LMFDB - Embedded newform 98.13.d.a.31.7

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			31.7
Root			$-295.555 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.31
Dual form			98.13.d.a.19.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(22.6274 + 39.1918i) q^{2} +(444.082 + 256.391i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(12687.9 - 7325.35i) q^{5} +23205.9i q^{6} -92681.9 q^{8} +(-134248. - 232524. i) q^{9} +O(q^{10})$	\(q+(22.6274 + 39.1918i) q^{2} +(444.082 + 256.391i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(12687.9 - 7325.35i) q^{5} +23205.9i q^{6} -92681.9 q^{8} +(-134248. - 232524. i) q^{9} +(574187. + 331507. i) q^{10} +(1.34149e6 - 2.32353e6i) q^{11} +(-909481. + 525089. i) q^{12} +1.34691e6i q^{13} +7.51261e6 q^{15} +(-2.09715e6 - 3.63237e6i) q^{16} +(-6.20477e6 - 3.58233e6i) q^{17} +(6.07536e6 - 1.05228e7i) q^{18} +(-6.33442e7 + 3.65718e7i) q^{19} +3.00046e7i q^{20} +1.21418e8 q^{22} +(-1.14112e8 - 1.97648e8i) q^{23} +(-4.11584e7 - 2.37628e7i) q^{24} +(-1.47489e7 + 2.55459e7i) q^{25} +(-5.27880e7 + 3.04772e7i) q^{26} -4.10193e8i q^{27} -5.69081e8 q^{29} +(1.69991e8 + 2.94433e8i) q^{30} +(-2.67528e8 - 1.54457e8i) q^{31} +(9.49063e7 - 1.64382e8i) q^{32} +(1.19146e9 - 6.87891e8i) q^{33} -3.24235e8i q^{34} +5.49879e8 q^{36} +(-8.51831e8 - 1.47542e9i) q^{37} +(-2.86663e9 - 1.65505e9i) q^{38} +(-3.45336e8 + 5.98140e8i) q^{39} +(-1.17594e9 + 6.78927e8i) q^{40} +5.37658e9i q^{41} -9.19904e9 q^{43} +(2.74737e9 + 4.75858e9i) q^{44} +(-3.40664e9 - 1.96682e9i) q^{45} +(5.16414e9 - 8.94455e9i) q^{46} +(-9.45381e9 + 5.45816e9i) q^{47} -2.15076e9i q^{48} -1.33492e9 q^{50} +(-1.83695e9 - 3.18170e9i) q^{51} +(-2.38891e9 - 1.37924e9i) q^{52} +(7.92816e9 - 1.37320e10i) q^{53} +(1.60762e10 - 9.28161e9i) q^{54} -3.93075e10i q^{55} -3.75067e10 q^{57} +(-1.28768e10 - 2.23033e10i) q^{58} +(-1.75457e10 - 1.01300e10i) q^{59} +(-7.69292e9 + 1.33245e10i) q^{60} +(-2.38455e10 + 1.37672e10i) q^{61} -1.39799e10i q^{62} +8.58993e9 q^{64} +(9.86660e9 + 1.70895e10i) q^{65} +(5.39194e10 + 3.11304e10i) q^{66} +(-3.35056e10 + 5.80333e10i) q^{67} +(1.27074e10 - 7.33661e9i) q^{68} -1.17030e11i q^{69} +7.34393e10 q^{71} +(1.24423e10 + 2.15508e10i) q^{72} +(-5.62093e10 - 3.24525e10i) q^{73} +(3.85495e10 - 6.67697e10i) q^{74} +(-1.30995e10 + 7.56300e9i) q^{75} -1.49798e11i q^{76} -3.12563e10 q^{78} +(-3.16413e9 - 5.48043e9i) q^{79} +(-5.32168e10 - 3.07247e10i) q^{80} +(3.38251e10 - 5.85869e10i) q^{81} +(-2.10718e11 + 1.21658e11i) q^{82} +5.07191e11i q^{83} -1.04967e11 q^{85} +(-2.08151e11 - 3.60527e11i) q^{86} +(-2.52719e11 - 1.45907e11i) q^{87} +(-1.24332e11 + 2.15349e11i) q^{88} +(5.49695e11 - 3.17367e11i) q^{89} -1.78016e11i q^{90} +4.67404e11 q^{92} +(-7.92030e10 - 1.37184e11i) q^{93} +(-4.27831e11 - 2.47008e11i) q^{94} +(-5.35802e11 + 9.28037e11i) q^{95} +(8.42924e10 - 4.86662e10i) q^{96} -3.89725e11i q^{97} -7.20367e11 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 $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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
$3$	444.082	+	256.391i	0.609167	+	0.351702i	0.772639	−	0.634845i	$-0.218936\pi$
$3$	444.082	+	256.391i	0.609167	+	0.351702i	−0.163473	+	0.986548i	$0.552270\pi$
$4$	−1024.00	+	1773.62i	−0.250000	+	0.433013i
$5$	12687.9	−	7325.35i	0.812024	−	0.468822i	−0.0356345	−	0.999365i	$-0.511345\pi$
$5$	12687.9	−	7325.35i	0.812024	−	0.468822i	0.847658	+	0.530543i	$0.178012\pi$
$6$			23205.9i			0.497382i
$7$		0			0
$7$		0			0
$8$	−92681.9			−0.353553
$9$	−134248.	−	232524.i	−0.252611	−	0.437535i
$10$	574187.	+	331507.i	0.574187	+	0.331507i
$11$	1.34149e6	−	2.32353e6i	0.757235	−	1.31157i	−0.187020	−	0.982356i	$-0.559883\pi$
$11$	1.34149e6	−	2.32353e6i	0.757235	−	1.31157i	0.944255	−	0.329214i	$-0.106784\pi$
$12$	−909481.	+	525089.i	−0.304583	+	0.175851i
$13$			1.34691e6i			0.279048i	0.990219	+	0.139524i	$0.0445573\pi$
$13$			1.34691e6i			0.279048i	−0.990219	+	0.139524i	$0.955443\pi$
$14$		0			0
$15$	7.51261e6			0.659544
$16$	−2.09715e6	−	3.63237e6i	−0.125000	−	0.216506i
$17$	−6.20477e6	−	3.58233e6i	−0.257059	−	0.148413i	0.365933	−	0.930641i	$-0.380750\pi$
$17$	−6.20477e6	−	3.58233e6i	−0.257059	−	0.148413i	−0.622992	+	0.782228i	$0.714083\pi$
$18$	6.07536e6	−	1.05228e7i	0.178623	−	0.309384i
$19$	−6.33442e7	+	3.65718e7i	−1.34644	+	0.777365i	−0.987743	−	0.156091i	$-0.950111\pi$
$19$	−6.33442e7	+	3.65718e7i	−1.34644	+	0.777365i	−0.358692	+	0.933456i	$0.616777\pi$
$20$			3.00046e7i			0.468822i
$21$		0			0
$22$	1.21418e8			1.07089
$23$	−1.14112e8	−	1.97648e8i	−0.770843	−	1.33514i	−0.937102	−	0.349057i	$-0.886502\pi$
$23$	−1.14112e8	−	1.97648e8i	−0.770843	−	1.33514i	0.166259	−	0.986082i	$-0.446831\pi$
$24$	−4.11584e7	−	2.37628e7i	−0.215373	−	0.124346i
$25$	−1.47489e7	+	2.55459e7i	−0.0604117	+	0.104636i
$26$	−5.27880e7	+	3.04772e7i	−0.170881	+	0.0986585i
$27$		−	4.10193e8i		−	1.05878i
$28$		0			0
$29$	−5.69081e8			−0.956723			−0.478362	−	0.878163i	$-0.658769\pi$
$29$	−5.69081e8			−0.956723			−0.478362	+	0.878163i	$0.658769\pi$
$30$	1.69991e8	+	2.94433e8i	0.233184	+	0.403886i
$31$	−2.67528e8	−	1.54457e8i	−0.301439	−	0.174036i	0.341650	−	0.939827i	$-0.389014\pi$
$31$	−2.67528e8	−	1.54457e8i	−0.301439	−	0.174036i	−0.643089	+	0.765791i	$0.722347\pi$
$32$	9.49063e7	−	1.64382e8i	0.0883883	−	0.153093i
$33$	1.19146e9	−	6.87891e8i	0.922565	−	0.532643i
$34$		−	3.24235e8i		−	0.209888i
$35$		0			0
$36$	5.49879e8			0.252611
$37$	−8.51831e8	−	1.47542e9i	−0.332004	−	0.575048i	0.650901	−	0.759163i	$-0.274391\pi$
$37$	−8.51831e8	−	1.47542e9i	−0.332004	−	0.575048i	−0.982905	+	0.184115i	$0.941058\pi$
$38$	−2.86663e9	−	1.65505e9i	−0.952073	−	0.549680i
$39$	−3.45336e8	+	5.98140e8i	−0.0981420	+	0.169987i
$40$	−1.17594e9	+	6.78927e8i	−0.287094	+	0.165754i
$41$			5.37658e9i			1.13189i	0.824444	+	0.565944i	$0.191488\pi$
$41$			5.37658e9i			1.13189i	−0.824444	+	0.565944i	$0.808512\pi$
$42$		0			0
$43$	−9.19904e9			−1.45523			−0.727615	−	0.685985i	$-0.759371\pi$
$43$	−9.19904e9			−1.45523			−0.727615	+	0.685985i	$0.759371\pi$
$44$	2.74737e9	+	4.75858e9i	0.378618	+	0.655785i
$45$	−3.40664e9	−	1.96682e9i	−0.410252	−	0.236859i
$46$	5.16414e9	−	8.94455e9i	0.545068	−	0.944086i
$47$	−9.45381e9	+	5.45816e9i	−0.877041	+	0.506360i	−0.869682	−	0.493613i	$-0.835676\pi$
$47$	−9.45381e9	+	5.45816e9i	−0.877041	+	0.506360i	−0.00735915	+	0.999973i	$0.502343\pi$
$48$		−	2.15076e9i		−	0.175851i
$49$		0			0
$50$	−1.33492e9			−0.0854350
$51$	−1.83695e9	−	3.18170e9i	−0.104394	−	0.180816i
$52$	−2.38891e9	−	1.37924e9i	−0.120831	−	0.0697621i
$53$	7.92816e9	−	1.37320e10i	0.357698	−	0.619552i	−0.629877	−	0.776695i	$-0.716895\pi$
$53$	7.92816e9	−	1.37320e10i	0.357698	−	0.619552i	0.987576	+	0.157143i	$0.0502282\pi$
$54$	1.60762e10	−	9.28161e9i	0.648368	−	0.374335i
$55$		−	3.93075e10i		−	1.42003i
$56$		0			0
$57$	−3.75067e10			−1.09360
$58$	−1.28768e10	−	2.23033e10i	−0.338253	−	0.585871i
$59$	−1.75457e10	−	1.01300e10i	−0.415967	−	0.240159i	0.277383	−	0.960759i	$-0.410533\pi$
$59$	−1.75457e10	−	1.01300e10i	−0.415967	−	0.240159i	−0.693350	+	0.720601i	$0.743866\pi$
$60$	−7.69292e9	+	1.33245e10i	−0.164886	+	0.285591i
$61$	−2.38455e10	+	1.37672e10i	−0.462837	+	0.267219i	−0.713236	−	0.700924i	$-0.752771\pi$
$61$	−2.38455e10	+	1.37672e10i	−0.462837	+	0.267219i	0.250399	+	0.968143i	$0.419438\pi$
$62$		−	1.39799e10i		−	0.246124i
$63$		0			0
$64$	8.58993e9			0.125000
$65$	9.86660e9	+	1.70895e10i	0.130824	+	0.226594i
$66$	5.39194e10	+	3.11304e10i	0.652352	+	0.376635i
$67$	−3.35056e10	+	5.80333e10i	−0.370398	+	0.641547i	−0.989627	−	0.143663i	$-0.954112\pi$
$67$	−3.35056e10	+	5.80333e10i	−0.370398	+	0.641547i	0.619229	+	0.785210i	$0.287445\pi$
$68$	1.27074e10	−	7.33661e9i	0.128529	−	0.0742065i
$69$		−	1.17030e11i		−	1.08443i
$70$		0			0
$71$	7.34393e10			0.573295			0.286648	−	0.958036i	$-0.407459\pi$
$71$	7.34393e10			0.573295			0.286648	+	0.958036i	$0.407459\pi$
$72$	1.24423e10	+	2.15508e10i	0.0893114	+	0.154692i
$73$	−5.62093e10	−	3.24525e10i	−0.371425	−	0.214442i	0.302656	−	0.953100i	$-0.402127\pi$
$73$	−5.62093e10	−	3.24525e10i	−0.371425	−	0.214442i	−0.674081	+	0.738658i	$0.735460\pi$
$74$	3.85495e10	−	6.67697e10i	0.234762	−	0.406620i
$75$	−1.30995e10	+	7.56300e9i	−0.0736015	+	0.0424939i
$76$		−	1.49798e11i		−	0.777365i
$77$		0			0
$78$	−3.12563e10			−0.138794
$79$	−3.16413e9	−	5.48043e9i	−0.0130164	−	0.0225451i	0.859444	−	0.511230i	$-0.170810\pi$
$79$	−3.16413e9	−	5.48043e9i	−0.0130164	−	0.0225451i	−0.872460	+	0.488685i	$0.837477\pi$
$80$	−5.32168e10	−	3.07247e10i	−0.203006	−	0.117206i
$81$	3.38251e10	−	5.85869e10i	0.119765	−	0.207439i
$82$	−2.10718e11	+	1.21658e11i	−0.693136	+	0.400183i
$83$			5.07191e11i			1.55133i	0.631147	+	0.775663i	$0.282585\pi$
$83$			5.07191e11i			1.55133i	−0.631147	+	0.775663i	$0.717415\pi$
$84$		0			0
$85$	−1.04967e11			−0.278317
$86$	−2.08151e11	−	3.60527e11i	−0.514502	−	0.891143i
$87$	−2.52719e11	−	1.45907e11i	−0.582804	−	0.336482i
$88$	−1.24332e11	+	2.15349e11i	−0.267723	+	0.463710i
$89$	5.49695e11	−	3.17367e11i	1.10607	−	0.638589i	0.168260	−	0.985743i	$-0.446185\pi$
$89$	5.49695e11	−	3.17367e11i	1.10607	−	0.638589i	0.937808	+	0.347154i	$0.112852\pi$
$90$		−	1.78016e11i		−	0.334969i
$91$		0			0
$92$	4.67404e11			0.770843
$93$	−7.92030e10	−	1.37184e11i	−0.122418	−	0.212033i
$94$	−4.27831e11	−	2.47008e11i	−0.620161	−	0.358050i
$95$	−5.35802e11	+	9.28037e11i	−0.728891	+	1.26248i
$96$	8.42924e10	−	4.86662e10i	0.107686	−	0.0621728i
$97$		−	3.89725e11i		−	0.467873i	−0.972252	−	0.233937i	$-0.924839\pi$
$97$		−	3.89725e11i		−	0.467873i	0.972252	−	0.233937i	$-0.0751609\pi$
$98$		0			0
$99$	−7.20367e11			−0.765143
$100$	−3.02058e10	−	5.23180e10i	−0.0302058	−	0.0523180i
$101$	−2.37129e9	−	1.36906e9i	−0.00223386	−	0.00128972i	0.498883	−	0.866670i	$-0.333744\pi$
$101$	−2.37129e9	−	1.36906e9i	−0.00223386	−	0.00128972i	−0.501117	+	0.865380i	$0.667077\pi$
$102$	8.31310e10	−	1.43987e11i	0.0738180	−	0.127856i
$103$	1.83996e12	−	1.06230e12i	1.54094	−	0.889663i	0.542161	−	0.840274i	$-0.317606\pi$
$103$	1.83996e12	−	1.06230e12i	1.54094	−	0.889663i	0.998780	−	0.0493885i	$-0.0157272\pi$
$104$		−	1.24834e11i		−	0.0986585i
$105$		0			0
$106$	7.17575e11			0.505862
$107$	−9.41831e11	−	1.63130e12i	−0.627582	−	1.08700i	−0.988035	−	0.154227i	$-0.950711\pi$
$107$	−9.41831e11	−	1.63130e12i	−0.627582	−	1.08700i	0.360453	−	0.932777i	$-0.382622\pi$
$108$	7.27527e11	+	4.20038e11i	0.458465	+	0.264695i
$109$	1.30905e12	−	2.26734e12i	0.780544	−	1.35194i	−0.151081	−	0.988521i	$-0.548276\pi$
$109$	1.30905e12	−	2.26734e12i	0.780544	−	1.35194i	0.931625	−	0.363420i	$-0.118391\pi$
$110$	1.54053e12	−	8.89426e11i	0.869590	−	0.502058i
$111$		−	8.73608e11i		−	0.467067i
$112$		0			0
$113$	2.59357e12			1.24574			0.622869	−	0.782326i	$-0.285967\pi$
$113$	2.59357e12			1.24574			0.622869	+	0.782326i	$0.285967\pi$
$114$	−8.48681e11	−	1.46996e12i	−0.386647	−	0.669693i
$115$	−2.89569e12	−	1.67183e12i	−1.25189	−	0.722776i
$116$	5.82739e11	−	1.00933e12i	0.239181	−	0.414273i
$117$	3.13189e11	−	1.80820e11i	0.122093	−	0.0704906i
$118$		−	9.16865e11i		−	0.339636i
$119$		0			0
$120$	−6.96283e11			−0.233184
$121$	−2.02997e12	−	3.51600e12i	−0.646810	−	1.12031i
$122$	−1.07913e12	−	6.23034e11i	−0.327275	−	0.188952i
$123$	−1.37851e12	+	2.38765e12i	−0.398087	+	0.689508i
$124$	5.47897e11	−	3.16329e11i	0.150719	−	0.0870179i
$125$			4.00899e12i			1.05093i
$126$		0			0
$127$	6.80221e12			1.62117			0.810583	−	0.585623i	$-0.199150\pi$
$127$	6.80221e12			1.62117			0.810583	+	0.585623i	$0.199150\pi$
$128$	1.94368e11	+	3.36655e11i	0.0441942	+	0.0765466i
$129$	−4.08513e12	−	2.35855e12i	−0.886478	−	0.511808i
$130$	−4.46511e11	+	7.73381e11i	−0.0925066	+	0.160226i
$131$	7.06312e12	−	4.07789e12i	1.39755	−	0.806878i	0.403418	−	0.915016i	$-0.367822\pi$
$131$	7.06312e12	−	4.07789e12i	1.39755	−	0.806878i	0.994136	+	0.108137i	$0.0344886\pi$
$132$			2.81760e12i			0.532643i
$133$		0			0
$134$	−3.03258e12			−0.523821
$135$	−3.00481e12	−	5.20448e12i	−0.496380	−	0.859755i
$136$	5.75070e11	+	3.32017e11i	0.0908840	+	0.0524719i
$137$	−4.07097e12	+	7.05112e12i	−0.615707	+	1.06644i	0.374553	+	0.927206i	$0.377796\pi$
$137$	−4.07097e12	+	7.05112e12i	−0.615707	+	1.06644i	−0.990260	+	0.139230i	$0.955537\pi$
$138$	4.58661e12	−	2.64808e12i	0.664075	−	0.383404i
$139$		−	1.24727e13i		−	1.72930i	−0.502371	−	0.864652i	$-0.667539\pi$
$139$		−	1.24727e13i		−	1.72930i	0.502371	−	0.864652i	$-0.332461\pi$
$140$		0			0
$141$	−5.59769e12			−0.712352
$142$	1.66174e12	+	2.87822e12i	0.202691	+	0.351070i
$143$	3.12959e12	+	1.80687e12i	0.365991	+	0.211305i
$144$	−5.63076e11	+	9.75276e11i	−0.0631527	+	0.109384i
$145$	−7.22043e12	+	4.16872e12i	−0.776882	+	0.448533i
$146$		−	2.93726e12i		−	0.303267i
$147$		0			0
$148$	3.48910e12			0.332004
$149$	−2.91858e12	−	5.05512e12i	−0.266719	−	0.461970i	0.701294	−	0.712872i	$-0.252606\pi$
$149$	−2.91858e12	−	5.05512e12i	−0.266719	−	0.461970i	−0.968012	+	0.250902i	$0.919273\pi$
$150$	−5.92815e11	−	3.42262e11i	−0.0520441	−	0.0300477i
$151$	−4.06127e12	+	7.03433e12i	−0.342610	+	0.593419i	−0.984917	−	0.173029i	$-0.944644\pi$
$151$	−4.06127e12	+	7.03433e12i	−0.342610	+	0.593419i	0.642306	+	0.766448i	$0.277978\pi$
$152$	5.87086e12	−	3.38954e12i	0.476037	−	0.274840i
$153$			1.92368e12i			0.149963i
$154$		0			0
$155$	−4.52581e12			−0.326367
$156$	−7.07249e11	−	1.22499e12i	−0.0490710	−	0.0849934i
$157$	−2.00528e13	−	1.15775e13i	−1.33899	−	0.773065i	−0.352330	−	0.935876i	$-0.614610\pi$
$157$	−2.00528e13	−	1.15775e13i	−1.33899	−	0.773065i	−0.986657	+	0.162811i	$0.947944\pi$
$158$	1.43192e11	−	2.48016e11i	0.00920400	−	0.0159418i
$159$	7.04151e12	−	4.06542e12i	0.435796	−	0.251607i
$160$		−	2.78088e12i		−	0.165754i
$161$		0			0
$162$	3.06150e12			0.169373
$163$	−4.26181e12	−	7.38166e12i	−0.227231	−	0.393576i	0.729755	−	0.683708i	$-0.239634\pi$
$163$	−4.26181e12	−	7.38166e12i	−0.227231	−	0.393576i	−0.956987	+	0.290132i	$0.906301\pi$
$164$	−9.53601e12	−	5.50562e12i	−0.490121	−	0.282972i
$165$	1.00781e13	−	1.74557e13i	0.499430	−	0.865037i
$166$	−1.98778e13	+	1.14764e13i	−0.949990	+	0.548477i
$167$		−	2.04015e13i		−	0.940509i	−0.882531	−	0.470255i	$-0.844162\pi$
$167$		−	2.04015e13i		−	0.940509i	0.882531	−	0.470255i	$-0.155838\pi$
$168$		0			0
$169$	2.14839e13			0.922132
$170$	−2.37514e12	−	4.11385e12i	−0.0983999	−	0.170434i
$171$	1.70076e13	+	9.81936e12i	0.680248	+	0.392741i
$172$	9.41982e12	−	1.63156e13i	0.363808	−	0.630133i
$173$	7.36291e12	−	4.25098e12i	0.274646	−	0.158567i	−0.356351	−	0.934352i	$-0.615979\pi$
$173$	7.36291e12	−	4.25098e12i	0.274646	−	0.158567i	0.630997	+	0.775785i	$0.282646\pi$
$174$		−	1.32060e13i		−	0.475857i
$175$		0			0
$176$	−1.12532e13			−0.378618
$177$	−5.19449e12	−	8.99713e12i	−0.168929	−	0.292593i
$178$	2.48764e13	+	1.43624e13i	0.782108	+	0.451550i
$179$	9.88862e12	−	1.71276e13i	0.300620	−	0.520689i	−0.675657	−	0.737216i	$-0.736140\pi$
$179$	9.88862e12	−	1.71276e13i	0.300620	−	0.520689i	0.976276	+	0.216528i	$0.0694731\pi$
$180$	6.97679e12	−	4.02805e12i	0.205126	−	0.118430i
$181$			2.46719e13i			0.701667i	0.936438	+	0.350833i	$0.114102\pi$
$181$			2.46719e13i			0.701667i	−0.936438	+	0.350833i	$0.885898\pi$
$182$		0			0
$183$	−1.41192e13			−0.375926
$184$	1.05762e13	+	1.83184e13i	0.272534	+	0.472043i
$185$	−2.16159e13	−	1.24799e13i	−0.539190	−	0.311302i
$186$	3.58432e12	−	6.20822e12i	0.0865623	−	0.149930i
$187$	−1.66473e13	+	9.61130e12i	−0.389308	+	0.224767i
$188$		−	2.23566e13i		−	0.506360i
$189$		0			0
$190$	−4.84953e13			−1.03081
$191$	2.07509e13	+	3.59417e13i	0.427403	+	0.740283i	0.996641	−	0.0818891i	$-0.0260953\pi$
$191$	2.07509e13	+	3.59417e13i	0.427403	+	0.740283i	−0.569239	+	0.822172i	$0.692762\pi$
$192$	3.81464e12	+	2.20238e12i	0.0761458	+	0.0439628i
$193$	−2.98993e13	+	5.17871e13i	−0.578519	+	1.00202i	0.417131	+	0.908846i	$0.363036\pi$
$193$	−2.98993e13	+	5.17871e13i	−0.578519	+	1.00202i	−0.995650	+	0.0931772i	$0.970298\pi$
$194$	1.52741e13	−	8.81848e12i	0.286513	−	0.165418i
$195$			1.01188e13i			0.184045i
$196$		0			0
$197$	−5.28263e13			−0.903760			−0.451880	−	0.892079i	$-0.649246\pi$
$197$	−5.28263e13			−0.903760			−0.451880	+	0.892079i	$0.649246\pi$
$198$	−1.63000e13	−	2.82325e13i	−0.270519	−	0.468552i
$199$	−6.62250e13	−	3.82350e13i	−1.06636	−	0.615663i	−0.139175	−	0.990268i	$-0.544445\pi$
$199$	−6.62250e13	−	3.82350e13i	−1.06636	−	0.615663i	−0.927185	+	0.374605i	$0.877778\pi$
$200$	1.36696e12	−	2.36764e12i	0.0213588	−	0.0369944i
$201$	−2.97585e13	+	1.71811e13i	−0.451268	+	0.260539i
$202$		−	1.23913e11i		−	0.00182394i
$203$		0			0
$204$	7.52416e12			0.104394
$205$	3.93853e13	+	6.82174e13i	0.530654	+	0.919119i
$206$	8.32673e13	+	4.80744e13i	1.08961	+	0.629087i
$207$	−3.06387e13	+	5.30677e13i	−0.389446	+	0.674541i
$208$	4.89249e12	−	2.82468e12i	0.0604157	−	0.0348810i
$209$			1.96243e14i			2.35459i
$210$		0			0
$211$	5.17345e13			0.586254			0.293127	−	0.956074i	$-0.405304\pi$
$211$	5.17345e13			0.586254			0.293127	+	0.956074i	$0.405304\pi$
$212$	1.62369e13	+	2.81231e13i	0.178849	+	0.309776i
$213$	3.26131e13	+	1.88292e13i	0.349232	+	0.201629i
$214$	4.26224e13	−	7.38242e13i	0.443768	−	0.768628i
$215$	−1.16716e14	+	6.73862e13i	−1.18168	+	0.682244i
$216$			3.80175e13i			0.374335i
$217$		0			0
$218$	1.18482e14			1.10386
$219$	−1.66410e13	−	2.88231e13i	−0.150840	−	0.261262i
$220$	6.97165e13	+	4.02508e13i	0.614893	+	0.355009i
$221$	4.82508e12	−	8.35729e12i	0.0414144	−	0.0717318i
$222$	3.42383e13	−	1.97675e13i	0.286019	−	0.165133i
$223$			6.07846e13i			0.494270i	0.968981	+	0.247135i	$0.0794891\pi$
$223$			6.07846e13i			0.494270i	−0.968981	+	0.247135i	$0.920511\pi$
$224$		0			0
$225$	7.92005e12			0.0610425
$226$	5.86857e13	+	1.01647e14i	0.440435	+	0.762856i
$227$	1.40116e14	+	8.08961e13i	1.02408	+	0.591251i	0.915282	−	0.402813i	$-0.131967\pi$
$227$	1.40116e14	+	8.08961e13i	1.02408	+	0.591251i	0.108795	+	0.994064i	$0.465301\pi$
$228$	3.84069e13	−	6.65227e13i	0.273401	−	0.473545i
$229$	−7.46197e13	+	4.30817e13i	−0.517417	+	0.298731i	−0.735877	−	0.677115i	$-0.763230\pi$
$229$	−7.46197e13	+	4.30817e13i	−0.517417	+	0.298731i	0.218460	+	0.975846i	$0.429897\pi$
$230$		−	1.51316e14i		−	1.02216i
$231$		0			0
$232$	5.27435e13			0.338253
$233$	7.78131e13	+	1.34776e14i	0.486314	+	0.842321i	0.999876	−	0.0157316i	$-0.00500772\pi$
$233$	7.78131e13	+	1.34776e14i	0.486314	+	0.842321i	−0.513562	+	0.858052i	$0.671674\pi$
$234$	1.41733e13	+	8.18298e12i	0.0863330	+	0.0498444i
$235$	−7.99658e13	+	1.38505e14i	−0.474785	+	0.822352i
$236$	3.59336e13	−	2.07463e13i	0.207983	−	0.120079i
$237$		−	3.24502e12i		−	0.0183116i
$238$		0			0
$239$	2.13466e14			1.14536			0.572679	−	0.819780i	$-0.305904\pi$
$239$	2.13466e14			1.14536			0.572679	+	0.819780i	$0.305904\pi$
$240$	−1.57551e13	−	2.72886e13i	−0.0824429	−	0.142795i
$241$	9.99225e13	+	5.76903e13i	0.509989	+	0.294442i	0.732829	−	0.680413i	$-0.238199\pi$
$241$	9.99225e13	+	5.76903e13i	0.509989	+	0.294442i	−0.222840	+	0.974855i	$0.571533\pi$
$242$	9.18658e13	−	1.59116e14i	0.457364	−	0.792177i
$243$	−1.58746e14	+	9.16518e13i	−0.771017	+	0.445147i
$244$		−	5.63906e13i		−	0.267219i
$245$		0			0
$246$	−1.24768e14			−0.562981
$247$	−4.92590e13	−	8.53192e13i	−0.216922	−	0.375720i
$248$	2.47950e13	+	1.43154e13i	0.106575	+	0.0615309i
$249$	−1.30039e14	+	2.25235e14i	−0.545605	+	0.945016i
$250$	−1.57120e14	+	9.07132e13i	−0.643563	+	0.371561i
$251$			3.21279e14i			1.28481i	0.766364	+	0.642406i	$0.222064\pi$
$251$			3.21279e14i			1.28481i	−0.766364	+	0.642406i	$0.777936\pi$
$252$		0			0
$253$	−6.12322e14			−2.33484
$254$	1.53916e14	+	2.66591e14i	0.573169	+	0.992758i
$255$	−4.66141e13	−	2.69126e13i	−0.169541	−	0.0978848i
$256$	−8.79609e12	+	1.52353e13i	−0.0312500	+	0.0541266i
$257$	2.96288e14	−	1.71062e14i	1.02829	−	0.593683i	0.111795	−	0.993731i	$-0.464340\pi$
$257$	2.96288e14	−	1.71062e14i	1.02829	−	0.593683i	0.916494	+	0.400049i	$0.131007\pi$
$258$		−	2.13472e14i		−	0.723806i
$259$		0			0
$260$	−4.04136e13			−0.130824
$261$	7.63979e13	+	1.32325e14i	0.241679	+	0.418600i
$262$	3.19640e14	+	1.84544e14i	0.988220	+	0.570549i
$263$	5.15761e13	−	8.93325e13i	0.155853	−	0.269945i	−0.777517	−	0.628863i	$-0.783521\pi$
$263$	5.15761e13	−	8.93325e13i	0.155853	−	0.269945i	0.933369	+	0.358918i	$0.116854\pi$
$264$	−1.10427e14	+	6.37551e13i	−0.326176	+	0.188318i
$265$		−	2.32306e14i		−	0.670788i
$266$		0			0
$267$	3.25480e14			0.898373
$268$	−6.86194e13	−	1.18852e14i	−0.185199	−	0.320774i
$269$	−4.05993e14	−	2.34400e14i	−1.07153	−	0.618650i	−0.142933	−	0.989732i	$-0.545653\pi$
$269$	−4.05993e14	−	2.34400e14i	−1.07153	−	0.618650i	−0.928600	+	0.371083i	$0.878987\pi$
$270$	1.35982e14	−	2.35528e14i	0.350993	−	0.607938i
$271$	−3.78122e14	+	2.18309e14i	−0.954589	+	0.551132i	−0.894503	−	0.447061i	$-0.852471\pi$
$271$	−3.78122e14	+	2.18309e14i	−0.954589	+	0.551132i	−0.0600855	+	0.998193i	$0.519137\pi$
$272$			3.00507e13i			0.0742065i
$273$		0			0
$274$	−3.68462e14			−0.870741
$275$	3.95711e13	+	6.85391e13i	0.0914917	+	0.158468i
$276$	2.07566e14	+	1.19838e14i	0.469572	+	0.271107i
$277$	9.87191e13	−	1.70986e14i	0.218536	−	0.378515i	−0.735825	−	0.677172i	$-0.763205\pi$
$277$	9.87191e13	−	1.70986e14i	0.218536	−	0.378515i	0.954361	+	0.298657i	$0.0965387\pi$
$278$	4.88828e14	−	2.82225e14i	1.05898	−	0.611401i
$279$			8.29422e13i			0.175853i
$280$		0			0
$281$	8.30058e13			0.168605			0.0843025	−	0.996440i	$-0.473134\pi$
$281$	8.30058e13			0.168605			0.0843025	+	0.996440i	$0.473134\pi$
$282$	−1.26661e14	−	2.19384e14i	−0.251854	−	0.436225i
$283$	−6.14491e14	−	3.54776e14i	−1.19618	−	0.690615i	−0.236479	−	0.971637i	$-0.575993\pi$
$283$	−6.14491e14	−	3.54776e14i	−1.19618	−	0.690615i	−0.959701	+	0.281022i	$0.909327\pi$
$284$	−7.52019e13	+	1.30253e14i	−0.143324	+	0.248244i
$285$	−4.75881e14	+	2.74750e14i	−0.888033	+	0.512706i
$286$			1.63539e14i			0.298831i
$287$		0			0
$288$	−5.09638e13			−0.0893114
$289$	−2.65645e14	−	4.60111e14i	−0.455947	−	0.789724i
$290$	−3.26759e14	−	1.88655e14i	−0.549339	−	0.317161i
$291$	9.99221e13	−	1.73070e14i	0.164552	−	0.285013i
$292$	1.15117e14	−	6.64626e13i	0.185712	−	0.107221i
$293$			1.90883e14i			0.301691i	0.988557	+	0.150845i	$0.0481996\pi$
$293$			1.90883e14i			0.301691i	−0.988557	+	0.150845i	$0.951800\pi$
$294$		0			0
$295$	−2.96824e14			−0.450367
$296$	7.89494e13	+	1.36744e14i	0.117381	+	0.203310i
$297$	−9.53094e14	−	5.50269e14i	−1.38866	−	0.801745i
$298$	1.32080e14	−	2.28769e14i	0.188599	−	0.326662i
$299$	2.66215e14	−	1.53699e14i	0.372568	−	0.215102i
$300$		−	3.09780e13i		−	0.0424939i
$301$		0			0
$302$	−3.67585e14			−0.484524
$303$	−7.02031e11	−	1.21595e12i	−0.000907195	−	0.00157131i
$304$	2.65685e14	+	1.53393e14i	0.336609	+	0.194341i
$305$	−2.01699e14	+	3.49354e14i	−0.250556	+	0.433976i
$306$	−7.53924e13	+	4.35278e13i	−0.0918331	+	0.0530199i
$307$		−	6.74575e14i		−	0.805750i	−0.915255	−	0.402875i	$-0.868011\pi$
$307$		−	6.74575e14i		−	0.805750i	0.915255	−	0.402875i	$-0.131989\pi$
$308$		0			0
$309$	1.08946e15			1.25159
$310$	−1.02407e14	−	1.77375e14i	−0.115388	−	0.199858i
$311$	5.62583e14	+	3.24807e14i	0.621762	+	0.358974i	0.777555	−	0.628815i	$-0.216460\pi$
$311$	5.62583e14	+	3.24807e14i	0.621762	+	0.358974i	−0.155793	+	0.987790i	$0.549793\pi$
$312$	3.20064e13	−	5.54368e13i	0.0346984	−	0.0600994i
$313$	1.00138e15	−	5.78145e14i	1.06496	−	0.614853i	0.138157	−	0.990410i	$-0.455882\pi$
$313$	1.00138e15	−	5.78145e14i	1.06496	−	0.614853i	0.926799	+	0.375558i	$0.122549\pi$
$314$		−	1.04787e15i		−	1.09328i
$315$		0			0
$316$	1.29603e13			0.0130164
$317$	−8.96159e14	−	1.55219e15i	−0.883140	−	1.52964i	−0.847831	−	0.530266i	$-0.822092\pi$
$317$	−8.96159e14	−	1.55219e15i	−0.883140	−	1.52964i	−0.0353083	−	0.999376i	$-0.511241\pi$
$318$	3.18662e14	+	1.83980e14i	0.308154	+	0.177913i
$319$	−7.63416e14	+	1.32228e15i	−0.724464	+	1.25481i
$320$	1.08988e14	−	6.29242e13i	0.101503	−	0.0586028i
$321$		−	9.65909e14i		−	0.882889i
$322$		0			0
$323$	5.24049e14			0.461484
$324$	6.92739e13	+	1.19986e14i	0.0598824	+	0.103719i
$325$	−3.44081e13	−	1.98655e13i	−0.0291985	−	0.0168578i
$326$	1.92867e14	−	3.34056e14i	0.160677	−	0.278300i
$327$	1.16265e15	−	6.71258e14i	0.950963	−	0.549038i
$328$		−	4.98312e14i		−	0.400183i
$329$		0			0
$330$	9.12164e14			0.706300
$331$	−1.33115e14	−	2.30561e14i	−0.101218	−	0.175315i	0.810969	−	0.585089i	$-0.198941\pi$
$331$	−1.33115e14	−	2.30561e14i	−0.101218	−	0.175315i	−0.912187	+	0.409775i	$0.865607\pi$
$332$	−8.99565e14	−	5.19364e14i	−0.671744	−	0.387832i
$333$	−2.28713e14	+	3.96142e14i	−0.167736	+	0.290527i
$334$	7.99572e14	−	4.61633e14i	0.575942	−	0.332520i
$335$			9.81759e14i			0.694602i
$336$		0			0
$337$	−2.34808e14			−0.160300			−0.0801498	−	0.996783i	$-0.525540\pi$
$337$	−2.34808e14			−0.160300			−0.0801498	+	0.996783i	$0.525540\pi$
$338$	4.86125e14	+	8.41994e14i	0.326023	+	0.564688i
$339$	1.15176e15	+	6.64968e14i	0.758862	+	0.438129i
$340$	1.07486e14	−	1.86172e14i	0.0695793	−	0.120515i
$341$	−7.17771e14	+	4.14405e14i	−0.456520	+	0.263572i
$342$			8.88747e14i			0.555420i
$343$		0			0
$344$	8.52585e14			0.514502
$345$	−8.57282e14	−	1.48486e15i	−0.508404	−	0.880582i
$346$	3.33207e14	+	1.92377e14i	0.194204	+	0.112124i
$347$	−6.63393e14	+	1.14903e15i	−0.380009	+	0.658195i	−0.991063	−	0.133394i	$-0.957413\pi$
$347$	−6.63393e14	+	1.14903e15i	−0.380009	+	0.658195i	0.611054	+	0.791589i	$0.290746\pi$
$348$	5.17569e14	−	2.98818e14i	0.291402	−	0.168241i
$349$			2.62751e15i			1.45409i	0.686590	+	0.727045i	$0.259107\pi$
$349$			2.62751e15i			1.45409i	−0.686590	+	0.727045i	$0.740893\pi$
$350$		0			0
$351$	5.52494e14			0.295451
$352$	−2.54631e14	−	4.41034e14i	−0.133862	−	0.231855i
$353$	−2.19800e15	−	1.26902e15i	−1.13601	−	0.655873i	−0.190567	−	0.981674i	$-0.561033\pi$
$353$	−2.19800e15	−	1.26902e15i	−1.13601	−	0.655873i	−0.945438	+	0.325801i	$0.894366\pi$
$354$	2.35076e14	−	4.07163e14i	0.119451	−	0.206895i
$355$	9.31789e14	−	5.37968e14i	0.465530	−	0.268774i
$356$			1.29993e15i			0.638589i
$357$		0			0
$358$	8.95016e14			0.425141
$359$	−5.80208e14	−	1.00495e15i	−0.271030	−	0.469437i	0.698096	−	0.716004i	$-0.254031\pi$
$359$	−5.80208e14	−	1.00495e15i	−0.271030	−	0.469437i	−0.969126	+	0.246567i	$0.920698\pi$
$360$	3.15733e14	+	1.82289e14i	0.145046	+	0.0837423i
$361$	1.56834e15	−	2.71644e15i	0.708592	−	1.22732i
$362$	−9.66936e14	+	5.58261e14i	−0.429681	+	0.248077i
$363$		−	2.08186e15i		−	0.909938i
$364$		0			0
$365$	−9.50902e14			−0.402141
$366$	−3.19481e14	−	5.53357e14i	−0.132910	−	0.230207i
$367$	−1.55002e15	−	8.94904e14i	−0.634367	−	0.366252i	0.148074	−	0.988976i	$-0.452693\pi$
$367$	−1.55002e15	−	8.94904e14i	−0.634367	−	0.366252i	−0.782441	+	0.622724i	$0.786026\pi$
$368$	−4.78622e14	+	8.28998e14i	−0.192711	+	0.333785i
$369$	1.25018e15	−	7.21794e14i	0.495240	−	0.285927i
$370$		−	1.12955e15i		−	0.440247i
$371$		0			0
$372$	3.24415e14			0.122418
$373$	2.39198e15	+	4.14303e15i	0.888187	+	1.53838i	0.842017	+	0.539451i	$0.181368\pi$
$373$	2.39198e15	+	4.14303e15i	0.888187	+	1.53838i	0.0461697	+	0.998934i	$0.485298\pi$
$374$	−7.53369e14	−	4.34958e14i	−0.275282	−	0.158934i
$375$	−1.02787e15	+	1.78032e15i	−0.369616	+	0.640194i
$376$	8.76197e14	−	5.05873e14i	0.310081	−	0.179025i
$377$		−	7.66503e14i		−	0.266972i
$378$		0			0
$379$	−1.31568e15			−0.443931			−0.221965	−	0.975055i	$-0.571247\pi$
$379$	−1.31568e15			−0.443931			−0.221965	+	0.975055i	$0.571247\pi$
$380$	−1.09732e15	−	1.90062e15i	−0.364446	−	0.631239i
$381$	3.02074e15	+	1.74403e15i	0.987560	+	0.570168i
$382$	−9.39080e14	+	1.62653e15i	−0.302219	+	0.523459i
$383$	1.31260e15	−	7.57832e14i	0.415854	−	0.240093i	−0.277448	−	0.960741i	$-0.589489\pi$
$383$	1.31260e15	−	7.57832e14i	0.415854	−	0.240093i	0.693302	+	0.720647i	$0.256155\pi$
$384$			1.99337e14i			0.0621728i
$385$		0			0
$386$	−2.70618e15			−0.818149
$387$	1.23495e15	+	2.13900e15i	0.367607	+	0.636714i
$388$	6.91225e14	+	3.99079e14i	0.202595	+	0.116968i
$389$	1.38559e15	−	2.39991e15i	0.399886	−	0.692622i	−0.593826	−	0.804594i	$-0.702383\pi$
$389$	1.38559e15	−	2.39991e15i	0.399886	−	0.692622i	0.993711	+	0.111971i	$0.0357165\pi$
$390$	−3.96576e14	+	2.28963e14i	−0.112704	+	0.0650696i
$391$			1.63515e15i			0.457612i
$392$		0			0
$393$	4.18214e15			1.13512
$394$	−1.19532e15	−	2.07036e15i	−0.319527	−	0.553438i
$395$	−8.02921e13	−	4.63567e13i	−0.0211393	−	0.0122048i
$396$	7.37656e14	−	1.27766e15i	0.191286	−	0.331317i
$397$	−3.04662e15	+	1.75897e15i	−0.778172	+	0.449278i	−0.835782	−	0.549062i	$-0.814985\pi$
$397$	−3.04662e15	+	1.75897e15i	−0.778172	+	0.449278i	0.0576103	+	0.998339i	$0.481652\pi$
$398$		−	3.46064e15i		−	0.870679i
$399$		0			0
$400$	1.23723e14			0.0302058
$401$	−2.45890e15	−	4.25894e15i	−0.591391	−	1.02432i	−0.994045	−	0.108967i	$-0.965246\pi$
$401$	−2.45890e15	−	4.25894e15i	−0.591391	−	1.02432i	0.402655	−	0.915352i	$-0.368087\pi$
$402$	−1.34671e15	−	7.77526e14i	−0.319094	−	0.184229i
$403$	2.08041e14	−	3.60337e14i	0.0485644	−	0.0841160i
$404$	4.85640e12	−	2.80384e12i	0.00111693	−	0.000644860i
$405$		−	9.91123e14i		−	0.224594i
$406$		0			0
$407$	−4.57089e15			−1.00562
$408$	1.70252e14	+	2.94886e14i	0.0369090	+	0.0639282i
$409$	−2.52087e15	−	1.45543e15i	−0.538532	−	0.310921i	0.205952	−	0.978562i	$-0.433971\pi$
$409$	−2.52087e15	−	1.45543e15i	−0.538532	−	0.310921i	−0.744484	+	0.667641i	$0.767304\pi$
$410$	−1.78238e15	+	3.08717e15i	−0.375229	+	0.649915i
$411$	−3.61569e15	+	2.08752e15i	−0.750136	+	0.433091i
$412$			4.35120e15i			0.889663i
$413$		0			0
$414$	−2.77310e15			−0.550760
$415$	3.71535e15	+	6.43518e15i	0.727296	+	1.25971i
$416$	2.21409e14	+	1.27830e14i	0.0427204	+	0.0246646i
$417$	3.19789e15	−	5.53890e15i	0.608201	−	1.05343i
$418$	−7.69111e15	+	4.44046e15i	−1.44189	+	0.832474i
$419$			1.87176e14i			0.0345912i	0.999850	+	0.0172956i	$0.00550564\pi$
$419$			1.87176e14i			0.0345912i	−0.999850	+	0.0172956i	$0.994494\pi$
$420$		0			0
$421$	−2.95025e15			−0.529866			−0.264933	−	0.964267i	$-0.585350\pi$
$421$	−2.95025e15			−0.529866			−0.264933	+	0.964267i	$0.585350\pi$
$422$	1.17062e15	+	2.02757e15i	0.207272	+	0.359006i
$423$	2.53830e15	+	1.46549e15i	0.443100	+	0.255824i
$424$	−7.34797e14	+	1.27271e15i	−0.126466	+	0.219045i
$425$	1.83028e14	−	1.05671e14i	0.0310587	−	0.0179317i
$426$			1.70422e15i			0.285147i
$427$		0			0
$428$	3.85774e15			0.627582
$429$	9.26530e14	+	1.60480e15i	0.148633	+	0.257440i
$430$	−5.28197e15	−	3.04955e15i	−0.835575	−	0.482420i
$431$	9.33046e14	−	1.61608e15i	0.145559	−	0.252116i	−0.784022	−	0.620733i	$-0.786835\pi$
$431$	9.33046e14	−	1.61608e15i	0.145559	−	0.252116i	0.929581	+	0.368617i	$0.120169\pi$
$432$	−1.48997e15	+	8.60237e14i	−0.229233	+	0.132348i
$433$		−	6.43623e15i		−	0.976572i	−0.872684	−	0.488286i	$-0.837622\pi$
$433$		−	6.43623e15i		−	0.976572i	0.872684	−	0.488286i	$-0.162378\pi$
$434$		0			0
$435$	−4.27529e15			−0.631001
$436$	2.68094e15	+	4.64352e15i	0.390272	+	0.675971i
$437$	1.44567e16	+	8.34659e15i	2.07578	+	1.19845i
$438$	7.53088e14	−	1.30439e15i	0.106660	−	0.184740i
$439$	−3.66616e15	+	2.11666e15i	−0.512181	+	0.295708i	−0.733730	−	0.679441i	$-0.762222\pi$
$439$	−3.66616e15	+	2.11666e15i	−0.512181	+	0.295708i	0.221548	+	0.975149i	$0.428889\pi$
$440$			3.64309e15i			0.502058i
$441$		0			0
$442$	4.36717e14			0.0585688
$443$	3.53638e15	+	6.12518e15i	0.467882	+	0.810395i	0.999326	−	0.0366980i	$-0.0116840\pi$
$443$	3.53638e15	+	6.12518e15i	0.467882	+	0.810395i	−0.531445	+	0.847093i	$0.678351\pi$
$444$	1.54945e15	+	8.94575e14i	0.202246	+	0.116767i
$445$	4.64964e15	−	8.05342e15i	0.598769	−	1.03710i
$446$	−2.38226e15	+	1.37540e15i	−0.302677	+	0.174751i
$447$		−	2.99319e15i		−	0.375223i
$448$		0			0
$449$	−7.31324e15			−0.892549			−0.446274	−	0.894896i	$-0.647249\pi$
$449$	−7.31324e15			−0.892549			−0.446274	+	0.894896i	$0.647249\pi$
$450$	1.79210e14	+	3.10401e14i	0.0215818	+	0.0373808i
$451$	1.24926e16	+	7.21262e15i	1.48455	+	0.857105i
$452$	−2.65581e15	+	4.60000e15i	−0.311435	+	0.539421i
$453$	−3.60708e15	+	2.08255e15i	−0.417414	+	0.240994i
$454$			7.32188e15i			0.836156i
$455$		0			0
$456$	3.47620e15			0.386647
$457$	6.51453e15	+	1.12835e16i	0.715131	+	1.23864i	0.962909	+	0.269827i	$0.0869665\pi$
$457$	6.51453e15	+	1.12835e16i	0.715131	+	1.23864i	−0.247777	+	0.968817i	$0.579700\pi$
$458$	−3.37690e15	−	1.94966e15i	−0.365869	−	0.211235i
$459$	−1.46945e15	+	2.54516e15i	−0.157137	+	0.272169i
$460$	5.93037e15	−	3.42390e15i	0.625943	−	0.361388i
$461$			2.39251e15i			0.249257i	0.992203	+	0.124629i	$0.0397739\pi$
$461$			2.39251e15i			0.249257i	−0.992203	+	0.124629i	$0.960226\pi$
$462$		0			0
$463$	7.43873e15			0.755115			0.377557	−	0.925986i	$-0.376764\pi$
$463$	7.43873e15			0.755115			0.377557	+	0.925986i	$0.376764\pi$
$464$	1.19345e15	+	2.06712e15i	0.119590	+	0.207137i
$465$	−2.00983e15	−	1.16038e15i	−0.198812	−	0.114784i
$466$	−3.52142e15	+	6.09927e15i	−0.343876	+	0.595611i
$467$	2.18404e15	−	1.26096e15i	0.210552	−	0.121562i	−0.391016	−	0.920384i	$-0.627876\pi$
$467$	2.18404e15	−	1.26096e15i	0.210552	−	0.121562i	0.601568	+	0.798822i	$0.294543\pi$
$468$			7.40639e14i			0.0704906i
$469$		0			0
$470$	−7.23768e15			−0.671448
$471$	−5.93672e15	−	1.02827e16i	−0.543777	−	0.941850i
$472$	1.62617e15	+	9.38869e14i	0.147067	+	0.0849089i
$473$	−1.23404e16	+	2.13742e16i	−1.10195	+	1.90864i
$474$	1.27178e14	−	7.34264e13i	0.0112135	−	0.00647414i
$475$		−	2.15758e15i		−	0.187848i
$476$		0			0
$477$	−4.25735e15			−0.361434
$478$	4.83018e15	+	8.36612e15i	0.404945	+	0.701385i
$479$	−2.43833e15	−	1.40777e15i	−0.201873	−	0.116552i	0.395656	−	0.918399i	$-0.370517\pi$
$479$	−2.43833e15	−	1.40777e15i	−0.201873	−	0.116552i	−0.597529	+	0.801847i	$0.703851\pi$
$480$	7.12994e14	−	1.23494e15i	0.0582960	−	0.100972i
$481$	1.98726e15	−	1.14734e15i	0.160466	−	0.0926452i
$482$			5.22153e15i			0.416404i
$483$		0			0
$484$	8.31474e15			0.646810
$485$	−2.85487e15	−	4.94479e15i	−0.219349	−	0.379924i
$486$	−7.18400e15	−	4.14769e15i	−0.545191	−	0.314766i
$487$	1.11137e16	−	1.92494e16i	0.833074	−	1.44293i	−0.0625147	−	0.998044i	$-0.519912\pi$
$487$	1.11137e16	−	1.92494e16i	0.833074	−	1.44293i	0.895589	−	0.444883i	$-0.146755\pi$
$488$	2.21005e15	−	1.27597e15i	0.163638	−	0.0944762i
$489$		−	4.37076e15i		−	0.319671i
$490$		0			0
$491$	2.73159e16			1.94952			0.974758	−	0.223265i	$-0.0716714\pi$
$491$	2.73159e16			1.94952			0.974758	+	0.223265i	$0.0716714\pi$
$492$	−2.82318e15	−	4.88990e15i	−0.199044	−	0.344754i
$493$	3.53102e15	+	2.03864e15i	0.245934	+	0.141990i
$494$	2.22921e15	−	3.86110e15i	0.153387	−	0.265674i
$495$	−9.13992e15	+	5.27694e15i	−0.621314	+	0.358716i
$496$			1.29568e15i			0.0870179i
$497$		0			0
$498$	−1.17698e16			−0.771603
$499$	−9.95390e15	−	1.72407e16i	−0.644748	−	1.11674i	−0.984360	−	0.176171i	$-0.943629\pi$
$499$	−9.95390e15	−	1.72407e16i	−0.644748	−	1.11674i	0.339612	−	0.940566i	$-0.389704\pi$
$500$	−7.11043e15	−	4.10521e15i	−0.455068	−	0.262733i
$501$	5.23076e15	−	9.05994e15i	0.330779	−	0.572927i
$502$	−1.25915e16	+	7.26971e15i	−0.786784	+	0.454250i
$503$		−	6.87587e15i		−	0.424541i	−0.977211	−	0.212271i	$-0.931914\pi$
$503$		−	6.87587e15i		−	0.424541i	0.977211	−	0.212271i	$-0.0680858\pi$
$504$		0			0
$505$	−4.01154e13			−0.00241860
$506$	−1.38553e16	−	2.39980e16i	−0.825490	−	1.42979i
$507$	9.54063e15	+	5.50828e15i	0.561732	+	0.324316i
$508$	−6.96546e15	+	1.20645e16i	−0.405292	+	0.701986i
$509$	6.71112e15	−	3.87467e15i	0.385912	−	0.222807i	−0.294475	−	0.955659i	$-0.595145\pi$
$509$	6.71112e15	−	3.87467e15i	0.385912	−	0.222807i	0.680387	+	0.732853i	$0.261812\pi$
$510$		−	2.43585e15i		−	0.138430i
$511$		0			0
$512$	−7.96131e14			−0.0441942
$513$	1.50015e16	+	2.59834e16i	0.823058	+	1.42558i
$514$	1.34085e16	+	7.74138e15i	0.727110	+	0.419797i
$515$	1.55635e16	−	2.69567e16i	0.834187	−	1.44485i
$516$	8.36635e15	−	4.83032e15i	0.443239	−	0.255904i
$517$			2.92882e16i			1.53373i
$518$		0			0
$519$	4.35965e15			0.223073
$520$	−9.14455e14	−	1.58388e15i	−0.0462533	−	0.0801130i
$521$	−2.06740e16	−	1.19361e16i	−1.03371	−	0.596811i	−0.115662	−	0.993289i	$-0.536899\pi$
$521$	−2.06740e16	−	1.19361e16i	−1.03371	−	0.596811i	−0.918044	+	0.396478i	$0.870232\pi$
$522$	−3.45737e15	+	5.98835e15i	−0.170893	+	0.295995i
$523$	1.80842e16	−	1.04409e16i	0.883670	−	0.510187i	0.0118030	−	0.999930i	$-0.496243\pi$
$523$	1.80842e16	−	1.04409e16i	0.883670	−	0.510187i	0.871867	+	0.489743i	$0.162910\pi$
$524$			1.67031e16i			0.806878i
$525$		0			0
$526$	4.66814e15			0.220409
$527$	1.10663e15	+	1.91675e15i	0.0516583	+	0.0894748i
$528$	−4.99736e15	−	2.88522e15i	−0.230641	−	0.133161i
$529$	−1.50860e16	+	2.61297e16i	−0.688398	+	1.19234i
$530$	9.10450e15	−	5.25648e15i	0.410772	−	0.237159i
$531$			5.43973e15i			0.242667i
$532$		0			0
$533$	−7.24179e15			−0.315851
$534$	7.36477e15	+	1.27562e16i	0.317623	+	0.550139i
$535$	−2.38997e16	−	1.37985e16i	−1.01922	−	0.588449i
$536$	3.10536e15	−	5.37864e15i	0.130955	−	0.226821i
$537$	8.78273e15	−	5.07071e15i	0.366255	−	0.211457i
$538$		−	2.12155e16i		−	0.874903i
$539$		0			0
$540$	1.23077e16			0.496380
$541$	−1.60100e16	−	2.77302e16i	−0.638569	−	1.10603i	−0.985747	−	0.168235i	$-0.946193\pi$
$541$	−1.60100e16	−	2.77302e16i	−0.638569	−	1.10603i	0.347177	−	0.937799i	$-0.387140\pi$
$542$	−1.71119e16	−	9.87954e15i	−0.674996	−	0.389709i
$543$	−6.32565e15	+	1.09564e16i	−0.246778	+	0.427432i
$544$	−1.17774e15	+	6.79971e14i	−0.0454420	+	0.0262359i
$545$		−	3.83570e16i		−	1.46375i
$546$		0			0
$547$	−3.33242e16			−1.24404			−0.622022	−	0.783000i	$-0.713688\pi$
$547$	−3.33242e16			−1.24404			−0.622022	+	0.783000i	$0.713688\pi$
$548$	−8.33734e15	−	1.44407e16i	−0.307854	−	0.533218i
$549$	6.40242e15	+	3.69644e15i	0.233835	+	0.135005i
$550$	−1.79078e15	+	3.10173e15i	−0.0646944	+	0.112054i
$551$	3.60480e16	−	2.08123e16i	1.28817	−	0.743723i
$552$			1.08465e16i			0.383404i
$553$		0			0
$554$	8.93503e15			0.309056
$555$	−6.39948e15	−	1.10842e16i	−0.218971	−	0.379269i
$556$	2.21218e16	+	1.27720e16i	0.748811	+	0.432326i
$557$	−1.50168e15	+	2.60098e15i	−0.0502857	+	0.0870975i	−0.890073	−	0.455819i	$-0.849347\pi$
$557$	−1.50168e15	+	2.60098e15i	−0.0502857	+	0.0870975i	0.839787	+	0.542916i	$0.182680\pi$
$558$	−3.25066e15	+	1.87677e15i	−0.107688	+	0.0621735i
$559$		−	1.23903e16i		−	0.406080i
$560$		0			0
$561$	−9.85701e15			−0.316204
$562$	1.87821e15	+	3.25315e15i	0.0596109	+	0.103249i
$563$	−2.59585e16	−	1.49872e16i	−0.815135	−	0.470618i	0.0336009	−	0.999435i	$-0.489302\pi$
$563$	−2.59585e16	−	1.49872e16i	−0.815135	−	0.470618i	−0.848736	+	0.528817i	$0.822636\pi$
$564$	5.73204e15	−	9.92818e15i	0.178088	−	0.308457i
$565$	3.29068e16	−	1.89988e16i	1.01157	−	0.584030i
$566$		−	3.21107e16i		−	0.976677i
$567$		0			0
$568$	−6.80650e15			−0.202691
$569$	1.35760e16	+	2.35144e16i	0.400037	+	0.692884i	0.993730	−	0.111808i	$-0.0356641\pi$
$569$	1.35760e16	+	2.35144e16i	0.400037	+	0.692884i	−0.593693	+	0.804691i	$0.702331\pi$
$570$	−2.15359e16	−	1.24338e16i	−0.627934	−	0.362538i
$571$	−3.50961e15	+	6.07881e15i	−0.101261	+	0.175389i	−0.912204	−	0.409735i	$-0.865621\pi$
$571$	−3.50961e15	+	6.07881e15i	−0.101261	+	0.175389i	0.810944	+	0.585124i	$0.198954\pi$
$572$	−6.40939e15	+	3.70046e15i	−0.182996	+	0.105653i
$573$			2.12814e16i			0.601274i
$574$		0			0
$575$	6.73215e15			0.186272
$576$	−1.15318e15	−	1.99736e15i	−0.0315763	−	0.0546918i
$577$	4.43026e16	+	2.55781e16i	1.20053	+	0.693129i	0.960674	−	0.277679i	$-0.0895650\pi$
$577$	4.43026e16	+	2.55781e16i	1.20053	+	0.693129i	0.239860	+	0.970807i	$0.422898\pi$
$578$	1.20217e16	−	2.08222e16i	0.322403	−	0.558419i
$579$	−2.65555e16	+	1.53318e16i	−0.704828	+	0.406933i
$580$		−	1.70751e16i		−	0.448533i
$581$		0			0
$582$	9.04392e15			0.232712
$583$	−2.12711e16	−	3.68426e16i	−0.541724	−	0.938293i
$584$	5.20959e15	+	3.00776e15i	0.131319	+	0.0758168i
$585$	2.64914e15	−	4.58844e15i	0.0660951	−	0.114480i
$586$	−7.48106e15	+	4.31919e15i	−0.184747	+	0.106664i
$587$		−	2.97094e16i		−	0.726216i	−0.931747	−	0.363108i	$-0.881716\pi$
$587$		−	2.97094e16i		−	0.726216i	0.931747	−	0.363108i	$-0.118284\pi$
$588$		0			0
$589$	2.25951e16			0.541157
$590$	−6.71635e15	−	1.16331e16i	−0.159229	−	0.275792i
$591$	−2.34592e16	−	1.35442e16i	−0.550540	−	0.317855i
$592$	−3.57284e15	+	6.18834e15i	−0.0830010	+	0.143762i
$593$	−4.00972e16	+	2.31501e16i	−0.922116	+	0.532384i	−0.884309	−	0.466901i	$-0.845370\pi$
$593$	−4.00972e16	+	2.31501e16i	−0.922116	+	0.532384i	−0.0378064	+	0.999285i	$0.512037\pi$
$594$		−	4.98047e16i		−	1.13384i
$595$		0			0
$596$	1.19545e16			0.266719
$597$	−1.96063e16	−	3.39590e16i	−0.433060	−	0.750083i
$598$	1.20475e16	+	6.95564e15i	0.263446	+	0.152100i
$599$	−2.05859e16	+	3.56558e16i	−0.445664	+	0.771914i	−0.998098	−	0.0616433i	$-0.980366\pi$
$599$	−2.05859e16	+	3.56558e16i	−0.445664	+	0.771914i	0.552434	+	0.833557i	$0.313699\pi$
$600$	1.21409e15	−	7.00953e14i	0.0260221	−	0.0150239i
$601$			1.89158e15i			0.0401402i	0.999799	+	0.0200701i	$0.00638893\pi$
$601$			1.89158e15i			0.0401402i	−0.999799	+	0.0200701i	$0.993611\pi$
$602$		0			0
$603$	1.79922e16			0.374266
$604$	−8.31749e15	−	1.44063e16i	−0.171305	−	0.296709i
$605$	−5.15119e16	−	2.97404e16i	−1.05045	−	0.606478i
$606$	3.17703e13	−	5.50278e13i	0.000641484	−	0.00111108i
$607$	−7.45528e15	+	4.30431e15i	−0.149050	+	0.0860541i	−0.572670	−	0.819786i	$-0.694092\pi$
$607$	−7.45528e15	+	4.30431e15i	−0.149050	+	0.0860541i	0.423620	+	0.905840i	$0.360759\pi$
$608$			1.38836e16i			0.274840i
$609$		0			0
$610$	−1.82557e16			−0.354340
$611$	−7.35167e15	−	1.27335e16i	−0.141299	−	0.244737i
$612$	−3.41187e15	−	1.96985e15i	−0.0649358	−	0.0374907i
$613$	7.75623e15	−	1.34342e16i	0.146180	−	0.253191i	−0.783633	−	0.621225i	$-0.786635\pi$
$613$	7.75623e15	−	1.34342e16i	0.146180	−	0.253191i	0.929813	+	0.368033i	$0.119969\pi$
$614$	2.64378e16	−	1.52639e16i	0.493419	−	0.284876i
$615$			4.03922e16i			0.746529i
$616$		0			0
$617$	6.49218e16			1.17674			0.588368	−	0.808593i	$-0.299770\pi$
$617$	6.49218e16			1.17674			0.588368	+	0.808593i	$0.299770\pi$
$618$	2.46517e16	+	4.26980e16i	0.442503	+	0.766437i
$619$	−3.01581e16	−	1.74118e16i	−0.536117	−	0.309527i	0.207387	−	0.978259i	$-0.433504\pi$
$619$	−3.01581e16	−	1.74118e16i	−0.536117	−	0.309527i	−0.743504	+	0.668732i	$0.766837\pi$
$620$	4.63443e15	−	8.02707e15i	0.0815918	−	0.141321i
$621$	−8.10741e16	+	4.68081e16i	−1.41362	+	0.816153i
$622$			2.93982e16i			0.507666i
$623$		0			0
$624$	2.89689e15			0.0490710
$625$	2.57664e16	+	4.46288e16i	0.432289	+	0.748747i
$626$	4.53172e16	+	2.61639e16i	0.753038	+	0.434766i
$627$	−5.03148e16	+	8.71479e16i	−0.828115	+	1.43434i
$628$	4.10681e16	−	2.37107e16i	0.669494	−	0.386532i
$629$			1.22062e16i			0.197095i
$630$		0			0
$631$	−6.99817e16			−1.10869			−0.554343	−	0.832289i	$-0.687030\pi$
$631$	−6.99817e16			−1.10869			−0.554343	+	0.832289i	$0.687030\pi$
$632$	2.93257e14	+	5.07937e14i	0.00460200	+	0.00797090i
$633$	2.29744e16	+	1.32643e16i	0.357126	+	0.206187i
$634$	4.05555e16	−	7.02442e16i	0.624474	−	1.08162i
$635$	8.63055e16	−	4.98285e16i	1.31643	−	0.760039i
$636$			1.66520e16i			0.251607i
$637$		0			0
$638$	−6.90965e16			−1.02455
$639$	−9.85906e15	−	1.70764e16i	−0.144821	−	0.250837i
$640$	4.93223e15	+	2.84763e15i	0.0717734	+	0.0414384i
$641$	−8.26267e15	+	1.43114e16i	−0.119117	+	0.206316i	−0.919418	−	0.393282i	$-0.871340\pi$
$641$	−8.26267e15	+	1.43114e16i	−0.119117	+	0.206316i	0.800301	+	0.599598i	$0.204673\pi$
$642$	3.78557e16	−	2.18560e16i	0.540657	−	0.312148i
$643$		−	2.58392e16i		−	0.365605i	−0.983150	−	0.182803i	$-0.941483\pi$
$643$		−	2.58392e16i		−	0.365605i	0.983150	−	0.182803i	$-0.0585170\pi$
$644$		0			0
$645$	−6.91088e16			−0.959788
$646$	1.18579e16	+	2.05384e16i	0.163159	+	0.282600i
$647$	−8.66866e16	−	5.00485e16i	−1.18175	−	0.682284i	−0.225332	−	0.974282i	$-0.572347\pi$
$647$	−8.66866e16	−	5.00485e16i	−1.18175	−	0.682284i	−0.956419	+	0.291998i	$0.905680\pi$
$648$	−3.13498e15	+	5.42994e15i	−0.0423433	+	0.0733407i
$649$	−4.70747e16	+	2.71786e16i	−0.629969	+	0.363713i
$650$		−	1.79802e15i		−	0.0238405i
$651$		0			0
$652$	1.74564e16			0.227231
$653$	−1.53565e16	−	2.65983e16i	−0.198068	−	0.343064i	0.749834	−	0.661626i	$-0.230133\pi$
$653$	−1.53565e16	−	2.65983e16i	−0.198068	−	0.343064i	−0.947902	+	0.318562i	$0.896800\pi$
$654$	5.26156e16	+	3.03777e16i	0.672432	+	0.388229i
$655$	5.97440e16	−	1.03480e17i	0.756565	−	1.31041i
$656$	1.95298e16	−	1.12755e16i	0.245061	−	0.141486i
$657$			1.74267e16i			0.216682i
$658$		0			0
$659$	1.64417e16			0.200740			0.100370	−	0.994950i	$-0.467997\pi$
$659$	1.64417e16			0.200740			0.100370	+	0.994950i	$0.467997\pi$
$660$	2.06399e16	+	3.57494e16i	0.249715	+	0.432519i
$661$	6.43528e16	+	3.71541e16i	0.771540	+	0.445449i	0.833424	−	0.552635i	$-0.186377\pi$
$661$	6.43528e16	+	3.71541e16i	0.771540	+	0.445449i	−0.0618837	+	0.998083i	$0.519711\pi$
$662$	6.02408e15	−	1.04340e16i	0.0715719	−	0.123966i
$663$	4.28547e15	−	2.47422e15i	0.0504565	−	0.0291311i
$664$		−	4.70075e16i		−	0.548477i
$665$		0			0
$666$	−2.07007e16			−0.237214
$667$	6.49392e16	+	1.12478e17i	0.737483	+	1.27736i
$668$	3.61845e16	+	2.08911e16i	0.407252	+	0.235127i
$669$	−1.55846e16	+	2.69934e16i	−0.173836	+	0.301093i
$670$	−3.84770e16	+	2.22147e16i	−0.425355	+	0.245579i
$671$			7.38743e16i			0.809391i
$672$		0			0
$673$	1.00460e17			1.08119			0.540596	−	0.841283i	$-0.318199\pi$
$673$	1.00460e17			1.08119			0.540596	+	0.841283i	$0.318199\pi$
$674$	−5.31309e15	−	9.20254e15i	−0.0566745	−	0.0981631i
$675$	1.04788e16	+	6.04992e15i	0.110787	+	0.0639627i
$676$	−2.19995e16	+	3.81043e16i	−0.230533	+	0.399295i
$677$	2.84629e16	−	1.64330e16i	0.295629	−	0.170681i	−0.344849	−	0.938658i	$-0.612070\pi$
$677$	2.84629e16	−	1.64330e16i	0.295629	−	0.170681i	0.640477	+	0.767977i	$0.278736\pi$
$678$			6.01860e16i			0.619608i
$679$		0			0
$680$	9.72855e15			0.0983999
$681$	4.14821e16	+	7.18490e16i	0.415889	+	0.720341i
$682$	−3.24826e16	−	1.87538e16i	−0.322808	−	0.186373i
$683$	−2.00945e16	+	3.48046e16i	−0.197949	+	0.342857i	−0.947863	−	0.318678i	$-0.896761\pi$
$683$	−2.00945e16	+	3.48046e16i	−0.197949	+	0.342857i	0.749915	+	0.661535i	$0.230095\pi$
$684$	−3.48316e16	+	2.01101e16i	−0.340124	+	0.196371i
$685$			1.19285e17i			1.15463i
$686$		0			0
$687$	−4.41831e16			−0.420258
$688$	1.92918e16	+	3.34144e16i	0.181904	+	0.315067i
$689$	1.84958e16	+	1.06785e16i	0.172885	+	0.0998152i
$690$	3.87962e16	−	6.71969e16i	0.359496	−	0.622666i
$691$	−1.38373e17	+	7.98899e16i	−1.27111	+	0.733878i	−0.975198	−	0.221336i	$-0.928958\pi$
$691$	−1.38373e17	+	7.98899e16i	−1.27111	+	0.733878i	−0.295916	+	0.955214i	$0.595625\pi$
$692$			1.74120e16i			0.158567i
$693$		0			0
$694$	−6.00435e16			−0.537414
$695$	−9.13668e16	−	1.58252e17i	−0.810736	−	1.40424i
$696$	2.34225e16	+	1.35230e16i	0.206052	+	0.118964i
$697$	1.92607e16	−	3.33605e16i	0.167987	−	0.290961i
$698$	−1.02977e17	+	5.94537e16i	−0.890444	+	0.514098i
$699$			7.98023e16i			0.684152i
$700$		0			0
$701$	1.35098e17			1.13852			0.569262	−	0.822156i	$-0.307229\pi$
$701$	1.35098e17			1.13852			0.569262	+	0.822156i	$0.307229\pi$
$702$	1.25015e16	+	2.16533e16i	0.104458	+	0.180926i
$703$	1.07917e17	+	6.23060e16i	0.894044	+	0.516176i
$704$	1.15233e16	−	1.99589e16i	0.0946544	−	0.163946i
$705$	−7.10228e16	+	4.10050e16i	−0.578447	+	0.333966i
$706$		−	1.14858e17i		−	0.927544i
$707$		0			0
$708$	2.12766e16			0.168929
$709$	3.51496e15	+	6.08809e15i	0.0276722	+	0.0479296i	0.879530	−	0.475844i	$-0.157857\pi$
$709$	3.51496e15	+	6.08809e15i	0.0276722	+	0.0479296i	−0.851858	+	0.523773i	$0.824524\pi$
$710$	4.21679e16	+	2.43457e16i	0.329179	+	0.190052i
$711$	−8.49554e14	+	1.47147e15i	−0.00657618	+	0.0113903i
$712$	−5.09468e16	+	2.94141e16i	−0.391054	+	0.225775i
$713$			7.05020e16i			0.536617i
$714$		0			0
$715$	5.29437e16			0.396258
$716$	2.02519e16	+	3.50773e16i	0.150310	+	0.260344i
$717$	9.47964e16	+	5.47307e16i	0.697713	+	0.402825i
$718$	2.62572e16	−	4.54788e16i	0.191647	−	0.331942i
$719$	1.36454e17	−	7.87819e16i	0.987675	−	0.570234i	0.0830962	−	0.996542i	$-0.473519\pi$
$719$	1.36454e17	−	7.87819e16i	0.987675	−	0.570234i	0.904578	+	0.426307i	$0.140186\pi$
$720$			1.64989e16i			0.118430i
$721$		0			0
$722$	1.41950e17			1.00210
$723$	2.95825e16	+	5.12385e16i	0.207112	+	0.358729i
$724$	−4.37585e16	−	2.52640e16i	−0.303831	−	0.175417i
$725$	8.39335e15	−	1.45377e16i	0.0577973	−	0.100108i
$726$	8.15920e16	−	4.71071e16i	0.557221	−	0.321712i
$727$		−	1.73285e17i		−	1.17370i	−0.809697	−	0.586848i	$-0.800369\pi$
$727$		−	1.73285e17i		−	1.17370i	0.809697	−	0.586848i	$-0.199631\pi$
$728$		0			0
$729$	−1.29947e17			−0.865767
$730$	−2.15165e16	−	3.72676e16i	−0.142178	−	0.246260i
$731$	5.70780e16	+	3.29540e16i	0.374080	+	0.215975i
$732$	1.44580e16	−	2.50421e16i	0.0939816	−	0.162781i
$733$	−1.32918e17	+	7.67401e16i	−0.856957	+	0.494764i	−0.862992	−	0.505217i	$-0.831412\pi$
$733$	−1.32918e17	+	7.67401e16i	−0.856957	+	0.494764i	0.00603505	+	0.999982i	$0.498079\pi$
$734$		−	8.09975e16i		−	0.517959i
$735$		0			0
$736$	−4.33199e16			−0.272534
$737$	8.98946e16	+	1.55702e17i	0.560956	+	0.971604i
$738$	5.65768e16	+	3.26647e16i	0.350187	+	0.202181i
$739$	−7.76288e16	+	1.34457e17i	−0.476602	+	0.825499i	−0.999641	−	0.0268099i	$-0.991465\pi$
$739$	−7.76288e16	+	1.34457e17i	−0.476602	+	0.825499i	0.523038	+	0.852309i	$0.324798\pi$
$740$	4.42693e16	−	2.55589e16i	0.269595	−	0.155651i
$741$		−	5.05183e16i		−	0.305168i
$742$		0			0
$743$	−1.55426e17			−0.923830			−0.461915	−	0.886924i	$-0.652838\pi$
$743$	−1.55426e17			−0.923830			−0.461915	+	0.886924i	$0.652838\pi$
$744$	7.34068e15	+	1.27144e16i	0.0432812	+	0.0749652i
$745$	−7.40610e16	−	4.27592e16i	−0.433164	−	0.250087i
$746$	−1.08249e17	+	1.87492e17i	−0.628043	+	1.08780i
$747$	1.17934e17	−	6.80893e16i	0.678759	−	0.391882i
$748$		−	3.93679e16i		−	0.224767i
$749$		0			0
$750$	−9.30322e16			−0.522716
$751$	1.48252e17	+	2.56780e17i	0.826344	+	1.43127i	0.900888	+	0.434051i	$0.142916\pi$
$751$	1.48252e17	+	2.56780e17i	0.826344	+	1.43127i	−0.0745445	+	0.997218i	$0.523750\pi$
$752$	3.96522e16	+	2.28932e16i	0.219260	+	0.126590i
$753$	−8.23731e16	+	1.42674e17i	−0.451872	+	0.782665i
$754$	3.00407e16	−	1.73440e16i	0.163486	−	0.0943889i
$755$			1.19001e17i			0.642493i
$756$		0			0
$757$	−2.70923e16			−0.143970			−0.0719848	−	0.997406i	$-0.522933\pi$
$757$	−2.70923e16			−0.143970			−0.0719848	+	0.997406i	$0.522933\pi$
$758$	−2.97705e16	−	5.15639e16i	−0.156953	−	0.271851i
$759$	−2.71921e17	−	1.56994e17i	−1.42230	−	0.821168i
$760$	4.96592e16	−	8.60122e16i	0.257702	−	0.446353i
$761$	−2.95361e17	+	1.70527e17i	−1.52071	+	0.877980i	−0.521004	+	0.853554i	$0.674442\pi$
$761$	−2.95361e17	+	1.70527e17i	−1.52071	+	0.877980i	−0.999702	+	0.0244255i	$0.992224\pi$
$762$			1.57851e17i			0.806340i
$763$		0			0
$764$	−8.49958e16			−0.427403
$765$	1.40916e16	+	2.44074e16i	0.0703059	+	0.121773i
$766$	5.94016e16	+	3.42955e16i	0.294053	+	0.169772i
$767$	1.36443e16	−	2.36325e16i	0.0670159	−	0.116075i
$768$	−7.81238e15	+	4.51048e15i	−0.0380729	+	0.0219814i
$769$		−	1.79123e17i		−	0.866153i	−0.901357	−	0.433076i	$-0.857428\pi$
$769$		−	1.79123e17i		−	0.866153i	0.901357	−	0.433076i	$-0.142572\pi$
$770$		0			0
$771$	1.75435e17			0.835199
$772$	−6.12338e16	−	1.06060e17i	−0.289259	−	0.501012i
$773$	5.21474e16	+	3.01073e16i	0.244431	+	0.141122i	0.617211	−	0.786797i	$-0.288262\pi$
$773$	5.21474e16	+	3.01073e16i	0.244431	+	0.141122i	−0.372781	+	0.927919i	$0.621596\pi$
$774$	−5.58875e16	+	9.67999e16i	−0.259937	+	0.450225i
$775$	7.89151e15	−	4.55617e15i	0.0364208	−	0.0210276i
$776$			3.61205e16i			0.165418i
$777$		0			0
$778$	1.25409e17			0.565524
$779$	−1.96631e17	−	3.40575e17i	−0.879889	−	1.52401i
$780$	−1.79470e16	−	1.03617e16i	−0.0796936	−	0.0460111i
$781$	9.85180e16	−	1.70638e17i	0.434119	−	0.751917i
$782$	−6.40846e16	+	3.69993e16i	−0.280229	+	0.161790i
$783$			2.33433e17i			1.01296i
$784$		0			0
$785$	−3.39236e17			−1.44972
$786$	9.46311e16	+	1.63906e17i	0.401327	+	0.695119i
$787$	−1.49941e16	−	8.65682e15i	−0.0631060	−	0.0364343i	0.468115	−	0.883668i	$-0.344933\pi$
$787$	−1.49941e16	−	8.65682e15i	−0.0631060	−	0.0364343i	−0.531221	+	0.847233i	$0.678267\pi$
$788$	5.40942e16	−	9.36938e16i	0.225940	−	0.391340i
$789$	4.58081e16	−	2.64473e16i	0.189880	−	0.109628i
$790$		−	4.19573e15i		−	0.0172602i
$791$		0			0
$792$	6.67650e16			0.270519
$793$	−1.85433e16	−	3.21179e16i	−0.0745670	−	0.129154i
$794$	−1.37874e17	−	7.96018e16i	−0.550250	−	0.317687i
$795$	5.95612e16	−	1.03163e17i	0.235918	−	0.408621i
$796$	1.35629e17	−	7.83054e16i	0.533180	−	0.307832i
$797$		−	1.59583e17i		−	0.622640i	−0.950305	−	0.311320i	$-0.899229\pi$
$797$		−	1.59583e17i		−	0.622640i	0.950305	−	0.311320i	$-0.100771\pi$
$798$		0			0
$799$	7.82117e16			0.300601
$800$	2.79953e15	+	4.84894e15i	0.0106794	+	0.0184972i
$801$	−1.47591e17	−	8.52115e16i	−0.558809	−	0.322629i
$802$	1.11277e17	−	1.92738e17i	0.418176	−	0.724303i
$803$	−1.50808e17	+	8.70692e16i	−0.562512	+	0.324766i
$804$		−	7.03736e16i		−	0.260539i
$805$		0			0
$806$	1.88297e16			0.0686804
$807$	−1.20196e17	−	2.08186e17i	−0.435161	−	0.753721i
$808$	2.19775e14	+	1.26887e14i	0.000789789	+	0.000455985i
$809$	9.64003e15	−	1.66970e16i	0.0343864	−	0.0595591i	−0.848320	−	0.529484i	$-0.822386\pi$
$809$	9.64003e15	−	1.66970e16i	0.0343864	−	0.0595591i	0.882706	+	0.469925i	$0.155719\pi$
$810$	3.88439e16	−	2.24266e16i	0.137535	−	0.0794058i
$811$		−	3.01693e17i		−	1.06033i	−0.847896	−	0.530163i	$-0.822131\pi$
$811$		−	3.01693e17i		−	1.06033i	0.847896	−	0.530163i	$-0.177869\pi$
$812$		0			0
$813$	−2.23890e17			−0.775338
$814$	−1.03427e17	−	1.79141e17i	−0.355540	−	0.615814i
$815$	−1.08146e17	−	6.24384e16i	−0.369034	−	0.213062i
$816$	−7.70474e15	+	1.33450e16i	−0.0260986	+	0.0452041i
$817$	5.82706e17	−	3.36426e17i	1.95937	−	1.13125i
$818$		−	1.31730e17i		−	0.439709i
$819$		0			0
$820$	−1.61322e17			−0.530654
$821$	8.00654e16	+	1.38677e17i	0.261448	+	0.452842i	0.966627	−	0.256188i	$-0.0824666\pi$
$821$	8.00654e16	+	1.38677e17i	0.261448	+	0.452842i	−0.705179	+	0.709030i	$0.749133\pi$
$822$	−1.63627e17	−	9.44703e16i	−0.530426	−	0.306242i
$823$	2.11116e17	−	3.65664e17i	0.679395	−	1.17675i	−0.295769	−	0.955260i	$-0.595576\pi$
$823$	2.11116e17	−	3.65664e17i	0.679395	−	1.17675i	0.975163	−	0.221486i	$-0.0710908\pi$
$824$	−1.70531e17	+	9.84563e16i	−0.544805	+	0.314543i
$825$			4.05827e16i			0.128711i
$826$		0			0
$827$	2.73276e17			0.854218			0.427109	−	0.904200i	$-0.359532\pi$
$827$	2.73276e17			0.854218			0.427109	+	0.904200i	$0.359532\pi$
$828$	−6.27480e16	−	1.08683e17i	−0.194723	−	0.337270i
$829$	3.32090e17	+	1.91732e17i	1.02312	+	0.590701i	0.915007	−	0.403438i	$-0.132185\pi$
$829$	3.32090e17	+	1.91732e17i	1.02312	+	0.590701i	0.108116	+	0.994138i	$0.465518\pi$
$830$	−1.68138e17	+	2.91223e17i	−0.514276	+	0.890752i
$831$	8.76788e16	−	5.06214e16i	0.266249	−	0.153719i
$832$			1.15699e16i			0.0348810i
$833$		0			0
$834$	2.89440e17			0.860125
$835$	−1.49448e17	−	2.58851e17i	−0.440932	−	0.763716i
$836$	−3.48060e17	−	2.00952e17i	−1.01957	−	0.588648i
$837$	−6.33574e16	+	1.09738e17i	−0.184266	+	0.319157i
$838$	−7.33577e15	+	4.23531e15i	−0.0211827	+	0.0122298i
$839$		−	3.51637e17i		−	1.00814i	−0.863662	−	0.504072i	$-0.831835\pi$
$839$		−	3.51637e17i		−	1.00814i	0.863662	−	0.504072i	$-0.168165\pi$
$840$		0			0
$841$	−2.99612e16			−0.0846804
$842$	−6.67565e16	−	1.15626e17i	−0.187336	−	0.324475i
$843$	3.68614e16	+	2.12820e16i	0.102709	+	0.0592988i
$844$	−5.29761e16	+	9.17574e16i	−0.146563	+	0.253855i
$845$	2.72585e17	−	1.57377e17i	0.748793	−	0.432316i
$846$			1.32641e17i			0.361789i
$847$		0			0
$848$	−6.65062e16			−0.178849
$849$	−1.81923e17	−	3.15100e17i	−0.485782	−	0.841399i
$850$	8.28289e15	+	4.78213e15i	0.0219618	+	0.0126797i
$851$	−1.94409e17	+	3.36726e17i	−0.511846	+	0.886543i
$852$	−6.67916e16	+	3.85622e16i	−0.174616	+	0.100815i
$853$			7.08810e13i			0.000184008i	1.00000		9.20038e-5i	$2.92857e-5\pi$
$853$			7.08810e13i			0.000184008i	−1.00000		9.20038e-5i	$0.999971\pi$
$854$		0			0
$855$	2.87721e17			0.736503
$856$	8.72907e16	+	1.51192e17i	0.221884	+	0.384314i
$857$	1.30185e14	+	7.51626e13i	0.000328607	+	0.000189722i	0.500164	−	0.865931i	$-0.333273\pi$
$857$	1.30185e14	+	7.51626e13i	0.000328607	+	0.000189722i	−0.499836	+	0.866120i	$0.666606\pi$
$858$	−4.19299e16	+	7.26248e16i	−0.105099	+	0.182038i
$859$	5.78263e17	−	3.33860e17i	1.43935	−	0.831009i	0.441546	−	0.897239i	$-0.354430\pi$
$859$	5.78263e17	−	3.33860e17i	1.43935	−	0.831009i	0.997804	+	0.0662290i	$0.0210968\pi$
$860$		−	2.76014e17i		−	0.682244i
$861$		0			0
$862$	8.44497e16			0.205852
$863$	−2.04823e17	−	3.54764e17i	−0.495808	−	0.858765i	0.504180	−	0.863599i	$-0.331795\pi$
$863$	−2.04823e17	−	3.54764e17i	−0.495808	−	0.858765i	−0.999988	+	0.00483322i	$0.998462\pi$
$864$	−6.74286e16	−	3.89299e16i	−0.162092	−	0.0935838i
$865$	6.22798e16	−	1.07872e17i	0.148679	−	0.257520i
$866$	2.52248e17	−	1.45635e17i	0.598025	−	0.345270i
$867$		−	2.72436e17i		−	0.641431i
$868$		0			0
$869$	−1.69786e16			−0.0394260
$870$	−9.67387e16	−	1.67556e17i	−0.223092	−	0.386407i
$871$	−7.81659e16	−	4.51291e16i	−0.179023	−	0.103359i
$872$	−1.21325e17	+	2.10142e17i	−0.275964	+	0.477984i
$873$	−9.06205e16	+	5.23198e16i	−0.204711	+	0.118190i
$874$			7.55447e17i			1.69487i
$875$		0			0
$876$	6.81617e16			0.150840
$877$	3.89946e17	+	6.75407e17i	0.857052	+	1.48446i	0.874728	+	0.484614i	$0.161040\pi$
$877$	3.89946e17	+	6.75407e17i	0.857052	+	1.48446i	−0.0176760	+	0.999844i	$0.505627\pi$
$878$	−1.65911e17	−	9.57889e16i	−0.362167	−	0.209097i
$879$	−4.89407e16	+	8.47679e16i	−0.106105	+	0.183780i
$880$	−1.42779e17	+	8.24337e16i	−0.307446	+	0.177504i
$881$			5.86771e17i			1.25491i	0.778652	+	0.627456i	$0.215904\pi$
$881$			5.86771e17i			1.25491i	−0.778652	+	0.627456i	$0.784096\pi$
$882$		0			0
$883$	1.02492e17			0.216235			0.108117	−	0.994138i	$-0.465518\pi$
$883$	1.02492e17			0.216235			0.108117	+	0.994138i	$0.465518\pi$
$884$	9.88177e15	+	1.71157e16i	0.0207072	+	0.0358659i
$885$	−1.31814e17	−	7.61029e16i	−0.274348	−	0.158395i
$886$	−1.60038e17	+	2.77194e17i	−0.330842	+	0.573036i
$887$	3.08202e17	−	1.77941e17i	0.632840	−	0.365370i	−0.149011	−	0.988836i	$-0.547609\pi$
$887$	3.08202e17	−	1.77941e17i	0.632840	−	0.365370i	0.781851	+	0.623465i	$0.214276\pi$
$888$			8.09676e16i			0.165133i
$889$		0			0
$890$	4.20837e17			0.846787
$891$	−9.07520e16	−	1.57187e17i	−0.181380	−	0.314160i
$892$	−1.07809e17	−	6.22434e16i	−0.214025	−	0.123567i
$893$	3.99230e17	−	6.91486e17i	0.787252	−	1.36356i
$894$	1.17309e17	−	6.77281e16i	0.229776	−	0.132661i
$895$		−	2.89750e17i		−	0.563749i
$896$		0			0
$897$	1.57629e17			0.302608
$898$	−1.65480e17	−	2.86619e17i	−0.315564	−	0.546572i
$899$	1.52245e17	+	8.78988e16i	0.288393	+	0.166504i
$900$	−8.11013e15	+	1.40472e16i	−0.0152606	+	0.0264322i
$901$	−9.83848e16	+	5.68025e16i	−0.183899	+	0.106174i
$902$			6.52812e17i			1.21213i
$903$		0			0
$904$	−2.40377e17			−0.440435
$905$	1.80730e17	+	3.13034e17i	0.328957	+	0.569770i
$906$	−1.63238e17	−	9.42454e16i	−0.295156	−	0.170408i
$907$	−1.17389e17	+	2.03324e17i	−0.210856	+	0.365213i	−0.951983	−	0.306152i	$-0.900958\pi$
$907$	−1.17389e17	+	2.03324e17i	−0.210856	+	0.365213i	0.741127	+	0.671365i	$0.234292\pi$
$908$	−2.86958e17	+	1.65675e17i	−0.512039	+	0.295626i
$909$			7.35175e14i			0.00130319i
$910$		0			0
$911$	2.85714e17			0.499829			0.249915	−	0.968268i	$-0.419597\pi$
$911$	2.85714e17			0.499829			0.249915	+	0.968268i	$0.419597\pi$
$912$	7.86573e16	+	1.36239e17i	0.136701	+	0.236772i
$913$	1.17847e18	+	6.80391e17i	2.03467	+	1.17472i
$914$	−2.94814e17	+	5.10633e17i	−0.505674	+	0.875854i
$915$	−1.79142e17	+	1.03428e17i	−0.305261	+	0.176243i
$916$		−	1.76463e17i		−	0.298731i
$917$		0			0
$918$	−1.32999e17			−0.222225
$919$	−2.02204e17	−	3.50228e17i	−0.335658	−	0.581377i	0.647953	−	0.761680i	$-0.275625\pi$
$919$	−2.02204e17	−	3.50228e17i	−0.335658	−	0.581377i	−0.983611	+	0.180304i	$0.942292\pi$
$920$	2.68378e17	+	1.54948e17i	0.442608	+	0.255540i
$921$	1.72955e17	−	2.99567e17i	0.283384	−	0.490836i
$922$	−9.37667e16	+	5.41362e16i	−0.152638	+	0.0881257i
$923$			9.89164e16i			0.159977i
$924$		0			0
$925$	5.02545e16			0.0802277
$926$	1.68319e17	+	2.91538e17i	0.266973	+	0.462411i
$927$	−4.94022e17	−	2.85224e17i	−0.778517	−	0.449477i
$928$	−5.40094e16	+	9.35470e16i	−0.0845632	+	0.146468i
$929$	−1.04979e18	+	6.06094e17i	−1.63308	+	0.942856i	−0.649938	+	0.759987i	$0.725205\pi$
$929$	−1.04979e18	+	6.06094e17i	−1.63308	+	0.942856i	−0.983137	+	0.182869i	$0.941462\pi$
$930$		−	1.05025e17i		−	0.162329i
$931$		0			0
$932$	−3.18722e17			−0.486314
$933$	1.66555e17	+	2.88482e17i	0.252504	+	0.437350i
$934$	9.88384e16	+	5.70644e16i	0.148883	+	0.0859575i
$935$	−1.40812e17	+	2.43894e17i	−0.210751	+	0.365032i
$936$	−2.90270e16	+	1.67587e16i	−0.0431665	+	0.0249222i
$937$		−	1.24564e17i		−	0.184058i	−0.995756	−	0.0920292i	$-0.970665\pi$
$937$		−	1.24564e17i		−	0.184058i	0.995756	−	0.0920292i	$-0.0293353\pi$
$938$		0			0
$939$	5.92925e17			0.864981
$940$	−1.63770e17	−	2.83658e17i	−0.237393	−	0.411176i
$941$	−6.82895e17	−	3.94269e17i	−0.983594	−	0.567878i	−0.0802409	−	0.996775i	$-0.525569\pi$
$941$	−6.82895e17	−	3.94269e17i	−0.983594	−	0.567878i	−0.903353	+	0.428897i	$0.858902\pi$
$942$	2.68665e17	−	4.65342e17i	0.384509	−	0.665989i
$943$	1.06267e18	−	6.13535e17i	1.51123	−	0.872507i
$944$			8.49768e16i			0.120079i
$945$		0			0
$946$	−1.11693e18			−1.55840
$947$	2.52162e17	+	4.36757e17i	0.349606	+	0.605536i	0.986180	−	0.165680i	$-0.0529820\pi$
$947$	2.52162e17	+	4.36757e17i	0.349606	+	0.605536i	−0.636573	+	0.771216i	$0.719649\pi$
$948$	5.75543e15	+	3.32290e15i	0.00792917	+	0.00457791i
$949$	4.37106e16	−	7.57090e16i	0.0598398	−	0.103646i
$950$	8.45596e16	−	4.88205e16i	0.115033	−	0.0664142i
$951$		−	9.19068e17i		−	1.24241i
$952$		0			0
$953$	−1.53450e17			−0.204837			−0.102419	−	0.994741i	$-0.532658\pi$
$953$	−1.53450e17			−0.204837			−0.102419	+	0.994741i	$0.532658\pi$
$954$	−9.63328e16	−	1.66853e17i	−0.127786	−	0.221332i
$955$	5.26570e17	+	3.04015e17i	0.694122	+	0.400752i
$956$	−2.18589e17	+	3.78607e17i	−0.286339	+	0.495954i
$957$	−6.78039e17	+	3.91466e17i	−0.882639	+	0.509592i
$958$		−	1.27417e17i		−	0.164829i
$959$		0			0
$960$	6.45329e16			0.0824429
$961$	−3.46117e17	−	5.99493e17i	−0.439423	−	0.761103i
$962$	8.99329e16	+	5.19228e16i	0.113467	+	0.0655100i
$963$	−2.52877e17	+	4.37997e17i	−0.317068	+	0.549178i
$964$	−2.04641e17	+	1.18150e17i	−0.254995	+	0.147221i
$965$			8.76091e17i			1.08489i
$966$		0			0
$967$	−7.09549e17			−0.867807			−0.433904	−	0.900959i	$-0.642864\pi$
$967$	−7.09549e17			−0.867807			−0.433904	+	0.900959i	$0.642864\pi$
$968$	1.88141e17	+	3.25870e17i	0.228682	+	0.396089i
$969$	2.32721e17	+	1.34361e17i	0.281121	+	0.162305i
$970$	1.29197e17	−	2.23775e17i	0.155103	−	0.268647i
$971$	1.82086e17	−	1.05128e17i	0.217251	−	0.125430i	−0.387426	−	0.921901i	$-0.626636\pi$
$971$	1.82086e17	−	1.05128e17i	0.217251	−	0.125430i	0.604677	+	0.796471i	$0.293302\pi$
$972$		−	3.75406e17i		−	0.445147i
$973$		0			0
$974$	1.00589e18			1.17814
$975$	−1.01867e16	−	1.76439e16i	−0.0118578	−	0.0205384i
$976$	1.00015e17	+	5.77439e16i	0.115709	+	0.0668048i
$977$	3.67280e17	−	6.36148e17i	0.422309	−	0.731460i	−0.573856	−	0.818956i	$-0.694553\pi$
$977$	3.67280e17	−	6.36148e17i	0.422309	−	0.731460i	0.996165	+	0.0874959i	$0.0278865\pi$
$978$	1.71298e17	−	9.88989e16i	0.195758	−	0.113021i
$979$		−	1.70297e18i		−	1.93425i
$980$		0			0
$981$	−7.02948e17			−0.788695
$982$	6.18089e17	+	1.07056e18i	0.689258	+	1.19383i
$983$	7.32090e17	+	4.22672e17i	0.811415	+	0.468471i	0.847447	−	0.530880i	$-0.178138\pi$
$983$	7.32090e17	+	4.22672e17i	0.811415	+	0.468471i	−0.0360317	+	0.999351i	$0.511472\pi$
$984$	1.27763e17	−	2.21291e17i	0.140745	−	0.243778i
$985$	−6.70254e17	+	3.86971e17i	−0.733875	+	0.423703i
$986$			1.84516e17i			0.200804i
$987$		0			0
$988$	2.01765e17			0.216922
$989$	1.04972e18	+	1.81818e18i	1.12175	+	1.94294i
$990$	−4.13626e17	−	2.38807e17i	−0.439335	−	0.253650i
$991$	7.85878e17	−	1.36118e18i	0.829685	−	1.43706i	−0.0686004	−	0.997644i	$-0.521853\pi$
$991$	7.85878e17	−	1.36118e18i	0.829685	−	1.43706i	0.898285	−	0.439412i	$-0.144813\pi$
$992$	−5.07802e16	+	2.93179e16i	−0.0532873	+	0.0307655i
$993$		−	1.36518e17i		−	0.142394i
$994$		0			0
$995$	−1.12034e18			−1.15455
$996$	−2.66321e17	−	4.61281e17i	−0.272803	−	0.472508i
$997$	4.43092e17	+	2.55819e17i	0.451152	+	0.260473i	0.708316	−	0.705895i	$-0.249455\pi$
$997$	4.43092e17	+	2.55819e17i	0.451152	+	0.260473i	−0.257165	+	0.966368i	$0.582788\pi$
$998$	4.50462e17	−	7.80223e17i	0.455906	−	0.789652i
$999$	−6.05205e17	+	3.49415e17i	−0.608849	+	0.351519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.13.d.a.31.7		16
7.2	even	3		14.13.d.a.5.6	yes	16
7.3	odd	6		98.13.b.c.97.6		16
7.4	even	3		98.13.b.c.97.3		16
7.5	odd	6	inner	98.13.d.a.19.7		16
7.6	odd	2		14.13.d.a.3.6	✓	16
21.2	odd	6		126.13.n.a.19.4		16
21.20	even	2		126.13.n.a.73.4		16
28.23	odd	6		112.13.s.c.33.6		16
28.27	even	2		112.13.s.c.17.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.d.a.3.6	✓	16	7.6	odd	2
14.13.d.a.5.6	yes	16	7.2	even	3
98.13.b.c.97.3		16	7.4	even	3
98.13.b.c.97.6		16	7.3	odd	6
98.13.d.a.19.7		16	7.5	odd	6	inner
98.13.d.a.31.7		16	1.1	even	1	trivial
112.13.s.c.17.6		16	28.27	even	2
112.13.s.c.33.6		16	28.23	odd	6
126.13.n.a.19.4		16	21.2	odd	6
126.13.n.a.73.4		16	21.20	even	2

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)

\(f(q)\)	\(=\)	\(q+(22.6274 + 39.1918i) q^{2} +(444.082 + 256.391i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(12687.9 - 7325.35i) q^{5} +23205.9i q^{6} -92681.9 q^{8} +(-134248. - 232524. i) q^{9} +O(q^{10})\)	\(q+(22.6274 + 39.1918i) q^{2} +(444.082 + 256.391i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(12687.9 - 7325.35i) q^{5} +23205.9i q^{6} -92681.9 q^{8} +(-134248. - 232524. i) q^{9} +(574187. + 331507. i) q^{10} +(1.34149e6 - 2.32353e6i) q^{11} +(-909481. + 525089. i) q^{12} +1.34691e6i q^{13} +7.51261e6 q^{15} +(-2.09715e6 - 3.63237e6i) q^{16} +(-6.20477e6 - 3.58233e6i) q^{17} +(6.07536e6 - 1.05228e7i) q^{18} +(-6.33442e7 + 3.65718e7i) q^{19} +3.00046e7i q^{20} +1.21418e8 q^{22} +(-1.14112e8 - 1.97648e8i) q^{23} +(-4.11584e7 - 2.37628e7i) q^{24} +(-1.47489e7 + 2.55459e7i) q^{25} +(-5.27880e7 + 3.04772e7i) q^{26} -4.10193e8i q^{27} -5.69081e8 q^{29} +(1.69991e8 + 2.94433e8i) q^{30} +(-2.67528e8 - 1.54457e8i) q^{31} +(9.49063e7 - 1.64382e8i) q^{32} +(1.19146e9 - 6.87891e8i) q^{33} -3.24235e8i q^{34} +5.49879e8 q^{36} +(-8.51831e8 - 1.47542e9i) q^{37} +(-2.86663e9 - 1.65505e9i) q^{38} +(-3.45336e8 + 5.98140e8i) q^{39} +(-1.17594e9 + 6.78927e8i) q^{40} +5.37658e9i q^{41} -9.19904e9 q^{43} +(2.74737e9 + 4.75858e9i) q^{44} +(-3.40664e9 - 1.96682e9i) q^{45} +(5.16414e9 - 8.94455e9i) q^{46} +(-9.45381e9 + 5.45816e9i) q^{47} -2.15076e9i q^{48} -1.33492e9 q^{50} +(-1.83695e9 - 3.18170e9i) q^{51} +(-2.38891e9 - 1.37924e9i) q^{52} +(7.92816e9 - 1.37320e10i) q^{53} +(1.60762e10 - 9.28161e9i) q^{54} -3.93075e10i q^{55} -3.75067e10 q^{57} +(-1.28768e10 - 2.23033e10i) q^{58} +(-1.75457e10 - 1.01300e10i) q^{59} +(-7.69292e9 + 1.33245e10i) q^{60} +(-2.38455e10 + 1.37672e10i) q^{61} -1.39799e10i q^{62} +8.58993e9 q^{64} +(9.86660e9 + 1.70895e10i) q^{65} +(5.39194e10 + 3.11304e10i) q^{66} +(-3.35056e10 + 5.80333e10i) q^{67} +(1.27074e10 - 7.33661e9i) q^{68} -1.17030e11i q^{69} +7.34393e10 q^{71} +(1.24423e10 + 2.15508e10i) q^{72} +(-5.62093e10 - 3.24525e10i) q^{73} +(3.85495e10 - 6.67697e10i) q^{74} +(-1.30995e10 + 7.56300e9i) q^{75} -1.49798e11i q^{76} -3.12563e10 q^{78} +(-3.16413e9 - 5.48043e9i) q^{79} +(-5.32168e10 - 3.07247e10i) q^{80} +(3.38251e10 - 5.85869e10i) q^{81} +(-2.10718e11 + 1.21658e11i) q^{82} +5.07191e11i q^{83} -1.04967e11 q^{85} +(-2.08151e11 - 3.60527e11i) q^{86} +(-2.52719e11 - 1.45907e11i) q^{87} +(-1.24332e11 + 2.15349e11i) q^{88} +(5.49695e11 - 3.17367e11i) q^{89} -1.78016e11i q^{90} +4.67404e11 q^{92} +(-7.92030e10 - 1.37184e11i) q^{93} +(-4.27831e11 - 2.47008e11i) q^{94} +(-5.35802e11 + 9.28037e11i) q^{95} +(8.42924e10 - 4.86662e10i) q^{96} -3.89725e11i q^{97} -7.20367e11 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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