LMFDB - Embedded newform 226.2.a.d.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [226,2,Mod(1,226)] 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("226.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(226, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 226 = 2 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	226.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,4,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$1.80461908568$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 5 $ x^4 - 5*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.17557$ of defining polynomial
Character	$\chi$	$=$	226.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.28408 q^{3} +1.00000 q^{4} +0.273457 q^{5} +1.28408 q^{6} +1.23607 q^{7} +1.00000 q^{8} -1.35114 q^{9} +0.273457 q^{10} -2.35114 q^{11} +1.28408 q^{12} -5.04029 q^{13} +1.23607 q^{14} +0.351141 q^{15} +1.00000 q^{16} +4.47214 q^{17} -1.35114 q^{18} +3.75621 q^{19} +0.273457 q^{20} +1.58721 q^{21} -2.35114 q^{22} -1.32739 q^{23} +1.28408 q^{24} -4.92522 q^{25} -5.04029 q^{26} -5.58721 q^{27} +1.23607 q^{28} +5.31375 q^{29} +0.351141 q^{30} -6.82328 q^{31} +1.00000 q^{32} -3.01905 q^{33} +4.47214 q^{34} +0.338012 q^{35} -1.35114 q^{36} +1.86067 q^{37} +3.75621 q^{38} -6.47214 q^{39} +0.273457 q^{40} +1.10194 q^{41} +1.58721 q^{42} +5.43945 q^{43} -2.35114 q^{44} -0.369480 q^{45} -1.32739 q^{46} -6.02967 q^{47} +1.28408 q^{48} -5.47214 q^{49} -4.92522 q^{50} +5.74258 q^{51} -5.04029 q^{52} +8.49338 q^{53} -5.58721 q^{54} -0.642937 q^{55} +1.23607 q^{56} +4.82328 q^{57} +5.31375 q^{58} +0.243785 q^{59} +0.351141 q^{60} -6.85765 q^{61} -6.82328 q^{62} -1.67010 q^{63} +1.00000 q^{64} -1.37831 q^{65} -3.01905 q^{66} -5.28408 q^{67} +4.47214 q^{68} -1.70447 q^{69} +0.338012 q^{70} +1.08540 q^{71} -1.35114 q^{72} +13.7638 q^{73} +1.86067 q^{74} -6.32437 q^{75} +3.75621 q^{76} -2.90617 q^{77} -6.47214 q^{78} -5.03186 q^{79} +0.273457 q^{80} -3.12099 q^{81} +1.10194 q^{82} -0.919299 q^{83} +1.58721 q^{84} +1.22294 q^{85} +5.43945 q^{86} +6.82328 q^{87} -2.35114 q^{88} +14.0000 q^{89} -0.369480 q^{90} -6.23015 q^{91} -1.32739 q^{92} -8.76163 q^{93} -6.02967 q^{94} +1.02717 q^{95} +1.28408 q^{96} +13.2917 q^{97} -5.47214 q^{98} +3.17672 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 4 q^{7} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{12} + 4 q^{13} - 4 q^{14} - 8 q^{15} + 4 q^{16} + 4 q^{18} - 6 q^{19} + 4 q^{20} - 12 q^{21} - 6 q^{23}+ \cdots + 40 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 4 * q^7 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 2 * q^12 + 4 * q^13 - 4 * q^14 - 8 * q^15 + 4 * q^16 + 4 * q^18 - 6 * q^19 + 4 * q^20 - 12 * q^21 - 6 * q^23 + 2 * q^24 + 4 * q^25 + 4 * q^26 - 4 * q^27 - 4 * q^28 - 8 * q^30 + 4 * q^32 - 4 * q^35 + 4 * q^36 - 8 * q^37 - 6 * q^38 - 8 * q^39 + 4 * q^40 + 8 * q^41 - 12 * q^42 - 6 * q^43 - 16 * q^45 - 6 * q^46 - 6 * q^47 + 2 * q^48 - 4 * q^49 + 4 * q^50 - 20 * q^51 + 4 * q^52 + 4 * q^53 - 4 * q^54 - 20 * q^55 - 4 * q^56 - 8 * q^57 + 22 * q^59 - 8 * q^60 + 16 * q^61 - 4 * q^63 + 4 * q^64 + 24 * q^65 - 18 * q^67 + 12 * q^69 - 4 * q^70 + 22 * q^71 + 4 * q^72 - 8 * q^74 + 2 * q^75 - 6 * q^76 - 8 * q^78 - 2 * q^79 + 4 * q^80 - 4 * q^81 + 8 * q^82 + 12 * q^83 - 12 * q^84 - 6 * q^86 + 56 * q^89 - 16 * q^90 - 24 * q^91 - 6 * q^92 + 20 * q^93 - 6 * q^94 - 16 * q^95 + 2 * q^96 + 16 * q^97 - 4 * q^98 + 40 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.28408	0.741363	0.370682	−	0.928760i	$-0.379124\pi$
$3$	1.28408	0.741363	0.370682	+	0.928760i	$0.379124\pi$
$4$	1.00000	0.500000
$5$	0.273457	0.122294	0.0611469	−	0.998129i	$-0.480524\pi$
$5$	0.273457	0.122294	0.0611469	+	0.998129i	$0.480524\pi$
$6$	1.28408	0.524223
$7$	1.23607	0.467190	0.233595	−	0.972334i	$-0.424951\pi$
$7$	1.23607	0.467190	0.233595	+	0.972334i	$0.424951\pi$
$8$	1.00000	0.353553
$9$	−1.35114	−0.450380
$10$	0.273457	0.0864748
$11$	−2.35114	−0.708896	−0.354448	−	0.935076i	$-0.615331\pi$
$11$	−2.35114	−0.708896	−0.354448	+	0.935076i	$0.615331\pi$
$12$	1.28408	0.370682
$13$	−5.04029	−1.39793	−0.698963	−	0.715158i	$-0.746355\pi$
$13$	−5.04029	−1.39793	−0.698963	+	0.715158i	$0.746355\pi$
$14$	1.23607	0.330353
$15$	0.351141	0.0906642
$16$	1.00000	0.250000
$17$	4.47214	1.08465	0.542326	−	0.840168i	$-0.317544\pi$
$17$	4.47214	1.08465	0.542326	+	0.840168i	$0.317544\pi$
$18$	−1.35114	−0.318467
$19$	3.75621	0.861735	0.430867	−	0.902415i	$-0.358208\pi$
$19$	3.75621	0.861735	0.430867	+	0.902415i	$0.358208\pi$
$20$	0.273457	0.0611469
$21$	1.58721	0.346357
$22$	−2.35114	−0.501265
$23$	−1.32739	−0.276780	−0.138390	−	0.990378i	$-0.544193\pi$
$23$	−1.32739	−0.276780	−0.138390	+	0.990378i	$0.544193\pi$
$24$	1.28408	0.262112
$25$	−4.92522	−0.985044
$26$	−5.04029	−0.988483
$27$	−5.58721	−1.07526
$28$	1.23607	0.233595
$29$	5.31375	0.986739	0.493369	−	0.869820i	$-0.335765\pi$
$29$	5.31375	0.986739	0.493369	+	0.869820i	$0.335765\pi$
$30$	0.351141	0.0641093
$31$	−6.82328	−1.22550	−0.612748	−	0.790278i	$-0.709936\pi$
$31$	−6.82328	−1.22550	−0.612748	+	0.790278i	$0.709936\pi$
$32$	1.00000	0.176777
$33$	−3.01905	−0.525549
$34$	4.47214	0.766965
$35$	0.338012	0.0571345
$36$	−1.35114	−0.225190
$37$	1.86067	0.305892	0.152946	−	0.988235i	$-0.451124\pi$
$37$	1.86067	0.305892	0.152946	+	0.988235i	$0.451124\pi$
$38$	3.75621	0.609339
$39$	−6.47214	−1.03637
$40$	0.273457	0.0432374
$41$	1.10194	0.172095	0.0860474	−	0.996291i	$-0.472576\pi$
$41$	1.10194	0.172095	0.0860474	+	0.996291i	$0.472576\pi$
$42$	1.58721	0.244912
$43$	5.43945	0.829508	0.414754	−	0.909934i	$-0.363868\pi$
$43$	5.43945	0.829508	0.414754	+	0.909934i	$0.363868\pi$
$44$	−2.35114	−0.354448
$45$	−0.369480	−0.0550788
$46$	−1.32739	−0.195713
$47$	−6.02967	−0.879518	−0.439759	−	0.898116i	$-0.644936\pi$
$47$	−6.02967	−0.879518	−0.439759	+	0.898116i	$0.644936\pi$
$48$	1.28408	0.185341
$49$	−5.47214	−0.781734
$50$	−4.92522	−0.696531
$51$	5.74258	0.804121
$52$	−5.04029	−0.698963
$53$	8.49338	1.16666	0.583328	−	0.812237i	$-0.301750\pi$
$53$	8.49338	1.16666	0.583328	+	0.812237i	$0.301750\pi$
$54$	−5.58721	−0.760323
$55$	−0.642937	−0.0866936
$56$	1.23607	0.165177
$57$	4.82328	0.638859
$58$	5.31375	0.697730
$59$	0.243785	0.0317381	0.0158691	−	0.999874i	$-0.494949\pi$
$59$	0.243785	0.0317381	0.0158691	+	0.999874i	$0.494949\pi$
$60$	0.351141	0.0453321
$61$	−6.85765	−0.878032	−0.439016	−	0.898479i	$-0.644673\pi$
$61$	−6.85765	−0.878032	−0.439016	+	0.898479i	$0.644673\pi$
$62$	−6.82328	−0.866557
$63$	−1.67010	−0.210413
$64$	1.00000	0.125000
$65$	−1.37831	−0.170958
$66$	−3.01905	−0.371619
$67$	−5.28408	−0.645553	−0.322777	−	0.946475i	$-0.604616\pi$
$67$	−5.28408	−0.645553	−0.322777	+	0.946475i	$0.604616\pi$
$68$	4.47214	0.542326
$69$	−1.70447	−0.205195
$70$	0.338012	0.0404002
$71$	1.08540	0.128813	0.0644067	−	0.997924i	$-0.479485\pi$
$71$	1.08540	0.128813	0.0644067	+	0.997924i	$0.479485\pi$
$72$	−1.35114	−0.159233
$73$	13.7638	1.61093	0.805467	−	0.592641i	$-0.201915\pi$
$73$	13.7638	1.61093	0.805467	+	0.592641i	$0.201915\pi$
$74$	1.86067	0.216298
$75$	−6.32437	−0.730276
$76$	3.75621	0.430867
$77$	−2.90617	−0.331189
$78$	−6.47214	−0.732825
$79$	−5.03186	−0.566129	−0.283065	−	0.959101i	$-0.591351\pi$
$79$	−5.03186	−0.566129	−0.283065	+	0.959101i	$0.591351\pi$
$80$	0.273457	0.0305735
$81$	−3.12099	−0.346777
$82$	1.10194	0.121689
$83$	−0.919299	−0.100906	−0.0504531	−	0.998726i	$-0.516067\pi$
$83$	−0.919299	−0.100906	−0.0504531	+	0.998726i	$0.516067\pi$
$84$	1.58721	0.173179
$85$	1.22294	0.132646
$86$	5.43945	0.586551
$87$	6.82328	0.731532
$88$	−2.35114	−0.250632
$89$	14.0000	1.48400	0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000	1.48400	0.741999	+	0.670402i	$0.233878\pi$
$90$	−0.369480	−0.0389466
$91$	−6.23015	−0.653097
$92$	−1.32739	−0.138390
$93$	−8.76163	−0.908538
$94$	−6.02967	−0.621913
$95$	1.02717	0.105385
$96$	1.28408	0.131056
$97$	13.2917	1.34957	0.674783	−	0.738016i	$-0.264237\pi$
$97$	13.2917	1.34957	0.674783	+	0.738016i	$0.264237\pi$
$98$	−5.47214	−0.552769
$99$	3.17672	0.319273
$100$	−4.92522	−0.492522
$101$	13.1311	1.30659	0.653297	−	0.757102i	$-0.273385\pi$
$101$	13.1311	1.30659	0.653297	+	0.757102i	$0.273385\pi$
$102$	5.74258	0.568600
$103$	10.3404	1.01887	0.509435	−	0.860509i	$-0.329854\pi$
$103$	10.3404	1.01887	0.509435	+	0.860509i	$0.329854\pi$
$104$	−5.04029	−0.494241
$105$	0.434034	0.0423574
$106$	8.49338	0.824950
$107$	−5.43945	−0.525851	−0.262926	−	0.964816i	$-0.584687\pi$
$107$	−5.43945	−0.525851	−0.262926	+	0.964816i	$0.584687\pi$
$108$	−5.58721	−0.537629
$109$	2.02124	0.193600	0.0968000	−	0.995304i	$-0.469139\pi$
$109$	2.02124	0.193600	0.0968000	+	0.995304i	$0.469139\pi$
$110$	−0.642937	−0.0613016
$111$	2.38924	0.226777
$112$	1.23607	0.116797
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	4.82328	0.451741
$115$	−0.362985	−0.0338485
$116$	5.31375	0.493369
$117$	6.81015	0.629598
$118$	0.243785	0.0224422
$119$	5.52786	0.506738
$120$	0.351141	0.0320546
$121$	−5.47214	−0.497467
$122$	−6.85765	−0.620862
$123$	1.41498	0.127585
$124$	−6.82328	−0.612748
$125$	−2.71413	−0.242759
$126$	−1.67010	−0.148785
$127$	−21.5468	−1.91197	−0.955985	−	0.293416i	$-0.905208\pi$
$127$	−21.5468	−1.91197	−0.955985	+	0.293416i	$0.905208\pi$
$128$	1.00000	0.0883883
$129$	6.98468	0.614967
$130$	−1.37831	−0.120885
$131$	18.4449	1.61153	0.805767	−	0.592232i	$-0.201753\pi$
$131$	18.4449	1.61153	0.805767	+	0.592232i	$0.201753\pi$
$132$	−3.01905	−0.262775
$133$	4.64294	0.402594
$134$	−5.28408	−0.456475
$135$	−1.52786	−0.131498
$136$	4.47214	0.383482
$137$	13.2169	1.12920	0.564598	−	0.825366i	$-0.309031\pi$
$137$	13.2169	1.12920	0.564598	+	0.825366i	$0.309031\pi$
$138$	−1.70447	−0.145094
$139$	−0.313039	−0.0265516	−0.0132758	−	0.999912i	$-0.504226\pi$
$139$	−0.313039	−0.0265516	−0.0132758	+	0.999912i	$0.504226\pi$
$140$	0.338012	0.0285672
$141$	−7.74258	−0.652043
$142$	1.08540	0.0910848
$143$	11.8504	0.990984
$144$	−1.35114	−0.112595
$145$	1.45309	0.120672
$146$	13.7638	1.13910
$147$	−7.02666	−0.579549
$148$	1.86067	0.152946
$149$	12.5850	1.03100	0.515502	−	0.856888i	$-0.327605\pi$
$149$	12.5850	1.03100	0.515502	+	0.856888i	$0.327605\pi$
$150$	−6.32437	−0.516383
$151$	−8.44246	−0.687038	−0.343519	−	0.939146i	$-0.611619\pi$
$151$	−8.44246	−0.687038	−0.343519	+	0.939146i	$0.611619\pi$
$152$	3.75621	0.304669
$153$	−6.04249	−0.488506
$154$	−2.90617	−0.234186
$155$	−1.86588	−0.149871
$156$	−6.47214	−0.518186
$157$	−0.997808	−0.0796337	−0.0398169	−	0.999207i	$-0.512677\pi$
$157$	−0.997808	−0.0796337	−0.0398169	+	0.999207i	$0.512677\pi$
$158$	−5.03186	−0.400314
$159$	10.9062	0.864916
$160$	0.273457	0.0216187
$161$	−1.64074	−0.129309
$162$	−3.12099	−0.245209
$163$	3.90398	0.305783	0.152892	−	0.988243i	$-0.451141\pi$
$163$	3.90398	0.305783	0.152892	+	0.988243i	$0.451141\pi$
$164$	1.10194	0.0860474
$165$	−0.825582	−0.0642715
$166$	−0.919299	−0.0713514
$167$	−14.2275	−1.10096	−0.550480	−	0.834849i	$-0.685555\pi$
$167$	−14.2275	−1.10096	−0.550480	+	0.834849i	$0.685555\pi$
$168$	1.58721	0.122456
$169$	12.4046	0.954197
$170$	1.22294	0.0937951
$171$	−5.07518	−0.388108
$172$	5.43945	0.414754
$173$	0.884927	0.0672798	0.0336399	−	0.999434i	$-0.489290\pi$
$173$	0.884927	0.0672798	0.0336399	+	0.999434i	$0.489290\pi$
$174$	6.82328	0.517271
$175$	−6.08791	−0.460203
$176$	−2.35114	−0.177224
$177$	0.313039	0.0235295
$178$	14.0000	1.04934
$179$	15.7027	1.17367	0.586837	−	0.809705i	$-0.300373\pi$
$179$	15.7027	1.17367	0.586837	+	0.809705i	$0.300373\pi$
$180$	−0.369480	−0.0275394
$181$	−10.4501	−0.776747	−0.388374	−	0.921502i	$-0.626963\pi$
$181$	−10.4501	−0.776747	−0.388374	+	0.921502i	$0.626963\pi$
$182$	−6.23015	−0.461809
$183$	−8.80576	−0.650941
$184$	−1.32739	−0.0978565
$185$	0.508813	0.0374087
$186$	−8.76163	−0.642434
$187$	−10.5146	−0.768905
$188$	−6.02967	−0.439759
$189$	−6.90617	−0.502350
$190$	1.02717	0.0745184
$191$	−14.9833	−1.08416	−0.542078	−	0.840328i	$-0.682362\pi$
$191$	−14.9833	−1.08416	−0.542078	+	0.840328i	$0.682362\pi$
$192$	1.28408	0.0926704
$193$	3.49119	0.251301	0.125651	−	0.992075i	$-0.459898\pi$
$193$	3.49119	0.251301	0.125651	+	0.992075i	$0.459898\pi$
$194$	13.2917	0.954287
$195$	−1.76985	−0.126742
$196$	−5.47214	−0.390867
$197$	−12.0279	−0.856951	−0.428475	−	0.903553i	$-0.640949\pi$
$197$	−12.0279	−0.856951	−0.428475	+	0.903553i	$0.640949\pi$
$198$	3.17672	0.225760
$199$	−5.44027	−0.385651	−0.192825	−	0.981233i	$-0.561765\pi$
$199$	−5.44027	−0.385651	−0.192825	+	0.981233i	$0.561765\pi$
$200$	−4.92522	−0.348266
$201$	−6.78518	−0.478589
$202$	13.1311	0.923901
$203$	6.56816	0.460994
$204$	5.74258	0.402061
$205$	0.301335	0.0210461
$206$	10.3404	0.720450
$207$	1.79349	0.124656
$208$	−5.04029	−0.349482
$209$	−8.83139	−0.610880
$210$	0.434034	0.0299512
$211$	1.83860	0.126574	0.0632872	−	0.997995i	$-0.479842\pi$
$211$	1.83860	0.126574	0.0632872	+	0.997995i	$0.479842\pi$
$212$	8.49338	0.583328
$213$	1.39374	0.0954975
$214$	−5.43945	−0.371833
$215$	1.48746	0.101444
$216$	−5.58721	−0.380161
$217$	−8.43403	−0.572540
$218$	2.02124	0.136896
$219$	17.6738	1.19429
$220$	−0.642937	−0.0433468
$221$	−22.5409	−1.51626
$222$	2.38924	0.160355
$223$	−20.1103	−1.34668	−0.673341	−	0.739332i	$-0.735142\pi$
$223$	−20.1103	−1.34668	−0.673341	+	0.739332i	$0.735142\pi$
$224$	1.23607	0.0825883
$225$	6.65467	0.443645
$226$	−1.00000	−0.0665190
$227$	−15.1744	−1.00716	−0.503581	−	0.863948i	$-0.667984\pi$
$227$	−15.1744	−1.00716	−0.503581	+	0.863948i	$0.667984\pi$
$228$	4.82328	0.319429
$229$	−7.08361	−0.468098	−0.234049	−	0.972225i	$-0.575198\pi$
$229$	−7.08361	−0.468098	−0.234049	+	0.972225i	$0.575198\pi$
$230$	−0.362985	−0.0239345
$231$	−3.73175	−0.245531
$232$	5.31375	0.348865
$233$	−19.8848	−1.30270	−0.651349	−	0.758779i	$-0.725796\pi$
$233$	−19.8848	−1.30270	−0.651349	+	0.758779i	$0.725796\pi$
$234$	6.81015	0.445193
$235$	−1.64886	−0.107560
$236$	0.243785	0.0158691
$237$	−6.46131	−0.419707
$238$	5.52786	0.358318
$239$	−5.09591	−0.329627	−0.164813	−	0.986325i	$-0.552702\pi$
$239$	−5.09591	−0.329627	−0.164813	+	0.986325i	$0.552702\pi$
$240$	0.351141	0.0226661
$241$	−3.01532	−0.194234	−0.0971170	−	0.995273i	$-0.530962\pi$
$241$	−3.01532	−0.194234	−0.0971170	+	0.995273i	$0.530962\pi$
$242$	−5.47214	−0.351762
$243$	12.7540	0.818171
$244$	−6.85765	−0.439016
$245$	−1.49640	−0.0956013
$246$	1.41498	0.0902160
$247$	−18.9324	−1.20464
$248$	−6.82328	−0.433279
$249$	−1.18045	−0.0748082
$250$	−2.71413	−0.171656
$251$	26.9288	1.69973	0.849867	−	0.526998i	$-0.176682\pi$
$251$	26.9288	1.69973	0.849867	+	0.526998i	$0.176682\pi$
$252$	−1.67010	−0.105207
$253$	3.12088	0.196208
$254$	−21.5468	−1.35197
$255$	1.57035	0.0983392
$256$	1.00000	0.0625000
$257$	20.2741	1.26466	0.632330	−	0.774699i	$-0.282099\pi$
$257$	20.2741	1.26466	0.632330	+	0.774699i	$0.282099\pi$
$258$	6.98468	0.434847
$259$	2.29991	0.142909
$260$	−1.37831	−0.0854789
$261$	−7.17963	−0.444408
$262$	18.4449	1.13953
$263$	−9.93365	−0.612535	−0.306268	−	0.951945i	$-0.599080\pi$
$263$	−9.93365	−0.612535	−0.306268	+	0.951945i	$0.599080\pi$
$264$	−3.01905	−0.185810
$265$	2.32258	0.142675
$266$	4.64294	0.284677
$267$	17.9771	1.10018
$268$	−5.28408	−0.322777
$269$	13.5924	0.828744	0.414372	−	0.910108i	$-0.364001\pi$
$269$	13.5924	0.828744	0.414372	+	0.910108i	$0.364001\pi$
$270$	−1.52786	−0.0929828
$271$	−29.1506	−1.77077	−0.885385	−	0.464858i	$-0.846105\pi$
$271$	−29.1506	−1.77077	−0.885385	+	0.464858i	$0.846105\pi$
$272$	4.47214	0.271163
$273$	−8.00000	−0.484182
$274$	13.2169	0.798462
$275$	11.5799	0.698294
$276$	−1.70447	−0.102597
$277$	−29.8825	−1.79547	−0.897733	−	0.440540i	$-0.854787\pi$
$277$	−29.8825	−1.79547	−0.897733	+	0.440540i	$0.854787\pi$
$278$	−0.313039	−0.0187748
$279$	9.21921	0.551940
$280$	0.338012	0.0202001
$281$	−21.2432	−1.26726	−0.633630	−	0.773636i	$-0.718436\pi$
$281$	−21.2432	−1.26726	−0.633630	+	0.773636i	$0.718436\pi$
$282$	−7.74258	−0.461064
$283$	−13.9061	−0.826629	−0.413315	−	0.910588i	$-0.635629\pi$
$283$	−13.9061	−0.826629	−0.413315	+	0.910588i	$0.635629\pi$
$284$	1.08540	0.0644067
$285$	1.31896	0.0781285
$286$	11.8504	0.700731
$287$	1.36208	0.0804009
$288$	−1.35114	−0.0796167
$289$	3.00000	0.176471
$290$	1.45309	0.0853281
$291$	17.0676	1.00052
$292$	13.7638	0.805467
$293$	−4.27346	−0.249658	−0.124829	−	0.992178i	$-0.539838\pi$
$293$	−4.27346	−0.249658	−0.124829	+	0.992178i	$0.539838\pi$
$294$	−7.02666	−0.409803
$295$	0.0666648	0.00388138
$296$	1.86067	0.108149
$297$	13.1363	0.762246
$298$	12.5850	0.729030
$299$	6.69044	0.386918
$300$	−6.32437	−0.365138
$301$	6.72353	0.387538
$302$	−8.44246	−0.485809
$303$	16.8614	0.968661
$304$	3.75621	0.215434
$305$	−1.87528	−0.107378
$306$	−6.04249	−0.345426
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	−2.90617	−0.165594
$309$	13.2779	0.755353
$310$	−1.86588	−0.105975
$311$	9.69636	0.549830	0.274915	−	0.961469i	$-0.411350\pi$
$311$	9.69636	0.549830	0.274915	+	0.961469i	$0.411350\pi$
$312$	−6.47214	−0.366413
$313$	18.5550	1.04879	0.524396	−	0.851474i	$-0.324291\pi$
$313$	18.5550	1.04879	0.524396	+	0.851474i	$0.324291\pi$
$314$	−0.997808	−0.0563095
$315$	−0.456702	−0.0257322
$316$	−5.03186	−0.283065
$317$	−10.8364	−0.608633	−0.304317	−	0.952571i	$-0.598428\pi$
$317$	−10.8364	−0.608633	−0.304317	+	0.952571i	$0.598428\pi$
$318$	10.9062	0.611588
$319$	−12.4934	−0.699495
$320$	0.273457	0.0152867
$321$	−6.98468	−0.389847
$322$	−1.64074	−0.0914351
$323$	16.7983	0.934683
$324$	−3.12099	−0.173389
$325$	24.8246	1.37702
$326$	3.90398	0.216221
$327$	2.59544	0.143528
$328$	1.10194	0.0608447
$329$	−7.45309	−0.410902
$330$	−0.825582	−0.0454468
$331$	23.3914	1.28571	0.642855	−	0.765988i	$-0.277750\pi$
$331$	23.3914	1.28571	0.642855	+	0.765988i	$0.277750\pi$
$332$	−0.919299	−0.0504531
$333$	−2.51402	−0.137768
$334$	−14.2275	−0.778496
$335$	−1.44497	−0.0789472
$336$	1.58721	0.0865893
$337$	−30.6939	−1.67201	−0.836003	−	0.548725i	$-0.815113\pi$
$337$	−30.6939	−1.67201	−0.836003	+	0.548725i	$0.815113\pi$
$338$	12.4046	0.674719
$339$	−1.28408	−0.0697416
$340$	1.22294	0.0663232
$341$	16.0425	0.868749
$342$	−5.07518	−0.274434
$343$	−15.4164	−0.832408
$344$	5.43945	0.293275
$345$	−0.466101	−0.0250940
$346$	0.884927	0.0475740
$347$	3.41641	0.183402	0.0917012	−	0.995787i	$-0.470770\pi$
$347$	3.41641	0.183402	0.0917012	+	0.995787i	$0.470770\pi$
$348$	6.82328	0.365766
$349$	36.2851	1.94230	0.971148	−	0.238478i	$-0.0766486\pi$
$349$	36.2851	1.94230	0.971148	+	0.238478i	$0.0766486\pi$
$350$	−6.08791	−0.325412
$351$	28.1612	1.50313
$352$	−2.35114	−0.125316
$353$	−16.4684	−0.876525	−0.438262	−	0.898847i	$-0.644406\pi$
$353$	−16.4684	−0.876525	−0.438262	+	0.898847i	$0.644406\pi$
$354$	0.313039	0.0166378
$355$	0.296811	0.0157531
$356$	14.0000	0.741999
$357$	7.09821	0.375677
$358$	15.7027	0.829912
$359$	24.1197	1.27299	0.636493	−	0.771282i	$-0.280384\pi$
$359$	24.1197	1.27299	0.636493	+	0.771282i	$0.280384\pi$
$360$	−0.369480	−0.0194733
$361$	−4.89085	−0.257413
$362$	−10.4501	−0.549243
$363$	−7.02666	−0.368804
$364$	−6.23015	−0.326548
$365$	3.76382	0.197007
$366$	−8.80576	−0.460285
$367$	34.4413	1.79782	0.898910	−	0.438134i	$-0.144360\pi$
$367$	34.4413	1.79782	0.898910	+	0.438134i	$0.144360\pi$
$368$	−1.32739	−0.0691950
$369$	−1.48888	−0.0775081
$370$	0.508813	0.0264519
$371$	10.4984	0.545049
$372$	−8.76163	−0.454269
$373$	26.3540	1.36456	0.682280	−	0.731091i	$-0.260988\pi$
$373$	26.3540	1.36456	0.682280	+	0.731091i	$0.260988\pi$
$374$	−10.5146	−0.543698
$375$	−3.48515	−0.179972
$376$	−6.02967	−0.310957
$377$	−26.7829	−1.37939
$378$	−6.90617	−0.355215
$379$	28.5509	1.46656	0.733281	−	0.679925i	$-0.237988\pi$
$379$	28.5509	1.46656	0.733281	+	0.679925i	$0.237988\pi$
$380$	1.02717	0.0526925
$381$	−27.6678	−1.41746
$382$	−14.9833	−0.766615
$383$	22.7425	1.16209	0.581043	−	0.813873i	$-0.302645\pi$
$383$	22.7425	1.16209	0.581043	+	0.813873i	$0.302645\pi$
$384$	1.28408	0.0655279
$385$	−0.794714	−0.0405024
$386$	3.49119	0.177697
$387$	−7.34946	−0.373594
$388$	13.2917	0.674783
$389$	−36.7249	−1.86203	−0.931014	−	0.364982i	$-0.881075\pi$
$389$	−36.7249	−1.86203	−0.931014	+	0.364982i	$0.881075\pi$
$390$	−1.76985	−0.0896200
$391$	−5.93627	−0.300210
$392$	−5.47214	−0.276385
$393$	23.6847	1.19473
$394$	−12.0279	−0.605956
$395$	−1.37600	−0.0692341
$396$	3.17672	0.159636
$397$	−14.7183	−0.738691	−0.369346	−	0.929292i	$-0.620418\pi$
$397$	−14.7183	−0.738691	−0.369346	+	0.929292i	$0.620418\pi$
$398$	−5.44027	−0.272696
$399$	5.96190	0.298468
$400$	−4.92522	−0.246261
$401$	−6.79702	−0.339427	−0.169713	−	0.985493i	$-0.554284\pi$
$401$	−6.79702	−0.339427	−0.169713	+	0.985493i	$0.554284\pi$
$402$	−6.78518	−0.338414
$403$	34.3913	1.71315
$404$	13.1311	0.653297
$405$	−0.853459	−0.0424087
$406$	6.56816	0.325972
$407$	−4.37469	−0.216845
$408$	5.74258	0.284300
$409$	9.91919	0.490472	0.245236	−	0.969463i	$-0.421135\pi$
$409$	9.91919	0.490472	0.245236	+	0.969463i	$0.421135\pi$
$410$	0.301335	0.0148819
$411$	16.9715	0.837145
$412$	10.3404	0.509435
$413$	0.301335	0.0148277
$414$	1.79349	0.0881453
$415$	−0.251389	−0.0123402
$416$	−5.04029	−0.247121
$417$	−0.401967	−0.0196844
$418$	−8.83139	−0.431957
$419$	−14.8498	−0.725461	−0.362731	−	0.931894i	$-0.618155\pi$
$419$	−14.8498	−0.725461	−0.362731	+	0.931894i	$0.618155\pi$
$420$	0.434034	0.0211787
$421$	3.49119	0.170150	0.0850750	−	0.996375i	$-0.472887\pi$
$421$	3.49119	0.170150	0.0850750	+	0.996375i	$0.472887\pi$
$422$	1.83860	0.0895016
$423$	8.14694	0.396118
$424$	8.49338	0.412475
$425$	−22.0263	−1.06843
$426$	1.39374	0.0675269
$427$	−8.47652	−0.410208
$428$	−5.43945	−0.262926
$429$	15.2169	0.734679
$430$	1.48746	0.0717316
$431$	−38.2963	−1.84467	−0.922333	−	0.386395i	$-0.873720\pi$
$431$	−38.2963	−1.84467	−0.922333	+	0.386395i	$0.873720\pi$
$432$	−5.58721	−0.268815
$433$	−39.4104	−1.89394	−0.946971	−	0.321320i	$-0.895874\pi$
$433$	−39.4104	−1.89394	−0.946971	+	0.321320i	$0.895874\pi$
$434$	−8.43403	−0.404847
$435$	1.86588	0.0894619
$436$	2.02124	0.0968000
$437$	−4.98596	−0.238511
$438$	17.6738	0.844488
$439$	32.1518	1.53452	0.767260	−	0.641336i	$-0.221619\pi$
$439$	32.1518	1.53452	0.767260	+	0.641336i	$0.221619\pi$
$440$	−0.642937	−0.0306508
$441$	7.39363	0.352077
$442$	−22.5409	−1.07216
$443$	−40.0402	−1.90237	−0.951183	−	0.308627i	$-0.900131\pi$
$443$	−40.0402	−1.90237	−0.951183	+	0.308627i	$0.900131\pi$
$444$	2.38924	0.113388
$445$	3.82840	0.181484
$446$	−20.1103	−0.952248
$447$	16.1602	0.764349
$448$	1.23607	0.0583987
$449$	4.86368	0.229531	0.114766	−	0.993393i	$-0.463388\pi$
$449$	4.86368	0.229531	0.114766	+	0.993393i	$0.463388\pi$
$450$	6.65467	0.313704
$451$	−2.59083	−0.121997
$452$	−1.00000	−0.0470360
$453$	−10.8408	−0.509345
$454$	−15.1744	−0.712171
$455$	−1.70368	−0.0798697
$456$	4.82328	0.225871
$457$	8.12472	0.380059	0.190029	−	0.981778i	$-0.439142\pi$
$457$	8.12472	0.380059	0.190029	+	0.981778i	$0.439142\pi$
$458$	−7.08361	−0.330995
$459$	−24.9868	−1.16628
$460$	−0.362985	−0.0169243
$461$	5.57177	0.259503	0.129752	−	0.991547i	$-0.458582\pi$
$461$	5.57177	0.259503	0.129752	+	0.991547i	$0.458582\pi$
$462$	−3.73175	−0.173617
$463$	−26.7235	−1.24195	−0.620974	−	0.783831i	$-0.713263\pi$
$463$	−26.7235	−1.24195	−0.620974	+	0.783831i	$0.713263\pi$
$464$	5.31375	0.246685
$465$	−2.39593	−0.111109
$466$	−19.8848	−0.921146
$467$	−28.4469	−1.31637	−0.658184	−	0.752857i	$-0.728675\pi$
$467$	−28.4469	−1.31637	−0.658184	+	0.752857i	$0.728675\pi$
$468$	6.81015	0.314799
$469$	−6.53148	−0.301596
$470$	−1.64886	−0.0760562
$471$	−1.28126	−0.0590375
$472$	0.243785	0.0112211
$473$	−12.7889	−0.588034
$474$	−6.46131	−0.296778
$475$	−18.5002	−0.848847
$476$	5.52786	0.253369
$477$	−11.4758	−0.525439
$478$	−5.09591	−0.233081
$479$	5.05812	0.231112	0.115556	−	0.993301i	$-0.463135\pi$
$479$	5.05812	0.231112	0.115556	+	0.993301i	$0.463135\pi$
$480$	0.351141	0.0160273
$481$	−9.37831	−0.427614
$482$	−3.01532	−0.137344
$483$	−2.10685	−0.0958648
$484$	−5.47214	−0.248733
$485$	3.63471	0.165044
$486$	12.7540	0.578534
$487$	−11.1660	−0.505979	−0.252990	−	0.967469i	$-0.581414\pi$
$487$	−11.1660	−0.505979	−0.252990	+	0.967469i	$0.581414\pi$
$488$	−6.85765	−0.310431
$489$	5.01302	0.226696
$490$	−1.49640	−0.0676003
$491$	−32.1169	−1.44942	−0.724708	−	0.689057i	$-0.758025\pi$
$491$	−32.1169	−1.44942	−0.724708	+	0.689057i	$0.758025\pi$
$492$	1.41498	0.0637924
$493$	23.7638	1.07027
$494$	−18.9324	−0.851810
$495$	0.868699	0.0390451
$496$	−6.82328	−0.306374
$497$	1.34163	0.0601803
$498$	−1.18045	−0.0528974
$499$	36.9671	1.65487	0.827437	−	0.561559i	$-0.189798\pi$
$499$	36.9671	1.65487	0.827437	+	0.561559i	$0.189798\pi$
$500$	−2.71413	−0.121379
$501$	−18.2693	−0.816211
$502$	26.9288	1.20189
$503$	−13.7793	−0.614387	−0.307193	−	0.951647i	$-0.599390\pi$
$503$	−13.7793	−0.614387	−0.307193	+	0.951647i	$0.599390\pi$
$504$	−1.67010	−0.0743923
$505$	3.59080	0.159788
$506$	3.12088	0.138740
$507$	15.9284	0.707407
$508$	−21.5468	−0.955985
$509$	13.6772	0.606231	0.303116	−	0.952954i	$-0.401973\pi$
$509$	13.6772	0.606231	0.303116	+	0.952954i	$0.401973\pi$
$510$	1.57035	0.0695363
$511$	17.0130	0.752612
$512$	1.00000	0.0441942
$513$	−20.9868	−0.926588
$514$	20.2741	0.894250
$515$	2.82766	0.124602
$516$	6.98468	0.307483
$517$	14.1766	0.623487
$518$	2.29991	0.101052
$519$	1.13632	0.0498787
$520$	−1.37831	−0.0604427
$521$	30.2360	1.32466	0.662331	−	0.749212i	$-0.269567\pi$
$521$	30.2360	1.32466	0.662331	+	0.749212i	$0.269567\pi$
$522$	−7.17963	−0.314244
$523$	25.1287	1.09880	0.549401	−	0.835559i	$-0.314856\pi$
$523$	25.1287	1.09880	0.549401	+	0.835559i	$0.314856\pi$
$524$	18.4449	0.805767
$525$	−7.81736	−0.341177
$526$	−9.93365	−0.433128
$527$	−30.5146	−1.32924
$528$	−3.01905	−0.131387
$529$	−21.2380	−0.923393
$530$	2.32258	0.100886
$531$	−0.329388	−0.0142942
$532$	4.64294	0.201297
$533$	−5.55412	−0.240576
$534$	17.9771	0.777945
$535$	−1.48746	−0.0643084
$536$	−5.28408	−0.228237
$537$	20.1635	0.870118
$538$	13.5924	0.586011
$539$	12.8658	0.554168
$540$	−1.52786	−0.0657488
$541$	43.1046	1.85321	0.926606	−	0.376033i	$-0.122712\pi$
$541$	43.1046	1.85321	0.926606	+	0.376033i	$0.122712\pi$
$542$	−29.1506	−1.25212
$543$	−13.4187	−0.575852
$544$	4.47214	0.191741
$545$	0.552724	0.0236761
$546$	−8.00000	−0.342368
$547$	−19.3217	−0.826135	−0.413067	−	0.910700i	$-0.635543\pi$
$547$	−19.3217	−0.826135	−0.413067	+	0.910700i	$0.635543\pi$
$548$	13.2169	0.564598
$549$	9.26565	0.395448
$550$	11.5799	0.493768
$551$	19.9596	0.850307
$552$	−1.70447	−0.0725472
$553$	−6.21973	−0.264490
$554$	−29.8825	−1.26959
$555$	0.653356	0.0277334
$556$	−0.313039	−0.0132758
$557$	−6.89677	−0.292226	−0.146113	−	0.989268i	$-0.546676\pi$
$557$	−6.89677	−0.292226	−0.146113	+	0.989268i	$0.546676\pi$
$558$	9.21921	0.390280
$559$	−27.4164	−1.15959
$560$	0.338012	0.0142836
$561$	−13.5016	−0.570038
$562$	−21.2432	−0.896089
$563$	1.36208	0.0574047	0.0287024	−	0.999588i	$-0.490862\pi$
$563$	1.36208	0.0574047	0.0287024	+	0.999588i	$0.490862\pi$
$564$	−7.74258	−0.326021
$565$	−0.273457	−0.0115044
$566$	−13.9061	−0.584515
$567$	−3.85776	−0.162011
$568$	1.08540	0.0455424
$569$	23.9633	1.00459	0.502297	−	0.864695i	$-0.332488\pi$
$569$	23.9633	1.00459	0.502297	+	0.864695i	$0.332488\pi$
$570$	1.31896	0.0552452
$571$	25.4028	1.06307	0.531536	−	0.847035i	$-0.321615\pi$
$571$	25.4028	1.06307	0.531536	+	0.847035i	$0.321615\pi$
$572$	11.8504	0.495492
$573$	−19.2398	−0.803754
$574$	1.36208	0.0568520
$575$	6.53769	0.272641
$576$	−1.35114	−0.0562975
$577$	32.6333	1.35854	0.679271	−	0.733887i	$-0.262296\pi$
$577$	32.6333	1.35854	0.679271	+	0.733887i	$0.262296\pi$
$578$	3.00000	0.124784
$579$	4.48296	0.186305
$580$	1.45309	0.0603361
$581$	−1.13632	−0.0471423
$582$	17.0676	0.707474
$583$	−19.9691	−0.827037
$584$	13.7638	0.569551
$585$	1.86229	0.0769960
$586$	−4.27346	−0.176535
$587$	14.2953	0.590030	0.295015	−	0.955493i	$-0.404675\pi$
$587$	14.2953	0.590030	0.295015	+	0.955493i	$0.404675\pi$
$588$	−7.02666	−0.289774
$589$	−25.6297	−1.05605
$590$	0.0666648	0.00274455
$591$	−15.4447	−0.635312
$592$	1.86067	0.0764729
$593$	4.34741	0.178527	0.0892634	−	0.996008i	$-0.471549\pi$
$593$	4.34741	0.178527	0.0892634	+	0.996008i	$0.471549\pi$
$594$	13.1363	0.538990
$595$	1.51164	0.0619710
$596$	12.5850	0.515502
$597$	−6.98574	−0.285907
$598$	6.69044	0.273592
$599$	18.1776	0.742716	0.371358	−	0.928490i	$-0.378892\pi$
$599$	18.1776	0.742716	0.371358	+	0.928490i	$0.378892\pi$
$600$	−6.32437	−0.258191
$601$	25.6145	1.04484	0.522418	−	0.852689i	$-0.325030\pi$
$601$	25.6145	1.04484	0.522418	+	0.852689i	$0.325030\pi$
$602$	6.72353	0.274030
$603$	7.13954	0.290744
$604$	−8.44246	−0.343519
$605$	−1.49640	−0.0608372
$606$	16.8614	0.684947
$607$	−13.2849	−0.539218	−0.269609	−	0.962970i	$-0.586894\pi$
$607$	−13.2849	−0.539218	−0.269609	+	0.962970i	$0.586894\pi$
$608$	3.75621	0.152335
$609$	8.43403	0.341764
$610$	−1.87528	−0.0759277
$611$	30.3913	1.22950
$612$	−6.04249	−0.244253
$613$	22.3871	0.904208	0.452104	−	0.891965i	$-0.350674\pi$
$613$	22.3871	0.904208	0.452104	+	0.891965i	$0.350674\pi$
$614$	4.00000	0.161427
$615$	0.386938	0.0156028
$616$	−2.90617	−0.117093
$617$	−21.4201	−0.862342	−0.431171	−	0.902270i	$-0.641899\pi$
$617$	−21.4201	−0.862342	−0.431171	+	0.902270i	$0.641899\pi$
$618$	13.2779	0.534115
$619$	6.03050	0.242386	0.121193	−	0.992629i	$-0.461328\pi$
$619$	6.03050	0.242386	0.121193	+	0.992629i	$0.461328\pi$
$620$	−1.86588	−0.0749354
$621$	7.41641	0.297610
$622$	9.69636	0.388789
$623$	17.3050	0.693308
$624$	−6.47214	−0.259093
$625$	23.8839	0.955356
$626$	18.5550	0.741608
$627$	−11.3402	−0.452884
$628$	−0.997808	−0.0398169
$629$	8.32115	0.331786
$630$	−0.456702	−0.0181954
$631$	6.17923	0.245991	0.122996	−	0.992407i	$-0.460750\pi$
$631$	6.17923	0.245991	0.122996	+	0.992407i	$0.460750\pi$
$632$	−5.03186	−0.200157
$633$	2.36091	0.0938376
$634$	−10.8364	−0.430369
$635$	−5.89213	−0.233822
$636$	10.9062	0.432458
$637$	27.5812	1.09281
$638$	−12.4934	−0.494618
$639$	−1.46653	−0.0580150
$640$	0.273457	0.0108094
$641$	−14.3549	−0.566983	−0.283492	−	0.958975i	$-0.591493\pi$
$641$	−14.3549	−0.566983	−0.283492	+	0.958975i	$0.591493\pi$
$642$	−6.98468	−0.275663
$643$	−38.5024	−1.51839	−0.759193	−	0.650865i	$-0.774406\pi$
$643$	−38.5024	−1.51839	−0.759193	+	0.650865i	$0.774406\pi$
$644$	−1.64074	−0.0646544
$645$	1.91001	0.0752067
$646$	16.7983	0.660920
$647$	−6.76601	−0.265999	−0.133000	−	0.991116i	$-0.542461\pi$
$647$	−6.76601	−0.265999	−0.133000	+	0.991116i	$0.542461\pi$
$648$	−3.12099	−0.122604
$649$	−0.573173	−0.0224990
$650$	24.8246	0.973699
$651$	−10.8300	−0.424460
$652$	3.90398	0.152892
$653$	−29.5718	−1.15723	−0.578616	−	0.815600i	$-0.696407\pi$
$653$	−29.5718	−1.15723	−0.578616	+	0.815600i	$0.696407\pi$
$654$	2.59544	0.101490
$655$	5.04388	0.197081
$656$	1.10194	0.0430237
$657$	−18.5969	−0.725533
$658$	−7.45309	−0.290552
$659$	−10.1953	−0.397151	−0.198576	−	0.980086i	$-0.563632\pi$
$659$	−10.1953	−0.397151	−0.198576	+	0.980086i	$0.563632\pi$
$660$	−0.825582	−0.0321357
$661$	−9.35624	−0.363915	−0.181958	−	0.983306i	$-0.558243\pi$
$661$	−9.35624	−0.363915	−0.181958	+	0.983306i	$0.558243\pi$
$662$	23.3914	0.909134
$663$	−28.9443	−1.12410
$664$	−0.919299	−0.0356757
$665$	1.26965	0.0492348
$666$	−2.51402	−0.0974164
$667$	−7.05342	−0.273110
$668$	−14.2275	−0.550480
$669$	−25.8232	−0.998381
$670$	−1.44497	−0.0558241
$671$	16.1233	0.622433
$672$	1.58721	0.0612279
$673$	−28.4280	−1.09582	−0.547909	−	0.836538i	$-0.684576\pi$
$673$	−28.4280	−1.09582	−0.547909	+	0.836538i	$0.684576\pi$
$674$	−30.6939	−1.18229
$675$	27.5182	1.05918
$676$	12.4046	0.477099
$677$	26.5453	1.02022	0.510109	−	0.860110i	$-0.329605\pi$
$677$	26.5453	1.02022	0.510109	+	0.860110i	$0.329605\pi$
$678$	−1.28408	−0.0493148
$679$	16.4294	0.630503
$680$	1.22294	0.0468976
$681$	−19.4852	−0.746673
$682$	16.0425	0.614299
$683$	−45.0433	−1.72353	−0.861767	−	0.507305i	$-0.830642\pi$
$683$	−45.0433	−1.72353	−0.861767	+	0.507305i	$0.830642\pi$
$684$	−5.07518	−0.194054
$685$	3.61426	0.138094
$686$	−15.4164	−0.588601
$687$	−9.09591	−0.347031
$688$	5.43945	0.207377
$689$	−42.8091	−1.63090
$690$	−0.466101	−0.0177442
$691$	18.9214	0.719803	0.359902	−	0.932990i	$-0.382810\pi$
$691$	18.9214	0.719803	0.359902	+	0.932990i	$0.382810\pi$
$692$	0.884927	0.0336399
$693$	3.92665	0.149161
$694$	3.41641	0.129685
$695$	−0.0856029	−0.00324710
$696$	6.82328	0.258636
$697$	4.92804	0.186663
$698$	36.2851	1.37341
$699$	−25.5337	−0.965772
$700$	−6.08791	−0.230101
$701$	−29.5285	−1.11527	−0.557637	−	0.830085i	$-0.688292\pi$
$701$	−29.5285	−1.11527	−0.557637	+	0.830085i	$0.688292\pi$
$702$	28.1612	1.06288
$703$	6.98906	0.263598
$704$	−2.35114	−0.0886120
$705$	−2.11727	−0.0797408
$706$	−16.4684	−0.619797
$707$	16.2309	0.610427
$708$	0.313039	0.0117647
$709$	37.3085	1.40115	0.700576	−	0.713578i	$-0.252927\pi$
$709$	37.3085	1.40115	0.700576	+	0.713578i	$0.252927\pi$
$710$	0.296811	0.0111391
$711$	6.79876	0.254973
$712$	14.0000	0.524672
$713$	9.05715	0.339193
$714$	7.09821	0.265644
$715$	3.24059	0.121191
$716$	15.7027	0.586837
$717$	−6.54355	−0.244373
$718$	24.1197	0.900138
$719$	3.72967	0.139093	0.0695467	−	0.997579i	$-0.477845\pi$
$719$	3.72967	0.139093	0.0695467	+	0.997579i	$0.477845\pi$
$720$	−0.369480	−0.0137697
$721$	12.7814	0.476006
$722$	−4.89085	−0.182019
$723$	−3.87191	−0.143998
$724$	−10.4501	−0.388374
$725$	−26.1714	−0.971981
$726$	−7.02666	−0.260784
$727$	−50.7068	−1.88061	−0.940306	−	0.340331i	$-0.889461\pi$
$727$	−50.7068	−1.88061	−0.940306	+	0.340331i	$0.889461\pi$
$728$	−6.23015	−0.230905
$729$	25.7402	0.953339
$730$	3.76382	0.139305
$731$	24.3259	0.899727
$732$	−8.80576	−0.325470
$733$	10.5036	0.387959	0.193980	−	0.981006i	$-0.437860\pi$
$733$	10.5036	0.387959	0.193980	+	0.981006i	$0.437860\pi$
$734$	34.4413	1.27125
$735$	−1.92149	−0.0708753
$736$	−1.32739	−0.0489283
$737$	12.4236	0.457630
$738$	−1.48888	−0.0548065
$739$	36.9036	1.35752	0.678761	−	0.734359i	$-0.262517\pi$
$739$	36.9036	1.35752	0.678761	+	0.734359i	$0.262517\pi$
$740$	0.508813	0.0187043
$741$	−24.3107	−0.893077
$742$	10.4984	0.385408
$743$	27.4306	1.00633	0.503166	−	0.864190i	$-0.332168\pi$
$743$	27.4306	1.00633	0.503166	+	0.864190i	$0.332168\pi$
$744$	−8.76163	−0.321217
$745$	3.44147	0.126086
$746$	26.3540	0.964890
$747$	1.24210	0.0454462
$748$	−10.5146	−0.384453
$749$	−6.72353	−0.245672
$750$	−3.48515	−0.127260
$751$	−15.0962	−0.550869	−0.275435	−	0.961320i	$-0.588822\pi$
$751$	−15.0962	−0.550869	−0.275435	+	0.961320i	$0.588822\pi$
$752$	−6.02967	−0.219880
$753$	34.5788	1.26012
$754$	−26.7829	−0.975375
$755$	−2.30865	−0.0840205
$756$	−6.90617	−0.251175
$757$	0.208303	0.00757092	0.00378546	−	0.999993i	$-0.498795\pi$
$757$	0.208303	0.00757092	0.00378546	+	0.999993i	$0.498795\pi$
$758$	28.5509	1.03702
$759$	4.00746	0.145462
$760$	1.02717	0.0372592
$761$	−41.3758	−1.49987	−0.749935	−	0.661511i	$-0.769915\pi$
$761$	−41.3758	−1.49987	−0.749935	+	0.661511i	$0.769915\pi$
$762$	−27.6678	−1.00230
$763$	2.49839	0.0904479
$764$	−14.9833	−0.542078
$765$	−1.65236	−0.0597413
$766$	22.7425	0.821719
$767$	−1.22875	−0.0443675
$768$	1.28408	0.0463352
$769$	−45.5051	−1.64096	−0.820478	−	0.571678i	$-0.806293\pi$
$769$	−45.5051	−1.64096	−0.820478	+	0.571678i	$0.806293\pi$
$770$	−0.794714	−0.0286395
$771$	26.0335	0.937573
$772$	3.49119	0.125651
$773$	46.8456	1.68492	0.842459	−	0.538760i	$-0.181107\pi$
$773$	46.8456	1.68492	0.842459	+	0.538760i	$0.181107\pi$
$774$	−7.34946	−0.264171
$775$	33.6061	1.20717
$776$	13.2917	0.477144
$777$	2.95327	0.105948
$778$	−36.7249	−1.31665
$779$	4.13914	0.148300
$780$	−1.76985	−0.0633709
$781$	−2.55193	−0.0913152
$782$	−5.93627	−0.212281
$783$	−29.6890	−1.06100
$784$	−5.47214	−0.195433
$785$	−0.272858	−0.00973872
$786$	23.6847	0.844804
$787$	−48.3311	−1.72282	−0.861409	−	0.507912i	$-0.830417\pi$
$787$	−48.3311	−1.72282	−0.861409	+	0.507912i	$0.830417\pi$
$788$	−12.0279	−0.428475
$789$	−12.7556	−0.454111
$790$	−1.37600	−0.0489559
$791$	−1.23607	−0.0439495
$792$	3.17672	0.112880
$793$	34.5646	1.22742
$794$	−14.7183	−0.522333
$795$	2.98237	0.105774
$796$	−5.44027	−0.192825
$797$	34.9772	1.23895	0.619477	−	0.785015i	$-0.287345\pi$
$797$	34.9772	1.23895	0.619477	+	0.785015i	$0.287345\pi$
$798$	5.96190	0.211049
$799$	−26.9655	−0.953971
$800$	−4.92522	−0.174133
$801$	−18.9160	−0.668363
$802$	−6.79702	−0.240011
$803$	−32.3607	−1.14198
$804$	−6.78518	−0.239295
$805$	−0.448674	−0.0158137
$806$	34.3913	1.21138
$807$	17.4537	0.614401
$808$	13.1311	0.461951
$809$	47.8115	1.68096	0.840481	−	0.541841i	$-0.182273\pi$
$809$	47.8115	1.68096	0.840481	+	0.541841i	$0.182273\pi$
$810$	−0.853459	−0.0299875
$811$	−12.7598	−0.448058	−0.224029	−	0.974582i	$-0.571921\pi$
$811$	−12.7598	−0.448058	−0.224029	+	0.974582i	$0.571921\pi$
$812$	6.56816	0.230497
$813$	−37.4316	−1.31278
$814$	−4.37469	−0.153333
$815$	1.06757	0.0373954
$816$	5.74258	0.201030
$817$	20.4317	0.714816
$818$	9.91919	0.346816
$819$	8.41781	0.294142
$820$	0.301335	0.0105231
$821$	43.5657	1.52045	0.760227	−	0.649657i	$-0.225088\pi$
$821$	43.5657	1.52045	0.760227	+	0.649657i	$0.225088\pi$
$822$	16.9715	0.591951
$823$	−1.44289	−0.0502960	−0.0251480	−	0.999684i	$-0.508006\pi$
$823$	−1.44289	−0.0502960	−0.0251480	+	0.999684i	$0.508006\pi$
$824$	10.3404	0.360225
$825$	14.8695	0.517689
$826$	0.301335	0.0104848
$827$	28.2397	0.981990	0.490995	−	0.871162i	$-0.336633\pi$
$827$	28.2397	0.981990	0.490995	+	0.871162i	$0.336633\pi$
$828$	1.79349	0.0623281
$829$	−6.33036	−0.219862	−0.109931	−	0.993939i	$-0.535063\pi$
$829$	−6.33036	−0.219862	−0.109931	+	0.993939i	$0.535063\pi$
$830$	−0.251389	−0.00872585
$831$	−38.3715	−1.33109
$832$	−5.04029	−0.174741
$833$	−24.4721	−0.847909
$834$	−0.401967	−0.0139190
$835$	−3.89062	−0.134641
$836$	−8.83139	−0.305440
$837$	38.1231	1.31773
$838$	−14.8498	−0.512978
$839$	−52.6519	−1.81775	−0.908873	−	0.417072i	$-0.863056\pi$
$839$	−52.6519	−1.81775	−0.908873	+	0.417072i	$0.863056\pi$
$840$	0.434034	0.0149756
$841$	−0.764045	−0.0263464
$842$	3.49119	0.120314
$843$	−27.2779	−0.939501
$844$	1.83860	0.0632872
$845$	3.39212	0.116693
$846$	8.14694	0.280097
$847$	−6.76393	−0.232411
$848$	8.49338	0.291664
$849$	−17.8565	−0.612833
$850$	−22.0263	−0.755494
$851$	−2.46983	−0.0846647
$852$	1.39374	0.0477487
$853$	21.1090	0.722760	0.361380	−	0.932419i	$-0.382306\pi$
$853$	21.1090	0.722760	0.361380	+	0.932419i	$0.382306\pi$
$854$	−8.47652	−0.290061
$855$	−1.38784	−0.0474633
$856$	−5.43945	−0.185916
$857$	7.29333	0.249136	0.124568	−	0.992211i	$-0.460246\pi$
$857$	7.29333	0.249136	0.124568	+	0.992211i	$0.460246\pi$
$858$	15.2169	0.519497
$859$	−1.13617	−0.0387657	−0.0193828	−	0.999812i	$-0.506170\pi$
$859$	−1.13617	−0.0387657	−0.0193828	+	0.999812i	$0.506170\pi$
$860$	1.48746	0.0507219
$861$	1.74902	0.0596063
$862$	−38.2963	−1.30438
$863$	1.73677	0.0591202	0.0295601	−	0.999563i	$-0.490589\pi$
$863$	1.73677	0.0591202	0.0295601	+	0.999563i	$0.490589\pi$
$864$	−5.58721	−0.190081
$865$	0.241990	0.00822790
$866$	−39.4104	−1.33922
$867$	3.85224	0.130829
$868$	−8.43403	−0.286270
$869$	11.8306	0.401326
$870$	1.86588	0.0632591
$871$	26.6333	0.902435
$872$	2.02124	0.0684479
$873$	−17.9589	−0.607818
$874$	−4.98596	−0.168653
$875$	−3.35484	−0.113414
$876$	17.6738	0.597143
$877$	2.27847	0.0769385	0.0384693	−	0.999260i	$-0.487752\pi$
$877$	2.27847	0.0769385	0.0384693	+	0.999260i	$0.487752\pi$
$878$	32.1518	1.08507
$879$	−5.48746	−0.185087
$880$	−0.642937	−0.0216734
$881$	28.9120	0.974069	0.487035	−	0.873383i	$-0.338079\pi$
$881$	28.9120	0.974069	0.487035	+	0.873383i	$0.338079\pi$
$882$	7.39363	0.248956
$883$	−41.0479	−1.38137	−0.690686	−	0.723155i	$-0.742691\pi$
$883$	−41.0479	−1.38137	−0.690686	+	0.723155i	$0.742691\pi$
$884$	−22.5409	−0.758132
$885$	0.0856029	0.00287751
$886$	−40.0402	−1.34518
$887$	23.4411	0.787074	0.393537	−	0.919309i	$-0.371251\pi$
$887$	23.4411	0.787074	0.393537	+	0.919309i	$0.371251\pi$
$888$	2.38924	0.0801777
$889$	−26.6333	−0.893253
$890$	3.82840	0.128328
$891$	7.33790	0.245829
$892$	−20.1103	−0.673341
$893$	−22.6487	−0.757911
$894$	16.1602	0.540476
$895$	4.29401	0.143533
$896$	1.23607	0.0412941
$897$	8.59105	0.286847
$898$	4.86368	0.162303
$899$	−36.2572	−1.20925
$900$	6.65467	0.221822
$901$	37.9835	1.26542
$902$	−2.59083	−0.0862651
$903$	8.63354	0.287306
$904$	−1.00000	−0.0332595
$905$	−2.85765	−0.0949915
$906$	−10.8408	−0.360161
$907$	−5.39798	−0.179237	−0.0896185	−	0.995976i	$-0.528565\pi$
$907$	−5.39798	−0.179237	−0.0896185	+	0.995976i	$0.528565\pi$
$908$	−15.1744	−0.503581
$909$	−17.7420	−0.588464
$910$	−1.70368	−0.0564764
$911$	5.06757	0.167896	0.0839481	−	0.996470i	$-0.473247\pi$
$911$	5.06757	0.167896	0.0839481	+	0.996470i	$0.473247\pi$
$912$	4.82328	0.159715
$913$	2.16140	0.0715320
$914$	8.12472	0.268742
$915$	−2.40800	−0.0796061
$916$	−7.08361	−0.234049
$917$	22.7991	0.752893
$918$	−24.9868	−0.824686
$919$	−45.2550	−1.49282	−0.746412	−	0.665484i	$-0.768225\pi$
$919$	−45.2550	−1.49282	−0.746412	+	0.665484i	$0.768225\pi$
$920$	−0.362985	−0.0119673
$921$	5.13632	0.169247
$922$	5.57177	0.183497
$923$	−5.47074	−0.180072
$924$	−3.73175	−0.122766
$925$	−9.16419	−0.301317
$926$	−26.7235	−0.878190
$927$	−13.9713	−0.458879
$928$	5.31375	0.174432
$929$	8.62169	0.282869	0.141434	−	0.989948i	$-0.454829\pi$
$929$	8.62169	0.282869	0.141434	+	0.989948i	$0.454829\pi$
$930$	−2.39593	−0.0785657
$931$	−20.5545	−0.673647
$932$	−19.8848	−0.651349
$933$	12.4509	0.407624
$934$	−28.4469	−0.930812
$935$	−2.87530	−0.0940324
$936$	6.81015	0.222597
$937$	−17.5481	−0.573271	−0.286636	−	0.958040i	$-0.592537\pi$
$937$	−17.5481	−0.573271	−0.286636	+	0.958040i	$0.592537\pi$
$938$	−6.53148	−0.213260
$939$	23.8261	0.777536
$940$	−1.64886	−0.0537799
$941$	−32.7029	−1.06608	−0.533042	−	0.846089i	$-0.678951\pi$
$941$	−32.7029	−1.06608	−0.533042	+	0.846089i	$0.678951\pi$
$942$	−1.28126	−0.0417458
$943$	−1.46271	−0.0476324
$944$	0.243785	0.00793453
$945$	−1.88854	−0.0614343
$946$	−12.7889	−0.415803
$947$	59.7085	1.94027	0.970133	−	0.242575i	$-0.0779921\pi$
$947$	59.7085	1.94027	0.970133	+	0.242575i	$0.0779921\pi$
$948$	−6.46131	−0.209854
$949$	−69.3737	−2.25197
$950$	−18.5002	−0.600225
$951$	−13.9148	−0.451218
$952$	5.52786	0.179159
$953$	−58.8800	−1.90731	−0.953654	−	0.300904i	$-0.902712\pi$
$953$	−58.8800	−1.90731	−0.953654	+	0.300904i	$0.902712\pi$
$954$	−11.4758	−0.371541
$955$	−4.09731	−0.132586
$956$	−5.09591	−0.164813
$957$	−16.0425	−0.518580
$958$	5.05812	0.163421
$959$	16.3370	0.527549
$960$	0.351141	0.0113330
$961$	15.5571	0.501842
$962$	−9.37831	−0.302369
$963$	7.34946	0.236833
$964$	−3.01532	−0.0971170
$965$	0.954691	0.0307326
$966$	−2.10685	−0.0677867
$967$	51.4799	1.65548	0.827741	−	0.561110i	$-0.189626\pi$
$967$	51.4799	1.65548	0.827741	+	0.561110i	$0.189626\pi$
$968$	−5.47214	−0.175881
$969$	21.5704	0.692939
$970$	3.63471	0.116704
$971$	27.1359	0.870834	0.435417	−	0.900229i	$-0.356601\pi$
$971$	27.1359	0.870834	0.435417	+	0.900229i	$0.356601\pi$
$972$	12.7540	0.409085
$973$	−0.386938	−0.0124047
$974$	−11.1660	−0.357781
$975$	31.8767	1.02087
$976$	−6.85765	−0.219508
$977$	25.8667	0.827548	0.413774	−	0.910380i	$-0.364210\pi$
$977$	25.8667	0.827548	0.413774	+	0.910380i	$0.364210\pi$
$978$	5.01302	0.160299
$979$	−32.9160	−1.05200
$980$	−1.49640	−0.0478006
$981$	−2.73098	−0.0871936
$982$	−32.1169	−1.02489
$983$	49.7983	1.58832	0.794159	−	0.607710i	$-0.207912\pi$
$983$	49.7983	1.58832	0.794159	+	0.607710i	$0.207912\pi$
$984$	1.41498	0.0451080
$985$	−3.28911	−0.104800
$986$	23.7638	0.756794
$987$	−9.57035	−0.304628
$988$	−18.9324	−0.602321
$989$	−7.22027	−0.229591
$990$	0.868699	0.0276091
$991$	36.7879	1.16861	0.584303	−	0.811536i	$-0.301368\pi$
$991$	36.7879	1.16861	0.584303	+	0.811536i	$0.301368\pi$
$992$	−6.82328	−0.216639
$993$	30.0365	0.953178
$994$	1.34163	0.0425539
$995$	−1.48768	−0.0471627
$996$	−1.18045	−0.0374041
$997$	6.45172	0.204328	0.102164	−	0.994768i	$-0.467423\pi$
$997$	6.45172	0.204328	0.102164	+	0.994768i	$0.467423\pi$
$998$	36.9671	1.17017
$999$	−10.3959	−0.328913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	226.2.a.d.1.3	✓	4
3.2	odd	2		2034.2.a.r.1.3		4
4.3	odd	2		1808.2.a.j.1.2		4
5.4	even	2		5650.2.a.o.1.2		4
8.3	odd	2		7232.2.a.v.1.3		4
8.5	even	2		7232.2.a.u.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
226.2.a.d.1.3	✓	4	1.1	even	1	trivial
1808.2.a.j.1.2		4	4.3	odd	2
2034.2.a.r.1.3		4	3.2	odd	2
5650.2.a.o.1.2		4	5.4	even	2
7232.2.a.u.1.2		4	8.5	even	2
7232.2.a.v.1.3		4	8.3	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:	\( N \)	\(=\)	\( 226 = 2 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	226.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.28408 q^{3} +1.00000 q^{4} +0.273457 q^{5} +1.28408 q^{6} +1.23607 q^{7} +1.00000 q^{8} -1.35114 q^{9} +0.273457 q^{10} -2.35114 q^{11} +1.28408 q^{12} -5.04029 q^{13} +1.23607 q^{14} +0.351141 q^{15} +1.00000 q^{16} +4.47214 q^{17} -1.35114 q^{18} +3.75621 q^{19} +0.273457 q^{20} +1.58721 q^{21} -2.35114 q^{22} -1.32739 q^{23} +1.28408 q^{24} -4.92522 q^{25} -5.04029 q^{26} -5.58721 q^{27} +1.23607 q^{28} +5.31375 q^{29} +0.351141 q^{30} -6.82328 q^{31} +1.00000 q^{32} -3.01905 q^{33} +4.47214 q^{34} +0.338012 q^{35} -1.35114 q^{36} +1.86067 q^{37} +3.75621 q^{38} -6.47214 q^{39} +0.273457 q^{40} +1.10194 q^{41} +1.58721 q^{42} +5.43945 q^{43} -2.35114 q^{44} -0.369480 q^{45} -1.32739 q^{46} -6.02967 q^{47} +1.28408 q^{48} -5.47214 q^{49} -4.92522 q^{50} +5.74258 q^{51} -5.04029 q^{52} +8.49338 q^{53} -5.58721 q^{54} -0.642937 q^{55} +1.23607 q^{56} +4.82328 q^{57} +5.31375 q^{58} +0.243785 q^{59} +0.351141 q^{60} -6.85765 q^{61} -6.82328 q^{62} -1.67010 q^{63} +1.00000 q^{64} -1.37831 q^{65} -3.01905 q^{66} -5.28408 q^{67} +4.47214 q^{68} -1.70447 q^{69} +0.338012 q^{70} +1.08540 q^{71} -1.35114 q^{72} +13.7638 q^{73} +1.86067 q^{74} -6.32437 q^{75} +3.75621 q^{76} -2.90617 q^{77} -6.47214 q^{78} -5.03186 q^{79} +0.273457 q^{80} -3.12099 q^{81} +1.10194 q^{82} -0.919299 q^{83} +1.58721 q^{84} +1.22294 q^{85} +5.43945 q^{86} +6.82328 q^{87} -2.35114 q^{88} +14.0000 q^{89} -0.369480 q^{90} -6.23015 q^{91} -1.32739 q^{92} -8.76163 q^{93} -6.02967 q^{94} +1.02717 q^{95} +1.28408 q^{96} +13.2917 q^{97} -5.47214 q^{98} +3.17672 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 4 q^{7} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{12} + 4 q^{13} - 4 q^{14} - 8 q^{15} + 4 q^{16} + 4 q^{18} - 6 q^{19} + 4 q^{20} - 12 q^{21} - 6 q^{23}+ \cdots + 40 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 4 * q^7 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 2 * q^12 + 4 * q^13 - 4 * q^14 - 8 * q^15 + 4 * q^16 + 4 * q^18 - 6 * q^19 + 4 * q^20 - 12 * q^21 - 6 * q^23 + 2 * q^24 + 4 * q^25 + 4 * q^26 - 4 * q^27 - 4 * q^28 - 8 * q^30 + 4 * q^32 - 4 * q^35 + 4 * q^36 - 8 * q^37 - 6 * q^38 - 8 * q^39 + 4 * q^40 + 8 * q^41 - 12 * q^42 - 6 * q^43 - 16 * q^45 - 6 * q^46 - 6 * q^47 + 2 * q^48 - 4 * q^49 + 4 * q^50 - 20 * q^51 + 4 * q^52 + 4 * q^53 - 4 * q^54 - 20 * q^55 - 4 * q^56 - 8 * q^57 + 22 * q^59 - 8 * q^60 + 16 * q^61 - 4 * q^63 + 4 * q^64 + 24 * q^65 - 18 * q^67 + 12 * q^69 - 4 * q^70 + 22 * q^71 + 4 * q^72 - 8 * q^74 + 2 * q^75 - 6 * q^76 - 8 * q^78 - 2 * q^79 + 4 * q^80 - 4 * q^81 + 8 * q^82 + 12 * q^83 - 12 * q^84 - 6 * q^86 + 56 * q^89 - 16 * q^90 - 24 * q^91 - 6 * q^92 + 20 * q^93 - 6 * q^94 - 16 * q^95 + 2 * q^96 + 16 * q^97 - 4 * q^98 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more