LMFDB - Embedded newform 91.8.a.c.1.9

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			1.9
Root			$16.1785$ 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)

$f(q)$	$=$	$q+14.1785 q^{2} +6.78261 q^{3} +73.0290 q^{4} -4.23520 q^{5} +96.1671 q^{6} +343.000 q^{7} -779.405 q^{8} -2141.00 q^{9} +O(q^{10})$	\(q+14.1785 q^{2} +6.78261 q^{3} +73.0290 q^{4} -4.23520 q^{5} +96.1671 q^{6} +343.000 q^{7} -779.405 q^{8} -2141.00 q^{9} -60.0487 q^{10} -7896.54 q^{11} +495.328 q^{12} -2197.00 q^{13} +4863.22 q^{14} -28.7257 q^{15} -20398.5 q^{16} +31982.0 q^{17} -30356.0 q^{18} -9142.53 q^{19} -309.293 q^{20} +2326.44 q^{21} -111961. q^{22} +28761.2 q^{23} -5286.40 q^{24} -78107.1 q^{25} -31150.1 q^{26} -29355.1 q^{27} +25048.9 q^{28} -13425.2 q^{29} -407.287 q^{30} -172793. q^{31} -189455. q^{32} -53559.2 q^{33} +453455. q^{34} -1452.67 q^{35} -156355. q^{36} -245025. q^{37} -129627. q^{38} -14901.4 q^{39} +3300.94 q^{40} -778150. q^{41} +32985.3 q^{42} +713663. q^{43} -576676. q^{44} +9067.55 q^{45} +407790. q^{46} +132602. q^{47} -138355. q^{48} +117649. q^{49} -1.10744e6 q^{50} +216921. q^{51} -160445. q^{52} +743372. q^{53} -416211. q^{54} +33443.4 q^{55} -267336. q^{56} -62010.2 q^{57} -190349. q^{58} +1.05200e6 q^{59} -2097.81 q^{60} +1.76584e6 q^{61} -2.44994e6 q^{62} -734362. q^{63} -75182.7 q^{64} +9304.74 q^{65} -759387. q^{66} +744278. q^{67} +2.33561e6 q^{68} +195076. q^{69} -20596.7 q^{70} +383299. q^{71} +1.66870e6 q^{72} -3.29444e6 q^{73} -3.47408e6 q^{74} -529770. q^{75} -667670. q^{76} -2.70851e6 q^{77} -211279. q^{78} -2.30144e6 q^{79} +86391.7 q^{80} +4.48325e6 q^{81} -1.10330e7 q^{82} -3.15382e6 q^{83} +169897. q^{84} -135450. q^{85} +1.01186e7 q^{86} -91058.3 q^{87} +6.15460e6 q^{88} -1.36538e6 q^{89} +128564. q^{90} -753571. q^{91} +2.10040e6 q^{92} -1.17199e6 q^{93} +1.88009e6 q^{94} +38720.5 q^{95} -1.28500e6 q^{96} -1.40862e6 q^{97} +1.66808e6 q^{98} +1.69065e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	14.1785	1.25321	0.626606	−	0.779336i	$-0.284444\pi$
$2$	14.1785	1.25321	0.626606	+	0.779336i	$0.284444\pi$
$3$	6.78261	0.145035	0.0725175	−	0.997367i	$-0.476897\pi$
$3$	6.78261	0.145035	0.0725175	+	0.997367i	$0.476897\pi$
$4$	73.0290	0.570539
$5$	−4.23520	−0.0151523	−0.00757616	−	0.999971i	$-0.502412\pi$
$5$	−4.23520	−0.0151523	−0.00757616	+	0.999971i	$0.502412\pi$
$6$	96.1671	0.181759
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−779.405	−0.538205
$9$	−2141.00	−0.978965
$10$	−60.0487	−0.0189891
$11$	−7896.54	−1.78880	−0.894401	−	0.447266i	$-0.852398\pi$
$11$	−7896.54	−1.78880	−0.894401	+	0.447266i	$0.852398\pi$
$12$	495.328	0.0827481
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	4863.22	0.473669
$15$	−28.7257	−0.00219762
$16$	−20398.5	−1.24502
$17$	31982.0	1.57883	0.789413	−	0.613863i	$-0.210385\pi$
$17$	31982.0	1.57883	0.789413	+	0.613863i	$0.210385\pi$
$18$	−30356.0	−1.22685
$19$	−9142.53	−0.305794	−0.152897	−	0.988242i	$-0.548860\pi$
$19$	−9142.53	−0.305794	−0.152897	+	0.988242i	$0.548860\pi$
$20$	−309.293	−0.00864499
$21$	2326.44	0.0548181
$22$	−111961.	−2.24175
$23$	28761.2	0.492901	0.246451	−	0.969155i	$-0.420736\pi$
$23$	28761.2	0.492901	0.246451	+	0.969155i	$0.420736\pi$
$24$	−5286.40	−0.0780586
$25$	−78107.1	−0.999770
$26$	−31150.1	−0.347578
$27$	−29355.1	−0.287019
$28$	25048.9	0.215644
$29$	−13425.2	−0.102218	−0.0511092	−	0.998693i	$-0.516276\pi$
$29$	−13425.2	−0.102218	−0.0511092	+	0.998693i	$0.516276\pi$
$30$	−407.287	−0.00275408
$31$	−172793.	−1.04174	−0.520871	−	0.853636i	$-0.674393\pi$
$31$	−172793.	−1.04174	−0.520871	+	0.853636i	$0.674393\pi$
$32$	−189455.	−1.02207
$33$	−53559.2	−0.259439
$34$	453455.	1.97860
$35$	−1452.67	−0.00572704
$36$	−156355.	−0.558538
$37$	−245025.	−0.795251	−0.397626	−	0.917548i	$-0.630166\pi$
$37$	−245025.	−0.795251	−0.397626	+	0.917548i	$0.630166\pi$
$38$	−129627.	−0.383224
$39$	−14901.4	−0.0402255
$40$	3300.94	0.00815506
$41$	−778150.	−1.76327	−0.881637	−	0.471928i	$-0.843558\pi$
$41$	−778150.	−1.76327	−0.881637	+	0.471928i	$0.843558\pi$
$42$	32985.3	0.0686986
$43$	713663.	1.36884	0.684421	−	0.729087i	$-0.260055\pi$
$43$	713663.	1.36884	0.684421	+	0.729087i	$0.260055\pi$
$44$	−576676.	−1.02058
$45$	9067.55	0.0148336
$46$	407790.	0.617709
$47$	132602.	0.186297	0.0931486	−	0.995652i	$-0.470307\pi$
$47$	132602.	0.186297	0.0931486	+	0.995652i	$0.470307\pi$
$48$	−138355.	−0.180572
$49$	117649.	0.142857
$50$	−1.10744e6	−1.25292
$51$	216921.	0.228985
$52$	−160445.	−0.158239
$53$	743372.	0.685868	0.342934	−	0.939359i	$-0.388579\pi$
$53$	743372.	0.685868	0.342934	+	0.939359i	$0.388579\pi$
$54$	−416211.	−0.359696
$55$	33443.4	0.0271045
$56$	−267336.	−0.203422
$57$	−62010.2	−0.0443508
$58$	−190349.	−0.128101
$59$	1.05200e6	0.666860	0.333430	−	0.942775i	$-0.391794\pi$
$59$	1.05200e6	0.666860	0.333430	+	0.942775i	$0.391794\pi$
$60$	−2097.81	−0.00125383
$61$	1.76584e6	0.996083	0.498042	−	0.867153i	$-0.334053\pi$
$61$	1.76584e6	0.996083	0.498042	+	0.867153i	$0.334053\pi$
$62$	−2.44994e6	−1.30552
$63$	−734362.	−0.370014
$64$	−75182.7	−0.0358499
$65$	9304.74	0.00420250
$66$	−759387.	−0.325132
$67$	744278.	0.302325	0.151162	−	0.988509i	$-0.451698\pi$
$67$	744278.	0.302325	0.151162	+	0.988509i	$0.451698\pi$
$68$	2.33561e6	0.900782
$69$	195076.	0.0714879
$70$	−20596.7	−0.00717719
$71$	383299.	0.127097	0.0635483	−	0.997979i	$-0.479758\pi$
$71$	383299.	0.127097	0.0635483	+	0.997979i	$0.479758\pi$
$72$	1.66870e6	0.526884
$73$	−3.29444e6	−0.991177	−0.495588	−	0.868557i	$-0.665048\pi$
$73$	−3.29444e6	−0.991177	−0.495588	+	0.868557i	$0.665048\pi$
$74$	−3.47408e6	−0.996618
$75$	−529770.	−0.145002
$76$	−667670.	−0.174467
$77$	−2.70851e6	−0.676104
$78$	−211279.	−0.0504110
$79$	−2.30144e6	−0.525175	−0.262588	−	0.964908i	$-0.584576\pi$
$79$	−2.30144e6	−0.525175	−0.262588	+	0.964908i	$0.584576\pi$
$80$	86391.7	0.0188650
$81$	4.48325e6	0.937337
$82$	−1.10330e7	−2.20976
$83$	−3.15382e6	−0.605429	−0.302715	−	0.953081i	$-0.597893\pi$
$83$	−3.15382e6	−0.605429	−0.302715	+	0.953081i	$0.597893\pi$
$84$	169897.	0.0312758
$85$	−135450.	−0.0239229
$86$	1.01186e7	1.71545
$87$	−91058.3	−0.0148252
$88$	6.15460e6	0.962743
$89$	−1.36538e6	−0.205300	−0.102650	−	0.994718i	$-0.532732\pi$
$89$	−1.36538e6	−0.205300	−0.102650	+	0.994718i	$0.532732\pi$
$90$	128564.	0.0185896
$91$	−753571.	−0.104828
$92$	2.10040e6	0.281219
$93$	−1.17199e6	−0.151089
$94$	1.88009e6	0.233470
$95$	38720.5	0.00463349
$96$	−1.28500e6	−0.148236
$97$	−1.40862e6	−0.156709	−0.0783543	−	0.996926i	$-0.524967\pi$
$97$	−1.40862e6	−0.156709	−0.0783543	+	0.996926i	$0.524967\pi$
$98$	1.66808e6	0.179030
$99$	1.69065e7	1.75117
$100$	−5.70408e6	−0.570408
$101$	1.57617e7	1.52222	0.761112	−	0.648620i	$-0.224654\pi$
$101$	1.57617e7	1.52222	0.761112	+	0.648620i	$0.224654\pi$
$102$	3.07561e6	0.286966
$103$	8.44811e6	0.761780	0.380890	−	0.924620i	$-0.375618\pi$
$103$	8.44811e6	0.761780	0.380890	+	0.924620i	$0.375618\pi$
$104$	1.71235e6	0.149271
$105$	−9852.93	−0.000830621 0
$106$	1.05399e7	0.859538
$107$	−2.23508e7	−1.76380	−0.881899	−	0.471437i	$-0.843735\pi$
$107$	−2.23508e7	−1.76380	−0.881899	+	0.471437i	$0.843735\pi$
$108$	−2.14378e6	−0.163756
$109$	2.67222e6	0.197642	0.0988210	−	0.995105i	$-0.468493\pi$
$109$	2.67222e6	0.197642	0.0988210	+	0.995105i	$0.468493\pi$
$110$	474177.	0.0339677
$111$	−1.66191e6	−0.115339
$112$	−6.99668e6	−0.470575
$113$	1.75901e7	1.14682	0.573409	−	0.819269i	$-0.305620\pi$
$113$	1.75901e7	1.14682	0.573409	+	0.819269i	$0.305620\pi$
$114$	−879210.	−0.0555809
$115$	−121810.	−0.00746860
$116$	−980432.	−0.0583196
$117$	4.70377e6	0.271516
$118$	1.49158e7	0.835716
$119$	1.09698e7	0.596740
$120$	22389.0	0.00118277
$121$	4.28681e7	2.19981
$122$	2.50368e7	1.24830
$123$	−5.27789e6	−0.255736
$124$	−1.26189e7	−0.594354
$125$	661675.	0.0303012
$126$	−1.04121e7	−0.463706
$127$	−1.88365e7	−0.815994	−0.407997	−	0.912983i	$-0.633773\pi$
$127$	−1.88365e7	−0.815994	−0.407997	+	0.912983i	$0.633773\pi$
$128$	2.31843e7	0.977146
$129$	4.84050e6	0.198530
$130$	131927.	0.00526662
$131$	−2.92085e7	−1.13517	−0.567584	−	0.823316i	$-0.692122\pi$
$131$	−2.92085e7	−1.13517	−0.567584	+	0.823316i	$0.692122\pi$
$132$	−3.91137e6	−0.148020
$133$	−3.13589e6	−0.115579
$134$	1.05527e7	0.378877
$135$	124325.	0.00434901
$136$	−2.49269e7	−0.849732
$137$	−3.09166e7	−1.02724	−0.513618	−	0.858019i	$-0.671695\pi$
$137$	−3.09166e7	−1.02724	−0.513618	+	0.858019i	$0.671695\pi$
$138$	2.76588e6	0.0895894
$139$	4.72180e6	0.149127	0.0745635	−	0.997216i	$-0.476244\pi$
$139$	4.72180e6	0.149127	0.0745635	+	0.997216i	$0.476244\pi$
$140$	−106087.	−0.00326750
$141$	899386.	0.0270196
$142$	5.43460e6	0.159279
$143$	1.73487e7	0.496124
$144$	4.36731e7	1.21883
$145$	56858.6	0.00154885
$146$	−4.67101e7	−1.24215
$147$	797968.	0.0207193
$148$	−1.78939e7	−0.453722
$149$	−6.35120e7	−1.57291	−0.786455	−	0.617648i	$-0.788086\pi$
$149$	−6.35120e7	−1.57291	−0.786455	+	0.617648i	$0.788086\pi$
$150$	−7.51133e6	−0.181718
$151$	1.03388e7	0.244371	0.122185	−	0.992507i	$-0.461010\pi$
$151$	1.03388e7	0.244371	0.122185	+	0.992507i	$0.461010\pi$
$152$	7.12573e6	0.164580
$153$	−6.84733e7	−1.54561
$154$	−3.84026e7	−0.847301
$155$	731813.	0.0157848
$156$	−1.08823e6	−0.0229502
$157$	1.07253e7	0.221188	0.110594	−	0.993866i	$-0.464725\pi$
$157$	1.07253e7	0.221188	0.110594	+	0.993866i	$0.464725\pi$
$158$	−3.26309e7	−0.658156
$159$	5.04201e6	0.0994749
$160$	802382.	0.0154868
$161$	9.86509e6	0.186299
$162$	6.35657e7	1.17468
$163$	−8.36920e7	−1.51366	−0.756828	−	0.653614i	$-0.773252\pi$
$163$	−8.36920e7	−1.51366	−0.756828	+	0.653614i	$0.773252\pi$
$164$	−5.68275e7	−1.00602
$165$	226834.	0.00393110
$166$	−4.47163e7	−0.758731
$167$	2.58014e7	0.428683	0.214342	−	0.976759i	$-0.431239\pi$
$167$	2.58014e7	0.428683	0.214342	+	0.976759i	$0.431239\pi$
$168$	−1.81324e6	−0.0295034
$169$	4.82681e6	0.0769231
$170$	−1.92048e6	−0.0299804
$171$	1.95741e7	0.299361
$172$	5.21181e7	0.780978
$173$	−1.19610e8	−1.75632	−0.878162	−	0.478364i	$-0.841230\pi$
$173$	−1.19610e8	−1.75632	−0.878162	+	0.478364i	$0.841230\pi$
$174$	−1.29107e6	−0.0185792
$175$	−2.67907e7	−0.377878
$176$	1.61077e8	2.22710
$177$	7.13532e6	0.0967180
$178$	−1.93590e7	−0.257284
$179$	3.97906e6	0.0518555	0.0259278	−	0.999664i	$-0.491746\pi$
$179$	3.97906e6	0.0518555	0.0259278	+	0.999664i	$0.491746\pi$
$180$	662194.	0.00846315
$181$	−1.44074e8	−1.80596	−0.902982	−	0.429678i	$-0.858627\pi$
$181$	−1.44074e8	−1.80596	−0.902982	+	0.429678i	$0.858627\pi$
$182$	−1.06845e7	−0.131372
$183$	1.19770e7	0.144467
$184$	−2.24166e7	−0.265282
$185$	1.03773e6	0.0120499
$186$	−1.66170e7	−0.189346
$187$	−2.52547e8	−2.82421
$188$	9.68377e6	0.106290
$189$	−1.00688e7	−0.108483
$190$	548997.	0.00580674
$191$	−6.58290e7	−0.683597	−0.341799	−	0.939773i	$-0.611036\pi$
$191$	−6.58290e7	−0.683597	−0.341799	+	0.939773i	$0.611036\pi$
$192$	−509935.	−0.00519949
$193$	−1.22231e8	−1.22386	−0.611931	−	0.790911i	$-0.709607\pi$
$193$	−1.22231e8	−1.22386	−0.611931	+	0.790911i	$0.709607\pi$
$194$	−1.99721e7	−0.196389
$195$	63110.5	0.000609509 0
$196$	8.59179e6	0.0815056
$197$	2.12664e8	1.98181	0.990903	−	0.134576i	$-0.0429673\pi$
$197$	2.12664e8	1.98181	0.990903	+	0.134576i	$0.0429673\pi$
$198$	2.39708e8	2.19459
$199$	1.33715e8	1.20280	0.601400	−	0.798948i	$-0.294610\pi$
$199$	1.33715e8	1.20280	0.601400	+	0.798948i	$0.294610\pi$
$200$	6.08770e7	0.538082
$201$	5.04815e6	0.0438476
$202$	2.23477e8	1.90767
$203$	−4.60486e6	−0.0386349
$204$	1.58416e7	0.130645
$205$	3.29562e6	0.0267177
$206$	1.19781e8	0.954671
$207$	−6.15776e7	−0.482533
$208$	4.48155e7	0.345308
$209$	7.21943e7	0.547005
$210$	−139700.	−0.00104094
$211$	9.13240e7	0.669262	0.334631	−	0.942349i	$-0.391388\pi$
$211$	9.13240e7	0.669262	0.334631	+	0.942349i	$0.391388\pi$
$212$	5.42877e7	0.391315
$213$	2.59977e6	0.0184334
$214$	−3.16900e8	−2.21041
$215$	−3.02251e6	−0.0207411
$216$	2.28795e7	0.154475
$217$	−5.92680e7	−0.393741
$218$	3.78880e7	0.247687
$219$	−2.23449e7	−0.143755
$220$	2.44234e6	0.0154642
$221$	−7.02644e7	−0.437887
$222$	−2.35633e7	−0.144544
$223$	1.77088e8	1.06935	0.534677	−	0.845057i	$-0.320433\pi$
$223$	1.77088e8	1.06935	0.534677	+	0.845057i	$0.320433\pi$
$224$	−6.49832e7	−0.386307
$225$	1.67227e8	0.978740
$226$	2.49401e8	1.43721
$227$	−1.07588e8	−0.610484	−0.305242	−	0.952275i	$-0.598737\pi$
$227$	−1.07588e8	−0.610484	−0.305242	+	0.952275i	$0.598737\pi$
$228$	−4.52855e6	−0.0253039
$229$	1.45669e7	0.0801572	0.0400786	−	0.999197i	$-0.487239\pi$
$229$	1.45669e7	0.0801572	0.0400786	+	0.999197i	$0.487239\pi$
$230$	−1.72707e6	−0.00935973
$231$	−1.83708e7	−0.0980587
$232$	1.04637e7	0.0550145
$233$	2.07312e8	1.07369	0.536845	−	0.843681i	$-0.319616\pi$
$233$	2.07312e8	1.07369	0.536845	+	0.843681i	$0.319616\pi$
$234$	6.66922e7	0.340267
$235$	−561595.	−0.00282284
$236$	7.68267e7	0.380470
$237$	−1.56098e7	−0.0761688
$238$	1.55535e8	0.747841
$239$	−9.60165e7	−0.454939	−0.227469	−	0.973785i	$-0.573045\pi$
$239$	−9.60165e7	−0.454939	−0.227469	+	0.973785i	$0.573045\pi$
$240$	585962.	0.00273609
$241$	−3.30651e8	−1.52163	−0.760816	−	0.648967i	$-0.775201\pi$
$241$	−3.30651e8	−1.52163	−0.760816	+	0.648967i	$0.775201\pi$
$242$	6.07805e8	2.75683
$243$	9.46078e7	0.422966
$244$	1.28957e8	0.568305
$245$	−498267.	−0.00216462
$246$	−7.48324e7	−0.320492
$247$	2.00861e7	0.0848120
$248$	1.34676e8	0.560671
$249$	−2.13911e7	−0.0878084
$250$	9.38153e6	0.0379738
$251$	−2.91957e8	−1.16536	−0.582681	−	0.812701i	$-0.697996\pi$
$251$	−2.91957e8	−1.16536	−0.582681	+	0.812701i	$0.697996\pi$
$252$	−5.36297e7	−0.211107
$253$	−2.27114e8	−0.881702
$254$	−2.67073e8	−1.02261
$255$	−918706.	−0.00346965
$256$	3.38342e8	1.26042
$257$	−4.45549e8	−1.63731	−0.818653	−	0.574289i	$-0.805279\pi$
$257$	−4.45549e8	−1.63731	−0.818653	+	0.574289i	$0.805279\pi$
$258$	6.86309e7	0.248800
$259$	−8.40436e7	−0.300577
$260$	679516.	0.00239769
$261$	2.87434e7	0.100068
$262$	−4.14132e8	−1.42261
$263$	7.86991e7	0.266762	0.133381	−	0.991065i	$-0.457417\pi$
$263$	7.86991e7	0.266762	0.133381	+	0.991065i	$0.457417\pi$
$264$	4.17443e7	0.139631
$265$	−3.14833e6	−0.0103925
$266$	−4.44621e7	−0.144845
$267$	−9.26083e6	−0.0297756
$268$	5.43539e7	0.172488
$269$	−5.41542e8	−1.69629	−0.848144	−	0.529766i	$-0.822280\pi$
$269$	−5.41542e8	−1.69629	−0.848144	+	0.529766i	$0.822280\pi$
$270$	1.76274e6	0.00545022
$271$	4.01239e8	1.22465	0.612323	−	0.790608i	$-0.290235\pi$
$271$	4.01239e8	1.22465	0.612323	+	0.790608i	$0.290235\pi$
$272$	−6.52384e8	−1.96568
$273$	−5.11118e6	−0.0152038
$274$	−4.38351e8	−1.28734
$275$	6.16775e8	1.78839
$276$	1.42462e7	0.0407866
$277$	−2.09709e8	−0.592841	−0.296420	−	0.955058i	$-0.595793\pi$
$277$	−2.09709e8	−0.592841	−0.296420	+	0.955058i	$0.595793\pi$
$278$	6.69480e7	0.186888
$279$	3.69949e8	1.01983
$280$	1.13222e6	0.00308232
$281$	4.84561e7	0.130279	0.0651397	−	0.997876i	$-0.479251\pi$
$281$	4.84561e7	0.130279	0.0651397	+	0.997876i	$0.479251\pi$
$282$	1.27519e7	0.0338613
$283$	−5.91245e8	−1.55065	−0.775327	−	0.631560i	$-0.782415\pi$
$283$	−5.91245e8	−1.55065	−0.775327	+	0.631560i	$0.782415\pi$
$284$	2.79920e7	0.0725136
$285$	262626.	0.000672018 0
$286$	2.45978e8	0.621749
$287$	−2.66906e8	−0.666455
$288$	4.05623e8	1.00057
$289$	6.12508e8	1.49269
$290$	806169.	0.00194103
$291$	−9.55413e6	−0.0227282
$292$	−2.40589e8	−0.565505
$293$	4.23336e8	0.983215	0.491607	−	0.870817i	$-0.336410\pi$
$293$	4.23336e8	0.983215	0.491607	+	0.870817i	$0.336410\pi$
$294$	1.13140e7	0.0259656
$295$	−4.45544e6	−0.0101045
$296$	1.90974e8	0.428008
$297$	2.31804e8	0.513420
$298$	−9.00503e8	−1.97119
$299$	−6.31884e7	−0.136706
$300$	−3.86886e7	−0.0827291
$301$	2.44786e8	0.517374
$302$	1.46588e8	0.306249
$303$	1.06906e8	0.220776
$304$	1.86494e8	0.380721
$305$	−7.47867e6	−0.0150930
$306$	−9.70846e8	−1.93698
$307$	2.05699e8	0.405741	0.202870	−	0.979206i	$-0.434973\pi$
$307$	2.05699e8	0.405741	0.202870	+	0.979206i	$0.434973\pi$
$308$	−1.97800e8	−0.385744
$309$	5.73003e7	0.110485
$310$	1.03760e7	0.0197817
$311$	−9.59049e6	−0.0180792	−0.00903961	−	0.999959i	$-0.502877\pi$
$311$	−9.59049e6	−0.0180792	−0.00903961	+	0.999959i	$0.502877\pi$
$312$	1.16142e7	0.0216496
$313$	−1.75652e8	−0.323778	−0.161889	−	0.986809i	$-0.551759\pi$
$313$	−1.75652e8	−0.323778	−0.161889	+	0.986809i	$0.551759\pi$
$314$	1.52068e8	0.277195
$315$	3.11017e6	0.00560657
$316$	−1.68072e8	−0.299633
$317$	2.37691e8	0.419087	0.209544	−	0.977799i	$-0.432802\pi$
$317$	2.37691e8	0.419087	0.209544	+	0.977799i	$0.432802\pi$
$318$	7.14879e7	0.124663
$319$	1.06013e8	0.182849
$320$	318414.	0.000543210 0
$321$	−1.51597e8	−0.255813
$322$	1.39872e8	0.233472
$323$	−2.92396e8	−0.482795
$324$	3.27408e8	0.534787
$325$	1.71601e8	0.277286
$326$	−1.18662e9	−1.89693
$327$	1.81246e7	0.0286650
$328$	6.06494e8	0.949004
$329$	4.54824e7	0.0704137
$330$	3.21616e6	0.00492650
$331$	−2.39476e8	−0.362965	−0.181482	−	0.983394i	$-0.558090\pi$
$331$	−2.39476e8	−0.362965	−0.181482	+	0.983394i	$0.558090\pi$
$332$	−2.30320e8	−0.345421
$333$	5.24598e8	0.778523
$334$	3.65825e8	0.537231
$335$	−3.15217e6	−0.00458092
$336$	−4.74558e7	−0.0682498
$337$	−1.11824e9	−1.59158	−0.795791	−	0.605571i	$-0.792945\pi$
$337$	−1.11824e9	−1.59158	−0.795791	+	0.605571i	$0.792945\pi$
$338$	6.84368e7	0.0964009
$339$	1.19307e8	0.166329
$340$	−9.89179e6	−0.0136489
$341$	1.36447e9	1.86347
$342$	2.77531e8	0.375163
$343$	4.03536e7	0.0539949
$344$	−5.56232e8	−0.736718
$345$	−826187.	−0.00108321
$346$	−1.69588e9	−2.20104
$347$	−2.13142e8	−0.273852	−0.136926	−	0.990581i	$-0.543722\pi$
$347$	−2.13142e8	−0.273852	−0.136926	+	0.990581i	$0.543722\pi$
$348$	−6.64989e6	−0.00845838
$349$	7.18720e8	0.905046	0.452523	−	0.891753i	$-0.350524\pi$
$349$	7.18720e8	0.905046	0.452523	+	0.891753i	$0.350524\pi$
$350$	−3.79851e8	−0.473561
$351$	6.44932e7	0.0796048
$352$	1.49604e9	1.82829
$353$	−4.62333e8	−0.559428	−0.279714	−	0.960083i	$-0.590240\pi$
$353$	−4.62333e8	−0.559428	−0.279714	+	0.960083i	$0.590240\pi$
$354$	1.01168e8	0.121208
$355$	−1.62335e6	−0.00192581
$356$	−9.97122e7	−0.117131
$357$	7.44040e7	0.0865481
$358$	5.64170e7	0.0649859
$359$	−5.22700e7	−0.0596241	−0.0298120	−	0.999556i	$-0.509491\pi$
$359$	−5.22700e7	−0.0596241	−0.0298120	+	0.999556i	$0.509491\pi$
$360$	−7.06729e6	−0.00798352
$361$	−8.10286e8	−0.906490
$362$	−2.04274e9	−2.26326
$363$	2.90758e8	0.319050
$364$	−5.50325e7	−0.0598088
$365$	1.39526e7	0.0150186
$366$	1.69815e8	0.181048
$367$	1.14754e9	1.21182	0.605910	−	0.795533i	$-0.292809\pi$
$367$	1.14754e9	1.21182	0.605910	+	0.795533i	$0.292809\pi$
$368$	−5.86685e8	−0.613674
$369$	1.66602e9	1.72618
$370$	1.47134e7	0.0151011
$371$	2.54977e8	0.259234
$372$	−8.55891e7	−0.0862021
$373$	1.45073e9	1.44746	0.723731	−	0.690082i	$-0.242426\pi$
$373$	1.45073e9	1.44746	0.723731	+	0.690082i	$0.242426\pi$
$374$	−3.58073e9	−3.53933
$375$	4.48788e6	0.00439473
$376$	−1.03350e8	−0.100266
$377$	2.94953e7	0.0283503
$378$	−1.42760e8	−0.135952
$379$	4.04404e8	0.381574	0.190787	−	0.981631i	$-0.438896\pi$
$379$	4.04404e8	0.381574	0.190787	+	0.981631i	$0.438896\pi$
$380$	2.82772e6	0.00264359
$381$	−1.27761e8	−0.118348
$382$	−9.33354e8	−0.856692
$383$	−1.75951e9	−1.60028	−0.800138	−	0.599816i	$-0.795240\pi$
$383$	−1.75951e9	−1.60028	−0.800138	+	0.599816i	$0.795240\pi$
$384$	1.57250e8	0.141720
$385$	1.14711e7	0.0102445
$386$	−1.73305e9	−1.53376
$387$	−1.52795e9	−1.34005
$388$	−1.02870e8	−0.0894084
$389$	−1.35193e9	−1.16448	−0.582238	−	0.813019i	$-0.697823\pi$
$389$	−1.35193e9	−1.16448	−0.582238	+	0.813019i	$0.697823\pi$
$390$	894810.	0.000763844 0
$391$	9.19840e8	0.778205
$392$	−9.16962e7	−0.0768865
$393$	−1.98110e8	−0.164639
$394$	3.01524e9	2.48362
$395$	9.74705e6	0.00795763
$396$	1.23466e9	0.999114
$397$	−1.06139e8	−0.0851350	−0.0425675	−	0.999094i	$-0.513554\pi$
$397$	−1.06139e8	−0.0851350	−0.0425675	+	0.999094i	$0.513554\pi$
$398$	1.89587e9	1.50736
$399$	−2.12695e7	−0.0167630
$400$	1.59327e9	1.24474
$401$	1.62632e9	1.25951	0.629755	−	0.776794i	$-0.283155\pi$
$401$	1.62632e9	1.25951	0.629755	+	0.776794i	$0.283155\pi$
$402$	7.15751e7	0.0549504
$403$	3.79626e8	0.288927
$404$	1.15106e9	0.868488
$405$	−1.89875e7	−0.0142028
$406$	−6.52899e7	−0.0484177
$407$	1.93485e9	1.42255
$408$	−1.69070e8	−0.123241
$409$	−3.64660e8	−0.263546	−0.131773	−	0.991280i	$-0.542067\pi$
$409$	−3.64660e8	−0.263546	−0.131773	+	0.991280i	$0.542067\pi$
$410$	4.67269e7	0.0334829
$411$	−2.09696e8	−0.148985
$412$	6.16957e8	0.434625
$413$	3.60837e8	0.252049
$414$	−8.73077e8	−0.604716
$415$	1.33571e7	0.00917366
$416$	4.16234e8	0.283472
$417$	3.20262e7	0.0216286
$418$	1.02361e9	0.685513
$419$	−2.17097e7	−0.0144180	−0.00720899	−	0.999974i	$-0.502295\pi$
$419$	−2.17097e7	−0.0144180	−0.00720899	+	0.999974i	$0.502295\pi$
$420$	−719550.	−0.000473902 0
$421$	−8.42655e8	−0.550380	−0.275190	−	0.961390i	$-0.588741\pi$
$421$	−8.42655e8	−0.550380	−0.275190	+	0.961390i	$0.588741\pi$
$422$	1.29483e9	0.838727
$423$	−2.83900e8	−0.182378
$424$	−5.79388e8	−0.369138
$425$	−2.49802e9	−1.57846
$426$	3.68608e7	0.0231010
$427$	6.05681e8	0.376484
$428$	−1.63225e9	−1.00632
$429$	1.17669e8	0.0719554
$430$	−4.28545e7	−0.0259930
$431$	7.78311e8	0.468255	0.234128	−	0.972206i	$-0.424777\pi$
$431$	7.78311e8	0.468255	0.234128	+	0.972206i	$0.424777\pi$
$432$	5.98800e8	0.357346
$433$	1.08344e8	0.0641353	0.0320677	−	0.999486i	$-0.489791\pi$
$433$	1.08344e8	0.0641353	0.0320677	+	0.999486i	$0.489791\pi$
$434$	−8.40329e8	−0.493441
$435$	385650.	0.000224637 0
$436$	1.95149e8	0.112762
$437$	−2.62950e8	−0.150726
$438$	−3.16816e8	−0.180156
$439$	2.99962e9	1.69216	0.846079	−	0.533058i	$-0.178957\pi$
$439$	2.99962e9	1.69216	0.846079	+	0.533058i	$0.178957\pi$
$440$	−2.60660e7	−0.0145878
$441$	−2.51886e8	−0.139852
$442$	−9.96242e8	−0.548765
$443$	−1.32632e9	−0.724827	−0.362413	−	0.932017i	$-0.618047\pi$
$443$	−1.32632e9	−0.724827	−0.362413	+	0.932017i	$0.618047\pi$
$444$	−1.21368e8	−0.0658055
$445$	5.78266e6	0.00311077
$446$	2.51083e9	1.34013
$447$	−4.30777e8	−0.228127
$448$	−2.57877e7	−0.0135500
$449$	−2.05878e9	−1.07337	−0.536683	−	0.843784i	$-0.680323\pi$
$449$	−2.05878e9	−1.07337	−0.536683	+	0.843784i	$0.680323\pi$
$450$	2.37102e9	1.22657
$451$	6.14469e9	3.15415
$452$	1.28459e9	0.654305
$453$	7.01239e7	0.0354423
$454$	−1.52544e9	−0.765065
$455$	3.19153e6	0.00158840
$456$	4.83311e7	0.0238698
$457$	−1.73861e9	−0.852111	−0.426055	−	0.904697i	$-0.640097\pi$
$457$	−1.73861e9	−0.852111	−0.426055	+	0.904697i	$0.640097\pi$
$458$	2.06536e8	0.100454
$459$	−9.38835e8	−0.453153
$460$	−8.89563e6	−0.00426113
$461$	3.26227e9	1.55084	0.775419	−	0.631448i	$-0.217539\pi$
$461$	3.26227e9	1.55084	0.775419	+	0.631448i	$0.217539\pi$
$462$	−2.60470e8	−0.122888
$463$	4.02274e9	1.88360	0.941799	−	0.336177i	$-0.109134\pi$
$463$	4.02274e9	1.88360	0.941799	+	0.336177i	$0.109134\pi$
$464$	2.73855e8	0.127264
$465$	4.96361e6	0.00228935
$466$	2.93937e9	1.34556
$467$	−3.53786e9	−1.60743	−0.803715	−	0.595015i	$-0.797146\pi$
$467$	−3.53786e9	−1.60743	−0.803715	+	0.595015i	$0.797146\pi$
$468$	3.43512e8	0.154910
$469$	2.55287e8	0.114268
$470$	−7.96256e6	−0.00353761
$471$	7.27456e7	0.0320799
$472$	−8.19935e8	−0.358907
$473$	−5.63547e9	−2.44859
$474$	−2.21322e8	−0.0954556
$475$	7.14096e8	0.305724
$476$	8.01115e8	0.340463
$477$	−1.59156e9	−0.671441
$478$	−1.36137e9	−0.570135
$479$	−3.37375e9	−1.40261	−0.701307	−	0.712860i	$-0.747400\pi$
$479$	−3.37375e9	−1.40261	−0.701307	+	0.712860i	$0.747400\pi$
$480$	5.44225e6	0.00224613
$481$	5.38320e8	0.220563
$482$	−4.68812e9	−1.90693
$483$	6.69111e7	0.0270199
$484$	3.13062e9	1.25508
$485$	5.96580e6	0.00237450
$486$	1.34139e9	0.530066
$487$	1.44875e9	0.568384	0.284192	−	0.958767i	$-0.408275\pi$
$487$	1.44875e9	0.568384	0.284192	+	0.958767i	$0.408275\pi$
$488$	−1.37630e9	−0.536097
$489$	−5.67650e8	−0.219533
$490$	−7.06467e6	−0.00271272
$491$	3.69191e9	1.40756	0.703779	−	0.710419i	$-0.251495\pi$
$491$	3.69191e9	1.40756	0.703779	+	0.710419i	$0.251495\pi$
$492$	−3.85439e8	−0.145908
$493$	−4.29366e8	−0.161385
$494$	2.84791e8	0.106287
$495$	−7.16023e7	−0.0265344
$496$	3.52471e9	1.29699
$497$	1.31472e8	0.0480380
$498$	−3.03294e8	−0.110043
$499$	3.77246e9	1.35917	0.679583	−	0.733599i	$-0.262161\pi$
$499$	3.77246e9	1.35917	0.679583	+	0.733599i	$0.262161\pi$
$500$	4.83214e7	0.0172880
$501$	1.75001e8	0.0621740
$502$	−4.13951e9	−1.46045
$503$	2.38391e9	0.835223	0.417611	−	0.908626i	$-0.362867\pi$
$503$	2.38391e9	0.835223	0.417611	+	0.908626i	$0.362867\pi$
$504$	5.72365e8	0.199143
$505$	−6.67541e7	−0.0230652
$506$	−3.22013e9	−1.10496
$507$	3.27384e7	0.0111565
$508$	−1.37561e9	−0.465556
$509$	−1.98641e9	−0.667663	−0.333831	−	0.942633i	$-0.608342\pi$
$509$	−1.98641e9	−0.667663	−0.333831	+	0.942633i	$0.608342\pi$
$510$	−1.30258e7	−0.00434821
$511$	−1.12999e9	−0.374630
$512$	1.82957e9	0.602427
$513$	2.68380e8	0.0877687
$514$	−6.31721e9	−2.05189
$515$	−3.57795e7	−0.0115427
$516$	3.53497e8	0.113269
$517$	−1.04709e9	−0.333249
$518$	−1.19161e9	−0.376686
$519$	−8.11265e8	−0.254728
$520$	−7.25216e6	−0.00226181
$521$	1.17398e9	0.363688	0.181844	−	0.983327i	$-0.441793\pi$
$521$	1.17398e9	0.363688	0.181844	+	0.983327i	$0.441793\pi$
$522$	4.07537e8	0.125407
$523$	−4.23345e9	−1.29401	−0.647006	−	0.762485i	$-0.723979\pi$
$523$	−4.23345e9	−1.29401	−0.647006	+	0.762485i	$0.723979\pi$
$524$	−2.13307e9	−0.647658
$525$	−1.81711e8	−0.0548055
$526$	1.11583e9	0.334310
$527$	−5.52626e9	−1.64473
$528$	1.09253e9	0.323008
$529$	−2.57762e9	−0.757049
$530$	−4.46385e7	−0.0130240
$531$	−2.25233e9	−0.652832
$532$	−2.29011e8	−0.0659425
$533$	1.70960e9	0.489044
$534$	−1.31304e8	−0.0373151
$535$	9.46600e7	0.0267257
$536$	−5.80094e8	−0.162713
$537$	2.69884e7	0.00752086
$538$	−7.67824e9	−2.12581
$539$	−9.29020e8	−0.255543
$540$	9.07933e6	0.00248128
$541$	−4.48035e9	−1.21653	−0.608263	−	0.793736i	$-0.708133\pi$
$541$	−4.48035e9	−1.21653	−0.608263	+	0.793736i	$0.708133\pi$
$542$	5.68895e9	1.53474
$543$	−9.77195e8	−0.261928
$544$	−6.05916e9	−1.61368
$545$	−1.13174e7	−0.00299473
$546$	−7.24687e7	−0.0190536
$547$	6.39802e9	1.67144	0.835718	−	0.549159i	$-0.185052\pi$
$547$	6.39802e9	1.67144	0.835718	+	0.549159i	$0.185052\pi$
$548$	−2.25781e9	−0.586078
$549$	−3.78065e9	−0.975131
$550$	8.74493e9	2.24123
$551$	1.22741e8	0.0312578
$552$	−1.52043e8	−0.0384752
$553$	−7.89393e8	−0.198498
$554$	−2.97335e9	−0.742955
$555$	7.03853e6	0.00174766
$556$	3.44829e8	0.0850828
$557$	−2.53397e9	−0.621311	−0.310655	−	0.950523i	$-0.600548\pi$
$557$	−2.53397e9	−0.621311	−0.310655	+	0.950523i	$0.600548\pi$
$558$	5.24531e9	1.27806
$559$	−1.56792e9	−0.379649
$560$	2.96324e7	0.00713030
$561$	−1.71293e9	−0.409609
$562$	6.87033e8	0.163268
$563$	4.29257e9	1.01377	0.506883	−	0.862015i	$-0.330798\pi$
$563$	4.29257e9	1.01377	0.506883	+	0.862015i	$0.330798\pi$
$564$	6.56813e7	0.0154157
$565$	−7.44978e7	−0.0173770
$566$	−8.38295e9	−1.94330
$567$	1.53776e9	0.354280
$568$	−2.98745e8	−0.0684041
$569$	3.31946e9	0.755396	0.377698	−	0.925929i	$-0.376716\pi$
$569$	3.31946e9	0.755396	0.377698	+	0.925929i	$0.376716\pi$
$570$	3.72364e6	0.000842180 0
$571$	1.51995e8	0.0341668	0.0170834	−	0.999854i	$-0.494562\pi$
$571$	1.51995e8	0.0341668	0.0170834	+	0.999854i	$0.494562\pi$
$572$	1.26696e9	0.283058
$573$	−4.46492e8	−0.0991455
$574$	−3.78431e9	−0.835209
$575$	−2.24645e9	−0.492788
$576$	1.60966e8	0.0350958
$577$	−5.73397e8	−0.124263	−0.0621313	−	0.998068i	$-0.519790\pi$
$577$	−5.73397e8	−0.124263	−0.0621313	+	0.998068i	$0.519790\pi$
$578$	8.68443e9	1.87066
$579$	−8.29049e8	−0.177503
$580$	4.15233e6	0.000883678 0
$581$	−1.08176e9	−0.228831
$582$	−1.35463e8	−0.0284833
$583$	−5.87007e9	−1.22688
$584$	2.56770e9	0.533457
$585$	−1.99214e7	−0.00411410
$586$	6.00225e9	1.23218
$587$	−4.92920e9	−1.00587	−0.502936	−	0.864324i	$-0.667747\pi$
$587$	−4.92920e9	−1.00587	−0.502936	+	0.864324i	$0.667747\pi$
$588$	5.82748e7	0.0118212
$589$	1.57976e9	0.318558
$590$	−6.31714e7	−0.0126630
$591$	1.44241e9	0.287431
$592$	4.99814e9	0.990107
$593$	−1.67170e7	−0.00329205	−0.00164603	−	0.999999i	$-0.500524\pi$
$593$	−1.67170e7	−0.00329205	−0.00164603	+	0.999999i	$0.500524\pi$
$594$	3.28662e9	0.643424
$595$	−4.64594e7	−0.00904200
$596$	−4.63822e9	−0.897406
$597$	9.06935e8	0.174448
$598$	−8.95914e8	−0.171322
$599$	7.62725e8	0.145002	0.0725010	−	0.997368i	$-0.476902\pi$
$599$	7.62725e8	0.145002	0.0725010	+	0.997368i	$0.476902\pi$
$600$	4.12905e8	0.0780407
$601$	9.05252e9	1.70102	0.850509	−	0.525960i	$-0.176294\pi$
$601$	9.05252e9	1.70102	0.850509	+	0.525960i	$0.176294\pi$
$602$	3.47070e9	0.648379
$603$	−1.59350e9	−0.295965
$604$	7.55030e8	0.139423
$605$	−1.81555e8	−0.0333323
$606$	1.51576e9	0.276679
$607$	6.84926e9	1.24303	0.621517	−	0.783401i	$-0.286517\pi$
$607$	6.84926e9	1.24303	0.621517	+	0.783401i	$0.286517\pi$
$608$	1.73210e9	0.312544
$609$	−3.12330e7	−0.00560342
$610$	−1.06036e8	−0.0189147
$611$	−2.91326e8	−0.0516696
$612$	−5.00054e9	−0.881834
$613$	−1.74317e9	−0.305653	−0.152826	−	0.988253i	$-0.548838\pi$
$613$	−1.74317e9	−0.305653	−0.152826	+	0.988253i	$0.548838\pi$
$614$	2.91650e9	0.508479
$615$	2.23529e7	0.00387500
$616$	2.11103e9	0.363883
$617$	7.09852e9	1.21666	0.608331	−	0.793684i	$-0.291839\pi$
$617$	7.09852e9	1.21666	0.608331	+	0.793684i	$0.291839\pi$
$618$	8.12430e8	0.138461
$619$	9.12322e9	1.54608	0.773038	−	0.634360i	$-0.218736\pi$
$619$	9.12322e9	1.54608	0.773038	+	0.634360i	$0.218736\pi$
$620$	5.34436e7	0.00900585
$621$	−8.44289e8	−0.141472
$622$	−1.35979e8	−0.0226571
$623$	−4.68325e8	−0.0775959
$624$	3.03966e8	0.0500817
$625$	6.09931e9	0.999311
$626$	−2.49048e9	−0.405763
$627$	4.89666e8	0.0793348
$628$	7.83258e8	0.126196
$629$	−7.83638e9	−1.25556
$630$	4.40975e7	0.00702622
$631$	3.81738e9	0.604871	0.302435	−	0.953170i	$-0.402200\pi$
$631$	3.81738e9	0.604871	0.302435	+	0.953170i	$0.402200\pi$
$632$	1.79375e9	0.282652
$633$	6.19416e8	0.0970665
$634$	3.37009e9	0.525205
$635$	7.97764e7	0.0123642
$636$	3.68213e8	0.0567543
$637$	−2.58475e8	−0.0396214
$638$	1.50310e9	0.229148
$639$	−8.20643e8	−0.124423
$640$	−9.81903e7	−0.0148060
$641$	1.10940e10	1.66373	0.831866	−	0.554976i	$-0.187273\pi$
$641$	1.10940e10	1.66373	0.831866	+	0.554976i	$0.187273\pi$
$642$	−2.14941e9	−0.320587
$643$	2.55934e9	0.379655	0.189827	−	0.981817i	$-0.439207\pi$
$643$	2.55934e9	0.379655	0.189827	+	0.981817i	$0.439207\pi$
$644$	7.20438e8	0.106291
$645$	−2.05005e7	−0.00300819
$646$	−4.14573e9	−0.605044
$647$	2.73789e9	0.397421	0.198710	−	0.980058i	$-0.436325\pi$
$647$	2.73789e9	0.397421	0.198710	+	0.980058i	$0.436325\pi$
$648$	−3.49427e9	−0.504480
$649$	−8.30717e9	−1.19288
$650$	2.43304e9	0.347499
$651$	−4.01992e8	−0.0571062
$652$	−6.11194e9	−0.863600
$653$	−1.05682e10	−1.48526	−0.742632	−	0.669700i	$-0.766423\pi$
$653$	−1.05682e10	−1.48526	−0.742632	+	0.669700i	$0.766423\pi$
$654$	2.56979e8	0.0359233
$655$	1.23704e8	0.0172004
$656$	1.58731e10	2.19532
$657$	7.05338e9	0.970327
$658$	6.44870e8	0.0882433
$659$	1.20741e10	1.64344	0.821722	−	0.569888i	$-0.193013\pi$
$659$	1.20741e10	1.64344	0.821722	+	0.569888i	$0.193013\pi$
$660$	1.65655e7	0.00224285
$661$	5.35648e9	0.721397	0.360699	−	0.932682i	$-0.382538\pi$
$661$	5.35648e9	0.721397	0.360699	+	0.932682i	$0.382538\pi$
$662$	−3.39541e9	−0.454872
$663$	−4.76576e8	−0.0635090
$664$	2.45810e9	0.325845
$665$	1.32811e7	0.00175129
$666$	7.43799e9	0.975654
$667$	−3.86126e8	−0.0503836
$668$	1.88425e9	0.244580
$669$	1.20112e9	0.155094
$670$	−4.46929e7	−0.00574086
$671$	−1.39440e10	−1.78180
$672$	−4.40756e8	−0.0560281
$673$	1.55353e9	0.196457	0.0982287	−	0.995164i	$-0.468682\pi$
$673$	1.55353e9	0.196457	0.0982287	+	0.995164i	$0.468682\pi$
$674$	−1.58549e10	−1.99459
$675$	2.29284e9	0.286953
$676$	3.52497e8	0.0438876
$677$	−9.46059e9	−1.17181	−0.585906	−	0.810379i	$-0.699261\pi$
$677$	−9.46059e9	−1.17181	−0.585906	+	0.810379i	$0.699261\pi$
$678$	1.69159e9	0.208445
$679$	−4.83157e8	−0.0592303
$680$	1.05570e8	0.0128754
$681$	−7.29729e8	−0.0885415
$682$	1.93460e10	2.33532
$683$	−2.99091e9	−0.359196	−0.179598	−	0.983740i	$-0.557480\pi$
$683$	−2.99091e9	−0.359196	−0.179598	+	0.983740i	$0.557480\pi$
$684$	1.42948e9	0.170797
$685$	1.30938e8	0.0155650
$686$	5.72152e8	0.0676671
$687$	9.88016e7	0.0116256
$688$	−1.45576e10	−1.70424
$689$	−1.63319e9	−0.190226
$690$	−1.17141e7	−0.00135749
$691$	−4.13933e9	−0.477262	−0.238631	−	0.971110i	$-0.576699\pi$
$691$	−4.13933e9	−0.477262	−0.238631	+	0.971110i	$0.576699\pi$
$692$	−8.73496e9	−1.00205
$693$	5.79891e9	0.661882
$694$	−3.02203e9	−0.343194
$695$	−1.99978e7	−0.00225962
$696$	7.09712e7	0.00797903
$697$	−2.48868e10	−2.78390
$698$	1.01904e10	1.13421
$699$	1.40612e9	0.155723
$700$	−1.95650e9	−0.215594
$701$	4.65534e9	0.510432	0.255216	−	0.966884i	$-0.417853\pi$
$701$	4.65534e9	0.510432	0.255216	+	0.966884i	$0.417853\pi$
$702$	9.14415e8	0.0997616
$703$	2.24015e9	0.243183
$704$	5.93683e8	0.0641284
$705$	−3.80908e6	−0.000409410 0
$706$	−6.55518e9	−0.701081
$707$	5.40627e9	0.575347
$708$	5.21086e8	0.0551814
$709$	−1.78640e10	−1.88243	−0.941213	−	0.337813i	$-0.890313\pi$
$709$	−1.78640e10	−1.88243	−0.941213	+	0.337813i	$0.890313\pi$
$710$	−2.30166e7	−0.00241345
$711$	4.92737e9	0.514128
$712$	1.06418e9	0.110493
$713$	−4.96973e9	−0.513475
$714$	1.05494e9	0.108463
$715$	−7.34752e7	−0.00751744
$716$	2.90587e8	0.0295856
$717$	−6.51243e8	−0.0659821
$718$	−7.41108e8	−0.0747216
$719$	−1.18738e10	−1.19134	−0.595672	−	0.803228i	$-0.703114\pi$
$719$	−1.18738e10	−1.19134	−0.595672	+	0.803228i	$0.703114\pi$
$720$	−1.84964e8	−0.0184682
$721$	2.89770e9	0.287926
$722$	−1.14886e10	−1.13602
$723$	−2.24268e9	−0.220690
$724$	−1.05215e10	−1.03037
$725$	1.04861e9	0.102195
$726$	4.12250e9	0.399837
$727$	−7.11104e8	−0.0686377	−0.0343189	−	0.999411i	$-0.510926\pi$
$727$	−7.11104e8	−0.0686377	−0.0343189	+	0.999411i	$0.510926\pi$
$728$	5.87337e8	0.0564192
$729$	−9.16319e9	−0.875992
$730$	1.97827e8	0.0188215
$731$	2.28243e10	2.16116
$732$	8.74667e8	0.0824240
$733$	−1.05216e10	−0.986772	−0.493386	−	0.869810i	$-0.664241\pi$
$733$	−1.05216e10	−0.986772	−0.493386	+	0.869810i	$0.664241\pi$
$734$	1.62704e10	1.51867
$735$	−3.37956e6	−0.000313945 0
$736$	−5.44897e9	−0.503781
$737$	−5.87722e9	−0.540799
$738$	2.36216e10	2.16327
$739$	−2.00163e9	−0.182444	−0.0912218	−	0.995831i	$-0.529077\pi$
$739$	−2.00163e9	−0.182444	−0.0912218	+	0.995831i	$0.529077\pi$
$740$	7.57844e7	0.00687494
$741$	1.36237e8	0.0123007
$742$	3.61518e9	0.324875
$743$	1.94561e9	0.174018	0.0870092	−	0.996208i	$-0.472269\pi$
$743$	1.94561e9	0.174018	0.0870092	+	0.996208i	$0.472269\pi$
$744$	9.13452e8	0.0813169
$745$	2.68986e8	0.0238332
$746$	2.05692e10	1.81398
$747$	6.75231e9	0.592694
$748$	−1.84432e10	−1.61132
$749$	−7.66631e9	−0.666653
$750$	6.36313e7	0.00550753
$751$	1.36710e10	1.17777	0.588884	−	0.808218i	$-0.299568\pi$
$751$	1.36710e10	1.17777	0.588884	+	0.808218i	$0.299568\pi$
$752$	−2.70487e9	−0.231945
$753$	−1.98023e9	−0.169018
$754$	4.18198e8	0.0355289
$755$	−4.37868e7	−0.00370279
$756$	−7.35315e8	−0.0618938
$757$	−1.83919e10	−1.54096	−0.770481	−	0.637463i	$-0.779984\pi$
$757$	−1.83919e10	−1.54096	−0.770481	+	0.637463i	$0.779984\pi$
$758$	5.73383e9	0.478193
$759$	−1.54043e9	−0.127878
$760$	−3.01789e7	−0.00249377
$761$	5.42592e9	0.446300	0.223150	−	0.974784i	$-0.428366\pi$
$761$	5.42592e9	0.446300	0.223150	+	0.974784i	$0.428366\pi$
$762$	−1.81145e9	−0.148315
$763$	9.16571e8	0.0747016
$764$	−4.80742e9	−0.390019
$765$	2.89998e8	0.0234197
$766$	−2.49471e10	−2.00548
$767$	−2.31125e9	−0.184954
$768$	2.29484e9	0.182805
$769$	−5.18738e9	−0.411345	−0.205672	−	0.978621i	$-0.565938\pi$
$769$	−5.18738e9	−0.411345	−0.205672	+	0.978621i	$0.565938\pi$
$770$	1.62643e8	0.0128386
$771$	−3.02199e9	−0.237467
$772$	−8.92644e9	−0.698261
$773$	−1.79029e10	−1.39411	−0.697053	−	0.717020i	$-0.745506\pi$
$773$	−1.79029e10	−1.39411	−0.697053	+	0.717020i	$0.745506\pi$
$774$	−2.16640e10	−1.67936
$775$	1.34963e10	1.04150
$776$	1.09789e9	0.0843414
$777$	−5.70035e8	−0.0435941
$778$	−1.91683e10	−1.45933
$779$	7.11426e9	0.539199
$780$	4.60890e6	0.000347749 0
$781$	−3.02674e9	−0.227351
$782$	1.30419e10	0.975255
$783$	3.94100e8	0.0293386
$784$	−2.39986e9	−0.177861
$785$	−4.54239e7	−0.00335151
$786$	−2.80890e9	−0.206328
$787$	−1.13894e10	−0.832890	−0.416445	−	0.909161i	$-0.636724\pi$
$787$	−1.13894e10	−0.832890	−0.416445	+	0.909161i	$0.636724\pi$
$788$	1.55306e10	1.13070
$789$	5.33786e8	0.0386899
$790$	1.38198e8	0.00997259
$791$	6.03342e9	0.433457
$792$	−1.31770e10	−0.942491
$793$	−3.87954e9	−0.276264
$794$	−1.50489e9	−0.106692
$795$	−2.13539e7	−0.00150728
$796$	9.76505e9	0.686244
$797$	1.82526e10	1.27709	0.638544	−	0.769585i	$-0.279537\pi$
$797$	1.82526e10	1.27709	0.638544	+	0.769585i	$0.279537\pi$
$798$	−3.01569e8	−0.0210076
$799$	4.24086e9	0.294131
$800$	1.47978e10	1.02184
$801$	2.92327e9	0.200981
$802$	2.30588e10	1.57843
$803$	2.60146e10	1.77302
$804$	3.68661e8	0.0250168
$805$	−4.17807e7	−0.00282286
$806$	5.38252e9	0.362087
$807$	−3.67307e9	−0.246021
$808$	−1.22847e10	−0.819269
$809$	−3.19068e9	−0.211867	−0.105934	−	0.994373i	$-0.533783\pi$
$809$	−3.19068e9	−0.211867	−0.105934	+	0.994373i	$0.533783\pi$
$810$	−2.69214e8	−0.0177992
$811$	8.78229e9	0.578142	0.289071	−	0.957308i	$-0.406654\pi$
$811$	8.78229e9	0.578142	0.289071	+	0.957308i	$0.406654\pi$
$812$	−3.36288e8	−0.0220427
$813$	2.72145e9	0.177616
$814$	2.74332e10	1.78275
$815$	3.54453e8	0.0229354
$816$	−4.42487e9	−0.285092
$817$	−6.52468e9	−0.418584
$818$	−5.17032e9	−0.330279
$819$	1.61339e9	0.102623
$820$	2.40676e8	0.0152435
$821$	−1.84405e10	−1.16298	−0.581489	−	0.813554i	$-0.697530\pi$
$821$	−1.84405e10	−1.16298	−0.581489	+	0.813554i	$0.697530\pi$
$822$	−2.97316e9	−0.186710
$823$	−7.73606e9	−0.483749	−0.241875	−	0.970308i	$-0.577762\pi$
$823$	−7.73606e9	−0.483749	−0.241875	+	0.970308i	$0.577762\pi$
$824$	−6.58450e9	−0.409994
$825$	4.18335e9	0.259379
$826$	5.11611e9	0.315871
$827$	−2.71320e10	−1.66806	−0.834030	−	0.551719i	$-0.813972\pi$
$827$	−2.71320e10	−1.66806	−0.834030	+	0.551719i	$0.813972\pi$
$828$	−4.49695e9	−0.275304
$829$	1.50861e10	0.919680	0.459840	−	0.888002i	$-0.347907\pi$
$829$	1.50861e10	0.919680	0.459840	+	0.888002i	$0.347907\pi$
$830$	1.89383e8	0.0114965
$831$	−1.42238e9	−0.0859826
$832$	1.65176e8	0.00994298
$833$	3.76265e9	0.225546
$834$	4.54082e8	0.0271052
$835$	−1.09274e8	−0.00649554
$836$	5.27228e9	0.312088
$837$	5.07236e9	0.299000
$838$	−3.07810e8	−0.0180688
$839$	1.73769e10	1.01580	0.507898	−	0.861417i	$-0.330423\pi$
$839$	1.73769e10	1.01580	0.507898	+	0.861417i	$0.330423\pi$
$840$	7.67942e6	0.000447045 0
$841$	−1.70696e10	−0.989551
$842$	−1.19476e10	−0.689742
$843$	3.28659e8	0.0188951
$844$	6.66930e9	0.381840
$845$	−2.04425e7	−0.00116556
$846$	−4.02526e9	−0.228559
$847$	1.47038e10	0.831451
$848$	−1.51637e10	−0.853923
$849$	−4.01019e9	−0.224899
$850$	−3.54181e10	−1.97815
$851$	−7.04721e9	−0.391980
$852$	1.89859e8	0.0105170
$853$	−4.19213e9	−0.231267	−0.115633	−	0.993292i	$-0.536890\pi$
$853$	−4.19213e9	−0.231267	−0.115633	+	0.993292i	$0.536890\pi$
$854$	8.58764e9	0.471814
$855$	−8.29004e7	−0.00453602
$856$	1.74203e10	0.949286
$857$	−2.55881e8	−0.0138869	−0.00694343	−	0.999976i	$-0.502210\pi$
$857$	−2.55881e8	−0.0138869	−0.00694343	+	0.999976i	$0.502210\pi$
$858$	1.66837e9	0.0901753
$859$	3.29449e9	0.177342	0.0886711	−	0.996061i	$-0.471738\pi$
$859$	3.29449e9	0.177342	0.0886711	+	0.996061i	$0.471738\pi$
$860$	−2.20731e8	−0.0118336
$861$	−1.81032e9	−0.0966593
$862$	1.10353e10	0.586823
$863$	−3.39290e10	−1.79694	−0.898469	−	0.439038i	$-0.855319\pi$
$863$	−3.39290e10	−1.79694	−0.898469	+	0.439038i	$0.855319\pi$
$864$	5.56149e9	0.293355
$865$	5.06571e8	0.0266124
$866$	1.53615e9	0.0803751
$867$	4.15441e9	0.216492
$868$	−4.32828e9	−0.224645
$869$	1.81734e10	0.939435
$870$	5.46793e6	0.000281518 0
$871$	−1.63518e9	−0.0838497
$872$	−2.08274e9	−0.106372
$873$	3.01585e9	0.153412
$874$	−3.72823e9	−0.188892
$875$	2.26954e8	0.0114528
$876$	−1.63183e9	−0.0820180
$877$	2.89806e10	1.45081	0.725403	−	0.688324i	$-0.241653\pi$
$877$	2.89806e10	1.45081	0.725403	+	0.688324i	$0.241653\pi$
$878$	4.25300e10	2.12063
$879$	2.87132e9	0.142601
$880$	−6.82195e8	−0.0337458
$881$	−3.24339e10	−1.59803	−0.799013	−	0.601313i	$-0.794644\pi$
$881$	−3.24339e10	−1.59803	−0.799013	+	0.601313i	$0.794644\pi$
$882$	−3.57136e9	−0.175264
$883$	−1.73371e9	−0.0847451	−0.0423725	−	0.999102i	$-0.513492\pi$
$883$	−1.73371e9	−0.0847451	−0.0423725	+	0.999102i	$0.513492\pi$
$884$	−5.13134e9	−0.249832
$885$	−3.02195e7	−0.00146550
$886$	−1.88051e10	−0.908361
$887$	2.31382e10	1.11326	0.556631	−	0.830760i	$-0.312094\pi$
$887$	2.31382e10	1.11326	0.556631	+	0.830760i	$0.312094\pi$
$888$	1.29530e9	0.0620762
$889$	−6.46092e9	−0.308417
$890$	8.19892e7	0.00389845
$891$	−3.54022e10	−1.67671
$892$	1.29325e10	0.610108
$893$	−1.21231e9	−0.0569686
$894$	−6.10776e9	−0.285891
$895$	−1.68521e7	−0.000785731 0
$896$	7.95222e9	0.369326
$897$	−4.28582e8	−0.0198272
$898$	−2.91904e10	−1.34516
$899$	2.31979e9	0.106485
$900$	1.22124e10	0.558410
$901$	2.37745e10	1.08287
$902$	8.71223e10	3.95282
$903$	1.66029e9	0.0750373
$904$	−1.37098e10	−0.617224
$905$	6.10181e8	0.0273646
$906$	9.94250e8	0.0444167
$907$	−3.04752e10	−1.35619	−0.678096	−	0.734973i	$-0.737195\pi$
$907$	−3.04752e10	−1.35619	−0.678096	+	0.734973i	$0.737195\pi$
$908$	−7.85706e9	−0.348305
$909$	−3.37458e10	−1.49020
$910$	4.52510e7	0.00199060
$911$	8.72533e9	0.382356	0.191178	−	0.981555i	$-0.438769\pi$
$911$	8.72533e9	0.382356	0.191178	+	0.981555i	$0.438769\pi$
$912$	1.26491e9	0.0552178
$913$	2.49042e10	1.08299
$914$	−2.46509e10	−1.06787
$915$	−5.07249e7	−0.00218901
$916$	1.06381e9	0.0457328
$917$	−1.00185e10	−0.429053
$918$	−1.33112e10	−0.567897
$919$	3.73817e10	1.58875	0.794373	−	0.607431i	$-0.207800\pi$
$919$	3.73817e10	1.58875	0.794373	+	0.607431i	$0.207800\pi$
$920$	9.49389e7	0.00401964
$921$	1.39518e9	0.0588466
$922$	4.62539e10	1.94353
$923$	−8.42109e8	−0.0352503
$924$	−1.34160e9	−0.0559463
$925$	1.91382e10	0.795069
$926$	5.70363e10	2.36055
$927$	−1.80874e10	−0.745756
$928$	2.54349e9	0.104475
$929$	−3.60450e10	−1.47499	−0.737497	−	0.675350i	$-0.763993\pi$
$929$	−3.60450e10	−1.47499	−0.737497	+	0.675350i	$0.763993\pi$
$930$	7.03763e7	0.00286904
$931$	−1.07561e9	−0.0436848
$932$	1.51398e10	0.612582
$933$	−6.50486e7	−0.00262212
$934$	−5.01615e10	−2.01445
$935$	1.06959e9	0.0427933
$936$	−3.66614e9	−0.146131
$937$	3.50259e10	1.39092	0.695458	−	0.718567i	$-0.255202\pi$
$937$	3.50259e10	1.39092	0.695458	+	0.718567i	$0.255202\pi$
$938$	3.61958e9	0.143202
$939$	−1.19138e9	−0.0469592
$940$	−4.10127e7	−0.00161054
$941$	−3.32485e9	−0.130079	−0.0650396	−	0.997883i	$-0.520717\pi$
$941$	−3.32485e9	−0.130079	−0.0650396	+	0.997883i	$0.520717\pi$
$942$	1.03142e9	0.0402030
$943$	−2.23805e10	−0.869120
$944$	−2.14592e10	−0.830257
$945$	4.26435e7	0.00164377
$946$	−7.99023e10	−3.06860
$947$	2.58279e10	0.988245	0.494123	−	0.869392i	$-0.335489\pi$
$947$	2.58279e10	0.988245	0.494123	+	0.869392i	$0.335489\pi$
$948$	−1.13997e9	−0.0434573
$949$	7.23788e9	0.274903
$950$	1.01248e10	0.383136
$951$	1.61216e9	0.0607823
$952$	−8.54993e9	−0.321169
$953$	3.55136e10	1.32914	0.664569	−	0.747227i	$-0.268615\pi$
$953$	3.55136e10	1.32914	0.664569	+	0.747227i	$0.268615\pi$
$954$	−2.25658e10	−0.841458
$955$	2.78799e8	0.0103581
$956$	−7.01199e9	−0.259560
$957$	7.19045e8	0.0265194
$958$	−4.78346e10	−1.75777
$959$	−1.06044e10	−0.388259
$960$	2.15968e6	7.87844e−5 0
$961$	2.34477e9	0.0852253
$962$	7.63255e9	0.276412
$963$	4.78529e10	1.72670
$964$	−2.41471e10	−0.868151
$965$	5.17675e8	0.0185443
$966$	9.48697e8	0.0338616
$967$	2.74905e10	0.977664	0.488832	−	0.872378i	$-0.337423\pi$
$967$	2.74905e10	0.977664	0.488832	+	0.872378i	$0.337423\pi$
$968$	−3.34116e10	−1.18395
$969$	−1.98321e9	−0.0700222
$970$	8.45859e7	0.00297575
$971$	−1.03435e10	−0.362576	−0.181288	−	0.983430i	$-0.558027\pi$
$971$	−1.03435e10	−0.362576	−0.181288	+	0.983430i	$0.558027\pi$
$972$	6.90912e9	0.241318
$973$	1.61958e9	0.0563647
$974$	2.05410e10	0.712305
$975$	1.16390e9	0.0402162
$976$	−3.60203e10	−1.24015
$977$	3.21256e10	1.10210	0.551050	−	0.834472i	$-0.314227\pi$
$977$	3.21256e10	1.10210	0.551050	+	0.834472i	$0.314227\pi$
$978$	−8.04841e9	−0.275121
$979$	1.07818e10	0.367240
$980$	−3.63880e7	−0.00123500
$981$	−5.72121e9	−0.193485
$982$	5.23457e10	1.76397
$983$	4.63147e10	1.55518	0.777592	−	0.628769i	$-0.216441\pi$
$983$	4.63147e10	1.55518	0.777592	+	0.628769i	$0.216441\pi$
$984$	4.11361e9	0.137639
$985$	−9.00673e8	−0.0300290
$986$	−6.08775e9	−0.202250
$987$	3.08489e8	0.0102125
$988$	1.46687e9	0.0483885
$989$	2.05258e10	0.674704
$990$	−1.01521e9	−0.0332532
$991$	5.46722e10	1.78447	0.892234	−	0.451573i	$-0.149137\pi$
$991$	5.46722e10	1.78447	0.892234	+	0.451573i	$0.149137\pi$
$992$	3.27365e10	1.06474
$993$	−1.62427e9	−0.0526426
$994$	1.86407e9	0.0602018
$995$	−5.66309e8	−0.0182252
$996$	−1.56217e9	−0.0500981
$997$	−1.10862e10	−0.354282	−0.177141	−	0.984185i	$-0.556685\pi$
$997$	−1.10862e10	−0.354282	−0.177141	+	0.984185i	$0.556685\pi$
$998$	5.34877e10	1.70332
$999$	7.19274e9	0.228252

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.c.1.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.c.1.9	✓	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)

\(f(q)\)	\(=\)	\(q+14.1785 q^{2} +6.78261 q^{3} +73.0290 q^{4} -4.23520 q^{5} +96.1671 q^{6} +343.000 q^{7} -779.405 q^{8} -2141.00 q^{9} +O(q^{10})\)	\(q+14.1785 q^{2} +6.78261 q^{3} +73.0290 q^{4} -4.23520 q^{5} +96.1671 q^{6} +343.000 q^{7} -779.405 q^{8} -2141.00 q^{9} -60.0487 q^{10} -7896.54 q^{11} +495.328 q^{12} -2197.00 q^{13} +4863.22 q^{14} -28.7257 q^{15} -20398.5 q^{16} +31982.0 q^{17} -30356.0 q^{18} -9142.53 q^{19} -309.293 q^{20} +2326.44 q^{21} -111961. q^{22} +28761.2 q^{23} -5286.40 q^{24} -78107.1 q^{25} -31150.1 q^{26} -29355.1 q^{27} +25048.9 q^{28} -13425.2 q^{29} -407.287 q^{30} -172793. q^{31} -189455. q^{32} -53559.2 q^{33} +453455. q^{34} -1452.67 q^{35} -156355. q^{36} -245025. q^{37} -129627. q^{38} -14901.4 q^{39} +3300.94 q^{40} -778150. q^{41} +32985.3 q^{42} +713663. q^{43} -576676. q^{44} +9067.55 q^{45} +407790. q^{46} +132602. q^{47} -138355. q^{48} +117649. q^{49} -1.10744e6 q^{50} +216921. q^{51} -160445. q^{52} +743372. q^{53} -416211. q^{54} +33443.4 q^{55} -267336. q^{56} -62010.2 q^{57} -190349. q^{58} +1.05200e6 q^{59} -2097.81 q^{60} +1.76584e6 q^{61} -2.44994e6 q^{62} -734362. q^{63} -75182.7 q^{64} +9304.74 q^{65} -759387. q^{66} +744278. q^{67} +2.33561e6 q^{68} +195076. q^{69} -20596.7 q^{70} +383299. q^{71} +1.66870e6 q^{72} -3.29444e6 q^{73} -3.47408e6 q^{74} -529770. q^{75} -667670. q^{76} -2.70851e6 q^{77} -211279. q^{78} -2.30144e6 q^{79} +86391.7 q^{80} +4.48325e6 q^{81} -1.10330e7 q^{82} -3.15382e6 q^{83} +169897. q^{84} -135450. q^{85} +1.01186e7 q^{86} -91058.3 q^{87} +6.15460e6 q^{88} -1.36538e6 q^{89} +128564. q^{90} -753571. q^{91} +2.10040e6 q^{92} -1.17199e6 q^{93} +1.88009e6 q^{94} +38720.5 q^{95} -1.28500e6 q^{96} -1.40862e6 q^{97} +1.66808e6 q^{98} +1.69065e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9}+O(q^{10}) \) 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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