LMFDB - Embedded newform 17.16.c.a.4.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,16,Mod(4,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("17.4");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	17.c (of order $4$, degree $2$, 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:	$24.2578958670$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			4.5
Character	$\chi$	$=$	17.4
Dual form			17.16.c.a.13.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-235.953i q^{2} +(1501.32 - 1501.32i) q^{3} -22905.8 q^{4} +(44470.0 - 44470.0i) q^{5} +(-354242. - 354242. i) q^{6} +(-175577. - 175577. i) q^{7} -2.32702e6i q^{8} +9.84096e6i q^{9} +O(q^{10})$	\(q-235.953i q^{2} +(1501.32 - 1501.32i) q^{3} -22905.8 q^{4} +(44470.0 - 44470.0i) q^{5} +(-354242. - 354242. i) q^{6} +(-175577. - 175577. i) q^{7} -2.32702e6i q^{8} +9.84096e6i q^{9} +(-1.04928e7 - 1.04928e7i) q^{10} +(-3.82927e7 - 3.82927e7i) q^{11} +(-3.43890e7 + 3.43890e7i) q^{12} -2.65197e8 q^{13} +(-4.14278e7 + 4.14278e7i) q^{14} -1.33528e8i q^{15} -1.29964e9 q^{16} +(-1.64424e9 - 3.98611e8i) q^{17} +2.32200e9 q^{18} -4.03873e9i q^{19} +(-1.01862e9 + 1.01862e9i) q^{20} -5.27195e8 q^{21} +(-9.03527e9 + 9.03527e9i) q^{22} +(3.73876e9 + 3.73876e9i) q^{23} +(-3.49361e9 - 3.49361e9i) q^{24} +2.65624e10i q^{25} +6.25741e10i q^{26} +(3.63168e10 + 3.63168e10i) q^{27} +(4.02172e9 + 4.02172e9i) q^{28} +(-2.52760e8 + 2.52760e8i) q^{29} -3.15063e10 q^{30} +(7.99705e10 - 7.99705e10i) q^{31} +2.30403e11i q^{32} -1.14979e11 q^{33} +(-9.40533e10 + 3.87964e11i) q^{34} -1.56158e10 q^{35} -2.25415e11i q^{36} +(-4.54652e11 + 4.54652e11i) q^{37} -9.52950e11 q^{38} +(-3.98147e11 + 3.98147e11i) q^{39} +(-1.03483e11 - 1.03483e11i) q^{40} +(-2.35684e11 - 2.35684e11i) q^{41} +1.24393e11i q^{42} -1.09954e12i q^{43} +(8.77123e11 + 8.77123e11i) q^{44} +(4.37628e11 + 4.37628e11i) q^{45} +(8.82171e11 - 8.82171e11i) q^{46} +4.36717e12 q^{47} +(-1.95119e12 + 1.95119e12i) q^{48} -4.68591e12i q^{49} +6.26748e12 q^{50} +(-3.06698e12 + 1.87010e12i) q^{51} +6.07455e12 q^{52} -4.05639e12i q^{53} +(8.56906e12 - 8.56906e12i) q^{54} -3.40575e12 q^{55} +(-4.08571e11 + 4.08571e11i) q^{56} +(-6.06344e12 - 6.06344e12i) q^{57} +(5.96394e10 + 5.96394e10i) q^{58} -3.81023e12i q^{59} +3.05856e12i q^{60} +(-2.45852e13 - 2.45852e13i) q^{61} +(-1.88693e13 - 1.88693e13i) q^{62} +(1.72784e12 - 1.72784e12i) q^{63} +1.17775e13 q^{64} +(-1.17933e13 + 1.17933e13i) q^{65} +2.71297e13i q^{66} -1.49091e13 q^{67} +(3.76626e13 + 9.13048e12i) q^{68} +1.12262e13 q^{69} +3.68460e12i q^{70} +(-4.53167e13 + 4.53167e13i) q^{71} +2.29001e13 q^{72} +(-1.68696e13 + 1.68696e13i) q^{73} +(1.07276e14 + 1.07276e14i) q^{74} +(3.98788e13 + 3.98788e13i) q^{75} +9.25102e13i q^{76} +1.34466e13i q^{77} +(9.39440e13 + 9.39440e13i) q^{78} +(-1.71150e14 - 1.71150e14i) q^{79} +(-5.77952e13 + 5.77952e13i) q^{80} -3.21603e13 q^{81} +(-5.56103e13 + 5.56103e13i) q^{82} -1.11784e14i q^{83} +1.20758e13 q^{84} +(-9.08457e13 + 5.53933e13i) q^{85} -2.59439e14 q^{86} +7.58949e11i q^{87} +(-8.91079e13 + 8.91079e13i) q^{88} +1.89313e14 q^{89} +(1.03260e14 - 1.03260e14i) q^{90} +(4.65625e13 + 4.65625e13i) q^{91} +(-8.56391e13 - 8.56391e13i) q^{92} -2.40123e14i q^{93} -1.03045e15i q^{94} +(-1.79602e14 - 1.79602e14i) q^{95} +(3.45909e14 + 3.45909e14i) q^{96} +(4.74848e14 - 4.74848e14i) q^{97} -1.10565e15 q^{98} +(3.76837e14 - 3.76837e14i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 5256 q^{3} - 720900 q^{4} - 252126 q^{5} - 1017326 q^{6} + 1854722 q^{7}+O(q^{10}) $ 44 * q + 5256 * q^3 - 720900 * q^4 - 252126 * q^5 - 1017326 * q^6 + 1854722 * q^7	\( 44 q + 5256 q^{3} - 720900 q^{4} - 252126 q^{5} - 1017326 q^{6} + 1854722 q^{7} + 8409498 q^{10} - 9729300 q^{11} - 82056486 q^{12} + 146863304 q^{13} - 1773752796 q^{14} + 16082152452 q^{16} + 1961077578 q^{17} - 7034899972 q^{18} + 21230427174 q^{20} - 47057263940 q^{21} - 3442343910 q^{22} - 15842736534 q^{23} + 94553484290 q^{24} - 294640558020 q^{27} - 17774164556 q^{28} + 102726169530 q^{29} - 643189839240 q^{30} - 385043642942 q^{31} + 2378676720192 q^{33} + 158249007174 q^{34} + 408521183892 q^{35} + 1375134180422 q^{37} + 1543745804832 q^{38} + 603440813444 q^{39} - 8303553806742 q^{40} + 1443758220300 q^{41} - 4657636435362 q^{44} + 6106558559866 q^{45} + 9604057332832 q^{46} - 21302607302640 q^{47} + 25515630744334 q^{48} - 18255254395212 q^{50} + 19158460873088 q^{51} - 48159060495244 q^{52} - 78998282739512 q^{54} + 13393057779764 q^{55} + 137860752160332 q^{56} + 31257866131908 q^{57} - 69211880377042 q^{58} + 38643830633662 q^{61} + 238390785941076 q^{62} - 71567394446902 q^{63} - 498262566925124 q^{64} + 178535375770548 q^{65} + 57983772499388 q^{67} + 261849713539554 q^{68} - 115652283503244 q^{69} - 44377197355566 q^{71} + 93677094320796 q^{72} + 405163878377696 q^{73} - 405068893451898 q^{74} + 225803653508132 q^{75} - 802546741257484 q^{78} - 155549526248110 q^{79} - 124920621818622 q^{80} - 10\!\cdots\!28 q^{81}+ \cdots + 173739293641872 q^{99}+O(q^{100}) \) 44 * q + 5256 * q^3 - 720900 * q^4 - 252126 * q^5 - 1017326 * q^6 + 1854722 * q^7 + 8409498 * q^10 - 9729300 * q^11 - 82056486 * q^12 + 146863304 * q^13 - 1773752796 * q^14 + 16082152452 * q^16 + 1961077578 * q^17 - 7034899972 * q^18 + 21230427174 * q^20 - 47057263940 * q^21 - 3442343910 * q^22 - 15842736534 * q^23 + 94553484290 * q^24 - 294640558020 * q^27 - 17774164556 * q^28 + 102726169530 * q^29 - 643189839240 * q^30 - 385043642942 * q^31 + 2378676720192 * q^33 + 158249007174 * q^34 + 408521183892 * q^35 + 1375134180422 * q^37 + 1543745804832 * q^38 + 603440813444 * q^39 - 8303553806742 * q^40 + 1443758220300 * q^41 - 4657636435362 * q^44 + 6106558559866 * q^45 + 9604057332832 * q^46 - 21302607302640 * q^47 + 25515630744334 * q^48 - 18255254395212 * q^50 + 19158460873088 * q^51 - 48159060495244 * q^52 - 78998282739512 * q^54 + 13393057779764 * q^55 + 137860752160332 * q^56 + 31257866131908 * q^57 - 69211880377042 * q^58 + 38643830633662 * q^61 + 238390785941076 * q^62 - 71567394446902 * q^63 - 498262566925124 * q^64 + 178535375770548 * q^65 + 57983772499388 * q^67 + 261849713539554 * q^68 - 115652283503244 * q^69 - 44377197355566 * q^71 + 93677094320796 * q^72 + 405163878377696 * q^73 - 405068893451898 * q^74 + 225803653508132 * q^75 - 802546741257484 * q^78 - 155549526248110 * q^79 - 124920621818622 * q^80 - 1098726050204828 * q^81 - 575036459162320 * q^82 + 1901862557545176 * q^84 - 939038947054838 * q^85 + 1783857741230148 * q^86 + 1466099551935802 * q^88 - 1809234886116972 * q^89 - 156603181182342 * q^90 + 2736989931074496 * q^91 + 4441473764128152 * q^92 + 2349942705291804 * q^95 - 7961673687938290 * q^96 - 2718145106426904 * q^97 - 2118270343699824 * q^98 + 173739293641872 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	235.953i		−	1.30347i	−0.758448	−	0.651734i	$-0.774042\pi$
$2$		−	235.953i		−	1.30347i	0.758448	−	0.651734i	$-0.225958\pi$
$3$	1501.32	−	1501.32i	0.396337	−	0.396337i	−0.480602	−	0.876939i	$-0.659582\pi$
$3$	1501.32	−	1501.32i	0.396337	−	0.396337i	0.876939	+	0.480602i	$0.159582\pi$
$4$	−22905.8			−0.699029
$5$	44470.0	−	44470.0i	0.254561	−	0.254561i	−0.568276	−	0.822838i	$-0.692390\pi$
$5$	44470.0	−	44470.0i	0.254561	−	0.254561i	0.822838	+	0.568276i	$0.192390\pi$
$6$	−354242.	−	354242.i	−0.516613	−	0.516613i
$7$	−175577.	−	175577.i	−0.0805808	−	0.0805808i	0.665668	−	0.746248i	$-0.268147\pi$
$7$	−175577.	−	175577.i	−0.0805808	−	0.0805808i	−0.746248	+	0.665668i	$0.768147\pi$
$8$		−	2.32702e6i		−	0.392307i
$9$			9.84096e6i			0.685833i
$10$	−1.04928e7	−	1.04928e7i	−0.331813	−	0.331813i
$11$	−3.82927e7	−	3.82927e7i	−0.592476	−	0.592476i	0.345824	−	0.938299i	$-0.387599\pi$
$11$	−3.82927e7	−	3.82927e7i	−0.592476	−	0.592476i	−0.938299	+	0.345824i	$0.887599\pi$
$12$	−3.43890e7	+	3.43890e7i	−0.277051	+	0.277051i
$13$	−2.65197e8			−1.17218			−0.586090	−	0.810246i	$-0.699333\pi$
$13$	−2.65197e8			−1.17218			−0.586090	+	0.810246i	$0.699333\pi$
$14$	−4.14278e7	+	4.14278e7i	−0.105035	+	0.105035i
$15$		−	1.33528e8i		−	0.201784i
$16$	−1.29964e9			−1.21039
$17$	−1.64424e9	−	3.98611e8i	−0.971849	−	0.235604i
$17$	−1.64424e9	−	3.98611e8i	−0.971849	−	0.235604i
$18$	2.32200e9			0.893962
$19$		−	4.03873e9i		−	1.03656i	−0.855212	−	0.518278i	$-0.826573\pi$
$19$		−	4.03873e9i		−	1.03656i	0.855212	−	0.518278i	$-0.173427\pi$
$20$	−1.01862e9	+	1.01862e9i	−0.177946	+	0.177946i
$21$	−5.27195e8			−0.0638744
$22$	−9.03527e9	+	9.03527e9i	−0.772273	+	0.772273i
$23$	3.73876e9	+	3.73876e9i	0.228965	+	0.228965i	0.812260	−	0.583295i	$-0.198237\pi$
$23$	3.73876e9	+	3.73876e9i	0.228965	+	0.228965i	−0.583295	+	0.812260i	$0.698237\pi$
$24$	−3.49361e9	−	3.49361e9i	−0.155486	−	0.155486i
$25$			2.65624e10i			0.870397i
$26$			6.25741e10i			1.52790i
$27$	3.63168e10	+	3.63168e10i	0.668159	+	0.668159i
$28$	4.02172e9	+	4.02172e9i	0.0563283	+	0.0563283i
$29$	−2.52760e8	+	2.52760e8i	−0.00272097	+	0.00272097i	−0.708466	−	0.705745i	$-0.750612\pi$
$29$	−2.52760e8	+	2.52760e8i	−0.00272097	+	0.00272097i	0.705745	+	0.708466i	$0.250612\pi$
$30$	−3.15063e10			−0.263019
$31$	7.99705e10	−	7.99705e10i	0.522056	−	0.522056i	−0.396136	−	0.918192i	$-0.629649\pi$
$31$	7.99705e10	−	7.99705e10i	0.522056	−	0.522056i	0.918192	+	0.396136i	$0.129649\pi$
$32$			2.30403e11i			1.18539i
$33$	−1.14979e11			−0.469641
$34$	−9.40533e10	+	3.87964e11i	−0.307102	+	1.26677i
$35$	−1.56158e10			−0.0410255
$36$		−	2.25415e11i		−	0.479417i
$37$	−4.54652e11	+	4.54652e11i	−0.787346	+	0.787346i	−0.981058	−	0.193712i	$-0.937947\pi$
$37$	−4.54652e11	+	4.54652e11i	−0.787346	+	0.787346i	0.193712	+	0.981058i	$0.437947\pi$
$38$	−9.52950e11			−1.35112
$39$	−3.98147e11	+	3.98147e11i	−0.464579	+	0.464579i
$40$	−1.03483e11	−	1.03483e11i	−0.0998661	−	0.0998661i
$41$	−2.35684e11	−	2.35684e11i	−0.188995	−	0.188995i	0.606266	−	0.795262i	$-0.292667\pi$
$41$	−2.35684e11	−	2.35684e11i	−0.188995	−	0.188995i	−0.795262	+	0.606266i	$0.792667\pi$
$42$			1.24393e11i			0.0832582i
$43$		−	1.09954e12i		−	0.616874i	−0.951245	−	0.308437i	$-0.900194\pi$
$43$		−	1.09954e12i		−	0.616874i	0.951245	−	0.308437i	$-0.0998059\pi$
$44$	8.77123e11	+	8.77123e11i	0.414157	+	0.414157i
$45$	4.37628e11	+	4.37628e11i	0.174587	+	0.174587i
$46$	8.82171e11	−	8.82171e11i	0.298448	−	0.298448i
$47$	4.36717e12			1.25738			0.628690	−	0.777656i	$-0.283591\pi$
$47$	4.36717e12			1.25738			0.628690	+	0.777656i	$0.283591\pi$
$48$	−1.95119e12	+	1.95119e12i	−0.479722	+	0.479722i
$49$		−	4.68591e12i		−	0.987013i
$50$	6.26748e12			1.13453
$51$	−3.06698e12	+	1.87010e12i	−0.478559	+	0.291802i
$52$	6.07455e12			0.819387
$53$		−	4.05639e12i		−	0.474320i	−0.971471	−	0.237160i	$-0.923784\pi$
$53$		−	4.05639e12i		−	0.474320i	0.971471	−	0.237160i	$-0.0762165\pi$
$54$	8.56906e12	−	8.56906e12i	0.870924	−	0.870924i
$55$	−3.40575e12			−0.301643
$56$	−4.08571e11	+	4.08571e11i	−0.0316124	+	0.0316124i
$57$	−6.06344e12	−	6.06344e12i	−0.410826	−	0.410826i
$58$	5.96394e10	+	5.96394e10i	0.00354669	+	0.00354669i
$59$		−	3.81023e12i		−	0.199325i	−0.995021	−	0.0996624i	$-0.968224\pi$
$59$		−	3.81023e12i		−	0.199325i	0.995021	−	0.0996624i	$-0.0317763\pi$
$60$			3.05856e12i			0.141053i
$61$	−2.45852e13	−	2.45852e13i	−1.00161	−	1.00161i	−0.999999	−	0.00161565i	$-0.999486\pi$
$61$	−2.45852e13	−	2.45852e13i	−1.00161	−	1.00161i	−0.00161565	−	0.999999i	$-0.500514\pi$
$62$	−1.88693e13	−	1.88693e13i	−0.680483	−	0.680483i
$63$	1.72784e12	−	1.72784e12i	0.0552650	−	0.0552650i
$64$	1.17775e13			0.334737
$65$	−1.17933e13	+	1.17933e13i	−0.298392	+	0.298392i
$66$			2.71297e13i			0.612161i
$67$	−1.49091e13			−0.300532			−0.150266	−	0.988646i	$-0.548013\pi$
$67$	−1.49091e13			−0.300532			−0.150266	+	0.988646i	$0.548013\pi$
$68$	3.76626e13	+	9.13048e12i	0.679350	+	0.164694i
$69$	1.12262e13			0.181495
$70$			3.68460e12i			0.0534755i
$71$	−4.53167e13	+	4.53167e13i	−0.591317	+	0.591317i	−0.937987	−	0.346670i	$-0.887312\pi$
$71$	−4.53167e13	+	4.53167e13i	−0.591317	+	0.591317i	0.346670	+	0.937987i	$0.387312\pi$
$72$	2.29001e13			0.269057
$73$	−1.68696e13	+	1.68696e13i	−0.178725	+	0.178725i	−0.790800	−	0.612075i	$-0.790335\pi$
$73$	−1.68696e13	+	1.68696e13i	−0.178725	+	0.178725i	0.612075	+	0.790800i	$0.290335\pi$
$74$	1.07276e14	+	1.07276e14i	1.02628	+	1.02628i
$75$	3.98788e13	+	3.98788e13i	0.344971	+	0.344971i
$76$			9.25102e13i			0.724582i
$77$			1.34466e13i			0.0954844i
$78$	9.39440e13	+	9.39440e13i	0.605563	+	0.605563i
$79$	−1.71150e14	−	1.71150e14i	−1.00271	−	1.00271i	−0.999996	−	0.00270982i	$-0.999137\pi$
$79$	−1.71150e14	−	1.71150e14i	−1.00271	−	1.00271i	−0.00270982	−	0.999996i	$-0.500863\pi$
$80$	−5.77952e13	+	5.77952e13i	−0.308118	+	0.308118i
$81$	−3.21603e13			−0.156200
$82$	−5.56103e13	+	5.56103e13i	−0.246349	+	0.246349i
$83$		−	1.11784e14i		−	0.452161i	−0.974109	−	0.226080i	$-0.927409\pi$
$83$		−	1.11784e14i		−	0.452161i	0.974109	−	0.226080i	$-0.0725912\pi$
$84$	1.20758e13			0.0446500
$85$	−9.08457e13	+	5.53933e13i	−0.307371	+	0.187420i
$86$	−2.59439e14			−0.804076
$87$			7.58949e11i			0.00215684i
$88$	−8.91079e13	+	8.91079e13i	−0.232432	+	0.232432i
$89$	1.89313e14			0.453686			0.226843	−	0.973931i	$-0.427160\pi$
$89$	1.89313e14			0.453686			0.226843	+	0.973931i	$0.427160\pi$
$90$	1.03260e14	−	1.03260e14i	0.227568	−	0.227568i
$91$	4.65625e13	+	4.65625e13i	0.0944552	+	0.0944552i
$92$	−8.56391e13	−	8.56391e13i	−0.160053	−	0.160053i
$93$		−	2.40123e14i		−	0.413821i
$94$		−	1.03045e15i		−	1.63895i
$95$	−1.79602e14	−	1.79602e14i	−0.263867	−	0.263867i
$96$	3.45909e14	+	3.45909e14i	0.469816	+	0.469816i
$97$	4.74848e14	−	4.74848e14i	0.596714	−	0.596714i	−0.342723	−	0.939437i	$-0.611349\pi$
$97$	4.74848e14	−	4.74848e14i	0.596714	−	0.596714i	0.939437	+	0.342723i	$0.111349\pi$
$98$	−1.10565e15			−1.28654
$99$	3.76837e14	−	3.76837e14i	0.406339	−	0.406339i
$100$		−	6.08432e14i		−	0.608432i
$101$	1.29320e15			1.20021			0.600104	−	0.799922i	$-0.295126\pi$
$101$	1.29320e15			1.20021			0.600104	+	0.799922i	$0.295126\pi$
$102$	4.41255e14	+	7.23664e14i	0.380354	+	0.623786i
$103$	1.23182e15			0.986890			0.493445	−	0.869777i	$-0.335737\pi$
$103$	1.23182e15			0.986890			0.493445	+	0.869777i	$0.335737\pi$
$104$			6.17120e14i			0.459854i
$105$	−2.34444e13	+	2.34444e13i	−0.0162600	+	0.0162600i
$106$	−9.57118e14			−0.618260
$107$	6.99653e14	−	6.99653e14i	0.421216	−	0.421216i	−0.464407	−	0.885622i	$-0.653732\pi$
$107$	6.99653e14	−	6.99653e14i	0.421216	−	0.421216i	0.885622	+	0.464407i	$0.153732\pi$
$108$	−8.31865e14	−	8.31865e14i	−0.467062	−	0.467062i
$109$	1.55551e15	+	1.55551e15i	0.815030	+	0.815030i	0.985383	−	0.170353i	$-0.0544909\pi$
$109$	1.55551e15	+	1.55551e15i	0.815030	+	0.815030i	−0.170353	+	0.985383i	$0.554491\pi$
$110$			8.03597e14i			0.393182i
$111$			1.36516e15i			0.624110i
$112$	2.28187e14	+	2.28187e14i	0.0975340	+	0.0975340i
$113$	−2.00421e15	−	2.00421e15i	−0.801412	−	0.801412i	0.181904	−	0.983316i	$-0.441774\pi$
$113$	−2.00421e15	−	2.00421e15i	−0.801412	−	0.801412i	−0.983316	+	0.181904i	$0.941774\pi$
$114$	−1.43069e15	+	1.43069e15i	−0.535499	+	0.535499i
$115$	3.32525e14			0.116571
$116$	5.78966e12	−	5.78966e12i	0.00190203	−	0.00190203i
$117$		−	2.60980e15i		−	0.803920i
$118$	−8.99035e14			−0.259813
$119$	2.18704e14	+	3.58678e14i	0.0593273	+	0.0972976i
$120$	−3.10722e14			−0.0791613
$121$		−	1.24459e15i		−	0.297945i
$122$	−5.80096e15	+	5.80096e15i	−1.30557	+	1.30557i
$123$	−7.07675e14			−0.149812
$124$	−1.83178e15	+	1.83178e15i	−0.364932	+	0.364932i
$125$	2.53835e15	+	2.53835e15i	0.476131	+	0.476131i
$126$	−4.07690e14	−	4.07690e14i	−0.0720362	−	0.0720362i
$127$		−	7.39424e15i		−	1.23130i	−0.788018	−	0.615652i	$-0.788893\pi$
$127$		−	7.39424e15i		−	1.23130i	0.788018	−	0.615652i	$-0.211107\pi$
$128$			4.77091e15i			0.749077i
$129$	−1.65076e15	−	1.65076e15i	−0.244490	−	0.244490i
$130$	2.78267e15	+	2.78267e15i	0.388944	+	0.388944i
$131$	−7.17530e15	+	7.17530e15i	−0.946903	+	0.946903i	−0.998660	−	0.0517565i	$-0.983518\pi$
$131$	−7.17530e15	+	7.17530e15i	−0.946903	+	0.946903i	0.0517565	+	0.998660i	$0.483518\pi$
$132$	2.63369e15			0.328292
$133$	−7.09107e14	+	7.09107e14i	−0.0835266	+	0.0835266i
$134$			3.51784e15i			0.391733i
$135$	3.23002e15			0.340175
$136$	−9.27576e14	+	3.82619e15i	−0.0924288	+	0.381263i
$137$	−4.27178e15			−0.402907			−0.201454	−	0.979498i	$-0.564567\pi$
$137$	−4.27178e15			−0.402907			−0.201454	+	0.979498i	$0.564567\pi$
$138$		−	2.64885e15i		−	0.236572i
$139$	1.41138e16	−	1.41138e16i	1.19408	−	1.19408i	0.218171	−	0.975911i	$-0.429991\pi$
$139$	1.41138e16	−	1.41138e16i	1.19408	−	1.19408i	0.975911	−	0.218171i	$-0.0700091\pi$
$140$	3.57692e14			0.0286780
$141$	6.55654e15	−	6.55654e15i	0.498347	−	0.498347i
$142$	1.06926e16	+	1.06926e16i	0.770763	+	0.770763i
$143$	1.01551e16	+	1.01551e16i	0.694488	+	0.694488i
$144$		−	1.27897e16i		−	0.830124i
$145$			2.24805e13i			0.00138531i
$146$	3.98044e15	+	3.98044e15i	0.232962	+	0.232962i
$147$	−7.03507e15	−	7.03507e15i	−0.391190	−	0.391190i
$148$	1.04141e16	−	1.04141e16i	0.550377	−	0.550377i
$149$	−1.32310e16			−0.664807			−0.332403	−	0.943137i	$-0.607860\pi$
$149$	−1.32310e16			−0.664807			−0.332403	+	0.943137i	$0.607860\pi$
$150$	9.40952e15	−	9.40952e15i	0.449659	−	0.449659i
$151$		−	3.16527e16i		−	1.43908i	−0.694453	−	0.719538i	$-0.744354\pi$
$151$		−	3.16527e16i		−	1.43908i	0.694453	−	0.719538i	$-0.255646\pi$
$152$	−9.39821e15			−0.406648
$153$	3.92271e15	−	1.61809e16i	0.161585	−	0.666526i
$154$	3.17277e15			0.124461
$155$		−	7.11258e15i		−	0.265790i
$156$	9.11987e15	−	9.11987e15i	0.324754	−	0.324754i
$157$	−4.15690e16			−1.41098			−0.705492	−	0.708718i	$-0.749274\pi$
$157$	−4.15690e16			−1.41098			−0.705492	+	0.708718i	$0.749274\pi$
$158$	−4.03833e16	+	4.03833e16i	−1.30700	+	1.30700i
$159$	−6.08996e15	−	6.08996e15i	−0.187991	−	0.187991i
$160$	1.02460e16	+	1.02460e16i	0.301756	+	0.301756i
$161$		−	1.31288e15i		−	0.0369003i
$162$			7.58831e15i			0.203602i
$163$	−5.73662e15	−	5.73662e15i	−0.146977	−	0.146977i	0.629789	−	0.776766i	$-0.283141\pi$
$163$	−5.73662e15	−	5.73662e15i	−0.146977	−	0.146977i	−0.776766	+	0.629789i	$0.783141\pi$
$164$	5.39852e15	+	5.39852e15i	0.132113	+	0.132113i
$165$	−5.11314e15	+	5.11314e15i	−0.119552	+	0.119552i
$166$	−2.63757e16			−0.589377
$167$	2.16235e16	−	2.16235e16i	0.461904	−	0.461904i	−0.437375	−	0.899279i	$-0.644092\pi$
$167$	2.16235e16	−	2.16235e16i	0.461904	−	0.461904i	0.899279	+	0.437375i	$0.144092\pi$
$168$			1.22680e15i			0.0250584i
$169$	1.91438e16			0.374005
$170$	1.30702e16	+	2.14353e16i	0.244296	+	0.400648i
$171$	3.97450e16			0.710905
$172$			2.51858e16i			0.431213i
$173$	−1.14860e16	+	1.14860e16i	−0.188288	+	0.188288i	−0.794956	−	0.606667i	$-0.792506\pi$
$173$	−1.14860e16	+	1.14860e16i	−0.188288	+	0.188288i	0.606667	+	0.794956i	$0.292506\pi$
$174$	1.79076e14			0.00281137
$175$	4.66374e15	−	4.66374e15i	0.0701373	−	0.0701373i
$176$	4.97668e16	+	4.97668e16i	0.717125	+	0.717125i
$177$	−5.72039e15	−	5.72039e15i	−0.0789999	−	0.0789999i
$178$		−	4.46689e16i		−	0.591364i
$179$			1.09455e17i			1.38944i	0.719281	+	0.694719i	$0.244471\pi$
$179$			1.09455e17i			1.38944i	−0.719281	+	0.694719i	$0.755529\pi$
$180$	−1.00242e16	−	1.00242e16i	−0.122041	−	0.122041i
$181$	7.47356e16	+	7.47356e16i	0.872847	+	0.872847i	0.992782	−	0.119935i	$-0.0382685\pi$
$181$	7.47356e16	+	7.47356e16i	0.872847	+	0.872847i	−0.119935	+	0.992782i	$0.538268\pi$
$182$	1.09866e16	−	1.09866e16i	0.123119	−	0.123119i
$183$	−7.38208e16			−0.793955
$184$	8.70017e15	−	8.70017e15i	0.0898243	−	0.0898243i
$185$			4.04367e16i			0.400856i
$186$	−5.66578e16			−0.539402
$187$	4.76986e16	+	7.82263e16i	0.436208	+	0.715386i
$188$	−1.00033e17			−0.878945
$189$		−	1.27528e16i		−	0.107682i
$190$	−4.23777e16	+	4.23777e16i	−0.343942	+	0.343942i
$191$	9.53522e15			0.0744013			0.0372006	−	0.999308i	$-0.488156\pi$
$191$	9.53522e15			0.0744013			0.0372006	+	0.999308i	$0.488156\pi$
$192$	1.76818e16	−	1.76818e16i	0.132669	−	0.132669i
$193$	−3.51737e16	−	3.51737e16i	−0.253827	−	0.253827i	0.568710	−	0.822538i	$-0.307442\pi$
$193$	−3.51737e16	−	3.51737e16i	−0.253827	−	0.253827i	−0.822538	+	0.568710i	$0.807442\pi$
$194$	−1.12042e17	−	1.12042e17i	−0.777797	−	0.777797i
$195$			3.54112e16i			0.236527i
$196$			1.07334e17i			0.689951i
$197$	−1.16675e17	−	1.16675e17i	−0.721909	−	0.721909i	0.247085	−	0.968994i	$-0.420527\pi$
$197$	−1.16675e17	−	1.16675e17i	−0.721909	−	0.721909i	−0.968994	+	0.247085i	$0.920527\pi$
$198$	−8.89157e16	−	8.89157e16i	−0.529650	−	0.529650i
$199$	1.34437e17	−	1.34437e17i	0.771116	−	0.771116i	−0.207186	−	0.978302i	$-0.566430\pi$
$199$	1.34437e17	−	1.34437e17i	0.771116	−	0.771116i	0.978302	+	0.207186i	$0.0664305\pi$
$200$	6.18113e16			0.341462
$201$	−2.23834e16	+	2.23834e16i	−0.119112	+	0.119112i
$202$		−	3.05135e17i		−	1.56443i
$203$	8.87575e13			0.000438516
$204$	7.02516e16	−	4.28360e16i	0.334526	−	0.203978i
$205$	−2.09617e16			−0.0962217
$206$		−	2.90652e17i		−	1.28638i
$207$	−3.67929e16	+	3.67929e16i	−0.157032	+	0.157032i
$208$	3.44662e17			1.41879
$209$	−1.54654e17	+	1.54654e17i	−0.614134	+	0.614134i
$210$	5.53177e15	+	5.53177e15i	0.0211943	+	0.0211943i
$211$	2.90991e17	+	2.90991e17i	1.07587	+	1.07587i	0.996875	+	0.0789985i	$0.0251722\pi$
$211$	2.90991e17	+	2.90991e17i	1.07587	+	1.07587i	0.0789985	+	0.996875i	$0.474828\pi$
$212$			9.29148e16i			0.331563i
$213$			1.36070e17i			0.468722i
$214$	−1.65085e17	−	1.65085e17i	−0.549041	−	0.549041i
$215$	−4.88965e16	−	4.88965e16i	−0.157032	−	0.157032i
$216$	8.45101e16	−	8.45101e16i	0.262123	−	0.262123i
$217$	−2.80819e16			−0.0841354
$218$	3.67027e17	−	3.67027e17i	1.06237	−	1.06237i
$219$			5.06536e16i			0.141671i
$220$	7.80114e16			0.210857
$221$	4.36049e17	+	1.05710e17i	1.13918	+	0.276170i
$222$	3.22113e17			0.813507
$223$		−	1.51846e17i		−	0.370780i	−0.982665	−	0.185390i	$-0.940645\pi$
$223$		−	1.51846e17i		−	0.370780i	0.982665	−	0.185390i	$-0.0593548\pi$
$224$	4.04534e16	−	4.04534e16i	0.0955201	−	0.0955201i
$225$	−2.61400e17			−0.596947
$226$	−4.72900e17	+	4.72900e17i	−1.04462	+	1.04462i
$227$	−4.29442e17	−	4.29442e17i	−0.917721	−	0.917721i	0.0791424	−	0.996863i	$-0.474782\pi$
$227$	−4.29442e17	−	4.29442e17i	−0.917721	−	0.917721i	−0.996863	+	0.0791424i	$0.974782\pi$
$228$	1.38888e17	+	1.38888e17i	0.287179	+	0.287179i
$229$			9.44340e17i			1.88957i	0.327694	+	0.944784i	$0.393728\pi$
$229$			9.44340e17i			1.88957i	−0.327694	+	0.944784i	$0.606272\pi$
$230$		−	7.84603e16i		−	0.151947i
$231$	2.01877e16	+	2.01877e16i	0.0378440	+	0.0378440i
$232$	5.88178e14	+	5.88178e14i	0.00106745	+	0.00106745i
$233$	4.50515e17	−	4.50515e17i	0.791662	−	0.791662i	−0.190102	−	0.981764i	$-0.560882\pi$
$233$	4.50515e17	−	4.50515e17i	0.791662	−	0.791662i	0.981764	+	0.190102i	$0.0608819\pi$
$234$	−6.15789e17			−1.04788
$235$	1.94208e17	−	1.94208e17i	0.320080	−	0.320080i
$236$			8.72763e16i			0.139334i
$237$	−5.13903e17			−0.794820
$238$	8.46310e16	−	5.16038e16i	0.126824	−	0.0773312i
$239$	−9.24480e17			−1.34250			−0.671249	−	0.741232i	$-0.734242\pi$
$239$	−9.24480e17			−1.34250			−0.671249	+	0.741232i	$0.734242\pi$
$240$			1.73539e17i			0.244237i
$241$	−1.54258e17	+	1.54258e17i	−0.210436	+	0.210436i	−0.804453	−	0.594017i	$-0.797541\pi$
$241$	−1.54258e17	+	1.54258e17i	−0.210436	+	0.210436i	0.594017	+	0.804453i	$0.297541\pi$
$242$	−2.93665e17			−0.388362
$243$	−5.69390e17	+	5.69390e17i	−0.730067	+	0.730067i
$244$	5.63144e17	+	5.63144e17i	0.700157	+	0.700157i
$245$	−2.08382e17	−	2.08382e17i	−0.251255	−	0.251255i
$246$			1.66978e17i			0.195275i
$247$			1.07106e18i			1.21503i
$248$	−1.86093e17	−	1.86093e17i	−0.204806	−	0.204806i
$249$	−1.67824e17	−	1.67824e17i	−0.179208	−	0.179208i
$250$	5.98931e17	−	5.98931e17i	0.620621	−	0.620621i
$251$	6.42613e17			0.646245			0.323122	−	0.946357i	$-0.395267\pi$
$251$	6.42613e17			0.646245			0.323122	+	0.946357i	$0.395267\pi$
$252$	−3.95776e16	+	3.95776e16i	−0.0386318	+	0.0386318i
$253$		−	2.86334e17i		−	0.271312i
$254$	−1.74469e18			−1.60497
$255$	−5.32256e16	+	2.19552e17i	−0.0475411	+	0.196104i
$256$	1.51163e18			1.31113
$257$		−	1.37561e18i		−	1.15877i	−0.815054	−	0.579385i	$-0.803293\pi$
$257$		−	1.37561e18i		−	1.15877i	0.815054	−	0.579385i	$-0.196707\pi$
$258$	−3.89502e17	+	3.89502e17i	−0.318685	+	0.318685i
$259$	1.59652e17			0.126890
$260$	2.70135e17	−	2.70135e17i	0.208584	−	0.208584i
$261$	−2.48740e15	−	2.48740e15i	−0.00186613	−	0.00186613i
$262$	1.69303e18	+	1.69303e18i	1.23426	+	1.23426i
$263$			6.25694e17i			0.443296i	0.975127	+	0.221648i	$0.0711436\pi$
$263$			6.25694e17i			0.443296i	−0.975127	+	0.221648i	$0.928856\pi$
$264$			2.67560e17i			0.184243i
$265$	−1.80388e17	−	1.80388e17i	−0.120743	−	0.120743i
$266$	1.67316e17	+	1.67316e17i	0.108874	+	0.108874i
$267$	2.84220e17	−	2.84220e17i	0.179813	−	0.179813i
$268$	3.41504e17			0.210080
$269$	2.08033e18	−	2.08033e18i	1.24449	−	1.24449i	0.286369	−	0.958119i	$-0.407552\pi$
$269$	2.08033e18	−	2.08033e18i	1.24449	−	1.24449i	0.958119	−	0.286369i	$-0.0924484\pi$
$270$		−	7.62133e17i		−	0.443407i
$271$	−2.88491e18			−1.63254			−0.816268	−	0.577674i	$-0.803961\pi$
$271$	−2.88491e18			−1.63254			−0.816268	+	0.577674i	$0.803961\pi$
$272$	2.13693e18	+	5.18052e17i	1.17631	+	0.285172i
$273$	1.39811e17			0.0748723
$274$			1.00794e18i			0.525176i
$275$	1.01715e18	−	1.01715e18i	0.515689	−	0.515689i
$276$	−2.57144e17			−0.126870
$277$	1.00995e18	−	1.00995e18i	0.484953	−	0.484953i	−0.421756	−	0.906709i	$-0.638586\pi$
$277$	1.00995e18	−	1.00995e18i	0.484953	−	0.484953i	0.906709	+	0.421756i	$0.138586\pi$
$278$	−3.33020e18	−	3.33020e18i	−1.55645	−	1.55645i
$279$	7.86986e17	+	7.86986e17i	0.358043	+	0.358043i
$280$			3.63383e16i			0.0160946i
$281$			3.23323e18i			1.39424i	0.716952	+	0.697122i	$0.245536\pi$
$281$			3.23323e18i			1.39424i	−0.716952	+	0.697122i	$0.754464\pi$
$282$	−1.54704e18	−	1.54704e18i	−0.649579	−	0.649579i
$283$	−1.09837e18	−	1.09837e18i	−0.449106	−	0.449106i	0.445951	−	0.895057i	$-0.352866\pi$
$283$	−1.09837e18	−	1.09837e18i	−0.449106	−	0.449106i	−0.895057	+	0.445951i	$0.852866\pi$
$284$	1.03801e18	−	1.03801e18i	0.413348	−	0.413348i
$285$	−5.39283e17			−0.209161
$286$	2.39613e18	−	2.39613e18i	0.905242	−	0.905242i
$287$			8.27612e16i			0.0304588i
$288$	−2.26738e18			−0.812983
$289$	2.54464e18	+	1.31082e18i	0.888982	+	0.457942i
$290$	5.30434e15			0.00180570
$291$		−	1.42580e18i		−	0.473000i
$292$	3.86412e17	−	3.86412e17i	0.124934	−	0.124934i
$293$	−7.36988e17			−0.232249			−0.116124	−	0.993235i	$-0.537047\pi$
$293$	−7.36988e17			−0.232249			−0.116124	+	0.993235i	$0.537047\pi$
$294$	−1.65994e18	+	1.65994e18i	−0.509904	+	0.509904i
$295$	−1.69441e17	−	1.69441e17i	−0.0507404	−	0.0507404i
$296$	1.05798e18	+	1.05798e18i	0.308881	+	0.308881i
$297$		−	2.78134e18i		−	0.791736i
$298$			3.12189e18i			0.866554i
$299$	−9.91509e17	−	9.91509e17i	−0.268388	−	0.268388i
$300$	−9.13454e17	−	9.13454e17i	−0.241145	−	0.241145i
$301$	−1.93053e17	+	1.93053e17i	−0.0497082	+	0.0497082i
$302$	−7.46855e18			−1.87579
$303$	1.94152e18	−	1.94152e18i	0.475688	−	0.475688i
$304$			5.24891e18i			1.25463i
$305$	−2.18661e18			−0.509945
$306$	−3.81793e18	−	9.25575e17i	−0.868796	−	0.210621i
$307$	7.09684e18			1.57589			0.787947	−	0.615743i	$-0.211144\pi$
$307$	7.09684e18			1.57589			0.787947	+	0.615743i	$0.211144\pi$
$308$		−	3.08005e17i		−	0.0667463i
$309$	1.84936e18	−	1.84936e18i	0.391141	−	0.391141i
$310$	−1.67823e18			−0.346449
$311$	−2.06994e18	+	2.06994e18i	−0.417114	+	0.417114i	−0.884208	−	0.467094i	$-0.845301\pi$
$311$	−2.06994e18	+	2.06994e18i	−0.417114	+	0.417114i	0.467094	+	0.884208i	$0.345301\pi$
$312$	9.26498e17	+	9.26498e17i	0.182257	+	0.182257i
$313$	6.44380e18	+	6.44380e18i	1.23754	+	1.23754i	0.961003	+	0.276537i	$0.0891867\pi$
$313$	6.44380e18	+	6.44380e18i	1.23754	+	1.23754i	0.276537	+	0.961003i	$0.410813\pi$
$314$			9.80832e18i			1.83917i
$315$		−	1.53675e17i		−	0.0281367i
$316$	3.92032e18	+	3.92032e18i	0.700920	+	0.700920i
$317$	−4.26166e17	−	4.26166e17i	−0.0744106	−	0.0744106i	0.668922	−	0.743333i	$-0.266756\pi$
$317$	−4.26166e17	−	4.26166e17i	−0.0744106	−	0.0744106i	−0.743333	+	0.668922i	$0.766756\pi$
$318$	−1.43694e18	+	1.43694e18i	−0.245040	+	0.245040i
$319$	1.93577e16			0.00322421
$320$	5.23746e17	−	5.23746e17i	0.0852110	−	0.0852110i
$321$		−	2.10081e18i		−	0.333887i
$322$	−3.09777e17			−0.0480984
$323$	−1.60988e18	+	6.64065e18i	−0.244216	+	1.00738i
$324$	7.36656e17			0.109189
$325$		−	7.04428e18i		−	1.02026i
$326$	−1.35357e18	+	1.35357e18i	−0.191580	+	0.191580i
$327$	4.67064e18			0.646054
$328$	−5.48441e17	+	5.48441e17i	−0.0741440	+	0.0741440i
$329$	−7.66774e17	−	7.66774e17i	−0.101321	−	0.101321i
$330$	1.20646e18	+	1.20646e18i	0.155833	+	0.155833i
$331$			1.00610e18i			0.127038i	0.997981	+	0.0635189i	$0.0202323\pi$
$331$			1.00610e18i			0.127038i	−0.997981	+	0.0635189i	$0.979768\pi$
$332$			2.56049e18i			0.316073i
$333$	−4.47421e18	−	4.47421e18i	−0.539988	−	0.539988i
$334$	−5.10212e18	−	5.10212e18i	−0.602077	−	0.602077i
$335$	−6.63008e17	+	6.63008e17i	−0.0765037	+	0.0765037i
$336$	6.85166e17			0.0773128
$337$	1.03642e19	−	1.03642e19i	1.14370	−	1.14370i	0.155933	−	0.987768i	$-0.450162\pi$
$337$	1.03642e19	−	1.03642e19i	1.14370	−	1.14370i	0.987768	−	0.155933i	$-0.0498383\pi$
$338$		−	4.51703e18i		−	0.487503i
$339$	−6.01795e18			−0.635259
$340$	2.08089e18	−	1.26883e18i	0.214861	−	0.131012i
$341$	−6.12456e18			−0.618611
$342$		−	9.37794e18i		−	0.926641i
$343$	−1.65630e18	+	1.65630e18i	−0.160115	+	0.160115i
$344$	−2.55865e18			−0.242004
$345$	4.99228e17	−	4.99228e17i	0.0462015	−	0.0462015i
$346$	2.71016e18	+	2.71016e18i	0.245428	+	0.245428i
$347$	−6.26534e17	−	6.26534e17i	−0.0555231	−	0.0555231i	0.678800	−	0.734323i	$-0.262500\pi$
$347$	−6.26534e17	−	6.26534e17i	−0.0555231	−	0.0555231i	−0.734323	+	0.678800i	$0.762500\pi$
$348$		−	1.73843e16i		−	0.00150769i
$349$			1.74813e18i			0.148383i	0.997244	+	0.0741915i	$0.0236376\pi$
$349$			1.74813e18i			0.148383i	−0.997244	+	0.0741915i	$0.976362\pi$
$350$	−1.10042e18	−	1.10042e18i	−0.0914218	−	0.0914218i
$351$	−9.63113e18	−	9.63113e18i	−0.783202	−	0.783202i
$352$	8.82274e18	−	8.82274e18i	0.702318	−	0.702318i
$353$	−1.70858e19			−1.33145			−0.665724	−	0.746198i	$-0.731877\pi$
$353$	−1.70858e19			−1.33145			−0.665724	+	0.746198i	$0.731877\pi$
$354$	−1.34974e18	+	1.34974e18i	−0.102974	+	0.102974i
$355$			4.03047e18i			0.301053i
$356$	−4.33635e18			−0.317139
$357$	8.66837e17	+	2.10146e17i	0.0620763	+	0.0150490i
$358$	2.58263e19			1.81109
$359$			1.20842e19i			0.829869i	0.909851	+	0.414934i	$0.136195\pi$
$359$			1.20842e19i			0.829869i	−0.909851	+	0.414934i	$0.863805\pi$
$360$	1.01837e18	−	1.01837e18i	0.0684915	−	0.0684915i
$361$	−1.13021e18			−0.0744486
$362$	1.76341e19	−	1.76341e19i	1.13773	−	1.13773i
$363$	−1.86854e18	−	1.86854e18i	−0.118087	−	0.118087i
$364$	−1.06655e18	−	1.06655e18i	−0.0660269	−	0.0660269i
$365$			1.50039e18i			0.0909927i
$366$			1.74182e19i			1.03489i
$367$	−3.36749e18	−	3.36749e18i	−0.196025	−	0.196025i	0.602269	−	0.798293i	$-0.294264\pi$
$367$	−3.36749e18	−	3.36749e18i	−0.196025	−	0.196025i	−0.798293	+	0.602269i	$0.794264\pi$
$368$	−4.85905e18	−	4.85905e18i	−0.277136	−	0.277136i
$369$	2.31935e18	−	2.31935e18i	0.129619	−	0.129619i
$370$	9.54116e18			0.522503
$371$	−7.12208e17	+	7.12208e17i	−0.0382211	+	0.0382211i
$372$			5.50021e18i			0.289272i
$373$	2.46901e19			1.27265			0.636323	−	0.771423i	$-0.280455\pi$
$373$	2.46901e19			1.27265			0.636323	+	0.771423i	$0.280455\pi$
$374$	1.84577e19	−	1.12546e19i	0.932483	−	0.568583i
$375$	7.62177e18			0.377417
$376$		−	1.01625e19i		−	0.493278i
$377$	6.70313e16	−	6.70313e16i	0.00318946	−	0.00318946i
$378$	−3.00906e18			−0.140360
$379$	−2.05599e19	+	2.05599e19i	−0.940216	+	0.940216i	−0.998311	−	0.0580952i	$-0.981497\pi$
$379$	−2.05599e19	+	2.05599e19i	−0.940216	+	0.940216i	0.0580952	+	0.998311i	$0.481497\pi$
$380$	4.11393e18	+	4.11393e18i	0.184451	+	0.184451i
$381$	−1.11011e19	−	1.11011e19i	−0.488012	−	0.488012i
$382$		−	2.24986e18i		−	0.0969797i
$383$			8.19984e18i			0.346589i	0.984870	+	0.173294i	$0.0554412\pi$
$383$			8.19984e18i			0.346589i	−0.984870	+	0.173294i	$0.944559\pi$
$384$	7.16268e18	+	7.16268e18i	0.296887	+	0.296887i
$385$	5.97971e17	+	5.97971e17i	0.0243066	+	0.0243066i
$386$	−8.29934e18	+	8.29934e18i	−0.330856	+	0.330856i
$387$	1.08205e19			0.423073
$388$	−1.08767e19	+	1.08767e19i	−0.417120	+	0.417120i
$389$			3.54182e19i			1.33231i	0.745814	+	0.666155i	$0.232061\pi$
$389$			3.54182e19i			1.33231i	−0.745814	+	0.666155i	$0.767939\pi$
$390$	8.35539e18			0.308306
$391$	−4.65711e18	−	7.63773e18i	−0.168574	−	0.276464i
$392$	−1.09042e19			−0.387212
$393$			2.15449e19i			0.750586i
$394$	−2.75299e19	+	2.75299e19i	−0.940985	+	0.940985i
$395$	−1.52221e19			−0.510500
$396$	−8.63173e18	+	8.63173e18i	−0.284043	+	0.284043i
$397$	−2.16863e19	−	2.16863e19i	−0.700256	−	0.700256i	0.264210	−	0.964465i	$-0.414889\pi$
$397$	−2.16863e19	−	2.16863e19i	−0.700256	−	0.700256i	−0.964465	+	0.264210i	$0.914889\pi$
$398$	−3.17207e19	−	3.17207e19i	−1.00512	−	1.00512i
$399$			2.12920e18i			0.0662094i
$400$		−	3.45217e19i		−	1.05352i
$401$	1.59715e19	+	1.59715e19i	0.478368	+	0.478368i	0.904609	−	0.426241i	$-0.140163\pi$
$401$	1.59715e19	+	1.59715e19i	0.478368	+	0.478368i	−0.426241	+	0.904609i	$0.640163\pi$
$402$	5.28142e18	+	5.28142e18i	0.155259	+	0.155259i
$403$	−2.12080e19	+	2.12080e19i	−0.611943	+	0.611943i
$404$	−2.96218e19			−0.838980
$405$	−1.43017e18	+	1.43017e18i	−0.0397626	+	0.0397626i
$406$		−	2.09426e16i		−	0.000571591i
$407$	3.48196e19			0.932967
$408$	4.35176e18	+	7.13694e18i	0.114476	+	0.187742i
$409$	−4.39748e19			−1.13574			−0.567871	−	0.823118i	$-0.692233\pi$
$409$	−4.39748e19			−1.13574			−0.567871	+	0.823118i	$0.692233\pi$
$410$			4.94598e18i			0.125422i
$411$	−6.41333e18	+	6.41333e18i	−0.159687	+	0.159687i
$412$	−2.82158e19			−0.689864
$413$	−6.68988e17	+	6.68988e17i	−0.0160618	+	0.0160618i
$414$	8.68140e18	+	8.68140e18i	0.204686	+	0.204686i
$415$	−4.97103e18	−	4.97103e18i	−0.115103	−	0.115103i
$416$		−	6.11022e19i		−	1.38950i
$417$		−	4.23789e19i		−	0.946519i
$418$	3.64910e19	+	3.64910e19i	0.800504	+	0.800504i
$419$	3.65899e19	+	3.65899e19i	0.788418	+	0.788418i	0.981235	−	0.192817i	$-0.0617623\pi$
$419$	3.65899e19	+	3.65899e19i	0.788418	+	0.788418i	−0.192817	+	0.981235i	$0.561762\pi$
$420$	5.37012e17	−	5.37012e17i	0.0113662	−	0.0113662i
$421$	7.69595e19			1.60010			0.800049	−	0.599935i	$-0.204807\pi$
$421$	7.69595e19			1.60010			0.800049	+	0.599935i	$0.204807\pi$
$422$	6.86602e19	−	6.86602e19i	1.40237	−	1.40237i
$423$			4.29772e19i			0.862353i
$424$	−9.43932e18			−0.186079
$425$	1.05881e19	−	4.36750e19i	0.205069	−	0.845895i
$426$	3.21061e19			0.610965
$427$			8.63319e18i			0.161422i
$428$	−1.60261e19	+	1.60261e19i	−0.294442	+	0.294442i
$429$	3.04922e19			0.550503
$430$	−1.15373e19	+	1.15373e19i	−0.204687	+	0.204687i
$431$	3.95233e19	+	3.95233e19i	0.689086	+	0.689086i	0.962030	−	0.272944i	$-0.0879974\pi$
$431$	3.95233e19	+	3.95233e19i	0.689086	+	0.689086i	−0.272944	+	0.962030i	$0.587997\pi$
$432$	−4.71989e19	−	4.71989e19i	−0.808731	−	0.808731i
$433$			2.96281e18i			0.0498936i	0.999689	+	0.0249468i	$0.00794164\pi$
$433$			2.96281e18i			0.0498936i	−0.999689	+	0.0249468i	$0.992058\pi$
$434$			6.62601e18i			0.109668i
$435$	3.37505e16	+	3.37505e16i	0.000549049	+	0.000549049i
$436$	−3.56301e19	−	3.56301e19i	−0.569729	−	0.569729i
$437$	1.50998e19	−	1.50998e19i	0.237335	−	0.237335i
$438$	1.19519e19			0.184663
$439$	−3.47735e19	+	3.47735e19i	−0.528159	+	0.528159i	−0.920023	−	0.391864i	$-0.871830\pi$
$439$	−3.47735e19	+	3.47735e19i	−0.528159	+	0.528159i	0.391864	+	0.920023i	$0.371830\pi$
$440$			7.92526e18i			0.118336i
$441$	4.61138e19			0.676927
$442$	2.49427e19	−	1.02887e20i	0.359978	−	1.48489i
$443$	5.09742e19			0.723307			0.361653	−	0.932313i	$-0.382212\pi$
$443$	5.09742e19			0.723307			0.361653	+	0.932313i	$0.382212\pi$
$444$		−	3.12700e19i		−	0.436270i
$445$	8.41875e18	−	8.41875e18i	0.115491	−	0.115491i
$446$	−3.58284e19			−0.483300
$447$	−1.98640e19	+	1.98640e19i	−0.263488	+	0.263488i
$448$	−2.06785e18	−	2.06785e18i	−0.0269734	−	0.0269734i
$449$	−9.06479e19	−	9.06479e19i	−1.16281	−	1.16281i	−0.983857	−	0.178956i	$-0.942728\pi$
$449$	−9.06479e19	−	9.06479e19i	−1.16281	−	1.16281i	−0.178956	−	0.983857i	$-0.557272\pi$
$450$			6.16780e19i			0.778102i
$451$			1.80499e19i			0.223950i
$452$	4.59081e19	+	4.59081e19i	0.560210	+	0.560210i
$453$	−4.75210e19	−	4.75210e19i	−0.570360	−	0.570360i
$454$	−1.01328e20	+	1.01328e20i	−1.19622	+	1.19622i
$455$	4.14127e18			0.0480893
$456$	−1.41098e19	+	1.41098e19i	−0.161170	+	0.161170i
$457$		−	1.48528e18i		−	0.0166893i	−0.999965	−	0.00834463i	$-0.997344\pi$
$457$		−	1.48528e18i		−	0.0166893i	0.999965	−	0.00834463i	$-0.00265621\pi$
$458$	2.22820e20			2.46299
$459$	−4.52374e19	−	7.41899e19i	−0.491929	−	0.806770i
$460$	−7.61675e18			−0.0814865
$461$		−	1.97199e19i		−	0.207562i	−0.994600	−	0.103781i	$-0.966906\pi$
$461$		−	1.97199e19i		−	0.207562i	0.994600	−	0.103781i	$-0.0330941\pi$
$462$	4.76335e18	−	4.76335e18i	0.0493285	−	0.0493285i
$463$	−7.39763e19			−0.753763			−0.376882	−	0.926261i	$-0.623004\pi$
$463$	−7.39763e19			−0.753763			−0.376882	+	0.926261i	$0.623004\pi$
$464$	3.28498e17	−	3.28498e17i	0.00329342	−	0.00329342i
$465$	−1.06783e19	−	1.06783e19i	−0.105343	−	0.105343i
$466$	−1.06300e20	−	1.06300e20i	−1.03191	−	1.03191i
$467$		−	1.57543e20i		−	1.50496i	−0.658617	−	0.752478i	$-0.728858\pi$
$467$		−	1.57543e20i		−	1.50496i	0.658617	−	0.752478i	$-0.271142\pi$
$468$			5.97794e19i			0.561963i
$469$	2.61769e18	+	2.61769e18i	0.0242171	+	0.0242171i
$470$	−4.58240e19	−	4.58240e19i	−0.417214	−	0.417214i
$471$	−6.24085e19	+	6.24085e19i	−0.559226	+	0.559226i
$472$	−8.86649e18			−0.0781964
$473$	−4.21042e19	+	4.21042e19i	−0.365483	+	0.365483i
$474$			1.21257e20i			1.03602i
$475$	1.07278e20			0.902215
$476$	−5.00958e18	−	8.21578e18i	−0.0414715	−	0.0680138i
$477$	3.99188e19			0.325304
$478$			2.18134e20i			1.74990i
$479$	−1.60199e20	+	1.60199e20i	−1.26516	+	1.26516i	−0.316598	+	0.948560i	$0.602541\pi$
$479$	−1.60199e20	+	1.60199e20i	−1.26516	+	1.26516i	−0.948560	+	0.316598i	$0.897459\pi$
$480$	3.07652e19			0.239194
$481$	1.20572e20	−	1.20572e20i	0.922911	−	0.922911i
$482$	3.63976e19	+	3.63976e19i	0.274296	+	0.274296i
$483$	−1.97106e18	−	1.97106e18i	−0.0146250	−	0.0146250i
$484$			2.85083e19i			0.208272i
$485$		−	4.22330e19i		−	0.303801i
$486$	1.34349e20	+	1.34349e20i	0.951619	+	0.951619i
$487$	−7.62532e19	−	7.62532e19i	−0.531852	−	0.531852i	0.389271	−	0.921123i	$-0.372727\pi$
$487$	−7.62532e19	−	7.62532e19i	−0.531852	−	0.531852i	−0.921123	+	0.389271i	$0.872727\pi$
$488$	−5.72104e19	+	5.72104e19i	−0.392940	+	0.392940i
$489$	−1.72251e19			−0.116505
$490$	−4.91684e19	+	4.91684e19i	−0.327503	+	0.327503i
$491$			2.05449e20i			1.34770i	0.738869	+	0.673849i	$0.235360\pi$
$491$			2.05449e20i			1.34770i	−0.738869	+	0.673849i	$0.764640\pi$
$492$	1.62099e19			0.104723
$493$	5.16351e17	−	3.14846e17i	0.00328544	−	0.00200330i
$494$	2.52720e20			1.58375
$495$		−	3.35159e19i		−	0.206877i
$496$	−1.03933e20	+	1.03933e20i	−0.631890	+	0.631890i
$497$	1.59131e19			0.0952977
$498$	−3.95985e19	+	3.95985e19i	−0.233592	+	0.233592i
$499$	1.33061e19	+	1.33061e19i	0.0773210	+	0.0773210i	0.744710	−	0.667389i	$-0.232588\pi$
$499$	1.33061e19	+	1.33061e19i	0.0773210	+	0.0773210i	−0.667389	+	0.744710i	$0.732588\pi$
$500$	−5.81428e19	−	5.81428e19i	−0.332829	−	0.332829i
$501$		−	6.49277e19i		−	0.366140i
$502$		−	1.51626e20i		−	0.842359i
$503$	5.84697e19	+	5.84697e19i	0.320015	+	0.320015i	0.848773	−	0.528758i	$-0.177342\pi$
$503$	5.84697e19	+	5.84697e19i	0.320015	+	0.320015i	−0.528758	+	0.848773i	$0.677342\pi$
$504$	−4.02073e18	−	4.02073e18i	−0.0216808	−	0.0216808i
$505$	5.75088e19	−	5.75088e19i	0.305527	−	0.305527i
$506$	−6.75613e19			−0.353646
$507$	2.87410e19	−	2.87410e19i	0.148232	−	0.148232i
$508$			1.69371e20i			0.860717i
$509$	1.77737e20			0.890007			0.445004	−	0.895529i	$-0.353202\pi$
$509$	1.77737e20			0.890007			0.445004	+	0.895529i	$0.353202\pi$
$510$	5.18040e19	+	1.25587e19i	0.255615	+	0.0619683i
$511$	5.92383e18			0.0288036
$512$		−	2.00341e20i		−	0.959944i
$513$	1.46674e20	−	1.46674e20i	0.692584	−	0.692584i
$514$	−3.24579e20			−1.51042
$515$	5.47792e19	−	5.47792e19i	0.251224	−	0.251224i
$516$	3.78120e19	+	3.78120e19i	0.170906	+	0.170906i
$517$	−1.67231e20	−	1.67231e20i	−0.744967	−	0.744967i
$518$		−	3.76705e19i		−	0.165397i
$519$			3.44885e19i			0.149251i
$520$	2.74434e19	+	2.74434e19i	0.117061	+	0.117061i
$521$	−9.11048e19	−	9.11048e19i	−0.383052	−	0.383052i	0.489148	−	0.872201i	$-0.337308\pi$
$521$	−9.11048e19	−	9.11048e19i	−0.383052	−	0.383052i	−0.872201	+	0.489148i	$0.837308\pi$
$522$	−5.86909e17	+	5.86909e17i	−0.00243244	+	0.00243244i
$523$	−3.23379e20			−1.32114			−0.660570	−	0.750765i	$-0.729685\pi$
$523$	−3.23379e20			−1.32114			−0.660570	+	0.750765i	$0.729685\pi$
$524$	1.64356e20	−	1.64356e20i	0.661912	−	0.661912i
$525$		−	1.40036e19i		−	0.0555961i
$526$	1.47634e20			0.577822
$527$	−1.63368e20	+	9.96137e19i	−0.630358	+	0.384361i
$528$	1.49432e20			0.568447
$529$		−	2.38679e20i		−	0.895150i
$530$	−4.25631e19	+	4.25631e19i	−0.157385	+	0.157385i
$531$	3.74963e19			0.136704
$532$	1.62426e19	−	1.62426e19i	0.0583875	−	0.0583875i
$533$	6.25027e19	+	6.25027e19i	0.221536	+	0.221536i
$534$	−6.70625e19	−	6.70625e19i	−0.234380	−	0.234380i
$535$		−	6.22272e19i		−	0.214450i
$536$			3.46938e19i			0.117900i
$537$	1.64328e20	+	1.64328e20i	0.550687	+	0.550687i
$538$	−4.90861e20	−	4.90861e20i	−1.62215	−	1.62215i
$539$	−1.79436e20	+	1.79436e20i	−0.584781	+	0.584781i
$540$	−7.39861e19			−0.237792
$541$	4.37570e20	−	4.37570e20i	1.38697	−	1.38697i	0.555366	−	0.831606i	$-0.312578\pi$
$541$	4.37570e20	−	4.37570e20i	1.38697	−	1.38697i	0.831606	−	0.555366i	$-0.187422\pi$
$542$			6.80703e20i			2.12796i
$543$	2.24405e20			0.691884
$544$	9.18410e19	−	3.78838e20i	0.279283	−	1.15203i
$545$	1.38347e20			0.414950
$546$		−	3.29888e19i		−	0.0975936i
$547$	−6.53343e19	+	6.53343e19i	−0.190650	+	0.190650i	−0.795977	−	0.605327i	$-0.793042\pi$
$547$	−6.53343e19	+	6.53343e19i	−0.190650	+	0.190650i	0.605327	+	0.795977i	$0.293042\pi$
$548$	9.78485e19			0.281644
$549$	2.41942e20	−	2.41942e20i	0.686940	−	0.686940i
$550$	−2.39998e20	−	2.39998e20i	−0.672184	−	0.672184i
$551$	1.02083e18	+	1.02083e18i	0.00282043	+	0.00282043i
$552$		−	2.61236e19i		−	0.0712015i
$553$			6.00999e19i			0.161598i
$554$	−2.38299e20	−	2.38299e20i	−0.632121	−	0.632121i
$555$	6.07087e19	+	6.07087e19i	0.158874	+	0.158874i
$556$	−3.23288e20	+	3.23288e20i	−0.834697	+	0.834697i
$557$	5.51392e19			0.140458			0.0702291	−	0.997531i	$-0.477627\pi$
$557$	5.51392e19			0.140458			0.0702291	+	0.997531i	$0.477627\pi$
$558$	1.85692e20	−	1.85692e20i	0.466698	−	0.466698i
$559$			2.91594e20i			0.723087i
$560$	2.02950e19			0.0496568
$561$	1.89054e20	+	4.58320e19i	0.456420	+	0.110649i
$562$	7.62889e20			1.81735
$563$			6.43312e20i			1.51220i	0.654457	+	0.756099i	$0.272897\pi$
$563$			6.43312e20i			1.51220i	−0.654457	+	0.756099i	$0.727103\pi$
$564$	−1.50183e20	+	1.50183e20i	−0.348359	+	0.348359i
$565$	−1.78255e20			−0.408017
$566$	−2.59163e20	+	2.59163e20i	−0.585396	+	0.585396i
$567$	5.64660e18	+	5.64660e18i	0.0125868	+	0.0125868i
$568$	1.05453e20	+	1.05453e20i	0.231978	+	0.231978i
$569$			4.38134e20i			0.951184i	0.879666	+	0.475592i	$0.157766\pi$
$569$			4.38134e20i			0.951184i	−0.879666	+	0.475592i	$0.842234\pi$
$570$			1.27245e20i			0.272634i
$571$	3.62284e20	+	3.62284e20i	0.766088	+	0.766088i	0.977415	−	0.211328i	$-0.0677787\pi$
$571$	3.62284e20	+	3.62284e20i	0.766088	+	0.766088i	−0.211328	+	0.977415i	$0.567779\pi$
$572$	−2.32611e20	−	2.32611e20i	−0.485467	−	0.485467i
$573$	1.43155e19	−	1.43155e19i	0.0294880	−	0.0294880i
$574$	1.95277e19			0.0397020
$575$	−9.93104e19	+	9.93104e19i	−0.199290	+	0.199290i
$576$			1.15902e20i			0.229573i
$577$	−3.37295e20			−0.659464			−0.329732	−	0.944075i	$-0.606958\pi$
$577$	−3.37295e20			−0.659464			−0.329732	+	0.944075i	$0.606958\pi$
$578$	3.09293e20	−	6.00416e20i	0.596913	−	1.15876i
$579$	−1.05614e20			−0.201203
$580$		−	5.14933e17i		−	0.000968368i
$581$	−1.96266e19	+	1.96266e19i	−0.0364355	+	0.0364355i
$582$	−3.36422e20			−0.616541
$583$	−1.55330e20	+	1.55330e20i	−0.281023	+	0.281023i
$584$	3.92560e19	+	3.92560e19i	0.0701148	+	0.0701148i
$585$	−1.16058e20	−	1.16058e20i	−0.204647	−	0.204647i
$586$			1.73894e20i			0.302729i
$587$			9.26555e20i			1.59252i	0.604953	+	0.796261i	$0.293192\pi$
$587$			9.26555e20i			1.59252i	−0.604953	+	0.796261i	$0.706808\pi$
$588$	1.61144e20	+	1.61144e20i	0.273453	+	0.273453i
$589$	−3.22979e20	−	3.22979e20i	−0.541140	−	0.541140i
$590$	−3.99801e19	+	3.99801e19i	−0.0661384	+	0.0661384i
$591$	−3.50335e20			−0.572239
$592$	5.90885e20	−	5.90885e20i	0.952994	−	0.952994i
$593$		−	1.37685e20i		−	0.219269i	−0.993972	−	0.109635i	$-0.965032\pi$
$593$		−	1.37685e20i		−	0.219269i	0.993972	−	0.109635i	$-0.0349681\pi$
$594$	−6.56265e20			−1.03200
$595$	2.56762e19	+	6.22463e18i	0.0398706	+	0.00966576i
$596$	3.03066e20			0.464719
$597$		−	4.03666e20i		−	0.611244i
$598$	−2.33949e20	+	2.33949e20i	−0.349835	+	0.349835i
$599$	−5.27681e20			−0.779238			−0.389619	−	0.920976i	$-0.627393\pi$
$599$	−5.27681e20			−0.779238			−0.389619	+	0.920976i	$0.627393\pi$
$600$	9.27988e19	−	9.27988e19i	0.135334	−	0.135334i
$601$	−4.25982e20	−	4.25982e20i	−0.613526	−	0.613526i	0.330337	−	0.943863i	$-0.392837\pi$
$601$	−4.25982e20	−	4.25982e20i	−0.613526	−	0.613526i	−0.943863	+	0.330337i	$0.892837\pi$
$602$	4.55515e19	+	4.55515e19i	0.0647931	+	0.0647931i
$603$		−	1.46720e20i		−	0.206115i
$604$			7.25030e20i			1.00596i
$605$	−5.53470e19	−	5.53470e19i	−0.0758453	−	0.0758453i
$606$	−4.58107e20	−	4.58107e20i	−0.620044	−	0.620044i
$607$	2.69960e20	−	2.69960e20i	0.360898	−	0.360898i	−0.503245	−	0.864144i	$-0.667861\pi$
$607$	2.69960e20	−	2.69960e20i	0.360898	−	0.360898i	0.864144	+	0.503245i	$0.167861\pi$
$608$	9.30535e20			1.22873
$609$	1.33254e17	−	1.33254e17i	0.000173800	−	0.000173800i
$610$			5.15937e20i			0.664696i
$611$	−1.15816e21			−1.47387
$612$	−8.98527e19	+	3.70636e20i	−0.112952	+	0.465921i
$613$	1.14324e21			1.41966			0.709831	−	0.704372i	$-0.248771\pi$
$613$	1.14324e21			1.41966			0.709831	+	0.704372i	$0.248771\pi$
$614$		−	1.67452e21i		−	2.05413i
$615$	−3.14704e19	+	3.14704e19i	−0.0381363	+	0.0381363i
$616$	3.12905e19			0.0374591
$617$	−1.10869e21	+	1.10869e21i	−1.31121	+	1.31121i	−0.390688	+	0.920523i	$0.627763\pi$
$617$	−1.10869e21	+	1.10869e21i	−1.31121	+	1.31121i	−0.920523	+	0.390688i	$0.872237\pi$
$618$	−4.36363e20	−	4.36363e20i	−0.509840	−	0.509840i
$619$	7.83836e19	+	7.83836e19i	0.0904785	+	0.0904785i	0.750897	−	0.660419i	$-0.229621\pi$
$619$	7.83836e19	+	7.83836e19i	0.0904785	+	0.0904785i	−0.660419	+	0.750897i	$0.729621\pi$
$620$			1.62919e20i			0.185795i
$621$			2.71560e20i			0.305970i
$622$	4.88408e20	+	4.88408e20i	0.543695	+	0.543695i
$623$	−3.32389e19	−	3.32389e19i	−0.0365584	−	0.0365584i
$624$	5.17450e20	−	5.17450e20i	0.562320	−	0.562320i
$625$	−5.84860e20			−0.627988
$626$	1.52043e21	−	1.52043e21i	1.61309	−	1.61309i
$627$			4.64371e20i			0.486809i
$628$	9.52169e20			0.986318
$629$	9.28786e20	−	5.66328e20i	0.950683	−	0.579680i
$630$	−3.62599e19			−0.0366752
$631$		−	1.46137e20i		−	0.146063i	−0.997330	−	0.0730313i	$-0.976733\pi$
$631$		−	1.46137e20i		−	0.146063i	0.997330	−	0.0730313i	$-0.0232673\pi$
$632$	−3.98270e20	+	3.98270e20i	−0.393368	+	0.393368i
$633$	8.73744e20			0.852818
$634$	−1.00555e20	+	1.00555e20i	−0.0969918	+	0.0969918i
$635$	−3.28822e20	−	3.28822e20i	−0.313442	−	0.313442i
$636$	1.39495e20	+	1.39495e20i	0.131411	+	0.131411i
$637$			1.24269e21i			1.15696i
$638$		−	4.56751e18i		−	0.00420266i
$639$	−4.45960e20	−	4.45960e20i	−0.405545	−	0.405545i
$640$	2.12162e20	+	2.12162e20i	0.190686	+	0.190686i
$641$	1.21150e21	−	1.21150e21i	1.07619	−	1.07619i	0.0793408	−	0.996848i	$-0.474718\pi$
$641$	1.21150e21	−	1.21150e21i	1.07619	−	1.07619i	0.996848	−	0.0793408i	$-0.0252815\pi$
$642$	−4.95693e20			−0.435211
$643$	1.16658e21	−	1.16658e21i	1.01235	−	1.01235i	0.0124279	−	0.999923i	$-0.496044\pi$
$643$	1.16658e21	−	1.16658e21i	1.01235	−	1.01235i	0.999923	−	0.0124279i	$-0.00395602\pi$
$644$			3.00725e19i			0.0257944i
$645$	−1.46819e20			−0.124476
$646$	1.56688e21	+	3.79856e20i	1.31308	+	0.318328i
$647$	1.00309e21			0.830921			0.415460	−	0.909611i	$-0.363620\pi$
$647$	1.00309e21			0.830921			0.415460	+	0.909611i	$0.363620\pi$
$648$			7.48377e19i			0.0612784i
$649$	−1.45904e20	+	1.45904e20i	−0.118095	+	0.118095i
$650$	−1.66212e21			−1.32988
$651$	−4.21601e19	+	4.21601e19i	−0.0333460	+	0.0333460i
$652$	1.31402e20	+	1.31402e20i	0.102741	+	0.102741i
$653$	−1.03318e21	−	1.03318e21i	−0.798596	−	0.798596i	0.184278	−	0.982874i	$-0.441005\pi$
$653$	−1.03318e21	−	1.03318e21i	−0.798596	−	0.798596i	−0.982874	+	0.184278i	$0.941005\pi$
$654$		−	1.10205e21i		−	0.842110i
$655$			6.38172e20i			0.482090i
$656$	3.06305e20	+	3.06305e20i	0.228757	+	0.228757i
$657$	−1.66013e20	−	1.66013e20i	−0.122575	−	0.122575i
$658$	−1.80923e20	+	1.80923e20i	−0.132068	+	0.132068i
$659$	−1.45798e21			−1.05223			−0.526116	−	0.850413i	$-0.676352\pi$
$659$	−1.45798e21			−1.05223			−0.526116	+	0.850413i	$0.676352\pi$
$660$	1.17120e20	−	1.17120e20i	0.0835705	−	0.0835705i
$661$			6.92403e20i			0.488482i	0.969715	+	0.244241i	$0.0785387\pi$
$661$			6.92403e20i			0.488482i	−0.969715	+	0.244241i	$0.921461\pi$
$662$	2.37393e20			0.165590
$663$	8.13356e20	−	4.95945e20i	0.560957	−	0.342044i
$664$	−2.60123e20			−0.177386
$665$			6.30680e19i			0.0425253i
$666$	−1.05570e21	+	1.05570e21i	−0.703857	+	0.703857i
$667$	−1.89002e18			−0.00124601
$668$	−4.95302e20	+	4.95302e20i	−0.322884	+	0.322884i
$669$	−2.27970e20	−	2.27970e20i	−0.146954	−	0.146954i
$670$	1.56439e20	+	1.56439e20i	0.0997201	+	0.0997201i
$671$			1.88287e21i			1.18686i
$672$		−	1.21467e20i		−	0.0757164i
$673$	−1.62323e21	−	1.62323e21i	−1.00062	−	1.00062i	−1.00000		0.000617345i	$-0.999803\pi$
$673$	−1.62323e21	−	1.62323e21i	−1.00062	−	1.00062i	−0.000617345	−	1.00000i	$-0.500197\pi$
$674$	−2.44547e21	−	2.44547e21i	−1.49078	−	1.49078i
$675$	−9.64663e20	+	9.64663e20i	−0.581564	+	0.581564i
$676$	−4.38503e20			−0.261440
$677$	1.61757e20	−	1.61757e20i	0.0953779	−	0.0953779i	−0.657808	−	0.753186i	$-0.728516\pi$
$677$	1.61757e20	−	1.61757e20i	0.0953779	−	0.0953779i	0.753186	+	0.657808i	$0.228516\pi$
$678$			1.41995e21i			0.828040i
$679$	−1.66744e20			−0.0961674
$680$	1.28901e20	+	2.11400e20i	0.0735260	+	0.120584i
$681$	−1.28946e21			−0.727454
$682$			1.44511e21i			0.806339i
$683$	9.01936e20	−	9.01936e20i	0.497761	−	0.497761i	−0.412980	−	0.910740i	$-0.635512\pi$
$683$	9.01936e20	−	9.01936e20i	0.497761	−	0.497761i	0.910740	+	0.412980i	$0.135512\pi$
$684$	−9.10389e20			−0.496943
$685$	−1.89966e20	+	1.89966e20i	−0.102565	+	0.102565i
$686$	3.90808e20	+	3.90808e20i	0.208705	+	0.208705i
$687$	1.41776e21	+	1.41776e21i	0.748906	+	0.748906i
$688$			1.42901e21i			0.746657i
$689$			1.07574e21i			0.555988i
$690$	−1.17794e20	−	1.17794e20i	−0.0602222	−	0.0602222i
$691$	8.11997e20	+	8.11997e20i	0.410647	+	0.410647i	0.881964	−	0.471317i	$-0.156221\pi$
$691$	8.11997e20	+	8.11997e20i	0.410647	+	0.410647i	−0.471317	+	0.881964i	$0.656221\pi$
$692$	2.63096e20	−	2.63096e20i	0.131619	−	0.131619i
$693$	−1.32327e20			−0.0654863
$694$	−1.47832e20	+	1.47832e20i	−0.0723725	+	0.0723725i
$695$		−	1.25529e21i		−	0.607934i
$696$	1.76609e18			0.000846143
$697$	2.93575e20	+	4.81467e20i	0.139147	+	0.228203i
$698$	4.12477e20			0.193412
$699$		−	1.35274e21i		−	0.627531i
$700$	−1.06827e20	+	1.06827e20i	−0.0490280	+	0.0490280i
$701$	1.37832e21			0.625842			0.312921	−	0.949779i	$-0.398693\pi$
$701$	1.37832e21			0.625842			0.312921	+	0.949779i	$0.398693\pi$
$702$	−2.27249e21	+	2.27249e21i	−1.02088	+	1.02088i
$703$	1.83621e21	+	1.83621e21i	0.816128	+	0.816128i
$704$	−4.50992e20	−	4.50992e20i	−0.198323	−	0.198323i
$705$		−	5.83140e20i		−	0.253720i
$706$			4.03143e21i			1.73550i
$707$	−2.27057e20	−	2.27057e20i	−0.0967138	−	0.0967138i
$708$	1.31030e20	+	1.31030e20i	0.0552232	+	0.0552232i
$709$	2.46673e21	−	2.46673e21i	1.02867	−	1.02867i	0.0290899	−	0.999577i	$-0.490739\pi$
$709$	2.46673e21	−	2.46673e21i	1.02867	−	1.02867i	0.999577	−	0.0290899i	$-0.00926091\pi$
$710$	9.51001e20			0.392413
$711$	1.68428e21	−	1.68428e21i	0.687689	−	0.687689i
$712$		−	4.40535e20i		−	0.177984i
$713$	5.97980e20			0.239065
$714$	4.95845e19	−	2.04533e20i	0.0196159	−	0.0809145i
$715$	9.03197e20			0.353579
$716$		−	2.50716e21i		−	0.971257i
$717$	−1.38794e21	+	1.38794e21i	−0.532082	+	0.532082i
$718$	2.85130e21			1.08171
$719$	2.39870e21	−	2.39870e21i	0.900553	−	0.900553i	−0.0949309	−	0.995484i	$-0.530263\pi$
$719$	2.39870e21	−	2.39870e21i	0.900553	−	0.900553i	0.995484	+	0.0949309i	$0.0302630\pi$
$720$	−5.68760e20	−	5.68760e20i	−0.211317	−	0.211317i
$721$	−2.16279e20	−	2.16279e20i	−0.0795244	−	0.0795244i
$722$			2.66677e20i			0.0970414i
$723$			4.63182e20i			0.166807i
$724$	−1.71188e21	−	1.71188e21i	−0.610145	−	0.610145i
$725$	−6.71391e18	−	6.71391e18i	−0.00236832	−	0.00236832i
$726$	−4.40886e20	+	4.40886e20i	−0.153922	+	0.153922i
$727$	−3.42604e21			−1.18381			−0.591907	−	0.806006i	$-0.701625\pi$
$727$	−3.42604e21			−1.18381			−0.591907	+	0.806006i	$0.701625\pi$
$728$	1.08352e20	−	1.08352e20i	0.0370554	−	0.0370554i
$729$			1.24821e21i			0.422505i
$730$	3.54021e20			0.118606
$731$	−4.38287e20	+	1.80791e21i	−0.145338	+	0.599509i
$732$	1.69092e21			0.554997
$733$		−	1.15800e20i		−	0.0376207i	−0.999823	−	0.0188104i	$-0.994012\pi$
$733$		−	1.15800e20i		−	0.0376207i	0.999823	−	0.0188104i	$-0.00598788\pi$
$734$	−7.94569e20	+	7.94569e20i	−0.255512	+	0.255512i
$735$	−6.25699e20			−0.199164
$736$	−8.61420e20	+	8.61420e20i	−0.271414	+	0.271414i
$737$	5.70909e20	+	5.70909e20i	0.178058	+	0.178058i
$738$	−5.47258e20	−	5.47258e20i	−0.168954	−	0.168954i
$739$		−	6.52646e21i		−	1.99455i	−0.0737840	−	0.997274i	$-0.523508\pi$
$739$		−	6.52646e21i		−	1.99455i	0.0737840	−	0.997274i	$-0.476492\pi$
$740$		−	9.26235e20i		−	0.280210i
$741$	1.60801e21	+	1.60801e21i	0.481562	+	0.481562i
$742$	1.68048e20	+	1.68048e20i	0.0498199	+	0.0498199i
$743$	−2.33253e21	+	2.33253e21i	−0.684559	+	0.684559i	−0.961024	−	0.276465i	$-0.910837\pi$
$743$	−2.33253e21	+	2.33253e21i	−0.684559	+	0.684559i	0.276465	+	0.961024i	$0.410837\pi$
$744$	−5.58772e20			−0.162345
$745$	−5.88383e20	+	5.88383e20i	−0.169234	+	0.169234i
$746$		−	5.82571e21i		−	1.65885i
$747$	1.10006e21			0.310107
$748$	−1.09257e21	−	1.79183e21i	−0.304922	−	0.500076i
$749$	−2.45686e20			−0.0678838
$750$		−	1.79838e21i		−	0.491951i
$751$	2.25597e21	−	2.25597e21i	0.610991	−	0.610991i	−0.332214	−	0.943204i	$-0.607795\pi$
$751$	2.25597e21	−	2.25597e21i	0.610991	−	0.610991i	0.943204	+	0.332214i	$0.107795\pi$
$752$	−5.67577e21			−1.52192
$753$	9.64771e20	−	9.64771e20i	0.256131	−	0.256131i
$754$	−1.58162e19	−	1.58162e19i	−0.00415736	−	0.00415736i
$755$	−1.40760e21	−	1.40760e21i	−0.366333	−	0.366333i
$756$			2.92112e20i			0.0752725i
$757$		−	3.41812e21i		−	0.872105i	−0.899921	−	0.436053i	$-0.856376\pi$
$757$		−	3.41812e21i		−	0.872105i	0.899921	−	0.436053i	$-0.143624\pi$
$758$	4.85118e21	+	4.85118e21i	1.22554	+	1.22554i
$759$	−4.29880e20	−	4.29880e20i	−0.107531	−	0.107531i
$760$	−4.17939e20	+	4.17939e20i	−0.103517	+	0.103517i
$761$	−2.58841e20			−0.0634817			−0.0317408	−	0.999496i	$-0.510105\pi$
$761$	−2.58841e20			−0.0634817			−0.0317408	+	0.999496i	$0.510105\pi$
$762$	−2.61935e21	+	2.61935e21i	−0.636108	+	0.636108i
$763$		−	5.46222e20i		−	0.131352i
$764$	−2.18411e20			−0.0520086
$765$	−5.45123e20	−	8.94009e20i	−0.128539	−	0.210805i
$766$	1.93478e21			0.451767
$767$			1.01046e21i			0.233644i
$768$	2.26945e21	−	2.26945e21i	0.519651	−	0.519651i
$769$	−3.29022e21			−0.746066			−0.373033	−	0.927818i	$-0.621682\pi$
$769$	−3.29022e21			−0.746066			−0.373033	+	0.927818i	$0.621682\pi$
$770$	1.41093e20	−	1.41093e20i	0.0316829	−	0.0316829i
$771$	−2.06524e21	−	2.06524e21i	−0.459264	−	0.459264i
$772$	8.05681e20	+	8.05681e20i	0.177433	+	0.177433i
$773$		−	2.05288e21i		−	0.447731i	−0.974620	−	0.223865i	$-0.928132\pi$
$773$		−	2.05288e21i		−	0.447731i	0.974620	−	0.223865i	$-0.0718676\pi$
$774$		−	2.55313e21i		−	0.551462i
$775$	2.12421e21	+	2.12421e21i	0.454396	+	0.454396i
$776$	−1.10498e21	−	1.10498e21i	−0.234095	−	0.234095i
$777$	2.39690e20	−	2.39690e20i	0.0502913	−	0.0502913i
$778$	8.35704e21			1.73662
$779$	−9.51863e20	+	9.51863e20i	−0.195904	+	0.195904i
$780$		−	8.11122e20i		−	0.165339i
$781$	3.47059e21			0.700682
$782$	−1.80214e21	+	1.09886e21i	−0.360362	+	0.219731i
$783$	−1.83589e19			−0.00363608
$784$			6.09001e21i			1.19467i
$785$	−1.84857e21	+	1.84857e21i	−0.359182	+	0.359182i
$786$	5.08359e21			0.978365
$787$	−2.63988e20	+	2.63988e20i	−0.0503238	+	0.0503238i	−0.731821	−	0.681497i	$-0.761329\pi$
$787$	−2.63988e20	+	2.63988e20i	−0.0503238	+	0.0503238i	0.681497	+	0.731821i	$0.261329\pi$
$788$	2.67254e21	+	2.67254e21i	0.504635	+	0.504635i
$789$	9.39369e20	+	9.39369e20i	0.175695	+	0.175695i
$790$			3.59170e21i			0.665421i
$791$			7.03787e20i			0.129157i
$792$	−8.76907e20	−	8.76907e20i	−0.159410	−	0.159410i
$793$	6.51994e21	+	6.51994e21i	1.17407	+	1.17407i
$794$	−5.11695e21	+	5.11695e21i	−0.912761	+	0.912761i
$795$	−5.41642e20			−0.0957103
$796$	−3.07938e21	+	3.07938e21i	−0.539032	+	0.539032i
$797$			1.12732e22i			1.95483i	0.211335	+	0.977414i	$0.432219\pi$
$797$			1.12732e22i			1.95483i	−0.211335	+	0.977414i	$0.567781\pi$
$798$	5.02391e20			0.0863018
$799$	−7.18069e21	−	1.74080e21i	−1.22198	−	0.296243i
$800$	−6.12006e21			−1.03176
$801$			1.86302e21i			0.311153i
$802$	3.76852e21	−	3.76852e21i	0.623537	−	0.623537i
$803$	1.29197e21			0.211780
$804$	5.12708e20	−	5.12708e20i	0.0832626	−	0.0832626i
$805$	−5.83837e19	−	5.83837e19i	−0.00939340	−	0.00939340i
$806$	5.00408e21	+	5.00408e21i	0.797648	+	0.797648i
$807$		−	6.24651e21i		−	0.986475i
$808$		−	3.00931e21i		−	0.470850i
$809$	−7.39291e21	−	7.39291e21i	−1.14604	−	1.14604i	−0.987323	−	0.158722i	$-0.949263\pi$
$809$	−7.39291e21	−	7.39291e21i	−1.14604	−	1.14604i	−0.158722	−	0.987323i	$-0.550737\pi$
$810$	3.37452e20	+	3.37452e20i	0.0518292	+	0.0518292i
$811$	−5.24747e21	+	5.24747e21i	−0.798534	+	0.798534i	−0.982864	−	0.184330i	$-0.940988\pi$
$811$	−5.24747e21	+	5.24747e21i	−0.798534	+	0.798534i	0.184330	+	0.982864i	$0.440988\pi$
$812$	−2.03306e18			−0.000306535
$813$	−4.33119e21	+	4.33119e21i	−0.647035	+	0.647035i
$814$		−	8.21579e21i		−	1.21609i
$815$	−5.10216e20			−0.0748293
$816$	3.98599e21	−	2.43046e21i	0.579242	−	0.353193i
$817$	−4.44074e21			−0.639425
$818$			1.03760e22i			1.48040i
$819$	−4.58220e20	+	4.58220e20i	−0.0647805	+	0.0647805i
$820$	4.80144e20			0.0672617
$821$	5.58541e21	−	5.58541e21i	0.775321	−	0.775321i	−0.203710	−	0.979031i	$-0.565300\pi$
$821$	5.58541e21	−	5.58541e21i	0.775321	−	0.775321i	0.979031	+	0.203710i	$0.0653001\pi$
$822$	1.51324e21	+	1.51324e21i	0.208147	+	0.208147i
$823$	−6.74080e21	−	6.74080e21i	−0.918783	−	0.918783i	0.0781580	−	0.996941i	$-0.475096\pi$
$823$	−6.74080e21	−	6.74080e21i	−0.918783	−	0.918783i	−0.996941	+	0.0781580i	$0.975096\pi$
$824$		−	2.86648e21i		−	0.387163i
$825$		−	3.05413e21i		−	0.408774i
$826$	1.57850e20	+	1.57850e20i	0.0209360	+	0.0209360i
$827$	7.43577e21	+	7.43577e21i	0.977315	+	0.977315i	0.999748	−	0.0224333i	$-0.00714134\pi$
$827$	7.43577e21	+	7.43577e21i	0.977315	+	0.977315i	−0.0224333	+	0.999748i	$0.507141\pi$
$828$	8.42771e20	−	8.42771e20i	0.109770	−	0.109770i
$829$	−5.03425e21			−0.649795			−0.324897	−	0.945749i	$-0.605330\pi$
$829$	−5.03425e21			−0.649795			−0.324897	+	0.945749i	$0.605330\pi$
$830$	−1.17293e21	+	1.17293e21i	−0.150033	+	0.150033i
$831$		−	3.03251e21i		−	0.384410i
$832$	−3.12336e21			−0.392371
$833$	−1.86785e21	+	7.70477e21i	−0.232544	+	0.959228i
$834$	−9.99942e21			−1.23376
$835$		−	1.92319e21i		−	0.235166i
$836$	3.54246e21	−	3.54246e21i	0.429297	−	0.429297i
$837$	5.80855e21			0.697632
$838$	8.63350e21	−	8.63350e21i	1.02768	−	1.02768i
$839$	−6.42457e19	−	6.42457e19i	−0.00757930	−	0.00757930i	0.703307	−	0.710886i	$-0.251706\pi$
$839$	−6.42457e19	−	6.42457e19i	−0.00757930	−	0.00757930i	−0.710886	+	0.703307i	$0.751706\pi$
$840$	5.45556e19	+	5.45556e19i	0.00637889	+	0.00637889i
$841$			8.62906e21i			0.999985i
$842$		−	1.81588e22i		−	2.08568i
$843$	4.85412e21	+	4.85412e21i	0.552591	+	0.552591i
$844$	−6.66537e21	−	6.66537e21i	−0.752066	−	0.752066i
$845$	8.51324e20	−	8.51324e20i	0.0952071	−	0.0952071i
$846$	1.01406e22			1.12405
$847$	−2.18521e20	+	2.18521e20i	−0.0240087	+	0.0240087i
$848$			5.27187e21i			0.574111i
$849$	−3.29801e21			−0.355995
$850$	−1.03053e22	−	2.49828e21i	−1.10260	−	0.267300i
$851$	−3.39966e21			−0.360549
$852$		−	3.11679e21i		−	0.327650i
$853$	−6.52857e21	+	6.52857e21i	−0.680300	+	0.680300i	−0.960068	−	0.279768i	$-0.909743\pi$
$853$	−6.52857e21	+	6.52857e21i	−0.680300	+	0.680300i	0.279768	+	0.960068i	$0.409743\pi$
$854$	2.03703e21			0.210408
$855$	1.76746e21	−	1.76746e21i	0.180969	−	0.180969i
$856$	−1.62811e21	−	1.62811e21i	−0.165246	−	0.165246i
$857$	−1.55176e21	−	1.55176e21i	−0.156124	−	0.156124i	0.624723	−	0.780846i	$-0.285212\pi$
$857$	−1.55176e21	−	1.55176e21i	−0.156124	−	0.156124i	−0.780846	+	0.624723i	$0.785212\pi$
$858$		−	7.19473e21i		−	0.717563i
$859$		−	7.44581e21i		−	0.736145i	−0.929797	−	0.368072i	$-0.880018\pi$
$859$		−	7.44581e21i		−	0.736145i	0.929797	−	0.368072i	$-0.119982\pi$
$860$	1.12001e21	+	1.12001e21i	0.109770	+	0.109770i
$861$	1.24251e20	+	1.24251e20i	0.0120720	+	0.0120720i
$862$	9.32563e21	−	9.32563e21i	0.898201	−	0.898201i
$863$	1.88198e22			1.79694			0.898472	−	0.439031i	$-0.144678\pi$
$863$	1.88198e22			1.79694			0.898472	+	0.439031i	$0.144678\pi$
$864$	−8.36750e21	+	8.36750e21i	−0.792032	+	0.792032i
$865$			1.02157e21i			0.0958619i
$866$	6.99084e20			0.0650347
$867$	5.78831e21	−	1.85236e21i	0.533837	−	0.170837i
$868$	6.43238e20			0.0588130
$869$			1.31076e22i			1.18816i
$870$	7.96353e18	−	7.96353e18i	0.000715667	−	0.000715667i
$871$	3.95385e21			0.352277
$872$	3.61970e21	−	3.61970e21i	0.319742	−	0.319742i
$873$	4.67295e21	+	4.67295e21i	0.409246	+	0.409246i
$874$	−3.56285e21	−	3.56285e21i	−0.309358	−	0.309358i
$875$		−	8.91350e20i		−	0.0767340i
$876$		−	1.16026e21i		−	0.0990317i
$877$	−5.34124e19	−	5.34124e19i	−0.00452007	−	0.00452007i	0.704843	−	0.709363i	$-0.251017\pi$
$877$	−5.34124e19	−	5.34124e19i	−0.00452007	−	0.00452007i	−0.709363	+	0.704843i	$0.751017\pi$
$878$	8.20490e21	+	8.20490e21i	0.688438	+	0.688438i
$879$	−1.10646e21	+	1.10646e21i	−0.0920489	+	0.0920489i
$880$	4.42626e21			0.365105
$881$	−9.62890e21	+	9.62890e21i	−0.787512	+	0.787512i	−0.981086	−	0.193574i	$-0.937992\pi$
$881$	−9.62890e21	+	9.62890e21i	−0.787512	+	0.787512i	0.193574	+	0.981086i	$0.437992\pi$
$882$		−	1.08807e22i		−	0.882352i
$883$	1.28537e22			1.03353			0.516765	−	0.856127i	$-0.327136\pi$
$883$	1.28537e22			1.03353			0.516765	+	0.856127i	$0.327136\pi$
$884$	−9.98803e21	−	2.42138e21i	−0.796321	−	0.193051i
$885$	−5.08772e20			−0.0402206
$886$		−	1.20275e22i		−	0.942807i
$887$	9.89480e21	−	9.89480e21i	0.769095	−	0.769095i	−0.208852	−	0.977947i	$-0.566973\pi$
$887$	9.89480e21	−	9.89480e21i	0.769095	−	0.769095i	0.977947	+	0.208852i	$0.0669728\pi$
$888$	3.17675e21			0.244842
$889$	−1.29826e21	+	1.29826e21i	−0.0992195	+	0.0992195i
$890$	−1.98643e21	−	1.98643e21i	−0.150539	−	0.150539i
$891$	1.23150e21	+	1.23150e21i	0.0925449	+	0.0925449i
$892$			3.47814e21i			0.259186i
$893$		−	1.76378e22i		−	1.30334i
$894$	4.68697e21	+	4.68697e21i	0.343448	+	0.343448i
$895$	4.86748e21	+	4.86748e21i	0.353697	+	0.353697i
$896$	8.37660e20	−	8.37660e20i	0.0603612	−	0.0603612i
$897$	−2.97715e21			−0.212744
$898$	−2.13886e22	+	2.13886e22i	−1.51569	+	1.51569i
$899$			4.04267e19i			0.00284099i
$900$	5.98756e21			0.417283
$901$	−1.61692e21	+	6.66969e21i	−0.111751	+	0.460967i
$902$	4.25893e21			0.291912
$903$			5.79671e20i			0.0394025i
$904$	−4.66385e21	+	4.66385e21i	−0.314399	+	0.314399i
$905$	6.64699e21			0.444386
$906$	−1.12127e22	+	1.12127e22i	−0.743446	+	0.743446i
$907$	−1.39255e22	−	1.39255e22i	−0.915706	−	0.915706i	0.0810074	−	0.996713i	$-0.474186\pi$
$907$	−1.39255e22	−	1.39255e22i	−0.915706	−	0.915706i	−0.996713	+	0.0810074i	$0.974186\pi$
$908$	9.83670e21	+	9.83670e21i	0.641513	+	0.641513i
$909$			1.27264e22i			0.823143i
$910$		−	9.77145e20i		−	0.0626828i
$911$	−1.03530e22	−	1.03530e22i	−0.658689	−	0.658689i	0.296381	−	0.955070i	$-0.404220\pi$
$911$	−1.03530e22	−	1.03530e22i	−0.658689	−	0.658689i	−0.955070	+	0.296381i	$0.904220\pi$
$912$	7.88032e21	+	7.88032e21i	0.497259	+	0.497259i
$913$	−4.28050e21	+	4.28050e21i	−0.267894	+	0.267894i
$914$	−3.50456e20			−0.0217539
$915$	−3.28281e21	+	3.28281e21i	−0.202110	+	0.202110i
$916$		−	2.16308e22i		−	1.32086i
$917$	2.51963e21			0.152605
$918$	−1.75053e22	+	1.06739e22i	−1.05160	+	0.641214i
$919$	−2.20928e22			−1.31639			−0.658194	−	0.752849i	$-0.728679\pi$
$919$	−2.20928e22			−1.31639			−0.658194	+	0.752849i	$0.728679\pi$
$920$		−	7.73794e20i		−	0.0457316i
$921$	1.06547e22	−	1.06547e22i	0.624586	−	0.624586i
$922$	−4.65297e21			−0.270551
$923$	1.20179e22	−	1.20179e22i	0.693130	−	0.693130i
$924$	−4.62415e20	−	4.62415e20i	−0.0264541	−	0.0264541i
$925$	−1.20766e22	−	1.20766e22i	−0.685304	−	0.685304i
$926$			1.74549e22i			0.982506i
$927$			1.21223e22i			0.676842i
$928$	−5.82366e19	−	5.82366e19i	−0.00322542	−	0.00322542i
$929$	6.27776e21	+	6.27776e21i	0.344895	+	0.344895i	0.858204	−	0.513309i	$-0.171580\pi$
$929$	6.27776e21	+	6.27776e21i	0.344895	+	0.344895i	−0.513309	+	0.858204i	$0.671580\pi$
$930$	−2.51957e21	+	2.51957e21i	−0.137311	+	0.137311i
$931$	−1.89251e22			−1.02309
$932$	−1.03194e22	+	1.03194e22i	−0.553394	+	0.553394i
$933$			6.21530e21i			0.330636i
$934$	−3.71728e22			−1.96166
$935$	5.59988e21	+	1.35757e21i	0.293151	+	0.0710681i
$936$	−6.07305e21			−0.315383
$937$			2.00286e22i			1.03182i	0.856643	+	0.515910i	$0.172546\pi$
$937$			2.00286e22i			1.03182i	−0.856643	+	0.515910i	$0.827454\pi$
$938$	6.17651e20	−	6.17651e20i	0.0315662	−	0.0315662i
$939$	1.93485e22			0.980967
$940$	−4.44849e21	+	4.44849e21i	−0.223745	+	0.223745i
$941$	−5.57246e21	−	5.57246e21i	−0.278051	−	0.278051i	0.554279	−	0.832331i	$-0.312994\pi$
$941$	−5.57246e21	−	5.57246e21i	−0.278051	−	0.278051i	−0.832331	+	0.554279i	$0.812994\pi$
$942$	1.47255e22	+	1.47255e22i	0.728933	+	0.728933i
$943$		−	1.76233e21i		−	0.0865464i
$944$			4.95194e21i			0.241260i
$945$	−5.67117e20	−	5.67117e20i	−0.0274116	−	0.0274116i
$946$	9.93461e21	+	9.93461e21i	0.476395	+	0.476395i
$947$	2.59895e22	−	2.59895e22i	1.23644	−	1.23644i	0.274994	−	0.961446i	$-0.411324\pi$
$947$	2.59895e22	−	2.59895e22i	1.23644	−	1.23644i	0.961446	−	0.274994i	$-0.0886760\pi$
$948$	1.17714e22			0.555602
$949$	4.47378e21	−	4.47378e21i	0.209497	−	0.209497i
$950$		−	2.53127e22i		−	1.17601i
$951$	−1.27963e21			−0.0589834
$952$	8.34650e20	−	5.08929e20i	0.0381705	−	0.0232745i
$953$	−1.43234e22			−0.649906			−0.324953	−	0.945730i	$-0.605348\pi$
$953$	−1.43234e22			−0.649906			−0.324953	+	0.945730i	$0.605348\pi$
$954$		−	9.41895e21i		−	0.424023i
$955$	4.24031e20	−	4.24031e20i	0.0189397	−	0.0189397i
$956$	2.11759e22			0.938444
$957$	2.90622e19	−	2.90622e19i	0.00127788	−	0.00127788i
$958$	3.77995e22	+	3.77995e22i	1.64909	+	1.64909i
$959$	7.50026e20	+	7.50026e20i	0.0324666	+	0.0324666i
$960$		−	1.57262e21i		−	0.0675446i
$961$			1.06747e22i			0.454916i
$962$	−2.84494e22	−	2.84494e22i	−1.20298	−	1.20298i
$963$	6.88526e21	+	6.88526e21i	0.288884	+	0.288884i
$964$	3.53339e21	−	3.53339e21i	0.147101	−	0.147101i
$965$	−3.12835e21			−0.129229
$966$	−4.65076e20	+	4.65076e20i	−0.0190632	+	0.0190632i
$967$		−	2.32021e22i		−	0.943687i	−0.881682	−	0.471844i	$-0.843589\pi$
$967$		−	2.32021e22i		−	0.943687i	0.881682	−	0.471844i	$-0.156411\pi$
$968$	−2.89619e21			−0.116886
$969$	7.55282e21	+	1.23867e22i	0.302469	+	0.496053i
$970$	−9.96499e21			−0.395994
$971$			5.22610e21i			0.206079i	0.994677	+	0.103039i	$0.0328568\pi$
$971$			5.22610e21i			0.206079i	−0.994677	+	0.103039i	$0.967143\pi$
$972$	1.30423e22	−	1.30423e22i	0.510338	−	0.510338i
$973$	−4.95612e21			−0.192440
$974$	−1.79922e22	+	1.79922e22i	−0.693252	+	0.693252i
$975$	−1.05758e22	−	1.05758e22i	−0.404368	−	0.404368i
$976$	3.19520e22	+	3.19520e22i	1.21234	+	1.21234i
$977$		−	3.95363e22i		−	1.48863i	−0.667828	−	0.744316i	$-0.732776\pi$
$977$		−	3.95363e22i		−	1.48863i	0.667828	−	0.744316i	$-0.267224\pi$
$978$			4.06431e21i			0.151861i
$979$	−7.24929e21	−	7.24929e21i	−0.268798	−	0.268798i
$980$	4.77316e21	+	4.77316e21i	0.175635	+	0.175635i
$981$	−1.53077e22	+	1.53077e22i	−0.558974	+	0.558974i
$982$	4.84763e22			1.75668
$983$	2.98904e22	−	2.98904e22i	1.07493	−	1.07493i	0.0779762	−	0.996955i	$-0.475154\pi$
$983$	2.98904e22	−	2.98904e22i	1.07493	−	1.07493i	0.996955	−	0.0779762i	$-0.0248458\pi$
$984$			1.64678e21i			0.0587721i
$985$	−1.03771e22			−0.367540
$986$	−7.42888e19	−	1.21835e20i	−0.00261124	−	0.00428246i
$987$	−2.30235e21			−0.0803144
$988$		−	2.45335e22i		−	0.849341i
$989$	4.11090e21	−	4.11090e21i	0.141242	−	0.141242i
$990$	−7.90816e21			−0.269657
$991$	1.39451e22	−	1.39451e22i	0.471921	−	0.471921i	−0.430615	−	0.902536i	$-0.641703\pi$
$991$	1.39451e22	−	1.39451e22i	0.471921	−	0.471921i	0.902536	+	0.430615i	$0.141703\pi$
$992$	1.84254e22	+	1.84254e22i	0.618842	+	0.618842i
$993$	1.51049e21	+	1.51049e21i	0.0503498	+	0.0503498i
$994$		−	3.75475e21i		−	0.124217i
$995$		−	1.19568e22i		−	0.392593i
$996$	3.84413e21	+	3.84413e21i	0.125272	+	0.125272i
$997$	−5.44227e21	−	5.44227e21i	−0.176022	−	0.176022i	0.613597	−	0.789619i	$-0.289722\pi$
$997$	−5.44227e21	−	5.44227e21i	−0.176022	−	0.176022i	−0.789619	+	0.613597i	$0.789722\pi$
$998$	3.13962e21	−	3.13962e21i	0.100785	−	0.100785i
$999$	−3.30230e22			−1.05214

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.16.c.a.4.5	✓	44
17.13	even	4	inner	17.16.c.a.13.18	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.16.c.a.4.5	✓	44	1.1	even	1	trivial
17.16.c.a.13.18	yes	44	17.13	even	4	inner

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-235.953i q^{2} +(1501.32 - 1501.32i) q^{3} -22905.8 q^{4} +(44470.0 - 44470.0i) q^{5} +(-354242. - 354242. i) q^{6} +(-175577. - 175577. i) q^{7} -2.32702e6i q^{8} +9.84096e6i q^{9} +O(q^{10})\)	\(q-235.953i q^{2} +(1501.32 - 1501.32i) q^{3} -22905.8 q^{4} +(44470.0 - 44470.0i) q^{5} +(-354242. - 354242. i) q^{6} +(-175577. - 175577. i) q^{7} -2.32702e6i q^{8} +9.84096e6i q^{9} +(-1.04928e7 - 1.04928e7i) q^{10} +(-3.82927e7 - 3.82927e7i) q^{11} +(-3.43890e7 + 3.43890e7i) q^{12} -2.65197e8 q^{13} +(-4.14278e7 + 4.14278e7i) q^{14} -1.33528e8i q^{15} -1.29964e9 q^{16} +(-1.64424e9 - 3.98611e8i) q^{17} +2.32200e9 q^{18} -4.03873e9i q^{19} +(-1.01862e9 + 1.01862e9i) q^{20} -5.27195e8 q^{21} +(-9.03527e9 + 9.03527e9i) q^{22} +(3.73876e9 + 3.73876e9i) q^{23} +(-3.49361e9 - 3.49361e9i) q^{24} +2.65624e10i q^{25} +6.25741e10i q^{26} +(3.63168e10 + 3.63168e10i) q^{27} +(4.02172e9 + 4.02172e9i) q^{28} +(-2.52760e8 + 2.52760e8i) q^{29} -3.15063e10 q^{30} +(7.99705e10 - 7.99705e10i) q^{31} +2.30403e11i q^{32} -1.14979e11 q^{33} +(-9.40533e10 + 3.87964e11i) q^{34} -1.56158e10 q^{35} -2.25415e11i q^{36} +(-4.54652e11 + 4.54652e11i) q^{37} -9.52950e11 q^{38} +(-3.98147e11 + 3.98147e11i) q^{39} +(-1.03483e11 - 1.03483e11i) q^{40} +(-2.35684e11 - 2.35684e11i) q^{41} +1.24393e11i q^{42} -1.09954e12i q^{43} +(8.77123e11 + 8.77123e11i) q^{44} +(4.37628e11 + 4.37628e11i) q^{45} +(8.82171e11 - 8.82171e11i) q^{46} +4.36717e12 q^{47} +(-1.95119e12 + 1.95119e12i) q^{48} -4.68591e12i q^{49} +6.26748e12 q^{50} +(-3.06698e12 + 1.87010e12i) q^{51} +6.07455e12 q^{52} -4.05639e12i q^{53} +(8.56906e12 - 8.56906e12i) q^{54} -3.40575e12 q^{55} +(-4.08571e11 + 4.08571e11i) q^{56} +(-6.06344e12 - 6.06344e12i) q^{57} +(5.96394e10 + 5.96394e10i) q^{58} -3.81023e12i q^{59} +3.05856e12i q^{60} +(-2.45852e13 - 2.45852e13i) q^{61} +(-1.88693e13 - 1.88693e13i) q^{62} +(1.72784e12 - 1.72784e12i) q^{63} +1.17775e13 q^{64} +(-1.17933e13 + 1.17933e13i) q^{65} +2.71297e13i q^{66} -1.49091e13 q^{67} +(3.76626e13 + 9.13048e12i) q^{68} +1.12262e13 q^{69} +3.68460e12i q^{70} +(-4.53167e13 + 4.53167e13i) q^{71} +2.29001e13 q^{72} +(-1.68696e13 + 1.68696e13i) q^{73} +(1.07276e14 + 1.07276e14i) q^{74} +(3.98788e13 + 3.98788e13i) q^{75} +9.25102e13i q^{76} +1.34466e13i q^{77} +(9.39440e13 + 9.39440e13i) q^{78} +(-1.71150e14 - 1.71150e14i) q^{79} +(-5.77952e13 + 5.77952e13i) q^{80} -3.21603e13 q^{81} +(-5.56103e13 + 5.56103e13i) q^{82} -1.11784e14i q^{83} +1.20758e13 q^{84} +(-9.08457e13 + 5.53933e13i) q^{85} -2.59439e14 q^{86} +7.58949e11i q^{87} +(-8.91079e13 + 8.91079e13i) q^{88} +1.89313e14 q^{89} +(1.03260e14 - 1.03260e14i) q^{90} +(4.65625e13 + 4.65625e13i) q^{91} +(-8.56391e13 - 8.56391e13i) q^{92} -2.40123e14i q^{93} -1.03045e15i q^{94} +(-1.79602e14 - 1.79602e14i) q^{95} +(3.45909e14 + 3.45909e14i) q^{96} +(4.74848e14 - 4.74848e14i) q^{97} -1.10565e15 q^{98} +(3.76837e14 - 3.76837e14i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 5256 q^{3} - 720900 q^{4} - 252126 q^{5} - 1017326 q^{6} + 1854722 q^{7}+O(q^{10}) \) 44 * q + 5256 * q^3 - 720900 * q^4 - 252126 * q^5 - 1017326 * q^6 + 1854722 * q^7	\( 44 q + 5256 q^{3} - 720900 q^{4} - 252126 q^{5} - 1017326 q^{6} + 1854722 q^{7} + 8409498 q^{10} - 9729300 q^{11} - 82056486 q^{12} + 146863304 q^{13} - 1773752796 q^{14} + 16082152452 q^{16} + 1961077578 q^{17} - 7034899972 q^{18} + 21230427174 q^{20} - 47057263940 q^{21} - 3442343910 q^{22} - 15842736534 q^{23} + 94553484290 q^{24} - 294640558020 q^{27} - 17774164556 q^{28} + 102726169530 q^{29} - 643189839240 q^{30} - 385043642942 q^{31} + 2378676720192 q^{33} + 158249007174 q^{34} + 408521183892 q^{35} + 1375134180422 q^{37} + 1543745804832 q^{38} + 603440813444 q^{39} - 8303553806742 q^{40} + 1443758220300 q^{41} - 4657636435362 q^{44} + 6106558559866 q^{45} + 9604057332832 q^{46} - 21302607302640 q^{47} + 25515630744334 q^{48} - 18255254395212 q^{50} + 19158460873088 q^{51} - 48159060495244 q^{52} - 78998282739512 q^{54} + 13393057779764 q^{55} + 137860752160332 q^{56} + 31257866131908 q^{57} - 69211880377042 q^{58} + 38643830633662 q^{61} + 238390785941076 q^{62} - 71567394446902 q^{63} - 498262566925124 q^{64} + 178535375770548 q^{65} + 57983772499388 q^{67} + 261849713539554 q^{68} - 115652283503244 q^{69} - 44377197355566 q^{71} + 93677094320796 q^{72} + 405163878377696 q^{73} - 405068893451898 q^{74} + 225803653508132 q^{75} - 802546741257484 q^{78} - 155549526248110 q^{79} - 124920621818622 q^{80} - 10\!\cdots\!28 q^{81}+ \cdots + 173739293641872 q^{99}+O(q^{100}) \) 44 * q + 5256 * q^3 - 720900 * q^4 - 252126 * q^5 - 1017326 * q^6 + 1854722 * q^7 + 8409498 * q^10 - 9729300 * q^11 - 82056486 * q^12 + 146863304 * q^13 - 1773752796 * q^14 + 16082152452 * q^16 + 1961077578 * q^17 - 7034899972 * q^18 + 21230427174 * q^20 - 47057263940 * q^21 - 3442343910 * q^22 - 15842736534 * q^23 + 94553484290 * q^24 - 294640558020 * q^27 - 17774164556 * q^28 + 102726169530 * q^29 - 643189839240 * q^30 - 385043642942 * q^31 + 2378676720192 * q^33 + 158249007174 * q^34 + 408521183892 * q^35 + 1375134180422 * q^37 + 1543745804832 * q^38 + 603440813444 * q^39 - 8303553806742 * q^40 + 1443758220300 * q^41 - 4657636435362 * q^44 + 6106558559866 * q^45 + 9604057332832 * q^46 - 21302607302640 * q^47 + 25515630744334 * q^48 - 18255254395212 * q^50 + 19158460873088 * q^51 - 48159060495244 * q^52 - 78998282739512 * q^54 + 13393057779764 * q^55 + 137860752160332 * q^56 + 31257866131908 * q^57 - 69211880377042 * q^58 + 38643830633662 * q^61 + 238390785941076 * q^62 - 71567394446902 * q^63 - 498262566925124 * q^64 + 178535375770548 * q^65 + 57983772499388 * q^67 + 261849713539554 * q^68 - 115652283503244 * q^69 - 44377197355566 * q^71 + 93677094320796 * q^72 + 405163878377696 * q^73 - 405068893451898 * q^74 + 225803653508132 * q^75 - 802546741257484 * q^78 - 155549526248110 * q^79 - 124920621818622 * q^80 - 1098726050204828 * q^81 - 575036459162320 * q^82 + 1901862557545176 * q^84 - 939038947054838 * q^85 + 1783857741230148 * q^86 + 1466099551935802 * q^88 - 1809234886116972 * q^89 - 156603181182342 * q^90 + 2736989931074496 * q^91 + 4441473764128152 * q^92 + 2349942705291804 * q^95 - 7961673687938290 * q^96 - 2718145106426904 * q^97 - 2118270343699824 * q^98 + 173739293641872 * q^99

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