LMFDB - Embedded newform 39.4.j.b.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,4,Mod(4,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("39.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	39.j (of order $6$, 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:	$2.30107449022$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 17x^{2} + 289 $ x^4 - 17*x^2 + 289
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.2
Root			$3.57071 + 2.06155i$ of defining polynomial
Character	$\chi$	$=$	39.4
Dual form			39.4.j.b.10.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.57071 + 2.06155i) q^{2} +(1.50000 - 2.59808i) q^{3} +(4.50000 + 7.79423i) q^{4} +3.05006i q^{5} +(10.7121 - 6.18466i) q^{6} +(-5.78786 + 3.34162i) q^{7} +4.12311i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(3.57071 + 2.06155i) q^{2} +(1.50000 - 2.59808i) q^{3} +(4.50000 + 7.79423i) q^{4} +3.05006i q^{5} +(10.7121 - 6.18466i) q^{6} +(-5.78786 + 3.34162i) q^{7} +4.12311i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-6.28786 + 10.8909i) q^{10} +(-27.9293 - 16.1250i) q^{11} +27.0000 q^{12} +(-22.1364 + 41.3156i) q^{13} -27.5557 q^{14} +(7.92429 + 4.57509i) q^{15} +(27.5000 - 47.6314i) q^{16} +(-14.4293 - 24.9923i) q^{17} -37.1080i q^{18} +(87.6364 - 50.5969i) q^{19} +(-23.7729 + 13.7253i) q^{20} +20.0497i q^{21} +(-66.4850 - 115.155i) q^{22} +(-59.4950 + 103.048i) q^{23} +(10.7121 + 6.18466i) q^{24} +115.697 q^{25} +(-164.217 + 101.891i) q^{26} -27.0000 q^{27} +(-52.0907 - 30.0746i) q^{28} +(-80.0557 + 138.661i) q^{29} +(18.8636 + 32.6727i) q^{30} +38.0705i q^{31} +(224.955 - 129.878i) q^{32} +(-83.7879 + 48.3749i) q^{33} -118.987i q^{34} +(-10.1921 - 17.6533i) q^{35} +(40.5000 - 70.1481i) q^{36} +(283.682 + 163.784i) q^{37} +417.233 q^{38} +(74.1364 + 119.486i) q^{39} -12.5757 q^{40} +(48.5707 + 28.0423i) q^{41} +(-41.3336 + 71.5918i) q^{42} +(63.9393 + 110.746i) q^{43} -290.250i q^{44} +(23.7729 - 13.7253i) q^{45} +(-424.879 + 245.304i) q^{46} -517.983i q^{47} +(-82.5000 - 142.894i) q^{48} +(-149.167 + 258.365i) q^{49} +(413.121 + 238.516i) q^{50} -86.5757 q^{51} +(-421.637 + 13.3838i) q^{52} -695.546 q^{53} +(-96.4093 - 55.6619i) q^{54} +(49.1821 - 85.1860i) q^{55} +(-13.7779 - 23.8639i) q^{56} -303.581i q^{57} +(-571.712 + 330.078i) q^{58} +(568.566 - 328.262i) q^{59} +82.3516i q^{60} +(-350.652 - 607.347i) q^{61} +(-78.4843 + 135.939i) q^{62} +(52.0907 + 30.0746i) q^{63} +631.000 q^{64} +(-126.015 - 67.5174i) q^{65} -398.910 q^{66} +(-49.5150 - 28.5875i) q^{67} +(129.864 - 224.930i) q^{68} +(178.485 + 309.145i) q^{69} -84.0465i q^{70} +(-267.798 + 154.613i) q^{71} +(32.1364 - 18.5540i) q^{72} -389.711i q^{73} +(675.299 + 1169.65i) q^{74} +(173.546 - 300.590i) q^{75} +(788.728 + 455.372i) q^{76} +215.534 q^{77} +(18.3943 + 579.485i) q^{78} +901.820 q^{79} +(145.279 + 83.8766i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(115.621 + 200.262i) q^{82} -687.095i q^{83} +(-156.272 + 90.2238i) q^{84} +(76.2279 - 44.0102i) q^{85} +527.257i q^{86} +(240.167 + 415.982i) q^{87} +(66.4850 - 115.155i) q^{88} +(-927.113 - 535.269i) q^{89} +113.181 q^{90} +(-9.93858 - 313.100i) q^{91} -1070.91 q^{92} +(98.9100 + 57.1057i) q^{93} +(1067.85 - 1849.57i) q^{94} +(154.324 + 267.296i) q^{95} -779.267i q^{96} +(-1519.43 + 877.242i) q^{97} +(-1065.27 + 615.032i) q^{98} +290.250i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} + 18 q^{4} - 66 q^{7} - 18 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 + 18 * q^4 - 66 * q^7 - 18 * q^9	$ 4 q + 6 q^{3} + 18 q^{4} - 66 q^{7} - 18 q^{9} - 68 q^{10} - 126 q^{11} + 108 q^{12} + 40 q^{13} + 204 q^{14} - 54 q^{15} + 110 q^{16} - 72 q^{17} + 222 q^{19} + 162 q^{20} + 34 q^{22} - 138 q^{23} + 120 q^{25} - 714 q^{26} - 108 q^{27} - 594 q^{28} - 6 q^{29} + 204 q^{30} - 378 q^{33} + 402 q^{35} + 162 q^{36} + 492 q^{37} + 612 q^{38} + 168 q^{39} - 136 q^{40} + 180 q^{41} + 306 q^{42} + 470 q^{43} - 162 q^{45} - 714 q^{46} - 330 q^{48} + 346 q^{49} + 1224 q^{50} - 432 q^{51} - 144 q^{52} - 2268 q^{53} - 446 q^{55} + 102 q^{56} - 2244 q^{58} + 2160 q^{59} - 160 q^{61} - 1428 q^{62} + 594 q^{63} + 2524 q^{64} - 804 q^{65} + 204 q^{66} - 498 q^{67} + 648 q^{68} + 414 q^{69} - 1314 q^{71} + 1530 q^{74} + 180 q^{75} + 1998 q^{76} + 2976 q^{77} - 612 q^{78} + 8 q^{79} - 990 q^{80} - 162 q^{81} + 34 q^{82} - 1782 q^{84} - 852 q^{85} + 18 q^{87} - 34 q^{88} - 252 q^{89} + 1224 q^{90} - 1668 q^{91} - 2484 q^{92} - 1404 q^{93} + 2686 q^{94} - 54 q^{95} - 336 q^{97} - 6732 q^{98}+O(q^{100}) $ 4 * q + 6 * q^3 + 18 * q^4 - 66 * q^7 - 18 * q^9 - 68 * q^10 - 126 * q^11 + 108 * q^12 + 40 * q^13 + 204 * q^14 - 54 * q^15 + 110 * q^16 - 72 * q^17 + 222 * q^19 + 162 * q^20 + 34 * q^22 - 138 * q^23 + 120 * q^25 - 714 * q^26 - 108 * q^27 - 594 * q^28 - 6 * q^29 + 204 * q^30 - 378 * q^33 + 402 * q^35 + 162 * q^36 + 492 * q^37 + 612 * q^38 + 168 * q^39 - 136 * q^40 + 180 * q^41 + 306 * q^42 + 470 * q^43 - 162 * q^45 - 714 * q^46 - 330 * q^48 + 346 * q^49 + 1224 * q^50 - 432 * q^51 - 144 * q^52 - 2268 * q^53 - 446 * q^55 + 102 * q^56 - 2244 * q^58 + 2160 * q^59 - 160 * q^61 - 1428 * q^62 + 594 * q^63 + 2524 * q^64 - 804 * q^65 + 204 * q^66 - 498 * q^67 + 648 * q^68 + 414 * q^69 - 1314 * q^71 + 1530 * q^74 + 180 * q^75 + 1998 * q^76 + 2976 * q^77 - 612 * q^78 + 8 * q^79 - 990 * q^80 - 162 * q^81 + 34 * q^82 - 1782 * q^84 - 852 * q^85 + 18 * q^87 - 34 * q^88 - 252 * q^89 + 1224 * q^90 - 1668 * q^91 - 2484 * q^92 - 1404 * q^93 + 2686 * q^94 - 54 * q^95 - 336 * q^97 - 6732 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	3.57071	+	2.06155i	1.26244	+	0.728869i	0.973546	−	0.228493i	$-0.0733797\pi$
$2$	3.57071	+	2.06155i	1.26244	+	0.728869i	0.288892	+	0.957362i	$0.406713\pi$
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$	4.50000	+	7.79423i	0.562500	+	0.974279i
$5$			3.05006i			0.272806i	0.990653	+	0.136403i	$0.0435541\pi$
$5$			3.05006i			0.272806i	−0.990653	+	0.136403i	$0.956446\pi$
$6$	10.7121	−	6.18466i	0.728869	−	0.420813i
$7$	−5.78786	+	3.34162i	−0.312515	+	0.180431i	−0.648051	−	0.761597i	$-0.724416\pi$
$7$	−5.78786	+	3.34162i	−0.312515	+	0.180431i	0.335536	+	0.942027i	$0.391082\pi$
$8$			4.12311i			0.182217i
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−6.28786	+	10.8909i	−0.198840	+	0.344400i
$11$	−27.9293	−	16.1250i	−0.765545	−	0.441988i	0.0657380	−	0.997837i	$-0.479060\pi$
$11$	−27.9293	−	16.1250i	−0.765545	−	0.441988i	−0.831283	+	0.555849i	$0.812393\pi$
$12$	27.0000			0.649519
$13$	−22.1364	+	41.3156i	−0.472272	+	0.881453i
$13$	−22.1364	+	41.3156i	−0.472272	+	0.881453i
$14$	−27.5557			−0.526041
$15$	7.92429	+	4.57509i	0.136403	+	0.0787522i
$16$	27.5000	−	47.6314i	0.429688	−	0.744241i
$17$	−14.4293	−	24.9923i	−0.205860	−	0.356560i	0.744547	−	0.667571i	$-0.232666\pi$
$17$	−14.4293	−	24.9923i	−0.205860	−	0.356560i	−0.950406	+	0.311011i	$0.899332\pi$
$18$		−	37.1080i		−	0.485913i
$19$	87.6364	−	50.5969i	1.05817	−	0.610933i	0.133242	−	0.991083i	$-0.457461\pi$
$19$	87.6364	−	50.5969i	1.05817	−	0.610933i	0.924925	+	0.380150i	$0.124128\pi$
$20$	−23.7729	+	13.7253i	−0.265789	+	0.153453i
$21$			20.0497i			0.208343i
$22$	−66.4850	−	115.155i	−0.644302	−	1.11596i
$23$	−59.4950	+	103.048i	−0.539372	+	0.934220i	0.459566	+	0.888144i	$0.348005\pi$
$23$	−59.4950	+	103.048i	−0.539372	+	0.934220i	−0.998938	+	0.0460765i	$0.985328\pi$
$24$	10.7121	+	6.18466i	0.0911086	+	0.0526016i
$25$	115.697			0.925577
$26$	−164.217	+	101.891i	−1.23868	+	0.768555i
$27$	−27.0000			−0.192450
$28$	−52.0907	−	30.0746i	−0.351579	−	0.202984i
$29$	−80.0557	+	138.661i	−0.512620	+	0.887883i	0.487273	+	0.873250i	$0.337992\pi$
$29$	−80.0557	+	138.661i	−0.512620	+	0.887883i	−0.999893	+	0.0146339i	$0.995342\pi$
$30$	18.8636	+	32.6727i	0.114800	+	0.198840i
$31$			38.0705i			0.220570i	0.993900	+	0.110285i	$0.0351763\pi$
$31$			38.0705i			0.220570i	−0.993900	+	0.110285i	$0.964824\pi$
$32$	224.955	−	129.878i	1.24271	−	0.717480i
$33$	−83.7879	+	48.3749i	−0.441988	+	0.255182i
$34$		−	118.987i		−	0.600179i
$35$	−10.1921	−	17.6533i	−0.0492225	−	0.0852558i
$36$	40.5000	−	70.1481i	0.187500	−	0.324760i
$37$	283.682	+	163.784i	1.26046	+	0.727727i	0.973164	−	0.230114i	$-0.0739099\pi$
$37$	283.682	+	163.784i	1.26046	+	0.727727i	0.287297	+	0.957841i	$0.407243\pi$
$38$	417.233			1.78116
$39$	74.1364	+	119.486i	0.304393	+	0.490590i
$40$	−12.5757			−0.0497099
$41$	48.5707	+	28.0423i	0.185011	+	0.106816i	0.589645	−	0.807662i	$-0.299268\pi$
$41$	48.5707	+	28.0423i	0.185011	+	0.106816i	−0.404634	+	0.914479i	$0.632601\pi$
$42$	−41.3336	+	71.5918i	−0.151855	+	0.263021i
$43$	63.9393	+	110.746i	0.226759	+	0.392759i	0.956846	−	0.290596i	$-0.0938536\pi$
$43$	63.9393	+	110.746i	0.226759	+	0.392759i	−0.730087	+	0.683355i	$0.760520\pi$
$44$		−	290.250i		−	0.994472i
$45$	23.7729	−	13.7253i	0.0787522	−	0.0454676i
$46$	−424.879	+	245.304i	−1.36185	+	0.786264i
$47$		−	517.983i		−	1.60757i	−0.594923	−	0.803783i	$-0.702817\pi$
$47$		−	517.983i		−	1.60757i	0.594923	−	0.803783i	$-0.297183\pi$
$48$	−82.5000	−	142.894i	−0.248080	−	0.429688i
$49$	−149.167	+	258.365i	−0.434890	+	0.753251i
$50$	413.121	+	238.516i	1.16848	+	0.674624i
$51$	−86.5757			−0.237706
$52$	−421.637	+	13.3838i	−1.12443	+	0.0356923i
$53$	−695.546			−1.80265			−0.901326	−	0.433141i	$-0.857405\pi$
$53$	−695.546			−1.80265			−0.901326	+	0.433141i	$0.857405\pi$
$54$	−96.4093	−	55.6619i	−0.242956	−	0.140271i
$55$	49.1821	−	85.1860i	0.120577	−	0.208845i
$56$	−13.7779	−	23.8639i	−0.0328776	−	0.0569456i
$57$		−	303.581i		−	0.705445i
$58$	−571.712	+	330.078i	−1.29430	+	0.747265i
$59$	568.566	−	328.262i	1.25459	−	0.724339i	0.282574	−	0.959245i	$-0.408812\pi$
$59$	568.566	−	328.262i	1.25459	−	0.724339i	0.972018	+	0.234906i	$0.0754783\pi$
$60$			82.3516i			0.177192i
$61$	−350.652	−	607.347i	−0.736007	−	1.27480i	−0.954280	−	0.298913i	$-0.903376\pi$
$61$	−350.652	−	607.347i	−0.736007	−	1.27480i	0.218274	−	0.975888i	$-0.429957\pi$
$62$	−78.4843	+	135.939i	−0.160766	+	0.278456i
$63$	52.0907	+	30.0746i	0.104172	+	0.0601435i
$64$	631.000			1.23242
$65$	−126.015	−	67.5174i	−0.240465	−	0.128839i
$66$	−398.910			−0.743976
$67$	−49.5150	−	28.5875i	−0.0902869	−	0.0521271i	0.454177	−	0.890912i	$-0.349933\pi$
$67$	−49.5150	−	28.5875i	−0.0902869	−	0.0521271i	−0.544464	+	0.838784i	$0.683267\pi$
$68$	129.864	−	224.930i	0.231592	−	0.401130i
$69$	178.485	+	309.145i	0.311407	+	0.539372i
$70$		−	84.0465i		−	0.143507i
$71$	−267.798	+	154.613i	−0.447630	+	0.258440i	−0.706829	−	0.707385i	$-0.749875\pi$
$71$	−267.798	+	154.613i	−0.447630	+	0.258440i	0.259199	+	0.965824i	$0.416542\pi$
$72$	32.1364	−	18.5540i	0.0526016	−	0.0303695i
$73$		−	389.711i		−	0.624826i	−0.949946	−	0.312413i	$-0.898863\pi$
$73$		−	389.711i		−	0.624826i	0.949946	−	0.312413i	$-0.101137\pi$
$74$	675.299	+	1169.65i	1.06084	+	1.83742i
$75$	173.546	−	300.590i	0.267191	−	0.462789i
$76$	788.728	+	455.372i	1.19044	+	0.687300i
$77$	215.534			0.318992
$78$	18.3943	+	579.485i	0.0267018	+	0.841202i
$79$	901.820			1.28434			0.642169	−	0.766563i	$-0.278035\pi$
$79$	901.820			1.28434			0.642169	+	0.766563i	$0.278035\pi$
$80$	145.279	+	83.8766i	0.203033	+	0.117221i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	115.621	+	200.262i	0.155710	+	0.269698i
$83$		−	687.095i		−	0.908657i	−0.890834	−	0.454328i	$-0.849879\pi$
$83$		−	687.095i		−	0.908657i	0.890834	−	0.454328i	$-0.150121\pi$
$84$	−156.272	+	90.2238i	−0.202984	+	0.117193i
$85$	76.2279	−	44.0102i	0.0972714	−	0.0561597i
$86$			527.257i			0.661111i
$87$	240.167	+	415.982i	0.295961	+	0.512620i
$88$	66.4850	−	115.155i	0.0805378	−	0.139496i
$89$	−927.113	−	535.269i	−1.10420	−	0.637510i	−0.166879	−	0.985977i	$-0.553369\pi$
$89$	−927.113	−	535.269i	−1.10420	−	0.637510i	−0.937321	+	0.348467i	$0.886702\pi$
$90$	113.181			0.132560
$91$	−9.93858	−	313.100i	−0.0114489	−	0.360679i
$92$	−1070.91			−1.21359
$93$	98.9100	+	57.1057i	0.110285	+	0.0636730i
$94$	1067.85	−	1849.57i	1.17170	−	2.02945i
$95$	154.324	+	267.296i	0.166666	+	0.288674i
$96$		−	779.267i		−	0.828475i
$97$	−1519.43	+	877.242i	−1.59046	+	0.918251i	−0.597230	+	0.802070i	$0.703732\pi$
$97$	−1519.43	+	877.242i	−1.59046	+	0.918251i	−0.993228	+	0.116182i	$0.962935\pi$
$98$	−1065.27	+	615.032i	−1.09804	+	0.633955i
$99$			290.250i			0.294658i
$100$	520.637	+	901.770i	0.520637	+	0.901770i
$101$	−320.420	+	554.984i	−0.315673	+	0.546762i	−0.979580	−	0.201053i	$-0.935564\pi$
$101$	−320.420	+	554.984i	−0.315673	+	0.546762i	0.663907	+	0.747815i	$0.268897\pi$
$102$	−309.137	−	178.480i	−0.300090	−	0.173257i
$103$	693.153			0.663091			0.331546	−	0.943439i	$-0.392430\pi$
$103$	693.153			0.663091			0.331546	+	0.943439i	$0.392430\pi$
$104$	−170.349	−	91.2708i	−0.160616	−	0.0860562i
$105$	−61.1528			−0.0568372
$106$	−2483.59	−	1433.90i	−2.27574	−	1.31390i
$107$	202.838	−	351.325i	0.183262	−	0.317420i	−0.759727	−	0.650242i	$-0.774668\pi$
$107$	202.838	−	351.325i	0.183262	−	0.317420i	0.942990	+	0.332822i	$0.108001\pi$
$108$	−121.500	−	210.444i	−0.108253	−	0.187500i
$109$			479.516i			0.421370i	0.977554	+	0.210685i	$0.0675694\pi$
$109$			479.516i			0.421370i	−0.977554	+	0.210685i	$0.932431\pi$
$110$	351.231	−	202.783i	0.304441	−	0.175769i
$111$	851.046	−	491.352i	0.727727	−	0.420154i
$112$			367.578i			0.310115i
$113$	773.602	+	1339.92i	0.644021	+	1.11548i	0.984527	+	0.175235i	$0.0560684\pi$
$113$	773.602	+	1339.92i	0.644021	+	1.11548i	−0.340506	+	0.940242i	$0.610598\pi$
$114$	625.849	−	1084.00i	0.514177	−	0.890580i
$115$	−314.304	−	181.463i	−0.254861	−	0.147144i
$116$	−1441.00			−1.15339
$117$	421.637	−	13.3838i	0.333166	−	0.0105755i
$118$	2706.91			2.11179
$119$	167.029	+	96.4344i	0.128668	+	0.0742868i
$120$	−18.8636	+	32.6727i	−0.0143500	+	0.0248549i
$121$	−145.470	−	251.961i	−0.109294	−	0.189302i
$122$		−	2891.55i		−	2.14581i
$123$	145.712	−	84.1269i	0.106816	−	0.0616705i
$124$	−296.730	+	171.317i	−0.214896	+	0.124070i
$125$			734.140i			0.525308i
$126$	124.001	+	214.776i	0.0876735	+	0.151855i
$127$	−1247.58	+	2160.87i	−0.871690	+	1.50981i	−0.0114416	+	0.999935i	$0.503642\pi$
$127$	−1247.58	+	2160.87i	−0.871690	+	1.50981i	−0.860248	+	0.509876i	$0.829691\pi$
$128$	453.481	+	261.817i	0.313144	+	0.180794i
$129$	383.636			0.261839
$130$	−310.773	−	500.872i	−0.209666	−	0.337918i
$131$	43.7571			0.0291838			0.0145919	−	0.999894i	$-0.495355\pi$
$131$	43.7571			0.0291838			0.0145919	+	0.999894i	$0.495355\pi$
$132$	−754.091	−	435.374i	−0.497236	−	0.287079i
$133$	−338.151	+	585.695i	−0.220462	+	0.381851i
$134$	−117.869	−	204.156i	−0.0759877	−	0.131615i
$135$		−	82.3516i		−	0.0525015i
$136$	103.046	−	59.4935i	0.0649713	−	0.0375112i
$137$	−178.569	+	103.097i	−0.111359	+	0.0642932i	−0.554645	−	0.832087i	$-0.687146\pi$
$137$	−178.569	+	103.097i	−0.111359	+	0.0642932i	0.443286	+	0.896380i	$0.353813\pi$
$138$			1471.83i			0.907899i
$139$	50.0000	+	86.6025i	0.0305104	+	0.0528456i	0.880877	−	0.473344i	$-0.156953\pi$
$139$	50.0000	+	86.6025i	0.0305104	+	0.0528456i	−0.850367	+	0.526190i	$0.823620\pi$
$140$	91.7293	−	158.880i	0.0553753	−	0.0959128i
$141$	−1345.76	−	776.974i	−0.803783	−	0.464064i
$142$	−1274.97			−0.753474
$143$	1284.47	−	796.966i	0.751137	−	0.466053i
$144$	−495.000			−0.286458
$145$	−422.923	−	244.175i	−0.242220	−	0.139846i
$146$	803.411	−	1391.55i	0.455416	−	0.788804i
$147$	447.501	+	775.095i	0.251084	+	0.434890i
$148$			2948.11i			1.63739i
$149$	−329.480	+	190.225i	−0.181155	+	0.104590i	−0.587835	−	0.808981i	$-0.700020\pi$
$149$	−329.480	+	190.225i	−0.181155	+	0.104590i	0.406680	+	0.913571i	$0.366686\pi$
$150$	1239.36	−	715.547i	0.674624	−	0.389495i
$151$		−	1517.45i		−	0.817805i	−0.912578	−	0.408902i	$-0.865912\pi$
$151$		−	1517.45i		−	0.817805i	0.912578	−	0.408902i	$-0.134088\pi$
$152$	208.616	+	361.334i	0.111323	+	0.192816i
$153$	−129.864	+	224.930i	−0.0686199	+	0.118853i
$154$	769.611	+	444.335i	0.402708	+	0.232504i
$155$	−116.117			−0.0601726
$156$	−597.684	+	1115.52i	−0.306750	+	0.572520i
$157$	1450.16			0.737166			0.368583	−	0.929595i	$-0.379843\pi$
$157$	1450.16			0.737166			0.368583	+	0.929595i	$0.379843\pi$
$158$	3220.14	+	1859.15i	1.62140	+	0.936114i
$159$	−1043.32	+	1807.08i	−0.520381	+	0.901326i
$160$	396.135	+	686.126i	0.195733	+	0.339019i
$161$		−	795.239i		−	0.389277i
$162$	−289.228	+	166.986i	−0.140271	+	0.0809854i
$163$	2028.54	−	1171.18i	0.974772	−	0.562785i	0.0740844	−	0.997252i	$-0.476397\pi$
$163$	2028.54	−	1171.18i	0.974772	−	0.562785i	0.900688	+	0.434467i	$0.143063\pi$
$164$			504.762i			0.240337i
$165$	−147.546	−	255.558i	−0.0696150	−	0.120577i
$166$	1416.48	−	2453.42i	0.662292	−	1.14712i
$167$	34.7043	+	20.0365i	0.0160808	+	0.00928428i	0.508019	−	0.861346i	$-0.330378\pi$
$167$	34.7043	+	20.0365i	0.0160808	+	0.00928428i	−0.491938	+	0.870630i	$0.663711\pi$
$168$	−82.6671			−0.0379637
$169$	−1216.96	−	1829.16i	−0.553918	−	0.832571i
$170$	362.917			0.163732
$171$	−788.728	−	455.372i	−0.352722	−	0.203644i
$172$	−575.454	+	996.715i	−0.255104	+	0.441853i
$173$	954.770	+	1653.71i	0.419594	+	0.726759i	0.995899	−	0.0904765i	$-0.0288390\pi$
$173$	954.770	+	1653.71i	0.419594	+	0.726759i	−0.576304	+	0.817235i	$0.695506\pi$
$174$			1980.47i			0.862868i
$175$	−669.639	+	386.616i	−0.289257	+	0.167002i
$176$	−1536.11	+	886.874i	−0.657890	+	0.379833i
$177$		−	1969.57i		−	0.836395i
$178$	−2206.97	−	3822.58i	−0.929322	−	1.60963i
$179$	−254.979	+	441.637i	−0.106470	+	0.184411i	−0.914338	−	0.404953i	$-0.867288\pi$
$179$	−254.979	+	441.637i	−0.106470	+	0.184411i	0.807868	+	0.589363i	$0.200621\pi$
$180$	213.956	+	123.527i	0.0885962	+	0.0511510i
$181$	2136.88			0.877531			0.438766	−	0.898602i	$-0.355416\pi$
$181$	2136.88			0.877531			0.438766	+	0.898602i	$0.355416\pi$
$182$	609.985	−	1138.48i	0.248435	−	0.463680i
$183$	−2103.91			−0.849867
$184$	−424.879	−	245.304i	−0.170231	−	0.0982830i
$185$	−499.551	+	865.247i	−0.198528	+	0.343861i
$186$	235.453	+	407.816i	0.0928185	+	0.160766i
$187$			930.688i			0.363950i
$188$	4037.28	−	2330.92i	1.56622	−	0.904256i
$189$	156.272	−	90.2238i	0.0601435	−	0.0347239i
$190$			1272.58i			0.485911i
$191$	−2028.87	−	3514.11i	−0.768607	−	1.33127i	−0.938318	−	0.345773i	$-0.887617\pi$
$191$	−2028.87	−	3514.11i	−0.768607	−	1.33127i	0.169711	−	0.985494i	$-0.445717\pi$
$192$	946.500	−	1639.39i	0.355770	−	0.616211i
$193$	−756.381	−	436.697i	−0.282101	−	0.162871i	0.352273	−	0.935897i	$-0.385409\pi$
$193$	−756.381	−	436.697i	−0.282101	−	0.162871i	−0.634374	+	0.773026i	$0.718742\pi$
$194$	−7233.92			−2.67714
$195$	−364.438	+	226.120i	−0.133836	+	0.0830401i
$196$	−2685.01			−0.978502
$197$	3591.62	+	2073.62i	1.29895	+	0.749947i	0.980222	−	0.197901i	$-0.0634124\pi$
$197$	3591.62	+	2073.62i	1.29895	+	0.749947i	0.318724	+	0.947848i	$0.396746\pi$
$198$	−598.365	+	1036.40i	−0.214767	+	0.371988i
$199$	−1202.03	−	2081.98i	−0.428189	−	0.741646i	0.568523	−	0.822667i	$-0.307515\pi$
$199$	−1202.03	−	2081.98i	−0.428189	−	0.741646i	−0.996712	+	0.0810216i	$0.974182\pi$
$200$			477.032i			0.168656i
$201$	−148.545	+	85.7625i	−0.0521271	+	0.0300956i
$202$	−2288.26	+	1321.13i	−0.797035	+	0.460169i
$203$		−	1070.06i		−	0.369969i
$204$	−389.591	−	674.791i	−0.133710	−	0.231592i
$205$	−85.5307	+	148.144i	−0.0291401	+	0.0504722i
$206$	2475.05	+	1428.97i	0.837111	+	0.483307i
$207$	1070.91			0.359582
$208$	1359.17	+	2190.57i	0.453083	+	0.730233i
$209$	−3263.50			−1.08010
$210$	−218.359	−	126.070i	−0.0717535	−	0.0414269i
$211$	−1934.43	+	3350.53i	−0.631144	+	1.09317i	0.356174	+	0.934420i	$0.384081\pi$
$211$	−1934.43	+	3350.53i	−0.631144	+	1.09317i	−0.987318	+	0.158754i	$0.949252\pi$
$212$	−3129.96	−	5421.24i	−1.01399	−	1.75629i
$213$			927.679i			0.298420i
$214$	1448.55	−	836.322i	0.462715	−	0.267149i
$215$	−337.782	+	195.019i	−0.107147	+	0.0618612i
$216$		−	111.324i		−	0.0350677i
$217$	−127.217	−	220.346i	−0.0397975	−	0.0689313i
$218$	−988.547	+	1712.21i	−0.307123	+	0.531953i
$219$	−1012.50	−	584.567i	−0.312413	−	0.180372i
$220$	885.279			0.271298
$221$	1351.98	−	42.9153i	0.411512	−	0.0130624i
$222$	4051.79			1.22495
$223$	2436.61	+	1406.78i	0.731692	+	0.422443i	0.819041	−	0.573735i	$-0.194506\pi$
$223$	2436.61	+	1406.78i	0.731692	+	0.422443i	−0.0873487	+	0.996178i	$0.527839\pi$
$224$	−868.005	+	1503.43i	−0.258911	+	0.448447i
$225$	−520.637	−	901.770i	−0.154263	−	0.267191i
$226$			6379.29i			1.87763i
$227$	3913.02	−	2259.19i	1.14413	−	0.660561i	0.196677	−	0.980468i	$-0.436985\pi$
$227$	3913.02	−	2259.19i	1.14413	−	0.660561i	0.947449	+	0.319907i	$0.103652\pi$
$228$	2366.18	−	1366.12i	0.687300	−	0.396813i
$229$		−	1305.27i		−	0.376658i	−0.982106	−	0.188329i	$-0.939693\pi$
$229$		−	1305.27i		−	0.376658i	0.982106	−	0.188329i	$-0.0603070\pi$
$230$	−748.192	−	1295.91i	−0.214497	−	0.371520i
$231$	323.301	−	559.975i	0.0920852	−	0.159496i
$232$	−571.712	−	330.078i	−0.161788	−	0.0934082i
$233$	3360.55			0.944879			0.472440	−	0.881363i	$-0.343373\pi$
$233$	3360.55			0.944879			0.472440	+	0.881363i	$0.343373\pi$
$234$	1533.14	+	821.437i	0.428309	+	0.229483i
$235$	1579.88			0.438553
$236$	5117.09	+	2954.35i	1.41142	+	0.814882i
$237$	1352.73	−	2343.00i	0.370756	−	0.642169i
$238$	397.609	+	688.679i	0.108291	+	0.187565i
$239$			4737.17i			1.28210i	0.767499	+	0.641050i	$0.221501\pi$
$239$			4737.17i			1.28210i	−0.767499	+	0.641050i	$0.778499\pi$
$240$	435.836	−	251.630i	0.117221	−	0.0676777i
$241$	4144.17	−	2392.64i	1.10767	−	0.639516i	0.169448	−	0.985539i	$-0.445801\pi$
$241$	4144.17	−	2392.64i	1.10767	−	0.639516i	0.938226	+	0.346023i	$0.112468\pi$
$242$		−	1199.58i		−	0.318643i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	3155.87	−	5466.13i	0.828007	−	1.43415i
$245$	−788.029	−	454.969i	−0.205491	−	0.118640i
$246$	693.729			0.179799
$247$	150.484	+	4740.79i	0.0387655	+	1.22125i
$248$	−156.969			−0.0401916
$249$	−1785.13	−	1030.64i	−0.454328	−	0.262307i
$250$	−1513.47	+	2621.41i	−0.382881	+	0.663169i
$251$	−1636.93	−	2835.25i	−0.411642	−	0.712985i	0.583428	−	0.812165i	$-0.301711\pi$
$251$	−1636.93	−	2835.25i	−0.411642	−	0.712985i	−0.995069	+	0.0991805i	$0.968378\pi$
$252$			541.343i			0.135323i
$253$	3323.31	−	1918.71i	0.825828	−	0.476792i
$254$	−8909.48	+	5143.89i	−2.20091	+	1.27069i
$255$		−	264.061i		−	0.0648476i
$256$	−1444.50	−	2501.95i	−0.352661	−	0.610827i
$257$	−3272.91	+	5668.84i	−0.794390	+	1.37592i	0.128835	+	0.991666i	$0.458876\pi$
$257$	−3272.91	+	5668.84i	−0.794390	+	1.37592i	−0.923226	+	0.384258i	$0.874457\pi$
$258$	1369.85	+	790.885i	0.330556	+	0.190846i
$259$	−2189.22			−0.525217
$260$	−40.8214	−	1286.02i	−0.00973706	−	0.306752i
$261$	1441.00			0.341746
$262$	156.244	+	90.2077i	0.0368428	+	0.0212712i
$263$	−44.1007	+	76.3847i	−0.0103398	+	0.0179091i	−0.871149	−	0.491019i	$-0.836625\pi$
$263$	−44.1007	+	76.3847i	−0.0103398	+	0.0179091i	0.860809	+	0.508928i	$0.169958\pi$
$264$	−199.455	−	345.466i	−0.0464985	−	0.0805378i
$265$		−	2121.46i		−	0.491773i
$266$	−2414.88	+	1394.23i	−0.556639	+	0.321376i
$267$	−2781.34	+	1605.81i	−0.637510	+	0.368067i
$268$		−	514.575i		−	0.117286i
$269$	2263.80	+	3921.01i	0.513109	+	0.888730i	0.999884	+	0.0152033i	$0.00483956\pi$
$269$	2263.80	+	3921.01i	0.513109	+	0.888730i	−0.486776	+	0.873527i	$0.661827\pi$
$270$	169.772	−	294.054i	0.0382667	−	0.0662798i
$271$	−7206.91	−	4160.91i	−1.61546	−	0.932684i	−0.988075	−	0.153971i	$-0.950794\pi$
$271$	−7206.91	−	4160.91i	−1.61546	−	0.932684i	−0.627380	−	0.778713i	$-0.715873\pi$
$272$	−1587.22			−0.353821
$273$	−828.366	−	443.829i	−0.183645	−	0.0983948i
$274$	−850.160			−0.187445
$275$	−3231.34	−	1865.61i	−0.708571	−	0.409094i
$276$	−1606.36	+	2782.31i	−0.350333	+	0.606794i
$277$	−1440.65	−	2495.29i	−0.312493	−	0.541254i	0.666408	−	0.745587i	$-0.267831\pi$
$277$	−1440.65	−	2495.29i	−0.312493	−	0.541254i	−0.978901	+	0.204333i	$0.934497\pi$
$278$			412.311i			0.0889523i
$279$	296.730	−	171.317i	0.0636730	−	0.0367616i
$280$	72.7864	−	42.0233i	0.0155351	−	0.00896918i
$281$		−	2817.99i		−	0.598247i	−0.954214	−	0.299123i	$-0.903306\pi$
$281$		−	2817.99i		−	0.598247i	0.954214	−	0.299123i	$-0.0966942\pi$
$282$	−3203.55	−	5548.71i	−0.676484	−	1.17170i
$283$	132.301	−	229.152i	0.0277896	−	0.0481330i	−0.851796	−	0.523873i	$-0.824486\pi$
$283$	132.301	−	229.152i	0.0277896	−	0.0481330i	0.879586	+	0.475740i	$0.157820\pi$
$284$	−2410.18	−	1391.52i	−0.503584	−	0.290744i
$285$	925.941			0.192449
$286$	6229.45	−	197.738i	1.28796	−	0.0408829i
$287$	−374.827			−0.0770918
$288$	−2024.59	−	1168.90i	−0.414238	−	0.239160i
$289$	2040.09	−	3533.54i	0.415244	−	0.719223i
$290$	−1006.76	−	1743.76i	−0.203858	−	0.353093i
$291$			5263.45i			1.06031i
$292$	3037.50	−	1753.70i	0.608754	−	0.351464i
$293$	3717.43	−	2146.26i	0.741211	−	0.427938i	−0.0812984	−	0.996690i	$-0.525907\pi$
$293$	3717.43	−	2146.26i	0.741211	−	0.427938i	0.822509	+	0.568751i	$0.192573\pi$
$294$			3690.19i			0.732028i
$295$	1001.22	+	1734.16i	0.197604	+	0.342260i
$296$	−675.299	+	1169.65i	−0.132604	+	0.229678i
$297$	754.091	+	435.374i	0.147329	+	0.0850606i
$298$	−1568.64			−0.304929
$299$	−2940.50	−	4739.19i	−0.568740	−	0.916638i
$300$	3123.82			0.601180
$301$	−740.143	−	427.322i	−0.141731	−	0.0818286i
$302$	3128.31	−	5418.39i	0.596072	−	1.03243i
$303$	961.260	+	1664.95i	0.182254	+	0.315673i
$304$		−	5565.66i		−	1.05004i
$305$	1852.45	−	1069.51i	0.347773	−	0.200787i
$306$	−927.411	+	535.441i	−0.173257	+	0.100030i
$307$			7026.26i			1.30622i	0.757263	+	0.653110i	$0.226536\pi$
$307$			7026.26i			1.30622i	−0.757263	+	0.653110i	$0.773464\pi$
$308$	969.904	+	1679.92i	0.179433	+	0.310787i
$309$	1039.73	−	1800.86i	0.191418	−	0.331546i
$310$	−414.621	−	239.382i	−0.0759642	−	0.0438580i
$311$	1133.21			0.206618			0.103309	−	0.994649i	$-0.467057\pi$
$311$	1133.21			0.206618			0.103309	+	0.994649i	$0.467057\pi$
$312$	−492.651	+	305.672i	−0.0893939	+	0.0554657i
$313$	−5285.95			−0.954566			−0.477283	−	0.878750i	$-0.658378\pi$
$313$	−5285.95			−0.954566			−0.477283	+	0.878750i	$0.658378\pi$
$314$	5178.09	+	2989.57i	0.930626	+	0.537297i
$315$	−91.7293	+	158.880i	−0.0164075	+	0.0284186i
$316$	4058.19	+	7028.99i	0.722440	+	1.25130i
$317$			4782.16i			0.847296i	0.905827	+	0.423648i	$0.139251\pi$
$317$			4782.16i			0.847296i	−0.905827	+	0.423648i	$0.860749\pi$
$318$	−7450.78	+	4301.71i	−1.31390	+	0.758579i
$319$	4471.80	−	2581.79i	0.784867	−	0.453143i
$320$			1924.59i			0.336212i
$321$	−608.514	−	1053.98i	−0.105807	−	0.183262i
$322$	1639.43	−	2839.57i	0.283732	−	0.491438i
$323$	−2529.06	−	1460.15i	−0.435668	−	0.251533i
$324$	−729.000			−0.125000
$325$	−2561.12	+	4780.10i	−0.437124	+	0.815852i
$326$	9657.80			1.64079
$327$	1245.82	+	719.274i	0.210685	+	0.121639i
$328$	−115.621	+	200.262i	−0.0194638	+	0.0337123i
$329$	1730.90	+	2998.01i	0.290054	+	0.502388i
$330$		−	1216.70i		−	0.202961i
$331$	−7508.43	+	4334.99i	−1.24683	+	0.719857i	−0.970476	−	0.241199i	$-0.922459\pi$
$331$	−7508.43	+	4334.99i	−1.24683	+	0.719857i	−0.276353	+	0.961056i	$0.589126\pi$
$332$	5355.38	−	3091.93i	0.885285	−	0.511120i
$333$		−	2948.11i		−	0.485152i
$334$	82.6128	+	143.090i	0.0135340	+	0.0234417i
$335$	87.1936	−	151.024i	0.0142206	−	0.0246308i
$336$	954.996	+	551.367i	0.155058	+	0.0895225i
$337$	−8526.59			−1.37826			−0.689129	−	0.724639i	$-0.742007\pi$
$337$	−8526.59			−1.37826			−0.689129	+	0.724639i	$0.742007\pi$
$338$	−574.497	−	9040.23i	−0.0924513	−	1.45480i
$339$	4641.61			0.743651
$340$	686.051	+	396.092i	0.109430	+	0.0631796i
$341$	613.886	−	1063.28i	0.0974891	−	0.168856i
$342$	−1877.55	−	3252.01i	−0.296860	−	0.514177i
$343$		−	4286.19i		−	0.674731i
$344$	−456.618	+	263.628i	−0.0715674	+	0.0413195i
$345$	−942.911	+	544.390i	−0.147144	+	0.0849535i
$346$			7873.23i			1.22332i
$347$	6290.74	+	10895.9i	0.973213	+	1.68565i	0.685711	+	0.727874i	$0.259491\pi$
$347$	6290.74	+	10895.9i	0.973213	+	1.68565i	0.287501	+	0.957780i	$0.407175\pi$
$348$	−2161.50	+	3743.84i	−0.332956	+	0.576697i
$349$	7760.61	+	4480.59i	1.19030	+	0.687222i	0.958375	−	0.285511i	$-0.0921633\pi$
$349$	7760.61	+	4480.59i	1.19030	+	0.687222i	0.231928	+	0.972733i	$0.425497\pi$
$350$	−3188.12			−0.486892
$351$	597.684	−	1115.52i	0.0908889	−	0.169636i
$352$	−8377.11			−1.26847
$353$	−4640.16	−	2679.00i	−0.699634	−	0.403934i	0.107577	−	0.994197i	$-0.465691\pi$
$353$	−4640.16	−	2679.00i	−0.699634	−	0.403934i	−0.807211	+	0.590263i	$0.799024\pi$
$354$	4060.37	−	7032.77i	0.609622	−	1.05590i
$355$	−471.579	−	816.799i	−0.0705037	−	0.122116i
$356$		−	9634.84i		−	1.43440i
$357$	501.088	−	289.303i	0.0742868	−	0.0428895i
$358$	−1820.92	+	1051.31i	−0.268822	+	0.155205i
$359$		−	2705.40i		−	0.397731i	−0.980027	−	0.198866i	$-0.936274\pi$
$359$		−	2705.40i		−	0.397731i	0.980027	−	0.198866i	$-0.0637257\pi$
$360$	56.5907	+	98.0180i	0.00828498	+	0.0143500i
$361$	1690.60	−	2928.20i	0.246478	−	0.426913i
$362$	7630.19	+	4405.29i	1.10783	+	0.639605i
$363$	−872.820			−0.126202
$364$	2395.65	−	1486.42i	0.344962	−	0.214037i
$365$	1188.64			0.170456
$366$	−7512.47	−	4337.33i	−1.07290	−	0.619442i
$367$	−5236.88	+	9070.54i	−0.744858	+	1.29013i	0.205403	+	0.978678i	$0.434150\pi$
$367$	−5236.88	+	9070.54i	−0.744858	+	1.29013i	−0.950261	+	0.311455i	$0.899184\pi$
$368$	3272.22	+	5667.66i	0.463523	+	0.802846i
$369$		−	504.762i		−	0.0712110i
$370$	−3567.51	+	2059.70i	−0.501259	+	0.289402i
$371$	4025.72	−	2324.25i	0.563356	−	0.325254i
$372$			1027.90i			0.143264i
$373$	6381.51	+	11053.1i	0.885850	+	1.53434i	0.844737	+	0.535182i	$0.179757\pi$
$373$	6381.51	+	11053.1i	0.885850	+	1.53434i	0.0411127	+	0.999155i	$0.486910\pi$
$374$	−1918.66	+	3323.22i	−0.265272	+	0.459464i
$375$	1907.35	+	1101.21i	0.262654	+	0.151643i
$376$	2135.70			0.292926
$377$	−3956.70	−	6377.00i	−0.540531	−	0.871173i
$378$	744.004			0.101237
$379$	−2007.47	−	1159.01i	−0.272076	−	0.157083i	0.357755	−	0.933816i	$-0.383542\pi$
$379$	−2007.47	−	1159.01i	−0.272076	−	0.157083i	−0.629831	+	0.776733i	$0.716876\pi$
$380$	−1388.91	+	2405.67i	−0.187499	+	0.324758i
$381$	3742.73	+	6482.60i	0.503270	+	0.871690i
$382$		−	16730.5i		−	2.24086i
$383$	−1717.63	+	991.672i	−0.229156	+	0.132303i	−0.610183	−	0.792261i	$-0.708904\pi$
$383$	−1717.63	+	991.672i	−0.229156	+	0.132303i	0.381027	+	0.924564i	$0.375571\pi$
$384$	1360.44	−	785.452i	0.180794	−	0.104381i
$385$			657.392i			0.0870229i
$386$	−1800.55	−	3118.64i	−0.237424	−	0.411230i
$387$	575.454	−	996.715i	0.0755864	−	0.130920i
$388$	−13674.8	−	7895.17i	−1.78927	−	1.03303i
$389$	3244.51			0.422887			0.211444	−	0.977390i	$-0.432184\pi$
$389$	3244.51			0.422887			0.211444	+	0.977390i	$0.432184\pi$
$390$	−1767.46	+	56.1036i	−0.229485	+	0.00728441i
$391$	3433.88			0.444140
$392$	−1065.27	−	615.032i	−0.137255	−	0.0792444i
$393$	65.6357	−	113.684i	0.00842464	−	0.0145919i
$394$	8549.77	+	14808.6i	1.09323	+	1.89352i
$395$			2750.60i			0.350374i
$396$	−2262.27	+	1306.12i	−0.287079	+	0.165745i
$397$	3256.02	−	1879.86i	0.411624	−	0.237651i	−0.279863	−	0.960040i	$-0.590289\pi$
$397$	3256.02	−	1879.86i	0.411624	−	0.237651i	0.691487	+	0.722389i	$0.256956\pi$
$398$		−	9912.20i		−	1.24838i
$399$	1014.45	+	1757.09i	0.127284	+	0.220462i
$400$	3181.67	−	5510.82i	0.397709	−	0.688852i
$401$	1729.93	+	998.773i	0.215432	+	0.124380i	0.603833	−	0.797110i	$-0.293639\pi$
$401$	1729.93	+	998.773i	0.215432	+	0.124380i	−0.388401	+	0.921490i	$0.626973\pi$
$402$	−707.216			−0.0877431
$403$	−1572.90	−	842.744i	−0.194422	−	0.104169i
$404$	−5767.56			−0.710264
$405$	−213.956	−	123.527i	−0.0262507	−	0.0151559i
$406$	2205.99	−	3820.89i	0.269659	−	0.467063i
$407$	−5282.03	−	9148.74i	−0.643293	−	1.11422i
$408$		−	356.961i		−	0.0433142i
$409$	4499.20	−	2597.62i	0.543940	−	0.314044i	−0.202735	−	0.979234i	$-0.564983\pi$
$409$	4499.20	−	2597.62i	0.543940	−	0.314044i	0.746674	+	0.665190i	$0.231650\pi$
$410$	−610.811	+	352.652i	−0.0735752	+	0.0424787i
$411$			618.582i			0.0742394i
$412$	3119.19	+	5402.59i	0.372989	+	0.646035i
$413$	−2193.85	+	3799.86i	−0.261386	+	0.452734i
$414$	3823.91	+	2207.74i	0.453950	+	0.262088i
$415$	2095.68			0.247887
$416$	386.280	+	12169.2i	0.0455263	+	1.43424i
$417$	300.000			0.0352304
$418$	−11653.0	−	6727.87i	−1.36356	−	0.787251i
$419$	3411.05	−	5908.12i	0.397711	−	0.688855i	−0.595732	−	0.803183i	$-0.703138\pi$
$419$	3411.05	−	5908.12i	0.397711	−	0.688855i	0.993443	+	0.114328i	$0.0364714\pi$
$420$	−275.188	−	476.639i	−0.0319709	−	0.0553753i
$421$		−	7537.70i		−	0.872601i	−0.899801	−	0.436300i	$-0.856288\pi$
$421$		−	7537.70i		−	0.872601i	0.899801	−	0.436300i	$-0.143712\pi$
$422$	−13814.6	+	7975.85i	−1.59356	+	0.920043i
$423$	−4037.28	+	2330.92i	−0.464064	+	0.267928i
$424$		−	2867.81i		−	0.328474i
$425$	−1669.43	−	2891.53i	−0.190539	−	0.330023i
$426$	−1912.46	+	3312.48i	−0.217509	+	0.376737i
$427$	4059.05	+	2343.49i	0.460026	+	0.265596i
$428$	3651.08			0.412340
$429$	−143.876	−	4532.59i	−0.0161920	−	0.510107i
$430$	−1608.16			−0.180355
$431$	−11608.4	−	6702.10i	−1.29735	−	0.749023i	−0.317401	−	0.948291i	$-0.602810\pi$
$431$	−11608.4	−	6702.10i	−1.29735	−	0.749023i	−0.979945	+	0.199268i	$0.936143\pi$
$432$	−742.500	+	1286.05i	−0.0826934	+	0.143229i
$433$	−8857.97	−	15342.5i	−0.983110	−	1.70280i	−0.650050	−	0.759892i	$-0.725252\pi$
$433$	−8857.97	−	15342.5i	−0.983110	−	1.70280i	−0.333061	−	0.942905i	$-0.608081\pi$
$434$		−	1049.06i		−	0.116029i
$435$	−1268.77	+	732.524i	−0.139846	+	0.0807398i
$436$	−3737.46	+	2157.82i	−0.410531	+	0.237020i
$437$			12041.1i			1.31808i
$438$	−2410.23	−	4174.64i	−0.262935	−	0.455416i
$439$	3581.73	−	6203.75i	0.389401	−	0.674462i	−0.602968	−	0.797765i	$-0.706015\pi$
$439$	3581.73	−	6203.75i	0.389401	−	0.674462i	0.992369	+	0.123303i	$0.0393488\pi$
$440$	351.231	+	202.783i	0.0380552	+	0.0219712i
$441$	2685.01			0.289926
$442$	4916.02	+	2633.95i	0.529030	+	0.283448i
$443$	−10169.2			−1.09064			−0.545321	−	0.838227i	$-0.683592\pi$
$443$	−10169.2			−1.09064			−0.545321	+	0.838227i	$0.683592\pi$
$444$	7659.42	+	4422.17i	0.818693	+	0.472673i
$445$	1632.60	−	2827.75i	0.173916	−	0.301232i
$446$	5800.29	+	10046.4i	0.615811	+	1.06662i
$447$			1141.35i			0.120770i
$448$	−3652.14	+	2108.56i	−0.385150	+	0.222367i
$449$	−14845.8	+	8571.24i	−1.56040	+	0.900895i	−0.563179	+	0.826335i	$0.690422\pi$
$449$	−14845.8	+	8571.24i	−1.56040	+	0.900895i	−0.997217	+	0.0745603i	$0.976245\pi$
$450$		−	4293.28i		−	0.449750i
$451$	−904.364	−	1566.40i	−0.0944231	−	0.163546i
$452$	−6962.42	+	12059.3i	−0.724524	+	1.25491i
$453$	−3942.46	−	2276.18i	−0.408902	−	0.236080i
$454$	18629.7			1.92585
$455$	954.974	−	30.3133i	0.0983954	−	0.00312331i
$456$	1251.70			0.128544
$457$	12203.3	+	7045.57i	1.24912	+	0.721177i	0.970933	−	0.239351i	$-0.0769346\pi$
$457$	12203.3	+	7045.57i	1.24912	+	0.721177i	0.278183	+	0.960528i	$0.410268\pi$
$458$	2690.88	−	4660.74i	0.274534	−	0.475507i
$459$	389.591	+	674.791i	0.0396177	+	0.0686199i
$460$		−	3266.34i		−	0.331074i
$461$	2530.72	−	1461.11i	0.255678	−	0.147616i	−0.366684	−	0.930346i	$-0.619507\pi$
$461$	2530.72	−	1461.11i	0.255678	−	0.147616i	0.622361	+	0.782730i	$0.286174\pi$
$462$	2308.83	−	1333.01i	0.232504	−	0.134236i
$463$		−	2072.61i		−	0.208040i	−0.994575	−	0.104020i	$-0.966829\pi$
$463$		−	2072.61i		−	0.208040i	0.994575	−	0.104020i	$-0.0331706\pi$
$464$	4403.06	+	7626.33i	0.440533	+	0.763025i
$465$	−174.176	+	301.681i	−0.0173703	+	0.0300863i
$466$	11999.6	+	6927.95i	1.19285	+	0.688693i
$467$	2664.19			0.263992			0.131996	−	0.991250i	$-0.457861\pi$
$467$	2664.19			0.263992			0.131996	+	0.991250i	$0.457861\pi$
$468$	2001.68	+	3226.11i	0.197709	+	0.318647i
$469$	382.114			0.0376213
$470$	5641.29	+	3257.00i	0.553646	+	0.319648i
$471$	2175.23	−	3767.61i	0.212801	−	0.368583i
$472$	1353.46	+	2344.26i	0.131987	+	0.228608i
$473$		−	4124.08i		−	0.400899i
$474$	9660.42	−	5577.45i	0.936114	−	0.540466i
$475$	10139.3	−	5853.92i	0.979415	−	0.565466i
$476$			1735.82i			0.167145i
$477$	3129.96	+	5421.24i	0.300442	+	0.520381i
$478$	−9765.92	+	16915.1i	−0.934483	+	1.61857i
$479$	4521.26	+	2610.35i	0.431277	+	0.248998i	0.699890	−	0.714250i	$-0.253232\pi$
$479$	4521.26	+	2610.35i	0.431277	+	0.248998i	−0.268614	+	0.963248i	$0.586566\pi$
$480$	2376.81			0.226013
$481$	−13046.5	+	8094.91i	−1.23674	+	0.767351i
$482$	19730.2			1.86449
$483$	−2066.09	−	1192.86i	−0.194639	−	0.112375i
$484$	1309.23	−	2267.65i	0.122955	−	0.212965i
$485$	−2675.64	−	4634.34i	−0.250504	−	0.433886i
$486$			1001.91i			0.0935139i
$487$	10586.8	−	6112.30i	0.985081	−	0.568737i	0.0812808	−	0.996691i	$-0.474099\pi$
$487$	10586.8	−	6112.30i	0.985081	−	0.568737i	0.903800	+	0.427954i	$0.140766\pi$
$488$	2504.16	−	1445.78i	0.232291	−	0.134113i
$489$		−	7027.08i		−	0.649848i
$490$	−1875.88	−	3249.13i	−0.172946	−	0.299552i
$491$	9826.61	−	17020.2i	0.903195	−	1.56438i	0.0798720	−	0.996805i	$-0.474549\pi$
$491$	9826.61	−	17020.2i	0.903195	−	1.56438i	0.823323	−	0.567574i	$-0.192118\pi$
$492$	1311.41	+	757.143i	0.120168	+	0.0693793i
$493$	4620.59			0.422111
$494$	−9236.04	+	17238.2i	−0.841193	+	1.57001i
$495$	−885.279			−0.0803845
$496$	1813.35	+	1046.94i	0.164157	+	0.0947760i
$497$	1033.32	−	1789.76i	0.0932608	−	0.161532i
$498$	−4249.45	−	7360.26i	−0.382374	−	0.662292i
$499$			11713.6i			1.05084i	0.850842	+	0.525422i	$0.176093\pi$
$499$			11713.6i			1.05084i	−0.850842	+	0.525422i	$0.823907\pi$
$500$	−5722.06	+	3303.63i	−0.511796	+	0.295486i
$501$	104.113	−	60.1096i	0.00928428	−	0.00536028i
$502$		−	13498.5i		−	1.20013i
$503$	−6501.67	−	11261.2i	−0.576332	−	0.998236i	−0.995896	−	0.0905104i	$-0.971150\pi$
$503$	−6501.67	−	11261.2i	−0.576332	−	0.998236i	0.419563	−	0.907726i	$-0.362183\pi$
$504$	−124.001	+	214.776i	−0.0109592	+	0.0189819i
$505$	−1692.73	−	977.300i	−0.149160	−	0.0861174i
$506$	15822.1			1.39008
$507$	−6577.73	+	418.008i	−0.576188	+	0.0366162i
$508$	−22456.4			−1.96130
$509$	−4614.99	−	2664.47i	−0.401878	−	0.232024i	0.285416	−	0.958404i	$-0.407868\pi$
$509$	−4614.99	−	2664.47i	−0.401878	−	0.232024i	−0.687294	+	0.726379i	$0.741202\pi$
$510$	544.376	−	942.886i	0.0472654	−	0.0818661i
$511$	1302.27	+	2255.59i	0.112738	+	0.195267i
$512$		−	16100.7i		−	1.38976i
$513$	−2366.18	+	1366.12i	−0.203644	+	0.117574i
$514$	−23373.2	+	13494.5i	−2.00574	+	1.15801i
$515$			2114.16i			0.180895i
$516$	1726.36	+	2990.14i	0.147284	+	0.255104i
$517$	−8352.47	+	14466.9i	−0.710524	+	1.23066i
$518$	−7817.06	−	4513.18i	−0.663054	−	0.382814i
$519$	5728.62			0.484506
$520$	278.381	−	519.573i	0.0234766	−	0.0438169i
$521$	−11700.3			−0.983876			−0.491938	−	0.870630i	$-0.663711\pi$
$521$	−11700.3			−0.983876			−0.491938	+	0.870630i	$0.663711\pi$
$522$	5145.41	+	2970.70i	0.431434	+	0.249088i
$523$	2267.52	−	3927.46i	0.189583	−	0.328367i	−0.755528	−	0.655116i	$-0.772620\pi$
$523$	2267.52	−	3927.46i	0.189583	−	0.328367i	0.945111	+	0.326749i	$0.105953\pi$
$524$	196.907	+	341.053i	0.0164159	+	0.0284332i
$525$			2319.70i			0.192838i
$526$	−314.942	+	181.832i	−0.0261067	+	0.0150727i
$527$	951.467	−	549.330i	0.0786462	−	0.0454064i
$528$			5321.24i			0.438594i
$529$	−995.810	−	1724.79i	−0.0818451	−	0.141760i
$530$	4373.49	−	7575.11i	0.358438	−	0.620834i
$531$	−5117.09	−	2954.35i	−0.418197	−	0.241446i
$532$	−6086.73			−0.496040
$533$	−2233.77	+	1385.97i	−0.181529	+	0.112632i
$534$	−13241.8			−1.07309
$535$	1071.56	+	618.667i	0.0865939	+	0.0499950i
$536$	117.869	−	204.156i	0.00949847	−	0.0164518i
$537$	764.938	+	1324.91i	0.0614702	+	0.106470i
$538$			18667.8i			1.49596i
$539$	8332.26	−	4810.63i	0.665855	−	0.384432i
$540$	641.867	−	370.582i	0.0511510	−	0.0295321i
$541$		−	5184.89i		−	0.412044i	−0.978547	−	0.206022i	$-0.933948\pi$
$541$		−	5184.89i		−	0.412044i	0.978547	−	0.206022i	$-0.0660519\pi$
$542$	−17155.9	−	29714.8i	−1.35961	−	2.35491i
$543$	3205.32	−	5551.78i	0.253321	−	0.438766i
$544$	−6491.88	−	3748.09i	−0.511649	−	0.295401i
$545$	−1462.55			−0.114952
$546$	−2042.88	−	3292.51i	−0.160123	−	0.258070i
$547$	5609.12			0.438443			0.219222	−	0.975675i	$-0.429648\pi$
$547$	5609.12			0.438443			0.219222	+	0.975675i	$0.429648\pi$
$548$	−1607.12	−	927.873i	−0.125279	−	0.0723299i
$549$	−3155.87	+	5466.13i	−0.245336	+	0.424934i
$550$	−7692.12	−	13323.2i	−0.596351	−	1.03291i
$551$			16202.3i			1.25271i
$552$	−1274.64	+	735.913i	−0.0982830	+	0.0567437i
$553$	−5219.61	+	3013.54i	−0.401375	+	0.231734i
$554$		−	11879.9i		−	0.911066i
$555$	1498.65	+	2595.74i	0.114620	+	0.198528i
$556$	−450.000	+	779.423i	−0.0343242	+	0.0594512i
$557$	17450.9	+	10075.3i	1.32750	+	0.766432i	0.984912	−	0.173055i	$-0.0553637\pi$
$557$	17450.9	+	10075.3i	1.32750	+	0.766432i	0.342586	+	0.939486i	$0.388697\pi$
$558$	1412.72			0.107178
$559$	−5990.93	+	190.167i	−0.453290	+	0.0143886i
$560$	−1121.14			−0.0846011
$561$	2418.00	+	1396.03i	0.181975	+	0.105063i
$562$	5809.44	−	10062.2i	0.436044	−	0.755250i
$563$	8146.10	+	14109.5i	0.609800	+	1.05620i	0.991273	+	0.131824i	$0.0420834\pi$
$563$	8146.10	+	14109.5i	0.609800	+	1.05620i	−0.381474	+	0.924380i	$0.624583\pi$
$564$		−	13985.5i		−	1.04414i
$565$	−4086.83	+	2359.53i	−0.304308	+	0.175692i
$566$	944.816	−	545.490i	0.0701654	−	0.0405100i
$567$		−	541.343i		−	0.0400957i
$568$	−637.486	−	1104.16i	−0.0470921	−	0.0815660i
$569$	5230.27	−	9059.09i	0.385350	−	0.667446i	−0.606468	−	0.795108i	$-0.707414\pi$
$569$	5230.27	−	9059.09i	0.385350	−	0.667446i	0.991818	+	0.127662i	$0.0407474\pi$
$570$	3306.27	+	1908.88i	0.242955	+	0.140270i
$571$	−2225.96			−0.163141			−0.0815705	−	0.996668i	$-0.525994\pi$
$571$	−2225.96			−0.163141			−0.0815705	+	0.996668i	$0.525994\pi$
$572$	11991.8	+	6425.09i	0.876580	+	0.469662i
$573$	−12173.2			−0.887511
$574$	−1338.40	−	772.726i	−0.0973236	−	0.0561898i
$575$	−6883.40	+	11922.4i	−0.499231	+	0.864693i
$576$	−2839.50	−	4918.16i	−0.205404	−	0.355770i
$577$		−	4686.23i		−	0.338112i	−0.985606	−	0.169056i	$-0.945928\pi$
$577$		−	4686.23i		−	0.338112i	0.985606	−	0.169056i	$-0.0540718\pi$
$578$	14569.2	−	8411.51i	1.04844	−	0.605316i
$579$	−2269.14	+	1310.09i	−0.162871	+	0.0940337i
$580$		−	4395.14i		−	0.314652i
$581$	2296.01	+	3976.81i	0.163949	+	0.283969i
$582$	−10850.9	+	18794.3i	−0.772824	+	1.33857i
$583$	19426.1	+	11215.7i	1.38001	+	0.796750i
$584$	1606.82			0.113854
$585$	40.8214	+	1286.02i	0.00288505	+	0.0908894i
$586$	17698.5			1.24764
$587$	10470.7	+	6045.28i	0.736241	+	0.425069i	0.820701	−	0.571358i	$-0.193583\pi$
$587$	10470.7	+	6045.28i	0.736241	+	0.425069i	−0.0844601	+	0.996427i	$0.526917\pi$
$588$	−4027.51	+	6975.86i	−0.282469	+	0.489251i
$589$	1926.25	+	3336.36i	0.134753	+	0.233400i
$590$			8256.25i			0.576109i
$591$	10774.9	−	6220.87i	0.749947	−	0.432982i
$592$	15602.5	−	9008.12i	1.08321	−	0.625391i
$593$			6135.97i			0.424914i	0.977170	+	0.212457i	$0.0681466\pi$
$593$			6135.97i			0.424914i	−0.977170	+	0.212457i	$0.931853\pi$
$594$	1795.09	+	3109.20i	0.123996	+	0.214767i
$595$	−294.131	+	509.449i	−0.0202658	+	0.0351015i
$596$	−2965.32	−	1712.03i	−0.203799	−	0.117663i
$597$	−7212.18			−0.494431
$598$	−729.579	−	22984.3i	−0.0498908	−	1.57174i
$599$	−6198.80			−0.422831			−0.211416	−	0.977396i	$-0.567807\pi$
$599$	−6198.80			−0.422831			−0.211416	+	0.977396i	$0.567807\pi$
$600$	1239.36	+	715.547i	0.0843281	+	0.0486868i
$601$	−9172.69	+	15887.6i	−0.622565	+	1.07831i	0.366441	+	0.930441i	$0.380576\pi$
$601$	−9172.69	+	15887.6i	−0.622565	+	1.07831i	−0.989006	+	0.147873i	$0.952757\pi$
$602$	−1761.89	−	3051.69i	−0.119285	−	0.206607i
$603$			514.575i			0.0347514i
$604$	11827.4	−	6828.53i	0.796770	−	0.460015i
$605$	768.497	−	443.692i	0.0516427	−	0.0298159i
$606$			7926.75i			0.531357i
$607$	−5194.06	−	8996.38i	−0.347315	−	0.601568i	0.638456	−	0.769658i	$-0.279573\pi$
$607$	−5194.06	−	8996.38i	−0.347315	−	0.601568i	−0.985772	+	0.168090i	$0.946240\pi$
$608$	13142.8	−	22764.1i	0.876665	−	1.51843i
$609$	−2780.11	−	1605.10i	−0.184985	−	0.106801i
$610$	8819.40			0.585389
$611$	21400.8	+	11466.3i	1.41699	+	0.759209i
$612$	−2337.54			−0.154395
$613$	−696.701	−	402.240i	−0.0459045	−	0.0265030i	0.476872	−	0.878973i	$-0.341770\pi$
$613$	−696.701	−	402.240i	−0.0459045	−	0.0265030i	−0.522777	+	0.852470i	$0.675104\pi$
$614$	−14485.0	+	25088.8i	−0.952064	+	1.64902i
$615$	256.592	+	444.431i	0.0168241	+	0.0291401i
$616$			888.671i			0.0581259i
$617$	−13179.4	+	7609.13i	−0.859940	+	0.496486i	−0.863992	−	0.503505i	$-0.832043\pi$
$617$	−13179.4	+	7609.13i	−0.859940	+	0.496486i	0.00405239	+	0.999992i	$0.498710\pi$
$618$	7425.15	−	4286.91i	0.483307	−	0.279037i
$619$		−	11462.5i		−	0.744291i	−0.928174	−	0.372145i	$-0.878622\pi$
$619$		−	11462.5i		−	0.744291i	0.928174	−	0.372145i	$-0.121378\pi$
$620$	−522.527	−	905.044i	−0.0338471	−	0.0586249i
$621$	1606.36	−	2782.31i	0.103802	−	0.179791i
$622$	4046.36	+	2336.17i	0.260843	+	0.150598i
$623$	7154.66			0.460105
$624$	7730.01	−	245.370i	0.495911	−	0.0157414i
$625$	12223.0			0.782270
$626$	−18874.6	−	10897.3i	−1.20508	−	0.695754i
$627$	−4895.25	+	8478.81i	−0.311798	+	0.540050i
$628$	6525.70	+	11302.8i	0.414656	+	0.718205i
$629$		−	9453.14i		−	0.599239i
$630$	−655.078	+	378.209i	−0.0414269	+	0.0239178i
$631$	−3869.99	+	2234.34i	−0.244155	+	0.140963i	−0.617085	−	0.786896i	$-0.711687\pi$
$631$	−3869.99	+	2234.34i	−0.244155	+	0.140963i	0.372930	+	0.927860i	$0.378353\pi$
$632$			3718.30i			0.234028i
$633$	5803.28	+	10051.6i	0.364391	+	0.631144i
$634$	−9858.67	+	17075.7i	−0.617568	+	1.06966i
$635$	−6590.77	−	3805.18i	−0.411885	−	0.237802i
$636$	−18779.7			−1.17086
$637$	−7372.48	−	11882.2i	−0.458569	−	0.739074i
$638$	21290.0			1.32113
$639$	2410.18	+	1391.52i	0.149210	+	0.0861465i
$640$	−798.558	+	1383.14i	−0.0493215	+	0.0854274i
$641$	3071.18	+	5319.44i	0.189242	+	0.327777i	0.944998	−	0.327077i	$-0.106064\pi$
$641$	3071.18	+	5319.44i	0.189242	+	0.327777i	−0.755756	+	0.654854i	$0.772730\pi$
$642$		−	5017.93i		−	0.308477i
$643$	−17959.8	+	10369.1i	−1.10150	+	0.635951i	−0.936615	−	0.350361i	$-0.886059\pi$
$643$	−17959.8	+	10369.1i	−1.10150	+	0.635951i	−0.164886	+	0.986313i	$0.552726\pi$
$644$	6198.27	−	3578.58i	0.379264	−	0.218968i
$645$			1170.11i			0.0714312i
$646$	−6020.37	−	10427.6i	−0.366669	−	0.635090i
$647$	426.379	−	738.509i	0.0259083	−	0.0448745i	−0.852781	−	0.522269i	$-0.825086\pi$
$647$	426.379	−	738.509i	0.0259083	−	0.0448745i	0.878689	+	0.477395i	$0.158419\pi$
$648$	−289.228	−	166.986i	−0.0175339	−	0.0101232i
$649$	−21172.8			−1.28060
$650$	−18999.5	+	11788.5i	−1.14649	+	0.711357i
$651$	−763.303			−0.0459542
$652$	18256.9	+	10540.6i	1.09662	+	0.633133i
$653$	3672.88	−	6361.61i	0.220108	−	0.381239i	−0.734732	−	0.678357i	$-0.762692\pi$
$653$	3672.88	−	6361.61i	0.220108	−	0.381239i	0.954841	+	0.297118i	$0.0960256\pi$
$654$	2965.64	+	5136.64i	0.177318	+	0.307123i
$655$			133.462i			0.00796151i
$656$	2671.39	−	1542.33i	0.158994	−	0.0917954i
$657$	−3037.50	+	1753.70i	−0.180372	+	0.104138i
$658$			14273.4i			0.845645i
$659$	−6270.33	−	10860.5i	−0.370648	−	0.641982i	0.619017	−	0.785378i	$-0.287531\pi$
$659$	−6270.33	−	10860.5i	−0.370648	−	0.641982i	−0.989665	+	0.143396i	$0.954198\pi$
$660$	1327.92	−	2300.02i	0.0783169	−	0.135649i
$661$	1942.45	+	1121.48i	0.114301	+	0.0659915i	0.556060	−	0.831142i	$-0.312312\pi$
$661$	1942.45	+	1121.48i	0.114301	+	0.0659915i	−0.441760	+	0.897133i	$0.645646\pi$
$662$	−35747.3			−2.09873
$663$	1916.48	−	3576.93i	0.112262	−	0.209527i
$664$	2832.97			0.165573
$665$	−1786.41	−	1031.38i	−0.104171	−	0.0601433i
$666$	6077.69	−	10526.9i	0.353612	−	0.612474i
$667$	−9525.83	−	16499.2i	−0.552986	−	0.957800i
$668$			360.658i			0.0208896i
$669$	7309.83	−	4220.33i	0.422443	−	0.243897i
$670$	622.687	−	359.508i	0.0359052	−	0.0207299i
$671$			22617.0i			1.30122i
$672$	2604.01	+	4510.29i	0.149482	+	0.258911i
$673$	−2388.23	+	4136.53i	−0.136790	+	0.236927i	−0.926280	−	0.376837i	$-0.877012\pi$
$673$	−2388.23	+	4136.53i	−0.136790	+	0.236927i	0.789490	+	0.613763i	$0.210345\pi$
$674$	−30446.0	−	17578.0i	−1.73997	−	1.00457i
$675$	−3123.82			−0.178127
$676$	8780.58	−	17716.5i	0.499578	−	1.00799i
$677$	−7933.57			−0.450387			−0.225193	−	0.974314i	$-0.572301\pi$
$677$	−7933.57			−0.450387			−0.225193	+	0.974314i	$0.572301\pi$
$678$	16573.9	+	9568.93i	0.938814	+	0.542024i
$679$	5862.82	−	10154.7i	0.331361	−	0.573935i
$680$	181.459	+	314.295i	0.0102333	+	0.0177245i
$681$		−	13555.1i		−	0.762750i
$682$	4384.02	−	2531.12i	0.246148	−	0.142114i
$683$	20415.5	−	11786.9i	1.14374	−	0.660340i	0.196388	−	0.980526i	$-0.437079\pi$
$683$	20415.5	−	11786.9i	1.14374	−	0.660340i	0.947355	+	0.320186i	$0.103745\pi$
$684$		−	8196.70i		−	0.458200i
$685$	−314.452	−	544.647i	−0.0175396	−	0.0303794i
$686$	8836.21	−	15304.8i	0.491790	−	0.851806i
$687$	−3391.19	−	1957.90i	−0.188329	−	0.108732i
$688$	7033.32			0.389743
$689$	15396.9	−	28736.9i	0.851343	−	1.58895i
$690$	−4489.15			−0.247680
$691$	−10863.2	−	6271.89i	−0.598056	−	0.345288i	0.170221	−	0.985406i	$-0.445552\pi$
$691$	−10863.2	−	6271.89i	−0.598056	−	0.345288i	−0.768276	+	0.640118i	$0.778885\pi$
$692$	−8592.93	+	14883.4i	−0.472044	+	0.817604i
$693$	−969.904	−	1679.92i	−0.0531654	−	0.0920852i
$694$			51874.8i			2.83738i
$695$	−264.143	+	152.503i	−0.0144166	+	0.00832340i
$696$	−1715.14	+	990.234i	−0.0934082	+	0.0539292i
$697$		−	1618.52i		−	0.0879568i
$698$	18473.9	+	31997.8i	1.00179	+	1.73515i
$699$	5040.82	−	8730.96i	0.272763	−	0.472440i
$700$	−6026.75	−	3479.54i	−0.325414	−	0.187878i
$701$	581.786			0.0313463			0.0156731	−	0.999877i	$-0.495011\pi$
$701$	581.786			0.0313463			0.0156731	+	0.999877i	$0.495011\pi$
$702$	4433.86	−	2751.05i	0.238384	−	0.147908i
$703$	33147.9			1.77837
$704$	−17623.4	−	10174.9i	−0.943475	−	0.544715i
$705$	2369.82	−	4104.64i	0.126599	−	0.219276i
$706$	−11045.8	−	19131.9i	−0.588830	−	1.01988i
$707$		−	4282.89i		−	0.227828i
$708$	15351.3	−	8863.06i	0.814882	−	0.470472i
$709$	−17963.1	+	10371.0i	−0.951507	+	0.549353i	−0.893549	−	0.448966i	$-0.851792\pi$
$709$	−17963.1	+	10371.0i	−0.951507	+	0.549353i	−0.0579583	+	0.998319i	$0.518459\pi$
$710$		−	3888.74i		−	0.205552i
$711$	−4058.19	−	7028.99i	−0.214056	−	0.370756i
$712$	2206.97	−	3822.58i	0.116165	−	0.201204i
$713$	−3923.10	−	2265.00i	−0.206061	−	0.118969i
$714$	2385.66			0.125043
$715$	2430.79	+	3917.70i	0.127142	+	0.204914i
$716$	−4589.63			−0.239556
$717$	12307.5	+	7105.75i	0.641050	+	0.370110i
$718$	5577.32	−	9660.21i	0.289894	−	0.502111i
$719$	12675.1	+	21953.9i	0.657443	+	1.13872i	0.981275	+	0.192610i	$0.0616953\pi$
$719$	12675.1	+	21953.9i	0.657443	+	1.13872i	−0.323832	+	0.946114i	$0.604971\pi$
$720$		−	1509.78i		−	0.0781474i
$721$	−4011.87	+	2316.25i	−0.207226	+	0.119642i
$722$	12073.3	−	6970.50i	0.622328	−	0.359301i
$723$		−	14355.8i		−	0.738449i
$724$	9615.97	+	16655.3i	0.493611	+	0.854960i
$725$	−9262.22	+	16042.6i	−0.474469	+	0.821805i
$726$	−3116.59	−	1799.36i	−0.159322	−	0.0919844i
$727$	−33428.2			−1.70534			−0.852672	−	0.522447i	$-0.825019\pi$
$727$	−33428.2			−1.70534			−0.852672	+	0.522447i	$0.825019\pi$
$728$	1290.95	−	40.9778i	0.0657220	−	0.00208618i
$729$	729.000			0.0370370
$730$	4244.30	+	2450.45i	0.215190	+	0.124240i
$731$	1845.20	−	3195.97i	0.0933612	−	0.161706i
$732$	−9467.61	−	16398.4i	−0.478050	−	0.828007i
$733$			3842.67i			0.193632i	0.995302	+	0.0968160i	$0.0308658\pi$
$733$			3842.67i			0.193632i	−0.995302	+	0.0968160i	$0.969134\pi$
$734$	−37398.8	+	21592.2i	−1.88067	+	1.08581i
$735$	−2364.09	+	1364.91i	−0.118640	+	0.0684970i
$736$			30908.3i			1.54796i
$737$	921.946	+	1596.86i	0.0460791	+	0.0798114i
$738$	1040.59	−	1802.36i	0.0519035	−	0.0898994i
$739$	−25140.4	−	14514.8i	−1.25143	−	0.722511i	−0.280034	−	0.959990i	$-0.590346\pi$
$739$	−25140.4	−	14514.8i	−1.25143	−	0.722511i	−0.971393	+	0.237479i	$0.923679\pi$
$740$	−8991.91			−0.446688
$741$	12542.7	+	6720.21i	0.621816	+	0.333162i
$742$	19166.3			0.948269
$743$	−30308.0	−	17498.3i	−1.49649	−	0.864000i	−0.496500	−	0.868037i	$-0.665382\pi$
$743$	−30308.0	−	17498.3i	−1.49649	−	0.864000i	−0.999992	+	0.00403656i	$0.998715\pi$
$744$	−235.453	+	407.816i	−0.0116023	+	0.0200958i
$745$	−580.199	−	1004.93i	−0.0285327	−	0.0494200i
$746$			52623.2i			2.58267i
$747$	−5355.38	+	3091.93i	−0.262307	+	0.151443i
$748$	−7253.99	+	4188.10i	−0.354589	+	0.204722i
$749$			2711.23i			0.132265i
$750$	4540.41	+	7864.22i	0.221056	+	0.382881i
$751$	5227.06	−	9053.52i	0.253979	−	0.439904i	−0.710639	−	0.703557i	$-0.751594\pi$
$751$	5227.06	−	9053.52i	0.253979	−	0.439904i	0.964618	+	0.263653i	$0.0849274\pi$
$752$	−24672.3	−	14244.5i	−1.19642	−	0.690751i
$753$	−9821.58			−0.475323
$754$	−981.712	−	30927.4i	−0.0474162	−	1.49378i
$755$	4628.32			0.223102
$756$	1406.45	+	812.014i	0.0676615	+	0.0390644i
$757$	14065.2	−	24361.6i	0.675308	−	1.16967i	−0.301071	−	0.953602i	$-0.597344\pi$
$757$	14065.2	−	24361.6i	0.675308	−	1.16967i	0.976379	−	0.216065i	$-0.0693225\pi$
$758$	−4778.73	−	8277.00i	−0.228986	−	0.396615i
$759$		−	11512.3i		−	0.550552i
$760$	−1102.09	+	636.292i	−0.0526014	+	0.0303694i
$761$	18261.9	−	10543.5i	0.869899	−	0.502236i	0.00258400	−	0.999997i	$-0.499177\pi$
$761$	18261.9	−	10543.5i	0.869899	−	0.502236i	0.867315	+	0.497761i	$0.165844\pi$
$762$			30863.4i			1.46727i
$763$	−1602.36	−	2775.37i	−0.0760280	−	0.131684i
$764$	18259.8	−	31627.0i	0.864683	−	1.49768i
$765$	−686.051	−	396.092i	−0.0324238	−	0.0187199i
$766$	−8177.54			−0.385727
$767$	976.309	+	30757.2i	0.0459615	+	1.44795i
$768$	−8667.00			−0.407218
$769$	16911.7	+	9763.96i	0.793044	+	0.457864i	0.841033	−	0.540984i	$-0.181948\pi$
$769$	16911.7	+	9763.96i	0.793044	+	0.457864i	−0.0479893	+	0.998848i	$0.515281\pi$
$770$	−1355.25	+	2347.36i	−0.0634283	+	0.109861i
$771$	9818.72	+	17006.5i	0.458641	+	0.794390i
$772$		−	7860.55i		−	0.366460i
$773$	25419.6	−	14676.0i	1.18277	−	0.682870i	0.226113	−	0.974101i	$-0.427398\pi$
$773$	25419.6	−	14676.0i	1.18277	−	0.682870i	0.956653	+	0.291231i	$0.0940648\pi$
$774$	4109.56	−	2372.66i	0.190846	−	0.110185i
$775$			4404.64i			0.204154i
$776$	−3616.96	−	6264.76i	−0.167321	−	0.289809i
$777$	−3283.82	+	5687.75i	−0.151617	+	0.262609i
$778$	11585.2	+	6688.73i	0.533869	+	0.308229i
$779$	5675.42			0.261031
$780$	−3402.41	−	1822.97i	−0.156187	−	0.0836831i
$781$	9972.54			0.456908
$782$	12261.4	+	7079.13i	0.560700	+	0.323720i
$783$	2161.50	−	3743.84i	0.0986537	−	0.170873i
$784$	8204.19	+	14210.1i	0.373733	+	0.647325i
$785$			4423.06i			0.201103i
$786$	468.733	−	270.623i	0.0212712	−	0.0122809i
$787$	3865.18	−	2231.56i	0.175068	−	0.101076i	−0.409905	−	0.912128i	$-0.634438\pi$
$787$	3865.18	−	2231.56i	0.175068	−	0.101076i	0.584974	+	0.811052i	$0.301105\pi$
$788$			37325.2i			1.68738i
$789$	132.302	+	229.154i	0.00596968	+	0.0103398i
$790$	−5670.52	+	9821.62i	−0.255377	+	0.442326i
$791$	−8955.00	−	5170.17i	−0.402532	−	0.232402i
$792$	−1196.73			−0.0536919
$793$	32855.1	−	1042.90i	1.47127	−	0.0467018i
$794$	15501.7			0.692866
$795$	−5511.70	−	3182.18i	−0.245887	−	0.141963i
$796$	10818.3	−	18737.8i	0.481713	−	0.834352i
$797$	−17392.7	−	30125.1i	−0.773002	−	1.33888i	−0.935911	−	0.352237i	$-0.885421\pi$
$797$	−17392.7	−	30125.1i	−0.773002	−	1.33888i	0.162909	−	0.986641i	$-0.447912\pi$
$798$			8365.40i			0.371093i
$799$	−12945.6	+	7474.12i	−0.573193	+	0.330933i
$800$	26026.6	−	15026.5i	1.15023	−	0.664083i
$801$			9634.84i			0.425007i
$802$	4118.05	+	7132.66i	0.181313	+	0.314044i
$803$	−6284.09	+	10884.4i	−0.276165	+	0.478332i
$804$	−1336.91	−	771.862i	−0.0586430	−	0.0338576i
$805$	2425.53			0.106197
$806$	−3879.03	−	6251.82i	−0.169520	−	0.273215i
$807$	13582.8			0.592487
$808$	−2288.26	−	1321.13i	−0.0996294	−	0.0575211i
$809$	5309.98	−	9197.15i	0.230765	−	0.399697i	−0.727268	−	0.686353i	$-0.759210\pi$
$809$	5309.98	−	9197.15i	0.230765	−	0.399697i	0.958033	+	0.286656i	$0.0925438\pi$
$810$	−509.316	−	882.162i	−0.0220933	−	0.0382667i
$811$		−	5497.87i		−	0.238047i	−0.992891	−	0.119024i	$-0.962024\pi$
$811$		−	5497.87i		−	0.238047i	0.992891	−	0.119024i	$-0.0379764\pi$
$812$	8340.32	−	4815.29i	0.360453	−	0.208108i
$813$	−21620.7	+	12482.7i	−0.932684	+	0.538485i
$814$		−	43556.7i		−	1.87551i
$815$	3572.17	+	6187.18i	0.153531	+	0.265923i
$816$	−2380.83	+	4123.72i	−0.102139	+	0.176911i
$817$	11206.8	+	6470.26i	0.479898	+	0.277070i
$818$	21420.5			0.915587
$819$	−2395.65	+	1486.42i	−0.102211	+	0.0634182i
$820$	−1539.55			−0.0655653
$821$	18451.0	+	10652.7i	0.784340	+	0.452839i	0.837966	−	0.545722i	$-0.183745\pi$
$821$	18451.0	+	10652.7i	0.784340	+	0.452839i	−0.0536261	+	0.998561i	$0.517078\pi$
$822$	−1275.24	+	2208.78i	−0.0541108	+	0.0937227i
$823$	8671.28	+	15019.1i	0.367268	+	0.636127i	0.989137	−	0.146994i	$-0.0469597\pi$
$823$	8671.28	+	15019.1i	0.367268	+	0.636127i	−0.621869	+	0.783121i	$0.713626\pi$
$824$			2857.94i			0.120827i
$825$	−9694.02	+	5596.84i	−0.409094	+	0.236190i
$826$	−15667.2	+	9045.48i	−0.659967	+	0.381032i
$827$			5129.96i			0.215703i	0.994167	+	0.107851i	$0.0343971\pi$
$827$			5129.96i			0.215703i	−0.994167	+	0.107851i	$0.965603\pi$
$828$	4819.09	+	8346.92i	0.202265	+	0.350333i
$829$	−4235.90	+	7336.80i	−0.177466	+	0.307380i	−0.941012	−	0.338374i	$-0.890123\pi$
$829$	−4235.90	+	7336.80i	−0.177466	+	0.307380i	0.763546	+	0.645753i	$0.223457\pi$
$830$	7483.08	+	4320.36i	0.312942	+	0.180677i
$831$	−8643.93			−0.360836
$832$	−13968.1	+	26070.1i	−0.582039	+	1.08632i
$833$	8609.50			0.358105
$834$	1071.21	+	618.466i	0.0444762	+	0.0256783i
$835$	−61.1126	+	105.850i	−0.00253280	+	0.00438694i
$836$	−14685.7	−	25436.4i	−0.607556	−	1.05232i
$837$		−	1027.90i		−	0.0424486i
$838$	24359.8	−	14064.1i	1.00417	−	0.579758i
$839$	−16588.8	+	9577.52i	−0.682607	+	0.394103i	−0.800837	−	0.598883i	$-0.795611\pi$
$839$	−16588.8	+	9577.52i	−0.682607	+	0.394103i	0.118230	+	0.992986i	$0.462278\pi$
$840$		−	252.140i		−	0.0103567i
$841$	−623.334	−	1079.65i	−0.0255580	−	0.0442678i
$842$	15539.4	−	26915.0i	0.636012	−	1.10160i
$843$	−7321.36	−	4226.99i	−0.299123	−	0.172699i
$844$	−34819.7			−1.42007
$845$	5579.04	−	3711.79i	0.227130	−	0.151112i
$846$	−19221.3			−0.781136
$847$	1683.92	+	972.211i	0.0683119	+	0.0394399i
$848$	−19127.5	+	33129.8i	−0.774577	+	1.34161i
$849$	−396.902	−	687.455i	−0.0160443	−	0.0277896i
$850$		−	13766.4i		−	0.555512i
$851$	−33755.3	+	19488.7i	−1.35972	+	0.785032i
$852$	−7230.54	+	4174.56i	−0.290744	+	0.167861i
$853$		−	18075.1i		−	0.725532i	−0.931880	−	0.362766i	$-0.881832\pi$
$853$		−	18075.1i		−	0.725532i	0.931880	−	0.362766i	$-0.118168\pi$
$854$	9662.47	+	16735.9i	0.387170	+	0.670598i
$855$	1388.91	−	2405.67i	0.0555553	−	0.0962246i
$856$	1448.55	+	836.322i	0.0578394	+	0.0333936i
$857$	21054.6			0.839219			0.419609	−	0.907705i	$-0.362167\pi$
$857$	21054.6			0.839219			0.419609	+	0.907705i	$0.362167\pi$
$858$	8830.44	−	16481.2i	0.351359	−	0.655780i
$859$	920.322			0.0365553			0.0182776	−	0.999833i	$-0.494182\pi$
$859$	920.322			0.0365553			0.0182776	+	0.999833i	$0.494182\pi$
$860$	−3040.04	−	1755.17i	−0.120540	−	0.0695938i
$861$	−562.241	+	973.830i	−0.0222545	+	0.0385459i
$862$	−27633.5	−	47862.6i	−1.09188	−	1.89119i
$863$			19427.5i			0.766304i	0.923685	+	0.383152i	$0.125161\pi$
$863$			19427.5i			0.766304i	−0.923685	+	0.383152i	$0.874839\pi$
$864$	−6073.78	+	3506.70i	−0.239160	+	0.138079i
$865$	−5043.91	+	2912.10i	−0.198264	+	0.114468i
$866$		−	73044.7i		−	2.86623i
$867$	−6120.27	−	10600.6i	−0.239741	−	0.415244i
$868$	1144.95	−	1983.12i	0.0447722	−	0.0775477i
$869$	−25187.2	−	14541.8i	−0.983218	−	0.567661i
$870$	−6040.55			−0.235395
$871$	2277.19	−	1412.92i	0.0885876	−	0.0549654i
$872$	−1977.09			−0.0767808
$873$	13674.8	+	7895.17i	0.530153	+	0.306084i
$874$	−24823.3	+	42995.2i	−0.960709	+	1.66400i
$875$	−2453.22	−	4249.10i	−0.0947816	−	0.164167i
$876$		−	10522.2i		−	0.405836i
$877$	−12879.7	+	7436.09i	−0.495914	+	0.286316i	−0.727024	−	0.686612i	$-0.759097\pi$
$877$	−12879.7	+	7436.09i	−0.495914	+	0.286316i	0.231111	+	0.972927i	$0.425764\pi$
$878$	25578.7	−	14767.9i	0.983188	−	0.567644i
$879$		−	12877.6i		−	0.494141i
$880$	−2705.02	−	4685.23i	−0.103621	−	0.179476i
$881$	−6470.30	+	11206.9i	−0.247435	+	0.428570i	−0.962813	−	0.270167i	$-0.912921\pi$
$881$	−6470.30	+	11206.9i	−0.247435	+	0.428570i	0.715379	+	0.698737i	$0.246254\pi$
$882$	9587.40	+	5535.29i	0.366014	+	0.211318i
$883$	25585.5			0.975108			0.487554	−	0.873093i	$-0.337889\pi$
$883$	25585.5			0.975108			0.487554	+	0.873093i	$0.337889\pi$
$884$	6418.41	+	10344.5i	0.244202	+	0.393580i
$885$	6007.30			0.228173
$886$	−36311.4	−	20964.4i	−1.37687	−	0.794935i
$887$	−1858.23	+	3218.55i	−0.0703418	+	0.121836i	−0.899051	−	0.437844i	$-0.855742\pi$
$887$	−1858.23	+	3218.55i	−0.0703418	+	0.121836i	0.828709	+	0.559679i	$0.189076\pi$
$888$	2025.90	+	3508.95i	0.0765592	+	0.132604i
$889$		−	16675.7i		−	0.629118i
$890$	11659.1	−	6731.39i	0.439117	−	0.253524i
$891$	2262.27	−	1306.12i	0.0850606	−	0.0491097i
$892$			25322.0i			0.950496i
$893$	−26208.3	−	45394.2i	−0.982115	−	1.70107i
$894$	−2352.96	+	4075.44i	−0.0880254	+	0.152464i
$895$	−1347.02	−	777.702i	−0.0503082	−	0.0290455i
$896$	−3499.58			−0.130483
$897$	−16723.5	+	530.846i	−0.622500	+	0.0197597i
$898$	−70680.3			−2.62654
$899$	−5278.87	−	3047.76i	−0.195840	−	0.113068i
$900$	4685.73	−	8115.93i	0.173546	−	0.300590i
$901$	10036.2	+	17383.3i	0.371093	+	0.642753i
$902$		−	7457.57i		−	0.275288i
$903$	−2220.43	+	1281.97i	−0.0818286	+	0.0472438i
$904$	−5524.62	+	3189.64i	−0.203259	+	0.117352i
$905$			6517.61i			0.239395i
$906$	−9384.92	−	16255.2i	−0.344143	−	0.596072i
$907$	−6480.21	+	11224.0i	−0.237235	+	0.410902i	−0.959920	−	0.280275i	$-0.909574\pi$
$907$	−6480.21	+	11224.0i	−0.237235	+	0.410902i	0.722685	+	0.691177i	$0.242908\pi$
$908$	35217.2	+	20332.7i	1.28714	+	0.743131i
$909$	5767.56			0.210449
$910$	3472.43	+	1860.49i	0.126495	+	0.0677743i
$911$	−36607.1			−1.33134			−0.665668	−	0.746248i	$-0.731853\pi$
$911$	−36607.1			−1.33134			−0.665668	+	0.746248i	$0.731853\pi$
$912$	−14460.0	−	8348.49i	−0.525021	−	0.303121i
$913$	−11079.4	+	19190.1i	−0.401615	+	0.695618i
$914$	29049.6	+	50315.5i	1.05129	+	1.82088i
$915$		−	6417.06i		−	0.231849i
$916$	10173.6	−	5873.71i	0.366969	−	0.211870i
$917$	−253.260	+	146.220i	−0.00912038	+	0.00526565i
$918$			3212.65i			0.115505i
$919$	−10178.1	−	17629.0i	−0.365338	−	0.632784i	0.623492	−	0.781830i	$-0.285713\pi$
$919$	−10178.1	−	17629.0i	−0.365338	−	0.632784i	−0.988830	+	0.149045i	$0.952380\pi$
$920$	748.192	−	1295.91i	0.0268121	−	0.0464400i
$921$	18254.8	+	10539.4i	0.653110	+	0.377073i
$922$	12048.6			0.430370
$923$	−459.847	−	14486.8i	−0.0163988	−	0.516619i
$924$	5819.43			0.207192
$925$	32821.2	+	18949.3i	1.16665	+	0.673568i
$926$	4272.80	−	7400.71i	0.151634	−	0.262638i
$927$	−3119.19	−	5402.59i	−0.110515	−	0.191418i
$928$			41589.8i			1.47118i
$929$	39031.5	−	22534.8i	1.37845	−	0.795849i	0.386478	−	0.922298i	$-0.373691\pi$
$929$	39031.5	−	22534.8i	1.37845	−	0.795849i	0.991973	+	0.126449i	$0.0403580\pi$
$930$	−1243.86	+	718.145i	−0.0438580	+	0.0253214i
$931$			30189.6i			1.06275i
$932$	15122.5	+	26192.9i	0.531495	+	0.920576i
$933$	1699.81	−	2944.16i	0.0596456	−	0.103309i
$934$	9513.07	+	5492.37i	0.333273	+	0.192415i
$935$	−2838.65			−0.0992876
$936$	55.1828	+	1738.45i	0.00192704	+	0.0607085i
$937$	−6771.10			−0.236075			−0.118037	−	0.993009i	$-0.537660\pi$
$937$	−6771.10			−0.236075			−0.118037	+	0.993009i	$0.537660\pi$
$938$	1364.42	+	787.749i	0.0474946	+	0.0274210i
$939$	−7928.92	+	13733.3i	−0.275560	+	0.477283i
$940$	7109.45	+	12313.9i	0.246686	+	0.427273i
$941$		−	36690.7i		−	1.27108i	−0.772070	−	0.635538i	$-0.780778\pi$
$941$		−	36690.7i		−	1.27108i	0.772070	−	0.635538i	$-0.219222\pi$
$942$	15534.3	−	8968.72i	0.537297	−	0.310209i
$943$	−5779.43	+	3336.76i	−0.199580	+	0.115228i
$944$		−	36108.8i		−	1.24496i
$945$	275.188	+	476.639i	0.00947287	+	0.0164075i
$946$	8502.01	−	14725.9i	0.292203	−	0.506111i
$947$	44047.1	+	25430.6i	1.51145	+	0.872634i	0.999911	+	0.0133718i	$0.00425649\pi$
$947$	44047.1	+	25430.6i	1.51145	+	0.872634i	0.511536	+	0.859262i	$0.329077\pi$
$948$	24349.1			0.834202
$949$	16101.2	+	8626.82i	0.550754	+	0.295088i
$950$	48272.6			1.64860
$951$	12424.4	+	7173.24i	0.423648	+	0.244593i
$952$	−397.609	+	688.679i	−0.0135363	+	0.0234456i
$953$	5927.79	+	10267.2i	0.201490	+	0.348991i	0.949009	−	0.315250i	$-0.102088\pi$
$953$	5927.79	+	10267.2i	0.201490	+	0.348991i	−0.747519	+	0.664241i	$0.768755\pi$
$954$			25810.3i			0.875931i
$955$	10718.2	−	6188.18i	0.363177	−	0.209680i
$956$	−36922.6	+	21317.3i	−1.24912	+	0.721181i
$957$		−	15490.8i		−	0.523245i
$958$	10762.7	+	18641.6i	0.362973	+	0.628688i
$959$	689.022	−	1193.42i	0.0232009	−	0.0401852i
$960$	5000.22	+	2886.88i	0.168106	+	0.0970559i
$961$	28341.6			0.951349
$962$	−63273.5	+	2008.46i	−2.12060	+	0.0673132i
$963$	−3651.08			−0.122175
$964$	37297.5	+	21533.7i	1.24613	+	0.719455i
$965$	1331.95	−	2307.01i	0.0444322	−	0.0769588i
$966$	−4918.28	−	8518.71i	−0.163813	−	0.283732i
$967$		−	40661.7i		−	1.35221i	−0.736803	−	0.676107i	$-0.763666\pi$
$967$		−	40661.7i		−	1.35221i	0.736803	−	0.676107i	$-0.236334\pi$
$968$	1038.86	−	599.788i	0.0344942	−	0.0199152i
$969$	−7587.19	+	4380.46i	−0.251533	+	0.145223i
$970$		−	22063.9i		−	0.730339i
$971$	−28659.1	−	49639.1i	−0.947184	−	1.64057i	−0.751318	−	0.659940i	$-0.770582\pi$
$971$	−28659.1	−	49639.1i	−0.947184	−	1.64057i	−0.195866	−	0.980631i	$-0.562752\pi$
$972$	−1093.50	+	1894.00i	−0.0360844	+	0.0625000i
$973$	−578.786	−	334.162i	−0.0190699	−	0.0110100i
$974$	50403.3			1.65814
$975$	8577.37	+	13824.1i	0.281739	+	0.454079i
$976$	−38571.7			−1.26501
$977$	−2621.23	−	1513.37i	−0.0858347	−	0.0495567i	0.456468	−	0.889740i	$-0.349114\pi$
$977$	−2621.23	−	1513.37i	−0.0858347	−	0.0495567i	−0.542303	+	0.840183i	$0.682448\pi$
$978$	14486.7	−	25091.7i	0.473654	−	0.820393i
$979$	17262.4	+	29899.4i	0.563543	+	0.976085i
$980$		−	8189.43i		−	0.266941i
$981$	3737.46	−	2157.82i	0.121639	−	0.0702283i
$982$	70176.0	−	40516.1i	2.28045	−	1.31662i
$983$			33942.5i			1.10132i	0.834730	+	0.550659i	$0.185624\pi$
$983$			33942.5i			1.10132i	−0.834730	+	0.550659i	$0.814376\pi$
$984$	346.864	+	600.787i	0.0112374	+	0.0194638i
$985$	−6324.67	+	10954.7i	−0.204590	+	0.354360i
$986$	16498.8	+	9525.58i	0.532889	+	0.307664i
$987$	10385.4			0.334925
$988$	−36273.6	+	22506.4i	−1.16803	+	0.724722i
$989$	−15216.3			−0.489231
$990$	−3161.08	−	1825.05i	−0.101480	−	0.0585897i
$991$	−10818.7	+	18738.6i	−0.346790	+	0.600658i	−0.985677	−	0.168642i	$-0.946062\pi$
$991$	−10818.7	+	18738.6i	−0.346790	+	0.600658i	0.638887	+	0.769300i	$0.279395\pi$
$992$	4944.51	+	8564.14i	0.158254	+	0.274105i
$993$			26009.9i			0.831219i
$994$	7379.36	−	4260.48i	0.235472	−	0.135950i
$995$	6350.16	−	3666.26i	0.202325	−	0.116812i
$996$		−	18551.6i		−	0.590190i
$997$	−9812.31	−	16995.4i	−0.311694	−	0.539870i	0.667035	−	0.745026i	$-0.267563\pi$
$997$	−9812.31	−	16995.4i	−0.311694	−	0.539870i	−0.978729	+	0.205156i	$0.934230\pi$
$998$	−24148.1	+	41825.8i	−0.765928	+	1.32663i
$999$	−7659.42	−	4422.17i	−0.242576	−	0.140051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.j.b.4.2	✓	4
3.2	odd	2		117.4.q.d.82.1		4
4.3	odd	2		624.4.bv.c.433.2		4
13.4	even	6		507.4.b.e.337.4		4
13.6	odd	12		507.4.a.k.1.1		4
13.7	odd	12		507.4.a.k.1.4		4
13.9	even	3		507.4.b.e.337.1		4
13.10	even	6	inner	39.4.j.b.10.2	yes	4
39.20	even	12		1521.4.a.z.1.1		4
39.23	odd	6		117.4.q.d.10.1		4
39.32	even	12		1521.4.a.z.1.4		4
52.23	odd	6		624.4.bv.c.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.b.4.2	✓	4	1.1	even	1	trivial
39.4.j.b.10.2	yes	4	13.10	even	6	inner
117.4.q.d.10.1		4	39.23	odd	6
117.4.q.d.82.1		4	3.2	odd	2
507.4.a.k.1.1		4	13.6	odd	12
507.4.a.k.1.4		4	13.7	odd	12
507.4.b.e.337.1		4	13.9	even	3
507.4.b.e.337.4		4	13.4	even	6
624.4.bv.c.49.1		4	52.23	odd	6
624.4.bv.c.433.2		4	4.3	odd	2
1521.4.a.z.1.1		4	39.20	even	12
1521.4.a.z.1.4		4	39.32	even	12

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:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	39.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.57071 + 2.06155i) q^{2} +(1.50000 - 2.59808i) q^{3} +(4.50000 + 7.79423i) q^{4} +3.05006i q^{5} +(10.7121 - 6.18466i) q^{6} +(-5.78786 + 3.34162i) q^{7} +4.12311i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(3.57071 + 2.06155i) q^{2} +(1.50000 - 2.59808i) q^{3} +(4.50000 + 7.79423i) q^{4} +3.05006i q^{5} +(10.7121 - 6.18466i) q^{6} +(-5.78786 + 3.34162i) q^{7} +4.12311i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-6.28786 + 10.8909i) q^{10} +(-27.9293 - 16.1250i) q^{11} +27.0000 q^{12} +(-22.1364 + 41.3156i) q^{13} -27.5557 q^{14} +(7.92429 + 4.57509i) q^{15} +(27.5000 - 47.6314i) q^{16} +(-14.4293 - 24.9923i) q^{17} -37.1080i q^{18} +(87.6364 - 50.5969i) q^{19} +(-23.7729 + 13.7253i) q^{20} +20.0497i q^{21} +(-66.4850 - 115.155i) q^{22} +(-59.4950 + 103.048i) q^{23} +(10.7121 + 6.18466i) q^{24} +115.697 q^{25} +(-164.217 + 101.891i) q^{26} -27.0000 q^{27} +(-52.0907 - 30.0746i) q^{28} +(-80.0557 + 138.661i) q^{29} +(18.8636 + 32.6727i) q^{30} +38.0705i q^{31} +(224.955 - 129.878i) q^{32} +(-83.7879 + 48.3749i) q^{33} -118.987i q^{34} +(-10.1921 - 17.6533i) q^{35} +(40.5000 - 70.1481i) q^{36} +(283.682 + 163.784i) q^{37} +417.233 q^{38} +(74.1364 + 119.486i) q^{39} -12.5757 q^{40} +(48.5707 + 28.0423i) q^{41} +(-41.3336 + 71.5918i) q^{42} +(63.9393 + 110.746i) q^{43} -290.250i q^{44} +(23.7729 - 13.7253i) q^{45} +(-424.879 + 245.304i) q^{46} -517.983i q^{47} +(-82.5000 - 142.894i) q^{48} +(-149.167 + 258.365i) q^{49} +(413.121 + 238.516i) q^{50} -86.5757 q^{51} +(-421.637 + 13.3838i) q^{52} -695.546 q^{53} +(-96.4093 - 55.6619i) q^{54} +(49.1821 - 85.1860i) q^{55} +(-13.7779 - 23.8639i) q^{56} -303.581i q^{57} +(-571.712 + 330.078i) q^{58} +(568.566 - 328.262i) q^{59} +82.3516i q^{60} +(-350.652 - 607.347i) q^{61} +(-78.4843 + 135.939i) q^{62} +(52.0907 + 30.0746i) q^{63} +631.000 q^{64} +(-126.015 - 67.5174i) q^{65} -398.910 q^{66} +(-49.5150 - 28.5875i) q^{67} +(129.864 - 224.930i) q^{68} +(178.485 + 309.145i) q^{69} -84.0465i q^{70} +(-267.798 + 154.613i) q^{71} +(32.1364 - 18.5540i) q^{72} -389.711i q^{73} +(675.299 + 1169.65i) q^{74} +(173.546 - 300.590i) q^{75} +(788.728 + 455.372i) q^{76} +215.534 q^{77} +(18.3943 + 579.485i) q^{78} +901.820 q^{79} +(145.279 + 83.8766i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(115.621 + 200.262i) q^{82} -687.095i q^{83} +(-156.272 + 90.2238i) q^{84} +(76.2279 - 44.0102i) q^{85} +527.257i q^{86} +(240.167 + 415.982i) q^{87} +(66.4850 - 115.155i) q^{88} +(-927.113 - 535.269i) q^{89} +113.181 q^{90} +(-9.93858 - 313.100i) q^{91} -1070.91 q^{92} +(98.9100 + 57.1057i) q^{93} +(1067.85 - 1849.57i) q^{94} +(154.324 + 267.296i) q^{95} -779.267i q^{96} +(-1519.43 + 877.242i) q^{97} +(-1065.27 + 615.032i) q^{98} +290.250i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 18 q^{4} - 66 q^{7} - 18 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 + 18 * q^4 - 66 * q^7 - 18 * q^9	\( 4 q + 6 q^{3} + 18 q^{4} - 66 q^{7} - 18 q^{9} - 68 q^{10} - 126 q^{11} + 108 q^{12} + 40 q^{13} + 204 q^{14} - 54 q^{15} + 110 q^{16} - 72 q^{17} + 222 q^{19} + 162 q^{20} + 34 q^{22} - 138 q^{23} + 120 q^{25} - 714 q^{26} - 108 q^{27} - 594 q^{28} - 6 q^{29} + 204 q^{30} - 378 q^{33} + 402 q^{35} + 162 q^{36} + 492 q^{37} + 612 q^{38} + 168 q^{39} - 136 q^{40} + 180 q^{41} + 306 q^{42} + 470 q^{43} - 162 q^{45} - 714 q^{46} - 330 q^{48} + 346 q^{49} + 1224 q^{50} - 432 q^{51} - 144 q^{52} - 2268 q^{53} - 446 q^{55} + 102 q^{56} - 2244 q^{58} + 2160 q^{59} - 160 q^{61} - 1428 q^{62} + 594 q^{63} + 2524 q^{64} - 804 q^{65} + 204 q^{66} - 498 q^{67} + 648 q^{68} + 414 q^{69} - 1314 q^{71} + 1530 q^{74} + 180 q^{75} + 1998 q^{76} + 2976 q^{77} - 612 q^{78} + 8 q^{79} - 990 q^{80} - 162 q^{81} + 34 q^{82} - 1782 q^{84} - 852 q^{85} + 18 q^{87} - 34 q^{88} - 252 q^{89} + 1224 q^{90} - 1668 q^{91} - 2484 q^{92} - 1404 q^{93} + 2686 q^{94} - 54 q^{95} - 336 q^{97} - 6732 q^{98}+O(q^{100}) \) 4 * q + 6 * q^3 + 18 * q^4 - 66 * q^7 - 18 * q^9 - 68 * q^10 - 126 * q^11 + 108 * q^12 + 40 * q^13 + 204 * q^14 - 54 * q^15 + 110 * q^16 - 72 * q^17 + 222 * q^19 + 162 * q^20 + 34 * q^22 - 138 * q^23 + 120 * q^25 - 714 * q^26 - 108 * q^27 - 594 * q^28 - 6 * q^29 + 204 * q^30 - 378 * q^33 + 402 * q^35 + 162 * q^36 + 492 * q^37 + 612 * q^38 + 168 * q^39 - 136 * q^40 + 180 * q^41 + 306 * q^42 + 470 * q^43 - 162 * q^45 - 714 * q^46 - 330 * q^48 + 346 * q^49 + 1224 * q^50 - 432 * q^51 - 144 * q^52 - 2268 * q^53 - 446 * q^55 + 102 * q^56 - 2244 * q^58 + 2160 * q^59 - 160 * q^61 - 1428 * q^62 + 594 * q^63 + 2524 * q^64 - 804 * q^65 + 204 * q^66 - 498 * q^67 + 648 * q^68 + 414 * q^69 - 1314 * q^71 + 1530 * q^74 + 180 * q^75 + 1998 * q^76 + 2976 * q^77 - 612 * q^78 + 8 * q^79 - 990 * q^80 - 162 * q^81 + 34 * q^82 - 1782 * q^84 - 852 * q^85 + 18 * q^87 - 34 * q^88 - 252 * q^89 + 1224 * q^90 - 1668 * q^91 - 2484 * q^92 - 1404 * q^93 + 2686 * q^94 - 54 * q^95 - 336 * q^97 - 6732 * q^98

Introduction

L-functions

Modular forms

Varieties

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