LMFDB - Embedded newform 98.7.b.c.97.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,7,Mod(97,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.97"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	98.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,256,0,0,0,0,-1512] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$22.5453001947$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 285x^{6} + 282x^{5} + 62091x^{4} + 29260x^{3} + 4838750x^{2} + 2401000x + 294122500 $ x^8 - 2x^7 + 285x^6 + 282x^5 + 62091x^4 + 29260x^3 + 4838750x^2 + 2401000*x + 294122500
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			97.2
Root			$7.51287 - 13.0127i$ of defining polynomial
Character	$\chi$	$=$	98.97
Dual form			98.7.b.c.97.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.65685 q^{2} -25.2754i q^{3} +32.0000 q^{4} -12.4115i q^{5} +142.979i q^{6} -181.019 q^{8} +90.1550 q^{9} +70.2099i q^{10} -1549.66 q^{11} -808.812i q^{12} -2770.09i q^{13} -313.705 q^{15} +1024.00 q^{16} +126.573i q^{17} -509.994 q^{18} -1325.37i q^{19} -397.167i q^{20} +8766.21 q^{22} -14239.5 q^{23} +4575.33i q^{24} +15471.0 q^{25} +15670.0i q^{26} -20704.5i q^{27} -7479.03 q^{29} +1774.58 q^{30} +56859.7i q^{31} -5792.62 q^{32} +39168.3i q^{33} -716.004i q^{34} +2884.96 q^{36} -90011.5 q^{37} +7497.44i q^{38} -70015.2 q^{39} +2246.72i q^{40} +35783.9i q^{41} -79422.8 q^{43} -49589.2 q^{44} -1118.96i q^{45} +80550.9 q^{46} +145878. i q^{47} -25882.0i q^{48} -87516.9 q^{50} +3199.17 q^{51} -88643.0i q^{52} -170181. q^{53} +117122. i q^{54} +19233.6i q^{55} -33499.3 q^{57} +42307.8 q^{58} +216991. i q^{59} -10038.5 q^{60} -199177. i q^{61} -321647. i q^{62} +32768.0 q^{64} -34380.9 q^{65} -221569. i q^{66} +144438. q^{67} +4050.33i q^{68} +359909. i q^{69} +407591. q^{71} -16319.8 q^{72} +186753. i q^{73} +509182. q^{74} -391034. i q^{75} -42411.9i q^{76} +396066. q^{78} +83858.5 q^{79} -12709.3i q^{80} -457590. q^{81} -202424. i q^{82} +162495. i q^{83} +1570.95 q^{85} +449283. q^{86} +189035. i q^{87} +280519. q^{88} -507844. i q^{89} +6329.77i q^{90} -455665. q^{92} +1.43715e6 q^{93} -825210. i q^{94} -16449.8 q^{95} +146411. i q^{96} -509740. i q^{97} -139710. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 256 q^{4} - 1512 q^{9} + 2712 q^{11} + 27144 q^{15} + 8192 q^{16} + 13632 q^{18} + 25248 q^{22} + 8256 q^{23} - 9328 q^{25} - 30312 q^{29} - 19296 q^{30} - 48384 q^{36} + 12248 q^{37} - 201528 q^{39}+ \cdots - 4625928 q^{99}+O(q^{100}) $ 8 * q + 256 * q^4 - 1512 * q^9 + 2712 * q^11 + 27144 * q^15 + 8192 * q^16 + 13632 * q^18 + 25248 * q^22 + 8256 * q^23 - 9328 * q^25 - 30312 * q^29 - 19296 * q^30 - 48384 * q^36 + 12248 * q^37 - 201528 * q^39 - 297376 * q^43 + 86784 * q^44 + 388128 * q^46 + 38784 * q^50 - 507384 * q^51 - 556968 * q^53 - 81288 * q^57 + 339648 * q^58 + 868608 * q^60 + 262144 * q^64 - 16632 * q^65 - 1297616 * q^67 + 190128 * q^71 + 436224 * q^72 + 2316288 * q^74 + 1122432 * q^78 - 140192 * q^79 - 2355840 * q^81 + 2190984 * q^85 + 1146048 * q^86 + 807936 * q^88 + 264192 * q^92 + 46728 * q^93 - 1451280 * q^95 - 4625928 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−5.65685	−0.707107
$2$	−5.65685	−0.707107
$3$	− 25.2754i	− 0.936125i	−0.883695	−	0.468063i	$-0.844952\pi$
$3$	− 25.2754i	− 0.936125i	0.883695	−	0.468063i	$-0.155048\pi$
$4$	32.0000	0.500000
$5$	− 12.4115i	− 0.0992917i	−0.998767	−	0.0496459i	$-0.984191\pi$
$5$	− 12.4115i	− 0.0992917i	0.998767	−	0.0496459i	$-0.0158093\pi$
$6$	142.979i	0.661941i
$7$	0	0
$7$	0	0
$8$	−181.019	−0.353553
$9$	90.1550	0.123669
$10$	70.2099i	0.0702099i
$11$	−1549.66	−1.16428	−0.582142	−	0.813087i	$-0.697785\pi$
$11$	−1549.66	−1.16428	−0.582142	+	0.813087i	$0.697785\pi$
$12$	− 808.812i	− 0.468063i
$13$	− 2770.09i	− 1.26085i	−0.776249	−	0.630427i	$-0.782880\pi$
$13$	− 2770.09i	− 1.26085i	0.776249	−	0.630427i	$-0.217120\pi$
$14$	0	0
$15$	−313.705	−0.0929495
$16$	1024.00	0.250000
$17$	126.573i	0.0257628i	0.999917	+	0.0128814i	$0.00410039\pi$
$17$	126.573i	0.0257628i	−0.999917	+	0.0128814i	$0.995900\pi$
$18$	−509.994	−0.0874475
$19$	− 1325.37i	− 0.193231i	−0.995322	−	0.0966156i	$-0.969198\pi$
$19$	− 1325.37i	− 0.193231i	0.995322	−	0.0966156i	$-0.0308018\pi$
$20$	− 397.167i	− 0.0496459i
$21$	0	0
$22$	8766.21	0.823273
$23$	−14239.5	−1.17034	−0.585170	−	0.810911i	$-0.698972\pi$
$23$	−14239.5	−1.17034	−0.585170	+	0.810911i	$0.698972\pi$
$24$	4575.33i	0.330970i
$25$	15471.0	0.990141
$26$	15670.0i	0.891558i
$27$	− 20704.5i	− 1.05190i
$28$	0	0
$29$	−7479.03	−0.306656	−0.153328	−	0.988175i	$-0.548999\pi$
$29$	−7479.03	−0.306656	−0.153328	+	0.988175i	$0.548999\pi$
$30$	1774.58	0.0657252
$31$	56859.7i	1.90862i	0.298820	+	0.954309i	$0.403407\pi$
$31$	56859.7i	1.90862i	−0.298820	+	0.954309i	$0.596593\pi$
$32$	−5792.62	−0.176777
$33$	39168.3i	1.08992i
$34$	− 716.004i	− 0.0182171i
$35$	0	0
$36$	2884.96	0.0618347
$37$	−90011.5	−1.77702	−0.888511	−	0.458855i	$-0.848260\pi$
$37$	−90011.5	−1.77702	−0.888511	+	0.458855i	$0.848260\pi$
$38$	7497.44i	0.136635i
$39$	−70015.2	−1.18032
$40$	2246.72i	0.0351049i
$41$	35783.9i	0.519202i	0.965716	+	0.259601i	$0.0835910\pi$
$41$	35783.9i	0.519202i	−0.965716	+	0.259601i	$0.916409\pi$
$42$	0	0
$43$	−79422.8	−0.998942	−0.499471	−	0.866331i	$-0.666472\pi$
$43$	−79422.8	−0.998942	−0.499471	+	0.866331i	$0.666472\pi$
$44$	−49589.2	−0.582142
$45$	− 1118.96i	− 0.0122794i
$46$	80550.9	0.827555
$47$	145878.i	1.40506i	0.711652	+	0.702532i	$0.247947\pi$
$47$	145878.i	1.40506i	−0.711652	+	0.702532i	$0.752053\pi$
$48$	− 25882.0i	− 0.234031i
$49$	0	0
$50$	−87516.9	−0.700136
$51$	3199.17	0.0241172
$52$	− 88643.0i	− 0.630427i
$53$	−170181.	−1.14309	−0.571547	−	0.820569i	$-0.693657\pi$
$53$	−170181.	−1.14309	−0.571547	+	0.820569i	$0.693657\pi$
$54$	117122.i	0.743802i
$55$	19233.6i	0.115604i
$56$	0	0
$57$	−33499.3	−0.180889
$58$	42307.8	0.216839
$59$	216991.i	1.05654i	0.849077	+	0.528269i	$0.177159\pi$
$59$	216991.i	1.05654i	−0.849077	+	0.528269i	$0.822841\pi$
$60$	−10038.5	−0.0464747
$61$	− 199177.i	− 0.877505i	−0.898608	−	0.438753i	$-0.855420\pi$
$61$	− 199177.i	− 0.877505i	0.898608	−	0.438753i	$-0.144580\pi$
$62$	− 321647.i	− 1.34960i
$63$	0	0
$64$	32768.0	0.125000
$65$	−34380.9	−0.125192
$66$	− 221569.i	− 0.770687i
$67$	144438.	0.480238	0.240119	−	0.970743i	$-0.422813\pi$
$67$	144438.	0.480238	0.240119	+	0.970743i	$0.422813\pi$
$68$	4050.33i	0.0128814i
$69$	359909.i	1.09558i
$70$	0	0
$71$	407591.	1.13880	0.569402	−	0.822059i	$-0.307175\pi$
$71$	407591.	1.13880	0.569402	+	0.822059i	$0.307175\pi$
$72$	−16319.8	−0.0437238
$73$	186753.i	0.480063i	0.970765	+	0.240032i	$0.0771578\pi$
$73$	186753.i	0.480063i	−0.970765	+	0.240032i	$0.922842\pi$
$74$	509182.	1.25654
$75$	− 391034.i	− 0.926896i
$76$	− 42411.9i	− 0.0966156i
$77$	0	0
$78$	396066.	0.834610
$79$	83858.5	0.170085	0.0850425	−	0.996377i	$-0.472897\pi$
$79$	83858.5	0.170085	0.0850425	+	0.996377i	$0.472897\pi$
$80$	− 12709.3i	− 0.0248229i
$81$	−457590.	−0.861036
$82$	− 202424.i	− 0.367131i
$83$	162495.i	0.284188i	0.989853	+	0.142094i	$0.0453836\pi$
$83$	162495.i	0.284188i	−0.989853	+	0.142094i	$0.954616\pi$
$84$	0	0
$85$	1570.95	0.00255804
$86$	449283.	0.706358
$87$	189035.i	0.287068i
$88$	280519.	0.411637
$89$	− 507844.i	− 0.720378i	−0.932879	−	0.360189i	$-0.882712\pi$
$89$	− 507844.i	− 0.720378i	0.932879	−	0.360189i	$-0.117288\pi$
$90$	6329.77i	0.00868281i
$91$	0	0
$92$	−455665.	−0.585170
$93$	1.43715e6	1.78671
$94$	− 825210.i	− 0.993530i
$95$	−16449.8	−0.0191863
$96$	146411.i	0.165485i
$97$	− 509740.i	− 0.558514i	−0.960216	−	0.279257i	$-0.909912\pi$
$97$	− 509740.i	− 0.558514i	0.960216	−	0.279257i	$-0.0900881\pi$
$98$	0	0
$99$	−139710.	−0.143986
$100$	495071.	0.495071
$101$	− 1.55951e6i	− 1.51364i	−0.653622	−	0.756821i	$-0.726751\pi$
$101$	− 1.55951e6i	− 1.51364i	0.653622	−	0.756821i	$-0.273249\pi$
$102$	−18097.3	−0.0170535
$103$	− 727252.i	− 0.665539i	−0.943008	−	0.332769i	$-0.892017\pi$
$103$	− 727252.i	− 0.665539i	0.943008	−	0.332769i	$-0.107983\pi$
$104$	501441.i	0.445779i
$105$	0	0
$106$	962686.	0.808290
$107$	−1.74964e6	−1.42823	−0.714116	−	0.700028i	$-0.753171\pi$
$107$	−1.74964e6	−1.42823	−0.714116	+	0.700028i	$0.753171\pi$
$108$	− 662543.i	− 0.525948i
$109$	−772852.	−0.596783	−0.298392	−	0.954444i	$-0.596450\pi$
$109$	−772852.	−0.596783	−0.298392	+	0.954444i	$0.596450\pi$
$110$	− 108802.i	− 0.0817442i
$111$	2.27508e6i	1.66352i
$112$	0	0
$113$	−2.26586e6	−1.57035	−0.785176	−	0.619273i	$-0.787428\pi$
$113$	−2.26586e6	−1.57035	−0.785176	+	0.619273i	$0.787428\pi$
$114$	189501.	0.127908
$115$	176733.i	0.116205i
$116$	−239329.	−0.153328
$117$	− 249738.i	− 0.155929i
$118$	− 1.22748e6i	− 0.747085i
$119$	0	0
$120$	56786.6	0.0328626
$121$	629893.	0.355558
$122$	1.12672e6i	0.620490i
$123$	904452.	0.486038
$124$	1.81951e6i	0.954309i
$125$	− 385946.i	− 0.197605i
$126$	0	0
$127$	813391.	0.397089	0.198545	−	0.980092i	$-0.436379\pi$
$127$	813391.	0.397089	0.198545	+	0.980092i	$0.436379\pi$
$128$	−185364.	−0.0883883
$129$	2.00744e6i	0.935134i
$130$	194488.	0.0885243
$131$	3.06778e6i	1.36461i	0.731066	+	0.682307i	$0.239023\pi$
$131$	3.06778e6i	1.36461i	−0.731066	+	0.682307i	$0.760977\pi$
$132$	1.25339e6i	0.544958i
$133$	0	0
$134$	−817064.	−0.339580
$135$	−256973.	−0.104445
$136$	− 22912.1i	− 0.00910853i
$137$	−628001.	−0.244230	−0.122115	−	0.992516i	$-0.538968\pi$
$137$	−628001.	−0.244230	−0.122115	+	0.992516i	$0.538968\pi$
$138$	− 2.03595e6i	− 0.774695i
$139$	− 2.79572e6i	− 1.04100i	−0.853863	−	0.520498i	$-0.825746\pi$
$139$	− 2.79572e6i	− 1.04100i	0.853863	−	0.520498i	$-0.174254\pi$
$140$	0	0
$141$	3.68712e6	1.31532
$142$	−2.30568e6	−0.805257
$143$	4.29271e6i	1.46799i
$144$	92318.8	0.0309174
$145$	92825.8i	0.0304484i
$146$	− 1.05643e6i	− 0.339456i
$147$	0	0
$148$	−2.88037e6	−0.888511
$149$	−4.09077e6	−1.23665	−0.618324	−	0.785924i	$-0.712188\pi$
$149$	−4.09077e6	−1.23665	−0.618324	+	0.785924i	$0.712188\pi$
$150$	2.21202e6i	0.655415i
$151$	1.63874e6	0.475969	0.237985	−	0.971269i	$-0.423513\pi$
$151$	1.63874e6	0.475969	0.237985	+	0.971269i	$0.423513\pi$
$152$	239918.i	0.0683176i
$153$	11411.2i	0.00318607i
$154$	0	0
$155$	705712.	0.189510
$156$	−2.24049e6	−0.590158
$157$	− 5.75442e6i	− 1.48697i	−0.668752	−	0.743485i	$-0.733171\pi$
$157$	− 5.75442e6i	− 1.48697i	0.668752	−	0.743485i	$-0.266829\pi$
$158$	−474375.	−0.120268
$159$	4.30138e6i	1.07008i
$160$	71894.9i	0.0175525i
$161$	0	0
$162$	2.58852e6	0.608845
$163$	957939.	0.221195	0.110597	−	0.993865i	$-0.464724\pi$
$163$	957939.	0.221195	0.110597	+	0.993865i	$0.464724\pi$
$164$	1.14508e6i	0.259601i
$165$	486136.	0.108220
$166$	− 919212.i	− 0.200951i
$167$	− 6.70923e6i	− 1.44053i	−0.693698	−	0.720266i	$-0.744020\pi$
$167$	− 6.70923e6i	− 1.44053i	0.693698	−	0.720266i	$-0.255980\pi$
$168$	0	0
$169$	−2.84662e6	−0.589751
$170$	−8886.65	−0.00180880
$171$	− 119489.i	− 0.0238968i
$172$	−2.54153e6	−0.499471
$173$	− 347094.i	− 0.0670362i	−0.999438	−	0.0335181i	$-0.989329\pi$
$173$	− 347094.i	− 0.0670362i	0.999438	−	0.0335181i	$-0.0106711\pi$
$174$	− 1.06935e6i	− 0.202988i
$175$	0	0
$176$	−1.58685e6	−0.291071
$177$	5.48452e6	0.989052
$178$	2.87280e6i	0.509384i
$179$	−2.94540e6	−0.513554	−0.256777	−	0.966471i	$-0.582661\pi$
$179$	−2.94540e6	−0.513554	−0.256777	+	0.966471i	$0.582661\pi$
$180$	− 35806.6i	− 0.00613968i
$181$	2.88805e6i	0.487046i	0.969895	+	0.243523i	$0.0783031\pi$
$181$	2.88805e6i	0.487046i	−0.969895	+	0.243523i	$0.921697\pi$
$182$	0	0
$183$	−5.03428e6	−0.821455
$184$	2.57763e6	0.413777
$185$	1.11717e6i	0.176444i
$186$	−8.12975e6	−1.26339
$187$	− 196145.i	− 0.0299953i
$188$	4.66810e6i	0.702532i
$189$	0	0
$190$	93054.3	0.0135667
$191$	−5.66730e6	−0.813347	−0.406674	−	0.913574i	$-0.633311\pi$
$191$	−5.66730e6	−0.813347	−0.406674	+	0.913574i	$0.633311\pi$
$192$	− 828224.i	− 0.117016i
$193$	1.30863e7	1.82030	0.910152	−	0.414274i	$-0.135965\pi$
$193$	1.30863e7	1.82030	0.910152	+	0.414274i	$0.135965\pi$
$194$	2.88353e6i	0.394929i
$195$	868991.i	0.117196i
$196$	0	0
$197$	4.47088e6	0.584783	0.292391	−	0.956299i	$-0.405549\pi$
$197$	4.47088e6	0.584783	0.292391	+	0.956299i	$0.405549\pi$
$198$	790318.	0.101814
$199$	− 8.05760e6i	− 1.02246i	−0.859444	−	0.511230i	$-0.829190\pi$
$199$	− 8.05760e6i	− 1.02246i	0.859444	−	0.511230i	$-0.170810\pi$
$200$	−2.80054e6	−0.350068
$201$	− 3.65072e6i	− 0.449563i
$202$	8.82191e6i	1.07031i
$203$	0	0
$204$	102374.	0.0120586
$205$	444131.	0.0515524
$206$	4.11396e6i	0.470607i
$207$	−1.28376e6	−0.144735
$208$	− 2.83658e6i	− 0.315213i
$209$	2.05388e6i	0.224976i
$210$	0	0
$211$	421809.	0.0449023	0.0224511	−	0.999748i	$-0.492853\pi$
$211$	421809.	0.0449023	0.0224511	+	0.999748i	$0.492853\pi$
$212$	−5.44578e6	−0.571547
$213$	− 1.03020e7i	− 1.06606i
$214$	9.89749e6	1.00991
$215$	985754.i	0.0991866i
$216$	3.74791e6i	0.371901i
$217$	0	0
$218$	4.37191e6	0.421990
$219$	4.72025e6	0.449399
$220$	615475.i	0.0578019i
$221$	350619.	0.0324831
$222$	− 1.28698e7i	− 1.17628i
$223$	− 4.49399e6i	− 0.405245i	−0.979257	−	0.202622i	$-0.935054\pi$
$223$	− 4.49399e6i	− 0.405245i	0.979257	−	0.202622i	$-0.0649464\pi$
$224$	0	0
$225$	1.39478e6	0.122450
$226$	1.28176e7	1.11041
$227$	3.89219e6i	0.332749i	0.986063	+	0.166375i	$0.0532061\pi$
$227$	3.89219e6i	0.332749i	−0.986063	+	0.166375i	$0.946794\pi$
$228$	−1.07198e6	−0.0904443
$229$	− 2.46566e6i	− 0.205318i	−0.994717	−	0.102659i	$-0.967265\pi$
$229$	− 2.46566e6i	− 0.205318i	0.994717	−	0.102659i	$-0.0327351\pi$
$230$	− 999755.i	− 0.0821694i
$231$	0	0
$232$	1.35385e6	0.108419
$233$	2.26972e7	1.79434	0.897170	−	0.441685i	$-0.145619\pi$
$233$	2.26972e7	1.79434	0.897170	+	0.441685i	$0.145619\pi$
$234$	1.41273e6i	0.110259i
$235$	1.81056e6	0.139511
$236$	6.94370e6i	0.528269i
$237$	− 2.11956e6i	− 0.159221i
$238$	0	0
$239$	−3.91448e6	−0.286734	−0.143367	−	0.989670i	$-0.545793\pi$
$239$	−3.91448e6	−0.286734	−0.143367	+	0.989670i	$0.545793\pi$
$240$	−321233.	−0.0232374
$241$	− 9.82635e6i	− 0.702006i	−0.936374	−	0.351003i	$-0.885841\pi$
$241$	− 9.82635e6i	− 0.702006i	0.936374	−	0.351003i	$-0.114159\pi$
$242$	−3.56321e6	−0.251417
$243$	− 3.52779e6i	− 0.245857i
$244$	− 6.37367e6i	− 0.438753i
$245$	0	0
$246$	−5.11635e6	−0.343681
$247$	−3.67141e6	−0.243636
$248$	− 1.02927e7i	− 0.674799i
$249$	4.10713e6	0.266036
$250$	2.18324e6i	0.139728i
$251$	1.12666e7i	0.712477i	0.934395	+	0.356238i	$0.115941\pi$
$251$	1.12666e7i	0.712477i	−0.934395	+	0.356238i	$0.884059\pi$
$252$	0	0
$253$	2.20664e7	1.36261
$254$	−4.60124e6	−0.280785
$255$	− 39706.4i	− 0.00239464i
$256$	1.04858e6	0.0625000
$257$	− 3.11879e7i	− 1.83733i	−0.395039	−	0.918665i	$-0.629269\pi$
$257$	− 3.11879e7i	− 1.83733i	0.395039	−	0.918665i	$-0.370731\pi$
$258$	− 1.13558e7i	− 0.661240i
$259$	0	0
$260$	−1.10019e6	−0.0625962
$261$	−674273.	−0.0379240
$262$	− 1.73540e7i	− 0.964928i
$263$	−1.35186e7	−0.743127	−0.371564	−	0.928407i	$-0.621178\pi$
$263$	−1.35186e7	−0.743127	−0.371564	+	0.928407i	$0.621178\pi$
$264$	− 7.09022e6i	− 0.385343i
$265$	2.11219e6i	0.113500i
$266$	0	0
$267$	−1.28360e7	−0.674364
$268$	4.62201e6	0.240119
$269$	2.60752e7i	1.33958i	0.742548	+	0.669792i	$0.233617\pi$
$269$	2.60752e7i	1.33958i	−0.742548	+	0.669792i	$0.766383\pi$
$270$	1.45366e6	0.0738534
$271$	1.10455e7i	0.554979i	0.960729	+	0.277490i	$0.0895024\pi$
$271$	1.10455e7i	0.554979i	−0.960729	+	0.277490i	$0.910498\pi$
$272$	129611.i	0.00644071i
$273$	0	0
$274$	3.55251e6	0.172696
$275$	−2.39748e7	−1.15281
$276$	1.15171e7i	0.547792i
$277$	−1.59471e7	−0.750311	−0.375155	−	0.926962i	$-0.622411\pi$
$277$	−1.59471e7	−0.750311	−0.375155	+	0.926962i	$0.622411\pi$
$278$	1.58150e7i	0.736095i
$279$	5.12618e6i	0.236038i
$280$	0	0
$281$	−1.25628e6	−0.0566198	−0.0283099	−	0.999599i	$-0.509013\pi$
$281$	−1.25628e6	−0.0566198	−0.0283099	+	0.999599i	$0.509013\pi$
$282$	−2.08575e7	−0.930069
$283$	− 337339.i	− 0.0148836i	−0.999972	−	0.00744179i	$-0.997631\pi$
$283$	− 337339.i	− 0.0148836i	0.999972	−	0.00744179i	$-0.00236882\pi$
$284$	1.30429e7	0.569402
$285$	415776.i	0.0179607i
$286$	− 2.42832e7i	− 1.03803i
$287$	0	0
$288$	−522234.	−0.0218619
$289$	2.41215e7	0.999336
$290$	− 525102.i	− 0.0215303i
$291$	−1.28839e7	−0.522839
$292$	5.97609e6i	0.240032i
$293$	1.30355e7i	0.518233i	0.965846	+	0.259117i	$0.0834314\pi$
$293$	1.30355e7i	0.518233i	−0.965846	+	0.259117i	$0.916569\pi$
$294$	0	0
$295$	2.69317e6	0.104905
$296$	1.62938e7	0.628272
$297$	3.20849e7i	1.22471i
$298$	2.31409e7	0.874442
$299$	3.94448e7i	1.47563i
$300$	− 1.25131e7i	− 0.463448i
$301$	0	0
$302$	−9.27010e6	−0.336561
$303$	−3.94172e7	−1.41696
$304$	− 1.35718e6i	− 0.0483078i
$305$	−2.47208e6	−0.0871290
$306$	− 64551.3i	− 0.00225290i
$307$	− 3.48621e7i	− 1.20487i	−0.798170	−	0.602433i	$-0.794198\pi$
$307$	− 3.48621e7i	− 1.20487i	0.798170	−	0.602433i	$-0.205802\pi$
$308$	0	0
$309$	−1.83816e7	−0.623028
$310$	−3.99211e6	−0.134004
$311$	4.41060e7i	1.46628i	0.680079	+	0.733139i	$0.261945\pi$
$311$	4.41060e7i	1.46628i	−0.680079	+	0.733139i	$0.738055\pi$
$312$	1.26741e7	0.417305
$313$	4.35412e7i	1.41993i	0.704237	+	0.709965i	$0.251289\pi$
$313$	4.35412e7i	1.41993i	−0.704237	+	0.709965i	$0.748711\pi$
$314$	3.25519e7i	1.05145i
$315$	0	0
$316$	2.68347e6	0.0850425
$317$	−3.27393e7	−1.02776	−0.513880	−	0.857862i	$-0.671792\pi$
$317$	−3.27393e7	−1.02776	−0.513880	+	0.857862i	$0.671792\pi$
$318$	− 2.43323e7i	− 0.756661i
$319$	1.15900e7	0.357035
$320$	− 406699.i	− 0.0124115i
$321$	4.42229e7i	1.33700i
$322$	0	0
$323$	167756.	0.00497818
$324$	−1.46429e7	−0.430518
$325$	− 4.28560e7i	− 1.24842i
$326$	−5.41892e6	−0.156408
$327$	1.95341e7i	0.558664i
$328$	− 6.47758e6i	− 0.183565i
$329$	0	0
$330$	−2.75000e6	−0.0765228
$331$	−3.16254e7	−0.872072	−0.436036	−	0.899929i	$-0.643618\pi$
$331$	−3.16254e7	−0.872072	−0.436036	+	0.899929i	$0.643618\pi$
$332$	5.19985e6i	0.142094i
$333$	−8.11499e6	−0.219763
$334$	3.79531e7i	1.01861i
$335$	− 1.79269e6i	− 0.0476837i
$336$	0	0
$337$	−8.23591e6	−0.215190	−0.107595	−	0.994195i	$-0.534315\pi$
$337$	−8.23591e6	−0.215190	−0.107595	+	0.994195i	$0.534315\pi$
$338$	1.61029e7	0.417017
$339$	5.72704e7i	1.47005i
$340$	50270.5	0.00127902
$341$	− 8.81133e7i	− 2.22217i
$342$	675932.i	0.0168976i
$343$	0	0
$344$	1.43771e7	0.353179
$345$	4.46700e6	0.108782
$346$	1.96346e6i	0.0474017i
$347$	−6.25010e7	−1.49589	−0.747943	−	0.663763i	$-0.768958\pi$
$347$	−6.25010e7	−1.49589	−0.747943	+	0.663763i	$0.768958\pi$
$348$	6.04913e6i	0.143534i
$349$	− 2.49010e7i	− 0.585788i	−0.956145	−	0.292894i	$-0.905382\pi$
$349$	− 2.49010e7i	− 0.585788i	0.956145	−	0.292894i	$-0.0946183\pi$
$350$	0	0
$351$	−5.73533e7	−1.32629
$352$	8.97660e6	0.205818
$353$	− 6.92552e7i	− 1.57445i	−0.616668	−	0.787224i	$-0.711518\pi$
$353$	− 6.92552e7i	− 1.57445i	0.616668	−	0.787224i	$-0.288482\pi$
$354$	−3.10251e7	−0.699365
$355$	− 5.05880e6i	− 0.113074i
$356$	− 1.62510e7i	− 0.360189i
$357$	0	0
$358$	1.66617e7	0.363137
$359$	3.00933e7	0.650408	0.325204	−	0.945644i	$-0.394567\pi$
$359$	3.00933e7	0.650408	0.325204	+	0.945644i	$0.394567\pi$
$360$	202553.i	0.00434141i
$361$	4.52893e7	0.962662
$362$	− 1.63373e7i	− 0.344393i
$363$	− 1.59208e7i	− 0.332847i
$364$	0	0
$365$	2.31787e6	0.0476663
$366$	2.84782e7	0.580856
$367$	2.12124e7i	0.429132i	0.976709	+	0.214566i	$0.0688338\pi$
$367$	2.12124e7i	0.429132i	−0.976709	+	0.214566i	$0.931166\pi$
$368$	−1.45813e7	−0.292585
$369$	3.22610e6i	0.0642094i
$370$	− 6.31969e6i	− 0.124764i
$371$	0	0
$372$	4.59888e7	0.893353
$373$	4.88411e7	0.941151	0.470575	−	0.882360i	$-0.344046\pi$
$373$	4.88411e7	0.941151	0.470575	+	0.882360i	$0.344046\pi$
$374$	1.10956e6i	0.0212098i
$375$	−9.75494e6	−0.184983
$376$	− 2.64067e7i	− 0.496765i
$377$	2.07176e7i	0.386648i
$378$	0	0
$379$	8.40563e6	0.154402	0.0772009	−	0.997016i	$-0.475402\pi$
$379$	8.40563e6	0.154402	0.0772009	+	0.997016i	$0.475402\pi$
$380$	−526394.	−0.00959313
$381$	− 2.05588e7i	− 0.371725i
$382$	3.20591e7	0.575123
$383$	1.70184e7i	0.302917i	0.988464	+	0.151458i	$0.0483969\pi$
$383$	1.70184e7i	0.302917i	−0.988464	+	0.151458i	$0.951603\pi$
$384$	4.68514e6i	0.0827426i
$385$	0	0
$386$	−7.40271e7	−1.28715
$387$	−7.16037e6	−0.123539
$388$	− 1.63117e7i	− 0.279257i
$389$	5.98291e6	0.101640	0.0508199	−	0.998708i	$-0.483817\pi$
$389$	5.98291e6	0.101640	0.0508199	+	0.998708i	$0.483817\pi$
$390$	− 4.91576e6i	− 0.0828699i
$391$	− 1.80234e6i	− 0.0301513i
$392$	0	0
$393$	7.75392e7	1.27745
$394$	−2.52911e7	−0.413504
$395$	− 1.04081e6i	− 0.0168880i
$396$	−4.47072e6	−0.0719932
$397$	− 1.05663e8i	− 1.68869i	−0.535798	−	0.844346i	$-0.679989\pi$
$397$	− 1.05663e8i	− 1.68869i	0.535798	−	0.844346i	$-0.320011\pi$
$398$	4.55807e7i	0.722989i
$399$	0	0
$400$	1.58423e7	0.247535
$401$	6.12686e7	0.950177	0.475089	−	0.879938i	$-0.342416\pi$
$401$	6.12686e7	0.950177	0.475089	+	0.879938i	$0.342416\pi$
$402$	2.06516e7i	0.317889i
$403$	1.57507e8	2.40649
$404$	− 4.99042e7i	− 0.756821i
$405$	5.67936e6i	0.0854938i
$406$	0	0
$407$	1.39487e8	2.06896
$408$	−579113.	−0.00852673
$409$	− 1.09398e8i	− 1.59897i	−0.600685	−	0.799486i	$-0.705106\pi$
$409$	− 1.09398e8i	− 1.59897i	0.600685	−	0.799486i	$-0.294894\pi$
$410$	−2.51238e6	−0.0364531
$411$	1.58730e7i	0.228630i
$412$	− 2.32721e7i	− 0.332769i
$413$	0	0
$414$	7.26207e6	0.102343
$415$	2.01680e6	0.0282175
$416$	1.60461e7i	0.222889i
$417$	−7.06628e7	−0.974502
$418$	− 1.16185e7i	− 0.159082i
$419$	− 2.04457e7i	− 0.277946i	−0.990296	−	0.138973i	$-0.955620\pi$
$419$	− 2.04457e7i	− 0.277946i	0.990296	−	0.138973i	$-0.0443802\pi$
$420$	0	0
$421$	−3.19255e7	−0.427850	−0.213925	−	0.976850i	$-0.568625\pi$
$421$	−3.19255e7	−0.427850	−0.213925	+	0.976850i	$0.568625\pi$
$422$	−2.38611e6	−0.0317507
$423$	1.31516e7i	0.173764i
$424$	3.08060e7	0.404145
$425$	1.95820e6i	0.0255088i
$426$	5.82770e7i	0.753821i
$427$	0	0
$428$	−5.59886e7	−0.714116
$429$	1.08500e8	1.37422
$430$	− 5.57627e6i	− 0.0701355i
$431$	311283.	0.00388798	0.00194399	−	0.999998i	$-0.499381\pi$
$431$	311283.	0.00388798	0.00194399	+	0.999998i	$0.499381\pi$
$432$	− 2.12014e7i	− 0.262974i
$433$	− 5.06252e7i	− 0.623596i	−0.950148	−	0.311798i	$-0.899069\pi$
$433$	− 5.06252e7i	− 0.623596i	0.950148	−	0.311798i	$-0.100931\pi$
$434$	0	0
$435$	2.34621e6	0.0285035
$436$	−2.47313e7	−0.298392
$437$	1.88727e7i	0.226146i
$438$	−2.67017e7	−0.317773
$439$	8.09571e7i	0.956889i	0.878118	+	0.478445i	$0.158799\pi$
$439$	8.09571e7i	0.956889i	−0.878118	+	0.478445i	$0.841201\pi$
$440$	− 3.48165e6i	− 0.0408721i
$441$	0	0
$442$	−1.98340e6	−0.0229691
$443$	−2.56743e6	−0.0295317	−0.0147658	−	0.999891i	$-0.504700\pi$
$443$	−2.56743e6	−0.0295317	−0.0147658	+	0.999891i	$0.504700\pi$
$444$	7.28024e7i	0.831758i
$445$	−6.30309e6	−0.0715276
$446$	2.54218e7i	0.286551i
$447$	1.03396e8i	1.15766i
$448$	0	0
$449$	−6.11330e7	−0.675362	−0.337681	−	0.941261i	$-0.609643\pi$
$449$	−6.11330e7	−0.675362	−0.337681	+	0.941261i	$0.609643\pi$
$450$	−7.89009e6	−0.0865854
$451$	− 5.54530e7i	− 0.604498i
$452$	−7.25074e7	−0.785176
$453$	− 4.14197e7i	− 0.445567i
$454$	− 2.20176e7i	− 0.235289i
$455$	0	0
$456$	6.06402e6	0.0639538
$457$	9.59719e6	0.100553	0.0502765	−	0.998735i	$-0.483990\pi$
$457$	9.59719e6	0.100553	0.0502765	+	0.998735i	$0.483990\pi$
$458$	1.39479e7i	0.145182i
$459$	2.62062e6	0.0270998
$460$	5.65547e6i	0.0581025i
$461$	6.04509e7i	0.617021i	0.951221	+	0.308510i	$0.0998304\pi$
$461$	6.04509e7i	0.617021i	−0.951221	+	0.308510i	$0.900170\pi$
$462$	0	0
$463$	−1.14757e8	−1.15621	−0.578104	−	0.815963i	$-0.696207\pi$
$463$	−1.14757e8	−1.15621	−0.578104	+	0.815963i	$0.696207\pi$
$464$	−7.65853e6	−0.0766640
$465$	− 1.78371e7i	− 0.177405i
$466$	−1.28395e8	−1.26879
$467$	− 6.85435e7i	− 0.673001i	−0.941683	−	0.336500i	$-0.890757\pi$
$467$	− 6.85435e7i	− 0.673001i	0.941683	−	0.336500i	$-0.109243\pi$
$468$	− 7.99162e6i	− 0.0779645i
$469$	0	0
$470$	−1.02421e7	−0.0986493
$471$	−1.45445e8	−1.39199
$472$	− 3.92795e7i	− 0.373543i
$473$	1.23079e8	1.16305
$474$	1.19900e7i	0.112586i
$475$	− 2.05048e7i	− 0.191326i
$476$	0	0
$477$	−1.53426e7	−0.141366
$478$	2.21436e7	0.202752
$479$	− 9.77893e7i	− 0.889784i	−0.895584	−	0.444892i	$-0.853242\pi$
$479$	− 9.77893e7i	− 0.889784i	0.895584	−	0.444892i	$-0.146758\pi$
$480$	1.81717e6	0.0164313
$481$	2.49340e8i	2.24056i
$482$	5.55862e7i	0.496393i
$483$	0	0
$484$	2.01566e7	0.177779
$485$	−6.32662e6	−0.0554558
$486$	1.99562e7i	0.173847i
$487$	2.28183e7	0.197559	0.0987794	−	0.995109i	$-0.468506\pi$
$487$	2.28183e7	0.197559	0.0987794	+	0.995109i	$0.468506\pi$
$488$	3.60549e7i	0.310245i
$489$	− 2.42123e7i	− 0.207066i
$490$	0	0
$491$	1.11615e7	0.0942930	0.0471465	−	0.998888i	$-0.484987\pi$
$491$	1.11615e7	0.0942930	0.0471465	+	0.998888i	$0.484987\pi$
$492$	2.89425e7	0.243019
$493$	− 946642.i	− 0.00790032i
$494$	2.07686e7	0.172277
$495$	1.73400e6i	0.0142967i
$496$	5.82243e7i	0.477155i
$497$	0	0
$498$	−2.32334e7	−0.188116
$499$	−4.33257e7	−0.348693	−0.174347	−	0.984684i	$-0.555781\pi$
$499$	−4.33257e7	−0.348693	−0.174347	+	0.984684i	$0.555781\pi$
$500$	− 1.23503e7i	− 0.0988023i
$501$	−1.69578e8	−1.34852
$502$	− 6.37334e7i	− 0.503797i
$503$	− 2.32014e8i	− 1.82310i	−0.411192	−	0.911549i	$-0.634887\pi$
$503$	− 2.32014e8i	− 1.82310i	0.411192	−	0.911549i	$-0.365113\pi$
$504$	0	0
$505$	−1.93558e7	−0.150292
$506$	−1.24827e8	−0.963509
$507$	7.19493e7i	0.552081i
$508$	2.60285e7	0.198545
$509$	− 1.17917e8i	− 0.894179i	−0.894489	−	0.447089i	$-0.852461\pi$
$509$	− 1.17917e8i	− 0.894179i	0.894489	−	0.447089i	$-0.147539\pi$
$510$	224614.i	0.00169327i
$511$	0	0
$512$	−5.93164e6	−0.0441942
$513$	−2.74411e7	−0.203259
$514$	1.76425e8i	1.29919i
$515$	−9.02627e6	−0.0660825
$516$	6.42382e7i	0.467567i
$517$	− 2.26062e8i	− 1.63589i
$518$	0	0
$519$	−8.77294e6	−0.0627542
$520$	6.22361e6	0.0442622
$521$	2.24136e8i	1.58489i	0.609946	+	0.792443i	$0.291191\pi$
$521$	2.24136e8i	1.58489i	−0.609946	+	0.792443i	$0.708809\pi$
$522$	3.81426e6	0.0268163
$523$	1.82109e8i	1.27299i	0.771279	+	0.636497i	$0.219617\pi$
$523$	1.82109e8i	1.27299i	−0.771279	+	0.636497i	$0.780383\pi$
$524$	9.81688e7i	0.682307i
$525$	0	0
$526$	7.64725e7	0.525470
$527$	−7.19688e6	−0.0491714
$528$	4.01083e7i	0.272479i
$529$	5.47281e7	0.369695
$530$	− 1.19483e7i	− 0.0802565i
$531$	1.95628e7i	0.130661i
$532$	0	0
$533$	9.91248e7	0.654637
$534$	7.26111e7	0.476848
$535$	2.17157e7i	0.141812i
$536$	−2.61461e7	−0.169790
$537$	7.44462e7i	0.480750i
$538$	− 1.47503e8i	− 0.947229i
$539$	0	0
$540$	−8.22312e6	−0.0522223
$541$	−2.45350e8	−1.54951	−0.774756	−	0.632261i	$-0.782127\pi$
$541$	−2.45350e8	−1.54951	−0.774756	+	0.632261i	$0.782127\pi$
$542$	− 6.24827e7i	− 0.392430i
$543$	7.29967e7	0.455936
$544$	− 733188.i	− 0.00455427i
$545$	9.59222e6i	0.0592556i
$546$	0	0
$547$	1.02069e8	0.623637	0.311819	−	0.950142i	$-0.399062\pi$
$547$	1.02069e8	0.623637	0.311819	+	0.950142i	$0.399062\pi$
$548$	−2.00960e7	−0.122115
$549$	− 1.79568e7i	− 0.108521i
$550$	1.35622e8	0.815157
$551$	9.91251e6i	0.0592555i
$552$	− 6.51505e7i	− 0.387348i
$553$	0	0
$554$	9.02102e7	0.530550
$555$	2.82370e7	0.165173
$556$	− 8.94629e7i	− 0.520498i
$557$	1.91412e8	1.10765	0.553826	−	0.832633i	$-0.313167\pi$
$557$	1.91412e8	1.10765	0.553826	+	0.832633i	$0.313167\pi$
$558$	− 2.89981e7i	− 0.166904i
$559$	2.20009e8i	1.25952i
$560$	0	0
$561$	−4.95764e6	−0.0280793
$562$	7.10660e6	0.0400362
$563$	1.92544e8i	1.07896i	0.842000	+	0.539478i	$0.181378\pi$
$563$	1.92544e8i	1.07896i	−0.842000	+	0.539478i	$0.818622\pi$
$564$	1.17988e8	0.657658
$565$	2.81226e7i	0.155923i
$566$	1.90828e6i	0.0105243i
$567$	0	0
$568$	−7.37818e7	−0.402628
$569$	−5.98416e7	−0.324837	−0.162419	−	0.986722i	$-0.551930\pi$
$569$	−5.98416e7	−0.324837	−0.162419	+	0.986722i	$0.551930\pi$
$570$	− 2.35198e6i	− 0.0127002i
$571$	−2.55691e8	−1.37343	−0.686716	−	0.726926i	$-0.740949\pi$
$571$	−2.55691e8	−1.37343	−0.686716	+	0.726926i	$0.740949\pi$
$572$	1.37367e8i	0.733996i
$573$	1.43243e8i	0.761395i
$574$	0	0
$575$	−2.20299e8	−1.15880
$576$	2.95420e6	0.0154587
$577$	3.23113e7i	0.168200i	0.996457	+	0.0841001i	$0.0268015\pi$
$577$	3.23113e7i	0.168200i	−0.996457	+	0.0841001i	$0.973198\pi$
$578$	−1.36452e8	−0.706637
$579$	− 3.30760e8i	− 1.70403i
$580$	2.97042e6i	0.0152242i
$581$	0	0
$582$	7.28822e7	0.369703
$583$	2.63722e8	1.33089
$584$	− 3.38058e7i	− 0.169728i
$585$	−3.09961e6	−0.0154825
$586$	− 7.37400e7i	− 0.366446i
$587$	− 9.56070e7i	− 0.472689i	−0.971669	−	0.236344i	$-0.924051\pi$
$587$	− 9.56070e7i	− 0.472689i	0.971669	−	0.236344i	$-0.0759493\pi$
$588$	0	0
$589$	7.53603e7	0.368805
$590$	−1.52349e7	−0.0741794
$591$	− 1.13003e8i	− 0.547430i
$592$	−9.21718e7	−0.444256
$593$	− 1.16277e8i	− 0.557610i	−0.960348	−	0.278805i	$-0.910062\pi$
$593$	− 1.16277e8i	− 0.557610i	0.960348	−	0.278805i	$-0.0899383\pi$
$594$	− 1.81500e8i	− 0.865997i
$595$	0	0
$596$	−1.30905e8	−0.618324
$597$	−2.03659e8	−0.957151
$598$	− 2.23134e8i	− 1.04343i
$599$	−3.59984e8	−1.67495	−0.837477	−	0.546472i	$-0.815971\pi$
$599$	−3.59984e8	−1.67495	−0.837477	+	0.546472i	$0.815971\pi$
$600$	7.07848e7i	0.327707i
$601$	3.47560e8i	1.60105i	0.599297	+	0.800527i	$0.295447\pi$
$601$	3.47560e8i	1.60105i	−0.599297	+	0.800527i	$0.704553\pi$
$602$	0	0
$603$	1.30218e7	0.0593908
$604$	5.24396e7	0.237985
$605$	− 7.81789e6i	− 0.0353040i
$606$	2.22977e8	1.00194
$607$	− 2.12644e8i	− 0.950796i	−0.879771	−	0.475398i	$-0.842304\pi$
$607$	− 2.12644e8i	− 0.950796i	0.879771	−	0.475398i	$-0.157696\pi$
$608$	7.67738e6i	0.0341588i
$609$	0	0
$610$	1.39842e7	0.0616095
$611$	4.04096e8	1.77158
$612$	365158.i	0.00159304i
$613$	−7.88548e7	−0.342332	−0.171166	−	0.985242i	$-0.554753\pi$
$613$	−7.88548e7	−0.342332	−0.171166	+	0.985242i	$0.554753\pi$
$614$	1.97210e8i	0.851968i
$615$	− 1.12256e7i	− 0.0482595i
$616$	0	0
$617$	4.19908e6	0.0178772	0.00893859	−	0.999960i	$-0.497155\pi$
$617$	4.19908e6	0.0178772	0.00893859	+	0.999960i	$0.497155\pi$
$618$	1.03982e8	0.440547
$619$	− 2.65849e8i	− 1.12089i	−0.828191	−	0.560446i	$-0.810630\pi$
$619$	− 2.65849e8i	− 1.12089i	0.828191	−	0.560446i	$-0.189370\pi$
$620$	2.25828e7	0.0947550
$621$	2.94822e8i	1.23107i
$622$	− 2.49501e8i	− 1.03681i
$623$	0	0
$624$	−7.16956e7	−0.295079
$625$	2.36944e8	0.970521
$626$	− 2.46306e8i	− 1.00404i
$627$	5.19126e7	0.210606
$628$	− 1.84141e8i	− 0.743485i
$629$	− 1.13930e7i	− 0.0457811i
$630$	0	0
$631$	−2.02533e8	−0.806135	−0.403068	−	0.915170i	$-0.632056\pi$
$631$	−2.02533e8	−0.806135	−0.403068	+	0.915170i	$0.632056\pi$
$632$	−1.51800e7	−0.0601341
$633$	− 1.06614e7i	− 0.0420342i
$634$	1.85202e8	0.726736
$635$	− 1.00954e7i	− 0.0394277i
$636$	1.37644e8i	0.535040i
$637$	0	0
$638$	−6.55628e7	−0.252462
$639$	3.67464e7	0.140835
$640$	2.30064e6i	0.00877623i
$641$	−2.31886e7	−0.0880441	−0.0440221	−	0.999031i	$-0.514017\pi$
$641$	−2.31886e7	−0.0880441	−0.0440221	+	0.999031i	$0.514017\pi$
$642$	− 2.50163e8i	− 0.945404i
$643$	3.10031e8i	1.16620i	0.812401	+	0.583100i	$0.198160\pi$
$643$	3.10031e8i	1.16620i	−0.812401	+	0.583100i	$0.801840\pi$
$644$	0	0
$645$	2.49153e7	0.0928511
$646$	−948972.	−0.00352011
$647$	− 1.48972e8i	− 0.550036i	−0.961439	−	0.275018i	$-0.911316\pi$
$647$	− 1.48972e8i	− 0.550036i	0.961439	−	0.275018i	$-0.0886838\pi$
$648$	8.28326e7	0.304422
$649$	− 3.36262e8i	− 1.23011i
$650$	2.42430e8i	0.882768i
$651$	0	0
$652$	3.06541e7	0.110597
$653$	−2.30223e8	−0.826817	−0.413408	−	0.910546i	$-0.635662\pi$
$653$	−2.30223e8	−0.826817	−0.413408	+	0.910546i	$0.635662\pi$
$654$	− 1.10502e8i	− 0.395035i
$655$	3.80756e7	0.135495
$656$	3.66427e7i	0.129800i
$657$	1.68367e7i	0.0593691i
$658$	0	0
$659$	4.63051e8	1.61798	0.808989	−	0.587824i	$-0.200015\pi$
$659$	4.63051e8	1.61798	0.808989	+	0.587824i	$0.200015\pi$
$660$	1.55564e7	0.0541098
$661$	3.29455e8i	1.14075i	0.821384	+	0.570376i	$0.193202\pi$
$661$	3.29455e8i	1.14075i	−0.821384	+	0.570376i	$0.806798\pi$
$662$	1.78900e8	0.616648
$663$	− 8.86202e6i	− 0.0304083i
$664$	− 2.94148e7i	− 0.100476i
$665$	0	0
$666$	4.59053e7	0.155396
$667$	1.06498e8	0.358892
$668$	− 2.14695e8i	− 0.720266i
$669$	−1.13587e8	−0.379360
$670$	1.01410e7i	0.0337175i
$671$	3.08657e8i	1.02167i
$672$	0	0
$673$	−8.50491e7	−0.279013	−0.139506	−	0.990221i	$-0.544552\pi$
$673$	−8.50491e7	−0.279013	−0.139506	+	0.990221i	$0.544552\pi$
$674$	4.65894e7	0.152162
$675$	− 3.20318e8i	− 1.04152i
$676$	−9.10917e7	−0.294876
$677$	3.96153e8i	1.27672i	0.769736	+	0.638362i	$0.220388\pi$
$677$	3.96153e8i	1.27672i	−0.769736	+	0.638362i	$0.779612\pi$
$678$	− 3.23970e8i	− 1.03948i
$679$	0	0
$680$	−284373.	−0.000904402 0
$681$	9.83767e7	0.311495
$682$	4.98444e8i	1.57131i
$683$	3.23361e8	1.01490	0.507452	−	0.861680i	$-0.330587\pi$
$683$	3.23361e8	1.01490	0.507452	+	0.861680i	$0.330587\pi$
$684$	− 3.82365e6i	− 0.0119484i
$685$	7.79441e6i	0.0242500i
$686$	0	0
$687$	−6.23206e7	−0.192204
$688$	−8.13290e7	−0.249735
$689$	4.71416e8i	1.44127i
$690$	−2.52692e7	−0.0769208
$691$	− 4.77634e8i	− 1.44764i	−0.689988	−	0.723821i	$-0.742384\pi$
$691$	− 4.77634e8i	− 1.44764i	0.689988	−	0.723821i	$-0.257616\pi$
$692$	− 1.11070e7i	− 0.0335181i
$693$	0	0
$694$	3.53559e8	1.05775
$695$	−3.46989e7	−0.103362
$696$	− 3.42191e7i	− 0.101494i
$697$	−4.52927e6	−0.0133761
$698$	1.40861e8i	0.414214i
$699$	− 5.73681e8i	− 1.67973i
$700$	0	0
$701$	1.25339e7	0.0363859	0.0181929	−	0.999834i	$-0.494209\pi$
$701$	1.25339e7	0.0363859	0.0181929	+	0.999834i	$0.494209\pi$
$702$	3.24439e8	0.937826
$703$	1.19299e8i	0.343376i
$704$	−5.07793e7	−0.145536
$705$	− 4.57626e7i	− 0.130600i
$706$	3.91766e8i	1.11330i
$707$	0	0
$708$	1.75505e8	0.494526
$709$	−1.94398e8	−0.545447	−0.272723	−	0.962093i	$-0.587924\pi$
$709$	−1.94398e8	−0.545447	−0.272723	+	0.962093i	$0.587924\pi$
$710$	2.86169e7i	0.0799553i
$711$	7.56027e6	0.0210343
$712$	9.19296e7i	0.254692i
$713$	− 8.09654e8i	− 2.23373i
$714$	0	0
$715$	5.32788e7	0.145759
$716$	−9.42529e7	−0.256777
$717$	9.89399e7i	0.268419i
$718$	−1.70233e8	−0.459908
$719$	− 2.41409e8i	− 0.649481i	−0.945803	−	0.324741i	$-0.894723\pi$
$719$	− 2.41409e8i	− 0.649481i	0.945803	−	0.324741i	$-0.105277\pi$
$720$	− 1.14581e6i	− 0.00306984i
$721$	0	0
$722$	−2.56195e8	−0.680705
$723$	−2.48365e8	−0.657166
$724$	9.24177e7i	0.243523i
$725$	−1.15708e8	−0.303633
$726$	9.00615e7i	0.235358i
$727$	3.89703e8i	1.01422i	0.861882	+	0.507109i	$0.169286\pi$
$727$	3.89703e8i	1.01422i	−0.861882	+	0.507109i	$0.830714\pi$
$728$	0	0
$729$	−4.22749e8	−1.09119
$730$	−1.31119e7	−0.0337052
$731$	− 1.00528e7i	− 0.0257356i
$732$	−1.61097e8	−0.410728
$733$	1.75227e8i	0.444927i	0.974941	+	0.222464i	$0.0714099\pi$
$733$	1.75227e8i	0.444927i	−0.974941	+	0.222464i	$0.928590\pi$
$734$	− 1.19995e8i	− 0.303442i
$735$	0	0
$736$	8.24841e7	0.206889
$737$	−2.23830e8	−0.559134
$738$	− 1.82496e7i	− 0.0454029i
$739$	7.66256e6	0.0189863	0.00949315	−	0.999955i	$-0.496978\pi$
$739$	7.66256e6	0.0189863	0.00949315	+	0.999955i	$0.496978\pi$
$740$	3.57496e7i	0.0882218i
$741$	9.27963e7i	0.228074i
$742$	0	0
$743$	4.78399e8	1.16634	0.583169	−	0.812351i	$-0.301813\pi$
$743$	4.78399e8	1.16634	0.583169	+	0.812351i	$0.301813\pi$
$744$	−2.60152e8	−0.631696
$745$	5.07724e7i	0.122789i
$746$	−2.76287e8	−0.665494
$747$	1.46498e7i	0.0351454i
$748$	− 6.27664e6i	− 0.0149976i
$749$	0	0
$750$	5.51823e7	0.130802
$751$	−7.01881e7	−0.165708	−0.0828540	−	0.996562i	$-0.526404\pi$
$751$	−7.01881e7	−0.165708	−0.0828540	+	0.996562i	$0.526404\pi$
$752$	1.49379e8i	0.351266i
$753$	2.84767e8	0.666968
$754$	− 1.17197e8i	− 0.273402i
$755$	− 2.03391e7i	− 0.0472598i
$756$	0	0
$757$	−5.44271e7	−0.125466	−0.0627332	−	0.998030i	$-0.519982\pi$
$757$	−5.44271e7	−0.125466	−0.0627332	+	0.998030i	$0.519982\pi$
$758$	−4.75494e7	−0.109179
$759$	− 5.57738e8i	− 1.27557i
$760$	2.97774e6	0.00678337
$761$	5.57740e8i	1.26555i	0.774338	+	0.632773i	$0.218083\pi$
$761$	5.57740e8i	1.26555i	−0.774338	+	0.632773i	$0.781917\pi$
$762$	1.16298e8i	0.262850i
$763$	0	0
$764$	−1.81354e8	−0.406674
$765$	141629.	0.000316351 0
$766$	− 9.62708e7i	− 0.214194i
$767$	6.01085e8	1.33214
$768$	− 2.65032e7i	− 0.0585078i
$769$	− 3.50325e8i	− 0.770356i	−0.922842	−	0.385178i	$-0.874140\pi$
$769$	− 3.50325e8i	− 0.770356i	0.922842	−	0.385178i	$-0.125860\pi$
$770$	0	0
$771$	−7.88286e8	−1.71997
$772$	4.18761e8	0.910152
$773$	− 5.70467e8i	− 1.23507i	−0.786543	−	0.617536i	$-0.788131\pi$
$773$	− 5.70467e8i	− 1.23507i	0.786543	−	0.617536i	$-0.211869\pi$
$774$	4.05052e7	0.0873550
$775$	8.79673e8i	1.88980i
$776$	9.22729e7i	0.197464i
$777$	0	0
$778$	−3.38444e7	−0.0718702
$779$	4.74270e7	0.100326
$780$	2.78077e7i	0.0585978i
$781$	−6.31628e8	−1.32589
$782$	1.01955e7i	0.0213202i
$783$	1.54849e8i	0.322570i
$784$	0	0
$785$	−7.14208e7	−0.147644
$786$	−4.38628e8	−0.903293
$787$	7.46413e8i	1.53128i	0.643268	+	0.765641i	$0.277578\pi$
$787$	7.46413e8i	1.53128i	−0.643268	+	0.765641i	$0.722422\pi$
$788$	1.43068e8	0.292391
$789$	3.41687e8i	0.695660i
$790$	5.88770e6i	0.0119416i
$791$	0	0
$792$	2.52902e7	0.0509069
$793$	−5.51739e8	−1.10641
$794$	5.97719e8i	1.19409i
$795$	5.33864e7	0.106250
$796$	− 2.57843e8i	− 0.511230i
$797$	− 8.52897e8i	− 1.68470i	−0.538934	−	0.842348i	$-0.681173\pi$
$797$	− 8.52897e8i	− 1.68470i	0.538934	−	0.842348i	$-0.318827\pi$
$798$	0	0
$799$	−1.84642e7	−0.0361984
$800$	−8.96173e7	−0.175034
$801$	− 4.57847e7i	− 0.0890888i
$802$	−3.46587e8	−0.671877
$803$	− 2.89404e8i	− 0.558930i
$804$	− 1.16823e8i	− 0.224782i
$805$	0	0
$806$	−8.90992e8	−1.70164
$807$	6.59060e8	1.25402
$808$	2.82301e8i	0.535154i
$809$	−5.37862e8	−1.01584	−0.507920	−	0.861404i	$-0.669586\pi$
$809$	−5.37862e8	−1.01584	−0.507920	+	0.861404i	$0.669586\pi$
$810$	− 3.21273e7i	− 0.0604532i
$811$	− 546840.i	− 0.00102517i	−1.00000		0.000512587i	$-0.999837\pi$
$811$	− 546840.i	− 0.00102517i	1.00000		0.000512587i	$-0.000163162\pi$
$812$	0	0
$813$	2.79179e8	0.519530
$814$	−7.89060e8	−1.46297
$815$	− 1.18894e7i	− 0.0219628i
$816$	3.27596e6	0.00602931
$817$	1.05265e8i	0.193027i
$818$	6.18850e8i	1.13064i
$819$	0	0
$820$	1.42122e7	0.0257762
$821$	−5.33076e7	−0.0963295	−0.0481648	−	0.998839i	$-0.515337\pi$
$821$	−5.33076e7	−0.0963295	−0.0481648	+	0.998839i	$0.515337\pi$
$822$	− 8.97910e7i	− 0.161666i
$823$	−7.66358e8	−1.37478	−0.687389	−	0.726290i	$-0.741243\pi$
$823$	−7.66358e8	−1.37478	−0.687389	+	0.726290i	$0.741243\pi$
$824$	1.31647e8i	0.235304i
$825$	6.05971e8i	1.07917i
$826$	0	0
$827$	1.00353e9	1.77425	0.887127	−	0.461526i	$-0.152698\pi$
$827$	1.00353e9	1.77425	0.887127	+	0.461526i	$0.152698\pi$
$828$	−4.10805e7	−0.0723676
$829$	1.48306e8i	0.260313i	0.991493	+	0.130157i	$0.0415480\pi$
$829$	1.48306e8i	0.260313i	−0.991493	+	0.130157i	$0.958452\pi$
$830$	−1.14088e7	−0.0199528
$831$	4.03068e8i	0.702385i
$832$	− 9.07705e7i	− 0.157607i
$833$	0	0
$834$	3.99729e8	0.689077
$835$	−8.32714e7	−0.143033
$836$	6.57242e7i	0.112488i
$837$	1.17725e9	2.00767
$838$	1.15659e8i	0.196538i
$839$	2.21066e8i	0.374315i	0.982330	+	0.187157i	$0.0599274\pi$
$839$	2.21066e8i	0.374315i	−0.982330	+	0.187157i	$0.940073\pi$
$840$	0	0
$841$	−5.38887e8	−0.905962
$842$	1.80598e8	0.302536
$843$	3.17530e7i	0.0530032i
$844$	1.34979e7	0.0224511
$845$	3.53307e7i	0.0585574i
$846$	− 7.43969e7i	− 0.122869i
$847$	0	0
$848$	−1.74265e8	−0.285774
$849$	−8.52637e6	−0.0139329
$850$	− 1.10773e7i	− 0.0180375i
$851$	1.28172e9	2.07972
$852$	− 3.29664e8i	− 0.533032i
$853$	9.10570e8i	1.46712i	0.679624	+	0.733561i	$0.262143\pi$
$853$	9.10570e8i	1.46712i	−0.679624	+	0.733561i	$0.737857\pi$
$854$	0	0
$855$	−1.48303e6	−0.00237276
$856$	3.16720e8	0.504956
$857$	− 1.94185e8i	− 0.308513i	−0.988031	−	0.154256i	$-0.950702\pi$
$857$	− 1.94185e8i	− 0.308513i	0.988031	−	0.154256i	$-0.0492981\pi$
$858$	−6.13768e8	−0.971723
$859$	− 7.22263e8i	− 1.13950i	−0.821816	−	0.569752i	$-0.807039\pi$
$859$	− 7.22263e8i	− 1.13950i	0.821816	−	0.569752i	$-0.192961\pi$
$860$	3.15441e7i	0.0495933i
$861$	0	0
$862$	−1.76088e6	−0.00274922
$863$	−1.94276e8	−0.302264	−0.151132	−	0.988514i	$-0.548292\pi$
$863$	−1.94276e8	−0.302264	−0.151132	+	0.988514i	$0.548292\pi$
$864$	1.19933e8i	0.185951i
$865$	−4.30795e6	−0.00665614
$866$	2.86380e8i	0.440949i
$867$	− 6.09681e8i	− 0.935504i
$868$	0	0
$869$	−1.29952e8	−0.198027
$870$	−1.32721e7	−0.0201550
$871$	− 4.00107e8i	− 0.605510i
$872$	1.39901e8	0.210995
$873$	− 4.59557e7i	− 0.0690711i
$874$	− 1.06760e8i	− 0.159909i
$875$	0	0
$876$	1.51048e8	0.224700
$877$	4.96734e8	0.736419	0.368210	−	0.929743i	$-0.379971\pi$
$877$	4.96734e8	0.736419	0.368210	+	0.929743i	$0.379971\pi$
$878$	− 4.57963e8i	− 0.676623i
$879$	3.29478e8	0.485131
$880$	1.96952e7i	0.0289009i
$881$	8.63809e7i	0.126325i	0.998003	+	0.0631626i	$0.0201187\pi$
$881$	8.63809e7i	0.126325i	−0.998003	+	0.0631626i	$0.979881\pi$
$882$	0	0
$883$	6.49219e8	0.942994	0.471497	−	0.881868i	$-0.343714\pi$
$883$	6.49219e8	0.942994	0.471497	+	0.881868i	$0.343714\pi$
$884$	1.12198e7	0.0162416
$885$	− 6.80710e7i	− 0.0982046i
$886$	1.45236e7	0.0208820
$887$	− 7.12881e8i	− 1.02152i	−0.859724	−	0.510759i	$-0.829364\pi$
$887$	− 7.12881e8i	− 1.02152i	0.859724	−	0.510759i	$-0.170636\pi$
$888$	− 4.11833e8i	− 0.588141i
$889$	0	0
$890$	3.56557e7	0.0505776
$891$	7.09110e8	1.00249
$892$	− 1.43808e8i	− 0.202622i
$893$	1.93343e8	0.271502
$894$	− 5.84894e8i	− 0.818587i
$895$	3.65568e7i	0.0509916i
$896$	0	0
$897$	9.96983e8	1.38137
$898$	3.45820e8	0.477553
$899$	− 4.25255e8i	− 0.585289i
$900$	4.46331e7	0.0612251
$901$	− 2.15402e7i	− 0.0294493i
$902$	3.13689e8i	0.427445i
$903$	0	0
$904$	4.10164e8	0.555203
$905$	3.58450e7	0.0483596
$906$	2.34305e8i	0.315063i
$907$	−8.28411e8	−1.11026	−0.555129	−	0.831764i	$-0.687331\pi$
$907$	−8.28411e8	−1.11026	−0.555129	+	0.831764i	$0.687331\pi$
$908$	1.24550e8i	0.166375i
$909$	− 1.40597e8i	− 0.187191i
$910$	0	0
$911$	−1.17587e9	−1.55526	−0.777631	−	0.628721i	$-0.783579\pi$
$911$	−1.17587e9	−1.55526	−0.777631	+	0.628721i	$0.783579\pi$
$912$	−3.43033e7	−0.0452222
$913$	− 2.51813e8i	− 0.330876i
$914$	−5.42899e7	−0.0711018
$915$	6.24827e7i	0.0815637i
$916$	− 7.89013e7i	− 0.102659i
$917$	0	0
$918$	−1.48245e7	−0.0191625
$919$	4.50920e8	0.580969	0.290485	−	0.956880i	$-0.406184\pi$
$919$	4.50920e8	0.580969	0.290485	+	0.956880i	$0.406184\pi$
$920$	− 3.19921e7i	− 0.0410847i
$921$	−8.81153e8	−1.12790
$922$	− 3.41962e8i	− 0.436299i
$923$	− 1.12907e9i	− 1.43587i
$924$	0	0
$925$	−1.39256e9	−1.75950
$926$	6.49163e8	0.817562
$927$	− 6.55655e7i	− 0.0823068i
$928$	4.33232e7	0.0542096
$929$	− 1.19419e9i	− 1.48945i	−0.667372	−	0.744725i	$-0.732581\pi$
$929$	− 1.19419e9i	− 1.48945i	0.667372	−	0.744725i	$-0.267419\pi$
$930$	1.00902e8i	0.125444i
$931$	0	0
$932$	7.26311e8	0.897170
$933$	1.11480e9	1.37262
$934$	3.87740e8i	0.475883i
$935$	−2.43445e6	−0.00297828
$936$	4.52074e7i	0.0551293i
$937$	− 5.57908e8i	− 0.678178i	−0.940754	−	0.339089i	$-0.889881\pi$
$937$	− 5.57908e8i	− 0.678178i	0.940754	−	0.339089i	$-0.110119\pi$
$938$	0	0
$939$	1.10052e9	1.32923
$940$	5.79379e7	0.0697556
$941$	− 1.06009e9i	− 1.27226i	−0.771583	−	0.636128i	$-0.780535\pi$
$941$	− 1.06009e9i	− 1.27226i	0.771583	−	0.636128i	$-0.219465\pi$
$942$	8.22762e8	0.984286
$943$	− 5.09545e8i	− 0.607642i
$944$	2.22198e8i	0.264134i
$945$	0	0
$946$	−6.96238e8	−0.822402
$947$	8.16869e8	0.961839	0.480919	−	0.876765i	$-0.340303\pi$
$947$	8.16869e8	0.961839	0.480919	+	0.876765i	$0.340303\pi$
$948$	− 6.78258e7i	− 0.0796104i
$949$	5.17323e8	0.605289
$950$	1.15993e8i	0.135288i
$951$	8.27499e8i	0.962112i
$952$	0	0
$953$	1.23336e9	1.42499	0.712494	−	0.701678i	$-0.247565\pi$
$953$	1.23336e9	1.42499	0.712494	+	0.701678i	$0.247565\pi$
$954$	8.67910e7	0.0999608
$955$	7.03395e7i	0.0807586i
$956$	−1.25263e8	−0.143367
$957$	− 2.92941e8i	− 0.334229i
$958$	5.53180e8i	0.629173i
$959$	0	0
$960$	−1.02795e7	−0.0116187
$961$	−2.34552e9	−2.64283
$962$	− 1.41048e9i	− 1.58432i
$963$	−1.57739e8	−0.176629
$964$	− 3.14443e8i	− 0.351003i
$965$	− 1.62420e8i	− 0.180741i
$966$	0	0
$967$	−5.82431e8	−0.644118	−0.322059	−	0.946720i	$-0.604375\pi$
$967$	−5.82431e8	−0.644118	−0.322059	+	0.946720i	$0.604375\pi$
$968$	−1.14023e8	−0.125709
$969$	− 4.24010e6i	− 0.00466020i
$970$	3.57888e7	0.0392132
$971$	3.43898e7i	0.0375640i	0.999824	+	0.0187820i	$0.00597884\pi$
$971$	3.43898e7i	0.0375640i	−0.999824	+	0.0187820i	$0.994021\pi$
$972$	− 1.12889e8i	− 0.122929i
$973$	0	0
$974$	−1.29080e8	−0.139695
$975$	−1.08320e9	−1.16868
$976$	− 2.03957e8i	− 0.219376i
$977$	−5.21206e8	−0.558889	−0.279444	−	0.960162i	$-0.590150\pi$
$977$	−5.21206e8	−0.558889	−0.279444	+	0.960162i	$0.590150\pi$
$978$	1.36965e8i	0.146418i
$979$	7.86987e8i	0.838725i
$980$	0	0
$981$	−6.96765e7	−0.0738039
$982$	−6.31392e7	−0.0666753
$983$	6.23594e8i	0.656510i	0.944589	+	0.328255i	$0.106460\pi$
$983$	6.23594e8i	0.656510i	−0.944589	+	0.328255i	$0.893540\pi$
$984$	−1.63723e8	−0.171840
$985$	− 5.54902e7i	− 0.0580641i
$986$	5.35501e6i	0.00558637i
$987$	0	0
$988$	−1.17485e8	−0.121818
$989$	1.13094e9	1.16910
$990$	− 9.80901e6i	− 0.0101093i
$991$	1.39866e8	0.143712	0.0718559	−	0.997415i	$-0.477108\pi$
$991$	1.39866e8	0.143712	0.0718559	+	0.997415i	$0.477108\pi$
$992$	− 3.29366e8i	− 0.337399i
$993$	7.99344e8i	0.816368i
$994$	0	0
$995$	−1.00007e8	−0.101522
$996$	1.31428e8	0.133018
$997$	1.94311e9i	1.96071i	0.197249	+	0.980353i	$0.436799\pi$
$997$	1.94311e9i	1.96071i	−0.197249	+	0.980353i	$0.563201\pi$
$998$	2.45087e8	0.246563
$999$	1.86364e9i	1.86924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.7.b.c.97.2		8
7.2	even	3		14.7.d.a.3.4	✓	8
7.3	odd	6		14.7.d.a.5.4	yes	8
7.4	even	3		98.7.d.c.19.3		8
7.5	odd	6		98.7.d.c.31.3		8
7.6	odd	2	inner	98.7.b.c.97.3		8
21.2	odd	6		126.7.n.c.73.1		8
21.17	even	6		126.7.n.c.19.1		8
28.3	even	6		112.7.s.c.33.2		8
28.23	odd	6		112.7.s.c.17.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.7.d.a.3.4	✓	8	7.2	even	3
14.7.d.a.5.4	yes	8	7.3	odd	6
98.7.b.c.97.2		8	1.1	even	1	trivial
98.7.b.c.97.3		8	7.6	odd	2	inner
98.7.d.c.19.3		8	7.4	even	3
98.7.d.c.31.3		8	7.5	odd	6
112.7.s.c.17.2		8	28.23	odd	6
112.7.s.c.33.2		8	28.3	even	6
126.7.n.c.19.1		8	21.17	even	6
126.7.n.c.73.1		8	21.2	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	98.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.65685 q^{2} -25.2754i q^{3} +32.0000 q^{4} -12.4115i q^{5} +142.979i q^{6} -181.019 q^{8} +90.1550 q^{9} +70.2099i q^{10} -1549.66 q^{11} -808.812i q^{12} -2770.09i q^{13} -313.705 q^{15} +1024.00 q^{16} +126.573i q^{17} -509.994 q^{18} -1325.37i q^{19} -397.167i q^{20} +8766.21 q^{22} -14239.5 q^{23} +4575.33i q^{24} +15471.0 q^{25} +15670.0i q^{26} -20704.5i q^{27} -7479.03 q^{29} +1774.58 q^{30} +56859.7i q^{31} -5792.62 q^{32} +39168.3i q^{33} -716.004i q^{34} +2884.96 q^{36} -90011.5 q^{37} +7497.44i q^{38} -70015.2 q^{39} +2246.72i q^{40} +35783.9i q^{41} -79422.8 q^{43} -49589.2 q^{44} -1118.96i q^{45} +80550.9 q^{46} +145878. i q^{47} -25882.0i q^{48} -87516.9 q^{50} +3199.17 q^{51} -88643.0i q^{52} -170181. q^{53} +117122. i q^{54} +19233.6i q^{55} -33499.3 q^{57} +42307.8 q^{58} +216991. i q^{59} -10038.5 q^{60} -199177. i q^{61} -321647. i q^{62} +32768.0 q^{64} -34380.9 q^{65} -221569. i q^{66} +144438. q^{67} +4050.33i q^{68} +359909. i q^{69} +407591. q^{71} -16319.8 q^{72} +186753. i q^{73} +509182. q^{74} -391034. i q^{75} -42411.9i q^{76} +396066. q^{78} +83858.5 q^{79} -12709.3i q^{80} -457590. q^{81} -202424. i q^{82} +162495. i q^{83} +1570.95 q^{85} +449283. q^{86} +189035. i q^{87} +280519. q^{88} -507844. i q^{89} +6329.77i q^{90} -455665. q^{92} +1.43715e6 q^{93} -825210. i q^{94} -16449.8 q^{95} +146411. i q^{96} -509740. i q^{97} -139710. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 256 q^{4} - 1512 q^{9} + 2712 q^{11} + 27144 q^{15} + 8192 q^{16} + 13632 q^{18} + 25248 q^{22} + 8256 q^{23} - 9328 q^{25} - 30312 q^{29} - 19296 q^{30} - 48384 q^{36} + 12248 q^{37} - 201528 q^{39}+ \cdots - 4625928 q^{99}+O(q^{100}) \) 8 * q + 256 * q^4 - 1512 * q^9 + 2712 * q^11 + 27144 * q^15 + 8192 * q^16 + 13632 * q^18 + 25248 * q^22 + 8256 * q^23 - 9328 * q^25 - 30312 * q^29 - 19296 * q^30 - 48384 * q^36 + 12248 * q^37 - 201528 * q^39 - 297376 * q^43 + 86784 * q^44 + 388128 * q^46 + 38784 * q^50 - 507384 * q^51 - 556968 * q^53 - 81288 * q^57 + 339648 * q^58 + 868608 * q^60 + 262144 * q^64 - 16632 * q^65 - 1297616 * q^67 + 190128 * q^71 + 436224 * q^72 + 2316288 * q^74 + 1122432 * q^78 - 140192 * q^79 - 2355840 * q^81 + 2190984 * q^85 + 1146048 * q^86 + 807936 * q^88 + 264192 * q^92 + 46728 * q^93 - 1451280 * q^95 - 4625928 * q^99

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