LMFDB - Embedded newform 671.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, 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("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 5 x^{18} - 18 x^{17} + 122 x^{16} + 78 x^{15} - 1177 x^{14} + 387 x^{13} + 5755 x^{12} + \cdots - 43 $ x^19 - 5x^18 - 18x^17 + 122x^16 + 78x^15 - 1177x^14 + 387x^13 + 5755x^12 - 4673x^11 - 15053x^10 + 16875x^9 + 20141x^8 - 28019x^7 - 11589x^6 + 21077x^5 + 1674x^4 - 6404x^3 + 241x^2 + 643x - 43
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			1.9
Root			$0.0681863$ of defining polynomial
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0681863 q^{2} +0.0544406 q^{3} -1.99535 q^{4} -3.91488 q^{5} +0.00371210 q^{6} +0.303195 q^{7} -0.272428 q^{8} -2.99704 q^{9} +O(q^{10})$	\(q+0.0681863 q^{2} +0.0544406 q^{3} -1.99535 q^{4} -3.91488 q^{5} +0.00371210 q^{6} +0.303195 q^{7} -0.272428 q^{8} -2.99704 q^{9} -0.266941 q^{10} +1.00000 q^{11} -0.108628 q^{12} +6.79933 q^{13} +0.0206738 q^{14} -0.213128 q^{15} +3.97213 q^{16} -6.53047 q^{17} -0.204357 q^{18} +7.01323 q^{19} +7.81155 q^{20} +0.0165061 q^{21} +0.0681863 q^{22} +3.70369 q^{23} -0.0148312 q^{24} +10.3263 q^{25} +0.463622 q^{26} -0.326482 q^{27} -0.604981 q^{28} -3.05727 q^{29} -0.0145324 q^{30} -1.27972 q^{31} +0.815701 q^{32} +0.0544406 q^{33} -0.445289 q^{34} -1.18697 q^{35} +5.98014 q^{36} +4.27553 q^{37} +0.478207 q^{38} +0.370160 q^{39} +1.06652 q^{40} -4.70664 q^{41} +0.00112549 q^{42} +5.86092 q^{43} -1.99535 q^{44} +11.7330 q^{45} +0.252541 q^{46} +3.88981 q^{47} +0.216245 q^{48} -6.90807 q^{49} +0.704109 q^{50} -0.355523 q^{51} -13.5671 q^{52} +2.62341 q^{53} -0.0222616 q^{54} -3.91488 q^{55} -0.0825990 q^{56} +0.381804 q^{57} -0.208464 q^{58} +12.7861 q^{59} +0.425265 q^{60} -1.00000 q^{61} -0.0872597 q^{62} -0.908687 q^{63} -7.88863 q^{64} -26.6185 q^{65} +0.00371210 q^{66} -8.24324 q^{67} +13.0306 q^{68} +0.201631 q^{69} -0.0809352 q^{70} +6.32123 q^{71} +0.816478 q^{72} -6.92845 q^{73} +0.291533 q^{74} +0.562167 q^{75} -13.9939 q^{76} +0.303195 q^{77} +0.0252398 q^{78} +10.1935 q^{79} -15.5504 q^{80} +8.97333 q^{81} -0.320928 q^{82} +1.99577 q^{83} -0.0329355 q^{84} +25.5660 q^{85} +0.399635 q^{86} -0.166440 q^{87} -0.272428 q^{88} +3.32883 q^{89} +0.800032 q^{90} +2.06153 q^{91} -7.39015 q^{92} -0.0696689 q^{93} +0.265232 q^{94} -27.4559 q^{95} +0.0444072 q^{96} +1.03501 q^{97} -0.471036 q^{98} -2.99704 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) $ 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9} + 7 q^{10} + 19 q^{11} - 4 q^{12} + 8 q^{13} - 11 q^{14} - 5 q^{15} + 31 q^{16} + 9 q^{17} + 10 q^{18} + 17 q^{19} - 6 q^{20} + 18 q^{21} + 5 q^{22} - 10 q^{23} + 26 q^{24} + 45 q^{25} + 5 q^{26} - 33 q^{27} + 36 q^{28} + 27 q^{29} - 30 q^{30} + 7 q^{31} + 8 q^{32} - 5 q^{34} + 17 q^{35} + 38 q^{36} + 20 q^{37} - 37 q^{38} + 24 q^{39} + 10 q^{40} + 19 q^{41} + 21 q^{42} + 20 q^{43} + 23 q^{44} - 32 q^{45} + 41 q^{46} - 19 q^{47} + 5 q^{48} + 42 q^{49} + 36 q^{50} + 47 q^{51} - 28 q^{52} + 3 q^{53} - 33 q^{54} - 44 q^{56} + 11 q^{57} + 23 q^{58} - 28 q^{59} - 96 q^{60} - 19 q^{61} - 11 q^{62} - 32 q^{63} + 47 q^{64} + 25 q^{65} + q^{66} + 3 q^{67} + 38 q^{68} + 3 q^{70} - 19 q^{71} + 34 q^{72} + 20 q^{73} - 22 q^{74} - 50 q^{75} - 25 q^{76} + 9 q^{77} - 94 q^{78} + 69 q^{79} - 36 q^{80} + 47 q^{81} - 61 q^{82} + q^{83} - 28 q^{84} + 24 q^{85} - 27 q^{86} - 58 q^{87} + 9 q^{88} + 36 q^{90} + 24 q^{91} - 67 q^{92} - 14 q^{93} + 64 q^{94} - 3 q^{95} - 26 q^{96} + 21 q^{97} - 87 q^{98} + 29 q^{99}+O(q^{100}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9 + 7 * q^10 + 19 * q^11 - 4 * q^12 + 8 * q^13 - 11 * q^14 - 5 * q^15 + 31 * q^16 + 9 * q^17 + 10 * q^18 + 17 * q^19 - 6 * q^20 + 18 * q^21 + 5 * q^22 - 10 * q^23 + 26 * q^24 + 45 * q^25 + 5 * q^26 - 33 * q^27 + 36 * q^28 + 27 * q^29 - 30 * q^30 + 7 * q^31 + 8 * q^32 - 5 * q^34 + 17 * q^35 + 38 * q^36 + 20 * q^37 - 37 * q^38 + 24 * q^39 + 10 * q^40 + 19 * q^41 + 21 * q^42 + 20 * q^43 + 23 * q^44 - 32 * q^45 + 41 * q^46 - 19 * q^47 + 5 * q^48 + 42 * q^49 + 36 * q^50 + 47 * q^51 - 28 * q^52 + 3 * q^53 - 33 * q^54 - 44 * q^56 + 11 * q^57 + 23 * q^58 - 28 * q^59 - 96 * q^60 - 19 * q^61 - 11 * q^62 - 32 * q^63 + 47 * q^64 + 25 * q^65 + q^66 + 3 * q^67 + 38 * q^68 + 3 * q^70 - 19 * q^71 + 34 * q^72 + 20 * q^73 - 22 * q^74 - 50 * q^75 - 25 * q^76 + 9 * q^77 - 94 * q^78 + 69 * q^79 - 36 * q^80 + 47 * q^81 - 61 * q^82 + q^83 - 28 * q^84 + 24 * q^85 - 27 * q^86 - 58 * q^87 + 9 * q^88 + 36 * q^90 + 24 * q^91 - 67 * q^92 - 14 * q^93 + 64 * q^94 - 3 * q^95 - 26 * q^96 + 21 * q^97 - 87 * q^98 + 29 * 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 $

$2$	0.0681863	0.0482150	0.0241075	−	0.999709i	$-0.492326\pi$
$2$	0.0681863	0.0482150	0.0241075	+	0.999709i	$0.492326\pi$
$3$	0.0544406	0.0314313	0.0157156	−	0.999877i	$-0.494997\pi$
$3$	0.0544406	0.0314313	0.0157156	+	0.999877i	$0.494997\pi$
$4$	−1.99535	−0.997675
$5$	−3.91488	−1.75079	−0.875393	−	0.483412i	$-0.839397\pi$
$5$	−3.91488	−1.75079	−0.875393	+	0.483412i	$0.839397\pi$
$6$	0.00371210	0.00151546
$7$	0.303195	0.114597	0.0572985	−	0.998357i	$-0.481751\pi$
$7$	0.303195	0.114597	0.0572985	+	0.998357i	$0.481751\pi$
$8$	−0.272428	−0.0963180
$9$	−2.99704	−0.999012
$10$	−0.266941	−0.0844142
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.108628	−0.0313582
$13$	6.79933	1.88580	0.942898	−	0.333082i	$-0.108088\pi$
$13$	6.79933	1.88580	0.942898	+	0.333082i	$0.108088\pi$
$14$	0.0206738	0.00552530
$15$	−0.213128	−0.0550294
$16$	3.97213	0.993031
$17$	−6.53047	−1.58387	−0.791936	−	0.610604i	$-0.790927\pi$
$17$	−6.53047	−1.58387	−0.791936	+	0.610604i	$0.790927\pi$
$18$	−0.204357	−0.0481674
$19$	7.01323	1.60895	0.804473	−	0.593990i	$-0.202448\pi$
$19$	7.01323	1.60895	0.804473	+	0.593990i	$0.202448\pi$
$20$	7.81155	1.74672
$21$	0.0165061	0.00360193
$22$	0.0681863	0.0145374
$23$	3.70369	0.772272	0.386136	−	0.922442i	$-0.373810\pi$
$23$	3.70369	0.772272	0.386136	+	0.922442i	$0.373810\pi$
$24$	−0.0148312	−0.00302740
$25$	10.3263	2.06525
$26$	0.463622	0.0909237
$27$	−0.326482	−0.0628315
$28$	−0.604981	−0.114331
$29$	−3.05727	−0.567721	−0.283860	−	0.958866i	$-0.591615\pi$
$29$	−3.05727	−0.567721	−0.283860	+	0.958866i	$0.591615\pi$
$30$	−0.0145324	−0.00265324
$31$	−1.27972	−0.229845	−0.114923	−	0.993374i	$-0.536662\pi$
$31$	−1.27972	−0.229845	−0.114923	+	0.993374i	$0.536662\pi$
$32$	0.815701	0.144197
$33$	0.0544406	0.00947689
$34$	−0.445289	−0.0763664
$35$	−1.18697	−0.200635
$36$	5.98014	0.996690
$37$	4.27553	0.702893	0.351447	−	0.936208i	$-0.385690\pi$
$37$	4.27553	0.702893	0.351447	+	0.936208i	$0.385690\pi$
$38$	0.478207	0.0775753
$39$	0.370160	0.0592730
$40$	1.06652	0.168632
$41$	−4.70664	−0.735053	−0.367527	−	0.930013i	$-0.619795\pi$
$41$	−4.70664	−0.735053	−0.367527	+	0.930013i	$0.619795\pi$
$42$	0.00112549	0.000173667 0
$43$	5.86092	0.893782	0.446891	−	0.894588i	$-0.352531\pi$
$43$	5.86092	0.893782	0.446891	+	0.894588i	$0.352531\pi$
$44$	−1.99535	−0.300810
$45$	11.7330	1.74906
$46$	0.252541	0.0372351
$47$	3.88981	0.567386	0.283693	−	0.958915i	$-0.408440\pi$
$47$	3.88981	0.567386	0.283693	+	0.958915i	$0.408440\pi$
$48$	0.216245	0.0312122
$49$	−6.90807	−0.986868
$50$	0.704109	0.0995761
$51$	−0.355523	−0.0497831
$52$	−13.5671	−1.88141
$53$	2.62341	0.360353	0.180177	−	0.983634i	$-0.442333\pi$
$53$	2.62341	0.360353	0.180177	+	0.983634i	$0.442333\pi$
$54$	−0.0222616	−0.00302942
$55$	−3.91488	−0.527882
$56$	−0.0825990	−0.0110378
$57$	0.381804	0.0505712
$58$	−0.208464	−0.0273727
$59$	12.7861	1.66461	0.832304	−	0.554319i	$-0.187021\pi$
$59$	12.7861	1.66461	0.832304	+	0.554319i	$0.187021\pi$
$60$	0.425265	0.0549015
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−0.0872597	−0.0110820
$63$	−0.908687	−0.114484
$64$	−7.88863	−0.986079
$65$	−26.6185	−3.30162
$66$	0.00371210	0.000456928 0
$67$	−8.24324	−1.00707	−0.503536	−	0.863974i	$-0.667968\pi$
$67$	−8.24324	−1.00707	−0.503536	+	0.863974i	$0.667968\pi$
$68$	13.0306	1.58019
$69$	0.201631	0.0242735
$70$	−0.0809352	−0.00967361
$71$	6.32123	0.750192	0.375096	−	0.926986i	$-0.377610\pi$
$71$	6.32123	0.750192	0.375096	+	0.926986i	$0.377610\pi$
$72$	0.816478	0.0962228
$73$	−6.92845	−0.810914	−0.405457	−	0.914114i	$-0.632888\pi$
$73$	−6.92845	−0.810914	−0.405457	+	0.914114i	$0.632888\pi$
$74$	0.291533	0.0338900
$75$	0.562167	0.0649135
$76$	−13.9939	−1.60521
$77$	0.303195	0.0345523
$78$	0.0252398	0.00285785
$79$	10.1935	1.14686	0.573431	−	0.819254i	$-0.305612\pi$
$79$	10.1935	1.14686	0.573431	+	0.819254i	$0.305612\pi$
$80$	−15.5504	−1.73859
$81$	8.97333	0.997037
$82$	−0.320928	−0.0354406
$83$	1.99577	0.219064	0.109532	−	0.993983i	$-0.465065\pi$
$83$	1.99577	0.219064	0.109532	+	0.993983i	$0.465065\pi$
$84$	−0.0329355	−0.00359356
$85$	25.5660	2.77302
$86$	0.399635	0.0430937
$87$	−0.166440	−0.0178442
$88$	−0.272428	−0.0290410
$89$	3.32883	0.352855	0.176428	−	0.984314i	$-0.443546\pi$
$89$	3.32883	0.352855	0.176428	+	0.984314i	$0.443546\pi$
$90$	0.800032	0.0843308
$91$	2.06153	0.216107
$92$	−7.39015	−0.770477
$93$	−0.0696689	−0.00722433
$94$	0.265232	0.0273566
$95$	−27.4559	−2.81692
$96$	0.0444072	0.00453230
$97$	1.03501	0.105089	0.0525447	−	0.998619i	$-0.483267\pi$
$97$	1.03501	0.105089	0.0525447	+	0.998619i	$0.483267\pi$
$98$	−0.471036	−0.0475818
$99$	−2.99704	−0.301213
$100$	−20.6045	−2.06045
$101$	−10.9799	−1.09254	−0.546272	−	0.837608i	$-0.683954\pi$
$101$	−10.9799	−1.09254	−0.546272	+	0.837608i	$0.683954\pi$
$102$	−0.0242418	−0.00240029
$103$	15.4079	1.51819	0.759093	−	0.650982i	$-0.225643\pi$
$103$	15.4079	1.51819	0.759093	+	0.650982i	$0.225643\pi$
$104$	−1.85233	−0.181636
$105$	−0.0646194	−0.00630621
$106$	0.178881	0.0173744
$107$	11.9839	1.15853	0.579266	−	0.815139i	$-0.303339\pi$
$107$	11.9839	1.15853	0.579266	+	0.815139i	$0.303339\pi$
$108$	0.651446	0.0626854
$109$	−7.94865	−0.761343	−0.380672	−	0.924710i	$-0.624307\pi$
$109$	−7.94865	−0.761343	−0.380672	+	0.924710i	$0.624307\pi$
$110$	−0.266941	−0.0254518
$111$	0.232762	0.0220928
$112$	1.20433	0.113798
$113$	10.9070	1.02605	0.513023	−	0.858375i	$-0.328526\pi$
$113$	10.9070	1.02605	0.513023	+	0.858375i	$0.328526\pi$
$114$	0.0260338	0.00243829
$115$	−14.4995	−1.35208
$116$	6.10033	0.566401
$117$	−20.3779	−1.88393
$118$	0.871837	0.0802591
$119$	−1.98001	−0.181507
$120$	0.0580621	0.00530032
$121$	1.00000	0.0909091
$122$	−0.0681863	−0.00617330
$123$	−0.256232	−0.0231037
$124$	2.55350	0.229311
$125$	−20.8516	−1.86503
$126$	−0.0619600	−0.00551984
$127$	3.10238	0.275291	0.137646	−	0.990482i	$-0.456046\pi$
$127$	3.10238	0.275291	0.137646	+	0.990482i	$0.456046\pi$
$128$	−2.16930	−0.191741
$129$	0.319072	0.0280927
$130$	−1.81502	−0.159188
$131$	13.4836	1.17807	0.589036	−	0.808107i	$-0.299508\pi$
$131$	13.4836	1.17807	0.589036	+	0.808107i	$0.299508\pi$
$132$	−0.108628	−0.00945485
$133$	2.12638	0.184380
$134$	−0.562077	−0.0485560
$135$	1.27814	0.110004
$136$	1.77909	0.152555
$137$	7.96517	0.680510	0.340255	−	0.940333i	$-0.389487\pi$
$137$	7.96517	0.680510	0.340255	+	0.940333i	$0.389487\pi$
$138$	0.0137485	0.00117035
$139$	17.9562	1.52302	0.761512	−	0.648151i	$-0.224458\pi$
$139$	17.9562	1.52302	0.761512	+	0.648151i	$0.224458\pi$
$140$	2.36842	0.200168
$141$	0.211763	0.0178337
$142$	0.431022	0.0361705
$143$	6.79933	0.568589
$144$	−11.9046	−0.992050
$145$	11.9688	0.993958
$146$	−0.472426	−0.0390982
$147$	−0.376079	−0.0310185
$148$	−8.53119	−0.701259
$149$	4.31977	0.353889	0.176945	−	0.984221i	$-0.443379\pi$
$149$	4.31977	0.353889	0.176945	+	0.984221i	$0.443379\pi$
$150$	0.0383321	0.00312980
$151$	−12.6813	−1.03199	−0.515994	−	0.856592i	$-0.672577\pi$
$151$	−12.6813	−1.03199	−0.515994	+	0.856592i	$0.672577\pi$
$152$	−1.91060	−0.154970
$153$	19.5721	1.58231
$154$	0.0206738	0.00166594
$155$	5.00996	0.402410
$156$	−0.738598	−0.0591352
$157$	15.5765	1.24314	0.621569	−	0.783359i	$-0.286496\pi$
$157$	15.5765	1.24314	0.621569	+	0.783359i	$0.286496\pi$
$158$	0.695059	0.0552960
$159$	0.142820	0.0113264
$160$	−3.19337	−0.252458
$161$	1.12294	0.0885001
$162$	0.611859	0.0480722
$163$	−20.6082	−1.61416	−0.807081	−	0.590440i	$-0.798954\pi$
$163$	−20.6082	−1.61416	−0.807081	+	0.590440i	$0.798954\pi$
$164$	9.39139	0.733345
$165$	−0.213128	−0.0165920
$166$	0.136084	0.0105622
$167$	8.95293	0.692799	0.346399	−	0.938087i	$-0.387404\pi$
$167$	8.95293	0.692799	0.346399	+	0.938087i	$0.387404\pi$
$168$	−0.00449673	−0.000346931 0
$169$	33.2309	2.55623
$170$	1.74325	0.133701
$171$	−21.0189	−1.60736
$172$	−11.6946	−0.891704
$173$	6.55106	0.498068	0.249034	−	0.968495i	$-0.419887\pi$
$173$	6.55106	0.498068	0.249034	+	0.968495i	$0.419887\pi$
$174$	−0.0113489	−0.000860358 0
$175$	3.13087	0.236672
$176$	3.97213	0.299410
$177$	0.696082	0.0523208
$178$	0.226981	0.0170129
$179$	−7.86025	−0.587502	−0.293751	−	0.955882i	$-0.594904\pi$
$179$	−7.86025	−0.587502	−0.293751	+	0.955882i	$0.594904\pi$
$180$	−23.4115	−1.74499
$181$	−21.1964	−1.57551	−0.787756	−	0.615987i	$-0.788757\pi$
$181$	−21.1964	−1.57551	−0.787756	+	0.615987i	$0.788757\pi$
$182$	0.140568	0.0104196
$183$	−0.0544406	−0.00402436
$184$	−1.00899	−0.0743837
$185$	−16.7382	−1.23062
$186$	−0.00475047	−0.000348321 0
$187$	−6.53047	−0.477555
$188$	−7.76153	−0.566067
$189$	−0.0989878	−0.00720030
$190$	−1.87212	−0.135818
$191$	−19.4126	−1.40464	−0.702322	−	0.711859i	$-0.747853\pi$
$191$	−19.4126	−1.40464	−0.702322	+	0.711859i	$0.747853\pi$
$192$	−0.429462	−0.0309937
$193$	17.8215	1.28282	0.641411	−	0.767198i	$-0.278349\pi$
$193$	17.8215	1.28282	0.641411	+	0.767198i	$0.278349\pi$
$194$	0.0705736	0.00506689
$195$	−1.44913	−0.103774
$196$	13.7840	0.984573
$197$	−19.0557	−1.35766	−0.678832	−	0.734294i	$-0.737514\pi$
$197$	−19.0557	−1.35766	−0.678832	+	0.734294i	$0.737514\pi$
$198$	−0.204357	−0.0145230
$199$	−21.2212	−1.50433	−0.752167	−	0.658973i	$-0.770991\pi$
$199$	−21.2212	−1.50433	−0.752167	+	0.658973i	$0.770991\pi$
$200$	−2.81316	−0.198921
$201$	−0.448767	−0.0316536
$202$	−0.748682	−0.0526771
$203$	−0.926950	−0.0650591
$204$	0.709392	0.0496674
$205$	18.4259	1.28692
$206$	1.05061	0.0731994
$207$	−11.1001	−0.771509
$208$	27.0078	1.87265
$209$	7.01323	0.485115
$210$	−0.00440616	−0.000304054 0
$211$	5.35619	0.368735	0.184368	−	0.982857i	$-0.440976\pi$
$211$	5.35619	0.368735	0.184368	+	0.982857i	$0.440976\pi$
$212$	−5.23463	−0.359516
$213$	0.344131	0.0235795
$214$	0.817141	0.0558586
$215$	−22.9448	−1.56482
$216$	0.0889430	0.00605180
$217$	−0.388006	−0.0263396
$218$	−0.541990	−0.0367082
$219$	−0.377189	−0.0254881
$220$	7.81155	0.526655
$221$	−44.4029	−2.98686
$222$	0.0158712	0.00106521
$223$	2.30793	0.154550	0.0772751	−	0.997010i	$-0.475378\pi$
$223$	2.30793	0.154550	0.0772751	+	0.997010i	$0.475378\pi$
$224$	0.247317	0.0165245
$225$	−30.9482	−2.06321
$226$	0.743710	0.0494708
$227$	−2.61947	−0.173860	−0.0869302	−	0.996214i	$-0.527706\pi$
$227$	−2.61947	−0.173860	−0.0869302	+	0.996214i	$0.527706\pi$
$228$	−0.761833	−0.0504536
$229$	−4.04845	−0.267529	−0.133764	−	0.991013i	$-0.542707\pi$
$229$	−4.04845	−0.267529	−0.133764	+	0.991013i	$0.542707\pi$
$230$	−0.988666	−0.0651907
$231$	0.0165061	0.00108602
$232$	0.832887	0.0546817
$233$	3.99185	0.261515	0.130757	−	0.991414i	$-0.458259\pi$
$233$	3.99185	0.261515	0.130757	+	0.991414i	$0.458259\pi$
$234$	−1.38949	−0.0908339
$235$	−15.2281	−0.993372
$236$	−25.5127	−1.66074
$237$	0.554941	0.0360473
$238$	−0.135009	−0.00875136
$239$	5.95641	0.385288	0.192644	−	0.981269i	$-0.438294\pi$
$239$	5.95641	0.385288	0.192644	+	0.981269i	$0.438294\pi$
$240$	−0.846571	−0.0546459
$241$	−25.6876	−1.65468	−0.827342	−	0.561698i	$-0.810148\pi$
$241$	−25.6876	−1.65468	−0.827342	+	0.561698i	$0.810148\pi$
$242$	0.0681863	0.00438318
$243$	1.46796	0.0941696
$244$	1.99535	0.127739
$245$	27.0442	1.72779
$246$	−0.0174715	−0.00111394
$247$	47.6853	3.03414
$248$	0.348633	0.0221382
$249$	0.108651	0.00688547
$250$	−1.42180	−0.0899222
$251$	26.8930	1.69747	0.848734	−	0.528819i	$-0.177365\pi$
$251$	26.8930	1.69747	0.848734	+	0.528819i	$0.177365\pi$
$252$	1.81315	0.114218
$253$	3.70369	0.232849
$254$	0.211540	0.0132732
$255$	1.39183	0.0871596
$256$	15.6293	0.976834
$257$	2.92965	0.182746	0.0913732	−	0.995817i	$-0.470874\pi$
$257$	2.92965	0.182746	0.0913732	+	0.995817i	$0.470874\pi$
$258$	0.0217563	0.00135449
$259$	1.29632	0.0805495
$260$	53.1133	3.29395
$261$	9.16275	0.567160
$262$	0.919400	0.0568007
$263$	1.10601	0.0681998	0.0340999	−	0.999418i	$-0.489144\pi$
$263$	1.10601	0.0681998	0.0340999	+	0.999418i	$0.489144\pi$
$264$	−0.0148312	−0.000912794 0
$265$	−10.2703	−0.630902
$266$	0.144990	0.00888990
$267$	0.181223	0.0110907
$268$	16.4482	1.00473
$269$	24.8350	1.51422	0.757110	−	0.653288i	$-0.226611\pi$
$269$	24.8350	1.51422	0.757110	+	0.653288i	$0.226611\pi$
$270$	0.0871515	0.00530387
$271$	8.66608	0.526427	0.263213	−	0.964738i	$-0.415218\pi$
$271$	8.66608	0.526427	0.263213	+	0.964738i	$0.415218\pi$
$272$	−25.9399	−1.57283
$273$	0.112231	0.00679251
$274$	0.543116	0.0328108
$275$	10.3263	0.622696
$276$	−0.402324	−0.0242171
$277$	−7.12404	−0.428042	−0.214021	−	0.976829i	$-0.568656\pi$
$277$	−7.12404	−0.428042	−0.214021	+	0.976829i	$0.568656\pi$
$278$	1.22437	0.0734326
$279$	3.83538	0.229618
$280$	0.323365	0.0193247
$281$	−13.4644	−0.803216	−0.401608	−	0.915812i	$-0.631549\pi$
$281$	−13.4644	−0.803216	−0.401608	+	0.915812i	$0.631549\pi$
$282$	0.0144394	0.000859851 0
$283$	−19.4500	−1.15618	−0.578091	−	0.815972i	$-0.696202\pi$
$283$	−19.4500	−1.15618	−0.578091	+	0.815972i	$0.696202\pi$
$284$	−12.6131	−0.748448
$285$	−1.49472	−0.0885393
$286$	0.463622	0.0274145
$287$	−1.42703	−0.0842349
$288$	−2.44469	−0.144055
$289$	25.6471	1.50865
$290$	0.816111	0.0479237
$291$	0.0563466	0.00330310
$292$	13.8247	0.809029
$293$	−0.0105302	−0.000615181 0	−0.000307590	−	1.00000i	$-0.500098\pi$
$293$	−0.0105302	−0.000615181 0	−0.000307590		1.00000i	$0.500098\pi$
$294$	−0.0256435	−0.00149556
$295$	−50.0560	−2.91437
$296$	−1.16478	−0.0677013
$297$	−0.326482	−0.0189444
$298$	0.294549	0.0170628
$299$	25.1826	1.45635
$300$	−1.12172	−0.0647626
$301$	1.77700	0.102425
$302$	−0.864690	−0.0497573
$303$	−0.597754	−0.0343401
$304$	27.8574	1.59773
$305$	3.91488	0.224165
$306$	1.33455	0.0762910
$307$	11.4927	0.655921	0.327960	−	0.944691i	$-0.393639\pi$
$307$	11.4927	0.655921	0.327960	+	0.944691i	$0.393639\pi$
$308$	−0.604981	−0.0344720
$309$	0.838815	0.0477185
$310$	0.341611	0.0194022
$311$	10.1036	0.572924	0.286462	−	0.958092i	$-0.407521\pi$
$311$	10.1036	0.572924	0.286462	+	0.958092i	$0.407521\pi$
$312$	−0.100842	−0.00570905
$313$	−7.79436	−0.440563	−0.220282	−	0.975436i	$-0.570698\pi$
$313$	−7.79436	−0.440563	−0.220282	+	0.975436i	$0.570698\pi$
$314$	1.06210	0.0599379
$315$	3.55740	0.200437
$316$	−20.3397	−1.14420
$317$	3.87259	0.217507	0.108753	−	0.994069i	$-0.465314\pi$
$317$	3.87259	0.217507	0.108753	+	0.994069i	$0.465314\pi$
$318$	0.00973838	0.000546101 0
$319$	−3.05727	−0.171174
$320$	30.8830	1.72641
$321$	0.652412	0.0364141
$322$	0.0765692	0.00426703
$323$	−45.7997	−2.54836
$324$	−17.9049	−0.994719
$325$	70.2116	3.89464
$326$	−1.40520	−0.0778269
$327$	−0.432729	−0.0239300
$328$	1.28222	0.0707988
$329$	1.17937	0.0650208
$330$	−0.0145324	−0.000799983 0
$331$	25.4503	1.39888	0.699439	−	0.714693i	$-0.253433\pi$
$331$	25.4503	1.39888	0.699439	+	0.714693i	$0.253433\pi$
$332$	−3.98226	−0.218555
$333$	−12.8139	−0.702199
$334$	0.610468	0.0334033
$335$	32.2713	1.76317
$336$	0.0655644	0.00357683
$337$	26.5230	1.44480	0.722400	−	0.691475i	$-0.243039\pi$
$337$	26.5230	1.44480	0.722400	+	0.691475i	$0.243039\pi$
$338$	2.26590	0.123249
$339$	0.593784	0.0322499
$340$	−51.0131	−2.76657
$341$	−1.27972	−0.0693009
$342$	−1.43320	−0.0774987
$343$	−4.21686	−0.227689
$344$	−1.59668	−0.0860873
$345$	−0.789360	−0.0424977
$346$	0.446693	0.0240144
$347$	−11.3447	−0.609016	−0.304508	−	0.952510i	$-0.598492\pi$
$347$	−11.3447	−0.609016	−0.304508	+	0.952510i	$0.598492\pi$
$348$	0.332105	0.0178027
$349$	4.09107	0.218990	0.109495	−	0.993987i	$-0.465077\pi$
$349$	4.09107	0.218990	0.109495	+	0.993987i	$0.465077\pi$
$350$	0.213483	0.0114111
$351$	−2.21986	−0.118487
$352$	0.815701	0.0434770
$353$	22.6163	1.20374	0.601871	−	0.798593i	$-0.294422\pi$
$353$	22.6163	1.20374	0.601871	+	0.798593i	$0.294422\pi$
$354$	0.0474633	0.00252265
$355$	−24.7468	−1.31343
$356$	−6.64218	−0.352035
$357$	−0.107793	−0.00570500
$358$	−0.535961	−0.0283264
$359$	19.3253	1.01995	0.509974	−	0.860190i	$-0.329655\pi$
$359$	19.3253	1.01995	0.509974	+	0.860190i	$0.329655\pi$
$360$	−3.19641	−0.168466
$361$	30.1854	1.58871
$362$	−1.44530	−0.0759634
$363$	0.0544406	0.00285739
$364$	−4.11347	−0.215604
$365$	27.1240	1.41974
$366$	−0.00371210	−0.000194035 0
$367$	−0.677877	−0.0353849	−0.0176925	−	0.999843i	$-0.505632\pi$
$367$	−0.677877	−0.0353849	−0.0176925	+	0.999843i	$0.505632\pi$
$368$	14.7115	0.766890
$369$	14.1060	0.734327
$370$	−1.14132	−0.0593342
$371$	0.795406	0.0412954
$372$	0.139014	0.00720753
$373$	28.1562	1.45787	0.728935	−	0.684582i	$-0.240015\pi$
$373$	28.1562	1.45787	0.728935	+	0.684582i	$0.240015\pi$
$374$	−0.445289	−0.0230253
$375$	−1.13517	−0.0586201
$376$	−1.05969	−0.0546495
$377$	−20.7874	−1.07061
$378$	−0.00674961	−0.000347163 0
$379$	6.18358	0.317629	0.158815	−	0.987308i	$-0.449233\pi$
$379$	6.18358	0.317629	0.158815	+	0.987308i	$0.449233\pi$
$380$	54.7842	2.81037
$381$	0.168895	0.00865276
$382$	−1.32367	−0.0677249
$383$	−27.3143	−1.39570	−0.697848	−	0.716246i	$-0.745859\pi$
$383$	−27.3143	−1.39570	−0.697848	+	0.716246i	$0.745859\pi$
$384$	−0.118098	−0.00602666
$385$	−1.18697	−0.0604937
$386$	1.21518	0.0618513
$387$	−17.5654	−0.892899
$388$	−2.06521	−0.104845
$389$	−20.4658	−1.03766	−0.518828	−	0.854879i	$-0.673631\pi$
$389$	−20.4658	−1.03766	−0.518828	+	0.854879i	$0.673631\pi$
$390$	−0.0988108	−0.00500348
$391$	−24.1868	−1.22318
$392$	1.88195	0.0950531
$393$	0.734057	0.0370283
$394$	−1.29934	−0.0654598
$395$	−39.9064	−2.00791
$396$	5.98014	0.300513
$397$	−38.3339	−1.92393	−0.961963	−	0.273181i	$-0.911924\pi$
$397$	−38.3339	−1.92393	−0.961963	+	0.273181i	$0.911924\pi$
$398$	−1.44700	−0.0725315
$399$	0.115761	0.00579531
$400$	41.0172	2.05086
$401$	31.3382	1.56496	0.782478	−	0.622678i	$-0.213956\pi$
$401$	31.3382	1.56496	0.782478	+	0.622678i	$0.213956\pi$
$402$	−0.0305998	−0.00152618
$403$	−8.70127	−0.433441
$404$	21.9088	1.09000
$405$	−35.1295	−1.74560
$406$	−0.0632053	−0.00313683
$407$	4.27553	0.211930
$408$	0.0968544	0.00479501
$409$	1.76760	0.0874024	0.0437012	−	0.999045i	$-0.486085\pi$
$409$	1.76760	0.0874024	0.0437012	+	0.999045i	$0.486085\pi$
$410$	1.25640	0.0620489
$411$	0.433628	0.0213893
$412$	−30.7442	−1.51466
$413$	3.87668	0.190759
$414$	−0.756874	−0.0371983
$415$	−7.81320	−0.383535
$416$	5.54623	0.271926
$417$	0.977544	0.0478706
$418$	0.478207	0.0233898
$419$	−16.3781	−0.800121	−0.400060	−	0.916489i	$-0.631011\pi$
$419$	−16.3781	−0.800121	−0.400060	+	0.916489i	$0.631011\pi$
$420$	0.128938	0.00629155
$421$	34.7756	1.69486	0.847430	−	0.530907i	$-0.178149\pi$
$421$	34.7756	1.69486	0.847430	+	0.530907i	$0.178149\pi$
$422$	0.365219	0.0177786
$423$	−11.6579	−0.566826
$424$	−0.714692	−0.0347085
$425$	−67.4353	−3.27109
$426$	0.0234651	0.00113689
$427$	−0.303195	−0.0146726
$428$	−23.9122	−1.15584
$429$	0.370160	0.0178715
$430$	−1.56452	−0.0754479
$431$	28.2610	1.36128	0.680642	−	0.732616i	$-0.261701\pi$
$431$	28.2610	1.36128	0.680642	+	0.732616i	$0.261701\pi$
$432$	−1.29683	−0.0623936
$433$	−5.07667	−0.243969	−0.121984	−	0.992532i	$-0.538926\pi$
$433$	−5.07667	−0.243969	−0.121984	+	0.992532i	$0.538926\pi$
$434$	−0.0264567	−0.00126996
$435$	0.651590	0.0312414
$436$	15.8604	0.759573
$437$	25.9748	1.24254
$438$	−0.0257191	−0.00122891
$439$	−13.4300	−0.640977	−0.320489	−	0.947252i	$-0.603847\pi$
$439$	−13.4300	−0.640977	−0.320489	+	0.947252i	$0.603847\pi$
$440$	1.06652	0.0508445
$441$	20.7037	0.985893
$442$	−3.02767	−0.144011
$443$	22.3941	1.06397	0.531987	−	0.846752i	$-0.321445\pi$
$443$	22.3941	1.06397	0.531987	+	0.846752i	$0.321445\pi$
$444$	−0.464443	−0.0220415
$445$	−13.0320	−0.617774
$446$	0.157369	0.00745164
$447$	0.235171	0.0111232
$448$	−2.39180	−0.113002
$449$	2.03117	0.0958571	0.0479285	−	0.998851i	$-0.484738\pi$
$449$	2.03117	0.0958571	0.0479285	+	0.998851i	$0.484738\pi$
$450$	−2.11024	−0.0994777
$451$	−4.70664	−0.221627
$452$	−21.7633	−1.02366
$453$	−0.690376	−0.0324367
$454$	−0.178612	−0.00838268
$455$	−8.07062	−0.378356
$456$	−0.104014	−0.00487092
$457$	6.51608	0.304809	0.152405	−	0.988318i	$-0.451298\pi$
$457$	6.51608	0.304809	0.152405	+	0.988318i	$0.451298\pi$
$458$	−0.276049	−0.0128989
$459$	2.13208	0.0995170
$460$	28.9315	1.34894
$461$	−18.8472	−0.877800	−0.438900	−	0.898536i	$-0.644632\pi$
$461$	−18.8472	−0.877800	−0.438900	+	0.898536i	$0.644632\pi$
$462$	0.00112549	5.23626e−5 0
$463$	−19.3076	−0.897299	−0.448649	−	0.893708i	$-0.648095\pi$
$463$	−19.3076	−0.897299	−0.448649	+	0.893708i	$0.648095\pi$
$464$	−12.1439	−0.563765
$465$	0.272745	0.0126482
$466$	0.272190	0.0126090
$467$	−32.6438	−1.51057	−0.755287	−	0.655394i	$-0.772502\pi$
$467$	−32.6438	−1.51057	−0.755287	+	0.655394i	$0.772502\pi$
$468$	40.6610	1.87955
$469$	−2.49931	−0.115407
$470$	−1.03835	−0.0478955
$471$	0.847992	0.0390734
$472$	−3.48330	−0.160332
$473$	5.86092	0.269485
$474$	0.0378394	0.00173802
$475$	72.4204	3.32288
$476$	3.95081	0.181085
$477$	−7.86246	−0.359997
$478$	0.406146	0.0185767
$479$	−4.50704	−0.205932	−0.102966	−	0.994685i	$-0.532833\pi$
$479$	−4.50704	−0.205932	−0.102966	+	0.994685i	$0.532833\pi$
$480$	−0.173849	−0.00793508
$481$	29.0708	1.32551
$482$	−1.75154	−0.0797807
$483$	0.0611335	0.00278167
$484$	−1.99535	−0.0906978
$485$	−4.05194	−0.183989
$486$	0.100095	0.00454039
$487$	−12.5364	−0.568080	−0.284040	−	0.958813i	$-0.591675\pi$
$487$	−12.5364	−0.568080	−0.284040	+	0.958813i	$0.591675\pi$
$488$	0.272428	0.0123323
$489$	−1.12192	−0.0507352
$490$	1.84405	0.0833056
$491$	3.77887	0.170538	0.0852691	−	0.996358i	$-0.472825\pi$
$491$	3.77887	0.170538	0.0852691	+	0.996358i	$0.472825\pi$
$492$	0.511273	0.0230500
$493$	19.9654	0.899197
$494$	3.25149	0.146291
$495$	11.7330	0.527360
$496$	−5.08322	−0.228243
$497$	1.91657	0.0859698
$498$	0.00740851	0.000331983 0
$499$	13.1799	0.590014	0.295007	−	0.955495i	$-0.404678\pi$
$499$	13.1799	0.590014	0.295007	+	0.955495i	$0.404678\pi$
$500$	41.6063	1.86069
$501$	0.487403	0.0217756
$502$	1.83373	0.0818435
$503$	−33.4595	−1.49189	−0.745943	−	0.666010i	$-0.768001\pi$
$503$	−33.4595	−1.49189	−0.745943	+	0.666010i	$0.768001\pi$
$504$	0.247552	0.0110268
$505$	42.9851	1.91281
$506$	0.252541	0.0112268
$507$	1.80911	0.0803455
$508$	−6.19033	−0.274651
$509$	−17.0686	−0.756554	−0.378277	−	0.925693i	$-0.623483\pi$
$509$	−17.0686	−0.756554	−0.378277	+	0.925693i	$0.623483\pi$
$510$	0.0949036	0.00420240
$511$	−2.10067	−0.0929283
$512$	5.40431	0.238839
$513$	−2.28969	−0.101092
$514$	0.199762	0.00881112
$515$	−60.3200	−2.65802
$516$	−0.636660	−0.0280274
$517$	3.88981	0.171073
$518$	0.0883914	0.00388370
$519$	0.356644	0.0156549
$520$	7.25165	0.318006
$521$	23.6849	1.03765	0.518827	−	0.854879i	$-0.326369\pi$
$521$	23.6849	1.03765	0.518827	+	0.854879i	$0.326369\pi$
$522$	0.624774	0.0273456
$523$	−12.6251	−0.552056	−0.276028	−	0.961150i	$-0.589018\pi$
$523$	−12.6251	−0.552056	−0.276028	+	0.961150i	$0.589018\pi$
$524$	−26.9046	−1.17533
$525$	0.170446	0.00743889
$526$	0.0754151	0.00328825
$527$	8.35720	0.364045
$528$	0.216245	0.00941084
$529$	−9.28270	−0.403596
$530$	−0.700296	−0.0304189
$531$	−38.3204	−1.66296
$532$	−4.24287	−0.183952
$533$	−32.0020	−1.38616
$534$	0.0123570	0.000534738 0
$535$	−46.9156	−2.02834
$536$	2.24569	0.0969992
$537$	−0.427916	−0.0184659
$538$	1.69341	0.0730081
$539$	−6.90807	−0.297552
$540$	−2.55033	−0.109749
$541$	−16.5491	−0.711500	−0.355750	−	0.934581i	$-0.615775\pi$
$541$	−16.5491	−0.711500	−0.355750	+	0.934581i	$0.615775\pi$
$542$	0.590908	0.0253817
$543$	−1.15394	−0.0495204
$544$	−5.32691	−0.228390
$545$	31.1180	1.33295
$546$	0.00765259	0.000327501 0
$547$	−19.5438	−0.835632	−0.417816	−	0.908532i	$-0.637204\pi$
$547$	−19.5438	−0.835632	−0.417816	+	0.908532i	$0.637204\pi$
$548$	−15.8933	−0.678928
$549$	2.99704	0.127910
$550$	0.704109	0.0300233
$551$	−21.4413	−0.913432
$552$	−0.0549299	−0.00233797
$553$	3.09063	0.131427
$554$	−0.485762	−0.0206380
$555$	−0.911236	−0.0386798
$556$	−35.8289	−1.51948
$557$	23.8951	1.01247	0.506234	−	0.862396i	$-0.331037\pi$
$557$	23.8951	1.01247	0.506234	+	0.862396i	$0.331037\pi$
$558$	0.261520	0.0110710
$559$	39.8504	1.68549
$560$	−4.71480	−0.199237
$561$	−0.355523	−0.0150102
$562$	−0.918085	−0.0387271
$563$	−27.2351	−1.14782	−0.573912	−	0.818917i	$-0.694575\pi$
$563$	−27.2351	−1.14782	−0.573912	+	0.818917i	$0.694575\pi$
$564$	−0.422542	−0.0177922
$565$	−42.6996	−1.79639
$566$	−1.32622	−0.0557454
$567$	2.72067	0.114257
$568$	−1.72208	−0.0722570
$569$	16.7989	0.704245	0.352123	−	0.935954i	$-0.385460\pi$
$569$	16.7989	0.704245	0.352123	+	0.935954i	$0.385460\pi$
$570$	−0.101919	−0.00426893
$571$	22.4289	0.938621	0.469310	−	0.883033i	$-0.344503\pi$
$571$	22.4289	0.938621	0.469310	+	0.883033i	$0.344503\pi$
$572$	−13.5671	−0.567267
$573$	−1.05683	−0.0441498
$574$	−0.0973040	−0.00406139
$575$	38.2452	1.59494
$576$	23.6425	0.985105
$577$	5.88874	0.245151	0.122576	−	0.992459i	$-0.460885\pi$
$577$	5.88874	0.245151	0.122576	+	0.992459i	$0.460885\pi$
$578$	1.74878	0.0727396
$579$	0.970214	0.0403207
$580$	−23.8820	−0.991647
$581$	0.605108	0.0251041
$582$	0.00384207	0.000159259 0
$583$	2.62341	0.108651
$584$	1.88751	0.0781056
$585$	79.7768	3.29836
$586$	−0.000718016 0	−2.96610e−5 0
$587$	−43.3846	−1.79067	−0.895337	−	0.445390i	$-0.853065\pi$
$587$	−43.3846	−1.79067	−0.895337	+	0.445390i	$0.853065\pi$
$588$	0.750410	0.0309464
$589$	−8.97500	−0.369808
$590$	−3.41313	−0.140517
$591$	−1.03740	−0.0426731
$592$	16.9830	0.697995
$593$	26.0295	1.06890	0.534452	−	0.845199i	$-0.320518\pi$
$593$	26.0295	1.06890	0.534452	+	0.845199i	$0.320518\pi$
$594$	−0.0222616	−0.000913405 0
$595$	7.75148	0.317780
$596$	−8.61945	−0.353067
$597$	−1.15530	−0.0472831
$598$	1.71711	0.0702178
$599$	−17.5791	−0.718264	−0.359132	−	0.933287i	$-0.616927\pi$
$599$	−17.5791	−0.718264	−0.359132	+	0.933287i	$0.616927\pi$
$600$	−0.153150	−0.00625233
$601$	24.2650	0.989792	0.494896	−	0.868952i	$-0.335206\pi$
$601$	24.2650	0.989792	0.494896	+	0.868952i	$0.335206\pi$
$602$	0.121167	0.00493841
$603$	24.7053	1.00608
$604$	25.3036	1.02959
$605$	−3.91488	−0.159162
$606$	−0.0407586	−0.00165571
$607$	−45.0861	−1.82999	−0.914995	−	0.403466i	$-0.867805\pi$
$607$	−45.0861	−1.82999	−0.914995	+	0.403466i	$0.867805\pi$
$608$	5.72070	0.232005
$609$	−0.0504637	−0.00204489
$610$	0.266941	0.0108081
$611$	26.4481	1.06998
$612$	−39.0531	−1.57863
$613$	−0.613943	−0.0247969	−0.0123985	−	0.999923i	$-0.503947\pi$
$613$	−0.613943	−0.0247969	−0.0123985	+	0.999923i	$0.503947\pi$
$614$	0.783643	0.0316252
$615$	1.00312	0.0404496
$616$	−0.0825990	−0.00332801
$617$	−43.8722	−1.76623	−0.883113	−	0.469160i	$-0.844557\pi$
$617$	−43.8722	−1.76623	−0.883113	+	0.469160i	$0.844557\pi$
$618$	0.0571957	0.00230075
$619$	−35.6911	−1.43455	−0.717274	−	0.696792i	$-0.754610\pi$
$619$	−35.6911	−1.43455	−0.717274	+	0.696792i	$0.754610\pi$
$620$	−9.99663	−0.401474
$621$	−1.20919	−0.0485230
$622$	0.688929	0.0276235
$623$	1.00929	0.0404362
$624$	1.47032	0.0588599
$625$	30.0002	1.20001
$626$	−0.531469	−0.0212418
$627$	0.381804	0.0152478
$628$	−31.0805	−1.24025
$629$	−27.9213	−1.11329
$630$	0.242566	0.00966406
$631$	38.3278	1.52581	0.762904	−	0.646512i	$-0.223773\pi$
$631$	38.3278	1.52581	0.762904	+	0.646512i	$0.223773\pi$
$632$	−2.77701	−0.110463
$633$	0.291594	0.0115898
$634$	0.264058	0.0104871
$635$	−12.1454	−0.481976
$636$	−0.284976	−0.0113000
$637$	−46.9703	−1.86103
$638$	−0.208464	−0.00825317
$639$	−18.9450	−0.749451
$640$	8.49254	0.335697
$641$	3.98918	0.157563	0.0787816	−	0.996892i	$-0.474897\pi$
$641$	3.98918	0.157563	0.0787816	+	0.996892i	$0.474897\pi$
$642$	0.0444856	0.00175571
$643$	17.4155	0.686800	0.343400	−	0.939189i	$-0.388421\pi$
$643$	17.4155	0.686800	0.343400	+	0.939189i	$0.388421\pi$
$644$	−2.24066	−0.0882944
$645$	−1.24913	−0.0491843
$646$	−3.12291	−0.122869
$647$	0.461061	0.0181262	0.00906309	−	0.999959i	$-0.497115\pi$
$647$	0.461061	0.0181262	0.00906309	+	0.999959i	$0.497115\pi$
$648$	−2.44459	−0.0960326
$649$	12.7861	0.501898
$650$	4.78748	0.187780
$651$	−0.0211233	−0.000827886 0
$652$	41.1207	1.61041
$653$	−14.7783	−0.578320	−0.289160	−	0.957281i	$-0.593376\pi$
$653$	−14.7783	−0.578320	−0.289160	+	0.957281i	$0.593376\pi$
$654$	−0.0295062	−0.00115378
$655$	−52.7868	−2.06255
$656$	−18.6954	−0.729931
$657$	20.7648	0.810113
$658$	0.0804170	0.00313498
$659$	10.4530	0.407192	0.203596	−	0.979055i	$-0.434737\pi$
$659$	10.4530	0.407192	0.203596	+	0.979055i	$0.434737\pi$
$660$	0.425265	0.0165534
$661$	19.8241	0.771069	0.385535	−	0.922693i	$-0.374017\pi$
$661$	19.8241	0.771069	0.385535	+	0.922693i	$0.374017\pi$
$662$	1.73537	0.0674469
$663$	−2.41732	−0.0938808
$664$	−0.543705	−0.0210998
$665$	−8.32451	−0.322810
$666$	−0.873735	−0.0338565
$667$	−11.3232	−0.438435
$668$	−17.8642	−0.691188
$669$	0.125645	0.00485771
$670$	2.20046	0.0850112
$671$	−1.00000	−0.0386046
$672$	0.0134641	0.000519388 0
$673$	25.9931	1.00196	0.500981	−	0.865458i	$-0.332973\pi$
$673$	25.9931	1.00196	0.500981	+	0.865458i	$0.332973\pi$
$674$	1.80851	0.0696611
$675$	−3.37134	−0.129763
$676$	−66.3074	−2.55028
$677$	−41.5759	−1.59789	−0.798946	−	0.601403i	$-0.794609\pi$
$677$	−41.5759	−1.59789	−0.798946	+	0.601403i	$0.794609\pi$
$678$	0.0404880	0.00155493
$679$	0.313810	0.0120429
$680$	−6.96490	−0.267092
$681$	−0.142605	−0.00546465
$682$	−0.0872597	−0.00334135
$683$	10.7333	0.410697	0.205348	−	0.978689i	$-0.434167\pi$
$683$	10.7333	0.410697	0.205348	+	0.978689i	$0.434167\pi$
$684$	41.9401	1.60362
$685$	−31.1827	−1.19143
$686$	−0.287532	−0.0109780
$687$	−0.220400	−0.00840877
$688$	23.2803	0.887554
$689$	17.8375	0.679553
$690$	−0.0538235	−0.00204903
$691$	−6.52559	−0.248245	−0.124123	−	0.992267i	$-0.539612\pi$
$691$	−6.52559	−0.248245	−0.124123	+	0.992267i	$0.539612\pi$
$692$	−13.0717	−0.496910
$693$	−0.908687	−0.0345182
$694$	−0.773555	−0.0293637
$695$	−70.2962	−2.66649
$696$	0.0453428	0.00171872
$697$	30.7366	1.16423
$698$	0.278955	0.0105586
$699$	0.217319	0.00821975
$700$	−6.24718	−0.236121
$701$	−24.5074	−0.925630	−0.462815	−	0.886455i	$-0.653161\pi$
$701$	−24.5074	−0.925630	−0.462815	+	0.886455i	$0.653161\pi$
$702$	−0.151364	−0.00571287
$703$	29.9853	1.13092
$704$	−7.88863	−0.297314
$705$	−0.829027	−0.0312230
$706$	1.54212	0.0580385
$707$	−3.32906	−0.125202
$708$	−1.38893	−0.0521991
$709$	−18.7316	−0.703481	−0.351741	−	0.936098i	$-0.614410\pi$
$709$	−18.7316	−0.703481	−0.351741	+	0.936098i	$0.614410\pi$
$710$	−1.68740	−0.0633269
$711$	−30.5504	−1.14573
$712$	−0.906868	−0.0339863
$713$	−4.73970	−0.177503
$714$	−0.00734999	−0.000275067 0
$715$	−26.6185	−0.995477
$716$	15.6839	0.586137
$717$	0.324270	0.0121101
$718$	1.31772	0.0491769
$719$	45.0553	1.68028	0.840140	−	0.542370i	$-0.182473\pi$
$719$	45.0553	1.68028	0.840140	+	0.542370i	$0.182473\pi$
$720$	46.6050	1.73687
$721$	4.67160	0.173980
$722$	2.05823	0.0765995
$723$	−1.39845	−0.0520088
$724$	42.2942	1.57185
$725$	−31.5702	−1.17249
$726$	0.00371210	0.000137769 0
$727$	8.92480	0.331002	0.165501	−	0.986210i	$-0.447076\pi$
$727$	8.92480	0.331002	0.165501	+	0.986210i	$0.447076\pi$
$728$	−0.561618	−0.0208149
$729$	−26.8401	−0.994077
$730$	1.84949	0.0684526
$731$	−38.2746	−1.41564
$732$	0.108628	0.00401501
$733$	1.03943	0.0383922	0.0191961	−	0.999816i	$-0.493889\pi$
$733$	1.03943	0.0383922	0.0191961	+	0.999816i	$0.493889\pi$
$734$	−0.0462220	−0.00170608
$735$	1.47230	0.0543068
$736$	3.02110	0.111359
$737$	−8.24324	−0.303644
$738$	0.961834	0.0354056
$739$	31.1002	1.14404	0.572020	−	0.820240i	$-0.306160\pi$
$739$	31.1002	1.14404	0.572020	+	0.820240i	$0.306160\pi$
$740$	33.3985	1.22776
$741$	2.59601	0.0953670
$742$	0.0542358	0.00199106
$743$	−9.81050	−0.359912	−0.179956	−	0.983675i	$-0.557596\pi$
$743$	−9.81050	−0.359912	−0.179956	+	0.983675i	$0.557596\pi$
$744$	0.0189798	0.000695832 0
$745$	−16.9114	−0.619584
$746$	1.91987	0.0702913
$747$	−5.98140	−0.218848
$748$	13.0306	0.476445
$749$	3.63347	0.132764
$750$	−0.0774033	−0.00282637
$751$	24.2550	0.885077	0.442539	−	0.896749i	$-0.354078\pi$
$751$	24.2550	0.885077	0.442539	+	0.896749i	$0.354078\pi$
$752$	15.4508	0.563433
$753$	1.46407	0.0533536
$754$	−1.41742	−0.0516193
$755$	49.6456	1.80679
$756$	0.197515	0.00718356
$757$	15.2208	0.553210	0.276605	−	0.960984i	$-0.410791\pi$
$757$	15.2208	0.553210	0.276605	+	0.960984i	$0.410791\pi$
$758$	0.421635	0.0153145
$759$	0.201631	0.00731873
$760$	7.47977	0.271320
$761$	33.5732	1.21703	0.608513	−	0.793544i	$-0.291766\pi$
$761$	33.5732	1.21703	0.608513	+	0.793544i	$0.291766\pi$
$762$	0.0115163	0.000417193 0
$763$	−2.40999	−0.0872476
$764$	38.7349	1.40138
$765$	−76.6222	−2.77028
$766$	−1.86246	−0.0672935
$767$	86.9370	3.13911
$768$	0.850870	0.0307031
$769$	−41.5447	−1.49814	−0.749069	−	0.662492i	$-0.769499\pi$
$769$	−41.5447	−1.49814	−0.749069	+	0.662492i	$0.769499\pi$
$770$	−0.0809352	−0.00291670
$771$	0.159492	0.00574395
$772$	−35.5602	−1.27984
$773$	−14.4356	−0.519214	−0.259607	−	0.965714i	$-0.583593\pi$
$773$	−14.4356	−0.519214	−0.259607	+	0.965714i	$0.583593\pi$
$774$	−1.19772	−0.0430512
$775$	−13.2148	−0.474688
$776$	−0.281966	−0.0101220
$777$	0.0705725	0.00253177
$778$	−1.39549	−0.0500306
$779$	−33.0087	−1.18266
$780$	2.89152	0.103533
$781$	6.32123	0.226191
$782$	−1.64921	−0.0589757
$783$	0.998144	0.0356708
$784$	−27.4397	−0.979990
$785$	−60.9800	−2.17647
$786$	0.0500527	0.00178532
$787$	3.08181	0.109855	0.0549273	−	0.998490i	$-0.482507\pi$
$787$	3.08181	0.109855	0.0549273	+	0.998490i	$0.482507\pi$
$788$	38.0229	1.35451
$789$	0.0602121	0.00214361
$790$	−2.72107	−0.0968114
$791$	3.30696	0.117582
$792$	0.816478	0.0290123
$793$	−6.79933	−0.241451
$794$	−2.61385	−0.0927621
$795$	−0.559123	−0.0198300
$796$	42.3438	1.50084
$797$	−14.1563	−0.501443	−0.250721	−	0.968059i	$-0.580668\pi$
$797$	−14.1563	−0.501443	−0.250721	+	0.968059i	$0.580668\pi$
$798$	0.00789333	0.000279421 0
$799$	−25.4023	−0.898668
$800$	8.42314	0.297803
$801$	−9.97662	−0.352507
$802$	2.13684	0.0754544
$803$	−6.92845	−0.244500
$804$	0.895447	0.0315800
$805$	−4.39617	−0.154945
$806$	−0.593308	−0.0208984
$807$	1.35203	0.0475938
$808$	2.99125	0.105232
$809$	16.0096	0.562868	0.281434	−	0.959581i	$-0.409190\pi$
$809$	16.0096	0.562868	0.281434	+	0.959581i	$0.409190\pi$
$810$	−2.39535	−0.0841641
$811$	−28.5859	−1.00379	−0.501894	−	0.864929i	$-0.667363\pi$
$811$	−28.5859	−1.00379	−0.501894	+	0.864929i	$0.667363\pi$
$812$	1.84959	0.0649079
$813$	0.471786	0.0165463
$814$	0.291533	0.0102182
$815$	80.6787	2.82605
$816$	−1.41218	−0.0494362
$817$	41.1040	1.43805
$818$	0.120526	0.00421411
$819$	−6.17847	−0.215893
$820$	−36.7661	−1.28393
$821$	16.2518	0.567192	0.283596	−	0.958944i	$-0.408472\pi$
$821$	16.2518	0.567192	0.283596	+	0.958944i	$0.408472\pi$
$822$	0.0295675	0.00103129
$823$	8.26290	0.288027	0.144013	−	0.989576i	$-0.453999\pi$
$823$	8.26290	0.288027	0.144013	+	0.989576i	$0.453999\pi$
$824$	−4.19755	−0.146229
$825$	0.562167	0.0195721
$826$	0.264337	0.00919746
$827$	25.5526	0.888550	0.444275	−	0.895891i	$-0.353461\pi$
$827$	25.5526	0.888550	0.444275	+	0.895891i	$0.353461\pi$
$828$	22.1486	0.769716
$829$	−31.4801	−1.09335	−0.546675	−	0.837345i	$-0.684107\pi$
$829$	−31.4801	−1.09335	−0.546675	+	0.837345i	$0.684107\pi$
$830$	−0.532753	−0.0184921
$831$	−0.387837	−0.0134539
$832$	−53.6374	−1.85954
$833$	45.1130	1.56307
$834$	0.0666552	0.00230808
$835$	−35.0496	−1.21294
$836$	−13.9939	−0.483988
$837$	0.417807	0.0144415
$838$	−1.11676	−0.0385778
$839$	24.9428	0.861122	0.430561	−	0.902562i	$-0.358316\pi$
$839$	24.9428	0.861122	0.430561	+	0.902562i	$0.358316\pi$
$840$	0.0176042	0.000607401 0
$841$	−19.6531	−0.677693
$842$	2.37122	0.0817177
$843$	−0.733007	−0.0252461
$844$	−10.6875	−0.367878
$845$	−130.095	−4.47541
$846$	−0.794909	−0.0273295
$847$	0.303195	0.0104179
$848$	10.4205	0.357842
$849$	−1.05887	−0.0363403
$850$	−4.59817	−0.157716
$851$	15.8352	0.542825
$852$	−0.686663	−0.0235247
$853$	16.4256	0.562400	0.281200	−	0.959649i	$-0.409268\pi$
$853$	16.4256	0.562400	0.281200	+	0.959649i	$0.409268\pi$
$854$	−0.0206738	−0.000707442 0
$855$	82.2864	2.81414
$856$	−3.26476	−0.111587
$857$	−34.3235	−1.17247	−0.586234	−	0.810142i	$-0.699390\pi$
$857$	−34.3235	−1.17247	−0.586234	+	0.810142i	$0.699390\pi$
$858$	0.0252398	0.000861674 0
$859$	51.4625	1.75588	0.877938	−	0.478774i	$-0.158919\pi$
$859$	51.4625	1.75588	0.877938	+	0.478774i	$0.158919\pi$
$860$	45.7829	1.56118
$861$	−0.0776883	−0.00264761
$862$	1.92701	0.0656343
$863$	4.40577	0.149974	0.0749870	−	0.997185i	$-0.476108\pi$
$863$	4.40577	0.149974	0.0749870	+	0.997185i	$0.476108\pi$
$864$	−0.266312	−0.00906011
$865$	−25.6466	−0.872010
$866$	−0.346159	−0.0117630
$867$	1.39624	0.0474188
$868$	0.774208	0.0262783
$869$	10.1935	0.345792
$870$	0.0444295	0.00150630
$871$	−56.0486	−1.89913
$872$	2.16544	0.0733310
$873$	−3.10197	−0.104986
$874$	1.77113	0.0599093
$875$	−6.32211	−0.213726
$876$	0.752624	0.0254288
$877$	−38.6518	−1.30518	−0.652589	−	0.757712i	$-0.726317\pi$
$877$	−38.6518	−1.30518	−0.652589	+	0.757712i	$0.726317\pi$
$878$	−0.915740	−0.0309047
$879$	−0.000573270 0	−1.93359e−5 0
$880$	−15.5504	−0.524203
$881$	10.9617	0.369309	0.184654	−	0.982804i	$-0.440883\pi$
$881$	10.9617	0.369309	0.184654	+	0.982804i	$0.440883\pi$
$882$	1.41171	0.0475348
$883$	−41.7435	−1.40478	−0.702391	−	0.711791i	$-0.747884\pi$
$883$	−41.7435	−1.40478	−0.702391	+	0.711791i	$0.747884\pi$
$884$	88.5993	2.97992
$885$	−2.72508	−0.0916024
$886$	1.52697	0.0512996
$887$	−58.1584	−1.95277	−0.976384	−	0.216043i	$-0.930685\pi$
$887$	−58.1584	−1.95277	−0.976384	+	0.216043i	$0.930685\pi$
$888$	−0.0634111	−0.00212794
$889$	0.940626	0.0315476
$890$	−0.888601	−0.0297860
$891$	8.97333	0.300618
$892$	−4.60512	−0.154191
$893$	27.2801	0.912894
$894$	0.0160354	0.000536305 0
$895$	30.7719	1.02859
$896$	−0.657721	−0.0219729
$897$	1.37096	0.0457749
$898$	0.138498	0.00462175
$899$	3.91246	0.130488
$900$	61.7524	2.05841
$901$	−17.1321	−0.570754
$902$	−0.320928	−0.0106857
$903$	0.0967411	0.00321934
$904$	−2.97138	−0.0988266
$905$	82.9811	2.75838
$906$	−0.0470742	−0.00156394
$907$	−5.54303	−0.184053	−0.0920267	−	0.995757i	$-0.529335\pi$
$907$	−5.54303	−0.184053	−0.0920267	+	0.995757i	$0.529335\pi$
$908$	5.22676	0.173456
$909$	32.9073	1.09147
$910$	−0.550306	−0.0182425
$911$	31.7084	1.05055	0.525274	−	0.850933i	$-0.323963\pi$
$911$	31.7084	1.05055	0.525274	+	0.850933i	$0.323963\pi$
$912$	1.51657	0.0502188
$913$	1.99577	0.0660504
$914$	0.444308	0.0146964
$915$	0.213128	0.00704580
$916$	8.07807	0.266907
$917$	4.08818	0.135003
$918$	0.145379	0.00479822
$919$	−48.8169	−1.61032	−0.805160	−	0.593058i	$-0.797920\pi$
$919$	−48.8169	−1.61032	−0.805160	+	0.593058i	$0.797920\pi$
$920$	3.95007	0.130230
$921$	0.625667	0.0206164
$922$	−1.28512	−0.0423231
$923$	42.9802	1.41471
$924$	−0.0329355	−0.00108350
$925$	44.1502	1.45165
$926$	−1.31651	−0.0432633
$927$	−46.1780	−1.51669
$928$	−2.49382	−0.0818636
$929$	−22.6953	−0.744607	−0.372304	−	0.928111i	$-0.621432\pi$
$929$	−22.6953	−0.744607	−0.372304	+	0.928111i	$0.621432\pi$
$930$	0.0185975	0.000609836 0
$931$	−48.4479	−1.58782
$932$	−7.96515	−0.260907
$933$	0.550047	0.0180077
$934$	−2.22586	−0.0728323
$935$	25.5660	0.836097
$936$	5.55150	0.181457
$937$	38.7282	1.26520	0.632598	−	0.774480i	$-0.281989\pi$
$937$	38.7282	1.26520	0.632598	+	0.774480i	$0.281989\pi$
$938$	−0.170419	−0.00556438
$939$	−0.424329	−0.0138475
$940$	30.3854	0.991063
$941$	37.9671	1.23769	0.618846	−	0.785513i	$-0.287601\pi$
$941$	37.9671	1.23769	0.618846	+	0.785513i	$0.287601\pi$
$942$	0.0578215	0.00188393
$943$	−17.4319	−0.567661
$944$	50.7880	1.65301
$945$	0.387525	0.0126062
$946$	0.399635	0.0129932
$947$	27.6736	0.899271	0.449635	−	0.893212i	$-0.351554\pi$
$947$	27.6736	0.899271	0.449635	+	0.893212i	$0.351554\pi$
$948$	−1.10730	−0.0359635
$949$	−47.1088	−1.52922
$950$	4.93808	0.160213
$951$	0.210826	0.00683651
$952$	0.539410	0.0174824
$953$	34.7510	1.12569	0.562847	−	0.826561i	$-0.309706\pi$
$953$	34.7510	1.12569	0.562847	+	0.826561i	$0.309706\pi$
$954$	−0.536112	−0.0173573
$955$	75.9978	2.45923
$956$	−11.8851	−0.384392
$957$	−0.166440	−0.00538023
$958$	−0.307319	−0.00992901
$959$	2.41500	0.0779845
$960$	1.68129	0.0542634
$961$	−29.3623	−0.947171
$962$	1.98223	0.0639097
$963$	−35.9163	−1.15739
$964$	51.2558	1.65084
$965$	−69.7691	−2.24595
$966$	0.00416847	0.000134118 0
$967$	51.1014	1.64331	0.821654	−	0.569986i	$-0.193051\pi$
$967$	51.1014	1.64331	0.821654	+	0.569986i	$0.193051\pi$
$968$	−0.272428	−0.00875618
$969$	−2.49336	−0.0800983
$970$	−0.276287	−0.00887104
$971$	−13.5996	−0.436432	−0.218216	−	0.975900i	$-0.570024\pi$
$971$	−13.5996	−0.436432	−0.218216	+	0.975900i	$0.570024\pi$
$972$	−2.92909	−0.0939507
$973$	5.44423	0.174534
$974$	−0.854813	−0.0273900
$975$	3.82236	0.122414
$976$	−3.97213	−0.127145
$977$	−2.51589	−0.0804906	−0.0402453	−	0.999190i	$-0.512814\pi$
$977$	−2.51589	−0.0804906	−0.0402453	+	0.999190i	$0.512814\pi$
$978$	−0.0764999	−0.00244620
$979$	3.32883	0.106390
$980$	−53.9628	−1.72378
$981$	23.8224	0.760591
$982$	0.257668	0.00822250
$983$	−25.4275	−0.811011	−0.405506	−	0.914093i	$-0.632905\pi$
$983$	−25.4275	−0.811011	−0.405506	+	0.914093i	$0.632905\pi$
$984$	0.0698049	0.00222530
$985$	74.6008	2.37698
$986$	1.36137	0.0433548
$987$	0.0642056	0.00204369
$988$	−95.1489	−3.02709
$989$	21.7070	0.690243
$990$	0.800032	0.0254267
$991$	−23.1853	−0.736506	−0.368253	−	0.929726i	$-0.620044\pi$
$991$	−23.1853	−0.736506	−0.368253	+	0.929726i	$0.620044\pi$
$992$	−1.04387	−0.0331430
$993$	1.38553	0.0439685
$994$	0.130684	0.00414504
$995$	83.0785	2.63377
$996$	−0.216797	−0.00686947
$997$	−29.2808	−0.927334	−0.463667	−	0.886010i	$-0.653467\pi$
$997$	−29.2808	−0.927334	−0.463667	+	0.886010i	$0.653467\pi$
$998$	0.898691	0.0284476
$999$	−1.39589	−0.0441638

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.c.1.9	✓	19
3.2	odd	2		6039.2.a.k.1.11		19
11.10	odd	2		7381.2.a.i.1.11		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.c.1.9	✓	19	1.1	even	1	trivial
6039.2.a.k.1.11		19	3.2	odd	2
7381.2.a.i.1.11		19	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0681863 q^{2} +0.0544406 q^{3} -1.99535 q^{4} -3.91488 q^{5} +0.00371210 q^{6} +0.303195 q^{7} -0.272428 q^{8} -2.99704 q^{9} +O(q^{10})\)	\(q+0.0681863 q^{2} +0.0544406 q^{3} -1.99535 q^{4} -3.91488 q^{5} +0.00371210 q^{6} +0.303195 q^{7} -0.272428 q^{8} -2.99704 q^{9} -0.266941 q^{10} +1.00000 q^{11} -0.108628 q^{12} +6.79933 q^{13} +0.0206738 q^{14} -0.213128 q^{15} +3.97213 q^{16} -6.53047 q^{17} -0.204357 q^{18} +7.01323 q^{19} +7.81155 q^{20} +0.0165061 q^{21} +0.0681863 q^{22} +3.70369 q^{23} -0.0148312 q^{24} +10.3263 q^{25} +0.463622 q^{26} -0.326482 q^{27} -0.604981 q^{28} -3.05727 q^{29} -0.0145324 q^{30} -1.27972 q^{31} +0.815701 q^{32} +0.0544406 q^{33} -0.445289 q^{34} -1.18697 q^{35} +5.98014 q^{36} +4.27553 q^{37} +0.478207 q^{38} +0.370160 q^{39} +1.06652 q^{40} -4.70664 q^{41} +0.00112549 q^{42} +5.86092 q^{43} -1.99535 q^{44} +11.7330 q^{45} +0.252541 q^{46} +3.88981 q^{47} +0.216245 q^{48} -6.90807 q^{49} +0.704109 q^{50} -0.355523 q^{51} -13.5671 q^{52} +2.62341 q^{53} -0.0222616 q^{54} -3.91488 q^{55} -0.0825990 q^{56} +0.381804 q^{57} -0.208464 q^{58} +12.7861 q^{59} +0.425265 q^{60} -1.00000 q^{61} -0.0872597 q^{62} -0.908687 q^{63} -7.88863 q^{64} -26.6185 q^{65} +0.00371210 q^{66} -8.24324 q^{67} +13.0306 q^{68} +0.201631 q^{69} -0.0809352 q^{70} +6.32123 q^{71} +0.816478 q^{72} -6.92845 q^{73} +0.291533 q^{74} +0.562167 q^{75} -13.9939 q^{76} +0.303195 q^{77} +0.0252398 q^{78} +10.1935 q^{79} -15.5504 q^{80} +8.97333 q^{81} -0.320928 q^{82} +1.99577 q^{83} -0.0329355 q^{84} +25.5660 q^{85} +0.399635 q^{86} -0.166440 q^{87} -0.272428 q^{88} +3.32883 q^{89} +0.800032 q^{90} +2.06153 q^{91} -7.39015 q^{92} -0.0696689 q^{93} +0.265232 q^{94} -27.4559 q^{95} +0.0444072 q^{96} +1.03501 q^{97} -0.471036 q^{98} -2.99704 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9} + 7 q^{10} + 19 q^{11} - 4 q^{12} + 8 q^{13} - 11 q^{14} - 5 q^{15} + 31 q^{16} + 9 q^{17} + 10 q^{18} + 17 q^{19} - 6 q^{20} + 18 q^{21} + 5 q^{22} - 10 q^{23} + 26 q^{24} + 45 q^{25} + 5 q^{26} - 33 q^{27} + 36 q^{28} + 27 q^{29} - 30 q^{30} + 7 q^{31} + 8 q^{32} - 5 q^{34} + 17 q^{35} + 38 q^{36} + 20 q^{37} - 37 q^{38} + 24 q^{39} + 10 q^{40} + 19 q^{41} + 21 q^{42} + 20 q^{43} + 23 q^{44} - 32 q^{45} + 41 q^{46} - 19 q^{47} + 5 q^{48} + 42 q^{49} + 36 q^{50} + 47 q^{51} - 28 q^{52} + 3 q^{53} - 33 q^{54} - 44 q^{56} + 11 q^{57} + 23 q^{58} - 28 q^{59} - 96 q^{60} - 19 q^{61} - 11 q^{62} - 32 q^{63} + 47 q^{64} + 25 q^{65} + q^{66} + 3 q^{67} + 38 q^{68} + 3 q^{70} - 19 q^{71} + 34 q^{72} + 20 q^{73} - 22 q^{74} - 50 q^{75} - 25 q^{76} + 9 q^{77} - 94 q^{78} + 69 q^{79} - 36 q^{80} + 47 q^{81} - 61 q^{82} + q^{83} - 28 q^{84} + 24 q^{85} - 27 q^{86} - 58 q^{87} + 9 q^{88} + 36 q^{90} + 24 q^{91} - 67 q^{92} - 14 q^{93} + 64 q^{94} - 3 q^{95} - 26 q^{96} + 21 q^{97} - 87 q^{98} + 29 q^{99}+O(q^{100}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9 + 7 * q^10 + 19 * q^11 - 4 * q^12 + 8 * q^13 - 11 * q^14 - 5 * q^15 + 31 * q^16 + 9 * q^17 + 10 * q^18 + 17 * q^19 - 6 * q^20 + 18 * q^21 + 5 * q^22 - 10 * q^23 + 26 * q^24 + 45 * q^25 + 5 * q^26 - 33 * q^27 + 36 * q^28 + 27 * q^29 - 30 * q^30 + 7 * q^31 + 8 * q^32 - 5 * q^34 + 17 * q^35 + 38 * q^36 + 20 * q^37 - 37 * q^38 + 24 * q^39 + 10 * q^40 + 19 * q^41 + 21 * q^42 + 20 * q^43 + 23 * q^44 - 32 * q^45 + 41 * q^46 - 19 * q^47 + 5 * q^48 + 42 * q^49 + 36 * q^50 + 47 * q^51 - 28 * q^52 + 3 * q^53 - 33 * q^54 - 44 * q^56 + 11 * q^57 + 23 * q^58 - 28 * q^59 - 96 * q^60 - 19 * q^61 - 11 * q^62 - 32 * q^63 + 47 * q^64 + 25 * q^65 + q^66 + 3 * q^67 + 38 * q^68 + 3 * q^70 - 19 * q^71 + 34 * q^72 + 20 * q^73 - 22 * q^74 - 50 * q^75 - 25 * q^76 + 9 * q^77 - 94 * q^78 + 69 * q^79 - 36 * q^80 + 47 * q^81 - 61 * q^82 + q^83 - 28 * q^84 + 24 * q^85 - 27 * q^86 - 58 * q^87 + 9 * q^88 + 36 * q^90 + 24 * q^91 - 67 * q^92 - 14 * q^93 + 64 * q^94 - 3 * q^95 - 26 * q^96 + 21 * q^97 - 87 * q^98 + 29 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more