LMFDB - Embedded newform 91.8.a.b.1.9

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			1.9
Root			$20.7278$ 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)

$f(q)$	$=$	$q+19.7278 q^{2} +5.55266 q^{3} +261.185 q^{4} -428.566 q^{5} +109.542 q^{6} -343.000 q^{7} +2627.45 q^{8} -2156.17 q^{9} +O(q^{10})$	\(q+19.7278 q^{2} +5.55266 q^{3} +261.185 q^{4} -428.566 q^{5} +109.542 q^{6} -343.000 q^{7} +2627.45 q^{8} -2156.17 q^{9} -8454.65 q^{10} -6102.17 q^{11} +1450.27 q^{12} +2197.00 q^{13} -6766.63 q^{14} -2379.68 q^{15} +18402.1 q^{16} -2313.44 q^{17} -42536.4 q^{18} +28599.2 q^{19} -111935. q^{20} -1904.56 q^{21} -120382. q^{22} -64881.5 q^{23} +14589.3 q^{24} +105544. q^{25} +43341.9 q^{26} -24116.1 q^{27} -89586.6 q^{28} -25381.1 q^{29} -46945.8 q^{30} +275914. q^{31} +26718.1 q^{32} -33883.3 q^{33} -45639.0 q^{34} +146998. q^{35} -563160. q^{36} -89482.8 q^{37} +564198. q^{38} +12199.2 q^{39} -1.12604e6 q^{40} -567947. q^{41} -37572.8 q^{42} -398454. q^{43} -1.59380e6 q^{44} +924060. q^{45} -1.27997e6 q^{46} +922136. q^{47} +102180. q^{48} +117649. q^{49} +2.08214e6 q^{50} -12845.7 q^{51} +573824. q^{52} +793297. q^{53} -475758. q^{54} +2.61518e6 q^{55} -901216. q^{56} +158801. q^{57} -500713. q^{58} -1.62799e6 q^{59} -621537. q^{60} -368362. q^{61} +5.44317e6 q^{62} +739566. q^{63} -1.82838e6 q^{64} -941559. q^{65} -668442. q^{66} -2.48020e6 q^{67} -604236. q^{68} -360265. q^{69} +2.89995e6 q^{70} -3.76058e6 q^{71} -5.66523e6 q^{72} +208897. q^{73} -1.76530e6 q^{74} +586047. q^{75} +7.46968e6 q^{76} +2.09305e6 q^{77} +240663. q^{78} +5.15548e6 q^{79} -7.88649e6 q^{80} +4.58163e6 q^{81} -1.12043e7 q^{82} -3.78417e6 q^{83} -497444. q^{84} +991459. q^{85} -7.86062e6 q^{86} -140933. q^{87} -1.60332e7 q^{88} -1.12865e7 q^{89} +1.82296e7 q^{90} -753571. q^{91} -1.69461e7 q^{92} +1.53206e6 q^{93} +1.81917e7 q^{94} -1.22566e7 q^{95} +148357. q^{96} +1.55068e7 q^{97} +2.32095e6 q^{98} +1.31573e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	19.7278	1.74371	0.871853	−	0.489768i	$-0.162918\pi$
$2$	19.7278	1.74371	0.871853	+	0.489768i	$0.162918\pi$
$3$	5.55266	0.118734	0.0593672	−	0.998236i	$-0.481092\pi$
$3$	5.55266	0.118734	0.0593672	+	0.998236i	$0.481092\pi$
$4$	261.185	2.04051
$5$	−428.566	−1.53328	−0.766642	−	0.642075i	$-0.778074\pi$
$5$	−428.566	−1.53328	−0.766642	+	0.642075i	$0.778074\pi$
$6$	109.542	0.207038
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	2627.45	1.81434
$9$	−2156.17	−0.985902
$10$	−8454.65	−2.67360
$11$	−6102.17	−1.38233	−0.691163	−	0.722699i	$-0.742901\pi$
$11$	−6102.17	−1.38233	−0.691163	+	0.722699i	$0.742901\pi$
$12$	1450.27	0.242279
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−6766.63	−0.659059
$15$	−2379.68	−0.182053
$16$	18402.1	1.12317
$17$	−2313.44	−0.114205	−0.0571027	−	0.998368i	$-0.518186\pi$
$17$	−2313.44	−0.114205	−0.0571027	+	0.998368i	$0.518186\pi$
$18$	−42536.4	−1.71912
$19$	28599.2	0.956567	0.478284	−	0.878205i	$-0.341259\pi$
$19$	28599.2	0.956567	0.478284	+	0.878205i	$0.341259\pi$
$20$	−111935.	−3.12868
$21$	−1904.56	−0.0448774
$22$	−120382.	−2.41037
$23$	−64881.5	−1.11192	−0.555959	−	0.831209i	$-0.687649\pi$
$23$	−64881.5	−1.11192	−0.555959	+	0.831209i	$0.687649\pi$
$24$	14589.3	0.215425
$25$	105544.	1.35096
$26$	43341.9	0.483617
$27$	−24116.1	−0.235795
$28$	−89586.6	−0.771241
$29$	−25381.1	−0.193249	−0.0966245	−	0.995321i	$-0.530805\pi$
$29$	−25381.1	−0.193249	−0.0966245	+	0.995321i	$0.530805\pi$
$30$	−46945.8	−0.317448
$31$	275914.	1.66344	0.831721	−	0.555194i	$-0.187356\pi$
$31$	275914.	1.66344	0.831721	+	0.555194i	$0.187356\pi$
$32$	26718.1	0.144139
$33$	−33883.3	−0.164130
$34$	−45639.0	−0.199140
$35$	146998.	0.579527
$36$	−563160.	−2.01174
$37$	−89482.8	−0.290425	−0.145212	−	0.989401i	$-0.546387\pi$
$37$	−89482.8	−0.290425	−0.145212	+	0.989401i	$0.546387\pi$
$38$	564198.	1.66797
$39$	12199.2	0.0329310
$40$	−1.12604e6	−2.78190
$41$	−567947.	−1.28696	−0.643479	−	0.765464i	$-0.722510\pi$
$41$	−567947.	−1.28696	−0.643479	+	0.765464i	$0.722510\pi$
$42$	−37572.8	−0.0782530
$43$	−398454.	−0.764256	−0.382128	−	0.924109i	$-0.624809\pi$
$43$	−398454.	−0.764256	−0.382128	+	0.924109i	$0.624809\pi$
$44$	−1.59380e6	−2.82065
$45$	924060.	1.51167
$46$	−1.27997e6	−1.93886
$47$	922136.	1.29555	0.647773	−	0.761834i	$-0.275701\pi$
$47$	922136.	1.29555	0.647773	+	0.761834i	$0.275701\pi$
$48$	102180.	0.133359
$49$	117649.	0.142857
$50$	2.08214e6	2.35567
$51$	−12845.7	−0.0135601
$52$	573824.	0.565936
$53$	793297.	0.731931	0.365965	−	0.930628i	$-0.380739\pi$
$53$	793297.	0.731931	0.365965	+	0.930628i	$0.380739\pi$
$54$	−475758.	−0.411157
$55$	2.61518e6	2.11950
$56$	−901216.	−0.685758
$57$	158801.	0.113577
$58$	−500713.	−0.336970
$59$	−1.62799e6	−1.03198	−0.515988	−	0.856596i	$-0.672575\pi$
$59$	−1.62799e6	−1.03198	−0.515988	+	0.856596i	$0.672575\pi$
$60$	−621537.	−0.371482
$61$	−368362.	−0.207788	−0.103894	−	0.994588i	$-0.533130\pi$
$61$	−368362.	−0.207788	−0.103894	+	0.994588i	$0.533130\pi$
$62$	5.44317e6	2.90055
$63$	739566.	0.372636
$64$	−1.82838e6	−0.871837
$65$	−941559.	−0.425256
$66$	−668442.	−0.286194
$67$	−2.48020e6	−1.00745	−0.503727	−	0.863863i	$-0.668038\pi$
$67$	−2.48020e6	−1.00745	−0.503727	+	0.863863i	$0.668038\pi$
$68$	−604236.	−0.233037
$69$	−360265.	−0.132023
$70$	2.89995e6	1.01052
$71$	−3.76058e6	−1.24696	−0.623478	−	0.781841i	$-0.714281\pi$
$71$	−3.76058e6	−1.24696	−0.623478	+	0.781841i	$0.714281\pi$
$72$	−5.66523e6	−1.78877
$73$	208897.	0.0628495	0.0314247	−	0.999506i	$-0.489996\pi$
$73$	208897.	0.0628495	0.0314247	+	0.999506i	$0.489996\pi$
$74$	−1.76530e6	−0.506415
$75$	586047.	0.160405
$76$	7.46968e6	1.95189
$77$	2.09305e6	0.522470
$78$	240663.	0.0574220
$79$	5.15548e6	1.17645	0.588226	−	0.808697i	$-0.299827\pi$
$79$	5.15548e6	1.17645	0.588226	+	0.808697i	$0.299827\pi$
$80$	−7.88649e6	−1.72214
$81$	4.58163e6	0.957905
$82$	−1.12043e7	−2.24408
$83$	−3.78417e6	−0.726436	−0.363218	−	0.931704i	$-0.618322\pi$
$83$	−3.78417e6	−0.726436	−0.363218	+	0.931704i	$0.618322\pi$
$84$	−497444.	−0.0915728
$85$	991459.	0.175109
$86$	−7.86062e6	−1.33264
$87$	−140933.	−0.0229453
$88$	−1.60332e7	−2.50801
$89$	−1.12865e7	−1.69704	−0.848522	−	0.529160i	$-0.822507\pi$
$89$	−1.12865e7	−1.69704	−0.848522	+	0.529160i	$0.822507\pi$
$90$	1.82296e7	2.63590
$91$	−753571.	−0.104828
$92$	−1.69461e7	−2.26888
$93$	1.53206e6	0.197508
$94$	1.81917e7	2.25905
$95$	−1.22566e7	−1.46669
$96$	148357.	0.0171142
$97$	1.55068e7	1.72513	0.862564	−	0.505949i	$-0.168857\pi$
$97$	1.55068e7	1.72513	0.862564	+	0.505949i	$0.168857\pi$
$98$	2.32095e6	0.249101
$99$	1.31573e7	1.36284
$100$	2.75664e7	2.75664
$101$	−4.49875e6	−0.434478	−0.217239	−	0.976118i	$-0.569705\pi$
$101$	−4.49875e6	−0.434478	−0.217239	+	0.976118i	$0.569705\pi$
$102$	−253418.	−0.0236448
$103$	4.03519e6	0.363859	0.181930	−	0.983312i	$-0.441766\pi$
$103$	4.03519e6	0.363859	0.181930	+	0.983312i	$0.441766\pi$
$104$	5.77251e6	0.503209
$105$	816230.	0.0688098
$106$	1.56500e7	1.27627
$107$	8.03287e6	0.633910	0.316955	−	0.948441i	$-0.397340\pi$
$107$	8.03287e6	0.633910	0.316955	+	0.948441i	$0.397340\pi$
$108$	−6.29878e6	−0.481142
$109$	1.08446e7	0.802087	0.401044	−	0.916059i	$-0.368648\pi$
$109$	1.08446e7	0.802087	0.401044	+	0.916059i	$0.368648\pi$
$110$	5.15918e7	3.69578
$111$	−496867.	−0.0344834
$112$	−6.31191e6	−0.424519
$113$	3.38301e6	0.220561	0.110281	−	0.993900i	$-0.464825\pi$
$113$	3.38301e6	0.220561	0.110281	+	0.993900i	$0.464825\pi$
$114$	3.13280e6	0.198046
$115$	2.78060e7	1.70489
$116$	−6.62917e6	−0.394327
$117$	−4.73710e6	−0.273440
$118$	−3.21166e7	−1.79946
$119$	793509.	0.0431655
$120$	−6.25249e6	−0.330308
$121$	1.77494e7	0.910823
$122$	−7.26697e6	−0.362321
$123$	−3.15362e6	−0.152806
$124$	7.20646e7	3.39427
$125$	−1.17506e7	−0.538117
$126$	1.45900e7	0.649768
$127$	−4.36705e7	−1.89180	−0.945900	−	0.324457i	$-0.894818\pi$
$127$	−4.36705e7	−1.89180	−0.945900	+	0.324457i	$0.894818\pi$
$128$	−3.94897e7	−1.66437
$129$	−2.21248e6	−0.0907435
$130$	−1.85749e7	−0.741522
$131$	−2.95763e7	−1.14946	−0.574731	−	0.818342i	$-0.694893\pi$
$131$	−2.95763e7	−1.14946	−0.574731	+	0.818342i	$0.694893\pi$
$132$	−8.84982e6	−0.334908
$133$	−9.80951e6	−0.361548
$134$	−4.89289e7	−1.75670
$135$	1.03353e7	0.361540
$136$	−6.07844e6	−0.207208
$137$	3.73078e7	1.23959	0.619794	−	0.784764i	$-0.287216\pi$
$137$	3.73078e7	1.23959	0.619794	+	0.784764i	$0.287216\pi$
$138$	−7.10722e6	−0.230209
$139$	−446331.	−0.0140963	−0.00704815	−	0.999975i	$-0.502244\pi$
$139$	−446331.	−0.0140963	−0.00704815	+	0.999975i	$0.502244\pi$
$140$	3.83937e7	1.18253
$141$	5.12031e6	0.153826
$142$	−7.41880e7	−2.17432
$143$	−1.34065e7	−0.383388
$144$	−3.96779e7	−1.10734
$145$	1.08775e7	0.296306
$146$	4.12107e6	0.109591
$147$	653265.	0.0169621
$148$	−2.33716e7	−0.592615
$149$	7.50230e7	1.85799	0.928993	−	0.370096i	$-0.120675\pi$
$149$	7.50230e7	1.85799	0.928993	+	0.370096i	$0.120675\pi$
$150$	1.15614e7	0.279699
$151$	−4.15805e7	−0.982812	−0.491406	−	0.870931i	$-0.663517\pi$
$151$	−4.15805e7	−0.982812	−0.491406	+	0.870931i	$0.663517\pi$
$152$	7.51429e7	1.73554
$153$	4.98816e6	0.112595
$154$	4.12912e7	0.911034
$155$	−1.18247e8	−2.55053
$156$	3.18625e6	0.0671961
$157$	−9.04582e6	−0.186552	−0.0932758	−	0.995640i	$-0.529734\pi$
$157$	−9.04582e6	−0.186552	−0.0932758	+	0.995640i	$0.529734\pi$
$158$	1.01706e8	2.05138
$159$	4.40491e6	0.0869054
$160$	−1.14505e7	−0.221006
$161$	2.22543e7	0.420266
$162$	9.03854e7	1.67030
$163$	−3.34765e6	−0.0605458	−0.0302729	−	0.999542i	$-0.509638\pi$
$163$	−3.34765e6	−0.0605458	−0.0302729	+	0.999542i	$0.509638\pi$
$164$	−1.48340e8	−2.62605
$165$	1.45212e7	0.251657
$166$	−7.46533e7	−1.26669
$167$	−4.42628e7	−0.735412	−0.367706	−	0.929942i	$-0.619857\pi$
$167$	−4.42628e7	−0.735412	−0.367706	+	0.929942i	$0.619857\pi$
$168$	−5.00414e6	−0.0814231
$169$	4.82681e6	0.0769231
$170$	1.95593e7	0.305339
$171$	−6.16646e7	−0.943082
$172$	−1.04070e8	−1.55947
$173$	−7.41968e7	−1.08949	−0.544745	−	0.838601i	$-0.683374\pi$
$173$	−7.41968e7	−1.08949	−0.544745	+	0.838601i	$0.683374\pi$
$174$	−2.78029e6	−0.0400099
$175$	−3.62014e7	−0.510614
$176$	−1.12293e8	−1.55259
$177$	−9.03966e6	−0.122531
$178$	−2.22657e8	−2.95915
$179$	1.40643e8	1.83287	0.916436	−	0.400180i	$-0.131053\pi$
$179$	1.40643e8	1.83287	0.916436	+	0.400180i	$0.131053\pi$
$180$	2.41351e8	3.08457
$181$	−1.09790e8	−1.37622	−0.688111	−	0.725606i	$-0.741560\pi$
$181$	−1.09790e8	−1.37622	−0.688111	+	0.725606i	$0.741560\pi$
$182$	−1.48663e7	−0.182790
$183$	−2.04539e6	−0.0246716
$184$	−1.70473e8	−2.01740
$185$	3.83493e7	0.445303
$186$	3.02240e7	0.344395
$187$	1.41170e7	0.157869
$188$	2.40849e8	2.64357
$189$	8.27183e6	0.0891221
$190$	−2.41796e8	−2.55747
$191$	−1.28305e8	−1.33237	−0.666186	−	0.745785i	$-0.732074\pi$
$191$	−1.28305e8	−1.33237	−0.666186	+	0.745785i	$0.732074\pi$
$192$	−1.01523e7	−0.103517
$193$	−1.61200e8	−1.61404	−0.807021	−	0.590523i	$-0.798922\pi$
$193$	−1.61200e8	−1.61404	−0.807021	+	0.590523i	$0.798922\pi$
$194$	3.05915e8	3.00811
$195$	−5.22816e6	−0.0504926
$196$	3.07282e7	0.291502
$197$	−1.93705e8	−1.80513	−0.902566	−	0.430551i	$-0.858319\pi$
$197$	−1.93705e8	−1.80513	−0.902566	+	0.430551i	$0.858319\pi$
$198$	2.59565e8	2.37639
$199$	−1.33837e8	−1.20390	−0.601950	−	0.798534i	$-0.705609\pi$
$199$	−1.33837e8	−1.20390	−0.601950	+	0.798534i	$0.705609\pi$
$200$	2.77311e8	2.45110
$201$	−1.37717e7	−0.119620
$202$	−8.87504e7	−0.757601
$203$	8.70572e6	0.0730413
$204$	−3.35511e6	−0.0276695
$205$	2.43403e8	1.97327
$206$	7.96053e7	0.634464
$207$	1.39895e8	1.09624
$208$	4.04293e7	0.311512
$209$	−1.74517e8	−1.32229
$210$	1.61024e7	0.119984
$211$	−1.77902e8	−1.30374	−0.651872	−	0.758329i	$-0.726016\pi$
$211$	−1.77902e8	−1.30374	−0.651872	+	0.758329i	$0.726016\pi$
$212$	2.07197e8	1.49351
$213$	−2.08812e7	−0.148057
$214$	1.58471e8	1.10535
$215$	1.70764e8	1.17182
$216$	−6.33640e7	−0.427813
$217$	−9.46384e7	−0.628722
$218$	2.13940e8	1.39860
$219$	1.15993e6	0.00746240
$220$	6.83047e8	4.32485
$221$	−5.08262e6	−0.0316749
$222$	−9.80209e6	−0.0601289
$223$	2.20034e8	1.32869	0.664343	−	0.747428i	$-0.268711\pi$
$223$	2.20034e8	1.32869	0.664343	+	0.747428i	$0.268711\pi$
$224$	−9.16432e6	−0.0544794
$225$	−2.27570e8	−1.33191
$226$	6.67394e7	0.384594
$227$	−8.05820e7	−0.457244	−0.228622	−	0.973515i	$-0.573422\pi$
$227$	−8.05820e7	−0.457244	−0.228622	+	0.973515i	$0.573422\pi$
$228$	4.14766e7	0.231756
$229$	5.14203e7	0.282951	0.141475	−	0.989942i	$-0.454815\pi$
$229$	5.14203e7	0.282951	0.141475	+	0.989942i	$0.454815\pi$
$230$	5.48550e8	2.97282
$231$	1.16220e7	0.0620352
$232$	−6.66876e7	−0.350620
$233$	−3.14157e8	−1.62705	−0.813526	−	0.581529i	$-0.802455\pi$
$233$	−3.14157e8	−1.62705	−0.813526	+	0.581529i	$0.802455\pi$
$234$	−9.34525e7	−0.476799
$235$	−3.95196e8	−1.98644
$236$	−4.25207e8	−2.10576
$237$	2.86266e7	0.139685
$238$	1.56542e7	0.0752680
$239$	−2.19255e8	−1.03886	−0.519430	−	0.854513i	$-0.673856\pi$
$239$	−2.19255e8	−1.03886	−0.519430	+	0.854513i	$0.673856\pi$
$240$	−4.37910e7	−0.204478
$241$	1.68452e8	0.775204	0.387602	−	0.921827i	$-0.373304\pi$
$241$	1.68452e8	0.775204	0.387602	+	0.921827i	$0.373304\pi$
$242$	3.50156e8	1.58821
$243$	7.81822e7	0.349531
$244$	−9.62108e7	−0.423994
$245$	−5.04203e7	−0.219040
$246$	−6.22139e7	−0.266449
$247$	6.28323e7	0.265304
$248$	7.24950e8	3.01806
$249$	−2.10122e7	−0.0862529
$250$	−2.31814e8	−0.938318
$251$	4.34461e8	1.73417	0.867086	−	0.498158i	$-0.165990\pi$
$251$	4.34461e8	1.73417	0.867086	+	0.498158i	$0.165990\pi$
$252$	1.93164e8	0.760368
$253$	3.95918e8	1.53703
$254$	−8.61523e8	−3.29874
$255$	5.50524e6	0.0207915
$256$	−5.45012e8	−2.03033
$257$	2.35781e8	0.866449	0.433225	−	0.901286i	$-0.357376\pi$
$257$	2.35781e8	0.866449	0.433225	+	0.901286i	$0.357376\pi$
$258$	−4.36473e7	−0.158230
$259$	3.06926e7	0.109770
$260$	−2.45921e8	−0.867740
$261$	5.47259e7	0.190525
$262$	−5.83475e8	−2.00432
$263$	−1.86046e8	−0.630632	−0.315316	−	0.948987i	$-0.602110\pi$
$263$	−1.86046e8	−0.630632	−0.315316	+	0.948987i	$0.602110\pi$
$264$	−8.90267e7	−0.297788
$265$	−3.39980e8	−1.12226
$266$	−1.93520e8	−0.630434
$267$	−6.26699e7	−0.201498
$268$	−6.47793e8	−2.05572
$269$	2.15028e8	0.673539	0.336769	−	0.941587i	$-0.390666\pi$
$269$	2.15028e8	0.673539	0.336769	+	0.941587i	$0.390666\pi$
$270$	2.03893e8	0.630420
$271$	2.43199e8	0.742283	0.371141	−	0.928576i	$-0.378967\pi$
$271$	2.43199e8	0.742283	0.371141	+	0.928576i	$0.378967\pi$
$272$	−4.25720e7	−0.128272
$273$	−4.18432e6	−0.0124467
$274$	7.36000e8	2.16148
$275$	−6.44045e8	−1.86746
$276$	−9.40958e7	−0.269394
$277$	−2.89067e8	−0.817182	−0.408591	−	0.912718i	$-0.633980\pi$
$277$	−2.89067e8	−0.817182	−0.408591	+	0.912718i	$0.633980\pi$
$278$	−8.80512e6	−0.0245798
$279$	−5.94916e8	−1.63999
$280$	3.86230e8	1.05146
$281$	5.79400e8	1.55778	0.778890	−	0.627160i	$-0.215783\pi$
$281$	5.79400e8	1.55778	0.778890	+	0.627160i	$0.215783\pi$
$282$	1.01012e8	0.268227
$283$	5.30718e8	1.39191	0.695955	−	0.718085i	$-0.254981\pi$
$283$	5.30718e8	1.39191	0.695955	+	0.718085i	$0.254981\pi$
$284$	−9.82209e8	−2.54443
$285$	−6.80568e7	−0.174146
$286$	−2.64480e8	−0.668516
$287$	1.94806e8	0.486425
$288$	−5.76088e7	−0.142107
$289$	−4.04987e8	−0.986957
$290$	2.14588e8	0.516670
$291$	8.61040e7	0.204832
$292$	5.45608e7	0.128245
$293$	1.45974e8	0.339030	0.169515	−	0.985528i	$-0.445780\pi$
$293$	1.45974e8	0.339030	0.169515	+	0.985528i	$0.445780\pi$
$294$	1.28875e7	0.0295768
$295$	6.97700e8	1.58231
$296$	−2.35112e8	−0.526930
$297$	1.47161e8	0.325945
$298$	1.48004e9	3.23978
$299$	−1.42545e8	−0.308391
$300$	1.53067e8	0.327308
$301$	1.36670e8	0.288862
$302$	−8.20291e8	−1.71374
$303$	−2.49800e7	−0.0515875
$304$	5.26283e8	1.07439
$305$	1.57867e8	0.318598
$306$	9.84053e7	0.196333
$307$	−3.51571e8	−0.693472	−0.346736	−	0.937963i	$-0.612710\pi$
$307$	−3.51571e8	−0.693472	−0.346736	+	0.937963i	$0.612710\pi$
$308$	5.46673e8	1.06611
$309$	2.24060e7	0.0432026
$310$	−2.33275e9	−4.44737
$311$	4.78523e8	0.902073	0.451037	−	0.892505i	$-0.351054\pi$
$311$	4.78523e8	0.902073	0.451037	+	0.892505i	$0.351054\pi$
$312$	3.20528e7	0.0597482
$313$	−1.77481e8	−0.327150	−0.163575	−	0.986531i	$-0.552303\pi$
$313$	−1.77481e8	−0.327150	−0.163575	+	0.986531i	$0.552303\pi$
$314$	−1.78454e8	−0.325291
$315$	−3.16952e8	−0.571356
$316$	1.34653e9	2.40056
$317$	1.94234e8	0.342466	0.171233	−	0.985231i	$-0.445225\pi$
$317$	1.94234e8	0.342466	0.171233	+	0.985231i	$0.445225\pi$
$318$	8.68990e7	0.151537
$319$	1.54880e8	0.267133
$320$	7.83579e8	1.33677
$321$	4.46038e7	0.0752669
$322$	4.39029e8	0.732820
$323$	−6.61623e7	−0.109245
$324$	1.19665e9	1.95462
$325$	2.31879e8	0.374688
$326$	−6.60418e7	−0.105574
$327$	6.02165e7	0.0952354
$328$	−1.49225e9	−2.33499
$329$	−3.16293e8	−0.489670
$330$	2.86471e8	0.438816
$331$	6.78259e8	1.02801	0.514005	−	0.857787i	$-0.328161\pi$
$331$	6.78259e8	1.02801	0.514005	+	0.857787i	$0.328161\pi$
$332$	−9.88370e8	−1.48230
$333$	1.92940e8	0.286330
$334$	−8.73206e8	−1.28234
$335$	1.06293e9	1.54471
$336$	−3.50479e7	−0.0504051
$337$	−4.45161e8	−0.633596	−0.316798	−	0.948493i	$-0.602608\pi$
$337$	−4.45161e8	−0.633596	−0.316798	+	0.948493i	$0.602608\pi$
$338$	9.52222e7	0.134131
$339$	1.87847e7	0.0261882
$340$	2.58955e8	0.357312
$341$	−1.68367e9	−2.29942
$342$	−1.21651e9	−1.64446
$343$	−4.03536e7	−0.0539949
$344$	−1.04692e9	−1.38662
$345$	1.54397e8	0.202429
$346$	−1.46374e9	−1.89975
$347$	−6.43829e8	−0.827213	−0.413607	−	0.910456i	$-0.635731\pi$
$347$	−6.43829e8	−0.827213	−0.413607	+	0.910456i	$0.635731\pi$
$348$	−3.68095e7	−0.0468202
$349$	1.45251e8	0.182907	0.0914536	−	0.995809i	$-0.470849\pi$
$349$	1.45251e8	0.182907	0.0914536	+	0.995809i	$0.470849\pi$
$350$	−7.14174e8	−0.890361
$351$	−5.29831e7	−0.0653977
$352$	−1.63039e8	−0.199247
$353$	8.01038e8	0.969263	0.484632	−	0.874718i	$-0.338954\pi$
$353$	8.01038e8	0.969263	0.484632	+	0.874718i	$0.338954\pi$
$354$	−1.78333e8	−0.213658
$355$	1.61166e9	1.91194
$356$	−2.94786e9	−3.46284
$357$	4.40608e6	0.00512524
$358$	2.77457e9	3.19599
$359$	1.33252e9	1.52000	0.759998	−	0.649925i	$-0.225200\pi$
$359$	1.33252e9	1.52000	0.759998	+	0.649925i	$0.225200\pi$
$360$	2.42792e9	2.74269
$361$	−7.59603e7	−0.0849790
$362$	−2.16592e9	−2.39973
$363$	9.85562e7	0.108146
$364$	−1.96822e8	−0.213904
$365$	−8.95260e7	−0.0963661
$366$	−4.03510e7	−0.0430200
$367$	2.08163e8	0.219823	0.109912	−	0.993941i	$-0.464943\pi$
$367$	2.08163e8	0.219823	0.109912	+	0.993941i	$0.464943\pi$
$368$	−1.19395e9	−1.24888
$369$	1.22459e9	1.26882
$370$	7.56546e8	0.776478
$371$	−2.72101e8	−0.276644
$372$	4.00150e8	0.403017
$373$	−8.95253e8	−0.893233	−0.446617	−	0.894725i	$-0.647371\pi$
$373$	−8.95253e8	−0.893233	−0.446617	+	0.894725i	$0.647371\pi$
$374$	2.78497e8	0.275277
$375$	−6.52473e7	−0.0638930
$376$	2.42287e9	2.35057
$377$	−5.57623e7	−0.0535977
$378$	1.63185e8	0.155403
$379$	5.98555e8	0.564764	0.282382	−	0.959302i	$-0.408875\pi$
$379$	5.98555e8	0.564764	0.282382	+	0.959302i	$0.408875\pi$
$380$	−3.20125e9	−2.99279
$381$	−2.42488e8	−0.224622
$382$	−2.53117e9	−2.32327
$383$	1.67170e9	1.52042	0.760208	−	0.649680i	$-0.225097\pi$
$383$	1.67170e9	1.52042	0.760208	+	0.649680i	$0.225097\pi$
$384$	−2.19273e8	−0.197618
$385$	−8.97008e8	−0.801094
$386$	−3.18012e9	−2.81441
$387$	8.59134e8	0.753482
$388$	4.05015e9	3.52014
$389$	1.44628e9	1.24575	0.622873	−	0.782323i	$-0.285965\pi$
$389$	1.44628e9	1.24575	0.622873	+	0.782323i	$0.285965\pi$
$390$	−1.03140e8	−0.0880442
$391$	1.50099e8	0.126987
$392$	3.09117e8	0.259192
$393$	−1.64227e8	−0.136481
$394$	−3.82137e9	−3.14762
$395$	−2.20946e9	−1.80383
$396$	3.43650e9	2.78088
$397$	−1.26723e9	−1.01646	−0.508228	−	0.861222i	$-0.669699\pi$
$397$	−1.26723e9	−1.01646	−0.508228	+	0.861222i	$0.669699\pi$
$398$	−2.64031e9	−2.09925
$399$	−5.44689e7	−0.0429282
$400$	1.94222e9	1.51736
$401$	1.76704e9	1.36849	0.684244	−	0.729253i	$-0.260132\pi$
$401$	1.76704e9	1.36849	0.684244	+	0.729253i	$0.260132\pi$
$402$	−2.71686e8	−0.208581
$403$	6.06183e8	0.461356
$404$	−1.17501e9	−0.886556
$405$	−1.96353e9	−1.46874
$406$	1.71744e8	0.127363
$407$	5.46040e8	0.401461
$408$	−3.37515e7	−0.0246027
$409$	1.47944e7	0.0106922	0.00534609	−	0.999986i	$-0.498298\pi$
$409$	1.47944e7	0.0106922	0.00534609	+	0.999986i	$0.498298\pi$
$410$	4.80180e9	3.44081
$411$	2.07157e8	0.147182
$412$	1.05393e9	0.742459
$413$	5.58400e8	0.390050
$414$	2.75982e9	1.91153
$415$	1.62177e9	1.11383
$416$	5.86997e7	0.0399769
$417$	−2.47832e6	−0.00167372
$418$	−3.44283e9	−2.30568
$419$	−2.59010e9	−1.72016	−0.860078	−	0.510163i	$-0.829585\pi$
$419$	−2.59010e9	−1.72016	−0.860078	+	0.510163i	$0.829585\pi$
$420$	2.13187e8	0.140407
$421$	−2.31820e8	−0.151413	−0.0757065	−	0.997130i	$-0.524121\pi$
$421$	−2.31820e8	−0.151413	−0.0757065	+	0.997130i	$0.524121\pi$
$422$	−3.50961e9	−2.27335
$423$	−1.98828e9	−1.27728
$424$	2.08435e9	1.32797
$425$	−2.44168e8	−0.154286
$426$	−4.11940e8	−0.258167
$427$	1.26348e8	0.0785365
$428$	2.09807e9	1.29350
$429$	−7.44416e7	−0.0455214
$430$	3.36879e9	2.04331
$431$	1.70825e9	1.02774	0.513869	−	0.857869i	$-0.328212\pi$
$431$	1.70825e9	1.02774	0.513869	+	0.857869i	$0.328212\pi$
$432$	−4.43787e8	−0.264838
$433$	1.98682e8	0.117612	0.0588058	−	0.998269i	$-0.481271\pi$
$433$	1.98682e8	0.117612	0.0588058	+	0.998269i	$0.481271\pi$
$434$	−1.86701e9	−1.09631
$435$	6.03989e7	0.0351817
$436$	2.83246e9	1.63667
$437$	−1.85555e9	−1.06363
$438$	2.28829e7	0.0130122
$439$	−2.60601e9	−1.47011	−0.735057	−	0.678005i	$-0.762845\pi$
$439$	−2.60601e9	−1.47011	−0.735057	+	0.678005i	$0.762845\pi$
$440$	6.87127e9	3.84550
$441$	−2.53671e8	−0.140843
$442$	−1.00269e8	−0.0552316
$443$	5.85677e8	0.320070	0.160035	−	0.987111i	$-0.448839\pi$
$443$	5.85677e8	0.320070	0.160035	+	0.987111i	$0.448839\pi$
$444$	−1.29775e8	−0.0703638
$445$	4.83700e9	2.60205
$446$	4.34078e9	2.31684
$447$	4.16577e8	0.220607
$448$	6.27133e8	0.329523
$449$	−3.10283e9	−1.61769	−0.808847	−	0.588020i	$-0.799908\pi$
$449$	−3.10283e9	−1.61769	−0.808847	+	0.588020i	$0.799908\pi$
$450$	−4.48944e9	−2.32246
$451$	3.46571e9	1.77900
$452$	8.83594e8	0.450058
$453$	−2.30882e8	−0.116694
$454$	−1.58970e9	−0.797298
$455$	3.22955e8	0.160732
$456$	4.17243e8	0.206069
$457$	9.66348e8	0.473617	0.236808	−	0.971556i	$-0.423899\pi$
$457$	9.66348e8	0.473617	0.236808	+	0.971556i	$0.423899\pi$
$458$	1.01441e9	0.493383
$459$	5.57911e7	0.0269290
$460$	7.26251e9	3.47884
$461$	−1.24626e9	−0.592455	−0.296228	−	0.955117i	$-0.595729\pi$
$461$	−1.24626e9	−0.592455	−0.296228	+	0.955117i	$0.595729\pi$
$462$	2.29276e8	0.108171
$463$	−1.90865e9	−0.893702	−0.446851	−	0.894608i	$-0.647455\pi$
$463$	−1.90865e9	−0.893702	−0.446851	+	0.894608i	$0.647455\pi$
$464$	−4.67065e8	−0.217052
$465$	−6.56586e8	−0.302835
$466$	−6.19762e9	−2.83710
$467$	1.82985e9	0.831394	0.415697	−	0.909503i	$-0.363538\pi$
$467$	1.82985e9	0.831394	0.415697	+	0.909503i	$0.363538\pi$
$468$	−1.23726e9	−0.557957
$469$	8.50710e8	0.380782
$470$	−7.79634e9	−3.46376
$471$	−5.02283e7	−0.0221501
$472$	−4.27746e9	−1.87236
$473$	2.43144e9	1.05645
$474$	5.64739e8	0.243570
$475$	3.01846e9	1.29228
$476$	2.07253e8	0.0880798
$477$	−1.71048e9	−0.721612
$478$	−4.32542e9	−1.81147
$479$	−3.37796e9	−1.40436	−0.702182	−	0.711997i	$-0.747791\pi$
$479$	−3.37796e9	−1.40436	−0.702182	+	0.711997i	$0.747791\pi$
$480$	−6.35806e7	−0.0262410
$481$	−1.96594e8	−0.0805493
$482$	3.32318e9	1.35173
$483$	1.23571e8	0.0499000
$484$	4.63587e9	1.85854
$485$	−6.64568e9	−2.64511
$486$	1.54236e9	0.609480
$487$	2.85462e9	1.11995	0.559973	−	0.828511i	$-0.310811\pi$
$487$	2.85462e9	1.11995	0.559973	+	0.828511i	$0.310811\pi$
$488$	−9.67854e8	−0.376999
$489$	−1.85884e7	−0.00718887
$490$	−9.94681e8	−0.381942
$491$	2.02162e9	0.770751	0.385376	−	0.922760i	$-0.374072\pi$
$491$	2.02162e9	0.770751	0.385376	+	0.922760i	$0.374072\pi$
$492$	−8.23679e8	−0.311803
$493$	5.87176e7	0.0220701
$494$	1.23954e9	0.462612
$495$	−5.63877e9	−2.08962
$496$	5.07738e9	1.86833
$497$	1.28988e9	0.471305
$498$	−4.14524e8	−0.150400
$499$	3.15183e9	1.13556	0.567781	−	0.823179i	$-0.307802\pi$
$499$	3.15183e9	1.13556	0.567781	+	0.823179i	$0.307802\pi$
$500$	−3.06910e9	−1.09803
$501$	−2.45776e8	−0.0873188
$502$	8.57094e9	3.02389
$503$	−7.16205e7	−0.0250928	−0.0125464	−	0.999921i	$-0.503994\pi$
$503$	−7.16205e7	−0.0250928	−0.0125464	+	0.999921i	$0.503994\pi$
$504$	1.94317e9	0.676090
$505$	1.92801e9	0.666177
$506$	7.81058e9	2.68013
$507$	2.68016e7	0.00913342
$508$	−1.14061e10	−3.86024
$509$	3.06746e9	1.03102	0.515509	−	0.856884i	$-0.327603\pi$
$509$	3.06746e9	1.03102	0.515509	+	0.856884i	$0.327603\pi$
$510$	1.08606e8	0.0362542
$511$	−7.16516e7	−0.0237549
$512$	−5.69720e9	−1.87593
$513$	−6.89701e8	−0.225554
$514$	4.65144e9	1.51083
$515$	−1.72934e9	−0.557899
$516$	−5.77867e8	−0.185163
$517$	−5.62704e9	−1.79087
$518$	6.05497e8	0.191407
$519$	−4.11989e8	−0.129360
$520$	−2.47390e9	−0.771561
$521$	−2.29774e7	−0.00711817	−0.00355908	−	0.999994i	$-0.501133\pi$
$521$	−2.29774e7	−0.00711817	−0.00355908	+	0.999994i	$0.501133\pi$
$522$	1.07962e9	0.332219
$523$	1.36063e9	0.415895	0.207948	−	0.978140i	$-0.433322\pi$
$523$	1.36063e9	0.415895	0.207948	+	0.978140i	$0.433322\pi$
$524$	−7.72490e9	−2.34549
$525$	−2.01014e8	−0.0606274
$526$	−3.67028e9	−1.09964
$527$	−6.38309e8	−0.189974
$528$	−6.23523e8	−0.184346
$529$	8.04778e8	0.236364
$530$	−6.70705e9	−1.95689
$531$	3.51022e9	1.01743
$532$	−2.56210e9	−0.737743
$533$	−1.24778e9	−0.356938
$534$	−1.23634e9	−0.351353
$535$	−3.44261e9	−0.971964
$536$	−6.51662e9	−1.82787
$537$	7.80942e8	0.217625
$538$	4.24203e9	1.17445
$539$	−7.17915e8	−0.197475
$540$	2.69944e9	0.737727
$541$	1.62138e9	0.440246	0.220123	−	0.975472i	$-0.429354\pi$
$541$	1.62138e9	0.440246	0.220123	+	0.975472i	$0.429354\pi$
$542$	4.79778e9	1.29432
$543$	−6.09627e8	−0.163405
$544$	−6.18107e7	−0.0164614
$545$	−4.64763e9	−1.22983
$546$	−8.25474e7	−0.0217035
$547$	−4.40640e9	−1.15114	−0.575571	−	0.817752i	$-0.695220\pi$
$547$	−4.40640e9	−1.15114	−0.575571	+	0.817752i	$0.695220\pi$
$548$	9.74425e9	2.52939
$549$	7.94251e8	0.204859
$550$	−1.27056e10	−3.25631
$551$	−7.25878e8	−0.184856
$552$	−9.46578e8	−0.239535
$553$	−1.76833e9	−0.444657
$554$	−5.70265e9	−1.42493
$555$	2.12940e8	0.0528728
$556$	−1.16575e8	−0.0287637
$557$	−3.90176e9	−0.956681	−0.478341	−	0.878174i	$-0.658762\pi$
$557$	−3.90176e9	−0.956681	−0.478341	+	0.878174i	$0.658762\pi$
$558$	−1.17364e10	−2.85966
$559$	−8.75404e8	−0.211966
$560$	2.70507e9	0.650909
$561$	7.83868e7	0.0187445
$562$	1.14303e10	2.71631
$563$	−4.55103e9	−1.07481	−0.537403	−	0.843325i	$-0.680595\pi$
$563$	−4.55103e9	−1.07481	−0.537403	+	0.843325i	$0.680595\pi$
$564$	1.33735e9	0.313883
$565$	−1.44984e9	−0.338183
$566$	1.04699e10	2.42708
$567$	−1.57150e9	−0.362054
$568$	−9.88075e9	−2.26241
$569$	1.92072e9	0.437090	0.218545	−	0.975827i	$-0.429869\pi$
$569$	1.92072e9	0.437090	0.218545	+	0.975827i	$0.429869\pi$
$570$	−1.34261e9	−0.303660
$571$	1.07182e9	0.240933	0.120466	−	0.992717i	$-0.461561\pi$
$571$	1.07182e9	0.240933	0.120466	+	0.992717i	$0.461561\pi$
$572$	−3.50158e9	−0.782307
$573$	−7.12432e8	−0.158198
$574$	3.84309e9	0.848182
$575$	−6.84782e9	−1.50216
$576$	3.94228e9	0.859546
$577$	4.34334e9	0.941257	0.470628	−	0.882332i	$-0.344027\pi$
$577$	4.34334e9	0.941257	0.470628	+	0.882332i	$0.344027\pi$
$578$	−7.98949e9	−1.72096
$579$	−8.95089e8	−0.191642
$580$	2.84104e9	0.604615
$581$	1.29797e9	0.274567
$582$	1.69864e9	0.357167
$583$	−4.84083e9	−1.01177
$584$	5.48866e8	0.114031
$585$	2.03016e9	0.419261
$586$	2.87974e9	0.591168
$587$	6.75535e8	0.137853	0.0689263	−	0.997622i	$-0.478043\pi$
$587$	6.75535e8	0.137853	0.0689263	+	0.997622i	$0.478043\pi$
$588$	1.70623e8	0.0346113
$589$	7.89090e9	1.59119
$590$	1.37641e10	2.75908
$591$	−1.07558e9	−0.214331
$592$	−1.64667e9	−0.326197
$593$	5.40575e9	1.06455	0.532273	−	0.846573i	$-0.321338\pi$
$593$	5.40575e9	1.06455	0.532273	+	0.846573i	$0.321338\pi$
$594$	2.90316e9	0.568353
$595$	−3.40071e8	−0.0661850
$596$	1.95949e10	3.79124
$597$	−7.43151e8	−0.142944
$598$	−2.81209e9	−0.537743
$599$	5.53835e9	1.05290	0.526449	−	0.850207i	$-0.323523\pi$
$599$	5.53835e9	1.05290	0.526449	+	0.850207i	$0.323523\pi$
$600$	1.53981e9	0.291030
$601$	7.45958e9	1.40170	0.700848	−	0.713311i	$-0.252805\pi$
$601$	7.45958e9	1.40170	0.700848	+	0.713311i	$0.252805\pi$
$602$	2.69619e9	0.503690
$603$	5.34774e9	0.993252
$604$	−1.08602e10	−2.00544
$605$	−7.60677e9	−1.39655
$606$	−4.92801e8	−0.0899534
$607$	6.96586e9	1.26420	0.632098	−	0.774888i	$-0.282194\pi$
$607$	6.96586e9	1.26420	0.632098	+	0.774888i	$0.282194\pi$
$608$	7.64116e8	0.137879
$609$	4.83399e7	0.00867252
$610$	3.11437e9	0.555541
$611$	2.02593e9	0.359320
$612$	1.30283e9	0.229752
$613$	−2.92486e8	−0.0512854	−0.0256427	−	0.999671i	$-0.508163\pi$
$613$	−2.92486e8	−0.0512854	−0.0256427	+	0.999671i	$0.508163\pi$
$614$	−6.93572e9	−1.20921
$615$	1.35153e9	0.234295
$616$	5.49938e9	0.947940
$617$	−2.33359e9	−0.399969	−0.199985	−	0.979799i	$-0.564089\pi$
$617$	−2.33359e9	−0.399969	−0.199985	+	0.979799i	$0.564089\pi$
$618$	4.42021e8	0.0753327
$619$	−3.98246e9	−0.674892	−0.337446	−	0.941345i	$-0.609563\pi$
$619$	−3.98246e9	−0.674892	−0.337446	+	0.941345i	$0.609563\pi$
$620$	−3.08844e10	−5.20438
$621$	1.56469e9	0.262185
$622$	9.44020e9	1.57295
$623$	3.87126e9	0.641423
$624$	2.24490e8	0.0369872
$625$	−3.20966e9	−0.525871
$626$	−3.50131e9	−0.570454
$627$	−9.69033e8	−0.157001
$628$	−2.36263e9	−0.380661
$629$	2.07013e8	0.0331680
$630$	−6.25277e9	−0.996278
$631$	6.48026e8	0.102681	0.0513405	−	0.998681i	$-0.483651\pi$
$631$	6.48026e8	0.102681	0.0513405	+	0.998681i	$0.483651\pi$
$632$	1.35458e10	2.13449
$633$	−9.87829e8	−0.154799
$634$	3.83181e9	0.597161
$635$	1.87157e10	2.90067
$636$	1.15050e9	0.177331
$637$	2.58475e8	0.0396214
$638$	3.05544e9	0.465802
$639$	8.10845e9	1.22938
$640$	1.69239e10	2.55195
$641$	4.71120e9	0.706526	0.353263	−	0.935524i	$-0.385072\pi$
$641$	4.71120e9	0.706526	0.353263	+	0.935524i	$0.385072\pi$
$642$	8.79934e8	0.131243
$643$	5.76156e9	0.854676	0.427338	−	0.904092i	$-0.359451\pi$
$643$	5.76156e9	0.854676	0.427338	+	0.904092i	$0.359451\pi$
$644$	5.81251e9	0.857557
$645$	9.48193e8	0.139135
$646$	−1.30524e9	−0.190491
$647$	−7.59360e9	−1.10226	−0.551128	−	0.834421i	$-0.685802\pi$
$647$	−7.59360e9	−1.10226	−0.551128	+	0.834421i	$0.685802\pi$
$648$	1.20380e10	1.73797
$649$	9.93427e9	1.42653
$650$	4.57446e9	0.653346
$651$	−5.25495e8	−0.0746509
$652$	−8.74358e8	−0.123544
$653$	−5.91232e9	−0.830925	−0.415462	−	0.909610i	$-0.636380\pi$
$653$	−5.91232e9	−0.830925	−0.415462	+	0.909610i	$0.636380\pi$
$654$	1.18794e9	0.166062
$655$	1.26754e10	1.76245
$656$	−1.04514e10	−1.44548
$657$	−4.50417e8	−0.0619634
$658$	−6.23975e9	−0.853841
$659$	−1.44165e10	−1.96228	−0.981140	−	0.193300i	$-0.938081\pi$
$659$	−1.44165e10	−1.96228	−0.981140	+	0.193300i	$0.938081\pi$
$660$	3.79273e9	0.513509
$661$	−3.90799e8	−0.0526318	−0.0263159	−	0.999654i	$-0.508378\pi$
$661$	−3.90799e8	−0.0526318	−0.0263159	+	0.999654i	$0.508378\pi$
$662$	1.33805e10	1.79255
$663$	−2.82221e7	−0.00376090
$664$	−9.94272e9	−1.31801
$665$	4.20402e9	0.554356
$666$	3.80628e9	0.499276
$667$	1.64676e9	0.214877
$668$	−1.15608e10	−1.50062
$669$	1.22177e9	0.157761
$670$	2.09693e10	2.69353
$671$	2.24781e9	0.287231
$672$	−5.08863e7	−0.00646858
$673$	−5.90309e9	−0.746495	−0.373247	−	0.927732i	$-0.621756\pi$
$673$	−5.90309e9	−0.746495	−0.373247	+	0.927732i	$0.621756\pi$
$674$	−8.78203e9	−1.10480
$675$	−2.54530e9	−0.318549
$676$	1.26069e9	0.156962
$677$	−1.29502e10	−1.60405	−0.802024	−	0.597292i	$-0.796243\pi$
$677$	−1.29502e10	−1.60405	−0.802024	+	0.597292i	$0.796243\pi$
$678$	3.70581e8	0.0456645
$679$	−5.31883e9	−0.652037
$680$	2.60501e9	0.317708
$681$	−4.47445e8	−0.0542906
$682$	−3.32152e10	−4.00951
$683$	3.55157e9	0.426529	0.213264	−	0.976995i	$-0.431590\pi$
$683$	3.55157e9	0.426529	0.213264	+	0.976995i	$0.431590\pi$
$684$	−1.61059e10	−1.92437
$685$	−1.59888e10	−1.90064
$686$	−7.96087e8	−0.0941513
$687$	2.85520e8	0.0335960
$688$	−7.33238e9	−0.858392
$689$	1.74287e9	0.203001
$690$	3.04591e9	0.352976
$691$	−5.93381e8	−0.0684165	−0.0342082	−	0.999415i	$-0.510891\pi$
$691$	−5.93381e8	−0.0684165	−0.0342082	+	0.999415i	$0.510891\pi$
$692$	−1.93791e10	−2.22312
$693$	−4.51296e9	−0.515104
$694$	−1.27013e10	−1.44242
$695$	1.91282e8	0.0216136
$696$	−3.70294e8	−0.0416307
$697$	1.31391e9	0.146977
$698$	2.86549e9	0.318936
$699$	−1.74441e9	−0.193187
$700$	−9.45529e9	−1.04191
$701$	−9.64162e9	−1.05715	−0.528575	−	0.848886i	$-0.677274\pi$
$701$	−9.64162e9	−1.05715	−0.528575	+	0.848886i	$0.677274\pi$
$702$	−1.04524e9	−0.114034
$703$	−2.55913e9	−0.277811
$704$	1.11571e10	1.20516
$705$	−2.19439e9	−0.235859
$706$	1.58027e10	1.69011
$707$	1.54307e9	0.164217
$708$	−2.36103e9	−0.250026
$709$	−9.33637e9	−0.983821	−0.491910	−	0.870646i	$-0.663701\pi$
$709$	−9.33637e9	−0.983821	−0.491910	+	0.870646i	$0.663701\pi$
$710$	3.17944e10	3.33385
$711$	−1.11161e10	−1.15987
$712$	−2.96547e10	−3.07902
$713$	−1.79017e10	−1.84961
$714$	8.69222e7	0.00893690
$715$	5.74556e9	0.587842
$716$	3.67339e10	3.74000
$717$	−1.21745e9	−0.123349
$718$	2.62876e10	2.65043
$719$	9.55205e9	0.958397	0.479199	−	0.877707i	$-0.340927\pi$
$719$	9.55205e9	0.958397	0.479199	+	0.877707i	$0.340927\pi$
$720$	1.70046e10	1.69786
$721$	−1.38407e9	−0.137526
$722$	−1.49853e9	−0.148178
$723$	9.35355e8	0.0920434
$724$	−2.86756e10	−2.80820
$725$	−2.67881e9	−0.261071
$726$	1.94429e9	0.188575
$727$	−3.40515e9	−0.328674	−0.164337	−	0.986404i	$-0.552548\pi$
$727$	−3.40515e9	−0.328674	−0.164337	+	0.986404i	$0.552548\pi$
$728$	−1.97997e9	−0.190195
$729$	−9.58591e9	−0.916404
$730$	−1.76615e9	−0.168034
$731$	9.21798e8	0.0872821
$732$	−5.34226e8	−0.0503427
$733$	−1.61343e10	−1.51317	−0.756584	−	0.653896i	$-0.773133\pi$
$733$	−1.61343e10	−1.51317	−0.756584	+	0.653896i	$0.773133\pi$
$734$	4.10660e9	0.383307
$735$	−2.79967e8	−0.0260076
$736$	−1.73351e9	−0.160271
$737$	1.51346e10	1.39263
$738$	2.41584e10	2.21244
$739$	4.30616e9	0.392496	0.196248	−	0.980554i	$-0.437124\pi$
$739$	4.30616e9	0.392496	0.196248	+	0.980554i	$0.437124\pi$
$740$	1.00163e10	0.908646
$741$	3.48887e8	0.0315007
$742$	−5.36794e9	−0.482386
$743$	1.34403e10	1.20212	0.601060	−	0.799204i	$-0.294745\pi$
$743$	1.34403e10	1.20212	0.601060	+	0.799204i	$0.294745\pi$
$744$	4.02540e9	0.358347
$745$	−3.21523e10	−2.84882
$746$	−1.76614e10	−1.55754
$747$	8.15931e9	0.716195
$748$	3.68715e9	0.322133
$749$	−2.75528e9	−0.239595
$750$	−1.28719e9	−0.111411
$751$	1.45347e10	1.25218	0.626090	−	0.779751i	$-0.284654\pi$
$751$	1.45347e10	1.25218	0.626090	+	0.779751i	$0.284654\pi$
$752$	1.69692e10	1.45512
$753$	2.41241e9	0.205906
$754$	−1.10007e9	−0.0934586
$755$	1.78200e10	1.50693
$756$	2.16048e9	0.181855
$757$	−5.70997e9	−0.478408	−0.239204	−	0.970969i	$-0.576886\pi$
$757$	−5.70997e9	−0.478408	−0.239204	+	0.970969i	$0.576886\pi$
$758$	1.18082e10	0.984782
$759$	2.19840e9	0.182499
$760$	−3.22037e10	−2.66108
$761$	−3.66090e9	−0.301122	−0.150561	−	0.988601i	$-0.548108\pi$
$761$	−3.66090e9	−0.301122	−0.150561	+	0.988601i	$0.548108\pi$
$762$	−4.78374e9	−0.391675
$763$	−3.71970e9	−0.303160
$764$	−3.35113e10	−2.71872
$765$	−2.13775e9	−0.172640
$766$	3.29789e10	2.65116
$767$	−3.57669e9	−0.286218
$768$	−3.02627e9	−0.241070
$769$	8.01646e9	0.635683	0.317842	−	0.948144i	$-0.397042\pi$
$769$	8.01646e9	0.635683	0.317842	+	0.948144i	$0.397042\pi$
$770$	−1.76960e10	−1.39687
$771$	1.30921e9	0.102877
$772$	−4.21031e10	−3.29347
$773$	−1.14038e10	−0.888020	−0.444010	−	0.896022i	$-0.646445\pi$
$773$	−1.14038e10	−0.888020	−0.444010	+	0.896022i	$0.646445\pi$
$774$	1.69488e10	1.31385
$775$	2.91209e10	2.24724
$776$	4.07434e10	3.12998
$777$	1.70426e8	0.0130335
$778$	2.85320e10	2.17222
$779$	−1.62428e10	−1.23106
$780$	−1.36552e9	−0.103031
$781$	2.29477e10	1.72370
$782$	2.96112e9	0.221428
$783$	6.12094e8	0.0455672
$784$	2.16498e9	0.160453
$785$	3.87673e9	0.286036
$786$	−3.23984e9	−0.237982
$787$	7.18095e9	0.525134	0.262567	−	0.964914i	$-0.415431\pi$
$787$	7.18095e9	0.525134	0.262567	+	0.964914i	$0.415431\pi$
$788$	−5.05929e10	−3.68339
$789$	−1.03305e9	−0.0748777
$790$	−4.35877e10	−3.14535
$791$	−1.16037e9	−0.0833643
$792$	3.45702e10	2.47266
$793$	−8.09292e8	−0.0576301
$794$	−2.49996e10	−1.77240
$795$	−1.88779e9	−0.133251
$796$	−3.49563e10	−2.45657
$797$	−1.04044e10	−0.727968	−0.363984	−	0.931405i	$-0.618584\pi$
$797$	−1.04044e10	−0.727968	−0.363984	+	0.931405i	$0.618584\pi$
$798$	−1.07455e9	−0.0748542
$799$	−2.13330e9	−0.147958
$800$	2.81993e9	0.194725
$801$	2.43355e10	1.67312
$802$	3.48598e10	2.38624
$803$	−1.27472e9	−0.0868784
$804$	−3.59697e9	−0.244085
$805$	−9.53745e9	−0.644387
$806$	1.19586e10	0.804468
$807$	1.19398e9	0.0799722
$808$	−1.18203e10	−0.788292
$809$	−2.54027e10	−1.68679	−0.843394	−	0.537296i	$-0.819446\pi$
$809$	−2.54027e10	−1.68679	−0.843394	+	0.537296i	$0.819446\pi$
$810$	−3.87361e10	−2.56105
$811$	−1.14291e10	−0.752383	−0.376191	−	0.926542i	$-0.622766\pi$
$811$	−1.14291e10	−0.752383	−0.376191	+	0.926542i	$0.622766\pi$
$812$	2.27381e9	0.149042
$813$	1.35040e9	0.0881345
$814$	1.07722e10	0.700031
$815$	1.43469e9	0.0928338
$816$	−2.36388e8	−0.0152303
$817$	−1.13955e10	−0.731062
$818$	2.91861e8	0.0186440
$819$	1.62483e9	0.103351
$820$	6.35732e10	4.02648
$821$	−1.10447e10	−0.696550	−0.348275	−	0.937392i	$-0.613232\pi$
$821$	−1.10447e10	−0.696550	−0.348275	+	0.937392i	$0.613232\pi$
$822$	4.08676e9	0.256642
$823$	1.63880e10	1.02477	0.512384	−	0.858757i	$-0.328763\pi$
$823$	1.63880e10	1.02477	0.512384	+	0.858757i	$0.328763\pi$
$824$	1.06023e10	0.660166
$825$	−3.57616e9	−0.221732
$826$	1.10160e10	0.680132
$827$	5.05483e9	0.310769	0.155384	−	0.987854i	$-0.450338\pi$
$827$	5.05483e9	0.310769	0.155384	+	0.987854i	$0.450338\pi$
$828$	3.65386e10	2.23690
$829$	−1.03800e10	−0.632783	−0.316391	−	0.948629i	$-0.602471\pi$
$829$	−1.03800e10	−0.632783	−0.316391	+	0.948629i	$0.602471\pi$
$830$	3.19938e10	1.94220
$831$	−1.60509e9	−0.0970277
$832$	−4.01694e9	−0.241804
$833$	−2.72173e8	−0.0163150
$834$	−4.88918e7	−0.00291847
$835$	1.89695e10	1.12760
$836$	−4.55813e10	−2.69814
$837$	−6.65397e9	−0.392231
$838$	−5.10969e10	−2.99944
$839$	1.27181e10	0.743454	0.371727	−	0.928342i	$-0.378766\pi$
$839$	1.27181e10	0.743454	0.371727	+	0.928342i	$0.378766\pi$
$840$	2.14460e9	0.124845
$841$	−1.66057e10	−0.962655
$842$	−4.57329e9	−0.264020
$843$	3.21721e9	0.184962
$844$	−4.64654e10	−2.66030
$845$	−2.06860e9	−0.117945
$846$	−3.92244e10	−2.22720
$847$	−6.08803e9	−0.344259
$848$	1.45983e10	0.822085
$849$	2.94690e9	0.165268
$850$	−4.81690e9	−0.269030
$851$	5.80577e9	0.322929
$852$	−5.45387e9	−0.302111
$853$	−1.13899e9	−0.0628347	−0.0314174	−	0.999506i	$-0.510002\pi$
$853$	−1.13899e9	−0.0628347	−0.0314174	+	0.999506i	$0.510002\pi$
$854$	2.49257e9	0.136945
$855$	2.64273e10	1.44601
$856$	2.11060e10	1.15013
$857$	2.80478e10	1.52218	0.761089	−	0.648648i	$-0.224665\pi$
$857$	2.80478e10	1.52218	0.761089	+	0.648648i	$0.224665\pi$
$858$	−1.46857e9	−0.0793759
$859$	−9.52790e9	−0.512886	−0.256443	−	0.966559i	$-0.582551\pi$
$859$	−9.52790e9	−0.512886	−0.256443	+	0.966559i	$0.582551\pi$
$860$	4.46010e10	2.39111
$861$	1.08169e9	0.0577553
$862$	3.37001e10	1.79207
$863$	1.84605e10	0.977701	0.488851	−	0.872368i	$-0.337416\pi$
$863$	1.84605e10	0.977701	0.488851	+	0.872368i	$0.337416\pi$
$864$	−6.44338e8	−0.0339872
$865$	3.17982e10	1.67050
$866$	3.91955e9	0.205080
$867$	−2.24875e9	−0.117186
$868$	−2.47182e10	−1.28291
$869$	−3.14596e10	−1.62624
$870$	1.19154e9	0.0613465
$871$	−5.44901e9	−0.279418
$872$	2.84937e10	1.45526
$873$	−3.34353e10	−1.70081
$874$	−3.66060e10	−1.85465
$875$	4.03047e9	0.203389
$876$	3.02957e8	0.0152271
$877$	−1.78759e10	−0.894890	−0.447445	−	0.894311i	$-0.647666\pi$
$877$	−1.78759e10	−0.894890	−0.447445	+	0.894311i	$0.647666\pi$
$878$	−5.14109e10	−2.56345
$879$	8.10542e8	0.0402545
$880$	4.81248e10	2.38056
$881$	8.16173e9	0.402130	0.201065	−	0.979578i	$-0.435560\pi$
$881$	8.16173e9	0.402130	0.201065	+	0.979578i	$0.435560\pi$
$882$	−5.00437e9	−0.245589
$883$	1.00317e10	0.490356	0.245178	−	0.969478i	$-0.421154\pi$
$883$	1.00317e10	0.490356	0.245178	+	0.969478i	$0.421154\pi$
$884$	−1.32751e9	−0.0646329
$885$	3.87409e9	0.187875
$886$	1.15541e10	0.558108
$887$	9.79101e9	0.471080	0.235540	−	0.971865i	$-0.424314\pi$
$887$	9.79101e9	0.471080	0.235540	+	0.971865i	$0.424314\pi$
$888$	−1.30550e9	−0.0625648
$889$	1.49790e10	0.715034
$890$	9.54232e10	4.53721
$891$	−2.79579e10	−1.32414
$892$	5.74696e10	2.71120
$893$	2.63723e10	1.23928
$894$	8.21814e9	0.384674
$895$	−6.02747e10	−2.81031
$896$	1.35450e10	0.629071
$897$	−7.91501e8	−0.0366166
$898$	−6.12120e10	−2.82078
$899$	−7.00300e9	−0.321458
$900$	−5.94379e10	−2.71778
$901$	−1.83524e9	−0.0835904
$902$	6.83708e10	3.10204
$903$	7.58881e8	0.0342978
$904$	8.88871e9	0.400174
$905$	4.70523e10	2.11014
$906$	−4.55480e9	−0.203479
$907$	−3.96185e10	−1.76308	−0.881542	−	0.472106i	$-0.843494\pi$
$907$	−3.96185e10	−1.76308	−0.881542	+	0.472106i	$0.843494\pi$
$908$	−2.10468e10	−0.933010
$909$	9.70007e9	0.428352
$910$	6.37118e9	0.280269
$911$	−3.78717e10	−1.65959	−0.829793	−	0.558071i	$-0.811542\pi$
$911$	−3.78717e10	−1.65959	−0.829793	+	0.558071i	$0.811542\pi$
$912$	2.92227e9	0.127567
$913$	2.30917e10	1.00417
$914$	1.90639e10	0.825848
$915$	8.76584e8	0.0378286
$916$	1.34302e10	0.577364
$917$	1.01447e10	0.434456
$918$	1.10064e9	0.0469563
$919$	−1.66526e10	−0.707746	−0.353873	−	0.935293i	$-0.615136\pi$
$919$	−1.66526e10	−0.707746	−0.353873	+	0.935293i	$0.615136\pi$
$920$	7.30588e10	3.09325
$921$	−1.95215e9	−0.0823390
$922$	−2.45860e10	−1.03307
$923$	−8.26200e9	−0.345843
$924$	3.03549e9	0.126583
$925$	−9.44433e9	−0.392351
$926$	−3.76534e10	−1.55835
$927$	−8.70054e9	−0.358730
$928$	−6.78135e8	−0.0278547
$929$	−9.92062e9	−0.405960	−0.202980	−	0.979183i	$-0.565063\pi$
$929$	−9.92062e9	−0.405960	−0.202980	+	0.979183i	$0.565063\pi$
$930$	−1.29530e10	−0.528056
$931$	3.36466e9	0.136652
$932$	−8.20532e10	−3.32002
$933$	2.65708e9	0.107107
$934$	3.60989e10	1.44971
$935$	−6.05006e9	−0.242058
$936$	−1.24465e10	−0.496114
$937$	−4.67128e10	−1.85501	−0.927507	−	0.373806i	$-0.878053\pi$
$937$	−4.67128e10	−1.85501	−0.927507	+	0.373806i	$0.878053\pi$
$938$	1.67826e10	0.663972
$939$	−9.85494e8	−0.0388440
$940$	−1.03219e11	−4.05335
$941$	−3.78424e10	−1.48052	−0.740261	−	0.672320i	$-0.765298\pi$
$941$	−3.78424e10	−1.48052	−0.740261	+	0.672320i	$0.765298\pi$
$942$	−9.90894e8	−0.0386233
$943$	3.68492e10	1.43099
$944$	−2.99583e10	−1.15909
$945$	−3.54502e9	−0.136649
$946$	4.79669e10	1.84214
$947$	1.23857e10	0.473909	0.236955	−	0.971521i	$-0.423851\pi$
$947$	1.23857e10	0.473909	0.236955	+	0.971521i	$0.423851\pi$
$948$	7.47685e9	0.285029
$949$	4.58946e8	0.0174313
$950$	5.95474e10	2.25336
$951$	1.07852e9	0.0406626
$952$	2.08491e9	0.0783172
$953$	−2.94194e10	−1.10105	−0.550527	−	0.834817i	$-0.685573\pi$
$953$	−2.94194e10	−1.10105	−0.550527	+	0.834817i	$0.685573\pi$
$954$	−3.37440e10	−1.25828
$955$	5.49870e10	2.04290
$956$	−5.72663e10	−2.11981
$957$	8.59995e8	0.0317179
$958$	−6.66396e10	−2.44880
$959$	−1.27966e10	−0.468520
$960$	4.35095e9	0.158721
$961$	4.86158e10	1.76704
$962$	−3.87836e9	−0.140454
$963$	−1.73202e10	−0.624973
$964$	4.39971e10	1.58181
$965$	6.90849e10	2.47478
$966$	2.43778e9	0.0870110
$967$	−2.84009e10	−1.01004	−0.505022	−	0.863107i	$-0.668516\pi$
$967$	−2.84009e10	−1.01004	−0.505022	+	0.863107i	$0.668516\pi$
$968$	4.66356e10	1.65255
$969$	−3.67377e8	−0.0129711
$970$	−1.31105e11	−4.61229
$971$	−1.34425e10	−0.471210	−0.235605	−	0.971849i	$-0.575707\pi$
$971$	−1.34425e10	−0.471210	−0.235605	+	0.971849i	$0.575707\pi$
$972$	2.04200e10	0.713222
$973$	1.53092e8	0.00532790
$974$	5.63154e10	1.95286
$975$	1.28755e9	0.0444884
$976$	−6.77863e9	−0.233382
$977$	−1.14812e9	−0.0393874	−0.0196937	−	0.999806i	$-0.506269\pi$
$977$	−1.14812e9	−0.0393874	−0.0196937	+	0.999806i	$0.506269\pi$
$978$	−3.66708e8	−0.0125353
$979$	6.88720e10	2.34587
$980$	−1.31691e10	−0.446954
$981$	−2.33828e10	−0.790780
$982$	3.98821e10	1.34396
$983$	2.86412e10	0.961730	0.480865	−	0.876795i	$-0.340323\pi$
$983$	2.86412e10	0.961730	0.480865	+	0.876795i	$0.340323\pi$
$984$	−8.28598e9	−0.277243
$985$	8.30153e10	2.76778
$986$	1.15837e9	0.0384837
$987$	−1.75627e9	−0.0581407
$988$	1.64109e10	0.541356
$989$	2.58523e10	0.849791
$990$	−1.11240e11	−3.64368
$991$	2.86118e10	0.933871	0.466935	−	0.884291i	$-0.345358\pi$
$991$	2.86118e10	0.933871	0.466935	+	0.884291i	$0.345358\pi$
$992$	7.37190e9	0.239767
$993$	3.76614e9	0.122060
$994$	2.54465e10	0.821817
$995$	5.73580e10	1.84592
$996$	−5.48808e9	−0.176000
$997$	6.11174e10	1.95313	0.976567	−	0.215215i	$-0.0690453\pi$
$997$	6.11174e10	1.95313	0.976567	+	0.215215i	$0.0690453\pi$
$998$	6.21786e10	1.98009
$999$	2.15798e9	0.0684807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.b.1.9	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.b.1.9	✓	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)

\(f(q)\)	\(=\)	\(q+19.7278 q^{2} +5.55266 q^{3} +261.185 q^{4} -428.566 q^{5} +109.542 q^{6} -343.000 q^{7} +2627.45 q^{8} -2156.17 q^{9} +O(q^{10})\)	\(q+19.7278 q^{2} +5.55266 q^{3} +261.185 q^{4} -428.566 q^{5} +109.542 q^{6} -343.000 q^{7} +2627.45 q^{8} -2156.17 q^{9} -8454.65 q^{10} -6102.17 q^{11} +1450.27 q^{12} +2197.00 q^{13} -6766.63 q^{14} -2379.68 q^{15} +18402.1 q^{16} -2313.44 q^{17} -42536.4 q^{18} +28599.2 q^{19} -111935. q^{20} -1904.56 q^{21} -120382. q^{22} -64881.5 q^{23} +14589.3 q^{24} +105544. q^{25} +43341.9 q^{26} -24116.1 q^{27} -89586.6 q^{28} -25381.1 q^{29} -46945.8 q^{30} +275914. q^{31} +26718.1 q^{32} -33883.3 q^{33} -45639.0 q^{34} +146998. q^{35} -563160. q^{36} -89482.8 q^{37} +564198. q^{38} +12199.2 q^{39} -1.12604e6 q^{40} -567947. q^{41} -37572.8 q^{42} -398454. q^{43} -1.59380e6 q^{44} +924060. q^{45} -1.27997e6 q^{46} +922136. q^{47} +102180. q^{48} +117649. q^{49} +2.08214e6 q^{50} -12845.7 q^{51} +573824. q^{52} +793297. q^{53} -475758. q^{54} +2.61518e6 q^{55} -901216. q^{56} +158801. q^{57} -500713. q^{58} -1.62799e6 q^{59} -621537. q^{60} -368362. q^{61} +5.44317e6 q^{62} +739566. q^{63} -1.82838e6 q^{64} -941559. q^{65} -668442. q^{66} -2.48020e6 q^{67} -604236. q^{68} -360265. q^{69} +2.89995e6 q^{70} -3.76058e6 q^{71} -5.66523e6 q^{72} +208897. q^{73} -1.76530e6 q^{74} +586047. q^{75} +7.46968e6 q^{76} +2.09305e6 q^{77} +240663. q^{78} +5.15548e6 q^{79} -7.88649e6 q^{80} +4.58163e6 q^{81} -1.12043e7 q^{82} -3.78417e6 q^{83} -497444. q^{84} +991459. q^{85} -7.86062e6 q^{86} -140933. q^{87} -1.60332e7 q^{88} -1.12865e7 q^{89} +1.82296e7 q^{90} -753571. q^{91} -1.69461e7 q^{92} +1.53206e6 q^{93} +1.81917e7 q^{94} -1.22566e7 q^{95} +148357. q^{96} +1.55068e7 q^{97} +2.32095e6 q^{98} +1.31573e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 5 q^{2} - 26 q^{3} + 393 q^{4} - 181 q^{5} + 703 q^{6} - 3087 q^{7} + 1197 q^{8} + 3211 q^{9}+O(q^{10}) \) 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

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