LMFDB - Embedded newform 4235.2.a.be.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:	$0$
Dimension:	$5$
Coefficient field:	5.5.173513.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 3x^{2} + 3x - 1 $ x^5 - 2x^4 - 5x^3 + 3x^2 + 3x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.18986$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.686507 q^{2} +0.347661 q^{3} -1.52871 q^{4} -1.00000 q^{5} +0.238671 q^{6} -1.00000 q^{7} -2.42248 q^{8} -2.87913 q^{9} +O(q^{10})$	\(q+0.686507 q^{2} +0.347661 q^{3} -1.52871 q^{4} -1.00000 q^{5} +0.238671 q^{6} -1.00000 q^{7} -2.42248 q^{8} -2.87913 q^{9} -0.686507 q^{10} -0.531472 q^{12} +6.93189 q^{13} -0.686507 q^{14} -0.347661 q^{15} +1.39437 q^{16} -1.96001 q^{17} -1.97654 q^{18} -6.62306 q^{19} +1.52871 q^{20} -0.347661 q^{21} +0.784785 q^{23} -0.842202 q^{24} +1.00000 q^{25} +4.75879 q^{26} -2.04394 q^{27} +1.52871 q^{28} -7.86778 q^{29} -0.238671 q^{30} -0.764092 q^{31} +5.80221 q^{32} -1.34556 q^{34} +1.00000 q^{35} +4.40135 q^{36} +3.82290 q^{37} -4.54677 q^{38} +2.40994 q^{39} +2.42248 q^{40} +7.61257 q^{41} -0.238671 q^{42} -10.0009 q^{43} +2.87913 q^{45} +0.538760 q^{46} -10.7534 q^{47} +0.484766 q^{48} +1.00000 q^{49} +0.686507 q^{50} -0.681416 q^{51} -10.5968 q^{52} +6.15759 q^{53} -1.40318 q^{54} +2.42248 q^{56} -2.30258 q^{57} -5.40128 q^{58} +7.75135 q^{59} +0.531472 q^{60} +5.45060 q^{61} -0.524554 q^{62} +2.87913 q^{63} +1.19452 q^{64} -6.93189 q^{65} -5.70880 q^{67} +2.99628 q^{68} +0.272839 q^{69} +0.686507 q^{70} +4.77809 q^{71} +6.97465 q^{72} +11.6223 q^{73} +2.62445 q^{74} +0.347661 q^{75} +10.1247 q^{76} +1.65444 q^{78} +3.19473 q^{79} -1.39437 q^{80} +7.92680 q^{81} +5.22608 q^{82} +3.50736 q^{83} +0.531472 q^{84} +1.96001 q^{85} -6.86567 q^{86} -2.73532 q^{87} +5.50249 q^{89} +1.97654 q^{90} -6.93189 q^{91} -1.19971 q^{92} -0.265645 q^{93} -7.38228 q^{94} +6.62306 q^{95} +2.01720 q^{96} +11.5544 q^{97} +0.686507 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 5 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 5 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9	$ 5 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} + 11 q^{12} + 12 q^{13} - 2 q^{14} + 2 q^{15} + 2 q^{16} + 14 q^{17} + 7 q^{18} + 9 q^{19} - 4 q^{20} + 2 q^{21} + 17 q^{23} + 6 q^{24} + 5 q^{25} - 11 q^{26} - 11 q^{27} - 4 q^{28} + 3 q^{29} - 5 q^{30} + 2 q^{31} - 5 q^{32} + 16 q^{34} + 5 q^{35} - 15 q^{36} + 4 q^{37} - 11 q^{38} + 2 q^{39} + 6 q^{40} - 15 q^{41} - 5 q^{42} + 4 q^{43} - 3 q^{45} - 10 q^{46} - 2 q^{47} - 10 q^{48} + 5 q^{49} + 2 q^{50} - 18 q^{51} + 4 q^{52} + 6 q^{53} + 4 q^{54} + 6 q^{56} - 32 q^{58} - 6 q^{59} - 11 q^{60} + 20 q^{61} + 21 q^{62} - 3 q^{63} - 26 q^{64} - 12 q^{65} + 3 q^{67} + 5 q^{68} + 2 q^{70} - 6 q^{71} + 34 q^{72} + 11 q^{73} - 15 q^{74} - 2 q^{75} + 47 q^{76} + 31 q^{78} + 19 q^{79} - 2 q^{80} + 33 q^{81} + 8 q^{83} - 11 q^{84} - 14 q^{85} + 27 q^{86} - 30 q^{87} + q^{89} - 7 q^{90} - 12 q^{91} + 44 q^{92} + 3 q^{93} + 28 q^{94} - 9 q^{95} - 4 q^{96} - 7 q^{97} + 2 q^{98}+O(q^{100}) $ 5 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 5 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 + 11 * q^12 + 12 * q^13 - 2 * q^14 + 2 * q^15 + 2 * q^16 + 14 * q^17 + 7 * q^18 + 9 * q^19 - 4 * q^20 + 2 * q^21 + 17 * q^23 + 6 * q^24 + 5 * q^25 - 11 * q^26 - 11 * q^27 - 4 * q^28 + 3 * q^29 - 5 * q^30 + 2 * q^31 - 5 * q^32 + 16 * q^34 + 5 * q^35 - 15 * q^36 + 4 * q^37 - 11 * q^38 + 2 * q^39 + 6 * q^40 - 15 * q^41 - 5 * q^42 + 4 * q^43 - 3 * q^45 - 10 * q^46 - 2 * q^47 - 10 * q^48 + 5 * q^49 + 2 * q^50 - 18 * q^51 + 4 * q^52 + 6 * q^53 + 4 * q^54 + 6 * q^56 - 32 * q^58 - 6 * q^59 - 11 * q^60 + 20 * q^61 + 21 * q^62 - 3 * q^63 - 26 * q^64 - 12 * q^65 + 3 * q^67 + 5 * q^68 + 2 * q^70 - 6 * q^71 + 34 * q^72 + 11 * q^73 - 15 * q^74 - 2 * q^75 + 47 * q^76 + 31 * q^78 + 19 * q^79 - 2 * q^80 + 33 * q^81 + 8 * q^83 - 11 * q^84 - 14 * q^85 + 27 * q^86 - 30 * q^87 + q^89 - 7 * q^90 - 12 * q^91 + 44 * q^92 + 3 * q^93 + 28 * q^94 - 9 * q^95 - 4 * q^96 - 7 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.686507	0.485434	0.242717	−	0.970097i	$-0.421961\pi$
$2$	0.686507	0.485434	0.242717	+	0.970097i	$0.421961\pi$
$3$	0.347661	0.200722	0.100361	−	0.994951i	$-0.468000\pi$
$3$	0.347661	0.200722	0.100361	+	0.994951i	$0.468000\pi$
$4$	−1.52871	−0.764354
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.238671	0.0974372
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.42248	−0.856477
$9$	−2.87913	−0.959711
$10$	−0.686507	−0.217093
$11$	0	0
$11$	0	0
$12$	−0.531472	−0.153423
$13$	6.93189	1.92256	0.961280	−	0.275573i	$-0.0888677\pi$
$13$	6.93189	1.92256	0.961280	+	0.275573i	$0.0888677\pi$
$14$	−0.686507	−0.183477
$15$	−0.347661	−0.0897656
$16$	1.39437	0.348592
$17$	−1.96001	−0.475371	−0.237686	−	0.971342i	$-0.576389\pi$
$17$	−1.96001	−0.475371	−0.237686	+	0.971342i	$0.576389\pi$
$18$	−1.97654	−0.465876
$19$	−6.62306	−1.51943	−0.759717	−	0.650254i	$-0.774662\pi$
$19$	−6.62306	−1.51943	−0.759717	+	0.650254i	$0.774662\pi$
$20$	1.52871	0.341830
$21$	−0.347661	−0.0758658
$22$	0	0
$23$	0.784785	0.163639	0.0818195	−	0.996647i	$-0.473927\pi$
$23$	0.784785	0.163639	0.0818195	+	0.996647i	$0.473927\pi$
$24$	−0.842202	−0.171914
$25$	1.00000	0.200000
$26$	4.75879	0.933275
$27$	−2.04394	−0.393357
$28$	1.52871	0.288899
$29$	−7.86778	−1.46101	−0.730505	−	0.682907i	$-0.760715\pi$
$29$	−7.86778	−1.46101	−0.730505	+	0.682907i	$0.760715\pi$
$30$	−0.238671	−0.0435752
$31$	−0.764092	−0.137235	−0.0686175	−	0.997643i	$-0.521859\pi$
$31$	−0.764092	−0.137235	−0.0686175	+	0.997643i	$0.521859\pi$
$32$	5.80221	1.02569
$33$	0	0
$34$	−1.34556	−0.230761
$35$	1.00000	0.169031
$36$	4.40135	0.733559
$37$	3.82290	0.628481	0.314240	−	0.949343i	$-0.398250\pi$
$37$	3.82290	0.628481	0.314240	+	0.949343i	$0.398250\pi$
$38$	−4.54677	−0.737584
$39$	2.40994	0.385900
$40$	2.42248	0.383028
$41$	7.61257	1.18888	0.594442	−	0.804139i	$-0.297373\pi$
$41$	7.61257	1.18888	0.594442	+	0.804139i	$0.297373\pi$
$42$	−0.238671	−0.0368278
$43$	−10.0009	−1.52512	−0.762560	−	0.646917i	$-0.776058\pi$
$43$	−10.0009	−1.52512	−0.762560	+	0.646917i	$0.776058\pi$
$44$	0	0
$45$	2.87913	0.429196
$46$	0.538760	0.0794358
$47$	−10.7534	−1.56854	−0.784272	−	0.620417i	$-0.786963\pi$
$47$	−10.7534	−1.56854	−0.784272	+	0.620417i	$0.786963\pi$
$48$	0.484766	0.0699700
$49$	1.00000	0.142857
$50$	0.686507	0.0970867
$51$	−0.681416	−0.0954174
$52$	−10.5968	−1.46952
$53$	6.15759	0.845810	0.422905	−	0.906174i	$-0.361010\pi$
$53$	6.15759	0.845810	0.422905	+	0.906174i	$0.361010\pi$
$54$	−1.40318	−0.190949
$55$	0	0
$56$	2.42248	0.323718
$57$	−2.30258	−0.304984
$58$	−5.40128	−0.709223
$59$	7.75135	1.00914	0.504570	−	0.863371i	$-0.331651\pi$
$59$	7.75135	1.00914	0.504570	+	0.863371i	$0.331651\pi$
$60$	0.531472	0.0686127
$61$	5.45060	0.697878	0.348939	−	0.937146i	$-0.386542\pi$
$61$	5.45060	0.697878	0.348939	+	0.937146i	$0.386542\pi$
$62$	−0.524554	−0.0666185
$63$	2.87913	0.362737
$64$	1.19452	0.149315
$65$	−6.93189	−0.859795
$66$	0	0
$67$	−5.70880	−0.697440	−0.348720	−	0.937227i	$-0.613384\pi$
$67$	−5.70880	−0.697440	−0.348720	+	0.937227i	$0.613384\pi$
$68$	2.99628	0.363352
$69$	0.272839	0.0328459
$70$	0.686507	0.0820533
$71$	4.77809	0.567055	0.283528	−	0.958964i	$-0.408495\pi$
$71$	4.77809	0.567055	0.283528	+	0.958964i	$0.408495\pi$
$72$	6.97465	0.821970
$73$	11.6223	1.36029	0.680146	−	0.733077i	$-0.261916\pi$
$73$	11.6223	1.36029	0.680146	+	0.733077i	$0.261916\pi$
$74$	2.62445	0.305086
$75$	0.347661	0.0401444
$76$	10.1247	1.16139
$77$	0	0
$78$	1.65444	0.187329
$79$	3.19473	0.359435	0.179718	−	0.983718i	$-0.442482\pi$
$79$	3.19473	0.359435	0.179718	+	0.983718i	$0.442482\pi$
$80$	−1.39437	−0.155895
$81$	7.92680	0.880755
$82$	5.22608	0.577124
$83$	3.50736	0.384982	0.192491	−	0.981299i	$-0.438343\pi$
$83$	3.50736	0.384982	0.192491	+	0.981299i	$0.438343\pi$
$84$	0.531472	0.0579883
$85$	1.96001	0.212592
$86$	−6.86567	−0.740345
$87$	−2.73532	−0.293257
$88$	0	0
$89$	5.50249	0.583263	0.291631	−	0.956531i	$-0.405802\pi$
$89$	5.50249	0.583263	0.291631	+	0.956531i	$0.405802\pi$
$90$	1.97654	0.208346
$91$	−6.93189	−0.726659
$92$	−1.19971	−0.125078
$93$	−0.265645	−0.0275461
$94$	−7.38228	−0.761424
$95$	6.62306	0.679511
$96$	2.01720	0.205879
$97$	11.5544	1.17317	0.586587	−	0.809886i	$-0.300471\pi$
$97$	11.5544	1.17317	0.586587	+	0.809886i	$0.300471\pi$
$98$	0.686507	0.0693477
$99$	0	0
$100$	−1.52871	−0.152871
$101$	11.7895	1.17310	0.586548	−	0.809915i	$-0.300487\pi$
$101$	11.7895	1.17310	0.586548	+	0.809915i	$0.300487\pi$
$102$	−0.467797	−0.0463188
$103$	−4.40135	−0.433678	−0.216839	−	0.976207i	$-0.569575\pi$
$103$	−4.40135	−0.433678	−0.216839	+	0.976207i	$0.569575\pi$
$104$	−16.7924	−1.64663
$105$	0.347661	0.0339282
$106$	4.22723	0.410585
$107$	−5.43253	−0.525183	−0.262591	−	0.964907i	$-0.584577\pi$
$107$	−5.43253	−0.525183	−0.262591	+	0.964907i	$0.584577\pi$
$108$	3.12459	0.300664
$109$	15.0021	1.43694	0.718471	−	0.695557i	$-0.244842\pi$
$109$	15.0021	1.43694	0.718471	+	0.695557i	$0.244842\pi$
$110$	0	0
$111$	1.32907	0.126150
$112$	−1.39437	−0.131755
$113$	−11.1067	−1.04483	−0.522414	−	0.852692i	$-0.674968\pi$
$113$	−11.1067	−1.04483	−0.522414	+	0.852692i	$0.674968\pi$
$114$	−1.58073	−0.148049
$115$	−0.784785	−0.0731816
$116$	12.0275	1.11673
$117$	−19.9578	−1.84510
$118$	5.32135	0.489870
$119$	1.96001	0.179673
$120$	0.842202	0.0768821
$121$	0	0
$122$	3.74187	0.338773
$123$	2.64659	0.238635
$124$	1.16807	0.104896
$125$	−1.00000	−0.0894427
$126$	1.97654	0.176085
$127$	18.5364	1.64484	0.822418	−	0.568884i	$-0.192625\pi$
$127$	18.5364	1.64484	0.822418	+	0.568884i	$0.192625\pi$
$128$	−10.7844	−0.953212
$129$	−3.47691	−0.306125
$130$	−4.75879	−0.417373
$131$	16.3467	1.42822	0.714110	−	0.700034i	$-0.246832\pi$
$131$	16.3467	1.42822	0.714110	+	0.700034i	$0.246832\pi$
$132$	0	0
$133$	6.62306	0.574292
$134$	−3.91913	−0.338561
$135$	2.04394	0.175915
$136$	4.74808	0.407144
$137$	−5.63493	−0.481425	−0.240712	−	0.970596i	$-0.577381\pi$
$137$	−5.63493	−0.481425	−0.240712	+	0.970596i	$0.577381\pi$
$138$	0.187306	0.0159445
$139$	0.724551	0.0614557	0.0307278	−	0.999528i	$-0.490217\pi$
$139$	0.724551	0.0614557	0.0307278	+	0.999528i	$0.490217\pi$
$140$	−1.52871	−0.129199
$141$	−3.73853	−0.314841
$142$	3.28019	0.275268
$143$	0	0
$144$	−4.01456	−0.334547
$145$	7.86778	0.653383
$146$	7.97882	0.660332
$147$	0.347661	0.0286746
$148$	−5.84410	−0.480382
$149$	14.5961	1.19576	0.597881	−	0.801585i	$-0.296010\pi$
$149$	14.5961	1.19576	0.597881	+	0.801585i	$0.296010\pi$
$150$	0.238671	0.0194874
$151$	−13.6298	−1.10917	−0.554587	−	0.832126i	$-0.687124\pi$
$151$	−13.6298	−1.10917	−0.554587	+	0.832126i	$0.687124\pi$
$152$	16.0442	1.30136
$153$	5.64311	0.456219
$154$	0	0
$155$	0.764092	0.0613733
$156$	−3.68410	−0.294964
$157$	16.6716	1.33054	0.665269	−	0.746603i	$-0.268317\pi$
$157$	16.6716	1.33054	0.665269	+	0.746603i	$0.268317\pi$
$158$	2.19320	0.174482
$159$	2.14075	0.169773
$160$	−5.80221	−0.458705
$161$	−0.784785	−0.0618497
$162$	5.44180	0.427548
$163$	4.39756	0.344443	0.172222	−	0.985058i	$-0.444905\pi$
$163$	4.39756	0.344443	0.172222	+	0.985058i	$0.444905\pi$
$164$	−11.6374	−0.908728
$165$	0	0
$166$	2.40782	0.186883
$167$	9.16565	0.709259	0.354630	−	0.935007i	$-0.384607\pi$
$167$	9.16565	0.709259	0.354630	+	0.935007i	$0.384607\pi$
$168$	0.842202	0.0649773
$169$	35.0511	2.69624
$170$	1.34556	0.103199
$171$	19.0687	1.45822
$172$	15.2884	1.16573
$173$	−7.24312	−0.550684	−0.275342	−	0.961346i	$-0.588791\pi$
$173$	−7.24312	−0.550684	−0.275342	+	0.961346i	$0.588791\pi$
$174$	−1.87781	−0.142357
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	2.69484	0.202556
$178$	3.77750	0.283135
$179$	14.7251	1.10061	0.550304	−	0.834964i	$-0.314512\pi$
$179$	14.7251	1.10061	0.550304	+	0.834964i	$0.314512\pi$
$180$	−4.40135	−0.328058
$181$	4.64185	0.345026	0.172513	−	0.985007i	$-0.444811\pi$
$181$	4.64185	0.345026	0.172513	+	0.985007i	$0.444811\pi$
$182$	−4.75879	−0.352745
$183$	1.89496	0.140079
$184$	−1.90113	−0.140153
$185$	−3.82290	−0.281065
$186$	−0.182367	−0.0133718
$187$	0	0
$188$	16.4388	1.19892
$189$	2.04394	0.148675
$190$	4.54677	0.329858
$191$	−24.6025	−1.78018	−0.890088	−	0.455788i	$-0.849358\pi$
$191$	−24.6025	−1.78018	−0.890088	+	0.455788i	$0.849358\pi$
$192$	0.415288	0.0299708
$193$	4.32354	0.311216	0.155608	−	0.987819i	$-0.450266\pi$
$193$	4.32354	0.311216	0.155608	+	0.987819i	$0.450266\pi$
$194$	7.93219	0.569498
$195$	−2.40994	−0.172580
$196$	−1.52871	−0.109193
$197$	−8.69393	−0.619417	−0.309708	−	0.950832i	$-0.600231\pi$
$197$	−8.69393	−0.619417	−0.309708	+	0.950832i	$0.600231\pi$
$198$	0	0
$199$	4.04154	0.286497	0.143248	−	0.989687i	$-0.454245\pi$
$199$	4.04154	0.286497	0.143248	+	0.989687i	$0.454245\pi$
$200$	−2.42248	−0.171295
$201$	−1.98472	−0.139992
$202$	8.09355	0.569460
$203$	7.86778	0.552210
$204$	1.04169	0.0729327
$205$	−7.61257	−0.531685
$206$	−3.02156	−0.210522
$207$	−2.25950	−0.157046
$208$	9.66559	0.670188
$209$	0	0
$210$	0.238671	0.0164699
$211$	6.14639	0.423135	0.211568	−	0.977363i	$-0.432143\pi$
$211$	6.14639	0.423135	0.211568	+	0.977363i	$0.432143\pi$
$212$	−9.41316	−0.646499
$213$	1.66115	0.113820
$214$	−3.72947	−0.254941
$215$	10.0009	0.682055
$216$	4.95141	0.336901
$217$	0.764092	0.0518699
$218$	10.2991	0.697540
$219$	4.04063	0.273040
$220$	0	0
$221$	−13.5865	−0.913929
$222$	0.912417	0.0612374
$223$	−0.809255	−0.0541917	−0.0270959	−	0.999633i	$-0.508626\pi$
$223$	−0.809255	−0.0541917	−0.0270959	+	0.999633i	$0.508626\pi$
$224$	−5.80221	−0.387676
$225$	−2.87913	−0.191942
$226$	−7.62481	−0.507195
$227$	20.5303	1.36264	0.681322	−	0.731984i	$-0.261405\pi$
$227$	20.5303	1.36264	0.681322	+	0.731984i	$0.261405\pi$
$228$	3.51997	0.233115
$229$	−24.9573	−1.64922	−0.824611	−	0.565700i	$-0.808606\pi$
$229$	−24.9573	−1.64922	−0.824611	+	0.565700i	$0.808606\pi$
$230$	−0.538760	−0.0355248
$231$	0	0
$232$	19.0596	1.25132
$233$	5.66931	0.371409	0.185705	−	0.982606i	$-0.440543\pi$
$233$	5.66931	0.371409	0.185705	+	0.982606i	$0.440543\pi$
$234$	−13.7012	−0.895674
$235$	10.7534	0.701474
$236$	−11.8495	−0.771340
$237$	1.11068	0.0721465
$238$	1.34556	0.0872195
$239$	−28.3802	−1.83576	−0.917880	−	0.396857i	$-0.870101\pi$
$239$	−28.3802	−1.83576	−0.917880	+	0.396857i	$0.870101\pi$
$240$	−0.484766	−0.0312915
$241$	2.81378	0.181252	0.0906259	−	0.995885i	$-0.471113\pi$
$241$	2.81378	0.181252	0.0906259	+	0.995885i	$0.471113\pi$
$242$	0	0
$243$	8.88766	0.570144
$244$	−8.33238	−0.533426
$245$	−1.00000	−0.0638877
$246$	1.81690	0.115841
$247$	−45.9103	−2.92120
$248$	1.85100	0.117539
$249$	1.21937	0.0772744
$250$	−0.686507	−0.0434185
$251$	−17.6689	−1.11525	−0.557625	−	0.830093i	$-0.688287\pi$
$251$	−17.6689	−1.11525	−0.557625	+	0.830093i	$0.688287\pi$
$252$	−4.40135	−0.277259
$253$	0	0
$254$	12.7253	0.798458
$255$	0.681416	0.0426720
$256$	−9.79259	−0.612037
$257$	−10.2273	−0.637963	−0.318981	−	0.947761i	$-0.603341\pi$
$257$	−10.2273	−0.637963	−0.318981	+	0.947761i	$0.603341\pi$
$258$	−2.38692	−0.148603
$259$	−3.82290	−0.237543
$260$	10.5968	0.657188
$261$	22.6524	1.40215
$262$	11.2221	0.693306
$263$	17.1774	1.05920	0.529602	−	0.848246i	$-0.322341\pi$
$263$	17.1774	1.05920	0.529602	+	0.848246i	$0.322341\pi$
$264$	0	0
$265$	−6.15759	−0.378258
$266$	4.54677	0.278781
$267$	1.91300	0.117074
$268$	8.72708	0.533091
$269$	−0.321070	−0.0195760	−0.00978799	−	0.999952i	$-0.503116\pi$
$269$	−0.321070	−0.0195760	−0.00978799	+	0.999952i	$0.503116\pi$
$270$	1.40318	0.0853948
$271$	22.4824	1.36571	0.682854	−	0.730555i	$-0.260738\pi$
$271$	22.4824	1.36571	0.682854	+	0.730555i	$0.260738\pi$
$272$	−2.73296	−0.165710
$273$	−2.40994	−0.145856
$274$	−3.86842	−0.233700
$275$	0	0
$276$	−0.417091	−0.0251059
$277$	−9.83239	−0.590771	−0.295386	−	0.955378i	$-0.595448\pi$
$277$	−9.83239	−0.590771	−0.295386	+	0.955378i	$0.595448\pi$
$278$	0.497410	0.0298326
$279$	2.19992	0.131706
$280$	−2.42248	−0.144771
$281$	8.33492	0.497219	0.248610	−	0.968604i	$-0.420026\pi$
$281$	8.33492	0.497219	0.248610	+	0.968604i	$0.420026\pi$
$282$	−2.56653	−0.152835
$283$	20.7471	1.23329	0.616645	−	0.787242i	$-0.288492\pi$
$283$	20.7471	1.23329	0.616645	+	0.787242i	$0.288492\pi$
$284$	−7.30431	−0.433431
$285$	2.30258	0.136393
$286$	0	0
$287$	−7.61257	−0.449356
$288$	−16.7053	−0.984370
$289$	−13.1584	−0.774022
$290$	5.40128	0.317174
$291$	4.01702	0.235482
$292$	−17.7672	−1.03975
$293$	−26.8926	−1.57108	−0.785540	−	0.618810i	$-0.787615\pi$
$293$	−26.8926	−1.57108	−0.785540	+	0.618810i	$0.787615\pi$
$294$	0.238671	0.0139196
$295$	−7.75135	−0.451301
$296$	−9.26091	−0.538279
$297$	0	0
$298$	10.0203	0.580463
$299$	5.44004	0.314606
$300$	−0.531472	−0.0306845
$301$	10.0009	0.576441
$302$	−9.35693	−0.538431
$303$	4.09873	0.235466
$304$	−9.23496	−0.529662
$305$	−5.45060	−0.312100
$306$	3.87404	0.221464
$307$	0.949294	0.0541791	0.0270895	−	0.999633i	$-0.491376\pi$
$307$	0.949294	0.0541791	0.0270895	+	0.999633i	$0.491376\pi$
$308$	0	0
$309$	−1.53018	−0.0870487
$310$	0.524554	0.0297927
$311$	−31.8174	−1.80420	−0.902099	−	0.431530i	$-0.857974\pi$
$311$	−31.8174	−1.80420	−0.902099	+	0.431530i	$0.857974\pi$
$312$	−5.83805	−0.330514
$313$	12.2944	0.694921	0.347461	−	0.937695i	$-0.387044\pi$
$313$	12.2944	0.694921	0.347461	+	0.937695i	$0.387044\pi$
$314$	11.4452	0.645888
$315$	−2.87913	−0.162221
$316$	−4.88381	−0.274736
$317$	−11.8070	−0.663148	−0.331574	−	0.943429i	$-0.607580\pi$
$317$	−11.8070	−0.663148	−0.331574	+	0.943429i	$0.607580\pi$
$318$	1.46964	0.0824134
$319$	0	0
$320$	−1.19452	−0.0667758
$321$	−1.88868	−0.105416
$322$	−0.538760	−0.0300239
$323$	12.9812	0.722295
$324$	−12.1178	−0.673209
$325$	6.93189	0.384512
$326$	3.01895	0.167204
$327$	5.21565	0.288426
$328$	−18.4413	−1.01825
$329$	10.7534	0.592854
$330$	0	0
$331$	−31.3047	−1.72066	−0.860331	−	0.509736i	$-0.829743\pi$
$331$	−31.3047	−1.72066	−0.860331	+	0.509736i	$0.829743\pi$
$332$	−5.36172	−0.294263
$333$	−11.0066	−0.603160
$334$	6.29228	0.344298
$335$	5.70880	0.311905
$336$	−0.484766	−0.0264462
$337$	14.1641	0.771570	0.385785	−	0.922589i	$-0.373931\pi$
$337$	14.1641	0.771570	0.385785	+	0.922589i	$0.373931\pi$
$338$	24.0628	1.30884
$339$	−3.86135	−0.209720
$340$	−2.99628	−0.162496
$341$	0	0
$342$	13.0908	0.707867
$343$	−1.00000	−0.0539949
$344$	24.2270	1.30623
$345$	−0.272839	−0.0146891
$346$	−4.97245	−0.267321
$347$	−10.9391	−0.587242	−0.293621	−	0.955922i	$-0.594860\pi$
$347$	−10.9391	−0.587242	−0.293621	+	0.955922i	$0.594860\pi$
$348$	4.18150	0.224152
$349$	3.63142	0.194385	0.0971927	−	0.995266i	$-0.469014\pi$
$349$	3.63142	0.194385	0.0971927	+	0.995266i	$0.469014\pi$
$350$	−0.686507	−0.0366953
$351$	−14.1684	−0.756252
$352$	0	0
$353$	0.0881447	0.00469147	0.00234573	−	0.999997i	$-0.499253\pi$
$353$	0.0881447	0.00469147	0.00234573	+	0.999997i	$0.499253\pi$
$354$	1.85002	0.0983277
$355$	−4.77809	−0.253595
$356$	−8.41170	−0.445819
$357$	0.681416	0.0360644
$358$	10.1089	0.534272
$359$	23.3127	1.23040	0.615198	−	0.788372i	$-0.289076\pi$
$359$	23.3127	1.23040	0.615198	+	0.788372i	$0.289076\pi$
$360$	−6.97465	−0.367596
$361$	24.8649	1.30868
$362$	3.18666	0.167487
$363$	0	0
$364$	10.5968	0.555425
$365$	−11.6223	−0.608341
$366$	1.30090	0.0679992
$367$	−31.5373	−1.64624	−0.823118	−	0.567871i	$-0.807767\pi$
$367$	−31.5373	−1.64624	−0.823118	+	0.567871i	$0.807767\pi$
$368$	1.09428	0.0570431
$369$	−21.9176	−1.14098
$370$	−2.62445	−0.136438
$371$	−6.15759	−0.319686
$372$	0.406093	0.0210549
$373$	21.1123	1.09315	0.546576	−	0.837409i	$-0.315931\pi$
$373$	21.1123	1.09315	0.546576	+	0.837409i	$0.315931\pi$
$374$	0	0
$375$	−0.347661	−0.0179531
$376$	26.0499	1.34342
$377$	−54.5386	−2.80888
$378$	1.40318	0.0721718
$379$	−14.7915	−0.759789	−0.379894	−	0.925030i	$-0.624040\pi$
$379$	−14.7915	−0.759789	−0.379894	+	0.925030i	$0.624040\pi$
$380$	−10.1247	−0.519387
$381$	6.44436	0.330155
$382$	−16.8898	−0.864158
$383$	4.39482	0.224565	0.112282	−	0.993676i	$-0.464184\pi$
$383$	4.39482	0.224565	0.112282	+	0.993676i	$0.464184\pi$
$384$	−3.74930	−0.191331
$385$	0	0
$386$	2.96814	0.151075
$387$	28.7939	1.46367
$388$	−17.6633	−0.896720
$389$	12.7478	0.646341	0.323170	−	0.946341i	$-0.395251\pi$
$389$	12.7478	0.646341	0.323170	+	0.946341i	$0.395251\pi$
$390$	−1.65444	−0.0837760
$391$	−1.53818	−0.0777892
$392$	−2.42248	−0.122354
$393$	5.68311	0.286675
$394$	−5.96844	−0.300686
$395$	−3.19473	−0.160744
$396$	0	0
$397$	−24.4701	−1.22812	−0.614060	−	0.789259i	$-0.710465\pi$
$397$	−24.4701	−1.22812	−0.614060	+	0.789259i	$0.710465\pi$
$398$	2.77454	0.139075
$399$	2.30258	0.115273
$400$	1.39437	0.0697183
$401$	17.8417	0.890972	0.445486	−	0.895289i	$-0.353031\pi$
$401$	17.8417	0.890972	0.445486	+	0.895289i	$0.353031\pi$
$402$	−1.36253	−0.0679566
$403$	−5.29660	−0.263842
$404$	−18.0226	−0.896660
$405$	−7.92680	−0.393886
$406$	5.40128	0.268061
$407$	0	0
$408$	1.65072	0.0817228
$409$	−31.6080	−1.56291	−0.781457	−	0.623959i	$-0.785523\pi$
$409$	−31.6080	−1.56291	−0.781457	+	0.623959i	$0.785523\pi$
$410$	−5.22608	−0.258098
$411$	−1.95904	−0.0966325
$412$	6.72839	0.331484
$413$	−7.75135	−0.381419
$414$	−1.55116	−0.0762354
$415$	−3.50736	−0.172169
$416$	40.2203	1.97196
$417$	0.251898	0.0123355
$418$	0	0
$419$	18.8692	0.921820	0.460910	−	0.887447i	$-0.347523\pi$
$419$	18.8692	0.921820	0.460910	+	0.887447i	$0.347523\pi$
$420$	−0.531472	−0.0259332
$421$	27.6839	1.34923	0.674616	−	0.738169i	$-0.264309\pi$
$421$	27.6839	1.34923	0.674616	+	0.738169i	$0.264309\pi$
$422$	4.21954	0.205404
$423$	30.9605	1.50535
$424$	−14.9167	−0.724417
$425$	−1.96001	−0.0950742
$426$	1.14039	0.0552522
$427$	−5.45060	−0.263773
$428$	8.30476	0.401426
$429$	0	0
$430$	6.86567	0.331092
$431$	12.7060	0.612025	0.306013	−	0.952027i	$-0.401005\pi$
$431$	12.7060	0.612025	0.306013	+	0.952027i	$0.401005\pi$
$432$	−2.85000	−0.137121
$433$	−11.9990	−0.576634	−0.288317	−	0.957535i	$-0.593096\pi$
$433$	−11.9990	−0.576634	−0.288317	+	0.957535i	$0.593096\pi$
$434$	0.524554	0.0251794
$435$	2.73532	0.131148
$436$	−22.9339	−1.09833
$437$	−5.19767	−0.248638
$438$	2.77392	0.132543
$439$	11.9673	0.571167	0.285583	−	0.958354i	$-0.407813\pi$
$439$	11.9673	0.571167	0.285583	+	0.958354i	$0.407813\pi$
$440$	0	0
$441$	−2.87913	−0.137102
$442$	−9.32725	−0.443652
$443$	1.33944	0.0636385	0.0318193	−	0.999494i	$-0.489870\pi$
$443$	1.33944	0.0636385	0.0318193	+	0.999494i	$0.489870\pi$
$444$	−2.03176	−0.0964232
$445$	−5.50249	−0.260843
$446$	−0.555559	−0.0263065
$447$	5.07450	0.240015
$448$	−1.19452	−0.0564359
$449$	38.2241	1.80390	0.901952	−	0.431836i	$-0.142134\pi$
$449$	38.2241	1.80390	0.901952	+	0.431836i	$0.142134\pi$
$450$	−1.97654	−0.0931752
$451$	0	0
$452$	16.9789	0.798619
$453$	−4.73853	−0.222636
$454$	14.0942	0.661473
$455$	6.93189	0.324972
$456$	5.57795	0.261211
$457$	34.9281	1.63387	0.816933	−	0.576733i	$-0.195673\pi$
$457$	34.9281	1.63387	0.816933	+	0.576733i	$0.195673\pi$
$458$	−17.1333	−0.800588
$459$	4.00614	0.186990
$460$	1.19971	0.0559366
$461$	−39.7510	−1.85139	−0.925695	−	0.378271i	$-0.876519\pi$
$461$	−39.7510	−1.85139	−0.925695	+	0.378271i	$0.876519\pi$
$462$	0	0
$463$	−37.4127	−1.73871	−0.869357	−	0.494185i	$-0.835466\pi$
$463$	−37.4127	−1.73871	−0.869357	+	0.494185i	$0.835466\pi$
$464$	−10.9706	−0.509296
$465$	0.265645	0.0123190
$466$	3.89202	0.180294
$467$	−16.7157	−0.773511	−0.386755	−	0.922182i	$-0.626404\pi$
$467$	−16.7157	−0.773511	−0.386755	+	0.922182i	$0.626404\pi$
$468$	30.5097	1.41031
$469$	5.70880	0.263608
$470$	7.38228	0.340519
$471$	5.79606	0.267068
$472$	−18.7775	−0.864305
$473$	0	0
$474$	0.762490	0.0350223
$475$	−6.62306	−0.303887
$476$	−2.99628	−0.137334
$477$	−17.7285	−0.811733
$478$	−19.4832	−0.891140
$479$	−2.62221	−0.119812	−0.0599059	−	0.998204i	$-0.519080\pi$
$479$	−2.62221	−0.119812	−0.0599059	+	0.998204i	$0.519080\pi$
$480$	−2.01720	−0.0920721
$481$	26.4999	1.20829
$482$	1.93168	0.0879857
$483$	−0.272839	−0.0124146
$484$	0	0
$485$	−11.5544	−0.524659
$486$	6.10144	0.276767
$487$	24.2244	1.09771	0.548857	−	0.835916i	$-0.315063\pi$
$487$	24.2244	1.09771	0.548857	+	0.835916i	$0.315063\pi$
$488$	−13.2040	−0.597716
$489$	1.52886	0.0691373
$490$	−0.686507	−0.0310132
$491$	−9.61841	−0.434073	−0.217036	−	0.976164i	$-0.569639\pi$
$491$	−9.61841	−0.434073	−0.217036	+	0.976164i	$0.569639\pi$
$492$	−4.04586	−0.182402
$493$	15.4209	0.694522
$494$	−31.5177	−1.41805
$495$	0	0
$496$	−1.06542	−0.0478389
$497$	−4.77809	−0.214327
$498$	0.837105	0.0375116
$499$	35.3936	1.58443	0.792217	−	0.610239i	$-0.208927\pi$
$499$	35.3936	1.58443	0.792217	+	0.610239i	$0.208927\pi$
$500$	1.52871	0.0683659
$501$	3.18654	0.142364
$502$	−12.1298	−0.541380
$503$	1.76125	0.0785303	0.0392651	−	0.999229i	$-0.487498\pi$
$503$	1.76125	0.0785303	0.0392651	+	0.999229i	$0.487498\pi$
$504$	−6.97465	−0.310675
$505$	−11.7895	−0.524624
$506$	0	0
$507$	12.1859	0.541194
$508$	−28.3367	−1.25724
$509$	18.0742	0.801127	0.400563	−	0.916269i	$-0.368814\pi$
$509$	18.0742	0.801127	0.400563	+	0.916269i	$0.368814\pi$
$510$	0.467797	0.0207144
$511$	−11.6223	−0.514142
$512$	14.8461	0.656109
$513$	13.5371	0.597679
$514$	−7.02112	−0.309688
$515$	4.40135	0.193947
$516$	5.31519	0.233988
$517$	0	0
$518$	−2.62445	−0.115312
$519$	−2.51815	−0.110534
$520$	16.7924	0.736395
$521$	26.7783	1.17318	0.586590	−	0.809884i	$-0.300470\pi$
$521$	26.7783	1.17318	0.586590	+	0.809884i	$0.300470\pi$
$522$	15.5510	0.680649
$523$	8.74460	0.382375	0.191187	−	0.981554i	$-0.438766\pi$
$523$	8.74460	0.382375	0.191187	+	0.981554i	$0.438766\pi$
$524$	−24.9894	−1.09167
$525$	−0.347661	−0.0151732
$526$	11.7924	0.514173
$527$	1.49762	0.0652375
$528$	0	0
$529$	−22.3841	−0.973222
$530$	−4.22723	−0.183619
$531$	−22.3172	−0.968482
$532$	−10.1247	−0.438962
$533$	52.7695	2.28570
$534$	1.31329	0.0568315
$535$	5.43253	0.234869
$536$	13.8295	0.597342
$537$	5.11935	0.220916
$538$	−0.220417	−0.00950284
$539$	0	0
$540$	−3.12459	−0.134461
$541$	6.10540	0.262492	0.131246	−	0.991350i	$-0.458102\pi$
$541$	6.10540	0.262492	0.131246	+	0.991350i	$0.458102\pi$
$542$	15.4343	0.662961
$543$	1.61379	0.0692543
$544$	−11.3724	−0.487586
$545$	−15.0021	−0.642620
$546$	−1.65444	−0.0708036
$547$	31.3647	1.34106	0.670528	−	0.741884i	$-0.266068\pi$
$547$	31.3647	1.34106	0.670528	+	0.741884i	$0.266068\pi$
$548$	8.61417	0.367979
$549$	−15.6930	−0.669761
$550$	0	0
$551$	52.1087	2.21991
$552$	−0.660947	−0.0281318
$553$	−3.19473	−0.135854
$554$	−6.75000	−0.286780
$555$	−1.32907	−0.0564159
$556$	−1.10763	−0.0469739
$557$	28.0774	1.18968	0.594840	−	0.803844i	$-0.297215\pi$
$557$	28.0774	1.18968	0.594840	+	0.803844i	$0.297215\pi$
$558$	1.51026	0.0639345
$559$	−69.3250	−2.93214
$560$	1.39437	0.0589227
$561$	0	0
$562$	5.72198	0.241367
$563$	−17.8205	−0.751044	−0.375522	−	0.926814i	$-0.622536\pi$
$563$	−17.8205	−0.751044	−0.375522	+	0.926814i	$0.622536\pi$
$564$	5.71513	0.240650
$565$	11.1067	0.467261
$566$	14.2430	0.598680
$567$	−7.92680	−0.332894
$568$	−11.5748	−0.485670
$569$	−16.0142	−0.671350	−0.335675	−	0.941978i	$-0.608964\pi$
$569$	−16.0142	−0.671350	−0.335675	+	0.941978i	$0.608964\pi$
$570$	1.58073	0.0662096
$571$	9.85306	0.412338	0.206169	−	0.978516i	$-0.433900\pi$
$571$	9.85306	0.412338	0.206169	+	0.978516i	$0.433900\pi$
$572$	0	0
$573$	−8.55333	−0.357320
$574$	−5.22608	−0.218132
$575$	0.784785	0.0327278
$576$	−3.43919	−0.143299
$577$	40.2269	1.67467	0.837334	−	0.546692i	$-0.184113\pi$
$577$	40.2269	1.67467	0.837334	+	0.546692i	$0.184113\pi$
$578$	−9.03332	−0.375736
$579$	1.50313	0.0624678
$580$	−12.0275	−0.499416
$581$	−3.50736	−0.145510
$582$	2.75771	0.114311
$583$	0	0
$584$	−28.1549	−1.16506
$585$	19.9578	0.825154
$586$	−18.4619	−0.762655
$587$	15.8825	0.655541	0.327770	−	0.944757i	$-0.393703\pi$
$587$	15.8825	0.655541	0.327770	+	0.944757i	$0.393703\pi$
$588$	−0.531472	−0.0219175
$589$	5.06062	0.208519
$590$	−5.32135	−0.219077
$591$	−3.02254	−0.124331
$592$	5.33052	0.219083
$593$	27.4115	1.12566	0.562828	−	0.826574i	$-0.309713\pi$
$593$	27.4115	1.12566	0.562828	+	0.826574i	$0.309713\pi$
$594$	0	0
$595$	−1.96001	−0.0803524
$596$	−22.3132	−0.913985
$597$	1.40508	0.0575062
$598$	3.73463	0.152720
$599$	11.8185	0.482889	0.241445	−	0.970415i	$-0.422379\pi$
$599$	11.8185	0.482889	0.241445	+	0.970415i	$0.422379\pi$
$600$	−0.842202	−0.0343827
$601$	−35.7342	−1.45763	−0.728813	−	0.684712i	$-0.759928\pi$
$601$	−35.7342	−1.45763	−0.728813	+	0.684712i	$0.759928\pi$
$602$	6.86567	0.279824
$603$	16.4364	0.669341
$604$	20.8359	0.847802
$605$	0	0
$606$	2.81381	0.114303
$607$	46.0107	1.86752	0.933759	−	0.357903i	$-0.116508\pi$
$607$	46.0107	1.86752	0.933759	+	0.357903i	$0.116508\pi$
$608$	−38.4283	−1.55847
$609$	2.73532	0.110841
$610$	−3.74187	−0.151504
$611$	−74.5414	−3.01562
$612$	−8.62667	−0.348713
$613$	33.5403	1.35468	0.677339	−	0.735671i	$-0.263133\pi$
$613$	33.5403	1.35468	0.677339	+	0.735671i	$0.263133\pi$
$614$	0.651697	0.0263003
$615$	−2.64659	−0.106721
$616$	0	0
$617$	−37.9684	−1.52855	−0.764275	−	0.644890i	$-0.776903\pi$
$617$	−37.9684	−1.52855	−0.764275	+	0.644890i	$0.776903\pi$
$618$	−1.05048	−0.0422564
$619$	24.2899	0.976295	0.488148	−	0.872761i	$-0.337673\pi$
$619$	24.2899	0.976295	0.488148	+	0.872761i	$0.337673\pi$
$620$	−1.16807	−0.0469110
$621$	−1.60405	−0.0643685
$622$	−21.8428	−0.875818
$623$	−5.50249	−0.220453
$624$	3.36034	0.134521
$625$	1.00000	0.0400000
$626$	8.44020	0.337338
$627$	0	0
$628$	−25.4860	−1.01700
$629$	−7.49290	−0.298762
$630$	−1.97654	−0.0787474
$631$	8.98145	0.357546	0.178773	−	0.983890i	$-0.442787\pi$
$631$	8.98145	0.357546	0.178773	+	0.983890i	$0.442787\pi$
$632$	−7.73917	−0.307848
$633$	2.13686	0.0849325
$634$	−8.10560	−0.321914
$635$	−18.5364	−0.735593
$636$	−3.27259	−0.129766
$637$	6.93189	0.274651
$638$	0	0
$639$	−13.7568	−0.544209
$640$	10.7844	0.426289
$641$	−2.90135	−0.114596	−0.0572982	−	0.998357i	$-0.518249\pi$
$641$	−2.90135	−0.114596	−0.0572982	+	0.998357i	$0.518249\pi$
$642$	−1.29659	−0.0511723
$643$	−9.24001	−0.364390	−0.182195	−	0.983262i	$-0.558320\pi$
$643$	−9.24001	−0.364390	−0.182195	+	0.983262i	$0.558320\pi$
$644$	1.19971	0.0472751
$645$	3.47691	0.136903
$646$	8.91170	0.350626
$647$	−24.1075	−0.947764	−0.473882	−	0.880588i	$-0.657148\pi$
$647$	−24.1075	−0.947764	−0.473882	+	0.880588i	$0.657148\pi$
$648$	−19.2025	−0.754347
$649$	0	0
$650$	4.75879	0.186655
$651$	0.265645	0.0104114
$652$	−6.72259	−0.263277
$653$	−48.7740	−1.90868	−0.954338	−	0.298730i	$-0.903437\pi$
$653$	−48.7740	−1.90868	−0.954338	+	0.298730i	$0.903437\pi$
$654$	3.58058	0.140012
$655$	−16.3467	−0.638719
$656$	10.6147	0.414435
$657$	−33.4623	−1.30549
$658$	7.38228	0.287791
$659$	−23.9454	−0.932782	−0.466391	−	0.884579i	$-0.654446\pi$
$659$	−23.9454	−0.932782	−0.466391	+	0.884579i	$0.654446\pi$
$660$	0	0
$661$	−5.19486	−0.202057	−0.101028	−	0.994884i	$-0.532213\pi$
$661$	−5.19486	−0.202057	−0.101028	+	0.994884i	$0.532213\pi$
$662$	−21.4909	−0.835267
$663$	−4.72350	−0.183446
$664$	−8.49651	−0.329728
$665$	−6.62306	−0.256831
$666$	−7.55613	−0.292794
$667$	−6.17451	−0.239078
$668$	−14.0116	−0.542125
$669$	−0.281346	−0.0108775
$670$	3.91913	0.151409
$671$	0	0
$672$	−2.01720	−0.0778151
$673$	0.376972	0.0145312	0.00726561	−	0.999974i	$-0.497687\pi$
$673$	0.376972	0.0145312	0.00726561	+	0.999974i	$0.497687\pi$
$674$	9.72378	0.374546
$675$	−2.04394	−0.0786714
$676$	−53.5829	−2.06088
$677$	−45.1303	−1.73450	−0.867249	−	0.497874i	$-0.834114\pi$
$677$	−45.1303	−1.73450	−0.867249	+	0.497874i	$0.834114\pi$
$678$	−2.65084	−0.101805
$679$	−11.5544	−0.443418
$680$	−4.74808	−0.182080
$681$	7.13758	0.273513
$682$	0	0
$683$	3.83855	0.146878	0.0734391	−	0.997300i	$-0.476603\pi$
$683$	3.83855	0.146878	0.0734391	+	0.997300i	$0.476603\pi$
$684$	−29.1504	−1.11459
$685$	5.63493	0.215300
$686$	−0.686507	−0.0262110
$687$	−8.67665	−0.331035
$688$	−13.9449	−0.531644
$689$	42.6837	1.62612
$690$	−0.187306	−0.00713060
$691$	−37.6116	−1.43081	−0.715406	−	0.698709i	$-0.753758\pi$
$691$	−37.6116	−1.43081	−0.715406	+	0.698709i	$0.753758\pi$
$692$	11.0726	0.420918
$693$	0	0
$694$	−7.50977	−0.285067
$695$	−0.724551	−0.0274838
$696$	6.62625	0.251168
$697$	−14.9207	−0.565161
$698$	2.49299	0.0943612
$699$	1.97100	0.0745500
$700$	1.52871	0.0577797
$701$	43.4361	1.64056	0.820280	−	0.571962i	$-0.193818\pi$
$701$	43.4361	1.64056	0.820280	+	0.571962i	$0.193818\pi$
$702$	−9.72669	−0.367110
$703$	−25.3193	−0.954935
$704$	0	0
$705$	3.73853	0.140801
$706$	0.0605119	0.00227740
$707$	−11.7895	−0.443388
$708$	−4.11962	−0.154825
$709$	−26.5940	−0.998759	−0.499379	−	0.866383i	$-0.666439\pi$
$709$	−26.5940	−0.998759	−0.499379	+	0.866383i	$0.666439\pi$
$710$	−3.28019	−0.123103
$711$	−9.19805	−0.344954
$712$	−13.3297	−0.499551
$713$	−0.599648	−0.0224570
$714$	0.467797	0.0175069
$715$	0	0
$716$	−22.5104	−0.841254
$717$	−9.86667	−0.368477
$718$	16.0043	0.597276
$719$	32.9627	1.22930	0.614651	−	0.788800i	$-0.289297\pi$
$719$	32.9627	1.22930	0.614651	+	0.788800i	$0.289297\pi$
$720$	4.01456	0.149614
$721$	4.40135	0.163915
$722$	17.0699	0.635276
$723$	0.978242	0.0363812
$724$	−7.09604	−0.263722
$725$	−7.86778	−0.292202
$726$	0	0
$727$	−11.0077	−0.408252	−0.204126	−	0.978945i	$-0.565435\pi$
$727$	−11.0077	−0.408252	−0.204126	+	0.978945i	$0.565435\pi$
$728$	16.7924	0.622367
$729$	−20.6905	−0.766315
$730$	−7.97882	−0.295309
$731$	19.6018	0.724998
$732$	−2.89684	−0.107070
$733$	−7.63798	−0.282115	−0.141058	−	0.990001i	$-0.545050\pi$
$733$	−7.63798	−0.282115	−0.141058	+	0.990001i	$0.545050\pi$
$734$	−21.6506	−0.799138
$735$	−0.347661	−0.0128237
$736$	4.55348	0.167844
$737$	0	0
$738$	−15.0466	−0.553872
$739$	−10.7655	−0.396015	−0.198007	−	0.980201i	$-0.563447\pi$
$739$	−10.7655	−0.396015	−0.198007	+	0.980201i	$0.563447\pi$
$740$	5.84410	0.214833
$741$	−15.9612	−0.586349
$742$	−4.22723	−0.155186
$743$	45.6506	1.67476	0.837379	−	0.546623i	$-0.184087\pi$
$743$	45.6506	1.67476	0.837379	+	0.546623i	$0.184087\pi$
$744$	0.643519	0.0235926
$745$	−14.5961	−0.534761
$746$	14.4937	0.530653
$747$	−10.0981	−0.369472
$748$	0	0
$749$	5.43253	0.198500
$750$	−0.238671	−0.00871505
$751$	27.6573	1.00923	0.504615	−	0.863345i	$-0.331635\pi$
$751$	27.6573	1.00923	0.504615	+	0.863345i	$0.331635\pi$
$752$	−14.9942	−0.546781
$753$	−6.14278	−0.223855
$754$	−37.4411	−1.36352
$755$	13.6298	0.496038
$756$	−3.12459	−0.113640
$757$	31.9269	1.16040	0.580202	−	0.814473i	$-0.302974\pi$
$757$	31.9269	1.16040	0.580202	+	0.814473i	$0.302974\pi$
$758$	−10.1545	−0.368827
$759$	0	0
$760$	−16.0442	−0.581986
$761$	7.34997	0.266436	0.133218	−	0.991087i	$-0.457469\pi$
$761$	7.34997	0.266436	0.133218	+	0.991087i	$0.457469\pi$
$762$	4.42410	0.160268
$763$	−15.0021	−0.543113
$764$	37.6101	1.36069
$765$	−5.64311	−0.204027
$766$	3.01707	0.109011
$767$	53.7315	1.94013
$768$	−3.40450	−0.122849
$769$	−24.8933	−0.897677	−0.448839	−	0.893613i	$-0.648162\pi$
$769$	−24.8933	−0.897677	−0.448839	+	0.893613i	$0.648162\pi$
$770$	0	0
$771$	−3.55563	−0.128053
$772$	−6.60944	−0.237879
$773$	−16.2506	−0.584493	−0.292247	−	0.956343i	$-0.594403\pi$
$773$	−16.2506	−0.584493	−0.292247	+	0.956343i	$0.594403\pi$
$774$	19.7672	0.710517
$775$	−0.764092	−0.0274470
$776$	−27.9904	−1.00480
$777$	−1.32907	−0.0476802
$778$	8.75147	0.313755
$779$	−50.4185	−1.80643
$780$	3.68410	0.131912
$781$	0	0
$782$	−1.05597	−0.0377615
$783$	16.0813	0.574698
$784$	1.39437	0.0497988
$785$	−16.6716	−0.595035
$786$	3.90149	0.139162
$787$	3.95549	0.140998	0.0704990	−	0.997512i	$-0.477541\pi$
$787$	3.95549	0.140998	0.0704990	+	0.997512i	$0.477541\pi$
$788$	13.2905	0.473454
$789$	5.97190	0.212605
$790$	−2.19320	−0.0780307
$791$	11.1067	0.394908
$792$	0	0
$793$	37.7829	1.34171
$794$	−16.7989	−0.596171
$795$	−2.14075	−0.0759246
$796$	−6.17833	−0.218985
$797$	8.71439	0.308680	0.154340	−	0.988018i	$-0.450675\pi$
$797$	8.71439	0.308680	0.154340	+	0.988018i	$0.450675\pi$
$798$	1.58073	0.0559574
$799$	21.0767	0.745641
$800$	5.80221	0.205139
$801$	−15.8424	−0.559763
$802$	12.2484	0.432508
$803$	0	0
$804$	3.03406	0.107003
$805$	0.784785	0.0276600
$806$	−3.63615	−0.128078
$807$	−0.111623	−0.00392933
$808$	−28.5598	−1.00473
$809$	6.03333	0.212121	0.106060	−	0.994360i	$-0.466176\pi$
$809$	6.03333	0.212121	0.106060	+	0.994360i	$0.466176\pi$
$810$	−5.44180	−0.191205
$811$	22.5947	0.793406	0.396703	−	0.917947i	$-0.370154\pi$
$811$	22.5947	0.793406	0.396703	+	0.917947i	$0.370154\pi$
$812$	−12.0275	−0.422084
$813$	7.81624	0.274128
$814$	0	0
$815$	−4.39756	−0.154040
$816$	−0.950144	−0.0332617
$817$	66.2364	2.31732
$818$	−21.6991	−0.758691
$819$	19.9578	0.697383
$820$	11.6374	0.406396
$821$	−29.8311	−1.04111	−0.520555	−	0.853828i	$-0.674275\pi$
$821$	−29.8311	−1.04111	−0.520555	+	0.853828i	$0.674275\pi$
$822$	−1.34490	−0.0469087
$823$	32.8406	1.14475	0.572376	−	0.819992i	$-0.306022\pi$
$823$	32.8406	1.14475	0.572376	+	0.819992i	$0.306022\pi$
$824$	10.6622	0.371435
$825$	0	0
$826$	−5.32135	−0.185154
$827$	−18.7126	−0.650700	−0.325350	−	0.945594i	$-0.605482\pi$
$827$	−18.7126	−0.650700	−0.325350	+	0.945594i	$0.605482\pi$
$828$	3.45412	0.120039
$829$	0.271335	0.00942387	0.00471194	−	0.999989i	$-0.498500\pi$
$829$	0.271335	0.00942387	0.00471194	+	0.999989i	$0.498500\pi$
$830$	−2.40782	−0.0835768
$831$	−3.41833	−0.118581
$832$	8.28030	0.287068
$833$	−1.96001	−0.0679101
$834$	0.172930	0.00598806
$835$	−9.16565	−0.317190
$836$	0	0
$837$	1.56176	0.0539823
$838$	12.9538	0.447482
$839$	42.3565	1.46231	0.731155	−	0.682212i	$-0.238982\pi$
$839$	42.3565	1.46231	0.731155	+	0.682212i	$0.238982\pi$
$840$	−0.842202	−0.0290587
$841$	32.9019	1.13455
$842$	19.0052	0.654963
$843$	2.89772	0.0998028
$844$	−9.39604	−0.323425
$845$	−35.0511	−1.20579
$846$	21.2546	0.730747
$847$	0	0
$848$	8.58594	0.294842
$849$	7.21296	0.247548
$850$	−1.34556	−0.0461522
$851$	3.00015	0.102844
$852$	−2.53942	−0.0869991
$853$	−28.1208	−0.962837	−0.481418	−	0.876491i	$-0.659878\pi$
$853$	−28.1208	−0.962837	−0.481418	+	0.876491i	$0.659878\pi$
$854$	−3.74187	−0.128044
$855$	−19.0687	−0.652134
$856$	13.1602	0.449807
$857$	0.647160	0.0221066	0.0110533	−	0.999939i	$-0.496482\pi$
$857$	0.647160	0.0221066	0.0110533	+	0.999939i	$0.496482\pi$
$858$	0	0
$859$	−41.2100	−1.40607	−0.703033	−	0.711157i	$-0.748171\pi$
$859$	−41.2100	−1.40607	−0.703033	+	0.711157i	$0.748171\pi$
$860$	−15.2884	−0.521331
$861$	−2.64659	−0.0901955
$862$	8.72274	0.297098
$863$	32.3321	1.10060	0.550299	−	0.834967i	$-0.314514\pi$
$863$	32.3321	1.10060	0.550299	+	0.834967i	$0.314514\pi$
$864$	−11.8594	−0.403464
$865$	7.24312	0.246273
$866$	−8.23739	−0.279918
$867$	−4.57465	−0.155363
$868$	−1.16807	−0.0396470
$869$	0	0
$870$	1.87781	0.0636638
$871$	−39.5727	−1.34087
$872$	−36.3424	−1.23071
$873$	−33.2667	−1.12591
$874$	−3.56824	−0.120697
$875$	1.00000	0.0338062
$876$	−6.17695	−0.208700
$877$	11.1898	0.377853	0.188927	−	0.981991i	$-0.439499\pi$
$877$	11.1898	0.377853	0.188927	+	0.981991i	$0.439499\pi$
$878$	8.21561	0.277263
$879$	−9.34949	−0.315350
$880$	0	0
$881$	2.71373	0.0914280	0.0457140	−	0.998955i	$-0.485444\pi$
$881$	2.71373	0.0914280	0.0457140	+	0.998955i	$0.485444\pi$
$882$	−1.97654	−0.0665537
$883$	33.4154	1.12452	0.562259	−	0.826961i	$-0.309932\pi$
$883$	33.4154	1.12452	0.562259	+	0.826961i	$0.309932\pi$
$884$	20.7699	0.698566
$885$	−2.69484	−0.0905860
$886$	0.919532	0.0308923
$887$	−27.8490	−0.935077	−0.467538	−	0.883973i	$-0.654859\pi$
$887$	−27.8490	−0.935077	−0.467538	+	0.883973i	$0.654859\pi$
$888$	−3.21965	−0.108044
$889$	−18.5364	−0.621689
$890$	−3.77750	−0.126622
$891$	0	0
$892$	1.23711	0.0414217
$893$	71.2203	2.38330
$894$	3.48368	0.116512
$895$	−14.7251	−0.492207
$896$	10.7844	0.360280
$897$	1.89129	0.0631483
$898$	26.2411	0.875676
$899$	6.01171	0.200502
$900$	4.40135	0.146712
$901$	−12.0689	−0.402074
$902$	0	0
$903$	3.47691	0.115704
$904$	26.9057	0.894871
$905$	−4.64185	−0.154300
$906$	−3.25303	−0.108075
$907$	39.9247	1.32568	0.662839	−	0.748762i	$-0.269351\pi$
$907$	39.9247	1.32568	0.662839	+	0.748762i	$0.269351\pi$
$908$	−31.3848	−1.04154
$909$	−33.9434	−1.12583
$910$	4.75879	0.157752
$911$	46.7616	1.54928	0.774641	−	0.632402i	$-0.217931\pi$
$911$	46.7616	1.54928	0.774641	+	0.632402i	$0.217931\pi$
$912$	−3.21063	−0.106315
$913$	0	0
$914$	23.9783	0.793133
$915$	−1.89496	−0.0626454
$916$	38.1524	1.26059
$917$	−16.3467	−0.539816
$918$	2.75024	0.0907715
$919$	−43.6332	−1.43933	−0.719664	−	0.694322i	$-0.755704\pi$
$919$	−43.6332	−1.43933	−0.719664	+	0.694322i	$0.755704\pi$
$920$	1.90113	0.0626783
$921$	0.330032	0.0108749
$922$	−27.2894	−0.898727
$923$	33.1212	1.09020
$924$	0	0
$925$	3.82290	0.125696
$926$	−25.6840	−0.844030
$927$	12.6721	0.416206
$928$	−45.6505	−1.49855
$929$	22.5732	0.740602	0.370301	−	0.928912i	$-0.379255\pi$
$929$	22.5732	0.740602	0.370301	+	0.928912i	$0.379255\pi$
$930$	0.182367	0.00598004
$931$	−6.62306	−0.217062
$932$	−8.66673	−0.283888
$933$	−11.0616	−0.362142
$934$	−11.4755	−0.375488
$935$	0	0
$936$	48.3475	1.58029
$937$	34.9192	1.14076	0.570380	−	0.821381i	$-0.306796\pi$
$937$	34.9192	1.14076	0.570380	+	0.821381i	$0.306796\pi$
$938$	3.91913	0.127964
$939$	4.27428	0.139486
$940$	−16.4388	−0.536175
$941$	57.5803	1.87706	0.938531	−	0.345194i	$-0.112187\pi$
$941$	57.5803	1.87706	0.938531	+	0.345194i	$0.112187\pi$
$942$	3.97903	0.129644
$943$	5.97423	0.194548
$944$	10.8082	0.351777
$945$	−2.04394	−0.0664894
$946$	0	0
$947$	5.60101	0.182009	0.0910043	−	0.995851i	$-0.470992\pi$
$947$	5.60101	0.182009	0.0910043	+	0.995851i	$0.470992\pi$
$948$	−1.69791	−0.0551455
$949$	80.5648	2.61524
$950$	−4.54677	−0.147517
$951$	−4.10484	−0.133108
$952$	−4.74808	−0.153886
$953$	−8.78117	−0.284450	−0.142225	−	0.989834i	$-0.545426\pi$
$953$	−8.78117	−0.284450	−0.142225	+	0.989834i	$0.545426\pi$
$954$	−12.1708	−0.394043
$955$	24.6025	0.796119
$956$	43.3850	1.40317
$957$	0	0
$958$	−1.80016	−0.0581606
$959$	5.63493	0.181962
$960$	−0.415288	−0.0134034
$961$	−30.4162	−0.981167
$962$	18.1924	0.586546
$963$	15.6410	0.504024
$964$	−4.30146	−0.138541
$965$	−4.32354	−0.139180
$966$	−0.187306	−0.00602646
$967$	−35.9168	−1.15501	−0.577503	−	0.816388i	$-0.695973\pi$
$967$	−35.9168	−1.15501	−0.577503	+	0.816388i	$0.695973\pi$
$968$	0	0
$969$	4.51306	0.144980
$970$	−7.93219	−0.254687
$971$	16.1609	0.518630	0.259315	−	0.965793i	$-0.416503\pi$
$971$	16.1609	0.518630	0.259315	+	0.965793i	$0.416503\pi$
$972$	−13.5866	−0.435792
$973$	−0.724551	−0.0232281
$974$	16.6302	0.532867
$975$	2.40994	0.0771800
$976$	7.60013	0.243274
$977$	21.3894	0.684307	0.342153	−	0.939644i	$-0.388844\pi$
$977$	21.3894	0.684307	0.342153	+	0.939644i	$0.388844\pi$
$978$	1.04957	0.0335616
$979$	0	0
$980$	1.52871	0.0488328
$981$	−43.1931	−1.37905
$982$	−6.60311	−0.210714
$983$	9.94885	0.317319	0.158659	−	0.987333i	$-0.449283\pi$
$983$	9.94885	0.317319	0.158659	+	0.987333i	$0.449283\pi$
$984$	−6.41132	−0.204385
$985$	8.69393	0.277012
$986$	10.5865	0.337144
$987$	3.73853	0.118999
$988$	70.1834	2.23283
$989$	−7.84854	−0.249569
$990$	0	0
$991$	−16.1989	−0.514575	−0.257288	−	0.966335i	$-0.582829\pi$
$991$	−16.1989	−0.514575	−0.257288	+	0.966335i	$0.582829\pi$
$992$	−4.43342	−0.140761
$993$	−10.8834	−0.345375
$994$	−3.28019	−0.104041
$995$	−4.04154	−0.128125
$996$	−1.86406	−0.0590650
$997$	−24.2743	−0.768773	−0.384387	−	0.923172i	$-0.625587\pi$
$997$	−24.2743	−0.768773	−0.384387	+	0.923172i	$0.625587\pi$
$998$	24.2979	0.769138
$999$	−7.81379	−0.247217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.be.1.3	yes	5
11.10	odd	2		4235.2.a.y.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.y.1.3	✓	5	11.10	odd	2
4235.2.a.be.1.3	yes	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.686507 q^{2} +0.347661 q^{3} -1.52871 q^{4} -1.00000 q^{5} +0.238671 q^{6} -1.00000 q^{7} -2.42248 q^{8} -2.87913 q^{9} +O(q^{10})\)	\(q+0.686507 q^{2} +0.347661 q^{3} -1.52871 q^{4} -1.00000 q^{5} +0.238671 q^{6} -1.00000 q^{7} -2.42248 q^{8} -2.87913 q^{9} -0.686507 q^{10} -0.531472 q^{12} +6.93189 q^{13} -0.686507 q^{14} -0.347661 q^{15} +1.39437 q^{16} -1.96001 q^{17} -1.97654 q^{18} -6.62306 q^{19} +1.52871 q^{20} -0.347661 q^{21} +0.784785 q^{23} -0.842202 q^{24} +1.00000 q^{25} +4.75879 q^{26} -2.04394 q^{27} +1.52871 q^{28} -7.86778 q^{29} -0.238671 q^{30} -0.764092 q^{31} +5.80221 q^{32} -1.34556 q^{34} +1.00000 q^{35} +4.40135 q^{36} +3.82290 q^{37} -4.54677 q^{38} +2.40994 q^{39} +2.42248 q^{40} +7.61257 q^{41} -0.238671 q^{42} -10.0009 q^{43} +2.87913 q^{45} +0.538760 q^{46} -10.7534 q^{47} +0.484766 q^{48} +1.00000 q^{49} +0.686507 q^{50} -0.681416 q^{51} -10.5968 q^{52} +6.15759 q^{53} -1.40318 q^{54} +2.42248 q^{56} -2.30258 q^{57} -5.40128 q^{58} +7.75135 q^{59} +0.531472 q^{60} +5.45060 q^{61} -0.524554 q^{62} +2.87913 q^{63} +1.19452 q^{64} -6.93189 q^{65} -5.70880 q^{67} +2.99628 q^{68} +0.272839 q^{69} +0.686507 q^{70} +4.77809 q^{71} +6.97465 q^{72} +11.6223 q^{73} +2.62445 q^{74} +0.347661 q^{75} +10.1247 q^{76} +1.65444 q^{78} +3.19473 q^{79} -1.39437 q^{80} +7.92680 q^{81} +5.22608 q^{82} +3.50736 q^{83} +0.531472 q^{84} +1.96001 q^{85} -6.86567 q^{86} -2.73532 q^{87} +5.50249 q^{89} +1.97654 q^{90} -6.93189 q^{91} -1.19971 q^{92} -0.265645 q^{93} -7.38228 q^{94} +6.62306 q^{95} +2.01720 q^{96} +11.5544 q^{97} +0.686507 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 5 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 5 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9	\( 5 q + 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} + 11 q^{12} + 12 q^{13} - 2 q^{14} + 2 q^{15} + 2 q^{16} + 14 q^{17} + 7 q^{18} + 9 q^{19} - 4 q^{20} + 2 q^{21} + 17 q^{23} + 6 q^{24} + 5 q^{25} - 11 q^{26} - 11 q^{27} - 4 q^{28} + 3 q^{29} - 5 q^{30} + 2 q^{31} - 5 q^{32} + 16 q^{34} + 5 q^{35} - 15 q^{36} + 4 q^{37} - 11 q^{38} + 2 q^{39} + 6 q^{40} - 15 q^{41} - 5 q^{42} + 4 q^{43} - 3 q^{45} - 10 q^{46} - 2 q^{47} - 10 q^{48} + 5 q^{49} + 2 q^{50} - 18 q^{51} + 4 q^{52} + 6 q^{53} + 4 q^{54} + 6 q^{56} - 32 q^{58} - 6 q^{59} - 11 q^{60} + 20 q^{61} + 21 q^{62} - 3 q^{63} - 26 q^{64} - 12 q^{65} + 3 q^{67} + 5 q^{68} + 2 q^{70} - 6 q^{71} + 34 q^{72} + 11 q^{73} - 15 q^{74} - 2 q^{75} + 47 q^{76} + 31 q^{78} + 19 q^{79} - 2 q^{80} + 33 q^{81} + 8 q^{83} - 11 q^{84} - 14 q^{85} + 27 q^{86} - 30 q^{87} + q^{89} - 7 q^{90} - 12 q^{91} + 44 q^{92} + 3 q^{93} + 28 q^{94} - 9 q^{95} - 4 q^{96} - 7 q^{97} + 2 q^{98}+O(q^{100}) \) 5 * q + 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 5 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 + 11 * q^12 + 12 * q^13 - 2 * q^14 + 2 * q^15 + 2 * q^16 + 14 * q^17 + 7 * q^18 + 9 * q^19 - 4 * q^20 + 2 * q^21 + 17 * q^23 + 6 * q^24 + 5 * q^25 - 11 * q^26 - 11 * q^27 - 4 * q^28 + 3 * q^29 - 5 * q^30 + 2 * q^31 - 5 * q^32 + 16 * q^34 + 5 * q^35 - 15 * q^36 + 4 * q^37 - 11 * q^38 + 2 * q^39 + 6 * q^40 - 15 * q^41 - 5 * q^42 + 4 * q^43 - 3 * q^45 - 10 * q^46 - 2 * q^47 - 10 * q^48 + 5 * q^49 + 2 * q^50 - 18 * q^51 + 4 * q^52 + 6 * q^53 + 4 * q^54 + 6 * q^56 - 32 * q^58 - 6 * q^59 - 11 * q^60 + 20 * q^61 + 21 * q^62 - 3 * q^63 - 26 * q^64 - 12 * q^65 + 3 * q^67 + 5 * q^68 + 2 * q^70 - 6 * q^71 + 34 * q^72 + 11 * q^73 - 15 * q^74 - 2 * q^75 + 47 * q^76 + 31 * q^78 + 19 * q^79 - 2 * q^80 + 33 * q^81 + 8 * q^83 - 11 * q^84 - 14 * q^85 + 27 * q^86 - 30 * q^87 + q^89 - 7 * q^90 - 12 * q^91 + 44 * q^92 + 3 * q^93 + 28 * q^94 - 9 * q^95 - 4 * q^96 - 7 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

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Database

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