LMFDB - Embedded newform 91.8.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(1,91)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.4270373191$
Analytic rank:	$1$
Dimension:	$10$
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			1.3
Root			$-11.8703$ 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)

$f(q)$	$=$	$q-13.8703 q^{2} +79.8279 q^{3} +64.3848 q^{4} -355.678 q^{5} -1107.24 q^{6} +343.000 q^{7} +882.360 q^{8} +4185.49 q^{9} +O(q^{10})$	\(q-13.8703 q^{2} +79.8279 q^{3} +64.3848 q^{4} -355.678 q^{5} -1107.24 q^{6} +343.000 q^{7} +882.360 q^{8} +4185.49 q^{9} +4933.36 q^{10} -3979.36 q^{11} +5139.70 q^{12} -2197.00 q^{13} -4757.51 q^{14} -28393.0 q^{15} -20479.9 q^{16} +32013.6 q^{17} -58053.9 q^{18} -34677.2 q^{19} -22900.3 q^{20} +27381.0 q^{21} +55194.8 q^{22} -35204.9 q^{23} +70436.9 q^{24} +48382.1 q^{25} +30473.0 q^{26} +159535. q^{27} +22084.0 q^{28} -161052. q^{29} +393820. q^{30} +315216. q^{31} +171119. q^{32} -317663. q^{33} -444038. q^{34} -121998. q^{35} +269482. q^{36} -447106. q^{37} +480982. q^{38} -175382. q^{39} -313836. q^{40} -587312. q^{41} -379782. q^{42} +431518. q^{43} -256210. q^{44} -1.48869e6 q^{45} +488302. q^{46} -1.09626e6 q^{47} -1.63486e6 q^{48} +117649. q^{49} -671074. q^{50} +2.55558e6 q^{51} -141454. q^{52} -1.10769e6 q^{53} -2.21280e6 q^{54} +1.41537e6 q^{55} +302650. q^{56} -2.76820e6 q^{57} +2.23383e6 q^{58} -2.03028e6 q^{59} -1.82808e6 q^{60} -110314. q^{61} -4.37214e6 q^{62} +1.43562e6 q^{63} +247948. q^{64} +781425. q^{65} +4.40608e6 q^{66} -1.31986e6 q^{67} +2.06119e6 q^{68} -2.81033e6 q^{69} +1.69214e6 q^{70} -3.26258e6 q^{71} +3.69311e6 q^{72} +407628. q^{73} +6.20149e6 q^{74} +3.86224e6 q^{75} -2.23268e6 q^{76} -1.36492e6 q^{77} +2.43260e6 q^{78} -4.59608e6 q^{79} +7.28424e6 q^{80} +3.58167e6 q^{81} +8.14619e6 q^{82} -2.19125e6 q^{83} +1.76292e6 q^{84} -1.13866e7 q^{85} -5.98528e6 q^{86} -1.28564e7 q^{87} -3.51123e6 q^{88} +8.51992e6 q^{89} +2.06485e7 q^{90} -753571. q^{91} -2.26666e6 q^{92} +2.51630e7 q^{93} +1.52055e7 q^{94} +1.23339e7 q^{95} +1.36601e7 q^{96} +873334. q^{97} -1.63183e6 q^{98} -1.66555e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−13.8703	−1.22597	−0.612986	−	0.790094i	$-0.710032\pi$
$2$	−13.8703	−1.22597	−0.612986	+	0.790094i	$0.710032\pi$
$3$	79.8279	1.70699	0.853493	−	0.521104i	$-0.174480\pi$
$3$	79.8279	1.70699	0.853493	+	0.521104i	$0.174480\pi$
$4$	64.3848	0.503007
$5$	−355.678	−1.27251	−0.636257	−	0.771477i	$-0.719518\pi$
$5$	−355.678	−1.27251	−0.636257	+	0.771477i	$0.719518\pi$
$6$	−1107.24	−2.09272
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	882.360	0.609300
$9$	4185.49	1.91380
$10$	4933.36	1.56007
$11$	−3979.36	−0.901443	−0.450722	−	0.892665i	$-0.648833\pi$
$11$	−3979.36	−0.901443	−0.450722	+	0.892665i	$0.648833\pi$
$12$	5139.70	0.858626
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−4757.51	−0.463374
$15$	−28393.0	−2.17216
$16$	−20479.9	−1.24999
$17$	32013.6	1.58039	0.790194	−	0.612857i	$-0.209980\pi$
$17$	32013.6	1.58039	0.790194	+	0.612857i	$0.209980\pi$
$18$	−58053.9	−2.34627
$19$	−34677.2	−1.15986	−0.579930	−	0.814666i	$-0.696920\pi$
$19$	−34677.2	−1.15986	−0.579930	+	0.814666i	$0.696920\pi$
$20$	−22900.3	−0.640083
$21$	27381.0	0.645180
$22$	55194.8	1.10514
$23$	−35204.9	−0.603331	−0.301666	−	0.953414i	$-0.597543\pi$
$23$	−35204.9	−0.603331	−0.301666	+	0.953414i	$0.597543\pi$
$24$	70436.9	1.04007
$25$	48382.1	0.619291
$26$	30473.0	0.340023
$27$	159535.	1.55985
$28$	22084.0	0.190119
$29$	−161052.	−1.22623	−0.613116	−	0.789993i	$-0.710084\pi$
$29$	−161052.	−1.22623	−0.613116	+	0.789993i	$0.710084\pi$
$30$	393820.	2.66301
$31$	315216.	1.90039	0.950195	−	0.311656i	$-0.100884\pi$
$31$	315216.	1.90039	0.950195	+	0.311656i	$0.100884\pi$
$32$	171119.	0.923154
$33$	−317663.	−1.53875
$34$	−444038.	−1.93751
$35$	−121998.	−0.480965
$36$	269482.	0.962656
$37$	−447106.	−1.45112	−0.725562	−	0.688156i	$-0.758420\pi$
$37$	−447106.	−1.45112	−0.725562	+	0.688156i	$0.758420\pi$
$38$	480982.	1.42196
$39$	−175382.	−0.473433
$40$	−313836.	−0.775342
$41$	−587312.	−1.33084	−0.665419	−	0.746470i	$-0.731747\pi$
$41$	−587312.	−1.33084	−0.665419	+	0.746470i	$0.731747\pi$
$42$	−379782.	−0.790973
$43$	431518.	0.827674	0.413837	−	0.910351i	$-0.364188\pi$
$43$	431518.	0.827674	0.413837	+	0.910351i	$0.364188\pi$
$44$	−256210.	−0.453432
$45$	−1.48869e6	−2.43534
$46$	488302.	0.739667
$47$	−1.09626e6	−1.54018	−0.770092	−	0.637933i	$-0.779790\pi$
$47$	−1.09626e6	−1.54018	−0.770092	+	0.637933i	$0.779790\pi$
$48$	−1.63486e6	−2.13372
$49$	117649.	0.142857
$50$	−671074.	−0.759233
$51$	2.55558e6	2.69770
$52$	−141454.	−0.139509
$53$	−1.10769e6	−1.02200	−0.511001	−	0.859580i	$-0.670725\pi$
$53$	−1.10769e6	−1.02200	−0.511001	+	0.859580i	$0.670725\pi$
$54$	−2.21280e6	−1.91233
$55$	1.41537e6	1.14710
$56$	302650.	0.230294
$57$	−2.76820e6	−1.97987
$58$	2.23383e6	1.50333
$59$	−2.03028e6	−1.28698	−0.643492	−	0.765453i	$-0.722515\pi$
$59$	−2.03028e6	−1.28698	−0.643492	+	0.765453i	$0.722515\pi$
$60$	−1.82808e6	−1.09261
$61$	−110314.	−0.0622268	−0.0311134	−	0.999516i	$-0.509905\pi$
$61$	−110314.	−0.0622268	−0.0311134	+	0.999516i	$0.509905\pi$
$62$	−4.37214e6	−2.32982
$63$	1.43562e6	0.723350
$64$	247948.	0.118231
$65$	781425.	0.352932
$66$	4.40608e6	1.88647
$67$	−1.31986e6	−0.536124	−0.268062	−	0.963402i	$-0.586383\pi$
$67$	−1.31986e6	−0.536124	−0.268062	+	0.963402i	$0.586383\pi$
$68$	2.06119e6	0.794946
$69$	−2.81033e6	−1.02988
$70$	1.69214e6	0.589649
$71$	−3.26258e6	−1.08182	−0.540912	−	0.841079i	$-0.681921\pi$
$71$	−3.26258e6	−1.08182	−0.540912	+	0.841079i	$0.681921\pi$
$72$	3.69311e6	1.16608
$73$	407628.	0.122640	0.0613202	−	0.998118i	$-0.480469\pi$
$73$	407628.	0.122640	0.0613202	+	0.998118i	$0.480469\pi$
$74$	6.20149e6	1.77904
$75$	3.86224e6	1.05712
$76$	−2.23268e6	−0.583418
$77$	−1.36492e6	−0.340714
$78$	2.43260e6	0.580415
$79$	−4.59608e6	−1.04880	−0.524400	−	0.851472i	$-0.675710\pi$
$79$	−4.59608e6	−1.04880	−0.524400	+	0.851472i	$0.675710\pi$
$80$	7.28424e6	1.59063
$81$	3.58167e6	0.748839
$82$	8.14619e6	1.63157
$83$	−2.19125e6	−0.420647	−0.210324	−	0.977632i	$-0.567452\pi$
$83$	−2.19125e6	−0.420647	−0.210324	+	0.977632i	$0.567452\pi$
$84$	1.76292e6	0.324530
$85$	−1.13866e7	−2.01107
$86$	−5.98528e6	−1.01471
$87$	−1.28564e7	−2.09316
$88$	−3.51123e6	−0.549249
$89$	8.51992e6	1.28106	0.640531	−	0.767932i	$-0.278714\pi$
$89$	8.51992e6	1.28106	0.640531	+	0.767932i	$0.278714\pi$
$90$	2.06485e7	2.98566
$91$	−753571.	−0.104828
$92$	−2.26666e6	−0.303480
$93$	2.51630e7	3.24394
$94$	1.52055e7	1.88822
$95$	1.23339e7	1.47594
$96$	1.36601e7	1.57581
$97$	873334.	0.0971582	0.0485791	−	0.998819i	$-0.484531\pi$
$97$	873334.	0.0971582	0.0485791	+	0.998819i	$0.484531\pi$
$98$	−1.63183e6	−0.175139
$99$	−1.66555e7	−1.72518
$100$	3.11507e6	0.311507
$101$	−5.58428e6	−0.539314	−0.269657	−	0.962956i	$-0.586910\pi$
$101$	−5.58428e6	−0.539314	−0.269657	+	0.962956i	$0.586910\pi$
$102$	−3.54466e7	−3.30731
$103$	1.80633e6	0.162880	0.0814400	−	0.996678i	$-0.474048\pi$
$103$	1.80633e6	0.162880	0.0814400	+	0.996678i	$0.474048\pi$
$104$	−1.93855e6	−0.168989
$105$	−9.73881e6	−0.821001
$106$	1.53639e7	1.25294
$107$	−9.37855e6	−0.740104	−0.370052	−	0.929011i	$-0.620660\pi$
$107$	−9.37855e6	−0.740104	−0.370052	+	0.929011i	$0.620660\pi$
$108$	1.02716e7	0.784615
$109$	1.54390e6	0.114189	0.0570947	−	0.998369i	$-0.481816\pi$
$109$	1.54390e6	0.114189	0.0570947	+	0.998369i	$0.481816\pi$
$110$	−1.96316e7	−1.40631
$111$	−3.56915e7	−2.47705
$112$	−7.02459e6	−0.472452
$113$	−9.80155e6	−0.639029	−0.319514	−	0.947581i	$-0.603520\pi$
$113$	−9.80155e6	−0.639029	−0.319514	+	0.947581i	$0.603520\pi$
$114$	3.83958e7	2.42726
$115$	1.25216e7	0.767747
$116$	−1.03693e7	−0.616803
$117$	−9.19552e6	−0.530793
$118$	2.81605e7	1.57781
$119$	1.09807e7	0.597331
$120$	−2.50529e7	−1.32350
$121$	−3.65190e6	−0.187400
$122$	1.53009e6	0.0762884
$123$	−4.68839e7	−2.27172
$124$	2.02952e7	0.955909
$125$	1.05789e7	0.484458
$126$	−1.99125e7	−0.886806
$127$	3.75328e7	1.62592	0.812958	−	0.582322i	$-0.197856\pi$
$127$	3.75328e7	1.62592	0.812958	+	0.582322i	$0.197856\pi$
$128$	−2.53424e7	−1.06810
$129$	3.44472e7	1.41283
$130$	−1.08386e7	−0.432684
$131$	4.29410e7	1.66887	0.834435	−	0.551106i	$-0.185794\pi$
$131$	4.29410e7	1.66887	0.834435	+	0.551106i	$0.185794\pi$
$132$	−2.04527e7	−0.774002
$133$	−1.18943e7	−0.438386
$134$	1.83068e7	0.657273
$135$	−5.67431e7	−1.98493
$136$	2.82476e7	0.962930
$137$	7.74050e6	0.257186	0.128593	−	0.991697i	$-0.458954\pi$
$137$	7.74050e6	0.257186	0.128593	+	0.991697i	$0.458954\pi$
$138$	3.89801e7	1.26260
$139$	4.54639e7	1.43587	0.717934	−	0.696111i	$-0.245088\pi$
$139$	4.54639e7	1.43587	0.717934	+	0.696111i	$0.245088\pi$
$140$	−7.85480e6	−0.241929
$141$	−8.75124e7	−2.62907
$142$	4.52529e7	1.32629
$143$	8.74265e6	0.250015
$144$	−8.57182e7	−2.39224
$145$	5.72826e7	1.56040
$146$	−5.65391e6	−0.150354
$147$	9.39167e6	0.243855
$148$	−2.87869e7	−0.729925
$149$	5.27216e7	1.30568	0.652840	−	0.757496i	$-0.273577\pi$
$149$	5.27216e7	1.30568	0.652840	+	0.757496i	$0.273577\pi$
$150$	−5.35704e7	−1.29600
$151$	4.93290e7	1.16596	0.582980	−	0.812487i	$-0.301887\pi$
$151$	4.93290e7	1.16596	0.582980	+	0.812487i	$0.301887\pi$
$152$	−3.05978e7	−0.706703
$153$	1.33993e8	3.02455
$154$	1.89318e7	0.417705
$155$	−1.12116e8	−2.41827
$156$	−1.12919e7	−0.238140
$157$	−3.07184e7	−0.633504	−0.316752	−	0.948508i	$-0.602592\pi$
$157$	−3.07184e7	−0.633504	−0.316752	+	0.948508i	$0.602592\pi$
$158$	6.37489e7	1.28580
$159$	−8.84243e7	−1.74454
$160$	−6.08634e7	−1.17473
$161$	−1.20753e7	−0.228038
$162$	−4.96788e7	−0.918055
$163$	3.29657e7	0.596220	0.298110	−	0.954532i	$-0.403644\pi$
$163$	3.29657e7	0.596220	0.298110	+	0.954532i	$0.403644\pi$
$164$	−3.78140e7	−0.669421
$165$	1.12986e8	1.95808
$166$	3.03932e7	0.515702
$167$	−9.08175e7	−1.50890	−0.754452	−	0.656355i	$-0.772097\pi$
$167$	−9.08175e7	−1.50890	−0.754452	+	0.656355i	$0.772097\pi$
$168$	2.41599e7	0.393108
$169$	4.82681e6	0.0769231
$170$	1.57935e8	2.46551
$171$	−1.45141e8	−2.21975
$172$	2.77832e7	0.416326
$173$	−1.39067e7	−0.204203	−0.102102	−	0.994774i	$-0.532557\pi$
$173$	−1.39067e7	−0.204203	−0.102102	+	0.994774i	$0.532557\pi$
$174$	1.78322e8	2.56616
$175$	1.65951e7	0.234070
$176$	8.14966e7	1.12680
$177$	−1.62073e8	−2.19687
$178$	−1.18174e8	−1.57055
$179$	2.69587e7	0.351328	0.175664	−	0.984450i	$-0.443793\pi$
$179$	2.69587e7	0.351328	0.175664	+	0.984450i	$0.443793\pi$
$180$	−9.58489e7	−1.22499
$181$	3.88926e7	0.487520	0.243760	−	0.969836i	$-0.421619\pi$
$181$	3.88926e7	0.487520	0.243760	+	0.969836i	$0.421619\pi$
$182$	1.04522e7	0.128517
$183$	−8.80616e6	−0.106220
$184$	−3.10634e7	−0.367610
$185$	1.59026e8	1.84658
$186$	−3.49019e8	−3.97698
$187$	−1.27394e8	−1.42463
$188$	−7.05828e7	−0.774723
$189$	5.47205e7	0.589568
$190$	−1.71075e8	−1.80946
$191$	−2.69097e7	−0.279442	−0.139721	−	0.990191i	$-0.544621\pi$
$191$	−2.69097e7	−0.279442	−0.139721	+	0.990191i	$0.544621\pi$
$192$	1.97931e7	0.201818
$193$	1.04743e7	0.104876	0.0524379	−	0.998624i	$-0.483301\pi$
$193$	1.04743e7	0.104876	0.0524379	+	0.998624i	$0.483301\pi$
$194$	−1.21134e7	−0.119113
$195$	6.23795e7	0.602450
$196$	7.57481e6	0.0718581
$197$	−1.22552e8	−1.14206	−0.571028	−	0.820931i	$-0.693455\pi$
$197$	−1.22552e8	−1.14206	−0.571028	+	0.820931i	$0.693455\pi$
$198$	2.31017e8	2.11503
$199$	−9.91158e7	−0.891573	−0.445787	−	0.895139i	$-0.647076\pi$
$199$	−9.91158e7	−0.891573	−0.445787	+	0.895139i	$0.647076\pi$
$200$	4.26904e7	0.377334
$201$	−1.05361e8	−0.915157
$202$	7.74555e7	0.661184
$203$	−5.52408e7	−0.463472
$204$	1.64541e8	1.35696
$205$	2.08894e8	1.69351
$206$	−2.50544e7	−0.199686
$207$	−1.47350e8	−1.15466
$208$	4.49942e7	0.346685
$209$	1.37993e8	1.04555
$210$	1.35080e8	1.00652
$211$	−1.01960e8	−0.747208	−0.373604	−	0.927588i	$-0.621878\pi$
$211$	−1.01960e8	−0.747208	−0.373604	+	0.927588i	$0.621878\pi$
$212$	−7.13183e7	−0.514074
$213$	−2.60445e8	−1.84666
$214$	1.30083e8	0.907346
$215$	−1.53482e8	−1.05323
$216$	1.40767e8	0.950416
$217$	1.08119e8	0.718280
$218$	−2.14143e7	−0.139993
$219$	3.25400e7	0.209345
$220$	9.11284e7	0.576998
$221$	−7.03340e7	−0.438321
$222$	4.95052e8	3.03679
$223$	5.67905e7	0.342933	0.171466	−	0.985190i	$-0.445150\pi$
$223$	5.67905e7	0.342933	0.171466	+	0.985190i	$0.445150\pi$
$224$	5.86939e7	0.348919
$225$	2.02503e8	1.18520
$226$	1.35950e8	0.783431
$227$	−1.67421e8	−0.949991	−0.474996	−	0.879988i	$-0.657550\pi$
$227$	−1.67421e8	−0.949991	−0.474996	+	0.879988i	$0.657550\pi$
$228$	−1.78230e8	−0.995886
$229$	1.05222e8	0.579006	0.289503	−	0.957177i	$-0.406510\pi$
$229$	1.05222e8	0.579006	0.289503	+	0.957177i	$0.406510\pi$
$230$	−1.73679e8	−0.941237
$231$	−1.08959e8	−0.581593
$232$	−1.42106e8	−0.747143
$233$	3.42604e7	0.177438	0.0887190	−	0.996057i	$-0.471723\pi$
$233$	3.42604e7	0.177438	0.0887190	+	0.996057i	$0.471723\pi$
$234$	1.27544e8	0.650738
$235$	3.89917e8	1.95991
$236$	−1.30719e8	−0.647362
$237$	−3.66895e8	−1.79029
$238$	−1.52305e8	−0.732310
$239$	3.17143e7	0.150267	0.0751333	−	0.997174i	$-0.476062\pi$
$239$	3.17143e7	0.150267	0.0751333	+	0.997174i	$0.476062\pi$
$240$	5.81485e8	2.71518
$241$	2.50536e8	1.15295	0.576475	−	0.817115i	$-0.304428\pi$
$241$	2.50536e8	1.15295	0.576475	+	0.817115i	$0.304428\pi$
$242$	5.06528e7	0.229747
$243$	−6.29856e7	−0.281591
$244$	−7.10258e6	−0.0313005
$245$	−4.18452e7	−0.181788
$246$	6.50293e8	2.78507
$247$	7.61857e7	0.321688
$248$	2.78134e8	1.15791
$249$	−1.74923e8	−0.718039
$250$	−1.46732e8	−0.593931
$251$	2.16608e8	0.864604	0.432302	−	0.901729i	$-0.357701\pi$
$251$	2.16608e8	0.864604	0.432302	+	0.901729i	$0.357701\pi$
$252$	9.24323e7	0.363850
$253$	1.40093e8	0.543869
$254$	−5.20591e8	−1.99333
$255$	−9.08965e8	−3.43286
$256$	3.19769e8	1.19123
$257$	3.60809e8	1.32590	0.662951	−	0.748663i	$-0.269304\pi$
$257$	3.60809e8	1.32590	0.662951	+	0.748663i	$0.269304\pi$
$258$	−4.77792e8	−1.73209
$259$	−1.53357e8	−0.548474
$260$	5.03120e7	0.177527
$261$	−6.74080e8	−2.34677
$262$	−5.95604e8	−2.04599
$263$	−1.31833e8	−0.446868	−0.223434	−	0.974719i	$-0.571727\pi$
$263$	−1.31833e8	−0.446868	−0.223434	+	0.974719i	$0.571727\pi$
$264$	−2.80294e8	−0.937561
$265$	3.93980e8	1.30051
$266$	1.64977e8	0.537449
$267$	6.80127e8	2.18676
$268$	−8.49789e7	−0.269674
$269$	−4.41342e8	−1.38243	−0.691214	−	0.722650i	$-0.742924\pi$
$269$	−4.41342e8	−1.38243	−0.691214	+	0.722650i	$0.742924\pi$
$270$	7.87043e8	2.43347
$271$	9.33068e7	0.284787	0.142394	−	0.989810i	$-0.454520\pi$
$271$	9.33068e7	0.284787	0.142394	+	0.989810i	$0.454520\pi$
$272$	−6.55635e8	−1.97547
$273$	−6.01560e7	−0.178941
$274$	−1.07363e8	−0.315303
$275$	−1.92530e8	−0.558256
$276$	−1.80943e8	−0.518036
$277$	−3.16655e8	−0.895173	−0.447587	−	0.894241i	$-0.647716\pi$
$277$	−3.16655e8	−0.895173	−0.447587	+	0.894241i	$0.647716\pi$
$278$	−6.30597e8	−1.76033
$279$	1.31933e9	3.63697
$280$	−1.07646e8	−0.293052
$281$	3.44291e8	0.925665	0.462833	−	0.886446i	$-0.346833\pi$
$281$	3.44291e8	0.925665	0.462833	+	0.886446i	$0.346833\pi$
$282$	1.21382e9	3.22317
$283$	−1.03740e8	−0.272077	−0.136039	−	0.990704i	$-0.543437\pi$
$283$	−1.03740e8	−0.272077	−0.136039	+	0.990704i	$0.543437\pi$
$284$	−2.10061e8	−0.544165
$285$	9.84590e8	2.51941
$286$	−1.21263e8	−0.306512
$287$	−2.01448e8	−0.503010
$288$	7.16218e8	1.76673
$289$	6.14534e8	1.49763
$290$	−7.94527e8	−1.91300
$291$	6.97164e7	0.165848
$292$	2.62450e7	0.0616889
$293$	8.26629e8	1.91988	0.959940	−	0.280206i	$-0.0904027\pi$
$293$	8.26629e8	1.91988	0.959940	+	0.280206i	$0.0904027\pi$
$294$	−1.30265e8	−0.298960
$295$	7.22126e8	1.63771
$296$	−3.94509e8	−0.884170
$297$	−6.34846e8	−1.40612
$298$	−7.31264e8	−1.60073
$299$	7.73452e7	0.167334
$300$	2.48670e8	0.531739
$301$	1.48011e8	0.312831
$302$	−6.84208e8	−1.42943
$303$	−4.45781e8	−0.920602
$304$	7.10183e8	1.44982
$305$	3.92364e7	0.0791845
$306$	−1.85852e9	−3.70801
$307$	−3.32980e8	−0.656801	−0.328400	−	0.944539i	$-0.606510\pi$
$307$	−3.32980e8	−0.656801	−0.328400	+	0.944539i	$0.606510\pi$
$308$	−8.78801e7	−0.171381
$309$	1.44196e8	0.278034
$310$	1.55508e9	2.96473
$311$	2.81834e8	0.531290	0.265645	−	0.964071i	$-0.414415\pi$
$311$	2.81834e8	0.531290	0.265645	+	0.964071i	$0.414415\pi$
$312$	−1.54750e8	−0.288463
$313$	−6.61795e8	−1.21988	−0.609941	−	0.792447i	$-0.708807\pi$
$313$	−6.61795e8	−1.21988	−0.609941	+	0.792447i	$0.708807\pi$
$314$	4.26073e8	0.776658
$315$	−5.10620e8	−0.920472
$316$	−2.95918e8	−0.527553
$317$	−9.51839e8	−1.67825	−0.839124	−	0.543940i	$-0.816932\pi$
$317$	−9.51839e8	−1.67825	−0.839124	+	0.543940i	$0.816932\pi$
$318$	1.22647e9	2.13876
$319$	6.40882e8	1.10538
$320$	−8.81896e7	−0.150450
$321$	−7.48670e8	−1.26335
$322$	1.67488e8	0.279568
$323$	−1.11014e9	−1.83303
$324$	2.30605e8	0.376671
$325$	−1.06295e8	−0.171760
$326$	−4.57244e8	−0.730948
$327$	1.23246e8	0.194920
$328$	−5.18221e8	−0.810880
$329$	−3.76019e8	−0.582135
$330$	−1.56715e9	−2.40055
$331$	−5.21849e8	−0.790945	−0.395473	−	0.918478i	$-0.629419\pi$
$331$	−5.21849e8	−0.790945	−0.395473	+	0.918478i	$0.629419\pi$
$332$	−1.41083e8	−0.211588
$333$	−1.87136e9	−2.77717
$334$	1.25966e9	1.84987
$335$	4.69445e8	0.682225
$336$	−5.60758e8	−0.806469
$337$	−1.51522e7	−0.0215661	−0.0107830	−	0.999942i	$-0.503432\pi$
$337$	−1.51522e7	−0.0215661	−0.0107830	+	0.999942i	$0.503432\pi$
$338$	−6.69492e7	−0.0943055
$339$	−7.82437e8	−1.09081
$340$	−7.33122e8	−1.01158
$341$	−1.25436e9	−1.71309
$342$	2.01314e9	2.72135
$343$	4.03536e7	0.0539949
$344$	3.80754e8	0.504302
$345$	9.99575e8	1.31053
$346$	1.92890e8	0.250347
$347$	−4.81716e8	−0.618925	−0.309462	−	0.950912i	$-0.600149\pi$
$347$	−4.81716e8	−0.618925	−0.309462	+	0.950912i	$0.600149\pi$
$348$	−8.27759e8	−1.05287
$349$	−1.16083e9	−1.46177	−0.730886	−	0.682499i	$-0.760893\pi$
$349$	−1.16083e9	−1.46177	−0.730886	+	0.682499i	$0.760893\pi$
$350$	−2.30178e8	−0.286963
$351$	−3.50498e8	−0.432624
$352$	−6.80945e8	−0.832171
$353$	4.71997e8	0.571121	0.285561	−	0.958361i	$-0.407820\pi$
$353$	4.71997e8	0.571121	0.285561	+	0.958361i	$0.407820\pi$
$354$	2.24799e9	2.69329
$355$	1.16043e9	1.37664
$356$	5.48554e8	0.644383
$357$	8.76564e8	1.01964
$358$	−3.73924e8	−0.430718
$359$	2.49562e8	0.284674	0.142337	−	0.989818i	$-0.454538\pi$
$359$	2.49562e8	0.284674	0.142337	+	0.989818i	$0.454538\pi$
$360$	−1.31356e9	−1.48385
$361$	3.08634e8	0.345277
$362$	−5.39452e8	−0.597686
$363$	−2.91523e8	−0.319889
$364$	−4.85186e7	−0.0527294
$365$	−1.44984e8	−0.156062
$366$	1.22144e8	0.130223
$367$	1.03603e9	1.09406	0.547030	−	0.837113i	$-0.315758\pi$
$367$	1.03603e9	1.09406	0.547030	+	0.837113i	$0.315758\pi$
$368$	7.20991e8	0.754159
$369$	−2.45819e9	−2.54696
$370$	−2.20574e9	−2.26385
$371$	−3.79937e8	−0.386280
$372$	1.62012e9	1.63172
$373$	7.96214e8	0.794417	0.397209	−	0.917728i	$-0.369979\pi$
$373$	7.96214e8	0.794417	0.397209	+	0.917728i	$0.369979\pi$
$374$	1.76699e9	1.74656
$375$	8.44491e8	0.826962
$376$	−9.67300e8	−0.938434
$377$	3.53831e8	0.340095
$378$	−7.58989e8	−0.722793
$379$	−3.99800e8	−0.377230	−0.188615	−	0.982051i	$-0.560400\pi$
$379$	−3.99800e8	−0.377230	−0.188615	+	0.982051i	$0.560400\pi$
$380$	7.94117e8	0.742407
$381$	2.99617e9	2.77542
$382$	3.73245e8	0.342588
$383$	5.56148e8	0.505818	0.252909	−	0.967490i	$-0.418613\pi$
$383$	5.56148e8	0.505818	0.252909	+	0.967490i	$0.418613\pi$
$384$	−2.02303e9	−1.82323
$385$	4.85472e8	0.433563
$386$	−1.45282e8	−0.128575
$387$	1.80611e9	1.58401
$388$	5.62295e7	0.0488712
$389$	3.61828e7	0.0311658	0.0155829	−	0.999879i	$-0.495040\pi$
$389$	3.61828e7	0.0311658	0.0155829	+	0.999879i	$0.495040\pi$
$390$	−8.65222e8	−0.738586
$391$	−1.12704e9	−0.953498
$392$	1.03809e8	0.0870428
$393$	3.42789e9	2.84874
$394$	1.69983e9	1.40013
$395$	1.63472e9	1.33461
$396$	−1.07236e9	−0.867779
$397$	6.93301e8	0.556103	0.278052	−	0.960566i	$-0.410311\pi$
$397$	6.93301e8	0.556103	0.278052	+	0.960566i	$0.410311\pi$
$398$	1.37476e9	1.09304
$399$	−9.49494e8	−0.748319
$400$	−9.90858e8	−0.774108
$401$	−1.39417e9	−1.07971	−0.539857	−	0.841756i	$-0.681522\pi$
$401$	−1.39417e9	−1.07971	−0.539857	+	0.841756i	$0.681522\pi$
$402$	1.46139e9	1.12196
$403$	−6.92530e8	−0.527073
$404$	−3.59543e8	−0.271279
$405$	−1.27392e9	−0.952908
$406$	7.66205e8	0.568204
$407$	1.77920e9	1.30811
$408$	2.25494e9	1.64371
$409$	2.29542e9	1.65894	0.829470	−	0.558551i	$-0.188642\pi$
$409$	2.29542e9	1.65894	0.829470	+	0.558551i	$0.188642\pi$
$410$	−2.89742e9	−2.07620
$411$	6.17908e8	0.439013
$412$	1.16301e8	0.0819297
$413$	−6.96385e8	−0.486434
$414$	2.04378e9	1.41558
$415$	7.79379e8	0.535279
$416$	−3.75949e8	−0.256037
$417$	3.62928e9	2.45101
$418$	−1.91400e9	−1.28181
$419$	−2.94771e9	−1.95765	−0.978826	−	0.204693i	$-0.934380\pi$
$419$	−2.94771e9	−1.95765	−0.978826	+	0.204693i	$0.934380\pi$
$420$	−6.27032e8	−0.412969
$421$	−2.28626e9	−1.49327	−0.746636	−	0.665233i	$-0.768332\pi$
$421$	−2.28626e9	−1.49327	−0.746636	+	0.665233i	$0.768332\pi$
$422$	1.41421e9	0.916055
$423$	−4.58840e9	−2.94761
$424$	−9.77379e8	−0.622705
$425$	1.54889e9	0.978720
$426$	3.61244e9	2.26395
$427$	−3.78378e7	−0.0235195
$428$	−6.03837e8	−0.372277
$429$	6.97907e8	0.426773
$430$	2.12883e9	1.29123
$431$	−2.26694e9	−1.36386	−0.681929	−	0.731418i	$-0.738859\pi$
$431$	−2.26694e9	−1.36386	−0.681929	+	0.731418i	$0.738859\pi$
$432$	−3.26725e9	−1.94980
$433$	7.80139e8	0.461811	0.230905	−	0.972976i	$-0.425831\pi$
$433$	7.80139e8	0.461811	0.230905	+	0.972976i	$0.425831\pi$
$434$	−1.49964e9	−0.880591
$435$	4.57275e9	2.66358
$436$	9.94036e7	0.0574380
$437$	1.22081e9	0.699780
$438$	−4.51340e8	−0.256652
$439$	−2.33356e9	−1.31642	−0.658209	−	0.752835i	$-0.728686\pi$
$439$	−2.33356e9	−1.31642	−0.658209	+	0.752835i	$0.728686\pi$
$440$	1.24887e9	0.698927
$441$	4.92418e8	0.273400
$442$	9.75552e8	0.537369
$443$	1.11476e9	0.609211	0.304605	−	0.952479i	$-0.401475\pi$
$443$	1.11476e9	0.609211	0.304605	+	0.952479i	$0.401475\pi$
$444$	−2.29799e9	−1.24597
$445$	−3.03035e9	−1.63017
$446$	−7.87701e8	−0.420426
$447$	4.20865e9	2.22878
$448$	8.50460e7	0.0446870
$449$	3.62362e9	1.88921	0.944604	−	0.328211i	$-0.106446\pi$
$449$	3.62362e9	1.88921	0.944604	+	0.328211i	$0.106446\pi$
$450$	−2.80877e9	−1.45302
$451$	2.33712e9	1.19968
$452$	−6.31071e8	−0.321436
$453$	3.93783e9	1.99028
$454$	2.32218e9	1.16466
$455$	2.68029e8	0.133396
$456$	−2.44255e9	−1.20633
$457$	6.19268e7	0.0303509	0.0151755	−	0.999885i	$-0.495169\pi$
$457$	6.19268e7	0.0303509	0.0151755	+	0.999885i	$0.495169\pi$
$458$	−1.45946e9	−0.709846
$459$	5.10729e9	2.46517
$460$	8.06203e8	0.386182
$461$	−3.37017e9	−1.60213	−0.801067	−	0.598575i	$-0.795734\pi$
$461$	−3.37017e9	−1.60213	−0.801067	+	0.598575i	$0.795734\pi$
$462$	1.51129e9	0.713017
$463$	−3.87277e8	−0.181338	−0.0906688	−	0.995881i	$-0.528900\pi$
$463$	−3.87277e8	−0.181338	−0.0906688	+	0.995881i	$0.528900\pi$
$464$	3.29832e9	1.53278
$465$	−8.94995e9	−4.12796
$466$	−4.75202e8	−0.217534
$467$	−1.48458e9	−0.674518	−0.337259	−	0.941412i	$-0.609500\pi$
$467$	−1.48458e9	−0.674518	−0.337259	+	0.941412i	$0.609500\pi$
$468$	−5.92052e8	−0.266993
$469$	−4.52711e8	−0.202636
$470$	−5.40827e9	−2.40279
$471$	−2.45218e9	−1.08138
$472$	−1.79144e9	−0.784160
$473$	−1.71716e9	−0.746101
$474$	5.08894e9	2.19484
$475$	−1.67775e9	−0.718291
$476$	7.06989e8	0.300461
$477$	−4.63621e9	−1.95591
$478$	−4.39886e8	−0.184223
$479$	−2.52079e9	−1.04800	−0.524002	−	0.851717i	$-0.675562\pi$
$479$	−2.52079e9	−1.04800	−0.524002	+	0.851717i	$0.675562\pi$
$480$	−4.85860e9	−2.00524
$481$	9.82292e8	0.402470
$482$	−3.47501e9	−1.41348
$483$	−9.63944e8	−0.389257
$484$	−2.35127e8	−0.0942634
$485$	−3.10626e8	−0.123635
$486$	8.73629e8	0.345223
$487$	3.03517e9	1.19078	0.595390	−	0.803437i	$-0.296997\pi$
$487$	3.03517e9	1.19078	0.595390	+	0.803437i	$0.296997\pi$
$488$	−9.73371e7	−0.0379148
$489$	2.63159e9	1.01774
$490$	5.80405e8	0.222867
$491$	9.06913e8	0.345764	0.172882	−	0.984943i	$-0.444692\pi$
$491$	9.06913e8	0.345764	0.172882	+	0.984943i	$0.444692\pi$
$492$	−3.01861e9	−1.14269
$493$	−5.15585e9	−1.93792
$494$	−1.05672e9	−0.394380
$495$	5.92402e9	2.19532
$496$	−6.45558e9	−2.37547
$497$	−1.11906e9	−0.408891
$498$	2.42623e9	0.880296
$499$	9.07352e8	0.326907	0.163453	−	0.986551i	$-0.447737\pi$
$499$	9.07352e8	0.326907	0.163453	+	0.986551i	$0.447737\pi$
$500$	6.81121e8	0.243685
$501$	−7.24976e9	−2.57568
$502$	−3.00442e9	−1.05998
$503$	−1.96375e9	−0.688016	−0.344008	−	0.938967i	$-0.611785\pi$
$503$	−1.96375e9	−0.688016	−0.344008	+	0.938967i	$0.611785\pi$
$504$	1.26674e9	0.440737
$505$	1.98621e9	0.686285
$506$	−1.94313e9	−0.666768
$507$	3.85314e8	0.131307
$508$	2.41655e9	0.817847
$509$	4.92017e9	1.65374	0.826872	−	0.562390i	$-0.190118\pi$
$509$	4.92017e9	1.65374	0.826872	+	0.562390i	$0.190118\pi$
$510$	1.26076e10	4.20859
$511$	1.39816e8	0.0463537
$512$	−1.19146e9	−0.392315
$513$	−5.53222e9	−1.80921
$514$	−5.00452e9	−1.62552
$515$	−6.42474e8	−0.207267
$516$	2.21788e9	0.710662
$517$	4.36242e9	1.38839
$518$	2.12711e9	0.672413
$519$	−1.11014e9	−0.348572
$520$	6.89499e8	0.215041
$521$	2.55759e9	0.792316	0.396158	−	0.918182i	$-0.370343\pi$
$521$	2.55759e9	0.792316	0.396158	+	0.918182i	$0.370343\pi$
$522$	9.34968e9	2.87707
$523$	7.61152e8	0.232657	0.116328	−	0.993211i	$-0.462888\pi$
$523$	7.61152e8	0.232657	0.116328	+	0.993211i	$0.462888\pi$
$524$	2.76475e9	0.839453
$525$	1.32475e9	0.399554
$526$	1.82856e9	0.547847
$527$	1.00912e10	3.00335
$528$	6.50570e9	1.92343
$529$	−2.16544e9	−0.635991
$530$	−5.46462e9	−1.59439
$531$	−8.49770e9	−2.46304
$532$	−7.65811e8	−0.220511
$533$	1.29032e9	0.369108
$534$	−9.43355e9	−2.68090
$535$	3.33575e9	0.941792
$536$	−1.16459e9	−0.326660
$537$	2.15205e9	0.599712
$538$	6.12155e9	1.69482
$539$	−4.68167e8	−0.128778
$540$	−3.65340e9	−0.998433
$541$	−2.60116e9	−0.706278	−0.353139	−	0.935571i	$-0.614886\pi$
$541$	−2.60116e9	−0.706278	−0.353139	+	0.935571i	$0.614886\pi$
$542$	−1.29419e9	−0.349141
$543$	3.10472e9	0.832190
$544$	5.47815e9	1.45894
$545$	−5.49131e8	−0.145307
$546$	8.34380e8	0.219376
$547$	3.77194e9	0.985392	0.492696	−	0.870201i	$-0.336011\pi$
$547$	3.77194e9	0.985392	0.492696	+	0.870201i	$0.336011\pi$
$548$	4.98371e8	0.129366
$549$	−4.61720e8	−0.119090
$550$	2.67044e9	0.684406
$551$	5.58482e9	1.42226
$552$	−2.47973e9	−0.627505
$553$	−1.57645e9	−0.396409
$554$	4.39210e9	1.09746
$555$	1.26947e10	3.15208
$556$	2.92718e9	0.722251
$557$	2.72127e9	0.667235	0.333618	−	0.942709i	$-0.391731\pi$
$557$	2.72127e9	0.667235	0.333618	+	0.942709i	$0.391731\pi$
$558$	−1.82995e10	−4.45882
$559$	−9.48045e8	−0.229555
$560$	2.49849e9	0.601202
$561$	−1.01696e10	−2.43182
$562$	−4.77542e9	−1.13484
$563$	−2.33124e9	−0.550565	−0.275282	−	0.961363i	$-0.588771\pi$
$563$	−2.33124e9	−0.550565	−0.275282	+	0.961363i	$0.588771\pi$
$564$	−5.63447e9	−1.32244
$565$	3.48620e9	0.813172
$566$	1.43890e9	0.333559
$567$	1.22851e9	0.283035
$568$	−2.87877e9	−0.659155
$569$	−2.53570e9	−0.577040	−0.288520	−	0.957474i	$-0.593163\pi$
$569$	−2.53570e9	−0.577040	−0.288520	+	0.957474i	$0.593163\pi$
$570$	−1.36565e10	−3.08872
$571$	−1.31643e9	−0.295917	−0.147959	−	0.988994i	$-0.547270\pi$
$571$	−1.31643e9	−0.295917	−0.147959	+	0.988994i	$0.547270\pi$
$572$	5.62894e8	0.125759
$573$	−2.14814e9	−0.477004
$574$	2.79414e9	0.616676
$575$	−1.70329e9	−0.373638
$576$	1.03778e9	0.226270
$577$	−2.68545e9	−0.581972	−0.290986	−	0.956727i	$-0.593983\pi$
$577$	−2.68545e9	−0.581972	−0.290986	+	0.956727i	$0.593983\pi$
$578$	−8.52376e9	−1.83605
$579$	8.36143e8	0.179022
$580$	3.68813e9	0.784890
$581$	−7.51598e8	−0.158990
$582$	−9.66987e8	−0.203325
$583$	4.40788e9	0.921276
$584$	3.59674e8	0.0747248
$585$	3.27065e9	0.675442
$586$	−1.14656e10	−2.35372
$587$	7.60284e8	0.155147	0.0775734	−	0.996987i	$-0.475283\pi$
$587$	7.60284e8	0.155147	0.0775734	+	0.996987i	$0.475283\pi$
$588$	6.04681e8	0.122661
$589$	−1.09308e10	−2.20419
$590$	−1.00161e10	−2.00778
$591$	−9.78303e9	−1.94947
$592$	9.15667e9	1.81389
$593$	7.30842e9	1.43924	0.719618	−	0.694370i	$-0.244317\pi$
$593$	7.30842e9	1.43924	0.719618	+	0.694370i	$0.244317\pi$
$594$	8.80550e9	1.72386
$595$	−3.90559e9	−0.760111
$596$	3.39447e9	0.656766
$597$	−7.91220e9	−1.52190
$598$	−1.07280e9	−0.205147
$599$	9.14855e9	1.73924	0.869618	−	0.493725i	$-0.164365\pi$
$599$	9.14855e9	1.73924	0.869618	+	0.493725i	$0.164365\pi$
$600$	3.40789e9	0.644104
$601$	−3.61454e9	−0.679192	−0.339596	−	0.940571i	$-0.610290\pi$
$601$	−3.61454e9	−0.679192	−0.339596	+	0.940571i	$0.610290\pi$
$602$	−2.05295e9	−0.383522
$603$	−5.52425e9	−1.02604
$604$	3.17604e9	0.586485
$605$	1.29890e9	0.238469
$606$	6.18311e9	1.12863
$607$	−7.27446e9	−1.32020	−0.660101	−	0.751177i	$-0.729486\pi$
$607$	−7.27446e9	−1.32020	−0.660101	+	0.751177i	$0.729486\pi$
$608$	−5.93393e9	−1.07073
$609$	−4.40975e9	−0.791140
$610$	−5.44221e8	−0.0970780
$611$	2.40849e9	0.427170
$612$	8.62710e9	1.52137
$613$	1.07483e10	1.88465	0.942323	−	0.334704i	$-0.108636\pi$
$613$	1.07483e10	1.88465	0.942323	+	0.334704i	$0.108636\pi$
$614$	4.61853e9	0.805219
$615$	1.66756e10	2.89080
$616$	−1.20435e9	−0.207597
$617$	5.04425e9	0.864567	0.432284	−	0.901738i	$-0.357708\pi$
$617$	5.04425e9	0.864567	0.432284	+	0.901738i	$0.357708\pi$
$618$	−2.00004e9	−0.340862
$619$	8.76035e9	1.48458	0.742291	−	0.670078i	$-0.233739\pi$
$619$	8.76035e9	1.48458	0.742291	+	0.670078i	$0.233739\pi$
$620$	−7.21855e9	−1.21641
$621$	−5.61641e9	−0.941106
$622$	−3.90912e9	−0.651347
$623$	2.92233e9	0.484196
$624$	3.59179e9	0.591787
$625$	−7.54254e9	−1.23577
$626$	9.17928e9	1.49554
$627$	1.10157e10	1.78474
$628$	−1.97780e9	−0.318657
$629$	−1.43135e10	−2.29334
$630$	7.08244e9	1.12847
$631$	−5.98002e9	−0.947545	−0.473772	−	0.880647i	$-0.657108\pi$
$631$	−5.98002e9	−0.947545	−0.473772	+	0.880647i	$0.657108\pi$
$632$	−4.05539e9	−0.639033
$633$	−8.13925e9	−1.27547
$634$	1.32023e10	2.05748
$635$	−1.33496e10	−2.06900
$636$	−5.69318e9	−0.877517
$637$	−2.58475e8	−0.0396214
$638$	−8.88922e9	−1.35516
$639$	−1.36555e10	−2.07040
$640$	9.01373e9	1.35917
$641$	4.46662e9	0.669847	0.334924	−	0.942245i	$-0.391289\pi$
$641$	4.46662e9	0.669847	0.334924	+	0.942245i	$0.391289\pi$
$642$	1.03843e10	1.54883
$643$	3.62227e9	0.537332	0.268666	−	0.963233i	$-0.413417\pi$
$643$	3.62227e9	0.537332	0.268666	+	0.963233i	$0.413417\pi$
$644$	−7.77465e8	−0.114705
$645$	−1.22521e10	−1.79784
$646$	1.53980e10	2.24724
$647$	−1.16389e10	−1.68946	−0.844730	−	0.535193i	$-0.820239\pi$
$647$	−1.16389e10	−1.68946	−0.844730	+	0.535193i	$0.820239\pi$
$648$	3.16033e9	0.456267
$649$	8.07920e9	1.16014
$650$	1.47435e9	0.210573
$651$	8.63092e9	1.22609
$652$	2.12249e9	0.299902
$653$	3.12872e8	0.0439714	0.0219857	−	0.999758i	$-0.493001\pi$
$653$	3.12872e8	0.0439714	0.0219857	+	0.999758i	$0.493001\pi$
$654$	−1.70946e9	−0.238966
$655$	−1.52732e10	−2.12366
$656$	1.20281e10	1.66354
$657$	1.70612e9	0.234710
$658$	5.21548e9	0.713681
$659$	6.98565e9	0.950842	0.475421	−	0.879759i	$-0.342296\pi$
$659$	6.98565e9	0.950842	0.475421	+	0.879759i	$0.342296\pi$
$660$	7.27459e9	0.984928
$661$	8.18942e9	1.10293	0.551465	−	0.834198i	$-0.314069\pi$
$661$	8.18942e9	1.10293	0.551465	+	0.834198i	$0.314069\pi$
$662$	7.23819e9	0.969677
$663$	−5.61461e9	−0.748208
$664$	−1.93347e9	−0.256300
$665$	4.23053e9	0.557852
$666$	2.59563e10	3.40473
$667$	5.66981e9	0.739824
$668$	−5.84727e9	−0.758989
$669$	4.53347e9	0.585382
$670$	−6.51134e9	−0.836389
$671$	4.38980e8	0.0560940
$672$	4.68541e9	0.595601
$673$	1.64526e9	0.208057	0.104029	−	0.994574i	$-0.466827\pi$
$673$	1.64526e9	0.208057	0.104029	+	0.994574i	$0.466827\pi$
$674$	2.10165e8	0.0264394
$675$	7.71864e9	0.966001
$676$	3.10773e8	0.0386928
$677$	4.30944e9	0.533778	0.266889	−	0.963727i	$-0.414004\pi$
$677$	4.30944e9	0.533778	0.266889	+	0.963727i	$0.414004\pi$
$678$	1.08526e10	1.33731
$679$	2.99554e8	0.0367224
$680$	−1.00470e10	−1.22534
$681$	−1.33649e10	−1.62162
$682$	1.73983e10	2.10020
$683$	−1.26812e10	−1.52296	−0.761480	−	0.648188i	$-0.775527\pi$
$683$	−1.26812e10	−1.52296	−0.761480	+	0.648188i	$0.775527\pi$
$684$	−9.34487e9	−1.11655
$685$	−2.75313e9	−0.327272
$686$	−5.59716e8	−0.0661963
$687$	8.39967e9	0.988356
$688$	−8.83743e9	−1.03459
$689$	2.43359e9	0.283452
$690$	−1.38644e10	−1.60668
$691$	1.55284e10	1.79042	0.895209	−	0.445647i	$-0.147026\pi$
$691$	1.55284e10	1.79042	0.895209	+	0.445647i	$0.147026\pi$
$692$	−8.95380e8	−0.102716
$693$	−5.71285e9	−0.652059
$694$	6.68154e9	0.758784
$695$	−1.61705e10	−1.82716
$696$	−1.13440e10	−1.27536
$697$	−1.88020e10	−2.10324
$698$	1.61010e10	1.79209
$699$	2.73494e9	0.302884
$700$	1.06847e9	0.117739
$701$	−5.65285e9	−0.619804	−0.309902	−	0.950769i	$-0.600296\pi$
$701$	−5.65285e9	−0.619804	−0.309902	+	0.950769i	$0.600296\pi$
$702$	4.86151e9	0.530385
$703$	1.55044e10	1.68310
$704$	−9.86671e8	−0.106578
$705$	3.11263e10	3.34553
$706$	−6.54674e9	−0.700178
$707$	−1.91541e9	−0.203842
$708$	−1.04350e10	−1.10504
$709$	4.37424e9	0.460936	0.230468	−	0.973080i	$-0.425974\pi$
$709$	4.37424e9	0.460936	0.230468	+	0.973080i	$0.425974\pi$
$710$	−1.60955e10	−1.68772
$711$	−1.92368e10	−2.00719
$712$	7.51764e9	0.780551
$713$	−1.10972e10	−1.14656
$714$	−1.21582e10	−1.25004
$715$	−3.10957e9	−0.318148
$716$	1.73573e9	0.176720
$717$	2.53168e9	0.256503
$718$	−3.46150e9	−0.349003
$719$	−6.65546e9	−0.667770	−0.333885	−	0.942614i	$-0.608360\pi$
$719$	−6.65546e9	−0.667770	−0.333885	+	0.942614i	$0.608360\pi$
$720$	3.04881e10	3.04415
$721$	6.19572e8	0.0615628
$722$	−4.28084e9	−0.423300
$723$	1.99998e10	1.96807
$724$	2.50410e9	0.245226
$725$	−7.79202e9	−0.759394
$726$	4.04351e9	0.392175
$727$	−1.50514e10	−1.45280	−0.726399	−	0.687273i	$-0.758808\pi$
$727$	−1.50514e10	−1.45280	−0.726399	+	0.687273i	$0.758808\pi$
$728$	−6.64921e8	−0.0638720
$729$	−1.28611e10	−1.22951
$730$	2.01097e9	0.191327
$731$	1.38145e10	1.30805
$732$	−5.66983e8	−0.0534296
$733$	−1.99602e10	−1.87198	−0.935991	−	0.352025i	$-0.885493\pi$
$733$	−1.99602e10	−1.87198	−0.935991	+	0.352025i	$0.885493\pi$
$734$	−1.43700e10	−1.34129
$735$	−3.34041e9	−0.310309
$736$	−6.02424e9	−0.556968
$737$	5.25218e9	0.483286
$738$	3.40958e10	3.12250
$739$	−1.39895e10	−1.27511	−0.637555	−	0.770405i	$-0.720054\pi$
$739$	−1.39895e10	−1.27511	−0.637555	+	0.770405i	$0.720054\pi$
$740$	1.02389e10	0.928840
$741$	6.08174e9	0.549116
$742$	5.26983e9	0.473569
$743$	1.54926e10	1.38568	0.692841	−	0.721091i	$-0.256359\pi$
$743$	1.54926e10	1.38568	0.692841	+	0.721091i	$0.256359\pi$
$744$	2.22029e10	1.97653
$745$	−1.87519e10	−1.66150
$746$	−1.10437e10	−0.973933
$747$	−9.17144e9	−0.805036
$748$	−8.20222e9	−0.716598
$749$	−3.21684e9	−0.279733
$750$	−1.17133e10	−1.01383
$751$	−6.31113e9	−0.543710	−0.271855	−	0.962338i	$-0.587637\pi$
$751$	−6.31113e9	−0.543710	−0.271855	+	0.962338i	$0.587637\pi$
$752$	2.24513e10	1.92522
$753$	1.72914e10	1.47587
$754$	−4.90773e9	−0.416947
$755$	−1.75453e10	−1.48370
$756$	3.52317e9	0.296556
$757$	−8.02329e9	−0.672229	−0.336114	−	0.941821i	$-0.609113\pi$
$757$	−8.02329e9	−0.672229	−0.336114	+	0.941821i	$0.609113\pi$
$758$	5.54534e9	0.462473
$759$	1.11833e10	0.928377
$760$	1.08830e10	0.899289
$761$	−1.64685e10	−1.35459	−0.677297	−	0.735710i	$-0.736849\pi$
$761$	−1.64685e10	−1.35459	−0.677297	+	0.735710i	$0.736849\pi$
$762$	−4.15577e10	−3.40258
$763$	5.29557e8	0.0431595
$764$	−1.73258e9	−0.140561
$765$	−4.76583e10	−3.84878
$766$	−7.71393e9	−0.620119
$767$	4.46052e9	0.356945
$768$	2.55264e10	2.03342
$769$	9.23686e9	0.732457	0.366229	−	0.930525i	$-0.380649\pi$
$769$	9.23686e9	0.732457	0.366229	+	0.930525i	$0.380649\pi$
$770$	−6.73364e9	−0.531536
$771$	2.88026e10	2.26330
$772$	6.74388e8	0.0527532
$773$	4.93736e9	0.384474	0.192237	−	0.981349i	$-0.438426\pi$
$773$	4.93736e9	0.384474	0.192237	+	0.981349i	$0.438426\pi$
$774$	−2.50513e10	−1.94195
$775$	1.52508e10	1.17689
$776$	7.70596e8	0.0591985
$777$	−1.22422e10	−0.936237
$778$	−5.01866e8	−0.0382084
$779$	2.03663e10	1.54359
$780$	4.01630e9	0.303036
$781$	1.29830e10	0.975203
$782$	1.56323e10	1.16896
$783$	−2.56934e10	−1.91274
$784$	−2.40943e9	−0.178570
$785$	1.09259e10	0.806143
$786$	−4.75458e10	−3.49247
$787$	−1.30865e10	−0.957003	−0.478502	−	0.878087i	$-0.658820\pi$
$787$	−1.30865e10	−0.957003	−0.478502	+	0.878087i	$0.658820\pi$
$788$	−7.89047e9	−0.574462
$789$	−1.05239e10	−0.762797
$790$	−2.26741e10	−1.63620
$791$	−3.36193e9	−0.241530
$792$	−1.46962e10	−1.05115
$793$	2.42361e8	0.0172586
$794$	−9.61629e9	−0.681767
$795$	3.14506e10	2.21995
$796$	−6.38155e9	−0.448467
$797$	1.35142e10	0.945550	0.472775	−	0.881183i	$-0.343252\pi$
$797$	1.35142e10	0.945550	0.472775	+	0.881183i	$0.343252\pi$
$798$	1.31698e10	0.917418
$799$	−3.50954e10	−2.43409
$800$	8.27911e9	0.571701
$801$	3.56600e10	2.45170
$802$	1.93375e10	1.32370
$803$	−1.62210e9	−0.110553
$804$	−6.78368e9	−0.460330
$805$	4.29492e9	0.290181
$806$	9.60559e9	0.646177
$807$	−3.52314e10	−2.35979
$808$	−4.92734e9	−0.328604
$809$	5.55535e9	0.368886	0.184443	−	0.982843i	$-0.440952\pi$
$809$	5.55535e9	0.368886	0.184443	+	0.982843i	$0.440952\pi$
$810$	1.76697e10	1.16824
$811$	5.08438e9	0.334707	0.167354	−	0.985897i	$-0.446478\pi$
$811$	5.08438e9	0.334707	0.167354	+	0.985897i	$0.446478\pi$
$812$	−3.55667e9	−0.233129
$813$	7.44848e9	0.486128
$814$	−2.46779e10	−1.60370
$815$	−1.17252e10	−0.758698
$816$	−5.23379e10	−3.37210
$817$	−1.49638e10	−0.959987
$818$	−3.18382e10	−2.03381
$819$	−3.15406e9	−0.200621
$820$	1.34496e10	0.851847
$821$	−1.95761e10	−1.23459	−0.617297	−	0.786730i	$-0.711772\pi$
$821$	−1.95761e10	−1.23459	−0.617297	+	0.786730i	$0.711772\pi$
$822$	−8.57056e9	−0.538217
$823$	−3.29140e9	−0.205817	−0.102909	−	0.994691i	$-0.532815\pi$
$823$	−3.29140e9	−0.205817	−0.102909	+	0.994691i	$0.532815\pi$
$824$	1.59384e9	0.0992427
$825$	−1.53692e10	−0.952935
$826$	9.65906e9	0.596355
$827$	1.88024e10	1.15597	0.577983	−	0.816049i	$-0.303840\pi$
$827$	1.88024e10	1.15597	0.577983	+	0.816049i	$0.303840\pi$
$828$	−9.48709e9	−0.580800
$829$	1.44850e10	0.883033	0.441517	−	0.897253i	$-0.354441\pi$
$829$	1.44850e10	0.883033	0.441517	+	0.897253i	$0.354441\pi$
$830$	−1.08102e10	−0.656237
$831$	−2.52779e10	−1.52805
$832$	−5.44741e8	−0.0327913
$833$	3.76637e9	0.225770
$834$	−5.03392e10	−3.00487
$835$	3.23018e10	1.92010
$836$	8.88464e9	0.525918
$837$	5.02880e10	2.96432
$838$	4.08856e10	2.40003
$839$	1.50854e10	0.881838	0.440919	−	0.897547i	$-0.354653\pi$
$839$	1.50854e10	0.881838	0.440919	+	0.897547i	$0.354653\pi$
$840$	−8.59314e9	−0.500236
$841$	8.68780e9	0.503644
$842$	3.17111e10	1.83071
$843$	2.74840e10	1.58010
$844$	−6.56468e9	−0.375850
$845$	−1.71679e9	−0.0978857
$846$	6.36424e10	3.61368
$847$	−1.25260e9	−0.0708305
$848$	2.26853e10	1.27749
$849$	−8.28131e9	−0.464432
$850$	−2.14835e10	−1.19988
$851$	1.57403e10	0.875509
$852$	−1.67687e10	−0.928882
$853$	2.11820e9	0.116854	0.0584272	−	0.998292i	$-0.481391\pi$
$853$	2.11820e9	0.116854	0.0584272	+	0.998292i	$0.481391\pi$
$854$	5.24822e8	0.0288343
$855$	5.16234e10	2.82466
$856$	−8.27526e9	−0.450945
$857$	−1.79107e10	−0.972032	−0.486016	−	0.873950i	$-0.661550\pi$
$857$	−1.79107e10	−0.972032	−0.486016	+	0.873950i	$0.661550\pi$
$858$	−9.68017e9	−0.523211
$859$	−1.71791e10	−0.924749	−0.462375	−	0.886685i	$-0.653002\pi$
$859$	−1.71791e10	−0.924749	−0.462375	+	0.886685i	$0.653002\pi$
$860$	−9.88189e9	−0.529780
$861$	−1.60812e10	−0.858631
$862$	3.14431e10	1.67205
$863$	2.38549e10	1.26339	0.631697	−	0.775215i	$-0.282359\pi$
$863$	2.38549e10	1.26339	0.631697	+	0.775215i	$0.282359\pi$
$864$	2.72995e10	1.43998
$865$	4.94631e9	0.259851
$866$	−1.08207e10	−0.566167
$867$	4.90569e10	2.55643
$868$	6.96124e9	0.361300
$869$	1.82894e10	0.945433
$870$	−6.34254e10	−3.26547
$871$	2.89973e9	0.148694
$872$	1.36227e9	0.0695755
$873$	3.65533e9	0.185942
$874$	−1.69329e10	−0.857911
$875$	3.62856e9	0.183108
$876$	2.09509e9	0.105302
$877$	1.14442e10	0.572912	0.286456	−	0.958093i	$-0.407523\pi$
$877$	1.14442e10	0.572912	0.286456	+	0.958093i	$0.407523\pi$
$878$	3.23672e10	1.61389
$879$	6.59880e10	3.27721
$880$	−2.89866e10	−1.43386
$881$	1.39502e10	0.687328	0.343664	−	0.939093i	$-0.388332\pi$
$881$	1.39502e10	0.687328	0.343664	+	0.939093i	$0.388332\pi$
$882$	−6.82998e9	−0.335181
$883$	2.05515e10	1.00457	0.502285	−	0.864702i	$-0.332493\pi$
$883$	2.05515e10	1.00457	0.502285	+	0.864702i	$0.332493\pi$
$884$	−4.52844e9	−0.220478
$885$	5.76458e10	2.79554
$886$	−1.54620e10	−0.746875
$887$	−3.63953e10	−1.75110	−0.875552	−	0.483123i	$-0.839502\pi$
$887$	−3.63953e10	−1.75110	−0.875552	+	0.483123i	$0.839502\pi$
$888$	−3.14928e10	−1.50927
$889$	1.28738e10	0.614539
$890$	4.20318e10	1.99854
$891$	−1.42528e10	−0.675036
$892$	3.65645e9	0.172497
$893$	3.80153e10	1.78640
$894$	−5.83752e10	−2.73242
$895$	−9.58861e9	−0.447070
$896$	−8.69243e9	−0.403704
$897$	6.17430e9	0.285637
$898$	−5.02606e10	−2.31612
$899$	−5.07661e10	−2.33032
$900$	1.30381e10	0.596164
$901$	−3.54611e10	−1.61516
$902$	−3.24166e10	−1.47077
$903$	1.18154e10	0.533999
$904$	−8.64850e9	−0.389360
$905$	−1.38333e10	−0.620376
$906$	−5.46188e10	−2.44002
$907$	1.45838e10	0.648999	0.324500	−	0.945886i	$-0.394804\pi$
$907$	1.45838e10	0.648999	0.324500	+	0.945886i	$0.394804\pi$
$908$	−1.07794e10	−0.477852
$909$	−2.33729e10	−1.03214
$910$	−3.71764e9	−0.163539
$911$	−2.58170e10	−1.13134	−0.565668	−	0.824633i	$-0.691382\pi$
$911$	−2.58170e10	−1.13134	−0.565668	+	0.824633i	$0.691382\pi$
$912$	5.66924e10	2.47482
$913$	8.71976e9	0.379190
$914$	−8.58943e8	−0.0372094
$915$	3.13216e9	0.135167
$916$	6.77472e9	0.291244
$917$	1.47288e10	0.630774
$918$	−7.08396e10	−3.02223
$919$	1.33367e10	0.566820	0.283410	−	0.958999i	$-0.408534\pi$
$919$	1.33367e10	0.566820	0.283410	+	0.958999i	$0.408534\pi$
$920$	1.10486e10	0.467788
$921$	−2.65811e10	−1.12115
$922$	4.67452e10	1.96417
$923$	7.16788e9	0.300044
$924$	−7.01528e9	−0.292545
$925$	−2.16319e10	−0.898668
$926$	5.37164e9	0.222315
$927$	7.56039e9	0.311720
$928$	−2.75591e10	−1.13200
$929$	−1.42831e10	−0.584476	−0.292238	−	0.956346i	$-0.594400\pi$
$929$	−1.42831e10	−0.584476	−0.292238	+	0.956346i	$0.594400\pi$
$930$	1.24138e11	5.06076
$931$	−4.07973e9	−0.165694
$932$	2.20585e9	0.0892525
$933$	2.24982e10	0.906906
$934$	2.05915e10	0.826940
$935$	4.53112e10	1.81286
$936$	−8.11376e9	−0.323412
$937$	−1.65052e10	−0.655440	−0.327720	−	0.944775i	$-0.606280\pi$
$937$	−1.65052e10	−0.655440	−0.327720	+	0.944775i	$0.606280\pi$
$938$	6.27923e9	0.248426
$939$	−5.28297e10	−2.08232
$940$	2.51048e10	0.985845
$941$	−4.07115e10	−1.59277	−0.796385	−	0.604790i	$-0.793257\pi$
$941$	−4.07115e10	−1.59277	−0.796385	+	0.604790i	$0.793257\pi$
$942$	3.40125e10	1.32575
$943$	2.06763e10	0.802937
$944$	4.15798e10	1.60872
$945$	−1.94629e10	−0.750233
$946$	2.38176e10	0.914699
$947$	3.92358e10	1.50127	0.750634	−	0.660719i	$-0.229748\pi$
$947$	3.92358e10	1.50127	0.750634	+	0.660719i	$0.229748\pi$
$948$	−2.36225e10	−0.900526
$949$	−8.95558e8	−0.0340143
$950$	2.32709e10	0.880605
$951$	−7.59833e10	−2.86475
$952$	9.68891e9	0.363953
$953$	1.57430e10	0.589199	0.294600	−	0.955621i	$-0.404814\pi$
$953$	1.57430e10	0.589199	0.294600	+	0.955621i	$0.404814\pi$
$954$	6.43056e10	2.39789
$955$	9.57119e9	0.355594
$956$	2.04192e9	0.0755851
$957$	5.11603e10	1.88687
$958$	3.49641e10	1.28482
$959$	2.65499e9	0.0972071
$960$	−7.03998e9	−0.256816
$961$	7.18487e10	2.61148
$962$	−1.36247e10	−0.493416
$963$	−3.92538e10	−1.41641
$964$	1.61307e10	0.579942
$965$	−3.72549e9	−0.133456
$966$	1.33702e10	0.477219
$967$	−3.52009e10	−1.25187	−0.625937	−	0.779874i	$-0.715283\pi$
$967$	−3.52009e10	−1.25187	−0.625937	+	0.779874i	$0.715283\pi$
$968$	−3.22229e9	−0.114183
$969$	−8.86203e10	−3.12896
$970$	4.30847e9	0.151573
$971$	−3.09529e9	−0.108501	−0.0542505	−	0.998527i	$-0.517277\pi$
$971$	−3.09529e9	−0.108501	−0.0542505	+	0.998527i	$0.517277\pi$
$972$	−4.05532e9	−0.141642
$973$	1.55941e10	0.542707
$974$	−4.20987e10	−1.45986
$975$	−8.48534e9	−0.293193
$976$	2.25922e9	0.0777830
$977$	1.87196e10	0.642193	0.321096	−	0.947047i	$-0.395949\pi$
$977$	1.87196e10	0.642193	0.321096	+	0.947047i	$0.395949\pi$
$978$	−3.65008e10	−1.24772
$979$	−3.39038e10	−1.15481
$980$	−2.69420e9	−0.0914404
$981$	6.46196e9	0.218536
$982$	−1.25791e10	−0.423897
$983$	4.53735e10	1.52358	0.761789	−	0.647826i	$-0.224321\pi$
$983$	4.53735e10	1.52358	0.761789	+	0.647826i	$0.224321\pi$
$984$	−4.13685e10	−1.38416
$985$	4.35890e10	1.45328
$986$	7.15132e10	2.37584
$987$	−3.00168e10	−0.993696
$988$	4.90521e9	0.161811
$989$	−1.51916e10	−0.499362
$990$	−8.21678e10	−2.69140
$991$	−3.11177e9	−0.101566	−0.0507831	−	0.998710i	$-0.516172\pi$
$991$	−3.11177e9	−0.101566	−0.0507831	+	0.998710i	$0.516172\pi$
$992$	5.39396e10	1.75435
$993$	−4.16581e10	−1.35013
$994$	1.55217e10	0.501289
$995$	3.52533e10	1.13454
$996$	−1.12624e10	−0.361179
$997$	−1.81745e10	−0.580803	−0.290402	−	0.956905i	$-0.593789\pi$
$997$	−1.81745e10	−0.580803	−0.290402	+	0.956905i	$0.593789\pi$
$998$	−1.25852e10	−0.400779
$999$	−7.13291e10	−2.26354

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.c.1.3	✓	10

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

\(f(q)\)	\(=\)	\(q-13.8703 q^{2} +79.8279 q^{3} +64.3848 q^{4} -355.678 q^{5} -1107.24 q^{6} +343.000 q^{7} +882.360 q^{8} +4185.49 q^{9} +O(q^{10})\)	\(q-13.8703 q^{2} +79.8279 q^{3} +64.3848 q^{4} -355.678 q^{5} -1107.24 q^{6} +343.000 q^{7} +882.360 q^{8} +4185.49 q^{9} +4933.36 q^{10} -3979.36 q^{11} +5139.70 q^{12} -2197.00 q^{13} -4757.51 q^{14} -28393.0 q^{15} -20479.9 q^{16} +32013.6 q^{17} -58053.9 q^{18} -34677.2 q^{19} -22900.3 q^{20} +27381.0 q^{21} +55194.8 q^{22} -35204.9 q^{23} +70436.9 q^{24} +48382.1 q^{25} +30473.0 q^{26} +159535. q^{27} +22084.0 q^{28} -161052. q^{29} +393820. q^{30} +315216. q^{31} +171119. q^{32} -317663. q^{33} -444038. q^{34} -121998. q^{35} +269482. q^{36} -447106. q^{37} +480982. q^{38} -175382. q^{39} -313836. q^{40} -587312. q^{41} -379782. q^{42} +431518. q^{43} -256210. q^{44} -1.48869e6 q^{45} +488302. q^{46} -1.09626e6 q^{47} -1.63486e6 q^{48} +117649. q^{49} -671074. q^{50} +2.55558e6 q^{51} -141454. q^{52} -1.10769e6 q^{53} -2.21280e6 q^{54} +1.41537e6 q^{55} +302650. q^{56} -2.76820e6 q^{57} +2.23383e6 q^{58} -2.03028e6 q^{59} -1.82808e6 q^{60} -110314. q^{61} -4.37214e6 q^{62} +1.43562e6 q^{63} +247948. q^{64} +781425. q^{65} +4.40608e6 q^{66} -1.31986e6 q^{67} +2.06119e6 q^{68} -2.81033e6 q^{69} +1.69214e6 q^{70} -3.26258e6 q^{71} +3.69311e6 q^{72} +407628. q^{73} +6.20149e6 q^{74} +3.86224e6 q^{75} -2.23268e6 q^{76} -1.36492e6 q^{77} +2.43260e6 q^{78} -4.59608e6 q^{79} +7.28424e6 q^{80} +3.58167e6 q^{81} +8.14619e6 q^{82} -2.19125e6 q^{83} +1.76292e6 q^{84} -1.13866e7 q^{85} -5.98528e6 q^{86} -1.28564e7 q^{87} -3.51123e6 q^{88} +8.51992e6 q^{89} +2.06485e7 q^{90} -753571. q^{91} -2.26666e6 q^{92} +2.51630e7 q^{93} +1.52055e7 q^{94} +1.23339e7 q^{95} +1.36601e7 q^{96} +873334. q^{97} -1.63183e6 q^{98} -1.66555e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9}+O(q^{10}) \) 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

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