LMFDB - Embedded newform 91.8.a.b.1.5

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			1.5
Root			$-0.950186$ 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)

$f(q)$	$=$	$q-1.95019 q^{2} -76.8097 q^{3} -124.197 q^{4} +57.0015 q^{5} +149.793 q^{6} -343.000 q^{7} +491.831 q^{8} +3712.72 q^{9} +O(q^{10})$	\(q-1.95019 q^{2} -76.8097 q^{3} -124.197 q^{4} +57.0015 q^{5} +149.793 q^{6} -343.000 q^{7} +491.831 q^{8} +3712.72 q^{9} -111.163 q^{10} +2077.87 q^{11} +9539.51 q^{12} +2197.00 q^{13} +668.914 q^{14} -4378.26 q^{15} +14938.0 q^{16} -58.2568 q^{17} -7240.51 q^{18} +25380.1 q^{19} -7079.40 q^{20} +26345.7 q^{21} -4052.23 q^{22} +32152.3 q^{23} -37777.4 q^{24} -74875.8 q^{25} -4284.56 q^{26} -117190. q^{27} +42599.5 q^{28} -83770.6 q^{29} +8538.43 q^{30} -122027. q^{31} -92086.3 q^{32} -159600. q^{33} +113.612 q^{34} -19551.5 q^{35} -461108. q^{36} -14733.4 q^{37} -49495.9 q^{38} -168751. q^{39} +28035.1 q^{40} +175209. q^{41} -51379.1 q^{42} -255441. q^{43} -258064. q^{44} +211631. q^{45} -62703.1 q^{46} +1.02485e6 q^{47} -1.14738e6 q^{48} +117649. q^{49} +146022. q^{50} +4474.69 q^{51} -272860. q^{52} +726394. q^{53} +228543. q^{54} +118441. q^{55} -168698. q^{56} -1.94944e6 q^{57} +163368. q^{58} +259522. q^{59} +543766. q^{60} -3.06383e6 q^{61} +237975. q^{62} -1.27346e6 q^{63} -1.73248e6 q^{64} +125232. q^{65} +311250. q^{66} +345489. q^{67} +7235.31 q^{68} -2.46961e6 q^{69} +38129.1 q^{70} +1.83038e6 q^{71} +1.82603e6 q^{72} +2.08708e6 q^{73} +28732.9 q^{74} +5.75119e6 q^{75} -3.15212e6 q^{76} -712708. q^{77} +329096. q^{78} +184600. q^{79} +851489. q^{80} +881628. q^{81} -341691. q^{82} -4.16666e6 q^{83} -3.27205e6 q^{84} -3320.72 q^{85} +498158. q^{86} +6.43439e6 q^{87} +1.02196e6 q^{88} -7.37484e6 q^{89} -412719. q^{90} -753571. q^{91} -3.99322e6 q^{92} +9.37285e6 q^{93} -1.99865e6 q^{94} +1.44670e6 q^{95} +7.07312e6 q^{96} -1.09582e7 q^{97} -229437. q^{98} +7.71454e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.95019	−0.172374	−0.0861869	−	0.996279i	$-0.527468\pi$
$2$	−1.95019	−0.172374	−0.0861869	+	0.996279i	$0.527468\pi$
$3$	−76.8097	−1.64245	−0.821224	−	0.570606i	$-0.806708\pi$
$3$	−76.8097	−1.64245	−0.821224	+	0.570606i	$0.806708\pi$
$4$	−124.197	−0.970287
$5$	57.0015	0.203935	0.101967	−	0.994788i	$-0.467486\pi$
$5$	57.0015	0.203935	0.101967	+	0.994788i	$0.467486\pi$
$6$	149.793	0.283115
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	491.831	0.339626
$9$	3712.72	1.69763
$10$	−111.163	−0.0351530
$11$	2077.87	0.470699	0.235349	−	0.971911i	$-0.424377\pi$
$11$	2077.87	0.470699	0.235349	+	0.971911i	$0.424377\pi$
$12$	9539.51	1.59365
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	668.914	0.0651512
$15$	−4378.26	−0.334952
$16$	14938.0	0.911745
$17$	−58.2568	−0.00287591	−0.00143796	−	0.999999i	$-0.500458\pi$
$17$	−58.2568	−0.00287591	−0.00143796	+	0.999999i	$0.500458\pi$
$18$	−7240.51	−0.292628
$19$	25380.1	0.848898	0.424449	−	0.905452i	$-0.360468\pi$
$19$	25380.1	0.848898	0.424449	+	0.905452i	$0.360468\pi$
$20$	−7079.40	−0.197875
$21$	26345.7	0.620787
$22$	−4052.23	−0.0811361
$23$	32152.3	0.551017	0.275509	−	0.961299i	$-0.411154\pi$
$23$	32152.3	0.551017	0.275509	+	0.961299i	$0.411154\pi$
$24$	−37777.4	−0.557818
$25$	−74875.8	−0.958411
$26$	−4284.56	−0.0478079
$27$	−117190.	−1.14583
$28$	42599.5	0.366734
$29$	−83770.6	−0.637821	−0.318910	−	0.947785i	$-0.603317\pi$
$29$	−83770.6	−0.637821	−0.318910	+	0.947785i	$0.603317\pi$
$30$	8538.43	0.0577369
$31$	−122027.	−0.735681	−0.367841	−	0.929889i	$-0.619903\pi$
$31$	−122027.	−0.735681	−0.367841	+	0.929889i	$0.619903\pi$
$32$	−92086.3	−0.496787
$33$	−159600.	−0.773098
$34$	113.612	0.000495732 0
$35$	−19551.5	−0.0770800
$36$	−461108.	−1.64719
$37$	−14733.4	−0.0478186	−0.0239093	−	0.999714i	$-0.507611\pi$
$37$	−14733.4	−0.0478186	−0.0239093	+	0.999714i	$0.507611\pi$
$38$	−49495.9	−0.146328
$39$	−168751.	−0.455533
$40$	28035.1	0.0692615
$41$	175209.	0.397021	0.198511	−	0.980099i	$-0.436390\pi$
$41$	175209.	0.397021	0.198511	+	0.980099i	$0.436390\pi$
$42$	−51379.1	−0.107007
$43$	−255441.	−0.489950	−0.244975	−	0.969529i	$-0.578780\pi$
$43$	−255441.	−0.489950	−0.244975	+	0.969529i	$0.578780\pi$
$44$	−258064.	−0.456713
$45$	211631.	0.346206
$46$	−62703.1	−0.0949809
$47$	1.02485e6	1.43985	0.719925	−	0.694052i	$-0.244176\pi$
$47$	1.02485e6	1.43985	0.719925	+	0.694052i	$0.244176\pi$
$48$	−1.14738e6	−1.49749
$49$	117649.	0.142857
$50$	146022.	0.165205
$51$	4474.69	0.00472354
$52$	−272860.	−0.269109
$53$	726394.	0.670204	0.335102	−	0.942182i	$-0.391229\pi$
$53$	726394.	0.670204	0.335102	+	0.942182i	$0.391229\pi$
$54$	228543.	0.197510
$55$	118441.	0.0959918
$56$	−168698.	−0.128366
$57$	−1.94944e6	−1.39427
$58$	163368.	0.109944
$59$	259522.	0.164510	0.0822551	−	0.996611i	$-0.473788\pi$
$59$	259522.	0.164510	0.0822551	+	0.996611i	$0.473788\pi$
$60$	543766.	0.325000
$61$	−3.06383e6	−1.72826	−0.864132	−	0.503265i	$-0.832132\pi$
$61$	−3.06383e6	−1.72826	−0.864132	+	0.503265i	$0.832132\pi$
$62$	237975.	0.126812
$63$	−1.27346e6	−0.641645
$64$	−1.73248e6	−0.826112
$65$	125232.	0.0565613
$66$	311250.	0.133262
$67$	345489.	0.140337	0.0701685	−	0.997535i	$-0.477646\pi$
$67$	345489.	0.140337	0.0701685	+	0.997535i	$0.477646\pi$
$68$	7235.31	0.00279046
$69$	−2.46961e6	−0.905017
$70$	38129.1	0.0132866
$71$	1.83038e6	0.606929	0.303464	−	0.952843i	$-0.401857\pi$
$71$	1.83038e6	0.606929	0.303464	+	0.952843i	$0.401857\pi$
$72$	1.82603e6	0.576560
$73$	2.08708e6	0.627926	0.313963	−	0.949435i	$-0.398343\pi$
$73$	2.08708e6	0.627926	0.313963	+	0.949435i	$0.398343\pi$
$74$	28732.9	0.00824267
$75$	5.75119e6	1.57414
$76$	−3.15212e6	−0.823675
$77$	−712708.	−0.177907
$78$	329096.	0.0785219
$79$	184600.	0.0421247	0.0210624	−	0.999778i	$-0.493295\pi$
$79$	184600.	0.0421247	0.0210624	+	0.999778i	$0.493295\pi$
$80$	851489.	0.185936
$81$	881628.	0.184326
$82$	−341691.	−0.0684360
$83$	−4.16666e6	−0.799862	−0.399931	−	0.916545i	$-0.630966\pi$
$83$	−4.16666e6	−0.799862	−0.399931	+	0.916545i	$0.630966\pi$
$84$	−3.27205e6	−0.602342
$85$	−3320.72	−0.000586498 0
$86$	498158.	0.0844545
$87$	6.43439e6	1.04759
$88$	1.02196e6	0.159861
$89$	−7.37484e6	−1.10889	−0.554444	−	0.832221i	$-0.687069\pi$
$89$	−7.37484e6	−1.10889	−0.554444	+	0.832221i	$0.687069\pi$
$90$	−412719.	−0.0596769
$91$	−753571.	−0.104828
$92$	−3.99322e6	−0.534645
$93$	9.37285e6	1.20832
$94$	−1.99865e6	−0.248192
$95$	1.44670e6	0.173120
$96$	7.07312e6	0.815946
$97$	−1.09582e7	−1.21910	−0.609550	−	0.792748i	$-0.708650\pi$
$97$	−1.09582e7	−1.21910	−0.609550	+	0.792748i	$0.708650\pi$
$98$	−229437.	−0.0246248
$99$	7.71454e6	0.799074
$100$	9.29934e6	0.929934
$101$	1.79566e7	1.73420	0.867101	−	0.498133i	$-0.165981\pi$
$101$	1.79566e7	1.73420	0.867101	+	0.498133i	$0.165981\pi$
$102$	−8726.48	−0.000814214 0
$103$	1.74347e7	1.57212	0.786058	−	0.618153i	$-0.212119\pi$
$103$	1.74347e7	1.57212	0.786058	+	0.618153i	$0.212119\pi$
$104$	1.08055e6	0.0941953
$105$	1.50174e6	0.126600
$106$	−1.41660e6	−0.115526
$107$	5.78842e6	0.456790	0.228395	−	0.973569i	$-0.426652\pi$
$107$	5.78842e6	0.456790	0.228395	+	0.973569i	$0.426652\pi$
$108$	1.45547e7	1.11178
$109$	−1.19429e7	−0.883317	−0.441658	−	0.897183i	$-0.645610\pi$
$109$	−1.19429e7	−0.883317	−0.441658	+	0.897183i	$0.645610\pi$
$110$	−230983.	−0.0165465
$111$	1.13167e6	0.0785395
$112$	−5.12374e6	−0.344607
$113$	−1.03882e7	−0.677278	−0.338639	−	0.940916i	$-0.609966\pi$
$113$	−1.03882e7	−0.677278	−0.338639	+	0.940916i	$0.609966\pi$
$114$	3.80176e6	0.240336
$115$	1.83273e6	0.112372
$116$	1.04040e7	0.618870
$117$	8.15686e6	0.470839
$118$	−506117.	−0.0283572
$119$	19982.1	0.00108699
$120$	−2.15336e6	−0.113758
$121$	−1.51696e7	−0.778443
$122$	5.97504e6	0.297907
$123$	−1.34578e7	−0.652087
$124$	1.51553e7	0.713822
$125$	−8.72127e6	−0.399388
$126$	2.48349e6	0.110603
$127$	−2.64452e7	−1.14560	−0.572801	−	0.819694i	$-0.694143\pi$
$127$	−2.64452e7	−1.14560	−0.572801	+	0.819694i	$0.694143\pi$
$128$	1.51657e7	0.639187
$129$	1.96204e7	0.804717
$130$	−244226.	−0.00974968
$131$	4.88540e6	0.189868	0.0949338	−	0.995484i	$-0.469736\pi$
$131$	4.88540e6	0.189868	0.0949338	+	0.995484i	$0.469736\pi$
$132$	1.98218e7	0.750127
$133$	−8.70537e6	−0.320853
$134$	−673768.	−0.0241904
$135$	−6.68003e6	−0.233674
$136$	−28652.5	−0.000976734 0
$137$	−3.71923e7	−1.23575	−0.617875	−	0.786276i	$-0.712006\pi$
$137$	−3.71923e7	−1.23575	−0.617875	+	0.786276i	$0.712006\pi$
$138$	4.81620e6	0.156001
$139$	7.22810e6	0.228282	0.114141	−	0.993465i	$-0.463588\pi$
$139$	7.22810e6	0.228282	0.114141	+	0.993465i	$0.463588\pi$
$140$	2.42823e6	0.0747898
$141$	−7.87183e7	−2.36488
$142$	−3.56959e6	−0.104619
$143$	4.56507e6	0.130548
$144$	5.54608e7	1.54781
$145$	−4.77505e6	−0.130074
$146$	−4.07019e6	−0.108238
$147$	−9.03658e6	−0.234635
$148$	1.82984e6	0.0463978
$149$	−6.55575e7	−1.62357	−0.811784	−	0.583958i	$-0.801503\pi$
$149$	−6.55575e7	−1.62357	−0.811784	+	0.583958i	$0.801503\pi$
$150$	−1.12159e7	−0.271340
$151$	−6.98807e7	−1.65173	−0.825863	−	0.563871i	$-0.809311\pi$
$151$	−6.98807e7	−1.65173	−0.825863	+	0.563871i	$0.809311\pi$
$152$	1.24827e7	0.288308
$153$	−216292.	−0.00488225
$154$	1.38991e6	0.0306666
$155$	−6.95571e6	−0.150031
$156$	2.09583e7	0.441998
$157$	4.72050e7	0.973507	0.486753	−	0.873539i	$-0.338181\pi$
$157$	4.72050e7	0.973507	0.486753	+	0.873539i	$0.338181\pi$
$158$	−360005.	−0.00726120
$159$	−5.57941e7	−1.10077
$160$	−5.24905e6	−0.101312
$161$	−1.10283e7	−0.208265
$162$	−1.71934e6	−0.0317731
$163$	−4.07094e7	−0.736273	−0.368136	−	0.929772i	$-0.620004\pi$
$163$	−4.07094e7	−0.736273	−0.368136	+	0.929772i	$0.620004\pi$
$164$	−2.17604e7	−0.385225
$165$	−9.09744e6	−0.157661
$166$	8.12577e6	0.137875
$167$	−3.08502e7	−0.512567	−0.256283	−	0.966602i	$-0.582498\pi$
$167$	−3.08502e7	−0.512567	−0.256283	+	0.966602i	$0.582498\pi$
$168$	1.29576e7	0.210835
$169$	4.82681e6	0.0769231
$170$	6476.03	0.000101097 0
$171$	9.42292e7	1.44112
$172$	3.17250e7	0.475392
$173$	−7.70788e7	−1.13181	−0.565905	−	0.824470i	$-0.691473\pi$
$173$	−7.70788e7	−1.13181	−0.565905	+	0.824470i	$0.691473\pi$
$174$	−1.25483e7	−0.180577
$175$	2.56824e7	0.362245
$176$	3.10392e7	0.429157
$177$	−1.99338e7	−0.270199
$178$	1.43823e7	0.191143
$179$	1.63247e7	0.212745	0.106372	−	0.994326i	$-0.466076\pi$
$179$	1.63247e7	0.212745	0.106372	+	0.994326i	$0.466076\pi$
$180$	−2.62839e7	−0.335920
$181$	−17278.8	−0.000216591 0	−0.000108295	−	1.00000i	$-0.500034\pi$
$181$	−17278.8	−0.000216591 0	−0.000108295		1.00000i	$0.500034\pi$
$182$	1.46960e6	0.0180697
$183$	2.35332e8	2.83858
$184$	1.58135e7	0.187140
$185$	−839825.	−0.00975187
$186$	−1.82788e7	−0.208282
$187$	−121050.	−0.00135369
$188$	−1.27283e8	−1.39707
$189$	4.01963e7	0.433082
$190$	−2.82134e6	−0.0298413
$191$	−1.27488e8	−1.32390	−0.661948	−	0.749550i	$-0.730270\pi$
$191$	−1.27488e8	−1.32390	−0.661948	+	0.749550i	$0.730270\pi$
$192$	1.33071e8	1.35685
$193$	−8.09100e7	−0.810124	−0.405062	−	0.914289i	$-0.632750\pi$
$193$	−8.09100e7	−0.810124	−0.405062	+	0.914289i	$0.632750\pi$
$194$	2.13706e7	0.210141
$195$	−9.61904e6	−0.0928989
$196$	−1.46116e7	−0.138612
$197$	9.77949e7	0.911348	0.455674	−	0.890147i	$-0.349398\pi$
$197$	9.77949e7	0.911348	0.455674	+	0.890147i	$0.349398\pi$
$198$	−1.50448e7	−0.137739
$199$	−1.54509e8	−1.38985	−0.694926	−	0.719081i	$-0.744563\pi$
$199$	−1.54509e8	−1.38985	−0.694926	+	0.719081i	$0.744563\pi$
$200$	−3.68262e7	−0.325501
$201$	−2.65369e7	−0.230496
$202$	−3.50187e7	−0.298931
$203$	2.87333e7	0.241074
$204$	−555742.	−0.00458319
$205$	9.98719e6	0.0809664
$206$	−3.40009e7	−0.270991
$207$	1.19373e8	0.935426
$208$	3.28188e7	0.252872
$209$	5.27364e7	0.399575
$210$	−2.92868e6	−0.0218225
$211$	1.40699e8	1.03110	0.515552	−	0.856858i	$-0.327587\pi$
$211$	1.40699e8	1.03110	0.515552	+	0.856858i	$0.327587\pi$
$212$	−9.02158e7	−0.650290
$213$	−1.40591e8	−0.996849
$214$	−1.12885e7	−0.0787386
$215$	−1.45605e7	−0.0999177
$216$	−5.76379e7	−0.389152
$217$	4.18552e7	0.278061
$218$	2.32909e7	0.152261
$219$	−1.60308e8	−1.03133
$220$	−1.47100e7	−0.0931396
$221$	−127990.	−0.000797635 0
$222$	−2.20696e6	−0.0135382
$223$	1.98794e8	1.20043	0.600215	−	0.799839i	$-0.295082\pi$
$223$	1.98794e8	1.20043	0.600215	+	0.799839i	$0.295082\pi$
$224$	3.15856e7	0.187768
$225$	−2.77993e8	−1.62703
$226$	2.02590e7	0.116745
$227$	−2.68936e7	−0.152601	−0.0763007	−	0.997085i	$-0.524311\pi$
$227$	−2.68936e7	−0.152601	−0.0763007	+	0.997085i	$0.524311\pi$
$228$	2.42114e8	1.35284
$229$	2.06354e7	0.113550	0.0567752	−	0.998387i	$-0.481918\pi$
$229$	2.06354e7	0.113550	0.0567752	+	0.998387i	$0.481918\pi$
$230$	−3.57417e6	−0.0193699
$231$	5.47429e7	0.292204
$232$	−4.12010e7	−0.216620
$233$	−1.84690e8	−0.956526	−0.478263	−	0.878217i	$-0.658733\pi$
$233$	−1.84690e8	−0.956526	−0.478263	+	0.878217i	$0.658733\pi$
$234$	−1.59074e7	−0.0811603
$235$	5.84179e7	0.293635
$236$	−3.22318e7	−0.159622
$237$	−1.41791e7	−0.0691877
$238$	−38968.8	−0.000187369 0
$239$	−2.48542e8	−1.17762	−0.588812	−	0.808270i	$-0.700404\pi$
$239$	−2.48542e8	−1.17762	−0.588812	+	0.808270i	$0.700404\pi$
$240$	−6.54026e7	−0.305391
$241$	1.27864e8	0.588421	0.294211	−	0.955741i	$-0.404943\pi$
$241$	1.27864e8	0.588421	0.294211	+	0.955741i	$0.404943\pi$
$242$	2.95836e7	0.134183
$243$	1.88578e8	0.843080
$244$	3.80518e8	1.67691
$245$	6.70616e6	0.0291335
$246$	2.62452e7	0.112403
$247$	5.57600e7	0.235442
$248$	−6.00166e7	−0.249856
$249$	3.20040e8	1.31373
$250$	1.70081e7	0.0688440
$251$	1.80445e8	0.720257	0.360129	−	0.932903i	$-0.382733\pi$
$251$	1.80445e8	0.720257	0.360129	+	0.932903i	$0.382733\pi$
$252$	1.58160e8	0.622580
$253$	6.68083e7	0.259363
$254$	5.15731e7	0.197472
$255$	255064.	0.000963292 0
$256$	1.92182e8	0.715933
$257$	5.00130e8	1.83788	0.918940	−	0.394397i	$-0.129046\pi$
$257$	5.00130e8	1.83788	0.918940	+	0.394397i	$0.129046\pi$
$258$	−3.82634e7	−0.138712
$259$	5.05356e6	0.0180737
$260$	−1.55534e7	−0.0548807
$261$	−3.11017e8	−1.08279
$262$	−9.52745e6	−0.0327282
$263$	2.93269e8	0.994078	0.497039	−	0.867728i	$-0.334421\pi$
$263$	2.93269e8	0.994078	0.497039	+	0.867728i	$0.334421\pi$
$264$	−7.84963e7	−0.262564
$265$	4.14055e7	0.136678
$266$	1.69771e7	0.0553067
$267$	5.66459e8	1.82129
$268$	−4.29086e7	−0.136167
$269$	−5.21772e8	−1.63436	−0.817180	−	0.576382i	$-0.804464\pi$
$269$	−5.21772e8	−1.63436	−0.817180	+	0.576382i	$0.804464\pi$
$270$	1.30273e7	0.0402792
$271$	5.87031e8	1.79171	0.895857	−	0.444343i	$-0.146563\pi$
$271$	5.87031e8	1.79171	0.895857	+	0.444343i	$0.146563\pi$
$272$	−870242.	−0.00262210
$273$	5.78815e7	0.172175
$274$	7.25318e7	0.213011
$275$	−1.55582e8	−0.451123
$276$	3.06718e8	0.878127
$277$	−4.79114e7	−0.135444	−0.0677220	−	0.997704i	$-0.521573\pi$
$277$	−4.79114e7	−0.135444	−0.0677220	+	0.997704i	$0.521573\pi$
$278$	−1.40961e7	−0.0393499
$279$	−4.53052e8	−1.24892
$280$	−9.61603e6	−0.0261784
$281$	5.36862e7	0.144341	0.0721706	−	0.997392i	$-0.477007\pi$
$281$	5.36862e7	0.144341	0.0721706	+	0.997392i	$0.477007\pi$
$282$	1.53515e8	0.407643
$283$	−1.91865e8	−0.503204	−0.251602	−	0.967831i	$-0.580957\pi$
$283$	−1.91865e8	−0.503204	−0.251602	+	0.967831i	$0.580957\pi$
$284$	−2.27328e8	−0.588895
$285$	−1.11121e8	−0.284340
$286$	−8.90274e6	−0.0225031
$287$	−6.00968e7	−0.150060
$288$	−3.41891e8	−0.843362
$289$	−4.10335e8	−0.999992
$290$	9.31223e6	0.0224213
$291$	8.41698e8	2.00231
$292$	−2.59208e8	−0.609268
$293$	−7.48571e8	−1.73859	−0.869293	−	0.494297i	$-0.835426\pi$
$293$	−7.48571e8	−1.73859	−0.869293	+	0.494297i	$0.835426\pi$
$294$	1.76230e7	0.0404450
$295$	1.47931e7	0.0335493
$296$	−7.24634e6	−0.0162404
$297$	−2.43506e8	−0.539339
$298$	1.27849e8	0.279861
$299$	7.06387e7	0.152825
$300$	−7.14279e8	−1.52737
$301$	8.76164e7	0.185184
$302$	1.36280e8	0.284714
$303$	−1.37924e9	−2.84834
$304$	3.79128e8	0.773978
$305$	−1.74643e8	−0.352453
$306$	421809.	0.000841571 0
$307$	−6.13923e8	−1.21096	−0.605480	−	0.795861i	$-0.707019\pi$
$307$	−6.13923e8	−1.21096	−0.605480	+	0.795861i	$0.707019\pi$
$308$	8.85160e7	0.172621
$309$	−1.33915e9	−2.58212
$310$	1.35649e7	0.0258614
$311$	3.55168e8	0.669533	0.334766	−	0.942301i	$-0.391343\pi$
$311$	3.55168e8	0.669533	0.334766	+	0.942301i	$0.391343\pi$
$312$	−8.29968e7	−0.154711
$313$	1.06933e8	0.197109	0.0985546	−	0.995132i	$-0.468578\pi$
$313$	1.06933e8	0.197109	0.0985546	+	0.995132i	$0.468578\pi$
$314$	−9.20585e7	−0.167807
$315$	−7.25893e7	−0.130854
$316$	−2.29267e7	−0.0408731
$317$	−5.20022e8	−0.916884	−0.458442	−	0.888724i	$-0.651592\pi$
$317$	−5.20022e8	−0.916884	−0.458442	+	0.888724i	$0.651592\pi$
$318$	1.08809e8	0.189745
$319$	−1.74064e8	−0.300222
$320$	−9.87540e7	−0.168473
$321$	−4.44607e8	−0.750254
$322$	2.15072e7	0.0358994
$323$	−1.47856e6	−0.00244136
$324$	−1.09495e8	−0.178850
$325$	−1.64502e8	−0.265815
$326$	7.93910e7	0.126914
$327$	9.17329e8	1.45080
$328$	8.61733e7	0.134839
$329$	−3.51523e8	−0.544212
$330$	1.77417e7	0.0271767
$331$	8.94128e8	1.35520	0.677598	−	0.735433i	$-0.263021\pi$
$331$	8.94128e8	1.35520	0.677598	+	0.735433i	$0.263021\pi$
$332$	5.17486e8	0.776096
$333$	−5.47010e7	−0.0811785
$334$	6.01636e7	0.0883530
$335$	1.96934e7	0.0286196
$336$	3.93553e8	0.565999
$337$	4.69571e8	0.668338	0.334169	−	0.942513i	$-0.391544\pi$
$337$	4.69571e8	0.668338	0.334169	+	0.942513i	$0.391544\pi$
$338$	−9.41318e6	−0.0132595
$339$	7.97916e8	1.11239
$340$	412423.	0.000569072 0
$341$	−2.53556e8	−0.346284
$342$	−1.83765e8	−0.248411
$343$	−4.03536e7	−0.0539949
$344$	−1.25634e8	−0.166400
$345$	−1.40771e8	−0.184564
$346$	1.50318e8	0.195094
$347$	−9.32789e8	−1.19848	−0.599239	−	0.800570i	$-0.704530\pi$
$347$	−9.32789e8	−1.19848	−0.599239	+	0.800570i	$0.704530\pi$
$348$	−7.99131e8	−1.01646
$349$	7.88074e7	0.0992380	0.0496190	−	0.998768i	$-0.484199\pi$
$349$	7.88074e7	0.0992380	0.0496190	+	0.998768i	$0.484199\pi$
$350$	−5.00855e7	−0.0624416
$351$	−2.57467e8	−0.317795
$352$	−1.91343e8	−0.233837
$353$	3.11290e8	0.376664	0.188332	−	0.982105i	$-0.439692\pi$
$353$	3.11290e8	0.376664	0.188332	+	0.982105i	$0.439692\pi$
$354$	3.88747e7	0.0465753
$355$	1.04334e8	0.123774
$356$	9.15932e8	1.07594
$357$	−1.53482e6	−0.00178533
$358$	−3.18361e7	−0.0366716
$359$	−6.79280e8	−0.774851	−0.387426	−	0.921901i	$-0.626636\pi$
$359$	−6.79280e8	−0.774851	−0.387426	+	0.921901i	$0.626636\pi$
$360$	1.04087e8	0.117581
$361$	−2.49723e8	−0.279373
$362$	33697.0	3.73345e−5 0
$363$	1.16518e9	1.27855
$364$	9.35911e7	0.101714
$365$	1.18966e8	0.128056
$366$	−4.58941e8	−0.489297
$367$	1.40088e9	1.47934	0.739672	−	0.672968i	$-0.234981\pi$
$367$	1.40088e9	1.47934	0.739672	+	0.672968i	$0.234981\pi$
$368$	4.80293e8	0.502387
$369$	6.50504e8	0.673997
$370$	1.63782e6	0.00168097
$371$	−2.49153e8	−0.253313
$372$	−1.16408e9	−1.17242
$373$	−9.54859e7	−0.0952705	−0.0476353	−	0.998865i	$-0.515169\pi$
$373$	−9.54859e7	−0.0952705	−0.0476353	+	0.998865i	$0.515169\pi$
$374$	236070.	0.000233340 0
$375$	6.69878e8	0.655973
$376$	5.04052e8	0.489010
$377$	−1.84044e8	−0.176900
$378$	−7.83903e7	−0.0746519
$379$	−1.21115e9	−1.14278	−0.571390	−	0.820679i	$-0.693596\pi$
$379$	−1.21115e9	−1.14278	−0.571390	+	0.820679i	$0.693596\pi$
$380$	−1.79676e8	−0.167976
$381$	2.03125e9	1.88159
$382$	2.48626e8	0.228205
$383$	1.31422e9	1.19529	0.597643	−	0.801762i	$-0.296104\pi$
$383$	1.31422e9	1.19529	0.597643	+	0.801762i	$0.296104\pi$
$384$	−1.16487e9	−1.04983
$385$	−4.06254e7	−0.0362815
$386$	1.57790e8	0.139644
$387$	−9.48383e8	−0.831755
$388$	1.36098e9	1.18288
$389$	−1.89135e8	−0.162910	−0.0814552	−	0.996677i	$-0.525957\pi$
$389$	−1.89135e8	−0.162910	−0.0814552	+	0.996677i	$0.525957\pi$
$390$	1.87589e7	0.0160133
$391$	−1.87309e6	−0.00158468
$392$	5.78634e7	0.0485180
$393$	−3.75246e8	−0.311848
$394$	−1.90718e8	−0.157093
$395$	1.05225e7	0.00859069
$396$	−9.58122e8	−0.775332
$397$	1.13134e9	0.907458	0.453729	−	0.891140i	$-0.350093\pi$
$397$	1.13134e9	0.907458	0.453729	+	0.891140i	$0.350093\pi$
$398$	3.01322e8	0.239574
$399$	6.68656e8	0.526984
$400$	−1.11850e9	−0.873826
$401$	2.21791e9	1.71767	0.858834	−	0.512254i	$-0.171189\pi$
$401$	2.21791e9	1.71767	0.858834	+	0.512254i	$0.171189\pi$
$402$	5.17519e7	0.0397315
$403$	−2.68093e8	−0.204041
$404$	−2.23015e9	−1.68267
$405$	5.02541e7	0.0375906
$406$	−5.60353e7	−0.0415548
$407$	−3.06140e7	−0.0225082
$408$	2.20079e6	0.00160423
$409$	−1.28786e9	−0.930759	−0.465379	−	0.885111i	$-0.654082\pi$
$409$	−1.28786e9	−0.930759	−0.465379	+	0.885111i	$0.654082\pi$
$410$	−1.94769e7	−0.0139565
$411$	2.85672e9	2.02965
$412$	−2.16533e9	−1.52540
$413$	−8.90161e7	−0.0621790
$414$	−2.32799e8	−0.161243
$415$	−2.37506e8	−0.163120
$416$	−2.02314e8	−0.137784
$417$	−5.55188e8	−0.374942
$418$	−1.02846e8	−0.0688763
$419$	−2.59761e9	−1.72514	−0.862570	−	0.505938i	$-0.831146\pi$
$419$	−2.59761e9	−1.72514	−0.862570	+	0.505938i	$0.831146\pi$
$420$	−1.86512e8	−0.122838
$421$	−1.72411e9	−1.12610	−0.563052	−	0.826421i	$-0.690373\pi$
$421$	−1.72411e9	−1.12610	−0.563052	+	0.826421i	$0.690373\pi$
$422$	−2.74389e8	−0.177735
$423$	3.80498e9	2.44434
$424$	3.57263e8	0.227618
$425$	4.36203e6	0.00275631
$426$	2.74179e8	0.171831
$427$	1.05089e9	0.653223
$428$	−7.18903e8	−0.443218
$429$	−3.50642e8	−0.214419
$430$	2.83957e7	0.0172232
$431$	−2.29828e9	−1.38272	−0.691358	−	0.722512i	$-0.742987\pi$
$431$	−2.29828e9	−1.38272	−0.691358	+	0.722512i	$0.742987\pi$
$432$	−1.75059e9	−1.04470
$433$	2.94415e9	1.74282	0.871410	−	0.490555i	$-0.163206\pi$
$433$	2.94415e9	1.74282	0.871410	+	0.490555i	$0.163206\pi$
$434$	−8.16255e7	−0.0479305
$435$	3.66770e8	0.213639
$436$	1.48327e9	0.857071
$437$	8.16029e8	0.467757
$438$	3.12630e8	0.177775
$439$	−1.20346e8	−0.0678897	−0.0339449	−	0.999424i	$-0.510807\pi$
$439$	−1.20346e8	−0.0678897	−0.0339449	+	0.999424i	$0.510807\pi$
$440$	5.82531e7	0.0326013
$441$	4.36798e8	0.242519
$442$	249605.	0.000137491 0
$443$	−7.44024e8	−0.406606	−0.203303	−	0.979116i	$-0.565168\pi$
$443$	−7.44024e8	−0.406606	−0.203303	+	0.979116i	$0.565168\pi$
$444$	−1.40549e8	−0.0762059
$445$	−4.20377e8	−0.226141
$446$	−3.87686e8	−0.206923
$447$	5.03545e9	2.66663
$448$	5.94241e8	0.312241
$449$	3.24812e9	1.69344	0.846720	−	0.532039i	$-0.178574\pi$
$449$	3.24812e9	1.69344	0.846720	+	0.532039i	$0.178574\pi$
$450$	5.42139e8	0.280457
$451$	3.64061e8	0.186877
$452$	1.29018e9	0.657154
$453$	5.36751e9	2.71287
$454$	5.24476e7	0.0263045
$455$	−4.29546e7	−0.0213782
$456$	−9.58792e8	−0.473530
$457$	4.39637e8	0.215470	0.107735	−	0.994180i	$-0.465640\pi$
$457$	4.39637e8	0.215470	0.107735	+	0.994180i	$0.465640\pi$
$458$	−4.02429e7	−0.0195731
$459$	6.82714e6	0.00329530
$460$	−2.27619e8	−0.109033
$461$	−4.12716e9	−1.96200	−0.980998	−	0.194019i	$-0.937848\pi$
$461$	−4.12716e9	−1.96200	−0.980998	+	0.194019i	$0.937848\pi$
$462$	−1.06759e8	−0.0503682
$463$	2.19609e9	1.02829	0.514146	−	0.857703i	$-0.328109\pi$
$463$	2.19609e9	1.02829	0.514146	+	0.857703i	$0.328109\pi$
$464$	−1.25137e9	−0.581530
$465$	5.34266e8	0.246418
$466$	3.60179e8	0.164880
$467$	9.70330e8	0.440870	0.220435	−	0.975402i	$-0.429252\pi$
$467$	9.70330e8	0.440870	0.220435	+	0.975402i	$0.429252\pi$
$468$	−1.01306e9	−0.456849
$469$	−1.18503e8	−0.0530424
$470$	−1.13926e8	−0.0506150
$471$	−3.62580e9	−1.59893
$472$	1.27641e8	0.0558719
$473$	−5.30773e8	−0.230619
$474$	2.76518e7	0.0119261
$475$	−1.90035e9	−0.813593
$476$	−2.48171e6	−0.00105470
$477$	2.69690e9	1.13776
$478$	4.84703e8	0.202992
$479$	−2.39597e9	−0.996109	−0.498054	−	0.867146i	$-0.665952\pi$
$479$	−2.39597e9	−0.996109	−0.498054	+	0.867146i	$0.665952\pi$
$480$	4.03178e8	0.166400
$481$	−3.23693e7	−0.0132625
$482$	−2.49358e8	−0.101428
$483$	8.47077e8	0.342064
$484$	1.88402e9	0.755313
$485$	−6.24635e8	−0.248617
$486$	−3.67762e8	−0.145325
$487$	−2.19882e9	−0.862656	−0.431328	−	0.902195i	$-0.641955\pi$
$487$	−2.19882e9	−0.862656	−0.431328	+	0.902195i	$0.641955\pi$
$488$	−1.50689e9	−0.586963
$489$	3.12688e9	1.20929
$490$	−1.30783e7	−0.00502185
$491$	−2.57328e9	−0.981076	−0.490538	−	0.871420i	$-0.663200\pi$
$491$	−2.57328e9	−0.981076	−0.490538	+	0.871420i	$0.663200\pi$
$492$	1.67141e9	0.632711
$493$	4.88021e6	0.00183432
$494$	−1.08742e8	−0.0405840
$495$	4.39740e8	0.162959
$496$	−1.82284e9	−0.670753
$497$	−6.27821e8	−0.229398
$498$	−6.24138e8	−0.226453
$499$	−4.10067e9	−1.47742	−0.738708	−	0.674025i	$-0.764564\pi$
$499$	−4.10067e9	−1.47742	−0.738708	+	0.674025i	$0.764564\pi$
$500$	1.08315e9	0.387521
$501$	2.36959e9	0.841864
$502$	−3.51902e8	−0.124153
$503$	−3.78813e9	−1.32720	−0.663600	−	0.748087i	$-0.730972\pi$
$503$	−3.78813e9	−1.32720	−0.663600	+	0.748087i	$0.730972\pi$
$504$	−6.26329e8	−0.217919
$505$	1.02355e9	0.353664
$506$	−1.30289e8	−0.0447074
$507$	−3.70746e8	−0.126342
$508$	3.28441e9	1.11156
$509$	−4.70157e9	−1.58027	−0.790134	−	0.612934i	$-0.789989\pi$
$509$	−4.70157e9	−1.58027	−0.790134	+	0.612934i	$0.789989\pi$
$510$	−497422.	−0.000166046 0
$511$	−7.15867e8	−0.237334
$512$	−2.31600e9	−0.762595
$513$	−2.97430e9	−0.972690
$514$	−9.75347e8	−0.316802
$515$	9.93804e8	0.320609
$516$	−2.43679e9	−0.780806
$517$	2.12950e9	0.677736
$518$	−9.85537e6	−0.00311544
$519$	5.92040e9	1.85894
$520$	6.15930e7	0.0192097
$521$	−3.71798e9	−1.15180	−0.575898	−	0.817522i	$-0.695347\pi$
$521$	−3.71798e9	−1.15180	−0.575898	+	0.817522i	$0.695347\pi$
$522$	6.06542e8	0.186644
$523$	−2.90721e9	−0.888630	−0.444315	−	0.895871i	$-0.646553\pi$
$523$	−2.90721e9	−0.888630	−0.444315	+	0.895871i	$0.646553\pi$
$524$	−6.06751e8	−0.184226
$525$	−1.97266e9	−0.594969
$526$	−5.71929e8	−0.171353
$527$	7.10890e6	0.00211575
$528$	−2.38411e9	−0.704868
$529$	−2.37105e9	−0.696380
$530$	−8.07485e7	−0.0235597
$531$	9.63535e8	0.279278
$532$	1.08118e9	0.311320
$533$	3.84935e8	0.110114
$534$	−1.10470e9	−0.313943
$535$	3.29948e8	0.0931553
$536$	1.69922e8	0.0476621
$537$	−1.25389e9	−0.349422
$538$	1.01755e9	0.281721
$539$	2.44459e8	0.0672427
$540$	8.29638e8	0.226731
$541$	1.82129e9	0.494526	0.247263	−	0.968948i	$-0.420469\pi$
$541$	1.82129e9	0.494526	0.247263	+	0.968948i	$0.420469\pi$
$542$	−1.14482e9	−0.308844
$543$	1.32718e6	0.000355739 0
$544$	5.36465e6	0.00142872
$545$	−6.80762e8	−0.180139
$546$	−1.12880e8	−0.0296785
$547$	−1.05837e9	−0.276493	−0.138246	−	0.990398i	$-0.544147\pi$
$547$	−1.05837e9	−0.276493	−0.138246	+	0.990398i	$0.544147\pi$
$548$	4.61916e9	1.19903
$549$	−1.13752e10	−2.93396
$550$	3.03414e8	0.0777617
$551$	−2.12610e9	−0.541445
$552$	−1.21463e9	−0.307367
$553$	−6.33178e7	−0.0159217
$554$	9.34362e7	0.0233470
$555$	6.45067e7	0.0160169
$556$	−8.97707e8	−0.221500
$557$	−2.82181e9	−0.691886	−0.345943	−	0.938255i	$-0.612441\pi$
$557$	−2.82181e9	−0.691886	−0.345943	+	0.938255i	$0.612441\pi$
$558$	8.83536e8	0.215281
$559$	−5.61205e8	−0.135888
$560$	−2.92061e8	−0.0702773
$561$	9.29780e6	0.00222336
$562$	−1.04698e8	−0.0248806
$563$	−3.83839e8	−0.0906505	−0.0453253	−	0.998972i	$-0.514432\pi$
$563$	−3.83839e8	−0.0906505	−0.0453253	+	0.998972i	$0.514432\pi$
$564$	9.77656e9	2.29461
$565$	−5.92144e8	−0.138120
$566$	3.74173e8	0.0867391
$567$	−3.02398e8	−0.0696689
$568$	9.00239e8	0.206129
$569$	−7.58997e9	−1.72722	−0.863609	−	0.504163i	$-0.831801\pi$
$569$	−7.58997e9	−1.72722	−0.863609	+	0.504163i	$0.831801\pi$
$570$	2.16706e8	0.0490127
$571$	6.39287e9	1.43704	0.718521	−	0.695505i	$-0.244819\pi$
$571$	6.39287e9	1.43704	0.718521	+	0.695505i	$0.244819\pi$
$572$	−5.66967e8	−0.126669
$573$	9.79234e9	2.17443
$574$	1.17200e8	0.0258664
$575$	−2.40743e9	−0.528101
$576$	−6.43223e9	−1.40244
$577$	1.74582e9	0.378341	0.189171	−	0.981944i	$-0.439420\pi$
$577$	1.74582e9	0.378341	0.189171	+	0.981944i	$0.439420\pi$
$578$	8.00230e8	0.172372
$579$	6.21467e9	1.33059
$580$	5.93046e8	0.126209
$581$	1.42917e9	0.302320
$582$	−1.64147e9	−0.345145
$583$	1.50935e9	0.315464
$584$	1.02649e9	0.213260
$585$	4.64953e8	0.0960203
$586$	1.45985e9	0.299687
$587$	1.04323e9	0.212885	0.106443	−	0.994319i	$-0.466054\pi$
$587$	1.04323e9	0.212885	0.106443	+	0.994319i	$0.466054\pi$
$588$	1.12231e9	0.227664
$589$	−3.09705e9	−0.624518
$590$	−2.88494e7	−0.00578302
$591$	−7.51159e9	−1.49684
$592$	−2.20088e8	−0.0435984
$593$	−3.64787e9	−0.718370	−0.359185	−	0.933266i	$-0.616945\pi$
$593$	−3.64787e9	−0.718370	−0.359185	+	0.933266i	$0.616945\pi$
$594$	4.74882e8	0.0929679
$595$	1.13901e6	0.000221675 0
$596$	8.14203e9	1.57533
$597$	1.18678e10	2.28276
$598$	−1.37759e8	−0.0263430
$599$	3.84661e9	0.731281	0.365641	−	0.930756i	$-0.380850\pi$
$599$	3.84661e9	0.731281	0.365641	+	0.930756i	$0.380850\pi$
$600$	2.82861e9	0.534618
$601$	1.13563e9	0.213391	0.106695	−	0.994292i	$-0.465973\pi$
$601$	1.13563e9	0.213391	0.106695	+	0.994292i	$0.465973\pi$
$602$	−1.70868e8	−0.0319208
$603$	1.28271e9	0.238241
$604$	8.67895e9	1.60265
$605$	−8.64692e8	−0.158751
$606$	2.68978e9	0.490978
$607$	4.04207e9	0.733572	0.366786	−	0.930305i	$-0.380458\pi$
$607$	4.04207e9	0.733572	0.366786	+	0.930305i	$0.380458\pi$
$608$	−2.33716e9	−0.421721
$609$	−2.20700e9	−0.395951
$610$	3.40586e8	0.0607536
$611$	2.25159e9	0.399343
$612$	2.68627e7	0.00473718
$613$	−6.93424e9	−1.21587	−0.607935	−	0.793987i	$-0.708002\pi$
$613$	−6.93424e9	−1.21587	−0.607935	+	0.793987i	$0.708002\pi$
$614$	1.19726e9	0.208738
$615$	−7.67113e8	−0.132983
$616$	−3.50532e8	−0.0604220
$617$	−3.48575e9	−0.597446	−0.298723	−	0.954340i	$-0.596561\pi$
$617$	−3.48575e9	−0.597446	−0.298723	+	0.954340i	$0.596561\pi$
$618$	2.61160e9	0.445089
$619$	−6.99959e9	−1.18619	−0.593097	−	0.805131i	$-0.702095\pi$
$619$	−6.99959e9	−1.18619	−0.593097	+	0.805131i	$0.702095\pi$
$620$	8.63877e8	0.145573
$621$	−3.76795e9	−0.631370
$622$	−6.92643e8	−0.115410
$623$	2.52957e9	0.419120
$624$	−2.52080e9	−0.415330
$625$	5.35255e9	0.876962
$626$	−2.08539e8	−0.0339765
$627$	−4.05067e9	−0.656281
$628$	−5.86270e9	−0.944581
$629$	858321.	0.000137522 0
$630$	1.41563e8	0.0225557
$631$	4.46313e8	0.0707191	0.0353596	−	0.999375i	$-0.488742\pi$
$631$	4.46313e8	0.0707191	0.0353596	+	0.999375i	$0.488742\pi$
$632$	9.07920e7	0.0143066
$633$	−1.08070e10	−1.69353
$634$	1.01414e9	0.158047
$635$	−1.50741e9	−0.233628
$636$	6.92945e9	1.06807
$637$	2.58475e8	0.0396214
$638$	3.39457e8	0.0517503
$639$	6.79571e9	1.03034
$640$	8.64467e8	0.130352
$641$	−4.39550e9	−0.659181	−0.329591	−	0.944124i	$-0.606911\pi$
$641$	−4.39550e9	−0.659181	−0.329591	+	0.944124i	$0.606911\pi$
$642$	8.67066e8	0.129324
$643$	−6.26600e9	−0.929506	−0.464753	−	0.885440i	$-0.653857\pi$
$643$	−6.26600e9	−0.929506	−0.464753	+	0.885440i	$0.653857\pi$
$644$	1.36967e9	0.202077
$645$	1.11839e9	0.164110
$646$	2.88347e6	0.000420826 0
$647$	9.60638e9	1.39442	0.697212	−	0.716865i	$-0.254424\pi$
$647$	9.60638e9	1.39442	0.697212	+	0.716865i	$0.254424\pi$
$648$	4.33612e8	0.0626020
$649$	5.39252e8	0.0774347
$650$	3.20810e8	0.0458196
$651$	−3.21489e9	−0.456701
$652$	5.05598e9	0.714396
$653$	3.69135e9	0.518786	0.259393	−	0.965772i	$-0.416477\pi$
$653$	3.69135e9	0.518786	0.259393	+	0.965772i	$0.416477\pi$
$654$	−1.78896e9	−0.250080
$655$	2.78475e8	0.0387206
$656$	2.61728e9	0.361982
$657$	7.74874e9	1.06599
$658$	6.85536e8	0.0938079
$659$	3.36279e9	0.457721	0.228861	−	0.973459i	$-0.426500\pi$
$659$	3.36279e9	0.457721	0.228861	+	0.973459i	$0.426500\pi$
$660$	1.12987e9	0.152977
$661$	−9.09130e7	−0.0122439	−0.00612197	−	0.999981i	$-0.501949\pi$
$661$	−9.09130e7	−0.0122439	−0.00612197	+	0.999981i	$0.501949\pi$
$662$	−1.74372e9	−0.233600
$663$	9.83089e6	0.00131007
$664$	−2.04929e9	−0.271654
$665$	−4.96219e8	−0.0654331
$666$	1.06677e8	0.0139930
$667$	−2.69342e9	−0.351450
$668$	3.83150e9	0.497337
$669$	−1.52693e10	−1.97164
$670$	−3.84058e7	−0.00493327
$671$	−6.36623e9	−0.813492
$672$	−2.42608e9	−0.308399
$673$	4.23216e9	0.535192	0.267596	−	0.963531i	$-0.413771\pi$
$673$	4.23216e9	0.535192	0.267596	+	0.963531i	$0.413771\pi$
$674$	−9.15750e8	−0.115204
$675$	8.77473e9	1.09817
$676$	−5.99474e8	−0.0746375
$677$	1.09780e9	0.135976	0.0679880	−	0.997686i	$-0.478342\pi$
$677$	1.09780e9	0.135976	0.0679880	+	0.997686i	$0.478342\pi$
$678$	−1.55609e9	−0.191747
$679$	3.75867e9	0.460776
$680$	−1.63323e6	−0.000199190 0
$681$	2.06569e9	0.250640
$682$	4.94481e8	0.0596903
$683$	3.81168e9	0.457767	0.228883	−	0.973454i	$-0.426493\pi$
$683$	3.81168e9	0.457767	0.228883	+	0.973454i	$0.426493\pi$
$684$	−1.17030e10	−1.39830
$685$	−2.12001e9	−0.252012
$686$	7.86971e7	0.00930731
$687$	−1.58500e9	−0.186501
$688$	−3.81579e9	−0.446709
$689$	1.59589e9	0.185881
$690$	2.74531e8	0.0318140
$691$	−2.40671e9	−0.277492	−0.138746	−	0.990328i	$-0.544307\pi$
$691$	−2.40671e9	−0.277492	−0.138746	+	0.990328i	$0.544307\pi$
$692$	9.57294e9	1.09818
$693$	−2.64609e9	−0.302022
$694$	1.81911e9	0.206586
$695$	4.12012e8	0.0465547
$696$	3.16463e9	0.355788
$697$	−1.02071e7	−0.00114180
$698$	−1.53689e8	−0.0171060
$699$	1.41860e10	1.57104
$700$	−3.18967e9	−0.351482
$701$	1.00755e10	1.10472	0.552361	−	0.833605i	$-0.313727\pi$
$701$	1.00755e10	1.10472	0.552361	+	0.833605i	$0.313727\pi$
$702$	5.02109e8	0.0547795
$703$	−3.73935e8	−0.0405931
$704$	−3.59986e9	−0.388850
$705$	−4.48706e9	−0.482281
$706$	−6.07074e8	−0.0649270
$707$	−6.15912e9	−0.655467
$708$	2.47572e9	0.262171
$709$	1.53834e10	1.62103	0.810513	−	0.585721i	$-0.199189\pi$
$709$	1.53834e10	1.62103	0.810513	+	0.585721i	$0.199189\pi$
$710$	−2.03472e8	−0.0213354
$711$	6.85370e8	0.0715124
$712$	−3.62718e9	−0.376607
$713$	−3.92345e9	−0.405373
$714$	2.99318e6	0.000307744 0
$715$	2.60216e8	0.0266233
$716$	−2.02747e9	−0.206423
$717$	1.90904e10	1.93419
$718$	1.32472e9	0.133564
$719$	−1.74992e9	−0.175577	−0.0877886	−	0.996139i	$-0.527980\pi$
$719$	−1.74992e9	−0.175577	−0.0877886	+	0.996139i	$0.527980\pi$
$720$	3.16135e9	0.315652
$721$	−5.98011e9	−0.594204
$722$	4.87007e8	0.0481565
$723$	−9.82118e9	−0.966451
$724$	2.14598e6	0.000210155 0
$725$	6.27240e9	0.611294
$726$	−2.27231e9	−0.220389
$727$	5.41111e9	0.522295	0.261148	−	0.965299i	$-0.415899\pi$
$727$	5.41111e9	0.522295	0.261148	+	0.965299i	$0.415899\pi$
$728$	−3.70629e8	−0.0356025
$729$	−1.64127e10	−1.56904
$730$	−2.32007e8	−0.0220735
$731$	1.48812e7	0.00140905
$732$	−2.92274e10	−2.75424
$733$	−1.44007e9	−0.135058	−0.0675291	−	0.997717i	$-0.521512\pi$
$733$	−1.44007e9	−0.135058	−0.0675291	+	0.997717i	$0.521512\pi$
$734$	−2.73197e9	−0.255000
$735$	−5.15098e8	−0.0478503
$736$	−2.96079e9	−0.273738
$737$	7.17880e8	0.0660565
$738$	−1.26860e9	−0.116179
$739$	−4.45323e9	−0.405900	−0.202950	−	0.979189i	$-0.565053\pi$
$739$	−4.45323e9	−0.405900	−0.202950	+	0.979189i	$0.565053\pi$
$740$	1.04304e8	0.00946211
$741$	−4.28291e9	−0.386701
$742$	4.85895e8	0.0436645
$743$	1.92386e10	1.72073	0.860363	−	0.509682i	$-0.170237\pi$
$743$	1.92386e10	1.72073	0.860363	+	0.509682i	$0.170237\pi$
$744$	4.60985e9	0.410376
$745$	−3.73687e9	−0.331102
$746$	1.86215e8	0.0164221
$747$	−1.54697e10	−1.35787
$748$	1.50340e7	0.00131347
$749$	−1.98543e9	−0.172650
$750$	−1.30639e9	−0.113073
$751$	1.88968e10	1.62797	0.813987	−	0.580882i	$-0.197292\pi$
$751$	1.88968e10	1.62797	0.813987	+	0.580882i	$0.197292\pi$
$752$	1.53092e10	1.31278
$753$	−1.38600e10	−1.18299
$754$	3.58920e8	0.0304929
$755$	−3.98330e9	−0.336844
$756$	−4.99225e9	−0.420214
$757$	−1.45836e10	−1.22188	−0.610942	−	0.791676i	$-0.709209\pi$
$757$	−1.45836e10	−1.22188	−0.610942	+	0.791676i	$0.709209\pi$
$758$	2.36198e9	0.196985
$759$	−5.13152e9	−0.425990
$760$	7.11532e8	0.0587959
$761$	1.78465e10	1.46793	0.733967	−	0.679185i	$-0.237667\pi$
$761$	1.78465e10	1.46793	0.733967	+	0.679185i	$0.237667\pi$
$762$	−3.96131e9	−0.324337
$763$	4.09641e9	0.333862
$764$	1.58337e10	1.28456
$765$	−1.23289e7	−0.000995659 0
$766$	−2.56297e9	−0.206036
$767$	5.70170e8	0.0456269
$768$	−1.47614e10	−1.17588
$769$	7.27717e9	0.577059	0.288530	−	0.957471i	$-0.406834\pi$
$769$	7.27717e9	0.577059	0.288530	+	0.957471i	$0.406834\pi$
$770$	7.92271e7	0.00625398
$771$	−3.84148e10	−3.01862
$772$	1.00488e10	0.786053
$773$	−1.36532e9	−0.106318	−0.0531588	−	0.998586i	$-0.516929\pi$
$773$	−1.36532e9	−0.106318	−0.0531588	+	0.998586i	$0.516929\pi$
$774$	1.84952e9	0.143373
$775$	9.13687e9	0.705085
$776$	−5.38959e9	−0.414038
$777$	−3.88162e8	−0.0296852
$778$	3.68849e8	0.0280815
$779$	4.44683e9	0.337030
$780$	1.19465e9	0.0901387
$781$	3.80329e9	0.285681
$782$	3.65288e6	0.000273157 0
$783$	9.81711e9	0.730832
$784$	1.75744e9	0.130249
$785$	2.69075e9	0.198532
$786$	7.31800e8	0.0537543
$787$	7.33877e9	0.536675	0.268338	−	0.963325i	$-0.413526\pi$
$787$	7.33877e9	0.536675	0.268338	+	0.963325i	$0.413526\pi$
$788$	−1.21458e10	−0.884270
$789$	−2.25259e10	−1.63272
$790$	−2.05208e7	−0.00148081
$791$	3.56316e9	0.255987
$792$	3.79425e9	0.271386
$793$	−6.73123e9	−0.479334
$794$	−2.20633e9	−0.156422
$795$	−3.18034e9	−0.224486
$796$	1.91895e10	1.34856
$797$	−1.95756e9	−0.136965	−0.0684827	−	0.997652i	$-0.521816\pi$
$797$	−1.95756e9	−0.136965	−0.0684827	+	0.997652i	$0.521816\pi$
$798$	−1.30400e9	−0.0908383
$799$	−5.97045e7	−0.00414088
$800$	6.89504e9	0.476126
$801$	−2.73808e10	−1.88249
$802$	−4.32534e9	−0.296081
$803$	4.33666e9	0.295564
$804$	3.29580e9	0.223648
$805$	−6.28627e8	−0.0424724
$806$	5.22832e8	0.0351714
$807$	4.00771e10	2.68435
$808$	8.83161e9	0.588980
$809$	−2.55817e10	−1.69867	−0.849337	−	0.527850i	$-0.822998\pi$
$809$	−2.55817e10	−1.69867	−0.849337	+	0.527850i	$0.822998\pi$
$810$	−9.80048e7	−0.00647963
$811$	−2.72384e10	−1.79311	−0.896557	−	0.442928i	$-0.853940\pi$
$811$	−2.72384e10	−1.79311	−0.896557	+	0.442928i	$0.853940\pi$
$812$	−3.56859e9	−0.233911
$813$	−4.50897e10	−2.94280
$814$	5.97031e7	0.00387982
$815$	−2.32050e9	−0.150151
$816$	6.68430e7	0.00430666
$817$	−6.48312e9	−0.415917
$818$	2.51157e9	0.160438
$819$	−2.79780e9	−0.177960
$820$	−1.24038e9	−0.0785606
$821$	−7.12972e9	−0.449647	−0.224823	−	0.974400i	$-0.572180\pi$
$821$	−7.12972e9	−0.449647	−0.224823	+	0.974400i	$0.572180\pi$
$822$	−5.57115e9	−0.349859
$823$	−1.83696e10	−1.14868	−0.574341	−	0.818616i	$-0.694742\pi$
$823$	−1.83696e10	−1.14868	−0.574341	+	0.818616i	$0.694742\pi$
$824$	8.57493e9	0.533931
$825$	1.19502e10	0.740945
$826$	1.73598e8	0.0107180
$827$	1.61354e10	0.991998	0.495999	−	0.868323i	$-0.334802\pi$
$827$	1.61354e10	0.991998	0.495999	+	0.868323i	$0.334802\pi$
$828$	−1.48257e10	−0.907632
$829$	−2.31880e10	−1.41359	−0.706793	−	0.707421i	$-0.749859\pi$
$829$	−2.31880e10	−1.41359	−0.706793	+	0.707421i	$0.749859\pi$
$830$	4.63181e8	0.0281175
$831$	3.68006e9	0.222460
$832$	−3.80626e9	−0.229122
$833$	−6.85386e6	−0.000410845 0
$834$	1.08272e9	0.0646301
$835$	−1.75851e9	−0.104530
$836$	−6.54969e9	−0.387703
$837$	1.43004e10	0.842963
$838$	5.06582e9	0.297369
$839$	−1.28219e9	−0.0749524	−0.0374762	−	0.999298i	$-0.511932\pi$
$839$	−1.28219e9	−0.0749524	−0.0374762	+	0.999298i	$0.511932\pi$
$840$	7.38604e8	0.0429966
$841$	−1.02324e10	−0.593185
$842$	3.36235e9	0.194111
$843$	−4.12362e9	−0.237073
$844$	−1.74744e10	−1.00047
$845$	2.75135e8	0.0156873
$846$	−7.42042e9	−0.421340
$847$	5.20319e9	0.294224
$848$	1.08509e10	0.611055
$849$	1.47371e10	0.826485
$850$	−8.50677e6	−0.000475115 0
$851$	−4.73713e8	−0.0263489
$852$	1.74610e10	0.967230
$853$	9.34612e9	0.515596	0.257798	−	0.966199i	$-0.417003\pi$
$853$	9.34612e9	0.515596	0.257798	+	0.966199i	$0.417003\pi$
$854$	−2.04944e9	−0.112598
$855$	5.37120e9	0.293894
$856$	2.84692e9	0.155138
$857$	6.53038e9	0.354410	0.177205	−	0.984174i	$-0.443294\pi$
$857$	6.53038e9	0.354410	0.177205	+	0.984174i	$0.443294\pi$
$858$	6.83817e8	0.0369602
$859$	2.38505e10	1.28387	0.641937	−	0.766757i	$-0.278131\pi$
$859$	2.38505e10	1.28387	0.641937	+	0.766757i	$0.278131\pi$
$860$	1.80837e9	0.0969489
$861$	4.61602e9	0.246466
$862$	4.48208e9	0.238344
$863$	2.13694e10	1.13176	0.565880	−	0.824488i	$-0.308537\pi$
$863$	2.13694e10	1.13176	0.565880	+	0.824488i	$0.308537\pi$
$864$	1.07916e10	0.569231
$865$	−4.39361e9	−0.230815
$866$	−5.74165e9	−0.300417
$867$	3.15177e10	1.64243
$868$	−5.19828e9	−0.269799
$869$	3.83574e8	0.0198281
$870$	−7.15270e8	−0.0368258
$871$	7.59039e8	0.0389225
$872$	−5.87388e9	−0.299997
$873$	−4.06849e10	−2.06958
$874$	−1.59141e9	−0.0806291
$875$	2.99140e9	0.150954
$876$	1.99097e10	1.00069
$877$	4.37384e9	0.218960	0.109480	−	0.993989i	$-0.465082\pi$
$877$	4.37384e9	0.218960	0.109480	+	0.993989i	$0.465082\pi$
$878$	2.34696e8	0.0117024
$879$	5.74975e10	2.85554
$880$	1.76928e9	0.0875200
$881$	−3.53082e10	−1.73964	−0.869822	−	0.493366i	$-0.835766\pi$
$881$	−3.53082e10	−1.73964	−0.869822	+	0.493366i	$0.835766\pi$
$882$	−8.51838e8	−0.0418039
$883$	−1.10320e10	−0.539253	−0.269627	−	0.962965i	$-0.586900\pi$
$883$	−1.10320e10	−0.539253	−0.269627	+	0.962965i	$0.586900\pi$
$884$	1.58960e7	0.000773935 0
$885$	−1.13626e9	−0.0551030
$886$	1.45099e9	0.0700882
$887$	−8.07442e9	−0.388489	−0.194244	−	0.980953i	$-0.562225\pi$
$887$	−8.07442e9	−0.388489	−0.194244	+	0.980953i	$0.562225\pi$
$888$	5.56589e8	0.0266741
$889$	9.07070e9	0.432997
$890$	8.19813e8	0.0389807
$891$	1.83190e9	0.0867623
$892$	−2.46896e10	−1.16476
$893$	2.60107e10	1.22229
$894$	−9.82007e9	−0.459656
$895$	9.30530e8	0.0433860
$896$	−5.20184e9	−0.241590
$897$	−5.42574e9	−0.251007
$898$	−6.33444e9	−0.291905
$899$	1.02223e10	0.469233
$900$	3.45259e10	1.57869
$901$	−4.23174e7	−0.00192745
$902$	−7.09988e8	−0.0322128
$903$	−6.72978e9	−0.304154
$904$	−5.10925e9	−0.230021
$905$	−984919.	−4.41703e−5 0
$906$	−1.04676e10	−0.467628
$907$	7.05851e8	0.0314114	0.0157057	−	0.999877i	$-0.495001\pi$
$907$	7.05851e8	0.0314114	0.0157057	+	0.999877i	$0.495001\pi$
$908$	3.34010e9	0.148067
$909$	6.66680e10	2.94404
$910$	8.37696e7	0.00368503
$911$	1.46117e10	0.640306	0.320153	−	0.947366i	$-0.396266\pi$
$911$	1.46117e10	0.640306	0.320153	+	0.947366i	$0.396266\pi$
$912$	−2.91207e10	−1.27122
$913$	−8.65777e9	−0.376494
$914$	−8.57375e8	−0.0371415
$915$	1.34143e10	0.578886
$916$	−2.56285e9	−0.110176
$917$	−1.67569e9	−0.0717632
$918$	−1.33142e7	−0.000568023 0
$919$	−1.42287e10	−0.604730	−0.302365	−	0.953192i	$-0.597776\pi$
$919$	−1.42287e10	−0.604730	−0.302365	+	0.953192i	$0.597776\pi$
$920$	9.01393e8	0.0381643
$921$	4.71552e10	1.98894
$922$	8.04873e9	0.338197
$923$	4.02135e9	0.168332
$924$	−6.79889e9	−0.283521
$925$	1.10318e9	0.0458299
$926$	−4.28278e9	−0.177251
$927$	6.47303e10	2.66888
$928$	7.71412e9	0.316861
$929$	−1.13794e10	−0.465653	−0.232827	−	0.972518i	$-0.574797\pi$
$929$	−1.13794e10	−0.465653	−0.232827	+	0.972518i	$0.574797\pi$
$930$	−1.04192e9	−0.0424760
$931$	2.98594e9	0.121271
$932$	2.29379e10	0.928105
$933$	−2.72803e10	−1.09967
$934$	−1.89233e9	−0.0759944
$935$	−6.90002e6	−0.000276064 0
$936$	4.01179e9	0.159909
$937$	−1.90844e10	−0.757863	−0.378931	−	0.925425i	$-0.623708\pi$
$937$	−1.90844e10	−0.757863	−0.378931	+	0.925425i	$0.623708\pi$
$938$	2.31102e8	0.00914312
$939$	−8.21350e9	−0.323742
$940$	−7.25531e9	−0.284911
$941$	−1.59667e10	−0.624672	−0.312336	−	0.949972i	$-0.601112\pi$
$941$	−1.59667e10	−0.624672	−0.312336	+	0.949972i	$0.601112\pi$
$942$	7.07098e9	0.275614
$943$	5.63339e9	0.218766
$944$	3.87675e9	0.149991
$945$	2.29125e9	0.0883204
$946$	1.03511e9	0.0397526
$947$	8.14110e9	0.311500	0.155750	−	0.987796i	$-0.450221\pi$
$947$	8.14110e9	0.311500	0.155750	+	0.987796i	$0.450221\pi$
$948$	1.76100e9	0.0671319
$949$	4.58531e9	0.174155
$950$	3.70605e9	0.140242
$951$	3.99427e10	1.50593
$952$	9.82781e6	0.000369171 0
$953$	4.19591e10	1.57037	0.785183	−	0.619264i	$-0.212569\pi$
$953$	4.19591e10	1.57037	0.785183	+	0.619264i	$0.212569\pi$
$954$	−5.25946e9	−0.196120
$955$	−7.26703e9	−0.269988
$956$	3.08681e10	1.14263
$957$	1.33698e10	0.493098
$958$	4.67259e9	0.171703
$959$	1.27569e10	0.467069
$960$	7.58526e9	0.276708
$961$	−1.26221e10	−0.458773
$962$	6.31261e7	0.00228611
$963$	2.14908e10	0.775462
$964$	−1.58803e10	−0.570938
$965$	−4.61199e9	−0.165212
$966$	−1.65196e9	−0.0589629
$967$	1.30731e10	0.464930	0.232465	−	0.972605i	$-0.425321\pi$
$967$	1.30731e10	0.464930	0.232465	+	0.972605i	$0.425321\pi$
$968$	−7.46090e9	−0.264379
$969$	1.13568e8	0.00400980
$970$	1.21815e9	0.0428550
$971$	−9.07547e9	−0.318128	−0.159064	−	0.987268i	$-0.550848\pi$
$971$	−9.07547e9	−0.318128	−0.159064	+	0.987268i	$0.550848\pi$
$972$	−2.34208e10	−0.818030
$973$	−2.47924e9	−0.0862826
$974$	4.28810e9	0.148699
$975$	1.26354e10	0.436588
$976$	−4.57676e10	−1.57574
$977$	−4.95923e10	−1.70131	−0.850655	−	0.525724i	$-0.823795\pi$
$977$	−4.95923e10	−1.70131	−0.850655	+	0.525724i	$0.823795\pi$
$978$	−6.09800e9	−0.208450
$979$	−1.53239e10	−0.521952
$980$	−8.32884e8	−0.0282679
$981$	−4.43407e10	−1.49955
$982$	5.01838e9	0.169112
$983$	−2.51636e10	−0.844957	−0.422479	−	0.906373i	$-0.638840\pi$
$983$	−2.51636e10	−0.844957	−0.422479	+	0.906373i	$0.638840\pi$
$984$	−6.61895e9	−0.221465
$985$	5.57445e9	0.185855
$986$	−9.51732e6	−0.000316188 0
$987$	2.70004e10	0.893840
$988$	−6.92522e9	−0.228446
$989$	−8.21304e9	−0.269971
$990$	−8.57576e8	−0.0280898
$991$	−2.28538e10	−0.745935	−0.372967	−	0.927844i	$-0.621660\pi$
$991$	−2.28538e10	−0.745935	−0.372967	+	0.927844i	$0.621660\pi$
$992$	1.12370e10	0.365477
$993$	−6.86777e10	−2.22584
$994$	1.22437e9	0.0395421
$995$	−8.80725e9	−0.283439
$996$	−3.97480e10	−1.27470
$997$	−8.74517e9	−0.279470	−0.139735	−	0.990189i	$-0.544625\pi$
$997$	−8.74517e9	−0.279470	−0.139735	+	0.990189i	$0.544625\pi$
$998$	7.99707e9	0.254668
$999$	1.72661e9	0.0547918

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.b.1.5	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.b.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-1.95019 q^{2} -76.8097 q^{3} -124.197 q^{4} +57.0015 q^{5} +149.793 q^{6} -343.000 q^{7} +491.831 q^{8} +3712.72 q^{9} +O(q^{10})\)	\(q-1.95019 q^{2} -76.8097 q^{3} -124.197 q^{4} +57.0015 q^{5} +149.793 q^{6} -343.000 q^{7} +491.831 q^{8} +3712.72 q^{9} -111.163 q^{10} +2077.87 q^{11} +9539.51 q^{12} +2197.00 q^{13} +668.914 q^{14} -4378.26 q^{15} +14938.0 q^{16} -58.2568 q^{17} -7240.51 q^{18} +25380.1 q^{19} -7079.40 q^{20} +26345.7 q^{21} -4052.23 q^{22} +32152.3 q^{23} -37777.4 q^{24} -74875.8 q^{25} -4284.56 q^{26} -117190. q^{27} +42599.5 q^{28} -83770.6 q^{29} +8538.43 q^{30} -122027. q^{31} -92086.3 q^{32} -159600. q^{33} +113.612 q^{34} -19551.5 q^{35} -461108. q^{36} -14733.4 q^{37} -49495.9 q^{38} -168751. q^{39} +28035.1 q^{40} +175209. q^{41} -51379.1 q^{42} -255441. q^{43} -258064. q^{44} +211631. q^{45} -62703.1 q^{46} +1.02485e6 q^{47} -1.14738e6 q^{48} +117649. q^{49} +146022. q^{50} +4474.69 q^{51} -272860. q^{52} +726394. q^{53} +228543. q^{54} +118441. q^{55} -168698. q^{56} -1.94944e6 q^{57} +163368. q^{58} +259522. q^{59} +543766. q^{60} -3.06383e6 q^{61} +237975. q^{62} -1.27346e6 q^{63} -1.73248e6 q^{64} +125232. q^{65} +311250. q^{66} +345489. q^{67} +7235.31 q^{68} -2.46961e6 q^{69} +38129.1 q^{70} +1.83038e6 q^{71} +1.82603e6 q^{72} +2.08708e6 q^{73} +28732.9 q^{74} +5.75119e6 q^{75} -3.15212e6 q^{76} -712708. q^{77} +329096. q^{78} +184600. q^{79} +851489. q^{80} +881628. q^{81} -341691. q^{82} -4.16666e6 q^{83} -3.27205e6 q^{84} -3320.72 q^{85} +498158. q^{86} +6.43439e6 q^{87} +1.02196e6 q^{88} -7.37484e6 q^{89} -412719. q^{90} -753571. q^{91} -3.99322e6 q^{92} +9.37285e6 q^{93} -1.99865e6 q^{94} +1.44670e6 q^{95} +7.07312e6 q^{96} -1.09582e7 q^{97} -229437. q^{98} +7.71454e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 5 q^{2} - 26 q^{3} + 393 q^{4} - 181 q^{5} + 703 q^{6} - 3087 q^{7} + 1197 q^{8} + 3211 q^{9}+O(q^{10}) \) 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