LMFDB - Embedded newform 33.8.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,8,Mod(1,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, 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("33.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	33.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:	$10.3087058410$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.115512.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 70x - 194 $ x^3 - x^2 - 70*x - 194
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.66999$ of defining polynomial
Character	$\chi$	$=$	33.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.51124 q^{2} -27.0000 q^{3} -85.6037 q^{4} -22.9029 q^{5} +175.804 q^{6} -1466.13 q^{7} +1390.83 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-6.51124 q^{2} -27.0000 q^{3} -85.6037 q^{4} -22.9029 q^{5} +175.804 q^{6} -1466.13 q^{7} +1390.83 q^{8} +729.000 q^{9} +149.126 q^{10} -1331.00 q^{11} +2311.30 q^{12} +10497.7 q^{13} +9546.34 q^{14} +618.377 q^{15} +1901.28 q^{16} -14269.6 q^{17} -4746.70 q^{18} +50530.6 q^{19} +1960.57 q^{20} +39585.6 q^{21} +8666.46 q^{22} +96125.6 q^{23} -37552.3 q^{24} -77600.5 q^{25} -68352.7 q^{26} -19683.0 q^{27} +125506. q^{28} -230613. q^{29} -4026.41 q^{30} +84260.8 q^{31} -190405. q^{32} +35937.0 q^{33} +92912.5 q^{34} +33578.6 q^{35} -62405.1 q^{36} -105490. q^{37} -329017. q^{38} -283437. q^{39} -31853.9 q^{40} -106391. q^{41} -257751. q^{42} +573565. q^{43} +113939. q^{44} -16696.2 q^{45} -625897. q^{46} +369766. q^{47} -51334.4 q^{48} +1.32600e6 q^{49} +505275. q^{50} +385278. q^{51} -898638. q^{52} +321116. q^{53} +128161. q^{54} +30483.7 q^{55} -2.03913e6 q^{56} -1.36433e6 q^{57} +1.50158e6 q^{58} +2.03704e6 q^{59} -52935.4 q^{60} +3.00081e6 q^{61} -548643. q^{62} -1.06881e6 q^{63} +996412. q^{64} -240426. q^{65} -233995. q^{66} +2.19360e6 q^{67} +1.22153e6 q^{68} -2.59539e6 q^{69} -218639. q^{70} -4.26371e6 q^{71} +1.01391e6 q^{72} -278806. q^{73} +686872. q^{74} +2.09521e6 q^{75} -4.32561e6 q^{76} +1.95142e6 q^{77} +1.84552e6 q^{78} -283782. q^{79} -43544.7 q^{80} +531441. q^{81} +692735. q^{82} +5.87262e6 q^{83} -3.38867e6 q^{84} +326814. q^{85} -3.73462e6 q^{86} +6.22656e6 q^{87} -1.85119e6 q^{88} -8.64670e6 q^{89} +108713. q^{90} -1.53909e7 q^{91} -8.22871e6 q^{92} -2.27504e6 q^{93} -2.40764e6 q^{94} -1.15730e6 q^{95} +5.14094e6 q^{96} +37857.4 q^{97} -8.63391e6 q^{98} -970299. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 9 q^{2} - 81 q^{3} - 15 q^{4} - 444 q^{5} - 243 q^{6} + 1614 q^{7} + 3153 q^{8} + 2187 q^{9}+O(q^{10}) $ 3 * q + 9 * q^2 - 81 * q^3 - 15 * q^4 - 444 * q^5 - 243 * q^6 + 1614 * q^7 + 3153 * q^8 + 2187 * q^9	\( 3 q + 9 q^{2} - 81 q^{3} - 15 q^{4} - 444 q^{5} - 243 q^{6} + 1614 q^{7} + 3153 q^{8} + 2187 q^{9} + 2880 q^{10} - 3993 q^{11} + 405 q^{12} + 20772 q^{13} + 36258 q^{14} + 11988 q^{15} + 12225 q^{16} - 14538 q^{17} + 6561 q^{18} + 24492 q^{19} + 80112 q^{20} - 43578 q^{21} - 11979 q^{22} + 35094 q^{23} - 85131 q^{24} + 29121 q^{25} + 203832 q^{26} - 59049 q^{27} + 278034 q^{28} - 179862 q^{29} - 77760 q^{30} + 288888 q^{31} - 519567 q^{32} + 107811 q^{33} - 491586 q^{34} - 532872 q^{35} - 10935 q^{36} + 107562 q^{37} - 686328 q^{38} - 560844 q^{39} - 237360 q^{40} - 135198 q^{41} - 978966 q^{42} + 193536 q^{43} + 19965 q^{44} - 323676 q^{45} + 16422 q^{46} - 591486 q^{47} - 330075 q^{48} + 4461159 q^{49} - 1192245 q^{50} + 392526 q^{51} + 2449992 q^{52} + 79044 q^{53} - 177147 q^{54} + 590964 q^{55} + 752658 q^{56} - 661284 q^{57} + 2289930 q^{58} + 2532768 q^{59} - 2163024 q^{60} + 6678792 q^{61} - 2660808 q^{62} + 1176606 q^{63} - 3966303 q^{64} + 3191832 q^{65} + 323433 q^{66} + 7150356 q^{67} - 7821954 q^{68} - 947538 q^{69} + 4029120 q^{70} + 1390398 q^{71} + 2298537 q^{72} - 6429114 q^{73} + 2507478 q^{74} - 786267 q^{75} - 7654728 q^{76} - 2148234 q^{77} - 5503464 q^{78} + 6873186 q^{79} - 7556016 q^{80} + 1594323 q^{81} - 1774590 q^{82} + 6505596 q^{83} - 7506918 q^{84} - 16546032 q^{85} - 6519468 q^{86} + 4856274 q^{87} - 4196643 q^{88} - 8842962 q^{89} + 2099520 q^{90} + 3066648 q^{91} + 6921990 q^{92} - 7799976 q^{93} - 24038238 q^{94} - 190968 q^{95} + 14028309 q^{96} - 1764774 q^{97} + 24377397 q^{98} - 2910897 q^{99}+O(q^{100}) \) 3 * q + 9 * q^2 - 81 * q^3 - 15 * q^4 - 444 * q^5 - 243 * q^6 + 1614 * q^7 + 3153 * q^8 + 2187 * q^9 + 2880 * q^10 - 3993 * q^11 + 405 * q^12 + 20772 * q^13 + 36258 * q^14 + 11988 * q^15 + 12225 * q^16 - 14538 * q^17 + 6561 * q^18 + 24492 * q^19 + 80112 * q^20 - 43578 * q^21 - 11979 * q^22 + 35094 * q^23 - 85131 * q^24 + 29121 * q^25 + 203832 * q^26 - 59049 * q^27 + 278034 * q^28 - 179862 * q^29 - 77760 * q^30 + 288888 * q^31 - 519567 * q^32 + 107811 * q^33 - 491586 * q^34 - 532872 * q^35 - 10935 * q^36 + 107562 * q^37 - 686328 * q^38 - 560844 * q^39 - 237360 * q^40 - 135198 * q^41 - 978966 * q^42 + 193536 * q^43 + 19965 * q^44 - 323676 * q^45 + 16422 * q^46 - 591486 * q^47 - 330075 * q^48 + 4461159 * q^49 - 1192245 * q^50 + 392526 * q^51 + 2449992 * q^52 + 79044 * q^53 - 177147 * q^54 + 590964 * q^55 + 752658 * q^56 - 661284 * q^57 + 2289930 * q^58 + 2532768 * q^59 - 2163024 * q^60 + 6678792 * q^61 - 2660808 * q^62 + 1176606 * q^63 - 3966303 * q^64 + 3191832 * q^65 + 323433 * q^66 + 7150356 * q^67 - 7821954 * q^68 - 947538 * q^69 + 4029120 * q^70 + 1390398 * q^71 + 2298537 * q^72 - 6429114 * q^73 + 2507478 * q^74 - 786267 * q^75 - 7654728 * q^76 - 2148234 * q^77 - 5503464 * q^78 + 6873186 * q^79 - 7556016 * q^80 + 1594323 * q^81 - 1774590 * q^82 + 6505596 * q^83 - 7506918 * q^84 - 16546032 * q^85 - 6519468 * q^86 + 4856274 * q^87 - 4196643 * q^88 - 8842962 * q^89 + 2099520 * q^90 + 3066648 * q^91 + 6921990 * q^92 - 7799976 * q^93 - 24038238 * q^94 - 190968 * q^95 + 14028309 * q^96 - 1764774 * q^97 + 24377397 * q^98 - 2910897 * 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 $

$2$	−6.51124	−0.575518	−0.287759	−	0.957703i	$-0.592910\pi$
$2$	−6.51124	−0.575518	−0.287759	+	0.957703i	$0.592910\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−85.6037	−0.668779
$5$	−22.9029	−0.0819398	−0.0409699	−	0.999160i	$-0.513045\pi$
$5$	−22.9029	−0.0819398	−0.0409699	+	0.999160i	$0.513045\pi$
$6$	175.804	0.332275
$7$	−1466.13	−1.61559	−0.807793	−	0.589467i	$-0.799338\pi$
$7$	−1466.13	−1.61559	−0.807793	+	0.589467i	$0.799338\pi$
$8$	1390.83	0.960412
$9$	729.000	0.333333
$10$	149.126	0.0471578
$11$	−1331.00	−0.301511
$11$	−1331.00	−0.301511
$12$	2311.30	0.386120
$13$	10497.7	1.32523	0.662614	−	0.748961i	$-0.269447\pi$
$13$	10497.7	1.32523	0.662614	+	0.748961i	$0.269447\pi$
$14$	9546.34	0.929798
$15$	618.377	0.0473080
$16$	1901.28	0.116045
$17$	−14269.6	−0.704432	−0.352216	−	0.935919i	$-0.614572\pi$
$17$	−14269.6	−0.704432	−0.352216	+	0.935919i	$0.614572\pi$
$18$	−4746.70	−0.191839
$19$	50530.6	1.69012	0.845059	−	0.534673i	$-0.179565\pi$
$19$	50530.6	1.69012	0.845059	+	0.534673i	$0.179565\pi$
$20$	1960.57	0.0547996
$21$	39585.6	0.932759
$22$	8666.46	0.173525
$23$	96125.6	1.64737	0.823686	−	0.567046i	$-0.191914\pi$
$23$	96125.6	1.64737	0.823686	+	0.567046i	$0.191914\pi$
$24$	−37552.3	−0.554494
$25$	−77600.5	−0.993286
$26$	−68352.7	−0.762692
$27$	−19683.0	−0.192450
$28$	125506.	1.08047
$29$	−230613.	−1.75587	−0.877934	−	0.478782i	$-0.841078\pi$
$29$	−230613.	−1.75587	−0.877934	+	0.478782i	$0.841078\pi$
$30$	−4026.41	−0.0272266
$31$	84260.8	0.507995	0.253998	−	0.967205i	$-0.418254\pi$
$31$	84260.8	0.507995	0.253998	+	0.967205i	$0.418254\pi$
$32$	−190405.	−1.02720
$33$	35937.0	0.174078
$34$	92912.5	0.405413
$35$	33578.6	0.132381
$36$	−62405.1	−0.222926
$37$	−105490.	−0.342378	−0.171189	−	0.985238i	$-0.554761\pi$
$37$	−105490.	−0.342378	−0.171189	+	0.985238i	$0.554761\pi$
$38$	−329017.	−0.972693
$39$	−283437.	−0.765120
$40$	−31853.9	−0.0786960
$41$	−106391.	−0.241079	−0.120540	−	0.992709i	$-0.538463\pi$
$41$	−106391.	−0.241079	−0.120540	+	0.992709i	$0.538463\pi$
$42$	−257751.	−0.536819
$43$	573565.	1.10013	0.550064	−	0.835122i	$-0.314603\pi$
$43$	573565.	1.10013	0.550064	+	0.835122i	$0.314603\pi$
$44$	113939.	0.201644
$45$	−16696.2	−0.0273133
$46$	−625897.	−0.948092
$47$	369766.	0.519499	0.259749	−	0.965676i	$-0.416360\pi$
$47$	369766.	0.519499	0.259749	+	0.965676i	$0.416360\pi$
$48$	−51334.4	−0.0669984
$49$	1.32600e6	1.61012
$50$	505275.	0.571654
$51$	385278.	0.406704
$52$	−898638.	−0.886284
$53$	321116.	0.296276	0.148138	−	0.988967i	$-0.452672\pi$
$53$	321116.	0.296276	0.148138	+	0.988967i	$0.452672\pi$
$54$	128161.	0.110758
$55$	30483.7	0.0247058
$56$	−2.03913e6	−1.55163
$57$	−1.36433e6	−0.975790
$58$	1.50158e6	1.01053
$59$	2.03704e6	1.29127	0.645636	−	0.763646i	$-0.276592\pi$
$59$	2.03704e6	1.29127	0.645636	+	0.763646i	$0.276592\pi$
$60$	−52935.4	−0.0316386
$61$	3.00081e6	1.69271	0.846357	−	0.532616i	$-0.178791\pi$
$61$	3.00081e6	1.69271	0.846357	+	0.532616i	$0.178791\pi$
$62$	−548643.	−0.292361
$63$	−1.06881e6	−0.538529
$64$	996412.	0.475126
$65$	−240426.	−0.108589
$66$	−233995.	−0.100185
$67$	2.19360e6	0.891036	0.445518	−	0.895273i	$-0.353019\pi$
$67$	2.19360e6	0.891036	0.445518	+	0.895273i	$0.353019\pi$
$68$	1.22153e6	0.471110
$69$	−2.59539e6	−0.951111
$70$	−218639.	−0.0761875
$71$	−4.26371e6	−1.41379	−0.706893	−	0.707321i	$-0.749904\pi$
$71$	−4.26371e6	−1.41379	−0.706893	+	0.707321i	$0.749904\pi$
$72$	1.01391e6	0.320137
$73$	−278806.	−0.0838825	−0.0419413	−	0.999120i	$-0.513354\pi$
$73$	−278806.	−0.0838825	−0.0419413	+	0.999120i	$0.513354\pi$
$74$	686872.	0.197045
$75$	2.09521e6	0.573474
$76$	−4.32561e6	−1.13032
$77$	1.95142e6	0.487117
$78$	1.84552e6	0.440341
$79$	−283782.	−0.0647575	−0.0323788	−	0.999476i	$-0.510308\pi$
$79$	−283782.	−0.0647575	−0.0323788	+	0.999476i	$0.510308\pi$
$80$	−43544.7	−0.00950867
$81$	531441.	0.111111
$82$	692735.	0.138745
$83$	5.87262e6	1.12735	0.563675	−	0.825997i	$-0.309387\pi$
$83$	5.87262e6	1.12735	0.563675	+	0.825997i	$0.309387\pi$
$84$	−3.38867e6	−0.623810
$85$	326814.	0.0577210
$86$	−3.73462e6	−0.633144
$87$	6.22656e6	1.01375
$88$	−1.85119e6	−0.289575
$89$	−8.64670e6	−1.30013	−0.650063	−	0.759880i	$-0.725257\pi$
$89$	−8.64670e6	−1.30013	−0.650063	+	0.759880i	$0.725257\pi$
$90$	108713.	0.0157193
$91$	−1.53909e7	−2.14102
$92$	−8.22871e6	−1.10173
$93$	−2.27504e6	−0.293291
$94$	−2.40764e6	−0.298981
$95$	−1.15730e6	−0.138488
$96$	5.14094e6	0.593053
$97$	37857.4	0.00421162	0.00210581	−	0.999998i	$-0.499330\pi$
$97$	37857.4	0.00421162	0.00210581	+	0.999998i	$0.499330\pi$
$98$	−8.63391e6	−0.926651
$99$	−970299.	−0.100504
$100$	6.64289e6	0.664289
$101$	9.01395e6	0.870543	0.435272	−	0.900299i	$-0.356652\pi$
$101$	9.01395e6	0.870543	0.435272	+	0.900299i	$0.356652\pi$
$102$	−2.50864e6	−0.234066
$103$	−5.26940e6	−0.475150	−0.237575	−	0.971369i	$-0.576353\pi$
$103$	−5.26940e6	−0.475150	−0.237575	+	0.971369i	$0.576353\pi$
$104$	1.46004e7	1.27276
$105$	−906623.	−0.0764301
$106$	−2.09087e6	−0.170512
$107$	1.56526e7	1.23522	0.617608	−	0.786486i	$-0.288102\pi$
$107$	1.56526e7	1.23522	0.617608	+	0.786486i	$0.288102\pi$
$108$	1.68494e6	0.128707
$109$	1.44413e7	1.06811	0.534054	−	0.845451i	$-0.320668\pi$
$109$	1.44413e7	1.06811	0.534054	+	0.845451i	$0.320668\pi$
$110$	−198487.	−0.0142186
$111$	2.84824e6	0.197672
$112$	−2.78752e6	−0.187480
$113$	−6.12092e6	−0.399064	−0.199532	−	0.979891i	$-0.563942\pi$
$113$	−6.12092e6	−0.399064	−0.199532	+	0.979891i	$0.563942\pi$
$114$	8.88346e6	0.561585
$115$	−2.20155e6	−0.134985
$116$	1.97414e7	1.17429
$117$	7.65279e6	0.441742
$118$	−1.32637e7	−0.743150
$119$	2.09211e7	1.13807
$120$	860055.	0.0454351
$121$	1.77156e6	0.0909091
$122$	−1.95390e7	−0.974187
$123$	2.87255e6	0.139187
$124$	−7.21304e6	−0.339737
$125$	3.56656e6	0.163329
$126$	6.95928e6	0.309933
$127$	3.21582e7	1.39309	0.696545	−	0.717513i	$-0.254720\pi$
$127$	3.21582e7	1.39309	0.696545	+	0.717513i	$0.254720\pi$
$128$	1.78840e7	0.753754
$129$	−1.54863e7	−0.635159
$130$	1.56547e6	0.0624948
$131$	8.62966e6	0.335385	0.167693	−	0.985839i	$-0.446368\pi$
$131$	8.62966e6	0.335385	0.167693	+	0.985839i	$0.446368\pi$
$132$	−3.07634e6	−0.116420
$133$	−7.40846e7	−2.73053
$134$	−1.42831e7	−0.512807
$135$	450797.	0.0157693
$136$	−1.98465e7	−0.676545
$137$	1.01093e6	0.0335891	0.0167946	−	0.999859i	$-0.494654\pi$
$137$	1.01093e6	0.0335891	0.0167946	+	0.999859i	$0.494654\pi$
$138$	1.68992e7	0.547381
$139$	−8.19986e6	−0.258973	−0.129486	−	0.991581i	$-0.541333\pi$
$139$	−8.19986e6	−0.258973	−0.129486	+	0.991581i	$0.541333\pi$
$140$	−2.87446e6	−0.0885335
$141$	−9.98368e6	−0.299933
$142$	2.77620e7	0.813659
$143$	−1.39724e7	−0.399571
$144$	1.38603e6	0.0386815
$145$	5.28171e6	0.143875
$146$	1.81537e6	0.0482759
$147$	−3.58020e7	−0.929601
$148$	9.03035e6	0.228975
$149$	−5.18686e7	−1.28455	−0.642277	−	0.766473i	$-0.722010\pi$
$149$	−5.18686e7	−1.28455	−0.642277	+	0.766473i	$0.722010\pi$
$150$	−1.36424e7	−0.330044
$151$	1.99247e7	0.470947	0.235473	−	0.971881i	$-0.424336\pi$
$151$	1.99247e7	0.470947	0.235473	+	0.971881i	$0.424336\pi$
$152$	7.02793e7	1.62321
$153$	−1.04025e7	−0.234811
$154$	−1.27062e7	−0.280345
$155$	−1.92981e6	−0.0416250
$156$	2.42632e7	0.511697
$157$	1.99000e7	0.410397	0.205199	−	0.978720i	$-0.434216\pi$
$157$	1.99000e7	0.410397	0.205199	+	0.978720i	$0.434216\pi$
$158$	1.84777e6	0.0372691
$159$	−8.67014e6	−0.171055
$160$	4.36083e6	0.0841684
$161$	−1.40933e8	−2.66147
$162$	−3.46034e6	−0.0639464
$163$	−2.85113e7	−0.515657	−0.257829	−	0.966191i	$-0.583007\pi$
$163$	−2.85113e7	−0.515657	−0.257829	+	0.966191i	$0.583007\pi$
$164$	9.10744e6	0.161229
$165$	−823060.	−0.0142639
$166$	−3.82381e7	−0.648810
$167$	−3.46095e7	−0.575027	−0.287513	−	0.957777i	$-0.592829\pi$
$167$	−3.46095e7	−0.575027	−0.287513	+	0.957777i	$0.592829\pi$
$168$	5.50566e7	0.895833
$169$	4.74522e7	0.756228
$170$	−2.12796e6	−0.0332195
$171$	3.68368e7	0.563373
$172$	−4.90993e7	−0.735743
$173$	7.55804e7	1.10981	0.554904	−	0.831915i	$-0.312755\pi$
$173$	7.55804e7	1.10981	0.554904	+	0.831915i	$0.312755\pi$
$174$	−4.05427e7	−0.583432
$175$	1.13773e8	1.60474
$176$	−2.53060e6	−0.0349888
$177$	−5.50001e7	−0.745516
$178$	5.63008e7	0.748246
$179$	−1.10056e8	−1.43426	−0.717131	−	0.696938i	$-0.754545\pi$
$179$	−1.10056e8	−1.43426	−0.717131	+	0.696938i	$0.754545\pi$
$180$	1.42926e6	0.0182665
$181$	1.15485e8	1.44761	0.723806	−	0.690004i	$-0.242391\pi$
$181$	1.15485e8	1.44761	0.723806	+	0.690004i	$0.242391\pi$
$182$	1.00214e8	1.23219
$183$	−8.10218e7	−0.977289
$184$	1.33694e8	1.58216
$185$	2.41603e6	0.0280544
$186$	1.48134e7	0.168794
$187$	1.89928e7	0.212394
$188$	−3.16534e7	−0.347430
$189$	2.88579e7	0.310920
$190$	7.53544e6	0.0797023
$191$	−1.04151e8	−1.08155	−0.540775	−	0.841167i	$-0.681869\pi$
$191$	−1.04151e8	−1.08155	−0.540775	+	0.841167i	$0.681869\pi$
$192$	−2.69031e7	−0.274314
$193$	1.05802e8	1.05936	0.529678	−	0.848199i	$-0.322313\pi$
$193$	1.05802e8	1.05936	0.529678	+	0.848199i	$0.322313\pi$
$194$	−246498.	−0.00242386
$195$	6.49151e6	0.0626938
$196$	−1.13511e8	−1.07681
$197$	3.92196e7	0.365486	0.182743	−	0.983161i	$-0.441502\pi$
$197$	3.92196e7	0.365486	0.182743	+	0.983161i	$0.441502\pi$
$198$	6.31785e6	0.0578417
$199$	1.74839e7	0.157272	0.0786361	−	0.996903i	$-0.474943\pi$
$199$	1.74839e7	0.157272	0.0786361	+	0.996903i	$0.474943\pi$
$200$	−1.07929e8	−0.953964
$201$	−5.92272e7	−0.514440
$202$	−5.86920e7	−0.501013
$203$	3.38110e8	2.83675
$204$	−3.29812e7	−0.271995
$205$	2.43665e6	0.0197540
$206$	3.43103e7	0.273457
$207$	7.00756e7	0.549124
$208$	1.99589e7	0.153786
$209$	−6.72563e7	−0.509590
$210$	5.90324e6	0.0439869
$211$	−8.52190e7	−0.624522	−0.312261	−	0.949996i	$-0.601086\pi$
$211$	−8.52190e7	−0.624522	−0.312261	+	0.949996i	$0.601086\pi$
$212$	−2.74888e7	−0.198143
$213$	1.15120e8	0.816249
$214$	−1.01918e8	−0.710889
$215$	−1.31363e7	−0.0901443
$216$	−2.73756e7	−0.184831
$217$	−1.23538e8	−0.820710
$218$	−9.40311e7	−0.614715
$219$	7.52775e6	0.0484296
$220$	−2.60952e6	−0.0165227
$221$	−1.49797e8	−0.933533
$222$	−1.85455e7	−0.113764
$223$	8.83128e7	0.533282	0.266641	−	0.963796i	$-0.414086\pi$
$223$	8.83128e7	0.533282	0.266641	+	0.963796i	$0.414086\pi$
$224$	2.79159e8	1.65953
$225$	−5.65707e7	−0.331095
$226$	3.98548e7	0.229668
$227$	−1.76040e7	−0.0998896	−0.0499448	−	0.998752i	$-0.515905\pi$
$227$	−1.76040e7	−0.0998896	−0.0499448	+	0.998752i	$0.515905\pi$
$228$	1.16791e8	0.652588
$229$	4.87412e7	0.268208	0.134104	−	0.990967i	$-0.457184\pi$
$229$	4.87412e7	0.268208	0.134104	+	0.990967i	$0.457184\pi$
$230$	1.43348e7	0.0776865
$231$	−5.26884e7	−0.281237
$232$	−3.20743e8	−1.68636
$233$	4.83355e7	0.250334	0.125167	−	0.992136i	$-0.460053\pi$
$233$	4.83355e7	0.250334	0.125167	+	0.992136i	$0.460053\pi$
$234$	−4.98292e7	−0.254231
$235$	−8.46870e6	−0.0425676
$236$	−1.74378e8	−0.863575
$237$	7.66212e6	0.0373878
$238$	−1.36222e8	−0.654980
$239$	1.90542e8	0.902815	0.451407	−	0.892318i	$-0.350922\pi$
$239$	1.90542e8	0.902815	0.451407	+	0.892318i	$0.350922\pi$
$240$	1.17571e6	0.00548983
$241$	−1.61022e8	−0.741014	−0.370507	−	0.928830i	$-0.620816\pi$
$241$	−1.61022e8	−0.741014	−0.370507	+	0.928830i	$0.620816\pi$
$242$	−1.15351e7	−0.0523198
$243$	−1.43489e7	−0.0641500
$244$	−2.56880e8	−1.13205
$245$	−3.03692e7	−0.131933
$246$	−1.87039e7	−0.0801047
$247$	5.30453e8	2.23979
$248$	1.17192e8	0.487885
$249$	−1.58561e8	−0.650876
$250$	−2.32227e7	−0.0939990
$251$	−1.96074e8	−0.782640	−0.391320	−	0.920255i	$-0.627981\pi$
$251$	−1.96074e8	−0.782640	−0.391320	+	0.920255i	$0.627981\pi$
$252$	9.14941e7	0.360157
$253$	−1.27943e8	−0.496701
$254$	−2.09390e8	−0.801748
$255$	−8.82397e6	−0.0333253
$256$	−2.43988e8	−0.908925
$257$	2.41346e8	0.886900	0.443450	−	0.896299i	$-0.353754\pi$
$257$	2.41346e8	0.886900	0.443450	+	0.896299i	$0.353754\pi$
$258$	1.00835e8	0.365546
$259$	1.54663e8	0.553141
$260$	2.05814e7	0.0726220
$261$	−1.68117e8	−0.585289
$262$	−5.61898e7	−0.193020
$263$	−3.44355e7	−0.116724	−0.0583621	−	0.998295i	$-0.518588\pi$
$263$	−3.44355e7	−0.116724	−0.0583621	+	0.998295i	$0.518588\pi$
$264$	4.99821e7	0.167186
$265$	−7.35449e6	−0.0242768
$266$	4.82383e8	1.57147
$267$	2.33461e8	0.750628
$268$	−1.87780e8	−0.595906
$269$	−5.11883e8	−1.60338	−0.801692	−	0.597737i	$-0.796067\pi$
$269$	−5.11883e8	−1.60338	−0.801692	+	0.597737i	$0.796067\pi$
$270$	−2.93525e6	−0.00907553
$271$	1.26396e8	0.385782	0.192891	−	0.981220i	$-0.438214\pi$
$271$	1.26396e8	0.385782	0.192891	+	0.981220i	$0.438214\pi$
$272$	−2.71304e7	−0.0817456
$273$	4.15555e8	1.23612
$274$	−6.58240e6	−0.0193311
$275$	1.03286e8	0.299487
$276$	2.22175e8	0.636083
$277$	−1.36972e8	−0.387216	−0.193608	−	0.981079i	$-0.562019\pi$
$277$	−1.36972e8	−0.387216	−0.193608	+	0.981079i	$0.562019\pi$
$278$	5.33912e7	0.149044
$279$	6.14262e7	0.169332
$280$	4.67020e7	0.127140
$281$	2.62615e8	0.706070	0.353035	−	0.935610i	$-0.385150\pi$
$281$	2.62615e8	0.706070	0.353035	+	0.935610i	$0.385150\pi$
$282$	6.50062e7	0.172617
$283$	1.77203e8	0.464749	0.232375	−	0.972626i	$-0.425350\pi$
$283$	1.77203e8	0.464749	0.232375	+	0.972626i	$0.425350\pi$
$284$	3.64989e8	0.945510
$285$	3.12470e7	0.0799560
$286$	9.09775e7	0.229960
$287$	1.55983e8	0.389484
$288$	−1.38805e8	−0.342399
$289$	−2.06718e8	−0.503775
$290$	−3.43905e7	−0.0828029
$291$	−1.02215e6	−0.00243158
$292$	2.38668e7	0.0560989
$293$	−2.63396e8	−0.611748	−0.305874	−	0.952072i	$-0.598949\pi$
$293$	−2.63396e8	−0.611748	−0.305874	+	0.952072i	$0.598949\pi$
$294$	2.33116e8	0.535002
$295$	−4.66541e7	−0.105807
$296$	−1.46718e8	−0.328824
$297$	2.61981e7	0.0580259
$298$	3.37729e8	0.739284
$299$	1.00909e9	2.18314
$300$	−1.79358e8	−0.383527
$301$	−8.40923e8	−1.77735
$302$	−1.29734e8	−0.271038
$303$	−2.43377e8	−0.502608
$304$	9.60726e7	0.196129
$305$	−6.87271e7	−0.138701
$306$	6.77332e7	0.135138
$307$	8.90623e8	1.75675	0.878374	−	0.477974i	$-0.158629\pi$
$307$	8.90623e8	1.75675	0.878374	+	0.477974i	$0.158629\pi$
$308$	−1.67049e8	−0.325774
$309$	1.42274e8	0.274328
$310$	1.25655e7	0.0239560
$311$	−5.94300e8	−1.12033	−0.560163	−	0.828383i	$-0.689261\pi$
$311$	−5.94300e8	−1.12033	−0.560163	+	0.828383i	$0.689261\pi$
$312$	−3.94211e8	−0.734831
$313$	4.92264e7	0.0907388	0.0453694	−	0.998970i	$-0.485554\pi$
$313$	4.92264e7	0.0907388	0.0453694	+	0.998970i	$0.485554\pi$
$314$	−1.29574e8	−0.236191
$315$	2.44788e7	0.0441269
$316$	2.42928e7	0.0433085
$317$	−4.18014e8	−0.737027	−0.368513	−	0.929622i	$-0.620133\pi$
$317$	−4.18014e8	−0.737027	−0.368513	+	0.929622i	$0.620133\pi$
$318$	5.64534e7	0.0984453
$319$	3.06947e8	0.529414
$320$	−2.28207e7	−0.0389317
$321$	−4.22620e8	−0.713153
$322$	9.17648e8	1.53172
$323$	−7.21050e8	−1.19057
$324$	−4.54933e7	−0.0743088
$325$	−8.14623e8	−1.31633
$326$	1.85644e8	0.296770
$327$	−3.89916e8	−0.616672
$328$	−1.47971e8	−0.231536
$329$	−5.42126e8	−0.839295
$330$	5.35915e6	0.00820912
$331$	−7.83135e8	−1.18697	−0.593484	−	0.804846i	$-0.702248\pi$
$331$	−7.83135e8	−1.18697	−0.593484	+	0.804846i	$0.702248\pi$
$332$	−5.02718e8	−0.753948
$333$	−7.69023e7	−0.114126
$334$	2.25351e8	0.330938
$335$	−5.02397e7	−0.0730113
$336$	7.52630e7	0.108242
$337$	1.03792e9	1.47726	0.738631	−	0.674109i	$-0.235472\pi$
$337$	1.03792e9	1.47726	0.738631	+	0.674109i	$0.235472\pi$
$338$	−3.08973e8	−0.435223
$339$	1.65265e8	0.230399
$340$	−2.79765e7	−0.0386026
$341$	−1.12151e8	−0.153166
$342$	−2.39854e8	−0.324231
$343$	−7.36669e8	−0.985696
$344$	7.97729e8	1.05658
$345$	5.94419e7	0.0779338
$346$	−4.92122e8	−0.638714
$347$	−6.64048e7	−0.0853191	−0.0426596	−	0.999090i	$-0.513583\pi$
$347$	−6.64048e7	−0.0853191	−0.0426596	+	0.999090i	$0.513583\pi$
$348$	−5.33017e8	−0.677975
$349$	−1.46818e9	−1.84880	−0.924400	−	0.381424i	$-0.875434\pi$
$349$	−1.46818e9	−1.84880	−0.924400	+	0.381424i	$0.875434\pi$
$350$	−7.40800e8	−0.923556
$351$	−2.06625e8	−0.255040
$352$	2.53430e8	0.309712
$353$	1.42534e9	1.72468	0.862338	−	0.506334i	$-0.169000\pi$
$353$	1.42534e9	1.72468	0.862338	+	0.506334i	$0.169000\pi$
$354$	3.58119e8	0.429058
$355$	9.76512e7	0.115845
$356$	7.40190e8	0.869497
$357$	−5.64868e8	−0.657065
$358$	7.16602e8	0.825443
$359$	1.35677e9	1.54766	0.773830	−	0.633394i	$-0.218339\pi$
$359$	1.35677e9	1.54766	0.773830	+	0.633394i	$0.218339\pi$
$360$	−2.32215e7	−0.0262320
$361$	1.65947e9	1.85650
$362$	−7.51953e8	−0.833126
$363$	−4.78321e7	−0.0524864
$364$	1.31752e9	1.43187
$365$	6.38545e6	0.00687332
$366$	5.27552e8	0.562447
$367$	8.30382e8	0.876893	0.438446	−	0.898757i	$-0.355529\pi$
$367$	8.30382e8	0.876893	0.438446	+	0.898757i	$0.355529\pi$
$368$	1.82761e8	0.191169
$369$	−7.75588e7	−0.0803598
$370$	−1.57313e7	−0.0161458
$371$	−4.70799e8	−0.478660
$372$	1.94752e8	0.196147
$373$	5.28884e8	0.527691	0.263845	−	0.964565i	$-0.415009\pi$
$373$	5.28884e8	0.527691	0.263845	+	0.964565i	$0.415009\pi$
$374$	−1.23667e8	−0.122237
$375$	−9.62971e7	−0.0942983
$376$	5.14280e8	0.498933
$377$	−2.42090e9	−2.32692
$378$	−1.87901e8	−0.178940
$379$	−1.11808e9	−1.05496	−0.527480	−	0.849567i	$-0.676863\pi$
$379$	−1.11808e9	−1.05496	−0.527480	+	0.849567i	$0.676863\pi$
$380$	9.90689e7	0.0926178
$381$	−8.68272e8	−0.804301
$382$	6.78153e8	0.622452
$383$	1.68891e9	1.53607	0.768034	−	0.640409i	$-0.221235\pi$
$383$	1.68891e9	1.53607	0.768034	+	0.640409i	$0.221235\pi$
$384$	−4.82868e8	−0.435180
$385$	−4.46932e7	−0.0399143
$386$	−6.88900e8	−0.609678
$387$	4.18129e8	0.366709
$388$	−3.24073e6	−0.00281664
$389$	1.20012e9	1.03372	0.516858	−	0.856071i	$-0.327102\pi$
$389$	1.20012e9	1.03372	0.516858	+	0.856071i	$0.327102\pi$
$390$	−4.22678e7	−0.0360814
$391$	−1.37167e9	−1.16046
$392$	1.84424e9	1.54638
$393$	−2.33001e8	−0.193635
$394$	−2.55368e8	−0.210344
$395$	6.49942e6	0.00530622
$396$	8.30612e7	0.0672148
$397$	6.39914e8	0.513281	0.256640	−	0.966507i	$-0.417384\pi$
$397$	6.39914e8	0.513281	0.256640	+	0.966507i	$0.417384\pi$
$398$	−1.13842e8	−0.0905130
$399$	2.00028e9	1.57647
$400$	−1.47540e8	−0.115265
$401$	−6.93705e8	−0.537241	−0.268621	−	0.963246i	$-0.586568\pi$
$401$	−6.93705e8	−0.537241	−0.268621	+	0.963246i	$0.586568\pi$
$402$	3.85642e8	0.296069
$403$	8.84541e8	0.673210
$404$	−7.71628e8	−0.582201
$405$	−1.21715e7	−0.00910442
$406$	−2.20151e9	−1.63260
$407$	1.40407e8	0.103231
$408$	5.35855e8	0.390604
$409$	6.30962e8	0.456007	0.228004	−	0.973660i	$-0.426780\pi$
$409$	6.30962e8	0.456007	0.228004	+	0.973660i	$0.426780\pi$
$410$	−1.58656e7	−0.0113688
$411$	−2.72951e7	−0.0193927
$412$	4.51080e8	0.317771
$413$	−2.98657e9	−2.08616
$414$	−4.56279e8	−0.316031
$415$	−1.34500e8	−0.0923748
$416$	−1.99881e9	−1.36127
$417$	2.21396e8	0.149518
$418$	4.37922e8	0.293278
$419$	2.67057e9	1.77360	0.886799	−	0.462156i	$-0.152924\pi$
$419$	2.67057e9	1.77360	0.886799	+	0.462156i	$0.152924\pi$
$420$	7.76103e7	0.0511148
$421$	1.82965e9	1.19503	0.597517	−	0.801857i	$-0.296154\pi$
$421$	1.82965e9	1.19503	0.597517	+	0.801857i	$0.296154\pi$
$422$	5.54882e8	0.359424
$423$	2.69559e8	0.173166
$424$	4.46617e8	0.284547
$425$	1.10732e9	0.699703
$426$	−7.49575e8	−0.469766
$427$	−4.39958e9	−2.73472
$428$	−1.33992e9	−0.826087
$429$	3.77254e8	0.230692
$430$	8.55336e7	0.0518797
$431$	−1.18514e9	−0.713015	−0.356508	−	0.934292i	$-0.616033\pi$
$431$	−1.18514e9	−0.713015	−0.356508	+	0.934292i	$0.616033\pi$
$432$	−3.74228e7	−0.0223328
$433$	−3.02434e8	−0.179029	−0.0895143	−	0.995986i	$-0.528531\pi$
$433$	−3.02434e8	−0.179029	−0.0895143	+	0.995986i	$0.528531\pi$
$434$	8.04383e8	0.472333
$435$	−1.42606e8	−0.0830665
$436$	−1.23623e9	−0.714328
$437$	4.85729e9	2.78425
$438$	−4.90150e7	−0.0278721
$439$	−7.56157e8	−0.426566	−0.213283	−	0.976990i	$-0.568416\pi$
$439$	−7.56157e8	−0.426566	−0.213283	+	0.976990i	$0.568416\pi$
$440$	4.23975e7	0.0237277
$441$	9.66654e8	0.536706
$442$	9.75363e8	0.537265
$443$	−2.13366e9	−1.16604	−0.583018	−	0.812459i	$-0.698128\pi$
$443$	−2.13366e9	−1.16604	−0.583018	+	0.812459i	$0.698128\pi$
$444$	−2.43820e8	−0.132199
$445$	1.98034e8	0.106532
$446$	−5.75026e8	−0.306913
$447$	1.40045e9	0.741637
$448$	−1.46087e9	−0.767607
$449$	−9.63080e8	−0.502112	−0.251056	−	0.967973i	$-0.580778\pi$
$449$	−9.63080e8	−0.502112	−0.251056	+	0.967973i	$0.580778\pi$
$450$	3.68346e8	0.190551
$451$	1.41606e8	0.0726882
$452$	5.23974e8	0.266885
$453$	−5.37966e8	−0.271901
$454$	1.14624e8	0.0574883
$455$	3.52497e8	0.175435
$456$	−1.89754e9	−0.937161
$457$	−1.40297e9	−0.687609	−0.343805	−	0.939041i	$-0.611716\pi$
$457$	−1.40297e9	−0.687609	−0.343805	+	0.939041i	$0.611716\pi$
$458$	−3.17366e8	−0.154359
$459$	2.80868e8	0.135568
$460$	1.88461e8	0.0902754
$461$	−2.52827e9	−1.20191	−0.600953	−	0.799284i	$-0.705212\pi$
$461$	−2.52827e9	−1.20191	−0.600953	+	0.799284i	$0.705212\pi$
$462$	3.43067e8	0.161857
$463$	2.99988e8	0.140466	0.0702329	−	0.997531i	$-0.477626\pi$
$463$	2.99988e8	0.140466	0.0702329	+	0.997531i	$0.477626\pi$
$464$	−4.38460e8	−0.203759
$465$	5.21050e7	0.0240322
$466$	−3.14724e8	−0.144072
$467$	9.43831e8	0.428830	0.214415	−	0.976743i	$-0.431216\pi$
$467$	9.43831e8	0.428830	0.214415	+	0.976743i	$0.431216\pi$
$468$	−6.55107e8	−0.295428
$469$	−3.21611e9	−1.43955
$470$	5.51418e7	0.0244984
$471$	−5.37300e8	−0.236943
$472$	2.83317e9	1.24015
$473$	−7.63416e8	−0.331701
$474$	−4.98899e7	−0.0215173
$475$	−3.92120e9	−1.67877
$476$	−1.79092e9	−0.761118
$477$	2.34094e8	0.0987588
$478$	−1.24067e9	−0.519586
$479$	−2.70997e6	−0.00112665	−0.000563326	−	1.00000i	$-0.500179\pi$
$479$	−2.70997e6	−0.00112665	−0.000563326		1.00000i	$0.500179\pi$
$480$	−1.17742e8	−0.0485946
$481$	−1.10740e9	−0.453729
$482$	1.04845e9	0.426467
$483$	3.80519e9	1.53660
$484$	−1.51652e8	−0.0607981
$485$	−867042.	−0.000345099 0
$486$	9.34292e7	0.0369195
$487$	4.14451e9	1.62600	0.813002	−	0.582261i	$-0.197832\pi$
$487$	4.14451e9	1.62600	0.813002	+	0.582261i	$0.197832\pi$
$488$	4.17360e9	1.62570
$489$	7.69806e8	0.297715
$490$	1.97741e8	0.0759296
$491$	5.05782e9	1.92831	0.964157	−	0.265332i	$-0.0854815\pi$
$491$	5.05782e9	1.92831	0.964157	+	0.265332i	$0.0854815\pi$
$492$	−2.45901e8	−0.0930855
$493$	3.29075e9	1.23689
$494$	−3.45391e9	−1.28904
$495$	2.22226e7	0.00823526
$496$	1.60203e8	0.0589501
$497$	6.25116e9	2.28409
$498$	1.03243e9	0.374591
$499$	−5.07724e9	−1.82926	−0.914631	−	0.404290i	$-0.867519\pi$
$499$	−5.07724e9	−1.82926	−0.914631	+	0.404290i	$0.867519\pi$
$500$	−3.05311e8	−0.109231
$501$	9.34457e8	0.331992
$502$	1.27668e9	0.450423
$503$	−1.20032e9	−0.420542	−0.210271	−	0.977643i	$-0.567435\pi$
$503$	−1.20032e9	−0.420542	−0.210271	+	0.977643i	$0.567435\pi$
$504$	−1.48653e9	−0.517209
$505$	−2.06445e8	−0.0713321
$506$	8.33069e8	0.285861
$507$	−1.28121e9	−0.436608
$508$	−2.75286e9	−0.931669
$509$	3.95700e9	1.33001	0.665003	−	0.746841i	$-0.268430\pi$
$509$	3.95700e9	1.33001	0.665003	+	0.746841i	$0.268430\pi$
$510$	5.74550e7	0.0191793
$511$	4.08766e8	0.135519
$512$	−7.00489e8	−0.230651
$513$	−9.94594e8	−0.325263
$514$	−1.57146e9	−0.510427
$515$	1.20684e8	0.0389337
$516$	1.32568e9	0.424781
$517$	−4.92159e8	−0.156635
$518$	−1.00705e9	−0.318343
$519$	−2.04067e9	−0.640748
$520$	−3.34391e8	−0.104290
$521$	−5.64143e8	−0.174766	−0.0873830	−	0.996175i	$-0.527850\pi$
$521$	−5.64143e8	−0.174766	−0.0873830	+	0.996175i	$0.527850\pi$
$522$	1.09465e9	0.336844
$523$	−1.78145e9	−0.544526	−0.272263	−	0.962223i	$-0.587772\pi$
$523$	−1.78145e9	−0.544526	−0.272263	+	0.962223i	$0.587772\pi$
$524$	−7.38731e8	−0.224299
$525$	−3.07186e9	−0.926496
$526$	2.24218e8	0.0671768
$527$	−1.20236e9	−0.357848
$528$	6.83261e7	0.0202008
$529$	5.83531e9	1.71384
$530$	4.78868e7	0.0139717
$531$	1.48500e9	0.430424
$532$	6.34192e9	1.82612
$533$	−1.11685e9	−0.319485
$534$	−1.52012e9	−0.432000
$535$	−3.58489e8	−0.101213
$536$	3.05091e9	0.855762
$537$	2.97151e9	0.828072
$538$	3.33299e9	0.922777
$539$	−1.76491e9	−0.485468
$540$	−3.85899e7	−0.0105462
$541$	6.13363e9	1.66543	0.832717	−	0.553699i	$-0.186784\pi$
$541$	6.13363e9	1.66543	0.832717	+	0.553699i	$0.186784\pi$
$542$	−8.22998e8	−0.222025
$543$	−3.11811e9	−0.835779
$544$	2.71700e9	0.723591
$545$	−3.30748e8	−0.0875205
$546$	−2.70578e9	−0.711408
$547$	−1.02383e9	−0.267467	−0.133734	−	0.991017i	$-0.542697\pi$
$547$	−1.02383e9	−0.267467	−0.133734	+	0.991017i	$0.542697\pi$
$548$	−8.65393e7	−0.0224637
$549$	2.18759e9	0.564238
$550$	−6.72522e8	−0.172360
$551$	−1.16530e10	−2.96762
$552$	−3.60974e9	−0.913459
$553$	4.16062e8	0.104621
$554$	8.91859e8	0.222850
$555$	−6.52328e7	−0.0161972
$556$	7.01938e8	0.173196
$557$	8.68740e8	0.213008	0.106504	−	0.994312i	$-0.466034\pi$
$557$	8.68740e8	0.213008	0.106504	+	0.994312i	$0.466034\pi$
$558$	−3.99961e8	−0.0974535
$559$	6.02109e9	1.45792
$560$	6.38422e7	0.0153621
$561$	−5.12805e8	−0.122626
$562$	−1.70995e9	−0.406356
$563$	−7.92129e8	−0.187075	−0.0935376	−	0.995616i	$-0.529818\pi$
$563$	−7.92129e8	−0.187075	−0.0935376	+	0.995616i	$0.529818\pi$
$564$	8.54640e8	0.200589
$565$	1.40187e8	0.0326992
$566$	−1.15381e9	−0.267471
$567$	−7.79163e8	−0.179510
$568$	−5.93008e9	−1.35782
$569$	3.06956e9	0.698526	0.349263	−	0.937025i	$-0.386432\pi$
$569$	3.06956e9	0.698526	0.349263	+	0.937025i	$0.386432\pi$
$570$	−2.03457e8	−0.0460161
$571$	1.36993e9	0.307943	0.153972	−	0.988075i	$-0.450794\pi$
$571$	1.36993e9	0.307943	0.153972	+	0.988075i	$0.450794\pi$
$572$	1.19609e9	0.267225
$573$	2.81208e9	0.624434
$574$	−1.01564e9	−0.224155
$575$	−7.45939e9	−1.63631
$576$	7.26384e8	0.158375
$577$	−7.02749e9	−1.52295	−0.761473	−	0.648196i	$-0.775524\pi$
$577$	−7.02749e9	−1.52295	−0.761473	+	0.648196i	$0.775524\pi$
$578$	1.34599e9	0.289932
$579$	−2.85664e9	−0.611619
$580$	−4.52134e8	−0.0962209
$581$	−8.61004e9	−1.82133
$582$	6.65546e6	0.00139942
$583$	−4.27406e8	−0.0893307
$584$	−3.87770e8	−0.0805618
$585$	−1.75271e8	−0.0361963
$586$	1.71504e9	0.352072
$587$	−5.15208e9	−1.05135	−0.525677	−	0.850684i	$-0.676188\pi$
$587$	−5.15208e9	−1.05135	−0.525677	+	0.850684i	$0.676188\pi$
$588$	3.06479e9	0.621698
$589$	4.25775e9	0.858572
$590$	3.03776e8	0.0608935
$591$	−1.05893e9	−0.211014
$592$	−2.00566e8	−0.0397311
$593$	−2.10968e9	−0.415457	−0.207728	−	0.978187i	$-0.566607\pi$
$593$	−2.10968e9	−0.415457	−0.207728	+	0.978187i	$0.566607\pi$
$594$	−1.70582e8	−0.0333949
$595$	−4.79152e8	−0.0932533
$596$	4.44014e9	0.859083
$597$	−4.72065e8	−0.0908012
$598$	−6.57045e9	−1.25644
$599$	9.31625e9	1.77112	0.885558	−	0.464529i	$-0.153776\pi$
$599$	9.31625e9	1.77112	0.885558	+	0.464529i	$0.153776\pi$
$600$	2.91407e9	0.550771
$601$	−3.64612e9	−0.685127	−0.342563	−	0.939495i	$-0.611295\pi$
$601$	−3.64612e9	−0.685127	−0.342563	+	0.939495i	$0.611295\pi$
$602$	5.47545e9	1.02290
$603$	1.59913e9	0.297012
$604$	−1.70563e9	−0.314959
$605$	−4.05738e7	−0.00744907
$606$	1.58468e9	0.289260
$607$	1.09624e9	0.198951	0.0994755	−	0.995040i	$-0.468284\pi$
$607$	1.09624e9	0.198951	0.0994755	+	0.995040i	$0.468284\pi$
$608$	−9.62130e9	−1.73609
$609$	−9.12896e9	−1.63780
$610$	4.47499e8	0.0798247
$611$	3.88167e9	0.688454
$612$	8.90493e8	0.157037
$613$	6.44955e9	1.13088	0.565442	−	0.824788i	$-0.308706\pi$
$613$	6.44955e9	1.13088	0.565442	+	0.824788i	$0.308706\pi$
$614$	−5.79906e9	−1.01104
$615$	−6.57896e7	−0.0114050
$616$	2.71409e9	0.467834
$617$	−7.65657e9	−1.31231	−0.656155	−	0.754626i	$-0.727818\pi$
$617$	−7.65657e9	−1.31231	−0.656155	+	0.754626i	$0.727818\pi$
$618$	−9.26379e8	−0.157881
$619$	−6.11175e9	−1.03573	−0.517867	−	0.855461i	$-0.673274\pi$
$619$	−6.11175e9	−1.03573	−0.517867	+	0.855461i	$0.673274\pi$
$620$	1.65199e8	0.0278380
$621$	−1.89204e9	−0.317037
$622$	3.86963e9	0.644767
$623$	1.26772e10	2.10046
$624$	−5.38891e8	−0.0887881
$625$	5.98085e9	0.979903
$626$	−3.20525e8	−0.0522218
$627$	1.81592e9	0.294212
$628$	−1.70351e9	−0.274465
$629$	1.50530e9	0.241182
$630$	−1.59388e8	−0.0253958
$631$	−1.23495e9	−0.195680	−0.0978399	−	0.995202i	$-0.531193\pi$
$631$	−1.23495e9	−0.195680	−0.0978399	+	0.995202i	$0.531193\pi$
$632$	−3.94691e8	−0.0621939
$633$	2.30091e9	0.360568
$634$	2.72179e9	0.424172
$635$	−7.36516e8	−0.114149
$636$	7.42196e8	0.114398
$637$	1.39199e10	2.13377
$638$	−1.99860e9	−0.304687
$639$	−3.10824e9	−0.471262
$640$	−4.09595e8	−0.0617625
$641$	−3.11269e9	−0.466802	−0.233401	−	0.972381i	$-0.574985\pi$
$641$	−3.11269e9	−0.466802	−0.233401	+	0.972381i	$0.574985\pi$
$642$	2.75178e9	0.410432
$643$	2.24869e9	0.333574	0.166787	−	0.985993i	$-0.446661\pi$
$643$	2.24869e9	0.333574	0.166787	+	0.985993i	$0.446661\pi$
$644$	1.20644e10	1.77994
$645$	3.54680e8	0.0520448
$646$	4.69493e9	0.685197
$647$	3.45334e9	0.501274	0.250637	−	0.968081i	$-0.419360\pi$
$647$	3.45334e9	0.501274	0.250637	+	0.968081i	$0.419360\pi$
$648$	7.39142e8	0.106712
$649$	−2.71130e9	−0.389333
$650$	5.30420e9	0.757571
$651$	3.33551e9	0.473837
$652$	2.44068e9	0.344861
$653$	4.81658e9	0.676929	0.338464	−	0.940979i	$-0.390093\pi$
$653$	4.81658e9	0.676929	0.338464	+	0.940979i	$0.390093\pi$
$654$	2.53884e9	0.354906
$655$	−1.97644e8	−0.0274814
$656$	−2.02278e8	−0.0279760
$657$	−2.03249e8	−0.0279608
$658$	3.52991e9	0.483029
$659$	−5.84569e9	−0.795677	−0.397838	−	0.917456i	$-0.630239\pi$
$659$	−5.84569e9	−0.795677	−0.397838	+	0.917456i	$0.630239\pi$
$660$	7.04570e7	0.00953939
$661$	−1.39642e10	−1.88067	−0.940334	−	0.340252i	$-0.889488\pi$
$661$	−1.39642e10	−1.88067	−0.940334	+	0.340252i	$0.889488\pi$
$662$	5.09918e9	0.683121
$663$	4.04451e9	0.538975
$664$	8.16780e9	1.08272
$665$	1.69675e9	0.223739
$666$	5.00730e8	0.0656816
$667$	−2.21679e10	−2.89257
$668$	2.96270e9	0.384566
$669$	−2.38445e9	−0.307890
$670$	3.27123e8	0.0420193
$671$	−3.99407e9	−0.510372
$672$	−7.53730e9	−0.958128
$673$	−6.23105e9	−0.787967	−0.393984	−	0.919117i	$-0.628903\pi$
$673$	−6.23105e9	−0.787967	−0.393984	+	0.919117i	$0.628903\pi$
$674$	−6.75813e9	−0.850191
$675$	1.52741e9	0.191158
$676$	−4.06208e9	−0.505749
$677$	3.65484e9	0.452698	0.226349	−	0.974046i	$-0.427321\pi$
$677$	3.65484e9	0.452698	0.226349	+	0.974046i	$0.427321\pi$
$678$	−1.07608e9	−0.132599
$679$	−5.55039e7	−0.00680423
$680$	4.54541e8	0.0554360
$681$	4.75307e8	0.0576713
$682$	7.30243e8	0.0881500
$683$	7.30759e9	0.877611	0.438805	−	0.898582i	$-0.355402\pi$
$683$	7.30759e9	0.877611	0.438805	+	0.898582i	$0.355402\pi$
$684$	−3.15337e9	−0.376772
$685$	−2.31532e7	−0.00275228
$686$	4.79663e9	0.567286
$687$	−1.31601e9	−0.154850
$688$	1.09051e9	0.127664
$689$	3.37097e9	0.392633
$690$	−3.87041e8	−0.0448523
$691$	1.66378e9	0.191833	0.0959163	−	0.995389i	$-0.469422\pi$
$691$	1.66378e9	0.191833	0.0959163	+	0.995389i	$0.469422\pi$
$692$	−6.46996e9	−0.742216
$693$	1.42259e9	0.162372
$694$	4.32378e8	0.0491027
$695$	1.87800e8	0.0212202
$696$	8.66006e9	0.973618
$697$	1.51815e9	0.169824
$698$	9.55967e9	1.06402
$699$	−1.30506e9	−0.144531
$700$	−9.73935e9	−1.07322
$701$	−7.01449e9	−0.769100	−0.384550	−	0.923104i	$-0.625643\pi$
$701$	−7.01449e9	−0.769100	−0.384550	+	0.923104i	$0.625643\pi$
$702$	1.34539e9	0.146780
$703$	−5.33049e9	−0.578660
$704$	−1.32622e9	−0.143256
$705$	2.28655e8	0.0245764
$706$	−9.28074e9	−0.992582
$707$	−1.32156e10	−1.40644
$708$	4.70821e9	0.498585
$709$	5.76802e8	0.0607806	0.0303903	−	0.999538i	$-0.490325\pi$
$709$	5.76802e8	0.0607806	0.0303903	+	0.999538i	$0.490325\pi$
$710$	−6.35830e8	−0.0666710
$711$	−2.06877e8	−0.0215858
$712$	−1.20261e10	−1.24866
$713$	8.09963e9	0.836858
$714$	3.67800e9	0.378153
$715$	3.20007e8	0.0327408
$716$	9.42121e9	0.959204
$717$	−5.14464e9	−0.521240
$718$	−8.83425e9	−0.890706
$719$	9.27391e9	0.930490	0.465245	−	0.885182i	$-0.345966\pi$
$719$	9.27391e9	0.930490	0.465245	+	0.885182i	$0.345966\pi$
$720$	−3.17441e7	−0.00316956
$721$	7.72564e9	0.767646
$722$	−1.08052e10	−1.06845
$723$	4.34760e9	0.427824
$724$	−9.88598e9	−0.968132
$725$	1.78957e10	1.74408
$726$	3.11447e8	0.0302069
$727$	−1.35691e10	−1.30972	−0.654862	−	0.755749i	$-0.727273\pi$
$727$	−1.35691e10	−1.30972	−0.654862	+	0.755749i	$0.727273\pi$
$728$	−2.14061e10	−2.05626
$729$	3.87420e8	0.0370370
$730$	−4.15772e7	−0.00395572
$731$	−8.18452e9	−0.774966
$732$	6.93577e9	0.653590
$733$	1.86948e10	1.75330	0.876651	−	0.481126i	$-0.159772\pi$
$733$	1.86948e10	1.75330	0.876651	+	0.481126i	$0.159772\pi$
$734$	−5.40682e9	−0.504668
$735$	8.19969e8	0.0761713
$736$	−1.83028e10	−1.69218
$737$	−2.91968e9	−0.268658
$738$	5.05004e8	0.0462485
$739$	2.11872e10	1.93116	0.965578	−	0.260115i	$-0.0837605\pi$
$739$	2.11872e10	1.93116	0.965578	+	0.260115i	$0.0837605\pi$
$740$	−2.06821e8	−0.0187622
$741$	−1.43222e10	−1.29314
$742$	3.06549e9	0.275477
$743$	−4.13191e9	−0.369565	−0.184782	−	0.982779i	$-0.559158\pi$
$743$	−4.13191e9	−0.369565	−0.184782	+	0.982779i	$0.559158\pi$
$744$	−3.16419e9	−0.281681
$745$	1.18794e9	0.105256
$746$	−3.44369e9	−0.303695
$747$	4.28114e9	0.375783
$748$	−1.62585e9	−0.142045
$749$	−2.29488e10	−1.99560
$750$	6.27014e8	0.0542704
$751$	1.78743e10	1.53989	0.769946	−	0.638109i	$-0.220283\pi$
$751$	1.78743e10	1.53989	0.769946	+	0.638109i	$0.220283\pi$
$752$	7.03027e8	0.0602850
$753$	5.29400e9	0.451857
$754$	1.57631e10	1.33919
$755$	−4.56332e8	−0.0385893
$756$	−2.47034e9	−0.207937
$757$	7.62595e9	0.638938	0.319469	−	0.947597i	$-0.396496\pi$
$757$	7.62595e9	0.638938	0.319469	+	0.947597i	$0.396496\pi$
$758$	7.28010e9	0.607148
$759$	3.45447e9	0.286771
$760$	−1.60960e9	−0.133006
$761$	1.24031e10	1.02020	0.510099	−	0.860116i	$-0.329609\pi$
$761$	1.24031e10	1.02020	0.510099	+	0.860116i	$0.329609\pi$
$762$	5.65353e9	0.462889
$763$	−2.11729e10	−1.72562
$764$	8.91572e9	0.723319
$765$	2.38247e8	0.0192403
$766$	−1.09969e10	−0.884035
$767$	2.13841e10	1.71123
$768$	6.58767e9	0.524768
$769$	1.10128e10	0.873283	0.436641	−	0.899636i	$-0.356168\pi$
$769$	1.10128e10	0.873283	0.436641	+	0.899636i	$0.356168\pi$
$770$	2.91008e8	0.0229714
$771$	−6.51635e9	−0.512052
$772$	−9.05701e9	−0.708475
$773$	−8.73173e9	−0.679942	−0.339971	−	0.940436i	$-0.610417\pi$
$773$	−8.73173e9	−0.679942	−0.339971	+	0.940436i	$0.610417\pi$
$774$	−2.72254e9	−0.211048
$775$	−6.53868e9	−0.504585
$776$	5.26530e7	0.00404489
$777$	−4.17589e9	−0.319356
$778$	−7.81427e9	−0.594922
$779$	−5.37599e9	−0.407453
$780$	−5.55697e8	−0.0419283
$781$	5.67500e9	0.426272
$782$	8.93128e9	0.667867
$783$	4.53916e9	0.337917
$784$	2.52109e9	0.186845
$785$	−4.55767e8	−0.0336279
$786$	1.51713e9	0.111440
$787$	−2.15808e10	−1.57818	−0.789089	−	0.614278i	$-0.789447\pi$
$787$	−2.15808e10	−1.57818	−0.789089	+	0.614278i	$0.789447\pi$
$788$	−3.35734e9	−0.244430
$789$	9.29757e8	0.0673907
$790$	−4.23193e7	−0.00305382
$791$	8.97408e9	0.644721
$792$	−1.34952e9	−0.0965251
$793$	3.15014e10	2.24323
$794$	−4.16664e9	−0.295402
$795$	1.98571e8	0.0140162
$796$	−1.49669e9	−0.105180
$797$	−1.43410e10	−1.00340	−0.501702	−	0.865040i	$-0.667293\pi$
$797$	−1.43410e10	−1.00340	−0.501702	+	0.865040i	$0.667293\pi$
$798$	−1.30243e10	−0.907288
$799$	−5.27640e9	−0.365952
$800$	1.47755e10	1.02030
$801$	−6.30344e9	−0.433375
$802$	4.51688e9	0.309192
$803$	3.71090e8	0.0252915
$804$	5.07007e9	0.344047
$805$	3.22777e9	0.218080
$806$	−5.75946e9	−0.387444
$807$	1.38208e10	0.925715
$808$	1.25368e10	0.836080
$809$	−7.87747e9	−0.523079	−0.261539	−	0.965193i	$-0.584230\pi$
$809$	−7.87747e9	−0.523079	−0.261539	+	0.965193i	$0.584230\pi$
$810$	7.92517e7	0.00523976
$811$	1.79798e10	1.18362	0.591810	−	0.806077i	$-0.298413\pi$
$811$	1.79798e10	1.18362	0.591810	+	0.806077i	$0.298413\pi$
$812$	−2.89435e10	−1.89716
$813$	−3.41270e9	−0.222731
$814$	−9.14227e8	−0.0594112
$815$	6.52992e8	0.0422528
$816$	7.32519e8	0.0471958
$817$	2.89826e10	1.85935
$818$	−4.10835e9	−0.262440
$819$	−1.12200e10	−0.713673
$820$	−2.08586e8	−0.0132111
$821$	1.51047e10	0.952603	0.476302	−	0.879282i	$-0.341977\pi$
$821$	1.51047e10	0.952603	0.476302	+	0.879282i	$0.341977\pi$
$822$	1.77725e8	0.0111608
$823$	−2.28969e9	−0.143178	−0.0715891	−	0.997434i	$-0.522807\pi$
$823$	−2.28969e9	−0.143178	−0.0715891	+	0.997434i	$0.522807\pi$
$824$	−7.32882e9	−0.456340
$825$	−2.78873e9	−0.172909
$826$	1.94463e10	1.20062
$827$	1.65291e10	1.01620	0.508100	−	0.861298i	$-0.330348\pi$
$827$	1.65291e10	1.01620	0.508100	+	0.861298i	$0.330348\pi$
$828$	−5.99873e9	−0.367243
$829$	6.28590e8	0.0383201	0.0191600	−	0.999816i	$-0.493901\pi$
$829$	6.28590e8	0.0383201	0.0191600	+	0.999816i	$0.493901\pi$
$830$	8.75762e8	0.0531634
$831$	3.69825e9	0.223559
$832$	1.04600e10	0.629650
$833$	−1.89214e10	−1.13422
$834$	−1.44156e9	−0.0860503
$835$	7.92657e8	0.0471176
$836$	5.75739e9	0.340803
$837$	−1.65851e9	−0.0977638
$838$	−1.73887e10	−1.02074
$839$	2.41206e10	1.41001	0.705005	−	0.709202i	$-0.250945\pi$
$839$	2.41206e10	1.41001	0.705005	+	0.709202i	$0.250945\pi$
$840$	−1.26095e9	−0.0734044
$841$	3.59327e10	2.08307
$842$	−1.19133e10	−0.687763
$843$	−7.09061e9	−0.407650
$844$	7.29507e9	0.417667
$845$	−1.08679e9	−0.0619651
$846$	−1.75517e9	−0.0996603
$847$	−2.59734e9	−0.146871
$848$	6.10531e8	0.0343813
$849$	−4.78448e9	−0.268323
$850$	−7.21006e9	−0.402691
$851$	−1.01403e10	−0.564024
$852$	−9.85472e9	−0.545890
$853$	−2.75650e10	−1.52067	−0.760337	−	0.649529i	$-0.774966\pi$
$853$	−2.75650e10	−1.52067	−0.760337	+	0.649529i	$0.774966\pi$
$854$	2.86467e10	1.57388
$855$	−8.43669e8	−0.0461626
$856$	2.17700e10	1.18632
$857$	−3.29561e10	−1.78856	−0.894280	−	0.447508i	$-0.852312\pi$
$857$	−3.29561e10	−1.78856	−0.894280	+	0.447508i	$0.852312\pi$
$858$	−2.45639e9	−0.132768
$859$	−1.74671e10	−0.940251	−0.470126	−	0.882599i	$-0.655791\pi$
$859$	−1.74671e10	−0.940251	−0.470126	+	0.882599i	$0.655791\pi$
$860$	1.12452e9	0.0602866
$861$	−4.21153e9	−0.224869
$862$	7.71672e9	0.410353
$863$	1.33149e10	0.705179	0.352589	−	0.935778i	$-0.385301\pi$
$863$	1.33149e10	0.705179	0.352589	+	0.935778i	$0.385301\pi$
$864$	3.74775e9	0.197684
$865$	−1.73101e9	−0.0909374
$866$	1.96922e9	0.103034
$867$	5.58140e9	0.290855
$868$	1.05753e10	0.548874
$869$	3.77714e8	0.0195251
$870$	9.28543e8	0.0478063
$871$	2.30276e10	1.18083
$872$	2.00854e10	1.02582
$873$	2.75980e7	0.00140387
$874$	−3.16270e10	−1.60239
$875$	−5.22905e9	−0.263873
$876$	−6.44404e8	−0.0323887
$877$	−2.16552e10	−1.08409	−0.542043	−	0.840351i	$-0.682349\pi$
$877$	−2.16552e10	−1.08409	−0.542043	+	0.840351i	$0.682349\pi$
$878$	4.92352e9	0.245496
$879$	7.11170e9	0.353193
$880$	5.79579e7	0.00286697
$881$	−1.89906e10	−0.935670	−0.467835	−	0.883816i	$-0.654966\pi$
$881$	−1.89906e10	−0.935670	−0.467835	+	0.883816i	$0.654966\pi$
$882$	−6.29412e9	−0.308884
$883$	−1.59282e10	−0.778580	−0.389290	−	0.921115i	$-0.627280\pi$
$883$	−1.59282e10	−0.778580	−0.389290	+	0.921115i	$0.627280\pi$
$884$	1.28232e10	0.624327
$885$	1.25966e9	0.0610874
$886$	1.38928e10	0.671074
$887$	−1.80968e10	−0.870703	−0.435352	−	0.900260i	$-0.643376\pi$
$887$	−1.80968e10	−0.870703	−0.435352	+	0.900260i	$0.643376\pi$
$888$	3.96140e9	0.189847
$889$	−4.71482e10	−2.25066
$890$	−1.28945e9	−0.0613111
$891$	−7.07348e8	−0.0335013
$892$	−7.55990e9	−0.356648
$893$	1.86845e10	0.878014
$894$	−9.11868e9	−0.426826
$895$	2.52060e9	0.117523
$896$	−2.62203e10	−1.21775
$897$	−2.72455e10	−1.26044
$898$	6.27085e9	0.288974
$899$	−1.94317e10	−0.891973
$900$	4.84267e9	0.221430
$901$	−4.58219e9	−0.208707
$902$	−9.22031e8	−0.0418333
$903$	2.27049e10	1.02615
$904$	−8.51313e9	−0.383266
$905$	−2.64495e9	−0.118617
$906$	3.50283e9	0.156484
$907$	−1.96520e10	−0.874544	−0.437272	−	0.899329i	$-0.644055\pi$
$907$	−1.96520e10	−0.874544	−0.437272	+	0.899329i	$0.644055\pi$
$908$	1.50697e9	0.0668041
$909$	6.57117e9	0.290181
$910$	−2.29519e9	−0.100966
$911$	3.74053e10	1.63915	0.819576	−	0.572971i	$-0.194209\pi$
$911$	3.74053e10	1.63915	0.819576	+	0.572971i	$0.194209\pi$
$912$	−2.59396e9	−0.113235
$913$	−7.81646e9	−0.339909
$914$	9.13508e9	0.395731
$915$	1.85563e9	0.0800788
$916$	−4.17243e9	−0.179372
$917$	−1.26522e10	−0.541844
$918$	−1.82880e9	−0.0780218
$919$	−4.10744e10	−1.74569	−0.872845	−	0.487998i	$-0.837727\pi$
$919$	−4.10744e10	−1.74569	−0.872845	+	0.487998i	$0.837727\pi$
$920$	−3.06198e9	−0.129642
$921$	−2.40468e10	−1.01426
$922$	1.64622e10	0.691719
$923$	−4.47589e10	−1.87359
$924$	4.51032e9	0.188086
$925$	8.18609e9	0.340079
$926$	−1.95329e9	−0.0808405
$927$	−3.84139e9	−0.158383
$928$	4.39100e10	1.80362
$929$	−1.49524e10	−0.611864	−0.305932	−	0.952053i	$-0.598968\pi$
$929$	−1.49524e10	−0.611864	−0.305932	+	0.952053i	$0.598968\pi$
$930$	−3.39268e8	−0.0138310
$931$	6.70036e10	2.72129
$932$	−4.13770e9	−0.167418
$933$	1.60461e10	0.646820
$934$	−6.14551e9	−0.246799
$935$	−4.34989e8	−0.0174035
$936$	1.06437e10	0.424255
$937$	−1.06439e10	−0.422679	−0.211339	−	0.977413i	$-0.567783\pi$
$937$	−1.06439e10	−0.422679	−0.211339	+	0.977413i	$0.567783\pi$
$938$	2.09408e10	0.828484
$939$	−1.32911e9	−0.0523881
$940$	7.24952e8	0.0284683
$941$	−1.23064e10	−0.481468	−0.240734	−	0.970591i	$-0.577388\pi$
$941$	−1.23064e10	−0.481468	−0.240734	+	0.970591i	$0.577388\pi$
$942$	3.49849e9	0.136365
$943$	−1.02269e10	−0.397147
$944$	3.87297e9	0.149845
$945$	−6.60928e8	−0.0254767
$946$	4.97078e9	0.190900
$947$	3.69429e10	1.41353	0.706766	−	0.707447i	$-0.250153\pi$
$947$	3.69429e10	1.41353	0.706766	+	0.707447i	$0.250153\pi$
$948$	−6.55906e8	−0.0250042
$949$	−2.92680e9	−0.111163
$950$	2.55319e10	0.966163
$951$	1.12864e10	0.425523
$952$	2.90975e10	1.09302
$953$	8.91918e9	0.333810	0.166905	−	0.985973i	$-0.446623\pi$
$953$	8.91918e9	0.333810	0.166905	+	0.985973i	$0.446623\pi$
$954$	−1.52424e9	−0.0568374
$955$	2.38536e9	0.0886220
$956$	−1.63111e10	−0.603784
$957$	−8.28756e9	−0.305657
$958$	1.76453e7	0.000648409 0
$959$	−1.48216e9	−0.0542661
$960$	6.16159e8	0.0224773
$961$	−2.04127e10	−0.741941
$962$	7.21054e9	0.261129
$963$	1.14107e10	0.411739
$964$	1.37841e10	0.495574
$965$	−2.42316e9	−0.0868034
$966$	−2.47765e10	−0.884341
$967$	9.73150e9	0.346088	0.173044	−	0.984914i	$-0.444640\pi$
$967$	9.73150e9	0.346088	0.173044	+	0.984914i	$0.444640\pi$
$968$	2.46393e9	0.0873102
$969$	1.94683e10	0.687378
$970$	5.64552e6	0.000198611 0
$971$	2.82145e10	0.989021	0.494510	−	0.869172i	$-0.335347\pi$
$971$	2.82145e10	0.989021	0.494510	+	0.869172i	$0.335347\pi$
$972$	1.22832e9	0.0429022
$973$	1.20221e10	0.418393
$974$	−2.69859e10	−0.935794
$975$	2.19948e10	0.759983
$976$	5.70536e9	0.196430
$977$	−1.91767e10	−0.657873	−0.328936	−	0.944352i	$-0.606690\pi$
$977$	−1.91767e10	−0.657873	−0.328936	+	0.944352i	$0.606690\pi$
$978$	−5.01240e9	−0.171340
$979$	1.15088e10	0.392003
$980$	2.59972e9	0.0882338
$981$	1.05277e10	0.356036
$982$	−3.29327e10	−1.10978
$983$	−1.90138e10	−0.638457	−0.319228	−	0.947678i	$-0.603424\pi$
$983$	−1.90138e10	−0.638457	−0.319228	+	0.947678i	$0.603424\pi$
$984$	3.99521e9	0.133677
$985$	−8.98241e8	−0.0299479
$986$	−2.14269e10	−0.711852
$987$	1.46374e10	0.484567
$988$	−4.54087e10	−1.49793
$989$	5.51343e10	1.81232
$990$	−1.44697e8	−0.00473954
$991$	2.54270e10	0.829922	0.414961	−	0.909839i	$-0.363795\pi$
$991$	2.54270e10	0.829922	0.414961	+	0.909839i	$0.363795\pi$
$992$	−1.60437e10	−0.521812
$993$	2.11447e10	0.685296
$994$	−4.07028e10	−1.31454
$995$	−4.00431e8	−0.0128869
$996$	1.35734e10	0.435292
$997$	1.76129e10	0.562858	0.281429	−	0.959582i	$-0.409192\pi$
$997$	1.76129e10	0.562858	0.281429	+	0.959582i	$0.409192\pi$
$998$	3.30591e10	1.05277
$999$	2.07636e9	0.0658907

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.a.d.1.1	✓	3
3.2	odd	2		99.8.a.e.1.3		3
4.3	odd	2		528.8.a.o.1.2		3
11.10	odd	2		363.8.a.e.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.a.d.1.1	✓	3	1.1	even	1	trivial
99.8.a.e.1.3		3	3.2	odd	2
363.8.a.e.1.3		3	11.10	odd	2
528.8.a.o.1.2		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	33.a (trivial)

\(f(q)\)	\(=\)	\(q-6.51124 q^{2} -27.0000 q^{3} -85.6037 q^{4} -22.9029 q^{5} +175.804 q^{6} -1466.13 q^{7} +1390.83 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-6.51124 q^{2} -27.0000 q^{3} -85.6037 q^{4} -22.9029 q^{5} +175.804 q^{6} -1466.13 q^{7} +1390.83 q^{8} +729.000 q^{9} +149.126 q^{10} -1331.00 q^{11} +2311.30 q^{12} +10497.7 q^{13} +9546.34 q^{14} +618.377 q^{15} +1901.28 q^{16} -14269.6 q^{17} -4746.70 q^{18} +50530.6 q^{19} +1960.57 q^{20} +39585.6 q^{21} +8666.46 q^{22} +96125.6 q^{23} -37552.3 q^{24} -77600.5 q^{25} -68352.7 q^{26} -19683.0 q^{27} +125506. q^{28} -230613. q^{29} -4026.41 q^{30} +84260.8 q^{31} -190405. q^{32} +35937.0 q^{33} +92912.5 q^{34} +33578.6 q^{35} -62405.1 q^{36} -105490. q^{37} -329017. q^{38} -283437. q^{39} -31853.9 q^{40} -106391. q^{41} -257751. q^{42} +573565. q^{43} +113939. q^{44} -16696.2 q^{45} -625897. q^{46} +369766. q^{47} -51334.4 q^{48} +1.32600e6 q^{49} +505275. q^{50} +385278. q^{51} -898638. q^{52} +321116. q^{53} +128161. q^{54} +30483.7 q^{55} -2.03913e6 q^{56} -1.36433e6 q^{57} +1.50158e6 q^{58} +2.03704e6 q^{59} -52935.4 q^{60} +3.00081e6 q^{61} -548643. q^{62} -1.06881e6 q^{63} +996412. q^{64} -240426. q^{65} -233995. q^{66} +2.19360e6 q^{67} +1.22153e6 q^{68} -2.59539e6 q^{69} -218639. q^{70} -4.26371e6 q^{71} +1.01391e6 q^{72} -278806. q^{73} +686872. q^{74} +2.09521e6 q^{75} -4.32561e6 q^{76} +1.95142e6 q^{77} +1.84552e6 q^{78} -283782. q^{79} -43544.7 q^{80} +531441. q^{81} +692735. q^{82} +5.87262e6 q^{83} -3.38867e6 q^{84} +326814. q^{85} -3.73462e6 q^{86} +6.22656e6 q^{87} -1.85119e6 q^{88} -8.64670e6 q^{89} +108713. q^{90} -1.53909e7 q^{91} -8.22871e6 q^{92} -2.27504e6 q^{93} -2.40764e6 q^{94} -1.15730e6 q^{95} +5.14094e6 q^{96} +37857.4 q^{97} -8.63391e6 q^{98} -970299. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 9 q^{2} - 81 q^{3} - 15 q^{4} - 444 q^{5} - 243 q^{6} + 1614 q^{7} + 3153 q^{8} + 2187 q^{9}+O(q^{10}) \) 3 * q + 9 * q^2 - 81 * q^3 - 15 * q^4 - 444 * q^5 - 243 * q^6 + 1614 * q^7 + 3153 * q^8 + 2187 * q^9	\( 3 q + 9 q^{2} - 81 q^{3} - 15 q^{4} - 444 q^{5} - 243 q^{6} + 1614 q^{7} + 3153 q^{8} + 2187 q^{9} + 2880 q^{10} - 3993 q^{11} + 405 q^{12} + 20772 q^{13} + 36258 q^{14} + 11988 q^{15} + 12225 q^{16} - 14538 q^{17} + 6561 q^{18} + 24492 q^{19} + 80112 q^{20} - 43578 q^{21} - 11979 q^{22} + 35094 q^{23} - 85131 q^{24} + 29121 q^{25} + 203832 q^{26} - 59049 q^{27} + 278034 q^{28} - 179862 q^{29} - 77760 q^{30} + 288888 q^{31} - 519567 q^{32} + 107811 q^{33} - 491586 q^{34} - 532872 q^{35} - 10935 q^{36} + 107562 q^{37} - 686328 q^{38} - 560844 q^{39} - 237360 q^{40} - 135198 q^{41} - 978966 q^{42} + 193536 q^{43} + 19965 q^{44} - 323676 q^{45} + 16422 q^{46} - 591486 q^{47} - 330075 q^{48} + 4461159 q^{49} - 1192245 q^{50} + 392526 q^{51} + 2449992 q^{52} + 79044 q^{53} - 177147 q^{54} + 590964 q^{55} + 752658 q^{56} - 661284 q^{57} + 2289930 q^{58} + 2532768 q^{59} - 2163024 q^{60} + 6678792 q^{61} - 2660808 q^{62} + 1176606 q^{63} - 3966303 q^{64} + 3191832 q^{65} + 323433 q^{66} + 7150356 q^{67} - 7821954 q^{68} - 947538 q^{69} + 4029120 q^{70} + 1390398 q^{71} + 2298537 q^{72} - 6429114 q^{73} + 2507478 q^{74} - 786267 q^{75} - 7654728 q^{76} - 2148234 q^{77} - 5503464 q^{78} + 6873186 q^{79} - 7556016 q^{80} + 1594323 q^{81} - 1774590 q^{82} + 6505596 q^{83} - 7506918 q^{84} - 16546032 q^{85} - 6519468 q^{86} + 4856274 q^{87} - 4196643 q^{88} - 8842962 q^{89} + 2099520 q^{90} + 3066648 q^{91} + 6921990 q^{92} - 7799976 q^{93} - 24038238 q^{94} - 190968 q^{95} + 14028309 q^{96} - 1764774 q^{97} + 24377397 q^{98} - 2910897 q^{99}+O(q^{100}) \) 3 * q + 9 * q^2 - 81 * q^3 - 15 * q^4 - 444 * q^5 - 243 * q^6 + 1614 * q^7 + 3153 * q^8 + 2187 * q^9 + 2880 * q^10 - 3993 * q^11 + 405 * q^12 + 20772 * q^13 + 36258 * q^14 + 11988 * q^15 + 12225 * q^16 - 14538 * q^17 + 6561 * q^18 + 24492 * q^19 + 80112 * q^20 - 43578 * q^21 - 11979 * q^22 + 35094 * q^23 - 85131 * q^24 + 29121 * q^25 + 203832 * q^26 - 59049 * q^27 + 278034 * q^28 - 179862 * q^29 - 77760 * q^30 + 288888 * q^31 - 519567 * q^32 + 107811 * q^33 - 491586 * q^34 - 532872 * q^35 - 10935 * q^36 + 107562 * q^37 - 686328 * q^38 - 560844 * q^39 - 237360 * q^40 - 135198 * q^41 - 978966 * q^42 + 193536 * q^43 + 19965 * q^44 - 323676 * q^45 + 16422 * q^46 - 591486 * q^47 - 330075 * q^48 + 4461159 * q^49 - 1192245 * q^50 + 392526 * q^51 + 2449992 * q^52 + 79044 * q^53 - 177147 * q^54 + 590964 * q^55 + 752658 * q^56 - 661284 * q^57 + 2289930 * q^58 + 2532768 * q^59 - 2163024 * q^60 + 6678792 * q^61 - 2660808 * q^62 + 1176606 * q^63 - 3966303 * q^64 + 3191832 * q^65 + 323433 * q^66 + 7150356 * q^67 - 7821954 * q^68 - 947538 * q^69 + 4029120 * q^70 + 1390398 * q^71 + 2298537 * q^72 - 6429114 * q^73 + 2507478 * q^74 - 786267 * q^75 - 7654728 * q^76 - 2148234 * q^77 - 5503464 * q^78 + 6873186 * q^79 - 7556016 * q^80 + 1594323 * q^81 - 1774590 * q^82 + 6505596 * q^83 - 7506918 * q^84 - 16546032 * q^85 - 6519468 * q^86 + 4856274 * q^87 - 4196643 * q^88 - 8842962 * q^89 + 2099520 * q^90 + 3066648 * q^91 + 6921990 * q^92 - 7799976 * q^93 - 24038238 * q^94 - 190968 * q^95 + 14028309 * q^96 - 1764774 * q^97 + 24377397 * q^98 - 2910897 * q^99

Introduction

L-functions

Modular forms

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