LMFDB - Embedded newform 91.8.a.b.1.2

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			1.2
Root			$-11.7379$ 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)

$f(q)$	$=$	$q-12.7379 q^{2} -48.2951 q^{3} +34.2551 q^{4} -506.573 q^{5} +615.180 q^{6} -343.000 q^{7} +1194.12 q^{8} +145.416 q^{9} +O(q^{10})$	\(q-12.7379 q^{2} -48.2951 q^{3} +34.2551 q^{4} -506.573 q^{5} +615.180 q^{6} -343.000 q^{7} +1194.12 q^{8} +145.416 q^{9} +6452.69 q^{10} +1352.60 q^{11} -1654.35 q^{12} +2197.00 q^{13} +4369.11 q^{14} +24465.0 q^{15} -19595.2 q^{16} +10549.6 q^{17} -1852.31 q^{18} +14208.4 q^{19} -17352.7 q^{20} +16565.2 q^{21} -17229.4 q^{22} -8973.52 q^{23} -57670.0 q^{24} +178491. q^{25} -27985.3 q^{26} +98598.5 q^{27} -11749.5 q^{28} -23816.2 q^{29} -311633. q^{30} +30954.1 q^{31} +96756.0 q^{32} -65324.1 q^{33} -134380. q^{34} +173754. q^{35} +4981.26 q^{36} -149814. q^{37} -180986. q^{38} -106104. q^{39} -604907. q^{40} +228713. q^{41} -211007. q^{42} -273187. q^{43} +46333.5 q^{44} -73664.0 q^{45} +114304. q^{46} -1.24344e6 q^{47} +946354. q^{48} +117649. q^{49} -2.27361e6 q^{50} -509493. q^{51} +75258.5 q^{52} -1.40014e6 q^{53} -1.25594e6 q^{54} -685191. q^{55} -409582. q^{56} -686196. q^{57} +303370. q^{58} +1.73935e6 q^{59} +838050. q^{60} +2.75981e6 q^{61} -394291. q^{62} -49877.9 q^{63} +1.27572e6 q^{64} -1.11294e6 q^{65} +832094. q^{66} +3.37432e6 q^{67} +361377. q^{68} +433377. q^{69} -2.21327e6 q^{70} -3.17998e6 q^{71} +173644. q^{72} +4.53392e6 q^{73} +1.90833e6 q^{74} -8.62024e6 q^{75} +486710. q^{76} -463943. q^{77} +1.35155e6 q^{78} -3.35790e6 q^{79} +9.92642e6 q^{80} -5.07985e6 q^{81} -2.91334e6 q^{82} +27902.9 q^{83} +567443. q^{84} -5.34413e6 q^{85} +3.47983e6 q^{86} +1.15021e6 q^{87} +1.61516e6 q^{88} +6.49633e6 q^{89} +938328. q^{90} -753571. q^{91} -307389. q^{92} -1.49493e6 q^{93} +1.58388e7 q^{94} -7.19758e6 q^{95} -4.67284e6 q^{96} +1.51501e7 q^{97} -1.49861e6 q^{98} +196691. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−12.7379	−1.12589	−0.562943	−	0.826496i	$-0.690331\pi$
$2$	−12.7379	−1.12589	−0.562943	+	0.826496i	$0.690331\pi$
$3$	−48.2951	−1.03271	−0.516355	−	0.856374i	$-0.672712\pi$
$3$	−48.2951	−1.03271	−0.516355	+	0.856374i	$0.672712\pi$
$4$	34.2551	0.267618
$5$	−506.573	−1.81237	−0.906185	−	0.422882i	$-0.861019\pi$
$5$	−506.573	−1.81237	−0.906185	+	0.422882i	$0.861019\pi$
$6$	615.180	1.16271
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	1194.12	0.824578
$9$	145.416	0.0664913
$10$	6452.69	2.04052
$11$	1352.60	0.306405	0.153202	−	0.988195i	$-0.451041\pi$
$11$	1352.60	0.306405	0.153202	+	0.988195i	$0.451041\pi$
$12$	−1654.35	−0.276372
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	4369.11	0.425545
$15$	24465.0	1.87165
$16$	−19595.2	−1.19600
$17$	10549.6	0.520791	0.260396	−	0.965502i	$-0.416147\pi$
$17$	10549.6	0.520791	0.260396	+	0.965502i	$0.416147\pi$
$18$	−1852.31	−0.0748616
$19$	14208.4	0.475234	0.237617	−	0.971359i	$-0.423634\pi$
$19$	14208.4	0.475234	0.237617	+	0.971359i	$0.423634\pi$
$20$	−17352.7	−0.485023
$21$	16565.2	0.390328
$22$	−17229.4	−0.344977
$23$	−8973.52	−0.153785	−0.0768927	−	0.997039i	$-0.524500\pi$
$23$	−8973.52	−0.153785	−0.0768927	+	0.997039i	$0.524500\pi$
$24$	−57670.0	−0.851551
$25$	178491.	2.28468
$26$	−27985.3	−0.312264
$27$	98598.5	0.964044
$28$	−11749.5	−0.101150
$29$	−23816.2	−0.181334	−0.0906672	−	0.995881i	$-0.528900\pi$
$29$	−23816.2	−0.181334	−0.0906672	+	0.995881i	$0.528900\pi$
$30$	−311633.	−2.10727
$31$	30954.1	0.186617	0.0933087	−	0.995637i	$-0.470256\pi$
$31$	30954.1	0.186617	0.0933087	+	0.995637i	$0.470256\pi$
$32$	96756.0	0.521979
$33$	−65324.1	−0.316428
$34$	−134380.	−0.586351
$35$	173754.	0.685011
$36$	4981.26	0.0177943
$37$	−149814.	−0.486236	−0.243118	−	0.969997i	$-0.578170\pi$
$37$	−149814.	−0.486236	−0.243118	+	0.969997i	$0.578170\pi$
$38$	−180986.	−0.535059
$39$	−106104.	−0.286422
$40$	−604907.	−1.49444
$41$	228713.	0.518261	0.259130	−	0.965842i	$-0.416564\pi$
$41$	228713.	0.518261	0.259130	+	0.965842i	$0.416564\pi$
$42$	−211007.	−0.439465
$43$	−273187.	−0.523986	−0.261993	−	0.965070i	$-0.584380\pi$
$43$	−273187.	−0.523986	−0.261993	+	0.965070i	$0.584380\pi$
$44$	46333.5	0.0819995
$45$	−73664.0	−0.120507
$46$	114304.	0.173145
$47$	−1.24344e6	−1.74696	−0.873478	−	0.486864i	$-0.838141\pi$
$47$	−1.24344e6	−1.74696	−0.873478	+	0.486864i	$0.838141\pi$
$48$	946354.	1.23512
$49$	117649.	0.142857
$50$	−2.27361e6	−2.57229
$51$	−509493.	−0.537827
$52$	75258.5	0.0742239
$53$	−1.40014e6	−1.29183	−0.645914	−	0.763410i	$-0.723523\pi$
$53$	−1.40014e6	−1.29183	−0.645914	+	0.763410i	$0.723523\pi$
$54$	−1.25594e6	−1.08540
$55$	−685191.	−0.555319
$56$	−409582.	−0.311661
$57$	−686196.	−0.490779
$58$	303370.	0.204162
$59$	1.73935e6	1.10257	0.551283	−	0.834318i	$-0.314138\pi$
$59$	1.73935e6	1.10257	0.551283	+	0.834318i	$0.314138\pi$
$60$	838050.	0.500888
$61$	2.75981e6	1.55677	0.778386	−	0.627786i	$-0.216039\pi$
$61$	2.75981e6	1.55677	0.778386	+	0.627786i	$0.216039\pi$
$62$	−394291.	−0.210110
$63$	−49877.9	−0.0251314
$64$	1.27572e6	0.608310
$65$	−1.11294e6	−0.502661
$66$	832094.	0.356261
$67$	3.37432e6	1.37064	0.685322	−	0.728240i	$-0.259661\pi$
$67$	3.37432e6	1.37064	0.685322	+	0.728240i	$0.259661\pi$
$68$	361377.	0.139373
$69$	433377.	0.158816
$70$	−2.21327e6	−0.771244
$71$	−3.17998e6	−1.05444	−0.527219	−	0.849730i	$-0.676765\pi$
$71$	−3.17998e6	−1.05444	−0.527219	+	0.849730i	$0.676765\pi$
$72$	173644.	0.0548273
$73$	4.53392e6	1.36409	0.682047	−	0.731309i	$-0.261090\pi$
$73$	4.53392e6	1.36409	0.682047	+	0.731309i	$0.261090\pi$
$74$	1.90833e6	0.547446
$75$	−8.62024e6	−2.35942
$76$	486710.	0.127181
$77$	−463943.	−0.115810
$78$	1.35155e6	0.322479
$79$	−3.35790e6	−0.766255	−0.383127	−	0.923696i	$-0.625153\pi$
$79$	−3.35790e6	−0.766255	−0.383127	+	0.923696i	$0.625153\pi$
$80$	9.92642e6	2.16759
$81$	−5.07985e6	−1.06207
$82$	−2.91334e6	−0.583502
$83$	27902.9	0.00535644	0.00267822	−	0.999996i	$-0.499147\pi$
$83$	27902.9	0.00535644	0.00267822	+	0.999996i	$0.499147\pi$
$84$	567443.	0.104459
$85$	−5.34413e6	−0.943867
$86$	3.47983e6	0.589948
$87$	1.15021e6	0.187266
$88$	1.61516e6	0.252655
$89$	6.49633e6	0.976794	0.488397	−	0.872622i	$-0.337582\pi$
$89$	6.49633e6	0.976794	0.488397	+	0.872622i	$0.337582\pi$
$90$	938328.	0.135677
$91$	−753571.	−0.104828
$92$	−307389.	−0.0411558
$93$	−1.49493e6	−0.192722
$94$	1.58388e7	1.96687
$95$	−7.19758e6	−0.861299
$96$	−4.67284e6	−0.539053
$97$	1.51501e7	1.68544	0.842721	−	0.538350i	$-0.180952\pi$
$97$	1.51501e7	1.68544	0.842721	+	0.538350i	$0.180952\pi$
$98$	−1.49861e6	−0.160841
$99$	196691.	0.0203733
$100$	6.11423e6	0.611423
$101$	−1.24987e7	−1.20709	−0.603545	−	0.797329i	$-0.706246\pi$
$101$	−1.24987e7	−1.20709	−0.603545	+	0.797329i	$0.706246\pi$
$102$	6.48989e6	0.605531
$103$	1.38337e7	1.24741	0.623705	−	0.781660i	$-0.285627\pi$
$103$	1.38337e7	1.24741	0.623705	+	0.781660i	$0.285627\pi$
$104$	2.62347e6	0.228697
$105$	−8.39149e6	−0.707419
$106$	1.78348e7	1.45445
$107$	1.36810e7	1.07963	0.539813	−	0.841785i	$-0.318495\pi$
$107$	1.36810e7	1.07963	0.539813	+	0.841785i	$0.318495\pi$
$108$	3.37750e6	0.257996
$109$	−9.05114e6	−0.669438	−0.334719	−	0.942318i	$-0.608641\pi$
$109$	−9.05114e6	−0.669438	−0.334719	+	0.942318i	$0.608641\pi$
$110$	8.72793e6	0.625226
$111$	7.23530e6	0.502141
$112$	6.72117e6	0.452045
$113$	1.46842e7	0.957363	0.478682	−	0.877988i	$-0.341115\pi$
$113$	1.46842e7	0.957363	0.478682	+	0.877988i	$0.341115\pi$
$114$	8.74072e6	0.552561
$115$	4.54574e6	0.278716
$116$	−815828.	−0.0485284
$117$	319480.	0.0184414
$118$	−2.21557e7	−1.24136
$119$	−3.61850e6	−0.196841
$120$	2.92140e7	1.54332
$121$	−1.76576e7	−0.906116
$122$	−3.51543e7	−1.75275
$123$	−1.10457e7	−0.535213
$124$	1.06034e6	0.0499422
$125$	−5.08427e7	−2.32832
$126$	635341.	0.0282950
$127$	1.19573e7	0.517990	0.258995	−	0.965879i	$-0.416609\pi$
$127$	1.19573e7	0.517990	0.258995	+	0.965879i	$0.416609\pi$
$128$	−2.86348e7	−1.20687
$129$	1.31936e7	0.541126
$130$	1.41766e7	0.565939
$131$	−1.38918e7	−0.539894	−0.269947	−	0.962875i	$-0.587006\pi$
$131$	−1.38918e7	−0.539894	−0.269947	+	0.962875i	$0.587006\pi$
$132$	−2.23768e6	−0.0846817
$133$	−4.87348e6	−0.179621
$134$	−4.29819e7	−1.54319
$135$	−4.99473e7	−1.74720
$136$	1.25974e7	0.429433
$137$	−2.41193e7	−0.801387	−0.400694	−	0.916212i	$-0.631231\pi$
$137$	−2.41193e7	−0.801387	−0.400694	+	0.916212i	$0.631231\pi$
$138$	−5.52033e6	−0.178808
$139$	−5.30983e7	−1.67698	−0.838491	−	0.544915i	$-0.816562\pi$
$139$	−5.30983e7	−1.67698	−0.838491	+	0.544915i	$0.816562\pi$
$140$	5.95198e6	0.183321
$141$	6.00520e7	1.80410
$142$	4.05064e7	1.18718
$143$	2.97167e6	0.0849814
$144$	−2.84947e6	−0.0795235
$145$	1.20647e7	0.328645
$146$	−5.77528e7	−1.53581
$147$	−5.68187e6	−0.147530
$148$	−5.13191e6	−0.130126
$149$	−185227.	−0.00458725	−0.00229362	−	0.999997i	$-0.500730\pi$
$149$	−185227.	−0.00458725	−0.00229362	+	0.999997i	$0.500730\pi$
$150$	1.09804e8	2.65643
$151$	−3.94267e7	−0.931905	−0.465952	−	0.884810i	$-0.654288\pi$
$151$	−3.94267e7	−0.931905	−0.465952	+	0.884810i	$0.654288\pi$
$152$	1.69665e7	0.391867
$153$	1.53408e6	0.0346281
$154$	5.90967e6	0.130389
$155$	−1.56805e7	−0.338220
$156$	−3.63461e6	−0.0766518
$157$	8.66429e7	1.78683	0.893417	−	0.449228i	$-0.148301\pi$
$157$	8.66429e7	1.78683	0.893417	+	0.449228i	$0.148301\pi$
$158$	4.27727e7	0.862715
$159$	6.76197e7	1.33408
$160$	−4.90140e7	−0.946019
$161$	3.07792e6	0.0581254
$162$	6.47068e7	1.19577
$163$	−3.66794e7	−0.663385	−0.331693	−	0.943388i	$-0.607620\pi$
$163$	−3.66794e7	−0.663385	−0.331693	+	0.943388i	$0.607620\pi$
$164$	7.83460e6	0.138696
$165$	3.30914e7	0.573484
$166$	−355426.	−0.00603074
$167$	−2.76739e7	−0.459794	−0.229897	−	0.973215i	$-0.573839\pi$
$167$	−2.76739e7	−0.459794	−0.229897	+	0.973215i	$0.573839\pi$
$168$	1.97808e7	0.321856
$169$	4.82681e6	0.0769231
$170$	6.80732e7	1.06269
$171$	2.06613e6	0.0315989
$172$	−9.35804e6	−0.140228
$173$	−1.02168e8	−1.50022	−0.750108	−	0.661315i	$-0.769999\pi$
$173$	−1.02168e8	−1.50022	−0.750108	+	0.661315i	$0.769999\pi$
$174$	−1.46513e7	−0.210840
$175$	−6.12224e7	−0.863530
$176$	−2.65046e7	−0.366460
$177$	−8.40020e7	−1.13863
$178$	−8.27498e7	−1.09976
$179$	−4.99917e7	−0.651497	−0.325748	−	0.945456i	$-0.605616\pi$
$179$	−4.99917e7	−0.651497	−0.325748	+	0.945456i	$0.605616\pi$
$180$	−2.52337e6	−0.0322498
$181$	−1.36188e8	−1.70712	−0.853562	−	0.520992i	$-0.825562\pi$
$181$	−1.36188e8	−1.70712	−0.853562	+	0.520992i	$0.825562\pi$
$182$	9.59894e6	0.118025
$183$	−1.33285e8	−1.60770
$184$	−1.07154e7	−0.126808
$185$	7.58919e7	0.881240
$186$	1.90423e7	0.216983
$187$	1.42694e7	0.159573
$188$	−4.25941e7	−0.467517
$189$	−3.38193e7	−0.364375
$190$	9.16824e7	0.969724
$191$	9.02332e7	0.937021	0.468511	−	0.883458i	$-0.344791\pi$
$191$	9.02332e7	0.937021	0.468511	+	0.883458i	$0.344791\pi$
$192$	−6.16109e7	−0.628208
$193$	1.37689e8	1.37863	0.689317	−	0.724460i	$-0.257911\pi$
$193$	1.37689e8	1.37863	0.689317	+	0.724460i	$0.257911\pi$
$194$	−1.92981e8	−1.89761
$195$	5.37496e7	0.519103
$196$	4.03008e6	0.0382311
$197$	1.35026e8	1.25830	0.629152	−	0.777282i	$-0.283402\pi$
$197$	1.35026e8	1.25830	0.629152	+	0.777282i	$0.283402\pi$
$198$	−2.50543e6	−0.0229380
$199$	3.70999e7	0.333723	0.166862	−	0.985980i	$-0.446637\pi$
$199$	3.70999e7	0.333723	0.166862	+	0.985980i	$0.446637\pi$
$200$	2.13139e8	1.88390
$201$	−1.62963e8	−1.41548
$202$	1.59208e8	1.35905
$203$	8.16897e6	0.0685380
$204$	−1.74527e7	−0.143932
$205$	−1.15860e8	−0.939280
$206$	−1.76213e8	−1.40444
$207$	−1.30490e6	−0.0102254
$208$	−4.30507e7	−0.331710
$209$	1.92183e7	0.145614
$210$	1.06890e8	0.796472
$211$	−3.86260e7	−0.283068	−0.141534	−	0.989933i	$-0.545203\pi$
$211$	−3.86260e7	−0.283068	−0.141534	+	0.989933i	$0.545203\pi$
$212$	−4.79618e7	−0.345716
$213$	1.53578e8	1.08893
$214$	−1.74267e8	−1.21553
$215$	1.38389e8	0.949657
$216$	1.17738e8	0.794930
$217$	−1.06172e7	−0.0705347
$218$	1.15293e8	0.753711
$219$	−2.18966e8	−1.40871
$220$	−2.34713e7	−0.148613
$221$	2.31774e7	0.144442
$222$	−9.21628e7	−0.565354
$223$	1.12450e8	0.679035	0.339517	−	0.940600i	$-0.389736\pi$
$223$	1.12450e8	0.679035	0.339517	+	0.940600i	$0.389736\pi$
$224$	−3.31873e7	−0.197290
$225$	2.59555e7	0.151912
$226$	−1.87047e8	−1.07788
$227$	−1.20984e8	−0.686495	−0.343248	−	0.939245i	$-0.611527\pi$
$227$	−1.20984e8	−0.686495	−0.343248	+	0.939245i	$0.611527\pi$
$228$	−2.35057e7	−0.131341
$229$	−1.89671e8	−1.04370	−0.521850	−	0.853037i	$-0.674758\pi$
$229$	−1.89671e8	−1.04370	−0.521850	+	0.853037i	$0.674758\pi$
$230$	−5.79034e7	−0.313802
$231$	2.24061e7	0.119598
$232$	−2.84394e7	−0.149524
$233$	−1.95446e8	−1.01224	−0.506118	−	0.862464i	$-0.668920\pi$
$233$	−1.95446e8	−1.01224	−0.506118	+	0.862464i	$0.668920\pi$
$234$	−4.06952e6	−0.0207629
$235$	6.29892e8	3.16613
$236$	5.95816e7	0.295067
$237$	1.62170e8	0.791319
$238$	4.60923e7	0.221620
$239$	3.22577e8	1.52841	0.764206	−	0.644972i	$-0.223131\pi$
$239$	3.22577e8	1.52841	0.764206	+	0.644972i	$0.223131\pi$
$240$	−4.79397e8	−2.23850
$241$	9.27797e7	0.426966	0.213483	−	0.976947i	$-0.431519\pi$
$241$	9.27797e7	0.426966	0.213483	+	0.976947i	$0.431519\pi$
$242$	2.24922e8	1.02018
$243$	2.96969e7	0.132767
$244$	9.45377e7	0.416620
$245$	−5.95978e7	−0.258910
$246$	1.40700e8	0.602589
$247$	3.12158e7	0.131806
$248$	3.69628e7	0.153881
$249$	−1.34757e6	−0.00553165
$250$	6.47631e8	2.62143
$251$	−2.72214e8	−1.08656	−0.543278	−	0.839553i	$-0.682817\pi$
$251$	−2.72214e8	−1.08656	−0.543278	+	0.839553i	$0.682817\pi$
$252$	−1.70857e6	−0.00672560
$253$	−1.21376e7	−0.0471206
$254$	−1.52312e8	−0.583197
$255$	2.58095e8	0.974741
$256$	2.01456e8	0.750483
$257$	−1.78994e8	−0.657768	−0.328884	−	0.944370i	$-0.606673\pi$
$257$	−1.78994e8	−0.657768	−0.328884	+	0.944370i	$0.606673\pi$
$258$	−1.68059e8	−0.609246
$259$	5.13863e7	0.183780
$260$	−3.81239e7	−0.134521
$261$	−3.46327e6	−0.0120572
$262$	1.76953e8	0.607859
$263$	−1.77354e8	−0.601168	−0.300584	−	0.953755i	$-0.597182\pi$
$263$	−1.77354e8	−0.601168	−0.300584	+	0.953755i	$0.597182\pi$
$264$	−7.80045e7	−0.260919
$265$	7.09270e8	2.34127
$266$	6.20781e7	0.202233
$267$	−3.13741e8	−1.00875
$268$	1.15588e8	0.366809
$269$	−2.34198e8	−0.733584	−0.366792	−	0.930303i	$-0.619544\pi$
$269$	−2.34198e8	−0.733584	−0.366792	+	0.930303i	$0.619544\pi$
$270$	6.36226e8	1.96715
$271$	4.86888e8	1.48606	0.743031	−	0.669257i	$-0.233388\pi$
$271$	4.86888e8	1.48606	0.743031	+	0.669257i	$0.233388\pi$
$272$	−2.06722e8	−0.622866
$273$	3.63938e7	0.108257
$274$	3.07230e8	0.902270
$275$	2.41427e8	0.700038
$276$	1.48454e7	0.0425020
$277$	−3.11143e8	−0.879591	−0.439795	−	0.898098i	$-0.644949\pi$
$277$	−3.11143e8	−0.879591	−0.439795	+	0.898098i	$0.644949\pi$
$278$	6.76362e8	1.88809
$279$	4.50123e6	0.0124084
$280$	2.07483e8	0.564845
$281$	−5.72605e8	−1.53951	−0.769756	−	0.638338i	$-0.779622\pi$
$281$	−5.72605e8	−1.53951	−0.769756	+	0.638338i	$0.779622\pi$
$282$	−7.64939e8	−2.03121
$283$	5.38922e8	1.41343	0.706714	−	0.707499i	$-0.250177\pi$
$283$	5.38922e8	1.41343	0.706714	+	0.707499i	$0.250177\pi$
$284$	−1.08931e8	−0.282186
$285$	3.47608e8	0.889473
$286$	−3.78529e7	−0.0956793
$287$	−7.84487e7	−0.195884
$288$	1.40699e7	0.0347071
$289$	−2.99045e8	−0.728776
$290$	−1.53679e8	−0.370017
$291$	−7.31675e8	−1.74057
$292$	1.55310e8	0.365056
$293$	−4.77980e8	−1.11013	−0.555064	−	0.831807i	$-0.687306\pi$
$293$	−4.77980e8	−1.11013	−0.555064	+	0.831807i	$0.687306\pi$
$294$	7.23753e7	0.166102
$295$	−8.81107e8	−1.99826
$296$	−1.78896e8	−0.400940
$297$	1.33365e8	0.295388
$298$	2.35941e6	0.00516472
$299$	−1.97148e7	−0.0426524
$300$	−2.95287e8	−0.631423
$301$	9.37030e7	0.198048
$302$	5.02215e8	1.04922
$303$	6.03626e8	1.24658
$304$	−2.78417e8	−0.568379
$305$	−1.39805e9	−2.82145
$306$	−1.95410e7	−0.0389873
$307$	8.72777e8	1.72155	0.860774	−	0.508988i	$-0.169980\pi$
$307$	8.72777e8	1.72155	0.860774	+	0.508988i	$0.169980\pi$
$308$	−1.58924e7	−0.0309929
$309$	−6.68102e8	−1.28821
$310$	1.99737e8	0.380797
$311$	4.89634e8	0.923018	0.461509	−	0.887136i	$-0.347308\pi$
$311$	4.89634e8	0.923018	0.461509	+	0.887136i	$0.347308\pi$
$312$	−1.26701e8	−0.236178
$313$	−3.85929e8	−0.711381	−0.355691	−	0.934604i	$-0.615754\pi$
$313$	−3.85929e8	−0.711381	−0.355691	+	0.934604i	$0.615754\pi$
$314$	−1.10365e9	−2.01177
$315$	2.52668e7	0.0455473
$316$	−1.15025e8	−0.205064
$317$	−4.06719e8	−0.717112	−0.358556	−	0.933508i	$-0.616731\pi$
$317$	−4.06719e8	−0.717112	−0.358556	+	0.933508i	$0.616731\pi$
$318$	−8.61335e8	−1.50203
$319$	−3.22139e7	−0.0555618
$320$	−6.46244e8	−1.10248
$321$	−6.60723e8	−1.11494
$322$	−3.92063e7	−0.0654426
$323$	1.49893e8	0.247498
$324$	−1.74011e8	−0.284229
$325$	3.92145e8	0.633657
$326$	4.67220e8	0.746896
$327$	4.37126e8	0.691336
$328$	2.73111e8	0.427346
$329$	4.26500e8	0.660287
$330$	−4.21516e8	−0.645677
$331$	−9.08264e8	−1.37662	−0.688310	−	0.725416i	$-0.741647\pi$
$331$	−9.08264e8	−1.37662	−0.688310	+	0.725416i	$0.741647\pi$
$332$	955817.	0.00143348
$333$	−2.17855e7	−0.0323305
$334$	3.52509e8	0.517675
$335$	−1.70934e9	−2.48411
$336$	−3.24599e8	−0.466832
$337$	1.32075e8	0.187981	0.0939907	−	0.995573i	$-0.470038\pi$
$337$	1.32075e8	0.187981	0.0939907	+	0.995573i	$0.470038\pi$
$338$	−6.14836e7	−0.0866066
$339$	−7.09177e8	−0.988679
$340$	−1.83064e8	−0.252596
$341$	4.18686e7	0.0571805
$342$	−2.63183e7	−0.0355768
$343$	−4.03536e7	−0.0539949
$344$	−3.26217e8	−0.432068
$345$	−2.19537e8	−0.287833
$346$	1.30141e9	1.68907
$347$	3.83825e8	0.493151	0.246576	−	0.969124i	$-0.420695\pi$
$347$	3.83825e8	0.493151	0.246576	+	0.969124i	$0.420695\pi$
$348$	3.94005e7	0.0501158
$349$	−5.21822e8	−0.657103	−0.328551	−	0.944486i	$-0.606560\pi$
$349$	−5.21822e8	−0.657103	−0.328551	+	0.944486i	$0.606560\pi$
$350$	7.79847e8	0.972235
$351$	2.16621e8	0.267378
$352$	1.30872e8	0.159937
$353$	6.08680e8	0.736508	0.368254	−	0.929725i	$-0.379956\pi$
$353$	6.08680e8	0.736508	0.368254	+	0.929725i	$0.379956\pi$
$354$	1.07001e9	1.28197
$355$	1.61089e9	1.91103
$356$	2.22532e8	0.261408
$357$	1.74756e8	0.203279
$358$	6.36791e8	0.733511
$359$	−2.43667e7	−0.0277950	−0.0138975	−	0.999903i	$-0.504424\pi$
$359$	−2.43667e7	−0.0277950	−0.0138975	+	0.999903i	$0.504424\pi$
$360$	−8.79635e7	−0.0993673
$361$	−6.91993e8	−0.774153
$362$	1.73476e9	1.92203
$363$	8.52777e8	0.935756
$364$	−2.58137e7	−0.0280540
$365$	−2.29676e9	−2.47224
$366$	1.69778e9	1.81008
$367$	−1.16862e9	−1.23407	−0.617037	−	0.786934i	$-0.711667\pi$
$367$	−1.16862e9	−1.23407	−0.617037	+	0.786934i	$0.711667\pi$
$368$	1.75838e8	0.183927
$369$	3.32587e7	0.0344598
$370$	−9.66706e8	−0.992175
$371$	4.80246e8	0.488265
$372$	−5.12090e7	−0.0515758
$373$	2.21325e8	0.220825	0.110413	−	0.993886i	$-0.464783\pi$
$373$	2.21325e8	0.220825	0.110413	+	0.993886i	$0.464783\pi$
$374$	−1.81763e8	−0.179661
$375$	2.45545e9	2.40448
$376$	−1.48481e9	−1.44050
$377$	−5.23243e7	−0.0502931
$378$	4.30788e8	0.410244
$379$	1.18354e9	1.11672	0.558361	−	0.829598i	$-0.311430\pi$
$379$	1.18354e9	1.11672	0.558361	+	0.829598i	$0.311430\pi$
$380$	−2.46554e8	−0.230499
$381$	−5.77481e8	−0.534934
$382$	−1.14938e9	−1.05498
$383$	4.83941e8	0.440146	0.220073	−	0.975483i	$-0.429370\pi$
$383$	4.83941e8	0.440146	0.220073	+	0.975483i	$0.429370\pi$
$384$	1.38292e9	1.24634
$385$	2.35021e8	0.209891
$386$	−1.75387e9	−1.55218
$387$	−3.97258e7	−0.0348405
$388$	5.18968e8	0.451055
$389$	−2.19180e9	−1.88789	−0.943945	−	0.330102i	$-0.892917\pi$
$389$	−2.19180e9	−1.88789	−0.943945	+	0.330102i	$0.892917\pi$
$390$	−6.84659e8	−0.584451
$391$	−9.46668e7	−0.0800901
$392$	1.40487e8	0.117797
$393$	6.70905e8	0.557554
$394$	−1.71995e9	−1.41671
$395$	1.70102e9	1.38874
$396$	6.73766e6	0.00545225
$397$	1.41026e9	1.13118	0.565589	−	0.824687i	$-0.308649\pi$
$397$	1.41026e9	1.13118	0.565589	+	0.824687i	$0.308649\pi$
$398$	−4.72576e8	−0.375734
$399$	2.35365e8	0.185497
$400$	−3.49757e9	−2.73248
$401$	1.44678e9	1.12046	0.560230	−	0.828337i	$-0.310713\pi$
$401$	1.44678e9	1.12046	0.560230	+	0.828337i	$0.310713\pi$
$402$	2.07582e9	1.59367
$403$	6.80061e7	0.0517583
$404$	−4.28144e8	−0.323039
$405$	2.57331e9	1.92486
$406$	−1.04056e8	−0.0771659
$407$	−2.02639e8	−0.148985
$408$	−6.08394e8	−0.443480
$409$	2.05610e9	1.48598	0.742991	−	0.669301i	$-0.233406\pi$
$409$	2.05610e9	1.48598	0.742991	+	0.669301i	$0.233406\pi$
$410$	1.47582e9	1.05752
$411$	1.16484e9	0.827601
$412$	4.73876e8	0.333829
$413$	−5.96597e8	−0.416731
$414$	1.66217e7	0.0115126
$415$	−1.41349e7	−0.00970785
$416$	2.12573e8	0.144771
$417$	2.56439e9	1.73184
$418$	−2.44802e8	−0.163945
$419$	−6.51972e8	−0.432992	−0.216496	−	0.976284i	$-0.569463\pi$
$419$	−6.51972e8	−0.432992	−0.216496	+	0.976284i	$0.569463\pi$
$420$	−2.87451e8	−0.189318
$421$	−4.66558e8	−0.304732	−0.152366	−	0.988324i	$-0.548689\pi$
$421$	−4.66558e8	−0.304732	−0.152366	+	0.988324i	$0.548689\pi$
$422$	4.92015e8	0.318702
$423$	−1.80817e8	−0.116157
$424$	−1.67193e9	−1.06521
$425$	1.88300e9	1.18984
$426$	−1.95626e9	−1.22601
$427$	−9.46616e8	−0.588405
$428$	4.68643e8	0.288927
$429$	−1.43517e8	−0.0877612
$430$	−1.76279e9	−1.06920
$431$	7.84003e7	0.0471680	0.0235840	−	0.999722i	$-0.492492\pi$
$431$	7.84003e7	0.0471680	0.0235840	+	0.999722i	$0.492492\pi$
$432$	−1.93206e9	−1.15300
$433$	−4.58045e8	−0.271144	−0.135572	−	0.990767i	$-0.543287\pi$
$433$	−4.58045e8	−0.271144	−0.135572	+	0.990767i	$0.543287\pi$
$434$	1.35242e8	0.0794140
$435$	−5.82664e8	−0.339395
$436$	−3.10048e8	−0.179154
$437$	−1.27499e8	−0.0730840
$438$	2.78918e9	1.58605
$439$	1.85433e9	1.04607	0.523035	−	0.852311i	$-0.324800\pi$
$439$	1.85433e9	1.04607	0.523035	+	0.852311i	$0.324800\pi$
$440$	−8.18199e8	−0.457904
$441$	1.71081e7	0.00949876
$442$	−2.95233e8	−0.162625
$443$	9.42961e8	0.515325	0.257662	−	0.966235i	$-0.417048\pi$
$443$	9.42961e8	0.515325	0.257662	+	0.966235i	$0.417048\pi$
$444$	2.47846e8	0.134382
$445$	−3.29086e9	−1.77031
$446$	−1.43238e9	−0.764516
$447$	8.94555e6	0.00473730
$448$	−4.37571e8	−0.229920
$449$	−1.75008e8	−0.0912421	−0.0456210	−	0.998959i	$-0.514527\pi$
$449$	−1.75008e8	−0.0912421	−0.0456210	+	0.998959i	$0.514527\pi$
$450$	−3.30620e8	−0.171035
$451$	3.09358e8	0.158798
$452$	5.03010e8	0.256208
$453$	1.90412e9	0.962388
$454$	1.54109e9	0.772915
$455$	3.81739e8	0.189988
$456$	−8.19398e8	−0.404686
$457$	1.26386e8	0.0619428	0.0309714	−	0.999520i	$-0.490140\pi$
$457$	1.26386e8	0.0619428	0.0309714	+	0.999520i	$0.490140\pi$
$458$	2.41601e9	1.17509
$459$	1.04017e9	0.502066
$460$	1.55715e8	0.0745895
$461$	3.35390e9	1.59440	0.797199	−	0.603716i	$-0.206314\pi$
$461$	3.35390e9	1.59440	0.797199	+	0.603716i	$0.206314\pi$
$462$	−2.85408e8	−0.134654
$463$	3.09786e9	1.45054	0.725268	−	0.688467i	$-0.241716\pi$
$463$	3.09786e9	1.45054	0.725268	+	0.688467i	$0.241716\pi$
$464$	4.66685e8	0.216876
$465$	7.57291e8	0.349283
$466$	2.48958e9	1.13966
$467$	−7.83551e8	−0.356007	−0.178003	−	0.984030i	$-0.556964\pi$
$467$	−7.83551e8	−0.356007	−0.178003	+	0.984030i	$0.556964\pi$
$468$	1.09438e7	0.00493524
$469$	−1.15739e9	−0.518055
$470$	−8.02353e9	−3.56470
$471$	−4.18443e9	−1.84528
$472$	2.07699e9	0.909152
$473$	−3.69513e8	−0.160552
$474$	−2.06571e9	−0.890935
$475$	2.53607e9	1.08576
$476$	−1.23952e8	−0.0526781
$477$	−2.03603e8	−0.0858953
$478$	−4.10896e9	−1.72082
$479$	1.15860e9	0.481681	0.240841	−	0.970565i	$-0.422577\pi$
$479$	1.15860e9	0.481681	0.240841	+	0.970565i	$0.422577\pi$
$480$	2.36713e9	0.976964
$481$	−3.29142e8	−0.134858
$482$	−1.18182e9	−0.480715
$483$	−1.48648e8	−0.0600268
$484$	−6.04864e8	−0.242493
$485$	−7.67462e9	−3.05464
$486$	−3.78278e8	−0.149480
$487$	−4.60255e9	−1.80571	−0.902853	−	0.429948i	$-0.858532\pi$
$487$	−4.60255e9	−1.80571	−0.902853	+	0.429948i	$0.858532\pi$
$488$	3.29554e9	1.28368
$489$	1.77144e9	0.685085
$490$	7.59153e8	0.291503
$491$	3.93309e9	1.49951	0.749753	−	0.661718i	$-0.230172\pi$
$491$	3.93309e9	1.49951	0.749753	+	0.661718i	$0.230172\pi$
$492$	−3.78373e8	−0.143233
$493$	−2.51251e8	−0.0944374
$494$	−3.97625e8	−0.148399
$495$	−9.96381e7	−0.0369239
$496$	−6.06553e8	−0.223194
$497$	1.09073e9	0.398540
$498$	1.71653e7	0.00622801
$499$	−6.20501e8	−0.223558	−0.111779	−	0.993733i	$-0.535655\pi$
$499$	−6.20501e8	−0.223558	−0.111779	+	0.993733i	$0.535655\pi$
$500$	−1.74162e9	−0.623101
$501$	1.33651e9	0.474834
$502$	3.46744e9	1.22334
$503$	−4.59717e9	−1.61065	−0.805327	−	0.592830i	$-0.798010\pi$
$503$	−4.59717e9	−1.61065	−0.805327	+	0.592830i	$0.798010\pi$
$504$	−5.95600e7	−0.0207228
$505$	6.33150e9	2.18769
$506$	1.54608e8	0.0530524
$507$	−2.33111e8	−0.0794393
$508$	4.09600e8	0.138623
$509$	−1.19648e9	−0.402154	−0.201077	−	0.979575i	$-0.564444\pi$
$509$	−1.19648e9	−0.402154	−0.201077	+	0.979575i	$0.564444\pi$
$510$	−3.28760e9	−1.09745
$511$	−1.55514e9	−0.515579
$512$	1.09911e9	0.361908
$513$	1.40093e9	0.458146
$514$	2.28002e9	0.740571
$515$	−7.00779e9	−2.26077
$516$	4.51947e8	0.144815
$517$	−1.68188e9	−0.535276
$518$	−6.54556e8	−0.206915
$519$	4.93422e9	1.54929
$520$	−1.32898e9	−0.414483
$521$	−3.94765e9	−1.22294	−0.611472	−	0.791266i	$-0.709422\pi$
$521$	−3.94765e9	−1.22294	−0.611472	+	0.791266i	$0.709422\pi$
$522$	4.41150e7	0.0135750
$523$	−1.89006e9	−0.577724	−0.288862	−	0.957371i	$-0.593277\pi$
$523$	−1.89006e9	−0.577724	−0.288862	+	0.957371i	$0.593277\pi$
$524$	−4.75865e8	−0.144485
$525$	2.95674e9	0.891776
$526$	2.25913e9	0.676847
$527$	3.26552e8	0.0971887
$528$	1.28004e9	0.378447
$529$	−3.32430e9	−0.976350
$530$	−9.03464e9	−2.63600
$531$	2.52930e8	0.0733111
$532$	−1.66941e8	−0.0480699
$533$	5.02484e8	0.143740
$534$	3.99641e9	1.13573
$535$	−6.93040e9	−1.95668
$536$	4.02933e9	1.13020
$537$	2.41435e9	0.672808
$538$	2.98320e9	0.825932
$539$	1.59132e8	0.0437721
$540$	−1.71095e9	−0.467584
$541$	1.25116e9	0.339721	0.169860	−	0.985468i	$-0.445668\pi$
$541$	1.25116e9	0.339721	0.169860	+	0.985468i	$0.445668\pi$
$542$	−6.20195e9	−1.67314
$543$	6.57723e9	1.76296
$544$	1.02074e9	0.271842
$545$	4.58506e9	1.21327
$546$	−4.63582e8	−0.121886
$547$	4.85382e9	1.26803	0.634013	−	0.773322i	$-0.281407\pi$
$547$	4.85382e9	1.26803	0.634013	+	0.773322i	$0.281407\pi$
$548$	−8.26209e8	−0.214466
$549$	4.01322e8	0.103512
$550$	−3.07529e9	−0.788163
$551$	−3.38391e8	−0.0861762
$552$	5.17503e8	0.130956
$553$	1.15176e9	0.289617
$554$	3.96332e9	0.990319
$555$	−3.66520e9	−0.910066
$556$	−1.81889e9	−0.448791
$557$	7.42127e9	1.81964	0.909819	−	0.415006i	$-0.136221\pi$
$557$	7.42127e9	1.81964	0.909819	+	0.415006i	$0.136221\pi$
$558$	−5.73364e7	−0.0139705
$559$	−6.00191e8	−0.145328
$560$	−3.40476e9	−0.819273
$561$	−6.89141e8	−0.164793
$562$	7.29381e9	1.73331
$563$	−3.88620e9	−0.917796	−0.458898	−	0.888489i	$-0.651756\pi$
$563$	−3.88620e9	−0.917796	−0.458898	+	0.888489i	$0.651756\pi$
$564$	2.05709e9	0.482810
$565$	−7.43864e9	−1.73510
$566$	−6.86476e9	−1.59136
$567$	1.74239e9	0.401425
$568$	−3.79727e9	−0.869466
$569$	4.62670e9	1.05288	0.526440	−	0.850213i	$-0.323527\pi$
$569$	4.62670e9	1.05288	0.526440	+	0.850213i	$0.323527\pi$
$570$	−4.42781e9	−1.00144
$571$	−6.13711e9	−1.37955	−0.689775	−	0.724024i	$-0.742291\pi$
$571$	−6.13711e9	−1.37955	−0.689775	+	0.724024i	$0.742291\pi$
$572$	1.01795e8	0.0227426
$573$	−4.35782e9	−0.967672
$574$	9.99275e8	0.220543
$575$	−1.60169e9	−0.351351
$576$	1.85510e8	0.0404473
$577$	−4.25413e9	−0.921924	−0.460962	−	0.887420i	$-0.652496\pi$
$577$	−4.25413e9	−0.921924	−0.460962	+	0.887420i	$0.652496\pi$
$578$	3.80922e9	0.820519
$579$	−6.64971e9	−1.42373
$580$	4.13276e8	0.0879513
$581$	−9.57070e6	−0.00202454
$582$	9.32003e9	1.95969
$583$	−1.89383e9	−0.395822
$584$	5.41403e9	1.12480
$585$	−1.61840e8	−0.0334226
$586$	6.08849e9	1.24988
$587$	8.26096e9	1.68576	0.842882	−	0.538098i	$-0.180857\pi$
$587$	8.26096e9	1.68576	0.842882	+	0.538098i	$0.180857\pi$
$588$	−1.94633e8	−0.0394817
$589$	4.39808e8	0.0886868
$590$	1.12235e10	2.24981
$591$	−6.52110e9	−1.29946
$592$	2.93565e9	0.581538
$593$	−4.87048e9	−0.959136	−0.479568	−	0.877505i	$-0.659207\pi$
$593$	−4.87048e9	−0.959136	−0.479568	+	0.877505i	$0.659207\pi$
$594$	−1.69879e9	−0.332573
$595$	1.83304e9	0.356748
$596$	−6.34497e6	−0.00122763
$597$	−1.79174e9	−0.344640
$598$	2.51126e8	0.0480217
$599$	−3.09919e9	−0.589188	−0.294594	−	0.955623i	$-0.595184\pi$
$599$	−3.09919e9	−0.589188	−0.294594	+	0.955623i	$0.595184\pi$
$600$	−1.02936e10	−1.94552
$601$	−9.45451e9	−1.77655	−0.888277	−	0.459309i	$-0.848097\pi$
$601$	−9.45451e9	−1.77655	−0.888277	+	0.459309i	$0.848097\pi$
$602$	−1.19358e9	−0.222980
$603$	4.90682e8	0.0911359
$604$	−1.35057e9	−0.249394
$605$	8.94488e9	1.64222
$606$	−7.68895e9	−1.40350
$607$	6.38242e9	1.15831	0.579155	−	0.815217i	$-0.303382\pi$
$607$	6.38242e9	1.15831	0.579155	+	0.815217i	$0.303382\pi$
$608$	1.37475e9	0.248062
$609$	−3.94521e8	−0.0707799
$610$	1.78082e10	3.17663
$611$	−2.73184e9	−0.484518
$612$	5.25502e7	0.00926710
$613$	−2.79140e9	−0.489453	−0.244726	−	0.969592i	$-0.578698\pi$
$613$	−2.79140e9	−0.489453	−0.244726	+	0.969592i	$0.578698\pi$
$614$	−1.11174e10	−1.93827
$615$	5.59547e9	0.970005
$616$	−5.54002e8	−0.0954945
$617$	4.67462e9	0.801213	0.400606	−	0.916250i	$-0.368799\pi$
$617$	4.67462e9	0.801213	0.400606	+	0.916250i	$0.368799\pi$
$618$	8.51024e9	1.45038
$619$	−2.72483e9	−0.461767	−0.230883	−	0.972981i	$-0.574162\pi$
$619$	−2.72483e9	−0.461767	−0.230883	+	0.972981i	$0.574162\pi$
$620$	−5.37137e8	−0.0905137
$621$	−8.84775e8	−0.148256
$622$	−6.23693e9	−1.03921
$623$	−2.22824e9	−0.369193
$624$	2.07914e9	0.342561
$625$	1.18109e10	1.93510
$626$	4.91594e9	0.800934
$627$	−9.28150e8	−0.150377
$628$	2.96796e9	0.478189
$629$	−1.58048e9	−0.253228
$630$	−3.21846e8	−0.0512810
$631$	−1.00895e9	−0.159870	−0.0799349	−	0.996800i	$-0.525471\pi$
$631$	−1.00895e9	−0.159870	−0.0799349	+	0.996800i	$0.525471\pi$
$632$	−4.00973e9	−0.631837
$633$	1.86545e9	0.292327
$634$	5.18076e9	0.807386
$635$	−6.05726e9	−0.938789
$636$	2.31632e9	0.357025
$637$	2.58475e8	0.0396214
$638$	4.10339e8	0.0625562
$639$	−4.62422e8	−0.0701109
$640$	1.45056e10	2.18729
$641$	−5.66358e9	−0.849353	−0.424676	−	0.905345i	$-0.639612\pi$
$641$	−5.66358e9	−0.849353	−0.424676	+	0.905345i	$0.639612\pi$
$642$	8.41625e9	1.25530
$643$	−8.85244e9	−1.31318	−0.656590	−	0.754247i	$-0.728002\pi$
$643$	−8.85244e9	−1.31318	−0.656590	+	0.754247i	$0.728002\pi$
$644$	1.05434e8	0.0155554
$645$	−6.68351e9	−0.980721
$646$	−1.90932e9	−0.278654
$647$	1.34221e10	1.94830	0.974152	−	0.225894i	$-0.0725303\pi$
$647$	1.34221e10	1.94830	0.974152	+	0.225894i	$0.0725303\pi$
$648$	−6.06593e9	−0.875760
$649$	2.35265e9	0.337832
$650$	−4.99512e9	−0.713426
$651$	5.12761e8	0.0728420
$652$	−1.25646e9	−0.177534
$653$	−8.74745e9	−1.22938	−0.614689	−	0.788770i	$-0.710718\pi$
$653$	−8.74745e9	−1.22938	−0.614689	+	0.788770i	$0.710718\pi$
$654$	−5.56808e9	−0.778365
$655$	7.03720e9	0.978488
$656$	−4.48170e9	−0.619839
$657$	6.59307e8	0.0907003
$658$	−5.43273e9	−0.743408
$659$	−1.19393e10	−1.62509	−0.812546	−	0.582897i	$-0.801919\pi$
$659$	−1.19393e10	−1.62509	−0.812546	+	0.582897i	$0.801919\pi$
$660$	1.13355e9	0.153475
$661$	−1.08843e10	−1.46586	−0.732932	−	0.680302i	$-0.761849\pi$
$661$	−1.08843e10	−1.46586	−0.732932	+	0.680302i	$0.761849\pi$
$662$	1.15694e10	1.54992
$663$	−1.11936e9	−0.149166
$664$	3.33193e7	0.00441680
$665$	2.46877e9	0.325541
$666$	2.77502e8	0.0364004
$667$	2.13715e8	0.0278866
$668$	−9.47973e8	−0.123049
$669$	−5.43078e9	−0.701247
$670$	2.17735e10	2.79683
$671$	3.73293e9	0.477003
$672$	1.60279e9	0.203743
$673$	−2.15292e9	−0.272255	−0.136127	−	0.990691i	$-0.543466\pi$
$673$	−2.15292e9	−0.272255	−0.136127	+	0.990691i	$0.543466\pi$
$674$	−1.68236e9	−0.211645
$675$	1.75989e10	2.20254
$676$	1.65343e8	0.0205860
$677$	−8.32794e9	−1.03152	−0.515760	−	0.856733i	$-0.672490\pi$
$677$	−8.32794e9	−1.03152	−0.515760	+	0.856733i	$0.672490\pi$
$678$	9.03345e9	1.11314
$679$	−5.19648e9	−0.637037
$680$	−6.38151e9	−0.778292
$681$	5.84293e9	0.708951
$682$	−5.33319e8	−0.0643786
$683$	−4.60623e9	−0.553189	−0.276594	−	0.960987i	$-0.589206\pi$
$683$	−4.60623e9	−0.553189	−0.276594	+	0.960987i	$0.589206\pi$
$684$	7.07756e7	0.00845644
$685$	1.22182e10	1.45241
$686$	5.14022e8	0.0607921
$687$	9.16016e9	1.07784
$688$	5.35316e9	0.626687
$689$	−3.07610e9	−0.358288
$690$	2.79645e9	0.324067
$691$	9.98497e9	1.15126	0.575630	−	0.817710i	$-0.304757\pi$
$691$	9.98497e9	1.15126	0.575630	+	0.817710i	$0.304757\pi$
$692$	−3.49978e9	−0.401485
$693$	−6.74649e7	−0.00770037
$694$	−4.88914e9	−0.555232
$695$	2.68981e10	3.03931
$696$	1.37348e9	0.154415
$697$	2.41283e9	0.269906
$698$	6.64694e9	0.739822
$699$	9.43910e9	1.04535
$700$	−2.09718e9	−0.231096
$701$	−7.47201e9	−0.819265	−0.409633	−	0.912251i	$-0.634343\pi$
$701$	−7.47201e9	−0.819265	−0.409633	+	0.912251i	$0.634343\pi$
$702$	−2.75930e9	−0.301037
$703$	−2.12862e9	−0.231076
$704$	1.72554e9	0.186389
$705$	−3.04207e10	−3.26970
$706$	−7.75333e9	−0.829224
$707$	4.28705e9	0.456237
$708$	−2.87750e9	−0.304718
$709$	−1.50499e10	−1.58588	−0.792940	−	0.609299i	$-0.791451\pi$
$709$	−1.50499e10	−1.58588	−0.792940	+	0.609299i	$0.791451\pi$
$710$	−2.05195e10	−2.15160
$711$	−4.88294e8	−0.0509493
$712$	7.75738e9	0.805443
$713$	−2.77767e8	−0.0286990
$714$	−2.22603e9	−0.228869
$715$	−1.50537e9	−0.154018
$716$	−1.71247e9	−0.174352
$717$	−1.55789e10	−1.57841
$718$	3.10382e8	0.0312940
$719$	7.96474e9	0.799136	0.399568	−	0.916704i	$-0.369160\pi$
$719$	7.96474e9	0.799136	0.399568	+	0.916704i	$0.369160\pi$
$720$	1.44346e9	0.144126
$721$	−4.74497e9	−0.471477
$722$	8.81457e9	0.871607
$723$	−4.48080e9	−0.440932
$724$	−4.66515e9	−0.456857
$725$	−4.25098e9	−0.414292
$726$	−1.08626e10	−1.05355
$727$	1.76490e10	1.70353	0.851765	−	0.523923i	$-0.175532\pi$
$727$	1.76490e10	1.70353	0.851765	+	0.523923i	$0.175532\pi$
$728$	−8.99852e8	−0.0864393
$729$	9.67541e9	0.924960
$730$	2.92560e10	2.78346
$731$	−2.88200e9	−0.272888
$732$	−4.56571e9	−0.430248
$733$	−1.43841e10	−1.34902	−0.674509	−	0.738266i	$-0.735645\pi$
$733$	−1.43841e10	−1.34902	−0.674509	+	0.738266i	$0.735645\pi$
$734$	1.48858e10	1.38943
$735$	2.87828e9	0.267379
$736$	−8.68242e8	−0.0802728
$737$	4.56411e9	0.419972
$738$	−4.23647e8	−0.0387978
$739$	−6.90717e9	−0.629571	−0.314786	−	0.949163i	$-0.601933\pi$
$739$	−6.90717e9	−0.629571	−0.314786	+	0.949163i	$0.601933\pi$
$740$	2.59968e9	0.235836
$741$	−1.50757e9	−0.136118
$742$	−6.11735e9	−0.549730
$743$	3.22593e9	0.288532	0.144266	−	0.989539i	$-0.453918\pi$
$743$	3.22593e9	0.288532	0.144266	+	0.989539i	$0.453918\pi$
$744$	−1.78512e9	−0.158914
$745$	9.38309e7	0.00831379
$746$	−2.81922e9	−0.248624
$747$	4.05754e6	0.000356157 0
$748$	4.88799e8	0.0427046
$749$	−4.69257e9	−0.408060
$750$	−3.12774e10	−2.70717
$751$	−1.09718e10	−0.945228	−0.472614	−	0.881270i	$-0.656690\pi$
$751$	−1.09718e10	−0.945228	−0.472614	+	0.881270i	$0.656690\pi$
$752$	2.43655e10	2.08936
$753$	1.31466e10	1.12210
$754$	6.66504e8	0.0566243
$755$	1.99725e10	1.68896
$756$	−1.15848e9	−0.0975132
$757$	1.21251e10	1.01589	0.507947	−	0.861388i	$-0.330405\pi$
$757$	1.21251e10	1.01589	0.507947	+	0.861388i	$0.330405\pi$
$758$	−1.50758e10	−1.25730
$759$	5.86186e8	0.0486620
$760$	−8.59476e9	−0.710209
$761$	6.02906e9	0.495910	0.247955	−	0.968772i	$-0.420241\pi$
$761$	6.02906e9	0.495910	0.247955	+	0.968772i	$0.420241\pi$
$762$	7.35591e9	0.602274
$763$	3.10454e9	0.253024
$764$	3.09095e9	0.250764
$765$	−7.77124e8	−0.0627589
$766$	−6.16441e9	−0.495554
$767$	3.82135e9	0.305797
$768$	−9.72935e9	−0.775032
$769$	1.18054e10	0.936134	0.468067	−	0.883693i	$-0.344951\pi$
$769$	1.18054e10	0.936134	0.468067	+	0.883693i	$0.344951\pi$
$770$	−2.99368e9	−0.236313
$771$	8.64454e9	0.679284
$772$	4.71655e9	0.368947
$773$	−2.02253e10	−1.57495	−0.787474	−	0.616348i	$-0.788611\pi$
$773$	−2.02253e10	−1.57495	−0.787474	+	0.616348i	$0.788611\pi$
$774$	5.06025e8	0.0392264
$775$	5.52502e9	0.426362
$776$	1.80910e10	1.38978
$777$	−2.48171e9	−0.189792
$778$	2.79190e10	2.12555
$779$	3.24965e9	0.246295
$780$	1.84120e9	0.138921
$781$	−4.30125e9	−0.323085
$782$	1.20586e9	0.0901723
$783$	−2.34825e9	−0.174814
$784$	−2.30536e9	−0.170857
$785$	−4.38909e10	−3.23840
$786$	−8.54595e9	−0.627742
$787$	−1.53971e10	−1.12597	−0.562987	−	0.826466i	$-0.690348\pi$
$787$	−1.53971e10	−1.12597	−0.562987	+	0.826466i	$0.690348\pi$
$788$	4.62533e9	0.336745
$789$	8.56533e9	0.620833
$790$	−2.16675e10	−1.56356
$791$	−5.03669e9	−0.361849
$792$	2.34872e8	0.0167993
$793$	6.06331e9	0.431771
$794$	−1.79637e10	−1.27358
$795$	−3.42543e10	−2.41785
$796$	1.27086e9	0.0893104
$797$	−1.00216e10	−0.701188	−0.350594	−	0.936528i	$-0.614020\pi$
$797$	−1.00216e10	−0.701188	−0.350594	+	0.936528i	$0.614020\pi$
$798$	−2.99807e9	−0.208848
$799$	−1.31178e10	−0.909800
$800$	1.72701e10	1.19256
$801$	9.44673e8	0.0649483
$802$	−1.84290e10	−1.26151
$803$	6.13259e9	0.417965
$804$	−5.58232e9	−0.378808
$805$	−1.55919e9	−0.105345
$806$	−8.66258e8	−0.0582740
$807$	1.13106e10	0.757580
$808$	−1.49249e10	−0.995341
$809$	−4.04763e9	−0.268770	−0.134385	−	0.990929i	$-0.542906\pi$
$809$	−4.04763e9	−0.268770	−0.134385	+	0.990929i	$0.542906\pi$
$810$	−3.27787e10	−2.16718
$811$	−8.70517e9	−0.573066	−0.286533	−	0.958070i	$-0.592503\pi$
$811$	−8.70517e9	−0.573066	−0.286533	+	0.958070i	$0.592503\pi$
$812$	2.79829e8	0.0183420
$813$	−2.35143e10	−1.53467
$814$	2.58121e9	0.167740
$815$	1.85808e10	1.20230
$816$	9.98364e9	0.643240
$817$	−3.88154e9	−0.249016
$818$	−2.61905e10	−1.67305
$819$	−1.09582e8	−0.00697018
$820$	−3.96880e9	−0.251368
$821$	1.01574e10	0.640590	0.320295	−	0.947318i	$-0.396218\pi$
$821$	1.01574e10	0.640590	0.320295	+	0.947318i	$0.396218\pi$
$822$	−1.48377e10	−0.931784
$823$	−2.75916e10	−1.72535	−0.862674	−	0.505760i	$-0.831212\pi$
$823$	−2.75916e10	−1.72535	−0.862674	+	0.505760i	$0.831212\pi$
$824$	1.65191e10	1.02859
$825$	−1.16598e10	−0.722937
$826$	7.59941e9	0.469191
$827$	−1.64448e10	−1.01102	−0.505511	−	0.862820i	$-0.668696\pi$
$827$	−1.64448e10	−1.01102	−0.505511	+	0.862820i	$0.668696\pi$
$828$	−4.46994e7	−0.00273650
$829$	8.87302e9	0.540917	0.270458	−	0.962732i	$-0.412825\pi$
$829$	8.87302e9	0.540917	0.270458	+	0.962732i	$0.412825\pi$
$830$	1.80049e8	0.0109299
$831$	1.50267e10	0.908363
$832$	2.80275e9	0.168715
$833$	1.24115e9	0.0743988
$834$	−3.26650e10	−1.94985
$835$	1.40189e10	0.833316
$836$	6.58325e8	0.0389689
$837$	3.05202e9	0.179907
$838$	8.30478e9	0.487499
$839$	2.24983e10	1.31517	0.657586	−	0.753380i	$-0.271578\pi$
$839$	2.24983e10	1.31517	0.657586	+	0.753380i	$0.271578\pi$
$840$	−1.00204e10	−0.583322
$841$	−1.66827e10	−0.967118
$842$	5.94299e9	0.343093
$843$	2.76540e10	1.58987
$844$	−1.32314e9	−0.0757541
$845$	−2.44513e9	−0.139413
$846$	2.30323e9	0.130780
$847$	6.05657e9	0.342480
$848$	2.74360e10	1.54502
$849$	−2.60273e10	−1.45966
$850$	−2.39856e10	−1.33963
$851$	1.34436e9	0.0747761
$852$	5.26082e9	0.291417
$853$	−1.37743e10	−0.759882	−0.379941	−	0.925011i	$-0.624056\pi$
$853$	−1.37743e10	−0.759882	−0.379941	+	0.925011i	$0.624056\pi$
$854$	1.20579e10	0.662476
$855$	−1.04665e9	−0.0572689
$856$	1.63367e10	0.890236
$857$	1.83998e10	0.998573	0.499286	−	0.866437i	$-0.333596\pi$
$857$	1.83998e10	0.998573	0.499286	+	0.866437i	$0.333596\pi$
$858$	1.82811e9	0.0988091
$859$	−2.04068e10	−1.09850	−0.549249	−	0.835658i	$-0.685086\pi$
$859$	−2.04068e10	−1.09850	−0.549249	+	0.835658i	$0.685086\pi$
$860$	4.74053e9	0.254145
$861$	3.78869e9	0.202292
$862$	−9.98659e8	−0.0531058
$863$	9.30571e9	0.492846	0.246423	−	0.969162i	$-0.420745\pi$
$863$	9.30571e9	0.492846	0.246423	+	0.969162i	$0.420745\pi$
$864$	9.54000e9	0.503211
$865$	5.17556e10	2.71895
$866$	5.83455e9	0.305277
$867$	1.44424e10	0.752615
$868$	−3.63695e8	−0.0188764
$869$	−4.54190e9	−0.234784
$870$	7.42194e9	0.382120
$871$	7.41338e9	0.380148
$872$	−1.08081e10	−0.552004
$873$	2.20307e9	0.112067
$874$	1.62408e9	0.0822843
$875$	1.74390e10	0.880023
$876$	−7.50071e9	−0.376997
$877$	1.84999e10	0.926126	0.463063	−	0.886325i	$-0.346750\pi$
$877$	1.84999e10	0.926126	0.463063	+	0.886325i	$0.346750\pi$
$878$	−2.36203e10	−1.17775
$879$	2.30841e10	1.14644
$880$	1.34265e10	0.664161
$881$	−2.23823e9	−0.110278	−0.0551390	−	0.998479i	$-0.517560\pi$
$881$	−2.23823e9	−0.110278	−0.0551390	+	0.998479i	$0.517560\pi$
$882$	−2.17922e8	−0.0106945
$883$	2.23693e10	1.09343	0.546714	−	0.837320i	$-0.315879\pi$
$883$	2.23693e10	1.09343	0.546714	+	0.837320i	$0.315879\pi$
$884$	7.93945e8	0.0386552
$885$	4.25531e10	2.06362
$886$	−1.20114e10	−0.580196
$887$	3.46241e10	1.66589	0.832944	−	0.553358i	$-0.186654\pi$
$887$	3.46241e10	1.66589	0.832944	+	0.553358i	$0.186654\pi$
$888$	8.63979e9	0.414055
$889$	−4.10137e9	−0.195782
$890$	4.19188e10	1.99317
$891$	−6.87101e9	−0.325423
$892$	3.85198e9	0.181722
$893$	−1.76673e10	−0.830212
$894$	−1.13948e8	−0.00533366
$895$	2.53244e10	1.18075
$896$	9.82173e9	0.456153
$897$	9.52129e8	0.0440476
$898$	2.22924e9	0.102728
$899$	−7.37210e8	−0.0338401
$900$	8.89109e8	0.0406543
$901$	−1.47708e10	−0.672773
$902$	−3.94059e9	−0.178788
$903$	−4.52540e9	−0.204526
$904$	1.75347e10	0.789421
$905$	6.89893e10	3.09394
$906$	−2.42545e10	−1.08354
$907$	−2.74395e10	−1.22110	−0.610550	−	0.791978i	$-0.709052\pi$
$907$	−2.74395e10	−1.22110	−0.610550	+	0.791978i	$0.709052\pi$
$908$	−4.14432e9	−0.183718
$909$	−1.81752e9	−0.0802610
$910$	−4.86256e9	−0.213905
$911$	2.08668e10	0.914409	0.457205	−	0.889362i	$-0.348851\pi$
$911$	2.08668e10	0.914409	0.457205	+	0.889362i	$0.348851\pi$
$912$	1.34462e10	0.586971
$913$	3.77415e7	0.00164124
$914$	−1.60989e9	−0.0697405
$915$	6.75188e10	2.91374
$916$	−6.49719e9	−0.279313
$917$	4.76488e9	0.204061
$918$	−1.32497e10	−0.565269
$919$	2.92165e10	1.24172	0.620860	−	0.783921i	$-0.286783\pi$
$919$	2.92165e10	1.24172	0.620860	+	0.783921i	$0.286783\pi$
$920$	5.42814e9	0.229823
$921$	−4.21509e10	−1.77786
$922$	−4.27218e10	−1.79511
$923$	−6.98642e9	−0.292448
$924$	7.67525e8	0.0320067
$925$	−2.67405e10	−1.11090
$926$	−3.94604e10	−1.63314
$927$	2.01165e9	0.0829419
$928$	−2.30437e9	−0.0946528
$929$	−6.17818e9	−0.252817	−0.126408	−	0.991978i	$-0.540345\pi$
$929$	−6.17818e9	−0.252817	−0.126408	+	0.991978i	$0.540345\pi$
$930$	−9.64633e9	−0.393253
$931$	1.67160e9	0.0678905
$932$	−6.69504e9	−0.270893
$933$	−2.36469e10	−0.953210
$934$	9.98083e9	0.400823
$935$	−7.22848e9	−0.289205
$936$	3.81496e8	0.0152064
$937$	4.01039e10	1.59257	0.796284	−	0.604924i	$-0.206796\pi$
$937$	4.01039e10	1.59257	0.796284	+	0.604924i	$0.206796\pi$
$938$	1.47428e10	0.583270
$939$	1.86385e10	0.734651
$940$	2.15770e10	0.847313
$941$	−2.77410e10	−1.08532	−0.542661	−	0.839952i	$-0.682583\pi$
$941$	−2.77410e10	−1.08532	−0.542661	+	0.839952i	$0.682583\pi$
$942$	5.33010e10	2.07758
$943$	−2.05236e9	−0.0797010
$944$	−3.40830e10	−1.31867
$945$	1.71319e10	0.660381
$946$	4.70683e9	0.180763
$947$	−1.43030e10	−0.547272	−0.273636	−	0.961833i	$-0.588226\pi$
$947$	−1.43030e10	−0.547272	−0.273636	+	0.961833i	$0.588226\pi$
$948$	5.55516e9	0.211771
$949$	9.96103e9	0.378331
$950$	−3.23043e10	−1.22244
$951$	1.96425e10	0.740569
$952$	−4.32092e9	−0.162311
$953$	−9.73458e9	−0.364328	−0.182164	−	0.983268i	$-0.558310\pi$
$953$	−9.73458e9	−0.364328	−0.182164	+	0.983268i	$0.558310\pi$
$954$	2.59348e9	0.0967083
$955$	−4.57097e10	−1.69823
$956$	1.10499e10	0.409031
$957$	1.55577e9	0.0573792
$958$	−1.47582e10	−0.542318
$959$	8.27292e9	0.302896
$960$	3.12104e10	1.13855
$961$	−2.65545e10	−0.965174
$962$	4.19259e9	0.151834
$963$	1.98944e9	0.0717857
$964$	3.17818e9	0.114264
$965$	−6.97495e10	−2.49859
$966$	1.89347e9	0.0675833
$967$	−2.13948e10	−0.760878	−0.380439	−	0.924806i	$-0.624227\pi$
$967$	−2.13948e10	−0.760878	−0.380439	+	0.924806i	$0.624227\pi$
$968$	−2.10853e10	−0.747164
$969$	−7.23907e9	−0.255593
$970$	9.77588e10	3.43918
$971$	3.22018e10	1.12879	0.564394	−	0.825506i	$-0.309110\pi$
$971$	3.22018e10	1.12879	0.564394	+	0.825506i	$0.309110\pi$
$972$	1.01727e9	0.0355308
$973$	1.82127e10	0.633840
$974$	5.86270e10	2.03302
$975$	−1.89387e10	−0.654385
$976$	−5.40792e10	−1.86190
$977$	−2.86578e10	−0.983133	−0.491567	−	0.870840i	$-0.663576\pi$
$977$	−2.86578e10	−0.983133	−0.491567	+	0.870840i	$0.663576\pi$
$978$	−2.25644e10	−0.771327
$979$	8.78695e9	0.299294
$980$	−2.04153e9	−0.0692890
$981$	−1.31618e9	−0.0445118
$982$	−5.00994e10	−1.68827
$983$	−5.78754e9	−0.194337	−0.0971687	−	0.995268i	$-0.530979\pi$
$983$	−5.78754e9	−0.194337	−0.0971687	+	0.995268i	$0.530979\pi$
$984$	−1.31899e10	−0.441325
$985$	−6.84005e10	−2.28051
$986$	3.20042e9	0.106326
$987$	−2.05978e10	−0.681886
$988$	1.06930e9	0.0352737
$989$	2.45144e9	0.0805815
$990$	1.26918e9	0.0415721
$991$	−2.79012e10	−0.910678	−0.455339	−	0.890318i	$-0.650482\pi$
$991$	−2.79012e10	−0.910678	−0.455339	+	0.890318i	$0.650482\pi$
$992$	2.99499e9	0.0974104
$993$	4.38647e10	1.42165
$994$	−1.38937e10	−0.448710
$995$	−1.87938e10	−0.604830
$996$	−4.61613e7	−0.00148037
$997$	9.90754e9	0.316616	0.158308	−	0.987390i	$-0.449396\pi$
$997$	9.90754e9	0.316616	0.158308	+	0.987390i	$0.449396\pi$
$998$	7.90391e9	0.251701
$999$	−1.47715e10	−0.468753

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.b.1.2	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.b.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-12.7379 q^{2} -48.2951 q^{3} +34.2551 q^{4} -506.573 q^{5} +615.180 q^{6} -343.000 q^{7} +1194.12 q^{8} +145.416 q^{9} +O(q^{10})\)	\(q-12.7379 q^{2} -48.2951 q^{3} +34.2551 q^{4} -506.573 q^{5} +615.180 q^{6} -343.000 q^{7} +1194.12 q^{8} +145.416 q^{9} +6452.69 q^{10} +1352.60 q^{11} -1654.35 q^{12} +2197.00 q^{13} +4369.11 q^{14} +24465.0 q^{15} -19595.2 q^{16} +10549.6 q^{17} -1852.31 q^{18} +14208.4 q^{19} -17352.7 q^{20} +16565.2 q^{21} -17229.4 q^{22} -8973.52 q^{23} -57670.0 q^{24} +178491. q^{25} -27985.3 q^{26} +98598.5 q^{27} -11749.5 q^{28} -23816.2 q^{29} -311633. q^{30} +30954.1 q^{31} +96756.0 q^{32} -65324.1 q^{33} -134380. q^{34} +173754. q^{35} +4981.26 q^{36} -149814. q^{37} -180986. q^{38} -106104. q^{39} -604907. q^{40} +228713. q^{41} -211007. q^{42} -273187. q^{43} +46333.5 q^{44} -73664.0 q^{45} +114304. q^{46} -1.24344e6 q^{47} +946354. q^{48} +117649. q^{49} -2.27361e6 q^{50} -509493. q^{51} +75258.5 q^{52} -1.40014e6 q^{53} -1.25594e6 q^{54} -685191. q^{55} -409582. q^{56} -686196. q^{57} +303370. q^{58} +1.73935e6 q^{59} +838050. q^{60} +2.75981e6 q^{61} -394291. q^{62} -49877.9 q^{63} +1.27572e6 q^{64} -1.11294e6 q^{65} +832094. q^{66} +3.37432e6 q^{67} +361377. q^{68} +433377. q^{69} -2.21327e6 q^{70} -3.17998e6 q^{71} +173644. q^{72} +4.53392e6 q^{73} +1.90833e6 q^{74} -8.62024e6 q^{75} +486710. q^{76} -463943. q^{77} +1.35155e6 q^{78} -3.35790e6 q^{79} +9.92642e6 q^{80} -5.07985e6 q^{81} -2.91334e6 q^{82} +27902.9 q^{83} +567443. q^{84} -5.34413e6 q^{85} +3.47983e6 q^{86} +1.15021e6 q^{87} +1.61516e6 q^{88} +6.49633e6 q^{89} +938328. q^{90} -753571. q^{91} -307389. q^{92} -1.49493e6 q^{93} +1.58388e7 q^{94} -7.19758e6 q^{95} -4.67284e6 q^{96} +1.51501e7 q^{97} -1.49861e6 q^{98} +196691. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 5 q^{2} - 26 q^{3} + 393 q^{4} - 181 q^{5} + 703 q^{6} - 3087 q^{7} + 1197 q^{8} + 3211 q^{9}+O(q^{10}) \) 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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