LMFDB - Embedded newform 98.13.d.a.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,13,Mod(19,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("98.19");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	98.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$89.5713940931$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} - 2204556 x^{14} - 87623088 x^{13} + 1948666431190 x^{12} + 195028079162640 x^{11} + \cdots + 24\!\cdots\!25 $ x^16 - 8x^15 - 2204556x^14 - 87623088x^13 + 1948666431190x^12 + 195028079162640x^11 - 880028445307457796x^10 - 151849761581608663584x^9 + 211028190361269390536623x^8 + 54528516937299786222168960x^7 - 23832744423106572444860463196x^6 - 9141197551096679767843476458896x^5 + 523508549551073444838291611810734x^4 + 566732587460008152706924066069468392x^3 + 73514373627956541910802883627148139944x^2 + 2445664577552004486793879639585121170640*x + 24120197826518417347025654428599335187025
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{48}\cdot 3^{8}\cdot 7^{8} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.6
Root			$-22.0174 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.19
Dual form			98.13.d.a.31.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(22.6274 - 39.1918i) q^{2} +(33.7761 - 19.5006i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(-2481.87 - 1432.91i) q^{5} -1764.99i q^{6} -92681.9 q^{8} +(-264960. + 458924. i) q^{9} +O(q^{10})$	\(q+(22.6274 - 39.1918i) q^{2} +(33.7761 - 19.5006i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(-2481.87 - 1432.91i) q^{5} -1764.99i q^{6} -92681.9 q^{8} +(-264960. + 458924. i) q^{9} +(-112317. + 64846.2i) q^{10} +(-1.70644e6 - 2.95565e6i) q^{11} +(-69173.4 - 39937.3i) q^{12} -6.97895e6i q^{13} -111771. q^{15} +(-2.09715e6 + 3.63237e6i) q^{16} +(2.47314e7 - 1.42787e7i) q^{17} +(1.19907e7 + 2.07685e7i) q^{18} +(4.55136e7 + 2.62773e7i) q^{19} +5.86920e6i q^{20} -1.54450e8 q^{22} +(-1.55977e7 + 2.70160e7i) q^{23} +(-3.13043e6 + 1.80735e6i) q^{24} +(-1.17964e8 - 2.04319e8i) q^{25} +(-2.73518e8 - 1.57916e8i) q^{26} +4.13944e7i q^{27} +4.56209e8 q^{29} +(-2.52908e6 + 4.38050e6i) q^{30} +(-1.51818e9 + 8.76523e8i) q^{31} +(9.49063e7 + 1.64382e8i) q^{32} +(-1.15274e8 - 6.65534e7i) q^{33} -1.29236e9i q^{34} +1.08528e9 q^{36} +(9.08379e8 - 1.57336e9i) q^{37} +(2.05971e9 - 1.18918e9i) q^{38} +(-1.36094e8 - 2.35721e8i) q^{39} +(2.30025e8 + 1.32805e8i) q^{40} +5.14132e9i q^{41} -7.27073e9 q^{43} +(-3.49480e9 + 6.05317e9i) q^{44} +(1.31519e9 - 7.59328e8i) q^{45} +(7.05871e8 + 1.22260e9i) q^{46} +(-3.70838e9 - 2.14103e9i) q^{47} +1.63583e8i q^{48} -1.06769e10 q^{50} +(5.56887e8 - 9.64556e8i) q^{51} +(-1.23780e10 + 7.14644e9i) q^{52} +(3.61377e9 + 6.25923e9i) q^{53} +(1.62232e9 + 9.36648e8i) q^{54} +9.78073e9i q^{55} +2.04970e9 q^{57} +(1.03228e10 - 1.78797e10i) q^{58} +(4.46587e9 - 2.57837e9i) q^{59} +(1.14453e8 + 1.98239e8i) q^{60} +(-4.42661e9 - 2.55570e9i) q^{61} +7.93338e10i q^{62} +8.58993e9 q^{64} +(-1.00002e10 + 1.73209e10i) q^{65} +(-5.21670e9 + 3.01186e9i) q^{66} +(3.79522e10 + 6.57352e10i) q^{67} +(-5.06500e10 - 2.92428e10i) q^{68} +1.21666e9i q^{69} -1.13092e11 q^{71} +(2.45570e10 - 4.25340e10i) q^{72} +(-1.51188e11 + 8.72887e10i) q^{73} +(-4.11085e10 - 7.12021e10i) q^{74} +(-7.96871e9 - 4.60074e9i) q^{75} -1.07632e11i q^{76} -1.23178e10 q^{78} +(-1.13044e11 + 1.95798e11i) q^{79} +(1.04097e10 - 6.01006e9i) q^{80} +(-1.40003e11 - 2.42493e11i) q^{81} +(2.01498e11 + 1.16335e11i) q^{82} +4.13229e11i q^{83} -8.18404e10 q^{85} +(-1.64518e11 + 2.84953e11i) q^{86} +(1.54090e10 - 8.89637e9i) q^{87} +(1.58156e11 + 2.73935e11i) q^{88} +(2.25422e11 + 1.30148e11i) q^{89} -6.87265e10i q^{90} +6.38882e10 q^{92} +(-3.41855e10 + 5.92110e10i) q^{93} +(-1.67822e11 + 9.68921e10i) q^{94} +(-7.53061e10 - 1.30434e11i) q^{95} +(6.41112e9 + 3.70146e9i) q^{96} -4.10959e11i q^{97} +1.80856e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16384 q^{4} - 18144 q^{5} + 2362248 q^{9}+O(q^{10}) $ 16 * q - 16384 * q^4 - 18144 * q^5 + 2362248 * q^9	\( 16 q - 16384 q^{4} - 18144 q^{5} + 2362248 q^{9} + 2290176 q^{10} + 2072088 q^{11} - 27163728 q^{15} - 33554432 q^{16} + 101561040 q^{17} - 4592640 q^{18} - 174931848 q^{19} + 62776320 q^{22} + 25630560 q^{23} - 242221056 q^{24} + 521205808 q^{25} + 1434682368 q^{26} + 532360944 q^{29} - 2151917568 q^{30} - 4583818344 q^{31} - 6054957720 q^{33} - 9675767808 q^{36} + 5764524040 q^{37} + 149506560 q^{38} + 10526083272 q^{39} - 4690280448 q^{40} - 66929432000 q^{43} + 4243636224 q^{44} - 57253352184 q^{45} + 7203213312 q^{46} - 18116171640 q^{47} - 99248080896 q^{50} - 23299256376 q^{51} - 8269578240 q^{52} + 39134161800 q^{53} - 105152205312 q^{54} - 328243960080 q^{57} + 29637396480 q^{58} - 201845459088 q^{59} + 27815657472 q^{60} - 336780254328 q^{61} + 137438953472 q^{64} + 158322703896 q^{65} - 268884080640 q^{66} + 107767119920 q^{67} - 207997009920 q^{68} - 1150259029344 q^{71} - 9405726720 q^{72} + 738414283320 q^{73} + 4902778368 q^{74} - 1537028640000 q^{75} - 786088888320 q^{78} + 227632064768 q^{79} + 76101451776 q^{80} - 391984178400 q^{81} + 302578053120 q^{82} + 710209696080 q^{85} - 38105192448 q^{86} - 1957017683880 q^{87} - 64282951680 q^{88} + 2485007442792 q^{89} - 104982773760 q^{92} - 458668768680 q^{93} + 2021298693120 q^{94} - 186503862960 q^{95} + 496068722688 q^{96} + 3921180354576 q^{99}+O(q^{100}) \) 16 * q - 16384 * q^4 - 18144 * q^5 + 2362248 * q^9 + 2290176 * q^10 + 2072088 * q^11 - 27163728 * q^15 - 33554432 * q^16 + 101561040 * q^17 - 4592640 * q^18 - 174931848 * q^19 + 62776320 * q^22 + 25630560 * q^23 - 242221056 * q^24 + 521205808 * q^25 + 1434682368 * q^26 + 532360944 * q^29 - 2151917568 * q^30 - 4583818344 * q^31 - 6054957720 * q^33 - 9675767808 * q^36 + 5764524040 * q^37 + 149506560 * q^38 + 10526083272 * q^39 - 4690280448 * q^40 - 66929432000 * q^43 + 4243636224 * q^44 - 57253352184 * q^45 + 7203213312 * q^46 - 18116171640 * q^47 - 99248080896 * q^50 - 23299256376 * q^51 - 8269578240 * q^52 + 39134161800 * q^53 - 105152205312 * q^54 - 328243960080 * q^57 + 29637396480 * q^58 - 201845459088 * q^59 + 27815657472 * q^60 - 336780254328 * q^61 + 137438953472 * q^64 + 158322703896 * q^65 - 268884080640 * q^66 + 107767119920 * q^67 - 207997009920 * q^68 - 1150259029344 * q^71 - 9405726720 * q^72 + 738414283320 * q^73 + 4902778368 * q^74 - 1537028640000 * q^75 - 786088888320 * q^78 + 227632064768 * q^79 + 76101451776 * q^80 - 391984178400 * q^81 + 302578053120 * q^82 + 710209696080 * q^85 - 38105192448 * q^86 - 1957017683880 * q^87 - 64282951680 * q^88 + 2485007442792 * q^89 - 104982773760 * q^92 - 458668768680 * q^93 + 2021298693120 * q^94 - 186503862960 * q^95 + 496068722688 * q^96 + 3921180354576 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	22.6274	−	39.1918i	0.353553	−	0.612372i
$2$	22.6274	−	39.1918i	0.353553	−	0.612372i
$3$	33.7761	−	19.5006i	0.0463321	−	0.0267498i	−0.476655	−	0.879090i	$-0.658151\pi$
$3$	33.7761	−	19.5006i	0.0463321	−	0.0267498i	0.522987	+	0.852341i	$0.324818\pi$
$4$	−1024.00	−	1773.62i	−0.250000	−	0.433013i
$5$	−2481.87	−	1432.91i	−0.158840	−	0.0917063i	0.418473	−	0.908229i	$-0.362565\pi$
$5$	−2481.87	−	1432.91i	−0.158840	−	0.0917063i	−0.577313	+	0.816523i	$0.695899\pi$
$6$		−	1764.99i		−	0.0378300i
$7$		0			0
$7$		0			0
$8$	−92681.9			−0.353553
$9$	−264960.	+	458924.i	−0.498569	+	0.863547i
$10$	−112317.	+	64846.2i	−0.112317	+	0.0648462i
$11$	−1.70644e6	−	2.95565e6i	−0.963243	−	1.66839i	−0.714263	−	0.699878i	$-0.753238\pi$
$11$	−1.70644e6	−	2.95565e6i	−0.963243	−	1.66839i	−0.248980	−	0.968509i	$-0.580095\pi$
$12$	−69173.4	−	39937.3i	−0.0231660	−	0.0133749i
$13$		−	6.97895e6i		−	1.44587i	−0.690915	−	0.722936i	$-0.742792\pi$
$13$		−	6.97895e6i		−	1.44587i	0.690915	−	0.722936i	$-0.257208\pi$
$14$		0			0
$15$	−111771.			−0.00981251
$16$	−2.09715e6	+	3.63237e6i	−0.125000	+	0.216506i
$17$	2.47314e7	−	1.42787e7i	1.02460	−	0.591555i	0.109169	−	0.994023i	$-0.465181\pi$
$17$	2.47314e7	−	1.42787e7i	1.02460	−	0.591555i	0.915434	+	0.402468i	$0.131848\pi$
$18$	1.19907e7	+	2.07685e7i	0.352541	+	0.610620i
$19$	4.55136e7	+	2.62773e7i	0.967431	+	0.558546i	0.898452	−	0.439072i	$-0.144693\pi$
$19$	4.55136e7	+	2.62773e7i	0.967431	+	0.558546i	0.0689787	+	0.997618i	$0.478026\pi$
$20$			5.86920e6i			0.0917063i
$21$		0			0
$22$	−1.54450e8			−1.36223
$23$	−1.55977e7	+	2.70160e7i	−0.105364	+	0.182496i	−0.913887	−	0.405969i	$-0.866934\pi$
$23$	−1.55977e7	+	2.70160e7i	−0.105364	+	0.182496i	0.808523	+	0.588465i	$0.200268\pi$
$24$	−3.13043e6	+	1.80735e6i	−0.0163809	+	0.00945749i
$25$	−1.17964e8	−	2.04319e8i	−0.483180	−	0.836892i
$26$	−2.73518e8	−	1.57916e8i	−0.885412	−	0.511193i
$27$			4.13944e7i			0.106846i
$28$		0			0
$29$	4.56209e8			0.766966			0.383483	−	0.923548i	$-0.374724\pi$
$29$	4.56209e8			0.766966			0.383483	+	0.923548i	$0.374724\pi$
$30$	−2.52908e6	+	4.38050e6i	−0.00346925	+	0.00600891i
$31$	−1.51818e9	+	8.76523e8i	−1.71062	+	0.987628i	−0.776902	+	0.629622i	$0.783210\pi$
$31$	−1.51818e9	+	8.76523e8i	−1.71062	+	0.987628i	−0.933719	+	0.358006i	$0.883457\pi$
$32$	9.49063e7	+	1.64382e8i	0.0883883	+	0.153093i
$33$	−1.15274e8	−	6.65534e7i	−0.0892581	−	0.0515332i
$34$		−	1.29236e9i		−	0.836585i
$35$		0			0
$36$	1.08528e9			0.498569
$37$	9.08379e8	−	1.57336e9i	0.354043	−	0.613221i	−0.632910	−	0.774225i	$-0.718140\pi$
$37$	9.08379e8	−	1.57336e9i	0.354043	−	0.613221i	0.986954	+	0.161004i	$0.0514731\pi$
$38$	2.05971e9	−	1.18918e9i	0.684077	−	0.394952i
$39$	−1.36094e8	−	2.35721e8i	−0.0386768	−	0.0669902i
$40$	2.30025e8	+	1.32805e8i	0.0561584	+	0.0324231i
$41$			5.14132e9i			1.08236i	0.840907	+	0.541180i	$0.182022\pi$
$41$			5.14132e9i			1.08236i	−0.840907	+	0.541180i	$0.817978\pi$
$42$		0			0
$43$	−7.27073e9			−1.15018			−0.575092	−	0.818089i	$-0.695034\pi$
$43$	−7.27073e9			−1.15018			−0.575092	+	0.818089i	$0.695034\pi$
$44$	−3.49480e9	+	6.05317e9i	−0.481622	+	0.834193i
$45$	1.31519e9	−	7.59328e8i	0.158385	−	0.0914438i
$46$	7.05871e8	+	1.22260e9i	0.0745038	+	0.129044i
$47$	−3.70838e9	−	2.14103e9i	−0.344031	−	0.198626i	0.318022	−	0.948083i	$-0.396981\pi$
$47$	−3.70838e9	−	2.14103e9i	−0.344031	−	0.198626i	−0.662053	+	0.749457i	$0.730315\pi$
$48$			1.63583e8i			0.0133749i
$49$		0			0
$50$	−1.06769e10			−0.683320
$51$	5.56887e8	−	9.64556e8i	0.0316480	−	0.0548159i
$52$	−1.23780e10	+	7.14644e9i	−0.626081	+	0.361468i
$53$	3.61377e9	+	6.25923e9i	0.163044	+	0.282401i	0.935959	−	0.352109i	$-0.114535\pi$
$53$	3.61377e9	+	6.25923e9i	0.163044	+	0.282401i	−0.772915	+	0.634510i	$0.781202\pi$
$54$	1.62232e9	+	9.36648e8i	0.0654297	+	0.0377758i
$55$			9.78073e9i			0.353342i
$56$		0			0
$57$	2.04970e9			0.0597641
$58$	1.03228e10	−	1.78797e10i	0.271163	−	0.469669i
$59$	4.46587e9	−	2.57837e9i	0.105875	−	0.0611270i	−0.446127	−	0.894969i	$-0.647197\pi$
$59$	4.46587e9	−	2.57837e9i	0.105875	−	0.0611270i	0.552003	+	0.833842i	$0.313864\pi$
$60$	1.14453e8	+	1.98239e8i	0.00245313	+	0.00424894i
$61$	−4.42661e9	−	2.55570e9i	−0.0859196	−	0.0496057i	0.456425	−	0.889762i	$-0.349130\pi$
$61$	−4.42661e9	−	2.55570e9i	−0.0859196	−	0.0496057i	−0.542344	+	0.840156i	$0.682463\pi$
$62$			7.93338e10i			1.39672i
$63$		0			0
$64$	8.58993e9			0.125000
$65$	−1.00002e10	+	1.73209e10i	−0.132596	+	0.229662i
$66$	−5.21670e9	+	3.01186e9i	−0.0631150	+	0.0364395i
$67$	3.79522e10	+	6.57352e10i	0.419555	+	0.726690i	0.995895	−	0.0905201i	$-0.0288529\pi$
$67$	3.79522e10	+	6.57352e10i	0.419555	+	0.726690i	−0.576340	+	0.817210i	$0.695520\pi$
$68$	−5.06500e10	−	2.92428e10i	−0.512301	−	0.295777i
$69$			1.21666e9i			0.0112739i
$70$		0			0
$71$	−1.13092e11			−0.882838			−0.441419	−	0.897301i	$-0.645525\pi$
$71$	−1.13092e11			−0.882838			−0.441419	+	0.897301i	$0.645525\pi$
$72$	2.45570e10	−	4.25340e10i	0.176271	−	0.305310i
$73$	−1.51188e11	+	8.72887e10i	−0.999037	+	0.576794i	−0.907963	−	0.419050i	$-0.862363\pi$
$73$	−1.51188e11	+	8.72887e10i	−0.999037	+	0.576794i	−0.0910734	+	0.995844i	$0.529030\pi$
$74$	−4.11085e10	−	7.12021e10i	−0.250347	−	0.433613i
$75$	−7.96871e9	−	4.60074e9i	−0.0447734	−	0.0258500i
$76$		−	1.07632e11i		−	0.558546i
$77$		0			0
$78$	−1.23178e10			−0.0546973
$79$	−1.13044e11	+	1.95798e11i	−0.465036	+	0.805465i	−0.999203	−	0.0399134i	$-0.987292\pi$
$79$	−1.13044e11	+	1.95798e11i	−0.465036	+	0.805465i	0.534168	+	0.845379i	$0.320625\pi$
$80$	1.04097e10	−	6.01006e9i	0.0397100	−	0.0229266i
$81$	−1.40003e11	−	2.42493e11i	−0.495711	−	0.858596i
$82$	2.01498e11	+	1.16335e11i	0.662807	+	0.382672i
$83$			4.13229e11i			1.26393i	0.774998	+	0.631964i	$0.217751\pi$
$83$			4.13229e11i			1.26393i	−0.774998	+	0.631964i	$0.782249\pi$
$84$		0			0
$85$	−8.18404e10			−0.216997
$86$	−1.64518e11	+	2.84953e11i	−0.406652	+	0.704341i
$87$	1.54090e10	−	8.89637e9i	0.0355351	−	0.0205162i
$88$	1.58156e11	+	2.73935e11i	0.340558	+	0.589864i
$89$	2.25422e11	+	1.30148e11i	0.453583	+	0.261876i	0.709342	−	0.704864i	$-0.248992\pi$
$89$	2.25422e11	+	1.30148e11i	0.453583	+	0.261876i	−0.255759	+	0.966741i	$0.582325\pi$
$90$		−	6.87265e10i		−	0.129321i
$91$		0			0
$92$	6.38882e10			0.105364
$93$	−3.41855e10	+	5.92110e10i	−0.0528377	+	0.0915176i
$94$	−1.67822e11	+	9.68921e10i	−0.243266	+	0.140450i
$95$	−7.53061e10	−	1.30434e11i	−0.102444	−	0.177439i
$96$	6.41112e9	+	3.70146e9i	0.00819043	+	0.00472875i
$97$		−	4.10959e11i		−	0.493364i	−0.969096	−	0.246682i	$-0.920660\pi$
$97$		−	4.10959e11i		−	0.493364i	0.969096	−	0.246682i	$-0.0793404\pi$
$98$		0			0
$99$	1.80856e12			1.92097
$100$	−2.41590e11	+	4.18446e11i	−0.241590	+	0.418446i
$101$	−1.20728e12	+	6.97024e11i	−1.13731	+	0.656628i	−0.945764	−	0.324855i	$-0.894685\pi$
$101$	−1.20728e12	+	6.97024e11i	−1.13731	+	0.656628i	−0.191550	+	0.981483i	$0.561351\pi$
$102$	−2.52018e10	−	4.36508e10i	−0.0223785	−	0.0387607i
$103$	1.25187e12	+	7.22767e11i	1.04842	+	0.605306i	0.922207	−	0.386698i	$-0.126384\pi$
$103$	1.25187e12	+	7.22767e11i	1.04842	+	0.605306i	0.126213	+	0.992003i	$0.459718\pi$
$104$			6.46822e11i			0.511193i
$105$		0			0
$106$	3.27081e11			0.230579
$107$	−2.85284e11	+	4.94126e11i	−0.190097	+	0.329257i	−0.945282	−	0.326254i	$-0.894213\pi$
$107$	−2.85284e11	+	4.94126e11i	−0.190097	+	0.329257i	0.755186	+	0.655511i	$0.227547\pi$
$108$	7.34179e10	−	4.23879e10i	0.0462658	−	0.0267115i
$109$	−1.41409e11	−	2.44928e11i	−0.0843176	−	0.146042i	0.820783	−	0.571241i	$-0.193538\pi$
$109$	−1.41409e11	−	2.44928e11i	−0.0843176	−	0.146042i	−0.905100	+	0.425198i	$0.860204\pi$
$110$	3.83325e11	+	2.21313e11i	0.216377	+	0.124925i
$111$		−	7.08558e10i		−	0.0378824i
$112$		0			0
$113$	−1.58024e12			−0.759017			−0.379509	−	0.925188i	$-0.623907\pi$
$113$	−1.58024e12			−0.759017			−0.379509	+	0.925188i	$0.623907\pi$
$114$	4.63793e10	−	8.03313e10i	0.0211298	−	0.0365979i
$115$	7.74231e10	−	4.47002e10i	0.0334721	−	0.0193251i
$116$	−4.67158e11	−	8.09142e11i	−0.191742	−	0.332106i
$117$	3.20281e12	+	1.84914e12i	1.24858	+	0.720867i
$118$		−	2.33367e11i		−	0.0864466i
$119$		0			0
$120$	1.03591e10			0.00346925
$121$	−4.25469e12	+	7.36934e12i	−1.35567	+	2.34810i
$122$	−2.00325e11	+	1.15658e11i	−0.0607543	+	0.0350765i
$123$	1.00259e11	+	1.73654e11i	0.0289529	+	0.0501479i
$124$	3.10924e12	+	1.79512e12i	0.855311	+	0.493814i
$125$			1.37579e12i			0.360655i
$126$		0			0
$127$	5.21870e12			1.24377			0.621885	−	0.783109i	$-0.286367\pi$
$127$	5.21870e12			1.24377			0.621885	+	0.783109i	$0.286367\pi$
$128$	1.94368e11	−	3.36655e11i	0.0441942	−	0.0765466i
$129$	−2.45577e11	+	1.41784e11i	−0.0532904	+	0.0307672i
$130$	4.52558e11	+	7.83853e11i	0.0937592	+	0.162396i
$131$	3.96077e12	+	2.28675e12i	0.783703	+	0.452471i	0.837741	−	0.546068i	$-0.183876\pi$
$131$	3.96077e12	+	2.28675e12i	0.783703	+	0.452471i	−0.0540381	+	0.998539i	$0.517209\pi$
$132$			2.72603e11i			0.0515332i
$133$		0			0
$134$	3.43504e12			0.593340
$135$	5.93145e10	−	1.02736e11i	0.00979847	−	0.0169714i
$136$	−2.29216e12	+	1.32338e12i	−0.362252	+	0.209146i
$137$	−2.84567e12	−	4.92884e12i	−0.430389	−	0.745455i	0.566518	−	0.824049i	$-0.308290\pi$
$137$	−2.84567e12	−	4.92884e12i	−0.430389	−	0.745455i	−0.996907	+	0.0785942i	$0.974957\pi$
$138$	4.76831e10	+	2.75299e10i	0.00690383	+	0.00398593i
$139$		−	3.77435e12i		−	0.523304i	−0.965162	−	0.261652i	$-0.915733\pi$
$139$		−	3.77435e12i		−	0.523304i	0.965162	−	0.261652i	$-0.0842672\pi$
$140$		0			0
$141$	−1.67006e11			−0.0212529
$142$	−2.55897e12	+	4.43227e12i	−0.312130	+	0.540625i
$143$	−2.06273e13	+	1.19092e13i	−2.41227	+	1.39273i
$144$	−1.11132e12	−	1.92487e12i	−0.124642	−	0.215887i
$145$	−1.13225e12	−	6.53707e11i	−0.121825	−	0.0703356i
$146$			7.90047e12i			0.815710i
$147$		0			0
$148$	−3.72072e12			−0.354043
$149$	−3.34471e12	+	5.79320e12i	−0.305661	+	0.529421i	−0.977408	−	0.211360i	$-0.932211\pi$
$149$	−3.34471e12	+	5.79320e12i	−0.305661	+	0.529421i	0.671747	+	0.740781i	$0.265544\pi$
$150$	−3.60623e11	+	2.08206e11i	−0.0316596	+	0.0182787i
$151$	−2.61840e11	−	4.53520e11i	−0.0220889	−	0.0382591i	0.854770	−	0.519008i	$-0.173698\pi$
$151$	−2.61840e11	−	4.53520e11i	−0.0220889	−	0.0382591i	−0.876859	+	0.480748i	$0.840365\pi$
$152$	−4.21829e12	−	2.43543e12i	−0.342038	−	0.197476i
$153$			1.51331e13i			1.17972i
$154$		0			0
$155$	5.02392e12			0.362287
$156$	−2.78720e11	+	4.82757e11i	−0.0193384	+	0.0334951i
$157$	1.35363e13	−	7.81517e12i	0.903860	−	0.521844i	0.0254094	−	0.999677i	$-0.491911\pi$
$157$	1.35363e13	−	7.81517e12i	0.903860	−	0.521844i	0.878450	+	0.477833i	$0.158578\pi$
$158$	5.11580e12	+	8.86083e12i	0.328830	+	0.569550i
$159$	2.44118e11	+	1.40941e11i	0.0151083	+	0.00872280i
$160$		−	5.43969e11i		−	0.0324231i
$161$		0			0
$162$	−1.26717e13			−0.701041
$163$	−1.21647e12	+	2.10698e12i	−0.0648597	+	0.112340i	−0.896632	−	0.442777i	$-0.853993\pi$
$163$	−1.21647e12	+	2.10698e12i	−0.0648597	+	0.112340i	0.831772	+	0.555117i	$0.187327\pi$
$164$	9.11875e12	−	5.26471e12i	0.468675	−	0.270590i
$165$	1.90730e11	+	3.30355e11i	0.00945183	+	0.0163711i
$166$	1.61952e13	+	9.35031e12i	0.773995	+	0.446866i
$167$			5.39380e12i			0.248654i	0.992241	+	0.124327i	$0.0396772\pi$
$167$			5.39380e12i			0.248654i	−0.992241	+	0.124327i	$0.960323\pi$
$168$		0			0
$169$	−2.54076e13			−1.09055
$170$	−1.85184e12	+	3.20748e12i	−0.0767201	+	0.132883i
$171$	−2.41186e13	+	1.39249e13i	−0.964662	+	0.556948i
$172$	7.44523e12	+	1.28955e13i	0.287546	+	0.498045i
$173$	2.20779e13	+	1.27467e13i	0.823533	+	0.475467i	0.851633	−	0.524138i	$-0.175612\pi$
$173$	2.20779e13	+	1.27467e13i	0.823533	+	0.475467i	−0.0281004	+	0.999605i	$0.508946\pi$
$174$		−	8.05207e11i		−	0.0290143i
$175$		0			0
$176$	1.43147e13			0.481622
$177$	1.00560e11	−	1.74174e11i	0.00327027	−	0.00566428i
$178$	1.02015e13	−	5.88981e12i	0.320732	−	0.185175i
$179$	−1.79942e13	−	3.11668e13i	−0.547033	−	0.947489i	−0.998476	−	0.0551891i	$-0.982424\pi$
$179$	−1.79942e13	−	3.11668e13i	−0.547033	−	0.947489i	0.451443	−	0.892300i	$-0.350910\pi$
$180$	−2.69352e12	−	1.55510e12i	−0.0791927	−	0.0457219i
$181$		−	1.12708e13i		−	0.320542i	−0.987073	−	0.160271i	$-0.948763\pi$
$181$		−	1.12708e13i		−	0.320542i	0.987073	−	0.160271i	$-0.0512368\pi$
$182$		0			0
$183$	−1.99351e11			−0.00530777
$184$	1.44562e12	−	2.50389e12i	0.0372519	−	0.0645222i
$185$	−4.50896e12	+	2.60325e12i	−0.112473	+	0.0649360i
$186$	1.54706e12	+	2.67958e12i	0.0373619	+	0.0647127i
$187$	−8.44056e13	−	4.87316e13i	−1.97388	−	1.13962i
$188$			8.76967e12i			0.198626i
$189$		0			0
$190$	−6.81593e12			−0.144878
$191$	4.94665e12	−	8.56784e12i	0.101885	−	0.176470i	−0.810576	−	0.585633i	$-0.800846\pi$
$191$	4.94665e12	−	8.56784e12i	0.101885	−	0.176470i	0.912461	+	0.409163i	$0.134179\pi$
$192$	2.90134e11	−	1.67509e11i	0.00579151	−	0.00334373i
$193$	2.19536e13	+	3.80247e13i	0.424777	+	0.735736i	0.996400	−	0.0847810i	$-0.0270191\pi$
$193$	2.19536e13	+	3.80247e13i	0.424777	+	0.735736i	−0.571622	+	0.820517i	$0.693686\pi$
$194$	−1.61062e13	−	9.29893e12i	−0.302123	−	0.174431i
$195$			7.80041e11i			0.0141876i
$196$		0			0
$197$	3.88271e13			0.664259			0.332129	−	0.943234i	$-0.392233\pi$
$197$	3.88271e13			0.664259			0.332129	+	0.943234i	$0.392233\pi$
$198$	4.09230e13	−	7.08807e13i	0.679166	−	1.17635i
$199$	1.63961e13	−	9.46629e12i	0.264011	−	0.152427i	−0.362152	−	0.932119i	$-0.617958\pi$
$199$	1.63961e13	−	9.46629e12i	0.264011	−	0.152427i	0.626163	+	0.779692i	$0.284624\pi$
$200$	1.09331e13	+	1.89367e13i	0.170830	+	0.295886i
$201$	2.56375e12	+	1.48018e12i	0.0388777	+	0.0224460i
$202$			6.30874e13i			0.928613i
$203$		0			0
$204$	−2.28101e12			−0.0316480
$205$	7.36706e12	−	1.27601e13i	0.0992592	−	0.171922i
$206$	5.66531e13	−	3.27087e13i	0.741345	−	0.428016i
$207$	−8.26553e12	−	1.43163e13i	−0.105063	−	0.181974i
$208$	2.53501e13	+	1.46359e13i	0.313040	+	0.180734i
$209$		−	1.79363e14i		−	2.15206i
$210$		0			0
$211$	−3.19733e13			−0.362320			−0.181160	−	0.983454i	$-0.557985\pi$
$211$	−3.19733e13			−0.362320			−0.181160	+	0.983454i	$0.557985\pi$
$212$	7.40099e12	−	1.28189e13i	0.0815220	−	0.141200i
$213$	−3.81980e12	+	2.20536e12i	−0.0409037	+	0.0236158i
$214$	1.29105e13	+	2.23616e13i	0.134419	+	0.232820i
$215$	1.80451e13	+	1.04183e13i	0.182695	+	0.105479i
$216$		−	3.83651e12i		−	0.0377758i
$217$		0			0
$218$	−1.27989e13			−0.119243
$219$	−3.40437e12	+	5.89654e12i	−0.0308583	+	0.0534481i
$220$	1.73473e13	−	1.00155e13i	0.153002	−	0.0883355i
$221$	−9.96503e13	−	1.72599e14i	−0.855313	−	1.48144i
$222$	−2.77697e12	−	1.60328e12i	−0.0231981	−	0.0133935i
$223$		−	1.78662e14i		−	1.45279i	−0.687279	−	0.726394i	$-0.741195\pi$
$223$		−	1.78662e14i		−	1.45279i	0.687279	−	0.726394i	$-0.258805\pi$
$224$		0			0
$225$	1.25023e14			0.963594
$226$	−3.57567e13	+	6.19324e13i	−0.268353	+	0.464801i
$227$	1.41352e14	−	8.16094e13i	1.03311	−	0.596465i	0.115234	−	0.993338i	$-0.463238\pi$
$227$	1.41352e14	−	8.16094e13i	1.03311	−	0.596465i	0.917873	+	0.396873i	$0.129905\pi$
$228$	−2.09889e12	−	3.63538e12i	−0.0149410	−	0.0258786i
$229$	−1.71369e14	−	9.89401e13i	−1.18828	−	0.686056i	−0.230367	−	0.973104i	$-0.573993\pi$
$229$	−1.71369e14	−	9.89401e13i	−1.18828	−	0.686056i	−0.957916	+	0.287048i	$0.907326\pi$
$230$		−	4.04580e12i		−	0.0273299i
$231$		0			0
$232$	−4.22823e13			−0.271163
$233$	9.54556e13	−	1.65334e14i	0.596576	−	1.03330i	−0.396746	−	0.917928i	$-0.629861\pi$
$233$	9.54556e13	−	1.65334e14i	0.596576	−	1.03330i	0.993322	−	0.115372i	$-0.0368059\pi$
$234$	1.44943e14	−	8.36826e13i	0.882878	−	0.509730i
$235$	6.13582e12	+	1.06276e13i	0.0364305	+	0.0630995i
$236$	−9.14610e12	−	5.28050e12i	−0.0529375	−	0.0305635i
$237$			8.81774e12i			0.0497585i
$238$		0			0
$239$	−1.79102e14			−0.960979			−0.480490	−	0.877000i	$-0.659541\pi$
$239$	−1.79102e14			−0.960979			−0.480490	+	0.877000i	$0.659541\pi$
$240$	2.34400e11	−	4.05993e11i	0.00122656	−	0.00212447i
$241$	−1.71712e14	+	9.91377e13i	−0.876390	+	0.505984i	−0.869466	−	0.493992i	$-0.835537\pi$
$241$	−1.71712e14	+	9.91377e13i	−0.876390	+	0.505984i	−0.00692345	+	0.999976i	$0.502204\pi$
$242$	1.92545e14	+	3.33498e14i	0.958607	+	1.66036i
$243$	−2.85089e13	−	1.64596e13i	−0.138466	−	0.0799434i
$244$			1.04682e13i			0.0496057i
$245$		0			0
$246$	9.07440e12			0.0409456
$247$	1.83388e14	−	3.17637e14i	0.807587	−	1.39878i
$248$	1.40708e14	−	8.12378e13i	0.604796	−	0.349179i
$249$	8.05823e12	+	1.39573e13i	0.0338099	+	0.0585604i
$250$	5.39198e13	+	3.11306e13i	0.220855	+	0.127511i
$251$			2.18276e14i			0.872897i	0.899729	+	0.436448i	$0.143764\pi$
$251$			2.18276e14i			0.872897i	−0.899729	+	0.436448i	$0.856236\pi$
$252$		0			0
$253$	1.06466e14			0.405966
$254$	1.18086e14	−	2.04530e14i	0.439739	−	0.761650i
$255$	−2.76425e12	+	1.59594e12i	−0.0100539	+	0.00580464i
$256$	−8.79609e12	−	1.52353e13i	−0.0312500	−	0.0541266i
$257$	−3.59299e14	−	2.07441e14i	−1.24697	−	0.719941i	−0.276469	−	0.961023i	$-0.589164\pi$
$257$	−3.59299e14	−	2.07441e14i	−1.24697	−	0.719941i	−0.970505	+	0.241082i	$0.922498\pi$
$258$			1.28328e13i			0.0435114i
$259$		0			0
$260$	4.09609e13			0.132596
$261$	−1.20877e14	+	2.09365e14i	−0.382385	+	0.662311i
$262$	1.79244e14	−	1.03486e14i	0.554162	−	0.319945i
$263$	−5.88475e13	−	1.01927e14i	−0.177825	−	0.308003i	0.763310	−	0.646032i	$-0.223573\pi$
$263$	−5.88475e13	−	1.01927e14i	−0.177825	−	0.308003i	−0.941135	+	0.338030i	$0.890240\pi$
$264$	1.06838e13	+	6.16830e12i	0.0315575	+	0.0182197i
$265$		−	2.07128e13i		−	0.0598087i
$266$		0			0
$267$	1.01518e13			0.0280206
$268$	7.77262e13	−	1.34626e14i	0.209777	−	0.363345i
$269$	−3.43540e14	+	1.98343e14i	−0.906700	+	0.523483i	−0.879368	−	0.476143i	$-0.842034\pi$
$269$	−3.43540e14	+	1.98343e14i	−0.906700	+	0.523483i	−0.0273318	+	0.999626i	$0.508701\pi$
$270$	−2.68427e12	−	4.64929e12i	−0.00692856	−	0.0120006i
$271$	1.79827e14	+	1.03823e14i	0.453983	+	0.262107i	0.709511	−	0.704694i	$-0.248916\pi$
$271$	1.79827e14	+	1.03823e14i	0.453983	+	0.262107i	−0.255528	+	0.966802i	$0.582249\pi$
$272$			1.19778e14i			0.295777i
$273$		0			0
$274$	−2.57561e14			−0.608662
$275$	−4.02597e14	+	6.97319e14i	−0.930839	+	1.61226i
$276$	2.15789e12	−	1.24586e12i	0.00488175	−	0.00281848i
$277$	−1.57997e14	−	2.73658e14i	−0.349759	−	0.605801i	0.636447	−	0.771320i	$-0.280403\pi$
$277$	−1.57997e14	−	2.73658e14i	−0.349759	−	0.605801i	−0.986207	+	0.165520i	$0.947070\pi$
$278$	−1.47924e14	−	8.54039e13i	−0.320457	−	0.185016i
$279$		−	9.28974e14i		−	1.96960i
$280$		0			0
$281$	−3.27034e14			−0.664286			−0.332143	−	0.943229i	$-0.607772\pi$
$281$	−3.27034e14			−0.664286			−0.332143	+	0.943229i	$0.607772\pi$
$282$	−3.77891e12	+	6.54527e12i	−0.00751402	+	0.0130147i
$283$	−6.95128e13	+	4.01332e13i	−0.135315	+	0.0781242i	−0.566129	−	0.824316i	$-0.691560\pi$
$283$	−6.95128e13	+	4.01332e13i	−0.135315	+	0.0781242i	0.430814	+	0.902441i	$0.358226\pi$
$284$	1.15806e14	+	2.00582e14i	0.220709	+	0.382280i
$285$	−5.08709e12	−	2.93703e12i	−0.00949292	−	0.00548074i
$286$			1.07790e15i			1.96961i
$287$		0			0
$288$	−1.00585e14			−0.176271
$289$	1.16451e14	−	2.01699e14i	0.199874	−	0.346192i
$290$	−5.12400e13	+	2.95834e13i	−0.0861432	+	0.0497348i
$291$	−8.01395e12	−	1.38806e13i	−0.0131974	−	0.0228586i
$292$	3.09634e14	+	1.78767e14i	0.499518	+	0.288397i
$293$			3.68606e14i			0.582581i	0.956635	+	0.291290i	$0.0940846\pi$
$293$			3.68606e14i			0.582581i	−0.956635	+	0.291290i	$0.905915\pi$
$294$		0			0
$295$	−1.47783e13			−0.0224229
$296$	−8.41903e13	+	1.45822e14i	−0.125173	+	0.216806i
$297$	1.22347e14	−	7.06372e13i	0.178261	−	0.102919i
$298$	1.51364e14	+	2.62170e14i	0.216135	+	0.374357i
$299$	1.88543e14	+	1.08856e14i	0.263866	+	0.152343i
$300$			1.88446e13i			0.0258500i
$301$		0			0
$302$	−2.36990e13			−0.0312384
$303$	−2.71848e13	+	4.70855e13i	−0.0351294	+	0.0608459i
$304$	−1.90898e14	+	1.10215e14i	−0.241858	+	0.139637i
$305$	7.32419e12	+	1.26859e13i	0.00909831	+	0.0157587i
$306$	5.93095e14	+	3.42424e14i	0.722430	+	0.417095i
$307$			6.36629e14i			0.760425i	0.924899	+	0.380212i	$0.124149\pi$
$307$			6.36629e14i			0.760425i	−0.924899	+	0.380212i	$0.875851\pi$
$308$		0			0
$309$	5.63776e13			0.0647673
$310$	1.13678e14	−	1.96897e14i	0.128088	−	0.221854i
$311$	−1.14101e15	+	6.58762e14i	−1.26103	+	0.728059i	−0.973275	−	0.229644i	$-0.926244\pi$
$311$	−1.14101e15	+	6.58762e14i	−1.26103	+	0.728059i	−0.287760	+	0.957703i	$0.592911\pi$
$312$	1.26134e13	+	2.18471e13i	0.0136743	+	0.0236846i
$313$	−6.11719e14	−	3.53176e14i	−0.650558	−	0.375600i	0.138112	−	0.990417i	$-0.455897\pi$
$313$	−6.11719e14	−	3.53176e14i	−0.650558	−	0.375600i	−0.788670	+	0.614817i	$0.789230\pi$
$314$		−	7.07348e14i		−	0.737999i
$315$		0			0
$316$	4.63030e14			0.465036
$317$	−3.73216e14	+	6.46429e14i	−0.367794	+	0.637038i	−0.989220	−	0.146435i	$-0.953220\pi$
$317$	−3.73216e14	+	6.46429e14i	−0.367794	+	0.637038i	0.621426	+	0.783473i	$0.286554\pi$
$318$	1.10475e13	−	6.37828e12i	0.0106832	−	0.00616795i
$319$	−7.78496e14	−	1.34839e15i	−0.738775	−	1.27960i
$320$	−2.13191e13	−	1.23086e13i	−0.0198550	−	0.0114633i
$321$			2.22528e13i			0.0203402i
$322$		0			0
$323$	1.50082e15			1.32164
$324$	−2.86727e14	+	4.96626e14i	−0.247855	+	0.429298i
$325$	−1.42593e15	+	8.23264e14i	−1.21004	+	0.698616i
$326$	5.50510e13	+	9.53512e13i	0.0458627	+	0.0794366i
$327$	−9.55249e12	−	5.51513e12i	−0.00781322	−	0.00451096i
$328$		−	4.76507e14i		−	0.382672i
$329$		0			0
$330$	1.72629e13			0.0133669
$331$	−5.66623e14	+	9.81420e14i	−0.430850	+	0.746255i	−0.996947	−	0.0780844i	$-0.975120\pi$
$331$	−5.66623e14	+	9.81420e14i	−0.430850	+	0.746255i	0.566096	+	0.824339i	$0.308453\pi$
$332$	7.32912e14	−	4.23147e14i	0.547297	−	0.315982i
$333$	4.81368e14	+	8.33754e14i	0.353030	+	0.611466i
$334$	2.11393e14	+	1.22048e14i	0.152269	+	0.0879126i
$335$		−	2.17529e14i		−	0.153903i
$336$		0			0
$337$	−5.02783e13			−0.0343242			−0.0171621	−	0.999853i	$-0.505463\pi$
$337$	−5.02783e13			−0.0343242			−0.0171621	+	0.999853i	$0.505463\pi$
$338$	−5.74909e14	+	9.95772e14i	−0.385566	+	0.667820i
$339$	−5.33742e13	+	3.08156e13i	−0.0351668	+	0.0203036i
$340$	8.38046e13	+	1.45154e14i	0.0542493	+	0.0939626i
$341$	5.18139e15	+	2.99148e15i	3.29549	+	1.90265i
$342$			1.26034e15i			0.787643i
$343$		0			0
$344$	6.73865e14			0.406652
$345$	1.74336e12	−	3.01960e12i	0.00103389	−	0.00179075i
$346$	9.99131e14	−	5.76849e14i	0.582326	−	0.336206i
$347$	−4.20033e14	−	7.27518e14i	−0.240606	−	0.416742i	0.720281	−	0.693682i	$-0.244013\pi$
$347$	−4.20033e14	−	7.27518e14i	−0.240606	−	0.416742i	−0.960887	+	0.276941i	$0.910679\pi$
$348$	−3.15575e13	−	1.82198e13i	−0.0177676	−	0.0102581i
$349$			4.32312e14i			0.239246i	0.992819	+	0.119623i	$0.0381686\pi$
$349$			4.32312e14i			0.239246i	−0.992819	+	0.119623i	$0.961831\pi$
$350$		0			0
$351$	2.88889e14			0.154486
$352$	3.23904e14	−	5.61019e14i	0.170279	−	0.294932i
$353$	2.08818e15	−	1.20561e15i	1.07925	−	0.623103i	0.148553	−	0.988904i	$-0.452538\pi$
$353$	2.08818e15	−	1.20561e15i	1.07925	−	0.623103i	0.930693	+	0.365802i	$0.119205\pi$
$354$	−4.55081e12	−	7.88223e12i	−0.00231243	−	0.00400525i
$355$	2.80680e14	+	1.62050e14i	0.140230	+	0.0809618i
$356$		−	5.33085e14i		−	0.261876i
$357$		0			0
$358$	−1.62865e15			−0.773622
$359$	−3.22382e14	+	5.58381e14i	−0.150593	+	0.260834i	−0.931445	−	0.363881i	$-0.881451\pi$
$359$	−3.22382e14	+	5.58381e14i	−0.150593	+	0.260834i	0.780853	+	0.624715i	$0.214785\pi$
$360$	−1.21895e14	+	7.03760e13i	−0.0559977	+	0.0323303i
$361$	2.74336e14	+	4.75164e14i	0.123948	+	0.214684i
$362$	−4.41725e14	−	2.55030e14i	−0.196291	−	0.113329i
$363$			3.31876e14i			0.145056i
$364$		0			0
$365$	5.00308e14			0.211583
$366$	−4.51080e12	+	7.81294e12i	−0.00187658	+	0.00325033i
$367$	−1.22970e15	+	7.09969e14i	−0.503273	+	0.290565i	−0.730064	−	0.683379i	$-0.760510\pi$
$367$	−1.22970e15	+	7.09969e14i	−0.503273	+	0.290565i	0.226791	+	0.973943i	$0.427177\pi$
$368$	−6.54215e13	−	1.13313e14i	−0.0263411	−	0.0456241i
$369$	−2.35948e15	−	1.36224e15i	−0.934668	−	0.539631i
$370$			2.35619e14i			0.0918334i
$371$		0			0
$372$	1.40024e14			0.0528377
$373$	−1.45705e15	+	2.52368e15i	−0.541030	+	0.937092i	0.457815	+	0.889047i	$0.348632\pi$
$373$	−1.45705e15	+	2.52368e15i	−0.541030	+	0.937092i	−0.998845	+	0.0480443i	$0.984701\pi$
$374$	−3.81976e15	+	2.20534e15i	−1.39575	+	0.805835i
$375$	2.68288e13	+	4.64688e13i	0.00964746	+	0.0167099i
$376$	3.43700e14	+	1.98435e14i	0.121633	+	0.0702249i
$377$		−	3.18386e15i		−	1.10893i
$378$		0			0
$379$	1.27572e15			0.430446			0.215223	−	0.976565i	$-0.430952\pi$
$379$	1.27572e15			0.430446			0.215223	+	0.976565i	$0.430952\pi$
$380$	−1.54227e14	+	2.67129e14i	−0.0512222	+	0.0887195i
$381$	1.76267e14	−	1.01768e14i	0.0576264	−	0.0332706i
$382$	−2.23860e14	−	3.87736e14i	−0.0720437	−	0.124783i
$383$	−2.23693e15	−	1.29149e15i	−0.708696	−	0.409166i	0.101882	−	0.994797i	$-0.467514\pi$
$383$	−2.23693e15	−	1.29149e15i	−0.708696	−	0.409166i	−0.810578	+	0.585630i	$0.800847\pi$
$384$		−	1.51612e13i		−	0.00472875i
$385$		0			0
$386$	1.98701e15			0.600726
$387$	1.92645e15	−	3.33672e15i	0.573446	−	0.993238i
$388$	−7.28885e14	+	4.20822e14i	−0.213633	+	0.123341i
$389$	−1.93820e15	−	3.35706e15i	−0.559373	−	0.968862i	−0.997549	−	0.0699729i	$-0.977709\pi$
$389$	−1.93820e15	−	3.35706e15i	−0.559373	−	0.968862i	0.438176	−	0.898889i	$-0.355625\pi$
$390$	3.05713e13	+	1.76503e13i	0.00868812	+	0.00501609i
$391$			8.90859e14i			0.249315i
$392$		0			0
$393$	1.78372e14			0.0484141
$394$	8.78556e14	−	1.52170e15i	0.234851	−	0.406774i
$395$	5.61124e14	−	3.23965e14i	0.147732	−	0.0852934i
$396$	−1.85196e15	−	3.20769e15i	−0.480243	−	0.831805i
$397$	−6.39369e13	−	3.69140e13i	−0.0163308	−	0.00942861i	0.491812	−	0.870701i	$-0.336335\pi$
$397$	−6.39369e13	−	3.69140e13i	−0.0163308	−	0.00942861i	−0.508143	+	0.861273i	$0.669668\pi$
$398$		−	8.56791e14i		−	0.215564i
$399$		0			0
$400$	9.89552e14			0.241590
$401$	2.01262e15	−	3.48596e15i	0.484055	−	0.838409i	−0.515777	−	0.856723i	$-0.672497\pi$
$401$	2.01262e15	−	3.48596e15i	0.484055	−	0.838409i	0.999832	+	0.0183143i	$0.00582995\pi$
$402$	1.16022e14	−	6.69855e13i	0.0274907	−	0.0158717i
$403$	6.11721e15	+	1.05953e16i	1.42798	+	2.47334i
$404$	2.47251e15	+	1.42751e15i	0.568657	+	0.328314i
$405$			8.02449e14i			0.181839i
$406$		0			0
$407$	−6.20039e15			−1.36412
$408$	−5.16133e13	+	8.93969e13i	−0.0111892	+	0.0193803i
$409$	4.98822e15	−	2.87995e15i	1.06563	−	0.615240i	0.138644	−	0.990342i	$-0.455726\pi$
$409$	4.98822e15	−	2.87995e15i	1.06563	−	0.615240i	0.926984	+	0.375102i	$0.122392\pi$
$410$	−3.33395e14	−	5.77457e14i	−0.0701869	−	0.121567i
$411$	−1.92231e14	−	1.10985e14i	−0.0398816	−	0.0230256i
$412$		−	2.96045e15i		−	0.605306i
$413$		0			0
$414$	−7.48110e14			−0.148581
$415$	5.92121e14	−	1.02558e15i	0.115910	−	0.200762i
$416$	1.14722e15	−	6.62346e14i	0.221353	−	0.127798i
$417$	−7.36023e13	−	1.27483e14i	−0.0139983	−	0.0242457i
$418$	−7.02957e15	−	4.05852e15i	−1.31786	−	0.760870i
$419$			9.49384e15i			1.75452i	0.480018	+	0.877259i	$0.340630\pi$
$419$			9.49384e15i			1.75452i	−0.480018	+	0.877259i	$0.659370\pi$
$420$		0			0
$421$	−8.68328e15			−1.55952			−0.779761	−	0.626078i	$-0.784659\pi$
$421$	−8.68328e15			−1.55952			−0.779761	+	0.626078i	$0.784659\pi$
$422$	−7.23473e14	+	1.25309e15i	−0.128100	+	0.221875i
$423$	1.96514e15	−	1.13458e15i	0.343046	−	0.198058i
$424$	−3.34931e14	−	5.80117e14i	−0.0576448	−	0.0998437i
$425$	−5.83483e15	−	3.36874e15i	−0.990135	−	0.571655i
$426$			1.99606e14i			0.0333977i
$427$		0			0
$428$	1.16852e15			0.190097
$429$	−4.64473e14	+	8.04491e14i	−0.0745104	+	0.129056i
$430$	8.16626e14	−	4.71479e14i	0.129185	−	0.0745850i
$431$	−1.34756e14	−	2.33405e14i	−0.0210226	−	0.0364121i	0.855323	−	0.518096i	$-0.173359\pi$
$431$	−1.34756e14	−	2.33405e14i	−0.0210226	−	0.0364121i	−0.876345	+	0.481683i	$0.840026\pi$
$432$	−1.50360e14	−	8.68103e13i	−0.0231329	−	0.0133558i
$433$		−	5.06968e15i		−	0.769224i	−0.923078	−	0.384612i	$-0.874335\pi$
$433$		−	5.06968e15i		−	0.769224i	0.923078	−	0.384612i	$-0.125665\pi$
$434$		0			0
$435$	−5.09908e13			−0.00752586
$436$	−2.89606e14	+	5.01612e14i	−0.0421588	+	0.0730212i
$437$	−1.41982e15	+	8.19731e14i	−0.203865	+	0.117702i
$438$	1.54064e14	+	2.66847e14i	0.0218201	+	0.0377935i
$439$	−1.41866e14	−	8.19063e13i	−0.0198194	−	0.0114427i	0.490058	−	0.871690i	$-0.336976\pi$
$439$	−1.41866e14	−	8.19063e13i	−0.0198194	−	0.0114427i	−0.509877	+	0.860247i	$0.670309\pi$
$440$		−	9.06497e14i		−	0.124925i
$441$		0			0
$442$	−9.01931e15			−1.20959
$443$	4.35743e15	−	7.54729e15i	0.576512	−	0.998548i	−0.419364	−	0.907818i	$-0.637747\pi$
$443$	4.35743e15	−	7.54729e15i	0.576512	−	0.998548i	0.995876	−	0.0907297i	$-0.0289199\pi$
$444$	−1.25671e14	+	7.25563e13i	−0.0164036	+	0.00947060i
$445$	−3.72980e14	−	6.46020e14i	−0.0480314	−	0.0831929i
$446$	−7.00208e15	−	4.04265e15i	−0.889647	−	0.513638i
$447$			2.60895e14i			0.0327055i
$448$		0			0
$449$	5.38504e15			0.657220			0.328610	−	0.944466i	$-0.393420\pi$
$449$	5.38504e15			0.657220			0.328610	+	0.944466i	$0.393420\pi$
$450$	2.82894e15	−	4.89987e15i	0.340682	−	0.590078i
$451$	1.51959e16	−	8.77338e15i	1.80579	−	1.04258i
$452$	1.61816e15	+	2.80274e15i	0.189754	+	0.328664i
$453$	−1.76878e13	−	1.02121e13i	−0.00204685	−	0.00118175i
$454$		−	7.38644e15i		−	0.843529i
$455$		0			0
$456$	−1.89970e14			−0.0211298
$457$	6.62808e15	−	1.14802e16i	0.727596	−	1.26023i	−0.230300	−	0.973120i	$-0.573971\pi$
$457$	6.62808e15	−	1.14802e16i	0.727596	−	1.26023i	0.957896	−	0.287114i	$-0.0926959\pi$
$458$	−7.75529e15	+	4.47752e15i	−0.840243	+	0.485115i
$459$	5.91058e14	+	1.02374e15i	0.0632054	+	0.109475i
$460$	−1.58562e14	−	9.15461e13i	−0.0167361	−	0.00966257i
$461$			1.36310e16i			1.42011i	0.704144	+	0.710057i	$0.251331\pi$
$461$			1.36310e16i			1.42011i	−0.704144	+	0.710057i	$0.748669\pi$
$462$		0			0
$463$	1.32894e16			1.34902			0.674511	−	0.738265i	$-0.264354\pi$
$463$	1.32894e16			1.34902			0.674511	+	0.738265i	$0.264354\pi$
$464$	−9.56740e14	+	1.65712e15i	−0.0958708	+	0.166053i
$465$	1.69688e14	−	9.79695e13i	0.0167855	−	0.00969111i
$466$	−4.31983e15	−	7.48216e15i	−0.421843	−	0.730654i
$467$	5.95361e15	+	3.43732e15i	0.573957	+	0.331374i	0.758728	−	0.651407i	$-0.225821\pi$
$467$	5.95361e15	+	3.43732e15i	0.573957	+	0.331374i	−0.184771	+	0.982782i	$0.559154\pi$
$468$		−	7.57408e15i		−	0.720867i
$469$		0			0
$470$	5.55351e14			0.0515206
$471$	3.04801e14	−	5.27931e14i	0.0279185	−	0.0483562i
$472$	−4.13905e14	+	2.38968e14i	−0.0374325	+	0.0216117i
$473$	1.24071e16	+	2.14897e16i	1.10791	+	1.91895i
$474$	3.45583e14	+	1.99523e14i	0.0304707	+	0.0175923i
$475$		−	1.23991e16i		−	1.07951i
$476$		0			0
$477$	−3.83001e15			−0.325155
$478$	−4.05263e15	+	7.01935e15i	−0.339758	+	0.588477i
$479$	−2.96526e15	+	1.71199e15i	−0.245499	+	0.141739i	−0.617701	−	0.786413i	$-0.711936\pi$
$479$	−2.96526e15	+	1.71199e15i	−0.245499	+	0.141739i	0.372203	+	0.928151i	$0.378603\pi$
$480$	−1.06077e13	−	1.83731e13i	−0.000867312	−	0.00150223i
$481$	−1.09804e16	−	6.33953e15i	−0.886640	−	0.511902i
$482$			8.97292e15i			0.715569i
$483$		0			0
$484$	1.74272e16			1.35567
$485$	−5.88867e14	+	1.01995e15i	−0.0452446	+	0.0783660i
$486$	−1.29017e15	+	7.44879e14i	−0.0979103	+	0.0565285i
$487$	−7.91361e15	−	1.37068e16i	−0.593200	−	1.02745i	−0.993798	−	0.111199i	$-0.964531\pi$
$487$	−7.91361e15	−	1.37068e16i	−0.593200	−	1.02745i	0.400598	−	0.916254i	$-0.368802\pi$
$488$	4.10266e14	+	2.36867e14i	0.0303772	+	0.0175383i
$489$			9.48875e13i			0.00693994i
$490$		0			0
$491$	−2.26555e16			−1.61690			−0.808452	−	0.588563i	$-0.799694\pi$
$491$	−2.26555e16			−1.61690			−0.808452	+	0.588563i	$0.799694\pi$
$492$	2.05330e14	−	3.55643e14i	0.0144765	−	0.0250740i
$493$	1.12827e16	−	6.51407e15i	0.785836	−	0.453702i
$494$	−8.29919e15	−	1.43746e16i	−0.571050	−	0.989088i
$495$	−4.48861e15	−	2.59150e15i	−0.305127	−	0.176165i
$496$		−	7.35281e15i		−	0.493814i
$497$		0			0
$498$	7.29347e14			0.0478144
$499$	−4.53576e15	+	7.85617e15i	−0.293797	+	0.508871i	−0.974704	−	0.223498i	$-0.928252\pi$
$499$	−4.53576e15	+	7.85617e15i	−0.293797	+	0.508871i	0.680907	+	0.732369i	$0.261586\pi$
$500$	2.44013e15	−	1.40881e15i	0.156168	−	0.0901638i
$501$	1.05182e14	+	1.82181e14i	0.00665146	+	0.0115207i
$502$	8.55462e15	+	4.93901e15i	0.534538	+	0.308616i
$503$		−	2.00202e16i		−	1.23612i	−0.786131	−	0.618060i	$-0.787919\pi$
$503$		−	2.00202e16i		−	1.23612i	0.786131	−	0.618060i	$-0.212081\pi$
$504$		0			0
$505$	3.99509e15			0.240868
$506$	2.40906e15	−	4.17261e15i	0.143531	−	0.248602i
$507$	−8.58170e14	+	4.95465e14i	−0.0505272	+	0.0291719i
$508$	−5.34395e15	−	9.25599e15i	−0.310942	−	0.538568i
$509$	1.95778e16	+	1.13032e16i	1.12579	+	0.649973i	0.942872	−	0.333155i	$-0.108113\pi$
$509$	1.95778e16	+	1.13032e16i	1.12579	+	0.649973i	0.182915	+	0.983129i	$0.441447\pi$
$510$			1.44448e14i			0.00820900i
$511$		0			0
$512$	−7.96131e14			−0.0441942
$513$	−1.08773e15	+	1.88401e15i	−0.0596785	+	0.103366i
$514$	−1.62600e16	+	9.38773e15i	−0.881744	+	0.509075i
$515$	−2.07132e15	−	3.58763e15i	−0.111021	−	0.192293i
$516$	5.02941e14	+	2.90373e14i	0.0266452	+	0.0153836i
$517$			1.46142e16i			0.765301i
$518$		0			0
$519$	9.94272e14			0.0508746
$520$	9.26839e14	−	1.60533e15i	0.0468796	−	0.0811979i
$521$	−4.18618e15	+	2.41689e15i	−0.209311	+	0.120846i	−0.600991	−	0.799256i	$-0.705227\pi$
$521$	−4.18618e15	+	2.41689e15i	−0.209311	+	0.120846i	0.391680	+	0.920101i	$0.371894\pi$
$522$	5.47028e15	+	9.47480e15i	0.270387	+	0.468325i
$523$	1.78991e16	+	1.03340e16i	0.874623	+	0.504964i	0.868882	−	0.495020i	$-0.164839\pi$
$523$	1.78991e16	+	1.03340e16i	0.874623	+	0.504964i	0.00574101	+	0.999984i	$0.498173\pi$
$524$		−	9.36653e15i		−	0.452471i
$525$		0			0
$526$	−5.32627e15			−0.251483
$527$	−2.50312e16	+	4.33553e16i	−1.16847	+	2.02385i
$528$	4.83494e14	−	2.79145e14i	0.0223145	−	0.0128833i
$529$	1.04707e16	+	1.81358e16i	0.477797	+	0.827568i
$530$	−8.11774e14	−	4.68678e14i	−0.0366252	−	0.0211456i
$531$			2.73266e15i			0.121904i
$532$		0			0
$533$	3.58810e16			1.56495
$534$	2.29710e14	−	3.97869e14i	0.00990677	−	0.0171590i
$535$	1.41608e15	−	8.17572e14i	0.0603899	−	0.0348661i
$536$	−3.51749e15	−	6.09246e15i	−0.148335	−	0.256924i
$537$	−1.21554e15	−	7.01795e14i	−0.0506903	−	0.0292661i
$538$			1.79519e16i			0.740317i
$539$		0			0
$540$	−2.42952e14			−0.00979847
$541$	2.06290e16	−	3.57305e16i	0.822801	−	1.42513i	−0.0807865	−	0.996731i	$-0.525743\pi$
$541$	2.06290e16	−	3.57305e16i	0.822801	−	1.42513i	0.903588	−	0.428403i	$-0.140923\pi$
$542$	8.13805e15	−	4.69851e15i	0.321015	−	0.185338i
$543$	−2.19789e14	−	3.80685e14i	−0.00857445	−	0.0148514i
$544$	4.69433e15	+	2.71028e15i	0.181126	+	0.104573i
$545$			8.10507e14i			0.0309298i
$546$		0			0
$547$	1.32093e16			0.493124			0.246562	−	0.969127i	$-0.420699\pi$
$547$	1.32093e16			0.493124			0.246562	+	0.969127i	$0.420699\pi$
$548$	−5.82793e15	+	1.00943e16i	−0.215194	+	0.372728i
$549$	2.34575e15	−	1.35432e15i	0.0856737	−	0.0494637i
$550$	1.82195e16	+	3.15571e16i	0.658203	+	1.14004i
$551$	2.07637e16	+	1.19880e16i	0.741987	+	0.428386i
$552$		−	1.12762e14i		−	0.00398593i
$553$		0			0
$554$	−1.43002e16			−0.494634
$555$	−1.01530e14	+	1.75855e14i	−0.00347406	+	0.00601724i
$556$	−6.69427e15	+	3.86494e15i	−0.226597	+	0.130826i
$557$	−1.83976e16	−	3.18655e16i	−0.616069	−	1.06706i	−0.990196	−	0.139685i	$-0.955391\pi$
$557$	−1.83976e16	−	3.18655e16i	−0.616069	−	1.06706i	0.374127	−	0.927378i	$-0.377942\pi$
$558$	−3.64082e16	−	2.10203e16i	−1.20613	−	0.696359i
$559$			5.07421e16i			1.66302i
$560$		0			0
$561$	−3.80118e15			−0.121939
$562$	−7.39994e15	+	1.28171e16i	−0.234861	+	0.406790i
$563$	−4.52579e16	+	2.61296e16i	−1.42116	+	0.820508i	−0.996398	−	0.0847958i	$-0.972976\pi$
$563$	−4.52579e16	+	2.61296e16i	−1.42116	+	0.820508i	−0.424764	+	0.905304i	$0.639643\pi$
$564$	1.71014e14	+	2.96205e14i	0.00531321	+	0.00920276i
$565$	3.92195e15	+	2.26434e15i	0.120562	+	0.0696067i
$566$			3.63244e15i			0.110484i
$567$		0			0
$568$	1.04816e16			0.312130
$569$	−3.10411e16	+	5.37648e16i	−0.914669	+	1.58425i	−0.107284	+	0.994228i	$0.534215\pi$
$569$	−3.10411e16	+	5.37648e16i	−0.914669	+	1.58425i	−0.807385	+	0.590024i	$0.799118\pi$
$570$	−2.30215e14	+	1.32915e14i	−0.00671251	+	0.00387547i
$571$	−4.60260e15	−	7.97194e15i	−0.132796	−	0.230010i	0.791957	−	0.610577i	$-0.209062\pi$
$571$	−4.60260e15	−	7.97194e15i	−0.132796	−	0.230010i	−0.924754	+	0.380567i	$0.875729\pi$
$572$	4.22447e16	+	2.43900e16i	1.20614	+	0.696363i
$573$		−	3.85851e14i		−	0.0109016i
$574$		0			0
$575$	7.35986e15			0.203640
$576$	−2.27599e15	+	3.94213e15i	−0.0623211	+	0.107943i
$577$	−5.12969e16	+	2.96163e16i	−1.39007	+	0.802556i	−0.993322	−	0.115373i	$-0.963194\pi$
$577$	−5.12969e16	+	2.96163e16i	−1.39007	+	0.802556i	−0.396746	+	0.917929i	$0.629860\pi$
$578$	−5.26998e15	−	9.12787e15i	−0.141332	−	0.244795i
$579$	1.48301e15	+	8.56217e14i	0.0393616	+	0.0227254i
$580$			2.67759e15i			0.0703356i
$581$		0			0
$582$	−7.25340e14			−0.0186640
$583$	1.23334e16	−	2.13620e16i	0.314102	−	0.544041i
$584$	1.40124e16	−	8.09008e15i	0.353213	−	0.203927i
$585$	−5.29931e15	−	9.17868e15i	−0.132216	−	0.229005i
$586$	1.44463e16	+	8.34059e15i	0.356756	+	0.205973i
$587$			1.82380e16i			0.445808i	0.974840	+	0.222904i	$0.0715536\pi$
$587$			1.82380e16i			0.445808i	−0.974840	+	0.222904i	$0.928446\pi$
$588$		0			0
$589$	−9.21307e16			−2.20654
$590$	−3.34395e14	+	5.79189e14i	−0.00792770	+	0.0137312i
$591$	1.31143e15	−	7.57152e14i	0.0307765	−	0.0177688i
$592$	3.81002e15	+	6.59914e15i	0.0885109	+	0.153305i
$593$	−2.24308e16	−	1.29504e16i	−0.515842	−	0.297822i	0.219390	−	0.975637i	$-0.429593\pi$
$593$	−2.24308e16	−	1.29504e16i	−0.515842	−	0.297822i	−0.735232	+	0.677816i	$0.762927\pi$
$594$		−	6.39335e15i		−	0.145549i
$595$		0			0
$596$	1.36999e16			0.305661
$597$	3.69197e14	−	6.39468e14i	0.00815478	−	0.0141245i
$598$	8.53250e15	−	4.92624e15i	0.186582	−	0.107723i
$599$	2.44690e16	+	4.23816e16i	0.529732	+	0.917523i	0.999399	+	0.0346788i	$0.0110408\pi$
$599$	2.44690e16	+	4.23816e16i	0.529732	+	0.917523i	−0.469667	+	0.882844i	$0.655626\pi$
$600$	7.38555e14	+	4.26405e14i	0.0158298	+	0.00913934i
$601$		−	2.83221e16i		−	0.601005i	−0.953781	−	0.300503i	$-0.902846\pi$
$601$		−	2.83221e16i		−	0.601005i	0.953781	−	0.300503i	$-0.0971544\pi$
$602$		0			0
$603$	−4.02233e16			−0.836708
$604$	−5.36248e14	+	9.28809e14i	−0.0110444	+	0.0191295i
$605$	2.11192e16	−	1.21932e16i	0.430671	−	0.248648i
$606$	1.23024e15	+	2.13085e15i	0.0248402	+	0.0430245i
$607$	−5.41690e15	−	3.12745e15i	−0.108298	−	0.0625256i	0.444873	−	0.895594i	$-0.353249\pi$
$607$	−5.41690e15	−	3.12745e15i	−0.108298	−	0.0625256i	−0.553170	+	0.833068i	$0.686582\pi$
$608$			9.97552e15i			0.197476i
$609$		0			0
$610$	6.62910e14			0.0128670
$611$	−1.49422e16	+	2.58806e16i	−0.287188	+	0.497424i
$612$	2.68404e16	−	1.54963e16i	0.510835	−	0.294931i
$613$	−2.77793e16	−	4.81152e16i	−0.523551	−	0.906816i	−0.999624	−	0.0274109i	$-0.991274\pi$
$613$	−2.77793e16	−	4.81152e16i	−0.523551	−	0.906816i	0.476074	−	0.879405i	$-0.342060\pi$
$614$	2.49507e16	+	1.44053e16i	0.465663	+	0.268851i
$615$		−	5.74649e14i		−	0.0106207i
$616$		0			0
$617$	8.06869e16			1.46249			0.731243	−	0.682117i	$-0.238940\pi$
$617$	8.06869e16			1.46249			0.731243	+	0.682117i	$0.238940\pi$
$618$	1.27568e15	−	2.20954e15i	0.0228987	−	0.0396617i
$619$	3.40981e15	−	1.96865e15i	0.0606158	−	0.0349966i	−0.469386	−	0.882993i	$-0.655525\pi$
$619$	3.40981e15	−	1.96865e15i	0.0606158	−	0.0349966i	0.530002	+	0.847997i	$0.322191\pi$
$620$	−5.14449e15	−	8.91052e15i	−0.0905717	−	0.156875i
$621$	−1.11831e15	−	6.45657e14i	−0.0194990	−	0.0112578i
$622$			5.96244e16i			1.02963i
$623$		0			0
$624$	1.14164e15			0.0193384
$625$	−2.68284e16	+	4.64681e16i	−0.450106	+	0.779606i
$626$	−2.76833e16	+	1.59829e16i	−0.460014	+	0.265589i
$627$	−3.49769e15	−	6.05818e15i	−0.0575673	−	0.0997095i
$628$	−2.77223e16	−	1.60055e16i	−0.451930	−	0.260922i
$629$		−	5.18818e16i		−	0.837744i
$630$		0			0
$631$	6.92232e16			1.09667			0.548334	−	0.836259i	$-0.315262\pi$
$631$	6.92232e16			1.09667			0.548334	+	0.836259i	$0.315262\pi$
$632$	1.04772e16	−	1.81470e16i	0.164415	−	0.284775i
$633$	−1.07993e15	+	6.23499e14i	−0.0167870	+	0.00969200i
$634$	1.68898e16	+	2.92540e16i	0.260070	+	0.450454i
$635$	−1.29522e16	−	7.47793e15i	−0.197560	−	0.114062i
$636$		−	5.77296e14i		−	0.00872280i
$637$		0			0
$638$	−7.04614e16			−1.04479
$639$	2.99648e16	−	5.19005e16i	0.440155	−	0.762372i
$640$	−9.64794e14	+	5.57024e14i	−0.0140396	+	0.00810577i
$641$	−1.58433e16	−	2.74413e16i	−0.228400	−	0.395600i	0.728934	−	0.684584i	$-0.240016\pi$
$641$	−1.58433e16	−	2.74413e16i	−0.228400	−	0.395600i	−0.957334	+	0.288983i	$0.906683\pi$
$642$	8.72129e14	+	5.03524e14i	0.0124558	+	0.00719135i
$643$		−	5.19233e16i		−	0.734678i	−0.930087	−	0.367339i	$-0.880269\pi$
$643$		−	5.19233e16i		−	0.734678i	0.930087	−	0.367339i	$-0.119731\pi$
$644$		0			0
$645$	8.12655e14			0.0112862
$646$	3.39597e16	−	5.88200e16i	0.467271	−	0.809338i
$647$	−1.04748e17	+	6.04762e16i	−1.42797	+	0.824439i	−0.996961	−	0.0779084i	$-0.975176\pi$
$647$	−1.04748e17	+	6.04762e16i	−1.42797	+	0.824439i	−0.431010	+	0.902347i	$0.641842\pi$
$648$	1.29758e16	+	2.24747e16i	0.175260	+	0.303560i
$649$	−1.52415e16	−	8.79969e15i	−0.203967	−	0.117760i
$650$			7.45133e16i			0.987993i
$651$		0			0
$652$	4.98265e15			0.0648597
$653$	2.32580e16	−	4.02840e16i	0.299980	−	0.519581i	−0.676151	−	0.736763i	$-0.736353\pi$
$653$	2.32580e16	−	4.02840e16i	0.299980	−	0.519581i	0.976131	+	0.217182i	$0.0696866\pi$
$654$	−4.32296e14	+	2.49586e14i	−0.00552478	+	0.00318973i
$655$	−6.55342e15	−	1.13509e16i	−0.0829889	−	0.143741i
$656$	−1.86752e16	−	1.07821e16i	−0.234338	−	0.135295i
$657$		−	9.25120e16i		−	1.15029i
$658$		0			0
$659$	3.88240e16			0.474011			0.237005	−	0.971508i	$-0.423834\pi$
$659$	3.88240e16			0.474011			0.237005	+	0.971508i	$0.423834\pi$
$660$	3.90616e14	−	6.76566e14i	0.00472592	−	0.00818553i
$661$	9.43195e16	−	5.44554e16i	1.13082	−	0.652878i	0.186677	−	0.982421i	$-0.440228\pi$
$661$	9.43195e16	−	5.44554e16i	1.13082	−	0.652878i	0.944140	+	0.329543i	$0.106895\pi$
$662$	2.56424e16	+	4.44140e16i	0.304657	+	0.527682i
$663$	−6.73159e15	−	3.88648e15i	−0.0792568	−	0.0457589i
$664$		−	3.82989e16i		−	0.446866i
$665$		0			0
$666$	4.35685e16			0.499260
$667$	−7.11582e15	+	1.23250e16i	−0.0808109	+	0.139969i
$668$	9.56655e15	−	5.52325e15i	0.107670	−	0.0621636i
$669$	−3.48401e15	−	6.03449e15i	−0.0388618	−	0.0673106i
$670$	−8.52535e15	−	4.92211e15i	−0.0942461	−	0.0544130i
$671$			1.74447e16i			0.191129i
$672$		0			0
$673$	−4.67477e16			−0.503118			−0.251559	−	0.967842i	$-0.580943\pi$
$673$	−4.67477e16			−0.503118			−0.251559	+	0.967842i	$0.580943\pi$
$674$	−1.13767e15	+	1.97050e15i	−0.0121355	+	0.0210192i
$675$	8.45768e15	−	4.88304e15i	0.0894187	−	0.0516259i
$676$	2.60174e16	+	4.50635e16i	0.272636	+	0.472220i
$677$	−5.40258e16	−	3.11918e16i	−0.561137	−	0.323973i	0.192465	−	0.981304i	$-0.438352\pi$
$677$	−5.40258e16	−	3.11918e16i	−0.561137	−	0.323973i	−0.753602	+	0.657331i	$0.771685\pi$
$678$			2.78911e15i			0.0287136i
$679$		0			0
$680$	7.58512e15			0.0767201
$681$	3.18287e15	−	5.51289e15i	0.0319107	−	0.0552709i
$682$	2.34483e17	−	1.35379e17i	2.33026	−	1.34538i
$683$	−3.36676e16	−	5.83140e16i	−0.331656	−	0.574445i	0.651181	−	0.758923i	$-0.274274\pi$
$683$	−3.36676e16	−	5.83140e16i	−0.331656	−	0.574445i	−0.982837	+	0.184478i	$0.940941\pi$
$684$	4.93948e16	+	2.85181e16i	0.482331	+	0.278474i
$685$			1.63104e16i			0.157877i
$686$		0			0
$687$	−7.71758e15			−0.0734075
$688$	1.52478e16	−	2.64100e16i	0.143773	−	0.249022i
$689$	4.36828e16	−	2.52203e16i	0.408315	−	0.235741i
$690$	−7.88957e13	−	1.36651e14i	−0.000731070	−	0.00126625i
$691$	−2.07049e16	−	1.19540e16i	−0.190197	−	0.109810i	0.401878	−	0.915693i	$-0.368358\pi$
$691$	−2.07049e16	−	1.19540e16i	−0.190197	−	0.109810i	−0.592075	+	0.805883i	$0.701691\pi$
$692$		−	5.22104e16i		−	0.475467i
$693$		0			0
$694$	−3.80170e16			−0.340268
$695$	−5.40831e15	+	9.36747e15i	−0.0479903	+	0.0831216i
$696$	−1.42813e15	+	8.24532e14i	−0.0125636	+	0.00725358i
$697$	7.34113e16	+	1.27152e17i	0.640275	+	1.10899i
$698$	1.69431e16	+	9.78210e15i	0.146508	+	0.0845862i
$699$		−	7.44577e15i		−	0.0638332i
$700$		0			0
$701$	−1.42561e17			−1.20141			−0.600707	−	0.799469i	$-0.705114\pi$
$701$	−1.42561e17			−1.20141			−0.600707	+	0.799469i	$0.705114\pi$
$702$	6.53682e15	−	1.13221e16i	0.0546190	−	0.0946029i
$703$	8.26872e16	−	4.77395e16i	0.685025	−	0.395499i
$704$	−1.46582e16	−	2.53888e16i	−0.120405	−	0.208548i
$705$	4.14488e14	+	2.39305e14i	0.00337580	+	0.00194902i
$706$		−	1.09120e17i		−	0.881201i
$707$		0			0
$708$	−4.11892e14			−0.00327027
$709$	1.08427e17	−	1.87800e17i	0.853607	−	1.47849i	−0.0243234	−	0.999704i	$-0.507743\pi$
$709$	1.08427e17	−	1.87800e17i	0.853607	−	1.47849i	0.877931	−	0.478787i	$-0.158924\pi$
$710$	1.27021e16	−	7.33357e15i	0.0991575	−	0.0572486i
$711$	−5.99044e16	−	1.03758e17i	−0.463705	−	0.803160i
$712$	−2.08926e16	−	1.20623e16i	−0.160366	−	0.0925873i
$713$		−	5.46870e16i		−	0.416243i
$714$		0			0
$715$	6.82592e16			0.510887
$716$	−3.68521e16	+	6.38296e16i	−0.273517	+	0.473745i
$717$	−6.04938e15	+	3.49261e15i	−0.0445241	+	0.0257060i
$718$	1.45893e16	+	2.52694e16i	0.106485	+	0.184437i
$719$	−1.49791e16	−	8.64816e15i	−0.108420	−	0.0625966i	0.444809	−	0.895625i	$-0.353271\pi$
$719$	−1.49791e16	−	8.64816e15i	−0.108420	−	0.0625966i	−0.553230	+	0.833029i	$0.686605\pi$
$720$			6.36971e15i			0.0457219i
$721$		0			0
$722$	2.48301e16			0.175289
$723$	−3.86649e15	+	6.69697e15i	−0.0270700	+	0.0468865i
$724$	−1.99902e16	+	1.15413e16i	−0.138799	+	0.0801355i
$725$	−5.38162e16	−	9.32124e16i	−0.370583	−	0.641868i
$726$	1.30068e16	+	7.50950e15i	0.0888284	+	0.0512851i
$727$		−	1.17362e17i		−	0.794915i	−0.917621	−	0.397458i	$-0.869893\pi$
$727$		−	1.17362e17i		−	0.794915i	0.917621	−	0.397458i	$-0.130107\pi$
$728$		0			0
$729$	1.47523e17			0.982868
$730$	1.13207e16	−	1.96080e16i	0.0748057	−	0.129567i
$731$	−1.79816e17	+	1.03817e17i	−1.17848	+	0.680397i
$732$	2.04136e14	+	3.53573e14i	0.00132694	+	0.00229833i
$733$	−1.49527e17	−	8.63296e16i	−0.964044	−	0.556591i	−0.0666284	−	0.997778i	$-0.521224\pi$
$733$	−1.49527e17	−	8.63296e16i	−0.964044	−	0.556591i	−0.897415	+	0.441187i	$0.854558\pi$
$734$			6.42591e16i			0.410921i
$735$		0			0
$736$	−5.92128e15			−0.0372519
$737$	1.29527e17	−	2.24347e17i	0.808266	−	1.39996i
$738$	−1.06778e17	+	6.16481e16i	−0.660910	+	0.381577i
$739$	9.54432e15	+	1.65313e16i	0.0585974	+	0.101494i	0.893836	−	0.448394i	$-0.148004\pi$
$739$	9.54432e15	+	1.65313e16i	0.0585974	+	0.101494i	−0.835239	+	0.549888i	$0.814671\pi$
$740$	9.23436e15	+	5.33146e15i	0.0562363	+	0.0324680i
$741$		−	1.43047e16i		−	0.0864112i
$742$		0			0
$743$	−5.56299e16			−0.330655			−0.165328	−	0.986239i	$-0.552868\pi$
$743$	−5.56299e16			−0.330655			−0.165328	+	0.986239i	$0.552868\pi$
$744$	3.16838e15	−	5.48779e15i	0.0186810	−	0.0323564i
$745$	1.66023e16	−	9.58534e15i	0.0971025	−	0.0560621i
$746$	6.59386e16	+	1.14209e17i	0.382566	+	0.662624i
$747$	−1.89641e17	−	1.09489e17i	−1.09146	−	0.630155i
$748$			1.99605e17i			1.13962i
$749$		0			0
$750$	2.42826e15			0.0136436
$751$	−1.36551e17	+	2.36514e17i	−0.761125	+	1.31831i	0.181146	+	0.983456i	$0.442019\pi$
$751$	−1.36551e17	+	2.36514e17i	−0.761125	+	1.31831i	−0.942271	+	0.334851i	$0.891314\pi$
$752$	1.55541e16	−	8.98015e15i	0.0860076	−	0.0496565i
$753$	4.25651e15	+	7.37249e15i	0.0233498	+	0.0404431i
$754$	−1.24781e17	−	7.20426e16i	−0.679081	−	0.392068i
$755$			1.50077e15i			0.00810276i
$756$		0			0
$757$	−9.53508e16			−0.506698			−0.253349	−	0.967375i	$-0.581532\pi$
$757$	−9.53508e16			−0.506698			−0.253349	+	0.967375i	$0.581532\pi$
$758$	2.88662e16	−	4.99977e16i	0.152186	−	0.263593i
$759$	3.59602e15	−	2.07616e15i	0.0188092	−	0.0108595i
$760$	6.97951e15	+	1.20889e16i	0.0362196	+	0.0627342i
$761$	−7.55592e16	−	4.36241e16i	−0.389026	−	0.224605i	0.292712	−	0.956201i	$-0.405442\pi$
$761$	−7.55592e16	−	4.36241e16i	−0.389026	−	0.224605i	−0.681738	+	0.731596i	$0.738776\pi$
$762$		−	9.21098e15i		−	0.0470518i
$763$		0			0
$764$	−2.02615e16			−0.101885
$765$	2.16844e16	−	3.75585e16i	0.108188	−	0.187387i
$766$	−1.01232e17	+	5.84463e16i	−0.501124	+	0.289324i
$767$	−1.79943e16	−	3.11671e16i	−0.0883818	−	0.153082i
$768$	−5.94195e14	−	3.43059e14i	−0.00289575	−	0.00167186i
$769$			2.35317e17i			1.13787i	0.822381	+	0.568937i	$0.192645\pi$
$769$			2.35317e17i			1.13787i	−0.822381	+	0.568937i	$0.807355\pi$
$770$		0			0
$771$	−1.61809e16			−0.0770331
$772$	4.49609e16	−	7.78746e16i	0.212389	−	0.367868i
$773$	1.91385e17	−	1.10496e17i	0.897080	−	0.517929i	0.0208283	−	0.999783i	$-0.493370\pi$
$773$	1.91385e17	−	1.10496e17i	0.897080	−	0.517929i	0.876252	+	0.481854i	$0.160036\pi$
$774$	−8.71813e16	−	1.51002e17i	−0.405488	−	0.702325i
$775$	3.58181e17	+	2.06796e17i	1.65308	+	0.954404i
$776$			3.80884e16i			0.174431i
$777$		0			0
$778$	−1.75426e17			−0.791072
$779$	−1.35100e17	+	2.34000e17i	−0.604548	+	1.04711i
$780$	1.38350e15	−	7.98762e14i	0.00614343	−	0.00354691i
$781$	1.92985e17	+	3.34259e17i	0.850387	+	1.47291i
$782$	3.49144e16	+	2.01578e16i	0.152674	+	0.0881462i
$783$			1.88845e16i			0.0819474i
$784$		0			0
$785$	−4.47938e16			−0.191425
$786$	4.03610e15	−	6.99073e15i	0.0171170	−	0.0296475i
$787$	1.58831e16	−	9.17012e15i	0.0668478	−	0.0385946i	−0.466204	−	0.884677i	$-0.654379\pi$
$787$	1.58831e16	−	9.17012e15i	0.0668478	−	0.0385946i	0.533051	+	0.846083i	$0.321045\pi$
$788$	−3.97589e16	−	6.88645e16i	−0.166065	−	0.287633i
$789$	−3.97528e15	−	2.29513e15i	−0.0164780	−	0.00951360i
$790$		−	2.93220e16i		−	0.120623i
$791$		0			0
$792$	−1.67621e17			−0.679166
$793$	−1.78361e16	+	3.08931e16i	−0.0717235	+	0.124229i
$794$	−2.89345e15	+	1.67054e15i	−0.0115476	+	0.00666704i
$795$	−4.03913e14	−	6.99598e14i	−0.00159987	−	0.00277106i
$796$	−3.35792e16	−	1.93870e16i	−0.132006	−	0.0762134i
$797$		−	9.39084e16i		−	0.366399i	−0.983076	−	0.183200i	$-0.941355\pi$
$797$		−	9.39084e16i		−	0.366399i	0.983076	−	0.183200i	$-0.0586454\pi$
$798$		0			0
$799$	−1.22285e17			−0.469993
$800$	2.23910e16	−	3.87824e16i	0.0854149	−	0.147943i
$801$	−1.19456e17	+	6.89678e16i	−0.452285	+	0.261127i
$802$	−9.10807e16	−	1.57756e17i	−0.342279	−	0.592844i
$803$	5.15989e17	+	2.97906e17i	1.92463	+	1.11119i
$804$		−	6.06284e15i		−	0.0224460i
$805$		0			0
$806$	5.53667e17			2.01947
$807$	−7.73562e15	+	1.33985e16i	−0.0280062	+	0.0485081i
$808$	1.11893e17	−	6.46015e16i	0.402101	−	0.232153i
$809$	−5.04324e16	−	8.73514e16i	−0.179895	−	0.311587i	0.761950	−	0.647636i	$-0.224242\pi$
$809$	−5.04324e16	−	8.73514e16i	−0.179895	−	0.311587i	−0.941844	+	0.336050i	$0.890909\pi$
$810$	3.14495e16	+	1.81574e16i	0.111353	+	0.0642899i
$811$			2.30062e17i			0.808572i	0.914633	+	0.404286i	$0.132480\pi$
$811$			2.30062e17i			0.808572i	−0.914633	+	0.404286i	$0.867520\pi$
$812$		0			0
$813$	8.09848e15			0.0280453
$814$	−1.40299e17	+	2.43005e17i	−0.482289	+	0.835349i
$815$	6.03824e15	−	3.48618e15i	0.0206046	−	0.0118961i
$816$	2.33575e15	+	4.04564e15i	0.00791199	+	0.0137040i
$817$	−3.30918e17	−	1.91055e17i	−1.11272	−	0.642431i
$818$		−	2.60663e17i		−	0.870081i
$819$		0			0
$820$	−3.01755e16			−0.0992592
$821$	−7.59952e16	+	1.31628e17i	−0.248157	+	0.429821i	−0.963015	−	0.269449i	$-0.913158\pi$
$821$	−7.59952e16	+	1.31628e17i	−0.248157	+	0.429821i	0.714857	+	0.699270i	$0.246492\pi$
$822$	−8.69938e15	+	5.02259e15i	−0.0282005	+	0.0162816i
$823$	8.24296e16	+	1.42772e17i	0.265268	+	0.459457i	0.967634	−	0.252359i	$-0.0812064\pi$
$823$	8.24296e16	+	1.42772e17i	0.265268	+	0.459457i	−0.702366	+	0.711816i	$0.747873\pi$
$824$	−1.16026e17	−	6.69874e16i	−0.370672	−	0.214008i
$825$			3.14036e16i			0.0995992i
$826$		0			0
$827$	6.48794e16			0.202803			0.101401	−	0.994846i	$-0.467667\pi$
$827$	6.48794e16			0.202803			0.101401	+	0.994846i	$0.467667\pi$
$828$	−1.69278e16	+	2.93198e16i	−0.0525314	+	0.0909870i
$829$	−3.94012e17	+	2.27483e17i	−1.21390	+	0.700844i	−0.963606	−	0.267327i	$-0.913860\pi$
$829$	−3.94012e17	+	2.27483e17i	−1.21390	+	0.700844i	−0.250291	+	0.968171i	$0.580526\pi$
$830$	−2.67963e16	−	4.64126e16i	−0.0819609	−	0.141960i
$831$	−1.06730e16	−	6.16206e15i	−0.0324101	−	0.0187120i
$832$		−	5.99487e16i		−	0.180734i
$833$		0			0
$834$	−6.66172e15			−0.0197966
$835$	7.72883e15	−	1.33867e16i	0.0228032	−	0.0394962i
$836$	−3.18122e17	+	1.83668e17i	−0.931871	+	0.538016i
$837$	−3.62831e16	−	6.28443e16i	−0.105524	−	0.182773i
$838$	3.72081e17	+	2.14821e17i	1.07442	+	0.620316i
$839$			4.60417e17i			1.32002i	0.751259	+	0.660008i	$0.229447\pi$
$839$			4.60417e17i			1.32002i	−0.751259	+	0.660008i	$0.770553\pi$
$840$		0			0
$841$	−1.45688e17			−0.411763
$842$	−1.96480e17	+	3.40314e17i	−0.551374	+	0.955008i
$843$	−1.10459e16	+	6.37737e15i	−0.0307777	+	0.0177695i
$844$	3.27406e16	+	5.67085e16i	0.0905800	+	0.156889i
$845$	6.30586e16	+	3.64069e16i	0.173222	+	0.100010i
$846$		−	1.02690e17i		−	0.280096i
$847$		0			0
$848$	−3.03145e16			−0.0815220
$849$	−1.56525e15	+	2.71108e15i	−0.00417962	+	0.00723931i
$850$	−2.64054e17	+	1.52452e17i	−0.700131	+	0.404221i
$851$	2.83372e16	+	4.90815e16i	0.0746071	+	0.129223i
$852$	7.82294e15	+	4.51658e15i	0.0204518	+	0.0118079i
$853$			4.56236e17i			1.18439i	0.805794	+	0.592196i	$0.201739\pi$
$853$			4.56236e17i			1.18439i	−0.805794	+	0.592196i	$0.798261\pi$
$854$		0			0
$855$	7.98124e16			0.204302
$856$	2.64406e16	−	4.57965e16i	0.0672093	−	0.116410i
$857$	1.55206e17	−	8.96082e16i	0.391763	−	0.226184i	−0.291161	−	0.956674i	$-0.594041\pi$
$857$	1.55206e17	−	8.96082e16i	0.391763	−	0.226184i	0.682924	+	0.730490i	$0.260708\pi$
$858$	2.10196e16	+	3.64071e16i	0.0526868	+	0.0912562i
$859$	5.84979e17	+	3.37738e17i	1.45607	+	0.840660i	0.998815	−	0.0486771i	$-0.0155005\pi$
$859$	5.84979e17	+	3.37738e17i	1.45607	+	0.840660i	0.457252	+	0.889337i	$0.348834\pi$
$860$		−	4.26734e16i		−	0.105479i
$861$		0			0
$862$	−1.21968e16			−0.0297304
$863$	1.04495e17	−	1.80991e17i	0.252948	−	0.438118i	−0.711388	−	0.702799i	$-0.751933\pi$
$863$	1.04495e17	−	1.80991e17i	0.252948	−	0.438118i	0.964336	+	0.264681i	$0.0852666\pi$
$864$	−6.80451e15	+	3.92859e15i	−0.0163574	+	0.00944396i
$865$	−3.65297e16	−	6.32713e16i	−0.0872066	−	0.151046i
$866$	−1.98690e17	−	1.14714e17i	−0.471052	−	0.271962i
$867$		−	9.08348e15i		−	0.0213864i
$868$		0			0
$869$	7.71615e17			1.79177
$870$	−1.15379e15	+	1.99842e15i	−0.00266079	+	0.00460863i
$871$	4.58763e17	−	2.64867e17i	1.05070	−	0.606622i
$872$	1.31061e16	+	2.27004e16i	0.0298108	+	0.0516338i
$873$	1.88599e17	+	1.08888e17i	0.426043	+	0.245976i
$874$			7.41936e16i			0.166455i
$875$		0			0
$876$	1.39443e16			0.0308583
$877$	1.11780e17	−	1.93609e17i	0.245679	−	0.425529i	−0.716643	−	0.697440i	$-0.754322\pi$
$877$	1.11780e17	−	1.93609e17i	0.245679	−	0.425529i	0.962322	+	0.271911i	$0.0876557\pi$
$878$	−6.42012e15	+	3.70666e15i	−0.0140144	+	0.00809124i
$879$	7.18804e15	+	1.24500e16i	0.0155839	+	0.0269922i
$880$	−3.55273e16	−	2.05117e16i	−0.0765008	−	0.0441677i
$881$		−	9.10277e17i		−	1.94678i	−0.229144	−	0.973392i	$-0.573593\pi$
$881$		−	9.10277e17i		−	1.94678i	0.229144	−	0.973392i	$-0.426407\pi$
$882$		0			0
$883$	4.97000e17			1.04856			0.524279	−	0.851547i	$-0.324335\pi$
$883$	4.97000e17			1.04856			0.524279	+	0.851547i	$0.324335\pi$
$884$	−2.04084e17	+	3.53483e17i	−0.427656	+	0.740722i
$885$	−4.99153e14	+	2.88186e14i	−0.00103890	+	0.000599809i
$886$	−1.97195e17	−	3.41552e17i	−0.407656	−	0.706080i
$887$	2.48013e17	+	1.43190e17i	0.509252	+	0.294017i	0.732526	−	0.680739i	$-0.238341\pi$
$887$	2.48013e17	+	1.43190e17i	0.509252	+	0.294017i	−0.223274	+	0.974756i	$0.571675\pi$
$888$			6.56705e15i			0.0133935i
$889$		0			0
$890$	−3.37583e16			−0.0679267
$891$	−4.77816e17	+	8.27601e17i	−0.954980	+	1.65407i
$892$	−3.16878e17	+	1.82950e17i	−0.629076	+	0.363197i
$893$	−1.12521e17	−	1.94892e17i	−0.221884	−	0.384314i
$894$	1.02250e16	+	5.90339e15i	0.0200280	+	0.0115632i
$895$			1.03136e17i			0.200666i
$896$		0			0
$897$	8.49100e15			0.0163006
$898$	1.21849e17	−	2.11049e17i	0.232362	−	0.402463i
$899$	−6.92609e17	+	3.99878e17i	−1.31199	+	0.757477i
$900$	−1.28023e17	−	2.21743e17i	−0.240898	−	0.417248i
$901$	1.78747e17	+	1.03200e17i	0.334111	+	0.192899i
$902$		−	7.94075e17i		−	1.47442i
$903$		0			0
$904$	1.46459e17			0.268353
$905$	−1.61501e16	+	2.79728e16i	−0.0293957	+	0.0509149i
$906$	−8.00460e14	+	4.62146e14i	−0.00144734	+	0.000835622i
$907$	1.65405e17	+	2.86490e17i	0.297102	+	0.514595i	0.975472	−	0.220126i	$-0.0706467\pi$
$907$	1.65405e17	+	2.86490e17i	0.297102	+	0.514595i	−0.678370	+	0.734720i	$0.737313\pi$
$908$	−2.89488e17	−	1.67136e17i	−0.516554	−	0.298233i
$909$		−	7.38734e17i		−	1.30950i
$910$		0			0
$911$	−7.13090e17			−1.24748			−0.623741	−	0.781631i	$-0.714388\pi$
$911$	−7.13090e17			−1.24748			−0.623741	+	0.781631i	$0.714388\pi$
$912$	−4.29852e15	+	7.44526e15i	−0.00747051	+	0.0129393i
$913$	1.22136e18	−	7.05153e17i	2.10872	−	1.21747i
$914$	−2.99953e17	−	5.19533e17i	−0.514488	−	0.891120i
$915$	4.94765e14	+	2.85653e14i	0.000843087	+	0.000486756i
$916$			4.05259e17i			0.686056i
$917$		0			0
$918$	5.34965e16			0.0893859
$919$	−1.91376e17	+	3.31473e17i	−0.317684	+	0.550244i	−0.980004	−	0.198976i	$-0.936238\pi$
$919$	−1.91376e17	+	3.31473e17i	−0.317684	+	0.550244i	0.662321	+	0.749220i	$0.269572\pi$
$920$	−7.17572e15	+	4.14290e15i	−0.0118342	+	0.00683247i
$921$	1.24147e16	+	2.15028e16i	0.0203412	+	0.0352320i
$922$	5.34225e17	+	3.08435e17i	0.869639	+	0.502086i
$923$			7.89262e17i			1.27647i
$924$		0			0
$925$	−4.28623e17			−0.684267
$926$	3.00705e17	−	5.20836e17i	0.476951	−	0.826104i
$927$	−6.63390e17	+	3.83008e17i	−1.04542	+	0.603573i
$928$	4.32971e16	+	7.49928e16i	0.0677909	+	0.117417i
$929$	−4.43731e17	−	2.56188e17i	−0.690281	−	0.398534i	0.113436	−	0.993545i	$-0.463814\pi$
$929$	−4.43731e17	−	2.56188e17i	−0.690281	−	0.398534i	−0.803717	+	0.595011i	$0.797148\pi$
$930$		−	8.86719e15i		−	0.0137053i
$931$		0			0
$932$	−3.90986e17			−0.596576
$933$	−2.56926e16	+	4.45008e16i	−0.0389509	+	0.0674649i
$934$	2.69430e17	−	1.55555e17i	0.405849	−	0.234317i
$935$	1.39656e17	+	2.41891e17i	0.209021	+	0.362035i
$936$	−2.96842e17	−	1.71382e17i	−0.441439	−	0.254865i
$937$			1.03036e18i			1.52248i	0.648471	+	0.761239i	$0.275409\pi$
$937$			1.03036e18i			1.52248i	−0.648471	+	0.761239i	$0.724591\pi$
$938$		0			0
$939$	−2.75486e16			−0.0401889
$940$	1.25662e16	−	2.17652e16i	0.0182153	−	0.0315498i
$941$	8.34992e17	−	4.82083e17i	1.20266	−	0.694359i	0.241518	−	0.970396i	$-0.422355\pi$
$941$	8.34992e17	−	4.82083e17i	1.20266	−	0.694359i	0.961147	+	0.276038i	$0.0890214\pi$
$942$	−1.37937e16	−	2.38914e16i	−0.0197413	−	0.0341930i
$943$	−1.38898e17	−	8.01928e16i	−0.197527	−	0.114042i
$944$			2.16289e16i			0.0305635i
$945$		0			0
$946$	1.12296e18			1.56682
$947$	1.23888e17	−	2.14580e17i	0.171763	−	0.297502i	−0.767273	−	0.641320i	$-0.778387\pi$
$947$	1.23888e17	−	2.14580e17i	0.171763	−	0.297502i	0.939036	+	0.343818i	$0.111720\pi$
$948$	1.56393e16	−	9.02936e15i	0.0215461	−	0.0124396i
$949$	6.09183e17	+	1.05514e18i	0.833970	+	1.44448i
$950$	−4.85943e17	−	2.80559e17i	−0.661064	−	0.381666i
$951$			2.91118e16i			0.0393537i
$952$		0			0
$953$	−1.21407e18			−1.62064			−0.810320	−	0.585988i	$-0.800707\pi$
$953$	−1.21407e18			−1.62064			−0.810320	+	0.585988i	$0.800707\pi$
$954$	−8.66633e16	+	1.50105e17i	−0.114960	+	0.199116i
$955$	−2.45539e16	+	1.41762e16i	−0.0323669	+	0.0186870i
$956$	1.83401e17	+	3.17660e17i	0.240245	+	0.416116i
$957$	−5.25890e16	−	3.03623e16i	−0.0684579	−	0.0395242i
$958$			1.54952e17i			0.200449i
$959$		0			0
$960$	−9.60102e14			−0.00122656
$961$	1.14275e18	−	1.97931e18i	1.45082	−	2.51289i
$962$	−4.96915e17	+	2.86894e17i	−0.626949	+	0.361969i
$963$	−1.51177e17	−	2.61847e17i	−0.189552	−	0.328314i
$964$	3.51665e17	+	2.03034e17i	0.438195	+	0.252992i
$965$		−	1.25830e17i		−	0.155819i
$966$		0			0
$967$	1.21549e18			1.48660			0.743298	−	0.668960i	$-0.233260\pi$
$967$	1.21549e18			1.48660			0.743298	+	0.668960i	$0.233260\pi$
$968$	3.94333e17	−	6.83004e17i	0.479303	−	0.830178i
$969$	5.06919e16	−	2.92670e16i	0.0612344	−	0.0353537i
$970$	2.66491e16	+	4.61576e16i	0.0319928	+	0.0554131i
$971$	−1.14900e18	−	6.63374e17i	−1.37089	−	0.791486i	−0.379854	−	0.925047i	$-0.624026\pi$
$971$	−1.14900e18	−	6.63374e17i	−1.37089	−	0.791486i	−0.991041	+	0.133560i	$0.957359\pi$
$972$			6.74187e16i			0.0799434i
$973$		0			0
$974$	−7.16259e17			−0.838911
$975$	−3.21083e16	+	5.56132e16i	−0.0373757	+	0.0647367i
$976$	1.85665e16	−	1.07194e16i	0.0214799	−	0.0124014i
$977$	2.13451e17	+	3.69708e17i	0.245432	+	0.425100i	0.962253	−	0.272157i	$-0.0877370\pi$
$977$	2.13451e17	+	3.69708e17i	0.245432	+	0.425100i	−0.716821	+	0.697257i	$0.754404\pi$
$978$	3.71881e15	+	2.14706e15i	0.00424983	+	0.00245364i
$979$		−	8.88359e17i		−	1.00900i
$980$		0			0
$981$	1.49871e17			0.168153
$982$	−5.12635e17	+	8.87909e17i	−0.571662	+	0.990147i
$983$	−5.22072e17	+	3.01418e17i	−0.578641	+	0.334079i	−0.760593	−	0.649229i	$-0.775092\pi$
$983$	−5.22072e17	+	3.01418e17i	−0.578641	+	0.334079i	0.181952	+	0.983307i	$0.441758\pi$
$984$	−9.29219e15	−	1.60945e16i	−0.0102364	−	0.0177300i
$985$	−9.63639e16	−	5.56358e16i	−0.105511	−	0.0609167i
$986$		−	5.89587e17i		−	0.641632i
$987$		0			0
$988$	−7.51157e17			−0.807587
$989$	1.13407e17	−	1.96426e17i	0.121188	−	0.209904i
$990$	−2.03131e17	+	1.17278e17i	−0.215758	+	0.124568i
$991$	−3.24511e17	−	5.62069e17i	−0.342600	−	0.593400i	0.642315	−	0.766441i	$-0.277974\pi$
$991$	−3.24511e17	−	5.62069e17i	−0.342600	−	0.593400i	−0.984915	+	0.173041i	$0.944641\pi$
$992$	−2.88170e17	−	1.66375e17i	−0.302398	−	0.174590i
$993$			4.41980e16i			0.0461007i
$994$		0			0
$995$	−5.42574e16			−0.0559140
$996$	1.65032e16	−	2.85845e16i	0.0169049	−	0.0292802i
$997$	9.77523e17	−	5.64373e17i	0.995304	−	0.574639i	0.0884486	−	0.996081i	$-0.471809\pi$
$997$	9.77523e17	−	5.64373e17i	0.995304	−	0.574639i	0.906856	+	0.421442i	$0.138476\pi$
$998$	2.05265e17	+	3.55530e17i	0.207746	+	0.359826i
$999$	6.51282e16	+	3.76018e16i	0.0655203	+	0.0378282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.13.d.a.19.6		16
7.2	even	3		98.13.b.c.97.5		16
7.3	odd	6	inner	98.13.d.a.31.6		16
7.4	even	3		14.13.d.a.3.7	✓	16
7.5	odd	6		98.13.b.c.97.4		16
7.6	odd	2		14.13.d.a.5.7	yes	16
21.11	odd	6		126.13.n.a.73.2		16
21.20	even	2		126.13.n.a.19.2		16
28.11	odd	6		112.13.s.c.17.4		16
28.27	even	2		112.13.s.c.33.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.d.a.3.7	✓	16	7.4	even	3
14.13.d.a.5.7	yes	16	7.6	odd	2
98.13.b.c.97.4		16	7.5	odd	6
98.13.b.c.97.5		16	7.2	even	3
98.13.d.a.19.6		16	1.1	even	1	trivial
98.13.d.a.31.6		16	7.3	odd	6	inner
112.13.s.c.17.4		16	28.11	odd	6
112.13.s.c.33.4		16	28.27	even	2
126.13.n.a.19.2		16	21.20	even	2
126.13.n.a.73.2		16	21.11	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	98.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(22.6274 - 39.1918i) q^{2} +(33.7761 - 19.5006i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(-2481.87 - 1432.91i) q^{5} -1764.99i q^{6} -92681.9 q^{8} +(-264960. + 458924. i) q^{9} +O(q^{10})\)	\(q+(22.6274 - 39.1918i) q^{2} +(33.7761 - 19.5006i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(-2481.87 - 1432.91i) q^{5} -1764.99i q^{6} -92681.9 q^{8} +(-264960. + 458924. i) q^{9} +(-112317. + 64846.2i) q^{10} +(-1.70644e6 - 2.95565e6i) q^{11} +(-69173.4 - 39937.3i) q^{12} -6.97895e6i q^{13} -111771. q^{15} +(-2.09715e6 + 3.63237e6i) q^{16} +(2.47314e7 - 1.42787e7i) q^{17} +(1.19907e7 + 2.07685e7i) q^{18} +(4.55136e7 + 2.62773e7i) q^{19} +5.86920e6i q^{20} -1.54450e8 q^{22} +(-1.55977e7 + 2.70160e7i) q^{23} +(-3.13043e6 + 1.80735e6i) q^{24} +(-1.17964e8 - 2.04319e8i) q^{25} +(-2.73518e8 - 1.57916e8i) q^{26} +4.13944e7i q^{27} +4.56209e8 q^{29} +(-2.52908e6 + 4.38050e6i) q^{30} +(-1.51818e9 + 8.76523e8i) q^{31} +(9.49063e7 + 1.64382e8i) q^{32} +(-1.15274e8 - 6.65534e7i) q^{33} -1.29236e9i q^{34} +1.08528e9 q^{36} +(9.08379e8 - 1.57336e9i) q^{37} +(2.05971e9 - 1.18918e9i) q^{38} +(-1.36094e8 - 2.35721e8i) q^{39} +(2.30025e8 + 1.32805e8i) q^{40} +5.14132e9i q^{41} -7.27073e9 q^{43} +(-3.49480e9 + 6.05317e9i) q^{44} +(1.31519e9 - 7.59328e8i) q^{45} +(7.05871e8 + 1.22260e9i) q^{46} +(-3.70838e9 - 2.14103e9i) q^{47} +1.63583e8i q^{48} -1.06769e10 q^{50} +(5.56887e8 - 9.64556e8i) q^{51} +(-1.23780e10 + 7.14644e9i) q^{52} +(3.61377e9 + 6.25923e9i) q^{53} +(1.62232e9 + 9.36648e8i) q^{54} +9.78073e9i q^{55} +2.04970e9 q^{57} +(1.03228e10 - 1.78797e10i) q^{58} +(4.46587e9 - 2.57837e9i) q^{59} +(1.14453e8 + 1.98239e8i) q^{60} +(-4.42661e9 - 2.55570e9i) q^{61} +7.93338e10i q^{62} +8.58993e9 q^{64} +(-1.00002e10 + 1.73209e10i) q^{65} +(-5.21670e9 + 3.01186e9i) q^{66} +(3.79522e10 + 6.57352e10i) q^{67} +(-5.06500e10 - 2.92428e10i) q^{68} +1.21666e9i q^{69} -1.13092e11 q^{71} +(2.45570e10 - 4.25340e10i) q^{72} +(-1.51188e11 + 8.72887e10i) q^{73} +(-4.11085e10 - 7.12021e10i) q^{74} +(-7.96871e9 - 4.60074e9i) q^{75} -1.07632e11i q^{76} -1.23178e10 q^{78} +(-1.13044e11 + 1.95798e11i) q^{79} +(1.04097e10 - 6.01006e9i) q^{80} +(-1.40003e11 - 2.42493e11i) q^{81} +(2.01498e11 + 1.16335e11i) q^{82} +4.13229e11i q^{83} -8.18404e10 q^{85} +(-1.64518e11 + 2.84953e11i) q^{86} +(1.54090e10 - 8.89637e9i) q^{87} +(1.58156e11 + 2.73935e11i) q^{88} +(2.25422e11 + 1.30148e11i) q^{89} -6.87265e10i q^{90} +6.38882e10 q^{92} +(-3.41855e10 + 5.92110e10i) q^{93} +(-1.67822e11 + 9.68921e10i) q^{94} +(-7.53061e10 - 1.30434e11i) q^{95} +(6.41112e9 + 3.70146e9i) q^{96} -4.10959e11i q^{97} +1.80856e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16384 q^{4} - 18144 q^{5} + 2362248 q^{9}+O(q^{10}) \) 16 * q - 16384 * q^4 - 18144 * q^5 + 2362248 * q^9	\( 16 q - 16384 q^{4} - 18144 q^{5} + 2362248 q^{9} + 2290176 q^{10} + 2072088 q^{11} - 27163728 q^{15} - 33554432 q^{16} + 101561040 q^{17} - 4592640 q^{18} - 174931848 q^{19} + 62776320 q^{22} + 25630560 q^{23} - 242221056 q^{24} + 521205808 q^{25} + 1434682368 q^{26} + 532360944 q^{29} - 2151917568 q^{30} - 4583818344 q^{31} - 6054957720 q^{33} - 9675767808 q^{36} + 5764524040 q^{37} + 149506560 q^{38} + 10526083272 q^{39} - 4690280448 q^{40} - 66929432000 q^{43} + 4243636224 q^{44} - 57253352184 q^{45} + 7203213312 q^{46} - 18116171640 q^{47} - 99248080896 q^{50} - 23299256376 q^{51} - 8269578240 q^{52} + 39134161800 q^{53} - 105152205312 q^{54} - 328243960080 q^{57} + 29637396480 q^{58} - 201845459088 q^{59} + 27815657472 q^{60} - 336780254328 q^{61} + 137438953472 q^{64} + 158322703896 q^{65} - 268884080640 q^{66} + 107767119920 q^{67} - 207997009920 q^{68} - 1150259029344 q^{71} - 9405726720 q^{72} + 738414283320 q^{73} + 4902778368 q^{74} - 1537028640000 q^{75} - 786088888320 q^{78} + 227632064768 q^{79} + 76101451776 q^{80} - 391984178400 q^{81} + 302578053120 q^{82} + 710209696080 q^{85} - 38105192448 q^{86} - 1957017683880 q^{87} - 64282951680 q^{88} + 2485007442792 q^{89} - 104982773760 q^{92} - 458668768680 q^{93} + 2021298693120 q^{94} - 186503862960 q^{95} + 496068722688 q^{96} + 3921180354576 q^{99}+O(q^{100}) \) 16 * q - 16384 * q^4 - 18144 * q^5 + 2362248 * q^9 + 2290176 * q^10 + 2072088 * q^11 - 27163728 * q^15 - 33554432 * q^16 + 101561040 * q^17 - 4592640 * q^18 - 174931848 * q^19 + 62776320 * q^22 + 25630560 * q^23 - 242221056 * q^24 + 521205808 * q^25 + 1434682368 * q^26 + 532360944 * q^29 - 2151917568 * q^30 - 4583818344 * q^31 - 6054957720 * q^33 - 9675767808 * q^36 + 5764524040 * q^37 + 149506560 * q^38 + 10526083272 * q^39 - 4690280448 * q^40 - 66929432000 * q^43 + 4243636224 * q^44 - 57253352184 * q^45 + 7203213312 * q^46 - 18116171640 * q^47 - 99248080896 * q^50 - 23299256376 * q^51 - 8269578240 * q^52 + 39134161800 * q^53 - 105152205312 * q^54 - 328243960080 * q^57 + 29637396480 * q^58 - 201845459088 * q^59 + 27815657472 * q^60 - 336780254328 * q^61 + 137438953472 * q^64 + 158322703896 * q^65 - 268884080640 * q^66 + 107767119920 * q^67 - 207997009920 * q^68 - 1150259029344 * q^71 - 9405726720 * q^72 + 738414283320 * q^73 + 4902778368 * q^74 - 1537028640000 * q^75 - 786088888320 * q^78 + 227632064768 * q^79 + 76101451776 * q^80 - 391984178400 * q^81 + 302578053120 * q^82 + 710209696080 * q^85 - 38105192448 * q^86 - 1957017683880 * q^87 - 64282951680 * q^88 + 2485007442792 * q^89 - 104982773760 * q^92 - 458668768680 * q^93 + 2021298693120 * q^94 - 186503862960 * q^95 + 496068722688 * q^96 + 3921180354576 * q^99

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