LMFDB - Embedded newform 4235.2.a.bj.1.3

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:	$10$
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			1.3
Root			$1.78795$ 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)

$f(q)$	$=$	$q-1.78795 q^{2} +0.315097 q^{3} +1.19678 q^{4} -1.00000 q^{5} -0.563380 q^{6} -1.00000 q^{7} +1.43612 q^{8} -2.90071 q^{9} +O(q^{10})$	\(q-1.78795 q^{2} +0.315097 q^{3} +1.19678 q^{4} -1.00000 q^{5} -0.563380 q^{6} -1.00000 q^{7} +1.43612 q^{8} -2.90071 q^{9} +1.78795 q^{10} +0.377102 q^{12} +0.918329 q^{13} +1.78795 q^{14} -0.315097 q^{15} -4.96128 q^{16} -2.10123 q^{17} +5.18634 q^{18} -1.48063 q^{19} -1.19678 q^{20} -0.315097 q^{21} +7.48177 q^{23} +0.452518 q^{24} +1.00000 q^{25} -1.64193 q^{26} -1.85930 q^{27} -1.19678 q^{28} -4.91413 q^{29} +0.563380 q^{30} +8.31153 q^{31} +5.99829 q^{32} +3.75690 q^{34} +1.00000 q^{35} -3.47151 q^{36} +2.36802 q^{37} +2.64731 q^{38} +0.289363 q^{39} -1.43612 q^{40} +0.211635 q^{41} +0.563380 q^{42} -1.18998 q^{43} +2.90071 q^{45} -13.3771 q^{46} -3.29122 q^{47} -1.56329 q^{48} +1.00000 q^{49} -1.78795 q^{50} -0.662091 q^{51} +1.09904 q^{52} +8.80435 q^{53} +3.32434 q^{54} -1.43612 q^{56} -0.466544 q^{57} +8.78624 q^{58} +0.639624 q^{59} -0.377102 q^{60} +3.61846 q^{61} -14.8606 q^{62} +2.90071 q^{63} -0.802113 q^{64} -0.918329 q^{65} +2.10256 q^{67} -2.51470 q^{68} +2.35749 q^{69} -1.78795 q^{70} -7.73556 q^{71} -4.16578 q^{72} -10.4138 q^{73} -4.23391 q^{74} +0.315097 q^{75} -1.77199 q^{76} -0.517368 q^{78} -13.5005 q^{79} +4.96128 q^{80} +8.11628 q^{81} -0.378394 q^{82} -2.69888 q^{83} -0.377102 q^{84} +2.10123 q^{85} +2.12762 q^{86} -1.54843 q^{87} +16.4716 q^{89} -5.18634 q^{90} -0.918329 q^{91} +8.95403 q^{92} +2.61894 q^{93} +5.88456 q^{94} +1.48063 q^{95} +1.89005 q^{96} -12.2952 q^{97} -1.78795 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.78795	−1.26427	−0.632137	−	0.774857i	$-0.717822\pi$
$2$	−1.78795	−1.26427	−0.632137	+	0.774857i	$0.717822\pi$
$3$	0.315097	0.181922	0.0909608	−	0.995854i	$-0.471006\pi$
$3$	0.315097	0.181922	0.0909608	+	0.995854i	$0.471006\pi$
$4$	1.19678	0.598389
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.563380	−0.229999
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.43612	0.507746
$9$	−2.90071	−0.966905
$10$	1.78795	0.565401
$11$	0	0
$11$	0	0
$12$	0.377102	0.108860
$13$	0.918329	0.254699	0.127349	−	0.991858i	$-0.459353\pi$
$13$	0.918329	0.254699	0.127349	+	0.991858i	$0.459353\pi$
$14$	1.78795	0.477851
$15$	−0.315097	−0.0813578
$16$	−4.96128	−1.24032
$17$	−2.10123	−0.509622	−0.254811	−	0.966991i	$-0.582013\pi$
$17$	−2.10123	−0.509622	−0.254811	+	0.966991i	$0.582013\pi$
$18$	5.18634	1.22243
$19$	−1.48063	−0.339681	−0.169840	−	0.985472i	$-0.554325\pi$
$19$	−1.48063	−0.339681	−0.169840	+	0.985472i	$0.554325\pi$
$20$	−1.19678	−0.267608
$21$	−0.315097	−0.0687599
$22$	0	0
$23$	7.48177	1.56006	0.780029	−	0.625744i	$-0.215204\pi$
$23$	7.48177	1.56006	0.780029	+	0.625744i	$0.215204\pi$
$24$	0.452518	0.0923699
$25$	1.00000	0.200000
$26$	−1.64193	−0.322009
$27$	−1.85930	−0.357822
$28$	−1.19678	−0.226170
$29$	−4.91413	−0.912531	−0.456265	−	0.889844i	$-0.650813\pi$
$29$	−4.91413	−0.912531	−0.456265	+	0.889844i	$0.650813\pi$
$30$	0.563380	0.102859
$31$	8.31153	1.49279	0.746397	−	0.665501i	$-0.231782\pi$
$31$	8.31153	1.49279	0.746397	+	0.665501i	$0.231782\pi$
$32$	5.99829	1.06036
$33$	0	0
$34$	3.75690	0.644302
$35$	1.00000	0.169031
$36$	−3.47151	−0.578586
$37$	2.36802	0.389300	0.194650	−	0.980873i	$-0.437643\pi$
$37$	2.36802	0.389300	0.194650	+	0.980873i	$0.437643\pi$
$38$	2.64731	0.429450
$39$	0.289363	0.0463352
$40$	−1.43612	−0.227071
$41$	0.211635	0.0330519	0.0165259	−	0.999863i	$-0.494739\pi$
$41$	0.211635	0.0330519	0.0165259	+	0.999863i	$0.494739\pi$
$42$	0.563380	0.0869314
$43$	−1.18998	−0.181470	−0.0907349	−	0.995875i	$-0.528922\pi$
$43$	−1.18998	−0.181470	−0.0907349	+	0.995875i	$0.528922\pi$
$44$	0	0
$45$	2.90071	0.432413
$46$	−13.3771	−1.97234
$47$	−3.29122	−0.480074	−0.240037	−	0.970764i	$-0.577160\pi$
$47$	−3.29122	−0.480074	−0.240037	+	0.970764i	$0.577160\pi$
$48$	−1.56329	−0.225641
$49$	1.00000	0.142857
$50$	−1.78795	−0.252855
$51$	−0.662091	−0.0927113
$52$	1.09904	0.152409
$53$	8.80435	1.20937	0.604685	−	0.796465i	$-0.293299\pi$
$53$	8.80435	1.20937	0.604685	+	0.796465i	$0.293299\pi$
$54$	3.32434	0.452386
$55$	0	0
$56$	−1.43612	−0.191910
$57$	−0.466544	−0.0617953
$58$	8.78624	1.15369
$59$	0.639624	0.0832719	0.0416360	−	0.999133i	$-0.486743\pi$
$59$	0.639624	0.0832719	0.0416360	+	0.999133i	$0.486743\pi$
$60$	−0.377102	−0.0486837
$61$	3.61846	0.463297	0.231648	−	0.972800i	$-0.425588\pi$
$61$	3.61846	0.463297	0.231648	+	0.972800i	$0.425588\pi$
$62$	−14.8606	−1.88730
$63$	2.90071	0.365456
$64$	−0.802113	−0.100264
$65$	−0.918329	−0.113905
$66$	0	0
$67$	2.10256	0.256869	0.128434	−	0.991718i	$-0.459005\pi$
$67$	2.10256	0.256869	0.128434	+	0.991718i	$0.459005\pi$
$68$	−2.51470	−0.304953
$69$	2.35749	0.283808
$70$	−1.78795	−0.213701
$71$	−7.73556	−0.918042	−0.459021	−	0.888425i	$-0.651800\pi$
$71$	−7.73556	−0.918042	−0.459021	+	0.888425i	$0.651800\pi$
$72$	−4.16578	−0.490942
$73$	−10.4138	−1.21885	−0.609423	−	0.792845i	$-0.708599\pi$
$73$	−10.4138	−1.21885	−0.609423	+	0.792845i	$0.708599\pi$
$74$	−4.23391	−0.492182
$75$	0.315097	0.0363843
$76$	−1.77199	−0.203261
$77$	0	0
$78$	−0.517368	−0.0585804
$79$	−13.5005	−1.51893	−0.759463	−	0.650550i	$-0.774538\pi$
$79$	−13.5005	−1.51893	−0.759463	+	0.650550i	$0.774538\pi$
$80$	4.96128	0.554688
$81$	8.11628	0.901809
$82$	−0.378394	−0.0417866
$83$	−2.69888	−0.296241	−0.148120	−	0.988969i	$-0.547322\pi$
$83$	−2.69888	−0.296241	−0.148120	+	0.988969i	$0.547322\pi$
$84$	−0.377102	−0.0411452
$85$	2.10123	0.227910
$86$	2.12762	0.229428
$87$	−1.54843	−0.166009
$88$	0	0
$89$	16.4716	1.74598	0.872992	−	0.487734i	$-0.162176\pi$
$89$	16.4716	1.74598	0.872992	+	0.487734i	$0.162176\pi$
$90$	−5.18634	−0.546688
$91$	−0.918329	−0.0962670
$92$	8.95403	0.933522
$93$	2.61894	0.271572
$94$	5.88456	0.606946
$95$	1.48063	0.151910
$96$	1.89005	0.192902
$97$	−12.2952	−1.24839	−0.624193	−	0.781270i	$-0.714572\pi$
$97$	−12.2952	−1.24839	−0.624193	+	0.781270i	$0.714572\pi$
$98$	−1.78795	−0.180611
$99$	0	0
$100$	1.19678	0.119678
$101$	8.58741	0.854479	0.427240	−	0.904138i	$-0.359486\pi$
$101$	8.58741	0.854479	0.427240	+	0.904138i	$0.359486\pi$
$102$	1.18379	0.117213
$103$	12.4950	1.23117	0.615586	−	0.788070i	$-0.288920\pi$
$103$	12.4950	1.23117	0.615586	+	0.788070i	$0.288920\pi$
$104$	1.31883	0.129322
$105$	0.315097	0.0307504
$106$	−15.7418	−1.52898
$107$	0.673328	0.0650931	0.0325465	−	0.999470i	$-0.489638\pi$
$107$	0.673328	0.0650931	0.0325465	+	0.999470i	$0.489638\pi$
$108$	−2.22517	−0.214117
$109$	4.70312	0.450478	0.225239	−	0.974304i	$-0.427684\pi$
$109$	4.70312	0.450478	0.225239	+	0.974304i	$0.427684\pi$
$110$	0	0
$111$	0.746156	0.0708220
$112$	4.96128	0.468797
$113$	−3.03659	−0.285658	−0.142829	−	0.989747i	$-0.545620\pi$
$113$	−3.03659	−0.285658	−0.142829	+	0.989747i	$0.545620\pi$
$114$	0.834160	0.0781262
$115$	−7.48177	−0.697679
$116$	−5.88113	−0.546049
$117$	−2.66381	−0.246269
$118$	−1.14362	−0.105279
$119$	2.10123	0.192619
$120$	−0.452518	−0.0413091
$121$	0	0
$122$	−6.46965	−0.585734
$123$	0.0666857	0.00601285
$124$	9.94706	0.893273
$125$	−1.00000	−0.0894427
$126$	−5.18634	−0.462036
$127$	−6.34073	−0.562649	−0.281325	−	0.959613i	$-0.590774\pi$
$127$	−6.34073	−0.562649	−0.281325	+	0.959613i	$0.590774\pi$
$128$	−10.5624	−0.933597
$129$	−0.374959	−0.0330133
$130$	1.64193	0.144007
$131$	−3.03000	−0.264732	−0.132366	−	0.991201i	$-0.542257\pi$
$131$	−3.03000	−0.264732	−0.132366	+	0.991201i	$0.542257\pi$
$132$	0	0
$133$	1.48063	0.128387
$134$	−3.75928	−0.324753
$135$	1.85930	0.160023
$136$	−3.01762	−0.258759
$137$	−15.2194	−1.30028	−0.650142	−	0.759813i	$-0.725290\pi$
$137$	−15.2194	−1.30028	−0.650142	+	0.759813i	$0.725290\pi$
$138$	−4.21508	−0.358811
$139$	−18.1117	−1.53621	−0.768106	−	0.640323i	$-0.778800\pi$
$139$	−18.1117	−1.53621	−0.768106	+	0.640323i	$0.778800\pi$
$140$	1.19678	0.101146
$141$	−1.03706	−0.0873359
$142$	13.8308	1.16066
$143$	0	0
$144$	14.3912	1.19927
$145$	4.91413	0.408096
$146$	18.6194	1.54095
$147$	0.315097	0.0259888
$148$	2.83399	0.232953
$149$	2.99034	0.244979	0.122489	−	0.992470i	$-0.460912\pi$
$149$	2.99034	0.244979	0.122489	+	0.992470i	$0.460912\pi$
$150$	−0.563380	−0.0459998
$151$	19.1345	1.55715	0.778573	−	0.627554i	$-0.215944\pi$
$151$	19.1345	1.55715	0.778573	+	0.627554i	$0.215944\pi$
$152$	−2.12637	−0.172472
$153$	6.09506	0.492756
$154$	0	0
$155$	−8.31153	−0.667598
$156$	0.346304	0.0277265
$157$	−15.4203	−1.23067	−0.615336	−	0.788265i	$-0.710980\pi$
$157$	−15.4203	−1.23067	−0.615336	+	0.788265i	$0.710980\pi$
$158$	24.1383	1.92034
$159$	2.77423	0.220011
$160$	−5.99829	−0.474207
$161$	−7.48177	−0.589646
$162$	−14.5115	−1.14013
$163$	−7.15127	−0.560131	−0.280065	−	0.959981i	$-0.590356\pi$
$163$	−7.15127	−0.560131	−0.280065	+	0.959981i	$0.590356\pi$
$164$	0.253281	0.0197779
$165$	0	0
$166$	4.82547	0.374529
$167$	9.40229	0.727571	0.363785	−	0.931483i	$-0.381484\pi$
$167$	9.40229	0.727571	0.363785	+	0.931483i	$0.381484\pi$
$168$	−0.452518	−0.0349126
$169$	−12.1567	−0.935129
$170$	−3.75690	−0.288141
$171$	4.29490	0.328439
$172$	−1.42414	−0.108590
$173$	−3.66870	−0.278926	−0.139463	−	0.990227i	$-0.544538\pi$
$173$	−3.66870	−0.278926	−0.139463	+	0.990227i	$0.544538\pi$
$174$	2.76852	0.209881
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	0.201544	0.0151490
$178$	−29.4504	−2.20740
$179$	5.99184	0.447851	0.223925	−	0.974606i	$-0.428113\pi$
$179$	5.99184	0.447851	0.223925	+	0.974606i	$0.428113\pi$
$180$	3.47151	0.258751
$181$	16.7601	1.24577	0.622885	−	0.782313i	$-0.285960\pi$
$181$	16.7601	1.24577	0.622885	+	0.782313i	$0.285960\pi$
$182$	1.64193	0.121708
$183$	1.14017	0.0842837
$184$	10.7447	0.792113
$185$	−2.36802	−0.174100
$186$	−4.68255	−0.343341
$187$	0	0
$188$	−3.93887	−0.287271
$189$	1.85930	0.135244
$190$	−2.64731	−0.192056
$191$	−17.5517	−1.27000	−0.634999	−	0.772513i	$-0.719000\pi$
$191$	−17.5517	−1.27000	−0.634999	+	0.772513i	$0.719000\pi$
$192$	−0.252744	−0.0182402
$193$	21.0546	1.51554	0.757770	−	0.652521i	$-0.226289\pi$
$193$	21.0546	1.51554	0.757770	+	0.652521i	$0.226289\pi$
$194$	21.9832	1.57830
$195$	−0.289363	−0.0207217
$196$	1.19678	0.0854842
$197$	3.19019	0.227292	0.113646	−	0.993521i	$-0.463747\pi$
$197$	3.19019	0.227292	0.113646	+	0.993521i	$0.463747\pi$
$198$	0	0
$199$	7.98869	0.566303	0.283152	−	0.959075i	$-0.408620\pi$
$199$	7.98869	0.566303	0.283152	+	0.959075i	$0.408620\pi$
$200$	1.43612	0.101549
$201$	0.662512	0.0467300
$202$	−15.3539	−1.08030
$203$	4.91413	0.344904
$204$	−0.792377	−0.0554775
$205$	−0.211635	−0.0147812
$206$	−22.3405	−1.55654
$207$	−21.7025	−1.50843
$208$	−4.55608	−0.315908
$209$	0	0
$210$	−0.563380	−0.0388769
$211$	−22.4597	−1.54619	−0.773093	−	0.634292i	$-0.781292\pi$
$211$	−22.4597	−1.54619	−0.773093	+	0.634292i	$0.781292\pi$
$212$	10.5369	0.723674
$213$	−2.43746	−0.167012
$214$	−1.20388	−0.0822955
$215$	1.18998	0.0811558
$216$	−2.67018	−0.181683
$217$	−8.31153	−0.564223
$218$	−8.40897	−0.569527
$219$	−3.28137	−0.221734
$220$	0	0
$221$	−1.92962	−0.129800
$222$	−1.33409	−0.0895385
$223$	−21.4117	−1.43383	−0.716917	−	0.697159i	$-0.754447\pi$
$223$	−21.4117	−1.43383	−0.716917	+	0.697159i	$0.754447\pi$
$224$	−5.99829	−0.400778
$225$	−2.90071	−0.193381
$226$	5.42928	0.361150
$227$	−28.0844	−1.86403	−0.932014	−	0.362422i	$-0.881950\pi$
$227$	−28.0844	−1.86403	−0.932014	+	0.362422i	$0.881950\pi$
$228$	−0.558350	−0.0369777
$229$	−10.1049	−0.667754	−0.333877	−	0.942617i	$-0.608357\pi$
$229$	−10.1049	−0.667754	−0.333877	+	0.942617i	$0.608357\pi$
$230$	13.3771	0.882057
$231$	0	0
$232$	−7.05729	−0.463334
$233$	−16.6261	−1.08922	−0.544608	−	0.838691i	$-0.683321\pi$
$233$	−16.6261	−1.08922	−0.544608	+	0.838691i	$0.683321\pi$
$234$	4.76277	0.311352
$235$	3.29122	0.214696
$236$	0.765488	0.0498290
$237$	−4.25398	−0.276326
$238$	−3.75690	−0.243523
$239$	−14.9409	−0.966444	−0.483222	−	0.875498i	$-0.660534\pi$
$239$	−14.9409	−0.966444	−0.483222	+	0.875498i	$0.660534\pi$
$240$	1.56329	0.100910
$241$	10.1514	0.653907	0.326953	−	0.945040i	$-0.393978\pi$
$241$	10.1514	0.653907	0.326953	+	0.945040i	$0.393978\pi$
$242$	0	0
$243$	8.13532	0.521881
$244$	4.33050	0.277232
$245$	−1.00000	−0.0638877
$246$	−0.119231	−0.00760189
$247$	−1.35971	−0.0865162
$248$	11.9364	0.757960
$249$	−0.850410	−0.0538926
$250$	1.78795	0.113080
$251$	1.92390	0.121436	0.0607179	−	0.998155i	$-0.480661\pi$
$251$	1.92390	0.121436	0.0607179	+	0.998155i	$0.480661\pi$
$252$	3.47151	0.218685
$253$	0	0
$254$	11.3369	0.711343
$255$	0.662091	0.0414618
$256$	20.4894	1.28059
$257$	23.2898	1.45278	0.726390	−	0.687283i	$-0.241197\pi$
$257$	23.2898	1.45278	0.726390	+	0.687283i	$0.241197\pi$
$258$	0.670409	0.0417378
$259$	−2.36802	−0.147141
$260$	−1.09904	−0.0681593
$261$	14.2545	0.882330
$262$	5.41750	0.334694
$263$	−6.68796	−0.412397	−0.206199	−	0.978510i	$-0.566109\pi$
$263$	−6.68796	−0.412397	−0.206199	+	0.978510i	$0.566109\pi$
$264$	0	0
$265$	−8.80435	−0.540847
$266$	−2.64731	−0.162317
$267$	5.19016	0.317632
$268$	2.51630	0.153708
$269$	8.27692	0.504653	0.252326	−	0.967642i	$-0.418804\pi$
$269$	8.27692	0.504653	0.252326	+	0.967642i	$0.418804\pi$
$270$	−3.32434	−0.202313
$271$	−6.36287	−0.386517	−0.193258	−	0.981148i	$-0.561906\pi$
$271$	−6.36287	−0.386517	−0.193258	+	0.981148i	$0.561906\pi$
$272$	10.4248	0.632095
$273$	−0.289363	−0.0175130
$274$	27.2116	1.64391
$275$	0	0
$276$	2.82139	0.169828
$277$	20.2172	1.21473	0.607366	−	0.794422i	$-0.292226\pi$
$277$	20.2172	1.21473	0.607366	+	0.794422i	$0.292226\pi$
$278$	32.3828	1.94219
$279$	−24.1094	−1.44339
$280$	1.43612	0.0858247
$281$	18.6914	1.11504	0.557518	−	0.830165i	$-0.311754\pi$
$281$	18.6914	1.11504	0.557518	+	0.830165i	$0.311754\pi$
$282$	1.85421	0.110417
$283$	−30.3536	−1.80433	−0.902167	−	0.431388i	$-0.858024\pi$
$283$	−30.3536	−1.80433	−0.902167	+	0.431388i	$0.858024\pi$
$284$	−9.25776	−0.549347
$285$	0.466544	0.0276357
$286$	0	0
$287$	−0.211635	−0.0124924
$288$	−17.3993	−1.02527
$289$	−12.5848	−0.740285
$290$	−8.78624	−0.515946
$291$	−3.87418	−0.227109
$292$	−12.4630	−0.729344
$293$	4.17105	0.243675	0.121838	−	0.992550i	$-0.461121\pi$
$293$	4.17105	0.243675	0.121838	+	0.992550i	$0.461121\pi$
$294$	−0.563380	−0.0328570
$295$	−0.639624	−0.0372403
$296$	3.40076	0.197665
$297$	0	0
$298$	−5.34660	−0.309720
$299$	6.87073	0.397344
$300$	0.377102	0.0217720
$301$	1.18998	0.0685891
$302$	−34.2117	−1.96866
$303$	2.70587	0.155448
$304$	7.34584	0.421313
$305$	−3.61846	−0.207193
$306$	−10.8977	−0.622979
$307$	−13.0645	−0.745630	−0.372815	−	0.927906i	$-0.621607\pi$
$307$	−13.0645	−0.745630	−0.372815	+	0.927906i	$0.621607\pi$
$308$	0	0
$309$	3.93715	0.223977
$310$	14.8606	0.844027
$311$	19.1029	1.08323	0.541614	−	0.840627i	$-0.317814\pi$
$311$	19.1029	1.08323	0.541614	+	0.840627i	$0.317814\pi$
$312$	0.415561	0.0235265
$313$	−5.78321	−0.326886	−0.163443	−	0.986553i	$-0.552260\pi$
$313$	−5.78321	−0.326886	−0.163443	+	0.986553i	$0.552260\pi$
$314$	27.5707	1.55591
$315$	−2.90071	−0.163437
$316$	−16.1571	−0.908910
$317$	−11.8045	−0.663009	−0.331504	−	0.943454i	$-0.607556\pi$
$317$	−11.8045	−0.663009	−0.331504	+	0.943454i	$0.607556\pi$
$318$	−4.96019	−0.278154
$319$	0	0
$320$	0.802113	0.0448395
$321$	0.212164	0.0118418
$322$	13.3771	0.745475
$323$	3.11115	0.173109
$324$	9.71339	0.539633
$325$	0.918329	0.0509397
$326$	12.7861	0.708159
$327$	1.48194	0.0819516
$328$	0.303934	0.0167820
$329$	3.29122	0.181451
$330$	0	0
$331$	−0.927740	−0.0509932	−0.0254966	−	0.999675i	$-0.508117\pi$
$331$	−0.927740	−0.0509932	−0.0254966	+	0.999675i	$0.508117\pi$
$332$	−3.22996	−0.177267
$333$	−6.86894	−0.376416
$334$	−16.8109	−0.919849
$335$	−2.10256	−0.114875
$336$	1.56329	0.0852842
$337$	−9.55990	−0.520761	−0.260380	−	0.965506i	$-0.583848\pi$
$337$	−9.55990	−0.520761	−0.260380	+	0.965506i	$0.583848\pi$
$338$	21.7356	1.18226
$339$	−0.956821	−0.0519674
$340$	2.51470	0.136379
$341$	0	0
$342$	−7.67908	−0.415237
$343$	−1.00000	−0.0539949
$344$	−1.70895	−0.0921405
$345$	−2.35749	−0.126923
$346$	6.55947	0.352639
$347$	−8.45057	−0.453651	−0.226825	−	0.973935i	$-0.572835\pi$
$347$	−8.45057	−0.453651	−0.226825	+	0.973935i	$0.572835\pi$
$348$	−1.85313	−0.0993381
$349$	−27.6041	−1.47761	−0.738807	−	0.673917i	$-0.764610\pi$
$349$	−27.6041	−1.47761	−0.738807	+	0.673917i	$0.764610\pi$
$350$	1.78795	0.0955702
$351$	−1.70745	−0.0911368
$352$	0	0
$353$	−20.9875	−1.11705	−0.558525	−	0.829488i	$-0.688632\pi$
$353$	−20.9875	−1.11705	−0.558525	+	0.829488i	$0.688632\pi$
$354$	−0.360351	−0.0191524
$355$	7.73556	0.410561
$356$	19.7128	1.04478
$357$	0.662091	0.0350416
$358$	−10.7131	−0.566206
$359$	35.1589	1.85562	0.927809	−	0.373056i	$-0.121690\pi$
$359$	35.1589	1.85562	0.927809	+	0.373056i	$0.121690\pi$
$360$	4.16578	0.219556
$361$	−16.8077	−0.884617
$362$	−29.9663	−1.57500
$363$	0	0
$364$	−1.09904	−0.0576052
$365$	10.4138	0.545084
$366$	−2.03857	−0.106558
$367$	6.07720	0.317227	0.158614	−	0.987341i	$-0.449298\pi$
$367$	6.07720	0.317227	0.158614	+	0.987341i	$0.449298\pi$
$368$	−37.1192	−1.93497
$369$	−0.613893	−0.0319580
$370$	4.23391	0.220110
$371$	−8.80435	−0.457099
$372$	3.13429	0.162506
$373$	−36.5490	−1.89244	−0.946218	−	0.323530i	$-0.895130\pi$
$373$	−36.5490	−1.89244	−0.946218	+	0.323530i	$0.895130\pi$
$374$	0	0
$375$	−0.315097	−0.0162716
$376$	−4.72660	−0.243756
$377$	−4.51279	−0.232420
$378$	−3.32434	−0.170986
$379$	12.6390	0.649224	0.324612	−	0.945847i	$-0.394766\pi$
$379$	12.6390	0.649224	0.324612	+	0.945847i	$0.394766\pi$
$380$	1.77199	0.0909013
$381$	−1.99795	−0.102358
$382$	31.3817	1.60563
$383$	−3.07147	−0.156945	−0.0784723	−	0.996916i	$-0.525004\pi$
$383$	−3.07147	−0.156945	−0.0784723	+	0.996916i	$0.525004\pi$
$384$	−3.32820	−0.169841
$385$	0	0
$386$	−37.6446	−1.91606
$387$	3.45178	0.175464
$388$	−14.7146	−0.747022
$389$	21.8103	1.10583	0.552913	−	0.833239i	$-0.313516\pi$
$389$	21.8103	1.10583	0.552913	+	0.833239i	$0.313516\pi$
$390$	0.517368	0.0261979
$391$	−15.7209	−0.795040
$392$	1.43612	0.0725351
$393$	−0.954745	−0.0481605
$394$	−5.70392	−0.287359
$395$	13.5005	0.679285
$396$	0	0
$397$	−21.2134	−1.06467	−0.532335	−	0.846534i	$-0.678685\pi$
$397$	−21.2134	−1.06467	−0.532335	+	0.846534i	$0.678685\pi$
$398$	−14.2834	−0.715963
$399$	0.466544	0.0233564
$400$	−4.96128	−0.248064
$401$	0.543215	0.0271269	0.0135634	−	0.999908i	$-0.495682\pi$
$401$	0.543215	0.0271269	0.0135634	+	0.999908i	$0.495682\pi$
$402$	−1.18454	−0.0590795
$403$	7.63271	0.380213
$404$	10.2772	0.511311
$405$	−8.11628	−0.403301
$406$	−8.78624	−0.436054
$407$	0	0
$408$	−0.950844	−0.0470738
$409$	−24.6331	−1.21803	−0.609014	−	0.793159i	$-0.708435\pi$
$409$	−24.6331	−1.21803	−0.609014	+	0.793159i	$0.708435\pi$
$410$	0.378394	0.0186876
$411$	−4.79560	−0.236550
$412$	14.9538	0.736720
$413$	−0.639624	−0.0314738
$414$	38.8030	1.90706
$415$	2.69888	0.132483
$416$	5.50840	0.270072
$417$	−5.70694	−0.279470
$418$	0	0
$419$	33.7352	1.64807	0.824036	−	0.566538i	$-0.191718\pi$
$419$	33.7352	1.64807	0.824036	+	0.566538i	$0.191718\pi$
$420$	0.377102	0.0184007
$421$	−37.9328	−1.84873	−0.924366	−	0.381508i	$-0.875405\pi$
$421$	−37.9328	−1.84873	−0.924366	+	0.381508i	$0.875405\pi$
$422$	40.1568	1.95480
$423$	9.54690	0.464186
$424$	12.6441	0.614053
$425$	−2.10123	−0.101924
$426$	4.35806	0.211149
$427$	−3.61846	−0.175110
$428$	0.805825	0.0389510
$429$	0	0
$430$	−2.12762	−0.102603
$431$	2.75951	0.132921	0.0664604	−	0.997789i	$-0.478829\pi$
$431$	2.75951	0.132921	0.0664604	+	0.997789i	$0.478829\pi$
$432$	9.22450	0.443814
$433$	−6.85539	−0.329449	−0.164724	−	0.986340i	$-0.552673\pi$
$433$	−6.85539	−0.329449	−0.164724	+	0.986340i	$0.552673\pi$
$434$	14.8606	0.713333
$435$	1.54843	0.0742415
$436$	5.62860	0.269561
$437$	−11.0778	−0.529922
$438$	5.86693	0.280333
$439$	−30.3391	−1.44801	−0.724004	−	0.689796i	$-0.757700\pi$
$439$	−30.3391	−1.44801	−0.724004	+	0.689796i	$0.757700\pi$
$440$	0	0
$441$	−2.90071	−0.138129
$442$	3.45007	0.164103
$443$	−6.31289	−0.299934	−0.149967	−	0.988691i	$-0.547917\pi$
$443$	−6.31289	−0.299934	−0.149967	+	0.988691i	$0.547917\pi$
$444$	0.892984	0.0423792
$445$	−16.4716	−0.780828
$446$	38.2831	1.81276
$447$	0.942250	0.0445669
$448$	0.802113	0.0378963
$449$	13.3253	0.628858	0.314429	−	0.949281i	$-0.398187\pi$
$449$	13.3253	0.628858	0.314429	+	0.949281i	$0.398187\pi$
$450$	5.18634	0.244487
$451$	0	0
$452$	−3.63413	−0.170935
$453$	6.02924	0.283279
$454$	50.2136	2.35664
$455$	0.918329	0.0430519
$456$	−0.670014	−0.0313763
$457$	−31.5147	−1.47420	−0.737099	−	0.675785i	$-0.763805\pi$
$457$	−31.5147	−1.47420	−0.737099	+	0.675785i	$0.763805\pi$
$458$	18.0672	0.844224
$459$	3.90681	0.182354
$460$	−8.95403	−0.417484
$461$	−20.9736	−0.976839	−0.488419	−	0.872609i	$-0.662426\pi$
$461$	−20.9736	−0.976839	−0.488419	+	0.872609i	$0.662426\pi$
$462$	0	0
$463$	2.38853	0.111005	0.0555023	−	0.998459i	$-0.482324\pi$
$463$	2.38853	0.111005	0.0555023	+	0.998459i	$0.482324\pi$
$464$	24.3804	1.13183
$465$	−2.61894	−0.121451
$466$	29.7268	1.37707
$467$	−29.2701	−1.35446	−0.677230	−	0.735772i	$-0.736820\pi$
$467$	−29.2701	−1.35446	−0.677230	+	0.735772i	$0.736820\pi$
$468$	−3.18799	−0.147365
$469$	−2.10256	−0.0970873
$470$	−5.88456	−0.271434
$471$	−4.85889	−0.223886
$472$	0.918578	0.0422810
$473$	0	0
$474$	7.60592	0.349351
$475$	−1.48063	−0.0679362
$476$	2.51470	0.115261
$477$	−25.5389	−1.16935
$478$	26.7136	1.22185
$479$	28.1414	1.28581	0.642906	−	0.765945i	$-0.277729\pi$
$479$	28.1414	1.28581	0.642906	+	0.765945i	$0.277729\pi$
$480$	−1.89005	−0.0862684
$481$	2.17462	0.0991541
$482$	−18.1502	−0.826717
$483$	−2.35749	−0.107269
$484$	0	0
$485$	12.2952	0.558296
$486$	−14.5456	−0.659801
$487$	−24.1566	−1.09464	−0.547320	−	0.836923i	$-0.684352\pi$
$487$	−24.1566	−1.09464	−0.547320	+	0.836923i	$0.684352\pi$
$488$	5.19656	0.235237
$489$	−2.25335	−0.101900
$490$	1.78795	0.0807715
$491$	4.56026	0.205801	0.102901	−	0.994692i	$-0.467188\pi$
$491$	4.56026	0.205801	0.102901	+	0.994692i	$0.467188\pi$
$492$	0.0798081	0.00359803
$493$	10.3257	0.465046
$494$	2.43110	0.109380
$495$	0	0
$496$	−41.2358	−1.85154
$497$	7.73556	0.346987
$498$	1.52049	0.0681350
$499$	−38.7695	−1.73556	−0.867780	−	0.496948i	$-0.834454\pi$
$499$	−38.7695	−1.73556	−0.867780	+	0.496948i	$0.834454\pi$
$500$	−1.19678	−0.0535216
$501$	2.96264	0.132361
$502$	−3.43985	−0.153528
$503$	−20.7525	−0.925306	−0.462653	−	0.886539i	$-0.653102\pi$
$503$	−20.7525	−0.925306	−0.462653	+	0.886539i	$0.653102\pi$
$504$	4.16578	0.185559
$505$	−8.58741	−0.382135
$506$	0	0
$507$	−3.83054	−0.170120
$508$	−7.58846	−0.336683
$509$	−7.95919	−0.352785	−0.176392	−	0.984320i	$-0.556443\pi$
$509$	−7.95919	−0.352785	−0.176392	+	0.984320i	$0.556443\pi$
$510$	−1.18379	−0.0524190
$511$	10.4138	0.460680
$512$	−15.5092	−0.685416
$513$	2.75294	0.121545
$514$	−41.6411	−1.83671
$515$	−12.4950	−0.550596
$516$	−0.448743	−0.0197548
$517$	0	0
$518$	4.23391	0.186027
$519$	−1.15600	−0.0507427
$520$	−1.31883	−0.0578346
$521$	−9.98053	−0.437255	−0.218627	−	0.975808i	$-0.570158\pi$
$521$	−9.98053	−0.437255	−0.218627	+	0.975808i	$0.570158\pi$
$522$	−25.4864	−1.11551
$523$	17.0472	0.745422	0.372711	−	0.927947i	$-0.378428\pi$
$523$	17.0472	0.745422	0.372711	+	0.927947i	$0.378428\pi$
$524$	−3.62624	−0.158413
$525$	−0.315097	−0.0137520
$526$	11.9578	0.521383
$527$	−17.4644	−0.760762
$528$	0	0
$529$	32.9769	1.43378
$530$	15.7418	0.683779
$531$	−1.85537	−0.0805160
$532$	1.77199	0.0768256
$533$	0.194351	0.00841826
$534$	−9.27976	−0.401574
$535$	−0.673328	−0.0291105
$536$	3.01953	0.130424
$537$	1.88801	0.0814737
$538$	−14.7987	−0.638019
$539$	0	0
$540$	2.22517	0.0957561
$541$	−28.0627	−1.20651	−0.603256	−	0.797548i	$-0.706130\pi$
$541$	−28.0627	−1.20651	−0.603256	+	0.797548i	$0.706130\pi$
$542$	11.3765	0.488663
$543$	5.28107	0.226633
$544$	−12.6038	−0.540382
$545$	−4.70312	−0.201460
$546$	0.517368	0.0221413
$547$	−30.4956	−1.30390	−0.651950	−	0.758262i	$-0.726049\pi$
$547$	−30.4956	−1.30390	−0.651950	+	0.758262i	$0.726049\pi$
$548$	−18.2143	−0.778076
$549$	−10.4961	−0.447964
$550$	0	0
$551$	7.27603	0.309969
$552$	3.38564	0.144102
$553$	13.5005	0.574100
$554$	−36.1474	−1.53575
$555$	−0.746156	−0.0316726
$556$	−21.6757	−0.919253
$557$	29.2525	1.23947	0.619734	−	0.784812i	$-0.287241\pi$
$557$	29.2525	1.23947	0.619734	+	0.784812i	$0.287241\pi$
$558$	43.1064	1.82484
$559$	−1.09279	−0.0462201
$560$	−4.96128	−0.209652
$561$	0	0
$562$	−33.4194	−1.40971
$563$	36.3643	1.53257	0.766287	−	0.642498i	$-0.222102\pi$
$563$	36.3643	1.53257	0.766287	+	0.642498i	$0.222102\pi$
$564$	−1.24113	−0.0522609
$565$	3.03659	0.127750
$566$	54.2708	2.28117
$567$	−8.11628	−0.340852
$568$	−11.1092	−0.466132
$569$	−10.4493	−0.438059	−0.219030	−	0.975718i	$-0.570289\pi$
$569$	−10.4493	−0.438059	−0.219030	+	0.975718i	$0.570289\pi$
$570$	−0.834160	−0.0349391
$571$	−8.73993	−0.365755	−0.182877	−	0.983136i	$-0.558541\pi$
$571$	−8.73993	−0.365755	−0.182877	+	0.983136i	$0.558541\pi$
$572$	0	0
$573$	−5.53050	−0.231040
$574$	0.378394	0.0157939
$575$	7.48177	0.312011
$576$	2.32670	0.0969459
$577$	9.32705	0.388290	0.194145	−	0.980973i	$-0.437807\pi$
$577$	9.32705	0.388290	0.194145	+	0.980973i	$0.437807\pi$
$578$	22.5011	0.935923
$579$	6.63424	0.275710
$580$	5.88113	0.244201
$581$	2.69888	0.111968
$582$	6.92686	0.287127
$583$	0	0
$584$	−14.9555	−0.618864
$585$	2.66381	0.110135
$586$	−7.45764	−0.308072
$587$	−47.2098	−1.94856	−0.974279	−	0.225347i	$-0.927648\pi$
$587$	−47.2098	−1.94856	−0.974279	+	0.225347i	$0.927648\pi$
$588$	0.377102	0.0155514
$589$	−12.3063	−0.507074
$590$	1.14362	0.0470820
$591$	1.00522	0.0413493
$592$	−11.7484	−0.482856
$593$	−35.6810	−1.46524	−0.732621	−	0.680637i	$-0.761703\pi$
$593$	−35.6810	−1.46524	−0.732621	+	0.680637i	$0.761703\pi$
$594$	0	0
$595$	−2.10123	−0.0861419
$596$	3.57878	0.146593
$597$	2.51722	0.103023
$598$	−12.2845	−0.502352
$599$	−44.7669	−1.82913	−0.914563	−	0.404442i	$-0.867466\pi$
$599$	−44.7669	−1.82913	−0.914563	+	0.404442i	$0.867466\pi$
$600$	0.452518	0.0184740
$601$	−3.86874	−0.157809	−0.0789046	−	0.996882i	$-0.525142\pi$
$601$	−3.86874	−0.157809	−0.0789046	+	0.996882i	$0.525142\pi$
$602$	−2.12762	−0.0867155
$603$	−6.09893	−0.248368
$604$	22.8998	0.931780
$605$	0	0
$606$	−4.83797	−0.196529
$607$	26.8218	1.08866	0.544332	−	0.838870i	$-0.316783\pi$
$607$	26.8218	1.08866	0.544332	+	0.838870i	$0.316783\pi$
$608$	−8.88128	−0.360183
$609$	1.54843	0.0627455
$610$	6.46965	0.261948
$611$	−3.02242	−0.122274
$612$	7.29444	0.294860
$613$	11.2197	0.453158	0.226579	−	0.973993i	$-0.427246\pi$
$613$	11.2197	0.453158	0.226579	+	0.973993i	$0.427246\pi$
$614$	23.3587	0.942681
$615$	−0.0666857	−0.00268903
$616$	0	0
$617$	−43.6299	−1.75648	−0.878238	−	0.478225i	$-0.841280\pi$
$617$	−43.6299	−1.75648	−0.878238	+	0.478225i	$0.841280\pi$
$618$	−7.03944	−0.283168
$619$	17.2057	0.691554	0.345777	−	0.938317i	$-0.387615\pi$
$619$	17.2057	0.691554	0.345777	+	0.938317i	$0.387615\pi$
$620$	−9.94706	−0.399484
$621$	−13.9109	−0.558224
$622$	−34.1552	−1.36950
$623$	−16.4716	−0.659920
$624$	−1.43561	−0.0574704
$625$	1.00000	0.0400000
$626$	10.3401	0.413274
$627$	0	0
$628$	−18.4547	−0.736421
$629$	−4.97574	−0.198396
$630$	5.18634	0.206629
$631$	1.97660	0.0786872	0.0393436	−	0.999226i	$-0.487473\pi$
$631$	1.97660	0.0786872	0.0393436	+	0.999226i	$0.487473\pi$
$632$	−19.3884	−0.771229
$633$	−7.07698	−0.281285
$634$	21.1060	0.838225
$635$	6.34073	0.251624
$636$	3.32014	0.131652
$637$	0.918329	0.0363855
$638$	0	0
$639$	22.4386	0.887659
$640$	10.5624	0.417517
$641$	−43.5408	−1.71976	−0.859878	−	0.510499i	$-0.829461\pi$
$641$	−43.5408	−1.71976	−0.859878	+	0.510499i	$0.829461\pi$
$642$	−0.379339	−0.0149713
$643$	41.5096	1.63698	0.818490	−	0.574520i	$-0.194811\pi$
$643$	41.5096	1.63698	0.818490	+	0.574520i	$0.194811\pi$
$644$	−8.95403	−0.352838
$645$	0.374959	0.0147640
$646$	−5.56259	−0.218857
$647$	18.8615	0.741524	0.370762	−	0.928728i	$-0.379097\pi$
$647$	18.8615	0.741524	0.370762	+	0.928728i	$0.379097\pi$
$648$	11.6560	0.457890
$649$	0	0
$650$	−1.64193	−0.0644018
$651$	−2.61894	−0.102644
$652$	−8.55849	−0.335177
$653$	10.8061	0.422877	0.211439	−	0.977391i	$-0.432185\pi$
$653$	10.8061	0.422877	0.211439	+	0.977391i	$0.432185\pi$
$654$	−2.64964	−0.103609
$655$	3.03000	0.118392
$656$	−1.04998	−0.0409949
$657$	30.2075	1.17851
$658$	−5.88456	−0.229404
$659$	42.5404	1.65714	0.828570	−	0.559886i	$-0.189155\pi$
$659$	42.5404	1.65714	0.828570	+	0.559886i	$0.189155\pi$
$660$	0	0
$661$	3.71322	0.144427	0.0722137	−	0.997389i	$-0.476994\pi$
$661$	3.71322	0.144427	0.0722137	+	0.997389i	$0.476994\pi$
$662$	1.65876	0.0644694
$663$	−0.608017	−0.0236134
$664$	−3.87592	−0.150415
$665$	−1.48063	−0.0574165
$666$	12.2814	0.475893
$667$	−36.7664	−1.42360
$668$	11.2525	0.435371
$669$	−6.74677	−0.260845
$670$	3.75928	0.145234
$671$	0	0
$672$	−1.89005	−0.0729101
$673$	−26.9699	−1.03961	−0.519806	−	0.854284i	$-0.673996\pi$
$673$	−26.9699	−1.03961	−0.519806	+	0.854284i	$0.673996\pi$
$674$	17.0927	0.658385
$675$	−1.85930	−0.0715645
$676$	−14.5489	−0.559571
$677$	3.26462	0.125470	0.0627348	−	0.998030i	$-0.480018\pi$
$677$	3.26462	0.125470	0.0627348	+	0.998030i	$0.480018\pi$
$678$	1.71075	0.0657010
$679$	12.2952	0.471846
$680$	3.01762	0.115720
$681$	−8.84933	−0.339107
$682$	0	0
$683$	9.27074	0.354735	0.177367	−	0.984145i	$-0.443242\pi$
$683$	9.27074	0.354735	0.177367	+	0.984145i	$0.443242\pi$
$684$	5.14004	0.196534
$685$	15.2194	0.581504
$686$	1.78795	0.0682644
$687$	−3.18404	−0.121479
$688$	5.90381	0.225081
$689$	8.08528	0.308025
$690$	4.21508	0.160465
$691$	−30.9029	−1.17560	−0.587802	−	0.809005i	$-0.700007\pi$
$691$	−30.9029	−1.17560	−0.587802	+	0.809005i	$0.700007\pi$
$692$	−4.39062	−0.166906
$693$	0	0
$694$	15.1092	0.573539
$695$	18.1117	0.687015
$696$	−2.22373	−0.0842904
$697$	−0.444694	−0.0168440
$698$	49.3549	1.86811
$699$	−5.23886	−0.198152
$700$	−1.19678	−0.0452340
$701$	−12.7277	−0.480717	−0.240359	−	0.970684i	$-0.577265\pi$
$701$	−12.7277	−0.480717	−0.240359	+	0.970684i	$0.577265\pi$
$702$	3.05284	0.115222
$703$	−3.50617	−0.132238
$704$	0	0
$705$	1.03706	0.0390578
$706$	37.5246	1.41226
$707$	−8.58741	−0.322963
$708$	0.241203	0.00906498
$709$	1.33317	0.0500683	0.0250341	−	0.999687i	$-0.492031\pi$
$709$	1.33317	0.0500683	0.0250341	+	0.999687i	$0.492031\pi$
$710$	−13.8308	−0.519062
$711$	39.1611	1.46866
$712$	23.6552	0.886516
$713$	62.1850	2.32885
$714$	−1.18379	−0.0443022
$715$	0	0
$716$	7.17090	0.267989
$717$	−4.70783	−0.175817
$718$	−62.8626	−2.34601
$719$	−3.93671	−0.146814	−0.0734072	−	0.997302i	$-0.523387\pi$
$719$	−3.93671	−0.146814	−0.0734072	+	0.997302i	$0.523387\pi$
$720$	−14.3912	−0.536330
$721$	−12.4950	−0.465339
$722$	30.0514	1.11840
$723$	3.19867	0.118960
$724$	20.0582	0.745456
$725$	−4.91413	−0.182506
$726$	0	0
$727$	−6.93696	−0.257278	−0.128639	−	0.991692i	$-0.541061\pi$
$727$	−6.93696	−0.257278	−0.128639	+	0.991692i	$0.541061\pi$
$728$	−1.31883	−0.0488792
$729$	−21.7854	−0.806867
$730$	−18.6194	−0.689136
$731$	2.50041	0.0924811
$732$	1.36453	0.0504345
$733$	37.9597	1.40207	0.701036	−	0.713126i	$-0.252721\pi$
$733$	37.9597	1.40207	0.701036	+	0.713126i	$0.252721\pi$
$734$	−10.8658	−0.401062
$735$	−0.315097	−0.0116225
$736$	44.8779	1.65422
$737$	0	0
$738$	1.09761	0.0404037
$739$	7.98080	0.293579	0.146789	−	0.989168i	$-0.453106\pi$
$739$	7.98080	0.293579	0.146789	+	0.989168i	$0.453106\pi$
$740$	−2.83399	−0.104180
$741$	−0.428441	−0.0157392
$742$	15.7418	0.577899
$743$	8.59700	0.315393	0.157697	−	0.987488i	$-0.449593\pi$
$743$	8.59700	0.315393	0.157697	+	0.987488i	$0.449593\pi$
$744$	3.76112	0.137889
$745$	−2.99034	−0.109558
$746$	65.3479	2.39256
$747$	7.82868	0.286436
$748$	0	0
$749$	−0.673328	−0.0246029
$750$	0.563380	0.0205717
$751$	5.68860	0.207580	0.103790	−	0.994599i	$-0.466903\pi$
$751$	5.68860	0.207580	0.103790	+	0.994599i	$0.466903\pi$
$752$	16.3287	0.595445
$753$	0.606217	0.0220918
$754$	8.06865	0.293843
$755$	−19.1345	−0.696377
$756$	2.22517	0.0809287
$757$	7.19618	0.261550	0.130775	−	0.991412i	$-0.458254\pi$
$757$	7.19618	0.261550	0.130775	+	0.991412i	$0.458254\pi$
$758$	−22.5980	−0.820797
$759$	0	0
$760$	2.12637	0.0771316
$761$	20.6373	0.748100	0.374050	−	0.927409i	$-0.377969\pi$
$761$	20.6373	0.748100	0.374050	+	0.927409i	$0.377969\pi$
$762$	3.57224	0.129409
$763$	−4.70312	−0.170265
$764$	−21.0055	−0.759954
$765$	−6.09506	−0.220367
$766$	5.49164	0.198421
$767$	0.587385	0.0212092
$768$	6.45615	0.232966
$769$	13.4597	0.485369	0.242684	−	0.970105i	$-0.421972\pi$
$769$	13.4597	0.485369	0.242684	+	0.970105i	$0.421972\pi$
$770$	0	0
$771$	7.33856	0.264292
$772$	25.1977	0.906884
$773$	−47.3411	−1.70274	−0.851370	−	0.524565i	$-0.824228\pi$
$773$	−47.3411	−1.70274	−0.851370	+	0.524565i	$0.824228\pi$
$774$	−6.17163	−0.221835
$775$	8.31153	0.298559
$776$	−17.6574	−0.633863
$777$	−0.746156	−0.0267682
$778$	−38.9958	−1.39807
$779$	−0.313355	−0.0112271
$780$	−0.346304	−0.0123997
$781$	0	0
$782$	28.1082	1.00515
$783$	9.13684	0.326524
$784$	−4.96128	−0.177189
$785$	15.4203	0.550373
$786$	1.70704	0.0608881
$787$	−51.6864	−1.84242	−0.921210	−	0.389065i	$-0.872798\pi$
$787$	−51.6864	−1.84242	−0.921210	+	0.389065i	$0.872798\pi$
$788$	3.81796	0.136009
$789$	−2.10736	−0.0750239
$790$	−24.1383	−0.858802
$791$	3.03659	0.107969
$792$	0	0
$793$	3.32294	0.118001
$794$	37.9286	1.34603
$795$	−2.77423	−0.0983917
$796$	9.56070	0.338870
$797$	29.6219	1.04926	0.524631	−	0.851330i	$-0.324203\pi$
$797$	29.6219	1.04926	0.524631	+	0.851330i	$0.324203\pi$
$798$	−0.834160	−0.0295289
$799$	6.91561	0.244657
$800$	5.99829	0.212072
$801$	−47.7794	−1.68820
$802$	−0.971244	−0.0342958
$803$	0	0
$804$	0.792880	0.0279627
$805$	7.48177	0.263698
$806$	−13.6469	−0.480693
$807$	2.60804	0.0918072
$808$	12.3326	0.433858
$809$	37.3162	1.31197	0.655983	−	0.754776i	$-0.272254\pi$
$809$	37.3162	1.31197	0.655983	+	0.754776i	$0.272254\pi$
$810$	14.5115	0.509883
$811$	35.9228	1.26142	0.630710	−	0.776019i	$-0.282764\pi$
$811$	35.9228	1.26142	0.630710	+	0.776019i	$0.282764\pi$
$812$	5.88113	0.206387
$813$	−2.00492	−0.0703158
$814$	0	0
$815$	7.15127	0.250498
$816$	3.28482	0.114992
$817$	1.76192	0.0616418
$818$	44.0428	1.53992
$819$	2.66381	0.0930810
$820$	−0.253281	−0.00884494
$821$	10.4371	0.364256	0.182128	−	0.983275i	$-0.441701\pi$
$821$	10.4371	0.364256	0.182128	+	0.983275i	$0.441701\pi$
$822$	8.57431	0.299064
$823$	−2.18573	−0.0761897	−0.0380949	−	0.999274i	$-0.512129\pi$
$823$	−2.18573	−0.0761897	−0.0380949	+	0.999274i	$0.512129\pi$
$824$	17.9444	0.625122
$825$	0	0
$826$	1.14362	0.0397915
$827$	15.6554	0.544393	0.272196	−	0.962242i	$-0.412250\pi$
$827$	15.6554	0.544393	0.272196	+	0.962242i	$0.412250\pi$
$828$	−25.9731	−0.902627
$829$	−42.7165	−1.48360	−0.741802	−	0.670618i	$-0.766029\pi$
$829$	−42.7165	−1.48360	−0.741802	+	0.670618i	$0.766029\pi$
$830$	−4.82547	−0.167495
$831$	6.37038	0.220986
$832$	−0.736603	−0.0255371
$833$	−2.10123	−0.0728032
$834$	10.2037	0.353327
$835$	−9.40229	−0.325380
$836$	0	0
$837$	−15.4536	−0.534155
$838$	−60.3169	−2.08361
$839$	45.3289	1.56493	0.782464	−	0.622695i	$-0.213962\pi$
$839$	45.3289	1.56493	0.782464	+	0.622695i	$0.213962\pi$
$840$	0.452518	0.0156134
$841$	−4.85133	−0.167287
$842$	67.8221	2.33730
$843$	5.88962	0.202849
$844$	−26.8793	−0.925222
$845$	12.1567	0.418202
$846$	−17.0694	−0.586858
$847$	0	0
$848$	−43.6808	−1.50001
$849$	−9.56434	−0.328247
$850$	3.75690	0.128860
$851$	17.7170	0.607330
$852$	−2.91710	−0.0999380
$853$	−10.8363	−0.371026	−0.185513	−	0.982642i	$-0.559395\pi$
$853$	−10.8363	−0.371026	−0.185513	+	0.982642i	$0.559395\pi$
$854$	6.46965	0.221387
$855$	−4.29490	−0.146882
$856$	0.966981	0.0330507
$857$	48.0540	1.64150	0.820748	−	0.571291i	$-0.193557\pi$
$857$	48.0540	1.64150	0.820748	+	0.571291i	$0.193557\pi$
$858$	0	0
$859$	9.79481	0.334195	0.167097	−	0.985940i	$-0.446561\pi$
$859$	9.79481	0.334195	0.167097	+	0.985940i	$0.446561\pi$
$860$	1.42414	0.0485628
$861$	−0.0666857	−0.00227264
$862$	−4.93387	−0.168048
$863$	−28.3613	−0.965429	−0.482715	−	0.875778i	$-0.660349\pi$
$863$	−28.3613	−0.965429	−0.482715	+	0.875778i	$0.660349\pi$
$864$	−11.1526	−0.379420
$865$	3.66870	0.124740
$866$	12.2571	0.416514
$867$	−3.96545	−0.134674
$868$	−9.94706	−0.337625
$869$	0	0
$870$	−2.76852	−0.0938617
$871$	1.93084	0.0654241
$872$	6.75426	0.228728
$873$	35.6648	1.20707
$874$	19.8065	0.669966
$875$	1.00000	0.0338062
$876$	−3.92707	−0.132683
$877$	26.4807	0.894191	0.447095	−	0.894486i	$-0.352458\pi$
$877$	26.4807	0.894191	0.447095	+	0.894486i	$0.352458\pi$
$878$	54.2450	1.83068
$879$	1.31429	0.0443298
$880$	0	0
$881$	26.2788	0.885355	0.442678	−	0.896681i	$-0.354029\pi$
$881$	26.2788	0.885355	0.442678	+	0.896681i	$0.354029\pi$
$882$	5.18634	0.174633
$883$	−1.82199	−0.0613148	−0.0306574	−	0.999530i	$-0.509760\pi$
$883$	−1.82199	−0.0613148	−0.0306574	+	0.999530i	$0.509760\pi$
$884$	−2.30932	−0.0776710
$885$	−0.201544	−0.00677482
$886$	11.2872	0.379199
$887$	−20.4113	−0.685343	−0.342672	−	0.939455i	$-0.611332\pi$
$887$	−20.4113	−0.685343	−0.342672	+	0.939455i	$0.611332\pi$
$888$	1.07157	0.0359596
$889$	6.34073	0.212661
$890$	29.4504	0.987181
$891$	0	0
$892$	−25.6251	−0.857991
$893$	4.87310	0.163072
$894$	−1.68470	−0.0563448
$895$	−5.99184	−0.200285
$896$	10.5624	0.352866
$897$	2.16495	0.0722855
$898$	−23.8250	−0.795049
$899$	−40.8439	−1.36222
$900$	−3.47151	−0.115717
$901$	−18.4999	−0.616322
$902$	0	0
$903$	0.374959	0.0124778
$904$	−4.36091	−0.145042
$905$	−16.7601	−0.557126
$906$	−10.7800	−0.358142
$907$	15.2706	0.507054	0.253527	−	0.967328i	$-0.418409\pi$
$907$	15.2706	0.507054	0.253527	+	0.967328i	$0.418409\pi$
$908$	−33.6108	−1.11542
$909$	−24.9096	−0.826200
$910$	−1.64193	−0.0544294
$911$	6.59784	0.218596	0.109298	−	0.994009i	$-0.465140\pi$
$911$	6.59784	0.218596	0.109298	+	0.994009i	$0.465140\pi$
$912$	2.31466	0.0766459
$913$	0	0
$914$	56.3469	1.86379
$915$	−1.14017	−0.0376928
$916$	−12.0934	−0.399577
$917$	3.03000	0.100059
$918$	−6.98520	−0.230546
$919$	3.48818	0.115065	0.0575323	−	0.998344i	$-0.481677\pi$
$919$	3.48818	0.115065	0.0575323	+	0.998344i	$0.481677\pi$
$920$	−10.7447	−0.354244
$921$	−4.11659	−0.135646
$922$	37.4999	1.23499
$923$	−7.10379	−0.233824
$924$	0	0
$925$	2.36802	0.0778599
$926$	−4.27059	−0.140340
$927$	−36.2445	−1.19043
$928$	−29.4764	−0.967610
$929$	55.9724	1.83640	0.918198	−	0.396122i	$-0.129644\pi$
$929$	55.9724	1.83640	0.918198	+	0.396122i	$0.129644\pi$
$930$	4.68255	0.153547
$931$	−1.48063	−0.0485258
$932$	−19.8978	−0.651775
$933$	6.01928	0.197063
$934$	52.3336	1.71241
$935$	0	0
$936$	−3.82555	−0.125042
$937$	−21.7799	−0.711517	−0.355759	−	0.934578i	$-0.615777\pi$
$937$	−21.7799	−0.711517	−0.355759	+	0.934578i	$0.615777\pi$
$938$	3.75928	0.122745
$939$	−1.82228	−0.0594677
$940$	3.93887	0.128472
$941$	−26.1584	−0.852740	−0.426370	−	0.904549i	$-0.640208\pi$
$941$	−26.1584	−0.852740	−0.426370	+	0.904549i	$0.640208\pi$
$942$	8.68747	0.283053
$943$	1.58341	0.0515628
$944$	−3.17335	−0.103284
$945$	−1.85930	−0.0604830
$946$	0	0
$947$	51.0785	1.65983	0.829914	−	0.557891i	$-0.188389\pi$
$947$	51.0785	1.65983	0.829914	+	0.557891i	$0.188389\pi$
$948$	−5.09107	−0.165350
$949$	−9.56331	−0.310438
$950$	2.64731	0.0858900
$951$	−3.71958	−0.120616
$952$	3.01762	0.0978016
$953$	−25.6253	−0.830085	−0.415042	−	0.909802i	$-0.636233\pi$
$953$	−25.6253	−0.830085	−0.415042	+	0.909802i	$0.636233\pi$
$954$	45.6624	1.47837
$955$	17.5517	0.567961
$956$	−17.8809	−0.578310
$957$	0	0
$958$	−50.3155	−1.62562
$959$	15.2194	0.491461
$960$	0.252744	0.00815727
$961$	38.0815	1.22844
$962$	−3.88812	−0.125358
$963$	−1.95313	−0.0629388
$964$	12.1489	0.391291
$965$	−21.0546	−0.677770
$966$	4.21508	0.135618
$967$	29.8751	0.960719	0.480360	−	0.877072i	$-0.340506\pi$
$967$	29.8751	0.960719	0.480360	+	0.877072i	$0.340506\pi$
$968$	0	0
$969$	0.980315	0.0314923
$970$	−21.9832	−0.705839
$971$	−23.4246	−0.751731	−0.375865	−	0.926674i	$-0.622654\pi$
$971$	−23.4246	−0.751731	−0.375865	+	0.926674i	$0.622654\pi$
$972$	9.73618	0.312288
$973$	18.1117	0.580633
$974$	43.1909	1.38393
$975$	0.289363	0.00926703
$976$	−17.9522	−0.574636
$977$	−9.94778	−0.318258	−0.159129	−	0.987258i	$-0.550869\pi$
$977$	−9.94778	−0.318258	−0.159129	+	0.987258i	$0.550869\pi$
$978$	4.02888	0.128829
$979$	0	0
$980$	−1.19678	−0.0382297
$981$	−13.6424	−0.435569
$982$	−8.15353	−0.260190
$983$	23.0926	0.736539	0.368269	−	0.929719i	$-0.379950\pi$
$983$	23.0926	0.736539	0.368269	+	0.929719i	$0.379950\pi$
$984$	0.0957689	0.00305300
$985$	−3.19019	−0.101648
$986$	−18.4619	−0.587946
$987$	1.03706	0.0330099
$988$	−1.62727	−0.0517704
$989$	−8.90314	−0.283103
$990$	0	0
$991$	44.9621	1.42827	0.714134	−	0.700009i	$-0.246821\pi$
$991$	44.9621	1.42827	0.714134	+	0.700009i	$0.246821\pi$
$992$	49.8550	1.58290
$993$	−0.292328	−0.00927676
$994$	−13.8308	−0.438687
$995$	−7.98869	−0.253258
$996$	−1.01775	−0.0322487
$997$	−43.1356	−1.36612	−0.683060	−	0.730363i	$-0.739351\pi$
$997$	−43.1356	−1.36612	−0.683060	+	0.730363i	$0.739351\pi$
$998$	69.3180	2.19422
$999$	−4.40286	−0.139300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bj.1.3	✓	10
11.10	odd	2		4235.2.a.bl.1.8	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.bj.1.3	✓	10	1.1	even	1	trivial
4235.2.a.bl.1.8	yes	10	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)

\(f(q)\)	\(=\)	\(q-1.78795 q^{2} +0.315097 q^{3} +1.19678 q^{4} -1.00000 q^{5} -0.563380 q^{6} -1.00000 q^{7} +1.43612 q^{8} -2.90071 q^{9} +O(q^{10})\)	\(q-1.78795 q^{2} +0.315097 q^{3} +1.19678 q^{4} -1.00000 q^{5} -0.563380 q^{6} -1.00000 q^{7} +1.43612 q^{8} -2.90071 q^{9} +1.78795 q^{10} +0.377102 q^{12} +0.918329 q^{13} +1.78795 q^{14} -0.315097 q^{15} -4.96128 q^{16} -2.10123 q^{17} +5.18634 q^{18} -1.48063 q^{19} -1.19678 q^{20} -0.315097 q^{21} +7.48177 q^{23} +0.452518 q^{24} +1.00000 q^{25} -1.64193 q^{26} -1.85930 q^{27} -1.19678 q^{28} -4.91413 q^{29} +0.563380 q^{30} +8.31153 q^{31} +5.99829 q^{32} +3.75690 q^{34} +1.00000 q^{35} -3.47151 q^{36} +2.36802 q^{37} +2.64731 q^{38} +0.289363 q^{39} -1.43612 q^{40} +0.211635 q^{41} +0.563380 q^{42} -1.18998 q^{43} +2.90071 q^{45} -13.3771 q^{46} -3.29122 q^{47} -1.56329 q^{48} +1.00000 q^{49} -1.78795 q^{50} -0.662091 q^{51} +1.09904 q^{52} +8.80435 q^{53} +3.32434 q^{54} -1.43612 q^{56} -0.466544 q^{57} +8.78624 q^{58} +0.639624 q^{59} -0.377102 q^{60} +3.61846 q^{61} -14.8606 q^{62} +2.90071 q^{63} -0.802113 q^{64} -0.918329 q^{65} +2.10256 q^{67} -2.51470 q^{68} +2.35749 q^{69} -1.78795 q^{70} -7.73556 q^{71} -4.16578 q^{72} -10.4138 q^{73} -4.23391 q^{74} +0.315097 q^{75} -1.77199 q^{76} -0.517368 q^{78} -13.5005 q^{79} +4.96128 q^{80} +8.11628 q^{81} -0.378394 q^{82} -2.69888 q^{83} -0.377102 q^{84} +2.10123 q^{85} +2.12762 q^{86} -1.54843 q^{87} +16.4716 q^{89} -5.18634 q^{90} -0.918329 q^{91} +8.95403 q^{92} +2.61894 q^{93} +5.88456 q^{94} +1.48063 q^{95} +1.89005 q^{96} -12.2952 q^{97} -1.78795 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 4 q^{3} + 12 q^{4} - 10 q^{5} - 10 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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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