LMFDB - Embedded newform 96.3.p.a.5.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [96,3,Mod(5,96)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(96, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("96.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	96.p (of order $8$, degree $4$, 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:	$2.61581053786$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$30$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			5.17
Character	$\chi$	$=$	96.5
Dual form			96.3.p.a.77.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.369569 - 1.96556i) q^{2} +(2.79336 - 1.09413i) q^{3} +(-3.72684 - 1.45282i) q^{4} +(0.710186 - 1.71454i) q^{5} +(-1.11823 - 5.89488i) q^{6} +(-3.31956 - 3.31956i) q^{7} +(-4.23292 + 6.78840i) q^{8} +(6.60576 - 6.11260i) q^{9} +O(q^{10})$	\(q+(0.369569 - 1.96556i) q^{2} +(2.79336 - 1.09413i) q^{3} +(-3.72684 - 1.45282i) q^{4} +(0.710186 - 1.71454i) q^{5} +(-1.11823 - 5.89488i) q^{6} +(-3.31956 - 3.31956i) q^{7} +(-4.23292 + 6.78840i) q^{8} +(6.60576 - 6.11260i) q^{9} +(-3.10757 - 2.02955i) q^{10} +(10.7191 + 4.43999i) q^{11} +(-12.0000 + 0.0193925i) q^{12} +(-4.02050 + 1.66535i) q^{13} +(-7.75159 + 5.29798i) q^{14} +(0.107879 - 5.56637i) q^{15} +(11.7786 + 10.8288i) q^{16} +9.30385 q^{17} +(-9.57339 - 15.2430i) q^{18} +(-19.5621 + 8.10288i) q^{19} +(-5.13767 + 5.35805i) q^{20} +(-12.9048 - 5.64071i) q^{21} +(12.6885 - 19.4281i) q^{22} +(10.2920 + 10.2920i) q^{23} +(-4.39670 + 23.5938i) q^{24} +(15.2424 + 15.2424i) q^{25} +(1.78748 + 8.51799i) q^{26} +(11.7643 - 24.3023i) q^{27} +(7.54874 + 17.1942i) q^{28} +(24.5730 - 10.1785i) q^{29} +(-10.9012 - 2.26920i) q^{30} -33.0986 q^{31} +(25.6377 - 19.1496i) q^{32} +(34.8002 + 0.674445i) q^{33} +(3.43841 - 18.2873i) q^{34} +(-8.04902 + 3.33401i) q^{35} +(-33.4991 + 13.1837i) q^{36} +(34.7694 + 14.4020i) q^{37} +(8.69715 + 41.4450i) q^{38} +(-9.40862 + 9.05087i) q^{39} +(8.63283 + 12.0786i) q^{40} +(45.9556 + 45.9556i) q^{41} +(-15.8563 + 23.2804i) q^{42} +(-16.8272 + 40.6245i) q^{43} +(-33.4978 - 32.1200i) q^{44} +(-5.78899 - 15.6669i) q^{45} +(24.0330 - 16.4259i) q^{46} -89.1816 q^{47} +(44.7502 + 17.3615i) q^{48} -26.9611i q^{49} +(35.5929 - 24.3267i) q^{50} +(25.9890 - 10.1796i) q^{51} +(17.4032 - 0.365418i) q^{52} +(-67.3508 - 27.8976i) q^{53} +(-43.4198 - 32.1048i) q^{54} +(15.2251 - 15.2251i) q^{55} +(36.5859 - 8.48306i) q^{56} +(-45.7784 + 44.0377i) q^{57} +(-10.9249 - 52.0612i) q^{58} +(18.8842 - 45.5906i) q^{59} +(-8.48898 + 20.5882i) q^{60} +(-18.9284 - 45.6972i) q^{61} +(-12.2322 + 65.0572i) q^{62} +(-42.2193 - 1.63708i) q^{63} +(-28.1648 - 57.4695i) q^{64} +8.07602i q^{65} +(14.1867 - 68.1526i) q^{66} +(-45.3348 - 109.448i) q^{67} +(-34.6739 - 13.5168i) q^{68} +(40.0099 + 17.4885i) q^{69} +(3.57853 + 17.0530i) q^{70} +(-55.3980 + 55.3980i) q^{71} +(13.5331 + 70.7167i) q^{72} +(-90.2492 + 90.2492i) q^{73} +(41.1576 - 63.0188i) q^{74} +(59.2546 + 25.9004i) q^{75} +(84.6767 - 1.77797i) q^{76} +(-20.8438 - 50.3214i) q^{77} +(14.3129 + 21.8381i) q^{78} +91.8469i q^{79} +(26.9315 - 12.5045i) q^{80} +(6.27220 - 80.7568i) q^{81} +(107.312 - 73.3447i) q^{82} +(3.02564 + 7.30454i) q^{83} +(39.8990 + 39.7703i) q^{84} +(6.60747 - 15.9518i) q^{85} +(73.6310 + 48.0884i) q^{86} +(57.5047 - 55.3181i) q^{87} +(-75.5134 + 53.9713i) q^{88} +(23.9892 - 23.9892i) q^{89} +(-32.9337 + 5.58858i) q^{90} +(18.8745 + 7.81807i) q^{91} +(-23.4041 - 53.3088i) q^{92} +(-92.4564 + 36.2141i) q^{93} +(-32.9587 + 175.292i) q^{94} +39.2946i q^{95} +(50.6633 - 81.5428i) q^{96} -41.8801 q^{97} +(-52.9936 - 9.96398i) q^{98} +(97.9476 - 36.1920i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9}+O(q^{10}) $ 120 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9	$ 120 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} + 32 q^{10} - 4 q^{12} - 8 q^{13} - 40 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} - 120 q^{22} - 144 q^{24} - 8 q^{25} + 92 q^{27} - 8 q^{28} - 60 q^{30} - 16 q^{31} - 8 q^{33} - 40 q^{34} + 64 q^{36} - 8 q^{37} - 196 q^{39} - 232 q^{40} + 16 q^{42} - 8 q^{43} - 4 q^{45} - 40 q^{46} + 48 q^{48} - 40 q^{51} - 112 q^{52} + 304 q^{54} - 264 q^{55} - 4 q^{57} - 16 q^{58} + 424 q^{60} + 56 q^{61} - 8 q^{63} + 40 q^{64} + 428 q^{66} + 248 q^{67} - 4 q^{69} + 328 q^{70} + 416 q^{72} - 8 q^{73} - 104 q^{75} + 720 q^{76} + 276 q^{78} + 512 q^{82} + 232 q^{84} - 208 q^{85} - 452 q^{87} + 272 q^{88} - 304 q^{90} - 200 q^{91} - 40 q^{93} + 416 q^{94} - 616 q^{96} - 16 q^{97} + 252 q^{99}+O(q^{100}) $ 120 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9 + 32 * q^10 - 4 * q^12 - 8 * q^13 - 40 * q^16 - 4 * q^18 - 8 * q^19 - 4 * q^21 - 120 * q^22 - 144 * q^24 - 8 * q^25 + 92 * q^27 - 8 * q^28 - 60 * q^30 - 16 * q^31 - 8 * q^33 - 40 * q^34 + 64 * q^36 - 8 * q^37 - 196 * q^39 - 232 * q^40 + 16 * q^42 - 8 * q^43 - 4 * q^45 - 40 * q^46 + 48 * q^48 - 40 * q^51 - 112 * q^52 + 304 * q^54 - 264 * q^55 - 4 * q^57 - 16 * q^58 + 424 * q^60 + 56 * q^61 - 8 * q^63 + 40 * q^64 + 428 * q^66 + 248 * q^67 - 4 * q^69 + 328 * q^70 + 416 * q^72 - 8 * q^73 - 104 * q^75 + 720 * q^76 + 276 * q^78 + 512 * q^82 + 232 * q^84 - 208 * q^85 - 452 * q^87 + 272 * q^88 - 304 * q^90 - 200 * q^91 - 40 * q^93 + 416 * q^94 - 616 * q^96 - 16 * q^97 + 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.369569	−	1.96556i	0.184784	−	0.982779i
$2$	0.369569	−	1.96556i	0.184784	−	0.982779i
$3$	2.79336	−	1.09413i	0.931121	−	0.364710i
$3$	2.79336	−	1.09413i	0.931121	−	0.364710i
$4$	−3.72684	−	1.45282i	−0.931709	−	0.363205i
$5$	0.710186	−	1.71454i	0.142037	−	0.342908i	−0.836812	−	0.547490i	$-0.815583\pi$
$5$	0.710186	−	1.71454i	0.142037	−	0.342908i	0.978849	+	0.204582i	$0.0655834\pi$
$6$	−1.11823	−	5.89488i	−0.186372	−	0.982479i
$7$	−3.31956	−	3.31956i	−0.474222	−	0.474222i	0.429056	−	0.903278i	$-0.358846\pi$
$7$	−3.31956	−	3.31956i	−0.474222	−	0.474222i	−0.903278	+	0.429056i	$0.858846\pi$
$8$	−4.23292	+	6.78840i	−0.529115	+	0.848550i
$9$	6.60576	−	6.11260i	0.733974	−	0.679178i
$10$	−3.10757	−	2.02955i	−0.310757	−	0.202955i
$11$	10.7191	+	4.43999i	0.974462	+	0.403635i	0.812371	−	0.583141i	$-0.198176\pi$
$11$	10.7191	+	4.43999i	0.974462	+	0.403635i	0.162091	+	0.986776i	$0.448176\pi$
$12$	−12.0000	+	0.0193925i	−0.999999	+	0.00161604i
$13$	−4.02050	+	1.66535i	−0.309269	+	0.128104i	−0.531920	−	0.846795i	$-0.678529\pi$
$13$	−4.02050	+	1.66535i	−0.309269	+	0.128104i	0.222650	+	0.974898i	$0.428529\pi$
$14$	−7.75159	+	5.29798i	−0.553685	+	0.378427i
$15$	0.107879	−	5.56637i	0.00719193	−	0.371092i
$16$	11.7786	+	10.8288i	0.736165	+	0.676802i
$17$	9.30385			0.547285			0.273643	−	0.961831i	$-0.411771\pi$
$17$	9.30385			0.547285			0.273643	+	0.961831i	$0.411771\pi$
$18$	−9.57339	−	15.2430i	−0.531855	−	0.846835i
$19$	−19.5621	+	8.10288i	−1.02958	+	0.426467i	−0.832562	−	0.553932i	$-0.813127\pi$
$19$	−19.5621	+	8.10288i	−1.02958	+	0.426467i	−0.197021	+	0.980399i	$0.563127\pi$
$20$	−5.13767	+	5.35805i	−0.256883	+	0.267902i
$21$	−12.9048	−	5.64071i	−0.614512	−	0.268605i
$22$	12.6885	−	19.4281i	0.576750	−	0.883095i
$23$	10.2920	+	10.2920i	0.447477	+	0.447477i	0.894515	−	0.447038i	$-0.147521\pi$
$23$	10.2920	+	10.2920i	0.447477	+	0.447477i	−0.447038	+	0.894515i	$0.647521\pi$
$24$	−4.39670	+	23.5938i	−0.183196	+	0.983076i
$25$	15.2424	+	15.2424i	0.609695	+	0.609695i
$26$	1.78748	+	8.51799i	0.0687493	+	0.327615i
$27$	11.7643	−	24.3023i	0.435716	−	0.900084i
$28$	7.54874	+	17.1942i	0.269598	+	0.614077i
$29$	24.5730	−	10.1785i	0.847343	−	0.350981i	0.0835986	−	0.996500i	$-0.473359\pi$
$29$	24.5730	−	10.1785i	0.847343	−	0.350981i	0.763745	+	0.645518i	$0.223359\pi$
$30$	−10.9012	−	2.26920i	−0.363372	−	0.0756400i
$31$	−33.0986			−1.06770			−0.533848	−	0.845580i	$-0.679255\pi$
$31$	−33.0986			−1.06770			−0.533848	+	0.845580i	$0.679255\pi$
$32$	25.6377	−	19.1496i	0.801179	−	0.598425i
$33$	34.8002	+	0.674445i	1.05455	+	0.0204377i
$34$	3.43841	−	18.2873i	0.101130	−	0.537861i
$35$	−8.04902	+	3.33401i	−0.229972	+	0.0952576i
$36$	−33.4991	+	13.1837i	−0.930531	+	0.366214i
$37$	34.7694	+	14.4020i	0.939714	+	0.389242i	0.799355	−	0.600859i	$-0.205175\pi$
$37$	34.7694	+	14.4020i	0.939714	+	0.389242i	0.140358	+	0.990101i	$0.455175\pi$
$38$	8.69715	+	41.4450i	0.228872	+	1.09066i
$39$	−9.40862	+	9.05087i	−0.241247	+	0.232073i
$40$	8.63283	+	12.0786i	0.215821	+	0.301964i
$41$	45.9556	+	45.9556i	1.12087	+	1.12087i	0.991611	+	0.129257i	$0.0412593\pi$
$41$	45.9556	+	45.9556i	1.12087	+	1.12087i	0.129257	+	0.991611i	$0.458741\pi$
$42$	−15.8563	+	23.2804i	−0.377532	+	0.554296i
$43$	−16.8272	+	40.6245i	−0.391330	+	0.944755i	0.598320	+	0.801257i	$0.295835\pi$
$43$	−16.8272	+	40.6245i	−0.391330	+	0.944755i	−0.989651	+	0.143498i	$0.954165\pi$
$44$	−33.4978	−	32.1200i	−0.761313	−	0.730000i
$45$	−5.78899	−	15.6669i	−0.128644	−	0.348154i
$46$	24.0330	−	16.4259i	0.522457	−	0.357084i
$47$	−89.1816			−1.89748			−0.948741	−	0.316056i	$-0.897641\pi$
$47$	−89.1816			−1.89748			−0.948741	+	0.316056i	$0.897641\pi$
$48$	44.7502	+	17.3615i	0.932295	+	0.361698i
$49$		−	26.9611i		−	0.550226i
$50$	35.5929	−	24.3267i	0.711858	−	0.486534i
$51$	25.9890	−	10.1796i	0.509589	−	0.199600i
$52$	17.4032	−	0.365418i	0.334677	−	0.00702727i
$53$	−67.3508	−	27.8976i	−1.27077	−	0.526370i	−0.357571	−	0.933886i	$-0.616395\pi$
$53$	−67.3508	−	27.8976i	−1.27077	−	0.526370i	−0.913198	+	0.407516i	$0.866395\pi$
$54$	−43.4198	−	32.1048i	−0.804071	−	0.594534i
$55$	15.2251	−	15.2251i	0.276820	−	0.276820i
$56$	36.5859	−	8.48306i	0.653320	−	0.151483i
$57$	−45.7784	+	44.0377i	−0.803130	+	0.772592i
$58$	−10.9249	−	52.0612i	−0.188361	−	0.897607i
$59$	18.8842	−	45.5906i	0.320072	−	0.772722i	−0.679177	−	0.733974i	$-0.737663\pi$
$59$	18.8842	−	45.5906i	0.320072	−	0.772722i	0.999249	−	0.0387475i	$-0.0123368\pi$
$60$	−8.48898	+	20.5882i	−0.141483	+	0.343137i
$61$	−18.9284	−	45.6972i	−0.310302	−	0.749135i	−0.999694	−	0.0247462i	$-0.992122\pi$
$61$	−18.9284	−	45.6972i	−0.310302	−	0.749135i	0.689392	−	0.724388i	$-0.257878\pi$
$62$	−12.2322	+	65.0572i	−0.197294	+	1.04931i
$63$	−42.2193	−	1.63708i	−0.670148	−	0.0259853i
$64$	−28.1648	−	57.4695i	−0.440074	−	0.897961i
$65$			8.07602i			0.124247i
$66$	14.1867	−	68.1526i	0.214950	−	1.03261i
$67$	−45.3348	−	109.448i	−0.676639	−	1.63355i	−0.770097	−	0.637927i	$-0.779792\pi$
$67$	−45.3348	−	109.448i	−0.676639	−	1.63355i	0.0934584	−	0.995623i	$-0.470208\pi$
$68$	−34.6739	−	13.5168i	−0.509911	−	0.198776i
$69$	40.0099	+	17.4885i	0.579854	+	0.253456i
$70$	3.57853	+	17.0530i	0.0511219	+	0.243614i
$71$	−55.3980	+	55.3980i	−0.780253	+	0.780253i	−0.979873	−	0.199620i	$-0.936029\pi$
$71$	−55.3980	+	55.3980i	−0.780253	+	0.780253i	0.199620	+	0.979873i	$0.436029\pi$
$72$	13.5331	+	70.7167i	0.187960	+	0.982177i
$73$	−90.2492	+	90.2492i	−1.23629	+	1.23629i	−0.274784	+	0.961506i	$0.588606\pi$
$73$	−90.2492	+	90.2492i	−1.23629	+	1.23629i	−0.961506	+	0.274784i	$0.911394\pi$
$74$	41.1576	−	63.0188i	0.556184	−	0.851605i
$75$	59.2546	+	25.9004i	0.790062	+	0.345338i
$76$	84.6767	−	1.77797i	1.11417	−	0.0233944i
$77$	−20.8438	−	50.3214i	−0.270699	−	0.653524i
$78$	14.3129	+	21.8381i	0.183498	+	0.279976i
$79$			91.8469i			1.16262i	0.813683	+	0.581309i	$0.197459\pi$
$79$			91.8469i			1.16262i	−0.813683	+	0.581309i	$0.802541\pi$
$80$	26.9315	−	12.5045i	0.336644	−	0.156306i
$81$	6.27220	−	80.7568i	0.0774346	−	0.996997i
$82$	107.312	−	73.3447i	1.30869	−	0.894447i
$83$	3.02564	+	7.30454i	0.0364535	+	0.0880065i	0.941058	−	0.338246i	$-0.109834\pi$
$83$	3.02564	+	7.30454i	0.0364535	+	0.0880065i	−0.904604	+	0.426252i	$0.859834\pi$
$84$	39.8990	+	39.7703i	0.474988	+	0.473455i
$85$	6.60747	−	15.9518i	0.0777349	−	0.187669i
$86$	73.6310	+	48.0884i	0.856174	+	0.559167i
$87$	57.5047	−	55.3181i	0.660973	−	0.635840i
$88$	−75.5134	+	53.9713i	−0.858107	+	0.613310i
$89$	23.9892	−	23.9892i	0.269542	−	0.269542i	−0.559374	−	0.828916i	$-0.688958\pi$
$89$	23.9892	−	23.9892i	0.269542	−	0.269542i	0.828916	+	0.559374i	$0.188958\pi$
$90$	−32.9337	+	5.58858i	−0.365930	+	0.0620953i
$91$	18.8745	+	7.81807i	0.207412	+	0.0859129i
$92$	−23.4041	−	53.3088i	−0.254393	−	0.579444i
$93$	−92.4564	+	36.2141i	−0.994155	+	0.389399i
$94$	−32.9587	+	175.292i	−0.350625	+	1.86480i
$95$			39.2946i			0.413627i
$96$	50.6633	−	81.5428i	0.527743	−	0.849404i
$97$	−41.8801			−0.431754			−0.215877	−	0.976421i	$-0.569261\pi$
$97$	−41.8801			−0.431754			−0.215877	+	0.976421i	$0.569261\pi$
$98$	−52.9936	−	9.96398i	−0.540751	−	0.101673i
$99$	97.9476	−	36.1920i	0.989369	−	0.365575i
$100$	−34.6615	−	78.9503i	−0.346615	−	0.789503i
$101$	27.9447	−	67.4645i	0.276680	−	0.667965i	−0.723059	−	0.690786i	$-0.757265\pi$
$101$	27.9447	−	67.4645i	0.276680	−	0.667965i	0.999740	+	0.0228207i	$0.00726469\pi$
$102$	−10.4039	−	54.8450i	−0.101999	−	0.537696i
$103$	105.463	+	105.463i	1.02391	+	1.02391i	0.999707	+	0.0242046i	$0.00770532\pi$
$103$	105.463	+	105.463i	1.02391	+	1.02391i	0.0242046	+	0.999707i	$0.492295\pi$
$104$	5.71343	−	34.3421i	0.0549368	−	0.330212i
$105$	−18.8360	+	18.1198i	−0.179391	+	0.172569i
$106$	−79.7251	+	122.072i	−0.752124	+	1.15162i
$107$	−46.2628	−	19.1627i	−0.432363	−	0.179091i	0.155878	−	0.987776i	$-0.450179\pi$
$107$	−46.2628	−	19.1627i	−0.432363	−	0.179091i	−0.588241	+	0.808686i	$0.700179\pi$
$108$	−79.1505	+	73.4792i	−0.732875	+	0.680363i
$109$	−53.3231	+	22.0872i	−0.489203	+	0.202635i	−0.613629	−	0.789594i	$-0.710291\pi$
$109$	−53.3231	+	22.0872i	−0.489203	+	0.202635i	0.124426	+	0.992229i	$0.460291\pi$
$110$	−24.2991	−	35.5525i	−0.220901	−	0.323205i
$111$	112.881	+	2.18769i	1.01695	+	0.0197089i
$112$	−3.15293	−	75.0468i	−0.0281512	−	0.670061i
$113$	54.0961			0.478726			0.239363	−	0.970930i	$-0.423061\pi$
$113$	54.0961			0.478726			0.239363	+	0.970930i	$0.423061\pi$
$114$	69.6405	+	106.255i	0.610881	+	0.932062i
$115$	24.9552	−	10.3368i	0.217002	−	0.0898851i
$116$	−106.367	+	2.23340i	−0.916956	+	0.0192535i
$117$	−16.3789	+	35.5766i	−0.139990	+	0.304074i
$118$	−82.6319	−	53.9669i	−0.700271	−	0.457347i
$119$	−30.8847	−	30.8847i	−0.259535	−	0.259535i
$120$	37.3301	+	24.2944i	0.311084	+	0.202453i
$121$	9.62525	+	9.62525i	0.0795475	+	0.0795475i
$122$	−96.8159	+	20.3166i	−0.793573	+	0.166530i
$123$	178.652	+	78.0894i	1.45246	+	0.634873i
$124$	123.353	+	48.0862i	0.994783	+	0.387792i
$125$	79.8222	−	33.0634i	0.638577	−	0.264507i
$126$	−18.8207	+	82.3795i	−0.149371	+	0.653806i
$127$	54.1831			0.426638			0.213319	−	0.976983i	$-0.431573\pi$
$127$	54.1831			0.426638			0.213319	+	0.976983i	$0.431573\pi$
$128$	−123.369	+	34.1205i	−0.963817	+	0.266567i
$129$	−2.55609	+	131.890i	−0.0198147	+	1.02240i
$130$	15.8739	+	2.98465i	0.122107	+	0.0229588i
$131$	16.6818	−	6.90981i	0.127342	−	0.0527466i	−0.318103	−	0.948056i	$-0.603046\pi$
$131$	16.6818	−	6.90981i	0.127342	−	0.0527466i	0.445444	+	0.895310i	$0.353046\pi$
$132$	−128.715	−	53.0719i	−0.975113	−	0.402060i
$133$	91.8354	+	38.0395i	0.690492	+	0.286011i
$134$	−231.880	+	48.6596i	−1.73045	+	0.363132i
$135$	−33.3124	−	37.4296i	−0.246759	−	0.277256i
$136$	−39.3825	+	63.1583i	−0.289577	+	0.464399i
$137$	38.4961	+	38.4961i	0.280993	+	0.280993i	0.833505	−	0.552512i	$-0.186331\pi$
$137$	38.4961	+	38.4961i	0.280993	+	0.280993i	−0.552512	+	0.833505i	$0.686331\pi$
$138$	49.1610	−	72.1787i	0.356239	−	0.523034i
$139$	−5.47215	+	13.2109i	−0.0393680	+	0.0950427i	−0.942341	−	0.334655i	$-0.891380\pi$
$139$	−5.47215	+	13.2109i	−0.0393680	+	0.0950427i	0.902973	+	0.429698i	$0.141380\pi$
$140$	34.8411	−	0.731565i	0.248865	−	0.00522547i
$141$	−249.117	+	97.5762i	−1.76678	+	0.692030i
$142$	88.4146	+	129.361i	0.622638	+	0.910995i
$143$	−50.4902			−0.353078
$144$	143.999	−	0.465420i	0.999995	−	0.00323208i
$145$		−	49.3600i		−	0.340414i
$146$	144.037	+	210.743i	0.986553	+	1.44345i
$147$	−29.4989	−	75.3121i	−0.200673	−	0.512327i
$148$	−108.657	−	104.187i	−0.734166	−	0.703969i
$149$	193.116	+	79.9912i	1.29608	+	0.536854i	0.920792	−	0.390055i	$-0.127544\pi$
$149$	193.116	+	79.9912i	1.29608	+	0.536854i	0.375287	+	0.926908i	$0.377544\pi$
$150$	72.8074	−	106.896i	0.485383	−	0.712643i
$151$	153.471	−	153.471i	1.01636	−	1.01636i	0.0164997	−	0.999864i	$-0.494748\pi$
$151$	153.471	−	153.471i	1.01636	−	1.01636i	0.999864	−	0.0164997i	$-0.00525224\pi$
$152$	27.7992	−	167.094i	0.182889	−	1.09930i
$153$	61.4590	−	56.8707i	0.401693	−	0.371704i
$154$	−106.613	+	22.3725i	−0.692291	+	0.145276i
$155$	−23.5062	+	56.7489i	−0.151653	+	0.366122i
$156$	48.2137	−	20.0621i	0.309062	−	0.128603i
$157$	−97.3627	−	235.054i	−0.620145	−	1.49716i	−0.851533	−	0.524300i	$-0.824327\pi$
$157$	−97.3627	−	235.054i	−0.620145	−	1.49716i	0.231389	−	0.972861i	$-0.425673\pi$
$158$	180.530	+	33.9437i	1.14260	+	0.214834i
$159$	−218.659	−	4.23771i	−1.37521	−	0.0266523i
$160$	−14.6252	−	57.5567i	−0.0914077	−	0.359730i
$161$		−	68.3295i		−	0.424407i
$162$	−156.414	−	42.1736i	−0.965520	−	0.260331i
$163$	−60.3273	−	145.643i	−0.370106	−	0.893515i	−0.993732	−	0.111792i	$-0.964341\pi$
$163$	−60.3273	−	145.643i	−0.370106	−	0.893515i	0.623626	−	0.781723i	$-0.285659\pi$
$164$	−104.504	−	238.034i	−0.637219	−	1.45143i
$165$	25.8710	−	59.1874i	0.156794	−	0.358712i
$166$	15.4757	−	3.24754i	0.0932270	−	0.0195635i
$167$	99.4493	−	99.4493i	0.595505	−	0.595505i	−0.343608	−	0.939113i	$-0.611649\pi$
$167$	99.4493	−	99.4493i	0.595505	−	0.595505i	0.939113	+	0.343608i	$0.111649\pi$
$168$	92.9162	−	63.7260i	0.553072	−	0.379321i
$169$	−106.110	+	106.110i	−0.627870	+	0.627870i
$170$	−28.9124	−	18.8827i	−0.170073	−	0.111074i
$171$	−79.6928	+	173.101i	−0.466040	+	1.01229i
$172$	121.732	−	126.954i	0.707746	−	0.738104i
$173$	8.79723	+	21.2384i	0.0508510	+	0.122765i	0.947264	−	0.320455i	$-0.103836\pi$
$173$	8.79723	+	21.2384i	0.0508510	+	0.122765i	−0.896413	+	0.443220i	$0.853836\pi$
$174$	−87.4790	−	133.473i	−0.502753	−	0.767084i
$175$		−	101.196i		−	0.578262i
$176$	78.1763	+	168.372i	0.444183	+	0.956660i
$177$	2.86856	−	148.013i	0.0162066	−	0.836231i
$178$	−38.2865	−	56.0179i	−0.215093	−	0.314707i
$179$	35.4592	+	85.6060i	0.198096	+	0.478246i	0.991446	−	0.130520i	$-0.0416648\pi$
$179$	35.4592	+	85.6060i	0.198096	+	0.478246i	−0.793350	+	0.608766i	$0.791665\pi$
$180$	−1.18660	+	66.7985i	−0.00659222	+	0.371103i
$181$	32.1195	−	77.5433i	0.177456	−	0.428416i	−0.809976	−	0.586463i	$-0.800520\pi$
$181$	32.1195	−	77.5433i	0.177456	−	0.428416i	0.987432	+	0.158047i	$0.0505198\pi$
$182$	22.3423	−	34.2096i	0.122760	−	0.187965i
$183$	−102.873	−	106.939i	−0.562145	−	0.584365i
$184$	−113.431	+	26.3009i	−0.616473	+	0.142940i
$185$	49.3855	−	49.3855i	0.266949	−	0.266949i
$186$	37.0120	+	195.112i	0.198989	+	1.04899i
$187$	99.7287	+	41.3090i	0.533309	+	0.220904i
$188$	332.365	+	129.565i	1.76790	+	0.689174i
$189$	−119.725	+	41.6205i	−0.633466	+	0.220214i
$190$	77.2357	+	14.5220i	0.406504	+	0.0764318i
$191$			81.9805i			0.429218i	0.976700	+	0.214609i	$0.0688476\pi$
$191$			81.9805i			0.429218i	−0.976700	+	0.214609i	$0.931152\pi$
$192$	−141.553	−	129.717i	−0.737258	−	0.675612i
$193$	157.757			0.817395			0.408697	−	0.912670i	$-0.365983\pi$
$193$	157.757			0.817395			0.408697	+	0.912670i	$0.365983\pi$
$194$	−15.4776	+	82.3178i	−0.0797813	+	0.424318i
$195$	8.83621	+	22.5593i	0.0453139	+	0.115689i
$196$	−39.1696	+	100.480i	−0.199845	+	0.512651i
$197$	−100.906	+	243.608i	−0.512212	+	1.23659i	0.430381	+	0.902647i	$0.358379\pi$
$197$	−100.906	+	243.608i	−0.512212	+	1.23659i	−0.942593	+	0.333943i	$0.891621\pi$
$198$	−34.9390	−	205.897i	−0.176460	−	1.03988i
$199$	87.0618	+	87.0618i	0.437496	+	0.437496i	0.891169	−	0.453672i	$-0.149886\pi$
$199$	87.0618	+	87.0618i	0.437496	+	0.437496i	−0.453672	+	0.891169i	$0.649886\pi$
$200$	−167.991	+	38.9516i	−0.839956	+	0.194758i
$201$	−246.387	−	256.126i	−1.22580	−	1.27426i
$202$	−122.278	−	79.8597i	−0.605336	−	0.395345i
$203$	−115.359	−	47.7834i	−0.568272	−	0.235386i
$204$	−111.646	+	0.180425i	−0.547285	+	0.000884437i
$205$	111.430	−	46.1558i	0.543560	−	0.225150i
$206$	246.269	−	168.318i	1.19548	−	0.817076i
$207$	130.897	+	5.07560i	0.632352	+	0.0245198i
$208$	−65.3898	−	23.9218i	−0.314374	−	0.115009i
$209$	−245.664			−1.17543
$210$	28.6543	+	43.7198i	0.136449	+	0.208189i
$211$	−43.6713	+	18.0892i	−0.206973	+	0.0857310i	−0.483762	−	0.875200i	$-0.660730\pi$
$211$	−43.6713	+	18.0892i	−0.206973	+	0.0857310i	0.276789	+	0.960931i	$0.410730\pi$
$212$	210.475	+	201.818i	0.992808	+	0.951973i
$213$	−94.1342	+	215.359i	−0.441945	+	1.01108i
$214$	−54.7627	+	83.8503i	−0.255900	+	0.391824i
$215$	57.7019	+	57.7019i	0.268381	+	0.268381i
$216$	115.176	+	182.731i	0.533223	+	0.845975i
$217$	109.873	+	109.873i	0.506325	+	0.506325i
$218$	23.7070	+	112.972i	0.108748	+	0.518222i
$219$	−153.355	+	350.843i	−0.700249	+	1.60202i
$220$	−78.8607	+	34.6222i	−0.358458	+	0.157373i
$221$	−37.4061	+	15.4941i	−0.169259	+	0.0701092i
$222$	46.0174	−	221.066i	0.207286	−	0.995793i
$223$	−188.617			−0.845815			−0.422907	−	0.906173i	$-0.638990\pi$
$223$	−188.617			−0.845815			−0.422907	+	0.906173i	$0.638990\pi$
$224$	−148.674	−	21.5377i	−0.663723	−	0.0961504i
$225$	193.858	+	7.51695i	0.861592	+	0.0334087i
$226$	19.9922	−	106.329i	0.0884612	−	0.470482i
$227$	−225.835	+	93.5437i	−0.994866	+	0.412087i	−0.819912	−	0.572490i	$-0.805978\pi$
$227$	−225.835	+	93.5437i	−0.994866	+	0.412087i	−0.174954	+	0.984577i	$0.555978\pi$
$228$	234.588	−	97.6138i	1.02889	−	0.428131i
$229$	228.152	+	94.5035i	0.996295	+	0.412679i	0.820437	−	0.571737i	$-0.193730\pi$
$229$	228.152	+	94.5035i	0.996295	+	0.412679i	0.175858	+	0.984416i	$0.443730\pi$
$230$	−11.0949	−	52.8711i	−0.0482387	−	0.229874i
$231$	−113.282	−	117.760i	−0.490400	−	0.509784i
$232$	−34.9200	+	209.896i	−0.150517	+	0.904723i
$233$	−101.354	−	101.354i	−0.434994	−	0.434994i	0.455329	−	0.890323i	$-0.349522\pi$
$233$	−101.354	−	101.354i	−0.434994	−	0.434994i	−0.890323	+	0.455329i	$0.849522\pi$
$234$	63.8748	+	45.3416i	0.272969	+	0.193768i
$235$	−63.3356	+	152.906i	−0.269513	+	0.650662i
$236$	−136.613	+	142.473i	−0.578870	+	0.603701i
$237$	100.492	+	256.562i	0.424018	+	1.08254i
$238$	−72.1196	+	49.2916i	−0.303023	+	0.207107i
$239$	148.221			0.620170			0.310085	−	0.950709i	$-0.399642\pi$
$239$	148.221			0.620170			0.310085	+	0.950709i	$0.399642\pi$
$240$	61.5480	−	64.3961i	0.256450	−	0.268317i
$241$		−	22.8439i		−	0.0947879i	−0.998876	−	0.0473940i	$-0.984908\pi$
$241$		−	22.8439i		−	0.0947879i	0.998876	−	0.0473940i	$-0.0150916\pi$
$242$	22.4762	−	15.3618i	0.0928768	−	0.0634785i
$243$	−70.8378	−	232.446i	−0.291514	−	0.956567i
$244$	4.15336	+	197.806i	0.0170220	+	0.810679i
$245$	−46.2259	−	19.1474i	−0.188677	−	0.0781526i
$246$	219.513	−	322.292i	0.892331	−	1.31013i
$247$	65.1553	−	65.1553i	0.263787	−	0.263787i
$248$	140.104	−	224.686i	0.564934	−	0.905994i
$249$	16.4438	+	17.0938i	0.0660394	+	0.0686498i
$250$	−35.4883	−	169.114i	−0.141953	−	0.676457i
$251$	32.5584	−	78.6029i	0.129715	−	0.313159i	−0.845657	−	0.533727i	$-0.820791\pi$
$251$	32.5584	−	78.6029i	0.129715	−	0.313159i	0.975372	+	0.220568i	$0.0707910\pi$
$252$	154.966	+	67.4381i	0.614945	+	0.267612i
$253$	64.6242	+	156.017i	0.255432	+	0.616666i
$254$	20.0244	−	106.500i	0.0788361	−	0.419291i
$255$	1.00369	−	51.7887i	0.00393604	−	0.203093i
$256$	21.4727	+	255.098i	0.0838777	+	0.996476i
$257$		−	163.708i		−	0.636995i	−0.947924	−	0.318498i	$-0.896822\pi$
$257$		−	163.708i		−	0.636995i	0.947924	−	0.318498i	$-0.103178\pi$
$258$	258.293	+	53.7666i	1.00114	+	0.208398i
$259$	−67.6109	−	163.227i	−0.261046	−	0.630221i
$260$	11.7330	−	30.0980i	0.0451269	−	0.115762i
$261$	100.106	−	217.441i	0.383549	−	0.833108i
$262$	−7.41657	−	35.3426i	−0.0283075	−	0.134895i
$263$	149.627	−	149.627i	0.568925	−	0.568925i	−0.362902	−	0.931827i	$-0.618214\pi$
$263$	149.627	−	149.627i	0.568925	−	0.568925i	0.931827	+	0.362902i	$0.118214\pi$
$264$	−151.885	+	233.383i	−0.575322	+	0.884026i
$265$	−95.6632	+	95.6632i	−0.360993	+	0.360993i
$266$	108.708	−	166.450i	0.408678	−	0.625750i
$267$	40.7633	−	93.2579i	0.152672	−	0.349281i
$268$	9.94757	+	473.758i	0.0371178	+	1.76775i
$269$	−3.15620	−	7.61974i	−0.0117331	−	0.0283262i	0.917904	−	0.396802i	$-0.129880\pi$
$269$	−3.15620	−	7.61974i	−0.0117331	−	0.0283262i	−0.929638	+	0.368475i	$0.879880\pi$
$270$	−85.8812	+	51.6447i	−0.318079	+	0.191277i
$271$			454.602i			1.67750i	0.544519	+	0.838748i	$0.316712\pi$
$271$			454.602i			1.67750i	−0.544519	+	0.838748i	$0.683288\pi$
$272$	109.587	+	100.750i	0.402892	+	0.370404i
$273$	61.2773	+	1.18758i	0.224459	+	0.00435012i
$274$	89.8933	−	61.4394i	0.328078	−	0.224231i
$275$	95.7083	+	231.060i	0.348030	+	0.840219i
$276$	−123.703	−	123.304i	−0.448199	−	0.446753i
$277$	154.853	−	373.847i	0.559035	−	1.34963i	−0.351497	−	0.936189i	$-0.614327\pi$
$277$	154.853	−	373.847i	0.559035	−	1.34963i	0.910531	−	0.413440i	$-0.135673\pi$
$278$	23.9445	+	15.6382i	0.0861314	+	0.0562524i
$279$	−218.641	+	202.318i	−0.783661	+	0.725156i
$280$	11.4383	−	68.7526i	0.0408509	−	0.245545i
$281$	−102.165	+	102.165i	−0.363577	+	0.363577i	−0.865128	−	0.501551i	$-0.832763\pi$
$281$	−102.165	+	102.165i	−0.363577	+	0.363577i	0.501551	+	0.865128i	$0.332763\pi$
$282$	99.7259	+	525.714i	0.353638	+	1.86424i
$283$	−460.095	−	190.578i	−1.62578	−	0.673420i	−0.631029	−	0.775759i	$-0.717367\pi$
$283$	−460.095	−	190.578i	−1.62578	−	0.673420i	−0.994750	+	0.102339i	$0.967367\pi$
$284$	286.943	−	125.976i	1.01036	−	0.443578i
$285$	42.9933	+	109.764i	0.150854	+	0.385137i
$286$	−18.6596	+	99.2414i	−0.0652434	+	0.346998i
$287$		−	305.104i		−	1.06308i
$288$	52.3028	−	283.211i	0.181607	−	0.983371i
$289$	−202.438			−0.700479
$290$	−97.0199	−	18.2419i	−0.334551	−	0.0629031i
$291$	−116.986	+	45.8222i	−0.402015	+	0.157465i
$292$	467.460	−	205.228i	1.60089	−	0.702837i
$293$	−111.907	+	270.167i	−0.381935	+	0.922072i	0.609657	+	0.792665i	$0.291307\pi$
$293$	−111.907	+	270.167i	−0.381935	+	0.922072i	−0.991592	+	0.129407i	$0.958693\pi$
$294$	−158.932	+	30.1488i	−0.540586	+	0.102547i
$295$	−64.7556	−	64.7556i	−0.219511	−	0.219511i
$296$	−244.942	+	175.066i	−0.827508	+	0.591440i
$297$	234.005	−	208.265i	0.787894	−	0.701228i
$298$	228.597	−	350.018i	0.767104	−	1.17456i
$299$	−58.5185	−	24.2392i	−0.195714	−	0.0810675i
$300$	−183.204	−	182.613i	−0.610680	−	0.608709i
$301$	190.714	−	78.9964i	0.633602	−	0.262446i
$302$	−244.938	−	358.374i	−0.811053	−	1.18667i
$303$	4.24487	−	219.028i	0.0140095	−	0.722865i
$304$	−318.159	−	116.394i	−1.04658	−	0.382874i
$305$	−91.7925			−0.300959
$306$	−89.0694	−	141.819i	−0.291076	−	0.463461i
$307$	−253.247	+	104.898i	−0.824909	+	0.341689i	−0.754885	−	0.655857i	$-0.772308\pi$
$307$	−253.247	+	104.898i	−0.824909	+	0.341689i	−0.0700240	+	0.997545i	$0.522308\pi$
$308$	4.57365	+	217.822i	0.0148495	+	0.707214i
$309$	409.986	+	179.206i	1.32682	+	0.579955i
$310$	102.856	+	67.1754i	0.331794	+	0.216695i
$311$	219.931	+	219.931i	0.707175	+	0.707175i	0.965940	−	0.258766i	$-0.0833157\pi$
$311$	219.931	+	219.931i	0.707175	+	0.707175i	−0.258766	+	0.965940i	$0.583316\pi$
$312$	−21.6150	−	102.181i	−0.0692787	−	0.327503i
$313$	−61.5130	−	61.5130i	−0.196527	−	0.196527i	0.601982	−	0.798509i	$-0.294378\pi$
$313$	−61.5130	−	61.5130i	−0.196527	−	0.196527i	−0.798509	+	0.601982i	$0.794378\pi$
$314$	−497.995	+	104.503i	−1.58597	+	0.332813i
$315$	−32.7904	+	71.2242i	−0.104097	+	0.226108i
$316$	133.437	−	342.298i	0.422268	−	1.08322i
$317$	453.882	−	188.004i	1.43180	−	0.593073i	0.474008	−	0.880521i	$-0.342807\pi$
$317$	453.882	−	188.004i	1.43180	−	0.593073i	0.957796	+	0.287448i	$0.0928069\pi$
$318$	−89.1390	+	428.221i	−0.280311	+	1.34661i
$319$	308.592			0.967372
$320$	−118.536	+	7.47557i	−0.370425	+	0.0233611i
$321$	−150.195	−	2.91086i	−0.467898	−	0.00906809i
$322$	−134.306	−	25.2525i	−0.417098	−	0.0784238i
$323$	−182.003	+	75.3880i	−0.563476	+	0.233399i
$324$	−140.700	+	291.855i	−0.434261	+	0.900787i
$325$	−86.6659	−	35.8982i	−0.266664	−	0.110456i
$326$	−308.565	+	64.7517i	−0.946517	+	0.198625i
$327$	−124.785	+	120.040i	−0.381605	+	0.367094i
$328$	−506.491	+	117.439i	−1.54418	+	0.358044i
$329$	296.043	+	296.043i	0.899828	+	0.899828i
$330$	−106.775	−	72.7248i	−0.323561	−	0.220378i
$331$	182.672	−	441.009i	0.551879	−	1.33235i	−0.364187	−	0.931326i	$-0.618653\pi$
$331$	182.672	−	441.009i	0.551879	−	1.33235i	0.916066	−	0.401028i	$-0.131347\pi$
$332$	−0.663900	−	31.6185i	−0.00199970	−	0.0952366i
$333$	317.712	−	117.396i	0.954090	−	0.352539i
$334$	−158.720	−	232.227i	−0.475210	−	0.695290i
$335$	−219.849			−0.656266
$336$	−90.9182	−	206.183i	−0.270590	−	0.613641i
$337$			255.982i			0.759591i	0.925071	+	0.379795i	$0.124006\pi$
$337$			255.982i			0.759591i	−0.925071	+	0.379795i	$0.875994\pi$
$338$	169.350	+	247.780i	0.501037	+	0.733078i
$339$	151.110	−	59.1881i	0.445752	−	0.174596i
$340$	−47.8001	+	49.8505i	−0.140588	+	0.146619i
$341$	−354.786	−	146.957i	−1.04043	−	0.430960i
$342$	310.788	+	220.614i	0.908737	+	0.645069i
$343$	−252.157	+	252.157i	−0.735152	+	0.735152i
$344$	−204.547	−	286.190i	−0.594613	−	0.831948i
$345$	58.3992	−	56.1786i	0.169273	−	0.162837i
$346$	44.9965	−	9.44242i	0.130048	−	0.0272902i
$347$	220.467	−	532.255i	0.635353	−	1.53388i	−0.197453	−	0.980312i	$-0.563267\pi$
$347$	220.467	−	532.255i	0.635353	−	1.53388i	0.832806	−	0.553565i	$-0.186733\pi$
$348$	−294.678	+	122.618i	−0.846775	+	0.352350i
$349$	21.6460	+	52.2581i	0.0620229	+	0.149737i	0.951852	−	0.306557i	$-0.0991769\pi$
$349$	21.6460	+	52.2581i	0.0620229	+	0.149737i	−0.889830	+	0.456293i	$0.849177\pi$
$350$	−198.906	−	37.3988i	−0.568304	−	0.106854i
$351$	−6.82677	+	117.299i	−0.0194495	+	0.334185i
$352$	359.837	−	91.4349i	1.02226	−	0.259758i
$353$		−	666.011i		−	1.88672i	−0.331777	−	0.943358i	$-0.607648\pi$
$353$		−	666.011i		−	1.88672i	0.331777	−	0.943358i	$-0.392352\pi$
$354$	−289.868	−	60.3393i	−0.818836	−	0.170450i
$355$	55.6393	+	134.325i	0.156730	+	0.378381i
$356$	−124.256	+	54.5520i	−0.349033	+	0.153236i
$357$	−120.064	−	52.4803i	−0.336313	−	0.147004i
$358$	181.368	−	38.0597i	0.506615	−	0.106312i
$359$	316.755	−	316.755i	0.882326	−	0.882326i	−0.111445	−	0.993771i	$-0.535548\pi$
$359$	316.755	−	316.755i	0.882326	−	0.882326i	0.993771	+	0.111445i	$0.0355478\pi$
$360$	130.858	+	27.0190i	0.363494	+	0.0750527i
$361$	61.7528	−	61.7528i	0.171060	−	0.171060i
$362$	−140.546	−	91.7903i	−0.388247	−	0.253564i
$363$	37.4181	+	16.3556i	0.103080	+	0.0450566i
$364$	−58.9839	−	56.5579i	−0.162044	−	0.155379i
$365$	90.6422	+	218.830i	0.248335	+	0.599534i
$366$	−248.213	+	162.681i	−0.678178	+	0.444483i
$367$		−	299.475i		−	0.816009i	−0.912980	−	0.408004i	$-0.866225\pi$
$367$		−	299.475i		−	0.816009i	0.912980	−	0.408004i	$-0.133775\pi$
$368$	9.77536	+	232.675i	0.0265635	+	0.632270i
$369$	584.480	+	22.6635i	1.58396	+	0.0614188i
$370$	−78.8188	−	115.321i	−0.213024	−	0.311680i
$371$	130.967	+	316.182i	0.353011	+	0.852244i
$372$	397.182	−	0.641865i	1.06769	−	0.00172544i
$373$	−95.1781	+	229.780i	−0.255169	+	0.616033i	−0.998607	−	0.0527728i	$-0.983194\pi$
$373$	−95.1781	+	229.780i	−0.255169	+	0.616033i	0.743437	+	0.668805i	$0.233194\pi$
$374$	118.052	−	180.756i	0.315647	−	0.483305i
$375$	186.797	−	179.694i	0.498125	−	0.479184i
$376$	377.499	−	605.400i	1.00399	−	1.61011i
$377$	−81.8450	+	81.8450i	−0.217095	+	0.217095i
$378$	37.5607	+	250.708i	0.0993670	+	0.663250i
$379$	213.487	+	88.4290i	0.563289	+	0.233322i	0.646112	−	0.763242i	$-0.276394\pi$
$379$	213.487	+	88.4290i	0.563289	+	0.233322i	−0.0828233	+	0.996564i	$0.526394\pi$
$380$	57.0878	−	146.444i	0.150231	−	0.385380i
$381$	151.353	−	59.2833i	0.397252	−	0.155599i
$382$	161.138	+	30.2975i	0.421826	+	0.0793127i
$383$		−	364.818i		−	0.952528i	−0.879302	−	0.476264i	$-0.841991\pi$
$383$		−	364.818i		−	0.952528i	0.879302	−	0.476264i	$-0.158009\pi$
$384$	−307.281	+	230.292i	−0.800211	+	0.599719i
$385$	−101.081			−0.262548
$386$	58.3021	−	310.081i	0.151042	−	0.803318i
$387$	137.165	+	371.214i	0.354431	+	0.959208i
$388$	156.080	+	60.8442i	0.402269	+	0.156815i
$389$	−83.2313	+	200.938i	−0.213962	+	0.516550i	−0.994025	−	0.109151i	$-0.965187\pi$
$389$	−83.2313	+	200.938i	−0.213962	+	0.516550i	0.780063	+	0.625701i	$0.215187\pi$
$390$	47.6072	−	9.03089i	0.122070	−	0.0231561i
$391$	95.7549	+	95.7549i	0.244897	+	0.244897i
$392$	183.023	+	114.124i	0.466895	+	0.291133i
$393$	39.0380	−	37.5536i	0.0993333	−	0.0955562i
$394$	441.535	+	288.366i	1.12065	+	0.731894i
$395$	157.475	+	65.2284i	0.398672	+	0.165135i
$396$	−417.615	−	7.41846i	−1.05458	−	0.0187335i
$397$	−327.910	+	135.825i	−0.825970	+	0.342128i	−0.755306	−	0.655372i	$-0.772512\pi$
$397$	−327.910	+	135.825i	−0.825970	+	0.342128i	−0.0706638	+	0.997500i	$0.522512\pi$
$398$	203.300	−	138.950i	0.510805	−	0.349120i
$399$	298.150	+	5.77829i	0.747243	+	0.0144819i
$400$	14.4773	+	344.592i	0.0361932	+	0.861479i
$401$	−577.659			−1.44055			−0.720274	−	0.693690i	$-0.755984\pi$
$401$	−577.659			−1.44055			−0.720274	+	0.693690i	$0.755984\pi$
$402$	−594.486	+	389.631i	−1.47882	+	0.969232i
$403$	133.073	−	55.1206i	0.330206	−	0.136776i
$404$	−202.159	+	210.831i	−0.500394	+	0.521858i
$405$	−134.006	−	68.1063i	−0.330880	−	0.168164i
$406$	−136.554	+	209.086i	−0.336340	+	0.514990i
$407$	308.752	+	308.752i	0.758603	+	0.758603i
$408$	−40.9063	+	219.513i	−0.100260	+	0.538023i
$409$	−183.918	−	183.918i	−0.449678	−	0.449678i	0.445569	−	0.895248i	$-0.353001\pi$
$409$	−183.918	−	183.918i	−0.449678	−	0.449678i	−0.895248	+	0.445569i	$0.853001\pi$
$410$	−49.5408	−	236.080i	−0.120831	−	0.575804i
$411$	149.653	+	65.4139i	0.364120	+	0.159158i
$412$	−239.825	−	546.262i	−0.582099	−	1.32588i
$413$	−214.028	+	88.6532i	−0.518227	+	0.214657i
$414$	58.3518	−	255.410i	0.140946	−	0.616932i
$415$	14.6727			0.0353559
$416$	−71.1858	+	119.687i	−0.171120	+	0.287708i
$417$	−0.831233	+	42.8902i	−0.00199336	+	0.102854i
$418$	−90.7898	+	482.867i	−0.217201	+	1.15518i
$419$	321.845	−	133.312i	0.768126	−	0.318168i	0.0360129	−	0.999351i	$-0.488534\pi$
$419$	321.845	−	133.312i	0.768126	−	0.318168i	0.732113	+	0.681183i	$0.238534\pi$
$420$	96.5235	−	40.1642i	0.229818	−	0.0956291i
$421$	−551.627	−	228.491i	−1.31028	−	0.542735i	−0.385312	−	0.922786i	$-0.625906\pi$
$421$	−551.627	−	228.491i	−1.31028	−	0.542735i	−0.924965	+	0.380052i	$0.875906\pi$
$422$	19.4159	+	92.5236i	0.0460092	+	0.219250i
$423$	−589.113	+	545.132i	−1.39270	+	1.28873i
$424$	474.471	−	339.116i	1.11903	−	0.799801i
$425$	141.813	+	141.813i	0.333677	+	0.333677i
$426$	388.512	+	264.616i	0.912000	+	0.621165i
$427$	−88.8606	+	214.528i	−0.208104	+	0.502408i
$428$	144.574	+	138.628i	0.337790	+	0.323897i
$429$	−141.037	+	55.2428i	−0.328759	+	0.128771i
$430$	134.741	−	92.0916i	0.313352	−	0.214167i
$431$	−542.607			−1.25895			−0.629475	−	0.777021i	$-0.716730\pi$
$431$	−542.607			−1.25895			−0.629475	+	0.777021i	$0.716730\pi$
$432$	401.733	−	158.854i	0.929938	−	0.367717i
$433$			583.456i			1.34747i	0.738971	+	0.673737i	$0.235312\pi$
$433$			583.456i			1.34747i	−0.738971	+	0.673737i	$0.764688\pi$
$434$	256.567	−	175.356i	0.591167	−	0.404045i
$435$	−54.0062	−	137.880i	−0.124152	−	0.316966i
$436$	230.815	−	4.84647i	0.529393	−	0.0111158i
$437$	−284.727	−	117.938i	−0.651549	−	0.269880i
$438$	632.927	+	431.088i	1.44504	+	0.984219i
$439$	−183.924	+	183.924i	−0.418961	+	0.418961i	−0.884846	−	0.465884i	$-0.845736\pi$
$439$	−183.924	+	183.924i	−0.418961	+	0.418961i	0.465884	+	0.884846i	$0.345736\pi$
$440$	38.9074	+	167.801i	0.0884259	+	0.381365i
$441$	−164.802	−	178.099i	−0.373702	−	0.403852i
$442$	16.6305	+	79.2501i	0.0376255	+	0.179299i
$443$	43.3926	−	104.759i	0.0979516	−	0.236476i	−0.867306	−	0.497775i	$-0.834151\pi$
$443$	43.3926	−	104.759i	0.0979516	−	0.236476i	0.965258	+	0.261299i	$0.0841507\pi$
$444$	−417.512	−	172.149i	−0.940342	−	0.387723i
$445$	−24.0937	−	58.1673i	−0.0541432	−	0.130713i
$446$	−69.7069	+	370.737i	−0.156293	+	0.831249i
$447$	626.963	+	12.1508i	1.40260	+	0.0271831i
$448$	−97.2789	+	284.268i	−0.217140	+	0.634526i
$449$			669.975i			1.49215i	0.665863	+	0.746074i	$0.268064\pi$
$449$			669.975i			1.49215i	−0.665863	+	0.746074i	$0.731936\pi$
$450$	86.4189	−	378.261i	0.192042	−	0.840581i
$451$	288.559	+	696.644i	0.639821	+	1.54467i
$452$	−201.607	−	78.5918i	−0.446034	−	0.173876i
$453$	260.783	−	596.617i	0.575680	−	1.31704i
$454$	100.404	+	478.462i	0.221155	+	1.05388i
$455$	26.8088	−	26.8088i	0.0589205	−	0.0589205i
$456$	−105.169	−	497.170i	−0.230634	−	1.09029i
$457$	320.952	−	320.952i	0.702302	−	0.702302i	−0.262602	−	0.964904i	$-0.584581\pi$
$457$	320.952	−	320.952i	0.702302	−	0.702302i	0.964904	+	0.262602i	$0.0845806\pi$
$458$	270.070	−	413.520i	0.589672	−	0.902881i
$459$	109.453	−	226.105i	0.238461	−	0.492603i
$460$	−108.022	+	2.26815i	−0.234829	+	0.00493076i
$461$	−321.487	−	776.139i	−0.697369	−	1.68360i	−0.729378	−	0.684111i	$-0.760190\pi$
$461$	−321.487	−	776.139i	−0.697369	−	1.68360i	0.0320082	−	0.999488i	$-0.489810\pi$
$462$	−273.330	+	179.143i	−0.591623	+	0.387755i
$463$		−	300.320i		−	0.648638i	−0.945948	−	0.324319i	$-0.894865\pi$
$463$		−	300.320i		−	0.648638i	0.945948	−	0.324319i	$-0.105135\pi$
$464$	399.657	+	146.208i	0.861329	+	0.315104i
$465$	−3.57064	+	184.239i	−0.00767880	+	0.396213i
$466$	−236.673	+	161.759i	−0.507883	+	0.347123i
$467$	−80.2670	−	193.782i	−0.171878	−	0.414950i	0.814343	−	0.580384i	$-0.197098\pi$
$467$	−80.2670	−	193.782i	−0.171878	−	0.414950i	−0.986221	+	0.165434i	$0.947098\pi$
$468$	112.728	−	108.793i	0.240871	−	0.232463i
$469$	−212.827	+	513.810i	−0.453789	+	1.09554i
$470$	277.138	+	180.999i	0.589655	+	0.385104i
$471$	−529.149	−	550.065i	−1.12346	−	1.16787i
$472$	229.552	+	321.175i	0.486338	+	0.680456i
$473$	−360.744	+	360.744i	−0.762673	+	0.762673i
$474$	541.426	−	102.706i	1.14225	−	0.216680i
$475$	−421.680	−	174.666i	−0.887747	−	0.367717i
$476$	70.2323	+	159.972i	0.147547	+	0.336075i
$477$	−615.430	+	227.404i	−1.29021	+	0.476737i
$478$	54.7778	−	291.336i	0.114598	−	0.609490i
$479$			823.626i			1.71947i	0.510741	+	0.859734i	$0.329371\pi$
$479$			823.626i			1.71947i	−0.510741	+	0.859734i	$0.670629\pi$
$480$	−103.828	−	144.775i	−0.216309	−	0.301615i
$481$	−163.775			−0.340488
$482$	−44.9010	−	8.44239i	−0.0931556	−	0.0175153i
$483$	−74.7613	−	190.869i	−0.154785	−	0.395174i
$484$	−21.8880	−	49.8555i	−0.0452232	−	0.103007i
$485$	−29.7427	+	71.8052i	−0.0613251	+	0.148052i
$486$	−483.065	+	53.3312i	−0.993961	+	0.109735i
$487$	−114.692	−	114.692i	−0.235508	−	0.235508i	0.579479	−	0.814987i	$-0.303256\pi$
$487$	−114.692	−	114.692i	−0.235508	−	0.235508i	−0.814987	+	0.579479i	$0.803256\pi$
$488$	390.333	+	64.9391i	0.799864	+	0.133072i
$489$	−327.868	−	340.828i	−0.670487	−	0.696989i
$490$	−54.7190	+	83.7834i	−0.111671	+	0.170987i
$491$	214.991	+	89.0522i	0.437864	+	0.181369i	0.590715	−	0.806880i	$-0.298846\pi$
$491$	214.991	+	89.0522i	0.437864	+	0.181369i	−0.152852	+	0.988249i	$0.548846\pi$
$492$	−552.358	−	550.575i	−1.12268	−	1.11906i
$493$	228.623	−	94.6988i	0.463739	−	0.192087i
$494$	−103.987	−	152.146i	−0.210500	−	0.307988i
$495$	7.50842	−	193.638i	0.0151685	−	0.391188i
$496$	−389.856	−	358.419i	−0.786001	−	0.722619i
$497$	367.794			0.740027
$498$	39.6760	−	26.0040i	0.0796706	−	0.0522168i
$499$	278.730	−	115.454i	0.558577	−	0.231370i	−0.0854903	−	0.996339i	$-0.527246\pi$
$499$	278.730	−	115.454i	0.558577	−	0.231370i	0.644067	+	0.764969i	$0.277246\pi$
$500$	−345.519	+	7.25494i	−0.691039	+	0.0145099i
$501$	168.988	−	386.608i	0.337301	−	0.771673i
$502$	−142.466	−	93.0446i	−0.283797	−	0.185348i
$503$	−68.9715	−	68.9715i	−0.137120	−	0.137120i	0.635215	−	0.772335i	$-0.280911\pi$
$503$	−68.9715	−	68.9715i	−0.137120	−	0.137120i	−0.772335	+	0.635215i	$0.780911\pi$
$504$	189.824	−	279.672i	0.376635	−	0.554905i
$505$	−95.8247	−	95.8247i	−0.189752	−	0.189752i
$506$	330.543	−	69.3637i	0.653247	−	0.137082i
$507$	−180.306	+	412.502i	−0.355633	+	0.813613i
$508$	−201.932	−	78.7181i	−0.397503	−	0.154957i
$509$	228.236	−	94.5382i	0.448400	−	0.185733i	−0.147044	−	0.989130i	$-0.546976\pi$
$509$	228.236	−	94.5382i	0.448400	−	0.185733i	0.595444	+	0.803397i	$0.296976\pi$
$510$	−101.423	−	21.1123i	−0.198868	−	0.0413967i
$511$	599.175			1.17255
$512$	509.345	+	52.0704i	0.994815	+	0.101700i
$513$	−33.2162	+	570.728i	−0.0647490	+	1.11253i
$514$	−321.777	−	60.5013i	−0.626026	−	0.117707i
$515$	255.719	−	105.922i	0.496541	−	0.205674i
$516$	201.138	−	487.819i	0.389803	−	0.945386i
$517$	−955.945	−	395.965i	−1.84902	−	0.765890i
$518$	−345.819	+	72.5695i	−0.667605	+	0.140096i
$519$	47.8114	+	49.7012i	0.0921221	+	0.0957634i
$520$	−54.8233	−	34.1852i	−0.105429	−	0.0657407i
$521$	347.432	+	347.432i	0.666857	+	0.666857i	0.956987	−	0.290131i	$-0.0936987\pi$
$521$	347.432	+	347.432i	0.666857	+	0.666857i	−0.290131	+	0.956987i	$0.593699\pi$
$522$	−390.397	−	277.124i	−0.747887	−	0.530889i
$523$	162.057	−	391.239i	0.309860	−	0.748068i	−0.689849	−	0.723953i	$-0.742323\pi$
$523$	162.057	−	391.239i	0.309860	−	0.748068i	0.999709	−	0.0241148i	$-0.00767672\pi$
$524$	−72.2089	+	1.51618i	−0.137803	+	0.00289348i
$525$	−110.721	−	282.677i	−0.210898	−	0.538432i
$526$	−238.804	−	349.399i	−0.453999	−	0.664256i
$527$	−307.944			−0.584334
$528$	402.596	+	384.790i	0.762492	+	0.728768i
$529$		−	317.151i		−	0.599529i
$530$	152.677	+	223.386i	0.288071	+	0.421483i
$531$	−153.932	−	416.592i	−0.289891	−	0.784543i
$532$	−286.991	−	275.187i	−0.539457	−	0.517269i
$533$	−261.297	−	108.233i	−0.490237	−	0.203063i
$534$	−168.239	−	114.588i	−0.315054	−	0.214584i
$535$	−65.7105	+	65.7105i	−0.122823	+	0.122823i
$536$	934.874	+	155.533i	1.74417	+	0.290174i
$537$	192.714	+	200.332i	0.358872	+	0.373057i
$538$	−16.1435	+	3.38767i	−0.0300064	+	0.00629679i
$539$	119.707	−	288.998i	0.222091	−	0.536174i
$540$	69.7716	+	187.891i	0.129207	+	0.347946i
$541$	329.107	+	794.536i	0.608332	+	1.46864i	0.864813	+	0.502093i	$0.167437\pi$
$541$	329.107	+	794.536i	0.608332	+	1.46864i	−0.256482	+	0.966549i	$0.582563\pi$
$542$	893.546	+	168.007i	1.64861	+	0.309975i
$543$	4.87903	−	251.750i	0.00898532	−	0.463627i
$544$	238.530	−	178.165i	0.438473	−	0.327509i
$545$			107.111i			0.196533i
$546$	24.9804	−	120.005i	0.0457517	−	0.219790i
$547$	263.735	+	636.712i	0.482148	+	1.16401i	0.958587	+	0.284800i	$0.0919273\pi$
$547$	263.735	+	636.712i	0.482148	+	1.16401i	−0.476439	+	0.879208i	$0.658073\pi$
$548$	−87.5409	−	199.397i	−0.159746	−	0.363862i
$549$	−404.365	−	186.163i	−0.736549	−	0.339095i
$550$	489.533	−	102.728i	0.890060	−	0.186777i
$551$	−398.223	+	398.223i	−0.722729	+	0.722729i
$552$	−288.078	+	197.576i	−0.521880	+	0.357928i
$553$	304.891	−	304.891i	0.551340	−	0.551340i
$554$	−677.590	−	442.534i	−1.22309	−	0.798798i
$555$	83.9176	−	191.986i	0.151203	−	0.345921i
$556$	39.5869	−	41.2850i	0.0711995	−	0.0742536i
$557$	150.031	+	362.206i	0.269355	+	0.650280i	0.999453	−	0.0330618i	$-0.0105258\pi$
$557$	150.031	+	362.206i	0.269355	+	0.650280i	−0.730098	+	0.683342i	$0.760526\pi$
$558$	316.866	+	504.523i	0.567860	+	0.904163i
$559$		−	191.354i		−	0.342315i
$560$	−130.910	−	47.8914i	−0.233768	−	0.0855203i
$561$	323.776	+	6.27493i	0.577141	+	0.0111853i
$562$	163.055	+	238.569i	0.290133	+	0.424499i
$563$	7.20103	+	17.3848i	0.0127905	+	0.0308789i	0.930146	−	0.367191i	$-0.119680\pi$
$563$	7.20103	+	17.3848i	0.0127905	+	0.0308789i	−0.917355	+	0.398069i	$0.869680\pi$
$564$	1070.18	−	1.72946i	1.89748	−	0.00306641i
$565$	38.4183	−	92.7500i	0.0679970	−	0.164159i
$566$	−544.629	+	833.913i	−0.962241	+	1.47334i
$567$	−288.898	+	247.256i	−0.509520	+	0.436077i
$568$	−141.568	−	610.559i	−0.249240	−	1.07493i
$569$	736.438	−	736.438i	1.29427	−	1.29427i	0.362146	−	0.932121i	$-0.382044\pi$
$569$	736.438	−	736.438i	1.29427	−	1.29427i	0.932121	−	0.362146i	$-0.117956\pi$
$570$	231.637	−	43.9405i	0.406380	−	0.0770886i
$571$	67.6067	+	28.0036i	0.118401	+	0.0490431i	0.441097	−	0.897459i	$-0.354589\pi$
$571$	67.6067	+	28.0036i	0.118401	+	0.0490431i	−0.322697	+	0.946502i	$0.604589\pi$
$572$	188.169	+	73.3531i	0.328966	+	0.128240i
$573$	89.6973	+	229.001i	0.156540	+	0.399654i
$574$	−599.701	−	112.757i	−1.04477	−	0.196441i
$575$			313.748i			0.545649i
$576$	−537.338	−	207.470i	−0.932878	−	0.360191i
$577$	−198.526			−0.344066			−0.172033	−	0.985091i	$-0.555034\pi$
$577$	−198.526			−0.344066			−0.172033	+	0.985091i	$0.555034\pi$
$578$	−74.8149	+	397.904i	−0.129438	+	0.688416i
$579$	440.673	−	172.607i	0.761093	−	0.298112i
$580$	−71.7110	+	183.957i	−0.123640	+	0.317166i
$581$	14.2041	−	34.2916i	0.0244476	−	0.0590217i
$582$	46.8318	+	246.878i	0.0804669	+	0.424189i
$583$	−598.073	−	598.073i	−1.02585	−	1.02585i
$584$	−230.630	−	994.665i	−0.394914	−	1.70319i
$585$	49.3655	+	53.3483i	0.0843855	+	0.0911937i
$586$	489.672	+	319.805i	0.835618	+	0.545742i
$587$	−449.792	−	186.310i	−0.766255	−	0.317393i	−0.0349005	−	0.999391i	$-0.511111\pi$
$587$	−449.792	−	186.310i	−0.766255	−	0.317393i	−0.731354	+	0.681998i	$0.761111\pi$
$588$	0.522844	+	323.533i	0.000889190	+	0.550226i
$589$	647.477	−	268.194i	1.09928	−	0.455338i
$590$	−151.213	+	103.349i	−0.256293	+	0.175168i
$591$	−15.3278	+	790.891i	−0.0259354	+	1.33822i
$592$	253.580	+	546.148i	0.428344	+	0.922547i
$593$	−196.908			−0.332054			−0.166027	−	0.986121i	$-0.553094\pi$
$593$	−196.908			−0.332054			−0.166027	+	0.986121i	$0.553094\pi$
$594$	−322.875	−	536.918i	−0.543561	−	0.903902i
$595$	−74.8869	+	31.0192i	−0.125860	+	0.0521331i
$596$	−603.499	−	578.676i	−1.01258	−	0.970933i
$597$	338.452	+	147.938i	0.566921	+	0.247803i
$598$	−69.2701	+	106.064i	−0.115836	+	0.177364i
$599$	−192.040	−	192.040i	−0.320602	−	0.320602i	0.528396	−	0.848998i	$-0.322794\pi$
$599$	−192.040	−	192.040i	−0.320602	−	0.320602i	−0.848998	+	0.528396i	$0.822794\pi$
$600$	−426.642	+	292.610i	−0.711071	+	0.487683i
$601$	−192.637	−	192.637i	−0.320528	−	0.320528i	0.528442	−	0.848969i	$-0.322776\pi$
$601$	−192.637	−	192.637i	−0.320528	−	0.320528i	−0.848969	+	0.528442i	$0.822776\pi$
$602$	−84.7900	−	404.054i	−0.140847	−	0.671186i
$603$	−968.482	−	445.873i	−1.60611	−	0.739425i
$604$	−794.926	+	348.996i	−1.31610	+	0.577808i
$605$	23.3386	−	9.66717i	0.0385762	−	0.0159788i
$606$	−428.943	−	89.2894i	−0.707828	−	0.147342i
$607$	297.333			0.489840			0.244920	−	0.969543i	$-0.421238\pi$
$607$	297.333			0.489840			0.244920	+	0.969543i	$0.421238\pi$
$608$	−346.360	+	582.345i	−0.569672	+	0.957805i
$609$	−374.522	−	7.25841i	−0.614978	−	0.0119186i
$610$	−33.9236	+	180.423i	−0.0556125	+	0.295776i
$611$	358.555	−	148.518i	0.586833	−	0.243074i
$612$	−311.671	+	122.659i	−0.509266	+	0.200424i
$613$	584.752	+	242.212i	0.953918	+	0.395126i	0.804702	−	0.593679i	$-0.202325\pi$
$613$	584.752	+	242.212i	0.953918	+	0.395126i	0.149216	+	0.988805i	$0.452325\pi$
$614$	112.592	+	536.539i	0.183374	+	0.873842i
$615$	260.764	−	250.848i	0.424006	−	0.407884i
$616$	429.832	+	71.5104i	0.697779	+	0.116088i
$617$	146.927	+	146.927i	0.238131	+	0.238131i	0.816076	−	0.577945i	$-0.196145\pi$
$617$	146.927	+	146.927i	0.238131	+	0.238131i	−0.577945	+	0.816076i	$0.696145\pi$
$618$	503.758	−	739.623i	0.815143	−	1.19680i
$619$	61.7515	−	149.081i	0.0997600	−	0.240842i	−0.866118	−	0.499840i	$-0.833392\pi$
$619$	61.7515	−	149.081i	0.0997600	−	0.240842i	0.965878	+	0.258998i	$0.0833922\pi$
$620$	170.049	−	177.344i	0.274273	−	0.286038i
$621$	371.196	−	129.040i	0.597739	−	0.207794i
$622$	513.567	−	351.008i	0.825671	−	0.564322i
$623$	−159.267			−0.255646
$624$	−208.831	+	4.72250i	−0.334665	+	0.00756812i
$625$			378.560i			0.605696i
$626$	−143.641	+	98.1742i	−0.229458	+	0.156828i
$627$	−686.229	+	268.788i	−1.09446	+	0.428690i
$628$	21.3638	+	1017.46i	0.0340188	+	1.62016i
$629$	323.489	+	133.994i	0.514291	+	0.213027i
$630$	127.877	+	90.7737i	0.202979	+	0.144085i
$631$	−595.746	+	595.746i	−0.944130	+	0.944130i	−0.998520	−	0.0543894i	$-0.982679\pi$
$631$	−595.746	+	595.746i	−0.944130	+	0.944130i	0.0543894	+	0.998520i	$0.482679\pi$
$632$	−623.493	−	388.781i	−0.986540	−	0.615159i
$633$	−102.198	+	98.3118i	−0.161450	+	0.155311i
$634$	−201.792	−	961.612i	−0.318284	−	1.51674i
$635$	38.4801	−	92.8991i	0.0605986	−	0.146298i
$636$	808.749	+	333.465i	1.27162	+	0.524316i
$637$	44.8995	+	108.397i	0.0704859	+	0.170168i
$638$	114.046	−	606.555i	0.178755	−	0.950713i
$639$	−27.3201	+	704.572i	−0.0427545	+	1.10262i
$640$	−29.1136	+	235.752i	−0.0454900	+	0.368363i
$641$			574.164i			0.895732i	0.894101	+	0.447866i	$0.147816\pi$
$641$			574.164i			0.895732i	−0.894101	+	0.447866i	$0.852184\pi$
$642$	−61.2290	+	294.142i	−0.0953723	+	0.458165i
$643$	−229.033	−	552.935i	−0.356194	−	0.859930i	−0.995828	−	0.0912496i	$-0.970914\pi$
$643$	−229.033	−	552.935i	−0.356194	−	0.859930i	0.639634	−	0.768680i	$-0.279086\pi$
$644$	−99.2704	+	254.653i	−0.154147	+	0.395424i
$645$	224.316	+	98.0491i	0.347776	+	0.152014i
$646$	80.9169	+	385.598i	0.125258	+	0.596901i
$647$	109.550	−	109.550i	0.169320	−	0.169320i	−0.617360	−	0.786681i	$-0.711798\pi$
$647$	109.550	−	109.550i	0.169320	−	0.169320i	0.786681	+	0.617360i	$0.211798\pi$
$648$	521.660	+	384.415i	0.805030	+	0.593234i
$649$	404.843	−	404.843i	0.623796	−	0.623796i
$650$	−102.589	+	157.080i	−0.157829	+	0.241661i
$651$	427.129	+	186.699i	0.656112	+	0.286789i
$652$	13.2373	+	630.432i	0.0203026	+	0.966920i
$653$	−316.240	−	763.470i	−0.484288	−	1.16917i	−0.957554	−	0.288254i	$-0.906925\pi$
$653$	−316.240	−	763.470i	−0.484288	−	1.16917i	0.473266	−	0.880919i	$-0.343075\pi$
$654$	189.829	+	289.635i	0.290258	+	0.442866i
$655$		−	33.5088i		−	0.0511585i
$656$	43.6489	+	1038.94i	0.0665379	+	1.58375i
$657$	−44.5074	+	1147.82i	−0.0677434	+	1.74707i
$658$	691.299	−	472.482i	1.05061	−	0.718058i
$659$	198.327	+	478.804i	0.300952	+	0.726562i	0.999935	+	0.0114237i	$0.00363634\pi$
$659$	198.327	+	478.804i	0.300952	+	0.726562i	−0.698983	+	0.715138i	$0.746364\pi$
$660$	−182.406	+	182.996i	−0.276372	+	0.277267i
$661$	225.481	−	544.359i	0.341121	−	0.823538i	−0.656482	−	0.754341i	$-0.727956\pi$
$661$	225.481	−	544.359i	0.341121	−	0.823538i	0.997603	−	0.0691966i	$-0.0220436\pi$
$662$	−799.319	−	522.036i	−1.20743	−	0.788574i
$663$	−87.5364	+	84.2079i	−0.132031	+	0.127010i
$664$	−62.3934	−	10.3803i	−0.0939660	−	0.0156330i
$665$	130.441	−	130.441i	0.196151	−	0.196151i
$666$	−113.331	−	667.867i	−0.170167	−	1.00280i
$667$	357.660	+	148.148i	0.536222	+	0.222111i
$668$	−515.113	+	226.150i	−0.771127	+	0.338547i
$669$	−526.875	+	206.371i	−0.787556	+	0.308477i
$670$	−81.2494	+	432.126i	−0.121268	+	0.644964i
$671$		−	573.874i		−	0.855252i
$672$	−438.866	+	102.506i	−0.653074	+	0.152539i
$673$	577.336			0.857855			0.428927	−	0.903339i	$-0.358892\pi$
$673$	577.336			0.857855			0.428927	+	0.903339i	$0.358892\pi$
$674$	503.148	+	94.6030i	0.746510	+	0.140361i
$675$	549.741	−	191.108i	0.814431	−	0.283123i
$676$	549.613	−	241.296i	0.813037	−	0.356947i
$677$	119.747	−	289.095i	0.176879	−	0.427023i	−0.810430	−	0.585835i	$-0.800766\pi$
$677$	119.747	−	289.095i	0.176879	−	0.427023i	0.987309	+	0.158812i	$0.0507665\pi$
$678$	−60.4921	−	318.890i	−0.0892214	−	0.470339i
$679$	139.023	+	139.023i	0.204747	+	0.204747i
$680$	80.3186	+	112.377i	0.118116	+	0.165260i
$681$	−528.489	+	508.394i	−0.776049	+	0.746540i
$682$	−419.971	+	643.042i	−0.615793	+	0.942877i
$683$	466.059	+	193.048i	0.682371	+	0.282647i	0.696817	−	0.717248i	$-0.254599\pi$
$683$	466.059	+	193.048i	0.682371	+	0.282647i	−0.0144469	+	0.999896i	$0.504599\pi$
$684$	548.486	−	529.340i	0.801880	−	0.773889i
$685$	93.3426	−	38.6638i	0.136267	−	0.0564434i
$686$	402.440	+	588.819i	0.586647	+	0.858337i
$687$	740.709	+	14.3553i	1.07818	+	0.0208956i
$688$	−638.117	+	296.282i	−0.927496	+	0.430642i
$689$	317.243			0.460440
$690$	−88.8399	−	135.549i	−0.128753	−	0.196448i
$691$	442.227	−	183.176i	0.639981	−	0.265089i	−0.0390059	−	0.999239i	$-0.512419\pi$
$691$	442.227	−	183.176i	0.639981	−	0.265089i	0.678987	+	0.734150i	$0.262419\pi$
$692$	−1.93033	−	91.9328i	−0.00278949	−	0.132851i
$693$	−445.284	−	205.001i	−0.642545	−	0.295817i
$694$	−964.701	−	630.047i	−1.39006	−	0.907848i
$695$	18.7645	+	18.7645i	0.0269992	+	0.0269992i
$696$	132.109	+	624.522i	0.189811	+	0.897302i
$697$	427.564	+	427.564i	0.613435	+	0.613435i
$698$	110.716	−	23.2335i	0.158619	−	0.0332858i
$699$	−394.011	−	172.223i	−0.563679	−	0.246386i
$700$	−147.019	+	377.141i	−0.210027	+	0.538772i
$701$	577.819	−	239.340i	0.824278	−	0.341427i	0.0696432	−	0.997572i	$-0.477814\pi$
$701$	577.819	−	239.340i	0.824278	−	0.341427i	0.754635	+	0.656145i	$0.227814\pi$
$702$	228.035	+	56.7685i	0.324836	+	0.0808668i
$703$	−796.859			−1.13351
$704$	−46.7362	−	741.072i	−0.0663867	−	1.05266i
$705$	−9.62082	+	496.418i	−0.0136466	+	0.704139i
$706$	−1309.08	−	246.137i	−1.85422	−	0.348636i
$707$	−316.716	+	131.188i	−0.447972	+	0.185556i
$708$	−225.726	+	547.453i	−0.318823	+	0.773238i
$709$	817.355	+	338.559i	1.15283	+	0.477517i	0.875481	−	0.483253i	$-0.160545\pi$
$709$	817.355	+	338.559i	1.15283	+	0.477517i	0.277347	+	0.960770i	$0.410545\pi$
$710$	284.586	−	59.7199i	0.400826	−	0.0841125i
$711$	561.423	+	606.719i	0.789625	+	0.853331i
$712$	61.3040	+	264.393i	0.0861011	+	0.371338i
$713$	−340.649	−	340.649i	−0.477769	−	0.477769i
$714$	−147.525	+	216.597i	−0.206618	+	0.303358i
$715$	−35.8574	+	86.5675i	−0.0501503	+	0.121073i
$716$	−7.78062	−	370.555i	−0.0108668	−	0.517536i
$717$	414.034	−	162.173i	0.577454	−	0.226182i
$718$	−505.538	−	739.663i	−0.704091	−	1.03017i
$719$	493.903			0.686931			0.343465	−	0.939165i	$-0.388399\pi$
$719$	493.903			0.686931			0.343465	+	0.939165i	$0.388399\pi$
$720$	101.468	−	247.223i	0.140928	−	0.343366i
$721$		−	700.180i		−	0.971124i
$722$	−98.5568	−	144.201i	−0.136505	−	0.199724i
$723$	−24.9942	−	63.8113i	−0.0345701	−	0.0882590i
$724$	−232.360	+	242.328i	−0.320940	+	0.334707i
$725$	529.694	+	219.407i	0.730613	+	0.302630i
$726$	45.9764	−	67.5029i	0.0633283	−	0.0929793i
$727$	266.150	−	266.150i	0.366093	−	0.366093i	−0.499957	−	0.866050i	$-0.666651\pi$
$727$	266.150	−	266.150i	0.366093	−	0.366093i	0.866050	+	0.499957i	$0.166651\pi$
$728$	−132.966	+	95.0343i	−0.182646	+	0.130542i
$729$	−452.201	−	571.800i	−0.620304	−	0.784362i
$730$	463.621	−	97.2900i	0.635097	−	0.133274i
$731$	−156.558	+	377.964i	−0.214169	+	0.517051i
$732$	228.027	+	547.999i	0.311512	+	0.748632i
$733$	−153.494	−	370.568i	−0.209406	−	0.505550i	0.783924	−	0.620856i	$-0.213215\pi$
$733$	−153.494	−	370.568i	−0.209406	−	0.505550i	−0.993330	+	0.115307i	$0.963215\pi$
$734$	−588.636	−	110.677i	−0.801957	−	0.150786i
$735$	−150.076	−	2.90854i	−0.204184	−	0.00395719i
$736$	460.950	+	66.7755i	0.626290	+	0.0907276i
$737$		−	1374.47i		−	1.86495i
$738$	260.552	−	1140.45i	0.353052	−	1.54533i
$739$	44.2681	+	106.873i	0.0599027	+	0.144618i	0.950997	−	0.309201i	$-0.100061\pi$
$739$	44.2681	+	106.873i	0.0599027	+	0.144618i	−0.891094	+	0.453818i	$0.850061\pi$
$740$	−255.800	+	112.304i	−0.345676	+	0.151762i
$741$	110.714	−	253.291i	0.149412	−	0.341823i
$742$	669.876	−	140.572i	0.902798	−	0.189450i
$743$	47.8447	−	47.8447i	0.0643940	−	0.0643940i	−0.674176	−	0.738570i	$-0.735501\pi$
$743$	47.8447	−	47.8447i	0.0643940	−	0.0643940i	0.738570	+	0.674176i	$0.235501\pi$
$744$	145.525	−	780.922i	0.195598	−	1.04963i
$745$	274.296	−	274.296i	0.368183	−	0.368183i
$746$	416.471	+	271.998i	0.558273	+	0.364608i
$747$	64.6364	+	29.7575i	0.0865280	+	0.0398360i
$748$	−311.658	−	298.840i	−0.416655	−	0.399518i
$749$	89.9604	+	217.184i	0.120107	+	0.289965i
$750$	−284.165	−	433.569i	−0.378886	−	0.578092i
$751$		−	357.049i		−	0.475431i	−0.971335	−	0.237716i	$-0.923601\pi$
$751$		−	357.049i		−	0.475431i	0.971335	−	0.237716i	$-0.0763986\pi$
$752$	−1050.44	−	965.733i	−1.39686	−	1.28422i
$753$	4.94570	−	255.190i	0.00656799	−	0.338897i
$754$	130.624	+	191.118i	0.173241	+	0.253473i
$755$	−154.139	−	372.125i	−0.204158	−	0.492881i
$756$	506.663	+	18.8262i	0.670189	+	0.0249023i
$757$	−339.528	+	819.694i	−0.448518	+	1.08282i	0.524359	+	0.851497i	$0.324305\pi$
$757$	−339.528	+	819.694i	−0.448518	+	1.08282i	−0.972877	+	0.231322i	$0.925695\pi$
$758$	252.710	−	386.940i	0.333391	−	0.510475i
$759$	351.221	+	365.104i	0.462742	+	0.481033i
$760$	−266.747	−	166.331i	−0.350983	−	0.218856i
$761$	−794.277	+	794.277i	−1.04373	+	1.04373i	−0.0447288	+	0.998999i	$0.514242\pi$
$761$	−794.277	+	794.277i	−1.04373	+	1.04373i	−0.998999	+	0.0447288i	$0.985758\pi$
$762$	−60.5894	−	319.402i	−0.0795136	−	0.419163i
$763$	250.329	+	103.690i	0.328085	+	0.135897i
$764$	119.103	−	305.528i	0.155894	−	0.399906i
$765$	−53.8599	−	145.763i	−0.0704051	−	0.190540i
$766$	−717.071	−	134.825i	−0.936124	−	0.176012i
$767$			214.746i			0.279982i
$768$	339.091	+	689.087i	0.441525	+	0.897249i
$769$	556.538			0.723717			0.361859	−	0.932233i	$-0.382142\pi$
$769$	556.538			0.723717			0.361859	+	0.932233i	$0.382142\pi$
$770$	−37.3564	+	198.681i	−0.0485148	+	0.258027i
$771$	−179.117	−	457.295i	−0.232318	−	0.593120i
$772$	−587.935	−	229.192i	−0.761574	−	0.296881i
$773$	7.40246	−	17.8711i	0.00957627	−	0.0231192i	−0.919019	−	0.394213i	$-0.871017\pi$
$773$	7.40246	−	17.8711i	0.00957627	−	0.0231192i	0.928595	+	0.371094i	$0.121017\pi$
$774$	780.334	−	132.416i	1.00818	−	0.171080i
$775$	−504.501	−	504.501i	−0.650969	−	0.650969i
$776$	177.275	−	284.299i	0.228447	−	0.366364i
$777$	−367.453	−	381.978i	−0.472913	−	0.491606i
$778$	364.196	+	237.856i	0.468118	+	0.305728i
$779$	−1271.36	−	526.615i	−1.63204	−	0.676014i
$780$	−0.156615	−	96.9122i	−0.000200788	−	0.124246i
$781$	−839.782	+	347.849i	−1.07526	+	0.445389i
$782$	223.600	−	152.824i	0.285933	−	0.195427i
$783$	41.7246	−	716.921i	0.0532882	−	0.915608i
$784$	291.957	−	317.565i	0.372394	−	0.405057i
$785$	−472.156			−0.601473
$786$	−59.3866	−	90.6101i	−0.0755554	−	0.115280i
$787$	−988.014	+	409.249i	−1.25542	+	0.520011i	−0.908500	−	0.417885i	$-0.862772\pi$
$787$	−988.014	+	409.249i	−1.25542	+	0.520011i	−0.346918	+	0.937896i	$0.612772\pi$
$788$	729.978	−	761.291i	0.926368	−	0.966105i
$789$	254.252	−	581.675i	0.322246	−	0.737231i
$790$	186.408	−	285.420i	0.235960	−	0.361292i
$791$	−179.575	−	179.575i	−0.227023	−	0.227023i
$792$	−168.919	+	818.105i	−0.213281	+	1.03296i
$793$	152.203	+	152.203i	0.191934	+	0.191934i
$794$	145.786	+	694.723i	0.183610	+	0.874966i
$795$	−162.554	+	371.890i	−0.204471	+	0.467786i
$796$	−197.980	−	450.950i	−0.248719	−	0.566520i
$797$	−982.564	+	406.991i	−1.23283	+	0.510654i	−0.901466	−	0.432850i	$-0.857508\pi$
$797$	−982.564	+	406.991i	−1.23283	+	0.510654i	−0.331362	+	0.943504i	$0.607508\pi$
$798$	121.544	−	583.895i	0.152311	−	0.731698i
$799$	−829.732			−1.03846
$800$	682.665	+	98.8944i	0.853332	+	0.123618i
$801$	11.8306	−	305.104i	0.0147697	−	0.380903i
$802$	−213.485	+	1135.42i	−0.266191	+	1.41574i
$803$	−1368.09	+	566.683i	−1.70373	+	0.705707i
$804$	546.139	+	1312.49i	0.679278	+	1.63245i
$805$	−117.154	−	48.5267i	−0.145533	−	0.0602816i
$806$	−59.1631	−	281.933i	−0.0734034	−	0.349793i
$807$	−17.1534	−	17.8314i	−0.0212557	−	0.0220959i
$808$	339.688	+	475.272i	0.420406	+	0.588208i
$809$	158.403	+	158.403i	0.195801	+	0.195801i	0.798197	−	0.602396i	$-0.205787\pi$
$809$	158.403	+	158.403i	0.195801	+	0.195801i	−0.602396	+	0.798197i	$0.705787\pi$
$810$	−183.392	+	238.228i	−0.226409	+	0.294108i
$811$	−154.779	+	373.671i	−0.190850	+	0.460753i	−0.990121	−	0.140219i	$-0.955219\pi$
$811$	−154.779	+	373.671i	−0.190850	+	0.460753i	0.799270	+	0.600972i	$0.205219\pi$
$812$	360.505	+	345.677i	0.443971	+	0.425710i
$813$	497.393	+	1269.87i	0.611799	+	1.56195i
$814$	720.974	−	492.764i	0.885717	−	0.605361i
$815$	−292.554			−0.358962
$816$	416.349	+	161.529i	0.510231	+	0.197952i
$817$		−	931.048i		−	1.13959i
$818$	−429.473	+	293.532i	−0.525028	+	0.358841i
$819$	172.469	−	63.7279i	0.210585	−	0.0778119i
$820$	−482.337	+	10.1277i	−0.588216	+	0.0123509i
$821$	227.727	+	94.3275i	0.277377	+	0.114893i	0.517036	−	0.855964i	$-0.327035\pi$
$821$	227.727	+	94.3275i	0.277377	+	0.114893i	−0.239658	+	0.970857i	$0.577035\pi$
$822$	183.882	−	269.977i	0.223701	−	0.328440i
$823$	423.153	−	423.153i	0.514159	−	0.514159i	−0.401639	−	0.915798i	$-0.631559\pi$
$823$	423.153	−	423.153i	0.514159	−	0.514159i	0.915798	+	0.401639i	$0.131559\pi$
$824$	−1162.34	+	269.508i	−1.41061	+	0.327073i
$825$	520.158	+	540.718i	0.630494	+	0.655416i
$826$	95.1551	+	453.448i	0.115200	+	0.548968i
$827$	−149.235	+	360.286i	−0.180454	+	0.435654i	−0.988060	−	0.154068i	$-0.950763\pi$
$827$	−149.235	+	360.286i	−0.180454	+	0.435654i	0.807606	+	0.589722i	$0.200763\pi$
$828$	−480.458	−	209.085i	−0.580263	−	0.252519i
$829$	−48.9973	−	118.290i	−0.0591041	−	0.142690i	0.891569	−	0.452886i	$-0.149605\pi$
$829$	−48.9973	−	118.290i	−0.0591041	−	0.142690i	−0.950673	+	0.310196i	$0.899605\pi$
$830$	5.42257	−	28.8401i	0.00653322	−	0.0347471i
$831$	23.5225	−	1213.72i	0.0283062	−	1.46055i
$832$	208.943	+	184.152i	0.251134	+	0.221337i
$833$		−	250.842i		−	0.301131i
$834$	83.9960	+	17.4847i	0.100715	+	0.0209649i
$835$	−99.8824	−	241.138i	−0.119620	−	0.288787i
$836$	915.551	+	356.905i	1.09516	+	0.426920i
$837$	−389.382	+	804.371i	−0.465212	+	0.961017i
$838$	−143.090	−	681.873i	−0.170751	−	0.813691i
$839$	−59.1440	+	59.1440i	−0.0704934	+	0.0704934i	−0.741474	−	0.670981i	$-0.765873\pi$
$839$	−59.1440	+	59.1440i	−0.0704934	+	0.0704934i	0.670981	+	0.741474i	$0.265873\pi$
$840$	−43.2730	−	204.566i	−0.0515155	−	0.243531i
$841$	−94.4475	+	94.4475i	−0.112304	+	0.112304i
$842$	−652.977	+	999.811i	−0.775507	+	1.18742i
$843$	−173.603	+	397.166i	−0.205934	+	0.471135i
$844$	189.036	−	3.96923i	0.223976	−	0.00470287i
$845$	106.572	+	257.288i	0.126121	+	0.304483i
$846$	853.770	+	1359.40i	1.00918	+	1.60685i
$847$		−	63.9031i		−	0.0754464i
$848$	−491.202	−	1057.93i	−0.579248	−	1.24755i
$849$	−1493.73	−	28.9492i	−1.75940	−	0.0340980i
$850$	331.151	−	226.332i	0.389589	−	0.266273i
$851$	209.621	+	506.070i	0.246323	+	0.594677i
$852$	663.701	−	665.849i	0.778992	−	0.781513i
$853$	−263.908	+	637.131i	−0.309388	+	0.746929i	0.690337	+	0.723488i	$0.257462\pi$
$853$	−263.908	+	637.131i	−0.309388	+	0.746929i	−0.999725	+	0.0234414i	$0.992538\pi$
$854$	388.828	+	253.944i	0.455302	+	0.297358i
$855$	240.192	+	259.571i	0.280926	+	0.303591i
$856$	325.911	−	232.936i	0.380737	−	0.272122i
$857$	842.638	−	842.638i	0.983241	−	0.983241i	−0.0166209	−	0.999862i	$-0.505291\pi$
$857$	842.638	−	842.638i	0.983241	−	0.983241i	0.999862	+	0.0166209i	$0.00529084\pi$
$858$	56.4599	+	297.633i	0.0658040	+	0.346892i
$859$	914.408	+	378.760i	1.06450	+	0.440931i	0.845048	−	0.534691i	$-0.179572\pi$
$859$	914.408	+	378.760i	1.06450	+	0.440931i	0.219455	+	0.975623i	$0.429572\pi$
$860$	−131.215	−	298.876i	−0.152576	−	0.347530i
$861$	−333.824	−	852.268i	−0.387716	−	0.989858i
$862$	−200.531	+	1066.53i	−0.232634	+	1.23727i
$863$		−	482.513i		−	0.559111i	−0.960129	−	0.279556i	$-0.909813\pi$
$863$		−	482.513i		−	0.559111i	0.960129	−	0.279556i	$-0.0901872\pi$
$864$	−163.768	−	848.337i	−0.189547	−	0.981872i
$865$	42.6618			0.0493200
$866$	1146.82	+	215.627i	1.32427	+	0.248992i
$867$	−565.484	+	221.494i	−0.652231	+	0.255471i
$868$	−249.852	−	569.102i	−0.287848	−	0.655648i
$869$	−407.799	+	984.514i	−0.469274	+	1.13293i
$870$	−290.971	+	55.1960i	−0.334449	+	0.0634437i
$871$	364.537	+	364.537i	0.418527	+	0.418527i
$872$	75.7761	−	455.472i	0.0868992	−	0.522330i
$873$	−276.650	+	255.996i	−0.316896	+	0.293237i
$874$	−337.040	+	516.061i	−0.385629	+	0.590459i
$875$	−374.730	−	155.218i	−0.428263	−	0.177392i
$876$	1081.24	−	1084.74i	1.23429	−	1.23829i
$877$	−1406.14	+	582.442i	−1.60335	+	0.664130i	−0.991885	−	0.127140i	$-0.959420\pi$
$877$	−1406.14	+	582.442i	−1.60335	+	0.664130i	−0.611467	+	0.791270i	$0.709420\pi$
$878$	293.541	+	429.486i	0.334329	+	0.489164i
$879$	−16.9989	+	877.116i	−0.0193389	+	0.997856i
$880$	344.201	−	14.4609i	0.391137	−	0.0164328i
$881$	1370.72			1.55587			0.777933	−	0.628347i	$-0.216268\pi$
$881$	1370.72			1.55587			0.777933	+	0.628347i	$0.216268\pi$
$882$	−410.969	+	258.109i	−0.465951	+	0.292641i
$883$	1216.61	−	503.935i	1.37781	−	0.570708i	0.433916	−	0.900953i	$-0.357132\pi$
$883$	1216.61	−	503.935i	1.37781	−	0.570708i	0.943895	+	0.330245i	$0.107132\pi$
$884$	161.917	−	3.39980i	0.183164	−	0.00384592i
$885$	−251.737	−	110.035i	−0.284449	−	0.124333i
$886$	−189.873	−	124.006i	−0.214304	−	0.139962i
$887$	−126.214	−	126.214i	−0.142293	−	0.142293i	0.632372	−	0.774665i	$-0.282081\pi$
$887$	−126.214	−	126.214i	−0.142293	−	0.142293i	−0.774665	+	0.632372i	$0.782081\pi$
$888$	−492.668	+	757.023i	−0.554807	+	0.852503i
$889$	−179.864	−	179.864i	−0.202321	−	0.202321i
$890$	−123.236	+	25.8607i	−0.138467	+	0.0290570i
$891$	425.791	−	837.790i	0.477880	−	0.940281i
$892$	702.944	+	274.026i	0.788054	+	0.307204i
$893$	1744.58	−	722.628i	1.95361	−	0.809214i
$894$	255.589	−	1227.84i	0.285894	−	1.37343i
$895$	171.958			0.192132
$896$	522.794	+	296.264i	0.583475	+	0.330652i
$897$	−189.984	−	3.68199i	−0.211800	−	0.00410478i
$898$	1316.87	+	247.602i	1.46645	+	0.275726i
$899$	−813.330	+	336.892i	−0.904705	+	0.374741i
$900$	−711.557	−	309.655i	−0.790619	−	0.344061i
$901$	−626.622	−	259.555i	−0.695473	−	0.288075i
$902$	1475.94	−	309.722i	1.63629	−	0.343373i
$903$	446.302	−	429.331i	0.494243	−	0.475450i
$904$	−228.984	+	367.226i	−0.253301	+	0.406223i
$905$	−110.140	−	110.140i	−0.121702	−	0.121702i
$906$	−1076.31	−	733.075i	−1.18798	−	0.809134i
$907$	−301.385	+	727.607i	−0.332287	+	0.802213i	0.666123	+	0.745842i	$0.267953\pi$
$907$	−301.385	+	727.607i	−0.332287	+	0.802213i	−0.998410	+	0.0563703i	$0.982047\pi$
$908$	977.551	−	20.5258i	1.07660	−	0.0226055i
$909$	−227.787	−	616.469i	−0.250591	−	0.678184i
$910$	−42.7866	−	62.6020i	−0.0470182	−	0.0687934i
$911$	−864.601			−0.949068			−0.474534	−	0.880237i	$-0.657383\pi$
$911$	−864.601			−0.949068			−0.474534	+	0.880237i	$0.657383\pi$
$912$	−1016.08	+	22.9777i	−1.11413	+	0.0251949i
$913$			91.7317i			0.100473i
$914$	−512.236	−	749.464i	−0.560434	−	0.819983i
$915$	−256.410	+	100.433i	−0.280229	+	0.109763i
$916$	−712.988	−	683.662i	−0.778371	−	0.746356i
$917$	−78.3135	−	32.4385i	−0.0854019	−	0.0353746i
$918$	−403.971	−	298.698i	−0.440056	−	0.325380i
$919$	662.872	−	662.872i	0.721297	−	0.721297i	−0.247572	−	0.968869i	$-0.579633\pi$
$919$	662.872	−	662.872i	0.721297	−	0.721297i	0.968869	+	0.247572i	$0.0796328\pi$
$920$	−35.4632	+	213.161i	−0.0385470	+	0.231697i
$921$	−592.639	+	570.105i	−0.643474	+	0.619006i
$922$	−1644.36	+	345.065i	−1.78347	+	0.374257i
$923$	130.471	−	314.985i	0.141355	−	0.341262i
$924$	251.101	+	603.452i	0.271754	+	0.653086i
$925$	310.448	+	749.489i	0.335620	+	0.810258i
$926$	−590.296	−	110.989i	−0.637468	−	0.119858i
$927$	1341.32	+	52.0102i	1.44694	+	0.0561059i
$928$	435.081	−	731.515i	0.468838	−	0.788270i
$929$		−	1520.53i		−	1.63674i	−0.574693	−	0.818369i	$-0.694879\pi$
$929$		−	1520.53i		−	1.63674i	0.574693	−	0.818369i	$-0.305121\pi$
$930$	360.813	+	75.1073i	0.387971	+	0.0807606i
$931$	218.462	+	527.415i	0.234654	+	0.566504i
$932$	230.480	+	524.977i	0.247296	+	0.563280i
$933$	854.981	+	373.715i	0.916379	+	0.400552i
$934$	−410.553	+	86.1538i	−0.439564	+	0.0922417i
$935$	141.652	−	141.652i	0.151499	−	0.151499i
$936$	−172.178	−	261.779i	−0.183951	−	0.279679i
$937$	−428.097	+	428.097i	−0.456880	+	0.456880i	−0.897630	−	0.440750i	$-0.854713\pi$
$937$	−428.097	+	428.097i	−0.456880	+	0.456880i	0.440750	+	0.897630i	$0.354713\pi$
$938$	931.269	+	608.212i	0.992824	+	0.648413i
$939$	−239.132	−	104.525i	−0.254666	−	0.111315i
$940$	458.185	−	477.839i	0.487431	−	0.508340i
$941$	574.159	+	1386.14i	0.610159	+	1.47305i	0.862827	+	0.505500i	$0.168692\pi$
$941$	574.159	+	1386.14i	0.610159	+	1.47305i	−0.252668	+	0.967553i	$0.581308\pi$
$942$	−1276.74	+	836.787i	−1.35535	+	0.888309i
$943$			945.947i			1.00312i
$944$	716.124	−	332.501i	0.758605	−	0.352225i
$945$	−13.6672	+	234.832i	−0.0144626	+	0.248499i
$946$	575.744	+	842.384i	0.608609	+	0.890469i
$947$	202.456	+	488.773i	0.213787	+	0.516128i	0.993999	−	0.109387i	$-0.0348889\pi$
$947$	202.456	+	488.773i	0.213787	+	0.516128i	−0.780212	+	0.625515i	$0.784889\pi$
$948$	−1.78114	−	1102.16i	−0.00187884	−	1.16262i
$949$	212.551	−	513.143i	0.223973	−	0.540720i
$950$	−499.155	+	764.285i	−0.525426	+	0.804511i
$951$	1062.16	−	1021.77i	1.11688	−	1.07442i
$952$	340.390	−	78.9251i	0.357552	−	0.0829045i
$953$	−755.761	+	755.761i	−0.793033	+	0.793033i	−0.981986	−	0.188953i	$-0.939491\pi$
$953$	−755.761	+	755.761i	−0.793033	+	0.793033i	0.188953	+	0.981986i	$0.439491\pi$
$954$	219.531	+	1293.71i	0.230116	+	1.35609i
$955$	140.559	+	58.2215i	0.147182	+	0.0609649i
$956$	−552.395	−	215.338i	−0.577819	−	0.225249i
$957$	862.009	−	337.639i	0.900741	−	0.352810i
$958$	1618.88	+	304.386i	1.68986	+	0.317731i
$959$		−	255.580i		−	0.266507i
$960$	−322.935	+	150.576i	−0.336391	+	0.156850i
$961$	134.516			0.139975
$962$	−60.5260	+	321.909i	−0.0629169	+	0.334624i
$963$	−422.735	+	156.202i	−0.438977	+	0.162204i
$964$	−33.1880	+	85.1355i	−0.0344274	+	0.0883148i
$965$	112.037	−	270.481i	0.116101	−	0.280291i
$966$	−402.794	+	76.4084i	−0.416971	+	0.0790977i
$967$	−137.364	−	137.364i	−0.142052	−	0.142052i	0.632505	−	0.774557i	$-0.282027\pi$
$967$	−137.364	−	137.364i	−0.142052	−	0.142052i	−0.774557	+	0.632505i	$0.782027\pi$
$968$	−106.083	+	24.5971i	−0.109590	+	0.0254103i
$969$	−425.915	+	409.720i	−0.439541	+	0.422828i
$970$	130.145	+	84.9979i	0.134170	+	0.0876267i
$971$	1359.17	+	562.987i	1.39976	+	0.579801i	0.949690	−	0.313191i	$-0.101398\pi$
$971$	1359.17	+	562.987i	1.39976	+	0.579801i	0.450073	+	0.892992i	$0.351398\pi$
$972$	−73.7003	+	969.202i	−0.0758233	+	0.997121i
$973$	62.0196	−	25.6893i	0.0637406	−	0.0264022i
$974$	−267.821	+	183.048i	−0.274970	+	0.187934i
$975$	−281.366	−	5.45302i	−0.288581	−	0.00559284i
$976$	271.897	−	743.224i	0.278583	−	0.761500i
$977$	−1291.79			−1.32220			−0.661098	−	0.750299i	$-0.729909\pi$
$977$	−1291.79			−1.32220			−0.661098	+	0.750299i	$0.729909\pi$
$978$	−791.087	+	518.485i	−0.808882	+	0.530148i
$979$	363.654	−	150.631i	0.371455	−	0.153862i
$980$	144.459	+	138.517i	0.147407	+	0.141344i
$981$	−217.230	+	471.846i	−0.221437	+	0.480984i
$982$	254.491	−	389.666i	0.259156	−	0.396809i
$983$	1137.44	+	1137.44i	1.15711	+	1.15711i	0.985095	+	0.172012i	$0.0550269\pi$
$983$	1137.44	+	1137.44i	1.15711	+	1.15711i	0.172012	+	0.985095i	$0.444973\pi$
$984$	−1286.32	+	882.216i	−1.30724	+	0.896561i
$985$	346.015	+	346.015i	0.351284	+	0.351284i
$986$	−101.644	−	484.370i	−0.103087	−	0.491247i
$987$	1150.87	+	503.047i	1.16602	+	0.509673i
$988$	−337.482	+	148.164i	−0.341581	+	0.149964i
$989$	−591.291	+	244.921i	−0.597867	+	0.247645i
$990$	−377.832	−	86.3209i	−0.381649	−	0.0871928i
$991$	−625.243			−0.630921			−0.315461	−	0.948939i	$-0.602159\pi$
$991$	−625.243			−0.630921			−0.315461	+	0.948939i	$0.602159\pi$
$992$	−848.572	+	633.825i	−0.855416	+	0.638936i
$993$	27.7483	−	1431.77i	0.0279439	−	1.44186i
$994$	135.925	−	722.920i	0.136746	−	0.727283i
$995$	211.101	−	87.4409i	0.212162	−	0.0878803i
$996$	−36.4493	−	87.5957i	−0.0365957	−	0.0879475i
$997$	−363.892	−	150.729i	−0.364987	−	0.151183i	0.192650	−	0.981268i	$-0.438292\pi$
$997$	−363.892	−	150.729i	−0.364987	−	0.151183i	−0.557637	+	0.830085i	$0.688292\pi$
$998$	−123.921	−	590.528i	−0.124169	−	0.591711i
$999$	759.039	−	675.547i	0.759799	−	0.676223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.3.p.a.5.17	yes	120
3.2	odd	2	inner	96.3.p.a.5.14	✓	120
4.3	odd	2		384.3.p.a.113.4		120
12.11	even	2		384.3.p.a.113.27		120
32.13	even	8	inner	96.3.p.a.77.14	yes	120
32.19	odd	8		384.3.p.a.17.27		120
96.77	odd	8	inner	96.3.p.a.77.17	yes	120
96.83	even	8		384.3.p.a.17.4		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.3.p.a.5.14	✓	120	3.2	odd	2	inner
96.3.p.a.5.17	yes	120	1.1	even	1	trivial
96.3.p.a.77.14	yes	120	32.13	even	8	inner
96.3.p.a.77.17	yes	120	96.77	odd	8	inner
384.3.p.a.17.4		120	96.83	even	8
384.3.p.a.17.27		120	32.19	odd	8
384.3.p.a.113.4		120	4.3	odd	2
384.3.p.a.113.27		120	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	96.p (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.369569 - 1.96556i) q^{2} +(2.79336 - 1.09413i) q^{3} +(-3.72684 - 1.45282i) q^{4} +(0.710186 - 1.71454i) q^{5} +(-1.11823 - 5.89488i) q^{6} +(-3.31956 - 3.31956i) q^{7} +(-4.23292 + 6.78840i) q^{8} +(6.60576 - 6.11260i) q^{9} +O(q^{10})\)	\(q+(0.369569 - 1.96556i) q^{2} +(2.79336 - 1.09413i) q^{3} +(-3.72684 - 1.45282i) q^{4} +(0.710186 - 1.71454i) q^{5} +(-1.11823 - 5.89488i) q^{6} +(-3.31956 - 3.31956i) q^{7} +(-4.23292 + 6.78840i) q^{8} +(6.60576 - 6.11260i) q^{9} +(-3.10757 - 2.02955i) q^{10} +(10.7191 + 4.43999i) q^{11} +(-12.0000 + 0.0193925i) q^{12} +(-4.02050 + 1.66535i) q^{13} +(-7.75159 + 5.29798i) q^{14} +(0.107879 - 5.56637i) q^{15} +(11.7786 + 10.8288i) q^{16} +9.30385 q^{17} +(-9.57339 - 15.2430i) q^{18} +(-19.5621 + 8.10288i) q^{19} +(-5.13767 + 5.35805i) q^{20} +(-12.9048 - 5.64071i) q^{21} +(12.6885 - 19.4281i) q^{22} +(10.2920 + 10.2920i) q^{23} +(-4.39670 + 23.5938i) q^{24} +(15.2424 + 15.2424i) q^{25} +(1.78748 + 8.51799i) q^{26} +(11.7643 - 24.3023i) q^{27} +(7.54874 + 17.1942i) q^{28} +(24.5730 - 10.1785i) q^{29} +(-10.9012 - 2.26920i) q^{30} -33.0986 q^{31} +(25.6377 - 19.1496i) q^{32} +(34.8002 + 0.674445i) q^{33} +(3.43841 - 18.2873i) q^{34} +(-8.04902 + 3.33401i) q^{35} +(-33.4991 + 13.1837i) q^{36} +(34.7694 + 14.4020i) q^{37} +(8.69715 + 41.4450i) q^{38} +(-9.40862 + 9.05087i) q^{39} +(8.63283 + 12.0786i) q^{40} +(45.9556 + 45.9556i) q^{41} +(-15.8563 + 23.2804i) q^{42} +(-16.8272 + 40.6245i) q^{43} +(-33.4978 - 32.1200i) q^{44} +(-5.78899 - 15.6669i) q^{45} +(24.0330 - 16.4259i) q^{46} -89.1816 q^{47} +(44.7502 + 17.3615i) q^{48} -26.9611i q^{49} +(35.5929 - 24.3267i) q^{50} +(25.9890 - 10.1796i) q^{51} +(17.4032 - 0.365418i) q^{52} +(-67.3508 - 27.8976i) q^{53} +(-43.4198 - 32.1048i) q^{54} +(15.2251 - 15.2251i) q^{55} +(36.5859 - 8.48306i) q^{56} +(-45.7784 + 44.0377i) q^{57} +(-10.9249 - 52.0612i) q^{58} +(18.8842 - 45.5906i) q^{59} +(-8.48898 + 20.5882i) q^{60} +(-18.9284 - 45.6972i) q^{61} +(-12.2322 + 65.0572i) q^{62} +(-42.2193 - 1.63708i) q^{63} +(-28.1648 - 57.4695i) q^{64} +8.07602i q^{65} +(14.1867 - 68.1526i) q^{66} +(-45.3348 - 109.448i) q^{67} +(-34.6739 - 13.5168i) q^{68} +(40.0099 + 17.4885i) q^{69} +(3.57853 + 17.0530i) q^{70} +(-55.3980 + 55.3980i) q^{71} +(13.5331 + 70.7167i) q^{72} +(-90.2492 + 90.2492i) q^{73} +(41.1576 - 63.0188i) q^{74} +(59.2546 + 25.9004i) q^{75} +(84.6767 - 1.77797i) q^{76} +(-20.8438 - 50.3214i) q^{77} +(14.3129 + 21.8381i) q^{78} +91.8469i q^{79} +(26.9315 - 12.5045i) q^{80} +(6.27220 - 80.7568i) q^{81} +(107.312 - 73.3447i) q^{82} +(3.02564 + 7.30454i) q^{83} +(39.8990 + 39.7703i) q^{84} +(6.60747 - 15.9518i) q^{85} +(73.6310 + 48.0884i) q^{86} +(57.5047 - 55.3181i) q^{87} +(-75.5134 + 53.9713i) q^{88} +(23.9892 - 23.9892i) q^{89} +(-32.9337 + 5.58858i) q^{90} +(18.8745 + 7.81807i) q^{91} +(-23.4041 - 53.3088i) q^{92} +(-92.4564 + 36.2141i) q^{93} +(-32.9587 + 175.292i) q^{94} +39.2946i q^{95} +(50.6633 - 81.5428i) q^{96} -41.8801 q^{97} +(-52.9936 - 9.96398i) q^{98} +(97.9476 - 36.1920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) 120 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9	\( 120 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} + 32 q^{10} - 4 q^{12} - 8 q^{13} - 40 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} - 120 q^{22} - 144 q^{24} - 8 q^{25} + 92 q^{27} - 8 q^{28} - 60 q^{30} - 16 q^{31} - 8 q^{33} - 40 q^{34} + 64 q^{36} - 8 q^{37} - 196 q^{39} - 232 q^{40} + 16 q^{42} - 8 q^{43} - 4 q^{45} - 40 q^{46} + 48 q^{48} - 40 q^{51} - 112 q^{52} + 304 q^{54} - 264 q^{55} - 4 q^{57} - 16 q^{58} + 424 q^{60} + 56 q^{61} - 8 q^{63} + 40 q^{64} + 428 q^{66} + 248 q^{67} - 4 q^{69} + 328 q^{70} + 416 q^{72} - 8 q^{73} - 104 q^{75} + 720 q^{76} + 276 q^{78} + 512 q^{82} + 232 q^{84} - 208 q^{85} - 452 q^{87} + 272 q^{88} - 304 q^{90} - 200 q^{91} - 40 q^{93} + 416 q^{94} - 616 q^{96} - 16 q^{97} + 252 q^{99}+O(q^{100}) \) 120 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9 + 32 * q^10 - 4 * q^12 - 8 * q^13 - 40 * q^16 - 4 * q^18 - 8 * q^19 - 4 * q^21 - 120 * q^22 - 144 * q^24 - 8 * q^25 + 92 * q^27 - 8 * q^28 - 60 * q^30 - 16 * q^31 - 8 * q^33 - 40 * q^34 + 64 * q^36 - 8 * q^37 - 196 * q^39 - 232 * q^40 + 16 * q^42 - 8 * q^43 - 4 * q^45 - 40 * q^46 + 48 * q^48 - 40 * q^51 - 112 * q^52 + 304 * q^54 - 264 * q^55 - 4 * q^57 - 16 * q^58 + 424 * q^60 + 56 * q^61 - 8 * q^63 + 40 * q^64 + 428 * q^66 + 248 * q^67 - 4 * q^69 + 328 * q^70 + 416 * q^72 - 8 * q^73 - 104 * q^75 + 720 * q^76 + 276 * q^78 + 512 * q^82 + 232 * q^84 - 208 * q^85 - 452 * q^87 + 272 * q^88 - 304 * q^90 - 200 * q^91 - 40 * q^93 + 416 * q^94 - 616 * q^96 - 16 * q^97 + 252 * q^99

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