LMFDB - Embedded newform 37.10.a.a.1.2

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			1.2
Root			$38.3784$ 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)

$f(q)$	$=$	$q-40.3784 q^{2} +50.3948 q^{3} +1118.42 q^{4} -1136.25 q^{5} -2034.86 q^{6} +800.534 q^{7} -24486.1 q^{8} -17143.4 q^{9} +O(q^{10})$	\(q-40.3784 q^{2} +50.3948 q^{3} +1118.42 q^{4} -1136.25 q^{5} -2034.86 q^{6} +800.534 q^{7} -24486.1 q^{8} -17143.4 q^{9} +45879.8 q^{10} +46888.8 q^{11} +56362.3 q^{12} +125499. q^{13} -32324.3 q^{14} -57260.9 q^{15} +416081. q^{16} +75049.5 q^{17} +692222. q^{18} +404923. q^{19} -1.27080e6 q^{20} +40342.8 q^{21} -1.89330e6 q^{22} -1.49268e6 q^{23} -1.23397e6 q^{24} -662070. q^{25} -5.06744e6 q^{26} -1.85586e6 q^{27} +895330. q^{28} -1.62342e6 q^{29} +2.31210e6 q^{30} +2.87183e6 q^{31} -4.26380e6 q^{32} +2.36295e6 q^{33} -3.03038e6 q^{34} -909604. q^{35} -1.91734e7 q^{36} -1.87416e6 q^{37} -1.63501e7 q^{38} +6.32449e6 q^{39} +2.78222e7 q^{40} -2.75969e7 q^{41} -1.62898e6 q^{42} +4.56953e6 q^{43} +5.24412e7 q^{44} +1.94791e7 q^{45} +6.02721e7 q^{46} -3.06309e7 q^{47} +2.09683e7 q^{48} -3.97128e7 q^{49} +2.67333e7 q^{50} +3.78210e6 q^{51} +1.40360e8 q^{52} -1.04627e8 q^{53} +7.49366e7 q^{54} -5.32773e7 q^{55} -1.96020e7 q^{56} +2.04060e7 q^{57} +6.55511e7 q^{58} +1.36231e7 q^{59} -6.40415e7 q^{60} -8.83091e7 q^{61} -1.15960e8 q^{62} -1.37238e7 q^{63} -4.08679e7 q^{64} -1.42598e8 q^{65} -9.54123e7 q^{66} +7.75239e7 q^{67} +8.39366e7 q^{68} -7.52233e7 q^{69} +3.67284e7 q^{70} +7.73617e7 q^{71} +4.19774e8 q^{72} -9.50405e7 q^{73} +7.56756e7 q^{74} -3.33649e7 q^{75} +4.52872e8 q^{76} +3.75361e7 q^{77} -2.55373e8 q^{78} +2.71542e8 q^{79} -4.72770e8 q^{80} +2.43907e8 q^{81} +1.11432e9 q^{82} -2.31731e8 q^{83} +4.51200e7 q^{84} -8.52747e7 q^{85} -1.84510e8 q^{86} -8.18119e7 q^{87} -1.14813e9 q^{88} -8.23276e8 q^{89} -7.86534e8 q^{90} +1.00466e8 q^{91} -1.66944e9 q^{92} +1.44726e8 q^{93} +1.23683e9 q^{94} -4.60092e8 q^{95} -2.14874e8 q^{96} -7.78331e8 q^{97} +1.60354e9 q^{98} -8.03833e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−40.3784	−1.78449	−0.892245	−	0.451551i	$-0.850871\pi$
$2$	−40.3784	−1.78449	−0.892245	+	0.451551i	$0.850871\pi$
$3$	50.3948	0.359203	0.179602	−	0.983739i	$-0.442519\pi$
$3$	50.3948	0.359203	0.179602	+	0.983739i	$0.442519\pi$
$4$	1118.42	2.18441
$5$	−1136.25	−0.813031	−0.406516	−	0.913644i	$-0.633256\pi$
$5$	−1136.25	−0.813031	−0.406516	+	0.913644i	$0.633256\pi$
$6$	−2034.86	−0.640994
$7$	800.534	0.126020	0.0630099	−	0.998013i	$-0.479930\pi$
$7$	800.534	0.126020	0.0630099	+	0.998013i	$0.479930\pi$
$8$	−24486.1	−2.11356
$9$	−17143.4	−0.870973
$10$	45879.8	1.45085
$11$	46888.8	0.965612	0.482806	−	0.875727i	$-0.339618\pi$
$11$	46888.8	0.965612	0.482806	+	0.875727i	$0.339618\pi$
$12$	56362.3	0.784645
$13$	125499.	1.21869	0.609347	−	0.792904i	$-0.291432\pi$
$13$	125499.	1.21869	0.609347	+	0.792904i	$0.291432\pi$
$14$	−32324.3	−0.224881
$15$	−57260.9	−0.292043
$16$	416081.	1.58722
$17$	75049.5	0.217935	0.108968	−	0.994045i	$-0.465246\pi$
$17$	75049.5	0.217935	0.108968	+	0.994045i	$0.465246\pi$
$18$	692222.	1.55424
$19$	404923.	0.712821	0.356411	−	0.934329i	$-0.384000\pi$
$19$	404923.	0.712821	0.356411	+	0.934329i	$0.384000\pi$
$20$	−1.27080e6	−1.77599
$21$	40342.8	0.0452667
$22$	−1.89330e6	−1.72312
$23$	−1.49268e6	−1.11222	−0.556111	−	0.831108i	$-0.687707\pi$
$23$	−1.49268e6	−1.11222	−0.556111	+	0.831108i	$0.687707\pi$
$24$	−1.23397e6	−0.759198
$25$	−662070.	−0.338980
$26$	−5.06744e6	−2.17475
$27$	−1.85586e6	−0.672059
$28$	895330.	0.275278
$29$	−1.62342e6	−0.426226	−0.213113	−	0.977028i	$-0.568360\pi$
$29$	−1.62342e6	−0.426226	−0.213113	+	0.977028i	$0.568360\pi$
$30$	2.31210e6	0.521149
$31$	2.87183e6	0.558511	0.279256	−	0.960217i	$-0.409912\pi$
$31$	2.87183e6	0.558511	0.279256	+	0.960217i	$0.409912\pi$
$32$	−4.26380e6	−0.718824
$33$	2.36295e6	0.346851
$34$	−3.03038e6	−0.388904
$35$	−909604.	−0.102458
$36$	−1.91734e7	−1.90256
$37$	−1.87416e6	−0.164399
$37$	−1.87416e6	−0.164399
$38$	−1.63501e7	−1.27202
$39$	6.32449e6	0.437759
$40$	2.78222e7	1.71839
$41$	−2.75969e7	−1.52522	−0.762610	−	0.646859i	$-0.776082\pi$
$41$	−2.75969e7	−1.52522	−0.762610	+	0.646859i	$0.776082\pi$
$42$	−1.62898e6	−0.0807780
$43$	4.56953e6	0.203828	0.101914	−	0.994793i	$-0.467503\pi$
$43$	4.56953e6	0.203828	0.101914	+	0.994793i	$0.467503\pi$
$44$	5.24412e7	2.10929
$45$	1.94791e7	0.708128
$46$	6.02721e7	1.98475
$47$	−3.06309e7	−0.915629	−0.457814	−	0.889048i	$-0.651368\pi$
$47$	−3.06309e7	−0.915629	−0.457814	+	0.889048i	$0.651368\pi$
$48$	2.09683e7	0.570135
$49$	−3.97128e7	−0.984119
$50$	2.67333e7	0.604906
$51$	3.78210e6	0.0782831
$52$	1.40360e8	2.66212
$53$	−1.04627e8	−1.82139	−0.910697	−	0.413076i	$-0.864454\pi$
$53$	−1.04627e8	−1.82139	−0.910697	+	0.413076i	$0.864454\pi$
$54$	7.49366e7	1.19928
$55$	−5.32773e7	−0.785073
$56$	−1.96020e7	−0.266350
$57$	2.04060e7	0.256048
$58$	6.55511e7	0.760596
$59$	1.36231e7	0.146366	0.0731832	−	0.997319i	$-0.476684\pi$
$59$	1.36231e7	0.146366	0.0731832	+	0.997319i	$0.476684\pi$
$60$	−6.40415e7	−0.637941
$61$	−8.83091e7	−0.816622	−0.408311	−	0.912843i	$-0.633882\pi$
$61$	−8.83091e7	−0.816622	−0.408311	+	0.912843i	$0.633882\pi$
$62$	−1.15960e8	−0.996658
$63$	−1.37238e7	−0.109760
$64$	−4.08679e7	−0.304489
$65$	−1.42598e8	−0.990836
$66$	−9.54123e7	−0.618952
$67$	7.75239e7	0.470001	0.235001	−	0.971995i	$-0.424491\pi$
$67$	7.75239e7	0.470001	0.235001	+	0.971995i	$0.424491\pi$
$68$	8.39366e7	0.476059
$69$	−7.52233e7	−0.399514
$70$	3.67284e7	0.182835
$71$	7.73617e7	0.361296	0.180648	−	0.983548i	$-0.442180\pi$
$71$	7.73617e7	0.361296	0.180648	+	0.983548i	$0.442180\pi$
$72$	4.19774e8	1.84085
$73$	−9.50405e7	−0.391702	−0.195851	−	0.980634i	$-0.562747\pi$
$73$	−9.50405e7	−0.391702	−0.195851	+	0.980634i	$0.562747\pi$
$74$	7.56756e7	0.293368
$75$	−3.33649e7	−0.121763
$76$	4.52872e8	1.55709
$77$	3.75361e7	0.121686
$78$	−2.55373e8	−0.781176
$79$	2.71542e8	0.784360	0.392180	−	0.919889i	$-0.371721\pi$
$79$	2.71542e8	0.784360	0.392180	+	0.919889i	$0.371721\pi$
$80$	−4.72770e8	−1.29046
$81$	2.43907e8	0.629567
$82$	1.11432e9	2.72174
$83$	−2.31731e8	−0.535960	−0.267980	−	0.963425i	$-0.586356\pi$
$83$	−2.31731e8	−0.535960	−0.267980	+	0.963425i	$0.586356\pi$
$84$	4.51200e7	0.0988808
$85$	−8.52747e7	−0.177188
$86$	−1.84510e8	−0.363729
$87$	−8.18119e7	−0.153102
$88$	−1.14813e9	−2.04088
$89$	−8.23276e8	−1.39088	−0.695441	−	0.718583i	$-0.744791\pi$
$89$	−8.23276e8	−1.39088	−0.695441	+	0.718583i	$0.744791\pi$
$90$	−7.86534e8	−1.26365
$91$	1.00466e8	0.153580
$92$	−1.66944e9	−2.42954
$93$	1.44726e8	0.200619
$94$	1.23683e9	1.63393
$95$	−4.60092e8	−0.579546
$96$	−2.14874e8	−0.258204
$97$	−7.78331e8	−0.892671	−0.446336	−	0.894866i	$-0.647271\pi$
$97$	−7.78331e8	−0.892671	−0.446336	+	0.894866i	$0.647271\pi$
$98$	1.60354e9	1.75615
$99$	−8.03833e8	−0.841022
$100$	−7.40470e8	−0.740470
$101$	1.93447e9	1.84976	0.924880	−	0.380260i	$-0.124165\pi$
$101$	1.93447e9	1.84976	0.924880	+	0.380260i	$0.124165\pi$
$102$	−1.52715e8	−0.139695
$103$	−4.06349e8	−0.355740	−0.177870	−	0.984054i	$-0.556921\pi$
$103$	−4.06349e8	−0.355740	−0.177870	+	0.984054i	$0.556921\pi$
$104$	−3.07298e9	−2.57578
$105$	−4.58393e7	−0.0368032
$106$	4.22469e9	3.25026
$107$	8.42547e8	0.621394	0.310697	−	0.950509i	$-0.399437\pi$
$107$	8.42547e8	0.621394	0.310697	+	0.950509i	$0.399437\pi$
$108$	−2.07562e9	−1.46805
$109$	6.58247e8	0.446652	0.223326	−	0.974744i	$-0.428308\pi$
$109$	6.58247e8	0.446652	0.223326	+	0.974744i	$0.428308\pi$
$110$	2.15125e9	1.40095
$111$	−9.44480e7	−0.0590526
$112$	3.33087e8	0.200022
$113$	−1.16368e9	−0.671398	−0.335699	−	0.941969i	$-0.608973\pi$
$113$	−1.16368e9	−0.671398	−0.335699	+	0.941969i	$0.608973\pi$
$114$	−8.23961e8	−0.456915
$115$	1.69605e9	0.904272
$116$	−1.81566e9	−0.931050
$117$	−2.15147e9	−1.06145
$118$	−5.50079e8	−0.261190
$119$	6.00797e7	0.0274642
$120$	1.40210e9	0.617251
$121$	−1.59383e8	−0.0675942
$122$	3.56578e9	1.45725
$123$	−1.39074e9	−0.547863
$124$	3.21191e9	1.22002
$125$	2.97150e9	1.08863
$126$	5.54147e8	0.195865
$127$	−5.36695e9	−1.83067	−0.915336	−	0.402691i	$-0.868075\pi$
$127$	−5.36695e9	−1.83067	−0.915336	+	0.402691i	$0.868075\pi$
$128$	3.83325e9	1.26218
$129$	2.30281e8	0.0732156
$130$	5.75786e9	1.76814
$131$	5.56134e9	1.64990	0.824951	−	0.565204i	$-0.191202\pi$
$131$	5.56134e9	1.64990	0.824951	+	0.565204i	$0.191202\pi$
$132$	2.64277e9	0.757663
$133$	3.24154e8	0.0898296
$134$	−3.13029e9	−0.838712
$135$	2.10871e9	0.546405
$136$	−1.83767e9	−0.460620
$137$	−7.66808e9	−1.85971	−0.929853	−	0.367932i	$-0.880066\pi$
$137$	−7.66808e9	−1.85971	−0.929853	+	0.367932i	$0.880066\pi$
$138$	3.03740e9	0.712928
$139$	6.16588e9	1.40097	0.700484	−	0.713668i	$-0.252967\pi$
$139$	6.16588e9	1.40097	0.700484	+	0.713668i	$0.252967\pi$
$140$	−1.01732e9	−0.223810
$141$	−1.54364e9	−0.328897
$142$	−3.12374e9	−0.644730
$143$	5.88450e9	1.17678
$144$	−7.13303e9	−1.38243
$145$	1.84460e9	0.346535
$146$	3.83758e9	0.698989
$147$	−2.00132e9	−0.353499
$148$	−2.09609e9	−0.359114
$149$	−7.02935e9	−1.16836	−0.584180	−	0.811624i	$-0.698584\pi$
$149$	−7.02935e9	−1.16836	−0.584180	+	0.811624i	$0.698584\pi$
$150$	1.34722e9	0.217284
$151$	−6.55525e9	−1.02611	−0.513054	−	0.858356i	$-0.671486\pi$
$151$	−6.55525e9	−1.02611	−0.513054	+	0.858356i	$0.671486\pi$
$152$	−9.91498e9	−1.50659
$153$	−1.28660e9	−0.189816
$154$	−1.51565e9	−0.217148
$155$	−3.26311e9	−0.454087
$156$	7.07341e9	0.956243
$157$	−3.62788e9	−0.476546	−0.238273	−	0.971198i	$-0.576581\pi$
$157$	−3.62788e9	−0.476546	−0.238273	+	0.971198i	$0.576581\pi$
$158$	−1.09644e10	−1.39968
$159$	−5.27267e9	−0.654250
$160$	4.84473e9	0.584426
$161$	−1.19494e9	−0.140162
$162$	−9.84859e9	−1.12346
$163$	7.51980e9	0.834377	0.417189	−	0.908820i	$-0.363015\pi$
$163$	7.51980e9	0.834377	0.417189	+	0.908820i	$0.363015\pi$
$164$	−3.08648e10	−3.33170
$165$	−2.68490e9	−0.282001
$166$	9.35691e9	0.956415
$167$	−1.18795e10	−1.18188	−0.590939	−	0.806716i	$-0.701243\pi$
$167$	−1.18795e10	−1.18188	−0.590939	+	0.806716i	$0.701243\pi$
$168$	−9.87837e8	−0.0956739
$169$	5.14546e9	0.485215
$170$	3.44326e9	0.316191
$171$	−6.94173e9	−0.620848
$172$	5.11064e9	0.445243
$173$	9.58241e9	0.813331	0.406666	−	0.913577i	$-0.366691\pi$
$173$	9.58241e9	0.813331	0.406666	+	0.913577i	$0.366691\pi$
$174$	3.30343e9	0.273208
$175$	−5.30010e8	−0.0427182
$176$	1.95096e10	1.53264
$177$	6.86533e8	0.0525753
$178$	3.32426e10	2.48202
$179$	−1.67661e10	−1.22066	−0.610329	−	0.792148i	$-0.708963\pi$
$179$	−1.67661e10	−1.22066	−0.610329	+	0.792148i	$0.708963\pi$
$180$	2.17857e10	1.54684
$181$	1.36007e10	0.941907	0.470953	−	0.882158i	$-0.343910\pi$
$181$	1.36007e10	0.941907	0.470953	+	0.882158i	$0.343910\pi$
$182$	−4.05666e9	−0.274061
$183$	−4.45032e9	−0.293333
$184$	3.65499e10	2.35075
$185$	2.12951e9	0.133662
$186$	−5.84379e9	−0.358003
$187$	3.51898e9	0.210441
$188$	−3.42581e10	−2.00010
$189$	−1.48568e9	−0.0846928
$190$	1.85778e10	1.03419
$191$	8.41372e9	0.457444	0.228722	−	0.973492i	$-0.426545\pi$
$191$	8.41372e9	0.457444	0.228722	+	0.973492i	$0.426545\pi$
$192$	−2.05953e9	−0.109374
$193$	−1.46218e9	−0.0758564	−0.0379282	−	0.999280i	$-0.512076\pi$
$193$	−1.46218e9	−0.0758564	−0.0379282	+	0.999280i	$0.512076\pi$
$194$	3.14278e10	1.59296
$195$	−7.18617e9	−0.355911
$196$	−4.44154e10	−2.14972
$197$	−3.23987e10	−1.53260	−0.766300	−	0.642483i	$-0.777904\pi$
$197$	−3.23987e10	−1.53260	−0.766300	+	0.642483i	$0.777904\pi$
$198$	3.24575e10	1.50080
$199$	4.77171e9	0.215693	0.107846	−	0.994168i	$-0.465605\pi$
$199$	4.77171e9	0.215693	0.107846	+	0.994168i	$0.465605\pi$
$200$	1.62115e10	0.716455
$201$	3.90680e9	0.168826
$202$	−7.81107e10	−3.30088
$203$	−1.29960e9	−0.0537129
$204$	4.22997e9	0.171002
$205$	3.13568e10	1.24005
$206$	1.64077e10	0.634814
$207$	2.55896e10	0.968716
$208$	5.22177e10	1.93434
$209$	1.89864e10	0.688309
$210$	1.85092e9	0.0656750
$211$	−2.63931e9	−0.0916685	−0.0458343	−	0.998949i	$-0.514595\pi$
$211$	−2.63931e9	−0.0916685	−0.0458343	+	0.998949i	$0.514595\pi$
$212$	−1.17017e11	−3.97866
$213$	3.89863e9	0.129779
$214$	−3.40207e10	−1.10887
$215$	−5.19211e9	−0.165718
$216$	4.54427e10	1.42044
$217$	2.29900e9	0.0703835
$218$	−2.65790e10	−0.797047
$219$	−4.78955e9	−0.140701
$220$	−5.95861e10	−1.71492
$221$	9.41863e9	0.265596
$222$	3.81366e9	0.105379
$223$	−5.42102e10	−1.46794	−0.733971	−	0.679181i	$-0.762335\pi$
$223$	−5.42102e10	−1.46794	−0.733971	+	0.679181i	$0.762335\pi$
$224$	−3.41332e9	−0.0905860
$225$	1.13501e10	0.295242
$226$	4.69875e10	1.19810
$227$	6.10866e10	1.52697	0.763483	−	0.645828i	$-0.223488\pi$
$227$	6.10866e10	1.52697	0.763483	+	0.645828i	$0.223488\pi$
$228$	2.28224e10	0.559312
$229$	2.66952e10	0.641466	0.320733	−	0.947170i	$-0.396071\pi$
$229$	2.66952e10	0.641466	0.320733	+	0.947170i	$0.396071\pi$
$230$	−6.84839e10	−1.61366
$231$	1.89163e9	0.0437101
$232$	3.97512e10	0.900854
$233$	2.99218e10	0.665099	0.332549	−	0.943086i	$-0.392091\pi$
$233$	2.99218e10	0.665099	0.332549	+	0.943086i	$0.392091\pi$
$234$	8.68730e10	1.89415
$235$	3.48042e10	0.744435
$236$	1.52363e10	0.319724
$237$	1.36843e10	0.281744
$238$	−2.42592e9	−0.0490095
$239$	−5.94206e10	−1.17800	−0.589001	−	0.808132i	$-0.700479\pi$
$239$	−5.94206e10	−1.17800	−0.589001	+	0.808132i	$0.700479\pi$
$240$	−2.38252e10	−0.463538
$241$	−4.57857e10	−0.874286	−0.437143	−	0.899392i	$-0.644010\pi$
$241$	−4.57857e10	−0.874286	−0.437143	+	0.899392i	$0.644010\pi$
$242$	6.43565e9	0.120621
$243$	4.88205e10	0.898202
$244$	−9.87663e10	−1.78383
$245$	4.51235e10	0.800120
$246$	5.61558e10	0.977657
$247$	5.08173e10	0.868711
$248$	−7.03200e10	−1.18045
$249$	−1.16780e10	−0.192518
$250$	−1.19985e11	−1.94265
$251$	2.97565e10	0.473206	0.236603	−	0.971606i	$-0.423966\pi$
$251$	2.97565e10	0.473206	0.236603	+	0.971606i	$0.423966\pi$
$252$	−1.53490e10	−0.239760
$253$	−6.99901e10	−1.07397
$254$	2.16709e11	3.26682
$255$	−4.29740e9	−0.0636466
$256$	−1.33856e11	−1.94786
$257$	−7.59800e10	−1.08643	−0.543213	−	0.839595i	$-0.682792\pi$
$257$	−7.59800e10	−1.08643	−0.543213	+	0.839595i	$0.682792\pi$
$258$	−9.29837e9	−0.130653
$259$	−1.50033e9	−0.0207175
$260$	−1.59483e11	−2.16439
$261$	2.78309e10	0.371231
$262$	−2.24558e11	−2.94424
$263$	7.66520e10	0.987921	0.493961	−	0.869484i	$-0.335549\pi$
$263$	7.66520e10	0.987921	0.493961	+	0.869484i	$0.335549\pi$
$264$	−5.78595e10	−0.733090
$265$	1.18882e11	1.48085
$266$	−1.30888e10	−0.160300
$267$	−4.14888e10	−0.499609
$268$	8.67039e10	1.02667
$269$	1.50781e11	1.75574	0.877872	−	0.478896i	$-0.158963\pi$
$269$	1.50781e11	1.75574	0.877872	+	0.478896i	$0.158963\pi$
$270$	−8.51464e10	−0.975055
$271$	1.54469e11	1.73972	0.869858	−	0.493302i	$-0.164210\pi$
$271$	1.54469e11	1.73972	0.869858	+	0.493302i	$0.164210\pi$
$272$	3.12267e10	0.345912
$273$	5.06297e9	0.0551662
$274$	3.09625e11	3.31863
$275$	−3.10437e10	−0.327323
$276$	−8.41310e10	−0.872700
$277$	−6.13690e9	−0.0626311	−0.0313156	−	0.999510i	$-0.509970\pi$
$277$	−6.13690e9	−0.0626311	−0.0313156	+	0.999510i	$0.509970\pi$
$278$	−2.48968e11	−2.50001
$279$	−4.92329e10	−0.486448
$280$	2.22727e10	0.216551
$281$	1.64996e11	1.57869	0.789343	−	0.613952i	$-0.210421\pi$
$281$	1.64996e11	1.57869	0.789343	+	0.613952i	$0.210421\pi$
$282$	6.23296e10	0.586913
$283$	−1.62244e11	−1.50359	−0.751794	−	0.659398i	$-0.770811\pi$
$283$	−1.62244e11	−1.50359	−0.751794	+	0.659398i	$0.770811\pi$
$284$	8.65226e10	0.789218
$285$	−2.31862e10	−0.208175
$286$	−2.37607e11	−2.09996
$287$	−2.20922e10	−0.192208
$288$	7.30959e10	0.626076
$289$	−1.12955e11	−0.952504
$290$	−7.44821e10	−0.618388
$291$	−3.92238e10	−0.320650
$292$	−1.06295e11	−0.855636
$293$	−1.89963e11	−1.50579	−0.752896	−	0.658139i	$-0.771344\pi$
$293$	−1.89963e11	−1.50579	−0.752896	+	0.658139i	$0.771344\pi$
$294$	8.08100e10	0.630815
$295$	−1.54792e10	−0.119001
$296$	4.58909e10	0.347467
$297$	−8.70190e10	−0.648948
$298$	2.83834e11	2.08493
$299$	−1.87330e11	−1.35546
$300$	−3.73158e10	−0.265979
$301$	3.65807e9	0.0256863
$302$	2.64691e11	1.83108
$303$	9.74871e10	0.664439
$304$	1.68481e11	1.13141
$305$	1.00341e11	0.663939
$306$	5.19509e10	0.338725
$307$	−1.00092e11	−0.643097	−0.321549	−	0.946893i	$-0.604203\pi$
$307$	−1.00092e11	−0.643097	−0.321549	+	0.946893i	$0.604203\pi$
$308$	4.19810e10	0.265812
$309$	−2.04779e10	−0.127783
$310$	1.31759e11	0.810314
$311$	7.13241e10	0.432329	0.216165	−	0.976357i	$-0.430645\pi$
$311$	7.13241e10	0.432329	0.216165	+	0.976357i	$0.430645\pi$
$312$	−1.54862e11	−0.925229
$313$	−3.34324e10	−0.196887	−0.0984436	−	0.995143i	$-0.531386\pi$
$313$	−3.34324e10	−0.196887	−0.0984436	+	0.995143i	$0.531386\pi$
$314$	1.46488e11	0.850391
$315$	1.55937e10	0.0892382
$316$	3.03697e11	1.71336
$317$	1.54602e11	0.859900	0.429950	−	0.902853i	$-0.358531\pi$
$317$	1.54602e11	0.859900	0.429950	+	0.902853i	$0.358531\pi$
$318$	2.12902e11	1.16750
$319$	−7.61203e10	−0.411569
$320$	4.64360e10	0.247559
$321$	4.24600e10	0.223207
$322$	4.82498e10	0.250118
$323$	3.03892e10	0.155349
$324$	2.72790e11	1.37523
$325$	−8.30890e10	−0.413113
$326$	−3.03638e11	−1.48894
$327$	3.31722e10	0.160439
$328$	6.75740e11	3.22364
$329$	−2.45211e10	−0.115387
$330$	1.08412e11	0.503227
$331$	−3.99258e11	−1.82822	−0.914109	−	0.405468i	$-0.867109\pi$
$331$	−3.99258e11	−1.82822	−0.914109	+	0.405468i	$0.867109\pi$
$332$	−2.59171e11	−1.17075
$333$	3.21294e10	0.143187
$334$	4.79674e11	2.10905
$335$	−8.80862e10	−0.382126
$336$	1.67859e10	0.0718484
$337$	−8.72916e10	−0.368670	−0.184335	−	0.982863i	$-0.559013\pi$
$337$	−8.72916e10	−0.368670	−0.184335	+	0.982863i	$0.559013\pi$
$338$	−2.07765e11	−0.865861
$339$	−5.86434e10	−0.241168
$340$	−9.53726e10	−0.387051
$341$	1.34657e11	0.539305
$342$	2.80296e11	1.10790
$343$	−6.40959e10	−0.250038
$344$	−1.11890e11	−0.430803
$345$	8.54722e10	0.324817
$346$	−3.86923e11	−1.45138
$347$	−4.88075e11	−1.80719	−0.903595	−	0.428388i	$-0.859081\pi$
$347$	−4.88075e11	−1.80719	−0.903595	+	0.428388i	$0.859081\pi$
$348$	−9.14997e10	−0.334436
$349$	−5.32048e11	−1.91971	−0.959856	−	0.280493i	$-0.909502\pi$
$349$	−5.32048e11	−1.91971	−0.959856	+	0.280493i	$0.909502\pi$
$350$	2.14010e10	0.0762302
$351$	−2.32908e11	−0.819035
$352$	−1.99925e11	−0.694104
$353$	3.09116e11	1.05959	0.529793	−	0.848127i	$-0.322270\pi$
$353$	3.09116e11	1.05959	0.529793	+	0.848127i	$0.322270\pi$
$354$	−2.77211e10	−0.0938201
$355$	−8.79019e10	−0.293745
$356$	−9.20764e11	−3.03825
$357$	3.02770e9	0.00986521
$358$	6.76989e11	2.17825
$359$	−3.81338e11	−1.21167	−0.605836	−	0.795589i	$-0.707161\pi$
$359$	−3.81338e11	−1.21167	−0.605836	+	0.795589i	$0.707161\pi$
$360$	−4.76967e11	−1.49667
$361$	−1.58725e11	−0.491886
$362$	−5.49175e11	−1.68082
$363$	−8.03210e9	−0.0242800
$364$	1.12363e11	0.335480
$365$	1.07989e11	0.318466
$366$	1.79697e11	0.523450
$367$	5.27302e10	0.151727	0.0758634	−	0.997118i	$-0.475829\pi$
$367$	5.27302e10	0.151727	0.0758634	+	0.997118i	$0.475829\pi$
$368$	−6.21076e11	−1.76534
$369$	4.73103e11	1.32842
$370$	−8.59861e10	−0.238518
$371$	−8.37578e10	−0.229532
$372$	1.61863e11	0.438233
$373$	1.59327e11	0.426186	0.213093	−	0.977032i	$-0.431646\pi$
$373$	1.59327e11	0.426186	0.213093	+	0.977032i	$0.431646\pi$
$374$	−1.42091e11	−0.375530
$375$	1.49748e11	0.391040
$376$	7.50031e11	1.93524
$377$	−2.03737e11	−0.519439
$378$	5.99893e10	0.151133
$379$	4.61244e11	1.14830	0.574149	−	0.818751i	$-0.305333\pi$
$379$	4.61244e11	1.14830	0.574149	+	0.818751i	$0.305333\pi$
$380$	−5.14574e11	−1.26596
$381$	−2.70466e11	−0.657583
$382$	−3.39733e11	−0.816304
$383$	3.85053e11	0.914378	0.457189	−	0.889370i	$-0.348856\pi$
$383$	3.85053e11	0.914378	0.457189	+	0.889370i	$0.348856\pi$
$384$	1.93176e11	0.453380
$385$	−4.26503e10	−0.0989347
$386$	5.90404e10	0.135365
$387$	−7.83371e10	−0.177529
$388$	−8.70498e11	−1.94996
$389$	7.60426e11	1.68377	0.841887	−	0.539654i	$-0.181445\pi$
$389$	7.60426e11	1.68377	0.841887	+	0.539654i	$0.181445\pi$
$390$	2.90166e11	0.635121
$391$	−1.12025e11	−0.242393
$392$	9.72411e11	2.08000
$393$	2.80262e11	0.592650
$394$	1.30821e12	2.73491
$395$	−3.08539e11	−0.637709
$396$	−8.99019e11	−1.83713
$397$	2.76424e11	0.558493	0.279247	−	0.960219i	$-0.409915\pi$
$397$	2.76424e11	0.558493	0.279247	+	0.960219i	$0.409915\pi$
$398$	−1.92674e11	−0.384902
$399$	1.63357e10	0.0322671
$400$	−2.75475e11	−0.538037
$401$	3.99684e11	0.771910	0.385955	−	0.922518i	$-0.373872\pi$
$401$	3.99684e11	0.771910	0.385955	+	0.922518i	$0.373872\pi$
$402$	−1.57750e11	−0.301268
$403$	3.60412e11	0.680654
$404$	2.16354e12	4.04063
$405$	−2.77139e11	−0.511858
$406$	5.24759e10	0.0958501
$407$	−8.78773e10	−0.158746
$408$	−9.26090e10	−0.165456
$409$	1.18586e11	0.209545	0.104773	−	0.994496i	$-0.466589\pi$
$409$	1.18586e11	0.209545	0.104773	+	0.994496i	$0.466589\pi$
$410$	−1.26614e12	−2.21286
$411$	−3.86431e11	−0.668012
$412$	−4.54468e11	−0.777080
$413$	1.09057e10	0.0184451
$414$	−1.03327e12	−1.72866
$415$	2.63303e11	0.435752
$416$	−5.35102e11	−0.876026
$417$	3.10728e11	0.503232
$418$	−7.66639e11	−1.22828
$419$	−3.30035e11	−0.523115	−0.261558	−	0.965188i	$-0.584236\pi$
$419$	−3.30035e11	−0.523115	−0.261558	+	0.965188i	$0.584236\pi$
$420$	−5.12674e10	−0.0803932
$421$	4.76740e11	0.739625	0.369813	−	0.929106i	$-0.379422\pi$
$421$	4.76740e11	0.739625	0.369813	+	0.929106i	$0.379422\pi$
$422$	1.06571e11	0.163582
$423$	5.25117e11	0.797488
$424$	2.56192e12	3.84963
$425$	−4.96880e10	−0.0738757
$426$	−1.57420e11	−0.231589
$427$	−7.06944e10	−0.102911
$428$	9.42318e11	1.35738
$429$	2.96548e11	0.422705
$430$	2.09649e11	0.295723
$431$	−1.30520e12	−1.82191	−0.910957	−	0.412501i	$-0.864655\pi$
$431$	−1.30520e12	−1.82191	−0.910957	+	0.412501i	$0.864655\pi$
$432$	−7.72187e11	−1.06671
$433$	−3.14353e10	−0.0429756	−0.0214878	−	0.999769i	$-0.506840\pi$
$433$	−3.14353e10	−0.0429756	−0.0214878	+	0.999769i	$0.506840\pi$
$434$	−9.28300e10	−0.125599
$435$	9.29584e10	0.124476
$436$	7.36194e11	0.975670
$437$	−6.04420e11	−0.792816
$438$	1.93394e11	0.251079
$439$	8.48576e11	1.09044	0.545218	−	0.838294i	$-0.316447\pi$
$439$	8.48576e11	1.09044	0.545218	+	0.838294i	$0.316447\pi$
$440$	1.30455e12	1.65930
$441$	6.80810e11	0.857141
$442$	−3.80309e11	−0.473954
$443$	−1.03200e11	−0.127310	−0.0636550	−	0.997972i	$-0.520276\pi$
$443$	−1.03200e11	−0.127310	−0.0636550	+	0.997972i	$0.520276\pi$
$444$	−1.05632e11	−0.128995
$445$	9.35444e11	1.13083
$446$	2.18892e12	2.61953
$447$	−3.54243e11	−0.419679
$448$	−3.27161e10	−0.0383717
$449$	2.69145e11	0.312520	0.156260	−	0.987716i	$-0.450056\pi$
$449$	2.69145e11	0.312520	0.156260	+	0.987716i	$0.450056\pi$
$450$	−4.58299e11	−0.526857
$451$	−1.29398e12	−1.47277
$452$	−1.30148e12	−1.46661
$453$	−3.30351e11	−0.368581
$454$	−2.46658e12	−2.72486
$455$	−1.14154e11	−0.124865
$456$	−4.99663e11	−0.541172
$457$	−1.55811e12	−1.67099	−0.835497	−	0.549496i	$-0.814820\pi$
$457$	−1.55811e12	−1.67099	−0.835497	+	0.549496i	$0.814820\pi$
$458$	−1.07791e12	−1.14469
$459$	−1.39281e11	−0.146465
$460$	1.89689e12	1.97530
$461$	1.71765e12	1.77126	0.885628	−	0.464395i	$-0.153728\pi$
$461$	1.71765e12	1.77126	0.885628	+	0.464395i	$0.153728\pi$
$462$	−7.63808e10	−0.0780002
$463$	−5.09878e10	−0.0515646	−0.0257823	−	0.999668i	$-0.508208\pi$
$463$	−5.09878e10	−0.0515646	−0.0257823	+	0.999668i	$0.508208\pi$
$464$	−6.75474e11	−0.676515
$465$	−1.64444e11	−0.163109
$466$	−1.20819e12	−1.18686
$467$	1.98389e11	0.193016	0.0965078	−	0.995332i	$-0.469233\pi$
$467$	1.98389e11	0.193016	0.0965078	+	0.995332i	$0.469233\pi$
$468$	−2.40624e12	−2.31864
$469$	6.20605e10	0.0592294
$470$	−1.40534e12	−1.32844
$471$	−1.82826e11	−0.171177
$472$	−3.33576e11	−0.309354
$473$	2.14260e11	0.196819
$474$	−5.52551e11	−0.502770
$475$	−2.68087e11	−0.241632
$476$	6.71941e10	0.0599929
$477$	1.79366e12	1.58638
$478$	2.39931e12	2.10213
$479$	4.07451e11	0.353644	0.176822	−	0.984243i	$-0.443418\pi$
$479$	4.07451e11	0.353644	0.176822	+	0.984243i	$0.443418\pi$
$480$	2.44149e11	0.209928
$481$	−2.35205e11	−0.200352
$482$	1.84876e12	1.56015
$483$	−6.02188e10	−0.0503466
$484$	−1.78257e11	−0.147653
$485$	8.84375e11	0.725770
$486$	−1.97129e12	−1.60283
$487$	−1.72342e12	−1.38838	−0.694192	−	0.719790i	$-0.744238\pi$
$487$	−1.72342e12	−1.38838	−0.694192	+	0.719790i	$0.744238\pi$
$488$	2.16235e12	1.72598
$489$	3.78959e11	0.299711
$490$	−1.82201e12	−1.42781
$491$	2.04206e12	1.58563	0.792813	−	0.609465i	$-0.208616\pi$
$491$	2.04206e12	1.58563	0.792813	+	0.609465i	$0.208616\pi$
$492$	−1.55542e12	−1.19676
$493$	−1.21837e11	−0.0928897
$494$	−2.05192e12	−1.55021
$495$	9.13352e11	0.683777
$496$	1.19492e12	0.886482
$497$	6.19307e10	0.0455305
$498$	4.71540e11	0.343547
$499$	−2.26534e12	−1.63562	−0.817808	−	0.575491i	$-0.804811\pi$
$499$	−2.26534e12	−1.63562	−0.817808	+	0.575491i	$0.804811\pi$
$500$	3.32338e12	2.37802
$501$	−5.98663e11	−0.424534
$502$	−1.20152e12	−0.844431
$503$	5.78891e11	0.403219	0.201609	−	0.979466i	$-0.435383\pi$
$503$	5.78891e11	0.403219	0.201609	+	0.979466i	$0.435383\pi$
$504$	3.36044e11	0.231984
$505$	−2.19803e12	−1.50391
$506$	2.82609e12	1.91650
$507$	2.59304e11	0.174291
$508$	−6.00248e12	−3.99893
$509$	3.98496e11	0.263144	0.131572	−	0.991307i	$-0.457997\pi$
$509$	3.98496e11	0.263144	0.131572	+	0.991307i	$0.457997\pi$
$510$	1.73522e11	0.113577
$511$	−7.60832e10	−0.0493622
$512$	3.44227e12	2.21376
$513$	−7.51478e11	−0.479058
$514$	3.06795e12	1.93872
$515$	4.61713e11	0.289227
$516$	2.57550e11	0.159933
$517$	−1.43625e12	−0.884142
$518$	6.05809e10	0.0369702
$519$	4.82904e11	0.292151
$520$	3.49166e12	2.09419
$521$	1.78068e12	1.05881	0.529403	−	0.848371i	$-0.322416\pi$
$521$	1.78068e12	1.05881	0.529403	+	0.848371i	$0.322416\pi$
$522$	−1.12377e12	−0.662458
$523$	1.47669e12	0.863039	0.431520	−	0.902104i	$-0.357978\pi$
$523$	1.47669e12	0.863039	0.431520	+	0.902104i	$0.357978\pi$
$524$	6.21989e12	3.60406
$525$	−2.67097e10	−0.0153445
$526$	−3.09508e12	−1.76294
$527$	2.15530e11	0.121719
$528$	9.83180e11	0.550529
$529$	4.26942e11	0.237038
$530$	−4.80028e12	−2.64256
$531$	−2.33546e11	−0.127481
$532$	3.62539e11	0.196224
$533$	−3.46337e12	−1.85878
$534$	1.67525e12	0.891548
$535$	−9.57341e11	−0.505213
$536$	−1.89826e12	−0.993376
$537$	−8.44925e11	−0.438464
$538$	−6.08829e12	−3.13311
$539$	−1.86209e12	−0.950277
$540$	2.35841e12	1.19357
$541$	2.21174e12	1.11006	0.555029	−	0.831831i	$-0.312707\pi$
$541$	2.21174e12	1.11006	0.555029	+	0.831831i	$0.312707\pi$
$542$	−6.23720e12	−3.10451
$543$	6.85405e11	0.338336
$544$	−3.19996e11	−0.156657
$545$	−7.47931e11	−0.363142
$546$	−2.04435e11	−0.0984436
$547$	−9.65971e11	−0.461340	−0.230670	−	0.973032i	$-0.574092\pi$
$547$	−9.65971e11	−0.461340	−0.230670	+	0.973032i	$0.574092\pi$
$548$	−8.57610e12	−4.06235
$549$	1.51391e12	0.711256
$550$	1.25350e12	0.584105
$551$	−6.57359e11	−0.303823
$552$	1.84193e12	0.844396
$553$	2.17379e11	0.0988448
$554$	2.47798e11	0.111765
$555$	1.07316e11	0.0480116
$556$	6.89601e12	3.06028
$557$	2.49214e12	1.09704	0.548521	−	0.836137i	$-0.315191\pi$
$557$	2.49214e12	1.09704	0.548521	+	0.836137i	$0.315191\pi$
$558$	1.98795e12	0.868062
$559$	5.73471e11	0.248404
$560$	−3.78469e11	−0.162624
$561$	1.77339e11	0.0755910
$562$	−6.66229e12	−2.81715
$563$	−1.50009e12	−0.629259	−0.314629	−	0.949215i	$-0.601880\pi$
$563$	−1.50009e12	−0.629259	−0.314629	+	0.949215i	$0.601880\pi$
$564$	−1.72643e12	−0.718444
$565$	1.32223e12	0.545868
$566$	6.55115e12	2.68314
$567$	1.95256e11	0.0793379
$568$	−1.89429e12	−0.763622
$569$	−2.15499e12	−0.861868	−0.430934	−	0.902383i	$-0.641816\pi$
$569$	−2.15499e12	−0.861868	−0.430934	+	0.902383i	$0.641816\pi$
$570$	9.36223e11	0.371486
$571$	9.33658e11	0.367557	0.183779	−	0.982968i	$-0.441167\pi$
$571$	9.33658e11	0.367557	0.183779	+	0.982968i	$0.441167\pi$
$572$	6.58131e12	2.57058
$573$	4.24008e11	0.164315
$574$	8.92049e11	0.342993
$575$	9.88259e11	0.377021
$576$	7.00613e11	0.265202
$577$	1.95126e12	0.732865	0.366432	−	0.930445i	$-0.380579\pi$
$577$	1.95126e12	0.732865	0.366432	+	0.930445i	$0.380579\pi$
$578$	4.56096e12	1.69973
$579$	−7.36862e10	−0.0272479
$580$	2.06303e12	0.756973
$581$	−1.85508e11	−0.0675415
$582$	1.58380e12	0.572197
$583$	−4.90586e12	−1.75876
$584$	2.32717e12	0.827886
$585$	2.44460e12	0.862992
$586$	7.67041e12	2.68707
$587$	−2.48705e10	−0.00864596	−0.00432298	−	0.999991i	$-0.501376\pi$
$587$	−2.48705e10	−0.00864596	−0.00432298	+	0.999991i	$0.501376\pi$
$588$	−2.23830e12	−0.772184
$589$	1.16287e12	0.398119
$590$	6.25025e11	0.212355
$591$	−1.63272e12	−0.550515
$592$	−7.79803e11	−0.260938
$593$	3.86162e12	1.28240	0.641200	−	0.767374i	$-0.278437\pi$
$593$	3.86162e12	1.28240	0.641200	+	0.767374i	$0.278437\pi$
$594$	3.51369e12	1.15804
$595$	−6.82653e10	−0.0223292
$596$	−7.86174e12	−2.55217
$597$	2.40470e11	0.0774775
$598$	7.56407e12	2.41880
$599$	1.98719e12	0.630692	0.315346	−	0.948977i	$-0.397879\pi$
$599$	1.98719e12	0.630692	0.315346	+	0.948977i	$0.397879\pi$
$600$	8.16976e11	0.257353
$601$	−1.16212e12	−0.363341	−0.181671	−	0.983359i	$-0.558150\pi$
$601$	−1.16212e12	−0.363341	−0.181671	+	0.983359i	$0.558150\pi$
$602$	−1.47707e11	−0.0458370
$603$	−1.32902e12	−0.409358
$604$	−7.33150e12	−2.24144
$605$	1.81099e11	0.0549562
$606$	−3.93637e12	−1.18569
$607$	−2.40847e12	−0.720099	−0.360049	−	0.932933i	$-0.617240\pi$
$607$	−2.40847e12	−0.720099	−0.360049	+	0.932933i	$0.617240\pi$
$608$	−1.72651e12	−0.512393
$609$	−6.54932e10	−0.0192938
$610$	−4.05160e12	−1.18479
$611$	−3.84414e12	−1.11587
$612$	−1.43895e12	−0.414635
$613$	1.45367e12	0.415809	0.207904	−	0.978149i	$-0.433336\pi$
$613$	1.45367e12	0.415809	0.207904	+	0.978149i	$0.433336\pi$
$614$	4.04156e12	1.14760
$615$	1.58022e12	0.445430
$616$	−9.19114e11	−0.257191
$617$	4.45918e12	1.23871	0.619357	−	0.785109i	$-0.287393\pi$
$617$	4.45918e12	1.23871	0.619357	+	0.785109i	$0.287393\pi$
$618$	8.26865e11	0.228027
$619$	−2.55636e12	−0.699864	−0.349932	−	0.936775i	$-0.613795\pi$
$619$	−2.55636e12	−0.699864	−0.349932	+	0.936775i	$0.613795\pi$
$620$	−3.64951e12	−0.991910
$621$	2.77020e12	0.747479
$622$	−2.87995e12	−0.771488
$623$	−6.59060e11	−0.175279
$624$	2.63150e12	0.694821
$625$	−2.08325e12	−0.546113
$626$	1.34995e12	0.351343
$627$	9.56813e11	0.247243
$628$	−4.05748e12	−1.04097
$629$	−1.40655e11	−0.0358284
$630$	−6.29647e11	−0.159245
$631$	5.28493e12	1.32711	0.663555	−	0.748127i	$-0.269047\pi$
$631$	5.28493e12	1.32711	0.663555	+	0.748127i	$0.269047\pi$
$632$	−6.64901e12	−1.65779
$633$	−1.33008e11	−0.0329276
$634$	−6.24258e12	−1.53448
$635$	6.09817e12	1.48839
$636$	−5.89704e12	−1.42915
$637$	−4.98390e12	−1.19934
$638$	3.07361e12	0.734440
$639$	−1.32624e12	−0.314679
$640$	−4.35551e12	−1.02619
$641$	−9.70546e11	−0.227068	−0.113534	−	0.993534i	$-0.536217\pi$
$641$	−9.70546e11	−0.227068	−0.113534	+	0.993534i	$0.536217\pi$
$642$	−1.71447e12	−0.398310
$643$	8.63581e11	0.199230	0.0996148	−	0.995026i	$-0.468239\pi$
$643$	8.63581e11	0.199230	0.0996148	+	0.995026i	$0.468239\pi$
$644$	−1.33644e12	−0.306171
$645$	−2.61655e11	−0.0595266
$646$	−1.22707e12	−0.277219
$647$	−1.67738e12	−0.376325	−0.188162	−	0.982138i	$-0.560253\pi$
$647$	−1.67738e12	−0.376325	−0.188162	+	0.982138i	$0.560253\pi$
$648$	−5.97234e12	−1.33063
$649$	6.38771e11	0.141333
$650$	3.35500e12	0.737196
$651$	1.15858e11	0.0252820
$652$	8.41027e12	1.82262
$653$	1.31136e12	0.282236	0.141118	−	0.989993i	$-0.454930\pi$
$653$	1.31136e12	0.282236	0.141118	+	0.989993i	$0.454930\pi$
$654$	−1.33944e12	−0.286302
$655$	−6.31905e12	−1.34142
$656$	−1.14825e13	−2.42086
$657$	1.62931e12	0.341162
$658$	9.90122e11	0.205908
$659$	−6.35115e12	−1.31180	−0.655901	−	0.754847i	$-0.727711\pi$
$659$	−6.35115e12	−1.31180	−0.655901	+	0.754847i	$0.727711\pi$
$660$	−3.00283e12	−0.616004
$661$	−5.53840e10	−0.0112844	−0.00564219	−	0.999984i	$-0.501796\pi$
$661$	−5.53840e10	−0.0112844	−0.00564219	+	0.999984i	$0.501796\pi$
$662$	1.61214e13	3.26244
$663$	4.74650e11	0.0954031
$664$	5.67418e12	1.13278
$665$	−3.68319e11	−0.0730343
$666$	−1.29733e12	−0.255516
$667$	2.42325e12	0.474058
$668$	−1.32862e13	−2.58170
$669$	−2.73191e12	−0.527290
$670$	3.55678e12	0.681900
$671$	−4.14071e12	−0.788540
$672$	−1.72014e11	−0.0325388
$673$	−1.36186e12	−0.255896	−0.127948	−	0.991781i	$-0.540839\pi$
$673$	−1.36186e12	−0.255896	−0.127948	+	0.991781i	$0.540839\pi$
$674$	3.52470e12	0.657888
$675$	1.22871e12	0.227815
$676$	5.75476e12	1.05991
$677$	−1.16341e12	−0.212855	−0.106428	−	0.994320i	$-0.533941\pi$
$677$	−1.16341e12	−0.212855	−0.106428	+	0.994320i	$0.533941\pi$
$678$	2.36793e12	0.430363
$679$	−6.23081e11	−0.112494
$680$	2.08805e12	0.374498
$681$	3.07845e12	0.548491
$682$	−5.43724e12	−0.962384
$683$	9.16047e12	1.61074	0.805369	−	0.592774i	$-0.201967\pi$
$683$	9.16047e12	1.61074	0.805369	+	0.592774i	$0.201967\pi$
$684$	−7.76375e12	−1.35618
$685$	8.71283e12	1.51200
$686$	2.58809e12	0.446191
$687$	1.34530e12	0.230417
$688$	1.90130e12	0.323520
$689$	−1.31306e13	−2.21972
$690$	−3.45123e12	−0.579633
$691$	−9.43076e12	−1.57360	−0.786802	−	0.617206i	$-0.788265\pi$
$691$	−9.43076e12	−1.57360	−0.786802	+	0.617206i	$0.788265\pi$
$692$	1.07171e13	1.77665
$693$	−6.43496e11	−0.105985
$694$	1.97077e13	3.22491
$695$	−7.00595e12	−1.13903
$696$	2.00325e12	0.323590
$697$	−2.07113e12	−0.332399
$698$	2.14832e13	3.42571
$699$	1.50790e12	0.238905
$700$	−5.92771e11	−0.0933138
$701$	−2.42958e12	−0.380015	−0.190008	−	0.981783i	$-0.560851\pi$
$701$	−2.42958e12	−0.380015	−0.190008	+	0.981783i	$0.560851\pi$
$702$	9.40445e12	1.46156
$703$	−7.58890e11	−0.117187
$704$	−1.91625e12	−0.294019
$705$	1.75395e12	0.267403
$706$	−1.24816e13	−1.89082
$707$	1.54861e12	0.233106
$708$	7.67829e11	0.114846
$709$	−1.98109e12	−0.294440	−0.147220	−	0.989104i	$-0.547032\pi$
$709$	−1.98109e12	−0.294440	−0.147220	+	0.989104i	$0.547032\pi$
$710$	3.54934e12	0.524186
$711$	−4.65515e12	−0.683156
$712$	2.01588e13	2.93971
$713$	−4.28673e12	−0.621188
$714$	−1.22254e11	−0.0176044
$715$	−6.68623e12	−0.956763
$716$	−1.87515e13	−2.66641
$717$	−2.99449e12	−0.423142
$718$	1.53978e13	2.16222
$719$	−2.11719e12	−0.295447	−0.147724	−	0.989029i	$-0.547195\pi$
$719$	−2.11719e12	−0.295447	−0.147724	+	0.989029i	$0.547195\pi$
$720$	8.10487e12	1.12396
$721$	−3.25297e11	−0.0448302
$722$	6.40908e12	0.877765
$723$	−2.30736e12	−0.314046
$724$	1.52112e13	2.05751
$725$	1.07482e12	0.144482
$726$	3.24323e11	0.0433275
$727$	9.36052e12	1.24278	0.621391	−	0.783500i	$-0.286568\pi$
$727$	9.36052e12	1.24278	0.621391	+	0.783500i	$0.286568\pi$
$728$	−2.46002e12	−0.324600
$729$	−2.34053e12	−0.306930
$730$	−4.36044e12	−0.568300
$731$	3.42941e11	0.0444213
$732$	−4.97731e12	−0.640759
$733$	2.06000e11	0.0263572	0.0131786	−	0.999913i	$-0.495805\pi$
$733$	2.06000e11	0.0263572	0.0131786	+	0.999913i	$0.495805\pi$
$734$	−2.12916e12	−0.270755
$735$	2.27399e12	0.287405
$736$	6.36450e12	0.799491
$737$	3.63501e12	0.453839
$738$	−1.91031e13	−2.37056
$739$	1.32647e13	1.63605	0.818027	−	0.575180i	$-0.195068\pi$
$739$	1.32647e13	1.63605	0.818027	+	0.575180i	$0.195068\pi$
$740$	2.38168e12	0.291971
$741$	2.56093e12	0.312044
$742$	3.38201e12	0.409597
$743$	−1.44270e12	−0.173670	−0.0868352	−	0.996223i	$-0.527675\pi$
$743$	−1.44270e12	−0.173670	−0.0868352	+	0.996223i	$0.527675\pi$
$744$	−3.54376e12	−0.424020
$745$	7.98707e12	0.949914
$746$	−6.43337e12	−0.760526
$747$	3.97264e12	0.466806
$748$	3.93569e12	0.459688
$749$	6.74488e11	0.0783080
$750$	−6.04660e12	−0.697808
$751$	−1.61096e12	−0.184801	−0.0924007	−	0.995722i	$-0.529454\pi$
$751$	−1.61096e12	−0.184801	−0.0924007	+	0.995722i	$0.529454\pi$
$752$	−1.27449e13	−1.45331
$753$	1.49957e12	0.169977
$754$	8.22658e12	0.926933
$755$	7.44838e12	0.834258
$756$	−1.66160e12	−0.185003
$757$	−8.27527e12	−0.915906	−0.457953	−	0.888976i	$-0.651417\pi$
$757$	−8.27527e12	−0.915906	−0.457953	+	0.888976i	$0.651417\pi$
$758$	−1.86243e13	−2.04913
$759$	−3.52714e12	−0.385775
$760$	1.12659e13	1.22491
$761$	−1.41047e13	−1.52452	−0.762259	−	0.647272i	$-0.775910\pi$
$761$	−1.41047e13	−1.52452	−0.762259	+	0.647272i	$0.775910\pi$
$762$	1.09210e13	1.17345
$763$	5.26949e11	0.0562870
$764$	9.41004e12	0.999243
$765$	1.46190e12	0.154326
$766$	−1.55478e13	−1.63170
$767$	1.70968e12	0.178376
$768$	−6.74565e12	−0.699678
$769$	5.45961e12	0.562980	0.281490	−	0.959564i	$-0.409171\pi$
$769$	5.45961e12	0.562980	0.281490	+	0.959564i	$0.409171\pi$
$770$	1.72215e12	0.176548
$771$	−3.82900e12	−0.390248
$772$	−1.63532e12	−0.165701
$773$	−1.76648e13	−1.77951	−0.889755	−	0.456439i	$-0.849125\pi$
$773$	−1.76648e13	−1.77951	−0.889755	+	0.456439i	$0.849125\pi$
$774$	3.16313e12	0.316798
$775$	−1.90136e12	−0.189324
$776$	1.90583e13	1.88671
$777$	−7.56088e10	−0.00744180
$778$	−3.07048e13	−3.00468
$779$	−1.11746e13	−1.08721
$780$	−8.03713e12	−0.777455
$781$	3.62740e12	0.348872
$782$	4.52339e12	0.432547
$783$	3.01283e12	0.286449
$784$	−1.65237e13	−1.56202
$785$	4.12217e12	0.387447
$786$	−1.13166e13	−1.05758
$787$	9.80705e12	0.911281	0.455640	−	0.890164i	$-0.349410\pi$
$787$	9.80705e12	0.911281	0.455640	+	0.890164i	$0.349410\pi$
$788$	−3.62352e13	−3.34782
$789$	3.86286e12	0.354864
$790$	1.24583e13	1.13799
$791$	−9.31565e11	−0.0846095
$792$	1.96827e13	1.77755
$793$	−1.10827e13	−0.995212
$794$	−1.11615e13	−0.996626
$795$	5.99105e12	0.531926
$796$	5.33676e12	0.471160
$797$	6.35228e12	0.557657	0.278828	−	0.960341i	$-0.410054\pi$
$797$	6.35228e12	0.557657	0.278828	+	0.960341i	$0.410054\pi$
$798$	−6.59609e11	−0.0575803
$799$	−2.29883e12	−0.199548
$800$	2.82294e12	0.243667
$801$	1.41137e13	1.21142
$802$	−1.61386e13	−1.37747
$803$	−4.45634e12	−0.378232
$804$	4.36943e12	0.368784
$805$	1.35775e12	0.113956
$806$	−1.45529e13	−1.21462
$807$	7.59857e12	0.630668
$808$	−4.73676e13	−3.90958
$809$	1.06091e13	0.870781	0.435390	−	0.900242i	$-0.356610\pi$
$809$	1.06091e13	0.870781	0.435390	+	0.900242i	$0.356610\pi$
$810$	1.11904e13	0.913406
$811$	−1.11718e12	−0.0906835	−0.0453417	−	0.998972i	$-0.514438\pi$
$811$	−1.11718e12	−0.0906835	−0.0453417	+	0.998972i	$0.514438\pi$
$812$	−1.45350e12	−0.117331
$813$	7.78442e12	0.624912
$814$	3.54834e12	0.283280
$815$	−8.54435e12	−0.678375
$816$	1.57366e12	0.124253
$817$	1.85031e12	0.145293
$818$	−4.78831e12	−0.373932
$819$	−1.72233e12	−0.133764
$820$	3.50700e13	2.70877
$821$	−7.60871e12	−0.584476	−0.292238	−	0.956346i	$-0.594400\pi$
$821$	−7.60871e12	−0.584476	−0.292238	+	0.956346i	$0.594400\pi$
$822$	1.56035e13	1.19206
$823$	2.32810e13	1.76890	0.884448	−	0.466639i	$-0.154535\pi$
$823$	2.32810e13	1.76890	0.884448	+	0.466639i	$0.154535\pi$
$824$	9.94992e12	0.751877
$825$	−1.56444e12	−0.117575
$826$	−4.40357e11	−0.0329150
$827$	2.29429e13	1.70559	0.852793	−	0.522249i	$-0.174907\pi$
$827$	2.29429e13	1.70559	0.852793	+	0.522249i	$0.174907\pi$
$828$	2.86198e13	2.11607
$829$	8.31740e12	0.611635	0.305817	−	0.952090i	$-0.401070\pi$
$829$	8.31740e12	0.611635	0.305817	+	0.952090i	$0.401070\pi$
$830$	−1.06318e13	−0.777595
$831$	−3.09268e11	−0.0224973
$832$	−5.12887e12	−0.371079
$833$	−2.98042e12	−0.214474
$834$	−1.25467e13	−0.898013
$835$	1.34980e13	0.960904
$836$	2.12346e13	1.50355
$837$	−5.32972e12	−0.375353
$838$	1.33263e13	0.933494
$839$	1.09177e13	0.760682	0.380341	−	0.924846i	$-0.375807\pi$
$839$	1.09177e13	0.760682	0.380341	+	0.924846i	$0.375807\pi$
$840$	1.12243e12	0.0777859
$841$	−1.18717e13	−0.818332
$842$	−1.92500e13	−1.31985
$843$	8.31496e12	0.567069
$844$	−2.95185e12	−0.200241
$845$	−5.84651e12	−0.394495
$846$	−2.12034e13	−1.42311
$847$	−1.27592e11	−0.00851820
$848$	−4.35334e13	−2.89096
$849$	−8.17624e12	−0.540094
$850$	2.00632e12	0.131831
$851$	2.79752e12	0.182848
$852$	4.36029e12	0.283489
$853$	−9.23071e12	−0.596986	−0.298493	−	0.954412i	$-0.596484\pi$
$853$	−9.23071e12	−0.596986	−0.298493	+	0.954412i	$0.596484\pi$
$854$	2.85453e12	0.183643
$855$	7.88752e12	0.504769
$856$	−2.06307e13	−1.31335
$857$	7.12039e12	0.450911	0.225455	−	0.974254i	$-0.427613\pi$
$857$	7.12039e12	0.450911	0.225455	+	0.974254i	$0.427613\pi$
$858$	−1.19741e13	−0.754313
$859$	1.25176e11	0.00784425	0.00392213	−	0.999992i	$-0.498752\pi$
$859$	1.25176e11	0.00784425	0.00392213	+	0.999992i	$0.498752\pi$
$860$	−5.80694e12	−0.361996
$861$	−1.11333e12	−0.0690416
$862$	5.27017e13	3.25119
$863$	1.64135e13	1.00729	0.503644	−	0.863912i	$-0.331992\pi$
$863$	1.64135e13	1.00729	0.503644	+	0.863912i	$0.331992\pi$
$864$	7.91301e12	0.483092
$865$	−1.08880e13	−0.661264
$866$	1.26931e12	0.0766895
$867$	−5.69237e12	−0.342142
$868$	2.57124e12	0.153746
$869$	1.27323e13	0.757387
$870$	−3.75351e12	−0.222127
$871$	9.72916e12	0.572787
$872$	−1.61179e13	−0.944027
$873$	1.33432e13	0.777493
$874$	2.44055e13	1.41477
$875$	2.37879e12	0.137189
$876$	−5.35671e12	−0.307347
$877$	−3.83733e12	−0.219044	−0.109522	−	0.993984i	$-0.534932\pi$
$877$	−3.83733e12	−0.219044	−0.109522	+	0.993984i	$0.534932\pi$
$878$	−3.42642e13	−1.94587
$879$	−9.57316e12	−0.540885
$880$	−2.21677e13	−1.24609
$881$	−5.38444e12	−0.301126	−0.150563	−	0.988600i	$-0.548109\pi$
$881$	−5.38444e12	−0.301126	−0.150563	+	0.988600i	$0.548109\pi$
$882$	−2.74900e13	−1.52956
$883$	2.15422e13	1.19252	0.596261	−	0.802790i	$-0.296652\pi$
$883$	2.15422e13	1.19252	0.596261	+	0.802790i	$0.296652\pi$
$884$	1.05339e13	0.580170
$885$	−7.80070e11	−0.0427454
$886$	4.16705e12	0.227184
$887$	−5.79459e12	−0.314316	−0.157158	−	0.987573i	$-0.550233\pi$
$887$	−5.79459e12	−0.314316	−0.157158	+	0.987573i	$0.550233\pi$
$888$	2.31266e12	0.124811
$889$	−4.29643e12	−0.230701
$890$	−3.77717e13	−2.01796
$891$	1.14365e13	0.607918
$892$	−6.06295e13	−3.20658
$893$	−1.24031e13	−0.652680
$894$	1.43038e13	0.748913
$895$	1.90504e13	0.992433
$896$	3.06865e12	0.159060
$897$	−9.44044e12	−0.486885
$898$	−1.08676e13	−0.557689
$899$	−4.66219e12	−0.238052
$900$	1.26941e13	0.644929
$901$	−7.85223e12	−0.396946
$902$	5.22490e13	2.62814
$903$	1.84348e11	0.00922662
$904$	2.84940e13	1.41904
$905$	−1.54538e13	−0.765800
$906$	1.33390e13	0.657730
$907$	−2.75707e13	−1.35274	−0.676370	−	0.736562i	$-0.736448\pi$
$907$	−2.75707e13	−1.35274	−0.676370	+	0.736562i	$0.736448\pi$
$908$	6.83202e13	3.33551
$909$	−3.31633e13	−1.61109
$910$	4.60937e12	0.222820
$911$	−8.26381e12	−0.397510	−0.198755	−	0.980049i	$-0.563690\pi$
$911$	−8.26381e12	−0.397510	−0.198755	+	0.980049i	$0.563690\pi$
$912$	8.49055e12	0.406405
$913$	−1.08656e13	−0.517529
$914$	6.29139e13	2.98187
$915$	5.05666e12	0.238489
$916$	2.98564e13	1.40122
$917$	4.45204e12	0.207920
$918$	5.62395e12	0.261366
$919$	3.72227e13	1.72142	0.860712	−	0.509092i	$-0.170019\pi$
$919$	3.72227e13	1.72142	0.860712	+	0.509092i	$0.170019\pi$
$920$	−4.15297e13	−1.91123
$921$	−5.04412e12	−0.231003
$922$	−6.93561e13	−3.16079
$923$	9.70881e12	0.440310
$924$	2.11562e12	0.0954805
$925$	1.24083e12	0.0557280
$926$	2.05881e12	0.0920166
$927$	6.96620e12	0.309840
$928$	6.92194e12	0.306381
$929$	−5.03796e12	−0.221913	−0.110957	−	0.993825i	$-0.535391\pi$
$929$	−5.03796e12	−0.221913	−0.110957	+	0.993825i	$0.535391\pi$
$930$	6.63998e12	0.291067
$931$	−1.60806e13	−0.701501
$932$	3.34650e13	1.45285
$933$	3.59437e12	0.155294
$934$	−8.01064e12	−0.344434
$935$	−3.99843e12	−0.171095
$936$	5.26812e13	2.24344
$937$	−2.42422e13	−1.02741	−0.513706	−	0.857966i	$-0.671728\pi$
$937$	−2.42422e13	−1.02741	−0.513706	+	0.857966i	$0.671728\pi$
$938$	−2.50591e12	−0.105694
$939$	−1.68482e12	−0.0707225
$940$	3.89256e13	1.62615
$941$	4.50046e13	1.87113	0.935565	−	0.353155i	$-0.114891\pi$
$941$	4.50046e13	1.87113	0.935565	+	0.353155i	$0.114891\pi$
$942$	7.38224e12	0.305463
$943$	4.11933e13	1.69638
$944$	5.66831e12	0.232316
$945$	1.68809e12	0.0688579
$946$	−8.65148e12	−0.351221
$947$	−2.28138e13	−0.921770	−0.460885	−	0.887460i	$-0.652468\pi$
$947$	−2.28138e13	−0.921770	−0.460885	+	0.887460i	$0.652468\pi$
$948$	1.53047e13	0.615444
$949$	−1.19275e13	−0.477365
$950$	1.08249e13	0.431190
$951$	7.79113e12	0.308879
$952$	−1.47112e12	−0.0580472
$953$	1.77163e13	0.695754	0.347877	−	0.937540i	$-0.386903\pi$
$953$	1.77163e13	0.695754	0.347877	+	0.937540i	$0.386903\pi$
$954$	−7.24253e13	−2.83089
$955$	−9.56006e12	−0.371916
$956$	−6.64569e13	−2.57324
$957$	−3.83607e12	−0.147837
$958$	−1.64522e13	−0.631074
$959$	−6.13856e12	−0.234360
$960$	2.34013e12	0.0889241
$961$	−1.81922e13	−0.688065
$962$	9.49720e12	0.357526
$963$	−1.44441e13	−0.541218
$964$	−5.12075e13	−1.90980
$965$	1.66139e12	0.0616736
$966$	2.43154e12	0.0898431
$967$	−2.54945e13	−0.937619	−0.468810	−	0.883299i	$-0.655317\pi$
$967$	−2.54945e13	−0.937619	−0.468810	+	0.883299i	$0.655317\pi$
$968$	3.90268e12	0.142864
$969$	1.53146e12	0.0558018
$970$	−3.57097e13	−1.29513
$971$	5.46928e12	0.197444	0.0987220	−	0.995115i	$-0.468525\pi$
$971$	5.46928e12	0.197444	0.0987220	+	0.995115i	$0.468525\pi$
$972$	5.46016e13	1.96204
$973$	4.93600e12	0.176550
$974$	6.95888e13	2.47756
$975$	−4.18726e12	−0.148391
$976$	−3.67437e13	−1.29616
$977$	−4.12413e13	−1.44813	−0.724064	−	0.689733i	$-0.757728\pi$
$977$	−4.12413e13	−1.44813	−0.724064	+	0.689733i	$0.757728\pi$
$978$	−1.53018e13	−0.534831
$979$	−3.86024e13	−1.34305
$980$	5.04668e13	1.74779
$981$	−1.12846e13	−0.389022
$982$	−8.24549e13	−2.82953
$983$	−2.16600e13	−0.739890	−0.369945	−	0.929054i	$-0.620624\pi$
$983$	−2.16600e13	−0.739890	−0.369945	+	0.929054i	$0.620624\pi$
$984$	3.40538e13	1.15794
$985$	3.68128e13	1.24605
$986$	4.91958e12	0.165761
$987$	−1.23574e12	−0.0414475
$988$	5.68349e13	1.89762
$989$	−6.82085e12	−0.226702
$990$	−3.68797e13	−1.22019
$991$	2.81911e13	0.928497	0.464248	−	0.885705i	$-0.346324\pi$
$991$	2.81911e13	0.928497	0.464248	+	0.885705i	$0.346324\pi$
$992$	−1.22449e13	−0.401471
$993$	−2.01206e13	−0.656702
$994$	−2.50066e12	−0.0812487
$995$	−5.42184e12	−0.175365
$996$	−1.30609e13	−0.420538
$997$	3.62936e13	1.16333	0.581663	−	0.813430i	$-0.302402\pi$
$997$	3.62936e13	1.16333	0.581663	+	0.813430i	$0.302402\pi$
$998$	9.14709e13	2.91874
$999$	3.47818e12	0.110486

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.a.a.1.2	✓	13	1.1	even	1	trivial
333.10.a.c.1.12		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)

\(f(q)\)	\(=\)	\(q-40.3784 q^{2} +50.3948 q^{3} +1118.42 q^{4} -1136.25 q^{5} -2034.86 q^{6} +800.534 q^{7} -24486.1 q^{8} -17143.4 q^{9} +O(q^{10})\)	\(q-40.3784 q^{2} +50.3948 q^{3} +1118.42 q^{4} -1136.25 q^{5} -2034.86 q^{6} +800.534 q^{7} -24486.1 q^{8} -17143.4 q^{9} +45879.8 q^{10} +46888.8 q^{11} +56362.3 q^{12} +125499. q^{13} -32324.3 q^{14} -57260.9 q^{15} +416081. q^{16} +75049.5 q^{17} +692222. q^{18} +404923. q^{19} -1.27080e6 q^{20} +40342.8 q^{21} -1.89330e6 q^{22} -1.49268e6 q^{23} -1.23397e6 q^{24} -662070. q^{25} -5.06744e6 q^{26} -1.85586e6 q^{27} +895330. q^{28} -1.62342e6 q^{29} +2.31210e6 q^{30} +2.87183e6 q^{31} -4.26380e6 q^{32} +2.36295e6 q^{33} -3.03038e6 q^{34} -909604. q^{35} -1.91734e7 q^{36} -1.87416e6 q^{37} -1.63501e7 q^{38} +6.32449e6 q^{39} +2.78222e7 q^{40} -2.75969e7 q^{41} -1.62898e6 q^{42} +4.56953e6 q^{43} +5.24412e7 q^{44} +1.94791e7 q^{45} +6.02721e7 q^{46} -3.06309e7 q^{47} +2.09683e7 q^{48} -3.97128e7 q^{49} +2.67333e7 q^{50} +3.78210e6 q^{51} +1.40360e8 q^{52} -1.04627e8 q^{53} +7.49366e7 q^{54} -5.32773e7 q^{55} -1.96020e7 q^{56} +2.04060e7 q^{57} +6.55511e7 q^{58} +1.36231e7 q^{59} -6.40415e7 q^{60} -8.83091e7 q^{61} -1.15960e8 q^{62} -1.37238e7 q^{63} -4.08679e7 q^{64} -1.42598e8 q^{65} -9.54123e7 q^{66} +7.75239e7 q^{67} +8.39366e7 q^{68} -7.52233e7 q^{69} +3.67284e7 q^{70} +7.73617e7 q^{71} +4.19774e8 q^{72} -9.50405e7 q^{73} +7.56756e7 q^{74} -3.33649e7 q^{75} +4.52872e8 q^{76} +3.75361e7 q^{77} -2.55373e8 q^{78} +2.71542e8 q^{79} -4.72770e8 q^{80} +2.43907e8 q^{81} +1.11432e9 q^{82} -2.31731e8 q^{83} +4.51200e7 q^{84} -8.52747e7 q^{85} -1.84510e8 q^{86} -8.18119e7 q^{87} -1.14813e9 q^{88} -8.23276e8 q^{89} -7.86534e8 q^{90} +1.00466e8 q^{91} -1.66944e9 q^{92} +1.44726e8 q^{93} +1.23683e9 q^{94} -4.60092e8 q^{95} -2.14874e8 q^{96} -7.78331e8 q^{97} +1.60354e9 q^{98} -8.03833e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 32 q^{2} - 251 q^{3} + 2730 q^{4} - 2159 q^{5} - 4401 q^{6} - 12576 q^{7} - 20394 q^{8} + 69112 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more