LMFDB - Embedded newform 737.2.a.f.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [737,2,Mod(1,737)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(737, 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("737.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 737 = 11 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	737.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:	$5.88497462897$
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:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.0213052$ of defining polynomial
Character	$\chi$	$=$	737.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0213052 q^{2} -0.490641 q^{3} -1.99955 q^{4} -1.68894 q^{5} +0.0104532 q^{6} -3.23910 q^{7} +0.0852109 q^{8} -2.75927 q^{9} +O(q^{10})$	\(q-0.0213052 q^{2} -0.490641 q^{3} -1.99955 q^{4} -1.68894 q^{5} +0.0104532 q^{6} -3.23910 q^{7} +0.0852109 q^{8} -2.75927 q^{9} +0.0359832 q^{10} +1.00000 q^{11} +0.981059 q^{12} -0.729835 q^{13} +0.0690095 q^{14} +0.828664 q^{15} +3.99728 q^{16} +5.52036 q^{17} +0.0587867 q^{18} +4.57010 q^{19} +3.37712 q^{20} +1.58923 q^{21} -0.0213052 q^{22} +2.78230 q^{23} -0.0418080 q^{24} -2.14748 q^{25} +0.0155493 q^{26} +2.82573 q^{27} +6.47673 q^{28} +3.98163 q^{29} -0.0176548 q^{30} -3.98681 q^{31} -0.255584 q^{32} -0.490641 q^{33} -0.117612 q^{34} +5.47065 q^{35} +5.51729 q^{36} +1.37287 q^{37} -0.0973667 q^{38} +0.358087 q^{39} -0.143916 q^{40} -6.10913 q^{41} -0.0338589 q^{42} -2.58984 q^{43} -1.99955 q^{44} +4.66025 q^{45} -0.0592774 q^{46} -4.60719 q^{47} -1.96123 q^{48} +3.49177 q^{49} +0.0457523 q^{50} -2.70852 q^{51} +1.45934 q^{52} +5.81037 q^{53} -0.0602027 q^{54} -1.68894 q^{55} -0.276007 q^{56} -2.24228 q^{57} -0.0848291 q^{58} +2.36004 q^{59} -1.65695 q^{60} +13.1551 q^{61} +0.0849396 q^{62} +8.93756 q^{63} -7.98911 q^{64} +1.23265 q^{65} +0.0104532 q^{66} -1.00000 q^{67} -11.0382 q^{68} -1.36511 q^{69} -0.116553 q^{70} +9.41869 q^{71} -0.235120 q^{72} +3.79882 q^{73} -0.0292491 q^{74} +1.05364 q^{75} -9.13813 q^{76} -3.23910 q^{77} -0.00762910 q^{78} +1.84987 q^{79} -6.75117 q^{80} +6.89140 q^{81} +0.130156 q^{82} +3.66734 q^{83} -3.17775 q^{84} -9.32357 q^{85} +0.0551769 q^{86} -1.95355 q^{87} +0.0852109 q^{88} -15.6158 q^{89} -0.0992873 q^{90} +2.36401 q^{91} -5.56334 q^{92} +1.95609 q^{93} +0.0981568 q^{94} -7.71863 q^{95} +0.125400 q^{96} -5.47596 q^{97} -0.0743928 q^{98} -2.75927 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 17 q + q^{2} + 10 q^{3} + 19 q^{4} + 10 q^{5} - 6 q^{6} + 20 q^{7} + 25 q^{9} + 10 q^{10} + 17 q^{11} + 18 q^{12} + q^{13} - 11 q^{14} + 7 q^{15} + 19 q^{16} + 2 q^{17} - 24 q^{18} + 13 q^{19} + 3 q^{20} + 5 q^{21} + q^{22} + 16 q^{23} - 36 q^{24} + 33 q^{25} + 12 q^{26} + 19 q^{27} + 44 q^{28} - 5 q^{29} + 3 q^{30} + 16 q^{31} - 24 q^{32} + 10 q^{33} + 4 q^{34} - 2 q^{35} + 25 q^{36} + 29 q^{37} - 19 q^{38} + 2 q^{39} + 31 q^{40} - 6 q^{41} - 26 q^{42} + 19 q^{43} + 19 q^{44} + 20 q^{45} - 33 q^{46} + 40 q^{47} + 81 q^{48} + 23 q^{49} - 3 q^{50} - q^{51} - 28 q^{52} + 15 q^{53} - 27 q^{54} + 10 q^{55} - 38 q^{56} - 27 q^{57} - 12 q^{58} - 2 q^{59} - 59 q^{60} - 6 q^{61} + 3 q^{62} + 32 q^{63} - 4 q^{64} - 30 q^{65} - 6 q^{66} - 17 q^{67} - 13 q^{68} + 5 q^{69} + 71 q^{70} + 2 q^{71} - 47 q^{72} + 41 q^{73} - 13 q^{74} - 6 q^{75} + 21 q^{76} + 20 q^{77} + 31 q^{78} + 41 q^{79} - 23 q^{80} + 37 q^{81} - 8 q^{82} + 2 q^{83} - 16 q^{84} - 36 q^{85} - 54 q^{86} + 32 q^{87} + q^{89} - 44 q^{90} + 16 q^{91} + 36 q^{92} + 26 q^{93} + 12 q^{94} - 31 q^{95} - 72 q^{96} + 3 q^{97} - 64 q^{98} + 25 q^{99}+O(q^{100}) \) 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 + 17 * q^11 + 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 + q^22 + 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 + 10 * q^33 + 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 + 19 * q^44 + 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 + 10 * q^55 - 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 - 6 * q^66 - 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 + 20 * q^77 + 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 + 25 * 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 $

$2$	−0.0213052	−0.0150650	−0.00753251	−	0.999972i	$-0.502398\pi$
$2$	−0.0213052	−0.0150650	−0.00753251	+	0.999972i	$0.502398\pi$
$3$	−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	$-0.709688\pi$
$7$	−3.23910	−1.22427	−0.612133	+	0.790755i	$0.709688\pi$
$8$	0.0852109	0.0301266
$9$	−2.75927	−0.919757
$10$	0.0359832	0.0113789
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.981059	0.283207
$13$	−0.729835	−0.202420	−0.101210	−	0.994865i	$-0.532271\pi$
$13$	−0.729835	−0.202420	−0.101210	+	0.994865i	$0.532271\pi$
$14$	0.0690095	0.0184436
$15$	0.828664	0.213960
$16$	3.99728	0.999319
$17$	5.52036	1.33888	0.669442	−	0.742864i	$-0.266533\pi$
$17$	5.52036	1.33888	0.669442	+	0.742864i	$0.266533\pi$
$18$	0.0587867	0.0138562
$19$	4.57010	1.04845	0.524226	−	0.851579i	$-0.324355\pi$
$19$	4.57010	1.04845	0.524226	+	0.851579i	$0.324355\pi$
$20$	3.37712	0.755146
$21$	1.58923	0.346799
$22$	−0.0213052	−0.00454227
$23$	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	$-0.379466\pi$
$29$	3.98163	0.739369	0.369685	+	0.929157i	$0.379466\pi$
$30$	−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
$33$	−0.490641	−0.0854096
$34$	−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	$-0.658291\pi$
$41$	−6.10913	−0.954085	−0.477043	+	0.878880i	$0.658291\pi$
$42$	−0.0338589	−0.00522454
$43$	−2.58984	−0.394946	−0.197473	−	0.980308i	$-0.563274\pi$
$43$	−2.58984	−0.394946	−0.197473	+	0.980308i	$0.563274\pi$
$44$	−1.99955	−0.301443
$45$	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
$55$	−1.68894	−0.227737
$56$	−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	$-0.181277\pi$
$61$	13.1551	1.68434	0.842171	+	0.539210i	$0.181277\pi$
$62$	0.0849396	0.0107873
$63$	8.93756	1.12603
$64$	−7.98911	−0.998639
$65$	1.23265	0.152891
$66$	0.0104532	0.00128670
$67$	−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	$-0.428641\pi$
$73$	3.79882	0.444618	0.222309	+	0.974976i	$0.428641\pi$
$74$	−0.0292491	−0.00340014
$75$	1.05364	0.121664
$76$	−9.13813	−1.04821
$77$	−3.23910	−0.369130
$78$	−0.00762910	−0.000863825 0
$79$	1.84987	0.208126	0.104063	−	0.994571i	$-0.466816\pi$
$79$	1.84987	0.208126	0.104063	+	0.994571i	$0.466816\pi$
$80$	−6.75117	−0.754803
$81$	6.89140	0.765711
$82$	0.130156	0.0143733
$83$	3.66734	0.402542	0.201271	−	0.979536i	$-0.435493\pi$
$83$	3.66734	0.402542	0.201271	+	0.979536i	$0.435493\pi$
$84$	−3.17775	−0.346721
$85$	−9.32357	−1.01128
$86$	0.0551769	0.00594987
$87$	−1.95355	−0.209442
$88$	0.0852109	0.00908352
$89$	−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
$99$	−2.75927	−0.277317
$100$	4.29398	0.429398
$101$	13.3662	1.32999	0.664995	−	0.746847i	$-0.268433\pi$
$101$	13.3662	1.32999	0.664995	+	0.746847i	$0.268433\pi$
$102$	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	$-0.397942\pi$
$107$	6.52010	0.630322	0.315161	+	0.949038i	$0.397942\pi$
$108$	−5.65018	−0.543689
$109$	−10.9067	−1.04467	−0.522334	−	0.852741i	$-0.674939\pi$
$109$	−10.9067	−1.04467	−0.522334	+	0.852741i	$0.674939\pi$
$110$	0.0359832	0.00343086
$111$	−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
$121$	1.00000	0.0909091
$122$	−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	$-0.168601\pi$
$127$	19.4504	1.72594	0.862970	+	0.505254i	$0.168601\pi$
$128$	0.681378	0.0602259
$129$	1.27068	0.111877
$130$	−0.0262618	−0.00230331
$131$	4.51463	0.394445	0.197223	−	0.980359i	$-0.436808\pi$
$131$	4.51463	0.394445	0.197223	+	0.980359i	$0.436808\pi$
$132$	0.981059	0.0853902
$133$	−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	$-0.648615\pi$
$139$	−10.6134	−0.900221	−0.450110	+	0.892973i	$0.648615\pi$
$140$	−10.9388	−0.924499
$141$	2.26047	0.190366
$142$	−0.200667	−0.0168396
$143$	−0.729835	−0.0610319
$144$	−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	$-0.559332\pi$
$149$	−4.52419	−0.370636	−0.185318	+	0.982679i	$0.559332\pi$
$150$	−0.0224479	−0.00183287
$151$	21.7361	1.76886	0.884428	−	0.466677i	$-0.154549\pi$
$151$	21.7361	1.76886	0.884428	+	0.466677i	$0.154549\pi$
$152$	0.389423	0.0315863
$153$	−15.2322	−1.23145
$154$	0.0690095	0.00556095
$155$	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
$165$	0.828664	0.0645114
$166$	−0.0781331	−0.00606431
$167$	−19.2420	−1.48899	−0.744494	−	0.667629i	$-0.767309\pi$
$167$	−19.2420	−1.48899	−0.744494	+	0.667629i	$0.767309\pi$
$168$	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	$-0.394611\pi$
$173$	8.55134	0.650147	0.325073	+	0.945689i	$0.394611\pi$
$174$	0.0416206	0.00315525
$175$	6.95589	0.525816
$176$	3.99728	0.301306
$177$	−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
$187$	5.52036	0.403689
$188$	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	$-0.145175\pi$
$193$	24.9449	1.79557	0.897785	+	0.440434i	$0.145175\pi$
$194$	0.116666	0.00837615
$195$	−0.604788	−0.0433098
$196$	−6.98196	−0.498712
$197$	7.39429	0.526821	0.263411	−	0.964684i	$-0.415153\pi$
$197$	7.39429	0.526821	0.263411	+	0.964684i	$0.415153\pi$
$198$	0.0587867	0.00417779
$199$	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
$209$	4.57010	0.316120
$210$	0.0571857	0.00394619
$211$	−6.45727	−0.444537	−0.222268	−	0.974986i	$-0.571346\pi$
$211$	−6.45727	−0.444537	−0.222268	+	0.974986i	$0.571346\pi$
$212$	−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
$220$	3.37712	0.227685
$221$	−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	$-0.679360\pi$
$227$	−16.0949	−1.06826	−0.534128	+	0.845404i	$0.679360\pi$
$228$	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
$231$	1.58923	0.104564
$232$	0.339278	0.0222747
$233$	−27.0638	−1.77301	−0.886505	−	0.462719i	$-0.846874\pi$
$233$	−27.0638	−1.77301	−0.886505	+	0.462719i	$0.846874\pi$
$234$	−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	$-0.652169\pi$
$239$	−14.2244	−0.920101	−0.460051	+	0.887893i	$0.652169\pi$
$240$	3.31240	0.213814
$241$	−14.6234	−0.941973	−0.470987	−	0.882140i	$-0.656102\pi$
$241$	−14.6234	−0.941973	−0.470987	+	0.882140i	$0.656102\pi$
$242$	−0.0213052	−0.00136955
$243$	−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
$253$	2.78230	0.174922
$254$	−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	$-0.478859\pi$
$263$	2.15265	0.132738	0.0663691	+	0.997795i	$0.478859\pi$
$264$	−0.0418080	−0.00257310
$265$	−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	$-0.540201\pi$
$271$	−4.14708	−0.251917	−0.125959	+	0.992035i	$0.540201\pi$
$272$	22.0664	1.33797
$273$	−1.15988	−0.0701991
$274$	0.000516880 0	3.12258e−5 0
$275$	−2.14748	−0.129498
$276$	2.72960	0.164303
$277$	12.2158	0.733974	0.366987	−	0.930226i	$-0.380389\pi$
$277$	12.2158	0.733974	0.366987	+	0.930226i	$0.380389\pi$
$278$	0.226121	0.0135618
$279$	11.0007	0.658594
$280$	0.466159	0.0278584
$281$	−4.12060	−0.245814	−0.122907	−	0.992418i	$-0.539222\pi$
$281$	−4.12060	−0.245814	−0.122907	+	0.992418i	$0.539222\pi$
$282$	−0.0481597	−0.00286787
$283$	4.79827	0.285227	0.142614	−	0.989778i	$-0.454449\pi$
$283$	4.79827	0.285227	0.142614	+	0.989778i	$0.454449\pi$
$284$	−18.8331	−1.11754
$285$	3.78708	0.224327
$286$	0.0155493	0.000919446 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	$-0.818273\pi$
$293$	−28.8052	−1.68282	−0.841409	+	0.540399i	$0.818273\pi$
$294$	0.0365001	0.00212873
$295$	−3.98596	−0.232072
$296$	0.116983	0.00679951
$297$	2.82573	0.163966
$298$	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	$-0.407748\pi$
$307$	10.0145	0.571558	0.285779	+	0.958296i	$0.407748\pi$
$308$	6.47673	0.369046
$309$	−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
$319$	3.98163	0.222928
$320$	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
$330$	−0.0176548	−0.000971865 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	$-0.454207\pi$
$337$	5.26378	0.286736	0.143368	+	0.989669i	$0.454207\pi$
$338$	0.265619	0.0144477
$339$	1.35193	0.0734266
$340$	18.6429	1.01105
$341$	−3.98681	−0.215898
$342$	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	$-0.627820\pi$
$347$	−14.5616	−0.781707	−0.390854	+	0.920453i	$0.627820\pi$
$348$	3.90621	0.209395
$349$	−13.3885	−0.716671	−0.358335	−	0.933593i	$-0.616656\pi$
$349$	−13.3885	−0.716671	−0.358335	+	0.933593i	$0.616656\pi$
$350$	−0.148196	−0.00792143
$351$	−2.06232	−0.110078
$352$	−0.255584	−0.0136227
$353$	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	$-0.406575\pi$
$359$	10.9632	0.578617	0.289309	+	0.957236i	$0.406575\pi$
$360$	0.397104	0.0209292
$361$	1.88581	0.0992533
$362$	0.145149	0.00762887
$363$	−0.490641	−0.0257520
$364$	−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	$-0.439465\pi$
$373$	7.30167	0.378066	0.189033	+	0.981971i	$0.439465\pi$
$374$	−0.117612	−0.00608158
$375$	−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
$385$	5.47065	0.278810
$386$	−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
$396$	5.51729	0.277254
$397$	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
$407$	1.37287	0.0680504
$408$	−0.230795	−0.0114261
$409$	16.6409	0.822840	0.411420	−	0.911446i	$-0.365033\pi$
$409$	16.6409	0.822840	0.411420	+	0.911446i	$0.365033\pi$
$410$	−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
$418$	−0.0973667	−0.00476236
$419$	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
$429$	0.358087	0.0172886
$430$	−0.0931905	−0.00449404
$431$	−4.91498	−0.236746	−0.118373	−	0.992969i	$-0.537768\pi$
$431$	−4.91498	−0.236746	−0.118373	+	0.992969i	$0.537768\pi$
$432$	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	$-0.574662\pi$
$439$	−9.73914	−0.464824	−0.232412	+	0.972617i	$0.574662\pi$
$440$	−0.143916	−0.00686094
$441$	−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
$451$	−6.10913	−0.287668
$452$	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	$-0.516486\pi$
$457$	−2.21336	−0.103536	−0.0517682	+	0.998659i	$0.516486\pi$
$458$	−0.317544	−0.0148379
$459$	15.5991	0.728102
$460$	9.39616	0.438098
$461$	0.291926	0.0135964	0.00679818	−	0.999977i	$-0.497836\pi$
$461$	0.291926	0.0135964	0.00679818	+	0.999977i	$0.497836\pi$
$462$	−0.0338589	−0.00157526
$463$	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
$473$	−2.58984	−0.119081
$474$	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	$-0.479307\pi$
$479$	2.84358	0.129926	0.0649632	+	0.997888i	$0.479307\pi$
$480$	−0.211794	−0.00966701
$481$	−1.00197	−0.0456857
$482$	0.311553	0.0141908
$483$	4.42173	0.201196
$484$	−1.99955	−0.0908885
$485$	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	$-0.567061\pi$
$491$	−9.26772	−0.418246	−0.209123	+	0.977889i	$0.567061\pi$
$492$	−5.99341	−0.270204
$493$	21.9800	0.989930
$494$	0.0710616	0.00319721
$495$	4.66025	0.209463
$496$	−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	$-0.821076\pi$
$503$	−37.9536	−1.69227	−0.846134	+	0.532971i	$0.821076\pi$
$504$	0.761578	0.0339234
$505$	−22.5748	−1.00457
$506$	−0.0592774	−0.00263520
$507$	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
$517$	−4.60719	−0.202624
$518$	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	$-0.343963\pi$
$523$	21.5339	0.941610	0.470805	+	0.882237i	$0.343963\pi$
$524$	−9.02722	−0.394356
$525$	−3.41284	−0.148949
$526$	−0.0458626	−0.00199970
$527$	−22.0086	−0.958711
$528$	−1.96123	−0.0853514
$529$	−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
$539$	3.49177	0.150401
$540$	9.54283	0.410658
$541$	5.66794	0.243684	0.121842	−	0.992550i	$-0.461120\pi$
$541$	5.66794	0.243684	0.121842	+	0.992550i	$0.461120\pi$
$542$	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	$-0.483498\pi$
$547$	2.42389	0.103638	0.0518190	+	0.998656i	$0.483498\pi$
$548$	0.0485106	0.00207227
$549$	−36.2986	−1.54919
$550$	0.0457523	0.00195088
$551$	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	$-0.471360\pi$
$557$	4.24123	0.179707	0.0898533	+	0.995955i	$0.471360\pi$
$558$	−0.234371	−0.00992173
$559$	1.89015	0.0799450
$560$	21.8677	0.924080
$561$	−2.70852	−0.114354
$562$	0.0877900	0.00370320
$563$	−19.3999	−0.817609	−0.408805	−	0.912622i	$-0.634054\pi$
$563$	−19.3999	−0.817609	−0.408805	+	0.912622i	$0.634054\pi$
$564$	−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	$-0.820213\pi$
$569$	−40.2978	−1.68937	−0.844686	+	0.535262i	$0.820213\pi$
$570$	−0.0806842	−0.00337949
$571$	−40.3296	−1.68774	−0.843870	−	0.536548i	$-0.819728\pi$
$571$	−40.3296	−1.68774	−0.843870	+	0.536548i	$0.819728\pi$
$572$	1.45934	0.0610180
$573$	−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
$583$	5.81037	0.240641
$584$	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	$-0.295899\pi$
$593$	29.1322	1.19632	0.598159	+	0.801378i	$0.295899\pi$
$594$	−0.0602027	−0.00247015
$595$	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	$-0.903995\pi$
$601$	−46.8174	−1.90972	−0.954860	+	0.297056i	$0.903995\pi$
$602$	−0.178723	−0.00728422
$603$	2.75927	0.112366
$604$	−43.4623	−1.76845
$605$	−1.68894	−0.0686652
$606$	0.139720	0.00567572
$607$	23.7040	0.962115	0.481057	−	0.876689i	$-0.340253\pi$
$607$	23.7040	0.962115	0.481057	+	0.876689i	$0.340253\pi$
$608$	−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	$-0.481123\pi$
$613$	2.93484	0.118537	0.0592685	+	0.998242i	$0.481123\pi$
$614$	−0.213361	−0.00861053
$615$	−5.06241	−0.204136
$616$	−0.276007	−0.0111206
$617$	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
$627$	−2.24228	−0.0895479
$628$	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
$638$	−0.0848291	−0.00335842
$639$	−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
$649$	2.36004	0.0926395
$650$	−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	$-0.574604\pi$
$659$	−11.9234	−0.464471	−0.232235	+	0.972660i	$0.574604\pi$
$660$	−1.65695	−0.0644967
$661$	−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
$671$	13.1551	0.507848
$672$	−0.406184	−0.0156689
$673$	37.7695	1.45591	0.727953	−	0.685627i	$-0.240472\pi$
$673$	37.7695	1.45591	0.727953	+	0.685627i	$0.240472\pi$
$674$	−0.112146	−0.00431969
$675$	−6.06819	−0.233565
$676$	24.9290	0.958809
$677$	15.3913	0.591534	0.295767	−	0.955260i	$-0.404425\pi$
$677$	15.3913	0.591534	0.295767	+	0.955260i	$0.404425\pi$
$678$	−0.0288030	−0.00110617
$679$	17.7372	0.680691
$680$	−0.794470	−0.0304666
$681$	7.89682	0.302607
$682$	0.0849396	0.00325251
$683$	−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
$693$	8.93756	0.339510
$694$	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	$-0.673982\pi$
$701$	−27.5233	−1.03954	−0.519770	+	0.854306i	$0.673982\pi$
$702$	0.0439380	0.00165833
$703$	6.27413	0.236633
$704$	−7.98911	−0.301101
$705$	−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
$715$	1.23265	0.0460985
$716$	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
$726$	0.0104532	0.000387954 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	$-0.380127\pi$
$733$	19.9131	0.735509	0.367754	+	0.929923i	$0.380127\pi$
$734$	−0.588947	−0.0217384
$735$	2.89351	0.106729
$736$	−0.711114	−0.0262120
$737$	−1.00000	−0.0368355
$738$	−0.359136	−0.0132200
$739$	−10.8311	−0.398427	−0.199213	−	0.979956i	$-0.563839\pi$
$739$	−10.8311	−0.398427	−0.199213	+	0.979956i	$0.563839\pi$
$740$	4.63633	0.170435
$741$	1.63649	0.0601181
$742$	0.400971	0.0147201
$743$	−40.7728	−1.49581	−0.747904	−	0.663806i	$-0.768940\pi$
$743$	−40.7728	−1.49581	−0.747904	+	0.663806i	$0.768940\pi$
$744$	0.166680	0.00611080
$745$	7.64110	0.279948
$746$	−0.155563	−0.00569557
$747$	−10.1192	−0.370241
$748$	−11.0382	−0.403597
$749$	−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
$759$	−1.36511	−0.0495504
$760$	−0.657712	−0.0238577
$761$	−14.0722	−0.510115	−0.255058	−	0.966926i	$-0.582094\pi$
$761$	−14.0722	−0.510115	−0.255058	+	0.966926i	$0.582094\pi$
$762$	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	$-0.750933\pi$
$769$	−39.3322	−1.41835	−0.709177	+	0.705031i	$0.750933\pi$
$770$	−0.116553	−0.00420028
$771$	−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
$781$	9.41869	0.337027
$782$	−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	$-0.393290\pi$
$787$	18.4590	0.657991	0.328995	+	0.944332i	$0.393290\pi$
$788$	−14.7852	−0.526701
$789$	−1.05618	−0.0376010
$790$	0.0665640	0.00236824
$791$	8.92513	0.317341
$792$	−0.235120	−0.00835463
$793$	−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
$803$	3.79882	0.134057
$804$	−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	$-0.320758\pi$
$809$	30.3665	1.06763	0.533815	+	0.845601i	$0.320758\pi$
$810$	0.247974	0.00871293
$811$	−25.7742	−0.905056	−0.452528	−	0.891750i	$-0.649478\pi$
$811$	−25.7742	−0.905056	−0.452528	+	0.891750i	$0.649478\pi$
$812$	25.7879	0.904979
$813$	2.03473	0.0713610
$814$	−0.0292491	−0.00102518
$815$	−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	$-0.415773\pi$
$821$	14.9872	0.523058	0.261529	+	0.965196i	$0.415773\pi$
$822$	−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
$825$	1.05364	0.0366830
$826$	0.162865	0.00566680
$827$	−6.82458	−0.237314	−0.118657	−	0.992935i	$-0.537859\pi$
$827$	−6.82458	−0.237314	−0.118657	+	0.992935i	$0.537859\pi$
$828$	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
$836$	−9.13813	−0.316049
$837$	−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
$847$	−3.23910	−0.111297
$848$	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	$-0.515240\pi$
$853$	−2.79550	−0.0957161	−0.0478580	+	0.998854i	$0.515240\pi$
$854$	0.907830	0.0310653
$855$	21.2978	0.728370
$856$	0.555584	0.0189895
$857$	56.8900	1.94333	0.971663	−	0.236372i	$-0.0759584\pi$
$857$	56.8900	1.94333	0.971663	+	0.236372i	$0.0759584\pi$
$858$	−0.00762910	−0.000260453 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
$869$	1.84987	0.0627524
$870$	−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	$-0.214095\pi$
$877$	46.3287	1.56441	0.782205	+	0.623022i	$0.214095\pi$
$878$	0.207494	0.00700258
$879$	14.1330	0.476694
$880$	−6.75117	−0.227582
$881$	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	$-0.530081\pi$
$887$	−5.62070	−0.188725	−0.0943624	+	0.995538i	$0.530081\pi$
$888$	−0.0573967	−0.00192611
$889$	−63.0017	−2.11301
$890$	−0.561907	−0.0188352
$891$	6.89140	0.230870
$892$	−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
$902$	0.130156	0.00433372
$903$	−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
$913$	3.66734	0.121371
$914$	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	$-0.307951\pi$
$919$	34.4013	1.13479	0.567396	+	0.823445i	$0.307951\pi$
$920$	−0.400419	−0.0132014
$921$	−4.91352	−0.161906
$922$	−0.00621953	−0.000204829 0
$923$	−6.87409	−0.226264
$924$	−3.17775	−0.104540
$925$	−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
$935$	−9.32357	−0.304913
$936$	0.171599	0.00560889
$937$	−11.6150	−0.379446	−0.189723	−	0.981838i	$-0.560759\pi$
$937$	−11.6150	−0.379446	−0.189723	+	0.981838i	$0.560759\pi$
$938$	−0.0690095	−0.00225324
$939$	5.97201	0.194889
$940$	−15.5590	−0.507479
$941$	−14.8692	−0.484722	−0.242361	−	0.970186i	$-0.577922\pi$
$941$	−14.8692	−0.484722	−0.242361	+	0.970186i	$0.577922\pi$
$942$	−0.0339167	−0.00110507
$943$	−16.9974	−0.553513
$944$	9.43371	0.307041
$945$	15.4586	0.502868
$946$	0.0551769	0.00179395
$947$	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	$-0.490907\pi$
$953$	1.76356	0.0571274	0.0285637	+	0.999592i	$0.490907\pi$
$954$	0.341573	0.0110588
$955$	−35.6384	−1.15323
$956$	28.4424	0.919892
$957$	−1.95355	−0.0631492
$958$	−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	$-0.401497\pi$
$967$	18.9404	0.609081	0.304540	+	0.952499i	$0.401497\pi$
$968$	0.0852109	0.00273878
$969$	−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
$979$	−15.6158	−0.499085
$980$	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
$990$	−0.0992873	−0.00315556
$991$	−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	$-0.422346\pi$
$997$	15.2536	0.483088	0.241544	+	0.970390i	$0.422346\pi$
$998$	−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	737.2.a.f.1.8	✓	17
3.2	odd	2		6633.2.a.w.1.10		17
11.10	odd	2		8107.2.a.o.1.10		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
737.2.a.f.1.8	✓	17	1.1	even	1	trivial
6633.2.a.w.1.10		17	3.2	odd	2
8107.2.a.o.1.10		17	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 737 = 11 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	737.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0213052 q^{2} -0.490641 q^{3} -1.99955 q^{4} -1.68894 q^{5} +0.0104532 q^{6} -3.23910 q^{7} +0.0852109 q^{8} -2.75927 q^{9} +O(q^{10})\)	\(q-0.0213052 q^{2} -0.490641 q^{3} -1.99955 q^{4} -1.68894 q^{5} +0.0104532 q^{6} -3.23910 q^{7} +0.0852109 q^{8} -2.75927 q^{9} +0.0359832 q^{10} +1.00000 q^{11} +0.981059 q^{12} -0.729835 q^{13} +0.0690095 q^{14} +0.828664 q^{15} +3.99728 q^{16} +5.52036 q^{17} +0.0587867 q^{18} +4.57010 q^{19} +3.37712 q^{20} +1.58923 q^{21} -0.0213052 q^{22} +2.78230 q^{23} -0.0418080 q^{24} -2.14748 q^{25} +0.0155493 q^{26} +2.82573 q^{27} +6.47673 q^{28} +3.98163 q^{29} -0.0176548 q^{30} -3.98681 q^{31} -0.255584 q^{32} -0.490641 q^{33} -0.117612 q^{34} +5.47065 q^{35} +5.51729 q^{36} +1.37287 q^{37} -0.0973667 q^{38} +0.358087 q^{39} -0.143916 q^{40} -6.10913 q^{41} -0.0338589 q^{42} -2.58984 q^{43} -1.99955 q^{44} +4.66025 q^{45} -0.0592774 q^{46} -4.60719 q^{47} -1.96123 q^{48} +3.49177 q^{49} +0.0457523 q^{50} -2.70852 q^{51} +1.45934 q^{52} +5.81037 q^{53} -0.0602027 q^{54} -1.68894 q^{55} -0.276007 q^{56} -2.24228 q^{57} -0.0848291 q^{58} +2.36004 q^{59} -1.65695 q^{60} +13.1551 q^{61} +0.0849396 q^{62} +8.93756 q^{63} -7.98911 q^{64} +1.23265 q^{65} +0.0104532 q^{66} -1.00000 q^{67} -11.0382 q^{68} -1.36511 q^{69} -0.116553 q^{70} +9.41869 q^{71} -0.235120 q^{72} +3.79882 q^{73} -0.0292491 q^{74} +1.05364 q^{75} -9.13813 q^{76} -3.23910 q^{77} -0.00762910 q^{78} +1.84987 q^{79} -6.75117 q^{80} +6.89140 q^{81} +0.130156 q^{82} +3.66734 q^{83} -3.17775 q^{84} -9.32357 q^{85} +0.0551769 q^{86} -1.95355 q^{87} +0.0852109 q^{88} -15.6158 q^{89} -0.0992873 q^{90} +2.36401 q^{91} -5.56334 q^{92} +1.95609 q^{93} +0.0981568 q^{94} -7.71863 q^{95} +0.125400 q^{96} -5.47596 q^{97} -0.0743928 q^{98} -2.75927 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + q^{2} + 10 q^{3} + 19 q^{4} + 10 q^{5} - 6 q^{6} + 20 q^{7} + 25 q^{9}+O(q^{10}) \) 17 * q + q^2 + 10 * q^3 + 19 * q^4 + 10 * q^5 - 6 * q^6 + 20 * q^7 + 25 * q^9	\( 17 q + q^{2} + 10 q^{3} + 19 q^{4} + 10 q^{5} - 6 q^{6} + 20 q^{7} + 25 q^{9} + 10 q^{10} + 17 q^{11} + 18 q^{12} + q^{13} - 11 q^{14} + 7 q^{15} + 19 q^{16} + 2 q^{17} - 24 q^{18} + 13 q^{19} + 3 q^{20} + 5 q^{21} + q^{22} + 16 q^{23} - 36 q^{24} + 33 q^{25} + 12 q^{26} + 19 q^{27} + 44 q^{28} - 5 q^{29} + 3 q^{30} + 16 q^{31} - 24 q^{32} + 10 q^{33} + 4 q^{34} - 2 q^{35} + 25 q^{36} + 29 q^{37} - 19 q^{38} + 2 q^{39} + 31 q^{40} - 6 q^{41} - 26 q^{42} + 19 q^{43} + 19 q^{44} + 20 q^{45} - 33 q^{46} + 40 q^{47} + 81 q^{48} + 23 q^{49} - 3 q^{50} - q^{51} - 28 q^{52} + 15 q^{53} - 27 q^{54} + 10 q^{55} - 38 q^{56} - 27 q^{57} - 12 q^{58} - 2 q^{59} - 59 q^{60} - 6 q^{61} + 3 q^{62} + 32 q^{63} - 4 q^{64} - 30 q^{65} - 6 q^{66} - 17 q^{67} - 13 q^{68} + 5 q^{69} + 71 q^{70} + 2 q^{71} - 47 q^{72} + 41 q^{73} - 13 q^{74} - 6 q^{75} + 21 q^{76} + 20 q^{77} + 31 q^{78} + 41 q^{79} - 23 q^{80} + 37 q^{81} - 8 q^{82} + 2 q^{83} - 16 q^{84} - 36 q^{85} - 54 q^{86} + 32 q^{87} + q^{89} - 44 q^{90} + 16 q^{91} + 36 q^{92} + 26 q^{93} + 12 q^{94} - 31 q^{95} - 72 q^{96} + 3 q^{97} - 64 q^{98} + 25 q^{99}+O(q^{100}) \) 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 + 17 * q^11 + 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 + q^22 + 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 + 10 * q^33 + 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 + 19 * q^44 + 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 + 10 * q^55 - 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 - 6 * q^66 - 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 + 20 * q^77 + 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 + 25 * q^99

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