LMFDB - Embedded newform 242.8.a.m.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [242,8,Mod(1,242)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(242, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("242.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	242.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:	$75.5971761672$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 935x^{2} - 10836x - 31788 $ x^4 - 2x^3 - 935x^2 - 10836*x - 31788
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 11 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-21.3016$ of defining polynomial
Character	$\chi$	$=$	242.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.00000 q^{2} +47.3597 q^{3} +64.0000 q^{4} +499.352 q^{5} +378.877 q^{6} +1391.56 q^{7} +512.000 q^{8} +55.9387 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +47.3597 q^{3} +64.0000 q^{4} +499.352 q^{5} +378.877 q^{6} +1391.56 q^{7} +512.000 q^{8} +55.9387 q^{9} +3994.81 q^{10} +3031.02 q^{12} +471.238 q^{13} +11132.5 q^{14} +23649.1 q^{15} +4096.00 q^{16} -17724.0 q^{17} +447.509 q^{18} +37409.8 q^{19} +31958.5 q^{20} +65904.0 q^{21} -31452.2 q^{23} +24248.2 q^{24} +171227. q^{25} +3769.91 q^{26} -100926. q^{27} +89060.0 q^{28} +161324. q^{29} +189193. q^{30} -265823. q^{31} +32768.0 q^{32} -141792. q^{34} +694879. q^{35} +3580.07 q^{36} -176651. q^{37} +299278. q^{38} +22317.7 q^{39} +255668. q^{40} -746391. q^{41} +527232. q^{42} -325064. q^{43} +27933.1 q^{45} -251618. q^{46} -578602. q^{47} +193985. q^{48} +1.11290e6 q^{49} +1.36982e6 q^{50} -839401. q^{51} +30159.2 q^{52} -2.03356e6 q^{53} -807411. q^{54} +712480. q^{56} +1.77172e6 q^{57} +1.29059e6 q^{58} +488428. q^{59} +1.51354e6 q^{60} +1.46176e6 q^{61} -2.12659e6 q^{62} +77842.2 q^{63} +262144. q^{64} +235314. q^{65} +2.85356e6 q^{67} -1.13433e6 q^{68} -1.48957e6 q^{69} +5.55903e6 q^{70} -3.90552e6 q^{71} +28640.6 q^{72} -2.92809e6 q^{73} -1.41321e6 q^{74} +8.10926e6 q^{75} +2.39423e6 q^{76} +178542. q^{78} +6.61578e6 q^{79} +2.04534e6 q^{80} -4.90218e6 q^{81} -5.97113e6 q^{82} +1.74078e6 q^{83} +4.21785e6 q^{84} -8.85049e6 q^{85} -2.60051e6 q^{86} +7.64026e6 q^{87} +1.02874e6 q^{89} +223465. q^{90} +655758. q^{91} -2.01294e6 q^{92} -1.25893e7 q^{93} -4.62882e6 q^{94} +1.86806e7 q^{95} +1.55188e6 q^{96} +1.21361e7 q^{97} +8.90324e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} + 16 q^{3} + 256 q^{4} + 404 q^{5} + 128 q^{6} - 656 q^{7} + 2048 q^{8} + 8116 q^{9}+O(q^{10}) $ 4 * q + 32 * q^2 + 16 * q^3 + 256 * q^4 + 404 * q^5 + 128 * q^6 - 656 * q^7 + 2048 * q^8 + 8116 * q^9	\( 4 q + 32 q^{2} + 16 q^{3} + 256 q^{4} + 404 q^{5} + 128 q^{6} - 656 q^{7} + 2048 q^{8} + 8116 q^{9} + 3232 q^{10} + 1024 q^{12} + 7556 q^{13} - 5248 q^{14} - 33600 q^{15} + 16384 q^{16} + 37308 q^{17} + 64928 q^{18} + 55424 q^{19} + 25856 q^{20} + 36416 q^{21} + 35456 q^{23} + 8192 q^{24} + 266784 q^{25} + 60448 q^{26} - 213344 q^{27} - 41984 q^{28} + 57188 q^{29} - 268800 q^{30} - 493456 q^{31} + 131072 q^{32} + 298464 q^{34} + 589344 q^{35} + 519424 q^{36} - 411052 q^{37} + 443392 q^{38} + 962336 q^{39} + 206848 q^{40} - 292244 q^{41} + 291328 q^{42} + 920400 q^{43} + 1837284 q^{45} + 283648 q^{46} + 83264 q^{47} + 65536 q^{48} + 1816644 q^{49} + 2134272 q^{50} - 2594928 q^{51} + 483584 q^{52} + 2585748 q^{53} - 1706752 q^{54} - 335872 q^{56} + 6623840 q^{57} + 457504 q^{58} + 1539984 q^{59} - 2150400 q^{60} + 4488024 q^{61} - 3947648 q^{62} - 12133840 q^{63} + 1048576 q^{64} - 312188 q^{65} + 4619264 q^{67} + 2387712 q^{68} + 2993472 q^{69} + 4714752 q^{70} - 5025488 q^{71} + 4155392 q^{72} - 3281912 q^{73} - 3288416 q^{74} - 718496 q^{75} + 3547136 q^{76} + 7698688 q^{78} + 15899968 q^{79} + 1654784 q^{80} + 16623940 q^{81} - 2337952 q^{82} + 18549088 q^{83} + 2330624 q^{84} - 4934868 q^{85} + 7363200 q^{86} + 22272672 q^{87} + 6384940 q^{89} + 14698272 q^{90} - 23874048 q^{91} + 2269184 q^{92} - 31055680 q^{93} + 666112 q^{94} + 7874608 q^{95} + 524288 q^{96} + 20254236 q^{97} + 14533152 q^{98}+O(q^{100}) \) 4 * q + 32 * q^2 + 16 * q^3 + 256 * q^4 + 404 * q^5 + 128 * q^6 - 656 * q^7 + 2048 * q^8 + 8116 * q^9 + 3232 * q^10 + 1024 * q^12 + 7556 * q^13 - 5248 * q^14 - 33600 * q^15 + 16384 * q^16 + 37308 * q^17 + 64928 * q^18 + 55424 * q^19 + 25856 * q^20 + 36416 * q^21 + 35456 * q^23 + 8192 * q^24 + 266784 * q^25 + 60448 * q^26 - 213344 * q^27 - 41984 * q^28 + 57188 * q^29 - 268800 * q^30 - 493456 * q^31 + 131072 * q^32 + 298464 * q^34 + 589344 * q^35 + 519424 * q^36 - 411052 * q^37 + 443392 * q^38 + 962336 * q^39 + 206848 * q^40 - 292244 * q^41 + 291328 * q^42 + 920400 * q^43 + 1837284 * q^45 + 283648 * q^46 + 83264 * q^47 + 65536 * q^48 + 1816644 * q^49 + 2134272 * q^50 - 2594928 * q^51 + 483584 * q^52 + 2585748 * q^53 - 1706752 * q^54 - 335872 * q^56 + 6623840 * q^57 + 457504 * q^58 + 1539984 * q^59 - 2150400 * q^60 + 4488024 * q^61 - 3947648 * q^62 - 12133840 * q^63 + 1048576 * q^64 - 312188 * q^65 + 4619264 * q^67 + 2387712 * q^68 + 2993472 * q^69 + 4714752 * q^70 - 5025488 * q^71 + 4155392 * q^72 - 3281912 * q^73 - 3288416 * q^74 - 718496 * q^75 + 3547136 * q^76 + 7698688 * q^78 + 15899968 * q^79 + 1654784 * q^80 + 16623940 * q^81 - 2337952 * q^82 + 18549088 * q^83 + 2330624 * q^84 - 4934868 * q^85 + 7363200 * q^86 + 22272672 * q^87 + 6384940 * q^89 + 14698272 * q^90 - 23874048 * q^91 + 2269184 * q^92 - 31055680 * q^93 + 666112 * q^94 + 7874608 * q^95 + 524288 * q^96 + 20254236 * q^97 + 14533152 * q^98

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 $

$2$	8.00000	0.707107
$2$	8.00000	0.707107
$3$	47.3597	1.01271	0.506354	−	0.862326i	$-0.330993\pi$
$3$	47.3597	1.01271	0.506354	+	0.862326i	$0.330993\pi$
$4$	64.0000	0.500000
$5$	499.352	1.78653	0.893267	−	0.449526i	$-0.148407\pi$
$5$	499.352	1.78653	0.893267	+	0.449526i	$0.148407\pi$
$6$	378.877	0.716093
$7$	1391.56	1.53342	0.766708	−	0.641997i	$-0.221894\pi$
$7$	1391.56	1.53342	0.766708	+	0.641997i	$0.221894\pi$
$8$	512.000	0.353553
$9$	55.9387	0.0255778
$10$	3994.81	1.26327
$11$	0	0
$11$	0	0
$12$	3031.02	0.506354
$13$	471.238	0.0594893	0.0297446	−	0.999558i	$-0.490531\pi$
$13$	471.238	0.0594893	0.0297446	+	0.999558i	$0.490531\pi$
$14$	11132.5	1.08429
$15$	23649.1	1.80924
$16$	4096.00	0.250000
$17$	−17724.0	−0.874962	−0.437481	−	0.899228i	$-0.644129\pi$
$17$	−17724.0	−0.874962	−0.437481	+	0.899228i	$0.644129\pi$
$18$	447.509	0.0180862
$19$	37409.8	1.25126	0.625630	−	0.780120i	$-0.284842\pi$
$19$	37409.8	1.25126	0.625630	+	0.780120i	$0.284842\pi$
$20$	31958.5	0.893267
$21$	65904.0	1.55290
$22$	0	0
$23$	−31452.2	−0.539019	−0.269509	−	0.962998i	$-0.586862\pi$
$23$	−31452.2	−0.539019	−0.269509	+	0.962998i	$0.586862\pi$
$24$	24248.2	0.358046
$25$	171227.	2.19171
$26$	3769.91	0.0420653
$27$	−100926.	−0.986805
$28$	89060.0	0.766708
$29$	161324.	1.22830	0.614152	−	0.789187i	$-0.289498\pi$
$29$	161324.	1.22830	0.614152	+	0.789187i	$0.289498\pi$
$30$	189193.	1.27932
$31$	−265823.	−1.60261	−0.801303	−	0.598258i	$-0.795860\pi$
$31$	−265823.	−1.60261	−0.801303	+	0.598258i	$0.795860\pi$
$32$	32768.0	0.176777
$33$	0	0
$34$	−141792.	−0.618692
$35$	694879.	2.73950
$36$	3580.07	0.0127889
$37$	−176651.	−0.573338	−0.286669	−	0.958030i	$-0.592548\pi$
$37$	−176651.	−0.573338	−0.286669	+	0.958030i	$0.592548\pi$
$38$	299278.	0.884775
$39$	22317.7	0.0602453
$40$	255668.	0.631635
$41$	−746391.	−1.69131	−0.845655	−	0.533730i	$-0.820790\pi$
$41$	−746391.	−1.69131	−0.845655	+	0.533730i	$0.820790\pi$
$42$	527232.	1.09807
$43$	−325064.	−0.623489	−0.311745	−	0.950166i	$-0.600913\pi$
$43$	−325064.	−0.623489	−0.311745	+	0.950166i	$0.600913\pi$
$44$	0	0
$45$	27933.1	0.0456956
$46$	−251618.	−0.381144
$47$	−578602.	−0.812901	−0.406451	−	0.913673i	$-0.633234\pi$
$47$	−578602.	−0.812901	−0.406451	+	0.913673i	$0.633234\pi$
$48$	193985.	0.253177
$49$	1.11290e6	1.35136
$50$	1.36982e6	1.54977
$51$	−839401.	−0.886082
$52$	30159.2	0.0297446
$53$	−2.03356e6	−1.87625	−0.938126	−	0.346294i	$-0.887440\pi$
$53$	−2.03356e6	−1.87625	−0.938126	+	0.346294i	$0.887440\pi$
$54$	−807411.	−0.697777
$55$	0	0
$56$	712480.	0.542144
$57$	1.77172e6	1.26716
$58$	1.29059e6	0.868543
$59$	488428.	0.309613	0.154806	−	0.987945i	$-0.450525\pi$
$59$	488428.	0.309613	0.154806	+	0.987945i	$0.450525\pi$
$60$	1.51354e6	0.904619
$61$	1.46176e6	0.824560	0.412280	−	0.911057i	$-0.364733\pi$
$61$	1.46176e6	0.824560	0.412280	+	0.911057i	$0.364733\pi$
$62$	−2.12659e6	−1.13321
$63$	77842.2	0.0392214
$64$	262144.	0.125000
$65$	235314.	0.106280
$66$	0	0
$67$	2.85356e6	1.15911	0.579555	−	0.814933i	$-0.303226\pi$
$67$	2.85356e6	1.15911	0.579555	+	0.814933i	$0.303226\pi$
$68$	−1.13433e6	−0.437481
$69$	−1.48957e6	−0.545869
$70$	5.55903e6	1.93712
$71$	−3.90552e6	−1.29502	−0.647508	−	0.762059i	$-0.724189\pi$
$71$	−3.90552e6	−1.29502	−0.647508	+	0.762059i	$0.724189\pi$
$72$	28640.6	0.00904312
$73$	−2.92809e6	−0.880956	−0.440478	−	0.897763i	$-0.645191\pi$
$73$	−2.92809e6	−0.880956	−0.440478	+	0.897763i	$0.645191\pi$
$74$	−1.41321e6	−0.405411
$75$	8.10926e6	2.21956
$76$	2.39423e6	0.625630
$77$	0	0
$78$	178542.	0.0425999
$79$	6.61578e6	1.50968	0.754842	−	0.655906i	$-0.227713\pi$
$79$	6.61578e6	1.50968	0.754842	+	0.655906i	$0.227713\pi$
$80$	2.04534e6	0.446634
$81$	−4.90218e6	−1.02492
$82$	−5.97113e6	−1.19594
$83$	1.74078e6	0.334173	0.167086	−	0.985942i	$-0.446564\pi$
$83$	1.74078e6	0.334173	0.167086	+	0.985942i	$0.446564\pi$
$84$	4.21785e6	0.776451
$85$	−8.85049e6	−1.56315
$86$	−2.60051e6	−0.440874
$87$	7.64026e6	1.24391
$88$	0	0
$89$	1.02874e6	0.154682	0.0773408	−	0.997005i	$-0.475357\pi$
$89$	1.02874e6	0.154682	0.0773408	+	0.997005i	$0.475357\pi$
$90$	223465.	0.0323117
$91$	655758.	0.0912218
$92$	−2.01294e6	−0.269509
$93$	−1.25893e7	−1.62297
$94$	−4.62882e6	−0.574808
$95$	1.86806e7	2.23542
$96$	1.55188e6	0.179023
$97$	1.21361e7	1.35013	0.675066	−	0.737757i	$-0.264115\pi$
$97$	1.21361e7	1.35013	0.675066	+	0.737757i	$0.264115\pi$
$98$	8.90324e6	0.955557
$99$	0	0
$100$	1.09585e7	1.09585
$101$	−2.63659e6	−0.254635	−0.127317	−	0.991862i	$-0.540637\pi$
$101$	−2.63659e6	−0.254635	−0.127317	+	0.991862i	$0.540637\pi$
$102$	−6.71520e6	−0.626554
$103$	5.43850e6	0.490398	0.245199	−	0.969473i	$-0.421147\pi$
$103$	5.43850e6	0.490398	0.245199	+	0.969473i	$0.421147\pi$
$104$	241274.	0.0210326
$105$	3.29093e7	2.77431
$106$	−1.62685e7	−1.32671
$107$	−2.20681e6	−0.174149	−0.0870747	−	0.996202i	$-0.527752\pi$
$107$	−2.20681e6	−0.174149	−0.0870747	+	0.996202i	$0.527752\pi$
$108$	−6.45929e6	−0.493403
$109$	−1.26458e7	−0.935307	−0.467653	−	0.883912i	$-0.654900\pi$
$109$	−1.26458e7	−0.935307	−0.467653	+	0.883912i	$0.654900\pi$
$110$	0	0
$111$	−8.36615e6	−0.580624
$112$	5.69984e6	0.383354
$113$	−2.22480e7	−1.45049	−0.725247	−	0.688489i	$-0.758274\pi$
$113$	−2.22480e7	−1.45049	−0.725247	+	0.688489i	$0.758274\pi$
$114$	1.41737e7	0.896019
$115$	−1.57057e7	−0.962976
$116$	1.03247e7	0.614152
$117$	26360.4	0.00152161
$118$	3.90743e6	0.218929
$119$	−2.46640e7	−1.34168
$120$	1.21084e7	0.639662
$121$	0	0
$122$	1.16941e7	0.583052
$123$	−3.53489e7	−1.71280
$124$	−1.70127e7	−0.801303
$125$	4.64907e7	2.12903
$126$	622737.	0.0277337
$127$	1.83656e7	0.795594	0.397797	−	0.917474i	$-0.369775\pi$
$127$	1.83656e7	0.795594	0.397797	+	0.917474i	$0.369775\pi$
$128$	2.09715e6	0.0883883
$129$	−1.53949e7	−0.631413
$130$	1.88251e6	0.0751511
$131$	6.25036e6	0.242916	0.121458	−	0.992597i	$-0.461243\pi$
$131$	6.25036e6	0.242916	0.121458	+	0.992597i	$0.461243\pi$
$132$	0	0
$133$	5.20581e7	1.91870
$134$	2.28285e7	0.819615
$135$	−5.03978e7	−1.76296
$136$	−9.07466e6	−0.309346
$137$	4.02314e7	1.33673	0.668364	−	0.743834i	$-0.266995\pi$
$137$	4.02314e7	1.33673	0.668364	+	0.743834i	$0.266995\pi$
$138$	−1.19165e7	−0.385987
$139$	3.61116e7	1.14050	0.570249	−	0.821472i	$-0.306847\pi$
$139$	3.61116e7	1.14050	0.570249	+	0.821472i	$0.306847\pi$
$140$	4.44723e7	1.36975
$141$	−2.74024e7	−0.823232
$142$	−3.12442e7	−0.915714
$143$	0	0
$144$	229125.	0.00639445
$145$	8.05574e7	2.19441
$146$	−2.34247e7	−0.622930
$147$	5.27068e7	1.36854
$148$	−1.13057e7	−0.286669
$149$	3.00572e7	0.744383	0.372192	−	0.928156i	$-0.378606\pi$
$149$	3.00572e7	0.744383	0.372192	+	0.928156i	$0.378606\pi$
$150$	6.48741e7	1.56947
$151$	3.33188e6	0.0787536	0.0393768	−	0.999224i	$-0.487463\pi$
$151$	3.33188e6	0.0787536	0.0393768	+	0.999224i	$0.487463\pi$
$152$	1.91538e7	0.442387
$153$	−991454.	−0.0223796
$154$	0	0
$155$	−1.32739e8	−2.86311
$156$	1.42833e6	0.0301226
$157$	−4.12875e6	−0.0851471	−0.0425735	−	0.999093i	$-0.513556\pi$
$157$	−4.12875e6	−0.0851471	−0.0425735	+	0.999093i	$0.513556\pi$
$158$	5.29262e7	1.06751
$159$	−9.63087e7	−1.90010
$160$	1.63628e7	0.315818
$161$	−4.37677e7	−0.826539
$162$	−3.92174e7	−0.724730
$163$	3.24159e7	0.586276	0.293138	−	0.956070i	$-0.405300\pi$
$163$	3.24159e7	0.586276	0.293138	+	0.956070i	$0.405300\pi$
$164$	−4.77691e7	−0.845655
$165$	0	0
$166$	1.39262e7	0.236296
$167$	5.42238e7	0.900911	0.450456	−	0.892799i	$-0.351262\pi$
$167$	5.42238e7	0.900911	0.450456	+	0.892799i	$0.351262\pi$
$168$	3.37428e7	0.549034
$169$	−6.25265e7	−0.996461
$170$	−7.08039e7	−1.10531
$171$	2.09265e6	0.0320045
$172$	−2.08041e7	−0.311745
$173$	5.13247e6	0.0753642	0.0376821	−	0.999290i	$-0.488003\pi$
$173$	5.13247e6	0.0753642	0.0376821	+	0.999290i	$0.488003\pi$
$174$	6.11220e7	0.879580
$175$	2.38273e8	3.36080
$176$	0	0
$177$	2.31318e7	0.313547
$178$	8.22988e6	0.109376
$179$	−7.53726e7	−0.982264	−0.491132	−	0.871085i	$-0.663417\pi$
$179$	−7.53726e7	−0.982264	−0.491132	+	0.871085i	$0.663417\pi$
$180$	1.78772e6	0.0228478
$181$	−6.12283e6	−0.0767497	−0.0383749	−	0.999263i	$-0.512218\pi$
$181$	−6.12283e6	−0.0767497	−0.0383749	+	0.999263i	$0.512218\pi$
$182$	5.24606e6	0.0645035
$183$	6.92285e7	0.835038
$184$	−1.61035e7	−0.190572
$185$	−8.82112e7	−1.02429
$186$	−1.00714e8	−1.14762
$187$	0	0
$188$	−3.70306e7	−0.406451
$189$	−1.40445e8	−1.51318
$190$	1.49445e8	1.58068
$191$	5.89721e7	0.612392	0.306196	−	0.951968i	$-0.400944\pi$
$191$	5.89721e7	0.612392	0.306196	+	0.951968i	$0.400944\pi$
$192$	1.24151e7	0.126589
$193$	1.20037e8	1.20189	0.600944	−	0.799291i	$-0.294792\pi$
$193$	1.20037e8	1.20189	0.600944	+	0.799291i	$0.294792\pi$
$194$	9.70884e7	0.954688
$195$	1.11444e7	0.107630
$196$	7.12259e7	0.675681
$197$	9.45692e7	0.881288	0.440644	−	0.897682i	$-0.354750\pi$
$197$	9.45692e7	0.881288	0.440644	+	0.897682i	$0.354750\pi$
$198$	0	0
$199$	8.75460e7	0.787500	0.393750	−	0.919218i	$-0.371178\pi$
$199$	8.75460e7	0.787500	0.393750	+	0.919218i	$0.371178\pi$
$200$	8.76683e7	0.774885
$201$	1.35144e8	1.17384
$202$	−2.10927e7	−0.180054
$203$	2.24493e8	1.88350
$204$	−5.37216e7	−0.443041
$205$	−3.72712e8	−3.02158
$206$	4.35080e7	0.346764
$207$	−1.75940e6	−0.0137869
$208$	1.93019e6	0.0148723
$209$	0	0
$210$	2.63274e8	1.96174
$211$	−2.23264e8	−1.63617	−0.818087	−	0.575095i	$-0.804965\pi$
$211$	−2.23264e8	−1.63617	−0.818087	+	0.575095i	$0.804965\pi$
$212$	−1.30148e8	−0.938126
$213$	−1.84964e8	−1.31147
$214$	−1.76545e7	−0.123142
$215$	−1.62321e8	−1.11389
$216$	−5.16743e7	−0.348888
$217$	−3.69910e8	−2.45746
$218$	−1.01167e8	−0.661362
$219$	−1.38673e8	−0.892151
$220$	0	0
$221$	−8.35220e6	−0.0520509
$222$	−6.69292e7	−0.410564
$223$	−9.01340e7	−0.544279	−0.272139	−	0.962258i	$-0.587731\pi$
$223$	−9.01340e7	−0.544279	−0.272139	+	0.962258i	$0.587731\pi$
$224$	4.55987e7	0.271072
$225$	9.57822e6	0.0560591
$226$	−1.77984e8	−1.02565
$227$	9.36984e7	0.531669	0.265835	−	0.964019i	$-0.414352\pi$
$227$	9.36984e7	0.531669	0.265835	+	0.964019i	$0.414352\pi$
$228$	1.13390e8	0.633581
$229$	9.72710e7	0.535253	0.267627	−	0.963523i	$-0.413761\pi$
$229$	9.72710e7	0.535253	0.267627	+	0.963523i	$0.413761\pi$
$230$	−1.25646e8	−0.680927
$231$	0	0
$232$	8.25979e7	0.434271
$233$	1.86730e8	0.967091	0.483546	−	0.875319i	$-0.339349\pi$
$233$	1.86730e8	0.967091	0.483546	+	0.875319i	$0.339349\pi$
$234$	210884.	0.00107594
$235$	−2.88926e8	−1.45228
$236$	3.12594e7	0.154806
$237$	3.13321e8	1.52887
$238$	−1.97312e8	−0.948711
$239$	−8.57905e6	−0.0406487	−0.0203243	−	0.999793i	$-0.506470\pi$
$239$	−8.57905e6	−0.0406487	−0.0203243	+	0.999793i	$0.506470\pi$
$240$	9.68668e7	0.452310
$241$	−2.70317e8	−1.24398	−0.621990	−	0.783025i	$-0.713676\pi$
$241$	−2.70317e8	−1.24398	−0.621990	+	0.783025i	$0.713676\pi$
$242$	0	0
$243$	−1.14396e7	−0.0511432
$244$	9.35527e7	0.412280
$245$	5.55731e8	2.41426
$246$	−2.82791e8	−1.21113
$247$	1.76289e7	0.0744366
$248$	−1.36101e8	−0.566607
$249$	8.24428e7	0.338419
$250$	3.71925e8	1.50545
$251$	−1.39083e8	−0.555159	−0.277579	−	0.960703i	$-0.589532\pi$
$251$	−1.39083e8	−0.555159	−0.277579	+	0.960703i	$0.589532\pi$
$252$	4.98190e6	0.0196107
$253$	0	0
$254$	1.46925e8	0.562570
$255$	−4.19156e8	−1.58302
$256$	1.67772e7	0.0625000
$257$	−1.38314e8	−0.508277	−0.254139	−	0.967168i	$-0.581792\pi$
$257$	−1.38314e8	−0.508277	−0.254139	+	0.967168i	$0.581792\pi$
$258$	−1.23159e8	−0.446476
$259$	−2.45822e8	−0.879166
$260$	1.50601e7	0.0531398
$261$	9.02425e6	0.0314174
$262$	5.00029e7	0.171767
$263$	−3.05008e8	−1.03387	−0.516935	−	0.856025i	$-0.672927\pi$
$263$	−3.05008e8	−1.03387	−0.516935	+	0.856025i	$0.672927\pi$
$264$	0	0
$265$	−1.01546e9	−3.35199
$266$	4.16465e8	1.35673
$267$	4.87206e7	0.156647
$268$	1.82628e8	0.579555
$269$	3.75565e8	1.17639	0.588195	−	0.808719i	$-0.299839\pi$
$269$	3.75565e8	1.17639	0.588195	+	0.808719i	$0.299839\pi$
$270$	−4.03182e8	−1.24660
$271$	2.99003e8	0.912606	0.456303	−	0.889824i	$-0.349173\pi$
$271$	2.99003e8	0.912606	0.456303	+	0.889824i	$0.349173\pi$
$272$	−7.25973e7	−0.218741
$273$	3.10565e7	0.0923810
$274$	3.21851e8	0.945210
$275$	0	0
$276$	−9.53323e7	−0.272934
$277$	−1.47777e7	−0.0417762	−0.0208881	−	0.999782i	$-0.506649\pi$
$277$	−1.47777e7	−0.0417762	−0.0208881	+	0.999782i	$0.506649\pi$
$278$	2.88892e8	0.806454
$279$	−1.48698e7	−0.0409912
$280$	3.55778e8	0.968559
$281$	−3.45376e8	−0.928581	−0.464291	−	0.885683i	$-0.653691\pi$
$281$	−3.45376e8	−0.928581	−0.464291	+	0.885683i	$0.653691\pi$
$282$	−2.19219e8	−0.582113
$283$	−1.51120e8	−0.396343	−0.198171	−	0.980167i	$-0.563500\pi$
$283$	−1.51120e8	−0.396343	−0.198171	+	0.980167i	$0.563500\pi$
$284$	−2.49954e8	−0.647508
$285$	8.84709e8	2.26383
$286$	0	0
$287$	−1.03865e9	−2.59348
$288$	1.83300e6	0.00452156
$289$	−9.62002e7	−0.234441
$290$	6.44460e8	1.55168
$291$	5.74760e8	1.36729
$292$	−1.87398e8	−0.440478
$293$	−1.64818e8	−0.382796	−0.191398	−	0.981513i	$-0.561302\pi$
$293$	−1.64818e8	−0.382796	−0.191398	+	0.981513i	$0.561302\pi$
$294$	4.21654e8	0.967701
$295$	2.43898e8	0.553134
$296$	−9.04455e7	−0.202706
$297$	0	0
$298$	2.40458e8	0.526358
$299$	−1.48215e7	−0.0320658
$300$	5.18993e8	1.10978
$301$	−4.52347e8	−0.956068
$302$	2.66551e7	0.0556872
$303$	−1.24868e8	−0.257870
$304$	1.53231e8	0.312815
$305$	7.29933e8	1.47310
$306$	−7.93163e6	−0.0158248
$307$	−1.33404e7	−0.0263138	−0.0131569	−	0.999913i	$-0.504188\pi$
$307$	−1.33404e7	−0.0263138	−0.0131569	+	0.999913i	$0.504188\pi$
$308$	0	0
$309$	2.57565e8	0.496630
$310$	−1.06191e9	−2.02453
$311$	−4.14486e8	−0.781355	−0.390677	−	0.920528i	$-0.627759\pi$
$311$	−4.14486e8	−0.781355	−0.390677	+	0.920528i	$0.627759\pi$
$312$	1.14267e7	0.0212999
$313$	−8.89685e8	−1.63995	−0.819976	−	0.572398i	$-0.806013\pi$
$313$	−8.89685e8	−1.63995	−0.819976	+	0.572398i	$0.806013\pi$
$314$	−3.30300e7	−0.0602081
$315$	3.88706e7	0.0700704
$316$	4.23410e8	0.754842
$317$	−6.47560e8	−1.14175	−0.570877	−	0.821036i	$-0.693397\pi$
$317$	−6.47560e8	−1.14175	−0.570877	+	0.821036i	$0.693397\pi$
$318$	−7.70469e8	−1.34357
$319$	0	0
$320$	1.30902e8	0.223317
$321$	−1.04514e8	−0.176363
$322$	−3.50142e8	−0.584452
$323$	−6.63049e8	−1.09481
$324$	−3.13739e8	−0.512462
$325$	8.06888e7	0.130383
$326$	2.59328e8	0.414560
$327$	−5.98902e8	−0.947193
$328$	−3.82152e8	−0.597968
$329$	−8.05162e8	−1.24651
$330$	0	0
$331$	3.56476e8	0.540297	0.270149	−	0.962819i	$-0.412927\pi$
$331$	3.56476e8	0.540297	0.270149	+	0.962819i	$0.412927\pi$
$332$	1.11410e8	0.167086
$333$	−9.88164e6	−0.0146647
$334$	4.33790e8	0.637040
$335$	1.42493e9	2.07079
$336$	2.69943e8	0.388225
$337$	−1.96157e8	−0.279190	−0.139595	−	0.990209i	$-0.544580\pi$
$337$	−1.96157e8	−0.279190	−0.139595	+	0.990209i	$0.544580\pi$
$338$	−5.00212e8	−0.704604
$339$	−1.05366e9	−1.46893
$340$	−5.66431e8	−0.781575
$341$	0	0
$342$	1.67412e7	0.0226306
$343$	4.02665e8	0.538784
$344$	−1.66433e8	−0.220437
$345$	−7.43818e8	−0.975213
$346$	4.10597e7	0.0532905
$347$	−1.79682e8	−0.230861	−0.115431	−	0.993316i	$-0.536825\pi$
$347$	−1.79682e8	−0.230861	−0.115431	+	0.993316i	$0.536825\pi$
$348$	4.88976e8	0.621957
$349$	1.06243e9	1.33787	0.668934	−	0.743322i	$-0.266751\pi$
$349$	1.06243e9	1.33787	0.668934	+	0.743322i	$0.266751\pi$
$350$	1.90619e9	2.37644
$351$	−4.75604e7	−0.0587043
$352$	0	0
$353$	1.05404e8	0.127540	0.0637700	−	0.997965i	$-0.479688\pi$
$353$	1.05404e8	0.127540	0.0637700	+	0.997965i	$0.479688\pi$
$354$	1.85054e8	0.221712
$355$	−1.95023e9	−2.31359
$356$	6.58390e7	0.0773408
$357$	−1.16808e9	−1.35873
$358$	−6.02981e8	−0.694565
$359$	−2.71875e8	−0.310127	−0.155063	−	0.987905i	$-0.549558\pi$
$359$	−2.71875e8	−0.310127	−0.155063	+	0.987905i	$0.549558\pi$
$360$	1.43017e7	0.0161559
$361$	5.05621e8	0.565653
$362$	−4.89826e7	−0.0542703
$363$	0	0
$364$	4.19685e7	0.0456109
$365$	−1.46215e9	−1.57386
$366$	5.53828e8	0.590461
$367$	−6.81828e7	−0.0720018	−0.0360009	−	0.999352i	$-0.511462\pi$
$367$	−6.81828e7	−0.0720018	−0.0360009	+	0.999352i	$0.511462\pi$
$368$	−1.28828e8	−0.134755
$369$	−4.17521e7	−0.0432600
$370$	−7.05689e8	−0.724282
$371$	−2.82983e9	−2.87707
$372$	−8.05715e8	−0.811486
$373$	6.73457e7	0.0671937	0.0335969	−	0.999435i	$-0.489304\pi$
$373$	6.73457e7	0.0671937	0.0335969	+	0.999435i	$0.489304\pi$
$374$	0	0
$375$	2.20178e9	2.15608
$376$	−2.96244e8	−0.287404
$377$	7.60221e7	0.0730710
$378$	−1.12356e9	−1.06998
$379$	−9.60253e8	−0.906043	−0.453021	−	0.891500i	$-0.649654\pi$
$379$	−9.60253e8	−0.906043	−0.453021	+	0.891500i	$0.649654\pi$
$380$	1.19556e9	1.11771
$381$	8.69787e8	0.805704
$382$	4.71777e8	0.433027
$383$	1.63835e9	1.49008	0.745041	−	0.667018i	$-0.232430\pi$
$383$	1.63835e9	1.49008	0.745041	+	0.667018i	$0.232430\pi$
$384$	9.93204e7	0.0895116
$385$	0	0
$386$	9.60294e8	0.849863
$387$	−1.81836e7	−0.0159475
$388$	7.76708e8	0.675066
$389$	2.20298e9	1.89753	0.948763	−	0.315988i	$-0.102336\pi$
$389$	2.20298e9	1.89753	0.948763	+	0.315988i	$0.102336\pi$
$390$	8.91550e7	0.0761061
$391$	5.57458e8	0.471621
$392$	5.69807e8	0.477779
$393$	2.96015e8	0.246003
$394$	7.56554e8	0.623165
$395$	3.30360e9	2.69710
$396$	0	0
$397$	−1.63096e9	−1.30821	−0.654105	−	0.756403i	$-0.726955\pi$
$397$	−1.63096e9	−1.30821	−0.654105	+	0.756403i	$0.726955\pi$
$398$	7.00368e8	0.556847
$399$	2.46545e9	1.94309
$400$	7.01346e8	0.547927
$401$	−1.13099e9	−0.875900	−0.437950	−	0.898999i	$-0.644295\pi$
$401$	−1.13099e9	−0.875900	−0.437950	+	0.898999i	$0.644295\pi$
$402$	1.08115e9	0.830030
$403$	−1.25266e8	−0.0953379
$404$	−1.68742e8	−0.127317
$405$	−2.44791e9	−1.83106
$406$	1.79594e9	1.33184
$407$	0	0
$408$	−4.29773e8	−0.313277
$409$	6.92226e8	0.500284	0.250142	−	0.968209i	$-0.419523\pi$
$409$	6.92226e8	0.500284	0.250142	+	0.968209i	$0.419523\pi$
$410$	−2.98169e9	−2.13658
$411$	1.90535e9	1.35372
$412$	3.48064e8	0.245199
$413$	6.79679e8	0.474765
$414$	−1.40752e7	−0.00974882
$415$	8.69262e8	0.597011
$416$	1.54415e7	0.0105163
$417$	1.71023e9	1.15499
$418$	0	0
$419$	2.76027e8	0.183317	0.0916583	−	0.995791i	$-0.470783\pi$
$419$	2.76027e8	0.183317	0.0916583	+	0.995791i	$0.470783\pi$
$420$	2.10619e9	1.38716
$421$	4.21081e8	0.275029	0.137515	−	0.990500i	$-0.456089\pi$
$421$	4.21081e8	0.275029	0.137515	+	0.990500i	$0.456089\pi$
$422$	−1.78611e9	−1.15695
$423$	−3.23662e7	−0.0207922
$424$	−1.04118e9	−0.663355
$425$	−3.03482e9	−1.91766
$426$	−1.47971e9	−0.927351
$427$	2.03413e9	1.26439
$428$	−1.41236e8	−0.0870747
$429$	0	0
$430$	−1.29857e9	−0.787636
$431$	2.29633e9	1.38154	0.690769	−	0.723075i	$-0.257272\pi$
$431$	2.29633e9	1.38154	0.690769	+	0.723075i	$0.257272\pi$
$432$	−4.13394e8	−0.246701
$433$	2.95345e9	1.74832	0.874161	−	0.485636i	$-0.161412\pi$
$433$	2.95345e9	1.74832	0.874161	+	0.485636i	$0.161412\pi$
$434$	−2.95928e9	−1.73769
$435$	3.81517e9	2.22230
$436$	−8.09332e8	−0.467653
$437$	−1.17662e9	−0.674453
$438$	−1.10939e9	−0.630846
$439$	−3.06504e9	−1.72906	−0.864532	−	0.502578i	$-0.832385\pi$
$439$	−3.06504e9	−1.72906	−0.864532	+	0.502578i	$0.832385\pi$
$440$	0	0
$441$	6.22544e7	0.0345649
$442$	−6.68176e7	−0.0368055
$443$	2.83824e9	1.55109	0.775544	−	0.631293i	$-0.217476\pi$
$443$	2.83824e9	1.55109	0.775544	+	0.631293i	$0.217476\pi$
$444$	−5.35434e8	−0.290312
$445$	5.13701e8	0.276344
$446$	−7.21072e8	−0.384863
$447$	1.42350e9	0.753843
$448$	3.64790e8	0.191677
$449$	2.78041e9	1.44959	0.724797	−	0.688962i	$-0.241933\pi$
$449$	2.78041e9	1.44959	0.724797	+	0.688962i	$0.241933\pi$
$450$	7.66257e7	0.0396397
$451$	0	0
$452$	−1.42387e9	−0.725247
$453$	1.57797e8	0.0797544
$454$	7.49587e8	0.375947
$455$	3.27454e8	0.162971
$456$	9.07118e8	0.448009
$457$	2.73664e9	1.34126	0.670628	−	0.741794i	$-0.266025\pi$
$457$	2.73664e9	1.34126	0.670628	+	0.741794i	$0.266025\pi$
$458$	7.78168e8	0.378481
$459$	1.78881e9	0.863417
$460$	−1.00517e9	−0.481488
$461$	−2.13412e9	−1.01453	−0.507266	−	0.861790i	$-0.669344\pi$
$461$	−2.13412e9	−1.01453	−0.507266	+	0.861790i	$0.669344\pi$
$462$	0	0
$463$	2.36016e9	1.10512	0.552558	−	0.833474i	$-0.313652\pi$
$463$	2.36016e9	1.10512	0.552558	+	0.833474i	$0.313652\pi$
$464$	6.60783e8	0.307076
$465$	−6.28649e9	−2.89950
$466$	1.49384e9	0.683837
$467$	1.59558e9	0.724952	0.362476	−	0.931993i	$-0.381932\pi$
$467$	1.59558e9	0.724952	0.362476	+	0.931993i	$0.381932\pi$
$468$	1.68707e6	0.000760803 0
$469$	3.97090e9	1.77740
$470$	−2.31141e9	−1.02691
$471$	−1.95536e8	−0.0862291
$472$	2.50075e8	0.109465
$473$	0	0
$474$	2.50657e9	1.08107
$475$	6.40557e9	2.74240
$476$	−1.57850e9	−0.670840
$477$	−1.13755e8	−0.0479904
$478$	−6.86324e7	−0.0287430
$479$	−3.47495e9	−1.44469	−0.722344	−	0.691534i	$-0.756935\pi$
$479$	−3.47495e9	−1.44469	−0.722344	+	0.691534i	$0.756935\pi$
$480$	7.74935e8	0.319831
$481$	−8.32449e7	−0.0341075
$482$	−2.16254e9	−0.879627
$483$	−2.07283e9	−0.837043
$484$	0	0
$485$	6.06016e9	2.41206
$486$	−9.15165e7	−0.0361637
$487$	7.70620e8	0.302335	0.151168	−	0.988508i	$-0.451697\pi$
$487$	7.70620e8	0.302335	0.151168	+	0.988508i	$0.451697\pi$
$488$	7.48422e8	0.291526
$489$	1.53521e9	0.593726
$490$	4.44585e9	1.70714
$491$	5.17606e8	0.197339	0.0986697	−	0.995120i	$-0.468541\pi$
$491$	5.17606e8	0.197339	0.0986697	+	0.995120i	$0.468541\pi$
$492$	−2.26233e9	−0.856402
$493$	−2.85930e9	−1.07472
$494$	1.41031e8	0.0526346
$495$	0	0
$496$	−1.08881e9	−0.400652
$497$	−5.43478e9	−1.98580
$498$	6.59543e8	0.239299
$499$	−8.84619e8	−0.318716	−0.159358	−	0.987221i	$-0.550942\pi$
$499$	−8.84619e8	−0.318716	−0.159358	+	0.987221i	$0.550942\pi$
$500$	2.97540e9	1.06451
$501$	2.56802e9	0.912360
$502$	−1.11267e9	−0.392557
$503$	4.49239e8	0.157394	0.0786972	−	0.996899i	$-0.474924\pi$
$503$	4.49239e8	0.157394	0.0786972	+	0.996899i	$0.474924\pi$
$504$	3.98552e7	0.0138669
$505$	−1.31658e9	−0.454913
$506$	0	0
$507$	−2.96123e9	−1.00912
$508$	1.17540e9	0.397797
$509$	−4.40533e9	−1.48070	−0.740348	−	0.672223i	$-0.765339\pi$
$509$	−4.40533e9	−1.48070	−0.740348	+	0.672223i	$0.765339\pi$
$510$	−3.35325e9	−1.11936
$511$	−4.07462e9	−1.35087
$512$	1.34218e8	0.0441942
$513$	−3.77564e9	−1.23475
$514$	−1.10651e9	−0.359406
$515$	2.71572e9	0.876113
$516$	−9.85275e8	−0.315706
$517$	0	0
$518$	−1.96657e9	−0.621664
$519$	2.43072e8	0.0763219
$520$	1.20481e8	0.0375755
$521$	4.71751e9	1.46144	0.730719	−	0.682678i	$-0.239185\pi$
$521$	4.71751e9	1.46144	0.730719	+	0.682678i	$0.239185\pi$
$522$	7.21940e7	0.0222154
$523$	−1.29677e9	−0.396376	−0.198188	−	0.980164i	$-0.563506\pi$
$523$	−1.29677e9	−0.396376	−0.198188	+	0.980164i	$0.563506\pi$
$524$	4.00023e8	0.121458
$525$	1.12845e10	3.40351
$526$	−2.44006e9	−0.731056
$527$	4.71144e9	1.40222
$528$	0	0
$529$	−2.41558e9	−0.709459
$530$	−8.12369e9	−2.37021
$531$	2.73220e7	0.00791922
$532$	3.33172e9	0.959351
$533$	−3.51728e8	−0.100615
$534$	3.89764e8	0.110766
$535$	−1.10197e9	−0.311124
$536$	1.46102e9	0.409807
$537$	−3.56962e9	−0.994747
$538$	3.00452e9	0.831834
$539$	0	0
$540$	−3.22546e9	−0.881481
$541$	2.28738e9	0.621080	0.310540	−	0.950560i	$-0.399490\pi$
$541$	2.28738e9	0.621080	0.310540	+	0.950560i	$0.399490\pi$
$542$	2.39203e9	0.645310
$543$	−2.89975e8	−0.0777251
$544$	−5.80778e8	−0.154673
$545$	−6.31471e9	−1.67096
$546$	2.48452e8	0.0653233
$547$	−7.52670e9	−1.96630	−0.983149	−	0.182808i	$-0.941481\pi$
$547$	−7.52670e9	−1.96630	−0.983149	+	0.182808i	$0.941481\pi$
$548$	2.57481e9	0.668364
$549$	8.17690e7	0.0210904
$550$	0	0
$551$	6.03510e9	1.53693
$552$	−7.62658e8	−0.192994
$553$	9.20627e9	2.31497
$554$	−1.18222e8	−0.0295402
$555$	−4.17765e9	−1.03731
$556$	2.31114e9	0.570249
$557$	4.29128e9	1.05219	0.526094	−	0.850426i	$-0.323656\pi$
$557$	4.29128e9	1.05219	0.526094	+	0.850426i	$0.323656\pi$
$558$	−1.18958e8	−0.0289851
$559$	−1.53183e8	−0.0370909
$560$	2.84623e9	0.684875
$561$	0	0
$562$	−2.76301e9	−0.656606
$563$	−4.63396e9	−1.09439	−0.547196	−	0.837005i	$-0.684305\pi$
$563$	−4.63396e9	−1.09439	−0.547196	+	0.837005i	$0.684305\pi$
$564$	−1.75375e9	−0.411616
$565$	−1.11096e10	−2.59136
$566$	−1.20896e9	−0.280256
$567$	−6.82169e9	−1.57163
$568$	−1.99963e9	−0.457857
$569$	−2.62163e9	−0.596592	−0.298296	−	0.954473i	$-0.596418\pi$
$569$	−2.62163e9	−0.596592	−0.298296	+	0.954473i	$0.596418\pi$
$570$	7.07767e9	1.60077
$571$	1.43643e9	0.322892	0.161446	−	0.986882i	$-0.448384\pi$
$571$	1.43643e9	0.322892	0.161446	+	0.986882i	$0.448384\pi$
$572$	0	0
$573$	2.79290e9	0.620175
$574$	−8.30921e9	−1.83387
$575$	−5.38547e9	−1.18137
$576$	1.46640e7	0.00319723
$577$	−2.42313e9	−0.525124	−0.262562	−	0.964915i	$-0.584567\pi$
$577$	−2.42313e9	−0.525124	−0.262562	+	0.964915i	$0.584567\pi$
$578$	−7.69601e8	−0.165775
$579$	5.68490e9	1.21716
$580$	5.15568e9	1.09720
$581$	2.42241e9	0.512425
$582$	4.59808e9	0.966820
$583$	0	0
$584$	−1.49918e9	−0.311465
$585$	1.31631e7	0.00271840
$586$	−1.31854e9	−0.270678
$587$	−5.81974e9	−1.18760	−0.593800	−	0.804613i	$-0.702373\pi$
$587$	−5.81974e9	−1.18760	−0.593800	+	0.804613i	$0.702373\pi$
$588$	3.37324e9	0.684268
$589$	−9.94439e9	−2.00528
$590$	1.95118e9	0.391125
$591$	4.47877e9	0.892488
$592$	−7.23564e8	−0.143335
$593$	−2.43450e9	−0.479422	−0.239711	−	0.970844i	$-0.577053\pi$
$593$	−2.43450e9	−0.479422	−0.239711	+	0.970844i	$0.577053\pi$
$594$	0	0
$595$	−1.23160e10	−2.39696
$596$	1.92366e9	0.372192
$597$	4.14615e9	0.797508
$598$	−1.18572e8	−0.0226740
$599$	−4.25024e9	−0.808015	−0.404007	−	0.914756i	$-0.632383\pi$
$599$	−4.25024e9	−0.808015	−0.404007	+	0.914756i	$0.632383\pi$
$600$	4.15194e9	0.784733
$601$	−4.95742e9	−0.931527	−0.465763	−	0.884909i	$-0.654220\pi$
$601$	−4.95742e9	−0.931527	−0.465763	+	0.884909i	$0.654220\pi$
$602$	−3.61878e9	−0.676042
$603$	1.59624e8	0.0296475
$604$	2.13241e8	0.0393768
$605$	0	0
$606$	−9.98943e8	−0.182342
$607$	4.76094e9	0.864037	0.432019	−	0.901865i	$-0.357802\pi$
$607$	4.76094e9	0.864037	0.432019	+	0.901865i	$0.357802\pi$
$608$	1.22584e9	0.221194
$609$	1.06319e10	1.90744
$610$	5.83946e9	1.04164
$611$	−2.72660e8	−0.0483589
$612$	−6.34531e7	−0.0111898
$613$	−4.99529e9	−0.875890	−0.437945	−	0.899002i	$-0.644293\pi$
$613$	−4.99529e9	−0.875890	−0.437945	+	0.899002i	$0.644293\pi$
$614$	−1.06723e8	−0.0186066
$615$	−1.76515e10	−3.05998
$616$	0	0
$617$	3.06556e9	0.525427	0.262713	−	0.964874i	$-0.415383\pi$
$617$	3.06556e9	0.525427	0.262713	+	0.964874i	$0.415383\pi$
$618$	2.06052e9	0.351170
$619$	1.56276e9	0.264835	0.132417	−	0.991194i	$-0.457726\pi$
$619$	1.56276e9	0.264835	0.132417	+	0.991194i	$0.457726\pi$
$620$	−8.49531e9	−1.43156
$621$	3.17436e9	0.531907
$622$	−3.31589e9	−0.552501
$623$	1.43155e9	0.237191
$624$	9.14133e7	0.0150613
$625$	9.83808e9	1.61187
$626$	−7.11748e9	−1.15962
$627$	0	0
$628$	−2.64240e8	−0.0425735
$629$	3.13096e9	0.501650
$630$	3.10965e8	0.0495473
$631$	−2.26420e9	−0.358767	−0.179384	−	0.983779i	$-0.557410\pi$
$631$	−2.26420e9	−0.358767	−0.179384	+	0.983779i	$0.557410\pi$
$632$	3.38728e9	0.533754
$633$	−1.05737e10	−1.65697
$634$	−5.18048e9	−0.807342
$635$	9.17088e9	1.42136
$636$	−6.16376e9	−0.950048
$637$	5.24443e8	0.0803916
$638$	0	0
$639$	−2.18470e8	−0.0331237
$640$	1.04722e9	0.157909
$641$	−3.07284e8	−0.0460825	−0.0230413	−	0.999735i	$-0.507335\pi$
$641$	−3.07284e8	−0.0460825	−0.0230413	+	0.999735i	$0.507335\pi$
$642$	−8.36111e8	−0.124707
$643$	2.60241e9	0.386044	0.193022	−	0.981194i	$-0.438171\pi$
$643$	2.60241e9	0.386044	0.193022	+	0.981194i	$0.438171\pi$
$644$	−2.80114e9	−0.413270
$645$	−7.68748e9	−1.12804
$646$	−5.30440e9	−0.774145
$647$	−6.93480e9	−1.00663	−0.503314	−	0.864104i	$-0.667886\pi$
$647$	−6.93480e9	−1.00663	−0.503314	+	0.864104i	$0.667886\pi$
$648$	−2.50992e9	−0.362365
$649$	0	0
$650$	6.45510e8	0.0921948
$651$	−1.75188e10	−2.48869
$652$	2.07462e9	0.293138
$653$	−3.18235e9	−0.447252	−0.223626	−	0.974675i	$-0.571789\pi$
$653$	−3.18235e9	−0.447252	−0.223626	+	0.974675i	$0.571789\pi$
$654$	−4.79121e9	−0.669766
$655$	3.12113e9	0.433977
$656$	−3.05722e9	−0.422827
$657$	−1.63793e8	−0.0225329
$658$	−6.44129e9	−0.881419
$659$	−7.05545e9	−0.960342	−0.480171	−	0.877175i	$-0.659425\pi$
$659$	−7.05545e9	−0.960342	−0.480171	+	0.877175i	$0.659425\pi$
$660$	0	0
$661$	1.09030e10	1.46839	0.734195	−	0.678938i	$-0.237560\pi$
$661$	1.09030e10	1.46839	0.734195	+	0.678938i	$0.237560\pi$
$662$	2.85181e9	0.382048
$663$	−3.95558e8	−0.0527124
$664$	8.91280e8	0.118148
$665$	2.59953e10	3.42783
$666$	−7.90532e7	−0.0103695
$667$	−5.07400e9	−0.662079
$668$	3.47032e9	0.450456
$669$	−4.26871e9	−0.551196
$670$	1.13994e10	1.46427
$671$	0	0
$672$	2.15954e9	0.274517
$673$	−3.02859e9	−0.382991	−0.191495	−	0.981494i	$-0.561334\pi$
$673$	−3.02859e9	−0.382991	−0.191495	+	0.981494i	$0.561334\pi$
$674$	−1.56926e9	−0.197417
$675$	−1.72813e10	−2.16279
$676$	−4.00169e9	−0.498231
$677$	1.29454e10	1.60345	0.801726	−	0.597692i	$-0.203915\pi$
$677$	1.29454e10	1.60345	0.801726	+	0.597692i	$0.203915\pi$
$678$	−8.42925e9	−1.03869
$679$	1.68881e10	2.07031
$680$	−4.53145e9	−0.552657
$681$	4.43753e9	0.538426
$682$	0	0
$683$	−4.71393e9	−0.566122	−0.283061	−	0.959102i	$-0.591350\pi$
$683$	−4.71393e9	−0.566122	−0.283061	+	0.959102i	$0.591350\pi$
$684$	1.33930e8	0.0160023
$685$	2.00896e10	2.38811
$686$	3.22132e9	0.380978
$687$	4.60672e9	0.542055
$688$	−1.33146e9	−0.155872
$689$	−9.58291e8	−0.111617
$690$	−5.95054e9	−0.689580
$691$	−9.77818e9	−1.12742	−0.563709	−	0.825974i	$-0.690626\pi$
$691$	−9.77818e9	−1.12742	−0.563709	+	0.825974i	$0.690626\pi$
$692$	3.28478e8	0.0376821
$693$	0	0
$694$	−1.43745e9	−0.163243
$695$	1.80324e10	2.03754
$696$	3.91181e9	0.439790
$697$	1.32290e10	1.47983
$698$	8.49948e9	0.946016
$699$	8.84345e9	0.979381
$700$	1.52495e10	1.68040
$701$	−1.12617e10	−1.23479	−0.617393	−	0.786655i	$-0.711811\pi$
$701$	−1.12617e10	−1.23479	−0.617393	+	0.786655i	$0.711811\pi$
$702$	−3.80483e8	−0.0415102
$703$	−6.60849e9	−0.717396
$704$	0	0
$705$	−1.36834e10	−1.47073
$706$	8.43234e8	0.0901844
$707$	−3.66898e9	−0.390460
$708$	1.48044e9	0.156774
$709$	6.00315e9	0.632582	0.316291	−	0.948662i	$-0.397562\pi$
$709$	6.00315e9	0.632582	0.316291	+	0.948662i	$0.397562\pi$
$710$	−1.56018e10	−1.63596
$711$	3.70078e8	0.0386144
$712$	5.26712e8	0.0546882
$713$	8.36073e9	0.863835
$714$	−9.34463e9	−0.960768
$715$	0	0
$716$	−4.82385e9	−0.491132
$717$	−4.06301e8	−0.0411652
$718$	−2.17500e9	−0.219293
$719$	1.03445e10	1.03791	0.518954	−	0.854802i	$-0.326322\pi$
$719$	1.03445e10	1.03791	0.518954	+	0.854802i	$0.326322\pi$
$720$	1.14414e8	0.0114239
$721$	7.56801e9	0.751984
$722$	4.04497e9	0.399977
$723$	−1.28021e10	−1.25979
$724$	−3.91861e8	−0.0383749
$725$	2.76231e10	2.69208
$726$	0	0
$727$	4.68555e9	0.452262	0.226131	−	0.974097i	$-0.427392\pi$
$727$	4.68555e9	0.452262	0.226131	+	0.974097i	$0.427392\pi$
$728$	3.35748e8	0.0322518
$729$	1.01793e10	0.973130
$730$	−1.16972e10	−1.11289
$731$	5.76142e9	0.545530
$732$	4.43063e9	0.417519
$733$	9.48605e9	0.889654	0.444827	−	0.895616i	$-0.353265\pi$
$733$	9.48605e9	0.889654	0.444827	+	0.895616i	$0.353265\pi$
$734$	−5.45462e8	−0.0509130
$735$	2.63192e10	2.44494
$736$	−1.03063e9	−0.0952859
$737$	0	0
$738$	−3.34017e8	−0.0305894
$739$	−5.50919e9	−0.502148	−0.251074	−	0.967968i	$-0.580784\pi$
$739$	−5.50919e9	−0.502148	−0.251074	+	0.967968i	$0.580784\pi$
$740$	−5.64551e9	−0.512145
$741$	8.34900e8	0.0753826
$742$	−2.26386e10	−2.03440
$743$	−1.20483e10	−1.07762	−0.538810	−	0.842427i	$-0.681126\pi$
$743$	−1.20483e10	−1.07762	−0.538810	+	0.842427i	$0.681126\pi$
$744$	−6.44572e9	−0.573808
$745$	1.50091e10	1.32987
$746$	5.38765e8	0.0475131
$747$	9.73770e7	0.00854740
$748$	0	0
$749$	−3.07092e9	−0.267043
$750$	1.76143e10	1.52458
$751$	4.42334e9	0.381075	0.190537	−	0.981680i	$-0.438977\pi$
$751$	4.42334e9	0.381075	0.190537	+	0.981680i	$0.438977\pi$
$752$	−2.36996e9	−0.203225
$753$	−6.58694e9	−0.562214
$754$	6.08177e8	0.0516690
$755$	1.66378e9	0.140696
$756$	−8.98851e9	−0.756591
$757$	−1.46813e9	−0.123007	−0.0615034	−	0.998107i	$-0.519589\pi$
$757$	−1.46813e9	−0.123007	−0.0615034	+	0.998107i	$0.519589\pi$
$758$	−7.68203e9	−0.640669
$759$	0	0
$760$	9.56449e9	0.790341
$761$	1.30863e10	1.07639	0.538197	−	0.842819i	$-0.319106\pi$
$761$	1.30863e10	1.07639	0.538197	+	0.842819i	$0.319106\pi$
$762$	6.95830e9	0.569719
$763$	−1.75974e10	−1.43421
$764$	3.77421e9	0.306196
$765$	−4.95084e8	−0.0399820
$766$	1.31068e10	1.05365
$767$	2.30166e8	0.0184186
$768$	7.94563e8	0.0632943
$769$	2.36251e10	1.87340	0.936701	−	0.350130i	$-0.113862\pi$
$769$	2.36251e10	1.87340	0.936701	+	0.350130i	$0.113862\pi$
$770$	0	0
$771$	−6.55051e9	−0.514737
$772$	7.68235e9	0.600944
$773$	1.06760e10	0.831345	0.415672	−	0.909514i	$-0.363546\pi$
$773$	1.06760e10	0.831345	0.415672	+	0.909514i	$0.363546\pi$
$774$	−1.45469e8	−0.0112766
$775$	−4.55161e10	−3.51244
$776$	6.21366e9	0.477344
$777$	−1.16420e10	−0.890338
$778$	1.76239e10	1.34175
$779$	−2.79224e10	−2.11627
$780$	7.13240e8	0.0538152
$781$	0	0
$782$	4.45966e9	0.333486
$783$	−1.62819e10	−1.21210
$784$	4.55846e9	0.337840
$785$	−2.06170e9	−0.152118
$786$	2.36812e9	0.173950
$787$	−5.98565e9	−0.437723	−0.218862	−	0.975756i	$-0.570234\pi$
$787$	−5.98565e9	−0.437723	−0.218862	+	0.975756i	$0.570234\pi$
$788$	6.05243e9	0.440644
$789$	−1.44451e10	−1.04701
$790$	2.64288e10	1.90714
$791$	−3.09595e10	−2.22421
$792$	0	0
$793$	6.88838e8	0.0490525
$794$	−1.30477e10	−0.925045
$795$	−4.80919e10	−3.39459
$796$	5.60294e9	0.393750
$797$	−6.26823e9	−0.438572	−0.219286	−	0.975661i	$-0.570373\pi$
$797$	−6.26823e9	−0.438572	−0.219286	+	0.975661i	$0.570373\pi$
$798$	1.97236e10	1.37397
$799$	1.02551e10	0.711258
$800$	5.61077e9	0.387443
$801$	5.75461e7	0.00395642
$802$	−9.04794e9	−0.619355
$803$	0	0
$804$	8.64919e9	0.586920
$805$	−2.18555e10	−1.47664
$806$	−1.00213e9	−0.0674141
$807$	1.77866e10	1.19134
$808$	−1.34993e9	−0.0900269
$809$	2.43765e10	1.61864	0.809321	−	0.587366i	$-0.199835\pi$
$809$	2.43765e10	1.61864	0.809321	+	0.587366i	$0.199835\pi$
$810$	−1.95833e10	−1.29476
$811$	−1.84392e10	−1.21386	−0.606931	−	0.794755i	$-0.707599\pi$
$811$	−1.84392e10	−1.21386	−0.606931	+	0.794755i	$0.707599\pi$
$812$	1.43675e10	0.941751
$813$	1.41607e10	0.924204
$814$	0	0
$815$	1.61870e10	1.04740
$816$	−3.43818e9	−0.221520
$817$	−1.21606e10	−0.780148
$818$	5.53781e9	0.353754
$819$	3.66822e7	0.00233325
$820$	−2.38536e10	−1.51079
$821$	−1.12084e10	−0.706875	−0.353437	−	0.935458i	$-0.614987\pi$
$821$	−1.12084e10	−0.706875	−0.353437	+	0.935458i	$0.614987\pi$
$822$	1.52428e10	0.957222
$823$	−1.60964e9	−0.100653	−0.0503267	−	0.998733i	$-0.516026\pi$
$823$	−1.60964e9	−0.100653	−0.0503267	+	0.998733i	$0.516026\pi$
$824$	2.78451e9	0.173382
$825$	0	0
$826$	5.43743e9	0.335710
$827$	1.82202e10	1.12017	0.560085	−	0.828435i	$-0.310769\pi$
$827$	1.82202e10	1.12017	0.560085	+	0.828435i	$0.310769\pi$
$828$	−1.12601e8	−0.00689346
$829$	2.91557e10	1.77739	0.888695	−	0.458499i	$-0.151613\pi$
$829$	2.91557e10	1.77739	0.888695	+	0.458499i	$0.151613\pi$
$830$	6.95410e9	0.422151
$831$	−6.99869e8	−0.0423071
$832$	1.23532e8	0.00743616
$833$	−1.97251e10	−1.18239
$834$	1.36819e10	0.816702
$835$	2.70767e10	1.60951
$836$	0	0
$837$	2.68286e10	1.58146
$838$	2.20821e9	0.129624
$839$	−7.75212e9	−0.453162	−0.226581	−	0.973992i	$-0.572755\pi$
$839$	−7.75212e9	−0.453162	−0.226581	+	0.973992i	$0.572755\pi$
$840$	1.68495e10	0.980868
$841$	8.77558e9	0.508733
$842$	3.36865e9	0.194475
$843$	−1.63569e10	−0.940382
$844$	−1.42889e10	−0.818087
$845$	−3.12227e10	−1.78021
$846$	−2.58930e8	−0.0147023
$847$	0	0
$848$	−8.32946e9	−0.469063
$849$	−7.15701e9	−0.401379
$850$	−2.42786e10	−1.35599
$851$	5.55608e9	0.309040
$852$	−1.18377e10	−0.655737
$853$	−2.21313e10	−1.22091	−0.610457	−	0.792049i	$-0.709014\pi$
$853$	−2.21313e10	−1.22091	−0.610457	+	0.792049i	$0.709014\pi$
$854$	1.62731e10	0.894060
$855$	1.04497e9	0.0571772
$856$	−1.12989e9	−0.0615711
$857$	−4.61092e9	−0.250239	−0.125119	−	0.992142i	$-0.539931\pi$
$857$	−4.61092e9	−0.250239	−0.125119	+	0.992142i	$0.539931\pi$
$858$	0	0
$859$	−3.36265e10	−1.81011	−0.905057	−	0.425290i	$-0.860172\pi$
$859$	−3.36265e10	−1.81011	−0.905057	+	0.425290i	$0.860172\pi$
$860$	−1.03886e10	−0.556943
$861$	−4.91902e10	−2.62644
$862$	1.83706e10	0.976895
$863$	1.09818e10	0.581614	0.290807	−	0.956782i	$-0.406076\pi$
$863$	1.09818e10	0.581614	0.290807	+	0.956782i	$0.406076\pi$
$864$	−3.30716e9	−0.174444
$865$	2.56291e9	0.134641
$866$	2.36276e10	1.23625
$867$	−4.55601e9	−0.237420
$868$	−2.36742e10	−1.22873
$869$	0	0
$870$	3.05214e10	1.57140
$871$	1.34471e9	0.0689546
$872$	−6.47466e9	−0.330681
$873$	6.78875e8	0.0345334
$874$	−9.41297e9	−0.476910
$875$	6.46947e10	3.26468
$876$	−8.87509e9	−0.446075
$877$	1.57068e10	0.786302	0.393151	−	0.919474i	$-0.371385\pi$
$877$	1.57068e10	0.786302	0.393151	+	0.919474i	$0.371385\pi$
$878$	−2.45204e10	−1.22263
$879$	−7.80571e9	−0.387661
$880$	0	0
$881$	1.32714e10	0.653886	0.326943	−	0.945044i	$-0.393982\pi$
$881$	1.32714e10	0.653886	0.326943	+	0.945044i	$0.393982\pi$
$882$	4.98035e8	0.0244411
$883$	1.12453e10	0.549677	0.274838	−	0.961490i	$-0.411376\pi$
$883$	1.12453e10	0.549677	0.274838	+	0.961490i	$0.411376\pi$
$884$	−5.34541e8	−0.0260254
$885$	1.15509e10	0.560163
$886$	2.27059e10	1.09678
$887$	2.90437e10	1.39740	0.698698	−	0.715417i	$-0.253763\pi$
$887$	2.90437e10	1.39740	0.698698	+	0.715417i	$0.253763\pi$
$888$	−4.28347e9	−0.205282
$889$	2.55568e10	1.21998
$890$	4.10960e9	0.195405
$891$	0	0
$892$	−5.76857e9	−0.272139
$893$	−2.16454e10	−1.01715
$894$	1.13880e10	0.533047
$895$	−3.76375e10	−1.75485
$896$	2.91832e9	0.135536
$897$	−7.01941e8	−0.0324733
$898$	2.22433e10	1.02502
$899$	−4.28837e10	−1.96849
$900$	6.13006e8	0.0280295
$901$	3.60427e10	1.64165
$902$	0	0
$903$	−2.14230e10	−0.968218
$904$	−1.13910e10	−0.512827
$905$	−3.05744e9	−0.137116
$906$	1.26238e9	0.0563949
$907$	−4.44257e10	−1.97701	−0.988505	−	0.151185i	$-0.951691\pi$
$907$	−4.44257e10	−1.97701	−0.988505	+	0.151185i	$0.951691\pi$
$908$	5.99670e9	0.265835
$909$	−1.47487e8	−0.00651299
$910$	2.61963e9	0.115238
$911$	1.04893e10	0.459653	0.229827	−	0.973232i	$-0.426184\pi$
$911$	1.04893e10	0.459653	0.229827	+	0.973232i	$0.426184\pi$
$912$	7.25695e9	0.316790
$913$	0	0
$914$	2.18932e10	0.948411
$915$	3.45694e10	1.49182
$916$	6.22535e9	0.267627
$917$	8.69777e9	0.372490
$918$	1.43105e10	0.610528
$919$	3.49809e10	1.48671	0.743355	−	0.668897i	$-0.233233\pi$
$919$	3.49809e10	1.48671	0.743355	+	0.668897i	$0.233233\pi$
$920$	−8.04133e9	−0.340463
$921$	−6.31795e8	−0.0266482
$922$	−1.70730e10	−0.717382
$923$	−1.84043e9	−0.0770396
$924$	0	0
$925$	−3.02475e10	−1.25659
$926$	1.88813e10	0.781436
$927$	3.04222e8	0.0125433
$928$	5.28627e9	0.217136
$929$	−5.15987e9	−0.211147	−0.105573	−	0.994412i	$-0.533668\pi$
$929$	−5.15987e9	−0.211147	−0.105573	+	0.994412i	$0.533668\pi$
$930$	−5.02919e10	−2.05025
$931$	4.16335e10	1.69091
$932$	1.19507e10	0.483546
$933$	−1.96299e10	−0.791285
$934$	1.27646e10	0.512618
$935$	0	0
$936$	1.34965e7	0.000537969 0
$937$	9.98335e9	0.396450	0.198225	−	0.980157i	$-0.436482\pi$
$937$	9.98335e9	0.396450	0.198225	+	0.980157i	$0.436482\pi$
$938$	3.17672e10	1.25681
$939$	−4.21352e10	−1.66079
$940$	−1.84913e10	−0.726138
$941$	−1.49742e9	−0.0585841	−0.0292920	−	0.999571i	$-0.509325\pi$
$941$	−1.49742e9	−0.0585841	−0.0292920	+	0.999571i	$0.509325\pi$
$942$	−1.56429e9	−0.0609732
$943$	2.34757e10	0.911648
$944$	2.00060e9	0.0774032
$945$	−7.01316e10	−2.70335
$946$	0	0
$947$	−3.02935e10	−1.15911	−0.579556	−	0.814933i	$-0.696774\pi$
$947$	−3.02935e10	−1.15911	−0.579556	+	0.814933i	$0.696774\pi$
$948$	2.00526e10	0.764435
$949$	−1.37983e9	−0.0524074
$950$	5.12446e10	1.93917
$951$	−3.06682e10	−1.15626
$952$	−1.26280e10	−0.474356
$953$	2.90556e10	1.08744	0.543719	−	0.839267i	$-0.317016\pi$
$953$	2.90556e10	1.08744	0.543719	+	0.839267i	$0.317016\pi$
$954$	−9.10037e8	−0.0339344
$955$	2.94478e10	1.09406
$956$	−5.49059e8	−0.0203243
$957$	0	0
$958$	−2.77996e10	−1.02155
$959$	5.59845e10	2.04976
$960$	6.19948e9	0.226155
$961$	4.31494e10	1.56835
$962$	−6.65959e8	−0.0241176
$963$	−1.23446e8	−0.00445436
$964$	−1.73003e10	−0.621990
$965$	5.99406e10	2.14721
$966$	−1.65826e10	−0.591879
$967$	4.78012e10	1.69999	0.849994	−	0.526792i	$-0.176605\pi$
$967$	4.78012e10	1.69999	0.849994	+	0.526792i	$0.176605\pi$
$968$	0	0
$969$	−3.14018e10	−1.10872
$970$	4.84813e10	1.70558
$971$	−5.52383e9	−0.193630	−0.0968150	−	0.995302i	$-0.530866\pi$
$971$	−5.52383e9	−0.193630	−0.0968150	+	0.995302i	$0.530866\pi$
$972$	−7.32132e8	−0.0255716
$973$	5.02515e10	1.74886
$974$	6.16496e9	0.213783
$975$	3.82139e9	0.132040
$976$	5.98737e9	0.206140
$977$	2.66938e9	0.0915756	0.0457878	−	0.998951i	$-0.485420\pi$
$977$	2.66938e9	0.0915756	0.0457878	+	0.998951i	$0.485420\pi$
$978$	1.22817e10	0.419828
$979$	0	0
$980$	3.55668e10	1.20713
$981$	−7.07390e8	−0.0239231
$982$	4.14084e9	0.139540
$983$	−5.34734e10	−1.79556	−0.897781	−	0.440442i	$-0.854822\pi$
$983$	−5.34734e10	−1.79556	−0.897781	+	0.440442i	$0.854822\pi$
$984$	−1.80986e10	−0.605567
$985$	4.72233e10	1.57445
$986$	−2.28744e10	−0.759942
$987$	−3.81322e10	−1.26236
$988$	1.12825e9	0.0372183
$989$	1.02240e10	0.336072
$990$	0	0
$991$	4.32159e10	1.41054	0.705271	−	0.708938i	$-0.250825\pi$
$991$	4.32159e10	1.41054	0.705271	+	0.708938i	$0.250825\pi$
$992$	−8.71049e9	−0.283304
$993$	1.68826e10	0.547164
$994$	−4.34783e10	−1.40417
$995$	4.37162e10	1.40690
$996$	5.27634e9	0.169210
$997$	−2.46827e10	−0.788786	−0.394393	−	0.918942i	$-0.629045\pi$
$997$	−2.46827e10	−0.788786	−0.394393	+	0.918942i	$0.629045\pi$
$998$	−7.07695e9	−0.225366
$999$	1.78288e10	0.565773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.8.a.m.1.3	yes	4
11.10	odd	2		242.8.a.l.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
242.8.a.l.1.3	✓	4	11.10	odd	2
242.8.a.m.1.3	yes	4	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:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	242.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +47.3597 q^{3} +64.0000 q^{4} +499.352 q^{5} +378.877 q^{6} +1391.56 q^{7} +512.000 q^{8} +55.9387 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +47.3597 q^{3} +64.0000 q^{4} +499.352 q^{5} +378.877 q^{6} +1391.56 q^{7} +512.000 q^{8} +55.9387 q^{9} +3994.81 q^{10} +3031.02 q^{12} +471.238 q^{13} +11132.5 q^{14} +23649.1 q^{15} +4096.00 q^{16} -17724.0 q^{17} +447.509 q^{18} +37409.8 q^{19} +31958.5 q^{20} +65904.0 q^{21} -31452.2 q^{23} +24248.2 q^{24} +171227. q^{25} +3769.91 q^{26} -100926. q^{27} +89060.0 q^{28} +161324. q^{29} +189193. q^{30} -265823. q^{31} +32768.0 q^{32} -141792. q^{34} +694879. q^{35} +3580.07 q^{36} -176651. q^{37} +299278. q^{38} +22317.7 q^{39} +255668. q^{40} -746391. q^{41} +527232. q^{42} -325064. q^{43} +27933.1 q^{45} -251618. q^{46} -578602. q^{47} +193985. q^{48} +1.11290e6 q^{49} +1.36982e6 q^{50} -839401. q^{51} +30159.2 q^{52} -2.03356e6 q^{53} -807411. q^{54} +712480. q^{56} +1.77172e6 q^{57} +1.29059e6 q^{58} +488428. q^{59} +1.51354e6 q^{60} +1.46176e6 q^{61} -2.12659e6 q^{62} +77842.2 q^{63} +262144. q^{64} +235314. q^{65} +2.85356e6 q^{67} -1.13433e6 q^{68} -1.48957e6 q^{69} +5.55903e6 q^{70} -3.90552e6 q^{71} +28640.6 q^{72} -2.92809e6 q^{73} -1.41321e6 q^{74} +8.10926e6 q^{75} +2.39423e6 q^{76} +178542. q^{78} +6.61578e6 q^{79} +2.04534e6 q^{80} -4.90218e6 q^{81} -5.97113e6 q^{82} +1.74078e6 q^{83} +4.21785e6 q^{84} -8.85049e6 q^{85} -2.60051e6 q^{86} +7.64026e6 q^{87} +1.02874e6 q^{89} +223465. q^{90} +655758. q^{91} -2.01294e6 q^{92} -1.25893e7 q^{93} -4.62882e6 q^{94} +1.86806e7 q^{95} +1.55188e6 q^{96} +1.21361e7 q^{97} +8.90324e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} + 16 q^{3} + 256 q^{4} + 404 q^{5} + 128 q^{6} - 656 q^{7} + 2048 q^{8} + 8116 q^{9}+O(q^{10}) \) 4 * q + 32 * q^2 + 16 * q^3 + 256 * q^4 + 404 * q^5 + 128 * q^6 - 656 * q^7 + 2048 * q^8 + 8116 * q^9	\( 4 q + 32 q^{2} + 16 q^{3} + 256 q^{4} + 404 q^{5} + 128 q^{6} - 656 q^{7} + 2048 q^{8} + 8116 q^{9} + 3232 q^{10} + 1024 q^{12} + 7556 q^{13} - 5248 q^{14} - 33600 q^{15} + 16384 q^{16} + 37308 q^{17} + 64928 q^{18} + 55424 q^{19} + 25856 q^{20} + 36416 q^{21} + 35456 q^{23} + 8192 q^{24} + 266784 q^{25} + 60448 q^{26} - 213344 q^{27} - 41984 q^{28} + 57188 q^{29} - 268800 q^{30} - 493456 q^{31} + 131072 q^{32} + 298464 q^{34} + 589344 q^{35} + 519424 q^{36} - 411052 q^{37} + 443392 q^{38} + 962336 q^{39} + 206848 q^{40} - 292244 q^{41} + 291328 q^{42} + 920400 q^{43} + 1837284 q^{45} + 283648 q^{46} + 83264 q^{47} + 65536 q^{48} + 1816644 q^{49} + 2134272 q^{50} - 2594928 q^{51} + 483584 q^{52} + 2585748 q^{53} - 1706752 q^{54} - 335872 q^{56} + 6623840 q^{57} + 457504 q^{58} + 1539984 q^{59} - 2150400 q^{60} + 4488024 q^{61} - 3947648 q^{62} - 12133840 q^{63} + 1048576 q^{64} - 312188 q^{65} + 4619264 q^{67} + 2387712 q^{68} + 2993472 q^{69} + 4714752 q^{70} - 5025488 q^{71} + 4155392 q^{72} - 3281912 q^{73} - 3288416 q^{74} - 718496 q^{75} + 3547136 q^{76} + 7698688 q^{78} + 15899968 q^{79} + 1654784 q^{80} + 16623940 q^{81} - 2337952 q^{82} + 18549088 q^{83} + 2330624 q^{84} - 4934868 q^{85} + 7363200 q^{86} + 22272672 q^{87} + 6384940 q^{89} + 14698272 q^{90} - 23874048 q^{91} + 2269184 q^{92} - 31055680 q^{93} + 666112 q^{94} + 7874608 q^{95} + 524288 q^{96} + 20254236 q^{97} + 14533152 q^{98}+O(q^{100}) \) 4 * q + 32 * q^2 + 16 * q^3 + 256 * q^4 + 404 * q^5 + 128 * q^6 - 656 * q^7 + 2048 * q^8 + 8116 * q^9 + 3232 * q^10 + 1024 * q^12 + 7556 * q^13 - 5248 * q^14 - 33600 * q^15 + 16384 * q^16 + 37308 * q^17 + 64928 * q^18 + 55424 * q^19 + 25856 * q^20 + 36416 * q^21 + 35456 * q^23 + 8192 * q^24 + 266784 * q^25 + 60448 * q^26 - 213344 * q^27 - 41984 * q^28 + 57188 * q^29 - 268800 * q^30 - 493456 * q^31 + 131072 * q^32 + 298464 * q^34 + 589344 * q^35 + 519424 * q^36 - 411052 * q^37 + 443392 * q^38 + 962336 * q^39 + 206848 * q^40 - 292244 * q^41 + 291328 * q^42 + 920400 * q^43 + 1837284 * q^45 + 283648 * q^46 + 83264 * q^47 + 65536 * q^48 + 1816644 * q^49 + 2134272 * q^50 - 2594928 * q^51 + 483584 * q^52 + 2585748 * q^53 - 1706752 * q^54 - 335872 * q^56 + 6623840 * q^57 + 457504 * q^58 + 1539984 * q^59 - 2150400 * q^60 + 4488024 * q^61 - 3947648 * q^62 - 12133840 * q^63 + 1048576 * q^64 - 312188 * q^65 + 4619264 * q^67 + 2387712 * q^68 + 2993472 * q^69 + 4714752 * q^70 - 5025488 * q^71 + 4155392 * q^72 - 3281912 * q^73 - 3288416 * q^74 - 718496 * q^75 + 3547136 * q^76 + 7698688 * q^78 + 15899968 * q^79 + 1654784 * q^80 + 16623940 * q^81 - 2337952 * q^82 + 18549088 * q^83 + 2330624 * q^84 - 4934868 * q^85 + 7363200 * q^86 + 22272672 * q^87 + 6384940 * q^89 + 14698272 * q^90 - 23874048 * q^91 + 2269184 * q^92 - 31055680 * q^93 + 666112 * q^94 + 7874608 * q^95 + 524288 * q^96 + 20254236 * q^97 + 14533152 * q^98

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