LMFDB - Embedded newform 37.8.a.a.1.5

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			1.5
Root			$9.55485$ 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)

$f(q)$	$=$	$q-11.5549 q^{2} -22.2601 q^{3} +5.51464 q^{4} +118.339 q^{5} +257.212 q^{6} +925.681 q^{7} +1415.30 q^{8} -1691.49 q^{9} +O(q^{10})$	\(q-11.5549 q^{2} -22.2601 q^{3} +5.51464 q^{4} +118.339 q^{5} +257.212 q^{6} +925.681 q^{7} +1415.30 q^{8} -1691.49 q^{9} -1367.39 q^{10} -1635.15 q^{11} -122.756 q^{12} +11098.5 q^{13} -10696.1 q^{14} -2634.23 q^{15} -17059.5 q^{16} -29875.3 q^{17} +19544.9 q^{18} -52852.4 q^{19} +652.596 q^{20} -20605.7 q^{21} +18893.9 q^{22} +14424.2 q^{23} -31504.7 q^{24} -64120.9 q^{25} -128242. q^{26} +86335.5 q^{27} +5104.80 q^{28} +150062. q^{29} +30438.2 q^{30} -182903. q^{31} +15961.1 q^{32} +36398.6 q^{33} +345205. q^{34} +109544. q^{35} -9327.95 q^{36} +50653.0 q^{37} +610702. q^{38} -247054. q^{39} +167485. q^{40} -736946. q^{41} +238096. q^{42} +945654. q^{43} -9017.27 q^{44} -200169. q^{45} -166669. q^{46} -718695. q^{47} +379745. q^{48} +33341.8 q^{49} +740908. q^{50} +665027. q^{51} +61204.4 q^{52} -2.12533e6 q^{53} -997594. q^{54} -193502. q^{55} +1.31012e6 q^{56} +1.17650e6 q^{57} -1.73394e6 q^{58} -1.83818e6 q^{59} -14526.8 q^{60} -690185. q^{61} +2.11342e6 q^{62} -1.56578e6 q^{63} +1.99918e6 q^{64} +1.31339e6 q^{65} -420581. q^{66} +271528. q^{67} -164752. q^{68} -321084. q^{69} -1.26576e6 q^{70} -3.00007e6 q^{71} -2.39396e6 q^{72} +2.99192e6 q^{73} -585288. q^{74} +1.42734e6 q^{75} -291462. q^{76} -1.51363e6 q^{77} +2.85468e6 q^{78} -1.72287e6 q^{79} -2.01880e6 q^{80} +1.77745e6 q^{81} +8.51531e6 q^{82} -6.90954e6 q^{83} -113633. q^{84} -3.53541e6 q^{85} -1.09269e7 q^{86} -3.34039e6 q^{87} -2.31423e6 q^{88} +3.85082e6 q^{89} +2.31292e6 q^{90} +1.02737e7 q^{91} +79544.2 q^{92} +4.07144e6 q^{93} +8.30442e6 q^{94} -6.25449e6 q^{95} -355297. q^{96} +1.00422e7 q^{97} -385260. q^{98} +2.76584e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−11.5549	−1.02131	−0.510657	−	0.859784i	$-0.670598\pi$
$2$	−11.5549	−1.02131	−0.510657	+	0.859784i	$0.670598\pi$
$3$	−22.2601	−0.475995	−0.237998	−	0.971266i	$-0.576491\pi$
$3$	−22.2601	−0.475995	−0.237998	+	0.971266i	$0.576491\pi$
$4$	5.51464	0.0430831
$5$	118.339	0.423382	0.211691	−	0.977337i	$-0.432103\pi$
$5$	118.339	0.423382	0.211691	+	0.977337i	$0.432103\pi$
$6$	257.212	0.486141
$7$	925.681	1.02004	0.510021	−	0.860162i	$-0.329638\pi$
$7$	925.681	1.02004	0.510021	+	0.860162i	$0.329638\pi$
$8$	1415.30	0.977313
$9$	−1691.49	−0.773429
$10$	−1367.39	−0.432406
$11$	−1635.15	−0.370411	−0.185205	−	0.982700i	$-0.559295\pi$
$11$	−1635.15	−0.370411	−0.185205	+	0.982700i	$0.559295\pi$
$12$	−122.756	−0.0205074
$13$	11098.5	1.40108	0.700541	−	0.713612i	$-0.252942\pi$
$13$	11098.5	1.40108	0.700541	+	0.713612i	$0.252942\pi$
$14$	−10696.1	−1.04178
$15$	−2634.23	−0.201528
$16$	−17059.5	−1.04123
$17$	−29875.3	−1.47483	−0.737414	−	0.675441i	$-0.763953\pi$
$17$	−29875.3	−1.47483	−0.737414	+	0.675441i	$0.763953\pi$
$18$	19544.9	0.789914
$19$	−52852.4	−1.76778	−0.883888	−	0.467698i	$-0.845083\pi$
$19$	−52852.4	−1.76778	−0.883888	+	0.467698i	$0.845083\pi$
$20$	652.596	0.0182406
$21$	−20605.7	−0.485535
$22$	18893.9	0.378306
$23$	14424.2	0.247197	0.123599	−	0.992332i	$-0.460556\pi$
$23$	14424.2	0.247197	0.123599	+	0.992332i	$0.460556\pi$
$24$	−31504.7	−0.465196
$25$	−64120.9	−0.820748
$26$	−128242.	−1.43095
$27$	86335.5	0.844144
$28$	5104.80	0.0439466
$29$	150062.	1.14255	0.571277	−	0.820757i	$-0.306448\pi$
$29$	150062.	1.14255	0.571277	+	0.820757i	$0.306448\pi$
$30$	30438.2	0.205823
$31$	−182903.	−1.10269	−0.551347	−	0.834276i	$-0.685886\pi$
$31$	−182903.	−1.10269	−0.551347	+	0.834276i	$0.685886\pi$
$32$	15961.1	0.0861071
$33$	36398.6	0.176314
$34$	345205.	1.50626
$35$	109544.	0.431867
$36$	−9327.95	−0.0333217
$37$	50653.0	0.164399
$37$	50653.0	0.164399
$38$	610702.	1.80546
$39$	−247054.	−0.666908
$40$	167485.	0.413777
$41$	−736946.	−1.66991	−0.834953	−	0.550321i	$-0.814506\pi$
$41$	−736946.	−1.66991	−0.834953	+	0.550321i	$0.814506\pi$
$42$	238096.	0.495884
$43$	945654.	1.81381	0.906906	−	0.421332i	$-0.138437\pi$
$43$	945654.	1.81381	0.906906	+	0.421332i	$0.138437\pi$
$44$	−9017.27	−0.0159585
$45$	−200169.	−0.327456
$46$	−166669.	−0.252466
$47$	−718695.	−1.00972	−0.504862	−	0.863200i	$-0.668456\pi$
$47$	−718695.	−1.00972	−0.504862	+	0.863200i	$0.668456\pi$
$48$	379745.	0.495619
$49$	33341.8	0.0404859
$50$	740908.	0.838242
$51$	665027.	0.702011
$52$	61204.4	0.0603630
$53$	−2.12533e6	−1.96092	−0.980460	−	0.196717i	$-0.936972\pi$
$53$	−2.12533e6	−1.96092	−0.980460	+	0.196717i	$0.936972\pi$
$54$	−997594.	−0.862136
$55$	−193502.	−0.156825
$56$	1.31012e6	0.996900
$57$	1.17650e6	0.841453
$58$	−1.73394e6	−1.16691
$59$	−1.83818e6	−1.16522	−0.582608	−	0.812753i	$-0.697968\pi$
$59$	−1.83818e6	−1.16522	−0.582608	+	0.812753i	$0.697968\pi$
$60$	−14526.8	−0.00868245
$61$	−690185.	−0.389324	−0.194662	−	0.980870i	$-0.562361\pi$
$61$	−690185.	−0.389324	−0.194662	+	0.980870i	$0.562361\pi$
$62$	2.11342e6	1.12620
$63$	−1.56578e6	−0.788930
$64$	1.99918e6	0.953285
$65$	1.31339e6	0.593193
$66$	−420581.	−0.180072
$67$	271528.	0.110294	0.0551470	−	0.998478i	$-0.482437\pi$
$67$	271528.	0.110294	0.0551470	+	0.998478i	$0.482437\pi$
$68$	−164752.	−0.0635402
$69$	−321084.	−0.117665
$70$	−1.26576e6	−0.441072
$71$	−3.00007e6	−0.994782	−0.497391	−	0.867527i	$-0.665708\pi$
$71$	−3.00007e6	−0.994782	−0.497391	+	0.867527i	$0.665708\pi$
$72$	−2.39396e6	−0.755882
$73$	2.99192e6	0.900160	0.450080	−	0.892988i	$-0.351395\pi$
$73$	2.99192e6	0.900160	0.450080	+	0.892988i	$0.351395\pi$
$74$	−585288.	−0.167903
$75$	1.42734e6	0.390672
$76$	−291462.	−0.0761613
$77$	−1.51363e6	−0.377835
$78$	2.85468e6	0.681123
$79$	−1.72287e6	−0.393149	−0.196574	−	0.980489i	$-0.562982\pi$
$79$	−1.72287e6	−0.393149	−0.196574	+	0.980489i	$0.562982\pi$
$80$	−2.01880e6	−0.440837
$81$	1.77745e6	0.371620
$82$	8.51531e6	1.70550
$83$	−6.90954e6	−1.32640	−0.663202	−	0.748440i	$-0.730803\pi$
$83$	−6.90954e6	−1.32640	−0.663202	+	0.748440i	$0.730803\pi$
$84$	−113633.	−0.0209184
$85$	−3.53541e6	−0.624415
$86$	−1.09269e7	−1.85247
$87$	−3.34039e6	−0.543850
$88$	−2.31423e6	−0.362007
$89$	3.85082e6	0.579012	0.289506	−	0.957176i	$-0.406509\pi$
$89$	3.85082e6	0.579012	0.289506	+	0.957176i	$0.406509\pi$
$90$	2.31292e6	0.334435
$91$	1.02737e7	1.42916
$92$	79544.2	0.0106500
$93$	4.07144e6	0.524877
$94$	8.30442e6	1.03124
$95$	−6.25449e6	−0.748445
$96$	−355297.	−0.0409866
$97$	1.00422e7	1.11720	0.558599	−	0.829438i	$-0.311339\pi$
$97$	1.00422e7	1.11720	0.558599	+	0.829438i	$0.311339\pi$
$98$	−385260.	−0.0413488
$99$	2.76584e6	0.286486
$100$	−353604.	−0.0353604
$101$	8.35242e6	0.806654	0.403327	−	0.915056i	$-0.367854\pi$
$101$	8.35242e6	0.806654	0.403327	+	0.915056i	$0.367854\pi$
$102$	−7.68429e6	−0.716974
$103$	−6.39754e6	−0.576876	−0.288438	−	0.957499i	$-0.593136\pi$
$103$	−6.39754e6	−0.576876	−0.288438	+	0.957499i	$0.593136\pi$
$104$	1.57077e7	1.36930
$105$	−2.43846e6	−0.205567
$106$	2.45578e7	2.00272
$107$	−1.55811e6	−0.122958	−0.0614789	−	0.998108i	$-0.519582\pi$
$107$	−1.55811e6	−0.122958	−0.0614789	+	0.998108i	$0.519582\pi$
$108$	476109.	0.0363683
$109$	1.70168e7	1.25859	0.629294	−	0.777167i	$-0.283344\pi$
$109$	1.70168e7	1.25859	0.629294	+	0.777167i	$0.283344\pi$
$110$	2.23589e6	0.160168
$111$	−1.12754e6	−0.0782531
$112$	−1.57916e7	−1.06210
$113$	−681271.	−0.0444166	−0.0222083	−	0.999753i	$-0.507070\pi$
$113$	−681271.	−0.0444166	−0.0222083	+	0.999753i	$0.507070\pi$
$114$	−1.35943e7	−0.859388
$115$	1.70694e6	0.104659
$116$	827536.	0.0492248
$117$	−1.87730e7	−1.08364
$118$	2.12399e7	1.19005
$119$	−2.76550e7	−1.50439
$120$	−3.72823e6	−0.196956
$121$	−1.68134e7	−0.862796
$122$	7.97499e6	0.397622
$123$	1.64045e7	0.794868
$124$	−1.00864e6	−0.0475075
$125$	−1.68332e7	−0.770872
$126$	1.80923e7	0.805745
$127$	−5.67446e6	−0.245817	−0.122908	−	0.992418i	$-0.539222\pi$
$127$	−5.67446e6	−0.245817	−0.122908	+	0.992418i	$0.539222\pi$
$128$	−2.51433e7	−1.05971
$129$	−2.10503e7	−0.863366
$130$	−1.51760e7	−0.605836
$131$	8.23834e6	0.320177	0.160088	−	0.987103i	$-0.448822\pi$
$131$	8.23834e6	0.320177	0.160088	+	0.987103i	$0.448822\pi$
$132$	200725.	0.00759615
$133$	−4.89245e7	−1.80321
$134$	−3.13746e6	−0.112645
$135$	1.02168e7	0.357395
$136$	−4.22825e7	−1.44137
$137$	−5.10992e6	−0.169782	−0.0848910	−	0.996390i	$-0.527054\pi$
$137$	−5.10992e6	−0.169782	−0.0848910	+	0.996390i	$0.527054\pi$
$138$	3.71008e6	0.120173
$139$	9.33958e6	0.294969	0.147484	−	0.989064i	$-0.452882\pi$
$139$	9.33958e6	0.294969	0.147484	+	0.989064i	$0.452882\pi$
$140$	604096.	0.0186062
$141$	1.59982e7	0.480624
$142$	3.46654e7	1.01598
$143$	−1.81478e7	−0.518976
$144$	2.88559e7	0.805315
$145$	1.77581e7	0.483737
$146$	−3.45712e7	−0.919346
$147$	−742193.	−0.0192711
$148$	279333.	0.00708282
$149$	4.20171e7	1.04058	0.520289	−	0.853990i	$-0.325824\pi$
$149$	4.20171e7	1.04058	0.520289	+	0.853990i	$0.325824\pi$
$150$	−1.64927e7	−0.398999
$151$	5.53579e7	1.30846	0.654230	−	0.756296i	$-0.272993\pi$
$151$	5.53579e7	1.30846	0.654230	+	0.756296i	$0.272993\pi$
$152$	−7.48021e7	−1.72767
$153$	5.05337e7	1.14067
$154$	1.74898e7	0.385888
$155$	−2.16445e7	−0.466861
$156$	−1.36241e6	−0.0287325
$157$	1.86566e7	0.384755	0.192377	−	0.981321i	$-0.438380\pi$
$157$	1.86566e7	0.384755	0.192377	+	0.981321i	$0.438380\pi$
$158$	1.99075e7	0.401528
$159$	4.73100e7	0.933389
$160$	1.88882e6	0.0364562
$161$	1.33522e7	0.252152
$162$	−2.05381e7	−0.379541
$163$	−5.74875e7	−1.03972	−0.519860	−	0.854251i	$-0.674016\pi$
$163$	−5.74875e7	−1.03972	−0.519860	+	0.854251i	$0.674016\pi$
$164$	−4.06399e6	−0.0719448
$165$	4.30737e6	0.0746481
$166$	7.98388e7	1.35468
$167$	−2.84648e7	−0.472934	−0.236467	−	0.971640i	$-0.575989\pi$
$167$	−2.84648e7	−0.472934	−0.236467	+	0.971640i	$0.575989\pi$
$168$	−2.91633e7	−0.474520
$169$	6.04287e7	0.963030
$170$	4.08511e7	0.637724
$171$	8.93993e7	1.36725
$172$	5.21494e6	0.0781447
$173$	8.91590e7	1.30919	0.654597	−	0.755978i	$-0.272839\pi$
$173$	8.91590e7	1.30919	0.654597	+	0.755978i	$0.272839\pi$
$174$	3.85977e7	0.555442
$175$	−5.93555e7	−0.837197
$176$	2.78948e7	0.385682
$177$	4.09181e7	0.554637
$178$	−4.44956e7	−0.591354
$179$	−1.06602e8	−1.38925	−0.694627	−	0.719370i	$-0.744430\pi$
$179$	−1.06602e8	−1.38925	−0.694627	+	0.719370i	$0.744430\pi$
$180$	−1.10386e6	−0.0141078
$181$	−1.40982e8	−1.76722	−0.883609	−	0.468226i	$-0.844893\pi$
$181$	−1.40982e8	−1.76722	−0.883609	+	0.468226i	$0.844893\pi$
$182$	−1.18711e8	−1.45962
$183$	1.53636e7	0.185316
$184$	2.04146e7	0.241589
$185$	5.99422e6	0.0696036
$186$	−4.70449e7	−0.536065
$187$	4.88507e7	0.546292
$188$	−3.96335e6	−0.0435020
$189$	7.99191e7	0.861062
$190$	7.22698e7	0.764397
$191$	−7.73485e7	−0.803221	−0.401611	−	0.915810i	$-0.631549\pi$
$191$	−7.73485e7	−0.803221	−0.401611	+	0.915810i	$0.631549\pi$
$192$	−4.45020e7	−0.453759
$193$	1.02788e8	1.02918	0.514590	−	0.857436i	$-0.327944\pi$
$193$	1.02788e8	1.02918	0.514590	+	0.857436i	$0.327944\pi$
$194$	−1.16037e8	−1.14101
$195$	−2.92361e7	−0.282357
$196$	183868.	0.00174426
$197$	5.28531e7	0.492537	0.246268	−	0.969202i	$-0.420796\pi$
$197$	5.28531e7	0.492537	0.246268	+	0.969202i	$0.420796\pi$
$198$	−3.19589e7	−0.292593
$199$	1.09533e8	0.985276	0.492638	−	0.870234i	$-0.336033\pi$
$199$	1.09533e8	0.985276	0.492638	+	0.870234i	$0.336033\pi$
$200$	−9.07504e7	−0.802127
$201$	−6.04423e6	−0.0524994
$202$	−9.65109e7	−0.823847
$203$	1.38909e8	1.16545
$204$	3.66739e6	0.0302448
$205$	−8.72094e7	−0.707008
$206$	7.39226e7	0.589172
$207$	−2.43983e7	−0.191189
$208$	−1.89335e8	−1.45884
$209$	8.64217e7	0.654804
$210$	2.81760e7	0.209948
$211$	3.03119e7	0.222139	0.111070	−	0.993813i	$-0.464572\pi$
$211$	3.03119e7	0.222139	0.111070	+	0.993813i	$0.464572\pi$
$212$	−1.17204e7	−0.0844826
$213$	6.67819e7	0.473511
$214$	1.80038e7	0.125579
$215$	1.11908e8	0.767936
$216$	1.22191e8	0.824992
$217$	−1.69310e8	−1.12479
$218$	−1.96626e8	−1.28541
$219$	−6.66004e7	−0.428472
$220$	−1.06709e6	−0.00675652
$221$	−3.31572e8	−2.06635
$222$	1.30286e7	0.0799211
$223$	−1.39101e8	−0.839971	−0.419986	−	0.907531i	$-0.637965\pi$
$223$	−1.39101e8	−0.839971	−0.419986	+	0.907531i	$0.637965\pi$
$224$	1.47749e7	0.0878329
$225$	1.08460e8	0.634790
$226$	7.87198e6	0.0453633
$227$	−1.70943e8	−0.969973	−0.484986	−	0.874522i	$-0.661175\pi$
$227$	−1.70943e8	−0.969973	−0.484986	+	0.874522i	$0.661175\pi$
$228$	6.48797e6	0.0362524
$229$	−7.48116e7	−0.411666	−0.205833	−	0.978587i	$-0.565990\pi$
$229$	−7.48116e7	−0.411666	−0.205833	+	0.978587i	$0.565990\pi$
$230$	−1.97235e7	−0.106890
$231$	3.36935e7	0.179847
$232$	2.12382e8	1.11663
$233$	2.30985e8	1.19629	0.598147	−	0.801386i	$-0.295904\pi$
$233$	2.30985e8	1.19629	0.598147	+	0.801386i	$0.295904\pi$
$234$	2.16920e8	1.10673
$235$	−8.50496e7	−0.427499
$236$	−1.01369e7	−0.0502011
$237$	3.83512e7	0.187137
$238$	3.19549e8	1.53645
$239$	4.37278e7	0.207188	0.103594	−	0.994620i	$-0.466966\pi$
$239$	4.37278e7	0.207188	0.103594	+	0.994620i	$0.466966\pi$
$240$	4.49386e7	0.209836
$241$	2.22817e8	1.02539	0.512694	−	0.858572i	$-0.328648\pi$
$241$	2.22817e8	1.02539	0.512694	+	0.858572i	$0.328648\pi$
$242$	1.94277e8	0.881186
$243$	−2.28382e8	−1.02103
$244$	−3.80612e6	−0.0167733
$245$	3.94563e6	0.0171410
$246$	−1.89552e8	−0.811810
$247$	−5.86584e8	−2.47680
$248$	−2.58863e8	−1.07768
$249$	1.53807e8	0.631362
$250$	1.94505e8	0.787302
$251$	−3.05532e8	−1.21955	−0.609773	−	0.792576i	$-0.708739\pi$
$251$	−3.05532e8	−1.21955	−0.609773	+	0.792576i	$0.708739\pi$
$252$	−8.63470e6	−0.0339896
$253$	−2.35857e7	−0.0915646
$254$	6.55676e7	0.251056
$255$	7.86986e7	0.297219
$256$	3.46316e7	0.129013
$257$	2.25865e8	0.830009	0.415005	−	0.909819i	$-0.363780\pi$
$257$	2.25865e8	0.830009	0.415005	+	0.909819i	$0.363780\pi$
$258$	2.43234e8	0.881769
$259$	4.68885e7	0.167694
$260$	7.24285e6	0.0255566
$261$	−2.53828e8	−0.883684
$262$	−9.51928e7	−0.327001
$263$	−1.04961e8	−0.355782	−0.177891	−	0.984050i	$-0.556927\pi$
$263$	−1.04961e8	−0.355782	−0.177891	+	0.984050i	$0.556927\pi$
$264$	5.15150e7	0.172314
$265$	−2.51509e8	−0.830218
$266$	5.65315e8	1.84164
$267$	−8.57196e7	−0.275607
$268$	1.49738e6	0.00475181
$269$	1.02373e8	0.320667	0.160333	−	0.987063i	$-0.448743\pi$
$269$	1.02373e8	0.320667	0.160333	+	0.987063i	$0.448743\pi$
$270$	−1.18054e8	−0.365013
$271$	2.40511e8	0.734078	0.367039	−	0.930206i	$-0.380372\pi$
$271$	2.40511e8	0.734078	0.367039	+	0.930206i	$0.380372\pi$
$272$	5.09657e8	1.53563
$273$	−2.28693e8	−0.680275
$274$	5.90443e7	0.173401
$275$	1.04847e8	0.304014
$276$	−1.77066e6	−0.00506937
$277$	4.27350e8	1.20810	0.604052	−	0.796945i	$-0.293552\pi$
$277$	4.27350e8	1.20810	0.604052	+	0.796945i	$0.293552\pi$
$278$	−1.07918e8	−0.301256
$279$	3.09378e8	0.852855
$280$	1.55038e8	0.422070
$281$	−6.00458e8	−1.61440	−0.807199	−	0.590280i	$-0.799018\pi$
$281$	−6.00458e8	−1.61440	−0.807199	+	0.590280i	$0.799018\pi$
$282$	−1.84857e8	−0.490868
$283$	5.29302e8	1.38820	0.694098	−	0.719881i	$-0.255803\pi$
$283$	5.29302e8	1.38820	0.694098	+	0.719881i	$0.255803\pi$
$284$	−1.65443e7	−0.0428583
$285$	1.39226e8	0.356256
$286$	2.09695e8	0.530038
$287$	−6.82177e8	−1.70338
$288$	−2.69981e7	−0.0665977
$289$	4.82196e8	1.17512
$290$	−2.05193e8	−0.494047
$291$	−2.23541e8	−0.531781
$292$	1.64994e7	0.0387817
$293$	1.65076e8	0.383397	0.191698	−	0.981454i	$-0.438600\pi$
$293$	1.65076e8	0.383397	0.191698	+	0.981454i	$0.438600\pi$
$294$	8.57593e6	0.0196818
$295$	−2.17528e8	−0.493331
$296$	7.16892e7	0.160669
$297$	−1.41172e8	−0.312680
$298$	−4.85502e8	−1.06276
$299$	1.60087e8	0.346344
$300$	7.87125e6	0.0168314
$301$	8.75373e8	1.85017
$302$	−6.39652e8	−1.33635
$303$	−1.85926e8	−0.383964
$304$	9.01634e8	1.84066
$305$	−8.16757e7	−0.164833
$306$	−5.83910e8	−1.16499
$307$	−5.60445e8	−1.10548	−0.552738	−	0.833355i	$-0.686417\pi$
$307$	−5.60445e8	−1.10548	−0.552738	+	0.833355i	$0.686417\pi$
$308$	−8.34712e6	−0.0162783
$309$	1.42410e8	0.274590
$310$	2.50099e8	0.476812
$311$	−3.06987e8	−0.578707	−0.289354	−	0.957222i	$-0.593440\pi$
$311$	−3.06987e8	−0.578707	−0.289354	+	0.957222i	$0.593440\pi$
$312$	−3.49656e8	−0.651778
$313$	−4.28573e8	−0.789987	−0.394994	−	0.918684i	$-0.629253\pi$
$313$	−4.28573e8	−0.789987	−0.394994	+	0.918684i	$0.629253\pi$
$314$	−2.15575e8	−0.392956
$315$	−1.85292e8	−0.334019
$316$	−9.50099e6	−0.0169381
$317$	−2.28615e8	−0.403086	−0.201543	−	0.979480i	$-0.564596\pi$
$317$	−2.28615e8	−0.403086	−0.201543	+	0.979480i	$0.564596\pi$
$318$	−5.46660e8	−0.953284
$319$	−2.45374e8	−0.423214
$320$	2.36581e8	0.403603
$321$	3.46838e7	0.0585274
$322$	−1.54283e8	−0.257526
$323$	1.57898e9	2.60717
$324$	9.80198e6	0.0160106
$325$	−7.11648e8	−1.14993
$326$	6.64260e8	1.06188
$327$	−3.78794e8	−0.599082
$328$	−1.04300e9	−1.63202
$329$	−6.65283e8	−1.02996
$330$	−4.97711e7	−0.0762392
$331$	−7.43301e8	−1.12659	−0.563296	−	0.826255i	$-0.690467\pi$
$331$	−7.43301e8	−1.12659	−0.563296	+	0.826255i	$0.690467\pi$
$332$	−3.81036e7	−0.0571457
$333$	−8.56789e7	−0.127151
$334$	3.28906e8	0.483014
$335$	3.21323e7	0.0466965
$336$	3.51523e8	0.505552
$337$	7.28354e8	1.03666	0.518332	−	0.855179i	$-0.326553\pi$
$337$	7.28354e8	1.03666	0.518332	+	0.855179i	$0.326553\pi$
$338$	−6.98245e8	−0.983557
$339$	1.51651e7	0.0211421
$340$	−1.94965e7	−0.0269018
$341$	2.99074e8	0.408450
$342$	−1.03300e9	−1.39639
$343$	−7.31474e8	−0.978745
$344$	1.33838e9	1.77266
$345$	−3.79967e7	−0.0498171
$346$	−1.03022e9	−1.33710
$347$	1.12493e8	0.144534	0.0722672	−	0.997385i	$-0.476977\pi$
$347$	1.12493e8	0.144534	0.0722672	+	0.997385i	$0.476977\pi$
$348$	−1.84210e7	−0.0234308
$349$	2.59612e8	0.326916	0.163458	−	0.986550i	$-0.447735\pi$
$349$	2.59612e8	0.326916	0.163458	+	0.986550i	$0.447735\pi$
$350$	6.85844e8	0.855042
$351$	9.58197e8	1.18271
$352$	−2.60989e7	−0.0318950
$353$	3.23378e8	0.391290	0.195645	−	0.980675i	$-0.437320\pi$
$353$	3.23378e8	0.391290	0.195645	+	0.980675i	$0.437320\pi$
$354$	−4.72803e8	−0.566459
$355$	−3.55025e8	−0.421173
$356$	2.12359e7	0.0249457
$357$	6.15603e8	0.716081
$358$	1.23178e9	1.41886
$359$	1.13077e9	1.28986	0.644929	−	0.764242i	$-0.276887\pi$
$359$	1.13077e9	1.28986	0.644929	+	0.764242i	$0.276887\pi$
$360$	−2.83299e8	−0.320027
$361$	1.89951e9	2.12503
$362$	1.62903e9	1.80488
$363$	3.74269e8	0.410687
$364$	5.66557e7	0.0615728
$365$	3.54060e8	0.381111
$366$	−1.77524e8	−0.189266
$367$	−1.79664e9	−1.89728	−0.948639	−	0.316360i	$-0.897539\pi$
$367$	−1.79664e9	−1.89728	−0.948639	+	0.316360i	$0.897539\pi$
$368$	−2.46069e8	−0.257389
$369$	1.24654e9	1.29155
$370$	−6.92623e7	−0.0710871
$371$	−1.96737e9	−2.00022
$372$	2.24525e7	0.0226133
$373$	1.18494e9	1.18226	0.591132	−	0.806575i	$-0.298681\pi$
$373$	1.18494e9	1.18226	0.591132	+	0.806575i	$0.298681\pi$
$374$	−5.64462e8	−0.557936
$375$	3.74709e8	0.366931
$376$	−1.01717e9	−0.986816
$377$	1.66546e9	1.60081
$378$	−9.23454e8	−0.879415
$379$	6.46583e8	0.610081	0.305040	−	0.952339i	$-0.401330\pi$
$379$	6.46583e8	0.610081	0.305040	+	0.952339i	$0.401330\pi$
$380$	−3.44913e7	−0.0322453
$381$	1.26314e8	0.117008
$382$	8.93751e8	0.820342
$383$	1.48505e9	1.35065	0.675327	−	0.737519i	$-0.264003\pi$
$383$	1.48505e9	1.35065	0.675327	+	0.737519i	$0.264003\pi$
$384$	5.59692e8	0.504417
$385$	−1.79121e8	−0.159968
$386$	−1.18770e9	−1.05112
$387$	−1.59956e9	−1.40285
$388$	5.53794e7	0.0481324
$389$	1.82621e8	0.157300	0.0786499	−	0.996902i	$-0.474939\pi$
$389$	1.82621e8	0.157300	0.0786499	+	0.996902i	$0.474939\pi$
$390$	3.37819e8	0.288375
$391$	−4.30927e8	−0.364573
$392$	4.71887e7	0.0395673
$393$	−1.83386e8	−0.152403
$394$	−6.10710e8	−0.503035
$395$	−2.03882e8	−0.166452
$396$	1.52526e7	0.0123427
$397$	1.45384e9	1.16614	0.583068	−	0.812424i	$-0.301852\pi$
$397$	1.45384e9	1.16614	0.583068	+	0.812424i	$0.301852\pi$
$398$	−1.26563e9	−1.00628
$399$	1.08906e9	0.858318
$400$	1.09387e9	0.854585
$401$	−1.09551e9	−0.848420	−0.424210	−	0.905564i	$-0.639448\pi$
$401$	−1.09551e9	−0.848420	−0.424210	+	0.905564i	$0.639448\pi$
$402$	6.98402e7	0.0536184
$403$	−2.02995e9	−1.54496
$404$	4.60606e7	0.0347532
$405$	2.10341e8	0.157337
$406$	−1.60508e9	−1.19029
$407$	−8.28253e7	−0.0608952
$408$	9.41213e8	0.686084
$409$	−1.93352e9	−1.39739	−0.698693	−	0.715421i	$-0.746235\pi$
$409$	−1.93352e9	−1.39739	−0.698693	+	0.715421i	$0.746235\pi$
$410$	1.00769e9	0.722078
$411$	1.13747e8	0.0808155
$412$	−3.52801e7	−0.0248536
$413$	−1.70157e9	−1.18857
$414$	2.81919e8	0.195265
$415$	−8.17667e8	−0.561576
$416$	1.77145e8	0.120643
$417$	−2.07900e8	−0.140404
$418$	−9.98591e8	−0.668760
$419$	2.35866e9	1.56645	0.783225	−	0.621738i	$-0.213573\pi$
$419$	2.35866e9	1.56645	0.783225	+	0.621738i	$0.213573\pi$
$420$	−1.34472e7	−0.00885646
$421$	−2.62705e9	−1.71586	−0.857929	−	0.513769i	$-0.828249\pi$
$421$	−2.62705e9	−1.71586	−0.857929	+	0.513769i	$0.828249\pi$
$422$	−3.50250e8	−0.226874
$423$	1.21566e9	0.780949
$424$	−3.00797e9	−1.91643
$425$	1.91563e9	1.21046
$426$	−7.71655e8	−0.483604
$427$	−6.38891e8	−0.397127
$428$	−8.59244e6	−0.00529741
$429$	4.03971e8	0.247030
$430$	−1.29308e9	−0.784304
$431$	5.27516e7	0.0317370	0.0158685	−	0.999874i	$-0.494949\pi$
$431$	5.27516e7	0.0317370	0.0158685	+	0.999874i	$0.494949\pi$
$432$	−1.47284e9	−0.878945
$433$	1.46655e9	0.868138	0.434069	−	0.900880i	$-0.357077\pi$
$433$	1.46655e9	0.868138	0.434069	+	0.900880i	$0.357077\pi$
$434$	1.95635e9	1.14877
$435$	−3.95298e8	−0.230256
$436$	9.38412e7	0.0542239
$437$	−7.62353e8	−0.436990
$438$	7.69558e8	0.437605
$439$	−1.02933e9	−0.580667	−0.290333	−	0.956926i	$-0.593766\pi$
$439$	−1.02933e9	−0.580667	−0.290333	+	0.956926i	$0.593766\pi$
$440$	−2.73863e8	−0.153267
$441$	−5.63973e7	−0.0313129
$442$	3.83126e9	2.11040
$443$	−2.05723e9	−1.12427	−0.562134	−	0.827046i	$-0.690020\pi$
$443$	−2.05723e9	−1.12427	−0.562134	+	0.827046i	$0.690020\pi$
$444$	−6.21798e6	−0.00337139
$445$	4.55701e8	0.245143
$446$	1.60730e9	0.857875
$447$	−9.35305e8	−0.495310
$448$	1.85060e9	0.972390
$449$	2.92368e8	0.152429	0.0762146	−	0.997091i	$-0.475717\pi$
$449$	2.92368e8	0.152429	0.0762146	+	0.997091i	$0.475717\pi$
$450$	−1.25324e9	−0.648320
$451$	1.20502e9	0.618552
$452$	−3.75696e6	−0.00191360
$453$	−1.23227e9	−0.622820
$454$	1.97522e9	0.990647
$455$	1.21578e9	0.605082
$456$	1.66510e9	0.822363
$457$	6.29451e8	0.308500	0.154250	−	0.988032i	$-0.450704\pi$
$457$	6.29451e8	0.308500	0.154250	+	0.988032i	$0.450704\pi$
$458$	8.64437e8	0.420440
$459$	−2.57930e9	−1.24497
$460$	9.41316e6	0.00450903
$461$	−8.22753e8	−0.391126	−0.195563	−	0.980691i	$-0.562653\pi$
$461$	−8.22753e8	−0.391126	−0.195563	+	0.980691i	$0.562653\pi$
$462$	−3.89324e8	−0.183681
$463$	−2.25780e9	−1.05719	−0.528593	−	0.848876i	$-0.677280\pi$
$463$	−2.25780e9	−1.05719	−0.528593	+	0.848876i	$0.677280\pi$
$464$	−2.55997e9	−1.18966
$465$	4.81809e8	0.222223
$466$	−2.66900e9	−1.22179
$467$	1.63894e9	0.744655	0.372327	−	0.928101i	$-0.378560\pi$
$467$	1.63894e9	0.744655	0.372327	+	0.928101i	$0.378560\pi$
$468$	−1.03526e8	−0.0466864
$469$	2.51348e8	0.112505
$470$	9.82735e8	0.436610
$471$	−4.15298e8	−0.183142
$472$	−2.60158e9	−1.13878
$473$	−1.54629e9	−0.671856
$474$	−4.43142e8	−0.191126
$475$	3.38895e9	1.45090
$476$	−1.52507e8	−0.0648136
$477$	3.59496e9	1.51663
$478$	−5.05269e8	−0.211604
$479$	1.33549e9	0.555224	0.277612	−	0.960693i	$-0.410457\pi$
$479$	1.33549e9	0.555224	0.277612	+	0.960693i	$0.410457\pi$
$480$	−4.20454e7	−0.0173530
$481$	5.62174e8	0.230336
$482$	−2.57461e9	−1.04724
$483$	−2.97221e8	−0.120023
$484$	−9.27201e7	−0.0371719
$485$	1.18839e9	0.473001
$486$	2.63892e9	1.04280
$487$	−6.37479e8	−0.250101	−0.125050	−	0.992150i	$-0.539909\pi$
$487$	−6.37479e8	−0.250101	−0.125050	+	0.992150i	$0.539909\pi$
$488$	−9.76819e8	−0.380491
$489$	1.27968e9	0.494902
$490$	−4.55912e7	−0.0175063
$491$	1.03337e9	0.393977	0.196989	−	0.980406i	$-0.436884\pi$
$491$	1.03337e9	0.393977	0.196989	+	0.980406i	$0.436884\pi$
$492$	9.04649e7	0.0342454
$493$	−4.48314e9	−1.68507
$494$	6.77789e9	2.52959
$495$	3.27306e8	0.121293
$496$	3.12023e9	1.14815
$497$	−2.77711e9	−1.01472
$498$	−1.77722e9	−0.644819
$499$	−3.38081e8	−0.121806	−0.0609030	−	0.998144i	$-0.519398\pi$
$499$	−3.38081e8	−0.121806	−0.0609030	+	0.998144i	$0.519398\pi$
$500$	−9.28291e7	−0.0332116
$501$	6.33629e8	0.225114
$502$	3.53037e9	1.24554
$503$	−2.19336e9	−0.768461	−0.384230	−	0.923237i	$-0.625533\pi$
$503$	−2.19336e9	−0.768461	−0.384230	+	0.923237i	$0.625533\pi$
$504$	−2.21605e9	−0.771031
$505$	9.88415e8	0.341523
$506$	2.72530e8	0.0935162
$507$	−1.34515e9	−0.458398
$508$	−3.12926e7	−0.0105906
$509$	7.28807e8	0.244963	0.122481	−	0.992471i	$-0.460915\pi$
$509$	7.28807e8	0.244963	0.122481	+	0.992471i	$0.460915\pi$
$510$	−9.09350e8	−0.303554
$511$	2.76956e9	0.918201
$512$	2.81818e9	0.927948
$513$	−4.56304e9	−1.49226
$514$	−2.60984e9	−0.847700
$515$	−7.57077e8	−0.244239
$516$	−1.16085e8	−0.0371965
$517$	1.17518e9	0.374012
$518$	−5.41790e8	−0.171268
$519$	−1.98469e9	−0.623170
$520$	1.85884e9	0.579735
$521$	1.23382e9	0.382226	0.191113	−	0.981568i	$-0.438790\pi$
$521$	1.23382e9	0.382226	0.191113	+	0.981568i	$0.438790\pi$
$522$	2.93294e9	0.902519
$523$	1.47934e8	0.0452180	0.0226090	−	0.999744i	$-0.492803\pi$
$523$	1.47934e8	0.0452180	0.0226090	+	0.999744i	$0.492803\pi$
$524$	4.54315e7	0.0137942
$525$	1.32126e9	0.398502
$526$	1.21281e9	0.363365
$527$	5.46429e9	1.62628
$528$	−6.20941e8	−0.183583
$529$	−3.19677e9	−0.938893
$530$	2.90615e9	0.847914
$531$	3.10926e9	0.901211
$532$	−2.69801e8	−0.0776878
$533$	−8.17902e9	−2.33968
$534$	9.90477e8	0.281482
$535$	−1.84386e8	−0.0520581
$536$	3.84293e8	0.107792
$537$	2.37298e9	0.661278
$538$	−1.18291e9	−0.327502
$539$	−5.45190e7	−0.0149964
$540$	5.63422e7	0.0153977
$541$	−3.94925e9	−1.07232	−0.536159	−	0.844117i	$-0.680125\pi$
$541$	−3.94925e9	−1.07232	−0.536159	+	0.844117i	$0.680125\pi$
$542$	−2.77907e9	−0.749724
$543$	3.13828e9	0.841187
$544$	−4.76844e8	−0.126993
$545$	2.01374e9	0.532864
$546$	2.64252e9	0.694774
$547$	6.48367e9	1.69381	0.846906	−	0.531742i	$-0.178462\pi$
$547$	6.48367e9	1.69381	0.846906	+	0.531742i	$0.178462\pi$
$548$	−2.81793e7	−0.00731474
$549$	1.16744e9	0.301114
$550$	−1.21150e9	−0.310494
$551$	−7.93112e9	−2.01978
$552$	−4.54430e8	−0.114995
$553$	−1.59482e9	−0.401028
$554$	−4.93796e9	−1.23385
$555$	−1.33432e8	−0.0331310
$556$	5.15044e7	0.0127082
$557$	−2.10458e9	−0.516027	−0.258013	−	0.966141i	$-0.583068\pi$
$557$	−2.10458e9	−0.516027	−0.258013	+	0.966141i	$0.583068\pi$
$558$	−3.57482e9	−0.871033
$559$	1.04954e10	2.54130
$560$	−1.86876e9	−0.449672
$561$	−1.08742e9	−0.260032
$562$	6.93820e9	1.64881
$563$	−3.95132e8	−0.0933175	−0.0466588	−	0.998911i	$-0.514857\pi$
$563$	−3.95132e8	−0.0933175	−0.0466588	+	0.998911i	$0.514857\pi$
$564$	8.82245e7	0.0207068
$565$	−8.06208e7	−0.0188052
$566$	−6.11600e9	−1.41778
$567$	1.64535e9	0.379068
$568$	−4.24601e9	−0.972213
$569$	−1.61609e9	−0.367767	−0.183883	−	0.982948i	$-0.558867\pi$
$569$	−1.61609e9	−0.367767	−0.183883	+	0.982948i	$0.558867\pi$
$570$	−1.60873e9	−0.363849
$571$	−3.90742e9	−0.878341	−0.439171	−	0.898404i	$-0.644728\pi$
$571$	−3.90742e9	−0.878341	−0.439171	+	0.898404i	$0.644728\pi$
$572$	−1.00078e8	−0.0223591
$573$	1.72179e9	0.382330
$574$	7.88245e9	1.73968
$575$	−9.24892e8	−0.202887
$576$	−3.38159e9	−0.737297
$577$	−4.52534e9	−0.980699	−0.490350	−	0.871526i	$-0.663131\pi$
$577$	−4.52534e9	−0.980699	−0.490350	+	0.871526i	$0.663131\pi$
$578$	−5.57170e9	−1.20016
$579$	−2.28807e9	−0.489885
$580$	9.79297e7	0.0208409
$581$	−6.39603e9	−1.35299
$582$	2.58299e9	0.543115
$583$	3.47523e9	0.726346
$584$	4.23446e9	0.879738
$585$	−2.22158e9	−0.458792
$586$	−1.90743e9	−0.391569
$587$	−1.64936e9	−0.336574	−0.168287	−	0.985738i	$-0.553824\pi$
$587$	−1.64936e9	−0.336574	−0.168287	+	0.985738i	$0.553824\pi$
$588$	−4.09292e6	−0.000830258 0
$589$	9.66687e9	1.94932
$590$	2.51351e9	0.503846
$591$	−1.17652e9	−0.234445
$592$	−8.64113e8	−0.171177
$593$	6.56810e9	1.29345	0.646723	−	0.762725i	$-0.276139\pi$
$593$	6.56810e9	1.29345	0.646723	+	0.762725i	$0.276139\pi$
$594$	1.63122e9	0.319345
$595$	−3.27266e9	−0.636930
$596$	2.31709e8	0.0448313
$597$	−2.43821e9	−0.468986
$598$	−1.84978e9	−0.353726
$599$	−6.92403e9	−1.31633	−0.658166	−	0.752873i	$-0.728667\pi$
$599$	−6.92403e9	−1.31633	−0.658166	+	0.752873i	$0.728667\pi$
$600$	2.02011e9	0.381809
$601$	−2.79378e9	−0.524967	−0.262483	−	0.964936i	$-0.584542\pi$
$601$	−2.79378e9	−0.524967	−0.262483	+	0.964936i	$0.584542\pi$
$602$	−1.01148e10	−1.88960
$603$	−4.59286e8	−0.0853046
$604$	3.05279e8	0.0563725
$605$	−1.98968e9	−0.365292
$606$	2.14834e9	0.392147
$607$	1.38554e9	0.251454	0.125727	−	0.992065i	$-0.459874\pi$
$607$	1.38554e9	0.251454	0.125727	+	0.992065i	$0.459874\pi$
$608$	−8.43585e8	−0.152218
$609$	−3.09213e9	−0.554750
$610$	9.43751e8	0.168346
$611$	−7.97646e9	−1.41470
$612$	2.78675e8	0.0491438
$613$	−2.34850e9	−0.411792	−0.205896	−	0.978574i	$-0.566011\pi$
$613$	−2.34850e9	−0.411792	−0.205896	+	0.978574i	$0.566011\pi$
$614$	6.47586e9	1.12904
$615$	1.94129e9	0.336533
$616$	−2.14224e9	−0.369263
$617$	2.46850e9	0.423093	0.211546	−	0.977368i	$-0.432150\pi$
$617$	2.46850e9	0.423093	0.211546	+	0.977368i	$0.432150\pi$
$618$	−1.64552e9	−0.280443
$619$	4.53246e9	0.768098	0.384049	−	0.923313i	$-0.374529\pi$
$619$	4.53246e9	0.768098	0.384049	+	0.923313i	$0.374529\pi$
$620$	−1.19362e8	−0.0201138
$621$	1.24532e9	0.208670
$622$	3.54719e9	0.591042
$623$	3.56463e9	0.590617
$624$	4.21461e9	0.694403
$625$	3.01742e9	0.494375
$626$	4.95210e9	0.806825
$627$	−1.92376e9	−0.311683
$628$	1.02885e8	0.0165764
$629$	−1.51327e9	−0.242460
$630$	2.14103e9	0.341138
$631$	7.91501e9	1.25415	0.627074	−	0.778960i	$-0.284252\pi$
$631$	7.91501e9	1.25415	0.627074	+	0.778960i	$0.284252\pi$
$632$	−2.43837e9	−0.384229
$633$	−6.74746e8	−0.105737
$634$	2.64161e9	0.411677
$635$	−6.71509e8	−0.104074
$636$	2.60897e8	0.0402133
$637$	3.70045e8	0.0567240
$638$	2.83526e9	0.432235
$639$	5.07459e9	0.769392
$640$	−2.97543e9	−0.448662
$641$	9.98936e9	1.49808	0.749039	−	0.662525i	$-0.230515\pi$
$641$	9.98936e9	1.49808	0.749039	+	0.662525i	$0.230515\pi$
$642$	−4.00766e8	−0.0597748
$643$	−4.11877e9	−0.610983	−0.305492	−	0.952195i	$-0.598821\pi$
$643$	−4.11877e9	−0.610983	−0.305492	+	0.952195i	$0.598821\pi$
$644$	7.36325e7	0.0108635
$645$	−2.49107e9	−0.365534
$646$	−1.82449e10	−2.66274
$647$	−7.20336e9	−1.04561	−0.522805	−	0.852452i	$-0.675114\pi$
$647$	−7.20336e9	−1.04561	−0.522805	+	0.852452i	$0.675114\pi$
$648$	2.51562e9	0.363189
$649$	3.00571e9	0.431609
$650$	8.22298e9	1.17444
$651$	3.76885e9	0.535397
$652$	−3.17023e8	−0.0447944
$653$	−9.65263e8	−0.135659	−0.0678296	−	0.997697i	$-0.521607\pi$
$653$	−9.65263e8	−0.135659	−0.0678296	+	0.997697i	$0.521607\pi$
$654$	4.37691e9	0.611851
$655$	9.74915e8	0.135557
$656$	1.25719e10	1.73875
$657$	−5.06079e9	−0.696209
$658$	7.68724e9	1.05191
$659$	−9.26318e8	−0.126084	−0.0630421	−	0.998011i	$-0.520080\pi$
$659$	−9.26318e8	−0.126084	−0.0630421	+	0.998011i	$0.520080\pi$
$660$	2.37536e7	0.00321607
$661$	1.22544e10	1.65039	0.825194	−	0.564849i	$-0.191066\pi$
$661$	1.22544e10	1.65039	0.825194	+	0.564849i	$0.191066\pi$
$662$	8.58873e9	1.15060
$663$	7.38082e9	0.983575
$664$	−9.77908e9	−1.29631
$665$	−5.78967e9	−0.763445
$666$	9.90008e8	0.129861
$667$	2.16452e9	0.282436
$668$	−1.56973e8	−0.0203755
$669$	3.09641e9	0.399822
$670$	−3.71283e8	−0.0476918
$671$	1.12856e9	0.144210
$672$	−3.28891e8	−0.0418080
$673$	4.54245e9	0.574431	0.287215	−	0.957866i	$-0.407270\pi$
$673$	4.54245e9	0.574431	0.287215	+	0.957866i	$0.407270\pi$
$674$	−8.41603e9	−1.05876
$675$	−5.53591e9	−0.692829
$676$	3.33243e8	0.0414904
$677$	−1.52955e10	−1.89454	−0.947272	−	0.320431i	$-0.896172\pi$
$677$	−1.52955e10	−1.89454	−0.947272	+	0.320431i	$0.896172\pi$
$678$	−1.75231e8	−0.0215927
$679$	9.29592e9	1.13959
$680$	−5.00367e9	−0.610249
$681$	3.80520e9	0.461703
$682$	−3.45576e9	−0.417156
$683$	1.47521e10	1.77166	0.885832	−	0.464006i	$-0.153589\pi$
$683$	1.47521e10	1.77166	0.885832	+	0.464006i	$0.153589\pi$
$684$	4.93005e8	0.0589053
$685$	−6.04702e8	−0.0718827
$686$	8.45207e9	0.999606
$687$	1.66531e9	0.195951
$688$	−1.61323e10	−1.88859
$689$	−2.35880e10	−2.74741
$690$	4.39046e8	0.0508790
$691$	9.33058e9	1.07581	0.537905	−	0.843006i	$-0.319216\pi$
$691$	9.33058e9	1.07581	0.537905	+	0.843006i	$0.319216\pi$
$692$	4.91680e8	0.0564041
$693$	2.56028e9	0.292228
$694$	−1.29984e9	−0.147615
$695$	1.10524e9	0.124884
$696$	−4.72765e9	−0.531512
$697$	2.20165e10	2.46282
$698$	−2.99978e9	−0.333884
$699$	−5.14175e9	−0.569430
$700$	−3.27324e8	−0.0360691
$701$	−6.12415e9	−0.671480	−0.335740	−	0.941955i	$-0.608986\pi$
$701$	−6.12415e9	−0.671480	−0.335740	+	0.941955i	$0.608986\pi$
$702$	−1.10718e10	−1.20792
$703$	−2.67713e9	−0.290621
$704$	−3.26897e9	−0.353107
$705$	1.89321e9	0.203487
$706$	−3.73659e9	−0.399631
$707$	7.73167e9	0.822821
$708$	2.25649e8	0.0238955
$709$	−3.70804e9	−0.390736	−0.195368	−	0.980730i	$-0.562590\pi$
$709$	−3.70804e9	−0.390736	−0.195368	+	0.980730i	$0.562590\pi$
$710$	4.10226e9	0.430150
$711$	2.91421e9	0.304072
$712$	5.45006e9	0.565876
$713$	−2.63823e9	−0.272583
$714$	−7.11320e9	−0.731344
$715$	−2.14759e9	−0.219725
$716$	−5.87874e8	−0.0598534
$717$	−9.73386e8	−0.0986207
$718$	−1.30658e10	−1.31735
$719$	7.41676e9	0.744154	0.372077	−	0.928202i	$-0.378646\pi$
$719$	7.41676e9	0.744154	0.372077	+	0.928202i	$0.378646\pi$
$720$	3.41477e9	0.340956
$721$	−5.92208e9	−0.588438
$722$	−2.19485e10	−2.17033
$723$	−4.95992e9	−0.488079
$724$	−7.77467e8	−0.0761372
$725$	−9.62209e9	−0.937749
$726$	−4.32462e9	−0.419440
$727$	−1.23745e10	−1.19442	−0.597212	−	0.802084i	$-0.703725\pi$
$727$	−1.23745e10	−1.19442	−0.597212	+	0.802084i	$0.703725\pi$
$728$	1.45404e10	1.39674
$729$	1.19653e9	0.114387
$730$	−4.09111e9	−0.389235
$731$	−2.82517e10	−2.67506
$732$	8.47246e7	0.00798401
$733$	−9.50315e9	−0.891258	−0.445629	−	0.895218i	$-0.647020\pi$
$733$	−9.50315e9	−0.891258	−0.445629	+	0.895218i	$0.647020\pi$
$734$	2.07600e10	1.93772
$735$	−8.78302e7	−0.00815902
$736$	2.30226e8	0.0212854
$737$	−4.43989e8	−0.0408541
$738$	−1.44035e10	−1.31908
$739$	−1.26702e10	−1.15486	−0.577429	−	0.816441i	$-0.695944\pi$
$739$	−1.26702e10	−1.15486	−0.577429	+	0.816441i	$0.695944\pi$
$740$	3.30559e7	0.00299874
$741$	1.30574e10	1.17894
$742$	2.27327e10	2.04286
$743$	1.40706e10	1.25850	0.629248	−	0.777204i	$-0.283363\pi$
$743$	1.40706e10	1.25850	0.629248	+	0.777204i	$0.283363\pi$
$744$	5.76231e9	0.512969
$745$	4.97226e9	0.440562
$746$	−1.36918e10	−1.20746
$747$	1.16874e10	1.02588
$748$	2.69394e8	0.0235360
$749$	−1.44232e9	−0.125422
$750$	−4.32971e9	−0.374752
$751$	1.94055e9	0.167180	0.0835901	−	0.996500i	$-0.473361\pi$
$751$	1.94055e9	0.167180	0.0835901	+	0.996500i	$0.473361\pi$
$752$	1.22606e10	1.05135
$753$	6.80116e9	0.580498
$754$	−1.92442e10	−1.63493
$755$	6.55099e9	0.553978
$756$	4.40725e8	0.0370972
$757$	1.06109e9	0.0889030	0.0444515	−	0.999012i	$-0.485846\pi$
$757$	1.06109e9	0.0889030	0.0444515	+	0.999012i	$0.485846\pi$
$758$	−7.47118e9	−0.623084
$759$	5.25021e8	0.0435843
$760$	−8.85199e9	−0.731465
$761$	9.14246e9	0.751998	0.375999	−	0.926620i	$-0.377300\pi$
$761$	9.14246e9	0.751998	0.375999	+	0.926620i	$0.377300\pi$
$762$	−1.45954e9	−0.119502
$763$	1.57521e10	1.28381
$764$	−4.26549e8	−0.0346053
$765$	5.98010e9	0.482941
$766$	−1.71595e10	−1.37944
$767$	−2.04011e10	−1.63256
$768$	−7.70904e8	−0.0614095
$769$	−1.22762e10	−0.973467	−0.486734	−	0.873550i	$-0.661812\pi$
$769$	−1.22762e10	−0.973467	−0.486734	+	0.873550i	$0.661812\pi$
$770$	2.06972e9	0.163378
$771$	−5.02778e9	−0.395080
$772$	5.66838e8	0.0443403
$773$	7.58717e8	0.0590815	0.0295408	−	0.999564i	$-0.490596\pi$
$773$	7.58717e8	0.0590815	0.0295408	+	0.999564i	$0.490596\pi$
$774$	1.84827e10	1.43276
$775$	1.17279e10	0.905034
$776$	1.42128e10	1.09185
$777$	−1.04374e9	−0.0798215
$778$	−2.11016e9	−0.160652
$779$	3.89494e10	2.95202
$780$	−1.61227e8	−0.0121648
$781$	4.90558e9	0.368478
$782$	4.97930e9	0.372344
$783$	1.29557e10	0.964480
$784$	−5.68794e8	−0.0421550
$785$	2.20780e9	0.162898
$786$	2.11900e9	0.155651
$787$	−9.04663e9	−0.661569	−0.330784	−	0.943706i	$-0.607313\pi$
$787$	−9.04663e9	−0.661569	−0.330784	+	0.943706i	$0.607313\pi$
$788$	2.91466e8	0.0212200
$789$	2.33645e9	0.169350
$790$	2.35583e9	0.170000
$791$	−6.30639e8	−0.0453068
$792$	3.91449e9	0.279987
$793$	−7.66004e9	−0.545475
$794$	−1.67989e10	−1.19099
$795$	5.59861e9	0.395180
$796$	6.04033e8	0.0424487
$797$	3.36932e9	0.235743	0.117871	−	0.993029i	$-0.462393\pi$
$797$	3.36932e9	0.235743	0.117871	+	0.993029i	$0.462393\pi$
$798$	−1.25840e10	−0.876612
$799$	2.14713e10	1.48917
$800$	−1.02344e9	−0.0706722
$801$	−6.51361e9	−0.447825
$802$	1.26585e10	0.866504
$803$	−4.89224e9	−0.333429
$804$	−3.33317e7	−0.00226184
$805$	1.58008e9	0.106756
$806$	2.34558e10	1.57789
$807$	−2.27884e9	−0.152636
$808$	1.18212e10	0.788353
$809$	2.19747e10	1.45916	0.729582	−	0.683894i	$-0.239715\pi$
$809$	2.19747e10	1.45916	0.729582	+	0.683894i	$0.239715\pi$
$810$	−2.43046e9	−0.160691
$811$	−1.15529e10	−0.760534	−0.380267	−	0.924877i	$-0.624168\pi$
$811$	−1.15529e10	−0.760534	−0.380267	+	0.924877i	$0.624168\pi$
$812$	7.66034e8	0.0502114
$813$	−5.35380e9	−0.349418
$814$	9.57035e8	0.0621931
$815$	−6.80300e9	−0.440199
$816$	−1.13450e10	−0.730953
$817$	−4.99801e10	−3.20642
$818$	2.23415e10	1.42717
$819$	−1.73778e10	−1.10535
$820$	−4.80928e8	−0.0304601
$821$	6.81179e9	0.429596	0.214798	−	0.976658i	$-0.431091\pi$
$821$	6.81179e9	0.429596	0.214798	+	0.976658i	$0.431091\pi$
$822$	−1.31433e9	−0.0825380
$823$	1.51865e9	0.0949641	0.0474820	−	0.998872i	$-0.484880\pi$
$823$	1.51865e9	0.0949641	0.0474820	+	0.998872i	$0.484880\pi$
$824$	−9.05444e9	−0.563789
$825$	−2.33391e9	−0.144709
$826$	1.96614e10	1.21390
$827$	−2.47726e10	−1.52301	−0.761506	−	0.648158i	$-0.775540\pi$
$827$	−2.47726e10	−1.52301	−0.761506	+	0.648158i	$0.775540\pi$
$828$	−1.34548e8	−0.00823704
$829$	−2.39666e10	−1.46105	−0.730527	−	0.682884i	$-0.760725\pi$
$829$	−2.39666e10	−1.46105	−0.730527	+	0.682884i	$0.760725\pi$
$830$	9.44803e9	0.573545
$831$	−9.51284e9	−0.575052
$832$	2.21880e10	1.33563
$833$	−9.96098e8	−0.0597096
$834$	2.40225e9	0.143396
$835$	−3.36849e9	−0.200232
$836$	4.76585e8	0.0282110
$837$	−1.57910e10	−0.930832
$838$	−2.72540e10	−1.59984
$839$	1.73745e10	1.01566	0.507828	−	0.861459i	$-0.330449\pi$
$839$	1.73745e10	1.01566	0.507828	+	0.861459i	$0.330449\pi$
$840$	−3.45115e9	−0.200903
$841$	5.26863e9	0.305430
$842$	3.03552e10	1.75243
$843$	1.33663e10	0.768446
$844$	1.67159e8	0.00957044
$845$	7.15107e9	0.407730
$846$	−1.40468e10	−0.797594
$847$	−1.55639e10	−0.880088
$848$	3.62569e10	2.04176
$849$	−1.17823e10	−0.660775
$850$	−2.21349e10	−1.23626
$851$	7.30628e8	0.0406390
$852$	3.68278e8	0.0204003
$853$	1.94445e10	1.07269	0.536347	−	0.843998i	$-0.319804\pi$
$853$	1.94445e10	1.07269	0.536347	+	0.843998i	$0.319804\pi$
$854$	7.38229e9	0.405591
$855$	1.05794e10	0.578868
$856$	−2.20520e9	−0.120168
$857$	−3.05945e9	−0.166039	−0.0830195	−	0.996548i	$-0.526456\pi$
$857$	−3.05945e9	−0.166039	−0.0830195	+	0.996548i	$0.526456\pi$
$858$	−4.66783e9	−0.252295
$859$	−4.71535e9	−0.253827	−0.126914	−	0.991914i	$-0.540507\pi$
$859$	−4.71535e9	−0.253827	−0.126914	+	0.991914i	$0.540507\pi$
$860$	6.17130e8	0.0330851
$861$	1.51853e10	0.810799
$862$	−6.09537e8	−0.0324134
$863$	1.54364e10	0.817541	0.408770	−	0.912637i	$-0.365958\pi$
$863$	1.54364e10	0.817541	0.408770	+	0.912637i	$0.365958\pi$
$864$	1.37801e9	0.0726868
$865$	1.05510e10	0.554289
$866$	−1.69458e10	−0.886642
$867$	−1.07337e10	−0.559350
$868$	−9.33683e8	−0.0484596
$869$	2.81715e9	0.145627
$870$	4.56761e9	0.235164
$871$	3.01355e9	0.154531
$872$	2.40838e10	1.23004
$873$	−1.69863e10	−0.864072
$874$	8.80888e9	0.446304
$875$	−1.55822e10	−0.786322
$876$	−3.67277e8	−0.0184599
$877$	−3.71762e10	−1.86108	−0.930542	−	0.366184i	$-0.880664\pi$
$877$	−3.71762e10	−1.86108	−0.930542	+	0.366184i	$0.880664\pi$
$878$	1.18937e10	0.593043
$879$	−3.67462e9	−0.182495
$880$	3.30104e9	0.163291
$881$	−2.87634e10	−1.41718	−0.708588	−	0.705622i	$-0.750667\pi$
$881$	−2.87634e10	−1.41718	−0.708588	+	0.705622i	$0.750667\pi$
$882$	6.51663e8	0.0319803
$883$	−6.24977e8	−0.0305493	−0.0152747	−	0.999883i	$-0.504862\pi$
$883$	−6.24977e8	−0.0305493	−0.0152747	+	0.999883i	$0.504862\pi$
$884$	−1.82850e9	−0.0890250
$885$	4.84220e9	0.234823
$886$	2.37710e10	1.14823
$887$	−2.07411e10	−0.997929	−0.498965	−	0.866622i	$-0.666286\pi$
$887$	−2.07411e10	−0.997929	−0.498965	+	0.866622i	$0.666286\pi$
$888$	−1.59581e9	−0.0764778
$889$	−5.25274e9	−0.250743
$890$	−5.26556e9	−0.250368
$891$	−2.90640e9	−0.137652
$892$	−7.67094e8	−0.0361886
$893$	3.79848e10	1.78496
$894$	1.08073e10	0.505867
$895$	−1.26152e10	−0.588185
$896$	−2.32747e10	−1.08095
$897$	−3.56356e9	−0.164858
$898$	−3.37828e9	−0.155678
$899$	−2.74467e10	−1.25989
$900$	5.98117e8	0.0273487
$901$	6.34948e10	2.89202
$902$	−1.39238e10	−0.631736
$903$	−1.94859e10	−0.880670
$904$	−9.64202e8	−0.0434089
$905$	−1.66837e10	−0.748208
$906$	1.42387e10	0.636096
$907$	1.65595e10	0.736924	0.368462	−	0.929643i	$-0.379884\pi$
$907$	1.65595e10	0.736924	0.368462	+	0.929643i	$0.379884\pi$
$908$	−9.42686e8	−0.0417895
$909$	−1.41280e10	−0.623889
$910$	−1.40481e10	−0.617978
$911$	−2.98228e10	−1.30687	−0.653437	−	0.756981i	$-0.726674\pi$
$911$	−2.98228e10	−1.30687	−0.653437	+	0.756981i	$0.726674\pi$
$912$	−2.00705e10	−0.876144
$913$	1.12982e10	0.491315
$914$	−7.27322e9	−0.315076
$915$	1.81811e9	0.0784596
$916$	−4.12559e8	−0.0177358
$917$	7.62607e9	0.326594
$918$	2.98034e10	1.27150
$919$	2.51077e10	1.06710	0.533548	−	0.845770i	$-0.320858\pi$
$919$	2.51077e10	1.06710	0.533548	+	0.845770i	$0.320858\pi$
$920$	2.41583e9	0.102284
$921$	1.24756e10	0.526201
$922$	9.50679e9	0.399462
$923$	−3.32964e10	−1.39377
$924$	1.85808e8	0.00774839
$925$	−3.24792e9	−0.134930
$926$	2.60885e10	1.07972
$927$	1.08214e10	0.446173
$928$	2.39516e9	0.0983820
$929$	−2.03107e10	−0.831131	−0.415566	−	0.909563i	$-0.636416\pi$
$929$	−2.03107e10	−0.831131	−0.415566	+	0.909563i	$0.636416\pi$
$930$	−5.56724e9	−0.226960
$931$	−1.76220e9	−0.0715699
$932$	1.27380e9	0.0515401
$933$	6.83357e9	0.275462
$934$	−1.89378e10	−0.760527
$935$	5.78093e9	0.231290
$936$	−2.65695e10	−1.05905
$937$	−1.80983e10	−0.718702	−0.359351	−	0.933202i	$-0.617002\pi$
$937$	−1.80983e10	−0.718702	−0.359351	+	0.933202i	$0.617002\pi$
$938$	−2.90429e9	−0.114903
$939$	9.54009e9	0.376030
$940$	−4.69018e8	−0.0184180
$941$	−2.13805e10	−0.836479	−0.418240	−	0.908337i	$-0.637353\pi$
$941$	−2.13805e10	−0.836479	−0.418240	+	0.908337i	$0.637353\pi$
$942$	4.79871e9	0.187045
$943$	−1.06298e10	−0.412797
$944$	3.13584e10	1.21325
$945$	9.45754e9	0.364558
$946$	1.78671e10	0.686176
$947$	−6.42112e9	−0.245689	−0.122845	−	0.992426i	$-0.539202\pi$
$947$	−6.42112e9	−0.245689	−0.122845	+	0.992426i	$0.539202\pi$
$948$	2.11493e8	0.00806244
$949$	3.32059e10	1.26120
$950$	−3.91588e10	−1.48182
$951$	5.08900e9	0.191867
$952$	−3.91401e10	−1.47026
$953$	2.10566e10	0.788067	0.394033	−	0.919096i	$-0.371079\pi$
$953$	2.10566e10	0.788067	0.394033	+	0.919096i	$0.371079\pi$
$954$	−4.15393e10	−1.54896
$955$	−9.15334e9	−0.340069
$956$	2.41143e8	0.00892632
$957$	5.46204e9	0.201448
$958$	−1.54314e10	−0.567058
$959$	−4.73015e9	−0.173185
$960$	−5.26631e9	−0.192113
$961$	5.94091e9	0.215934
$962$	−6.49583e9	−0.235246
$963$	2.63553e9	0.0950991
$964$	1.22875e9	0.0441769
$965$	1.21638e10	0.435736
$966$	3.43435e9	0.122581
$967$	5.47953e9	0.194872	0.0974362	−	0.995242i	$-0.468936\pi$
$967$	5.47953e9	0.194872	0.0974362	+	0.995242i	$0.468936\pi$
$968$	−2.37961e10	−0.843222
$969$	−3.51483e10	−1.24100
$970$	−1.37317e10	−0.483083
$971$	−1.28320e10	−0.449806	−0.224903	−	0.974381i	$-0.572207\pi$
$971$	−1.28320e10	−0.449806	−0.224903	+	0.974381i	$0.572207\pi$
$972$	−1.25944e9	−0.0439893
$973$	8.64547e9	0.300880
$974$	7.36598e9	0.255431
$975$	1.58413e10	0.547364
$976$	1.17742e10	0.405375
$977$	4.08944e10	1.40292	0.701460	−	0.712708i	$-0.252532\pi$
$977$	4.08944e10	1.40292	0.701460	+	0.712708i	$0.252532\pi$
$978$	−1.47865e10	−0.505451
$979$	−6.29667e9	−0.214472
$980$	2.17588e7	0.000738487 0
$981$	−2.87836e10	−0.973428
$982$	−1.19405e10	−0.402375
$983$	2.49526e10	0.837872	0.418936	−	0.908016i	$-0.362403\pi$
$983$	2.49526e10	0.837872	0.418936	+	0.908016i	$0.362403\pi$
$984$	2.32173e10	0.776835
$985$	6.25457e9	0.208531
$986$	5.18020e10	1.72099
$987$	1.48093e10	0.490256
$988$	−3.23480e9	−0.106708
$989$	1.36403e10	0.448370
$990$	−3.78198e9	−0.123878
$991$	1.20122e10	0.392070	0.196035	−	0.980597i	$-0.437193\pi$
$991$	1.20122e10	0.392070	0.196035	+	0.980597i	$0.437193\pi$
$992$	−2.91934e9	−0.0949498
$993$	1.65459e10	0.536252
$994$	3.20891e10	1.03635
$995$	1.29620e10	0.417148
$996$	8.48191e8	0.0272011
$997$	2.25949e10	0.722066	0.361033	−	0.932553i	$-0.382424\pi$
$997$	2.25949e10	0.722066	0.361033	+	0.932553i	$0.382424\pi$
$998$	3.90648e9	0.124402
$999$	4.37315e9	0.138776

Twists

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

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

\(f(q)\)	\(=\)	\(q-11.5549 q^{2} -22.2601 q^{3} +5.51464 q^{4} +118.339 q^{5} +257.212 q^{6} +925.681 q^{7} +1415.30 q^{8} -1691.49 q^{9} +O(q^{10})\)	\(q-11.5549 q^{2} -22.2601 q^{3} +5.51464 q^{4} +118.339 q^{5} +257.212 q^{6} +925.681 q^{7} +1415.30 q^{8} -1691.49 q^{9} -1367.39 q^{10} -1635.15 q^{11} -122.756 q^{12} +11098.5 q^{13} -10696.1 q^{14} -2634.23 q^{15} -17059.5 q^{16} -29875.3 q^{17} +19544.9 q^{18} -52852.4 q^{19} +652.596 q^{20} -20605.7 q^{21} +18893.9 q^{22} +14424.2 q^{23} -31504.7 q^{24} -64120.9 q^{25} -128242. q^{26} +86335.5 q^{27} +5104.80 q^{28} +150062. q^{29} +30438.2 q^{30} -182903. q^{31} +15961.1 q^{32} +36398.6 q^{33} +345205. q^{34} +109544. q^{35} -9327.95 q^{36} +50653.0 q^{37} +610702. q^{38} -247054. q^{39} +167485. q^{40} -736946. q^{41} +238096. q^{42} +945654. q^{43} -9017.27 q^{44} -200169. q^{45} -166669. q^{46} -718695. q^{47} +379745. q^{48} +33341.8 q^{49} +740908. q^{50} +665027. q^{51} +61204.4 q^{52} -2.12533e6 q^{53} -997594. q^{54} -193502. q^{55} +1.31012e6 q^{56} +1.17650e6 q^{57} -1.73394e6 q^{58} -1.83818e6 q^{59} -14526.8 q^{60} -690185. q^{61} +2.11342e6 q^{62} -1.56578e6 q^{63} +1.99918e6 q^{64} +1.31339e6 q^{65} -420581. q^{66} +271528. q^{67} -164752. q^{68} -321084. q^{69} -1.26576e6 q^{70} -3.00007e6 q^{71} -2.39396e6 q^{72} +2.99192e6 q^{73} -585288. q^{74} +1.42734e6 q^{75} -291462. q^{76} -1.51363e6 q^{77} +2.85468e6 q^{78} -1.72287e6 q^{79} -2.01880e6 q^{80} +1.77745e6 q^{81} +8.51531e6 q^{82} -6.90954e6 q^{83} -113633. q^{84} -3.53541e6 q^{85} -1.09269e7 q^{86} -3.34039e6 q^{87} -2.31423e6 q^{88} +3.85082e6 q^{89} +2.31292e6 q^{90} +1.02737e7 q^{91} +79544.2 q^{92} +4.07144e6 q^{93} +8.30442e6 q^{94} -6.25449e6 q^{95} -355297. q^{96} +1.00422e7 q^{97} -385260. q^{98} +2.76584e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 24 q^{2} - 95 q^{3} + 602 q^{4} - 624 q^{5} - 777 q^{6} - 501 q^{7} - 3810 q^{8} + 6181 q^{9}+O(q^{10}) \) 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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