LMFDB - Embedded newform 91.8.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(1,91)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.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:	$28.4270373191$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4 x^{8} - 764 x^{7} + 1562 x^{6} + 176422 x^{5} + 56746 x^{4} - 13204236 x^{3} + \cdots + 176334338 $ x^9 - 4x^8 - 764x^7 + 1562x^6 + 176422x^5 + 56746x^4 - 13204236x^3 - 22500802x^2 + 176026849x + 176334338
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$10.6825$ of defining polynomial
Character	$\chi$	$=$	91.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.68252 q^{2} +60.1290 q^{3} -34.2488 q^{4} -158.582 q^{5} +582.200 q^{6} -343.000 q^{7} -1570.98 q^{8} +1428.50 q^{9} +O(q^{10})$	\(q+9.68252 q^{2} +60.1290 q^{3} -34.2488 q^{4} -158.582 q^{5} +582.200 q^{6} -343.000 q^{7} -1570.98 q^{8} +1428.50 q^{9} -1535.48 q^{10} -4072.24 q^{11} -2059.35 q^{12} +2197.00 q^{13} -3321.10 q^{14} -9535.40 q^{15} -10827.2 q^{16} +945.853 q^{17} +13831.5 q^{18} -55952.9 q^{19} +5431.26 q^{20} -20624.3 q^{21} -39429.5 q^{22} +44746.7 q^{23} -94461.3 q^{24} -52976.6 q^{25} +21272.5 q^{26} -45608.0 q^{27} +11747.3 q^{28} -99583.7 q^{29} -92326.7 q^{30} +150775. q^{31} +96250.8 q^{32} -244860. q^{33} +9158.24 q^{34} +54393.8 q^{35} -48924.4 q^{36} +505908. q^{37} -541765. q^{38} +132103. q^{39} +249129. q^{40} +101017. q^{41} -199695. q^{42} -140944. q^{43} +139469. q^{44} -226535. q^{45} +433260. q^{46} -440509. q^{47} -651027. q^{48} +117649. q^{49} -512947. q^{50} +56873.2 q^{51} -75244.7 q^{52} -1.59520e6 q^{53} -441600. q^{54} +645785. q^{55} +538845. q^{56} -3.36439e6 q^{57} -964221. q^{58} +457981. q^{59} +326576. q^{60} -3.45027e6 q^{61} +1.45988e6 q^{62} -489975. q^{63} +2.31783e6 q^{64} -348406. q^{65} -2.37086e6 q^{66} +3.63713e6 q^{67} -32394.3 q^{68} +2.69057e6 q^{69} +526669. q^{70} +4.81142e6 q^{71} -2.24414e6 q^{72} -655263. q^{73} +4.89847e6 q^{74} -3.18543e6 q^{75} +1.91632e6 q^{76} +1.39678e6 q^{77} +1.27909e6 q^{78} -4.77387e6 q^{79} +1.71700e6 q^{80} -5.86649e6 q^{81} +978097. q^{82} -7.87248e6 q^{83} +706356. q^{84} -149996. q^{85} -1.36469e6 q^{86} -5.98787e6 q^{87} +6.39740e6 q^{88} +6.57523e6 q^{89} -2.19343e6 q^{90} -753571. q^{91} -1.53252e6 q^{92} +9.06594e6 q^{93} -4.26523e6 q^{94} +8.87315e6 q^{95} +5.78747e6 q^{96} +6.29434e6 q^{97} +1.13914e6 q^{98} -5.81719e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 5 q^{2} - 26 q^{3} + 393 q^{4} - 181 q^{5} + 703 q^{6} - 3087 q^{7} + 1197 q^{8} + 3211 q^{9}+O(q^{10}) $ 9 * q - 5 * q^2 - 26 * q^3 + 393 * q^4 - 181 * q^5 + 703 * q^6 - 3087 * q^7 + 1197 * q^8 + 3211 * q^9	\( 9 q - 5 q^{2} - 26 q^{3} + 393 q^{4} - 181 q^{5} + 703 q^{6} - 3087 q^{7} + 1197 q^{8} + 3211 q^{9} - 5124 q^{10} - 9826 q^{11} - 20919 q^{12} + 19773 q^{13} + 1715 q^{14} - 20346 q^{15} + 31113 q^{16} - 22766 q^{17} - 12978 q^{18} - 17769 q^{19} - 44204 q^{20} + 8918 q^{21} - 203553 q^{22} - 49103 q^{23} + 52737 q^{24} + 227466 q^{25} - 10985 q^{26} + 103624 q^{27} - 134799 q^{28} - 487455 q^{29} - 287992 q^{30} - 63843 q^{31} - 587099 q^{32} - 314392 q^{33} - 576240 q^{34} + 62083 q^{35} - 1514926 q^{36} - 796926 q^{37} - 766702 q^{38} - 57122 q^{39} - 2887296 q^{40} - 1567546 q^{41} - 241129 q^{42} - 277899 q^{43} - 1281195 q^{44} - 1650593 q^{45} - 1907445 q^{46} + 1077367 q^{47} - 1110835 q^{48} + 1058841 q^{49} - 267459 q^{50} - 3054368 q^{51} + 863421 q^{52} - 7322659 q^{53} - 3355387 q^{54} - 2613324 q^{55} - 410571 q^{56} - 3751946 q^{57} - 2992332 q^{58} - 169804 q^{59} - 2754416 q^{60} - 6352284 q^{61} + 6001087 q^{62} - 1101373 q^{63} + 1657017 q^{64} - 397657 q^{65} - 5962713 q^{66} + 921120 q^{67} + 5615224 q^{68} - 5202780 q^{69} + 1757532 q^{70} + 3786654 q^{71} + 2229758 q^{72} + 5792889 q^{73} - 1991961 q^{74} + 145628 q^{75} - 2806026 q^{76} + 3370318 q^{77} + 1544491 q^{78} + 3464037 q^{79} + 15422512 q^{80} - 5010363 q^{81} - 12539943 q^{82} + 6834945 q^{83} + 7175217 q^{84} + 3880662 q^{85} - 7977524 q^{86} + 3727078 q^{87} + 7013709 q^{88} - 20408371 q^{89} + 34910060 q^{90} - 6782139 q^{91} - 3544371 q^{92} + 3121742 q^{93} + 61343967 q^{94} + 3360807 q^{95} + 23547905 q^{96} + 41644125 q^{97} - 588245 q^{98} + 50754068 q^{99}+O(q^{100}) \) 9 * q - 5 * q^2 - 26 * q^3 + 393 * q^4 - 181 * q^5 + 703 * q^6 - 3087 * q^7 + 1197 * q^8 + 3211 * q^9 - 5124 * q^10 - 9826 * q^11 - 20919 * q^12 + 19773 * q^13 + 1715 * q^14 - 20346 * q^15 + 31113 * q^16 - 22766 * q^17 - 12978 * q^18 - 17769 * q^19 - 44204 * q^20 + 8918 * q^21 - 203553 * q^22 - 49103 * q^23 + 52737 * q^24 + 227466 * q^25 - 10985 * q^26 + 103624 * q^27 - 134799 * q^28 - 487455 * q^29 - 287992 * q^30 - 63843 * q^31 - 587099 * q^32 - 314392 * q^33 - 576240 * q^34 + 62083 * q^35 - 1514926 * q^36 - 796926 * q^37 - 766702 * q^38 - 57122 * q^39 - 2887296 * q^40 - 1567546 * q^41 - 241129 * q^42 - 277899 * q^43 - 1281195 * q^44 - 1650593 * q^45 - 1907445 * q^46 + 1077367 * q^47 - 1110835 * q^48 + 1058841 * q^49 - 267459 * q^50 - 3054368 * q^51 + 863421 * q^52 - 7322659 * q^53 - 3355387 * q^54 - 2613324 * q^55 - 410571 * q^56 - 3751946 * q^57 - 2992332 * q^58 - 169804 * q^59 - 2754416 * q^60 - 6352284 * q^61 + 6001087 * q^62 - 1101373 * q^63 + 1657017 * q^64 - 397657 * q^65 - 5962713 * q^66 + 921120 * q^67 + 5615224 * q^68 - 5202780 * q^69 + 1757532 * q^70 + 3786654 * q^71 + 2229758 * q^72 + 5792889 * q^73 - 1991961 * q^74 + 145628 * q^75 - 2806026 * q^76 + 3370318 * q^77 + 1544491 * q^78 + 3464037 * q^79 + 15422512 * q^80 - 5010363 * q^81 - 12539943 * q^82 + 6834945 * q^83 + 7175217 * q^84 + 3880662 * q^85 - 7977524 * q^86 + 3727078 * q^87 + 7013709 * q^88 - 20408371 * q^89 + 34910060 * q^90 - 6782139 * q^91 - 3544371 * q^92 + 3121742 * q^93 + 61343967 * q^94 + 3360807 * q^95 + 23547905 * q^96 + 41644125 * q^97 - 588245 * q^98 + 50754068 * 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 $

$2$	9.68252	0.855822	0.427911	−	0.903821i	$-0.359250\pi$
$2$	9.68252	0.855822	0.427911	+	0.903821i	$0.359250\pi$
$3$	60.1290	1.28576	0.642880	−	0.765967i	$-0.277740\pi$
$3$	60.1290	1.28576	0.642880	+	0.765967i	$0.277740\pi$
$4$	−34.2488	−0.267569
$5$	−158.582	−0.567362	−0.283681	−	0.958919i	$-0.591556\pi$
$5$	−158.582	−0.567362	−0.283681	+	0.958919i	$0.591556\pi$
$6$	582.200	1.10038
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	−1570.98	−1.08481
$9$	1428.50	0.653177
$10$	−1535.48	−0.485560
$11$	−4072.24	−0.922484	−0.461242	−	0.887274i	$-0.652596\pi$
$11$	−4072.24	−0.922484	−0.461242	+	0.887274i	$0.652596\pi$
$12$	−2059.35	−0.344029
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−3321.10	−0.323470
$15$	−9535.40	−0.729490
$16$	−10827.2	−0.660838
$17$	945.853	0.0466931	0.0233465	−	0.999727i	$-0.492568\pi$
$17$	945.853	0.0466931	0.0233465	+	0.999727i	$0.492568\pi$
$18$	13831.5	0.559003
$19$	−55952.9	−1.87148	−0.935740	−	0.352691i	$-0.885267\pi$
$19$	−55952.9	−1.87148	−0.935740	+	0.352691i	$0.885267\pi$
$20$	5431.26	0.151808
$21$	−20624.3	−0.485971
$22$	−39429.5	−0.789482
$23$	44746.7	0.766855	0.383427	−	0.923571i	$-0.374744\pi$
$23$	44746.7	0.766855	0.383427	+	0.923571i	$0.374744\pi$
$24$	−94461.3	−1.39481
$25$	−52976.6	−0.678101
$26$	21272.5	0.237362
$27$	−45608.0	−0.445931
$28$	11747.3	0.101132
$29$	−99583.7	−0.758220	−0.379110	−	0.925352i	$-0.623770\pi$
$29$	−99583.7	−0.758220	−0.379110	+	0.925352i	$0.623770\pi$
$30$	−92326.7	−0.624314
$31$	150775.	0.908997	0.454499	−	0.890747i	$-0.349818\pi$
$31$	150775.	0.908997	0.454499	+	0.890747i	$0.349818\pi$
$32$	96250.8	0.519254
$33$	−244860.	−1.18609
$34$	9158.24	0.0399609
$35$	54393.8	0.214443
$36$	−48924.4	−0.174770
$37$	505908.	1.64197	0.820986	−	0.570949i	$-0.193424\pi$
$37$	505908.	1.64197	0.820986	+	0.570949i	$0.193424\pi$
$38$	−541765.	−1.60165
$39$	132103.	0.356605
$40$	249129.	0.615481
$41$	101017.	0.228902	0.114451	−	0.993429i	$-0.463489\pi$
$41$	101017.	0.228902	0.114451	+	0.993429i	$0.463489\pi$
$42$	−199695.	−0.415905
$43$	−140944.	−0.270337	−0.135169	−	0.990823i	$-0.543158\pi$
$43$	−140944.	−0.270337	−0.135169	+	0.990823i	$0.543158\pi$
$44$	139469.	0.246828
$45$	−226535.	−0.370588
$46$	433260.	0.656291
$47$	−440509.	−0.618888	−0.309444	−	0.950918i	$-0.600143\pi$
$47$	−440509.	−0.618888	−0.309444	+	0.950918i	$0.600143\pi$
$48$	−651027.	−0.849679
$49$	117649.	0.142857
$50$	−512947.	−0.580334
$51$	56873.2	0.0600360
$52$	−75244.7	−0.0742103
$53$	−1.59520e6	−1.47180	−0.735899	−	0.677091i	$-0.763240\pi$
$53$	−1.59520e6	−1.47180	−0.735899	+	0.677091i	$0.763240\pi$
$54$	−441600.	−0.381637
$55$	645785.	0.523382
$56$	538845.	0.410021
$57$	−3.36439e6	−2.40627
$58$	−964221.	−0.648901
$59$	457981.	0.290312	0.145156	−	0.989409i	$-0.453632\pi$
$59$	457981.	0.290312	0.145156	+	0.989409i	$0.453632\pi$
$60$	326576.	0.195189
$61$	−3.45027e6	−1.94625	−0.973126	−	0.230275i	$-0.926038\pi$
$61$	−3.45027e6	−1.94625	−0.973126	+	0.230275i	$0.926038\pi$
$62$	1.45988e6	0.777940
$63$	−489975.	−0.246878
$64$	2.31783e6	1.10523
$65$	−348406.	−0.157358
$66$	−2.37086e6	−1.01508
$67$	3.63713e6	1.47740	0.738698	−	0.674036i	$-0.235441\pi$
$67$	3.63713e6	1.47740	0.738698	+	0.674036i	$0.235441\pi$
$68$	−32394.3	−0.0124936
$69$	2.69057e6	0.985991
$70$	526669.	0.183525
$71$	4.81142e6	1.59540	0.797699	−	0.603055i	$-0.206050\pi$
$71$	4.81142e6	1.59540	0.797699	+	0.603055i	$0.206050\pi$
$72$	−2.24414e6	−0.708575
$73$	−655263.	−0.197145	−0.0985725	−	0.995130i	$-0.531428\pi$
$73$	−655263.	−0.197145	−0.0985725	+	0.995130i	$0.531428\pi$
$74$	4.89847e6	1.40524
$75$	−3.18543e6	−0.871874
$76$	1.91632e6	0.500750
$77$	1.39678e6	0.348666
$78$	1.27909e6	0.305191
$79$	−4.77387e6	−1.08937	−0.544685	−	0.838640i	$-0.683351\pi$
$79$	−4.77387e6	−1.08937	−0.544685	+	0.838640i	$0.683351\pi$
$80$	1.71700e6	0.374934
$81$	−5.86649e6	−1.22654
$82$	978097.	0.195900
$83$	−7.87248e6	−1.51126	−0.755628	−	0.655001i	$-0.772668\pi$
$83$	−7.87248e6	−1.51126	−0.755628	+	0.655001i	$0.772668\pi$
$84$	706356.	0.130031
$85$	−149996.	−0.0264919
$86$	−1.36469e6	−0.231361
$87$	−5.98787e6	−0.974889
$88$	6.39740e6	1.00072
$89$	6.57523e6	0.988657	0.494329	−	0.869275i	$-0.335414\pi$
$89$	6.57523e6	0.988657	0.494329	+	0.869275i	$0.335414\pi$
$90$	−2.19343e6	−0.317157
$91$	−753571.	−0.104828
$92$	−1.53252e6	−0.205186
$93$	9.06594e6	1.16875
$94$	−4.26523e6	−0.529658
$95$	8.87315e6	1.06181
$96$	5.78747e6	0.667635
$97$	6.29434e6	0.700243	0.350122	−	0.936704i	$-0.386140\pi$
$97$	6.29434e6	0.700243	0.350122	+	0.936704i	$0.386140\pi$
$98$	1.13914e6	0.122260
$99$	−5.81719e6	−0.602546
$100$	1.81439e6	0.181439
$101$	−3.72792e6	−0.360032	−0.180016	−	0.983664i	$-0.557615\pi$
$101$	−3.72792e6	−0.360032	−0.180016	+	0.983664i	$0.557615\pi$
$102$	550676.	0.0513802
$103$	1.47589e7	1.33084	0.665419	−	0.746470i	$-0.268253\pi$
$103$	1.47589e7	1.33084	0.665419	+	0.746470i	$0.268253\pi$
$104$	−3.45144e6	−0.300873
$105$	3.27064e6	0.275721
$106$	−1.54455e7	−1.25960
$107$	−5.08577e6	−0.401341	−0.200671	−	0.979659i	$-0.564312\pi$
$107$	−5.08577e6	−0.401341	−0.200671	+	0.979659i	$0.564312\pi$
$108$	1.56202e6	0.119317
$109$	7.29545e6	0.539584	0.269792	−	0.962919i	$-0.413045\pi$
$109$	7.29545e6	0.539584	0.269792	+	0.962919i	$0.413045\pi$
$110$	6.25283e6	0.447922
$111$	3.04198e7	2.11118
$112$	3.71372e6	0.249773
$113$	1.57819e7	1.02893	0.514465	−	0.857512i	$-0.327991\pi$
$113$	1.57819e7	1.02893	0.514465	+	0.857512i	$0.327991\pi$
$114$	−3.25758e7	−2.05934
$115$	−7.09603e6	−0.435084
$116$	3.41062e6	0.202876
$117$	3.13841e6	0.181159
$118$	4.43441e6	0.248456
$119$	−324428.	−0.0176483
$120$	1.49799e7	0.791361
$121$	−2.90404e6	−0.149023
$122$	−3.34073e7	−1.66564
$123$	6.07404e6	0.294313
$124$	−5.16386e6	−0.243219
$125$	2.07904e7	0.952090
$126$	−4.74419e6	−0.211283
$127$	−4379.98	−0.000189740 0	−9.48699e−5	−	1.00000i	$-0.500030\pi$
$127$	−4379.98	−0.000189740 0	−9.48699e−5		1.00000i	$0.500030\pi$
$128$	1.01223e7	0.426623
$129$	−8.47481e6	−0.347589
$130$	−3.37344e6	−0.134670
$131$	4.28329e6	0.166467	0.0832334	−	0.996530i	$-0.473475\pi$
$131$	4.28329e6	0.166467	0.0832334	+	0.996530i	$0.473475\pi$
$132$	8.38616e6	0.317361
$133$	1.91919e7	0.707353
$134$	3.52166e7	1.26439
$135$	7.23262e6	0.253004
$136$	−1.48591e6	−0.0506533
$137$	−2.42792e7	−0.806700	−0.403350	−	0.915046i	$-0.632154\pi$
$137$	−2.42792e7	−0.806700	−0.403350	+	0.915046i	$0.632154\pi$
$138$	2.60515e7	0.843832
$139$	−3.64498e7	−1.15118	−0.575590	−	0.817738i	$-0.695228\pi$
$139$	−3.64498e7	−1.15118	−0.575590	+	0.817738i	$0.695228\pi$
$140$	−1.86292e6	−0.0573782
$141$	−2.64873e7	−0.795741
$142$	4.65867e7	1.36538
$143$	−8.94671e6	−0.255851
$144$	−1.54666e7	−0.431644
$145$	1.57922e7	0.430185
$146$	−6.34460e6	−0.168721
$147$	7.07412e6	0.183680
$148$	−1.73268e7	−0.439340
$149$	1.04606e7	0.259062	0.129531	−	0.991575i	$-0.458653\pi$
$149$	1.04606e7	0.259062	0.129531	+	0.991575i	$0.458653\pi$
$150$	−3.08430e7	−0.746169
$151$	−3.31276e7	−0.783017	−0.391508	−	0.920174i	$-0.628047\pi$
$151$	−3.31276e7	−0.783017	−0.391508	+	0.920174i	$0.628047\pi$
$152$	8.79008e7	2.03021
$153$	1.35115e6	0.0304988
$154$	1.35243e7	0.298396
$155$	−2.39102e7	−0.515730
$156$	−4.52439e6	−0.0954165
$157$	−2.52725e7	−0.521194	−0.260597	−	0.965448i	$-0.583919\pi$
$157$	−2.52725e7	−0.521194	−0.260597	+	0.965448i	$0.583919\pi$
$158$	−4.62231e7	−0.932307
$159$	−9.59176e7	−1.89238
$160$	−1.52637e7	−0.294605
$161$	−1.53481e7	−0.289844
$162$	−5.68024e7	−1.04970
$163$	−7.37068e7	−1.33306	−0.666532	−	0.745477i	$-0.732222\pi$
$163$	−7.37068e7	−1.33306	−0.666532	+	0.745477i	$0.732222\pi$
$164$	−3.45971e6	−0.0612471
$165$	3.88304e7	0.672943
$166$	−7.62254e7	−1.29337
$167$	8.65855e7	1.43859	0.719296	−	0.694704i	$-0.244465\pi$
$167$	8.65855e7	1.43859	0.719296	+	0.694704i	$0.244465\pi$
$168$	3.24002e7	0.527188
$169$	4.82681e6	0.0769231
$170$	−1.45234e6	−0.0226723
$171$	−7.99287e7	−1.22241
$172$	4.82715e6	0.0723339
$173$	−6.83184e7	−1.00317	−0.501587	−	0.865107i	$-0.667250\pi$
$173$	−6.83184e7	−1.00317	−0.501587	+	0.865107i	$0.667250\pi$
$174$	−5.79777e7	−0.834331
$175$	1.81710e7	0.256298
$176$	4.40908e7	0.609613
$177$	2.75379e7	0.373272
$178$	6.36648e7	0.846115
$179$	−8.34071e7	−1.08697	−0.543485	−	0.839419i	$-0.682896\pi$
$179$	−8.34071e7	−1.08697	−0.543485	+	0.839419i	$0.682896\pi$
$180$	7.75855e6	0.0991577
$181$	−8.33656e7	−1.04499	−0.522495	−	0.852643i	$-0.674999\pi$
$181$	−8.33656e7	−1.04499	−0.522495	+	0.852643i	$0.674999\pi$
$182$	−7.29647e6	−0.0897145
$183$	−2.07461e8	−2.50241
$184$	−7.02960e7	−0.831894
$185$	−8.02281e7	−0.931592
$186$	8.77811e7	1.00024
$187$	−3.85174e6	−0.0430736
$188$	1.50869e7	0.165595
$189$	1.56435e7	0.168546
$190$	8.59144e7	0.908717
$191$	−5.69985e7	−0.591898	−0.295949	−	0.955204i	$-0.595636\pi$
$191$	−5.69985e7	−0.591898	−0.295949	+	0.955204i	$0.595636\pi$
$192$	1.39369e8	1.42106
$193$	6.48032e7	0.648852	0.324426	−	0.945911i	$-0.394829\pi$
$193$	6.48032e7	0.648852	0.324426	+	0.945911i	$0.394829\pi$
$194$	6.09451e7	0.599284
$195$	−2.09493e7	−0.202324
$196$	−4.02934e6	−0.0382241
$197$	−1.99495e8	−1.85908	−0.929542	−	0.368715i	$-0.879798\pi$
$197$	−1.99495e8	−1.85908	−0.929542	+	0.368715i	$0.879798\pi$
$198$	−5.63250e7	−0.515672
$199$	1.36764e8	1.23023	0.615117	−	0.788436i	$-0.289109\pi$
$199$	1.36764e8	1.23023	0.615117	+	0.788436i	$0.289109\pi$
$200$	8.32251e7	0.735613
$201$	2.18697e8	1.89958
$202$	−3.60956e7	−0.308123
$203$	3.41572e7	0.286580
$204$	−1.94784e6	−0.0160638
$205$	−1.60195e7	−0.129870
$206$	1.42904e8	1.13896
$207$	6.39205e7	0.500892
$208$	−2.37873e7	−0.183283
$209$	2.27854e8	1.72641
$210$	3.16681e7	0.235968
$211$	−1.58872e8	−1.16428	−0.582142	−	0.813087i	$-0.697785\pi$
$211$	−1.58872e8	−1.16428	−0.582142	+	0.813087i	$0.697785\pi$
$212$	5.46336e7	0.393808
$213$	2.89306e8	2.05130
$214$	−4.92431e7	−0.343477
$215$	2.23512e7	0.153379
$216$	7.16491e7	0.483752
$217$	−5.17157e7	−0.343569
$218$	7.06383e7	0.461788
$219$	−3.94003e7	−0.253481
$220$	−2.21174e7	−0.140041
$221$	2.07804e6	0.0129503
$222$	2.94540e8	1.80679
$223$	−2.14582e8	−1.29577	−0.647883	−	0.761740i	$-0.724345\pi$
$223$	−2.14582e8	−1.29577	−0.647883	+	0.761740i	$0.724345\pi$
$224$	−3.30140e7	−0.196259
$225$	−7.56770e7	−0.442920
$226$	1.52809e8	0.880580
$227$	1.55420e8	0.881892	0.440946	−	0.897534i	$-0.354643\pi$
$227$	1.55420e8	0.881892	0.440946	+	0.897534i	$0.354643\pi$
$228$	1.15227e8	0.643844
$229$	1.44900e8	0.797342	0.398671	−	0.917094i	$-0.369471\pi$
$229$	1.44900e8	0.797342	0.398671	+	0.917094i	$0.369471\pi$
$230$	−6.87075e7	−0.372354
$231$	8.39869e7	0.448301
$232$	1.56444e8	0.822527
$233$	−9.48325e7	−0.491147	−0.245573	−	0.969378i	$-0.578976\pi$
$233$	−9.48325e7	−0.491147	−0.245573	+	0.969378i	$0.578976\pi$
$234$	3.03877e7	0.155040
$235$	6.98569e7	0.351133
$236$	−1.56853e7	−0.0776785
$237$	−2.87048e8	−1.40067
$238$	−3.14128e6	−0.0151038
$239$	−3.77564e8	−1.78895	−0.894474	−	0.447119i	$-0.852450\pi$
$239$	−3.77564e8	−1.78895	−0.894474	+	0.447119i	$0.852450\pi$
$240$	1.03241e8	0.482075
$241$	2.14392e8	0.986616	0.493308	−	0.869855i	$-0.335788\pi$
$241$	2.14392e8	0.986616	0.493308	+	0.869855i	$0.335788\pi$
$242$	−2.81184e7	−0.127537
$243$	−2.53002e8	−1.13110
$244$	1.18168e8	0.520756
$245$	−1.86571e7	−0.0810517
$246$	5.88120e7	0.251880
$247$	−1.22929e8	−0.519055
$248$	−2.36864e8	−0.986092
$249$	−4.73364e8	−1.94311
$250$	2.01304e8	0.814819
$251$	777675.	0.00310413	0.00155207	−	0.999999i	$-0.499506\pi$
$251$	777675.	0.00310413	0.00155207	+	0.999999i	$0.499506\pi$
$252$	1.67811e7	0.0660568
$253$	−1.82219e8	−0.707411
$254$	−42409.2	−0.000162384 0
$255$	−9.01909e6	−0.0340621
$256$	−1.98673e8	−0.740113
$257$	1.06228e8	0.390368	0.195184	−	0.980767i	$-0.437470\pi$
$257$	1.06228e8	0.390368	0.195184	+	0.980767i	$0.437470\pi$
$258$	−8.20575e7	−0.297474
$259$	−1.73526e8	−0.620607
$260$	1.19325e7	0.0421041
$261$	−1.42255e8	−0.495252
$262$	4.14730e7	0.142466
$263$	6.55675e6	0.0222251	0.0111126	−	0.999938i	$-0.496463\pi$
$263$	6.55675e6	0.0222251	0.0111126	+	0.999938i	$0.496463\pi$
$264$	3.84669e8	1.28669
$265$	2.52970e8	0.835042
$266$	1.85825e8	0.605368
$267$	3.95362e8	1.27118
$268$	−1.24567e8	−0.395305
$269$	4.84481e8	1.51755	0.758776	−	0.651351i	$-0.225798\pi$
$269$	4.84481e8	1.51755	0.758776	+	0.651351i	$0.225798\pi$
$270$	7.00300e7	0.216526
$271$	−8.75355e7	−0.267172	−0.133586	−	0.991037i	$-0.542649\pi$
$271$	−8.75355e7	−0.267172	−0.133586	+	0.991037i	$0.542649\pi$
$272$	−1.02409e7	−0.0308566
$273$	−4.53115e7	−0.134784
$274$	−2.35084e8	−0.690391
$275$	2.15733e8	0.625537
$276$	−9.21489e7	−0.263820
$277$	1.08587e8	0.306972	0.153486	−	0.988151i	$-0.450950\pi$
$277$	1.08587e8	0.306972	0.153486	+	0.988151i	$0.450950\pi$
$278$	−3.52926e8	−0.985205
$279$	2.15381e8	0.593736
$280$	−8.54514e7	−0.232630
$281$	−3.20045e8	−0.860477	−0.430239	−	0.902715i	$-0.641571\pi$
$281$	−3.20045e8	−0.860477	−0.430239	+	0.902715i	$0.641571\pi$
$282$	−2.56464e8	−0.681012
$283$	−2.72694e8	−0.715194	−0.357597	−	0.933876i	$-0.616404\pi$
$283$	−2.72694e8	−0.715194	−0.357597	+	0.933876i	$0.616404\pi$
$284$	−1.64786e8	−0.426879
$285$	5.33534e8	1.36523
$286$	−8.66267e7	−0.218963
$287$	−3.46488e7	−0.0865169
$288$	1.37494e8	0.339165
$289$	−4.09444e8	−0.997820
$290$	1.52908e8	0.368162
$291$	3.78472e8	0.900345
$292$	2.24420e7	0.0527498
$293$	−4.65534e8	−1.08122	−0.540611	−	0.841273i	$-0.681807\pi$
$293$	−4.65534e8	−1.08122	−0.540611	+	0.841273i	$0.681807\pi$
$294$	6.84953e7	0.157197
$295$	−7.26277e7	−0.164712
$296$	−7.94770e8	−1.78123
$297$	1.85726e8	0.411364
$298$	1.01285e8	0.221711
$299$	9.83084e7	0.212687
$300$	1.09097e8	0.233286
$301$	4.83437e7	0.102178
$302$	−3.20759e8	−0.670123
$303$	−2.24156e8	−0.462915
$304$	6.05812e8	1.23675
$305$	5.47152e8	1.10423
$306$	1.30825e7	0.0261016
$307$	−5.16462e8	−1.01872	−0.509359	−	0.860554i	$-0.670118\pi$
$307$	−5.16462e8	−1.01872	−0.509359	+	0.860554i	$0.670118\pi$
$308$	−4.78380e7	−0.0932922
$309$	8.87441e8	1.71114
$310$	−2.31511e8	−0.441373
$311$	5.35033e8	1.00860	0.504300	−	0.863528i	$-0.331750\pi$
$311$	5.35033e8	1.00860	0.504300	+	0.863528i	$0.331750\pi$
$312$	−2.07532e8	−0.386850
$313$	−1.58594e8	−0.292336	−0.146168	−	0.989260i	$-0.546694\pi$
$313$	−1.58594e8	−0.292336	−0.146168	+	0.989260i	$0.546694\pi$
$314$	−2.44701e8	−0.446049
$315$	7.77014e7	0.140069
$316$	1.63499e8	0.291482
$317$	−8.04318e8	−1.41814	−0.709072	−	0.705136i	$-0.750886\pi$
$317$	−8.04318e8	−1.41814	−0.709072	+	0.705136i	$0.750886\pi$
$318$	−9.28724e8	−1.61954
$319$	4.05529e8	0.699446
$320$	−3.67567e8	−0.627063
$321$	−3.05802e8	−0.516028
$322$	−1.48608e8	−0.248055
$323$	−5.29232e7	−0.0873851
$324$	2.00920e8	0.328183
$325$	−1.16390e8	−0.188071
$326$	−7.13667e8	−1.14086
$327$	4.38668e8	0.693775
$328$	−1.58695e8	−0.248316
$329$	1.51094e8	0.233918
$330$	3.75976e8	0.575920
$331$	8.25452e8	1.25110	0.625552	−	0.780182i	$-0.284874\pi$
$331$	8.25452e8	1.25110	0.625552	+	0.780182i	$0.284874\pi$
$332$	2.69623e8	0.404365
$333$	7.22689e8	1.07250
$334$	8.38365e8	1.23118
$335$	−5.76785e8	−0.838218
$336$	2.23302e8	0.321148
$337$	9.07034e8	1.29098	0.645489	−	0.763770i	$-0.276654\pi$
$337$	9.07034e8	1.29098	0.645489	+	0.763770i	$0.276654\pi$
$338$	4.67357e7	0.0658325
$339$	9.48952e8	1.32296
$340$	5.13717e6	0.00708840
$341$	−6.13991e8	−0.838536
$342$	−7.73911e8	−1.04616
$343$	−4.03536e7	−0.0539949
$344$	2.21419e8	0.293266
$345$	−4.26677e8	−0.559413
$346$	−6.61494e8	−0.858538
$347$	−4.22105e8	−0.542335	−0.271167	−	0.962532i	$-0.587410\pi$
$347$	−4.22105e8	−0.542335	−0.271167	+	0.962532i	$0.587410\pi$
$348$	2.05077e8	0.260850
$349$	−8.74993e8	−1.10183	−0.550916	−	0.834561i	$-0.685722\pi$
$349$	−8.74993e8	−1.10183	−0.550916	+	0.834561i	$0.685722\pi$
$350$	1.75941e8	0.219345
$351$	−1.00201e8	−0.123679
$352$	−3.91956e8	−0.479003
$353$	−7.95940e8	−0.963094	−0.481547	−	0.876420i	$-0.659925\pi$
$353$	−7.95940e8	−0.963094	−0.481547	+	0.876420i	$0.659925\pi$
$354$	2.66637e8	0.319454
$355$	−7.63007e8	−0.905168
$356$	−2.25194e8	−0.264534
$357$	−1.95075e7	−0.0226915
$358$	−8.07591e8	−0.930253
$359$	−1.20912e9	−1.37923	−0.689616	−	0.724175i	$-0.742221\pi$
$359$	−1.20912e9	−1.37923	−0.689616	+	0.724175i	$0.742221\pi$
$360$	3.55881e8	0.402018
$361$	2.23686e9	2.50244
$362$	−8.07189e8	−0.894325
$363$	−1.74617e8	−0.191608
$364$	2.58089e7	0.0280488
$365$	1.03913e8	0.111852
$366$	−2.00875e9	−2.14162
$367$	1.28565e8	0.135766	0.0678829	−	0.997693i	$-0.478376\pi$
$367$	1.28565e8	0.135766	0.0678829	+	0.997693i	$0.478376\pi$
$368$	−4.84480e8	−0.506767
$369$	1.44302e8	0.149514
$370$	−7.76810e8	−0.797276
$371$	5.47152e8	0.556288
$372$	−3.10498e8	−0.312722
$373$	−2.64164e8	−0.263568	−0.131784	−	0.991278i	$-0.542071\pi$
$373$	−2.64164e8	−0.263568	−0.131784	+	0.991278i	$0.542071\pi$
$374$	−3.72945e7	−0.0368633
$375$	1.25011e9	1.22416
$376$	6.92029e8	0.671377
$377$	−2.18785e8	−0.210292
$378$	1.51469e8	0.144245
$379$	1.10613e9	1.04368	0.521840	−	0.853044i	$-0.325246\pi$
$379$	1.10613e9	1.04368	0.521840	+	0.853044i	$0.325246\pi$
$380$	−3.03895e8	−0.284106
$381$	−263364.	−0.000243960 0
$382$	−5.51889e8	−0.506559
$383$	−1.25880e9	−1.14488	−0.572440	−	0.819947i	$-0.694003\pi$
$383$	−1.25880e9	−1.14488	−0.572440	+	0.819947i	$0.694003\pi$
$384$	6.08645e8	0.548535
$385$	−2.21504e8	−0.197820
$386$	6.27458e8	0.555302
$387$	−2.01338e8	−0.176578
$388$	−2.15574e8	−0.187363
$389$	7.12560e8	0.613759	0.306880	−	0.951748i	$-0.400715\pi$
$389$	7.12560e8	0.613759	0.306880	+	0.951748i	$0.400715\pi$
$390$	−2.02842e8	−0.173154
$391$	4.23238e7	0.0358068
$392$	−1.84824e8	−0.154973
$393$	2.57550e8	0.214036
$394$	−1.93161e9	−1.59105
$395$	7.57052e8	0.618067
$396$	1.99232e8	0.161222
$397$	6.43855e8	0.516442	0.258221	−	0.966086i	$-0.416864\pi$
$397$	6.43855e8	0.516442	0.258221	+	0.966086i	$0.416864\pi$
$398$	1.32422e9	1.05286
$399$	1.15399e9	0.909486
$400$	5.73587e8	0.448115
$401$	7.98206e8	0.618172	0.309086	−	0.951034i	$-0.399977\pi$
$401$	7.98206e8	0.618172	0.309086	+	0.951034i	$0.399977\pi$
$402$	2.11754e9	1.62570
$403$	3.31252e8	0.252111
$404$	1.27677e8	0.0963334
$405$	9.30322e8	0.695890
$406$	3.30728e8	0.245262
$407$	−2.06018e9	−1.51469
$408$	−8.93465e7	−0.0651279
$409$	2.01053e9	1.45305	0.726523	−	0.687142i	$-0.241135\pi$
$409$	2.01053e9	1.45305	0.726523	+	0.687142i	$0.241135\pi$
$410$	−1.55109e8	−0.111146
$411$	−1.45988e9	−1.03722
$412$	−5.05476e8	−0.356091
$413$	−1.57087e8	−0.109728
$414$	6.18912e8	0.428674
$415$	1.24844e9	0.857429
$416$	2.11463e8	0.144015
$417$	−2.19169e9	−1.48014
$418$	2.20620e9	1.47750
$419$	−1.83473e7	−0.0121849	−0.00609247	−	0.999981i	$-0.501939\pi$
$419$	−1.83473e7	−0.0121849	−0.00609247	+	0.999981i	$0.501939\pi$
$420$	−1.12016e8	−0.0737745
$421$	−8.63091e8	−0.563728	−0.281864	−	0.959454i	$-0.590953\pi$
$421$	−8.63091e8	−0.563728	−0.281864	+	0.959454i	$0.590953\pi$
$422$	−1.53828e9	−0.996420
$423$	−6.29266e8	−0.404243
$424$	2.50602e9	1.59663
$425$	−5.01081e7	−0.0316626
$426$	2.80121e9	1.75555
$427$	1.18344e9	0.735614
$428$	1.74182e8	0.107386
$429$	−5.37957e8	−0.328963
$430$	2.16416e8	0.131265
$431$	2.55870e9	1.53939	0.769695	−	0.638412i	$-0.220408\pi$
$431$	2.55870e9	1.53939	0.769695	+	0.638412i	$0.220408\pi$
$432$	4.93805e8	0.294688
$433$	−5.33692e8	−0.315924	−0.157962	−	0.987445i	$-0.550492\pi$
$433$	−5.33692e8	−0.315924	−0.157962	+	0.987445i	$0.550492\pi$
$434$	−5.00739e8	−0.294034
$435$	9.49571e8	0.553114
$436$	−2.49860e8	−0.144376
$437$	−2.50371e9	−1.43515
$438$	−3.81494e8	−0.216935
$439$	2.58126e9	1.45615	0.728076	−	0.685497i	$-0.240415\pi$
$439$	2.58126e9	1.45615	0.728076	+	0.685497i	$0.240415\pi$
$440$	−1.01451e9	−0.567772
$441$	1.68061e8	0.0933110
$442$	2.01207e7	0.0110832
$443$	4.89582e8	0.267554	0.133777	−	0.991011i	$-0.457289\pi$
$443$	4.89582e8	0.267554	0.133777	+	0.991011i	$0.457289\pi$
$444$	−1.04184e9	−0.564886
$445$	−1.04272e9	−0.560926
$446$	−2.07770e9	−1.10894
$447$	6.28985e8	0.333092
$448$	−7.95015e8	−0.417736
$449$	1.01796e8	0.0530726	0.0265363	−	0.999648i	$-0.491552\pi$
$449$	1.01796e8	0.0530726	0.0265363	+	0.999648i	$0.491552\pi$
$450$	−7.32744e8	−0.379061
$451$	−4.11364e8	−0.211159
$452$	−5.40513e8	−0.275310
$453$	−1.99193e9	−1.00677
$454$	1.50485e9	0.754742
$455$	1.19503e8	0.0594757
$456$	5.28539e9	2.61036
$457$	2.74038e9	1.34309	0.671544	−	0.740965i	$-0.265631\pi$
$457$	2.74038e9	1.34309	0.671544	+	0.740965i	$0.265631\pi$
$458$	1.40300e9	0.682383
$459$	−4.31384e7	−0.0208219
$460$	2.43031e8	0.116415
$461$	−2.21087e9	−1.05102	−0.525509	−	0.850788i	$-0.676125\pi$
$461$	−2.21087e9	−1.05102	−0.525509	+	0.850788i	$0.676125\pi$
$462$	8.13205e8	0.383666
$463$	7.03373e8	0.329346	0.164673	−	0.986348i	$-0.447343\pi$
$463$	7.03373e8	0.329346	0.164673	+	0.986348i	$0.447343\pi$
$464$	1.07821e9	0.501061
$465$	−1.43770e9	−0.663105
$466$	−9.18217e8	−0.420334
$467$	1.68775e9	0.766829	0.383415	−	0.923576i	$-0.374748\pi$
$467$	1.68775e9	0.766829	0.383415	+	0.923576i	$0.374748\pi$
$468$	−1.07487e8	−0.0484724
$469$	−1.24754e9	−0.558403
$470$	6.76391e8	0.300507
$471$	−1.51961e9	−0.670130
$472$	−7.19478e8	−0.314935
$473$	5.73956e8	0.249382
$474$	−2.77935e9	−1.19872
$475$	2.96420e9	1.26905
$476$	1.11113e7	0.00472214
$477$	−2.27873e9	−0.961345
$478$	−3.65577e9	−1.53102
$479$	3.05369e9	1.26955	0.634775	−	0.772697i	$-0.281093\pi$
$479$	3.05369e9	1.26955	0.634775	+	0.772697i	$0.281093\pi$
$480$	−9.17790e8	−0.378791
$481$	1.11148e9	0.455401
$482$	2.07585e9	0.844368
$483$	−9.22866e8	−0.372669
$484$	9.94599e7	0.0398739
$485$	−9.98171e8	−0.397291
$486$	−2.44969e9	−0.968020
$487$	−7.66235e8	−0.300615	−0.150307	−	0.988639i	$-0.548026\pi$
$487$	−7.66235e8	−0.300615	−0.150307	+	0.988639i	$0.548026\pi$
$488$	5.42030e9	2.11132
$489$	−4.43192e9	−1.71400
$490$	−1.80647e8	−0.0693658
$491$	−1.36941e9	−0.522092	−0.261046	−	0.965326i	$-0.584067\pi$
$491$	−1.36941e9	−0.522092	−0.261046	+	0.965326i	$0.584067\pi$
$492$	−2.08029e8	−0.0787490
$493$	−9.41915e7	−0.0354036
$494$	−1.19026e9	−0.444219
$495$	9.22503e8	0.341861
$496$	−1.63246e9	−0.600700
$497$	−1.65032e9	−0.603004
$498$	−4.58336e9	−1.66296
$499$	2.25940e8	0.0814031	0.0407015	−	0.999171i	$-0.487041\pi$
$499$	2.25940e8	0.0814031	0.0407015	+	0.999171i	$0.487041\pi$
$500$	−7.12047e8	−0.254750
$501$	5.20630e9	1.84968
$502$	7.52985e6	0.00265658
$503$	−3.04172e9	−1.06569	−0.532845	−	0.846213i	$-0.678877\pi$
$503$	−3.04172e9	−1.06569	−0.532845	+	0.846213i	$0.678877\pi$
$504$	7.69740e8	0.267816
$505$	5.91182e8	0.204268
$506$	−1.76434e9	−0.605418
$507$	2.90231e8	0.0989046
$508$	150009.	5.07685e−5 0
$509$	−4.45687e9	−1.49802	−0.749009	−	0.662559i	$-0.769470\pi$
$509$	−4.45687e9	−1.49802	−0.749009	+	0.662559i	$0.769470\pi$
$510$	−8.73275e7	−0.0291511
$511$	2.24755e8	0.0745138
$512$	−3.21931e9	−1.06003
$513$	2.55190e9	0.834550
$514$	1.02856e9	0.334086
$515$	−2.34051e9	−0.755066
$516$	2.90252e8	0.0930039
$517$	1.79386e9	0.570914
$518$	−1.68017e9	−0.531129
$519$	−4.10792e9	−1.28984
$520$	5.47337e8	0.170704
$521$	1.00624e9	0.311725	0.155862	−	0.987779i	$-0.450184\pi$
$521$	1.00624e9	0.311725	0.155862	+	0.987779i	$0.450184\pi$
$522$	−1.37739e9	−0.423848
$523$	4.09704e9	1.25232	0.626158	−	0.779696i	$-0.284627\pi$
$523$	4.09704e9	1.25232	0.626158	+	0.779696i	$0.284627\pi$
$524$	−1.46697e8	−0.0445413
$525$	1.09260e9	0.329538
$526$	6.34859e7	0.0190207
$527$	1.42611e8	0.0424439
$528$	2.65114e9	0.783815
$529$	−1.40256e9	−0.411934
$530$	2.44939e9	0.714647
$531$	6.54225e8	0.189625
$532$	−6.57298e8	−0.189266
$533$	2.21934e8	0.0634860
$534$	3.82810e9	1.08790
$535$	8.06514e8	0.227706
$536$	−5.71385e9	−1.60270
$537$	−5.01519e9	−1.39758
$538$	4.69100e9	1.29875
$539$	−4.79095e8	−0.131783
$540$	−2.47709e8	−0.0676960
$541$	5.76662e9	1.56578	0.782891	−	0.622159i	$-0.213744\pi$
$541$	5.76662e9	1.56578	0.782891	+	0.622159i	$0.213744\pi$
$542$	−8.47564e8	−0.228652
$543$	−5.01269e9	−1.34361
$544$	9.10391e7	0.0242455
$545$	−1.15693e9	−0.306139
$546$	−4.38729e8	−0.115351
$547$	−2.80452e9	−0.732661	−0.366331	−	0.930485i	$-0.619386\pi$
$547$	−2.80452e9	−0.732661	−0.366331	+	0.930485i	$0.619386\pi$
$548$	8.31533e8	0.215848
$549$	−4.92871e9	−1.27125
$550$	2.08884e9	0.535348
$551$	5.57200e9	1.41899
$552$	−4.22683e9	−1.06962
$553$	1.63744e9	0.411743
$554$	1.05140e9	0.262714
$555$	−4.82404e9	−1.19780
$556$	1.24836e9	0.308020
$557$	−3.75599e9	−0.920941	−0.460470	−	0.887675i	$-0.652319\pi$
$557$	−3.75599e9	−0.920941	−0.460470	+	0.887675i	$0.652319\pi$
$558$	2.08544e9	0.508133
$559$	−3.09653e8	−0.0749781
$560$	−5.88930e8	−0.141712
$561$	−2.31601e8	−0.0553823
$562$	−3.09884e9	−0.736415
$563$	9.24936e8	0.218440	0.109220	−	0.994018i	$-0.465165\pi$
$563$	9.24936e8	0.218440	0.109220	+	0.994018i	$0.465165\pi$
$564$	9.07160e8	0.212915
$565$	−2.50274e9	−0.583775
$566$	−2.64037e9	−0.612078
$567$	2.01221e9	0.463587
$568$	−7.55864e9	−1.73071
$569$	−2.45454e9	−0.558570	−0.279285	−	0.960208i	$-0.590097\pi$
$569$	−2.45454e9	−0.558570	−0.279285	+	0.960208i	$0.590097\pi$
$570$	5.16595e9	1.16839
$571$	8.04588e9	1.80862	0.904310	−	0.426876i	$-0.140386\pi$
$571$	8.04588e9	1.80862	0.904310	+	0.426876i	$0.140386\pi$
$572$	3.06414e8	0.0684578
$573$	−3.42726e9	−0.761038
$574$	−3.35487e8	−0.0740431
$575$	−2.37053e9	−0.520005
$576$	3.31101e9	0.721909
$577$	7.49095e9	1.62339	0.811693	−	0.584084i	$-0.198546\pi$
$577$	7.49095e9	1.62339	0.811693	+	0.584084i	$0.198546\pi$
$578$	−3.96445e9	−0.853956
$579$	3.89655e9	0.834268
$580$	−5.40865e8	−0.115104
$581$	2.70026e9	0.571201
$582$	3.66457e9	0.770535
$583$	6.49602e9	1.35771
$584$	1.02940e9	0.213865
$585$	−4.97697e8	−0.102783
$586$	−4.50754e9	−0.925334
$587$	6.58854e9	1.34448	0.672242	−	0.740331i	$-0.265331\pi$
$587$	6.58854e9	1.34448	0.672242	+	0.740331i	$0.265331\pi$
$588$	−2.42280e8	−0.0491470
$589$	−8.43629e9	−1.70117
$590$	−7.03219e8	−0.140964
$591$	−1.19954e10	−2.39034
$592$	−5.47755e9	−1.08508
$593$	−8.13097e9	−1.60122	−0.800610	−	0.599186i	$-0.795491\pi$
$593$	−8.13097e9	−1.60122	−0.800610	+	0.599186i	$0.795491\pi$
$594$	1.79830e9	0.352054
$595$	5.14485e7	0.0100130
$596$	−3.58263e8	−0.0693170
$597$	8.22351e9	1.58178
$598$	9.51873e8	0.182022
$599$	−1.40804e9	−0.267682	−0.133841	−	0.991003i	$-0.542731\pi$
$599$	−1.40804e9	−0.267682	−0.133841	+	0.991003i	$0.542731\pi$
$600$	5.00424e9	0.945821
$601$	−1.51844e9	−0.285323	−0.142662	−	0.989772i	$-0.545566\pi$
$601$	−1.51844e9	−0.285323	−0.142662	+	0.989772i	$0.545566\pi$
$602$	4.68089e8	0.0874461
$603$	5.19563e9	0.965001
$604$	1.13458e9	0.209511
$605$	4.60529e8	0.0845500
$606$	−2.17039e9	−0.396173
$607$	8.46324e9	1.53595	0.767973	−	0.640482i	$-0.221265\pi$
$607$	8.46324e9	1.53595	0.767973	+	0.640482i	$0.221265\pi$
$608$	−5.38551e9	−0.971773
$609$	2.05384e9	0.368473
$610$	5.29781e9	0.945023
$611$	−9.67797e8	−0.171649
$612$	−4.62753e7	−0.00816054
$613$	−2.97029e9	−0.520819	−0.260410	−	0.965498i	$-0.583858\pi$
$613$	−2.97029e9	−0.520819	−0.260410	+	0.965498i	$0.583858\pi$
$614$	−5.00065e9	−0.871841
$615$	−9.63236e8	−0.166982
$616$	−2.19431e9	−0.378238
$617$	−5.41266e9	−0.927710	−0.463855	−	0.885911i	$-0.653534\pi$
$617$	−5.41266e9	−0.927710	−0.463855	+	0.885911i	$0.653534\pi$
$618$	8.59266e9	1.46443
$619$	1.86658e9	0.316322	0.158161	−	0.987413i	$-0.449443\pi$
$619$	1.86658e9	0.316322	0.158161	+	0.987413i	$0.449443\pi$
$620$	8.18897e8	0.137993
$621$	−2.04080e9	−0.341964
$622$	5.18047e9	0.863183
$623$	−2.25530e9	−0.373677
$624$	−1.43031e9	−0.235658
$625$	8.41806e8	0.137922
$626$	−1.53559e9	−0.250188
$627$	1.37006e10	2.21975
$628$	8.65553e8	0.139455
$629$	4.78515e8	0.0766687
$630$	7.52345e8	0.119874
$631$	7.25572e8	0.114968	0.0574841	−	0.998346i	$-0.481692\pi$
$631$	7.25572e8	0.114968	0.0574841	+	0.998346i	$0.481692\pi$
$632$	7.49964e9	1.18176
$633$	−9.55283e9	−1.49699
$634$	−7.78782e9	−1.21368
$635$	694587.	0.000107651 0
$636$	3.28506e9	0.506342
$637$	2.58475e8	0.0396214
$638$	3.92654e9	0.598601
$639$	6.87311e9	1.04208
$640$	−1.60522e9	−0.242050
$641$	9.95321e9	1.49266	0.746329	−	0.665578i	$-0.231815\pi$
$641$	9.95321e9	1.49266	0.746329	+	0.665578i	$0.231815\pi$
$642$	−2.96094e9	−0.441628
$643$	4.14868e9	0.615420	0.307710	−	0.951480i	$-0.400437\pi$
$643$	4.14868e9	0.615420	0.307710	+	0.951480i	$0.400437\pi$
$644$	5.25654e8	0.0775532
$645$	1.34395e9	0.197209
$646$	−5.12430e8	−0.0747861
$647$	3.44569e9	0.500162	0.250081	−	0.968225i	$-0.419543\pi$
$647$	3.44569e9	0.500162	0.250081	+	0.968225i	$0.419543\pi$
$648$	9.21612e9	1.33056
$649$	−1.86501e9	−0.267808
$650$	−1.12695e9	−0.160956
$651$	−3.10962e9	−0.441747
$652$	2.52437e9	0.356686
$653$	4.62121e9	0.649471	0.324735	−	0.945805i	$-0.394725\pi$
$653$	4.62121e9	0.649471	0.324735	+	0.945805i	$0.394725\pi$
$654$	4.24741e9	0.593748
$655$	−6.79254e8	−0.0944468
$656$	−1.09373e9	−0.151267
$657$	−9.36042e8	−0.128771
$658$	1.46297e9	0.200192
$659$	−3.84079e9	−0.522783	−0.261391	−	0.965233i	$-0.584181\pi$
$659$	−3.84079e9	−0.522783	−0.261391	+	0.965233i	$0.584181\pi$
$660$	−1.32990e9	−0.180059
$661$	2.02282e8	0.0272429	0.0136214	−	0.999907i	$-0.495664\pi$
$661$	2.02282e8	0.0272429	0.0136214	+	0.999907i	$0.495664\pi$
$662$	7.99245e9	1.07072
$663$	1.24950e8	0.0166510
$664$	1.23675e10	1.63943
$665$	−3.04349e9	−0.401325
$666$	6.99745e9	0.917867
$667$	−4.45604e9	−0.581445
$668$	−2.96545e9	−0.384922
$669$	−1.29026e10	−1.66604
$670$	−5.58473e9	−0.717365
$671$	1.40503e10	1.79539
$672$	−1.98510e9	−0.252342
$673$	−1.06311e10	−1.34439	−0.672197	−	0.740372i	$-0.734649\pi$
$673$	−1.06311e10	−1.34439	−0.672197	+	0.740372i	$0.734649\pi$
$674$	8.78237e9	1.10485
$675$	2.41616e9	0.302386
$676$	−1.65313e8	−0.0205822
$677$	−6.32522e9	−0.783457	−0.391728	−	0.920081i	$-0.628123\pi$
$677$	−6.32522e9	−0.783457	−0.391728	+	0.920081i	$0.628123\pi$
$678$	9.18825e9	1.13221
$679$	−2.15896e9	−0.264667
$680$	2.35640e8	0.0287387
$681$	9.34522e9	1.13390
$682$	−5.94498e9	−0.717637
$683$	−3.64924e9	−0.438258	−0.219129	−	0.975696i	$-0.570321\pi$
$683$	−3.64924e9	−0.438258	−0.219129	+	0.975696i	$0.570321\pi$
$684$	2.73746e9	0.327078
$685$	3.85025e9	0.457691
$686$	−3.90725e8	−0.0462100
$687$	8.71271e9	1.02519
$688$	1.52602e9	0.178649
$689$	−3.50465e9	−0.408204
$690$	−4.13131e9	−0.478758
$691$	1.16764e10	1.34629	0.673143	−	0.739513i	$-0.264944\pi$
$691$	1.16764e10	1.34629	0.673143	+	0.739513i	$0.264944\pi$
$692$	2.33982e9	0.268418
$693$	1.99530e9	0.227741
$694$	−4.08704e9	−0.464142
$695$	5.78029e9	0.653135
$696$	9.40681e9	1.05757
$697$	9.55470e7	0.0106881
$698$	−8.47213e9	−0.942972
$699$	−5.70218e9	−0.631497
$700$	−6.22335e8	−0.0685774
$701$	9.11625e9	0.999547	0.499774	−	0.866156i	$-0.333417\pi$
$701$	9.11625e9	0.999547	0.499774	+	0.866156i	$0.333417\pi$
$702$	−9.70195e8	−0.105847
$703$	−2.83070e10	−3.07292
$704$	−9.43875e9	−1.01955
$705$	4.20043e9	0.451473
$706$	−7.70670e9	−0.824237
$707$	1.27868e9	0.136079
$708$	−9.43142e8	−0.0998759
$709$	−1.61812e10	−1.70510	−0.852550	−	0.522645i	$-0.824945\pi$
$709$	−1.61812e10	−1.70510	−0.852550	+	0.522645i	$0.824945\pi$
$710$	−7.38783e9	−0.774663
$711$	−6.81946e9	−0.711552
$712$	−1.03295e10	−1.07251
$713$	6.74667e9	0.697069
$714$	−1.88882e8	−0.0194199
$715$	1.41879e9	0.145160
$716$	2.85660e9	0.290839
$717$	−2.27025e10	−2.30016
$718$	−1.17073e10	−1.18038
$719$	−9.67769e9	−0.971003	−0.485502	−	0.874236i	$-0.661363\pi$
$719$	−9.67769e9	−0.971003	−0.485502	+	0.874236i	$0.661363\pi$
$720$	2.45273e9	0.244898
$721$	−5.06232e9	−0.503009
$722$	2.16584e10	2.14164
$723$	1.28912e10	1.26855
$724$	2.85517e9	0.279607
$725$	5.27561e9	0.514150
$726$	−1.69073e9	−0.163982
$727$	−1.42338e10	−1.37388	−0.686942	−	0.726712i	$-0.741047\pi$
$727$	−1.42338e10	−1.37388	−0.686942	+	0.726712i	$0.741047\pi$
$728$	1.18384e9	0.113719
$729$	−2.38272e9	−0.227786
$730$	1.00614e9	0.0957258
$731$	−1.33312e8	−0.0126229
$732$	7.10531e9	0.669567
$733$	−1.38139e9	−0.129554	−0.0647770	−	0.997900i	$-0.520634\pi$
$733$	−1.38139e9	−0.129554	−0.0647770	+	0.997900i	$0.520634\pi$
$734$	1.24483e9	0.116191
$735$	−1.12183e9	−0.104213
$736$	4.30690e9	0.398192
$737$	−1.48113e10	−1.36287
$738$	1.39721e9	0.127957
$739$	1.72241e10	1.56993	0.784966	−	0.619538i	$-0.212680\pi$
$739$	1.72241e10	1.56993	0.784966	+	0.619538i	$0.212680\pi$
$740$	2.74772e9	0.249265
$741$	−7.39157e9	−0.667380
$742$	5.29781e9	0.476083
$743$	−9.46077e9	−0.846185	−0.423093	−	0.906086i	$-0.639056\pi$
$743$	−9.46077e9	−0.846185	−0.423093	+	0.906086i	$0.639056\pi$
$744$	−1.42424e10	−1.26788
$745$	−1.65886e9	−0.146982
$746$	−2.55778e9	−0.225568
$747$	−1.12458e10	−0.987118
$748$	1.31918e8	0.0115252
$749$	1.74442e9	0.151693
$750$	1.21042e10	1.04766
$751$	−1.33540e10	−1.15046	−0.575229	−	0.817993i	$-0.695087\pi$
$751$	−1.33540e10	−1.15046	−0.575229	+	0.817993i	$0.695087\pi$
$752$	4.76946e9	0.408984
$753$	4.67608e7	0.00399116
$754$	−2.11839e9	−0.179973
$755$	5.25346e9	0.444254
$756$	−5.35772e8	−0.0450977
$757$	3.38355e9	0.283490	0.141745	−	0.989903i	$-0.454729\pi$
$757$	3.38355e9	0.283490	0.141745	+	0.989903i	$0.454729\pi$
$758$	1.07101e10	0.893204
$759$	−1.09567e10	−0.909561
$760$	−1.39395e10	−1.15186
$761$	8.75788e9	0.720365	0.360183	−	0.932882i	$-0.382714\pi$
$761$	8.75788e9	0.720365	0.360183	+	0.932882i	$0.382714\pi$
$762$	−2.55002e6	−0.000208786 0
$763$	−2.50234e9	−0.203944
$764$	1.95213e9	0.158373
$765$	−2.14269e8	−0.0173039
$766$	−1.21883e10	−0.979813
$767$	1.00618e9	0.0805181
$768$	−1.19460e10	−0.951607
$769$	−3.75707e9	−0.297925	−0.148962	−	0.988843i	$-0.547593\pi$
$769$	−3.75707e9	−0.297925	−0.148962	+	0.988843i	$0.547593\pi$
$770$	−2.14472e9	−0.169299
$771$	6.38741e9	0.501920
$772$	−2.21943e9	−0.173613
$773$	−1.91238e9	−0.148917	−0.0744587	−	0.997224i	$-0.523723\pi$
$773$	−1.91238e9	−0.148917	−0.0744587	+	0.997224i	$0.523723\pi$
$774$	−1.94946e9	−0.151119
$775$	−7.98754e9	−0.616392
$776$	−9.88826e9	−0.759633
$777$	−1.04340e10	−0.797951
$778$	6.89938e9	0.525269
$779$	−5.65218e9	−0.428386
$780$	7.17488e8	0.0541357
$781$	−1.95933e10	−1.47173
$782$	4.09801e8	0.0306442
$783$	4.54181e9	0.338114
$784$	−1.27381e9	−0.0944054
$785$	4.00777e9	0.295705
$786$	2.49373e9	0.183177
$787$	2.61356e10	1.91126	0.955631	−	0.294565i	$-0.0951748\pi$
$787$	2.61356e10	1.91126	0.955631	+	0.294565i	$0.0951748\pi$
$788$	6.83245e9	0.497433
$789$	3.94251e8	0.0285761
$790$	7.33017e9	0.528955
$791$	−5.41320e9	−0.388899
$792$	9.13867e9	0.653649
$793$	−7.58025e9	−0.539793
$794$	6.23414e9	0.441982
$795$	1.52108e10	1.07366
$796$	−4.68402e9	−0.329172
$797$	1.83284e8	0.0128239	0.00641195	−	0.999979i	$-0.497959\pi$
$797$	1.83284e8	0.0128239	0.00641195	+	0.999979i	$0.497959\pi$
$798$	1.11735e10	0.778358
$799$	−4.16656e8	−0.0288978
$800$	−5.09904e9	−0.352106
$801$	9.39270e9	0.645768
$802$	7.72864e9	0.529045
$803$	2.66839e9	0.181863
$804$	−7.49011e9	−0.508267
$805$	2.43394e9	0.164446
$806$	3.20736e9	0.215762
$807$	2.91314e10	1.95121
$808$	5.85647e9	0.390568
$809$	6.67855e9	0.443468	0.221734	−	0.975107i	$-0.428828\pi$
$809$	6.67855e9	0.443468	0.221734	+	0.975107i	$0.428828\pi$
$810$	9.00786e9	0.595558
$811$	2.20728e10	1.45306	0.726532	−	0.687133i	$-0.241131\pi$
$811$	2.20728e10	1.45306	0.726532	+	0.687133i	$0.241131\pi$
$812$	−1.16984e9	−0.0766800
$813$	−5.26342e9	−0.343519
$814$	−1.99477e10	−1.29631
$815$	1.16886e10	0.756329
$816$	−6.15776e8	−0.0396741
$817$	7.88621e9	0.505931
$818$	1.94670e10	1.24355
$819$	−1.07647e9	−0.0684716
$820$	5.48648e8	0.0347493
$821$	2.47811e10	1.56286	0.781429	−	0.623994i	$-0.214491\pi$
$821$	2.47811e10	1.56286	0.781429	+	0.623994i	$0.214491\pi$
$822$	−1.41353e10	−0.887677
$823$	−2.31661e10	−1.44862	−0.724309	−	0.689475i	$-0.757841\pi$
$823$	−2.31661e10	−1.44862	−0.724309	+	0.689475i	$0.757841\pi$
$824$	−2.31860e10	−1.44371
$825$	1.29718e10	0.804290
$826$	−1.52100e9	−0.0939074
$827$	−1.42406e10	−0.875507	−0.437753	−	0.899095i	$-0.644226\pi$
$827$	−1.42406e10	−0.875507	−0.437753	+	0.899095i	$0.644226\pi$
$828$	−2.18920e9	−0.134023
$829$	−1.35506e10	−0.826071	−0.413036	−	0.910715i	$-0.635532\pi$
$829$	−1.35506e10	−0.826071	−0.413036	+	0.910715i	$0.635532\pi$
$830$	1.20880e10	0.733806
$831$	6.52924e9	0.394692
$832$	5.09227e9	0.306535
$833$	1.11279e8	0.00667044
$834$	−2.12211e10	−1.26674
$835$	−1.37309e10	−0.816201
$836$	−7.80372e9	−0.461934
$837$	−6.87653e9	−0.405350
$838$	−1.77648e8	−0.0104281
$839$	1.93669e10	1.13212	0.566061	−	0.824363i	$-0.308467\pi$
$839$	1.93669e10	1.13212	0.566061	+	0.824363i	$0.308467\pi$
$840$	−5.13811e9	−0.299106
$841$	−7.33296e9	−0.425102
$842$	−8.35690e9	−0.482451
$843$	−1.92440e10	−1.10637
$844$	5.44118e9	0.311526
$845$	−7.65447e8	−0.0436432
$846$	−6.09288e9	−0.345960
$847$	9.96085e8	0.0563254
$848$	1.72715e10	0.972621
$849$	−1.63968e10	−0.919567
$850$	−4.85173e8	−0.0270976
$851$	2.26377e10	1.25915
$852$	−9.90839e9	−0.548864
$853$	5.54166e9	0.305716	0.152858	−	0.988248i	$-0.451152\pi$
$853$	5.54166e9	0.305716	0.152858	+	0.988248i	$0.451152\pi$
$854$	1.14587e10	0.629554
$855$	1.26753e10	0.693547
$856$	7.98963e9	0.435380
$857$	−2.67901e10	−1.45392	−0.726962	−	0.686677i	$-0.759068\pi$
$857$	−2.67901e10	−1.45392	−0.726962	+	0.686677i	$0.759068\pi$
$858$	−5.20878e9	−0.281534
$859$	−5.71143e9	−0.307446	−0.153723	−	0.988114i	$-0.549126\pi$
$859$	−5.71143e9	−0.307446	−0.153723	+	0.988114i	$0.549126\pi$
$860$	−7.65502e8	−0.0410395
$861$	−2.08340e9	−0.111240
$862$	2.47747e10	1.31744
$863$	3.79383e9	0.200928	0.100464	−	0.994941i	$-0.467967\pi$
$863$	3.79383e9	0.200928	0.100464	+	0.994941i	$0.467967\pi$
$864$	−4.38980e9	−0.231551
$865$	1.08341e10	0.569163
$866$	−5.16748e9	−0.270375
$867$	−2.46195e10	−1.28296
$868$	1.77120e9	0.0919283
$869$	1.94403e10	1.00493
$870$	9.19424e9	0.473367
$871$	7.99077e9	0.409756
$872$	−1.14610e10	−0.585348
$873$	8.99145e9	0.457383
$874$	−2.42422e10	−1.22824
$875$	−7.13111e9	−0.359856
$876$	1.34941e9	0.0678236
$877$	1.79564e10	0.898919	0.449459	−	0.893301i	$-0.351617\pi$
$877$	1.79564e10	0.898919	0.449459	+	0.893301i	$0.351617\pi$
$878$	2.49931e10	1.24621
$879$	−2.79921e10	−1.39019
$880$	−6.99203e9	−0.345871
$881$	−3.54190e10	−1.74510	−0.872551	−	0.488524i	$-0.837536\pi$
$881$	−3.54190e10	−1.74510	−0.872551	+	0.488524i	$0.837536\pi$
$882$	1.62726e9	0.0798576
$883$	2.30773e10	1.12804	0.564018	−	0.825762i	$-0.309255\pi$
$883$	2.30773e10	1.12804	0.564018	+	0.825762i	$0.309255\pi$
$884$	−7.11704e7	−0.00346510
$885$	−4.36703e9	−0.211780
$886$	4.74039e9	0.228979
$887$	−2.08348e10	−1.00244	−0.501219	−	0.865321i	$-0.667115\pi$
$887$	−2.08348e10	−1.00244	−0.501219	+	0.865321i	$0.667115\pi$
$888$	−4.77887e10	−2.29024
$889$	1.50233e6	7.17149e−5 0
$890$	−1.00961e10	−0.480053
$891$	2.38897e10	1.13146
$892$	7.34919e9	0.346707
$893$	2.46477e10	1.15824
$894$	6.09016e9	0.285067
$895$	1.32269e10	0.616705
$896$	−3.47195e9	−0.161249
$897$	5.91119e9	0.273465
$898$	9.85646e8	0.0454207
$899$	−1.50147e10	−0.689220
$900$	2.59185e9	0.118512
$901$	−1.50882e9	−0.0687228
$902$	−3.98304e9	−0.180714
$903$	2.90686e9	0.131376
$904$	−2.47931e10	−1.11620
$905$	1.32203e10	0.592887
$906$	−1.92869e10	−0.861617
$907$	1.79557e10	0.799054	0.399527	−	0.916721i	$-0.369174\pi$
$907$	1.79557e10	0.799054	0.399527	+	0.916721i	$0.369174\pi$
$908$	−5.32294e9	−0.235967
$909$	−5.32532e9	−0.235165
$910$	1.15709e9	0.0509006
$911$	9.32582e9	0.408670	0.204335	−	0.978901i	$-0.434497\pi$
$911$	9.32582e9	0.408670	0.204335	+	0.978901i	$0.434497\pi$
$912$	3.64269e10	1.59016
$913$	3.20586e10	1.39411
$914$	2.65338e10	1.14944
$915$	3.28997e10	1.41977
$916$	−4.96266e9	−0.213344
$917$	−1.46917e9	−0.0629185
$918$	−4.17689e8	−0.0178198
$919$	−5.10451e9	−0.216945	−0.108473	−	0.994099i	$-0.534596\pi$
$919$	−5.10451e9	−0.216945	−0.108473	+	0.994099i	$0.534596\pi$
$920$	1.11477e10	0.471985
$921$	−3.10544e10	−1.30983
$922$	−2.14068e10	−0.899485
$923$	1.05707e10	0.442484
$924$	−2.87645e9	−0.119951
$925$	−2.68013e10	−1.11342
$926$	6.81042e9	0.281861
$927$	2.10831e10	0.869273
$928$	−9.58501e9	−0.393708
$929$	−2.19029e10	−0.896286	−0.448143	−	0.893962i	$-0.647914\pi$
$929$	−2.19029e10	−0.896286	−0.448143	+	0.893962i	$0.647914\pi$
$930$	−1.39205e10	−0.567500
$931$	−6.58281e9	−0.267354
$932$	3.24790e9	0.131416
$933$	3.21710e10	1.29682
$934$	1.63417e10	0.656269
$935$	6.10818e8	0.0244383
$936$	−4.93037e9	−0.196523
$937$	2.37446e10	0.942922	0.471461	−	0.881887i	$-0.343727\pi$
$937$	2.37446e10	0.942922	0.471461	+	0.881887i	$0.343727\pi$
$938$	−1.20793e10	−0.477894
$939$	−9.53612e9	−0.375874
$940$	−2.39252e9	−0.0939523
$941$	3.76249e10	1.47201	0.736006	−	0.676975i	$-0.236710\pi$
$941$	3.76249e10	1.47201	0.736006	+	0.676975i	$0.236710\pi$
$942$	−1.47137e10	−0.573512
$943$	4.52016e9	0.175535
$944$	−4.95864e9	−0.191849
$945$	−2.48079e9	−0.0956265
$946$	5.55734e9	0.213426
$947$	−1.83964e10	−0.703896	−0.351948	−	0.936019i	$-0.614481\pi$
$947$	−1.83964e10	−0.703896	−0.351948	+	0.936019i	$0.614481\pi$
$948$	9.83106e9	0.374775
$949$	−1.43961e9	−0.0546782
$950$	2.87009e10	1.08608
$951$	−4.83628e10	−1.82339
$952$	5.09668e8	0.0191451
$953$	−3.26553e10	−1.22216	−0.611081	−	0.791568i	$-0.709265\pi$
$953$	−3.26553e10	−1.22216	−0.611081	+	0.791568i	$0.709265\pi$
$954$	−2.20639e10	−0.822740
$955$	9.03896e9	0.335820
$956$	1.29311e10	0.478667
$957$	2.43840e10	0.899319
$958$	2.95674e10	1.08651
$959$	8.32776e9	0.304904
$960$	−2.21014e10	−0.806252
$961$	−4.77959e9	−0.173724
$962$	1.07619e10	0.389742
$963$	−7.26502e9	−0.262147
$964$	−7.34266e9	−0.263988
$965$	−1.02766e10	−0.368134
$966$	−8.93567e9	−0.318939
$967$	1.51103e10	0.537379	0.268689	−	0.963227i	$-0.413410\pi$
$967$	1.51103e10	0.537379	0.268689	+	0.963227i	$0.413410\pi$
$968$	4.56218e9	0.161662
$969$	−3.18222e9	−0.112356
$970$	−9.66481e9	−0.340011
$971$	3.87728e10	1.35912	0.679562	−	0.733618i	$-0.262170\pi$
$971$	3.87728e10	1.35912	0.679562	+	0.733618i	$0.262170\pi$
$972$	8.66500e9	0.302647
$973$	1.25023e10	0.435105
$974$	−7.41908e9	−0.257273
$975$	−6.99839e9	−0.241814
$976$	3.73567e10	1.28616
$977$	2.19721e10	0.753773	0.376887	−	0.926259i	$-0.376995\pi$
$977$	2.19721e10	0.753773	0.376887	+	0.926259i	$0.376995\pi$
$978$	−4.29121e10	−1.46688
$979$	−2.67759e10	−0.912021
$980$	6.38982e8	0.0216869
$981$	1.04215e10	0.352444
$982$	−1.32593e10	−0.446817
$983$	−6.50384e9	−0.218390	−0.109195	−	0.994020i	$-0.534827\pi$
$983$	−6.50384e9	−0.218390	−0.109195	+	0.994020i	$0.534827\pi$
$984$	−9.54218e9	−0.319275
$985$	3.16363e10	1.05477
$986$	−9.12011e8	−0.0302992
$987$	9.08516e9	0.300762
$988$	4.21016e9	0.138883
$989$	−6.30676e9	−0.207309
$990$	8.93216e9	0.292572
$991$	4.14755e10	1.35374	0.676868	−	0.736104i	$-0.263337\pi$
$991$	4.14755e10	1.35374	0.676868	+	0.736104i	$0.263337\pi$
$992$	1.45122e10	0.472000
$993$	4.96336e10	1.60862
$994$	−1.59792e10	−0.516064
$995$	−2.16884e10	−0.697987
$996$	1.62122e10	0.519916
$997$	−1.91930e10	−0.613352	−0.306676	−	0.951814i	$-0.599217\pi$
$997$	−1.91930e10	−0.613352	−0.306676	+	0.951814i	$0.599217\pi$
$998$	2.18767e9	0.0696665
$999$	−2.30734e10	−0.732206

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.b.1.7	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.b.1.7	✓	9	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q+9.68252 q^{2} +60.1290 q^{3} -34.2488 q^{4} -158.582 q^{5} +582.200 q^{6} -343.000 q^{7} -1570.98 q^{8} +1428.50 q^{9} +O(q^{10})\)	\(q+9.68252 q^{2} +60.1290 q^{3} -34.2488 q^{4} -158.582 q^{5} +582.200 q^{6} -343.000 q^{7} -1570.98 q^{8} +1428.50 q^{9} -1535.48 q^{10} -4072.24 q^{11} -2059.35 q^{12} +2197.00 q^{13} -3321.10 q^{14} -9535.40 q^{15} -10827.2 q^{16} +945.853 q^{17} +13831.5 q^{18} -55952.9 q^{19} +5431.26 q^{20} -20624.3 q^{21} -39429.5 q^{22} +44746.7 q^{23} -94461.3 q^{24} -52976.6 q^{25} +21272.5 q^{26} -45608.0 q^{27} +11747.3 q^{28} -99583.7 q^{29} -92326.7 q^{30} +150775. q^{31} +96250.8 q^{32} -244860. q^{33} +9158.24 q^{34} +54393.8 q^{35} -48924.4 q^{36} +505908. q^{37} -541765. q^{38} +132103. q^{39} +249129. q^{40} +101017. q^{41} -199695. q^{42} -140944. q^{43} +139469. q^{44} -226535. q^{45} +433260. q^{46} -440509. q^{47} -651027. q^{48} +117649. q^{49} -512947. q^{50} +56873.2 q^{51} -75244.7 q^{52} -1.59520e6 q^{53} -441600. q^{54} +645785. q^{55} +538845. q^{56} -3.36439e6 q^{57} -964221. q^{58} +457981. q^{59} +326576. q^{60} -3.45027e6 q^{61} +1.45988e6 q^{62} -489975. q^{63} +2.31783e6 q^{64} -348406. q^{65} -2.37086e6 q^{66} +3.63713e6 q^{67} -32394.3 q^{68} +2.69057e6 q^{69} +526669. q^{70} +4.81142e6 q^{71} -2.24414e6 q^{72} -655263. q^{73} +4.89847e6 q^{74} -3.18543e6 q^{75} +1.91632e6 q^{76} +1.39678e6 q^{77} +1.27909e6 q^{78} -4.77387e6 q^{79} +1.71700e6 q^{80} -5.86649e6 q^{81} +978097. q^{82} -7.87248e6 q^{83} +706356. q^{84} -149996. q^{85} -1.36469e6 q^{86} -5.98787e6 q^{87} +6.39740e6 q^{88} +6.57523e6 q^{89} -2.19343e6 q^{90} -753571. q^{91} -1.53252e6 q^{92} +9.06594e6 q^{93} -4.26523e6 q^{94} +8.87315e6 q^{95} +5.78747e6 q^{96} +6.29434e6 q^{97} +1.13914e6 q^{98} -5.81719e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 5 q^{2} - 26 q^{3} + 393 q^{4} - 181 q^{5} + 703 q^{6} - 3087 q^{7} + 1197 q^{8} + 3211 q^{9}+O(q^{10}) \) 9 * q - 5 * q^2 - 26 * q^3 + 393 * q^4 - 181 * q^5 + 703 * q^6 - 3087 * q^7 + 1197 * q^8 + 3211 * q^9	\( 9 q - 5 q^{2} - 26 q^{3} + 393 q^{4} - 181 q^{5} + 703 q^{6} - 3087 q^{7} + 1197 q^{8} + 3211 q^{9} - 5124 q^{10} - 9826 q^{11} - 20919 q^{12} + 19773 q^{13} + 1715 q^{14} - 20346 q^{15} + 31113 q^{16} - 22766 q^{17} - 12978 q^{18} - 17769 q^{19} - 44204 q^{20} + 8918 q^{21} - 203553 q^{22} - 49103 q^{23} + 52737 q^{24} + 227466 q^{25} - 10985 q^{26} + 103624 q^{27} - 134799 q^{28} - 487455 q^{29} - 287992 q^{30} - 63843 q^{31} - 587099 q^{32} - 314392 q^{33} - 576240 q^{34} + 62083 q^{35} - 1514926 q^{36} - 796926 q^{37} - 766702 q^{38} - 57122 q^{39} - 2887296 q^{40} - 1567546 q^{41} - 241129 q^{42} - 277899 q^{43} - 1281195 q^{44} - 1650593 q^{45} - 1907445 q^{46} + 1077367 q^{47} - 1110835 q^{48} + 1058841 q^{49} - 267459 q^{50} - 3054368 q^{51} + 863421 q^{52} - 7322659 q^{53} - 3355387 q^{54} - 2613324 q^{55} - 410571 q^{56} - 3751946 q^{57} - 2992332 q^{58} - 169804 q^{59} - 2754416 q^{60} - 6352284 q^{61} + 6001087 q^{62} - 1101373 q^{63} + 1657017 q^{64} - 397657 q^{65} - 5962713 q^{66} + 921120 q^{67} + 5615224 q^{68} - 5202780 q^{69} + 1757532 q^{70} + 3786654 q^{71} + 2229758 q^{72} + 5792889 q^{73} - 1991961 q^{74} + 145628 q^{75} - 2806026 q^{76} + 3370318 q^{77} + 1544491 q^{78} + 3464037 q^{79} + 15422512 q^{80} - 5010363 q^{81} - 12539943 q^{82} + 6834945 q^{83} + 7175217 q^{84} + 3880662 q^{85} - 7977524 q^{86} + 3727078 q^{87} + 7013709 q^{88} - 20408371 q^{89} + 34910060 q^{90} - 6782139 q^{91} - 3544371 q^{92} + 3121742 q^{93} + 61343967 q^{94} + 3360807 q^{95} + 23547905 q^{96} + 41644125 q^{97} - 588245 q^{98} + 50754068 q^{99}+O(q^{100}) \) 9 * q - 5 * q^2 - 26 * q^3 + 393 * q^4 - 181 * q^5 + 703 * q^6 - 3087 * q^7 + 1197 * q^8 + 3211 * q^9 - 5124 * q^10 - 9826 * q^11 - 20919 * q^12 + 19773 * q^13 + 1715 * q^14 - 20346 * q^15 + 31113 * q^16 - 22766 * q^17 - 12978 * q^18 - 17769 * q^19 - 44204 * q^20 + 8918 * q^21 - 203553 * q^22 - 49103 * q^23 + 52737 * q^24 + 227466 * q^25 - 10985 * q^26 + 103624 * q^27 - 134799 * q^28 - 487455 * q^29 - 287992 * q^30 - 63843 * q^31 - 587099 * q^32 - 314392 * q^33 - 576240 * q^34 + 62083 * q^35 - 1514926 * q^36 - 796926 * q^37 - 766702 * q^38 - 57122 * q^39 - 2887296 * q^40 - 1567546 * q^41 - 241129 * q^42 - 277899 * q^43 - 1281195 * q^44 - 1650593 * q^45 - 1907445 * q^46 + 1077367 * q^47 - 1110835 * q^48 + 1058841 * q^49 - 267459 * q^50 - 3054368 * q^51 + 863421 * q^52 - 7322659 * q^53 - 3355387 * q^54 - 2613324 * q^55 - 410571 * q^56 - 3751946 * q^57 - 2992332 * q^58 - 169804 * q^59 - 2754416 * q^60 - 6352284 * q^61 + 6001087 * q^62 - 1101373 * q^63 + 1657017 * q^64 - 397657 * q^65 - 5962713 * q^66 + 921120 * q^67 + 5615224 * q^68 - 5202780 * q^69 + 1757532 * q^70 + 3786654 * q^71 + 2229758 * q^72 + 5792889 * q^73 - 1991961 * q^74 + 145628 * q^75 - 2806026 * q^76 + 3370318 * q^77 + 1544491 * q^78 + 3464037 * q^79 + 15422512 * q^80 - 5010363 * q^81 - 12539943 * q^82 + 6834945 * q^83 + 7175217 * q^84 + 3880662 * q^85 - 7977524 * q^86 + 3727078 * q^87 + 7013709 * q^88 - 20408371 * q^89 + 34910060 * q^90 - 6782139 * q^91 - 3544371 * q^92 + 3121742 * q^93 + 61343967 * q^94 + 3360807 * q^95 + 23547905 * q^96 + 41644125 * q^97 - 588245 * q^98 + 50754068 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more