LMFDB - Embedded newform 6027.2.a.y.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 16x^{4} + 14x^{3} - 20x^{2} - 10x + 4 $ x^7 - 3x^6 - 6x^5 + 16x^4 + 14x^3 - 20x^2 - 10x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.762978$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.76298 q^{2} -1.00000 q^{3} +1.10809 q^{4} -3.51322 q^{5} -1.76298 q^{6} -1.57241 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.76298 q^{2} -1.00000 q^{3} +1.10809 q^{4} -3.51322 q^{5} -1.76298 q^{6} -1.57241 q^{8} +1.00000 q^{9} -6.19372 q^{10} -0.153259 q^{11} -1.10809 q^{12} +2.35241 q^{13} +3.51322 q^{15} -4.98832 q^{16} -2.14700 q^{17} +1.76298 q^{18} -1.53924 q^{19} -3.89296 q^{20} -0.270193 q^{22} -3.30805 q^{23} +1.57241 q^{24} +7.34269 q^{25} +4.14724 q^{26} -1.00000 q^{27} -4.53129 q^{29} +6.19372 q^{30} +0.462221 q^{31} -5.64946 q^{32} +0.153259 q^{33} -3.78511 q^{34} +1.10809 q^{36} -7.31083 q^{37} -2.71365 q^{38} -2.35241 q^{39} +5.52423 q^{40} -1.00000 q^{41} +3.68806 q^{43} -0.169825 q^{44} -3.51322 q^{45} -5.83202 q^{46} +0.200461 q^{47} +4.98832 q^{48} +12.9450 q^{50} +2.14700 q^{51} +2.60668 q^{52} -8.09875 q^{53} -1.76298 q^{54} +0.538433 q^{55} +1.53924 q^{57} -7.98856 q^{58} -0.519212 q^{59} +3.89296 q^{60} -2.10590 q^{61} +0.814885 q^{62} +0.0167549 q^{64} -8.26451 q^{65} +0.270193 q^{66} +14.3401 q^{67} -2.37907 q^{68} +3.30805 q^{69} +5.11775 q^{71} -1.57241 q^{72} +6.70809 q^{73} -12.8888 q^{74} -7.34269 q^{75} -1.70562 q^{76} -4.14724 q^{78} -2.88889 q^{79} +17.5250 q^{80} +1.00000 q^{81} -1.76298 q^{82} +0.349683 q^{83} +7.54287 q^{85} +6.50196 q^{86} +4.53129 q^{87} +0.240987 q^{88} +1.87138 q^{89} -6.19372 q^{90} -3.66562 q^{92} -0.462221 q^{93} +0.353409 q^{94} +5.40770 q^{95} +5.64946 q^{96} -9.30390 q^{97} -0.153259 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9	$ 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9} + 3 q^{10} + 11 q^{11} - 8 q^{12} + 7 q^{13} + q^{15} + 6 q^{16} - 11 q^{17} + 4 q^{18} - 4 q^{19} + 7 q^{20} + 6 q^{22} + 7 q^{23} - 12 q^{24} + 2 q^{25} + 13 q^{26} - 7 q^{27} + 4 q^{29} - 3 q^{30} + 7 q^{31} + 18 q^{32} - 11 q^{33} + 20 q^{34} + 8 q^{36} - 4 q^{38} - 7 q^{39} + 9 q^{40} - 7 q^{41} + q^{43} + 18 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 6 q^{48} + 19 q^{50} + 11 q^{51} + 27 q^{52} + 23 q^{53} - 4 q^{54} + 30 q^{55} + 4 q^{57} - 3 q^{58} - 8 q^{59} - 7 q^{60} + 3 q^{61} + 16 q^{62} + 6 q^{64} + 15 q^{65} - 6 q^{66} + 3 q^{67} - 7 q^{69} + 7 q^{71} + 12 q^{72} + 11 q^{73} - 13 q^{74} - 2 q^{75} + 40 q^{76} - 13 q^{78} - q^{79} + 43 q^{80} + 7 q^{81} - 4 q^{82} - 10 q^{85} - 12 q^{86} - 4 q^{87} + 10 q^{88} - 32 q^{89} + 3 q^{90} - 19 q^{92} - 7 q^{93} - 21 q^{94} - 8 q^{95} - 18 q^{96} + 25 q^{97} + 11 q^{99}+O(q^{100}) $ 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9 + 3 * q^10 + 11 * q^11 - 8 * q^12 + 7 * q^13 + q^15 + 6 * q^16 - 11 * q^17 + 4 * q^18 - 4 * q^19 + 7 * q^20 + 6 * q^22 + 7 * q^23 - 12 * q^24 + 2 * q^25 + 13 * q^26 - 7 * q^27 + 4 * q^29 - 3 * q^30 + 7 * q^31 + 18 * q^32 - 11 * q^33 + 20 * q^34 + 8 * q^36 - 4 * q^38 - 7 * q^39 + 9 * q^40 - 7 * q^41 + q^43 + 18 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 6 * q^48 + 19 * q^50 + 11 * q^51 + 27 * q^52 + 23 * q^53 - 4 * q^54 + 30 * q^55 + 4 * q^57 - 3 * q^58 - 8 * q^59 - 7 * q^60 + 3 * q^61 + 16 * q^62 + 6 * q^64 + 15 * q^65 - 6 * q^66 + 3 * q^67 - 7 * q^69 + 7 * q^71 + 12 * q^72 + 11 * q^73 - 13 * q^74 - 2 * q^75 + 40 * q^76 - 13 * q^78 - q^79 + 43 * q^80 + 7 * q^81 - 4 * q^82 - 10 * q^85 - 12 * q^86 - 4 * q^87 + 10 * q^88 - 32 * q^89 + 3 * q^90 - 19 * q^92 - 7 * q^93 - 21 * q^94 - 8 * q^95 - 18 * q^96 + 25 * q^97 + 11 * q^99

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 $

$2$	1.76298	1.24661	0.623307	−	0.781977i	$-0.285789\pi$
$2$	1.76298	1.24661	0.623307	+	0.781977i	$0.285789\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.10809	0.554046
$5$	−3.51322	−1.57116	−0.785579	−	0.618761i	$-0.787635\pi$
$5$	−3.51322	−1.57116	−0.785579	+	0.618761i	$0.787635\pi$
$6$	−1.76298	−0.719733
$7$	0	0
$7$	0	0
$8$	−1.57241	−0.555933
$9$	1.00000	0.333333
$10$	−6.19372	−1.95863
$11$	−0.153259	−0.0462094	−0.0231047	−	0.999733i	$-0.507355\pi$
$11$	−0.153259	−0.0462094	−0.0231047	+	0.999733i	$0.507355\pi$
$12$	−1.10809	−0.319878
$13$	2.35241	0.652440	0.326220	−	0.945294i	$-0.394225\pi$
$13$	2.35241	0.652440	0.326220	+	0.945294i	$0.394225\pi$
$14$	0	0
$15$	3.51322	0.907108
$16$	−4.98832	−1.24708
$17$	−2.14700	−0.520724	−0.260362	−	0.965511i	$-0.583842\pi$
$17$	−2.14700	−0.520724	−0.260362	+	0.965511i	$0.583842\pi$
$18$	1.76298	0.415538
$19$	−1.53924	−0.353127	−0.176563	−	0.984289i	$-0.556498\pi$
$19$	−1.53924	−0.353127	−0.176563	+	0.984289i	$0.556498\pi$
$20$	−3.89296	−0.870493
$21$	0	0
$22$	−0.270193	−0.0576053
$23$	−3.30805	−0.689776	−0.344888	−	0.938644i	$-0.612083\pi$
$23$	−3.30805	−0.689776	−0.344888	+	0.938644i	$0.612083\pi$
$24$	1.57241	0.320968
$25$	7.34269	1.46854
$26$	4.14724	0.813341
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−4.53129	−0.841439	−0.420719	−	0.907191i	$-0.638222\pi$
$29$	−4.53129	−0.841439	−0.420719	+	0.907191i	$0.638222\pi$
$30$	6.19372	1.13081
$31$	0.462221	0.0830173	0.0415086	−	0.999138i	$-0.486784\pi$
$31$	0.462221	0.0830173	0.0415086	+	0.999138i	$0.486784\pi$
$32$	−5.64946	−0.998693
$33$	0.153259	0.0266790
$34$	−3.78511	−0.649142
$35$	0	0
$36$	1.10809	0.184682
$37$	−7.31083	−1.20189	−0.600946	−	0.799289i	$-0.705210\pi$
$37$	−7.31083	−1.20189	−0.600946	+	0.799289i	$0.705210\pi$
$38$	−2.71365	−0.440213
$39$	−2.35241	−0.376686
$40$	5.52423	0.873458
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	3.68806	0.562423	0.281212	−	0.959646i	$-0.409264\pi$
$43$	3.68806	0.562423	0.281212	+	0.959646i	$0.409264\pi$
$44$	−0.169825	−0.0256021
$45$	−3.51322	−0.523719
$46$	−5.83202	−0.859884
$47$	0.200461	0.0292403	0.0146201	−	0.999893i	$-0.495346\pi$
$47$	0.200461	0.0292403	0.0146201	+	0.999893i	$0.495346\pi$
$48$	4.98832	0.720001
$49$	0	0
$50$	12.9450	1.83070
$51$	2.14700	0.300640
$52$	2.60668	0.361482
$53$	−8.09875	−1.11245	−0.556224	−	0.831032i	$-0.687751\pi$
$53$	−8.09875	−1.11245	−0.556224	+	0.831032i	$0.687751\pi$
$54$	−1.76298	−0.239911
$55$	0.538433	0.0726023
$56$	0	0
$57$	1.53924	0.203878
$58$	−7.98856	−1.04895
$59$	−0.519212	−0.0675956	−0.0337978	−	0.999429i	$-0.510760\pi$
$59$	−0.519212	−0.0675956	−0.0337978	+	0.999429i	$0.510760\pi$
$60$	3.89296	0.502580
$61$	−2.10590	−0.269633	−0.134816	−	0.990871i	$-0.543044\pi$
$61$	−2.10590	−0.269633	−0.134816	+	0.990871i	$0.543044\pi$
$62$	0.814885	0.103490
$63$	0	0
$64$	0.0167549	0.00209436
$65$	−8.26451	−1.02509
$66$	0.270193	0.0332584
$67$	14.3401	1.75192	0.875958	−	0.482387i	$-0.160230\pi$
$67$	14.3401	1.75192	0.875958	+	0.482387i	$0.160230\pi$
$68$	−2.37907	−0.288505
$69$	3.30805	0.398242
$70$	0	0
$71$	5.11775	0.607365	0.303682	−	0.952773i	$-0.401784\pi$
$71$	5.11775	0.607365	0.303682	+	0.952773i	$0.401784\pi$
$72$	−1.57241	−0.185311
$73$	6.70809	0.785123	0.392561	−	0.919726i	$-0.371589\pi$
$73$	6.70809	0.785123	0.392561	+	0.919726i	$0.371589\pi$
$74$	−12.8888	−1.49830
$75$	−7.34269	−0.847860
$76$	−1.70562	−0.195648
$77$	0	0
$78$	−4.14724	−0.469582
$79$	−2.88889	−0.325026	−0.162513	−	0.986706i	$-0.551960\pi$
$79$	−2.88889	−0.325026	−0.162513	+	0.986706i	$0.551960\pi$
$80$	17.5250	1.95936
$81$	1.00000	0.111111
$82$	−1.76298	−0.194688
$83$	0.349683	0.0383827	0.0191913	−	0.999816i	$-0.493891\pi$
$83$	0.349683	0.0383827	0.0191913	+	0.999816i	$0.493891\pi$
$84$	0	0
$85$	7.54287	0.818140
$86$	6.50196	0.701125
$87$	4.53129	0.485805
$88$	0.240987	0.0256893
$89$	1.87138	0.198366	0.0991831	−	0.995069i	$-0.468377\pi$
$89$	1.87138	0.198366	0.0991831	+	0.995069i	$0.468377\pi$
$90$	−6.19372	−0.652876
$91$	0	0
$92$	−3.66562	−0.382168
$93$	−0.462221	−0.0479300
$94$	0.353409	0.0364514
$95$	5.40770	0.554818
$96$	5.64946	0.576596
$97$	−9.30390	−0.944668	−0.472334	−	0.881420i	$-0.656588\pi$
$97$	−9.30390	−0.944668	−0.472334	+	0.881420i	$0.656588\pi$
$98$	0	0
$99$	−0.153259	−0.0154031
$100$	8.13637	0.813637
$101$	15.8760	1.57972	0.789858	−	0.613289i	$-0.210154\pi$
$101$	15.8760	1.57972	0.789858	+	0.613289i	$0.210154\pi$
$102$	3.78511	0.374782
$103$	18.7078	1.84333	0.921667	−	0.387981i	$-0.126827\pi$
$103$	18.7078	1.84333	0.921667	+	0.387981i	$0.126827\pi$
$104$	−3.69896	−0.362713
$105$	0	0
$106$	−14.2779	−1.38679
$107$	6.80514	0.657877	0.328939	−	0.944351i	$-0.393309\pi$
$107$	6.80514	0.657877	0.328939	+	0.944351i	$0.393309\pi$
$108$	−1.10809	−0.106626
$109$	14.4970	1.38856	0.694280	−	0.719705i	$-0.255723\pi$
$109$	14.4970	1.38856	0.694280	+	0.719705i	$0.255723\pi$
$110$	0.949245	0.0905070
$111$	7.31083	0.693913
$112$	0	0
$113$	10.9043	1.02579	0.512896	−	0.858451i	$-0.328573\pi$
$113$	10.9043	1.02579	0.512896	+	0.858451i	$0.328573\pi$
$114$	2.71365	0.254157
$115$	11.6219	1.08375
$116$	−5.02108	−0.466195
$117$	2.35241	0.217480
$118$	−0.915359	−0.0842656
$119$	0	0
$120$	−5.52423	−0.504291
$121$	−10.9765	−0.997865
$122$	−3.71265	−0.336128
$123$	1.00000	0.0901670
$124$	0.512183	0.0459954
$125$	−8.23036	−0.736146
$126$	0	0
$127$	−2.69248	−0.238919	−0.119459	−	0.992839i	$-0.538116\pi$
$127$	−2.69248	−0.238919	−0.119459	+	0.992839i	$0.538116\pi$
$128$	11.3285	1.00130
$129$	−3.68806	−0.324715
$130$	−14.5701	−1.27789
$131$	−14.1990	−1.24057	−0.620287	−	0.784375i	$-0.712984\pi$
$131$	−14.1990	−1.24057	−0.620287	+	0.784375i	$0.712984\pi$
$132$	0.169825	0.0147814
$133$	0	0
$134$	25.2812	2.18396
$135$	3.51322	0.302369
$136$	3.37597	0.289487
$137$	−9.57507	−0.818054	−0.409027	−	0.912522i	$-0.634132\pi$
$137$	−9.57507	−0.818054	−0.409027	+	0.912522i	$0.634132\pi$
$138$	5.83202	0.496454
$139$	18.0900	1.53438	0.767189	−	0.641421i	$-0.221655\pi$
$139$	18.0900	1.53438	0.767189	+	0.641421i	$0.221655\pi$
$140$	0	0
$141$	−0.200461	−0.0168819
$142$	9.02247	0.757149
$143$	−0.360528	−0.0301489
$144$	−4.98832	−0.415693
$145$	15.9194	1.32203
$146$	11.8262	0.978745
$147$	0	0
$148$	−8.10107	−0.665904
$149$	7.52984	0.616868	0.308434	−	0.951246i	$-0.400195\pi$
$149$	7.52984	0.616868	0.308434	+	0.951246i	$0.400195\pi$
$150$	−12.9450	−1.05695
$151$	7.18861	0.585000	0.292500	−	0.956265i	$-0.405513\pi$
$151$	7.18861	0.585000	0.292500	+	0.956265i	$0.405513\pi$
$152$	2.42033	0.196315
$153$	−2.14700	−0.173575
$154$	0	0
$155$	−1.62388	−0.130433
$156$	−2.60668	−0.208702
$157$	21.9904	1.75503	0.877513	−	0.479554i	$-0.159201\pi$
$157$	21.9904	1.75503	0.877513	+	0.479554i	$0.159201\pi$
$158$	−5.09306	−0.405182
$159$	8.09875	0.642273
$160$	19.8478	1.56910
$161$	0	0
$162$	1.76298	0.138513
$163$	−8.91625	−0.698374	−0.349187	−	0.937053i	$-0.613542\pi$
$163$	−8.91625	−0.698374	−0.349187	+	0.937053i	$0.613542\pi$
$164$	−1.10809	−0.0865274
$165$	−0.538433	−0.0419169
$166$	0.616483	0.0478483
$167$	3.01514	0.233318	0.116659	−	0.993172i	$-0.462781\pi$
$167$	3.01514	0.233318	0.116659	+	0.993172i	$0.462781\pi$
$168$	0	0
$169$	−7.46619	−0.574322
$170$	13.2979	1.01990
$171$	−1.53924	−0.117709
$172$	4.08671	0.311608
$173$	2.42150	0.184103	0.0920516	−	0.995754i	$-0.470658\pi$
$173$	2.42150	0.184103	0.0920516	+	0.995754i	$0.470658\pi$
$174$	7.98856	0.605611
$175$	0	0
$176$	0.764505	0.0576268
$177$	0.519212	0.0390263
$178$	3.29921	0.247286
$179$	17.7746	1.32854	0.664268	−	0.747495i	$-0.268744\pi$
$179$	17.7746	1.32854	0.664268	+	0.747495i	$0.268744\pi$
$180$	−3.89296	−0.290164
$181$	18.9450	1.40817	0.704087	−	0.710114i	$-0.251356\pi$
$181$	18.9450	1.40817	0.704087	+	0.710114i	$0.251356\pi$
$182$	0	0
$183$	2.10590	0.155672
$184$	5.20163	0.383469
$185$	25.6845	1.88836
$186$	−0.814885	−0.0597502
$187$	0.329048	0.0240623
$188$	0.222130	0.0162005
$189$	0	0
$190$	9.53365	0.691644
$191$	−9.12762	−0.660451	−0.330226	−	0.943902i	$-0.607125\pi$
$191$	−9.12762	−0.660451	−0.330226	+	0.943902i	$0.607125\pi$
$192$	−0.0167549	−0.00120918
$193$	−15.0315	−1.08199	−0.540996	−	0.841025i	$-0.681953\pi$
$193$	−15.0315	−1.08199	−0.540996	+	0.841025i	$0.681953\pi$
$194$	−16.4026	−1.17764
$195$	8.26451	0.591834
$196$	0	0
$197$	6.19254	0.441200	0.220600	−	0.975364i	$-0.429198\pi$
$197$	6.19254	0.441200	0.220600	+	0.975364i	$0.429198\pi$
$198$	−0.270193	−0.0192018
$199$	−20.8642	−1.47903	−0.739513	−	0.673143i	$-0.764944\pi$
$199$	−20.8642	−1.47903	−0.739513	+	0.673143i	$0.764944\pi$
$200$	−11.5457	−0.816408
$201$	−14.3401	−1.01147
$202$	27.9890	1.96930
$203$	0	0
$204$	2.37907	0.166568
$205$	3.51322	0.245374
$206$	32.9814	2.29793
$207$	−3.30805	−0.229925
$208$	−11.7345	−0.813644
$209$	0.235903	0.0163178
$210$	0	0
$211$	15.0775	1.03798	0.518989	−	0.854781i	$-0.326309\pi$
$211$	15.0775	1.03798	0.518989	+	0.854781i	$0.326309\pi$
$212$	−8.97416	−0.616348
$213$	−5.11775	−0.350662
$214$	11.9973	0.820119
$215$	−12.9569	−0.883656
$216$	1.57241	0.106989
$217$	0	0
$218$	25.5579	1.73100
$219$	−6.70809	−0.453291
$220$	0.596633	0.0402250
$221$	−5.05062	−0.339741
$222$	12.8888	0.865042
$223$	−6.22227	−0.416674	−0.208337	−	0.978057i	$-0.566805\pi$
$223$	−6.22227	−0.416674	−0.208337	+	0.978057i	$0.566805\pi$
$224$	0	0
$225$	7.34269	0.489512
$226$	19.2241	1.27877
$227$	−22.2786	−1.47868	−0.739340	−	0.673332i	$-0.764862\pi$
$227$	−22.2786	−1.47868	−0.739340	+	0.673332i	$0.764862\pi$
$228$	1.70562	0.112958
$229$	−22.3029	−1.47382	−0.736910	−	0.675991i	$-0.763716\pi$
$229$	−22.3029	−1.47382	−0.736910	+	0.675991i	$0.763716\pi$
$230$	20.4891	1.35101
$231$	0	0
$232$	7.12506	0.467783
$233$	9.54073	0.625034	0.312517	−	0.949912i	$-0.398828\pi$
$233$	9.54073	0.625034	0.312517	+	0.949912i	$0.398828\pi$
$234$	4.14724	0.271114
$235$	−0.704264	−0.0459411
$236$	−0.575334	−0.0374510
$237$	2.88889	0.187654
$238$	0	0
$239$	7.33462	0.474437	0.237219	−	0.971456i	$-0.423764\pi$
$239$	7.33462	0.474437	0.237219	+	0.971456i	$0.423764\pi$
$240$	−17.5250	−1.13124
$241$	10.6267	0.684524	0.342262	−	0.939605i	$-0.388807\pi$
$241$	10.6267	0.684524	0.342262	+	0.939605i	$0.388807\pi$
$242$	−19.3513	−1.24395
$243$	−1.00000	−0.0641500
$244$	−2.33353	−0.149389
$245$	0	0
$246$	1.76298	0.112403
$247$	−3.62093	−0.230394
$248$	−0.726803	−0.0461520
$249$	−0.349683	−0.0221602
$250$	−14.5099	−0.917689
$251$	−24.9505	−1.57486	−0.787432	−	0.616401i	$-0.788590\pi$
$251$	−24.9505	−1.57486	−0.787432	+	0.616401i	$0.788590\pi$
$252$	0	0
$253$	0.506989	0.0318741
$254$	−4.74678	−0.297840
$255$	−7.54287	−0.472353
$256$	19.9383	1.24615
$257$	−16.9251	−1.05576	−0.527880	−	0.849319i	$-0.677013\pi$
$257$	−16.9251	−1.05576	−0.527880	+	0.849319i	$0.677013\pi$
$258$	−6.50196	−0.404795
$259$	0	0
$260$	−9.15783	−0.567945
$261$	−4.53129	−0.280480
$262$	−25.0326	−1.54652
$263$	8.88776	0.548043	0.274021	−	0.961724i	$-0.411646\pi$
$263$	8.88776	0.548043	0.274021	+	0.961724i	$0.411646\pi$
$264$	−0.240987	−0.0148317
$265$	28.4527	1.74783
$266$	0	0
$267$	−1.87138	−0.114527
$268$	15.8901	0.970642
$269$	1.00992	0.0615760	0.0307880	−	0.999526i	$-0.490198\pi$
$269$	1.00992	0.0615760	0.0307880	+	0.999526i	$0.490198\pi$
$270$	6.19372	0.376938
$271$	5.34824	0.324882	0.162441	−	0.986718i	$-0.448063\pi$
$271$	5.34824	0.324882	0.162441	+	0.986718i	$0.448063\pi$
$272$	10.7099	0.649384
$273$	0	0
$274$	−16.8806	−1.01980
$275$	−1.12533	−0.0678602
$276$	3.66562	0.220645
$277$	22.6002	1.35792	0.678958	−	0.734177i	$-0.262432\pi$
$277$	22.6002	1.35792	0.678958	+	0.734177i	$0.262432\pi$
$278$	31.8924	1.91278
$279$	0.462221	0.0276724
$280$	0	0
$281$	22.8887	1.36542	0.682712	−	0.730688i	$-0.260800\pi$
$281$	22.8887	1.36542	0.682712	+	0.730688i	$0.260800\pi$
$282$	−0.353409	−0.0210452
$283$	5.82600	0.346320	0.173160	−	0.984894i	$-0.444602\pi$
$283$	5.82600	0.346320	0.173160	+	0.984894i	$0.444602\pi$
$284$	5.67093	0.336508
$285$	−5.40770	−0.320324
$286$	−0.635603	−0.0375840
$287$	0	0
$288$	−5.64946	−0.332898
$289$	−12.3904	−0.728847
$290$	28.0655	1.64806
$291$	9.30390	0.545404
$292$	7.43318	0.434994
$293$	−14.4075	−0.841695	−0.420848	−	0.907131i	$-0.638267\pi$
$293$	−14.4075	−0.841695	−0.420848	+	0.907131i	$0.638267\pi$
$294$	0	0
$295$	1.82410	0.106203
$296$	11.4957	0.668172
$297$	0.153259	0.00889300
$298$	13.2749	0.768996
$299$	−7.78188	−0.450038
$300$	−8.13637	−0.469753
$301$	0	0
$302$	12.6734	0.729270
$303$	−15.8760	−0.912050
$304$	7.67824	0.440377
$305$	7.39848	0.423635
$306$	−3.78511	−0.216381
$307$	28.0043	1.59829	0.799145	−	0.601139i	$-0.205286\pi$
$307$	28.0043	1.59829	0.799145	+	0.601139i	$0.205286\pi$
$308$	0	0
$309$	−18.7078	−1.06425
$310$	−2.86287	−0.162600
$311$	−5.44438	−0.308723	−0.154361	−	0.988014i	$-0.549332\pi$
$311$	−5.44438	−0.308723	−0.154361	+	0.988014i	$0.549332\pi$
$312$	3.69896	0.209412
$313$	−10.2875	−0.581487	−0.290743	−	0.956801i	$-0.593903\pi$
$313$	−10.2875	−0.581487	−0.290743	+	0.956801i	$0.593903\pi$
$314$	38.7686	2.18784
$315$	0	0
$316$	−3.20116	−0.180079
$317$	−6.28867	−0.353207	−0.176603	−	0.984282i	$-0.556511\pi$
$317$	−6.28867	−0.353207	−0.176603	+	0.984282i	$0.556511\pi$
$318$	14.2779	0.800666
$319$	0.694461	0.0388824
$320$	−0.0588636	−0.00329058
$321$	−6.80514	−0.379826
$322$	0	0
$323$	3.30476	0.183882
$324$	1.10809	0.0615606
$325$	17.2730	0.958132
$326$	−15.7191	−0.870603
$327$	−14.4970	−0.801686
$328$	1.57241	0.0868221
$329$	0	0
$330$	−0.949245	−0.0522542
$331$	−10.4513	−0.574455	−0.287227	−	0.957862i	$-0.592734\pi$
$331$	−10.4513	−0.574455	−0.287227	+	0.957862i	$0.592734\pi$
$332$	0.387480	0.0212657
$333$	−7.31083	−0.400631
$334$	5.31562	0.290858
$335$	−50.3797	−2.75254
$336$	0	0
$337$	20.2234	1.10164	0.550819	−	0.834625i	$-0.314316\pi$
$337$	20.2234	1.10164	0.550819	+	0.834625i	$0.314316\pi$
$338$	−13.1627	−0.715958
$339$	−10.9043	−0.592242
$340$	8.35820	0.453287
$341$	−0.0708396	−0.00383618
$342$	−2.71365	−0.146738
$343$	0	0
$344$	−5.79916	−0.312670
$345$	−11.6219	−0.625702
$346$	4.26905	0.229506
$347$	−27.0279	−1.45093	−0.725466	−	0.688258i	$-0.758376\pi$
$347$	−27.0279	−1.45093	−0.725466	+	0.688258i	$0.758376\pi$
$348$	5.02108	0.269158
$349$	3.37370	0.180590	0.0902950	−	0.995915i	$-0.471219\pi$
$349$	3.37370	0.180590	0.0902950	+	0.995915i	$0.471219\pi$
$350$	0	0
$351$	−2.35241	−0.125562
$352$	0.865832	0.0461490
$353$	5.94112	0.316214	0.158107	−	0.987422i	$-0.449461\pi$
$353$	5.94112	0.316214	0.158107	+	0.987422i	$0.449461\pi$
$354$	0.915359	0.0486508
$355$	−17.9797	−0.954266
$356$	2.07366	0.109904
$357$	0	0
$358$	31.3362	1.65617
$359$	29.5196	1.55798	0.778991	−	0.627035i	$-0.215732\pi$
$359$	29.5196	1.55798	0.778991	+	0.627035i	$0.215732\pi$
$360$	5.52423	0.291153
$361$	−16.6307	−0.875301
$362$	33.3997	1.75545
$363$	10.9765	0.576117
$364$	0	0
$365$	−23.5670	−1.23355
$366$	3.71265	0.194063
$367$	36.7303	1.91731	0.958653	−	0.284577i	$-0.0918532\pi$
$367$	36.7303	1.91731	0.958653	+	0.284577i	$0.0918532\pi$
$368$	16.5016	0.860205
$369$	−1.00000	−0.0520579
$370$	45.2812	2.35406
$371$	0	0
$372$	−0.512183	−0.0265554
$373$	3.94562	0.204296	0.102148	−	0.994769i	$-0.467428\pi$
$373$	3.94562	0.204296	0.102148	+	0.994769i	$0.467428\pi$
$374$	0.580104	0.0299964
$375$	8.23036	0.425014
$376$	−0.315208	−0.0162556
$377$	−10.6594	−0.548988
$378$	0	0
$379$	18.5735	0.954057	0.477029	−	0.878888i	$-0.341714\pi$
$379$	18.5735	0.954057	0.477029	+	0.878888i	$0.341714\pi$
$380$	5.99222	0.307395
$381$	2.69248	0.137940
$382$	−16.0918	−0.823327
$383$	−32.0391	−1.63712	−0.818560	−	0.574421i	$-0.805227\pi$
$383$	−32.0391	−1.63712	−0.818560	+	0.574421i	$0.805227\pi$
$384$	−11.3285	−0.578103
$385$	0	0
$386$	−26.5002	−1.34883
$387$	3.68806	0.187474
$388$	−10.3096	−0.523389
$389$	6.04608	0.306549	0.153274	−	0.988184i	$-0.451018\pi$
$389$	6.04608	0.306549	0.153274	+	0.988184i	$0.451018\pi$
$390$	14.5701	0.737788
$391$	7.10238	0.359183
$392$	0	0
$393$	14.1990	0.716246
$394$	10.9173	0.550006
$395$	10.1493	0.510667
$396$	−0.169825	−0.00853404
$397$	−12.0690	−0.605725	−0.302862	−	0.953034i	$-0.597942\pi$
$397$	−12.0690	−0.605725	−0.302862	+	0.953034i	$0.597942\pi$
$398$	−36.7832	−1.84377
$399$	0	0
$400$	−36.6276	−1.83138
$401$	−12.2878	−0.613625	−0.306813	−	0.951770i	$-0.599262\pi$
$401$	−12.2878	−0.613625	−0.306813	+	0.951770i	$0.599262\pi$
$402$	−25.2812	−1.26091
$403$	1.08733	0.0541638
$404$	17.5920	0.875235
$405$	−3.51322	−0.174573
$406$	0	0
$407$	1.12045	0.0555387
$408$	−3.37597	−0.167136
$409$	−10.8267	−0.535344	−0.267672	−	0.963510i	$-0.586254\pi$
$409$	−10.8267	−0.535344	−0.267672	+	0.963510i	$0.586254\pi$
$410$	6.19372	0.305886
$411$	9.57507	0.472303
$412$	20.7300	1.02129
$413$	0	0
$414$	−5.83202	−0.286628
$415$	−1.22851	−0.0603052
$416$	−13.2898	−0.651587
$417$	−18.0900	−0.885873
$418$	0.415892	0.0203420
$419$	6.22595	0.304157	0.152079	−	0.988368i	$-0.451403\pi$
$419$	6.22595	0.304157	0.152079	+	0.988368i	$0.451403\pi$
$420$	0	0
$421$	15.7312	0.766692	0.383346	−	0.923605i	$-0.374772\pi$
$421$	15.7312	0.766692	0.383346	+	0.923605i	$0.374772\pi$
$422$	26.5813	1.29396
$423$	0.200461	0.00974677
$424$	12.7346	0.618447
$425$	−15.7647	−0.764702
$426$	−9.02247	−0.437140
$427$	0	0
$428$	7.54071	0.364494
$429$	0.360528	0.0174065
$430$	−22.8428	−1.10158
$431$	3.48632	0.167930	0.0839652	−	0.996469i	$-0.473242\pi$
$431$	3.48632	0.167930	0.0839652	+	0.996469i	$0.473242\pi$
$432$	4.98832	0.240000
$433$	4.30477	0.206874	0.103437	−	0.994636i	$-0.467016\pi$
$433$	4.30477	0.206874	0.103437	+	0.994636i	$0.467016\pi$
$434$	0	0
$435$	−15.9194	−0.763276
$436$	16.0640	0.769326
$437$	5.09190	0.243578
$438$	−11.8262	−0.565078
$439$	−15.4484	−0.737314	−0.368657	−	0.929566i	$-0.620182\pi$
$439$	−15.4484	−0.737314	−0.368657	+	0.929566i	$0.620182\pi$
$440$	−0.846640	−0.0403620
$441$	0	0
$442$	−8.90412	−0.423526
$443$	26.4331	1.25587	0.627936	−	0.778265i	$-0.283900\pi$
$443$	26.4331	1.25587	0.627936	+	0.778265i	$0.283900\pi$
$444$	8.10107	0.384460
$445$	−6.57457	−0.311665
$446$	−10.9697	−0.519432
$447$	−7.52984	−0.356149
$448$	0	0
$449$	−24.3795	−1.15054	−0.575271	−	0.817963i	$-0.695103\pi$
$449$	−24.3795	−1.15054	−0.575271	+	0.817963i	$0.695103\pi$
$450$	12.9450	0.610233
$451$	0.153259	0.00721669
$452$	12.0830	0.568336
$453$	−7.18861	−0.337750
$454$	−39.2766	−1.84334
$455$	0	0
$456$	−2.42033	−0.113342
$457$	2.04659	0.0957355	0.0478678	−	0.998854i	$-0.484757\pi$
$457$	2.04659	0.0957355	0.0478678	+	0.998854i	$0.484757\pi$
$458$	−39.3196	−1.83728
$459$	2.14700	0.100213
$460$	12.8781	0.600446
$461$	9.05983	0.421958	0.210979	−	0.977491i	$-0.432335\pi$
$461$	9.05983	0.421958	0.210979	+	0.977491i	$0.432335\pi$
$462$	0	0
$463$	34.2073	1.58975	0.794874	−	0.606775i	$-0.207537\pi$
$463$	34.2073	1.58975	0.794874	+	0.606775i	$0.207537\pi$
$464$	22.6035	1.04934
$465$	1.62388	0.0753057
$466$	16.8201	0.779176
$467$	−18.2381	−0.843961	−0.421980	−	0.906605i	$-0.638665\pi$
$467$	−18.2381	−0.843961	−0.421980	+	0.906605i	$0.638665\pi$
$468$	2.60668	0.120494
$469$	0	0
$470$	−1.24160	−0.0572708
$471$	−21.9904	−1.01326
$472$	0.816416	0.0375786
$473$	−0.565229	−0.0259892
$474$	5.09306	0.233932
$475$	−11.3022	−0.518580
$476$	0	0
$477$	−8.09875	−0.370816
$478$	12.9308	0.591440
$479$	−17.6864	−0.808110	−0.404055	−	0.914735i	$-0.632400\pi$
$479$	−17.6864	−0.808110	−0.404055	+	0.914735i	$0.632400\pi$
$480$	−19.8478	−0.905923
$481$	−17.1980	−0.784163
$482$	18.7346	0.853337
$483$	0	0
$484$	−12.1630	−0.552863
$485$	32.6866	1.48422
$486$	−1.76298	−0.0799703
$487$	−36.2629	−1.64323	−0.821615	−	0.570043i	$-0.806927\pi$
$487$	−36.2629	−1.64323	−0.821615	+	0.570043i	$0.806927\pi$
$488$	3.31135	0.149898
$489$	8.91625	0.403207
$490$	0	0
$491$	−36.2157	−1.63439	−0.817195	−	0.576361i	$-0.804472\pi$
$491$	−36.2157	−1.63439	−0.817195	+	0.576361i	$0.804472\pi$
$492$	1.10809	0.0499566
$493$	9.72867	0.438157
$494$	−6.38362	−0.287212
$495$	0.538433	0.0242008
$496$	−2.30570	−0.103529
$497$	0	0
$498$	−0.616483	−0.0276253
$499$	−5.27117	−0.235970	−0.117985	−	0.993015i	$-0.537643\pi$
$499$	−5.27117	−0.235970	−0.117985	+	0.993015i	$0.537643\pi$
$500$	−9.11999	−0.407858
$501$	−3.01514	−0.134706
$502$	−43.9873	−1.96325
$503$	8.59294	0.383140	0.191570	−	0.981479i	$-0.438642\pi$
$503$	8.59294	0.383140	0.191570	+	0.981479i	$0.438642\pi$
$504$	0	0
$505$	−55.7757	−2.48198
$506$	0.893811	0.0397347
$507$	7.46619	0.331585
$508$	−2.98351	−0.132372
$509$	35.7148	1.58303	0.791515	−	0.611150i	$-0.209293\pi$
$509$	35.7148	1.58303	0.791515	+	0.611150i	$0.209293\pi$
$510$	−13.2979	−0.588842
$511$	0	0
$512$	12.4939	0.552157
$513$	1.53924	0.0679593
$514$	−29.8386	−1.31613
$515$	−65.7246	−2.89617
$516$	−4.08671	−0.179907
$517$	−0.0307226	−0.00135118
$518$	0	0
$519$	−2.42150	−0.106292
$520$	12.9952	0.569879
$521$	−4.85721	−0.212798	−0.106399	−	0.994324i	$-0.533932\pi$
$521$	−4.85721	−0.212798	−0.106399	+	0.994324i	$0.533932\pi$
$522$	−7.98856	−0.349650
$523$	−13.7918	−0.603073	−0.301537	−	0.953455i	$-0.597500\pi$
$523$	−13.7918	−0.603073	−0.301537	+	0.953455i	$0.597500\pi$
$524$	−15.7338	−0.687335
$525$	0	0
$526$	15.6689	0.683197
$527$	−0.992387	−0.0432291
$528$	−0.764505	−0.0332708
$529$	−12.0568	−0.524209
$530$	50.1614	2.17887
$531$	−0.519212	−0.0225319
$532$	0	0
$533$	−2.35241	−0.101894
$534$	−3.29921	−0.142771
$535$	−23.9079	−1.03363
$536$	−22.5485	−0.973948
$537$	−17.7746	−0.767030
$538$	1.78047	0.0767615
$539$	0	0
$540$	3.89296	0.167527
$541$	13.9611	0.600235	0.300117	−	0.953902i	$-0.402974\pi$
$541$	13.9611	0.600235	0.300117	+	0.953902i	$0.402974\pi$
$542$	9.42882	0.405003
$543$	−18.9450	−0.813010
$544$	12.1294	0.520043
$545$	−50.9311	−2.18165
$546$	0	0
$547$	37.3982	1.59903	0.799516	−	0.600644i	$-0.205089\pi$
$547$	37.3982	1.59903	0.799516	+	0.600644i	$0.205089\pi$
$548$	−10.6101	−0.453239
$549$	−2.10590	−0.0898775
$550$	−1.98394	−0.0845955
$551$	6.97476	0.297135
$552$	−5.20163	−0.221396
$553$	0	0
$554$	39.8437	1.69280
$555$	−25.6845	−1.09025
$556$	20.0454	0.850116
$557$	1.73041	0.0733200	0.0366600	−	0.999328i	$-0.488328\pi$
$557$	1.73041	0.0733200	0.0366600	+	0.999328i	$0.488328\pi$
$558$	0.814885	0.0344968
$559$	8.67581	0.366948
$560$	0	0
$561$	−0.329048	−0.0138924
$562$	40.3522	1.70216
$563$	9.87388	0.416134	0.208067	−	0.978115i	$-0.433283\pi$
$563$	9.87388	0.416134	0.208067	+	0.978115i	$0.433283\pi$
$564$	−0.222130	−0.00935334
$565$	−38.3092	−1.61168
$566$	10.2711	0.431727
$567$	0	0
$568$	−8.04722	−0.337654
$569$	36.4363	1.52749	0.763744	−	0.645519i	$-0.223359\pi$
$569$	36.4363	1.52749	0.763744	+	0.645519i	$0.223359\pi$
$570$	−9.53365	−0.399321
$571$	−29.8704	−1.25004	−0.625019	−	0.780610i	$-0.714909\pi$
$571$	−29.8704	−1.25004	−0.625019	+	0.780610i	$0.714909\pi$
$572$	−0.399498	−0.0167038
$573$	9.12762	0.381312
$574$	0	0
$575$	−24.2900	−1.01296
$576$	0.0167549	0.000698121 0
$577$	20.4964	0.853277	0.426638	−	0.904422i	$-0.359698\pi$
$577$	20.4964	0.853277	0.426638	+	0.904422i	$0.359698\pi$
$578$	−21.8440	−0.908590
$579$	15.0315	0.624688
$580$	17.6401	0.732467
$581$	0	0
$582$	16.4026	0.679909
$583$	1.24121	0.0514056
$584$	−10.5479	−0.436475
$585$	−8.26451	−0.341695
$586$	−25.4001	−1.04927
$587$	5.59113	0.230771	0.115385	−	0.993321i	$-0.463190\pi$
$587$	5.59113	0.230771	0.115385	+	0.993321i	$0.463190\pi$
$588$	0	0
$589$	−0.711470	−0.0293156
$590$	3.21585	0.132395
$591$	−6.19254	−0.254727
$592$	36.4687	1.49886
$593$	−7.14936	−0.293589	−0.146794	−	0.989167i	$-0.546896\pi$
$593$	−7.14936	−0.293589	−0.146794	+	0.989167i	$0.546896\pi$
$594$	0.270193	0.0110861
$595$	0	0
$596$	8.34375	0.341773
$597$	20.8642	0.853916
$598$	−13.7193	−0.561023
$599$	32.9077	1.34457	0.672287	−	0.740291i	$-0.265312\pi$
$599$	32.9077	1.34457	0.672287	+	0.740291i	$0.265312\pi$
$600$	11.5457	0.471353
$601$	−40.7143	−1.66077	−0.830386	−	0.557188i	$-0.811880\pi$
$601$	−40.7143	−1.66077	−0.830386	+	0.557188i	$0.811880\pi$
$602$	0	0
$603$	14.3401	0.583972
$604$	7.96563	0.324117
$605$	38.5629	1.56780
$606$	−27.9890	−1.13697
$607$	−6.02578	−0.244579	−0.122289	−	0.992494i	$-0.539024\pi$
$607$	−6.02578	−0.244579	−0.122289	+	0.992494i	$0.539024\pi$
$608$	8.69590	0.352665
$609$	0	0
$610$	13.0433	0.528110
$611$	0.471567	0.0190775
$612$	−2.37907	−0.0961683
$613$	12.1435	0.490471	0.245235	−	0.969464i	$-0.421135\pi$
$613$	12.1435	0.490471	0.245235	+	0.969464i	$0.421135\pi$
$614$	49.3710	1.99245
$615$	−3.51322	−0.141667
$616$	0	0
$617$	31.7612	1.27866	0.639329	−	0.768933i	$-0.279212\pi$
$617$	31.7612	1.27866	0.639329	+	0.768933i	$0.279212\pi$
$618$	−32.9814	−1.32671
$619$	13.2321	0.531842	0.265921	−	0.963995i	$-0.414324\pi$
$619$	13.2321	0.531842	0.265921	+	0.963995i	$0.414324\pi$
$620$	−1.79941	−0.0722660
$621$	3.30805	0.132747
$622$	−9.59832	−0.384858
$623$	0	0
$624$	11.7345	0.469758
$625$	−7.79840	−0.311936
$626$	−18.1367	−0.724889
$627$	−0.235903	−0.00942107
$628$	24.3674	0.972364
$629$	15.6963	0.625854
$630$	0	0
$631$	4.27005	0.169988	0.0849940	−	0.996381i	$-0.472913\pi$
$631$	4.27005	0.169988	0.0849940	+	0.996381i	$0.472913\pi$
$632$	4.54254	0.180693
$633$	−15.0775	−0.599277
$634$	−11.0868	−0.440312
$635$	9.45926	0.375379
$636$	8.97416	0.355849
$637$	0	0
$638$	1.22432	0.0484713
$639$	5.11775	0.202455
$640$	−39.7993	−1.57321
$641$	−30.8242	−1.21748	−0.608741	−	0.793369i	$-0.708325\pi$
$641$	−30.8242	−1.21748	−0.608741	+	0.793369i	$0.708325\pi$
$642$	−11.9973	−0.473496
$643$	−40.6982	−1.60498	−0.802490	−	0.596666i	$-0.796492\pi$
$643$	−40.6982	−1.60498	−0.802490	+	0.596666i	$0.796492\pi$
$644$	0	0
$645$	12.9569	0.510179
$646$	5.82621	0.229229
$647$	−2.71221	−0.106628	−0.0533141	−	0.998578i	$-0.516978\pi$
$647$	−2.71221	−0.106628	−0.0533141	+	0.998578i	$0.516978\pi$
$648$	−1.57241	−0.0617703
$649$	0.0795740	0.00312355
$650$	30.4519	1.19442
$651$	0	0
$652$	−9.88002	−0.386931
$653$	28.3292	1.10861	0.554303	−	0.832315i	$-0.312985\pi$
$653$	28.3292	1.10861	0.554303	+	0.832315i	$0.312985\pi$
$654$	−25.5579	−0.999393
$655$	49.8843	1.94914
$656$	4.98832	0.194761
$657$	6.70809	0.261708
$658$	0	0
$659$	19.3189	0.752559	0.376279	−	0.926506i	$-0.377203\pi$
$659$	19.3189	0.752559	0.376279	+	0.926506i	$0.377203\pi$
$660$	−0.596633	−0.0232239
$661$	−17.0248	−0.662188	−0.331094	−	0.943598i	$-0.607418\pi$
$661$	−17.0248	−0.662188	−0.331094	+	0.943598i	$0.607418\pi$
$662$	−18.4254	−0.716123
$663$	5.05062	0.196150
$664$	−0.549846	−0.0213382
$665$	0	0
$666$	−12.8888	−0.499432
$667$	14.9897	0.580404
$668$	3.34105	0.129269
$669$	6.22227	0.240567
$670$	−88.8183	−3.43135
$671$	0.322748	0.0124596
$672$	0	0
$673$	−49.7452	−1.91754	−0.958768	−	0.284190i	$-0.908275\pi$
$673$	−49.7452	−1.91754	−0.958768	+	0.284190i	$0.908275\pi$
$674$	35.6534	1.37332
$675$	−7.34269	−0.282620
$676$	−8.27322	−0.318201
$677$	29.5251	1.13474	0.567372	−	0.823462i	$-0.307960\pi$
$677$	29.5251	1.13474	0.567372	+	0.823462i	$0.307960\pi$
$678$	−19.2241	−0.738296
$679$	0	0
$680$	−11.8605	−0.454830
$681$	22.2786	0.853717
$682$	−0.124889	−0.00478223
$683$	−22.1250	−0.846589	−0.423294	−	0.905992i	$-0.639126\pi$
$683$	−22.1250	−0.846589	−0.423294	+	0.905992i	$0.639126\pi$
$684$	−1.70562	−0.0652161
$685$	33.6393	1.28529
$686$	0	0
$687$	22.3029	0.850911
$688$	−18.3972	−0.701386
$689$	−19.0516	−0.725806
$690$	−20.4891	−0.780008
$691$	46.6462	1.77450	0.887252	−	0.461285i	$-0.152611\pi$
$691$	46.6462	1.77450	0.887252	+	0.461285i	$0.152611\pi$
$692$	2.68324	0.102002
$693$	0	0
$694$	−47.6495	−1.80875
$695$	−63.5542	−2.41075
$696$	−7.12506	−0.270075
$697$	2.14700	0.0813234
$698$	5.94776	0.225126
$699$	−9.54073	−0.360864
$700$	0	0
$701$	−37.0007	−1.39750	−0.698748	−	0.715368i	$-0.746259\pi$
$701$	−37.0007	−1.39750	−0.698748	+	0.715368i	$0.746259\pi$
$702$	−4.14724	−0.156527
$703$	11.2532	0.424421
$704$	−0.00256784	−9.67793e−5 0
$705$	0.704264	0.0265241
$706$	10.4741	0.394197
$707$	0	0
$708$	0.575334	0.0216224
$709$	20.1599	0.757123	0.378561	−	0.925576i	$-0.376419\pi$
$709$	20.1599	0.757123	0.378561	+	0.925576i	$0.376419\pi$
$710$	−31.6979	−1.18960
$711$	−2.88889	−0.108342
$712$	−2.94259	−0.110278
$713$	−1.52905	−0.0572633
$714$	0	0
$715$	1.26661	0.0473686
$716$	19.6959	0.736069
$717$	−7.33462	−0.273917
$718$	52.0423	1.94220
$719$	41.6127	1.55189	0.775946	−	0.630799i	$-0.217273\pi$
$719$	41.6127	1.55189	0.775946	+	0.630799i	$0.217273\pi$
$720$	17.5250	0.653119
$721$	0	0
$722$	−29.3196	−1.09116
$723$	−10.6267	−0.395210
$724$	20.9928	0.780193
$725$	−33.2718	−1.23568
$726$	19.3513	0.718196
$727$	13.1809	0.488853	0.244427	−	0.969668i	$-0.421400\pi$
$727$	13.1809	0.488853	0.244427	+	0.969668i	$0.421400\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−41.5480	−1.53776
$731$	−7.91826	−0.292867
$732$	2.33353	0.0862497
$733$	46.8015	1.72865	0.864327	−	0.502930i	$-0.167745\pi$
$733$	46.8015	1.72865	0.864327	+	0.502930i	$0.167745\pi$
$734$	64.7547	2.39014
$735$	0	0
$736$	18.6887	0.688875
$737$	−2.19775	−0.0809550
$738$	−1.76298	−0.0648961
$739$	26.0375	0.957807	0.478903	−	0.877868i	$-0.341034\pi$
$739$	26.0375	0.957807	0.478903	+	0.877868i	$0.341034\pi$
$740$	28.4608	1.04624
$741$	3.62093	0.133018
$742$	0	0
$743$	23.6043	0.865956	0.432978	−	0.901404i	$-0.357463\pi$
$743$	23.6043	0.865956	0.432978	+	0.901404i	$0.357463\pi$
$744$	0.726803	0.0266459
$745$	−26.4539	−0.969197
$746$	6.95604	0.254679
$747$	0.349683	0.0127942
$748$	0.364615	0.0133316
$749$	0	0
$750$	14.5099	0.529828
$751$	−5.74126	−0.209502	−0.104751	−	0.994498i	$-0.533405\pi$
$751$	−5.74126	−0.209502	−0.104751	+	0.994498i	$0.533405\pi$
$752$	−0.999965	−0.0364650
$753$	24.9505	0.909248
$754$	−18.7923	−0.684376
$755$	−25.2551	−0.919128
$756$	0	0
$757$	−34.2154	−1.24358	−0.621791	−	0.783183i	$-0.713595\pi$
$757$	−34.2154	−1.24358	−0.621791	+	0.783183i	$0.713595\pi$
$758$	32.7447	1.18934
$759$	−0.506989	−0.0184025
$760$	−8.50314	−0.308441
$761$	20.5043	0.743280	0.371640	−	0.928377i	$-0.378796\pi$
$761$	20.5043	0.743280	0.371640	+	0.928377i	$0.378796\pi$
$762$	4.74678	0.171958
$763$	0	0
$764$	−10.1142	−0.365920
$765$	7.54287	0.272713
$766$	−56.4842	−2.04086
$767$	−1.22140	−0.0441021
$768$	−19.9383	−0.719462
$769$	5.59555	0.201781	0.100890	−	0.994898i	$-0.467831\pi$
$769$	5.59555	0.201781	0.100890	+	0.994898i	$0.467831\pi$
$770$	0	0
$771$	16.9251	0.609544
$772$	−16.6563	−0.599473
$773$	14.0158	0.504114	0.252057	−	0.967712i	$-0.418893\pi$
$773$	14.0158	0.504114	0.252057	+	0.967712i	$0.418893\pi$
$774$	6.50196	0.233708
$775$	3.39394	0.121914
$776$	14.6296	0.525172
$777$	0	0
$778$	10.6591	0.382148
$779$	1.53924	0.0551491
$780$	9.15783	0.327903
$781$	−0.784342	−0.0280659
$782$	12.5213	0.447762
$783$	4.53129	0.161935
$784$	0	0
$785$	−77.2570	−2.75742
$786$	25.0326	0.892882
$787$	−0.00890650	−0.000317482 0	−0.000158741	−	1.00000i	$-0.500051\pi$
$787$	−0.00890650	−0.000317482 0	−0.000158741		1.00000i	$0.500051\pi$
$788$	6.86190	0.244445
$789$	−8.88776	−0.316413
$790$	17.8930	0.636605
$791$	0	0
$792$	0.240987	0.00856310
$793$	−4.95393	−0.175919
$794$	−21.2774	−0.755105
$795$	−28.4527	−1.00911
$796$	−23.1195	−0.819448
$797$	−47.0451	−1.66642	−0.833211	−	0.552954i	$-0.813500\pi$
$797$	−47.0451	−1.66642	−0.833211	+	0.552954i	$0.813500\pi$
$798$	0	0
$799$	−0.430391	−0.0152261
$800$	−41.4822	−1.46662
$801$	1.87138	0.0661221
$802$	−21.6632	−0.764953
$803$	−1.02808	−0.0362800
$804$	−15.8901	−0.560400
$805$	0	0
$806$	1.91694	0.0675213
$807$	−1.00992	−0.0355509
$808$	−24.9636	−0.878216
$809$	−19.5973	−0.689006	−0.344503	−	0.938785i	$-0.611953\pi$
$809$	−19.5973	−0.689006	−0.344503	+	0.938785i	$0.611953\pi$
$810$	−6.19372	−0.217625
$811$	−19.1670	−0.673046	−0.336523	−	0.941675i	$-0.609251\pi$
$811$	−19.1670	−0.673046	−0.336523	+	0.941675i	$0.609251\pi$
$812$	0	0
$813$	−5.34824	−0.187571
$814$	1.97533	0.0692354
$815$	31.3247	1.09726
$816$	−10.7099	−0.374922
$817$	−5.67682	−0.198607
$818$	−19.0872	−0.667367
$819$	0	0
$820$	3.89296	0.135948
$821$	−26.7619	−0.933996	−0.466998	−	0.884258i	$-0.654665\pi$
$821$	−26.7619	−0.933996	−0.466998	+	0.884258i	$0.654665\pi$
$822$	16.8806	0.588780
$823$	−49.8669	−1.73825	−0.869125	−	0.494592i	$-0.835317\pi$
$823$	−49.8669	−1.73825	−0.869125	+	0.494592i	$0.835317\pi$
$824$	−29.4164	−1.02477
$825$	1.12533	0.0391791
$826$	0	0
$827$	11.5217	0.400650	0.200325	−	0.979729i	$-0.435800\pi$
$827$	11.5217	0.400650	0.200325	+	0.979729i	$0.435800\pi$
$828$	−3.66562	−0.127389
$829$	36.8850	1.28107	0.640535	−	0.767929i	$-0.278713\pi$
$829$	36.8850	1.28107	0.640535	+	0.767929i	$0.278713\pi$
$830$	−2.16584	−0.0751773
$831$	−22.6002	−0.783993
$832$	0.0394144	0.00136645
$833$	0	0
$834$	−31.8924	−1.10434
$835$	−10.5928	−0.366580
$836$	0.261403	0.00904080
$837$	−0.462221	−0.0159767
$838$	10.9762	0.379167
$839$	−20.8081	−0.718377	−0.359188	−	0.933265i	$-0.616946\pi$
$839$	−20.8081	−0.718377	−0.359188	+	0.933265i	$0.616946\pi$
$840$	0	0
$841$	−8.46745	−0.291981
$842$	27.7338	0.955769
$843$	−22.8887	−0.788328
$844$	16.7073	0.575087
$845$	26.2303	0.902351
$846$	0.353409	0.0121505
$847$	0	0
$848$	40.3991	1.38731
$849$	−5.82600	−0.199948
$850$	−27.7929	−0.953289
$851$	24.1846	0.829037
$852$	−5.67093	−0.194283
$853$	46.0297	1.57603	0.788014	−	0.615658i	$-0.211110\pi$
$853$	46.0297	1.57603	0.788014	+	0.615658i	$0.211110\pi$
$854$	0	0
$855$	5.40770	0.184939
$856$	−10.7005	−0.365735
$857$	−8.16902	−0.279048	−0.139524	−	0.990219i	$-0.544557\pi$
$857$	−8.16902	−0.279048	−0.139524	+	0.990219i	$0.544557\pi$
$858$	0.635603	0.0216991
$859$	−19.6237	−0.669551	−0.334776	−	0.942298i	$-0.608661\pi$
$859$	−19.6237	−0.669551	−0.334776	+	0.942298i	$0.608661\pi$
$860$	−14.3575	−0.489586
$861$	0	0
$862$	6.14631	0.209344
$863$	−38.9104	−1.32452	−0.662262	−	0.749272i	$-0.730403\pi$
$863$	−38.9104	−1.32452	−0.662262	+	0.749272i	$0.730403\pi$
$864$	5.64946	0.192199
$865$	−8.50725	−0.289255
$866$	7.58922	0.257892
$867$	12.3904	0.420800
$868$	0	0
$869$	0.442750	0.0150193
$870$	−28.0655	−0.951510
$871$	33.7336	1.14302
$872$	−22.7953	−0.771946
$873$	−9.30390	−0.314889
$874$	8.97690	0.303648
$875$	0	0
$876$	−7.43318	−0.251144
$877$	−30.9324	−1.04451	−0.522256	−	0.852789i	$-0.674909\pi$
$877$	−30.9324	−1.04451	−0.522256	+	0.852789i	$0.674909\pi$
$878$	−27.2353	−0.919145
$879$	14.4075	0.485953
$880$	−2.68587	−0.0905407
$881$	36.6380	1.23437	0.617183	−	0.786819i	$-0.288274\pi$
$881$	36.6380	1.23437	0.617183	+	0.786819i	$0.288274\pi$
$882$	0	0
$883$	−7.63457	−0.256924	−0.128462	−	0.991714i	$-0.541004\pi$
$883$	−7.63457	−0.256924	−0.128462	+	0.991714i	$0.541004\pi$
$884$	−5.59654	−0.188232
$885$	−1.82410	−0.0613165
$886$	46.6009	1.56559
$887$	6.73740	0.226220	0.113110	−	0.993582i	$-0.463919\pi$
$887$	6.73740	0.226220	0.113110	+	0.993582i	$0.463919\pi$
$888$	−11.4957	−0.385769
$889$	0	0
$890$	−11.5908	−0.388525
$891$	−0.153259	−0.00513438
$892$	−6.89485	−0.230857
$893$	−0.308559	−0.0103255
$894$	−13.2749	−0.443980
$895$	−62.4460	−2.08734
$896$	0	0
$897$	7.78188	0.259829
$898$	−42.9806	−1.43428
$899$	−2.09445	−0.0698539
$900$	8.13637	0.271212
$901$	17.3880	0.579279
$902$	0.270193	0.00899643
$903$	0	0
$904$	−17.1461	−0.570272
$905$	−66.5580	−2.21246
$906$	−12.6734	−0.421044
$907$	25.4475	0.844969	0.422485	−	0.906370i	$-0.361158\pi$
$907$	25.4475	0.844969	0.422485	+	0.906370i	$0.361158\pi$
$908$	−24.6867	−0.819257
$909$	15.8760	0.526572
$910$	0	0
$911$	−52.3981	−1.73603	−0.868013	−	0.496541i	$-0.834603\pi$
$911$	−52.3981	−1.73603	−0.868013	+	0.496541i	$0.834603\pi$
$912$	−7.67824	−0.254252
$913$	−0.0535921	−0.00177364
$914$	3.60810	0.119345
$915$	−7.39848	−0.244586
$916$	−24.7137	−0.816564
$917$	0	0
$918$	3.78511	0.124927
$919$	39.4875	1.30257	0.651286	−	0.758833i	$-0.274230\pi$
$919$	39.4875	1.30257	0.651286	+	0.758833i	$0.274230\pi$
$920$	−18.2744	−0.602490
$921$	−28.0043	−0.922773
$922$	15.9723	0.526019
$923$	12.0390	0.396269
$924$	0	0
$925$	−53.6811	−1.76502
$926$	60.3067	1.98180
$927$	18.7078	0.614445
$928$	25.5993	0.840339
$929$	−6.33471	−0.207835	−0.103917	−	0.994586i	$-0.533138\pi$
$929$	−6.33471	−0.207835	−0.103917	+	0.994586i	$0.533138\pi$
$930$	2.86287	0.0938771
$931$	0	0
$932$	10.5720	0.346297
$933$	5.44438	0.178241
$934$	−32.1534	−1.05209
$935$	−1.15601	−0.0378057
$936$	−3.69896	−0.120904
$937$	−11.7911	−0.385198	−0.192599	−	0.981278i	$-0.561692\pi$
$937$	−11.7911	−0.385198	−0.192599	+	0.981278i	$0.561692\pi$
$938$	0	0
$939$	10.2875	0.335721
$940$	−0.780389	−0.0254535
$941$	46.3405	1.51066	0.755329	−	0.655345i	$-0.227477\pi$
$941$	46.3405	1.51066	0.755329	+	0.655345i	$0.227477\pi$
$942$	−38.7686	−1.26315
$943$	3.30805	0.107725
$944$	2.58999	0.0842970
$945$	0	0
$946$	−0.996486	−0.0323985
$947$	−44.0358	−1.43097	−0.715485	−	0.698628i	$-0.753794\pi$
$947$	−44.0358	−1.43097	−0.715485	+	0.698628i	$0.753794\pi$
$948$	3.20116	0.103969
$949$	15.7802	0.512245
$950$	−19.9255	−0.646469
$951$	6.28867	0.203924
$952$	0	0
$953$	42.4278	1.37437	0.687185	−	0.726482i	$-0.258846\pi$
$953$	42.4278	1.37437	0.687185	+	0.726482i	$0.258846\pi$
$954$	−14.2779	−0.462265
$955$	32.0673	1.03767
$956$	8.12743	0.262860
$957$	−0.694461	−0.0224487
$958$	−31.1806	−1.00740
$959$	0	0
$960$	0.0588636	0.00189982
$961$	−30.7864	−0.993108
$962$	−30.3198	−0.977548
$963$	6.80514	0.219292
$964$	11.7753	0.379258
$965$	52.8089	1.69998
$966$	0	0
$967$	46.9193	1.50882	0.754412	−	0.656401i	$-0.227922\pi$
$967$	46.9193	1.50882	0.754412	+	0.656401i	$0.227922\pi$
$968$	17.2596	0.554746
$969$	−3.30476	−0.106164
$970$	57.6258	1.85025
$971$	50.5664	1.62275	0.811376	−	0.584525i	$-0.198719\pi$
$971$	50.5664	1.62275	0.811376	+	0.584525i	$0.198719\pi$
$972$	−1.10809	−0.0355421
$973$	0	0
$974$	−63.9308	−2.04847
$975$	−17.2730	−0.553178
$976$	10.5049	0.336253
$977$	41.0155	1.31220	0.656101	−	0.754673i	$-0.272205\pi$
$977$	41.0155	1.31220	0.656101	+	0.754673i	$0.272205\pi$
$978$	15.7191	0.502643
$979$	−0.286807	−0.00916638
$980$	0	0
$981$	14.4970	0.462854
$982$	−63.8474	−2.03745
$983$	−7.15597	−0.228240	−0.114120	−	0.993467i	$-0.536405\pi$
$983$	−7.15597	−0.228240	−0.114120	+	0.993467i	$0.536405\pi$
$984$	−1.57241	−0.0501268
$985$	−21.7557	−0.693195
$986$	17.1514	0.546213
$987$	0	0
$988$	−4.01232	−0.127649
$989$	−12.2003	−0.387946
$990$	0.949245	0.0301690
$991$	−0.649041	−0.0206175	−0.0103087	−	0.999947i	$-0.503281\pi$
$991$	−0.649041	−0.0206175	−0.0103087	+	0.999947i	$0.503281\pi$
$992$	−2.61130	−0.0829088
$993$	10.4513	0.331662
$994$	0	0
$995$	73.3005	2.32378
$996$	−0.387480	−0.0122778
$997$	29.1089	0.921887	0.460944	−	0.887429i	$-0.347511\pi$
$997$	29.1089	0.921887	0.460944	+	0.887429i	$0.347511\pi$
$998$	−9.29296	−0.294164
$999$	7.31083	0.231304

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.y.1.5		7
7.6	odd	2		861.2.a.m.1.5	✓	7
21.20	even	2		2583.2.a.u.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.a.m.1.5	✓	7	7.6	odd	2
2583.2.a.u.1.3		7	21.20	even	2
6027.2.a.y.1.5		7	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+1.76298 q^{2} -1.00000 q^{3} +1.10809 q^{4} -3.51322 q^{5} -1.76298 q^{6} -1.57241 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.76298 q^{2} -1.00000 q^{3} +1.10809 q^{4} -3.51322 q^{5} -1.76298 q^{6} -1.57241 q^{8} +1.00000 q^{9} -6.19372 q^{10} -0.153259 q^{11} -1.10809 q^{12} +2.35241 q^{13} +3.51322 q^{15} -4.98832 q^{16} -2.14700 q^{17} +1.76298 q^{18} -1.53924 q^{19} -3.89296 q^{20} -0.270193 q^{22} -3.30805 q^{23} +1.57241 q^{24} +7.34269 q^{25} +4.14724 q^{26} -1.00000 q^{27} -4.53129 q^{29} +6.19372 q^{30} +0.462221 q^{31} -5.64946 q^{32} +0.153259 q^{33} -3.78511 q^{34} +1.10809 q^{36} -7.31083 q^{37} -2.71365 q^{38} -2.35241 q^{39} +5.52423 q^{40} -1.00000 q^{41} +3.68806 q^{43} -0.169825 q^{44} -3.51322 q^{45} -5.83202 q^{46} +0.200461 q^{47} +4.98832 q^{48} +12.9450 q^{50} +2.14700 q^{51} +2.60668 q^{52} -8.09875 q^{53} -1.76298 q^{54} +0.538433 q^{55} +1.53924 q^{57} -7.98856 q^{58} -0.519212 q^{59} +3.89296 q^{60} -2.10590 q^{61} +0.814885 q^{62} +0.0167549 q^{64} -8.26451 q^{65} +0.270193 q^{66} +14.3401 q^{67} -2.37907 q^{68} +3.30805 q^{69} +5.11775 q^{71} -1.57241 q^{72} +6.70809 q^{73} -12.8888 q^{74} -7.34269 q^{75} -1.70562 q^{76} -4.14724 q^{78} -2.88889 q^{79} +17.5250 q^{80} +1.00000 q^{81} -1.76298 q^{82} +0.349683 q^{83} +7.54287 q^{85} +6.50196 q^{86} +4.53129 q^{87} +0.240987 q^{88} +1.87138 q^{89} -6.19372 q^{90} -3.66562 q^{92} -0.462221 q^{93} +0.353409 q^{94} +5.40770 q^{95} +5.64946 q^{96} -9.30390 q^{97} -0.153259 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9	\( 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9} + 3 q^{10} + 11 q^{11} - 8 q^{12} + 7 q^{13} + q^{15} + 6 q^{16} - 11 q^{17} + 4 q^{18} - 4 q^{19} + 7 q^{20} + 6 q^{22} + 7 q^{23} - 12 q^{24} + 2 q^{25} + 13 q^{26} - 7 q^{27} + 4 q^{29} - 3 q^{30} + 7 q^{31} + 18 q^{32} - 11 q^{33} + 20 q^{34} + 8 q^{36} - 4 q^{38} - 7 q^{39} + 9 q^{40} - 7 q^{41} + q^{43} + 18 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 6 q^{48} + 19 q^{50} + 11 q^{51} + 27 q^{52} + 23 q^{53} - 4 q^{54} + 30 q^{55} + 4 q^{57} - 3 q^{58} - 8 q^{59} - 7 q^{60} + 3 q^{61} + 16 q^{62} + 6 q^{64} + 15 q^{65} - 6 q^{66} + 3 q^{67} - 7 q^{69} + 7 q^{71} + 12 q^{72} + 11 q^{73} - 13 q^{74} - 2 q^{75} + 40 q^{76} - 13 q^{78} - q^{79} + 43 q^{80} + 7 q^{81} - 4 q^{82} - 10 q^{85} - 12 q^{86} - 4 q^{87} + 10 q^{88} - 32 q^{89} + 3 q^{90} - 19 q^{92} - 7 q^{93} - 21 q^{94} - 8 q^{95} - 18 q^{96} + 25 q^{97} + 11 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9 + 3 * q^10 + 11 * q^11 - 8 * q^12 + 7 * q^13 + q^15 + 6 * q^16 - 11 * q^17 + 4 * q^18 - 4 * q^19 + 7 * q^20 + 6 * q^22 + 7 * q^23 - 12 * q^24 + 2 * q^25 + 13 * q^26 - 7 * q^27 + 4 * q^29 - 3 * q^30 + 7 * q^31 + 18 * q^32 - 11 * q^33 + 20 * q^34 + 8 * q^36 - 4 * q^38 - 7 * q^39 + 9 * q^40 - 7 * q^41 + q^43 + 18 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 6 * q^48 + 19 * q^50 + 11 * q^51 + 27 * q^52 + 23 * q^53 - 4 * q^54 + 30 * q^55 + 4 * q^57 - 3 * q^58 - 8 * q^59 - 7 * q^60 + 3 * q^61 + 16 * q^62 + 6 * q^64 + 15 * q^65 - 6 * q^66 + 3 * q^67 - 7 * q^69 + 7 * q^71 + 12 * q^72 + 11 * q^73 - 13 * q^74 - 2 * q^75 + 40 * q^76 - 13 * q^78 - q^79 + 43 * q^80 + 7 * q^81 - 4 * q^82 - 10 * q^85 - 12 * q^86 - 4 * q^87 + 10 * q^88 - 32 * q^89 + 3 * q^90 - 19 * q^92 - 7 * q^93 - 21 * q^94 - 8 * q^95 - 18 * q^96 + 25 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more