LMFDB - Embedded newform 98.10.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,10,Mod(1,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("98.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	98.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:	$50.4735119441$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{2305}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 576 $ x^2 - x - 576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$24.5052$ of defining polynomial
Character	$\chi$	$=$	98.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0000 q^{2} +247.052 q^{3} +256.000 q^{4} +2373.22 q^{5} -3952.83 q^{6} -4096.00 q^{8} +41351.7 q^{9} +O(q^{10})$	\(q-16.0000 q^{2} +247.052 q^{3} +256.000 q^{4} +2373.22 q^{5} -3952.83 q^{6} -4096.00 q^{8} +41351.7 q^{9} -37971.5 q^{10} -27940.9 q^{11} +63245.3 q^{12} -60943.3 q^{13} +586309. q^{15} +65536.0 q^{16} +358867. q^{17} -661628. q^{18} +391593. q^{19} +607544. q^{20} +447055. q^{22} -302894. q^{23} -1.01193e6 q^{24} +3.67904e6 q^{25} +975093. q^{26} +5.35330e6 q^{27} +6.73993e6 q^{29} -9.38094e6 q^{30} -2.98262e6 q^{31} -1.04858e6 q^{32} -6.90287e6 q^{33} -5.74188e6 q^{34} +1.05860e7 q^{36} -3.49582e6 q^{37} -6.26549e6 q^{38} -1.50562e7 q^{39} -9.72070e6 q^{40} -3.43724e7 q^{41} -1.45085e7 q^{43} -7.15288e6 q^{44} +9.81367e7 q^{45} +4.84631e6 q^{46} +2.76485e7 q^{47} +1.61908e7 q^{48} -5.88647e7 q^{50} +8.86589e7 q^{51} -1.56015e7 q^{52} -2.39217e7 q^{53} -8.56529e7 q^{54} -6.63100e7 q^{55} +9.67439e7 q^{57} -1.07839e8 q^{58} +1.20580e8 q^{59} +1.50095e8 q^{60} -7.23140e7 q^{61} +4.77219e7 q^{62} +1.67772e7 q^{64} -1.44632e8 q^{65} +1.10446e8 q^{66} +8.70377e7 q^{67} +9.18701e7 q^{68} -7.48307e7 q^{69} +2.19622e8 q^{71} -1.69377e8 q^{72} -2.67792e8 q^{73} +5.59331e7 q^{74} +9.08915e8 q^{75} +1.00248e8 q^{76} +2.40899e8 q^{78} +2.85350e7 q^{79} +1.55531e8 q^{80} +5.08619e8 q^{81} +5.49959e8 q^{82} +3.83237e8 q^{83} +8.51671e8 q^{85} +2.32136e8 q^{86} +1.66511e9 q^{87} +1.14446e8 q^{88} -7.21581e8 q^{89} -1.57019e9 q^{90} -7.75410e7 q^{92} -7.36861e8 q^{93} -4.42377e8 q^{94} +9.29336e8 q^{95} -2.59053e8 q^{96} +6.73736e8 q^{97} -1.15541e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{2} + 14 q^{3} + 512 q^{4} + 2730 q^{5} - 224 q^{6} - 8192 q^{8} + 75982 q^{9}+O(q^{10}) $ 2 * q - 32 * q^2 + 14 * q^3 + 512 * q^4 + 2730 * q^5 - 224 * q^6 - 8192 * q^8 + 75982 * q^9	\( 2 q - 32 q^{2} + 14 q^{3} + 512 q^{4} + 2730 q^{5} - 224 q^{6} - 8192 q^{8} + 75982 q^{9} - 43680 q^{10} + 44940 q^{11} + 3584 q^{12} - 100282 q^{13} + 503160 q^{15} + 131072 q^{16} + 870408 q^{17} - 1215712 q^{18} - 508774 q^{19} + 698880 q^{20} - 719040 q^{22} + 79800 q^{23} - 57344 q^{24} + 1853210 q^{25} + 1604512 q^{26} + 1869812 q^{27} + 2006328 q^{29} - 8050560 q^{30} - 2188732 q^{31} - 2097152 q^{32} - 23887920 q^{33} - 13926528 q^{34} + 19451392 q^{36} - 20723576 q^{37} + 8140384 q^{38} - 5888224 q^{39} - 11182080 q^{40} - 19016592 q^{41} + 4193716 q^{43} + 11504640 q^{44} + 110492130 q^{45} - 1276800 q^{46} + 74542524 q^{47} + 917504 q^{48} - 29651360 q^{50} - 30556644 q^{51} - 25672192 q^{52} - 3239748 q^{53} - 29916992 q^{54} - 40307400 q^{55} + 306576332 q^{57} - 32101248 q^{58} + 133642362 q^{59} + 128808960 q^{60} - 227801686 q^{61} + 35019712 q^{62} + 33554432 q^{64} - 158667180 q^{65} + 382206720 q^{66} + 332930272 q^{67} + 222824448 q^{68} - 164018400 q^{69} - 167985720 q^{71} - 311222272 q^{72} + 44684276 q^{73} + 331577216 q^{74} + 1334428970 q^{75} - 130246144 q^{76} + 94211584 q^{78} + 269642776 q^{79} + 178913280 q^{80} + 638826478 q^{81} + 304265472 q^{82} + 183105762 q^{83} + 1034179020 q^{85} - 67099456 q^{86} + 2768288796 q^{87} - 184074240 q^{88} - 791657748 q^{89} - 1767874080 q^{90} + 20428800 q^{92} - 921877624 q^{93} - 1192680384 q^{94} + 608102040 q^{95} - 14680064 q^{96} + 4169480 q^{97} + 1368480540 q^{99}+O(q^{100}) \) 2 * q - 32 * q^2 + 14 * q^3 + 512 * q^4 + 2730 * q^5 - 224 * q^6 - 8192 * q^8 + 75982 * q^9 - 43680 * q^10 + 44940 * q^11 + 3584 * q^12 - 100282 * q^13 + 503160 * q^15 + 131072 * q^16 + 870408 * q^17 - 1215712 * q^18 - 508774 * q^19 + 698880 * q^20 - 719040 * q^22 + 79800 * q^23 - 57344 * q^24 + 1853210 * q^25 + 1604512 * q^26 + 1869812 * q^27 + 2006328 * q^29 - 8050560 * q^30 - 2188732 * q^31 - 2097152 * q^32 - 23887920 * q^33 - 13926528 * q^34 + 19451392 * q^36 - 20723576 * q^37 + 8140384 * q^38 - 5888224 * q^39 - 11182080 * q^40 - 19016592 * q^41 + 4193716 * q^43 + 11504640 * q^44 + 110492130 * q^45 - 1276800 * q^46 + 74542524 * q^47 + 917504 * q^48 - 29651360 * q^50 - 30556644 * q^51 - 25672192 * q^52 - 3239748 * q^53 - 29916992 * q^54 - 40307400 * q^55 + 306576332 * q^57 - 32101248 * q^58 + 133642362 * q^59 + 128808960 * q^60 - 227801686 * q^61 + 35019712 * q^62 + 33554432 * q^64 - 158667180 * q^65 + 382206720 * q^66 + 332930272 * q^67 + 222824448 * q^68 - 164018400 * q^69 - 167985720 * q^71 - 311222272 * q^72 + 44684276 * q^73 + 331577216 * q^74 + 1334428970 * q^75 - 130246144 * q^76 + 94211584 * q^78 + 269642776 * q^79 + 178913280 * q^80 + 638826478 * q^81 + 304265472 * q^82 + 183105762 * q^83 + 1034179020 * q^85 - 67099456 * q^86 + 2768288796 * q^87 - 184074240 * q^88 - 791657748 * q^89 - 1767874080 * q^90 + 20428800 * q^92 - 921877624 * q^93 - 1192680384 * q^94 + 608102040 * q^95 - 14680064 * q^96 + 4169480 * q^97 + 1368480540 * 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 $

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	247.052	1.76093	0.880467	−	0.474108i	$-0.157229\pi$
$3$	247.052	1.76093	0.880467	+	0.474108i	$0.157229\pi$
$4$	256.000	0.500000
$5$	2373.22	1.69814	0.849069	−	0.528283i	$-0.177164\pi$
$5$	2373.22	1.69814	0.849069	+	0.528283i	$0.177164\pi$
$6$	−3952.83	−1.24517
$7$	0	0
$7$	0	0
$8$	−4096.00	−0.353553
$9$	41351.7	2.10089
$10$	−37971.5	−1.20076
$11$	−27940.9	−0.575405	−0.287703	−	0.957720i	$-0.592891\pi$
$11$	−27940.9	−0.575405	−0.287703	+	0.957720i	$0.592891\pi$
$12$	63245.3	0.880467
$13$	−60943.3	−0.591808	−0.295904	−	0.955218i	$-0.595621\pi$
$13$	−60943.3	−0.591808	−0.295904	+	0.955218i	$0.595621\pi$
$14$	0	0
$15$	586309.	2.99031
$16$	65536.0	0.250000
$17$	358867.	1.04211	0.521055	−	0.853523i	$-0.325538\pi$
$17$	358867.	1.04211	0.521055	+	0.853523i	$0.325538\pi$
$18$	−661628.	−1.48555
$19$	391593.	0.689356	0.344678	−	0.938721i	$-0.387988\pi$
$19$	391593.	0.689356	0.344678	+	0.938721i	$0.387988\pi$
$20$	607544.	0.849069
$21$	0	0
$22$	447055.	0.406873
$23$	−302894.	−0.225692	−0.112846	−	0.993612i	$-0.535997\pi$
$23$	−302894.	−0.225692	−0.112846	+	0.993612i	$0.535997\pi$
$24$	−1.01193e6	−0.622584
$25$	3.67904e6	1.88367
$26$	975093.	0.418472
$27$	5.35330e6	1.93859
$28$	0	0
$29$	6.73993e6	1.76956	0.884778	−	0.466013i	$-0.154310\pi$
$29$	6.73993e6	1.76956	0.884778	+	0.466013i	$0.154310\pi$
$30$	−9.38094e6	−2.11447
$31$	−2.98262e6	−0.580056	−0.290028	−	0.957018i	$-0.593665\pi$
$31$	−2.98262e6	−0.580056	−0.290028	+	0.957018i	$0.593665\pi$
$32$	−1.04858e6	−0.176777
$33$	−6.90287e6	−1.01325
$34$	−5.74188e6	−0.736884
$35$	0	0
$36$	1.05860e7	1.05044
$37$	−3.49582e6	−0.306649	−0.153324	−	0.988176i	$-0.548998\pi$
$37$	−3.49582e6	−0.306649	−0.153324	+	0.988176i	$0.548998\pi$
$38$	−6.26549e6	−0.487449
$39$	−1.50562e7	−1.04214
$40$	−9.72070e6	−0.600382
$41$	−3.43724e7	−1.89969	−0.949845	−	0.312722i	$-0.898759\pi$
$41$	−3.43724e7	−1.89969	−0.949845	+	0.312722i	$0.898759\pi$
$42$	0	0
$43$	−1.45085e7	−0.647164	−0.323582	−	0.946200i	$-0.604887\pi$
$43$	−1.45085e7	−0.647164	−0.323582	+	0.946200i	$0.604887\pi$
$44$	−7.15288e6	−0.287703
$45$	9.81367e7	3.56759
$46$	4.84631e6	0.159588
$47$	2.76485e7	0.826479	0.413239	−	0.910622i	$-0.364397\pi$
$47$	2.76485e7	0.826479	0.413239	+	0.910622i	$0.364397\pi$
$48$	1.61908e7	0.440233
$49$	0	0
$50$	−5.88647e7	−1.33196
$51$	8.86589e7	1.83509
$52$	−1.56015e7	−0.295904
$53$	−2.39217e7	−0.416438	−0.208219	−	0.978082i	$-0.566767\pi$
$53$	−2.39217e7	−0.416438	−0.208219	+	0.978082i	$0.566767\pi$
$54$	−8.56529e7	−1.37079
$55$	−6.63100e7	−0.977117
$56$	0	0
$57$	9.67439e7	1.21391
$58$	−1.07839e8	−1.25127
$59$	1.20580e8	1.29551	0.647756	−	0.761848i	$-0.275707\pi$
$59$	1.20580e8	1.29551	0.647756	+	0.761848i	$0.275707\pi$
$60$	1.50095e8	1.49515
$61$	−7.23140e7	−0.668710	−0.334355	−	0.942447i	$-0.608518\pi$
$61$	−7.23140e7	−0.668710	−0.334355	+	0.942447i	$0.608518\pi$
$62$	4.77219e7	0.410161
$63$	0	0
$64$	1.67772e7	0.125000
$65$	−1.44632e8	−1.00497
$66$	1.10446e8	0.716476
$67$	8.70377e7	0.527680	0.263840	−	0.964566i	$-0.415011\pi$
$67$	8.70377e7	0.527680	0.263840	+	0.964566i	$0.415011\pi$
$68$	9.18701e7	0.521055
$69$	−7.48307e7	−0.397428
$70$	0	0
$71$	2.19622e8	1.02568	0.512842	−	0.858483i	$-0.328593\pi$
$71$	2.19622e8	1.02568	0.512842	+	0.858483i	$0.328593\pi$
$72$	−1.69377e8	−0.742775
$73$	−2.67792e8	−1.10368	−0.551841	−	0.833949i	$-0.686074\pi$
$73$	−2.67792e8	−1.10368	−0.551841	+	0.833949i	$0.686074\pi$
$74$	5.59331e7	0.216833
$75$	9.08915e8	3.31702
$76$	1.00248e8	0.344678
$77$	0	0
$78$	2.40899e8	0.736901
$79$	2.85350e7	0.0824243	0.0412122	−	0.999150i	$-0.486878\pi$
$79$	2.85350e7	0.0824243	0.0412122	+	0.999150i	$0.486878\pi$
$80$	1.55531e8	0.424534
$81$	5.08619e8	1.31283
$82$	5.49959e8	1.34328
$83$	3.83237e8	0.886372	0.443186	−	0.896430i	$-0.353848\pi$
$83$	3.83237e8	0.886372	0.443186	+	0.896430i	$0.353848\pi$
$84$	0	0
$85$	8.51671e8	1.76965
$86$	2.32136e8	0.457614
$87$	1.66511e9	3.11607
$88$	1.14446e8	0.203437
$89$	−7.21581e8	−1.21907	−0.609537	−	0.792757i	$-0.708645\pi$
$89$	−7.21581e8	−1.21907	−0.609537	+	0.792757i	$0.708645\pi$
$90$	−1.57019e9	−2.52267
$91$	0	0
$92$	−7.75410e7	−0.112846
$93$	−7.36861e8	−1.02144
$94$	−4.42377e8	−0.584409
$95$	9.29336e8	1.17062
$96$	−2.59053e8	−0.311292
$97$	6.73736e8	0.772710	0.386355	−	0.922350i	$-0.373734\pi$
$97$	6.73736e8	0.772710	0.386355	+	0.922350i	$0.373734\pi$
$98$	0	0
$99$	−1.15541e9	−1.20886
$100$	9.41835e8	0.941835
$101$	1.04805e7	0.0100216	0.00501081	−	0.999987i	$-0.498405\pi$
$101$	1.04805e7	0.0100216	0.00501081	+	0.999987i	$0.498405\pi$
$102$	−1.41854e9	−1.29760
$103$	−1.39782e9	−1.22373	−0.611864	−	0.790963i	$-0.709580\pi$
$103$	−1.39782e9	−1.22373	−0.611864	+	0.790963i	$0.709580\pi$
$104$	2.49624e8	0.209236
$105$	0	0
$106$	3.82747e8	0.294466
$107$	−4.84414e8	−0.357264	−0.178632	−	0.983916i	$-0.557167\pi$
$107$	−4.84414e8	−0.357264	−0.178632	+	0.983916i	$0.557167\pi$
$108$	1.37045e9	0.969293
$109$	−1.96298e8	−0.133198	−0.0665989	−	0.997780i	$-0.521215\pi$
$109$	−1.96298e8	−0.133198	−0.0665989	+	0.997780i	$0.521215\pi$
$110$	1.06096e9	0.690926
$111$	−8.63649e8	−0.539988
$112$	0	0
$113$	−5.80849e8	−0.335128	−0.167564	−	0.985861i	$-0.553590\pi$
$113$	−5.80849e8	−0.335128	−0.167564	+	0.985861i	$0.553590\pi$
$114$	−1.54790e9	−0.858364
$115$	−7.18835e8	−0.383256
$116$	1.72542e9	0.884778
$117$	−2.52011e9	−1.24332
$118$	−1.92928e9	−0.916066
$119$	0	0
$120$	−2.40152e9	−1.05723
$121$	−1.57725e9	−0.668909
$122$	1.15702e9	0.472850
$123$	−8.49178e9	−3.34523
$124$	−7.63550e8	−0.290028
$125$	4.09598e9	1.50059
$126$	0	0
$127$	2.59088e9	0.883751	0.441876	−	0.897076i	$-0.354313\pi$
$127$	2.59088e9	0.883751	0.441876	+	0.897076i	$0.354313\pi$
$128$	−2.68435e8	−0.0883883
$129$	−3.58436e9	−1.13961
$130$	2.31411e9	0.710622
$131$	−2.45598e9	−0.728626	−0.364313	−	0.931277i	$-0.618696\pi$
$131$	−2.45598e9	−0.728626	−0.364313	+	0.931277i	$0.618696\pi$
$132$	−1.76713e9	−0.506625
$133$	0	0
$134$	−1.39260e9	−0.373126
$135$	1.27046e10	3.29198
$136$	−1.46992e9	−0.368442
$137$	6.08364e9	1.47544	0.737719	−	0.675108i	$-0.235903\pi$
$137$	6.08364e9	1.47544	0.737719	+	0.675108i	$0.235903\pi$
$138$	1.19729e9	0.281024
$139$	−2.25249e9	−0.511796	−0.255898	−	0.966704i	$-0.582371\pi$
$139$	−2.25249e9	−0.511796	−0.255898	+	0.966704i	$0.582371\pi$
$140$	0	0
$141$	6.83063e9	1.45537
$142$	−3.51395e9	−0.725268
$143$	1.70281e9	0.340530
$144$	2.71003e9	0.525221
$145$	1.59953e10	3.00495
$146$	4.28466e9	0.780421
$147$	0	0
$148$	−8.94930e8	−0.153324
$149$	−3.13517e9	−0.521103	−0.260551	−	0.965460i	$-0.583904\pi$
$149$	−3.13517e9	−0.521103	−0.260551	+	0.965460i	$0.583904\pi$
$150$	−1.45426e10	−2.34548
$151$	−6.20938e9	−0.971969	−0.485984	−	0.873968i	$-0.661539\pi$
$151$	−6.20938e9	−0.971969	−0.485984	+	0.873968i	$0.661539\pi$
$152$	−1.60397e9	−0.243724
$153$	1.48398e10	2.18936
$154$	0	0
$155$	−7.07840e9	−0.985014
$156$	−3.85438e9	−0.521068
$157$	−1.33378e10	−1.75201	−0.876006	−	0.482300i	$-0.839802\pi$
$157$	−1.33378e10	−1.75201	−0.876006	+	0.482300i	$0.839802\pi$
$158$	−4.56560e8	−0.0582828
$159$	−5.90990e9	−0.733319
$160$	−2.48850e9	−0.300191
$161$	0	0
$162$	−8.13790e9	−0.928314
$163$	7.33621e9	0.814006	0.407003	−	0.913427i	$-0.366574\pi$
$163$	7.33621e9	0.814006	0.407003	+	0.913427i	$0.366574\pi$
$164$	−8.79934e9	−0.949845
$165$	−1.63820e10	−1.72064
$166$	−6.13179e9	−0.626760
$167$	6.42205e9	0.638925	0.319462	−	0.947599i	$-0.396498\pi$
$167$	6.42205e9	0.638925	0.319462	+	0.947599i	$0.396498\pi$
$168$	0	0
$169$	−6.89041e9	−0.649763
$170$	−1.36267e10	−1.25133
$171$	1.61931e10	1.44826
$172$	−3.71418e9	−0.323582
$173$	−1.91846e10	−1.62834	−0.814171	−	0.580626i	$-0.802808\pi$
$173$	−1.91846e10	−1.62834	−0.814171	+	0.580626i	$0.802808\pi$
$174$	−2.66418e10	−2.20339
$175$	0	0
$176$	−1.83114e9	−0.143851
$177$	2.97896e10	2.28131
$178$	1.15453e10	0.862016
$179$	1.53377e10	1.11666	0.558330	−	0.829619i	$-0.311442\pi$
$179$	1.53377e10	1.11666	0.558330	+	0.829619i	$0.311442\pi$
$180$	2.51230e10	1.78380
$181$	1.73475e10	1.20139	0.600694	−	0.799479i	$-0.294891\pi$
$181$	1.73475e10	1.20139	0.600694	+	0.799479i	$0.294891\pi$
$182$	0	0
$183$	−1.78653e10	−1.17755
$184$	1.24066e9	0.0797941
$185$	−8.29634e9	−0.520732
$186$	1.17898e10	0.722267
$187$	−1.00271e10	−0.599636
$188$	7.07802e9	0.413239
$189$	0	0
$190$	−1.48694e10	−0.827755
$191$	2.70138e10	1.46871	0.734355	−	0.678765i	$-0.237485\pi$
$191$	2.70138e10	1.46871	0.734355	+	0.678765i	$0.237485\pi$
$192$	4.14485e9	0.220117
$193$	2.70232e9	0.140194	0.0700970	−	0.997540i	$-0.477669\pi$
$193$	2.70232e9	0.140194	0.0700970	+	0.997540i	$0.477669\pi$
$194$	−1.07798e10	−0.546389
$195$	−3.57316e10	−1.76969
$196$	0	0
$197$	2.39047e10	1.13080	0.565399	−	0.824818i	$-0.308722\pi$
$197$	2.39047e10	1.13080	0.565399	+	0.824818i	$0.308722\pi$
$198$	1.84865e10	0.854794
$199$	2.16111e9	0.0976872	0.0488436	−	0.998806i	$-0.484446\pi$
$199$	2.16111e9	0.0976872	0.0488436	+	0.998806i	$0.484446\pi$
$200$	−1.50694e10	−0.665978
$201$	2.15028e10	0.929209
$202$	−1.67689e8	−0.00708635
$203$	0	0
$204$	2.26967e10	0.917544
$205$	−8.15732e10	−3.22593
$206$	2.23652e10	0.865306
$207$	−1.25252e10	−0.474153
$208$	−3.99398e9	−0.147952
$209$	−1.09415e10	−0.396659
$210$	0	0
$211$	3.61055e9	0.125401	0.0627007	−	0.998032i	$-0.480029\pi$
$211$	3.61055e9	0.125401	0.0627007	+	0.998032i	$0.480029\pi$
$212$	−6.12395e9	−0.208219
$213$	5.42581e10	1.80616
$214$	7.75062e9	0.252624
$215$	−3.44319e10	−1.09897
$216$	−2.19271e10	−0.685394
$217$	0	0
$218$	3.14077e9	0.0941851
$219$	−6.61585e10	−1.94351
$220$	−1.69753e10	−0.488559
$221$	−2.18706e10	−0.616730
$222$	1.38184e10	0.381829
$223$	7.13001e10	1.93072	0.965358	−	0.260929i	$-0.0840287\pi$
$223$	7.13001e10	1.93072	0.965358	+	0.260929i	$0.0840287\pi$
$224$	0	0
$225$	1.52135e11	3.95737
$226$	9.29359e9	0.236971
$227$	−7.15361e10	−1.78817	−0.894086	−	0.447896i	$-0.852173\pi$
$227$	−7.15361e10	−1.78817	−0.894086	+	0.447896i	$0.852173\pi$
$228$	2.47664e10	0.606955
$229$	3.56020e10	0.855491	0.427745	−	0.903899i	$-0.359308\pi$
$229$	3.56020e10	0.855491	0.427745	+	0.903899i	$0.359308\pi$
$230$	1.15014e10	0.271003
$231$	0	0
$232$	−2.76067e10	−0.625633
$233$	−3.80069e10	−0.844814	−0.422407	−	0.906406i	$-0.638815\pi$
$233$	−3.80069e10	−0.844814	−0.422407	+	0.906406i	$0.638815\pi$
$234$	4.03218e10	0.879161
$235$	6.56160e10	1.40347
$236$	3.08685e10	0.647756
$237$	7.04962e9	0.145144
$238$	0	0
$239$	−8.67126e10	−1.71906	−0.859531	−	0.511083i	$-0.829244\pi$
$239$	−8.67126e10	−1.71906	−0.859531	+	0.511083i	$0.829244\pi$
$240$	3.84243e10	0.747576
$241$	8.18418e9	0.156278	0.0781391	−	0.996942i	$-0.475102\pi$
$241$	8.18418e9	0.156278	0.0781391	+	0.996942i	$0.475102\pi$
$242$	2.52360e10	0.472990
$243$	2.02863e10	0.373228
$244$	−1.85124e10	−0.334355
$245$	0	0
$246$	1.35868e11	2.36543
$247$	−2.38650e10	−0.407967
$248$	1.22168e10	0.205081
$249$	9.46795e10	1.56084
$250$	−6.55357e10	−1.06108
$251$	−9.75467e10	−1.55125	−0.775624	−	0.631196i	$-0.782565\pi$
$251$	−9.75467e10	−1.55125	−0.775624	+	0.631196i	$0.782565\pi$
$252$	0	0
$253$	8.46315e9	0.129864
$254$	−4.14540e10	−0.624907
$255$	2.10407e11	3.11623
$256$	4.29497e9	0.0625000
$257$	4.43042e9	0.0633499	0.0316750	−	0.999498i	$-0.489916\pi$
$257$	4.43042e9	0.0633499	0.0316750	+	0.999498i	$0.489916\pi$
$258$	5.73497e10	0.805828
$259$	0	0
$260$	−3.70258e10	−0.502486
$261$	2.78708e11	3.71763
$262$	3.92957e10	0.515216
$263$	−1.20620e11	−1.55460	−0.777301	−	0.629129i	$-0.783412\pi$
$263$	−1.20620e11	−1.55460	−0.777301	+	0.629129i	$0.783412\pi$
$264$	2.82741e10	0.358238
$265$	−5.67714e10	−0.707168
$266$	0	0
$267$	−1.78268e11	−2.14671
$268$	2.22816e10	0.263840
$269$	−7.59025e10	−0.883835	−0.441917	−	0.897056i	$-0.645702\pi$
$269$	−7.59025e10	−0.883835	−0.441917	+	0.897056i	$0.645702\pi$
$270$	−2.03273e11	−2.32778
$271$	−7.11397e10	−0.801217	−0.400608	−	0.916249i	$-0.631201\pi$
$271$	−7.11397e10	−0.801217	−0.400608	+	0.916249i	$0.631201\pi$
$272$	2.35187e10	0.260528
$273$	0	0
$274$	−9.73382e10	−1.04329
$275$	−1.02796e11	−1.08387
$276$	−1.91567e10	−0.198714
$277$	8.61542e10	0.879261	0.439630	−	0.898179i	$-0.355109\pi$
$277$	8.61542e10	0.879261	0.439630	+	0.898179i	$0.355109\pi$
$278$	3.60399e10	0.361894
$279$	−1.23336e11	−1.21863
$280$	0	0
$281$	−1.00179e11	−0.958511	−0.479256	−	0.877675i	$-0.659093\pi$
$281$	−1.00179e11	−0.958511	−0.479256	+	0.877675i	$0.659093\pi$
$282$	−1.09290e11	−1.02910
$283$	4.57444e10	0.423935	0.211967	−	0.977277i	$-0.432013\pi$
$283$	4.57444e10	0.423935	0.211967	+	0.977277i	$0.432013\pi$
$284$	5.62233e10	0.512842
$285$	2.29594e11	2.06139
$286$	−2.72450e10	−0.240791
$287$	0	0
$288$	−4.33604e10	−0.371388
$289$	1.01980e10	0.0859950
$290$	−2.55925e11	−2.12482
$291$	1.66448e11	1.36069
$292$	−6.85546e10	−0.551841
$293$	1.01615e10	0.0805476	0.0402738	−	0.999189i	$-0.487177\pi$
$293$	1.01615e10	0.0805476	0.0402738	+	0.999189i	$0.487177\pi$
$294$	0	0
$295$	2.86163e11	2.19996
$296$	1.43189e10	0.108417
$297$	−1.49576e11	−1.11547
$298$	5.01628e10	0.368475
$299$	1.84594e10	0.133566
$300$	2.32682e11	1.65851
$301$	0	0
$302$	9.93501e10	0.687286
$303$	2.58924e9	0.0176474
$304$	2.56634e10	0.172339
$305$	−1.71617e11	−1.13556
$306$	−2.37437e11	−1.54811
$307$	3.68957e10	0.237057	0.118529	−	0.992951i	$-0.462182\pi$
$307$	3.68957e10	0.237057	0.118529	+	0.992951i	$0.462182\pi$
$308$	0	0
$309$	−3.45335e11	−2.15490
$310$	1.13254e11	0.696510
$311$	−1.88558e11	−1.14294	−0.571469	−	0.820624i	$-0.693626\pi$
$311$	−1.88558e11	−1.14294	−0.571469	+	0.820624i	$0.693626\pi$
$312$	6.16701e10	0.368450
$313$	−1.31778e11	−0.776058	−0.388029	−	0.921647i	$-0.626844\pi$
$313$	−1.31778e11	−0.776058	−0.388029	+	0.921647i	$0.626844\pi$
$314$	2.13405e11	1.23886
$315$	0	0
$316$	7.30495e9	0.0412122
$317$	−1.50686e11	−0.838118	−0.419059	−	0.907959i	$-0.637640\pi$
$317$	−1.50686e11	−0.838118	−0.419059	+	0.907959i	$0.637640\pi$
$318$	9.45584e10	0.518535
$319$	−1.88320e11	−1.01821
$320$	3.98160e10	0.212267
$321$	−1.19675e11	−0.629118
$322$	0	0
$323$	1.40530e11	0.718386
$324$	1.30206e11	0.656417
$325$	−2.24213e11	−1.11477
$326$	−1.17379e11	−0.575589
$327$	−4.84959e10	−0.234552
$328$	1.40789e11	0.671642
$329$	0	0
$330$	2.62112e11	1.21667
$331$	3.38877e10	0.155173	0.0775865	−	0.996986i	$-0.475279\pi$
$331$	3.38877e10	0.155173	0.0775865	+	0.996986i	$0.475279\pi$
$332$	9.81087e10	0.443186
$333$	−1.44558e11	−0.644234
$334$	−1.02753e11	−0.451788
$335$	2.06559e11	0.896073
$336$	0	0
$337$	1.98312e11	0.837555	0.418778	−	0.908089i	$-0.362459\pi$
$337$	1.98312e11	0.837555	0.418778	+	0.908089i	$0.362459\pi$
$338$	1.10247e11	0.459452
$339$	−1.43500e11	−0.590138
$340$	2.18028e11	0.884824
$341$	8.33371e10	0.333767
$342$	−2.59089e11	−1.02407
$343$	0	0
$344$	5.94268e10	0.228807
$345$	−1.77590e11	−0.674888
$346$	3.06954e11	1.15141
$347$	−1.71762e11	−0.635981	−0.317990	−	0.948094i	$-0.603008\pi$
$347$	−1.71762e11	−0.635981	−0.317990	+	0.948094i	$0.603008\pi$
$348$	4.26269e11	1.55803
$349$	1.88189e11	0.679014	0.339507	−	0.940603i	$-0.389740\pi$
$349$	1.88189e11	0.679014	0.339507	+	0.940603i	$0.389740\pi$
$350$	0	0
$351$	−3.26248e11	−1.14727
$352$	2.92982e10	0.101718
$353$	−1.97995e11	−0.678686	−0.339343	−	0.940663i	$-0.610205\pi$
$353$	−1.97995e11	−0.678686	−0.339343	+	0.940663i	$0.610205\pi$
$354$	−4.76633e11	−1.61313
$355$	5.21211e11	1.74175
$356$	−1.84725e11	−0.609537
$357$	0	0
$358$	−2.45403e11	−0.789598
$359$	4.34669e11	1.38113	0.690563	−	0.723272i	$-0.257363\pi$
$359$	4.34669e11	1.38113	0.690563	+	0.723272i	$0.257363\pi$
$360$	−4.01968e11	−1.26133
$361$	−1.69343e11	−0.524788
$362$	−2.77560e11	−0.849510
$363$	−3.89663e11	−1.17790
$364$	0	0
$365$	−6.35528e11	−1.87420
$366$	2.85845e11	0.832657
$367$	−6.02066e10	−0.173240	−0.0866198	−	0.996241i	$-0.527607\pi$
$367$	−6.02066e10	−0.173240	−0.0866198	+	0.996241i	$0.527607\pi$
$368$	−1.98505e10	−0.0564230
$369$	−1.42136e12	−3.99103
$370$	1.32741e11	0.368213
$371$	0	0
$372$	−1.88637e11	−0.510720
$373$	−6.85521e11	−1.83371	−0.916855	−	0.399219i	$-0.869281\pi$
$373$	−6.85521e11	−1.83371	−0.916855	+	0.399219i	$0.869281\pi$
$374$	1.60433e11	0.424007
$375$	1.01192e12	2.64244
$376$	−1.13248e11	−0.292204
$377$	−4.10754e11	−1.04724
$378$	0	0
$379$	5.05522e11	1.25853	0.629266	−	0.777190i	$-0.283356\pi$
$379$	5.05522e11	1.25853	0.629266	+	0.777190i	$0.283356\pi$
$380$	2.37910e11	0.585311
$381$	6.40082e11	1.55623
$382$	−4.32221e11	−1.03854
$383$	−2.02054e11	−0.479814	−0.239907	−	0.970796i	$-0.577117\pi$
$383$	−2.02054e11	−0.479814	−0.239907	+	0.970796i	$0.577117\pi$
$384$	−6.63175e10	−0.155646
$385$	0	0
$386$	−4.32371e10	−0.0991321
$387$	−5.99952e11	−1.35962
$388$	1.72476e11	0.386355
$389$	5.51954e11	1.22216	0.611082	−	0.791567i	$-0.290735\pi$
$389$	5.51954e11	1.22216	0.611082	+	0.791567i	$0.290735\pi$
$390$	5.71706e11	1.25136
$391$	−1.08699e11	−0.235196
$392$	0	0
$393$	−6.06756e11	−1.28306
$394$	−3.82475e11	−0.799595
$395$	6.77197e10	0.139968
$396$	−2.95784e11	−0.604430
$397$	−1.26816e11	−0.256222	−0.128111	−	0.991760i	$-0.540891\pi$
$397$	−1.26816e11	−0.256222	−0.128111	+	0.991760i	$0.540891\pi$
$398$	−3.45777e10	−0.0690753
$399$	0	0
$400$	2.41110e11	0.470917
$401$	5.86957e11	1.13359	0.566795	−	0.823859i	$-0.308183\pi$
$401$	5.86957e11	1.13359	0.566795	+	0.823859i	$0.308183\pi$
$402$	−3.44045e11	−0.657050
$403$	1.81771e11	0.343282
$404$	2.68302e9	0.00501081
$405$	1.20706e12	2.22937
$406$	0	0
$407$	9.76764e10	0.176447
$408$	−3.63147e11	−0.648801
$409$	9.08262e10	0.160493	0.0802465	−	0.996775i	$-0.474429\pi$
$409$	9.08262e10	0.160493	0.0802465	+	0.996775i	$0.474429\pi$
$410$	1.30517e12	2.28108
$411$	1.50298e12	2.59815
$412$	−3.57843e11	−0.611864
$413$	0	0
$414$	2.00403e11	0.335277
$415$	9.09505e11	1.50518
$416$	6.39037e10	0.104618
$417$	−5.56483e11	−0.901238
$418$	1.75064e11	0.280481
$419$	8.34669e11	1.32297	0.661487	−	0.749957i	$-0.269926\pi$
$419$	8.34669e11	1.32297	0.661487	+	0.749957i	$0.269926\pi$
$420$	0	0
$421$	−1.61360e10	−0.0250337	−0.0125169	−	0.999922i	$-0.503984\pi$
$421$	−1.61360e10	−0.0250337	−0.0125169	+	0.999922i	$0.503984\pi$
$422$	−5.77688e10	−0.0886722
$423$	1.14331e12	1.73634
$424$	9.79832e10	0.147233
$425$	1.32029e12	1.96299
$426$	−8.68130e11	−1.27715
$427$	0	0
$428$	−1.24010e11	−0.178632
$429$	4.20684e11	0.599650
$430$	5.50910e11	0.777092
$431$	−4.81935e11	−0.672730	−0.336365	−	0.941732i	$-0.609198\pi$
$431$	−4.81935e11	−0.672730	−0.336365	+	0.941732i	$0.609198\pi$
$432$	3.50834e11	0.484646
$433$	−6.68314e11	−0.913661	−0.456830	−	0.889554i	$-0.651015\pi$
$433$	−6.68314e11	−0.913661	−0.456830	+	0.889554i	$0.651015\pi$
$434$	0	0
$435$	3.95168e12	5.29151
$436$	−5.02523e10	−0.0665989
$437$	−1.18611e11	−0.155582
$438$	1.05854e12	1.37427
$439$	4.79819e11	0.616577	0.308288	−	0.951293i	$-0.400244\pi$
$439$	4.79819e11	0.616577	0.308288	+	0.951293i	$0.400244\pi$
$440$	2.71606e11	0.345463
$441$	0	0
$442$	3.49929e11	0.436094
$443$	−6.53598e11	−0.806295	−0.403148	−	0.915135i	$-0.632084\pi$
$443$	−6.53598e11	−0.806295	−0.403148	+	0.915135i	$0.632084\pi$
$444$	−2.21094e11	−0.269994
$445$	−1.71247e12	−2.07016
$446$	−1.14080e12	−1.36522
$447$	−7.74551e11	−0.917627
$448$	0	0
$449$	−1.88660e11	−0.219064	−0.109532	−	0.993983i	$-0.534935\pi$
$449$	−1.88660e11	−0.219064	−0.109532	+	0.993983i	$0.534935\pi$
$450$	−2.43416e12	−2.79829
$451$	9.60397e11	1.09309
$452$	−1.48697e11	−0.167564
$453$	−1.53404e12	−1.71157
$454$	1.14458e12	1.26443
$455$	0	0
$456$	−3.96263e11	−0.429182
$457$	1.31205e12	1.40711	0.703556	−	0.710639i	$-0.251594\pi$
$457$	1.31205e12	1.40711	0.703556	+	0.710639i	$0.251594\pi$
$458$	−5.69633e11	−0.604923
$459$	1.92113e12	2.02022
$460$	−1.84022e11	−0.191628
$461$	−1.16594e12	−1.20233	−0.601165	−	0.799125i	$-0.705297\pi$
$461$	−1.16594e12	−1.20233	−0.601165	+	0.799125i	$0.705297\pi$
$462$	0	0
$463$	−3.87318e10	−0.0391700	−0.0195850	−	0.999808i	$-0.506234\pi$
$463$	−3.87318e10	−0.0391700	−0.0195850	+	0.999808i	$0.506234\pi$
$464$	4.41708e11	0.442389
$465$	−1.74873e12	−1.73454
$466$	6.08111e11	0.597374
$467$	−1.17150e11	−0.113977	−0.0569883	−	0.998375i	$-0.518150\pi$
$467$	−1.17150e11	−0.113977	−0.0569883	+	0.998375i	$0.518150\pi$
$468$	−6.45149e11	−0.621661
$469$	0	0
$470$	−1.04986e12	−0.992406
$471$	−3.29514e12	−3.08518
$472$	−4.93896e11	−0.458033
$473$	4.05381e11	0.372382
$474$	−1.12794e11	−0.102632
$475$	1.44069e12	1.29852
$476$	0	0
$477$	−9.89203e11	−0.874888
$478$	1.38740e12	1.21556
$479$	1.94734e12	1.69018	0.845089	−	0.534626i	$-0.179548\pi$
$479$	1.94734e12	1.69018	0.845089	+	0.534626i	$0.179548\pi$
$480$	−6.14789e11	−0.528616
$481$	2.13047e11	0.181477
$482$	−1.30947e11	−0.110505
$483$	0	0
$484$	−4.03776e11	−0.334454
$485$	1.59892e12	1.31217
$486$	−3.24580e11	−0.263912
$487$	−1.95983e12	−1.57884	−0.789421	−	0.613852i	$-0.789619\pi$
$487$	−1.95983e12	−1.57884	−0.789421	+	0.613852i	$0.789619\pi$
$488$	2.96198e11	0.236425
$489$	1.81243e12	1.43341
$490$	0	0
$491$	−2.93589e11	−0.227967	−0.113984	−	0.993483i	$-0.536361\pi$
$491$	−2.93589e11	−0.227967	−0.113984	+	0.993483i	$0.536361\pi$
$492$	−2.17389e12	−1.67261
$493$	2.41874e12	1.84407
$494$	3.81840e11	0.288476
$495$	−2.74203e12	−2.05281
$496$	−1.95469e11	−0.145014
$497$	0	0
$498$	−1.51487e12	−1.10368
$499$	1.71390e12	1.23746	0.618732	−	0.785602i	$-0.287647\pi$
$499$	1.71390e12	1.23746	0.618732	+	0.785602i	$0.287647\pi$
$500$	1.04857e12	0.750296
$501$	1.58658e12	1.12510
$502$	1.56075e12	1.09690
$503$	−1.61385e12	−1.12411	−0.562053	−	0.827101i	$-0.689988\pi$
$503$	−1.61385e12	−1.12411	−0.562053	+	0.827101i	$0.689988\pi$
$504$	0	0
$505$	2.48726e10	0.0170181
$506$	−1.35410e11	−0.0918279
$507$	−1.70229e12	−1.14419
$508$	6.63265e11	0.441876
$509$	−1.17088e12	−0.773181	−0.386590	−	0.922252i	$-0.626347\pi$
$509$	−1.17088e12	−0.773181	−0.386590	+	0.922252i	$0.626347\pi$
$510$	−3.36651e12	−2.20351
$511$	0	0
$512$	−6.87195e10	−0.0441942
$513$	2.09632e12	1.33638
$514$	−7.08868e10	−0.0447952
$515$	−3.31734e12	−2.07806
$516$	−9.17595e11	−0.569807
$517$	−7.72526e11	−0.475560
$518$	0	0
$519$	−4.73960e12	−2.86740
$520$	5.92412e11	0.355311
$521$	−2.91339e12	−1.73232	−0.866161	−	0.499765i	$-0.833420\pi$
$521$	−2.91339e12	−1.73232	−0.866161	+	0.499765i	$0.833420\pi$
$522$	−4.45932e12	−2.62876
$523$	−2.53787e12	−1.48324	−0.741620	−	0.670820i	$-0.765942\pi$
$523$	−2.53787e12	−1.48324	−0.741620	+	0.670820i	$0.765942\pi$
$524$	−6.28732e11	−0.364313
$525$	0	0
$526$	1.92992e12	1.09927
$527$	−1.07036e12	−0.604482
$528$	−4.52386e11	−0.253313
$529$	−1.70941e12	−0.949063
$530$	9.08342e11	0.500044
$531$	4.98620e12	2.72172
$532$	0	0
$533$	2.09477e12	1.12425
$534$	2.85229e12	1.51795
$535$	−1.14962e12	−0.606683
$536$	−3.56506e11	−0.186563
$537$	3.78920e12	1.96636
$538$	1.21444e12	0.624965
$539$	0	0
$540$	3.25237e12	1.64599
$541$	1.11804e12	0.561136	0.280568	−	0.959834i	$-0.409477\pi$
$541$	1.11804e12	0.561136	0.280568	+	0.959834i	$0.409477\pi$
$542$	1.13823e12	0.566546
$543$	4.28574e12	2.11556
$544$	−3.76300e11	−0.184221
$545$	−4.65859e11	−0.226188
$546$	0	0
$547$	1.99438e12	0.952500	0.476250	−	0.879310i	$-0.341996\pi$
$547$	1.99438e12	0.952500	0.476250	+	0.879310i	$0.341996\pi$
$548$	1.55741e12	0.737719
$549$	−2.99031e12	−1.40488
$550$	1.64473e12	0.766414
$551$	2.63931e12	1.21985
$552$	3.06506e11	0.140512
$553$	0	0
$554$	−1.37847e12	−0.621731
$555$	−2.04963e12	−0.916973
$556$	−5.76638e11	−0.255898
$557$	−4.69088e11	−0.206493	−0.103247	−	0.994656i	$-0.532923\pi$
$557$	−4.69088e11	−0.206493	−0.103247	+	0.994656i	$0.532923\pi$
$558$	1.97338e12	0.861702
$559$	8.84197e11	0.382997
$560$	0	0
$561$	−2.47721e12	−1.05592
$562$	1.60286e12	0.677770
$563$	−1.74518e12	−0.732069	−0.366034	−	0.930601i	$-0.619285\pi$
$563$	−1.74518e12	−0.732069	−0.366034	+	0.930601i	$0.619285\pi$
$564$	1.74864e12	0.727687
$565$	−1.37848e12	−0.569093
$566$	−7.31911e11	−0.299767
$567$	0	0
$568$	−8.99572e11	−0.362634
$569$	−4.13341e12	−1.65311	−0.826557	−	0.562853i	$-0.809704\pi$
$569$	−4.13341e12	−1.65311	−0.826557	+	0.562853i	$0.809704\pi$
$570$	−3.67351e12	−1.45762
$571$	4.14262e12	1.63084	0.815422	−	0.578867i	$-0.196505\pi$
$571$	4.14262e12	1.63084	0.815422	+	0.578867i	$0.196505\pi$
$572$	4.35920e11	0.170265
$573$	6.67383e12	2.58630
$574$	0	0
$575$	−1.11436e12	−0.425129
$576$	6.93767e11	0.262611
$577$	−4.27130e12	−1.60424	−0.802120	−	0.597164i	$-0.796294\pi$
$577$	−4.27130e12	−1.60424	−0.802120	+	0.597164i	$0.796294\pi$
$578$	−1.63167e11	−0.0608076
$579$	6.67614e11	0.246872
$580$	4.09480e12	1.50247
$581$	0	0
$582$	−2.66316e12	−0.962154
$583$	6.68394e11	0.239621
$584$	1.09687e12	0.390211
$585$	−5.98078e12	−2.11133
$586$	−1.62584e11	−0.0569557
$587$	−5.32282e12	−1.85042	−0.925210	−	0.379455i	$-0.876111\pi$
$587$	−5.32282e12	−1.85042	−0.925210	+	0.379455i	$0.876111\pi$
$588$	0	0
$589$	−1.16797e12	−0.399865
$590$	−4.57861e12	−1.55561
$591$	5.90570e12	1.99126
$592$	−2.29102e11	−0.0766622
$593$	2.69262e11	0.0894190	0.0447095	−	0.999000i	$-0.485764\pi$
$593$	2.69262e11	0.0894190	0.0447095	+	0.999000i	$0.485764\pi$
$594$	2.39322e12	0.788758
$595$	0	0
$596$	−8.02605e11	−0.260551
$597$	5.33906e11	0.172021
$598$	−2.95350e11	−0.0944457
$599$	3.51807e12	1.11657	0.558283	−	0.829651i	$-0.311460\pi$
$599$	3.51807e12	1.11657	0.558283	+	0.829651i	$0.311460\pi$
$600$	−3.72292e12	−1.17274
$601$	1.97549e12	0.617645	0.308823	−	0.951120i	$-0.400065\pi$
$601$	1.97549e12	0.617645	0.308823	+	0.951120i	$0.400065\pi$
$602$	0	0
$603$	3.59916e12	1.10860
$604$	−1.58960e12	−0.485984
$605$	−3.74316e12	−1.13590
$606$	−4.14279e10	−0.0124786
$607$	1.20562e12	0.360464	0.180232	−	0.983624i	$-0.442315\pi$
$607$	1.20562e12	0.360464	0.180232	+	0.983624i	$0.442315\pi$
$608$	−4.10615e11	−0.121862
$609$	0	0
$610$	2.74587e12	0.802963
$611$	−1.68499e12	−0.489117
$612$	3.79899e12	1.09468
$613$	−5.02026e11	−0.143600	−0.0717999	−	0.997419i	$-0.522874\pi$
$613$	−5.02026e11	−0.143600	−0.0717999	+	0.997419i	$0.522874\pi$
$614$	−5.90332e11	−0.167625
$615$	−2.01528e13	−5.68065
$616$	0	0
$617$	5.17852e12	1.43854	0.719271	−	0.694730i	$-0.244476\pi$
$617$	5.17852e12	1.43854	0.719271	+	0.694730i	$0.244476\pi$
$618$	5.52536e12	1.52375
$619$	4.69963e12	1.28664	0.643318	−	0.765599i	$-0.277557\pi$
$619$	4.69963e12	1.28664	0.643318	+	0.765599i	$0.277557\pi$
$620$	−1.81207e12	−0.492507
$621$	−1.62149e12	−0.437523
$622$	3.01693e12	0.808179
$623$	0	0
$624$	−9.86722e11	−0.260534
$625$	2.53502e12	0.664541
$626$	2.10845e12	0.548756
$627$	−2.70312e12	−0.698491
$628$	−3.41449e12	−0.876006
$629$	−1.25454e12	−0.319562
$630$	0	0
$631$	−5.53678e12	−1.39035	−0.695177	−	0.718839i	$-0.744674\pi$
$631$	−5.53678e12	−1.39035	−0.695177	+	0.718839i	$0.744674\pi$
$632$	−1.16879e11	−0.0291414
$633$	8.91994e11	0.220823
$634$	2.41097e12	0.592639
$635$	6.14872e12	1.50073
$636$	−1.51293e12	−0.366660
$637$	0	0
$638$	3.01312e12	0.719985
$639$	9.08175e12	2.15484
$640$	−6.37056e11	−0.150096
$641$	−2.85506e12	−0.667966	−0.333983	−	0.942579i	$-0.608393\pi$
$641$	−2.85506e12	−0.667966	−0.333983	+	0.942579i	$0.608393\pi$
$642$	1.91481e12	0.444854
$643$	7.48209e12	1.72613	0.863065	−	0.505093i	$-0.168542\pi$
$643$	7.48209e12	1.72613	0.863065	+	0.505093i	$0.168542\pi$
$644$	0	0
$645$	−8.50646e12	−1.93522
$646$	−2.24848e12	−0.507976
$647$	3.83872e12	0.861225	0.430613	−	0.902537i	$-0.358297\pi$
$647$	3.83872e12	0.861225	0.430613	+	0.902537i	$0.358297\pi$
$648$	−2.08330e12	−0.464157
$649$	−3.36912e12	−0.745445
$650$	3.58741e12	0.788263
$651$	0	0
$652$	1.87807e12	0.407003
$653$	−1.09261e11	−0.0235157	−0.0117578	−	0.999931i	$-0.503743\pi$
$653$	−1.09261e11	−0.0235157	−0.0117578	+	0.999931i	$0.503743\pi$
$654$	7.75934e11	0.165854
$655$	−5.82859e12	−1.23731
$656$	−2.25263e12	−0.474922
$657$	−1.10736e13	−2.31871
$658$	0	0
$659$	−2.10319e12	−0.434403	−0.217202	−	0.976127i	$-0.569693\pi$
$659$	−2.10319e12	−0.434403	−0.217202	+	0.976127i	$0.569693\pi$
$660$	−4.19380e12	−0.860319
$661$	1.76045e12	0.358688	0.179344	−	0.983786i	$-0.442603\pi$
$661$	1.76045e12	0.358688	0.179344	+	0.983786i	$0.442603\pi$
$662$	−5.42203e11	−0.109724
$663$	−5.40317e12	−1.08602
$664$	−1.56974e12	−0.313380
$665$	0	0
$666$	2.31293e12	0.455542
$667$	−2.04149e12	−0.399374
$668$	1.64404e12	0.319462
$669$	1.76148e13	3.39986
$670$	−3.30495e12	−0.633619
$671$	2.02052e12	0.384779
$672$	0	0
$673$	8.52389e12	1.60166	0.800830	−	0.598892i	$-0.204392\pi$
$673$	8.52389e12	1.60166	0.800830	+	0.598892i	$0.204392\pi$
$674$	−3.17299e12	−0.592241
$675$	1.96950e13	3.65165
$676$	−1.76394e12	−0.324881
$677$	2.88497e12	0.527828	0.263914	−	0.964546i	$-0.414986\pi$
$677$	2.88497e12	0.527828	0.263914	+	0.964546i	$0.414986\pi$
$678$	2.29600e12	0.417290
$679$	0	0
$680$	−3.48844e12	−0.625665
$681$	−1.76732e13	−3.14885
$682$	−1.33339e12	−0.236009
$683$	1.03086e13	1.81262	0.906309	−	0.422616i	$-0.138888\pi$
$683$	1.03086e13	1.81262	0.906309	+	0.422616i	$0.138888\pi$
$684$	4.14542e12	0.724130
$685$	1.44378e13	2.50550
$686$	0	0
$687$	8.79556e12	1.50646
$688$	−9.50829e11	−0.161791
$689$	1.45787e12	0.246451
$690$	2.84143e12	0.477218
$691$	−7.85439e12	−1.31057	−0.655287	−	0.755380i	$-0.727452\pi$
$691$	−7.85439e12	−1.31057	−0.655287	+	0.755380i	$0.727452\pi$
$692$	−4.91126e12	−0.814171
$693$	0	0
$694$	2.74819e12	0.449706
$695$	−5.34566e12	−0.869099
$696$	−6.82030e12	−1.10170
$697$	−1.23351e13	−1.97969
$698$	−3.01102e12	−0.480136
$699$	−9.38969e12	−1.48766
$700$	0	0
$701$	1.69579e12	0.265242	0.132621	−	0.991167i	$-0.457661\pi$
$701$	1.69579e12	0.265242	0.132621	+	0.991167i	$0.457661\pi$
$702$	5.21997e12	0.811243
$703$	−1.36894e12	−0.211390
$704$	−4.68771e11	−0.0719257
$705$	1.62106e13	2.47142
$706$	3.16793e12	0.479904
$707$	0	0
$708$	7.62613e12	1.14066
$709$	−2.20703e12	−0.328020	−0.164010	−	0.986459i	$-0.552443\pi$
$709$	−2.20703e12	−0.328020	−0.164010	+	0.986459i	$0.552443\pi$
$710$	−8.33938e12	−1.23160
$711$	1.17997e12	0.173164
$712$	2.95560e12	0.431008
$713$	9.03417e11	0.130914
$714$	0	0
$715$	4.04115e12	0.578266
$716$	3.92644e12	0.558330
$717$	−2.14225e13	−3.02715
$718$	−6.95470e12	−0.976604
$719$	1.46869e12	0.204952	0.102476	−	0.994735i	$-0.467324\pi$
$719$	1.46869e12	0.204952	0.102476	+	0.994735i	$0.467324\pi$
$720$	6.43149e12	0.891898
$721$	0	0
$722$	2.70948e12	0.371081
$723$	2.02192e12	0.275195
$724$	4.44096e12	0.600694
$725$	2.47965e13	3.33326
$726$	6.23461e12	0.832904
$727$	4.97511e11	0.0660538	0.0330269	−	0.999454i	$-0.489485\pi$
$727$	4.97511e11	0.0660538	0.0330269	+	0.999454i	$0.489485\pi$
$728$	0	0
$729$	−4.99938e12	−0.655605
$730$	1.01684e13	1.32526
$731$	−5.20663e12	−0.674417
$732$	−4.57352e12	−0.588777
$733$	5.22437e12	0.668445	0.334223	−	0.942494i	$-0.391526\pi$
$733$	5.22437e12	0.668445	0.334223	+	0.942494i	$0.391526\pi$
$734$	9.63306e11	0.122499
$735$	0	0
$736$	3.17608e11	0.0398971
$737$	−2.43191e12	−0.303630
$738$	2.27417e13	2.82208
$739$	7.35495e11	0.0907152	0.0453576	−	0.998971i	$-0.485557\pi$
$739$	7.35495e11	0.0907152	0.0453576	+	0.998971i	$0.485557\pi$
$740$	−2.12386e12	−0.260366
$741$	−5.89590e12	−0.718403
$742$	0	0
$743$	−1.12076e12	−0.134916	−0.0674580	−	0.997722i	$-0.521489\pi$
$743$	−1.12076e12	−0.134916	−0.0674580	+	0.997722i	$0.521489\pi$
$744$	3.01818e12	0.361133
$745$	−7.44045e12	−0.884904
$746$	1.09683e13	1.29663
$747$	1.58475e13	1.86217
$748$	−2.56694e12	−0.299818
$749$	0	0
$750$	−1.61907e13	−1.86849
$751$	−1.62183e12	−0.186049	−0.0930244	−	0.995664i	$-0.529653\pi$
$751$	−1.62183e12	−0.186049	−0.0930244	+	0.995664i	$0.529653\pi$
$752$	1.81197e12	0.206620
$753$	−2.40991e13	−2.73164
$754$	6.57206e12	0.740509
$755$	−1.47362e13	−1.65054
$756$	0	0
$757$	−1.55150e12	−0.171720	−0.0858600	−	0.996307i	$-0.527364\pi$
$757$	−1.55150e12	−0.171720	−0.0858600	+	0.996307i	$0.527364\pi$
$758$	−8.08836e12	−0.889916
$759$	2.09084e12	0.228682
$760$	−3.80656e12	−0.413877
$761$	−1.62863e13	−1.76032	−0.880159	−	0.474679i	$-0.842564\pi$
$761$	−1.62863e13	−1.76032	−0.880159	+	0.474679i	$0.842564\pi$
$762$	−1.02413e13	−1.10042
$763$	0	0
$764$	6.91554e12	0.734355
$765$	3.52181e13	3.71783
$766$	3.23286e12	0.339280
$767$	−7.34856e12	−0.766695
$768$	1.06108e12	0.110058
$769$	1.32915e13	1.37059	0.685293	−	0.728267i	$-0.259674\pi$
$769$	1.32915e13	1.37059	0.685293	+	0.728267i	$0.259674\pi$
$770$	0	0
$771$	1.09455e12	0.111555
$772$	6.91794e11	0.0700970
$773$	7.58593e12	0.764190	0.382095	−	0.924123i	$-0.375203\pi$
$773$	7.58593e12	0.764190	0.382095	+	0.924123i	$0.375203\pi$
$774$	9.59923e12	0.961395
$775$	−1.09732e13	−1.09263
$776$	−2.75962e12	−0.273194
$777$	0	0
$778$	−8.83126e12	−0.864200
$779$	−1.34600e13	−1.30956
$780$	−9.14729e12	−0.884844
$781$	−6.13645e12	−0.590184
$782$	1.73918e12	0.166309
$783$	3.60809e13	3.43044
$784$	0	0
$785$	−3.16536e13	−2.97516
$786$	9.70809e12	0.907262
$787$	−3.30985e12	−0.307554	−0.153777	−	0.988106i	$-0.549144\pi$
$787$	−3.30985e12	−0.307554	−0.153777	+	0.988106i	$0.549144\pi$
$788$	6.11960e12	0.565399
$789$	−2.97995e13	−2.73755
$790$	−1.08352e12	−0.0989722
$791$	0	0
$792$	4.73254e12	0.427397
$793$	4.40706e12	0.395748
$794$	2.02906e12	0.181176
$795$	−1.40255e13	−1.24528
$796$	5.53244e11	0.0488436
$797$	3.26446e12	0.286582	0.143291	−	0.989681i	$-0.454232\pi$
$797$	3.26446e12	0.286582	0.143291	+	0.989681i	$0.454232\pi$
$798$	0	0
$799$	9.92216e12	0.861283
$800$	−3.85776e12	−0.332989
$801$	−2.98386e13	−2.56114
$802$	−9.39131e12	−0.801570
$803$	7.48235e12	0.635064
$804$	5.50473e12	0.464605
$805$	0	0
$806$	−2.90833e12	−0.242737
$807$	−1.87519e13	−1.55637
$808$	−4.29283e10	−0.00354318
$809$	3.46768e12	0.284624	0.142312	−	0.989822i	$-0.454546\pi$
$809$	3.46768e12	0.284624	0.142312	+	0.989822i	$0.454546\pi$
$810$	−1.93130e13	−1.57640
$811$	−1.02915e13	−0.835381	−0.417690	−	0.908589i	$-0.637160\pi$
$811$	−1.02915e13	−0.835381	−0.417690	+	0.908589i	$0.637160\pi$
$812$	0	0
$813$	−1.75752e13	−1.41089
$814$	−1.56282e12	−0.124767
$815$	1.74104e13	1.38229
$816$	5.81035e12	0.458772
$817$	−5.68143e12	−0.446127
$818$	−1.45322e12	−0.113486
$819$	0	0
$820$	−2.08828e13	−1.61297
$821$	6.23700e12	0.479106	0.239553	−	0.970883i	$-0.422999\pi$
$821$	6.23700e12	0.479106	0.239553	+	0.970883i	$0.422999\pi$
$822$	−2.40476e13	−1.83717
$823$	2.46689e13	1.87435	0.937175	−	0.348860i	$-0.113431\pi$
$823$	2.46689e13	1.87435	0.937175	+	0.348860i	$0.113431\pi$
$824$	5.72548e12	0.432653
$825$	−2.53959e13	−1.90863
$826$	0	0
$827$	−1.45027e13	−1.07814	−0.539068	−	0.842262i	$-0.681224\pi$
$827$	−1.45027e13	−1.07814	−0.539068	+	0.842262i	$0.681224\pi$
$828$	−3.20645e12	−0.237076
$829$	1.07681e13	0.791854	0.395927	−	0.918282i	$-0.370423\pi$
$829$	1.07681e13	0.791854	0.395927	+	0.918282i	$0.370423\pi$
$830$	−1.45521e13	−1.06432
$831$	2.12846e13	1.54832
$832$	−1.02246e12	−0.0739761
$833$	0	0
$834$	8.90373e12	0.637272
$835$	1.52409e13	1.08498
$836$	−2.80102e12	−0.198330
$837$	−1.59668e13	−1.12449
$838$	−1.33547e13	−0.935484
$839$	2.36129e13	1.64521	0.822603	−	0.568616i	$-0.192521\pi$
$839$	2.36129e13	1.64521	0.822603	+	0.568616i	$0.192521\pi$
$840$	0	0
$841$	3.09195e13	2.13133
$842$	2.58176e11	0.0177015
$843$	−2.47494e13	−1.68787
$844$	9.24301e11	0.0627007
$845$	−1.63524e13	−1.10339
$846$	−1.82930e13	−1.22778
$847$	0	0
$848$	−1.56773e12	−0.104109
$849$	1.13013e13	0.746521
$850$	−2.11246e13	−1.38805
$851$	1.05886e12	0.0692081
$852$	1.38901e13	0.903080
$853$	1.67503e13	1.08331	0.541655	−	0.840601i	$-0.317798\pi$
$853$	1.67503e13	1.08331	0.541655	+	0.840601i	$0.317798\pi$
$854$	0	0
$855$	3.84297e13	2.45934
$856$	1.98416e12	0.126312
$857$	1.16182e13	0.735742	0.367871	−	0.929877i	$-0.380087\pi$
$857$	1.16182e13	0.735742	0.367871	+	0.929877i	$0.380087\pi$
$858$	−6.73094e12	−0.424017
$859$	−1.58818e13	−0.995246	−0.497623	−	0.867393i	$-0.665794\pi$
$859$	−1.58818e13	−0.995246	−0.497623	+	0.867393i	$0.665794\pi$
$860$	−8.81455e12	−0.549487
$861$	0	0
$862$	7.71096e12	0.475692
$863$	1.35971e13	0.834446	0.417223	−	0.908804i	$-0.363003\pi$
$863$	1.35971e13	0.834446	0.417223	+	0.908804i	$0.363003\pi$
$864$	−5.61335e12	−0.342697
$865$	−4.55293e13	−2.76515
$866$	1.06930e13	0.646056
$867$	2.51943e12	0.151431
$868$	0	0
$869$	−7.97294e11	−0.0474274
$870$	−6.32269e13	−3.74167
$871$	−5.30437e12	−0.312285
$872$	8.04037e11	0.0470925
$873$	2.78601e13	1.62338
$874$	1.89778e12	0.110013
$875$	0	0
$876$	−1.69366e13	−0.971755
$877$	3.40277e12	0.194238	0.0971189	−	0.995273i	$-0.469037\pi$
$877$	3.40277e12	0.194238	0.0971189	+	0.995273i	$0.469037\pi$
$878$	−7.67711e12	−0.435986
$879$	2.51041e12	0.141839
$880$	−4.34569e12	−0.244279
$881$	−9.30779e12	−0.520541	−0.260270	−	0.965536i	$-0.583812\pi$
$881$	−9.30779e12	−0.520541	−0.260270	+	0.965536i	$0.583812\pi$
$882$	0	0
$883$	1.00154e13	0.554430	0.277215	−	0.960808i	$-0.410589\pi$
$883$	1.00154e13	0.554430	0.277215	+	0.960808i	$0.410589\pi$
$884$	−5.59887e12	−0.308365
$885$	7.06972e13	3.87398
$886$	1.04576e13	0.570137
$887$	2.58440e13	1.40186	0.700928	−	0.713232i	$-0.252769\pi$
$887$	2.58440e13	1.40186	0.700928	+	0.713232i	$0.252769\pi$
$888$	3.53751e12	0.190915
$889$	0	0
$890$	2.73995e13	1.46382
$891$	−1.42113e13	−0.755412
$892$	1.82528e13	0.965358
$893$	1.08270e13	0.569739
$894$	1.23928e13	0.648860
$895$	3.63997e13	1.89624
$896$	0	0
$897$	4.56043e12	0.235201
$898$	3.01855e12	0.154901
$899$	−2.01026e13	−1.02644
$900$	3.89465e13	1.97869
$901$	−8.58471e12	−0.433974
$902$	−1.53664e13	−0.772932
$903$	0	0
$904$	2.37916e12	0.118486
$905$	4.11694e13	2.04012
$906$	2.45447e13	1.21026
$907$	3.82049e13	1.87451	0.937253	−	0.348650i	$-0.113360\pi$
$907$	3.82049e13	1.87451	0.937253	+	0.348650i	$0.113360\pi$
$908$	−1.83133e13	−0.894086
$909$	4.33389e11	0.0210543
$910$	0	0
$911$	9.85478e12	0.474039	0.237020	−	0.971505i	$-0.423829\pi$
$911$	9.85478e12	0.474039	0.237020	+	0.971505i	$0.423829\pi$
$912$	6.34021e12	0.303478
$913$	−1.07080e13	−0.510023
$914$	−2.09929e13	−0.994979
$915$	−4.23983e13	−1.99965
$916$	9.11412e12	0.427745
$917$	0	0
$918$	−3.07380e13	−1.42851
$919$	2.60834e13	1.20627	0.603135	−	0.797639i	$-0.293918\pi$
$919$	2.60834e13	1.20627	0.603135	+	0.797639i	$0.293918\pi$
$920$	2.94435e12	0.135501
$921$	9.11517e12	0.417442
$922$	1.86551e13	0.850176
$923$	−1.33845e13	−0.607008
$924$	0	0
$925$	−1.28613e13	−0.577625
$926$	6.19709e11	0.0276974
$927$	−5.78024e13	−2.57091
$928$	−7.06733e12	−0.312816
$929$	3.60592e13	1.58835	0.794174	−	0.607690i	$-0.207904\pi$
$929$	3.60592e13	1.58835	0.794174	+	0.607690i	$0.207904\pi$
$930$	2.79797e13	1.22651
$931$	0	0
$932$	−9.72977e12	−0.422407
$933$	−4.65836e13	−2.01264
$934$	1.87440e12	0.0805936
$935$	−2.37965e13	−1.01826
$936$	1.03224e13	0.439581
$937$	−2.75358e13	−1.16700	−0.583499	−	0.812114i	$-0.698317\pi$
$937$	−2.75358e13	−1.16700	−0.583499	+	0.812114i	$0.698317\pi$
$938$	0	0
$939$	−3.25561e13	−1.36659
$940$	1.67977e13	0.701737
$941$	7.60157e12	0.316046	0.158023	−	0.987435i	$-0.449488\pi$
$941$	7.60157e12	0.316046	0.158023	+	0.987435i	$0.449488\pi$
$942$	5.27223e13	2.18155
$943$	1.04112e13	0.428745
$944$	7.90234e12	0.323878
$945$	0	0
$946$	−6.48610e12	−0.263314
$947$	−2.35269e13	−0.950582	−0.475291	−	0.879829i	$-0.657657\pi$
$947$	−2.35269e13	−0.950582	−0.475291	+	0.879829i	$0.657657\pi$
$948$	1.80470e12	0.0725719
$949$	1.63201e13	0.653168
$950$	−2.30510e13	−0.918192
$951$	−3.72272e13	−1.47587
$952$	0	0
$953$	3.76056e12	0.147684	0.0738422	−	0.997270i	$-0.476474\pi$
$953$	3.76056e12	0.147684	0.0738422	+	0.997270i	$0.476474\pi$
$954$	1.58272e13	0.618639
$955$	6.41098e13	2.49407
$956$	−2.21984e13	−0.859531
$957$	−4.65248e13	−1.79300
$958$	−3.11575e13	−1.19514
$959$	0	0
$960$	9.83663e12	0.373788
$961$	−1.75436e13	−0.663535
$962$	−3.40875e12	−0.128324
$963$	−2.00313e13	−0.750571
$964$	2.09515e12	0.0781391
$965$	6.41320e12	0.238068
$966$	0	0
$967$	3.59678e13	1.32280	0.661400	−	0.750033i	$-0.269963\pi$
$967$	3.59678e13	1.32280	0.661400	+	0.750033i	$0.269963\pi$
$968$	6.46042e12	0.236495
$969$	3.47182e13	1.26503
$970$	−2.55827e13	−0.927843
$971$	1.20049e13	0.433383	0.216692	−	0.976240i	$-0.430473\pi$
$971$	1.20049e13	0.433383	0.216692	+	0.976240i	$0.430473\pi$
$972$	5.19328e12	0.186614
$973$	0	0
$974$	3.13573e13	1.11641
$975$	−5.53923e13	−1.96304
$976$	−4.73917e12	−0.167178
$977$	−4.59954e12	−0.161506	−0.0807530	−	0.996734i	$-0.525732\pi$
$977$	−4.59954e12	−0.161506	−0.0807530	+	0.996734i	$0.525732\pi$
$978$	−2.89988e13	−1.01357
$979$	2.01617e13	0.701462
$980$	0	0
$981$	−8.11727e12	−0.279833
$982$	4.69742e12	0.161197
$983$	3.13830e12	0.107202	0.0536011	−	0.998562i	$-0.482930\pi$
$983$	3.13830e12	0.107202	0.0536011	+	0.998562i	$0.482930\pi$
$984$	3.47823e13	1.18272
$985$	5.67310e13	1.92025
$986$	−3.86999e13	−1.30396
$987$	0	0
$988$	−6.10944e12	−0.203984
$989$	4.39454e12	0.146060
$990$	4.38725e13	1.45156
$991$	1.38736e13	0.456939	0.228470	−	0.973551i	$-0.426628\pi$
$991$	1.38736e13	0.456939	0.228470	+	0.973551i	$0.426628\pi$
$992$	3.12750e12	0.102540
$993$	8.37203e12	0.273249
$994$	0	0
$995$	5.12878e12	0.165886
$996$	2.42380e13	0.780421
$997$	1.65453e13	0.530331	0.265166	−	0.964203i	$-0.414573\pi$
$997$	1.65453e13	0.530331	0.265166	+	0.964203i	$0.414573\pi$
$998$	−2.74224e13	−0.875019
$999$	−1.87142e13	−0.594465

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.a.e.1.2		2
7.2	even	3		98.10.c.h.67.1		4
7.3	odd	6		98.10.c.j.79.2		4
7.4	even	3		98.10.c.h.79.1		4
7.5	odd	6		98.10.c.j.67.2		4
7.6	odd	2		14.10.a.c.1.1	✓	2
21.20	even	2		126.10.a.o.1.2		2
28.27	even	2		112.10.a.c.1.2		2
35.13	even	4		350.10.c.j.99.3		4
35.27	even	4		350.10.c.j.99.2		4
35.34	odd	2		350.10.a.j.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.a.c.1.1	✓	2	7.6	odd	2
98.10.a.e.1.2		2	1.1	even	1	trivial
98.10.c.h.67.1		4	7.2	even	3
98.10.c.h.79.1		4	7.4	even	3
98.10.c.j.67.2		4	7.5	odd	6
98.10.c.j.79.2		4	7.3	odd	6
112.10.a.c.1.2		2	28.27	even	2
126.10.a.o.1.2		2	21.20	even	2
350.10.a.j.1.2		2	35.34	odd	2
350.10.c.j.99.2		4	35.27	even	4
350.10.c.j.99.3		4	35.13	even	4

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +247.052 q^{3} +256.000 q^{4} +2373.22 q^{5} -3952.83 q^{6} -4096.00 q^{8} +41351.7 q^{9} +O(q^{10})\)	\(q-16.0000 q^{2} +247.052 q^{3} +256.000 q^{4} +2373.22 q^{5} -3952.83 q^{6} -4096.00 q^{8} +41351.7 q^{9} -37971.5 q^{10} -27940.9 q^{11} +63245.3 q^{12} -60943.3 q^{13} +586309. q^{15} +65536.0 q^{16} +358867. q^{17} -661628. q^{18} +391593. q^{19} +607544. q^{20} +447055. q^{22} -302894. q^{23} -1.01193e6 q^{24} +3.67904e6 q^{25} +975093. q^{26} +5.35330e6 q^{27} +6.73993e6 q^{29} -9.38094e6 q^{30} -2.98262e6 q^{31} -1.04858e6 q^{32} -6.90287e6 q^{33} -5.74188e6 q^{34} +1.05860e7 q^{36} -3.49582e6 q^{37} -6.26549e6 q^{38} -1.50562e7 q^{39} -9.72070e6 q^{40} -3.43724e7 q^{41} -1.45085e7 q^{43} -7.15288e6 q^{44} +9.81367e7 q^{45} +4.84631e6 q^{46} +2.76485e7 q^{47} +1.61908e7 q^{48} -5.88647e7 q^{50} +8.86589e7 q^{51} -1.56015e7 q^{52} -2.39217e7 q^{53} -8.56529e7 q^{54} -6.63100e7 q^{55} +9.67439e7 q^{57} -1.07839e8 q^{58} +1.20580e8 q^{59} +1.50095e8 q^{60} -7.23140e7 q^{61} +4.77219e7 q^{62} +1.67772e7 q^{64} -1.44632e8 q^{65} +1.10446e8 q^{66} +8.70377e7 q^{67} +9.18701e7 q^{68} -7.48307e7 q^{69} +2.19622e8 q^{71} -1.69377e8 q^{72} -2.67792e8 q^{73} +5.59331e7 q^{74} +9.08915e8 q^{75} +1.00248e8 q^{76} +2.40899e8 q^{78} +2.85350e7 q^{79} +1.55531e8 q^{80} +5.08619e8 q^{81} +5.49959e8 q^{82} +3.83237e8 q^{83} +8.51671e8 q^{85} +2.32136e8 q^{86} +1.66511e9 q^{87} +1.14446e8 q^{88} -7.21581e8 q^{89} -1.57019e9 q^{90} -7.75410e7 q^{92} -7.36861e8 q^{93} -4.42377e8 q^{94} +9.29336e8 q^{95} -2.59053e8 q^{96} +6.73736e8 q^{97} -1.15541e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{2} + 14 q^{3} + 512 q^{4} + 2730 q^{5} - 224 q^{6} - 8192 q^{8} + 75982 q^{9}+O(q^{10}) \) 2 * q - 32 * q^2 + 14 * q^3 + 512 * q^4 + 2730 * q^5 - 224 * q^6 - 8192 * q^8 + 75982 * q^9	\( 2 q - 32 q^{2} + 14 q^{3} + 512 q^{4} + 2730 q^{5} - 224 q^{6} - 8192 q^{8} + 75982 q^{9} - 43680 q^{10} + 44940 q^{11} + 3584 q^{12} - 100282 q^{13} + 503160 q^{15} + 131072 q^{16} + 870408 q^{17} - 1215712 q^{18} - 508774 q^{19} + 698880 q^{20} - 719040 q^{22} + 79800 q^{23} - 57344 q^{24} + 1853210 q^{25} + 1604512 q^{26} + 1869812 q^{27} + 2006328 q^{29} - 8050560 q^{30} - 2188732 q^{31} - 2097152 q^{32} - 23887920 q^{33} - 13926528 q^{34} + 19451392 q^{36} - 20723576 q^{37} + 8140384 q^{38} - 5888224 q^{39} - 11182080 q^{40} - 19016592 q^{41} + 4193716 q^{43} + 11504640 q^{44} + 110492130 q^{45} - 1276800 q^{46} + 74542524 q^{47} + 917504 q^{48} - 29651360 q^{50} - 30556644 q^{51} - 25672192 q^{52} - 3239748 q^{53} - 29916992 q^{54} - 40307400 q^{55} + 306576332 q^{57} - 32101248 q^{58} + 133642362 q^{59} + 128808960 q^{60} - 227801686 q^{61} + 35019712 q^{62} + 33554432 q^{64} - 158667180 q^{65} + 382206720 q^{66} + 332930272 q^{67} + 222824448 q^{68} - 164018400 q^{69} - 167985720 q^{71} - 311222272 q^{72} + 44684276 q^{73} + 331577216 q^{74} + 1334428970 q^{75} - 130246144 q^{76} + 94211584 q^{78} + 269642776 q^{79} + 178913280 q^{80} + 638826478 q^{81} + 304265472 q^{82} + 183105762 q^{83} + 1034179020 q^{85} - 67099456 q^{86} + 2768288796 q^{87} - 184074240 q^{88} - 791657748 q^{89} - 1767874080 q^{90} + 20428800 q^{92} - 921877624 q^{93} - 1192680384 q^{94} + 608102040 q^{95} - 14680064 q^{96} + 4169480 q^{97} + 1368480540 q^{99}+O(q^{100}) \) 2 * q - 32 * q^2 + 14 * q^3 + 512 * q^4 + 2730 * q^5 - 224 * q^6 - 8192 * q^8 + 75982 * q^9 - 43680 * q^10 + 44940 * q^11 + 3584 * q^12 - 100282 * q^13 + 503160 * q^15 + 131072 * q^16 + 870408 * q^17 - 1215712 * q^18 - 508774 * q^19 + 698880 * q^20 - 719040 * q^22 + 79800 * q^23 - 57344 * q^24 + 1853210 * q^25 + 1604512 * q^26 + 1869812 * q^27 + 2006328 * q^29 - 8050560 * q^30 - 2188732 * q^31 - 2097152 * q^32 - 23887920 * q^33 - 13926528 * q^34 + 19451392 * q^36 - 20723576 * q^37 + 8140384 * q^38 - 5888224 * q^39 - 11182080 * q^40 - 19016592 * q^41 + 4193716 * q^43 + 11504640 * q^44 + 110492130 * q^45 - 1276800 * q^46 + 74542524 * q^47 + 917504 * q^48 - 29651360 * q^50 - 30556644 * q^51 - 25672192 * q^52 - 3239748 * q^53 - 29916992 * q^54 - 40307400 * q^55 + 306576332 * q^57 - 32101248 * q^58 + 133642362 * q^59 + 128808960 * q^60 - 227801686 * q^61 + 35019712 * q^62 + 33554432 * q^64 - 158667180 * q^65 + 382206720 * q^66 + 332930272 * q^67 + 222824448 * q^68 - 164018400 * q^69 - 167985720 * q^71 - 311222272 * q^72 + 44684276 * q^73 + 331577216 * q^74 + 1334428970 * q^75 - 130246144 * q^76 + 94211584 * q^78 + 269642776 * q^79 + 178913280 * q^80 + 638826478 * q^81 + 304265472 * q^82 + 183105762 * q^83 + 1034179020 * q^85 - 67099456 * q^86 + 2768288796 * q^87 - 184074240 * q^88 - 791657748 * q^89 - 1767874080 * q^90 + 20428800 * q^92 - 921877624 * q^93 - 1192680384 * q^94 + 608102040 * q^95 - 14680064 * q^96 + 4169480 * q^97 + 1368480540 * q^99

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