LMFDB - Embedded newform 37.8.a.a.1.3

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			1.3
Root			$10.5631$ 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)

$f(q)$	$=$	$q-12.5631 q^{2} -77.5936 q^{3} +29.8308 q^{4} +318.311 q^{5} +974.814 q^{6} -75.8943 q^{7} +1233.31 q^{8} +3833.76 q^{9} +O(q^{10})$	\(q-12.5631 q^{2} -77.5936 q^{3} +29.8308 q^{4} +318.311 q^{5} +974.814 q^{6} -75.8943 q^{7} +1233.31 q^{8} +3833.76 q^{9} -3998.96 q^{10} -266.520 q^{11} -2314.68 q^{12} -8015.96 q^{13} +953.465 q^{14} -24698.9 q^{15} -19312.5 q^{16} +35262.9 q^{17} -48163.9 q^{18} +9445.22 q^{19} +9495.47 q^{20} +5888.91 q^{21} +3348.31 q^{22} -83781.9 q^{23} -95696.7 q^{24} +23196.7 q^{25} +100705. q^{26} -127778. q^{27} -2263.99 q^{28} -73682.7 q^{29} +310294. q^{30} +102372. q^{31} +84760.7 q^{32} +20680.3 q^{33} -443011. q^{34} -24158.0 q^{35} +114364. q^{36} +50653.0 q^{37} -118661. q^{38} +621987. q^{39} +392575. q^{40} +478123. q^{41} -73982.8 q^{42} -555632. q^{43} -7950.51 q^{44} +1.22033e6 q^{45} +1.05256e6 q^{46} -1.25895e6 q^{47} +1.49852e6 q^{48} -817783. q^{49} -291422. q^{50} -2.73618e6 q^{51} -239123. q^{52} -1.59456e6 q^{53} +1.60529e6 q^{54} -84836.2 q^{55} -93600.9 q^{56} -732889. q^{57} +925681. q^{58} +613337. q^{59} -736787. q^{60} +822380. q^{61} -1.28611e6 q^{62} -290961. q^{63} +1.40714e6 q^{64} -2.55157e6 q^{65} -259808. q^{66} -4.31951e6 q^{67} +1.05192e6 q^{68} +6.50094e6 q^{69} +303498. q^{70} -730666. q^{71} +4.72821e6 q^{72} +930505. q^{73} -636357. q^{74} -1.79992e6 q^{75} +281759. q^{76} +20227.4 q^{77} -7.81407e6 q^{78} +3.74490e6 q^{79} -6.14737e6 q^{80} +1.53033e6 q^{81} -6.00669e6 q^{82} -6.81217e6 q^{83} +175671. q^{84} +1.12246e7 q^{85} +6.98045e6 q^{86} +5.71731e6 q^{87} -328701. q^{88} -1.08105e7 q^{89} -1.53311e7 q^{90} +608365. q^{91} -2.49928e6 q^{92} -7.94340e6 q^{93} +1.58163e7 q^{94} +3.00652e6 q^{95} -6.57688e6 q^{96} +1.09805e7 q^{97} +1.02739e7 q^{98} -1.02178e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−12.5631	−1.11043	−0.555215	−	0.831707i	$-0.687364\pi$
$2$	−12.5631	−1.11043	−0.555215	+	0.831707i	$0.687364\pi$
$3$	−77.5936	−1.65921	−0.829605	−	0.558351i	$-0.811434\pi$
$3$	−77.5936	−1.65921	−0.829605	+	0.558351i	$0.811434\pi$
$4$	29.8308	0.233053
$5$	318.311	1.13882	0.569412	−	0.822053i	$-0.307171\pi$
$5$	318.311	1.13882	0.569412	+	0.822053i	$0.307171\pi$
$6$	974.814	1.84244
$7$	−75.8943	−0.0836307	−0.0418154	−	0.999125i	$-0.513314\pi$
$7$	−75.8943	−0.0836307	−0.0418154	+	0.999125i	$0.513314\pi$
$8$	1233.31	0.851640
$9$	3833.76	1.75298
$10$	−3998.96	−1.26458
$11$	−266.520	−0.0603748	−0.0301874	−	0.999544i	$-0.509610\pi$
$11$	−266.520	−0.0603748	−0.0301874	+	0.999544i	$0.509610\pi$
$12$	−2314.68	−0.386684
$13$	−8015.96	−1.01194	−0.505969	−	0.862552i	$-0.668865\pi$
$13$	−8015.96	−1.01194	−0.505969	+	0.862552i	$0.668865\pi$
$14$	953.465	0.0928660
$15$	−24698.9	−1.88955
$16$	−19312.5	−1.17874
$17$	35262.9	1.74079	0.870396	−	0.492352i	$-0.163863\pi$
$17$	35262.9	1.74079	0.870396	+	0.492352i	$0.163863\pi$
$18$	−48163.9	−1.94656
$19$	9445.22	0.315918	0.157959	−	0.987446i	$-0.449509\pi$
$19$	9445.22	0.315918	0.157959	+	0.987446i	$0.449509\pi$
$20$	9495.47	0.265406
$21$	5888.91	0.138761
$22$	3348.31	0.0670419
$23$	−83781.9	−1.43583	−0.717915	−	0.696131i	$-0.754903\pi$
$23$	−83781.9	−1.43583	−0.717915	+	0.696131i	$0.754903\pi$
$24$	−95696.7	−1.41305
$25$	23196.7	0.296918
$26$	100705.	1.12369
$27$	−127778.	−1.24935
$28$	−2263.99	−0.0194904
$29$	−73682.7	−0.561013	−0.280506	−	0.959852i	$-0.590502\pi$
$29$	−73682.7	−0.561013	−0.280506	+	0.959852i	$0.590502\pi$
$30$	310294.	2.09821
$31$	102372.	0.617184	0.308592	−	0.951195i	$-0.400142\pi$
$31$	102372.	0.617184	0.308592	+	0.951195i	$0.400142\pi$
$32$	84760.7	0.457267
$33$	20680.3	0.100174
$34$	−443011.	−1.93303
$35$	−24158.0	−0.0952406
$36$	114364.	0.408537
$37$	50653.0	0.164399
$37$	50653.0	0.164399
$38$	−118661.	−0.350805
$39$	621987.	1.67902
$40$	392575.	0.969868
$41$	478123.	1.08342	0.541709	−	0.840566i	$-0.317778\pi$
$41$	478123.	1.08342	0.541709	+	0.840566i	$0.317778\pi$
$42$	−73982.8	−0.154084
$43$	−555632.	−1.06573	−0.532866	−	0.846200i	$-0.678885\pi$
$43$	−555632.	−1.06573	−0.532866	+	0.846200i	$0.678885\pi$
$44$	−7950.51	−0.0140705
$45$	1.22033e6	1.99633
$46$	1.05256e6	1.59439
$47$	−1.25895e6	−1.76875	−0.884373	−	0.466781i	$-0.845414\pi$
$47$	−1.25895e6	−1.76875	−0.884373	+	0.466781i	$0.845414\pi$
$48$	1.49852e6	1.95578
$49$	−817783.	−0.993006
$50$	−291422.	−0.329707
$51$	−2.73618e6	−2.88834
$52$	−239123.	−0.235835
$53$	−1.59456e6	−1.47121	−0.735605	−	0.677411i	$-0.763102\pi$
$53$	−1.59456e6	−1.47121	−0.735605	+	0.677411i	$0.763102\pi$
$54$	1.60529e6	1.38731
$55$	−84836.2	−0.0687562
$56$	−93600.9	−0.0712233
$57$	−732889.	−0.524175
$58$	925681.	0.622965
$59$	613337.	0.388792	0.194396	−	0.980923i	$-0.437725\pi$
$59$	613337.	0.388792	0.194396	+	0.980923i	$0.437725\pi$
$60$	−736787.	−0.440365
$61$	822380.	0.463893	0.231947	−	0.972729i	$-0.425491\pi$
$61$	822380.	0.463893	0.231947	+	0.972729i	$0.425491\pi$
$62$	−1.28611e6	−0.685339
$63$	−290961.	−0.146603
$64$	1.40714e6	0.670977
$65$	−2.55157e6	−1.15242
$66$	−259808.	−0.111237
$67$	−4.31951e6	−1.75458	−0.877289	−	0.479963i	$-0.840650\pi$
$67$	−4.31951e6	−1.75458	−0.877289	+	0.479963i	$0.840650\pi$
$68$	1.05192e6	0.405697
$69$	6.50094e6	2.38234
$70$	303498.	0.105758
$71$	−730666.	−0.242278	−0.121139	−	0.992636i	$-0.538655\pi$
$71$	−730666.	−0.242278	−0.121139	+	0.992636i	$0.538655\pi$
$72$	4.72821e6	1.49291
$73$	930505.	0.279955	0.139978	−	0.990155i	$-0.455297\pi$
$73$	930505.	0.279955	0.139978	+	0.990155i	$0.455297\pi$
$74$	−636357.	−0.182553
$75$	−1.79992e6	−0.492649
$76$	281759.	0.0736257
$77$	20227.4	0.00504919
$78$	−7.81407e6	−1.86443
$79$	3.74490e6	0.854565	0.427282	−	0.904118i	$-0.359471\pi$
$79$	3.74490e6	0.854565	0.427282	+	0.904118i	$0.359471\pi$
$80$	−6.14737e6	−1.34238
$81$	1.53033e6	0.319955
$82$	−6.00669e6	−1.20306
$83$	−6.81217e6	−1.30771	−0.653856	−	0.756619i	$-0.726850\pi$
$83$	−6.81217e6	−1.30771	−0.653856	+	0.756619i	$0.726850\pi$
$84$	175671.	0.0323387
$85$	1.12246e7	1.98246
$86$	6.98045e6	1.18342
$87$	5.71731e6	0.930838
$88$	−328701.	−0.0514176
$89$	−1.08105e7	−1.62547	−0.812737	−	0.582630i	$-0.802024\pi$
$89$	−1.08105e7	−1.62547	−0.812737	+	0.582630i	$0.802024\pi$
$90$	−1.53311e7	−2.21679
$91$	608365.	0.0846291
$92$	−2.49928e6	−0.334625
$93$	−7.94340e6	−1.02404
$94$	1.58163e7	1.96407
$95$	3.00652e6	0.359775
$96$	−6.57688e6	−0.758701
$97$	1.09805e7	1.22158	0.610791	−	0.791792i	$-0.290852\pi$
$97$	1.09805e7	1.22158	0.610791	+	0.791792i	$0.290852\pi$
$98$	1.02739e7	1.10266
$99$	−1.02178e6	−0.105836
$100$	691977.	0.0691977
$101$	6.48136e6	0.625952	0.312976	−	0.949761i	$-0.398674\pi$
$101$	6.48136e6	0.625952	0.312976	+	0.949761i	$0.398674\pi$
$102$	3.43748e7	3.20730
$103$	−4.93356e6	−0.444867	−0.222434	−	0.974948i	$-0.571400\pi$
$103$	−4.93356e6	−0.444867	−0.222434	+	0.974948i	$0.571400\pi$
$104$	−9.88614e6	−0.861807
$105$	1.87450e6	0.158024
$106$	2.00325e7	1.63368
$107$	2.58234e6	0.203784	0.101892	−	0.994795i	$-0.467510\pi$
$107$	2.58234e6	0.203784	0.101892	+	0.994795i	$0.467510\pi$
$108$	−3.81173e6	−0.291165
$109$	1.87769e7	1.38877	0.694385	−	0.719604i	$-0.255677\pi$
$109$	1.87769e7	1.38877	0.694385	+	0.719604i	$0.255677\pi$
$110$	1.06580e6	0.0763489
$111$	−3.93035e6	−0.272772
$112$	1.46571e6	0.0985788
$113$	2.21240e7	1.44241	0.721205	−	0.692721i	$-0.243588\pi$
$113$	2.21240e7	1.44241	0.721205	+	0.692721i	$0.243588\pi$
$114$	9.20733e6	0.582059
$115$	−2.66687e7	−1.63516
$116$	−2.19802e6	−0.130746
$117$	−3.07313e7	−1.77390
$118$	−7.70539e6	−0.431726
$119$	−2.67625e6	−0.145584
$120$	−3.04613e7	−1.60921
$121$	−1.94161e7	−0.996355
$122$	−1.03316e7	−0.515121
$123$	−3.70993e7	−1.79762
$124$	3.05384e6	0.143837
$125$	−1.74843e7	−0.800686
$126$	3.65536e6	0.162792
$127$	−412831.	−0.0178838	−0.00894190	−	0.999960i	$-0.502846\pi$
$127$	−412831.	−0.0178838	−0.00894190	+	0.999960i	$0.502846\pi$
$128$	−2.85274e7	−1.20234
$129$	4.31135e7	1.76827
$130$	3.20555e7	1.27968
$131$	−2.29312e7	−0.891204	−0.445602	−	0.895231i	$-0.647010\pi$
$131$	−2.29312e7	−0.891204	−0.445602	+	0.895231i	$0.647010\pi$
$132$	616909.	0.0233460
$133$	−716838.	−0.0264205
$134$	5.42663e7	1.94833
$135$	−4.06732e7	−1.42279
$136$	4.34900e7	1.48253
$137$	−3.44296e7	−1.14396	−0.571979	−	0.820268i	$-0.693824\pi$
$137$	−3.44296e7	−1.14396	−0.571979	+	0.820268i	$0.693824\pi$
$138$	−8.16718e7	−2.64542
$139$	−2.33834e7	−0.738509	−0.369255	−	0.929328i	$-0.620387\pi$
$139$	−2.33834e7	−0.738509	−0.369255	+	0.929328i	$0.620387\pi$
$140$	−720651.	−0.0221961
$141$	9.76863e7	2.93472
$142$	9.17941e6	0.269033
$143$	2.13641e6	0.0610955
$144$	−7.40394e7	−2.06630
$145$	−2.34540e7	−0.638894
$146$	−1.16900e7	−0.310870
$147$	6.34547e7	1.64761
$148$	1.51102e6	0.0383137
$149$	−5.58296e7	−1.38265	−0.691326	−	0.722543i	$-0.742973\pi$
$149$	−5.58296e7	−1.38265	−0.691326	+	0.722543i	$0.742973\pi$
$150$	2.26125e7	0.547052
$151$	−2.06455e7	−0.487984	−0.243992	−	0.969777i	$-0.578457\pi$
$151$	−2.06455e7	−0.487984	−0.243992	+	0.969777i	$0.578457\pi$
$152$	1.16489e7	0.269049
$153$	1.35190e8	3.05157
$154$	−254118.	−0.00560677
$155$	3.25861e7	0.702863
$156$	1.85544e7	0.391300
$157$	−5.93512e7	−1.22400	−0.611999	−	0.790859i	$-0.709634\pi$
$157$	−5.93512e7	−1.22400	−0.611999	+	0.790859i	$0.709634\pi$
$158$	−4.70474e7	−0.948934
$159$	1.23727e8	2.44105
$160$	2.69802e7	0.520746
$161$	6.35857e6	0.120079
$162$	−1.92257e7	−0.355287
$163$	−2.91078e6	−0.0526445	−0.0263223	−	0.999654i	$-0.508380\pi$
$163$	−2.91078e6	−0.0526445	−0.0263223	+	0.999654i	$0.508380\pi$
$164$	1.42628e7	0.252494
$165$	6.58275e6	0.114081
$166$	8.55818e7	1.45212
$167$	4.28810e7	0.712455	0.356227	−	0.934399i	$-0.384063\pi$
$167$	4.28810e7	0.712455	0.356227	+	0.934399i	$0.384063\pi$
$168$	7.26283e6	0.118174
$169$	1.50709e6	0.0240179
$170$	−1.41015e8	−2.20138
$171$	3.62108e7	0.553798
$172$	−1.65750e7	−0.248372
$173$	−1.18491e8	−1.73990	−0.869951	−	0.493138i	$-0.835850\pi$
$173$	−1.18491e8	−1.73990	−0.869951	+	0.493138i	$0.835850\pi$
$174$	−7.18269e7	−1.03363
$175$	−1.76050e6	−0.0248315
$176$	5.14716e6	0.0711662
$177$	−4.75910e7	−0.645087
$178$	1.35813e8	1.80498
$179$	9.78313e7	1.27495	0.637474	−	0.770472i	$-0.279980\pi$
$179$	9.78313e7	1.27495	0.637474	+	0.770472i	$0.279980\pi$
$180$	3.64034e7	0.465252
$181$	3.71610e7	0.465814	0.232907	−	0.972499i	$-0.425176\pi$
$181$	3.71610e7	0.465814	0.232907	+	0.972499i	$0.425176\pi$
$182$	−7.64294e6	−0.0939746
$183$	−6.38114e7	−0.769697
$184$	−1.03329e8	−1.22281
$185$	1.61234e7	0.187221
$186$	9.97935e7	1.13712
$187$	−9.39828e6	−0.105100
$188$	−3.75555e7	−0.412212
$189$	9.69764e6	0.104484
$190$	−3.77711e7	−0.399505
$191$	−4.63328e6	−0.0481141	−0.0240570	−	0.999711i	$-0.507658\pi$
$191$	−4.63328e6	−0.0481141	−0.0240570	+	0.999711i	$0.507658\pi$
$192$	−1.09185e8	−1.11329
$193$	−1.17961e8	−1.18111	−0.590553	−	0.806999i	$-0.701090\pi$
$193$	−1.17961e8	−1.18111	−0.590553	+	0.806999i	$0.701090\pi$
$194$	−1.37949e8	−1.35648
$195$	1.97985e8	1.91210
$196$	−2.43951e7	−0.231423
$197$	1.13166e8	1.05459	0.527295	−	0.849682i	$-0.323206\pi$
$197$	1.13166e8	1.05459	0.527295	+	0.849682i	$0.323206\pi$
$198$	1.28366e7	0.117523
$199$	2.33851e6	0.0210355	0.0105178	−	0.999945i	$-0.496652\pi$
$199$	2.33851e6	0.0210355	0.0105178	+	0.999945i	$0.496652\pi$
$200$	2.86087e7	0.252867
$201$	3.35166e8	2.91121
$202$	−8.14258e7	−0.695076
$203$	5.59210e6	0.0469179
$204$	−8.16224e7	−0.673137
$205$	1.52192e8	1.23382
$206$	6.19807e7	0.493993
$207$	−3.21200e8	−2.51698
$208$	1.54808e8	1.19281
$209$	−2.51734e6	−0.0190735
$210$	−2.35495e7	−0.175475
$211$	−1.43899e8	−1.05455	−0.527277	−	0.849693i	$-0.676787\pi$
$211$	−1.43899e8	−1.05455	−0.527277	+	0.849693i	$0.676787\pi$
$212$	−4.75670e7	−0.342870
$213$	5.66950e7	0.401991
$214$	−3.24421e7	−0.226288
$215$	−1.76864e8	−1.21368
$216$	−1.57590e8	−1.06400
$217$	−7.76944e6	−0.0516155
$218$	−2.35895e8	−1.54213
$219$	−7.22012e7	−0.464504
$220$	−2.53073e6	−0.0160239
$221$	−2.82666e8	−1.76157
$222$	4.93772e7	0.302895
$223$	3.31577e7	0.200225	0.100112	−	0.994976i	$-0.468080\pi$
$223$	3.31577e7	0.200225	0.100112	+	0.994976i	$0.468080\pi$
$224$	−6.43285e6	−0.0382415
$225$	8.89308e7	0.520491
$226$	−2.77945e8	−1.60170
$227$	1.90467e8	1.08076	0.540381	−	0.841420i	$-0.318280\pi$
$227$	1.90467e8	1.08076	0.540381	+	0.841420i	$0.318280\pi$
$228$	−2.18627e7	−0.122161
$229$	2.59140e8	1.42597	0.712986	−	0.701178i	$-0.247342\pi$
$229$	2.59140e8	1.42597	0.712986	+	0.701178i	$0.247342\pi$
$230$	3.35041e8	1.81573
$231$	−1.56951e6	−0.00837766
$232$	−9.08734e7	−0.477781
$233$	−4.29347e7	−0.222363	−0.111182	−	0.993800i	$-0.535463\pi$
$233$	−4.29347e7	−0.222363	−0.111182	+	0.993800i	$0.535463\pi$
$234$	3.86080e8	1.96980
$235$	−4.00737e8	−2.01429
$236$	1.82963e7	0.0906091
$237$	−2.90580e8	−1.41790
$238$	3.36220e7	0.161660
$239$	3.02972e8	1.43552	0.717760	−	0.696291i	$-0.245168\pi$
$239$	3.02972e8	1.43552	0.717760	+	0.696291i	$0.245168\pi$
$240$	4.76996e8	2.22728
$241$	−1.89991e8	−0.874327	−0.437164	−	0.899382i	$-0.644017\pi$
$241$	−1.89991e8	−0.874327	−0.437164	+	0.899382i	$0.644017\pi$
$242$	2.43926e8	1.10638
$243$	1.60707e8	0.718477
$244$	2.45323e7	0.108112
$245$	−2.60309e8	−1.13086
$246$	4.66081e8	1.99613
$247$	−7.57125e7	−0.319690
$248$	1.26256e8	0.525619
$249$	5.28580e8	2.16977
$250$	2.19656e8	0.889105
$251$	−4.40467e8	−1.75815	−0.879074	−	0.476685i	$-0.841838\pi$
$251$	−4.40467e8	−1.75815	−0.879074	+	0.476685i	$0.841838\pi$
$252$	−8.67959e6	−0.0341663
$253$	2.23296e7	0.0866879
$254$	5.18643e6	0.0198587
$255$	−8.70954e8	−3.28931
$256$	1.78278e8	0.664136
$257$	−4.06176e8	−1.49262	−0.746308	−	0.665601i	$-0.768175\pi$
$257$	−4.06176e8	−1.49262	−0.746308	+	0.665601i	$0.768175\pi$
$258$	−5.41638e8	−1.96354
$259$	−3.84427e6	−0.0137488
$260$	−7.61153e7	−0.268575
$261$	−2.82482e8	−0.983443
$262$	2.88086e8	0.989619
$263$	−2.25674e8	−0.764955	−0.382477	−	0.923965i	$-0.624929\pi$
$263$	−2.25674e8	−0.764955	−0.382477	+	0.923965i	$0.624929\pi$
$264$	2.55051e7	0.0853126
$265$	−5.07565e8	−1.67545
$266$	9.00569e6	0.0293381
$267$	8.38824e8	2.69700
$268$	−1.28854e8	−0.408910
$269$	5.18788e8	1.62501	0.812507	−	0.582952i	$-0.198102\pi$
$269$	5.18788e8	1.62501	0.812507	+	0.582952i	$0.198102\pi$
$270$	5.10980e8	1.57991
$271$	3.93988e8	1.20251	0.601257	−	0.799056i	$-0.294667\pi$
$271$	3.93988e8	1.20251	0.601257	+	0.799056i	$0.294667\pi$
$272$	−6.81014e8	−2.05194
$273$	−4.72052e7	−0.140417
$274$	4.32542e8	1.27029
$275$	−6.18240e6	−0.0179264
$276$	1.93928e8	0.555213
$277$	8.57998e6	0.0242553	0.0121277	−	0.999926i	$-0.496140\pi$
$277$	8.57998e6	0.0242553	0.0121277	+	0.999926i	$0.496140\pi$
$278$	2.93768e8	0.820063
$279$	3.92470e8	1.08191
$280$	−2.97942e7	−0.0811107
$281$	5.91771e8	1.59104	0.795521	−	0.605926i	$-0.207197\pi$
$281$	5.91771e8	1.59104	0.795521	+	0.605926i	$0.207197\pi$
$282$	−1.22724e9	−3.25880
$283$	2.84279e8	0.745578	0.372789	−	0.927916i	$-0.378402\pi$
$283$	2.84279e8	0.745578	0.372789	+	0.927916i	$0.378402\pi$
$284$	−2.17964e7	−0.0564637
$285$	−2.33286e8	−0.596942
$286$	−2.68399e7	−0.0678423
$287$	−3.62868e7	−0.0906070
$288$	3.24952e8	0.801578
$289$	8.33135e8	2.03036
$290$	2.94654e8	0.709447
$291$	−8.52019e8	−2.02686
$292$	2.77577e7	0.0652444
$293$	−4.19161e8	−0.973519	−0.486760	−	0.873536i	$-0.661821\pi$
$293$	−4.19161e8	−0.973519	−0.486760	+	0.873536i	$0.661821\pi$
$294$	−7.97186e8	−1.82955
$295$	1.95232e8	0.442765
$296$	6.24707e7	0.140009
$297$	3.40555e7	0.0754292
$298$	7.01392e8	1.53534
$299$	6.71593e8	1.45297
$300$	−5.36930e7	−0.114814
$301$	4.21693e7	0.0891279
$302$	2.59371e8	0.541872
$303$	−5.02912e8	−1.03859
$304$	−1.82411e8	−0.372385
$305$	2.61772e8	0.528292
$306$	−1.69840e9	−3.38856
$307$	4.11092e8	0.810876	0.405438	−	0.914123i	$-0.367119\pi$
$307$	4.11092e8	0.810876	0.405438	+	0.914123i	$0.367119\pi$
$308$	603398.	0.00117673
$309$	3.82813e8	0.738128
$310$	−4.09381e8	−0.780480
$311$	−9.69453e8	−1.82753	−0.913767	−	0.406239i	$-0.866840\pi$
$311$	−9.69453e8	−1.82753	−0.913767	+	0.406239i	$0.866840\pi$
$312$	7.67101e8	1.42992
$313$	−3.22228e8	−0.593961	−0.296981	−	0.954884i	$-0.595980\pi$
$313$	−3.22228e8	−0.593961	−0.296981	+	0.954884i	$0.595980\pi$
$314$	7.45633e8	1.35916
$315$	−9.26159e7	−0.166955
$316$	1.11713e8	0.199159
$317$	−1.16615e8	−0.205612	−0.102806	−	0.994701i	$-0.532782\pi$
$317$	−1.16615e8	−0.205612	−0.102806	+	0.994701i	$0.532782\pi$
$318$	−1.55440e9	−2.71061
$319$	1.96379e7	0.0338710
$320$	4.47908e8	0.764124
$321$	−2.00373e8	−0.338121
$322$	−7.98832e7	−0.133340
$323$	3.33066e8	0.549948
$324$	4.56511e7	0.0745665
$325$	−1.85944e8	−0.300463
$326$	3.65684e7	0.0584580
$327$	−1.45696e9	−2.30426
$328$	5.89672e8	0.922682
$329$	9.55470e7	0.147921
$330$	−8.26995e7	−0.126679
$331$	−2.63150e8	−0.398846	−0.199423	−	0.979914i	$-0.563907\pi$
$331$	−2.63150e8	−0.398846	−0.199423	+	0.979914i	$0.563907\pi$
$332$	−2.03212e8	−0.304766
$333$	1.94192e8	0.288188
$334$	−5.38717e8	−0.791131
$335$	−1.37495e9	−1.99815
$336$	−1.13729e8	−0.163563
$337$	1.77911e8	0.253219	0.126610	−	0.991953i	$-0.459590\pi$
$337$	1.77911e8	0.253219	0.126610	+	0.991953i	$0.459590\pi$
$338$	−1.89336e7	−0.0266702
$339$	−1.71668e9	−2.39326
$340$	3.34838e8	0.462018
$341$	−2.72842e7	−0.0372624
$342$	−4.54918e8	−0.614953
$343$	1.24567e8	0.166677
$344$	−6.85265e8	−0.907619
$345$	2.06932e9	2.71307
$346$	1.48861e9	1.93204
$347$	9.43151e7	0.121179	0.0605896	−	0.998163i	$-0.480702\pi$
$347$	9.43151e7	0.121179	0.0605896	+	0.998163i	$0.480702\pi$
$348$	1.70552e8	0.216935
$349$	−1.82324e8	−0.229591	−0.114795	−	0.993389i	$-0.536621\pi$
$349$	−1.82324e8	−0.229591	−0.114795	+	0.993389i	$0.536621\pi$
$350$	2.21173e7	0.0275736
$351$	1.02427e9	1.26426
$352$	−2.25904e7	−0.0276074
$353$	1.11920e9	1.35425	0.677124	−	0.735869i	$-0.263226\pi$
$353$	1.11920e9	1.35425	0.677124	+	0.735869i	$0.263226\pi$
$354$	5.97889e8	0.716323
$355$	−2.32579e8	−0.275912
$356$	−3.22486e8	−0.378822
$357$	2.07660e8	0.241554
$358$	−1.22906e9	−1.41574
$359$	2.27759e8	0.259804	0.129902	−	0.991527i	$-0.458534\pi$
$359$	2.27759e8	0.259804	0.129902	+	0.991527i	$0.458534\pi$
$360$	1.50504e9	1.70016
$361$	−8.04659e8	−0.900196
$362$	−4.66857e8	−0.517254
$363$	1.50657e9	1.65316
$364$	1.81480e7	0.0197231
$365$	2.96190e8	0.318819
$366$	8.01667e8	0.854694
$367$	3.07602e8	0.324831	0.162415	−	0.986722i	$-0.448072\pi$
$367$	3.07602e8	0.324831	0.162415	+	0.986722i	$0.448072\pi$
$368$	1.61804e9	1.69247
$369$	1.83301e9	1.89921
$370$	−2.02559e8	−0.207896
$371$	1.21018e8	0.123038
$372$	−2.36958e8	−0.238655
$373$	4.33666e8	0.432687	0.216344	−	0.976317i	$-0.430587\pi$
$373$	4.33666e8	0.432687	0.216344	+	0.976317i	$0.430587\pi$
$374$	1.18071e8	0.116706
$375$	1.35667e9	1.32851
$376$	−1.55267e9	−1.50634
$377$	5.90638e8	0.567710
$378$	−1.21832e8	−0.116022
$379$	−1.85131e9	−1.74680	−0.873398	−	0.487008i	$-0.838088\pi$
$379$	−1.85131e9	−1.74680	−0.873398	+	0.487008i	$0.838088\pi$
$380$	8.96868e7	0.0838467
$381$	3.20331e7	0.0296730
$382$	5.82083e7	0.0534273
$383$	1.78371e9	1.62229	0.811145	−	0.584844i	$-0.198844\pi$
$383$	1.78371e9	1.62229	0.811145	+	0.584844i	$0.198844\pi$
$384$	2.21354e9	1.99493
$385$	6.43858e6	0.00575013
$386$	1.48196e9	1.31154
$387$	−2.13016e9	−1.86820
$388$	3.27558e8	0.284694
$389$	−1.24758e8	−0.107460	−0.0537298	−	0.998556i	$-0.517111\pi$
$389$	−1.24758e8	−0.107460	−0.0537298	+	0.998556i	$0.517111\pi$
$390$	−2.48730e9	−2.12326
$391$	−2.95440e9	−2.49948
$392$	−1.00858e9	−0.845684
$393$	1.77931e9	1.47869
$394$	−1.42171e9	−1.17105
$395$	1.19204e9	0.973198
$396$	−3.04804e7	−0.0246654
$397$	−3.86599e8	−0.310094	−0.155047	−	0.987907i	$-0.549553\pi$
$397$	−3.86599e8	−0.310094	−0.155047	+	0.987907i	$0.549553\pi$
$398$	−2.93789e7	−0.0233585
$399$	5.56220e7	0.0438371
$400$	−4.47986e8	−0.349989
$401$	4.87329e8	0.377413	0.188707	−	0.982034i	$-0.439570\pi$
$401$	4.87329e8	0.377413	0.188707	+	0.982034i	$0.439570\pi$
$402$	−4.21072e9	−3.23270
$403$	−8.20609e8	−0.624552
$404$	1.93344e8	0.145880
$405$	4.87122e8	0.364372
$406$	−7.02539e7	−0.0520990
$407$	−1.35000e7	−0.00992556
$408$	−3.37454e9	−2.45983
$409$	9.19829e8	0.664777	0.332388	−	0.943143i	$-0.392146\pi$
$409$	9.19829e8	0.664777	0.332388	+	0.943143i	$0.392146\pi$
$410$	−1.91199e9	−1.37007
$411$	2.67152e9	1.89807
$412$	−1.47172e8	−0.103678
$413$	−4.65487e7	−0.0325149
$414$	4.03526e9	2.79493
$415$	−2.16839e9	−1.48925
$416$	−6.79438e8	−0.462725
$417$	1.81440e9	1.22534
$418$	3.16256e7	0.0211798
$419$	−1.39858e9	−0.928837	−0.464419	−	0.885616i	$-0.653737\pi$
$419$	−1.39858e9	−0.928837	−0.464419	+	0.885616i	$0.653737\pi$
$420$	5.59179e7	0.0368280
$421$	−4.15794e8	−0.271576	−0.135788	−	0.990738i	$-0.543357\pi$
$421$	−4.15794e8	−0.271576	−0.135788	+	0.990738i	$0.543357\pi$
$422$	1.80781e9	1.17101
$423$	−4.82651e9	−3.10057
$424$	−1.96658e9	−1.25294
$425$	8.17984e8	0.516873
$426$	−7.12263e8	−0.446382
$427$	−6.24139e7	−0.0387957
$428$	7.70333e7	0.0474925
$429$	−1.65772e8	−0.101370
$430$	2.22195e9	1.34770
$431$	3.45553e7	0.0207895	0.0103947	−	0.999946i	$-0.496691\pi$
$431$	3.45553e7	0.0207895	0.0103947	+	0.999946i	$0.496691\pi$
$432$	2.46771e9	1.47266
$433$	1.03991e9	0.615582	0.307791	−	0.951454i	$-0.400410\pi$
$433$	1.03991e9	0.615582	0.307791	+	0.951454i	$0.400410\pi$
$434$	9.76080e7	0.0573154
$435$	1.81988e9	1.06006
$436$	5.60129e8	0.323657
$437$	−7.91339e8	−0.453605
$438$	9.07069e8	0.515799
$439$	1.03813e9	0.585632	0.292816	−	0.956169i	$-0.405408\pi$
$439$	1.03813e9	0.585632	0.292816	+	0.956169i	$0.405408\pi$
$440$	−1.04629e8	−0.0585556
$441$	−3.13519e9	−1.74072
$442$	3.55116e9	1.95610
$443$	−7.59816e8	−0.415236	−0.207618	−	0.978210i	$-0.566571\pi$
$443$	−7.59816e8	−0.415236	−0.207618	+	0.978210i	$0.566571\pi$
$444$	−1.17245e8	−0.0635705
$445$	−3.44109e9	−1.85113
$446$	−4.16563e8	−0.222335
$447$	4.33202e9	2.29411
$448$	−1.06794e8	−0.0561143
$449$	1.39253e8	0.0726012	0.0363006	−	0.999341i	$-0.488443\pi$
$449$	1.39253e8	0.0726012	0.0363006	+	0.999341i	$0.488443\pi$
$450$	−1.11724e9	−0.577968
$451$	−1.27429e8	−0.0654111
$452$	6.59977e8	0.336159
$453$	1.60196e9	0.809668
$454$	−2.39286e9	−1.20011
$455$	1.93649e8	0.0963775
$456$	−9.03877e8	−0.446408
$457$	3.73041e9	1.82831	0.914155	−	0.405365i	$-0.132856\pi$
$457$	3.73041e9	1.82831	0.914155	+	0.405365i	$0.132856\pi$
$458$	−3.25560e9	−1.58344
$459$	−4.50584e9	−2.17486
$460$	−7.95549e8	−0.381078
$461$	−1.34927e9	−0.641423	−0.320711	−	0.947177i	$-0.603922\pi$
$461$	−1.34927e9	−0.641423	−0.320711	+	0.947177i	$0.603922\pi$
$462$	1.97179e7	0.00930280
$463$	1.56567e9	0.733104	0.366552	−	0.930398i	$-0.380538\pi$
$463$	1.56567e9	0.733104	0.366552	+	0.930398i	$0.380538\pi$
$464$	1.42300e9	0.661288
$465$	−2.52847e9	−1.16620
$466$	5.39392e8	0.246918
$467$	−3.38752e9	−1.53912	−0.769561	−	0.638574i	$-0.779525\pi$
$467$	−3.38752e9	−1.53912	−0.769561	+	0.638574i	$0.779525\pi$
$468$	−9.16739e8	−0.413414
$469$	3.27826e8	0.146737
$470$	5.03449e9	2.23673
$471$	4.60527e9	2.03087
$472$	7.56432e8	0.331111
$473$	1.48087e8	0.0643433
$474$	3.65058e9	1.57448
$475$	2.19098e8	0.0938018
$476$	−7.98348e7	−0.0339288
$477$	−6.11316e9	−2.57900
$478$	−3.80625e9	−1.59404
$479$	3.27880e9	1.36314	0.681570	−	0.731753i	$-0.261298\pi$
$479$	3.27880e9	1.36314	0.681570	+	0.731753i	$0.261298\pi$
$480$	−2.09349e9	−0.864027
$481$	−4.06032e8	−0.166362
$482$	2.38687e9	0.970879
$483$	−4.93384e8	−0.199237
$484$	−5.79199e8	−0.232204
$485$	3.49522e9	1.39117
$486$	−2.01897e9	−0.797818
$487$	1.31796e9	0.517071	0.258536	−	0.966002i	$-0.416760\pi$
$487$	1.31796e9	0.517071	0.258536	+	0.966002i	$0.416760\pi$
$488$	1.01425e9	0.395070
$489$	2.25858e8	0.0873483
$490$	3.27028e9	1.25574
$491$	−1.29994e8	−0.0495609	−0.0247805	−	0.999693i	$-0.507889\pi$
$491$	−1.29994e8	−0.0495609	−0.0247805	+	0.999693i	$0.507889\pi$
$492$	−1.10670e9	−0.418941
$493$	−2.59827e9	−0.976607
$494$	9.51182e8	0.354993
$495$	−3.25242e8	−0.120528
$496$	−1.97705e9	−0.727499
$497$	5.54534e7	0.0202619
$498$	−6.64060e9	−2.40937
$499$	−1.47680e9	−0.532072	−0.266036	−	0.963963i	$-0.585714\pi$
$499$	−1.47680e9	−0.532072	−0.266036	+	0.963963i	$0.585714\pi$
$500$	−5.21570e8	−0.186602
$501$	−3.32729e9	−1.18211
$502$	5.53362e9	1.95230
$503$	1.02924e9	0.360604	0.180302	−	0.983611i	$-0.442293\pi$
$503$	1.02924e9	0.360604	0.180302	+	0.983611i	$0.442293\pi$
$504$	−3.58844e8	−0.124853
$505$	2.06309e9	0.712849
$506$	−2.80528e8	−0.0962608
$507$	−1.16940e8	−0.0398507
$508$	−1.23151e7	−0.00416788
$509$	−5.44407e9	−1.82983	−0.914917	−	0.403643i	$-0.867744\pi$
$509$	−5.44407e9	−1.82983	−0.914917	+	0.403643i	$0.867744\pi$
$510$	1.09419e10	3.65255
$511$	−7.06200e7	−0.0234129
$512$	1.41179e9	0.464864
$513$	−1.20689e9	−0.394692
$514$	5.10282e9	1.65744
$515$	−1.57041e9	−0.506625
$516$	1.28611e9	0.412101
$517$	3.35535e8	0.106788
$518$	4.82959e7	0.0152671
$519$	9.19416e9	2.88686
$520$	−3.14686e9	−0.981446
$521$	−1.06716e8	−0.0330596	−0.0165298	−	0.999863i	$-0.505262\pi$
$521$	−1.06716e8	−0.0330596	−0.0165298	+	0.999863i	$0.505262\pi$
$522$	3.54884e9	1.09204
$523$	−1.81163e8	−0.0553751	−0.0276875	−	0.999617i	$-0.508814\pi$
$523$	−1.81163e8	−0.0553751	−0.0276875	+	0.999617i	$0.508814\pi$
$524$	−6.84056e8	−0.207698
$525$	1.36603e8	0.0412006
$526$	2.83515e9	0.849428
$527$	3.60993e9	1.07439
$528$	−3.99387e8	−0.118080
$529$	3.61459e9	1.06161
$530$	6.37658e9	1.86047
$531$	2.35139e9	0.681543
$532$	−2.13839e7	−0.00615737
$533$	−3.83261e9	−1.09635
$534$	−1.05382e10	−2.99483
$535$	8.21987e8	0.232074
$536$	−5.32728e9	−1.49427
$537$	−7.59108e9	−2.11541
$538$	−6.51757e9	−1.80446
$539$	2.17956e8	0.0599525
$540$	−1.21331e9	−0.331585
$541$	−1.82680e9	−0.496020	−0.248010	−	0.968757i	$-0.579777\pi$
$541$	−1.82680e9	−0.496020	−0.248010	+	0.968757i	$0.579777\pi$
$542$	−4.94969e9	−1.33531
$543$	−2.88346e9	−0.772883
$544$	2.98891e9	0.796006
$545$	5.97687e9	1.58156
$546$	5.93043e8	0.155924
$547$	−3.35372e8	−0.0876136	−0.0438068	−	0.999040i	$-0.513949\pi$
$547$	−3.35372e8	−0.0876136	−0.0438068	+	0.999040i	$0.513949\pi$
$548$	−1.02706e9	−0.266603
$549$	3.15281e9	0.813195
$550$	7.76699e7	0.0199060
$551$	−6.95950e8	−0.177234
$552$	8.01765e9	2.02890
$553$	−2.84216e8	−0.0714679
$554$	−1.07791e8	−0.0269338
$555$	−1.25107e9	−0.310640
$556$	−6.97546e8	−0.172112
$557$	−5.53200e9	−1.35640	−0.678202	−	0.734876i	$-0.737240\pi$
$557$	−5.53200e9	−1.35640	−0.678202	+	0.734876i	$0.737240\pi$
$558$	−4.93062e9	−1.20138
$559$	4.45392e9	1.07845
$560$	4.66550e8	0.112264
$561$	7.29246e8	0.174383
$562$	−7.43447e9	−1.76674
$563$	−4.34714e9	−1.02665	−0.513327	−	0.858193i	$-0.671587\pi$
$563$	−4.34714e9	−1.02665	−0.513327	+	0.858193i	$0.671587\pi$
$564$	2.91406e9	0.683946
$565$	7.04231e9	1.64265
$566$	−3.57142e9	−0.827911
$567$	−1.16144e8	−0.0267581
$568$	−9.01135e8	−0.206334
$569$	−6.35578e9	−1.44636	−0.723179	−	0.690661i	$-0.757320\pi$
$569$	−6.35578e9	−1.44636	−0.723179	+	0.690661i	$0.757320\pi$
$570$	2.93079e9	0.662862
$571$	2.65678e9	0.597213	0.298606	−	0.954376i	$-0.403478\pi$
$571$	2.65678e9	0.597213	0.298606	+	0.954376i	$0.403478\pi$
$572$	6.37310e7	0.0142385
$573$	3.59513e8	0.0798314
$574$	4.55873e8	0.100613
$575$	−1.94347e9	−0.426324
$576$	5.39465e9	1.17621
$577$	−4.40565e9	−0.954761	−0.477381	−	0.878697i	$-0.658414\pi$
$577$	−4.40565e9	−0.954761	−0.477381	+	0.878697i	$0.658414\pi$
$578$	−1.04667e10	−2.25457
$579$	9.15304e9	1.95970
$580$	−6.99652e8	−0.148896
$581$	5.17004e8	0.109365
$582$	1.07040e10	2.25069
$583$	4.24982e8	0.0888240
$584$	1.14760e9	0.238421
$585$	−9.78210e9	−2.02016
$586$	5.26595e9	1.08102
$587$	2.88303e9	0.588323	0.294162	−	0.955756i	$-0.404960\pi$
$587$	2.88303e9	0.588323	0.294162	+	0.955756i	$0.404960\pi$
$588$	1.89291e9	0.383980
$589$	9.66925e8	0.194980
$590$	−2.45271e9	−0.491659
$591$	−8.78094e9	−1.74979
$592$	−9.78234e8	−0.193784
$593$	−5.53242e9	−1.08949	−0.544745	−	0.838602i	$-0.683374\pi$
$593$	−5.53242e9	−1.08949	−0.544745	+	0.838602i	$0.683374\pi$
$594$	−4.27842e8	−0.0837588
$595$	−8.51880e8	−0.165794
$596$	−1.66544e9	−0.322232
$597$	−1.81453e8	−0.0349024
$598$	−8.43727e9	−1.61342
$599$	9.62933e9	1.83064	0.915318	−	0.402732i	$-0.131939\pi$
$599$	9.62933e9	1.83064	0.915318	+	0.402732i	$0.131939\pi$
$600$	−2.21985e9	−0.419560
$601$	5.92488e9	1.11332	0.556659	−	0.830741i	$-0.312083\pi$
$601$	5.92488e9	1.11332	0.556659	+	0.830741i	$0.312083\pi$
$602$	−5.29776e8	−0.0989702
$603$	−1.65600e10	−3.07574
$604$	−6.15871e8	−0.113726
$605$	−6.18037e9	−1.13467
$606$	6.31812e9	1.15328
$607$	5.42764e9	0.985032	0.492516	−	0.870303i	$-0.336077\pi$
$607$	5.42764e9	0.985032	0.492516	+	0.870303i	$0.336077\pi$
$608$	8.00583e8	0.144459
$609$	−4.33911e8	−0.0778466
$610$	−3.28867e9	−0.586631
$611$	1.00917e10	1.78986
$612$	4.03282e9	0.711179
$613$	4.46675e9	0.783214	0.391607	−	0.920133i	$-0.371919\pi$
$613$	4.46675e9	0.783214	0.391607	+	0.920133i	$0.371919\pi$
$614$	−5.16457e9	−0.900420
$615$	−1.18091e10	−2.04717
$616$	2.49465e7	0.00430009
$617$	−4.25562e8	−0.0729399	−0.0364700	−	0.999335i	$-0.511611\pi$
$617$	−4.25562e8	−0.0729399	−0.0364700	+	0.999335i	$0.511611\pi$
$618$	−4.80930e9	−0.819639
$619$	2.29595e9	0.389085	0.194543	−	0.980894i	$-0.437678\pi$
$619$	2.29595e9	0.389085	0.194543	+	0.980894i	$0.437678\pi$
$620$	9.72069e8	0.163805
$621$	1.07055e10	1.79385
$622$	1.21793e10	2.02935
$623$	8.20454e8	0.135940
$624$	−1.20121e10	−1.97912
$625$	−7.37767e9	−1.20876
$626$	4.04817e9	0.659552
$627$	1.95330e8	0.0316469
$628$	−1.77049e9	−0.285256
$629$	1.78617e9	0.286185
$630$	1.16354e9	0.185391
$631$	1.13563e10	1.79942	0.899710	−	0.436487i	$-0.143778\pi$
$631$	1.13563e10	1.79942	0.899710	+	0.436487i	$0.143778\pi$
$632$	4.61861e9	0.727782
$633$	1.11656e10	1.74973
$634$	1.46505e9	0.228317
$635$	−1.31409e8	−0.0203665
$636$	3.69089e9	0.568894
$637$	6.55532e9	1.00486
$638$	−2.46713e8	−0.0376114
$639$	−2.80120e9	−0.424709
$640$	−9.08057e9	−1.36925
$641$	−1.17218e10	−1.75789	−0.878947	−	0.476919i	$-0.841754\pi$
$641$	−1.17218e10	−1.75789	−0.878947	+	0.476919i	$0.841754\pi$
$642$	2.51730e9	0.375459
$643$	8.78005e8	0.130244	0.0651222	−	0.997877i	$-0.479256\pi$
$643$	8.78005e8	0.130244	0.0651222	+	0.997877i	$0.479256\pi$
$644$	1.89681e8	0.0279849
$645$	1.37235e10	2.01375
$646$	−4.18433e9	−0.610679
$647$	−6.70870e9	−0.973809	−0.486904	−	0.873455i	$-0.661874\pi$
$647$	−6.70870e9	−0.973809	−0.486904	+	0.873455i	$0.661874\pi$
$648$	1.88737e9	0.272487
$649$	−1.63467e8	−0.0234732
$650$	2.33603e9	0.333642
$651$	6.02858e8	0.0856410
$652$	−8.68310e7	−0.0122690
$653$	−5.54487e9	−0.779284	−0.389642	−	0.920966i	$-0.627401\pi$
$653$	−5.54487e9	−0.779284	−0.389642	+	0.920966i	$0.627401\pi$
$654$	1.83039e10	2.55872
$655$	−7.29924e9	−1.01492
$656$	−9.23373e9	−1.27707
$657$	3.56733e9	0.490755
$658$	−1.20036e9	−0.164256
$659$	−6.33863e9	−0.862773	−0.431387	−	0.902167i	$-0.641975\pi$
$659$	−6.33863e9	−0.862773	−0.431387	+	0.902167i	$0.641975\pi$
$660$	1.96369e8	0.0265869
$661$	−6.93134e9	−0.933495	−0.466748	−	0.884391i	$-0.654574\pi$
$661$	−6.93134e9	−0.933495	−0.466748	+	0.884391i	$0.654574\pi$
$662$	3.30597e9	0.442890
$663$	2.19331e10	2.92282
$664$	−8.40149e9	−1.11370
$665$	−2.28177e8	−0.0300882
$666$	−2.43964e9	−0.320012
$667$	6.17328e9	0.805519
$668$	1.27918e9	0.166040
$669$	−2.57283e9	−0.332215
$670$	1.72735e10	2.21881
$671$	−2.19181e8	−0.0280075
$672$	4.99148e8	0.0634507
$673$	6.47288e9	0.818549	0.409275	−	0.912411i	$-0.365782\pi$
$673$	6.47288e9	0.818549	0.409275	+	0.912411i	$0.365782\pi$
$674$	−2.23510e9	−0.281182
$675$	−2.96404e9	−0.370954
$676$	4.49576e7	0.00559745
$677$	−1.35290e10	−1.67574	−0.837868	−	0.545874i	$-0.816198\pi$
$677$	−1.35290e10	−1.67574	−0.837868	+	0.545874i	$0.816198\pi$
$678$	2.15668e10	2.65755
$679$	−8.33360e8	−0.102162
$680$	1.38433e10	1.68834
$681$	−1.47790e10	−1.79321
$682$	3.42773e8	0.0413772
$683$	8.78333e9	1.05484	0.527420	−	0.849605i	$-0.323159\pi$
$683$	8.78333e9	1.05484	0.527420	+	0.849605i	$0.323159\pi$
$684$	1.08020e9	0.129064
$685$	−1.09593e10	−1.30277
$686$	−1.56495e9	−0.185082
$687$	−2.01076e10	−2.36599
$688$	1.07306e10	1.25622
$689$	1.27819e10	1.48877
$690$	−2.59970e10	−3.01267
$691$	−1.10753e9	−0.127697	−0.0638487	−	0.997960i	$-0.520338\pi$
$691$	−1.10753e9	−0.127697	−0.0638487	+	0.997960i	$0.520338\pi$
$692$	−3.53469e9	−0.405490
$693$	7.75469e7	0.00885112
$694$	−1.18489e9	−0.134561
$695$	−7.44319e9	−0.841032
$696$	7.05119e9	0.792739
$697$	1.68600e10	1.88601
$698$	2.29055e9	0.254945
$699$	3.33146e9	0.368947
$700$	−5.25171e7	−0.00578705
$701$	−2.65260e9	−0.290843	−0.145421	−	0.989370i	$-0.546454\pi$
$701$	−2.65260e9	−0.290843	−0.145421	+	0.989370i	$0.546454\pi$
$702$	−1.28679e10	−1.40388
$703$	4.78429e8	0.0519366
$704$	−3.75032e8	−0.0405101
$705$	3.10946e10	3.34213
$706$	−1.40607e10	−1.50380
$707$	−4.91898e8	−0.0523488
$708$	−1.41968e9	−0.150340
$709$	7.19365e9	0.758032	0.379016	−	0.925390i	$-0.376263\pi$
$709$	7.19365e9	0.758032	0.379016	+	0.925390i	$0.376263\pi$
$710$	2.92190e9	0.306381
$711$	1.43571e10	1.49803
$712$	−1.33326e10	−1.38432
$713$	−8.57691e9	−0.886171
$714$	−2.60885e9	−0.268229
$715$	6.80044e8	0.0695770
$716$	2.91839e9	0.297131
$717$	−2.35086e10	−2.38183
$718$	−2.86136e9	−0.288494
$719$	−7.85102e9	−0.787726	−0.393863	−	0.919169i	$-0.628861\pi$
$719$	−7.85102e9	−0.787726	−0.393863	+	0.919169i	$0.628861\pi$
$720$	−2.35675e10	−2.35316
$721$	3.74429e8	0.0372045
$722$	1.01090e10	0.999604
$723$	1.47421e10	1.45069
$724$	1.10854e9	0.108559
$725$	−1.70920e9	−0.166575
$726$	−1.89271e10	−1.83572
$727$	1.60212e9	0.154641	0.0773204	−	0.997006i	$-0.475364\pi$
$727$	1.60212e9	0.154641	0.0773204	+	0.997006i	$0.475364\pi$
$728$	7.50301e8	0.0720735
$729$	−1.58167e10	−1.51206
$730$	−3.72105e9	−0.354026
$731$	−1.95932e10	−1.85522
$732$	−1.90355e9	−0.179380
$733$	−5.15009e9	−0.483004	−0.241502	−	0.970400i	$-0.577640\pi$
$733$	−5.15009e9	−0.483004	−0.241502	+	0.970400i	$0.577640\pi$
$734$	−3.86442e9	−0.360702
$735$	2.01983e10	1.87633
$736$	−7.10141e9	−0.656557
$737$	1.15124e9	0.105932
$738$	−2.30282e10	−2.10894
$739$	−6.23785e9	−0.568564	−0.284282	−	0.958741i	$-0.591755\pi$
$739$	−6.23785e9	−0.568564	−0.284282	+	0.958741i	$0.591755\pi$
$740$	4.80974e8	0.0436325
$741$	5.87481e9	0.530432
$742$	−1.52036e9	−0.136625
$743$	−1.06146e9	−0.0949388	−0.0474694	−	0.998873i	$-0.515116\pi$
$743$	−1.06146e9	−0.0949388	−0.0474694	+	0.998873i	$0.515116\pi$
$744$	−9.79665e9	−0.872112
$745$	−1.77712e10	−1.57460
$746$	−5.44817e9	−0.480469
$747$	−2.61162e10	−2.29239
$748$	−2.80358e8	−0.0244939
$749$	−1.95985e8	−0.0170426
$750$	−1.70439e10	−1.47521
$751$	1.82567e10	1.57283	0.786415	−	0.617698i	$-0.211935\pi$
$751$	1.82567e10	1.57283	0.786415	+	0.617698i	$0.211935\pi$
$752$	2.43134e10	2.08489
$753$	3.41774e10	2.91714
$754$	−7.42023e9	−0.630402
$755$	−6.57168e9	−0.555728
$756$	2.89288e8	0.0243503
$757$	1.13322e10	0.949461	0.474730	−	0.880131i	$-0.342546\pi$
$757$	1.13322e10	0.949461	0.474730	+	0.880131i	$0.342546\pi$
$758$	2.32581e10	1.93969
$759$	−1.73263e9	−0.143833
$760$	3.70796e9	0.306399
$761$	−2.39708e9	−0.197168	−0.0985841	−	0.995129i	$-0.531431\pi$
$761$	−2.39708e9	−0.197168	−0.0985841	+	0.995129i	$0.531431\pi$
$762$	−4.02434e8	−0.0329497
$763$	−1.42506e9	−0.116144
$764$	−1.38215e8	−0.0112131
$765$	4.30323e10	3.47520
$766$	−2.24089e10	−1.80144
$767$	−4.91648e9	−0.393433
$768$	−1.38332e10	−1.10194
$769$	1.13037e10	0.896355	0.448177	−	0.893945i	$-0.352073\pi$
$769$	1.13037e10	0.896355	0.448177	+	0.893945i	$0.352073\pi$
$770$	−8.08884e7	−0.00638511
$771$	3.15166e10	2.47656
$772$	−3.51888e9	−0.275261
$773$	1.28680e10	1.00203	0.501017	−	0.865437i	$-0.332959\pi$
$773$	1.28680e10	1.00203	0.501017	+	0.865437i	$0.332959\pi$
$774$	2.67614e10	2.07451
$775$	2.37469e9	0.183253
$776$	1.35424e10	1.04035
$777$	2.98291e8	0.0228122
$778$	1.56734e9	0.119326
$779$	4.51598e9	0.342271
$780$	5.90606e9	0.445622
$781$	1.94737e8	0.0146275
$782$	3.71163e10	2.77550
$783$	9.41505e9	0.700901
$784$	1.57934e10	1.17050
$785$	−1.88921e10	−1.39392
$786$	−2.23536e10	−1.64199
$787$	−3.15080e9	−0.230414	−0.115207	−	0.993342i	$-0.536753\pi$
$787$	−3.15080e9	−0.230414	−0.115207	+	0.993342i	$0.536753\pi$
$788$	3.37583e9	0.245776
$789$	1.75108e10	1.26922
$790$	−1.49757e10	−1.08067
$791$	−1.67908e9	−0.120630
$792$	−1.26016e9	−0.0901340
$793$	−6.59216e9	−0.469431
$794$	4.85687e9	0.344338
$795$	3.93838e10	2.77992
$796$	6.97597e7	0.00490240
$797$	7.47013e9	0.522666	0.261333	−	0.965249i	$-0.415838\pi$
$797$	7.47013e9	0.522666	0.261333	+	0.965249i	$0.415838\pi$
$798$	−6.98784e8	−0.0486780
$799$	−4.43942e10	−3.07902
$800$	1.96617e9	0.135771
$801$	−4.14449e10	−2.84942
$802$	−6.12235e9	−0.419091
$803$	−2.47998e8	−0.0169022
$804$	9.99828e9	0.678468
$805$	2.02400e9	0.136749
$806$	1.03094e10	0.693521
$807$	−4.02546e10	−2.69624
$808$	7.99350e9	0.533086
$809$	1.17390e10	0.779490	0.389745	−	0.920923i	$-0.372563\pi$
$809$	1.17390e10	0.779490	0.389745	+	0.920923i	$0.372563\pi$
$810$	−6.11975e9	−0.404609
$811$	−2.38533e10	−1.57028	−0.785138	−	0.619321i	$-0.787408\pi$
$811$	−2.38533e10	−1.57028	−0.785138	+	0.619321i	$0.787408\pi$
$812$	1.66817e8	0.0109344
$813$	−3.05709e10	−1.99522
$814$	1.69602e8	0.0110216
$815$	−9.26533e8	−0.0599528
$816$	5.28423e10	3.40460
$817$	−5.24807e9	−0.336684
$818$	−1.15559e10	−0.738187
$819$	2.33233e9	0.148353
$820$	4.54000e9	0.287546
$821$	3.52152e9	0.222090	0.111045	−	0.993815i	$-0.464580\pi$
$821$	3.52152e9	0.222090	0.111045	+	0.993815i	$0.464580\pi$
$822$	−3.35625e10	−2.10767
$823$	1.57368e10	0.984050	0.492025	−	0.870581i	$-0.336257\pi$
$823$	1.57368e10	0.984050	0.492025	+	0.870581i	$0.336257\pi$
$824$	−6.08459e9	−0.378867
$825$	4.79714e8	0.0297436
$826$	5.84795e8	0.0361055
$827$	2.37800e10	1.46198	0.730991	−	0.682387i	$-0.239058\pi$
$827$	2.37800e10	1.46198	0.730991	+	0.682387i	$0.239058\pi$
$828$	−9.58166e9	−0.586590
$829$	−3.13207e9	−0.190937	−0.0954685	−	0.995432i	$-0.530435\pi$
$829$	−3.13207e9	−0.190937	−0.0954685	+	0.995432i	$0.530435\pi$
$830$	2.72416e10	1.65371
$831$	−6.65751e8	−0.0402447
$832$	−1.12796e10	−0.678987
$833$	−2.88374e10	−1.72862
$834$	−2.27945e10	−1.36066
$835$	1.36495e10	0.811360
$836$	−7.50944e7	−0.00444514
$837$	−1.30809e10	−0.771078
$838$	1.75705e10	1.03141
$839$	2.94133e10	1.71940	0.859699	−	0.510802i	$-0.170651\pi$
$839$	2.94133e10	1.71940	0.859699	+	0.510802i	$0.170651\pi$
$840$	2.31184e9	0.134580
$841$	−1.18207e10	−0.685265
$842$	5.22365e9	0.301565
$843$	−4.59177e10	−2.63987
$844$	−4.29262e9	−0.245767
$845$	4.79722e8	0.0273521
$846$	6.06358e10	3.44297
$847$	1.47357e9	0.0833259
$848$	3.07948e10	1.73417
$849$	−2.20583e10	−1.23707
$850$	−1.02764e10	−0.573951
$851$	−4.24381e9	−0.236049
$852$	1.69126e9	0.0936852
$853$	1.68977e10	0.932193	0.466096	−	0.884734i	$-0.345660\pi$
$853$	1.68977e10	0.932193	0.466096	+	0.884734i	$0.345660\pi$
$854$	7.84111e8	0.0430799
$855$	1.15263e10	0.630678
$856$	3.18482e9	0.173551
$857$	−3.21911e10	−1.74704	−0.873520	−	0.486788i	$-0.838168\pi$
$857$	−3.21911e10	−1.74704	−0.873520	+	0.486788i	$0.838168\pi$
$858$	2.08261e9	0.112565
$859$	1.70739e10	0.919090	0.459545	−	0.888155i	$-0.348013\pi$
$859$	1.70739e10	0.919090	0.459545	+	0.888155i	$0.348013\pi$
$860$	−5.27599e9	−0.282852
$861$	2.81562e9	0.150336
$862$	−4.34120e8	−0.0230853
$863$	1.37282e10	0.727069	0.363535	−	0.931581i	$-0.381570\pi$
$863$	1.37282e10	0.727069	0.363535	+	0.931581i	$0.381570\pi$
$864$	−1.08306e10	−0.571286
$865$	−3.77170e10	−1.98144
$866$	−1.30644e10	−0.683561
$867$	−6.46459e10	−3.36879
$868$	−2.31769e8	−0.0120292
$869$	−9.98091e8	−0.0515942
$870$	−2.28633e10	−1.17712
$871$	3.46250e10	1.77552
$872$	2.31576e10	1.18273
$873$	4.20968e10	2.14141
$874$	9.94165e9	0.503696
$875$	1.32695e9	0.0669619
$876$	−2.15382e9	−0.108254
$877$	−3.70821e9	−0.185637	−0.0928187	−	0.995683i	$-0.529588\pi$
$877$	−3.70821e9	−0.185637	−0.0928187	+	0.995683i	$0.529588\pi$
$878$	−1.30421e10	−0.650303
$879$	3.25242e10	1.61527
$880$	1.63840e9	0.0810457
$881$	−2.35175e8	−0.0115871	−0.00579355	−	0.999983i	$-0.501844\pi$
$881$	−2.35175e8	−0.0115871	−0.00579355	+	0.999983i	$0.501844\pi$
$882$	3.93876e10	1.93294
$883$	2.36484e10	1.15595	0.577976	−	0.816054i	$-0.303843\pi$
$883$	2.36484e10	1.15595	0.577976	+	0.816054i	$0.303843\pi$
$884$	−8.43216e9	−0.410540
$885$	−1.51487e10	−0.734640
$886$	9.54562e9	0.461090
$887$	4.04357e9	0.194550	0.0972751	−	0.995258i	$-0.468987\pi$
$887$	4.04357e9	0.194550	0.0972751	+	0.995258i	$0.468987\pi$
$888$	−4.84732e9	−0.232304
$889$	3.13315e7	0.00149563
$890$	4.32307e10	2.05555
$891$	−4.07865e8	−0.0193172
$892$	9.89122e8	0.0466630
$893$	−1.18911e10	−0.558779
$894$	−5.44235e10	−2.54745
$895$	3.11408e10	1.45194
$896$	2.16506e9	0.100552
$897$	−5.21113e10	−2.41078
$898$	−1.74945e9	−0.0806185
$899$	−7.54304e9	−0.346248
$900$	2.65288e9	0.121302
$901$	−5.62288e10	−2.56107
$902$	1.60090e9	0.0726344
$903$	−3.27207e9	−0.147882
$904$	2.72857e10	1.22842
$905$	1.18287e10	0.530480
$906$	−2.01255e10	−0.899079
$907$	−2.59707e9	−0.115573	−0.0577867	−	0.998329i	$-0.518404\pi$
$907$	−2.59707e9	−0.115573	−0.0577867	+	0.998329i	$0.518404\pi$
$908$	5.68180e9	0.251875
$909$	2.48480e10	1.09728
$910$	−2.43283e9	−0.107020
$911$	−6.56851e9	−0.287841	−0.143920	−	0.989589i	$-0.545971\pi$
$911$	−6.56851e9	−0.287841	−0.143920	+	0.989589i	$0.545971\pi$
$912$	1.41539e10	0.617865
$913$	1.81558e9	0.0789528
$914$	−4.68654e10	−2.03021
$915$	−2.03119e10	−0.876548
$916$	7.73037e9	0.332327
$917$	1.74035e9	0.0745320
$918$	5.66072e10	2.41503
$919$	−1.93988e10	−0.824464	−0.412232	−	0.911079i	$-0.635251\pi$
$919$	−1.93988e10	−0.824464	−0.412232	+	0.911079i	$0.635251\pi$
$920$	−3.28907e10	−1.39256
$921$	−3.18981e10	−1.34541
$922$	1.69509e10	0.712255
$923$	5.85699e9	0.245171
$924$	−4.68198e7	−0.00195244
$925$	1.17498e9	0.0488130
$926$	−1.96696e10	−0.814060
$927$	−1.89141e10	−0.779842
$928$	−6.24540e9	−0.256532
$929$	−1.57313e10	−0.643738	−0.321869	−	0.946784i	$-0.604311\pi$
$929$	−1.57313e10	−0.643738	−0.321869	+	0.946784i	$0.604311\pi$
$930$	3.17653e10	1.29498
$931$	−7.72414e9	−0.313709
$932$	−1.28078e9	−0.0518224
$933$	7.52233e10	3.03226
$934$	4.25577e10	1.70909
$935$	−2.99157e9	−0.119690
$936$	−3.79011e10	−1.51073
$937$	1.70691e10	0.677833	0.338917	−	0.940816i	$-0.389940\pi$
$937$	1.70691e10	0.677833	0.338917	+	0.940816i	$0.389940\pi$
$938$	−4.11850e9	−0.162941
$939$	2.50028e10	0.985506
$940$	−1.19543e10	−0.469436
$941$	1.80958e10	0.707967	0.353983	−	0.935252i	$-0.384827\pi$
$941$	1.80958e10	0.707967	0.353983	+	0.935252i	$0.384827\pi$
$942$	−5.78563e10	−2.25514
$943$	−4.00581e10	−1.55560
$944$	−1.18450e10	−0.458284
$945$	3.08686e9	0.118989
$946$	−1.86043e9	−0.0714487
$947$	−4.57524e10	−1.75061	−0.875305	−	0.483572i	$-0.839339\pi$
$947$	−4.57524e10	−1.75061	−0.875305	+	0.483572i	$0.839339\pi$
$948$	−8.66824e9	−0.330447
$949$	−7.45889e9	−0.283297
$950$	−2.75255e9	−0.104160
$951$	9.04859e9	0.341153
$952$	−3.30064e9	−0.123985
$953$	−2.56861e9	−0.0961331	−0.0480665	−	0.998844i	$-0.515306\pi$
$953$	−2.56861e9	−0.0961331	−0.0480665	+	0.998844i	$0.515306\pi$
$954$	7.68001e10	2.86380
$955$	−1.47482e9	−0.0547934
$956$	9.03789e9	0.334552
$957$	−1.52378e9	−0.0561992
$958$	−4.11918e10	−1.51367
$959$	2.61301e9	0.0956701
$960$	−3.47548e10	−1.26784
$961$	−1.70326e10	−0.619084
$962$	5.10101e9	0.184733
$963$	9.90009e9	0.357229
$964$	−5.66760e9	−0.203765
$965$	−3.75484e10	−1.34507
$966$	6.19842e9	0.221239
$967$	3.05525e10	1.08656	0.543280	−	0.839551i	$-0.317182\pi$
$967$	3.05525e10	1.08656	0.543280	+	0.839551i	$0.317182\pi$
$968$	−2.39461e10	−0.848536
$969$	−2.58438e10	−0.912480
$970$	−4.39107e10	−1.54479
$971$	3.10053e10	1.08685	0.543424	−	0.839458i	$-0.317128\pi$
$971$	3.10053e10	1.08685	0.543424	+	0.839458i	$0.317128\pi$
$972$	4.79402e9	0.167443
$973$	1.77467e9	0.0617621
$974$	−1.65576e10	−0.574171
$975$	1.44281e10	0.498531
$976$	−1.58822e10	−0.546809
$977$	1.90832e10	0.654668	0.327334	−	0.944909i	$-0.393850\pi$
$977$	1.90832e10	0.654668	0.327334	+	0.944909i	$0.393850\pi$
$978$	−2.83747e9	−0.0969941
$979$	2.88121e9	0.0981377
$980$	−7.76523e9	−0.263550
$981$	7.19860e10	2.43448
$982$	1.63313e9	0.0550339
$983$	3.64856e10	1.22514	0.612568	−	0.790418i	$-0.290137\pi$
$983$	3.64856e10	1.22514	0.612568	+	0.790418i	$0.290137\pi$
$984$	−4.57548e10	−1.53092
$985$	3.60219e10	1.20099
$986$	3.26422e10	1.08445
$987$	−7.41383e9	−0.245433
$988$	−2.25857e9	−0.0745047
$989$	4.65519e10	1.53021
$990$	4.08604e9	0.133838
$991$	2.65309e10	0.865954	0.432977	−	0.901405i	$-0.357463\pi$
$991$	2.65309e10	0.865954	0.432977	+	0.901405i	$0.357463\pi$
$992$	8.67711e9	0.282218
$993$	2.04187e10	0.661769
$994$	−6.96665e8	−0.0224994
$995$	7.44373e8	0.0239558
$996$	1.57680e10	0.505672
$997$	1.83369e10	0.585993	0.292997	−	0.956113i	$-0.405348\pi$
$997$	1.83369e10	0.585993	0.292997	+	0.956113i	$0.405348\pi$
$998$	1.85532e10	0.590829
$999$	−6.47235e9	−0.205392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.a.a.1.3	✓	10
3.2	odd	2		333.8.a.c.1.8		10
4.3	odd	2		592.8.a.f.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.a.a.1.3	✓	10	1.1	even	1	trivial
333.8.a.c.1.8		10	3.2	odd	2
592.8.a.f.1.10		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)

\(f(q)\)	\(=\)	\(q-12.5631 q^{2} -77.5936 q^{3} +29.8308 q^{4} +318.311 q^{5} +974.814 q^{6} -75.8943 q^{7} +1233.31 q^{8} +3833.76 q^{9} +O(q^{10})\)	\(q-12.5631 q^{2} -77.5936 q^{3} +29.8308 q^{4} +318.311 q^{5} +974.814 q^{6} -75.8943 q^{7} +1233.31 q^{8} +3833.76 q^{9} -3998.96 q^{10} -266.520 q^{11} -2314.68 q^{12} -8015.96 q^{13} +953.465 q^{14} -24698.9 q^{15} -19312.5 q^{16} +35262.9 q^{17} -48163.9 q^{18} +9445.22 q^{19} +9495.47 q^{20} +5888.91 q^{21} +3348.31 q^{22} -83781.9 q^{23} -95696.7 q^{24} +23196.7 q^{25} +100705. q^{26} -127778. q^{27} -2263.99 q^{28} -73682.7 q^{29} +310294. q^{30} +102372. q^{31} +84760.7 q^{32} +20680.3 q^{33} -443011. q^{34} -24158.0 q^{35} +114364. q^{36} +50653.0 q^{37} -118661. q^{38} +621987. q^{39} +392575. q^{40} +478123. q^{41} -73982.8 q^{42} -555632. q^{43} -7950.51 q^{44} +1.22033e6 q^{45} +1.05256e6 q^{46} -1.25895e6 q^{47} +1.49852e6 q^{48} -817783. q^{49} -291422. q^{50} -2.73618e6 q^{51} -239123. q^{52} -1.59456e6 q^{53} +1.60529e6 q^{54} -84836.2 q^{55} -93600.9 q^{56} -732889. q^{57} +925681. q^{58} +613337. q^{59} -736787. q^{60} +822380. q^{61} -1.28611e6 q^{62} -290961. q^{63} +1.40714e6 q^{64} -2.55157e6 q^{65} -259808. q^{66} -4.31951e6 q^{67} +1.05192e6 q^{68} +6.50094e6 q^{69} +303498. q^{70} -730666. q^{71} +4.72821e6 q^{72} +930505. q^{73} -636357. q^{74} -1.79992e6 q^{75} +281759. q^{76} +20227.4 q^{77} -7.81407e6 q^{78} +3.74490e6 q^{79} -6.14737e6 q^{80} +1.53033e6 q^{81} -6.00669e6 q^{82} -6.81217e6 q^{83} +175671. q^{84} +1.12246e7 q^{85} +6.98045e6 q^{86} +5.71731e6 q^{87} -328701. q^{88} -1.08105e7 q^{89} -1.53311e7 q^{90} +608365. q^{91} -2.49928e6 q^{92} -7.94340e6 q^{93} +1.58163e7 q^{94} +3.00652e6 q^{95} -6.57688e6 q^{96} +1.09805e7 q^{97} +1.02739e7 q^{98} -1.02178e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 24 q^{2} - 95 q^{3} + 602 q^{4} - 624 q^{5} - 777 q^{6} - 501 q^{7} - 3810 q^{8} + 6181 q^{9}+O(q^{10}) \) 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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