LMFDB - Embedded newform 37.8.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,8,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, 8, names="a")

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

chi := DirichletCharacter("37.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 8 $
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:	$11.5582459429$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4 x^{9} - 905 x^{8} + 4018 x^{7} + 291290 x^{6} - 1367036 x^{5} - 39566544 x^{4} + \cdots - 45399525376 $ x^10 - 4x^9 - 905x^8 + 4018x^7 + 291290x^6 - 1367036x^5 - 39566544x^4 + 175732512x^3 + 2143908736x^2 - 5929608704*x - 45399525376
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-5.27803$ 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)

$f(q)$	$=$	$q+3.27803 q^{2} -7.54665 q^{3} -117.254 q^{4} +243.887 q^{5} -24.7382 q^{6} +767.318 q^{7} -803.953 q^{8} -2130.05 q^{9} +O(q^{10})$	\(q+3.27803 q^{2} -7.54665 q^{3} -117.254 q^{4} +243.887 q^{5} -24.7382 q^{6} +767.318 q^{7} -803.953 q^{8} -2130.05 q^{9} +799.468 q^{10} -4752.74 q^{11} +884.879 q^{12} -14193.7 q^{13} +2515.30 q^{14} -1840.53 q^{15} +12373.2 q^{16} -7120.26 q^{17} -6982.37 q^{18} -6703.23 q^{19} -28596.8 q^{20} -5790.68 q^{21} -15579.6 q^{22} -2021.32 q^{23} +6067.15 q^{24} -18644.3 q^{25} -46527.5 q^{26} +32579.2 q^{27} -89971.5 q^{28} -82009.8 q^{29} -6033.31 q^{30} +53175.0 q^{31} +143466. q^{32} +35867.2 q^{33} -23340.5 q^{34} +187139. q^{35} +249758. q^{36} +50653.0 q^{37} -21973.4 q^{38} +107115. q^{39} -196073. q^{40} +395755. q^{41} -18982.1 q^{42} -627353. q^{43} +557280. q^{44} -519490. q^{45} -6625.95 q^{46} +1.03473e6 q^{47} -93376.1 q^{48} -234766. q^{49} -61116.8 q^{50} +53734.1 q^{51} +1.66428e6 q^{52} +1.68094e6 q^{53} +106796. q^{54} -1.15913e6 q^{55} -616887. q^{56} +50586.9 q^{57} -268831. q^{58} -2.56307e6 q^{59} +215810. q^{60} -1.25591e6 q^{61} +174309. q^{62} -1.63442e6 q^{63} -1.11348e6 q^{64} -3.46166e6 q^{65} +117574. q^{66} +1.77215e6 q^{67} +834883. q^{68} +15254.2 q^{69} +613447. q^{70} -3.84691e6 q^{71} +1.71246e6 q^{72} +834660. q^{73} +166042. q^{74} +140702. q^{75} +785984. q^{76} -3.64686e6 q^{77} +351127. q^{78} +436630. q^{79} +3.01766e6 q^{80} +4.41255e6 q^{81} +1.29730e6 q^{82} -2.27115e6 q^{83} +678983. q^{84} -1.73654e6 q^{85} -2.05648e6 q^{86} +618900. q^{87} +3.82098e6 q^{88} +7.02798e6 q^{89} -1.70291e6 q^{90} -1.08911e7 q^{91} +237009. q^{92} -401293. q^{93} +3.39189e6 q^{94} -1.63483e6 q^{95} -1.08269e6 q^{96} +1.50347e7 q^{97} -769570. q^{98} +1.01236e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 24 q^{2} - 95 q^{3} + 602 q^{4} - 624 q^{5} - 777 q^{6} - 501 q^{7} - 3810 q^{8} + 6181 q^{9}+O(q^{10}) $ 10 * q - 24 * q^2 - 95 * q^3 + 602 * q^4 - 624 * q^5 - 777 * q^6 - 501 * q^7 - 3810 * q^8 + 6181 * q^9	\( 10 q - 24 q^{2} - 95 q^{3} + 602 q^{4} - 624 q^{5} - 777 q^{6} - 501 q^{7} - 3810 q^{8} + 6181 q^{9} + 8595 q^{10} - 8325 q^{11} - 19645 q^{12} - 17108 q^{13} - 65418 q^{14} - 55756 q^{15} - 56998 q^{16} - 72924 q^{17} - 156165 q^{18} - 47786 q^{19} - 226209 q^{20} - 65313 q^{21} - 138973 q^{22} - 148086 q^{23} - 68031 q^{24} + 108736 q^{25} - 60237 q^{26} - 87329 q^{27} + 219974 q^{28} - 164154 q^{29} + 78864 q^{30} - 189560 q^{31} - 30114 q^{32} - 179737 q^{33} + 532624 q^{34} - 705156 q^{35} + 1923693 q^{36} + 506530 q^{37} + 1256412 q^{38} + 1322800 q^{39} + 2936777 q^{40} + 814263 q^{41} + 3415826 q^{42} - 590572 q^{43} + 610311 q^{44} - 250574 q^{45} + 2903897 q^{46} - 1534185 q^{47} + 2082419 q^{48} - 214337 q^{49} - 2313525 q^{50} + 722138 q^{51} + 149159 q^{52} - 2518209 q^{53} + 1095990 q^{54} - 3482468 q^{55} - 3645834 q^{56} - 9225638 q^{57} + 5626023 q^{58} - 5894748 q^{59} - 1289832 q^{60} - 2569480 q^{61} - 863697 q^{62} - 2836574 q^{63} - 4093742 q^{64} - 6774600 q^{65} + 17251556 q^{66} - 6983232 q^{67} - 8114412 q^{68} - 11557564 q^{69} + 8982748 q^{70} - 5013963 q^{71} - 7567137 q^{72} - 11678449 q^{73} - 1215672 q^{74} - 6586901 q^{75} + 4912252 q^{76} + 1333113 q^{77} - 7352119 q^{78} - 3853378 q^{79} - 11975661 q^{80} - 7381718 q^{81} + 564093 q^{82} - 15677895 q^{83} + 4781738 q^{84} + 11909320 q^{85} + 34274010 q^{86} - 12611710 q^{87} + 14448317 q^{88} - 25836 q^{89} + 64591590 q^{90} + 12335744 q^{91} + 7579845 q^{92} + 4592632 q^{93} + 26251718 q^{94} + 11723664 q^{95} + 42299113 q^{96} + 4648834 q^{97} + 15230184 q^{98} - 16904018 q^{99}+O(q^{100}) \) 10 * q - 24 * q^2 - 95 * q^3 + 602 * q^4 - 624 * q^5 - 777 * q^6 - 501 * q^7 - 3810 * q^8 + 6181 * q^9 + 8595 * q^10 - 8325 * q^11 - 19645 * q^12 - 17108 * q^13 - 65418 * q^14 - 55756 * q^15 - 56998 * q^16 - 72924 * q^17 - 156165 * q^18 - 47786 * q^19 - 226209 * q^20 - 65313 * q^21 - 138973 * q^22 - 148086 * q^23 - 68031 * q^24 + 108736 * q^25 - 60237 * q^26 - 87329 * q^27 + 219974 * q^28 - 164154 * q^29 + 78864 * q^30 - 189560 * q^31 - 30114 * q^32 - 179737 * q^33 + 532624 * q^34 - 705156 * q^35 + 1923693 * q^36 + 506530 * q^37 + 1256412 * q^38 + 1322800 * q^39 + 2936777 * q^40 + 814263 * q^41 + 3415826 * q^42 - 590572 * q^43 + 610311 * q^44 - 250574 * q^45 + 2903897 * q^46 - 1534185 * q^47 + 2082419 * q^48 - 214337 * q^49 - 2313525 * q^50 + 722138 * q^51 + 149159 * q^52 - 2518209 * q^53 + 1095990 * q^54 - 3482468 * q^55 - 3645834 * q^56 - 9225638 * q^57 + 5626023 * q^58 - 5894748 * q^59 - 1289832 * q^60 - 2569480 * q^61 - 863697 * q^62 - 2836574 * q^63 - 4093742 * q^64 - 6774600 * q^65 + 17251556 * q^66 - 6983232 * q^67 - 8114412 * q^68 - 11557564 * q^69 + 8982748 * q^70 - 5013963 * q^71 - 7567137 * q^72 - 11678449 * q^73 - 1215672 * q^74 - 6586901 * q^75 + 4912252 * q^76 + 1333113 * q^77 - 7352119 * q^78 - 3853378 * q^79 - 11975661 * q^80 - 7381718 * q^81 + 564093 * q^82 - 15677895 * q^83 + 4781738 * q^84 + 11909320 * q^85 + 34274010 * q^86 - 12611710 * q^87 + 14448317 * q^88 - 25836 * q^89 + 64591590 * q^90 + 12335744 * q^91 + 7579845 * q^92 + 4592632 * q^93 + 26251718 * q^94 + 11723664 * q^95 + 42299113 * q^96 + 4648834 * q^97 + 15230184 * q^98 - 16904018 * 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 $

$2$	3.27803	0.289740	0.144870	−	0.989451i	$-0.453724\pi$
$2$	3.27803	0.289740	0.144870	+	0.989451i	$0.453724\pi$
$3$	−7.54665	−0.161373	−0.0806863	−	0.996740i	$-0.525711\pi$
$3$	−7.54665	−0.161373	−0.0806863	+	0.996740i	$0.525711\pi$
$4$	−117.254	−0.916051
$5$	243.887	0.872555	0.436278	−	0.899812i	$-0.356297\pi$
$5$	243.887	0.872555	0.436278	+	0.899812i	$0.356297\pi$
$6$	−24.7382	−0.0467561
$7$	767.318	0.845537	0.422768	−	0.906238i	$-0.361058\pi$
$7$	767.318	0.845537	0.422768	+	0.906238i	$0.361058\pi$
$8$	−803.953	−0.555157
$9$	−2130.05	−0.973959
$10$	799.468	0.252814
$11$	−4752.74	−1.07664	−0.538319	−	0.842741i	$-0.680940\pi$
$11$	−4752.74	−1.07664	−0.538319	+	0.842741i	$0.680940\pi$
$12$	884.879	0.147825
$13$	−14193.7	−1.79182	−0.895911	−	0.444234i	$-0.853476\pi$
$13$	−14193.7	−1.79182	−0.895911	+	0.444234i	$0.853476\pi$
$14$	2515.30	0.244986
$15$	−1840.53	−0.140806
$16$	12373.2	0.755200
$17$	−7120.26	−0.351500	−0.175750	−	0.984435i	$-0.556235\pi$
$17$	−7120.26	−0.351500	−0.175750	+	0.984435i	$0.556235\pi$
$18$	−6982.37	−0.282195
$19$	−6703.23	−0.224206	−0.112103	−	0.993697i	$-0.535759\pi$
$19$	−6703.23	−0.224206	−0.112103	+	0.993697i	$0.535759\pi$
$20$	−28596.8	−0.799305
$21$	−5790.68	−0.136446
$22$	−15579.6	−0.311945
$23$	−2021.32	−0.0346408	−0.0173204	−	0.999850i	$-0.505514\pi$
$23$	−2021.32	−0.0346408	−0.0173204	+	0.999850i	$0.505514\pi$
$24$	6067.15	0.0895870
$25$	−18644.3	−0.238648
$26$	−46527.5	−0.519163
$27$	32579.2	0.318543
$28$	−89971.5	−0.774554
$29$	−82009.8	−0.624415	−0.312207	−	0.950014i	$-0.601068\pi$
$29$	−82009.8	−0.624415	−0.312207	+	0.950014i	$0.601068\pi$
$30$	−6033.31	−0.0407973
$31$	53175.0	0.320584	0.160292	−	0.987070i	$-0.448756\pi$
$31$	53175.0	0.320584	0.160292	+	0.987070i	$0.448756\pi$
$32$	143466.	0.773968
$33$	35867.2	0.173740
$34$	−23340.5	−0.101843
$35$	187139.	0.737777
$36$	249758.	0.892196
$37$	50653.0	0.164399
$37$	50653.0	0.164399
$38$	−21973.4	−0.0649614
$39$	107115.	0.289151
$40$	−196073.	−0.484405
$41$	395755.	0.896775	0.448387	−	0.893839i	$-0.351999\pi$
$41$	395755.	0.896775	0.448387	+	0.893839i	$0.351999\pi$
$42$	−18982.1	−0.0395340
$43$	−627353.	−1.20329	−0.601647	−	0.798762i	$-0.705489\pi$
$43$	−627353.	−1.20329	−0.601647	+	0.798762i	$0.705489\pi$
$44$	557280.	0.986254
$45$	−519490.	−0.849833
$46$	−6625.95	−0.0100368
$47$	1.03473e6	1.45374	0.726869	−	0.686776i	$-0.240975\pi$
$47$	1.03473e6	1.45374	0.726869	+	0.686776i	$0.240975\pi$
$48$	−93376.1	−0.121869
$49$	−234766.	−0.285068
$50$	−61116.8	−0.0691457
$51$	53734.1	0.0567224
$52$	1.66428e6	1.64140
$53$	1.68094e6	1.55091	0.775456	−	0.631402i	$-0.217520\pi$
$53$	1.68094e6	1.55091	0.775456	+	0.631402i	$0.217520\pi$
$54$	106796.	0.0922946
$55$	−1.15913e6	−0.939425
$56$	−616887.	−0.469405
$57$	50586.9	0.0361807
$58$	−268831.	−0.180918
$59$	−2.56307e6	−1.62472	−0.812361	−	0.583155i	$-0.801818\pi$
$59$	−2.56307e6	−1.62472	−0.812361	+	0.583155i	$0.801818\pi$
$60$	215810.	0.128986
$61$	−1.25591e6	−0.708441	−0.354220	−	0.935162i	$-0.615254\pi$
$61$	−1.25591e6	−0.708441	−0.354220	+	0.935162i	$0.615254\pi$
$62$	174309.	0.0928860
$63$	−1.63442e6	−0.823518
$64$	−1.11348e6	−0.530950
$65$	−3.46166e6	−1.56346
$66$	117574.	0.0503394
$67$	1.77215e6	0.719843	0.359921	−	0.932983i	$-0.382803\pi$
$67$	1.77215e6	0.719843	0.359921	+	0.932983i	$0.382803\pi$
$68$	834883.	0.321991
$69$	15254.2	0.00559007
$70$	613447.	0.213764
$71$	−3.84691e6	−1.27558	−0.637790	−	0.770211i	$-0.720151\pi$
$71$	−3.84691e6	−1.27558	−0.637790	+	0.770211i	$0.720151\pi$
$72$	1.71246e6	0.540700
$73$	834660.	0.251119	0.125559	−	0.992086i	$-0.459927\pi$
$73$	834660.	0.251119	0.125559	+	0.992086i	$0.459927\pi$
$74$	166042.	0.0476330
$75$	140702.	0.0385112
$76$	785984.	0.205384
$77$	−3.64686e6	−0.910336
$78$	351127.	0.0837786
$79$	436630.	0.0996366	0.0498183	−	0.998758i	$-0.484136\pi$
$79$	436630.	0.0996366	0.0498183	+	0.998758i	$0.484136\pi$
$80$	3.01766e6	0.658953
$81$	4.41255e6	0.922555
$82$	1.29730e6	0.259831
$83$	−2.27115e6	−0.435986	−0.217993	−	0.975950i	$-0.569951\pi$
$83$	−2.27115e6	−0.435986	−0.217993	+	0.975950i	$0.569951\pi$
$84$	678983.	0.124992
$85$	−1.73654e6	−0.306703
$86$	−2.05648e6	−0.348643
$87$	618900.	0.100763
$88$	3.82098e6	0.597702
$89$	7.02798e6	1.05673	0.528367	−	0.849016i	$-0.322805\pi$
$89$	7.02798e6	1.05673	0.528367	+	0.849016i	$0.322805\pi$
$90$	−1.70291e6	−0.246231
$91$	−1.08911e7	−1.51505
$92$	237009.	0.0317327
$93$	−401293.	−0.0517334
$94$	3.39189e6	0.421206
$95$	−1.63483e6	−0.195632
$96$	−1.08269e6	−0.124897
$97$	1.50347e7	1.67261	0.836305	−	0.548265i	$-0.184711\pi$
$97$	1.50347e7	1.67261	0.836305	+	0.548265i	$0.184711\pi$
$98$	−769570.	−0.0825956
$99$	1.01236e7	1.04860
$100$	2.18613e6	0.218613
$101$	−1.59536e6	−0.154075	−0.0770377	−	0.997028i	$-0.524546\pi$
$101$	−1.59536e6	−0.154075	−0.0770377	+	0.997028i	$0.524546\pi$
$102$	176142.	0.0164347
$103$	1.03708e7	0.935153	0.467577	−	0.883953i	$-0.345127\pi$
$103$	1.03708e7	0.935153	0.467577	+	0.883953i	$0.345127\pi$
$104$	1.14111e7	0.994742
$105$	−1.41227e6	−0.119057
$106$	5.51018e6	0.449361
$107$	−1.57376e7	−1.24192	−0.620961	−	0.783841i	$-0.713257\pi$
$107$	−1.57376e7	−1.24192	−0.620961	+	0.783841i	$0.713257\pi$
$108$	−3.82006e6	−0.291801
$109$	−1.91796e7	−1.41855	−0.709277	−	0.704930i	$-0.750979\pi$
$109$	−1.91796e7	−1.41855	−0.709277	+	0.704930i	$0.750979\pi$
$110$	−3.79966e6	−0.272189
$111$	−382260.	−0.0265295
$112$	9.49418e6	0.638549
$113$	−1.35094e7	−0.880768	−0.440384	−	0.897810i	$-0.645158\pi$
$113$	−1.35094e7	−0.880768	−0.440384	+	0.897810i	$0.645158\pi$
$114$	165826.	0.0104830
$115$	−492973.	−0.0302260
$116$	9.61602e6	0.571995
$117$	3.02333e7	1.74516
$118$	−8.40184e6	−0.470747
$119$	−5.46351e6	−0.297206
$120$	1.47970e6	0.0781696
$121$	3.10134e6	0.159148
$122$	−4.11691e6	−0.205264
$123$	−2.98663e6	−0.144715
$124$	−6.23501e6	−0.293671
$125$	−2.36007e7	−1.08079
$126$	−5.35770e6	−0.238606
$127$	−3.50334e7	−1.51764	−0.758822	−	0.651298i	$-0.774225\pi$
$127$	−3.50334e7	−1.51764	−0.758822	+	0.651298i	$0.774225\pi$
$128$	−2.20136e7	−0.927806
$129$	4.73441e6	0.194179
$130$	−1.13474e7	−0.452998
$131$	8.67115e6	0.336998	0.168499	−	0.985702i	$-0.446108\pi$
$131$	8.67115e6	0.336998	0.168499	+	0.985702i	$0.446108\pi$
$132$	−4.20560e6	−0.159154
$133$	−5.14351e6	−0.189574
$134$	5.80916e6	0.208567
$135$	7.94564e6	0.277946
$136$	5.72435e6	0.195137
$137$	7.13655e6	0.237119	0.118559	−	0.992947i	$-0.462172\pi$
$137$	7.13655e6	0.237119	0.118559	+	0.992947i	$0.462172\pi$
$138$	50003.8	0.00161967
$139$	5.57389e7	1.76038	0.880190	−	0.474622i	$-0.157415\pi$
$139$	5.57389e7	1.76038	0.880190	+	0.474622i	$0.157415\pi$
$140$	−2.19428e7	−0.675841
$141$	−7.80878e6	−0.234594
$142$	−1.26103e7	−0.369586
$143$	6.74591e7	1.92914
$144$	−2.63555e7	−0.735533
$145$	−2.00011e7	−0.544836
$146$	2.73604e6	0.0727592
$147$	1.77169e6	0.0460021
$148$	−5.93929e6	−0.150598
$149$	−5.00368e7	−1.23919	−0.619595	−	0.784922i	$-0.712703\pi$
$149$	−5.00368e7	−1.23919	−0.619595	+	0.784922i	$0.712703\pi$
$150$	461227.	0.0111582
$151$	−3.84432e7	−0.908658	−0.454329	−	0.890834i	$-0.650121\pi$
$151$	−3.84432e7	−0.908658	−0.454329	+	0.890834i	$0.650121\pi$
$152$	5.38908e6	0.124469
$153$	1.51665e7	0.342346
$154$	−1.19545e7	−0.263761
$155$	1.29687e7	0.279727
$156$	−1.25597e7	−0.264877
$157$	5.87230e7	1.21104	0.605521	−	0.795829i	$-0.292965\pi$
$157$	5.87230e7	1.21104	0.605521	+	0.795829i	$0.292965\pi$
$158$	1.43129e6	0.0288687
$159$	−1.26855e7	−0.250275
$160$	3.49893e7	0.675330
$161$	−1.55100e6	−0.0292900
$162$	1.44645e7	0.267301
$163$	3.76157e7	0.680319	0.340159	−	0.940368i	$-0.389519\pi$
$163$	3.76157e7	0.680319	0.340159	+	0.940368i	$0.389519\pi$
$164$	−4.64041e7	−0.821491
$165$	8.74754e6	0.151597
$166$	−7.44491e6	−0.126323
$167$	−4.33600e7	−0.720413	−0.360207	−	0.932873i	$-0.617294\pi$
$167$	−4.33600e7	−0.720413	−0.360207	+	0.932873i	$0.617294\pi$
$168$	4.65543e6	0.0757491
$169$	1.38714e8	2.21063
$170$	−5.69243e6	−0.0888641
$171$	1.42782e7	0.218367
$172$	7.35599e7	1.10228
$173$	−5.44826e7	−0.800012	−0.400006	−	0.916513i	$-0.630992\pi$
$173$	−5.44826e7	−0.800012	−0.400006	+	0.916513i	$0.630992\pi$
$174$	2.02877e6	0.0291952
$175$	−1.43061e7	−0.201785
$176$	−5.88065e7	−0.813076
$177$	1.93426e7	0.262186
$178$	2.30380e7	0.306178
$179$	4.31678e7	0.562567	0.281283	−	0.959625i	$-0.409240\pi$
$179$	4.31678e7	0.562567	0.281283	+	0.959625i	$0.409240\pi$
$180$	6.09126e7	0.778490
$181$	4.15791e7	0.521195	0.260597	−	0.965448i	$-0.416080\pi$
$181$	4.15791e7	0.521195	0.260597	+	0.965448i	$0.416080\pi$
$182$	−3.57014e7	−0.438971
$183$	9.47790e6	0.114323
$184$	1.62505e6	0.0192311
$185$	1.23536e7	0.143447
$186$	−1.31545e6	−0.0149892
$187$	3.38407e7	0.378438
$188$	−1.21327e8	−1.33170
$189$	2.49987e7	0.269340
$190$	−5.35902e6	−0.0566824
$191$	−1.05880e8	−1.09950	−0.549752	−	0.835328i	$-0.685278\pi$
$191$	−1.05880e8	−1.09950	−0.549752	+	0.835328i	$0.685278\pi$
$192$	8.40307e6	0.0856808
$193$	9.24094e7	0.925264	0.462632	−	0.886550i	$-0.346905\pi$
$193$	9.24094e7	0.925264	0.462632	+	0.886550i	$0.346905\pi$
$194$	4.92844e7	0.484622
$195$	2.61239e7	0.252300
$196$	2.75273e7	0.261137
$197$	−1.91658e7	−0.178605	−0.0893026	−	0.996005i	$-0.528464\pi$
$197$	−1.91658e7	−0.178605	−0.0893026	+	0.996005i	$0.528464\pi$
$198$	3.31854e7	0.303821
$199$	−1.33704e8	−1.20270	−0.601351	−	0.798985i	$-0.705371\pi$
$199$	−1.33704e8	−1.20270	−0.601351	+	0.798985i	$0.705371\pi$
$200$	1.49892e7	0.132487
$201$	−1.33738e7	−0.116163
$202$	−5.22964e6	−0.0446418
$203$	−6.29277e7	−0.527965
$204$	−6.30057e6	−0.0519606
$205$	9.65194e7	0.782485
$206$	3.39959e7	0.270951
$207$	4.30551e6	0.0337387
$208$	−1.75622e8	−1.35318
$209$	3.18587e7	0.241388
$210$	−4.62947e6	−0.0344956
$211$	−2.23944e8	−1.64116	−0.820581	−	0.571530i	$-0.806350\pi$
$211$	−2.23944e8	−1.64116	−0.820581	+	0.571530i	$0.806350\pi$
$212$	−1.97098e8	−1.42071
$213$	2.90313e7	0.205844
$214$	−5.15883e7	−0.359835
$215$	−1.53003e8	−1.04994
$216$	−2.61922e7	−0.176841
$217$	4.08022e7	0.271065
$218$	−6.28713e7	−0.411012
$219$	−6.29889e6	−0.0405237
$220$	1.35913e8	0.860561
$221$	1.01063e8	0.629825
$222$	−1.25306e6	−0.00768665
$223$	−2.20987e8	−1.33444	−0.667220	−	0.744861i	$-0.732516\pi$
$223$	−2.20987e8	−1.33444	−0.667220	+	0.744861i	$0.732516\pi$
$224$	1.10084e8	0.654418
$225$	3.97133e7	0.232433
$226$	−4.42843e7	−0.255194
$227$	6.89169e7	0.391053	0.195526	−	0.980698i	$-0.437358\pi$
$227$	6.89169e7	0.391053	0.195526	+	0.980698i	$0.437358\pi$
$228$	−5.93155e6	−0.0331433
$229$	−7.42019e7	−0.408311	−0.204156	−	0.978938i	$-0.565445\pi$
$229$	−7.42019e7	−0.408311	−0.204156	+	0.978938i	$0.565445\pi$
$230$	−1.61598e6	−0.00875768
$231$	2.75216e7	0.146903
$232$	6.59320e7	0.346648
$233$	−1.66560e8	−0.862630	−0.431315	−	0.902201i	$-0.641950\pi$
$233$	−1.66560e8	−0.862630	−0.431315	+	0.902201i	$0.641950\pi$
$234$	9.91059e7	0.505643
$235$	2.52358e8	1.26847
$236$	3.00532e8	1.48833
$237$	−3.29510e6	−0.0160786
$238$	−1.79096e7	−0.0861124
$239$	−2.75168e8	−1.30378	−0.651892	−	0.758312i	$-0.726025\pi$
$239$	−2.75168e8	−1.30378	−0.651892	+	0.758312i	$0.726025\pi$
$240$	−2.27732e7	−0.106337
$241$	1.25859e8	0.579196	0.289598	−	0.957148i	$-0.406478\pi$
$241$	1.25859e8	0.579196	0.289598	+	0.957148i	$0.406478\pi$
$242$	1.01663e7	0.0461115
$243$	−1.04551e8	−0.467418
$244$	1.47261e8	0.648968
$245$	−5.72562e7	−0.248737
$246$	−9.79026e6	−0.0419297
$247$	9.51439e7	0.401737
$248$	−4.27502e7	−0.177974
$249$	1.71396e7	0.0703562
$250$	−7.73640e7	−0.313148
$251$	1.51435e8	0.604462	0.302231	−	0.953235i	$-0.402269\pi$
$251$	1.51435e8	0.604462	0.302231	+	0.953235i	$0.402269\pi$
$252$	1.91644e8	0.754384
$253$	9.60680e6	0.0372955
$254$	−1.14841e8	−0.439722
$255$	1.31050e7	0.0494934
$256$	7.03644e7	0.262128
$257$	−4.73292e8	−1.73925	−0.869627	−	0.493709i	$-0.835641\pi$
$257$	−4.73292e8	−1.73925	−0.869627	+	0.493709i	$0.835641\pi$
$258$	1.55196e7	0.0562614
$259$	3.88670e7	0.139005
$260$	4.05895e8	1.43221
$261$	1.74685e8	0.608154
$262$	2.84243e7	0.0976418
$263$	1.28865e8	0.436807	0.218403	−	0.975859i	$-0.429915\pi$
$263$	1.28865e8	0.436807	0.218403	+	0.975859i	$0.429915\pi$
$264$	−2.88356e7	−0.0964528
$265$	4.09959e8	1.35326
$266$	−1.68606e7	−0.0549272
$267$	−5.30377e7	−0.170528
$268$	−2.07792e8	−0.659413
$269$	−1.83418e8	−0.574526	−0.287263	−	0.957852i	$-0.592745\pi$
$269$	−1.83418e8	−0.574526	−0.287263	+	0.957852i	$0.592745\pi$
$270$	2.60461e7	0.0805321
$271$	7.88474e7	0.240655	0.120328	−	0.992734i	$-0.461606\pi$
$271$	7.88474e7	0.240655	0.120328	+	0.992734i	$0.461606\pi$
$272$	−8.81004e7	−0.265452
$273$	8.21914e7	0.244488
$274$	2.33939e7	0.0687029
$275$	8.86117e7	0.256937
$276$	−1.78862e6	−0.00512079
$277$	4.75543e8	1.34435	0.672173	−	0.740395i	$-0.265361\pi$
$277$	4.75543e8	1.34435	0.672173	+	0.740395i	$0.265361\pi$
$278$	1.82714e8	0.510052
$279$	−1.13265e8	−0.312235
$280$	−1.50451e8	−0.409582
$281$	7.16458e7	0.192628	0.0963138	−	0.995351i	$-0.469295\pi$
$281$	7.16458e7	0.192628	0.0963138	+	0.995351i	$0.469295\pi$
$282$	−2.55974e7	−0.0679711
$283$	−5.38320e8	−1.41185	−0.705924	−	0.708288i	$-0.749468\pi$
$283$	−5.38320e8	−1.41185	−0.705924	+	0.708288i	$0.749468\pi$
$284$	4.51067e8	1.16850
$285$	1.23375e7	0.0315696
$286$	2.21133e8	0.558950
$287$	3.03670e8	0.758256
$288$	−3.05589e8	−0.753813
$289$	−3.59641e8	−0.876448
$290$	−6.55643e7	−0.157861
$291$	−1.13462e8	−0.269913
$292$	−9.78676e7	−0.230038
$293$	5.40361e8	1.25501	0.627506	−	0.778612i	$-0.284076\pi$
$293$	5.40361e8	1.25501	0.627506	+	0.778612i	$0.284076\pi$
$294$	5.80767e6	0.0133287
$295$	−6.25099e8	−1.41766
$296$	−4.07226e7	−0.0912672
$297$	−1.54841e8	−0.342955
$298$	−1.64022e8	−0.359043
$299$	2.86901e7	0.0620701
$300$	−1.64980e7	−0.0352782
$301$	−4.81379e8	−1.01743
$302$	−1.26018e8	−0.263274
$303$	1.20396e7	0.0248635
$304$	−8.29404e7	−0.169320
$305$	−3.06299e8	−0.618154
$306$	4.97163e7	0.0991914
$307$	−6.80410e8	−1.34210	−0.671052	−	0.741410i	$-0.734157\pi$
$307$	−6.80410e8	−1.34210	−0.671052	+	0.741410i	$0.734157\pi$
$308$	4.27611e8	0.833914
$309$	−7.82649e7	−0.150908
$310$	4.25117e7	0.0810481
$311$	−2.66989e8	−0.503306	−0.251653	−	0.967818i	$-0.580974\pi$
$311$	−2.66989e8	−0.503306	−0.251653	+	0.967818i	$0.580974\pi$
$312$	−8.61155e7	−0.160524
$313$	6.63117e8	1.22232	0.611160	−	0.791507i	$-0.290703\pi$
$313$	6.63117e8	1.22232	0.611160	+	0.791507i	$0.290703\pi$
$314$	1.92496e8	0.350887
$315$	−3.98614e8	−0.718565
$316$	−5.11969e7	−0.0912722
$317$	−4.54092e8	−0.800639	−0.400320	−	0.916376i	$-0.631101\pi$
$317$	−4.54092e8	−0.800639	−0.400320	+	0.916376i	$0.631101\pi$
$318$	−4.15834e7	−0.0725146
$319$	3.89771e8	0.672268
$320$	−2.71564e8	−0.463283
$321$	1.18766e8	0.200412
$322$	−5.08422e6	−0.00848650
$323$	4.77288e7	0.0788082
$324$	−5.17391e8	−0.845107
$325$	2.64633e8	0.427614
$326$	1.23306e8	0.197116
$327$	1.44741e8	0.228916
$328$	−3.18169e8	−0.497850
$329$	7.93970e8	1.22919
$330$	2.86747e7	0.0439239
$331$	−4.79847e8	−0.727286	−0.363643	−	0.931538i	$-0.618467\pi$
$331$	−4.79847e8	−0.727286	−0.363643	+	0.931538i	$0.618467\pi$
$332$	2.66303e8	0.399386
$333$	−1.07893e8	−0.160118
$334$	−1.42136e8	−0.208733
$335$	4.32203e8	0.628103
$336$	−7.16492e7	−0.103044
$337$	6.24493e8	0.888838	0.444419	−	0.895819i	$-0.353410\pi$
$337$	6.24493e8	0.888838	0.444419	+	0.895819i	$0.353410\pi$
$338$	4.54708e8	0.640507
$339$	1.01951e8	0.142132
$340$	2.03617e8	0.280955
$341$	−2.52727e8	−0.345152
$342$	4.68045e7	0.0632697
$343$	−8.12060e8	−1.08657
$344$	5.04362e8	0.668017
$345$	3.72029e6	0.00487765
$346$	−1.78596e8	−0.231795
$347$	−1.31121e9	−1.68469	−0.842343	−	0.538942i	$-0.818824\pi$
$347$	−1.31121e9	−1.68469	−0.842343	+	0.538942i	$0.818824\pi$
$348$	−7.25688e7	−0.0923044
$349$	1.27831e9	1.60971	0.804855	−	0.593472i	$-0.202243\pi$
$349$	1.27831e9	1.60971	0.804855	+	0.593472i	$0.202243\pi$
$350$	−4.68960e7	−0.0584653
$351$	−4.62421e8	−0.570772
$352$	−6.81855e8	−0.833283
$353$	1.12400e8	0.136005	0.0680027	−	0.997685i	$-0.478337\pi$
$353$	1.12400e8	0.136005	0.0680027	+	0.997685i	$0.478337\pi$
$354$	6.34058e7	0.0759656
$355$	−9.38209e8	−1.11301
$356$	−8.24063e8	−0.968022
$357$	4.12312e7	0.0479609
$358$	1.41505e8	0.162998
$359$	1.21643e9	1.38758	0.693790	−	0.720177i	$-0.255940\pi$
$359$	1.21643e9	1.38758	0.693790	+	0.720177i	$0.255940\pi$
$360$	4.17645e8	0.471790
$361$	−8.48938e8	−0.949732
$362$	1.36298e8	0.151011
$363$	−2.34047e7	−0.0256821
$364$	1.27703e9	1.38786
$365$	2.03562e8	0.219115
$366$	3.10689e7	0.0331239
$367$	1.03280e9	1.09065	0.545324	−	0.838225i	$-0.316407\pi$
$367$	1.03280e9	1.09065	0.545324	+	0.838225i	$0.316407\pi$
$368$	−2.50102e7	−0.0261607
$369$	−8.42978e8	−0.873422
$370$	4.04955e7	0.0415624
$371$	1.28982e9	1.31135
$372$	4.70534e7	0.0473905
$373$	6.05487e8	0.604121	0.302060	−	0.953289i	$-0.402326\pi$
$373$	6.05487e8	0.604121	0.302060	+	0.953289i	$0.402326\pi$
$374$	1.10931e8	0.109649
$375$	1.78107e8	0.174410
$376$	−8.31877e8	−0.807052
$377$	1.16403e9	1.11884
$378$	8.19464e7	0.0780385
$379$	1.34584e9	1.26986	0.634932	−	0.772568i	$-0.281028\pi$
$379$	1.34584e9	1.26986	0.634932	+	0.772568i	$0.281028\pi$
$380$	1.91691e8	0.179209
$381$	2.64385e8	0.244906
$382$	−3.47078e8	−0.318570
$383$	−9.42952e8	−0.857618	−0.428809	−	0.903395i	$-0.641067\pi$
$383$	−9.42952e8	−0.857618	−0.428809	+	0.903395i	$0.641067\pi$
$384$	1.66129e8	0.149722
$385$	−8.89421e8	−0.794318
$386$	3.02921e8	0.268086
$387$	1.33629e9	1.17196
$388$	−1.76289e9	−1.53220
$389$	4.01190e8	0.345562	0.172781	−	0.984960i	$-0.444725\pi$
$389$	4.01190e8	0.345562	0.172781	+	0.984960i	$0.444725\pi$
$390$	8.56352e7	0.0731014
$391$	1.43923e7	0.0121762
$392$	1.88740e8	0.158257
$393$	−6.54382e7	−0.0543822
$394$	−6.28260e7	−0.0517491
$395$	1.06488e8	0.0869385
$396$	−1.18703e9	−0.960571
$397$	1.35442e9	1.08640	0.543198	−	0.839605i	$-0.317213\pi$
$397$	1.35442e9	1.08640	0.543198	+	0.839605i	$0.317213\pi$
$398$	−4.38285e8	−0.348471
$399$	3.88163e7	0.0305921
$400$	−2.30690e8	−0.180227
$401$	1.55536e9	1.20455	0.602276	−	0.798288i	$-0.294261\pi$
$401$	1.55536e9	1.20455	0.602276	+	0.798288i	$0.294261\pi$
$402$	−4.38397e7	−0.0336570
$403$	−7.54752e8	−0.574429
$404$	1.87063e8	0.141141
$405$	1.07616e9	0.804980
$406$	−2.06279e8	−0.152973
$407$	−2.40740e8	−0.176998
$408$	−4.31997e7	−0.0314898
$409$	2.10885e9	1.52410	0.762051	−	0.647517i	$-0.224192\pi$
$409$	2.10885e9	1.52410	0.762051	+	0.647517i	$0.224192\pi$
$410$	3.16394e8	0.226717
$411$	−5.38570e7	−0.0382645
$412$	−1.21602e9	−0.856648
$413$	−1.96669e9	−1.37376
$414$	1.41136e7	0.00977545
$415$	−5.53903e8	−0.380422
$416$	−2.03631e9	−1.38681
$417$	−4.20642e8	−0.284077
$418$	1.04434e8	0.0699398
$419$	−2.10395e8	−0.139729	−0.0698644	−	0.997556i	$-0.522257\pi$
$419$	−2.10395e8	−0.139729	−0.0698644	+	0.997556i	$0.522257\pi$
$420$	1.65595e8	0.109062
$421$	−9.41293e8	−0.614805	−0.307402	−	0.951580i	$-0.599460\pi$
$421$	−9.41293e8	−0.614805	−0.307402	+	0.951580i	$0.599460\pi$
$422$	−7.34097e8	−0.475510
$423$	−2.20403e9	−1.41588
$424$	−1.35140e9	−0.860999
$425$	1.32753e8	0.0838845
$426$	9.51654e7	0.0596411
$427$	−9.63682e8	−0.599013
$428$	1.84530e9	1.13766
$429$	−5.09090e8	−0.311311
$430$	−5.01549e8	−0.304210
$431$	4.56614e8	0.274713	0.137356	−	0.990522i	$-0.456139\pi$
$431$	4.56614e8	0.274713	0.137356	+	0.990522i	$0.456139\pi$
$432$	4.03109e8	0.240563
$433$	−1.96250e9	−1.16172	−0.580860	−	0.814003i	$-0.697284\pi$
$433$	−1.96250e9	−1.16172	−0.580860	+	0.814003i	$0.697284\pi$
$434$	1.33751e8	0.0785385
$435$	1.50941e8	0.0879216
$436$	2.24889e9	1.29947
$437$	1.35494e7	0.00776666
$438$	−2.06480e7	−0.0117413
$439$	−1.86715e8	−0.105331	−0.0526653	−	0.998612i	$-0.516772\pi$
$439$	−1.86715e8	−0.105331	−0.0526653	+	0.998612i	$0.516772\pi$
$440$	9.31885e8	0.521528
$441$	5.00062e8	0.277644
$442$	3.31288e8	0.182485
$443$	−6.04204e8	−0.330195	−0.165097	−	0.986277i	$-0.552794\pi$
$443$	−6.04204e8	−0.330195	−0.165097	+	0.986277i	$0.552794\pi$
$444$	4.48218e7	0.0243024
$445$	1.71403e9	0.922059
$446$	−7.24402e8	−0.386641
$447$	3.77610e8	0.199971
$448$	−8.54396e8	−0.448938
$449$	2.33429e9	1.21700	0.608502	−	0.793552i	$-0.291771\pi$
$449$	2.33429e9	1.21700	0.608502	+	0.793552i	$0.291771\pi$
$450$	1.30182e8	0.0673451
$451$	−1.88092e9	−0.965501
$452$	1.58404e9	0.806828
$453$	2.90117e8	0.146632
$454$	2.25912e8	0.113304
$455$	−2.65620e9	−1.32197
$456$	−4.06695e7	−0.0200859
$457$	1.70366e9	0.834982	0.417491	−	0.908681i	$-0.362909\pi$
$457$	1.70366e9	0.834982	0.417491	+	0.908681i	$0.362909\pi$
$458$	−2.43236e8	−0.118304
$459$	−2.31973e8	−0.111968
$460$	5.78033e7	0.0276885
$461$	−3.05600e9	−1.45278	−0.726390	−	0.687283i	$-0.758803\pi$
$461$	−3.05600e9	−1.45278	−0.726390	+	0.687283i	$0.758803\pi$
$462$	9.02167e7	0.0425638
$463$	6.39902e8	0.299626	0.149813	−	0.988714i	$-0.452133\pi$
$463$	6.39902e8	0.299626	0.149813	+	0.988714i	$0.452133\pi$
$464$	−1.01472e9	−0.471558
$465$	−9.78700e7	−0.0451403
$466$	−5.45989e8	−0.249939
$467$	−3.14452e9	−1.42871	−0.714357	−	0.699781i	$-0.753281\pi$
$467$	−3.14452e9	−1.42871	−0.714357	+	0.699781i	$0.753281\pi$
$468$	−3.54499e9	−1.59866
$469$	1.35980e9	0.608654
$470$	8.27237e8	0.367526
$471$	−4.43162e8	−0.195429
$472$	2.06059e9	0.901975
$473$	2.98164e9	1.29551
$474$	−1.08014e7	−0.00465862
$475$	1.24977e8	0.0535062
$476$	6.40621e8	0.272256
$477$	−3.58049e9	−1.51052
$478$	−9.02011e8	−0.377759
$479$	1.34262e9	0.558186	0.279093	−	0.960264i	$-0.409966\pi$
$479$	1.34262e9	0.558186	0.279093	+	0.960264i	$0.409966\pi$
$480$	−2.64052e8	−0.108980
$481$	−7.18955e8	−0.294574
$482$	4.12571e8	0.167816
$483$	1.17048e7	0.00472661
$484$	−3.63646e8	−0.145787
$485$	3.66677e9	1.45944
$486$	−3.42721e8	−0.135430
$487$	1.00484e9	0.394226	0.197113	−	0.980381i	$-0.436843\pi$
$487$	1.00484e9	0.394226	0.197113	+	0.980381i	$0.436843\pi$
$488$	1.00969e9	0.393296
$489$	−2.83872e8	−0.109785
$490$	−1.87688e8	−0.0720692
$491$	1.76780e9	0.673981	0.336991	−	0.941508i	$-0.390591\pi$
$491$	1.76780e9	0.673981	0.336991	+	0.941508i	$0.390591\pi$
$492$	3.50195e8	0.132566
$493$	5.83932e8	0.219481
$494$	3.11885e8	0.116399
$495$	2.46900e9	0.914962
$496$	6.57944e8	0.242105
$497$	−2.95180e9	−1.07855
$498$	5.61841e7	0.0203850
$499$	4.42270e9	1.59344	0.796721	−	0.604348i	$-0.206566\pi$
$499$	4.42270e9	1.59344	0.796721	+	0.604348i	$0.206566\pi$
$500$	2.76729e9	0.990057
$501$	3.27223e8	0.116255
$502$	4.96410e8	0.175137
$503$	−1.56395e9	−0.547944	−0.273972	−	0.961738i	$-0.588338\pi$
$503$	−1.56395e9	−0.547944	−0.273972	+	0.961738i	$0.588338\pi$
$504$	1.31400e9	0.457181
$505$	−3.89086e8	−0.134439
$506$	3.14914e7	0.0108060
$507$	−1.04682e9	−0.356734
$508$	4.10783e9	1.39024
$509$	3.04461e9	1.02334	0.511670	−	0.859182i	$-0.329027\pi$
$509$	3.04461e9	1.02334	0.511670	+	0.859182i	$0.329027\pi$
$510$	4.29587e7	0.0143402
$511$	6.40450e8	0.212330
$512$	3.04840e9	1.00375
$513$	−2.18386e8	−0.0714191
$514$	−1.55147e9	−0.503931
$515$	2.52930e9	0.815973
$516$	−5.55131e8	−0.177878
$517$	−4.91782e9	−1.56515
$518$	1.27407e8	0.0402754
$519$	4.11161e8	0.129100
$520$	2.78301e9	0.867967
$521$	−5.57929e9	−1.72841	−0.864205	−	0.503141i	$-0.832178\pi$
$521$	−5.57929e9	−1.72841	−0.864205	+	0.503141i	$0.832178\pi$
$522$	5.72623e8	0.176207
$523$	4.12628e8	0.126125	0.0630627	−	0.998010i	$-0.479913\pi$
$523$	4.12628e8	0.126125	0.0630627	+	0.998010i	$0.479913\pi$
$524$	−1.01673e9	−0.308707
$525$	1.07963e8	0.0325626
$526$	4.22423e8	0.126560
$527$	−3.78620e8	−0.112685
$528$	4.43792e8	0.131208
$529$	−3.40074e9	−0.998800
$530$	1.34386e9	0.392092
$531$	5.45947e9	1.58241
$532$	6.03100e8	0.173660
$533$	−5.61725e9	−1.60686
$534$	−1.73859e8	−0.0494088
$535$	−3.83818e9	−1.08365
$536$	−1.42472e9	−0.399626
$537$	−3.25772e8	−0.0907828
$538$	−6.01252e8	−0.166463
$539$	1.11578e9	0.306915
$540$	−9.31662e8	−0.254613
$541$	−4.75113e8	−0.129005	−0.0645025	−	0.997918i	$-0.520546\pi$
$541$	−4.75113e8	−0.129005	−0.0645025	+	0.997918i	$0.520546\pi$
$542$	2.58465e8	0.0697274
$543$	−3.13783e8	−0.0841066
$544$	−1.02151e9	−0.272049
$545$	−4.67764e9	−1.23777
$546$	2.69426e8	0.0708379
$547$	−8.26414e8	−0.215895	−0.107947	−	0.994157i	$-0.534428\pi$
$547$	−8.26414e8	−0.215895	−0.107947	+	0.994157i	$0.534428\pi$
$548$	−8.36793e8	−0.217213
$549$	2.67515e9	0.689992
$550$	2.90472e8	0.0744449
$551$	5.49731e8	0.139997
$552$	−1.22636e7	−0.00310336
$553$	3.35034e8	0.0842464
$554$	1.55885e9	0.389511
$555$	−9.32282e7	−0.0231484
$556$	−6.53563e9	−1.61260
$557$	−1.27435e9	−0.312461	−0.156230	−	0.987721i	$-0.549934\pi$
$557$	−1.27435e9	−0.312461	−0.156230	+	0.987721i	$0.549934\pi$
$558$	−3.71288e8	−0.0904671
$559$	8.90447e9	2.15609
$560$	2.31550e9	0.557169
$561$	−2.55384e8	−0.0610695
$562$	2.34857e8	0.0558119
$563$	−2.76657e9	−0.653374	−0.326687	−	0.945133i	$-0.605932\pi$
$563$	−2.76657e9	−0.653374	−0.326687	+	0.945133i	$0.605932\pi$
$564$	9.15614e8	0.214900
$565$	−3.29476e9	−0.768518
$566$	−1.76463e9	−0.409069
$567$	3.38583e9	0.780054
$568$	3.09273e9	0.708146
$569$	−8.36822e9	−1.90432	−0.952160	−	0.305599i	$-0.901143\pi$
$569$	−8.36822e9	−1.90432	−0.952160	+	0.305599i	$0.901143\pi$
$570$	4.04427e7	0.00914698
$571$	−1.17152e9	−0.263345	−0.131672	−	0.991293i	$-0.542035\pi$
$571$	−1.17152e9	−0.263345	−0.131672	+	0.991293i	$0.542035\pi$
$572$	−7.90988e9	−1.76719
$573$	7.99038e8	0.177430
$574$	9.95442e8	0.219697
$575$	3.76862e7	0.00826694
$576$	2.37177e9	0.517124
$577$	−2.51408e9	−0.544833	−0.272417	−	0.962179i	$-0.587823\pi$
$577$	−2.51408e9	−0.544833	−0.272417	+	0.962179i	$0.587823\pi$
$578$	−1.17891e9	−0.253942
$579$	−6.97381e8	−0.149312
$580$	2.34522e9	0.499098
$581$	−1.74270e9	−0.368642
$582$	−3.71932e8	−0.0782047
$583$	−7.98907e9	−1.66977
$584$	−6.71027e8	−0.139410
$585$	7.37350e9	1.52275
$586$	1.77132e9	0.363627
$587$	−1.54715e9	−0.315719	−0.157859	−	0.987462i	$-0.550459\pi$
$587$	−1.54715e9	−0.315719	−0.157859	+	0.987462i	$0.550459\pi$
$588$	−2.07739e8	−0.0421403
$589$	−3.56444e8	−0.0718767
$590$	−2.04910e9	−0.410753
$591$	1.44637e8	0.0288220
$592$	6.26739e8	0.124154
$593$	−3.45350e9	−0.680093	−0.340046	−	0.940409i	$-0.610443\pi$
$593$	−3.45350e9	−0.680093	−0.340046	+	0.940409i	$0.610443\pi$
$594$	−5.07573e8	−0.0993678
$595$	−1.33248e9	−0.259328
$596$	5.86704e9	1.13516
$597$	1.00902e9	0.194083
$598$	9.40470e7	0.0179842
$599$	1.01161e10	1.92318	0.961590	−	0.274491i	$-0.0885092\pi$
$599$	1.01161e10	1.92318	0.961590	+	0.274491i	$0.0885092\pi$
$600$	−1.13118e8	−0.0213797
$601$	9.17326e9	1.72370	0.861852	−	0.507159i	$-0.169304\pi$
$601$	9.17326e9	1.72370	0.861852	+	0.507159i	$0.169304\pi$
$602$	−1.57798e9	−0.294790
$603$	−3.77476e9	−0.701097
$604$	4.50764e9	0.832376
$605$	7.56375e8	0.138865
$606$	3.94662e7	0.00720396
$607$	2.92095e8	0.0530107	0.0265053	−	0.999649i	$-0.491562\pi$
$607$	2.92095e8	0.0530107	0.0265053	+	0.999649i	$0.491562\pi$
$608$	−9.61684e8	−0.173528
$609$	4.74893e8	0.0851991
$610$	−1.00406e9	−0.179104
$611$	−1.46867e10	−2.60484
$612$	−1.77834e9	−0.313606
$613$	−2.23649e9	−0.392152	−0.196076	−	0.980589i	$-0.562820\pi$
$613$	−2.23649e9	−0.392152	−0.196076	+	0.980589i	$0.562820\pi$
$614$	−2.23041e9	−0.388861
$615$	−7.28398e8	−0.126272
$616$	2.93190e9	0.505379
$617$	4.47705e9	0.767350	0.383675	−	0.923468i	$-0.374658\pi$
$617$	4.47705e9	0.767350	0.383675	+	0.923468i	$0.374658\pi$
$618$	−2.56555e8	−0.0437241
$619$	8.78566e9	1.48887	0.744435	−	0.667695i	$-0.232719\pi$
$619$	8.78566e9	1.48887	0.744435	+	0.667695i	$0.232719\pi$
$620$	−1.52063e9	−0.256244
$621$	−6.58531e7	−0.0110346
$622$	−8.75199e8	−0.145828
$623$	5.39270e9	0.893507
$624$	1.32536e9	0.218367
$625$	−4.29932e9	−0.704400
$626$	2.17372e9	0.354155
$627$	−2.40426e8	−0.0389534
$628$	−6.88553e9	−1.10938
$629$	−3.60663e8	−0.0577862
$630$	−1.30667e9	−0.208197
$631$	6.83671e9	1.08329	0.541644	−	0.840608i	$-0.317802\pi$
$631$	6.83671e9	1.08329	0.541644	+	0.840608i	$0.317802\pi$
$632$	−3.51030e8	−0.0553139
$633$	1.69003e9	0.264839
$634$	−1.48853e9	−0.231977
$635$	−8.54419e9	−1.32423
$636$	1.48743e9	0.229264
$637$	3.33220e9	0.510791
$638$	1.27768e9	0.194783
$639$	8.19410e9	1.24236
$640$	−5.36883e9	−0.809562
$641$	8.91799e9	1.33741	0.668704	−	0.743529i	$-0.266850\pi$
$641$	8.91799e9	1.33741	0.668704	+	0.743529i	$0.266850\pi$
$642$	3.89319e8	0.0580674
$643$	−2.48489e9	−0.368611	−0.184305	−	0.982869i	$-0.559004\pi$
$643$	−2.48489e9	−0.368611	−0.184305	+	0.982869i	$0.559004\pi$
$644$	1.81861e8	0.0268312
$645$	1.15466e9	0.169432
$646$	1.56457e8	0.0228339
$647$	3.39781e9	0.493212	0.246606	−	0.969116i	$-0.420685\pi$
$647$	3.39781e9	0.493212	0.246606	+	0.969116i	$0.420685\pi$
$648$	−3.54748e9	−0.512162
$649$	1.21816e10	1.74924
$650$	8.67475e8	0.123897
$651$	−3.07920e8	−0.0437425
$652$	−4.41061e9	−0.623206
$653$	−1.18401e9	−0.166402	−0.0832011	−	0.996533i	$-0.526514\pi$
$653$	−1.18401e9	−0.166402	−0.0832011	+	0.996533i	$0.526514\pi$
$654$	4.74467e8	0.0663261
$655$	2.11478e9	0.294049
$656$	4.89676e9	0.677244
$657$	−1.77787e9	−0.244580
$658$	2.60266e9	0.356145
$659$	−5.20005e9	−0.707797	−0.353898	−	0.935284i	$-0.615144\pi$
$659$	−5.20005e9	−0.707797	−0.353898	+	0.935284i	$0.615144\pi$
$660$	−1.02569e9	−0.138871
$661$	−2.41813e9	−0.325668	−0.162834	−	0.986653i	$-0.552063\pi$
$661$	−2.41813e9	−0.325668	−0.162834	+	0.986653i	$0.552063\pi$
$662$	−1.57296e9	−0.210724
$663$	−7.62688e8	−0.101636
$664$	1.82590e9	0.242041
$665$	−1.25443e9	−0.165414
$666$	−3.53678e8	−0.0463925
$667$	1.65768e8	0.0216302
$668$	5.08416e9	0.659935
$669$	1.66771e9	0.215342
$670$	1.41677e9	0.181986
$671$	5.96900e9	0.762734
$672$	−8.30764e8	−0.105605
$673$	8.96524e9	1.13373	0.566865	−	0.823811i	$-0.308156\pi$
$673$	8.96524e9	1.13373	0.566865	+	0.823811i	$0.308156\pi$
$674$	2.04711e9	0.257532
$675$	−6.07419e8	−0.0760195
$676$	−1.62648e10	−2.02505
$677$	3.28740e9	0.407185	0.203593	−	0.979056i	$-0.434738\pi$
$677$	3.28740e9	0.407185	0.203593	+	0.979056i	$0.434738\pi$
$678$	3.34198e8	0.0411813
$679$	1.15364e10	1.41425
$680$	1.39609e9	0.170268
$681$	−5.20092e8	−0.0631052
$682$	−8.28447e8	−0.100004
$683$	−1.08548e10	−1.30361	−0.651807	−	0.758385i	$-0.725989\pi$
$683$	−1.08548e10	−1.30361	−0.651807	+	0.758385i	$0.725989\pi$
$684$	−1.67418e9	−0.200035
$685$	1.74051e9	0.206899
$686$	−2.66196e9	−0.314823
$687$	5.59976e8	0.0658902
$688$	−7.76235e9	−0.908728
$689$	−2.38588e10	−2.77896
$690$	1.21952e7	0.00141325
$691$	1.43801e10	1.65801	0.829007	−	0.559238i	$-0.188906\pi$
$691$	1.43801e10	1.65801	0.829007	+	0.559238i	$0.188906\pi$
$692$	6.38833e9	0.732851
$693$	7.76799e9	0.886630
$694$	−4.29819e9	−0.488121
$695$	1.35940e10	1.53603
$696$	−4.97566e8	−0.0559395
$697$	−2.81788e9	−0.315216
$698$	4.19035e9	0.466397
$699$	1.25697e9	0.139205
$700$	1.67746e9	0.184846
$701$	−1.65596e10	−1.81566	−0.907832	−	0.419333i	$-0.862264\pi$
$701$	−1.65596e10	−1.81566	−0.907832	+	0.419333i	$0.862264\pi$
$702$	−1.51583e9	−0.165376
$703$	−3.39539e8	−0.0368592
$704$	5.29209e9	0.571641
$705$	−1.90446e9	−0.204696
$706$	3.68452e8	0.0394062
$707$	−1.22415e9	−0.130276
$708$	−2.26801e9	−0.240175
$709$	−1.61276e10	−1.69945	−0.849723	−	0.527229i	$-0.823231\pi$
$709$	−1.61276e10	−1.69945	−0.849723	+	0.527229i	$0.823231\pi$
$710$	−3.07548e9	−0.322484
$711$	−9.30044e8	−0.0970420
$712$	−5.65016e9	−0.586653
$713$	−1.07484e8	−0.0111053
$714$	1.35157e8	0.0138962
$715$	1.64524e10	1.68328
$716$	−5.06161e9	−0.515340
$717$	2.07660e9	0.210395
$718$	3.98751e9	0.402037
$719$	−1.36505e10	−1.36961	−0.684807	−	0.728724i	$-0.740114\pi$
$719$	−1.36505e10	−1.36961	−0.684807	+	0.728724i	$0.740114\pi$
$720$	−6.42775e9	−0.641793
$721$	7.95772e9	0.790706
$722$	−2.78285e9	−0.275175
$723$	−9.49815e8	−0.0934663
$724$	−4.87534e9	−0.477441
$725$	1.52902e9	0.149015
$726$	−7.67215e7	−0.00744113
$727$	−6.56482e9	−0.633654	−0.316827	−	0.948483i	$-0.602617\pi$
$727$	−6.56482e9	−0.633654	−0.316827	+	0.948483i	$0.602617\pi$
$728$	8.75594e9	0.841090
$729$	−8.86124e9	−0.847126
$730$	6.67284e8	0.0634864
$731$	4.46692e9	0.422958
$732$	−1.11133e9	−0.104726
$733$	3.92413e9	0.368027	0.184013	−	0.982924i	$-0.441091\pi$
$733$	3.92413e9	0.368027	0.184013	+	0.982924i	$0.441091\pi$
$734$	3.38555e9	0.316004
$735$	4.32092e8	0.0401394
$736$	−2.89990e8	−0.0268109
$737$	−8.42255e9	−0.775010
$738$	−2.76331e9	−0.253065
$739$	−3.97265e9	−0.362097	−0.181048	−	0.983474i	$-0.557949\pi$
$739$	−3.97265e9	−0.362097	−0.181048	+	0.983474i	$0.557949\pi$
$740$	−1.44851e9	−0.131405
$741$	−7.18018e8	−0.0648293
$742$	4.22806e9	0.379951
$743$	1.70278e10	1.52299	0.761494	−	0.648172i	$-0.224466\pi$
$743$	1.70278e10	1.52299	0.761494	+	0.648172i	$0.224466\pi$
$744$	3.22621e8	0.0287202
$745$	−1.22033e10	−1.08126
$746$	1.98481e9	0.175038
$747$	4.83766e9	0.424633
$748$	−3.96798e9	−0.346668
$749$	−1.20757e10	−1.05009
$750$	5.83839e8	0.0505334
$751$	−1.93168e10	−1.66416	−0.832082	−	0.554653i	$-0.812851\pi$
$751$	−1.93168e10	−1.66416	−0.832082	+	0.554653i	$0.812851\pi$
$752$	1.28030e10	1.09786
$753$	−1.14283e9	−0.0975436
$754$	3.81572e9	0.324173
$755$	−9.37578e9	−0.792854
$756$	−2.93120e9	−0.246729
$757$	−9.17588e9	−0.768798	−0.384399	−	0.923167i	$-0.625591\pi$
$757$	−9.17588e9	−0.768798	−0.384399	+	0.923167i	$0.625591\pi$
$758$	4.41172e9	0.367930
$759$	−7.24992e7	−0.00601848
$760$	1.31432e9	0.108606
$761$	4.84148e8	0.0398228	0.0199114	−	0.999802i	$-0.493662\pi$
$761$	4.84148e8	0.0398228	0.0199114	+	0.999802i	$0.493662\pi$
$762$	8.66663e8	0.0709591
$763$	−1.47168e10	−1.19944
$764$	1.24149e10	1.00720
$765$	3.69891e9	0.298716
$766$	−3.09103e9	−0.248486
$767$	3.63796e10	2.91121
$768$	−5.31015e8	−0.0423002
$769$	1.53761e10	1.21928	0.609641	−	0.792678i	$-0.291314\pi$
$769$	1.53761e10	1.21928	0.609641	+	0.792678i	$0.291314\pi$
$770$	−2.91555e9	−0.230146
$771$	3.57177e9	0.280668
$772$	−1.08354e10	−0.847589
$773$	−1.93843e10	−1.50946	−0.754729	−	0.656037i	$-0.772232\pi$
$773$	−1.93843e10	−1.50946	−0.754729	+	0.656037i	$0.772232\pi$
$774$	4.38041e9	0.339564
$775$	−9.91413e8	−0.0765065
$776$	−1.20872e10	−0.928560
$777$	−2.93315e8	−0.0224317
$778$	1.31511e9	0.100123
$779$	−2.65284e9	−0.201062
$780$	−3.06315e9	−0.231120
$781$	1.82833e10	1.37334
$782$	4.71785e7	0.00352794
$783$	−2.67182e9	−0.198903
$784$	−2.90480e9	−0.215283
$785$	1.43217e10	1.05670
$786$	−2.14509e8	−0.0157567
$787$	−5.55676e9	−0.406359	−0.203180	−	0.979141i	$-0.565128\pi$
$787$	−5.55676e9	−0.406359	−0.203180	+	0.979141i	$0.565128\pi$
$788$	2.24727e9	0.163611
$789$	−9.72497e8	−0.0704886
$790$	3.49072e8	0.0251895
$791$	−1.03660e10	−0.744721
$792$	−8.13886e9	−0.582137
$793$	1.78260e10	1.26940
$794$	4.43985e9	0.314772
$795$	−3.09382e9	−0.218378
$796$	1.56774e10	1.10174
$797$	8.59205e9	0.601163	0.300582	−	0.953756i	$-0.402819\pi$
$797$	8.59205e9	0.601163	0.300582	+	0.953756i	$0.402819\pi$
$798$	1.27241e8	0.00886375
$799$	−7.36758e9	−0.510989
$800$	−2.67482e9	−0.184706
$801$	−1.49699e10	−1.02922
$802$	5.09852e9	0.349007
$803$	−3.96692e9	−0.270364
$804$	1.56813e9	0.106411
$805$	−3.78267e8	−0.0255572
$806$	−2.47410e9	−0.166435
$807$	1.38419e9	0.0927128
$808$	1.28259e9	0.0855360
$809$	3.75879e8	0.0249591	0.0124795	−	0.999922i	$-0.496028\pi$
$809$	3.75879e8	0.0249591	0.0124795	+	0.999922i	$0.496028\pi$
$810$	3.52770e9	0.233235
$811$	2.20119e10	1.44905	0.724526	−	0.689248i	$-0.242059\pi$
$811$	2.20119e10	1.44905	0.724526	+	0.689248i	$0.242059\pi$
$812$	7.37855e9	0.483643
$813$	−5.95034e8	−0.0388351
$814$	−7.89155e8	−0.0512834
$815$	9.17396e9	0.593616
$816$	6.64863e8	0.0428367
$817$	4.20529e9	0.269786
$818$	6.91288e9	0.441593
$819$	2.31986e10	1.47560
$820$	−1.13173e10	−0.716796
$821$	7.80179e9	0.492032	0.246016	−	0.969266i	$-0.420878\pi$
$821$	7.80179e9	0.492032	0.246016	+	0.969266i	$0.420878\pi$
$822$	−1.76545e8	−0.0110868
$823$	−6.19095e9	−0.387131	−0.193565	−	0.981087i	$-0.562005\pi$
$823$	−6.19095e9	−0.387131	−0.193565	+	0.981087i	$0.562005\pi$
$824$	−8.33764e9	−0.519156
$825$	−6.68721e8	−0.0414626
$826$	−6.44689e9	−0.398034
$827$	2.93491e10	1.80437	0.902186	−	0.431347i	$-0.141961\pi$
$827$	2.93491e10	1.80437	0.902186	+	0.431347i	$0.141961\pi$
$828$	−5.04840e8	−0.0309064
$829$	−2.49577e10	−1.52147	−0.760736	−	0.649062i	$-0.775162\pi$
$829$	−2.49577e10	−1.52147	−0.760736	+	0.649062i	$0.775162\pi$
$830$	−1.81571e9	−0.110223
$831$	−3.58876e9	−0.216940
$832$	1.58045e10	0.951368
$833$	1.67159e9	0.100201
$834$	−1.37888e9	−0.0823085
$835$	−1.05749e10	−0.628600
$836$	−3.73558e9	−0.221124
$837$	1.73240e9	0.102120
$838$	−6.89681e8	−0.0404850
$839$	−2.96970e10	−1.73598	−0.867991	−	0.496580i	$-0.834589\pi$
$839$	−2.96970e10	−1.73598	−0.867991	+	0.496580i	$0.834589\pi$
$840$	1.13540e9	0.0660953
$841$	−1.05243e10	−0.610106
$842$	−3.08559e9	−0.178134
$843$	−5.40686e8	−0.0310848
$844$	2.62585e10	1.50339
$845$	3.38304e10	1.92889
$846$	−7.22490e9	−0.410238
$847$	2.37972e9	0.134565
$848$	2.07986e10	1.17125
$849$	4.06251e9	0.227834
$850$	4.35168e8	0.0243047
$851$	−1.02386e8	−0.00569491
$852$	−3.40405e9	−0.188563
$853$	2.32424e10	1.28221	0.641105	−	0.767453i	$-0.278476\pi$
$853$	2.32424e10	1.28221	0.641105	+	0.767453i	$0.278476\pi$
$854$	−3.15898e9	−0.173558
$855$	3.48226e9	0.190537
$856$	1.26523e10	0.689461
$857$	−2.26338e10	−1.22836	−0.614179	−	0.789167i	$-0.710513\pi$
$857$	−2.26338e10	−1.22836	−0.614179	+	0.789167i	$0.710513\pi$
$858$	−1.66881e9	−0.0901992
$859$	3.63155e9	0.195486	0.0977432	−	0.995212i	$-0.468838\pi$
$859$	3.63155e9	0.195486	0.0977432	+	0.995212i	$0.468838\pi$
$860$	1.79403e10	0.961799
$861$	−2.29169e9	−0.122362
$862$	1.49680e9	0.0795953
$863$	5.19160e9	0.274956	0.137478	−	0.990505i	$-0.456100\pi$
$863$	5.19160e9	0.274956	0.137478	+	0.990505i	$0.456100\pi$
$864$	4.67400e9	0.246542
$865$	−1.32876e10	−0.698054
$866$	−6.43313e9	−0.336597
$867$	2.71408e9	0.141435
$868$	−4.78424e9	−0.248310
$869$	−2.07519e9	−0.107273
$870$	4.94791e8	0.0254744
$871$	−2.51534e10	−1.28983
$872$	1.54195e10	0.787520
$873$	−3.20247e10	−1.62905
$874$	4.44153e7	0.00225031
$875$	−1.81093e10	−0.913846
$876$	7.38573e8	0.0371218
$877$	−1.62883e10	−0.815412	−0.407706	−	0.913113i	$-0.633671\pi$
$877$	−1.62883e10	−0.815412	−0.407706	+	0.913113i	$0.633671\pi$
$878$	−6.12059e8	−0.0305185
$879$	−4.07792e9	−0.202524
$880$	−1.43421e10	−0.709454
$881$	9.99202e9	0.492309	0.246154	−	0.969231i	$-0.420833\pi$
$881$	9.99202e9	0.492309	0.246154	+	0.969231i	$0.420833\pi$
$882$	1.63922e9	0.0804447
$883$	−3.17375e10	−1.55135	−0.775677	−	0.631131i	$-0.782591\pi$
$883$	−3.17375e10	−1.55135	−0.775677	+	0.631131i	$0.782591\pi$
$884$	−1.18501e10	−0.576951
$885$	4.71740e9	0.228771
$886$	−1.98060e9	−0.0956707
$887$	−3.25815e10	−1.56761	−0.783805	−	0.621007i	$-0.786724\pi$
$887$	−3.25815e10	−1.56761	−0.783805	+	0.621007i	$0.786724\pi$
$888$	3.07319e8	0.0147280
$889$	−2.68818e10	−1.28322
$890$	5.61865e9	0.267157
$891$	−2.09717e10	−0.993257
$892$	2.59117e10	1.22242
$893$	−6.93606e9	−0.325936
$894$	1.23782e9	0.0579396
$895$	1.05280e10	0.490870
$896$	−1.68915e10	−0.784494
$897$	−2.16514e8	−0.0100164
$898$	7.65188e9	0.352615
$899$	−4.36087e9	−0.200177
$900$	−4.65657e9	−0.212920
$901$	−1.19687e10	−0.545145
$902$	−6.16572e9	−0.279744
$903$	3.63280e9	0.164185
$904$	1.08609e10	0.488964
$905$	1.01406e10	0.454771
$906$	9.51015e8	0.0424853
$907$	4.49147e9	0.199877	0.0999386	−	0.994994i	$-0.468135\pi$
$907$	4.49147e9	0.199877	0.0999386	+	0.994994i	$0.468135\pi$
$908$	−8.08082e9	−0.358224
$909$	3.39819e9	0.150063
$910$	−8.70710e9	−0.383026
$911$	9.99744e9	0.438101	0.219051	−	0.975714i	$-0.429704\pi$
$911$	9.99744e9	0.438101	0.219051	+	0.975714i	$0.429704\pi$
$912$	6.25922e8	0.0273236
$913$	1.07942e10	0.469399
$914$	5.58467e9	0.241928
$915$	2.31153e9	0.0997531
$916$	8.70051e9	0.374034
$917$	6.65354e9	0.284944
$918$	−7.60415e8	−0.0324415
$919$	1.88391e10	0.800675	0.400337	−	0.916368i	$-0.368893\pi$
$919$	1.88391e10	0.800675	0.400337	+	0.916368i	$0.368893\pi$
$920$	3.96327e8	0.0167802
$921$	5.13482e9	0.216579
$922$	−1.00177e10	−0.420928
$923$	5.46020e10	2.28561
$924$	−3.22703e9	−0.134571
$925$	−9.44392e8	−0.0392334
$926$	2.09762e9	0.0868137
$927$	−2.20903e10	−0.910801
$928$	−1.17656e10	−0.483277
$929$	5.58372e9	0.228491	0.114245	−	0.993453i	$-0.463555\pi$
$929$	5.58372e9	0.228491	0.114245	+	0.993453i	$0.463555\pi$
$930$	−3.20821e8	−0.0130789
$931$	1.57369e9	0.0639139
$932$	1.95299e10	0.790213
$933$	2.01487e9	0.0812197
$934$	−1.03078e10	−0.413956
$935$	8.25330e9	0.330208
$936$	−2.43062e10	−0.968838
$937$	7.80828e9	0.310075	0.155038	−	0.987909i	$-0.450450\pi$
$937$	7.80828e9	0.310075	0.155038	+	0.987909i	$0.450450\pi$
$938$	4.45747e9	0.176351
$939$	−5.00431e9	−0.197249
$940$	−2.95901e10	−1.16198
$941$	−3.57978e9	−0.140053	−0.0700265	−	0.997545i	$-0.522308\pi$
$941$	−3.57978e9	−0.140053	−0.0700265	+	0.997545i	$0.522308\pi$
$942$	−1.45270e9	−0.0566236
$943$	−7.99948e8	−0.0310650
$944$	−3.17134e10	−1.22699
$945$	6.09684e9	0.235014
$946$	9.77392e9	0.375362
$947$	−3.84595e10	−1.47156	−0.735781	−	0.677219i	$-0.763185\pi$
$947$	−3.84595e10	−1.47156	−0.735781	+	0.677219i	$0.763185\pi$
$948$	3.86365e8	0.0147288
$949$	−1.18469e10	−0.449961
$950$	4.09680e8	0.0155029
$951$	3.42688e9	0.129201
$952$	4.39240e9	0.164996
$953$	8.66853e9	0.324429	0.162215	−	0.986755i	$-0.448136\pi$
$953$	8.66853e9	0.324429	0.162215	+	0.986755i	$0.448136\pi$
$954$	−1.17370e10	−0.437659
$955$	−2.58227e10	−0.959377
$956$	3.22647e10	1.19433
$957$	−2.94147e9	−0.108486
$958$	4.40115e9	0.161729
$959$	5.47601e9	0.200493
$960$	2.04940e9	0.0747612
$961$	−2.46850e10	−0.897226
$962$	−2.35676e9	−0.0853498
$963$	3.35218e10	1.20958
$964$	−1.47576e10	−0.530573
$965$	2.25374e10	0.807344
$966$	3.83688e7	0.00136949
$967$	2.35896e10	0.838935	0.419467	−	0.907770i	$-0.362217\pi$
$967$	2.35896e10	0.838935	0.419467	+	0.907770i	$0.362217\pi$
$968$	−2.49333e9	−0.0883519
$969$	−3.60192e8	−0.0127175
$970$	1.20198e10	0.422859
$971$	−3.04851e9	−0.106861	−0.0534306	−	0.998572i	$-0.517016\pi$
$971$	−3.04851e9	−0.106861	−0.0534306	+	0.998572i	$0.517016\pi$
$972$	1.22590e10	0.428179
$973$	4.27695e10	1.48847
$974$	3.29389e9	0.114223
$975$	−1.99709e9	−0.0690052
$976$	−1.55396e10	−0.535014
$977$	−7.94635e9	−0.272607	−0.136303	−	0.990667i	$-0.543522\pi$
$977$	−7.94635e9	−0.272607	−0.136303	+	0.990667i	$0.543522\pi$
$978$	−9.30543e8	−0.0318090
$979$	−3.34022e10	−1.13772
$980$	6.71355e9	0.227856
$981$	4.08534e10	1.38161
$982$	5.79491e9	0.195279
$983$	2.91417e10	0.978537	0.489269	−	0.872133i	$-0.337264\pi$
$983$	2.91417e10	0.978537	0.489269	+	0.872133i	$0.337264\pi$
$984$	2.40111e9	0.0803394
$985$	−4.67427e9	−0.155843
$986$	1.91415e9	0.0635926
$987$	−5.99182e9	−0.198357
$988$	−1.11560e10	−0.368011
$989$	1.26808e9	0.0416831
$990$	8.09347e9	0.265101
$991$	3.10660e10	1.01397	0.506987	−	0.861953i	$-0.330759\pi$
$991$	3.10660e10	1.01397	0.506987	+	0.861953i	$0.330759\pi$
$992$	7.62879e9	0.248122
$993$	3.62124e9	0.117364
$994$	−9.67611e9	−0.312499
$995$	−3.26085e10	−1.04942
$996$	−2.00969e9	−0.0644499
$997$	−1.05277e10	−0.336434	−0.168217	−	0.985750i	$-0.553801\pi$
$997$	−1.05277e10	−0.336434	−0.168217	+	0.985750i	$0.553801\pi$
$998$	1.44978e10	0.461684
$999$	1.65024e9	0.0523681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.a.a.1.6	✓	10
3.2	odd	2		333.8.a.c.1.5		10
4.3	odd	2		592.8.a.f.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.a.a.1.6	✓	10	1.1	even	1	trivial
333.8.a.c.1.5		10	3.2	odd	2
592.8.a.f.1.5		10	4.3	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.a (trivial)

\(f(q)\)	\(=\)	\(q+3.27803 q^{2} -7.54665 q^{3} -117.254 q^{4} +243.887 q^{5} -24.7382 q^{6} +767.318 q^{7} -803.953 q^{8} -2130.05 q^{9} +O(q^{10})\)	\(q+3.27803 q^{2} -7.54665 q^{3} -117.254 q^{4} +243.887 q^{5} -24.7382 q^{6} +767.318 q^{7} -803.953 q^{8} -2130.05 q^{9} +799.468 q^{10} -4752.74 q^{11} +884.879 q^{12} -14193.7 q^{13} +2515.30 q^{14} -1840.53 q^{15} +12373.2 q^{16} -7120.26 q^{17} -6982.37 q^{18} -6703.23 q^{19} -28596.8 q^{20} -5790.68 q^{21} -15579.6 q^{22} -2021.32 q^{23} +6067.15 q^{24} -18644.3 q^{25} -46527.5 q^{26} +32579.2 q^{27} -89971.5 q^{28} -82009.8 q^{29} -6033.31 q^{30} +53175.0 q^{31} +143466. q^{32} +35867.2 q^{33} -23340.5 q^{34} +187139. q^{35} +249758. q^{36} +50653.0 q^{37} -21973.4 q^{38} +107115. q^{39} -196073. q^{40} +395755. q^{41} -18982.1 q^{42} -627353. q^{43} +557280. q^{44} -519490. q^{45} -6625.95 q^{46} +1.03473e6 q^{47} -93376.1 q^{48} -234766. q^{49} -61116.8 q^{50} +53734.1 q^{51} +1.66428e6 q^{52} +1.68094e6 q^{53} +106796. q^{54} -1.15913e6 q^{55} -616887. q^{56} +50586.9 q^{57} -268831. q^{58} -2.56307e6 q^{59} +215810. q^{60} -1.25591e6 q^{61} +174309. q^{62} -1.63442e6 q^{63} -1.11348e6 q^{64} -3.46166e6 q^{65} +117574. q^{66} +1.77215e6 q^{67} +834883. q^{68} +15254.2 q^{69} +613447. q^{70} -3.84691e6 q^{71} +1.71246e6 q^{72} +834660. q^{73} +166042. q^{74} +140702. q^{75} +785984. q^{76} -3.64686e6 q^{77} +351127. q^{78} +436630. q^{79} +3.01766e6 q^{80} +4.41255e6 q^{81} +1.29730e6 q^{82} -2.27115e6 q^{83} +678983. q^{84} -1.73654e6 q^{85} -2.05648e6 q^{86} +618900. q^{87} +3.82098e6 q^{88} +7.02798e6 q^{89} -1.70291e6 q^{90} -1.08911e7 q^{91} +237009. q^{92} -401293. q^{93} +3.39189e6 q^{94} -1.63483e6 q^{95} -1.08269e6 q^{96} +1.50347e7 q^{97} -769570. q^{98} +1.01236e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 24 q^{2} - 95 q^{3} + 602 q^{4} - 624 q^{5} - 777 q^{6} - 501 q^{7} - 3810 q^{8} + 6181 q^{9}+O(q^{10}) \) 10 * q - 24 * q^2 - 95 * q^3 + 602 * q^4 - 624 * q^5 - 777 * q^6 - 501 * q^7 - 3810 * q^8 + 6181 * q^9	\( 10 q - 24 q^{2} - 95 q^{3} + 602 q^{4} - 624 q^{5} - 777 q^{6} - 501 q^{7} - 3810 q^{8} + 6181 q^{9} + 8595 q^{10} - 8325 q^{11} - 19645 q^{12} - 17108 q^{13} - 65418 q^{14} - 55756 q^{15} - 56998 q^{16} - 72924 q^{17} - 156165 q^{18} - 47786 q^{19} - 226209 q^{20} - 65313 q^{21} - 138973 q^{22} - 148086 q^{23} - 68031 q^{24} + 108736 q^{25} - 60237 q^{26} - 87329 q^{27} + 219974 q^{28} - 164154 q^{29} + 78864 q^{30} - 189560 q^{31} - 30114 q^{32} - 179737 q^{33} + 532624 q^{34} - 705156 q^{35} + 1923693 q^{36} + 506530 q^{37} + 1256412 q^{38} + 1322800 q^{39} + 2936777 q^{40} + 814263 q^{41} + 3415826 q^{42} - 590572 q^{43} + 610311 q^{44} - 250574 q^{45} + 2903897 q^{46} - 1534185 q^{47} + 2082419 q^{48} - 214337 q^{49} - 2313525 q^{50} + 722138 q^{51} + 149159 q^{52} - 2518209 q^{53} + 1095990 q^{54} - 3482468 q^{55} - 3645834 q^{56} - 9225638 q^{57} + 5626023 q^{58} - 5894748 q^{59} - 1289832 q^{60} - 2569480 q^{61} - 863697 q^{62} - 2836574 q^{63} - 4093742 q^{64} - 6774600 q^{65} + 17251556 q^{66} - 6983232 q^{67} - 8114412 q^{68} - 11557564 q^{69} + 8982748 q^{70} - 5013963 q^{71} - 7567137 q^{72} - 11678449 q^{73} - 1215672 q^{74} - 6586901 q^{75} + 4912252 q^{76} + 1333113 q^{77} - 7352119 q^{78} - 3853378 q^{79} - 11975661 q^{80} - 7381718 q^{81} + 564093 q^{82} - 15677895 q^{83} + 4781738 q^{84} + 11909320 q^{85} + 34274010 q^{86} - 12611710 q^{87} + 14448317 q^{88} - 25836 q^{89} + 64591590 q^{90} + 12335744 q^{91} + 7579845 q^{92} + 4592632 q^{93} + 26251718 q^{94} + 11723664 q^{95} + 42299113 q^{96} + 4648834 q^{97} + 15230184 q^{98} - 16904018 q^{99}+O(q^{100}) \) 10 * q - 24 * q^2 - 95 * q^3 + 602 * q^4 - 624 * q^5 - 777 * q^6 - 501 * q^7 - 3810 * q^8 + 6181 * q^9 + 8595 * q^10 - 8325 * q^11 - 19645 * q^12 - 17108 * q^13 - 65418 * q^14 - 55756 * q^15 - 56998 * q^16 - 72924 * q^17 - 156165 * q^18 - 47786 * q^19 - 226209 * q^20 - 65313 * q^21 - 138973 * q^22 - 148086 * q^23 - 68031 * q^24 + 108736 * q^25 - 60237 * q^26 - 87329 * q^27 + 219974 * q^28 - 164154 * q^29 + 78864 * q^30 - 189560 * q^31 - 30114 * q^32 - 179737 * q^33 + 532624 * q^34 - 705156 * q^35 + 1923693 * q^36 + 506530 * q^37 + 1256412 * q^38 + 1322800 * q^39 + 2936777 * q^40 + 814263 * q^41 + 3415826 * q^42 - 590572 * q^43 + 610311 * q^44 - 250574 * q^45 + 2903897 * q^46 - 1534185 * q^47 + 2082419 * q^48 - 214337 * q^49 - 2313525 * q^50 + 722138 * q^51 + 149159 * q^52 - 2518209 * q^53 + 1095990 * q^54 - 3482468 * q^55 - 3645834 * q^56 - 9225638 * q^57 + 5626023 * q^58 - 5894748 * q^59 - 1289832 * q^60 - 2569480 * q^61 - 863697 * q^62 - 2836574 * q^63 - 4093742 * q^64 - 6774600 * q^65 + 17251556 * q^66 - 6983232 * q^67 - 8114412 * q^68 - 11557564 * q^69 + 8982748 * q^70 - 5013963 * q^71 - 7567137 * q^72 - 11678449 * q^73 - 1215672 * q^74 - 6586901 * q^75 + 4912252 * q^76 + 1333113 * q^77 - 7352119 * q^78 - 3853378 * q^79 - 11975661 * q^80 - 7381718 * q^81 + 564093 * q^82 - 15677895 * q^83 + 4781738 * q^84 + 11909320 * q^85 + 34274010 * q^86 - 12611710 * q^87 + 14448317 * q^88 - 25836 * q^89 + 64591590 * q^90 + 12335744 * q^91 + 7579845 * q^92 + 4592632 * q^93 + 26251718 * q^94 + 11723664 * q^95 + 42299113 * q^96 + 4648834 * q^97 + 15230184 * q^98 - 16904018 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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