LMFDB - Embedded newform 49.7.d.e.19.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,7,Mod(19,49)] 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("49.19"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	49.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$11.2726500974$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.4
Character	$\chi$	$=$	49.19
Dual form			49.7.d.e.31.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.49614 + 11.2516i) q^{2} +(40.4001 - 23.3250i) q^{3} +(-52.3997 - 90.7589i) q^{4} +(-26.6652 - 15.3952i) q^{5} +606.091i q^{6} +530.077 q^{8} +(723.614 - 1253.34i) q^{9} +(346.442 - 200.018i) q^{10} +(-726.315 - 1258.01i) q^{11} +(-4233.91 - 2444.45i) q^{12} -1874.30i q^{13} -1436.37 q^{15} +(-89.8745 + 155.667i) q^{16} +(5324.52 - 3074.11i) q^{17} +(9401.39 + 16283.7i) q^{18} +(1530.22 + 883.475i) q^{19} +3226.81i q^{20} +18873.0 q^{22} +(-4857.66 + 8413.72i) q^{23} +(21415.2 - 12364.1i) q^{24} +(-7338.48 - 12710.6i) q^{25} +(21089.0 + 12175.7i) q^{26} -33505.3i q^{27} +40048.9 q^{29} +(9330.87 - 16161.5i) q^{30} +(-27848.2 + 16078.2i) q^{31} +(15794.8 + 27357.4i) q^{32} +(-58686.4 - 33882.6i) q^{33} +79879.4i q^{34} -151668. q^{36} +(18886.2 - 32711.8i) q^{37} +(-19881.1 + 11478.4i) q^{38} +(-43718.1 - 75722.0i) q^{39} +(-14134.6 - 8160.62i) q^{40} -37007.6i q^{41} -44338.5 q^{43} +(-76117.4 + 131839. i) q^{44} +(-38590.6 + 22280.3i) q^{45} +(-63112.1 - 109313. i) q^{46} +(73660.5 + 42527.9i) q^{47} +8385.30i q^{48} +190687. q^{50} +(143407. - 248389. i) q^{51} +(-170110. + 98212.8i) q^{52} +(57979.3 + 100423. i) q^{53} +(376990. + 217655. i) q^{54} +44727.0i q^{55} +82428.3 q^{57} +(-260163. + 450616. i) q^{58} +(19940.5 - 11512.7i) q^{59} +(75265.4 + 130363. i) q^{60} +(-90546.8 - 52277.2i) q^{61} -417785. i q^{62} -421925. q^{64} +(-28855.2 + 49978.6i) q^{65} +(762471. - 440213. i) q^{66} +(-944.851 - 1636.53i) q^{67} +(-558006. - 322165. i) q^{68} +453221. i q^{69} -67013.1 q^{71} +(383571. - 664364. i) q^{72} +(-643419. + 371478. i) q^{73} +(245374. + 425001. i) q^{74} +(-592951. - 342340. i) q^{75} -185175. i q^{76} +1.13600e6 q^{78} +(138176. - 239328. i) q^{79} +(4793.04 - 2767.27i) q^{80} +(-253998. - 439938. i) q^{81} +(416396. + 240406. i) q^{82} +675103. i q^{83} -189306. q^{85} +(288029. - 498881. i) q^{86} +(1.61798e6 - 934142. i) q^{87} +(-385003. - 666845. i) q^{88} +(-608994. - 351603. i) q^{89} -578944. i q^{90} +1.01816e6 q^{92} +(-750048. + 1.29912e6i) q^{93} +(-957018. + 552535. i) q^{94} +(-27202.5 - 47116.1i) q^{95} +(1.27622e6 + 736828. i) q^{96} +543745. i q^{97} -2.10229e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{2} - 564 q^{4} + 1880 q^{8} + 1252 q^{9} + 3872 q^{11} + 44864 q^{15} - 37908 q^{16} + 19436 q^{18} + 159744 q^{22} - 40032 q^{23} + 28860 q^{25} + 68032 q^{29} - 21192 q^{30} + 82060 q^{32}+ \cdots - 8949984 q^{99}+O(q^{100}) $ 24 * q - 20 * q^2 - 564 * q^4 + 1880 * q^8 + 1252 * q^9 + 3872 * q^11 + 44864 * q^15 - 37908 * q^16 + 19436 * q^18 + 159744 * q^22 - 40032 * q^23 + 28860 * q^25 + 68032 * q^29 - 21192 * q^30 + 82060 * q^32 - 563240 * q^36 + 169632 * q^37 - 492128 * q^39 - 241536 * q^43 + 404312 * q^44 + 118872 * q^46 - 2091048 * q^50 + 539424 * q^51 + 15856 * q^53 + 1853888 * q^57 - 971304 * q^58 + 429912 * q^60 - 11496 * q^64 + 267904 * q^65 - 1508352 * q^67 + 5037248 * q^71 - 2550364 * q^72 + 3876024 * q^74 - 135184 * q^78 - 232224 * q^79 - 528204 * q^81 + 1508256 * q^85 + 1560848 * q^86 - 1812720 * q^88 + 7305776 * q^92 - 164384 * q^93 - 2305600 * q^95 - 8949984 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−6.49614	+	11.2516i	−0.812018	+	1.40646i	0.0994322	+	0.995044i	$0.468297\pi$
$2$	−6.49614	+	11.2516i	−0.812018	+	1.40646i	−0.911450	+	0.411411i	$0.865036\pi$
$3$	40.4001	−	23.3250i	1.49630	−	0.863890i	0.496310	−	0.868145i	$-0.334688\pi$
$3$	40.4001	−	23.3250i	1.49630	−	0.863890i	0.999991	+	0.00425554i	$0.00135459\pi$
$4$	−52.3997	−	90.7589i	−0.818745	−	1.41811i
$5$	−26.6652	−	15.3952i	−0.213322	−	0.123161i	0.389532	−	0.921013i	$-0.372637\pi$
$5$	−26.6652	−	15.3952i	−0.213322	−	0.123161i	−0.602854	+	0.797851i	$0.705970\pi$
$6$			606.091i			2.80597i
$7$		0			0
$7$		0			0
$8$	530.077			1.03531
$9$	723.614	−	1253.34i	0.992611	−	1.71925i
$10$	346.442	−	200.018i	0.346442	−	0.200018i
$11$	−726.315	−	1258.01i	−0.545691	−	0.945165i	−0.998563	−	0.0535894i	$-0.982934\pi$
$11$	−726.315	−	1258.01i	−0.545691	−	0.945165i	0.452872	−	0.891576i	$-0.350400\pi$
$12$	−4233.91	−	2444.45i	−2.45018	−	1.41461i
$13$		−	1874.30i		−	0.853118i	−0.904460	−	0.426559i	$-0.859726\pi$
$13$		−	1874.30i		−	0.853118i	0.904460	−	0.426559i	$-0.140274\pi$
$14$		0			0
$15$	−1436.37			−0.425591
$16$	−89.8745	+	155.667i	−0.0219420	+	0.0380047i
$17$	5324.52	−	3074.11i	1.08376	−	0.625710i	0.151852	−	0.988403i	$-0.451476\pi$
$17$	5324.52	−	3074.11i	1.08376	−	0.625710i	0.931908	+	0.362694i	$0.118143\pi$
$18$	9401.39	+	16283.7i	1.61204	+	2.79213i
$19$	1530.22	+	883.475i	0.223097	+	0.128805i	0.607384	−	0.794409i	$-0.292219\pi$
$19$	1530.22	+	883.475i	0.223097	+	0.128805i	−0.384286	+	0.923214i	$0.625552\pi$
$20$			3226.81i			0.403351i
$21$		0			0
$22$	18873.0			1.77244
$23$	−4857.66	+	8413.72i	−0.399249	+	0.691520i	−0.993633	−	0.112661i	$-0.964062\pi$
$23$	−4857.66	+	8413.72i	−0.399249	+	0.691520i	0.594384	+	0.804181i	$0.297396\pi$
$24$	21415.2	−	12364.1i	1.54913	−	0.894391i
$25$	−7338.48	−	12710.6i	−0.469663	−	0.813479i
$26$	21089.0	+	12175.7i	1.19987	+	0.692747i
$27$		−	33505.3i		−	1.70225i
$28$		0			0
$29$	40048.9			1.64209			0.821044	−	0.570864i	$-0.193392\pi$
$29$	40048.9			1.64209			0.821044	+	0.570864i	$0.193392\pi$
$30$	9330.87	−	16161.5i	0.345588	−	0.598575i
$31$	−27848.2	+	16078.2i	−0.934787	+	0.539699i	−0.888322	−	0.459221i	$-0.848129\pi$
$31$	−27848.2	+	16078.2i	−0.934787	+	0.539699i	−0.0464645	+	0.998920i	$0.514795\pi$
$32$	15794.8	+	27357.4i	0.482019	+	0.834881i
$33$	−58686.4	−	33882.6i	−1.63304	−	0.942834i
$34$			79879.4i			2.03235i
$35$		0			0
$36$	−151668.			−3.25078
$37$	18886.2	−	32711.8i	0.372854	−	0.645802i	−0.617149	−	0.786846i	$-0.711713\pi$
$37$	18886.2	−	32711.8i	0.372854	−	0.645802i	0.990003	+	0.141044i	$0.0450459\pi$
$38$	−19881.1	+	11478.4i	−0.362318	+	0.209184i
$39$	−43718.1	−	75722.0i	−0.737000	−	1.27652i
$40$	−14134.6	−	8160.62i	−0.220853	−	0.127510i
$41$		−	37007.6i		−	0.536956i	−0.963286	−	0.268478i	$-0.913479\pi$
$41$		−	37007.6i		−	0.536956i	0.963286	−	0.268478i	$-0.0865207\pi$
$42$		0			0
$43$	−44338.5			−0.557668			−0.278834	−	0.960339i	$-0.589948\pi$
$43$	−44338.5			−0.557668			−0.278834	+	0.960339i	$0.589948\pi$
$44$	−76117.4	+	131839.i	−0.893564	+	1.54770i
$45$	−38590.6	+	22280.3i	−0.423491	+	0.244503i
$46$	−63112.1	−	109313.i	−0.648395	−	1.12305i
$47$	73660.5	+	42527.9i	0.709481	+	0.409619i	0.810869	−	0.585228i	$-0.198995\pi$
$47$	73660.5	+	42527.9i	0.709481	+	0.409619i	−0.101388	+	0.994847i	$0.532328\pi$
$48$			8385.30i			0.0758219i
$49$		0			0
$50$	190687.			1.52550
$51$	143407.	−	248389.i	1.08109	−	1.87250i
$52$	−170110.	+	98212.8i	−1.20981	+	0.698487i
$53$	57979.3	+	100423.i	0.389444	+	0.674537i	0.992375	−	0.123256i	$-0.0393337\pi$
$53$	57979.3	+	100423.i	0.389444	+	0.674537i	−0.602931	+	0.797794i	$0.706000\pi$
$54$	376990.	+	217655.i	2.39413	+	1.38225i
$55$			44727.0i			0.268832i
$56$		0			0
$57$	82428.3			0.445094
$58$	−260163.	+	450616.i	−1.33340	+	2.30952i
$59$	19940.5	−	11512.7i	0.0970913	−	0.0560557i	−0.450668	−	0.892692i	$-0.648814\pi$
$59$	19940.5	−	11512.7i	0.0970913	−	0.0560557i	0.547759	+	0.836636i	$0.315481\pi$
$60$	75265.4	+	130363.i	0.348451	+	0.603535i
$61$	−90546.8	−	52277.2i	−0.398918	−	0.230315i	0.287099	−	0.957901i	$-0.407309\pi$
$61$	−90546.8	−	52277.2i	−0.398918	−	0.230315i	−0.686017	+	0.727586i	$0.740642\pi$
$62$		−	417785.i		−	1.75298i
$63$		0			0
$64$	−421925.			−1.60951
$65$	−28855.2	+	49978.6i	−0.105071	+	0.181989i
$66$	762471.	−	440213.i	2.65211	−	1.53120i
$67$	−944.851	−	1636.53i	−0.00314151	−	0.00544126i	0.864450	−	0.502718i	$-0.167667\pi$
$67$	−944.851	−	1636.53i	−0.00314151	−	0.00544126i	−0.867592	+	0.497277i	$0.834333\pi$
$68$	−558006.	−	322165.i	−1.77465	−	1.02459i
$69$			453221.i			1.37963i
$70$		0			0
$71$	−67013.1			−0.187234			−0.0936170	−	0.995608i	$-0.529843\pi$
$71$	−67013.1			−0.187234			−0.0936170	+	0.995608i	$0.529843\pi$
$72$	383571.	−	664364.i	1.02766	−	1.77995i
$73$	−643419.	+	371478.i	−1.65396	+	0.954915i	−0.678541	+	0.734563i	$0.737387\pi$
$73$	−643419.	+	371478.i	−1.65396	+	0.954915i	−0.975420	+	0.220352i	$0.929279\pi$
$74$	245374.	+	425001.i	0.605528	+	1.04880i
$75$	−592951.	−	342340.i	−1.40551	−	0.811473i
$76$		−	185175.i		−	0.421834i
$77$		0			0
$78$	1.13600e6			2.39383
$79$	138176.	−	239328.i	0.280254	−	0.485414i	−0.691193	−	0.722670i	$-0.742915\pi$
$79$	138176.	−	239328.i	0.280254	−	0.485414i	0.971447	+	0.237256i	$0.0762480\pi$
$80$	4793.04	−	2767.27i	0.00936141	−	0.00540481i
$81$	−253998.	−	439938.i	−0.477943	−	0.827821i
$82$	416396.	+	240406.i	0.755205	+	0.436018i
$83$			675103.i			1.18069i	0.807151	+	0.590345i	$0.201008\pi$
$83$			675103.i			1.18069i	−0.807151	+	0.590345i	$0.798992\pi$
$84$		0			0
$85$	−189306.			−0.308253
$86$	288029.	−	498881.i	0.452836	−	0.784335i
$87$	1.61798e6	−	934142.i	2.45706	−	1.41858i
$88$	−385003.	−	666845.i	−0.564958	−	0.978536i
$89$	−608994.	−	351603.i	−0.863859	−	0.498749i	0.00144385	−	0.999999i	$-0.499540\pi$
$89$	−608994.	−	351603.i	−0.863859	−	0.498749i	−0.865303	+	0.501250i	$0.832874\pi$
$90$		−	578944.i		−	0.794162i
$91$		0			0
$92$	1.01816e6			1.30753
$93$	−750048.	+	1.29912e6i	−0.932482	+	1.61511i
$94$	−957018.	+	552535.i	−1.15222	+	0.665236i
$95$	−27202.5	−	47116.1i	−0.0317276	−	0.0549539i
$96$	1.27622e6	+	736828.i	1.44249	+	0.832822i
$97$			543745.i			0.595772i	0.954601	+	0.297886i	$0.0962816\pi$
$97$			543745.i			0.595772i	−0.954601	+	0.297886i	$0.903718\pi$
$98$		0			0
$99$	−2.10229e6			−2.16664
$100$	−769068.	+	1.33206e6i	−0.769068	+	1.33206i
$101$	109259.	−	63080.6i	0.106045	−	0.0612254i	−0.446039	−	0.895013i	$-0.647166\pi$
$101$	109259.	−	63080.6i	0.106045	−	0.0612254i	0.552085	+	0.833788i	$0.313832\pi$
$102$	1.86319e6	+	3.22714e6i	1.75573	+	3.04101i
$103$	1.70385e6	+	983716.i	1.55926	+	0.900239i	0.997328	+	0.0730560i	$0.0232752\pi$
$103$	1.70385e6	+	983716.i	1.55926	+	0.900239i	0.561932	+	0.827183i	$0.310058\pi$
$104$		−	993524.i		−	0.883239i
$105$		0			0
$106$	−1.50657e6			−1.26494
$107$	887301.	−	1.53685e6i	0.724302	−	1.25453i	−0.234959	−	0.972005i	$-0.575496\pi$
$107$	887301.	−	1.53685e6i	0.724302	−	1.25453i	0.959261	−	0.282522i	$-0.0911710\pi$
$108$	−3.04091e6	+	1.75567e6i	−2.41397	+	1.39371i
$109$	−486972.	−	843460.i	−0.376032	−	0.651306i	0.614449	−	0.788956i	$-0.289378\pi$
$109$	−486972.	−	843460.i	−0.376032	−	0.651306i	−0.990481	+	0.137650i	$0.956045\pi$
$110$	−503252.	−	290553.i	−0.378101	−	0.218297i
$111$		−	1.76208e6i		−	1.28842i
$112$		0			0
$113$	1.57203e6			1.08950			0.544748	−	0.838600i	$-0.316625\pi$
$113$	1.57203e6			1.08950			0.544748	+	0.838600i	$0.316625\pi$
$114$	−535466.	+	927454.i	−0.361424	+	0.626005i
$115$	259061.	−	149569.i	0.170337	−	0.0983441i
$116$	−2.09855e6	−	3.63479e6i	−1.34445	−	2.32866i
$117$	−2.34913e6	−	1.35627e6i	−1.46673	−	0.846815i
$118$			299152.i			0.182073i
$119$		0			0
$120$	−761387.			−0.440617
$121$	−169287.	+	293213.i	−0.0955580	+	0.165511i
$122$	1.17641e6	−	679200.i	0.647857	−	0.374040i
$123$	−863202.	−	1.49511e6i	−0.463871	−	0.803448i
$124$	2.91848e6	+	1.68498e6i	1.53070	+	0.883753i
$125$			933007.i			0.477700i
$126$		0			0
$127$	−526054.			−0.256814			−0.128407	−	0.991722i	$-0.540986\pi$
$127$	−526054.			−0.256814			−0.128407	+	0.991722i	$0.540986\pi$
$128$	1.73002e6	−	2.99647e6i	0.824935	−	1.42883i
$129$	−1.79128e6	+	1.03420e6i	−0.834439	+	0.481763i
$130$	−374895.	−	649337.i	−0.170639	−	0.295556i
$131$	585393.	+	337977.i	0.260396	+	0.150339i	0.624515	−	0.781013i	$-0.285297\pi$
$131$	585393.	+	337977.i	0.260396	+	0.150339i	−0.364119	+	0.931352i	$0.618630\pi$
$132$			7.10176e6i			3.08776i
$133$		0			0
$134$	24551.5			0.0102039
$135$	−515820.	+	893427.i	−0.209651	+	0.363126i
$136$	2.82240e6	−	1.62952e6i	1.12202	−	0.647801i
$137$	1.57313e6	+	2.72475e6i	0.611792	+	1.05966i	0.990938	+	0.134319i	$0.0428845\pi$
$137$	1.57313e6	+	2.72475e6i	0.611792	+	1.05966i	−0.379146	+	0.925337i	$0.623782\pi$
$138$	−5.09948e6	−	2.94418e6i	−1.94039	−	1.12028i
$139$			3.59508e6i			1.33864i	0.742974	+	0.669320i	$0.233415\pi$
$139$			3.59508e6i			1.33864i	−0.742974	+	0.669320i	$0.766585\pi$
$140$		0			0
$141$	3.96786e6			1.41546
$142$	435327.	−	754008.i	0.152037	−	0.263336i
$143$	−2.35790e6	+	1.36133e6i	−0.806338	+	0.465539i
$144$	130069.	+	225286.i	0.0435598	+	0.0754477i
$145$	−1.06791e6	−	616560.i	−0.350293	−	0.202242i
$146$		−	9.65270e6i		−	3.10163i
$147$		0			0
$148$	−3.95852e6			−1.22109
$149$	526647.	−	912179.i	0.159207	−	0.275754i	−0.775376	−	0.631500i	$-0.782440\pi$
$149$	526647.	−	912179.i	0.159207	−	0.275754i	0.934583	+	0.355746i	$0.115773\pi$
$150$	7.70378e6	−	4.44778e6i	2.28260	−	1.31786i
$151$	1.99922e6	+	3.46275e6i	0.580671	+	1.00575i	0.995400	+	0.0958067i	$0.0305431\pi$
$151$	1.99922e6	+	3.46275e6i	0.580671	+	1.00575i	−0.414729	+	0.909945i	$0.636124\pi$
$152$	811136.	+	468310.i	0.230974	+	0.133353i
$153$		−	8.89787e6i		−	2.48435i
$154$		0			0
$155$	990106.			0.265880
$156$	−4.58163e6	+	7.93562e6i	−1.20683	+	2.09029i
$157$	−1.32516e6	+	765079.i	−0.342427	+	0.197700i	−0.661345	−	0.750082i	$-0.730014\pi$
$157$	−1.32516e6	+	765079.i	−0.342427	+	0.197700i	0.318918	+	0.947782i	$0.396681\pi$
$158$	1.79522e6	+	3.10942e6i	0.455142	+	0.788329i
$159$	4.68474e6	+	2.70474e6i	1.16545	+	0.672874i
$160$		−	972654.i		−	0.237464i
$161$		0			0
$162$	6.60003e6			1.55239
$163$	2.93051e6	−	5.07579e6i	0.676675	−	1.17203i	−0.299302	−	0.954159i	$-0.596754\pi$
$163$	2.93051e6	−	5.07579e6i	0.676675	−	1.17203i	0.975976	−	0.217876i	$-0.0699130\pi$
$164$	−3.35877e6	+	1.93918e6i	−0.761462	+	0.439630i
$165$	1.04326e6	+	1.80698e6i	0.232241	+	0.402254i
$166$	−7.59603e6	−	4.38557e6i	−1.66059	−	0.958741i
$167$		−	3.63135e6i		−	0.779684i	−0.920882	−	0.389842i	$-0.872530\pi$
$167$		−	3.63135e6i		−	0.779684i	0.920882	−	0.389842i	$-0.127470\pi$
$168$		0			0
$169$	1.31380e6			0.272189
$170$	1.22976e6	−	2.13000e6i	0.250307	−	0.433544i
$171$	2.21458e6	−	1.27859e6i	0.442897	−	0.255707i
$172$	2.32332e6	+	4.02411e6i	0.456588	+	0.790833i
$173$	8.76430e6	+	5.06007e6i	1.69270	+	0.977279i	0.952327	+	0.305078i	$0.0986827\pi$
$173$	8.76430e6	+	5.06007e6i	1.69270	+	0.977279i	0.740369	+	0.672200i	$0.234651\pi$
$174$			2.42733e7i			4.60766i
$175$		0			0
$176$	261109.			0.0478943
$177$	537066.	−	930226.i	0.0968519	−	0.167752i
$178$	7.91222e6	−	4.56812e6i	1.40294	−	0.809986i
$179$	−866055.	−	1.50005e6i	−0.151003	−	0.261545i	0.780593	−	0.625039i	$-0.214917\pi$
$179$	−866055.	−	1.50005e6i	−0.151003	−	0.261545i	−0.931597	+	0.363494i	$0.881584\pi$
$180$	4.04427e6	+	2.33496e6i	0.693462	+	0.400371i
$181$		−	590435.i		−	0.0995719i	−0.998760	−	0.0497859i	$-0.984146\pi$
$181$		−	590435.i		−	0.0995719i	0.998760	−	0.0497859i	$-0.0158539\pi$
$182$		0			0
$183$	−4.87747e6			−0.795868
$184$	−2.57494e6	+	4.45992e6i	−0.413345	+	0.715935i
$185$	−1.00721e6	+	581511.i	−0.159076	+	0.0918424i
$186$	−9.74484e6	−	1.68786e7i	−1.51438	−	2.62299i
$187$	−7.73455e6	−	4.46555e6i	−1.18280	−	0.682889i
$188$		−	8.91380e6i		−	1.34150i
$189$		0			0
$190$	706845.			0.103054
$191$	−6.18822e6	+	1.07183e7i	−0.888107	+	1.53825i	−0.0459970	+	0.998942i	$0.514646\pi$
$191$	−6.18822e6	+	1.07183e7i	−0.888107	+	1.53825i	−0.842110	+	0.539305i	$0.818687\pi$
$192$	−1.70458e7	+	9.84140e6i	−2.40832	+	1.39044i
$193$	−4.13638e6	−	7.16443e6i	−0.575372	−	0.996574i	−0.996001	−	0.0893411i	$-0.971524\pi$
$193$	−4.13638e6	−	7.16443e6i	−0.575372	−	0.996574i	0.420629	−	0.907233i	$-0.361809\pi$
$194$	−6.11803e6	−	3.53225e6i	−0.837927	−	0.483778i
$195$			2.69219e6i			0.363080i
$196$		0			0
$197$	1.47614e6			0.193077			0.0965383	−	0.995329i	$-0.469223\pi$
$197$	1.47614e6			0.193077			0.0965383	+	0.995329i	$0.469223\pi$
$198$	1.36567e7	−	2.36542e7i	1.75935	−	3.04728i
$199$	9.58684e6	−	5.53496e6i	1.21651	−	0.702353i	0.252342	−	0.967638i	$-0.418799\pi$
$199$	9.58684e6	−	5.53496e6i	1.21651	−	0.702353i	0.964170	+	0.265285i	$0.0854660\pi$
$200$	−3.88996e6	−	6.73760e6i	−0.486245	−	0.842201i
$201$	−76344.2	−	44077.3i	−0.00940130	−	0.00542784i
$202$			1.63912e6i			0.198864i
$203$		0			0
$204$	−3.00580e7			−3.54054
$205$	−569738.	+	986815.i	−0.0661323	+	0.114544i
$206$	−2.21368e7	+	1.27807e7i	−2.53229	+	1.46202i
$207$	7.03014e6	+	1.21766e7i	0.792598	+	1.37282i
$208$	291767.	+	168452.i	0.0324225	+	0.0187191i
$209$		−	2.56672e6i		−	0.281151i
$210$		0			0
$211$	7.69041e6			0.818657			0.409329	−	0.912387i	$-0.365763\pi$
$211$	7.69041e6			0.818657			0.409329	+	0.912387i	$0.365763\pi$
$212$	6.07619e6	−	1.05243e7i	0.637711	−	1.10455i
$213$	−2.70734e6	+	1.56308e6i	−0.280158	+	0.161750i
$214$	1.15281e7	+	1.99672e7i	1.17629	+	2.03740i
$215$	1.18230e6	+	682598.i	0.118963	+	0.0686831i
$216$		−	1.77604e7i		−	1.76235i
$217$		0			0
$218$	1.26538e7			1.22138
$219$	−1.73295e7	+	3.00155e7i	−1.64988	+	2.85768i
$220$	4.05937e6	−	2.34368e6i	0.381233	−	0.220105i
$221$	−5.76181e6	−	9.97975e6i	−0.533804	−	0.924576i
$222$	1.98263e7	+	1.14467e7i	1.81210	+	1.04622i
$223$			1.40475e7i			1.26673i	0.773853	+	0.633366i	$0.218327\pi$
$223$			1.40475e7i			1.26673i	−0.773853	+	0.633366i	$0.781673\pi$
$224$		0			0
$225$	−2.12409e7			−1.86477
$226$	−1.02121e7	+	1.76879e7i	−0.884690	+	1.53233i
$227$	−98812.7	+	57049.5i	−0.00844763	+	0.00487724i	−0.504218	−	0.863576i	$-0.668219\pi$
$227$	−98812.7	+	57049.5i	−0.00844763	+	0.00487724i	0.495770	+	0.868454i	$0.334886\pi$
$228$	−4.31922e6	−	7.48110e6i	−0.364418	−	0.631191i
$229$	8.85431e6	+	5.11204e6i	0.737306	+	0.425684i	0.821089	−	0.570800i	$-0.193367\pi$
$229$	8.85431e6	+	5.11204e6i	0.737306	+	0.425684i	−0.0837827	+	0.996484i	$0.526700\pi$
$230$			3.88649e6i			0.319429i
$231$		0			0
$232$	2.12290e7			1.70007
$233$	6.55425e6	−	1.13523e7i	0.518149	−	0.897461i	−0.481628	−	0.876376i	$-0.659954\pi$
$233$	6.55425e6	−	1.13523e7i	0.518149	−	0.897461i	0.999778	−	0.0210854i	$-0.00671219\pi$
$234$	3.05205e7	−	1.76210e7i	2.38202	−	1.37526i
$235$	−1.30945e6	−	2.26803e6i	−0.100899	−	0.174761i
$236$	−2.08975e6	−	1.20652e6i	−0.158986	−	0.0917907i
$237$		−	1.28918e7i		−	0.968434i
$238$		0			0
$239$	5.42281e6			0.397219			0.198610	−	0.980079i	$-0.436357\pi$
$239$	5.42281e6			0.397219			0.198610	+	0.980079i	$0.436357\pi$
$240$	129093.	−	223596.i	0.00933833	−	0.0161745i
$241$	1.13260e7	−	6.53909e6i	0.809146	−	0.467161i	−0.0375133	−	0.999296i	$-0.511944\pi$
$241$	1.13260e7	−	6.53909e6i	0.809146	−	0.467161i	0.846659	+	0.532136i	$0.178610\pi$
$242$	−2.19942e6	−	3.80951e6i	−0.155190	−	0.268796i
$243$	629875.	+	363659.i	0.0438971	+	0.0253440i
$244$			1.09572e7i			0.754278i
$245$		0			0
$246$	2.24299e7			1.50669
$247$	1.65590e6	−	2.86810e6i	0.109886	−	0.190328i
$248$	−1.47617e7	+	8.52268e6i	−0.967791	+	0.558754i
$249$	1.57468e7	+	2.72743e7i	1.01999	+	1.76667i
$250$	−1.04979e7	−	6.06095e6i	−0.671864	−	0.387901i
$251$			1.39585e7i			0.882711i	0.897332	+	0.441356i	$0.145502\pi$
$251$			1.39585e7i			0.882711i	−0.897332	+	0.441356i	$0.854498\pi$
$252$		0			0
$253$	1.41128e7			0.871467
$254$	3.41732e6	−	5.91897e6i	0.208538	−	0.361198i
$255$	−7.64798e6	+	4.41556e6i	−0.461239	+	0.266297i
$256$	8.97526e6	+	1.55456e7i	0.534967	+	0.926590i
$257$	−2.74896e6	−	1.58711e6i	−0.161946	−	0.0934993i	0.416837	−	0.908981i	$-0.363139\pi$
$257$	−2.74896e6	−	1.58711e6i	−0.161946	−	0.0934993i	−0.578782	+	0.815482i	$0.696472\pi$
$258$		−	2.68731e7i		−	1.56480i
$259$		0			0
$260$	6.04801e6			0.344106
$261$	2.89799e7	−	5.01947e7i	1.62996	−	2.82317i
$262$	−7.60559e6	+	4.39109e6i	−0.422892	+	0.244157i
$263$	−6.89127e6	−	1.19360e7i	−0.378819	−	0.656134i	0.612072	−	0.790802i	$-0.290336\pi$
$263$	−6.89127e6	−	1.19360e7i	−0.378819	−	0.656134i	−0.990891	+	0.134668i	$0.957003\pi$
$264$	−3.11083e7	−	1.79604e7i	−1.69069	−	0.976123i
$265$		−	3.57040e6i		−	0.191858i
$266$		0			0
$267$	−3.28046e7			−1.72346
$268$	−99019.8	+	171507.i	−0.00514420	+	0.00891001i
$269$	1.28733e7	−	7.43241e6i	0.661353	−	0.381832i	−0.131439	−	0.991324i	$-0.541960\pi$
$269$	1.28733e7	−	7.43241e6i	0.661353	−	0.381832i	0.792792	+	0.609492i	$0.208627\pi$
$270$	−6.70168e6	−	1.16077e7i	−0.340481	−	0.589730i
$271$	−2.19493e7	−	1.26724e7i	−1.10284	−	0.636724i	−0.165873	−	0.986147i	$-0.553044\pi$
$271$	−2.19493e7	−	1.26724e7i	−1.10284	−	0.636724i	−0.936965	+	0.349423i	$0.886378\pi$
$272$			1.10514e6i			0.0549173i
$273$		0			0
$274$	−4.08772e7			−1.98714
$275$	−1.06601e7	+	1.84638e7i	−0.512582	+	0.887817i
$276$	4.11338e7	−	2.37486e7i	1.95646	−	1.12956i
$277$	−1.19226e7	−	2.06506e7i	−0.560960	−	0.971612i	−0.997413	−	0.0718844i	$-0.977099\pi$
$277$	−1.19226e7	−	2.06506e7i	−0.560960	−	0.971612i	0.436453	−	0.899727i	$-0.356235\pi$
$278$	−4.04505e7	−	2.33541e7i	−1.88274	−	1.08700i
$279$			4.65376e7i			2.14285i
$280$		0			0
$281$	1.23157e6			0.0555059			0.0277529	−	0.999615i	$-0.491165\pi$
$281$	1.23157e6			0.0555059			0.0277529	+	0.999615i	$0.491165\pi$
$282$	−2.57758e7	+	4.46449e7i	−1.14938	+	1.99079i
$283$	−1.77636e7	+	1.02558e7i	−0.783739	+	0.452492i	−0.837754	−	0.546048i	$-0.816132\pi$
$283$	−1.77636e7	+	1.02558e7i	−0.783739	+	0.452492i	0.0540144	+	0.998540i	$0.482798\pi$
$284$	3.51147e6	+	6.08204e6i	0.153297	+	0.265518i
$285$	−2.19797e6	−	1.26900e6i	−0.0949482	−	0.0548184i
$286$		−	3.53737e7i		−	1.51210i
$287$		0			0
$288$	4.57173e7			1.91383
$289$	6.83154e6	−	1.18326e7i	0.283025	−	0.490214i
$290$	1.38746e7	−	8.01052e6i	0.568888	−	0.328448i
$291$	1.26829e7	+	2.19674e7i	0.514682	+	0.891455i
$292$	6.74299e7	+	3.89307e7i	2.70834	+	1.56366i
$293$		−	1.71525e7i		−	0.681904i	−0.940081	−	0.340952i	$-0.889251\pi$
$293$		−	1.71525e7i		−	0.681904i	0.940081	−	0.340952i	$-0.110749\pi$
$294$		0			0
$295$	−708958.			−0.0276156
$296$	1.00111e7	−	1.73398e7i	0.386018	−	0.668603i
$297$	−4.21502e7	+	2.43354e7i	−1.60890	+	0.928901i
$298$	6.84235e6	+	1.18513e7i	0.258557	+	0.447834i
$299$	1.57698e7	+	9.10473e6i	0.589948	+	0.340607i
$300$			7.17541e7i			2.65756i
$301$		0			0
$302$	−5.19489e7			−1.88606
$303$	2.94271e6	−	5.09693e6i	0.105784	−	0.183223i
$304$	−275056.	+	158804.i	−0.00979040	+	0.00565249i
$305$	1.60963e6	+	2.78797e6i	0.0567319	+	0.0982625i
$306$	1.00116e8	+	5.78018e7i	3.49412	+	2.01733i
$307$		−	8.94639e6i		−	0.309195i	−0.987978	−	0.154598i	$-0.950592\pi$
$307$		−	8.94639e6i		−	0.309195i	0.987978	−	0.154598i	$-0.0494081\pi$
$308$		0			0
$309$	9.17808e7			3.11083
$310$	−6.43186e6	+	1.11403e7i	−0.215900	+	0.373949i
$311$	−1.05103e6	+	606810.i	−0.0349408	+	0.0201731i	−0.517369	−	0.855763i	$-0.673088\pi$
$311$	−1.05103e6	+	606810.i	−0.0349408	+	0.0201731i	0.482428	+	0.875936i	$0.339755\pi$
$312$	−2.31740e7	−	4.01385e7i	−0.763021	−	1.32159i
$313$	−3.66811e7	−	2.11778e7i	−1.19621	−	0.690635i	−0.236505	−	0.971630i	$-0.576002\pi$
$313$	−3.66811e7	−	2.11778e7i	−1.19621	−	0.690635i	−0.959709	+	0.280996i	$0.909335\pi$
$314$		−	1.98802e7i		−	0.642144i
$315$		0			0
$316$	−2.89615e7			−0.917826
$317$	−4.97456e6	+	8.61619e6i	−0.156163	+	0.270482i	−0.933482	−	0.358625i	$-0.883246\pi$
$317$	−4.97456e6	+	8.61619e6i	−0.156163	+	0.270482i	0.777319	+	0.629106i	$0.216579\pi$
$318$	−6.08655e7	+	3.51407e7i	−1.89273	+	1.09277i
$319$	−2.90881e7	−	5.03821e7i	−0.896073	−	1.55204i
$320$	1.12507e7	+	6.49560e6i	0.343344	+	0.198230i
$321$		−	8.27852e7i		−	2.50287i
$322$		0			0
$323$	1.08636e7			0.322379
$324$	−2.66189e7	+	4.61052e7i	−0.782626	+	1.35555i
$325$	−2.38235e7	+	1.37545e7i	−0.693994	+	0.400678i
$326$	3.80740e7	+	6.59461e7i	1.09894	+	1.90343i
$327$	−3.93475e7	−	2.27173e7i	−1.12531	−	0.649700i
$328$		−	1.96169e7i		−	0.555914i
$329$		0			0
$330$	−2.71086e7			−0.754337
$331$	6.34727e6	−	1.09938e7i	0.175026	−	0.303154i	−0.765144	−	0.643859i	$-0.777332\pi$
$331$	6.34727e6	−	1.09938e7i	0.175026	−	0.303154i	0.940170	+	0.340705i	$0.110666\pi$
$332$	6.12717e7	−	3.53752e7i	1.67435	−	0.966685i
$333$	−2.73326e7	−	4.73414e7i	−0.740198	−	1.28206i
$334$	4.08586e7	+	2.35898e7i	1.09659	+	0.633117i
$335$			58184.6i			0.00154765i
$336$		0			0
$337$	−7.16152e7			−1.87118			−0.935590	−	0.353088i	$-0.885132\pi$
$337$	−7.16152e7			−1.87118			−0.935590	+	0.353088i	$0.885132\pi$
$338$	−8.53466e6	+	1.47825e7i	−0.221022	+	0.382822i
$339$	6.35102e7	−	3.66677e7i	1.63021	−	0.941205i
$340$	9.91957e6	+	1.71812e7i	0.252381	+	0.437136i
$341$	4.04532e7	+	2.33557e7i	1.02021	+	0.589019i
$342$			3.32236e7i			0.830554i
$343$		0			0
$344$	−2.35028e7			−0.577357
$345$	6.97741e6	−	1.20852e7i	0.169917	−	0.294305i
$346$	−1.13868e8	+	6.57419e7i	−2.74900	+	1.58714i
$347$	1.75485e7	+	3.03948e7i	0.420001	+	0.727464i	0.995939	−	0.0900298i	$-0.0286962\pi$
$347$	1.75485e7	+	3.03948e7i	0.420001	+	0.727464i	−0.575938	+	0.817494i	$0.695363\pi$
$348$	−1.69563e8	−	9.78974e7i	−4.02341	−	2.32292i
$349$			7.40536e7i			1.74209i	0.491206	+	0.871044i	$0.336556\pi$
$349$			7.40536e7i			1.74209i	−0.491206	+	0.871044i	$0.663444\pi$
$350$		0			0
$351$	−6.27991e7			−1.45222
$352$	2.29440e7	−	3.97402e7i	0.526067	−	0.911174i
$353$	−7.47792e6	+	4.31738e6i	−0.170003	+	0.0981513i	−0.582587	−	0.812768i	$-0.697960\pi$
$353$	−7.47792e6	+	4.31738e6i	−0.170003	+	0.0981513i	0.412584	+	0.910919i	$0.364626\pi$
$354$	6.97772e6	+	1.20858e7i	0.157291	+	0.272436i
$355$	1.78692e6	+	1.03168e6i	0.0399411	+	0.0230600i
$356$			7.36955e7i			1.63339i
$357$		0			0
$358$	2.25041e7			0.490469
$359$	8.51689e6	−	1.47517e7i	0.184076	−	0.318829i	−0.759189	−	0.650871i	$-0.774404\pi$
$359$	8.51689e6	−	1.47517e7i	0.184076	−	0.318829i	0.943265	+	0.332041i	$0.107737\pi$
$360$	−2.04560e7	+	1.18103e7i	−0.438443	+	0.253135i
$361$	−2.19619e7	−	3.80391e7i	−0.466818	−	0.808553i
$362$	6.64337e6	+	3.83555e6i	0.140043	+	0.0808541i
$363$			1.57945e7i			0.330206i
$364$		0			0
$365$	2.28759e7			0.470434
$366$	3.16847e7	−	5.48795e7i	0.646259	−	1.11935i
$367$	7.81169e7	−	4.51008e7i	1.58033	−	0.912402i	0.585516	−	0.810661i	$-0.300892\pi$
$367$	7.81169e7	−	4.51008e7i	1.58033	−	0.912402i	0.994811	−	0.101741i	$-0.0324413\pi$
$368$	−873160.	−	1.51236e6i	−0.0175207	−	0.0303467i
$369$	−4.63829e7	−	2.67792e7i	−0.923164	−	0.532989i
$370$		−	1.51103e7i		−	0.298310i
$371$		0			0
$372$	1.57209e8			3.05386
$373$	1.05025e7	−	1.81908e7i	0.202379	−	0.350530i	−0.746916	−	0.664919i	$-0.768466\pi$
$373$	1.05025e7	−	1.81908e7i	0.202379	−	0.350530i	0.949294	+	0.314389i	$0.101799\pi$
$374$	1.00490e8	−	5.80176e7i	1.92091	−	1.10904i
$375$	2.17624e7	+	3.76936e7i	0.412680	+	0.714783i
$376$	3.90457e7	+	2.25431e7i	0.734531	+	0.424082i
$377$		−	7.50637e7i		−	1.40090i
$378$		0			0
$379$	−6.45049e6			−0.118488			−0.0592441	−	0.998244i	$-0.518869\pi$
$379$	−6.45049e6			−0.118488			−0.0592441	+	0.998244i	$0.518869\pi$
$380$	−2.85080e6	+	4.93774e6i	−0.0519537	+	0.0899865i
$381$	−2.12526e7	+	1.22702e7i	−0.384271	+	0.221859i
$382$	−8.03991e7	−	1.39255e8i	−1.44232	−	2.49817i
$383$	5.99883e7	+	3.46342e7i	1.06775	+	0.616466i	0.927566	−	0.373659i	$-0.121897\pi$
$383$	5.99883e7	+	3.46342e7i	1.06775	+	0.616466i	0.140185	+	0.990125i	$0.455230\pi$
$384$		−	1.61411e8i		−	2.85061i
$385$		0			0
$386$	1.07482e8			1.86885
$387$	−3.20839e7	+	5.55710e7i	−0.553547	+	0.958772i
$388$	4.93497e7	−	2.84921e7i	0.844870	−	0.487786i
$389$	−7.70676e6	−	1.33485e7i	−0.130925	−	0.226769i	0.793108	−	0.609081i	$-0.208461\pi$
$389$	−7.70676e6	−	1.33485e7i	−0.130925	−	0.226769i	−0.924033	+	0.382312i	$0.875128\pi$
$390$	−3.02916e7	−	1.74889e7i	−0.510656	−	0.294827i
$391$			5.97320e7i			0.999256i
$392$		0			0
$393$	3.15333e7			0.519507
$394$	−9.58923e6	+	1.66090e7i	−0.156782	+	0.271554i
$395$	−7.36899e6	+	4.25449e6i	−0.119568	+	0.0690329i
$396$	1.10159e8	+	1.90801e8i	1.77392	+	3.07253i
$397$	−2.59562e7	−	1.49858e7i	−0.414829	−	0.239502i	0.278033	−	0.960571i	$-0.410317\pi$
$397$	−2.59562e7	−	1.49858e7i	−0.414829	−	0.239502i	−0.692863	+	0.721070i	$0.743651\pi$
$398$			1.43824e8i			2.28129i
$399$		0			0
$400$	2.63817e6			0.0412214
$401$	−5.23712e7	+	9.07096e7i	−0.812193	+	1.40676i	0.0991326	+	0.995074i	$0.468393\pi$
$401$	−5.23712e7	+	9.07096e7i	−0.812193	+	1.40676i	−0.911326	+	0.411686i	$0.864940\pi$
$402$	991885.	−	572665.i	0.0152680	−	0.00881501i
$403$	3.01354e7	+	5.21960e7i	0.460428	+	0.797484i
$404$	−1.14502e7	−	6.61080e6i	−0.173648	−	0.100256i
$405$			1.56414e7i			0.235456i
$406$		0			0
$407$	−5.48692e7			−0.813852
$408$	7.60170e7	−	1.31665e8i	1.11926	−	1.93861i
$409$	−1.07576e8	+	6.21089e7i	−1.57233	+	0.907786i	−0.576449	+	0.817133i	$0.695562\pi$
$409$	−1.07576e8	+	6.21089e7i	−1.57233	+	0.907786i	−0.995883	+	0.0906533i	$0.971104\pi$
$410$	−7.40219e6	−	1.28210e7i	−0.107401	−	0.186024i
$411$	1.27110e8	+	7.33868e7i	1.83085	+	1.05704i
$412$		−	2.06186e8i		−	2.94827i
$413$		0			0
$414$	−1.82675e8			−2.57441
$415$	1.03933e7	−	1.80018e7i	0.145415	−	0.251867i
$416$	5.12760e7	−	2.96042e7i	0.712252	−	0.411219i
$417$	8.38553e7	+	1.45242e8i	1.15644	+	2.00301i
$418$	2.88799e7	+	1.66738e7i	0.395427	+	0.228300i
$419$			8.30323e7i			1.12877i	0.825512	+	0.564384i	$0.190886\pi$
$419$			8.30323e7i			1.12877i	−0.825512	+	0.564384i	$0.809114\pi$
$420$		0			0
$421$	1.40657e8			1.88502			0.942511	−	0.334176i	$-0.108458\pi$
$421$	1.40657e8			1.88502			0.942511	+	0.334176i	$0.108458\pi$
$422$	−4.99580e7	+	8.65298e7i	−0.664764	+	1.15141i
$423$	1.06603e8	−	6.15475e7i	1.40848	−	0.813185i
$424$	3.07335e7	+	5.32320e7i	0.403194	+	0.698353i
$425$	−7.81477e7	−	4.51186e7i	−1.01800	−	0.587745i
$426$		−	4.06160e7i		−	0.525374i
$427$		0			0
$428$	−1.85977e8			−2.37207
$429$	−6.35063e7	+	1.09996e8i	−0.804349	+	1.39317i
$430$	−1.53607e7	+	8.86851e6i	−0.193199	+	0.111544i
$431$	2.09573e7	+	3.62991e7i	0.261760	+	0.453381i	0.966710	−	0.255876i	$-0.0823638\pi$
$431$	2.09573e7	+	3.62991e7i	0.261760	+	0.453381i	−0.704950	+	0.709257i	$0.749030\pi$
$432$	5.21568e6	+	3.01127e6i	0.0646933	+	0.0373507i
$433$		−	1.98782e6i		−	0.0244857i	−0.999925	−	0.0122429i	$-0.996103\pi$
$433$		−	1.98782e6i		−	0.0244857i	0.999925	−	0.0122429i	$-0.00389712\pi$
$434$		0			0
$435$	−5.75251e7			−0.698859
$436$	−5.10344e7	+	8.83941e7i	−0.615748	+	1.06651i
$437$	−1.48666e7	+	8.58325e6i	−0.178143	+	0.102851i
$438$	−2.25149e8	−	3.89970e8i	−2.67947	−	4.64097i
$439$	−3.07094e7	−	1.77301e7i	−0.362976	−	0.209564i	0.307410	−	0.951577i	$-0.400538\pi$
$439$	−3.07094e7	−	1.77301e7i	−0.362976	−	0.209564i	−0.670385	+	0.742013i	$0.733871\pi$
$440$			2.37087e7i			0.278324i
$441$		0			0
$442$	1.49718e8			1.73383
$443$	4.16962e7	−	7.22199e7i	0.479606	−	0.830703i	−0.520120	−	0.854093i	$-0.674113\pi$
$443$	4.16962e7	−	7.22199e7i	0.479606	−	0.830703i	0.999726	+	0.0233905i	$0.00744611\pi$
$444$	−1.59925e8	+	9.23325e7i	−1.82712	+	1.05489i
$445$	1.08260e7	+	1.87511e7i	0.122853	+	0.212788i
$446$	−1.58058e8	−	9.12546e7i	−1.78160	−	1.02861i
$447$		−	4.91362e7i		−	0.550148i
$448$		0			0
$449$	−4.99535e7			−0.551858			−0.275929	−	0.961178i	$-0.588985\pi$
$449$	−4.99535e7			−0.551858			−0.275929	+	0.961178i	$0.588985\pi$
$450$	1.37984e8	−	2.38995e8i	1.51423	−	2.62272i
$451$	−4.65561e7	+	2.68791e7i	−0.507512	+	0.293012i
$452$	−8.23739e7	−	1.42676e8i	−0.892020	−	1.54502i
$453$	1.61538e8	+	9.32638e7i	1.73772	+	1.00327i
$454$		−	1.48241e6i		−	0.0158416i
$455$		0			0
$456$	4.36933e7			0.460809
$457$	5.32988e7	−	9.23163e7i	0.558431	−	0.967230i	−0.439197	−	0.898391i	$-0.644737\pi$
$457$	5.32988e7	−	9.23163e7i	0.558431	−	0.967230i	0.997628	−	0.0688394i	$-0.0219296\pi$
$458$	−1.15038e8	+	6.64170e7i	−1.19741	+	0.691326i
$459$	−1.02999e8	−	1.78400e8i	−1.06511	−	1.84483i
$460$	−2.71495e7	−	1.56747e7i	−0.278925	−	0.161038i
$461$			9.86855e7i			1.00728i	0.863914	+	0.503640i	$0.168006\pi$
$461$			9.86855e7i			1.00728i	−0.863914	+	0.503640i	$0.831994\pi$
$462$		0			0
$463$	−1.02200e8			−1.02969			−0.514845	−	0.857283i	$-0.672151\pi$
$463$	−1.02200e8			−1.02969			−0.514845	+	0.857283i	$0.672151\pi$
$464$	−3.59937e6	+	6.23430e6i	−0.0360307	+	0.0624070i
$465$	4.00004e7	−	2.30942e7i	0.397837	−	0.229691i
$466$	8.51546e7	+	1.47492e8i	0.841493	+	1.45751i
$467$	4.81592e7	+	2.78047e7i	0.472856	+	0.273003i	0.717434	−	0.696626i	$-0.245316\pi$
$467$	4.81592e7	+	2.78047e7i	0.472856	+	0.273003i	−0.244579	+	0.969629i	$0.578650\pi$
$468$			2.84272e8i			2.77330i
$469$		0			0
$470$	3.40254e7			0.327726
$471$	−3.56910e7	+	6.18186e7i	−0.341583	+	0.591638i
$472$	1.05700e7	−	6.10260e6i	0.100519	−	0.0580348i
$473$	3.22037e7	+	5.57785e7i	0.304314	+	0.527088i
$474$	1.45054e8	+	8.37472e7i	1.36206	+	0.786385i
$475$		−	2.59334e7i		−	0.241980i
$476$		0			0
$477$	1.67818e8			1.54627
$478$	−3.52273e7	+	6.10155e7i	−0.322549	+	0.558672i
$479$	−1.09255e8	+	6.30783e7i	−0.994109	+	0.573949i	−0.906500	−	0.422206i	$-0.861256\pi$
$479$	−1.09255e8	+	6.30783e7i	−0.994109	+	0.573949i	−0.0876089	+	0.996155i	$0.527923\pi$
$480$	−2.26872e7	−	3.92953e7i	−0.205143	−	0.355318i
$481$	−6.13118e7	−	3.53984e7i	−0.550945	−	0.318089i
$482$			1.69915e8i			1.51737i
$483$		0			0
$484$	3.54823e7			0.312951
$485$	8.37105e6	−	1.44991e7i	0.0733761	−	0.127091i
$486$	−8.18352e6	+	4.72476e6i	−0.0712904	+	0.0411595i
$487$	6.52596e7	+	1.13033e8i	0.565012	+	0.978629i	0.997049	+	0.0767730i	$0.0244617\pi$
$487$	6.52596e7	+	1.13033e8i	0.565012	+	0.978629i	−0.432037	+	0.901856i	$0.642205\pi$
$488$	−4.79968e7	−	2.77109e7i	−0.413002	−	0.238447i
$489$		−	2.73417e8i		−	2.33829i
$490$		0			0
$491$	−1.47325e8			−1.24460			−0.622302	−	0.782778i	$-0.713802\pi$
$491$	−1.47325e8			−1.24460			−0.622302	+	0.782778i	$0.713802\pi$
$492$	−9.04631e7	+	1.56687e8i	−0.759584	+	1.31564i
$493$	2.13241e8	−	1.23115e8i	1.77963	−	1.02747i
$494$	2.15139e7	+	3.72631e7i	0.178459	+	0.309100i
$495$	5.60579e7	+	3.23650e7i	0.462191	+	0.266846i
$496$		−	5.78007e6i		−	0.0473684i
$497$		0			0
$498$	−4.09174e8			−3.31299
$499$	2.13462e7	−	3.69727e7i	0.171798	−	0.297564i	−0.767250	−	0.641348i	$-0.778376\pi$
$499$	2.13462e7	−	3.69727e7i	0.171798	−	0.297564i	0.939049	+	0.343784i	$0.111709\pi$
$500$	8.46787e7	−	4.88893e7i	0.677430	−	0.391114i
$501$	−8.47013e7	−	1.46707e8i	−0.673561	−	1.16664i
$502$	−1.57056e8	−	9.06766e7i	−1.24149	−	0.716777i
$503$		−	1.95808e8i		−	1.53860i	−0.638886	−	0.769301i	$-0.720605\pi$
$503$		−	1.95808e8i		−	1.53860i	0.638886	−	0.769301i	$-0.279395\pi$
$504$		0			0
$505$	−3.88454e6			−0.0301624
$506$	−9.16786e7	+	1.58792e8i	−0.707647	+	1.22568i
$507$	5.30778e7	−	3.06445e7i	0.407277	−	0.235141i
$508$	2.75651e7	+	4.77441e7i	0.210265	+	0.364190i
$509$	8.59044e7	+	4.95969e7i	0.651422	+	0.376098i	0.789001	−	0.614392i	$-0.210599\pi$
$509$	8.59044e7	+	4.95969e7i	0.651422	+	0.376098i	−0.137579	+	0.990491i	$0.543932\pi$
$510$		−	1.14736e8i		−	0.864950i
$511$		0			0
$512$	−1.17762e7			−0.0877392
$513$	2.96011e7	−	5.12706e7i	0.219258	−	0.379766i
$514$	3.57153e7	−	2.06202e7i	0.263005	−	0.151846i
$515$	−3.02889e7	−	5.24620e7i	−0.221749	−	0.384081i
$516$	1.87725e8	+	1.08383e8i	1.36639	+	0.788883i
$517$		−	1.23555e8i		−	0.894103i
$518$		0			0
$519$	4.72105e8			3.37704
$520$	−1.52955e7	+	2.64925e7i	−0.108781	+	0.188414i
$521$	−1.96465e8	+	1.13429e8i	−1.38922	+	0.802066i	−0.993227	−	0.116187i	$-0.962933\pi$
$521$	−1.96465e8	+	1.13429e8i	−1.38922	+	0.802066i	−0.395992	+	0.918254i	$0.629599\pi$
$522$	3.76515e8	+	6.52144e8i	2.64710	+	4.58492i
$523$	−2.18283e8	−	1.26026e8i	−1.52586	−	0.880958i	−0.999529	−	0.0306797i	$-0.990233\pi$
$523$	−2.18283e8	−	1.26026e8i	−1.52586	−	0.880958i	−0.526334	−	0.850278i	$-0.676434\pi$
$524$		−	7.08395e7i		−	0.492359i
$525$		0			0
$526$	1.79067e8			1.23043
$527$	−9.88523e7	+	1.71217e8i	−0.675390	+	1.16981i
$528$	1.05488e7	−	6.09037e6i	0.0716642	−	0.0413754i
$529$	2.68241e7	+	4.64608e7i	0.181200	+	0.313848i
$530$	4.01729e7	+	2.31938e7i	0.269840	+	0.155792i
$531$		−	3.33229e7i		−	0.222566i
$532$		0			0
$533$	−6.93633e7			−0.458087
$534$	2.13103e8	−	3.69105e8i	1.39948	−	2.42397i
$535$	−4.73201e7	+	2.73203e7i	−0.309019	+	0.178412i
$536$	−500844.	−	867487.i	−0.00325243	−	0.00563337i
$537$	−6.99775e7	−	4.04015e7i	−0.451893	−	0.260900i
$538$			1.93128e8i			1.24022i
$539$		0			0
$540$	1.08115e8			0.686603
$541$	1.25513e7	−	2.17394e7i	0.0792675	−	0.137295i	−0.823667	−	0.567074i	$-0.808075\pi$
$541$	1.25513e7	−	2.17394e7i	0.0792675	−	0.137295i	0.902934	+	0.429779i	$0.141409\pi$
$542$	2.85171e8	−	1.64643e8i	1.79105	−	1.03406i
$543$	−1.37719e7	−	2.38537e7i	−0.0860191	−	0.148989i
$544$	1.68199e8	+	9.71099e7i	1.04479	+	0.603207i
$545$			2.99881e7i			0.185250i
$546$		0			0
$547$	1.10837e8			0.677208			0.338604	−	0.940929i	$-0.390045\pi$
$547$	1.10837e8			0.677208			0.338604	+	0.940929i	$0.390045\pi$
$548$	1.64863e8	−	2.85552e8i	1.00180	−	1.73518i
$549$	−1.31042e8	+	7.56570e7i	−0.791941	+	0.457227i
$550$	−1.38499e8	−	2.39887e8i	−0.832450	−	1.44185i
$551$	6.12838e7	+	3.53822e7i	0.366345	+	0.211510i
$552$			2.40242e8i			1.42834i
$553$		0			0
$554$	3.09804e8			1.82204
$555$	−2.71275e7	+	4.69863e7i	−0.158683	+	0.274848i
$556$	3.26285e8	−	1.88381e8i	1.89834	−	1.09601i
$557$	−1.12339e8	−	1.94578e8i	−0.650080	−	1.12597i	−0.983103	−	0.183053i	$-0.941402\pi$
$557$	−1.12339e8	−	1.94578e8i	−0.650080	−	1.12597i	0.333023	−	0.942919i	$-0.391931\pi$
$558$	−5.23624e8	−	3.02315e8i	−3.01382	−	1.74003i
$559$			8.31037e7i			0.475757i
$560$		0			0
$561$	−4.16636e8			−2.35976
$562$	−8.00043e6	+	1.38572e7i	−0.0450718	+	0.0780666i
$563$	−1.16491e7	+	6.72563e6i	−0.0652782	+	0.0376884i	−0.532284	−	0.846566i	$-0.678666\pi$
$563$	−1.16491e7	+	6.72563e6i	−0.0652782	+	0.0376884i	0.467006	+	0.884254i	$0.345333\pi$
$564$	−2.07915e8	−	3.60118e8i	−1.15890	−	2.00728i
$565$	−4.19185e7	−	2.42017e7i	−0.232413	−	0.134184i
$566$		−	2.66493e8i		−	1.46973i
$567$		0			0
$568$	−3.55221e7			−0.193845
$569$	−1.81339e7	+	3.14089e7i	−0.0984362	+	0.170496i	−0.911038	−	0.412323i	$-0.864717\pi$
$569$	−1.81339e7	+	3.14089e7i	−0.0984362	+	0.170496i	0.812601	+	0.582820i	$0.198051\pi$
$570$	2.85566e7	−	1.64872e7i	0.154199	−	0.0890270i
$571$	−1.01486e7	−	1.75779e7i	−0.0545128	−	0.0944189i	0.837481	−	0.546466i	$-0.184027\pi$
$571$	−1.01486e7	−	1.75779e7i	−0.0545128	−	0.0944189i	−0.891994	+	0.452047i	$0.850694\pi$
$572$	2.47106e8	+	1.42667e8i	1.32037	+	0.762316i
$573$			5.77361e8i			3.06891i
$574$		0			0
$575$	1.42591e8			0.750049
$576$	−3.05310e8	+	5.28813e8i	−1.59762	+	2.76716i
$577$	2.32739e8	−	1.34372e8i	1.21155	−	0.699489i	0.248453	−	0.968644i	$-0.420078\pi$
$577$	2.32739e8	−	1.34372e8i	1.21155	−	0.699489i	0.963097	+	0.269155i	$0.0867444\pi$
$578$	8.87572e7	+	1.53732e8i	0.459643	+	0.796124i
$579$	−3.34221e8	−	1.92963e8i	−1.72186	−	0.994116i
$580$			1.29230e8i			0.662338i
$581$		0			0
$582$	−3.29559e8			−1.67172
$583$	8.42225e7	−	1.45878e8i	0.425033	−	0.736178i
$584$	−3.41062e8	+	1.96912e8i	−1.71236	+	0.988630i
$585$	4.17600e7	+	7.23304e7i	0.208590	+	0.361288i
$586$	1.92993e8	+	1.11425e8i	0.959068	+	0.553718i
$587$			8.55223e7i			0.422829i	0.977396	+	0.211415i	$0.0678071\pi$
$587$			8.55223e7i			0.422829i	−0.977396	+	0.211415i	$0.932193\pi$
$588$		0			0
$589$	−5.68187e7			−0.278064
$590$	4.60549e6	−	7.97694e6i	0.0224243	−	0.0388401i
$591$	5.96364e7	−	3.44311e7i	0.288901	−	0.166797i
$592$	3.39477e6	+	5.87991e6i	0.0163623	+	0.0283404i
$593$	1.32160e8	+	7.63026e7i	0.633776	+	0.365911i	0.782213	−	0.623011i	$-0.214091\pi$
$593$	1.32160e8	+	7.63026e7i	0.633776	+	0.365911i	−0.148437	+	0.988922i	$0.547424\pi$
$594$		−	6.32345e8i		−	3.01714i
$595$		0			0
$596$	−1.10385e8			−0.521398
$597$	2.58206e8	−	4.47227e8i	1.21351	−	2.10186i
$598$	−2.04886e8	+	1.18291e8i	−0.958097	+	0.553157i
$599$	1.38818e8	+	2.40440e8i	0.645901	+	1.11873i	0.984093	+	0.177656i	$0.0568516\pi$
$599$	1.38818e8	+	2.40440e8i	0.645901	+	1.11873i	−0.338191	+	0.941077i	$0.609815\pi$
$600$	−3.14310e8	−	1.81467e8i	−1.45514	−	0.840124i
$601$		−	1.55047e8i		−	0.714231i	−0.934060	−	0.357116i	$-0.883760\pi$
$601$		−	1.55047e8i		−	0.714231i	0.934060	−	0.357116i	$-0.116240\pi$
$602$		0			0
$603$	−2.73483e6			−0.0124732
$604$	2.09517e8	−	3.62894e8i	0.950843	−	1.64691i
$605$	9.02814e6	−	5.21240e6i	0.0407692	−	0.0235381i
$606$	3.82325e7	+	6.62207e7i	0.171797	+	0.297561i
$607$	7.21062e7	+	4.16305e7i	0.322408	+	0.186143i	0.652466	−	0.757818i	$-0.273735\pi$
$607$	7.21062e7	+	4.16305e7i	0.322408	+	0.186143i	−0.330057	+	0.943961i	$0.607068\pi$
$608$			5.58172e7i			0.248346i
$609$		0			0
$610$	−4.18256e7			−0.184269
$611$	7.97101e7	−	1.38062e8i	0.349454	−	0.605272i
$612$	−8.07561e8	+	4.66246e8i	−3.52307	+	2.03405i
$613$	6.01924e6	+	1.04256e7i	0.0261312	+	0.0452606i	0.878795	−	0.477199i	$-0.158348\pi$
$613$	6.01924e6	+	1.04256e7i	0.0261312	+	0.0452606i	−0.852664	+	0.522460i	$0.825015\pi$
$614$	1.00662e8	+	5.81170e7i	0.434869	+	0.251072i
$615$			5.31566e7i			0.228524i
$616$		0			0
$617$	−2.78131e8			−1.18412			−0.592058	−	0.805895i	$-0.701685\pi$
$617$	−2.78131e8			−1.18412			−0.592058	+	0.805895i	$0.701685\pi$
$618$	−5.96221e8	+	1.03268e9i	−2.52605	+	4.37524i
$619$	−3.53647e8	+	2.04178e8i	−1.49107	+	0.860870i	−0.999948	−	0.0102205i	$-0.996747\pi$
$619$	−3.53647e8	+	2.04178e8i	−1.49107	+	0.860870i	−0.491123	+	0.871090i	$0.663413\pi$
$620$	−5.18812e7	−	8.98609e7i	−0.217688	−	0.377047i
$621$	2.81904e8	+	1.62758e8i	1.17714	+	0.679621i
$622$		−	1.57677e7i		−	0.0655235i
$623$		0			0
$624$	1.57166e7			0.0646851
$625$	−1.00300e8	+	1.73725e8i	−0.410828	+	0.711576i
$626$	4.76571e8	−	2.75148e8i	1.94269	−	1.12161i
$627$	−5.98689e7	−	1.03696e8i	−0.242884	−	0.420687i
$628$	1.38875e8	+	8.01798e7i	0.560721	+	0.323732i
$629$		−	2.32233e8i		−	0.933193i
$630$		0			0
$631$	−1.50267e8			−0.598102			−0.299051	−	0.954237i	$-0.596670\pi$
$631$	−1.50267e8			−0.598102			−0.299051	+	0.954237i	$0.596670\pi$
$632$	7.32440e7	−	1.26862e8i	0.290149	−	0.502552i
$633$	3.10694e8	−	1.79379e8i	1.22496	−	0.707230i
$634$	−6.46309e7	−	1.11944e8i	−0.253614	−	0.439271i
$635$	1.40273e7	+	8.09869e6i	0.0547840	+	0.0316296i
$636$		−	5.66910e8i		−	2.20365i
$637$		0			0
$638$	7.55842e8			2.91051
$639$	−4.84916e7	+	8.39899e7i	−0.185851	+	0.321903i
$640$	−9.22624e7	+	5.32677e7i	−0.351953	+	0.203200i
$641$	−6.41991e7	−	1.11196e8i	−0.243756	−	0.422197i	0.718025	−	0.696017i	$-0.245046\pi$
$641$	−6.41991e7	−	1.11196e8i	−0.243756	−	0.422197i	−0.961781	+	0.273820i	$0.911713\pi$
$642$	9.31470e8	+	5.37784e8i	3.52017	+	2.03237i
$643$			1.19057e8i			0.447841i	0.974607	+	0.223920i	$0.0718856\pi$
$643$			1.19057e8i			0.447841i	−0.974607	+	0.223920i	$0.928114\pi$
$644$		0			0
$645$	6.36865e7			0.237339
$646$	−7.05715e7	+	1.22233e8i	−0.261777	+	0.453411i
$647$	−1.17033e8	+	6.75689e7i	−0.432111	+	0.249479i	−0.700245	−	0.713902i	$-0.746926\pi$
$647$	−1.17033e8	+	6.75689e7i	−0.432111	+	0.249479i	0.268135	+	0.963381i	$0.413593\pi$
$648$	−1.34639e8	−	2.33201e8i	−0.494817	−	0.857048i
$649$	−2.89662e7	−	1.67236e7i	−0.105964	−	0.0611782i
$650$		−	3.57405e8i		−	1.30143i
$651$		0			0
$652$	−6.14231e8			−2.21610
$653$	−6.08680e7	+	1.05427e8i	−0.218600	+	0.378626i	−0.954380	−	0.298594i	$-0.903482\pi$
$653$	−6.08680e7	+	1.05427e8i	−0.218600	+	0.378626i	0.735780	+	0.677220i	$0.236816\pi$
$654$	5.11213e8	−	2.95149e8i	1.82755	−	1.05514i
$655$	−1.04064e7	−	1.80244e7i	−0.0370320	−	0.0641413i
$656$	5.76086e6	+	3.32603e6i	0.0204068	+	0.0117819i
$657$			1.07523e9i			3.79144i
$658$		0			0
$659$	−9.23112e7			−0.322551			−0.161275	−	0.986909i	$-0.551561\pi$
$659$	−9.23112e7			−0.322551			−0.161275	+	0.986909i	$0.551561\pi$
$660$	1.09333e8	−	1.89370e8i	0.380293	−	0.658687i
$661$	3.54056e8	−	2.04414e8i	1.22593	−	0.707793i	0.259757	−	0.965674i	$-0.416358\pi$
$661$	3.54056e8	−	2.04414e8i	1.22593	−	0.707793i	0.966177	+	0.257881i	$0.0830242\pi$
$662$	8.24656e7	+	1.42835e8i	0.284249	+	0.492333i
$663$	−4.65556e8	−	2.68789e8i	−1.59746	−	0.922296i
$664$			3.57857e8i			1.22238i
$665$		0			0
$666$	7.10225e8			2.40421
$667$	−1.94544e8	+	3.36960e8i	−0.655602	+	1.13554i
$668$	−3.29577e8	+	1.90282e8i	−1.10568	+	0.638362i
$669$	3.27658e8	+	5.67521e8i	1.09432	+	1.89541i
$670$	−654672.	−	377975.i	−0.00217670	−	0.00125672i
$671$			1.51879e8i			0.502724i
$672$		0			0
$673$	−1.99033e8			−0.652950			−0.326475	−	0.945206i	$-0.605861\pi$
$673$	−1.99033e8			−0.652950			−0.326475	+	0.945206i	$0.605861\pi$
$674$	4.65223e8	−	8.05789e8i	1.51943	−	2.63173i
$675$	−4.25873e8	+	2.45878e8i	−1.38474	+	0.799482i
$676$	−6.88429e7	−	1.19239e8i	−0.222853	−	0.385993i
$677$	−3.59101e8	−	2.07327e8i	−1.15731	−	0.668175i	−0.206654	−	0.978414i	$-0.566258\pi$
$677$	−3.59101e8	−	2.07327e8i	−1.15731	−	0.668175i	−0.950659	+	0.310239i	$0.899591\pi$
$678$			9.52793e8i			3.05710i
$679$		0			0
$680$	−1.00347e8			−0.319136
$681$	−2.66136e6	+	4.60962e6i	−0.00842680	+	0.0145957i
$682$	−5.25579e8	+	3.03443e8i	−1.65686	+	0.956587i
$683$	−2.49630e8	−	4.32372e8i	−0.783492	−	1.35705i	−0.929896	−	0.367823i	$-0.880103\pi$
$683$	−2.49630e8	−	4.32372e8i	−0.783492	−	1.35705i	0.146403	−	0.989225i	$-0.453230\pi$
$684$	−2.32087e8	−	1.33995e8i	−0.725240	−	0.418718i
$685$		−	9.68747e7i		−	0.301397i
$686$		0			0
$687$	4.76953e8			1.47098
$688$	3.98490e6	−	6.90204e6i	0.0122363	−	0.0211940i
$689$	1.88223e8	−	1.08671e8i	0.575460	−	0.332242i
$690$	9.06524e7	+	1.57015e8i	0.275951	+	0.477961i
$691$	3.51191e8	+	2.02760e8i	1.06441	+	0.614538i	0.926649	−	0.375927i	$-0.122676\pi$
$691$	3.51191e8	+	2.02760e8i	1.06441	+	0.614538i	0.137762	+	0.990465i	$0.456009\pi$
$692$		−	1.06058e9i		−	3.20057i
$693$		0			0
$694$	−4.55989e8			−1.36419
$695$	5.53468e7	−	9.58635e7i	0.164869	−	0.285561i
$696$	8.57654e8	−	4.95167e8i	2.54381	−	1.46867i
$697$	−1.13765e8	−	1.97047e8i	−0.335979	−	0.581932i
$698$	−8.33225e8	−	4.81063e8i	−2.45017	−	1.41461i
$699$		−	6.11512e8i		−	1.79050i
$700$		0			0
$701$	−2.52012e8			−0.731590			−0.365795	−	0.930695i	$-0.619203\pi$
$701$	−2.52012e8			−0.731590			−0.365795	+	0.930695i	$0.619203\pi$
$702$	4.07952e8	−	7.06593e8i	1.17923	−	2.04248i
$703$	5.78001e7	−	3.33709e7i	0.166365	−	0.0960510i
$704$	3.06450e8	+	5.30787e8i	0.878298	+	1.52126i
$705$	−1.05804e8	−	6.10858e7i	−0.301949	−	0.174330i
$706$		−	1.12185e8i		−	0.318802i
$707$		0			0
$708$	−1.12568e8			−0.317188
$709$	−2.83181e8	+	4.90484e8i	−0.794559	+	1.37622i	0.128561	+	0.991702i	$0.458964\pi$
$709$	−2.83181e8	+	4.90484e8i	−0.794559	+	1.37622i	−0.923119	+	0.384514i	$0.874369\pi$
$710$	−2.32162e7	+	1.34039e7i	−0.0648657	+	0.0374502i
$711$	−1.99972e8	−	3.46362e8i	−0.556366	−	0.963655i
$712$	−3.22813e8	−	1.86376e8i	−0.894359	−	0.516358i
$713$		−	3.12410e8i		−	0.861898i
$714$		0			0
$715$	8.38318e7			0.229346
$716$	−9.07620e7	+	1.57204e8i	−0.247266	+	0.428278i
$717$	2.19082e8	−	1.26487e8i	0.594360	−	0.343154i
$718$	1.10654e8	+	1.91658e8i	0.298946	+	0.517790i
$719$	−5.86941e8	−	3.38870e8i	−1.57909	−	0.911690i	−0.994986	−	0.100012i	$-0.968112\pi$
$719$	−5.86941e8	−	3.38870e8i	−1.57909	−	0.911690i	−0.584106	−	0.811677i	$-0.698555\pi$
$720$		−	8.00972e6i		−	0.0214595i
$721$		0			0
$722$	5.70670e8			1.51626
$723$	3.05049e8	−	5.28360e8i	0.807150	−	1.39803i
$724$	−5.35873e7	+	3.09386e7i	−0.141204	+	0.0815240i
$725$	−2.93898e8	−	5.09046e8i	−0.771228	−	1.33581i
$726$	−1.77714e8	−	1.02603e8i	−0.464421	−	0.268133i
$727$		−	3.86483e8i		−	1.00584i	−0.864334	−	0.502919i	$-0.832260\pi$
$727$		−	3.86483e8i		−	1.00584i	0.864334	−	0.502919i	$-0.167740\pi$
$728$		0			0
$729$	4.04259e8			1.04346
$730$	−1.48605e8	+	2.57391e8i	−0.382001	+	0.661645i
$731$	−2.36081e8	+	1.36301e8i	−0.604378	+	0.348938i
$732$	2.55578e8	+	4.42674e8i	0.651613	+	1.12863i
$733$	1.57315e8	+	9.08257e7i	0.399445	+	0.230620i	0.686245	−	0.727371i	$-0.259258\pi$
$733$	1.57315e8	+	9.08257e7i	0.399445	+	0.230620i	−0.286799	+	0.957991i	$0.592591\pi$
$734$			1.17193e9i			2.96355i
$735$		0			0
$736$	−3.06903e8			−0.769782
$737$	−1.37252e6	+	2.37727e6i	−0.00342859	+	0.00593850i
$738$	6.02619e8	−	3.47923e8i	1.49925	−	0.865592i
$739$	2.42028e8	+	4.19205e8i	0.599698	+	1.03871i	0.992865	+	0.119240i	$0.0380459\pi$
$739$	2.42028e8	+	4.19205e8i	0.599698	+	1.03871i	−0.393167	+	0.919467i	$0.628621\pi$
$740$	1.05555e8	+	6.09420e7i	0.260485	+	0.150391i
$741$		−	1.54495e8i		−	0.379718i
$742$		0			0
$743$	−1.12266e8			−0.273704			−0.136852	−	0.990592i	$-0.543698\pi$
$743$	−1.12266e8			−0.273704			−0.136852	+	0.990592i	$0.543698\pi$
$744$	−3.97583e8	+	6.88634e8i	−0.965404	+	1.67213i
$745$	−2.80863e7	+	1.62156e7i	−0.0679244	+	0.0392162i
$746$	1.36451e8	+	2.36340e8i	0.328670	+	0.569273i
$747$	8.46131e8	+	4.88514e8i	2.02991	+	1.17197i
$748$			9.35973e8i			2.23645i
$749$		0			0
$750$	−5.65487e8			−1.34041
$751$	2.46811e8	−	4.27489e8i	0.582699	−	1.00926i	−0.412459	−	0.910976i	$-0.635330\pi$
$751$	2.46811e8	−	4.27489e8i	0.582699	−	1.00926i	0.995158	−	0.0982882i	$-0.0313367\pi$
$752$	−1.32404e7	+	7.64435e6i	−0.0311349	+	0.0179757i
$753$	3.25583e8	+	5.63926e8i	0.762565	+	1.32080i
$754$	8.44590e8	+	4.87624e8i	1.97030	+	1.13755i
$755$		−	1.23113e8i		−	0.286065i
$756$		0			0
$757$	3.35326e8			0.773000			0.386500	−	0.922289i	$-0.373684\pi$
$757$	3.35326e8			0.773000			0.386500	+	0.922289i	$0.373684\pi$
$758$	4.19033e7	−	7.25786e7i	0.0962144	−	0.166648i
$759$	5.70158e8	−	3.29181e8i	1.30398	−	0.752851i
$760$	−1.44194e7	−	2.49752e7i	−0.0328478	−	0.0568941i
$761$	3.34254e8	+	1.92982e8i	0.758444	+	0.437888i	0.828737	−	0.559639i	$-0.189060\pi$
$761$	3.34254e8	+	1.92982e8i	0.758444	+	0.437888i	−0.0702931	+	0.997526i	$0.522393\pi$
$762$		−	3.18836e8i		−	0.720614i
$763$		0			0
$764$	1.29704e9			2.90853
$765$	−1.36984e8	+	2.37264e8i	−0.305975	+	0.529965i
$766$	−7.79384e8	+	4.49978e8i	−1.73407	+	1.00116i
$767$	−2.15782e7	−	3.73745e7i	−0.0478222	−	0.0828304i
$768$	7.25203e8	+	4.18696e8i	1.60094	+	0.924305i
$769$		−	4.67287e7i		−	0.102755i	−0.998679	−	0.0513777i	$-0.983639\pi$
$769$		−	4.67287e7i		−	0.102755i	0.998679	−	0.0513777i	$-0.0163612\pi$
$770$		0			0
$771$	−1.48078e8			−0.323092
$772$	−4.33490e8	+	7.50827e8i	−0.942166	+	1.63188i
$773$	−5.17660e8	+	2.98871e8i	−1.12074	+	0.647062i	−0.941591	−	0.336760i	$-0.890669\pi$
$773$	−5.17660e8	+	2.98871e8i	−1.12074	+	0.647062i	−0.179153	+	0.983821i	$0.557336\pi$
$774$	−4.16843e8	−	7.21994e8i	−0.898980	−	1.55708i
$775$	4.08727e8	+	2.35979e8i	0.878069	+	0.506953i
$776$			2.88227e8i			0.616807i
$777$		0			0
$778$	2.00257e8			0.425254
$779$	3.26952e7	−	5.66298e7i	0.0691627	−	0.119793i
$780$	2.44340e8	−	1.41070e8i	0.514886	−	0.297270i
$781$	4.86726e7	+	8.43035e7i	0.102172	+	0.176967i
$782$	−6.72083e8	−	3.88027e8i	−1.40541	−	0.811413i
$783$		−	1.34185e9i		−	2.79524i
$784$		0			0
$785$	4.71141e7			0.0973961
$786$	−2.04845e8	+	3.54801e8i	−0.421849	+	0.730663i
$787$	2.88080e8	−	1.66323e8i	0.591001	−	0.341215i	−0.174492	−	0.984659i	$-0.555828\pi$
$787$	2.88080e8	−	1.66323e8i	0.591001	−	0.341215i	0.765493	+	0.643444i	$0.222495\pi$
$788$	−7.73494e7	−	1.33973e8i	−0.158081	−	0.273804i
$789$	−5.56816e8	−	3.21478e8i	−1.13365	−	0.654516i
$790$		−	1.10551e8i		−	0.224224i
$791$		0			0
$792$	−1.11437e9			−2.24313
$793$	−9.79832e7	+	1.69712e8i	−0.196486	+	0.340324i
$794$	3.37230e8	−	1.94700e8i	0.673697	−	0.388959i
$795$	−8.32798e7	−	1.44245e8i	−0.165744	−	0.287077i
$796$	−1.00469e9	−	5.80061e8i	−1.99203	−	1.15010i
$797$			5.19774e8i			1.02669i	0.858182	+	0.513345i	$0.171594\pi$
$797$			5.19774e8i			1.02669i	−0.858182	+	0.513345i	$0.828406\pi$
$798$		0			0
$799$	5.22942e8			1.02521
$800$	2.31819e8	−	4.01523e8i	0.452772	−	0.784225i
$801$	−8.81352e8	+	5.08849e8i	−1.71495	+	0.990128i
$802$	−6.80421e8	−	1.17852e9i	−1.31903	−	2.28463i
$803$	9.34650e8	+	5.39620e8i	1.80510	+	1.04218i
$804$			9.23856e6i			0.0177761i
$805$		0			0
$806$	−7.83054e8			−1.49550
$807$	3.46722e8	−	6.00540e8i	0.659722	−	1.14267i
$808$	5.79155e7	−	3.34376e7i	0.109790	−	0.0633870i
$809$	−1.78242e8	−	3.08723e8i	−0.336638	−	0.583074i	0.647160	−	0.762354i	$-0.275957\pi$
$809$	−1.78242e8	−	3.08723e8i	−0.336638	−	0.583074i	−0.983798	+	0.179280i	$0.942623\pi$
$810$	−1.75991e8	−	1.01609e8i	−0.331159	−	0.191195i
$811$		−	2.56770e8i		−	0.481374i	−0.970603	−	0.240687i	$-0.922627\pi$
$811$		−	2.56770e8i		−	0.481374i	0.970603	−	0.240687i	$-0.0773727\pi$
$812$		0			0
$813$	−1.18234e9			−2.20024
$814$	3.56438e8	−	6.17369e8i	0.660863	−	1.14465i
$815$	−1.56285e8	+	9.02313e7i	−0.288699	+	0.166680i
$816$	2.57773e7	+	4.46477e7i	0.0474425	+	0.0821728i
$817$	−6.78478e7	−	3.91719e7i	−0.124414	−	0.0718305i
$818$		−	1.61387e9i		−	2.94855i
$819$		0			0
$820$	1.19416e8			0.216582
$821$	−2.06310e8	+	3.57340e8i	−0.372813	+	0.645731i	−0.989997	−	0.141088i	$-0.954940\pi$
$821$	−2.06310e8	+	3.57340e8i	−0.372813	+	0.645731i	0.617184	+	0.786819i	$0.288273\pi$
$822$	−1.65144e9	+	9.53462e8i	−2.97337	+	1.71667i
$823$	4.18340e8	+	7.24587e8i	0.750464	+	1.29984i	0.947598	+	0.319466i	$0.103504\pi$
$823$	4.18340e8	+	7.24587e8i	0.750464	+	1.29984i	−0.197133	+	0.980377i	$0.563163\pi$
$824$	9.03169e8	+	5.21445e8i	1.61431	+	0.932024i
$825$			9.94588e8i			1.77126i
$826$		0			0
$827$	5.94119e8			1.05041			0.525203	−	0.850977i	$-0.323989\pi$
$827$	5.94119e8			1.05041			0.525203	+	0.850977i	$0.323989\pi$
$828$	7.36755e8	−	1.27610e9i	1.29787	−	2.24798i
$829$	−3.32964e8	+	1.92237e8i	−0.584432	+	0.337422i	−0.762893	−	0.646525i	$-0.776222\pi$
$829$	−3.32964e8	+	1.92237e8i	−0.584432	+	0.337422i	0.178461	+	0.983947i	$0.442888\pi$
$830$	1.35033e8	+	2.33884e8i	0.236160	+	0.409041i
$831$	−9.63350e8	−	5.56190e8i	−1.67873	−	0.969216i
$832$			7.90814e8i			1.37311i
$833$		0			0
$834$	−2.17894e9			−3.75619
$835$	−5.59052e7	+	9.68307e7i	−0.0960269	+	0.166324i
$836$	−2.32953e8	+	1.34496e8i	−0.398703	+	0.230191i
$837$	5.38705e8	+	9.33064e8i	0.918702	+	1.59124i
$838$	−9.34250e8	−	5.39389e8i	−1.58756	−	0.916580i
$839$			8.54024e8i			1.44605i	0.690820	+	0.723027i	$0.257250\pi$
$839$			8.54024e8i			1.44605i	−0.690820	+	0.723027i	$0.742750\pi$
$840$		0			0
$841$	1.00909e9			1.69645
$842$	−9.13730e8	+	1.58263e9i	−1.53067	+	2.65120i
$843$	4.97555e7	−	2.87263e7i	0.0830535	−	0.0479510i
$844$	−4.02975e8	−	6.97973e8i	−0.670272	−	1.16094i
$845$	−3.50329e7	−	2.02262e7i	−0.0580638	−	0.0335232i
$846$			1.59929e9i			2.64128i
$847$		0			0
$848$	−2.08434e7			−0.0341808
$849$	−4.78435e8	+	8.28673e8i	−0.781807	+	1.35413i
$850$	1.01532e9	−	5.86193e8i	1.65327	−	0.954518i
$851$	1.83485e8	+	3.17806e8i	0.297723	+	0.515672i
$852$	2.83727e8	+	1.63810e8i	0.458757	+	0.264863i
$853$		−	1.79623e8i		−	0.289411i	−0.989475	−	0.144706i	$-0.953776\pi$
$853$		−	1.79623e8i		−	0.289411i	0.989475	−	0.144706i	$-0.0462235\pi$
$854$		0			0
$855$	−7.87363e7			−0.125973
$856$	4.70338e8	−	8.14649e8i	0.749874	−	1.29882i
$857$	4.78700e8	−	2.76378e8i	0.760538	−	0.439097i	−0.0689506	−	0.997620i	$-0.521965\pi$
$857$	4.78700e8	−	2.76378e8i	0.760538	−	0.439097i	0.829489	+	0.558523i	$0.188632\pi$
$858$	−8.25091e8	−	1.42910e9i	−1.30629	−	2.26256i
$859$	−3.17693e8	−	1.83420e8i	−0.501219	−	0.289379i	0.227998	−	0.973662i	$-0.426782\pi$
$859$	−3.17693e8	−	1.83420e8i	−0.501219	−	0.289379i	−0.729217	+	0.684283i	$0.760115\pi$
$860$		−	1.43072e8i		−	0.224936i
$861$		0			0
$862$	−5.44566e8			−0.850215
$863$	3.79917e8	−	6.58035e8i	0.591094	−	1.02380i	−0.402992	−	0.915204i	$-0.632030\pi$
$863$	3.79917e8	−	6.58035e8i	0.591094	−	1.02380i	0.994085	−	0.108601i	$-0.0346369\pi$
$864$	9.16618e8	−	5.29210e8i	1.42117	−	0.820515i
$865$	−1.55801e8	−	2.69856e8i	−0.240726	−	0.416950i
$866$	2.23662e7	+	1.29132e7i	0.0344381	+	0.0198828i
$867$		−	6.37383e8i		−	0.978010i
$868$		0			0
$869$	−4.01438e8			−0.611728
$870$	3.73691e8	−	6.47252e8i	0.567486	−	0.982914i
$871$	−3.06735e6	+	1.77094e6i	−0.00464204	+	0.00268008i
$872$	−2.58133e8	−	4.47099e8i	−0.389308	−	0.674302i
$873$	6.81495e8	+	3.93462e8i	1.02428	+	0.591370i
$874$		−	2.23032e8i		−	0.334066i
$875$		0			0
$876$	3.63224e9			5.40333
$877$	−2.43692e8	+	4.22088e8i	−0.361279	+	0.625754i	−0.988172	−	0.153352i	$-0.950993\pi$
$877$	−2.43692e8	+	4.22088e8i	−0.361279	+	0.625754i	0.626892	+	0.779106i	$0.284327\pi$
$878$	3.98985e8	−	2.30354e8i	0.589485	−	0.340339i
$879$	−4.00081e8	−	6.92961e8i	−0.589090	−	1.02033i
$880$	−6.96252e6	−	4.01981e6i	−0.0102169	−	0.00589872i
$881$			8.74830e7i			0.127937i	0.997952	+	0.0639684i	$0.0203757\pi$
$881$			8.74830e7i			0.127937i	−0.997952	+	0.0639684i	$0.979624\pi$
$882$		0			0
$883$	−2.63332e8			−0.382491			−0.191245	−	0.981542i	$-0.561253\pi$
$883$	−2.63332e8			−0.382491			−0.191245	+	0.981542i	$0.561253\pi$
$884$	−6.03834e8	+	1.04587e9i	−0.874100	+	1.51398i
$885$	−2.86420e7	+	1.65365e7i	−0.0413212	+	0.0238568i
$886$	5.41728e8	+	9.38301e8i	0.778898	+	1.34909i
$887$	4.82875e8	+	2.78788e8i	0.691933	+	0.399488i	0.804336	−	0.594175i	$-0.202521\pi$
$887$	4.82875e8	+	2.78788e8i	0.691933	+	0.399488i	−0.112403	+	0.993663i	$0.535855\pi$
$888$		−	9.34039e8i		−	1.33391i
$889$		0			0
$890$	−2.81308e8			−0.399036
$891$	−3.68966e8	+	6.39067e8i	−0.521618	+	0.903469i
$892$	1.27494e9	−	7.36085e8i	1.79636	−	1.03713i
$893$	7.51447e7	+	1.30154e8i	0.105522	+	0.182770i
$894$	5.52863e8	+	3.19196e8i	0.773758	+	0.446729i
$895$			5.33323e7i			0.0743911i
$896$		0			0
$897$	8.49472e8			1.17699
$898$	3.24505e8	−	5.62059e8i	0.448118	−	0.776164i
$899$	−1.11529e9	+	6.43914e8i	−1.53500	+	0.886234i
$900$	1.11302e9	+	1.92780e9i	1.52677	+	2.64444i
$901$	6.17424e8	+	3.56470e8i	0.844129	+	0.487358i
$902$		−	6.98443e8i		−	0.951725i
$903$		0			0
$904$	8.33297e8			1.12796
$905$	−9.08985e6	+	1.57441e7i	−0.0122634	+	0.0212408i
$906$	−2.09874e9	+	1.21171e9i	−2.82211	+	1.62935i
$907$	1.60683e8	+	2.78311e8i	0.215352	+	0.373000i	0.953381	−	0.301768i	$-0.0975769\pi$
$907$	1.60683e8	+	2.78311e8i	0.215352	+	0.373000i	−0.738030	+	0.674768i	$0.764244\pi$
$908$	1.03555e7	+	5.97876e6i	0.0138329	+	0.00798644i
$909$		−	1.82584e8i		−	0.243092i
$910$		0			0
$911$	−1.09356e9			−1.44640			−0.723198	−	0.690641i	$-0.757329\pi$
$911$	−1.09356e9			−1.44640			−0.723198	+	0.690641i	$0.757329\pi$
$912$	−7.40820e6	+	1.28314e7i	−0.00976625	+	0.0169156i
$913$	8.49290e8	−	4.90338e8i	1.11595	−	0.644293i
$914$	6.92474e8	+	1.19940e9i	0.906911	+	1.57082i
$915$	1.30059e8	+	7.50894e7i	0.169776	+	0.0980202i
$916$		−	1.07148e9i		−	1.39411i
$917$		0			0
$918$	2.67639e9			3.45956
$919$	3.73057e8	−	6.46154e8i	0.480650	−	0.832510i	−0.519104	−	0.854711i	$-0.673734\pi$
$919$	3.73057e8	−	6.46154e8i	0.480650	−	0.832510i	0.999754	+	0.0222016i	$0.00706757\pi$
$920$	1.37322e8	−	7.92831e7i	0.176351	−	0.101816i
$921$	−2.08675e8	−	3.61435e8i	−0.267110	−	0.462649i
$922$	−1.11037e9	−	6.41075e8i	−1.41670	−	0.817929i
$923$			1.25603e8i			0.159733i
$924$		0			0
$925$	−5.54383e8			−0.700462
$926$	6.63904e8	−	1.14991e9i	0.836127	−	1.44821i
$927$	2.46585e9	−	1.42366e9i	3.09548	−	1.78717i
$928$	6.32564e8	+	1.09563e9i	0.791517	+	1.37095i
$929$	8.93145e7	+	5.15657e7i	0.111397	+	0.0643153i	0.554663	−	0.832075i	$-0.312847\pi$
$929$	8.93145e7	+	5.15657e7i	0.111397	+	0.0643153i	−0.443266	+	0.896390i	$0.646180\pi$
$930$			6.00094e8i			0.746054i
$931$		0			0
$932$	−1.37376e9			−1.69693
$933$	−2.83077e7	+	4.90304e7i	−0.0348546	+	0.0603699i
$934$	−6.25698e8	+	3.61247e8i	−0.767934	+	0.443367i
$935$	1.37496e8	+	2.38150e8i	0.168211	+	0.291350i
$936$	−1.24522e9	−	7.18927e8i	−1.51851	−	0.876713i
$937$			4.08495e8i			0.496556i	0.968689	+	0.248278i	$0.0798647\pi$
$937$			4.08495e8i			0.496556i	−0.968689	+	0.248278i	$0.920135\pi$
$938$		0			0
$939$	−1.97589e9			−2.38653
$940$	−1.37229e8	+	2.37688e8i	−0.165220	+	0.286170i
$941$	5.76909e8	−	3.33078e8i	0.692370	−	0.399740i	−0.112129	−	0.993694i	$-0.535767\pi$
$941$	5.76909e8	−	3.33078e8i	0.692370	−	0.399740i	0.804499	+	0.593954i	$0.202434\pi$
$942$	−4.63707e8	−	8.03164e8i	−0.554742	−	0.960841i
$943$	3.11371e8	+	1.79770e8i	0.371316	+	0.214379i
$944$			4.13878e6i			0.00491990i
$945$		0			0
$946$	−8.36799e8			−0.988435
$947$	−2.09394e8	+	3.62681e8i	−0.246555	+	0.427046i	−0.962568	−	0.271041i	$-0.912632\pi$
$947$	−2.09394e8	+	3.62681e8i	−0.246555	+	0.427046i	0.716013	+	0.698087i	$0.245965\pi$
$948$	−1.17005e9	+	6.75529e8i	−1.37334	+	0.792900i
$949$	6.96262e8	+	1.20596e9i	0.814655	+	1.41102i
$950$	2.91794e8	+	1.68467e8i	0.340334	+	0.196492i
$951$			4.64127e8i			0.539629i
$952$		0			0
$953$	6.31833e8			0.730001			0.365001	−	0.931007i	$-0.381069\pi$
$953$	6.31833e8			0.730001			0.365001	+	0.931007i	$0.381069\pi$
$954$	−1.09017e9	+	1.88823e9i	−1.25560	+	2.17476i
$955$	3.30020e8	−	1.90537e8i	0.378905	−	0.218761i
$956$	−2.84153e8	−	4.92168e8i	−0.325221	−	0.563300i
$957$	−2.35033e9	−	1.35696e9i	−2.68159	−	1.54822i
$958$		−	1.63906e9i		−	1.86423i
$959$		0			0
$960$	6.06040e8			0.684995
$961$	7.32642e7	−	1.26897e8i	0.0825509	−	0.142982i
$962$	7.96580e8	−	4.59906e8i	0.894755	−	0.516587i
$963$	−1.28413e9	−	2.22417e9i	−1.43790	−	2.49052i
$964$	−1.18696e9	−	6.85293e8i	−1.32497	−	0.764971i
$965$			2.54721e8i			0.283454i
$966$		0			0
$967$	1.49395e9			1.65218			0.826090	−	0.563538i	$-0.190560\pi$
$967$	1.49395e9			1.65218			0.826090	+	0.563538i	$0.190560\pi$
$968$	−8.97350e7	+	1.55426e8i	−0.0989318	+	0.171355i
$969$	4.38891e8	−	2.53394e8i	0.482375	−	0.278500i
$970$	1.08759e8	+	1.88376e8i	0.119165	+	0.206401i
$971$	3.30927e8	+	1.91061e8i	0.361472	+	0.208696i	0.669726	−	0.742608i	$-0.266412\pi$
$971$	3.30927e8	+	1.91061e8i	0.361472	+	0.208696i	−0.308255	+	0.951304i	$0.599745\pi$
$972$		−	7.62224e7i		−	0.0830011i
$973$		0			0
$974$	−1.69574e9			−1.83520
$975$	−6.41649e8	+	1.11137e9i	−0.692283	+	1.19907i
$976$	1.62757e7	−	9.39677e6i	0.0175061	−	0.0101072i
$977$	−6.68910e8	−	1.15859e9i	−0.717272	−	1.24235i	−0.962077	−	0.272779i	$-0.912057\pi$
$977$	−6.68910e8	−	1.15859e9i	−0.717272	−	1.24235i	0.244805	−	0.969572i	$-0.421276\pi$
$978$	3.07639e9	+	1.77615e9i	3.28870	+	1.89873i
$979$			1.02150e9i			1.08865i
$980$		0			0
$981$	−1.40952e9			−1.49301
$982$	9.57042e8	−	1.65764e9i	1.01064	−	1.75048i
$983$	−1.26792e9	+	7.32032e8i	−1.33484	+	0.770672i	−0.986038	−	0.166523i	$-0.946746\pi$
$983$	−1.26792e9	+	7.32032e8i	−1.33484	+	0.770672i	−0.348805	+	0.937195i	$0.613413\pi$
$984$	−4.57564e8	−	7.92523e8i	−0.480249	−	0.831815i
$985$	−3.93617e7	−	2.27255e7i	−0.0411874	−	0.0237796i
$986$			3.19908e9i			3.33730i
$987$		0			0
$988$	−3.47074e8			−0.359875
$989$	2.15381e8	−	3.73052e8i	0.222648	−	0.385638i
$990$	−7.28320e8	+	4.20496e8i	−0.750614	+	0.433367i
$991$	1.09479e8	+	1.89624e8i	0.112489	+	0.194837i	0.916773	−	0.399408i	$-0.130784\pi$
$991$	1.09479e8	+	1.89624e8i	0.112489	+	0.194837i	−0.804284	+	0.594245i	$0.797451\pi$
$992$	−8.79714e8	−	5.07903e8i	−0.901169	−	0.520290i
$993$		−	5.92201e8i		−	0.604814i
$994$		0			0
$995$	−3.40847e8			−0.346011
$996$	1.65026e9	−	2.85833e9i	1.67022	−	2.89290i
$997$	−7.36590e7	+	4.25270e7i	−0.0743259	+	0.0429121i	−0.536702	−	0.843772i	$-0.680330\pi$
$997$	−7.36590e7	+	4.25270e7i	−0.0743259	+	0.0429121i	0.462376	+	0.886684i	$0.346997\pi$
$998$	2.77336e8	+	4.80360e8i	0.279007	+	0.483254i
$999$	−1.09602e9	−	6.32787e8i	−1.09931	−	0.634689i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.7.d.e.19.4		24
7.2	even	3		49.7.b.c.48.10	yes	12
7.3	odd	6	inner	49.7.d.e.31.4		24
7.4	even	3	inner	49.7.d.e.31.3		24
7.5	odd	6		49.7.b.c.48.9	✓	12
7.6	odd	2	inner	49.7.d.e.19.3		24
21.2	odd	6		441.7.d.e.244.3		12
21.5	even	6		441.7.d.e.244.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.7.b.c.48.9	✓	12	7.5	odd	6
49.7.b.c.48.10	yes	12	7.2	even	3
49.7.d.e.19.3		24	7.6	odd	2	inner
49.7.d.e.19.4		24	1.1	even	1	trivial
49.7.d.e.31.3		24	7.4	even	3	inner
49.7.d.e.31.4		24	7.3	odd	6	inner
441.7.d.e.244.3		12	21.2	odd	6
441.7.d.e.244.4		12	21.5	even	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	49.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-6.49614 + 11.2516i) q^{2} +(40.4001 - 23.3250i) q^{3} +(-52.3997 - 90.7589i) q^{4} +(-26.6652 - 15.3952i) q^{5} +606.091i q^{6} +530.077 q^{8} +(723.614 - 1253.34i) q^{9} +(346.442 - 200.018i) q^{10} +(-726.315 - 1258.01i) q^{11} +(-4233.91 - 2444.45i) q^{12} -1874.30i q^{13} -1436.37 q^{15} +(-89.8745 + 155.667i) q^{16} +(5324.52 - 3074.11i) q^{17} +(9401.39 + 16283.7i) q^{18} +(1530.22 + 883.475i) q^{19} +3226.81i q^{20} +18873.0 q^{22} +(-4857.66 + 8413.72i) q^{23} +(21415.2 - 12364.1i) q^{24} +(-7338.48 - 12710.6i) q^{25} +(21089.0 + 12175.7i) q^{26} -33505.3i q^{27} +40048.9 q^{29} +(9330.87 - 16161.5i) q^{30} +(-27848.2 + 16078.2i) q^{31} +(15794.8 + 27357.4i) q^{32} +(-58686.4 - 33882.6i) q^{33} +79879.4i q^{34} -151668. q^{36} +(18886.2 - 32711.8i) q^{37} +(-19881.1 + 11478.4i) q^{38} +(-43718.1 - 75722.0i) q^{39} +(-14134.6 - 8160.62i) q^{40} -37007.6i q^{41} -44338.5 q^{43} +(-76117.4 + 131839. i) q^{44} +(-38590.6 + 22280.3i) q^{45} +(-63112.1 - 109313. i) q^{46} +(73660.5 + 42527.9i) q^{47} +8385.30i q^{48} +190687. q^{50} +(143407. - 248389. i) q^{51} +(-170110. + 98212.8i) q^{52} +(57979.3 + 100423. i) q^{53} +(376990. + 217655. i) q^{54} +44727.0i q^{55} +82428.3 q^{57} +(-260163. + 450616. i) q^{58} +(19940.5 - 11512.7i) q^{59} +(75265.4 + 130363. i) q^{60} +(-90546.8 - 52277.2i) q^{61} -417785. i q^{62} -421925. q^{64} +(-28855.2 + 49978.6i) q^{65} +(762471. - 440213. i) q^{66} +(-944.851 - 1636.53i) q^{67} +(-558006. - 322165. i) q^{68} +453221. i q^{69} -67013.1 q^{71} +(383571. - 664364. i) q^{72} +(-643419. + 371478. i) q^{73} +(245374. + 425001. i) q^{74} +(-592951. - 342340. i) q^{75} -185175. i q^{76} +1.13600e6 q^{78} +(138176. - 239328. i) q^{79} +(4793.04 - 2767.27i) q^{80} +(-253998. - 439938. i) q^{81} +(416396. + 240406. i) q^{82} +675103. i q^{83} -189306. q^{85} +(288029. - 498881. i) q^{86} +(1.61798e6 - 934142. i) q^{87} +(-385003. - 666845. i) q^{88} +(-608994. - 351603. i) q^{89} -578944. i q^{90} +1.01816e6 q^{92} +(-750048. + 1.29912e6i) q^{93} +(-957018. + 552535. i) q^{94} +(-27202.5 - 47116.1i) q^{95} +(1.27622e6 + 736828. i) q^{96} +543745. i q^{97} -2.10229e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{2} - 564 q^{4} + 1880 q^{8} + 1252 q^{9} + 3872 q^{11} + 44864 q^{15} - 37908 q^{16} + 19436 q^{18} + 159744 q^{22} - 40032 q^{23} + 28860 q^{25} + 68032 q^{29} - 21192 q^{30} + 82060 q^{32}+ \cdots - 8949984 q^{99}+O(q^{100}) \) 24 * q - 20 * q^2 - 564 * q^4 + 1880 * q^8 + 1252 * q^9 + 3872 * q^11 + 44864 * q^15 - 37908 * q^16 + 19436 * q^18 + 159744 * q^22 - 40032 * q^23 + 28860 * q^25 + 68032 * q^29 - 21192 * q^30 + 82060 * q^32 - 563240 * q^36 + 169632 * q^37 - 492128 * q^39 - 241536 * q^43 + 404312 * q^44 + 118872 * q^46 - 2091048 * q^50 + 539424 * q^51 + 15856 * q^53 + 1853888 * q^57 - 971304 * q^58 + 429912 * q^60 - 11496 * q^64 + 267904 * q^65 - 1508352 * q^67 + 5037248 * q^71 - 2550364 * q^72 + 3876024 * q^74 - 135184 * q^78 - 232224 * q^79 - 528204 * q^81 + 1508256 * q^85 + 1560848 * q^86 - 1812720 * q^88 + 7305776 * q^92 - 164384 * q^93 - 2305600 * q^95 - 8949984 * q^99

Introduction

L-functions

Modular forms

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