LMFDB - Embedded newform 7.17.b.b.6.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,17,Mod(6,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 17, names="a")

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

chi := DirichletCharacter("7.6");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	7.b (of order $2$, degree $1$, 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:	$11.3627180700$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5365384x^{6} + 10449491370210x^{4} + 8743024230718881600x^{2} + 2655236149032650377194000 $ x^8 + 5365384x^6 + 10449491370210x^4 + 8743024230718881600*x^2 + 2655236149032650377194000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{17}\cdot 3^{5}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			6.3
Root			$-923.458i$ of defining polynomial
Character	$\chi$	$=$	7.6
Dual form			7.17.b.b.6.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-174.041 q^{2} -5540.75i q^{3} -35245.9 q^{4} -367486. i q^{5} +964315. i q^{6} +(-2.61707e6 - 5.13652e6i) q^{7} +1.75401e7 q^{8} +1.23468e7 q^{9} +O(q^{10})$	\(q-174.041 q^{2} -5540.75i q^{3} -35245.9 q^{4} -367486. i q^{5} +964315. i q^{6} +(-2.61707e6 - 5.13652e6i) q^{7} +1.75401e7 q^{8} +1.23468e7 q^{9} +6.39575e7i q^{10} -3.60366e8 q^{11} +1.95288e8i q^{12} +1.13015e9i q^{13} +(4.55477e8 + 8.93964e8i) q^{14} -2.03615e9 q^{15} -7.42823e8 q^{16} +9.01276e9i q^{17} -2.14885e9 q^{18} -2.00035e10i q^{19} +1.29524e10i q^{20} +(-2.84602e10 + 1.45005e10i) q^{21} +6.27183e10 q^{22} +1.48036e10 q^{23} -9.71855e10i q^{24} +1.75419e10 q^{25} -1.96692e11i q^{26} -3.06922e11i q^{27} +(9.22409e10 + 1.81041e11i) q^{28} -2.91164e10 q^{29} +3.54372e11 q^{30} +9.80084e11i q^{31} -1.02023e12 q^{32} +1.99670e12i q^{33} -1.56859e12i q^{34} +(-1.88760e12 + 9.61737e11i) q^{35} -4.35175e11 q^{36} -2.13410e11 q^{37} +3.48142e12i q^{38} +6.26187e12 q^{39} -6.44575e12i q^{40} -5.34761e12i q^{41} +(4.95323e12 - 2.52368e12i) q^{42} -1.30167e13 q^{43} +1.27014e13 q^{44} -4.53729e12i q^{45} -2.57644e12 q^{46} -1.07979e13i q^{47} +4.11580e12i q^{48} +(-1.95348e13 + 2.68853e13i) q^{49} -3.05301e12 q^{50} +4.99374e13 q^{51} -3.98331e13i q^{52} -2.07131e13 q^{53} +5.34168e13i q^{54} +1.32429e14i q^{55} +(-4.59038e13 - 9.00953e13i) q^{56} -1.10834e14 q^{57} +5.06744e12 q^{58} +8.42298e13i q^{59} +7.17658e13 q^{60} +9.13503e13i q^{61} -1.70574e14i q^{62} +(-3.23126e13 - 6.34198e13i) q^{63} +2.26243e14 q^{64} +4.15314e14 q^{65} -3.47506e14i q^{66} -5.28775e14 q^{67} -3.17663e14i q^{68} -8.20232e13i q^{69} +(3.28519e14 - 1.67381e14i) q^{70} -4.01228e14 q^{71} +2.16565e14 q^{72} +6.43508e14i q^{73} +3.71420e13 q^{74} -9.71954e13i q^{75} +7.05039e14i q^{76} +(9.43103e14 + 1.85103e15i) q^{77} -1.08982e15 q^{78} -1.62095e15 q^{79} +2.72977e14i q^{80} -1.16908e15 q^{81} +9.30702e14i q^{82} -2.83944e15i q^{83} +(1.00310e15 - 5.11084e14i) q^{84} +3.31206e15 q^{85} +2.26543e15 q^{86} +1.61327e14i q^{87} -6.32087e15 q^{88} -3.51833e15i q^{89} +7.89673e14i q^{90} +(5.80504e15 - 2.95768e15i) q^{91} -5.21767e14 q^{92} +5.43040e15 q^{93} +1.87927e15i q^{94} -7.35099e15 q^{95} +5.65283e15i q^{96} -1.19129e15i q^{97} +(3.39985e15 - 4.67913e15i) q^{98} -4.44938e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 544 q^{2} + 18784 q^{4} - 3034472 q^{7} - 35863808 q^{8} - 41933880 q^{9}+O(q^{10}) $ 8 * q - 544 * q^2 + 18784 * q^4 - 3034472 * q^7 - 35863808 * q^8 - 41933880 * q^9	$ 8 q - 544 q^{2} + 18784 q^{4} - 3034472 q^{7} - 35863808 q^{8} - 41933880 q^{9} + 430398704 q^{11} - 2080234240 q^{14} + 83393280 q^{15} - 4357080832 q^{16} - 7232400864 q^{18} + 45847234944 q^{21} - 34275403968 q^{22} + 89765082416 q^{23} + 61966251080 q^{25} - 376785722656 q^{28} - 22437591664 q^{29} - 192018300480 q^{30} + 941689387008 q^{32} + 371925382080 q^{35} - 4527659399328 q^{36} + 5737866534416 q^{37} - 7975804007808 q^{39} - 13160568536640 q^{42} - 3976952110864 q^{43} + 45337613120448 q^{44} + 35817469755072 q^{46} - 27450534789496 q^{49} - 96564765668320 q^{50} + 58670380591488 q^{51} - 108679841507824 q^{53} - 15117119134208 q^{56} - 196163055495360 q^{57} + 650847682404672 q^{58} - 335782392744960 q^{60} + 223739049782808 q^{63} - 460533940742144 q^{64} + 573279455461440 q^{65} - 722120065643024 q^{67} + 12\!\cdots\!60 q^{70}+ \cdots - 15\!\cdots\!92 q^{99}+O(q^{100}) $ 8 * q - 544 * q^2 + 18784 * q^4 - 3034472 * q^7 - 35863808 * q^8 - 41933880 * q^9 + 430398704 * q^11 - 2080234240 * q^14 + 83393280 * q^15 - 4357080832 * q^16 - 7232400864 * q^18 + 45847234944 * q^21 - 34275403968 * q^22 + 89765082416 * q^23 + 61966251080 * q^25 - 376785722656 * q^28 - 22437591664 * q^29 - 192018300480 * q^30 + 941689387008 * q^32 + 371925382080 * q^35 - 4527659399328 * q^36 + 5737866534416 * q^37 - 7975804007808 * q^39 - 13160568536640 * q^42 - 3976952110864 * q^43 + 45337613120448 * q^44 + 35817469755072 * q^46 - 27450534789496 * q^49 - 96564765668320 * q^50 + 58670380591488 * q^51 - 108679841507824 * q^53 - 15117119134208 * q^56 - 196163055495360 * q^57 + 650847682404672 * q^58 - 335782392744960 * q^60 + 223739049782808 * q^63 - 460533940742144 * q^64 + 573279455461440 * q^65 - 722120065643024 * q^67 + 1268642086877760 * q^70 - 289095246669136 * q^71 + 1560006716205312 * q^72 - 5411665863643328 * q^74 + 4485628262682896 * q^77 + 192459573633600 * q^78 + 5832776866563376 * q^79 - 14617034931574584 * q^81 + 12924747561148416 * q^84 - 5815379514337920 * q^85 + 7508453217752512 * q^86 - 24665635192321536 * q^88 + 23929798963272384 * q^91 + 1197288221450688 * q^92 + 27012151562451840 * q^93 - 53204702857107840 * q^95 + 43278421367298656 * q^98 - 15738606124789392 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−174.041			−0.679846			−0.339923	−	0.940453i	$-0.610401\pi$
$2$	−174.041			−0.679846			−0.339923	+	0.940453i	$0.610401\pi$
$3$		−	5540.75i		−	0.844497i	−0.906480	−	0.422249i	$-0.861241\pi$
$3$		−	5540.75i		−	0.844497i	0.906480	−	0.422249i	$-0.138759\pi$
$4$	−35245.9			−0.537809
$5$		−	367486.i		−	0.940764i	−0.882463	−	0.470382i	$-0.844116\pi$
$5$		−	367486.i		−	0.940764i	0.882463	−	0.470382i	$-0.155884\pi$
$6$			964315.i			0.574128i
$7$	−2.61707e6	−	5.13652e6i	−0.453974	−	0.891015i
$7$	−2.61707e6	−	5.13652e6i	−0.453974	−	0.891015i
$8$	1.75401e7			1.04547
$9$	1.23468e7			0.286824
$10$			6.39575e7i			0.639575i
$11$	−3.60366e8			−1.68113			−0.840567	−	0.541708i	$-0.817778\pi$
$11$	−3.60366e8			−1.68113			−0.840567	+	0.541708i	$0.817778\pi$
$12$			1.95288e8i			0.454178i
$13$			1.13015e9i			1.38544i	0.721205	+	0.692722i	$0.243589\pi$
$13$			1.13015e9i			1.38544i	−0.721205	+	0.692722i	$0.756411\pi$
$14$	4.55477e8	+	8.93964e8i	0.308633	+	0.605753i
$15$	−2.03615e9			−0.794473
$16$	−7.42823e8			−0.172952
$17$			9.01276e9i			1.29201i	0.763332	+	0.646006i	$0.223562\pi$
$17$			9.01276e9i			1.29201i	−0.763332	+	0.646006i	$0.776438\pi$
$18$	−2.14885e9			−0.194996
$19$		−	2.00035e10i		−	1.17781i	−0.808201	−	0.588907i	$-0.799559\pi$
$19$		−	2.00035e10i		−	1.17781i	0.808201	−	0.588907i	$-0.200441\pi$
$20$			1.29524e10i			0.505952i
$21$	−2.84602e10	+	1.45005e10i	−0.752460	+	0.383380i
$22$	6.27183e10			1.14291
$23$	1.48036e10			0.189037			0.0945183	−	0.995523i	$-0.469869\pi$
$23$	1.48036e10			0.189037			0.0945183	+	0.995523i	$0.469869\pi$
$24$		−	9.71855e10i		−	0.882900i
$25$	1.75419e10			0.114963
$26$		−	1.96692e11i		−	0.941889i
$27$		−	3.06922e11i		−	1.08672i
$28$	9.22409e10	+	1.81041e11i	0.244151	+	0.479196i
$29$	−2.91164e10			−0.0582042			−0.0291021	−	0.999576i	$-0.509265\pi$
$29$	−2.91164e10			−0.0582042			−0.0291021	+	0.999576i	$0.509265\pi$
$30$	3.54372e11			0.540119
$31$			9.80084e11i			1.14913i	0.818459	+	0.574566i	$0.194829\pi$
$31$			9.80084e11i			1.14913i	−0.818459	+	0.574566i	$0.805171\pi$
$32$	−1.02023e12			−0.927893
$33$			1.99670e12i			1.41971i
$34$		−	1.56859e12i		−	0.878369i
$35$	−1.88760e12	+	9.61737e11i	−0.838235	+	0.427083i
$36$	−4.35175e11			−0.154257
$37$	−2.13410e11			−0.0607577			−0.0303789	−	0.999538i	$-0.509671\pi$
$37$	−2.13410e11			−0.0607577			−0.0303789	+	0.999538i	$0.509671\pi$
$38$			3.48142e12i			0.800732i
$39$	6.26187e12			1.17000
$40$		−	6.44575e12i		−	0.983544i
$41$		−	5.34761e12i		−	0.669714i	−0.942269	−	0.334857i	$-0.891312\pi$
$41$		−	5.34761e12i		−	0.669714i	0.942269	−	0.334857i	$-0.108688\pi$
$42$	4.95323e12	−	2.52368e12i	0.511557	−	0.260639i
$43$	−1.30167e13			−1.11366			−0.556829	−	0.830627i	$-0.687982\pi$
$43$	−1.30167e13			−1.11366			−0.556829	+	0.830627i	$0.687982\pi$
$44$	1.27014e13			0.904129
$45$		−	4.53729e12i		−	0.269834i
$46$	−2.57644e12			−0.128516
$47$		−	1.07979e13i		−	0.453477i	−0.973956	−	0.226738i	$-0.927194\pi$
$47$		−	1.07979e13i		−	0.453477i	0.973956	−	0.226738i	$-0.0728062\pi$
$48$			4.11580e12i			0.146058i
$49$	−1.95348e13	+	2.68853e13i	−0.587815	+	0.808995i
$50$	−3.05301e12			−0.0781570
$51$	4.99374e13			1.09110
$52$		−	3.98331e13i		−	0.745104i
$53$	−2.07131e13			−0.332689			−0.166344	−	0.986068i	$-0.553196\pi$
$53$	−2.07131e13			−0.332689			−0.166344	+	0.986068i	$0.553196\pi$
$54$			5.34168e13i			0.738802i
$55$			1.32429e14i			1.58155i
$56$	−4.59038e13	−	9.00953e13i	−0.474618	−	0.931533i
$57$	−1.10834e14			−0.994660
$58$	5.06744e12			0.0395699
$59$			8.42298e13i			0.573653i	0.957983	+	0.286827i	$0.0926004\pi$
$59$			8.42298e13i			0.573653i	−0.957983	+	0.286827i	$0.907400\pi$
$60$	7.17658e13			0.427275
$61$			9.13503e13i			0.476509i	0.971203	+	0.238255i	$0.0765753\pi$
$61$			9.13503e13i			0.476509i	−0.971203	+	0.238255i	$0.923425\pi$
$62$		−	1.70574e14i		−	0.781232i
$63$	−3.23126e13	−	6.34198e13i	−0.130211	−	0.255565i
$64$	2.26243e14			0.803776
$65$	4.15314e14			1.30338
$66$		−	3.47506e14i		−	0.965186i
$67$	−5.28775e14			−1.30218			−0.651092	−	0.758998i	$-0.725689\pi$
$67$	−5.28775e14			−1.30218			−0.651092	+	0.758998i	$0.725689\pi$
$68$		−	3.17663e14i		−	0.694856i
$69$		−	8.20232e13i		−	0.159641i
$70$	3.28519e14	−	1.67381e14i	0.569871	−	0.290350i
$71$	−4.01228e14			−0.621332			−0.310666	−	0.950519i	$-0.600552\pi$
$71$	−4.01228e14			−0.621332			−0.310666	+	0.950519i	$0.600552\pi$
$72$	2.16565e14			0.299867
$73$			6.43508e14i			0.797941i	0.916964	+	0.398971i	$0.130632\pi$
$73$			6.43508e14i			0.797941i	−0.916964	+	0.398971i	$0.869368\pi$
$74$	3.71420e13			0.0413059
$75$		−	9.71954e13i		−	0.0970858i
$76$			7.05039e14i			0.633439i
$77$	9.43103e14	+	1.85103e15i	0.763191	+	1.49792i
$78$	−1.08982e15			−0.795423
$79$	−1.62095e15			−1.06845			−0.534224	−	0.845343i	$-0.679396\pi$
$79$	−1.62095e15			−1.06845			−0.534224	+	0.845343i	$0.679396\pi$
$80$			2.72977e14i			0.162707i
$81$	−1.16908e15			−0.630908
$82$			9.30702e14i			0.455302i
$83$		−	2.83944e15i		−	1.26069i	−0.776316	−	0.630344i	$-0.782914\pi$
$83$		−	2.83944e15i		−	1.26069i	0.776316	−	0.630344i	$-0.217086\pi$
$84$	1.00310e15	−	5.11084e14i	0.404680	−	0.206185i
$85$	3.31206e15			1.21548
$86$	2.26543e15			0.757116
$87$			1.61327e14i			0.0491533i
$88$	−6.32087e15			−1.75758
$89$		−	3.51833e15i		−	0.893752i	−0.894596	−	0.446876i	$-0.852537\pi$
$89$		−	3.51833e15i		−	0.893752i	0.894596	−	0.446876i	$-0.147463\pi$
$90$			7.89673e14i			0.183446i
$91$	5.80504e15	−	2.95768e15i	1.23445	−	0.628956i
$92$	−5.21767e14			−0.101666
$93$	5.43040e15			0.970438
$94$			1.87927e15i			0.308294i
$95$	−7.35099e15			−1.10804
$96$			5.65283e15i			0.783603i
$97$		−	1.19129e15i		−	0.152000i	−0.997108	−	0.0759999i	$-0.975785\pi$
$97$		−	1.19129e15i		−	0.152000i	0.997108	−	0.0759999i	$-0.0242149\pi$
$98$	3.39985e15	−	4.67913e15i	0.399624	−	0.549992i
$99$	−4.44938e15			−0.482190
$100$	−6.18281e14			−0.0618281
$101$		−	1.34658e16i		−	1.24355i	−0.783196	−	0.621774i	$-0.786412\pi$
$101$		−	1.34658e16i		−	1.24355i	0.783196	−	0.621774i	$-0.213588\pi$
$102$	−8.69114e15			−0.741781
$103$			7.66102e15i			0.604768i	0.953186	+	0.302384i	$0.0977824\pi$
$103$			7.66102e15i			0.604768i	−0.953186	+	0.302384i	$0.902218\pi$
$104$			1.98230e16i			1.44845i
$105$	5.32874e15	+	1.04587e16i	0.360670	+	0.707887i
$106$	3.60492e15			0.226177
$107$	2.32738e16			1.35456			0.677278	−	0.735728i	$-0.263160\pi$
$107$	2.32738e16			1.35456			0.677278	+	0.735728i	$0.263160\pi$
$108$			1.08177e16i			0.584448i
$109$	−3.24462e16			−1.62836			−0.814182	−	0.580609i	$-0.802814\pi$
$109$	−3.24462e16			−1.62836			−0.814182	+	0.580609i	$0.802814\pi$
$110$		−	2.30481e16i		−	1.07521i
$111$			1.18245e15i			0.0513097i
$112$	1.94402e15	+	3.81553e15i	0.0785157	+	0.154103i
$113$	−3.49168e16			−1.31343			−0.656714	−	0.754140i	$-0.728054\pi$
$113$	−3.49168e16			−1.31343			−0.656714	+	0.754140i	$0.728054\pi$
$114$	1.92896e16			0.676216
$115$		−	5.44013e15i		−	0.177839i
$116$	1.02623e15			0.0313027
$117$			1.39538e16i			0.397379i
$118$		−	1.46594e16i		−	0.389996i
$119$	4.62943e16	−	2.35870e16i	1.15120	−	0.586540i
$120$	−3.57143e16			−0.830600
$121$	8.39139e16			1.82621
$122$		−	1.58987e16i		−	0.323953i
$123$	−2.96298e16			−0.565571
$124$		−	3.45439e16i		−	0.618013i
$125$		−	6.25203e16i		−	1.04892i
$126$	5.62370e15	+	1.10376e16i	0.0885233	+	0.173745i
$127$	−2.07036e15			−0.0305925			−0.0152963	−	0.999883i	$-0.504869\pi$
$127$	−2.07036e15			−0.0305925			−0.0152963	+	0.999883i	$0.504869\pi$
$128$	2.74863e16			0.381449
$129$			7.21220e16i			0.940481i
$130$	−7.22815e16			−0.886095
$131$			6.88094e16i			0.793373i	0.917954	+	0.396686i	$0.129840\pi$
$131$			6.88094e16i			0.793373i	−0.917954	+	0.396686i	$0.870160\pi$
$132$		−	7.03753e16i		−	0.763535i
$133$	−1.02748e17	+	5.23505e16i	−1.04945	+	0.534697i
$134$	9.20284e16			0.885285
$135$	−1.12789e17			−1.02235
$136$			1.58085e17i			1.35076i
$137$	1.85465e16			0.149450			0.0747251	−	0.997204i	$-0.476192\pi$
$137$	1.85465e16			0.149450			0.0747251	+	0.997204i	$0.476192\pi$
$138$			1.42754e16i			0.108531i
$139$			2.30860e17i			1.65665i	0.560250	+	0.828323i	$0.310705\pi$
$139$			2.30860e17i			1.65665i	−0.560250	+	0.828323i	$0.689295\pi$
$140$	6.65301e16	−	3.38972e16i	0.450810	−	0.229689i
$141$	−5.98282e16			−0.382960
$142$	6.98299e16			0.422410
$143$		−	4.07267e17i		−	2.32912i
$144$	−9.17152e15			−0.0496068
$145$			1.06999e16i			0.0547564i
$146$		−	1.11996e17i		−	0.542477i
$147$	1.48965e17	+	1.08237e17i	0.683194	+	0.496408i
$148$	7.52183e15			0.0326761
$149$	−1.68826e17			−0.694942			−0.347471	−	0.937691i	$-0.612959\pi$
$149$	−1.68826e17			−0.694942			−0.347471	+	0.937691i	$0.612959\pi$
$150$			1.69159e16i			0.0660034i
$151$	1.26320e17			0.467364			0.233682	−	0.972313i	$-0.424923\pi$
$151$	1.26320e17			0.467364			0.233682	+	0.972313i	$0.424923\pi$
$152$		−	3.50864e17i		−	1.23137i
$153$			1.11279e17i			0.370580i
$154$	−1.64138e17	−	3.22154e17i	−0.518853	−	1.01835i
$155$	3.60167e17			1.08106
$156$	−2.20705e17			−0.629239
$157$			8.66808e16i			0.234815i	0.993084	+	0.117407i	$0.0374584\pi$
$157$			8.66808e16i			0.234815i	−0.993084	+	0.117407i	$0.962542\pi$
$158$	2.82111e17			0.726380
$159$			1.14766e17i			0.280955i
$160$			3.74920e17i			0.872928i
$161$	−3.87422e16	−	7.60393e16i	−0.0858177	−	0.168434i
$162$	2.03468e17			0.428920
$163$	−7.38163e17			−1.48133			−0.740665	−	0.671875i	$-0.765489\pi$
$163$	−7.38163e17			−1.48133			−0.740665	+	0.671875i	$0.765489\pi$
$164$			1.88481e17i			0.360178i
$165$	7.33758e17			1.33561
$166$			4.94178e17i			0.857074i
$167$		−	5.23460e17i		−	0.865270i	−0.901569	−	0.432635i	$-0.857584\pi$
$167$		−	5.23460e17i		−	0.865270i	0.901569	−	0.432635i	$-0.142416\pi$
$168$	−4.99195e17	+	2.54341e17i	−0.786677	+	0.400814i
$169$	−6.11821e17			−0.919455
$170$	−5.76434e17			−0.826338
$171$		−	2.46980e17i		−	0.337825i
$172$	4.58783e17			0.598935
$173$			4.61800e17i			0.575552i	0.957698	+	0.287776i	$0.0929159\pi$
$173$			4.61800e17i			0.575552i	−0.957698	+	0.287776i	$0.907084\pi$
$174$		−	2.80774e16i		−	0.0334167i
$175$	−4.59085e16	−	9.01045e16i	−0.0521901	−	0.102434i
$176$	2.67688e17			0.290755
$177$	4.66696e17			0.484449
$178$			6.12333e17i			0.607614i
$179$	7.84542e17			0.744375			0.372188	−	0.928158i	$-0.378608\pi$
$179$	7.84542e17			0.744375			0.372188	+	0.928158i	$0.378608\pi$
$180$			1.59921e17i			0.145119i
$181$		−	6.10930e17i		−	0.530350i	−0.964200	−	0.265175i	$-0.914570\pi$
$181$		−	6.10930e17i		−	0.530350i	0.964200	−	0.265175i	$-0.0854298\pi$
$182$	−1.01031e18	+	5.14756e17i	−0.839237	+	0.427593i
$183$	5.06149e17			0.402411
$184$	2.59658e17			0.197633
$185$			7.84253e16i			0.0571587i
$186$	−9.45109e17			−0.659749
$187$		−	3.24789e18i		−	2.17204i
$188$			3.80580e17i			0.243884i
$189$	−1.57651e18	+	8.03236e17i	−0.968283	+	0.493343i
$190$	1.27937e18			0.753300
$191$	−1.58935e16			−0.00897333			−0.00448666	−	0.999990i	$-0.501428\pi$
$191$	−1.58935e16			−0.00897333			−0.00448666	+	0.999990i	$0.501428\pi$
$192$		−	1.25355e18i		−	0.678787i
$193$	3.10120e18			1.61091			0.805456	−	0.592655i	$-0.201920\pi$
$193$	3.10120e18			1.61091			0.805456	+	0.592655i	$0.201920\pi$
$194$			2.07333e17i			0.103337i
$195$		−	2.30115e18i		−	1.10070i
$196$	6.88521e17	−	9.47595e17i	0.316132	−	0.435085i
$197$	−1.98958e18			−0.877065			−0.438533	−	0.898715i	$-0.644502\pi$
$197$	−1.98958e18			−0.877065			−0.438533	+	0.898715i	$0.644502\pi$
$198$	7.74373e17			0.327815
$199$			1.81196e18i			0.736756i	0.929676	+	0.368378i	$0.120087\pi$
$199$			1.81196e18i			0.736756i	−0.929676	+	0.368378i	$0.879913\pi$
$200$	3.07688e17			0.120191
$201$			2.92981e18i			1.09969i
$202$			2.34360e18i			0.845422i
$203$	7.61997e16	+	1.49557e17i	0.0264232	+	0.0518608i
$204$	−1.76009e18			−0.586804
$205$	−1.96517e18			−0.630043
$206$		−	1.33333e18i		−	0.411149i
$207$	1.82778e17			0.0542203
$208$		−	8.39501e17i		−	0.239615i
$209$			7.20857e18i			1.98006i
$210$	−9.27417e17	−	1.82024e18i	−0.245200	−	0.481254i
$211$	−2.71875e18			−0.692006			−0.346003	−	0.938233i	$-0.612461\pi$
$211$	−2.71875e18			−0.692006			−0.346003	+	0.938233i	$0.612461\pi$
$212$	7.30051e17			0.178923
$213$			2.22310e18i			0.524714i
$214$	−4.05058e18			−0.920889
$215$			4.78344e18i			1.04769i
$216$		−	5.38345e18i		−	1.13614i
$217$	5.03422e18	−	2.56495e18i	1.02389	−	0.521676i
$218$	5.64695e18			1.10704
$219$	3.56551e18			0.673859
$220$		−	4.66759e18i		−	0.850572i
$221$	−1.01858e19			−1.79001
$222$		−	2.05795e17i		−	0.0348827i
$223$		−	4.95777e18i		−	0.810676i	−0.914167	−	0.405338i	$-0.867154\pi$
$223$		−	4.95777e18i		−	0.810676i	0.914167	−	0.405338i	$-0.132846\pi$
$224$	2.67001e18	+	5.24043e18i	0.421239	+	0.826766i
$225$	2.16587e17			0.0329741
$226$	6.07693e18			0.892929
$227$		−	4.11057e18i		−	0.583036i	−0.956565	−	0.291518i	$-0.905840\pi$
$227$		−	4.11057e18i		−	0.583036i	0.956565	−	0.291518i	$-0.0941603\pi$
$228$	3.90645e18			0.534937
$229$		−	6.34792e18i		−	0.839359i	−0.907672	−	0.419680i	$-0.862142\pi$
$229$		−	6.34792e18i		−	0.839359i	0.907672	−	0.419680i	$-0.137858\pi$
$230$			9.46804e17i			0.120903i
$231$	1.02561e19	−	5.22549e18i	1.26499	−	0.644513i
$232$	−5.10706e17			−0.0608509
$233$	−1.17065e19			−1.34765			−0.673827	−	0.738889i	$-0.735351\pi$
$233$	−1.17065e19			−1.34765			−0.673827	+	0.738889i	$0.735351\pi$
$234$		−	2.42852e18i		−	0.270157i
$235$	−3.96806e18			−0.426615
$236$		−	2.96875e18i		−	0.308516i
$237$			8.98128e18i			0.902301i
$238$	−8.05708e18	+	4.10510e18i	−0.782640	+	0.398757i
$239$	6.00995e17			0.0564530			0.0282265	−	0.999602i	$-0.491014\pi$
$239$	6.00995e17			0.0564530			0.0282265	+	0.999602i	$0.491014\pi$
$240$	1.51250e18			0.137406
$241$			1.64063e19i			1.44170i	0.693090	+	0.720851i	$0.256249\pi$
$241$			1.64063e19i			1.44170i	−0.693090	+	0.720851i	$0.743751\pi$
$242$	−1.46044e19			−1.24154
$243$		−	6.73437e18i		−	0.553920i
$244$		−	3.21972e18i		−	0.256271i
$245$	9.87997e18	+	7.17877e18i	0.761074	+	0.552995i
$246$	5.15678e18			0.384501
$247$	2.26069e19			1.63179
$248$			1.71908e19i			1.20139i
$249$	−1.57326e19			−1.06465
$250$			1.08811e19i			0.713102i
$251$		−	8.96109e18i		−	0.568815i	−0.958704	−	0.284407i	$-0.908203\pi$
$251$		−	8.96109e18i		−	0.568815i	0.958704	−	0.284407i	$-0.0917968\pi$
$252$	1.13888e18	+	2.23529e18i	0.0700286	+	0.137445i
$253$	−5.33473e18			−0.317796
$254$	3.60326e17			0.0207982
$255$		−	1.83513e19i		−	1.02647i
$256$	−1.96108e19			−1.06310
$257$		−	5.19384e18i		−	0.272913i	−0.990646	−	0.136456i	$-0.956429\pi$
$257$		−	5.19384e18i		−	0.272913i	0.990646	−	0.136456i	$-0.0435713\pi$
$258$		−	1.25522e19i		−	0.639382i
$259$	5.58510e17	+	1.09619e18i	0.0275824	+	0.0541360i
$260$	−1.46381e19			−0.700968
$261$	−3.59496e17			−0.0166944
$262$		−	1.19756e19i		−	0.539372i
$263$	3.08614e19			1.34825			0.674125	−	0.738617i	$-0.264521\pi$
$263$	3.08614e19			1.34825			0.674125	+	0.738617i	$0.264521\pi$
$264$			3.50223e19i			1.48427i
$265$			7.61177e18i			0.312982i
$266$	1.78824e19	−	9.11111e18i	0.713464	−	0.363512i
$267$	−1.94942e19			−0.754771
$268$	1.86371e19			0.700327
$269$			5.74844e18i			0.209668i	0.994490	+	0.104834i	$0.0334311\pi$
$269$			5.74844e18i			0.209668i	−0.994490	+	0.104834i	$0.966569\pi$
$270$	1.96299e19			0.695039
$271$		−	1.72000e19i		−	0.591256i	−0.955303	−	0.295628i	$-0.904471\pi$
$271$		−	1.72000e19i		−	0.591256i	0.955303	−	0.295628i	$-0.0955288\pi$
$272$		−	6.69489e18i		−	0.223456i
$273$	−1.63878e19	−	3.21642e19i	−0.531151	−	1.04249i
$274$	−3.22784e18			−0.101603
$275$	−6.32151e18			−0.193268
$276$			2.89098e18i			0.0858564i
$277$	1.20292e19			0.347055			0.173528	−	0.984829i	$-0.444483\pi$
$277$	1.20292e19			0.347055			0.173528	+	0.984829i	$0.444483\pi$
$278$		−	4.01790e19i		−	1.12627i
$279$			1.21009e19i			0.329599i
$280$	−3.31088e19	+	1.68690e19i	−0.876352	+	0.446504i
$281$	3.05469e19			0.785809			0.392904	−	0.919579i	$-0.371470\pi$
$281$	3.05469e19			0.785809			0.392904	+	0.919579i	$0.371470\pi$
$282$	1.04125e19			0.260354
$283$		−	5.31823e19i		−	1.29263i	−0.763069	−	0.646317i	$-0.776309\pi$
$283$		−	5.31823e19i		−	1.29263i	0.763069	−	0.646317i	$-0.223691\pi$
$284$	1.41416e19			0.334158
$285$			4.07300e19i			0.935741i
$286$			7.08810e19i			1.58344i
$287$	−2.74681e19	+	1.39951e19i	−0.596725	+	0.304033i
$288$	−1.25966e19			−0.266142
$289$	−3.25687e19			−0.669295
$290$		−	1.86221e18i		−	0.0372259i
$291$	−6.60063e18			−0.128363
$292$		−	2.26810e19i		−	0.429140i
$293$		−	6.75815e18i		−	0.124419i	−0.998063	−	0.0622095i	$-0.980185\pi$
$293$		−	6.75815e18i		−	0.124419i	0.998063	−	0.0622095i	$-0.0198147\pi$
$294$	−2.59259e19	−	1.88377e19i	−0.464467	−	0.337481i
$295$	3.09533e19			0.539672
$296$	−3.74324e18			−0.0635206
$297$			1.10604e20i			1.82692i
$298$	2.93825e19			0.472454
$299$			1.67303e19i			0.261900i
$300$			3.42574e18i			0.0522136i
$301$	3.40655e19	+	6.68604e19i	0.505572	+	0.992286i
$302$	−2.19847e19			−0.317735
$303$	−7.46109e19			−1.05017
$304$			1.48590e19i			0.203705i
$305$	3.35700e19			0.448283
$306$		−	1.93671e19i		−	0.251938i
$307$		−	7.49638e19i		−	0.950046i	−0.879973	−	0.475023i	$-0.842440\pi$
$307$		−	7.49638e19i		−	0.950046i	0.879973	−	0.475023i	$-0.157560\pi$
$308$	−3.32405e19	−	6.52411e19i	−0.410451	−	0.805593i
$309$	4.24478e19			0.510725
$310$	−6.26837e19			−0.734955
$311$		−	1.10461e20i		−	1.26219i	−0.775706	−	0.631094i	$-0.782606\pi$
$311$		−	1.10461e20i		−	1.26219i	0.775706	−	0.631094i	$-0.217394\pi$
$312$	1.09834e20			1.22321
$313$			1.45602e19i			0.158057i	0.996872	+	0.0790283i	$0.0251818\pi$
$313$			1.45602e19i			0.158057i	−0.996872	+	0.0790283i	$0.974818\pi$
$314$		−	1.50860e19i		−	0.159638i
$315$	−2.33059e19	+	1.18744e19i	−0.240426	+	0.122498i
$316$	5.71318e19			0.574621
$317$	−7.06744e19			−0.693087			−0.346543	−	0.938034i	$-0.612645\pi$
$317$	−7.06744e19			−0.693087			−0.346543	+	0.938034i	$0.612645\pi$
$318$		−	1.99740e19i		−	0.191006i
$319$	1.04926e19			0.0978490
$320$		−	8.31411e19i		−	0.756164i
$321$		−	1.28954e20i		−	1.14392i
$322$	6.74271e18	+	1.32339e19i	0.0583428	+	0.114509i
$323$	1.80286e20			1.52175
$324$	4.12054e19			0.339308
$325$			1.98250e19i			0.159275i
$326$	1.28470e20			1.00708
$327$			1.79776e20i			1.37515i
$328$		−	9.37979e19i		−	0.700168i
$329$	−5.54635e19	+	2.82588e19i	−0.404054	+	0.205867i
$330$	−1.27704e20			−0.908013
$331$	−2.53869e20			−1.76192			−0.880958	−	0.473194i	$-0.843101\pi$
$331$	−2.53869e20			−1.76192			−0.880958	+	0.473194i	$0.843101\pi$
$332$			1.00078e20i			0.678010i
$333$	−2.63494e18			−0.0174268
$334$			9.11033e19i			0.588250i
$335$			1.94317e20i			1.22505i
$336$	2.11409e19	−	1.07713e19i	0.130139	−	0.0663063i
$337$	−1.26391e20			−0.759763			−0.379881	−	0.925035i	$-0.624035\pi$
$337$	−1.26391e20			−0.759763			−0.379881	+	0.925035i	$0.624035\pi$
$338$	1.06482e20			0.625088
$339$			1.93465e20i			1.10919i
$340$	−1.16737e20			−0.653696
$341$		−	3.53189e20i		−	1.93184i
$342$			4.29845e19i			0.229669i
$343$	1.89221e20	+	2.99804e19i	0.987680	+	0.156489i
$344$	−2.28314e20			−1.16430
$345$	−3.01424e19			−0.150184
$346$		−	8.03719e19i		−	0.391287i
$347$	−9.77646e19			−0.465099			−0.232550	−	0.972585i	$-0.574707\pi$
$347$	−9.77646e19			−0.465099			−0.232550	+	0.972585i	$0.574707\pi$
$348$		−	5.68610e18i		−	0.0264351i
$349$			3.53078e20i			1.60423i	0.597167	+	0.802117i	$0.296293\pi$
$349$			3.53078e20i			1.60423i	−0.597167	+	0.802117i	$0.703707\pi$
$350$	7.98994e18	+	1.56819e19i	0.0354813	+	0.0696391i
$351$	3.46867e20			1.50559
$352$	3.67656e20			1.55991
$353$		−	3.31924e20i		−	1.37671i	−0.725376	−	0.688353i	$-0.758334\pi$
$353$		−	3.31924e20i		−	1.37671i	0.725376	−	0.688353i	$-0.241666\pi$
$354$	−8.12240e19			−0.329351
$355$			1.47446e20i			0.584527i
$356$			1.24007e20i			0.480668i
$357$	−1.30690e20	−	2.56505e20i	−0.495331	−	0.972187i
$358$	−1.36542e20			−0.506061
$359$	1.01723e20			0.368691			0.184345	−	0.982862i	$-0.440984\pi$
$359$	1.01723e20			0.368691			0.184345	+	0.982862i	$0.440984\pi$
$360$		−	7.95847e19i		−	0.282104i
$361$	−1.11697e20			−0.387244
$362$			1.06327e20i			0.360557i
$363$		−	4.64945e20i		−	1.54223i
$364$	−2.04604e20	+	1.04246e20i	−0.663899	+	0.338258i
$365$	2.36480e20			0.750674
$366$	−8.80905e19			−0.273577
$367$		−	3.42419e20i		−	1.04047i	−0.854023	−	0.520235i	$-0.825844\pi$
$367$		−	3.42419e20i		−	1.04047i	0.854023	−	0.520235i	$-0.174156\pi$
$368$	−1.09965e19			−0.0326943
$369$		−	6.60261e19i		−	0.192090i
$370$		−	1.36492e19i		−	0.0388591i
$371$	5.42076e19	+	1.06393e20i	0.151032	+	0.296431i
$372$	−1.91399e20			−0.521911
$373$	7.27504e20			1.94162			0.970811	−	0.239845i	$-0.0770967\pi$
$373$	7.27504e20			1.94162			0.970811	+	0.239845i	$0.0770967\pi$
$374$			5.65265e20i			1.47666i
$375$	−3.46409e20			−0.885808
$376$		−	1.89396e20i		−	0.474098i
$377$		−	3.29059e19i		−	0.0806386i
$378$	2.74377e20	−	1.39796e20i	0.658284	−	0.335397i
$379$	−4.44081e20			−1.04315			−0.521577	−	0.853204i	$-0.674656\pi$
$379$	−4.44081e20			−1.04315			−0.521577	+	0.853204i	$0.674656\pi$
$380$	2.59092e20			0.595917
$381$			1.14713e19i			0.0258353i
$382$	2.76612e18			0.00610048
$383$			4.77417e20i			1.03112i	0.856855	+	0.515558i	$0.172415\pi$
$383$			4.77417e20i			1.03112i	−0.856855	+	0.515558i	$0.827585\pi$
$384$		−	1.52294e20i		−	0.322132i
$385$	6.80227e20	−	3.46577e20i	1.40918	−	0.717983i
$386$	−5.39735e20			−1.09517
$387$	−1.60715e20			−0.319424
$388$			4.19880e19i			0.0817469i
$389$	−7.08252e20			−1.35080			−0.675400	−	0.737451i	$-0.736029\pi$
$389$	−7.08252e20			−1.35080			−0.675400	+	0.737451i	$0.736029\pi$
$390$			4.00494e20i			0.748305i
$391$			1.33422e20i			0.244238i
$392$	−3.42643e20	+	4.71572e20i	−0.614545	+	0.845783i
$393$	3.81255e20			0.670001
$394$	3.46268e20			0.596269
$395$			5.95677e20i			1.00516i
$396$	1.56822e20			0.259326
$397$		−	1.09356e21i		−	1.77223i	−0.463464	−	0.886116i	$-0.653394\pi$
$397$		−	1.09356e21i		−	1.77223i	0.463464	−	0.886116i	$-0.346606\pi$
$398$		−	3.15354e20i		−	0.500880i
$399$	2.90061e20	+	5.69302e20i	0.451550	+	0.886257i
$400$	−1.30306e19			−0.0198831
$401$	−7.00609e20			−1.04790			−0.523951	−	0.851748i	$-0.675543\pi$
$401$	−7.00609e20			−1.04790			−0.523951	+	0.851748i	$0.675543\pi$
$402$		−	5.09906e20i		−	0.747621i
$403$	−1.10764e21			−1.59206
$404$			4.74616e20i			0.668792i
$405$			4.29622e20i			0.593535i
$406$	−1.32618e19	−	2.60290e19i	−0.0179637	−	0.0352574i
$407$	7.69058e19			0.102142
$408$	8.75909e20			1.14072
$409$			1.03302e21i			1.31924i	0.751600	+	0.659619i	$0.229282\pi$
$409$			1.03302e21i			1.31924i	−0.751600	+	0.659619i	$0.770718\pi$
$410$	3.42020e20			0.428332
$411$		−	1.02761e20i		−	0.126210i
$412$		−	2.70019e20i		−	0.325250i
$413$	4.32648e20	−	2.20435e20i	0.511134	−	0.260424i
$414$	−3.18108e19			−0.0368614
$415$	−1.04345e21			−1.18601
$416$		−	1.15301e21i		−	1.28554i
$417$	1.27914e21			1.39903
$418$		−	1.25458e21i		−	1.34614i
$419$			1.37671e20i			0.144921i	0.997371	+	0.0724604i	$0.0230851\pi$
$419$			1.37671e20i			0.144921i	−0.997371	+	0.0724604i	$0.976915\pi$
$420$	−1.87816e20	−	3.68627e20i	−0.193972	−	0.380708i
$421$	1.38936e21			1.40785			0.703926	−	0.710273i	$-0.251429\pi$
$421$	1.38936e21			1.40785			0.703926	+	0.710273i	$0.251429\pi$
$422$	4.73173e20			0.470458
$423$		−	1.33320e20i		−	0.130068i
$424$	−3.63311e20			−0.347817
$425$			1.58101e20i			0.148533i
$426$		−	3.86910e20i		−	0.356724i
$427$	4.69223e20	−	2.39070e20i	0.424577	−	0.216323i
$428$	−8.20305e20			−0.728492
$429$	−2.25656e21			−1.96693
$430$		−	8.32513e20i		−	0.712268i
$431$	1.02995e21			0.864965			0.432482	−	0.901642i	$-0.357638\pi$
$431$	1.02995e21			0.864965			0.432482	+	0.901642i	$0.357638\pi$
$432$			2.27989e20i			0.187950i
$433$		−	8.17699e20i		−	0.661745i	−0.943676	−	0.330872i	$-0.892657\pi$
$433$		−	8.17699e20i		−	0.661745i	0.943676	−	0.330872i	$-0.107343\pi$
$434$	−8.76159e20	+	4.46405e20i	−0.696090	+	0.354659i
$435$	5.92853e19			0.0462416
$436$	1.14359e21			0.875750
$437$		−	2.96124e20i		−	0.222650i
$438$	−6.20544e20			−0.458121
$439$			2.43697e21i			1.76658i	0.468826	+	0.883291i	$0.344677\pi$
$439$			2.43697e21i			1.76658i	−0.468826	+	0.883291i	$0.655323\pi$
$440$			2.32283e21i			1.65347i
$441$	−2.41193e20	+	3.31948e20i	−0.168600	+	0.232039i
$442$	1.77274e21			1.21693
$443$	−7.58059e20			−0.511062			−0.255531	−	0.966801i	$-0.582250\pi$
$443$	−7.58059e20			−0.511062			−0.255531	+	0.966801i	$0.582250\pi$
$444$		−	4.16765e19i		−	0.0275948i
$445$	−1.29294e21			−0.840809
$446$			8.62853e20i			0.551135i
$447$			9.35421e20i			0.586877i
$448$	−5.92094e20	−	1.16210e21i	−0.364894	−	0.716177i
$449$	7.60182e20			0.460200			0.230100	−	0.973167i	$-0.426095\pi$
$449$	7.60182e20			0.460200			0.230100	+	0.973167i	$0.426095\pi$
$450$	−3.76950e19			−0.0224173
$451$			1.92710e21i			1.12588i
$452$	1.23067e21			0.706374
$453$		−	6.99905e20i		−	0.394687i
$454$			7.15407e20i			0.396375i
$455$	−1.08691e21	−	2.13327e21i	−0.591699	−	1.16133i
$456$	−1.94405e21			−1.03989
$457$	−1.63080e21			−0.857177			−0.428588	−	0.903500i	$-0.640989\pi$
$457$	−1.63080e21			−0.857177			−0.428588	+	0.903500i	$0.640989\pi$
$458$			1.10480e21i			0.570635i
$459$	2.76621e21			1.40405
$460$			1.91742e20i			0.0956434i
$461$		−	2.48199e21i		−	1.21673i	−0.793659	−	0.608363i	$-0.791827\pi$
$461$		−	2.48199e21i		−	1.21673i	0.793659	−	0.608363i	$-0.208173\pi$
$462$	−1.78497e21	+	9.09448e20i	−0.859995	+	0.438170i
$463$	−1.27051e21			−0.601632			−0.300816	−	0.953682i	$-0.597259\pi$
$463$	−1.27051e21			−0.601632			−0.300816	+	0.953682i	$0.597259\pi$
$464$	2.16284e19			0.0100665
$465$		−	1.99559e21i		−	0.912953i
$466$	2.03740e21			0.916198
$467$		−	3.33173e21i		−	1.47277i	−0.676563	−	0.736384i	$-0.736532\pi$
$467$		−	3.33173e21i		−	1.47277i	0.676563	−	0.736384i	$-0.263468\pi$
$468$		−	4.91813e20i		−	0.213714i
$469$	1.38384e21	+	2.71607e21i	0.591158	+	1.16027i
$470$	6.90604e20			0.290032
$471$	4.80276e20			0.198301
$472$			1.47740e21i			0.599739i
$473$	4.69076e21			1.87221
$474$		−	1.56311e21i		−	0.613426i
$475$		−	3.50899e20i		−	0.135405i
$476$	−1.63168e21	+	8.31345e20i	−0.619127	+	0.315447i
$477$	−2.55741e20			−0.0954232
$478$	−1.04597e20			−0.0383794
$479$		−	3.26906e21i		−	1.17961i	−0.807545	−	0.589805i	$-0.799204\pi$
$479$		−	3.26906e21i		−	1.17961i	0.807545	−	0.589805i	$-0.200796\pi$
$480$	2.07734e21			0.737186
$481$		−	2.41185e20i		−	0.0841764i
$482$		−	2.85537e21i		−	0.980136i
$483$	−4.21314e20	+	2.14661e20i	−0.142242	+	0.0724728i
$484$	−2.95762e21			−0.982153
$485$	−4.37782e20			−0.142996
$486$			1.17205e21i			0.376580i
$487$	−2.52389e21			−0.797699			−0.398850	−	0.917016i	$-0.630590\pi$
$487$	−2.52389e21			−0.797699			−0.398850	+	0.917016i	$0.630590\pi$
$488$			1.60230e21i			0.498178i
$489$			4.08998e21i			1.25098i
$490$	−1.71952e21	−	1.24940e21i	−0.517413	−	0.375952i
$491$	3.53856e21			1.04755			0.523774	−	0.851857i	$-0.324524\pi$
$491$	3.53856e21			1.04755			0.523774	+	0.851857i	$0.324524\pi$
$492$	1.04433e21			0.304169
$493$		−	2.62419e20i		−	0.0752005i
$494$	−3.93452e21			−1.10937
$495$			1.63509e21i			0.453627i
$496$		−	7.28029e20i		−	0.198745i
$497$	1.05004e21	+	2.06091e21i	0.282069	+	0.553616i
$498$	2.73811e21			0.723797
$499$	1.61553e21			0.420253			0.210126	−	0.977674i	$-0.432612\pi$
$499$	1.61553e21			0.420253			0.210126	+	0.977674i	$0.432612\pi$
$500$			2.20358e21i			0.564117i
$501$	−2.90036e21			−0.730718
$502$			1.55959e21i			0.386707i
$503$		−	4.93570e21i		−	1.20449i	−0.798310	−	0.602247i	$-0.794272\pi$
$503$		−	4.93570e21i		−	1.20449i	0.798310	−	0.602247i	$-0.205728\pi$
$504$	−5.66767e20	−	1.11239e21i	−0.136132	−	0.267186i
$505$	−4.94851e21			−1.16989
$506$	9.28459e20			0.216052
$507$			3.38994e21i			0.776477i
$508$	7.29715e19			0.0164529
$509$		−	2.72550e20i		−	0.0604929i	−0.999542	−	0.0302464i	$-0.990371\pi$
$509$		−	2.72550e20i		−	0.0604929i	0.999542	−	0.0302464i	$-0.00962921\pi$
$510$			3.19387e21i			0.697841i
$511$	3.30539e21	−	1.68410e21i	0.710977	−	0.362245i
$512$	1.61173e21			0.341298
$513$	−6.13950e21			−1.27995
$514$			9.03939e20i			0.185539i
$515$	2.81532e21			0.568944
$516$		−	2.54200e21i		−	0.505799i
$517$			3.89118e21i			0.762355i
$518$	−9.72034e19	−	1.90781e20i	−0.0187518	−	0.0368042i
$519$	2.55872e21			0.486052
$520$	7.28466e21			1.36265
$521$		−	3.39955e21i		−	0.626209i	−0.949719	−	0.313104i	$-0.898631\pi$
$521$		−	3.39955e21i		−	0.626209i	0.949719	−	0.313104i	$-0.101369\pi$
$522$	6.25669e19			0.0113496
$523$			8.07239e21i			1.44208i	0.692895	+	0.721038i	$0.256335\pi$
$523$			8.07239e21i			1.44208i	−0.692895	+	0.721038i	$0.743665\pi$
$524$		−	2.42525e21i		−	0.426683i
$525$	−4.99247e20	+	2.54367e20i	−0.0865049	+	0.0440744i
$526$	−5.37115e21			−0.916602
$527$	−8.83326e21			−1.48469
$528$		−	1.48319e21i		−	0.245542i
$529$	−5.91346e21			−0.964265
$530$		−	1.32476e21i		−	0.212779i
$531$			1.03997e21i			0.164538i
$532$	3.62145e21	−	1.84514e21i	0.564403	−	0.287565i
$533$	6.04360e21			0.927851
$534$	3.39278e21			0.513128
$535$		−	8.55279e21i		−	1.27432i
$536$	−9.27479e21			−1.36140
$537$		−	4.34695e21i		−	0.628623i
$538$		−	1.00046e21i		−	0.142542i
$539$	7.03968e21	−	9.68854e21i	0.988196	−	1.36003i
$540$	3.97536e21			0.549828
$541$	1.04588e22			1.42529			0.712645	−	0.701525i	$-0.247497\pi$
$541$	1.04588e22			1.42529			0.712645	+	0.701525i	$0.247497\pi$
$542$			2.99351e21i			0.401963i
$543$	−3.38501e21			−0.447879
$544$		−	9.19508e21i		−	1.19885i
$545$			1.19235e22i			1.53191i
$546$	2.85214e21	+	5.59788e21i	0.361101	+	0.708733i
$547$	1.93294e21			0.241168			0.120584	−	0.992703i	$-0.461523\pi$
$547$	1.93294e21			0.241168			0.120584	+	0.992703i	$0.461523\pi$
$548$	−6.53686e20			−0.0803757
$549$			1.12789e21i			0.136674i
$550$	1.10020e21			0.131392
$551$			5.82429e20i			0.0685536i
$552$		−	1.43870e21i		−	0.166900i
$553$	4.24214e21	+	8.32606e21i	0.485048	+	0.952003i
$554$	−2.09357e21			−0.235944
$555$	4.34535e20			0.0482704
$556$		−	8.13685e21i		−	0.890960i
$557$	−8.48372e21			−0.915682			−0.457841	−	0.889034i	$-0.651377\pi$
$557$	−8.48372e21			−0.915682			−0.457841	+	0.889034i	$0.651377\pi$
$558$		−	2.10605e21i		−	0.224076i
$559$		−	1.47108e22i		−	1.54291i
$560$	1.40215e21	−	7.14400e20i	0.144974	−	0.0738648i
$561$	−1.79957e22			−1.83429
$562$	−5.31640e21			−0.534229
$563$			1.50971e22i			1.49564i	0.663904	+	0.747818i	$0.268899\pi$
$563$			1.50971e22i			1.49564i	−0.663904	+	0.747818i	$0.731101\pi$
$564$	2.10870e21			0.205959
$565$			1.28314e22i			1.23563i
$566$			9.25587e21i			0.878792i
$567$	3.05958e21	+	6.00503e21i	0.286416	+	0.562148i
$568$	−7.03759e21			−0.649587
$569$	9.99853e21			0.909993			0.454996	−	0.890493i	$-0.349641\pi$
$569$	9.99853e21			0.909993			0.454996	+	0.890493i	$0.349641\pi$
$570$		−	7.08867e21i		−	0.636160i
$571$	−1.12919e22			−0.999263			−0.499631	−	0.866238i	$-0.666531\pi$
$571$	−1.12919e22			−0.999263			−0.499631	+	0.866238i	$0.666531\pi$
$572$			1.43545e22i			1.25262i
$573$			8.80621e19i			0.00757795i
$574$	4.78057e21	−	2.43571e21i	0.405681	−	0.206695i
$575$	2.59684e20			0.0217322
$576$	2.79339e21			0.230543
$577$			6.72532e21i			0.547402i	0.961815	+	0.273701i	$0.0882479\pi$
$577$			6.72532e21i			0.547402i	−0.961815	+	0.273701i	$0.911752\pi$
$578$	5.66827e21			0.455017
$579$		−	1.71830e22i		−	1.36041i
$580$		−	3.77126e20i		−	0.0294485i
$581$	−1.45848e22	+	7.43101e21i	−1.12329	+	0.572320i
$582$	1.14878e21			0.0872674
$583$	7.46429e21			0.559294
$584$			1.12872e22i			0.834226i
$585$	5.12782e21			0.373840
$586$			1.17619e21i			0.0845858i
$587$		−	1.49311e22i		−	1.05922i	−0.848242	−	0.529609i	$-0.822339\pi$
$587$		−	1.49311e22i		−	1.05922i	0.848242	−	0.529609i	$-0.177661\pi$
$588$	−5.25039e21	−	3.81492e21i	−0.367428	−	0.266973i
$589$	1.96051e22			1.35346
$590$	−5.38712e21			−0.366894
$591$			1.10238e22i			0.740679i
$592$	1.58526e20			0.0105082
$593$		−	4.51828e21i		−	0.295485i	−0.989026	−	0.147743i	$-0.952799\pi$
$593$		−	4.51828e21i		−	0.295485i	0.989026	−	0.147743i	$-0.0472007\pi$
$594$		−	1.92496e22i		−	1.24203i
$595$	−8.66790e21	−	1.70125e22i	−0.551796	−	1.08301i
$596$	5.95041e21			0.373746
$597$	1.00396e22			0.622188
$598$		−	2.91176e21i		−	0.178051i
$599$	2.74440e21			0.165589			0.0827947	−	0.996567i	$-0.473615\pi$
$599$	2.74440e21			0.165589			0.0827947	+	0.996567i	$0.473615\pi$
$600$		−	1.70482e21i		−	0.101501i
$601$		−	1.84898e21i		−	0.108627i	−0.998524	−	0.0543134i	$-0.982703\pi$
$601$		−	1.84898e21i		−	0.108627i	0.998524	−	0.0543134i	$-0.0172970\pi$
$602$	−5.92878e21	−	1.16364e22i	−0.343711	−	0.674602i
$603$	−6.52870e21			−0.373498
$604$	−4.45224e21			−0.251353
$605$		−	3.08372e22i		−	1.71803i
$606$	1.29853e22			0.713956
$607$		−	4.82981e21i		−	0.262072i	−0.991378	−	0.131036i	$-0.958170\pi$
$607$		−	4.82981e21i		−	0.262072i	0.991378	−	0.131036i	$-0.0418303\pi$
$608$			2.04081e22i			1.09288i
$609$	8.28659e20	−	4.22203e20i	0.0437963	−	0.0223143i
$610$	−5.84254e21			−0.304763
$611$	1.22032e22			0.628266
$612$		−	3.92213e21i		−	0.199302i
$613$	2.41660e21			0.121205			0.0606025	−	0.998162i	$-0.480698\pi$
$613$	2.41660e21			0.121205			0.0606025	+	0.998162i	$0.480698\pi$
$614$			1.30467e22i			0.645885i
$615$			1.08885e22i			0.532069i
$616$	1.65422e22	+	3.24673e22i	0.797896	+	1.56603i
$617$	−8.49801e21			−0.404609			−0.202305	−	0.979323i	$-0.564843\pi$
$617$	−8.49801e21			−0.404609			−0.202305	+	0.979323i	$0.564843\pi$
$618$	−7.38763e21			−0.347214
$619$			1.36191e21i			0.0631865i	0.999501	+	0.0315933i	$0.0100581\pi$
$619$			1.36191e21i			0.0631865i	−0.999501	+	0.0315933i	$0.989942\pi$
$620$	−1.26944e22			−0.581405
$621$		−	4.54356e21i		−	0.205430i
$622$			1.92246e22i			0.858094i
$623$	−1.80720e22	+	9.20772e21i	−0.796346	+	0.405740i
$624$	−4.65146e21			−0.202355
$625$	−2.02987e22			−0.871821
$626$		−	2.53407e21i		−	0.107454i
$627$	3.99408e22			1.67216
$628$		−	3.05514e21i		−	0.126286i
$629$		−	1.92342e21i		−	0.0784997i
$630$	4.05617e21	−	2.06663e21i	0.163453	−	0.0832795i
$631$	3.08583e21			0.122783			0.0613913	−	0.998114i	$-0.480446\pi$
$631$	3.08583e21			0.122783			0.0613913	+	0.998114i	$0.480446\pi$
$632$	−2.84317e22			−1.11703
$633$			1.50639e22i			0.584397i
$634$	1.23002e22			0.471193
$635$			7.60827e20i			0.0287804i
$636$		−	4.04503e21i		−	0.151100i
$637$	−3.03844e22	−	2.20773e22i	−1.12082	−	0.814385i
$638$	−1.82613e21			−0.0665223
$639$	−4.95389e21			−0.178213
$640$		−	1.01008e22i		−	0.358853i
$641$	2.90821e22			1.02038			0.510190	−	0.860062i	$-0.329575\pi$
$641$	2.90821e22			1.02038			0.510190	+	0.860062i	$0.329575\pi$
$642$			2.24433e22i			0.777688i
$643$			3.23267e22i			1.10630i	0.833081	+	0.553150i	$0.186575\pi$
$643$			3.23267e22i			1.10630i	−0.833081	+	0.553150i	$0.813425\pi$
$644$	1.36550e21	+	2.68007e21i	0.0461536	+	0.0905856i
$645$	2.65038e22			0.884771
$646$	−3.13772e22			−1.03456
$647$			1.29517e22i			0.421787i	0.977509	+	0.210894i	$0.0676373\pi$
$647$			1.29517e22i			0.421787i	−0.977509	+	0.210894i	$0.932363\pi$
$648$	−2.05059e22			−0.659597
$649$		−	3.03535e22i		−	0.964388i
$650$		−	3.45036e21i		−	0.108282i
$651$	−1.42117e22	−	2.78934e22i	−0.440554	−	0.864675i
$652$	2.60172e22			0.796673
$653$	−1.20860e22			−0.365574			−0.182787	−	0.983153i	$-0.558512\pi$
$653$	−1.20860e22			−0.365574			−0.182787	+	0.983153i	$0.558512\pi$
$654$		−	3.12883e22i		−	0.934890i
$655$	2.52865e22			0.746377
$656$			3.97233e21i			0.115828i
$657$			7.94529e21i			0.228869i
$658$	9.65290e21	−	4.91817e21i	0.274695	−	0.139958i
$659$	1.06225e22			0.298637			0.149319	−	0.988789i	$-0.452292\pi$
$659$	1.06225e22			0.298637			0.149319	+	0.988789i	$0.452292\pi$
$660$	−2.58619e22			−0.718306
$661$			5.33887e21i			0.146500i	0.997314	+	0.0732500i	$0.0233371\pi$
$661$			5.33887e21i			0.146500i	−0.997314	+	0.0732500i	$0.976663\pi$
$662$	4.41835e22			1.19783
$663$			5.64367e22i			1.51166i
$664$		−	4.98042e22i		−	1.31802i
$665$	1.92381e22	+	3.77586e22i	0.503024	+	0.987284i
$666$	4.58587e20			0.0118475
$667$	−4.31029e20			−0.0110027
$668$			1.84498e22i			0.465350i
$669$	−2.74697e22			−0.684613
$670$		−	3.38191e22i		−	0.832845i
$671$		−	3.29195e22i		−	0.801076i
$672$	2.90359e22	−	1.47939e22i	0.698202	−	0.355736i
$673$	−4.54780e22			−1.08064			−0.540320	−	0.841460i	$-0.681697\pi$
$673$	−4.54780e22			−1.08064			−0.540320	+	0.841460i	$0.681697\pi$
$674$	2.19972e22			0.516522
$675$		−	5.38400e21i		−	0.124932i
$676$	2.15641e22			0.494491
$677$		−	6.74484e22i		−	1.52849i	−0.644927	−	0.764244i	$-0.723112\pi$
$677$		−	6.74484e22i		−	1.52849i	0.644927	−	0.764244i	$-0.276888\pi$
$678$		−	3.36707e22i		−	0.754076i
$679$	−6.11908e21	+	3.11769e21i	−0.135434	+	0.0690040i
$680$	5.80941e22			1.27075
$681$	−2.27756e22			−0.492372
$682$			6.14692e22i			1.31336i
$683$	−8.98950e22			−1.89832			−0.949161	−	0.314792i	$-0.898065\pi$
$683$	−8.98950e22			−1.89832			−0.949161	+	0.314792i	$0.898065\pi$
$684$			8.70501e21i			0.181686i
$685$		−	6.81556e21i		−	0.140597i
$686$	−3.29321e22	−	5.21780e21i	−0.671470	−	0.106388i
$687$	−3.51722e22			−0.708837
$688$	9.66908e21			0.192609
$689$		−	2.34089e22i		−	0.460922i
$690$	5.24600e21			0.102102
$691$			1.00961e23i			1.94236i	0.238357	+	0.971178i	$0.423391\pi$
$691$			1.00961e23i			1.94236i	−0.238357	+	0.971178i	$0.576609\pi$
$692$		−	1.62765e22i		−	0.309537i
$693$	1.16443e22	+	2.28544e22i	0.218902	+	0.429638i
$694$	1.70150e22			0.316196
$695$	8.48378e22			1.55851
$696$			2.82969e21i			0.0513884i
$697$	4.81968e22			0.865278
$698$		−	6.14500e22i		−	1.09063i
$699$			6.48626e22i			1.13809i
$700$	1.61808e21	+	3.17581e21i	0.0280683	+	0.0550897i
$701$	6.29642e22			1.07982			0.539908	−	0.841724i	$-0.318459\pi$
$701$	6.29642e22			1.07982			0.539908	+	0.841724i	$0.318459\pi$
$702$	−6.03690e22			−1.02357
$703$			4.26894e21i			0.0715612i
$704$	−8.15302e22			−1.35126
$705$			2.19860e22i			0.360275i
$706$			5.77683e22i			0.935949i
$707$	−6.91677e22	+	3.52411e22i	−1.10802	+	0.564539i
$708$	−1.64491e22			−0.260541
$709$	6.54941e22			1.02573			0.512864	−	0.858470i	$-0.328585\pi$
$709$	6.54941e22			1.02573			0.512864	+	0.858470i	$0.328585\pi$
$710$		−	2.56615e22i		−	0.397389i
$711$	−2.00136e22			−0.306457
$712$		−	6.17120e22i		−	0.934394i
$713$			1.45088e22i			0.217228i
$714$	2.27453e22	+	4.46422e22i	0.336749	+	0.660937i
$715$	−1.49665e23			−2.19115
$716$	−2.76519e22			−0.400332
$717$		−	3.32996e21i		−	0.0476744i
$718$	−1.77039e22			−0.250653
$719$			2.46182e22i			0.344688i	0.985037	+	0.172344i	$0.0551340\pi$
$719$			2.46182e22i			0.344688i	−0.985037	+	0.172344i	$0.944866\pi$
$720$			3.37041e21i			0.0466683i
$721$	3.93510e22	−	2.00494e22i	0.538857	−	0.274549i
$722$	1.94399e22			0.263266
$723$	9.09034e22			1.21751
$724$			2.15328e22i			0.285227i
$725$	−5.10758e20			−0.00669131
$726$			8.09194e22i			1.04848i
$727$		−	4.63414e22i		−	0.593873i	−0.954897	−	0.296936i	$-0.904035\pi$
$727$		−	4.63414e22i		−	0.593873i	0.954897	−	0.296936i	$-0.0959650\pi$
$728$	1.01821e23	−	5.18781e22i	1.29059	−	0.657557i
$729$	−8.76387e22			−1.09869
$730$	−4.11571e22			−0.510343
$731$		−	1.17316e23i		−	1.43886i
$732$	−1.78397e22			−0.216420
$733$		−	1.02806e23i		−	1.23364i	−0.787105	−	0.616819i	$-0.788421\pi$
$733$		−	1.02806e23i		−	1.23364i	0.787105	−	0.616819i	$-0.211579\pi$
$734$			5.95948e22i			0.707360i
$735$	3.97758e22	−	5.47424e22i	0.467003	−	0.642725i
$736$	−1.51031e22			−0.175406
$737$	1.90553e23			2.18915
$738$			1.14912e22i			0.130592i
$739$	6.48478e22			0.729020			0.364510	−	0.931199i	$-0.381236\pi$
$739$	6.48478e22			0.729020			0.364510	+	0.931199i	$0.381236\pi$
$740$		−	2.76417e21i		−	0.0307405i
$741$		−	1.25259e23i		−	1.37805i
$742$	−9.43433e21	−	1.85168e22i	−0.102679	−	0.201527i
$743$	1.25952e22			0.135611			0.0678057	−	0.997699i	$-0.478400\pi$
$743$	1.25952e22			0.135611			0.0678057	+	0.997699i	$0.478400\pi$
$744$	9.52499e22			1.01457
$745$			6.20411e22i			0.653776i
$746$	−1.26615e23			−1.32000
$747$		−	3.50581e22i		−	0.361596i
$748$			1.14475e23i			1.16815i
$749$	−6.09091e22	−	1.19546e23i	−0.614933	−	1.20693i
$750$	6.02893e22			0.602213
$751$	−9.77052e22			−0.965602			−0.482801	−	0.875730i	$-0.660381\pi$
$751$	−9.77052e22			−0.965602			−0.482801	+	0.875730i	$0.660381\pi$
$752$			8.02090e21i			0.0784297i
$753$	−4.96511e22			−0.480363
$754$			5.72696e21i			0.0548218i
$755$		−	4.64207e22i		−	0.439679i
$756$	5.55655e22	−	2.83107e22i	0.520752	−	0.265324i
$757$	−4.39944e22			−0.407972			−0.203986	−	0.978974i	$-0.565390\pi$
$757$	−4.39944e22			−0.407972			−0.203986	+	0.978974i	$0.565390\pi$
$758$	7.72881e22			0.709184
$759$			2.95584e22i			0.268378i
$760$	−1.28937e23			−1.15843
$761$			1.43561e23i			1.27632i	0.769903	+	0.638161i	$0.220305\pi$
$761$			1.43561e23i			1.27632i	−0.769903	+	0.638161i	$0.779695\pi$
$762$		−	1.99648e21i		−	0.0175640i
$763$	8.49140e22	+	1.66661e23i	0.739235	+	1.45090i
$764$	5.60181e20			0.00482594
$765$	4.08935e22			0.348629
$766$		−	8.30899e22i		−	0.701000i
$767$	−9.51922e22			−0.794764
$768$			1.08658e23i			0.897787i
$769$			6.81582e22i			0.557324i	0.960389	+	0.278662i	$0.0898909\pi$
$769$			6.81582e22i			0.557324i	−0.960389	+	0.278662i	$0.910109\pi$
$770$	−1.18387e23	+	6.03185e22i	−0.958029	+	0.488118i
$771$	−2.87778e22			−0.230474
$772$	−1.09305e23			−0.866363
$773$		−	1.72831e22i		−	0.135577i	−0.997700	−	0.0677886i	$-0.978406\pi$
$773$		−	1.72831e22i		−	0.135577i	0.997700	−	0.0677886i	$-0.0215943\pi$
$774$	2.79709e22			0.217159
$775$			1.71926e22i			0.132107i
$776$		−	2.08954e22i		−	0.158912i
$777$	6.07369e21	−	3.09456e21i	0.0457177	−	0.0232933i
$778$	1.23265e23			0.918336
$779$	−1.06971e23			−0.788798
$780$			8.11060e22i			0.591965i
$781$	1.44589e23			1.04454
$782$		−	2.32208e22i		−	0.166044i
$783$			8.93646e21i			0.0632516i
$784$	1.45109e22	−	1.99710e22i	0.101664	−	0.139917i
$785$	3.18540e22			0.220906
$786$	−6.63539e22			−0.455498
$787$		−	3.63971e22i		−	0.247325i	−0.992324	−	0.123663i	$-0.960536\pi$
$787$		−	3.63971e22i		−	0.247325i	0.992324	−	0.123663i	$-0.0394641\pi$
$788$	7.01245e22			0.471694
$789$		−	1.70995e23i		−	1.13859i
$790$		−	1.03672e23i		−	0.683352i
$791$	9.13796e22	+	1.79351e23i	0.596262	+	1.17028i
$792$	−7.80428e22			−0.504117
$793$	−1.03239e23			−0.660177
$794$			1.90325e23i			1.20484i
$795$	4.21749e22			0.264312
$796$		−	6.38640e22i		−	0.396234i
$797$			1.43259e23i			0.879946i	0.898011	+	0.439973i	$0.145012\pi$
$797$			1.43259e23i			0.879946i	−0.898011	+	0.439973i	$0.854988\pi$
$798$	−5.04824e22	−	9.90817e22i	−0.306985	−	0.602518i
$799$	9.73186e22			0.585897
$800$	−1.78968e22			−0.106673
$801$		−	4.34403e22i		−	0.256350i
$802$	1.21934e23			0.712412
$803$		−	2.31898e23i		−	1.34145i
$804$		−	1.03264e23i		−	0.591424i
$805$	−2.79434e22	+	1.42372e22i	−0.158457	+	0.0807342i
$806$	1.92774e23			1.08235
$807$	3.18507e22			0.177064
$808$		−	2.36193e23i		−	1.30010i
$809$	−3.56555e23			−1.94329			−0.971645	−	0.236443i	$-0.924018\pi$
$809$	−3.56555e23			−1.94329			−0.971645	+	0.236443i	$0.924018\pi$
$810$		−	7.47717e22i		−	0.403513i
$811$		−	2.17261e23i		−	1.16095i	−0.814277	−	0.580477i	$-0.802866\pi$
$811$		−	2.17261e23i		−	1.16095i	0.814277	−	0.580477i	$-0.197134\pi$
$812$	−2.68573e21	−	5.27127e21i	−0.0142106	−	0.0278912i
$813$	−9.53011e22			−0.499314
$814$	−1.33847e22			−0.0694407
$815$			2.71265e23i			1.39358i
$816$	−3.70947e22			−0.188708
$817$			2.60378e23i			1.31168i
$818$		−	1.79788e23i		−	0.896879i
$819$	7.16739e22	−	3.65180e22i	0.354071	−	0.180400i
$820$	6.92642e22			0.338843
$821$	−1.07355e22			−0.0520090			−0.0260045	−	0.999662i	$-0.508278\pi$
$821$	−1.07355e22			−0.0520090			−0.0260045	+	0.999662i	$0.508278\pi$
$822$			1.78846e22i			0.0858036i
$823$	4.01771e23			1.90889			0.954443	−	0.298392i	$-0.0964502\pi$
$823$	4.01771e23			1.90889			0.954443	+	0.298392i	$0.0964502\pi$
$824$			1.34375e23i			0.632269i
$825$			3.50259e22i			0.163214i
$826$	−7.52984e22	+	3.83647e22i	−0.347492	+	0.177048i
$827$	2.00374e23			0.915794			0.457897	−	0.889005i	$-0.348603\pi$
$827$	2.00374e23			0.915794			0.457897	+	0.889005i	$0.348603\pi$
$828$	−6.44218e21			−0.0291602
$829$			7.03835e20i			0.00315526i	0.999999	+	0.00157763i	$0.000502175\pi$
$829$			7.03835e20i			0.00315526i	−0.999999	+	0.00157763i	$0.999498\pi$
$830$	1.81603e23			0.806305
$831$		−	6.66508e22i		−	0.293087i
$832$			2.55688e23i			1.11359i
$833$	−2.42311e23	−	1.76063e23i	−1.04523	−	0.759464i
$834$	−2.22622e23			−0.951128
$835$	−1.92364e23			−0.814015
$836$		−	2.54072e23i		−	1.06490i
$837$	3.00809e23			1.24878
$838$		−	2.39604e22i		−	0.0985238i
$839$			4.12335e23i			1.67940i	0.543050	+	0.839700i	$0.317269\pi$
$839$			4.12335e23i			1.67940i	−0.543050	+	0.839700i	$0.682731\pi$
$840$	9.34668e22	+	1.83447e23i	0.377071	+	0.740077i
$841$	−2.49399e23			−0.996612
$842$	−2.41805e23			−0.957123
$843$		−	1.69253e23i		−	0.663613i
$844$	9.58247e22			0.372167
$845$			2.24835e23i			0.864990i
$846$			2.32030e22i			0.0884263i
$847$	−2.19608e23	−	4.31026e23i	−0.829052	−	1.62718i
$848$	1.53862e22			0.0575392
$849$	−2.94669e23			−1.09163
$850$		−	2.75160e22i		−	0.100980i
$851$	−3.15925e21			−0.0114854
$852$		−	7.83551e22i		−	0.282196i
$853$		−	2.48008e23i		−	0.884858i	−0.896804	−	0.442429i	$-0.854117\pi$
$853$		−	2.48008e23i		−	0.884858i	0.896804	−	0.442429i	$-0.145883\pi$
$854$	−8.16639e22	+	4.16079e22i	−0.288647	+	0.147066i
$855$	−9.07616e22			−0.317814
$856$	4.08225e23			1.41615
$857$			5.39493e23i			1.85413i	0.374906	+	0.927063i	$0.377675\pi$
$857$			5.39493e23i			1.85413i	−0.374906	+	0.927063i	$0.622325\pi$
$858$	3.92734e23			1.33721
$859$			2.30253e23i			0.776712i	0.921510	+	0.388356i	$0.126957\pi$
$859$			2.30253e23i			0.776712i	−0.921510	+	0.388356i	$0.873043\pi$
$860$		−	1.68596e23i		−	0.563457i
$861$	7.75432e22	+	1.52194e23i	0.256755	+	0.503932i
$862$	−1.79253e23			−0.588043
$863$	−1.39736e23			−0.454175			−0.227087	−	0.973874i	$-0.572920\pi$
$863$	−1.39736e23			−0.454175			−0.227087	+	0.973874i	$0.572920\pi$
$864$			3.13130e23i			1.00836i
$865$	1.69705e23			0.541459
$866$			1.42313e23i			0.449885i
$867$			1.80455e23i			0.565218i
$868$	−1.77436e23	+	9.04038e22i	−0.550659	+	0.280562i
$869$	5.84136e23			1.79620
$870$	−1.03181e22			−0.0314372
$871$		−	5.97595e23i		−	1.80410i
$872$	−5.69111e23			−1.70241
$873$		−	1.47087e22i		−	0.0435972i
$874$			5.15376e22i			0.151368i
$875$	−3.21137e23	+	1.63620e23i	−0.934601	+	0.476181i
$876$	−1.25670e23			−0.362408
$877$	1.65989e23			0.474331			0.237166	−	0.971469i	$-0.423782\pi$
$877$	1.65989e23			0.474331			0.237166	+	0.971469i	$0.423782\pi$
$878$		−	4.24131e23i		−	1.20100i
$879$	−3.74452e22			−0.105072
$880$		−	9.83717e22i		−	0.273532i
$881$			3.30027e23i			0.909373i	0.890652	+	0.454687i	$0.150249\pi$
$881$			3.30027e23i			0.909373i	−0.890652	+	0.454687i	$0.849751\pi$
$882$	4.19774e22	−	5.77725e22i	0.114622	−	0.157751i
$883$	−3.37790e22			−0.0914031			−0.0457016	−	0.998955i	$-0.514552\pi$
$883$	−3.37790e22			−0.0914031			−0.0457016	+	0.998955i	$0.514552\pi$
$884$	3.59006e23			0.962684
$885$		−	1.71504e23i		−	0.455752i
$886$	1.31933e23			0.347443
$887$		−	6.66180e23i		−	1.73861i	−0.494275	−	0.869306i	$-0.664566\pi$
$887$		−	6.66180e23i		−	1.73861i	0.494275	−	0.869306i	$-0.335434\pi$
$888$			2.07404e22i			0.0536430i
$889$	5.41827e21	+	1.06344e22i	0.0138882	+	0.0272584i
$890$	2.25024e23			0.571621
$891$	4.21298e23			1.06064
$892$			1.74741e23i			0.435989i
$893$	−2.15995e23			−0.534111
$894$		−	1.62801e23i		−	0.398986i
$895$		−	2.88308e23i		−	0.700282i
$896$	−7.19335e22	−	1.41184e23i	−0.173168	−	0.339876i
$897$	9.26985e22			0.221174
$898$	−1.32303e23			−0.312865
$899$		−	2.85365e22i		−	0.0668842i
$900$	−7.63381e21			−0.0177338
$901$		−	1.86682e23i		−	0.429838i
$902$		−	3.35393e23i		−	0.765424i
$903$	3.70456e23	−	1.88748e23i	0.837983	−	0.426954i
$904$	−6.12445e23			−1.37315
$905$	−2.24508e23			−0.498935
$906$			1.21812e23i			0.268327i
$907$	6.62245e22			0.144597			0.0722987	−	0.997383i	$-0.476967\pi$
$907$	6.62245e22			0.144597			0.0722987	+	0.997383i	$0.476967\pi$
$908$			1.44881e23i			0.313562i
$909$		−	1.66261e23i		−	0.356680i
$910$	1.89166e23	+	3.71276e23i	0.402264	+	0.789524i
$911$	3.30568e23			0.696809			0.348405	−	0.937344i	$-0.386724\pi$
$911$	3.30568e23			0.696809			0.348405	+	0.937344i	$0.386724\pi$
$912$	8.23302e22			0.172029
$913$			1.02324e24i			2.11939i
$914$	2.83825e23			0.582748
$915$		−	1.86003e23i		−	0.378574i
$916$			2.23738e23i			0.451415i
$917$	3.53441e23	−	1.80079e23i	0.706907	−	0.360171i
$918$	−4.81433e23			−0.954541
$919$	−2.65843e23			−0.522518			−0.261259	−	0.965269i	$-0.584138\pi$
$919$	−2.65843e23			−0.522518			−0.261259	+	0.965269i	$0.584138\pi$
$920$		−	9.54207e22i		−	0.185926i
$921$	−4.15356e23			−0.802311
$922$			4.31967e23i			0.827186i
$923$		−	4.53447e23i		−	0.860821i
$924$	−3.61484e23	+	1.84177e23i	−0.680321	+	0.346625i
$925$	−3.74363e21			−0.00698488
$926$	2.21121e23			0.409017
$927$			9.45894e22i			0.173462i
$928$	2.97054e22			0.0540072
$929$			7.72614e23i			1.39263i	0.717734	+	0.696317i	$0.245179\pi$
$929$			7.72614e23i			1.39263i	−0.717734	+	0.696317i	$0.754821\pi$
$930$			3.47314e23i			0.620668i
$931$	5.37799e23	+	3.90764e23i	0.952846	+	0.692336i
$932$	4.12605e23			0.724781
$933$	−6.12034e23			−1.06591
$934$			5.79856e23i			1.00126i
$935$	−1.19355e24			−2.04338
$936$			2.44751e23i			0.415449i
$937$		−	4.32069e23i		−	0.727171i	−0.931561	−	0.363586i	$-0.881552\pi$
$937$		−	4.32069e23i		−	0.727171i	0.931561	−	0.363586i	$-0.118448\pi$
$938$	−2.40845e23	−	4.72706e23i	−0.401897	−	0.788802i
$939$	8.06744e22			0.133478
$940$	1.39858e23			0.229437
$941$		−	9.05962e23i		−	1.47364i	−0.676086	−	0.736822i	$-0.736325\pi$
$941$		−	9.05962e23i		−	1.47364i	0.676086	−	0.736822i	$-0.263675\pi$
$942$	−8.35876e22			−0.134814
$943$		−	7.91641e22i		−	0.126600i
$944$		−	6.25678e22i		−	0.0992145i
$945$	2.95178e23	+	5.79346e23i	0.464119	+	0.910926i
$946$	−8.16383e23			−1.27281
$947$	5.30216e23			0.819697			0.409848	−	0.912154i	$-0.365582\pi$
$947$	5.30216e23			0.819697			0.409848	+	0.912154i	$0.365582\pi$
$948$		−	3.16553e23i		−	0.485266i
$949$	−7.27260e23			−1.10550
$950$			6.10708e22i			0.0920544i
$951$			3.91589e23i			0.585310i
$952$	8.12008e23	−	4.13720e23i	1.20355	−	0.613212i
$953$	1.15658e24			1.69994			0.849971	−	0.526829i	$-0.176619\pi$
$953$	1.15658e24			1.69994			0.849971	+	0.526829i	$0.176619\pi$
$954$	4.45094e22			0.0648731
$955$			5.84065e21i			0.00844179i
$956$	−2.11826e22			−0.0303610
$957$		−	5.81367e22i		−	0.0826332i
$958$			5.68949e23i			0.801954i
$959$	−4.85374e22	−	9.52643e22i	−0.0678465	−	0.133162i
$960$	−4.60664e23			−0.638579
$961$	−2.33141e23			−0.320502
$962$			4.19761e22i			0.0572270i
$963$	2.87358e23			0.388519
$964$		−	5.78256e23i		−	0.775361i
$965$		−	1.13965e24i		−	1.51549i
$966$	7.33258e22	−	3.73597e22i	0.0967030	−	0.0492704i
$967$	−3.20006e23			−0.418549			−0.209274	−	0.977857i	$-0.567110\pi$
$967$	−3.20006e23			−0.418549			−0.209274	+	0.977857i	$0.567110\pi$
$968$	1.47186e24			1.90925
$969$		−	9.98922e23i		−	1.28511i
$970$	7.61918e22			0.0972153
$971$		−	3.16118e23i		−	0.400032i	−0.979793	−	0.200016i	$-0.935901\pi$
$971$		−	3.16118e23i		−	0.400032i	0.979793	−	0.200016i	$-0.0640995\pi$
$972$			2.37359e23i			0.297903i
$973$	1.18582e24	−	6.04176e23i	1.47610	−	0.752075i
$974$	4.39260e23			0.542313
$975$	1.09845e23			0.134507
$976$		−	6.78571e22i		−	0.0824132i
$977$	−7.89042e23			−0.950482			−0.475241	−	0.879856i	$-0.657639\pi$
$977$	−7.89042e23			−0.950482			−0.475241	+	0.879856i	$0.657639\pi$
$978$		−	7.11822e23i		−	0.850473i
$979$			1.26789e24i			1.50252i
$980$	−3.48228e23	−	2.53022e23i	−0.409313	−	0.297406i
$981$	−4.00608e23			−0.467054
$982$	−6.15852e23			−0.712172
$983$			8.45106e23i			0.969356i	0.874693	+	0.484678i	$0.161063\pi$
$983$			8.45106e23i			0.969356i	−0.874693	+	0.484678i	$0.838937\pi$
$984$	−5.19710e23			−0.591290
$985$			7.31143e23i			0.825111i
$986$			4.56716e22i			0.0511248i
$987$	1.56575e23	+	3.07309e23i	0.173854	+	0.341223i
$988$	−7.96800e23			−0.877594
$989$	−1.92694e23			−0.210522
$990$		−	2.84571e23i		−	0.308397i
$991$	7.19084e22			0.0773019			0.0386510	−	0.999253i	$-0.487694\pi$
$991$	7.19084e22			0.0773019			0.0386510	+	0.999253i	$0.487694\pi$
$992$		−	9.99910e23i		−	1.06627i
$993$			1.40662e24i			1.48793i
$994$	−1.82750e23	−	3.58683e23i	−0.191763	−	0.376374i
$995$	6.65869e23			0.693113
$996$	5.54510e23			0.572578
$997$		−	5.38342e23i		−	0.551438i	−0.961238	−	0.275719i	$-0.911084\pi$
$997$		−	5.38342e23i		−	0.551438i	0.961238	−	0.275719i	$-0.0889160\pi$
$998$	−2.81168e23			−0.285707
$999$			6.55002e22i			0.0660266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.17.b.b.6.3	✓	8
3.2	odd	2		63.17.d.c.55.6		8
4.3	odd	2		112.17.c.b.97.5		8
7.6	odd	2	inner	7.17.b.b.6.4	yes	8
21.20	even	2		63.17.d.c.55.5		8
28.27	even	2		112.17.c.b.97.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.17.b.b.6.3	✓	8	1.1	even	1	trivial
7.17.b.b.6.4	yes	8	7.6	odd	2	inner
63.17.d.c.55.5		8	21.20	even	2
63.17.d.c.55.6		8	3.2	odd	2
112.17.c.b.97.4		8	28.27	even	2
112.17.c.b.97.5		8	4.3	odd	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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	7.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-174.041 q^{2} -5540.75i q^{3} -35245.9 q^{4} -367486. i q^{5} +964315. i q^{6} +(-2.61707e6 - 5.13652e6i) q^{7} +1.75401e7 q^{8} +1.23468e7 q^{9} +O(q^{10})\)	\(q-174.041 q^{2} -5540.75i q^{3} -35245.9 q^{4} -367486. i q^{5} +964315. i q^{6} +(-2.61707e6 - 5.13652e6i) q^{7} +1.75401e7 q^{8} +1.23468e7 q^{9} +6.39575e7i q^{10} -3.60366e8 q^{11} +1.95288e8i q^{12} +1.13015e9i q^{13} +(4.55477e8 + 8.93964e8i) q^{14} -2.03615e9 q^{15} -7.42823e8 q^{16} +9.01276e9i q^{17} -2.14885e9 q^{18} -2.00035e10i q^{19} +1.29524e10i q^{20} +(-2.84602e10 + 1.45005e10i) q^{21} +6.27183e10 q^{22} +1.48036e10 q^{23} -9.71855e10i q^{24} +1.75419e10 q^{25} -1.96692e11i q^{26} -3.06922e11i q^{27} +(9.22409e10 + 1.81041e11i) q^{28} -2.91164e10 q^{29} +3.54372e11 q^{30} +9.80084e11i q^{31} -1.02023e12 q^{32} +1.99670e12i q^{33} -1.56859e12i q^{34} +(-1.88760e12 + 9.61737e11i) q^{35} -4.35175e11 q^{36} -2.13410e11 q^{37} +3.48142e12i q^{38} +6.26187e12 q^{39} -6.44575e12i q^{40} -5.34761e12i q^{41} +(4.95323e12 - 2.52368e12i) q^{42} -1.30167e13 q^{43} +1.27014e13 q^{44} -4.53729e12i q^{45} -2.57644e12 q^{46} -1.07979e13i q^{47} +4.11580e12i q^{48} +(-1.95348e13 + 2.68853e13i) q^{49} -3.05301e12 q^{50} +4.99374e13 q^{51} -3.98331e13i q^{52} -2.07131e13 q^{53} +5.34168e13i q^{54} +1.32429e14i q^{55} +(-4.59038e13 - 9.00953e13i) q^{56} -1.10834e14 q^{57} +5.06744e12 q^{58} +8.42298e13i q^{59} +7.17658e13 q^{60} +9.13503e13i q^{61} -1.70574e14i q^{62} +(-3.23126e13 - 6.34198e13i) q^{63} +2.26243e14 q^{64} +4.15314e14 q^{65} -3.47506e14i q^{66} -5.28775e14 q^{67} -3.17663e14i q^{68} -8.20232e13i q^{69} +(3.28519e14 - 1.67381e14i) q^{70} -4.01228e14 q^{71} +2.16565e14 q^{72} +6.43508e14i q^{73} +3.71420e13 q^{74} -9.71954e13i q^{75} +7.05039e14i q^{76} +(9.43103e14 + 1.85103e15i) q^{77} -1.08982e15 q^{78} -1.62095e15 q^{79} +2.72977e14i q^{80} -1.16908e15 q^{81} +9.30702e14i q^{82} -2.83944e15i q^{83} +(1.00310e15 - 5.11084e14i) q^{84} +3.31206e15 q^{85} +2.26543e15 q^{86} +1.61327e14i q^{87} -6.32087e15 q^{88} -3.51833e15i q^{89} +7.89673e14i q^{90} +(5.80504e15 - 2.95768e15i) q^{91} -5.21767e14 q^{92} +5.43040e15 q^{93} +1.87927e15i q^{94} -7.35099e15 q^{95} +5.65283e15i q^{96} -1.19129e15i q^{97} +(3.39985e15 - 4.67913e15i) q^{98} -4.44938e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 544 q^{2} + 18784 q^{4} - 3034472 q^{7} - 35863808 q^{8} - 41933880 q^{9}+O(q^{10}) \) 8 * q - 544 * q^2 + 18784 * q^4 - 3034472 * q^7 - 35863808 * q^8 - 41933880 * q^9	\( 8 q - 544 q^{2} + 18784 q^{4} - 3034472 q^{7} - 35863808 q^{8} - 41933880 q^{9} + 430398704 q^{11} - 2080234240 q^{14} + 83393280 q^{15} - 4357080832 q^{16} - 7232400864 q^{18} + 45847234944 q^{21} - 34275403968 q^{22} + 89765082416 q^{23} + 61966251080 q^{25} - 376785722656 q^{28} - 22437591664 q^{29} - 192018300480 q^{30} + 941689387008 q^{32} + 371925382080 q^{35} - 4527659399328 q^{36} + 5737866534416 q^{37} - 7975804007808 q^{39} - 13160568536640 q^{42} - 3976952110864 q^{43} + 45337613120448 q^{44} + 35817469755072 q^{46} - 27450534789496 q^{49} - 96564765668320 q^{50} + 58670380591488 q^{51} - 108679841507824 q^{53} - 15117119134208 q^{56} - 196163055495360 q^{57} + 650847682404672 q^{58} - 335782392744960 q^{60} + 223739049782808 q^{63} - 460533940742144 q^{64} + 573279455461440 q^{65} - 722120065643024 q^{67} + 12\!\cdots\!60 q^{70}+ \cdots - 15\!\cdots\!92 q^{99}+O(q^{100}) \) 8 * q - 544 * q^2 + 18784 * q^4 - 3034472 * q^7 - 35863808 * q^8 - 41933880 * q^9 + 430398704 * q^11 - 2080234240 * q^14 + 83393280 * q^15 - 4357080832 * q^16 - 7232400864 * q^18 + 45847234944 * q^21 - 34275403968 * q^22 + 89765082416 * q^23 + 61966251080 * q^25 - 376785722656 * q^28 - 22437591664 * q^29 - 192018300480 * q^30 + 941689387008 * q^32 + 371925382080 * q^35 - 4527659399328 * q^36 + 5737866534416 * q^37 - 7975804007808 * q^39 - 13160568536640 * q^42 - 3976952110864 * q^43 + 45337613120448 * q^44 + 35817469755072 * q^46 - 27450534789496 * q^49 - 96564765668320 * q^50 + 58670380591488 * q^51 - 108679841507824 * q^53 - 15117119134208 * q^56 - 196163055495360 * q^57 + 650847682404672 * q^58 - 335782392744960 * q^60 + 223739049782808 * q^63 - 460533940742144 * q^64 + 573279455461440 * q^65 - 722120065643024 * q^67 + 1268642086877760 * q^70 - 289095246669136 * q^71 + 1560006716205312 * q^72 - 5411665863643328 * q^74 + 4485628262682896 * q^77 + 192459573633600 * q^78 + 5832776866563376 * q^79 - 14617034931574584 * q^81 + 12924747561148416 * q^84 - 5815379514337920 * q^85 + 7508453217752512 * q^86 - 24665635192321536 * q^88 + 23929798963272384 * q^91 + 1197288221450688 * q^92 + 27012151562451840 * q^93 - 53204702857107840 * q^95 + 43278421367298656 * q^98 - 15738606124789392 * q^99

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