−0.0429312
$521$	1.60516e9	0.497264	0.248632	−	0.968598i	$-0.420019\pi$
$521$	1.60516e9	0.497264	0.248632	+	0.968598i	$0.420019\pi$
$522$	−5.81140e7	−0.0178827
$523$	−3.28673e9	−1.00463	−0.502317	−	0.864683i	$-0.667519\pi$
$523$	−3.28673e9	−1.00463	−0.502317	+	0.864683i	$0.667519\pi$
$524$	−5.53482e9	−1.68052
$525$	−1.38604e9	−0.418041
$526$	−9.20016e8	−0.275642
$527$	−3.77501e9	−1.12352
$528$	0	0
$529$	7.69224e9	2.25922
$530$	−2.86472e7	−0.00835827
$531$	7.02502e7	0.0203618
$532$	1.13100e9	0.325665
$533$	−6.38137e9	−1.82545
$534$	−1.88636e8	−0.0536081
$535$	2.12247e7	0.00599245
$536$	2.55706e9	0.717239
$537$	2.96802e9	0.827099
$538$	−9.50393e8	−0.263127
$539$	0	0
$540$	−1.11616e8	−0.0305035
$541$	4.98110e9	1.35249	0.676246	−	0.736676i	$-0.263606\pi$
$541$	4.98110e9	1.35249	0.676246	+	0.736676i	$0.263606\pi$
$542$	1.26542e9	0.341380
$543$	−4.65696e8	−0.124825
$544$	3.85192e9	1.02584
$545$	4.40997e8	0.116694
$546$	−4.66839e8	−0.122742
$547$	−1.81980e9	−0.475410	−0.237705	−	0.971337i	$-0.576395\pi$
$547$	−1.81980e9	−0.475410	−0.237705	+	0.971337i	$0.576395\pi$
$548$	−3.58177e9	−0.929748
$549$	1.86962e8	0.0482226
$550$	0	0
$551$	4.82340e8	0.122835
$552$	4.12187e9	1.04306
$553$	8.27188e7	0.0208001
$554$	4.57674e8	0.114359
$555$	−1.87916e8	−0.0466593
$556$	1.62755e9	0.401581
$557$	−4.89297e9	−1.19972	−0.599860	−	0.800105i	$-0.704777\pi$
$557$	−4.89297e9	−1.19972	−0.599860	+	0.800105i	$0.704777\pi$
$558$	−4.43245e8	−0.108000
$559$	7.12698e9	1.72570
$560$	−8.62426e7	−0.0207522
$561$	0	0
$562$	4.94671e8	0.117555
$563$	2.86546e9	0.676728	0.338364	−	0.941015i	$-0.390126\pi$
$563$	2.86546e9	0.676728	0.338364	+	0.941015i	$0.390126\pi$
$564$	5.92749e9	1.39121
$565$	−4.03776e8	−0.0941826
$566$	−6.12513e8	−0.141990
$567$	−1.72435e9	−0.397268
$568$	9.04136e8	0.207021
$569$	−3.39523e9	−0.772638	−0.386319	−	0.922365i	$-0.626254\pi$
$569$	−3.39523e9	−0.772638	−0.386319	+	0.922365i	$0.626254\pi$
$570$	1.04686e8	0.0236769
$571$	−4.54946e9	−1.02267	−0.511333	−	0.859383i	$-0.670848\pi$
$571$	−4.54946e9	−1.02267	−0.511333	+	0.859383i	$0.670848\pi$
$572$	0	0
$573$	6.54090e9	1.45243
$574$	4.85873e8	0.107234
$575$	8.18296e9	1.79503
$576$	−2.14344e9	−0.467340
$577$	5.84945e9	1.26765	0.633826	−	0.773476i	$-0.281484\pi$
$577$	5.84945e9	1.26765	0.633826	+	0.773476i	$0.281484\pi$
$578$	1.66402e9	0.358435
$579$	1.13280e9	0.242537
$580$	−3.90754e7	−0.00831583
$581$	−4.13625e8	−0.0874964
$582$	1.67944e9	0.353129
$583$	0	0
$584$	−3.13459e9	−0.651233
$585$	3.11557e8	0.0643416
$586$	−1.66272e9	−0.341331
$587$	−2.77867e9	−0.567027	−0.283513	−	0.958968i	$-0.591500\pi$
$587$	−2.77867e9	−0.567027	−0.283513	+	0.958968i	$0.591500\pi$
$588$	5.39609e9	1.09461
$589$	3.67888e9	0.741843
$590$	−2.62847e6	−0.000526890 0
$591$	6.67082e8	0.132930
$592$	2.03854e9	0.403825
$593$	−2.58203e9	−0.508475	−0.254238	−	0.967142i	$-0.581825\pi$
$593$	−2.58203e9	−0.508475	−0.254238	+	0.967142i	$0.581825\pi$
$594$	0	0
$595$	−2.02032e8	−0.0393198
$596$	−9.23666e9	−1.78712
$597$	−3.78946e9	−0.728898
$598$	2.75614e9	0.527043
$599$	−7.26236e9	−1.38065	−0.690326	−	0.723499i	$-0.742533\pi$
$599$	−7.26236e9	−1.38065	−0.690326	+	0.723499i	$0.742533\pi$
$600$	3.03946e9	0.574470
$601$	5.85287e9	1.09979	0.549893	−	0.835235i	$-0.314669\pi$
$601$	5.85287e9	1.09979	0.549893	+	0.835235i	$0.314669\pi$
$602$	−5.42643e8	−0.101374
$603$	−5.78753e9	−1.07494
$604$	7.81826e9	1.44371
$605$	0	0
$606$	5.92906e7	0.0108226
$607$	−4.30103e9	−0.780571	−0.390286	−	0.920694i	$-0.627624\pi$
$607$	−4.30103e9	−0.780571	−0.390286	+	0.920694i	$0.627624\pi$
$608$	−3.75383e9	−0.677348
$609$	−2.72417e8	−0.0488736
$610$	−6.99534e6	−0.00124783
$611$	8.14751e9	1.44504
$612$	−5.76021e9	−1.01580
$613$	7.75826e8	0.136036	0.0680178	−	0.997684i	$-0.478333\pi$
$613$	7.75826e8	0.136036	0.0680178	+	0.997684i	$0.478333\pi$
$614$	1.08426e9	0.189035
$615$	−8.08195e8	−0.140105
$616$	0	0
$617$	−7.13547e9	−1.22299	−0.611497	−	0.791247i	$-0.709432\pi$
$617$	−7.13547e9	−1.22299	−0.611497	+	0.791247i	$0.709432\pi$
$618$	−5.40355e7	−0.00920915
$619$	6.01601e9	1.01951	0.509754	−	0.860320i	$-0.329736\pi$
$619$	6.01601e9	1.01951	0.509754	+	0.860320i	$0.329736\pi$
$620$	−2.98034e8	−0.0502222
$621$	4.59401e9	0.769789
$622$	−2.76425e8	−0.0460587
$623$	−3.54777e8	−0.0587824
$624$	−8.42395e9	−1.38794
$625$	5.99929e9	0.982923
$626$	−1.16744e9	−0.190206
$627$	0	0
$628$	−4.78427e9	−0.770826
$629$	4.77550e9	0.765141
$630$	−2.37217e7	−0.00377967
$631$	−6.05087e9	−0.958771	−0.479385	−	0.877604i	$-0.659140\pi$
$631$	−6.05087e9	−0.958771	−0.479385	+	0.877604i	$0.659140\pi$
$632$	−1.81395e8	−0.0285834
$633$	−1.07800e10	−1.68930
$634$	−8.70458e8	−0.135655
$635$	−4.26215e8	−0.0660573
$636$	−3.82872e9	−0.590137
$637$	7.41708e9	1.13696
$638$	0	0
$639$	−2.04638e9	−0.310266
$640$	4.01227e8	0.0605007
$641$	9.52953e8	0.142912	0.0714560	−	0.997444i	$-0.477235\pi$
$641$	9.52953e8	0.142912	0.0714560	+	0.997444i	$0.477235\pi$
$642$	−1.57850e8	−0.0235436
$643$	−1.51044e9	−0.224060	−0.112030	−	0.993705i	$-0.535735\pi$
$643$	−1.51044e9	−0.224060	−0.112030	+	0.993705i	$0.535735\pi$
$644$	3.77118e9	0.556387
$645$	9.02626e8	0.132449
$646$	−2.66037e9	−0.388265
$647$	−5.19762e9	−0.754465	−0.377233	−	0.926118i	$-0.623124\pi$
$647$	−5.19762e9	−0.754465	−0.377233	+	0.926118i	$0.623124\pi$
$648$	3.78133e9	0.545924
$649$	0	0
$650$	2.03237e9	0.290272
$651$	−2.07777e9	−0.295165
$652$	−5.12867e9	−0.724667
$653$	7.07261e8	0.0993993	0.0496996	−	0.998764i	$-0.484174\pi$
$653$	7.07261e8	0.0993993	0.0496996	+	0.998764i	$0.484174\pi$
$654$	−3.27973e9	−0.458475
$655$	−9.63517e8	−0.133972
$656$	8.76741e9	1.21257
$657$	7.09471e9	0.976013
$658$	−6.20346e8	−0.0848874
$659$	−9.85786e9	−1.34179	−0.670894	−	0.741554i	$-0.734089\pi$
$659$	−9.85786e9	−1.34179	−0.670894	+	0.741554i	$0.734089\pi$
$660$	0	0
$661$	5.06942e8	0.0682737	0.0341368	−	0.999417i	$-0.489132\pi$
$661$	5.06942e8	0.0682737	0.0341368	+	0.999417i	$0.489132\pi$
$662$	−1.26946e8	−0.0170066
$663$	−1.97340e10	−2.62977
$664$	9.07040e8	0.120237
$665$	1.96888e8	0.0259623
$666$	5.60717e8	0.0735503
$667$	1.60830e9	0.209859
$668$	8.98226e9	1.16592
$669$	−1.25865e10	−1.62523
$670$	2.16545e8	0.0278155
$671$	0	0
$672$	2.12010e9	0.269503
$673$	−9.77343e9	−1.23593	−0.617966	−	0.786205i	$-0.712043\pi$
$673$	−9.77343e9	−1.23593	−0.617966	+	0.786205i	$0.712043\pi$
$674$	−1.55647e9	−0.195809
$675$	3.38762e9	0.423966
$676$	−4.69316e9	−0.584321
$677$	−2.69076e9	−0.333284	−0.166642	−	0.986017i	$-0.553292\pi$
$677$	−2.69076e9	−0.333284	−0.166642	+	0.986017i	$0.553292\pi$
$678$	3.00291e9	0.370032
$679$	3.15861e9	0.387214
$680$	4.43038e8	0.0540331
$681$	9.67162e9	1.17350
$682$	0	0
$683$	−1.47392e9	−0.177012	−0.0885059	−	0.996076i	$-0.528209\pi$
$683$	−1.47392e9	−0.177012	−0.0885059	+	0.996076i	$0.528209\pi$
$684$	5.61352e9	0.670717
$685$	−6.23524e8	−0.0741202
$686$	−1.19631e9	−0.141485
$687$	−9.17709e9	−1.07983
$688$	−9.79182e9	−1.14631
$689$	−5.26268e9	−0.612971
$690$	3.49062e8	0.0404511
$691$	5.23240e9	0.603292	0.301646	−	0.953420i	$-0.402464\pi$
$691$	5.23240e9	0.603292	0.301646	+	0.953420i	$0.402464\pi$
$692$	−1.40756e10	−1.61472
$693$	0	0
$694$	1.02587e9	0.116502
$695$	2.83329e8	0.0320143
$696$	5.97386e8	0.0671618
$697$	2.05386e10	2.29750
$698$	−2.06815e9	−0.230191
$699$	−1.75506e10	−1.94366
$700$	2.78086e9	0.306434
$701$	1.40020e10	1.53525	0.767623	−	0.640902i	$-0.221440\pi$
$701$	1.40020e10	1.53525	0.767623	+	0.640902i	$0.221440\pi$
$702$	1.14100e9	0.124481
$703$	−4.65389e9	−0.505210
$704$	0	0
$705$	1.03187e9	0.110909
$706$	−3.46874e9	−0.370985
$707$	1.11511e8	0.0118672
$708$	−3.51296e8	−0.0372012
$709$	1.67299e10	1.76292	0.881460	−	0.472258i	$-0.156561\pi$
$709$	1.67299e10	1.76292	0.881460	+	0.472258i	$0.156561\pi$
$710$	7.65670e7	0.00802855
$711$	4.10561e8	0.0428385
$712$	7.77993e8	0.0807785
$713$	1.22668e10	1.26741
$714$	1.50253e9	0.154483
$715$	0	0
$716$	−5.95484e9	−0.606282
$717$	−1.39230e10	−1.41064
$718$	−1.51121e9	−0.152366
$719$	−8.56461e9	−0.859323	−0.429662	−	0.902990i	$-0.641367\pi$
$719$	−8.56461e9	−0.859323	−0.429662	+	0.902990i	$0.641367\pi$
$720$	−4.28050e8	−0.0427397
$721$	−1.01627e8	−0.0100980
$722$	2.70756e8	0.0267731
$723$	1.41206e9	0.138954
$724$	9.34341e8	0.0914999
$725$	1.18596e9	0.115581
$726$	0	0
$727$	2.91423e9	0.281289	0.140645	−	0.990060i	$-0.455082\pi$
$727$	2.91423e9	0.281289	0.140645	+	0.990060i	$0.455082\pi$
$728$	1.92539e9	0.184952
$729$	−2.79448e9	−0.267150
$730$	−2.65454e8	−0.0252557
$731$	−2.29384e10	−2.17196
$732$	−9.34932e8	−0.0881031
$733$	1.29641e10	1.21584	0.607921	−	0.793997i	$-0.292004\pi$
$733$	1.29641e10	1.21584	0.607921	+	0.793997i	$0.292004\pi$
$734$	2.02435e9	0.188951
$735$	9.39366e8	0.0872628
$736$	−1.25167e10	−1.15722
$737$	0	0
$738$	2.41155e9	0.220851
$739$	4.46882e9	0.407322	0.203661	−	0.979042i	$-0.434716\pi$
$739$	4.46882e9	0.407322	0.203661	+	0.979042i	$0.434716\pi$
$740$	3.77022e8	0.0342023
$741$	1.92315e10	1.73640
$742$	4.00697e8	0.0360083
$743$	1.69242e10	1.51373	0.756864	−	0.653572i	$-0.226730\pi$
$743$	1.69242e10	1.51373	0.756864	+	0.653572i	$0.226730\pi$
$744$	4.55636e9	0.405613
$745$	−1.60794e9	−0.142470
$746$	5.73629e8	0.0505877
$747$	−2.05296e9	−0.180201
$748$	0	0
$749$	−2.96877e8	−0.0258161
$750$	5.16272e8	0.0446852
$751$	−1.83277e9	−0.157895	−0.0789475	−	0.996879i	$-0.525156\pi$
$751$	−1.83277e9	−0.157895	−0.0789475	+	0.996879i	$0.525156\pi$
$752$	−1.11939e10	−0.959887
$753$	1.49565e10	1.27658
$754$	3.99448e8	0.0339360
$755$	1.36103e9	0.115094
$756$	1.56121e9	0.131412
$757$	−4.45249e9	−0.373051	−0.186525	−	0.982450i	$-0.559723\pi$
$757$	−4.45249e9	−0.373051	−0.186525	+	0.982450i	$0.559723\pi$
$758$	2.51572e9	0.209807
$759$	0	0
$760$	−4.31756e8	−0.0356772
$761$	−1.04559e10	−0.860034	−0.430017	−	0.902821i	$-0.641492\pi$
$761$	−1.04559e10	−0.860034	−0.430017	+	0.902821i	$0.641492\pi$
$762$	3.16980e9	0.259531
$763$	−6.16836e9	−0.502728
$764$	−1.31232e10	−1.06467
$765$	−1.00275e9	−0.0809802
$766$	−3.99148e9	−0.320873
$767$	−4.82867e8	−0.0386406
$768$	8.33106e9	0.663645
$769$	1.36936e10	1.08586	0.542931	−	0.839777i	$-0.317315\pi$
$769$	1.36936e10	1.08586	0.542931	+	0.839777i	$0.317315\pi$
$770$	0	0
$771$	−2.09139e10	−1.64341
$772$	−2.27277e9	−0.177785
$773$	−1.14791e9	−0.0893883	−0.0446942	−	0.999001i	$-0.514231\pi$
$773$	−1.14791e9	−0.0893883	−0.0446942	+	0.999001i	$0.514231\pi$
$774$	−2.69332e9	−0.208783
$775$	9.04551e9	0.698035
$776$	−6.92652e9	−0.532107
$777$	2.62844e9	0.201013
$778$	1.43450e8	0.0109212
$779$	−2.00156e10	−1.51700
$780$	−1.55798e9	−0.117553
$781$	0	0
$782$	−8.87069e9	−0.663336
$783$	6.65813e8	0.0495662
$784$	−1.01904e10	−0.755239
$785$	−8.32859e8	−0.0614508
$786$	7.16576e9	0.526360
$787$	1.79626e10	1.31358	0.656790	−	0.754073i	$-0.271914\pi$
$787$	1.79626e10	1.31358	0.656790	+	0.754073i	$0.271914\pi$
$788$	−1.33839e9	−0.0974407
$789$	−2.14054e10	−1.55151
$790$	−1.53614e7	−0.00110850
$791$	5.64773e9	0.405748
$792$	0	0
$793$	−1.28509e9	−0.0915120
$794$	3.05666e9	0.216708
$795$	−6.66514e8	−0.0470462
$796$	7.60291e9	0.534298
$797$	1.22815e10	0.859308	0.429654	−	0.902994i	$-0.358635\pi$
$797$	1.22815e10	0.859308	0.429654	+	0.902994i	$0.358635\pi$
$798$	−1.46427e9	−0.102003
$799$	−2.62229e10	−1.81873
$800$	−9.22980e9	−0.637349
$801$	−1.76088e9	−0.121064
$802$	−4.18908e9	−0.286753
$803$	0	0
$804$	2.89414e10	1.96392
$805$	6.56498e8	0.0443556
$806$	3.04666e9	0.204951
$807$	−2.21121e10	−1.48106
$808$	−2.44533e8	−0.0163079
$809$	8.86347e9	0.588551	0.294275	−	0.955721i	$-0.404922\pi$
$809$	8.86347e9	0.588551	0.294275	+	0.955721i	$0.404922\pi$
$810$	3.20223e8	0.0211717
$811$	−8.71364e9	−0.573623	−0.286811	−	0.957987i	$-0.592595\pi$
$811$	−8.71364e9	−0.573623	−0.286811	+	0.957987i	$0.592595\pi$
$812$	5.46560e8	0.0358255
$813$	2.94417e10	1.92152
$814$	0	0
$815$	−8.92814e8	−0.0577710
$816$	2.71127e10	1.74686
$817$	2.23542e10	1.43411
$818$	2.01425e9	0.128670
$819$	−4.35784e9	−0.277190
$820$	1.62151e9	0.102700
$821$	−2.17356e10	−1.37079	−0.685394	−	0.728172i	$-0.740370\pi$
$821$	−2.17356e10	−1.37079	−0.685394	+	0.728172i	$0.740370\pi$
$822$	4.63720e9	0.291209
$823$	−8.02664e9	−0.501920	−0.250960	−	0.967997i	$-0.580746\pi$
$823$	−8.02664e9	−0.501920	−0.250960	+	0.967997i	$0.580746\pi$
$824$	2.22859e8	0.0138767
$825$	0	0
$826$	3.67651e7	0.00226990
$827$	5.04666e9	0.310266	0.155133	−	0.987894i	$-0.450419\pi$
$827$	5.04666e9	0.310266	0.155133	+	0.987894i	$0.450419\pi$
$828$	1.87176e10	1.14589
$829$	−1.32432e10	−0.807335	−0.403667	−	0.914906i	$-0.632265\pi$
$829$	−1.32432e10	−0.807335	−0.403667	+	0.914906i	$0.632265\pi$
$830$	7.68129e7	0.00466295
$831$	1.06484e10	0.643695
$832$	1.47330e10	0.886869
$833$	−2.38720e10	−1.43098
$834$	−2.10714e9	−0.125780
$835$	1.56366e9	0.0929477
$836$	0	0
$837$	5.07826e9	0.299348
$838$	5.29567e9	0.310861
$839$	1.08137e9	0.0632129	0.0316064	−	0.999500i	$-0.489938\pi$
$839$	1.08137e9	0.0632129	0.0316064	+	0.999500i	$0.489938\pi$
$840$	2.43849e8	0.0141952
$841$	−1.70168e10	−0.986487
$842$	−3.45169e9	−0.199269
$843$	1.15092e10	0.661679
$844$	2.16284e10	1.23830
$845$	−8.16998e8	−0.0465825
$846$	−3.07898e9	−0.174828
$847$	0	0
$848$	7.23044e9	0.407173
$849$	−1.42509e10	−0.799218
$850$	−6.54123e9	−0.365336
$851$	−1.55178e10	−0.863133
$852$	1.02332e10	0.566858
$853$	−2.00367e10	−1.10536	−0.552682	−	0.833392i	$-0.686396\pi$
$853$	−2.00367e10	−1.10536	−0.552682	+	0.833392i	$0.686396\pi$
$854$	9.78459e7	0.00537576
$855$	9.77218e8	0.0534700
$856$	6.51023e8	0.0354763
$857$	−1.47813e10	−0.802194	−0.401097	−	0.916036i	$-0.631371\pi$
$857$	−1.47813e10	−0.802194	−0.401097	+	0.916036i	$0.631371\pi$
$858$	0	0
$859$	−6.72649e8	−0.0362087	−0.0181043	−	0.999836i	$-0.505763\pi$
$859$	−6.72649e8	−0.0362087	−0.0181043	+	0.999836i	$0.505763\pi$
$860$	−1.81097e9	−0.0970881
$861$	1.13045e10	0.603586
$862$	−3.53348e9	−0.187900
$863$	1.47026e10	0.778674	0.389337	−	0.921095i	$-0.372704\pi$
$863$	1.47026e10	0.778674	0.389337	+	0.921095i	$0.372704\pi$
$864$	−5.18172e9	−0.273323
$865$	−2.45032e9	−0.128726
$866$	4.38233e9	0.229294
$867$	3.87155e10	2.01752
$868$	4.16870e9	0.216362
$869$	0	0
$870$	5.05898e7	0.00260463
$871$	3.97808e10	2.03990
$872$	1.35266e10	0.690847
$873$	1.56772e10	0.797478
$874$	8.64479e9	0.437990
$875$	9.70978e8	0.0489983
$876$	−3.54781e10	−1.78318
$877$	−1.13782e10	−0.569607	−0.284804	−	0.958586i	$-0.591928\pi$
$877$	−1.13782e10	−0.569607	−0.284804	+	0.958586i	$0.591928\pi$
$878$	4.00424e9	0.199659
$879$	−3.86852e10	−1.92125
$880$	0	0
$881$	3.18530e10	1.56941	0.784703	−	0.619873i	$-0.212816\pi$
$881$	3.18530e10	1.56941	0.784703	+	0.619873i	$0.212816\pi$
$882$	−2.80295e9	−0.137555
$883$	1.07971e10	0.527768	0.263884	−	0.964554i	$-0.414996\pi$
$883$	1.07971e10	0.527768	0.263884	+	0.964554i	$0.414996\pi$
$884$	3.95929e10	1.92768
$885$	−6.11547e7	−0.00296571
$886$	−3.47990e9	−0.168093
$887$	6.77567e9	0.326002	0.163001	−	0.986626i	$-0.447883\pi$
$887$	6.77567e9	0.326002	0.163001	+	0.986626i	$0.447883\pi$
$888$	−5.76392e9	−0.276231
$889$	5.96160e9	0.284581
$890$	6.58845e7	0.00313270
$891$	0	0
$892$	2.52528e10	1.19133
$893$	2.55552e10	1.20088
$894$	1.19584e10	0.559748
$895$	−1.03664e9	−0.0483332
$896$	−5.61208e9	−0.260643
$897$	6.41251e10	2.96657
$898$	−5.06695e9	−0.233496
$899$	1.77783e9	0.0816079
$900$	1.38023e10	0.631109
$901$	1.69381e10	0.771484
$902$	0	0
$903$	−1.26253e10	−0.570604
$904$	−1.23849e10	−0.557577
$905$	1.62653e8	0.00729443
$906$	−1.01221e10	−0.452189
$907$	−1.06048e10	−0.471929	−0.235964	−	0.971762i	$-0.575825\pi$
$907$	−1.06048e10	−0.471929	−0.235964	+	0.971762i	$0.575825\pi$
$908$	−1.94045e10	−0.860204
$909$	5.53465e8	0.0244409
$910$	1.63052e8	0.00717268
$911$	−9.07146e9	−0.397523	−0.198762	−	0.980048i	$-0.563692\pi$
$911$	−9.07146e9	−0.397523	−0.198762	+	0.980048i	$0.563692\pi$
$912$	−2.64222e10	−1.15342
$913$	0	0
$914$	2.05664e9	0.0890935
$915$	−1.62756e8	−0.00702364
$916$	1.84123e10	0.791541
$917$	1.34770e10	0.577166
$918$	−3.67232e9	−0.156672
$919$	−9.78493e9	−0.415866	−0.207933	−	0.978143i	$-0.566674\pi$
$919$	−9.78493e9	−0.415866	−0.207933	+	0.978143i	$0.566674\pi$
$920$	−1.43964e9	−0.0609532
$921$	2.52266e10	1.06402
$922$	9.83485e8	0.0413247
$923$	1.40659e10	0.588791
$924$	0	0
$925$	−1.14428e10	−0.475376
$926$	−6.81741e9	−0.282151
$927$	−5.04410e8	−0.0207972
$928$	−1.81405e9	−0.0745130
$929$	2.85741e10	1.16928	0.584638	−	0.811294i	$-0.301237\pi$
$929$	2.85741e10	1.16928	0.584638	+	0.811294i	$0.301237\pi$
$930$	3.85856e8	0.0157302
$931$	2.32641e10	0.944850
$932$	3.52123e10	1.42475
$933$	−6.43139e9	−0.259250
$934$	−1.23029e9	−0.0494074
$935$	0	0
$936$	9.55634e9	0.380913
$937$	−1.75648e10	−0.697516	−0.348758	−	0.937213i	$-0.613397\pi$
$937$	−1.75648e10	−0.697516	−0.348758	+	0.937213i	$0.613397\pi$
$938$	−3.02888e9	−0.119832
$939$	−2.71620e10	−1.07061
$940$	−2.07028e9	−0.0812985
$941$	−2.06702e10	−0.808686	−0.404343	−	0.914607i	$-0.632500\pi$
$941$	−2.06702e10	−0.808686	−0.404343	+	0.914607i	$0.632500\pi$
$942$	6.19404e9	0.241433
$943$	−6.67396e10	−2.59175
$944$	6.63414e8	0.0256675
$945$	2.71780e8	0.0104763
$946$	0	0
$947$	−2.61002e10	−0.998662	−0.499331	−	0.866411i	$-0.666421\pi$
$947$	−2.61002e10	−0.998662	−0.499331	+	0.866411i	$0.666421\pi$
$948$	−2.05307e9	−0.0782661
$949$	−4.87657e10	−1.85218
$950$	6.37465e9	0.241226
$951$	−2.02523e10	−0.763560
$952$	−6.19691e9	−0.232780
$953$	−3.69157e10	−1.38161	−0.690805	−	0.723041i	$-0.742744\pi$
$953$	−3.69157e10	−1.38161	−0.690805	+	0.723041i	$0.742744\pi$
$954$	1.98879e9	0.0741600
$955$	−2.28453e9	−0.0848759
$956$	2.79342e10	1.03403
$957$	0	0
$958$	7.68925e9	0.282556
$959$	8.72142e9	0.319317
$960$	1.86592e9	0.0680681
$961$	−1.39528e10	−0.507142
$962$	−3.85411e9	−0.139576
$963$	−1.47350e9	−0.0531689
$964$	−2.83307e9	−0.101856
$965$	−3.95651e8	−0.0141732
$966$	−4.88244e9	−0.174268
$967$	−2.24258e10	−0.797543	−0.398772	−	0.917050i	$-0.630563\pi$
$967$	−2.24258e10	−0.797543	−0.398772	+	0.917050i	$0.630563\pi$
$968$	0	0
$969$	−6.18969e10	−2.18542
$970$	−5.86574e8	−0.0206358
$971$	−3.46100e10	−1.21321	−0.606603	−	0.795005i	$-0.707468\pi$
$971$	−3.46100e10	−1.21321	−0.606603	+	0.795005i	$0.707468\pi$
$972$	3.12335e10	1.09091
$973$	−3.96301e9	−0.137921
$974$	−1.60700e9	−0.0557263
$975$	4.72857e10	1.63386
$976$	1.76560e9	0.0607879
$977$	−6.15266e9	−0.211073	−0.105536	−	0.994415i	$-0.533656\pi$
$977$	−6.15266e9	−0.211073	−0.105536	+	0.994415i	$0.533656\pi$
$978$	6.63994e9	0.226975
$979$	0	0
$980$	−1.88468e9	−0.0639656
$981$	−3.06156e10	−1.03538
$982$	−7.96507e9	−0.268410
$983$	−3.44287e10	−1.15607	−0.578034	−	0.816013i	$-0.696180\pi$
$983$	−3.44287e10	−1.15607	−0.578034	+	0.816013i	$0.696180\pi$
$984$	−2.47896e10	−0.829444
$985$	−2.32991e8	−0.00776804
$986$	−1.28563e9	−0.0427118
$987$	−1.44331e10	−0.477805
$988$	−3.85847e10	−1.27282
$989$	7.45376e10	2.45012
$990$	0	0
$991$	−1.98466e10	−0.647782	−0.323891	−	0.946094i	$-0.604991\pi$
$991$	−1.98466e10	−0.647782	−0.323891	+	0.946094i	$0.604991\pi$
$992$	−1.38361e10	−0.450010
$993$	−2.95357e9	−0.0957249
$994$	−1.07097e9	−0.0345878
$995$	1.32354e9	0.0425946
$996$	1.02661e10	0.329229
$997$	−3.52011e10	−1.12492	−0.562462	−	0.826823i	$-0.690146\pi$
$997$	−3.52011e10	−1.12492	−0.562462	+	0.826823i	$0.690146\pi$
$998$	−6.40841e9	−0.204077
$999$	−6.42414e9	−0.203862

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.8.a.d.1.3	✓	5
11.10	odd	2		121.8.a.e.1.3	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.8.a.d.1.3	✓	5	1.1	even	1	trivial
121.8.a.e.1.3	yes	5	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)

\(f(q)\)	\(=\)	\(q+2.59754 q^{2} +60.4351 q^{3} -121.253 q^{4} -21.1080 q^{5} +156.982 q^{6} +295.244 q^{7} -647.443 q^{8} +1465.40 q^{9} -54.8289 q^{10} -7327.92 q^{12} -10072.4 q^{13} +766.908 q^{14} -1275.67 q^{15} +13838.6 q^{16} +32418.4 q^{17} +3806.42 q^{18} -31592.8 q^{19} +2559.41 q^{20} +17843.1 q^{21} -105343. q^{23} -39128.3 q^{24} -77679.5 q^{25} -26163.5 q^{26} -43610.2 q^{27} -35799.2 q^{28} -15267.4 q^{29} -3313.59 q^{30} -116447. q^{31} +118819. q^{32} +84207.9 q^{34} -6232.03 q^{35} -177683. q^{36} +147308. q^{37} -82063.6 q^{38} -608729. q^{39} +13666.3 q^{40} +633548. q^{41} +46348.2 q^{42} -707573. q^{43} -30931.6 q^{45} -273631. q^{46} -808891. q^{47} +836337. q^{48} -736374. q^{49} -201775. q^{50} +1.95921e6 q^{51} +1.22131e6 q^{52} +522483. q^{53} -113279. q^{54} -191154. q^{56} -1.90932e6 q^{57} -39657.6 q^{58} +47939.4 q^{59} +154678. q^{60} +127585. q^{61} -302474. q^{62} +432650. q^{63} -1.46270e6 q^{64} +212609. q^{65} -3.94947e6 q^{67} -3.93082e6 q^{68} -6.36639e6 q^{69} -16187.9 q^{70} -1.39647e6 q^{71} -948761. q^{72} +4.84150e6 q^{73} +382639. q^{74} -4.69456e6 q^{75} +3.83072e6 q^{76} -1.58119e6 q^{78} +280171. q^{79} -292106. q^{80} -5.84040e6 q^{81} +1.64566e6 q^{82} -1.40096e6 q^{83} -2.16353e6 q^{84} -684288. q^{85} -1.83795e6 q^{86} -922684. q^{87} -1.20164e6 q^{89} -80346.0 q^{90} -2.97383e6 q^{91} +1.27731e7 q^{92} -7.03746e6 q^{93} -2.10113e6 q^{94} +666863. q^{95} +7.18083e6 q^{96} +1.06983e7 q^{97} -1.91276e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 8 q^{2} - 14 q^{3} + 166 q^{4} - 515 q^{5} - 692 q^{6} + 1286 q^{7} - 2334 q^{8} + 1133 q^{9} + 6836 q^{10} + 10496 q^{12} + 6533 q^{13} - 18668 q^{14} + 2074 q^{15} + 15010 q^{16} - 32705 q^{17}+ \cdots - 9136104 q^{98}+O(q^{100}) \) 5 * q - 8 * q^2 - 14 * q^3 + 166 * q^4 - 515 * q^5 - 692 * q^6 + 1286 * q^7 - 2334 * q^8 + 1133 * q^9 + 6836 * q^10 + 10496 * q^12 + 6533 * q^13 - 18668 * q^14 + 2074 * q^15 + 15010 * q^16 - 32705 * q^17 + 21848 * q^18 + 29910 * q^19 - 79078 * q^20 - 23132 * q^21 - 45214 * q^23 - 94992 * q^24 + 11764 * q^25 - 58196 * q^26 - 230348 * q^27 + 21856 * q^28 + 242061 * q^29 + 477220 * q^30 + 55310 * q^31 - 40750 * q^32 - 194608 * q^34 - 1092602 * q^35 - 1250618 * q^36 + 586689 * q^37 - 166692 * q^38 - 283790 * q^39 + 1951374 * q^40 + 565735 * q^41 - 1120208 * q^42 - 287040 * q^43 - 1566547 * q^45 - 1904780 * q^46 - 3182566 * q^47 + 949544 * q^48 - 765183 * q^49 - 4244056 * q^50 + 3141694 * q^51 + 4918498 * q^52 - 1220883 * q^53 + 913528 * q^54 - 5142192 * q^56 - 7377636 * q^57 - 10076868 * q^58 + 1304864 * q^59 - 7345528 * q^60 - 3437754 * q^61 + 4156516 * q^62 + 7075454 * q^63 - 4731286 * q^64 - 3342779 * q^65 - 5199446 * q^67 - 10501510 * q^68 - 11265124 * q^69 + 9858572 * q^70 - 3440220 * q^71 - 5576286 * q^72 + 9963974 * q^73 + 7512132 * q^74 - 241456 * q^75 - 7011480 * q^76 - 8493404 * q^78 - 7834562 * q^79 - 17690746 * q^80 + 4373321 * q^81 - 898480 * q^82 - 6230682 * q^83 + 19063160 * q^84 + 11708303 * q^85 + 6786552 * q^86 + 13109106 * q^87 - 13960869 * q^89 - 12112156 * q^90 + 573182 * q^91 - 3324824 * q^92 + 7120948 * q^93 - 9234428 * q^94 - 8171634 * q^95 - 4167472 * q^96 - 15733241 * q^97 - 9136104 * q^98

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