LMFDB - Embedded newform 8045.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8045,2,Mod(1,8045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8045, 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("8045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8045 = 5 \cdot 1609 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8045.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2396484261$
Analytic rank:	$1$
Dimension:	$127$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31881 q^{2} +0.00298266 q^{3} +3.37687 q^{4} +1.00000 q^{5} -0.00691620 q^{6} -0.956165 q^{7} -3.19269 q^{8} -2.99999 q^{9} +O(q^{10})$	\(q-2.31881 q^{2} +0.00298266 q^{3} +3.37687 q^{4} +1.00000 q^{5} -0.00691620 q^{6} -0.956165 q^{7} -3.19269 q^{8} -2.99999 q^{9} -2.31881 q^{10} +6.46086 q^{11} +0.0100720 q^{12} +3.33118 q^{13} +2.21716 q^{14} +0.00298266 q^{15} +0.649491 q^{16} +0.886427 q^{17} +6.95640 q^{18} +1.00573 q^{19} +3.37687 q^{20} -0.00285191 q^{21} -14.9815 q^{22} -2.24170 q^{23} -0.00952268 q^{24} +1.00000 q^{25} -7.72437 q^{26} -0.0178959 q^{27} -3.22884 q^{28} +1.41130 q^{29} -0.00691620 q^{30} +0.580960 q^{31} +4.87933 q^{32} +0.0192705 q^{33} -2.05545 q^{34} -0.956165 q^{35} -10.1306 q^{36} -1.44012 q^{37} -2.33208 q^{38} +0.00993577 q^{39} -3.19269 q^{40} -7.18477 q^{41} +0.00661303 q^{42} +4.27179 q^{43} +21.8175 q^{44} -2.99999 q^{45} +5.19808 q^{46} -9.01713 q^{47} +0.00193721 q^{48} -6.08575 q^{49} -2.31881 q^{50} +0.00264391 q^{51} +11.2490 q^{52} -13.2596 q^{53} +0.0414972 q^{54} +6.46086 q^{55} +3.05273 q^{56} +0.00299973 q^{57} -3.27253 q^{58} +5.17631 q^{59} +0.0100720 q^{60} -12.5050 q^{61} -1.34713 q^{62} +2.86849 q^{63} -12.6132 q^{64} +3.33118 q^{65} -0.0446846 q^{66} -13.3266 q^{67} +2.99334 q^{68} -0.00668623 q^{69} +2.21716 q^{70} -10.1984 q^{71} +9.57803 q^{72} +3.52767 q^{73} +3.33935 q^{74} +0.00298266 q^{75} +3.39620 q^{76} -6.17765 q^{77} -0.0230391 q^{78} +8.85913 q^{79} +0.649491 q^{80} +8.99992 q^{81} +16.6601 q^{82} -2.26555 q^{83} -0.00963052 q^{84} +0.886427 q^{85} -9.90545 q^{86} +0.00420942 q^{87} -20.6275 q^{88} +12.1786 q^{89} +6.95640 q^{90} -3.18516 q^{91} -7.56993 q^{92} +0.00173280 q^{93} +20.9090 q^{94} +1.00573 q^{95} +0.0145534 q^{96} +2.53413 q^{97} +14.1117 q^{98} -19.3825 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 127 q - 20 q^{2} - 31 q^{3} + 116 q^{4} + 127 q^{5} - 17 q^{6} - 63 q^{7} - 57 q^{8} + 122 q^{9}+O(q^{10}) $ 127 * q - 20 * q^2 - 31 * q^3 + 116 * q^4 + 127 * q^5 - 17 * q^6 - 63 * q^7 - 57 * q^8 + 122 * q^9	\( 127 q - 20 q^{2} - 31 q^{3} + 116 q^{4} + 127 q^{5} - 17 q^{6} - 63 q^{7} - 57 q^{8} + 122 q^{9} - 20 q^{10} - 32 q^{11} - 65 q^{12} - 49 q^{13} - 4 q^{14} - 31 q^{15} + 98 q^{16} - 53 q^{17} - 60 q^{18} - 126 q^{19} + 116 q^{20} - 24 q^{21} - 46 q^{22} - 121 q^{23} - 51 q^{24} + 127 q^{25} - 9 q^{26} - 112 q^{27} - 123 q^{28} - 6 q^{29} - 17 q^{30} - 54 q^{31} - 119 q^{32} - 57 q^{33} - 53 q^{34} - 63 q^{35} + 133 q^{36} - 61 q^{37} - 27 q^{38} - 33 q^{39} - 57 q^{40} - 8 q^{41} - 46 q^{42} - 208 q^{43} - 54 q^{44} + 122 q^{45} - 34 q^{46} - 116 q^{47} - 106 q^{48} + 110 q^{49} - 20 q^{50} - 54 q^{51} - 142 q^{52} - 60 q^{53} - 62 q^{54} - 32 q^{55} + 33 q^{56} - 56 q^{57} - 87 q^{58} - 53 q^{59} - 65 q^{60} - 76 q^{61} - 84 q^{62} - 215 q^{63} + 67 q^{64} - 49 q^{65} + 9 q^{66} - 145 q^{67} - 133 q^{68} + q^{69} - 4 q^{70} - 4 q^{71} - 167 q^{72} - 155 q^{73} - 14 q^{74} - 31 q^{75} - 199 q^{76} - 97 q^{77} - 24 q^{78} - 73 q^{79} + 98 q^{80} + 127 q^{81} - 69 q^{82} - 225 q^{83} - 59 q^{84} - 53 q^{85} + 30 q^{86} - 179 q^{87} - 119 q^{88} - 25 q^{89} - 60 q^{90} - 160 q^{91} - 188 q^{92} - 44 q^{93} - 32 q^{94} - 126 q^{95} - 43 q^{96} - 72 q^{97} - 111 q^{98} - 141 q^{99}+O(q^{100}) \) 127 * q - 20 * q^2 - 31 * q^3 + 116 * q^4 + 127 * q^5 - 17 * q^6 - 63 * q^7 - 57 * q^8 + 122 * q^9 - 20 * q^10 - 32 * q^11 - 65 * q^12 - 49 * q^13 - 4 * q^14 - 31 * q^15 + 98 * q^16 - 53 * q^17 - 60 * q^18 - 126 * q^19 + 116 * q^20 - 24 * q^21 - 46 * q^22 - 121 * q^23 - 51 * q^24 + 127 * q^25 - 9 * q^26 - 112 * q^27 - 123 * q^28 - 6 * q^29 - 17 * q^30 - 54 * q^31 - 119 * q^32 - 57 * q^33 - 53 * q^34 - 63 * q^35 + 133 * q^36 - 61 * q^37 - 27 * q^38 - 33 * q^39 - 57 * q^40 - 8 * q^41 - 46 * q^42 - 208 * q^43 - 54 * q^44 + 122 * q^45 - 34 * q^46 - 116 * q^47 - 106 * q^48 + 110 * q^49 - 20 * q^50 - 54 * q^51 - 142 * q^52 - 60 * q^53 - 62 * q^54 - 32 * q^55 + 33 * q^56 - 56 * q^57 - 87 * q^58 - 53 * q^59 - 65 * q^60 - 76 * q^61 - 84 * q^62 - 215 * q^63 + 67 * q^64 - 49 * q^65 + 9 * q^66 - 145 * q^67 - 133 * q^68 + q^69 - 4 * q^70 - 4 * q^71 - 167 * q^72 - 155 * q^73 - 14 * q^74 - 31 * q^75 - 199 * q^76 - 97 * q^77 - 24 * q^78 - 73 * q^79 + 98 * q^80 + 127 * q^81 - 69 * q^82 - 225 * q^83 - 59 * q^84 - 53 * q^85 + 30 * q^86 - 179 * q^87 - 119 * q^88 - 25 * q^89 - 60 * q^90 - 160 * q^91 - 188 * q^92 - 44 * q^93 - 32 * q^94 - 126 * q^95 - 43 * q^96 - 72 * q^97 - 111 * q^98 - 141 * 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 $

$2$	−2.31881	−1.63964	−0.819822	−	0.572618i	$-0.805928\pi$
$2$	−2.31881	−1.63964	−0.819822	+	0.572618i	$0.805928\pi$
$3$	0.00298266	0.00172204	0.000861019	−	1.00000i	$-0.499726\pi$
$3$	0.00298266	0.00172204	0.000861019		1.00000i	$0.499726\pi$
$4$	3.37687	1.68843
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.00691620	−0.00282353
$7$	−0.956165	−0.361396	−0.180698	−	0.983539i	$-0.557836\pi$
$7$	−0.956165	−0.361396	−0.180698	+	0.983539i	$0.557836\pi$
$8$	−3.19269	−1.12878
$9$	−2.99999	−0.999997
$10$	−2.31881	−0.733271
$11$	6.46086	1.94802	0.974012	−	0.226497i	$-0.0727273\pi$
$11$	6.46086	1.94802	0.974012	+	0.226497i	$0.0727273\pi$
$12$	0.0100720	0.00290754
$13$	3.33118	0.923904	0.461952	−	0.886905i	$-0.347149\pi$
$13$	3.33118	0.923904	0.461952	+	0.886905i	$0.347149\pi$
$14$	2.21716	0.592562
$15$	0.00298266	0.000770118 0
$16$	0.649491	0.162373
$17$	0.886427	0.214990	0.107495	−	0.994206i	$-0.465717\pi$
$17$	0.886427	0.214990	0.107495	+	0.994206i	$0.465717\pi$
$18$	6.95640	1.63964
$19$	1.00573	0.230729	0.115365	−	0.993323i	$-0.463196\pi$
$19$	1.00573	0.230729	0.115365	+	0.993323i	$0.463196\pi$
$20$	3.37687	0.755090
$21$	−0.00285191	−0.000622338 0
$22$	−14.9815	−3.19407
$23$	−2.24170	−0.467427	−0.233714	−	0.972305i	$-0.575088\pi$
$23$	−2.24170	−0.467427	−0.233714	+	0.972305i	$0.575088\pi$
$24$	−0.00952268	−0.00194381
$25$	1.00000	0.200000
$26$	−7.72437	−1.51487
$27$	−0.0178959	−0.00344407
$28$	−3.22884	−0.610194
$29$	1.41130	0.262072	0.131036	−	0.991378i	$-0.458170\pi$
$29$	1.41130	0.262072	0.131036	+	0.991378i	$0.458170\pi$
$30$	−0.00691620	−0.00126272
$31$	0.580960	0.104343	0.0521717	−	0.998638i	$-0.483386\pi$
$31$	0.580960	0.104343	0.0521717	+	0.998638i	$0.483386\pi$
$32$	4.87933	0.862552
$33$	0.0192705	0.00335457
$34$	−2.05545	−0.352507
$35$	−0.956165	−0.161621
$36$	−10.1306	−1.68843
$37$	−1.44012	−0.236753	−0.118377	−	0.992969i	$-0.537769\pi$
$37$	−1.44012	−0.236753	−0.118377	+	0.992969i	$0.537769\pi$
$38$	−2.33208	−0.378314
$39$	0.00993577	0.00159100
$40$	−3.19269	−0.504808
$41$	−7.18477	−1.12207	−0.561036	−	0.827791i	$-0.689597\pi$
$41$	−7.18477	−1.12207	−0.561036	+	0.827791i	$0.689597\pi$
$42$	0.00661303	0.00102041
$43$	4.27179	0.651441	0.325721	−	0.945466i	$-0.394393\pi$
$43$	4.27179	0.651441	0.325721	+	0.945466i	$0.394393\pi$
$44$	21.8175	3.28911
$45$	−2.99999	−0.447212
$46$	5.19808	0.766414
$47$	−9.01713	−1.31528	−0.657642	−	0.753331i	$-0.728446\pi$
$47$	−9.01713	−1.31528	−0.657642	+	0.753331i	$0.728446\pi$
$48$	0.00193721	0.000279612 0
$49$	−6.08575	−0.869393
$50$	−2.31881	−0.327929
$51$	0.00264391	0.000370221 0
$52$	11.2490	1.55995
$53$	−13.2596	−1.82134	−0.910670	−	0.413135i	$-0.864434\pi$
$53$	−13.2596	−1.82134	−0.910670	+	0.413135i	$0.864434\pi$
$54$	0.0414972	0.00564705
$55$	6.46086	0.871183
$56$	3.05273	0.407939
$57$	0.00299973	0.000397324 0
$58$	−3.27253	−0.429704
$59$	5.17631	0.673898	0.336949	−	0.941523i	$-0.390605\pi$
$59$	5.17631	0.673898	0.336949	+	0.941523i	$0.390605\pi$
$60$	0.0100720	0.00130029
$61$	−12.5050	−1.60111	−0.800553	−	0.599262i	$-0.795461\pi$
$61$	−12.5050	−1.60111	−0.800553	+	0.599262i	$0.795461\pi$
$62$	−1.34713	−0.171086
$63$	2.86849	0.361395
$64$	−12.6132	−1.57665
$65$	3.33118	0.413182
$66$	−0.0446846	−0.00550030
$67$	−13.3266	−1.62811	−0.814053	−	0.580791i	$-0.802743\pi$
$67$	−13.3266	−1.62811	−0.814053	+	0.580791i	$0.802743\pi$
$68$	2.99334	0.362996
$69$	−0.00668623	−0.000804927 0
$70$	2.21716	0.265002
$71$	−10.1984	−1.21033	−0.605165	−	0.796100i	$-0.706893\pi$
$71$	−10.1984	−1.21033	−0.605165	+	0.796100i	$0.706893\pi$
$72$	9.57803	1.12878
$73$	3.52767	0.412883	0.206441	−	0.978459i	$-0.433812\pi$
$73$	3.52767	0.412883	0.206441	+	0.978459i	$0.433812\pi$
$74$	3.33935	0.388191
$75$	0.00298266	0.000344407 0
$76$	3.39620	0.389571
$77$	−6.17765	−0.704009
$78$	−0.0230391	−0.00260867
$79$	8.85913	0.996730	0.498365	−	0.866967i	$-0.333934\pi$
$79$	8.85913	0.996730	0.498365	+	0.866967i	$0.333934\pi$
$80$	0.649491	0.0726153
$81$	8.99992	0.999991
$82$	16.6601	1.83980
$83$	−2.26555	−0.248676	−0.124338	−	0.992240i	$-0.539681\pi$
$83$	−2.26555	−0.248676	−0.124338	+	0.992240i	$0.539681\pi$
$84$	−0.00963052	−0.00105078
$85$	0.886427	0.0961465
$86$	−9.90545	−1.06813
$87$	0.00420942	0.000451297 0
$88$	−20.6275	−2.19890
$89$	12.1786	1.29093	0.645466	−	0.763789i	$-0.276663\pi$
$89$	12.1786	1.29093	0.645466	+	0.763789i	$0.276663\pi$
$90$	6.95640	0.733269
$91$	−3.18516	−0.333896
$92$	−7.56993	−0.789220
$93$	0.00173280	0.000179683 0
$94$	20.9090	2.15660
$95$	1.00573	0.103185
$96$	0.0145534	0.00148535
$97$	2.53413	0.257302	0.128651	−	0.991690i	$-0.458935\pi$
$97$	2.53413	0.257302	0.128651	+	0.991690i	$0.458935\pi$
$98$	14.1117	1.42549
$99$	−19.3825	−1.94802
$100$	3.37687	0.337687
$101$	−17.5034	−1.74165	−0.870827	−	0.491590i	$-0.836416\pi$
$101$	−17.5034	−1.74165	−0.870827	+	0.491590i	$0.836416\pi$
$102$	−0.00613071	−0.000607031 0
$103$	−5.91361	−0.582686	−0.291343	−	0.956619i	$-0.594102\pi$
$103$	−5.91361	−0.582686	−0.291343	+	0.956619i	$0.594102\pi$
$104$	−10.6354	−1.04289
$105$	−0.00285191	−0.000278318 0
$106$	30.7463	2.98635
$107$	−11.9432	−1.15459	−0.577296	−	0.816535i	$-0.695892\pi$
$107$	−11.9432	−1.15459	−0.577296	+	0.816535i	$0.695892\pi$
$108$	−0.0604321	−0.00581508
$109$	5.00623	0.479509	0.239755	−	0.970833i	$-0.422933\pi$
$109$	5.00623	0.479509	0.239755	+	0.970833i	$0.422933\pi$
$110$	−14.9815	−1.42843
$111$	−0.00429537	−0.000407698 0
$112$	−0.621020	−0.0586809
$113$	−16.3616	−1.53917	−0.769585	−	0.638545i	$-0.779537\pi$
$113$	−16.3616	−1.53917	−0.769585	+	0.638545i	$0.779537\pi$
$114$	−0.00695580	−0.000651470 0
$115$	−2.24170	−0.209040
$116$	4.76577	0.442490
$117$	−9.99352	−0.923901
$118$	−12.0029	−1.10495
$119$	−0.847570	−0.0776967
$120$	−0.00952268	−0.000869298 0
$121$	30.7428	2.79480
$122$	28.9968	2.62524
$123$	−0.0214297	−0.00193225
$124$	1.96182	0.176177
$125$	1.00000	0.0894427
$126$	−6.65147	−0.592560
$127$	−10.6430	−0.944416	−0.472208	−	0.881487i	$-0.656543\pi$
$127$	−10.6430	−0.944416	−0.472208	+	0.881487i	$0.656543\pi$
$128$	19.4889	1.72259
$129$	0.0127413	0.00112181
$130$	−7.72437	−0.677472
$131$	−3.23179	−0.282363	−0.141181	−	0.989984i	$-0.545090\pi$
$131$	−3.23179	−0.282363	−0.141181	+	0.989984i	$0.545090\pi$
$132$	0.0650740	0.00566396
$133$	−0.961639	−0.0833847
$134$	30.9019	2.66951
$135$	−0.0178959	−0.00154023
$136$	−2.83008	−0.242678
$137$	4.93467	0.421597	0.210799	−	0.977530i	$-0.432394\pi$
$137$	4.93467	0.421597	0.210799	+	0.977530i	$0.432394\pi$
$138$	0.0155041	0.00131979
$139$	5.17448	0.438893	0.219447	−	0.975625i	$-0.429575\pi$
$139$	5.17448	0.438893	0.219447	+	0.975625i	$0.429575\pi$
$140$	−3.22884	−0.272887
$141$	−0.0268950	−0.00226497
$142$	23.6482	1.98451
$143$	21.5223	1.79979
$144$	−1.94847	−0.162372
$145$	1.41130	0.117202
$146$	−8.17999	−0.676981
$147$	−0.0181517	−0.00149713
$148$	−4.86308	−0.399742
$149$	22.6629	1.85661	0.928307	−	0.371815i	$-0.121265\pi$
$149$	22.6629	1.85661	0.928307	+	0.371815i	$0.121265\pi$
$150$	−0.00691620	−0.000564706 0
$151$	16.1443	1.31381	0.656903	−	0.753975i	$-0.271866\pi$
$151$	16.1443	1.31381	0.656903	+	0.753975i	$0.271866\pi$
$152$	−3.21096	−0.260444
$153$	−2.65927	−0.214989
$154$	14.3248	1.15432
$155$	0.580960	0.0466638
$156$	0.0335518	0.00268629
$157$	−2.31014	−0.184369	−0.0921845	−	0.995742i	$-0.529385\pi$
$157$	−2.31014	−0.184369	−0.0921845	+	0.995742i	$0.529385\pi$
$158$	−20.5426	−1.63428
$159$	−0.0395487	−0.00313641
$160$	4.87933	0.385745
$161$	2.14344	0.168927
$162$	−20.8691	−1.63963
$163$	−24.6557	−1.93118	−0.965592	−	0.260062i	$-0.916257\pi$
$163$	−24.6557	−1.93118	−0.965592	+	0.260062i	$0.916257\pi$
$164$	−24.2620	−1.89454
$165$	0.0192705	0.00150021
$166$	5.25336	0.407740
$167$	−0.341502	−0.0264263	−0.0132131	−	0.999913i	$-0.504206\pi$
$167$	−0.341502	−0.0264263	−0.0132131	+	0.999913i	$0.504206\pi$
$168$	0.00910526	0.000702486 0
$169$	−1.90322	−0.146402
$170$	−2.05545	−0.157646
$171$	−3.01717	−0.230728
$172$	14.4253	1.09992
$173$	−13.1906	−1.00286	−0.501431	−	0.865198i	$-0.667193\pi$
$173$	−13.1906	−1.00286	−0.501431	+	0.865198i	$0.667193\pi$
$174$	−0.00976083	−0.000739967 0
$175$	−0.956165	−0.0722793
$176$	4.19627	0.316306
$177$	0.0154391	0.00116048
$178$	−28.2399	−2.11667
$179$	0.764422	0.0571356	0.0285678	−	0.999592i	$-0.490905\pi$
$179$	0.764422	0.0571356	0.0285678	+	0.999592i	$0.490905\pi$
$180$	−10.1306	−0.755088
$181$	−17.4998	−1.30075	−0.650376	−	0.759612i	$-0.725389\pi$
$181$	−17.4998	−1.30075	−0.650376	+	0.759612i	$0.725389\pi$
$182$	7.38577	0.547470
$183$	−0.0372982	−0.00275716
$184$	7.15705	0.527625
$185$	−1.44012	−0.105879
$186$	−0.00401803	−0.000294617 0
$187$	5.72708	0.418806
$188$	−30.4496	−2.22077
$189$	0.0171114	0.00124467
$190$	−2.33208	−0.169187
$191$	15.5965	1.12852	0.564262	−	0.825596i	$-0.309161\pi$
$191$	15.5965	1.12852	0.564262	+	0.825596i	$0.309161\pi$
$192$	−0.0376208	−0.00271505
$193$	−13.3912	−0.963921	−0.481961	−	0.876193i	$-0.660075\pi$
$193$	−13.3912	−0.963921	−0.481961	+	0.876193i	$0.660075\pi$
$194$	−5.87616	−0.421884
$195$	0.00993577	0.000711515 0
$196$	−20.5508	−1.46791
$197$	2.45734	0.175078	0.0875392	−	0.996161i	$-0.472100\pi$
$197$	2.45734	0.175078	0.0875392	+	0.996161i	$0.472100\pi$
$198$	44.9444	3.19406
$199$	−11.7365	−0.831976	−0.415988	−	0.909370i	$-0.636564\pi$
$199$	−11.7365	−0.831976	−0.415988	+	0.909370i	$0.636564\pi$
$200$	−3.19269	−0.225757
$201$	−0.0397487	−0.00280366
$202$	40.5870	2.85569
$203$	−1.34943	−0.0947118
$204$	0.00892812	0.000625093 0
$205$	−7.18477	−0.501806
$206$	13.7125	0.955397
$207$	6.72509	0.467426
$208$	2.16357	0.150017
$209$	6.49785	0.449466
$210$	0.00661303	0.000456343 0
$211$	16.8491	1.15994	0.579970	−	0.814638i	$-0.303064\pi$
$211$	16.8491	1.15994	0.579970	+	0.814638i	$0.303064\pi$
$212$	−44.7757	−3.07521
$213$	−0.0304184	−0.00208423
$214$	27.6940	1.89312
$215$	4.27179	0.291333
$216$	0.0571360	0.00388761
$217$	−0.555493	−0.0377093
$218$	−11.6085	−0.786225
$219$	0.0105218	0.000711000 0
$220$	21.8175	1.47093
$221$	2.95285	0.198630
$222$	0.00996013	0.000668480 0
$223$	1.76538	0.118219	0.0591093	−	0.998252i	$-0.481174\pi$
$223$	1.76538	0.118219	0.0591093	+	0.998252i	$0.481174\pi$
$224$	−4.66544	−0.311723
$225$	−2.99999	−0.199999
$226$	37.9394	2.52369
$227$	15.1924	1.00836	0.504178	−	0.863600i	$-0.331796\pi$
$227$	15.1924	1.00836	0.504178	+	0.863600i	$0.331796\pi$
$228$	0.0101297	0.000670855 0
$229$	−14.0914	−0.931186	−0.465593	−	0.884999i	$-0.654159\pi$
$229$	−14.0914	−0.931186	−0.465593	+	0.884999i	$0.654159\pi$
$230$	5.19808	0.342751
$231$	−0.0184258	−0.00121233
$232$	−4.50583	−0.295823
$233$	−3.41904	−0.223989	−0.111994	−	0.993709i	$-0.535724\pi$
$233$	−3.41904	−0.223989	−0.111994	+	0.993709i	$0.535724\pi$
$234$	23.1730	1.51487
$235$	−9.01713	−0.588213
$236$	17.4797	1.13783
$237$	0.0264237	0.00171641
$238$	1.96535	0.127395
$239$	17.7746	1.14975	0.574873	−	0.818243i	$-0.305052\pi$
$239$	17.7746	1.14975	0.574873	+	0.818243i	$0.305052\pi$
$240$	0.00193721	0.000125046 0
$241$	−27.4380	−1.76743	−0.883717	−	0.468022i	$-0.844967\pi$
$241$	−27.4380	−1.76743	−0.883717	+	0.468022i	$0.844967\pi$
$242$	−71.2865	−4.58247
$243$	0.0805314	0.00516609
$244$	−42.2278	−2.70336
$245$	−6.08575	−0.388804
$246$	0.0496913	0.00316820
$247$	3.35025	0.213172
$248$	−1.85482	−0.117781
$249$	−0.00675734	−0.000428229 0
$250$	−2.31881	−0.146654
$251$	−17.0229	−1.07448	−0.537239	−	0.843430i	$-0.680533\pi$
$251$	−17.0229	−1.07448	−0.537239	+	0.843430i	$0.680533\pi$
$252$	9.68649	0.610192
$253$	−14.4833	−0.910560
$254$	24.6791	1.54851
$255$	0.00264391	0.000165568 0
$256$	−19.9646	−1.24779
$257$	−5.98082	−0.373073	−0.186537	−	0.982448i	$-0.559726\pi$
$257$	−5.98082	−0.373073	−0.186537	+	0.982448i	$0.559726\pi$
$258$	−0.0295445	−0.00183936
$259$	1.37699	0.0855619
$260$	11.2490	0.697631
$261$	−4.23388	−0.262071
$262$	7.49390	0.462974
$263$	29.6935	1.83098	0.915490	−	0.402341i	$-0.131803\pi$
$263$	29.6935	1.83098	0.915490	+	0.402341i	$0.131803\pi$
$264$	−0.0615248	−0.00378659
$265$	−13.2596	−0.814528
$266$	2.22986	0.136721
$267$	0.0363247	0.00222303
$268$	−45.0022	−2.74895
$269$	8.72705	0.532098	0.266049	−	0.963960i	$-0.414282\pi$
$269$	8.72705	0.532098	0.266049	+	0.963960i	$0.414282\pi$
$270$	0.0414972	0.00252544
$271$	−1.63961	−0.0995991	−0.0497995	−	0.998759i	$-0.515858\pi$
$271$	−1.63961	−0.0995991	−0.0497995	+	0.998759i	$0.515858\pi$
$272$	0.575726	0.0349085
$273$	−0.00950024	−0.000574981 0
$274$	−11.4425	−0.691269
$275$	6.46086	0.389605
$276$	−0.0225785	−0.00135907
$277$	2.34824	0.141092	0.0705462	−	0.997509i	$-0.477526\pi$
$277$	2.34824	0.141092	0.0705462	+	0.997509i	$0.477526\pi$
$278$	−11.9986	−0.719629
$279$	−1.74287	−0.104343
$280$	3.05273	0.182436
$281$	−17.2851	−1.03114	−0.515571	−	0.856847i	$-0.672420\pi$
$281$	−17.2851	−1.03114	−0.515571	+	0.856847i	$0.672420\pi$
$282$	0.0623643	0.00371374
$283$	1.83313	0.108968	0.0544840	−	0.998515i	$-0.482649\pi$
$283$	1.83313	0.108968	0.0544840	+	0.998515i	$0.482649\pi$
$284$	−34.4387	−2.04356
$285$	0.00299973	0.000177689 0
$286$	−49.9061	−2.95101
$287$	6.86982	0.405513
$288$	−14.6379	−0.862549
$289$	−16.2142	−0.953779
$290$	−3.27253	−0.192170
$291$	0.00755844	0.000443083 0
$292$	11.9125	0.697125
$293$	4.66644	0.272616	0.136308	−	0.990666i	$-0.456476\pi$
$293$	4.66644	0.272616	0.136308	+	0.990666i	$0.456476\pi$
$294$	0.0420903	0.00245475
$295$	5.17631	0.301376
$296$	4.59784	0.267244
$297$	−0.115623	−0.00670913
$298$	−52.5508	−3.04419
$299$	−7.46752	−0.431858
$300$	0.0100720	0.000581509 0
$301$	−4.08453	−0.235429
$302$	−37.4356	−2.15417
$303$	−0.0522066	−0.00299919
$304$	0.653209	0.0374641
$305$	−12.5050	−0.716036
$306$	6.16634	0.352506
$307$	1.60940	0.0918535	0.0459268	−	0.998945i	$-0.485376\pi$
$307$	1.60940	0.0918535	0.0459268	+	0.998945i	$0.485376\pi$
$308$	−20.8611	−1.18867
$309$	−0.0176383	−0.00100341
$310$	−1.34713	−0.0765120
$311$	−8.69036	−0.492785	−0.246392	−	0.969170i	$-0.579245\pi$
$311$	−8.69036	−0.492785	−0.246392	+	0.969170i	$0.579245\pi$
$312$	−0.0317218	−0.00179589
$313$	−13.1795	−0.744950	−0.372475	−	0.928042i	$-0.621491\pi$
$313$	−13.1795	−0.744950	−0.372475	+	0.928042i	$0.621491\pi$
$314$	5.35676	0.302300
$315$	2.86849	0.161621
$316$	29.9161	1.68291
$317$	14.1994	0.797516	0.398758	−	0.917056i	$-0.369441\pi$
$317$	14.1994	0.797516	0.398758	+	0.917056i	$0.369441\pi$
$318$	0.0917058	0.00514260
$319$	9.11821	0.510522
$320$	−12.6132	−0.705099
$321$	−0.0356224	−0.00198825
$322$	−4.97022	−0.276979
$323$	0.891502	0.0496045
$324$	30.3915	1.68842
$325$	3.33118	0.184781
$326$	57.1718	3.16645
$327$	0.0149318	0.000825733 0
$328$	22.9387	1.26658
$329$	8.62186	0.475339
$330$	−0.0446846	−0.00245981
$331$	−10.1263	−0.556593	−0.278296	−	0.960495i	$-0.589770\pi$
$331$	−10.1263	−0.556593	−0.278296	+	0.960495i	$0.589770\pi$
$332$	−7.65044	−0.419873
$333$	4.32033	0.236753
$334$	0.791878	0.0433296
$335$	−13.3266	−0.728111
$336$	−0.00185229	−0.000101051 0
$337$	−14.5566	−0.792949	−0.396474	−	0.918046i	$-0.629766\pi$
$337$	−14.5566	−0.792949	−0.396474	+	0.918046i	$0.629766\pi$
$338$	4.41320	0.240047
$339$	−0.0488010	−0.00265051
$340$	2.99334	0.162337
$341$	3.75350	0.203263
$342$	6.99623	0.378313
$343$	12.5121	0.675592
$344$	−13.6385	−0.735337
$345$	−0.00668623	−0.000359974 0
$346$	30.5864	1.64434
$347$	−19.2263	−1.03212	−0.516062	−	0.856551i	$-0.672602\pi$
$347$	−19.2263	−1.03212	−0.516062	+	0.856551i	$0.672602\pi$
$348$	0.0142146	0.000761985 0
$349$	−6.44349	−0.344912	−0.172456	−	0.985017i	$-0.555170\pi$
$349$	−6.44349	−0.344912	−0.172456	+	0.985017i	$0.555170\pi$
$350$	2.21716	0.118512
$351$	−0.0596145	−0.00318199
$352$	31.5247	1.68027
$353$	−5.98266	−0.318425	−0.159212	−	0.987244i	$-0.550895\pi$
$353$	−5.98266	−0.318425	−0.159212	+	0.987244i	$0.550895\pi$
$354$	−0.0358004	−0.00190277
$355$	−10.1984	−0.541276
$356$	41.1256	2.17965
$357$	−0.00252801	−0.000133797 0
$358$	−1.77255	−0.0936820
$359$	13.8035	0.728519	0.364260	−	0.931297i	$-0.381322\pi$
$359$	13.8035	0.728519	0.364260	+	0.931297i	$0.381322\pi$
$360$	9.57803	0.504806
$361$	−17.9885	−0.946764
$362$	40.5788	2.13277
$363$	0.0916951	0.00481274
$364$	−10.7559	−0.563760
$365$	3.52767	0.184647
$366$	0.0864873	0.00452077
$367$	−35.8156	−1.86956	−0.934779	−	0.355230i	$-0.884403\pi$
$367$	−35.8156	−1.86956	−0.934779	+	0.355230i	$0.884403\pi$
$368$	−1.45596	−0.0758974
$369$	21.5542	1.12207
$370$	3.33935	0.173604
$371$	12.6783	0.658226
$372$	0.00585144	0.000303383 0
$373$	34.1310	1.76724	0.883618	−	0.468208i	$-0.155100\pi$
$373$	34.1310	1.76724	0.883618	+	0.468208i	$0.155100\pi$
$374$	−13.2800	−0.686693
$375$	0.00298266	0.000154024 0
$376$	28.7889	1.48467
$377$	4.70130	0.242129
$378$	−0.0396781	−0.00204082
$379$	−7.70523	−0.395791	−0.197895	−	0.980223i	$-0.563411\pi$
$379$	−7.70523	−0.395791	−0.197895	+	0.980223i	$0.563411\pi$
$380$	3.39620	0.174221
$381$	−0.0317445	−0.00162632
$382$	−36.1653	−1.85038
$383$	20.4923	1.04711	0.523554	−	0.851992i	$-0.324606\pi$
$383$	20.4923	1.04711	0.523554	+	0.851992i	$0.324606\pi$
$384$	0.0581287	0.00296637
$385$	−6.17765	−0.314842
$386$	31.0517	1.58049
$387$	−12.8153	−0.651440
$388$	8.55742	0.434437
$389$	8.90124	0.451311	0.225655	−	0.974207i	$-0.427548\pi$
$389$	8.90124	0.451311	0.225655	+	0.974207i	$0.427548\pi$
$390$	−0.0230391	−0.00116663
$391$	−1.98711	−0.100492
$392$	19.4299	0.981357
$393$	−0.00963931	−0.000486239 0
$394$	−5.69810	−0.287066
$395$	8.85913	0.445751
$396$	−65.4522	−3.28910
$397$	16.4162	0.823906	0.411953	−	0.911205i	$-0.364847\pi$
$397$	16.4162	0.823906	0.411953	+	0.911205i	$0.364847\pi$
$398$	27.2146	1.36414
$399$	−0.00286824	−0.000143592 0
$400$	0.649491	0.0324745
$401$	13.9236	0.695312	0.347656	−	0.937622i	$-0.386978\pi$
$401$	13.9236	0.695312	0.347656	+	0.937622i	$0.386978\pi$
$402$	0.0921696	0.00459700
$403$	1.93528	0.0964033
$404$	−59.1067	−2.94067
$405$	8.99992	0.447210
$406$	3.12908	0.155294
$407$	−9.30439	−0.461201
$408$	−0.00844116	−0.000417900 0
$409$	33.1825	1.64077	0.820386	−	0.571811i	$-0.193759\pi$
$409$	33.1825	1.64077	0.820386	+	0.571811i	$0.193759\pi$
$410$	16.6601	0.822783
$411$	0.0147184	0.000726006 0
$412$	−19.9695	−0.983826
$413$	−4.94940	−0.243544
$414$	−15.5942	−0.766412
$415$	−2.26555	−0.111211
$416$	16.2539	0.796915
$417$	0.0154337	0.000755790 0
$418$	−15.0673	−0.736964
$419$	27.4209	1.33960	0.669800	−	0.742541i	$-0.266380\pi$
$419$	27.4209	1.33960	0.669800	+	0.742541i	$0.266380\pi$
$420$	−0.00963052	−0.000469921 0
$421$	8.40916	0.409837	0.204919	−	0.978779i	$-0.434307\pi$
$421$	8.40916	0.409837	0.204919	+	0.978779i	$0.434307\pi$
$422$	−39.0698	−1.90189
$423$	27.0513	1.31528
$424$	42.3336	2.05590
$425$	0.886427	0.0429980
$426$	0.0705344	0.00341740
$427$	11.9569	0.578634
$428$	−40.3305	−1.94945
$429$	0.0641937	0.00309930
$430$	−9.90545	−0.477683
$431$	9.29558	0.447752	0.223876	−	0.974618i	$-0.428129\pi$
$431$	9.29558	0.447752	0.223876	+	0.974618i	$0.428129\pi$
$432$	−0.0116232	−0.000559223 0
$433$	22.1871	1.06624	0.533122	−	0.846039i	$-0.321019\pi$
$433$	22.1871	1.06624	0.533122	+	0.846039i	$0.321019\pi$
$434$	1.28808	0.0618299
$435$	0.00420942	0.000201826 0
$436$	16.9054	0.809619
$437$	−2.25454	−0.107849
$438$	−0.0243981	−0.00116579
$439$	21.1446	1.00917	0.504587	−	0.863361i	$-0.331645\pi$
$439$	21.1446	1.00917	0.504587	+	0.863361i	$0.331645\pi$
$440$	−20.6275	−0.983378
$441$	18.2572	0.869390
$442$	−6.84709	−0.325683
$443$	−9.66459	−0.459179	−0.229589	−	0.973288i	$-0.573738\pi$
$443$	−9.66459	−0.459179	−0.229589	+	0.973288i	$0.573738\pi$
$444$	−0.0145049	−0.000688371 0
$445$	12.1786	0.577322
$446$	−4.09357	−0.193836
$447$	0.0675955	0.00319716
$448$	12.0603	0.569796
$449$	10.2410	0.483305	0.241652	−	0.970363i	$-0.422311\pi$
$449$	10.2410	0.483305	0.241652	+	0.970363i	$0.422311\pi$
$450$	6.95640	0.327928
$451$	−46.4198	−2.18582
$452$	−55.2509	−2.59878
$453$	0.0481529	0.00226242
$454$	−35.2283	−1.65334
$455$	−3.18516	−0.149323
$456$	−0.00957720	−0.000448494 0
$457$	−35.3729	−1.65467	−0.827337	−	0.561706i	$-0.810145\pi$
$457$	−35.3729	−1.65467	−0.827337	+	0.561706i	$0.810145\pi$
$458$	32.6752	1.52681
$459$	−0.0158634	−0.000740441 0
$460$	−7.56993	−0.352950
$461$	−21.0864	−0.982091	−0.491045	−	0.871134i	$-0.663385\pi$
$461$	−21.0864	−0.982091	−0.491045	+	0.871134i	$0.663385\pi$
$462$	0.0427259	0.00198779
$463$	5.43332	0.252508	0.126254	−	0.991998i	$-0.459705\pi$
$463$	5.43332	0.252508	0.126254	+	0.991998i	$0.459705\pi$
$464$	0.916626	0.0425533
$465$	0.00173280	8.03568e−5 0
$466$	7.92809	0.367262
$467$	22.4133	1.03716	0.518581	−	0.855028i	$-0.326460\pi$
$467$	22.4133	1.03716	0.518581	+	0.855028i	$0.326460\pi$
$468$	−33.7468	−1.55995
$469$	12.7424	0.588392
$470$	20.9090	0.964459
$471$	−0.00689034	−0.000317490 0
$472$	−16.5263	−0.760686
$473$	27.5994	1.26902
$474$	−0.0612715	−0.00281429
$475$	1.00573	0.0461458
$476$	−2.86213	−0.131186
$477$	39.7785	1.82133
$478$	−41.2159	−1.88517
$479$	19.0089	0.868538	0.434269	−	0.900783i	$-0.357007\pi$
$479$	19.0089	0.868538	0.434269	+	0.900783i	$0.357007\pi$
$480$	0.0145534	0.000664267 0
$481$	−4.79729	−0.218737
$482$	63.6233	2.89796
$483$	0.00639314	0.000290898 0
$484$	103.814	4.71883
$485$	2.53413	0.115069
$486$	−0.186737	−0.00847055
$487$	−4.97207	−0.225306	−0.112653	−	0.993634i	$-0.535935\pi$
$487$	−4.97207	−0.225306	−0.112653	+	0.993634i	$0.535935\pi$
$488$	39.9246	1.80730
$489$	−0.0735395	−0.00332557
$490$	14.1117	0.637501
$491$	20.3938	0.920360	0.460180	−	0.887826i	$-0.347785\pi$
$491$	20.3938	0.920360	0.460180	+	0.887826i	$0.347785\pi$
$492$	−0.0723652	−0.00326247
$493$	1.25101	0.0563428
$494$	−7.76859	−0.349526
$495$	−19.3825	−0.871180
$496$	0.377328	0.0169425
$497$	9.75138	0.437409
$498$	0.0156690	0.000702144 0
$499$	20.0802	0.898913	0.449456	−	0.893302i	$-0.351618\pi$
$499$	20.0802	0.898913	0.449456	+	0.893302i	$0.351618\pi$
$500$	3.37687	0.151018
$501$	−0.00101858	−4.55070e−5 0
$502$	39.4729	1.76176
$503$	3.87715	0.172874	0.0864369	−	0.996257i	$-0.472452\pi$
$503$	3.87715	0.172874	0.0864369	+	0.996257i	$0.472452\pi$
$504$	−9.15818	−0.407938
$505$	−17.5034	−0.778891
$506$	33.5841	1.49299
$507$	−0.00567665	−0.000252109 0
$508$	−35.9401	−1.59458
$509$	27.1214	1.20213	0.601067	−	0.799199i	$-0.294743\pi$
$509$	27.1214	1.20213	0.601067	+	0.799199i	$0.294743\pi$
$510$	−0.00613071	−0.000271472 0
$511$	−3.37304	−0.149214
$512$	7.31632	0.323339
$513$	−0.0179984	−0.000794647 0
$514$	13.8684	0.611707
$515$	−5.91361	−0.260585
$516$	0.0430256	0.00189409
$517$	−58.2584	−2.56220
$518$	−3.19297	−0.140291
$519$	−0.0393430	−0.00172697
$520$	−10.6354	−0.466394
$521$	0.152248	0.00667012	0.00333506	−	0.999994i	$-0.498938\pi$
$521$	0.152248	0.00667012	0.00333506	+	0.999994i	$0.498938\pi$
$522$	9.81756	0.429703
$523$	−35.4855	−1.55167	−0.775835	−	0.630936i	$-0.782671\pi$
$523$	−35.4855	−1.55167	−0.775835	+	0.630936i	$0.782671\pi$
$524$	−10.9133	−0.476751
$525$	−0.00285191	−0.000124468 0
$526$	−68.8535	−3.00216
$527$	0.514978	0.0224328
$528$	0.0125160	0.000544690 0
$529$	−17.9748	−0.781512
$530$	30.7463	1.33554
$531$	−15.5289	−0.673896
$532$	−3.24733	−0.140789
$533$	−23.9338	−1.03669
$534$	−0.0842299	−0.00364498
$535$	−11.9432	−0.516349
$536$	42.5477	1.83778
$537$	0.00228001	9.83896e−5 0
$538$	−20.2364	−0.872451
$539$	−39.3192	−1.69360
$540$	−0.0604321	−0.00260058
$541$	38.6441	1.66144	0.830719	−	0.556692i	$-0.187930\pi$
$541$	38.6441	1.66144	0.830719	+	0.556692i	$0.187930\pi$
$542$	3.80193	0.163307
$543$	−0.0521960	−0.00223994
$544$	4.32517	0.185440
$545$	5.00623	0.214443
$546$	0.0220292	0.000942763 0
$547$	−38.1446	−1.63095	−0.815474	−	0.578794i	$-0.803523\pi$
$547$	−38.1446	−1.63095	−0.815474	+	0.578794i	$0.803523\pi$
$548$	16.6637	0.711838
$549$	37.5150	1.60110
$550$	−14.9815	−0.638813
$551$	1.41938	0.0604676
$552$	0.0213470	0.000908590 0
$553$	−8.47079	−0.360215
$554$	−5.44513	−0.231341
$555$	−0.00429537	−0.000182328 0
$556$	17.4735	0.741042
$557$	−21.6399	−0.916914	−0.458457	−	0.888717i	$-0.651598\pi$
$557$	−21.6399	−0.916914	−0.458457	+	0.888717i	$0.651598\pi$
$558$	4.04139	0.171086
$559$	14.2301	0.601869
$560$	−0.621020	−0.0262429
$561$	0.0170819	0.000721199 0
$562$	40.0808	1.69070
$563$	40.6293	1.71232	0.856160	−	0.516711i	$-0.172844\pi$
$563$	40.6293	1.71232	0.856160	+	0.516711i	$0.172844\pi$
$564$	−0.0908208	−0.00382424
$565$	−16.3616	−0.688337
$566$	−4.25067	−0.178669
$567$	−8.60541	−0.361393
$568$	32.5604	1.36620
$569$	29.9887	1.25719	0.628595	−	0.777733i	$-0.283630\pi$
$569$	29.9887	1.25719	0.628595	+	0.777733i	$0.283630\pi$
$570$	−0.00695580	−0.000291346 0
$571$	−31.8214	−1.33169	−0.665843	−	0.746092i	$-0.731928\pi$
$571$	−31.8214	−1.33169	−0.665843	+	0.746092i	$0.731928\pi$
$572$	72.6780	3.03882
$573$	0.0465190	0.00194336
$574$	−15.9298	−0.664897
$575$	−2.24170	−0.0934855
$576$	37.8395	1.57665
$577$	1.20131	0.0500112	0.0250056	−	0.999687i	$-0.492040\pi$
$577$	1.20131	0.0500112	0.0250056	+	0.999687i	$0.492040\pi$
$578$	37.5977	1.56386
$579$	−0.0399414	−0.00165991
$580$	4.76577	0.197888
$581$	2.16624	0.0898706
$582$	−0.0175266	−0.000726499 0
$583$	−85.6682	−3.54801
$584$	−11.2628	−0.466056
$585$	−9.99352	−0.413181
$586$	−10.8206	−0.446994
$587$	−42.1560	−1.73997	−0.869983	−	0.493081i	$-0.835870\pi$
$587$	−42.1560	−1.73997	−0.869983	+	0.493081i	$0.835870\pi$
$588$	−0.0612958	−0.00252780
$589$	0.584286	0.0240751
$590$	−12.0029	−0.494150
$591$	0.00732941	0.000301491 0
$592$	−0.935341	−0.0384423
$593$	−5.36457	−0.220297	−0.110148	−	0.993915i	$-0.535133\pi$
$593$	−5.36457	−0.220297	−0.110148	+	0.993915i	$0.535133\pi$
$594$	0.268107	0.0110006
$595$	−0.847570	−0.0347470
$596$	76.5294	3.13477
$597$	−0.0350058	−0.00143269
$598$	17.3157	0.708093
$599$	−31.4794	−1.28621	−0.643107	−	0.765776i	$-0.722355\pi$
$599$	−31.4794	−1.28621	−0.643107	+	0.765776i	$0.722355\pi$
$600$	−0.00952268	−0.000388762 0
$601$	−3.66379	−0.149449	−0.0747245	−	0.997204i	$-0.523808\pi$
$601$	−3.66379	−0.149449	−0.0747245	+	0.997204i	$0.523808\pi$
$602$	9.47125	0.386019
$603$	39.9797	1.62810
$604$	54.5172	2.21827
$605$	30.7428	1.24987
$606$	0.121057	0.00491761
$607$	−3.34527	−0.135780	−0.0678901	−	0.997693i	$-0.521627\pi$
$607$	−3.34527	−0.135780	−0.0678901	+	0.997693i	$0.521627\pi$
$608$	4.90726	0.199016
$609$	−0.00402490	−0.000163097 0
$610$	28.9968	1.17404
$611$	−30.0377	−1.21520
$612$	−8.98001	−0.362995
$613$	−9.72224	−0.392678	−0.196339	−	0.980536i	$-0.562905\pi$
$613$	−9.72224	−0.392678	−0.196339	+	0.980536i	$0.562905\pi$
$614$	−3.73190	−0.150607
$615$	−0.0214297	−0.000864128 0
$616$	19.7233	0.794675
$617$	−15.2503	−0.613953	−0.306976	−	0.951717i	$-0.599317\pi$
$617$	−15.2503	−0.613953	−0.306976	+	0.951717i	$0.599317\pi$
$618$	0.0408997	0.00164523
$619$	5.15404	0.207158	0.103579	−	0.994621i	$-0.466970\pi$
$619$	5.15404	0.207158	0.103579	+	0.994621i	$0.466970\pi$
$620$	1.96182	0.0787887
$621$	0.0401173	0.00160985
$622$	20.1513	0.807992
$623$	−11.6448	−0.466538
$624$	0.00645319	0.000258334 0
$625$	1.00000	0.0400000
$626$	30.5608	1.22145
$627$	0.0193809	0.000773997 0
$628$	−7.80102	−0.311295
$629$	−1.27656	−0.0508997
$630$	−6.65147	−0.265001
$631$	2.20085	0.0876144	0.0438072	−	0.999040i	$-0.486051\pi$
$631$	2.20085	0.0876144	0.0438072	+	0.999040i	$0.486051\pi$
$632$	−28.2844	−1.12509
$633$	0.0502551	0.00199746
$634$	−32.9256	−1.30764
$635$	−10.6430	−0.422356
$636$	−0.133551	−0.00529563
$637$	−20.2727	−0.803235
$638$	−21.1434	−0.837074
$639$	30.5952	1.21033
$640$	19.4889	0.770367
$641$	−22.6127	−0.893147	−0.446574	−	0.894747i	$-0.647356\pi$
$641$	−22.6127	−0.893147	−0.446574	+	0.894747i	$0.647356\pi$
$642$	0.0826015	0.00326002
$643$	−6.98630	−0.275513	−0.137756	−	0.990466i	$-0.543989\pi$
$643$	−6.98630	−0.275513	−0.137756	+	0.990466i	$0.543989\pi$
$644$	7.23810	0.285221
$645$	0.0127413	0.000501687 0
$646$	−2.06722	−0.0813337
$647$	−44.0709	−1.73260	−0.866302	−	0.499520i	$-0.833510\pi$
$647$	−44.0709	−1.73260	−0.866302	+	0.499520i	$0.833510\pi$
$648$	−28.7339	−1.12877
$649$	33.4434	1.31277
$650$	−7.72437	−0.302975
$651$	−0.00165684	−6.49369e−5 0
$652$	−83.2590	−3.26067
$653$	39.9733	1.56428	0.782139	−	0.623105i	$-0.214129\pi$
$653$	39.9733	1.56428	0.782139	+	0.623105i	$0.214129\pi$
$654$	−0.0346241	−0.00135391
$655$	−3.23179	−0.126276
$656$	−4.66644	−0.182194
$657$	−10.5830	−0.412882
$658$	−19.9924	−0.779386
$659$	−39.4124	−1.53529	−0.767644	−	0.640876i	$-0.778571\pi$
$659$	−39.4124	−1.53529	−0.767644	+	0.640876i	$0.778571\pi$
$660$	0.0650740	0.00253300
$661$	29.4339	1.14485	0.572423	−	0.819958i	$-0.306004\pi$
$661$	29.4339	1.14485	0.572423	+	0.819958i	$0.306004\pi$
$662$	23.4810	0.912614
$663$	0.00880733	0.000342049 0
$664$	7.23318	0.280702
$665$	−0.961639	−0.0372908
$666$	−10.0180	−0.388190
$667$	−3.16371	−0.122499
$668$	−1.15321	−0.0446190
$669$	0.00526552	0.000203577 0
$670$	30.9019	1.19384
$671$	−80.7933	−3.11899
$672$	−0.0139154	−0.000536799 0
$673$	30.1645	1.16276	0.581378	−	0.813633i	$-0.302514\pi$
$673$	30.1645	1.16276	0.581378	+	0.813633i	$0.302514\pi$
$674$	33.7540	1.30015
$675$	−0.0178959	−0.000688814 0
$676$	−6.42692	−0.247189
$677$	−0.0222922	−0.000856757 0	−0.000428379	−	1.00000i	$-0.500136\pi$
$677$	−0.0222922	−0.000856757 0	−0.000428379		1.00000i	$0.500136\pi$
$678$	0.113160	0.00434589
$679$	−2.42305	−0.0929880
$680$	−2.83008	−0.108529
$681$	0.0453137	0.00173643
$682$	−8.70364	−0.333280
$683$	10.1915	0.389968	0.194984	−	0.980806i	$-0.437535\pi$
$683$	10.1915	0.389968	0.194984	+	0.980806i	$0.437535\pi$
$684$	−10.1886	−0.389570
$685$	4.93467	0.188544
$686$	−29.0132	−1.10773
$687$	−0.0420298	−0.00160354
$688$	2.77449	0.105776
$689$	−44.1700	−1.68274
$690$	0.0155041	0.000590230 0
$691$	27.5852	1.04939	0.524695	−	0.851291i	$-0.324180\pi$
$691$	27.5852	1.04939	0.524695	+	0.851291i	$0.324180\pi$
$692$	−44.5429	−1.69327
$693$	18.5329	0.704007
$694$	44.5821	1.69231
$695$	5.17448	0.196279
$696$	−0.0134394	−0.000509417 0
$697$	−6.36877	−0.241234
$698$	14.9412	0.565533
$699$	−0.0101978	−0.000385717 0
$700$	−3.22884	−0.122039
$701$	−12.0342	−0.454525	−0.227262	−	0.973834i	$-0.572977\pi$
$701$	−12.0342	−0.454525	−0.227262	+	0.973834i	$0.572977\pi$
$702$	0.138235	0.00521733
$703$	−1.44836	−0.0546259
$704$	−81.4922	−3.07135
$705$	−0.0268950	−0.00101292
$706$	13.8726	0.522103
$707$	16.7361	0.629428
$708$	0.0521359	0.00195939
$709$	12.7140	0.477483	0.238742	−	0.971083i	$-0.423265\pi$
$709$	12.7140	0.477483	0.238742	+	0.971083i	$0.423265\pi$
$710$	23.6482	0.887501
$711$	−26.5773	−0.996727
$712$	−38.8825	−1.45718
$713$	−1.30234	−0.0487730
$714$	0.00586197	0.000219379 0
$715$	21.5223	0.804889
$716$	2.58135	0.0964696
$717$	0.0530156	0.00197990
$718$	−32.0076	−1.19451
$719$	3.58696	0.133771	0.0668856	−	0.997761i	$-0.478694\pi$
$719$	3.58696	0.133771	0.0668856	+	0.997761i	$0.478694\pi$
$720$	−1.94847	−0.0726150
$721$	5.65439	0.210580
$722$	41.7119	1.55236
$723$	−0.0818380	−0.00304359
$724$	−59.0946	−2.19623
$725$	1.41130	0.0524143
$726$	−0.212623	−0.00789119
$727$	5.30994	0.196935	0.0984673	−	0.995140i	$-0.468606\pi$
$727$	5.30994	0.196935	0.0984673	+	0.995140i	$0.468606\pi$
$728$	10.1692	0.376896
$729$	−26.9995	−0.999982
$730$	−8.17999	−0.302755
$731$	3.78663	0.140053
$732$	−0.125951	−0.00465528
$733$	−19.7765	−0.730463	−0.365231	−	0.930917i	$-0.619010\pi$
$733$	−19.7765	−0.730463	−0.365231	+	0.930917i	$0.619010\pi$
$734$	83.0494	3.06541
$735$	−0.0181517	−0.000669535 0
$736$	−10.9380	−0.403180
$737$	−86.1015	−3.17159
$738$	−49.9801	−1.83979
$739$	−51.3719	−1.88975	−0.944873	−	0.327437i	$-0.893815\pi$
$739$	−51.3719	−1.88975	−0.944873	+	0.327437i	$0.893815\pi$
$740$	−4.86308	−0.178770
$741$	0.00999265	0.000367089 0
$742$	−29.3986	−1.07926
$743$	0.292029	0.0107135	0.00535676	−	0.999986i	$-0.498295\pi$
$743$	0.292029	0.0107135	0.00535676	+	0.999986i	$0.498295\pi$
$744$	−0.00553229	−0.000202824 0
$745$	22.6629	0.830303
$746$	−79.1432	−2.89764
$747$	6.79662	0.248675
$748$	19.3396	0.707126
$749$	11.4197	0.417265
$750$	−0.00691620	−0.000252544 0
$751$	7.23130	0.263874	0.131937	−	0.991258i	$-0.457880\pi$
$751$	7.23130	0.263874	0.131937	+	0.991258i	$0.457880\pi$
$752$	−5.85654	−0.213566
$753$	−0.0507735	−0.00185029
$754$	−10.9014	−0.397005
$755$	16.1443	0.587552
$756$	0.0577830	0.00210155
$757$	−6.13742	−0.223068	−0.111534	−	0.993761i	$-0.535576\pi$
$757$	−6.13742	−0.223068	−0.111534	+	0.993761i	$0.535576\pi$
$758$	17.8669	0.648956
$759$	−0.0431988	−0.00156802
$760$	−3.21096	−0.116474
$761$	−15.7055	−0.569322	−0.284661	−	0.958628i	$-0.591881\pi$
$761$	−15.7055	−0.569322	−0.284661	+	0.958628i	$0.591881\pi$
$762$	0.0736094	0.00266659
$763$	−4.78678	−0.173293
$764$	52.6673	1.90544
$765$	−2.65927	−0.0961462
$766$	−47.5177	−1.71689
$767$	17.2432	0.622617
$768$	−0.0595477	−0.00214874
$769$	−21.0472	−0.758982	−0.379491	−	0.925195i	$-0.623901\pi$
$769$	−21.0472	−0.758982	−0.379491	+	0.925195i	$0.623901\pi$
$770$	14.3248	0.516229
$771$	−0.0178387	−0.000642446 0
$772$	−45.2204	−1.62752
$773$	−13.4369	−0.483291	−0.241645	−	0.970365i	$-0.577687\pi$
$773$	−13.4369	−0.483291	−0.241645	+	0.970365i	$0.577687\pi$
$774$	29.7163	1.06813
$775$	0.580960	0.0208687
$776$	−8.09068	−0.290438
$777$	0.00410708	0.000147341 0
$778$	−20.6403	−0.739989
$779$	−7.22590	−0.258895
$780$	0.0335518	0.00120135
$781$	−65.8907	−2.35775
$782$	4.60771	0.164772
$783$	−0.0252565	−0.000902593 0
$784$	−3.95264	−0.141166
$785$	−2.31014	−0.0824523
$786$	0.0223517	0.000797259 0
$787$	16.2511	0.579291	0.289645	−	0.957134i	$-0.406463\pi$
$787$	16.2511	0.579291	0.289645	+	0.957134i	$0.406463\pi$
$788$	8.29811	0.295608
$789$	0.0885655	0.00315302
$790$	−20.5426	−0.730873
$791$	15.6444	0.556250
$792$	61.8823	2.19889
$793$	−41.6566	−1.47927
$794$	−38.0660	−1.35091
$795$	−0.0395487	−0.00140265
$796$	−39.6325	−1.40474
$797$	−37.0423	−1.31210	−0.656052	−	0.754715i	$-0.727775\pi$
$797$	−37.0423	−1.31210	−0.656052	+	0.754715i	$0.727775\pi$
$798$	0.00665089	0.000235439 0
$799$	−7.99303	−0.282773
$800$	4.87933	0.172510
$801$	−36.5358	−1.29093
$802$	−32.2862	−1.14006
$803$	22.7918	0.804306
$804$	−0.134226	−0.00473379
$805$	2.14344	0.0755463
$806$	−4.48755	−0.158067
$807$	0.0260298	0.000916292 0
$808$	55.8829	1.96595
$809$	−23.7022	−0.833324	−0.416662	−	0.909062i	$-0.636800\pi$
$809$	−23.7022	−0.833324	−0.416662	+	0.909062i	$0.636800\pi$
$810$	−20.8691	−0.733265
$811$	−4.54814	−0.159707	−0.0798534	−	0.996807i	$-0.525445\pi$
$811$	−4.54814	−0.159707	−0.0798534	+	0.996807i	$0.525445\pi$
$812$	−4.55686	−0.159914
$813$	−0.00489039	−0.000171513 0
$814$	21.5751	0.756206
$815$	−24.6557	−0.863652
$816$	0.00171719	6.01138e−5 0
$817$	4.29624	0.150307
$818$	−76.9439	−2.69028
$819$	9.55545	0.333895
$820$	−24.2620	−0.847265
$821$	−34.7610	−1.21317	−0.606584	−	0.795020i	$-0.707461\pi$
$821$	−34.7610	−1.21317	−0.606584	+	0.795020i	$0.707461\pi$
$822$	−0.0341292	−0.00119039
$823$	−37.9994	−1.32458	−0.662288	−	0.749249i	$-0.730415\pi$
$823$	−37.9994	−1.32458	−0.662288	+	0.749249i	$0.730415\pi$
$824$	18.8803	0.657727
$825$	0.0192705	0.000670914 0
$826$	11.4767	0.399326
$827$	10.1684	0.353591	0.176796	−	0.984248i	$-0.443427\pi$
$827$	10.1684	0.353591	0.176796	+	0.984248i	$0.443427\pi$
$828$	22.7097	0.789217
$829$	33.2539	1.15496	0.577478	−	0.816406i	$-0.304037\pi$
$829$	33.2539	1.15496	0.577478	+	0.816406i	$0.304037\pi$
$830$	5.25336	0.182347
$831$	0.00700401	0.000242966 0
$832$	−42.0169	−1.45667
$833$	−5.39457	−0.186911
$834$	−0.0357877	−0.00123923
$835$	−0.341502	−0.0118182
$836$	21.9424	0.758893
$837$	−0.0103968	−0.000359366 0
$838$	−63.5839	−2.19647
$839$	−17.7244	−0.611914	−0.305957	−	0.952045i	$-0.598976\pi$
$839$	−17.7244	−0.611914	−0.305957	+	0.952045i	$0.598976\pi$
$840$	0.00910526	0.000314161 0
$841$	−27.0082	−0.931318
$842$	−19.4992	−0.671987
$843$	−0.0515554	−0.00177566
$844$	56.8972	1.95848
$845$	−1.90322	−0.0654728
$846$	−62.7268	−2.15659
$847$	−29.3952	−1.01003
$848$	−8.61196	−0.295736
$849$	0.00546759	0.000187647 0
$850$	−2.05545	−0.0705015
$851$	3.22831	0.110665
$852$	−0.102719	−0.00351909
$853$	−46.9791	−1.60853	−0.804266	−	0.594269i	$-0.797442\pi$
$853$	−46.9791	−1.60853	−0.804266	+	0.594269i	$0.797442\pi$
$854$	−27.7257	−0.948753
$855$	−3.01717	−0.103185
$856$	38.1309	1.30329
$857$	6.62983	0.226471	0.113235	−	0.993568i	$-0.463879\pi$
$857$	6.62983	0.226471	0.113235	+	0.993568i	$0.463879\pi$
$858$	−0.148853	−0.00508175
$859$	−39.9456	−1.36293	−0.681463	−	0.731853i	$-0.738656\pi$
$859$	−39.9456	−1.36293	−0.681463	+	0.731853i	$0.738656\pi$
$860$	14.4253	0.491897
$861$	0.0204903	0.000698308 0
$862$	−21.5546	−0.734154
$863$	16.9789	0.577969	0.288984	−	0.957334i	$-0.406682\pi$
$863$	16.9789	0.577969	0.288984	+	0.957334i	$0.406682\pi$
$864$	−0.0873200	−0.00297069
$865$	−13.1906	−0.448494
$866$	−51.4476	−1.74826
$867$	−0.0483615	−0.00164244
$868$	−1.87583	−0.0636697
$869$	57.2376	1.94165
$870$	−0.00976083	−0.000330923 0
$871$	−44.3934	−1.50421
$872$	−15.9833	−0.541263
$873$	−7.60237	−0.257301
$874$	5.22784	0.176834
$875$	−0.956165	−0.0323243
$876$	0.0355308	0.00120048
$877$	−11.0030	−0.371546	−0.185773	−	0.982593i	$-0.559479\pi$
$877$	−11.0030	−0.371546	−0.185773	+	0.982593i	$0.559479\pi$
$878$	−49.0302	−1.65469
$879$	0.0139184	0.000469456 0
$880$	4.19627	0.141456
$881$	19.3697	0.652581	0.326290	−	0.945270i	$-0.394201\pi$
$881$	19.3697	0.652581	0.326290	+	0.945270i	$0.394201\pi$
$882$	−42.3349	−1.42549
$883$	18.2106	0.612836	0.306418	−	0.951897i	$-0.400869\pi$
$883$	18.2106	0.612836	0.306418	+	0.951897i	$0.400869\pi$
$884$	9.97138	0.335374
$885$	0.0154391	0.000518981 0
$886$	22.4103	0.752890
$887$	−19.5294	−0.655732	−0.327866	−	0.944724i	$-0.606329\pi$
$887$	−19.5294	−0.655732	−0.327866	+	0.944724i	$0.606329\pi$
$888$	0.0137138	0.000460204 0
$889$	10.1765	0.341309
$890$	−28.2399	−0.946603
$891$	58.1473	1.94801
$892$	5.96145	0.199604
$893$	−9.06875	−0.303474
$894$	−0.156741	−0.00524220
$895$	0.764422	0.0255518
$896$	−18.6346	−0.622539
$897$	−0.0222730	−0.000743675 0
$898$	−23.7470	−0.792447
$899$	0.819908	0.0273455
$900$	−10.1306	−0.337686
$901$	−11.7536	−0.391570
$902$	107.639	3.58397
$903$	−0.0121828	−0.000405417 0
$904$	52.2374	1.73739
$905$	−17.4998	−0.581714
$906$	−0.111657	−0.00370957
$907$	5.89187	0.195636	0.0978182	−	0.995204i	$-0.468814\pi$
$907$	5.89187	0.195636	0.0978182	+	0.995204i	$0.468814\pi$
$908$	51.3027	1.70254
$909$	52.5101	1.74165
$910$	7.38577	0.244836
$911$	−24.2231	−0.802549	−0.401274	−	0.915958i	$-0.631433\pi$
$911$	−24.2231	−0.802549	−0.401274	+	0.915958i	$0.631433\pi$
$912$	0.00194830	6.45146e−5 0
$913$	−14.6374	−0.484427
$914$	82.0229	2.71308
$915$	−0.0372982	−0.00123304
$916$	−47.5848	−1.57225
$917$	3.09012	0.102045
$918$	0.0367842	0.00121406
$919$	6.22212	0.205249	0.102624	−	0.994720i	$-0.467276\pi$
$919$	6.22212	0.205249	0.102624	+	0.994720i	$0.467276\pi$
$920$	7.15705	0.235961
$921$	0.00480030	0.000158175 0
$922$	48.8952	1.61028
$923$	−33.9728	−1.11823
$924$	−0.0622215	−0.00204694
$925$	−1.44012	−0.0473507
$926$	−12.5988	−0.414023
$927$	17.7408	0.582684
$928$	6.88619	0.226050
$929$	23.0497	0.756237	0.378119	−	0.925757i	$-0.376571\pi$
$929$	23.0497	0.756237	0.378119	+	0.925757i	$0.376571\pi$
$930$	−0.00401803	−0.000131757 0
$931$	−6.12059	−0.200594
$932$	−11.5456	−0.378190
$933$	−0.0259203	−0.000848594 0
$934$	−51.9720	−1.70058
$935$	5.72708	0.187296
$936$	31.9062	1.04289
$937$	−38.2100	−1.24827	−0.624133	−	0.781318i	$-0.714548\pi$
$937$	−38.2100	−1.24827	−0.624133	+	0.781318i	$0.714548\pi$
$938$	−29.5473	−0.964753
$939$	−0.0393100	−0.00128283
$940$	−30.4496	−0.993157
$941$	50.7872	1.65562	0.827808	−	0.561011i	$-0.189588\pi$
$941$	50.7872	1.65562	0.827808	+	0.561011i	$0.189588\pi$
$942$	0.0159774	0.000520571 0
$943$	16.1061	0.524487
$944$	3.36196	0.109423
$945$	0.0171114	0.000556635 0
$946$	−63.9978	−2.08075
$947$	53.4118	1.73565	0.867825	−	0.496871i	$-0.165518\pi$
$947$	53.4118	1.73565	0.867825	+	0.496871i	$0.165518\pi$
$948$	0.0892294	0.00289804
$949$	11.7513	0.381464
$950$	−2.33208	−0.0756627
$951$	0.0423518	0.00137335
$952$	2.70603	0.0877028
$953$	1.79165	0.0580373	0.0290186	−	0.999579i	$-0.490762\pi$
$953$	1.79165	0.0580373	0.0290186	+	0.999579i	$0.490762\pi$
$954$	−92.2388	−2.98634
$955$	15.5965	0.504691
$956$	60.0225	1.94127
$957$	0.0271965	0.000879138 0
$958$	−44.0779	−1.42409
$959$	−4.71836	−0.152364
$960$	−0.0376208	−0.00121421
$961$	−30.6625	−0.989112
$962$	11.1240	0.358652
$963$	35.8295	1.15459
$964$	−92.6543	−2.98419
$965$	−13.3912	−0.431079
$966$	−0.0148245	−0.000476969 0
$967$	−30.8211	−0.991138	−0.495569	−	0.868568i	$-0.665041\pi$
$967$	−30.8211	−0.991138	−0.495569	+	0.868568i	$0.665041\pi$
$968$	−98.1520	−3.15472
$969$	0.00265904	8.54208e−5 0
$970$	−5.87616	−0.188672
$971$	−16.0277	−0.514354	−0.257177	−	0.966364i	$-0.582792\pi$
$971$	−16.0277	−0.514354	−0.257177	+	0.966364i	$0.582792\pi$
$972$	0.271944	0.00872260
$973$	−4.94765	−0.158614
$974$	11.5293	0.369422
$975$	0.00993577	0.000318199 0
$976$	−8.12190	−0.259976
$977$	22.5322	0.720871	0.360435	−	0.932784i	$-0.382628\pi$
$977$	22.5322	0.720871	0.360435	+	0.932784i	$0.382628\pi$
$978$	0.170524	0.00545275
$979$	78.6845	2.51477
$980$	−20.5508	−0.656470
$981$	−15.0186	−0.479508
$982$	−47.2893	−1.50906
$983$	−35.1157	−1.12002	−0.560008	−	0.828487i	$-0.689202\pi$
$983$	−35.1157	−1.12002	−0.560008	+	0.828487i	$0.689202\pi$
$984$	0.0684182	0.00218109
$985$	2.45734	0.0782974
$986$	−2.90086	−0.0923822
$987$	0.0257160	0.000818551 0
$988$	11.3134	0.359926
$989$	−9.57608	−0.304502
$990$	44.9444	1.42843
$991$	−37.8699	−1.20298	−0.601488	−	0.798882i	$-0.705425\pi$
$991$	−37.8699	−1.20298	−0.601488	+	0.798882i	$0.705425\pi$
$992$	2.83469	0.0900016
$993$	−0.0302033	−0.000958474 0
$994$	−22.6116	−0.717195
$995$	−11.7365	−0.372071
$996$	−0.0228186	−0.000723036 0
$997$	47.9326	1.51804	0.759021	−	0.651066i	$-0.225678\pi$
$997$	47.9326	1.51804	0.759021	+	0.651066i	$0.225678\pi$
$998$	−46.5621	−1.47390
$999$	0.0257722	0.000815395 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8045.2.a.c.1.17	✓	127

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8045.2.a.c.1.17	✓	127	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8045 = 5 \cdot 1609 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.31881 q^{2} +0.00298266 q^{3} +3.37687 q^{4} +1.00000 q^{5} -0.00691620 q^{6} -0.956165 q^{7} -3.19269 q^{8} -2.99999 q^{9} +O(q^{10})\)	\(q-2.31881 q^{2} +0.00298266 q^{3} +3.37687 q^{4} +1.00000 q^{5} -0.00691620 q^{6} -0.956165 q^{7} -3.19269 q^{8} -2.99999 q^{9} -2.31881 q^{10} +6.46086 q^{11} +0.0100720 q^{12} +3.33118 q^{13} +2.21716 q^{14} +0.00298266 q^{15} +0.649491 q^{16} +0.886427 q^{17} +6.95640 q^{18} +1.00573 q^{19} +3.37687 q^{20} -0.00285191 q^{21} -14.9815 q^{22} -2.24170 q^{23} -0.00952268 q^{24} +1.00000 q^{25} -7.72437 q^{26} -0.0178959 q^{27} -3.22884 q^{28} +1.41130 q^{29} -0.00691620 q^{30} +0.580960 q^{31} +4.87933 q^{32} +0.0192705 q^{33} -2.05545 q^{34} -0.956165 q^{35} -10.1306 q^{36} -1.44012 q^{37} -2.33208 q^{38} +0.00993577 q^{39} -3.19269 q^{40} -7.18477 q^{41} +0.00661303 q^{42} +4.27179 q^{43} +21.8175 q^{44} -2.99999 q^{45} +5.19808 q^{46} -9.01713 q^{47} +0.00193721 q^{48} -6.08575 q^{49} -2.31881 q^{50} +0.00264391 q^{51} +11.2490 q^{52} -13.2596 q^{53} +0.0414972 q^{54} +6.46086 q^{55} +3.05273 q^{56} +0.00299973 q^{57} -3.27253 q^{58} +5.17631 q^{59} +0.0100720 q^{60} -12.5050 q^{61} -1.34713 q^{62} +2.86849 q^{63} -12.6132 q^{64} +3.33118 q^{65} -0.0446846 q^{66} -13.3266 q^{67} +2.99334 q^{68} -0.00668623 q^{69} +2.21716 q^{70} -10.1984 q^{71} +9.57803 q^{72} +3.52767 q^{73} +3.33935 q^{74} +0.00298266 q^{75} +3.39620 q^{76} -6.17765 q^{77} -0.0230391 q^{78} +8.85913 q^{79} +0.649491 q^{80} +8.99992 q^{81} +16.6601 q^{82} -2.26555 q^{83} -0.00963052 q^{84} +0.886427 q^{85} -9.90545 q^{86} +0.00420942 q^{87} -20.6275 q^{88} +12.1786 q^{89} +6.95640 q^{90} -3.18516 q^{91} -7.56993 q^{92} +0.00173280 q^{93} +20.9090 q^{94} +1.00573 q^{95} +0.0145534 q^{96} +2.53413 q^{97} +14.1117 q^{98} -19.3825 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 127 q - 20 q^{2} - 31 q^{3} + 116 q^{4} + 127 q^{5} - 17 q^{6} - 63 q^{7} - 57 q^{8} + 122 q^{9}+O(q^{10}) \) 127 * q - 20 * q^2 - 31 * q^3 + 116 * q^4 + 127 * q^5 - 17 * q^6 - 63 * q^7 - 57 * q^8 + 122 * q^9	\( 127 q - 20 q^{2} - 31 q^{3} + 116 q^{4} + 127 q^{5} - 17 q^{6} - 63 q^{7} - 57 q^{8} + 122 q^{9} - 20 q^{10} - 32 q^{11} - 65 q^{12} - 49 q^{13} - 4 q^{14} - 31 q^{15} + 98 q^{16} - 53 q^{17} - 60 q^{18} - 126 q^{19} + 116 q^{20} - 24 q^{21} - 46 q^{22} - 121 q^{23} - 51 q^{24} + 127 q^{25} - 9 q^{26} - 112 q^{27} - 123 q^{28} - 6 q^{29} - 17 q^{30} - 54 q^{31} - 119 q^{32} - 57 q^{33} - 53 q^{34} - 63 q^{35} + 133 q^{36} - 61 q^{37} - 27 q^{38} - 33 q^{39} - 57 q^{40} - 8 q^{41} - 46 q^{42} - 208 q^{43} - 54 q^{44} + 122 q^{45} - 34 q^{46} - 116 q^{47} - 106 q^{48} + 110 q^{49} - 20 q^{50} - 54 q^{51} - 142 q^{52} - 60 q^{53} - 62 q^{54} - 32 q^{55} + 33 q^{56} - 56 q^{57} - 87 q^{58} - 53 q^{59} - 65 q^{60} - 76 q^{61} - 84 q^{62} - 215 q^{63} + 67 q^{64} - 49 q^{65} + 9 q^{66} - 145 q^{67} - 133 q^{68} + q^{69} - 4 q^{70} - 4 q^{71} - 167 q^{72} - 155 q^{73} - 14 q^{74} - 31 q^{75} - 199 q^{76} - 97 q^{77} - 24 q^{78} - 73 q^{79} + 98 q^{80} + 127 q^{81} - 69 q^{82} - 225 q^{83} - 59 q^{84} - 53 q^{85} + 30 q^{86} - 179 q^{87} - 119 q^{88} - 25 q^{89} - 60 q^{90} - 160 q^{91} - 188 q^{92} - 44 q^{93} - 32 q^{94} - 126 q^{95} - 43 q^{96} - 72 q^{97} - 111 q^{98} - 141 q^{99}+O(q^{100}) \) 127 * q - 20 * q^2 - 31 * q^3 + 116 * q^4 + 127 * q^5 - 17 * q^6 - 63 * q^7 - 57 * q^8 + 122 * q^9 - 20 * q^10 - 32 * q^11 - 65 * q^12 - 49 * q^13 - 4 * q^14 - 31 * q^15 + 98 * q^16 - 53 * q^17 - 60 * q^18 - 126 * q^19 + 116 * q^20 - 24 * q^21 - 46 * q^22 - 121 * q^23 - 51 * q^24 + 127 * q^25 - 9 * q^26 - 112 * q^27 - 123 * q^28 - 6 * q^29 - 17 * q^30 - 54 * q^31 - 119 * q^32 - 57 * q^33 - 53 * q^34 - 63 * q^35 + 133 * q^36 - 61 * q^37 - 27 * q^38 - 33 * q^39 - 57 * q^40 - 8 * q^41 - 46 * q^42 - 208 * q^43 - 54 * q^44 + 122 * q^45 - 34 * q^46 - 116 * q^47 - 106 * q^48 + 110 * q^49 - 20 * q^50 - 54 * q^51 - 142 * q^52 - 60 * q^53 - 62 * q^54 - 32 * q^55 + 33 * q^56 - 56 * q^57 - 87 * q^58 - 53 * q^59 - 65 * q^60 - 76 * q^61 - 84 * q^62 - 215 * q^63 + 67 * q^64 - 49 * q^65 + 9 * q^66 - 145 * q^67 - 133 * q^68 + q^69 - 4 * q^70 - 4 * q^71 - 167 * q^72 - 155 * q^73 - 14 * q^74 - 31 * q^75 - 199 * q^76 - 97 * q^77 - 24 * q^78 - 73 * q^79 + 98 * q^80 + 127 * q^81 - 69 * q^82 - 225 * q^83 - 59 * q^84 - 53 * q^85 + 30 * q^86 - 179 * q^87 - 119 * q^88 - 25 * q^89 - 60 * q^90 - 160 * q^91 - 188 * q^92 - 44 * q^93 - 32 * q^94 - 126 * q^95 - 43 * q^96 - 72 * q^97 - 111 * q^98 - 141 * q^99

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