LMFDB - Embedded newform 175.4.x.a.3.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$928$
Relative dimension:	$58$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.9
Character	$\chi$	$=$	175.3
Dual form			175.4.x.a.117.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.38969 + 3.67979i) q^{2} +(1.74074 - 4.53478i) q^{3} +(-4.57638 - 10.2787i) q^{4} +(10.9198 + 2.39967i) q^{5} +(12.5272 + 17.2422i) q^{6} +(14.0149 - 12.1072i) q^{7} +(14.0907 + 2.23174i) q^{8} +(2.53089 + 2.27882i) q^{9} +(-34.9251 + 34.4481i) q^{10} +(-36.0998 - 40.0929i) q^{11} +(-54.5780 + 2.86031i) q^{12} +(-41.9216 - 21.3601i) q^{13} +(11.0607 + 80.5041i) q^{14} +(29.8904 - 45.3416i) q^{15} +(18.3450 - 20.3742i) q^{16} +(26.2204 - 32.3795i) q^{17} +(-14.4336 + 3.86747i) q^{18} +(-17.8059 - 7.92768i) q^{19} +(-25.3076 - 123.223i) q^{20} +(-30.5071 - 84.6297i) q^{21} +(233.801 - 37.0304i) q^{22} +(-46.9954 - 30.5192i) q^{23} +(34.6486 - 60.0131i) q^{24} +(113.483 + 52.4077i) q^{25} +(178.780 - 103.219i) q^{26} +(131.595 - 67.0510i) q^{27} +(-188.584 - 88.6480i) q^{28} +(135.740 - 186.830i) q^{29} +(95.4188 + 218.343i) q^{30} +(-339.618 + 35.6953i) q^{31} +(60.6732 + 226.435i) q^{32} +(-244.653 + 93.9134i) q^{33} +(56.4913 + 173.862i) q^{34} +(182.092 - 98.5765i) q^{35} +(11.8411 - 36.4430i) q^{36} +(11.5807 + 220.973i) q^{37} +(71.7226 - 46.5772i) q^{38} +(-169.838 + 152.923i) q^{39} +(148.511 + 58.1830i) q^{40} +(462.687 - 150.336i) q^{41} +(384.322 + 89.9786i) q^{42} +(77.2715 + 77.2715i) q^{43} +(-246.897 + 554.541i) q^{44} +(22.1683 + 30.9575i) q^{45} +(224.608 - 100.002i) q^{46} +(321.172 - 260.080i) q^{47} +(-60.4586 - 118.657i) q^{48} +(49.8331 - 339.361i) q^{49} +(-464.039 + 292.357i) q^{50} +(-101.191 - 175.268i) q^{51} +(-27.7055 + 528.652i) q^{52} +(455.413 + 174.817i) q^{53} +(-67.7368 + 644.473i) q^{54} +(-297.992 - 524.433i) q^{55} +(224.499 - 139.320i) q^{56} +(-66.9455 + 66.9455i) q^{57} +(363.121 + 945.962i) q^{58} +(-820.595 - 174.423i) q^{59} +(-602.844 - 99.7351i) q^{60} +(6.26595 + 29.4790i) q^{61} +(680.228 - 1335.02i) q^{62} +(63.0601 + 1.29551i) q^{63} +(-769.630 - 250.068i) q^{64} +(-406.517 - 333.845i) q^{65} +(239.061 - 1124.69i) q^{66} +(122.712 + 99.3699i) q^{67} +(-452.815 - 121.331i) q^{68} +(-220.204 + 159.988i) q^{69} +(-72.4025 + 905.629i) q^{70} +(-343.827 - 249.805i) q^{71} +(30.5761 + 37.7584i) q^{72} +(417.016 + 21.8549i) q^{73} +(-840.810 - 485.442i) q^{74} +(435.202 - 423.393i) q^{75} +219.302i q^{76} +(-991.346 - 124.830i) q^{77} +(-156.865 - 990.404i) q^{78} +(-90.6505 - 9.52775i) q^{79} +(249.215 - 178.460i) q^{80} +(-65.3772 - 622.023i) q^{81} +(-552.471 + 2061.85i) q^{82} +(-85.5853 + 540.364i) q^{83} +(-730.273 + 700.872i) q^{84} +(364.021 - 290.657i) q^{85} +(-468.998 + 99.6886i) q^{86} +(-610.946 - 940.774i) q^{87} +(-419.193 - 645.501i) q^{88} +(398.955 - 84.8005i) q^{89} +(-166.892 + 7.59609i) q^{90} +(-846.136 + 208.192i) q^{91} +(-98.6292 + 622.720i) q^{92} +(-429.315 + 1602.23i) q^{93} +(189.540 + 1803.35i) q^{94} +(-175.412 - 129.297i) q^{95} +(1132.45 + 119.025i) q^{96} +(117.678 + 742.987i) q^{97} +(1129.69 + 994.341i) q^{98} -183.736i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) $ 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−2.38969	+	3.67979i	−0.844881	+	1.30100i	0.106914	+	0.994268i	$0.465903\pi$
$2$	−2.38969	+	3.67979i	−0.844881	+	1.30100i	−0.951795	+	0.306735i	$0.900764\pi$
$3$	1.74074	−	4.53478i	0.335005	−	0.872718i	−0.657824	−	0.753172i	$-0.728523\pi$
$3$	1.74074	−	4.53478i	0.335005	−	0.872718i	0.992829	−	0.119546i	$-0.0381439\pi$
$4$	−4.57638	−	10.2787i	−0.572048	−	1.28484i
$5$	10.9198	+	2.39967i	0.976695	+	0.214633i
$5$	10.9198	+	2.39967i	0.976695	+	0.214633i
$6$	12.5272	+	17.2422i	0.852369	+	1.17319i
$7$	14.0149	−	12.1072i	0.756732	−	0.653725i
$7$	14.0149	−	12.1072i	0.756732	−	0.653725i
$8$	14.0907	+	2.23174i	0.622725	+	0.0986300i
$9$	2.53089	+	2.27882i	0.0937365	+	0.0844007i
$10$	−34.9251	+	34.4481i	−1.10443	+	1.08934i
$11$	−36.0998	−	40.0929i	−0.989501	−	1.09895i	−0.995091	−	0.0989674i	$-0.968446\pi$
$11$	−36.0998	−	40.0929i	−0.989501	−	1.09895i	0.00559009	−	0.999984i	$-0.498221\pi$
$12$	−54.5780	+	2.86031i	−1.31294	+	0.0688084i
$13$	−41.9216	−	21.3601i	−0.894381	−	0.455710i	−0.0545206	−	0.998513i	$-0.517363\pi$
$13$	−41.9216	−	21.3601i	−0.894381	−	0.455710i	−0.839860	+	0.542803i	$0.817363\pi$
$14$	11.0607	+	80.5041i	0.211150	+	1.53683i
$15$	29.8904	−	45.3416i	0.514512	−	0.780476i
$16$	18.3450	−	20.3742i	0.286641	−	0.318347i
$17$	26.2204	−	32.3795i	0.374081	−	0.461952i	−0.554988	−	0.831859i	$-0.687277\pi$
$17$	26.2204	−	32.3795i	0.374081	−	0.461952i	0.929069	+	0.369907i	$0.120610\pi$
$18$	−14.4336	+	3.86747i	−0.189002	+	0.0506429i
$19$	−17.8059	−	7.92768i	−0.214997	−	0.0957228i	0.296412	−	0.955060i	$-0.404210\pi$
$19$	−17.8059	−	7.92768i	−0.214997	−	0.0957228i	−0.511409	+	0.859337i	$0.670876\pi$
$20$	−25.3076	−	123.223i	−0.282947	−	1.37768i
$21$	−30.5071	−	84.6297i	−0.317009	−	0.879415i
$22$	233.801	−	37.0304i	2.26575	−	0.358860i
$23$	−46.9954	−	30.5192i	−0.426053	−	0.276682i	0.313750	−	0.949506i	$-0.398415\pi$
$23$	−46.9954	−	30.5192i	−0.426053	−	0.276682i	−0.739803	+	0.672824i	$0.765081\pi$
$24$	34.6486	−	60.0131i	0.294692	−	0.510422i
$25$	113.483	+	52.4077i	0.907865	+	0.419262i
$26$	178.780	−	103.219i	1.34853	−	0.778571i
$27$	131.595	−	67.0510i	0.937980	−	0.477925i
$28$	−188.584	−	88.6480i	−1.27282	−	0.598318i
$29$	135.740	−	186.830i	0.869184	−	1.19633i	−0.110117	−	0.993919i	$-0.535123\pi$
$29$	135.740	−	186.830i	0.869184	−	1.19633i	0.979301	−	0.202410i	$-0.0648774\pi$
$30$	95.4188	+	218.343i	0.580700	+	1.32879i
$31$	−339.618	+	35.6953i	−1.96765	+	0.206808i	−0.999115	−	0.0420671i	$-0.986606\pi$
$31$	−339.618	+	35.6953i	−1.96765	+	0.206808i	−0.968535	+	0.248875i	$0.919939\pi$
$32$	60.6732	+	226.435i	0.335175	+	1.25089i
$33$	−244.653	+	93.9134i	−1.29056	+	0.495401i
$34$	56.4913	+	173.862i	0.284947	+	0.876976i
$35$	182.092	−	98.5765i	0.879407	−	0.476071i
$36$	11.8411	−	36.4430i	0.0548197	−	0.168718i
$37$	11.5807	+	220.973i	0.0514556	+	0.981831i	0.895361	+	0.445340i	$0.146917\pi$
$37$	11.5807	+	220.973i	0.0514556	+	0.981831i	−0.843906	+	0.536491i	$0.819749\pi$
$38$	71.7226	−	46.5772i	0.306183	−	0.198837i
$39$	−169.838	+	152.923i	−0.697328	+	0.627877i
$40$	148.511	+	58.1830i	0.587043	+	0.229989i
$41$	462.687	−	150.336i	1.76243	−	0.572648i	0.764982	−	0.644052i	$-0.222748\pi$
$41$	462.687	−	150.336i	1.76243	−	0.572648i	0.997447	+	0.0714038i	$0.0227479\pi$
$42$	384.322	+	89.9786i	1.41196	+	0.330571i
$43$	77.2715	+	77.2715i	0.274042	+	0.274042i	0.830725	−	0.556683i	$-0.187926\pi$
$43$	77.2715	+	77.2715i	0.274042	+	0.274042i	−0.556683	+	0.830725i	$0.687926\pi$
$44$	−246.897	+	554.541i	−0.845936	+	1.90000i
$45$	22.1683	+	30.9575i	0.0734368	+	0.102553i
$46$	224.608	−	100.002i	0.719928	−	0.320533i
$47$	321.172	−	260.080i	0.996759	−	0.807160i	0.0155055	−	0.999880i	$-0.495064\pi$
$47$	321.172	−	260.080i	0.996759	−	0.807160i	0.981254	+	0.192720i	$0.0617309\pi$
$48$	−60.4586	−	118.657i	−0.181801	−	0.356805i
$49$	49.8331	−	339.361i	0.145286	−	0.989390i
$50$	−464.039	+	292.357i	−1.31250	+	0.826910i
$51$	−101.191	−	175.268i	−0.277835	−	0.481224i
$52$	−27.7055	+	528.652i	−0.0738858	+	1.40982i
$53$	455.413	+	174.817i	1.18030	+	0.453074i	0.867833	−	0.496856i	$-0.165512\pi$
$53$	455.413	+	174.817i	1.18030	+	0.453074i	0.312464	+	0.949929i	$0.398845\pi$
$54$	−67.7368	+	644.473i	−0.170700	+	1.62410i
$55$	−297.992	−	524.433i	−0.730569	−	1.28572i
$56$	224.499	−	139.320i	0.535713	−	0.332455i
$57$	−66.9455	+	66.9455i	−0.155564	+	0.155564i
$58$	363.121	+	945.962i	0.822070	+	2.14157i
$59$	−820.595	−	174.423i	−1.81072	−	0.384880i	−0.826656	−	0.562707i	$-0.809760\pi$
$59$	−820.595	−	174.423i	−1.81072	−	0.384880i	−0.984062	+	0.177828i	$0.943093\pi$
$60$	−602.844	−	99.7351i	−1.29711	−	0.214596i
$61$	6.26595	+	29.4790i	0.0131520	+	0.0618753i	0.984234	−	0.176870i	$-0.0565972\pi$
$61$	6.26595	+	29.4790i	0.0131520	+	0.0618753i	−0.971082	+	0.238745i	$0.923264\pi$
$62$	680.228	−	1335.02i	1.39337	−	2.73465i
$63$	63.0601	+	1.29551i	0.126108	+	0.00259078i
$64$	−769.630	−	250.068i	−1.50318	−	0.488414i
$65$	−406.517	−	333.845i	−0.775727	−	0.637053i
$66$	239.061	−	1124.69i	0.445855	−	2.09758i
$67$	122.712	+	99.3699i	0.223755	+	0.181194i	0.734643	−	0.678454i	$-0.237350\pi$
$67$	122.712	+	99.3699i	0.223755	+	0.181194i	−0.510887	+	0.859648i	$0.670683\pi$
$68$	−452.815	−	121.331i	−0.807527	−	0.216376i
$69$	−220.204	+	159.988i	−0.384195	+	0.279134i
$70$	−72.4025	+	905.629i	−0.123625	+	1.54633i
$71$	−343.827	−	249.805i	−0.574715	−	0.417555i	0.262100	−	0.965041i	$-0.415585\pi$
$71$	−343.827	−	249.805i	−0.574715	−	0.417555i	−0.836815	+	0.547486i	$0.815585\pi$
$72$	30.5761	+	37.7584i	0.0500476	+	0.0618037i
$73$	417.016	+	21.8549i	0.668604	+	0.0350400i	0.383618	−	0.923492i	$-0.374678\pi$
$73$	417.016	+	21.8549i	0.668604	+	0.0350400i	0.284986	+	0.958532i	$0.408011\pi$
$74$	−840.810	−	485.442i	−1.32084	−	0.762587i
$75$	435.202	−	423.393i	0.670037	−	0.651856i
$76$			219.302i			0.330995i
$77$	−991.346	−	124.830i	−1.46720	−	0.184750i
$78$	−156.865	−	990.404i	−0.227711	−	1.43771i
$79$	−90.6505	−	9.52775i	−0.129101	−	0.0135691i	0.0397576	−	0.999209i	$-0.487341\pi$
$79$	−90.6505	−	9.52775i	−0.129101	−	0.0135691i	−0.168859	+	0.985640i	$0.554008\pi$
$80$	249.215	−	178.460i	0.348289	−	0.249405i
$81$	−65.3772	−	622.023i	−0.0896807	−	0.853255i
$82$	−552.471	+	2061.85i	−0.744027	+	2.77675i
$83$	−85.5853	+	540.364i	−0.113183	+	0.714611i	0.864202	+	0.503145i	$0.167824\pi$
$83$	−85.5853	+	540.364i	−0.113183	+	0.714611i	−0.977385	+	0.211466i	$0.932176\pi$
$84$	−730.273	+	700.872i	−0.948564	+	0.910374i
$85$	364.021	−	290.657i	0.464513	−	0.370896i
$86$	−468.998	+	99.6886i	−0.588062	+	0.124996i
$87$	−610.946	−	940.774i	−0.752877	−	1.15933i
$88$	−419.193	−	645.501i	−0.507797	−	0.781939i
$89$	398.955	−	84.8005i	0.475159	−	0.100998i	0.0358937	−	0.999356i	$-0.488572\pi$
$89$	398.955	−	84.8005i	0.475159	−	0.100998i	0.439265	+	0.898357i	$0.355239\pi$
$90$	−166.892	+	7.59609i	−0.195467	+	0.00889664i
$91$	−846.136	+	208.192i	−0.974715	+	0.239829i
$92$	−98.6292	+	622.720i	−0.111770	+	0.705686i
$93$	−429.315	+	1602.23i	−0.478687	+	1.78649i
$94$	189.540	+	1803.35i	0.207974	+	1.97874i
$95$	−175.412	−	129.297i	−0.189441	−	0.139637i
$96$	1132.45	+	119.025i	1.20396	+	0.126541i
$97$	117.678	+	742.987i	0.123179	+	0.777721i	0.969508	+	0.245060i	$0.0788077\pi$
$97$	117.678	+	742.987i	0.123179	+	0.777721i	−0.846329	+	0.532661i	$0.821192\pi$
$98$	1129.69	+	994.341i	1.16445	+	1.02493i
$99$		−	183.736i		−	0.186526i
$100$	19.3418	−	1406.30i	0.0193418	−	1.40630i
$101$	−121.849	−	70.3498i	−0.120044	−	0.0693076i	0.438776	−	0.898597i	$-0.355412\pi$
$101$	−121.849	−	70.3498i	−0.120044	−	0.0693076i	−0.558820	+	0.829289i	$0.688746\pi$
$102$	886.764	+	46.4733i	0.860811	+	0.0451132i
$103$	−163.183	−	201.514i	−0.156105	−	0.192774i	0.693093	−	0.720848i	$-0.256248\pi$
$103$	−163.183	−	201.514i	−0.156105	−	0.192774i	−0.849198	+	0.528074i	$0.822914\pi$
$104$	−543.032	−	394.536i	−0.512007	−	0.371995i
$105$	−130.047	−	997.344i	−0.120870	−	0.926960i
$106$	−1731.58	+	1258.07i	−1.58666	+	1.15278i
$107$	292.991	+	78.5067i	0.264715	+	0.0709302i	0.388735	−	0.921350i	$-0.372912\pi$
$107$	292.991	+	78.5067i	0.264715	+	0.0709302i	−0.124020	+	0.992280i	$0.539579\pi$
$108$	−1291.43	−	1045.78i	−1.15063	−	0.931759i
$109$	−108.809	+	511.906i	−0.0956148	+	0.449832i	0.904130	+	0.427257i	$0.140520\pi$
$109$	−108.809	+	511.906i	−0.0956148	+	0.449832i	−0.999745	+	0.0225755i	$0.992813\pi$
$110$	2641.91	+	156.680i	2.28997	+	0.135808i
$111$	1022.22	+	332.140i	0.874100	+	0.284012i
$112$	10.4292	−	507.648i	0.00879878	−	0.428288i
$113$	−125.249	+	245.814i	−0.104269	+	0.204640i	−0.937247	−	0.348667i	$-0.886634\pi$
$113$	−125.249	+	245.814i	−0.104269	+	0.204640i	0.832977	+	0.553307i	$0.186634\pi$
$114$	−86.3669	−	406.324i	−0.0709562	−	0.333823i
$115$	−439.943	−	446.036i	−0.356739	−	0.361679i
$116$	−2541.58	−	540.229i	−2.03431	−	0.432405i
$117$	−57.4229	−	149.592i	−0.0453739	−	0.118203i
$118$	2602.80	−	2602.80i	2.03057	−	2.03057i
$119$	−24.5484	−	771.249i	−0.0189105	−	0.594120i
$120$	522.367	−	572.185i	0.397378	−	0.435276i
$121$	−165.117	+	1570.99i	−0.124055	+	1.18030i
$122$	−123.450	−	47.3881i	−0.0916119	−	0.0351665i
$123$	123.676	−	2359.88i	0.0906625	−	1.72994i
$124$	1921.12	+	3327.48i	1.39131	+	2.40981i
$125$	1113.45	+	844.603i	0.796720	+	0.604348i
$126$	−155.461	+	228.952i	−0.109917	+	0.161878i
$127$	1257.70	+	2468.37i	0.878762	+	1.72467i	0.663598	+	0.748089i	$0.269029\pi$
$127$	1257.70	+	2468.37i	0.878762	+	1.72467i	0.215164	+	0.976578i	$0.430971\pi$
$128$	1301.92	−	1054.28i	0.899023	−	0.728014i
$129$	484.918	−	215.900i	0.330967	−	0.147356i
$130$	2199.93	−	698.113i	1.48420	−	0.470989i
$131$	−211.044	+	474.013i	−0.140756	+	0.316143i	−0.970144	−	0.242530i	$-0.922023\pi$
$131$	−211.044	+	474.013i	−0.140756	+	0.316143i	0.829388	+	0.558673i	$0.188689\pi$
$132$	2084.93	+	2084.93i	1.37477	+	1.37477i
$133$	−345.528	+	104.473i	−0.225271	+	0.0681125i
$134$	−658.903	+	214.091i	−0.424780	+	0.138019i
$135$	1597.89	−	416.398i	1.01870	−	0.265465i
$136$	441.726	−	397.731i	0.278512	−	0.250773i
$137$	−478.237	+	310.571i	−0.298238	+	0.193678i	−0.685080	−	0.728468i	$-0.740233\pi$
$137$	−478.237	+	310.571i	−0.298238	+	0.193678i	0.386842	+	0.922146i	$0.373566\pi$
$138$	−62.5029	−	1192.63i	−0.0385551	−	0.735674i
$139$	−700.153	+	2154.85i	−0.427239	+	1.31491i	0.473595	+	0.880743i	$0.342956\pi$
$139$	−700.153	+	2154.85i	−0.427239	+	1.31491i	−0.900834	+	0.434164i	$0.857044\pi$
$140$	−1846.57	−	1420.55i	−1.11474	−	0.857563i
$141$	−620.327	−	1909.17i	−0.370503	−	1.14029i
$142$	1740.87	−	668.256i	1.02881	−	0.394921i
$143$	656.972	+	2451.85i	0.384187	+	1.43381i
$144$	92.8583	−	9.75980i	0.0537375	−	0.00564803i
$145$	1930.58	−	1714.42i	1.10570	−	0.981893i
$146$	−1076.96	+	1482.31i	−0.610478	+	0.840251i
$147$	−1452.18	−	816.720i	−0.814787	−	0.458244i
$148$	2218.33	−	1130.29i	1.23206	−	0.627767i
$149$	−1725.03	+	995.947i	−0.948456	+	0.547591i	−0.892601	−	0.450847i	$-0.851122\pi$
$149$	−1725.03	+	995.947i	−0.948456	+	0.547591i	−0.0558552	+	0.998439i	$0.517789\pi$
$150$	518.003	+	2613.23i	0.281965	+	1.42246i
$151$	91.2824	−	158.106i	0.0491951	−	0.0852084i	−0.840379	−	0.541999i	$-0.817668\pi$
$151$	91.2824	−	158.106i	0.0491951	−	0.0852084i	0.889574	+	0.456790i	$0.151001\pi$
$152$	−233.204	−	151.444i	−0.124443	−	0.0808141i
$153$	140.148	−	22.1973i	0.0740542	−	0.0117290i
$154$	2828.35	−	3349.64i	1.47997	−	1.75274i
$155$	−3794.21	−	425.186i	−1.96618	−	0.220334i
$156$	2349.09	+	1045.88i	1.20563	+	0.536780i
$157$	240.922	−	64.5550i	0.122469	−	0.0328156i	−0.197064	−	0.980391i	$-0.563141\pi$
$157$	240.922	−	64.5550i	0.122469	−	0.0328156i	0.319533	+	0.947575i	$0.396474\pi$
$158$	251.686	−	310.807i	0.126728	−	0.156496i
$159$	1585.51	−	1760.89i	0.790811	−	0.878285i
$160$	119.168	+	2618.22i	0.0588816	+	1.29368i
$161$	−1028.13	+	141.259i	−0.503282	+	0.0691476i
$162$	2445.15	+	1245.86i	1.18586	+	0.604224i
$163$	−2858.85	+	149.826i	−1.37376	+	0.0719955i	−0.724867	−	0.688889i	$-0.758099\pi$
$163$	−2858.85	+	149.826i	−1.37376	+	0.0719955i	−0.648888	+	0.760884i	$0.724766\pi$
$164$	−3662.70	−	4067.84i	−1.74396	−	1.93686i
$165$	−2896.91	+	438.428i	−1.36682	+	0.206858i
$166$	−1783.91	−	1606.24i	−0.834084	−	0.751013i
$167$	−2333.66	−	369.615i	−1.08134	−	0.171267i	−0.409756	−	0.912195i	$-0.634386\pi$
$167$	−2333.66	−	369.615i	−1.08134	−	0.171267i	−0.671585	+	0.740928i	$0.734386\pi$
$168$	−240.993	−	1260.57i	−0.110673	−	0.578900i
$169$	9.79926	+	13.4875i	0.00446029	+	0.00613907i
$170$	199.661	+	2034.10i	0.0900781	+	0.917696i
$171$	−26.9988	−	60.6404i	−0.0120740	−	0.0271186i
$172$	440.629	−	1147.88i	0.195335	−	0.508865i
$173$	500.622	−	770.891i	0.220009	−	0.338785i	−0.711381	−	0.702807i	$-0.751930\pi$
$173$	500.622	−	770.891i	0.220009	−	0.338785i	0.931390	+	0.364022i	$0.118597\pi$
$174$	4921.82			2.14438
$175$	2224.96	−	639.472i	0.961093	−	0.276226i
$176$	−1479.11			−0.633480
$177$	−2219.41	+	3417.59i	−0.942491	+	1.45131i
$178$	−641.328	+	1670.72i	−0.270054	+	0.703514i
$179$	1351.66	+	3035.88i	0.564401	+	1.26767i	0.940092	+	0.340921i	$0.110739\pi$
$179$	1351.66	+	3035.88i	0.564401	+	1.26767i	−0.375691	+	0.926745i	$0.622595\pi$
$180$	216.753	−	369.535i	0.0897545	−	0.153020i
$181$	644.871	+	887.588i	0.264822	+	0.364497i	0.920633	−	0.390428i	$-0.127673\pi$
$181$	644.871	+	887.588i	0.264822	+	0.364497i	−0.655811	+	0.754925i	$0.727673\pi$
$182$	1255.89	−	3611.12i	0.511500	−	1.47074i
$183$	144.588	+	22.9005i	0.0584057	+	0.00925055i
$184$	−594.085	−	534.917i	−0.238025	−	0.214318i
$185$	−403.803	+	2440.77i	−0.160477	+	0.969994i
$186$	−4869.93	−	5408.61i	−1.91979	−	2.13214i
$187$	−2244.74	+	117.642i	−0.877817	+	0.0460044i
$188$	−4143.09	−	2111.01i	−1.60727	−	0.818943i
$189$	1032.49	−	2532.95i	0.397368	−	0.974842i
$190$	894.965	−	336.502i	0.341724	−	0.128487i
$191$	3086.47	−	3427.87i	1.16926	−	1.29860i	0.223141	−	0.974786i	$-0.428369\pi$
$191$	3086.47	−	3427.87i	1.16926	−	1.29860i	0.946122	−	0.323812i	$-0.104964\pi$
$192$	−2473.73	+	3054.80i	−0.929822	+	1.14823i
$193$	2128.02	−	570.200i	0.793668	−	0.212663i	0.160866	−	0.986976i	$-0.448571\pi$
$193$	2128.02	−	570.200i	0.793668	−	0.212663i	0.632802	+	0.774314i	$0.281905\pi$
$194$	−3015.25	−	1342.48i	−1.11589	−	0.496826i
$195$	−2221.55	+	1262.33i	−0.815840	+	0.463575i
$196$	−3716.25	+	1040.82i	−1.35432	+	0.379309i
$197$	3487.40	−	552.349i	1.26125	−	0.199763i	0.510229	−	0.860039i	$-0.329561\pi$
$197$	3487.40	−	552.349i	1.26125	−	0.199763i	0.751023	+	0.660276i	$0.229561\pi$
$198$	676.109	+	439.070i	0.242672	+	0.157593i
$199$	1378.72	−	2388.00i	0.491128	−	0.850659i	−0.508820	−	0.860873i	$-0.669918\pi$
$199$	1378.72	−	2388.00i	0.491128	−	0.850659i	0.999948	+	0.0102140i	$0.00325128\pi$
$200$	1482.09	+	991.724i	0.523999	+	0.350627i
$201$	664.229	−	383.493i	0.233090	−	0.134575i
$202$	550.054	−	280.267i	0.191592	−	0.0976213i
$203$	−359.605	−	4261.83i	−0.124332	−	1.47351i
$204$	−1338.44	+	1842.21i	−0.459361	+	0.632257i
$205$	5413.20	−	531.342i	1.84426	−	0.181027i
$206$	1131.48	−	118.924i	0.382690	−	0.0402224i
$207$	−49.3923	−	184.335i	−0.0165846	−	0.0618944i
$208$	−1204.25	+	462.267i	−0.401440	+	0.154098i
$209$	324.944	+	1000.08i	0.107545	+	0.330989i
$210$	3980.79	+	1904.79i	1.30810	+	0.625920i
$211$	−477.055	+	1468.22i	−0.155648	+	0.479036i	−0.998226	−	0.0595385i	$-0.981037\pi$
$211$	−477.055	+	1468.22i	−0.155648	+	0.479036i	0.842578	+	0.538575i	$0.181037\pi$
$212$	−287.252	−	5481.09i	−0.0930592	−	1.77567i
$213$	−1731.32	+	1124.33i	−0.556940	+	0.361681i
$214$	−989.044	+	890.540i	−0.315933	+	0.284467i
$215$	658.362	+	1029.21i	0.208837	+	0.326474i
$216$	2003.90	−	651.107i	0.631241	−	0.205103i
$217$	−4327.53	+	4612.07i	−1.35379	+	1.44280i
$218$	−1623.69	−	1623.69i	−0.504450	−	0.504450i
$219$	825.023	−	1853.03i	0.254566	−	0.571764i
$220$	−4026.78	+	5462.99i	−1.23402	+	1.67416i
$221$	−1790.83	+	797.329i	−0.545087	+	0.242688i
$222$	−3665.00	+	2967.86i	−1.10801	+	0.897250i
$223$	−655.685	−	1286.85i	−0.196896	−	0.386431i	0.771357	−	0.636403i	$-0.219579\pi$
$223$	−655.685	−	1286.85i	−0.196896	−	0.386431i	−0.968253	+	0.249972i	$0.919579\pi$
$224$	3591.82	+	2438.88i	1.07138	+	0.727476i
$225$	167.785	+	391.246i	0.0497142	+	0.115925i
$226$	−605.241	−	1048.31i	−0.178142	−	0.308551i
$227$	−87.5086	+	1669.76i	−0.0255866	+	0.488221i	0.955541	+	0.294859i	$0.0952726\pi$
$227$	−87.5086	+	1669.76i	−0.0255866	+	0.488221i	−0.981127	+	0.193362i	$0.938061\pi$
$228$	994.483	+	381.746i	0.288865	+	0.110885i
$229$	107.069	−	1018.69i	0.0308966	−	0.293962i	−0.968152	−	0.250362i	$-0.919451\pi$
$229$	107.069	−	1018.69i	0.0308966	−	0.293962i	0.999049	−	0.0436003i	$-0.0138828\pi$
$230$	2692.65	−	553.015i	0.771947	−	0.158542i
$231$	−2291.75	+	4278.23i	−0.652754	+	1.21856i
$232$	2329.63	−	2329.63i	0.659256	−	0.659256i
$233$	−1466.87	−	3821.33i	−0.412437	−	1.07443i	−0.969743	−	0.244128i	$-0.921498\pi$
$233$	−1466.87	−	3821.33i	−0.412437	−	1.07443i	0.557306	−	0.830307i	$-0.311835\pi$
$234$	687.689	+	146.173i	0.192118	+	0.0408360i
$235$	4131.23	−	2069.31i	1.14677	−	0.574411i
$236$	1962.51	+	9232.90i	0.541308	+	2.54665i
$237$	−201.005	+	394.494i	−0.0550914	+	0.108123i
$238$	2896.70	+	1752.71i	0.788929	+	0.477358i
$239$	4486.42	+	1457.73i	1.21424	+	0.394529i	0.844979	−	0.534799i	$-0.179613\pi$
$239$	4486.42	+	1457.73i	1.21424	+	0.394529i	0.369256	+	0.929328i	$0.379613\pi$
$240$	−375.458	−	1440.79i	−0.100982	−	0.387510i
$241$	742.520	−	3493.28i	0.198464	−	0.933702i	−0.760316	−	0.649554i	$-0.774956\pi$
$241$	742.520	−	3493.28i	0.198464	−	0.933702i	0.958780	−	0.284148i	$-0.0917108\pi$
$242$	−5386.32	−	4361.76i	−1.43077	−	1.15861i
$243$	917.279	+	245.784i	0.242154	+	0.0648850i
$244$	274.331	−	199.313i	0.0719764	−	0.0522939i
$245$	1358.52	−	3586.16i	0.354256	−	0.935149i
$246$	8388.32	+	6094.47i	2.17406	+	1.57955i
$247$	577.113	+	712.675i	0.148667	+	0.183589i
$248$	−4865.10	−	254.969i	−1.24570	−	0.0652845i
$249$	2301.45	+	1328.74i	0.585737	+	0.338175i
$250$	−5768.76	+	2078.93i	−1.45939	+	0.525933i
$251$		−	1239.79i		−	0.311772i	−0.987775	−	0.155886i	$-0.950177\pi$
$251$		−	1239.79i		−	0.311772i	0.987775	−	0.155886i	$-0.0498232\pi$
$252$	−275.271	−	654.106i	−0.0688113	−	0.163511i
$253$	472.923	+	2985.92i	0.117519	+	0.741989i
$254$	−12088.6	−	1270.56i	−2.98625	−	0.313867i
$255$	−684.398	−	2156.71i	−0.168073	−	0.529641i
$256$	91.6266	+	871.769i	0.0223698	+	0.212834i
$257$	−841.676	+	3141.18i	−0.204289	+	0.762418i	0.785376	+	0.619019i	$0.212470\pi$
$257$	−841.676	+	3141.18i	−0.204289	+	0.762418i	−0.989665	+	0.143399i	$0.954197\pi$
$258$	−364.337	+	2300.33i	−0.0879171	+	0.555087i
$259$	2837.66	+	2956.70i	0.680786	+	0.709345i
$260$	−1571.13	+	5706.28i	−0.374759	+	1.36111i
$261$	769.296	−	163.519i	0.182445	−	0.0387799i
$262$	−1239.94	−	1909.34i	−0.292381	−	0.450227i
$263$	−155.455	−	239.379i	−0.0364477	−	0.0561246i	0.819977	−	0.572396i	$-0.193986\pi$
$263$	−155.455	−	239.379i	−0.0364477	−	0.0561246i	−0.856425	+	0.516272i	$0.827319\pi$
$264$	−3656.91	+	777.300i	−0.852527	+	0.181210i
$265$	4553.51	+	3001.80i	1.05555	+	0.695846i
$266$	441.265	−	1521.13i	0.101713	−	0.350626i
$267$	309.924	−	1956.79i	0.0710377	−	0.448514i
$268$	459.821	−	1716.07i	0.104806	−	0.391142i
$269$	161.838	+	1539.79i	0.0366820	+	0.349006i	0.997434	+	0.0715961i	$0.0228092\pi$
$269$	161.838	+	1539.79i	0.0366820	+	0.349006i	−0.960752	+	0.277410i	$0.910524\pi$
$270$	−2286.19	+	6874.95i	−0.515308	+	1.54962i
$271$	−3701.27	−	389.019i	−0.829653	−	0.0872001i	−0.319825	−	0.947477i	$-0.603624\pi$
$271$	−3701.27	−	389.019i	−0.829653	−	0.0872001i	−0.509828	+	0.860276i	$0.670291\pi$
$272$	−178.693	−	1128.22i	−0.0398340	−	0.251502i
$273$	−528.795	+	4199.44i	−0.117231	+	0.930996i
$274$		−	2501.98i		−	0.551643i
$275$	−1995.55	−	6441.78i	−0.437585	−	1.41256i
$276$	2652.21	+	1531.25i	0.578421	+	0.333952i
$277$	−1053.72	−	55.2231i	−0.228563	−	0.0119785i	−0.0622891	−	0.998058i	$-0.519840\pi$
$277$	−1053.72	−	55.2231i	−0.228563	−	0.0119785i	−0.166273	+	0.986080i	$0.553173\pi$
$278$	−6256.26	−	7725.83i	−1.34973	−	1.66678i
$279$	−940.877	−	683.587i	−0.201895	−	0.146686i
$280$	2785.80	−	982.625i	0.594584	−	0.209725i
$281$	−865.847	+	629.074i	−0.183815	+	0.133550i	−0.675888	−	0.737005i	$-0.736240\pi$
$281$	−865.847	+	629.074i	−0.183815	+	0.133550i	0.492072	+	0.870554i	$0.336240\pi$
$282$	8507.74	+	2279.64i	1.79656	+	0.481386i
$283$	4551.69	+	3685.89i	0.956077	+	0.774216i	0.974216	−	0.225619i	$-0.0724405\pi$
$283$	4551.69	+	3685.89i	0.956077	+	0.774216i	−0.0181382	+	0.999835i	$0.505774\pi$
$284$	−994.192	+	4677.30i	−0.207727	+	0.977278i
$285$	−891.678	+	570.383i	−0.185328	+	0.118549i
$286$	−10592.3	−	3441.64i	−2.18998	−	0.711567i
$287$	4664.36	−	7708.77i	0.959332	−	1.58549i
$288$	−362.449	+	711.345i	−0.0741579	+	0.145543i
$289$	660.547	+	3107.63i	0.134449	+	0.632532i
$290$	1695.20	+	11201.1i	0.343261	+	2.26810i
$291$	3574.13	+	759.704i	0.719996	+	0.153040i
$292$	−1683.79	−	4386.41i	−0.337453	−	0.879094i
$293$	2157.44	−	2157.44i	0.430168	−	0.430168i	−0.458517	−	0.888685i	$-0.651619\pi$
$293$	2157.44	−	2157.44i	0.430168	−	0.430168i	0.888685	+	0.458517i	$0.151619\pi$
$294$	6475.61	−	3392.01i	1.28458	−	0.672878i
$295$	−8542.16	−	3873.81i	−1.68591	−	0.764550i
$296$	−329.975	+	3139.50i	−0.0647953	+	0.616486i
$297$	−7438.82	−	2855.50i	−1.45335	−	0.557888i
$298$	457.402	−	8727.75i	0.0889147	−	1.69659i
$299$	1318.23	+	2283.24i	0.254967	+	0.441616i
$300$	−6343.59	−	2535.71i	−1.22082	−	0.487998i
$301$	2018.49	+	147.411i	0.386524	+	0.0282281i
$302$	363.660	+	713.723i	0.0692924	+	0.135994i
$303$	−531.128	+	430.099i	−0.100701	+	0.0815464i
$304$	−488.169	+	217.347i	−0.0921000	+	0.0410056i
$305$	−2.31697	+	336.940i	−0.000434982	+	0.0632562i
$306$	−253.228	+	568.760i	−0.0473075	+	0.106254i
$307$	5112.51	+	5112.51i	0.950444	+	0.950444i	0.998829	−	0.0483844i	$-0.0154073\pi$
$307$	5112.51	+	5112.51i	0.950444	+	0.950444i	−0.0483844	+	0.998829i	$0.515407\pi$
$308$	3253.68	+	10761.0i	0.601934	+	1.99080i
$309$	−1197.88	+	389.214i	−0.220534	+	0.0716557i
$310$	10631.6	−	12945.8i	1.94785	−	2.37185i
$311$	2830.60	−	2548.68i	0.516104	−	0.464702i	−0.369442	−	0.929254i	$-0.620451\pi$
$311$	2830.60	−	2548.68i	0.516104	−	0.464702i	0.885546	+	0.464551i	$0.153784\pi$
$312$	−2734.41	+	1775.75i	−0.496171	+	0.322217i
$313$	−153.845	−	2935.54i	−0.0277823	−	0.530117i	−0.976702	−	0.214600i	$-0.931155\pi$
$313$	−153.845	−	2935.54i	−0.0277823	−	0.530117i	0.948920	−	0.315517i	$-0.102178\pi$
$314$	−338.180	+	1040.81i	−0.0607790	+	0.187058i
$315$	685.493	+	165.470i	0.122613	+	0.0295974i
$316$	316.918	+	975.374i	0.0564179	+	0.173636i
$317$	−4854.63	+	1863.52i	−0.860136	+	0.330175i	−0.748146	−	0.663534i	$-0.769056\pi$
$317$	−4854.63	+	1863.52i	−0.860136	+	0.330175i	−0.111990	+	0.993709i	$0.535723\pi$
$318$	2690.83	+	10042.3i	0.474510	+	1.77089i
$319$	−12390.8	+	1302.32i	−2.17477	+	0.228577i
$320$	−7804.11	−	4577.54i	−1.36332	−	0.799664i
$321$	866.030	−	1191.99i	0.150583	−	0.207260i
$322$	1937.12	−	4120.89i	0.335252	−	0.713193i
$323$	−723.571	+	368.678i	−0.124646	+	0.0635102i
$324$	−6094.41	+	3518.61i	−1.04500	+	0.603328i
$325$	−3637.96	−	4621.03i	−0.620916	−	0.788703i
$326$	6280.41	−	10878.0i	1.06699	−	1.84809i
$327$	2131.97	+	1384.52i	0.360545	+	0.234141i
$328$	6855.08	−	1085.74i	1.15399	−	0.182774i
$329$	1352.35	−	7533.46i	0.226619	−	1.26241i
$330$	5309.39	−	11707.7i	0.885674	−	1.95300i
$331$	2084.89	+	928.255i	0.346212	+	0.154143i	0.572474	−	0.819923i	$-0.305984\pi$
$331$	2084.89	+	928.255i	0.346212	+	0.154143i	−0.226262	+	0.974067i	$0.572650\pi$
$332$	5945.93	−	1593.21i	0.982907	−	0.263369i
$333$	−474.249	+	585.648i	−0.0780440	+	0.0963764i
$334$	6936.81	−	7704.11i	1.13642	−	1.26213i
$335$	1101.53	+	1379.57i	0.179651	+	0.224996i
$336$	−2283.92	−	930.976i	−0.370827	−	0.151157i
$337$	−7522.65	−	3832.98i	−1.21598	−	0.619572i	−0.276116	−	0.961124i	$-0.589048\pi$
$337$	−7522.65	−	3832.98i	−1.21598	−	0.619572i	−0.939863	+	0.341552i	$0.889048\pi$
$338$	−73.0485	+	3.82831i	−0.0117554	+	0.000616072i
$339$	896.688	+	995.873i	0.143662	+	0.159553i
$340$	−4653.48	−	2411.52i	−0.742266	−	0.384656i
$341$	13691.3	+	12327.7i	2.17426	+	1.95772i
$342$	287.663	+	45.5613i	0.0454825	+	0.00720372i
$343$	−3410.29	−	5359.43i	−0.536847	−	0.843680i
$344$	916.357	+	1261.26i	0.143624	+	0.197681i
$345$	−2788.50	+	1218.61i	−0.435153	+	0.190168i
$346$	1640.39	+	3684.37i	0.254878	+	0.572466i
$347$	1079.90	−	2813.23i	0.167066	−	0.435222i	−0.824332	−	0.566107i	$-0.808449\pi$
$347$	1079.90	−	2813.23i	0.167066	−	0.435222i	0.991397	+	0.130886i	$0.0417821\pi$
$348$	−6874.04	+	10585.1i	−1.05887	+	1.63052i
$349$	628.570			0.0964086			0.0482043	−	0.998837i	$-0.484650\pi$
$349$	628.570			0.0964086			0.0482043	+	0.998837i	$0.484650\pi$
$350$	−2963.83	+	9715.53i	−0.452638	+	1.48376i
$351$	−6948.88			−1.05671
$352$	6888.16	−	10606.8i	1.04301	−	1.60610i
$353$	−1919.14	+	4999.53i	−0.289364	+	0.753818i	0.709433	+	0.704773i	$0.248951\pi$
$353$	−1919.14	+	4999.53i	−0.289364	+	0.753818i	−0.998797	+	0.0490453i	$0.984382\pi$
$354$	−7272.33	−	16333.9i	−1.09186	−	2.45237i
$355$	−3155.06	−	3552.88i	−0.471700	−	0.531176i
$356$	−2697.41	−	3712.67i	−0.401580	−	0.552728i
$357$	−3540.18	−	1231.22i	−0.524835	−	0.182530i
$358$	−14401.4	−	2280.96i	−2.12609	−	0.336739i
$359$	4323.39	+	3892.79i	0.635598	+	0.572295i	0.922659	−	0.385618i	$-0.126012\pi$
$359$	4323.39	+	3892.79i	0.635598	+	0.572295i	−0.287061	+	0.957912i	$0.592678\pi$
$360$	243.277	+	485.686i	0.0356162	+	0.0711052i
$361$	−4335.37	−	4814.91i	−0.632070	−	0.701985i
$362$	−4807.18	+	251.934i	−0.697955	+	0.0365783i
$363$	6836.64	+	3483.44i	0.988514	+	0.503673i
$364$	6012.19	+	7744.43i	0.865727	+	1.11516i
$365$	4501.28	+	1239.35i	0.645501	+	0.177728i
$366$	−429.788	+	477.328i	−0.0613809	+	0.0681704i
$367$	−2391.49	+	2953.25i	−0.340149	+	0.420049i	−0.918303	−	0.395879i	$-0.870440\pi$
$367$	−2391.49	+	2953.25i	−0.340149	+	0.420049i	0.578154	+	0.815928i	$0.303773\pi$
$368$	−1483.94	+	397.619i	−0.210205	+	0.0563243i
$369$	1513.60	+	673.897i	0.213536	+	0.0950723i
$370$	−8016.56	−	7318.58i	−1.12638	−	1.02831i
$371$	8499.09	−	3063.73i	1.18935	−	0.428735i
$372$	18433.6	−	2919.59i	2.56918	−	0.406918i
$373$	9234.65	+	5997.05i	1.28191	+	0.832481i	0.992203	−	0.124634i	$-0.0397758\pi$
$373$	9234.65	+	5997.05i	1.28191	+	0.832481i	0.289706	+	0.957116i	$0.406442\pi$
$374$	4931.33	−	8541.31i	0.681799	−	1.18091i
$375$	5768.31	−	3579.02i	0.794331	−	0.492852i
$376$	5105.95	−	2947.92i	0.700317	−	0.404328i
$377$	−9681.16	+	4932.80i	−1.32256	+	0.673878i
$378$	6853.41	+	9852.30i	0.932544	+	1.34060i
$379$	−6220.69	+	8562.05i	−0.843102	+	1.16043i	0.142239	+	0.989832i	$0.454570\pi$
$379$	−6220.69	+	8562.05i	−0.843102	+	1.16043i	−0.985341	+	0.170598i	$0.945430\pi$
$380$	−526.251	+	2394.72i	−0.0710424	+	0.323281i
$381$	13382.8	−	1406.59i	1.79954	−	0.189139i
$382$	5238.17	+	19549.1i	0.701592	+	2.61838i
$383$	7784.40	−	2988.15i	1.03855	−	0.398662i	0.221458	−	0.975170i	$-0.428919\pi$
$383$	7784.40	−	2988.15i	1.03855	−	0.398662i	0.817091	+	0.576508i	$0.195585\pi$
$384$	−2514.60	−	7739.15i	−0.334174	−	1.02848i
$385$	−10525.7	−	3742.02i	−1.39335	−	0.495354i
$386$	−2987.07	+	9193.26i	−0.393880	+	1.21224i
$387$	19.4775	+	371.653i	0.00255839	+	0.0488171i
$388$	7098.42	−	4609.77i	0.928783	−	0.603159i
$389$	−9518.79	+	8570.76i	−1.24067	+	1.11711i	−0.251889	+	0.967756i	$0.581052\pi$
$389$	−9518.79	+	8570.76i	−1.24067	+	1.11711i	−0.988784	+	0.149351i	$0.952282\pi$
$390$	663.715	−	11191.4i	0.0861756	−	1.45308i
$391$	−2220.43	+	721.463i	−0.287192	+	0.0933144i
$392$	1459.55	−	4670.60i	0.188057	−	0.601788i
$393$	1782.17	+	1782.17i	0.228749	+	0.228749i
$394$	−6301.25	+	14152.8i	−0.805716	+	1.80967i
$395$	−967.020	−	321.572i	−0.123180	−	0.0409621i
$396$	−1888.57	+	840.845i	−0.239657	+	0.106702i
$397$	1017.53	−	823.979i	0.128636	−	0.104167i	−0.562844	−	0.826563i	$-0.690293\pi$
$397$	1017.53	−	823.979i	0.128636	−	0.104167i	0.691479	+	0.722396i	$0.256959\pi$
$398$	5492.67	+	10780.0i	0.691765	+	1.35767i
$399$	−127.712	+	1748.75i	−0.0160241	+	0.219416i
$400$	3149.62	−	1350.71i	0.393702	−	0.168839i
$401$	−2479.92	−	4295.34i	−0.308831	−	0.534910i	0.669276	−	0.743014i	$-0.266604\pi$
$401$	−2479.92	−	4295.34i	−0.308831	−	0.534910i	−0.978107	+	0.208103i	$0.933271\pi$
$402$	−176.124	+	3360.65i	−0.0218515	+	0.416951i
$403$	14999.8	+	5757.87i	1.85407	+	0.711712i
$404$	−165.477	+	1574.40i	−0.0203781	+	0.193885i
$405$	778.744	−	6949.24i	0.0955459	−	0.852618i
$406$	16542.0	+	8861.17i	2.02208	+	1.08318i
$407$	8441.40	−	8441.40i	1.02807	−	1.02807i
$408$	−1034.69	−	2695.47i	−0.125552	−	0.327073i
$409$	4337.34	+	921.930i	0.524371	+	0.111458i	0.462489	−	0.886625i	$-0.346956\pi$
$409$	4337.34	+	921.930i	0.524371	+	0.111458i	0.0618819	+	0.998083i	$0.480290\pi$
$410$	−10980.6	+	21189.2i	−1.32267	+	2.55234i
$411$	575.884	+	2709.32i	0.0691150	+	0.325160i
$412$	−1324.52	+	2599.51i	−0.158384	+	0.310847i
$413$	−13612.3	+	7490.56i	−1.62183	+	0.892461i
$414$	796.345	+	258.748i	0.0945368	+	0.0307169i
$415$	−2231.27	+	5695.28i	−0.263924	+	0.673664i
$416$	2293.17	−	10788.5i	0.270269	−	1.27151i
$417$	8552.98	+	6926.07i	1.00442	+	0.813360i
$418$	−4456.59	−	1194.14i	−0.521480	−	0.139730i
$419$	12773.8	−	9280.68i	1.48935	−	1.08208i	0.514963	−	0.857213i	$-0.327806\pi$
$419$	12773.8	−	9280.68i	1.48935	−	1.08208i	0.974390	−	0.224865i	$-0.0721943\pi$
$420$	−9656.28	+	5900.95i	−1.12185	+	0.685564i
$421$	−11656.0	−	8468.58i	−1.34936	−	0.980364i	−0.999043	−	0.0437307i	$-0.986076\pi$
$421$	−11656.0	−	8468.58i	−1.34936	−	0.980364i	−0.350312	−	0.936633i	$-0.613924\pi$
$422$	−4262.75	−	5264.05i	−0.491723	−	0.607228i
$423$	1405.52	+	73.6603i	0.161558	+	0.00846688i
$424$	6026.92	+	3479.65i	0.690314	+	0.398553i
$425$	4672.51	−	2300.38i	0.533294	−	0.262552i
$426$		−	9057.70i		−	1.03016i
$427$	444.723	+	337.281i	0.0504020	+	0.0382252i
$428$	−533.890	−	3370.85i	−0.0602957	−	0.380692i
$429$	12262.2	+	1288.81i	1.38001	+	0.145045i
$430$	−5360.57	−	36.8620i	−0.601185	−	0.00413406i
$431$	−861.817	−	8199.64i	−0.0963161	−	0.916387i	−0.930843	−	0.365419i	$-0.880926\pi$
$431$	−861.817	−	8199.64i	−0.0963161	−	0.916387i	0.834527	−	0.550967i	$-0.185741\pi$
$432$	1048.00	−	3911.19i	0.116718	−	0.435596i
$433$	−1888.48	+	11923.4i	−0.209595	+	1.32333i	0.628503	+	0.777807i	$0.283668\pi$
$433$	−1888.48	+	11923.4i	−0.209595	+	1.32333i	−0.838097	+	0.545521i	$0.816332\pi$
$434$	−6630.04	−	26945.8i	−0.733299	−	2.98028i
$435$	−4413.85	−	11739.1i	−0.486501	−	1.29390i
$436$	5759.69	−	1224.26i	0.632659	−	0.134476i
$437$	594.847	+	915.984i	0.0651153	+	0.100269i
$438$	4847.23	+	7464.08i	0.528789	+	0.814264i
$439$	9386.52	−	1995.17i	1.02049	−	0.216911i	0.332861	−	0.942976i	$-0.391986\pi$
$439$	9386.52	−	1995.17i	1.02049	−	0.216911i	0.687627	+	0.726065i	$0.258653\pi$
$440$	−3028.51	−	8054.66i	−0.328133	−	0.872706i
$441$	899.464	−	745.322i	0.0971238	−	0.0804797i
$442$	1345.52	−	8495.25i	0.144796	−	0.914203i
$443$	130.102	−	485.548i	0.0139534	−	0.0520747i	−0.958598	−	0.284762i	$-0.908085\pi$
$443$	130.102	−	485.548i	0.0139534	−	0.0520747i	0.972552	+	0.232688i	$0.0747520\pi$
$444$	−1264.10	−	12027.2i	−0.135117	−	1.28555i
$445$	4559.99	+	31.3568i	0.485763	+	0.00334035i
$446$	6302.23	+	662.392i	0.669102	+	0.0703254i
$447$	1513.57	+	9556.31i	0.160155	+	1.01118i
$448$	−13813.9	+	5813.37i	−1.45680	+	0.613071i
$449$			794.129i			0.0834683i	0.999129	+	0.0417342i	$0.0132883\pi$
$449$			794.129i			0.0834683i	−0.999129	+	0.0417342i	$0.986712\pi$
$450$	−1840.66	−	317.539i	−0.192821	−	0.0332643i
$451$	−22730.3	−	13123.4i	−2.37324	−	1.37019i
$452$	3099.85	+	162.456i	0.322576	+	0.0169055i
$453$	−558.076	−	689.166i	−0.0578823	−	0.0714787i
$454$	−5935.27	−	4312.22i	−0.613559	−	0.445777i
$455$	−9739.21	+	242.968i	−1.00347	+	0.0250341i
$456$	−1092.71	+	793.902i	−0.112217	+	0.0815304i
$457$	11326.6	+	3034.95i	1.15938	+	0.310654i	0.786717	−	0.617314i	$-0.211779\pi$
$457$	11326.6	+	3034.95i	1.15938	+	0.310654i	0.372659	+	0.927968i	$0.378446\pi$
$458$	3492.72	+	2828.35i	0.356341	+	0.288559i
$459$	1279.40	−	6019.08i	0.130103	−	0.612084i
$460$	−2571.33	+	6563.29i	−0.260628	+	0.665250i
$461$	5342.12	+	1735.76i	0.539712	+	0.175363i	0.566172	−	0.824287i	$-0.308424\pi$
$461$	5342.12	+	1735.76i	0.539712	+	0.175363i	−0.0264605	+	0.999650i	$0.508424\pi$
$462$	−10266.5	−	18656.8i	−1.03385	−	1.87877i
$463$	−689.404	+	1353.03i	−0.0691994	+	0.135811i	−0.923015	−	0.384764i	$-0.874283\pi$
$463$	−689.404	+	1353.03i	−0.0691994	+	0.135811i	0.853815	+	0.520576i	$0.174283\pi$
$464$	−1316.36	−	6193.01i	−0.131704	−	0.619619i
$465$	−8532.84	+	16465.7i	−0.850970	+	1.64211i
$466$	17567.0	+	3733.99i	1.74630	+	0.371188i
$467$	−2290.82	−	5967.78i	−0.226994	−	0.591341i	0.772026	−	0.635591i	$-0.219243\pi$
$467$	−2290.82	−	5967.78i	−0.226994	−	0.591341i	−0.999020	+	0.0442502i	$0.985910\pi$
$468$	−1274.82	+	1274.82i	−0.125916	+	0.125916i
$469$	2922.88	−	93.0334i	0.287774	−	0.00915967i
$470$	−2257.71	+	20147.1i	−0.221576	+	1.97726i
$471$	126.640	−	1204.90i	0.0123891	−	0.117875i
$472$	−11173.5	−	4289.09i	−1.08962	−	0.418265i
$473$	308.552	−	5887.53i	0.0299942	−	0.572323i
$474$	−971.319	−	1682.37i	−0.0941227	−	0.163025i
$475$	−1605.19	−	1832.82i	−0.155055	−	0.177043i
$476$	−7815.12	+	3781.86i	−0.752532	+	0.364162i
$477$	754.222	+	1480.24i	0.0723972	+	0.142088i
$478$	−16085.3	+	13025.6i	−1.53917	+	1.24639i
$479$	13122.4	−	5842.46i	1.25173	−	0.557304i	0.329573	−	0.944130i	$-0.393095\pi$
$479$	13122.4	−	5842.46i	1.25173	−	0.557304i	0.922153	+	0.386826i	$0.126429\pi$
$480$	12080.5	+	4017.23i	1.14874	+	0.382002i
$481$	4234.53	−	9510.91i	0.401409	−	0.901580i
$482$	11080.2	+	11080.2i	1.04707	+	1.04707i
$483$	−1149.14	+	4908.26i	−0.108256	+	0.462388i
$484$	16903.4	−	5492.24i	1.58747	−	0.515800i
$485$	−497.909	+	8395.64i	−0.0466163	+	0.786034i
$486$	−3096.44	+	2788.05i	−0.289007	+	0.260223i
$487$	−12193.7	+	7918.71i	−1.13460	+	0.736819i	−0.968432	−	0.249278i	$-0.919807\pi$
$487$	−12193.7	+	7918.71i	−1.13460	+	0.736819i	−0.166170	+	0.986097i	$0.553140\pi$
$488$	22.5019	+	429.362i	0.00208732	+	0.0398285i
$489$	−4297.07	+	13225.0i	−0.397383	+	1.22302i
$490$	9949.89	+	13568.9i	0.917327	+	1.25098i
$491$	6014.06	+	18509.4i	0.552771	+	1.70125i	0.701758	+	0.712415i	$0.252399\pi$
$491$	6014.06	+	18509.4i	0.552771	+	1.70125i	−0.148987	+	0.988839i	$0.547601\pi$
$492$	−24822.5	+	9528.48i	−2.27457	+	0.873124i
$493$	−2490.31	−	9293.97i	−0.227501	−	0.849045i
$494$	−4001.62	+	420.587i	−0.364456	+	0.0383059i
$495$	440.904	−	2006.35i	0.0400347	−	0.182179i
$496$	−5503.03	+	7574.28i	−0.498172	+	0.685675i
$497$	−7843.12	+	661.786i	−0.707871	+	0.0597287i
$498$	−10389.2	+	5293.58i	−0.934845	+	0.476327i
$499$	−2923.31	+	1687.77i	−0.262255	+	0.151413i	−0.625363	−	0.780334i	$-0.715049\pi$
$499$	−2923.31	+	1687.77i	−0.262255	+	0.151413i	0.363108	+	0.931747i	$0.381716\pi$
$500$	3585.86	−	15310.1i	0.320729	−	1.36938i
$501$	−5738.41	+	9939.21i	−0.511723	+	0.886330i
$502$	4562.16	+	2962.70i	0.405616	+	0.263410i
$503$	7669.38	−	1214.71i	0.679842	−	0.107676i	0.193043	−	0.981190i	$-0.438164\pi$
$503$	7669.38	−	1214.71i	0.679842	−	0.107676i	0.486799	+	0.873514i	$0.338164\pi$
$504$	885.667	+	158.988i	0.0782753	+	0.0140514i
$505$	−1161.75	−	1060.60i	−0.102371	−	0.0934578i
$506$	−12117.7	−	5395.15i	−1.06462	−	0.473999i
$507$	78.2209	−	20.9592i	0.00685189	−	0.00183596i
$508$	19616.0	−	24223.8i	1.71323	−	2.11566i
$509$	−10113.1	+	11231.8i	−0.880663	+	0.978075i	−0.999891	−	0.0147918i	$-0.995291\pi$
$509$	−10113.1	+	11231.8i	−0.880663	+	0.978075i	0.119228	+	0.992867i	$0.461958\pi$
$510$	9571.75	+	2635.42i	0.831067	+	0.228820i
$511$	6109.03	−	4742.59i	0.528860	−	0.410567i
$512$	8514.47	+	4338.34i	0.734942	+	0.374471i
$513$	−2874.72	+	150.658i	−0.247411	+	0.0129663i
$514$	−9547.55	−	10603.6i	−0.819308	−	0.909934i
$515$	−1298.35	−	2592.07i	−0.111092	−	0.221787i
$516$	−4438.35	−	3996.31i	−0.378658	−	0.340945i
$517$	−22021.6	−	3487.88i	−1.87332	−	0.296705i
$518$	−17661.2	+	3376.42i	−1.49804	+	0.286393i
$519$	−2624.37	−	3612.13i	−0.221959	−	0.305501i
$520$	−4983.04	−	5611.34i	−0.420232	−	0.473219i
$521$	4577.51	+	10281.3i	0.384922	+	0.864549i	0.997262	+	0.0739539i	$0.0235618\pi$
$521$	4577.51	+	10281.3i	0.384922	+	0.864549i	−0.612340	+	0.790595i	$0.709772\pi$
$522$	−1236.66	+	3221.61i	−0.103692	+	0.270126i
$523$	6345.75	−	9771.60i	0.530555	−	0.816983i	−0.467186	−	0.884159i	$-0.654732\pi$
$523$	6345.75	−	9771.60i	0.530555	−	0.816983i	0.997741	+	0.0671760i	$0.0213989\pi$
$524$	5838.07			0.486712
$525$	973.208	−	11202.9i	0.0809034	−	0.931300i
$526$	1252.35			0.103812
$527$	−7749.12	+	11932.6i	−0.640526	+	0.986323i
$528$	−2574.75	+	6707.45i	−0.212219	+	0.552849i
$529$	−3671.62	−	8246.59i	−0.301768	−	0.677783i
$530$	−21927.4	+	9582.61i	−1.79711	+	0.785362i
$531$	−1679.35	−	2311.43i	−0.137246	−	0.188903i
$532$	2655.12	+	3073.48i	0.216380	+	0.250474i
$533$	−22607.8	−	3580.72i	−1.83724	−	0.290991i
$534$	6459.95	+	5816.56i	0.523500	+	0.471362i
$535$	3011.01	+	1560.36i	0.243322	+	0.126094i
$536$	1507.32	+	1674.05i	0.121467	+	0.134903i
$537$	16119.9	−	844.809i	1.29539	−	0.0678886i
$538$	−6052.84	−	3084.08i	−0.485049	−	0.247145i
$539$	−15404.9	+	10252.9i	−1.23105	+	0.819339i
$540$	−11592.6	−	14518.7i	−0.923825	−	1.15701i
$541$	−16301.9	+	18105.1i	−1.29551	+	1.43881i	−0.461429	+	0.887177i	$0.652663\pi$
$541$	−16301.9	+	18105.1i	−1.29551	+	1.43881i	−0.834085	+	0.551637i	$0.814004\pi$
$542$	10276.4	−	12690.3i	0.814406	−	1.00571i
$543$	5147.56	−	1379.29i	0.406820	−	0.109007i
$544$	8922.74	+	3972.66i	0.703234	+	0.313100i
$545$	−2416.57	+	5328.80i	−0.189935	+	0.418827i
$546$	−14189.4	−	11981.2i	−1.11218	−	0.939099i
$547$	−2054.87	+	325.459i	−0.160621	+	0.0254399i	−0.236227	−	0.971698i	$-0.575911\pi$
$547$	−2054.87	+	325.459i	−0.160621	+	0.0254399i	0.0756058	+	0.997138i	$0.475911\pi$
$548$	5380.87	+	3494.38i	0.419451	+	0.272395i
$549$	−51.3188	+	88.8869i	−0.00398950	+	0.00691002i
$550$	28473.1	+	8050.63i	2.20745	+	0.624146i
$551$	−3898.10	+	2250.57i	−0.301388	+	0.174006i
$552$	−3459.87	+	1762.89i	−0.266779	+	0.135931i
$553$	−1385.81	+	963.990i	−0.106565	+	0.0741284i
$554$	2721.27	−	3745.50i	0.208692	−	0.287240i
$555$	10365.4	+	6079.89i	0.792770	+	0.465004i
$556$	25353.3	−	2664.74i	1.93385	−	0.203256i
$557$	−502.835	−	1876.61i	−0.0382510	−	0.142755i	0.944159	−	0.329489i	$-0.106876\pi$
$557$	−502.835	−	1876.61i	−0.0382510	−	0.142755i	−0.982411	+	0.186734i	$0.940210\pi$
$558$	4763.86	−	1828.67i	0.361416	−	0.138735i
$559$	−1588.82	−	4889.87i	−0.120214	−	0.369981i
$560$	1332.07	−	5518.38i	0.100518	−	0.416418i
$561$	−3374.02	+	10384.2i	−0.253924	+	0.781498i
$562$	−245.762	−	4689.43i	−0.0184464	−	0.351978i
$563$	21346.4	−	13862.5i	1.59794	−	1.03772i	0.633388	−	0.773835i	$-0.281664\pi$
$563$	21346.4	−	13862.5i	1.59794	−	1.03772i	0.964555	−	0.263881i	$-0.0850027\pi$
$564$	−16785.0	+	15113.3i	−1.25315	+	1.12834i
$565$	−1957.56	+	2383.68i	−0.145761	+	0.177491i
$566$	−24440.4	+	7941.17i	−1.81503	+	0.589739i
$567$	−8447.19	−	7926.04i	−0.625659	−	0.587059i
$568$	−4287.25	−	4287.25i	−0.316706	−	0.316706i
$569$	−10261.8	+	23048.5i	−0.756061	+	1.69814i	−0.0409171	+	0.999163i	$0.513028\pi$
$569$	−10261.8	+	23048.5i	−0.756061	+	1.69814i	−0.715144	+	0.698978i	$0.753639\pi$
$570$	31.9361	−	4644.23i	0.00234676	−	0.341272i
$571$	9680.21	−	4309.91i	0.709465	−	0.315874i	−0.0200884	−	0.999798i	$-0.506395\pi$
$571$	9680.21	−	4309.91i	0.709465	−	0.315874i	0.729553	+	0.683924i	$0.239728\pi$
$572$	22195.4	−	17973.5i	1.62244	−	1.31383i
$573$	−10171.9	−	19963.5i	−0.741601	−	1.45547i
$574$	17220.3	+	35585.4i	1.25220	+	2.58764i
$575$	−3733.75	−	5926.33i	−0.270797	−	0.429818i
$576$	−1377.99	−	2386.74i	−0.0996807	−	0.172652i
$577$	684.161	−	13054.6i	0.0493622	−	0.941887i	−0.855928	−	0.517094i	$-0.827014\pi$
$577$	684.161	−	13054.6i	0.0493622	−	0.941887i	0.905291	−	0.424793i	$-0.139653\pi$
$578$	−13013.9	−	4995.58i	−0.936520	−	0.359496i
$579$	1118.59	−	10642.6i	0.0802882	−	0.763891i
$580$	−26457.1	−	11998.1i	−1.89409	−	0.858957i
$581$	5342.81	+	8609.33i	0.381510	+	0.614759i
$582$	−11336.6	+	11336.6i	−0.807417	+	0.807417i
$583$	−9431.42	−	24569.7i	−0.669999	−	1.74541i
$584$	5827.26	+	1238.62i	0.412900	+	0.0877647i
$585$	−268.075	−	1771.30i	−0.0189462	−	0.125187i
$586$	2783.34	+	13094.6i	0.196209	+	0.923091i
$587$	8237.60	−	16167.2i	0.579220	−	1.13678i	−0.396556	−	0.918011i	$-0.629795\pi$
$587$	8237.60	−	16167.2i	0.579220	−	1.13678i	0.975776	−	0.218773i	$-0.0702054\pi$
$588$	−1749.12	+	18664.2i	−0.122674	+	1.30901i
$589$	6330.16	+	2056.80i	0.442835	+	0.143886i
$590$	34667.9	−	22176.2i	2.41908	−	1.54742i
$591$	3565.86	−	16776.1i	0.248189	−	1.16764i
$592$	4714.60	+	3817.81i	0.327312	+	0.265052i
$593$	9519.49	+	2550.74i	0.659222	+	0.176638i	0.572895	−	0.819629i	$-0.305820\pi$
$593$	9519.49	+	2550.74i	0.659222	+	0.176638i	0.0863273	+	0.996267i	$0.472487\pi$
$594$	28284.1	−	20549.6i	1.95372	−	1.41946i
$595$	1582.68	−	8480.78i	0.109048	−	0.584333i
$596$	18131.5	+	13173.3i	1.24613	+	0.905367i
$597$	−8429.09	−	10409.1i	−0.577855	−	0.713592i
$598$	−11552.0	−	605.414i	−0.789960	−	0.0414000i
$599$	−6524.84	−	3767.12i	−0.445071	−	0.256962i	0.260675	−	0.965427i	$-0.416055\pi$
$599$	−6524.84	−	3767.12i	−0.445071	−	0.256962i	−0.705746	+	0.708465i	$0.749388\pi$
$600$	7077.18	−	4994.63i	0.481541	−	0.339841i
$601$			14311.3i			0.971333i	0.874144	+	0.485667i	$0.161423\pi$
$601$			14311.3i			0.971333i	−0.874144	+	0.485667i	$0.838577\pi$
$602$	−5366.00	+	7075.36i	−0.363292	+	0.479020i
$603$	84.1230	+	531.132i	0.00568118	+	0.0358696i
$604$	−2042.87	−	214.714i	−0.137621	−	0.0144646i
$605$	−5572.89	+	16758.6i	−0.374496	+	1.12617i
$606$	−313.446	−	2982.24i	−0.0210114	−	0.199910i
$607$	2263.93	−	8449.11i	0.151384	−	0.564973i	−0.848004	−	0.529990i	$-0.822196\pi$
$607$	2263.93	−	8449.11i	0.151384	−	0.564973i	0.999388	−	0.0349831i	$-0.0111378\pi$
$608$	714.769	−	4512.87i	0.0476771	−	0.301022i
$609$	−19952.4	−	5788.01i	−1.32761	−	0.385126i
$610$	−1234.33	−	813.706i	−0.0819289	−	0.0540099i
$611$	−19019.3	+	4042.69i	−1.25931	+	0.267675i
$612$	−869.530	−	1338.96i	−0.0574325	−	0.0884383i
$613$	−4069.56	−	6266.57i	−0.268137	−	0.412894i	0.678796	−	0.734327i	$-0.262502\pi$
$613$	−4069.56	−	6266.57i	−0.268137	−	0.412894i	−0.946932	+	0.321433i	$0.895836\pi$
$614$	−31030.3	+	6595.69i	−2.03954	+	0.433518i
$615$	7013.44	−	25472.6i	0.459852	−	1.67017i
$616$	−13690.1	−	3971.37i	−0.895440	−	0.259758i
$617$	4196.44	−	26495.3i	0.273812	−	1.72878i	−0.340959	−	0.940078i	$-0.610752\pi$
$617$	4196.44	−	26495.3i	0.273812	−	1.72878i	0.614771	−	0.788705i	$-0.289248\pi$
$618$	1430.32	−	5338.04i	0.0931004	−	0.347456i
$619$	−1427.48	−	13581.5i	−0.0926901	−	0.881888i	−0.937772	−	0.347251i	$-0.887115\pi$
$619$	−1427.48	−	13581.5i	−0.0926901	−	0.881888i	0.845082	−	0.534637i	$-0.179551\pi$
$620$	12993.4	+	40945.4i	0.841657	+	2.65227i
$621$	−8230.69	−	865.081i	−0.531862	−	0.0559010i
$622$	2614.38	+	16506.6i	0.168532	+	1.06407i
$623$	4564.61	−	6018.68i	0.293543	−	0.387052i
$624$			6265.68i			0.401968i
$625$	10131.9	+	11894.8i	0.648439	+	0.761266i
$626$	11169.8	+	6448.90i	0.713157	+	0.411741i
$627$	5100.76	+	267.320i	0.324888	+	0.0170267i
$628$	−1766.10	−	2180.95i	−0.112221	−	0.138582i
$629$	7458.65	+	5419.03i	0.472808	+	0.343515i
$630$	−2247.01	+	2127.05i	−0.142100	+	0.134514i
$631$	−5365.34	+	3898.14i	−0.338495	+	0.245931i	−0.744027	−	0.668150i	$-0.767087\pi$
$631$	−5365.34	+	3898.14i	−0.338495	+	0.245931i	0.405531	+	0.914081i	$0.367087\pi$
$632$	−1256.06	−	336.561i	−0.0790561	−	0.0211830i
$633$	5827.64	+	4719.13i	0.365921	+	0.296317i
$634$	4743.68	−	22317.3i	0.297154	−	1.39800i
$635$	7810.52	+	29972.2i	0.488112	+	1.87308i
$636$	−25355.6	−	8238.52i	−1.58084	−	0.513646i
$637$	−9337.86	+	13162.1i	−0.580816	+	0.818683i
$638$	24817.8	−	48707.6i	1.54004	−	3.02250i
$639$	−300.926	−	1415.75i	−0.0186298	−	0.0876464i
$640$	16746.6	−	8388.29i	1.03433	−	0.518088i
$641$	10437.7	+	2218.59i	0.643155	+	0.136707i	0.517932	−	0.855422i	$-0.326702\pi$
$641$	10437.7	+	2218.59i	0.643155	+	0.136707i	0.125223	+	0.992129i	$0.460035\pi$
$642$	2316.73	+	6035.29i	0.142421	+	0.371019i
$643$	7026.33	−	7026.33i	0.430935	−	0.430935i	−0.458011	−	0.888946i	$-0.651438\pi$
$643$	7026.33	−	7026.33i	0.430935	−	0.430935i	0.888946	+	0.458011i	$0.151438\pi$
$644$	6157.10	+	9921.46i	0.376745	+	0.607081i
$645$	5813.29	−	1193.93i	0.354881	−	0.0728854i
$646$	372.449	−	3543.61i	0.0226839	−	0.215823i
$647$	−3502.44	−	1344.46i	−0.212821	−	0.0816943i	0.249622	−	0.968343i	$-0.419694\pi$
$647$	−3502.44	−	1344.46i	−0.212821	−	0.0816943i	−0.462443	+	0.886649i	$0.653027\pi$
$648$	466.986	−	8910.62i	0.0283101	−	0.540189i
$649$	22630.2	+	39196.7i	1.36874	+	2.37073i
$650$	25698.0	−	2344.14i	1.55070	−	0.141453i
$651$	13381.6	+	27652.8i	0.805633	+	1.66482i
$652$	14623.2	+	28699.6i	0.878357	+	1.72387i
$653$	−1627.13	+	1317.63i	−0.0975110	+	0.0789629i	−0.676836	−	0.736134i	$-0.736649\pi$
$653$	−1627.13	+	1317.63i	−0.0975110	+	0.0789629i	0.579325	+	0.815097i	$0.303316\pi$
$654$	−10189.5	+	4536.65i	−0.609236	+	0.271249i
$655$	−3442.03	+	4669.68i	−0.205330	+	0.278564i
$656$	5425.03	−	12184.8i	0.322884	−	0.725209i
$657$	1005.62	+	1005.62i	0.0597152	+	0.0597152i
$658$	24489.9	+	22979.0i	1.45093	+	1.36142i
$659$	−7212.76	+	2343.57i	−0.426357	+	0.138532i	−0.514333	−	0.857591i	$-0.671960\pi$
$659$	−7212.76	+	2343.57i	−0.426357	+	0.138532i	0.0879754	+	0.996123i	$0.471960\pi$
$660$	17763.9	+	27770.2i	1.04766	+	1.63781i
$661$	16058.0	−	14458.7i	0.944909	−	0.850800i	−0.0440439	−	0.999030i	$-0.514024\pi$
$661$	16058.0	−	14458.7i	0.944909	−	0.850800i	0.988953	+	0.148230i	$0.0473575\pi$
$662$	−8398.03	+	5453.74i	−0.493049	+	0.320190i
$663$	498.343	+	9508.95i	0.0291916	+	0.557009i
$664$	−2411.91	+	7423.08i	−0.140964	+	0.433843i
$665$	−4023.79	+	311.669i	−0.234641	+	0.0181744i
$666$	−1021.76	−	3144.65i	−0.0594480	−	0.182962i
$667$	−12081.1	+	4637.49i	−0.701321	+	0.269212i
$668$	6880.54	+	25678.5i	0.398527	+	1.48732i
$669$	−6976.97	+	733.309i	−0.403207	+	0.0423787i
$670$	−7708.82	+	756.673i	−0.444504	+	0.0436311i
$671$	955.698	−	1315.41i	0.0549841	−	0.0756791i
$672$	17312.2	−	12042.6i	0.993798	−	0.691301i
$673$	9734.36	−	4959.90i	0.557551	−	0.284086i	−0.152422	−	0.988316i	$-0.548707\pi$
$673$	9734.36	−	4959.90i	0.557551	−	0.284086i	0.709973	+	0.704229i	$0.248707\pi$
$674$	32081.4	−	18522.2i	1.83342	−	1.05853i
$675$	18447.8	−	712.569i	1.05193	−	0.0406323i
$676$	93.7894	−	162.448i	0.00533622	−	0.00924261i
$677$	−6059.93	−	3935.37i	−0.344021	−	0.223410i	0.361050	−	0.932546i	$-0.382418\pi$
$677$	−6059.93	−	3935.37i	−0.344021	−	0.223410i	−0.705071	+	0.709137i	$0.749085\pi$
$678$	−5807.41	+	919.803i	−0.328956	+	0.0521015i
$679$	10644.7	+	8988.13i	0.601629	+	0.508001i
$680$	5777.97	−	3283.15i	0.325846	−	0.185151i
$681$	7419.68	+	3303.45i	0.417508	+	0.185886i
$682$	−78081.1	+	20921.8i	−4.38399	+	1.17469i
$683$	−5029.36	+	6210.74i	−0.281761	+	0.347946i	−0.898303	−	0.439376i	$-0.855200\pi$
$683$	−5029.36	+	6210.74i	−0.281761	+	0.347946i	0.616542	+	0.787322i	$0.288533\pi$
$684$	−499.749	+	555.027i	−0.0279362	+	0.0310263i
$685$	−5967.51	+	2243.75i	−0.332857	+	0.125152i
$686$	27871.1	+	258.198i	1.55120	+	0.0143703i
$687$	−4433.17	−	2258.81i	−0.246195	−	0.125443i
$688$	2991.89	−	156.799i	0.165792	−	0.00868879i
$689$	−15357.5	−	17056.3i	−0.849165	−	0.943094i
$690$	2179.39	−	13173.2i	0.120243	−	0.726805i
$691$	−2356.45	−	2121.75i	−0.129730	−	0.116809i	0.601712	−	0.798713i	$-0.294486\pi$
$691$	−2356.45	−	2121.75i	−0.129730	−	0.116809i	−0.731442	+	0.681904i	$0.761152\pi$
$692$	−10214.8	−	1617.87i	−0.561140	−	0.0888759i
$693$	−2224.52	−	2575.03i	−0.121937	−	0.141151i
$694$	7771.48	+	10696.5i	0.425074	+	0.585064i
$695$	−12816.4	+	21850.4i	−0.699504	+	1.19256i
$696$	−6509.07	−	14619.6i	−0.354491	−	0.796199i
$697$	7264.04	−	18923.5i	0.394756	−	1.02837i
$698$	−1502.08	+	2313.01i	−0.0814538	+	0.125428i
$699$	−19882.3			−1.07585
$700$	−16755.2	−	19943.3i	−0.904698	−	1.07684i
$701$	22506.1			1.21262			0.606309	−	0.795230i	$-0.292650\pi$
$701$	22506.1			1.21262			0.606309	+	0.795230i	$0.292650\pi$
$702$	16605.6	−	25570.4i	0.892791	−	1.37478i
$703$	1545.60	−	4026.42i	0.0829209	−	0.216016i
$704$	17757.6	+	39884.1i	0.950658	+	2.13521i
$705$	−2192.46	−	22336.3i	−0.117125	−	1.19324i
$706$	−13811.1	−	19009.3i	−0.736242	−	1.01335i
$707$	−2559.44	+	489.308i	−0.136149	+	0.0260287i
$708$	45285.3	+	7172.49i	2.40385	+	0.380733i
$709$	−10609.3	−	9552.70i	−0.561978	−	0.506007i	0.338466	−	0.940979i	$-0.390092\pi$
$709$	−10609.3	−	9552.70i	−0.561978	−	0.506007i	−0.900444	+	0.434971i	$0.856759\pi$
$710$	20613.5	−	3119.71i	1.08959	−	0.164902i
$711$	−207.714	−	230.690i	−0.0109562	−	0.0121681i
$712$	5810.79	−	304.531i	0.305855	−	0.0160292i
$713$	17049.9	+	8687.34i	0.895543	+	0.456302i
$714$	12990.5	−	10084.9i	0.680895	−	0.528595i
$715$	1290.36	+	28350.2i	0.0674917	+	1.48285i
$716$	25019.2	−	27786.7i	1.30588	−	1.45033i
$717$	14420.1	−	17807.4i	0.751087	−	0.927516i
$718$	−24656.2	+	6606.61i	−1.28156	+	0.343394i
$719$	−4385.64	−	1952.61i	−0.227478	−	0.101280i	0.289833	−	0.957077i	$-0.406400\pi$
$719$	−4385.64	−	1952.61i	−0.227478	−	0.101280i	−0.517311	+	0.855797i	$0.673067\pi$
$720$	1037.41	+	116.254i	0.0536973	+	0.00601742i
$721$	−4726.74	−	848.510i	−0.244151	−	0.0438283i
$722$	28078.0	−	4447.12i	1.44731	−	0.229231i
$723$	−14548.7	−	9448.05i	−0.748372	−	0.485998i
$724$	6172.10	−	10690.4i	0.316829	−	0.548764i
$725$	25195.6	−	14088.3i	1.29068	−	0.721690i
$726$	−29155.8	+	16833.1i	−1.49046	+	0.860516i
$727$	−22907.1	+	11671.7i	−1.16861	+	0.595434i	−0.927045	−	0.374951i	$-0.877659\pi$
$727$	−22907.1	+	11671.7i	−1.16861	+	0.595434i	−0.241561	+	0.970386i	$0.577659\pi$
$728$	−12387.2	+	1045.21i	−0.630634	+	0.0532116i
$729$	12637.3	−	17393.8i	0.642043	−	0.883696i
$730$	−15317.2	+	13602.1i	−0.776596	+	0.689640i
$731$	4528.11	−	475.923i	0.229108	−	0.0240802i
$732$	−426.302	−	1590.98i	−0.0215254	−	0.0803338i
$733$	12084.0	−	4638.60i	0.608910	−	0.233739i	−0.0343207	−	0.999411i	$-0.510927\pi$
$733$	12084.0	−	4638.60i	0.608910	−	0.233739i	0.643231	+	0.765672i	$0.277593\pi$
$734$	−5152.42	−	15857.5i	−0.259100	−	0.797427i
$735$	−13897.6	−	12403.1i	−0.697444	−	0.622445i
$736$	4059.26	−	12493.1i	0.203297	−	0.625682i
$737$	−445.838	−	8507.10i	−0.0222831	−	0.425188i
$738$	−6096.82	+	3959.32i	−0.304102	+	0.197486i
$739$	−7285.01	+	6559.45i	−0.362630	+	0.326513i	−0.830224	−	0.557430i	$-0.811787\pi$
$739$	−7285.01	+	6559.45i	−0.362630	+	0.326513i	0.467594	+	0.883943i	$0.345121\pi$
$740$	26936.0	−	7019.31i	1.33809	−	0.348696i
$741$	4236.43	−	1376.50i	0.210026	−	0.0682415i
$742$	−9036.26	+	38596.2i	−0.447078	+	1.90958i
$743$	−19882.1	−	19882.1i	−0.981702	−	0.981702i	0.0181335	−	0.999836i	$-0.494228\pi$
$743$	−19882.1	−	19882.1i	−0.981702	−	0.981702i	−0.999836	+	0.0181335i	$0.994228\pi$
$744$	−9625.09	+	21618.3i	−0.474292	+	1.06528i
$745$	−21226.9	+	6736.02i	−1.04388	+	0.331260i
$746$	−44135.8	+	19650.5i	−2.16612	+	0.964419i
$747$	−1448.00	+	1172.57i	−0.0709231	+	0.0574324i
$748$	11482.0	+	22534.7i	0.561262	+	1.10154i
$749$	5056.72	−	2447.03i	0.246687	−	0.119376i
$750$	−614.402	+	29778.9i	−0.0299131	+	1.44983i
$751$	6006.28	+	10403.2i	0.291841	+	0.505483i	0.974245	−	0.225492i	$-0.0723990\pi$
$751$	6006.28	+	10403.2i	0.291841	+	0.505483i	−0.682404	+	0.730975i	$0.739066\pi$
$752$	592.983	−	11314.8i	0.0287551	−	0.548680i
$753$	−5622.16	−	2158.14i	−0.272089	−	0.104445i
$754$	4983.25	−	47412.5i	0.240689	−	2.29000i
$755$	1376.19	−	1507.43i	0.0663371	−	0.0726637i
$756$	−30760.6	+	979.092i	−1.47983	+	0.0471021i
$757$	−7887.16	+	7887.16i	−0.378684	+	0.378684i	−0.870627	−	0.491943i	$-0.836287\pi$
$757$	−7887.16	+	7887.16i	−0.378684	+	0.378684i	0.491943	+	0.870627i	$0.336287\pi$
$758$	−16641.1	−	43351.5i	−0.797402	−	2.07730i
$759$	14363.7	+	3053.10i	0.686916	+	0.146009i
$760$	−2183.12	−	2213.35i	−0.104197	−	0.105640i
$761$	−6700.50	−	31523.4i	−0.319176	−	1.50161i	−0.786539	−	0.617541i	$-0.788129\pi$
$761$	−6700.50	−	31523.4i	−0.319176	−	1.50161i	0.467363	−	0.884066i	$-0.345204\pi$
$762$	−26804.8	+	52607.4i	−1.27433	+	2.50100i
$763$	4672.79	+	8491.66i	0.221712	+	0.402908i
$764$	−49359.0	−	16037.7i	−2.33737	−	0.759456i
$765$	1583.65	+	93.9194i	0.0748458	+	0.00443878i
$766$	−7606.49	+	35785.7i	−0.358791	+	1.68798i
$767$	30674.9	+	24840.1i	1.44408	+	1.16939i
$768$	4112.77	+	1102.01i	0.193238	+	0.0517780i
$769$	275.453	−	200.128i	0.0129169	−	0.00938468i	−0.581308	−	0.813684i	$-0.697459\pi$
$769$	275.453	−	200.128i	0.0129169	−	0.00938468i	0.594225	+	0.804299i	$0.297459\pi$
$770$	38923.0	−	29790.2i	1.82167	−	1.39424i
$771$	12779.4	+	9284.78i	0.596938	+	0.433701i
$772$	−15599.6	−	19263.8i	−0.727254	−	0.898084i
$773$	14604.2	+	765.376i	0.679532	+	0.0356128i	0.388980	−	0.921246i	$-0.372828\pi$
$773$	14604.2	+	765.376i	0.679532	+	0.0356128i	0.290552	+	0.956859i	$0.406161\pi$
$774$	−1414.15	−	816.461i	−0.0656727	−	0.0379161i
$775$	−40411.6	−	13747.8i	−1.87307	−	0.637206i
$776$			10731.8i			0.496455i
$777$	18347.6	−	7721.32i	0.847125	−	0.356500i
$778$	−8791.70	−	55508.6i	−0.405138	−	2.55794i
$779$	−9430.36	−	991.170i	−0.433732	−	0.0455871i
$780$	23141.8	+	17057.9i	1.06232	+	0.783037i
$781$	2396.68	+	22802.9i	0.109808	+	1.04475i
$782$	2651.30	−	9894.80i	0.121241	−	0.452478i
$783$	5335.57	−	33687.4i	0.243522	−	1.53754i
$784$	−6000.02	−	7240.89i	−0.273324	−	0.329851i
$785$	2785.73	−	126.792i	0.126659	−	0.00576485i
$786$	−10816.8	+	2299.19i	−0.490870	+	0.104338i
$787$	3957.05	+	6093.33i	0.179230	+	0.275989i	0.916855	−	0.399221i	$-0.130719\pi$
$787$	3957.05	+	6093.33i	0.179230	+	0.275989i	−0.737625	+	0.675211i	$0.764053\pi$
$788$	−21637.1	−	33318.2i	−0.978160	−	1.50623i
$789$	−1356.14	+	288.256i	−0.0611911	+	0.0130066i
$790$	3494.19	−	2789.98i	0.157364	−	0.125649i
$791$	1220.77	+	4961.46i	0.0548744	+	0.223021i
$792$	410.050	−	2588.96i	0.0183971	−	0.116155i
$793$	366.995	−	1369.65i	0.0164343	−	0.0613336i
$794$	600.497	+	5713.35i	0.0268399	+	0.255364i
$795$	21538.9	−	15423.8i	0.960890	−	0.688082i
$796$	−30855.2	−	3243.01i	−1.37391	−	0.144404i
$797$	−36.2170	−	228.665i	−0.00160963	−	0.0101628i	0.986870	−	0.161514i	$-0.0516376\pi$
$797$	−36.2170	−	228.665i	−0.00160963	−	0.0101628i	−0.988480	+	0.151351i	$0.951638\pi$
$798$	−6129.86	−	4648.93i	−0.271923	−	0.206228i
$799$		−	17218.8i		−	0.762398i
$800$	−4981.57	+	28876.3i	−0.220156	+	1.27617i
$801$	1202.95	+	694.526i	0.0530640	+	0.0306365i
$802$	21732.2	+	1138.93i	0.956845	+	0.0501461i
$803$	−14178.0	−	17508.4i	−0.623077	−	0.769436i
$804$	−6981.59	−	5072.42i	−0.306246	−	0.222501i
$805$	−11566.0	−	924.667i	−0.506394	−	0.0404848i
$806$	−57032.5	+	41436.5i	−2.49241	+	1.81084i
$807$	7264.31	+	1946.47i	0.316872	+	0.0849056i
$808$	−1559.94	−	1263.21i	−0.0679188	−	0.0549995i
$809$	798.436	−	3756.35i	0.0346990	−	0.163246i	−0.957387	−	0.288810i	$-0.906741\pi$
$809$	798.436	−	3756.35i	0.0346990	−	0.163246i	0.992086	+	0.125564i	$0.0400739\pi$
$810$	23710.8	+	19472.1i	1.02853	+	0.844667i
$811$	27715.7	+	9005.39i	1.20004	+	0.389916i	0.839775	−	0.542935i	$-0.182687\pi$
$811$	27715.7	+	9005.39i	1.20004	+	0.389916i	0.360263	+	0.932851i	$0.382687\pi$
$812$	−42160.5	+	23200.1i	−1.82210	+	1.00266i
$813$	−8207.05	+	16107.2i	−0.354039	+	0.694841i
$814$	10890.3	+	51234.9i	0.468925	+	2.20612i
$815$	−31577.5	−	5224.22i	−1.35719	−	0.224535i
$816$	−5427.30	−	1153.61i	−0.232835	−	0.0494906i
$817$	−763.302	−	1988.47i	−0.0326861	−	0.0851502i
$818$	−13757.4	+	13757.4i	−0.588039	+	0.588039i
$819$	−2615.90	−	1401.28i	−0.111608	−	0.0597859i
$820$	−30234.4	−	53209.2i	−1.28760	−	2.26603i
$821$	4741.22	−	45109.6i	0.201546	−	1.91759i	−0.163405	−	0.986559i	$-0.552248\pi$
$821$	4741.22	−	45109.6i	0.201546	−	1.91759i	0.364952	−	0.931026i	$-0.381085\pi$
$822$	−11345.9	−	4355.29i	−0.481428	−	0.184803i
$823$	261.973	−	4998.74i	0.0110957	−	0.211719i	−0.987455	−	0.157901i	$-0.949527\pi$
$823$	261.973	−	4998.74i	0.0110957	−	0.211719i	0.998551	−	0.0538186i	$-0.0171393\pi$
$824$	−1849.62	−	3203.64i	−0.0781975	−	0.135442i
$825$	−32685.8	−	2164.10i	−1.37936	−	0.0913263i
$826$	4965.38	−	67990.5i	0.209162	−	2.86403i
$827$	19744.4	+	38750.5i	0.830204	+	1.62937i	0.775912	+	0.630842i	$0.217290\pi$
$827$	19744.4	+	38750.5i	0.830204	+	1.62937i	0.0542921	+	0.998525i	$0.482710\pi$
$828$	−1668.69	+	1351.28i	−0.0700373	+	0.0567151i
$829$	−20107.1	+	8952.24i	−0.842397	+	0.375059i	−0.782124	−	0.623123i	$-0.785864\pi$
$829$	−20107.1	+	8952.24i	−0.842397	+	0.375059i	−0.0602727	+	0.998182i	$0.519197\pi$
$830$	−15625.4	−	21820.5i	−0.653454	−	0.912532i
$831$	−2084.67	+	4682.25i	−0.0870234	+	0.195458i
$832$	26922.6	+	26922.6i	1.12184	+	1.12184i
$833$	−9681.69	−	10511.7i	−0.402702	−	0.437227i
$834$	−45925.4	+	14922.1i	−1.90680	+	0.619555i
$835$	−24596.1	−	9636.12i	−1.01938	−	0.399367i
$836$	8792.44	−	7916.75i	0.363747	−	0.327520i
$837$	−42298.6	+	27469.0i	−1.74678	+	1.13437i
$838$	3625.71	+	69182.7i	0.149461	+	2.85188i
$839$	4182.49	−	12872.4i	0.172104	−	0.529683i	−0.827385	−	0.561635i	$-0.810173\pi$
$839$	4182.49	−	12872.4i	0.172104	−	0.529683i	0.999489	+	0.0319524i	$0.0101725\pi$
$840$	393.362	−	14343.5i	0.0161575	−	0.589163i
$841$	−8943.57	−	27525.5i	−0.366705	−	1.12860i
$842$	59016.8	−	22654.4i	2.41550	−	0.927224i
$843$	1345.50	+	5021.47i	0.0549721	+	0.205159i
$844$	17274.7	−	1815.64i	0.704524	−	0.0740484i
$845$	74.6402	+	170.796i	0.00303870	+	0.00695332i
$846$	−3629.81	+	4996.01i	−0.147512	+	0.203033i
$847$	16706.1	+	24016.3i	0.677719	+	0.974272i
$848$	11916.3	−	6071.66i	0.482556	−	0.245875i
$849$	24638.0	−	14224.7i	0.995963	−	0.575020i
$850$	−2700.92	+	22691.1i	−0.108989	+	0.915643i
$851$	6199.68	−	10738.2i	0.249732	−	0.432549i
$852$	19479.9	+	12650.4i	0.783299	+	0.508680i
$853$	17380.3	−	2752.77i	0.697644	−	0.110496i	0.202468	−	0.979289i	$-0.435104\pi$
$853$	17380.3	−	2752.77i	0.697644	−	0.110496i	0.495176	+	0.868793i	$0.335104\pi$
$854$	−2303.87	+	830.493i	−0.0923148	+	0.0332774i
$855$	−149.305	−	726.968i	−0.00597205	−	0.0290781i
$856$	3953.23	+	1760.09i	0.157849	+	0.0702788i
$857$	20292.1	−	5437.25i	0.808828	−	0.216725i	0.169372	−	0.985552i	$-0.445826\pi$
$857$	20292.1	−	5437.25i	0.808828	−	0.216725i	0.639456	+	0.768828i	$0.279160\pi$
$858$	−34045.4	+	42042.6i	−1.35465	+	1.67286i
$859$	−21000.3	+	23323.2i	−0.834133	+	0.926399i	−0.998195	−	0.0600514i	$-0.980874\pi$
$859$	−21000.3	+	23323.2i	−0.834133	+	0.926399i	0.164062	+	0.986450i	$0.447540\pi$
$860$	7566.09	−	11477.2i	0.300002	−	0.455081i
$861$	−26838.1	−	34570.8i	−1.06230	−	1.36837i
$862$	32232.4	+	16423.2i	1.27360	+	0.648931i
$863$	−25094.6	+	1315.15i	−0.989837	+	0.0518751i	−0.540375	−	0.841424i	$-0.681718\pi$
$863$	−25094.6	+	1315.15i	−0.989837	+	0.0518751i	−0.449462	+	0.893300i	$0.648384\pi$
$864$	23167.0	+	25729.6i	0.912219	+	1.01312i
$865$	7316.57	−	7216.63i	0.287596	−	0.283668i
$866$	−39362.7	−	35442.3i	−1.54457	−	1.39074i
$867$	15242.3	+	2414.14i	0.597063	+	0.0945656i
$868$	67210.7	+	23374.9i	2.62820	+	0.914050i
$869$	2890.47	+	3978.39i	0.112834	+	0.155302i
$870$	53745.2	+	11810.7i	2.09441	+	0.460255i
$871$	−3021.71	−	6786.88i	−0.117551	−	0.264024i
$872$	−2675.63	+	6970.26i	−0.103909	+	0.270691i
$873$	−1395.31	+	2148.58i	−0.0540938	+	0.0832972i
$874$	−4792.13			−0.185465
$875$	25830.6	−	1643.73i	0.997981	−	0.0635066i
$876$	−22822.4			−0.880250
$877$	14079.8	−	21681.0i	0.542123	−	0.834795i	−0.456364	−	0.889793i	$-0.650848\pi$
$877$	14079.8	−	21681.0i	0.542123	−	0.834795i	0.998486	+	0.0549977i	$0.0175152\pi$
$878$	−15089.0	+	39308.3i	−0.579989	+	1.51092i
$879$	−6027.98	−	13539.1i	−0.231307	−	0.519524i
$880$	−16151.6	−	3549.38i	−0.618716	−	0.135966i
$881$	−3838.35	−	5283.03i	−0.146785	−	0.202032i	0.729293	−	0.684201i	$-0.239849\pi$
$881$	−3838.35	−	5283.03i	−0.146785	−	0.202032i	−0.876078	+	0.482169i	$0.839849\pi$
$882$	593.196	+	5090.93i	0.0226462	+	0.194354i
$883$	−37316.9	−	5910.41i	−1.42221	−	0.225256i	−0.602539	−	0.798090i	$-0.705844\pi$
$883$	−37316.9	−	5910.41i	−1.42221	−	0.225256i	−0.819672	+	0.572833i	$0.805844\pi$
$884$	16391.1	+	14758.6i	0.623632	+	0.561521i
$885$	−32436.5	+	31993.5i	−1.23202	+	1.21520i
$886$	1475.81	+	1639.06i	0.0559604	+	0.0621503i
$887$	42939.0	−	2250.34i	1.62542	−	0.0851849i	0.782300	−	0.622902i	$-0.214047\pi$
$887$	42939.0	−	2250.34i	1.62542	−	0.0851849i	0.843125	+	0.537718i	$0.180713\pi$
$888$	13662.5	+	6961.41i	0.516312	+	0.263074i
$889$	47511.5	+	19366.8i	1.79245	+	0.730642i
$890$	−11012.3	+	16704.9i	−0.414758	+	0.629156i
$891$	−22578.6	+	25076.1i	−0.848947	+	0.942851i
$892$	−10226.6	+	12628.7i	−0.383868	+	0.474038i
$893$	−7780.56	+	2084.79i	−0.291564	+	0.0781243i
$894$	−38782.2	−	17266.9i	−1.45086	−	0.645965i
$895$	7474.73	+	36394.7i	0.279165	+	1.35926i
$896$	5481.99	−	30538.2i	0.204398	−	1.13863i
$897$	12648.7	−	2003.35i	0.470821	−	0.0745707i
$898$	−2922.23	−	1897.72i	−0.108593	−	0.0705208i
$899$	−39430.8	+	68296.2i	−1.46284	+	2.53371i
$900$	3253.66	−	3515.11i	0.120506	−	0.130189i
$901$	17601.6	−	10162.3i	0.650826	−	0.375754i
$902$	102610.	−	52282.2i	3.78772	−	1.92994i
$903$	4182.14	−	8896.79i	0.154123	−	0.327870i
$904$	−2313.43	+	3184.17i	−0.0851146	+	0.117150i
$905$	4911.93	+	11239.7i	0.180418	+	0.412842i
$906$	3869.61	−	406.713i	0.141898	−	0.0149140i
$907$	−7771.40	−	29003.2i	−0.284504	−	1.06178i	−0.949201	−	0.314670i	$-0.898106\pi$
$907$	−7771.40	−	29003.2i	−0.284504	−	1.06178i	0.664697	−	0.747113i	$-0.268561\pi$
$908$	17563.5	−	6742.01i	0.641923	−	0.246411i
$909$	−148.072	−	455.720i	−0.00540292	−	0.0166285i
$910$	22379.6	−	36418.9i	0.815248	−	1.32667i
$911$	−15282.7	+	47035.3i	−0.555805	+	1.71059i	0.138003	+	0.990432i	$0.455932\pi$
$911$	−15282.7	+	47035.3i	−0.555805	+	1.71059i	−0.693808	+	0.720160i	$0.744068\pi$
$912$	135.845	+	2592.08i	0.00493233	+	0.0941144i
$913$	24754.4	−	16075.7i	0.897317	−	0.582725i
$914$	−38234.9	+	34426.9i	−1.38370	+	1.24589i
$915$	1523.91	+	597.031i	0.0550591	+	0.0215707i
$916$	−10960.9	+	3561.41i	−0.395369	+	0.128463i
$917$	2781.19	+	9198.37i	0.100156	+	0.331251i
$918$	19091.6	+	19091.6i	0.686402	+	0.686402i
$919$	10151.8	−	22801.4i	0.364394	−	0.818441i	−0.634567	−	0.772868i	$-0.718822\pi$
$919$	10151.8	−	22801.4i	0.364394	−	0.818441i	0.998961	−	0.0455739i	$-0.0145116\pi$
$920$	−5203.66	−	7266.78i	−0.186478	−	0.260412i
$921$	32083.6	−	14284.6i	1.14787	−	0.511066i
$922$	−19153.2	+	15510.0i	−0.684140	+	0.554006i
$923$	9077.90	+	17816.4i	0.323730	+	0.635356i
$924$	54462.7	+	3977.44i	1.93906	+	0.141611i
$925$	−10266.5	+	25683.7i	−0.364929	+	0.912944i
$926$	−3331.41	−	5770.18i	−0.118226	−	0.204773i
$927$	46.2170	−	881.872i	0.00163750	−	0.0312454i
$928$	50540.8	+	19400.8i	1.78781	+	0.686274i
$929$	−2979.91	+	28351.9i	−0.105240	+	1.00129i	0.806699	+	0.590962i	$0.201252\pi$
$929$	−2979.91	+	28351.9i	−0.105240	+	1.00129i	−0.911939	+	0.410326i	$0.865415\pi$
$930$	−40199.7	−	70747.0i	−1.41742	−	2.49450i
$931$	−3577.66	+	5647.54i	−0.125943	+	0.198809i
$932$	−32565.4	+	32565.4i	−1.14454	+	1.14454i
$933$	−6630.37	−	17272.7i	−0.232657	−	0.606091i
$934$	27434.5	+	5831.39i	0.961119	+	0.204292i
$935$	−24794.4	−	4102.01i	−0.867233	−	0.143476i
$936$	−475.276	−	2236.00i	−0.0165971	−	0.0780832i
$937$	−3074.90	+	6034.82i	−0.107207	+	0.210405i	−0.938377	−	0.345613i	$-0.887671\pi$
$937$	−3074.90	+	6034.82i	−0.107207	+	0.210405i	0.831171	+	0.556017i	$0.187671\pi$
$938$	−6642.41	+	10977.9i	−0.231218	+	0.382133i
$939$	−13579.8	−	4412.35i	−0.471950	−	0.153346i
$940$	−40175.9	−	32993.8i	−1.39404	−	1.14483i
$941$	1572.22	−	7396.69i	0.0544663	−	0.256244i	−0.942487	−	0.334242i	$-0.891520\pi$
$941$	1572.22	−	7396.69i	0.0544663	−	0.256244i	0.996953	+	0.0779986i	$0.0248530\pi$
$942$	4131.16	+	3345.35i	0.142888	+	0.115708i
$943$	−26332.3	−	7055.72i	−0.909330	−	0.243654i
$944$	−18607.6	+	13519.2i	−0.641551	+	0.466114i
$945$	17352.8	−	25181.6i	0.597340	−	0.866835i
$946$	20927.5	+	15204.8i	0.719253	+	0.522568i
$947$	27352.5	+	33777.6i	0.938582	+	1.15905i	0.987080	+	0.160229i	$0.0512234\pi$
$947$	27352.5	+	33777.6i	0.938582	+	1.15905i	−0.0484974	+	0.998823i	$0.515443\pi$
$948$	4974.77	+	260.717i	0.170436	+	0.00893216i
$949$	−17015.2	−	9823.71i	−0.582018	−	0.336028i
$950$	10580.3	−	1526.91i	0.361337	−	0.0521469i
$951$			25258.6i			0.861267i
$952$	1375.33	−	10922.2i	0.0468220	−	0.371839i
$953$	3590.78	+	22671.3i	0.122053	+	0.770614i	0.970459	+	0.241267i	$0.0775630\pi$
$953$	3590.78	+	22671.3i	0.122053	+	0.770614i	−0.848405	+	0.529347i	$0.822437\pi$
$954$	−7249.35	−	761.937i	−0.246023	−	0.0258581i
$955$	41929.3	−	30025.1i	1.42073	−	1.01737i
$956$	−5548.01	−	52785.8i	−0.187694	−	1.78579i
$957$	−15663.3	+	58456.4i	−0.529074	+	1.97453i
$958$	−9859.31	+	62249.2i	−0.332505	+	2.09935i
$959$	−2942.30	+	10142.7i	−0.0990738	+	0.341528i
$960$	−34343.0	+	27421.6i	−1.15460	+	0.921904i
$961$	84926.1	−	18051.6i	2.85073	−	0.605941i
$962$	24879.0	+	38310.3i	0.833815	+	1.28396i
$963$	562.624	+	866.365i	0.0188269	+	0.0289909i
$964$	−39304.6	+	8354.44i	−1.31319	+	0.279127i
$965$	24605.8	−	1119.93i	0.820816	−	0.0373593i
$966$	−15315.3	−	15957.8i	−0.510105	−	0.531504i
$967$	827.472	−	5224.46i	0.0275178	−	0.173741i	−0.970102	−	0.242699i	$-0.921967\pi$
$967$	827.472	−	5224.46i	0.0275178	−	0.173741i	0.997620	+	0.0689579i	$0.0219674\pi$
$968$	−5832.65	+	21767.7i	−0.193666	+	0.722770i
$969$	412.324	+	3923.00i	0.0136695	+	0.130057i
$970$	−29704.4	−	21895.1i	−0.983248	−	0.724753i
$971$	29517.5	+	3102.42i	0.975554	+	0.102535i	0.578870	−	0.815420i	$-0.303494\pi$
$971$	29517.5	+	3102.42i	0.975554	+	0.102535i	0.396684	+	0.917955i	$0.370161\pi$
$972$	−1671.47	−	10553.3i	−0.0551569	−	0.348247i
$973$	16276.6	+	38676.8i	0.536282	+	1.27433i
$974$		−	63793.7i		−	2.09865i
$975$	−27288.0	+	8453.34i	−0.896325	+	0.277665i
$976$	715.560	+	413.129i	0.0234677	+	0.0135491i
$977$	−4897.29	−	256.656i	−0.160367	−	0.00840446i	−0.0280164	−	0.999607i	$-0.508919\pi$
$977$	−4897.29	−	256.656i	−0.160367	−	0.00840446i	−0.132350	+	0.991203i	$0.542252\pi$
$978$	−38396.7	−	47416.0i	−1.25541	−	1.55030i
$979$	−17802.1	−	12934.0i	−0.581162	−	0.422239i
$980$	−43078.3	+	2447.79i	−1.40417	+	0.0797876i
$981$	−1441.92	+	1047.62i	−0.0469288	+	0.0340957i
$982$	−82482.3	−	22101.1i	−2.68036	−	0.718201i
$983$	−26103.0	−	21137.8i	−0.846956	−	0.685852i	0.104202	−	0.994556i	$-0.466771\pi$
$983$	−26103.0	−	21137.8i	−0.846956	−	0.685852i	−0.951158	+	0.308705i	$0.900105\pi$
$984$	7009.32	−	32976.2i	0.227082	−	1.06834i
$985$	39407.1	+	2337.06i	1.27473	+	0.0755990i
$986$	40150.9	+	13045.8i	1.29682	+	0.421363i
$987$	−31808.5	−	19246.4i	−1.02581	−	0.620688i
$988$	4684.30	−	9193.47i	0.150838	−	0.296036i
$989$	−1273.14	−	5989.67i	−0.0409339	−	0.192579i
$990$	6329.34	+	6416.99i	0.203191	+	0.206005i
$991$	9799.78	+	2083.01i	0.314127	+	0.0667698i	0.362278	−	0.932070i	$-0.381999\pi$
$991$	9799.78	+	2083.01i	0.314127	+	0.0667698i	−0.0481502	+	0.998840i	$0.515333\pi$
$992$	−28688.4	−	74735.7i	−0.918202	−	2.39200i
$993$	7838.68	−	7838.68i	0.250507	−	0.250507i
$994$	16307.3	−	30442.5i	0.520360	−	0.971406i
$995$	20785.7	−	22768.0i	0.662262	−	0.725422i
$996$	3125.46	−	29736.8i	0.0994318	−	0.946031i
$997$	−45198.7	−	17350.2i	−1.43577	−	0.551139i	−0.488778	−	0.872408i	$-0.662557\pi$
$997$	−45198.7	−	17350.2i	−1.43577	−	0.551139i	−0.946988	+	0.321269i	$0.895891\pi$
$998$	775.132	−	14790.4i	0.0245856	−	0.469120i
$999$	16340.4	+	28302.5i	0.517506	+	0.896346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.x.a.3.9	✓	928
7.5	odd	6	inner	175.4.x.a.103.50	yes	928
25.17	odd	20	inner	175.4.x.a.17.50	yes	928
175.117	even	60	inner	175.4.x.a.117.9	yes	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.x.a.3.9	✓	928	1.1	even	1	trivial
175.4.x.a.17.50	yes	928	25.17	odd	20	inner
175.4.x.a.103.50	yes	928	7.5	odd	6	inner
175.4.x.a.117.9	yes	928	175.117	even	60	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.38969 + 3.67979i) q^{2} +(1.74074 - 4.53478i) q^{3} +(-4.57638 - 10.2787i) q^{4} +(10.9198 + 2.39967i) q^{5} +(12.5272 + 17.2422i) q^{6} +(14.0149 - 12.1072i) q^{7} +(14.0907 + 2.23174i) q^{8} +(2.53089 + 2.27882i) q^{9} +(-34.9251 + 34.4481i) q^{10} +(-36.0998 - 40.0929i) q^{11} +(-54.5780 + 2.86031i) q^{12} +(-41.9216 - 21.3601i) q^{13} +(11.0607 + 80.5041i) q^{14} +(29.8904 - 45.3416i) q^{15} +(18.3450 - 20.3742i) q^{16} +(26.2204 - 32.3795i) q^{17} +(-14.4336 + 3.86747i) q^{18} +(-17.8059 - 7.92768i) q^{19} +(-25.3076 - 123.223i) q^{20} +(-30.5071 - 84.6297i) q^{21} +(233.801 - 37.0304i) q^{22} +(-46.9954 - 30.5192i) q^{23} +(34.6486 - 60.0131i) q^{24} +(113.483 + 52.4077i) q^{25} +(178.780 - 103.219i) q^{26} +(131.595 - 67.0510i) q^{27} +(-188.584 - 88.6480i) q^{28} +(135.740 - 186.830i) q^{29} +(95.4188 + 218.343i) q^{30} +(-339.618 + 35.6953i) q^{31} +(60.6732 + 226.435i) q^{32} +(-244.653 + 93.9134i) q^{33} +(56.4913 + 173.862i) q^{34} +(182.092 - 98.5765i) q^{35} +(11.8411 - 36.4430i) q^{36} +(11.5807 + 220.973i) q^{37} +(71.7226 - 46.5772i) q^{38} +(-169.838 + 152.923i) q^{39} +(148.511 + 58.1830i) q^{40} +(462.687 - 150.336i) q^{41} +(384.322 + 89.9786i) q^{42} +(77.2715 + 77.2715i) q^{43} +(-246.897 + 554.541i) q^{44} +(22.1683 + 30.9575i) q^{45} +(224.608 - 100.002i) q^{46} +(321.172 - 260.080i) q^{47} +(-60.4586 - 118.657i) q^{48} +(49.8331 - 339.361i) q^{49} +(-464.039 + 292.357i) q^{50} +(-101.191 - 175.268i) q^{51} +(-27.7055 + 528.652i) q^{52} +(455.413 + 174.817i) q^{53} +(-67.7368 + 644.473i) q^{54} +(-297.992 - 524.433i) q^{55} +(224.499 - 139.320i) q^{56} +(-66.9455 + 66.9455i) q^{57} +(363.121 + 945.962i) q^{58} +(-820.595 - 174.423i) q^{59} +(-602.844 - 99.7351i) q^{60} +(6.26595 + 29.4790i) q^{61} +(680.228 - 1335.02i) q^{62} +(63.0601 + 1.29551i) q^{63} +(-769.630 - 250.068i) q^{64} +(-406.517 - 333.845i) q^{65} +(239.061 - 1124.69i) q^{66} +(122.712 + 99.3699i) q^{67} +(-452.815 - 121.331i) q^{68} +(-220.204 + 159.988i) q^{69} +(-72.4025 + 905.629i) q^{70} +(-343.827 - 249.805i) q^{71} +(30.5761 + 37.7584i) q^{72} +(417.016 + 21.8549i) q^{73} +(-840.810 - 485.442i) q^{74} +(435.202 - 423.393i) q^{75} +219.302i q^{76} +(-991.346 - 124.830i) q^{77} +(-156.865 - 990.404i) q^{78} +(-90.6505 - 9.52775i) q^{79} +(249.215 - 178.460i) q^{80} +(-65.3772 - 622.023i) q^{81} +(-552.471 + 2061.85i) q^{82} +(-85.5853 + 540.364i) q^{83} +(-730.273 + 700.872i) q^{84} +(364.021 - 290.657i) q^{85} +(-468.998 + 99.6886i) q^{86} +(-610.946 - 940.774i) q^{87} +(-419.193 - 645.501i) q^{88} +(398.955 - 84.8005i) q^{89} +(-166.892 + 7.59609i) q^{90} +(-846.136 + 208.192i) q^{91} +(-98.6292 + 622.720i) q^{92} +(-429.315 + 1602.23i) q^{93} +(189.540 + 1803.35i) q^{94} +(-175.412 - 129.297i) q^{95} +(1132.45 + 119.025i) q^{96} +(117.678 + 742.987i) q^{97} +(1129.69 + 994.341i) q^{98} -183.736i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more