LMFDB - Embedded newform 91.8.a.b.1.3

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			1.3
Root			$-10.5479$ 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)

$f(q)$	$=$	$q-11.5479 q^{2} +14.0702 q^{3} +5.35382 q^{4} +200.806 q^{5} -162.481 q^{6} -343.000 q^{7} +1416.30 q^{8} -1989.03 q^{9} +O(q^{10})$	\(q-11.5479 q^{2} +14.0702 q^{3} +5.35382 q^{4} +200.806 q^{5} -162.481 q^{6} -343.000 q^{7} +1416.30 q^{8} -1989.03 q^{9} -2318.88 q^{10} -588.362 q^{11} +75.3292 q^{12} +2197.00 q^{13} +3960.93 q^{14} +2825.37 q^{15} -17040.6 q^{16} +20007.5 q^{17} +22969.1 q^{18} -9980.56 q^{19} +1075.08 q^{20} -4826.07 q^{21} +6794.35 q^{22} +42255.5 q^{23} +19927.6 q^{24} -37802.1 q^{25} -25370.7 q^{26} -58757.4 q^{27} -1836.36 q^{28} +163487. q^{29} -32627.0 q^{30} +126944. q^{31} +15496.3 q^{32} -8278.36 q^{33} -231045. q^{34} -68876.3 q^{35} -10648.9 q^{36} -480270. q^{37} +115254. q^{38} +30912.2 q^{39} +284402. q^{40} -600420. q^{41} +55730.9 q^{42} -980394. q^{43} -3149.99 q^{44} -399408. q^{45} -487962. q^{46} -179742. q^{47} -239764. q^{48} +117649. q^{49} +436535. q^{50} +281509. q^{51} +11762.3 q^{52} -663334. q^{53} +678525. q^{54} -118146. q^{55} -485793. q^{56} -140428. q^{57} -1.88794e6 q^{58} -1.90951e6 q^{59} +15126.5 q^{60} -2.41091e6 q^{61} -1.46593e6 q^{62} +682237. q^{63} +2.00225e6 q^{64} +441170. q^{65} +95597.6 q^{66} -3.97460e6 q^{67} +107117. q^{68} +594541. q^{69} +795376. q^{70} +3.28614e6 q^{71} -2.81707e6 q^{72} +636497. q^{73} +5.54611e6 q^{74} -531882. q^{75} -53434.1 q^{76} +201808. q^{77} -356970. q^{78} +2.10723e6 q^{79} -3.42185e6 q^{80} +3.52328e6 q^{81} +6.93359e6 q^{82} +2.27825e6 q^{83} -25837.9 q^{84} +4.01763e6 q^{85} +1.13215e7 q^{86} +2.30030e6 q^{87} -833301. q^{88} -1.81327e6 q^{89} +4.61232e6 q^{90} -753571. q^{91} +226228. q^{92} +1.78612e6 q^{93} +2.07564e6 q^{94} -2.00415e6 q^{95} +218035. q^{96} -1.02057e7 q^{97} -1.35860e6 q^{98} +1.17027e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−11.5479	−1.02070	−0.510350	−	0.859967i	$-0.670484\pi$
$2$	−11.5479	−1.02070	−0.510350	+	0.859967i	$0.670484\pi$
$3$	14.0702	0.300867	0.150434	−	0.988620i	$-0.451933\pi$
$3$	14.0702	0.300867	0.150434	+	0.988620i	$0.451933\pi$
$4$	5.35382	0.0418267
$5$	200.806	0.718424	0.359212	−	0.933256i	$-0.383046\pi$
$5$	200.806	0.718424	0.359212	+	0.933256i	$0.383046\pi$
$6$	−162.481	−0.307095
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	1416.30	0.978007
$9$	−1989.03	−0.909479
$10$	−2318.88	−0.733294
$11$	−588.362	−0.133282	−0.0666409	−	0.997777i	$-0.521228\pi$
$11$	−588.362	−0.133282	−0.0666409	+	0.997777i	$0.521228\pi$
$12$	75.3292	0.0125843
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	3960.93	0.385788
$15$	2825.37	0.216150
$16$	−17040.6	−1.04008
$17$	20007.5	0.987694	0.493847	−	0.869549i	$-0.335590\pi$
$17$	20007.5	0.987694	0.493847	+	0.869549i	$0.335590\pi$
$18$	22969.1	0.928304
$19$	−9980.56	−0.333824	−0.166912	−	0.985972i	$-0.553380\pi$
$19$	−9980.56	−0.333824	−0.166912	+	0.985972i	$0.553380\pi$
$20$	1075.08	0.0300493
$21$	−4826.07	−0.113717
$22$	6794.35	0.136041
$23$	42255.5	0.724161	0.362081	−	0.932147i	$-0.382066\pi$
$23$	42255.5	0.724161	0.362081	+	0.932147i	$0.382066\pi$
$24$	19927.6	0.294250
$25$	−37802.1	−0.483867
$26$	−25370.7	−0.283091
$27$	−58757.4	−0.574500
$28$	−1836.36	−0.0158090
$29$	163487.	1.24478	0.622388	−	0.782709i	$-0.286162\pi$
$29$	163487.	1.24478	0.622388	+	0.782709i	$0.286162\pi$
$30$	−32627.0	−0.220624
$31$	126944.	0.765323	0.382661	−	0.923889i	$-0.375008\pi$
$31$	126944.	0.765323	0.382661	+	0.923889i	$0.375008\pi$
$32$	15496.3	0.0835993
$33$	−8278.36	−0.0401001
$34$	−231045.	−1.00814
$35$	−68876.3	−0.271539
$36$	−10648.9	−0.0380405
$37$	−480270.	−1.55876	−0.779380	−	0.626551i	$-0.784466\pi$
$37$	−480270.	−1.55876	−0.779380	+	0.626551i	$0.784466\pi$
$38$	115254.	0.340734
$39$	30912.2	0.0834455
$40$	284402.	0.702623
$41$	−600420.	−1.36054	−0.680271	−	0.732961i	$-0.738138\pi$
$41$	−600420.	−1.36054	−0.680271	+	0.732961i	$0.738138\pi$
$42$	55730.9	0.116071
$43$	−980394.	−1.88045	−0.940224	−	0.340558i	$-0.889384\pi$
$43$	−980394.	−1.88045	−0.940224	+	0.340558i	$0.889384\pi$
$44$	−3149.99	−0.00557474
$45$	−399408.	−0.653391
$46$	−487962.	−0.739151
$47$	−179742.	−0.252526	−0.126263	−	0.991997i	$-0.540298\pi$
$47$	−179742.	−0.252526	−0.126263	+	0.991997i	$0.540298\pi$
$48$	−239764.	−0.312925
$49$	117649.	0.142857
$50$	436535.	0.493883
$51$	281509.	0.297165
$52$	11762.3	0.0116006
$53$	−663334.	−0.612022	−0.306011	−	0.952028i	$-0.598994\pi$
$53$	−663334.	−0.612022	−0.306011	+	0.952028i	$0.598994\pi$
$54$	678525.	0.586391
$55$	−118146.	−0.0957527
$56$	−485793.	−0.369652
$57$	−140428.	−0.100437
$58$	−1.88794e6	−1.27054
$59$	−1.90951e6	−1.21043	−0.605214	−	0.796063i	$-0.706912\pi$
$59$	−1.90951e6	−1.21043	−0.605214	+	0.796063i	$0.706912\pi$
$60$	15126.5	0.00904085
$61$	−2.41091e6	−1.35996	−0.679982	−	0.733229i	$-0.738012\pi$
$61$	−2.41091e6	−1.35996	−0.679982	+	0.733229i	$0.738012\pi$
$62$	−1.46593e6	−0.781164
$63$	682237.	0.343751
$64$	2.00225e6	0.954747
$65$	441170.	0.199255
$66$	95597.6	0.0409301
$67$	−3.97460e6	−1.61448	−0.807238	−	0.590227i	$-0.799038\pi$
$67$	−3.97460e6	−1.61448	−0.807238	+	0.590227i	$0.799038\pi$
$68$	107117.	0.0413120
$69$	594541.	0.217876
$70$	795376.	0.277159
$71$	3.28614e6	1.08964	0.544818	−	0.838554i	$-0.316599\pi$
$71$	3.28614e6	1.08964	0.544818	+	0.838554i	$0.316599\pi$
$72$	−2.81707e6	−0.889476
$73$	636497.	0.191499	0.0957495	−	0.995405i	$-0.469475\pi$
$73$	636497.	0.191499	0.0957495	+	0.995405i	$0.469475\pi$
$74$	5.54611e6	1.59103
$75$	−531882.	−0.145580
$76$	−53434.1	−0.0139628
$77$	201808.	0.0503757
$78$	−356970.	−0.0851728
$79$	2.10723e6	0.480859	0.240430	−	0.970667i	$-0.422712\pi$
$79$	2.10723e6	0.480859	0.240430	+	0.970667i	$0.422712\pi$
$80$	−3.42185e6	−0.747216
$81$	3.52328e6	0.736631
$82$	6.93359e6	1.38870
$83$	2.27825e6	0.437349	0.218674	−	0.975798i	$-0.429827\pi$
$83$	2.27825e6	0.437349	0.218674	+	0.975798i	$0.429827\pi$
$84$	−25837.9	−0.00475642
$85$	4.01763e6	0.709583
$86$	1.13215e7	1.91937
$87$	2.30030e6	0.374512
$88$	−833301.	−0.130350
$89$	−1.81327e6	−0.272646	−0.136323	−	0.990664i	$-0.543528\pi$
$89$	−1.81327e6	−0.272646	−0.136323	+	0.990664i	$0.543528\pi$
$90$	4.61232e6	0.666916
$91$	−753571.	−0.104828
$92$	226228.	0.0302893
$93$	1.78612e6	0.230261
$94$	2.07564e6	0.257753
$95$	−2.00415e6	−0.239827
$96$	218035.	0.0251523
$97$	−1.02057e7	−1.13538	−0.567688	−	0.823244i	$-0.692162\pi$
$97$	−1.02057e7	−1.13538	−0.567688	+	0.823244i	$0.692162\pi$
$98$	−1.35860e6	−0.145814
$99$	1.17027e6	0.121217
$100$	−202386.	−0.0202386
$101$	−1.26880e6	−0.122537	−0.0612685	−	0.998121i	$-0.519515\pi$
$101$	−1.26880e6	−0.122537	−0.0612685	+	0.998121i	$0.519515\pi$
$102$	−3.25084e6	−0.303316
$103$	−7.70938e6	−0.695167	−0.347584	−	0.937649i	$-0.612998\pi$
$103$	−7.70938e6	−0.695167	−0.347584	+	0.937649i	$0.612998\pi$
$104$	3.11162e6	0.271250
$105$	−969101.	−0.0816971
$106$	7.66011e6	0.624690
$107$	−1.66820e6	−0.131645	−0.0658225	−	0.997831i	$-0.520967\pi$
$107$	−1.66820e6	−0.131645	−0.0658225	+	0.997831i	$0.520967\pi$
$108$	−314577.	−0.0240294
$109$	1.79413e7	1.32697	0.663483	−	0.748191i	$-0.269077\pi$
$109$	1.79413e7	1.32697	0.663483	+	0.748191i	$0.269077\pi$
$110$	1.36434e6	0.0977347
$111$	−6.75748e6	−0.468980
$112$	5.84493e6	0.393112
$113$	−1.22125e7	−0.796215	−0.398108	−	0.917339i	$-0.630333\pi$
$113$	−1.22125e7	−0.796215	−0.398108	+	0.917339i	$0.630333\pi$
$114$	1.62165e6	0.102516
$115$	8.48513e6	0.520255
$116$	875283.	0.0520649
$117$	−4.36990e6	−0.252244
$118$	2.20508e7	1.23548
$119$	−6.86259e6	−0.373313
$120$	4.00158e6	0.211396
$121$	−1.91410e7	−0.982236
$122$	2.78410e7	1.38811
$123$	−8.44801e6	−0.409342
$124$	679633.	0.0320110
$125$	−2.32788e7	−1.06605
$126$	−7.87840e6	−0.350866
$127$	3.06409e7	1.32736	0.663679	−	0.748017i	$-0.268994\pi$
$127$	3.06409e7	1.32736	0.663679	+	0.748017i	$0.268994\pi$
$128$	−2.51053e7	−1.05811
$129$	−1.37943e7	−0.565765
$130$	−5.09458e6	−0.203379
$131$	−4.99739e7	−1.94220	−0.971100	−	0.238674i	$-0.923287\pi$
$131$	−4.99739e7	−1.94220	−0.971100	+	0.238674i	$0.923287\pi$
$132$	−44320.8	−0.00167726
$133$	3.42333e6	0.126174
$134$	4.58982e7	1.64789
$135$	−1.17988e7	−0.412734
$136$	2.83368e7	0.965972
$137$	2.17202e7	0.721675	0.360838	−	0.932629i	$-0.382491\pi$
$137$	2.17202e7	0.721675	0.360838	+	0.932629i	$0.382491\pi$
$138$	−6.86570e6	−0.222386
$139$	−2.36041e7	−0.745480	−0.372740	−	0.927936i	$-0.621582\pi$
$139$	−2.36041e7	−0.745480	−0.372740	+	0.927936i	$0.621582\pi$
$140$	−368751.	−0.0113576
$141$	−2.52899e6	−0.0759768
$142$	−3.79479e7	−1.11219
$143$	−1.29263e6	−0.0369657
$144$	3.38943e7	0.945928
$145$	3.28292e7	0.894277
$146$	−7.35020e6	−0.195463
$147$	1.65534e6	0.0429810
$148$	−2.57128e6	−0.0651979
$149$	−5.32522e7	−1.31882	−0.659410	−	0.751783i	$-0.729194\pi$
$149$	−5.32522e7	−1.31882	−0.659410	+	0.751783i	$0.729194\pi$
$150$	6.14212e6	0.148593
$151$	4.99295e7	1.18015	0.590076	−	0.807347i	$-0.299098\pi$
$151$	4.99295e7	1.18015	0.590076	+	0.807347i	$0.299098\pi$
$152$	−1.41355e7	−0.326482
$153$	−3.97956e7	−0.898287
$154$	−2.33046e6	−0.0514185
$155$	2.54910e7	0.549826
$156$	165498.	0.00349025
$157$	1.11496e7	0.229937	0.114969	−	0.993369i	$-0.463323\pi$
$157$	1.11496e7	0.229937	0.114969	+	0.993369i	$0.463323\pi$
$158$	−2.43341e7	−0.490812
$159$	−9.33322e6	−0.184137
$160$	3.11174e6	0.0600597
$161$	−1.44936e7	−0.273707
$162$	−4.06865e7	−0.751879
$163$	1.43793e7	0.260065	0.130033	−	0.991510i	$-0.458492\pi$
$163$	1.43793e7	0.260065	0.130033	+	0.991510i	$0.458492\pi$
$164$	−3.21454e6	−0.0569070
$165$	−1.66234e6	−0.0288089
$166$	−2.63090e7	−0.446402
$167$	6.92671e7	1.15085	0.575426	−	0.817854i	$-0.304836\pi$
$167$	6.92671e7	1.15085	0.575426	+	0.817854i	$0.304836\pi$
$168$	−6.83518e6	−0.111216
$169$	4.82681e6	0.0769231
$170$	−4.63951e7	−0.724271
$171$	1.98516e7	0.303606
$172$	−5.24886e6	−0.0786530
$173$	8.77920e6	0.128912	0.0644561	−	0.997921i	$-0.479469\pi$
$173$	8.77920e6	0.128912	0.0644561	+	0.997921i	$0.479469\pi$
$174$	−2.65636e7	−0.382265
$175$	1.29661e7	0.182885
$176$	1.00261e7	0.138623
$177$	−2.68671e7	−0.364178
$178$	2.09395e7	0.278289
$179$	−7.26491e6	−0.0946771	−0.0473385	−	0.998879i	$-0.515074\pi$
$179$	−7.26491e6	−0.0946771	−0.0473385	+	0.998879i	$0.515074\pi$
$180$	−2.13836e6	−0.0273292
$181$	−1.29031e8	−1.61740	−0.808700	−	0.588221i	$-0.799828\pi$
$181$	−1.29031e8	−1.61740	−0.808700	+	0.588221i	$0.799828\pi$
$182$	8.70216e6	0.106998
$183$	−3.39220e7	−0.409168
$184$	5.98466e7	0.708235
$185$	−9.64409e7	−1.11985
$186$	−2.06259e7	−0.235027
$187$	−1.17717e7	−0.131642
$188$	−962305.	−0.0105623
$189$	2.01538e7	0.217140
$190$	2.31437e7	0.244791
$191$	−8.88734e7	−0.922901	−0.461450	−	0.887166i	$-0.652671\pi$
$191$	−8.88734e7	−0.922901	−0.461450	+	0.887166i	$0.652671\pi$
$192$	2.81720e7	0.287252
$193$	6.62183e7	0.663022	0.331511	−	0.943451i	$-0.392442\pi$
$193$	6.62183e7	0.663022	0.331511	+	0.943451i	$0.392442\pi$
$194$	1.17854e8	1.15888
$195$	6.20733e6	0.0599492
$196$	629872.	0.00597525
$197$	3.29674e7	0.307222	0.153611	−	0.988131i	$-0.450910\pi$
$197$	3.29674e7	0.307222	0.153611	+	0.988131i	$0.450910\pi$
$198$	−1.35142e7	−0.123726
$199$	1.05985e8	0.953360	0.476680	−	0.879077i	$-0.341840\pi$
$199$	1.05985e8	0.953360	0.476680	+	0.879077i	$0.341840\pi$
$200$	−5.35394e7	−0.473226
$201$	−5.59233e7	−0.485743
$202$	1.46519e7	0.125073
$203$	−5.60762e7	−0.470481
$204$	1.50715e6	0.0124294
$205$	−1.20568e8	−0.977445
$206$	8.90271e7	0.709556
$207$	−8.40474e7	−0.658610
$208$	−3.74383e7	−0.288466
$209$	5.87218e6	0.0444926
$210$	1.11911e7	0.0833881
$211$	2.40198e8	1.76028	0.880139	−	0.474717i	$-0.157449\pi$
$211$	2.40198e8	1.76028	0.880139	+	0.474717i	$0.157449\pi$
$212$	−3.55137e6	−0.0255989
$213$	4.62365e7	0.327836
$214$	1.92642e7	0.134370
$215$	−1.96869e8	−1.35096
$216$	−8.32184e7	−0.561864
$217$	−4.35416e7	−0.289265
$218$	−2.07184e8	−1.35443
$219$	8.95562e6	0.0576158
$220$	−632535.	−0.00400502
$221$	4.39566e7	0.273937
$222$	7.80346e7	0.478687
$223$	−1.58098e8	−0.954682	−0.477341	−	0.878718i	$-0.658399\pi$
$223$	−1.58098e8	−0.954682	−0.477341	+	0.878718i	$0.658399\pi$
$224$	−5.31523e6	−0.0315976
$225$	7.51896e7	0.440067
$226$	1.41029e8	0.812696
$227$	−1.79222e8	−1.01696	−0.508478	−	0.861075i	$-0.669792\pi$
$227$	−1.79222e8	−1.01696	−0.508478	+	0.861075i	$0.669792\pi$
$228$	−751827.	−0.00420093
$229$	2.49422e8	1.37249	0.686246	−	0.727370i	$-0.259257\pi$
$229$	2.49422e8	1.37249	0.686246	+	0.727370i	$0.259257\pi$
$230$	−9.79854e7	−0.531024
$231$	2.83948e6	0.0151564
$232$	2.31548e8	1.21740
$233$	9.38820e7	0.486224	0.243112	−	0.969998i	$-0.421832\pi$
$233$	9.38820e7	0.486224	0.243112	+	0.969998i	$0.421832\pi$
$234$	5.04631e7	0.257465
$235$	−3.60931e7	−0.181421
$236$	−1.02232e7	−0.0506282
$237$	2.96491e7	0.144675
$238$	7.92484e7	0.381041
$239$	−2.79805e6	−0.0132575	−0.00662877	−	0.999978i	$-0.502110\pi$
$239$	−2.79805e6	−0.0132575	−0.00662877	+	0.999978i	$0.502110\pi$
$240$	−4.81460e7	−0.224813
$241$	3.52013e8	1.61994	0.809970	−	0.586471i	$-0.199483\pi$
$241$	3.52013e8	1.61994	0.809970	+	0.586471i	$0.199483\pi$
$242$	2.21038e8	1.00257
$243$	1.78076e8	0.796128
$244$	−1.29076e7	−0.0568828
$245$	2.36246e7	0.102632
$246$	9.75567e7	0.417815
$247$	−2.19273e7	−0.0925860
$248$	1.79791e8	0.748491
$249$	3.20553e7	0.131584
$250$	2.68821e8	1.08811
$251$	−2.61921e8	−1.04547	−0.522736	−	0.852495i	$-0.675089\pi$
$251$	−2.61921e8	−1.04547	−0.522736	+	0.852495i	$0.675089\pi$
$252$	3.65258e6	0.0143780
$253$	−2.48615e7	−0.0965175
$254$	−3.53838e8	−1.35483
$255$	5.65286e7	0.213490
$256$	3.36252e7	0.125264
$257$	−1.71594e8	−0.630573	−0.315286	−	0.948997i	$-0.602101\pi$
$257$	−1.71594e8	−0.630573	−0.315286	+	0.948997i	$0.602101\pi$
$258$	1.59295e8	0.577476
$259$	1.64733e8	0.589156
$260$	2.36194e6	0.00833418
$261$	−3.25182e8	−1.13210
$262$	5.77093e8	1.98240
$263$	4.18404e8	1.41824	0.709122	−	0.705086i	$-0.249092\pi$
$263$	4.18404e8	1.41824	0.709122	+	0.705086i	$0.249092\pi$
$264$	−1.17247e7	−0.0392182
$265$	−1.33201e8	−0.439691
$266$	−3.95323e7	−0.128785
$267$	−2.55131e7	−0.0820301
$268$	−2.12793e7	−0.0675282
$269$	4.21282e8	1.31959	0.659796	−	0.751445i	$-0.270643\pi$
$269$	4.21282e8	1.31959	0.659796	+	0.751445i	$0.270643\pi$
$270$	1.36251e8	0.421277
$271$	9.99340e7	0.305015	0.152507	−	0.988302i	$-0.451265\pi$
$271$	9.99340e7	0.305015	0.152507	+	0.988302i	$0.451265\pi$
$272$	−3.40941e8	−1.02728
$273$	−1.06029e7	−0.0315394
$274$	−2.50822e8	−0.736613
$275$	2.22414e7	0.0644907
$276$	3.18307e6	0.00911306
$277$	−4.19638e8	−1.18630	−0.593151	−	0.805091i	$-0.702116\pi$
$277$	−4.19638e8	−1.18630	−0.593151	+	0.805091i	$0.702116\pi$
$278$	2.72578e8	0.760911
$279$	−2.52495e8	−0.696045
$280$	−9.75498e7	−0.265567
$281$	−2.46337e8	−0.662303	−0.331152	−	0.943578i	$-0.607437\pi$
$281$	−2.46337e8	−0.662303	−0.331152	+	0.943578i	$0.607437\pi$
$282$	2.92046e7	0.0775494
$283$	−4.21579e8	−1.10567	−0.552836	−	0.833290i	$-0.686454\pi$
$283$	−4.21579e8	−1.10567	−0.552836	+	0.833290i	$0.686454\pi$
$284$	1.75934e7	0.0455759
$285$	−2.81987e7	−0.0721560
$286$	1.49272e7	0.0377309
$287$	2.05944e8	0.514236
$288$	−3.08226e7	−0.0760318
$289$	−1.00368e7	−0.0244599
$290$	−3.79108e8	−0.912788
$291$	−1.43595e8	−0.341598
$292$	3.40769e6	0.00800978
$293$	7.26293e8	1.68684	0.843422	−	0.537251i	$-0.180537\pi$
$293$	7.26293e8	1.68684	0.843422	+	0.537251i	$0.180537\pi$
$294$	−1.91157e7	−0.0438707
$295$	−3.83439e8	−0.869600
$296$	−6.80209e8	−1.52448
$297$	3.45707e7	0.0765703
$298$	6.14951e8	1.34612
$299$	9.28352e7	0.200846
$300$	−2.84760e6	−0.00608913
$301$	3.36275e8	0.710742
$302$	−5.76581e8	−1.20458
$303$	−1.78522e7	−0.0368674
$304$	1.70075e8	0.347202
$305$	−4.84125e8	−0.977030
$306$	4.59555e8	0.916881
$307$	6.53736e8	1.28949	0.644745	−	0.764397i	$-0.276963\pi$
$307$	6.53736e8	1.28949	0.644745	+	0.764397i	$0.276963\pi$
$308$	1.08045e6	0.00210705
$309$	−1.08472e8	−0.209153
$310$	−2.94367e8	−0.561207
$311$	−4.55953e8	−0.859526	−0.429763	−	0.902942i	$-0.641403\pi$
$311$	−4.55953e8	−0.859526	−0.429763	+	0.902942i	$0.641403\pi$
$312$	4.37810e7	0.0816103
$313$	−2.42543e8	−0.447079	−0.223539	−	0.974695i	$-0.571761\pi$
$313$	−2.42543e8	−0.447079	−0.223539	+	0.974695i	$0.571761\pi$
$314$	−1.28754e8	−0.234697
$315$	1.36997e8	0.246959
$316$	1.12818e7	0.0201128
$317$	−7.29505e8	−1.28624	−0.643119	−	0.765767i	$-0.722360\pi$
$317$	−7.29505e8	−1.28624	−0.643119	+	0.765767i	$0.722360\pi$
$318$	1.07779e8	0.187949
$319$	−9.61899e7	−0.165906
$320$	4.02063e8	0.685913
$321$	−2.34718e7	−0.0396077
$322$	1.67371e8	0.279373
$323$	−1.99686e8	−0.329716
$324$	1.88630e7	0.0308109
$325$	−8.30513e7	−0.134201
$326$	−1.66051e8	−0.265448
$327$	2.52436e8	0.399241
$328$	−8.50378e8	−1.33062
$329$	6.16514e7	0.0954459
$330$	1.91965e7	0.0294052
$331$	−1.03954e9	−1.57558	−0.787792	−	0.615942i	$-0.788776\pi$
$331$	−1.03954e9	−1.57558	−0.787792	+	0.615942i	$0.788776\pi$
$332$	1.21973e7	0.0182929
$333$	9.55272e8	1.41766
$334$	−7.99890e8	−1.17467
$335$	−7.98121e8	−1.15988
$336$	8.22392e7	0.118275
$337$	−8.72441e8	−1.24174	−0.620871	−	0.783913i	$-0.713221\pi$
$337$	−8.72441e8	−1.24174	−0.620871	+	0.783913i	$0.713221\pi$
$338$	−5.57395e7	−0.0785153
$339$	−1.71832e8	−0.239555
$340$	2.15097e7	0.0296795
$341$	−7.46888e7	−0.102004
$342$	−2.29245e8	−0.309890
$343$	−4.03536e7	−0.0539949
$344$	−1.38854e9	−1.83909
$345$	1.19387e8	0.156528
$346$	−1.01381e8	−0.131580
$347$	−3.21826e8	−0.413492	−0.206746	−	0.978395i	$-0.566287\pi$
$347$	−3.21826e8	−0.413492	−0.206746	+	0.978395i	$0.566287\pi$
$348$	1.23154e7	0.0156646
$349$	1.12631e9	1.41830	0.709150	−	0.705058i	$-0.249079\pi$
$349$	1.12631e9	1.41830	0.709150	+	0.705058i	$0.249079\pi$
$350$	−1.49732e8	−0.186670
$351$	−1.29090e8	−0.159337
$352$	−9.11744e6	−0.0111423
$353$	1.78446e8	0.215922	0.107961	−	0.994155i	$-0.465568\pi$
$353$	1.78446e8	0.215922	0.107961	+	0.994155i	$0.465568\pi$
$354$	3.10258e8	0.371716
$355$	6.59874e8	0.782820
$356$	−9.70795e6	−0.0114039
$357$	−9.65577e7	−0.112318
$358$	8.38944e7	0.0966368
$359$	−3.90807e8	−0.445791	−0.222896	−	0.974842i	$-0.571551\pi$
$359$	−3.90807e8	−0.445791	−0.222896	+	0.974842i	$0.571551\pi$
$360$	−5.65684e8	−0.639021
$361$	−7.94260e8	−0.888562
$362$	1.49003e9	1.65088
$363$	−2.69317e8	−0.295523
$364$	−4.03449e6	−0.00438463
$365$	1.27812e8	0.137577
$366$	3.91727e8	0.417638
$367$	1.17397e9	1.23973	0.619865	−	0.784709i	$-0.287188\pi$
$367$	1.17397e9	1.23973	0.619865	+	0.784709i	$0.287188\pi$
$368$	−7.20059e8	−0.753184
$369$	1.19425e9	1.23738
$370$	1.11369e9	1.14303
$371$	2.27524e8	0.231322
$372$	9.56255e6	0.00963105
$373$	−6.79811e8	−0.678277	−0.339138	−	0.940736i	$-0.610135\pi$
$373$	−6.79811e8	−0.678277	−0.339138	+	0.940736i	$0.610135\pi$
$374$	1.35938e8	0.134366
$375$	−3.27537e8	−0.320738
$376$	−2.54569e8	−0.246972
$377$	3.59182e8	0.345239
$378$	−2.32734e8	−0.221635
$379$	2.12085e8	0.200112	0.100056	−	0.994982i	$-0.468098\pi$
$379$	2.12085e8	0.200112	0.100056	+	0.994982i	$0.468098\pi$
$380$	−1.07299e7	−0.0100312
$381$	4.31122e8	0.399359
$382$	1.02630e9	0.942004
$383$	−1.71145e6	−0.00155657	−0.000778283	−	1.00000i	$-0.500248\pi$
$383$	−1.71145e6	−0.00155657	−0.000778283		1.00000i	$0.500248\pi$
$384$	−3.53236e8	−0.318350
$385$	4.05242e7	0.0361911
$386$	−7.64682e8	−0.676746
$387$	1.95003e9	1.71023
$388$	−5.46393e7	−0.0474891
$389$	9.35364e8	0.805670	0.402835	−	0.915273i	$-0.368025\pi$
$389$	9.35364e8	0.805670	0.402835	+	0.915273i	$0.368025\pi$
$390$	−7.16816e7	−0.0611901
$391$	8.45428e8	0.715250
$392$	1.66627e8	0.139715
$393$	−7.03141e8	−0.584344
$394$	−3.80704e8	−0.313581
$395$	4.23144e8	0.345461
$396$	6.26542e6	0.00507011
$397$	1.45605e9	1.16791	0.583956	−	0.811785i	$-0.301504\pi$
$397$	1.45605e9	1.16791	0.583956	+	0.811785i	$0.301504\pi$
$398$	−1.22390e9	−0.973093
$399$	4.81668e7	0.0379615
$400$	6.44172e8	0.503260
$401$	−9.87942e8	−0.765114	−0.382557	−	0.923932i	$-0.624956\pi$
$401$	−9.87942e8	−0.765114	−0.382557	+	0.923932i	$0.624956\pi$
$402$	6.45796e8	0.495797
$403$	2.78895e8	0.212262
$404$	−6.79292e6	−0.00512533
$405$	7.07495e8	0.529213
$406$	6.47562e8	0.480220
$407$	2.82573e8	0.207754
$408$	3.98703e8	0.290629
$409$	−1.30216e9	−0.941092	−0.470546	−	0.882376i	$-0.655943\pi$
$409$	−1.30216e9	−0.941092	−0.470546	+	0.882376i	$0.655943\pi$
$410$	1.39230e9	0.997677
$411$	3.05607e8	0.217128
$412$	−4.12747e7	−0.0290766
$413$	6.54960e8	0.457499
$414$	9.70570e8	0.672242
$415$	4.57485e8	0.314202
$416$	3.40454e7	0.0231863
$417$	−3.32114e8	−0.224291
$418$	−6.78114e7	−0.0454136
$419$	1.13143e9	0.751411	0.375706	−	0.926739i	$-0.377400\pi$
$419$	1.13143e9	0.751411	0.375706	+	0.926739i	$0.377400\pi$
$420$	−5.18839e6	−0.00341712
$421$	3.34093e8	0.218213	0.109106	−	0.994030i	$-0.465201\pi$
$421$	3.34093e8	0.218213	0.109106	+	0.994030i	$0.465201\pi$
$422$	−2.77378e9	−1.79671
$423$	3.57512e8	0.229667
$424$	−9.39484e8	−0.598561
$425$	−7.56328e8	−0.477913
$426$	−5.33934e8	−0.334622
$427$	8.26943e8	0.514018
$428$	−8.93123e6	−0.00550628
$429$	−1.81875e7	−0.0111218
$430$	2.27342e9	1.37892
$431$	2.17502e9	1.30856	0.654279	−	0.756253i	$-0.272972\pi$
$431$	2.17502e9	1.30856	0.654279	+	0.756253i	$0.272972\pi$
$432$	1.00126e9	0.597524
$433$	−1.88086e9	−1.11339	−0.556697	−	0.830716i	$-0.687932\pi$
$433$	−1.88086e9	−1.11339	−0.556697	+	0.830716i	$0.687932\pi$
$434$	5.02814e8	0.295252
$435$	4.61912e8	0.269059
$436$	9.60543e7	0.0555027
$437$	−4.21733e8	−0.241742
$438$	−1.03419e8	−0.0588084
$439$	−1.93330e9	−1.09062	−0.545309	−	0.838235i	$-0.683588\pi$
$439$	−1.93330e9	−1.09062	−0.545309	+	0.838235i	$0.683588\pi$
$440$	−1.67331e8	−0.0936468
$441$	−2.34007e8	−0.129926
$442$	−5.07606e8	−0.279607
$443$	8.54605e8	0.467038	0.233519	−	0.972352i	$-0.424976\pi$
$443$	8.54605e8	0.467038	0.233519	+	0.972352i	$0.424976\pi$
$444$	−3.61783e7	−0.0196159
$445$	−3.64115e8	−0.195875
$446$	1.82570e9	0.974443
$447$	−7.49268e8	−0.396790
$448$	−6.86772e8	−0.360861
$449$	2.11517e8	0.110277	0.0551383	−	0.998479i	$-0.482440\pi$
$449$	2.11517e8	0.110277	0.0551383	+	0.998479i	$0.482440\pi$
$450$	−8.68282e8	−0.449176
$451$	3.53265e8	0.181335
$452$	−6.53836e7	−0.0333031
$453$	7.02517e8	0.355069
$454$	2.06964e9	1.03801
$455$	−1.51321e8	−0.0753113
$456$	−1.98889e8	−0.0982277
$457$	−9.05828e8	−0.443955	−0.221978	−	0.975052i	$-0.571251\pi$
$457$	−9.05828e8	−0.443955	−0.221978	+	0.975052i	$0.571251\pi$
$458$	−2.88029e9	−1.40090
$459$	−1.17559e9	−0.567430
$460$	4.54279e7	0.0217606
$461$	−3.81152e9	−1.81194	−0.905972	−	0.423337i	$-0.860859\pi$
$461$	−3.81152e9	−1.81194	−0.905972	+	0.423337i	$0.860859\pi$
$462$	−3.27900e7	−0.0154701
$463$	−2.30234e8	−0.107804	−0.0539020	−	0.998546i	$-0.517166\pi$
$463$	−2.30234e8	−0.107804	−0.0539020	+	0.998546i	$0.517166\pi$
$464$	−2.78593e9	−1.29466
$465$	3.58662e8	0.165425
$466$	−1.08414e9	−0.496289
$467$	3.23310e9	1.46896	0.734481	−	0.678629i	$-0.237426\pi$
$467$	3.23310e9	1.46896	0.734481	+	0.678629i	$0.237426\pi$
$468$	−2.33957e7	−0.0105505
$469$	1.36329e9	0.610214
$470$	4.16799e8	0.185176
$471$	1.56876e8	0.0691806
$472$	−2.70444e9	−1.18381
$473$	5.76827e8	0.250629
$474$	−3.42385e8	−0.147669
$475$	3.77286e8	0.161526
$476$	−3.67411e7	−0.0156145
$477$	1.31939e9	0.556621
$478$	3.23116e7	0.0135320
$479$	3.81717e9	1.58697	0.793483	−	0.608593i	$-0.208266\pi$
$479$	3.81717e9	1.58697	0.793483	+	0.608593i	$0.208266\pi$
$480$	4.37827e7	0.0180700
$481$	−1.05515e9	−0.432322
$482$	−4.06501e9	−1.65347
$483$	−2.03928e8	−0.0823495
$484$	−1.02478e8	−0.0410837
$485$	−2.04935e9	−0.815681
$486$	−2.05640e9	−0.812607
$487$	1.98582e9	0.779093	0.389547	−	0.921007i	$-0.372632\pi$
$487$	1.98582e9	0.779093	0.389547	+	0.921007i	$0.372632\pi$
$488$	−3.41459e9	−1.33005
$489$	2.02320e8	0.0782451
$490$	−2.72814e8	−0.104756
$491$	−2.54628e9	−0.970780	−0.485390	−	0.874298i	$-0.661322\pi$
$491$	−2.54628e9	−0.970780	−0.485390	+	0.874298i	$0.661322\pi$
$492$	−4.52291e7	−0.0171214
$493$	3.27098e9	1.22946
$494$	2.53214e8	0.0945025
$495$	2.34997e8	0.0870851
$496$	−2.16320e9	−0.795995
$497$	−1.12714e9	−0.411844
$498$	−3.70172e8	−0.134308
$499$	3.33049e9	1.19993	0.599965	−	0.800026i	$-0.295181\pi$
$499$	3.33049e9	1.19993	0.599965	+	0.800026i	$0.295181\pi$
$500$	−1.24631e8	−0.0445892
$501$	9.74600e8	0.346254
$502$	3.02463e9	1.06711
$503$	2.93770e9	1.02925	0.514624	−	0.857416i	$-0.327931\pi$
$503$	2.93770e9	1.02925	0.514624	+	0.857416i	$0.327931\pi$
$504$	9.66256e8	0.336190
$505$	−2.54782e8	−0.0880335
$506$	2.87098e8	0.0985153
$507$	6.79140e7	0.0231436
$508$	1.64046e8	0.0555191
$509$	−3.78133e9	−1.27096	−0.635480	−	0.772117i	$-0.719198\pi$
$509$	−3.78133e9	−1.27096	−0.635480	+	0.772117i	$0.719198\pi$
$510$	−6.52787e8	−0.217909
$511$	−2.18319e8	−0.0723798
$512$	2.82518e9	0.930253
$513$	5.86432e8	0.191782
$514$	1.98154e9	0.643625
$515$	−1.54809e9	−0.499425
$516$	−7.38523e7	−0.0236641
$517$	1.05753e8	0.0336571
$518$	−1.90231e9	−0.601351
$519$	1.23525e8	0.0387854
$520$	6.24831e8	0.194873
$521$	−9.46499e7	−0.0293216	−0.0146608	−	0.999893i	$-0.504667\pi$
$521$	−9.46499e7	−0.0293216	−0.0146608	+	0.999893i	$0.504667\pi$
$522$	3.75516e9	1.15553
$523$	−3.69842e9	−1.13047	−0.565237	−	0.824929i	$-0.691215\pi$
$523$	−3.69842e9	−1.13047	−0.565237	+	0.824929i	$0.691215\pi$
$524$	−2.67551e8	−0.0812359
$525$	1.82436e8	0.0550240
$526$	−4.83168e9	−1.44760
$527$	2.53983e9	0.755905
$528$	1.41068e8	0.0417072
$529$	−1.61930e9	−0.475590
$530$	1.53819e9	0.448792
$531$	3.79806e9	1.10086
$532$	1.83279e7	0.00527743
$533$	−1.31912e9	−0.377346
$534$	2.94622e8	0.0837280
$535$	−3.34983e8	−0.0945769
$536$	−5.62924e9	−1.57897
$537$	−1.02219e8	−0.0284852
$538$	−4.86491e9	−1.34691
$539$	−6.92203e7	−0.0190402
$540$	−6.31688e7	−0.0172633
$541$	−3.54737e9	−0.963198	−0.481599	−	0.876392i	$-0.659944\pi$
$541$	−3.54737e9	−0.963198	−0.481599	+	0.876392i	$0.659944\pi$
$542$	−1.15403e9	−0.311328
$543$	−1.81548e9	−0.486622
$544$	3.10043e8	0.0825706
$545$	3.60270e9	0.953324
$546$	1.22441e8	0.0321923
$547$	1.39470e9	0.364356	0.182178	−	0.983266i	$-0.441685\pi$
$547$	1.39470e9	0.364356	0.182178	+	0.983266i	$0.441685\pi$
$548$	1.16286e8	0.0301853
$549$	4.79538e9	1.23686
$550$	−2.56841e8	−0.0658256
$551$	−1.63170e9	−0.415536
$552$	8.42052e8	0.213085
$553$	−7.22781e8	−0.181748
$554$	4.84593e9	1.21086
$555$	−1.35694e9	−0.336926
$556$	−1.26372e8	−0.0311810
$557$	−4.52627e9	−1.10981	−0.554904	−	0.831915i	$-0.687245\pi$
$557$	−4.52627e9	−1.10981	−0.554904	+	0.831915i	$0.687245\pi$
$558$	2.91578e9	0.710453
$559$	−2.15393e9	−0.521542
$560$	1.17370e9	0.282421
$561$	−1.65630e8	−0.0396066
$562$	2.84467e9	0.676012
$563$	−4.30871e9	−1.01758	−0.508790	−	0.860891i	$-0.669907\pi$
$563$	−4.30871e9	−1.01758	−0.508790	+	0.860891i	$0.669907\pi$
$564$	−1.35398e7	−0.00317786
$565$	−2.45234e9	−0.572020
$566$	4.86834e9	1.12856
$567$	−1.20849e9	−0.278420
$568$	4.65417e9	1.06567
$569$	2.92685e9	0.666051	0.333026	−	0.942918i	$-0.391930\pi$
$569$	2.92685e9	0.666051	0.333026	+	0.942918i	$0.391930\pi$
$570$	3.25636e8	0.0736496
$571$	1.91392e9	0.430227	0.215113	−	0.976589i	$-0.430988\pi$
$571$	1.91392e9	0.430227	0.215113	+	0.976589i	$0.430988\pi$
$572$	−6.92052e6	−0.00154615
$573$	−1.25046e9	−0.277671
$574$	−2.37822e9	−0.524881
$575$	−1.59735e9	−0.350398
$576$	−3.98254e9	−0.868323
$577$	1.23234e9	0.267064	0.133532	−	0.991044i	$-0.457368\pi$
$577$	1.23234e9	0.267064	0.133532	+	0.991044i	$0.457368\pi$
$578$	1.15904e8	0.0249662
$579$	9.31703e8	0.199481
$580$	1.75762e8	0.0374047
$581$	−7.81440e8	−0.165302
$582$	1.65822e9	0.348668
$583$	3.90281e8	0.0815713
$584$	9.01474e8	0.187287
$585$	−8.77500e8	−0.181218
$586$	−8.38715e9	−1.72176
$587$	1.71187e9	0.349331	0.174665	−	0.984628i	$-0.444116\pi$
$587$	1.71187e9	0.349331	0.174665	+	0.984628i	$0.444116\pi$
$588$	8.86240e6	0.00179776
$589$	−1.26697e9	−0.255483
$590$	4.42791e9	0.887600
$591$	4.63856e8	0.0924331
$592$	8.18410e9	1.62123
$593$	−3.78075e9	−0.744537	−0.372269	−	0.928125i	$-0.621420\pi$
$593$	−3.78075e9	−0.744537	−0.372269	+	0.928125i	$0.621420\pi$
$594$	−3.99218e8	−0.0781552
$595$	−1.37805e9	−0.268197
$596$	−2.85103e8	−0.0551620
$597$	1.49122e9	0.286835
$598$	−1.07205e9	−0.205004
$599$	−9.71022e8	−0.184602	−0.0923008	−	0.995731i	$-0.529422\pi$
$599$	−9.71022e8	−0.184602	−0.0923008	+	0.995731i	$0.529422\pi$
$600$	−7.53308e8	−0.142378
$601$	−3.22064e9	−0.605176	−0.302588	−	0.953121i	$-0.597851\pi$
$601$	−3.22064e9	−0.605176	−0.302588	+	0.953121i	$0.597851\pi$
$602$	−3.88327e9	−0.725454
$603$	7.90560e9	1.46833
$604$	2.67314e8	0.0493619
$605$	−3.84362e9	−0.705662
$606$	2.06155e8	0.0376305
$607$	−7.82533e9	−1.42018	−0.710089	−	0.704112i	$-0.751345\pi$
$607$	−7.82533e9	−1.42018	−0.710089	+	0.704112i	$0.751345\pi$
$608$	−1.54662e8	−0.0279074
$609$	−7.89001e8	−0.141552
$610$	5.59062e9	0.997254
$611$	−3.94892e8	−0.0700381
$612$	−2.13059e8	−0.0375724
$613$	1.54946e9	0.271686	0.135843	−	0.990730i	$-0.456626\pi$
$613$	1.54946e9	0.271686	0.135843	+	0.990730i	$0.456626\pi$
$614$	−7.54928e9	−1.31618
$615$	−1.69641e9	−0.294081
$616$	2.85822e8	0.0492678
$617$	6.32624e9	1.08429	0.542147	−	0.840283i	$-0.317611\pi$
$617$	6.32624e9	1.08429	0.542147	+	0.840283i	$0.317611\pi$
$618$	1.25263e9	0.213482
$619$	−5.72794e8	−0.0970691	−0.0485345	−	0.998822i	$-0.515455\pi$
$619$	−5.72794e8	−0.0970691	−0.0485345	+	0.998822i	$0.515455\pi$
$620$	1.36474e8	0.0229974
$621$	−2.48282e9	−0.416030
$622$	5.26530e9	0.877318
$623$	6.21953e8	0.103050
$624$	−5.26762e8	−0.0867898
$625$	−1.72122e9	−0.282005
$626$	2.80087e9	0.456333
$627$	8.26226e7	0.0133864
$628$	5.96928e7	0.00961753
$629$	−9.60902e9	−1.53958
$630$	−1.58203e9	−0.252070
$631$	8.66481e9	1.37296	0.686478	−	0.727151i	$-0.259156\pi$
$631$	8.66481e9	1.37296	0.686478	+	0.727151i	$0.259156\pi$
$632$	2.98449e9	0.470283
$633$	3.37963e9	0.529610
$634$	8.42425e9	1.31286
$635$	6.15286e9	0.953606
$636$	−4.99684e7	−0.00770186
$637$	2.58475e8	0.0396214
$638$	1.11079e9	0.169340
$639$	−6.53623e9	−0.991001
$640$	−5.04128e9	−0.760171
$641$	−1.09796e10	−1.64658	−0.823289	−	0.567622i	$-0.807863\pi$
$641$	−1.09796e10	−1.64658	−0.823289	+	0.567622i	$0.807863\pi$
$642$	2.71050e8	0.0404275
$643$	8.67979e9	1.28757	0.643785	−	0.765207i	$-0.277363\pi$
$643$	8.67979e9	1.28757	0.643785	+	0.765207i	$0.277363\pi$
$644$	−7.75963e7	−0.0114483
$645$	−2.76997e9	−0.406459
$646$	2.30596e9	0.336541
$647$	8.47493e9	1.23019	0.615094	−	0.788454i	$-0.289118\pi$
$647$	8.47493e9	1.23019	0.615094	+	0.788454i	$0.289118\pi$
$648$	4.99004e9	0.720430
$649$	1.12348e9	0.161328
$650$	9.59068e8	0.136979
$651$	−6.12638e8	−0.0870303
$652$	7.69844e7	0.0108777
$653$	−5.29960e9	−0.744813	−0.372407	−	0.928070i	$-0.621467\pi$
$653$	−5.29960e9	−0.744813	−0.372407	+	0.928070i	$0.621467\pi$
$654$	−2.91511e9	−0.407505
$655$	−1.00350e10	−1.39532
$656$	1.02315e10	1.41507
$657$	−1.26601e9	−0.174164
$658$	−7.11943e8	−0.0974215
$659$	−2.90477e9	−0.395379	−0.197689	−	0.980265i	$-0.563344\pi$
$659$	−2.90477e9	−0.395379	−0.197689	+	0.980265i	$0.563344\pi$
$660$	−8.89987e6	−0.00120498
$661$	−9.48249e9	−1.27708	−0.638539	−	0.769590i	$-0.720461\pi$
$661$	−9.48249e9	−1.27708	−0.638539	+	0.769590i	$0.720461\pi$
$662$	1.20044e10	1.60820
$663$	6.18476e8	0.0824187
$664$	3.22670e9	0.427730
$665$	6.87424e8	0.0906460
$666$	−1.10314e10	−1.44700
$667$	6.90824e9	0.901419
$668$	3.70844e8	0.0481364
$669$	−2.22446e9	−0.287232
$670$	9.21662e9	1.18389
$671$	1.41849e9	0.181258
$672$	−7.47861e7	−0.00950667
$673$	−3.38424e9	−0.427966	−0.213983	−	0.976837i	$-0.568644\pi$
$673$	−3.38424e9	−0.427966	−0.213983	+	0.976837i	$0.568644\pi$
$674$	1.00749e10	1.26744
$675$	2.22116e9	0.277982
$676$	2.58419e7	0.00321744
$677$	8.96596e9	1.11055	0.555273	−	0.831668i	$-0.312614\pi$
$677$	8.96596e9	1.11055	0.555273	+	0.831668i	$0.312614\pi$
$678$	1.98430e9	0.244514
$679$	3.50054e9	0.429132
$680$	5.69018e9	0.693977
$681$	−2.52169e9	−0.305968
$682$	8.62498e8	0.104115
$683$	1.13041e9	0.135757	0.0678785	−	0.997694i	$-0.478377\pi$
$683$	1.13041e9	0.135757	0.0678785	+	0.997694i	$0.478377\pi$
$684$	1.06282e8	0.0126988
$685$	4.36154e9	0.518468
$686$	4.65999e8	0.0551126
$687$	3.50940e9	0.412938
$688$	1.67065e10	1.95581
$689$	−1.45735e9	−0.169744
$690$	−1.37867e9	−0.159768
$691$	−1.22482e10	−1.41221	−0.706103	−	0.708109i	$-0.749548\pi$
$691$	−1.22482e10	−1.41221	−0.706103	+	0.708109i	$0.749548\pi$
$692$	4.70023e7	0.00539197
$693$	−4.01403e8	−0.0458157
$694$	3.71641e9	0.422051
$695$	−4.73984e9	−0.535571
$696$	3.25792e9	0.366276
$697$	−1.20129e10	−1.34380
$698$	−1.30065e10	−1.44766
$699$	1.32094e9	0.146289
$700$	6.94184e7	0.00764947
$701$	−2.18231e9	−0.239278	−0.119639	−	0.992817i	$-0.538174\pi$
$701$	−2.18231e9	−0.239278	−0.119639	+	0.992817i	$0.538174\pi$
$702$	1.49072e9	0.162636
$703$	4.79336e9	0.520351
$704$	−1.17805e9	−0.127250
$705$	−5.07836e8	−0.0545835
$706$	−2.06068e9	−0.220391
$707$	4.35198e8	0.0463147
$708$	−1.43841e8	−0.0152324
$709$	1.18778e10	1.25162	0.625810	−	0.779975i	$-0.284768\pi$
$709$	1.18778e10	1.25162	0.625810	+	0.779975i	$0.284768\pi$
$710$	−7.62016e9	−0.799024
$711$	−4.19135e9	−0.437331
$712$	−2.56815e9	−0.266649
$713$	5.36406e9	0.554217
$714$	1.11504e9	0.114643
$715$	−2.59568e8	−0.0265570
$716$	−3.88950e7	−0.00396003
$717$	−3.93690e7	−0.00398876
$718$	4.51299e9	0.455019
$719$	7.35320e8	0.0737777	0.0368888	−	0.999319i	$-0.488255\pi$
$719$	7.35320e8	0.0737777	0.0368888	+	0.999319i	$0.488255\pi$
$720$	6.80617e9	0.679577
$721$	2.64432e9	0.262748
$722$	9.17203e9	0.906954
$723$	4.95288e9	0.487387
$724$	−6.90806e8	−0.0676506
$725$	−6.18018e9	−0.602307
$726$	3.11004e9	0.301640
$727$	1.30938e10	1.26385	0.631926	−	0.775028i	$-0.282264\pi$
$727$	1.30938e10	1.26385	0.631926	+	0.775028i	$0.282264\pi$
$728$	−1.06729e9	−0.102523
$729$	−5.19987e9	−0.497102
$730$	−1.47596e9	−0.140425
$731$	−1.96153e10	−1.85731
$732$	−1.81612e8	−0.0171142
$733$	6.64908e9	0.623588	0.311794	−	0.950150i	$-0.399070\pi$
$733$	6.64908e9	0.623588	0.311794	+	0.950150i	$0.399070\pi$
$734$	−1.35569e10	−1.26539
$735$	3.32402e8	0.0308786
$736$	6.54803e8	0.0605394
$737$	2.33850e9	0.215180
$738$	−1.37911e10	−1.26300
$739$	4.63171e9	0.422169	0.211084	−	0.977468i	$-0.432301\pi$
$739$	4.63171e9	0.422169	0.211084	+	0.977468i	$0.432301\pi$
$740$	−5.16327e8	−0.0468397
$741$	−3.08521e8	−0.0278561
$742$	−2.62742e9	−0.236111
$743$	−5.85228e9	−0.523437	−0.261718	−	0.965144i	$-0.584289\pi$
$743$	−5.85228e9	−0.523437	−0.261718	+	0.965144i	$0.584289\pi$
$744$	2.52969e9	0.225196
$745$	−1.06933e10	−0.947472
$746$	7.85038e9	0.692317
$747$	−4.53151e9	−0.397760
$748$	−6.30235e7	−0.00550614
$749$	5.72192e8	0.0497571
$750$	3.78236e9	0.327377
$751$	2.14428e10	1.84732	0.923658	−	0.383217i	$-0.125184\pi$
$751$	2.14428e10	1.84732	0.923658	+	0.383217i	$0.125184\pi$
$752$	3.06291e9	0.262647
$753$	−3.68527e9	−0.314548
$754$	−4.14779e9	−0.352385
$755$	1.00261e10	0.847850
$756$	1.07900e8	0.00908227
$757$	−1.38619e10	−1.16142	−0.580709	−	0.814111i	$-0.697224\pi$
$757$	−1.38619e10	−1.16142	−0.580709	+	0.814111i	$0.697224\pi$
$758$	−2.44913e9	−0.204254
$759$	−3.49806e8	−0.0290389
$760$	−2.83849e9	−0.234552
$761$	−9.06999e9	−0.746037	−0.373019	−	0.927824i	$-0.621677\pi$
$761$	−9.06999e9	−0.746037	−0.373019	+	0.927824i	$0.621677\pi$
$762$	−4.97855e9	−0.407625
$763$	−6.15385e9	−0.501546
$764$	−4.75812e8	−0.0386019
$765$	−7.99118e9	−0.645351
$766$	1.97636e7	0.00158879
$767$	−4.19518e9	−0.335712
$768$	4.73113e8	0.0376877
$769$	−1.99016e10	−1.57814	−0.789069	−	0.614305i	$-0.789437\pi$
$769$	−1.99016e10	−1.57814	−0.789069	+	0.614305i	$0.789437\pi$
$770$	−4.67969e8	−0.0369403
$771$	−2.41435e9	−0.189719
$772$	3.54521e8	0.0277320
$773$	−8.11475e9	−0.631898	−0.315949	−	0.948776i	$-0.602323\pi$
$773$	−8.11475e9	−0.631898	−0.315949	+	0.948776i	$0.602323\pi$
$774$	−2.25188e10	−1.74563
$775$	−4.79874e9	−0.370315
$776$	−1.44543e10	−1.11041
$777$	2.31781e9	0.177258
$778$	−1.08015e10	−0.822346
$779$	5.99253e9	0.454181
$780$	3.32329e7	0.00250748
$781$	−1.93344e9	−0.145229
$782$	−9.76291e9	−0.730055
$783$	−9.60610e9	−0.715124
$784$	−2.00481e9	−0.148582
$785$	2.23890e9	0.165192
$786$	8.11980e9	0.596439
$787$	2.35662e9	0.172337	0.0861684	−	0.996281i	$-0.472538\pi$
$787$	2.35662e9	0.172337	0.0861684	+	0.996281i	$0.472538\pi$
$788$	1.76501e8	0.0128501
$789$	5.88701e9	0.426703
$790$	−4.88642e9	−0.352611
$791$	4.18889e9	0.300941
$792$	1.65746e9	0.118551
$793$	−5.29678e9	−0.377186
$794$	−1.68143e10	−1.19209
$795$	−1.87416e9	−0.132289
$796$	5.67422e8	0.0398759
$797$	1.63587e10	1.14457	0.572287	−	0.820053i	$-0.306056\pi$
$797$	1.63587e10	1.14457	0.572287	+	0.820053i	$0.306056\pi$
$798$	−5.56225e8	−0.0387472
$799$	−3.59619e9	−0.249419
$800$	−5.85793e8	−0.0404510
$801$	3.60666e9	0.247965
$802$	1.14087e10	0.780951
$803$	−3.74491e8	−0.0255233
$804$	−2.99403e8	−0.0203170
$805$	−2.91040e9	−0.196638
$806$	−3.22065e9	−0.216656
$807$	5.92750e9	0.397022
$808$	−1.79700e9	−0.119842
$809$	−7.83612e9	−0.520333	−0.260166	−	0.965564i	$-0.583777\pi$
$809$	−7.83612e9	−0.520333	−0.260166	+	0.965564i	$0.583777\pi$
$810$	−8.17007e9	−0.540167
$811$	2.67152e10	1.75867	0.879337	−	0.476200i	$-0.157986\pi$
$811$	2.67152e10	1.75867	0.879337	+	0.476200i	$0.157986\pi$
$812$	−3.00222e8	−0.0196787
$813$	1.40609e9	0.0917689
$814$	−3.26312e9	−0.212055
$815$	2.88745e9	0.186837
$816$	−4.79710e9	−0.309074
$817$	9.78488e9	0.627738
$818$	1.50372e10	0.960572
$819$	1.49888e9	0.0953393
$820$	−6.45498e8	−0.0408833
$821$	2.39063e10	1.50769	0.753845	−	0.657053i	$-0.228197\pi$
$821$	2.39063e10	1.50769	0.753845	+	0.657053i	$0.228197\pi$
$822$	−3.52911e9	−0.221623
$823$	5.20953e9	0.325761	0.162881	−	0.986646i	$-0.447921\pi$
$823$	5.20953e9	0.325761	0.162881	+	0.986646i	$0.447921\pi$
$824$	−1.09188e10	−0.679878
$825$	3.12940e8	0.0194031
$826$	−7.56341e9	−0.466969
$827$	−8.76573e9	−0.538913	−0.269457	−	0.963013i	$-0.586844\pi$
$827$	−8.76573e9	−0.538913	−0.269457	+	0.963013i	$0.586844\pi$
$828$	−4.49975e8	−0.0275475
$829$	−1.87801e10	−1.14487	−0.572436	−	0.819949i	$-0.694002\pi$
$829$	−1.87801e10	−1.14487	−0.572436	+	0.819949i	$0.694002\pi$
$830$	−5.28299e9	−0.320705
$831$	−5.90437e9	−0.356919
$832$	4.39894e9	0.264799
$833$	2.35387e9	0.141099
$834$	3.83522e9	0.228933
$835$	1.39092e10	0.826800
$836$	3.14386e7	0.00186098
$837$	−7.45888e9	−0.439678
$838$	−1.30656e10	−0.766965
$839$	1.46371e10	0.855631	0.427816	−	0.903866i	$-0.359283\pi$
$839$	1.46371e10	0.855631	0.427816	+	0.903866i	$0.359283\pi$
$840$	−1.37254e9	−0.0799003
$841$	9.47828e9	0.549469
$842$	−3.85807e9	−0.222729
$843$	−3.46600e9	−0.199265
$844$	1.28598e9	0.0736267
$845$	9.69250e8	0.0552634
$846$	−4.12850e9	−0.234421
$847$	6.56536e9	0.371250
$848$	1.13036e10	0.636550
$849$	−5.93168e9	−0.332660
$850$	8.73400e9	0.487806
$851$	−2.02940e10	−1.12879
$852$	2.47542e8	0.0137123
$853$	5.96060e9	0.328828	0.164414	−	0.986391i	$-0.447427\pi$
$853$	5.96060e9	0.328828	0.164414	+	0.986391i	$0.447427\pi$
$854$	−9.54945e9	−0.524658
$855$	3.98632e9	0.218117
$856$	−2.36268e9	−0.128750
$857$	−1.04626e10	−0.567815	−0.283907	−	0.958852i	$-0.591631\pi$
$857$	−1.04626e10	−0.567815	−0.283907	+	0.958852i	$0.591631\pi$
$858$	2.10028e8	0.0113520
$859$	2.04574e9	0.110122	0.0550611	−	0.998483i	$-0.482465\pi$
$859$	2.04574e9	0.110122	0.0550611	+	0.998483i	$0.482465\pi$
$860$	−1.05400e9	−0.0565062
$861$	2.89767e9	0.154717
$862$	−2.51169e10	−1.33564
$863$	1.78313e9	0.0944377	0.0472189	−	0.998885i	$-0.484964\pi$
$863$	1.78313e9	0.0944377	0.0472189	+	0.998885i	$0.484964\pi$
$864$	−9.10522e8	−0.0480278
$865$	1.76291e9	0.0926135
$866$	2.17200e10	1.13644
$867$	−1.41220e8	−0.00735917
$868$	−2.33114e8	−0.0120990
$869$	−1.23982e9	−0.0640897
$870$	−5.33411e9	−0.274628
$871$	−8.73219e9	−0.447775
$872$	2.54103e10	1.29778
$873$	2.02994e10	1.03260
$874$	4.87013e9	0.246746
$875$	7.98463e9	0.402927
$876$	4.79468e7	0.00240988
$877$	4.82318e9	0.241455	0.120727	−	0.992686i	$-0.461477\pi$
$877$	4.82318e9	0.241455	0.120727	+	0.992686i	$0.461477\pi$
$878$	2.23255e10	1.11319
$879$	1.02191e10	0.507516
$880$	2.01329e9	0.0995902
$881$	3.75657e10	1.85087	0.925434	−	0.378909i	$-0.123700\pi$
$881$	3.75657e10	1.85087	0.925434	+	0.378909i	$0.123700\pi$
$882$	2.70229e9	0.132615
$883$	−2.54765e9	−0.124531	−0.0622654	−	0.998060i	$-0.519833\pi$
$883$	−2.54765e9	−0.124531	−0.0622654	+	0.998060i	$0.519833\pi$
$884$	2.35336e8	0.0114579
$885$	−5.39505e9	−0.261634
$886$	−9.86889e9	−0.476706
$887$	2.67278e10	1.28597	0.642985	−	0.765878i	$-0.277696\pi$
$887$	2.67278e10	1.28597	0.642985	+	0.765878i	$0.277696\pi$
$888$	−9.57065e9	−0.458665
$889$	−1.05098e10	−0.501694
$890$	4.20477e9	0.199929
$891$	−2.07297e9	−0.0981794
$892$	−8.46427e8	−0.0399312
$893$	1.79392e9	0.0842992
$894$	8.65246e9	0.405003
$895$	−1.45883e9	−0.0680182
$896$	8.61112e9	0.399928
$897$	1.30621e9	0.0604280
$898$	−2.44258e9	−0.112559
$899$	2.07537e10	0.952656
$900$	4.02552e8	0.0184066
$901$	−1.32717e10	−0.604490
$902$	−4.07946e9	−0.185089
$903$	4.73145e9	0.213839
$904$	−1.72966e10	−0.778704
$905$	−2.59100e10	−1.16198
$906$	−8.11259e9	−0.362419
$907$	1.36112e10	0.605719	0.302859	−	0.953035i	$-0.402059\pi$
$907$	1.36112e10	0.605719	0.302859	+	0.953035i	$0.402059\pi$
$908$	−9.59525e8	−0.0425359
$909$	2.52368e9	0.111445
$910$	1.74744e9	0.0768701
$911$	−3.13727e10	−1.37479	−0.687397	−	0.726282i	$-0.741247\pi$
$911$	−3.13727e10	−1.37479	−0.687397	+	0.726282i	$0.741247\pi$
$912$	2.39298e9	0.104462
$913$	−1.34044e9	−0.0582906
$914$	1.04604e10	0.453145
$915$	−6.81172e9	−0.293956
$916$	1.33536e9	0.0574069
$917$	1.71411e10	0.734082
$918$	1.35756e10	0.579175
$919$	1.03132e10	0.438316	0.219158	−	0.975689i	$-0.429669\pi$
$919$	1.03132e10	0.438316	0.219158	+	0.975689i	$0.429669\pi$
$920$	1.20175e10	0.508813
$921$	9.19818e9	0.387965
$922$	4.40150e10	1.84945
$923$	7.21964e9	0.302211
$924$	1.52021e7	0.000633943 0
$925$	1.81552e10	0.754234
$926$	2.65871e9	0.110036
$927$	1.53342e10	0.632240
$928$	2.53345e9	0.104063
$929$	8.99804e9	0.368208	0.184104	−	0.982907i	$-0.441062\pi$
$929$	8.99804e9	0.368208	0.184104	+	0.982907i	$0.441062\pi$
$930$	−4.14179e9	−0.168849
$931$	−1.17420e9	−0.0476891
$932$	5.02628e8	0.0203372
$933$	−6.41534e9	−0.258603
$934$	−3.73355e10	−1.49937
$935$	−2.36382e9	−0.0945744
$936$	−6.18911e9	−0.246696
$937$	2.02199e10	0.802955	0.401478	−	0.915869i	$-0.368497\pi$
$937$	2.02199e10	0.802955	0.401478	+	0.915869i	$0.368497\pi$
$938$	−1.57431e10	−0.622845
$939$	−3.41263e9	−0.134511
$940$	−1.93236e8	−0.00758823
$941$	3.22483e10	1.26166	0.630831	−	0.775920i	$-0.282714\pi$
$941$	3.22483e10	1.26166	0.630831	+	0.775920i	$0.282714\pi$
$942$	−1.81159e9	−0.0706126
$943$	−2.53710e10	−0.985252
$944$	3.25392e10	1.25894
$945$	4.04699e9	0.155999
$946$	−6.66114e9	−0.255817
$947$	4.80145e10	1.83716	0.918580	−	0.395234i	$-0.129337\pi$
$947$	4.80145e10	1.83716	0.918580	+	0.395234i	$0.129337\pi$
$948$	1.58736e8	0.00605127
$949$	1.39838e9	0.0531123
$950$	−4.35686e9	−0.164870
$951$	−1.02643e10	−0.386987
$952$	−9.71952e9	−0.365103
$953$	1.22414e10	0.458147	0.229074	−	0.973409i	$-0.426430\pi$
$953$	1.22414e10	0.458147	0.229074	+	0.973409i	$0.426430\pi$
$954$	−1.52362e10	−0.568143
$955$	−1.78463e10	−0.663034
$956$	−1.49803e7	−0.000554519 0
$957$	−1.35341e9	−0.0499157
$958$	−4.40803e10	−1.61981
$959$	−7.45003e9	−0.272768
$960$	5.65709e9	0.206369
$961$	−1.13979e10	−0.414281
$962$	1.21848e10	0.441271
$963$	3.31810e9	0.119728
$964$	1.88462e9	0.0677568
$965$	1.32970e10	0.476330
$966$	2.35493e9	0.0840541
$967$	−3.45798e9	−0.122979	−0.0614893	−	0.998108i	$-0.519585\pi$
$967$	−3.45798e9	−0.122979	−0.0614893	+	0.998108i	$0.519585\pi$
$968$	−2.71095e10	−0.960633
$969$	−2.80962e9	−0.0992007
$970$	2.36657e10	0.832565
$971$	3.14586e10	1.10274	0.551368	−	0.834262i	$-0.314106\pi$
$971$	3.14586e10	1.10274	0.551368	+	0.834262i	$0.314106\pi$
$972$	9.53386e8	0.0332994
$973$	8.09622e9	0.281765
$974$	−2.29321e10	−0.795220
$975$	−1.16855e9	−0.0403766
$976$	4.10835e10	1.41447
$977$	2.28926e10	0.785352	0.392676	−	0.919677i	$-0.371549\pi$
$977$	2.28926e10	0.785352	0.392676	+	0.919677i	$0.371549\pi$
$978$	−2.33637e9	−0.0798647
$979$	1.06686e9	0.0363387
$980$	1.26482e8	0.00429276
$981$	−3.56857e10	−1.20685
$982$	2.94042e10	0.990874
$983$	5.36225e10	1.80057	0.900284	−	0.435303i	$-0.143359\pi$
$983$	5.36225e10	1.80057	0.900284	+	0.435303i	$0.143359\pi$
$984$	−1.19650e10	−0.400339
$985$	6.62003e9	0.220716
$986$	−3.77730e10	−1.25491
$987$	8.67445e8	0.0287165
$988$	−1.17395e8	−0.00387257
$989$	−4.14270e10	−1.36175
$990$	−2.71372e9	−0.0888877
$991$	−3.19499e10	−1.04283	−0.521413	−	0.853305i	$-0.674595\pi$
$991$	−3.19499e10	−1.04283	−0.521413	+	0.853305i	$0.674595\pi$
$992$	1.96715e9	0.0639805
$993$	−1.46264e10	−0.474041
$994$	1.30161e10	0.420368
$995$	2.12823e10	0.684916
$996$	1.71619e8	0.00550372
$997$	−3.93569e10	−1.25773	−0.628866	−	0.777514i	$-0.716480\pi$
$997$	−3.93569e10	−1.25773	−0.628866	+	0.777514i	$0.716480\pi$
$998$	−3.84601e10	−1.22477
$999$	2.82194e10	0.895507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.b.1.3	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.b.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-11.5479 q^{2} +14.0702 q^{3} +5.35382 q^{4} +200.806 q^{5} -162.481 q^{6} -343.000 q^{7} +1416.30 q^{8} -1989.03 q^{9} +O(q^{10})\)	\(q-11.5479 q^{2} +14.0702 q^{3} +5.35382 q^{4} +200.806 q^{5} -162.481 q^{6} -343.000 q^{7} +1416.30 q^{8} -1989.03 q^{9} -2318.88 q^{10} -588.362 q^{11} +75.3292 q^{12} +2197.00 q^{13} +3960.93 q^{14} +2825.37 q^{15} -17040.6 q^{16} +20007.5 q^{17} +22969.1 q^{18} -9980.56 q^{19} +1075.08 q^{20} -4826.07 q^{21} +6794.35 q^{22} +42255.5 q^{23} +19927.6 q^{24} -37802.1 q^{25} -25370.7 q^{26} -58757.4 q^{27} -1836.36 q^{28} +163487. q^{29} -32627.0 q^{30} +126944. q^{31} +15496.3 q^{32} -8278.36 q^{33} -231045. q^{34} -68876.3 q^{35} -10648.9 q^{36} -480270. q^{37} +115254. q^{38} +30912.2 q^{39} +284402. q^{40} -600420. q^{41} +55730.9 q^{42} -980394. q^{43} -3149.99 q^{44} -399408. q^{45} -487962. q^{46} -179742. q^{47} -239764. q^{48} +117649. q^{49} +436535. q^{50} +281509. q^{51} +11762.3 q^{52} -663334. q^{53} +678525. q^{54} -118146. q^{55} -485793. q^{56} -140428. q^{57} -1.88794e6 q^{58} -1.90951e6 q^{59} +15126.5 q^{60} -2.41091e6 q^{61} -1.46593e6 q^{62} +682237. q^{63} +2.00225e6 q^{64} +441170. q^{65} +95597.6 q^{66} -3.97460e6 q^{67} +107117. q^{68} +594541. q^{69} +795376. q^{70} +3.28614e6 q^{71} -2.81707e6 q^{72} +636497. q^{73} +5.54611e6 q^{74} -531882. q^{75} -53434.1 q^{76} +201808. q^{77} -356970. q^{78} +2.10723e6 q^{79} -3.42185e6 q^{80} +3.52328e6 q^{81} +6.93359e6 q^{82} +2.27825e6 q^{83} -25837.9 q^{84} +4.01763e6 q^{85} +1.13215e7 q^{86} +2.30030e6 q^{87} -833301. q^{88} -1.81327e6 q^{89} +4.61232e6 q^{90} -753571. q^{91} +226228. q^{92} +1.78612e6 q^{93} +2.07564e6 q^{94} -2.00415e6 q^{95} +218035. q^{96} -1.02057e7 q^{97} -1.35860e6 q^{98} +1.17027e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 5 q^{2} - 26 q^{3} + 393 q^{4} - 181 q^{5} + 703 q^{6} - 3087 q^{7} + 1197 q^{8} + 3211 q^{9}+O(q^{10}) \) 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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