LMFDB - Embedded newform 17.16.c.a.13.21

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			13.21
Character	$\chi$	$=$	17.13
Dual form			17.16.c.a.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+338.865i q^{2} +(-2552.04 - 2552.04i) q^{3} -82061.8 q^{4} +(-182025. - 182025. i) q^{5} +(864799. - 864799. i) q^{6} +(-103726. + 103726. i) q^{7} -1.67040e7i q^{8} -1.32307e6i q^{9} +O(q^{10})$	\(q+338.865i q^{2} +(-2552.04 - 2552.04i) q^{3} -82061.8 q^{4} +(-182025. - 182025. i) q^{5} +(864799. - 864799. i) q^{6} +(-103726. + 103726. i) q^{7} -1.67040e7i q^{8} -1.32307e6i q^{9} +(6.16820e7 - 6.16820e7i) q^{10} +(-8.12691e7 + 8.12691e7i) q^{11} +(2.09425e8 + 2.09425e8i) q^{12} -2.14152e8 q^{13} +(-3.51490e7 - 3.51490e7i) q^{14} +9.29071e8i q^{15} +2.97139e9 q^{16} +(8.89624e8 - 1.43909e9i) q^{17} +4.48344e8 q^{18} +1.52809e9i q^{19} +(1.49373e10 + 1.49373e10i) q^{20} +5.29424e8 q^{21} +(-2.75393e10 - 2.75393e10i) q^{22} +(2.12469e9 - 2.12469e9i) q^{23} +(-4.26292e10 + 4.26292e10i) q^{24} +3.57486e10i q^{25} -7.25687e10i q^{26} +(-3.99955e10 + 3.99955e10i) q^{27} +(8.51190e9 - 8.51190e9i) q^{28} +(4.59509e10 + 4.59509e10i) q^{29} -3.14830e11 q^{30} +(-1.73973e11 - 1.73973e11i) q^{31} +4.59547e11i q^{32} +4.14804e11 q^{33} +(4.87659e11 + 3.01463e11i) q^{34} +3.77613e10 q^{35} +1.08574e11i q^{36} +(3.28486e11 + 3.28486e11i) q^{37} -5.17815e11 q^{38} +(5.46524e11 + 5.46524e11i) q^{39} +(-3.04054e12 + 3.04054e12i) q^{40} +(1.27216e12 - 1.27216e12i) q^{41} +1.79403e11i q^{42} -1.58792e11i q^{43} +(6.66909e12 - 6.66909e12i) q^{44} +(-2.40833e11 + 2.40833e11i) q^{45} +(7.19985e11 + 7.19985e11i) q^{46} -3.48418e12 q^{47} +(-7.58312e12 - 7.58312e12i) q^{48} +4.72604e12i q^{49} -1.21140e13 q^{50} +(-5.94299e12 + 1.40227e12i) q^{51} +1.75737e13 q^{52} +7.92124e12i q^{53} +(-1.35531e13 - 1.35531e13i) q^{54} +2.95860e13 q^{55} +(1.73263e12 + 1.73263e12i) q^{56} +(3.89974e12 - 3.89974e12i) q^{57} +(-1.55712e13 + 1.55712e13i) q^{58} +2.56155e13i q^{59} -7.62412e13i q^{60} +(3.19310e13 - 3.19310e13i) q^{61} +(5.89534e13 - 5.89534e13i) q^{62} +(1.37237e11 + 1.37237e11i) q^{63} -5.83580e13 q^{64} +(3.89810e13 + 3.89810e13i) q^{65} +1.40563e14i q^{66} +1.81375e13 q^{67} +(-7.30041e13 + 1.18095e14i) q^{68} -1.08446e13 q^{69} +1.27960e13i q^{70} +(-5.19387e13 - 5.19387e13i) q^{71} -2.21006e13 q^{72} +(1.30482e13 + 1.30482e13i) q^{73} +(-1.11313e14 + 1.11313e14i) q^{74} +(9.12319e13 - 9.12319e13i) q^{75} -1.25397e14i q^{76} -1.68594e13i q^{77} +(-1.85198e14 + 1.85198e14i) q^{78} +(1.01817e13 - 1.01817e13i) q^{79} +(-5.40868e14 - 5.40868e14i) q^{80} +1.85156e14 q^{81} +(4.31092e14 + 4.31092e14i) q^{82} -1.42826e14i q^{83} -4.34455e13 q^{84} +(-4.23885e14 + 1.00017e14i) q^{85} +5.38090e13 q^{86} -2.34537e14i q^{87} +(1.35752e15 + 1.35752e15i) q^{88} +2.12607e14 q^{89} +(-8.16098e13 - 8.16098e13i) q^{90} +(2.22130e13 - 2.22130e13i) q^{91} +(-1.74356e14 + 1.74356e14i) q^{92} +8.87973e14i q^{93} -1.18067e15i q^{94} +(2.78150e14 - 2.78150e14i) q^{95} +(1.17278e15 - 1.17278e15i) q^{96} +(-2.33780e14 - 2.33780e14i) q^{97} -1.60149e15 q^{98} +(1.07525e14 + 1.07525e14i) 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 $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$			338.865i			1.87198i	0.352020	+	0.935992i	$0.385495\pi$
$2$			338.865i			1.87198i	−0.352020	+	0.935992i	$0.614505\pi$
$3$	−2552.04	−	2552.04i	−0.673718	−	0.673718i	0.284853	−	0.958571i	$-0.408055\pi$
$3$	−2552.04	−	2552.04i	−0.673718	−	0.673718i	−0.958571	+	0.284853i	$0.908055\pi$
$4$	−82061.8			−2.50433
$5$	−182025.	−	182025.i	−1.04197	−	1.04197i	−0.999080	−	0.0428920i	$-0.986343\pi$
$5$	−182025.	−	182025.i	−1.04197	−	1.04197i	−0.0428920	−	0.999080i	$-0.513657\pi$
$6$	864799.	−	864799.i	1.26119	−	1.26119i
$7$	−103726.	+	103726.i	−0.0476048	+	0.0476048i	−0.730508	−	0.682904i	$-0.760717\pi$
$7$	−103726.	+	103726.i	−0.0476048	+	0.0476048i	0.682904	+	0.730508i	$0.260717\pi$
$8$		−	1.67040e7i		−	2.81608i
$9$		−	1.32307e6i		−	0.0922073i
$10$	6.16820e7	−	6.16820e7i	1.95055	−	1.95055i
$11$	−8.12691e7	+	8.12691e7i	−1.25742	+	1.25742i	−0.305099	+	0.952321i	$0.598690\pi$
$11$	−8.12691e7	+	8.12691e7i	−1.25742	+	1.25742i	−0.952321	+	0.305099i	$0.901310\pi$
$12$	2.09425e8	+	2.09425e8i	1.68721	+	1.68721i
$13$	−2.14152e8			−0.946557			−0.473278	−	0.880913i	$-0.656930\pi$
$13$	−2.14152e8			−0.946557			−0.473278	+	0.880913i	$0.656930\pi$
$14$	−3.51490e7	−	3.51490e7i	−0.0891154	−	0.0891154i
$15$			9.29071e8i			1.40399i
$16$	2.97139e9			2.76732
$17$	8.89624e8	−	1.43909e9i	0.525823	−	0.850594i
$17$	8.89624e8	−	1.43909e9i	0.525823	−	0.850594i
$18$	4.48344e8			0.172611
$19$			1.52809e9i			0.392189i	0.980585	+	0.196095i	$0.0628260\pi$
$19$			1.52809e9i			0.392189i	−0.980585	+	0.196095i	$0.937174\pi$
$20$	1.49373e10	+	1.49373e10i	2.60944	+	2.60944i
$21$	5.29424e8			0.0641444
$22$	−2.75393e10	−	2.75393e10i	−2.35387	−	2.35387i
$23$	2.12469e9	−	2.12469e9i	0.130118	−	0.130118i	−0.639048	−	0.769166i	$-0.720672\pi$
$23$	2.12469e9	−	2.12469e9i	0.130118	−	0.130118i	0.769166	+	0.639048i	$0.220672\pi$
$24$	−4.26292e10	+	4.26292e10i	−1.89724	+	1.89724i
$25$			3.57486e10i			1.17141i
$26$		−	7.25687e10i		−	1.77194i
$27$	−3.99955e10	+	3.99955e10i	−0.735840	+	0.735840i
$28$	8.51190e9	−	8.51190e9i	0.119218	−	0.119218i
$29$	4.59509e10	+	4.59509e10i	0.494663	+	0.494663i	0.909772	−	0.415109i	$-0.136257\pi$
$29$	4.59509e10	+	4.59509e10i	0.494663	+	0.494663i	−0.415109	+	0.909772i	$0.636257\pi$
$30$	−3.14830e11			−2.62825
$31$	−1.73973e11	−	1.73973e11i	−1.13571	−	1.13571i	−0.989210	−	0.146504i	$-0.953198\pi$
$31$	−1.73973e11	−	1.73973e11i	−1.13571	−	1.13571i	−0.146504	−	0.989210i	$-0.546802\pi$
$32$			4.59547e11i			2.36431i
$33$	4.14804e11			1.69429
$34$	4.87659e11	+	3.01463e11i	1.59230	+	0.984333i
$35$	3.77613e10			0.0992057
$36$			1.08574e11i			0.230917i
$37$	3.28486e11	+	3.28486e11i	0.568858	+	0.568858i	0.931808	−	0.362950i	$-0.118231\pi$
$37$	3.28486e11	+	3.28486e11i	0.568858	+	0.568858i	−0.362950	+	0.931808i	$0.618231\pi$
$38$	−5.17815e11			−0.734172
$39$	5.46524e11	+	5.46524e11i	0.637713	+	0.637713i
$40$	−3.04054e12	+	3.04054e12i	−2.93427	+	2.93427i
$41$	1.27216e12	−	1.27216e12i	1.02015	−	1.02015i	0.0203563	−	0.999793i	$-0.493520\pi$
$41$	1.27216e12	−	1.27216e12i	1.02015	−	1.02015i	0.999793	−	0.0203563i	$-0.00648006\pi$
$42$			1.79403e11i			0.120077i
$43$		−	1.58792e11i		−	0.0890870i	−0.999007	−	0.0445435i	$-0.985817\pi$
$43$		−	1.58792e11i		−	0.0890870i	0.999007	−	0.0445435i	$-0.0141833\pi$
$44$	6.66909e12	−	6.66909e12i	3.14899	−	3.14899i
$45$	−2.40833e11	+	2.40833e11i	−0.0960774	+	0.0960774i
$46$	7.19985e11	+	7.19985e11i	0.243579	+	0.243579i
$47$	−3.48418e12			−1.00315			−0.501577	−	0.865113i	$-0.667246\pi$
$47$	−3.48418e12			−1.00315			−0.501577	+	0.865113i	$0.667246\pi$
$48$	−7.58312e12	−	7.58312e12i	−1.86440	−	1.86440i
$49$			4.72604e12i			0.995468i
$50$	−1.21140e13			−2.19286
$51$	−5.94299e12	+	1.40227e12i	−0.927317	+	0.218804i
$52$	1.75737e13			2.37049
$53$			7.92124e12i			0.926241i	0.886295	+	0.463121i	$0.153270\pi$
$53$			7.92124e12i			0.926241i	−0.886295	+	0.463121i	$0.846730\pi$
$54$	−1.35531e13	−	1.35531e13i	−1.37748	−	1.37748i
$55$	2.95860e13			2.62039
$56$	1.73263e12	+	1.73263e12i	0.134059	+	0.134059i
$57$	3.89974e12	−	3.89974e12i	0.264225	−	0.264225i
$58$	−1.55712e13	+	1.55712e13i	−0.926001	+	0.926001i
$59$			2.56155e13i			1.34002i	0.742351	+	0.670011i	$0.233711\pi$
$59$			2.56155e13i			1.34002i	−0.742351	+	0.670011i	$0.766289\pi$
$60$		−	7.62412e13i		−	3.51605i
$61$	3.19310e13	−	3.19310e13i	1.30089	−	1.30089i	0.373091	−	0.927795i	$-0.378298\pi$
$61$	3.19310e13	−	3.19310e13i	1.30089	−	1.30089i	0.927795	−	0.373091i	$-0.121702\pi$
$62$	5.89534e13	−	5.89534e13i	2.12604	−	2.12604i
$63$	1.37237e11	+	1.37237e11i	0.00438951	+	0.00438951i
$64$	−5.83580e13			−1.65863
$65$	3.89810e13	+	3.89810e13i	0.986285	+	0.986285i
$66$			1.40563e14i			3.17169i
$67$	1.81375e13			0.365608			0.182804	−	0.983149i	$-0.441483\pi$
$67$	1.81375e13			0.365608			0.182804	+	0.983149i	$0.441483\pi$
$68$	−7.30041e13	+	1.18095e14i	−1.31683	+	2.13017i
$69$	−1.08446e13			−0.175326
$70$			1.27960e13i			0.185711i
$71$	−5.19387e13	−	5.19387e13i	−0.677725	−	0.677725i	0.281760	−	0.959485i	$-0.409082\pi$
$71$	−5.19387e13	−	5.19387e13i	−0.677725	−	0.677725i	−0.959485	+	0.281760i	$0.909082\pi$
$72$	−2.21006e13			−0.259663
$73$	1.30482e13	+	1.30482e13i	0.138238	+	0.138238i	0.772840	−	0.634601i	$-0.218836\pi$
$73$	1.30482e13	+	1.30482e13i	0.138238	+	0.138238i	−0.634601	+	0.772840i	$0.718836\pi$
$74$	−1.11313e14	+	1.11313e14i	−1.06489	+	1.06489i
$75$	9.12319e13	−	9.12319e13i	0.789200	−	0.789200i
$76$		−	1.25397e14i		−	0.982170i
$77$		−	1.68594e13i		−	0.119718i
$78$	−1.85198e14	+	1.85198e14i	−1.19379	+	1.19379i
$79$	1.01817e13	−	1.01817e13i	0.0596506	−	0.0596506i	−0.676652	−	0.736303i	$-0.736570\pi$
$79$	1.01817e13	−	1.01817e13i	0.0596506	−	0.0596506i	0.736303	+	0.676652i	$0.236570\pi$
$80$	−5.40868e14	−	5.40868e14i	−2.88347	−	2.88347i
$81$	1.85156e14			0.899290
$82$	4.31092e14	+	4.31092e14i	1.90970	+	1.90970i
$83$		−	1.42826e14i		−	0.577727i	−0.957370	−	0.288863i	$-0.906723\pi$
$83$		−	1.42826e14i		−	0.577727i	0.957370	−	0.288863i	$-0.0932773\pi$
$84$	−4.34455e13			−0.160639
$85$	−4.23885e14	+	1.00017e14i	−1.43419	+	0.338402i
$86$	5.38090e13			0.166770
$87$		−	2.34537e14i		−	0.666527i
$88$	1.35752e15	+	1.35752e15i	3.54099	+	3.54099i
$89$	2.12607e14			0.509511			0.254755	−	0.967006i	$-0.418005\pi$
$89$	2.12607e14			0.509511			0.254755	+	0.967006i	$0.418005\pi$
$90$	−8.16098e13	−	8.16098e13i	−0.179856	−	0.179856i
$91$	2.22130e13	−	2.22130e13i	0.0450606	−	0.0450606i
$92$	−1.74356e14	+	1.74356e14i	−0.325858	+	0.325858i
$93$			8.87973e14i			1.53030i
$94$		−	1.18067e15i		−	1.87789i
$95$	2.78150e14	−	2.78150e14i	0.408650	−	0.408650i
$96$	1.17278e15	−	1.17278e15i	1.59288	−	1.59288i
$97$	−2.33780e14	−	2.33780e14i	−0.293778	−	0.293778i	0.544793	−	0.838571i	$-0.316608\pi$
$97$	−2.33780e14	−	2.33780e14i	−0.293778	−	0.293778i	−0.838571	+	0.544793i	$0.816608\pi$
$98$	−1.60149e15			−1.86350
$99$	1.07525e14	+	1.07525e14i	0.115943	+	0.115943i
$100$		−	2.93359e15i		−	2.93359i
$101$	5.47760e14			0.508370			0.254185	−	0.967156i	$-0.418193\pi$
$101$	5.47760e14			0.508370			0.254185	+	0.967156i	$0.418193\pi$
$102$	−4.75181e14	−	2.01387e15i	−0.409598	−	1.73592i
$103$	−1.23187e15			−0.986929			−0.493465	−	0.869766i	$-0.664270\pi$
$103$	−1.23187e15			−0.986929			−0.493465	+	0.869766i	$0.664270\pi$
$104$			3.57718e15i			2.66558i
$105$	−9.63684e13	−	9.63684e13i	−0.0668367	−	0.0668367i
$106$	−2.68423e15			−1.73391
$107$	−1.14188e15	−	1.14188e15i	−0.687452	−	0.687452i	0.274216	−	0.961668i	$-0.411582\pi$
$107$	−1.14188e15	−	1.14188e15i	−0.687452	−	0.687452i	−0.961668	+	0.274216i	$0.911582\pi$
$108$	3.28211e15	−	3.28211e15i	1.84278	−	1.84278i
$109$	1.75345e15	−	1.75345e15i	0.918743	−	0.918743i	−0.0781949	−	0.996938i	$-0.524916\pi$
$109$	1.75345e15	−	1.75345e15i	0.918743	−	0.918743i	0.996938	+	0.0781949i	$0.0249156\pi$
$110$			1.00257e16i			4.90533i
$111$		−	1.67662e15i		−	0.766500i
$112$	−3.08209e14	+	3.08209e14i	−0.131738	+	0.131738i
$113$	−2.00927e15	+	2.00927e15i	−0.803432	+	0.803432i	−0.983630	−	0.180198i	$-0.942326\pi$
$113$	−2.00927e15	+	2.00927e15i	−0.803432	+	0.803432i	0.180198	+	0.983630i	$0.442326\pi$
$114$	1.32149e15	+	1.32149e15i	0.494625	+	0.494625i
$115$	−7.73495e14			−0.271159
$116$	−3.77081e15	−	3.77081e15i	−1.23880	−	1.23880i
$117$			2.83339e14i			0.0872795i
$118$	−8.68019e15			−2.50850
$119$	5.69941e13	+	2.41548e14i	0.0154606	+	0.0655240i
$120$	1.55192e16			3.95374
$121$		−	9.03209e15i		−	2.16221i
$122$	1.08203e16	+	1.08203e16i	2.43524	+	2.43524i
$123$	−6.49322e15			−1.37459
$124$	1.42765e16	+	1.42765e16i	2.84420	+	2.84420i
$125$	9.52176e14	−	9.52176e14i	0.178604	−	0.178604i
$126$	−4.65048e13	+	4.65048e13i	−0.00821710	+	0.00821710i
$127$		−	6.32111e15i		−	1.05260i	−0.850297	−	0.526302i	$-0.823578\pi$
$127$		−	6.32111e15i		−	1.05260i	0.850297	−	0.526302i	$-0.176422\pi$
$128$		−	4.71706e15i		−	0.740622i
$129$	−4.05243e14	+	4.05243e14i	−0.0600196	+	0.0600196i
$130$	−1.32093e16	+	1.32093e16i	−1.84631	+	1.84631i
$131$	−1.06136e15	−	1.06136e15i	−0.140065	−	0.140065i	0.633598	−	0.773663i	$-0.281577\pi$
$131$	−1.06136e15	−	1.06136e15i	−0.140065	−	0.140065i	−0.773663	+	0.633598i	$0.781577\pi$
$132$	−3.40396e16			−4.24306
$133$	−1.58502e14	−	1.58502e14i	−0.0186701	−	0.0186701i
$134$			6.14616e15i			0.684413i
$135$	1.45604e16			1.53345
$136$	−2.40386e16	−	1.48602e16i	−2.39534	−	1.48076i
$137$	3.55914e15			0.335692			0.167846	−	0.985813i	$-0.446319\pi$
$137$	3.55914e15			0.335692			0.167846	+	0.985813i	$0.446319\pi$
$138$		−	3.67486e15i		−	0.328207i
$139$	2.52040e15	+	2.52040e15i	0.213235	+	0.213235i	0.805640	−	0.592405i	$-0.201821\pi$
$139$	2.52040e15	+	2.52040e15i	0.213235	+	0.213235i	−0.592405	+	0.805640i	$0.701821\pi$
$140$	−3.09876e15			−0.248443
$141$	8.89178e15	+	8.89178e15i	0.675843	+	0.675843i
$142$	1.76002e16	−	1.76002e16i	1.26869	−	1.26869i
$143$	1.74039e16	−	1.74039e16i	1.19022	−	1.19022i
$144$		−	3.93137e15i		−	0.255168i
$145$		−	1.67284e16i		−	1.03085i
$146$	−4.42158e15	+	4.42158e15i	−0.258780	+	0.258780i
$147$	1.20611e16	−	1.20611e16i	0.670665	−	0.670665i
$148$	−2.69561e16	−	2.69561e16i	−1.42461	−	1.42461i
$149$	−2.44499e16			−1.22851			−0.614256	−	0.789107i	$-0.710544\pi$
$149$	−2.44499e16			−1.22851			−0.614256	+	0.789107i	$0.710544\pi$
$150$	3.09153e16	+	3.09153e16i	1.47737	+	1.47737i
$151$			3.15659e16i			1.43513i	0.696492	+	0.717564i	$0.254743\pi$
$151$			3.15659e16i			1.43513i	−0.696492	+	0.717564i	$0.745257\pi$
$152$	2.55251e16			1.10443
$153$	−1.90403e15	−	1.17704e15i	−0.0784310	−	0.0484847i
$154$	5.71306e15			0.224111
$155$			6.33349e16i			2.36676i
$156$	−4.48488e16	−	4.48488e16i	−1.59704	−	1.59704i
$157$	3.91404e16			1.32855			0.664276	−	0.747488i	$-0.268740\pi$
$157$	3.91404e16			1.32855			0.664276	+	0.747488i	$0.268740\pi$
$158$	3.45021e15	+	3.45021e15i	0.111665	+	0.111665i
$159$	2.02153e16	−	2.02153e16i	0.624026	−	0.624026i
$160$	8.36490e16	−	8.36490e16i	2.46355	−	2.46355i
$161$			4.40770e14i			0.0123885i
$162$			6.27429e16i			1.68346i
$163$	1.02913e16	−	1.02913e16i	0.263672	−	0.263672i	−0.562872	−	0.826544i	$-0.690304\pi$
$163$	1.02913e16	−	1.02913e16i	0.263672	−	0.263672i	0.826544	+	0.562872i	$0.190304\pi$
$164$	−1.04396e17	+	1.04396e17i	−2.55479	+	2.55479i
$165$	−7.55047e16	−	7.55047e16i	−1.76541	−	1.76541i
$166$	4.83989e16			1.08150
$167$	3.73617e16	+	3.73617e16i	0.798092	+	0.798092i	0.982794	−	0.184702i	$-0.0591322\pi$
$167$	3.73617e16	+	3.73617e16i	0.798092	+	0.798092i	−0.184702	+	0.982794i	$0.559132\pi$
$168$		−	8.84347e15i		−	0.180636i
$169$	−5.32488e15			−0.104030
$170$	−3.38924e16	−	1.43640e17i	−0.633484	−	2.68478i
$171$	2.02177e15			0.0361627
$172$			1.30307e16i			0.223103i
$173$	−4.32205e15	−	4.32205e15i	−0.0708506	−	0.0708506i	0.670794	−	0.741644i	$-0.265954\pi$
$173$	−4.32205e15	−	4.32205e15i	−0.0708506	−	0.0708506i	−0.741644	+	0.670794i	$0.765954\pi$
$174$	7.94766e16			1.24773
$175$	−3.70804e15	−	3.70804e15i	−0.0557647	−	0.0557647i
$176$	−2.41482e17	+	2.41482e17i	−3.47969	+	3.47969i
$177$	6.53717e16	−	6.53717e16i	0.902797	−	0.902797i
$178$			7.20453e16i			0.953796i
$179$			8.63868e16i			1.09660i	0.836280	+	0.548302i	$0.184726\pi$
$179$			8.63868e16i			1.09660i	−0.836280	+	0.548302i	$0.815274\pi$
$180$	1.97632e16	−	1.97632e16i	0.240609	−	0.240609i
$181$	2.61737e16	−	2.61737e16i	0.305686	−	0.305686i	−0.537548	−	0.843233i	$-0.680649\pi$
$181$	2.61737e16	−	2.61737e16i	0.305686	−	0.305686i	0.843233	+	0.537548i	$0.180649\pi$
$182$	7.52723e15	+	7.52723e15i	0.0843528	+	0.0843528i
$183$	−1.62979e17			−1.75286
$184$	−3.54908e16	−	3.54908e16i	−0.366422	−	0.366422i
$185$		−	1.19585e17i		−	1.18547i
$186$	−3.00903e17			−2.86470
$187$	4.46549e16	+	1.89253e17i	0.408373	+	1.73073i
$188$	2.85918e17			2.51222
$189$		−	8.29712e15i		−	0.0700590i
$190$	9.42553e16	+	9.42553e16i	0.764987	+	0.764987i
$191$	−1.43860e17			−1.12251			−0.561253	−	0.827644i	$-0.689681\pi$
$191$	−1.43860e17			−1.12251			−0.561253	+	0.827644i	$0.689681\pi$
$192$	1.48932e17	+	1.48932e17i	1.11745	+	1.11745i
$193$	6.67349e16	−	6.67349e16i	0.481586	−	0.481586i	−0.424052	−	0.905638i	$-0.639393\pi$
$193$	6.67349e16	−	6.67349e16i	0.481586	−	0.481586i	0.905638	+	0.424052i	$0.139393\pi$
$194$	7.92199e16	−	7.92199e16i	0.549948	−	0.549948i
$195$		−	1.98962e17i		−	1.32896i
$196$		−	3.87827e17i		−	2.49298i
$197$	−1.52931e17	+	1.52931e17i	−0.946236	+	0.946236i	−0.998627	−	0.0523910i	$-0.983316\pi$
$197$	−1.52931e17	+	1.52931e17i	−0.946236	+	0.946236i	0.0523910	+	0.998627i	$0.483316\pi$
$198$	−3.64365e16	+	3.64365e16i	−0.217044	+	0.217044i
$199$	2.16875e17	+	2.16875e17i	1.24398	+	1.24398i	0.958338	+	0.285638i	$0.0922053\pi$
$199$	2.16875e17	+	2.16875e17i	1.24398	+	1.24398i	0.285638	+	0.958338i	$0.407795\pi$
$200$	5.97143e17			3.29878
$201$	−4.62876e16	−	4.62876e16i	−0.246317	−	0.246317i
$202$			1.85617e17i			0.951662i
$203$	−9.53257e15			−0.0470966
$204$	4.87692e17	−	1.15073e17i	2.32231	−	0.547957i
$205$	−4.63131e17			−2.12593
$206$		−	4.17438e17i		−	1.84752i
$207$	−2.81113e15	−	2.81113e15i	−0.0119978	−	0.0119978i
$208$	−6.36329e17			−2.61943
$209$	−1.24186e17	−	1.24186e17i	−0.493146	−	0.493146i
$210$	3.26559e16	−	3.26559e16i	0.125117	−	0.125117i
$211$	−1.05367e17	+	1.05367e17i	−0.389569	+	0.389569i	−0.874534	−	0.484964i	$-0.838833\pi$
$211$	−1.05367e17	+	1.05367e17i	−0.389569	+	0.389569i	0.484964	+	0.874534i	$0.338833\pi$
$212$		−	6.50031e17i		−	2.31961i
$213$			2.65100e17i			0.913192i
$214$	3.86944e17	−	3.86944e17i	1.28690	−	1.28690i
$215$	−2.89041e16	+	2.89041e16i	−0.0928262	+	0.0928262i
$216$	6.68084e17	+	6.68084e17i	2.07218	+	2.07218i
$217$	3.60909e16			0.108131
$218$	5.94183e17	+	5.94183e17i	1.71987	+	1.71987i
$219$		−	6.65990e16i		−	0.186267i
$220$	−2.42788e18			−6.56232
$221$	−1.90515e17	+	3.08185e17i	−0.497721	+	0.805136i
$222$	5.68148e17			1.43488
$223$		−	3.93343e17i		−	0.960474i	−0.877139	−	0.480237i	$-0.840551\pi$
$223$		−	3.93343e17i		−	0.960474i	0.877139	−	0.480237i	$-0.159449\pi$
$224$	−4.76668e16	−	4.76668e16i	−0.112553	−	0.112553i
$225$	4.72981e16			0.108013
$226$	−6.80871e17	−	6.80871e17i	−1.50401	−	1.50401i
$227$	1.67553e17	−	1.67553e17i	0.358063	−	0.358063i	−0.505036	−	0.863098i	$-0.668521\pi$
$227$	1.67553e17	−	1.67553e17i	0.358063	−	0.358063i	0.863098	+	0.505036i	$0.168521\pi$
$228$	−3.20019e17	+	3.20019e17i	−0.661706	+	0.661706i
$229$		−	1.71181e17i		−	0.342522i	−0.985226	−	0.171261i	$-0.945216\pi$
$229$		−	1.71181e17i		−	0.342522i	0.985226	−	0.171261i	$-0.0547841\pi$
$230$		−	2.62111e17i		−	0.507605i
$231$	−4.30258e16	+	4.30258e16i	−0.0806565	+	0.0806565i
$232$	7.67562e17	−	7.67562e17i	1.39301	−	1.39301i
$233$	6.21833e17	+	6.21833e17i	1.09271	+	1.09271i	0.995238	+	0.0974709i	$0.0310753\pi$
$233$	6.21833e17	+	6.21833e17i	1.09271	+	1.09271i	0.0974709	+	0.995238i	$0.468925\pi$
$234$	−9.60138e16			−0.163386
$235$	6.34209e17	+	6.34209e17i	1.04526	+	1.04526i
$236$		−	2.10205e18i		−	3.35585i
$237$	−5.19680e16			−0.0803754
$238$	−8.18521e16	+	1.93133e16i	−0.122660	+	0.0289421i
$239$	−6.59704e17			−0.957998			−0.478999	−	0.877815i	$-0.659000\pi$
$239$	−6.59704e17			−0.957998			−0.478999	+	0.877815i	$0.659000\pi$
$240$			2.76063e18i			3.88530i
$241$	9.54986e17	+	9.54986e17i	1.30277	+	1.30277i	0.926514	+	0.376260i	$0.122790\pi$
$241$	9.54986e17	+	9.54986e17i	1.30277	+	1.30277i	0.376260	+	0.926514i	$0.377210\pi$
$242$	3.06066e18			4.04762
$243$	1.01367e17	+	1.01367e17i	0.129972	+	0.129972i
$244$	−2.62032e18	+	2.62032e18i	−3.25784	+	3.25784i
$245$	8.60258e17	−	8.60258e17i	1.03725	−	1.03725i
$246$		−	2.20033e18i		−	2.57320i
$247$		−	3.27242e17i		−	0.371229i
$248$	−2.90604e18	+	2.90604e18i	−3.19826	+	3.19826i
$249$	−3.64499e17	+	3.64499e17i	−0.389225	+	0.389225i
$250$	3.22659e17	+	3.22659e17i	0.334345	+	0.334345i
$251$	−6.17682e17			−0.621172			−0.310586	−	0.950545i	$-0.600525\pi$
$251$	−6.17682e17			−0.621172			−0.310586	+	0.950545i	$0.600525\pi$
$252$	−1.12619e16	−	1.12619e16i	−0.0109928	−	0.0109928i
$253$			3.45344e17i			0.327226i
$254$	2.14201e18			1.97046
$255$	1.33702e18	+	8.26523e17i	1.19423	+	0.738251i
$256$	−3.13824e17			−0.272199
$257$			1.29819e18i			1.09355i	0.837279	+	0.546777i	$0.184145\pi$
$257$			1.29819e18i			1.09355i	−0.837279	+	0.546777i	$0.815855\pi$
$258$	−1.37323e17	−	1.37323e17i	−0.112356	−	0.112356i
$259$	−6.81448e16			−0.0541607
$260$	−3.19885e18	−	3.19885e18i	−2.46998	−	2.46998i
$261$	6.07965e16	−	6.07965e16i	0.0456115	−	0.0456115i
$262$	3.59659e17	−	3.59659e17i	0.262199	−	0.262199i
$263$		−	4.83427e17i		−	0.342502i	−0.985227	−	0.171251i	$-0.945219\pi$
$263$		−	4.83427e17i		−	0.342502i	0.985227	−	0.171251i	$-0.0547809\pi$
$264$		−	6.92887e18i		−	4.77126i
$265$	1.44186e18	−	1.44186e18i	0.965117	−	0.965117i
$266$	5.37107e16	−	5.37107e16i	0.0349501	−	0.0349501i
$267$	−5.42583e17	−	5.42583e17i	−0.343267	−	0.343267i
$268$	−1.48839e18			−0.915602
$269$	2.53261e17	+	2.53261e17i	0.151505	+	0.151505i	0.778790	−	0.627285i	$-0.215834\pi$
$269$	2.53261e17	+	2.53261e17i	0.151505	+	0.151505i	−0.627285	+	0.778790i	$0.715834\pi$
$270$			4.93401e18i			2.87059i
$271$	−1.85906e18			−1.05202			−0.526009	−	0.850479i	$-0.676312\pi$
$271$	−1.85906e18			−1.05202			−0.526009	+	0.850479i	$0.676312\pi$
$272$	2.64342e18	−	4.27611e18i	1.45512	−	2.35387i
$273$	−1.13377e17			−0.0607163
$274$			1.20607e18i			0.628411i
$275$	−2.90526e18	−	2.90526e18i	−1.47295	−	1.47295i
$276$	8.89928e17			0.439073
$277$	−2.62607e17	−	2.62607e17i	−0.126098	−	0.126098i	0.641241	−	0.767339i	$-0.278420\pi$
$277$	−2.62607e17	−	2.62607e17i	−0.126098	−	0.126098i	−0.767339	+	0.641241i	$0.778420\pi$
$278$	−8.54077e17	+	8.54077e17i	−0.399173	+	0.399173i
$279$	−2.30179e17	+	2.30179e17i	−0.104721	+	0.104721i
$280$		−	6.30763e17i		−	0.279371i
$281$			1.20777e18i			0.520821i	0.965498	+	0.260410i	$0.0838579\pi$
$281$			1.20777e18i			0.520821i	−0.965498	+	0.260410i	$0.916142\pi$
$282$	−3.01312e18	+	3.01312e18i	−1.26517	+	1.26517i
$283$	3.84866e17	−	3.84866e17i	0.157366	−	0.157366i	−0.624032	−	0.781398i	$-0.714507\pi$
$283$	3.84866e17	−	3.84866e17i	0.157366	−	0.157366i	0.781398	+	0.624032i	$0.214507\pi$
$284$	4.26218e18	+	4.26218e18i	1.69724	+	1.69724i
$285$	−1.41970e18			−0.550630
$286$	5.89759e18	+	5.89759e18i	2.22807	+	2.22807i
$287$			2.63912e17i			0.0971279i
$288$	6.08015e17			0.218007
$289$	−1.27956e18	−	2.56051e18i	−0.447020	−	0.894524i
$290$	5.66869e18			1.92973
$291$			1.19323e18i			0.395847i
$292$	−1.07076e18	−	1.07076e18i	−0.346194	−	0.346194i
$293$	3.11872e18			0.982809			0.491404	−	0.870932i	$-0.336484\pi$
$293$	3.11872e18			0.982809			0.491404	+	0.870932i	$0.336484\pi$
$294$	4.08708e18	+	4.08708e18i	1.25547	+	1.25547i
$295$	4.66265e18	−	4.66265e18i	1.39627	−	1.39627i
$296$	5.48701e18	−	5.48701e18i	1.60195	−	1.60195i
$297$		−	6.50080e18i		−	1.85052i
$298$		−	8.28521e18i		−	2.29976i
$299$	−4.55007e17	+	4.55007e17i	−0.123164	+	0.123164i
$300$	−7.48665e18	+	7.48665e18i	−1.97642	+	1.97642i
$301$	1.64708e16	+	1.64708e16i	0.00424097	+	0.00424097i
$302$	−1.06966e19			−2.68654
$303$	−1.39791e18	−	1.39791e18i	−0.342498	−	0.342498i
$304$			4.54054e18i			1.08531i
$305$	−1.16245e19			−2.71097
$306$	3.98858e17	−	6.45210e17i	0.0907627	−	0.146822i
$307$	6.39920e18			1.42098			0.710490	−	0.703708i	$-0.248473\pi$
$307$	6.39920e18			1.42098			0.710490	+	0.703708i	$0.248473\pi$
$308$			1.38351e18i			0.299814i
$309$	3.14379e18	+	3.14379e18i	0.664912	+	0.664912i
$310$	−2.14620e19			−4.43055
$311$	1.56367e18	+	1.56367e18i	0.315095	+	0.315095i	0.846880	−	0.531785i	$-0.178478\pi$
$311$	1.56367e18	+	1.56367e18i	0.315095	+	0.315095i	−0.531785	+	0.846880i	$0.678478\pi$
$312$	9.12912e18	−	9.12912e18i	1.79585	−	1.79585i
$313$	−1.38604e18	+	1.38604e18i	−0.266190	+	0.266190i	−0.827563	−	0.561373i	$-0.810273\pi$
$313$	−1.38604e18	+	1.38604e18i	−0.266190	+	0.266190i	0.561373	+	0.827563i	$0.310273\pi$
$314$			1.32633e19i			2.48703i
$315$		−	4.99610e16i		−	0.00914749i
$316$	−8.35524e17	+	8.35524e17i	−0.149385	+	0.149385i
$317$	1.51228e18	−	1.51228e18i	0.264051	−	0.264051i	−0.562647	−	0.826697i	$-0.690217\pi$
$317$	1.51228e18	−	1.51228e18i	0.264051	−	0.264051i	0.826697	+	0.562647i	$0.190217\pi$
$318$	6.85028e18	+	6.85028e18i	1.16817	+	1.16817i
$319$	−7.46878e18			−1.24400
$320$	1.06226e19	+	1.06226e19i	1.72825	+	1.72825i
$321$			5.82825e18i			0.926298i
$322$	−1.49362e17			−0.0231910
$323$	2.19906e18	+	1.35942e18i	0.333594	+	0.206222i
$324$	−1.51942e19			−2.25212
$325$		−	7.65563e18i		−	1.10881i
$326$	3.48737e18	+	3.48737e18i	0.493590	+	0.493590i
$327$	−8.94974e18			−1.23795
$328$	−2.12501e19	−	2.12501e19i	−2.87282	−	2.87282i
$329$	3.61399e17	−	3.61399e17i	0.0477549	−	0.0477549i
$330$	2.55859e19	−	2.55859e19i	3.30481	−	3.30481i
$331$			1.32542e19i			1.67357i	0.547534	+	0.836783i	$0.315567\pi$
$331$			1.32542e19i			1.67357i	−0.547534	+	0.836783i	$0.684433\pi$
$332$			1.17206e19i			1.44682i
$333$	4.34611e17	−	4.34611e17i	0.0524529	−	0.0524529i
$334$	−1.26606e19	+	1.26606e19i	−1.49402	+	1.49402i
$335$	−3.30147e18	−	3.30147e18i	−0.380953	−	0.380953i
$336$	1.57313e18			0.177508
$337$	−4.92171e18	−	4.92171e18i	−0.543115	−	0.543115i	0.381326	−	0.924441i	$-0.375468\pi$
$337$	−4.92171e18	−	4.92171e18i	−0.543115	−	0.543115i	−0.924441	+	0.381326i	$0.875468\pi$
$338$		−	1.80442e18i		−	0.194743i
$339$	1.02555e19			1.08257
$340$	3.47847e19	−	8.20760e18i	3.59167	−	0.847469i
$341$	2.82773e19			2.85614
$342$			6.85108e17i			0.0676961i
$343$	−9.82655e17	−	9.82655e17i	−0.0949938	−	0.0949938i
$344$	−2.65245e18			−0.250876
$345$	1.97399e18	+	1.97399e18i	0.182685	+	0.182685i
$346$	1.46459e18	−	1.46459e18i	0.132631	−	0.132631i
$347$	4.24944e17	−	4.24944e17i	0.0376583	−	0.0376583i	−0.688027	−	0.725685i	$-0.741523\pi$
$347$	4.24944e17	−	4.24944e17i	0.0376583	−	0.0376583i	0.725685	+	0.688027i	$0.241523\pi$
$348$			1.92465e19i			1.66920i
$349$		−	1.30735e19i		−	1.10969i	−0.831955	−	0.554843i	$-0.812778\pi$
$349$		−	1.30735e19i		−	1.10969i	0.831955	−	0.554843i	$-0.187222\pi$
$350$	1.25653e18	−	1.25653e18i	0.104391	−	0.104391i
$351$	8.56512e18	−	8.56512e18i	0.696514	−	0.696514i
$352$	−3.73470e19	−	3.73470e19i	−2.97293	−	2.97293i
$353$	8.39336e17			0.0654072			0.0327036	−	0.999465i	$-0.489588\pi$
$353$	8.39336e17			0.0654072			0.0327036	+	0.999465i	$0.489588\pi$
$354$	2.21522e19	+	2.21522e19i	1.69002	+	1.69002i
$355$			1.89083e19i			1.41234i
$356$	−1.74469e19			−1.27598
$357$	4.70988e17	−	7.61891e17i	0.0337286	−	0.0545609i
$358$	−2.92735e19			−2.05283
$359$			1.29563e18i			0.0889760i	0.999010	+	0.0444880i	$0.0141657\pi$
$359$			1.29563e18i			0.0889760i	−0.999010	+	0.0444880i	$0.985834\pi$
$360$	4.02286e18	+	4.02286e18i	0.270561	+	0.270561i
$361$	1.28461e19			0.846188
$362$	8.86935e18	+	8.86935e18i	0.572239	+	0.572239i
$363$	−2.30503e19	+	2.30503e19i	−1.45672	+	1.45672i
$364$	−1.82284e18	+	1.82284e18i	−0.112847	+	0.112847i
$365$		−	4.75019e18i		−	0.288081i
$366$		−	5.52278e19i		−	3.28133i
$367$	1.07840e19	−	1.07840e19i	0.627749	−	0.627749i	−0.319752	−	0.947501i	$-0.603600\pi$
$367$	1.07840e19	−	1.07840e19i	0.627749	−	0.627749i	0.947501	+	0.319752i	$0.103600\pi$
$368$	6.31330e18	−	6.31330e18i	0.360079	−	0.360079i
$369$	−1.68317e18	−	1.68317e18i	−0.0940652	−	0.0940652i
$370$	4.05233e19			2.21918
$371$	−8.21635e17	−	8.21635e17i	−0.0440935	−	0.0440935i
$372$		−	7.28686e19i		−	3.83238i
$373$	−1.10522e19			−0.569682			−0.284841	−	0.958575i	$-0.591941\pi$
$373$	−1.10522e19			−0.569682			−0.284841	+	0.958575i	$0.591941\pi$
$374$	−6.41312e19	+	1.51320e19i	−3.23991	+	0.764469i
$375$	−4.85998e18			−0.240658
$376$			5.81997e19i			2.82496i
$377$	−9.84048e18	−	9.84048e18i	−0.468226	−	0.468226i
$378$	2.81161e18			0.131149
$379$	1.30336e19	+	1.30336e19i	0.596031	+	0.596031i	0.939254	−	0.343223i	$-0.111519\pi$
$379$	1.30336e19	+	1.30336e19i	0.596031	+	0.596031i	−0.343223	+	0.939254i	$0.611519\pi$
$380$	−2.28255e19	+	2.28255e19i	−1.02339	+	1.02339i
$381$	−1.61317e19	+	1.61317e19i	−0.709159	+	0.709159i
$382$		−	4.87491e19i		−	2.10131i
$383$			1.92141e18i			0.0812137i	0.999175	+	0.0406068i	$0.0129291\pi$
$383$			1.92141e18i			0.0812137i	−0.999175	+	0.0406068i	$0.987071\pi$
$384$	−1.20381e19	+	1.20381e19i	−0.498971	+	0.498971i
$385$	−3.06883e18	+	3.06883e18i	−0.124743	+	0.124743i
$386$	2.26142e19	+	2.26142e19i	0.901521	+	0.901521i
$387$	−2.10093e17			−0.00821448
$388$	1.91844e19	+	1.91844e19i	0.735716	+	0.735716i
$389$			4.17968e19i			1.57225i	0.618068	+	0.786124i	$0.287916\pi$
$389$			4.17968e19i			1.57225i	−0.618068	+	0.786124i	$0.712084\pi$
$390$	6.74214e19			2.48779
$391$	−1.16746e18	−	4.94781e18i	−0.0422586	−	0.179097i
$392$	7.89436e19			2.80331
$393$			5.41728e18i			0.188728i
$394$	−5.18231e19	−	5.18231e19i	−1.77134	−	1.77134i
$395$	−3.70663e18			−0.124309
$396$	−8.82370e18	−	8.82370e18i	−0.290360	−	0.290360i
$397$	9.65416e18	−	9.65416e18i	0.311735	−	0.311735i	−0.533846	−	0.845581i	$-0.679254\pi$
$397$	9.65416e18	−	9.65416e18i	0.311735	−	0.311735i	0.845581	+	0.533846i	$0.179254\pi$
$398$	−7.34915e19	+	7.34915e19i	−2.32870	+	2.32870i
$399$			8.09005e17i			0.0251567i
$400$			1.06223e20i			3.24167i
$401$	1.42917e19	−	1.42917e19i	0.428055	−	0.428055i	−0.459910	−	0.887965i	$-0.652118\pi$
$401$	1.42917e19	−	1.42917e19i	0.428055	−	0.428055i	0.887965	+	0.459910i	$0.152118\pi$
$402$	1.56853e19	−	1.56853e19i	0.461101	−	0.461101i
$403$	3.72566e19	+	3.72566e19i	1.07502	+	1.07502i
$404$	−4.49502e19			−1.27313
$405$	−3.37030e19	−	3.37030e19i	−0.937035	−	0.937035i
$406$		−	3.23026e18i		−	0.0881642i
$407$	−5.33915e19			−1.43059
$408$	2.34235e19	+	9.92714e19i	0.616169	+	2.61140i
$409$	1.43779e19			0.371338			0.185669	−	0.982612i	$-0.440555\pi$
$409$	1.43779e19			0.371338			0.185669	+	0.982612i	$0.440555\pi$
$410$		−	1.56939e20i		−	3.97971i
$411$	−9.08308e18	−	9.08308e18i	−0.226162	−	0.226162i
$412$	1.01089e20			2.47159
$413$	−2.65698e18	−	2.65698e18i	−0.0637915	−	0.0637915i
$414$	9.52594e17	−	9.52594e17i	0.0224598	−	0.0224598i
$415$	−2.59979e19	+	2.59979e19i	−0.601975	+	0.601975i
$416$		−	9.84128e19i		−	2.23796i
$417$		−	1.28643e19i		−	0.287321i
$418$	4.20824e19	−	4.20824e19i	0.923163	−	0.923163i
$419$	5.17060e18	−	5.17060e18i	0.111413	−	0.111413i	−0.649203	−	0.760616i	$-0.724897\pi$
$419$	5.17060e18	−	5.17060e18i	0.111413	−	0.111413i	0.760616	+	0.649203i	$0.224897\pi$
$420$	7.90816e18	+	7.90816e18i	0.167381	+	0.167381i
$421$	−8.67992e18			−0.180468			−0.0902339	−	0.995921i	$-0.528761\pi$
$421$	−8.67992e18			−0.180468			−0.0902339	+	0.995921i	$0.528761\pi$
$422$	−3.57051e19	−	3.57051e19i	−0.729268	−	0.729268i
$423$			4.60984e18i			0.0924981i
$424$	1.32316e20			2.60837
$425$	5.14456e19	+	3.18028e19i	0.996394	+	0.615954i
$426$	−8.98331e19			−1.70948
$427$			6.62413e18i			0.123857i
$428$	9.37047e19	+	9.37047e19i	1.72160	+	1.72160i
$429$	−8.88311e19			−1.60375
$430$	−9.79459e18	−	9.79459e18i	−0.173769	−	0.173769i
$431$	−1.21009e19	+	1.21009e19i	−0.210979	+	0.210979i	−0.804683	−	0.593704i	$-0.797665\pi$
$431$	−1.21009e19	+	1.21009e19i	−0.210979	+	0.210979i	0.593704	+	0.804683i	$0.297665\pi$
$432$	−1.18842e20	+	1.18842e20i	−2.03631	+	2.03631i
$433$		−	8.39435e19i		−	1.41360i	−0.707411	−	0.706802i	$-0.750137\pi$
$433$		−	8.39435e19i		−	1.41360i	0.707411	−	0.706802i	$-0.249863\pi$
$434$			1.22300e19i			0.202419i
$435$	−4.26916e19	+	4.26916e19i	−0.694502	+	0.694502i
$436$	−1.43891e20	+	1.43891e20i	−2.30083	+	2.30083i
$437$	3.24671e18	+	3.24671e18i	0.0510309	+	0.0510309i
$438$	2.25681e19			0.348690
$439$	−7.88876e19	−	7.88876e19i	−1.19819	−	1.19819i	−0.974709	−	0.223479i	$-0.928259\pi$
$439$	−7.88876e19	−	7.88876e19i	−1.19819	−	1.19819i	−0.223479	−	0.974709i	$-0.571741\pi$
$440$		−	4.94203e20i		−	7.37922i
$441$	6.25291e18			0.0917894
$442$	−1.04433e20	−	6.45588e19i	−1.50720	−	0.931727i
$443$	3.05790e19			0.433905			0.216953	−	0.976182i	$-0.430388\pi$
$443$	3.05790e19			0.433905			0.216953	+	0.976182i	$0.430388\pi$
$444$			1.37586e20i			1.91957i
$445$	−3.86999e19	−	3.86999e19i	−0.530896	−	0.530896i
$446$	1.33290e20			1.79799
$447$	6.23971e19	+	6.23971e19i	0.827671	+	0.827671i
$448$	6.05321e18	−	6.05321e18i	0.0789588	−	0.0789588i
$449$	2.94299e19	−	2.94299e19i	0.377521	−	0.377521i	−0.492686	−	0.870207i	$-0.663985\pi$
$449$	2.94299e19	−	2.94299e19i	0.377521	−	0.377521i	0.870207	+	0.492686i	$0.163985\pi$
$450$			1.60277e19i			0.202198i
$451$			2.06775e20i			2.56551i
$452$	1.64884e20	−	1.64884e20i	2.01206	−	2.01206i
$453$	8.05575e19	−	8.05575e19i	0.966873	−	0.966873i
$454$	5.67780e19	+	5.67780e19i	0.670288	+	0.670288i
$455$	−8.08665e18			−0.0939038
$456$	−6.51410e19	−	6.51410e19i	−0.744078	−	0.744078i
$457$		−	9.60646e19i		−	1.07942i	−0.841850	−	0.539712i	$-0.818533\pi$
$457$		−	9.60646e19i		−	1.07942i	0.841850	−	0.539712i	$-0.181467\pi$
$458$	5.80072e19			0.641196
$459$	2.19764e19	+	9.31384e19i	0.238979	+	1.01282i
$460$	6.34743e19			0.679070
$461$			4.45463e19i			0.468872i	0.972132	+	0.234436i	$0.0753243\pi$
$461$			4.45463e19i			0.468872i	−0.972132	+	0.234436i	$0.924676\pi$
$462$	−1.45800e19	−	1.45800e19i	−0.150988	−	0.150988i
$463$	1.62811e19			0.165892			0.0829461	−	0.996554i	$-0.473567\pi$
$463$	1.62811e19			0.165892			0.0829461	+	0.996554i	$0.473567\pi$
$464$	1.36538e20	+	1.36538e20i	1.36889	+	1.36889i
$465$	1.61633e20	−	1.61633e20i	1.59453	−	1.59453i
$466$	−2.10718e20	+	2.10718e20i	−2.04553	+	2.04553i
$467$			3.91157e19i			0.373659i	0.982392	+	0.186829i	$0.0598211\pi$
$467$			3.91157e19i			0.373659i	−0.982392	+	0.186829i	$0.940179\pi$
$468$		−	2.32513e19i		−	0.218576i
$469$	−1.88132e18	+	1.88132e18i	−0.0174047	+	0.0174047i
$470$	−2.14911e20	+	2.14911e20i	−1.95671	+	1.95671i
$471$	−9.98880e19	−	9.98880e19i	−0.895069	−	0.895069i
$472$	4.27879e20			3.77360
$473$	1.29049e19	+	1.29049e19i	0.112020	+	0.112020i
$474$		−	1.76102e19i		−	0.150462i
$475$	−5.46269e19			−0.459414
$476$	−4.67704e18	−	1.98218e19i	−0.0387185	−	0.164094i
$477$	1.04804e19			0.0854062
$478$		−	2.23551e20i		−	1.79336i
$479$	1.00119e20	+	1.00119e20i	0.790683	+	0.790683i	0.981605	−	0.190922i	$-0.0611479\pi$
$479$	1.00119e20	+	1.00119e20i	0.790683	+	0.790683i	−0.190922	+	0.981605i	$0.561148\pi$
$480$	−4.26951e20			−3.31947
$481$	−7.03459e19	−	7.03459e19i	−0.538456	−	0.538456i
$482$	−3.23612e20	+	3.23612e20i	−2.43877	+	2.43877i
$483$	1.12486e18	−	1.12486e18i	0.00834635	−	0.00834635i
$484$			7.41189e20i			5.41488i
$485$			8.51076e19i			0.612217i
$486$	−3.43497e19	+	3.43497e19i	−0.243305	+	0.243305i
$487$	1.36833e20	−	1.36833e20i	0.954383	−	0.954383i	−0.0446214	−	0.999004i	$-0.514208\pi$
$487$	1.36833e20	−	1.36833e20i	0.954383	−	0.954383i	0.999004	+	0.0446214i	$0.0142081\pi$
$488$	−5.33374e20	−	5.33374e20i	−3.66339	−	3.66339i
$489$	−5.25278e19			−0.355281
$490$	2.91512e20	+	2.91512e20i	1.94171	+	1.94171i
$491$			9.24911e19i			0.606720i	0.952876	+	0.303360i	$0.0981085\pi$
$491$			9.24911e19i			0.606720i	−0.952876	+	0.303360i	$0.901891\pi$
$492$	5.32845e20			3.44241
$493$	1.07007e20	−	2.52487e19i	0.680862	−	0.160652i
$494$	1.10891e20			0.694936
$495$		−	3.91445e19i		−	0.241619i
$496$	−5.16942e20	−	5.16942e20i	−3.14289	−	3.14289i
$497$	1.07747e19			0.0645259
$498$	−1.23516e20	−	1.23516e20i	−0.728623	−	0.728623i
$499$	2.05772e20	−	2.05772e20i	1.19573	−	1.19573i	0.220293	−	0.975434i	$-0.429299\pi$
$499$	2.05772e20	−	2.05772e20i	1.19573	−	1.19573i	0.975434	−	0.220293i	$-0.0707015\pi$
$500$	−7.81372e19	+	7.81372e19i	−0.447284	+	0.447284i
$501$		−	1.90697e20i		−	1.07538i
$502$		−	2.09311e20i		−	1.16282i
$503$	−3.97420e19	+	3.97420e19i	−0.217515	+	0.217515i	−0.807451	−	0.589935i	$-0.799153\pi$
$503$	−3.97420e19	+	3.97420e19i	−0.217515	+	0.217515i	0.589935	+	0.807451i	$0.299153\pi$
$504$	2.29240e18	−	2.29240e18i	0.0123612	−	0.0123612i
$505$	−9.97061e19	−	9.97061e19i	−0.529708	−	0.529708i
$506$	−1.17025e20			−0.612562
$507$	1.35893e19	+	1.35893e19i	0.0700870	+	0.0700870i
$508$			5.18721e20i			2.63607i
$509$	1.78033e20			0.891492			0.445746	−	0.895159i	$-0.352938\pi$
$509$	1.78033e20			0.891492			0.445746	+	0.895159i	$0.352938\pi$
$510$	−2.80080e20	+	4.53070e20i	−1.38199	+	2.23557i
$511$	−2.70686e18			−0.0131616
$512$		−	2.60913e20i		−	1.25018i
$513$	−6.11166e19	−	6.11166e19i	−0.288588	−	0.288588i
$514$	−4.39912e20			−2.04711
$515$	2.24231e20	+	2.24231e20i	1.02835	+	1.02835i
$516$	3.32550e19	−	3.32550e19i	0.150309	−	0.150309i
$517$	2.83157e20	−	2.83157e20i	1.26138	−	1.26138i
$518$		−	2.30919e19i		−	0.101388i
$519$			2.20601e19i			0.0954667i
$520$	6.51137e20	−	6.51137e20i	2.77745	−	2.77745i
$521$	−3.06721e19	+	3.06721e19i	−0.128962	+	0.128962i	−0.768641	−	0.639680i	$-0.779067\pi$
$521$	−3.06721e19	+	3.06721e19i	−0.128962	+	0.128962i	0.639680	+	0.768641i	$0.279067\pi$
$522$	2.06018e19	+	2.06018e19i	0.0853841	+	0.0853841i
$523$	−1.73754e20			−0.709860			−0.354930	−	0.934893i	$-0.615495\pi$
$523$	−1.73754e20			−0.709860			−0.354930	+	0.934893i	$0.615495\pi$
$524$	8.70972e19	+	8.70972e19i	0.350768	+	0.350768i
$525$			1.89262e19i			0.0751394i
$526$	1.63817e20			0.641158
$527$	−4.05134e20	+	9.55930e19i	−1.56322	+	0.368847i
$528$	1.23255e21			4.68866
$529$			2.57607e20i			0.966139i
$530$	4.88598e20	+	4.88598e20i	1.80668	+	1.80668i
$531$	3.38912e19			0.123560
$532$	1.30069e19	+	1.30069e19i	0.0467560	+	0.0467560i
$533$	−2.72436e20	+	2.72436e20i	−0.965629	+	0.965629i
$534$	1.83863e20	−	1.83863e20i	0.642590	−	0.642590i
$535$			4.15701e20i			1.43261i
$536$		−	3.02967e20i		−	1.02958i
$537$	2.20463e20	−	2.20463e20i	0.738802	−	0.738802i
$538$	−8.58214e19	+	8.58214e19i	−0.283615	+	0.283615i
$539$	−3.84081e20	−	3.84081e20i	−1.25172	−	1.25172i
$540$	−1.19485e21			−3.84026
$541$	2.75803e20	+	2.75803e20i	0.874218	+	0.874218i	0.992929	−	0.118711i	$-0.0378762\pi$
$541$	2.75803e20	+	2.75803e20i	0.874218	+	0.874218i	−0.118711	+	0.992929i	$0.537876\pi$
$542$		−	6.29971e20i		−	1.96936i
$543$	−1.33593e20			−0.411892
$544$	6.61331e20	+	4.08824e20i	2.01107	+	1.24321i
$545$	−6.38343e20			−1.91461
$546$		−	3.84196e19i		−	0.113660i
$547$	−1.60317e20	−	1.60317e20i	−0.467816	−	0.467816i	0.433390	−	0.901206i	$-0.357317\pi$
$547$	−1.60317e20	−	1.60317e20i	−0.467816	−	0.467816i	−0.901206	+	0.433390i	$0.857317\pi$
$548$	−2.92070e20			−0.840683
$549$	−4.22471e19	−	4.22471e19i	−0.119951	−	0.119951i
$550$	9.84491e20	−	9.84491e20i	2.75735	−	2.75735i
$551$	−7.02169e19	+	7.02169e19i	−0.194001	+	0.194001i
$552$			1.81148e20i			0.493731i
$553$			2.11220e18i			0.00567931i
$554$	8.89883e19	−	8.89883e19i	0.236053	−	0.236053i
$555$	−3.05187e20	+	3.05187e20i	−0.798671	+	0.798671i
$556$	−2.06829e20	−	2.06829e20i	−0.534010	−	0.534010i
$557$	5.70368e19			0.145292			0.0726459	−	0.997358i	$-0.476856\pi$
$557$	5.70368e19			0.145292			0.0726459	+	0.997358i	$0.476856\pi$
$558$	−7.79998e19	−	7.79998e19i	−0.196036	−	0.196036i
$559$			3.40055e19i			0.0843259i
$560$	1.12204e20			0.274534
$561$	3.69020e20	−	5.96942e20i	0.890899	−	1.44116i
$562$	−4.09273e20			−0.974969
$563$			1.48519e19i			0.0349116i	0.999848	+	0.0174558i	$0.00555664\pi$
$563$			1.48519e19i			0.0349116i	−0.999848	+	0.0174558i	$0.994443\pi$
$564$	−7.29676e20	−	7.29676e20i	−1.69253	−	1.69253i
$565$	7.31473e20			1.67431
$566$	1.30418e20	+	1.30418e20i	0.294587	+	0.294587i
$567$	−1.92054e19	+	1.92054e19i	−0.0428105	+	0.0428105i
$568$	−8.67582e20	+	8.67582e20i	−1.90853	+	1.90853i
$569$		−	2.80728e20i		−	0.609458i	−0.952439	−	0.304729i	$-0.901434\pi$
$569$		−	2.80728e20i		−	0.609458i	0.952439	−	0.304729i	$-0.0985659\pi$
$570$		−	4.81087e20i		−	1.03077i
$571$	1.39777e20	−	1.39777e20i	0.295572	−	0.295572i	−0.543704	−	0.839277i	$-0.682979\pi$
$571$	1.39777e20	−	1.39777e20i	0.295572	−	0.295572i	0.839277	+	0.543704i	$0.182979\pi$
$572$	−1.42820e21	+	1.42820e21i	−2.98070	+	2.98070i
$573$	3.67136e20	+	3.67136e20i	0.756253	+	0.756253i
$574$	−8.94305e19			−0.181822
$575$	7.59548e19	+	7.59548e19i	0.152422	+	0.152422i
$576$			7.72119e19i			0.152938i
$577$	−6.88481e20			−1.34609			−0.673044	−	0.739602i	$-0.735014\pi$
$577$	−6.88481e20			−1.34609			−0.673044	+	0.739602i	$0.735014\pi$
$578$	8.67667e20	−	4.33599e20i	1.67453	−	0.836815i
$579$	−3.40621e20			−0.648906
$580$			1.37276e21i			2.58158i
$581$	1.48147e19	+	1.48147e19i	0.0275025	+	0.0275025i
$582$	−4.04345e20			−0.741020
$583$	−6.43752e20	−	6.43752e20i	−1.16467	−	1.16467i
$584$	2.17956e20	−	2.17956e20i	0.389290	−	0.389290i
$585$	5.15748e19	−	5.15748e19i	0.0909428	−	0.0909428i
$586$			1.05683e21i			1.83980i
$587$			8.80966e20i			1.51417i	0.653319	+	0.757083i	$0.273376\pi$
$587$			8.80966e20i			1.51417i	−0.653319	+	0.757083i	$0.726624\pi$
$588$	−9.89752e20	+	9.89752e20i	−1.67956	+	1.67956i
$589$	2.65846e20	−	2.65846e20i	0.445415	−	0.445415i
$590$	1.58001e21	+	1.58001e21i	2.61379	+	2.61379i
$591$	7.80573e20			1.27499
$592$	9.76061e20	+	9.76061e20i	1.57421	+	1.57421i
$593$		−	1.51910e20i		−	0.241923i	−0.992657	−	0.120961i	$-0.961402\pi$
$593$		−	1.51910e20i		−	0.241923i	0.992657	−	0.120961i	$-0.0385977\pi$
$594$	2.20290e21			3.46414
$595$	3.35933e19	−	5.43420e19i	0.0521646	−	0.0843837i
$596$	2.00640e21			3.07660
$597$		−	1.10695e21i		−	1.67618i
$598$	−1.54186e20	−	1.54186e20i	−0.230561	−	0.230561i
$599$	−1.02332e21			−1.51115			−0.755577	−	0.655060i	$-0.772643\pi$
$599$	−1.02332e21			−1.51115			−0.755577	+	0.655060i	$0.772643\pi$
$600$	−1.52393e21	−	1.52393e21i	−2.22245	−	2.22245i
$601$	−1.81897e20	+	1.81897e20i	−0.261980	+	0.261980i	−0.825858	−	0.563878i	$-0.809309\pi$
$601$	−1.81897e20	+	1.81897e20i	−0.261980	+	0.261980i	0.563878	+	0.825858i	$0.309309\pi$
$602$	−5.58137e18	+	5.58137e18i	−0.00793903	+	0.00793903i
$603$		−	2.39972e19i		−	0.0337117i
$604$		−	2.59035e21i		−	3.59403i
$605$	−1.64407e21	+	1.64407e21i	−2.25296	+	2.25296i
$606$	4.73702e20	−	4.73702e20i	0.641152	−	0.641152i
$607$	−3.08843e20	−	3.08843e20i	−0.412879	−	0.412879i	0.469861	−	0.882740i	$-0.344304\pi$
$607$	−3.08843e20	−	3.08843e20i	−0.412879	−	0.412879i	−0.882740	+	0.469861i	$0.844304\pi$
$608$	−7.02227e20			−0.927258
$609$	2.43275e19	+	2.43275e19i	0.0317299	+	0.0317299i
$610$		−	3.93914e21i		−	5.07490i
$611$	7.46145e20			0.949542
$612$	1.56248e20	+	9.65899e19i	0.196417	+	0.121422i
$613$	5.33048e20			0.661930			0.330965	−	0.943643i	$-0.392626\pi$
$613$	5.33048e20			0.661930			0.330965	+	0.943643i	$0.392626\pi$
$614$			2.16847e21i			2.66005i
$615$	1.18193e21	+	1.18193e21i	1.43228	+	1.43228i
$616$	−2.81618e20			−0.337136
$617$	3.76925e20	+	3.76925e20i	0.445776	+	0.445776i	0.893948	−	0.448172i	$-0.147925\pi$
$617$	3.76925e20	+	3.76925e20i	0.445776	+	0.445776i	−0.448172	+	0.893948i	$0.647925\pi$
$618$	−1.06532e21	+	1.06532e21i	−1.24471	+	1.24471i
$619$	−2.39488e20	+	2.39488e20i	−0.276442	+	0.276442i	−0.831687	−	0.555245i	$-0.812624\pi$
$619$	−2.39488e20	+	2.39488e20i	−0.276442	+	0.276442i	0.555245	+	0.831687i	$0.312624\pi$
$620$		−	5.19737e21i		−	5.92715i
$621$			1.69957e20i			0.191492i
$622$	−5.29873e20	+	5.29873e20i	−0.589853	+	0.589853i
$623$	−2.20528e19	+	2.20528e19i	−0.0242551	+	0.0242551i
$624$	1.62394e21	+	1.62394e21i	1.76476	+	1.76476i
$625$	7.44321e20			0.799209
$626$	−4.69680e20	−	4.69680e20i	−0.498304	−	0.498304i
$627$			6.33856e20i			0.664484i
$628$	−3.21193e21			−3.32713
$629$	7.64951e20	−	1.80493e20i	0.782986	−	0.184749i
$630$	1.69301e19			0.0171240
$631$			6.94969e20i			0.694617i	0.937751	+	0.347309i	$0.112904\pi$
$631$			6.94969e20i			0.694617i	−0.937751	+	0.347309i	$0.887096\pi$
$632$	−1.70074e20	−	1.70074e20i	−0.167981	−	0.167981i
$633$	5.37800e20			0.524920
$634$	5.12459e20	+	5.12459e20i	0.494299	+	0.494299i
$635$	−1.15060e21	+	1.15060e21i	−1.09678	+	1.09678i
$636$	−1.65891e21	+	1.65891e21i	−1.56276	+	1.56276i
$637$		−	1.01209e21i		−	0.942267i
$638$		−	2.53091e21i		−	2.32874i
$639$	−6.87188e19	+	6.87188e19i	−0.0624912	+	0.0624912i
$640$	−8.58623e20	+	8.58623e20i	−0.771707	+	0.771707i
$641$	2.44304e20	+	2.44304e20i	0.217018	+	0.217018i	0.807241	−	0.590223i	$-0.200960\pi$
$641$	2.44304e20	+	2.44304e20i	0.217018	+	0.217018i	−0.590223	+	0.807241i	$0.700960\pi$
$642$	−1.97499e21			−1.73401
$643$	8.12339e20	+	8.12339e20i	0.704945	+	0.704945i	0.965468	−	0.260523i	$-0.0838949\pi$
$643$	8.12339e20	+	8.12339e20i	0.704945	+	0.704945i	−0.260523	+	0.965468i	$0.583895\pi$
$644$		−	3.61704e19i		−	0.0310248i
$645$	1.47529e20			0.125077
$646$	−4.60661e20	+	7.45185e20i	−0.386045	+	0.624482i
$647$	1.70368e21			1.41126			0.705630	−	0.708580i	$-0.250664\pi$
$647$	1.70368e21			1.41126			0.705630	+	0.708580i	$0.250664\pi$
$648$		−	3.09284e21i		−	2.53247i
$649$	−2.08175e21	−	2.08175e21i	−1.68497	−	1.68497i
$650$	2.59423e21			2.07567
$651$	−9.21055e19	−	9.21055e19i	−0.0728497	−	0.0728497i
$652$	−8.44524e20	+	8.44524e20i	−0.660321	+	0.660321i
$653$	8.52968e20	−	8.52968e20i	0.659301	−	0.659301i	−0.295913	−	0.955215i	$-0.595624\pi$
$653$	8.52968e20	−	8.52968e20i	0.659301	−	0.659301i	0.955215	+	0.295913i	$0.0956240\pi$
$654$		−	3.03276e21i		−	2.31742i
$655$			3.86389e20i			0.291887i
$656$	3.78009e21	−	3.78009e21i	2.82308	−	2.82308i
$657$	1.72637e19	−	1.72637e19i	0.0127466	−	0.0127466i
$658$	1.22466e20	+	1.22466e20i	0.0893964	+	0.0893964i
$659$	1.27727e21			0.921814			0.460907	−	0.887448i	$-0.347524\pi$
$659$	1.27727e21			0.921814			0.460907	+	0.887448i	$0.347524\pi$
$660$	6.19605e21	+	6.19605e21i	4.42115	+	4.42115i
$661$			6.93405e20i			0.489188i	0.969626	+	0.244594i	$0.0786547\pi$
$661$			6.93405e20i			0.489188i	−0.969626	+	0.244594i	$0.921345\pi$
$662$	−4.49138e21			−3.13289
$663$	1.27270e21	−	3.00299e20i	0.877759	−	0.207111i
$664$	−2.38576e21			−1.62692
$665$			5.77025e19i			0.0389074i
$666$	1.47275e20	+	1.47275e20i	0.0981910	+	0.0981910i
$667$	1.95263e20			0.128729
$668$	−3.06597e21	−	3.06597e21i	−1.99868	−	1.99868i
$669$	−1.00383e21	+	1.00383e21i	−0.647089	+	0.647089i
$670$	1.11875e21	−	1.11875e21i	0.713138	−	0.713138i
$671$			5.19001e21i			3.27152i
$672$			2.43295e20i			0.151657i
$673$	1.32632e21	−	1.32632e21i	0.817589	−	0.817589i	−0.168169	−	0.985758i	$-0.553785\pi$
$673$	1.32632e21	−	1.32632e21i	0.817589	−	0.817589i	0.985758	+	0.168169i	$0.0537854\pi$
$674$	1.66780e21	−	1.66780e21i	1.01670	−	1.01670i
$675$	−1.42978e21	−	1.42978e21i	−0.861970	−	0.861970i
$676$	4.36969e20			0.260525
$677$	−2.14241e21	−	2.14241e21i	−1.26325	−	1.26325i	−0.949510	−	0.313737i	$-0.898419\pi$
$677$	−2.14241e21	−	2.14241e21i	−1.26325	−	1.26325i	−0.313737	−	0.949510i	$-0.601581\pi$
$678$			3.47522e21i			2.02656i
$679$	4.84979e19			0.0279705
$680$	1.67068e21	+	7.08055e21i	0.952966	+	4.03878i
$681$	−8.55206e20			−0.482467
$682$			9.58218e21i			5.34665i
$683$	−1.16281e21	−	1.16281e21i	−0.641733	−	0.641733i	0.309248	−	0.950981i	$-0.399923\pi$
$683$	−1.16281e21	−	1.16281e21i	−0.641733	−	0.641733i	−0.950981	+	0.309248i	$0.899923\pi$
$684$	−1.65910e20			−0.0905633
$685$	−6.47853e20	−	6.47853e20i	−0.349782	−	0.349782i
$686$	3.32988e20	−	3.32988e20i	0.177827	−	0.177827i
$687$	−4.36860e20	+	4.36860e20i	−0.230763	+	0.230763i
$688$		−	4.71832e20i		−	0.246533i
$689$		−	1.69635e21i		−	0.876740i
$690$	−6.68917e20	+	6.68917e20i	−0.341983	+	0.341983i
$691$	1.03129e21	−	1.03129e21i	0.521547	−	0.521547i	−0.396491	−	0.918039i	$-0.629772\pi$
$691$	1.03129e21	−	1.03129e21i	0.521547	−	0.521547i	0.918039	+	0.396491i	$0.129772\pi$
$692$	3.54675e20	+	3.54675e20i	0.177433	+	0.177433i
$693$	−2.23062e19			−0.0110389
$694$	1.43999e20	+	1.43999e20i	0.0704958	+	0.0704958i
$695$		−	9.17552e20i		−	0.444370i
$696$	−3.91770e21			−1.87699
$697$	−6.99015e20	−	2.96251e21i	−0.331315	−	1.40415i
$698$	4.43015e21			2.07732
$699$		−	3.17389e21i		−	1.47236i
$700$	3.04289e20	+	3.04289e20i	0.139653	+	0.139653i
$701$	−1.04946e21			−0.476521			−0.238260	−	0.971201i	$-0.576577\pi$
$701$	−1.04946e21			−0.476521			−0.238260	+	0.971201i	$0.576577\pi$
$702$	2.90242e21	+	2.90242e21i	1.30386	+	1.30386i
$703$	−5.01955e20	+	5.01955e20i	−0.223100	+	0.223100i
$704$	4.74270e21	−	4.74270e21i	2.08560	−	2.08560i
$705$		−	3.23705e21i		−	1.40842i
$706$			2.84422e20i			0.122441i
$707$	−5.68168e19	+	5.68168e19i	−0.0242009	+	0.0242009i
$708$	−5.36452e21	+	5.36452e21i	−2.26090	+	2.26090i
$709$	2.94349e21	+	2.94349e21i	1.22749	+	1.22749i	0.964912	+	0.262574i	$0.0845712\pi$
$709$	2.94349e21	+	2.94349e21i	1.22749	+	1.22749i	0.262574	+	0.964912i	$0.415429\pi$
$710$	−6.40736e21			−2.64388
$711$	−1.34711e19	−	1.34711e19i	−0.00550023	−	0.00550023i
$712$		−	3.55138e21i		−	1.43482i
$713$	−7.39279e20			−0.295554
$714$	2.58178e20	+	1.59602e20i	0.102137	+	0.0631394i
$715$	−6.33590e21			−2.48035
$716$		−	7.08906e21i		−	2.74625i
$717$	1.68359e21	+	1.68359e21i	0.645421	+	0.645421i
$718$	−4.39045e20			−0.166562
$719$	1.32942e21	+	1.32942e21i	0.499109	+	0.499109i	0.911160	−	0.412052i	$-0.135188\pi$
$719$	1.32942e21	+	1.32942e21i	0.499109	+	0.499109i	−0.412052	+	0.911160i	$0.635188\pi$
$720$	−7.15608e20	+	7.15608e20i	−0.265877	+	0.265877i
$721$	1.27777e20	−	1.27777e20i	0.0469825	−	0.0469825i
$722$			4.35309e21i			1.58405i
$723$		−	4.87433e21i		−	1.75541i
$724$	−2.14786e21	+	2.14786e21i	−0.765537	+	0.765537i
$725$	−1.64268e21	+	1.64268e21i	−0.579453	+	0.579453i
$726$	−7.81094e21	−	7.81094e21i	−2.72696	−	2.72696i
$727$	1.73386e21			0.599110			0.299555	−	0.954079i	$-0.403162\pi$
$727$	1.73386e21			0.599110			0.299555	+	0.954079i	$0.403162\pi$
$728$	−3.71045e20	−	3.71045e20i	−0.126894	−	0.126894i
$729$		−	3.17417e21i		−	1.07442i
$730$	1.60968e21			0.539283
$731$	−2.28516e20	−	1.41265e20i	−0.0757769	−	0.0468440i
$732$	1.33743e22			4.38974
$733$		−	3.60000e20i		−	0.116956i	−0.998289	−	0.0584780i	$-0.981375\pi$
$733$		−	3.60000e20i		−	0.116956i	0.998289	−	0.0584780i	$-0.0186248\pi$
$734$	3.65434e21	+	3.65434e21i	1.17514	+	1.17514i
$735$	−4.39083e21			−1.39763
$736$	9.76396e20	+	9.76396e20i	0.307640	+	0.307640i
$737$	−1.47402e21	+	1.47402e21i	−0.459723	+	0.459723i
$738$	5.70367e20	−	5.70367e20i	0.176089	−	0.176089i
$739$			2.42814e21i			0.742064i	0.928620	+	0.371032i	$0.120996\pi$
$739$			2.42814e21i			0.742064i	−0.928620	+	0.371032i	$0.879004\pi$
$740$			9.81338e21i			2.96880i
$741$	−8.35136e20	+	8.35136e20i	−0.250104	+	0.250104i
$742$	2.78424e20	−	2.78424e20i	0.0825424	−	0.0825424i
$743$	2.19999e21	+	2.19999e21i	0.645661	+	0.645661i	0.951941	−	0.306281i	$-0.0990846\pi$
$743$	2.19999e21	+	2.19999e21i	0.645661	+	0.645661i	−0.306281	+	0.951941i	$0.599085\pi$
$744$	1.48327e22			4.30945
$745$	4.45049e21	+	4.45049e21i	1.28007	+	1.28007i
$746$		−	3.74521e21i		−	1.06644i
$747$	−1.88970e20			−0.0532706
$748$	−3.66446e21	−	1.55304e22i	−1.02270	−	4.33432i
$749$	2.36884e20			0.0654520
$750$		−	1.64688e21i		−	0.450508i
$751$	−1.51418e21	−	1.51418e21i	−0.410088	−	0.410088i	0.471681	−	0.881769i	$-0.343647\pi$
$751$	−1.51418e21	−	1.51418e21i	−0.410088	−	0.410088i	−0.881769	+	0.471681i	$0.843647\pi$
$752$	−1.03529e22			−2.77605
$753$	1.57635e21	+	1.57635e21i	0.418495	+	0.418495i
$754$	3.33460e21	−	3.33460e21i	0.876513	−	0.876513i
$755$	5.74578e21	−	5.74578e21i	1.49536	−	1.49536i
$756$			6.80877e20i			0.175451i
$757$			5.55254e21i			1.41668i	0.705870	+	0.708342i	$0.250556\pi$
$757$			5.55254e21i			1.41668i	−0.705870	+	0.708342i	$0.749444\pi$
$758$	−4.41662e21	+	4.41662e21i	−1.11576	+	1.11576i
$759$	8.81332e20	−	8.81332e20i	0.220458	−	0.220458i
$760$	−4.64620e21	−	4.64620e21i	−1.15079	−	1.15079i
$761$	−6.31760e20			−0.154941			−0.0774707	−	0.996995i	$-0.524684\pi$
$761$	−6.31760e20			−0.154941			−0.0774707	+	0.996995i	$0.524684\pi$
$762$	−5.46649e21	−	5.46649e21i	−1.32754	−	1.32754i
$763$			3.63755e20i			0.0874731i
$764$	1.18054e22			2.81112
$765$	1.32330e20	+	5.60831e20i	0.0312032	+	0.132243i
$766$	−6.51099e20			−0.152031
$767$		−	5.48560e21i		−	1.26841i
$768$	8.00893e20	+	8.00893e20i	0.183386	+	0.183386i
$769$	2.33102e21			0.528565			0.264282	−	0.964445i	$-0.414865\pi$
$769$	2.33102e21			0.528565			0.264282	+	0.964445i	$0.414865\pi$
$770$	−1.03992e21	−	1.03992e21i	−0.233517	−	0.233517i
$771$	3.31304e21	−	3.31304e21i	0.736747	−	0.736747i
$772$	−5.47639e21	+	5.47639e21i	−1.20605	+	1.20605i
$773$			5.51693e21i			1.20324i	0.798784	+	0.601618i	$0.205477\pi$
$773$			5.51693e21i			1.20324i	−0.798784	+	0.601618i	$0.794523\pi$
$774$		−	7.11934e19i		−	0.0153774i
$775$	6.21929e21	−	6.21929e21i	1.33039	−	1.33039i
$776$	−3.90505e21	+	3.90505e21i	−0.827301	+	0.827301i
$777$	1.73908e20	+	1.73908e20i	0.0364891	+	0.0364891i
$778$	−1.41635e22			−2.94323
$779$	1.94397e21	+	1.94397e21i	0.400091	+	0.400091i
$780$			1.63272e22i			3.32814i
$781$	8.44203e21			1.70437
$782$	1.67664e21	−	3.95610e20i	0.335266	−	0.0791074i
$783$	−3.67566e21			−0.727985
$784$			1.40429e22i			2.75478i
$785$	−7.12454e21	−	7.12454e21i	−1.38431	−	1.38431i
$786$	−1.83573e21			−0.353297
$787$	5.53009e21	+	5.53009e21i	1.05420	+	1.05420i	0.998445	+	0.0557529i	$0.0177559\pi$
$787$	5.53009e21	+	5.53009e21i	1.05420	+	1.05420i	0.0557529	+	0.998445i	$0.482244\pi$
$788$	1.25498e22	−	1.25498e22i	2.36968	−	2.36968i
$789$	−1.23373e21	+	1.23373e21i	−0.230750	+	0.230750i
$790$		−	1.25605e21i		−	0.232704i
$791$		−	4.16825e20i		−	0.0764944i
$792$	1.79609e21	−	1.79609e21i	0.326505	−	0.326505i
$793$	−6.83809e21	+	6.83809e21i	−1.23136	+	1.23136i
$794$	3.27146e21	+	3.27146e21i	0.583563	+	0.583563i
$795$	−7.35939e21			−1.30043
$796$	−1.77972e22	−	1.77972e22i	−3.11532	−	3.11532i
$797$			7.23041e21i			1.25379i	0.779103	+	0.626896i	$0.215675\pi$
$797$			7.23041e21i			1.25379i	−0.779103	+	0.626896i	$0.784325\pi$
$798$	−2.74144e20			−0.0470930
$799$	−3.09961e21	+	5.01407e21i	−0.527481	+	0.853276i
$800$	−1.64282e22			−2.76958
$801$		−	2.81296e20i		−	0.0469806i
$802$	4.84295e21	+	4.84295e21i	0.801313	+	0.801313i
$803$	−2.12083e21			−0.347647
$804$	3.79844e21	+	3.79844e21i	0.616858	+	0.616858i
$805$	8.02312e19	−	8.02312e19i	0.0129084	−	0.0129084i
$806$	−1.26250e22	+	1.26250e22i	−2.01242	+	2.01242i
$807$		−	1.29267e21i		−	0.204143i
$808$		−	9.14976e21i		−	1.43161i
$809$	−3.63694e20	+	3.63694e20i	−0.0563796	+	0.0563796i	−0.734734	−	0.678355i	$-0.762693\pi$
$809$	−3.63694e20	+	3.63694e20i	−0.0563796	+	0.0563796i	0.678355	+	0.734734i	$0.262693\pi$
$810$	1.14208e22	−	1.14208e22i	1.75412	−	1.75412i
$811$	−3.09764e21	−	3.09764e21i	−0.471384	−	0.471384i	0.430978	−	0.902362i	$-0.358169\pi$
$811$	−3.09764e21	−	3.09764e21i	−0.471384	−	0.471384i	−0.902362	+	0.430978i	$0.858169\pi$
$812$	7.82260e20			0.117945
$813$	4.74439e21	+	4.74439e21i	0.708764	+	0.708764i
$814$		−	1.80925e22i		−	2.67804i
$815$	−3.74656e21			−0.549478
$816$	−1.76589e22	+	4.16670e21i	−2.56619	+	0.605502i
$817$	2.42647e20			0.0349390
$818$			4.87216e21i			0.695140i
$819$	−2.93895e19	−	2.93895e19i	−0.00415492	−	0.00415492i
$820$	3.80053e22			5.32403
$821$	−2.36270e20	−	2.36270e20i	−0.0327970	−	0.0327970i	0.690518	−	0.723315i	$-0.257383\pi$
$821$	−2.36270e20	−	2.36270e20i	−0.0327970	−	0.0327970i	−0.723315	+	0.690518i	$0.757383\pi$
$822$	3.07794e21	−	3.07794e21i	0.423372	−	0.423372i
$823$	6.24812e21	−	6.24812e21i	0.851629	−	0.851629i	−0.138705	−	0.990334i	$-0.544294\pi$
$823$	6.24812e21	−	6.24812e21i	0.851629	−	0.851629i	0.990334	+	0.138705i	$0.0442939\pi$
$824$			2.05771e22i			2.77927i
$825$			1.48287e22i			1.98471i
$826$	9.00358e20	−	9.00358e20i	0.119417	−	0.119417i
$827$	8.24126e21	−	8.24126e21i	1.08318	−	1.08318i	0.0869730	−	0.996211i	$-0.472281\pi$
$827$	8.24126e21	−	8.24126e21i	1.08318	−	1.08318i	0.996211	−	0.0869730i	$-0.0277194\pi$
$828$	2.30686e20	+	2.30686e20i	0.0300465	+	0.0300465i
$829$	−1.10855e22			−1.43086			−0.715431	−	0.698684i	$-0.753769\pi$
$829$	−1.10855e22			−1.43086			−0.715431	+	0.698684i	$0.753769\pi$
$830$	−8.80980e21	−	8.80980e21i	−1.12689	−	1.12689i
$831$			1.34037e21i			0.169909i
$832$	1.24975e22			1.56999
$833$	6.80122e21	+	4.20440e21i	0.846739	+	0.523440i
$834$	4.35928e21			0.537860
$835$		−	1.36015e22i		−	1.66318i
$836$	1.01909e22	+	1.01909e22i	1.23500	+	1.23500i
$837$	1.39163e22			1.67141
$838$	1.75214e21	+	1.75214e21i	0.208563	+	0.208563i
$839$	−5.33169e21	+	5.33169e21i	−0.629000	+	0.629000i	−0.947816	−	0.318817i	$-0.896715\pi$
$839$	−5.33169e21	+	5.33169e21i	−0.629000	+	0.629000i	0.318817	+	0.947816i	$0.396715\pi$
$840$	−1.60973e21	+	1.60973e21i	−0.188217	+	0.188217i
$841$		−	4.40621e21i		−	0.510617i
$842$		−	2.94132e21i		−	0.337833i
$843$	3.08229e21	−	3.08229e21i	0.350887	−	0.350887i
$844$	8.64658e21	−	8.64658e21i	0.975609	−	0.975609i
$845$	9.69260e20	+	9.69260e20i	0.108396	+	0.108396i
$846$	−1.56211e21			−0.173155
$847$	9.36858e20	+	9.36858e20i	0.102932	+	0.102932i
$848$			2.35371e22i			2.56321i
$849$	−1.96439e21			−0.212041
$850$	−1.07769e22	+	1.74331e22i	−1.15306	+	1.86523i
$851$	1.39586e21			0.148037
$852$		−	2.17545e22i		−	2.28693i
$853$	−4.49741e21	−	4.49741e21i	−0.468645	−	0.468645i	0.432830	−	0.901475i	$-0.357515\pi$
$853$	−4.49741e21	−	4.49741e21i	−0.468645	−	0.468645i	−0.901475	+	0.432830i	$0.857515\pi$
$854$	−2.24469e21			−0.231858
$855$	−3.68013e20	−	3.68013e20i	−0.0376805	−	0.0376805i
$856$	−1.90739e22	+	1.90739e22i	−1.93592	+	1.93592i
$857$	−8.89120e21	+	8.89120e21i	−0.894549	+	0.894549i	−0.994947	−	0.100398i	$-0.967988\pi$
$857$	−8.89120e21	+	8.89120e21i	−0.894549	+	0.894549i	0.100398	+	0.994947i	$0.467988\pi$
$858$		−	3.01018e22i		−	3.00219i
$859$			1.12786e22i			1.11508i	0.830149	+	0.557542i	$0.188255\pi$
$859$			1.12786e22i			1.11508i	−0.830149	+	0.557542i	$0.811745\pi$
$860$	2.37192e21	−	2.37192e21i	0.232467	−	0.232467i
$861$	6.73513e20	−	6.73513e20i	0.0654369	−	0.0654369i
$862$	−4.10058e21	−	4.10058e21i	−0.394949	−	0.394949i
$863$	−2.81462e21			−0.268744			−0.134372	−	0.990931i	$-0.542902\pi$
$863$	−2.81462e21			−0.268744			−0.134372	+	0.990931i	$0.542902\pi$
$864$	−1.83798e22	−	1.83798e22i	−1.73976	−	1.73976i
$865$			1.57344e21i			0.147649i
$866$	2.84455e22			2.64624
$867$	−3.26902e21	+	9.80001e21i	−0.301491	+	0.903823i
$868$	−2.96168e21			−0.270795
$869$			1.65491e21i			0.150012i
$870$	−1.44667e22	−	1.44667e22i	−1.30010	−	1.30010i
$871$	−3.88417e21			−0.346069
$872$	−2.92895e22	−	2.92895e22i	−2.58725	−	2.58725i
$873$	−3.09308e20	+	3.09308e20i	−0.0270885	+	0.0270885i
$874$	−1.10020e21	+	1.10020e21i	−0.0955290	+	0.0955290i
$875$			1.97530e20i			0.0170048i
$876$			5.46523e21i			0.466474i
$877$	9.78090e20	−	9.78090e20i	0.0827717	−	0.0827717i	−0.664509	−	0.747280i	$-0.731359\pi$
$877$	9.78090e20	−	9.78090e20i	0.0827717	−	0.0827717i	0.747280	+	0.664509i	$0.231359\pi$
$878$	2.67323e22	−	2.67323e22i	2.24299	−	2.24299i
$879$	−7.95910e21	−	7.95910e21i	−0.662136	−	0.662136i
$880$	8.79116e22			7.25147
$881$	−1.35985e22	−	1.35985e22i	−1.11217	−	1.11217i	−0.992856	−	0.119318i	$-0.961929\pi$
$881$	−1.35985e22	−	1.35985e22i	−1.11217	−	1.11217i	−0.119318	−	0.992856i	$-0.538071\pi$
$882$			2.11889e21i			0.171828i
$883$	−2.18318e22			−1.75544			−0.877718	−	0.479177i	$-0.840935\pi$
$883$	−2.18318e22			−1.75544			−0.877718	+	0.479177i	$0.840935\pi$
$884$	1.56340e22	−	2.52902e22i	1.24646	−	2.01632i
$885$	−2.37986e22			−1.88138
$886$			1.03621e22i			0.812264i
$887$	5.28344e20	+	5.28344e20i	0.0410667	+	0.0410667i	0.727342	−	0.686275i	$-0.240755\pi$
$887$	5.28344e20	+	5.28344e20i	0.0410667	+	0.0410667i	−0.686275	+	0.727342i	$0.740755\pi$
$888$	−2.80062e22			−2.15852
$889$	6.55661e20	+	6.55661e20i	0.0501090	+	0.0501090i
$890$	1.31140e22	−	1.31140e22i	0.993829	−	0.993829i
$891$	−1.50475e22	+	1.50475e22i	−1.13079	+	1.13079i
$892$			3.22785e22i			2.40534i
$893$		−	5.32413e21i		−	0.393426i
$894$	−2.11442e22	+	2.11442e22i	−1.54939	+	1.54939i
$895$	1.57246e22	−	1.57246e22i	1.14263	−	1.14263i
$896$	4.89280e20	+	4.89280e20i	0.0352572	+	0.0352572i
$897$	2.32239e21			0.165956
$898$	9.97278e21	+	9.97278e21i	0.706714	+	0.706714i
$899$		−	1.59884e22i		−	1.12359i
$900$	−3.88136e21			−0.270499
$901$	1.13994e22	+	7.04692e21i	0.787855	+	0.487039i
$902$	−7.00689e22			−4.80260
$903$		−	8.40681e19i		−	0.00571444i
$904$	3.35627e22	+	3.35627e22i	2.26253	+	2.26253i
$905$	−9.52852e21			−0.637032
$906$	2.72981e22	+	2.72981e22i	1.80997	+	1.80997i
$907$	1.59581e21	−	1.59581e21i	0.104936	−	0.104936i	−0.652689	−	0.757626i	$-0.726359\pi$
$907$	1.59581e21	−	1.59581e21i	0.104936	−	0.104936i	0.757626	+	0.652689i	$0.226359\pi$
$908$	−1.37497e22	+	1.37497e22i	−0.896706	+	0.896706i
$909$		−	7.24728e20i		−	0.0468755i
$910$		−	2.74029e21i		−	0.175786i
$911$	1.00326e22	−	1.00326e22i	0.638298	−	0.638298i	−0.311837	−	0.950135i	$-0.600944\pi$
$911$	1.00326e22	−	1.00326e22i	0.638298	−	0.638298i	0.950135	+	0.311837i	$0.100944\pi$
$912$	1.15876e22	−	1.15876e22i	0.731196	−	0.731196i
$913$	1.16074e22	+	1.16074e22i	0.726445	+	0.726445i
$914$	3.25530e22			2.02066
$915$	2.96662e22	+	2.96662e22i	1.82643	+	1.82643i
$916$			1.40474e22i			0.857787i
$917$	2.20181e20			0.0133355
$918$	−3.15614e22	+	7.44703e21i	−1.89599	+	0.447366i
$919$	2.34862e22			1.39942			0.699709	−	0.714428i	$-0.253313\pi$
$919$	2.34862e22			1.39942			0.699709	+	0.714428i	$0.253313\pi$
$920$			1.29204e22i			0.763603i
$921$	−1.63310e22	−	1.63310e22i	−0.957340	−	0.957340i
$922$	−1.50952e22			−0.877721
$923$	1.11228e22	+	1.11228e22i	0.641505	+	0.641505i
$924$	3.53077e21	−	3.53077e21i	0.201990	−	0.201990i
$925$	−1.17429e22	+	1.17429e22i	−0.666366	+	0.666366i
$926$			5.51710e21i			0.310548i
$927$			1.62986e21i			0.0910021i
$928$	−2.11166e22	+	2.11166e22i	−1.16954	+	1.16954i
$929$	−1.46982e22	+	1.46982e22i	−0.807507	+	0.807507i	−0.984256	−	0.176749i	$-0.943442\pi$
$929$	−1.46982e22	+	1.46982e22i	−0.807507	+	0.807507i	0.176749	+	0.984256i	$0.443442\pi$
$930$	5.47719e22	+	5.47719e22i	2.98494	+	2.98494i
$931$	−7.22180e21			−0.390412
$932$	−5.10287e22	−	5.10287e22i	−2.73650	−	2.73650i
$933$		−	7.98109e21i		−	0.424570i
$934$	−1.32550e22			−0.699483
$935$	2.63204e22	−	4.25771e22i	1.37786	−	2.22889i
$936$	4.73288e21			0.245786
$937$		−	3.66125e22i		−	1.88618i	−0.332545	−	0.943088i	$-0.607907\pi$
$937$		−	3.66125e22i		−	1.88618i	0.332545	−	0.943088i	$-0.392093\pi$
$938$	−6.37514e20	−	6.37514e20i	−0.0325813	−	0.0325813i
$939$	7.07444e21			0.358674
$940$	−5.20443e22	−	5.20443e22i	−2.61767	−	2.61767i
$941$	5.38399e21	−	5.38399e21i	0.268647	−	0.268647i	−0.559908	−	0.828555i	$-0.689163\pi$
$941$	5.38399e21	−	5.38399e21i	0.268647	−	0.268647i	0.828555	+	0.559908i	$0.189163\pi$
$942$	3.38486e22	−	3.38486e22i	1.67556	−	1.67556i
$943$		−	5.40591e21i		−	0.265480i
$944$			7.61136e22i			3.70828i
$945$	−1.51028e21	+	1.51028e21i	−0.0729995	+	0.0729995i
$946$	−4.37301e21	+	4.37301e21i	−0.209699	+	0.209699i
$947$	7.98114e21	+	7.98114e21i	0.379700	+	0.379700i	0.870994	−	0.491294i	$-0.163476\pi$
$947$	7.98114e21	+	7.98114e21i	0.379700	+	0.379700i	−0.491294	+	0.870994i	$0.663476\pi$
$948$	4.26459e21			0.201286
$949$	−2.79429e21	−	2.79429e21i	−0.130850	−	0.130850i
$950$		−	1.85112e22i		−	0.860017i
$951$	−7.71879e21			−0.355791
$952$	4.03480e21	−	9.52027e20i	0.184521	−	0.0435384i
$953$	2.17054e22			0.984852			0.492426	−	0.870354i	$-0.336110\pi$
$953$	2.17054e22			0.984852			0.492426	+	0.870354i	$0.336110\pi$
$954$			3.55144e21i			0.159879i
$955$	2.61860e22	+	2.61860e22i	1.16962	+	1.16962i
$956$	5.41365e22			2.39914
$957$	1.90606e22	+	1.90606e22i	0.838104	+	0.838104i
$958$	−3.39270e22	+	3.39270e22i	−1.48015	+	1.48015i
$959$	−3.69174e20	+	3.69174e20i	−0.0159806	+	0.0159806i
$960$		−	5.42187e22i		−	2.32871i
$961$			3.70679e22i			1.57969i
$962$	2.38378e22	−	2.38378e22i	1.00798	−	1.00798i
$963$	−1.51079e21	+	1.51079e21i	−0.0633881	+	0.0633881i
$964$	−7.83678e22	−	7.83678e22i	−3.26257	−	3.26257i
$965$	−2.42948e22			−1.00360
$966$	3.81177e20	+	3.81177e20i	0.0156242	+	0.0156242i
$967$			2.91250e21i			0.118459i	0.998244	+	0.0592294i	$0.0188643\pi$
$967$			2.91250e21i			0.118459i	−0.998244	+	0.0592294i	$0.981136\pi$
$968$	−1.50872e23			−6.08895
$969$	−2.14279e21	−	9.08139e21i	−0.0858126	−	0.363684i
$970$	−2.88400e22			−1.14606
$971$		−	4.78277e22i		−	1.88597i	−0.332834	−	0.942985i	$-0.608005\pi$
$971$		−	4.78277e22i		−	1.88597i	0.332834	−	0.942985i	$-0.391995\pi$
$972$	−8.31834e21	−	8.31834e21i	−0.325491	−	0.325491i
$973$	−5.22860e20			−0.0203020
$974$	4.63679e22	+	4.63679e22i	1.78659	+	1.78659i
$975$	−1.95375e22	+	1.95375e22i	−0.747023	+	0.747023i
$976$	9.48796e22	−	9.48796e22i	3.59997	−	3.59997i
$977$			1.44103e22i			0.542582i	0.962497	+	0.271291i	$0.0874505\pi$
$977$			1.44103e22i			0.542582i	−0.962497	+	0.271291i	$0.912549\pi$
$978$		−	1.77998e22i		−	0.665081i
$979$	−1.72784e22	+	1.72784e22i	−0.640669	+	0.640669i
$980$	−7.05943e22	+	7.05943e22i	−2.59761	+	2.59761i
$981$	−2.31994e21	−	2.31994e21i	−0.0847149	−	0.0847149i
$982$	−3.13420e22			−1.13577
$983$	−5.52448e21	−	5.52448e21i	−0.198674	−	0.198674i	0.600758	−	0.799431i	$-0.294866\pi$
$983$	−5.52448e21	−	5.52448e21i	−0.198674	−	0.198674i	−0.799431	+	0.600758i	$0.794866\pi$
$984$			1.08462e23i			3.87094i
$985$	5.56746e22			1.97190
$986$	8.55590e21	+	3.62609e22i	0.300738	+	1.27456i
$987$	−1.84461e21			−0.0643467
$988$			2.68541e22i			0.929679i
$989$	−3.37384e20	−	3.37384e20i	−0.0115918	−	0.0115918i
$990$	1.32647e22			0.452308
$991$	−1.86923e22	−	1.86923e22i	−0.632571	−	0.632571i	0.316141	−	0.948712i	$-0.397613\pi$
$991$	−1.86923e22	−	1.86923e22i	−0.632571	−	0.632571i	−0.948712	+	0.316141i	$0.897613\pi$
$992$	7.99487e22	−	7.99487e22i	2.68518	−	2.68518i
$993$	3.38252e22	−	3.38252e22i	1.12751	−	1.12751i
$994$			3.65119e21i			0.120792i
$995$		−	7.89534e22i		−	2.59237i
$996$	2.99114e22	−	2.99114e22i	0.974746	−	0.974746i
$997$	3.17320e22	−	3.17320e22i	1.02632	−	1.02632i	0.0266775	−	0.999644i	$-0.491507\pi$
$997$	3.17320e22	−	3.17320e22i	1.02632	−	1.02632i	0.999644	−	0.0266775i	$-0.00849273\pi$
$998$	6.97290e22	+	6.97290e22i	2.23838	+	2.23838i
$999$	−2.62760e22			−0.837177

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.16.c.a.13.21	yes	44
17.4	even	4	inner	17.16.c.a.4.2	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.16.c.a.4.2	✓	44	17.4	even	4	inner
17.16.c.a.13.21	yes	44	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+338.865i q^{2} +(-2552.04 - 2552.04i) q^{3} -82061.8 q^{4} +(-182025. - 182025. i) q^{5} +(864799. - 864799. i) q^{6} +(-103726. + 103726. i) q^{7} -1.67040e7i q^{8} -1.32307e6i q^{9} +O(q^{10})\)	\(q+338.865i q^{2} +(-2552.04 - 2552.04i) q^{3} -82061.8 q^{4} +(-182025. - 182025. i) q^{5} +(864799. - 864799. i) q^{6} +(-103726. + 103726. i) q^{7} -1.67040e7i q^{8} -1.32307e6i q^{9} +(6.16820e7 - 6.16820e7i) q^{10} +(-8.12691e7 + 8.12691e7i) q^{11} +(2.09425e8 + 2.09425e8i) q^{12} -2.14152e8 q^{13} +(-3.51490e7 - 3.51490e7i) q^{14} +9.29071e8i q^{15} +2.97139e9 q^{16} +(8.89624e8 - 1.43909e9i) q^{17} +4.48344e8 q^{18} +1.52809e9i q^{19} +(1.49373e10 + 1.49373e10i) q^{20} +5.29424e8 q^{21} +(-2.75393e10 - 2.75393e10i) q^{22} +(2.12469e9 - 2.12469e9i) q^{23} +(-4.26292e10 + 4.26292e10i) q^{24} +3.57486e10i q^{25} -7.25687e10i q^{26} +(-3.99955e10 + 3.99955e10i) q^{27} +(8.51190e9 - 8.51190e9i) q^{28} +(4.59509e10 + 4.59509e10i) q^{29} -3.14830e11 q^{30} +(-1.73973e11 - 1.73973e11i) q^{31} +4.59547e11i q^{32} +4.14804e11 q^{33} +(4.87659e11 + 3.01463e11i) q^{34} +3.77613e10 q^{35} +1.08574e11i q^{36} +(3.28486e11 + 3.28486e11i) q^{37} -5.17815e11 q^{38} +(5.46524e11 + 5.46524e11i) q^{39} +(-3.04054e12 + 3.04054e12i) q^{40} +(1.27216e12 - 1.27216e12i) q^{41} +1.79403e11i q^{42} -1.58792e11i q^{43} +(6.66909e12 - 6.66909e12i) q^{44} +(-2.40833e11 + 2.40833e11i) q^{45} +(7.19985e11 + 7.19985e11i) q^{46} -3.48418e12 q^{47} +(-7.58312e12 - 7.58312e12i) q^{48} +4.72604e12i q^{49} -1.21140e13 q^{50} +(-5.94299e12 + 1.40227e12i) q^{51} +1.75737e13 q^{52} +7.92124e12i q^{53} +(-1.35531e13 - 1.35531e13i) q^{54} +2.95860e13 q^{55} +(1.73263e12 + 1.73263e12i) q^{56} +(3.89974e12 - 3.89974e12i) q^{57} +(-1.55712e13 + 1.55712e13i) q^{58} +2.56155e13i q^{59} -7.62412e13i q^{60} +(3.19310e13 - 3.19310e13i) q^{61} +(5.89534e13 - 5.89534e13i) q^{62} +(1.37237e11 + 1.37237e11i) q^{63} -5.83580e13 q^{64} +(3.89810e13 + 3.89810e13i) q^{65} +1.40563e14i q^{66} +1.81375e13 q^{67} +(-7.30041e13 + 1.18095e14i) q^{68} -1.08446e13 q^{69} +1.27960e13i q^{70} +(-5.19387e13 - 5.19387e13i) q^{71} -2.21006e13 q^{72} +(1.30482e13 + 1.30482e13i) q^{73} +(-1.11313e14 + 1.11313e14i) q^{74} +(9.12319e13 - 9.12319e13i) q^{75} -1.25397e14i q^{76} -1.68594e13i q^{77} +(-1.85198e14 + 1.85198e14i) q^{78} +(1.01817e13 - 1.01817e13i) q^{79} +(-5.40868e14 - 5.40868e14i) q^{80} +1.85156e14 q^{81} +(4.31092e14 + 4.31092e14i) q^{82} -1.42826e14i q^{83} -4.34455e13 q^{84} +(-4.23885e14 + 1.00017e14i) q^{85} +5.38090e13 q^{86} -2.34537e14i q^{87} +(1.35752e15 + 1.35752e15i) q^{88} +2.12607e14 q^{89} +(-8.16098e13 - 8.16098e13i) q^{90} +(2.22130e13 - 2.22130e13i) q^{91} +(-1.74356e14 + 1.74356e14i) q^{92} +8.87973e14i q^{93} -1.18067e15i q^{94} +(2.78150e14 - 2.78150e14i) q^{95} +(1.17278e15 - 1.17278e15i) q^{96} +(-2.33780e14 - 2.33780e14i) q^{97} -1.60149e15 q^{98} +(1.07525e14 + 1.07525e14i) 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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