LMFDB - Embedded newform 91.8.a.c.1.6

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			1.6
Root			$1.45069$ 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)

$f(q)$	$=$	$q-0.549314 q^{2} -7.31646 q^{3} -127.698 q^{4} +243.344 q^{5} +4.01903 q^{6} +343.000 q^{7} +140.459 q^{8} -2133.47 q^{9} +O(q^{10})$	\(q-0.549314 q^{2} -7.31646 q^{3} -127.698 q^{4} +243.344 q^{5} +4.01903 q^{6} +343.000 q^{7} +140.459 q^{8} -2133.47 q^{9} -133.672 q^{10} +2740.76 q^{11} +934.299 q^{12} -2197.00 q^{13} -188.415 q^{14} -1780.42 q^{15} +16268.2 q^{16} +25231.7 q^{17} +1171.95 q^{18} -17430.7 q^{19} -31074.6 q^{20} -2509.55 q^{21} -1505.54 q^{22} -4191.76 q^{23} -1027.66 q^{24} -18908.7 q^{25} +1206.84 q^{26} +31610.5 q^{27} -43800.5 q^{28} -250442. q^{29} +978.008 q^{30} -229878. q^{31} -26915.1 q^{32} -20052.7 q^{33} -13860.1 q^{34} +83467.0 q^{35} +272440. q^{36} -234599. q^{37} +9574.95 q^{38} +16074.3 q^{39} +34179.8 q^{40} +620939. q^{41} +1378.53 q^{42} -907069. q^{43} -349990. q^{44} -519167. q^{45} +2302.59 q^{46} -244817. q^{47} -119026. q^{48} +117649. q^{49} +10386.8 q^{50} -184607. q^{51} +280553. q^{52} -1.52931e6 q^{53} -17364.1 q^{54} +666948. q^{55} +48177.3 q^{56} +127531. q^{57} +137572. q^{58} +285194. q^{59} +227356. q^{60} -1.90471e6 q^{61} +126275. q^{62} -731780. q^{63} -2.06755e6 q^{64} -534627. q^{65} +11015.2 q^{66} -3.25176e6 q^{67} -3.22205e6 q^{68} +30668.9 q^{69} -45849.6 q^{70} +4.62524e6 q^{71} -299664. q^{72} +3.62558e6 q^{73} +128869. q^{74} +138345. q^{75} +2.22587e6 q^{76} +940081. q^{77} -8829.82 q^{78} -7.90412e6 q^{79} +3.95877e6 q^{80} +4.43462e6 q^{81} -341091. q^{82} +3.60755e6 q^{83} +320465. q^{84} +6.13999e6 q^{85} +498266. q^{86} +1.83235e6 q^{87} +384964. q^{88} +5.88648e6 q^{89} +285186. q^{90} -753571. q^{91} +535281. q^{92} +1.68189e6 q^{93} +134482. q^{94} -4.24167e6 q^{95} +196923. q^{96} +1.40193e7 q^{97} -64626.3 q^{98} -5.84733e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.549314	−0.0485530	−0.0242765	−	0.999705i	$-0.507728\pi$
$2$	−0.549314	−0.0485530	−0.0242765	+	0.999705i	$0.507728\pi$
$3$	−7.31646	−0.156450	−0.0782252	−	0.996936i	$-0.524925\pi$
$3$	−7.31646	−0.156450	−0.0782252	+	0.996936i	$0.524925\pi$
$4$	−127.698	−0.997643
$5$	243.344	0.870614	0.435307	−	0.900282i	$-0.356640\pi$
$5$	243.344	0.870614	0.435307	+	0.900282i	$0.356640\pi$
$6$	4.01903	0.00759613
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	140.459	0.0969915
$9$	−2133.47	−0.975523
$10$	−133.672	−0.0422709
$11$	2740.76	0.620864	0.310432	−	0.950596i	$-0.399526\pi$
$11$	2740.76	0.620864	0.310432	+	0.950596i	$0.399526\pi$
$12$	934.299	0.156082
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−188.415	−0.0183513
$15$	−1780.42	−0.136208
$16$	16268.2	0.992933
$17$	25231.7	1.24559	0.622795	−	0.782385i	$-0.285997\pi$
$17$	25231.7	1.24559	0.622795	+	0.782385i	$0.285997\pi$
$18$	1171.95	0.0473646
$19$	−17430.7	−0.583013	−0.291506	−	0.956569i	$-0.594156\pi$
$19$	−17430.7	−0.583013	−0.291506	+	0.956569i	$0.594156\pi$
$20$	−31074.6	−0.868562
$21$	−2509.55	−0.0591327
$22$	−1505.54	−0.0301448
$23$	−4191.76	−0.0718372	−0.0359186	−	0.999355i	$-0.511436\pi$
$23$	−4191.76	−0.0718372	−0.0359186	+	0.999355i	$0.511436\pi$
$24$	−1027.66	−0.0151744
$25$	−18908.7	−0.242031
$26$	1206.84	0.0134662
$27$	31610.5	0.309071
$28$	−43800.5	−0.377073
$29$	−250442.	−1.90684	−0.953421	−	0.301641i	$-0.902465\pi$
$29$	−250442.	−1.90684	−0.953421	+	0.301641i	$0.902465\pi$
$30$	978.008	0.00661330
$31$	−229878.	−1.38590	−0.692950	−	0.720986i	$-0.743689\pi$
$31$	−229878.	−1.38590	−0.692950	+	0.720986i	$0.743689\pi$
$32$	−26915.1	−0.145201
$33$	−20052.7	−0.0971344
$34$	−13860.1	−0.0604771
$35$	83467.0	0.329061
$36$	272440.	0.973224
$37$	−234599.	−0.761414	−0.380707	−	0.924696i	$-0.624319\pi$
$37$	−234599.	−0.761414	−0.380707	+	0.924696i	$0.624319\pi$
$38$	9574.95	0.0283070
$39$	16074.3	0.0433915
$40$	34179.8	0.0844422
$41$	620939.	1.40704	0.703519	−	0.710677i	$-0.251611\pi$
$41$	620939.	1.40704	0.703519	+	0.710677i	$0.251611\pi$
$42$	1378.53	0.00287107
$43$	−907069.	−1.73981	−0.869903	−	0.493223i	$-0.835818\pi$
$43$	−907069.	−1.73981	−0.869903	+	0.493223i	$0.835818\pi$
$44$	−349990.	−0.619401
$45$	−519167.	−0.849304
$46$	2302.59	0.00348791
$47$	−244817.	−0.343954	−0.171977	−	0.985101i	$-0.555015\pi$
$47$	−244817.	−0.343954	−0.171977	+	0.985101i	$0.555015\pi$
$48$	−119026.	−0.155345
$49$	117649.	0.142857
$50$	10386.8	0.0117513
$51$	−184607.	−0.194873
$52$	280553.	0.276696
$53$	−1.52931e6	−1.41101	−0.705504	−	0.708706i	$-0.749279\pi$
$53$	−1.52931e6	−1.41101	−0.705504	+	0.708706i	$0.749279\pi$
$54$	−17364.1	−0.0150063
$55$	666948.	0.540533
$56$	48177.3	0.0366593
$57$	127531.	0.0912125
$58$	137572.	0.0925829
$59$	285194.	0.180783	0.0903917	−	0.995906i	$-0.471188\pi$
$59$	285194.	0.180783	0.0903917	+	0.995906i	$0.471188\pi$
$60$	227356.	0.135887
$61$	−1.90471e6	−1.07442	−0.537211	−	0.843448i	$-0.680522\pi$
$61$	−1.90471e6	−1.07442	−0.537211	+	0.843448i	$0.680522\pi$
$62$	126275.	0.0672895
$63$	−731780.	−0.368713
$64$	−2.06755e6	−0.985883
$65$	−534627.	−0.241465
$66$	11015.2	0.00471617
$67$	−3.25176e6	−1.32086	−0.660430	−	0.750887i	$-0.729626\pi$
$67$	−3.25176e6	−1.32086	−0.660430	+	0.750887i	$0.729626\pi$
$68$	−3.22205e6	−1.24265
$69$	30668.9	0.0112389
$70$	−45849.6	−0.0159769
$71$	4.62524e6	1.53366	0.766832	−	0.641848i	$-0.221832\pi$
$71$	4.62524e6	1.53366	0.766832	+	0.641848i	$0.221832\pi$
$72$	−299664.	−0.0946175
$73$	3.62558e6	1.09081	0.545403	−	0.838174i	$-0.316377\pi$
$73$	3.62558e6	1.09081	0.545403	+	0.838174i	$0.316377\pi$
$74$	128869.	0.0369689
$75$	138345.	0.0378658
$76$	2.22587e6	0.581638
$77$	940081.	0.234665
$78$	−8829.82	−0.00210679
$79$	−7.90412e6	−1.80368	−0.901839	−	0.432073i	$-0.857782\pi$
$79$	−7.90412e6	−1.80368	−0.901839	+	0.432073i	$0.857782\pi$
$80$	3.95877e6	0.864462
$81$	4.43462e6	0.927169
$82$	−341091.	−0.0683158
$83$	3.60755e6	0.692530	0.346265	−	0.938137i	$-0.387450\pi$
$83$	3.60755e6	0.692530	0.346265	+	0.938137i	$0.387450\pi$
$84$	320465.	0.0589933
$85$	6.13999e6	1.08443
$86$	498266.	0.0844727
$87$	1.83235e6	0.298326
$88$	384964.	0.0602186
$89$	5.88648e6	0.885097	0.442548	−	0.896745i	$-0.354074\pi$
$89$	5.88648e6	0.885097	0.442548	+	0.896745i	$0.354074\pi$
$90$	285186.	0.0412363
$91$	−753571.	−0.104828
$92$	535281.	0.0716678
$93$	1.68189e6	0.216824
$94$	134482.	0.0167000
$95$	−4.24167e6	−0.507579
$96$	196923.	0.0227168
$97$	1.40193e7	1.55964	0.779819	−	0.626005i	$-0.215311\pi$
$97$	1.40193e7	1.55964	0.779819	+	0.626005i	$0.215311\pi$
$98$	−64626.3	−0.00693614
$99$	−5.84733e6	−0.605667
$100$	2.41460e6	0.241460
$101$	−8.22592e6	−0.794437	−0.397219	−	0.917724i	$-0.630025\pi$
$101$	−8.22592e6	−0.794437	−0.397219	+	0.917724i	$0.630025\pi$
$102$	101407.	0.00946167
$103$	−1.74687e7	−1.57518	−0.787591	−	0.616199i	$-0.788672\pi$
$103$	−1.74687e7	−1.57518	−0.787591	+	0.616199i	$0.788672\pi$
$104$	−308588.	−0.0269006
$105$	−610683.	−0.0514817
$106$	840071.	0.0685086
$107$	2.10400e7	1.66036	0.830182	−	0.557493i	$-0.188237\pi$
$107$	2.10400e7	1.66036	0.830182	+	0.557493i	$0.188237\pi$
$108$	−4.03661e6	−0.308343
$109$	−1.61705e7	−1.19600	−0.597999	−	0.801497i	$-0.704037\pi$
$109$	−1.61705e7	−1.19600	−0.597999	+	0.801497i	$0.704037\pi$
$110$	−366364.	−0.0262445
$111$	1.71644e6	0.119123
$112$	5.58000e6	0.375294
$113$	7.20254e6	0.469582	0.234791	−	0.972046i	$-0.424559\pi$
$113$	7.20254e6	0.469582	0.234791	+	0.972046i	$0.424559\pi$
$114$	−70054.7	−0.00442864
$115$	−1.02004e6	−0.0625425
$116$	3.19811e7	1.90235
$117$	4.68723e6	0.270561
$118$	−156661.	−0.00877758
$119$	8.65448e6	0.470789
$120$	−250075.	−0.0132110
$121$	−1.19754e7	−0.614528
$122$	1.04628e6	0.0521664
$123$	−4.54308e6	−0.220131
$124$	2.93550e7	1.38263
$125$	−2.36126e7	−1.08133
$126$	401977.	0.0179021
$127$	−2.38263e6	−0.103215	−0.0516076	−	0.998667i	$-0.516435\pi$
$127$	−2.38263e6	−0.103215	−0.0516076	+	0.998667i	$0.516435\pi$
$128$	4.58086e6	0.193069
$129$	6.63653e6	0.272193
$130$	293678.	0.0117238
$131$	2.66770e7	1.03678	0.518392	−	0.855143i	$-0.326531\pi$
$131$	2.66770e7	1.03678	0.518392	+	0.855143i	$0.326531\pi$
$132$	2.56069e6	0.0969054
$133$	−5.97874e6	−0.220358
$134$	1.78624e6	0.0641317
$135$	7.69224e6	0.269082
$136$	3.54401e6	0.120812
$137$	−3.66957e7	−1.21925	−0.609625	−	0.792690i	$-0.708680\pi$
$137$	−3.66957e7	−1.21925	−0.609625	+	0.792690i	$0.708680\pi$
$138$	−16846.8	−0.000545684 0
$139$	1.74547e7	0.551265	0.275633	−	0.961263i	$-0.411113\pi$
$139$	1.74547e7	0.551265	0.275633	+	0.961263i	$0.411113\pi$
$140$	−1.06586e7	−0.328285
$141$	1.79120e6	0.0538116
$142$	−2.54071e6	−0.0744639
$143$	−6.02145e6	−0.172197
$144$	−3.47078e7	−0.968630
$145$	−6.09437e7	−1.66012
$146$	−1.99158e6	−0.0529619
$147$	−860774.	−0.0223500
$148$	2.99579e7	0.759619
$149$	6.81254e7	1.68716	0.843582	−	0.537000i	$-0.180443\pi$
$149$	6.81254e7	1.68716	0.843582	+	0.537000i	$0.180443\pi$
$150$	−75994.6	−0.00183850
$151$	−297107.	−0.00702253	−0.00351127	−	0.999994i	$-0.501118\pi$
$151$	−297107.	−0.00702253	−0.00351127	+	0.999994i	$0.501118\pi$
$152$	−2.44830e6	−0.0565473
$153$	−5.38311e7	−1.21510
$154$	−516400.	−0.0113937
$155$	−5.59395e7	−1.20658
$156$	−2.05265e6	−0.0432892
$157$	−7.92640e7	−1.63466	−0.817329	−	0.576171i	$-0.804546\pi$
$157$	−7.92640e7	−1.63466	−0.817329	+	0.576171i	$0.804546\pi$
$158$	4.34185e6	0.0875739
$159$	1.11891e7	0.220753
$160$	−6.54962e6	−0.126414
$161$	−1.43777e6	−0.0271519
$162$	−2.43600e6	−0.0450168
$163$	−3.56517e7	−0.644797	−0.322399	−	0.946604i	$-0.604489\pi$
$163$	−3.56517e7	−0.644797	−0.322399	+	0.946604i	$0.604489\pi$
$164$	−7.92928e7	−1.40372
$165$	−4.87969e6	−0.0845666
$166$	−1.98168e6	−0.0336244
$167$	−4.80961e6	−0.0799103	−0.0399551	−	0.999201i	$-0.512721\pi$
$167$	−4.80961e6	−0.0799103	−0.0399551	+	0.999201i	$0.512721\pi$
$168$	−352487.	−0.00573537
$169$	4.82681e6	0.0769231
$170$	−3.37278e6	−0.0526523
$171$	3.71879e7	0.568743
$172$	1.15831e8	1.73570
$173$	−1.24099e8	−1.82224	−0.911120	−	0.412140i	$-0.864781\pi$
$173$	−1.24099e8	−1.82224	−0.911120	+	0.412140i	$0.864781\pi$
$174$	−1.00654e6	−0.0144846
$175$	−6.48567e6	−0.0914791
$176$	4.45873e7	0.616477
$177$	−2.08661e6	−0.0282836
$178$	−3.23353e6	−0.0429741
$179$	−3.82375e7	−0.498315	−0.249157	−	0.968463i	$-0.580154\pi$
$179$	−3.82375e7	−0.498315	−0.249157	+	0.968463i	$0.580154\pi$
$180$	6.62967e7	0.847302
$181$	−4.79565e7	−0.601135	−0.300568	−	0.953761i	$-0.597176\pi$
$181$	−4.79565e7	−0.601135	−0.300568	+	0.953761i	$0.597176\pi$
$182$	413947.	0.00508974
$183$	1.39357e7	0.168094
$184$	−588769.	−0.00696759
$185$	−5.70884e7	−0.662898
$186$	−923888.	−0.0105275
$187$	6.91541e7	0.773343
$188$	3.12628e7	0.343143
$189$	1.08424e7	0.116818
$190$	2.33001e6	0.0246445
$191$	4.38692e7	0.455557	0.227779	−	0.973713i	$-0.426854\pi$
$191$	4.38692e7	0.455557	0.227779	+	0.973713i	$0.426854\pi$
$192$	1.51271e7	0.154242
$193$	8.57796e7	0.858882	0.429441	−	0.903095i	$-0.358711\pi$
$193$	8.57796e7	0.858882	0.429441	+	0.903095i	$0.358711\pi$
$194$	−7.70098e6	−0.0757251
$195$	3.91158e6	0.0377773
$196$	−1.50236e7	−0.142520
$197$	−1.36694e8	−1.27385	−0.636924	−	0.770926i	$-0.719794\pi$
$197$	−1.36694e8	−1.27385	−0.636924	+	0.770926i	$0.719794\pi$
$198$	3.21202e6	0.0294070
$199$	3.08643e7	0.277633	0.138816	−	0.990318i	$-0.455670\pi$
$199$	3.08643e7	0.277633	0.138816	+	0.990318i	$0.455670\pi$
$200$	−2.65589e6	−0.0234749
$201$	2.37914e7	0.206649
$202$	4.51861e6	0.0385723
$203$	−8.59018e7	−0.720719
$204$	2.35740e7	0.194414
$205$	1.51102e8	1.22499
$206$	9.59581e6	0.0764797
$207$	8.94300e6	0.0700788
$208$	−3.57413e7	−0.275390
$209$	−4.77735e7	−0.361972
$210$	335457.	0.00249959
$211$	1.50813e7	0.110522	0.0552610	−	0.998472i	$-0.482401\pi$
$211$	1.50813e7	0.110522	0.0552610	+	0.998472i	$0.482401\pi$
$212$	1.95290e8	1.40768
$213$	−3.38404e7	−0.239942
$214$	−1.15576e7	−0.0806156
$215$	−2.20730e8	−1.51470
$216$	4.43997e6	0.0299773
$217$	−7.88482e7	−0.523821
$218$	8.88268e6	0.0580693
$219$	−2.65264e7	−0.170657
$220$	−8.51681e7	−0.539259
$221$	−5.54341e7	−0.345465
$222$	−942863.	−0.00578380
$223$	2.52593e8	1.52530	0.762649	−	0.646812i	$-0.223898\pi$
$223$	2.52593e8	1.52530	0.762649	+	0.646812i	$0.223898\pi$
$224$	−9.23187e6	−0.0548810
$225$	4.03411e7	0.236107
$226$	−3.95646e6	−0.0227996
$227$	−3.57039e7	−0.202593	−0.101297	−	0.994856i	$-0.532299\pi$
$227$	−3.57039e7	−0.202593	−0.101297	+	0.994856i	$0.532299\pi$
$228$	−1.62855e7	−0.0909975
$229$	2.61521e8	1.43907	0.719536	−	0.694455i	$-0.244354\pi$
$229$	2.61521e8	1.43907	0.719536	+	0.694455i	$0.244354\pi$
$230$	560323.	0.00303662
$231$	−6.87806e6	−0.0367134
$232$	−3.51768e7	−0.184948
$233$	−9.90136e7	−0.512802	−0.256401	−	0.966571i	$-0.582537\pi$
$233$	−9.90136e7	−0.512802	−0.256401	+	0.966571i	$0.582537\pi$
$234$	−2.57476e6	−0.0131366
$235$	−5.95749e7	−0.299451
$236$	−3.64188e7	−0.180357
$237$	5.78302e7	0.282186
$238$	−4.75403e6	−0.0228582
$239$	1.29524e8	0.613700	0.306850	−	0.951758i	$-0.400725\pi$
$239$	1.29524e8	0.613700	0.306850	+	0.951758i	$0.400725\pi$
$240$	−2.89642e7	−0.135245
$241$	2.64372e8	1.21662	0.608312	−	0.793698i	$-0.291847\pi$
$241$	2.64372e8	1.21662	0.608312	+	0.793698i	$0.291847\pi$
$242$	6.57826e6	0.0298371
$243$	−1.01578e8	−0.454127
$244$	2.43228e8	1.07189
$245$	2.86292e7	0.124373
$246$	2.49558e6	0.0106880
$247$	3.82953e7	0.161699
$248$	−3.22884e7	−0.134420
$249$	−2.63945e7	−0.108347
$250$	1.29707e7	0.0525018
$251$	4.25352e8	1.69781	0.848907	−	0.528542i	$-0.177261\pi$
$251$	4.25352e8	1.69781	0.848907	+	0.528542i	$0.177261\pi$
$252$	9.34470e7	0.367844
$253$	−1.14886e7	−0.0446011
$254$	1.30881e6	0.00501141
$255$	−4.49230e7	−0.169659
$256$	2.62130e8	0.976509
$257$	−1.30564e7	−0.0479798	−0.0239899	−	0.999712i	$-0.507637\pi$
$257$	−1.30564e7	−0.0479798	−0.0239899	+	0.999712i	$0.507637\pi$
$258$	−3.64554e6	−0.0132158
$259$	−8.04676e7	−0.287787
$260$	6.82709e7	0.240896
$261$	5.34311e8	1.86017
$262$	−1.46541e7	−0.0503389
$263$	−1.94738e8	−0.660094	−0.330047	−	0.943965i	$-0.607065\pi$
$263$	−1.94738e8	−0.660094	−0.330047	+	0.943965i	$0.607065\pi$
$264$	−2.81657e6	−0.00942121
$265$	−3.72148e8	−1.22844
$266$	3.28421e6	0.0106990
$267$	−4.30682e7	−0.138474
$268$	4.15244e8	1.31775
$269$	−4.03123e8	−1.26271	−0.631356	−	0.775493i	$-0.717501\pi$
$269$	−4.03123e8	−1.26271	−0.631356	+	0.775493i	$0.717501\pi$
$270$	−4.22545e6	−0.0130647
$271$	−4.93578e8	−1.50648	−0.753240	−	0.657745i	$-0.771510\pi$
$271$	−4.93578e8	−1.50648	−0.753240	+	0.657745i	$0.771510\pi$
$272$	4.10475e8	1.23679
$273$	5.51347e6	0.0164005
$274$	2.01574e7	0.0591982
$275$	−5.18241e7	−0.150268
$276$	−3.91636e6	−0.0112125
$277$	−3.67841e8	−1.03988	−0.519938	−	0.854204i	$-0.674045\pi$
$277$	−3.67841e8	−1.03988	−0.519938	+	0.854204i	$0.674045\pi$
$278$	−9.58811e6	−0.0267656
$279$	4.90438e8	1.35198
$280$	1.17237e7	0.0319161
$281$	−8.19479e7	−0.220326	−0.110163	−	0.993914i	$-0.535137\pi$
$281$	−8.19479e7	−0.220326	−0.110163	+	0.993914i	$0.535137\pi$
$282$	−983930.	−0.00261272
$283$	7.09650e7	0.186119	0.0930597	−	0.995661i	$-0.470335\pi$
$283$	7.09650e7	0.186119	0.0930597	+	0.995661i	$0.470335\pi$
$284$	−5.90635e8	−1.53005
$285$	3.10340e7	0.0794109
$286$	3.30767e6	0.00836067
$287$	2.12982e8	0.531810
$288$	5.74225e7	0.141647
$289$	2.26300e8	0.551497
$290$	3.34772e7	0.0806040
$291$	−1.02571e8	−0.244006
$292$	−4.62980e8	−1.08823
$293$	−2.14281e8	−0.497676	−0.248838	−	0.968545i	$-0.580049\pi$
$293$	−2.14281e8	−0.497676	−0.248838	+	0.968545i	$0.580049\pi$
$294$	472835.	0.00108516
$295$	6.94003e7	0.157393
$296$	−3.29515e7	−0.0738507
$297$	8.66369e7	0.191891
$298$	−3.74223e7	−0.0819168
$299$	9.20930e6	0.0199240
$300$	−1.76664e7	−0.0377766
$301$	−3.11125e8	−0.657585
$302$	163205.	0.000340965 0
$303$	6.01846e7	0.124290
$304$	−2.83567e8	−0.578893
$305$	−4.63500e8	−0.935407
$306$	2.95702e7	0.0589969
$307$	−2.63780e8	−0.520305	−0.260152	−	0.965568i	$-0.583773\pi$
$307$	−2.63780e8	−0.520305	−0.260152	+	0.965568i	$0.583773\pi$
$308$	−1.20047e8	−0.234111
$309$	1.27809e8	0.246438
$310$	3.07283e7	0.0585832
$311$	−4.90398e8	−0.924458	−0.462229	−	0.886761i	$-0.652950\pi$
$311$	−4.90398e8	−0.924458	−0.462229	+	0.886761i	$0.652950\pi$
$312$	2.25777e6	0.00420861
$313$	−4.37902e8	−0.807183	−0.403591	−	0.914939i	$-0.632238\pi$
$313$	−4.37902e8	−0.807183	−0.403591	+	0.914939i	$0.632238\pi$
$314$	4.35408e7	0.0793676
$315$	−1.78074e8	−0.321007
$316$	1.00934e9	1.79943
$317$	9.68826e8	1.70820	0.854099	−	0.520110i	$-0.174109\pi$
$317$	9.68826e8	1.70820	0.854099	+	0.520110i	$0.174109\pi$
$318$	−6.14634e6	−0.0107182
$319$	−6.86403e8	−1.18389
$320$	−5.03125e8	−0.858324
$321$	−1.53939e8	−0.259764
$322$	789790.	0.00131831
$323$	−4.39807e8	−0.726195
$324$	−5.66293e8	−0.924983
$325$	4.15424e7	0.0671273
$326$	1.95840e7	0.0313068
$327$	1.18311e8	0.187114
$328$	8.72163e7	0.136471
$329$	−8.39724e7	−0.130002
$330$	2.68049e6	0.00410596
$331$	4.51159e8	0.683805	0.341902	−	0.939736i	$-0.388929\pi$
$331$	4.51159e8	0.683805	0.341902	+	0.939736i	$0.388929\pi$
$332$	−4.60677e8	−0.690897
$333$	5.00511e8	0.742777
$334$	2.64199e6	0.00387988
$335$	−7.91297e8	−1.14996
$336$	−4.08258e7	−0.0587148
$337$	5.41361e8	0.770517	0.385258	−	0.922809i	$-0.374112\pi$
$337$	5.41361e8	0.770517	0.385258	+	0.922809i	$0.374112\pi$
$338$	−2.65144e6	−0.00373484
$339$	−5.26971e7	−0.0734662
$340$	−7.84066e8	−1.08187
$341$	−6.30041e8	−0.860455
$342$	−2.04279e7	−0.0276141
$343$	4.03536e7	0.0539949
$344$	−1.27406e8	−0.168746
$345$	7.46308e6	0.00978479
$346$	6.81692e7	0.0884752
$347$	1.05442e9	1.35476	0.677380	−	0.735633i	$-0.263115\pi$
$347$	1.05442e9	1.35476	0.677380	+	0.735633i	$0.263115\pi$
$348$	−2.33988e8	−0.297623
$349$	9.18017e8	1.15601	0.578005	−	0.816033i	$-0.303831\pi$
$349$	9.18017e8	1.15601	0.578005	+	0.816033i	$0.303831\pi$
$350$	3.56267e6	0.00444158
$351$	−6.94483e7	−0.0857210
$352$	−7.37678e7	−0.0901503
$353$	−6.40375e7	−0.0774860	−0.0387430	−	0.999249i	$-0.512335\pi$
$353$	−6.40375e7	−0.0774860	−0.0387430	+	0.999249i	$0.512335\pi$
$354$	1.14621e6	0.00137325
$355$	1.12552e9	1.33523
$356$	−7.51693e8	−0.883010
$357$	−6.33201e7	−0.0736551
$358$	2.10044e7	0.0241947
$359$	6.45541e8	0.736365	0.368183	−	0.929753i	$-0.379980\pi$
$359$	6.45541e8	0.736365	0.368183	+	0.929753i	$0.379980\pi$
$360$	−7.29215e7	−0.0823753
$361$	−5.90041e8	−0.660096
$362$	2.63432e7	0.0291869
$363$	8.76176e7	0.0961431
$364$	9.62297e7	0.104581
$365$	8.82264e8	0.949671
$366$	−7.65510e6	−0.00816145
$367$	−6.66561e8	−0.703896	−0.351948	−	0.936019i	$-0.614481\pi$
$367$	−6.66561e8	−0.703896	−0.351948	+	0.936019i	$0.614481\pi$
$368$	−6.81925e7	−0.0713295
$369$	−1.32475e9	−1.37260
$370$	3.13594e7	0.0321857
$371$	−5.24553e8	−0.533311
$372$	−2.14775e8	−0.216313
$373$	8.94342e8	0.892325	0.446162	−	0.894952i	$-0.352790\pi$
$373$	8.94342e8	0.892325	0.446162	+	0.894952i	$0.352790\pi$
$374$	−3.79873e7	−0.0375481
$375$	1.72760e8	0.169174
$376$	−3.43867e7	−0.0333606
$377$	5.50222e8	0.528863
$378$	−5.95589e6	−0.00567186
$379$	3.81277e8	0.359752	0.179876	−	0.983689i	$-0.442430\pi$
$379$	3.81277e8	0.359752	0.179876	+	0.983689i	$0.442430\pi$
$380$	5.41653e8	0.506383
$381$	1.74324e7	0.0161481
$382$	−2.40980e7	−0.0221187
$383$	6.91741e8	0.629141	0.314570	−	0.949234i	$-0.398140\pi$
$383$	6.91741e8	0.629141	0.314570	+	0.949234i	$0.398140\pi$
$384$	−3.35157e7	−0.0302057
$385$	2.28763e8	0.204302
$386$	−4.71200e7	−0.0417013
$387$	1.93520e9	1.69722
$388$	−1.79023e9	−1.55596
$389$	−1.94684e8	−0.167690	−0.0838448	−	0.996479i	$-0.526720\pi$
$389$	−1.94684e8	−0.167690	−0.0838448	+	0.996479i	$0.526720\pi$
$390$	−2.14868e6	−0.00183420
$391$	−1.05765e8	−0.0894797
$392$	1.65248e7	0.0138559
$393$	−1.95181e8	−0.162205
$394$	7.50880e7	0.0618491
$395$	−1.92342e9	−1.57031
$396$	7.46694e8	0.604240
$397$	−1.30139e9	−1.04386	−0.521929	−	0.852989i	$-0.674787\pi$
$397$	−1.30139e9	−1.04386	−0.521929	+	0.852989i	$0.674787\pi$
$398$	−1.69542e7	−0.0134799
$399$	4.37432e7	0.0344751
$400$	−3.07610e8	−0.240321
$401$	−1.63849e8	−0.126893	−0.0634467	−	0.997985i	$-0.520209\pi$
$401$	−1.63849e8	−0.126893	−0.0634467	+	0.997985i	$0.520209\pi$
$402$	−1.30689e7	−0.0100334
$403$	5.05042e8	0.384379
$404$	1.05044e9	0.792564
$405$	1.07914e9	0.807206
$406$	4.71871e7	0.0349930
$407$	−6.42980e8	−0.472735
$408$	−2.59296e7	−0.0189010
$409$	7.62454e8	0.551039	0.275519	−	0.961296i	$-0.411150\pi$
$409$	7.62454e8	0.551039	0.275519	+	0.961296i	$0.411150\pi$
$410$	−8.30024e7	−0.0594767
$411$	2.68482e8	0.190752
$412$	2.23072e9	1.57147
$413$	9.78216e7	0.0683297
$414$	−4.91252e6	−0.00340254
$415$	8.77875e8	0.602926
$416$	5.91324e7	0.0402716
$417$	−1.27707e8	−0.0862456
$418$	2.62426e7	0.0175748
$419$	9.30565e8	0.618013	0.309006	−	0.951060i	$-0.400004\pi$
$419$	9.30565e8	0.618013	0.309006	+	0.951060i	$0.400004\pi$
$420$	7.79831e7	0.0513604
$421$	1.60411e9	1.04772	0.523862	−	0.851803i	$-0.324491\pi$
$421$	1.60411e9	1.04772	0.523862	+	0.851803i	$0.324491\pi$
$422$	−8.28435e6	−0.00536617
$423$	5.22310e8	0.335535
$424$	−2.14805e8	−0.136856
$425$	−4.77098e8	−0.301472
$426$	1.85890e7	0.0116499
$427$	−6.53316e8	−0.406093
$428$	−2.68678e9	−1.65645
$429$	4.40557e7	0.0269402
$430$	1.21250e8	0.0735432
$431$	1.35317e9	0.814107	0.407054	−	0.913404i	$-0.366556\pi$
$431$	1.35317e9	0.814107	0.407054	+	0.913404i	$0.366556\pi$
$432$	5.14247e8	0.306887
$433$	−1.05067e9	−0.621952	−0.310976	−	0.950418i	$-0.600656\pi$
$433$	−1.05067e9	−0.621952	−0.310976	+	0.950418i	$0.600656\pi$
$434$	4.33124e7	0.0254331
$435$	4.45892e8	0.259727
$436$	2.06494e9	1.19318
$437$	7.30655e7	0.0418820
$438$	1.45713e7	0.00828591
$439$	2.11797e9	1.19480	0.597399	−	0.801944i	$-0.296201\pi$
$439$	2.11797e9	1.19480	0.597399	+	0.801944i	$0.296201\pi$
$440$	9.36786e7	0.0524271
$441$	−2.51001e8	−0.139360
$442$	3.04507e7	0.0167733
$443$	6.02801e7	0.0329428	0.0164714	−	0.999864i	$-0.494757\pi$
$443$	6.02801e7	0.0329428	0.0164714	+	0.999864i	$0.494757\pi$
$444$	−2.19186e8	−0.118843
$445$	1.43244e9	0.770578
$446$	−1.38753e8	−0.0740578
$447$	−4.98437e8	−0.263957
$448$	−7.09169e8	−0.372629
$449$	−2.18822e9	−1.14085	−0.570425	−	0.821349i	$-0.693222\pi$
$449$	−2.18822e9	−1.14085	−0.570425	+	0.821349i	$0.693222\pi$
$450$	−2.21599e7	−0.0114637
$451$	1.70185e9	0.873579
$452$	−9.19752e8	−0.468475
$453$	2.17377e6	0.00109868
$454$	1.96126e7	0.00983650
$455$	−1.83377e8	−0.0912652
$456$	1.79129e7	0.00884684
$457$	3.94768e8	0.193480	0.0967398	−	0.995310i	$-0.469159\pi$
$457$	3.94768e8	0.193480	0.0967398	+	0.995310i	$0.469159\pi$
$458$	−1.43657e8	−0.0698713
$459$	7.97588e8	0.384976
$460$	1.30257e8	0.0623950
$461$	2.15334e9	1.02367	0.511834	−	0.859084i	$-0.328966\pi$
$461$	2.15334e9	1.02367	0.511834	+	0.859084i	$0.328966\pi$
$462$	3.77822e6	0.00178254
$463$	1.54486e9	0.723364	0.361682	−	0.932302i	$-0.382203\pi$
$463$	1.54486e9	0.723364	0.361682	+	0.932302i	$0.382203\pi$
$464$	−4.07425e9	−1.89337
$465$	4.09279e8	0.188770
$466$	5.43896e7	0.0248980
$467$	−4.06261e9	−1.84585	−0.922924	−	0.384982i	$-0.874208\pi$
$467$	−4.06261e9	−1.84585	−0.922924	+	0.384982i	$0.874208\pi$
$468$	−5.98551e8	−0.269924
$469$	−1.11535e9	−0.499238
$470$	3.27253e7	0.0145392
$471$	5.79932e8	0.255743
$472$	4.00580e7	0.0175345
$473$	−2.48606e9	−1.08018
$474$	−3.17669e7	−0.0137010
$475$	3.29592e8	0.141107
$476$	−1.10516e9	−0.469679
$477$	3.26273e9	1.37647
$478$	−7.11491e7	−0.0297970
$479$	−3.89840e7	−0.0162074	−0.00810368	−	0.999967i	$-0.502580\pi$
$479$	−3.89840e7	−0.0162074	−0.00810368	+	0.999967i	$0.502580\pi$
$480$	4.79201e7	0.0197776
$481$	5.15415e8	0.211178
$482$	−1.45224e8	−0.0590707
$483$	1.05194e7	0.00424792
$484$	1.52924e9	0.613079
$485$	3.41150e9	1.35784
$486$	5.57982e7	0.0220492
$487$	4.58654e9	1.79943	0.899713	−	0.436482i	$-0.143776\pi$
$487$	4.58654e9	1.79943	0.899713	+	0.436482i	$0.143776\pi$
$488$	−2.67533e8	−0.104210
$489$	2.60844e8	0.100879
$490$	−1.57264e7	−0.00603870
$491$	−9.55171e8	−0.364163	−0.182082	−	0.983283i	$-0.558283\pi$
$491$	−9.55171e8	−0.364163	−0.182082	+	0.983283i	$0.558283\pi$
$492$	5.80143e8	0.219612
$493$	−6.31909e9	−2.37515
$494$	−2.10362e7	−0.00785095
$495$	−1.42291e9	−0.527303
$496$	−3.73971e9	−1.37611
$497$	1.58646e9	0.579670
$498$	1.44989e7	0.00526055
$499$	−1.82336e9	−0.656934	−0.328467	−	0.944515i	$-0.606532\pi$
$499$	−1.82336e9	−0.656934	−0.328467	+	0.944515i	$0.606532\pi$
$500$	3.01528e9	1.07878
$501$	3.51893e7	0.0125020
$502$	−2.33652e8	−0.0824340
$503$	3.80411e9	1.33280	0.666400	−	0.745594i	$-0.267834\pi$
$503$	3.80411e9	1.33280	0.666400	+	0.745594i	$0.267834\pi$
$504$	−1.02785e8	−0.0357620
$505$	−2.00173e9	−0.691648
$506$	6.31086e6	0.00216552
$507$	−3.53151e7	−0.0120346
$508$	3.04258e8	0.102972
$509$	−5.07030e9	−1.70420	−0.852102	−	0.523376i	$-0.824672\pi$
$509$	−5.07030e9	−1.70420	−0.852102	+	0.523376i	$0.824672\pi$
$510$	2.46768e7	0.00823746
$511$	1.24357e9	0.412286
$512$	−7.30342e8	−0.240481
$513$	−5.50995e8	−0.180193
$514$	7.17208e6	0.00232956
$515$	−4.25091e9	−1.37138
$516$	−8.47473e8	−0.271551
$517$	−6.70986e8	−0.213548
$518$	4.42020e7	0.0139729
$519$	9.07963e8	0.285090
$520$	−7.50930e7	−0.0234200
$521$	−4.54339e9	−1.40750	−0.703749	−	0.710448i	$-0.748492\pi$
$521$	−4.54339e9	−1.40750	−0.703749	+	0.710448i	$0.748492\pi$
$522$	−2.93505e8	−0.0903168
$523$	4.58521e9	1.40153	0.700766	−	0.713391i	$-0.252842\pi$
$523$	4.58521e9	1.40153	0.700766	+	0.713391i	$0.252842\pi$
$524$	−3.40661e9	−1.03434
$525$	4.74522e7	0.0143119
$526$	1.06972e8	0.0320495
$527$	−5.80022e9	−1.72626
$528$	−3.26221e8	−0.0964480
$529$	−3.38725e9	−0.994839
$530$	2.04426e8	0.0596446
$531$	−6.08453e8	−0.176359
$532$	7.63475e8	0.219839
$533$	−1.36420e9	−0.390242
$534$	2.36580e7	0.00672331
$535$	5.11997e9	1.44554
$536$	−4.56738e8	−0.128112
$537$	2.79763e8	0.0779615
$538$	2.21441e8	0.0613084
$539$	3.22448e8	0.0886949
$540$	−9.82285e8	−0.268448
$541$	−5.40436e9	−1.46742	−0.733709	−	0.679464i	$-0.762212\pi$
$541$	−5.40436e9	−1.46742	−0.733709	+	0.679464i	$0.762212\pi$
$542$	2.71130e8	0.0731441
$543$	3.50871e8	0.0940478
$544$	−6.79113e8	−0.180862
$545$	−3.93499e9	−1.04125
$546$	−3.02863e6	−0.000796291 0
$547$	−2.94999e7	−0.00770664	−0.00385332	−	0.999993i	$-0.501227\pi$
$547$	−2.94999e7	−0.00770664	−0.00385332	+	0.999993i	$0.501227\pi$
$548$	4.68597e9	1.21638
$549$	4.06364e9	1.04812
$550$	2.84677e7	0.00729598
$551$	4.36540e9	1.11171
$552$	4.30771e6	0.00109008
$553$	−2.71111e9	−0.681726
$554$	2.02061e8	0.0504891
$555$	4.17685e8	0.103711
$556$	−2.22893e9	−0.549966
$557$	−1.91205e9	−0.468821	−0.234410	−	0.972138i	$-0.575316\pi$
$557$	−1.91205e9	−0.468821	−0.234410	+	0.972138i	$0.575316\pi$
$558$	−2.69405e8	−0.0656425
$559$	1.99283e9	0.482535
$560$	1.35786e9	0.326736
$561$	−5.05963e8	−0.120990
$562$	4.50151e7	0.0106975
$563$	3.26525e9	0.771147	0.385573	−	0.922677i	$-0.374004\pi$
$563$	3.26525e9	0.771147	0.385573	+	0.922677i	$0.374004\pi$
$564$	−2.28733e8	−0.0536848
$565$	1.75270e9	0.408824
$566$	−3.89821e7	−0.00903665
$567$	1.52107e9	0.350437
$568$	6.49655e8	0.148752
$569$	1.66131e9	0.378057	0.189029	−	0.981972i	$-0.439466\pi$
$569$	1.66131e9	0.378057	0.189029	+	0.981972i	$0.439466\pi$
$570$	−1.70474e7	−0.00385564
$571$	−7.20377e9	−1.61932	−0.809662	−	0.586897i	$-0.800349\pi$
$571$	−7.20377e9	−1.61932	−0.809662	+	0.586897i	$0.800349\pi$
$572$	7.68929e8	0.171791
$573$	−3.20967e8	−0.0712721
$574$	−1.16994e8	−0.0258210
$575$	7.92607e7	0.0173868
$576$	4.41105e9	0.961752
$577$	2.76895e9	0.600068	0.300034	−	0.953929i	$-0.403002\pi$
$577$	2.76895e9	0.600068	0.300034	+	0.953929i	$0.403002\pi$
$578$	−1.24310e8	−0.0267768
$579$	−6.27603e8	−0.134372
$580$	7.78240e9	1.65621
$581$	1.23739e9	0.261752
$582$	5.63439e7	0.0118472
$583$	−4.19147e9	−0.876044
$584$	5.09244e8	0.105799
$585$	1.14061e9	0.235555
$586$	1.17708e8	0.0241637
$587$	−5.20682e9	−1.06252	−0.531262	−	0.847207i	$-0.678282\pi$
$587$	−5.20682e9	−1.06252	−0.531262	+	0.847207i	$0.678282\pi$
$588$	1.09919e8	0.0222974
$589$	4.00694e9	0.807997
$590$	−3.81226e7	−0.00764188
$591$	1.00012e9	0.199294
$592$	−3.81651e9	−0.756033
$593$	−8.52472e8	−0.167876	−0.0839380	−	0.996471i	$-0.526750\pi$
$593$	−8.52472e8	−0.167876	−0.0839380	+	0.996471i	$0.526750\pi$
$594$	−4.75909e7	−0.00931689
$595$	2.10602e9	0.409876
$596$	−8.69950e9	−1.68319
$597$	−2.25817e8	−0.0434357
$598$	−5.05880e6	−0.000967372 0
$599$	−4.53512e8	−0.0862174	−0.0431087	−	0.999070i	$-0.513726\pi$
$599$	−4.53512e8	−0.0862174	−0.0431087	+	0.999070i	$0.513726\pi$
$600$	1.94317e7	0.00367266
$601$	1.07416e9	0.201841	0.100920	−	0.994895i	$-0.467821\pi$
$601$	1.07416e9	0.201841	0.100920	+	0.994895i	$0.467821\pi$
$602$	1.70905e8	0.0319277
$603$	6.93754e9	1.28853
$604$	3.79401e7	0.00700598
$605$	−2.91414e9	−0.535016
$606$	−3.30603e7	−0.00603465
$607$	−4.05620e9	−0.736138	−0.368069	−	0.929798i	$-0.619981\pi$
$607$	−4.05620e9	−0.736138	−0.368069	+	0.929798i	$0.619981\pi$
$608$	4.69150e8	0.0846543
$609$	6.28497e8	0.112757
$610$	2.54607e8	0.0454168
$611$	5.37864e8	0.0953955
$612$	6.87413e9	1.21224
$613$	1.86713e9	0.327388	0.163694	−	0.986511i	$-0.447659\pi$
$613$	1.86713e9	0.327388	0.163694	+	0.986511i	$0.447659\pi$
$614$	1.44898e8	0.0252623
$615$	−1.10553e9	−0.191650
$616$	1.32043e8	0.0227605
$617$	−7.78018e8	−0.133350	−0.0666748	−	0.997775i	$-0.521239\pi$
$617$	−7.78018e8	−0.133350	−0.0666748	+	0.997775i	$0.521239\pi$
$618$	−7.02073e7	−0.0119653
$619$	−4.72607e8	−0.0800908	−0.0400454	−	0.999198i	$-0.512750\pi$
$619$	−4.72607e8	−0.0800908	−0.0400454	+	0.999198i	$0.512750\pi$
$620$	7.14337e9	1.20374
$621$	−1.32504e8	−0.0222028
$622$	2.69382e8	0.0448852
$623$	2.01906e9	0.334535
$624$	2.61500e8	0.0430849
$625$	−4.26874e9	−0.699390
$626$	2.40546e8	0.0391911
$627$	3.49533e8	0.0566306
$628$	1.01219e10	1.63081
$629$	−5.91934e9	−0.948410
$630$	9.78188e7	0.0155858
$631$	−8.66628e9	−1.37319	−0.686594	−	0.727041i	$-0.740895\pi$
$631$	−8.66628e9	−1.37319	−0.686594	+	0.727041i	$0.740895\pi$
$632$	−1.11020e9	−0.174941
$633$	−1.10341e8	−0.0172912
$634$	−5.32190e8	−0.0829381
$635$	−5.79799e8	−0.0898607
$636$	−1.42883e9	−0.220232
$637$	−2.58475e8	−0.0396214
$638$	3.77051e8	0.0574814
$639$	−9.86781e9	−1.49612
$640$	1.11473e9	0.168089
$641$	3.87032e9	0.580422	0.290211	−	0.956963i	$-0.406274\pi$
$641$	3.87032e9	0.580422	0.290211	+	0.956963i	$0.406274\pi$
$642$	8.45606e7	0.0126123
$643$	6.03939e9	0.895890	0.447945	−	0.894061i	$-0.352156\pi$
$643$	6.03939e9	0.895890	0.447945	+	0.894061i	$0.352156\pi$
$644$	1.83601e8	0.0270879
$645$	1.61496e9	0.236975
$646$	2.41592e8	0.0352589
$647$	5.16440e9	0.749643	0.374822	−	0.927097i	$-0.377704\pi$
$647$	5.16440e9	0.749643	0.374822	+	0.927097i	$0.377704\pi$
$648$	6.22881e8	0.0899275
$649$	7.81649e8	0.112242
$650$	−2.28198e7	−0.00325923
$651$	5.76889e8	0.0819519
$652$	4.55265e9	0.643277
$653$	1.28056e9	0.179972	0.0899858	−	0.995943i	$-0.471318\pi$
$653$	1.28056e9	0.179972	0.0899858	+	0.995943i	$0.471318\pi$
$654$	−6.49898e7	−0.00908495
$655$	6.49170e9	0.902639
$656$	1.01016e10	1.39709
$657$	−7.73507e9	−1.06411
$658$	4.61272e7	0.00631199
$659$	7.64937e9	1.04118	0.520591	−	0.853806i	$-0.325712\pi$
$659$	7.64937e9	1.04118	0.520591	+	0.853806i	$0.325712\pi$
$660$	6.23128e8	0.0843672
$661$	−7.98447e8	−0.107533	−0.0537664	−	0.998554i	$-0.517123\pi$
$661$	−7.98447e8	−0.107533	−0.0537664	+	0.998554i	$0.517123\pi$
$662$	−2.47828e8	−0.0332007
$663$	4.05581e8	0.0540481
$664$	5.06711e8	0.0671695
$665$	−1.45489e9	−0.191847
$666$	−2.74938e8	−0.0360640
$667$	1.04980e9	0.136982
$668$	6.14179e8	0.0797219
$669$	−1.84809e9	−0.238633
$670$	4.34671e8	0.0558340
$671$	−5.22036e9	−0.667070
$672$	6.75446e7	0.00858614
$673$	8.12788e8	0.102784	0.0513919	−	0.998679i	$-0.483634\pi$
$673$	8.12788e8	0.102784	0.0513919	+	0.998679i	$0.483634\pi$
$674$	−2.97377e8	−0.0374109
$675$	−5.97713e8	−0.0748048
$676$	−6.16375e8	−0.0767417
$677$	2.14117e9	0.265211	0.132605	−	0.991169i	$-0.457666\pi$
$677$	2.14117e9	0.265211	0.132605	+	0.991169i	$0.457666\pi$
$678$	2.89473e7	0.00356700
$679$	4.80860e9	0.589488
$680$	8.62414e8	0.105180
$681$	2.61226e8	0.0316958
$682$	3.46090e8	0.0417777
$683$	7.62669e9	0.915933	0.457967	−	0.888969i	$-0.348578\pi$
$683$	7.62669e9	0.915933	0.457967	+	0.888969i	$0.348578\pi$
$684$	−4.74883e9	−0.567402
$685$	−8.92967e9	−1.06150
$686$	−2.21668e7	−0.00262161
$687$	−1.91341e9	−0.225143
$688$	−1.47564e10	−1.72751
$689$	3.35989e9	0.391343
$690$	−4.09958e6	−0.000475081 0
$691$	1.34525e10	1.55106	0.775531	−	0.631309i	$-0.217482\pi$
$691$	1.34525e10	1.55106	0.775531	+	0.631309i	$0.217482\pi$
$692$	1.58472e10	1.81794
$693$	−2.00563e9	−0.228921
$694$	−5.79211e8	−0.0657777
$695$	4.24750e9	0.479939
$696$	2.57370e8	0.0289351
$697$	1.56674e10	1.75259
$698$	−5.04280e8	−0.0561277
$699$	7.24429e8	0.0802280
$700$	8.28209e8	0.0912635
$701$	−1.59623e10	−1.75018	−0.875088	−	0.483963i	$-0.839197\pi$
$701$	−1.59623e10	−1.75018	−0.875088	+	0.483963i	$0.839197\pi$
$702$	3.81490e7	0.00416201
$703$	4.08924e9	0.443914
$704$	−5.66665e9	−0.612100
$705$	4.35877e8	0.0468492
$706$	3.51767e7	0.00376218
$707$	−2.82149e9	−0.300269
$708$	2.66457e8	0.0282170
$709$	−1.25005e10	−1.31724	−0.658618	−	0.752477i	$-0.728859\pi$
$709$	−1.25005e10	−1.31724	−0.658618	+	0.752477i	$0.728859\pi$
$710$	−6.18267e8	−0.0648294
$711$	1.68632e10	1.75953
$712$	8.26808e8	0.0858469
$713$	9.63594e8	0.0995591
$714$	3.47826e7	0.00357618
$715$	−1.46528e9	−0.149917
$716$	4.88286e9	0.497140
$717$	−9.47654e8	−0.0960136
$718$	−3.54605e8	−0.0357527
$719$	1.11043e10	1.11414	0.557072	−	0.830464i	$-0.311925\pi$
$719$	1.11043e10	1.11414	0.557072	+	0.830464i	$0.311925\pi$
$720$	−8.44592e9	−0.843303
$721$	−5.99177e9	−0.595363
$722$	3.24118e8	0.0320496
$723$	−1.93427e9	−0.190341
$724$	6.12396e9	0.599718
$725$	4.73553e9	0.461515
$726$	−4.81296e7	−0.00466803
$727$	−3.05192e9	−0.294579	−0.147290	−	0.989093i	$-0.547055\pi$
$727$	−3.05192e9	−0.294579	−0.147290	+	0.989093i	$0.547055\pi$
$728$	−1.05846e8	−0.0101675
$729$	−8.95532e9	−0.856121
$730$	−4.84640e8	−0.0461094
$731$	−2.28869e10	−2.16709
$732$	−1.77957e9	−0.167697
$733$	−1.80025e10	−1.68838	−0.844189	−	0.536046i	$-0.819918\pi$
$733$	−1.80025e10	−1.68838	−0.844189	+	0.536046i	$0.819918\pi$
$734$	3.66152e8	0.0341763
$735$	−2.09464e8	−0.0194583
$736$	1.12822e8	0.0104309
$737$	−8.91230e9	−0.820075
$738$	7.27707e8	0.0666437
$739$	−1.04908e10	−0.956213	−0.478106	−	0.878302i	$-0.658677\pi$
$739$	−1.04908e10	−0.956213	−0.478106	+	0.878302i	$0.658677\pi$
$740$	7.29008e9	0.661335
$741$	−2.80186e8	−0.0252978
$742$	2.88144e8	0.0258938
$743$	5.26602e9	0.471001	0.235501	−	0.971874i	$-0.424327\pi$
$743$	5.26602e9	0.471001	0.235501	+	0.971874i	$0.424327\pi$
$744$	2.36237e8	0.0210301
$745$	1.65779e10	1.46887
$746$	−4.91275e8	−0.0433250
$747$	−7.69659e9	−0.675579
$748$	−8.83085e9	−0.771520
$749$	7.21673e9	0.627558
$750$	−9.48997e7	−0.00821392
$751$	−1.01137e10	−0.871309	−0.435655	−	0.900114i	$-0.643483\pi$
$751$	−1.01137e10	−0.871309	−0.435655	+	0.900114i	$0.643483\pi$
$752$	−3.98274e9	−0.341523
$753$	−3.11207e9	−0.265624
$754$	−3.02245e8	−0.0256779
$755$	−7.22992e7	−0.00611391
$756$	−1.38456e9	−0.116543
$757$	3.93196e9	0.329437	0.164719	−	0.986341i	$-0.447328\pi$
$757$	3.93196e9	0.329437	0.164719	+	0.986341i	$0.447328\pi$
$758$	−2.09441e8	−0.0174670
$759$	8.40560e7	0.00697786
$760$	−5.95779e8	−0.0492309
$761$	−1.05300e10	−0.866130	−0.433065	−	0.901363i	$-0.642568\pi$
$761$	−1.05300e10	−0.866130	−0.433065	+	0.901363i	$0.642568\pi$
$762$	−9.57588e6	−0.000784037 0
$763$	−5.54648e9	−0.452045
$764$	−5.60202e9	−0.454483
$765$	−1.30995e10	−1.05789
$766$	−3.79983e8	−0.0305467
$767$	−6.26572e8	−0.0501403
$768$	−1.91786e9	−0.152775
$769$	−1.60174e10	−1.27014	−0.635068	−	0.772457i	$-0.719028\pi$
$769$	−1.60174e10	−1.27014	−0.635068	+	0.772457i	$0.719028\pi$
$770$	−1.25663e8	−0.00991949
$771$	9.55268e7	0.00750646
$772$	−1.09539e10	−0.856857
$773$	1.47196e10	1.14622	0.573110	−	0.819479i	$-0.305737\pi$
$773$	1.47196e10	1.14622	0.573110	+	0.819479i	$0.305737\pi$
$774$	−1.06303e9	−0.0824051
$775$	4.34669e9	0.335431
$776$	1.96913e9	0.151272
$777$	5.88738e8	0.0450244
$778$	1.06943e8	0.00814183
$779$	−1.08234e10	−0.820321
$780$	−4.99501e8	−0.0376882
$781$	1.26767e10	0.952197
$782$	5.80984e7	0.00434451
$783$	−7.91662e9	−0.589350
$784$	1.91394e9	0.141848
$785$	−1.92884e10	−1.42316
$786$	1.07216e8	0.00787554
$787$	2.43275e10	1.77904	0.889519	−	0.456898i	$-0.151039\pi$
$787$	2.43275e10	1.77904	0.889519	+	0.456898i	$0.151039\pi$
$788$	1.74556e10	1.27085
$789$	1.42479e9	0.103272
$790$	1.05656e9	0.0762431
$791$	2.47047e9	0.177485
$792$	−8.21308e8	−0.0587446
$793$	4.18465e9	0.297991
$794$	7.14873e8	0.0506824
$795$	2.72281e9	0.192190
$796$	−3.94132e9	−0.276978
$797$	1.68033e10	1.17568	0.587841	−	0.808977i	$-0.299978\pi$
$797$	1.68033e10	1.17568	0.587841	+	0.808977i	$0.299978\pi$
$798$	−2.40288e7	−0.00167387
$799$	−6.17716e9	−0.428425
$800$	5.08928e8	0.0351432
$801$	−1.25586e10	−0.863433
$802$	9.00047e7	0.00616106
$803$	9.93685e9	0.677243
$804$	−3.03812e9	−0.206162
$805$	−3.49874e8	−0.0236388
$806$	−2.77427e8	−0.0186628
$807$	2.94943e9	0.197552
$808$	−1.15540e9	−0.0770537
$809$	7.50895e9	0.498608	0.249304	−	0.968425i	$-0.419798\pi$
$809$	7.50895e9	0.498608	0.249304	+	0.968425i	$0.419798\pi$
$810$	−5.92786e8	−0.0391923
$811$	−6.75371e9	−0.444600	−0.222300	−	0.974978i	$-0.571356\pi$
$811$	−6.75371e9	−0.444600	−0.222300	+	0.974978i	$0.571356\pi$
$812$	1.09695e10	0.719020
$813$	3.61125e9	0.235689
$814$	3.53198e8	0.0229527
$815$	−8.67562e9	−0.561369
$816$	−3.00322e9	−0.193496
$817$	1.58109e10	1.01433
$818$	−4.18827e8	−0.0267546
$819$	1.60772e9	0.102263
$820$	−1.92954e10	−1.22210
$821$	−8.07832e9	−0.509471	−0.254736	−	0.967011i	$-0.581988\pi$
$821$	−8.07832e9	−0.509471	−0.254736	+	0.967011i	$0.581988\pi$
$822$	−1.47481e8	−0.00926158
$823$	−1.65521e10	−1.03503	−0.517515	−	0.855674i	$-0.673143\pi$
$823$	−1.65521e10	−1.03503	−0.517515	+	0.855674i	$0.673143\pi$
$824$	−2.45363e9	−0.152779
$825$	3.79169e8	0.0235095
$826$	−5.37348e7	−0.00331761
$827$	1.96996e10	1.21112	0.605562	−	0.795798i	$-0.292949\pi$
$827$	1.96996e10	1.21112	0.605562	+	0.795798i	$0.292949\pi$
$828$	−1.14201e9	−0.0699136
$829$	−2.44679e10	−1.49161	−0.745806	−	0.666163i	$-0.767936\pi$
$829$	−2.44679e10	−1.49161	−0.745806	+	0.666163i	$0.767936\pi$
$830$	−4.82229e8	−0.0292739
$831$	2.69130e9	0.162689
$832$	4.54240e9	0.273435
$833$	2.96849e9	0.177942
$834$	7.01510e7	0.00418748
$835$	−1.17039e9	−0.0695710
$836$	6.10059e9	0.361118
$837$	−7.26657e9	−0.428342
$838$	−5.11172e8	−0.0300064
$839$	−1.06062e10	−0.620000	−0.310000	−	0.950737i	$-0.600329\pi$
$839$	−1.06062e10	−0.620000	−0.310000	+	0.950737i	$0.600329\pi$
$840$	−8.57757e7	−0.00499329
$841$	4.54715e10	2.63605
$842$	−8.81160e8	−0.0508701
$843$	5.99568e8	0.0344701
$844$	−1.92585e9	−0.110261
$845$	1.17458e9	0.0669703
$846$	−2.86913e8	−0.0162912
$847$	−4.10756e9	−0.232270
$848$	−2.48791e10	−1.40104
$849$	−5.19212e8	−0.0291184
$850$	2.62077e8	0.0146373
$851$	9.83385e8	0.0546978
$852$	4.32136e9	0.239377
$853$	−1.19077e9	−0.0656910	−0.0328455	−	0.999460i	$-0.510457\pi$
$853$	−1.19077e9	−0.0656910	−0.0328455	+	0.999460i	$0.510457\pi$
$854$	3.58876e8	0.0197170
$855$	9.04946e9	0.495155
$856$	2.95526e9	0.161041
$857$	−7.42022e9	−0.402702	−0.201351	−	0.979519i	$-0.564533\pi$
$857$	−7.42022e9	−0.402702	−0.201351	+	0.979519i	$0.564533\pi$
$858$	−2.42004e7	−0.00130803
$859$	1.99014e10	1.07129	0.535647	−	0.844442i	$-0.320068\pi$
$859$	1.99014e10	1.07129	0.535647	+	0.844442i	$0.320068\pi$
$860$	2.81868e10	1.51113
$861$	−1.55827e9	−0.0832019
$862$	−7.43315e8	−0.0395273
$863$	−6.82432e9	−0.361428	−0.180714	−	0.983536i	$-0.557841\pi$
$863$	−6.82432e9	−0.361428	−0.180714	+	0.983536i	$0.557841\pi$
$864$	−8.50800e8	−0.0448776
$865$	−3.01987e10	−1.58647
$866$	5.77146e8	0.0301976
$867$	−1.65572e9	−0.0862818
$868$	1.00688e10	0.522586
$869$	−2.16633e10	−1.11984
$870$	−2.44935e8	−0.0126105
$871$	7.14412e9	0.366341
$872$	−2.27129e9	−0.116002
$873$	−2.99096e10	−1.52146
$874$	−4.01359e7	−0.00203350
$875$	−8.09911e9	−0.408704
$876$	3.38738e9	0.170255
$877$	1.82075e10	0.911490	0.455745	−	0.890110i	$-0.349373\pi$
$877$	1.82075e10	0.911490	0.455745	+	0.890110i	$0.349373\pi$
$878$	−1.16343e9	−0.0580110
$879$	1.56778e9	0.0778616
$880$	1.08501e10	0.536713
$881$	2.79623e9	0.137771	0.0688855	−	0.997625i	$-0.478056\pi$
$881$	2.79623e9	0.137771	0.0688855	+	0.997625i	$0.478056\pi$
$882$	1.37878e8	0.00676637
$883$	−7.65854e9	−0.374355	−0.187177	−	0.982326i	$-0.559934\pi$
$883$	−7.65854e9	−0.374355	−0.187177	+	0.982326i	$0.559934\pi$
$884$	7.07883e9	0.344650
$885$	−5.07765e8	−0.0246241
$886$	−3.31127e7	−0.00159947
$887$	3.53568e10	1.70114	0.850571	−	0.525861i	$-0.176257\pi$
$887$	3.53568e10	1.70114	0.850571	+	0.525861i	$0.176257\pi$
$888$	2.41088e8	0.0115540
$889$	−8.17243e8	−0.0390117
$890$	−7.86860e8	−0.0374139
$891$	1.21542e10	0.575646
$892$	−3.22557e10	−1.52170
$893$	4.26735e9	0.200529
$894$	2.73798e8	0.0128159
$895$	−9.30486e9	−0.433840
$896$	1.57124e9	0.0729732
$897$	−6.73795e7	−0.00311712
$898$	1.20202e9	0.0553917
$899$	5.75712e10	2.64269
$900$	−5.15148e9	−0.235550
$901$	−3.85871e10	−1.75754
$902$	−9.34848e8	−0.0424149
$903$	2.27633e9	0.102879
$904$	1.01166e9	0.0455454
$905$	−1.16699e10	−0.523357
$906$	−1.19408e6	−5.33441e−5 0
$907$	1.11669e10	0.496945	0.248472	−	0.968639i	$-0.420071\pi$
$907$	1.11669e10	0.496945	0.248472	+	0.968639i	$0.420071\pi$
$908$	4.55932e9	0.202116
$909$	1.75497e10	0.774992
$910$	1.00732e8	0.00443120
$911$	2.77023e10	1.21395	0.606975	−	0.794721i	$-0.292383\pi$
$911$	2.77023e10	1.21395	0.606975	+	0.794721i	$0.292383\pi$
$912$	2.07471e9	0.0905680
$913$	9.88742e9	0.429967
$914$	−2.16852e8	−0.00939401
$915$	3.39118e9	0.146345
$916$	−3.33958e10	−1.43568
$917$	9.15023e9	0.391867
$918$	−4.38126e8	−0.0186918
$919$	−1.11405e10	−0.473479	−0.236740	−	0.971573i	$-0.576079\pi$
$919$	−1.11405e10	−0.473479	−0.236740	+	0.971573i	$0.576079\pi$
$920$	−1.43274e8	−0.00606609
$921$	1.92994e9	0.0814018
$922$	−1.18286e9	−0.0497021
$923$	−1.01617e10	−0.425362
$924$	8.78316e8	0.0366268
$925$	4.43596e9	0.184286
$926$	−8.48616e8	−0.0351215
$927$	3.72690e10	1.53663
$928$	6.74068e9	0.276876
$929$	2.69601e10	1.10323	0.551615	−	0.834099i	$-0.314012\pi$
$929$	2.69601e10	1.10323	0.551615	+	0.834099i	$0.314012\pi$
$930$	−2.24823e8	−0.00916537
$931$	−2.05071e9	−0.0832875
$932$	1.26439e10	0.511593
$933$	3.58797e9	0.144632
$934$	2.23165e9	0.0896214
$935$	1.68282e10	0.673283
$936$	6.58363e8	0.0262422
$937$	−3.03153e9	−0.120385	−0.0601927	−	0.998187i	$-0.519172\pi$
$937$	−3.03153e9	−0.120385	−0.0601927	+	0.998187i	$0.519172\pi$
$938$	6.12680e8	0.0242395
$939$	3.20389e9	0.126284
$940$	7.60761e9	0.298745
$941$	4.57147e10	1.78851	0.894257	−	0.447554i	$-0.147705\pi$
$941$	4.57147e10	1.78851	0.894257	+	0.447554i	$0.147705\pi$
$942$	−3.18565e8	−0.0124171
$943$	−2.60283e9	−0.101078
$944$	4.63960e9	0.179506
$945$	2.63844e9	0.101703
$946$	1.36563e9	0.0524461
$947$	3.88161e10	1.48521	0.742603	−	0.669732i	$-0.233591\pi$
$947$	3.88161e10	1.48521	0.742603	+	0.669732i	$0.233591\pi$
$948$	−7.38481e9	−0.281521
$949$	−7.96540e9	−0.302535
$950$	−1.81050e8	−0.00685117
$951$	−7.08837e9	−0.267248
$952$	1.21560e9	0.0456625
$953$	−1.87841e10	−0.703015	−0.351507	−	0.936185i	$-0.614331\pi$
$953$	−1.87841e10	−0.703015	−0.351507	+	0.936185i	$0.614331\pi$
$954$	−1.79227e9	−0.0668318
$955$	1.06753e10	0.396615
$956$	−1.65399e10	−0.612253
$957$	5.02204e9	0.185220
$958$	2.14145e7	0.000786916 0
$959$	−1.25866e10	−0.460833
$960$	3.68110e9	0.134285
$961$	2.53313e10	0.920717
$962$	−2.83125e8	−0.0102533
$963$	−4.48883e10	−1.61972
$964$	−3.37599e10	−1.21376
$965$	2.08740e10	0.747755
$966$	−5.77847e6	−0.000206249 0
$967$	4.94026e10	1.75694	0.878470	−	0.477797i	$-0.158565\pi$
$967$	4.94026e10	1.75694	0.878470	+	0.477797i	$0.158565\pi$
$968$	−1.68205e9	−0.0596040
$969$	3.21783e9	0.113614
$970$	−1.87399e9	−0.0659273
$971$	−3.71001e10	−1.30049	−0.650246	−	0.759724i	$-0.725334\pi$
$971$	−3.71001e10	−1.30049	−0.650246	+	0.759724i	$0.725334\pi$
$972$	1.29713e10	0.453057
$973$	5.98696e9	0.208359
$974$	−2.51945e9	−0.0873675
$975$	−3.03943e8	−0.0105021
$976$	−3.09863e10	−1.06683
$977$	−2.83863e10	−0.973818	−0.486909	−	0.873453i	$-0.661876\pi$
$977$	−2.83863e10	−0.973818	−0.486909	+	0.873453i	$0.661876\pi$
$978$	−1.43285e8	−0.00489796
$979$	1.61334e10	0.549525
$980$	−3.65590e9	−0.124080
$981$	3.44992e10	1.16672
$982$	5.24689e8	0.0176812
$983$	−4.65415e10	−1.56280	−0.781399	−	0.624032i	$-0.785494\pi$
$983$	−4.65415e10	−1.56280	−0.781399	+	0.624032i	$0.785494\pi$
$984$	−6.38114e8	−0.0213509
$985$	−3.32637e10	−1.10903
$986$	3.47117e9	0.115320
$987$	6.14380e8	0.0203389
$988$	−4.89025e9	−0.161317
$989$	3.80222e9	0.124983
$990$	7.81626e8	0.0256021
$991$	5.09337e10	1.66245	0.831223	−	0.555939i	$-0.187641\pi$
$991$	5.09337e10	1.66245	0.831223	+	0.555939i	$0.187641\pi$
$992$	6.18719e9	0.201234
$993$	−3.30089e9	−0.106981
$994$	−8.71464e8	−0.0281447
$995$	7.51064e9	0.241711
$996$	3.37053e9	0.108091
$997$	−6.39183e9	−0.204264	−0.102132	−	0.994771i	$-0.532566\pi$
$997$	−6.39183e9	−0.204264	−0.102132	+	0.994771i	$0.532566\pi$
$998$	1.00160e9	0.0318961
$999$	−7.41581e9	−0.235331

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.c.1.6	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.c.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-0.549314 q^{2} -7.31646 q^{3} -127.698 q^{4} +243.344 q^{5} +4.01903 q^{6} +343.000 q^{7} +140.459 q^{8} -2133.47 q^{9} +O(q^{10})\)	\(q-0.549314 q^{2} -7.31646 q^{3} -127.698 q^{4} +243.344 q^{5} +4.01903 q^{6} +343.000 q^{7} +140.459 q^{8} -2133.47 q^{9} -133.672 q^{10} +2740.76 q^{11} +934.299 q^{12} -2197.00 q^{13} -188.415 q^{14} -1780.42 q^{15} +16268.2 q^{16} +25231.7 q^{17} +1171.95 q^{18} -17430.7 q^{19} -31074.6 q^{20} -2509.55 q^{21} -1505.54 q^{22} -4191.76 q^{23} -1027.66 q^{24} -18908.7 q^{25} +1206.84 q^{26} +31610.5 q^{27} -43800.5 q^{28} -250442. q^{29} +978.008 q^{30} -229878. q^{31} -26915.1 q^{32} -20052.7 q^{33} -13860.1 q^{34} +83467.0 q^{35} +272440. q^{36} -234599. q^{37} +9574.95 q^{38} +16074.3 q^{39} +34179.8 q^{40} +620939. q^{41} +1378.53 q^{42} -907069. q^{43} -349990. q^{44} -519167. q^{45} +2302.59 q^{46} -244817. q^{47} -119026. q^{48} +117649. q^{49} +10386.8 q^{50} -184607. q^{51} +280553. q^{52} -1.52931e6 q^{53} -17364.1 q^{54} +666948. q^{55} +48177.3 q^{56} +127531. q^{57} +137572. q^{58} +285194. q^{59} +227356. q^{60} -1.90471e6 q^{61} +126275. q^{62} -731780. q^{63} -2.06755e6 q^{64} -534627. q^{65} +11015.2 q^{66} -3.25176e6 q^{67} -3.22205e6 q^{68} +30668.9 q^{69} -45849.6 q^{70} +4.62524e6 q^{71} -299664. q^{72} +3.62558e6 q^{73} +128869. q^{74} +138345. q^{75} +2.22587e6 q^{76} +940081. q^{77} -8829.82 q^{78} -7.90412e6 q^{79} +3.95877e6 q^{80} +4.43462e6 q^{81} -341091. q^{82} +3.60755e6 q^{83} +320465. q^{84} +6.13999e6 q^{85} +498266. q^{86} +1.83235e6 q^{87} +384964. q^{88} +5.88648e6 q^{89} +285186. q^{90} -753571. q^{91} +535281. q^{92} +1.68189e6 q^{93} +134482. q^{94} -4.24167e6 q^{95} +196923. q^{96} +1.40193e7 q^{97} -64626.3 q^{98} -5.84733e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9}+O(q^{10}) \) 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

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more