LMFDB - Embedded newform 4235.2.a.bl.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 14x^{8} + 26x^{7} + 63x^{6} - 106x^{5} - 96x^{4} + 140x^{3} + 38x^{2} - 38x - 11 $ x^10 - 2x^9 - 14x^8 + 26x^7 + 63x^6 - 106x^5 - 96x^4 + 140x^3 + 38x^2 - 38*x - 11
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.330750$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.330750 q^{2} -2.01275 q^{3} -1.89060 q^{4} -1.00000 q^{5} +0.665719 q^{6} +1.00000 q^{7} +1.28682 q^{8} +1.05118 q^{9} +O(q^{10})$	\(q-0.330750 q^{2} -2.01275 q^{3} -1.89060 q^{4} -1.00000 q^{5} +0.665719 q^{6} +1.00000 q^{7} +1.28682 q^{8} +1.05118 q^{9} +0.330750 q^{10} +3.80532 q^{12} +5.87165 q^{13} -0.330750 q^{14} +2.01275 q^{15} +3.35559 q^{16} -4.59490 q^{17} -0.347678 q^{18} +1.01857 q^{19} +1.89060 q^{20} -2.01275 q^{21} -0.718654 q^{23} -2.59005 q^{24} +1.00000 q^{25} -1.94205 q^{26} +3.92250 q^{27} -1.89060 q^{28} +2.38921 q^{29} -0.665719 q^{30} +7.28253 q^{31} -3.68350 q^{32} +1.51976 q^{34} -1.00000 q^{35} -1.98737 q^{36} +5.20347 q^{37} -0.336894 q^{38} -11.8182 q^{39} -1.28682 q^{40} -8.67228 q^{41} +0.665719 q^{42} -2.10086 q^{43} -1.05118 q^{45} +0.237695 q^{46} -7.27317 q^{47} -6.75398 q^{48} +1.00000 q^{49} -0.330750 q^{50} +9.24841 q^{51} -11.1010 q^{52} -2.89777 q^{53} -1.29737 q^{54} +1.28682 q^{56} -2.05014 q^{57} -0.790233 q^{58} -4.47270 q^{59} -3.80532 q^{60} -0.582670 q^{61} -2.40870 q^{62} +1.05118 q^{63} -5.49287 q^{64} -5.87165 q^{65} -8.04324 q^{67} +8.68714 q^{68} +1.44647 q^{69} +0.330750 q^{70} +5.95360 q^{71} +1.35268 q^{72} +10.3957 q^{73} -1.72105 q^{74} -2.01275 q^{75} -1.92572 q^{76} +3.90887 q^{78} +4.72299 q^{79} -3.35559 q^{80} -11.0486 q^{81} +2.86836 q^{82} -11.3462 q^{83} +3.80532 q^{84} +4.59490 q^{85} +0.694862 q^{86} -4.80890 q^{87} +4.75655 q^{89} +0.347678 q^{90} +5.87165 q^{91} +1.35869 q^{92} -14.6579 q^{93} +2.40560 q^{94} -1.01857 q^{95} +7.41398 q^{96} +9.21735 q^{97} -0.330750 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 4 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 4 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^7 + 6 * q^8 + 6 * q^9	$ 10 q + 2 q^{2} + 4 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{7} + 6 q^{8} + 6 q^{9} - 2 q^{10} + 16 q^{12} + 26 q^{13} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 4 q^{17} + 8 q^{18} + 6 q^{19} - 12 q^{20} + 4 q^{21} - 8 q^{23} + 22 q^{24} + 10 q^{25} - 6 q^{26} + 10 q^{27} + 12 q^{28} - 4 q^{29} + 18 q^{31} + 24 q^{32} + 8 q^{34} - 10 q^{35} - 10 q^{36} - 16 q^{37} - 2 q^{38} + 16 q^{39} - 6 q^{40} - 30 q^{41} + 22 q^{43} - 6 q^{45} + 28 q^{46} + 14 q^{47} - 4 q^{48} + 10 q^{49} + 2 q^{50} + 36 q^{51} + 34 q^{52} - 10 q^{53} + 6 q^{54} + 6 q^{56} - 2 q^{57} - 38 q^{58} + 22 q^{59} - 16 q^{60} + 12 q^{61} - 6 q^{62} + 6 q^{63} + 8 q^{64} - 26 q^{65} - 14 q^{67} + 70 q^{68} + 8 q^{69} - 2 q^{70} - 8 q^{71} + 26 q^{72} + 30 q^{73} - 20 q^{74} + 4 q^{75} + 18 q^{76} - 32 q^{78} + 8 q^{79} - 20 q^{80} + 10 q^{81} - 28 q^{82} - 14 q^{83} + 16 q^{84} - 4 q^{85} - 14 q^{86} - 24 q^{87} - 6 q^{89} - 8 q^{90} + 26 q^{91} - 20 q^{92} + 14 q^{93} + 16 q^{94} - 6 q^{95} + 24 q^{96} + 20 q^{97} + 2 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 + 4 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^7 + 6 * q^8 + 6 * q^9 - 2 * q^10 + 16 * q^12 + 26 * q^13 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 4 * q^17 + 8 * q^18 + 6 * q^19 - 12 * q^20 + 4 * q^21 - 8 * q^23 + 22 * q^24 + 10 * q^25 - 6 * q^26 + 10 * q^27 + 12 * q^28 - 4 * q^29 + 18 * q^31 + 24 * q^32 + 8 * q^34 - 10 * q^35 - 10 * q^36 - 16 * q^37 - 2 * q^38 + 16 * q^39 - 6 * q^40 - 30 * q^41 + 22 * q^43 - 6 * q^45 + 28 * q^46 + 14 * q^47 - 4 * q^48 + 10 * q^49 + 2 * q^50 + 36 * q^51 + 34 * q^52 - 10 * q^53 + 6 * q^54 + 6 * q^56 - 2 * q^57 - 38 * q^58 + 22 * q^59 - 16 * q^60 + 12 * q^61 - 6 * q^62 + 6 * q^63 + 8 * q^64 - 26 * q^65 - 14 * q^67 + 70 * q^68 + 8 * q^69 - 2 * q^70 - 8 * q^71 + 26 * q^72 + 30 * q^73 - 20 * q^74 + 4 * q^75 + 18 * q^76 - 32 * q^78 + 8 * q^79 - 20 * q^80 + 10 * q^81 - 28 * q^82 - 14 * q^83 + 16 * q^84 - 4 * q^85 - 14 * q^86 - 24 * q^87 - 6 * q^89 - 8 * q^90 + 26 * q^91 - 20 * q^92 + 14 * q^93 + 16 * q^94 - 6 * q^95 + 24 * q^96 + 20 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.330750	−0.233876	−0.116938	−	0.993139i	$-0.537308\pi$
$2$	−0.330750	−0.233876	−0.116938	+	0.993139i	$0.537308\pi$
$3$	−2.01275	−1.16206	−0.581032	−	0.813881i	$-0.697351\pi$
$3$	−2.01275	−1.16206	−0.581032	+	0.813881i	$0.697351\pi$
$4$	−1.89060	−0.945302
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.665719	0.271779
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.28682	0.454959
$9$	1.05118	0.350393
$10$	0.330750	0.104592
$11$	0	0
$11$	0	0
$12$	3.80532	1.09850
$13$	5.87165	1.62850	0.814252	−	0.580512i	$-0.197147\pi$
$13$	5.87165	1.62850	0.814252	+	0.580512i	$0.197147\pi$
$14$	−0.330750	−0.0883967
$15$	2.01275	0.519691
$16$	3.35559	0.838898
$17$	−4.59490	−1.11443	−0.557214	−	0.830369i	$-0.688130\pi$
$17$	−4.59490	−1.11443	−0.557214	+	0.830369i	$0.688130\pi$
$18$	−0.347678	−0.0819485
$19$	1.01857	0.233677	0.116839	−	0.993151i	$-0.462724\pi$
$19$	1.01857	0.233677	0.116839	+	0.993151i	$0.462724\pi$
$20$	1.89060	0.422752
$21$	−2.01275	−0.439219
$22$	0	0
$23$	−0.718654	−0.149850	−0.0749248	−	0.997189i	$-0.523872\pi$
$23$	−0.718654	−0.149850	−0.0749248	+	0.997189i	$0.523872\pi$
$24$	−2.59005	−0.528692
$25$	1.00000	0.200000
$26$	−1.94205	−0.380868
$27$	3.92250	0.754885
$28$	−1.89060	−0.357291
$29$	2.38921	0.443666	0.221833	−	0.975085i	$-0.428796\pi$
$29$	2.38921	0.443666	0.221833	+	0.975085i	$0.428796\pi$
$30$	−0.665719	−0.121543
$31$	7.28253	1.30798	0.653990	−	0.756503i	$-0.273094\pi$
$31$	7.28253	1.30798	0.653990	+	0.756503i	$0.273094\pi$
$32$	−3.68350	−0.651157
$33$	0	0
$34$	1.51976	0.260638
$35$	−1.00000	−0.169031
$36$	−1.98737	−0.331228
$37$	5.20347	0.855445	0.427722	−	0.903910i	$-0.359316\pi$
$37$	5.20347	0.855445	0.427722	+	0.903910i	$0.359316\pi$
$38$	−0.336894	−0.0546514
$39$	−11.8182	−1.89243
$40$	−1.28682	−0.203464
$41$	−8.67228	−1.35438	−0.677191	−	0.735807i	$-0.736803\pi$
$41$	−8.67228	−1.35438	−0.677191	+	0.735807i	$0.736803\pi$
$42$	0.665719	0.102723
$43$	−2.10086	−0.320379	−0.160189	−	0.987086i	$-0.551211\pi$
$43$	−2.10086	−0.320379	−0.160189	+	0.987086i	$0.551211\pi$
$44$	0	0
$45$	−1.05118	−0.156701
$46$	0.237695	0.0350462
$47$	−7.27317	−1.06090	−0.530451	−	0.847716i	$-0.677977\pi$
$47$	−7.27317	−1.06090	−0.530451	+	0.847716i	$0.677977\pi$
$48$	−6.75398	−0.974854
$49$	1.00000	0.142857
$50$	−0.330750	−0.0467752
$51$	9.24841	1.29504
$52$	−11.1010	−1.53943
$53$	−2.89777	−0.398040	−0.199020	−	0.979995i	$-0.563776\pi$
$53$	−2.89777	−0.398040	−0.199020	+	0.979995i	$0.563776\pi$
$54$	−1.29737	−0.176549
$55$	0	0
$56$	1.28682	0.171958
$57$	−2.05014	−0.271548
$58$	−0.790233	−0.103763
$59$	−4.47270	−0.582297	−0.291148	−	0.956678i	$-0.594037\pi$
$59$	−4.47270	−0.582297	−0.291148	+	0.956678i	$0.594037\pi$
$60$	−3.80532	−0.491265
$61$	−0.582670	−0.0746032	−0.0373016	−	0.999304i	$-0.511876\pi$
$61$	−0.582670	−0.0746032	−0.0373016	+	0.999304i	$0.511876\pi$
$62$	−2.40870	−0.305905
$63$	1.05118	0.132436
$64$	−5.49287	−0.686608
$65$	−5.87165	−0.728289
$66$	0	0
$67$	−8.04324	−0.982639	−0.491319	−	0.870979i	$-0.663485\pi$
$67$	−8.04324	−0.982639	−0.491319	+	0.870979i	$0.663485\pi$
$68$	8.68714	1.05347
$69$	1.44647	0.174135
$70$	0.330750	0.0395322
$71$	5.95360	0.706563	0.353281	−	0.935517i	$-0.385066\pi$
$71$	5.95360	0.706563	0.353281	+	0.935517i	$0.385066\pi$
$72$	1.35268	0.159415
$73$	10.3957	1.21672	0.608362	−	0.793659i	$-0.291827\pi$
$73$	10.3957	1.21672	0.608362	+	0.793659i	$0.291827\pi$
$74$	−1.72105	−0.200068
$75$	−2.01275	−0.232413
$76$	−1.92572	−0.220895
$77$	0	0
$78$	3.90887	0.442593
$79$	4.72299	0.531378	0.265689	−	0.964059i	$-0.414401\pi$
$79$	4.72299	0.531378	0.265689	+	0.964059i	$0.414401\pi$
$80$	−3.35559	−0.375167
$81$	−11.0486	−1.22762
$82$	2.86836	0.316757
$83$	−11.3462	−1.24541	−0.622703	−	0.782458i	$-0.713965\pi$
$83$	−11.3462	−1.24541	−0.622703	+	0.782458i	$0.713965\pi$
$84$	3.80532	0.415195
$85$	4.59490	0.498387
$86$	0.694862	0.0749289
$87$	−4.80890	−0.515568
$88$	0	0
$89$	4.75655	0.504193	0.252097	−	0.967702i	$-0.418880\pi$
$89$	4.75655	0.504193	0.252097	+	0.967702i	$0.418880\pi$
$90$	0.347678	0.0366485
$91$	5.87165	0.615517
$92$	1.35869	0.141653
$93$	−14.6579	−1.51996
$94$	2.40560	0.248119
$95$	−1.01857	−0.104504
$96$	7.41398	0.756686
$97$	9.21735	0.935880	0.467940	−	0.883760i	$-0.344996\pi$
$97$	9.21735	0.935880	0.467940	+	0.883760i	$0.344996\pi$
$98$	−0.330750	−0.0334108
$99$	0	0
$100$	−1.89060	−0.189060
$101$	−13.4870	−1.34200	−0.671001	−	0.741456i	$-0.734135\pi$
$101$	−13.4870	−1.34200	−0.671001	+	0.741456i	$0.734135\pi$
$102$	−3.05891	−0.302878
$103$	14.8254	1.46079	0.730395	−	0.683025i	$-0.239336\pi$
$103$	14.8254	1.46079	0.730395	+	0.683025i	$0.239336\pi$
$104$	7.55575	0.740903
$105$	2.01275	0.196425
$106$	0.958439	0.0930918
$107$	−10.2695	−0.992791	−0.496396	−	0.868096i	$-0.665343\pi$
$107$	−10.2695	−0.992791	−0.496396	+	0.868096i	$0.665343\pi$
$108$	−7.41589	−0.713594
$109$	−9.82692	−0.941248	−0.470624	−	0.882334i	$-0.655971\pi$
$109$	−9.82692	−0.941248	−0.470624	+	0.882334i	$0.655971\pi$
$110$	0	0
$111$	−10.4733	−0.994082
$112$	3.35559	0.317074
$113$	−14.3624	−1.35110	−0.675549	−	0.737316i	$-0.736093\pi$
$113$	−14.3624	−1.35110	−0.675549	+	0.737316i	$0.736093\pi$
$114$	0.678085	0.0635084
$115$	0.718654	0.0670148
$116$	−4.51705	−0.419398
$117$	6.17216	0.570617
$118$	1.47935	0.136185
$119$	−4.59490	−0.421214
$120$	2.59005	0.236438
$121$	0	0
$122$	0.192718	0.0174479
$123$	17.4552	1.57388
$124$	−13.7684	−1.23644
$125$	−1.00000	−0.0894427
$126$	−0.347678	−0.0309736
$127$	1.81890	0.161402	0.0807008	−	0.996738i	$-0.474284\pi$
$127$	1.81890	0.161402	0.0807008	+	0.996738i	$0.474284\pi$
$128$	9.18377	0.811738
$129$	4.22852	0.372301
$130$	1.94205	0.170329
$131$	13.0503	1.14021	0.570104	−	0.821573i	$-0.306903\pi$
$131$	13.0503	1.14021	0.570104	+	0.821573i	$0.306903\pi$
$132$	0	0
$133$	1.01857	0.0883216
$134$	2.66031	0.229815
$135$	−3.92250	−0.337595
$136$	−5.91280	−0.507019
$137$	8.35509	0.713823	0.356912	−	0.934138i	$-0.383830\pi$
$137$	8.35509	0.713823	0.356912	+	0.934138i	$0.383830\pi$
$138$	−0.478421	−0.0407259
$139$	−12.4360	−1.05481	−0.527405	−	0.849614i	$-0.676835\pi$
$139$	−12.4360	−1.05481	−0.527405	+	0.849614i	$0.676835\pi$
$140$	1.89060	0.159785
$141$	14.6391	1.23284
$142$	−1.96916	−0.165248
$143$	0	0
$144$	3.52733	0.293944
$145$	−2.38921	−0.198413
$146$	−3.43838	−0.284562
$147$	−2.01275	−0.166009
$148$	−9.83770	−0.808654
$149$	9.09967	0.745474	0.372737	−	0.927937i	$-0.378419\pi$
$149$	9.09967	0.745474	0.372737	+	0.927937i	$0.378419\pi$
$150$	0.665719	0.0543557
$151$	8.55979	0.696586	0.348293	−	0.937386i	$-0.386761\pi$
$151$	8.55979	0.696586	0.348293	+	0.937386i	$0.386761\pi$
$152$	1.31072	0.106313
$153$	−4.83007	−0.390488
$154$	0	0
$155$	−7.28253	−0.584947
$156$	22.3435	1.78891
$157$	−22.6758	−1.80972	−0.904861	−	0.425707i	$-0.860025\pi$
$157$	−22.6758	−1.80972	−0.904861	+	0.425707i	$0.860025\pi$
$158$	−1.56213	−0.124276
$159$	5.83250	0.462548
$160$	3.68350	0.291206
$161$	−0.718654	−0.0566378
$162$	3.65431	0.287110
$163$	14.6417	1.14682	0.573412	−	0.819267i	$-0.305619\pi$
$163$	14.6417	1.14682	0.573412	+	0.819267i	$0.305619\pi$
$164$	16.3958	1.28030
$165$	0	0
$166$	3.75275	0.291270
$167$	7.72833	0.598036	0.299018	−	0.954247i	$-0.403341\pi$
$167$	7.72833	0.598036	0.299018	+	0.954247i	$0.403341\pi$
$168$	−2.59005	−0.199827
$169$	21.4763	1.65202
$170$	−1.51976	−0.116561
$171$	1.07071	0.0818789
$172$	3.97190	0.302855
$173$	20.0328	1.52306	0.761531	−	0.648128i	$-0.224448\pi$
$173$	20.0328	1.52306	0.761531	+	0.648128i	$0.224448\pi$
$174$	1.59054	0.120579
$175$	1.00000	0.0755929
$176$	0	0
$177$	9.00245	0.676666
$178$	−1.57323	−0.117919
$179$	−19.8218	−1.48155	−0.740776	−	0.671752i	$-0.765542\pi$
$179$	−19.8218	−1.48155	−0.740776	+	0.671752i	$0.765542\pi$
$180$	1.98737	0.148129
$181$	14.3178	1.06423	0.532117	−	0.846671i	$-0.321397\pi$
$181$	14.3178	1.06423	0.532117	+	0.846671i	$0.321397\pi$
$182$	−1.94205	−0.143954
$183$	1.17277	0.0866937
$184$	−0.924777	−0.0681755
$185$	−5.20347	−0.382567
$186$	4.84812	0.355481
$187$	0	0
$188$	13.7507	1.00287
$189$	3.92250	0.285320
$190$	0.336894	0.0244408
$191$	−3.10444	−0.224629	−0.112315	−	0.993673i	$-0.535826\pi$
$191$	−3.10444	−0.224629	−0.112315	+	0.993673i	$0.535826\pi$
$192$	11.0558	0.797883
$193$	23.5775	1.69715	0.848573	−	0.529079i	$-0.177463\pi$
$193$	23.5775	1.69715	0.848573	+	0.529079i	$0.177463\pi$
$194$	−3.04864	−0.218880
$195$	11.8182	0.846319
$196$	−1.89060	−0.135043
$197$	18.0015	1.28255	0.641277	−	0.767309i	$-0.278405\pi$
$197$	18.0015	1.28255	0.641277	+	0.767309i	$0.278405\pi$
$198$	0	0
$199$	−27.4047	−1.94267	−0.971333	−	0.237723i	$-0.923599\pi$
$199$	−27.4047	−1.94267	−0.971333	+	0.237723i	$0.923599\pi$
$200$	1.28682	0.0909918
$201$	16.1891	1.14189
$202$	4.46081	0.313862
$203$	2.38921	0.167690
$204$	−17.4851	−1.22420
$205$	8.67228	0.605698
$206$	−4.90350	−0.341643
$207$	−0.755434	−0.0525063
$208$	19.7029	1.36615
$209$	0	0
$210$	−0.665719	−0.0459390
$211$	11.9140	0.820192	0.410096	−	0.912042i	$-0.365495\pi$
$211$	11.9140	0.820192	0.410096	+	0.912042i	$0.365495\pi$
$212$	5.47854	0.376268
$213$	−11.9831	−0.821071
$214$	3.39664	0.232190
$215$	2.10086	0.143278
$216$	5.04754	0.343442
$217$	7.28253	0.494370
$218$	3.25026	0.220135
$219$	−20.9240	−1.41391
$220$	0	0
$221$	−26.9797	−1.81485
$222$	3.46405	0.232492
$223$	15.9984	1.07133	0.535667	−	0.844429i	$-0.320060\pi$
$223$	15.9984	1.07133	0.535667	+	0.844429i	$0.320060\pi$
$224$	−3.68350	−0.246114
$225$	1.05118	0.0700787
$226$	4.75035	0.315989
$227$	24.4085	1.62005	0.810026	−	0.586394i	$-0.199453\pi$
$227$	24.4085	1.62005	0.810026	+	0.586394i	$0.199453\pi$
$228$	3.87600	0.256695
$229$	16.6015	1.09706	0.548529	−	0.836132i	$-0.315188\pi$
$229$	16.6015	1.09706	0.548529	+	0.836132i	$0.315188\pi$
$230$	−0.237695	−0.0156731
$231$	0	0
$232$	3.07448	0.201850
$233$	6.46982	0.423852	0.211926	−	0.977286i	$-0.432026\pi$
$233$	6.46982	0.423852	0.211926	+	0.977286i	$0.432026\pi$
$234$	−2.04145	−0.133453
$235$	7.27317	0.474450
$236$	8.45611	0.550446
$237$	−9.50622	−0.617495
$238$	1.51976	0.0985117
$239$	−0.690748	−0.0446808	−0.0223404	−	0.999750i	$-0.507112\pi$
$239$	−0.690748	−0.0446808	−0.0223404	+	0.999750i	$0.507112\pi$
$240$	6.75398	0.435968
$241$	2.51621	0.162084	0.0810418	−	0.996711i	$-0.474175\pi$
$241$	2.51621	0.162084	0.0810418	+	0.996711i	$0.474175\pi$
$242$	0	0
$243$	10.4705	0.671686
$244$	1.10160	0.0705226
$245$	−1.00000	−0.0638877
$246$	−5.77330	−0.368092
$247$	5.98072	0.380544
$248$	9.37129	0.595077
$249$	22.8371	1.44724
$250$	0.330750	0.0209185
$251$	25.7918	1.62796	0.813982	−	0.580890i	$-0.197295\pi$
$251$	25.7918	1.62796	0.813982	+	0.580890i	$0.197295\pi$
$252$	−1.98737	−0.125192
$253$	0	0
$254$	−0.601603	−0.0377479
$255$	−9.24841	−0.579158
$256$	7.94820	0.496762
$257$	−19.3127	−1.20469	−0.602346	−	0.798235i	$-0.705767\pi$
$257$	−19.3127	−1.20469	−0.602346	+	0.798235i	$0.705767\pi$
$258$	−1.39859	−0.0870722
$259$	5.20347	0.323328
$260$	11.1010	0.688453
$261$	2.51149	0.155457
$262$	−4.31638	−0.266667
$263$	−8.45761	−0.521519	−0.260759	−	0.965404i	$-0.583973\pi$
$263$	−8.45761	−0.521519	−0.260759	+	0.965404i	$0.583973\pi$
$264$	0	0
$265$	2.89777	0.178009
$266$	−0.336894	−0.0206563
$267$	−9.57377	−0.585905
$268$	15.2066	0.928891
$269$	8.22807	0.501674	0.250837	−	0.968029i	$-0.419294\pi$
$269$	8.22807	0.501674	0.250837	+	0.968029i	$0.419294\pi$
$270$	1.29737	0.0789552
$271$	−28.7058	−1.74375	−0.871877	−	0.489726i	$-0.837097\pi$
$271$	−28.7058	−1.74375	−0.871877	+	0.489726i	$0.837097\pi$
$272$	−15.4186	−0.934891
$273$	−11.8182	−0.715270
$274$	−2.76345	−0.166946
$275$	0	0
$276$	−2.73471	−0.164610
$277$	−17.0348	−1.02352	−0.511762	−	0.859127i	$-0.671007\pi$
$277$	−17.0348	−1.02352	−0.511762	+	0.859127i	$0.671007\pi$
$278$	4.11322	0.246694
$279$	7.65524	0.458308
$280$	−1.28682	−0.0769021
$281$	13.4726	0.803707	0.401854	−	0.915704i	$-0.368366\pi$
$281$	13.4726	0.803707	0.401854	+	0.915704i	$0.368366\pi$
$282$	−4.84189	−0.288330
$283$	17.9067	1.06444	0.532221	−	0.846605i	$-0.321358\pi$
$283$	17.9067	1.06444	0.532221	+	0.846605i	$0.321358\pi$
$284$	−11.2559	−0.667915
$285$	2.05014	0.121440
$286$	0	0
$287$	−8.67228	−0.511908
$288$	−3.87202	−0.228161
$289$	4.11311	0.241948
$290$	0.790233	0.0464041
$291$	−18.5523	−1.08755
$292$	−19.6542	−1.15017
$293$	16.7640	0.979362	0.489681	−	0.871902i	$-0.337113\pi$
$293$	16.7640	0.979362	0.489681	+	0.871902i	$0.337113\pi$
$294$	0.665719	0.0388255
$295$	4.47270	0.260411
$296$	6.69592	0.389192
$297$	0	0
$298$	−3.00972	−0.174348
$299$	−4.21968	−0.244031
$300$	3.80532	0.219700
$301$	−2.10086	−0.121092
$302$	−2.83115	−0.162915
$303$	27.1459	1.55949
$304$	3.41792	0.196031
$305$	0.582670	0.0333636
$306$	1.59755	0.0913256
$307$	9.64553	0.550499	0.275250	−	0.961373i	$-0.411239\pi$
$307$	9.64553	0.550499	0.275250	+	0.961373i	$0.411239\pi$
$308$	0	0
$309$	−29.8399	−1.69753
$310$	2.40870	0.136805
$311$	17.4544	0.989749	0.494875	−	0.868964i	$-0.335214\pi$
$311$	17.4544	0.989749	0.494875	+	0.868964i	$0.335214\pi$
$312$	−15.2079	−0.860976
$313$	5.28721	0.298851	0.149425	−	0.988773i	$-0.452258\pi$
$313$	5.28721	0.298851	0.149425	+	0.988773i	$0.452258\pi$
$314$	7.50001	0.423250
$315$	−1.05118	−0.0592273
$316$	−8.92930	−0.502312
$317$	−33.7741	−1.89694	−0.948472	−	0.316860i	$-0.897372\pi$
$317$	−33.7741	−1.89694	−0.948472	+	0.316860i	$0.897372\pi$
$318$	−1.92910	−0.108179
$319$	0	0
$320$	5.49287	0.307061
$321$	20.6700	1.15369
$322$	0.237695	0.0132462
$323$	−4.68025	−0.260416
$324$	20.8885	1.16047
$325$	5.87165	0.325701
$326$	−4.84274	−0.268215
$327$	19.7792	1.09379
$328$	−11.1596	−0.616188
$329$	−7.27317	−0.400983
$330$	0	0
$331$	−33.8688	−1.86160	−0.930799	−	0.365532i	$-0.880887\pi$
$331$	−33.8688	−1.86160	−0.930799	+	0.365532i	$0.880887\pi$
$332$	21.4511	1.17728
$333$	5.46978	0.299742
$334$	−2.55615	−0.139866
$335$	8.04324	0.439449
$336$	−6.75398	−0.368460
$337$	−27.8610	−1.51768	−0.758842	−	0.651275i	$-0.774235\pi$
$337$	−27.8610	−1.51768	−0.758842	+	0.651275i	$0.774235\pi$
$338$	−7.10330	−0.386368
$339$	28.9079	1.57006
$340$	−8.68714	−0.471126
$341$	0	0
$342$	−0.354136	−0.0191495
$343$	1.00000	0.0539949
$344$	−2.70343	−0.145759
$345$	−1.44647	−0.0778755
$346$	−6.62584	−0.356207
$347$	15.8702	0.851957	0.425978	−	0.904733i	$-0.359930\pi$
$347$	15.8702	0.851957	0.425978	+	0.904733i	$0.359930\pi$
$348$	9.09172	0.487367
$349$	20.4354	1.09388	0.546941	−	0.837171i	$-0.315792\pi$
$349$	20.4354	1.09388	0.546941	+	0.837171i	$0.315792\pi$
$350$	−0.330750	−0.0176793
$351$	23.0315	1.22933
$352$	0	0
$353$	28.7818	1.53190	0.765949	−	0.642901i	$-0.222269\pi$
$353$	28.7818	1.53190	0.765949	+	0.642901i	$0.222269\pi$
$354$	−2.97756	−0.158256
$355$	−5.95360	−0.315984
$356$	−8.99275	−0.476615
$357$	9.24841	0.489478
$358$	6.55607	0.346499
$359$	−21.1079	−1.11403	−0.557017	−	0.830501i	$-0.688054\pi$
$359$	−21.1079	−1.11403	−0.557017	+	0.830501i	$0.688054\pi$
$360$	−1.35268	−0.0712924
$361$	−17.9625	−0.945395
$362$	−4.73562	−0.248899
$363$	0	0
$364$	−11.1010	−0.581849
$365$	−10.3957	−0.544136
$366$	−0.387894	−0.0202756
$367$	−13.6276	−0.711354	−0.355677	−	0.934609i	$-0.615750\pi$
$367$	−13.6276	−0.711354	−0.355677	+	0.934609i	$0.615750\pi$
$368$	−2.41151	−0.125709
$369$	−9.11612	−0.474566
$370$	1.72105	0.0894730
$371$	−2.89777	−0.150445
$372$	27.7124	1.43682
$373$	9.62780	0.498508	0.249254	−	0.968438i	$-0.419815\pi$
$373$	9.62780	0.498508	0.249254	+	0.968438i	$0.419815\pi$
$374$	0	0
$375$	2.01275	0.103938
$376$	−9.35926	−0.482667
$377$	14.0286	0.722511
$378$	−1.29737	−0.0667293
$379$	−10.9989	−0.564976	−0.282488	−	0.959271i	$-0.591160\pi$
$379$	−10.9989	−0.564976	−0.282488	+	0.959271i	$0.591160\pi$
$380$	1.92572	0.0987874
$381$	−3.66101	−0.187559
$382$	1.02679	0.0525353
$383$	22.2815	1.13853	0.569266	−	0.822153i	$-0.307227\pi$
$383$	22.2815	1.13853	0.569266	+	0.822153i	$0.307227\pi$
$384$	−18.4847	−0.943292
$385$	0	0
$386$	−7.79826	−0.396921
$387$	−2.20839	−0.112259
$388$	−17.4264	−0.884689
$389$	20.2773	1.02810	0.514049	−	0.857761i	$-0.328145\pi$
$389$	20.2773	1.02810	0.514049	+	0.857761i	$0.328145\pi$
$390$	−3.90887	−0.197933
$391$	3.30214	0.166996
$392$	1.28682	0.0649942
$393$	−26.2670	−1.32499
$394$	−5.95401	−0.299959
$395$	−4.72299	−0.237639
$396$	0	0
$397$	30.5070	1.53110	0.765550	−	0.643376i	$-0.222467\pi$
$397$	30.5070	1.53110	0.765550	+	0.643376i	$0.222467\pi$
$398$	9.06411	0.454343
$399$	−2.05014	−0.102635
$400$	3.35559	0.167780
$401$	26.2284	1.30978	0.654891	−	0.755723i	$-0.272715\pi$
$401$	26.2284	1.30978	0.654891	+	0.755723i	$0.272715\pi$
$402$	−5.35454	−0.267060
$403$	42.7605	2.13005
$404$	25.4985	1.26860
$405$	11.0486	0.549007
$406$	−0.790233	−0.0392186
$407$	0	0
$408$	11.9010	0.589188
$409$	−24.2001	−1.19662	−0.598310	−	0.801265i	$-0.704161\pi$
$409$	−24.2001	−1.19662	−0.598310	+	0.801265i	$0.704161\pi$
$410$	−2.86836	−0.141658
$411$	−16.8167	−0.829509
$412$	−28.0289	−1.38089
$413$	−4.47270	−0.220087
$414$	0.249860	0.0122800
$415$	11.3462	0.556962
$416$	−21.6282	−1.06041
$417$	25.0307	1.22576
$418$	0	0
$419$	−15.5499	−0.759664	−0.379832	−	0.925055i	$-0.624018\pi$
$419$	−15.5499	−0.759664	−0.379832	+	0.925055i	$0.624018\pi$
$420$	−3.80532	−0.185681
$421$	−20.0421	−0.976791	−0.488395	−	0.872622i	$-0.662418\pi$
$421$	−20.0421	−0.976791	−0.488395	+	0.872622i	$0.662418\pi$
$422$	−3.94055	−0.191823
$423$	−7.64542	−0.371733
$424$	−3.72891	−0.181092
$425$	−4.59490	−0.222885
$426$	3.96343	0.192029
$427$	−0.582670	−0.0281974
$428$	19.4156	0.938488
$429$	0	0
$430$	−0.694862	−0.0335092
$431$	−8.87276	−0.427386	−0.213693	−	0.976901i	$-0.568549\pi$
$431$	−8.87276	−0.427386	−0.213693	+	0.976901i	$0.568549\pi$
$432$	13.1623	0.633271
$433$	26.4754	1.27233	0.636163	−	0.771554i	$-0.280520\pi$
$433$	26.4754	1.27233	0.636163	+	0.771554i	$0.280520\pi$
$434$	−2.40870	−0.115621
$435$	4.80890	0.230569
$436$	18.5788	0.889764
$437$	−0.732002	−0.0350164
$438$	6.92062	0.330680
$439$	−23.5499	−1.12398	−0.561988	−	0.827146i	$-0.689963\pi$
$439$	−23.5499	−1.12398	−0.561988	+	0.827146i	$0.689963\pi$
$440$	0	0
$441$	1.05118	0.0500562
$442$	8.92353	0.424449
$443$	23.4485	1.11407	0.557035	−	0.830489i	$-0.311939\pi$
$443$	23.4485	1.11407	0.557035	+	0.830489i	$0.311939\pi$
$444$	19.8009	0.939708
$445$	−4.75655	−0.225482
$446$	−5.29149	−0.250559
$447$	−18.3154	−0.866288
$448$	−5.49287	−0.259514
$449$	33.0368	1.55910	0.779551	−	0.626339i	$-0.215447\pi$
$449$	33.0368	1.55910	0.779551	+	0.626339i	$0.215447\pi$
$450$	−0.347678	−0.0163897
$451$	0	0
$452$	27.1535	1.27719
$453$	−17.2288	−0.809477
$454$	−8.07313	−0.378891
$455$	−5.87165	−0.275267
$456$	−2.63816	−0.123543
$457$	11.1552	0.521818	0.260909	−	0.965363i	$-0.415978\pi$
$457$	11.1552	0.521818	0.260909	+	0.965363i	$0.415978\pi$
$458$	−5.49095	−0.256575
$459$	−18.0235	−0.841264
$460$	−1.35869	−0.0633492
$461$	19.0975	0.889457	0.444729	−	0.895665i	$-0.353300\pi$
$461$	19.0975	0.889457	0.444729	+	0.895665i	$0.353300\pi$
$462$	0	0
$463$	0.931169	0.0432751	0.0216375	−	0.999766i	$-0.493112\pi$
$463$	0.931169	0.0432751	0.0216375	+	0.999766i	$0.493112\pi$
$464$	8.01722	0.372190
$465$	14.6579	0.679745
$466$	−2.13989	−0.0991287
$467$	19.7138	0.912244	0.456122	−	0.889917i	$-0.349238\pi$
$467$	19.7138	0.912244	0.456122	+	0.889917i	$0.349238\pi$
$468$	−11.6691	−0.539405
$469$	−8.04324	−0.371403
$470$	−2.40560	−0.110962
$471$	45.6407	2.10301
$472$	−5.75556	−0.264921
$473$	0	0
$474$	3.14418	0.144417
$475$	1.01857	0.0467354
$476$	8.68714	0.398174
$477$	−3.04608	−0.139470
$478$	0.228465	0.0104498
$479$	−26.5606	−1.21358	−0.606792	−	0.794860i	$-0.707544\pi$
$479$	−26.5606	−1.21358	−0.606792	+	0.794860i	$0.707544\pi$
$480$	−7.41398	−0.338400
$481$	30.5530	1.39309
$482$	−0.832239	−0.0379074
$483$	1.44647	0.0658168
$484$	0	0
$485$	−9.21735	−0.418538
$486$	−3.46314	−0.157091
$487$	−6.94664	−0.314782	−0.157391	−	0.987536i	$-0.550308\pi$
$487$	−6.94664	−0.314782	−0.157391	+	0.987536i	$0.550308\pi$
$488$	−0.749790	−0.0339414
$489$	−29.4701	−1.33268
$490$	0.330750	0.0149418
$491$	−35.2938	−1.59279	−0.796393	−	0.604780i	$-0.793261\pi$
$491$	−35.2938	−1.59279	−0.796393	+	0.604780i	$0.793261\pi$
$492$	−33.0008	−1.48779
$493$	−10.9782	−0.494433
$494$	−1.97812	−0.0890000
$495$	0	0
$496$	24.4372	1.09726
$497$	5.95360	0.267056
$498$	−7.55337	−0.338475
$499$	17.8831	0.800559	0.400280	−	0.916393i	$-0.368913\pi$
$499$	17.8831	0.800559	0.400280	+	0.916393i	$0.368913\pi$
$500$	1.89060	0.0845504
$501$	−15.5552	−0.694957
$502$	−8.53065	−0.380742
$503$	29.9643	1.33604	0.668021	−	0.744142i	$-0.267141\pi$
$503$	29.9643	1.33604	0.668021	+	0.744142i	$0.267141\pi$
$504$	1.35268	0.0602531
$505$	13.4870	0.600162
$506$	0	0
$507$	−43.2265	−1.91976
$508$	−3.43883	−0.152573
$509$	−29.7021	−1.31652	−0.658260	−	0.752790i	$-0.728707\pi$
$509$	−29.7021	−1.31652	−0.658260	+	0.752790i	$0.728707\pi$
$510$	3.05891	0.135451
$511$	10.3957	0.459879
$512$	−20.9964	−0.927919
$513$	3.99535	0.176399
$514$	6.38767	0.281748
$515$	−14.8254	−0.653285
$516$	−7.99447	−0.351937
$517$	0	0
$518$	−1.72105	−0.0756185
$519$	−40.3210	−1.76990
$520$	−7.55575	−0.331342
$521$	−20.6680	−0.905482	−0.452741	−	0.891642i	$-0.649554\pi$
$521$	−20.6680	−0.905482	−0.452741	+	0.891642i	$0.649554\pi$
$522$	−0.830677	−0.0363577
$523$	−28.5626	−1.24896	−0.624478	−	0.781042i	$-0.714688\pi$
$523$	−28.5626	−1.24896	−0.624478	+	0.781042i	$0.714688\pi$
$524$	−24.6729	−1.07784
$525$	−2.01275	−0.0878438
$526$	2.79736	0.121971
$527$	−33.4625	−1.45765
$528$	0	0
$529$	−22.4835	−0.977545
$530$	−0.958439	−0.0416319
$531$	−4.70162	−0.204033
$532$	−1.92572	−0.0834906
$533$	−50.9206	−2.20562
$534$	3.16653	0.137029
$535$	10.2695	0.443990
$536$	−10.3502	−0.447060
$537$	39.8964	1.72166
$538$	−2.72144	−0.117330
$539$	0	0
$540$	7.41589	0.319129
$541$	25.9498	1.11567	0.557835	−	0.829952i	$-0.311632\pi$
$541$	25.9498	1.11567	0.557835	+	0.829952i	$0.311632\pi$
$542$	9.49445	0.407822
$543$	−28.8182	−1.23671
$544$	16.9253	0.725667
$545$	9.82692	0.420939
$546$	3.90887	0.167284
$547$	−20.2326	−0.865086	−0.432543	−	0.901613i	$-0.642384\pi$
$547$	−20.2326	−0.865086	−0.432543	+	0.901613i	$0.642384\pi$
$548$	−15.7962	−0.674779
$549$	−0.612491	−0.0261405
$550$	0	0
$551$	2.43359	0.103674
$552$	1.86135	0.0792243
$553$	4.72299	0.200842
$554$	5.63428	0.239377
$555$	10.4733	0.444567
$556$	23.5116	0.997114
$557$	30.0169	1.27186	0.635928	−	0.771749i	$-0.280618\pi$
$557$	30.0169	1.27186	0.635928	+	0.771749i	$0.280618\pi$
$558$	−2.53197	−0.107187
$559$	−12.3356	−0.521738
$560$	−3.35559	−0.141800
$561$	0	0
$562$	−4.45606	−0.187968
$563$	21.8155	0.919413	0.459706	−	0.888071i	$-0.347955\pi$
$563$	21.8155	0.919413	0.459706	+	0.888071i	$0.347955\pi$
$564$	−27.6768	−1.16540
$565$	14.3624	0.604229
$566$	−5.92264	−0.248947
$567$	−11.0486	−0.463996
$568$	7.66121	0.321457
$569$	−15.7505	−0.660296	−0.330148	−	0.943929i	$-0.607099\pi$
$569$	−15.7505	−0.660296	−0.330148	+	0.943929i	$0.607099\pi$
$570$	−0.678085	−0.0284018
$571$	14.6801	0.614343	0.307172	−	0.951654i	$-0.400617\pi$
$571$	14.6801	0.614343	0.307172	+	0.951654i	$0.400617\pi$
$572$	0	0
$573$	6.24847	0.261034
$574$	2.86836	0.119723
$575$	−0.718654	−0.0299699
$576$	−5.77399	−0.240583
$577$	−6.68008	−0.278096	−0.139048	−	0.990286i	$-0.544404\pi$
$577$	−6.68008	−0.278096	−0.139048	+	0.990286i	$0.544404\pi$
$578$	−1.36041	−0.0565857
$579$	−47.4557	−1.97219
$580$	4.51705	0.187560
$581$	−11.3462	−0.470719
$582$	6.13616	0.254352
$583$	0	0
$584$	13.3774	0.553560
$585$	−6.17216	−0.255188
$586$	−5.54469	−0.229049
$587$	21.2797	0.878307	0.439153	−	0.898412i	$-0.355278\pi$
$587$	21.2797	0.878307	0.439153	+	0.898412i	$0.355278\pi$
$588$	3.80532	0.156929
$589$	7.41780	0.305645
$590$	−1.47935	−0.0609038
$591$	−36.2326	−1.49041
$592$	17.4607	0.717631
$593$	15.4658	0.635102	0.317551	−	0.948241i	$-0.397139\pi$
$593$	15.4658	0.635102	0.317551	+	0.948241i	$0.397139\pi$
$594$	0	0
$595$	4.59490	0.188373
$596$	−17.2039	−0.704698
$597$	55.1589	2.25750
$598$	1.39566	0.0570729
$599$	10.8384	0.442844	0.221422	−	0.975178i	$-0.428930\pi$
$599$	10.8384	0.442844	0.221422	+	0.975178i	$0.428930\pi$
$600$	−2.59005	−0.105738
$601$	19.4788	0.794558	0.397279	−	0.917698i	$-0.369955\pi$
$601$	19.4788	0.794558	0.397279	+	0.917698i	$0.369955\pi$
$602$	0.694862	0.0283205
$603$	−8.45490	−0.344310
$604$	−16.1832	−0.658484
$605$	0	0
$606$	−8.97852	−0.364728
$607$	−5.90627	−0.239728	−0.119864	−	0.992790i	$-0.538246\pi$
$607$	−5.90627	−0.239728	−0.119864	+	0.992790i	$0.538246\pi$
$608$	−3.75192	−0.152160
$609$	−4.80890	−0.194866
$610$	−0.192718	−0.00780293
$611$	−42.7056	−1.72768
$612$	9.13175	0.369129
$613$	20.8940	0.843902	0.421951	−	0.906619i	$-0.361345\pi$
$613$	20.8940	0.843902	0.421951	+	0.906619i	$0.361345\pi$
$614$	−3.19026	−0.128748
$615$	−17.4552	−0.703860
$616$	0	0
$617$	8.83816	0.355811	0.177906	−	0.984048i	$-0.443068\pi$
$617$	8.83816	0.355811	0.177906	+	0.984048i	$0.443068\pi$
$618$	9.86955	0.397011
$619$	−3.58929	−0.144266	−0.0721328	−	0.997395i	$-0.522981\pi$
$619$	−3.58929	−0.144266	−0.0721328	+	0.997395i	$0.522981\pi$
$620$	13.7684	0.552951
$621$	−2.81892	−0.113119
$622$	−5.77305	−0.231478
$623$	4.75655	0.190567
$624$	−39.6571	−1.58755
$625$	1.00000	0.0400000
$626$	−1.74875	−0.0698939
$627$	0	0
$628$	42.8709	1.71073
$629$	−23.9094	−0.953331
$630$	0.347678	0.0138518
$631$	−21.4648	−0.854499	−0.427250	−	0.904134i	$-0.640517\pi$
$631$	−21.4648	−0.854499	−0.427250	+	0.904134i	$0.640517\pi$
$632$	6.07763	0.241755
$633$	−23.9799	−0.953115
$634$	11.1708	0.443649
$635$	−1.81890	−0.0721810
$636$	−11.0270	−0.437247
$637$	5.87165	0.232643
$638$	0	0
$639$	6.25831	0.247575
$640$	−9.18377	−0.363020
$641$	18.9450	0.748284	0.374142	−	0.927372i	$-0.377937\pi$
$641$	18.9450	0.748284	0.374142	+	0.927372i	$0.377937\pi$
$642$	−6.83661	−0.269819
$643$	25.9362	1.02282	0.511411	−	0.859336i	$-0.329123\pi$
$643$	25.9362	1.02282	0.511411	+	0.859336i	$0.329123\pi$
$644$	1.35869	0.0535399
$645$	−4.22852	−0.166498
$646$	1.54799	0.0609050
$647$	−22.7569	−0.894666	−0.447333	−	0.894367i	$-0.647626\pi$
$647$	−22.7569	−0.894666	−0.447333	+	0.894367i	$0.647626\pi$
$648$	−14.2175	−0.558516
$649$	0	0
$650$	−1.94205	−0.0761735
$651$	−14.6579	−0.574490
$652$	−27.6816	−1.08410
$653$	−37.7300	−1.47649	−0.738245	−	0.674532i	$-0.764345\pi$
$653$	−37.7300	−1.47649	−0.738245	+	0.674532i	$0.764345\pi$
$654$	−6.54197	−0.255811
$655$	−13.0503	−0.509917
$656$	−29.1006	−1.13619
$657$	10.9278	0.426332
$658$	2.40560	0.0937802
$659$	30.6835	1.19526	0.597630	−	0.801772i	$-0.296109\pi$
$659$	30.6835	1.19526	0.597630	+	0.801772i	$0.296109\pi$
$660$	0	0
$661$	29.0666	1.13056	0.565279	−	0.824900i	$-0.308768\pi$
$661$	29.0666	1.13056	0.565279	+	0.824900i	$0.308768\pi$
$662$	11.2021	0.435383
$663$	54.3034	2.10897
$664$	−14.6005	−0.566609
$665$	−1.01857	−0.0394986
$666$	−1.80913	−0.0701024
$667$	−1.71702	−0.0664831
$668$	−14.6112	−0.565325
$669$	−32.2009	−1.24496
$670$	−2.66031	−0.102777
$671$	0	0
$672$	7.41398	0.286001
$673$	16.4533	0.634228	0.317114	−	0.948387i	$-0.397286\pi$
$673$	16.4533	0.634228	0.317114	+	0.948387i	$0.397286\pi$
$674$	9.21503	0.354950
$675$	3.92250	0.150977
$676$	−40.6032	−1.56166
$677$	28.3173	1.08832	0.544161	−	0.838981i	$-0.316848\pi$
$677$	28.3173	1.08832	0.544161	+	0.838981i	$0.316848\pi$
$678$	−9.56130	−0.367199
$679$	9.21735	0.353729
$680$	5.91280	0.226746
$681$	−49.1284	−1.88260
$682$	0	0
$683$	−2.19092	−0.0838333	−0.0419166	−	0.999121i	$-0.513346\pi$
$683$	−2.19092	−0.0838333	−0.0419166	+	0.999121i	$0.513346\pi$
$684$	−2.02428	−0.0774003
$685$	−8.35509	−0.319232
$686$	−0.330750	−0.0126281
$687$	−33.4147	−1.27485
$688$	−7.04965	−0.268765
$689$	−17.0147	−0.648209
$690$	0.478421	0.0182132
$691$	−44.5032	−1.69298	−0.846491	−	0.532403i	$-0.821289\pi$
$691$	−44.5032	−1.69298	−0.846491	+	0.532403i	$0.821289\pi$
$692$	−37.8740	−1.43975
$693$	0	0
$694$	−5.24907	−0.199252
$695$	12.4360	0.471725
$696$	−6.18818	−0.234562
$697$	39.8483	1.50936
$698$	−6.75902	−0.255833
$699$	−13.0222	−0.492543
$700$	−1.89060	−0.0714581
$701$	−23.0878	−0.872015	−0.436007	−	0.899943i	$-0.643608\pi$
$701$	−23.0878	−0.872015	−0.436007	+	0.899943i	$0.643608\pi$
$702$	−7.61769	−0.287511
$703$	5.30012	0.199898
$704$	0	0
$705$	−14.6391	−0.551341
$706$	−9.51957	−0.358274
$707$	−13.4870	−0.507229
$708$	−17.0201	−0.639654
$709$	−26.0047	−0.976626	−0.488313	−	0.872669i	$-0.662388\pi$
$709$	−26.0047	−0.976626	−0.488313	+	0.872669i	$0.662388\pi$
$710$	1.96916	0.0739011
$711$	4.96471	0.186191
$712$	6.12082	0.229387
$713$	−5.23361	−0.196000
$714$	−3.05891	−0.114477
$715$	0	0
$716$	37.4752	1.40051
$717$	1.39031	0.0519220
$718$	6.98146	0.260546
$719$	31.7319	1.18340	0.591700	−	0.806158i	$-0.298457\pi$
$719$	31.7319	1.18340	0.591700	+	0.806158i	$0.298457\pi$
$720$	−3.52733	−0.131456
$721$	14.8254	0.552126
$722$	5.94110	0.221105
$723$	−5.06452	−0.188352
$724$	−27.0693	−1.00602
$725$	2.38921	0.0887331
$726$	0	0
$727$	31.7220	1.17650	0.588252	−	0.808678i	$-0.299816\pi$
$727$	31.7220	1.17650	0.588252	+	0.808678i	$0.299816\pi$
$728$	7.55575	0.280035
$729$	12.0710	0.447075
$730$	3.43838	0.127260
$731$	9.65327	0.357039
$732$	−2.21725	−0.0819518
$733$	24.2645	0.896228	0.448114	−	0.893976i	$-0.352096\pi$
$733$	24.2645	0.896228	0.448114	+	0.893976i	$0.352096\pi$
$734$	4.50733	0.166368
$735$	2.01275	0.0742416
$736$	2.64716	0.0975756
$737$	0	0
$738$	3.01516	0.110990
$739$	−32.1681	−1.18332	−0.591661	−	0.806187i	$-0.701527\pi$
$739$	−32.1681	−1.18332	−0.591661	+	0.806187i	$0.701527\pi$
$740$	9.83770	0.361641
$741$	−12.0377	−0.442216
$742$	0.958439	0.0351854
$743$	12.0217	0.441034	0.220517	−	0.975383i	$-0.429226\pi$
$743$	12.0217	0.441034	0.220517	+	0.975383i	$0.429226\pi$
$744$	−18.8621	−0.691518
$745$	−9.09967	−0.333386
$746$	−3.18440	−0.116589
$747$	−11.9269	−0.436382
$748$	0	0
$749$	−10.2695	−0.375240
$750$	−0.665719	−0.0243086
$751$	−2.04734	−0.0747084	−0.0373542	−	0.999302i	$-0.511893\pi$
$751$	−2.04734	−0.0747084	−0.0373542	+	0.999302i	$0.511893\pi$
$752$	−24.4058	−0.889988
$753$	−51.9126	−1.89180
$754$	−4.63997	−0.168978
$755$	−8.55979	−0.311523
$756$	−7.41589	−0.269713
$757$	−26.2120	−0.952691	−0.476346	−	0.879258i	$-0.658039\pi$
$757$	−26.2120	−0.952691	−0.476346	+	0.879258i	$0.658039\pi$
$758$	3.63790	0.132134
$759$	0	0
$760$	−1.31072	−0.0475448
$761$	50.6897	1.83750	0.918750	−	0.394840i	$-0.129200\pi$
$761$	50.6897	1.83750	0.918750	+	0.394840i	$0.129200\pi$
$762$	1.21088	0.0438655
$763$	−9.82692	−0.355758
$764$	5.86926	0.212342
$765$	4.83007	0.174631
$766$	−7.36962	−0.266275
$767$	−26.2622	−0.948272
$768$	−15.9978	−0.577270
$769$	−35.8421	−1.29250	−0.646249	−	0.763126i	$-0.723663\pi$
$769$	−35.8421	−1.29250	−0.646249	+	0.763126i	$0.723663\pi$
$770$	0	0
$771$	38.8717	1.39993
$772$	−44.5757	−1.60431
$773$	−21.1822	−0.761870	−0.380935	−	0.924602i	$-0.624398\pi$
$773$	−21.1822	−0.761870	−0.380935	+	0.924602i	$0.624398\pi$
$774$	0.730425	0.0262546
$775$	7.28253	0.261596
$776$	11.8611	0.425787
$777$	−10.4733	−0.375728
$778$	−6.70671	−0.240447
$779$	−8.83336	−0.316488
$780$	−22.3435	−0.800027
$781$	0	0
$782$	−1.09218	−0.0390564
$783$	9.37168	0.334916
$784$	3.35559	0.119843
$785$	22.6758	0.809332
$786$	8.68782	0.309884
$787$	43.4677	1.54945	0.774727	−	0.632295i	$-0.217887\pi$
$787$	43.4677	1.54945	0.774727	+	0.632295i	$0.217887\pi$
$788$	−34.0337	−1.21240
$789$	17.0231	0.606038
$790$	1.56213	0.0555781
$791$	−14.3624	−0.510667
$792$	0	0
$793$	−3.42124	−0.121492
$794$	−10.0902	−0.358087
$795$	−5.83250	−0.206858
$796$	51.8114	1.83641
$797$	17.5000	0.619881	0.309940	−	0.950756i	$-0.399691\pi$
$797$	17.5000	0.619881	0.309940	+	0.950756i	$0.399691\pi$
$798$	0.678085	0.0240039
$799$	33.4195	1.18230
$800$	−3.68350	−0.130231
$801$	4.99999	0.176666
$802$	−8.67504	−0.306326
$803$	0	0
$804$	−30.6071	−1.07943
$805$	0.718654	0.0253292
$806$	−14.1430	−0.498167
$807$	−16.5611	−0.582978
$808$	−17.3553	−0.610556
$809$	49.2786	1.73254	0.866272	−	0.499572i	$-0.166510\pi$
$809$	49.2786	1.73254	0.866272	+	0.499572i	$0.166510\pi$
$810$	−3.65431	−0.128400
$811$	−12.5219	−0.439704	−0.219852	−	0.975533i	$-0.570557\pi$
$811$	−12.5219	−0.439704	−0.219852	+	0.975533i	$0.570557\pi$
$812$	−4.51705	−0.158518
$813$	57.7777	2.02635
$814$	0	0
$815$	−14.6417	−0.512876
$816$	31.0339	1.08640
$817$	−2.13989	−0.0748652
$818$	8.00420	0.279860
$819$	6.17216	0.215673
$820$	−16.3958	−0.572568
$821$	6.61352	0.230813	0.115407	−	0.993318i	$-0.463183\pi$
$821$	6.61352	0.230813	0.115407	+	0.993318i	$0.463183\pi$
$822$	5.56214	0.194002
$823$	−36.3271	−1.26628	−0.633141	−	0.774037i	$-0.718235\pi$
$823$	−36.3271	−1.26628	−0.633141	+	0.774037i	$0.718235\pi$
$824$	19.0776	0.664599
$825$	0	0
$826$	1.47935	0.0514731
$827$	−34.7067	−1.20687	−0.603436	−	0.797411i	$-0.706202\pi$
$827$	−34.7067	−1.20687	−0.603436	+	0.797411i	$0.706202\pi$
$828$	1.42823	0.0496343
$829$	27.5745	0.957703	0.478851	−	0.877896i	$-0.341053\pi$
$829$	27.5745	0.957703	0.478851	+	0.877896i	$0.341053\pi$
$830$	−3.75275	−0.130260
$831$	34.2869	1.18940
$832$	−32.2522	−1.11814
$833$	−4.59490	−0.159204
$834$	−8.27890	−0.286675
$835$	−7.72833	−0.267450
$836$	0	0
$837$	28.5657	0.987374
$838$	5.14315	0.177667
$839$	36.3906	1.25634	0.628171	−	0.778075i	$-0.283804\pi$
$839$	36.3906	1.25634	0.628171	+	0.778075i	$0.283804\pi$
$840$	2.59005	0.0893652
$841$	−23.2917	−0.803161
$842$	6.62892	0.228448
$843$	−27.1170	−0.933959
$844$	−22.5246	−0.775329
$845$	−21.4763	−0.738808
$846$	2.52872	0.0869393
$847$	0	0
$848$	−9.72374	−0.333915
$849$	−36.0418	−1.23695
$850$	1.51976	0.0521275
$851$	−3.73949	−0.128188
$852$	22.6554	0.776160
$853$	11.8116	0.404420	0.202210	−	0.979342i	$-0.435188\pi$
$853$	11.8116	0.404420	0.202210	+	0.979342i	$0.435188\pi$
$854$	0.192718	0.00659468
$855$	−1.07071	−0.0366173
$856$	−13.2150	−0.451679
$857$	18.9187	0.646249	0.323125	−	0.946356i	$-0.395267\pi$
$857$	18.9187	0.646249	0.323125	+	0.946356i	$0.395267\pi$
$858$	0	0
$859$	35.4788	1.21052	0.605260	−	0.796028i	$-0.293069\pi$
$859$	35.4788	1.21052	0.605260	+	0.796028i	$0.293069\pi$
$860$	−3.97190	−0.135441
$861$	17.4552	0.594870
$862$	2.93467	0.0999551
$863$	−12.6623	−0.431028	−0.215514	−	0.976501i	$-0.569143\pi$
$863$	−12.6623	−0.431028	−0.215514	+	0.976501i	$0.569143\pi$
$864$	−14.4485	−0.491549
$865$	−20.0328	−0.681134
$866$	−8.75675	−0.297566
$867$	−8.27869	−0.281159
$868$	−13.7684	−0.467329
$869$	0	0
$870$	−1.59054	−0.0539245
$871$	−47.2271	−1.60023
$872$	−12.6455	−0.428229
$873$	9.68909	0.327926
$874$	0.242110	0.00818949
$875$	−1.00000	−0.0338062
$876$	39.5590	1.33657
$877$	41.0661	1.38670	0.693352	−	0.720599i	$-0.256133\pi$
$877$	41.0661	1.38670	0.693352	+	0.720599i	$0.256133\pi$
$878$	7.78914	0.262871
$879$	−33.7418	−1.13808
$880$	0	0
$881$	46.8952	1.57994	0.789969	−	0.613147i	$-0.210097\pi$
$881$	46.8952	1.57994	0.789969	+	0.613147i	$0.210097\pi$
$882$	−0.347678	−0.0117069
$883$	−13.3294	−0.448571	−0.224286	−	0.974523i	$-0.572005\pi$
$883$	−13.3294	−0.448571	−0.224286	+	0.974523i	$0.572005\pi$
$884$	51.0079	1.71558
$885$	−9.00245	−0.302614
$886$	−7.75559	−0.260554
$887$	−1.41678	−0.0475709	−0.0237855	−	0.999717i	$-0.507572\pi$
$887$	−1.41678	−0.0475709	−0.0237855	+	0.999717i	$0.507572\pi$
$888$	−13.4772	−0.452266
$889$	1.81890	0.0610041
$890$	1.57323	0.0527348
$891$	0	0
$892$	−30.2467	−1.01273
$893$	−7.40827	−0.247908
$894$	6.05782	0.202604
$895$	19.8218	0.662570
$896$	9.18377	0.306808
$897$	8.49319	0.283579
$898$	−10.9269	−0.364636
$899$	17.3995	0.580306
$900$	−1.98737	−0.0662455
$901$	13.3150	0.443586
$902$	0	0
$903$	4.22852	0.140716
$904$	−18.4818	−0.614694
$905$	−14.3178	−0.475940
$906$	5.69841	0.189317
$907$	41.2081	1.36829	0.684146	−	0.729345i	$-0.260175\pi$
$907$	41.2081	1.36829	0.684146	+	0.729345i	$0.260175\pi$
$908$	−46.1469	−1.53144
$909$	−14.1772	−0.470228
$910$	1.94205	0.0643784
$911$	−7.07088	−0.234269	−0.117134	−	0.993116i	$-0.537371\pi$
$911$	−7.07088	−0.234269	−0.117134	+	0.993116i	$0.537371\pi$
$912$	−6.87944	−0.227801
$913$	0	0
$914$	−3.68958	−0.122040
$915$	−1.17277	−0.0387706
$916$	−31.3869	−1.03705
$917$	13.0503	0.430958
$918$	5.96127	0.196751
$919$	−12.8853	−0.425048	−0.212524	−	0.977156i	$-0.568168\pi$
$919$	−12.8853	−0.425048	−0.212524	+	0.977156i	$0.568168\pi$
$920$	0.924777	0.0304890
$921$	−19.4141	−0.639716
$922$	−6.31649	−0.208023
$923$	34.9575	1.15064
$924$	0	0
$925$	5.20347	0.171089
$926$	−0.307984	−0.0101210
$927$	15.5842	0.511851
$928$	−8.80066	−0.288896
$929$	1.16713	0.0382922	0.0191461	−	0.999817i	$-0.493905\pi$
$929$	1.16713	0.0382922	0.0191461	+	0.999817i	$0.493905\pi$
$930$	−4.84812	−0.158976
$931$	1.01857	0.0333824
$932$	−12.2319	−0.400668
$933$	−35.1314	−1.15015
$934$	−6.52033	−0.213352
$935$	0	0
$936$	7.94246	0.259607
$937$	27.4563	0.896959	0.448480	−	0.893793i	$-0.351966\pi$
$937$	27.4563	0.896959	0.448480	+	0.893793i	$0.351966\pi$
$938$	2.66031	0.0868621
$939$	−10.6418	−0.347284
$940$	−13.7507	−0.448498
$941$	1.50273	0.0489877	0.0244938	−	0.999700i	$-0.492203\pi$
$941$	1.50273	0.0489877	0.0244938	+	0.999700i	$0.492203\pi$
$942$	−15.0957	−0.491844
$943$	6.23236	0.202954
$944$	−15.0086	−0.488487
$945$	−3.92250	−0.127599
$946$	0	0
$947$	−8.63389	−0.280564	−0.140282	−	0.990112i	$-0.544801\pi$
$947$	−8.63389	−0.280564	−0.140282	+	0.990112i	$0.544801\pi$
$948$	17.9725	0.583719
$949$	61.0400	1.98144
$950$	−0.336894	−0.0109303
$951$	67.9790	2.20437
$952$	−5.91280	−0.191635
$953$	−3.65094	−0.118266	−0.0591328	−	0.998250i	$-0.518834\pi$
$953$	−3.65094	−0.118266	−0.0591328	+	0.998250i	$0.518834\pi$
$954$	1.00749	0.0326188
$955$	3.10444	0.100457
$956$	1.30593	0.0422369
$957$	0	0
$958$	8.78493	0.283828
$959$	8.35509	0.269800
$960$	−11.0558	−0.356824
$961$	22.0352	0.710812
$962$	−10.1054	−0.325811
$963$	−10.7951	−0.347867
$964$	−4.75717	−0.153218
$965$	−23.5775	−0.758986
$966$	−0.478421	−0.0153930
$967$	33.7531	1.08543	0.542713	−	0.839918i	$-0.317397\pi$
$967$	33.7531	1.08543	0.542713	+	0.839918i	$0.317397\pi$
$968$	0	0
$969$	9.42019	0.302620
$970$	3.04864	0.0978860
$971$	48.1668	1.54575	0.772873	−	0.634561i	$-0.218819\pi$
$971$	48.1668	1.54575	0.772873	+	0.634561i	$0.218819\pi$
$972$	−19.7957	−0.634946
$973$	−12.4360	−0.398681
$974$	2.29760	0.0736200
$975$	−11.8182	−0.378485
$976$	−1.95520	−0.0625845
$977$	26.1738	0.837375	0.418687	−	0.908130i	$-0.362490\pi$
$977$	26.1738	0.837375	0.418687	+	0.908130i	$0.362490\pi$
$978$	9.74725	0.311683
$979$	0	0
$980$	1.89060	0.0603931
$981$	−10.3299	−0.329807
$982$	11.6734	0.372514
$983$	−39.4335	−1.25773	−0.628866	−	0.777513i	$-0.716481\pi$
$983$	−39.4335	−1.25773	−0.628866	+	0.777513i	$0.716481\pi$
$984$	22.4616	0.716051
$985$	−18.0015	−0.573576
$986$	3.63104	0.115636
$987$	14.6391	0.465968
$988$	−11.3072	−0.359729
$989$	1.50979	0.0480087
$990$	0	0
$991$	−20.2528	−0.643351	−0.321676	−	0.946850i	$-0.604246\pi$
$991$	−20.2528	−0.643351	−0.321676	+	0.946850i	$0.604246\pi$
$992$	−26.8252	−0.851701
$993$	68.1696	2.16330
$994$	−1.96916	−0.0624578
$995$	27.4047	0.868787
$996$	−43.1759	−1.36808
$997$	22.7964	0.721971	0.360985	−	0.932571i	$-0.382440\pi$
$997$	22.7964	0.721971	0.360985	+	0.932571i	$0.382440\pi$
$998$	−5.91486	−0.187231
$999$	20.4106	0.645762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bl.1.5	yes	10
11.10	odd	2		4235.2.a.bj.1.6	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.bj.1.6	✓	10	11.10	odd	2
4235.2.a.bl.1.5	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q-0.330750 q^{2} -2.01275 q^{3} -1.89060 q^{4} -1.00000 q^{5} +0.665719 q^{6} +1.00000 q^{7} +1.28682 q^{8} +1.05118 q^{9} +O(q^{10})\)	\(q-0.330750 q^{2} -2.01275 q^{3} -1.89060 q^{4} -1.00000 q^{5} +0.665719 q^{6} +1.00000 q^{7} +1.28682 q^{8} +1.05118 q^{9} +0.330750 q^{10} +3.80532 q^{12} +5.87165 q^{13} -0.330750 q^{14} +2.01275 q^{15} +3.35559 q^{16} -4.59490 q^{17} -0.347678 q^{18} +1.01857 q^{19} +1.89060 q^{20} -2.01275 q^{21} -0.718654 q^{23} -2.59005 q^{24} +1.00000 q^{25} -1.94205 q^{26} +3.92250 q^{27} -1.89060 q^{28} +2.38921 q^{29} -0.665719 q^{30} +7.28253 q^{31} -3.68350 q^{32} +1.51976 q^{34} -1.00000 q^{35} -1.98737 q^{36} +5.20347 q^{37} -0.336894 q^{38} -11.8182 q^{39} -1.28682 q^{40} -8.67228 q^{41} +0.665719 q^{42} -2.10086 q^{43} -1.05118 q^{45} +0.237695 q^{46} -7.27317 q^{47} -6.75398 q^{48} +1.00000 q^{49} -0.330750 q^{50} +9.24841 q^{51} -11.1010 q^{52} -2.89777 q^{53} -1.29737 q^{54} +1.28682 q^{56} -2.05014 q^{57} -0.790233 q^{58} -4.47270 q^{59} -3.80532 q^{60} -0.582670 q^{61} -2.40870 q^{62} +1.05118 q^{63} -5.49287 q^{64} -5.87165 q^{65} -8.04324 q^{67} +8.68714 q^{68} +1.44647 q^{69} +0.330750 q^{70} +5.95360 q^{71} +1.35268 q^{72} +10.3957 q^{73} -1.72105 q^{74} -2.01275 q^{75} -1.92572 q^{76} +3.90887 q^{78} +4.72299 q^{79} -3.35559 q^{80} -11.0486 q^{81} +2.86836 q^{82} -11.3462 q^{83} +3.80532 q^{84} +4.59490 q^{85} +0.694862 q^{86} -4.80890 q^{87} +4.75655 q^{89} +0.347678 q^{90} +5.87165 q^{91} +1.35869 q^{92} -14.6579 q^{93} +2.40560 q^{94} -1.01857 q^{95} +7.41398 q^{96} +9.21735 q^{97} -0.330750 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 4 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 4 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^7 + 6 * q^8 + 6 * q^9	\( 10 q + 2 q^{2} + 4 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{7} + 6 q^{8} + 6 q^{9} - 2 q^{10} + 16 q^{12} + 26 q^{13} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 4 q^{17} + 8 q^{18} + 6 q^{19} - 12 q^{20} + 4 q^{21} - 8 q^{23} + 22 q^{24} + 10 q^{25} - 6 q^{26} + 10 q^{27} + 12 q^{28} - 4 q^{29} + 18 q^{31} + 24 q^{32} + 8 q^{34} - 10 q^{35} - 10 q^{36} - 16 q^{37} - 2 q^{38} + 16 q^{39} - 6 q^{40} - 30 q^{41} + 22 q^{43} - 6 q^{45} + 28 q^{46} + 14 q^{47} - 4 q^{48} + 10 q^{49} + 2 q^{50} + 36 q^{51} + 34 q^{52} - 10 q^{53} + 6 q^{54} + 6 q^{56} - 2 q^{57} - 38 q^{58} + 22 q^{59} - 16 q^{60} + 12 q^{61} - 6 q^{62} + 6 q^{63} + 8 q^{64} - 26 q^{65} - 14 q^{67} + 70 q^{68} + 8 q^{69} - 2 q^{70} - 8 q^{71} + 26 q^{72} + 30 q^{73} - 20 q^{74} + 4 q^{75} + 18 q^{76} - 32 q^{78} + 8 q^{79} - 20 q^{80} + 10 q^{81} - 28 q^{82} - 14 q^{83} + 16 q^{84} - 4 q^{85} - 14 q^{86} - 24 q^{87} - 6 q^{89} - 8 q^{90} + 26 q^{91} - 20 q^{92} + 14 q^{93} + 16 q^{94} - 6 q^{95} + 24 q^{96} + 20 q^{97} + 2 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 + 4 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^7 + 6 * q^8 + 6 * q^9 - 2 * q^10 + 16 * q^12 + 26 * q^13 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 4 * q^17 + 8 * q^18 + 6 * q^19 - 12 * q^20 + 4 * q^21 - 8 * q^23 + 22 * q^24 + 10 * q^25 - 6 * q^26 + 10 * q^27 + 12 * q^28 - 4 * q^29 + 18 * q^31 + 24 * q^32 + 8 * q^34 - 10 * q^35 - 10 * q^36 - 16 * q^37 - 2 * q^38 + 16 * q^39 - 6 * q^40 - 30 * q^41 + 22 * q^43 - 6 * q^45 + 28 * q^46 + 14 * q^47 - 4 * q^48 + 10 * q^49 + 2 * q^50 + 36 * q^51 + 34 * q^52 - 10 * q^53 + 6 * q^54 + 6 * q^56 - 2 * q^57 - 38 * q^58 + 22 * q^59 - 16 * q^60 + 12 * q^61 - 6 * q^62 + 6 * q^63 + 8 * q^64 - 26 * q^65 - 14 * q^67 + 70 * q^68 + 8 * q^69 - 2 * q^70 - 8 * q^71 + 26 * q^72 + 30 * q^73 - 20 * q^74 + 4 * q^75 + 18 * q^76 - 32 * q^78 + 8 * q^79 - 20 * q^80 + 10 * q^81 - 28 * q^82 - 14 * q^83 + 16 * q^84 - 4 * q^85 - 14 * q^86 - 24 * q^87 - 6 * q^89 - 8 * q^90 + 26 * q^91 - 20 * q^92 + 14 * q^93 + 16 * q^94 - 6 * q^95 + 24 * q^96 + 20 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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