LMFDB - Embedded newform 49.28.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,28,Mod(1,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 28, names="a")

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

chi := DirichletCharacter("49.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	49.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:	$226.309231671$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{18209}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4552 $ x^2 - x - 4552
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-66.9704$ of defining polynomial
Character	$\chi$	$=$	49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+10433.6 q^{2} -2.15499e6 q^{3} -2.53577e7 q^{4} -4.86703e9 q^{5} -2.24843e10 q^{6} -1.66495e12 q^{8} -2.98161e12 q^{9} +O(q^{10})$	\(q+10433.6 q^{2} -2.15499e6 q^{3} -2.53577e7 q^{4} -4.86703e9 q^{5} -2.24843e10 q^{6} -1.66495e12 q^{8} -2.98161e12 q^{9} -5.07806e13 q^{10} -6.85469e13 q^{11} +5.46457e13 q^{12} +5.86777e14 q^{13} +1.04884e16 q^{15} -1.39679e16 q^{16} +2.42814e16 q^{17} -3.11089e16 q^{18} -2.43094e17 q^{19} +1.23417e17 q^{20} -7.15190e17 q^{22} +1.25668e17 q^{23} +3.58794e18 q^{24} +1.62374e19 q^{25} +6.12220e18 q^{26} +2.28584e19 q^{27} -1.25483e19 q^{29} +1.09432e20 q^{30} +6.23745e19 q^{31} +7.77296e19 q^{32} +1.47718e20 q^{33} +2.53343e20 q^{34} +7.56070e19 q^{36} +3.67692e20 q^{37} -2.53635e21 q^{38} -1.26450e21 q^{39} +8.10334e21 q^{40} -3.60988e21 q^{41} +1.19560e22 q^{43} +1.73819e21 q^{44} +1.45116e22 q^{45} +1.31117e21 q^{46} -8.26632e21 q^{47} +3.01007e22 q^{48} +1.69414e23 q^{50} -5.23263e22 q^{51} -1.48794e22 q^{52} +1.60547e23 q^{53} +2.38496e23 q^{54} +3.33619e23 q^{55} +5.23866e23 q^{57} -1.30923e23 q^{58} -1.09336e24 q^{59} -2.65962e23 q^{60} +1.32576e24 q^{61} +6.50790e23 q^{62} +2.68574e24 q^{64} -2.85586e24 q^{65} +1.54123e24 q^{66} +6.27072e24 q^{67} -6.15722e23 q^{68} -2.70814e23 q^{69} -1.65578e25 q^{71} +4.96422e24 q^{72} +7.93292e24 q^{73} +3.83635e24 q^{74} -3.49914e25 q^{75} +6.16433e24 q^{76} -1.31933e25 q^{78} +1.61913e25 q^{79} +6.79823e25 q^{80} -2.65232e25 q^{81} -3.76641e25 q^{82} -1.00338e26 q^{83} -1.18178e26 q^{85} +1.24744e26 q^{86} +2.70414e25 q^{87} +1.14127e26 q^{88} +1.72766e26 q^{89} +1.51408e26 q^{90} -3.18667e24 q^{92} -1.34416e26 q^{93} -8.62475e25 q^{94} +1.18315e27 q^{95} -1.67507e26 q^{96} +1.03077e27 q^{97} +2.04380e26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8280 q^{2} + 1286280 q^{3} + 190623296 q^{4} - 5443587900 q^{5} - 86882873184 q^{6} - 3195032348160 q^{8} + 1235136554154 q^{9}+O(q^{10}) $ 2 * q - 8280 * q^2 + 1286280 * q^3 + 190623296 * q^4 - 5443587900 * q^5 - 86882873184 * q^6 - 3195032348160 * q^8 + 1235136554154 * q^9	$ 2 q - 8280 q^{2} + 1286280 q^{3} + 190623296 q^{4} - 5443587900 q^{5} - 86882873184 q^{6} - 3195032348160 q^{8} + 1235136554154 q^{9} - 39991096148400 q^{10} + 138167337691944 q^{11} + 797895007176960 q^{12} + 753433801271060 q^{13} + 85\!\cdots\!00 q^{15}+ \cdots + 10\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 8280 * q^2 + 1286280 * q^3 + 190623296 * q^4 - 5443587900 * q^5 - 86882873184 * q^6 - 3195032348160 * q^8 + 1235136554154 * q^9 - 39991096148400 * q^10 + 138167337691944 * q^11 + 797895007176960 * q^12 + 753433801271060 * q^13 + 8504300488438800 * q^15 - 14322995785166848 * q^16 + 29753620331011740 * q^17 - 110019470226337080 * q^18 - 404565810372684760 * q^19 - 1109219331427200 * q^20 - 4583556785578779360 * q^22 + 2929078923121218960 * q^23 - 1677495533792532480 * q^24 + 9119218786673228750 * q^25 + 3003459254146640016 * q^26 + 11127665129740313040 * q^27 - 15546679995448558260 * q^29 + 146561411061600148800 * q^30 - 28544554594467385024 * q^31 + 289738949030869893120 * q^32 + 859077391009750054560 * q^33 + 150938335185934859568 * q^34 + 986344620988374211392 * q^36 + 1867697204682824566780 * q^37 + 485361223888169521440 * q^38 - 690990221801025527472 * q^39 + 8985527186071883904000 * q^40 - 9081343698046512254964 * q^41 + 5145612605801421773800 * q^43 + 46384541037574305299712 * q^44 + 12080376719602732775700 * q^45 - 51150723570313970279616 * q^46 + 1150251488862201070560 * q^47 + 28878849836569912688640 * q^48 + 302620649115949014735000 * q^50 - 33494974704727214464656 * q^51 + 21115266673184124022400 * q^52 + 106953735591470060758620 * q^53 + 458020779785618027135040 * q^54 + 214436254091483969701200 * q^55 - 31800538920577362634080 * q^57 - 74812163717162466470160 * q^58 - 2009620977624026488631880 * q^59 - 694490206253033569881600 * q^60 - 147857426692448940370444 * q^61 + 2352212714010270811080960 * q^62 - 1234057803938137445761024 * q^64 - 2951949350200452960922200 * q^65 - 11770868153144268253438848 * q^66 + 3051578535738098902157560 * q^67 + 566166870324676171716480 * q^68 + 9376480489705868528695872 * q^69 - 13175198820369338598286416 * q^71 - 1487763126543110308830720 * q^72 - 5284260812951286572116660 * q^73 - 24234145145448525537787728 * q^74 - 59486914888952006559645000 * q^75 - 28710432717942786872615680 * q^76 - 23925717325436558555851200 * q^78 + 62814351035720719918179040 * q^79 + 68186991639088251432345600 * q^80 - 99047155826597708238103278 * q^81 + 64726649726985190956760560 * q^82 - 171806873410054757883176280 * q^83 - 121333441005595565089302600 * q^85 + 252189883901197432712215584 * q^86 + 16722988656204557792643120 * q^87 - 202163623954874235550955520 * q^88 + 313473438761105539763494380 * q^89 + 196904738457998748777517200 * q^90 + 602296848225491467788034560 * q^92 - 447293490375807514724002560 * q^93 - 262465434750720041893579392 * q^94 + 1276245244260479145691314000 * q^95 + 562074901098402916384505856 * q^96 + 653202933397052842883888060 * q^97 + 1076041779280842335610479688 * 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 $

$2$	10433.6	0.900594	0.450297	−	0.892879i	$-0.351318\pi$
$2$	10433.6	0.900594	0.450297	+	0.892879i	$0.351318\pi$
$3$	−2.15499e6	−0.780384	−0.390192	−	0.920733i	$-0.627591\pi$
$3$	−2.15499e6	−0.780384	−0.390192	+	0.920733i	$0.627591\pi$
$4$	−2.53577e7	−0.188930
$5$	−4.86703e9	−1.78307	−0.891536	−	0.452950i	$-0.850371\pi$
$5$	−4.86703e9	−1.78307	−0.891536	+	0.452950i	$0.850371\pi$
$6$	−2.24843e10	−0.702810
$7$	0	0
$7$	0	0
$8$	−1.66495e12	−1.07074
$9$	−2.98161e12	−0.391000
$10$	−5.07806e13	−1.60582
$11$	−6.85469e13	−0.598668	−0.299334	−	0.954148i	$-0.596765\pi$
$11$	−6.85469e13	−0.598668	−0.299334	+	0.954148i	$0.596765\pi$
$12$	5.46457e13	0.147438
$13$	5.86777e14	0.537326	0.268663	−	0.963234i	$-0.413418\pi$
$13$	5.86777e14	0.537326	0.268663	+	0.963234i	$0.413418\pi$
$14$	0	0
$15$	1.04884e16	1.39148
$16$	−1.39679e16	−0.775376
$17$	2.42814e16	0.594585	0.297292	−	0.954786i	$-0.403916\pi$
$17$	2.42814e16	0.594585	0.297292	+	0.954786i	$0.403916\pi$
$18$	−3.11089e16	−0.352133
$19$	−2.43094e17	−1.32618	−0.663088	−	0.748541i	$-0.730755\pi$
$19$	−2.43094e17	−1.32618	−0.663088	+	0.748541i	$0.730755\pi$
$20$	1.23417e17	0.336876
$21$	0	0
$22$	−7.15190e17	−0.539157
$23$	1.25668e17	0.0519877	0.0259938	−	0.999662i	$-0.491725\pi$
$23$	1.25668e17	0.0519877	0.0259938	+	0.999662i	$0.491725\pi$
$24$	3.58794e18	0.835591
$25$	1.62374e19	2.17934
$26$	6.12220e18	0.483913
$27$	2.28584e19	1.08551
$28$	0	0
$29$	−1.25483e19	−0.227096	−0.113548	−	0.993532i	$-0.536222\pi$
$29$	−1.25483e19	−0.227096	−0.113548	+	0.993532i	$0.536222\pi$
$30$	1.09432e20	1.25316
$31$	6.23745e19	0.458801	0.229400	−	0.973332i	$-0.426323\pi$
$31$	6.23745e19	0.458801	0.229400	+	0.973332i	$0.426323\pi$
$32$	7.77296e19	0.372445
$33$	1.47718e20	0.467191
$34$	2.53343e20	0.535480
$35$	0	0
$36$	7.56070e19	0.0738717
$37$	3.67692e20	0.248177	0.124088	−	0.992271i	$-0.460399\pi$
$37$	3.67692e20	0.248177	0.124088	+	0.992271i	$0.460399\pi$
$38$	−2.53635e21	−1.19435
$39$	−1.26450e21	−0.419321
$40$	8.10334e21	1.90921
$41$	−3.60988e21	−0.609412	−0.304706	−	0.952446i	$-0.598558\pi$
$41$	−3.60988e21	−0.609412	−0.304706	+	0.952446i	$0.598558\pi$
$42$	0	0
$43$	1.19560e22	1.06111	0.530555	−	0.847651i	$-0.321984\pi$
$43$	1.19560e22	1.06111	0.530555	+	0.847651i	$0.321984\pi$
$44$	1.73819e21	0.113106
$45$	1.45116e22	0.697182
$46$	1.31117e21	0.0468198
$47$	−8.26632e21	−0.220796	−0.110398	−	0.993887i	$-0.535213\pi$
$47$	−8.26632e21	−0.220796	−0.110398	+	0.993887i	$0.535213\pi$
$48$	3.01007e22	0.605091
$49$	0	0
$50$	1.69414e23	1.96270
$51$	−5.23263e22	−0.464005
$52$	−1.48794e22	−0.101517
$53$	1.60547e23	0.846991	0.423496	−	0.905898i	$-0.360803\pi$
$53$	1.60547e23	0.846991	0.423496	+	0.905898i	$0.360803\pi$
$54$	2.38496e23	0.977608
$55$	3.33619e23	1.06747
$56$	0	0
$57$	5.23866e23	1.03493
$58$	−1.30923e23	−0.204522
$59$	−1.09336e24	−1.35601	−0.678004	−	0.735058i	$-0.737155\pi$
$59$	−1.09336e24	−1.35601	−0.678004	+	0.735058i	$0.737155\pi$
$60$	−2.65962e23	−0.262892
$61$	1.32576e24	1.04837	0.524183	−	0.851606i	$-0.324371\pi$
$61$	1.32576e24	1.04837	0.524183	+	0.851606i	$0.324371\pi$
$62$	6.50790e23	0.413193
$63$	0	0
$64$	2.68574e24	1.11080
$65$	−2.85586e24	−0.958091
$66$	1.54123e24	0.420750
$67$	6.27072e24	1.39736	0.698679	−	0.715435i	$-0.253771\pi$
$67$	6.27072e24	1.39736	0.698679	+	0.715435i	$0.253771\pi$
$68$	−6.15722e23	−0.112335
$69$	−2.70814e23	−0.0405704
$70$	0	0
$71$	−1.65578e25	−1.68661	−0.843303	−	0.537438i	$-0.819392\pi$
$71$	−1.65578e25	−1.68661	−0.843303	+	0.537438i	$0.819392\pi$
$72$	4.96422e24	0.418661
$73$	7.93292e24	0.555360	0.277680	−	0.960674i	$-0.410435\pi$
$73$	7.93292e24	0.555360	0.277680	+	0.960674i	$0.410435\pi$
$74$	3.83635e24	0.223506
$75$	−3.49914e25	−1.70073
$76$	6.16433e24	0.250554
$77$	0	0
$78$	−1.31933e25	−0.377638
$79$	1.61913e25	0.390227	0.195113	−	0.980781i	$-0.437493\pi$
$79$	1.61913e25	0.390227	0.195113	+	0.980781i	$0.437493\pi$
$80$	6.79823e25	1.38255
$81$	−2.65232e25	−0.456118
$82$	−3.76641e25	−0.548833
$83$	−1.00338e26	−1.24140	−0.620698	−	0.784049i	$-0.713151\pi$
$83$	−1.00338e26	−1.24140	−0.620698	+	0.784049i	$0.713151\pi$
$84$	0	0
$85$	−1.18178e26	−1.06019
$86$	1.24744e26	0.955630
$87$	2.70414e25	0.177223
$88$	1.14127e26	0.641020
$89$	1.72766e26	0.833092	0.416546	−	0.909115i	$-0.363241\pi$
$89$	1.72766e26	0.833092	0.416546	+	0.909115i	$0.363241\pi$
$90$	1.51408e26	0.627878
$91$	0	0
$92$	−3.18667e24	−0.00982203
$93$	−1.34416e26	−0.358041
$94$	−8.62475e25	−0.198848
$95$	1.18315e27	2.36467
$96$	−1.67507e26	−0.290650
$97$	1.03077e27	1.55505	0.777524	−	0.628853i	$-0.216475\pi$
$97$	1.03077e27	1.55505	0.777524	+	0.628853i	$0.216475\pi$
$98$	0	0
$99$	2.04380e26	0.234080
$100$	−4.11743e26	−0.411743
$101$	−4.65230e26	−0.406751	−0.203376	−	0.979101i	$-0.565191\pi$
$101$	−4.65230e26	−0.406751	−0.203376	+	0.979101i	$0.565191\pi$
$102$	−5.45951e26	−0.417880
$103$	−7.02209e26	−0.471155	−0.235577	−	0.971856i	$-0.575698\pi$
$103$	−7.02209e26	−0.471155	−0.235577	+	0.971856i	$0.575698\pi$
$104$	−9.76953e26	−0.575339
$105$	0	0
$106$	1.67509e27	0.762795
$107$	−3.21175e27	−1.28843	−0.644215	−	0.764845i	$-0.722816\pi$
$107$	−3.21175e27	−1.28843	−0.644215	+	0.764845i	$0.722816\pi$
$108$	−5.79639e26	−0.205086
$109$	1.11613e27	0.348705	0.174353	−	0.984683i	$-0.444217\pi$
$109$	1.11613e27	0.348705	0.174353	+	0.984683i	$0.444217\pi$
$110$	3.48085e27	0.961356
$111$	−7.92373e26	−0.193673
$112$	0	0
$113$	−3.24502e27	−0.623244	−0.311622	−	0.950206i	$-0.600872\pi$
$113$	−3.24502e27	−0.623244	−0.311622	+	0.950206i	$0.600872\pi$
$114$	5.46581e27	0.932050
$115$	−6.11632e26	−0.0926978
$116$	3.18196e26	0.0429053
$117$	−1.74954e27	−0.210095
$118$	−1.14077e28	−1.22121
$119$	0	0
$120$	−1.74626e28	−1.48992
$121$	−8.41132e27	−0.641596
$122$	1.38325e28	0.944152
$123$	7.77927e27	0.475576
$124$	−1.58168e27	−0.0866812
$125$	−4.27656e28	−2.10285
$126$	0	0
$127$	−3.05563e28	−1.21269	−0.606346	−	0.795201i	$-0.707365\pi$
$127$	−3.05563e28	−1.21269	−0.606346	+	0.795201i	$0.707365\pi$
$128$	1.75893e28	0.627933
$129$	−2.57650e28	−0.828074
$130$	−2.97969e28	−0.862852
$131$	3.92050e28	1.02371	0.511857	−	0.859071i	$-0.328958\pi$
$131$	3.92050e28	1.02371	0.511857	+	0.859071i	$0.328958\pi$
$132$	−3.74579e27	−0.0882664
$133$	0	0
$134$	6.54262e28	1.25845
$135$	−1.11253e29	−1.93555
$136$	−4.04273e28	−0.636648
$137$	−1.05475e28	−0.150461	−0.0752305	−	0.997166i	$-0.523969\pi$
$137$	−1.05475e28	−0.150461	−0.0752305	+	0.997166i	$0.523969\pi$
$138$	−2.82557e27	−0.0365374
$139$	−1.42615e29	−1.67289	−0.836443	−	0.548054i	$-0.815369\pi$
$139$	−1.42615e29	−1.67289	−0.836443	+	0.548054i	$0.815369\pi$
$140$	0	0
$141$	1.78138e28	0.172306
$142$	−1.72757e29	−1.51895
$143$	−4.02217e28	−0.321680
$144$	4.16469e28	0.303172
$145$	6.10727e28	0.404929
$146$	8.27689e28	0.500154
$147$	0	0
$148$	−9.32384e27	−0.0468880
$149$	1.04309e29	0.478968	0.239484	−	0.970900i	$-0.423022\pi$
$149$	1.04309e29	0.478968	0.239484	+	0.970900i	$0.423022\pi$
$150$	−3.65086e29	−1.53166
$151$	3.58958e29	1.37675	0.688374	−	0.725356i	$-0.258325\pi$
$151$	3.58958e29	1.37675	0.688374	+	0.725356i	$0.258325\pi$
$152$	4.04739e29	1.42000
$153$	−7.23978e28	−0.232483
$154$	0	0
$155$	−3.03578e29	−0.818074
$156$	3.20649e28	0.0792223
$157$	6.56383e29	1.48769	0.743844	−	0.668353i	$-0.233000\pi$
$157$	6.56383e29	1.48769	0.743844	+	0.668353i	$0.233000\pi$
$158$	1.68934e29	0.351436
$159$	−3.45978e29	−0.660979
$160$	−3.78312e29	−0.664096
$161$	0	0
$162$	−2.76732e29	−0.410778
$163$	3.98777e29	0.544750	0.272375	−	0.962191i	$-0.412191\pi$
$163$	3.98777e29	0.544750	0.272375	+	0.962191i	$0.412191\pi$
$164$	9.15385e28	0.115136
$165$	−7.18947e29	−0.833036
$166$	−1.04689e30	−1.11799
$167$	−6.97711e29	−0.687074	−0.343537	−	0.939139i	$-0.611625\pi$
$167$	−6.97711e29	−0.687074	−0.343537	+	0.939139i	$0.611625\pi$
$168$	0	0
$169$	−8.48226e29	−0.711280
$170$	−1.23303e30	−0.954799
$171$	7.24813e29	0.518536
$172$	−3.03176e29	−0.200475
$173$	−1.20460e30	−0.736580	−0.368290	−	0.929711i	$-0.620057\pi$
$173$	−1.20460e30	−0.736580	−0.368290	+	0.929711i	$0.620057\pi$
$174$	2.82139e29	0.159606
$175$	0	0
$176$	9.57457e29	0.464193
$177$	2.35619e30	1.05821
$178$	1.80257e30	0.750278
$179$	3.25033e30	1.25433	0.627164	−	0.778887i	$-0.284215\pi$
$179$	3.25033e30	1.25433	0.627164	+	0.778887i	$0.284215\pi$
$180$	−3.67981e29	−0.131718
$181$	5.16248e30	1.71474	0.857369	−	0.514702i	$-0.172097\pi$
$181$	5.16248e30	1.71474	0.857369	+	0.514702i	$0.172097\pi$
$182$	0	0
$183$	−2.85700e30	−0.818128
$184$	−2.09231e29	−0.0556655
$185$	−1.78957e30	−0.442517
$186$	−1.40245e30	−0.322450
$187$	−1.66442e30	−0.355959
$188$	2.09615e29	0.0417150
$189$	0	0
$190$	1.23445e31	2.12961
$191$	−5.77134e30	−0.927526	−0.463763	−	0.885959i	$-0.653501\pi$
$191$	−5.77134e30	−0.927526	−0.463763	+	0.885959i	$0.653501\pi$
$192$	−5.78775e30	−0.866849
$193$	−2.85746e30	−0.398985	−0.199492	−	0.979899i	$-0.563929\pi$
$193$	−2.85746e30	−0.398985	−0.199492	+	0.979899i	$0.563929\pi$
$194$	1.07547e31	1.40047
$195$	6.15436e30	0.747679
$196$	0	0
$197$	1.69381e31	1.79296	0.896482	−	0.443081i	$-0.146115\pi$
$197$	1.69381e31	1.79296	0.896482	+	0.443081i	$0.146115\pi$
$198$	2.13242e30	0.210811
$199$	8.37737e30	0.773733	0.386866	−	0.922136i	$-0.373557\pi$
$199$	8.37737e30	0.773733	0.386866	+	0.922136i	$0.373557\pi$
$200$	−2.70344e31	−2.33352
$201$	−1.35134e31	−1.09048
$202$	−4.85402e30	−0.366318
$203$	0	0
$204$	1.32688e30	0.0876644
$205$	1.75694e31	1.08663
$206$	−7.32657e30	−0.424319
$207$	−3.74695e29	−0.0203272
$208$	−8.19606e30	−0.416630
$209$	1.66634e31	0.793940
$210$	0	0
$211$	−1.95424e31	−0.818776	−0.409388	−	0.912360i	$-0.634258\pi$
$211$	−1.95424e31	−0.818776	−0.409388	+	0.912360i	$0.634258\pi$
$212$	−4.07112e30	−0.160022
$213$	3.56818e31	1.31620
$214$	−3.35101e31	−1.16035
$215$	−5.81900e31	−1.89204
$216$	−3.80581e31	−1.16231
$217$	0	0
$218$	1.16453e31	0.314042
$219$	−1.70954e31	−0.433394
$220$	−8.45984e30	−0.201677
$221$	1.42478e31	0.319486
$222$	−8.26730e30	−0.174421
$223$	5.21969e30	0.103640	0.0518202	−	0.998656i	$-0.483498\pi$
$223$	5.21969e30	0.103640	0.0518202	+	0.998656i	$0.483498\pi$
$224$	0	0
$225$	−4.84136e31	−0.852124
$226$	−3.38572e31	−0.561290
$227$	1.42268e31	0.222208	0.111104	−	0.993809i	$-0.464561\pi$
$227$	1.42268e31	0.222208	0.111104	+	0.993809i	$0.464561\pi$
$228$	−1.32841e31	−0.195529
$229$	−4.79201e31	−0.664874	−0.332437	−	0.943126i	$-0.607871\pi$
$229$	−4.79201e31	−0.664874	−0.332437	+	0.943126i	$0.607871\pi$
$230$	−6.38152e30	−0.0834831
$231$	0	0
$232$	2.08922e31	0.243162
$233$	−1.09089e31	−0.119805	−0.0599025	−	0.998204i	$-0.519079\pi$
$233$	−1.09089e31	−0.119805	−0.0599025	+	0.998204i	$0.519079\pi$
$234$	−1.82540e31	−0.189210
$235$	4.02324e31	0.393695
$236$	2.77252e31	0.256190
$237$	−3.48922e31	−0.304527
$238$	0	0
$239$	1.93175e32	1.50515	0.752573	−	0.658509i	$-0.228813\pi$
$239$	1.93175e32	1.50515	0.752573	+	0.658509i	$0.228813\pi$
$240$	−1.46501e32	−1.07892
$241$	1.37107e32	0.954619	0.477310	−	0.878735i	$-0.341612\pi$
$241$	1.37107e32	0.954619	0.477310	+	0.878735i	$0.341612\pi$
$242$	−8.77604e31	−0.577818
$243$	−1.17152e32	−0.729567
$244$	−3.36183e31	−0.198068
$245$	0	0
$246$	8.11657e31	0.428301
$247$	−1.42642e32	−0.712590
$248$	−1.03850e32	−0.491258
$249$	2.16227e32	0.968767
$250$	−4.46199e32	−1.89382
$251$	−6.44860e31	−0.259341	−0.129670	−	0.991557i	$-0.541392\pi$
$251$	−6.44860e31	−0.259341	−0.129670	+	0.991557i	$0.541392\pi$
$252$	0	0
$253$	−8.61418e30	−0.0311234
$254$	−3.18812e32	−1.09214
$255$	2.54673e32	0.827353
$256$	−1.76955e32	−0.545284
$257$	1.37557e32	0.402147	0.201073	−	0.979576i	$-0.435557\pi$
$257$	1.37557e32	0.402147	0.201073	+	0.979576i	$0.435557\pi$
$258$	−2.68822e32	−0.745758
$259$	0	0
$260$	7.24182e31	0.181012
$261$	3.74140e31	0.0887948
$262$	4.09049e32	0.921951
$263$	−6.29327e31	−0.134733	−0.0673665	−	0.997728i	$-0.521460\pi$
$263$	−6.29327e31	−0.134733	−0.0673665	+	0.997728i	$0.521460\pi$
$264$	−2.45942e32	−0.500242
$265$	−7.81388e32	−1.51025
$266$	0	0
$267$	−3.72309e32	−0.650132
$268$	−1.59011e32	−0.264003
$269$	−7.34021e32	−1.15892	−0.579459	−	0.815001i	$-0.696736\pi$
$269$	−7.34021e32	−1.15892	−0.579459	+	0.815001i	$0.696736\pi$
$270$	−1.16077e33	−1.74315
$271$	−6.75590e32	−0.965156	−0.482578	−	0.875853i	$-0.660300\pi$
$271$	−6.75590e32	−0.965156	−0.482578	+	0.875853i	$0.660300\pi$
$272$	−3.39161e32	−0.461027
$273$	0	0
$274$	−1.10049e32	−0.135504
$275$	−1.11302e33	−1.30470
$276$	6.86724e30	0.00766496
$277$	−1.48766e33	−1.58134	−0.790671	−	0.612241i	$-0.790268\pi$
$277$	−1.48766e33	−1.58134	−0.790671	+	0.612241i	$0.790268\pi$
$278$	−1.48799e33	−1.50659
$279$	−1.85976e32	−0.179391
$280$	0	0
$281$	9.53617e32	0.835293	0.417646	−	0.908610i	$-0.362855\pi$
$281$	9.53617e32	0.835293	0.417646	+	0.908610i	$0.362855\pi$
$282$	1.85863e32	0.155178
$283$	1.55041e33	1.23404	0.617022	−	0.786946i	$-0.288339\pi$
$283$	1.55041e33	1.23404	0.617022	+	0.786946i	$0.288339\pi$
$284$	4.19867e32	0.318650
$285$	−2.54967e33	−1.84535
$286$	−4.19658e32	−0.289703
$287$	0	0
$288$	−2.31760e32	−0.145626
$289$	−1.07812e33	−0.646469
$290$	6.37208e32	0.364677
$291$	−2.22130e33	−1.21354
$292$	−2.01161e32	−0.104924
$293$	2.76230e33	1.37581	0.687903	−	0.725802i	$-0.258531\pi$
$293$	2.76230e33	1.37581	0.687903	+	0.725802i	$0.258531\pi$
$294$	0	0
$295$	5.32143e33	2.41786
$296$	−6.12187e32	−0.265734
$297$	−1.56687e33	−0.649863
$298$	1.08832e33	0.431355
$299$	7.37394e31	0.0279344
$300$	8.87303e32	0.321318
$301$	0	0
$302$	3.74522e33	1.23989
$303$	1.00257e33	0.317422
$304$	3.39552e33	1.02828
$305$	−6.45252e33	−1.86931
$306$	−7.55370e32	−0.209373
$307$	−4.04426e33	−1.07268	−0.536341	−	0.844001i	$-0.680194\pi$
$307$	−4.04426e33	−1.07268	−0.536341	+	0.844001i	$0.680194\pi$
$308$	0	0
$309$	1.51325e33	0.367682
$310$	−3.16741e33	−0.736753
$311$	2.20209e33	0.490423	0.245211	−	0.969470i	$-0.421143\pi$
$311$	2.20209e33	0.490423	0.245211	+	0.969470i	$0.421143\pi$
$312$	2.10532e33	0.448985
$313$	−1.52934e33	−0.312361	−0.156180	−	0.987729i	$-0.549918\pi$
$313$	−1.52934e33	−0.312361	−0.156180	+	0.987729i	$0.549918\pi$
$314$	6.84844e33	1.33980
$315$	0	0
$316$	−4.10576e32	−0.0737255
$317$	5.64949e33	0.972096	0.486048	−	0.873932i	$-0.338438\pi$
$317$	5.64949e33	0.972096	0.486048	+	0.873932i	$0.338438\pi$
$318$	−3.60980e33	−0.595273
$319$	8.60143e32	0.135955
$320$	−1.30716e34	−1.98063
$321$	6.92129e33	1.00547
$322$	0	0
$323$	−5.90268e33	−0.788525
$324$	6.72568e32	0.0861744
$325$	9.52773e33	1.17102
$326$	4.16067e33	0.490598
$327$	−2.40526e33	−0.272124
$328$	6.01026e33	0.652524
$329$	0	0
$330$	−7.50120e33	−0.750227
$331$	−1.79482e33	−0.172323	−0.0861616	−	0.996281i	$-0.527460\pi$
$331$	−1.79482e33	−0.172323	−0.0861616	+	0.996281i	$0.527460\pi$
$332$	2.54434e33	0.234537
$333$	−1.09631e33	−0.0970372
$334$	−7.27964e33	−0.618775
$335$	−3.05198e34	−2.49159
$336$	0	0
$337$	3.56328e33	0.268439	0.134220	−	0.990952i	$-0.457147\pi$
$337$	3.56328e33	0.268439	0.134220	+	0.990952i	$0.457147\pi$
$338$	−8.85005e33	−0.640575
$339$	6.99298e33	0.486370
$340$	2.99674e33	0.200301
$341$	−4.27557e33	−0.274669
$342$	7.56241e33	0.466990
$343$	0	0
$344$	−1.99060e34	−1.13618
$345$	1.31806e33	0.0723399
$346$	−1.25683e34	−0.663359
$347$	−2.88728e34	−1.46569	−0.732843	−	0.680398i	$-0.761807\pi$
$347$	−2.88728e34	−1.46569	−0.732843	+	0.680398i	$0.761807\pi$
$348$	−6.85708e32	−0.0334826
$349$	−1.78587e34	−0.838893	−0.419447	−	0.907780i	$-0.637776\pi$
$349$	−1.78587e34	−0.838893	−0.419447	+	0.907780i	$0.637776\pi$
$350$	0	0
$351$	1.34128e34	0.583276
$352$	−5.32812e33	−0.222971
$353$	−2.71254e34	−1.09249	−0.546245	−	0.837626i	$-0.683943\pi$
$353$	−2.71254e34	−1.09249	−0.546245	+	0.837626i	$0.683943\pi$
$354$	2.45835e34	0.953015
$355$	8.05870e34	3.00734
$356$	−4.38095e33	−0.157396
$357$	0	0
$358$	3.39126e34	1.12964
$359$	2.08159e34	0.667760	0.333880	−	0.942616i	$-0.391642\pi$
$359$	2.08159e34	0.667760	0.333880	+	0.942616i	$0.391642\pi$
$360$	−2.41610e34	−0.746503
$361$	2.54943e34	0.758744
$362$	5.38633e34	1.54428
$363$	1.81263e34	0.500692
$364$	0	0
$365$	−3.86097e34	−0.990246
$366$	−2.98088e34	−0.736801
$367$	−1.50702e34	−0.359028	−0.179514	−	0.983755i	$-0.557453\pi$
$367$	−1.50702e34	−0.359028	−0.179514	+	0.983755i	$0.557453\pi$
$368$	−1.75533e33	−0.0403100
$369$	1.07633e34	0.238280
$370$	−1.86716e34	−0.398528
$371$	0	0
$372$	3.40850e33	0.0676446
$373$	3.06644e34	0.586901	0.293451	−	0.955974i	$-0.405196\pi$
$373$	3.06644e34	0.586901	0.293451	+	0.955974i	$0.405196\pi$
$374$	−1.73658e34	−0.320575
$375$	9.21594e34	1.64103
$376$	1.37630e34	0.236416
$377$	−7.36303e33	−0.122025
$378$	0	0
$379$	−2.54352e34	−0.392470	−0.196235	−	0.980557i	$-0.562872\pi$
$379$	−2.54352e34	−0.392470	−0.196235	+	0.980557i	$0.562872\pi$
$380$	−3.00020e34	−0.446757
$381$	6.58485e34	0.946365
$382$	−6.02158e34	−0.835325
$383$	−2.05837e34	−0.275638	−0.137819	−	0.990457i	$-0.544009\pi$
$383$	−2.05837e34	−0.275638	−0.137819	+	0.990457i	$0.544009\pi$
$384$	−3.79047e34	−0.490029
$385$	0	0
$386$	−2.98136e34	−0.359323
$387$	−3.56480e34	−0.414894
$388$	−2.61380e34	−0.293795
$389$	6.64448e34	0.721342	0.360671	−	0.932693i	$-0.382548\pi$
$389$	6.64448e34	0.721342	0.360671	+	0.932693i	$0.382548\pi$
$390$	6.42121e34	0.673356
$391$	3.05141e33	0.0309111
$392$	0	0
$393$	−8.44864e34	−0.798891
$394$	1.76726e35	1.61473
$395$	−7.88037e34	−0.695802
$396$	−5.18262e33	−0.0442246
$397$	7.11637e34	0.586931	0.293465	−	0.955970i	$-0.405191\pi$
$397$	7.11637e34	0.586931	0.293465	+	0.955970i	$0.405191\pi$
$398$	8.74061e34	0.696819
$399$	0	0
$400$	−2.26802e35	−1.68981
$401$	7.78771e34	0.560997	0.280499	−	0.959854i	$-0.409500\pi$
$401$	7.78771e34	0.560997	0.280499	+	0.959854i	$0.409500\pi$
$402$	−1.40993e35	−0.982077
$403$	3.65999e34	0.246526
$404$	1.17972e34	0.0768475
$405$	1.29089e35	0.813292
$406$	0	0
$407$	−2.52041e34	−0.148575
$408$	8.71204e34	0.496830
$409$	3.21718e35	1.77505	0.887526	−	0.460758i	$-0.152422\pi$
$409$	3.21718e35	1.77505	0.887526	+	0.460758i	$0.152422\pi$
$410$	1.83312e35	0.978609
$411$	2.27299e34	0.117417
$412$	1.78064e34	0.0890153
$413$	0	0
$414$	−3.90941e33	−0.0183066
$415$	4.88347e35	2.21350
$416$	4.56100e34	0.200124
$417$	3.07335e35	1.30549
$418$	1.73859e35	0.715018
$419$	4.31477e35	1.71818	0.859089	−	0.511827i	$-0.171031\pi$
$419$	4.31477e35	1.71818	0.859089	+	0.511827i	$0.171031\pi$
$420$	0	0
$421$	5.01390e35	1.87227	0.936133	−	0.351647i	$-0.114378\pi$
$421$	5.01390e35	1.87227	0.936133	+	0.351647i	$0.114378\pi$
$422$	−2.03898e35	−0.737385
$423$	2.46470e34	0.0863313
$424$	−2.67303e35	−0.906910
$425$	3.94267e35	1.29580
$426$	3.72290e35	1.18536
$427$	0	0
$428$	8.14427e34	0.243423
$429$	8.66775e34	0.251034
$430$	−6.07131e35	−1.70396
$431$	1.64027e35	0.446141	0.223070	−	0.974802i	$-0.428392\pi$
$431$	1.64027e35	0.446141	0.223070	+	0.974802i	$0.428392\pi$
$432$	−3.19285e35	−0.841682
$433$	1.75800e33	0.00449193	0.00224596	−	0.999997i	$-0.499285\pi$
$433$	1.75800e33	0.00449193	0.00224596	+	0.999997i	$0.499285\pi$
$434$	0	0
$435$	−1.31611e35	−0.316000
$436$	−2.83027e34	−0.0658809
$437$	−3.05493e34	−0.0689449
$438$	−1.78366e35	−0.390312
$439$	3.72911e35	0.791287	0.395644	−	0.918404i	$-0.370522\pi$
$439$	3.72911e35	0.791287	0.395644	+	0.918404i	$0.370522\pi$
$440$	−5.55459e35	−1.14298
$441$	0	0
$442$	1.48656e35	0.287727
$443$	−5.23878e35	−0.983513	−0.491756	−	0.870733i	$-0.663645\pi$
$443$	−5.23878e35	−0.983513	−0.491756	+	0.870733i	$0.663645\pi$
$444$	2.00928e34	0.0365907
$445$	−8.40856e35	−1.48546
$446$	5.44602e34	0.0933380
$447$	−2.24784e35	−0.373779
$448$	0	0
$449$	6.50462e35	1.01835	0.509174	−	0.860664i	$-0.329951\pi$
$449$	6.50462e35	1.01835	0.509174	+	0.860664i	$0.329951\pi$
$450$	−5.05128e35	−0.767418
$451$	2.47446e35	0.364836
$452$	8.22863e34	0.117749
$453$	−7.73550e35	−1.07439
$454$	1.48437e35	0.200119
$455$	0	0
$456$	−8.72209e35	−1.10814
$457$	9.00061e35	1.11020	0.555102	−	0.831782i	$-0.312679\pi$
$457$	9.00061e35	1.11020	0.555102	+	0.831782i	$0.312679\pi$
$458$	−4.99979e35	−0.598781
$459$	5.55036e35	0.645431
$460$	1.55096e34	0.0175134
$461$	−3.94034e35	−0.432087	−0.216043	−	0.976384i	$-0.569315\pi$
$461$	−3.94034e35	−0.432087	−0.216043	+	0.976384i	$0.569315\pi$
$462$	0	0
$463$	−1.39468e36	−1.44255	−0.721276	−	0.692648i	$-0.756444\pi$
$463$	−1.39468e36	−1.44255	−0.721276	+	0.692648i	$0.756444\pi$
$464$	1.75273e35	0.176085
$465$	6.54209e35	0.638412
$466$	−1.13819e35	−0.107896
$467$	−2.87062e35	−0.264361	−0.132180	−	0.991226i	$-0.542198\pi$
$467$	−2.87062e35	−0.264361	−0.132180	+	0.991226i	$0.542198\pi$
$468$	4.43645e34	0.0396932
$469$	0	0
$470$	4.19769e35	0.354559
$471$	−1.41450e36	−1.16097
$472$	1.82039e36	1.45194
$473$	−8.19544e35	−0.635253
$474$	−3.64051e35	−0.274255
$475$	−3.94722e36	−2.89020
$476$	0	0
$477$	−4.78690e35	−0.331174
$478$	2.01551e36	1.35553
$479$	−8.28285e35	−0.541565	−0.270782	−	0.962641i	$-0.587282\pi$
$479$	−8.28285e35	−0.541565	−0.270782	+	0.962641i	$0.587282\pi$
$480$	8.15259e35	0.518250
$481$	2.15753e35	0.133352
$482$	1.43052e36	0.859725
$483$	0	0
$484$	2.13292e35	0.121217
$485$	−5.01679e36	−2.77276
$486$	−1.22232e36	−0.657044
$487$	−1.69732e36	−0.887405	−0.443702	−	0.896174i	$-0.646335\pi$
$487$	−1.69732e36	−0.887405	−0.443702	+	0.896174i	$0.646335\pi$
$488$	−2.20732e36	−1.12253
$489$	−8.59360e35	−0.425114
$490$	0	0
$491$	2.68983e36	1.25929	0.629645	−	0.776883i	$-0.283201\pi$
$491$	2.68983e36	1.25929	0.629645	+	0.776883i	$0.283201\pi$
$492$	−1.97265e35	−0.0898505
$493$	−3.04690e35	−0.135028
$494$	−1.48827e36	−0.641754
$495$	−9.94724e35	−0.417381
$496$	−8.71242e35	−0.355743
$497$	0	0
$498$	2.25603e36	0.872466
$499$	−4.36140e35	−0.164160	−0.0820802	−	0.996626i	$-0.526156\pi$
$499$	−4.36140e35	−0.164160	−0.0820802	+	0.996626i	$0.526156\pi$
$500$	1.08444e36	0.397292
$501$	1.50356e36	0.536182
$502$	−6.72821e35	−0.233561
$503$	2.16228e36	0.730708	0.365354	−	0.930869i	$-0.380948\pi$
$503$	2.16228e36	0.730708	0.365354	+	0.930869i	$0.380948\pi$
$504$	0	0
$505$	2.26429e36	0.725267
$506$	−8.98769e34	−0.0280295
$507$	1.82792e36	0.555072
$508$	7.74839e35	0.229114
$509$	−4.49619e36	−1.29466	−0.647328	−	0.762211i	$-0.724114\pi$
$509$	−4.49619e36	−1.29466	−0.647328	+	0.762211i	$0.724114\pi$
$510$	2.65716e36	0.745110
$511$	0	0
$512$	−4.20707e36	−1.11901
$513$	−5.55676e36	−1.43958
$514$	1.43521e36	0.362171
$515$	3.41767e36	0.840103
$516$	6.53342e35	0.156448
$517$	5.66630e35	0.132184
$518$	0	0
$519$	2.59590e36	0.574815
$520$	4.75486e36	1.02587
$521$	−9.12580e35	−0.191850	−0.0959250	−	0.995389i	$-0.530581\pi$
$521$	−9.12580e35	−0.191850	−0.0959250	+	0.995389i	$0.530581\pi$
$522$	3.90363e35	0.0799681
$523$	−1.44280e35	−0.0288027	−0.0144013	−	0.999896i	$-0.504584\pi$
$523$	−1.44280e35	−0.0288027	−0.0144013	+	0.999896i	$0.504584\pi$
$524$	−9.94150e35	−0.193410
$525$	0	0
$526$	−6.56615e35	−0.121340
$527$	1.51454e36	0.272796
$528$	−2.06331e36	−0.362249
$529$	−5.82742e36	−0.997297
$530$	−8.15269e36	−1.36012
$531$	3.25998e36	0.530199
$532$	0	0
$533$	−2.11820e36	−0.327453
$534$	−3.88452e36	−0.585505
$535$	1.56317e37	2.29736
$536$	−1.04404e37	−1.49621
$537$	−7.00443e36	−0.978858
$538$	−7.65848e36	−1.04371
$539$	0	0
$540$	2.82112e36	0.365683
$541$	6.50406e36	0.822284	0.411142	−	0.911571i	$-0.365130\pi$
$541$	6.50406e36	0.822284	0.411142	+	0.911571i	$0.365130\pi$
$542$	−7.04883e36	−0.869214
$543$	−1.11251e37	−1.33815
$544$	1.88739e36	0.221450
$545$	−5.43226e36	−0.621767
$546$	0	0
$547$	1.22652e37	1.33612	0.668058	−	0.744109i	$-0.267126\pi$
$547$	1.22652e37	1.33612	0.668058	+	0.744109i	$0.267126\pi$
$548$	2.67462e35	0.0284266
$549$	−3.95291e36	−0.409911
$550$	−1.16128e37	−1.17501
$551$	3.05041e36	0.301170
$552$	4.50891e35	0.0434405
$553$	0	0
$554$	−1.55216e37	−1.42415
$555$	3.85650e36	0.345333
$556$	3.61640e36	0.316058
$557$	1.32843e37	1.13317	0.566585	−	0.824003i	$-0.308264\pi$
$557$	1.32843e37	1.13317	0.566585	+	0.824003i	$0.308264\pi$
$558$	−1.94040e36	−0.161559
$559$	7.01549e36	0.570162
$560$	0	0
$561$	3.58680e36	0.277785
$562$	9.94966e36	0.752260
$563$	1.08601e37	0.801624	0.400812	−	0.916160i	$-0.368728\pi$
$563$	1.08601e37	0.801624	0.400812	+	0.916160i	$0.368728\pi$
$564$	−4.51719e35	−0.0325537
$565$	1.57936e37	1.11129
$566$	1.61764e37	1.11137
$567$	0	0
$568$	2.75678e37	1.80592
$569$	−1.31614e37	−0.841948	−0.420974	−	0.907073i	$-0.638312\pi$
$569$	−1.31614e37	−0.841948	−0.420974	+	0.907073i	$0.638312\pi$
$570$	−2.66023e37	−1.66191
$571$	3.26297e37	1.99079	0.995395	−	0.0958616i	$-0.0305606\pi$
$571$	3.26297e37	1.99079	0.995395	+	0.0958616i	$0.0305606\pi$
$572$	1.01993e36	0.0607750
$573$	1.24372e37	0.723827
$574$	0	0
$575$	2.04053e36	0.113299
$576$	−8.00784e36	−0.434322
$577$	3.67195e36	0.194547	0.0972733	−	0.995258i	$-0.468988\pi$
$577$	3.67195e36	0.194547	0.0972733	+	0.995258i	$0.468988\pi$
$578$	−1.12487e37	−0.582206
$579$	6.15780e36	0.311361
$580$	−1.54867e36	−0.0765033
$581$	0	0
$582$	−2.31762e37	−1.09290
$583$	−1.10050e37	−0.507067
$584$	−1.32079e37	−0.594648
$585$	8.51507e36	0.374614
$586$	2.88207e37	1.23904
$587$	9.27744e36	0.389775	0.194888	−	0.980826i	$-0.437566\pi$
$587$	9.27744e36	0.389775	0.194888	+	0.980826i	$0.437566\pi$
$588$	0	0
$589$	−1.51629e37	−0.608451
$590$	5.55216e37	2.17751
$591$	−3.65015e37	−1.39920
$592$	−5.13589e36	−0.192430
$593$	5.24575e36	0.192119	0.0960593	−	0.995376i	$-0.469376\pi$
$593$	5.24575e36	0.192119	0.0960593	+	0.995376i	$0.469376\pi$
$594$	−1.63481e37	−0.585263
$595$	0	0
$596$	−2.64504e36	−0.0904913
$597$	−1.80531e37	−0.603809
$598$	7.69368e35	0.0251575
$599$	4.76000e37	1.52176	0.760878	−	0.648894i	$-0.224768\pi$
$599$	4.76000e37	1.52176	0.760878	+	0.648894i	$0.224768\pi$
$600$	5.82588e37	1.82104
$601$	−1.70669e37	−0.521613	−0.260807	−	0.965391i	$-0.583988\pi$
$601$	−1.70669e37	−0.521613	−0.260807	+	0.965391i	$0.583988\pi$
$602$	0	0
$603$	−1.86969e37	−0.546368
$604$	−9.10235e36	−0.260109
$605$	4.09381e37	1.14401
$606$	1.04604e37	0.285869
$607$	−1.00572e37	−0.268800	−0.134400	−	0.990927i	$-0.542911\pi$
$607$	−1.00572e37	−0.268800	−0.134400	+	0.990927i	$0.542911\pi$
$608$	−1.88956e37	−0.493928
$609$	0	0
$610$	−6.73230e37	−1.68349
$611$	−4.85049e36	−0.118640
$612$	1.83585e36	0.0439230
$613$	5.68669e37	1.33089	0.665447	−	0.746445i	$-0.268241\pi$
$613$	5.68669e37	1.33089	0.665447	+	0.746445i	$0.268241\pi$
$614$	−4.21962e37	−0.966052
$615$	−3.78619e37	−0.847985
$616$	0	0
$617$	−4.13930e37	−0.887315	−0.443657	−	0.896196i	$-0.646319\pi$
$617$	−4.13930e37	−0.887315	−0.443657	+	0.896196i	$0.646319\pi$
$618$	1.57887e37	0.331132
$619$	3.55328e37	0.729131	0.364565	−	0.931178i	$-0.381218\pi$
$619$	3.55328e37	0.729131	0.364565	+	0.931178i	$0.381218\pi$
$620$	7.69806e36	0.154559
$621$	2.87259e36	0.0564334
$622$	2.29758e37	0.441672
$623$	0	0
$624$	1.76624e37	0.325131
$625$	8.71634e37	1.57020
$626$	−1.59566e37	−0.281310
$627$	−3.59094e37	−0.619578
$628$	−1.66444e37	−0.281069
$629$	8.92809e36	0.147562
$630$	0	0
$631$	−7.29607e37	−1.15529	−0.577647	−	0.816287i	$-0.696029\pi$
$631$	−7.29607e37	−1.15529	−0.577647	+	0.816287i	$0.696029\pi$
$632$	−2.69577e37	−0.417833
$633$	4.21138e37	0.638960
$634$	5.89445e37	0.875464
$635$	1.48718e38	2.16232
$636$	8.77322e36	0.124879
$637$	0	0
$638$	8.97439e36	0.122441
$639$	4.93688e37	0.659464
$640$	−8.56075e37	−1.11965
$641$	1.83496e37	0.234987	0.117494	−	0.993074i	$-0.462514\pi$
$641$	1.83496e37	0.234987	0.117494	+	0.993074i	$0.462514\pi$
$642$	7.22140e37	0.905520
$643$	−5.85846e37	−0.719342	−0.359671	−	0.933079i	$-0.617111\pi$
$643$	−5.85846e37	−0.719342	−0.359671	+	0.933079i	$0.617111\pi$
$644$	0	0
$645$	1.25399e38	1.47651
$646$	−6.15862e37	−0.710141
$647$	−1.39594e38	−1.57637	−0.788187	−	0.615435i	$-0.788980\pi$
$647$	−1.39594e38	−1.57637	−0.788187	+	0.615435i	$0.788980\pi$
$648$	4.41596e37	0.488386
$649$	7.49466e37	0.811799
$650$	9.94085e37	1.05461
$651$	0	0
$652$	−1.01121e37	−0.102920
$653$	−8.62301e37	−0.859668	−0.429834	−	0.902908i	$-0.641428\pi$
$653$	−8.62301e37	−0.859668	−0.429834	+	0.902908i	$0.641428\pi$
$654$	−2.50955e37	−0.245074
$655$	−1.90812e38	−1.82536
$656$	5.04226e37	0.472523
$657$	−2.36529e37	−0.217146
$658$	0	0
$659$	1.30986e38	1.15418	0.577089	−	0.816681i	$-0.304189\pi$
$659$	1.30986e38	1.15418	0.577089	+	0.816681i	$0.304189\pi$
$660$	1.82309e37	0.157385
$661$	−1.01882e38	−0.861740	−0.430870	−	0.902414i	$-0.641793\pi$
$661$	−1.01882e38	−0.861740	−0.430870	+	0.902414i	$0.641793\pi$
$662$	−1.87265e37	−0.155193
$663$	−3.07039e37	−0.249322
$664$	1.67057e38	1.32922
$665$	0	0
$666$	−1.14385e37	−0.0873911
$667$	−1.57692e36	−0.0118062
$668$	1.76924e37	0.129809
$669$	−1.12484e37	−0.0808794
$670$	−3.18431e38	−2.24391
$671$	−9.08768e37	−0.627623
$672$	0	0
$673$	2.29828e36	0.0152476	0.00762378	−	0.999971i	$-0.497573\pi$
$673$	2.29828e36	0.0152476	0.00762378	+	0.999971i	$0.497573\pi$
$674$	3.71778e37	0.241755
$675$	3.71161e38	2.36571
$676$	2.15091e37	0.134382
$677$	−1.56923e37	−0.0961033	−0.0480516	−	0.998845i	$-0.515301\pi$
$677$	−1.56923e37	−0.0961033	−0.0480516	+	0.998845i	$0.515301\pi$
$678$	7.29619e37	0.438022
$679$	0	0
$680$	1.96761e38	1.13519
$681$	−3.06587e37	−0.173408
$682$	−4.46096e37	−0.247366
$683$	−1.85515e38	−1.00856	−0.504278	−	0.863542i	$-0.668241\pi$
$683$	−1.85515e38	−1.00856	−0.504278	+	0.863542i	$0.668241\pi$
$684$	−1.83796e37	−0.0979669
$685$	5.13352e37	0.268283
$686$	0	0
$687$	1.03267e38	0.518857
$688$	−1.67000e38	−0.822759
$689$	9.42055e37	0.455111
$690$	1.37521e37	0.0651489
$691$	−1.36613e38	−0.634655	−0.317328	−	0.948316i	$-0.602785\pi$
$691$	−1.36613e38	−0.634655	−0.317328	+	0.948316i	$0.602785\pi$
$692$	3.05459e37	0.139162
$693$	0	0
$694$	−3.01247e38	−1.31999
$695$	6.94113e38	2.98288
$696$	−4.50224e37	−0.189760
$697$	−8.76531e37	−0.362347
$698$	−1.86331e38	−0.755502
$699$	2.35085e37	0.0934940
$700$	0	0
$701$	−2.20458e38	−0.843594	−0.421797	−	0.906690i	$-0.638601\pi$
$701$	−2.20458e38	−0.843594	−0.421797	+	0.906690i	$0.638601\pi$
$702$	1.39944e38	0.525295
$703$	−8.93839e37	−0.329126
$704$	−1.84099e38	−0.664999
$705$	−8.67005e37	−0.307233
$706$	−2.83015e38	−0.983889
$707$	0	0
$708$	−5.97476e37	−0.199927
$709$	−5.82758e38	−1.91322	−0.956608	−	0.291376i	$-0.905887\pi$
$709$	−5.82758e38	−1.91322	−0.956608	+	0.291376i	$0.905887\pi$
$710$	8.40813e38	2.70839
$711$	−4.82763e37	−0.152579
$712$	−2.87646e38	−0.892027
$713$	7.83851e36	0.0238520
$714$	0	0
$715$	1.95760e38	0.573579
$716$	−8.24210e37	−0.236980
$717$	−4.16290e38	−1.17459
$718$	2.17185e38	0.601381
$719$	−2.83019e38	−0.769089	−0.384544	−	0.923107i	$-0.625641\pi$
$719$	−2.83019e38	−0.769089	−0.384544	+	0.923107i	$0.625641\pi$
$720$	−2.02697e38	−0.540578
$721$	0	0
$722$	2.65997e38	0.683321
$723$	−2.95465e38	−0.744970
$724$	−1.30909e38	−0.323965
$725$	−2.03751e38	−0.494921
$726$	1.89123e38	0.450920
$727$	2.87575e38	0.673032	0.336516	−	0.941678i	$-0.390751\pi$
$727$	2.87575e38	0.673032	0.336516	+	0.941678i	$0.390751\pi$
$728$	0	0
$729$	4.54717e38	1.02546
$730$	−4.02839e38	−0.891810
$731$	2.90308e38	0.630920
$732$	7.24472e37	0.154569
$733$	−6.09181e38	−1.27598	−0.637989	−	0.770046i	$-0.720233\pi$
$733$	−6.09181e38	−1.27598	−0.637989	+	0.770046i	$0.720233\pi$
$734$	−1.57237e38	−0.323339
$735$	0	0
$736$	9.76816e36	0.0193625
$737$	−4.29838e38	−0.836554
$738$	1.12300e38	0.214594
$739$	5.52340e38	1.03635	0.518175	−	0.855275i	$-0.326612\pi$
$739$	5.52340e38	1.03635	0.518175	+	0.855275i	$0.326612\pi$
$740$	4.53794e37	0.0836047
$741$	3.07393e38	0.556094
$742$	0	0
$743$	−4.68741e38	−0.817680	−0.408840	−	0.912606i	$-0.634067\pi$
$743$	−4.68741e38	−0.817680	−0.408840	+	0.912606i	$0.634067\pi$
$744$	2.23796e38	0.383370
$745$	−5.07674e38	−0.854033
$746$	3.19940e38	0.528560
$747$	2.99169e38	0.485387
$748$	4.22058e37	0.0672513
$749$	0	0
$750$	9.61555e38	1.47791
$751$	−7.49018e38	−1.13071	−0.565357	−	0.824846i	$-0.691262\pi$
$751$	−7.49018e38	−1.13071	−0.565357	+	0.824846i	$0.691262\pi$
$752$	1.15463e38	0.171200
$753$	1.38967e38	0.202385
$754$	−7.68229e37	−0.109895
$755$	−1.74706e39	−2.45484
$756$	0	0
$757$	−2.19892e38	−0.298137	−0.149068	−	0.988827i	$-0.547627\pi$
$757$	−2.19892e38	−0.298137	−0.149068	+	0.988827i	$0.547627\pi$
$758$	−2.65381e38	−0.353456
$759$	1.85635e37	0.0242882
$760$	−1.96988e39	−2.53195
$761$	−4.67111e38	−0.589830	−0.294915	−	0.955523i	$-0.595291\pi$
$761$	−4.67111e38	−0.589830	−0.294915	+	0.955523i	$0.595291\pi$
$762$	6.87037e38	0.852291
$763$	0	0
$764$	1.46348e38	0.175237
$765$	3.52362e38	0.414534
$766$	−2.14762e38	−0.248238
$767$	−6.41560e38	−0.728618
$768$	3.81336e38	0.425531
$769$	−9.38023e37	−0.102851	−0.0514254	−	0.998677i	$-0.516376\pi$
$769$	−9.38023e37	−0.102851	−0.0514254	+	0.998677i	$0.516376\pi$
$770$	0	0
$771$	−2.96433e38	−0.313829
$772$	7.24587e37	0.0753802
$773$	−1.06611e39	−1.08988	−0.544942	−	0.838474i	$-0.683448\pi$
$773$	−1.06611e39	−1.08988	−0.544942	+	0.838474i	$0.683448\pi$
$774$	−3.71937e38	−0.373652
$775$	1.01280e39	0.999885
$776$	−1.71618e39	−1.66506
$777$	0	0
$778$	6.93258e38	0.649637
$779$	8.77542e38	0.808188
$780$	−1.56061e38	−0.141259
$781$	1.13498e39	1.00972
$782$	3.18372e37	0.0278384
$783$	−2.86834e38	−0.246517
$784$	0	0
$785$	−3.19463e39	−2.65266
$786$	−8.81497e38	−0.719476
$787$	1.52283e39	1.22177	0.610887	−	0.791718i	$-0.290813\pi$
$787$	1.52283e39	1.22177	0.610887	+	0.791718i	$0.290813\pi$
$788$	−4.29513e38	−0.338744
$789$	1.35619e38	0.105143
$790$	−8.22206e38	−0.626635
$791$	0	0
$792$	−3.40282e38	−0.250639
$793$	7.77927e38	0.563314
$794$	7.42494e38	0.528586
$795$	1.68388e39	1.17857
$796$	−2.12431e38	−0.146181
$797$	2.14824e39	1.45343	0.726717	−	0.686937i	$-0.241045\pi$
$797$	2.14824e39	1.45343	0.726717	+	0.686937i	$0.241045\pi$
$798$	0	0
$799$	−2.00718e38	−0.131282
$800$	1.26213e39	0.811685
$801$	−5.15121e38	−0.325739
$802$	8.12538e38	0.505231
$803$	−5.43777e38	−0.332476
$804$	3.42668e38	0.206024
$805$	0	0
$806$	3.81869e38	0.222020
$807$	1.58181e39	0.904401
$808$	7.74583e38	0.435526
$809$	−1.44847e39	−0.800949	−0.400474	−	0.916308i	$-0.631155\pi$
$809$	−1.44847e39	−0.800949	−0.400474	+	0.916308i	$0.631155\pi$
$810$	1.34686e39	0.732446
$811$	4.08234e38	0.218337	0.109169	−	0.994023i	$-0.465181\pi$
$811$	4.08234e38	0.218337	0.109169	+	0.994023i	$0.465181\pi$
$812$	0	0
$813$	1.45589e39	0.753193
$814$	−2.62970e38	−0.133806
$815$	−1.94086e39	−0.971328
$816$	7.30889e38	0.359778
$817$	−2.90643e39	−1.40722
$818$	3.35668e39	1.59860
$819$	0	0
$820$	−4.45520e38	−0.205296
$821$	−2.94462e39	−1.33474	−0.667371	−	0.744726i	$-0.732580\pi$
$821$	−2.94462e39	−1.33474	−0.667371	+	0.744726i	$0.732580\pi$
$822$	2.37154e38	0.105745
$823$	−1.81936e39	−0.798032	−0.399016	−	0.916944i	$-0.630648\pi$
$823$	−1.81936e39	−0.798032	−0.399016	+	0.916944i	$0.630648\pi$
$824$	1.16914e39	0.504486
$825$	2.39855e39	1.01817
$826$	0	0
$827$	2.52233e39	1.03628	0.518141	−	0.855295i	$-0.326624\pi$
$827$	2.52233e39	1.03628	0.518141	+	0.855295i	$0.326624\pi$
$828$	9.50141e36	0.00384042
$829$	−1.02531e39	−0.407726	−0.203863	−	0.978999i	$-0.565350\pi$
$829$	−1.02531e39	−0.407726	−0.203863	+	0.978999i	$0.565350\pi$
$830$	5.09522e39	1.99346
$831$	3.20589e39	1.23405
$832$	1.57593e39	0.596861
$833$	0	0
$834$	3.20661e39	1.17572
$835$	3.39578e39	1.22510
$836$	−4.22545e38	−0.149999
$837$	1.42578e39	0.498035
$838$	4.50185e39	1.54738
$839$	1.22528e39	0.414429	0.207214	−	0.978296i	$-0.433560\pi$
$839$	1.22528e39	0.414429	0.207214	+	0.978296i	$0.433560\pi$
$840$	0	0
$841$	−2.89568e39	−0.948427
$842$	5.23130e39	1.68615
$843$	−2.05504e39	−0.651849
$844$	4.95552e38	0.154691
$845$	4.12834e39	1.26826
$846$	2.57156e38	0.0777495
$847$	0	0
$848$	−2.24251e39	−0.656736
$849$	−3.34112e39	−0.963028
$850$	4.11362e39	1.16699
$851$	4.62073e37	0.0129021
$852$	−9.04810e38	−0.248670
$853$	−2.17452e39	−0.588235	−0.294117	−	0.955769i	$-0.595026\pi$
$853$	−2.17452e39	−0.588235	−0.294117	+	0.955769i	$0.595026\pi$
$854$	0	0
$855$	−3.52769e39	−0.924586
$856$	5.34739e39	1.37958
$857$	−4.29564e39	−1.09091	−0.545453	−	0.838142i	$-0.683642\pi$
$857$	−4.29564e39	−1.09091	−0.545453	+	0.838142i	$0.683642\pi$
$858$	9.04358e38	0.226080
$859$	1.62483e39	0.399853	0.199927	−	0.979811i	$-0.435930\pi$
$859$	1.62483e39	0.399853	0.199927	+	0.979811i	$0.435930\pi$
$860$	1.47557e39	0.357462
$861$	0	0
$862$	1.71139e39	0.401792
$863$	3.68820e39	0.852450	0.426225	−	0.904617i	$-0.359843\pi$
$863$	3.68820e39	0.852450	0.426225	+	0.904617i	$0.359843\pi$
$864$	1.77678e39	0.404294
$865$	5.86281e39	1.31337
$866$	1.83423e37	0.00404541
$867$	2.32335e39	0.504494
$868$	0	0
$869$	−1.10987e39	−0.233616
$870$	−1.37318e39	−0.284588
$871$	3.67952e39	0.750838
$872$	−1.85830e39	−0.373374
$873$	−3.07336e39	−0.608024
$874$	−3.18739e38	−0.0620913
$875$	0	0
$876$	4.33500e38	0.0818811
$877$	−5.53156e39	−1.02885	−0.514426	−	0.857535i	$-0.671995\pi$
$877$	−5.53156e39	−1.02885	−0.514426	+	0.857535i	$0.671995\pi$
$878$	3.89080e39	0.712629
$879$	−5.95272e39	−1.07366
$880$	−4.65997e39	−0.827689
$881$	−9.22430e39	−1.61346	−0.806731	−	0.590919i	$-0.798765\pi$
$881$	−9.22430e39	−1.61346	−0.806731	+	0.590919i	$0.798765\pi$
$882$	0	0
$883$	−7.47767e39	−1.26852	−0.634259	−	0.773120i	$-0.718695\pi$
$883$	−7.47767e39	−1.26852	−0.634259	+	0.773120i	$0.718695\pi$
$884$	−3.61292e38	−0.0603605
$885$	−1.14676e40	−1.88686
$886$	−5.46593e39	−0.885746
$887$	3.52542e39	0.562655	0.281328	−	0.959612i	$-0.409225\pi$
$887$	3.52542e39	0.562655	0.281328	+	0.959612i	$0.409225\pi$
$888$	1.31926e39	0.207374
$889$	0	0
$890$	−8.77315e39	−1.33780
$891$	1.81808e39	0.273064
$892$	−1.32360e38	−0.0195808
$893$	2.00950e39	0.292814
$894$	−2.34531e39	−0.336623
$895$	−1.58194e40	−2.23656
$896$	0	0
$897$	−1.58908e38	−0.0217995
$898$	6.78666e39	0.917118
$899$	−7.82691e38	−0.104192
$900$	1.22766e39	0.160992
$901$	3.89832e39	0.503608
$902$	2.58175e39	0.328569
$903$	0	0
$904$	5.40278e39	0.667334
$905$	−2.51259e40	−3.05750
$906$	−8.07091e39	−0.967591
$907$	−1.16020e40	−1.37036	−0.685180	−	0.728374i	$-0.740276\pi$
$907$	−1.16020e40	−1.37036	−0.685180	+	0.728374i	$0.740276\pi$
$908$	−3.60761e38	−0.0419817
$909$	1.38713e39	0.159040
$910$	0	0
$911$	1.03198e40	1.14861	0.574306	−	0.818640i	$-0.305272\pi$
$911$	1.03198e40	1.14861	0.574306	+	0.818640i	$0.305272\pi$
$912$	−7.31732e39	−0.802457
$913$	6.87785e39	0.743185
$914$	9.39087e39	0.999844
$915$	1.39051e40	1.45878
$916$	1.21515e39	0.125615
$917$	0	0
$918$	5.79102e39	0.581271
$919$	1.74754e40	1.72850	0.864248	−	0.503067i	$-0.167795\pi$
$919$	1.74754e40	1.72850	0.864248	+	0.503067i	$0.167795\pi$
$920$	1.01833e39	0.0992555
$921$	8.71535e39	0.837104
$922$	−4.11119e39	−0.389135
$923$	−9.71572e39	−0.906258
$924$	0	0
$925$	5.97035e39	0.540862
$926$	−1.45515e40	−1.29915
$927$	2.09371e39	0.184222
$928$	−9.75371e38	−0.0845809
$929$	−8.87284e39	−0.758316	−0.379158	−	0.925332i	$-0.623786\pi$
$929$	−8.87284e39	−0.758316	−0.379158	+	0.925332i	$0.623786\pi$
$930$	6.82575e39	0.574951
$931$	0	0
$932$	2.76624e38	0.0226348
$933$	−4.74549e39	−0.382718
$934$	−2.99508e39	−0.238082
$935$	8.10076e39	0.634701
$936$	2.91289e39	0.224958
$937$	1.64530e39	0.125245	0.0626226	−	0.998037i	$-0.480054\pi$
$937$	1.64530e39	0.125245	0.0626226	+	0.998037i	$0.480054\pi$
$938$	0	0
$939$	3.29572e39	0.243761
$940$	−1.02020e39	−0.0743808
$941$	7.97642e38	0.0573255	0.0286628	−	0.999589i	$-0.490875\pi$
$941$	7.97642e38	0.0573255	0.0286628	+	0.999589i	$0.490875\pi$
$942$	−1.47583e40	−1.04556
$943$	−4.53648e38	−0.0316819
$944$	1.52720e40	1.05141
$945$	0	0
$946$	−8.55079e39	−0.572105
$947$	1.60271e40	1.05713	0.528566	−	0.848892i	$-0.322730\pi$
$947$	1.60271e40	1.05713	0.528566	+	0.848892i	$0.322730\pi$
$948$	8.84787e38	0.0575342
$949$	4.65486e39	0.298410
$950$	−4.11837e40	−2.60289
$951$	−1.21746e40	−0.758608
$952$	0	0
$953$	−8.74550e39	−0.529701	−0.264850	−	0.964290i	$-0.585323\pi$
$953$	−8.74550e39	−0.529701	−0.264850	+	0.964290i	$0.585323\pi$
$954$	−4.99446e39	−0.298253
$955$	2.80893e40	1.65384
$956$	−4.89847e39	−0.284367
$957$	−1.85360e39	−0.106098
$958$	−8.64200e39	−0.487730
$959$	0	0
$960$	2.81691e40	1.54565
$961$	−1.45921e40	−0.789502
$962$	2.25108e39	0.120096
$963$	9.57619e39	0.503776
$964$	−3.47673e39	−0.180356
$965$	1.39073e40	0.711419
$966$	0	0
$967$	1.60838e40	0.800075	0.400038	−	0.916499i	$-0.368997\pi$
$967$	1.60838e40	0.800075	0.400038	+	0.916499i	$0.368997\pi$
$968$	1.40044e40	0.686985
$969$	1.27202e40	0.615352
$970$	−5.23432e40	−2.49713
$971$	−1.28013e40	−0.602276	−0.301138	−	0.953581i	$-0.597367\pi$
$971$	−1.28013e40	−0.602276	−0.301138	+	0.953581i	$0.597367\pi$
$972$	2.97071e39	0.137837
$973$	0	0
$974$	−1.77091e40	−0.799192
$975$	−2.05322e40	−0.913845
$976$	−1.85181e40	−0.812877
$977$	−1.68476e40	−0.729392	−0.364696	−	0.931127i	$-0.618827\pi$
$977$	−1.68476e40	−0.729392	−0.364696	+	0.931127i	$0.618827\pi$
$978$	−8.96622e39	−0.382855
$979$	−1.18426e40	−0.498746
$980$	0	0
$981$	−3.32788e39	−0.136344
$982$	2.80647e40	1.13411
$983$	3.82928e40	1.52632	0.763159	−	0.646211i	$-0.223647\pi$
$983$	3.82928e40	1.52632	0.763159	+	0.646211i	$0.223647\pi$
$984$	−1.29521e40	−0.509219
$985$	−8.24383e40	−3.19698
$986$	−3.17901e39	−0.121606
$987$	0	0
$988$	3.61709e39	0.134630
$989$	1.50249e39	0.0551647
$990$	−1.03785e40	−0.375891
$991$	1.66034e40	0.593201	0.296600	−	0.955002i	$-0.404147\pi$
$991$	1.66034e40	0.593201	0.296600	+	0.955002i	$0.404147\pi$
$992$	4.84835e39	0.170878
$993$	3.86783e39	0.134478
$994$	0	0
$995$	−4.07729e40	−1.37962
$996$	−5.48304e39	−0.183029
$997$	4.81089e39	0.158431	0.0792156	−	0.996858i	$-0.474758\pi$
$997$	4.81089e39	0.158431	0.0792156	+	0.996858i	$0.474758\pi$
$998$	−4.55051e39	−0.147842
$999$	8.40486e39	0.269399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.28.a.b.1.2		2
7.6	odd	2		1.28.a.a.1.2	✓	2
21.20	even	2		9.28.a.d.1.1		2
28.27	even	2		16.28.a.d.1.1		2
35.13	even	4		25.28.b.a.24.2		4
35.27	even	4		25.28.b.a.24.3		4
35.34	odd	2		25.28.a.a.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.28.a.a.1.2	✓	2	7.6	odd	2
9.28.a.d.1.1		2	21.20	even	2
16.28.a.d.1.1		2	28.27	even	2
25.28.a.a.1.1		2	35.34	odd	2
25.28.b.a.24.2		4	35.13	even	4
25.28.b.a.24.3		4	35.27	even	4
49.28.a.b.1.2		2	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q+10433.6 q^{2} -2.15499e6 q^{3} -2.53577e7 q^{4} -4.86703e9 q^{5} -2.24843e10 q^{6} -1.66495e12 q^{8} -2.98161e12 q^{9} +O(q^{10})\)	\(q+10433.6 q^{2} -2.15499e6 q^{3} -2.53577e7 q^{4} -4.86703e9 q^{5} -2.24843e10 q^{6} -1.66495e12 q^{8} -2.98161e12 q^{9} -5.07806e13 q^{10} -6.85469e13 q^{11} +5.46457e13 q^{12} +5.86777e14 q^{13} +1.04884e16 q^{15} -1.39679e16 q^{16} +2.42814e16 q^{17} -3.11089e16 q^{18} -2.43094e17 q^{19} +1.23417e17 q^{20} -7.15190e17 q^{22} +1.25668e17 q^{23} +3.58794e18 q^{24} +1.62374e19 q^{25} +6.12220e18 q^{26} +2.28584e19 q^{27} -1.25483e19 q^{29} +1.09432e20 q^{30} +6.23745e19 q^{31} +7.77296e19 q^{32} +1.47718e20 q^{33} +2.53343e20 q^{34} +7.56070e19 q^{36} +3.67692e20 q^{37} -2.53635e21 q^{38} -1.26450e21 q^{39} +8.10334e21 q^{40} -3.60988e21 q^{41} +1.19560e22 q^{43} +1.73819e21 q^{44} +1.45116e22 q^{45} +1.31117e21 q^{46} -8.26632e21 q^{47} +3.01007e22 q^{48} +1.69414e23 q^{50} -5.23263e22 q^{51} -1.48794e22 q^{52} +1.60547e23 q^{53} +2.38496e23 q^{54} +3.33619e23 q^{55} +5.23866e23 q^{57} -1.30923e23 q^{58} -1.09336e24 q^{59} -2.65962e23 q^{60} +1.32576e24 q^{61} +6.50790e23 q^{62} +2.68574e24 q^{64} -2.85586e24 q^{65} +1.54123e24 q^{66} +6.27072e24 q^{67} -6.15722e23 q^{68} -2.70814e23 q^{69} -1.65578e25 q^{71} +4.96422e24 q^{72} +7.93292e24 q^{73} +3.83635e24 q^{74} -3.49914e25 q^{75} +6.16433e24 q^{76} -1.31933e25 q^{78} +1.61913e25 q^{79} +6.79823e25 q^{80} -2.65232e25 q^{81} -3.76641e25 q^{82} -1.00338e26 q^{83} -1.18178e26 q^{85} +1.24744e26 q^{86} +2.70414e25 q^{87} +1.14127e26 q^{88} +1.72766e26 q^{89} +1.51408e26 q^{90} -3.18667e24 q^{92} -1.34416e26 q^{93} -8.62475e25 q^{94} +1.18315e27 q^{95} -1.67507e26 q^{96} +1.03077e27 q^{97} +2.04380e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8280 q^{2} + 1286280 q^{3} + 190623296 q^{4} - 5443587900 q^{5} - 86882873184 q^{6} - 3195032348160 q^{8} + 1235136554154 q^{9}+O(q^{10}) \) 2 * q - 8280 * q^2 + 1286280 * q^3 + 190623296 * q^4 - 5443587900 * q^5 - 86882873184 * q^6 - 3195032348160 * q^8 + 1235136554154 * q^9	\( 2 q - 8280 q^{2} + 1286280 q^{3} + 190623296 q^{4} - 5443587900 q^{5} - 86882873184 q^{6} - 3195032348160 q^{8} + 1235136554154 q^{9} - 39991096148400 q^{10} + 138167337691944 q^{11} + 797895007176960 q^{12} + 753433801271060 q^{13} + 85\!\cdots\!00 q^{15}+ \cdots + 10\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 8280 * q^2 + 1286280 * q^3 + 190623296 * q^4 - 5443587900 * q^5 - 86882873184 * q^6 - 3195032348160 * q^8 + 1235136554154 * q^9 - 39991096148400 * q^10 + 138167337691944 * q^11 + 797895007176960 * q^12 + 753433801271060 * q^13 + 8504300488438800 * q^15 - 14322995785166848 * q^16 + 29753620331011740 * q^17 - 110019470226337080 * q^18 - 404565810372684760 * q^19 - 1109219331427200 * q^20 - 4583556785578779360 * q^22 + 2929078923121218960 * q^23 - 1677495533792532480 * q^24 + 9119218786673228750 * q^25 + 3003459254146640016 * q^26 + 11127665129740313040 * q^27 - 15546679995448558260 * q^29 + 146561411061600148800 * q^30 - 28544554594467385024 * q^31 + 289738949030869893120 * q^32 + 859077391009750054560 * q^33 + 150938335185934859568 * q^34 + 986344620988374211392 * q^36 + 1867697204682824566780 * q^37 + 485361223888169521440 * q^38 - 690990221801025527472 * q^39 + 8985527186071883904000 * q^40 - 9081343698046512254964 * q^41 + 5145612605801421773800 * q^43 + 46384541037574305299712 * q^44 + 12080376719602732775700 * q^45 - 51150723570313970279616 * q^46 + 1150251488862201070560 * q^47 + 28878849836569912688640 * q^48 + 302620649115949014735000 * q^50 - 33494974704727214464656 * q^51 + 21115266673184124022400 * q^52 + 106953735591470060758620 * q^53 + 458020779785618027135040 * q^54 + 214436254091483969701200 * q^55 - 31800538920577362634080 * q^57 - 74812163717162466470160 * q^58 - 2009620977624026488631880 * q^59 - 694490206253033569881600 * q^60 - 147857426692448940370444 * q^61 + 2352212714010270811080960 * q^62 - 1234057803938137445761024 * q^64 - 2951949350200452960922200 * q^65 - 11770868153144268253438848 * q^66 + 3051578535738098902157560 * q^67 + 566166870324676171716480 * q^68 + 9376480489705868528695872 * q^69 - 13175198820369338598286416 * q^71 - 1487763126543110308830720 * q^72 - 5284260812951286572116660 * q^73 - 24234145145448525537787728 * q^74 - 59486914888952006559645000 * q^75 - 28710432717942786872615680 * q^76 - 23925717325436558555851200 * q^78 + 62814351035720719918179040 * q^79 + 68186991639088251432345600 * q^80 - 99047155826597708238103278 * q^81 + 64726649726985190956760560 * q^82 - 171806873410054757883176280 * q^83 - 121333441005595565089302600 * q^85 + 252189883901197432712215584 * q^86 + 16722988656204557792643120 * q^87 - 202163623954874235550955520 * q^88 + 313473438761105539763494380 * q^89 + 196904738457998748777517200 * q^90 + 602296848225491467788034560 * q^92 - 447293490375807514724002560 * q^93 - 262465434750720041893579392 * q^94 + 1276245244260479145691314000 * q^95 + 562074901098402916384505856 * q^96 + 653202933397052842883888060 * q^97 + 1076041779280842335610479688 * q^99

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