LMFDB - Embedded newform 91.8.a.c.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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 957 x^{8} + 1224 x^{7} + 310102 x^{6} - 241884 x^{5} - 40367312 x^{4} + \cdots - 4516262912 $ x^10 - 2x^9 - 957x^8 + 1224x^7 + 310102x^6 - 241884x^5 - 40367312x^4 + 11067840x^3 + 1840757376x^2 + 541859072*x - 4516262912
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-16.8829$ 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)

$f(q)$	$=$	$q-18.8829 q^{2} +14.3398 q^{3} +228.563 q^{4} +382.689 q^{5} -270.777 q^{6} +343.000 q^{7} -1898.92 q^{8} -1981.37 q^{9} +O(q^{10})$	\(q-18.8829 q^{2} +14.3398 q^{3} +228.563 q^{4} +382.689 q^{5} -270.777 q^{6} +343.000 q^{7} -1898.92 q^{8} -1981.37 q^{9} -7226.26 q^{10} -3044.29 q^{11} +3277.55 q^{12} -2197.00 q^{13} -6476.83 q^{14} +5487.69 q^{15} +6600.94 q^{16} -11382.8 q^{17} +37413.9 q^{18} +4234.69 q^{19} +87468.4 q^{20} +4918.56 q^{21} +57484.9 q^{22} -31451.0 q^{23} -27230.1 q^{24} +68325.7 q^{25} +41485.7 q^{26} -59773.7 q^{27} +78397.1 q^{28} +18119.0 q^{29} -103623. q^{30} +41965.9 q^{31} +118416. q^{32} -43654.6 q^{33} +214940. q^{34} +131262. q^{35} -452867. q^{36} -353115. q^{37} -79963.2 q^{38} -31504.6 q^{39} -726694. q^{40} -175436. q^{41} -92876.6 q^{42} -669339. q^{43} -695812. q^{44} -758248. q^{45} +593885. q^{46} -76318.9 q^{47} +94656.5 q^{48} +117649. q^{49} -1.29018e6 q^{50} -163228. q^{51} -502153. q^{52} -196087. q^{53} +1.12870e6 q^{54} -1.16502e6 q^{55} -651328. q^{56} +60724.8 q^{57} -342139. q^{58} -511807. q^{59} +1.25428e6 q^{60} +2.45412e6 q^{61} -792437. q^{62} -679610. q^{63} -3.08096e6 q^{64} -840767. q^{65} +824324. q^{66} +390824. q^{67} -2.60169e6 q^{68} -451002. q^{69} -2.47861e6 q^{70} -3.29383e6 q^{71} +3.76245e6 q^{72} +1.50406e6 q^{73} +6.66783e6 q^{74} +979779. q^{75} +967894. q^{76} -1.04419e6 q^{77} +594898. q^{78} +1.73601e6 q^{79} +2.52611e6 q^{80} +3.47611e6 q^{81} +3.31273e6 q^{82} -4.50188e6 q^{83} +1.12420e6 q^{84} -4.35608e6 q^{85} +1.26390e7 q^{86} +259824. q^{87} +5.78085e6 q^{88} -8.85117e6 q^{89} +1.43179e7 q^{90} -753571. q^{91} -7.18853e6 q^{92} +601784. q^{93} +1.44112e6 q^{94} +1.62057e6 q^{95} +1.69807e6 q^{96} +6.74245e6 q^{97} -2.22155e6 q^{98} +6.03186e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9}+O(q^{10}) $ 10 * q - 18 * q^2 - 80 * q^3 + 670 * q^4 - 927 * q^5 - 1419 * q^6 + 3430 * q^7 - 4878 * q^8 + 3612 * q^9	\( 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9} + 9420 q^{10} + 876 q^{11} - 8765 q^{12} - 21970 q^{13} - 6174 q^{14} - 5320 q^{15} + 41370 q^{16} + 6294 q^{17} - 16027 q^{18} - 97401 q^{19} - 166650 q^{20} - 27440 q^{21} + 74171 q^{22} - 15255 q^{23} + 196187 q^{24} + 162145 q^{25} + 39546 q^{26} - 181820 q^{27} + 229810 q^{28} - 340533 q^{29} - 325020 q^{30} - 148675 q^{31} - 642762 q^{32} - 624400 q^{33} - 1161518 q^{34} - 317961 q^{35} - 773917 q^{36} - 621782 q^{37} - 805092 q^{38} + 175760 q^{39} - 350478 q^{40} - 2043336 q^{41} - 486717 q^{42} - 1801391 q^{43} - 3953667 q^{44} - 1908807 q^{45} - 2707731 q^{46} - 1624701 q^{47} - 6068625 q^{48} + 1176490 q^{49} - 6891516 q^{50} + 1811700 q^{51} - 1471990 q^{52} - 199965 q^{53} - 2895913 q^{54} + 739086 q^{55} - 1673154 q^{56} + 2159088 q^{57} + 2071092 q^{58} - 8098908 q^{59} + 8096436 q^{60} + 2271618 q^{61} - 8910225 q^{62} + 1238916 q^{63} + 8099930 q^{64} + 2036619 q^{65} - 5999191 q^{66} + 1970272 q^{67} - 1766238 q^{68} - 4622962 q^{69} + 3231060 q^{70} - 7145820 q^{71} + 984975 q^{72} + 1409431 q^{73} - 5498643 q^{74} - 8857892 q^{75} - 2749534 q^{76} + 300468 q^{77} + 3117543 q^{78} - 9011055 q^{79} - 23850522 q^{80} + 11613490 q^{81} + 27962597 q^{82} - 15006567 q^{83} - 3006395 q^{84} - 9416628 q^{85} + 38357850 q^{86} - 15828996 q^{87} + 42205269 q^{88} - 11472777 q^{89} + 53425712 q^{90} - 7535710 q^{91} + 16755837 q^{92} + 36339848 q^{93} + 5133371 q^{94} + 29637939 q^{95} + 65329611 q^{96} + 3228571 q^{97} - 2117682 q^{98} + 19367194 q^{99}+O(q^{100}) \) 10 * q - 18 * q^2 - 80 * q^3 + 670 * q^4 - 927 * q^5 - 1419 * q^6 + 3430 * q^7 - 4878 * q^8 + 3612 * q^9 + 9420 * q^10 + 876 * q^11 - 8765 * q^12 - 21970 * q^13 - 6174 * q^14 - 5320 * q^15 + 41370 * q^16 + 6294 * q^17 - 16027 * q^18 - 97401 * q^19 - 166650 * q^20 - 27440 * q^21 + 74171 * q^22 - 15255 * q^23 + 196187 * q^24 + 162145 * q^25 + 39546 * q^26 - 181820 * q^27 + 229810 * q^28 - 340533 * q^29 - 325020 * q^30 - 148675 * q^31 - 642762 * q^32 - 624400 * q^33 - 1161518 * q^34 - 317961 * q^35 - 773917 * q^36 - 621782 * q^37 - 805092 * q^38 + 175760 * q^39 - 350478 * q^40 - 2043336 * q^41 - 486717 * q^42 - 1801391 * q^43 - 3953667 * q^44 - 1908807 * q^45 - 2707731 * q^46 - 1624701 * q^47 - 6068625 * q^48 + 1176490 * q^49 - 6891516 * q^50 + 1811700 * q^51 - 1471990 * q^52 - 199965 * q^53 - 2895913 * q^54 + 739086 * q^55 - 1673154 * q^56 + 2159088 * q^57 + 2071092 * q^58 - 8098908 * q^59 + 8096436 * q^60 + 2271618 * q^61 - 8910225 * q^62 + 1238916 * q^63 + 8099930 * q^64 + 2036619 * q^65 - 5999191 * q^66 + 1970272 * q^67 - 1766238 * q^68 - 4622962 * q^69 + 3231060 * q^70 - 7145820 * q^71 + 984975 * q^72 + 1409431 * q^73 - 5498643 * q^74 - 8857892 * q^75 - 2749534 * q^76 + 300468 * q^77 + 3117543 * q^78 - 9011055 * q^79 - 23850522 * q^80 + 11613490 * q^81 + 27962597 * q^82 - 15006567 * q^83 - 3006395 * q^84 - 9416628 * q^85 + 38357850 * q^86 - 15828996 * q^87 + 42205269 * q^88 - 11472777 * q^89 + 53425712 * q^90 - 7535710 * q^91 + 16755837 * q^92 + 36339848 * q^93 + 5133371 * q^94 + 29637939 * q^95 + 65329611 * q^96 + 3228571 * q^97 - 2117682 * q^98 + 19367194 * 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 $

$2$	−18.8829	−1.66903	−0.834513	−	0.550988i	$-0.814251\pi$
$2$	−18.8829	−1.66903	−0.834513	+	0.550988i	$0.814251\pi$
$3$	14.3398	0.306634	0.153317	−	0.988177i	$-0.451004\pi$
$3$	14.3398	0.306634	0.153317	+	0.988177i	$0.451004\pi$
$4$	228.563	1.78565
$5$	382.689	1.36915	0.684574	−	0.728943i	$-0.259988\pi$
$5$	382.689	1.36915	0.684574	+	0.728943i	$0.259988\pi$
$6$	−270.777	−0.511780
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−1898.92	−1.31127
$9$	−1981.37	−0.905976
$10$	−7226.26	−2.28514
$11$	−3044.29	−0.689623	−0.344811	−	0.938672i	$-0.612057\pi$
$11$	−3044.29	−0.689623	−0.344811	+	0.938672i	$0.612057\pi$
$12$	3277.55	0.547540
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−6476.83	−0.630833
$15$	5487.69	0.419827
$16$	6600.94	0.402890
$17$	−11382.8	−0.561926	−0.280963	−	0.959719i	$-0.590654\pi$
$17$	−11382.8	−0.561926	−0.280963	+	0.959719i	$0.590654\pi$
$18$	37413.9	1.51210
$19$	4234.69	0.141639	0.0708197	−	0.997489i	$-0.477438\pi$
$19$	4234.69	0.141639	0.0708197	+	0.997489i	$0.477438\pi$
$20$	87468.4	2.44482
$21$	4918.56	0.115897
$22$	57484.9	1.15100
$23$	−31451.0	−0.538998	−0.269499	−	0.963001i	$-0.586858\pi$
$23$	−31451.0	−0.538998	−0.269499	+	0.963001i	$0.586858\pi$
$24$	−27230.1	−0.402078
$25$	68325.7	0.874569
$26$	41485.7	0.462905
$27$	−59773.7	−0.584436
$28$	78397.1	0.674911
$29$	18119.0	0.137956	0.0689782	−	0.997618i	$-0.478026\pi$
$29$	18119.0	0.137956	0.0689782	+	0.997618i	$0.478026\pi$
$30$	−103623.	−0.700702
$31$	41965.9	0.253006	0.126503	−	0.991966i	$-0.459625\pi$
$31$	41965.9	0.253006	0.126503	+	0.991966i	$0.459625\pi$
$32$	118416.	0.638833
$33$	−43654.6	−0.211462
$34$	214940.	0.937868
$35$	131262.	0.517490
$36$	−452867.	−1.61775
$37$	−353115.	−1.14607	−0.573034	−	0.819531i	$-0.694234\pi$
$37$	−353115.	−1.14607	−0.573034	+	0.819531i	$0.694234\pi$
$38$	−79963.2	−0.236400
$39$	−31504.6	−0.0850449
$40$	−726694.	−1.79532
$41$	−175436.	−0.397534	−0.198767	−	0.980047i	$-0.563694\pi$
$41$	−175436.	−0.397534	−0.198767	+	0.980047i	$0.563694\pi$
$42$	−92876.6	−0.193434
$43$	−669339.	−1.28383	−0.641913	−	0.766777i	$-0.721859\pi$
$43$	−669339.	−1.28383	−0.641913	+	0.766777i	$0.721859\pi$
$44$	−695812.	−1.23142
$45$	−758248.	−1.24042
$46$	593885.	0.899601
$47$	−76318.9	−0.107223	−0.0536117	−	0.998562i	$-0.517073\pi$
$47$	−76318.9	−0.107223	−0.0536117	+	0.998562i	$0.517073\pi$
$48$	94656.5	0.123540
$49$	117649.	0.142857
$50$	−1.29018e6	−1.45968
$51$	−163228.	−0.172305
$52$	−502153.	−0.495250
$53$	−196087.	−0.180919	−0.0904595	−	0.995900i	$-0.528834\pi$
$53$	−196087.	−0.180919	−0.0904595	+	0.995900i	$0.528834\pi$
$54$	1.12870e6	0.975439
$55$	−1.16502e6	−0.944196
$56$	−651328.	−0.495612
$57$	60724.8	0.0434314
$58$	−342139.	−0.230253
$59$	−511807.	−0.324433	−0.162216	−	0.986755i	$-0.551864\pi$
$59$	−511807.	−0.324433	−0.162216	+	0.986755i	$0.551864\pi$
$60$	1.25428e6	0.749663
$61$	2.45412e6	1.38433	0.692167	−	0.721737i	$-0.256656\pi$
$61$	2.45412e6	1.38433	0.692167	+	0.721737i	$0.256656\pi$
$62$	−792437.	−0.422274
$63$	−679610.	−0.342427
$64$	−3.08096e6	−1.46912
$65$	−840767.	−0.379734
$66$	824324.	0.352935
$67$	390824.	0.158752	0.0793760	−	0.996845i	$-0.474707\pi$
$67$	390824.	0.158752	0.0793760	+	0.996845i	$0.474707\pi$
$68$	−2.60169e6	−1.00340
$69$	−451002.	−0.165275
$70$	−2.47861e6	−0.863704
$71$	−3.29383e6	−1.09219	−0.546093	−	0.837724i	$-0.683886\pi$
$71$	−3.29383e6	−1.09219	−0.546093	+	0.837724i	$0.683886\pi$
$72$	3.76245e6	1.18798
$73$	1.50406e6	0.452517	0.226259	−	0.974067i	$-0.427351\pi$
$73$	1.50406e6	0.452517	0.226259	+	0.974067i	$0.427351\pi$
$74$	6.66783e6	1.91282
$75$	979779.	0.268172
$76$	967894.	0.252918
$77$	−1.04419e6	−0.260653
$78$	594898.	0.141942
$79$	1.73601e6	0.396149	0.198074	−	0.980187i	$-0.436531\pi$
$79$	1.73601e6	0.396149	0.198074	+	0.980187i	$0.436531\pi$
$80$	2.52611e6	0.551616
$81$	3.47611e6	0.726768
$82$	3.31273e6	0.663494
$83$	−4.50188e6	−0.864214	−0.432107	−	0.901822i	$-0.642230\pi$
$83$	−4.50188e6	−0.864214	−0.432107	+	0.901822i	$0.642230\pi$
$84$	1.12420e6	0.206951
$85$	−4.35608e6	−0.769360
$86$	1.26390e7	2.14274
$87$	259824.	0.0423020
$88$	5.78085e6	0.904279
$89$	−8.85117e6	−1.33087	−0.665435	−	0.746456i	$-0.731754\pi$
$89$	−8.85117e6	−1.33087	−0.665435	+	0.746456i	$0.731754\pi$
$90$	1.43179e7	2.07029
$91$	−753571.	−0.104828
$92$	−7.18853e6	−0.962460
$93$	601784.	0.0775802
$94$	1.44112e6	0.178959
$95$	1.62057e6	0.193926
$96$	1.69807e6	0.195888
$97$	6.74245e6	0.750096	0.375048	−	0.927005i	$-0.377626\pi$
$97$	6.74245e6	0.750096	0.375048	+	0.927005i	$0.377626\pi$
$98$	−2.22155e6	−0.238432
$99$	6.03186e6	0.624781
$100$	1.56167e7	1.56167
$101$	−1.14932e7	−1.10998	−0.554992	−	0.831856i	$-0.687279\pi$
$101$	−1.14932e7	−1.10998	−0.554992	+	0.831856i	$0.687279\pi$
$102$	3.08221e6	0.287582
$103$	2.09584e7	1.88985	0.944925	−	0.327286i	$-0.106134\pi$
$103$	2.09584e7	1.88985	0.944925	+	0.327286i	$0.106134\pi$
$104$	4.17192e6	0.363680
$105$	1.88228e6	0.158680
$106$	3.70269e6	0.301958
$107$	−1.86841e7	−1.47445	−0.737223	−	0.675650i	$-0.763863\pi$
$107$	−1.86841e7	−1.47445	−0.737223	+	0.675650i	$0.763863\pi$
$108$	−1.36621e7	−1.04360
$109$	−2.14677e7	−1.58779	−0.793894	−	0.608057i	$-0.791949\pi$
$109$	−2.14677e7	−1.58779	−0.793894	+	0.608057i	$0.791949\pi$
$110$	2.19988e7	1.57589
$111$	−5.06362e6	−0.351423
$112$	2.26412e6	0.152278
$113$	−1.61009e7	−1.04972	−0.524861	−	0.851188i	$-0.675883\pi$
$113$	−1.61009e7	−1.04972	−0.524861	+	0.851188i	$0.675883\pi$
$114$	−1.14666e6	−0.0724882
$115$	−1.20359e7	−0.737968
$116$	4.14133e6	0.246341
$117$	4.35307e6	0.251272
$118$	9.66440e6	0.541487
$119$	−3.90431e6	−0.212388
$120$	−1.04207e7	−0.550505
$121$	−1.02195e7	−0.524421
$122$	−4.63408e7	−2.31049
$123$	−2.51572e6	−0.121897
$124$	9.59185e6	0.451780
$125$	−3.75009e6	−0.171734
$126$	1.28330e7	0.571519
$127$	−1.66133e7	−0.719685	−0.359843	−	0.933013i	$-0.617170\pi$
$127$	−1.66133e7	−0.719685	−0.359843	+	0.933013i	$0.617170\pi$
$128$	4.30201e7	1.81316
$129$	−9.59821e6	−0.393664
$130$	1.58761e7	0.633785
$131$	1.74604e7	0.678586	0.339293	−	0.940681i	$-0.389812\pi$
$131$	1.74604e7	0.678586	0.339293	+	0.940681i	$0.389812\pi$
$132$	−9.97782e6	−0.377596
$133$	1.45250e6	0.0535347
$134$	−7.37988e6	−0.264961
$135$	−2.28747e7	−0.800180
$136$	2.16150e7	0.736834
$137$	−2.85718e7	−0.949327	−0.474663	−	0.880167i	$-0.657430\pi$
$137$	−2.85718e7	−0.949327	−0.474663	+	0.880167i	$0.657430\pi$
$138$	8.51622e6	0.275848
$139$	−1.88147e7	−0.594219	−0.297109	−	0.954843i	$-0.596023\pi$
$139$	−1.88147e7	−0.594219	−0.297109	+	0.954843i	$0.596023\pi$
$140$	3.00017e7	0.924054
$141$	−1.09440e6	−0.0328783
$142$	6.21969e7	1.82289
$143$	6.68830e6	0.191267
$144$	−1.30789e7	−0.365008
$145$	6.93394e6	0.188883
$146$	−2.84010e7	−0.755263
$147$	1.68707e6	0.0438048
$148$	−8.07091e7	−2.04647
$149$	−3.03911e7	−0.752653	−0.376327	−	0.926487i	$-0.622813\pi$
$149$	−3.03911e7	−0.752653	−0.376327	+	0.926487i	$0.622813\pi$
$150$	−1.85010e7	−0.447586
$151$	−4.52183e7	−1.06880	−0.534398	−	0.845233i	$-0.679462\pi$
$151$	−4.52183e7	−1.06880	−0.534398	+	0.845233i	$0.679462\pi$
$152$	−8.04133e6	−0.185727
$153$	2.25536e7	0.509091
$154$	1.97173e7	0.435036
$155$	1.60599e7	0.346403
$156$	−7.20079e6	−0.151860
$157$	6.86970e7	1.41674	0.708368	−	0.705843i	$-0.249432\pi$
$157$	6.86970e7	1.41674	0.708368	+	0.705843i	$0.249432\pi$
$158$	−3.27809e7	−0.661182
$159$	−2.81186e6	−0.0554758
$160$	4.53167e7	0.874657
$161$	−1.07877e7	−0.203722
$162$	−6.56389e7	−1.21299
$163$	9.89264e7	1.78919	0.894593	−	0.446881i	$-0.147465\pi$
$163$	9.89264e7	1.78919	0.894593	+	0.446881i	$0.147465\pi$
$164$	−4.00981e7	−0.709855
$165$	−1.67061e7	−0.289522
$166$	8.50085e7	1.44239
$167$	5.86668e7	0.974732	0.487366	−	0.873198i	$-0.337958\pi$
$167$	5.86668e7	0.974732	0.487366	+	0.873198i	$0.337958\pi$
$168$	−9.33994e6	−0.151971
$169$	4.82681e6	0.0769231
$170$	8.22553e7	1.28408
$171$	−8.39049e6	−0.128322
$172$	−1.52986e8	−2.29246
$173$	6.36332e7	0.934378	0.467189	−	0.884158i	$-0.345267\pi$
$173$	6.36332e7	0.934378	0.467189	+	0.884158i	$0.345267\pi$
$174$	−4.90622e6	−0.0706032
$175$	2.34357e7	0.330556
$176$	−2.00952e7	−0.277842
$177$	−7.33924e6	−0.0994820
$178$	1.67136e8	2.22126
$179$	−8.59424e7	−1.12001	−0.560005	−	0.828489i	$-0.689201\pi$
$179$	−8.59424e7	−1.12001	−0.560005	+	0.828489i	$0.689201\pi$
$180$	−1.73307e8	−2.21495
$181$	1.33657e8	1.67539	0.837695	−	0.546138i	$-0.183902\pi$
$181$	1.33657e8	1.67539	0.837695	+	0.546138i	$0.183902\pi$
$182$	1.42296e7	0.174961
$183$	3.51917e7	0.424484
$184$	5.97228e7	0.706770
$185$	−1.35133e8	−1.56914
$186$	−1.13634e7	−0.129483
$187$	3.46526e7	0.387517
$188$	−1.74437e7	−0.191463
$189$	−2.05024e7	−0.220896
$190$	−3.06010e7	−0.323667
$191$	1.85224e7	0.192345	0.0961723	−	0.995365i	$-0.469340\pi$
$191$	1.85224e7	0.192345	0.0961723	+	0.995365i	$0.469340\pi$
$192$	−4.41805e7	−0.450481
$193$	−1.26754e8	−1.26914	−0.634572	−	0.772864i	$-0.718824\pi$
$193$	−1.26754e8	−1.26914	−0.634572	+	0.772864i	$0.718824\pi$
$194$	−1.27317e8	−1.25193
$195$	−1.20565e7	−0.116439
$196$	2.68902e7	0.255093
$197$	−2.00593e8	−1.86932	−0.934659	−	0.355547i	$-0.884295\pi$
$197$	−2.00593e8	−1.86932	−0.934659	+	0.355547i	$0.884295\pi$
$198$	−1.13899e8	−1.04278
$199$	1.35077e8	1.21506	0.607529	−	0.794298i	$-0.292161\pi$
$199$	1.35077e8	1.21506	0.607529	+	0.794298i	$0.292161\pi$
$200$	−1.29745e8	−1.14679
$201$	5.60435e6	0.0486787
$202$	2.17025e8	1.85259
$203$	6.21482e6	0.0521426
$204$	−3.73078e7	−0.307677
$205$	−6.71372e7	−0.544283
$206$	−3.95755e8	−3.15421
$207$	6.23160e7	0.488319
$208$	−1.45023e7	−0.111741
$209$	−1.28916e7	−0.0976778
$210$	−3.55428e7	−0.264841
$211$	−1.56046e8	−1.14357	−0.571785	−	0.820403i	$-0.693749\pi$
$211$	−1.56046e8	−1.14357	−0.571785	+	0.820403i	$0.693749\pi$
$212$	−4.48183e7	−0.323057
$213$	−4.72330e7	−0.334901
$214$	3.52809e8	2.46089
$215$	−2.56148e8	−1.75775
$216$	1.13505e8	0.766352
$217$	1.43943e7	0.0956273
$218$	4.05371e8	2.65006
$219$	2.15680e7	0.138757
$220$	−2.66279e8	−1.68600
$221$	2.50081e7	0.155850
$222$	9.56157e7	0.586535
$223$	2.39824e8	1.44819	0.724095	−	0.689700i	$-0.242257\pi$
$223$	2.39824e8	1.44819	0.724095	+	0.689700i	$0.242257\pi$
$224$	4.06169e7	0.241456
$225$	−1.35378e8	−0.792338
$226$	3.04030e8	1.75201
$227$	1.47715e8	0.838172	0.419086	−	0.907947i	$-0.362351\pi$
$227$	1.47715e8	0.838172	0.419086	+	0.907947i	$0.362351\pi$
$228$	1.38794e7	0.0775532
$229$	−6.25985e7	−0.344461	−0.172231	−	0.985057i	$-0.555097\pi$
$229$	−6.25985e7	−0.344461	−0.172231	+	0.985057i	$0.555097\pi$
$230$	2.27273e8	1.23169
$231$	−1.49735e7	−0.0799249
$232$	−3.44065e7	−0.180897
$233$	3.33626e8	1.72788	0.863941	−	0.503593i	$-0.167989\pi$
$233$	3.33626e8	1.72788	0.863941	+	0.503593i	$0.167989\pi$
$234$	−8.21984e7	−0.419380
$235$	−2.92064e7	−0.146805
$236$	−1.16980e8	−0.579322
$237$	2.48941e7	0.121473
$238$	7.37246e7	0.354481
$239$	1.41210e8	0.669073	0.334537	−	0.942383i	$-0.391420\pi$
$239$	1.41210e8	0.669073	0.334537	+	0.942383i	$0.391420\pi$
$240$	3.62240e7	0.169144
$241$	−1.28796e8	−0.592709	−0.296354	−	0.955078i	$-0.595771\pi$
$241$	−1.28796e8	−0.592709	−0.296354	+	0.955078i	$0.595771\pi$
$242$	1.92973e8	0.875272
$243$	1.80572e8	0.807288
$244$	5.60920e8	2.47193
$245$	4.50229e7	0.195593
$246$	4.75040e7	0.203450
$247$	−9.30362e6	−0.0392837
$248$	−7.96898e7	−0.331758
$249$	−6.45563e7	−0.264997
$250$	7.08126e7	0.286629
$251$	−3.93242e8	−1.56965	−0.784823	−	0.619720i	$-0.787246\pi$
$251$	−3.93242e8	−1.56965	−0.784823	+	0.619720i	$0.787246\pi$
$252$	−1.55334e8	−0.611453
$253$	9.57459e7	0.371705
$254$	3.13707e8	1.20117
$255$	−6.24655e7	−0.235912
$256$	−4.17981e8	−1.55710
$257$	2.18524e8	0.803034	0.401517	−	0.915852i	$-0.368483\pi$
$257$	2.18524e8	0.803034	0.401517	+	0.915852i	$0.368483\pi$
$258$	1.81242e8	0.657036
$259$	−1.21119e8	−0.433173
$260$	−1.92168e8	−0.678070
$261$	−3.59005e7	−0.124985
$262$	−3.29702e8	−1.13258
$263$	2.14847e8	0.728255	0.364128	−	0.931349i	$-0.381367\pi$
$263$	2.14847e8	0.728255	0.364128	+	0.931349i	$0.381367\pi$
$264$	8.28964e7	0.277282
$265$	−7.50404e7	−0.247705
$266$	−2.74274e7	−0.0893508
$267$	−1.26924e8	−0.408090
$268$	8.93279e7	0.283475
$269$	4.83869e8	1.51564	0.757818	−	0.652466i	$-0.226266\pi$
$269$	4.83869e8	1.51564	0.757818	+	0.652466i	$0.226266\pi$
$270$	4.31941e8	1.33552
$271$	−1.06133e8	−0.323934	−0.161967	−	0.986796i	$-0.551784\pi$
$271$	−1.06133e8	−0.323934	−0.161967	+	0.986796i	$0.551784\pi$
$272$	−7.51374e7	−0.226394
$273$	−1.08061e7	−0.0321439
$274$	5.39518e8	1.58445
$275$	−2.08003e8	−0.603122
$276$	−1.03082e8	−0.295123
$277$	4.21798e8	1.19241	0.596205	−	0.802832i	$-0.296675\pi$
$277$	4.21798e8	1.19241	0.596205	+	0.802832i	$0.296675\pi$
$278$	3.55276e8	0.991766
$279$	−8.31500e7	−0.229217
$280$	−2.49256e8	−0.678567
$281$	−6.57371e8	−1.76741	−0.883707	−	0.468041i	$-0.844960\pi$
$281$	−6.57371e8	−1.76741	−0.883707	+	0.468041i	$0.844960\pi$
$282$	2.06654e7	0.0548748
$283$	−3.71514e7	−0.0974368	−0.0487184	−	0.998813i	$-0.515514\pi$
$283$	−3.71514e7	−0.0974368	−0.0487184	+	0.998813i	$0.515514\pi$
$284$	−7.52847e8	−1.95026
$285$	2.32387e7	0.0594641
$286$	−1.26294e8	−0.319229
$287$	−6.01744e7	−0.150254
$288$	−2.34627e8	−0.578767
$289$	−2.80770e8	−0.684240
$290$	−1.30933e8	−0.315250
$291$	9.66856e7	0.230005
$292$	3.43772e8	0.808037
$293$	−8.45368e8	−1.96340	−0.981701	−	0.190429i	$-0.939012\pi$
$293$	−8.45368e8	−1.96340	−0.981701	+	0.190429i	$0.939012\pi$
$294$	−3.18567e7	−0.0731114
$295$	−1.95863e8	−0.444197
$296$	6.70537e8	1.50280
$297$	1.81969e8	0.403041
$298$	5.73872e8	1.25620
$299$	6.90978e7	0.149491
$300$	2.23941e8	0.478861
$301$	−2.29583e8	−0.485241
$302$	8.53851e8	1.78385
$303$	−1.64811e8	−0.340358
$304$	2.79530e7	0.0570651
$305$	9.39163e8	1.89536
$306$	−4.25876e8	−0.849686
$307$	−7.88972e8	−1.55624	−0.778121	−	0.628114i	$-0.783827\pi$
$307$	−7.88972e8	−1.55624	−0.778121	+	0.628114i	$0.783827\pi$
$308$	−2.38663e8	−0.465434
$309$	3.00540e8	0.579492
$310$	−3.03257e8	−0.578155
$311$	6.04998e6	0.0114049	0.00570246	−	0.999984i	$-0.498185\pi$
$311$	6.04998e6	0.0114049	0.00570246	+	0.999984i	$0.498185\pi$
$312$	5.98246e7	0.111516
$313$	−4.03973e8	−0.744641	−0.372321	−	0.928104i	$-0.621438\pi$
$313$	−4.03973e8	−0.744641	−0.372321	+	0.928104i	$0.621438\pi$
$314$	−1.29720e9	−2.36457
$315$	−2.60079e8	−0.468833
$316$	3.96788e8	0.707382
$317$	8.34370e8	1.47113	0.735565	−	0.677454i	$-0.236917\pi$
$317$	8.34370e8	1.47113	0.735565	+	0.677454i	$0.236917\pi$
$318$	5.30960e7	0.0925906
$319$	−5.51595e7	−0.0951378
$320$	−1.17905e9	−2.01144
$321$	−2.67927e8	−0.452115
$322$	2.03703e8	0.340017
$323$	−4.82028e7	−0.0795908
$324$	7.94509e8	1.29775
$325$	−1.50111e8	−0.242562
$326$	−1.86801e9	−2.98620
$327$	−3.07843e8	−0.486869
$328$	3.33137e8	0.521273
$329$	−2.61774e7	−0.0405267
$330$	3.15460e8	0.483220
$331$	7.43274e8	1.12655	0.563276	−	0.826269i	$-0.309541\pi$
$331$	7.43274e8	1.12655	0.563276	+	0.826269i	$0.309541\pi$
$332$	−1.02896e9	−1.54318
$333$	6.99652e8	1.03831
$334$	−1.10780e9	−1.62685
$335$	1.49564e8	0.217355
$336$	3.24672e7	0.0466936
$337$	1.10288e8	0.156973	0.0784866	−	0.996915i	$-0.474991\pi$
$337$	1.10288e8	0.156973	0.0784866	+	0.996915i	$0.474991\pi$
$338$	−9.11440e7	−0.128387
$339$	−2.30884e8	−0.321880
$340$	−9.95638e8	−1.37381
$341$	−1.27756e8	−0.174479
$342$	1.58437e8	0.214173
$343$	4.03536e7	0.0539949
$344$	1.27102e9	1.68344
$345$	−1.72593e8	−0.226286
$346$	−1.20158e9	−1.55950
$347$	−6.25969e8	−0.804266	−0.402133	−	0.915581i	$-0.631731\pi$
$347$	−6.25969e8	−0.804266	−0.402133	+	0.915581i	$0.631731\pi$
$348$	5.93861e7	0.0755365
$349$	6.45976e8	0.813444	0.406722	−	0.913552i	$-0.366672\pi$
$349$	6.45976e8	0.813444	0.406722	+	0.913552i	$0.366672\pi$
$350$	−4.42533e8	−0.551706
$351$	1.31323e8	0.162093
$352$	−3.60494e8	−0.440554
$353$	7.10498e6	0.00859709	0.00429854	−	0.999991i	$-0.498632\pi$
$353$	7.10498e6	0.00859709	0.00429854	+	0.999991i	$0.498632\pi$
$354$	1.38586e8	0.166038
$355$	−1.26051e9	−1.49537
$356$	−2.02305e9	−2.37646
$357$	−5.59872e7	−0.0651253
$358$	1.62284e9	1.86932
$359$	−3.18847e8	−0.363707	−0.181854	−	0.983326i	$-0.558210\pi$
$359$	−3.18847e8	−0.363707	−0.181854	+	0.983326i	$0.558210\pi$
$360$	1.43985e9	1.62652
$361$	−8.75939e8	−0.979938
$362$	−2.52382e9	−2.79627
$363$	−1.46546e8	−0.160805
$364$	−1.72238e8	−0.187187
$365$	5.75587e8	0.619564
$366$	−6.64520e8	−0.708474
$367$	−4.18947e8	−0.442413	−0.221207	−	0.975227i	$-0.571000\pi$
$367$	−4.18947e8	−0.442413	−0.221207	+	0.975227i	$0.571000\pi$
$368$	−2.07606e8	−0.217157
$369$	3.47603e8	0.360156
$370$	2.55171e9	2.61893
$371$	−6.72580e7	−0.0683809
$372$	1.37546e8	0.138531
$373$	8.90034e8	0.888026	0.444013	−	0.896020i	$-0.353554\pi$
$373$	8.90034e8	0.888026	0.444013	+	0.896020i	$0.353554\pi$
$374$	−6.54341e8	−0.646775
$375$	−5.37757e7	−0.0526595
$376$	1.44923e8	0.140599
$377$	−3.98075e7	−0.0382622
$378$	3.87144e8	0.368681
$379$	1.60250e9	1.51204	0.756018	−	0.654551i	$-0.227142\pi$
$379$	1.60250e9	1.51204	0.756018	+	0.654551i	$0.227142\pi$
$380$	3.70402e8	0.346283
$381$	−2.38232e8	−0.220680
$382$	−3.49756e8	−0.321028
$383$	1.78718e9	1.62544	0.812722	−	0.582652i	$-0.197985\pi$
$383$	1.78718e9	1.62544	0.812722	+	0.582652i	$0.197985\pi$
$384$	6.16902e8	0.555977
$385$	−3.99600e8	−0.356873
$386$	2.39348e9	2.11823
$387$	1.32621e9	1.16312
$388$	1.54107e9	1.33941
$389$	1.37879e8	0.118761	0.0593804	−	0.998235i	$-0.481087\pi$
$389$	1.37879e8	0.118761	0.0593804	+	0.998235i	$0.481087\pi$
$390$	2.27661e8	0.194340
$391$	3.58001e8	0.302877
$392$	−2.23406e8	−0.187324
$393$	2.50379e8	0.208077
$394$	3.78776e9	3.11994
$395$	6.64353e8	0.542386
$396$	1.37866e9	1.11564
$397$	9.76505e8	0.783264	0.391632	−	0.920122i	$-0.371911\pi$
$397$	9.76505e8	0.783264	0.391632	+	0.920122i	$0.371911\pi$
$398$	−2.55065e9	−2.02796
$399$	2.08286e7	0.0164155
$400$	4.51014e8	0.352355
$401$	−5.70218e8	−0.441607	−0.220803	−	0.975318i	$-0.570868\pi$
$401$	−5.70218e8	−0.441607	−0.220803	+	0.975318i	$0.570868\pi$
$402$	−1.05826e8	−0.0812461
$403$	−9.21991e7	−0.0701712
$404$	−2.62692e9	−1.98204
$405$	1.33027e9	0.995054
$406$	−1.17354e8	−0.0870273
$407$	1.07499e9	0.790355
$408$	3.09956e8	0.225938
$409$	−1.53127e8	−0.110668	−0.0553338	−	0.998468i	$-0.517622\pi$
$409$	−1.53127e8	−0.110668	−0.0553338	+	0.998468i	$0.517622\pi$
$410$	1.26774e9	0.908422
$411$	−4.09715e8	−0.291096
$412$	4.79031e9	3.37461
$413$	−1.75550e8	−0.122624
$414$	−1.17671e9	−0.815017
$415$	−1.72282e9	−1.18324
$416$	−2.60161e8	−0.177180
$417$	−2.69800e8	−0.182207
$418$	2.43431e8	0.163027
$419$	−8.68003e8	−0.576464	−0.288232	−	0.957561i	$-0.593067\pi$
$419$	−8.68003e8	−0.576464	−0.288232	+	0.957561i	$0.593067\pi$
$420$	4.30219e8	0.283346
$421$	−1.69183e9	−1.10502	−0.552509	−	0.833507i	$-0.686329\pi$
$421$	−1.69183e9	−1.10502	−0.552509	+	0.833507i	$0.686329\pi$
$422$	2.94659e9	1.90865
$423$	1.51216e8	0.0971419
$424$	3.72353e8	0.237233
$425$	−7.77739e8	−0.491442
$426$	8.91894e8	0.558959
$427$	8.41763e8	0.523229
$428$	−4.27049e9	−2.63284
$429$	9.59092e7	0.0586489
$430$	4.83682e9	2.93373
$431$	1.14026e9	0.686014	0.343007	−	0.939333i	$-0.388554\pi$
$431$	1.14026e9	0.686014	0.343007	+	0.939333i	$0.388554\pi$
$432$	−3.94563e8	−0.235463
$433$	−4.39398e8	−0.260106	−0.130053	−	0.991507i	$-0.541515\pi$
$433$	−4.39398e8	−0.260106	−0.130053	+	0.991507i	$0.541515\pi$
$434$	−2.71806e8	−0.159604
$435$	9.94316e7	0.0579178
$436$	−4.90671e9	−2.83523
$437$	−1.33185e8	−0.0763434
$438$	−4.07266e8	−0.231589
$439$	1.53118e9	0.863774	0.431887	−	0.901928i	$-0.357848\pi$
$439$	1.53118e9	0.863774	0.431887	+	0.901928i	$0.357848\pi$
$440$	2.21227e9	1.23809
$441$	−2.33106e8	−0.129425
$442$	−4.72224e8	−0.260118
$443$	−1.76050e9	−0.962106	−0.481053	−	0.876692i	$-0.659745\pi$
$443$	−1.76050e9	−0.962106	−0.481053	+	0.876692i	$0.659745\pi$
$444$	−1.15736e9	−0.627518
$445$	−3.38724e9	−1.82216
$446$	−4.52857e9	−2.41707
$447$	−4.35804e8	−0.230789
$448$	−1.05677e9	−0.555275
$449$	1.18635e9	0.618513	0.309257	−	0.950979i	$-0.399920\pi$
$449$	1.18635e9	0.618513	0.309257	+	0.950979i	$0.399920\pi$
$450$	2.55633e9	1.32243
$451$	5.34077e8	0.274148
$452$	−3.68006e9	−1.87443
$453$	−6.48423e8	−0.327729
$454$	−2.78928e9	−1.39893
$455$	−2.88383e8	−0.143526
$456$	−1.15311e8	−0.0569502
$457$	−2.26795e9	−1.11154	−0.555772	−	0.831335i	$-0.687577\pi$
$457$	−2.26795e9	−1.11154	−0.555772	+	0.831335i	$0.687577\pi$
$458$	1.18204e9	0.574914
$459$	6.80394e8	0.328410
$460$	−2.75097e9	−1.31775
$461$	−9.15422e8	−0.435179	−0.217590	−	0.976040i	$-0.569819\pi$
$461$	−9.15422e8	−0.435179	−0.217590	+	0.976040i	$0.569819\pi$
$462$	2.82743e8	0.133397
$463$	4.41721e8	0.206830	0.103415	−	0.994638i	$-0.467023\pi$
$463$	4.41721e8	0.206830	0.103415	+	0.994638i	$0.467023\pi$
$464$	1.19603e8	0.0555812
$465$	2.30296e8	0.106219
$466$	−6.29982e9	−2.88388
$467$	4.27209e9	1.94103	0.970513	−	0.241051i	$-0.0774920\pi$
$467$	4.27209e9	1.94103	0.970513	+	0.241051i	$0.0774920\pi$
$468$	9.94950e8	0.448684
$469$	1.34053e8	0.0600026
$470$	5.51501e8	0.245021
$471$	9.85104e8	0.434419
$472$	9.71879e8	0.425418
$473$	2.03766e9	0.885356
$474$	−4.70073e8	−0.202741
$475$	2.89338e8	0.123873
$476$	−8.92380e8	−0.379250
$477$	3.88521e8	0.163908
$478$	−2.66646e9	−1.11670
$479$	2.94297e9	1.22352	0.611761	−	0.791043i	$-0.290462\pi$
$479$	2.94297e9	1.22352	0.611761	+	0.791043i	$0.290462\pi$
$480$	6.49833e8	0.268199
$481$	7.75795e8	0.317862
$482$	2.43203e9	0.989246
$483$	−1.54694e8	−0.0624680
$484$	−2.33579e9	−0.936430
$485$	2.58026e9	1.02699
$486$	−3.40972e9	−1.34738
$487$	1.93955e9	0.760939	0.380470	−	0.924793i	$-0.375762\pi$
$487$	1.93955e9	0.760939	0.380470	+	0.924793i	$0.375762\pi$
$488$	−4.66017e9	−1.81523
$489$	1.41859e9	0.548625
$490$	−8.50163e8	−0.326449
$491$	2.22678e9	0.848971	0.424486	−	0.905435i	$-0.360455\pi$
$491$	2.22678e9	0.848971	0.424486	+	0.905435i	$0.360455\pi$
$492$	−5.75000e8	−0.217666
$493$	−2.06246e8	−0.0775212
$494$	1.75679e8	0.0655655
$495$	2.30833e9	0.855419
$496$	2.77015e8	0.101934
$497$	−1.12978e9	−0.412808
$498$	1.21901e9	0.442287
$499$	−2.49275e9	−0.898106	−0.449053	−	0.893505i	$-0.648238\pi$
$499$	−2.49275e9	−0.898106	−0.449053	+	0.893505i	$0.648238\pi$
$500$	−8.57132e8	−0.306657
$501$	8.41273e8	0.298886
$502$	7.42554e9	2.61978
$503$	8.54875e8	0.299512	0.149756	−	0.988723i	$-0.452151\pi$
$503$	8.54875e8	0.299512	0.149756	+	0.988723i	$0.452151\pi$
$504$	1.29052e9	0.449013
$505$	−4.39832e9	−1.51973
$506$	−1.80796e9	−0.620385
$507$	6.92157e7	0.0235872
$508$	−3.79718e9	−1.28510
$509$	3.08879e9	1.03819	0.519093	−	0.854718i	$-0.326270\pi$
$509$	3.08879e9	1.03819	0.519093	+	0.854718i	$0.326270\pi$
$510$	1.17953e9	0.393743
$511$	5.15893e8	0.171036
$512$	2.38609e9	0.785675
$513$	−2.53123e8	−0.0827792
$514$	−4.12637e9	−1.34029
$515$	8.02054e9	2.58749
$516$	−2.19379e9	−0.702946
$517$	2.32337e8	0.0739437
$518$	2.28707e9	0.722977
$519$	9.12490e8	0.286512
$520$	1.59655e9	0.497932
$521$	−3.59743e9	−1.11445	−0.557224	−	0.830362i	$-0.688134\pi$
$521$	−3.59743e9	−1.11445	−0.557224	+	0.830362i	$0.688134\pi$
$522$	6.77904e8	0.208603
$523$	5.01384e9	1.53255	0.766275	−	0.642513i	$-0.222108\pi$
$523$	5.01384e9	1.53255	0.766275	+	0.642513i	$0.222108\pi$
$524$	3.99080e9	1.21171
$525$	3.36064e8	0.101360
$526$	−4.05692e9	−1.21548
$527$	−4.77691e8	−0.142171
$528$	−2.88162e8	−0.0851957
$529$	−2.41566e9	−0.709481
$530$	1.41698e9	0.413426
$531$	1.01408e9	0.293928
$532$	3.31987e8	0.0955941
$533$	3.85432e8	0.110256
$534$	2.39670e9	0.681112
$535$	−7.15019e9	−2.01874
$536$	−7.42142e8	−0.208166
$537$	−1.23240e9	−0.343433
$538$	−9.13684e9	−2.52964
$539$	−3.58158e8	−0.0985175
$540$	−5.22832e9	−1.42884
$541$	5.98705e9	1.62563	0.812816	−	0.582521i	$-0.197934\pi$
$541$	5.98705e9	1.62563	0.812816	+	0.582521i	$0.197934\pi$
$542$	2.00409e9	0.540654
$543$	1.91662e9	0.513731
$544$	−1.34791e9	−0.358977
$545$	−8.21544e9	−2.17392
$546$	2.04050e8	0.0536491
$547$	1.80005e9	0.470251	0.235125	−	0.971965i	$-0.424450\pi$
$547$	1.80005e9	0.470251	0.235125	+	0.971965i	$0.424450\pi$
$548$	−6.53046e9	−1.69516
$549$	−4.86251e9	−1.25417
$550$	3.92770e9	1.00663
$551$	7.67284e7	0.0195401
$552$	8.56415e8	0.216719
$553$	5.95452e8	0.149730
$554$	−7.96476e9	−1.99016
$555$	−1.93779e9	−0.481151
$556$	−4.30035e9	−1.06106
$557$	3.19141e9	0.782510	0.391255	−	0.920282i	$-0.372041\pi$
$557$	3.19141e9	0.782510	0.391255	+	0.920282i	$0.372041\pi$
$558$	1.57011e9	0.382570
$559$	1.47054e9	0.356069
$560$	8.66455e8	0.208491
$561$	4.96913e8	0.118826
$562$	1.24130e10	2.94986
$563$	−2.27739e9	−0.537846	−0.268923	−	0.963162i	$-0.586668\pi$
$563$	−2.27739e9	−0.537846	−0.268923	+	0.963162i	$0.586668\pi$
$564$	−2.50139e8	−0.0587091
$565$	−6.16161e9	−1.43723
$566$	7.01526e8	0.162625
$567$	1.19231e9	0.274692
$568$	6.25470e9	1.43215
$569$	2.63194e9	0.598939	0.299469	−	0.954106i	$-0.403190\pi$
$569$	2.63194e9	0.598939	0.299469	+	0.954106i	$0.403190\pi$
$570$	−4.38813e8	−0.0992471
$571$	1.72621e9	0.388032	0.194016	−	0.980998i	$-0.437849\pi$
$571$	1.72621e9	0.388032	0.194016	+	0.980998i	$0.437849\pi$
$572$	1.52870e9	0.341535
$573$	2.65608e8	0.0589793
$574$	1.13627e9	0.250777
$575$	−2.14891e9	−0.471391
$576$	6.10453e9	1.33099
$577$	−6.20138e9	−1.34392	−0.671959	−	0.740588i	$-0.734547\pi$
$577$	−6.20138e9	−1.34392	−0.671959	+	0.740588i	$0.734547\pi$
$578$	5.30174e9	1.14201
$579$	−1.81763e9	−0.389162
$580$	1.58484e9	0.337278
$581$	−1.54415e9	−0.326642
$582$	−1.82570e9	−0.383884
$583$	5.96947e8	0.124766
$584$	−2.85609e9	−0.593371
$585$	1.66587e9	0.344029
$586$	1.59630e10	3.27697
$587$	9.54893e7	0.0194859	0.00974297	−	0.999953i	$-0.496899\pi$
$587$	9.54893e7	0.0194859	0.00974297	+	0.999953i	$0.496899\pi$
$588$	3.85601e8	0.0782199
$589$	1.77713e8	0.0358356
$590$	3.69846e9	0.741376
$591$	−2.87646e9	−0.573196
$592$	−2.33090e9	−0.461739
$593$	−6.94305e9	−1.36728	−0.683642	−	0.729818i	$-0.739605\pi$
$593$	−6.94305e9	−1.36728	−0.683642	+	0.729818i	$0.739605\pi$
$594$	−3.43609e9	−0.672685
$595$	−1.49414e9	−0.290791
$596$	−6.94628e9	−1.34397
$597$	1.93699e9	0.372578
$598$	−1.30477e9	−0.249505
$599$	−6.43787e9	−1.22391	−0.611953	−	0.790894i	$-0.709616\pi$
$599$	−6.43787e9	−1.22391	−0.611953	+	0.790894i	$0.709616\pi$
$600$	−1.86052e9	−0.351645
$601$	−2.30144e9	−0.432454	−0.216227	−	0.976343i	$-0.569375\pi$
$601$	−2.30144e9	−0.432454	−0.216227	+	0.976343i	$0.569375\pi$
$602$	4.33519e9	0.809880
$603$	−7.74367e8	−0.143826
$604$	−1.03352e10	−1.90849
$605$	−3.91088e9	−0.718010
$606$	3.11210e9	0.568067
$607$	3.44611e9	0.625416	0.312708	−	0.949849i	$-0.398764\pi$
$607$	3.44611e9	0.625416	0.312708	+	0.949849i	$0.398764\pi$
$608$	5.01457e8	0.0904839
$609$	8.91195e7	0.0159887
$610$	−1.77341e10	−3.16341
$611$	1.67673e8	0.0297384
$612$	5.15491e9	0.909057
$613$	2.05627e9	0.360552	0.180276	−	0.983616i	$-0.442301\pi$
$613$	2.05627e9	0.360552	0.180276	+	0.983616i	$0.442301\pi$
$614$	1.48981e10	2.59741
$615$	−9.62737e8	−0.166895
$616$	1.98283e9	0.341785
$617$	−3.42191e9	−0.586503	−0.293251	−	0.956035i	$-0.594737\pi$
$617$	−3.42191e9	−0.586503	−0.293251	+	0.956035i	$0.594737\pi$
$618$	−5.67506e9	−0.967187
$619$	1.07748e10	1.82596	0.912979	−	0.408007i	$-0.133776\pi$
$619$	1.07748e10	1.82596	0.912979	+	0.408007i	$0.133776\pi$
$620$	3.67069e9	0.618553
$621$	1.87994e9	0.315010
$622$	−1.14241e8	−0.0190351
$623$	−3.03595e9	−0.503022
$624$	−2.07960e8	−0.0342637
$625$	−6.77306e9	−1.10970
$626$	7.62817e9	1.24283
$627$	−1.84864e8	−0.0299513
$628$	1.57016e10	2.52979
$629$	4.01945e9	0.644005
$630$	4.91104e9	0.782495
$631$	−1.74027e9	−0.275749	−0.137874	−	0.990450i	$-0.544027\pi$
$631$	−1.74027e9	−0.275749	−0.137874	+	0.990450i	$0.544027\pi$
$632$	−3.29654e9	−0.519456
$633$	−2.23767e9	−0.350657
$634$	−1.57553e10	−2.45535
$635$	−6.35772e9	−0.985356
$636$	−6.42687e8	−0.0990603
$637$	−2.58475e8	−0.0396214
$638$	1.04157e9	0.158787
$639$	6.52629e9	0.989494
$640$	1.64633e10	2.48249
$641$	5.30485e9	0.795554	0.397777	−	0.917482i	$-0.369782\pi$
$641$	5.30485e9	0.795554	0.397777	+	0.917482i	$0.369782\pi$
$642$	5.05923e9	0.754591
$643$	−7.37966e9	−1.09471	−0.547354	−	0.836901i	$-0.684365\pi$
$643$	−7.37966e9	−1.09471	−0.547354	+	0.836901i	$0.684365\pi$
$644$	−2.46567e9	−0.363776
$645$	−3.67313e9	−0.538985
$646$	9.10207e8	0.132839
$647$	−2.81811e8	−0.0409065	−0.0204532	−	0.999791i	$-0.506511\pi$
$647$	−2.81811e8	−0.0409065	−0.0204532	+	0.999791i	$0.506511\pi$
$648$	−6.60084e9	−0.952986
$649$	1.55809e9	0.223736
$650$	2.83454e9	0.404842
$651$	2.06412e8	0.0293225
$652$	2.26109e10	3.19486
$653$	−2.38630e9	−0.335374	−0.167687	−	0.985840i	$-0.553630\pi$
$653$	−2.38630e9	−0.335374	−0.167687	+	0.985840i	$0.553630\pi$
$654$	5.81296e9	0.812597
$655$	6.68190e9	0.929085
$656$	−1.15804e9	−0.160162
$657$	−2.98010e9	−0.409970
$658$	4.94304e8	0.0676400
$659$	−4.44831e9	−0.605475	−0.302738	−	0.953074i	$-0.597901\pi$
$659$	−4.44831e9	−0.605475	−0.302738	+	0.953074i	$0.597901\pi$
$660$	−3.81840e9	−0.516985
$661$	−8.08956e9	−1.08948	−0.544741	−	0.838605i	$-0.683372\pi$
$661$	−8.08956e9	−1.08948	−0.544741	+	0.838605i	$0.683372\pi$
$662$	−1.40352e10	−1.88024
$663$	3.58612e8	0.0477889
$664$	8.54870e9	1.13321
$665$	5.55855e8	0.0732970
$666$	−1.32114e10	−1.73297
$667$	−5.69861e8	−0.0743581
$668$	1.34091e10	1.74053
$669$	3.43904e9	0.444064
$670$	−2.82420e9	−0.362772
$671$	−7.47105e9	−0.954668
$672$	5.82439e8	0.0740386
$673$	−1.04821e10	−1.32555	−0.662777	−	0.748817i	$-0.730622\pi$
$673$	−1.04821e10	−1.32555	−0.662777	+	0.748817i	$0.730622\pi$
$674$	−2.08256e9	−0.261992
$675$	−4.08408e9	−0.511130
$676$	1.10323e9	0.137358
$677$	−6.17382e9	−0.764705	−0.382352	−	0.924017i	$-0.624886\pi$
$677$	−6.17382e9	−0.764705	−0.382352	+	0.924017i	$0.624886\pi$
$678$	4.35975e9	0.537226
$679$	2.31266e9	0.283510
$680$	8.27183e9	1.00884
$681$	2.11820e9	0.257012
$682$	2.41241e9	0.291209
$683$	3.23814e9	0.388887	0.194444	−	0.980914i	$-0.437710\pi$
$683$	3.23814e9	0.388887	0.194444	+	0.980914i	$0.437710\pi$
$684$	−1.91775e9	−0.229138
$685$	−1.09341e10	−1.29977
$686$	−7.61992e8	−0.0901189
$687$	−8.97653e8	−0.105623
$688$	−4.41827e9	−0.517241
$689$	4.30804e8	0.0501779
$690$	3.25906e9	0.377677
$691$	8.93383e9	1.03006	0.515032	−	0.857171i	$-0.327780\pi$
$691$	8.93383e9	1.03006	0.515032	+	0.857171i	$0.327780\pi$
$692$	1.45442e10	1.66847
$693$	2.06893e9	0.236145
$694$	1.18201e10	1.34234
$695$	−7.20019e9	−0.813574
$696$	−4.93383e8	−0.0554692
$697$	1.99695e9	0.223384
$698$	−1.21979e10	−1.35766
$699$	4.78414e9	0.529827
$700$	5.35653e9	0.590256
$701$	−7.06574e9	−0.774719	−0.387360	−	0.921929i	$-0.626613\pi$
$701$	−7.06574e9	−0.774719	−0.387360	+	0.921929i	$0.626613\pi$
$702$	−2.47975e9	−0.270538
$703$	−1.49534e9	−0.162329
$704$	9.37935e9	1.01314
$705$	−4.18815e8	−0.0450153
$706$	−1.34162e8	−0.0143488
$707$	−3.94217e9	−0.419534
$708$	−1.67748e9	−0.177640
$709$	5.18795e9	0.546681	0.273340	−	0.961917i	$-0.411871\pi$
$709$	5.18795e9	0.546681	0.273340	+	0.961917i	$0.411871\pi$
$710$	2.38021e10	2.49580
$711$	−3.43968e9	−0.358901
$712$	1.68076e10	1.74512
$713$	−1.31987e9	−0.136370
$714$	1.05720e9	0.108696
$715$	2.55954e9	0.261873
$716$	−1.96432e10	−1.99994
$717$	2.02493e9	0.205160
$718$	6.02075e9	0.607036
$719$	−3.93303e9	−0.394617	−0.197309	−	0.980341i	$-0.563220\pi$
$719$	−3.93303e9	−0.394617	−0.197309	+	0.980341i	$0.563220\pi$
$720$	−5.00515e9	−0.499751
$721$	7.18873e9	0.714296
$722$	1.65402e10	1.63554
$723$	−1.84691e9	−0.181744
$724$	3.05490e10	2.99166
$725$	1.23799e9	0.120652
$726$	2.76720e9	0.268388
$727$	1.29632e10	1.25124	0.625622	−	0.780126i	$-0.284845\pi$
$727$	1.29632e10	1.25124	0.625622	+	0.780126i	$0.284845\pi$
$728$	1.43097e9	0.137458
$729$	−5.01288e9	−0.479226
$730$	−1.08687e10	−1.03407
$731$	7.61897e9	0.721415
$732$	8.04351e9	0.757978
$733$	−3.12325e9	−0.292916	−0.146458	−	0.989217i	$-0.546787\pi$
$733$	−3.12325e9	−0.292916	−0.146458	+	0.989217i	$0.546787\pi$
$734$	7.91093e9	0.738399
$735$	6.45622e8	0.0599753
$736$	−3.72432e9	−0.344330
$737$	−1.18978e9	−0.109479
$738$	−6.56374e9	−0.601110
$739$	1.53207e10	1.39645	0.698223	−	0.715880i	$-0.253974\pi$
$739$	1.53207e10	1.39645	0.698223	+	0.715880i	$0.253974\pi$
$740$	−3.08865e10	−2.80193
$741$	−1.33412e8	−0.0120457
$742$	1.27002e9	0.114130
$743$	1.63391e10	1.46139	0.730697	−	0.682702i	$-0.239195\pi$
$743$	1.63391e10	1.46139	0.730697	+	0.682702i	$0.239195\pi$
$744$	−1.14274e9	−0.101728
$745$	−1.16303e10	−1.03049
$746$	−1.68064e10	−1.48214
$747$	8.91990e9	0.782957
$748$	7.92030e9	0.691968
$749$	−6.40864e9	−0.557288
$750$	1.01544e9	0.0878901
$751$	−1.51807e10	−1.30783	−0.653916	−	0.756567i	$-0.726875\pi$
$751$	−1.51807e10	−1.30783	−0.653916	+	0.756567i	$0.726875\pi$
$752$	−5.03777e8	−0.0431992
$753$	−5.63903e9	−0.481306
$754$	7.51679e8	0.0638606
$755$	−1.73045e10	−1.46334
$756$	−4.68609e9	−0.394443
$757$	9.07678e9	0.760495	0.380247	−	0.924885i	$-0.375839\pi$
$757$	9.07678e9	0.760495	0.380247	+	0.924885i	$0.375839\pi$
$758$	−3.02599e10	−2.52363
$759$	1.37298e9	0.113977
$760$	−3.07732e9	−0.254288
$761$	−1.52102e10	−1.25109	−0.625546	−	0.780187i	$-0.715124\pi$
$761$	−1.52102e10	−1.25109	−0.625546	+	0.780187i	$0.715124\pi$
$762$	4.49850e9	0.368320
$763$	−7.36341e9	−0.600127
$764$	4.23353e9	0.343460
$765$	8.63100e9	0.697021
$766$	−3.37470e10	−2.71291
$767$	1.12444e9	0.0899814
$768$	−5.99377e9	−0.477459
$769$	−4.82490e9	−0.382601	−0.191301	−	0.981531i	$-0.561271\pi$
$769$	−4.82490e9	−0.382601	−0.191301	+	0.981531i	$0.561271\pi$
$770$	7.54560e9	0.595630
$771$	3.13360e9	0.246237
$772$	−2.89712e10	−2.26624
$773$	1.07767e10	0.839181	0.419591	−	0.907713i	$-0.362174\pi$
$773$	1.07767e10	0.839181	0.419591	+	0.907713i	$0.362174\pi$
$774$	−2.50426e10	−1.94127
$775$	2.86735e9	0.221271
$776$	−1.28033e10	−0.983575
$777$	−1.73682e9	−0.132826
$778$	−2.60355e9	−0.198215
$779$	−7.42916e8	−0.0563065
$780$	−2.75566e9	−0.207919
$781$	1.00274e10	0.753196
$782$	−6.76009e9	−0.505509
$783$	−1.08304e9	−0.0806267
$784$	7.76595e8	0.0575557
$785$	2.62896e10	1.93972
$786$	−4.72788e9	−0.347286
$787$	−2.10639e10	−1.54037	−0.770187	−	0.637818i	$-0.779837\pi$
$787$	−2.10639e10	−1.54037	−0.770187	+	0.637818i	$0.779837\pi$
$788$	−4.58480e10	−3.33794
$789$	3.08087e9	0.223308
$790$	−1.25449e10	−0.905257
$791$	−5.52259e9	−0.396758
$792$	−1.14540e10	−0.819255
$793$	−5.39170e9	−0.383945
$794$	−1.84392e10	−1.30729
$795$	−1.07607e9	−0.0759547
$796$	3.08737e10	2.16967
$797$	3.19700e9	0.223686	0.111843	−	0.993726i	$-0.464325\pi$
$797$	3.19700e9	0.223686	0.111843	+	0.993726i	$0.464325\pi$
$798$	−3.93304e8	−0.0273980
$799$	8.68725e8	0.0602516
$800$	8.09089e9	0.558703
$801$	1.75374e10	1.20574
$802$	1.07674e10	0.737053
$803$	−4.57880e9	−0.312066
$804$	1.28095e9	0.0869231
$805$	−4.12833e9	−0.278926
$806$	1.74098e9	0.117118
$807$	6.93860e9	0.464745
$808$	2.18247e10	1.45548
$809$	9.36652e9	0.621954	0.310977	−	0.950417i	$-0.399344\pi$
$809$	9.36652e9	0.621954	0.310977	+	0.950417i	$0.399344\pi$
$810$	−2.51193e10	−1.66077
$811$	−2.86960e9	−0.188907	−0.0944536	−	0.995529i	$-0.530110\pi$
$811$	−2.86960e9	−0.188907	−0.0944536	+	0.995529i	$0.530110\pi$
$812$	1.42048e9	0.0931083
$813$	−1.52192e9	−0.0993290
$814$	−2.02988e10	−1.31912
$815$	3.78580e10	2.44966
$816$	−1.07746e9	−0.0694200
$817$	−2.83444e9	−0.181841
$818$	2.89148e9	0.184707
$819$	1.49310e9	0.0949721
$820$	−1.53451e10	−0.971898
$821$	−2.98369e10	−1.88171	−0.940855	−	0.338810i	$-0.889976\pi$
$821$	−2.98369e10	−1.88171	−0.940855	+	0.338810i	$0.889976\pi$
$822$	7.73660e9	0.485846
$823$	1.12227e10	0.701774	0.350887	−	0.936418i	$-0.385880\pi$
$823$	1.12227e10	0.701774	0.350887	+	0.936418i	$0.385880\pi$
$824$	−3.97982e10	−2.47810
$825$	−2.98273e9	−0.184938
$826$	3.31489e9	0.204663
$827$	2.26256e9	0.139101	0.0695505	−	0.997578i	$-0.477843\pi$
$827$	2.26256e9	0.139101	0.0695505	+	0.997578i	$0.477843\pi$
$828$	1.42431e10	0.871966
$829$	−2.17857e8	−0.0132810	−0.00664050	−	0.999978i	$-0.502114\pi$
$829$	−2.17857e8	−0.0132810	−0.00664050	+	0.999978i	$0.502114\pi$
$830$	3.25318e10	1.97485
$831$	6.04852e9	0.365633
$832$	6.76888e9	0.407460
$833$	−1.33918e9	−0.0802751
$834$	5.09460e9	0.304109
$835$	2.24511e10	1.33455
$836$	−2.94655e9	−0.174418
$837$	−2.50846e9	−0.147866
$838$	1.63904e10	0.962133
$839$	−4.16523e9	−0.243485	−0.121742	−	0.992562i	$-0.538848\pi$
$839$	−4.16523e9	−0.243485	−0.121742	+	0.992562i	$0.538848\pi$
$840$	−3.57429e9	−0.208071
$841$	−1.69216e10	−0.980968
$842$	3.19466e10	1.84430
$843$	−9.42659e9	−0.541949
$844$	−3.56662e10	−2.04201
$845$	1.84717e9	0.105319
$846$	−2.85539e9	−0.162132
$847$	−3.50528e9	−0.198212
$848$	−1.29436e9	−0.0728904
$849$	−5.32745e8	−0.0298774
$850$	1.46859e10	0.820230
$851$	1.11058e10	0.617729
$852$	−1.07957e10	−0.598015
$853$	−1.00137e10	−0.552426	−0.276213	−	0.961096i	$-0.589080\pi$
$853$	−1.00137e10	−0.552426	−0.276213	+	0.961096i	$0.589080\pi$
$854$	−1.58949e10	−0.873283
$855$	−3.21095e9	−0.175692
$856$	3.54795e10	1.93339
$857$	3.10201e10	1.68349	0.841744	−	0.539877i	$-0.181529\pi$
$857$	3.10201e10	1.68349	0.841744	+	0.539877i	$0.181529\pi$
$858$	−1.81104e9	−0.0978865
$859$	1.79309e10	0.965218	0.482609	−	0.875836i	$-0.339689\pi$
$859$	1.79309e10	0.965218	0.482609	+	0.875836i	$0.339689\pi$
$860$	−5.85460e10	−3.13872
$861$	−8.62891e8	−0.0460728
$862$	−2.15314e10	−1.14498
$863$	1.67534e10	0.887287	0.443643	−	0.896203i	$-0.353686\pi$
$863$	1.67534e10	0.887287	0.443643	+	0.896203i	$0.353686\pi$
$864$	−7.07820e9	−0.373357
$865$	2.43517e10	1.27930
$866$	8.29709e9	0.434123
$867$	−4.02620e9	−0.209811
$868$	3.29001e9	0.170757
$869$	−5.28493e9	−0.273193
$870$	−1.87755e9	−0.0966663
$871$	−8.58640e8	−0.0440299
$872$	4.07653e10	2.08201
$873$	−1.33593e10	−0.679569
$874$	2.51492e9	0.127419
$875$	−1.28628e9	−0.0649095
$876$	4.92964e9	0.247771
$877$	−5.88510e9	−0.294615	−0.147308	−	0.989091i	$-0.547061\pi$
$877$	−5.88510e9	−0.294615	−0.147308	+	0.989091i	$0.547061\pi$
$878$	−2.89131e10	−1.44166
$879$	−1.21224e10	−0.602045
$880$	−7.69020e9	−0.380407
$881$	−1.86505e10	−0.918912	−0.459456	−	0.888201i	$-0.651956\pi$
$881$	−1.86505e10	−0.918912	−0.459456	+	0.888201i	$0.651956\pi$
$882$	4.40171e9	0.216014
$883$	3.71193e10	1.81442	0.907208	−	0.420682i	$-0.138209\pi$
$883$	3.71193e10	1.81442	0.907208	+	0.420682i	$0.138209\pi$
$884$	5.71592e9	0.278293
$885$	−2.80864e9	−0.136206
$886$	3.32433e10	1.60578
$887$	2.32835e10	1.12025	0.560126	−	0.828408i	$-0.310753\pi$
$887$	2.32835e10	1.12025	0.560126	+	0.828408i	$0.310753\pi$
$888$	9.61539e9	0.460809
$889$	−5.69836e9	−0.272016
$890$	6.39609e10	3.04123
$891$	−1.05823e10	−0.501196
$892$	5.48149e10	2.58596
$893$	−3.23187e8	−0.0151871
$894$	8.22923e9	0.385192
$895$	−3.28892e10	−1.53346
$896$	1.47559e10	0.685311
$897$	9.90852e8	0.0458390
$898$	−2.24016e10	−1.03231
$899$	7.60381e8	0.0349038
$900$	−3.09425e10	−1.41484
$901$	2.23203e9	0.101663
$902$	−1.00849e10	−0.457561
$903$	−3.29219e9	−0.148791
$904$	3.05742e10	1.37646
$905$	5.11490e10	2.29386
$906$	1.22441e10	0.546988
$907$	1.74695e10	0.777419	0.388709	−	0.921360i	$-0.372921\pi$
$907$	1.74695e10	0.777419	0.388709	+	0.921360i	$0.372921\pi$
$908$	3.37621e10	1.49668
$909$	2.27723e10	1.00562
$910$	5.44550e9	0.239548
$911$	−7.84250e9	−0.343669	−0.171834	−	0.985126i	$-0.554969\pi$
$911$	−7.84250e9	−0.343669	−0.171834	+	0.985126i	$0.554969\pi$
$912$	4.00841e8	0.0174981
$913$	1.37050e10	0.595981
$914$	4.28254e10	1.85520
$915$	1.34675e10	0.581181
$916$	−1.43077e10	−0.615086
$917$	5.98892e9	0.256481
$918$	−1.28478e10	−0.548124
$919$	−1.66392e10	−0.707179	−0.353589	−	0.935401i	$-0.615039\pi$
$919$	−1.66392e10	−0.707179	−0.353589	+	0.935401i	$0.615039\pi$
$920$	2.28552e10	0.967673
$921$	−1.13137e10	−0.477196
$922$	1.72858e10	0.726325
$923$	7.23654e9	0.302918
$924$	−3.42239e9	−0.142718
$925$	−2.41268e10	−1.00232
$926$	−8.34095e9	−0.345205
$927$	−4.15263e10	−1.71216
$928$	2.14559e9	0.0881310
$929$	−3.96366e9	−0.162197	−0.0810983	−	0.996706i	$-0.525843\pi$
$929$	−3.96366e9	−0.162197	−0.0810983	+	0.996706i	$0.525843\pi$
$930$	−4.34865e9	−0.177282
$931$	4.98207e8	0.0202342
$932$	7.62545e10	3.08539
$933$	8.67557e7	0.00349713
$934$	−8.06693e10	−3.23962
$935$	1.32612e10	0.530568
$936$	−8.26611e9	−0.329485
$937$	−3.48536e9	−0.138407	−0.0692037	−	0.997603i	$-0.522046\pi$
$937$	−3.48536e9	−0.138407	−0.0692037	+	0.997603i	$0.522046\pi$
$938$	−2.53130e9	−0.100146
$939$	−5.79291e9	−0.228332
$940$	−6.67550e9	−0.262142
$941$	5.31458e9	0.207924	0.103962	−	0.994581i	$-0.466848\pi$
$941$	5.31458e9	0.207924	0.103962	+	0.994581i	$0.466848\pi$
$942$	−1.86016e10	−0.725057
$943$	5.51762e9	0.214270
$944$	−3.37841e9	−0.130711
$945$	−7.84603e9	−0.302440
$946$	−3.84769e10	−1.47768
$947$	−3.05870e10	−1.17034	−0.585170	−	0.810911i	$-0.698972\pi$
$947$	−3.05870e10	−1.17034	−0.585170	+	0.810911i	$0.698972\pi$
$948$	5.68988e9	0.216907
$949$	−3.30442e9	−0.125506
$950$	−5.46354e9	−0.206748
$951$	1.19647e10	0.451098
$952$	7.41396e9	0.278497
$953$	4.36681e10	1.63433	0.817165	−	0.576405i	$-0.195545\pi$
$953$	4.36681e10	1.63433	0.817165	+	0.576405i	$0.195545\pi$
$954$	−7.33640e9	−0.273567
$955$	7.08830e9	0.263348
$956$	3.22754e10	1.19473
$957$	−7.90978e8	−0.0291724
$958$	−5.55717e10	−2.04209
$959$	−9.80013e9	−0.358812
$960$	−1.69074e10	−0.616776
$961$	−2.57515e10	−0.935988
$962$	−1.46492e10	−0.530520
$963$	3.70201e10	1.33581
$964$	−2.94379e10	−1.05837
$965$	−4.85073e10	−1.73765
$966$	2.92106e9	0.104261
$967$	−3.36504e8	−0.0119673	−0.00598367	−	0.999982i	$-0.501905\pi$
$967$	−3.36504e8	−0.0119673	−0.00598367	+	0.999982i	$0.501905\pi$
$968$	1.94059e10	0.687655
$969$	−6.91220e8	−0.0244052
$970$	−4.87227e10	−1.71408
$971$	4.75130e10	1.66550	0.832752	−	0.553647i	$-0.186764\pi$
$971$	4.75130e10	1.66550	0.832752	+	0.553647i	$0.186764\pi$
$972$	4.12721e10	1.44153
$973$	−6.45345e9	−0.224593
$974$	−3.66243e10	−1.27003
$975$	−2.15257e9	−0.0743776
$976$	1.61995e10	0.557734
$977$	2.83106e10	0.971222	0.485611	−	0.874175i	$-0.338597\pi$
$977$	2.83106e10	0.971222	0.485611	+	0.874175i	$0.338597\pi$
$978$	−2.67870e10	−0.915669
$979$	2.69455e10	0.917798
$980$	1.02906e10	0.349260
$981$	4.25354e10	1.43850
$982$	−4.20481e10	−1.41696
$983$	3.67835e10	1.23514	0.617570	−	0.786516i	$-0.288117\pi$
$983$	3.67835e10	1.23514	0.617570	+	0.786516i	$0.288117\pi$
$984$	4.77714e9	0.159840
$985$	−7.67645e10	−2.55937
$986$	3.89451e9	0.129385
$987$	−3.75380e8	−0.0124268
$988$	−2.12646e9	−0.0701469
$989$	2.10514e10	0.691980
$990$	−4.35878e10	−1.42772
$991$	−4.45790e10	−1.45503	−0.727516	−	0.686091i	$-0.759325\pi$
$991$	−4.45790e10	−1.45503	−0.727516	+	0.686091i	$0.759325\pi$
$992$	4.96946e9	0.161629
$993$	1.06584e10	0.345439
$994$	2.13336e10	0.688987
$995$	5.16926e10	1.66360
$996$	−1.47552e10	−0.473191
$997$	−1.32610e10	−0.423782	−0.211891	−	0.977293i	$-0.567962\pi$
$997$	−1.32610e10	−0.423782	−0.211891	+	0.977293i	$0.567962\pi$
$998$	4.70703e10	1.49896
$999$	2.11070e10	0.669804

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.c.1.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.c.1.2	✓	10	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)

\(f(q)\)	\(=\)	\(q-18.8829 q^{2} +14.3398 q^{3} +228.563 q^{4} +382.689 q^{5} -270.777 q^{6} +343.000 q^{7} -1898.92 q^{8} -1981.37 q^{9} +O(q^{10})\)	\(q-18.8829 q^{2} +14.3398 q^{3} +228.563 q^{4} +382.689 q^{5} -270.777 q^{6} +343.000 q^{7} -1898.92 q^{8} -1981.37 q^{9} -7226.26 q^{10} -3044.29 q^{11} +3277.55 q^{12} -2197.00 q^{13} -6476.83 q^{14} +5487.69 q^{15} +6600.94 q^{16} -11382.8 q^{17} +37413.9 q^{18} +4234.69 q^{19} +87468.4 q^{20} +4918.56 q^{21} +57484.9 q^{22} -31451.0 q^{23} -27230.1 q^{24} +68325.7 q^{25} +41485.7 q^{26} -59773.7 q^{27} +78397.1 q^{28} +18119.0 q^{29} -103623. q^{30} +41965.9 q^{31} +118416. q^{32} -43654.6 q^{33} +214940. q^{34} +131262. q^{35} -452867. q^{36} -353115. q^{37} -79963.2 q^{38} -31504.6 q^{39} -726694. q^{40} -175436. q^{41} -92876.6 q^{42} -669339. q^{43} -695812. q^{44} -758248. q^{45} +593885. q^{46} -76318.9 q^{47} +94656.5 q^{48} +117649. q^{49} -1.29018e6 q^{50} -163228. q^{51} -502153. q^{52} -196087. q^{53} +1.12870e6 q^{54} -1.16502e6 q^{55} -651328. q^{56} +60724.8 q^{57} -342139. q^{58} -511807. q^{59} +1.25428e6 q^{60} +2.45412e6 q^{61} -792437. q^{62} -679610. q^{63} -3.08096e6 q^{64} -840767. q^{65} +824324. q^{66} +390824. q^{67} -2.60169e6 q^{68} -451002. q^{69} -2.47861e6 q^{70} -3.29383e6 q^{71} +3.76245e6 q^{72} +1.50406e6 q^{73} +6.66783e6 q^{74} +979779. q^{75} +967894. q^{76} -1.04419e6 q^{77} +594898. q^{78} +1.73601e6 q^{79} +2.52611e6 q^{80} +3.47611e6 q^{81} +3.31273e6 q^{82} -4.50188e6 q^{83} +1.12420e6 q^{84} -4.35608e6 q^{85} +1.26390e7 q^{86} +259824. q^{87} +5.78085e6 q^{88} -8.85117e6 q^{89} +1.43179e7 q^{90} -753571. q^{91} -7.18853e6 q^{92} +601784. q^{93} +1.44112e6 q^{94} +1.62057e6 q^{95} +1.69807e6 q^{96} +6.74245e6 q^{97} -2.22155e6 q^{98} +6.03186e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9}+O(q^{10}) \) 10 * q - 18 * q^2 - 80 * q^3 + 670 * q^4 - 927 * q^5 - 1419 * q^6 + 3430 * q^7 - 4878 * q^8 + 3612 * q^9	\( 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9} + 9420 q^{10} + 876 q^{11} - 8765 q^{12} - 21970 q^{13} - 6174 q^{14} - 5320 q^{15} + 41370 q^{16} + 6294 q^{17} - 16027 q^{18} - 97401 q^{19} - 166650 q^{20} - 27440 q^{21} + 74171 q^{22} - 15255 q^{23} + 196187 q^{24} + 162145 q^{25} + 39546 q^{26} - 181820 q^{27} + 229810 q^{28} - 340533 q^{29} - 325020 q^{30} - 148675 q^{31} - 642762 q^{32} - 624400 q^{33} - 1161518 q^{34} - 317961 q^{35} - 773917 q^{36} - 621782 q^{37} - 805092 q^{38} + 175760 q^{39} - 350478 q^{40} - 2043336 q^{41} - 486717 q^{42} - 1801391 q^{43} - 3953667 q^{44} - 1908807 q^{45} - 2707731 q^{46} - 1624701 q^{47} - 6068625 q^{48} + 1176490 q^{49} - 6891516 q^{50} + 1811700 q^{51} - 1471990 q^{52} - 199965 q^{53} - 2895913 q^{54} + 739086 q^{55} - 1673154 q^{56} + 2159088 q^{57} + 2071092 q^{58} - 8098908 q^{59} + 8096436 q^{60} + 2271618 q^{61} - 8910225 q^{62} + 1238916 q^{63} + 8099930 q^{64} + 2036619 q^{65} - 5999191 q^{66} + 1970272 q^{67} - 1766238 q^{68} - 4622962 q^{69} + 3231060 q^{70} - 7145820 q^{71} + 984975 q^{72} + 1409431 q^{73} - 5498643 q^{74} - 8857892 q^{75} - 2749534 q^{76} + 300468 q^{77} + 3117543 q^{78} - 9011055 q^{79} - 23850522 q^{80} + 11613490 q^{81} + 27962597 q^{82} - 15006567 q^{83} - 3006395 q^{84} - 9416628 q^{85} + 38357850 q^{86} - 15828996 q^{87} + 42205269 q^{88} - 11472777 q^{89} + 53425712 q^{90} - 7535710 q^{91} + 16755837 q^{92} + 36339848 q^{93} + 5133371 q^{94} + 29637939 q^{95} + 65329611 q^{96} + 3228571 q^{97} - 2117682 q^{98} + 19367194 q^{99}+O(q^{100}) \) 10 * q - 18 * q^2 - 80 * q^3 + 670 * q^4 - 927 * q^5 - 1419 * q^6 + 3430 * q^7 - 4878 * q^8 + 3612 * q^9 + 9420 * q^10 + 876 * q^11 - 8765 * q^12 - 21970 * q^13 - 6174 * q^14 - 5320 * q^15 + 41370 * q^16 + 6294 * q^17 - 16027 * q^18 - 97401 * q^19 - 166650 * q^20 - 27440 * q^21 + 74171 * q^22 - 15255 * q^23 + 196187 * q^24 + 162145 * q^25 + 39546 * q^26 - 181820 * q^27 + 229810 * q^28 - 340533 * q^29 - 325020 * q^30 - 148675 * q^31 - 642762 * q^32 - 624400 * q^33 - 1161518 * q^34 - 317961 * q^35 - 773917 * q^36 - 621782 * q^37 - 805092 * q^38 + 175760 * q^39 - 350478 * q^40 - 2043336 * q^41 - 486717 * q^42 - 1801391 * q^43 - 3953667 * q^44 - 1908807 * q^45 - 2707731 * q^46 - 1624701 * q^47 - 6068625 * q^48 + 1176490 * q^49 - 6891516 * q^50 + 1811700 * q^51 - 1471990 * q^52 - 199965 * q^53 - 2895913 * q^54 + 739086 * q^55 - 1673154 * q^56 + 2159088 * q^57 + 2071092 * q^58 - 8098908 * q^59 + 8096436 * q^60 + 2271618 * q^61 - 8910225 * q^62 + 1238916 * q^63 + 8099930 * q^64 + 2036619 * q^65 - 5999191 * q^66 + 1970272 * q^67 - 1766238 * q^68 - 4622962 * q^69 + 3231060 * q^70 - 7145820 * q^71 + 984975 * q^72 + 1409431 * q^73 - 5498643 * q^74 - 8857892 * q^75 - 2749534 * q^76 + 300468 * q^77 + 3117543 * q^78 - 9011055 * q^79 - 23850522 * q^80 + 11613490 * q^81 + 27962597 * q^82 - 15006567 * q^83 - 3006395 * q^84 - 9416628 * q^85 + 38357850 * q^86 - 15828996 * q^87 + 42205269 * q^88 - 11472777 * q^89 + 53425712 * q^90 - 7535710 * q^91 + 16755837 * q^92 + 36339848 * q^93 + 5133371 * q^94 + 29637939 * q^95 + 65329611 * q^96 + 3228571 * q^97 - 2117682 * q^98 + 19367194 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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