LMFDB - Embedded newform 8107.2.a.o.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8107,2,Mod(1,8107)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8107, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8107.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8107 = 11^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8107.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:	$64.7347209187$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - x^{16} - 26 x^{15} + 25 x^{14} + 272 x^{13} - 244 x^{12} - 1472 x^{11} + 1186 x^{10} + 4406 x^{9} + \cdots - 2 $ x^17 - x^16 - 26x^15 + 25x^14 + 272x^13 - 244x^12 - 1472x^11 + 1186x^10 + 4406x^9 - 3042x^8 - 7180x^7 + 4055x^6 + 5665x^5 - 2655x^4 - 1418x^3 + 810x^2 - 76*x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 737)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.0213052$ of defining polynomial
Character	$\chi$	$=$	8107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0213052 q^{2} -0.490641 q^{3} -1.99955 q^{4} -1.68894 q^{5} -0.0104532 q^{6} +3.23910 q^{7} -0.0852109 q^{8} -2.75927 q^{9} +O(q^{10})$	\(q+0.0213052 q^{2} -0.490641 q^{3} -1.99955 q^{4} -1.68894 q^{5} -0.0104532 q^{6} +3.23910 q^{7} -0.0852109 q^{8} -2.75927 q^{9} -0.0359832 q^{10} +0.981059 q^{12} +0.729835 q^{13} +0.0690095 q^{14} +0.828664 q^{15} +3.99728 q^{16} -5.52036 q^{17} -0.0587867 q^{18} -4.57010 q^{19} +3.37712 q^{20} -1.58923 q^{21} +2.78230 q^{23} +0.0418080 q^{24} -2.14748 q^{25} +0.0155493 q^{26} +2.82573 q^{27} -6.47673 q^{28} -3.98163 q^{29} +0.0176548 q^{30} -3.98681 q^{31} +0.255584 q^{32} -0.117612 q^{34} -5.47065 q^{35} +5.51729 q^{36} +1.37287 q^{37} -0.0973667 q^{38} -0.358087 q^{39} +0.143916 q^{40} +6.10913 q^{41} -0.0338589 q^{42} +2.58984 q^{43} +4.66025 q^{45} +0.0592774 q^{46} -4.60719 q^{47} -1.96123 q^{48} +3.49177 q^{49} -0.0457523 q^{50} +2.70852 q^{51} -1.45934 q^{52} +5.81037 q^{53} +0.0602027 q^{54} -0.276007 q^{56} +2.24228 q^{57} -0.0848291 q^{58} +2.36004 q^{59} -1.65695 q^{60} -13.1551 q^{61} -0.0849396 q^{62} -8.93756 q^{63} -7.98911 q^{64} -1.23265 q^{65} -1.00000 q^{67} +11.0382 q^{68} -1.36511 q^{69} -0.116553 q^{70} +9.41869 q^{71} +0.235120 q^{72} -3.79882 q^{73} +0.0292491 q^{74} +1.05364 q^{75} +9.13813 q^{76} -0.00762910 q^{78} -1.84987 q^{79} -6.75117 q^{80} +6.89140 q^{81} +0.130156 q^{82} -3.66734 q^{83} +3.17775 q^{84} +9.32357 q^{85} +0.0551769 q^{86} +1.95355 q^{87} -15.6158 q^{89} +0.0992873 q^{90} +2.36401 q^{91} -5.56334 q^{92} +1.95609 q^{93} -0.0981568 q^{94} +7.71863 q^{95} -0.125400 q^{96} -5.47596 q^{97} +0.0743928 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - q^{2} + 10 q^{3} + 19 q^{4} + 10 q^{5} + 6 q^{6} - 20 q^{7} + 25 q^{9}+O(q^{10}) $ 17 * q - q^2 + 10 * q^3 + 19 * q^4 + 10 * q^5 + 6 * q^6 - 20 * q^7 + 25 * q^9	\( 17 q - q^{2} + 10 q^{3} + 19 q^{4} + 10 q^{5} + 6 q^{6} - 20 q^{7} + 25 q^{9} - 10 q^{10} + 18 q^{12} - q^{13} - 11 q^{14} + 7 q^{15} + 19 q^{16} - 2 q^{17} + 24 q^{18} - 13 q^{19} + 3 q^{20} - 5 q^{21} + 16 q^{23} + 36 q^{24} + 33 q^{25} + 12 q^{26} + 19 q^{27} - 44 q^{28} + 5 q^{29} - 3 q^{30} + 16 q^{31} + 24 q^{32} + 4 q^{34} + 2 q^{35} + 25 q^{36} + 29 q^{37} - 19 q^{38} - 2 q^{39} - 31 q^{40} + 6 q^{41} - 26 q^{42} - 19 q^{43} + 20 q^{45} + 33 q^{46} + 40 q^{47} + 81 q^{48} + 23 q^{49} + 3 q^{50} + q^{51} + 28 q^{52} + 15 q^{53} + 27 q^{54} - 38 q^{56} + 27 q^{57} - 12 q^{58} - 2 q^{59} - 59 q^{60} + 6 q^{61} - 3 q^{62} - 32 q^{63} - 4 q^{64} + 30 q^{65} - 17 q^{67} + 13 q^{68} + 5 q^{69} + 71 q^{70} + 2 q^{71} + 47 q^{72} - 41 q^{73} + 13 q^{74} - 6 q^{75} - 21 q^{76} + 31 q^{78} - 41 q^{79} - 23 q^{80} + 37 q^{81} - 8 q^{82} - 2 q^{83} + 16 q^{84} + 36 q^{85} - 54 q^{86} - 32 q^{87} + q^{89} + 44 q^{90} + 16 q^{91} + 36 q^{92} + 26 q^{93} - 12 q^{94} + 31 q^{95} + 72 q^{96} + 3 q^{97} + 64 q^{98}+O(q^{100}) \) 17 * q - q^2 + 10 * q^3 + 19 * q^4 + 10 * q^5 + 6 * q^6 - 20 * q^7 + 25 * q^9 - 10 * q^10 + 18 * q^12 - q^13 - 11 * q^14 + 7 * q^15 + 19 * q^16 - 2 * q^17 + 24 * q^18 - 13 * q^19 + 3 * q^20 - 5 * q^21 + 16 * q^23 + 36 * q^24 + 33 * q^25 + 12 * q^26 + 19 * q^27 - 44 * q^28 + 5 * q^29 - 3 * q^30 + 16 * q^31 + 24 * q^32 + 4 * q^34 + 2 * q^35 + 25 * q^36 + 29 * q^37 - 19 * q^38 - 2 * q^39 - 31 * q^40 + 6 * q^41 - 26 * q^42 - 19 * q^43 + 20 * q^45 + 33 * q^46 + 40 * q^47 + 81 * q^48 + 23 * q^49 + 3 * q^50 + q^51 + 28 * q^52 + 15 * q^53 + 27 * q^54 - 38 * q^56 + 27 * q^57 - 12 * q^58 - 2 * q^59 - 59 * q^60 + 6 * q^61 - 3 * q^62 - 32 * q^63 - 4 * q^64 + 30 * q^65 - 17 * q^67 + 13 * q^68 + 5 * q^69 + 71 * q^70 + 2 * q^71 + 47 * q^72 - 41 * q^73 + 13 * q^74 - 6 * q^75 - 21 * q^76 + 31 * q^78 - 41 * q^79 - 23 * q^80 + 37 * q^81 - 8 * q^82 - 2 * q^83 + 16 * q^84 + 36 * q^85 - 54 * q^86 - 32 * q^87 + q^89 + 44 * q^90 + 16 * q^91 + 36 * q^92 + 26 * q^93 - 12 * q^94 + 31 * q^95 + 72 * q^96 + 3 * q^97 + 64 * 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 $

$2$	0.0213052	0.0150650	0.00753251	−	0.999972i	$-0.497602\pi$
$2$	0.0213052	0.0150650	0.00753251	+	0.999972i	$0.497602\pi$
$3$	−0.490641	−0.283272	−0.141636	−	0.989919i	$-0.545236\pi$
$3$	−0.490641	−0.283272	−0.141636	+	0.989919i	$0.545236\pi$
$4$	−1.99955	−0.999773
$5$	−1.68894	−0.755318	−0.377659	−	0.925945i	$-0.623271\pi$
$5$	−1.68894	−0.755318	−0.377659	+	0.925945i	$0.623271\pi$
$6$	−0.0104532	−0.00426749
$7$	3.23910	1.22427	0.612133	−	0.790755i	$-0.290312\pi$
$7$	3.23910	1.22427	0.612133	+	0.790755i	$0.290312\pi$
$8$	−0.0852109	−0.0301266
$9$	−2.75927	−0.919757
$10$	−0.0359832	−0.0113789
$11$	0	0
$11$	0	0
$12$	0.981059	0.283207
$13$	0.729835	0.202420	0.101210	−	0.994865i	$-0.467729\pi$
$13$	0.729835	0.202420	0.101210	+	0.994865i	$0.467729\pi$
$14$	0.0690095	0.0184436
$15$	0.828664	0.213960
$16$	3.99728	0.999319
$17$	−5.52036	−1.33888	−0.669442	−	0.742864i	$-0.733467\pi$
$17$	−5.52036	−1.33888	−0.669442	+	0.742864i	$0.733467\pi$
$18$	−0.0587867	−0.0138562
$19$	−4.57010	−1.04845	−0.524226	−	0.851579i	$-0.675645\pi$
$19$	−4.57010	−1.04845	−0.524226	+	0.851579i	$0.675645\pi$
$20$	3.37712	0.755146
$21$	−1.58923	−0.346799
$22$	0	0
$23$	2.78230	0.580150	0.290075	−	0.957004i	$-0.406320\pi$
$23$	2.78230	0.580150	0.290075	+	0.957004i	$0.406320\pi$
$24$	0.0418080	0.00853401
$25$	−2.14748	−0.429495
$26$	0.0155493	0.00304946
$27$	2.82573	0.543813
$28$	−6.47673	−1.22399
$29$	−3.98163	−0.739369	−0.369685	−	0.929157i	$-0.620534\pi$
$29$	−3.98163	−0.739369	−0.369685	+	0.929157i	$0.620534\pi$
$30$	0.0176548	0.00322331
$31$	−3.98681	−0.716052	−0.358026	−	0.933712i	$-0.616550\pi$
$31$	−3.98681	−0.716052	−0.358026	+	0.933712i	$0.616550\pi$
$32$	0.255584	0.0451814
$33$	0	0
$34$	−0.117612	−0.0201703
$35$	−5.47065	−0.924709
$36$	5.51729	0.919548
$37$	1.37287	0.225698	0.112849	−	0.993612i	$-0.464002\pi$
$37$	1.37287	0.225698	0.112849	+	0.993612i	$0.464002\pi$
$38$	−0.0973667	−0.0157950
$39$	−0.358087	−0.0573398
$40$	0.143916	0.0227552
$41$	6.10913	0.954085	0.477043	−	0.878880i	$-0.341709\pi$
$41$	6.10913	0.954085	0.477043	+	0.878880i	$0.341709\pi$
$42$	−0.0338589	−0.00522454
$43$	2.58984	0.394946	0.197473	−	0.980308i	$-0.436726\pi$
$43$	2.58984	0.394946	0.197473	+	0.980308i	$0.436726\pi$
$44$	0	0
$45$	4.66025	0.694709
$46$	0.0592774	0.00873998
$47$	−4.60719	−0.672027	−0.336014	−	0.941857i	$-0.609079\pi$
$47$	−4.60719	−0.672027	−0.336014	+	0.941857i	$0.609079\pi$
$48$	−1.96123	−0.283079
$49$	3.49177	0.498825
$50$	−0.0457523	−0.00647035
$51$	2.70852	0.379268
$52$	−1.45934	−0.202374
$53$	5.81037	0.798116	0.399058	−	0.916926i	$-0.369337\pi$
$53$	5.81037	0.798116	0.399058	+	0.916926i	$0.369337\pi$
$54$	0.0602027	0.00819255
$55$	0	0
$56$	−0.276007	−0.0368830
$57$	2.24228	0.296997
$58$	−0.0848291	−0.0111386
$59$	2.36004	0.307250	0.153625	−	0.988129i	$-0.450905\pi$
$59$	2.36004	0.307250	0.153625	+	0.988129i	$0.450905\pi$
$60$	−1.65695	−0.213911
$61$	−13.1551	−1.68434	−0.842171	−	0.539210i	$-0.818723\pi$
$61$	−13.1551	−1.68434	−0.842171	+	0.539210i	$0.818723\pi$
$62$	−0.0849396	−0.0107873
$63$	−8.93756	−1.12603
$64$	−7.98911	−0.998639
$65$	−1.23265	−0.152891
$66$	0	0
$67$	−1.00000	−0.122169
$67$	−1.00000	−0.122169
$68$	11.0382	1.33858
$69$	−1.36511	−0.164340
$70$	−0.116553	−0.0139308
$71$	9.41869	1.11779	0.558897	−	0.829237i	$-0.311225\pi$
$71$	9.41869	1.11779	0.558897	+	0.829237i	$0.311225\pi$
$72$	0.235120	0.0277092
$73$	−3.79882	−0.444618	−0.222309	−	0.974976i	$-0.571359\pi$
$73$	−3.79882	−0.444618	−0.222309	+	0.974976i	$0.571359\pi$
$74$	0.0292491	0.00340014
$75$	1.05364	0.121664
$76$	9.13813	1.04821
$77$	0	0
$78$	−0.00762910	−0.000863825 0
$79$	−1.84987	−0.208126	−0.104063	−	0.994571i	$-0.533184\pi$
$79$	−1.84987	−0.208126	−0.104063	+	0.994571i	$0.533184\pi$
$80$	−6.75117	−0.754803
$81$	6.89140	0.765711
$82$	0.130156	0.0143733
$83$	−3.66734	−0.402542	−0.201271	−	0.979536i	$-0.564507\pi$
$83$	−3.66734	−0.402542	−0.201271	+	0.979536i	$0.564507\pi$
$84$	3.17775	0.346721
$85$	9.32357	1.01128
$86$	0.0551769	0.00594987
$87$	1.95355	0.209442
$88$	0	0
$89$	−15.6158	−1.65528	−0.827638	−	0.561262i	$-0.810316\pi$
$89$	−15.6158	−1.65528	−0.827638	+	0.561262i	$0.810316\pi$
$90$	0.0992873	0.0104658
$91$	2.36401	0.247816
$92$	−5.56334	−0.580019
$93$	1.95609	0.202837
$94$	−0.0981568	−0.0101241
$95$	7.71863	0.791915
$96$	−0.125400	−0.0127986
$97$	−5.47596	−0.556000	−0.278000	−	0.960581i	$-0.589671\pi$
$97$	−5.47596	−0.556000	−0.278000	+	0.960581i	$0.589671\pi$
$98$	0.0743928	0.00751481
$99$	0	0
$100$	4.29398	0.429398
$101$	−13.3662	−1.32999	−0.664995	−	0.746847i	$-0.731567\pi$
$101$	−13.3662	−1.32999	−0.664995	+	0.746847i	$0.731567\pi$
$102$	0.0577053	0.00571368
$103$	18.1594	1.78930	0.894651	−	0.446766i	$-0.147424\pi$
$103$	18.1594	1.78930	0.894651	+	0.446766i	$0.147424\pi$
$104$	−0.0621899	−0.00609823
$105$	2.68412	0.261944
$106$	0.123791	0.0120236
$107$	−6.52010	−0.630322	−0.315161	−	0.949038i	$-0.602058\pi$
$107$	−6.52010	−0.630322	−0.315161	+	0.949038i	$0.602058\pi$
$108$	−5.65018	−0.543689
$109$	10.9067	1.04467	0.522334	−	0.852741i	$-0.325061\pi$
$109$	10.9067	1.04467	0.522334	+	0.852741i	$0.325061\pi$
$110$	0	0
$111$	−0.673584	−0.0639337
$112$	12.9476	1.22343
$113$	−2.75543	−0.259209	−0.129605	−	0.991566i	$-0.541371\pi$
$113$	−2.75543	−0.259209	−0.129605	+	0.991566i	$0.541371\pi$
$114$	0.0477721	0.00447426
$115$	−4.69915	−0.438198
$116$	7.96144	0.739201
$117$	−2.01381	−0.186177
$118$	0.0502809	0.00462873
$119$	−17.8810	−1.63915
$120$	−0.0706112	−0.00644589
$121$	0	0
$122$	−0.280272	−0.0253746
$123$	−2.99739	−0.270265
$124$	7.97181	0.715890
$125$	12.0717	1.07972
$126$	−0.190416	−0.0169636
$127$	−19.4504	−1.72594	−0.862970	−	0.505254i	$-0.831399\pi$
$127$	−19.4504	−1.72594	−0.862970	+	0.505254i	$0.831399\pi$
$128$	−0.681378	−0.0602259
$129$	−1.27068	−0.111877
$130$	−0.0262618	−0.00230331
$131$	−4.51463	−0.394445	−0.197223	−	0.980359i	$-0.563192\pi$
$131$	−4.51463	−0.394445	−0.197223	+	0.980359i	$0.563192\pi$
$132$	0	0
$133$	−14.8030	−1.28358
$134$	−0.0213052	−0.00184049
$135$	−4.77250	−0.410751
$136$	0.470395	0.0403361
$137$	−0.0242608	−0.00207274	−0.00103637	−	0.999999i	$-0.500330\pi$
$137$	−0.0242608	−0.00207274	−0.00103637	+	0.999999i	$0.500330\pi$
$138$	−0.0290839	−0.00247579
$139$	10.6134	0.900221	0.450110	−	0.892973i	$-0.351385\pi$
$139$	10.6134	0.900221	0.450110	+	0.892973i	$0.351385\pi$
$140$	10.9388	0.924499
$141$	2.26047	0.190366
$142$	0.200667	0.0168396
$143$	0	0
$144$	−11.0296	−0.919131
$145$	6.72473	0.558459
$146$	−0.0809345	−0.00669818
$147$	−1.71321	−0.141303
$148$	−2.74511	−0.225646
$149$	4.52419	0.370636	0.185318	−	0.982679i	$-0.440668\pi$
$149$	4.52419	0.370636	0.185318	+	0.982679i	$0.440668\pi$
$150$	0.0224479	0.00183287
$151$	−21.7361	−1.76886	−0.884428	−	0.466677i	$-0.845451\pi$
$151$	−21.7361	−1.76886	−0.884428	+	0.466677i	$0.845451\pi$
$152$	0.389423	0.0315863
$153$	15.2322	1.23145
$154$	0	0
$155$	6.73349	0.540847
$156$	0.716011	0.0573268
$157$	−3.24464	−0.258950	−0.129475	−	0.991583i	$-0.541329\pi$
$157$	−3.24464	−0.258950	−0.129475	+	0.991583i	$0.541329\pi$
$158$	−0.0394117	−0.00313542
$159$	−2.85080	−0.226084
$160$	−0.431667	−0.0341263
$161$	9.01216	0.710258
$162$	0.146822	0.0115354
$163$	17.9557	1.40640	0.703198	−	0.710994i	$-0.251755\pi$
$163$	17.9557	1.40640	0.703198	+	0.710994i	$0.251755\pi$
$164$	−12.2155	−0.953869
$165$	0	0
$166$	−0.0781331	−0.00606431
$167$	19.2420	1.48899	0.744494	−	0.667629i	$-0.232691\pi$
$167$	19.2420	1.48899	0.744494	+	0.667629i	$0.232691\pi$
$168$	0.135420	0.0104479
$169$	−12.4673	−0.959026
$170$	0.198640	0.0152350
$171$	12.6101	0.964322
$172$	−5.17850	−0.394857
$173$	−8.55134	−0.650147	−0.325073	−	0.945689i	$-0.605389\pi$
$173$	−8.55134	−0.650147	−0.325073	+	0.945689i	$0.605389\pi$
$174$	0.0416206	0.00315525
$175$	−6.95589	−0.525816
$176$	0	0
$177$	−1.15793	−0.0870353
$178$	−0.332698	−0.0249368
$179$	−23.6096	−1.76467	−0.882333	−	0.470626i	$-0.844028\pi$
$179$	−23.6096	−1.76467	−0.882333	+	0.470626i	$0.844028\pi$
$180$	−9.31838	−0.694551
$181$	−6.81286	−0.506396	−0.253198	−	0.967414i	$-0.581482\pi$
$181$	−6.81286	−0.506396	−0.253198	+	0.967414i	$0.581482\pi$
$182$	0.0503656	0.00373335
$183$	6.45444	0.477126
$184$	−0.237083	−0.0174780
$185$	−2.31869	−0.170473
$186$	0.0416748	0.00305575
$187$	0	0
$188$	9.21228	0.671875
$189$	9.15283	0.665771
$190$	0.164447	0.0119302
$191$	21.1010	1.52682	0.763408	−	0.645916i	$-0.223524\pi$
$191$	21.1010	1.52682	0.763408	+	0.645916i	$0.223524\pi$
$192$	3.91978	0.282886
$193$	−24.9449	−1.79557	−0.897785	−	0.440434i	$-0.854825\pi$
$193$	−24.9449	−1.79557	−0.897785	+	0.440434i	$0.854825\pi$
$194$	−0.116666	−0.00837615
$195$	0.604788	0.0433098
$196$	−6.98196	−0.498712
$197$	−7.39429	−0.526821	−0.263411	−	0.964684i	$-0.584847\pi$
$197$	−7.39429	−0.526821	−0.263411	+	0.964684i	$0.584847\pi$
$198$	0	0
$199$	19.3563	1.37213	0.686067	−	0.727538i	$-0.259336\pi$
$199$	19.3563	1.37213	0.686067	+	0.727538i	$0.259336\pi$
$200$	0.182988	0.0129392
$201$	0.490641	0.0346071
$202$	−0.284770	−0.0200363
$203$	−12.8969	−0.905184
$204$	−5.41580	−0.379182
$205$	−10.3180	−0.720638
$206$	0.386890	0.0269559
$207$	−7.67713	−0.533598
$208$	2.91735	0.202282
$209$	0	0
$210$	0.0571857	0.00394619
$211$	6.45727	0.444537	0.222268	−	0.974986i	$-0.428654\pi$
$211$	6.45727	0.444537	0.222268	+	0.974986i	$0.428654\pi$
$212$	−11.6181	−0.797935
$213$	−4.62120	−0.316639
$214$	−0.138912	−0.00949581
$215$	−4.37408	−0.298310
$216$	−0.240783	−0.0163832
$217$	−12.9137	−0.876638
$218$	0.232368	0.0157380
$219$	1.86386	0.125948
$220$	0	0
$221$	−4.02896	−0.271017
$222$	−0.0143508	−0.000963163 0
$223$	9.58533	0.641881	0.320941	−	0.947099i	$-0.396001\pi$
$223$	9.58533	0.641881	0.320941	+	0.947099i	$0.396001\pi$
$224$	0.827864	0.0553140
$225$	5.92547	0.395031
$226$	−0.0587049	−0.00390499
$227$	16.0949	1.06826	0.534128	−	0.845404i	$-0.320640\pi$
$227$	16.0949	1.06826	0.534128	+	0.845404i	$0.320640\pi$
$228$	−4.48354	−0.296929
$229$	14.9046	0.984922	0.492461	−	0.870334i	$-0.336097\pi$
$229$	14.9046	0.984922	0.492461	+	0.870334i	$0.336097\pi$
$230$	−0.100116	−0.00660146
$231$	0	0
$232$	0.339278	0.0222747
$233$	27.0638	1.77301	0.886505	−	0.462719i	$-0.153126\pi$
$233$	27.0638	1.77301	0.886505	+	0.462719i	$0.153126\pi$
$234$	−0.0429046	−0.00280476
$235$	7.78127	0.507594
$236$	−4.71900	−0.307181
$237$	0.907619	0.0589562
$238$	−0.380958	−0.0246938
$239$	14.2244	0.920101	0.460051	−	0.887893i	$-0.347831\pi$
$239$	14.2244	0.920101	0.460051	+	0.887893i	$0.347831\pi$
$240$	3.31240	0.213814
$241$	14.6234	0.941973	0.470987	−	0.882140i	$-0.343898\pi$
$241$	14.6234	0.941973	0.470987	+	0.882140i	$0.343898\pi$
$242$	0	0
$243$	−11.8584	−0.760717
$244$	26.3043	1.68396
$245$	−5.89740	−0.376771
$246$	−0.0638598	−0.00407155
$247$	−3.33542	−0.212228
$248$	0.339720	0.0215722
$249$	1.79934	0.114029
$250$	0.257189	0.0162660
$251$	18.0005	1.13618	0.568090	−	0.822967i	$-0.307683\pi$
$251$	18.0005	1.13618	0.568090	+	0.822967i	$0.307683\pi$
$252$	17.8711	1.12577
$253$	0	0
$254$	−0.414393	−0.0260013
$255$	−4.57452	−0.286468
$256$	15.9637	0.997731
$257$	1.27828	0.0797368	0.0398684	−	0.999205i	$-0.487306\pi$
$257$	1.27828	0.0797368	0.0398684	+	0.999205i	$0.487306\pi$
$258$	−0.0270720	−0.00168543
$259$	4.44685	0.276314
$260$	2.46474	0.152857
$261$	10.9864	0.680040
$262$	−0.0961849	−0.00594233
$263$	−2.15265	−0.132738	−0.0663691	−	0.997795i	$-0.521141\pi$
$263$	−2.15265	−0.132738	−0.0663691	+	0.997795i	$0.521141\pi$
$264$	0	0
$265$	−9.81338	−0.602831
$266$	−0.315381	−0.0193372
$267$	7.66177	0.468893
$268$	1.99955	0.122142
$269$	10.8551	0.661847	0.330923	−	0.943658i	$-0.392640\pi$
$269$	10.8551	0.661847	0.330923	+	0.943658i	$0.392640\pi$
$270$	−0.101679	−0.00618798
$271$	4.14708	0.251917	0.125959	−	0.992035i	$-0.459799\pi$
$271$	4.14708	0.251917	0.125959	+	0.992035i	$0.459799\pi$
$272$	−22.0664	−1.33797
$273$	−1.15988	−0.0701991
$274$	−0.000516880 0	−3.12258e−5 0
$275$	0	0
$276$	2.72960	0.164303
$277$	−12.2158	−0.733974	−0.366987	−	0.930226i	$-0.619611\pi$
$277$	−12.2158	−0.733974	−0.366987	+	0.930226i	$0.619611\pi$
$278$	0.226121	0.0135618
$279$	11.0007	0.658594
$280$	0.466159	0.0278584
$281$	4.12060	0.245814	0.122907	−	0.992418i	$-0.460778\pi$
$281$	4.12060	0.245814	0.122907	+	0.992418i	$0.460778\pi$
$282$	0.0481597	0.00286787
$283$	−4.79827	−0.285227	−0.142614	−	0.989778i	$-0.545551\pi$
$283$	−4.79827	−0.285227	−0.142614	+	0.989778i	$0.545551\pi$
$284$	−18.8331	−1.11754
$285$	−3.78708	−0.224327
$286$	0	0
$287$	19.7881	1.16805
$288$	−0.705227	−0.0415559
$289$	13.4744	0.792613
$290$	0.143271	0.00841319
$291$	2.68673	0.157499
$292$	7.59592	0.444517
$293$	28.8052	1.68282	0.841409	−	0.540399i	$-0.181727\pi$
$293$	28.8052	1.68282	0.841409	+	0.540399i	$0.181727\pi$
$294$	−0.0365001	−0.00212873
$295$	−3.98596	−0.232072
$296$	−0.116983	−0.00679951
$297$	0	0
$298$	0.0963887	0.00558365
$299$	2.03062	0.117434
$300$	−2.10680	−0.121636
$301$	8.38874	0.483519
$302$	−0.463090	−0.0266478
$303$	6.55802	0.376749
$304$	−18.2680	−1.04774
$305$	22.2183	1.27221
$306$	0.324524	0.0185518
$307$	−10.0145	−0.571558	−0.285779	−	0.958296i	$-0.592252\pi$
$307$	−10.0145	−0.571558	−0.285779	+	0.958296i	$0.592252\pi$
$308$	0	0
$309$	−8.90976	−0.506858
$310$	0.143458	0.00814787
$311$	21.8223	1.23743	0.618713	−	0.785617i	$-0.287654\pi$
$311$	21.8223	1.23743	0.618713	+	0.785617i	$0.287654\pi$
$312$	0.0305129	0.00172745
$313$	−12.1719	−0.687994	−0.343997	−	0.938971i	$-0.611781\pi$
$313$	−12.1719	−0.687994	−0.343997	+	0.938971i	$0.611781\pi$
$314$	−0.0691275	−0.00390109
$315$	15.0950	0.850508
$316$	3.69889	0.208079
$317$	−16.9133	−0.949945	−0.474972	−	0.880001i	$-0.657542\pi$
$317$	−16.9133	−0.949945	−0.474972	+	0.880001i	$0.657542\pi$
$318$	−0.0607368	−0.00340595
$319$	0	0
$320$	13.4931	0.754289
$321$	3.19903	0.178552
$322$	0.192006	0.0107000
$323$	25.2286	1.40376
$324$	−13.7797	−0.765537
$325$	−1.56730	−0.0869383
$326$	0.382548	0.0211874
$327$	−5.35125	−0.295925
$328$	−0.520565	−0.0287434
$329$	−14.9231	−0.822739
$330$	0	0
$331$	21.9687	1.20751	0.603753	−	0.797171i	$-0.293671\pi$
$331$	21.9687	1.20751	0.603753	+	0.797171i	$0.293671\pi$
$332$	7.33301	0.402451
$333$	−3.78811	−0.207587
$334$	0.409953	0.0224316
$335$	1.68894	0.0922767
$336$	−6.35261	−0.346563
$337$	−5.26378	−0.286736	−0.143368	−	0.989669i	$-0.545793\pi$
$337$	−5.26378	−0.286736	−0.143368	+	0.989669i	$0.545793\pi$
$338$	−0.265619	−0.0144477
$339$	1.35193	0.0734266
$340$	−18.6429	−1.01105
$341$	0	0
$342$	0.268661	0.0145275
$343$	−11.3635	−0.613571
$344$	−0.220682	−0.0118984
$345$	2.30559	0.124129
$346$	−0.182188	−0.00979447
$347$	14.5616	0.781707	0.390854	−	0.920453i	$-0.372180\pi$
$347$	14.5616	0.781707	0.390854	+	0.920453i	$0.372180\pi$
$348$	−3.90621	−0.209395
$349$	13.3885	0.716671	0.358335	−	0.933593i	$-0.383344\pi$
$349$	13.3885	0.716671	0.358335	+	0.933593i	$0.383344\pi$
$350$	−0.148196	−0.00792143
$351$	2.06232	0.110078
$352$	0	0
$353$	32.0925	1.70811	0.854056	−	0.520181i	$-0.174136\pi$
$353$	32.0925	1.70811	0.854056	+	0.520181i	$0.174136\pi$
$354$	−0.0246699	−0.00131119
$355$	−15.9076	−0.844289
$356$	31.2246	1.65490
$357$	8.77315	0.464325
$358$	−0.503007	−0.0265847
$359$	−10.9632	−0.578617	−0.289309	−	0.957236i	$-0.593425\pi$
$359$	−10.9632	−0.578617	−0.289309	+	0.957236i	$0.593425\pi$
$360$	−0.397104	−0.0209292
$361$	1.88581	0.0992533
$362$	−0.145149	−0.00762887
$363$	0	0
$364$	−4.72695	−0.247759
$365$	6.41599	0.335828
$366$	0.137513	0.00718792
$367$	27.6434	1.44297	0.721487	−	0.692428i	$-0.243459\pi$
$367$	27.6434	1.44297	0.721487	+	0.692428i	$0.243459\pi$
$368$	11.1216	0.579755
$369$	−16.8567	−0.877527
$370$	−0.0494000	−0.00256819
$371$	18.8204	0.977105
$372$	−3.91129	−0.202791
$373$	−7.30167	−0.378066	−0.189033	−	0.981971i	$-0.560535\pi$
$373$	−7.30167	−0.378066	−0.189033	+	0.981971i	$0.560535\pi$
$374$	0	0
$375$	−5.92285	−0.305855
$376$	0.392583	0.0202459
$377$	−2.90593	−0.149663
$378$	0.195003	0.0100298
$379$	2.58896	0.132986	0.0664930	−	0.997787i	$-0.478819\pi$
$379$	2.58896	0.132986	0.0664930	+	0.997787i	$0.478819\pi$
$380$	−15.4338	−0.791735
$381$	9.54314	0.488910
$382$	0.449561	0.0230015
$383$	5.51883	0.281999	0.141000	−	0.990010i	$-0.454968\pi$
$383$	5.51883	0.281999	0.141000	+	0.990010i	$0.454968\pi$
$384$	0.334312	0.0170603
$385$	0	0
$386$	−0.531454	−0.0270503
$387$	−7.14606	−0.363255
$388$	10.9494	0.555874
$389$	−16.9637	−0.860093	−0.430047	−	0.902807i	$-0.641503\pi$
$389$	−16.9637	−0.860093	−0.430047	+	0.902807i	$0.641503\pi$
$390$	0.0128851	0.000652462 0
$391$	−15.3593	−0.776755
$392$	−0.297537	−0.0150279
$393$	2.21506	0.111735
$394$	−0.157536	−0.00793657
$395$	3.12432	0.157201
$396$	0	0
$397$	30.4623	1.52886	0.764431	−	0.644706i	$-0.223020\pi$
$397$	30.4623	1.52886	0.764431	+	0.644706i	$0.223020\pi$
$398$	0.412390	0.0206712
$399$	7.26296	0.363603
$400$	−8.58406	−0.429203
$401$	−12.0438	−0.601438	−0.300719	−	0.953713i	$-0.597227\pi$
$401$	−12.0438	−0.601438	−0.300719	+	0.953713i	$0.597227\pi$
$402$	0.0104532	0.000521357 0
$403$	−2.90971	−0.144943
$404$	26.7264	1.32969
$405$	−11.6392	−0.578355
$406$	−0.274770	−0.0136366
$407$	0	0
$408$	−0.230795	−0.0114261
$409$	−16.6409	−0.822840	−0.411420	−	0.911446i	$-0.634967\pi$
$409$	−16.6409	−0.822840	−0.411420	+	0.911446i	$0.634967\pi$
$410$	−0.219826	−0.0108564
$411$	0.0119033	0.000587148 0
$412$	−36.3106	−1.78890
$413$	7.64439	0.376156
$414$	−0.163562	−0.00803866
$415$	6.19392	0.304047
$416$	0.186535	0.00914561
$417$	−5.20739	−0.255007
$418$	0	0
$419$	10.4342	0.509745	0.254872	−	0.966975i	$-0.417967\pi$
$419$	10.4342	0.509745	0.254872	+	0.966975i	$0.417967\pi$
$420$	−5.36703	−0.261884
$421$	−26.2693	−1.28029	−0.640144	−	0.768255i	$-0.721125\pi$
$421$	−26.2693	−1.28029	−0.640144	+	0.768255i	$0.721125\pi$
$422$	0.137573	0.00669695
$423$	12.7125	0.618102
$424$	−0.495107	−0.0240445
$425$	11.8548	0.575045
$426$	−0.0984553	−0.00477017
$427$	−42.6108	−2.06208
$428$	13.0372	0.630179
$429$	0	0
$430$	−0.0931905	−0.00449404
$431$	4.91498	0.236746	0.118373	−	0.992969i	$-0.462232\pi$
$431$	4.91498	0.236746	0.118373	+	0.992969i	$0.462232\pi$
$432$	11.2952	0.543442
$433$	19.6738	0.945463	0.472732	−	0.881206i	$-0.343268\pi$
$433$	19.6738	0.945463	0.472732	+	0.881206i	$0.343268\pi$
$434$	−0.275128	−0.0132066
$435$	−3.29943	−0.158195
$436$	−21.8084	−1.04443
$437$	−12.7154	−0.608260
$438$	0.0397097	0.00189740
$439$	9.73914	0.464824	0.232412	−	0.972617i	$-0.425338\pi$
$439$	9.73914	0.464824	0.232412	+	0.972617i	$0.425338\pi$
$440$	0	0
$441$	−9.63475	−0.458798
$442$	−0.0858375	−0.00408287
$443$	28.0339	1.33193	0.665964	−	0.745983i	$-0.268020\pi$
$443$	28.0339	1.33193	0.665964	+	0.745983i	$0.268020\pi$
$444$	1.34686	0.0639192
$445$	26.3742	1.25026
$446$	0.204217	0.00966995
$447$	−2.21975	−0.104991
$448$	−25.8775	−1.22260
$449$	−9.36598	−0.442008	−0.221004	−	0.975273i	$-0.570933\pi$
$449$	−9.36598	−0.442008	−0.221004	+	0.975273i	$0.570933\pi$
$450$	0.126243	0.00595115
$451$	0	0
$452$	5.50962	0.259151
$453$	10.6646	0.501066
$454$	0.342904	0.0160933
$455$	−3.99267	−0.187179
$456$	−0.191067	−0.00894751
$457$	2.21336	0.103536	0.0517682	−	0.998659i	$-0.483514\pi$
$457$	2.21336	0.103536	0.0517682	+	0.998659i	$0.483514\pi$
$458$	0.317544	0.0148379
$459$	−15.5991	−0.728102
$460$	9.39616	0.438098
$461$	−0.291926	−0.0135964	−0.00679818	−	0.999977i	$-0.502164\pi$
$461$	−0.291926	−0.0135964	−0.00679818	+	0.999977i	$0.502164\pi$
$462$	0	0
$463$	20.8938	0.971019	0.485509	−	0.874231i	$-0.338634\pi$
$463$	20.8938	0.971019	0.485509	+	0.874231i	$0.338634\pi$
$464$	−15.9157	−0.738866
$465$	−3.30372	−0.153207
$466$	0.576599	0.0267104
$467$	39.9976	1.85087	0.925435	−	0.378908i	$-0.123700\pi$
$467$	39.9976	1.85087	0.925435	+	0.378908i	$0.123700\pi$
$468$	4.02671	0.186135
$469$	−3.23910	−0.149568
$470$	0.165781	0.00764691
$471$	1.59195	0.0733532
$472$	−0.201101	−0.00925642
$473$	0	0
$474$	0.0193370	0.000888176 0
$475$	9.81418	0.450305
$476$	35.7539	1.63878
$477$	−16.0324	−0.734073
$478$	0.303053	0.0138613
$479$	−2.84358	−0.129926	−0.0649632	−	0.997888i	$-0.520693\pi$
$479$	−2.84358	−0.129926	−0.0649632	+	0.997888i	$0.520693\pi$
$480$	0.211794	0.00966701
$481$	1.00197	0.0456857
$482$	0.311553	0.0141908
$483$	−4.42173	−0.201196
$484$	0	0
$485$	9.24858	0.419956
$486$	−0.252645	−0.0114602
$487$	−14.1280	−0.640202	−0.320101	−	0.947383i	$-0.603717\pi$
$487$	−14.1280	−0.640202	−0.320101	+	0.947383i	$0.603717\pi$
$488$	1.12096	0.0507435
$489$	−8.80978	−0.398392
$490$	−0.125645	−0.00567607
$491$	9.26772	0.418246	0.209123	−	0.977889i	$-0.432939\pi$
$491$	9.26772	0.418246	0.209123	+	0.977889i	$0.432939\pi$
$492$	5.99341	0.270204
$493$	21.9800	0.989930
$494$	−0.0710616	−0.00319721
$495$	0	0
$496$	−15.9364	−0.715565
$497$	30.5081	1.36848
$498$	0.0383353	0.00171785
$499$	22.3962	1.00259	0.501295	−	0.865277i	$-0.332857\pi$
$499$	22.3962	1.00259	0.501295	+	0.865277i	$0.332857\pi$
$500$	−24.1379	−1.07948
$501$	−9.44089	−0.421788
$502$	0.383503	0.0171166
$503$	37.9536	1.69227	0.846134	−	0.532971i	$-0.178924\pi$
$503$	37.9536	1.69227	0.846134	+	0.532971i	$0.178924\pi$
$504$	0.761578	0.0339234
$505$	22.5748	1.00457
$506$	0	0
$507$	6.11698	0.271665
$508$	38.8919	1.72555
$509$	2.17080	0.0962190	0.0481095	−	0.998842i	$-0.484680\pi$
$509$	2.17080	0.0962190	0.0481095	+	0.998842i	$0.484680\pi$
$510$	−0.0974610	−0.00431564
$511$	−12.3048	−0.544331
$512$	1.70287	0.0752567
$513$	−12.9139	−0.570162
$514$	0.0272339	0.00120124
$515$	−30.6702	−1.35149
$516$	2.54078	0.111852
$517$	0	0
$518$	0.0947408	0.00416267
$519$	4.19564	0.184168
$520$	0.105035	0.00460610
$521$	4.26585	0.186890	0.0934451	−	0.995624i	$-0.470212\pi$
$521$	4.26585	0.186890	0.0934451	+	0.995624i	$0.470212\pi$
$522$	0.234067	0.0102448
$523$	−21.5339	−0.941610	−0.470805	−	0.882237i	$-0.656037\pi$
$523$	−21.5339	−0.941610	−0.470805	+	0.882237i	$0.656037\pi$
$524$	9.02722	0.394356
$525$	3.41284	0.148949
$526$	−0.0458626	−0.00199970
$527$	22.0086	0.958711
$528$	0	0
$529$	−15.2588	−0.663425
$530$	−0.209076	−0.00908166
$531$	−6.51198	−0.282596
$532$	29.5993	1.28329
$533$	4.45866	0.193126
$534$	0.163235	0.00706388
$535$	11.0121	0.476093
$536$	0.0852109	0.00368055
$537$	11.5838	0.499880
$538$	0.231269	0.00997073
$539$	0	0
$540$	9.54283	0.410658
$541$	−5.66794	−0.243684	−0.121842	−	0.992550i	$-0.538880\pi$
$541$	−5.66794	−0.243684	−0.121842	+	0.992550i	$0.538880\pi$
$542$	0.0883542	0.00379514
$543$	3.34267	0.143448
$544$	−1.41092	−0.0604927
$545$	−18.4207	−0.789057
$546$	−0.0247114	−0.00105755
$547$	−2.42389	−0.103638	−0.0518190	−	0.998656i	$-0.516502\pi$
$547$	−2.42389	−0.103638	−0.0518190	+	0.998656i	$0.516502\pi$
$548$	0.0485106	0.00207227
$549$	36.2986	1.54919
$550$	0	0
$551$	18.1964	0.775194
$552$	0.116322	0.00495101
$553$	−5.99190	−0.254802
$554$	−0.260259	−0.0110573
$555$	1.13764	0.0482903
$556$	−21.2221	−0.900017
$557$	−4.24123	−0.179707	−0.0898533	−	0.995955i	$-0.528640\pi$
$557$	−4.24123	−0.179707	−0.0898533	+	0.995955i	$0.528640\pi$
$558$	0.234371	0.00992173
$559$	1.89015	0.0799450
$560$	−21.8677	−0.924080
$561$	0	0
$562$	0.0877900	0.00370320
$563$	19.3999	0.817609	0.408805	−	0.912622i	$-0.365946\pi$
$563$	19.3999	0.817609	0.408805	+	0.912622i	$0.365946\pi$
$564$	−4.51992	−0.190323
$565$	4.65377	0.195785
$566$	−0.102228	−0.00429695
$567$	22.3219	0.937433
$568$	−0.802576	−0.0336753
$569$	40.2978	1.68937	0.844686	−	0.535262i	$-0.179787\pi$
$569$	40.2978	1.68937	0.844686	+	0.535262i	$0.179787\pi$
$570$	−0.0806842	−0.00337949
$571$	40.3296	1.68774	0.843870	−	0.536548i	$-0.180272\pi$
$571$	40.3296	1.68774	0.843870	+	0.536548i	$0.180272\pi$
$572$	0	0
$573$	−10.3530	−0.432504
$574$	0.421588	0.0175967
$575$	−5.97493	−0.249172
$576$	22.0441	0.918505
$577$	−4.68545	−0.195058	−0.0975289	−	0.995233i	$-0.531094\pi$
$577$	−4.68545	−0.195058	−0.0975289	+	0.995233i	$0.531094\pi$
$578$	0.287075	0.0119407
$579$	12.2390	0.508634
$580$	−13.4464	−0.558332
$581$	−11.8789	−0.492819
$582$	0.0572412	0.00237272
$583$	0	0
$584$	0.323701	0.0133948
$585$	3.40121	0.140623
$586$	0.613699	0.0253517
$587$	−35.0050	−1.44481	−0.722405	−	0.691471i	$-0.756963\pi$
$587$	−35.0050	−1.44481	−0.722405	+	0.691471i	$0.756963\pi$
$588$	3.42564	0.141271
$589$	18.2201	0.750747
$590$	−0.0849215	−0.00349616
$591$	3.62794	0.149233
$592$	5.48772	0.225544
$593$	−29.1322	−1.19632	−0.598159	−	0.801378i	$-0.704101\pi$
$593$	−29.1322	−1.19632	−0.598159	+	0.801378i	$0.704101\pi$
$594$	0	0
$595$	30.2000	1.23808
$596$	−9.04634	−0.370552
$597$	−9.49701	−0.388687
$598$	0.0432627	0.00176915
$599$	18.4534	0.753983	0.376992	−	0.926217i	$-0.376959\pi$
$599$	18.4534	0.753983	0.376992	+	0.926217i	$0.376959\pi$
$600$	−0.0897816	−0.00366532
$601$	46.8174	1.90972	0.954860	−	0.297056i	$-0.0960047\pi$
$601$	46.8174	1.90972	0.954860	+	0.297056i	$0.0960047\pi$
$602$	0.178723	0.00728422
$603$	2.75927	0.112366
$604$	43.4623	1.76845
$605$	0	0
$606$	0.139720	0.00567572
$607$	−23.7040	−0.962115	−0.481057	−	0.876689i	$-0.659747\pi$
$607$	−23.7040	−0.962115	−0.481057	+	0.876689i	$0.659747\pi$
$608$	−1.16805	−0.0473705
$609$	6.32774	0.256413
$610$	0.473363	0.0191659
$611$	−3.36249	−0.136032
$612$	−30.4575	−1.23117
$613$	−2.93484	−0.118537	−0.0592685	−	0.998242i	$-0.518877\pi$
$613$	−2.93484	−0.118537	−0.0592685	+	0.998242i	$0.518877\pi$
$614$	−0.213361	−0.00861053
$615$	5.06241	0.204136
$616$	0	0
$617$	13.8934	0.559326	0.279663	−	0.960098i	$-0.409777\pi$
$617$	13.8934	0.559326	0.279663	+	0.960098i	$0.409777\pi$
$618$	−0.189824	−0.00763583
$619$	37.0880	1.49069	0.745346	−	0.666678i	$-0.232284\pi$
$619$	37.0880	1.49069	0.745346	+	0.666678i	$0.232284\pi$
$620$	−13.4639	−0.540724
$621$	7.86205	0.315493
$622$	0.464926	0.0186419
$623$	−50.5813	−2.02650
$624$	−1.43137	−0.0573007
$625$	−9.65097	−0.386039
$626$	−0.259323	−0.0103646
$627$	0	0
$628$	6.48780	0.258891
$629$	−7.57872	−0.302183
$630$	0.321602	0.0128129
$631$	−38.6365	−1.53810	−0.769048	−	0.639191i	$-0.779269\pi$
$631$	−38.6365	−1.53810	−0.769048	+	0.639191i	$0.779269\pi$
$632$	0.157629	0.00627014
$633$	−3.16820	−0.125925
$634$	−0.360340	−0.0143109
$635$	32.8505	1.30363
$636$	5.70032	0.226032
$637$	2.54842	0.100972
$638$	0	0
$639$	−25.9887	−1.02810
$640$	1.15081	0.0454897
$641$	−18.5153	−0.731312	−0.365656	−	0.930750i	$-0.619155\pi$
$641$	−18.5153	−0.731312	−0.365656	+	0.930750i	$0.619155\pi$
$642$	0.0681557	0.00268989
$643$	23.9238	0.943464	0.471732	−	0.881742i	$-0.343629\pi$
$643$	23.9238	0.943464	0.471732	+	0.881742i	$0.343629\pi$
$644$	−18.0202	−0.710097
$645$	2.14610	0.0845027
$646$	0.537500	0.0211476
$647$	−26.5747	−1.04476	−0.522379	−	0.852713i	$-0.674956\pi$
$647$	−26.5747	−1.04476	−0.522379	+	0.852713i	$0.674956\pi$
$648$	−0.587222	−0.0230683
$649$	0	0
$650$	−0.0333916	−0.00130973
$651$	6.33598	0.248326
$652$	−35.9032	−1.40608
$653$	−13.5585	−0.530585	−0.265293	−	0.964168i	$-0.585469\pi$
$653$	−13.5585	−0.530585	−0.265293	+	0.964168i	$0.585469\pi$
$654$	−0.114009	−0.00445812
$655$	7.62495	0.297932
$656$	24.4199	0.953436
$657$	10.4820	0.408941
$658$	−0.317940	−0.0123946
$659$	11.9234	0.464471	0.232235	−	0.972660i	$-0.425396\pi$
$659$	11.9234	0.464471	0.232235	+	0.972660i	$0.425396\pi$
$660$	0	0
$661$	−37.4282	−1.45579	−0.727893	−	0.685690i	$-0.759500\pi$
$661$	−37.4282	−1.45579	−0.727893	+	0.685690i	$0.759500\pi$
$662$	0.468046	0.0181911
$663$	1.97677	0.0767714
$664$	0.312497	0.0121272
$665$	25.0014	0.969514
$666$	−0.0807062	−0.00312730
$667$	−11.0781	−0.428945
$668$	−38.4752	−1.48865
$669$	−4.70295	−0.181827
$670$	0.0359832	0.00139015
$671$	0	0
$672$	−0.406184	−0.0156689
$673$	−37.7695	−1.45591	−0.727953	−	0.685627i	$-0.759528\pi$
$673$	−37.7695	−1.45591	−0.727953	+	0.685627i	$0.759528\pi$
$674$	−0.112146	−0.00431969
$675$	−6.06819	−0.233565
$676$	24.9290	0.958809
$677$	−15.3913	−0.591534	−0.295767	−	0.955260i	$-0.595575\pi$
$677$	−15.3913	−0.591534	−0.295767	+	0.955260i	$0.595575\pi$
$678$	0.0288030	0.00110617
$679$	−17.7372	−0.680691
$680$	−0.794470	−0.0304666
$681$	−7.89682	−0.302607
$682$	0	0
$683$	−10.2969	−0.393998	−0.196999	−	0.980404i	$-0.563120\pi$
$683$	−10.2969	−0.393998	−0.196999	+	0.980404i	$0.563120\pi$
$684$	−25.2146	−0.964103
$685$	0.0409751	0.00156558
$686$	−0.242101	−0.00924346
$687$	−7.31279	−0.279000
$688$	10.3523	0.394677
$689$	4.24061	0.161555
$690$	0.0491210	0.00187001
$691$	20.3625	0.774626	0.387313	−	0.921948i	$-0.373403\pi$
$691$	20.3625	0.774626	0.387313	+	0.921948i	$0.373403\pi$
$692$	17.0988	0.649999
$693$	0	0
$694$	0.310237	0.0117764
$695$	−17.9255	−0.679953
$696$	−0.166464	−0.00630979
$697$	−33.7246	−1.27741
$698$	0.285244	0.0107967
$699$	−13.2786	−0.502243
$700$	13.9086	0.525697
$701$	27.5233	1.03954	0.519770	−	0.854306i	$-0.326018\pi$
$701$	27.5233	1.03954	0.519770	+	0.854306i	$0.326018\pi$
$702$	0.0439380	0.00165833
$703$	−6.27413	−0.236633
$704$	0	0
$705$	−3.81781	−0.143787
$706$	0.683736	0.0257327
$707$	−43.2946	−1.62826
$708$	2.31533	0.0870155
$709$	−18.8640	−0.708452	−0.354226	−	0.935160i	$-0.615256\pi$
$709$	−18.8640	−0.708452	−0.354226	+	0.935160i	$0.615256\pi$
$710$	−0.338914	−0.0127192
$711$	5.10428	0.191426
$712$	1.33064	0.0498679
$713$	−11.0925	−0.415418
$714$	0.186913	0.00699506
$715$	0	0
$716$	47.2085	1.76426
$717$	−6.97908	−0.260638
$718$	−0.233573	−0.00871688
$719$	26.0117	0.970072	0.485036	−	0.874494i	$-0.338807\pi$
$719$	26.0117	0.970072	0.485036	+	0.874494i	$0.338807\pi$
$720$	18.6283	0.694236
$721$	58.8202	2.19058
$722$	0.0401775	0.00149525
$723$	−7.17482	−0.266834
$724$	13.6226	0.506281
$725$	8.55044	0.317556
$726$	0	0
$727$	6.63210	0.245971	0.122985	−	0.992408i	$-0.460753\pi$
$727$	6.63210	0.245971	0.122985	+	0.992408i	$0.460753\pi$
$728$	−0.201440	−0.00746584
$729$	−14.8560	−0.550221
$730$	0.136694	0.00505926
$731$	−14.2968	−0.528788
$732$	−12.9060	−0.477018
$733$	−19.9131	−0.735509	−0.367754	−	0.929923i	$-0.619873\pi$
$733$	−19.9131	−0.735509	−0.367754	+	0.929923i	$0.619873\pi$
$734$	0.588947	0.0217384
$735$	2.89351	0.106729
$736$	0.711114	0.0262120
$737$	0	0
$738$	−0.359136	−0.0132200
$739$	10.8311	0.398427	0.199213	−	0.979956i	$-0.436161\pi$
$739$	10.8311	0.398427	0.199213	+	0.979956i	$0.436161\pi$
$740$	4.63633	0.170435
$741$	1.63649	0.0601181
$742$	0.400971	0.0147201
$743$	40.7728	1.49581	0.747904	−	0.663806i	$-0.231060\pi$
$743$	40.7728	1.49581	0.747904	+	0.663806i	$0.231060\pi$
$744$	−0.166680	−0.00611080
$745$	−7.64110	−0.279948
$746$	−0.155563	−0.00569557
$747$	10.1192	0.370241
$748$	0	0
$749$	−21.1193	−0.771681
$750$	−0.126187	−0.00460771
$751$	35.2767	1.28726	0.643632	−	0.765335i	$-0.277427\pi$
$751$	35.2767	1.28726	0.643632	+	0.765335i	$0.277427\pi$
$752$	−18.4162	−0.671570
$753$	−8.83176	−0.321847
$754$	−0.0619113	−0.00225468
$755$	36.7109	1.33605
$756$	−18.3015	−0.665620
$757$	11.3604	0.412900	0.206450	−	0.978457i	$-0.433809\pi$
$757$	11.3604	0.412900	0.206450	+	0.978457i	$0.433809\pi$
$758$	0.0551583	0.00200344
$759$	0	0
$760$	−0.657712	−0.0238577
$761$	14.0722	0.510115	0.255058	−	0.966926i	$-0.417906\pi$
$761$	14.0722	0.510115	0.255058	+	0.966926i	$0.417906\pi$
$762$	0.203318	0.00736544
$763$	35.3278	1.27895
$764$	−42.1925	−1.52647
$765$	−25.7263	−0.930135
$766$	0.117580	0.00424832
$767$	1.72244	0.0621936
$768$	−7.83244	−0.282629
$769$	39.3322	1.41835	0.709177	−	0.705031i	$-0.249067\pi$
$769$	39.3322	1.41835	0.709177	+	0.705031i	$0.249067\pi$
$770$	0	0
$771$	−0.627175	−0.0225872
$772$	49.8784	1.79516
$773$	−30.3126	−1.09027	−0.545134	−	0.838349i	$-0.683521\pi$
$773$	−30.3126	−1.09027	−0.545134	+	0.838349i	$0.683521\pi$
$774$	−0.152248	−0.00547244
$775$	8.56158	0.307541
$776$	0.466612	0.0167504
$777$	−2.18181	−0.0782718
$778$	−0.361414	−0.0129573
$779$	−27.9193	−1.00031
$780$	−1.20930	−0.0432999
$781$	0	0
$782$	−0.327233	−0.0117018
$783$	−11.2510	−0.402078
$784$	13.9576	0.498485
$785$	5.48000	0.195590
$786$	0.0471923	0.00168329
$787$	−18.4590	−0.657991	−0.328995	−	0.944332i	$-0.606710\pi$
$787$	−18.4590	−0.657991	−0.328995	+	0.944332i	$0.606710\pi$
$788$	14.7852	0.526701
$789$	1.05618	0.0376010
$790$	0.0665640	0.00236824
$791$	−8.92513	−0.317341
$792$	0	0
$793$	−9.60108	−0.340944
$794$	0.649005	0.0230323
$795$	4.81484	0.170765
$796$	−38.7039	−1.37182
$797$	−7.52953	−0.266709	−0.133355	−	0.991068i	$-0.542575\pi$
$797$	−7.52953	−0.266709	−0.133355	+	0.991068i	$0.542575\pi$
$798$	0.154739	0.00547768
$799$	25.4333	0.899767
$800$	−0.548862	−0.0194052
$801$	43.0884	1.52245
$802$	−0.256595	−0.00906067
$803$	0	0
$804$	−0.981059	−0.0345993
$805$	−15.2210	−0.536470
$806$	−0.0619919	−0.00218357
$807$	−5.32595	−0.187482
$808$	1.13895	0.0400681
$809$	−30.3665	−1.06763	−0.533815	−	0.845601i	$-0.679242\pi$
$809$	−30.3665	−1.06763	−0.533815	+	0.845601i	$0.679242\pi$
$810$	−0.247974	−0.00871293
$811$	25.7742	0.905056	0.452528	−	0.891750i	$-0.350522\pi$
$811$	25.7742	0.905056	0.452528	+	0.891750i	$0.350522\pi$
$812$	25.7879	0.904979
$813$	−2.03473	−0.0713610
$814$	0	0
$815$	−30.3261	−1.06228
$816$	10.8267	0.379010
$817$	−11.8358	−0.414082
$818$	−0.354537	−0.0123961
$819$	−6.52294	−0.227930
$820$	20.6312	0.720474
$821$	−14.9872	−0.523058	−0.261529	−	0.965196i	$-0.584227\pi$
$821$	−14.9872	−0.523058	−0.261529	+	0.965196i	$0.584227\pi$
$822$	0.000253602 0	8.84539e−6 0
$823$	−30.0200	−1.04643	−0.523216	−	0.852200i	$-0.675268\pi$
$823$	−30.0200	−1.04643	−0.523216	+	0.852200i	$0.675268\pi$
$824$	−1.54738	−0.0539056
$825$	0	0
$826$	0.162865	0.00566680
$827$	6.82458	0.237314	0.118657	−	0.992935i	$-0.462141\pi$
$827$	6.82458	0.237314	0.118657	+	0.992935i	$0.462141\pi$
$828$	15.3508	0.533476
$829$	−21.3151	−0.740303	−0.370151	−	0.928971i	$-0.620694\pi$
$829$	−21.3151	−0.740303	−0.370151	+	0.928971i	$0.620694\pi$
$830$	0.131962	0.00458048
$831$	5.99355	0.207914
$832$	−5.83073	−0.202144
$833$	−19.2759	−0.667869
$834$	−0.110944	−0.00384169
$835$	−32.4986	−1.12466
$836$	0	0
$837$	−11.2657	−0.389398
$838$	0.222303	0.00767931
$839$	12.1586	0.419761	0.209881	−	0.977727i	$-0.432692\pi$
$839$	12.1586	0.419761	0.209881	+	0.977727i	$0.432692\pi$
$840$	−0.228717	−0.00789148
$841$	−13.1467	−0.453333
$842$	−0.559671	−0.0192876
$843$	−2.02173	−0.0696322
$844$	−12.9116	−0.444436
$845$	21.0566	0.724369
$846$	0.270841	0.00931172
$847$	0	0
$848$	23.2257	0.797573
$849$	2.35422	0.0807968
$850$	0.252569	0.00866306
$851$	3.81973	0.130939
$852$	9.24029	0.316567
$853$	2.79550	0.0957161	0.0478580	−	0.998854i	$-0.484760\pi$
$853$	2.79550	0.0957161	0.0478580	+	0.998854i	$0.484760\pi$
$854$	−0.907830	−0.0310653
$855$	−21.2978	−0.728370
$856$	0.555584	0.0189895
$857$	−56.8900	−1.94333	−0.971663	−	0.236372i	$-0.924042\pi$
$857$	−56.8900	−1.94333	−0.971663	+	0.236372i	$0.924042\pi$
$858$	0	0
$859$	−23.0825	−0.787565	−0.393783	−	0.919204i	$-0.628834\pi$
$859$	−23.0825	−0.787565	−0.393783	+	0.919204i	$0.628834\pi$
$860$	8.74618	0.298242
$861$	−9.70884	−0.330876
$862$	0.104714	0.00356659
$863$	14.5240	0.494402	0.247201	−	0.968964i	$-0.420489\pi$
$863$	14.5240	0.494402	0.247201	+	0.968964i	$0.420489\pi$
$864$	0.722214	0.0245702
$865$	14.4427	0.491067
$866$	0.419154	0.0142434
$867$	−6.61110	−0.224525
$868$	25.8215	0.876439
$869$	0	0
$870$	−0.0702948	−0.00238322
$871$	−0.729835	−0.0247295
$872$	−0.929367	−0.0314723
$873$	15.1097	0.511385
$874$	−0.270904	−0.00916345
$875$	39.1014	1.32187
$876$	−3.72687	−0.125919
$877$	−46.3287	−1.56441	−0.782205	−	0.623022i	$-0.785905\pi$
$877$	−46.3287	−1.56441	−0.782205	+	0.623022i	$0.785905\pi$
$878$	0.207494	0.00700258
$879$	−14.1330	−0.476694
$880$	0	0
$881$	8.62388	0.290546	0.145273	−	0.989392i	$-0.453594\pi$
$881$	8.62388	0.290546	0.145273	+	0.989392i	$0.453594\pi$
$882$	−0.205270	−0.00691180
$883$	9.35621	0.314861	0.157431	−	0.987530i	$-0.449679\pi$
$883$	9.35621	0.314861	0.157431	+	0.987530i	$0.449679\pi$
$884$	8.05608	0.270955
$885$	1.95568	0.0657393
$886$	0.597266	0.0200655
$887$	5.62070	0.188725	0.0943624	−	0.995538i	$-0.469919\pi$
$887$	5.62070	0.188725	0.0943624	+	0.995538i	$0.469919\pi$
$888$	0.0573967	0.00192611
$889$	−63.0017	−2.11301
$890$	0.561907	0.0188352
$891$	0	0
$892$	−19.1663	−0.641735
$893$	21.0553	0.704589
$894$	−0.0472922	−0.00158169
$895$	39.8753	1.33288
$896$	−2.20705	−0.0737325
$897$	−0.996306	−0.0332657
$898$	−0.199544	−0.00665885
$899$	15.8740	0.529427
$900$	−11.8482	−0.394942
$901$	−32.0754	−1.06859
$902$	0	0
$903$	−4.11586	−0.136967
$904$	0.234793	0.00780910
$905$	11.5065	0.382490
$906$	0.227211	0.00754857
$907$	19.8426	0.658864	0.329432	−	0.944179i	$-0.393143\pi$
$907$	19.8426	0.658864	0.329432	+	0.944179i	$0.393143\pi$
$908$	−32.1825	−1.06801
$909$	36.8811	1.22327
$910$	−0.0850645	−0.00281986
$911$	51.6342	1.71072	0.855358	−	0.518037i	$-0.173337\pi$
$911$	51.6342	1.71072	0.855358	+	0.518037i	$0.173337\pi$
$912$	8.96300	0.296795
$913$	0	0
$914$	0.0471559	0.00155978
$915$	−10.9012	−0.360382
$916$	−29.8024	−0.984699
$917$	−14.6234	−0.482906
$918$	−0.332341	−0.0109689
$919$	−34.4013	−1.13479	−0.567396	−	0.823445i	$-0.692049\pi$
$919$	−34.4013	−1.13479	−0.567396	+	0.823445i	$0.692049\pi$
$920$	0.400419	0.0132014
$921$	4.91352	0.161906
$922$	−0.00621953	−0.000204829 0
$923$	6.87409	0.226264
$924$	0	0
$925$	−2.94820	−0.0969361
$926$	0.445146	0.0146284
$927$	−50.1068	−1.64572
$928$	−1.01764	−0.0334057
$929$	12.2043	0.400410	0.200205	−	0.979754i	$-0.435839\pi$
$929$	12.2043	0.400410	0.200205	+	0.979754i	$0.435839\pi$
$930$	−0.0703863	−0.00230806
$931$	−15.9578	−0.522994
$932$	−54.1154	−1.77261
$933$	−10.7069	−0.350528
$934$	0.852155	0.0278834
$935$	0	0
$936$	0.171599	0.00560889
$937$	11.6150	0.379446	0.189723	−	0.981838i	$-0.439241\pi$
$937$	11.6150	0.379446	0.189723	+	0.981838i	$0.439241\pi$
$938$	−0.0690095	−0.00225324
$939$	5.97201	0.194889
$940$	−15.5590	−0.507479
$941$	14.8692	0.484722	0.242361	−	0.970186i	$-0.422078\pi$
$941$	14.8692	0.484722	0.242361	+	0.970186i	$0.422078\pi$
$942$	0.0339167	0.00110507
$943$	16.9974	0.553513
$944$	9.43371	0.307041
$945$	−15.4586	−0.502868
$946$	0	0
$947$	54.2849	1.76402	0.882011	−	0.471228i	$-0.156189\pi$
$947$	54.2849	1.76402	0.882011	+	0.471228i	$0.156189\pi$
$948$	−1.81483	−0.0589428
$949$	−2.77251	−0.0899996
$950$	0.209093	0.00678386
$951$	8.29835	0.269092
$952$	1.52366	0.0493820
$953$	−1.76356	−0.0571274	−0.0285637	−	0.999592i	$-0.509093\pi$
$953$	−1.76356	−0.0571274	−0.0285637	+	0.999592i	$0.509093\pi$
$954$	−0.341573	−0.0110588
$955$	−35.6384	−1.15323
$956$	−28.4424	−0.919892
$957$	0	0
$958$	−0.0605829	−0.00195734
$959$	−0.0785831	−0.00253758
$960$	−6.62028	−0.213669
$961$	−15.1053	−0.487269
$962$	0.0213470	0.000688256 0
$963$	17.9907	0.579743
$964$	−29.2401	−0.941760
$965$	42.1304	1.35623
$966$	−0.0942057	−0.00303102
$967$	−18.9404	−0.609081	−0.304540	−	0.952499i	$-0.598503\pi$
$967$	−18.9404	−0.609081	−0.304540	+	0.952499i	$0.598503\pi$
$968$	0	0
$969$	−12.3782	−0.397645
$970$	0.197042	0.00632665
$971$	25.6428	0.822917	0.411459	−	0.911428i	$-0.365019\pi$
$971$	25.6428	0.822917	0.411459	+	0.911428i	$0.365019\pi$
$972$	23.7114	0.760544
$973$	34.3780	1.10211
$974$	−0.301000	−0.00964466
$975$	0.768983	0.0246272
$976$	−52.5847	−1.68320
$977$	28.9751	0.926996	0.463498	−	0.886098i	$-0.346594\pi$
$977$	28.9751	0.926996	0.463498	+	0.886098i	$0.346594\pi$
$978$	−0.187694	−0.00600178
$979$	0	0
$980$	11.7921	0.376686
$981$	−30.0944	−0.960842
$982$	0.197450	0.00630089
$983$	36.9212	1.17760	0.588802	−	0.808277i	$-0.299600\pi$
$983$	36.9212	1.17760	0.588802	+	0.808277i	$0.299600\pi$
$984$	0.255410	0.00814218
$985$	12.4885	0.397917
$986$	0.468288	0.0149133
$987$	7.32190	0.233059
$988$	6.66933	0.212179
$989$	7.20571	0.229128
$990$	0	0
$991$	−7.59922	−0.241397	−0.120699	−	0.992689i	$-0.538513\pi$
$991$	−7.59922	−0.241397	−0.120699	+	0.992689i	$0.538513\pi$
$992$	−1.01897	−0.0323522
$993$	−10.7787	−0.342052
$994$	0.649980	0.0206161
$995$	−32.6917	−1.03640
$996$	−3.59787	−0.114003
$997$	−15.2536	−0.483088	−0.241544	−	0.970390i	$-0.577654\pi$
$997$	−15.2536	−0.483088	−0.241544	+	0.970390i	$0.577654\pi$
$998$	0.477154	0.0151040
$999$	3.87935	0.122737

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8107.2.a.o.1.10		17
11.10	odd	2		737.2.a.f.1.8	✓	17
33.32	even	2		6633.2.a.w.1.10		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
737.2.a.f.1.8	✓	17	11.10	odd	2
6633.2.a.w.1.10		17	33.32	even	2
8107.2.a.o.1.10		17	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:	\( N \)	\(=\)	\( 8107 = 11^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8107.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0213052 q^{2} -0.490641 q^{3} -1.99955 q^{4} -1.68894 q^{5} -0.0104532 q^{6} +3.23910 q^{7} -0.0852109 q^{8} -2.75927 q^{9} +O(q^{10})\)	\(q+0.0213052 q^{2} -0.490641 q^{3} -1.99955 q^{4} -1.68894 q^{5} -0.0104532 q^{6} +3.23910 q^{7} -0.0852109 q^{8} -2.75927 q^{9} -0.0359832 q^{10} +0.981059 q^{12} +0.729835 q^{13} +0.0690095 q^{14} +0.828664 q^{15} +3.99728 q^{16} -5.52036 q^{17} -0.0587867 q^{18} -4.57010 q^{19} +3.37712 q^{20} -1.58923 q^{21} +2.78230 q^{23} +0.0418080 q^{24} -2.14748 q^{25} +0.0155493 q^{26} +2.82573 q^{27} -6.47673 q^{28} -3.98163 q^{29} +0.0176548 q^{30} -3.98681 q^{31} +0.255584 q^{32} -0.117612 q^{34} -5.47065 q^{35} +5.51729 q^{36} +1.37287 q^{37} -0.0973667 q^{38} -0.358087 q^{39} +0.143916 q^{40} +6.10913 q^{41} -0.0338589 q^{42} +2.58984 q^{43} +4.66025 q^{45} +0.0592774 q^{46} -4.60719 q^{47} -1.96123 q^{48} +3.49177 q^{49} -0.0457523 q^{50} +2.70852 q^{51} -1.45934 q^{52} +5.81037 q^{53} +0.0602027 q^{54} -0.276007 q^{56} +2.24228 q^{57} -0.0848291 q^{58} +2.36004 q^{59} -1.65695 q^{60} -13.1551 q^{61} -0.0849396 q^{62} -8.93756 q^{63} -7.98911 q^{64} -1.23265 q^{65} -1.00000 q^{67} +11.0382 q^{68} -1.36511 q^{69} -0.116553 q^{70} +9.41869 q^{71} +0.235120 q^{72} -3.79882 q^{73} +0.0292491 q^{74} +1.05364 q^{75} +9.13813 q^{76} -0.00762910 q^{78} -1.84987 q^{79} -6.75117 q^{80} +6.89140 q^{81} +0.130156 q^{82} -3.66734 q^{83} +3.17775 q^{84} +9.32357 q^{85} +0.0551769 q^{86} +1.95355 q^{87} -15.6158 q^{89} +0.0992873 q^{90} +2.36401 q^{91} -5.56334 q^{92} +1.95609 q^{93} -0.0981568 q^{94} +7.71863 q^{95} -0.125400 q^{96} -5.47596 q^{97} +0.0743928 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - q^{2} + 10 q^{3} + 19 q^{4} + 10 q^{5} + 6 q^{6} - 20 q^{7} + 25 q^{9}+O(q^{10}) \) 17 * q - q^2 + 10 * q^3 + 19 * q^4 + 10 * q^5 + 6 * q^6 - 20 * q^7 + 25 * q^9	\( 17 q - q^{2} + 10 q^{3} + 19 q^{4} + 10 q^{5} + 6 q^{6} - 20 q^{7} + 25 q^{9} - 10 q^{10} + 18 q^{12} - q^{13} - 11 q^{14} + 7 q^{15} + 19 q^{16} - 2 q^{17} + 24 q^{18} - 13 q^{19} + 3 q^{20} - 5 q^{21} + 16 q^{23} + 36 q^{24} + 33 q^{25} + 12 q^{26} + 19 q^{27} - 44 q^{28} + 5 q^{29} - 3 q^{30} + 16 q^{31} + 24 q^{32} + 4 q^{34} + 2 q^{35} + 25 q^{36} + 29 q^{37} - 19 q^{38} - 2 q^{39} - 31 q^{40} + 6 q^{41} - 26 q^{42} - 19 q^{43} + 20 q^{45} + 33 q^{46} + 40 q^{47} + 81 q^{48} + 23 q^{49} + 3 q^{50} + q^{51} + 28 q^{52} + 15 q^{53} + 27 q^{54} - 38 q^{56} + 27 q^{57} - 12 q^{58} - 2 q^{59} - 59 q^{60} + 6 q^{61} - 3 q^{62} - 32 q^{63} - 4 q^{64} + 30 q^{65} - 17 q^{67} + 13 q^{68} + 5 q^{69} + 71 q^{70} + 2 q^{71} + 47 q^{72} - 41 q^{73} + 13 q^{74} - 6 q^{75} - 21 q^{76} + 31 q^{78} - 41 q^{79} - 23 q^{80} + 37 q^{81} - 8 q^{82} - 2 q^{83} + 16 q^{84} + 36 q^{85} - 54 q^{86} - 32 q^{87} + q^{89} + 44 q^{90} + 16 q^{91} + 36 q^{92} + 26 q^{93} - 12 q^{94} + 31 q^{95} + 72 q^{96} + 3 q^{97} + 64 q^{98}+O(q^{100}) \) 17 * q - q^2 + 10 * q^3 + 19 * q^4 + 10 * q^5 + 6 * q^6 - 20 * q^7 + 25 * q^9 - 10 * q^10 + 18 * q^12 - q^13 - 11 * q^14 + 7 * q^15 + 19 * q^16 - 2 * q^17 + 24 * q^18 - 13 * q^19 + 3 * q^20 - 5 * q^21 + 16 * q^23 + 36 * q^24 + 33 * q^25 + 12 * q^26 + 19 * q^27 - 44 * q^28 + 5 * q^29 - 3 * q^30 + 16 * q^31 + 24 * q^32 + 4 * q^34 + 2 * q^35 + 25 * q^36 + 29 * q^37 - 19 * q^38 - 2 * q^39 - 31 * q^40 + 6 * q^41 - 26 * q^42 - 19 * q^43 + 20 * q^45 + 33 * q^46 + 40 * q^47 + 81 * q^48 + 23 * q^49 + 3 * q^50 + q^51 + 28 * q^52 + 15 * q^53 + 27 * q^54 - 38 * q^56 + 27 * q^57 - 12 * q^58 - 2 * q^59 - 59 * q^60 + 6 * q^61 - 3 * q^62 - 32 * q^63 - 4 * q^64 + 30 * q^65 - 17 * q^67 + 13 * q^68 + 5 * q^69 + 71 * q^70 + 2 * q^71 + 47 * q^72 - 41 * q^73 + 13 * q^74 - 6 * q^75 - 21 * q^76 + 31 * q^78 - 41 * q^79 - 23 * q^80 + 37 * q^81 - 8 * q^82 - 2 * q^83 + 16 * q^84 + 36 * q^85 - 54 * q^86 - 32 * q^87 + q^89 + 44 * q^90 + 16 * q^91 + 36 * q^92 + 26 * q^93 - 12 * q^94 + 31 * q^95 + 72 * q^96 + 3 * q^97 + 64 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more