LMFDB - Embedded newform 37.10.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,10,Mod(1,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("37.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	37.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:	$19.0563259381$
Analytic rank:	$1$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 6 x^{12} - 4637 x^{11} + 28852 x^{10} + 8006690 x^{9} - 52024972 x^{8} - 6415977160 x^{7} + \cdots - 99\!\cdots\!00 $ x^13 - 6x^12 - 4637x^11 + 28852x^10 + 8006690x^9 - 52024972x^8 - 6415977160x^7 + 44300013488x^6 + 2423840779488x^5 - 17813618433600x^4 - 361730826790528x^3 + 2726168160579840x^2 + 5682998922854400x - 9999214456320000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-36.3196$ of defining polynomial
Character	$\chi$	$=$	37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+34.3196 q^{2} -129.318 q^{3} +665.837 q^{4} -1076.40 q^{5} -4438.14 q^{6} +9336.44 q^{7} +5279.62 q^{8} -2959.93 q^{9} +O(q^{10})$	\(q+34.3196 q^{2} -129.318 q^{3} +665.837 q^{4} -1076.40 q^{5} -4438.14 q^{6} +9336.44 q^{7} +5279.62 q^{8} -2959.93 q^{9} -36941.6 q^{10} -58047.3 q^{11} -86104.5 q^{12} -108005. q^{13} +320423. q^{14} +139197. q^{15} -159714. q^{16} -668634. q^{17} -101584. q^{18} -243278. q^{19} -716706. q^{20} -1.20737e6 q^{21} -1.99216e6 q^{22} +2.32530e6 q^{23} -682749. q^{24} -794490. q^{25} -3.70670e6 q^{26} +2.92813e6 q^{27} +6.21655e6 q^{28} +2.01991e6 q^{29} +4.77721e6 q^{30} +8.33762e6 q^{31} -8.18448e6 q^{32} +7.50654e6 q^{33} -2.29473e7 q^{34} -1.00497e7 q^{35} -1.97083e6 q^{36} -1.87416e6 q^{37} -8.34923e6 q^{38} +1.39670e7 q^{39} -5.68298e6 q^{40} -7.34580e6 q^{41} -4.14364e7 q^{42} -8.69984e6 q^{43} -3.86500e7 q^{44} +3.18607e6 q^{45} +7.98035e7 q^{46} -4.36777e7 q^{47} +2.06538e7 q^{48} +4.68155e7 q^{49} -2.72666e7 q^{50} +8.64662e7 q^{51} -7.19139e7 q^{52} -2.04504e7 q^{53} +1.00492e8 q^{54} +6.24820e7 q^{55} +4.92929e7 q^{56} +3.14602e7 q^{57} +6.93225e7 q^{58} -1.49555e7 q^{59} +9.26828e7 q^{60} -1.03469e8 q^{61} +2.86144e8 q^{62} -2.76352e7 q^{63} -1.99115e8 q^{64} +1.16257e8 q^{65} +2.57622e8 q^{66} +1.75352e8 q^{67} -4.45201e8 q^{68} -3.00703e8 q^{69} -3.44903e8 q^{70} +6.24089e7 q^{71} -1.56273e7 q^{72} +4.17335e8 q^{73} -6.43205e7 q^{74} +1.02742e8 q^{75} -1.61984e8 q^{76} -5.41955e8 q^{77} +4.79342e8 q^{78} +2.96492e8 q^{79} +1.71916e8 q^{80} -3.20399e8 q^{81} -2.52105e8 q^{82} -8.94658e7 q^{83} -8.03910e8 q^{84} +7.19717e8 q^{85} -2.98575e8 q^{86} -2.61210e8 q^{87} -3.06468e8 q^{88} -9.24749e8 q^{89} +1.09345e8 q^{90} -1.00838e9 q^{91} +1.54827e9 q^{92} -1.07820e9 q^{93} -1.49900e9 q^{94} +2.61865e8 q^{95} +1.05840e9 q^{96} -6.81238e8 q^{97} +1.60669e9 q^{98} +1.71816e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 32 q^{2} - 251 q^{3} + 2730 q^{4} - 2159 q^{5} - 4401 q^{6} - 12576 q^{7} - 20394 q^{8} + 69112 q^{9}+O(q^{10}) $ 13 * q - 32 * q^2 - 251 * q^3 + 2730 * q^4 - 2159 * q^5 - 4401 * q^6 - 12576 * q^7 - 20394 * q^8 + 69112 * q^9	\( 13 q - 32 q^{2} - 251 q^{3} + 2730 q^{4} - 2159 q^{5} - 4401 q^{6} - 12576 q^{7} - 20394 q^{8} + 69112 q^{9} - 106605 q^{10} - 112451 q^{11} + 220963 q^{12} + 7129 q^{13} + 294824 q^{14} - 63644 q^{15} + 145178 q^{16} - 890862 q^{17} - 3066225 q^{18} - 1435874 q^{19} - 3193339 q^{20} - 4745036 q^{21} - 4350913 q^{22} - 2565799 q^{23} - 15286101 q^{24} - 1828304 q^{25} - 7543133 q^{26} - 10134680 q^{27} - 24344602 q^{28} - 2992323 q^{29} - 25604140 q^{30} - 8242245 q^{31} - 22320310 q^{32} - 18079398 q^{33} + 5045920 q^{34} - 26953204 q^{35} - 10407455 q^{36} - 24364093 q^{37} - 42175680 q^{38} - 79430765 q^{39} - 61032223 q^{40} - 50975109 q^{41} + 54850616 q^{42} - 18142836 q^{43} - 55265137 q^{44} + 136868596 q^{45} + 157343401 q^{46} - 14353596 q^{47} + 213610631 q^{48} + 213271999 q^{49} + 175451561 q^{50} + 151710418 q^{51} + 151573285 q^{52} + 74438872 q^{53} + 174228132 q^{54} + 118316889 q^{55} + 362406090 q^{56} + 248282906 q^{57} + 206405719 q^{58} - 251964328 q^{59} + 877937048 q^{60} + 202847323 q^{61} - 34418509 q^{62} - 227178410 q^{63} + 187231490 q^{64} - 341466470 q^{65} + 989905110 q^{66} - 12257509 q^{67} - 332496576 q^{68} - 768097033 q^{69} + 1098443332 q^{70} - 310979094 q^{71} - 588411507 q^{72} - 249752015 q^{73} + 59973152 q^{74} - 634307724 q^{75} + 365061440 q^{76} - 1143945802 q^{77} + 1471186393 q^{78} + 30429049 q^{79} + 885873041 q^{80} - 350972903 q^{81} - 1192633571 q^{82} - 2559788658 q^{83} - 2510580834 q^{84} - 3291393166 q^{85} - 1373534302 q^{86} - 1215098129 q^{87} + 107941215 q^{88} - 3063565514 q^{89} - 552233182 q^{90} - 1743876566 q^{91} - 2937303341 q^{92} - 1077794354 q^{93} + 49542148 q^{94} - 2168155374 q^{95} - 1504910121 q^{96} - 429307758 q^{97} - 1351241634 q^{98} - 3266142174 q^{99}+O(q^{100}) \) 13 * q - 32 * q^2 - 251 * q^3 + 2730 * q^4 - 2159 * q^5 - 4401 * q^6 - 12576 * q^7 - 20394 * q^8 + 69112 * q^9 - 106605 * q^10 - 112451 * q^11 + 220963 * q^12 + 7129 * q^13 + 294824 * q^14 - 63644 * q^15 + 145178 * q^16 - 890862 * q^17 - 3066225 * q^18 - 1435874 * q^19 - 3193339 * q^20 - 4745036 * q^21 - 4350913 * q^22 - 2565799 * q^23 - 15286101 * q^24 - 1828304 * q^25 - 7543133 * q^26 - 10134680 * q^27 - 24344602 * q^28 - 2992323 * q^29 - 25604140 * q^30 - 8242245 * q^31 - 22320310 * q^32 - 18079398 * q^33 + 5045920 * q^34 - 26953204 * q^35 - 10407455 * q^36 - 24364093 * q^37 - 42175680 * q^38 - 79430765 * q^39 - 61032223 * q^40 - 50975109 * q^41 + 54850616 * q^42 - 18142836 * q^43 - 55265137 * q^44 + 136868596 * q^45 + 157343401 * q^46 - 14353596 * q^47 + 213610631 * q^48 + 213271999 * q^49 + 175451561 * q^50 + 151710418 * q^51 + 151573285 * q^52 + 74438872 * q^53 + 174228132 * q^54 + 118316889 * q^55 + 362406090 * q^56 + 248282906 * q^57 + 206405719 * q^58 - 251964328 * q^59 + 877937048 * q^60 + 202847323 * q^61 - 34418509 * q^62 - 227178410 * q^63 + 187231490 * q^64 - 341466470 * q^65 + 989905110 * q^66 - 12257509 * q^67 - 332496576 * q^68 - 768097033 * q^69 + 1098443332 * q^70 - 310979094 * q^71 - 588411507 * q^72 - 249752015 * q^73 + 59973152 * q^74 - 634307724 * q^75 + 365061440 * q^76 - 1143945802 * q^77 + 1471186393 * q^78 + 30429049 * q^79 + 885873041 * q^80 - 350972903 * q^81 - 1192633571 * q^82 - 2559788658 * q^83 - 2510580834 * q^84 - 3291393166 * q^85 - 1373534302 * q^86 - 1215098129 * q^87 + 107941215 * q^88 - 3063565514 * q^89 - 552233182 * q^90 - 1743876566 * q^91 - 2937303341 * q^92 - 1077794354 * q^93 + 49542148 * q^94 - 2168155374 * q^95 - 1504910121 * q^96 - 429307758 * q^97 - 1351241634 * q^98 - 3266142174 * 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 $

$2$	34.3196	1.51673	0.758364	−	0.651832i	$-0.225999\pi$
$2$	34.3196	1.51673	0.758364	+	0.651832i	$0.225999\pi$
$3$	−129.318	−0.921748	−0.460874	−	0.887466i	$-0.652464\pi$
$3$	−129.318	−0.921748	−0.460874	+	0.887466i	$0.652464\pi$
$4$	665.837	1.30046
$5$	−1076.40	−0.770209	−0.385104	−	0.922873i	$-0.625835\pi$
$5$	−1076.40	−0.770209	−0.385104	+	0.922873i	$0.625835\pi$
$6$	−4438.14	−1.39804
$7$	9336.44	1.46974	0.734869	−	0.678209i	$-0.237243\pi$
$7$	9336.44	1.46974	0.734869	+	0.678209i	$0.237243\pi$
$8$	5279.62	0.455720
$9$	−2959.93	−0.150380
$10$	−36941.6	−1.16820
$11$	−58047.3	−1.19540	−0.597702	−	0.801718i	$-0.703919\pi$
$11$	−58047.3	−1.19540	−0.597702	+	0.801718i	$0.703919\pi$
$12$	−86104.5	−1.19870
$13$	−108005.	−1.04882	−0.524409	−	0.851467i	$-0.675714\pi$
$13$	−108005.	−1.04882	−0.524409	+	0.851467i	$0.675714\pi$
$14$	320423.	2.22919
$15$	139197.	0.709938
$16$	−159714.	−0.609260
$17$	−668634.	−1.94164	−0.970819	−	0.239814i	$-0.922914\pi$
$17$	−668634.	−1.94164	−0.970819	+	0.239814i	$0.922914\pi$
$18$	−101584.	−0.228086
$19$	−243278.	−0.428265	−0.214132	−	0.976805i	$-0.568692\pi$
$19$	−243278.	−0.428265	−0.214132	+	0.976805i	$0.568692\pi$
$20$	−716706.	−1.00163
$21$	−1.20737e6	−1.35473
$22$	−1.99216e6	−1.81310
$23$	2.32530e6	1.73262	0.866311	−	0.499505i	$-0.166485\pi$
$23$	2.32530e6	1.73262	0.866311	+	0.499505i	$0.166485\pi$
$24$	−682749.	−0.420059
$25$	−794490.	−0.406779
$26$	−3.70670e6	−1.59077
$27$	2.92813e6	1.06036
$28$	6.21655e6	1.91134
$29$	2.01991e6	0.530323	0.265161	−	0.964204i	$-0.414575\pi$
$29$	2.01991e6	0.530323	0.265161	+	0.964204i	$0.414575\pi$
$30$	4.77721e6	1.07678
$31$	8.33762e6	1.62149	0.810745	−	0.585399i	$-0.199062\pi$
$31$	8.33762e6	1.62149	0.810745	+	0.585399i	$0.199062\pi$
$32$	−8.18448e6	−1.37980
$33$	7.50654e6	1.10186
$34$	−2.29473e7	−2.94494
$35$	−1.00497e7	−1.13201
$36$	−1.97083e6	−0.195564
$37$	−1.87416e6	−0.164399
$37$	−1.87416e6	−0.164399
$38$	−8.34923e6	−0.649561
$39$	1.39670e7	0.966746
$40$	−5.68298e6	−0.351000
$41$	−7.34580e6	−0.405987	−0.202993	−	0.979180i	$-0.565067\pi$
$41$	−7.34580e6	−0.405987	−0.202993	+	0.979180i	$0.565067\pi$
$42$	−4.14364e7	−2.05476
$43$	−8.69984e6	−0.388064	−0.194032	−	0.980995i	$-0.562157\pi$
$43$	−8.69984e6	−0.388064	−0.194032	+	0.980995i	$0.562157\pi$
$44$	−3.86500e7	−1.55458
$45$	3.18607e6	0.115824
$46$	7.98035e7	2.62792
$47$	−4.36777e7	−1.30563	−0.652814	−	0.757518i	$-0.726412\pi$
$47$	−4.36777e7	−1.30563	−0.652814	+	0.757518i	$0.726412\pi$
$48$	2.06538e7	0.561584
$49$	4.68155e7	1.16013
$50$	−2.72666e7	−0.616972
$51$	8.64662e7	1.78970
$52$	−7.19139e7	−1.36395
$53$	−2.04504e7	−0.356009	−0.178004	−	0.984030i	$-0.556964\pi$
$53$	−2.04504e7	−0.356009	−0.178004	+	0.984030i	$0.556964\pi$
$54$	1.00492e8	1.60828
$55$	6.24820e7	0.920710
$56$	4.92929e7	0.669789
$57$	3.14602e7	0.394752
$58$	6.93225e7	0.804355
$59$	−1.49555e7	−0.160682	−0.0803408	−	0.996767i	$-0.525601\pi$
$59$	−1.49555e7	−0.160682	−0.0803408	+	0.996767i	$0.525601\pi$
$60$	9.26828e7	0.923248
$61$	−1.03469e8	−0.956807	−0.478403	−	0.878140i	$-0.658784\pi$
$61$	−1.03469e8	−0.956807	−0.478403	+	0.878140i	$0.658784\pi$
$62$	2.86144e8	2.45936
$63$	−2.76352e7	−0.221020
$64$	−1.99115e8	−1.48352
$65$	1.16257e8	0.807808
$66$	2.57622e8	1.67122
$67$	1.75352e8	1.06310	0.531549	−	0.847028i	$-0.321610\pi$
$67$	1.75352e8	1.06310	0.531549	+	0.847028i	$0.321610\pi$
$68$	−4.45201e8	−2.52503
$69$	−3.00703e8	−1.59704
$70$	−3.44903e8	−1.71694
$71$	6.24089e7	0.291464	0.145732	−	0.989324i	$-0.453446\pi$
$71$	6.24089e7	0.291464	0.145732	+	0.989324i	$0.453446\pi$
$72$	−1.56273e7	−0.0685313
$73$	4.17335e8	1.72001	0.860007	−	0.510282i	$-0.170459\pi$
$73$	4.17335e8	1.72001	0.860007	+	0.510282i	$0.170459\pi$
$74$	−6.43205e7	−0.249348
$75$	1.02742e8	0.374947
$76$	−1.61984e8	−0.556943
$77$	−5.41955e8	−1.75693
$78$	4.79342e8	1.46629
$79$	2.96492e8	0.856427	0.428214	−	0.903677i	$-0.359143\pi$
$79$	2.96492e8	0.856427	0.428214	+	0.903677i	$0.359143\pi$
$80$	1.71916e8	0.469257
$81$	−3.20399e8	−0.827006
$82$	−2.52105e8	−0.615771
$83$	−8.94658e7	−0.206921	−0.103461	−	0.994634i	$-0.532992\pi$
$83$	−8.94658e7	−0.206921	−0.103461	+	0.994634i	$0.532992\pi$
$84$	−8.03910e8	−1.76177
$85$	7.19717e8	1.49547
$86$	−2.98575e8	−0.588587
$87$	−2.61210e8	−0.488824
$88$	−3.06468e8	−0.544770
$89$	−9.24749e8	−1.56232	−0.781158	−	0.624333i	$-0.785371\pi$
$89$	−9.24749e8	−1.56232	−0.781158	+	0.624333i	$0.785371\pi$
$90$	1.09345e8	0.175674
$91$	−1.00838e9	−1.54149
$92$	1.54827e9	2.25321
$93$	−1.07820e9	−1.49461
$94$	−1.49900e9	−1.98028
$95$	2.61865e8	0.329853
$96$	1.05840e9	1.27183
$97$	−6.81238e8	−0.781315	−0.390658	−	0.920536i	$-0.627752\pi$
$97$	−6.81238e8	−0.781315	−0.390658	+	0.920536i	$0.627752\pi$
$98$	1.60669e9	1.75960
$99$	1.71816e8	0.179765
$100$	−5.29000e8	−0.529000
$101$	−8.72358e8	−0.834159	−0.417079	−	0.908870i	$-0.636946\pi$
$101$	−8.72358e8	−0.834159	−0.417079	+	0.908870i	$0.636946\pi$
$102$	2.96749e9	2.71449
$103$	−8.48087e7	−0.0742460	−0.0371230	−	0.999311i	$-0.511819\pi$
$103$	−8.48087e7	−0.0742460	−0.0371230	+	0.999311i	$0.511819\pi$
$104$	−5.70227e8	−0.477967
$105$	1.29961e9	1.04342
$106$	−7.01850e8	−0.539968
$107$	1.53011e9	1.12849	0.564243	−	0.825609i	$-0.309168\pi$
$107$	1.53011e9	1.12849	0.564243	+	0.825609i	$0.309168\pi$
$108$	1.94966e9	1.37896
$109$	−9.84674e8	−0.668149	−0.334074	−	0.942547i	$-0.608424\pi$
$109$	−9.84674e8	−0.668149	−0.334074	+	0.942547i	$0.608424\pi$
$110$	2.14436e9	1.39647
$111$	2.42362e8	0.151534
$112$	−1.49116e9	−0.895452
$113$	4.23223e8	0.244183	0.122092	−	0.992519i	$-0.461040\pi$
$113$	4.23223e8	0.244183	0.122092	+	0.992519i	$0.461040\pi$
$114$	1.07970e9	0.598732
$115$	−2.50295e9	−1.33448
$116$	1.34493e9	0.689665
$117$	3.19688e8	0.157721
$118$	−5.13267e8	−0.243710
$119$	−6.24266e9	−2.85370
$120$	7.34910e8	0.323533
$121$	1.01154e9	0.428991
$122$	−3.55100e9	−1.45121
$123$	9.49942e8	0.374217
$124$	5.55149e9	2.10869
$125$	2.95753e9	1.08351
$126$	−9.48431e8	−0.335227
$127$	−2.35378e9	−0.802876	−0.401438	−	0.915886i	$-0.631489\pi$
$127$	−2.35378e9	−0.802876	−0.401438	+	0.915886i	$0.631489\pi$
$128$	−2.64310e9	−0.870299
$129$	1.12504e9	0.357697
$130$	3.98989e9	1.22522
$131$	−3.81437e8	−0.113162	−0.0565812	−	0.998398i	$-0.518020\pi$
$131$	−3.81437e8	−0.113162	−0.0565812	+	0.998398i	$0.518020\pi$
$132$	4.99813e9	1.43293
$133$	−2.27136e9	−0.629438
$134$	6.01800e9	1.61243
$135$	−3.15184e9	−0.816699
$136$	−3.53014e9	−0.884843
$137$	5.95543e9	1.44434	0.722172	−	0.691714i	$-0.243144\pi$
$137$	5.95543e9	1.44434	0.722172	+	0.691714i	$0.243144\pi$
$138$	−1.03200e10	−2.42228
$139$	−5.54132e9	−1.25906	−0.629530	−	0.776976i	$-0.716753\pi$
$139$	−5.54132e9	−1.25906	−0.629530	+	0.776976i	$0.716753\pi$
$140$	−6.69149e9	−1.47213
$141$	5.64830e9	1.20346
$142$	2.14185e9	0.442071
$143$	6.26941e9	1.25376
$144$	4.72742e8	0.0916205
$145$	−2.17423e9	−0.408459
$146$	1.43228e10	2.60879
$147$	−6.05408e9	−1.06935
$148$	−1.24789e9	−0.213795
$149$	−1.13376e10	−1.88445	−0.942223	−	0.334986i	$-0.891268\pi$
$149$	−1.13376e10	−1.88445	−0.942223	+	0.334986i	$0.891268\pi$
$150$	3.52605e9	0.568693
$151$	2.20689e9	0.345450	0.172725	−	0.984970i	$-0.444743\pi$
$151$	2.20689e9	0.345450	0.172725	+	0.984970i	$0.444743\pi$
$152$	−1.28442e9	−0.195169
$153$	1.97911e9	0.291984
$154$	−1.85997e10	−2.66479
$155$	−8.97461e9	−1.24889
$156$	9.29974e9	1.25722
$157$	6.67257e8	0.0876485	0.0438243	−	0.999039i	$-0.486046\pi$
$157$	6.67257e8	0.0876485	0.0438243	+	0.999039i	$0.486046\pi$
$158$	1.01755e10	1.29897
$159$	2.64460e9	0.328150
$160$	8.80977e9	1.06273
$161$	2.17100e10	2.54650
$162$	−1.09960e10	−1.25434
$163$	4.54691e9	0.504513	0.252256	−	0.967660i	$-0.418827\pi$
$163$	4.54691e9	0.504513	0.252256	+	0.967660i	$0.418827\pi$
$164$	−4.89110e9	−0.527970
$165$	−8.08003e9	−0.848663
$166$	−3.07043e9	−0.313843
$167$	−1.23916e10	−1.23283	−0.616413	−	0.787423i	$-0.711415\pi$
$167$	−1.23916e10	−1.23283	−0.616413	+	0.787423i	$0.711415\pi$
$168$	−6.37445e9	−0.617377
$169$	1.06064e9	0.100018
$170$	2.47004e10	2.26822
$171$	7.20088e8	0.0644026
$172$	−5.79267e9	−0.504662
$173$	−1.67206e10	−1.41920	−0.709602	−	0.704603i	$-0.751125\pi$
$173$	−1.67206e10	−1.41920	−0.709602	+	0.704603i	$0.751125\pi$
$174$	−8.96462e9	−0.741413
$175$	−7.41770e9	−0.597858
$176$	9.27095e9	0.728311
$177$	1.93401e9	0.148108
$178$	−3.17371e10	−2.36961
$179$	−9.43404e9	−0.686846	−0.343423	−	0.939181i	$-0.611586\pi$
$179$	−9.43404e9	−0.686846	−0.343423	+	0.939181i	$0.611586\pi$
$180$	2.12140e9	0.150625
$181$	9.43961e9	0.653733	0.326867	−	0.945070i	$-0.394007\pi$
$181$	9.43961e9	0.653733	0.326867	+	0.945070i	$0.394007\pi$
$182$	−3.46074e10	−2.33802
$183$	1.33803e10	0.881935
$184$	1.22767e10	0.789591
$185$	2.01735e9	0.126622
$186$	−3.70035e10	−2.26691
$187$	3.88124e10	2.32104
$188$	−2.90822e10	−1.69792
$189$	2.73383e10	1.55845
$190$	8.98710e9	0.500298
$191$	1.33064e10	0.723453	0.361726	−	0.932284i	$-0.382187\pi$
$191$	1.33064e10	0.723453	0.361726	+	0.932284i	$0.382187\pi$
$192$	2.57491e10	1.36743
$193$	1.05626e10	0.547976	0.273988	−	0.961733i	$-0.411657\pi$
$193$	1.05626e10	0.547976	0.273988	+	0.961733i	$0.411657\pi$
$194$	−2.33798e10	−1.18504
$195$	−1.50341e10	−0.744596
$196$	3.11715e10	1.50871
$197$	−3.02661e10	−1.43172	−0.715861	−	0.698243i	$-0.753966\pi$
$197$	−3.02661e10	−1.43172	−0.715861	+	0.698243i	$0.753966\pi$
$198$	5.89666e9	0.272655
$199$	1.30242e10	0.588726	0.294363	−	0.955694i	$-0.404892\pi$
$199$	1.30242e10	0.588726	0.294363	+	0.955694i	$0.404892\pi$
$200$	−4.19461e9	−0.185377
$201$	−2.26761e10	−0.979909
$202$	−2.99390e10	−1.26519
$203$	1.88587e10	0.779436
$204$	5.75724e10	2.32744
$205$	7.90701e9	0.312694
$206$	−2.91060e9	−0.112611
$207$	−6.88273e9	−0.260552
$208$	1.72499e10	0.639002
$209$	1.41217e10	0.511950
$210$	4.46021e10	1.58259
$211$	−1.86716e10	−0.648502	−0.324251	−	0.945971i	$-0.605112\pi$
$211$	−1.86716e10	−0.648502	−0.324251	+	0.945971i	$0.605112\pi$
$212$	−1.36166e10	−0.462976
$213$	−8.07058e9	−0.268656
$214$	5.25129e10	1.71161
$215$	9.36450e9	0.298890
$216$	1.54594e10	0.483228
$217$	7.78437e10	2.38317
$218$	−3.37936e10	−1.01340
$219$	−5.39688e10	−1.58542
$220$	4.16028e10	1.19735
$221$	7.22160e10	2.03642
$222$	8.31778e9	0.229837
$223$	−1.12955e10	−0.305868	−0.152934	−	0.988236i	$-0.548872\pi$
$223$	−1.12955e10	−0.305868	−0.152934	+	0.988236i	$0.548872\pi$
$224$	−7.64139e10	−2.02795
$225$	2.35164e9	0.0611714
$226$	1.45249e10	0.370360
$227$	−2.45410e10	−0.613445	−0.306723	−	0.951799i	$-0.599232\pi$
$227$	−2.45410e10	−0.613445	−0.306723	+	0.951799i	$0.599232\pi$
$228$	2.09474e10	0.513361
$229$	3.55035e10	0.853123	0.426561	−	0.904459i	$-0.359725\pi$
$229$	3.55035e10	0.853123	0.426561	+	0.904459i	$0.359725\pi$
$230$	−8.59004e10	−2.02404
$231$	7.00844e10	1.61945
$232$	1.06644e10	0.241679
$233$	1.97421e10	0.438825	0.219413	−	0.975632i	$-0.429586\pi$
$233$	1.97421e10	0.438825	0.219413	+	0.975632i	$0.429586\pi$
$234$	1.09716e10	0.239220
$235$	4.70147e10	1.00561
$236$	−9.95791e9	−0.208961
$237$	−3.83416e10	−0.789410
$238$	−2.14246e11	−4.32829
$239$	−2.47767e10	−0.491194	−0.245597	−	0.969372i	$-0.578984\pi$
$239$	−2.47767e10	−0.491194	−0.245597	+	0.969372i	$0.578984\pi$
$240$	−2.22317e10	−0.432537
$241$	−1.01590e11	−1.93988	−0.969940	−	0.243343i	$-0.921756\pi$
$241$	−1.01590e11	−1.93988	−0.969940	+	0.243343i	$0.921756\pi$
$242$	3.47156e10	0.650662
$243$	−1.62012e10	−0.298070
$244$	−6.88932e10	−1.24429
$245$	−5.03922e10	−0.893544
$246$	3.26017e10	0.567586
$247$	2.62754e10	0.449172
$248$	4.40195e10	0.738946
$249$	1.15695e10	0.190729
$250$	1.01501e11	1.64339
$251$	−1.06726e11	−1.69722	−0.848612	−	0.529016i	$-0.822561\pi$
$251$	−1.06726e11	−1.69722	−0.848612	+	0.529016i	$0.822561\pi$
$252$	−1.84006e10	−0.287428
$253$	−1.34977e11	−2.07118
$254$	−8.07807e10	−1.21774
$255$	−9.30722e10	−1.37844
$256$	1.12368e10	0.163516
$257$	1.58787e10	0.227047	0.113524	−	0.993535i	$-0.463786\pi$
$257$	1.58787e10	0.227047	0.113524	+	0.993535i	$0.463786\pi$
$258$	3.86111e10	0.542529
$259$	−1.74980e10	−0.241624
$260$	7.74081e10	1.05052
$261$	−5.97879e9	−0.0797500
$262$	−1.30908e10	−0.171637
$263$	−6.87094e10	−0.885554	−0.442777	−	0.896632i	$-0.646007\pi$
$263$	−6.87094e10	−0.885554	−0.442777	+	0.896632i	$0.646007\pi$
$264$	3.96317e10	0.502140
$265$	2.20128e10	0.274201
$266$	−7.79521e10	−0.954685
$267$	1.19586e11	1.44006
$268$	1.16756e11	1.38252
$269$	−2.57655e10	−0.300022	−0.150011	−	0.988684i	$-0.547931\pi$
$269$	−2.57655e10	−0.300022	−0.150011	+	0.988684i	$0.547931\pi$
$270$	−1.08170e11	−1.23871
$271$	9.41053e10	1.05987	0.529934	−	0.848039i	$-0.322217\pi$
$271$	9.41053e10	1.05987	0.529934	+	0.848039i	$0.322217\pi$
$272$	1.06790e11	1.18296
$273$	1.30402e11	1.42086
$274$	2.04388e11	2.19068
$275$	4.61179e10	0.486265
$276$	−2.00219e11	−2.07689
$277$	−2.17075e10	−0.221540	−0.110770	−	0.993846i	$-0.535332\pi$
$277$	−2.17075e10	−0.221540	−0.110770	+	0.993846i	$0.535332\pi$
$278$	−1.90176e11	−1.90965
$279$	−2.46788e10	−0.243840
$280$	−5.30589e10	−0.515878
$281$	6.38970e10	0.611367	0.305684	−	0.952133i	$-0.401115\pi$
$281$	6.38970e10	0.611367	0.305684	+	0.952133i	$0.401115\pi$
$282$	1.93848e11	1.82532
$283$	9.07777e10	0.841280	0.420640	−	0.907228i	$-0.361806\pi$
$283$	9.07777e10	0.841280	0.420640	+	0.907228i	$0.361806\pi$
$284$	4.15542e10	0.379037
$285$	−3.38638e10	−0.304042
$286$	2.15164e11	1.90161
$287$	−6.85836e10	−0.596694
$288$	2.42255e10	0.207495
$289$	3.28483e11	2.76996
$290$	−7.46186e10	−0.619521
$291$	8.80962e10	0.720176
$292$	2.77877e11	2.23681
$293$	−7.63723e10	−0.605385	−0.302692	−	0.953088i	$-0.597885\pi$
$293$	−7.63723e10	−0.605385	−0.302692	+	0.953088i	$0.597885\pi$
$294$	−2.07774e11	−1.62191
$295$	1.60981e10	0.123758
$296$	−9.89487e9	−0.0749199
$297$	−1.69970e11	−1.26756
$298$	−3.89103e11	−2.85819
$299$	−2.51145e11	−1.81720
$300$	6.84091e10	0.487605
$301$	−8.12255e10	−0.570352
$302$	7.57398e10	0.523953
$303$	1.12811e11	0.768884
$304$	3.88549e10	0.260924
$305$	1.11373e11	0.736941
$306$	6.79224e10	0.442860
$307$	−3.03562e11	−1.95041	−0.975203	−	0.221312i	$-0.928966\pi$
$307$	−3.03562e11	−1.95041	−0.975203	+	0.221312i	$0.928966\pi$
$308$	−3.60854e11	−2.28482
$309$	1.09673e10	0.0684361
$310$	−3.08005e11	−1.89422
$311$	2.97890e11	1.80565	0.902827	−	0.430004i	$-0.141488\pi$
$311$	2.97890e11	1.80565	0.902827	+	0.430004i	$0.141488\pi$
$312$	7.37405e10	0.440565
$313$	−2.16129e10	−0.127281	−0.0636406	−	0.997973i	$-0.520271\pi$
$313$	−2.16129e10	−0.127281	−0.0636406	+	0.997973i	$0.520271\pi$
$314$	2.29000e10	0.132939
$315$	2.97466e10	0.170231
$316$	1.97415e11	1.11375
$317$	2.26531e11	1.25997	0.629986	−	0.776607i	$-0.283061\pi$
$317$	2.26531e11	1.25997	0.629986	+	0.776607i	$0.283061\pi$
$318$	9.07617e10	0.497715
$319$	−1.17250e11	−0.633950
$320$	2.14327e11	1.14262
$321$	−1.97871e11	−1.04018
$322$	7.45080e11	3.86235
$323$	1.62664e11	0.831535
$324$	−2.13333e11	−1.07549
$325$	8.58091e10	0.426636
$326$	1.56048e11	0.765208
$327$	1.27336e11	0.615865
$328$	−3.87831e10	−0.185016
$329$	−4.07795e11	−1.91893
$330$	−2.77304e11	−1.28719
$331$	1.24181e11	0.568631	0.284316	−	0.958731i	$-0.408234\pi$
$331$	1.24181e11	0.568631	0.284316	+	0.958731i	$0.408234\pi$
$332$	−5.95696e10	−0.269094
$333$	5.54739e9	0.0247223
$334$	−4.25274e11	−1.86986
$335$	−1.88748e11	−0.818807
$336$	1.92833e11	0.825382
$337$	1.42832e11	0.603240	0.301620	−	0.953428i	$-0.402473\pi$
$337$	1.42832e11	0.603240	0.301620	+	0.953428i	$0.402473\pi$
$338$	3.64007e10	0.151700
$339$	−5.47302e10	−0.225076
$340$	4.79214e11	1.94480
$341$	−4.83976e11	−1.93834
$342$	2.47132e10	0.0976811
$343$	6.03313e10	0.235353
$344$	−4.59319e10	−0.176848
$345$	3.23676e11	1.23006
$346$	−5.73845e11	−2.15255
$347$	3.42139e11	1.26683	0.633417	−	0.773810i	$-0.281652\pi$
$347$	3.42139e11	1.26683	0.633417	+	0.773810i	$0.281652\pi$
$348$	−1.73923e11	−0.635698
$349$	−2.29495e10	−0.0828055	−0.0414028	−	0.999143i	$-0.513183\pi$
$349$	−2.29495e10	−0.0828055	−0.0414028	+	0.999143i	$0.513183\pi$
$350$	−2.54573e11	−0.906788
$351$	−3.16254e11	−1.11212
$352$	4.75087e11	1.64942
$353$	−7.47849e9	−0.0256347	−0.0128173	−	0.999918i	$-0.504080\pi$
$353$	−7.47849e9	−0.0256347	−0.0128173	+	0.999918i	$0.504080\pi$
$354$	6.63744e10	0.224640
$355$	−6.71769e10	−0.224488
$356$	−6.15732e11	−2.03173
$357$	8.07287e11	2.63039
$358$	−3.23773e11	−1.04176
$359$	2.61976e10	0.0832409	0.0416204	−	0.999133i	$-0.486748\pi$
$359$	2.61976e10	0.0832409	0.0416204	+	0.999133i	$0.486748\pi$
$360$	1.68213e10	0.0527834
$361$	−2.63503e11	−0.816589
$362$	3.23964e11	0.991535
$363$	−1.30810e11	−0.395421
$364$	−6.71420e11	−2.00465
$365$	−4.49219e11	−1.32477
$366$	4.59207e11	1.33765
$367$	−2.23555e11	−0.643260	−0.321630	−	0.946865i	$-0.604231\pi$
$367$	−2.23555e11	−0.643260	−0.321630	+	0.946865i	$0.604231\pi$
$368$	−3.71382e11	−1.05562
$369$	2.17431e10	0.0610523
$370$	6.92346e10	0.192050
$371$	−1.90934e11	−0.523240
$372$	−7.17906e11	−1.94368
$373$	4.30341e11	1.15113	0.575563	−	0.817757i	$-0.304783\pi$
$373$	4.30341e11	1.15113	0.575563	+	0.817757i	$0.304783\pi$
$374$	1.33203e12	3.52039
$375$	−3.82461e11	−0.998726
$376$	−2.30602e11	−0.595001
$377$	−2.18161e11	−0.556212
$378$	9.38241e11	2.36375
$379$	2.25490e11	0.561373	0.280687	−	0.959799i	$-0.409438\pi$
$379$	2.25490e11	0.561373	0.280687	+	0.959799i	$0.409438\pi$
$380$	1.74359e11	0.428962
$381$	3.04385e11	0.740050
$382$	4.56671e11	1.09728
$383$	4.20977e11	0.999687	0.499843	−	0.866116i	$-0.333391\pi$
$383$	4.20977e11	0.999687	0.499843	+	0.866116i	$0.333391\pi$
$384$	3.41799e11	0.802196
$385$	5.83360e11	1.35320
$386$	3.62503e11	0.831130
$387$	2.57509e10	0.0583571
$388$	−4.53594e11	−1.01607
$389$	−6.16332e11	−1.36471	−0.682357	−	0.731019i	$-0.739045\pi$
$389$	−6.16332e11	−1.36471	−0.682357	+	0.731019i	$0.739045\pi$
$390$	−5.15963e11	−1.12935
$391$	−1.55477e12	−3.36412
$392$	2.47168e11	0.528696
$393$	4.93266e10	0.104307
$394$	−1.03872e12	−2.17153
$395$	−3.19143e11	−0.659628
$396$	1.14401e11	0.233778
$397$	−2.35545e10	−0.0475900	−0.0237950	−	0.999717i	$-0.507575\pi$
$397$	−2.35545e10	−0.0475900	−0.0237950	+	0.999717i	$0.507575\pi$
$398$	4.46987e11	0.892937
$399$	2.93726e11	0.580183
$400$	1.26891e11	0.247834
$401$	−1.46531e11	−0.282995	−0.141497	−	0.989939i	$-0.545192\pi$
$401$	−1.46531e11	−0.282995	−0.141497	+	0.989939i	$0.545192\pi$
$402$	−7.78234e11	−1.48625
$403$	−9.00507e11	−1.70065
$404$	−5.80848e11	−1.08479
$405$	3.44877e11	0.636967
$406$	6.47225e11	1.18219
$407$	1.08790e11	0.196523
$408$	4.56509e11	0.815603
$409$	1.24646e11	0.220253	0.110127	−	0.993918i	$-0.464874\pi$
$409$	1.24646e11	0.220253	0.110127	+	0.993918i	$0.464874\pi$
$410$	2.71366e11	0.474272
$411$	−7.70143e11	−1.33132
$412$	−5.64688e10	−0.0965541
$413$	−1.39631e11	−0.236160
$414$	−2.36213e11	−0.395186
$415$	9.63009e10	0.159373
$416$	8.83967e11	1.44716
$417$	7.16591e11	1.16054
$418$	4.84650e11	0.776488
$419$	−1.86536e11	−0.295664	−0.147832	−	0.989012i	$-0.547230\pi$
$419$	−1.86536e11	−0.295664	−0.147832	+	0.989012i	$0.547230\pi$
$420$	8.65328e11	1.35693
$421$	4.32115e11	0.670394	0.335197	−	0.942148i	$-0.391197\pi$
$421$	4.32115e11	0.670394	0.335197	+	0.942148i	$0.391197\pi$
$422$	−6.40803e11	−0.983600
$423$	1.29283e11	0.196341
$424$	−1.07970e11	−0.162240
$425$	5.31223e11	0.789817
$426$	−2.76979e11	−0.407478
$427$	−9.66028e11	−1.40626
$428$	1.01880e12	1.46755
$429$	−8.10746e11	−1.15565
$430$	3.21386e11	0.453335
$431$	4.77460e11	0.666483	0.333241	−	0.942842i	$-0.391858\pi$
$431$	4.77460e11	0.666483	0.333241	+	0.942842i	$0.391858\pi$
$432$	−4.67663e11	−0.646035
$433$	9.38153e10	0.128256	0.0641281	−	0.997942i	$-0.479573\pi$
$433$	9.38153e10	0.128256	0.0641281	+	0.997942i	$0.479573\pi$
$434$	2.67157e12	3.61462
$435$	2.81166e11	0.376497
$436$	−6.55632e11	−0.868902
$437$	−5.65696e11	−0.742021
$438$	−1.85219e12	−2.40465
$439$	−9.23783e11	−1.18708	−0.593540	−	0.804805i	$-0.702270\pi$
$439$	−9.23783e11	−1.18708	−0.593540	+	0.804805i	$0.702270\pi$
$440$	3.29882e11	0.419586
$441$	−1.38571e11	−0.174461
$442$	2.47843e12	3.08870
$443$	−3.26798e11	−0.403146	−0.201573	−	0.979473i	$-0.564605\pi$
$443$	−3.26798e11	−0.403146	−0.201573	+	0.979473i	$0.564605\pi$
$444$	1.61374e11	0.197065
$445$	9.95400e11	1.20331
$446$	−3.87658e11	−0.463919
$447$	1.46615e12	1.73698
$448$	−1.85903e12	−2.18039
$449$	3.50572e11	0.407070	0.203535	−	0.979068i	$-0.434757\pi$
$449$	3.50572e11	0.407070	0.203535	+	0.979068i	$0.434757\pi$
$450$	8.07073e10	0.0927804
$451$	4.26404e11	0.485318
$452$	2.81797e11	0.317552
$453$	−2.85390e11	−0.318418
$454$	−8.42238e11	−0.930430
$455$	1.08542e12	1.18727
$456$	1.66098e11	0.179897
$457$	5.37992e11	0.576970	0.288485	−	0.957484i	$-0.406848\pi$
$457$	5.37992e11	0.576970	0.288485	+	0.957484i	$0.406848\pi$
$458$	1.21847e12	1.29396
$459$	−1.95785e12	−2.05884
$460$	−1.66656e12	−1.73544
$461$	2.24837e11	0.231853	0.115927	−	0.993258i	$-0.463016\pi$
$461$	2.24837e11	0.231853	0.115927	+	0.993258i	$0.463016\pi$
$462$	2.40527e12	2.45626
$463$	5.19651e11	0.525530	0.262765	−	0.964860i	$-0.415366\pi$
$463$	5.19651e11	0.525530	0.262765	+	0.964860i	$0.415366\pi$
$464$	−3.22607e11	−0.323104
$465$	1.16058e12	1.15116
$466$	6.77542e11	0.665579
$467$	−1.05163e12	−1.02314	−0.511571	−	0.859241i	$-0.670936\pi$
$467$	−1.05163e12	−1.02314	−0.511571	+	0.859241i	$0.670936\pi$
$468$	2.12860e11	0.205111
$469$	1.63716e12	1.56248
$470$	1.61353e12	1.52523
$471$	−8.62881e10	−0.0807899
$472$	−7.89593e10	−0.0732259
$473$	5.05002e11	0.463893
$474$	−1.31587e12	−1.19732
$475$	1.93282e11	0.174209
$476$	−4.15659e12	−3.71113
$477$	6.05318e10	0.0535366
$478$	−8.50327e11	−0.745008
$479$	1.27153e12	1.10361	0.551807	−	0.833972i	$-0.313939\pi$
$479$	1.27153e12	1.10361	0.551807	+	0.833972i	$0.313939\pi$
$480$	−1.13926e12	−0.979574
$481$	2.02419e11	0.172425
$482$	−3.48654e12	−2.94227
$483$	−2.80749e12	−2.34723
$484$	6.73519e11	0.557886
$485$	7.33284e11	0.601776
$486$	−5.56018e11	−0.452091
$487$	−1.94977e12	−1.57074	−0.785369	−	0.619027i	$-0.787527\pi$
$487$	−1.94977e12	−1.57074	−0.785369	+	0.619027i	$0.787527\pi$
$488$	−5.46275e11	−0.436036
$489$	−5.87996e11	−0.465034
$490$	−1.72944e12	−1.35526
$491$	4.08089e11	0.316875	0.158438	−	0.987369i	$-0.449354\pi$
$491$	4.08089e11	0.316875	0.158438	+	0.987369i	$0.449354\pi$
$492$	6.32506e11	0.486656
$493$	−1.35058e12	−1.02969
$494$	9.01761e11	0.681271
$495$	−1.84943e11	−0.138457
$496$	−1.33163e12	−0.987908
$497$	5.82677e11	0.428375
$498$	3.97061e11	0.289285
$499$	1.98112e12	1.43040	0.715201	−	0.698919i	$-0.246335\pi$
$499$	1.98112e12	1.43040	0.715201	+	0.698919i	$0.246335\pi$
$500$	1.96923e12	1.40907
$501$	1.60245e12	1.13636
$502$	−3.66280e12	−2.57423
$503$	8.23536e11	0.573623	0.286811	−	0.957987i	$-0.407405\pi$
$503$	8.23536e11	0.573623	0.286811	+	0.957987i	$0.407405\pi$
$504$	−1.45904e11	−0.100723
$505$	9.39006e11	0.642476
$506$	−4.63237e12	−3.14142
$507$	−1.37159e11	−0.0921912
$508$	−1.56723e12	−1.04411
$509$	−8.61412e11	−0.568828	−0.284414	−	0.958702i	$-0.591799\pi$
$509$	−8.61412e11	−0.568828	−0.284414	+	0.958702i	$0.591799\pi$
$510$	−3.19420e12	−2.09072
$511$	3.89642e12	2.52797
$512$	1.73891e12	1.11831
$513$	−7.12352e11	−0.454115
$514$	5.44952e11	0.344369
$515$	9.12880e10	0.0571849
$516$	7.49095e11	0.465172
$517$	2.53537e12	1.56075
$518$	−6.00525e11	−0.366477
$519$	2.16227e12	1.30815
$520$	6.13792e11	0.368134
$521$	2.18788e12	1.30093	0.650463	−	0.759538i	$-0.274575\pi$
$521$	2.18788e12	1.30093	0.650463	+	0.759538i	$0.274575\pi$
$522$	−2.05190e11	−0.120959
$523$	−1.08120e11	−0.0631901	−0.0315951	−	0.999501i	$-0.510059\pi$
$523$	−1.08120e11	−0.0631901	−0.0315951	+	0.999501i	$0.510059\pi$
$524$	−2.53975e11	−0.147164
$525$	9.59240e11	0.551075
$526$	−2.35808e12	−1.34314
$527$	−5.57481e12	−3.14835
$528$	−1.19890e12	−0.671320
$529$	3.60587e12	2.00198
$530$	7.55471e11	0.415888
$531$	4.42672e10	0.0241633
$532$	−1.51235e12	−0.818560
$533$	7.93385e11	0.425806
$534$	4.10416e12	2.18418
$535$	−1.64701e12	−0.869170
$536$	9.25791e11	0.484475
$537$	1.21999e12	0.633099
$538$	−8.84263e11	−0.455052
$539$	−2.71751e12	−1.38683
$540$	−2.09861e12	−1.06209
$541$	−4.50335e11	−0.226021	−0.113010	−	0.993594i	$-0.536049\pi$
$541$	−4.50335e11	−0.226021	−0.113010	+	0.993594i	$0.536049\pi$
$542$	3.22966e12	1.60753
$543$	−1.22071e12	−0.602577
$544$	5.47242e12	2.67907
$545$	1.05990e12	0.514614
$546$	4.47535e12	2.15506
$547$	−2.31775e12	−1.10694	−0.553469	−	0.832870i	$-0.686696\pi$
$547$	−2.31775e12	−1.10694	−0.553469	+	0.832870i	$0.686696\pi$
$548$	3.96535e12	1.87832
$549$	3.06260e11	0.143885
$550$	1.58275e12	0.737531
$551$	−4.91400e11	−0.227119
$552$	−1.58760e12	−0.727804
$553$	2.76818e12	1.25872
$554$	−7.44994e11	−0.336015
$555$	−2.60878e11	−0.116713
$556$	−3.68962e12	−1.63736
$557$	−1.99632e12	−0.878782	−0.439391	−	0.898296i	$-0.644806\pi$
$557$	−1.99632e12	−0.878782	−0.439391	+	0.898296i	$0.644806\pi$
$558$	−8.46967e11	−0.369839
$559$	9.39628e11	0.407008
$560$	1.60508e12	0.689685
$561$	−5.01913e12	−2.13942
$562$	2.19292e12	0.927277
$563$	3.59948e12	1.50991	0.754957	−	0.655774i	$-0.227658\pi$
$563$	3.59948e12	1.50991	0.754957	+	0.655774i	$0.227658\pi$
$564$	3.76085e12	1.56506
$565$	−4.55557e11	−0.188072
$566$	3.11546e12	1.27599
$567$	−2.99139e12	−1.21548
$568$	3.29496e11	0.132826
$569$	−3.76278e12	−1.50489	−0.752443	−	0.658658i	$-0.771125\pi$
$569$	−3.76278e12	−1.50489	−0.752443	+	0.658658i	$0.771125\pi$
$570$	−1.16219e12	−0.461149
$571$	2.22709e12	0.876751	0.438375	−	0.898792i	$-0.355554\pi$
$571$	2.22709e12	0.876751	0.438375	+	0.898792i	$0.355554\pi$
$572$	4.17440e12	1.63047
$573$	−1.72075e12	−0.666842
$574$	−2.35376e12	−0.905023
$575$	−1.84743e12	−0.704794
$576$	5.89367e11	0.223092
$577$	2.46554e12	0.926021	0.463011	−	0.886353i	$-0.346769\pi$
$577$	2.46554e12	0.926021	0.463011	+	0.886353i	$0.346769\pi$
$578$	1.12734e13	4.20127
$579$	−1.36593e12	−0.505096
$580$	−1.44768e12	−0.531186
$581$	−8.35292e11	−0.304121
$582$	3.02343e12	1.09231
$583$	1.18709e12	0.425574
$584$	2.20337e12	0.783845
$585$	−3.44112e11	−0.121478
$586$	−2.62107e12	−0.918204
$587$	1.80230e12	0.626550	0.313275	−	0.949662i	$-0.398574\pi$
$587$	1.80230e12	0.626550	0.313275	+	0.949662i	$0.398574\pi$
$588$	−4.03103e12	−1.39065
$589$	−2.02836e12	−0.694427
$590$	5.52480e11	0.187708
$591$	3.91395e12	1.31969
$592$	2.99329e11	0.100162
$593$	−2.92045e12	−0.969848	−0.484924	−	0.874556i	$-0.661153\pi$
$593$	−2.92045e12	−0.969848	−0.484924	+	0.874556i	$0.661153\pi$
$594$	−5.83331e12	−1.92254
$595$	6.71960e12	2.19795
$596$	−7.54901e12	−2.45065
$597$	−1.68426e12	−0.542657
$598$	−8.61919e12	−2.75620
$599$	−4.02964e12	−1.27893	−0.639463	−	0.768822i	$-0.720843\pi$
$599$	−4.02964e12	−1.27893	−0.639463	+	0.768822i	$0.720843\pi$
$600$	5.42437e11	0.170871
$601$	−3.81051e12	−1.19137	−0.595686	−	0.803217i	$-0.703120\pi$
$601$	−3.81051e12	−1.19137	−0.595686	+	0.803217i	$0.703120\pi$
$602$	−2.78763e12	−0.865069
$603$	−5.19029e11	−0.159869
$604$	1.46943e12	0.449245
$605$	−1.08882e12	−0.330412
$606$	3.87164e12	1.16619
$607$	−5.59887e12	−1.67398	−0.836991	−	0.547216i	$-0.815687\pi$
$607$	−5.59887e12	−1.67398	−0.836991	+	0.547216i	$0.815687\pi$
$608$	1.99111e12	0.590920
$609$	−2.43877e12	−0.718444
$610$	3.82230e12	1.11774
$611$	4.71743e12	1.36937
$612$	1.31777e12	0.379714
$613$	1.65775e12	0.474185	0.237093	−	0.971487i	$-0.423806\pi$
$613$	1.65775e12	0.474185	0.237093	+	0.971487i	$0.423806\pi$
$614$	−1.04181e13	−2.95824
$615$	−1.02252e12	−0.288226
$616$	−2.86132e12	−0.800669
$617$	−6.21572e12	−1.72666	−0.863332	−	0.504636i	$-0.831627\pi$
$617$	−6.21572e12	−1.72666	−0.863332	+	0.504636i	$0.831627\pi$
$618$	3.76393e11	0.103799
$619$	4.17471e12	1.14293	0.571464	−	0.820627i	$-0.306376\pi$
$619$	4.17471e12	1.14293	0.571464	+	0.820627i	$0.306376\pi$
$620$	−5.97562e12	−1.62413
$621$	6.80879e12	1.83720
$622$	1.02235e13	2.73869
$623$	−8.63387e12	−2.29620
$624$	−2.23072e12	−0.588999
$625$	−1.63175e12	−0.427753
$626$	−7.41748e11	−0.193051
$627$	−1.82618e12	−0.471889
$628$	4.44284e11	0.113984
$629$	1.25313e12	0.319203
$630$	1.02089e12	0.258194
$631$	5.75695e12	1.44564	0.722820	−	0.691036i	$-0.242845\pi$
$631$	5.75695e12	1.44564	0.722820	+	0.691036i	$0.242845\pi$
$632$	1.56536e12	0.390291
$633$	2.41457e12	0.597755
$634$	7.77446e12	1.91103
$635$	2.53360e12	0.618382
$636$	1.76087e12	0.426747
$637$	−5.05632e12	−1.21677
$638$	−4.02398e12	−0.961530
$639$	−1.84726e11	−0.0438303
$640$	2.84503e12	0.670312
$641$	3.35199e12	0.784225	0.392113	−	0.919917i	$-0.371744\pi$
$641$	3.35199e12	0.784225	0.392113	+	0.919917i	$0.371744\pi$
$642$	−6.79084e12	−1.57767
$643$	1.74616e12	0.402842	0.201421	−	0.979505i	$-0.435444\pi$
$643$	1.74616e12	0.402842	0.201421	+	0.979505i	$0.435444\pi$
$644$	1.44553e13	3.31163
$645$	−1.21100e12	−0.275501
$646$	5.58258e12	1.26121
$647$	3.68639e11	0.0827050	0.0413525	−	0.999145i	$-0.486833\pi$
$647$	3.68639e11	0.0827050	0.0413525	+	0.999145i	$0.486833\pi$
$648$	−1.69159e12	−0.376883
$649$	8.68125e11	0.192080
$650$	2.94493e12	0.647091
$651$	−1.00666e13	−2.19668
$652$	3.02750e12	0.656100
$653$	3.37602e12	0.726601	0.363301	−	0.931672i	$-0.381650\pi$
$653$	3.37602e12	0.726601	0.363301	+	0.931672i	$0.381650\pi$
$654$	4.37011e12	0.934099
$655$	4.10579e11	0.0871587
$656$	1.17323e12	0.247351
$657$	−1.23528e12	−0.258656
$658$	−1.39954e13	−2.91050
$659$	−9.07216e11	−0.187381	−0.0936906	−	0.995601i	$-0.529866\pi$
$659$	−9.07216e11	−0.187381	−0.0936906	+	0.995601i	$0.529866\pi$
$660$	−5.37998e12	−1.10365
$661$	−3.66823e12	−0.747394	−0.373697	−	0.927551i	$-0.621910\pi$
$661$	−3.66823e12	−0.747394	−0.373697	+	0.927551i	$0.621910\pi$
$662$	4.26186e12	0.862458
$663$	−9.33880e12	−1.87707
$664$	−4.72346e11	−0.0942983
$665$	2.44489e12	0.484798
$666$	1.90384e11	0.0374971
$667$	4.69689e12	0.918849
$668$	−8.25076e12	−1.60325
$669$	1.46071e12	0.281934
$670$	−6.47778e12	−1.24191
$671$	6.00607e12	1.14377
$672$	9.88168e12	1.86926
$673$	6.92489e12	1.30120	0.650601	−	0.759419i	$-0.274517\pi$
$673$	6.92489e12	1.30120	0.650601	+	0.759419i	$0.274517\pi$
$674$	4.90193e12	0.914950
$675$	−2.32637e12	−0.431332
$676$	7.06212e11	0.130069
$677$	2.22502e12	0.407085	0.203542	−	0.979066i	$-0.434754\pi$
$677$	2.22502e12	0.407085	0.203542	+	0.979066i	$0.434754\pi$
$678$	−1.87832e12	−0.341379
$679$	−6.36034e12	−1.14833
$680$	3.79984e12	0.681514
$681$	3.17359e12	0.565442
$682$	−1.66099e13	−2.93993
$683$	−7.53860e12	−1.32555	−0.662777	−	0.748817i	$-0.730622\pi$
$683$	−7.53860e12	−1.32555	−0.662777	+	0.748817i	$0.730622\pi$
$684$	4.79461e11	0.0837531
$685$	−6.41042e12	−1.11245
$686$	2.07055e12	0.356966
$687$	−4.59123e12	−0.786365
$688$	1.38948e12	0.236432
$689$	2.20875e12	0.373388
$690$	1.11084e13	1.86566
$691$	−2.77605e11	−0.0463208	−0.0231604	−	0.999732i	$-0.507373\pi$
$691$	−2.77605e11	−0.0463208	−0.0231604	+	0.999732i	$0.507373\pi$
$692$	−1.11332e13	−1.84562
$693$	1.60415e12	0.264208
$694$	1.17421e13	1.92144
$695$	5.96467e12	0.969740
$696$	−1.37909e12	−0.222767
$697$	4.91165e12	0.788279
$698$	−7.87619e11	−0.125593
$699$	−2.55300e12	−0.404487
$700$	−4.93898e12	−0.777492
$701$	−8.90286e12	−1.39251	−0.696255	−	0.717794i	$-0.745152\pi$
$701$	−8.90286e12	−1.39251	−0.696255	+	0.717794i	$0.745152\pi$
$702$	−1.08537e13	−1.68679
$703$	4.55943e11	0.0704063
$704$	1.15581e13	1.77341
$705$	−6.07983e12	−0.926916
$706$	−2.56659e11	−0.0388808
$707$	−8.14472e12	−1.22600
$708$	1.28773e12	0.192609
$709$	−3.06048e12	−0.454864	−0.227432	−	0.973794i	$-0.573033\pi$
$709$	−3.06048e12	−0.454864	−0.227432	+	0.973794i	$0.573033\pi$
$710$	−2.30549e12	−0.340487
$711$	−8.77595e11	−0.128790
$712$	−4.88233e12	−0.711979
$713$	1.93875e13	2.80943
$714$	2.77058e13	3.98959
$715$	−6.74839e12	−0.965657
$716$	−6.28153e12	−0.893217
$717$	3.20407e12	0.452757
$718$	8.99092e11	0.126254
$719$	1.18782e13	1.65756	0.828782	−	0.559572i	$-0.189034\pi$
$719$	1.18782e13	1.65756	0.828782	+	0.559572i	$0.189034\pi$
$720$	−5.08859e11	−0.0705669
$721$	−7.91812e11	−0.109122
$722$	−9.04333e12	−1.23854
$723$	1.31374e13	1.78808
$724$	6.28524e12	0.850156
$725$	−1.60479e12	−0.215724
$726$	−4.48934e12	−0.599747
$727$	3.88538e12	0.515857	0.257928	−	0.966164i	$-0.416960\pi$
$727$	3.88538e12	0.515857	0.257928	+	0.966164i	$0.416960\pi$
$728$	−5.32389e12	−0.702487
$729$	8.40151e12	1.10175
$730$	−1.54170e13	−2.00932
$731$	5.81701e12	0.753479
$732$	8.90911e12	1.14692
$733$	−1.42676e13	−1.82550	−0.912752	−	0.408513i	$-0.866047\pi$
$733$	−1.42676e13	−1.82550	−0.912752	+	0.408513i	$0.866047\pi$
$734$	−7.67231e12	−0.975650
$735$	6.51660e12	0.823623
$736$	−1.90314e13	−2.39067
$737$	−1.01787e13	−1.27083
$738$	7.46214e11	0.0925998
$739$	1.15651e13	1.42643	0.713216	−	0.700945i	$-0.247238\pi$
$739$	1.15651e13	1.42643	0.713216	+	0.700945i	$0.247238\pi$
$740$	1.34322e12	0.164667
$741$	−3.39787e12	−0.414023
$742$	−6.55278e12	−0.793612
$743$	−3.25689e12	−0.392061	−0.196031	−	0.980598i	$-0.562805\pi$
$743$	−3.25689e12	−0.392061	−0.196031	+	0.980598i	$0.562805\pi$
$744$	−5.69250e12	−0.681122
$745$	1.22038e13	1.45142
$746$	1.47691e13	1.74595
$747$	2.64813e11	0.0311169
$748$	2.58427e13	3.01843
$749$	1.42858e13	1.65858
$750$	−1.31259e13	−1.51480
$751$	−1.38050e13	−1.58365	−0.791823	−	0.610751i	$-0.790868\pi$
$751$	−1.38050e13	−1.58365	−0.791823	+	0.610751i	$0.790868\pi$
$752$	6.97593e12	0.795467
$753$	1.38016e13	1.56441
$754$	−7.48719e12	−0.843622
$755$	−2.37550e12	−0.266069
$756$	1.82029e13	2.02671
$757$	2.07544e12	0.229709	0.114855	−	0.993382i	$-0.463360\pi$
$757$	2.07544e12	0.229709	0.114855	+	0.993382i	$0.463360\pi$
$758$	7.73875e12	0.851450
$759$	1.74550e13	1.90911
$760$	1.38255e12	0.150321
$761$	−1.05770e13	−1.14323	−0.571614	−	0.820523i	$-0.693683\pi$
$761$	−1.05770e13	−1.14323	−0.571614	+	0.820523i	$0.693683\pi$
$762$	1.04464e13	1.12245
$763$	−9.19335e12	−0.982004
$764$	8.85989e12	0.940824
$765$	−2.13031e12	−0.224888
$766$	1.44478e13	1.51625
$767$	1.61527e12	0.168526
$768$	−1.45311e12	−0.150721
$769$	−1.75639e13	−1.81114	−0.905571	−	0.424194i	$-0.860557\pi$
$769$	−1.75639e13	−1.81114	−0.905571	+	0.424194i	$0.860557\pi$
$770$	2.00207e13	2.05244
$771$	−2.05340e12	−0.209280
$772$	7.03295e12	0.712622
$773$	−1.89617e13	−1.91016	−0.955082	−	0.296342i	$-0.904233\pi$
$773$	−1.89617e13	−1.91016	−0.955082	+	0.296342i	$0.904233\pi$
$774$	8.83763e11	0.0885118
$775$	−6.62415e12	−0.659588
$776$	−3.59668e12	−0.356061
$777$	2.26280e12	0.222716
$778$	−2.11523e13	−2.06990
$779$	1.78708e12	0.173870
$780$	−1.00102e13	−0.968319
$781$	−3.62267e12	−0.348417
$782$	−5.33593e13	−5.10246
$783$	5.91455e12	0.562334
$784$	−7.47708e12	−0.706822
$785$	−7.18235e11	−0.0675076
$786$	1.69287e12	0.158206
$787$	1.53039e13	1.42205	0.711027	−	0.703165i	$-0.248230\pi$
$787$	1.53039e13	1.42205	0.711027	+	0.703165i	$0.248230\pi$
$788$	−2.01523e13	−1.86190
$789$	8.88534e12	0.816258
$790$	−1.09529e13	−1.00048
$791$	3.95140e12	0.358886
$792$	9.07124e11	0.0819225
$793$	1.11751e13	1.00352
$794$	−8.08381e11	−0.0721811
$795$	−2.84665e12	−0.252744
$796$	8.67202e12	0.765617
$797$	3.76037e11	0.0330117	0.0165059	−	0.999864i	$-0.494746\pi$
$797$	3.76037e11	0.0330117	0.0165059	+	0.999864i	$0.494746\pi$
$798$	1.00806e13	0.879980
$799$	2.92044e13	2.53506
$800$	6.50249e12	0.561273
$801$	2.73720e12	0.234941
$802$	−5.02887e12	−0.429226
$803$	−2.42252e13	−2.05611
$804$	−1.50986e13	−1.27433
$805$	−2.33687e13	−1.96134
$806$	−3.09051e13	−2.57942
$807$	3.33194e12	0.276545
$808$	−4.60572e12	−0.380143
$809$	8.16350e12	0.670051	0.335026	−	0.942209i	$-0.391255\pi$
$809$	8.16350e12	0.670051	0.335026	+	0.942209i	$0.391255\pi$
$810$	1.18361e13	0.966105
$811$	7.26498e11	0.0589713	0.0294856	−	0.999565i	$-0.490613\pi$
$811$	7.26498e11	0.0589713	0.0294856	+	0.999565i	$0.490613\pi$
$812$	1.25568e13	1.01363
$813$	−1.21695e13	−0.976932
$814$	3.73363e12	0.298072
$815$	−4.89429e12	−0.388580
$816$	−1.38098e13	−1.09039
$817$	2.11648e12	0.166194
$818$	4.27780e12	0.334064
$819$	2.98475e12	0.231809
$820$	5.26478e12	0.406647
$821$	−2.03191e13	−1.56084	−0.780422	−	0.625253i	$-0.784996\pi$
$821$	−2.03191e13	−1.56084	−0.780422	+	0.625253i	$0.784996\pi$
$822$	−2.64310e13	−2.01925
$823$	1.08873e13	0.827220	0.413610	−	0.910454i	$-0.364268\pi$
$823$	1.08873e13	0.827220	0.413610	+	0.910454i	$0.364268\pi$
$824$	−4.47758e11	−0.0338354
$825$	−5.96387e12	−0.448214
$826$	−4.79208e12	−0.358191
$827$	−9.13590e11	−0.0679167	−0.0339583	−	0.999423i	$-0.510811\pi$
$827$	−9.13590e11	−0.0679167	−0.0339583	+	0.999423i	$0.510811\pi$
$828$	−4.58278e12	−0.338838
$829$	1.57245e13	1.15633	0.578163	−	0.815921i	$-0.303770\pi$
$829$	1.57245e13	1.15633	0.578163	+	0.815921i	$0.303770\pi$
$830$	3.30501e12	0.241725
$831$	2.80717e12	0.204204
$832$	2.15055e13	1.55594
$833$	−3.13024e13	−2.25256
$834$	2.45931e13	1.76022
$835$	1.33383e13	0.949534
$836$	9.40272e12	0.665771
$837$	2.44136e13	1.71936
$838$	−6.40183e12	−0.448442
$839$	−3.47812e12	−0.242335	−0.121167	−	0.992632i	$-0.538664\pi$
$839$	−3.47812e12	−0.242335	−0.121167	+	0.992632i	$0.538664\pi$
$840$	6.86145e12	0.475509
$841$	−1.04271e13	−0.718758
$842$	1.48300e13	1.01681
$843$	−8.26301e12	−0.563527
$844$	−1.24323e13	−0.843352
$845$	−1.14167e12	−0.0770346
$846$	4.43695e12	0.297795
$847$	9.44416e12	0.630504
$848$	3.26621e12	0.216902
$849$	−1.17392e13	−0.775448
$850$	1.82314e13	1.19794
$851$	−4.35799e12	−0.284841
$852$	−5.37369e12	−0.349377
$853$	1.17204e13	0.758006	0.379003	−	0.925395i	$-0.376267\pi$
$853$	1.17204e13	0.758006	0.379003	+	0.925395i	$0.376267\pi$
$854$	−3.31537e13	−2.13291
$855$	−7.75102e11	−0.0496034
$856$	8.07842e12	0.514274
$857$	−1.27242e13	−0.805783	−0.402891	−	0.915248i	$-0.631995\pi$
$857$	−1.27242e13	−0.805783	−0.402891	+	0.915248i	$0.631995\pi$
$858$	−2.78245e13	−1.75281
$859$	2.65726e13	1.66519	0.832597	−	0.553879i	$-0.186853\pi$
$859$	2.65726e13	1.66519	0.832597	+	0.553879i	$0.186853\pi$
$860$	6.23523e12	0.388695
$861$	8.86908e12	0.550002
$862$	1.63862e13	1.01087
$863$	6.65761e12	0.408573	0.204287	−	0.978911i	$-0.434513\pi$
$863$	6.65761e12	0.408573	0.204287	+	0.978911i	$0.434513\pi$
$864$	−2.39652e13	−1.46309
$865$	1.79981e13	1.09308
$866$	3.21971e12	0.194530
$867$	−4.24787e13	−2.55320
$868$	5.18312e13	3.09922
$869$	−1.72105e13	−1.02378
$870$	9.64951e12	0.571043
$871$	−1.89389e13	−1.11500
$872$	−5.19871e12	−0.304489
$873$	2.01642e12	0.117494
$874$	−1.94145e13	−1.12544
$875$	2.76128e13	1.59248
$876$	−3.59344e13	−2.06178
$877$	−1.19094e13	−0.679819	−0.339909	−	0.940458i	$-0.610396\pi$
$877$	−1.19094e13	−0.679819	−0.339909	+	0.940458i	$0.610396\pi$
$878$	−3.17039e13	−1.80048
$879$	9.87629e12	0.558012
$880$	−9.97924e12	−0.560952
$881$	1.24700e13	0.697391	0.348696	−	0.937236i	$-0.386625\pi$
$881$	1.24700e13	0.697391	0.348696	+	0.937236i	$0.386625\pi$
$882$	−4.75570e12	−0.264610
$883$	3.32785e12	0.184222	0.0921108	−	0.995749i	$-0.470639\pi$
$883$	3.32785e12	0.184222	0.0921108	+	0.995749i	$0.470639\pi$
$884$	4.80841e13	2.64829
$885$	−2.08177e12	−0.114074
$886$	−1.12156e13	−0.611463
$887$	−5.24337e12	−0.284416	−0.142208	−	0.989837i	$-0.545420\pi$
$887$	−5.24337e12	−0.284416	−0.142208	+	0.989837i	$0.545420\pi$
$888$	1.27958e12	0.0690573
$889$	−2.19759e13	−1.18002
$890$	3.41617e13	1.82509
$891$	1.85983e13	0.988606
$892$	−7.52098e12	−0.397770
$893$	1.06259e13	0.559155
$894$	5.03179e13	2.63453
$895$	1.01548e13	0.529014
$896$	−2.46771e13	−1.27911
$897$	3.24775e13	1.67500
$898$	1.20315e13	0.617414
$899$	1.68412e13	0.859913
$900$	1.56581e12	0.0795512
$901$	1.36738e13	0.691240
$902$	1.46340e13	0.736095
$903$	1.05039e13	0.525721
$904$	2.23446e12	0.111279
$905$	−1.01608e13	−0.503511
$906$	−9.79449e12	−0.482953
$907$	2.17234e13	1.06585	0.532923	−	0.846164i	$-0.321094\pi$
$907$	2.17234e13	1.06585	0.532923	+	0.846164i	$0.321094\pi$
$908$	−1.63403e13	−0.797763
$909$	2.58212e12	0.125441
$910$	3.72514e13	1.80076
$911$	8.39548e12	0.403843	0.201922	−	0.979402i	$-0.435281\pi$
$911$	8.39548e12	0.403843	0.201922	+	0.979402i	$0.435281\pi$
$912$	−5.02463e12	−0.240507
$913$	5.19324e12	0.247355
$914$	1.84637e13	0.875106
$915$	−1.44026e13	−0.679274
$916$	2.36395e13	1.10945
$917$	−3.56127e12	−0.166319
$918$	−6.71926e13	−3.12269
$919$	−4.20773e13	−1.94593	−0.972967	−	0.230945i	$-0.925818\pi$
$919$	−4.20773e13	−1.94593	−0.972967	+	0.230945i	$0.925818\pi$
$920$	−1.32146e13	−0.608150
$921$	3.92560e13	1.79778
$922$	7.71631e12	0.351658
$923$	−6.74049e12	−0.305692
$924$	4.66648e13	2.10603
$925$	1.48900e12	0.0668740
$926$	1.78342e13	0.797085
$927$	2.51028e11	0.0111651
$928$	−1.65319e13	−0.731740
$929$	2.25599e13	0.993727	0.496863	−	0.867829i	$-0.334485\pi$
$929$	2.25599e13	0.993727	0.496863	+	0.867829i	$0.334485\pi$
$930$	3.98305e13	1.74599
$931$	−1.13892e13	−0.496844
$932$	1.31450e13	0.570676
$933$	−3.85225e13	−1.66436
$934$	−3.60915e13	−1.55183
$935$	−4.17776e13	−1.78769
$936$	1.68783e12	0.0718768
$937$	−3.05601e13	−1.29517	−0.647585	−	0.761993i	$-0.724221\pi$
$937$	−3.05601e13	−1.29517	−0.647585	+	0.761993i	$0.724221\pi$
$938$	5.61867e13	2.36985
$939$	2.79494e12	0.117321
$940$	3.13041e13	1.30775
$941$	3.36609e13	1.39950	0.699750	−	0.714388i	$-0.253295\pi$
$941$	3.36609e13	1.39950	0.699750	+	0.714388i	$0.253295\pi$
$942$	−2.96138e12	−0.122536
$943$	−1.70812e13	−0.703421
$944$	2.38860e12	0.0978968
$945$	−2.94270e13	−1.20033
$946$	1.73315e13	0.703599
$947$	−2.11821e13	−0.855843	−0.427921	−	0.903816i	$-0.640754\pi$
$947$	−2.11821e13	−0.855843	−0.427921	+	0.903816i	$0.640754\pi$
$948$	−2.55293e13	−1.02660
$949$	−4.50744e13	−1.80398
$950$	6.63337e12	0.264228
$951$	−2.92945e13	−1.16138
$952$	−3.29589e13	−1.30049
$953$	−1.54910e13	−0.608362	−0.304181	−	0.952614i	$-0.598383\pi$
$953$	−1.54910e13	−0.608362	−0.304181	+	0.952614i	$0.598383\pi$
$954$	2.07743e12	0.0812005
$955$	−1.43230e13	−0.557210
$956$	−1.64972e13	−0.638780
$957$	1.51625e13	0.584342
$958$	4.36384e13	1.67388
$959$	5.56025e13	2.12281
$960$	−2.77163e13	−1.05321
$961$	4.30762e13	1.62923
$962$	6.94695e12	0.261521
$963$	−4.52903e12	−0.169702
$964$	−6.76425e13	−2.52274
$965$	−1.13695e13	−0.422056
$966$	−9.63521e13	−3.56011
$967$	−3.03489e12	−0.111615	−0.0558077	−	0.998442i	$-0.517773\pi$
$967$	−3.03489e12	−0.111615	−0.0558077	+	0.998442i	$0.517773\pi$
$968$	5.34054e12	0.195500
$969$	−2.10354e13	−0.766466
$970$	2.51660e13	0.912730
$971$	−1.48960e13	−0.537755	−0.268877	−	0.963174i	$-0.586653\pi$
$971$	−1.48960e13	−0.537755	−0.268877	+	0.963174i	$0.586653\pi$
$972$	−1.07873e13	−0.387629
$973$	−5.17362e13	−1.85049
$974$	−6.69155e13	−2.38238
$975$	−1.10966e13	−0.393251
$976$	1.65253e13	0.582943
$977$	−5.30931e12	−0.186429	−0.0932144	−	0.995646i	$-0.529714\pi$
$977$	−5.30931e12	−0.186429	−0.0932144	+	0.995646i	$0.529714\pi$
$978$	−2.01798e13	−0.705329
$979$	5.36792e13	1.86760
$980$	−3.35530e13	−1.16202
$981$	2.91457e12	0.100476
$982$	1.40055e13	0.480614
$983$	−2.98890e13	−1.02099	−0.510495	−	0.859881i	$-0.670538\pi$
$983$	−2.98890e13	−1.02099	−0.510495	+	0.859881i	$0.670538\pi$
$984$	5.01534e12	0.170538
$985$	3.25784e13	1.10273
$986$	−4.63513e13	−1.56177
$987$	5.27351e13	1.76877
$988$	1.74951e13	0.584131
$989$	−2.02297e13	−0.672368
$990$	−6.34716e12	−0.210001
$991$	5.09698e13	1.67873	0.839367	−	0.543565i	$-0.182926\pi$
$991$	5.09698e13	1.67873	0.839367	+	0.543565i	$0.182926\pi$
$992$	−6.82391e13	−2.23733
$993$	−1.60589e13	−0.524135
$994$	1.99973e13	0.649729
$995$	−1.40193e13	−0.453442
$996$	7.70341e12	0.248037
$997$	−1.83136e12	−0.0587009	−0.0293505	−	0.999569i	$-0.509344\pi$
$997$	−1.83136e12	−0.0587009	−0.0293505	+	0.999569i	$0.509344\pi$
$998$	6.79913e13	2.16953
$999$	−5.48779e12	−0.174322

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.a.a.1.12	✓	13
3.2	odd	2		333.10.a.c.1.2		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.a.a.1.12	✓	13	1.1	even	1	trivial
333.10.a.c.1.2		13	3.2	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	37.a (trivial)

\(f(q)\)	\(=\)	\(q+34.3196 q^{2} -129.318 q^{3} +665.837 q^{4} -1076.40 q^{5} -4438.14 q^{6} +9336.44 q^{7} +5279.62 q^{8} -2959.93 q^{9} +O(q^{10})\)	\(q+34.3196 q^{2} -129.318 q^{3} +665.837 q^{4} -1076.40 q^{5} -4438.14 q^{6} +9336.44 q^{7} +5279.62 q^{8} -2959.93 q^{9} -36941.6 q^{10} -58047.3 q^{11} -86104.5 q^{12} -108005. q^{13} +320423. q^{14} +139197. q^{15} -159714. q^{16} -668634. q^{17} -101584. q^{18} -243278. q^{19} -716706. q^{20} -1.20737e6 q^{21} -1.99216e6 q^{22} +2.32530e6 q^{23} -682749. q^{24} -794490. q^{25} -3.70670e6 q^{26} +2.92813e6 q^{27} +6.21655e6 q^{28} +2.01991e6 q^{29} +4.77721e6 q^{30} +8.33762e6 q^{31} -8.18448e6 q^{32} +7.50654e6 q^{33} -2.29473e7 q^{34} -1.00497e7 q^{35} -1.97083e6 q^{36} -1.87416e6 q^{37} -8.34923e6 q^{38} +1.39670e7 q^{39} -5.68298e6 q^{40} -7.34580e6 q^{41} -4.14364e7 q^{42} -8.69984e6 q^{43} -3.86500e7 q^{44} +3.18607e6 q^{45} +7.98035e7 q^{46} -4.36777e7 q^{47} +2.06538e7 q^{48} +4.68155e7 q^{49} -2.72666e7 q^{50} +8.64662e7 q^{51} -7.19139e7 q^{52} -2.04504e7 q^{53} +1.00492e8 q^{54} +6.24820e7 q^{55} +4.92929e7 q^{56} +3.14602e7 q^{57} +6.93225e7 q^{58} -1.49555e7 q^{59} +9.26828e7 q^{60} -1.03469e8 q^{61} +2.86144e8 q^{62} -2.76352e7 q^{63} -1.99115e8 q^{64} +1.16257e8 q^{65} +2.57622e8 q^{66} +1.75352e8 q^{67} -4.45201e8 q^{68} -3.00703e8 q^{69} -3.44903e8 q^{70} +6.24089e7 q^{71} -1.56273e7 q^{72} +4.17335e8 q^{73} -6.43205e7 q^{74} +1.02742e8 q^{75} -1.61984e8 q^{76} -5.41955e8 q^{77} +4.79342e8 q^{78} +2.96492e8 q^{79} +1.71916e8 q^{80} -3.20399e8 q^{81} -2.52105e8 q^{82} -8.94658e7 q^{83} -8.03910e8 q^{84} +7.19717e8 q^{85} -2.98575e8 q^{86} -2.61210e8 q^{87} -3.06468e8 q^{88} -9.24749e8 q^{89} +1.09345e8 q^{90} -1.00838e9 q^{91} +1.54827e9 q^{92} -1.07820e9 q^{93} -1.49900e9 q^{94} +2.61865e8 q^{95} +1.05840e9 q^{96} -6.81238e8 q^{97} +1.60669e9 q^{98} +1.71816e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 32 q^{2} - 251 q^{3} + 2730 q^{4} - 2159 q^{5} - 4401 q^{6} - 12576 q^{7} - 20394 q^{8} + 69112 q^{9}+O(q^{10}) \) 13 * q - 32 * q^2 - 251 * q^3 + 2730 * q^4 - 2159 * q^5 - 4401 * q^6 - 12576 * q^7 - 20394 * q^8 + 69112 * q^9	\( 13 q - 32 q^{2} - 251 q^{3} + 2730 q^{4} - 2159 q^{5} - 4401 q^{6} - 12576 q^{7} - 20394 q^{8} + 69112 q^{9} - 106605 q^{10} - 112451 q^{11} + 220963 q^{12} + 7129 q^{13} + 294824 q^{14} - 63644 q^{15} + 145178 q^{16} - 890862 q^{17} - 3066225 q^{18} - 1435874 q^{19} - 3193339 q^{20} - 4745036 q^{21} - 4350913 q^{22} - 2565799 q^{23} - 15286101 q^{24} - 1828304 q^{25} - 7543133 q^{26} - 10134680 q^{27} - 24344602 q^{28} - 2992323 q^{29} - 25604140 q^{30} - 8242245 q^{31} - 22320310 q^{32} - 18079398 q^{33} + 5045920 q^{34} - 26953204 q^{35} - 10407455 q^{36} - 24364093 q^{37} - 42175680 q^{38} - 79430765 q^{39} - 61032223 q^{40} - 50975109 q^{41} + 54850616 q^{42} - 18142836 q^{43} - 55265137 q^{44} + 136868596 q^{45} + 157343401 q^{46} - 14353596 q^{47} + 213610631 q^{48} + 213271999 q^{49} + 175451561 q^{50} + 151710418 q^{51} + 151573285 q^{52} + 74438872 q^{53} + 174228132 q^{54} + 118316889 q^{55} + 362406090 q^{56} + 248282906 q^{57} + 206405719 q^{58} - 251964328 q^{59} + 877937048 q^{60} + 202847323 q^{61} - 34418509 q^{62} - 227178410 q^{63} + 187231490 q^{64} - 341466470 q^{65} + 989905110 q^{66} - 12257509 q^{67} - 332496576 q^{68} - 768097033 q^{69} + 1098443332 q^{70} - 310979094 q^{71} - 588411507 q^{72} - 249752015 q^{73} + 59973152 q^{74} - 634307724 q^{75} + 365061440 q^{76} - 1143945802 q^{77} + 1471186393 q^{78} + 30429049 q^{79} + 885873041 q^{80} - 350972903 q^{81} - 1192633571 q^{82} - 2559788658 q^{83} - 2510580834 q^{84} - 3291393166 q^{85} - 1373534302 q^{86} - 1215098129 q^{87} + 107941215 q^{88} - 3063565514 q^{89} - 552233182 q^{90} - 1743876566 q^{91} - 2937303341 q^{92} - 1077794354 q^{93} + 49542148 q^{94} - 2168155374 q^{95} - 1504910121 q^{96} - 429307758 q^{97} - 1351241634 q^{98} - 3266142174 q^{99}+O(q^{100}) \) 13 * q - 32 * q^2 - 251 * q^3 + 2730 * q^4 - 2159 * q^5 - 4401 * q^6 - 12576 * q^7 - 20394 * q^8 + 69112 * q^9 - 106605 * q^10 - 112451 * q^11 + 220963 * q^12 + 7129 * q^13 + 294824 * q^14 - 63644 * q^15 + 145178 * q^16 - 890862 * q^17 - 3066225 * q^18 - 1435874 * q^19 - 3193339 * q^20 - 4745036 * q^21 - 4350913 * q^22 - 2565799 * q^23 - 15286101 * q^24 - 1828304 * q^25 - 7543133 * q^26 - 10134680 * q^27 - 24344602 * q^28 - 2992323 * q^29 - 25604140 * q^30 - 8242245 * q^31 - 22320310 * q^32 - 18079398 * q^33 + 5045920 * q^34 - 26953204 * q^35 - 10407455 * q^36 - 24364093 * q^37 - 42175680 * q^38 - 79430765 * q^39 - 61032223 * q^40 - 50975109 * q^41 + 54850616 * q^42 - 18142836 * q^43 - 55265137 * q^44 + 136868596 * q^45 + 157343401 * q^46 - 14353596 * q^47 + 213610631 * q^48 + 213271999 * q^49 + 175451561 * q^50 + 151710418 * q^51 + 151573285 * q^52 + 74438872 * q^53 + 174228132 * q^54 + 118316889 * q^55 + 362406090 * q^56 + 248282906 * q^57 + 206405719 * q^58 - 251964328 * q^59 + 877937048 * q^60 + 202847323 * q^61 - 34418509 * q^62 - 227178410 * q^63 + 187231490 * q^64 - 341466470 * q^65 + 989905110 * q^66 - 12257509 * q^67 - 332496576 * q^68 - 768097033 * q^69 + 1098443332 * q^70 - 310979094 * q^71 - 588411507 * q^72 - 249752015 * q^73 + 59973152 * q^74 - 634307724 * q^75 + 365061440 * q^76 - 1143945802 * q^77 + 1471186393 * q^78 + 30429049 * q^79 + 885873041 * q^80 - 350972903 * q^81 - 1192633571 * q^82 - 2559788658 * q^83 - 2510580834 * q^84 - 3291393166 * q^85 - 1373534302 * q^86 - 1215098129 * q^87 + 107941215 * q^88 - 3063565514 * q^89 - 552233182 * q^90 - 1743876566 * q^91 - 2937303341 * q^92 - 1077794354 * q^93 + 49542148 * q^94 - 2168155374 * q^95 - 1504910121 * q^96 - 429307758 * q^97 - 1351241634 * q^98 - 3266142174 * q^99

Introduction

L-functions

Modular forms

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