LMFDB - Embedded newform 4235.2.a.t.1.2

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:	$1$
Dimension:	$4$
Coefficient field:	4.4.725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 3x^{2} + x + 1 $ x^4 - x^3 - 3*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.737640$ 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)

$f(q)$	$=$	$q-1.45589 q^{2} -2.35567 q^{3} +0.119606 q^{4} +1.00000 q^{5} +3.42960 q^{6} -1.00000 q^{7} +2.73764 q^{8} +2.54920 q^{9} +O(q^{10})$	\(q-1.45589 q^{2} -2.35567 q^{3} +0.119606 q^{4} +1.00000 q^{5} +3.42960 q^{6} -1.00000 q^{7} +2.73764 q^{8} +2.54920 q^{9} -1.45589 q^{10} -0.281754 q^{12} -0.899788 q^{13} +1.45589 q^{14} -2.35567 q^{15} -4.22491 q^{16} +0.644326 q^{17} -3.71135 q^{18} +0.219819 q^{19} +0.119606 q^{20} +2.35567 q^{21} +2.75389 q^{23} -6.44899 q^{24} +1.00000 q^{25} +1.30999 q^{26} +1.06193 q^{27} -0.119606 q^{28} +0.429595 q^{29} +3.42960 q^{30} -6.05077 q^{31} +0.675706 q^{32} -0.938065 q^{34} -1.00000 q^{35} +0.304901 q^{36} -0.527864 q^{37} -0.320031 q^{38} +2.11961 q^{39} +2.73764 q^{40} -9.74782 q^{41} -3.42960 q^{42} +2.94742 q^{43} +2.54920 q^{45} -4.00935 q^{46} +1.87664 q^{47} +9.95250 q^{48} +1.00000 q^{49} -1.45589 q^{50} -1.51782 q^{51} -0.107620 q^{52} -12.7409 q^{53} -1.54606 q^{54} -2.73764 q^{56} -0.517822 q^{57} -0.625442 q^{58} -1.93543 q^{59} -0.281754 q^{60} +13.5035 q^{61} +8.80924 q^{62} -2.54920 q^{63} +7.46606 q^{64} -0.899788 q^{65} +6.90570 q^{67} +0.0770654 q^{68} -6.48727 q^{69} +1.45589 q^{70} -0.408258 q^{71} +6.97880 q^{72} +8.18482 q^{73} +0.768510 q^{74} -2.35567 q^{75} +0.0262917 q^{76} -3.08591 q^{78} -15.6841 q^{79} -4.22491 q^{80} -10.1492 q^{81} +14.1917 q^{82} +8.13780 q^{83} +0.281754 q^{84} +0.644326 q^{85} -4.29110 q^{86} -1.01199 q^{87} -3.73945 q^{89} -3.71135 q^{90} +0.899788 q^{91} +0.329383 q^{92} +14.2537 q^{93} -2.73218 q^{94} +0.219819 q^{95} -1.59174 q^{96} -6.55722 q^{97} -1.45589 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 3 q^{3} + 3 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} + 9 q^{8} - 3 q^{9}+O(q^{10}) $ 4 * q - q^2 - 3 * q^3 + 3 * q^4 + 4 * q^5 - 2 * q^6 - 4 * q^7 + 9 * q^8 - 3 * q^9	$ 4 q - q^{2} - 3 q^{3} + 3 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} + 9 q^{8} - 3 q^{9} - q^{10} - 4 q^{12} - 2 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 9 q^{17} - 2 q^{18} + 5 q^{19} + 3 q^{20} + 3 q^{21} - 4 q^{23} - 11 q^{24} + 4 q^{25} - 13 q^{26} + 3 q^{27} - 3 q^{28} - 14 q^{29} - 2 q^{30} - 18 q^{31} + 2 q^{32} - 5 q^{34} - 4 q^{35} + q^{36} - 20 q^{37} - 7 q^{38} + 11 q^{39} + 9 q^{40} - q^{41} + 2 q^{42} - 10 q^{43} - 3 q^{45} + 7 q^{46} + 9 q^{47} + 4 q^{49} - q^{50} - 11 q^{52} - 3 q^{53} + 21 q^{54} - 9 q^{56} + 4 q^{57} - 7 q^{58} + 6 q^{59} - 4 q^{60} + 29 q^{61} - 3 q^{62} + 3 q^{63} - 11 q^{64} - 2 q^{65} - 5 q^{67} + 5 q^{68} - 14 q^{69} + q^{70} - 17 q^{71} - q^{72} - 12 q^{73} - 5 q^{74} - 3 q^{75} + 11 q^{76} + 5 q^{78} + 2 q^{79} - 3 q^{80} - 8 q^{81} + 22 q^{82} - 10 q^{83} + 4 q^{84} + 9 q^{85} + 3 q^{86} + 4 q^{87} - 41 q^{89} - 2 q^{90} + 2 q^{91} - 16 q^{92} + 21 q^{93} + 32 q^{94} + 5 q^{95} + 9 q^{96} - 4 q^{97} - q^{98}+O(q^{100}) $ 4 * q - q^2 - 3 * q^3 + 3 * q^4 + 4 * q^5 - 2 * q^6 - 4 * q^7 + 9 * q^8 - 3 * q^9 - q^10 - 4 * q^12 - 2 * q^13 + q^14 - 3 * q^15 - 3 * q^16 + 9 * q^17 - 2 * q^18 + 5 * q^19 + 3 * q^20 + 3 * q^21 - 4 * q^23 - 11 * q^24 + 4 * q^25 - 13 * q^26 + 3 * q^27 - 3 * q^28 - 14 * q^29 - 2 * q^30 - 18 * q^31 + 2 * q^32 - 5 * q^34 - 4 * q^35 + q^36 - 20 * q^37 - 7 * q^38 + 11 * q^39 + 9 * q^40 - q^41 + 2 * q^42 - 10 * q^43 - 3 * q^45 + 7 * q^46 + 9 * q^47 + 4 * q^49 - q^50 - 11 * q^52 - 3 * q^53 + 21 * q^54 - 9 * q^56 + 4 * q^57 - 7 * q^58 + 6 * q^59 - 4 * q^60 + 29 * q^61 - 3 * q^62 + 3 * q^63 - 11 * q^64 - 2 * q^65 - 5 * q^67 + 5 * q^68 - 14 * q^69 + q^70 - 17 * q^71 - q^72 - 12 * q^73 - 5 * q^74 - 3 * q^75 + 11 * q^76 + 5 * q^78 + 2 * q^79 - 3 * q^80 - 8 * q^81 + 22 * q^82 - 10 * q^83 + 4 * q^84 + 9 * q^85 + 3 * q^86 + 4 * q^87 - 41 * q^89 - 2 * q^90 + 2 * q^91 - 16 * q^92 + 21 * q^93 + 32 * q^94 + 5 * q^95 + 9 * q^96 - 4 * q^97 - 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 $

$2$	−1.45589	−1.02947	−0.514734	−	0.857350i	$-0.672109\pi$
$2$	−1.45589	−1.02947	−0.514734	+	0.857350i	$0.672109\pi$
$3$	−2.35567	−1.36005	−0.680025	−	0.733189i	$-0.738031\pi$
$3$	−2.35567	−1.36005	−0.680025	+	0.733189i	$0.738031\pi$
$4$	0.119606	0.0598032
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.42960	1.40013
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.73764	0.967902
$9$	2.54920	0.849734
$10$	−1.45589	−0.460392
$11$	0	0
$11$	0	0
$12$	−0.281754	−0.0813352
$13$	−0.899788	−0.249556	−0.124778	−	0.992185i	$-0.539822\pi$
$13$	−0.899788	−0.249556	−0.124778	+	0.992185i	$0.539822\pi$
$14$	1.45589	0.389102
$15$	−2.35567	−0.608232
$16$	−4.22491	−1.05623
$17$	0.644326	0.156272	0.0781360	−	0.996943i	$-0.475103\pi$
$17$	0.644326	0.156272	0.0781360	+	0.996943i	$0.475103\pi$
$18$	−3.71135	−0.874773
$19$	0.219819	0.0504299	0.0252149	−	0.999682i	$-0.491973\pi$
$19$	0.219819	0.0504299	0.0252149	+	0.999682i	$0.491973\pi$
$20$	0.119606	0.0267448
$21$	2.35567	0.514050
$22$	0	0
$23$	2.75389	0.574226	0.287113	−	0.957897i	$-0.407305\pi$
$23$	2.75389	0.574226	0.287113	+	0.957897i	$0.407305\pi$
$24$	−6.44899	−1.31639
$25$	1.00000	0.200000
$26$	1.30999	0.256910
$27$	1.06193	0.204369
$28$	−0.119606	−0.0226035
$29$	0.429595	0.0797738	0.0398869	−	0.999204i	$-0.487300\pi$
$29$	0.429595	0.0797738	0.0398869	+	0.999204i	$0.487300\pi$
$30$	3.42960	0.626156
$31$	−6.05077	−1.08675	−0.543376	−	0.839490i	$-0.682854\pi$
$31$	−6.05077	−1.08675	−0.543376	+	0.839490i	$0.682854\pi$
$32$	0.675706	0.119449
$33$	0	0
$34$	−0.938065	−0.160877
$35$	−1.00000	−0.169031
$36$	0.304901	0.0508168
$37$	−0.527864	−0.0867803	−0.0433902	−	0.999058i	$-0.513816\pi$
$37$	−0.527864	−0.0867803	−0.0433902	+	0.999058i	$0.513816\pi$
$38$	−0.320031	−0.0519159
$39$	2.11961	0.339409
$40$	2.73764	0.432859
$41$	−9.74782	−1.52235	−0.761177	−	0.648545i	$-0.775378\pi$
$41$	−9.74782	−1.52235	−0.761177	+	0.648545i	$0.775378\pi$
$42$	−3.42960	−0.529198
$43$	2.94742	0.449477	0.224738	−	0.974419i	$-0.427847\pi$
$43$	2.94742	0.449477	0.224738	+	0.974419i	$0.427847\pi$
$44$	0	0
$45$	2.54920	0.380013
$46$	−4.00935	−0.591147
$47$	1.87664	0.273736	0.136868	−	0.990589i	$-0.456296\pi$
$47$	1.87664	0.273736	0.136868	+	0.990589i	$0.456296\pi$
$48$	9.95250	1.43652
$49$	1.00000	0.142857
$50$	−1.45589	−0.205893
$51$	−1.51782	−0.212538
$52$	−0.107620	−0.0149242
$53$	−12.7409	−1.75010	−0.875050	−	0.484033i	$-0.839172\pi$
$53$	−12.7409	−1.75010	−0.875050	+	0.484033i	$0.839172\pi$
$54$	−1.54606	−0.210392
$55$	0	0
$56$	−2.73764	−0.365833
$57$	−0.517822	−0.0685871
$58$	−0.625442	−0.0821245
$59$	−1.93543	−0.251972	−0.125986	−	0.992032i	$-0.540209\pi$
$59$	−1.93543	−0.251972	−0.125986	+	0.992032i	$0.540209\pi$
$60$	−0.281754	−0.0363742
$61$	13.5035	1.72895	0.864474	−	0.502678i	$-0.167652\pi$
$61$	13.5035	1.72895	0.864474	+	0.502678i	$0.167652\pi$
$62$	8.80924	1.11877
$63$	−2.54920	−0.321169
$64$	7.46606	0.933258
$65$	−0.899788	−0.111605
$66$	0	0
$67$	6.90570	0.843666	0.421833	−	0.906674i	$-0.361387\pi$
$67$	6.90570	0.843666	0.421833	+	0.906674i	$0.361387\pi$
$68$	0.0770654	0.00934556
$69$	−6.48727	−0.780975
$70$	1.45589	0.174012
$71$	−0.408258	−0.0484513	−0.0242256	−	0.999707i	$-0.507712\pi$
$71$	−0.408258	−0.0484513	−0.0242256	+	0.999707i	$0.507712\pi$
$72$	6.97880	0.822459
$73$	8.18482	0.957961	0.478980	−	0.877826i	$-0.341007\pi$
$73$	8.18482	0.957961	0.478980	+	0.877826i	$0.341007\pi$
$74$	0.768510	0.0893375
$75$	−2.35567	−0.272010
$76$	0.0262917	0.00301587
$77$	0	0
$78$	−3.08591	−0.349410
$79$	−15.6841	−1.76460	−0.882298	−	0.470691i	$-0.844005\pi$
$79$	−15.6841	−1.76460	−0.882298	+	0.470691i	$0.844005\pi$
$80$	−4.22491	−0.472359
$81$	−10.1492	−1.12769
$82$	14.1917	1.56721
$83$	8.13780	0.893239	0.446620	−	0.894724i	$-0.352628\pi$
$83$	8.13780	0.893239	0.446620	+	0.894724i	$0.352628\pi$
$84$	0.281754	0.0307418
$85$	0.644326	0.0698869
$86$	−4.29110	−0.462722
$87$	−1.01199	−0.108496
$88$	0	0
$89$	−3.73945	−0.396381	−0.198190	−	0.980164i	$-0.563506\pi$
$89$	−3.73945	−0.396381	−0.198190	+	0.980164i	$0.563506\pi$
$90$	−3.71135	−0.391210
$91$	0.899788	0.0943234
$92$	0.329383	0.0343405
$93$	14.2537	1.47803
$94$	−2.73218	−0.281802
$95$	0.219819	0.0225529
$96$	−1.59174	−0.162457
$97$	−6.55722	−0.665785	−0.332892	−	0.942965i	$-0.608025\pi$
$97$	−6.55722	−0.665785	−0.332892	+	0.942965i	$0.608025\pi$
$98$	−1.45589	−0.147067
$99$	0	0
$100$	0.119606	0.0119606
$101$	11.6915	1.16335	0.581673	−	0.813423i	$-0.302398\pi$
$101$	11.6915	1.16335	0.581673	+	0.813423i	$0.302398\pi$
$102$	2.20978	0.218800
$103$	13.3576	1.31617	0.658083	−	0.752946i	$-0.271368\pi$
$103$	13.3576	1.31617	0.658083	+	0.752946i	$0.271368\pi$
$104$	−2.46329	−0.241546
$105$	2.35567	0.229890
$106$	18.5493	1.80167
$107$	7.02397	0.679033	0.339517	−	0.940600i	$-0.389737\pi$
$107$	7.02397	0.679033	0.339517	+	0.940600i	$0.389737\pi$
$108$	0.127014	0.0122219
$109$	−13.6827	−1.31057	−0.655284	−	0.755382i	$-0.727451\pi$
$109$	−13.6827	−1.31057	−0.655284	+	0.755382i	$0.727451\pi$
$110$	0	0
$111$	1.24348	0.118025
$112$	4.22491	0.399216
$113$	−5.45506	−0.513169	−0.256585	−	0.966522i	$-0.582597\pi$
$113$	−5.45506	−0.513169	−0.256585	+	0.966522i	$0.582597\pi$
$114$	0.753889	0.0706082
$115$	2.75389	0.256802
$116$	0.0513823	0.00477073
$117$	−2.29374	−0.212056
$118$	2.81777	0.259397
$119$	−0.644326	−0.0590652
$120$	−6.44899	−0.588709
$121$	0	0
$122$	−19.6596	−1.77990
$123$	22.9627	2.07048
$124$	−0.723711	−0.0649911
$125$	1.00000	0.0894427
$126$	3.71135	0.330633
$127$	20.8837	1.85313	0.926563	−	0.376139i	$-0.122749\pi$
$127$	20.8837	1.85313	0.926563	+	0.376139i	$0.122749\pi$
$128$	−12.2212	−1.08021
$129$	−6.94315	−0.611311
$130$	1.30999	0.114894
$131$	15.9627	1.39467	0.697333	−	0.716747i	$-0.254370\pi$
$131$	15.9627	1.39467	0.697333	+	0.716747i	$0.254370\pi$
$132$	0	0
$133$	−0.219819	−0.0190607
$134$	−10.0539	−0.868526
$135$	1.06193	0.0913968
$136$	1.76393	0.151256
$137$	−3.03087	−0.258945	−0.129472	−	0.991583i	$-0.541328\pi$
$137$	−3.03087	−0.258945	−0.129472	+	0.991583i	$0.541328\pi$
$138$	9.44473	0.803988
$139$	16.5899	1.40714	0.703570	−	0.710626i	$-0.251588\pi$
$139$	16.5899	1.40714	0.703570	+	0.710626i	$0.251588\pi$
$140$	−0.119606	−0.0101086
$141$	−4.42075	−0.372295
$142$	0.594377	0.0498790
$143$	0	0
$144$	−10.7701	−0.897512
$145$	0.429595	0.0356759
$146$	−11.9162	−0.986189
$147$	−2.35567	−0.194293
$148$	−0.0631359	−0.00518974
$149$	−1.23524	−0.101195	−0.0505975	−	0.998719i	$-0.516113\pi$
$149$	−1.23524	−0.101195	−0.0505975	+	0.998719i	$0.516113\pi$
$150$	3.42960	0.280025
$151$	8.72842	0.710309	0.355154	−	0.934808i	$-0.384428\pi$
$151$	8.72842	0.710309	0.355154	+	0.934808i	$0.384428\pi$
$152$	0.601785	0.0488112
$153$	1.64252	0.132790
$154$	0	0
$155$	−6.05077	−0.486010
$156$	0.253518	0.0202977
$157$	7.69838	0.614397	0.307199	−	0.951645i	$-0.400608\pi$
$157$	7.69838	0.614397	0.307199	+	0.951645i	$0.400608\pi$
$158$	22.8342	1.81659
$159$	30.0135	2.38022
$160$	0.675706	0.0534192
$161$	−2.75389	−0.217037
$162$	14.7761	1.16092
$163$	12.0792	0.946118	0.473059	−	0.881031i	$-0.343150\pi$
$163$	12.0792	0.946118	0.473059	+	0.881031i	$0.343150\pi$
$164$	−1.16590	−0.0910415
$165$	0	0
$166$	−11.8477	−0.919561
$167$	5.41433	0.418973	0.209487	−	0.977811i	$-0.432821\pi$
$167$	5.41433	0.418973	0.209487	+	0.977811i	$0.432821\pi$
$168$	6.44899	0.497550
$169$	−12.1904	−0.937722
$170$	−0.938065	−0.0719463
$171$	0.560362	0.0428520
$172$	0.352530	0.0268801
$173$	0.209776	0.0159490	0.00797450	−	0.999968i	$-0.497462\pi$
$173$	0.209776	0.0159490	0.00797450	+	0.999968i	$0.497462\pi$
$174$	1.47334	0.111693
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	4.55924	0.342694
$178$	5.44422	0.408061
$179$	−15.2474	−1.13964	−0.569821	−	0.821769i	$-0.692987\pi$
$179$	−15.2474	−1.13964	−0.569821	+	0.821769i	$0.692987\pi$
$180$	0.304901	0.0227259
$181$	−25.6992	−1.91021	−0.955103	−	0.296273i	$-0.904256\pi$
$181$	−25.6992	−1.91021	−0.955103	+	0.296273i	$0.904256\pi$
$182$	−1.30999	−0.0971028
$183$	−31.8099	−2.35145
$184$	7.53916	0.555794
$185$	−0.527864	−0.0388093
$186$	−20.7517	−1.52159
$187$	0	0
$188$	0.224458	0.0163703
$189$	−1.06193	−0.0772444
$190$	−0.320031	−0.0232175
$191$	21.1836	1.53279	0.766396	−	0.642368i	$-0.222048\pi$
$191$	21.1836	1.53279	0.766396	+	0.642368i	$0.222048\pi$
$192$	−17.5876	−1.26928
$193$	−6.41977	−0.462105	−0.231053	−	0.972941i	$-0.574217\pi$
$193$	−6.41977	−0.462105	−0.231053	+	0.972941i	$0.574217\pi$
$194$	9.54657	0.685404
$195$	2.11961	0.151788
$196$	0.119606	0.00854331
$197$	14.3741	1.02411	0.512056	−	0.858952i	$-0.328884\pi$
$197$	14.3741	1.02411	0.512056	+	0.858952i	$0.328884\pi$
$198$	0	0
$199$	−17.9288	−1.27094	−0.635471	−	0.772125i	$-0.719194\pi$
$199$	−17.9288	−1.27094	−0.635471	+	0.772125i	$0.719194\pi$
$200$	2.73764	0.193580
$201$	−16.2676	−1.14743
$202$	−17.0215	−1.19763
$203$	−0.429595	−0.0301517
$204$	−0.181541	−0.0127104
$205$	−9.74782	−0.680817
$206$	−19.4472	−1.35495
$207$	7.02022	0.487939
$208$	3.80152	0.263588
$209$	0	0
$210$	−3.42960	−0.236665
$211$	−8.28309	−0.570231	−0.285116	−	0.958493i	$-0.592032\pi$
$211$	−8.28309	−0.570231	−0.285116	+	0.958493i	$0.592032\pi$
$212$	−1.52389	−0.104661
$213$	0.961722	0.0658961
$214$	−10.2261	−0.699042
$215$	2.94742	0.201012
$216$	2.90720	0.197810
$217$	6.05077	0.410753
$218$	19.9205	1.34919
$219$	−19.2808	−1.30287
$220$	0	0
$221$	−0.579756	−0.0389986
$222$	−1.81036	−0.121503
$223$	−22.5820	−1.51220	−0.756102	−	0.654454i	$-0.772899\pi$
$223$	−22.5820	−1.51220	−0.756102	+	0.654454i	$0.772899\pi$
$224$	−0.675706	−0.0451475
$225$	2.54920	0.169947
$226$	7.94195	0.528291
$227$	−16.3775	−1.08701	−0.543507	−	0.839405i	$-0.682904\pi$
$227$	−16.3775	−1.08701	−0.543507	+	0.839405i	$0.682904\pi$
$228$	−0.0619347	−0.00410173
$229$	−16.6859	−1.10263	−0.551317	−	0.834296i	$-0.685875\pi$
$229$	−16.6859	−1.10263	−0.551317	+	0.834296i	$0.685875\pi$
$230$	−4.00935	−0.264369
$231$	0	0
$232$	1.17608	0.0772132
$233$	18.9466	1.24123	0.620616	−	0.784114i	$-0.286883\pi$
$233$	18.9466	1.24123	0.620616	+	0.784114i	$0.286883\pi$
$234$	3.33943	0.218305
$235$	1.87664	0.122419
$236$	−0.231490	−0.0150687
$237$	36.9466	2.39994
$238$	0.938065	0.0608057
$239$	−5.63774	−0.364675	−0.182338	−	0.983236i	$-0.558366\pi$
$239$	−5.63774	−0.364675	−0.182338	+	0.983236i	$0.558366\pi$
$240$	9.95250	0.642431
$241$	26.9629	1.73683	0.868416	−	0.495836i	$-0.165138\pi$
$241$	26.9629	1.73683	0.868416	+	0.495836i	$0.165138\pi$
$242$	0	0
$243$	20.7223	1.32934
$244$	1.61511	0.103397
$245$	1.00000	0.0638877
$246$	−33.4311	−2.13149
$247$	−0.197790	−0.0125851
$248$	−16.5648	−1.05187
$249$	−19.1700	−1.21485
$250$	−1.45589	−0.0920784
$251$	−16.2116	−1.02327	−0.511633	−	0.859204i	$-0.670959\pi$
$251$	−16.2116	−1.02327	−0.511633	+	0.859204i	$0.670959\pi$
$252$	−0.304901	−0.0192069
$253$	0	0
$254$	−30.4043	−1.90773
$255$	−1.51782	−0.0950497
$256$	2.86049	0.178781
$257$	−7.43154	−0.463567	−0.231783	−	0.972767i	$-0.574456\pi$
$257$	−7.43154	−0.463567	−0.231783	+	0.972767i	$0.574456\pi$
$258$	10.1084	0.629324
$259$	0.527864	0.0327999
$260$	−0.107620	−0.00667433
$261$	1.09512	0.0677865
$262$	−23.2399	−1.43576
$263$	−16.7681	−1.03397	−0.516983	−	0.855996i	$-0.672945\pi$
$263$	−16.7681	−1.03397	−0.516983	+	0.855996i	$0.672945\pi$
$264$	0	0
$265$	−12.7409	−0.782668
$266$	0.320031	0.0196224
$267$	8.80893	0.539098
$268$	0.825965	0.0504539
$269$	−25.6282	−1.56258	−0.781290	−	0.624168i	$-0.785438\pi$
$269$	−25.6282	−1.56258	−0.781290	+	0.624168i	$0.785438\pi$
$270$	−1.54606	−0.0940900
$271$	0.624107	0.0379118	0.0189559	−	0.999820i	$-0.493966\pi$
$271$	0.624107	0.0379118	0.0189559	+	0.999820i	$0.493966\pi$
$272$	−2.72222	−0.165059
$273$	−2.11961	−0.128284
$274$	4.41260	0.266575
$275$	0	0
$276$	−0.775918	−0.0467048
$277$	7.53519	0.452746	0.226373	−	0.974041i	$-0.427313\pi$
$277$	7.53519	0.452746	0.226373	+	0.974041i	$0.427313\pi$
$278$	−24.1531	−1.44860
$279$	−15.4246	−0.923449
$280$	−2.73764	−0.163605
$281$	−4.76841	−0.284460	−0.142230	−	0.989834i	$-0.545427\pi$
$281$	−4.76841	−0.284460	−0.142230	+	0.989834i	$0.545427\pi$
$282$	6.43612	0.383265
$283$	−5.87277	−0.349100	−0.174550	−	0.984648i	$-0.555847\pi$
$283$	−5.87277	−0.349100	−0.174550	+	0.984648i	$0.555847\pi$
$284$	−0.0488302	−0.00289754
$285$	−0.517822	−0.0306731
$286$	0	0
$287$	9.74782	0.575395
$288$	1.72251	0.101500
$289$	−16.5848	−0.975579
$290$	−0.625442	−0.0367272
$291$	15.4467	0.905500
$292$	0.978956	0.0572891
$293$	4.46180	0.260661	0.130331	−	0.991471i	$-0.458396\pi$
$293$	4.46180	0.260661	0.130331	+	0.991471i	$0.458396\pi$
$294$	3.42960	0.200018
$295$	−1.93543	−0.112685
$296$	−1.44510	−0.0839948
$297$	0	0
$298$	1.79837	0.104177
$299$	−2.47792	−0.143302
$300$	−0.281754	−0.0162670
$301$	−2.94742	−0.169886
$302$	−12.7076	−0.731240
$303$	−27.5413	−1.58221
$304$	−0.928714	−0.0532654
$305$	13.5035	0.773209
$306$	−2.39132	−0.136703
$307$	−21.6680	−1.23666	−0.618328	−	0.785920i	$-0.712190\pi$
$307$	−21.6680	−1.23666	−0.618328	+	0.785920i	$0.712190\pi$
$308$	0	0
$309$	−31.4662	−1.79005
$310$	8.80924	0.500331
$311$	−8.71196	−0.494010	−0.247005	−	0.969014i	$-0.579446\pi$
$311$	−8.71196	−0.494010	−0.247005	+	0.969014i	$0.579446\pi$
$312$	5.80272	0.328514
$313$	22.3056	1.26079	0.630395	−	0.776275i	$-0.282893\pi$
$313$	22.3056	1.26079	0.630395	+	0.776275i	$0.282893\pi$
$314$	−11.2080	−0.632502
$315$	−2.54920	−0.143631
$316$	−1.87591	−0.105528
$317$	−25.4066	−1.42698	−0.713488	−	0.700668i	$-0.752886\pi$
$317$	−25.4066	−1.42698	−0.713488	+	0.700668i	$0.752886\pi$
$318$	−43.6962	−2.45036
$319$	0	0
$320$	7.46606	0.417366
$321$	−16.5462	−0.923518
$322$	4.00935	0.223432
$323$	0.141635	0.00788078
$324$	−1.21391	−0.0674392
$325$	−0.899788	−0.0499112
$326$	−17.5860	−0.973998
$327$	32.2321	1.78244
$328$	−26.6860	−1.47349
$329$	−1.87664	−0.103463
$330$	0	0
$331$	10.3254	0.567536	0.283768	−	0.958893i	$-0.408415\pi$
$331$	10.3254	0.567536	0.283768	+	0.958893i	$0.408415\pi$
$332$	0.973332	0.0534185
$333$	−1.34563	−0.0737402
$334$	−7.88265	−0.431320
$335$	6.90570	0.377299
$336$	−9.95250	−0.542954
$337$	−28.0368	−1.52726	−0.763630	−	0.645654i	$-0.776585\pi$
$337$	−28.0368	−1.52726	−0.763630	+	0.645654i	$0.776585\pi$
$338$	17.7478	0.965354
$339$	12.8503	0.697935
$340$	0.0770654	0.00417946
$341$	0	0
$342$	−0.815824	−0.0441147
$343$	−1.00000	−0.0539949
$344$	8.06897	0.435050
$345$	−6.48727	−0.349263
$346$	−0.305410	−0.0164190
$347$	−22.0872	−1.18570	−0.592850	−	0.805313i	$-0.701997\pi$
$347$	−22.0872	−1.18570	−0.592850	+	0.805313i	$0.701997\pi$
$348$	−0.121040	−0.00648842
$349$	−14.3698	−0.769199	−0.384599	−	0.923084i	$-0.625660\pi$
$349$	−14.3698	−0.769199	−0.384599	+	0.923084i	$0.625660\pi$
$350$	1.45589	0.0778204
$351$	−0.955516	−0.0510016
$352$	0	0
$353$	29.1646	1.55227	0.776137	−	0.630565i	$-0.217177\pi$
$353$	29.1646	1.55227	0.776137	+	0.630565i	$0.217177\pi$
$354$	−6.63774	−0.352792
$355$	−0.408258	−0.0216681
$356$	−0.447262	−0.0237048
$357$	1.51782	0.0803316
$358$	22.1984	1.17322
$359$	−18.9788	−1.00166	−0.500831	−	0.865545i	$-0.666972\pi$
$359$	−18.9788	−1.00166	−0.500831	+	0.865545i	$0.666972\pi$
$360$	6.97880	0.367815
$361$	−18.9517	−0.997457
$362$	37.4151	1.96650
$363$	0	0
$364$	0.107620	0.00564083
$365$	8.18482	0.428413
$366$	46.3116	2.42075
$367$	−33.0934	−1.72746	−0.863732	−	0.503951i	$-0.831879\pi$
$367$	−33.0934	−1.72746	−0.863732	+	0.503951i	$0.831879\pi$
$368$	−11.6349	−0.606512
$369$	−24.8491	−1.29359
$370$	0.768510	0.0399529
$371$	12.7409	0.661476
$372$	1.70483	0.0883912
$373$	−23.7596	−1.23023	−0.615114	−	0.788438i	$-0.710890\pi$
$373$	−23.7596	−1.23023	−0.615114	+	0.788438i	$0.710890\pi$
$374$	0	0
$375$	−2.35567	−0.121646
$376$	5.13757	0.264950
$377$	−0.386544	−0.0199080
$378$	1.54606	0.0795206
$379$	9.53989	0.490031	0.245015	−	0.969519i	$-0.421207\pi$
$379$	9.53989	0.490031	0.245015	+	0.969519i	$0.421207\pi$
$380$	0.0262917	0.00134874
$381$	−49.1951	−2.52034
$382$	−30.8409	−1.57796
$383$	32.2316	1.64696	0.823479	−	0.567347i	$-0.192030\pi$
$383$	32.2316	1.64696	0.823479	+	0.567347i	$0.192030\pi$
$384$	28.7891	1.46914
$385$	0	0
$386$	9.34646	0.475722
$387$	7.51356	0.381936
$388$	−0.784285	−0.0398160
$389$	36.4823	1.84973	0.924863	−	0.380301i	$-0.124180\pi$
$389$	36.4823	1.84973	0.924863	+	0.380301i	$0.124180\pi$
$390$	−3.08591	−0.156261
$391$	1.77440	0.0897354
$392$	2.73764	0.138272
$393$	−37.6029	−1.89681
$394$	−20.9270	−1.05429
$395$	−15.6841	−0.789151
$396$	0	0
$397$	1.61774	0.0811921	0.0405960	−	0.999176i	$-0.487074\pi$
$397$	1.61774	0.0811921	0.0405960	+	0.999176i	$0.487074\pi$
$398$	26.1024	1.30839
$399$	0.517822	0.0259235
$400$	−4.22491	−0.211245
$401$	11.0800	0.553307	0.276654	−	0.960970i	$-0.410775\pi$
$401$	11.0800	0.553307	0.276654	+	0.960970i	$0.410775\pi$
$402$	23.6838	1.18124
$403$	5.44441	0.271205
$404$	1.39837	0.0695717
$405$	−10.1492	−0.504317
$406$	0.625442	0.0310402
$407$	0	0
$408$	−4.15525	−0.205715
$409$	−9.34115	−0.461890	−0.230945	−	0.972967i	$-0.574182\pi$
$409$	−9.34115	−0.461890	−0.230945	+	0.972967i	$0.574182\pi$
$410$	14.1917	0.700879
$411$	7.13974	0.352178
$412$	1.59766	0.0787108
$413$	1.93543	0.0952363
$414$	−10.2206	−0.502317
$415$	8.13780	0.399469
$416$	−0.607991	−0.0298092
$417$	−39.0805	−1.91378
$418$	0	0
$419$	25.3531	1.23858	0.619290	−	0.785162i	$-0.287421\pi$
$419$	25.3531	1.23858	0.619290	+	0.785162i	$0.287421\pi$
$420$	0.281754	0.0137482
$421$	−19.6601	−0.958175	−0.479087	−	0.877767i	$-0.659032\pi$
$421$	−19.6601	−0.958175	−0.479087	+	0.877767i	$0.659032\pi$
$422$	12.0592	0.587035
$423$	4.78393	0.232603
$424$	−34.8801	−1.69393
$425$	0.644326	0.0312544
$426$	−1.40016	−0.0678379
$427$	−13.5035	−0.653481
$428$	0.840111	0.0406083
$429$	0	0
$430$	−4.29110	−0.206935
$431$	34.1278	1.64388	0.821939	−	0.569576i	$-0.192892\pi$
$431$	34.1278	1.64388	0.821939	+	0.569576i	$0.192892\pi$
$432$	−4.48658	−0.215860
$433$	9.93556	0.477473	0.238736	−	0.971084i	$-0.423267\pi$
$433$	9.93556	0.477473	0.238736	+	0.971084i	$0.423267\pi$
$434$	−8.80924	−0.422857
$435$	−1.01199	−0.0485210
$436$	−1.63654	−0.0783761
$437$	0.605357	0.0289581
$438$	28.0706	1.34127
$439$	9.74028	0.464878	0.232439	−	0.972611i	$-0.425329\pi$
$439$	9.74028	0.464878	0.232439	+	0.972611i	$0.425329\pi$
$440$	0	0
$441$	2.54920	0.121391
$442$	0.844059	0.0401478
$443$	−29.5552	−1.40421	−0.702106	−	0.712072i	$-0.747757\pi$
$443$	−29.5552	−1.40421	−0.702106	+	0.712072i	$0.747757\pi$
$444$	0.148728	0.00705830
$445$	−3.73945	−0.177267
$446$	32.8769	1.55676
$447$	2.90983	0.137630
$448$	−7.46606	−0.352738
$449$	−22.9092	−1.08115	−0.540576	−	0.841295i	$-0.681794\pi$
$449$	−22.9092	−1.08115	−0.540576	+	0.841295i	$0.681794\pi$
$450$	−3.71135	−0.174955
$451$	0	0
$452$	−0.652460	−0.0306891
$453$	−20.5613	−0.966055
$454$	23.8438	1.11905
$455$	0.899788	0.0421827
$456$	−1.41761	−0.0663856
$457$	−35.5090	−1.66104	−0.830519	−	0.556990i	$-0.811956\pi$
$457$	−35.5090	−1.66104	−0.830519	+	0.556990i	$0.811956\pi$
$458$	24.2928	1.13513
$459$	0.684232	0.0319372
$460$	0.329383	0.0153575
$461$	11.0320	0.513811	0.256905	−	0.966437i	$-0.417297\pi$
$461$	11.0320	0.513811	0.256905	+	0.966437i	$0.417297\pi$
$462$	0	0
$463$	−1.20655	−0.0560733	−0.0280367	−	0.999607i	$-0.508926\pi$
$463$	−1.20655	−0.0560733	−0.0280367	+	0.999607i	$0.508926\pi$
$464$	−1.81500	−0.0842592
$465$	14.2537	0.660997
$466$	−27.5841	−1.27781
$467$	11.8043	0.546238	0.273119	−	0.961980i	$-0.411945\pi$
$467$	11.8043	0.546238	0.273119	+	0.961980i	$0.411945\pi$
$468$	−0.274346	−0.0126816
$469$	−6.90570	−0.318876
$470$	−2.73218	−0.126026
$471$	−18.1349	−0.835611
$472$	−5.29851	−0.243884
$473$	0	0
$474$	−53.7900	−2.47066
$475$	0.219819	0.0100860
$476$	−0.0770654	−0.00353229
$477$	−32.4792	−1.48712
$478$	8.20792	0.375421
$479$	−27.2596	−1.24552	−0.622762	−	0.782411i	$-0.713990\pi$
$479$	−27.2596	−1.24552	−0.622762	+	0.782411i	$0.713990\pi$
$480$	−1.59174	−0.0726528
$481$	0.474965	0.0216566
$482$	−39.2549	−1.78801
$483$	6.48727	0.295181
$484$	0	0
$485$	−6.55722	−0.297748
$486$	−30.1694	−1.36851
$487$	−3.76527	−0.170621	−0.0853103	−	0.996354i	$-0.527188\pi$
$487$	−3.76527	−0.170621	−0.0853103	+	0.996354i	$0.527188\pi$
$488$	36.9678	1.67345
$489$	−28.4547	−1.28677
$490$	−1.45589	−0.0657703
$491$	2.28887	0.103295	0.0516476	−	0.998665i	$-0.483553\pi$
$491$	2.28887	0.103295	0.0516476	+	0.998665i	$0.483553\pi$
$492$	2.74648	0.123821
$493$	0.276799	0.0124664
$494$	0.287960	0.0129559
$495$	0	0
$496$	25.5640	1.14786
$497$	0.408258	0.0183129
$498$	27.9094	1.25065
$499$	28.0997	1.25791	0.628957	−	0.777440i	$-0.283482\pi$
$499$	28.0997	1.25791	0.628957	+	0.777440i	$0.283482\pi$
$500$	0.119606	0.00534896
$501$	−12.7544	−0.569825
$502$	23.6022	1.05342
$503$	11.6624	0.520002	0.260001	−	0.965608i	$-0.416277\pi$
$503$	11.6624	0.520002	0.260001	+	0.965608i	$0.416277\pi$
$504$	−6.97880	−0.310860
$505$	11.6915	0.520264
$506$	0	0
$507$	28.7166	1.27535
$508$	2.49782	0.110823
$509$	−29.3908	−1.30273	−0.651363	−	0.758766i	$-0.725803\pi$
$509$	−29.3908	−1.30273	−0.651363	+	0.758766i	$0.725803\pi$
$510$	2.20978	0.0978505
$511$	−8.18482	−0.362075
$512$	20.2778	0.896159
$513$	0.233433	0.0103063
$514$	10.8195	0.477227
$515$	13.3576	0.588607
$516$	−0.830445	−0.0365583
$517$	0	0
$518$	−0.768510	−0.0337664
$519$	−0.494165	−0.0216914
$520$	−2.46329	−0.108023
$521$	−7.69765	−0.337240	−0.168620	−	0.985681i	$-0.553931\pi$
$521$	−7.69765	−0.337240	−0.168620	+	0.985681i	$0.553931\pi$
$522$	−1.59438	−0.0697840
$523$	10.4195	0.455611	0.227805	−	0.973707i	$-0.426845\pi$
$523$	10.4195	0.455611	0.227805	+	0.973707i	$0.426845\pi$
$524$	1.90924	0.0834054
$525$	2.35567	0.102810
$526$	24.4125	1.06443
$527$	−3.89867	−0.169829
$528$	0	0
$529$	−15.4161	−0.670265
$530$	18.5493	0.805732
$531$	−4.93380	−0.214109
$532$	−0.0262917	−0.00113989
$533$	8.77096	0.379913
$534$	−12.8248	−0.554983
$535$	7.02397	0.303673
$536$	18.9053	0.816586
$537$	35.9178	1.54997
$538$	37.3118	1.60862
$539$	0	0
$540$	0.127014	0.00546582
$541$	−41.4268	−1.78108	−0.890539	−	0.454908i	$-0.849672\pi$
$541$	−41.4268	−1.78108	−0.890539	+	0.454908i	$0.849672\pi$
$542$	−0.908629	−0.0390290
$543$	60.5390	2.59798
$544$	0.435374	0.0186665
$545$	−13.6827	−0.586104
$546$	3.08591	0.132065
$547$	−18.9756	−0.811337	−0.405668	−	0.914020i	$-0.632961\pi$
$547$	−18.9756	−0.811337	−0.405668	+	0.914020i	$0.632961\pi$
$548$	−0.362511	−0.0154857
$549$	34.4232	1.46915
$550$	0	0
$551$	0.0944331	0.00402298
$552$	−17.7598	−0.755907
$553$	15.6841	0.666955
$554$	−10.9704	−0.466087
$555$	1.24348	0.0527826
$556$	1.98426	0.0841514
$557$	−2.15879	−0.0914707	−0.0457354	−	0.998954i	$-0.514563\pi$
$557$	−2.15879	−0.0914707	−0.0457354	+	0.998954i	$0.514563\pi$
$558$	22.4565	0.950661
$559$	−2.65205	−0.112170
$560$	4.22491	0.178535
$561$	0	0
$562$	6.94227	0.292842
$563$	−25.0255	−1.05470	−0.527349	−	0.849649i	$-0.676814\pi$
$563$	−25.0255	−1.05470	−0.527349	+	0.849649i	$0.676814\pi$
$564$	−0.528750	−0.0222644
$565$	−5.45506	−0.229496
$566$	8.55009	0.359387
$567$	10.1492	0.426225
$568$	−1.11766	−0.0468961
$569$	−11.7312	−0.491799	−0.245899	−	0.969295i	$-0.579083\pi$
$569$	−11.7312	−0.491799	−0.245899	+	0.969295i	$0.579083\pi$
$570$	0.753889	0.0315770
$571$	−20.6183	−0.862847	−0.431423	−	0.902150i	$-0.641989\pi$
$571$	−20.6183	−0.862847	−0.431423	+	0.902150i	$0.641989\pi$
$572$	0	0
$573$	−49.9017	−2.08467
$574$	−14.1917	−0.592351
$575$	2.75389	0.114845
$576$	19.0325	0.793021
$577$	−23.4156	−0.974806	−0.487403	−	0.873177i	$-0.662056\pi$
$577$	−23.4156	−0.974806	−0.487403	+	0.873177i	$0.662056\pi$
$578$	24.1457	1.00433
$579$	15.1229	0.628486
$580$	0.0513823	0.00213353
$581$	−8.13780	−0.337613
$582$	−22.4886	−0.932183
$583$	0	0
$584$	22.4071	0.927212
$585$	−2.29374	−0.0948345
$586$	−6.49588	−0.268342
$587$	−27.6790	−1.14244	−0.571218	−	0.820799i	$-0.693529\pi$
$587$	−27.6790	−1.14244	−0.571218	+	0.820799i	$0.693529\pi$
$588$	−0.281754	−0.0116193
$589$	−1.33007	−0.0548047
$590$	2.81777	0.116006
$591$	−33.8607	−1.39284
$592$	2.23018	0.0916597
$593$	−19.8474	−0.815033	−0.407517	−	0.913198i	$-0.633605\pi$
$593$	−19.8474	−0.815033	−0.407517	+	0.913198i	$0.633605\pi$
$594$	0	0
$595$	−0.644326	−0.0264148
$596$	−0.147743	−0.00605178
$597$	42.2345	1.72854
$598$	3.60756	0.147524
$599$	−48.3237	−1.97445	−0.987227	−	0.159322i	$-0.949069\pi$
$599$	−48.3237	−1.97445	−0.987227	+	0.159322i	$0.949069\pi$
$600$	−6.44899	−0.263279
$601$	23.5429	0.960335	0.480168	−	0.877177i	$-0.340576\pi$
$601$	23.5429	0.960335	0.480168	+	0.877177i	$0.340576\pi$
$602$	4.29110	0.174892
$603$	17.6040	0.716891
$604$	1.04397	0.0424787
$605$	0	0
$606$	40.0970	1.62883
$607$	21.9404	0.890532	0.445266	−	0.895398i	$-0.353109\pi$
$607$	21.9404	0.890532	0.445266	+	0.895398i	$0.353109\pi$
$608$	0.148533	0.00602380
$609$	1.01199	0.0410077
$610$	−19.6596	−0.795994
$611$	−1.68858	−0.0683125
$612$	0.196455	0.00794123
$613$	−6.28468	−0.253836	−0.126918	−	0.991913i	$-0.540508\pi$
$613$	−6.28468	−0.253836	−0.126918	+	0.991913i	$0.540508\pi$
$614$	31.5461	1.27310
$615$	22.9627	0.925945
$616$	0	0
$617$	47.6580	1.91864	0.959319	−	0.282323i	$-0.0911050\pi$
$617$	47.6580	1.91864	0.959319	+	0.282323i	$0.0911050\pi$
$618$	45.8112	1.84280
$619$	−0.197497	−0.00793807	−0.00396903	−	0.999992i	$-0.501263\pi$
$619$	−0.197497	−0.00793807	−0.00396903	+	0.999992i	$0.501263\pi$
$620$	−0.723711	−0.0290649
$621$	2.92445	0.117354
$622$	12.6836	0.508567
$623$	3.73945	0.149818
$624$	−8.95514	−0.358492
$625$	1.00000	0.0400000
$626$	−32.4745	−1.29794
$627$	0	0
$628$	0.920775	0.0367429
$629$	−0.340116	−0.0135613
$630$	3.71135	0.147864
$631$	6.94531	0.276489	0.138244	−	0.990398i	$-0.455854\pi$
$631$	6.94531	0.276489	0.138244	+	0.990398i	$0.455854\pi$
$632$	−42.9373	−1.70796
$633$	19.5123	0.775543
$634$	36.9891	1.46903
$635$	20.8837	0.828743
$636$	3.58980	0.142345
$637$	−0.899788	−0.0356509
$638$	0	0
$639$	−1.04073	−0.0411707
$640$	−12.2212	−0.483084
$641$	31.6887	1.25163	0.625813	−	0.779973i	$-0.284767\pi$
$641$	31.6887	1.25163	0.625813	+	0.779973i	$0.284767\pi$
$642$	24.0894	0.950732
$643$	8.06028	0.317867	0.158933	−	0.987289i	$-0.449195\pi$
$643$	8.06028	0.317867	0.158933	+	0.987289i	$0.449195\pi$
$644$	−0.329383	−0.0129795
$645$	−6.94315	−0.273386
$646$	−0.206204	−0.00811300
$647$	20.0756	0.789255	0.394628	−	0.918841i	$-0.370874\pi$
$647$	20.0756	0.789255	0.394628	+	0.918841i	$0.370874\pi$
$648$	−27.7848	−1.09149
$649$	0	0
$650$	1.30999	0.0513820
$651$	−14.2537	−0.558645
$652$	1.44475	0.0565808
$653$	−38.0788	−1.49014	−0.745069	−	0.666987i	$-0.767584\pi$
$653$	−38.0788	−1.49014	−0.745069	+	0.666987i	$0.767584\pi$
$654$	−46.9262	−1.83496
$655$	15.9627	0.623714
$656$	41.1836	1.60795
$657$	20.8648	0.814012
$658$	2.73218	0.106511
$659$	−27.1641	−1.05816	−0.529082	−	0.848570i	$-0.677464\pi$
$659$	−27.1641	−1.05816	−0.529082	+	0.848570i	$0.677464\pi$
$660$	0	0
$661$	−19.7408	−0.767830	−0.383915	−	0.923368i	$-0.625424\pi$
$661$	−19.7408	−0.767830	−0.383915	+	0.923368i	$0.625424\pi$
$662$	−15.0326	−0.584260
$663$	1.36572	0.0530400
$664$	22.2784	0.864568
$665$	−0.219819	−0.00852421
$666$	1.95909	0.0759131
$667$	1.18306	0.0458082
$668$	0.647588	0.0250559
$669$	53.1959	2.05667
$670$	−10.0539	−0.388417
$671$	0	0
$672$	1.59174	0.0614028
$673$	−13.1547	−0.507078	−0.253539	−	0.967325i	$-0.581595\pi$
$673$	−13.1547	−0.507078	−0.253539	+	0.967325i	$0.581595\pi$
$674$	40.8184	1.57226
$675$	1.06193	0.0408739
$676$	−1.45805	−0.0560787
$677$	4.92411	0.189249	0.0946245	−	0.995513i	$-0.469835\pi$
$677$	4.92411	0.189249	0.0946245	+	0.995513i	$0.469835\pi$
$678$	−18.7087	−0.718501
$679$	6.55722	0.251643
$680$	1.76393	0.0676437
$681$	38.5801	1.47839
$682$	0	0
$683$	−20.3110	−0.777178	−0.388589	−	0.921411i	$-0.627037\pi$
$683$	−20.3110	−0.777178	−0.388589	+	0.921411i	$0.627037\pi$
$684$	0.0670229	0.00256268
$685$	−3.03087	−0.115804
$686$	1.45589	0.0555860
$687$	39.3065	1.49964
$688$	−12.4526	−0.474749
$689$	11.4641	0.436748
$690$	9.44473	0.359555
$691$	−6.97829	−0.265467	−0.132733	−	0.991152i	$-0.542375\pi$
$691$	−6.97829	−0.265467	−0.132733	+	0.991152i	$0.542375\pi$
$692$	0.0250906	0.000953800 0
$693$	0	0
$694$	32.1564	1.22064
$695$	16.5899	0.629292
$696$	−2.77045	−0.105014
$697$	−6.28077	−0.237901
$698$	20.9208	0.791865
$699$	−44.6320	−1.68814
$700$	−0.119606	−0.00452069
$701$	−29.3292	−1.10775	−0.553874	−	0.832601i	$-0.686851\pi$
$701$	−29.3292	−1.10775	−0.553874	+	0.832601i	$0.686851\pi$
$702$	1.39112	0.0525045
$703$	−0.116034	−0.00437632
$704$	0	0
$705$	−4.42075	−0.166495
$706$	−42.4603	−1.59802
$707$	−11.6915	−0.439703
$708$	0.545314	0.0204942
$709$	−40.0136	−1.50274	−0.751371	−	0.659880i	$-0.770607\pi$
$709$	−40.0136	−1.50274	−0.751371	+	0.659880i	$0.770607\pi$
$710$	0.594377	0.0223066
$711$	−39.9819	−1.49944
$712$	−10.2373	−0.383658
$713$	−16.6632	−0.624040
$714$	−2.20978	−0.0826988
$715$	0	0
$716$	−1.82368	−0.0681542
$717$	13.2807	0.495976
$718$	27.6310	1.03118
$719$	20.7126	0.772450	0.386225	−	0.922405i	$-0.373779\pi$
$719$	20.7126	0.772450	0.386225	+	0.922405i	$0.373779\pi$
$720$	−10.7701	−0.401379
$721$	−13.3576	−0.497464
$722$	27.5915	1.02685
$723$	−63.5158	−2.36218
$724$	−3.07379	−0.114236
$725$	0.429595	0.0159548
$726$	0	0
$727$	−17.4315	−0.646497	−0.323249	−	0.946314i	$-0.604775\pi$
$727$	−17.4315	−0.646497	−0.323249	+	0.946314i	$0.604775\pi$
$728$	2.46329	0.0912958
$729$	−18.3676	−0.680281
$730$	−11.9162	−0.441037
$731$	1.89910	0.0702406
$732$	−3.80466	−0.140624
$733$	21.9716	0.811540	0.405770	−	0.913975i	$-0.367003\pi$
$733$	21.9716	0.811540	0.405770	+	0.913975i	$0.367003\pi$
$734$	48.1803	1.77837
$735$	−2.35567	−0.0868904
$736$	1.86082	0.0685907
$737$	0	0
$738$	36.1775	1.33171
$739$	29.2876	1.07736	0.538681	−	0.842510i	$-0.318923\pi$
$739$	29.2876	1.07736	0.538681	+	0.842510i	$0.318923\pi$
$740$	−0.0631359	−0.00232092
$741$	0.465929	0.0171163
$742$	−18.5493	−0.680968
$743$	−14.0431	−0.515192	−0.257596	−	0.966253i	$-0.582930\pi$
$743$	−14.0431	−0.515192	−0.257596	+	0.966253i	$0.582930\pi$
$744$	39.0214	1.43059
$745$	−1.23524	−0.0452558
$746$	34.5914	1.26648
$747$	20.7449	0.759016
$748$	0	0
$749$	−7.02397	−0.256650
$750$	3.42960	0.125231
$751$	49.1953	1.79516	0.897582	−	0.440848i	$-0.145322\pi$
$751$	49.1953	1.79516	0.897582	+	0.440848i	$0.145322\pi$
$752$	−7.92863	−0.289127
$753$	38.1892	1.39169
$754$	0.562765	0.0204947
$755$	8.72842	0.317660
$756$	−0.127014	−0.00461946
$757$	−2.99363	−0.108805	−0.0544027	−	0.998519i	$-0.517325\pi$
$757$	−2.99363	−0.108805	−0.0544027	+	0.998519i	$0.517325\pi$
$758$	−13.8890	−0.504471
$759$	0	0
$760$	0.601785	0.0218290
$761$	46.5463	1.68730	0.843651	−	0.536891i	$-0.180401\pi$
$761$	46.5463	1.68730	0.843651	+	0.536891i	$0.180401\pi$
$762$	71.6225	2.59461
$763$	13.6827	0.495348
$764$	2.53369	0.0916659
$765$	1.64252	0.0593853
$766$	−46.9256	−1.69549
$767$	1.74148	0.0628811
$768$	−6.73838	−0.243150
$769$	51.5077	1.85742	0.928708	−	0.370812i	$-0.120920\pi$
$769$	51.5077	1.85742	0.928708	+	0.370812i	$0.120920\pi$
$770$	0	0
$771$	17.5063	0.630473
$772$	−0.767845	−0.0276353
$773$	29.1861	1.04975	0.524876	−	0.851179i	$-0.324112\pi$
$773$	29.1861	1.04975	0.524876	+	0.851179i	$0.324112\pi$
$774$	−10.9389	−0.393190
$775$	−6.05077	−0.217350
$776$	−17.9513	−0.644414
$777$	−1.24348	−0.0446094
$778$	−53.1141	−1.90423
$779$	−2.14275	−0.0767721
$780$	0.253518	0.00907741
$781$	0	0
$782$	−2.58333	−0.0923796
$783$	0.456202	0.0163033
$784$	−4.22491	−0.150890
$785$	7.69838	0.274767
$786$	54.7455	1.95271
$787$	2.30956	0.0823268	0.0411634	−	0.999152i	$-0.486894\pi$
$787$	2.30956	0.0823268	0.0411634	+	0.999152i	$0.486894\pi$
$788$	1.71923	0.0612451
$789$	39.5002	1.40624
$790$	22.8342	0.812406
$791$	5.45506	0.193960
$792$	0	0
$793$	−12.1503	−0.431470
$794$	−2.35525	−0.0835846
$795$	30.0135	1.06447
$796$	−2.14440	−0.0760064
$797$	29.0969	1.03067	0.515333	−	0.856990i	$-0.327668\pi$
$797$	29.0969	1.03067	0.515333	+	0.856990i	$0.327668\pi$
$798$	−0.753889	−0.0266874
$799$	1.20917	0.0427773
$800$	0.675706	0.0238898
$801$	−9.53261	−0.336818
$802$	−16.1312	−0.569612
$803$	0	0
$804$	−1.94571	−0.0686197
$805$	−2.75389	−0.0970619
$806$	−7.92645	−0.279197
$807$	60.3717	2.12519
$808$	32.0071	1.12600
$809$	−30.7537	−1.08124	−0.540621	−	0.841266i	$-0.681811\pi$
$809$	−30.7537	−1.08124	−0.540621	+	0.841266i	$0.681811\pi$
$810$	14.7761	0.519178
$811$	−25.8588	−0.908026	−0.454013	−	0.890995i	$-0.650008\pi$
$811$	−25.8588	−0.908026	−0.454013	+	0.890995i	$0.650008\pi$
$812$	−0.0513823	−0.00180316
$813$	−1.47019	−0.0515619
$814$	0	0
$815$	12.0792	0.423117
$816$	6.41265	0.224488
$817$	0.647898	0.0226671
$818$	13.5997	0.475501
$819$	2.29374	0.0801497
$820$	−1.16590	−0.0407150
$821$	40.6356	1.41819	0.709096	−	0.705112i	$-0.249103\pi$
$821$	40.6356	1.41819	0.709096	+	0.705112i	$0.249103\pi$
$822$	−10.3947	−0.362555
$823$	−1.29317	−0.0450769	−0.0225385	−	0.999746i	$-0.507175\pi$
$823$	−1.29317	−0.0450769	−0.0225385	+	0.999746i	$0.507175\pi$
$824$	36.5684	1.27392
$825$	0	0
$826$	−2.81777	−0.0980427
$827$	33.3613	1.16009	0.580043	−	0.814586i	$-0.303036\pi$
$827$	33.3613	1.16009	0.580043	+	0.814586i	$0.303036\pi$
$828$	0.839663	0.0291803
$829$	−36.5068	−1.26793	−0.633966	−	0.773361i	$-0.718574\pi$
$829$	−36.5068	−1.26793	−0.633966	+	0.773361i	$0.718574\pi$
$830$	−11.8477	−0.411240
$831$	−17.7505	−0.615756
$832$	−6.71787	−0.232900
$833$	0.644326	0.0223246
$834$	56.8968	1.97017
$835$	5.41433	0.187371
$836$	0	0
$837$	−6.42553	−0.222099
$838$	−36.9112	−1.27508
$839$	3.77010	0.130158	0.0650792	−	0.997880i	$-0.479270\pi$
$839$	3.77010	0.130158	0.0650792	+	0.997880i	$0.479270\pi$
$840$	6.44899	0.222511
$841$	−28.8154	−0.993636
$842$	28.6229	0.986410
$843$	11.2328	0.386879
$844$	−0.990710	−0.0341016
$845$	−12.1904	−0.419362
$846$	−6.96487	−0.239457
$847$	0	0
$848$	53.8292	1.84850
$849$	13.8343	0.474793
$850$	−0.938065	−0.0321754
$851$	−1.45368	−0.0498315
$852$	0.115028	0.00394080
$853$	17.6923	0.605774	0.302887	−	0.953026i	$-0.402050\pi$
$853$	17.6923	0.605774	0.302887	+	0.953026i	$0.402050\pi$
$854$	19.6596	0.672737
$855$	0.560362	0.0191640
$856$	19.2291	0.657237
$857$	16.3926	0.559961	0.279981	−	0.960006i	$-0.409672\pi$
$857$	16.3926	0.559961	0.279981	+	0.960006i	$0.409672\pi$
$858$	0	0
$859$	2.84010	0.0969028	0.0484514	−	0.998826i	$-0.484571\pi$
$859$	2.84010	0.0969028	0.0484514	+	0.998826i	$0.484571\pi$
$860$	0.352530	0.0120212
$861$	−22.9627	−0.782566
$862$	−49.6862	−1.69232
$863$	−2.81573	−0.0958484	−0.0479242	−	0.998851i	$-0.515261\pi$
$863$	−2.81573	−0.0958484	−0.0479242	+	0.998851i	$0.515261\pi$
$864$	0.717555	0.0244117
$865$	0.209776	0.00713261
$866$	−14.4651	−0.491543
$867$	39.0685	1.32684
$868$	0.723711	0.0245643
$869$	0	0
$870$	1.47334	0.0499508
$871$	−6.21366	−0.210542
$872$	−37.4584	−1.26850
$873$	−16.7157	−0.565740
$874$	−0.881331	−0.0298115
$875$	−1.00000	−0.0338062
$876$	−2.30610	−0.0779160
$877$	5.10432	0.172361	0.0861803	−	0.996280i	$-0.472534\pi$
$877$	5.10432	0.172361	0.0861803	+	0.996280i	$0.472534\pi$
$878$	−14.1807	−0.478577
$879$	−10.5105	−0.354512
$880$	0	0
$881$	−29.1705	−0.982778	−0.491389	−	0.870940i	$-0.663511\pi$
$881$	−29.1705	−0.982778	−0.491389	+	0.870940i	$0.663511\pi$
$882$	−3.71135	−0.124968
$883$	−37.8384	−1.27336	−0.636682	−	0.771126i	$-0.719694\pi$
$883$	−37.8384	−1.27336	−0.636682	+	0.771126i	$0.719694\pi$
$884$	−0.0693425	−0.00233224
$885$	4.55924	0.153257
$886$	43.0291	1.44559
$887$	−55.2277	−1.85436	−0.927182	−	0.374611i	$-0.877776\pi$
$887$	−55.2277	−1.85436	−0.927182	+	0.374611i	$0.877776\pi$
$888$	3.40419	0.114237
$889$	−20.8837	−0.700416
$890$	5.44422	0.182491
$891$	0	0
$892$	−2.70095	−0.0904345
$893$	0.412521	0.0138045
$894$	−4.23638	−0.141686
$895$	−15.2474	−0.509663
$896$	12.2212	0.408280
$897$	5.83716	0.194897
$898$	33.3532	1.11301
$899$	−2.59938	−0.0866943
$900$	0.304901	0.0101634
$901$	−8.20930	−0.273491
$902$	0	0
$903$	6.94315	0.231054
$904$	−14.9340	−0.496697
$905$	−25.6992	−0.854270
$906$	29.9350	0.994522
$907$	33.6101	1.11601	0.558003	−	0.829839i	$-0.311568\pi$
$907$	33.6101	1.11601	0.558003	+	0.829839i	$0.311568\pi$
$908$	−1.95886	−0.0650069
$909$	29.8039	0.988534
$910$	−1.30999	−0.0434257
$911$	6.10930	0.202410	0.101205	−	0.994866i	$-0.467730\pi$
$911$	6.10930	0.202410	0.101205	+	0.994866i	$0.467730\pi$
$912$	2.18775	0.0724436
$913$	0	0
$914$	51.6970	1.70999
$915$	−31.8099	−1.05160
$916$	−1.99574	−0.0659410
$917$	−15.9627	−0.527134
$918$	−0.996164	−0.0328783
$919$	−39.9157	−1.31670	−0.658348	−	0.752714i	$-0.728744\pi$
$919$	−39.9157	−1.31670	−0.658348	+	0.752714i	$0.728744\pi$
$920$	7.53916	0.248559
$921$	51.0426	1.68191
$922$	−16.0613	−0.528952
$923$	0.367345	0.0120913
$924$	0	0
$925$	−0.527864	−0.0173561
$926$	1.75661	0.0577257
$927$	34.0513	1.11839
$928$	0.290280	0.00952890
$929$	−11.3846	−0.373517	−0.186758	−	0.982406i	$-0.559798\pi$
$929$	−11.3846	−0.373517	−0.186758	+	0.982406i	$0.559798\pi$
$930$	−20.7517	−0.680475
$931$	0.219819	0.00720427
$932$	2.26613	0.0742296
$933$	20.5225	0.671878
$934$	−17.1857	−0.562335
$935$	0	0
$936$	−6.27943	−0.205250
$937$	−54.5073	−1.78068	−0.890338	−	0.455301i	$-0.849532\pi$
$937$	−54.5073	−1.78068	−0.890338	+	0.455301i	$0.849532\pi$
$938$	10.0539	0.328272
$939$	−52.5448	−1.71474
$940$	0.224458	0.00732101
$941$	−27.7248	−0.903803	−0.451901	−	0.892068i	$-0.649254\pi$
$941$	−27.7248	−0.903803	−0.451901	+	0.892068i	$0.649254\pi$
$942$	26.4023	0.860234
$943$	−26.8444	−0.874174
$944$	8.17701	0.266139
$945$	−1.06193	−0.0345447
$946$	0	0
$947$	20.0268	0.650784	0.325392	−	0.945579i	$-0.394504\pi$
$947$	20.0268	0.650784	0.325392	+	0.945579i	$0.394504\pi$
$948$	4.41904	0.143524
$949$	−7.36460	−0.239065
$950$	−0.320031	−0.0103832
$951$	59.8496	1.94076
$952$	−1.76393	−0.0571694
$953$	−29.4840	−0.955082	−0.477541	−	0.878610i	$-0.658472\pi$
$953$	−29.4840	−0.955082	−0.477541	+	0.878610i	$0.658472\pi$
$954$	47.2860	1.53094
$955$	21.1836	0.685486
$956$	−0.674310	−0.0218087
$957$	0	0
$958$	39.6870	1.28223
$959$	3.03087	0.0978719
$960$	−17.5876	−0.567638
$961$	5.61186	0.181028
$962$	−0.691496	−0.0222947
$963$	17.9055	0.576997
$964$	3.22493	0.103868
$965$	−6.41977	−0.206660
$966$	−9.44473	−0.303879
$967$	17.6179	0.566554	0.283277	−	0.959038i	$-0.408578\pi$
$967$	17.6179	0.566554	0.283277	+	0.959038i	$0.408578\pi$
$968$	0	0
$969$	−0.333646	−0.0107182
$970$	9.54657	0.306522
$971$	−28.5168	−0.915148	−0.457574	−	0.889172i	$-0.651282\pi$
$971$	−28.5168	−0.915148	−0.457574	+	0.889172i	$0.651282\pi$
$972$	2.47852	0.0794987
$973$	−16.5899	−0.531849
$974$	5.48180	0.175648
$975$	2.11961	0.0678817
$976$	−57.0511	−1.82616
$977$	55.5672	1.77775	0.888876	−	0.458148i	$-0.151487\pi$
$977$	55.5672	1.77775	0.888876	+	0.458148i	$0.151487\pi$
$978$	41.4269	1.32468
$979$	0	0
$980$	0.119606	0.00382068
$981$	−34.8801	−1.11363
$982$	−3.33233	−0.106339
$983$	−20.8499	−0.665008	−0.332504	−	0.943102i	$-0.607893\pi$
$983$	−20.8499	−0.665008	−0.332504	+	0.943102i	$0.607893\pi$
$984$	62.8636	2.00402
$985$	14.3741	0.457996
$986$	−0.402988	−0.0128338
$987$	4.42075	0.140714
$988$	−0.0236570	−0.000752628 0
$989$	8.11686	0.258101
$990$	0	0
$991$	5.85935	0.186128	0.0930642	−	0.995660i	$-0.470334\pi$
$991$	5.85935	0.186128	0.0930642	+	0.995660i	$0.470334\pi$
$992$	−4.08854	−0.129811
$993$	−24.3233	−0.771877
$994$	−0.594377	−0.0188525
$995$	−17.9288	−0.568383
$996$	−2.29285	−0.0726518
$997$	−28.1075	−0.890172	−0.445086	−	0.895488i	$-0.646827\pi$
$997$	−28.1075	−0.890172	−0.445086	+	0.895488i	$0.646827\pi$
$998$	−40.9099	−1.29498
$999$	−0.560557	−0.0177352

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.t.1.2		4
11.7	odd	10		385.2.n.c.71.2	✓	8
11.8	odd	10		385.2.n.c.141.2	yes	8
11.10	odd	2		4235.2.a.w.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.c.71.2	✓	8	11.7	odd	10
385.2.n.c.141.2	yes	8	11.8	odd	10
4235.2.a.t.1.2		4	1.1	even	1	trivial
4235.2.a.w.1.3		4	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.45589 q^{2} -2.35567 q^{3} +0.119606 q^{4} +1.00000 q^{5} +3.42960 q^{6} -1.00000 q^{7} +2.73764 q^{8} +2.54920 q^{9} +O(q^{10})\)	\(q-1.45589 q^{2} -2.35567 q^{3} +0.119606 q^{4} +1.00000 q^{5} +3.42960 q^{6} -1.00000 q^{7} +2.73764 q^{8} +2.54920 q^{9} -1.45589 q^{10} -0.281754 q^{12} -0.899788 q^{13} +1.45589 q^{14} -2.35567 q^{15} -4.22491 q^{16} +0.644326 q^{17} -3.71135 q^{18} +0.219819 q^{19} +0.119606 q^{20} +2.35567 q^{21} +2.75389 q^{23} -6.44899 q^{24} +1.00000 q^{25} +1.30999 q^{26} +1.06193 q^{27} -0.119606 q^{28} +0.429595 q^{29} +3.42960 q^{30} -6.05077 q^{31} +0.675706 q^{32} -0.938065 q^{34} -1.00000 q^{35} +0.304901 q^{36} -0.527864 q^{37} -0.320031 q^{38} +2.11961 q^{39} +2.73764 q^{40} -9.74782 q^{41} -3.42960 q^{42} +2.94742 q^{43} +2.54920 q^{45} -4.00935 q^{46} +1.87664 q^{47} +9.95250 q^{48} +1.00000 q^{49} -1.45589 q^{50} -1.51782 q^{51} -0.107620 q^{52} -12.7409 q^{53} -1.54606 q^{54} -2.73764 q^{56} -0.517822 q^{57} -0.625442 q^{58} -1.93543 q^{59} -0.281754 q^{60} +13.5035 q^{61} +8.80924 q^{62} -2.54920 q^{63} +7.46606 q^{64} -0.899788 q^{65} +6.90570 q^{67} +0.0770654 q^{68} -6.48727 q^{69} +1.45589 q^{70} -0.408258 q^{71} +6.97880 q^{72} +8.18482 q^{73} +0.768510 q^{74} -2.35567 q^{75} +0.0262917 q^{76} -3.08591 q^{78} -15.6841 q^{79} -4.22491 q^{80} -10.1492 q^{81} +14.1917 q^{82} +8.13780 q^{83} +0.281754 q^{84} +0.644326 q^{85} -4.29110 q^{86} -1.01199 q^{87} -3.73945 q^{89} -3.71135 q^{90} +0.899788 q^{91} +0.329383 q^{92} +14.2537 q^{93} -2.73218 q^{94} +0.219819 q^{95} -1.59174 q^{96} -6.55722 q^{97} -1.45589 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 3 q^{3} + 3 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} + 9 q^{8} - 3 q^{9}+O(q^{10}) \) 4 * q - q^2 - 3 * q^3 + 3 * q^4 + 4 * q^5 - 2 * q^6 - 4 * q^7 + 9 * q^8 - 3 * q^9	\( 4 q - q^{2} - 3 q^{3} + 3 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} + 9 q^{8} - 3 q^{9} - q^{10} - 4 q^{12} - 2 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 9 q^{17} - 2 q^{18} + 5 q^{19} + 3 q^{20} + 3 q^{21} - 4 q^{23} - 11 q^{24} + 4 q^{25} - 13 q^{26} + 3 q^{27} - 3 q^{28} - 14 q^{29} - 2 q^{30} - 18 q^{31} + 2 q^{32} - 5 q^{34} - 4 q^{35} + q^{36} - 20 q^{37} - 7 q^{38} + 11 q^{39} + 9 q^{40} - q^{41} + 2 q^{42} - 10 q^{43} - 3 q^{45} + 7 q^{46} + 9 q^{47} + 4 q^{49} - q^{50} - 11 q^{52} - 3 q^{53} + 21 q^{54} - 9 q^{56} + 4 q^{57} - 7 q^{58} + 6 q^{59} - 4 q^{60} + 29 q^{61} - 3 q^{62} + 3 q^{63} - 11 q^{64} - 2 q^{65} - 5 q^{67} + 5 q^{68} - 14 q^{69} + q^{70} - 17 q^{71} - q^{72} - 12 q^{73} - 5 q^{74} - 3 q^{75} + 11 q^{76} + 5 q^{78} + 2 q^{79} - 3 q^{80} - 8 q^{81} + 22 q^{82} - 10 q^{83} + 4 q^{84} + 9 q^{85} + 3 q^{86} + 4 q^{87} - 41 q^{89} - 2 q^{90} + 2 q^{91} - 16 q^{92} + 21 q^{93} + 32 q^{94} + 5 q^{95} + 9 q^{96} - 4 q^{97} - q^{98}+O(q^{100}) \) 4 * q - q^2 - 3 * q^3 + 3 * q^4 + 4 * q^5 - 2 * q^6 - 4 * q^7 + 9 * q^8 - 3 * q^9 - q^10 - 4 * q^12 - 2 * q^13 + q^14 - 3 * q^15 - 3 * q^16 + 9 * q^17 - 2 * q^18 + 5 * q^19 + 3 * q^20 + 3 * q^21 - 4 * q^23 - 11 * q^24 + 4 * q^25 - 13 * q^26 + 3 * q^27 - 3 * q^28 - 14 * q^29 - 2 * q^30 - 18 * q^31 + 2 * q^32 - 5 * q^34 - 4 * q^35 + q^36 - 20 * q^37 - 7 * q^38 + 11 * q^39 + 9 * q^40 - q^41 + 2 * q^42 - 10 * q^43 - 3 * q^45 + 7 * q^46 + 9 * q^47 + 4 * q^49 - q^50 - 11 * q^52 - 3 * q^53 + 21 * q^54 - 9 * q^56 + 4 * q^57 - 7 * q^58 + 6 * q^59 - 4 * q^60 + 29 * q^61 - 3 * q^62 + 3 * q^63 - 11 * q^64 - 2 * q^65 - 5 * q^67 + 5 * q^68 - 14 * q^69 + q^70 - 17 * q^71 - q^72 - 12 * q^73 - 5 * q^74 - 3 * q^75 + 11 * q^76 + 5 * q^78 + 2 * q^79 - 3 * q^80 - 8 * q^81 + 22 * q^82 - 10 * q^83 + 4 * q^84 + 9 * q^85 + 3 * q^86 + 4 * q^87 - 41 * q^89 - 2 * q^90 + 2 * q^91 - 16 * q^92 + 21 * q^93 + 32 * q^94 + 5 * q^95 + 9 * q^96 - 4 * q^97 - q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more