LMFDB - Embedded newform 37.10.a.a.1.3

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			1.3
Root			$25.8517$ 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)

$f(q)$	$=$	$q-27.8517 q^{2} -234.213 q^{3} +263.715 q^{4} -396.481 q^{5} +6523.22 q^{6} -10779.8 q^{7} +6915.15 q^{8} +35172.6 q^{9} +O(q^{10})$	\(q-27.8517 q^{2} -234.213 q^{3} +263.715 q^{4} -396.481 q^{5} +6523.22 q^{6} -10779.8 q^{7} +6915.15 q^{8} +35172.6 q^{9} +11042.7 q^{10} +82183.5 q^{11} -61765.4 q^{12} +66461.3 q^{13} +300234. q^{14} +92861.0 q^{15} -327620. q^{16} -368394. q^{17} -979616. q^{18} +224093. q^{19} -104558. q^{20} +2.52476e6 q^{21} -2.28895e6 q^{22} +282251. q^{23} -1.61962e6 q^{24} -1.79593e6 q^{25} -1.85106e6 q^{26} -3.62787e6 q^{27} -2.84278e6 q^{28} +4.60646e6 q^{29} -2.58633e6 q^{30} -389557. q^{31} +5.58422e6 q^{32} -1.92484e7 q^{33} +1.02604e7 q^{34} +4.27397e6 q^{35} +9.27555e6 q^{36} -1.87416e6 q^{37} -6.24137e6 q^{38} -1.55661e7 q^{39} -2.74173e6 q^{40} +9.64743e6 q^{41} -7.03187e7 q^{42} +2.41247e7 q^{43} +2.16730e7 q^{44} -1.39453e7 q^{45} -7.86115e6 q^{46} -5.05170e7 q^{47} +7.67329e7 q^{48} +7.58497e7 q^{49} +5.00196e7 q^{50} +8.62825e7 q^{51} +1.75268e7 q^{52} +9.67402e7 q^{53} +1.01042e8 q^{54} -3.25842e7 q^{55} -7.45437e7 q^{56} -5.24855e7 q^{57} -1.28297e8 q^{58} -1.34345e8 q^{59} +2.44888e7 q^{60} +1.24073e8 q^{61} +1.08498e7 q^{62} -3.79153e8 q^{63} +1.22120e7 q^{64} -2.63507e7 q^{65} +5.36100e8 q^{66} -6.87378e7 q^{67} -9.71510e7 q^{68} -6.61067e7 q^{69} -1.19037e8 q^{70} -3.78394e8 q^{71} +2.43224e8 q^{72} +2.94022e8 q^{73} +5.21985e7 q^{74} +4.20629e8 q^{75} +5.90968e7 q^{76} -8.85918e8 q^{77} +4.33541e8 q^{78} -1.03019e8 q^{79} +1.29895e8 q^{80} +1.57391e8 q^{81} -2.68697e8 q^{82} +3.92838e7 q^{83} +6.65817e8 q^{84} +1.46061e8 q^{85} -6.71913e8 q^{86} -1.07889e9 q^{87} +5.68311e8 q^{88} +7.11603e7 q^{89} +3.88400e8 q^{90} -7.16437e8 q^{91} +7.44338e7 q^{92} +9.12392e7 q^{93} +1.40698e9 q^{94} -8.88488e7 q^{95} -1.30790e9 q^{96} -5.91917e8 q^{97} -2.11254e9 q^{98} +2.89061e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−27.8517	−1.23088	−0.615441	−	0.788183i	$-0.711022\pi$
$2$	−27.8517	−1.23088	−0.615441	+	0.788183i	$0.711022\pi$
$3$	−234.213	−1.66942	−0.834709	−	0.550692i	$-0.814364\pi$
$3$	−234.213	−1.66942	−0.834709	+	0.550692i	$0.814364\pi$
$4$	263.715	0.515068
$5$	−396.481	−0.283699	−0.141849	−	0.989888i	$-0.545305\pi$
$5$	−396.481	−0.283699	−0.141849	+	0.989888i	$0.545305\pi$
$6$	6523.22	2.05485
$7$	−10779.8	−1.69695	−0.848473	−	0.529239i	$-0.822478\pi$
$7$	−10779.8	−1.69695	−0.848473	+	0.529239i	$0.822478\pi$
$8$	6915.15	0.596893
$9$	35172.6	1.78696
$10$	11042.7	0.349200
$11$	82183.5	1.69246	0.846228	−	0.532821i	$-0.178868\pi$
$11$	82183.5	1.69246	0.846228	+	0.532821i	$0.178868\pi$
$12$	−61765.4	−0.859864
$13$	66461.3	0.645392	0.322696	−	0.946503i	$-0.395411\pi$
$13$	66461.3	0.645392	0.322696	+	0.946503i	$0.395411\pi$
$14$	300234.	2.08874
$15$	92861.0	0.473612
$16$	−327620.	−1.24977
$17$	−368394.	−1.06977	−0.534887	−	0.844924i	$-0.679646\pi$
$17$	−368394.	−1.06977	−0.534887	+	0.844924i	$0.679646\pi$
$18$	−979616.	−2.19953
$19$	224093.	0.394492	0.197246	−	0.980354i	$-0.436800\pi$
$19$	224093.	0.394492	0.197246	+	0.980354i	$0.436800\pi$
$20$	−104558.	−0.146124
$21$	2.52476e6	2.83291
$22$	−2.28895e6	−2.08321
$23$	282251.	0.210310	0.105155	−	0.994456i	$-0.466466\pi$
$23$	282251.	0.210310	0.105155	+	0.994456i	$0.466466\pi$
$24$	−1.61962e6	−0.996464
$25$	−1.79593e6	−0.919515
$26$	−1.85106e6	−0.794401
$27$	−3.62787e6	−1.31376
$28$	−2.84278e6	−0.874043
$29$	4.60646e6	1.20942	0.604708	−	0.796447i	$-0.293290\pi$
$29$	4.60646e6	1.20942	0.604708	+	0.796447i	$0.293290\pi$
$30$	−2.58633e6	−0.582960
$31$	−389557.	−0.0757606	−0.0378803	−	0.999282i	$-0.512061\pi$
$31$	−389557.	−0.0757606	−0.0378803	+	0.999282i	$0.512061\pi$
$32$	5.58422e6	0.941429
$33$	−1.92484e7	−2.82542
$34$	1.02604e7	1.31676
$35$	4.27397e6	0.481422
$36$	9.27555e6	0.920404
$37$	−1.87416e6	−0.164399
$37$	−1.87416e6	−0.164399
$38$	−6.24137e6	−0.485572
$39$	−1.55661e7	−1.07743
$40$	−2.74173e6	−0.169338
$41$	9.64743e6	0.533193	0.266596	−	0.963808i	$-0.414101\pi$
$41$	9.64743e6	0.533193	0.266596	+	0.963808i	$0.414101\pi$
$42$	−7.03187e7	−3.48698
$43$	2.41247e7	1.07610	0.538052	−	0.842912i	$-0.319161\pi$
$43$	2.41247e7	1.07610	0.538052	+	0.842912i	$0.319161\pi$
$44$	2.16730e7	0.871730
$45$	−1.39453e7	−0.506957
$46$	−7.86115e6	−0.258867
$47$	−5.05170e7	−1.51007	−0.755035	−	0.655685i	$-0.772380\pi$
$47$	−5.05170e7	−1.51007	−0.755035	+	0.655685i	$0.772380\pi$
$48$	7.67329e7	2.08639
$49$	7.58497e7	1.87963
$50$	5.00196e7	1.13181
$51$	8.62825e7	1.78590
$52$	1.75268e7	0.332421
$53$	9.67402e7	1.68409	0.842046	−	0.539406i	$-0.181351\pi$
$53$	9.67402e7	1.68409	0.842046	+	0.539406i	$0.181351\pi$
$54$	1.01042e8	1.61708
$55$	−3.25842e7	−0.480148
$56$	−7.45437e7	−1.01290
$57$	−5.24855e7	−0.658571
$58$	−1.28297e8	−1.48865
$59$	−1.34345e8	−1.44340	−0.721700	−	0.692206i	$-0.756639\pi$
$59$	−1.34345e8	−1.44340	−0.721700	+	0.692206i	$0.756639\pi$
$60$	2.44888e7	0.243942
$61$	1.24073e8	1.14735	0.573673	−	0.819085i	$-0.305518\pi$
$61$	1.24073e8	1.14735	0.573673	+	0.819085i	$0.305518\pi$
$62$	1.08498e7	0.0932523
$63$	−3.79153e8	−3.03237
$64$	1.22120e7	0.0909862
$65$	−2.63507e7	−0.183097
$66$	5.36100e8	3.47775
$67$	−6.87378e7	−0.416734	−0.208367	−	0.978051i	$-0.566815\pi$
$67$	−6.87378e7	−0.416734	−0.208367	+	0.978051i	$0.566815\pi$
$68$	−9.71510e7	−0.551007
$69$	−6.61067e7	−0.351095
$70$	−1.19037e8	−0.592573
$71$	−3.78394e8	−1.76718	−0.883591	−	0.468259i	$-0.844881\pi$
$71$	−3.78394e8	−1.76718	−0.883591	+	0.468259i	$0.844881\pi$
$72$	2.43224e8	1.06662
$73$	2.94022e8	1.21179	0.605895	−	0.795544i	$-0.292815\pi$
$73$	2.94022e8	1.21179	0.605895	+	0.795544i	$0.292815\pi$
$74$	5.21985e7	0.202356
$75$	4.20629e8	1.53505
$76$	5.90968e7	0.203190
$77$	−8.85918e8	−2.87201
$78$	4.33541e8	1.32619
$79$	−1.03019e8	−0.297575	−0.148788	−	0.988869i	$-0.547537\pi$
$79$	−1.03019e8	−0.297575	−0.148788	+	0.988869i	$0.547537\pi$
$80$	1.29895e8	0.354559
$81$	1.57391e8	0.406254
$82$	−2.68697e8	−0.656297
$83$	3.92838e7	0.0908577	0.0454289	−	0.998968i	$-0.485535\pi$
$83$	3.92838e7	0.0908577	0.0454289	+	0.998968i	$0.485535\pi$
$84$	6.65817e8	1.45914
$85$	1.46061e8	0.303494
$86$	−6.71913e8	−1.32456
$87$	−1.07889e9	−2.01902
$88$	5.68311e8	1.01022
$89$	7.11603e7	0.120222	0.0601108	−	0.998192i	$-0.480855\pi$
$89$	7.11603e7	0.120222	0.0601108	+	0.998192i	$0.480855\pi$
$90$	3.88400e8	0.624004
$91$	−7.16437e8	−1.09520
$92$	7.44338e7	0.108324
$93$	9.12392e7	0.126476
$94$	1.40698e9	1.85872
$95$	−8.88488e7	−0.111917
$96$	−1.30790e9	−1.57164
$97$	−5.91917e8	−0.678873	−0.339436	−	0.940629i	$-0.610236\pi$
$97$	−5.91917e8	−0.678873	−0.339436	+	0.940629i	$0.610236\pi$
$98$	−2.11254e9	−2.31360
$99$	2.89061e9	3.02434
$100$	−4.73613e8	−0.473613
$101$	9.68630e8	0.926215	0.463108	−	0.886302i	$-0.346734\pi$
$101$	9.68630e8	0.926215	0.463108	+	0.886302i	$0.346734\pi$
$102$	−2.40311e9	−2.19823
$103$	−2.21399e9	−1.93824	−0.969121	−	0.246585i	$-0.920692\pi$
$103$	−2.21399e9	−1.93824	−0.969121	+	0.246585i	$0.920692\pi$
$104$	4.59590e8	0.385230
$105$	−1.00102e9	−0.803694
$106$	−2.69438e9	−2.07292
$107$	3.17101e8	0.233868	0.116934	−	0.993140i	$-0.462693\pi$
$107$	3.17101e8	0.233868	0.116934	+	0.993140i	$0.462693\pi$
$108$	−9.56724e8	−0.676674
$109$	−5.01820e8	−0.340509	−0.170255	−	0.985400i	$-0.554459\pi$
$109$	−5.01820e8	−0.340509	−0.170255	+	0.985400i	$0.554459\pi$
$110$	9.07524e8	0.591005
$111$	4.38953e8	0.274451
$112$	3.53167e9	2.12080
$113$	−1.05623e9	−0.609406	−0.304703	−	0.952447i	$-0.598557\pi$
$113$	−1.05623e9	−0.609406	−0.304703	+	0.952447i	$0.598557\pi$
$114$	1.46181e9	0.810623
$115$	−1.11907e8	−0.0596647
$116$	1.21479e9	0.622932
$117$	2.33762e9	1.15329
$118$	3.74172e9	1.77665
$119$	3.97120e9	1.81535
$120$	6.42148e8	0.282696
$121$	4.39617e9	1.86441
$122$	−3.45565e9	−1.41225
$123$	−2.25955e9	−0.890122
$124$	−1.02732e8	−0.0390219
$125$	1.48643e9	0.544564
$126$	1.05600e10	3.73248
$127$	3.21263e9	1.09583	0.547916	−	0.836533i	$-0.315421\pi$
$127$	3.21263e9	1.09583	0.547916	+	0.836533i	$0.315421\pi$
$128$	−3.19924e9	−1.05342
$129$	−5.65031e9	−1.79647
$130$	7.33910e8	0.225371
$131$	−4.77523e9	−1.41669	−0.708343	−	0.705868i	$-0.750557\pi$
$131$	−4.77523e9	−1.41669	−0.708343	+	0.705868i	$0.750557\pi$
$132$	−5.07610e9	−1.45528
$133$	−2.41567e9	−0.669431
$134$	1.91446e9	0.512950
$135$	1.43838e9	0.372711
$136$	−2.54750e9	−0.638541
$137$	−8.38192e8	−0.203283	−0.101642	−	0.994821i	$-0.532409\pi$
$137$	−8.38192e8	−0.203283	−0.101642	+	0.994821i	$0.532409\pi$
$138$	1.84118e9	0.432156
$139$	−5.06214e8	−0.115018	−0.0575092	−	0.998345i	$-0.518316\pi$
$139$	−5.06214e8	−0.115018	−0.0575092	+	0.998345i	$0.518316\pi$
$140$	1.12711e9	0.247965
$141$	1.18317e10	2.52094
$142$	1.05389e10	2.17519
$143$	5.46202e9	1.09230
$144$	−1.15233e10	−2.23329
$145$	−1.82637e9	−0.343110
$146$	−8.18901e9	−1.49157
$147$	−1.77650e10	−3.13788
$148$	−4.94244e8	−0.0846767
$149$	2.89651e9	0.481434	0.240717	−	0.970595i	$-0.422617\pi$
$149$	2.89651e9	0.481434	0.240717	+	0.970595i	$0.422617\pi$
$150$	−1.17152e10	−1.88947
$151$	−2.73564e9	−0.428216	−0.214108	−	0.976810i	$-0.568685\pi$
$151$	−2.73564e9	−0.428216	−0.214108	+	0.976810i	$0.568685\pi$
$152$	1.54964e9	0.235469
$153$	−1.29574e10	−1.91164
$154$	2.46743e10	3.53510
$155$	1.54452e8	0.0214932
$156$	−4.10501e9	−0.554950
$157$	1.26213e9	0.165789	0.0828943	−	0.996558i	$-0.473584\pi$
$157$	1.26213e9	0.165789	0.0828943	+	0.996558i	$0.473584\pi$
$158$	2.86926e9	0.366280
$159$	−2.26578e10	−2.81145
$160$	−2.21404e9	−0.267082
$161$	−3.04260e9	−0.356885
$162$	−4.38360e9	−0.500050
$163$	5.54254e9	0.614985	0.307493	−	0.951550i	$-0.400510\pi$
$163$	5.54254e9	0.614985	0.307493	+	0.951550i	$0.400510\pi$
$164$	2.54417e9	0.274631
$165$	7.63164e9	0.801567
$166$	−1.09412e9	−0.111835
$167$	−1.31375e10	−1.30704	−0.653520	−	0.756909i	$-0.726709\pi$
$167$	−1.31375e10	−1.30704	−0.653520	+	0.756909i	$0.726709\pi$
$168$	1.74591e10	1.69095
$169$	−6.18739e9	−0.583469
$170$	−4.06805e9	−0.373565
$171$	7.88196e9	0.704939
$172$	6.36205e9	0.554267
$173$	−1.79297e10	−1.52183	−0.760913	−	0.648854i	$-0.775248\pi$
$173$	−1.79297e10	−1.52183	−0.760913	+	0.648854i	$0.775248\pi$
$174$	3.00489e10	2.48518
$175$	1.93597e10	1.56037
$176$	−2.69250e10	−2.11519
$177$	3.14653e10	2.40964
$178$	−1.98193e9	−0.147979
$179$	−2.24379e10	−1.63359	−0.816797	−	0.576925i	$-0.804252\pi$
$179$	−2.24379e10	−1.63359	−0.816797	+	0.576925i	$0.804252\pi$
$180$	−3.67758e9	−0.261118
$181$	7.67539e9	0.531553	0.265777	−	0.964035i	$-0.414372\pi$
$181$	7.67539e9	0.531553	0.265777	+	0.964035i	$0.414372\pi$
$182$	1.99540e10	1.34806
$183$	−2.90596e10	−1.91540
$184$	1.95181e9	0.125533
$185$	7.43070e8	0.0466398
$186$	−2.54116e9	−0.155677
$187$	−3.02759e10	−1.81055
$188$	−1.33221e10	−0.777789
$189$	3.91076e10	2.22937
$190$	2.47459e9	0.137756
$191$	1.39055e10	0.756025	0.378013	−	0.925800i	$-0.376608\pi$
$191$	1.39055e10	0.756025	0.378013	+	0.925800i	$0.376608\pi$
$192$	−2.86020e9	−0.151894
$193$	9.01103e9	0.467484	0.233742	−	0.972299i	$-0.424903\pi$
$193$	9.01103e9	0.467484	0.233742	+	0.972299i	$0.424903\pi$
$194$	1.64859e10	0.835611
$195$	6.17166e9	0.305665
$196$	2.00027e10	0.968136
$197$	2.50955e10	1.18713	0.593564	−	0.804787i	$-0.297720\pi$
$197$	2.50955e10	1.18713	0.593564	+	0.804787i	$0.297720\pi$
$198$	−8.05083e10	−3.72261
$199$	2.24040e9	0.101272	0.0506358	−	0.998717i	$-0.483875\pi$
$199$	2.24040e9	0.101272	0.0506358	+	0.998717i	$0.483875\pi$
$200$	−1.24191e10	−0.548852
$201$	1.60993e10	0.695704
$202$	−2.69780e10	−1.14006
$203$	−4.96565e10	−2.05231
$204$	2.27540e10	0.919860
$205$	−3.82503e9	−0.151266
$206$	6.16633e10	2.38575
$207$	9.92750e9	0.375815
$208$	−2.17741e10	−0.806594
$209$	1.84168e10	0.667660
$210$	2.78801e10	0.989252
$211$	7.18822e9	0.249661	0.124830	−	0.992178i	$-0.460161\pi$
$211$	7.18822e9	0.249661	0.124830	+	0.992178i	$0.460161\pi$
$212$	2.55118e10	0.867422
$213$	8.86246e10	2.95016
$214$	−8.83178e9	−0.287863
$215$	−9.56499e9	−0.305289
$216$	−2.50873e10	−0.784173
$217$	4.19933e9	0.128562
$218$	1.39765e10	0.419126
$219$	−6.88638e10	−2.02298
$220$	−8.59294e9	−0.247309
$221$	−2.44839e10	−0.690424
$222$	−1.22256e10	−0.337816
$223$	4.41481e10	1.19547	0.597737	−	0.801692i	$-0.296067\pi$
$223$	4.41481e10	1.19547	0.597737	+	0.801692i	$0.296067\pi$
$224$	−6.01965e10	−1.59755
$225$	−6.31675e10	−1.64313
$226$	2.94178e10	0.750106
$227$	5.16891e10	1.29206	0.646029	−	0.763312i	$-0.276428\pi$
$227$	5.16891e10	1.29206	0.646029	+	0.763312i	$0.276428\pi$
$228$	−1.38412e10	−0.339209
$229$	−2.22782e10	−0.535330	−0.267665	−	0.963512i	$-0.586252\pi$
$229$	−2.22782e10	−0.535330	−0.267665	+	0.963512i	$0.586252\pi$
$230$	3.11680e9	0.0734402
$231$	2.07493e11	4.79458
$232$	3.18543e10	0.721893
$233$	−5.20999e10	−1.15807	−0.579036	−	0.815302i	$-0.696571\pi$
$233$	−5.20999e10	−1.15807	−0.579036	+	0.815302i	$0.696571\pi$
$234$	−6.51066e10	−1.41956
$235$	2.00290e10	0.428405
$236$	−3.54287e10	−0.743450
$237$	2.41285e10	0.496778
$238$	−1.10604e11	−2.23448
$239$	4.76832e10	0.945311	0.472656	−	0.881247i	$-0.343295\pi$
$239$	4.76832e10	0.945311	0.472656	+	0.881247i	$0.343295\pi$
$240$	−3.04232e10	−0.591907
$241$	−1.00759e11	−1.92401	−0.962005	−	0.273032i	$-0.911973\pi$
$241$	−1.00759e11	−1.92401	−0.962005	+	0.273032i	$0.911973\pi$
$242$	−1.22441e11	−2.29486
$243$	3.45444e10	0.635550
$244$	3.27200e10	0.590961
$245$	−3.00730e10	−0.533248
$246$	6.29323e10	1.09563
$247$	1.48935e10	0.254602
$248$	−2.69384e9	−0.0452210
$249$	−9.20076e9	−0.151679
$250$	−4.13995e10	−0.670294
$251$	2.26246e10	0.359790	0.179895	−	0.983686i	$-0.442424\pi$
$251$	2.26246e10	0.359790	0.179895	+	0.983686i	$0.442424\pi$
$252$	−9.99882e10	−1.56188
$253$	2.31963e10	0.355940
$254$	−8.94771e10	−1.34884
$255$	−3.42094e10	−0.506658
$256$	8.28517e10	1.20565
$257$	2.99537e10	0.428304	0.214152	−	0.976800i	$-0.431301\pi$
$257$	2.99537e10	0.428304	0.214152	+	0.976800i	$0.431301\pi$
$258$	1.57371e11	2.21124
$259$	2.02030e10	0.278976
$260$	−6.94906e9	−0.0943075
$261$	1.62021e11	2.16117
$262$	1.32998e11	1.74377
$263$	−9.48383e10	−1.22231	−0.611157	−	0.791509i	$-0.709296\pi$
$263$	−9.48383e10	−1.22231	−0.611157	+	0.791509i	$0.709296\pi$
$264$	−1.33106e11	−1.68647
$265$	−3.83557e10	−0.477775
$266$	6.72805e10	0.823990
$267$	−1.66666e10	−0.200700
$268$	−1.81272e10	−0.214647
$269$	−8.44184e10	−0.982997	−0.491498	−	0.870878i	$-0.663551\pi$
$269$	−8.44184e10	−0.982997	−0.491498	+	0.870878i	$0.663551\pi$
$270$	−4.00614e10	−0.458763
$271$	−4.89036e10	−0.550782	−0.275391	−	0.961332i	$-0.588807\pi$
$271$	−4.89036e10	−0.550782	−0.275391	+	0.961332i	$0.588807\pi$
$272$	1.20693e11	1.33697
$273$	1.67799e11	1.82834
$274$	2.33451e10	0.250217
$275$	−1.47596e11	−1.55624
$276$	−1.74333e10	−0.180838
$277$	−1.17261e11	−1.19672	−0.598361	−	0.801227i	$-0.704181\pi$
$277$	−1.17261e11	−1.19672	−0.598361	+	0.801227i	$0.704181\pi$
$278$	1.40989e10	0.141574
$279$	−1.37017e10	−0.135381
$280$	2.95552e10	0.287357
$281$	6.55587e10	0.627267	0.313633	−	0.949544i	$-0.398454\pi$
$281$	6.55587e10	0.627267	0.313633	+	0.949544i	$0.398454\pi$
$282$	−3.29533e11	−3.10297
$283$	−1.17682e10	−0.109061	−0.0545305	−	0.998512i	$-0.517366\pi$
$283$	−1.17682e10	−0.109061	−0.0545305	+	0.998512i	$0.517366\pi$
$284$	−9.97881e10	−0.910220
$285$	2.08095e10	0.186836
$286$	−1.52126e11	−1.34449
$287$	−1.03997e11	−0.904800
$288$	1.96412e11	1.68229
$289$	1.71261e10	0.144417
$290$	5.08675e10	0.422328
$291$	1.38635e11	1.13332
$292$	7.75381e10	0.624155
$293$	2.00566e10	0.158984	0.0794920	−	0.996836i	$-0.474670\pi$
$293$	2.00566e10	0.158984	0.0794920	+	0.996836i	$0.474670\pi$
$294$	4.94784e11	3.86236
$295$	5.32652e10	0.409491
$296$	−1.29601e10	−0.0981286
$297$	−2.98151e11	−2.22347
$298$	−8.06726e10	−0.592588
$299$	1.87588e10	0.135732
$300$	1.10926e11	0.790658
$301$	−2.60059e11	−1.82609
$302$	7.61922e10	0.527084
$303$	−2.26866e11	−1.54624
$304$	−7.34176e10	−0.493025
$305$	−4.91927e10	−0.325501
$306$	3.60885e11	2.35300
$307$	−1.24586e11	−0.800474	−0.400237	−	0.916412i	$-0.631072\pi$
$307$	−1.24586e11	−0.800474	−0.400237	+	0.916412i	$0.631072\pi$
$308$	−2.33630e11	−1.47928
$309$	5.18545e11	3.23574
$310$	−4.30174e9	−0.0264556
$311$	4.00774e10	0.242928	0.121464	−	0.992596i	$-0.461241\pi$
$311$	4.00774e10	0.242928	0.121464	+	0.992596i	$0.461241\pi$
$312$	−1.07642e11	−0.643110
$313$	−3.17006e11	−1.86689	−0.933445	−	0.358722i	$-0.883213\pi$
$313$	−3.17006e11	−1.86689	−0.933445	+	0.358722i	$0.883213\pi$
$314$	−3.51523e10	−0.204066
$315$	1.50327e11	0.860279
$316$	−2.71678e10	−0.153272
$317$	1.67527e10	0.0931789	0.0465894	−	0.998914i	$-0.485165\pi$
$317$	1.67527e10	0.0931789	0.0465894	+	0.998914i	$0.485165\pi$
$318$	6.31057e11	3.46056
$319$	3.78574e11	2.04688
$320$	−4.84181e9	−0.0258127
$321$	−7.42690e10	−0.390423
$322$	8.47414e10	0.439283
$323$	−8.25546e10	−0.422017
$324$	4.15063e10	0.209248
$325$	−1.19360e11	−0.593448
$326$	−1.54369e11	−0.756973
$327$	1.17533e11	0.568452
$328$	6.67135e10	0.318259
$329$	5.44561e11	2.56251
$330$	−2.12554e11	−0.986634
$331$	2.54738e11	1.16646	0.583228	−	0.812308i	$-0.301789\pi$
$331$	2.54738e11	1.16646	0.583228	+	0.812308i	$0.301789\pi$
$332$	1.03597e10	0.0467979
$333$	−6.59192e10	−0.293774
$334$	3.65902e11	1.60881
$335$	2.72533e10	0.118227
$336$	−8.27163e11	−3.54050
$337$	2.32048e11	0.980040	0.490020	−	0.871711i	$-0.336989\pi$
$337$	2.32048e11	0.980040	0.490020	+	0.871711i	$0.336989\pi$
$338$	1.72329e11	0.718181
$339$	2.47383e11	1.01735
$340$	3.85185e10	0.156320
$341$	−3.20151e10	−0.128221
$342$	−2.19526e11	−0.867696
$343$	−3.82639e11	−1.49268
$344$	1.66826e11	0.642319
$345$	2.62101e10	0.0996053
$346$	4.99371e11	1.87319
$347$	−1.89033e11	−0.699929	−0.349964	−	0.936763i	$-0.613806\pi$
$347$	−1.89033e11	−0.699929	−0.349964	+	0.936763i	$0.613806\pi$
$348$	−2.84520e11	−1.03993
$349$	−9.94946e10	−0.358992	−0.179496	−	0.983759i	$-0.557447\pi$
$349$	−9.94946e10	−0.358992	−0.179496	+	0.983759i	$0.557447\pi$
$350$	−5.39199e11	−1.92063
$351$	−2.41113e11	−0.847888
$352$	4.58930e11	1.59333
$353$	−2.87504e11	−0.985504	−0.492752	−	0.870170i	$-0.664009\pi$
$353$	−2.87504e11	−0.985504	−0.492752	+	0.870170i	$0.664009\pi$
$354$	−8.76360e11	−2.96598
$355$	1.50026e11	0.501348
$356$	1.87660e10	0.0619223
$357$	−9.30105e11	−3.03058
$358$	6.24934e11	2.01076
$359$	1.20405e10	0.0382576	0.0191288	−	0.999817i	$-0.493911\pi$
$359$	1.20405e10	0.0382576	0.0191288	+	0.999817i	$0.493911\pi$
$360$	−9.64338e10	−0.302599
$361$	−2.72470e11	−0.844376
$362$	−2.13772e11	−0.654279
$363$	−1.02964e12	−3.11247
$364$	−1.88935e11	−0.564101
$365$	−1.16574e11	−0.343784
$366$	8.09357e11	2.35763
$367$	−6.81722e10	−0.196160	−0.0980799	−	0.995179i	$-0.531270\pi$
$367$	−6.81722e10	−0.196160	−0.0980799	+	0.995179i	$0.531270\pi$
$368$	−9.24711e10	−0.262840
$369$	3.39326e11	0.952792
$370$	−2.06957e10	−0.0574081
$371$	−1.04284e12	−2.85781
$372$	2.40611e10	0.0651438
$373$	4.48773e11	1.20043	0.600215	−	0.799839i	$-0.295082\pi$
$373$	4.48773e11	1.20043	0.600215	+	0.799839i	$0.295082\pi$
$374$	8.43233e11	2.22857
$375$	−3.48141e11	−0.909105
$376$	−3.49333e11	−0.901351
$377$	3.06151e11	0.780548
$378$	−1.08921e12	−2.74409
$379$	7.13449e11	1.77618	0.888089	−	0.459671i	$-0.152033\pi$
$379$	7.13449e11	1.77618	0.888089	+	0.459671i	$0.152033\pi$
$380$	−2.34308e10	−0.0576448
$381$	−7.52439e11	−1.82940
$382$	−3.87291e11	−0.930577
$383$	4.13204e10	0.0981228	0.0490614	−	0.998796i	$-0.484377\pi$
$383$	4.13204e10	0.0981228	0.0490614	+	0.998796i	$0.484377\pi$
$384$	7.49304e11	1.75860
$385$	3.51250e11	0.814785
$386$	−2.50972e11	−0.575417
$387$	8.48529e11	1.92295
$388$	−1.56097e11	−0.349666
$389$	5.52272e11	1.22287	0.611434	−	0.791295i	$-0.290593\pi$
$389$	5.52272e11	1.22287	0.611434	+	0.791295i	$0.290593\pi$
$390$	−1.71891e11	−0.376238
$391$	−1.03979e11	−0.224984
$392$	5.24512e11	1.12194
$393$	1.11842e12	2.36504
$394$	−6.98951e11	−1.46121
$395$	4.08453e10	0.0844218
$396$	7.62297e11	1.55774
$397$	3.23090e10	0.0652780	0.0326390	−	0.999467i	$-0.489609\pi$
$397$	3.23090e10	0.0652780	0.0326390	+	0.999467i	$0.489609\pi$
$398$	−6.23989e10	−0.124653
$399$	5.65782e11	1.11756
$400$	5.88383e11	1.14918
$401$	−8.30085e11	−1.60315	−0.801573	−	0.597897i	$-0.796003\pi$
$401$	−8.30085e11	−1.60315	−0.801573	+	0.597897i	$0.796003\pi$
$402$	−4.48392e11	−0.856328
$403$	−2.58905e10	−0.0488953
$404$	2.55442e11	0.477064
$405$	−6.24026e10	−0.115254
$406$	1.38302e12	2.52616
$407$	−1.54025e11	−0.278238
$408$	5.96657e11	1.06599
$409$	9.03692e11	1.59685	0.798427	−	0.602091i	$-0.205666\pi$
$409$	9.03692e11	1.59685	0.798427	+	0.602091i	$0.205666\pi$
$410$	1.06533e11	0.186191
$411$	1.96315e11	0.339364
$412$	−5.83862e11	−0.998327
$413$	1.44820e12	2.44937
$414$	−2.76497e11	−0.462583
$415$	−1.55753e10	−0.0257762
$416$	3.71134e11	0.607591
$417$	1.18562e11	0.192014
$418$	−5.12938e11	−0.821810
$419$	−1.04552e12	−1.65718	−0.828589	−	0.559858i	$-0.810856\pi$
$419$	−1.04552e12	−1.65718	−0.828589	+	0.559858i	$0.810856\pi$
$420$	−2.63984e11	−0.413957
$421$	−8.38490e11	−1.30085	−0.650427	−	0.759569i	$-0.725410\pi$
$421$	−8.38490e11	−1.30085	−0.650427	+	0.759569i	$0.725410\pi$
$422$	−2.00204e11	−0.307303
$423$	−1.77682e12	−2.69843
$424$	6.68973e11	1.00522
$425$	6.61609e11	0.983673
$426$	−2.46834e12	−3.63130
$427$	−1.33748e12	−1.94698
$428$	8.36242e10	0.120458
$429$	−1.27927e12	−1.82350
$430$	2.66401e11	0.375775
$431$	3.96655e11	0.553688	0.276844	−	0.960915i	$-0.410712\pi$
$431$	3.96655e11	0.553688	0.276844	+	0.960915i	$0.410712\pi$
$432$	1.18857e12	1.64190
$433$	5.64725e11	0.772043	0.386022	−	0.922490i	$-0.373849\pi$
$433$	5.64725e11	0.772043	0.386022	+	0.922490i	$0.373849\pi$
$434$	−1.16958e11	−0.158244
$435$	4.27760e11	0.572794
$436$	−1.32337e11	−0.175385
$437$	6.32505e10	0.0829655
$438$	1.91797e12	2.49005
$439$	3.28569e11	0.422218	0.211109	−	0.977463i	$-0.432292\pi$
$439$	3.28569e11	0.422218	0.211109	+	0.977463i	$0.432292\pi$
$440$	−2.25325e11	−0.286597
$441$	2.66783e12	3.35881
$442$	6.81918e11	0.849830
$443$	−6.82781e11	−0.842296	−0.421148	−	0.906992i	$-0.638373\pi$
$443$	−6.82781e11	−0.842296	−0.421148	+	0.906992i	$0.638373\pi$
$444$	1.15758e11	0.141361
$445$	−2.82137e10	−0.0341067
$446$	−1.22960e12	−1.47149
$447$	−6.78399e11	−0.803714
$448$	−1.31642e11	−0.154399
$449$	1.81992e11	0.211322	0.105661	−	0.994402i	$-0.466304\pi$
$449$	1.81992e11	0.211322	0.105661	+	0.994402i	$0.466304\pi$
$450$	1.75932e12	2.02250
$451$	7.92859e11	0.902405
$452$	−2.78544e11	−0.313885
$453$	6.40723e11	0.714872
$454$	−1.43963e12	−1.59037
$455$	2.84054e11	0.310706
$456$	−3.62945e11	−0.393097
$457$	−1.27413e12	−1.36644	−0.683220	−	0.730213i	$-0.739421\pi$
$457$	−1.27413e12	−1.36644	−0.683220	+	0.730213i	$0.739421\pi$
$458$	6.20486e11	0.658927
$459$	1.33649e12	1.40542
$460$	−2.95116e10	−0.0307314
$461$	3.55884e11	0.366990	0.183495	−	0.983021i	$-0.441259\pi$
$461$	3.55884e11	0.366990	0.183495	+	0.983021i	$0.441259\pi$
$462$	−5.77903e12	−5.90155
$463$	−1.52165e12	−1.53886	−0.769430	−	0.638732i	$-0.779459\pi$
$463$	−1.52165e12	−1.53886	−0.769430	+	0.638732i	$0.779459\pi$
$464$	−1.50917e12	−1.51150
$465$	−3.61746e10	−0.0358811
$466$	1.45107e12	1.42545
$467$	−6.27735e11	−0.610732	−0.305366	−	0.952235i	$-0.598779\pi$
$467$	−6.27735e11	−0.610732	−0.305366	+	0.952235i	$0.598779\pi$
$468$	6.16465e11	0.594022
$469$	7.40978e11	0.707176
$470$	−5.57842e11	−0.527316
$471$	−2.95606e11	−0.276770
$472$	−9.29014e11	−0.861556
$473$	1.98265e12	1.82126
$474$	−6.72018e11	−0.611474
$475$	−4.02456e11	−0.362741
$476$	1.04726e12	0.935029
$477$	3.40261e12	3.00940
$478$	−1.32806e12	−1.16357
$479$	−2.05800e12	−1.78622	−0.893112	−	0.449834i	$-0.851483\pi$
$479$	−2.05800e12	−1.78622	−0.893112	+	0.449834i	$0.851483\pi$
$480$	5.18556e11	0.445872
$481$	−1.24559e11	−0.106102
$482$	2.80631e12	2.36823
$483$	7.12615e11	0.595790
$484$	1.15934e12	0.960296
$485$	2.34684e11	0.192595
$486$	−9.62120e11	−0.782286
$487$	−8.81476e11	−0.710117	−0.355059	−	0.934844i	$-0.615539\pi$
$487$	−8.81476e11	−0.710117	−0.355059	+	0.934844i	$0.615539\pi$
$488$	8.57986e11	0.684843
$489$	−1.29813e12	−1.02667
$490$	8.37582e11	0.656365
$491$	−1.24420e12	−0.966102	−0.483051	−	0.875592i	$-0.660471\pi$
$491$	−1.24420e12	−0.966102	−0.483051	+	0.875592i	$0.660471\pi$
$492$	−5.95878e11	−0.458474
$493$	−1.69699e12	−1.29380
$494$	−4.14810e11	−0.313385
$495$	−1.14607e12	−0.858003
$496$	1.27627e11	0.0946835
$497$	4.07899e12	2.99881
$498$	2.56257e11	0.186699
$499$	2.27561e11	0.164303	0.0821515	−	0.996620i	$-0.473821\pi$
$499$	2.27561e11	0.164303	0.0821515	+	0.996620i	$0.473821\pi$
$500$	3.91994e11	0.280488
$501$	3.07697e12	2.18200
$502$	−6.30133e11	−0.442859
$503$	2.60701e12	1.81588	0.907940	−	0.419101i	$-0.137655\pi$
$503$	2.60701e12	1.81588	0.907940	+	0.419101i	$0.137655\pi$
$504$	−2.62190e12	−1.81000
$505$	−3.84044e11	−0.262766
$506$	−6.46057e11	−0.438120
$507$	1.44917e12	0.974053
$508$	8.47218e11	0.564428
$509$	−1.71769e12	−1.13427	−0.567134	−	0.823625i	$-0.691948\pi$
$509$	−1.71769e12	−1.13427	−0.567134	+	0.823625i	$0.691948\pi$
$510$	9.52789e11	0.623636
$511$	−3.16949e12	−2.05634
$512$	−6.69545e11	−0.430591
$513$	−8.12982e11	−0.518266
$514$	−8.34261e11	−0.527191
$515$	8.77805e11	0.549877
$516$	−1.49007e12	−0.925303
$517$	−4.15166e12	−2.55573
$518$	−5.62687e11	−0.343387
$519$	4.19936e12	2.54056
$520$	−1.82219e11	−0.109289
$521$	−2.71498e12	−1.61434	−0.807172	−	0.590316i	$-0.799003\pi$
$521$	−2.71498e12	−1.61434	−0.807172	+	0.590316i	$0.799003\pi$
$522$	−4.51256e12	−2.66015
$523$	−1.10597e12	−0.646377	−0.323189	−	0.946335i	$-0.604755\pi$
$523$	−1.10597e12	−0.646377	−0.323189	+	0.946335i	$0.604755\pi$
$524$	−1.25930e12	−0.729690
$525$	−4.53428e12	−2.60490
$526$	2.64140e12	1.50452
$527$	1.43510e11	0.0810467
$528$	6.30618e12	3.53113
$529$	−1.72149e12	−0.955770
$530$	1.06827e12	0.588084
$531$	−4.72526e12	−2.57929
$532$	−6.37049e11	−0.344803
$533$	6.41181e11	0.344119
$534$	4.64194e11	0.247038
$535$	−1.25724e11	−0.0663480
$536$	−4.75332e11	−0.248746
$537$	5.25525e12	2.72715
$538$	2.35119e12	1.20995
$539$	6.23359e12	3.18118
$540$	3.79323e11	0.191972
$541$	−2.58444e11	−0.129712	−0.0648558	−	0.997895i	$-0.520659\pi$
$541$	−2.58444e11	−0.129712	−0.0648558	+	0.997895i	$0.520659\pi$
$542$	1.36205e12	0.677947
$543$	−1.79767e12	−0.887385
$544$	−2.05719e12	−1.00712
$545$	1.98962e11	0.0966021
$546$	−4.67347e12	−2.25047
$547$	−1.50797e12	−0.720192	−0.360096	−	0.932915i	$-0.617256\pi$
$547$	−1.50797e12	−0.720192	−0.360096	+	0.932915i	$0.617256\pi$
$548$	−2.21044e11	−0.104705
$549$	4.36399e12	2.05025
$550$	4.11078e12	1.91554
$551$	1.03228e12	0.477105
$552$	−4.57138e11	−0.209566
$553$	1.11052e12	0.504969
$554$	3.26590e12	1.47302
$555$	−1.74036e11	−0.0778613
$556$	−1.33496e11	−0.0592424
$557$	−2.08733e12	−0.918845	−0.459422	−	0.888218i	$-0.651944\pi$
$557$	−2.08733e12	−0.918845	−0.459422	+	0.888218i	$0.651944\pi$
$558$	3.81616e11	0.166638
$559$	1.60336e12	0.694509
$560$	−1.40024e12	−0.601668
$561$	7.09100e12	3.02256
$562$	−1.82592e12	−0.772091
$563$	−7.35288e11	−0.308439	−0.154220	−	0.988037i	$-0.549286\pi$
$563$	−7.35288e11	−0.308439	−0.154220	+	0.988037i	$0.549286\pi$
$564$	3.12020e12	1.29845
$565$	4.18776e11	0.172888
$566$	3.27763e11	0.134241
$567$	−1.69664e12	−0.689390
$568$	−2.61665e12	−1.05482
$569$	−1.44029e12	−0.576029	−0.288015	−	0.957626i	$-0.592995\pi$
$569$	−1.44029e12	−0.576029	−0.288015	+	0.957626i	$0.592995\pi$
$570$	−5.79580e11	−0.229973
$571$	−1.48887e12	−0.586131	−0.293066	−	0.956092i	$-0.594675\pi$
$571$	−1.48887e12	−0.586131	−0.293066	+	0.956092i	$0.594675\pi$
$572$	1.44042e12	0.562608
$573$	−3.25685e12	−1.26212
$574$	2.89649e12	1.11370
$575$	−5.06902e11	−0.193383
$576$	4.29527e11	0.162588
$577$	−5.32489e11	−0.199995	−0.0999976	−	0.994988i	$-0.531884\pi$
$577$	−5.32489e11	−0.199995	−0.0999976	+	0.994988i	$0.531884\pi$
$578$	−4.76990e11	−0.177760
$579$	−2.11050e12	−0.780425
$580$	−4.81642e11	−0.176725
$581$	−4.23470e11	−0.154181
$582$	−3.86120e12	−1.39498
$583$	7.95044e12	2.85025
$584$	2.03321e12	0.723310
$585$	−9.26822e11	−0.327186
$586$	−5.58610e11	−0.195690
$587$	−2.68729e11	−0.0934206	−0.0467103	−	0.998908i	$-0.514874\pi$
$587$	−2.68729e11	−0.0934206	−0.0467103	+	0.998908i	$0.514874\pi$
$588$	−4.68489e12	−1.61622
$589$	−8.72971e10	−0.0298869
$590$	−1.48352e12	−0.504035
$591$	−5.87768e12	−1.98181
$592$	6.14014e11	0.205461
$593$	2.45781e12	0.816211	0.408106	−	0.912935i	$-0.366190\pi$
$593$	2.45781e12	0.816211	0.408106	+	0.912935i	$0.366190\pi$
$594$	8.30400e12	2.73683
$595$	−1.57451e12	−0.515013
$596$	7.63853e11	0.247971
$597$	−5.24731e11	−0.169064
$598$	−5.22462e11	−0.167070
$599$	−2.88688e12	−0.916236	−0.458118	−	0.888891i	$-0.651476\pi$
$599$	−2.88688e12	−0.916236	−0.458118	+	0.888891i	$0.651476\pi$
$600$	2.90871e12	0.916264
$601$	−2.56318e12	−0.801389	−0.400695	−	0.916212i	$-0.631231\pi$
$601$	−2.56318e12	−0.801389	−0.400695	+	0.916212i	$0.631231\pi$
$602$	7.24306e12	2.24770
$603$	−2.41769e12	−0.744685
$604$	−7.21430e11	−0.220561
$605$	−1.74300e12	−0.528930
$606$	6.31858e12	1.90324
$607$	5.24723e12	1.56885	0.784424	−	0.620225i	$-0.212959\pi$
$607$	5.24723e12	1.56885	0.784424	+	0.620225i	$0.212959\pi$
$608$	1.25139e12	0.371386
$609$	1.16302e13	3.42617
$610$	1.37010e12	0.400653
$611$	−3.35742e12	−0.974587
$612$	−3.41706e12	−0.984624
$613$	−5.15143e12	−1.47352	−0.736760	−	0.676155i	$-0.763645\pi$
$613$	−5.15143e12	−1.47352	−0.736760	+	0.676155i	$0.763645\pi$
$614$	3.46993e12	0.985289
$615$	8.95870e11	0.252527
$616$	−6.12626e12	−1.71428
$617$	1.11280e12	0.309125	0.154563	−	0.987983i	$-0.450603\pi$
$617$	1.11280e12	0.309125	0.154563	+	0.987983i	$0.450603\pi$
$618$	−1.44423e13	−3.98281
$619$	−5.29938e12	−1.45083	−0.725417	−	0.688310i	$-0.758353\pi$
$619$	−5.29938e12	−1.45083	−0.725417	+	0.688310i	$0.758353\pi$
$620$	4.07313e10	0.0110705
$621$	−1.02397e12	−0.276296
$622$	−1.11622e12	−0.299015
$623$	−7.67091e11	−0.204010
$624$	5.09977e12	1.34654
$625$	2.91833e12	0.765023
$626$	8.82916e12	2.29792
$627$	−4.31344e12	−1.11460
$628$	3.32842e11	0.0853924
$629$	6.90429e11	0.175870
$630$	−4.18685e12	−1.05890
$631$	6.51971e12	1.63718	0.818589	−	0.574379i	$-0.194756\pi$
$631$	6.51971e12	1.63718	0.818589	+	0.574379i	$0.194756\pi$
$632$	−7.12394e11	−0.177621
$633$	−1.68357e12	−0.416788
$634$	−4.66590e11	−0.114692
$635$	−1.27375e12	−0.310886
$636$	−5.97520e12	−1.44809
$637$	5.04107e12	1.21310
$638$	−1.05439e13	−2.51947
$639$	−1.33091e13	−3.15788
$640$	1.26844e12	0.298855
$641$	1.70376e12	0.398610	0.199305	−	0.979938i	$-0.436132\pi$
$641$	1.70376e12	0.398610	0.199305	+	0.979938i	$0.436132\pi$
$642$	2.06852e12	0.480564
$643$	9.01144e11	0.207895	0.103948	−	0.994583i	$-0.466853\pi$
$643$	9.01144e11	0.207895	0.103948	+	0.994583i	$0.466853\pi$
$644$	−8.02378e11	−0.183820
$645$	2.24024e12	0.509655
$646$	2.29928e12	0.519453
$647$	3.24029e12	0.726967	0.363484	−	0.931601i	$-0.381587\pi$
$647$	3.24029e12	0.726967	0.363484	+	0.931601i	$0.381587\pi$
$648$	1.08838e12	0.242490
$649$	−1.10409e13	−2.44289
$650$	3.32437e12	0.730464
$651$	−9.83537e11	−0.214623
$652$	1.46165e12	0.316759
$653$	5.40681e11	0.116367	0.0581837	−	0.998306i	$-0.481469\pi$
$653$	5.40681e11	0.116367	0.0581837	+	0.998306i	$0.481469\pi$
$654$	−3.27348e12	−0.699697
$655$	1.89329e12	0.401912
$656$	−3.16070e12	−0.666370
$657$	1.03415e13	2.16542
$658$	−1.51669e13	−3.15414
$659$	1.29075e11	0.0266599	0.0133299	−	0.999911i	$-0.495757\pi$
$659$	1.29075e11	0.0266599	0.0133299	+	0.999911i	$0.495757\pi$
$660$	2.01258e12	0.412862
$661$	−2.20743e12	−0.449760	−0.224880	−	0.974386i	$-0.572199\pi$
$661$	−2.20743e12	−0.449760	−0.224880	+	0.974386i	$0.572199\pi$
$662$	−7.09489e12	−1.43577
$663$	5.73445e12	1.15261
$664$	2.71653e11	0.0542324
$665$	9.57769e11	0.189917
$666$	1.83596e12	0.361600
$667$	1.30018e12	0.254352
$668$	−3.46456e12	−0.673215
$669$	−1.03401e13	−1.99575
$670$	−7.59049e11	−0.145523
$671$	1.01968e13	1.94183
$672$	1.40988e13	2.66698
$673$	8.69580e12	1.63396	0.816980	−	0.576665i	$-0.195646\pi$
$673$	8.69580e12	1.63396	0.816980	+	0.576665i	$0.195646\pi$
$674$	−6.46293e12	−1.20631
$675$	6.51539e12	1.20802
$676$	−1.63171e12	−0.300526
$677$	−3.48801e12	−0.638159	−0.319080	−	0.947728i	$-0.603374\pi$
$677$	−3.48801e12	−0.638159	−0.319080	+	0.947728i	$0.603374\pi$
$678$	−6.89003e12	−1.25224
$679$	6.38073e12	1.15201
$680$	1.01004e12	0.181153
$681$	−1.21062e13	−2.15699
$682$	8.91675e11	0.157825
$683$	−4.34948e12	−0.764794	−0.382397	−	0.923998i	$-0.624901\pi$
$683$	−4.34948e12	−0.764794	−0.382397	+	0.923998i	$0.624901\pi$
$684$	2.07859e12	0.363092
$685$	3.32328e11	0.0576712
$686$	1.06571e13	1.83731
$687$	5.21785e12	0.893689
$688$	−7.90375e12	−1.34488
$689$	6.42948e12	1.08690
$690$	−7.29994e11	−0.122602
$691$	2.36435e12	0.394512	0.197256	−	0.980352i	$-0.436797\pi$
$691$	2.36435e12	0.394512	0.197256	+	0.980352i	$0.436797\pi$
$692$	−4.72832e12	−0.783844
$693$	−3.11601e13	−5.13215
$694$	5.26487e12	0.861529
$695$	2.00704e11	0.0326306
$696$	−7.46069e12	−1.20514
$697$	−3.55405e12	−0.570396
$698$	2.77109e12	0.441877
$699$	1.22025e13	1.93330
$700$	5.10544e12	0.803696
$701$	1.77595e12	0.277779	0.138889	−	0.990308i	$-0.455647\pi$
$701$	1.77595e12	0.277779	0.138889	+	0.990308i	$0.455647\pi$
$702$	6.71540e12	1.04365
$703$	−4.19987e11	−0.0648540
$704$	1.00362e12	0.153990
$705$	−4.69106e12	−0.715187
$706$	8.00748e12	1.21304
$707$	−1.04416e13	−1.57174
$708$	8.29786e12	1.24113
$709$	7.16551e12	1.06497	0.532487	−	0.846438i	$-0.321257\pi$
$709$	7.16551e12	1.06497	0.532487	+	0.846438i	$0.321257\pi$
$710$	−4.17847e12	−0.617099
$711$	−3.62346e12	−0.531754
$712$	4.92084e11	0.0717595
$713$	−1.09953e11	−0.0159332
$714$	2.59050e13	3.73028
$715$	−2.16559e12	−0.309884
$716$	−5.91722e12	−0.841413
$717$	−1.11680e13	−1.57812
$718$	−3.35347e11	−0.0470906
$719$	−3.55726e12	−0.496405	−0.248202	−	0.968708i	$-0.579840\pi$
$719$	−3.55726e12	−0.496405	−0.248202	+	0.968708i	$0.579840\pi$
$720$	4.56876e12	0.633581
$721$	2.38663e13	3.28909
$722$	7.58874e12	1.03933
$723$	2.35991e13	3.21198
$724$	2.02412e12	0.273786
$725$	−8.27286e12	−1.11208
$726$	2.86772e13	3.83108
$727$	−2.01512e12	−0.267544	−0.133772	−	0.991012i	$-0.542709\pi$
$727$	−2.01512e12	−0.267544	−0.133772	+	0.991012i	$0.542709\pi$
$728$	−4.95427e12	−0.653715
$729$	−1.11887e13	−1.46725
$730$	3.24679e12	0.423157
$731$	−8.88739e12	−1.15119
$732$	−7.66344e12	−0.986561
$733$	6.00143e12	0.767869	0.383935	−	0.923360i	$-0.374569\pi$
$733$	6.00143e12	0.767869	0.383935	+	0.923360i	$0.374569\pi$
$734$	1.89871e12	0.241449
$735$	7.04348e12	0.890213
$736$	1.57615e12	0.197992
$737$	−5.64911e12	−0.705304
$738$	−9.45078e12	−1.17277
$739$	1.21840e13	1.50276	0.751381	−	0.659869i	$-0.229388\pi$
$739$	1.21840e13	1.50276	0.751381	+	0.659869i	$0.229388\pi$
$740$	1.95959e11	0.0240227
$741$	−3.48826e12	−0.425037
$742$	2.90447e13	3.51763
$743$	−1.48611e13	−1.78896	−0.894482	−	0.447104i	$-0.852455\pi$
$743$	−1.48611e13	−1.78896	−0.894482	+	0.447104i	$0.852455\pi$
$744$	6.30933e11	0.0754927
$745$	−1.14841e12	−0.136582
$746$	−1.24991e13	−1.47759
$747$	1.38171e12	0.162359
$748$	−7.98420e12	−0.932555
$749$	−3.41827e12	−0.396861
$750$	9.69630e12	1.11900
$751$	−1.17910e13	−1.35260	−0.676302	−	0.736625i	$-0.736418\pi$
$751$	−1.17910e13	−1.35260	−0.676302	+	0.736625i	$0.736418\pi$
$752$	1.65504e13	1.88724
$753$	−5.29897e12	−0.600640
$754$	−8.52682e12	−0.960762
$755$	1.08463e12	0.121485
$756$	1.03133e13	1.14828
$757$	−2.97454e12	−0.329222	−0.164611	−	0.986359i	$-0.552637\pi$
$757$	−2.97454e12	−0.329222	−0.164611	+	0.986359i	$0.552637\pi$
$758$	−1.98707e13	−2.18626
$759$	−5.43288e12	−0.594213
$760$	−6.14403e11	−0.0668024
$761$	−6.17755e12	−0.667707	−0.333853	−	0.942625i	$-0.608349\pi$
$761$	−6.17755e12	−0.667707	−0.333853	+	0.942625i	$0.608349\pi$
$762$	2.09567e13	2.25177
$763$	5.40950e12	0.577826
$764$	3.66709e12	0.389405
$765$	5.13736e12	0.542330
$766$	−1.15084e12	−0.120777
$767$	−8.92873e12	−0.931559
$768$	−1.94049e13	−2.01273
$769$	−8.45487e12	−0.871843	−0.435922	−	0.899985i	$-0.643578\pi$
$769$	−8.45487e12	−0.871843	−0.435922	+	0.899985i	$0.643578\pi$
$770$	−9.78289e12	−1.00290
$771$	−7.01554e12	−0.715017
$772$	2.37634e12	0.240786
$773$	1.61419e13	1.62610	0.813049	−	0.582196i	$-0.197806\pi$
$773$	1.61419e13	1.62610	0.813049	+	0.582196i	$0.197806\pi$
$774$	−2.36330e13	−2.36692
$775$	6.99616e11	0.0696630
$776$	−4.09320e12	−0.405214
$777$	−4.73180e12	−0.465728
$778$	−1.53817e13	−1.50520
$779$	2.16193e12	0.210340
$780$	1.62756e12	0.157439
$781$	−3.10977e13	−2.99088
$782$	2.89600e12	0.276929
$783$	−1.67116e13	−1.58888
$784$	−2.48499e13	−2.34911
$785$	−5.00410e11	−0.0470340
$786$	−3.11499e13	−2.91109
$787$	−1.31712e13	−1.22388	−0.611941	−	0.790903i	$-0.709611\pi$
$787$	−1.31712e13	−1.22388	−0.611941	+	0.790903i	$0.709611\pi$
$788$	6.61806e12	0.611452
$789$	2.22123e13	2.04055
$790$	−1.13761e12	−0.103913
$791$	1.13859e13	1.03413
$792$	1.99890e13	1.80521
$793$	8.24608e12	0.740488
$794$	−8.99860e11	−0.0803494
$795$	8.98339e12	0.797606
$796$	5.90828e11	0.0521617
$797$	3.98086e12	0.349474	0.174737	−	0.984615i	$-0.444093\pi$
$797$	3.98086e12	0.349474	0.174737	+	0.984615i	$0.444093\pi$
$798$	−1.57580e13	−1.37558
$799$	1.86101e13	1.61543
$800$	−1.00289e13	−0.865658
$801$	2.50289e12	0.214831
$802$	2.31193e13	1.97328
$803$	2.41638e13	2.05090
$804$	4.24562e12	0.358335
$805$	1.20633e12	0.101248
$806$	7.21092e11	0.0601843
$807$	1.97719e13	1.64103
$808$	6.69822e12	0.552852
$809$	1.85829e13	1.52526	0.762630	−	0.646835i	$-0.223908\pi$
$809$	1.85829e13	1.52526	0.762630	+	0.646835i	$0.223908\pi$
$810$	1.73801e12	0.141864
$811$	7.85082e12	0.637267	0.318634	−	0.947878i	$-0.396776\pi$
$811$	7.85082e12	0.637267	0.318634	+	0.947878i	$0.396776\pi$
$812$	−1.30952e13	−1.05708
$813$	1.14539e13	0.919484
$814$	4.28985e12	0.342478
$815$	−2.19751e12	−0.174471
$816$	−2.82679e13	−2.23197
$817$	5.40619e12	0.424514
$818$	−2.51693e13	−1.96554
$819$	−2.51990e13	−1.95707
$820$	−1.00872e12	−0.0779125
$821$	−6.65240e12	−0.511015	−0.255508	−	0.966807i	$-0.582243\pi$
$821$	−6.65240e12	−0.511015	−0.255508	+	0.966807i	$0.582243\pi$
$822$	−5.46771e12	−0.417717
$823$	4.48999e12	0.341151	0.170575	−	0.985345i	$-0.445437\pi$
$823$	4.48999e12	0.341151	0.170575	+	0.985345i	$0.445437\pi$
$824$	−1.53101e13	−1.15692
$825$	3.45688e13	2.59801
$826$	−4.03349e13	−3.01489
$827$	3.32440e12	0.247137	0.123569	−	0.992336i	$-0.460566\pi$
$827$	3.32440e12	0.247137	0.123569	+	0.992336i	$0.460566\pi$
$828$	2.61803e12	0.193570
$829$	2.69063e13	1.97860	0.989300	−	0.145896i	$-0.0466065\pi$
$829$	2.69063e13	1.97860	0.989300	+	0.145896i	$0.0466065\pi$
$830$	4.33797e11	0.0317275
$831$	2.74639e13	1.99783
$832$	8.11623e11	0.0587218
$833$	−2.79425e13	−2.01078
$834$	−3.30214e12	−0.236346
$835$	5.20878e12	0.370806
$836$	4.85678e12	0.343890
$837$	1.41326e12	0.0995310
$838$	2.91195e13	2.03979
$839$	−1.77934e13	−1.23974	−0.619870	−	0.784704i	$-0.712815\pi$
$839$	−1.77934e13	−1.23974	−0.619870	+	0.784704i	$0.712815\pi$
$840$	−6.92220e12	−0.479719
$841$	6.71229e12	0.462688
$842$	2.33533e13	1.60120
$843$	−1.53547e13	−1.04717
$844$	1.89564e12	0.128592
$845$	2.45319e12	0.165529
$846$	4.94873e13	3.32144
$847$	−4.73897e13	−3.16380
$848$	−3.16941e13	−2.10473
$849$	2.75626e12	0.182068
$850$	−1.84269e13	−1.21078
$851$	−5.28983e11	−0.0345747
$852$	2.33716e13	1.51954
$853$	1.88591e13	1.21969	0.609847	−	0.792520i	$-0.291231\pi$
$853$	1.88591e13	1.21969	0.609847	+	0.792520i	$0.291231\pi$
$854$	3.72511e13	2.39650
$855$	−3.12505e12	−0.199990
$856$	2.19280e12	0.139594
$857$	−2.12797e12	−0.134757	−0.0673784	−	0.997727i	$-0.521463\pi$
$857$	−2.12797e12	−0.134757	−0.0673784	+	0.997727i	$0.521463\pi$
$858$	3.56299e13	2.24451
$859$	5.08343e12	0.318557	0.159279	−	0.987234i	$-0.449083\pi$
$859$	5.08343e12	0.318557	0.159279	+	0.987234i	$0.449083\pi$
$860$	−2.52243e12	−0.157245
$861$	2.43574e13	1.51049
$862$	−1.10475e13	−0.681524
$863$	−3.02368e12	−0.185561	−0.0927805	−	0.995687i	$-0.529575\pi$
$863$	−3.02368e12	−0.185561	−0.0927805	+	0.995687i	$0.529575\pi$
$864$	−2.02588e13	−1.23681
$865$	7.10878e12	0.431740
$866$	−1.57285e13	−0.950294
$867$	−4.01115e12	−0.241092
$868$	1.10743e12	0.0662180
$869$	−8.46649e12	−0.503633
$870$	−1.19138e13	−0.705041
$871$	−4.56841e12	−0.268957
$872$	−3.47016e12	−0.203248
$873$	−2.08193e13	−1.21311
$874$	−1.76163e12	−0.102121
$875$	−1.60234e13	−0.924096
$876$	−1.81604e13	−1.04198
$877$	1.33550e13	0.762337	0.381168	−	0.924506i	$-0.375522\pi$
$877$	1.33550e13	0.762337	0.381168	+	0.924506i	$0.375522\pi$
$878$	−9.15120e12	−0.519700
$879$	−4.69752e12	−0.265411
$880$	1.06753e13	0.600076
$881$	1.30554e13	0.730128	0.365064	−	0.930982i	$-0.381047\pi$
$881$	1.30554e13	0.730128	0.365064	+	0.930982i	$0.381047\pi$
$882$	−7.43036e13	−4.13429
$883$	−6.91014e12	−0.382529	−0.191264	−	0.981539i	$-0.561259\pi$
$883$	−6.91014e12	−0.382529	−0.191264	+	0.981539i	$0.561259\pi$
$884$	−6.45678e12	−0.355616
$885$	−1.24754e13	−0.683611
$886$	1.90166e13	1.03677
$887$	2.95901e13	1.60506	0.802529	−	0.596613i	$-0.203487\pi$
$887$	2.95901e13	1.60506	0.802529	+	0.596613i	$0.203487\pi$
$888$	3.03542e12	0.163818
$889$	−3.46314e13	−1.85957
$890$	7.85799e11	0.0419813
$891$	1.29349e13	0.687566
$892$	1.16425e13	0.615751
$893$	−1.13205e13	−0.595710
$894$	1.88946e13	0.989277
$895$	8.89622e12	0.463449
$896$	3.44871e13	1.78760
$897$	−4.39354e12	−0.226594
$898$	−5.06878e12	−0.260112
$899$	−1.79448e12	−0.0916261
$900$	−1.66582e13	−0.846325
$901$	−3.56385e13	−1.80160
$902$	−2.20824e13	−1.11075
$903$	6.09090e13	3.04851
$904$	−7.30400e12	−0.363750
$905$	−3.04315e12	−0.150801
$906$	−1.78452e13	−0.879923
$907$	1.02383e13	0.502335	0.251167	−	0.967944i	$-0.419186\pi$
$907$	1.02383e13	0.502335	0.251167	+	0.967944i	$0.419186\pi$
$908$	1.36312e13	0.665499
$909$	3.40693e13	1.65510
$910$	−7.91137e12	−0.382442
$911$	−1.19353e13	−0.574116	−0.287058	−	0.957913i	$-0.592677\pi$
$911$	−1.19353e13	−0.574116	−0.287058	+	0.957913i	$0.592677\pi$
$912$	1.71953e13	0.823065
$913$	3.22848e12	0.153773
$914$	3.54866e13	1.68192
$915$	1.15216e13	0.543396
$916$	−5.87511e12	−0.275731
$917$	5.14759e13	2.40404
$918$	−3.72233e13	−1.72991
$919$	−1.63702e13	−0.757067	−0.378534	−	0.925588i	$-0.623572\pi$
$919$	−1.63702e13	−0.757067	−0.378534	+	0.925588i	$0.623572\pi$
$920$	−7.73855e11	−0.0356135
$921$	2.91797e13	1.33633
$922$	−9.91195e12	−0.451721
$923$	−2.51485e13	−1.14053
$924$	5.47191e13	2.46953
$925$	3.36586e12	0.151167
$926$	4.23803e13	1.89415
$927$	−7.78719e13	−3.46355
$928$	2.57235e13	1.13858
$929$	−1.83004e13	−0.806102	−0.403051	−	0.915178i	$-0.632050\pi$
$929$	−1.83004e13	−0.806102	−0.403051	+	0.915178i	$0.632050\pi$
$930$	1.00752e12	0.0441654
$931$	1.69974e13	0.741497
$932$	−1.37395e13	−0.596486
$933$	−9.38663e12	−0.405548
$934$	1.74835e13	0.751738
$935$	1.20038e13	0.513650
$936$	1.61650e13	0.688389
$937$	−4.32736e12	−0.183398	−0.0916991	−	0.995787i	$-0.529230\pi$
$937$	−4.32736e12	−0.183398	−0.0916991	+	0.995787i	$0.529230\pi$
$938$	−2.06375e13	−0.870449
$939$	7.42470e13	3.11662
$940$	5.28196e12	0.220658
$941$	−3.39124e13	−1.40995	−0.704977	−	0.709230i	$-0.749043\pi$
$941$	−3.39124e13	−1.40995	−0.704977	+	0.709230i	$0.749043\pi$
$942$	8.23313e12	0.340671
$943$	2.72300e12	0.112136
$944$	4.40141e13	1.80392
$945$	−1.55054e13	−0.632471
$946$	−5.52201e13	−2.24175
$947$	2.14988e13	0.868639	0.434320	−	0.900759i	$-0.356989\pi$
$947$	2.14988e13	0.868639	0.434320	+	0.900759i	$0.356989\pi$
$948$	6.36304e12	0.255874
$949$	1.95411e13	0.782080
$950$	1.12091e13	0.446491
$951$	−3.92369e12	−0.155554
$952$	2.74614e13	1.08357
$953$	2.68404e11	0.0105407	0.00527036	−	0.999986i	$-0.498322\pi$
$953$	2.68404e11	0.0105407	0.00527036	+	0.999986i	$0.498322\pi$
$954$	−9.47683e13	−3.70421
$955$	−5.51327e12	−0.214484
$956$	1.25748e13	0.486900
$957$	−8.86670e13	−3.41710
$958$	5.73188e13	2.19863
$959$	9.03552e12	0.344960
$960$	1.13401e12	0.0430922
$961$	−2.62879e13	−0.994260
$962$	3.46918e12	0.130599
$963$	1.11533e13	0.417911
$964$	−2.65717e13	−0.990996
$965$	−3.57270e12	−0.132625
$966$	−1.98475e13	−0.733346
$967$	2.06519e13	0.759521	0.379761	−	0.925085i	$-0.376006\pi$
$967$	2.06519e13	0.759521	0.379761	+	0.925085i	$0.376006\pi$
$968$	3.04002e13	1.11285
$969$	1.93353e13	0.704523
$970$	−6.53634e12	−0.237062
$971$	1.06750e13	0.385375	0.192687	−	0.981260i	$-0.438280\pi$
$971$	1.06750e13	0.385375	0.192687	+	0.981260i	$0.438280\pi$
$972$	9.10988e12	0.327352
$973$	5.45687e12	0.195180
$974$	2.45506e13	0.874070
$975$	2.79556e13	0.990712
$976$	−4.06490e13	−1.43392
$977$	−5.33729e13	−1.87411	−0.937055	−	0.349182i	$-0.886459\pi$
$977$	−5.33729e13	−1.87411	−0.937055	+	0.349182i	$0.886459\pi$
$978$	3.61552e13	1.26370
$979$	5.84820e12	0.203470
$980$	−7.93069e12	−0.274659
$981$	−1.76503e13	−0.608474
$982$	3.46530e13	1.18916
$983$	−1.57157e13	−0.536839	−0.268419	−	0.963302i	$-0.586501\pi$
$983$	−1.57157e13	−0.536839	−0.268419	+	0.963302i	$0.586501\pi$
$984$	−1.56251e13	−0.531308
$985$	−9.94989e12	−0.336787
$986$	4.72640e13	1.59252
$987$	−1.27543e14	−4.27789
$988$	3.92765e12	0.131137
$989$	6.80922e12	0.226315
$990$	3.19200e13	1.05610
$991$	2.52142e13	0.830449	0.415225	−	0.909719i	$-0.363703\pi$
$991$	2.52142e13	0.830449	0.415225	+	0.909719i	$0.363703\pi$
$992$	−2.17537e12	−0.0713232
$993$	−5.96630e13	−1.94730
$994$	−1.13607e14	−3.69118
$995$	−8.88278e11	−0.0287306
$996$	−2.42638e12	−0.0781253
$997$	−3.95466e13	−1.26760	−0.633798	−	0.773499i	$-0.718505\pi$
$997$	−3.95466e13	−1.26760	−0.633798	+	0.773499i	$0.718505\pi$
$998$	−6.33795e12	−0.202237
$999$	6.79922e12	0.215980

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.a.a.1.3	✓	13
3.2	odd	2		333.10.a.c.1.11		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.a.a.1.3	✓	13	1.1	even	1	trivial
333.10.a.c.1.11		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)

\(f(q)\)	\(=\)	\(q-27.8517 q^{2} -234.213 q^{3} +263.715 q^{4} -396.481 q^{5} +6523.22 q^{6} -10779.8 q^{7} +6915.15 q^{8} +35172.6 q^{9} +O(q^{10})\)	\(q-27.8517 q^{2} -234.213 q^{3} +263.715 q^{4} -396.481 q^{5} +6523.22 q^{6} -10779.8 q^{7} +6915.15 q^{8} +35172.6 q^{9} +11042.7 q^{10} +82183.5 q^{11} -61765.4 q^{12} +66461.3 q^{13} +300234. q^{14} +92861.0 q^{15} -327620. q^{16} -368394. q^{17} -979616. q^{18} +224093. q^{19} -104558. q^{20} +2.52476e6 q^{21} -2.28895e6 q^{22} +282251. q^{23} -1.61962e6 q^{24} -1.79593e6 q^{25} -1.85106e6 q^{26} -3.62787e6 q^{27} -2.84278e6 q^{28} +4.60646e6 q^{29} -2.58633e6 q^{30} -389557. q^{31} +5.58422e6 q^{32} -1.92484e7 q^{33} +1.02604e7 q^{34} +4.27397e6 q^{35} +9.27555e6 q^{36} -1.87416e6 q^{37} -6.24137e6 q^{38} -1.55661e7 q^{39} -2.74173e6 q^{40} +9.64743e6 q^{41} -7.03187e7 q^{42} +2.41247e7 q^{43} +2.16730e7 q^{44} -1.39453e7 q^{45} -7.86115e6 q^{46} -5.05170e7 q^{47} +7.67329e7 q^{48} +7.58497e7 q^{49} +5.00196e7 q^{50} +8.62825e7 q^{51} +1.75268e7 q^{52} +9.67402e7 q^{53} +1.01042e8 q^{54} -3.25842e7 q^{55} -7.45437e7 q^{56} -5.24855e7 q^{57} -1.28297e8 q^{58} -1.34345e8 q^{59} +2.44888e7 q^{60} +1.24073e8 q^{61} +1.08498e7 q^{62} -3.79153e8 q^{63} +1.22120e7 q^{64} -2.63507e7 q^{65} +5.36100e8 q^{66} -6.87378e7 q^{67} -9.71510e7 q^{68} -6.61067e7 q^{69} -1.19037e8 q^{70} -3.78394e8 q^{71} +2.43224e8 q^{72} +2.94022e8 q^{73} +5.21985e7 q^{74} +4.20629e8 q^{75} +5.90968e7 q^{76} -8.85918e8 q^{77} +4.33541e8 q^{78} -1.03019e8 q^{79} +1.29895e8 q^{80} +1.57391e8 q^{81} -2.68697e8 q^{82} +3.92838e7 q^{83} +6.65817e8 q^{84} +1.46061e8 q^{85} -6.71913e8 q^{86} -1.07889e9 q^{87} +5.68311e8 q^{88} +7.11603e7 q^{89} +3.88400e8 q^{90} -7.16437e8 q^{91} +7.44338e7 q^{92} +9.12392e7 q^{93} +1.40698e9 q^{94} -8.88488e7 q^{95} -1.30790e9 q^{96} -5.91917e8 q^{97} -2.11254e9 q^{98} +2.89061e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 32 q^{2} - 251 q^{3} + 2730 q^{4} - 2159 q^{5} - 4401 q^{6} - 12576 q^{7} - 20394 q^{8} + 69112 q^{9}+O(q^{10}) \) 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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