LMFDB - Embedded newform 91.8.a.c.1.8

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			1.8
Root			$12.2698$ 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)

$f(q)$	$=$	$q+10.2698 q^{2} -81.6519 q^{3} -22.5320 q^{4} +313.060 q^{5} -838.546 q^{6} +343.000 q^{7} -1545.93 q^{8} +4480.04 q^{9} +O(q^{10})$	\(q+10.2698 q^{2} -81.6519 q^{3} -22.5320 q^{4} +313.060 q^{5} -838.546 q^{6} +343.000 q^{7} -1545.93 q^{8} +4480.04 q^{9} +3215.05 q^{10} +4589.73 q^{11} +1839.78 q^{12} -2197.00 q^{13} +3522.53 q^{14} -25561.9 q^{15} -12992.2 q^{16} -18394.3 q^{17} +46008.9 q^{18} +13502.3 q^{19} -7053.86 q^{20} -28006.6 q^{21} +47135.4 q^{22} -52047.6 q^{23} +126228. q^{24} +19881.5 q^{25} -22562.7 q^{26} -187231. q^{27} -7728.47 q^{28} -126389. q^{29} -262515. q^{30} -136335. q^{31} +64451.8 q^{32} -374760. q^{33} -188905. q^{34} +107380. q^{35} -100944. q^{36} -235595. q^{37} +138665. q^{38} +179389. q^{39} -483968. q^{40} -676470. q^{41} -287621. q^{42} +266146. q^{43} -103416. q^{44} +1.40252e6 q^{45} -534516. q^{46} -440980. q^{47} +1.06084e6 q^{48} +117649. q^{49} +204178. q^{50} +1.50193e6 q^{51} +49502.8 q^{52} +1.57803e6 q^{53} -1.92282e6 q^{54} +1.43686e6 q^{55} -530253. q^{56} -1.10249e6 q^{57} -1.29799e6 q^{58} -992625. q^{59} +575961. q^{60} -866239. q^{61} -1.40012e6 q^{62} +1.53665e6 q^{63} +2.32491e6 q^{64} -687793. q^{65} -3.84870e6 q^{66} +4.03078e6 q^{67} +414460. q^{68} +4.24978e6 q^{69} +1.10276e6 q^{70} -4.24947e6 q^{71} -6.92581e6 q^{72} -5.35477e6 q^{73} -2.41950e6 q^{74} -1.62336e6 q^{75} -304234. q^{76} +1.57428e6 q^{77} +1.84229e6 q^{78} -3.35025e6 q^{79} -4.06734e6 q^{80} +5.48992e6 q^{81} -6.94719e6 q^{82} +3.70208e6 q^{83} +631044. q^{84} -5.75852e6 q^{85} +2.73325e6 q^{86} +1.03199e7 q^{87} -7.09538e6 q^{88} +3.62636e6 q^{89} +1.44035e7 q^{90} -753571. q^{91} +1.17274e6 q^{92} +1.11320e7 q^{93} -4.52876e6 q^{94} +4.22703e6 q^{95} -5.26261e6 q^{96} -7.98420e6 q^{97} +1.20823e6 q^{98} +2.05621e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	10.2698	0.907727	0.453864	−	0.891071i	$-0.350045\pi$
$2$	10.2698	0.907727	0.453864	+	0.891071i	$0.350045\pi$
$3$	−81.6519	−1.74599	−0.872996	−	0.487728i	$-0.837826\pi$
$3$	−81.6519	−1.74599	−0.872996	+	0.487728i	$0.837826\pi$
$4$	−22.5320	−0.176031
$5$	313.060	1.12004	0.560019	−	0.828480i	$-0.310794\pi$
$5$	313.060	1.12004	0.560019	+	0.828480i	$0.310794\pi$
$6$	−838.546	−1.58488
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−1545.93	−1.06752
$9$	4480.04	2.04848
$10$	3215.05	1.01669
$11$	4589.73	1.03971	0.519855	−	0.854254i	$-0.325986\pi$
$11$	4589.73	1.03971	0.519855	+	0.854254i	$0.325986\pi$
$12$	1839.78	0.307349
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	3522.53	0.343089
$15$	−25561.9	−1.95557
$16$	−12992.2	−0.792982
$17$	−18394.3	−0.908055	−0.454027	−	0.890988i	$-0.650013\pi$
$17$	−18394.3	−0.908055	−0.454027	+	0.890988i	$0.650013\pi$
$18$	46008.9	1.85947
$19$	13502.3	0.451617	0.225808	−	0.974172i	$-0.427498\pi$
$19$	13502.3	0.451617	0.225808	+	0.974172i	$0.427498\pi$
$20$	−7053.86	−0.197161
$21$	−28006.6	−0.659923
$22$	47135.4	0.943773
$23$	−52047.6	−0.891976	−0.445988	−	0.895039i	$-0.647148\pi$
$23$	−52047.6	−0.891976	−0.445988	+	0.895039i	$0.647148\pi$
$24$	126228.	1.86387
$25$	19881.5	0.254483
$26$	−22562.7	−0.251758
$27$	−187231.	−1.83064
$28$	−7728.47	−0.0665335
$29$	−126389.	−0.962314	−0.481157	−	0.876634i	$-0.659783\pi$
$29$	−126389.	−0.962314	−0.481157	+	0.876634i	$0.659783\pi$
$30$	−262515.	−1.77513
$31$	−136335.	−0.821940	−0.410970	−	0.911649i	$-0.634810\pi$
$31$	−136335.	−0.821940	−0.410970	+	0.911649i	$0.634810\pi$
$32$	64451.8	0.347704
$33$	−374760.	−1.81532
$34$	−188905.	−0.824266
$35$	107380.	0.423334
$36$	−100944.	−0.360597
$37$	−235595.	−0.764645	−0.382323	−	0.924029i	$-0.624876\pi$
$37$	−235595.	−0.764645	−0.382323	+	0.924029i	$0.624876\pi$
$38$	138665.	0.409945
$39$	179389.	0.484251
$40$	−483968.	−1.19566
$41$	−676470.	−1.53287	−0.766435	−	0.642322i	$-0.777971\pi$
$41$	−676470.	−1.53287	−0.766435	+	0.642322i	$0.777971\pi$
$42$	−287621.	−0.599030
$43$	266146.	0.510481	0.255241	−	0.966878i	$-0.417845\pi$
$43$	266146.	0.510481	0.255241	+	0.966878i	$0.417845\pi$
$44$	−103416.	−0.183021
$45$	1.40252e6	2.29438
$46$	−534516.	−0.809671
$47$	−440980.	−0.619551	−0.309775	−	0.950810i	$-0.600254\pi$
$47$	−440980.	−0.619551	−0.309775	+	0.950810i	$0.600254\pi$
$48$	1.06084e6	1.38454
$49$	117649.	0.142857
$50$	204178.	0.231001
$51$	1.50193e6	1.58546
$52$	49502.8	0.0488222
$53$	1.57803e6	1.45596	0.727981	−	0.685597i	$-0.240459\pi$
$53$	1.57803e6	1.45596	0.727981	+	0.685597i	$0.240459\pi$
$54$	−1.92282e6	−1.66173
$55$	1.43686e6	1.16451
$56$	−530253.	−0.403483
$57$	−1.10249e6	−0.788519
$58$	−1.29799e6	−0.873519
$59$	−992625.	−0.629221	−0.314610	−	0.949221i	$-0.601874\pi$
$59$	−992625.	−0.629221	−0.314610	+	0.949221i	$0.601874\pi$
$60$	575961.	0.344242
$61$	−866239.	−0.488633	−0.244317	−	0.969696i	$-0.578564\pi$
$61$	−866239.	−0.488633	−0.244317	+	0.969696i	$0.578564\pi$
$62$	−1.40012e6	−0.746098
$63$	1.53665e6	0.774254
$64$	2.32491e6	1.10860
$65$	−687793.	−0.310642
$66$	−3.84870e6	−1.64782
$67$	4.03078e6	1.63729	0.818647	−	0.574297i	$-0.194724\pi$
$67$	4.03078e6	1.63729	0.818647	+	0.574297i	$0.194724\pi$
$68$	414460.	0.159846
$69$	4.24978e6	1.55738
$70$	1.10276e6	0.384272
$71$	−4.24947e6	−1.40906	−0.704531	−	0.709673i	$-0.748843\pi$
$71$	−4.24947e6	−1.40906	−0.704531	+	0.709673i	$0.748843\pi$
$72$	−6.92581e6	−2.18679
$73$	−5.35477e6	−1.61106	−0.805529	−	0.592556i	$-0.798119\pi$
$73$	−5.35477e6	−1.61106	−0.805529	+	0.592556i	$0.798119\pi$
$74$	−2.41950e6	−0.694090
$75$	−1.62336e6	−0.444325
$76$	−304234.	−0.0794986
$77$	1.57428e6	0.392974
$78$	1.84229e6	0.439568
$79$	−3.35025e6	−0.764509	−0.382255	−	0.924057i	$-0.624852\pi$
$79$	−3.35025e6	−0.764509	−0.382255	+	0.924057i	$0.624852\pi$
$80$	−4.06734e6	−0.888169
$81$	5.48992e6	1.14780
$82$	−6.94719e6	−1.39143
$83$	3.70208e6	0.710678	0.355339	−	0.934737i	$-0.384365\pi$
$83$	3.70208e6	0.710678	0.355339	+	0.934737i	$0.384365\pi$
$84$	631044.	0.116167
$85$	−5.75852e6	−1.01705
$86$	2.73325e6	0.463378
$87$	1.03199e7	1.68019
$88$	−7.09538e6	−1.10991
$89$	3.62636e6	0.545264	0.272632	−	0.962118i	$-0.412106\pi$
$89$	3.62636e6	0.545264	0.272632	+	0.962118i	$0.412106\pi$
$90$	1.44035e7	2.08267
$91$	−753571.	−0.104828
$92$	1.17274e6	0.157016
$93$	1.11320e7	1.43510
$94$	−4.52876e6	−0.562383
$95$	4.22703e6	0.505828
$96$	−5.26261e6	−0.607088
$97$	−7.98420e6	−0.888240	−0.444120	−	0.895967i	$-0.646484\pi$
$97$	−7.98420e6	−0.888240	−0.444120	+	0.895967i	$0.646484\pi$
$98$	1.20823e6	0.129675
$99$	2.05621e7	2.12983
$100$	−447970.	−0.0447970
$101$	−1.76227e7	−1.70196	−0.850978	−	0.525201i	$-0.823990\pi$
$101$	−1.76227e7	−1.70196	−0.850978	+	0.525201i	$0.823990\pi$
$102$	1.54245e7	1.43916
$103$	3.89505e6	0.351222	0.175611	−	0.984460i	$-0.443810\pi$
$103$	3.89505e6	0.351222	0.175611	+	0.984460i	$0.443810\pi$
$104$	3.39640e6	0.296076
$105$	−8.76775e6	−0.739138
$106$	1.62060e7	1.32162
$107$	−102980.	−0.00812662	−0.00406331	−	0.999992i	$-0.501293\pi$
$107$	−102980.	−0.00812662	−0.00406331	+	0.999992i	$0.501293\pi$
$108$	4.21868e6	0.322250
$109$	−2.18296e7	−1.61456	−0.807279	−	0.590170i	$-0.799061\pi$
$109$	−2.18296e7	−1.61456	−0.807279	+	0.590170i	$0.799061\pi$
$110$	1.47562e7	1.05706
$111$	1.92368e7	1.33506
$112$	−4.45633e6	−0.299719
$113$	2.74979e7	1.79277	0.896384	−	0.443278i	$-0.146184\pi$
$113$	2.74979e7	1.79277	0.896384	+	0.443278i	$0.146184\pi$
$114$	−1.13223e7	−0.715760
$115$	−1.62940e7	−0.999046
$116$	2.84780e6	0.169397
$117$	−9.84264e6	−0.568147
$118$	−1.01940e7	−0.571161
$119$	−6.30924e6	−0.343212
$120$	3.95169e7	2.08761
$121$	1.57841e6	0.0809975
$122$	−8.89606e6	−0.443546
$123$	5.52351e7	2.67638
$124$	3.07189e6	0.144687
$125$	−1.82337e7	−0.835007
$126$	1.57811e7	0.702812
$127$	−709688.	−0.0307436	−0.0153718	−	0.999882i	$-0.504893\pi$
$127$	−709688.	−0.0307436	−0.0153718	+	0.999882i	$0.504893\pi$
$128$	1.56264e7	0.658605
$129$	−2.17313e7	−0.891295
$130$	−7.06347e6	−0.281979
$131$	−1.58975e7	−0.617845	−0.308922	−	0.951087i	$-0.599968\pi$
$131$	−1.58975e7	−0.617845	−0.308922	+	0.951087i	$0.599968\pi$
$132$	8.44408e6	0.319554
$133$	4.63129e6	0.170695
$134$	4.13951e7	1.48622
$135$	−5.86145e7	−2.05039
$136$	2.84363e7	0.969362
$137$	3.76821e7	1.25202	0.626012	−	0.779813i	$-0.284686\pi$
$137$	3.76821e7	1.25202	0.626012	+	0.779813i	$0.284686\pi$
$138$	4.36443e7	1.41368
$139$	−3.25173e7	−1.02698	−0.513490	−	0.858096i	$-0.671648\pi$
$139$	−3.25173e7	−1.02698	−0.513490	+	0.858096i	$0.671648\pi$
$140$	−2.41947e6	−0.0745200
$141$	3.60069e7	1.08173
$142$	−4.36410e7	−1.27904
$143$	−1.00836e7	−0.288364
$144$	−5.82056e7	−1.62441
$145$	−3.95674e7	−1.07783
$146$	−5.49923e7	−1.46240
$147$	−9.60627e6	−0.249427
$148$	5.30842e6	0.134601
$149$	−5.31688e7	−1.31676	−0.658378	−	0.752688i	$-0.728757\pi$
$149$	−5.31688e7	−1.31676	−0.658378	+	0.752688i	$0.728757\pi$
$150$	−1.66715e7	−0.403326
$151$	−1.32378e7	−0.312893	−0.156446	−	0.987686i	$-0.550004\pi$
$151$	−1.32378e7	−0.312893	−0.156446	+	0.987686i	$0.550004\pi$
$152$	−2.08736e7	−0.482108
$153$	−8.24071e7	−1.86014
$154$	1.61674e7	0.356713
$155$	−4.26809e7	−0.920603
$156$	−4.04200e6	−0.0852432
$157$	−5.56831e7	−1.14835	−0.574176	−	0.818732i	$-0.694677\pi$
$157$	−5.56831e7	−1.14835	−0.574176	+	0.818732i	$0.694677\pi$
$158$	−3.44063e7	−0.693966
$159$	−1.28849e8	−2.54210
$160$	2.01773e7	0.389442
$161$	−1.78523e7	−0.337135
$162$	5.63801e7	1.04189
$163$	9.25998e7	1.67476	0.837382	−	0.546618i	$-0.184085\pi$
$163$	9.25998e7	1.67476	0.837382	+	0.546618i	$0.184085\pi$
$164$	1.52422e7	0.269833
$165$	−1.17322e8	−2.03323
$166$	3.80195e7	0.645102
$167$	4.52087e7	0.751128	0.375564	−	0.926796i	$-0.377449\pi$
$167$	4.52087e7	0.751128	0.375564	+	0.926796i	$0.377449\pi$
$168$	4.32962e7	0.704478
$169$	4.82681e6	0.0769231
$170$	−5.91386e7	−0.923208
$171$	6.04908e7	0.925130
$172$	−5.99679e6	−0.0898606
$173$	6.40319e7	0.940233	0.470116	−	0.882604i	$-0.344212\pi$
$173$	6.40319e7	0.940233	0.470116	+	0.882604i	$0.344212\pi$
$174$	1.05983e8	1.52516
$175$	6.81935e6	0.0961856
$176$	−5.96307e7	−0.824471
$177$	8.10497e7	1.09861
$178$	3.72419e7	0.494951
$179$	1.32169e8	1.72243	0.861217	−	0.508238i	$-0.169703\pi$
$179$	1.32169e8	1.72243	0.861217	+	0.508238i	$0.169703\pi$
$180$	−3.16015e7	−0.403882
$181$	−6.31845e7	−0.792019	−0.396009	−	0.918246i	$-0.629605\pi$
$181$	−6.31845e7	−0.792019	−0.396009	+	0.918246i	$0.629605\pi$
$182$	−7.73899e6	−0.0951557
$183$	7.07300e7	0.853149
$184$	8.04618e7	0.952198
$185$	−7.37554e7	−0.856431
$186$	1.14323e8	1.30268
$187$	−8.44248e7	−0.944114
$188$	9.93616e6	0.109060
$189$	−6.42202e7	−0.691919
$190$	4.34106e7	0.459154
$191$	1.32093e8	1.37171	0.685857	−	0.727736i	$-0.259427\pi$
$191$	1.32093e8	1.37171	0.685857	+	0.727736i	$0.259427\pi$
$192$	−1.89833e8	−1.93561
$193$	1.69461e8	1.69675	0.848377	−	0.529393i	$-0.177580\pi$
$193$	1.69461e8	1.69675	0.848377	+	0.529393i	$0.177580\pi$
$194$	−8.19958e7	−0.806279
$195$	5.61596e7	0.542379
$196$	−2.65087e6	−0.0251473
$197$	−1.93520e8	−1.80340	−0.901702	−	0.432357i	$-0.857682\pi$
$197$	−1.93520e8	−1.80340	−0.901702	+	0.432357i	$0.857682\pi$
$198$	2.11168e8	1.93331
$199$	5.72266e7	0.514769	0.257384	−	0.966309i	$-0.417139\pi$
$199$	5.72266e7	0.514769	0.257384	+	0.966309i	$0.417139\pi$
$200$	−3.07354e7	−0.271665
$201$	−3.29121e8	−2.85870
$202$	−1.80981e8	−1.54491
$203$	−4.33515e7	−0.363721
$204$	−3.38415e7	−0.279089
$205$	−2.11776e8	−1.71687
$206$	4.00012e7	0.318814
$207$	−2.33175e8	−1.82720
$208$	2.85439e7	0.219934
$209$	6.19718e7	0.469551
$210$	−9.00427e7	−0.670936
$211$	−7.29938e6	−0.0534931	−0.0267465	−	0.999642i	$-0.508515\pi$
$211$	−7.29938e6	−0.0534931	−0.0267465	+	0.999642i	$0.508515\pi$
$212$	−3.55562e7	−0.256295
$213$	3.46977e8	2.46021
$214$	−1.05758e6	−0.00737676
$215$	8.33195e7	0.571758
$216$	2.89445e8	1.95424
$217$	−4.67628e7	−0.310664
$218$	−2.24185e8	−1.46558
$219$	4.37228e8	2.81289
$220$	−3.23753e7	−0.204991
$221$	4.04123e7	0.251849
$222$	1.97557e8	1.21187
$223$	−3.12470e8	−1.88687	−0.943433	−	0.331564i	$-0.892424\pi$
$223$	−3.12470e8	−1.88687	−0.943433	+	0.331564i	$0.892424\pi$
$224$	2.21070e7	0.131420
$225$	8.90698e7	0.521305
$226$	2.82396e8	1.62734
$227$	1.95402e8	1.10877	0.554383	−	0.832262i	$-0.312954\pi$
$227$	1.95402e8	1.10877	0.554383	+	0.832262i	$0.312954\pi$
$228$	2.48413e7	0.138804
$229$	−2.46589e6	−0.0135690	−0.00678452	−	0.999977i	$-0.502160\pi$
$229$	−2.46589e6	−0.0135690	−0.00678452	+	0.999977i	$0.502160\pi$
$230$	−1.67336e8	−0.906861
$231$	−1.28543e8	−0.686128
$232$	1.95389e8	1.02729
$233$	−2.74313e8	−1.42069	−0.710347	−	0.703852i	$-0.751462\pi$
$233$	−2.74313e8	−1.42069	−0.710347	+	0.703852i	$0.751462\pi$
$234$	−1.01082e8	−0.515723
$235$	−1.38053e8	−0.693920
$236$	2.23658e7	0.110762
$237$	2.73555e8	1.33483
$238$	−6.47944e7	−0.311543
$239$	−9.43536e7	−0.447060	−0.223530	−	0.974697i	$-0.571758\pi$
$239$	−9.43536e7	−0.447060	−0.223530	+	0.974697i	$0.571758\pi$
$240$	3.32106e8	1.55074
$241$	1.74669e8	0.803813	0.401907	−	0.915681i	$-0.368348\pi$
$241$	1.74669e8	0.803813	0.401907	+	0.915681i	$0.368348\pi$
$242$	1.62099e7	0.0735236
$243$	−3.87884e7	−0.173412
$244$	1.95181e7	0.0860147
$245$	3.68312e7	0.160005
$246$	5.67251e8	2.42942
$247$	−2.96646e7	−0.125256
$248$	2.10763e8	0.877434
$249$	−3.02282e8	−1.24084
$250$	−1.87256e8	−0.757958
$251$	3.57106e8	1.42541	0.712703	−	0.701466i	$-0.247471\pi$
$251$	3.57106e8	1.42541	0.712703	+	0.701466i	$0.247471\pi$
$252$	−3.46238e7	−0.136293
$253$	−2.38884e8	−0.927397
$254$	−7.28833e6	−0.0279068
$255$	4.70194e8	1.77577
$256$	−1.37109e8	−0.510769
$257$	−1.10319e8	−0.405400	−0.202700	−	0.979241i	$-0.564972\pi$
$257$	−1.10319e8	−0.405400	−0.202700	+	0.979241i	$0.564972\pi$
$258$	−2.23175e8	−0.809053
$259$	−8.08091e7	−0.289009
$260$	1.54973e7	0.0546827
$261$	−5.66228e8	−1.97129
$262$	−1.63264e8	−0.560835
$263$	1.01578e8	0.344313	0.172157	−	0.985070i	$-0.444926\pi$
$263$	1.01578e8	0.344313	0.172157	+	0.985070i	$0.444926\pi$
$264$	5.79352e8	1.93789
$265$	4.94018e8	1.63073
$266$	4.75622e7	0.154945
$267$	−2.96100e8	−0.952025
$268$	−9.08214e7	−0.288215
$269$	2.76289e8	0.865428	0.432714	−	0.901531i	$-0.357556\pi$
$269$	2.76289e8	0.865428	0.432714	+	0.901531i	$0.357556\pi$
$270$	−6.01956e8	−1.86120
$271$	−1.96518e7	−0.0599804	−0.0299902	−	0.999550i	$-0.509548\pi$
$271$	−1.96518e7	−0.0599804	−0.0299902	+	0.999550i	$0.509548\pi$
$272$	2.38983e8	0.720071
$273$	6.15305e7	0.183030
$274$	3.86986e8	1.13650
$275$	9.12506e7	0.264589
$276$	−9.57561e7	−0.274148
$277$	−1.81403e8	−0.512819	−0.256410	−	0.966568i	$-0.582540\pi$
$277$	−1.81403e8	−0.512819	−0.256410	+	0.966568i	$0.582540\pi$
$278$	−3.33944e8	−0.932218
$279$	−6.10784e8	−1.68373
$280$	−1.66001e8	−0.451916
$281$	1.21888e8	0.327709	0.163855	−	0.986484i	$-0.447607\pi$
$281$	1.21888e8	0.327709	0.163855	+	0.986484i	$0.447607\pi$
$282$	3.69782e8	0.981916
$283$	1.21883e8	0.319663	0.159832	−	0.987144i	$-0.448905\pi$
$283$	1.21883e8	0.319663	0.159832	+	0.987144i	$0.448905\pi$
$284$	9.57489e7	0.248039
$285$	−3.45145e8	−0.883170
$286$	−1.03556e8	−0.261756
$287$	−2.32029e8	−0.579370
$288$	2.88746e8	0.712267
$289$	−7.19885e7	−0.175437
$290$	−4.06348e8	−0.978374
$291$	6.51925e8	1.55086
$292$	1.20654e8	0.283596
$293$	−1.48910e8	−0.345849	−0.172924	−	0.984935i	$-0.555322\pi$
$293$	−1.48910e8	−0.345849	−0.172924	+	0.984935i	$0.555322\pi$
$294$	−9.86541e7	−0.226412
$295$	−3.10751e8	−0.704751
$296$	3.64213e8	0.816271
$297$	−8.59338e8	−1.90334
$298$	−5.46031e8	−1.19525
$299$	1.14349e8	0.247390
$300$	3.65776e7	0.0782151
$301$	9.12879e7	0.192944
$302$	−1.35949e8	−0.284021
$303$	1.43893e9	2.97160
$304$	−1.75425e8	−0.358124
$305$	−2.71185e8	−0.547287
$306$	−8.46301e8	−1.68850
$307$	5.96397e8	1.17639	0.588195	−	0.808719i	$-0.299839\pi$
$307$	5.96397e8	1.17639	0.588195	+	0.808719i	$0.299839\pi$
$308$	−3.54716e7	−0.0691756
$309$	−3.18038e8	−0.613231
$310$	−4.38323e8	−0.835657
$311$	−9.92999e8	−1.87192	−0.935961	−	0.352105i	$-0.885466\pi$
$311$	−9.92999e8	−1.87192	−0.935961	+	0.352105i	$0.885466\pi$
$312$	−2.77323e8	−0.516945
$313$	2.68458e8	0.494847	0.247424	−	0.968907i	$-0.420416\pi$
$313$	2.68458e8	0.494847	0.247424	+	0.968907i	$0.420416\pi$
$314$	−5.71853e8	−1.04239
$315$	4.81064e8	0.867194
$316$	7.54879e7	0.134577
$317$	−1.76890e7	−0.0311886	−0.0155943	−	0.999878i	$-0.504964\pi$
$317$	−1.76890e7	−0.0311886	−0.0155943	+	0.999878i	$0.504964\pi$
$318$	−1.32325e9	−2.30753
$319$	−5.80092e8	−1.00053
$320$	7.27835e8	1.24168
$321$	8.40853e6	0.0141890
$322$	−1.83339e8	−0.306027
$323$	−2.48365e8	−0.410093
$324$	−1.23699e8	−0.202049
$325$	−4.36796e7	−0.0705809
$326$	9.50978e8	1.52023
$327$	1.78243e9	2.81900
$328$	1.04577e9	1.63636
$329$	−1.51256e8	−0.234168
$330$	−1.20487e9	−1.84562
$331$	1.00880e9	1.52900	0.764501	−	0.644622i	$-0.222985\pi$
$331$	1.00880e9	1.52900	0.764501	+	0.644622i	$0.222985\pi$
$332$	−8.34153e7	−0.125101
$333$	−1.05547e9	−1.56636
$334$	4.64282e8	0.681820
$335$	1.26187e9	1.83383
$336$	3.63868e8	0.523307
$337$	−6.77777e7	−0.0964677	−0.0482339	−	0.998836i	$-0.515359\pi$
$337$	−6.77777e7	−0.0964677	−0.0482339	+	0.998836i	$0.515359\pi$
$338$	4.95702e7	0.0698252
$339$	−2.24525e9	−3.13016
$340$	1.29751e8	0.179033
$341$	−6.25738e8	−0.854580
$342$	6.21226e8	0.839766
$343$	4.03536e7	0.0539949
$344$	−4.11442e8	−0.544947
$345$	1.33044e9	1.74433
$346$	6.57593e8	0.853475
$347$	−9.83522e8	−1.26366	−0.631831	−	0.775106i	$-0.717696\pi$
$347$	−9.83522e8	−1.26366	−0.631831	+	0.775106i	$0.717696\pi$
$348$	−2.32528e8	−0.295766
$349$	−4.65111e8	−0.585690	−0.292845	−	0.956160i	$-0.594602\pi$
$349$	−4.65111e8	−0.585690	−0.292845	+	0.956160i	$0.594602\pi$
$350$	7.00331e7	0.0873103
$351$	4.11346e8	0.507730
$352$	2.95816e8	0.361512
$353$	1.51364e9	1.83151	0.915756	−	0.401734i	$-0.131592\pi$
$353$	1.51364e9	1.83151	0.915756	+	0.401734i	$0.131592\pi$
$354$	8.32361e8	0.997242
$355$	−1.33034e9	−1.57820
$356$	−8.17092e7	−0.0959834
$357$	5.15162e8	0.599246
$358$	1.35734e9	1.56350
$359$	−1.43252e8	−0.163407	−0.0817035	−	0.996657i	$-0.526036\pi$
$359$	−1.43252e8	−0.163407	−0.0817035	+	0.996657i	$0.526036\pi$
$360$	−2.16819e9	−2.44929
$361$	−7.11560e8	−0.796042
$362$	−6.48890e8	−0.718937
$363$	−1.28880e8	−0.141421
$364$	1.69794e7	0.0184531
$365$	−1.67636e9	−1.80444
$366$	7.26381e8	0.774427
$367$	1.30066e9	1.37351	0.686757	−	0.726887i	$-0.259033\pi$
$367$	1.30066e9	1.37351	0.686757	+	0.726887i	$0.259033\pi$
$368$	6.76213e8	0.707321
$369$	−3.03061e9	−3.14006
$370$	−7.57450e8	−0.777406
$371$	5.41265e8	0.550302
$372$	−2.50826e8	−0.252622
$373$	1.07901e9	1.07657	0.538287	−	0.842762i	$-0.319072\pi$
$373$	1.07901e9	1.07657	0.538287	+	0.842762i	$0.319072\pi$
$374$	−8.67022e8	−0.856998
$375$	1.48882e9	1.45791
$376$	6.81724e8	0.661380
$377$	2.77677e8	0.266898
$378$	−6.59526e8	−0.628074
$379$	1.91623e9	1.80805	0.904025	−	0.427479i	$-0.140598\pi$
$379$	1.91623e9	1.80805	0.904025	+	0.427479i	$0.140598\pi$
$380$	−9.52433e7	−0.0890414
$381$	5.79474e7	0.0536780
$382$	1.35657e9	1.24514
$383$	−9.46193e8	−0.860565	−0.430283	−	0.902694i	$-0.641586\pi$
$383$	−9.46193e8	−0.860565	−0.430283	+	0.902694i	$0.641586\pi$
$384$	−1.27593e9	−1.14992
$385$	4.92843e8	0.440145
$386$	1.74032e9	1.54019
$387$	1.19234e9	1.04571
$388$	1.79900e8	0.156358
$389$	−8.33325e8	−0.717779	−0.358890	−	0.933380i	$-0.616845\pi$
$389$	−8.33325e8	−0.717779	−0.358890	+	0.933380i	$0.616845\pi$
$390$	5.76746e8	0.492332
$391$	9.57379e8	0.809963
$392$	−1.81877e8	−0.152502
$393$	1.29806e9	1.07875
$394$	−1.98740e9	−1.63700
$395$	−1.04883e9	−0.856279
$396$	−4.63306e8	−0.374916
$397$	2.56651e8	0.205862	0.102931	−	0.994688i	$-0.467178\pi$
$397$	2.56651e8	0.205862	0.102931	+	0.994688i	$0.467178\pi$
$398$	5.87703e8	0.467270
$399$	−3.78154e8	−0.298032
$400$	−2.58305e8	−0.201801
$401$	2.43641e9	1.88689	0.943443	−	0.331535i	$-0.107566\pi$
$401$	2.43641e9	1.88689	0.943443	+	0.331535i	$0.107566\pi$
$402$	−3.37999e9	−2.59492
$403$	2.99527e8	0.227965
$404$	3.97075e8	0.299597
$405$	1.71867e9	1.28558
$406$	−4.45210e8	−0.330159
$407$	−1.08132e9	−0.795010
$408$	−2.32187e9	−1.69250
$409$	2.10125e9	1.51861	0.759307	−	0.650733i	$-0.225538\pi$
$409$	2.10125e9	1.51861	0.759307	+	0.650733i	$0.225538\pi$
$410$	−2.17489e9	−1.55845
$411$	−3.07681e9	−2.18602
$412$	−8.77631e7	−0.0618261
$413$	−3.40470e8	−0.237823
$414$	−2.39465e9	−1.65860
$415$	1.15897e9	0.795986
$416$	−1.41601e8	−0.0964358
$417$	2.65510e9	1.79310
$418$	6.36436e8	0.426224
$419$	−1.78594e9	−1.18609	−0.593045	−	0.805169i	$-0.702075\pi$
$419$	−1.78594e9	−1.18609	−0.593045	+	0.805169i	$0.702075\pi$
$420$	1.97555e8	0.130111
$421$	3.17308e8	0.207250	0.103625	−	0.994616i	$-0.466956\pi$
$421$	3.17308e8	0.207250	0.103625	+	0.994616i	$0.466956\pi$
$422$	−7.49629e7	−0.0485571
$423$	−1.97561e9	−1.26914
$424$	−2.43952e9	−1.55426
$425$	−3.65706e8	−0.231085
$426$	3.56337e9	2.23320
$427$	−2.97120e8	−0.184686
$428$	2.32035e6	0.00143054
$429$	8.23348e8	0.503481
$430$	8.55672e8	0.519000
$431$	2.18378e8	0.131383	0.0656914	−	0.997840i	$-0.479075\pi$
$431$	2.18378e8	0.131383	0.0656914	+	0.997840i	$0.479075\pi$
$432$	2.43254e9	1.45167
$433$	2.23598e9	1.32361	0.661805	−	0.749676i	$-0.269791\pi$
$433$	2.23598e9	1.32361	0.661805	+	0.749676i	$0.269791\pi$
$434$	−4.80243e8	−0.281998
$435$	3.23075e9	1.88188
$436$	4.91865e8	0.284213
$437$	−7.02762e8	−0.402831
$438$	4.49022e9	2.55334
$439$	−5.96960e8	−0.336759	−0.168379	−	0.985722i	$-0.553853\pi$
$439$	−5.96960e8	−0.336759	−0.168379	+	0.985722i	$0.553853\pi$
$440$	−2.22128e9	−1.24314
$441$	5.27072e8	0.292641
$442$	4.15024e8	0.228610
$443$	−2.19850e9	−1.20147	−0.600736	−	0.799448i	$-0.705126\pi$
$443$	−2.19850e9	−1.20147	−0.600736	+	0.799448i	$0.705126\pi$
$444$	−4.33443e8	−0.235013
$445$	1.13527e9	0.610715
$446$	−3.20899e9	−1.71276
$447$	4.34134e9	2.29904
$448$	7.97443e8	0.419012
$449$	−4.40360e8	−0.229586	−0.114793	−	0.993389i	$-0.536620\pi$
$449$	−4.40360e8	−0.229586	−0.114793	+	0.993389i	$0.536620\pi$
$450$	9.14726e8	0.473203
$451$	−3.10481e9	−1.59374
$452$	−6.19581e8	−0.315583
$453$	1.08089e9	0.546308
$454$	2.00674e9	1.00646
$455$	−2.35913e8	−0.117412
$456$	1.70437e9	0.841756
$457$	−3.31421e9	−1.62433	−0.812164	−	0.583429i	$-0.801711\pi$
$457$	−3.31421e9	−1.62433	−0.812164	+	0.583429i	$0.801711\pi$
$458$	−2.53241e7	−0.0123170
$459$	3.44398e9	1.66233
$460$	3.67136e8	0.175863
$461$	−1.28896e8	−0.0612756	−0.0306378	−	0.999531i	$-0.509754\pi$
$461$	−1.28896e8	−0.0612756	−0.0306378	+	0.999531i	$0.509754\pi$
$462$	−1.32010e9	−0.622817
$463$	−4.66025e6	−0.00218210	−0.00109105	−	0.999999i	$-0.500347\pi$
$463$	−4.66025e6	−0.00218210	−0.00109105	+	0.999999i	$0.500347\pi$
$464$	1.64208e9	0.763098
$465$	3.48498e9	1.60737
$466$	−2.81713e9	−1.28960
$467$	−7.96908e8	−0.362076	−0.181038	−	0.983476i	$-0.557946\pi$
$467$	−7.96908e8	−0.362076	−0.181038	+	0.983476i	$0.557946\pi$
$468$	2.21774e8	0.100012
$469$	1.38256e9	0.618839
$470$	−1.41777e9	−0.629890
$471$	4.54664e9	2.00501
$472$	1.53453e9	0.671703
$473$	1.22154e9	0.530752
$474$	2.80934e9	1.21166
$475$	2.68446e8	0.114929
$476$	1.42160e8	0.0604161
$477$	7.06964e9	2.98252
$478$	−9.68989e8	−0.405809
$479$	−2.06306e9	−0.857706	−0.428853	−	0.903374i	$-0.641082\pi$
$479$	−2.06306e9	−0.857706	−0.428853	+	0.903374i	$0.641082\pi$
$480$	−1.64751e9	−0.679962
$481$	5.17602e8	0.212074
$482$	1.79380e9	0.729643
$483$	1.45768e9	0.588635
$484$	−3.55647e7	−0.0142581
$485$	−2.49953e9	−0.994861
$486$	−3.98347e8	−0.157411
$487$	−2.54278e9	−0.997602	−0.498801	−	0.866717i	$-0.666226\pi$
$487$	−2.54278e9	−0.997602	−0.498801	+	0.866717i	$0.666226\pi$
$488$	1.33914e9	0.521624
$489$	−7.56095e9	−2.92412
$490$	3.78247e8	0.145241
$491$	−4.70320e9	−1.79311	−0.896557	−	0.442929i	$-0.853940\pi$
$491$	−4.70320e9	−1.79311	−0.896557	+	0.442929i	$0.853940\pi$
$492$	−1.24456e9	−0.471125
$493$	2.32484e9	0.873834
$494$	−3.04648e8	−0.113698
$495$	6.43718e9	2.38549
$496$	1.77129e9	0.651784
$497$	−1.45757e9	−0.532575
$498$	−3.10437e9	−1.12634
$499$	−1.98530e9	−0.715276	−0.357638	−	0.933860i	$-0.616418\pi$
$499$	−1.98530e9	−0.715276	−0.357638	+	0.933860i	$0.616418\pi$
$500$	4.10842e8	0.146987
$501$	−3.69138e9	−1.31146
$502$	3.66739e9	1.29388
$503$	−4.16066e9	−1.45772	−0.728861	−	0.684662i	$-0.759950\pi$
$503$	−4.16066e9	−1.45772	−0.728861	+	0.684662i	$0.759950\pi$
$504$	−2.37555e9	−0.826529
$505$	−5.51697e9	−1.90625
$506$	−2.45328e9	−0.841823
$507$	−3.94118e8	−0.134307
$508$	1.59907e7	0.00541183
$509$	−4.25462e9	−1.43004	−0.715020	−	0.699104i	$-0.753582\pi$
$509$	−4.25462e9	−1.43004	−0.715020	+	0.699104i	$0.753582\pi$
$510$	4.82878e9	1.61191
$511$	−1.83669e9	−0.608923
$512$	−3.40825e9	−1.12224
$513$	−2.52805e9	−0.826750
$514$	−1.13295e9	−0.367993
$515$	1.21938e9	0.393382
$516$	4.89649e8	0.156896
$517$	−2.02398e9	−0.644153
$518$	−8.29890e8	−0.262341
$519$	−5.22833e9	−1.64164
$520$	1.06328e9	0.331616
$521$	5.46111e9	1.69180	0.845900	−	0.533342i	$-0.179064\pi$
$521$	5.46111e9	1.69180	0.845900	+	0.533342i	$0.179064\pi$
$522$	−5.81503e9	−1.78939
$523$	3.02180e9	0.923655	0.461827	−	0.886970i	$-0.347194\pi$
$523$	3.02180e9	0.923655	0.461827	+	0.886970i	$0.347194\pi$
$524$	3.58202e8	0.108760
$525$	−5.56813e8	−0.167939
$526$	1.04318e9	0.312543
$527$	2.50778e9	0.746367
$528$	4.86896e9	1.43952
$529$	−6.95875e8	−0.204379
$530$	5.07345e9	1.48026
$531$	−4.44700e9	−1.28895
$532$	−1.04352e8	−0.0300477
$533$	1.48620e9	0.425141
$534$	−3.04087e9	−0.864179
$535$	−3.22389e7	−0.00910212
$536$	−6.23129e9	−1.74784
$537$	−1.07918e10	−3.00735
$538$	2.83743e9	0.785573
$539$	5.39977e8	0.148530
$540$	1.32070e9	0.360932
$541$	1.07012e9	0.290564	0.145282	−	0.989390i	$-0.453591\pi$
$541$	1.07012e9	0.290564	0.145282	+	0.989390i	$0.453591\pi$
$542$	−2.01819e8	−0.0544458
$543$	5.15913e9	1.38286
$544$	−1.18555e9	−0.315734
$545$	−6.83398e9	−1.80837
$546$	6.31904e8	0.166141
$547$	−2.69290e9	−0.703502	−0.351751	−	0.936094i	$-0.614414\pi$
$547$	−2.69290e9	−0.703502	−0.351751	+	0.936094i	$0.614414\pi$
$548$	−8.49052e8	−0.220395
$549$	−3.88078e9	−1.00096
$550$	9.37122e8	0.240174
$551$	−1.70654e9	−0.434597
$552$	−6.56986e9	−1.66253
$553$	−1.14914e9	−0.288957
$554$	−1.86296e9	−0.465500
$555$	6.02227e9	1.49532
$556$	7.32678e8	0.180780
$557$	−1.35954e8	−0.0333349	−0.0166675	−	0.999861i	$-0.505306\pi$
$557$	−1.35954e8	−0.0333349	−0.0166675	+	0.999861i	$0.505306\pi$
$558$	−6.27261e9	−1.52837
$559$	−5.84722e8	−0.141582
$560$	−1.39510e9	−0.335696
$561$	6.89344e9	1.64841
$562$	1.25176e9	0.297471
$563$	4.16236e9	0.983016	0.491508	−	0.870873i	$-0.336446\pi$
$563$	4.16236e9	0.983016	0.491508	+	0.870873i	$0.336446\pi$
$564$	−8.11307e8	−0.190418
$565$	8.60847e9	2.00797
$566$	1.25171e9	0.290167
$567$	1.88304e9	0.433829
$568$	6.56937e9	1.50420
$569$	1.53271e9	0.348792	0.174396	−	0.984676i	$-0.444203\pi$
$569$	1.53271e9	0.348792	0.174396	+	0.984676i	$0.444203\pi$
$570$	−3.54456e9	−0.801678
$571$	−8.23790e9	−1.85178	−0.925891	−	0.377790i	$-0.876684\pi$
$571$	−8.23790e9	−1.85178	−0.925891	+	0.377790i	$0.876684\pi$
$572$	2.27204e8	0.0507610
$573$	−1.07857e10	−2.39500
$574$	−2.38289e9	−0.525910
$575$	−1.03478e9	−0.226993
$576$	1.04157e10	2.27096
$577$	−1.76248e9	−0.381953	−0.190976	−	0.981595i	$-0.561165\pi$
$577$	−1.76248e9	−0.381953	−0.190976	+	0.981595i	$0.561165\pi$
$578$	−7.39305e8	−0.159249
$579$	−1.38368e10	−2.96252
$580$	8.91532e8	0.189731
$581$	1.26981e9	0.268611
$582$	6.69511e9	1.40776
$583$	7.24273e9	1.51378
$584$	8.27809e9	1.71983
$585$	−3.08134e9	−0.636346
$586$	−1.52927e9	−0.313936
$587$	3.61639e8	0.0737976	0.0368988	−	0.999319i	$-0.488252\pi$
$587$	3.61639e8	0.0737976	0.0368988	+	0.999319i	$0.488252\pi$
$588$	2.16448e8	0.0439070
$589$	−1.84083e9	−0.371202
$590$	−3.19134e9	−0.639721
$591$	1.58012e10	3.14873
$592$	3.06090e9	0.606350
$593$	−7.82050e9	−1.54008	−0.770040	−	0.637996i	$-0.779764\pi$
$593$	−7.82050e9	−1.54008	−0.770040	+	0.637996i	$0.779764\pi$
$594$	−8.82520e9	−1.72771
$595$	−1.97517e9	−0.384411
$596$	1.19800e9	0.231790
$597$	−4.67266e9	−0.898781
$598$	1.17433e9	0.224562
$599$	4.01750e9	0.763769	0.381885	−	0.924210i	$-0.375275\pi$
$599$	4.01750e9	0.763769	0.381885	+	0.924210i	$0.375275\pi$
$600$	2.50960e9	0.474324
$601$	6.03440e9	1.13390	0.566949	−	0.823753i	$-0.308124\pi$
$601$	6.03440e9	1.13390	0.566949	+	0.823753i	$0.308124\pi$
$602$	9.37505e8	0.175140
$603$	1.80580e10	3.35397
$604$	2.98273e8	0.0550789
$605$	4.94137e8	0.0907202
$606$	1.47775e10	2.69740
$607$	−4.10286e9	−0.744606	−0.372303	−	0.928111i	$-0.621432\pi$
$607$	−4.10286e9	−0.744606	−0.372303	+	0.928111i	$0.621432\pi$
$608$	8.70247e8	0.157029
$609$	3.53973e9	0.635053
$610$	−2.78500e9	−0.496788
$611$	9.68834e8	0.171832
$612$	1.85680e9	0.327442
$613$	4.09137e9	0.717392	0.358696	−	0.933454i	$-0.383221\pi$
$613$	4.09137e9	0.717392	0.358696	+	0.933454i	$0.383221\pi$
$614$	6.12486e9	1.06784
$615$	1.72919e10	2.99764
$616$	−2.43372e9	−0.419505
$617$	3.58571e8	0.0614578	0.0307289	−	0.999528i	$-0.490217\pi$
$617$	3.58571e8	0.0614578	0.0307289	+	0.999528i	$0.490217\pi$
$618$	−3.26617e9	−0.556647
$619$	2.49746e8	0.0423234	0.0211617	−	0.999776i	$-0.493264\pi$
$619$	2.49746e8	0.0423234	0.0211617	+	0.999776i	$0.493264\pi$
$620$	9.61685e8	0.162055
$621$	9.74491e9	1.63289
$622$	−1.01979e10	−1.69919
$623$	1.24384e9	0.206090
$624$	−2.33066e9	−0.384002
$625$	−7.26148e9	−1.18972
$626$	2.75700e9	0.449186
$627$	−5.06012e9	−0.819831
$628$	1.25465e9	0.202146
$629$	4.33360e9	0.694340
$630$	4.94042e9	0.787175
$631$	5.35032e9	0.847768	0.423884	−	0.905717i	$-0.360666\pi$
$631$	5.35032e9	0.847768	0.423884	+	0.905717i	$0.360666\pi$
$632$	5.17925e9	0.816126
$633$	5.96009e8	0.0933984
$634$	−1.81662e8	−0.0283108
$635$	−2.22175e8	−0.0344340
$636$	2.90323e9	0.447488
$637$	−2.58475e8	−0.0396214
$638$	−5.95741e9	−0.908207
$639$	−1.90378e10	−2.88644
$640$	4.89201e9	0.737662
$641$	2.33908e9	0.350786	0.175393	−	0.984498i	$-0.443880\pi$
$641$	2.33908e9	0.350786	0.175393	+	0.984498i	$0.443880\pi$
$642$	8.63536e7	0.0128798
$643$	−1.17021e9	−0.173590	−0.0867950	−	0.996226i	$-0.527663\pi$
$643$	−1.17021e9	−0.173590	−0.0867950	+	0.996226i	$0.527663\pi$
$644$	4.02248e8	0.0593463
$645$	−6.80320e9	−0.998284
$646$	−2.55065e9	−0.372252
$647$	6.69685e8	0.0972088	0.0486044	−	0.998818i	$-0.484523\pi$
$647$	6.69685e8	0.0972088	0.0486044	+	0.998818i	$0.484523\pi$
$648$	−8.48701e9	−1.22530
$649$	−4.55588e9	−0.654207
$650$	−4.48580e8	−0.0640682
$651$	3.81827e9	0.542417
$652$	−2.08646e9	−0.294811
$653$	−1.19525e10	−1.67982	−0.839911	−	0.542724i	$-0.817393\pi$
$653$	−1.19525e10	−1.67982	−0.839911	+	0.542724i	$0.817393\pi$
$654$	1.83051e10	2.55889
$655$	−4.97687e9	−0.692009
$656$	8.78884e9	1.21554
$657$	−2.39896e10	−3.30023
$658$	−1.55337e9	−0.212561
$659$	−1.65668e8	−0.0225497	−0.0112748	−	0.999936i	$-0.503589\pi$
$659$	−1.65668e8	−0.0225497	−0.0112748	+	0.999936i	$0.503589\pi$
$660$	2.64350e9	0.357912
$661$	2.43595e9	0.328068	0.164034	−	0.986455i	$-0.447549\pi$
$661$	2.43595e9	0.328068	0.164034	+	0.986455i	$0.447549\pi$
$662$	1.03602e10	1.38792
$663$	−3.29974e9	−0.439726
$664$	−5.72315e9	−0.758660
$665$	1.44987e9	0.191185
$666$	−1.08395e10	−1.42183
$667$	6.57825e9	0.858361
$668$	−1.01864e9	−0.132222
$669$	2.55138e10	3.29445
$670$	1.29591e10	1.66462
$671$	−3.97580e9	−0.508037
$672$	−1.80508e9	−0.229458
$673$	−5.32344e9	−0.673193	−0.336597	−	0.941649i	$-0.609276\pi$
$673$	−5.32344e9	−0.673193	−0.336597	+	0.941649i	$0.609276\pi$
$674$	−6.96061e8	−0.0875664
$675$	−3.72243e9	−0.465868
$676$	−1.08758e8	−0.0135409
$677$	3.78528e9	0.468854	0.234427	−	0.972134i	$-0.424679\pi$
$677$	3.78528e9	0.468854	0.234427	+	0.972134i	$0.424679\pi$
$678$	−2.30582e10	−2.84133
$679$	−2.73858e9	−0.335723
$680$	8.90225e9	1.08572
$681$	−1.59550e10	−1.93589
$682$	−6.42619e9	−0.775725
$683$	−1.20873e10	−1.45164	−0.725819	−	0.687885i	$-0.758539\pi$
$683$	−1.20873e10	−1.45164	−0.725819	+	0.687885i	$0.758539\pi$
$684$	−1.36298e9	−0.162852
$685$	1.17967e10	1.40231
$686$	4.14422e8	0.0490127
$687$	2.01344e8	0.0236914
$688$	−3.45782e9	−0.404802
$689$	−3.46693e9	−0.403811
$690$	1.36633e10	1.58337
$691$	−1.26696e9	−0.146080	−0.0730398	−	0.997329i	$-0.523270\pi$
$691$	−1.26696e9	−0.146080	−0.0730398	+	0.997329i	$0.523270\pi$
$692$	−1.44277e9	−0.165510
$693$	7.05281e9	0.805000
$694$	−1.01005e10	−1.14706
$695$	−1.01798e10	−1.15026
$696$	−1.59539e10	−1.79363
$697$	1.24432e10	1.39193
$698$	−4.77658e9	−0.531647
$699$	2.23982e10	2.48052
$700$	−1.53654e8	−0.0169317
$701$	1.20182e10	1.31773	0.658867	−	0.752259i	$-0.271036\pi$
$701$	1.20182e10	1.31773	0.658867	+	0.752259i	$0.271036\pi$
$702$	4.22443e9	0.460880
$703$	−3.18107e9	−0.345327
$704$	1.06707e10	1.15263
$705$	1.12723e10	1.21158
$706$	1.55447e10	1.66251
$707$	−6.04460e9	−0.643279
$708$	−1.82621e9	−0.193390
$709$	1.03791e10	1.09370	0.546851	−	0.837230i	$-0.315826\pi$
$709$	1.03791e10	1.09370	0.546851	+	0.837230i	$0.315826\pi$
$710$	−1.36622e10	−1.43258
$711$	−1.50093e10	−1.56609
$712$	−5.60610e9	−0.582077
$713$	7.09589e9	0.733151
$714$	5.29059e9	0.543952
$715$	−3.15678e9	−0.322978
$716$	−2.97802e9	−0.303202
$717$	7.70415e9	0.780563
$718$	−1.47117e9	−0.148329
$719$	8.81182e9	0.884126	0.442063	−	0.896984i	$-0.354247\pi$
$719$	8.81182e9	0.884126	0.442063	+	0.896984i	$0.354247\pi$
$720$	−1.82218e10	−1.81940
$721$	1.33600e9	0.132750
$722$	−7.30755e9	−0.722589
$723$	−1.42620e10	−1.40345
$724$	1.42367e9	0.139420
$725$	−2.51281e9	−0.244893
$726$	−1.32357e9	−0.128372
$727$	1.68844e10	1.62973	0.814863	−	0.579653i	$-0.196812\pi$
$727$	1.68844e10	1.62973	0.814863	+	0.579653i	$0.196812\pi$
$728$	1.16497e9	0.111906
$729$	−8.83930e9	−0.845029
$730$	−1.72159e10	−1.63794
$731$	−4.89556e9	−0.463545
$732$	−1.59369e9	−0.150181
$733$	7.86610e9	0.737726	0.368863	−	0.929484i	$-0.379747\pi$
$733$	7.86610e9	0.737726	0.368863	+	0.929484i	$0.379747\pi$
$734$	1.33575e10	1.24678
$735$	−3.00734e9	−0.279368
$736$	−3.35456e9	−0.310144
$737$	1.85002e10	1.70231
$738$	−3.11236e10	−2.85032
$739$	1.38692e10	1.26414	0.632072	−	0.774910i	$-0.282205\pi$
$739$	1.38692e10	1.26414	0.632072	+	0.774910i	$0.282205\pi$
$740$	1.66185e9	0.150759
$741$	2.42217e9	0.218696
$742$	5.55866e9	0.499524
$743$	1.32825e9	0.118800	0.0594002	−	0.998234i	$-0.481081\pi$
$743$	1.32825e9	0.118800	0.0594002	+	0.998234i	$0.481081\pi$
$744$	−1.72092e10	−1.53199
$745$	−1.66450e10	−1.47481
$746$	1.10812e10	0.977235
$747$	1.65855e10	1.45581
$748$	1.90226e9	0.166193
$749$	−3.53222e7	−0.00307158
$750$	1.52898e10	1.32339
$751$	−8.67321e9	−0.747206	−0.373603	−	0.927589i	$-0.621878\pi$
$751$	−8.67321e9	−0.747206	−0.373603	+	0.927589i	$0.621878\pi$
$752$	5.72931e9	0.491292
$753$	−2.91584e10	−2.48875
$754$	2.85168e9	0.242271
$755$	−4.14422e9	−0.350452
$756$	1.44701e9	0.121799
$757$	1.28572e10	1.07724	0.538619	−	0.842549i	$-0.318946\pi$
$757$	1.28572e10	1.07724	0.538619	+	0.842549i	$0.318946\pi$
$758$	1.96792e10	1.64122
$759$	1.95053e10	1.61923
$760$	−6.53468e9	−0.539979
$761$	−1.80165e10	−1.48192	−0.740960	−	0.671549i	$-0.765629\pi$
$761$	−1.80165e10	−1.48192	−0.740960	+	0.671549i	$0.765629\pi$
$762$	5.95106e8	0.0487250
$763$	−7.48756e9	−0.610246
$764$	−2.97632e9	−0.241464
$765$	−2.57984e10	−2.08342
$766$	−9.71717e9	−0.781159
$767$	2.18080e9	0.174514
$768$	1.11952e10	0.891798
$769$	−8.49573e8	−0.0673688	−0.0336844	−	0.999433i	$-0.510724\pi$
$769$	−8.49573e8	−0.0673688	−0.0336844	+	0.999433i	$0.510724\pi$
$770$	5.06138e9	0.399532
$771$	9.00775e9	0.707825
$772$	−3.81829e9	−0.298681
$773$	1.35137e10	1.05232	0.526158	−	0.850387i	$-0.323632\pi$
$773$	1.35137e10	1.05232	0.526158	+	0.850387i	$0.323632\pi$
$774$	1.22451e10	0.949222
$775$	−2.71054e9	−0.209170
$776$	1.23430e10	0.948210
$777$	6.59822e9	0.504607
$778$	−8.55805e9	−0.651548
$779$	−9.13390e9	−0.692270
$780$	−1.26539e9	−0.0954756
$781$	−1.95039e10	−1.46502
$782$	9.83205e9	0.735225
$783$	2.36640e10	1.76166
$784$	−1.52852e9	−0.113283
$785$	−1.74322e10	−1.28620
$786$	1.33308e10	0.979212
$787$	−1.55023e10	−1.13367	−0.566834	−	0.823832i	$-0.691832\pi$
$787$	−1.55023e10	−1.13367	−0.566834	+	0.823832i	$0.691832\pi$
$788$	4.36038e9	0.317455
$789$	−8.29403e9	−0.601168
$790$	−1.07712e10	−0.777268
$791$	9.43176e9	0.677603
$792$	−3.17876e10	−2.27363
$793$	1.90313e9	0.135522
$794$	2.63575e9	0.186867
$795$	−4.03375e10	−2.84724
$796$	−1.28943e9	−0.0906153
$797$	−2.35640e10	−1.64872	−0.824358	−	0.566069i	$-0.808463\pi$
$797$	−2.35640e10	−1.64872	−0.824358	+	0.566069i	$0.808463\pi$
$798$	−3.88355e9	−0.270532
$799$	8.11152e9	0.562586
$800$	1.28140e9	0.0884849
$801$	1.62462e10	1.11696
$802$	2.50214e10	1.71278
$803$	−2.45769e10	−1.67503
$804$	7.41574e9	0.503220
$805$	−5.58885e9	−0.377604
$806$	3.07607e9	0.206930
$807$	−2.25596e10	−1.51103
$808$	2.72435e10	1.81686
$809$	2.64280e9	0.175487	0.0877434	−	0.996143i	$-0.472034\pi$
$809$	2.64280e9	0.175487	0.0877434	+	0.996143i	$0.472034\pi$
$810$	1.76504e10	1.16696
$811$	−1.52159e10	−1.00167	−0.500835	−	0.865543i	$-0.666974\pi$
$811$	−1.52159e10	−1.00167	−0.500835	+	0.865543i	$0.666974\pi$
$812$	9.76795e8	0.0640262
$813$	1.60461e9	0.104725
$814$	−1.11049e10	−0.721652
$815$	2.89893e10	1.87580
$816$	−1.95134e10	−1.25724
$817$	3.59358e9	0.230542
$818$	2.15794e10	1.37849
$819$	−3.37603e9	−0.214740
$820$	4.77173e9	0.302223
$821$	−2.39086e10	−1.50783	−0.753916	−	0.656971i	$-0.771837\pi$
$821$	−2.39086e10	−1.50783	−0.753916	+	0.656971i	$0.771837\pi$
$822$	−3.15982e10	−1.98431
$823$	3.77142e9	0.235833	0.117917	−	0.993023i	$-0.462378\pi$
$823$	3.77142e9	0.235833	0.117917	+	0.993023i	$0.462378\pi$
$824$	−6.02146e9	−0.374935
$825$	−7.45079e9	−0.461970
$826$	−3.49655e9	−0.215879
$827$	1.16688e10	0.717394	0.358697	−	0.933454i	$-0.383221\pi$
$827$	1.16688e10	0.717394	0.358697	+	0.933454i	$0.383221\pi$
$828$	5.25390e9	0.321644
$829$	−2.99904e10	−1.82827	−0.914137	−	0.405407i	$-0.867130\pi$
$829$	−2.99904e10	−1.82827	−0.914137	+	0.405407i	$0.867130\pi$
$830$	1.19024e10	0.722538
$831$	1.48119e10	0.895377
$832$	−5.10782e9	−0.307471
$833$	−2.16407e9	−0.129722
$834$	2.72672e10	1.62764
$835$	1.41530e10	0.841292
$836$	−1.39635e9	−0.0826555
$837$	2.55260e10	1.50468
$838$	−1.83412e10	−1.07665
$839$	1.21289e10	0.709016	0.354508	−	0.935053i	$-0.384648\pi$
$839$	1.21289e10	0.709016	0.354508	+	0.935053i	$0.384648\pi$
$840$	1.35543e10	0.789041
$841$	−1.27564e9	−0.0739508
$842$	3.25868e9	0.188126
$843$	−9.95239e9	−0.572178
$844$	1.64470e8	0.00941644
$845$	1.51108e9	0.0861567
$846$	−2.02890e10	−1.15203
$847$	5.41395e8	0.0306142
$848$	−2.05021e10	−1.15455
$849$	−9.95202e9	−0.558129
$850$	−3.75571e9	−0.209762
$851$	1.22622e10	0.682045
$852$	−7.81808e9	−0.433074
$853$	−1.26028e10	−0.695255	−0.347627	−	0.937633i	$-0.613013\pi$
$853$	−1.26028e10	−0.695255	−0.347627	+	0.937633i	$0.613013\pi$
$854$	−3.05135e9	−0.167645
$855$	1.89372e10	1.03618
$856$	1.59200e8	0.00867530
$857$	−8.91920e9	−0.484053	−0.242027	−	0.970270i	$-0.577812\pi$
$857$	−8.91920e9	−0.484053	−0.242027	+	0.970270i	$0.577812\pi$
$858$	8.45558e9	0.457023
$859$	2.25174e10	1.21211	0.606055	−	0.795422i	$-0.292751\pi$
$859$	2.25174e10	1.21211	0.606055	+	0.795422i	$0.292751\pi$
$860$	−1.87735e9	−0.100647
$861$	1.89456e10	1.01157
$862$	2.24269e9	0.119260
$863$	2.09033e10	1.10707	0.553537	−	0.832825i	$-0.313278\pi$
$863$	2.09033e10	1.10707	0.553537	+	0.832825i	$0.313278\pi$
$864$	−1.20674e10	−0.636523
$865$	2.00458e10	1.05310
$866$	2.29630e10	1.20148
$867$	5.87800e9	0.306311
$868$	1.05366e9	0.0546866
$869$	−1.53767e10	−0.794868
$870$	3.31791e10	1.70823
$871$	−8.85561e9	−0.454104
$872$	3.37470e10	1.72357
$873$	−3.57695e10	−1.81955
$874$	−7.21720e9	−0.365661
$875$	−6.25416e9	−0.315603
$876$	−9.85160e9	−0.495157
$877$	−2.71406e10	−1.35869	−0.679346	−	0.733818i	$-0.737736\pi$
$877$	−2.71406e10	−1.35869	−0.679346	+	0.733818i	$0.737736\pi$
$878$	−6.13063e9	−0.305685
$879$	1.21588e10	0.603849
$880$	−1.86680e10	−0.923439
$881$	1.57880e10	0.777879	0.388940	−	0.921263i	$-0.372841\pi$
$881$	1.57880e10	0.777879	0.388940	+	0.921263i	$0.372841\pi$
$882$	5.41290e9	0.265638
$883$	−4.74545e9	−0.231961	−0.115980	−	0.993251i	$-0.537001\pi$
$883$	−4.74545e9	−0.231961	−0.115980	+	0.993251i	$0.537001\pi$
$884$	−9.10569e8	−0.0443333
$885$	2.53734e10	1.23049
$886$	−2.25781e10	−1.09061
$887$	1.46137e9	0.0703117	0.0351559	−	0.999382i	$-0.488807\pi$
$887$	1.46137e9	0.0703117	0.0351559	+	0.999382i	$0.488807\pi$
$888$	−2.97387e10	−1.42520
$889$	−2.43423e8	−0.0116200
$890$	1.16589e10	0.554363
$891$	2.51972e10	1.19338
$892$	7.04056e9	0.332147
$893$	−5.95425e9	−0.279799
$894$	4.45845e10	2.08690
$895$	4.13767e10	1.92919
$896$	5.35986e9	0.248929
$897$	−9.33678e9	−0.431940
$898$	−4.52239e9	−0.208401
$899$	1.72312e10	0.790965
$900$	−2.00692e9	−0.0917659
$901$	−2.90268e10	−1.32209
$902$	−3.18857e10	−1.44668
$903$	−7.45384e9	−0.336878
$904$	−4.25097e10	−1.91381
$905$	−1.97805e10	−0.887090
$906$	1.11005e10	0.495899
$907$	7.34886e9	0.327035	0.163517	−	0.986540i	$-0.447716\pi$
$907$	7.34886e9	0.327035	0.163517	+	0.986540i	$0.447716\pi$
$908$	−4.40281e9	−0.195177
$909$	−7.89505e10	−3.48643
$910$	−2.42277e9	−0.106578
$911$	−1.14584e10	−0.502122	−0.251061	−	0.967971i	$-0.580779\pi$
$911$	−1.14584e10	−0.502122	−0.251061	+	0.967971i	$0.580779\pi$
$912$	1.43238e10	0.625281
$913$	1.69916e10	0.738899
$914$	−3.40362e10	−1.47445
$915$	2.21427e10	0.955559
$916$	5.55613e7	0.00238857
$917$	−5.45284e9	−0.233523
$918$	3.53688e10	1.50894
$919$	1.34600e10	0.572059	0.286030	−	0.958221i	$-0.407664\pi$
$919$	1.34600e10	0.572059	0.286030	+	0.958221i	$0.407664\pi$
$920$	2.51894e10	1.06650
$921$	−4.86970e10	−2.05397
$922$	−1.32374e9	−0.0556216
$923$	9.33608e9	0.390804
$924$	2.89632e9	0.120780
$925$	−4.68398e9	−0.194589
$926$	−4.78596e7	−0.00198075
$927$	1.74499e10	0.719474
$928$	−8.14601e9	−0.334601
$929$	1.58805e10	0.649843	0.324922	−	0.945741i	$-0.394662\pi$
$929$	1.58805e10	0.649843	0.324922	+	0.945741i	$0.394662\pi$
$930$	3.57899e10	1.45905
$931$	1.58853e9	0.0645167
$932$	6.18081e9	0.250086
$933$	8.10803e10	3.26836
$934$	−8.18406e9	−0.328666
$935$	−2.64300e10	−1.05744
$936$	1.52160e10	0.606506
$937$	−7.89338e8	−0.0313455	−0.0156727	−	0.999877i	$-0.504989\pi$
$937$	−7.89338e8	−0.0313455	−0.0156727	+	0.999877i	$0.504989\pi$
$938$	1.41985e10	0.561737
$939$	−2.19201e10	−0.863999
$940$	3.11061e9	0.122151
$941$	−2.61883e10	−1.02457	−0.512287	−	0.858814i	$-0.671202\pi$
$941$	−2.61883e10	−1.02457	−0.512287	+	0.858814i	$0.671202\pi$
$942$	4.66929e10	1.82000
$943$	3.52086e10	1.36728
$944$	1.28964e10	0.498961
$945$	−2.01048e10	−0.774975
$946$	1.25449e10	0.481779
$947$	1.53997e10	0.589233	0.294617	−	0.955616i	$-0.404808\pi$
$947$	1.53997e10	0.589233	0.294617	+	0.955616i	$0.404808\pi$
$948$	−6.16373e9	−0.234971
$949$	1.17644e10	0.446827
$950$	2.75688e9	0.104324
$951$	1.44434e9	0.0544551
$952$	9.75363e9	0.366385
$953$	1.33505e10	0.499658	0.249829	−	0.968290i	$-0.419626\pi$
$953$	1.33505e10	0.499658	0.249829	+	0.968290i	$0.419626\pi$
$954$	7.26035e10	2.70731
$955$	4.13531e10	1.53637
$956$	2.12597e9	0.0786965
$957$	4.73656e10	1.74691
$958$	−2.11872e10	−0.778563
$959$	1.29250e10	0.473221
$960$	−5.94292e10	−2.16796
$961$	−8.92549e9	−0.324414
$962$	5.31565e9	0.192506
$963$	−4.61355e8	−0.0166473
$964$	−3.93563e9	−0.141496
$965$	5.30514e10	1.90043
$966$	1.49700e10	0.534320
$967$	2.16430e10	0.769706	0.384853	−	0.922978i	$-0.374252\pi$
$967$	2.16430e10	0.769706	0.384853	+	0.922978i	$0.374252\pi$
$968$	−2.44011e9	−0.0864661
$969$	2.02795e10	0.716018
$970$	−2.56696e10	−0.903063
$971$	−1.02901e10	−0.360706	−0.180353	−	0.983602i	$-0.557724\pi$
$971$	−1.02901e10	−0.360706	−0.180353	+	0.983602i	$0.557724\pi$
$972$	8.73979e8	0.0305259
$973$	−1.11534e10	−0.388162
$974$	−2.61137e10	−0.905550
$975$	3.56653e9	0.123234
$976$	1.12544e10	0.387477
$977$	2.03940e10	0.699633	0.349817	−	0.936818i	$-0.386244\pi$
$977$	2.03940e10	0.699633	0.349817	+	0.936818i	$0.386244\pi$
$978$	−7.76492e10	−2.65431
$979$	1.66440e10	0.566916
$980$	−8.29880e8	−0.0281659
$981$	−9.77976e10	−3.30740
$982$	−4.83007e10	−1.62766
$983$	−3.02101e10	−1.01441	−0.507207	−	0.861824i	$-0.669322\pi$
$983$	−3.02101e10	−1.01441	−0.507207	+	0.861824i	$0.669322\pi$
$984$	−8.53894e10	−2.85707
$985$	−6.05832e10	−2.01988
$986$	2.38756e10	0.793203
$987$	1.23504e10	0.408855
$988$	6.68401e8	0.0220489
$989$	−1.38522e10	−0.455337
$990$	6.61083e10	2.16537
$991$	1.82822e10	0.596720	0.298360	−	0.954453i	$-0.403560\pi$
$991$	1.82822e10	0.596720	0.298360	+	0.954453i	$0.403560\pi$
$992$	−8.78701e9	−0.285792
$993$	−8.23707e10	−2.66963
$994$	−1.49689e10	−0.483433
$995$	1.79154e10	0.576560
$996$	6.81102e9	0.218426
$997$	2.76493e10	0.883592	0.441796	−	0.897116i	$-0.354342\pi$
$997$	2.76493e10	0.883592	0.441796	+	0.897116i	$0.354342\pi$
$998$	−2.03885e10	−0.649275
$999$	4.41106e10	1.39979

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.c.1.8	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.c.1.8	✓	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)

\(f(q)\)	\(=\)	\(q+10.2698 q^{2} -81.6519 q^{3} -22.5320 q^{4} +313.060 q^{5} -838.546 q^{6} +343.000 q^{7} -1545.93 q^{8} +4480.04 q^{9} +O(q^{10})\)	\(q+10.2698 q^{2} -81.6519 q^{3} -22.5320 q^{4} +313.060 q^{5} -838.546 q^{6} +343.000 q^{7} -1545.93 q^{8} +4480.04 q^{9} +3215.05 q^{10} +4589.73 q^{11} +1839.78 q^{12} -2197.00 q^{13} +3522.53 q^{14} -25561.9 q^{15} -12992.2 q^{16} -18394.3 q^{17} +46008.9 q^{18} +13502.3 q^{19} -7053.86 q^{20} -28006.6 q^{21} +47135.4 q^{22} -52047.6 q^{23} +126228. q^{24} +19881.5 q^{25} -22562.7 q^{26} -187231. q^{27} -7728.47 q^{28} -126389. q^{29} -262515. q^{30} -136335. q^{31} +64451.8 q^{32} -374760. q^{33} -188905. q^{34} +107380. q^{35} -100944. q^{36} -235595. q^{37} +138665. q^{38} +179389. q^{39} -483968. q^{40} -676470. q^{41} -287621. q^{42} +266146. q^{43} -103416. q^{44} +1.40252e6 q^{45} -534516. q^{46} -440980. q^{47} +1.06084e6 q^{48} +117649. q^{49} +204178. q^{50} +1.50193e6 q^{51} +49502.8 q^{52} +1.57803e6 q^{53} -1.92282e6 q^{54} +1.43686e6 q^{55} -530253. q^{56} -1.10249e6 q^{57} -1.29799e6 q^{58} -992625. q^{59} +575961. q^{60} -866239. q^{61} -1.40012e6 q^{62} +1.53665e6 q^{63} +2.32491e6 q^{64} -687793. q^{65} -3.84870e6 q^{66} +4.03078e6 q^{67} +414460. q^{68} +4.24978e6 q^{69} +1.10276e6 q^{70} -4.24947e6 q^{71} -6.92581e6 q^{72} -5.35477e6 q^{73} -2.41950e6 q^{74} -1.62336e6 q^{75} -304234. q^{76} +1.57428e6 q^{77} +1.84229e6 q^{78} -3.35025e6 q^{79} -4.06734e6 q^{80} +5.48992e6 q^{81} -6.94719e6 q^{82} +3.70208e6 q^{83} +631044. q^{84} -5.75852e6 q^{85} +2.73325e6 q^{86} +1.03199e7 q^{87} -7.09538e6 q^{88} +3.62636e6 q^{89} +1.44035e7 q^{90} -753571. q^{91} +1.17274e6 q^{92} +1.11320e7 q^{93} -4.52876e6 q^{94} +4.22703e6 q^{95} -5.26261e6 q^{96} -7.98420e6 q^{97} +1.20823e6 q^{98} +2.05621e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9}+O(q^{10}) \) 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

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Database

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