LMFDB - Embedded newform 80.3.i.a.13.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,3,Mod(13,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 3]))

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

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

chi := DirichletCharacter("80.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	80.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17984211488$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.18
Character	$\chi$	$=$	80.13
Dual form			80.3.i.a.37.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.47324 + 1.35261i) q^{2} -4.50609i q^{3} +(0.340894 + 3.98545i) q^{4} +(1.81773 - 4.65788i) q^{5} +(6.09498 - 6.63857i) q^{6} +(1.52625 + 1.52625i) q^{7} +(-4.88854 + 6.33263i) q^{8} -11.3048 q^{9} +O(q^{10})$	\(q+(1.47324 + 1.35261i) q^{2} -4.50609i q^{3} +(0.340894 + 3.98545i) q^{4} +(1.81773 - 4.65788i) q^{5} +(6.09498 - 6.63857i) q^{6} +(1.52625 + 1.52625i) q^{7} +(-4.88854 + 6.33263i) q^{8} -11.3048 q^{9} +(8.97825 - 4.40352i) q^{10} +(10.2610 - 10.2610i) q^{11} +(17.9588 - 1.53610i) q^{12} +21.4526i q^{13} +(0.184117 + 4.31294i) q^{14} +(-20.9888 - 8.19085i) q^{15} +(-15.7676 + 2.71723i) q^{16} +(-18.5474 + 18.5474i) q^{17} +(-16.6548 - 15.2910i) q^{18} +(-6.86774 + 6.86774i) q^{19} +(19.1834 + 5.65662i) q^{20} +(6.87740 - 6.87740i) q^{21} +(28.9960 - 1.23782i) q^{22} +(4.81049 - 4.81049i) q^{23} +(28.5354 + 22.0282i) q^{24} +(-18.3917 - 16.9335i) q^{25} +(-29.0169 + 31.6048i) q^{26} +10.3858i q^{27} +(-5.56248 + 6.60306i) q^{28} +(7.30552 - 7.30552i) q^{29} +(-19.8426 - 40.4568i) q^{30} +24.8935 q^{31} +(-26.9048 - 17.3242i) q^{32} +(-46.2368 - 46.2368i) q^{33} +(-52.4123 + 2.23745i) q^{34} +(9.88337 - 4.33477i) q^{35} +(-3.85375 - 45.0548i) q^{36} -0.818619i q^{37} +(-19.4072 + 0.828482i) q^{38} +96.6671 q^{39} +(20.6106 + 34.2812i) q^{40} +36.1925i q^{41} +(19.4345 - 0.829647i) q^{42} -35.2864 q^{43} +(44.3925 + 37.3967i) q^{44} +(-20.5491 + 52.6566i) q^{45} +(13.5937 - 0.580308i) q^{46} +(-9.49981 + 9.49981i) q^{47} +(12.2441 + 71.0501i) q^{48} -44.3412i q^{49} +(-4.19104 - 49.8240i) q^{50} +(83.5763 + 83.5763i) q^{51} +(-85.4980 + 7.31304i) q^{52} +81.0314 q^{53} +(-14.0479 + 15.3008i) q^{54} +(-29.1427 - 66.4460i) q^{55} +(-17.1263 + 2.20404i) q^{56} +(30.9466 + 30.9466i) q^{57} +(20.6443 - 0.881294i) q^{58} +(8.65405 + 8.65405i) q^{59} +(25.4892 - 86.4421i) q^{60} +(-16.3705 - 16.3705i) q^{61} +(36.6743 + 33.6713i) q^{62} +(-17.2539 - 17.2539i) q^{63} +(-16.2044 - 61.9146i) q^{64} +(99.9235 + 38.9949i) q^{65} +(-5.57773 - 130.659i) q^{66} -46.6786 q^{67} +(-80.2424 - 67.5970i) q^{68} +(-21.6765 - 21.6765i) q^{69} +(20.4239 + 6.98217i) q^{70} -80.8598i q^{71} +(55.2641 - 71.5894i) q^{72} +(-27.4939 + 27.4939i) q^{73} +(1.10727 - 1.20603i) q^{74} +(-76.3040 + 82.8748i) q^{75} +(-29.7122 - 25.0298i) q^{76} +31.3215 q^{77} +(142.414 + 130.753i) q^{78} -79.6266i q^{79} +(-16.0047 + 78.3827i) q^{80} -54.9442 q^{81} +(-48.9544 + 53.3204i) q^{82} -29.4998i q^{83} +(29.7540 + 25.0650i) q^{84} +(52.6775 + 120.106i) q^{85} +(-51.9855 - 47.7288i) q^{86} +(-32.9193 - 32.9193i) q^{87} +(14.8178 + 115.140i) q^{88} +29.5008 q^{89} +(-101.498 + 49.7810i) q^{90} +(-32.7419 + 32.7419i) q^{91} +(20.8118 + 17.5321i) q^{92} -112.173i q^{93} +(-26.8451 + 1.14600i) q^{94} +(19.5054 + 44.4728i) q^{95} +(-78.0646 + 121.236i) q^{96} +(11.6094 - 11.6094i) q^{97} +(59.9763 - 65.3253i) q^{98} +(-115.999 + 115.999i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9	$ 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9} + 6 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{15} + 24 q^{16} - 4 q^{17} + 22 q^{18} + 32 q^{19} + 40 q^{20} - 4 q^{21} + 92 q^{22} + 36 q^{24} - 52 q^{26} + 36 q^{28} - 28 q^{30} - 8 q^{31} - 132 q^{32} - 4 q^{33} - 88 q^{34} + 96 q^{35} - 116 q^{36} - 216 q^{38} + 72 q^{39} + 16 q^{40} + 16 q^{42} + 124 q^{43} - 168 q^{44} - 34 q^{45} + 108 q^{46} - 4 q^{47} + 340 q^{48} + 10 q^{50} - 100 q^{51} + 48 q^{52} - 4 q^{53} + 228 q^{54} - 172 q^{56} + 36 q^{57} + 16 q^{58} + 64 q^{59} + 136 q^{60} - 36 q^{61} - 356 q^{62} - 200 q^{63} - 176 q^{64} - 4 q^{65} + 276 q^{66} - 292 q^{67} - 72 q^{68} - 60 q^{69} - 92 q^{70} + 448 q^{72} + 48 q^{73} + 284 q^{74} + 96 q^{75} + 252 q^{76} + 192 q^{77} + 620 q^{78} + 4 q^{80} + 100 q^{81} - 240 q^{82} + 288 q^{84} + 48 q^{85} + 20 q^{86} + 36 q^{87} - 624 q^{88} - 578 q^{90} + 188 q^{91} - 412 q^{92} - 340 q^{94} + 380 q^{95} - 24 q^{96} - 4 q^{97} - 78 q^{98} - 92 q^{99}+O(q^{100}) $ 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9 + 6 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^15 + 24 * q^16 - 4 * q^17 + 22 * q^18 + 32 * q^19 + 40 * q^20 - 4 * q^21 + 92 * q^22 + 36 * q^24 - 52 * q^26 + 36 * q^28 - 28 * q^30 - 8 * q^31 - 132 * q^32 - 4 * q^33 - 88 * q^34 + 96 * q^35 - 116 * q^36 - 216 * q^38 + 72 * q^39 + 16 * q^40 + 16 * q^42 + 124 * q^43 - 168 * q^44 - 34 * q^45 + 108 * q^46 - 4 * q^47 + 340 * q^48 + 10 * q^50 - 100 * q^51 + 48 * q^52 - 4 * q^53 + 228 * q^54 - 172 * q^56 + 36 * q^57 + 16 * q^58 + 64 * q^59 + 136 * q^60 - 36 * q^61 - 356 * q^62 - 200 * q^63 - 176 * q^64 - 4 * q^65 + 276 * q^66 - 292 * q^67 - 72 * q^68 - 60 * q^69 - 92 * q^70 + 448 * q^72 + 48 * q^73 + 284 * q^74 + 96 * q^75 + 252 * q^76 + 192 * q^77 + 620 * q^78 + 4 * q^80 + 100 * q^81 - 240 * q^82 + 288 * q^84 + 48 * q^85 + 20 * q^86 + 36 * q^87 - 624 * q^88 - 578 * q^90 + 188 * q^91 - 412 * q^92 - 340 * q^94 + 380 * q^95 - 24 * q^96 - 4 * q^97 - 78 * q^98 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	1.47324	+	1.35261i	0.736622	+	0.676305i
$2$	1.47324	+	1.35261i	0.736622	+	0.676305i
$3$		−	4.50609i		−	1.50203i	−0.660285	−	0.751015i	$-0.729565\pi$
$3$		−	4.50609i		−	1.50203i	0.660285	−	0.751015i	$-0.270435\pi$
$4$	0.340894	+	3.98545i	0.0852234	+	0.996362i
$5$	1.81773	−	4.65788i	0.363546	−	0.931576i
$5$	1.81773	−	4.65788i	0.363546	−	0.931576i
$6$	6.09498	−	6.63857i	1.01583	−	1.10643i
$7$	1.52625	+	1.52625i	0.218035	+	0.218035i	0.807670	−	0.589635i	$-0.200728\pi$
$7$	1.52625	+	1.52625i	0.218035	+	0.218035i	−0.589635	+	0.807670i	$0.700728\pi$
$8$	−4.88854	+	6.33263i	−0.611067	+	0.791579i
$9$	−11.3048			−1.25609
$10$	8.97825	−	4.40352i	0.897825	−	0.440352i
$11$	10.2610	−	10.2610i	0.932816	−	0.932816i	−0.0650655	−	0.997881i	$-0.520726\pi$
$11$	10.2610	−	10.2610i	0.932816	−	0.932816i	0.997881	+	0.0650655i	$0.0207256\pi$
$12$	17.9588	−	1.53610i	1.49656	−	0.128008i
$13$			21.4526i			1.65020i	0.564989	+	0.825098i	$0.308880\pi$
$13$			21.4526i			1.65020i	−0.564989	+	0.825098i	$0.691120\pi$
$14$	0.184117	+	4.31294i	0.0131512	+	0.308067i
$15$	−20.9888	−	8.19085i	−1.39926	−	0.546056i
$16$	−15.7676	+	2.71723i	−0.985474	+	0.169827i
$17$	−18.5474	+	18.5474i	−1.09102	+	1.09102i	−0.0956051	+	0.995419i	$0.530479\pi$
$17$	−18.5474	+	18.5474i	−1.09102	+	1.09102i	−0.995419	+	0.0956051i	$0.969521\pi$
$18$	−16.6548	−	15.2910i	−0.925265	−	0.849502i
$19$	−6.86774	+	6.86774i	−0.361460	+	0.361460i	−0.864350	−	0.502890i	$-0.832270\pi$
$19$	−6.86774	+	6.86774i	−0.361460	+	0.361460i	0.502890	+	0.864350i	$0.332270\pi$
$20$	19.1834	+	5.65662i	0.959170	+	0.282831i
$21$	6.87740	−	6.87740i	0.327495	−	0.327495i
$22$	28.9960	−	1.23782i	1.31800	−	0.0562646i
$23$	4.81049	−	4.81049i	0.209152	−	0.209152i	−0.594755	−	0.803907i	$-0.702751\pi$
$23$	4.81049	−	4.81049i	0.209152	−	0.209152i	0.803907	+	0.594755i	$0.202751\pi$
$24$	28.5354	+	22.0282i	1.18897	+	0.917841i
$25$	−18.3917	−	16.9335i	−0.735669	−	0.677341i
$26$	−29.0169	+	31.6048i	−1.11604	+	1.21557i
$27$			10.3858i			0.384659i
$28$	−5.56248	+	6.60306i	−0.198660	+	0.235823i
$29$	7.30552	−	7.30552i	0.251915	−	0.251915i	−0.569841	−	0.821755i	$-0.692995\pi$
$29$	7.30552	−	7.30552i	0.251915	−	0.251915i	0.821755	+	0.569841i	$0.192995\pi$
$30$	−19.8426	−	40.4568i	−0.661421	−	1.34856i
$31$	24.8935			0.803018			0.401509	−	0.915855i	$-0.368486\pi$
$31$	24.8935			0.803018			0.401509	+	0.915855i	$0.368486\pi$
$32$	−26.9048	−	17.3242i	−0.840776	−	0.541383i
$33$	−46.2368	−	46.2368i	−1.40112	−	1.40112i
$34$	−52.4123	+	2.23745i	−1.54154	+	0.0658073i
$35$	9.88337	−	4.33477i	0.282382	−	0.123851i
$36$	−3.85375	−	45.0548i	−0.107049	−	1.25152i
$37$		−	0.818619i		−	0.0221248i	−0.999939	−	0.0110624i	$-0.996479\pi$
$37$		−	0.818619i		−	0.0221248i	0.999939	−	0.0110624i	$-0.00352135\pi$
$38$	−19.4072	+	0.828482i	−0.510717	+	0.0218022i
$39$	96.6671			2.47864
$40$	20.6106	+	34.2812i	0.515265	+	0.857031i
$41$			36.1925i			0.882744i	0.897324	+	0.441372i	$0.145508\pi$
$41$			36.1925i			0.882744i	−0.897324	+	0.441372i	$0.854492\pi$
$42$	19.4345	−	0.829647i	0.462726	−	0.0197535i
$43$	−35.2864			−0.820615			−0.410307	−	0.911947i	$-0.634579\pi$
$43$	−35.2864			−0.820615			−0.410307	+	0.911947i	$0.634579\pi$
$44$	44.3925	+	37.3967i	1.00892	+	0.849924i
$45$	−20.5491	+	52.6566i	−0.456647	+	1.17015i
$46$	13.5937	−	0.580308i	0.295516	−	0.0126154i
$47$	−9.49981	+	9.49981i	−0.202124	+	0.202124i	−0.800909	−	0.598786i	$-0.795650\pi$
$47$	−9.49981	+	9.49981i	−0.202124	+	0.202124i	0.598786	+	0.800909i	$0.295650\pi$
$48$	12.2441	+	71.0501i	0.255085	+	1.48021i
$49$		−	44.3412i		−	0.904921i
$50$	−4.19104	−	49.8240i	−0.0838207	−	0.996481i
$51$	83.5763	+	83.5763i	1.63875	+	1.63875i
$52$	−85.4980	+	7.31304i	−1.64419	+	0.140635i
$53$	81.0314			1.52889			0.764447	−	0.644686i	$-0.223012\pi$
$53$	81.0314			1.52889			0.764447	+	0.644686i	$0.223012\pi$
$54$	−14.0479	+	15.3008i	−0.260147	+	0.283348i
$55$	−29.1427	−	66.4460i	−0.529868	−	1.20811i
$56$	−17.1263	+	2.20404i	−0.305826	+	0.0393579i
$57$	30.9466	+	30.9466i	0.542924	+	0.542924i
$58$	20.6443	−	0.881294i	0.355937	−	0.0151947i
$59$	8.65405	+	8.65405i	0.146679	+	0.146679i	0.776633	−	0.629954i	$-0.216926\pi$
$59$	8.65405	+	8.65405i	0.146679	+	0.146679i	−0.629954	+	0.776633i	$0.716926\pi$
$60$	25.4892	−	86.4421i	0.424820	−	1.44070i
$61$	−16.3705	−	16.3705i	−0.268368	−	0.268368i	0.560074	−	0.828442i	$-0.310773\pi$
$61$	−16.3705	−	16.3705i	−0.268368	−	0.268368i	−0.828442	+	0.560074i	$0.810773\pi$
$62$	36.6743	+	33.6713i	0.591520	+	0.543085i
$63$	−17.2539	−	17.2539i	−0.273872	−	0.273872i
$64$	−16.2044	−	61.9146i	−0.253194	−	0.967415i
$65$	99.9235	+	38.9949i	1.53728	+	0.599922i
$66$	−5.57773	−	130.659i	−0.0845111	−	1.97967i
$67$	−46.6786			−0.696695			−0.348348	−	0.937365i	$-0.613257\pi$
$67$	−46.6786			−0.696695			−0.348348	+	0.937365i	$0.613257\pi$
$68$	−80.2424	−	67.5970i	−1.18004	−	0.994074i
$69$	−21.6765	−	21.6765i	−0.314152	−	0.314152i
$70$	20.4239	+	6.98217i	0.291769	+	0.0997453i
$71$		−	80.8598i		−	1.13887i	−0.822036	−	0.569435i	$-0.807162\pi$
$71$		−	80.8598i		−	1.13887i	0.822036	−	0.569435i	$-0.192838\pi$
$72$	55.2641	−	71.5894i	0.767557	−	0.994297i
$73$	−27.4939	+	27.4939i	−0.376629	+	0.376629i	−0.869884	−	0.493256i	$-0.835807\pi$
$73$	−27.4939	+	27.4939i	−0.376629	+	0.376629i	0.493256	+	0.869884i	$0.335807\pi$
$74$	1.10727	−	1.20603i	0.0149631	−	0.0162976i
$75$	−76.3040	+	82.8748i	−1.01739	+	1.10500i
$76$	−29.7122	−	25.0298i	−0.390950	−	0.329340i
$77$	31.3215			0.406773
$78$	142.414	+	130.753i	1.82582	+	1.67632i
$79$		−	79.6266i		−	1.00793i	−0.863724	−	0.503966i	$-0.831874\pi$
$79$		−	79.6266i		−	1.00793i	0.863724	−	0.503966i	$-0.168126\pi$
$80$	−16.0047	+	78.3827i	−0.200058	+	0.979784i
$81$	−54.9442			−0.678324
$82$	−48.9544	+	53.3204i	−0.597004	+	0.650249i
$83$		−	29.4998i		−	0.355420i	−0.984083	−	0.177710i	$-0.943131\pi$
$83$		−	29.4998i		−	0.355420i	0.984083	−	0.177710i	$-0.0568688\pi$
$84$	29.7540	+	25.0650i	0.354214	+	0.298393i
$85$	52.6775	+	120.106i	0.619735	+	1.41301i
$86$	−51.9855	−	47.7288i	−0.604483	−	0.554986i
$87$	−32.9193	−	32.9193i	−0.378383	−	0.378383i
$88$	14.8178	+	115.140i	0.168384	+	1.30841i
$89$	29.5008			0.331469			0.165735	−	0.986170i	$-0.447000\pi$
$89$	29.5008			0.331469			0.165735	+	0.986170i	$0.447000\pi$
$90$	−101.498	+	49.7810i	−1.12775	+	0.553123i
$91$	−32.7419	+	32.7419i	−0.359801	+	0.359801i
$92$	20.8118	+	17.5321i	0.226215	+	0.190566i
$93$		−	112.173i		−	1.20616i
$94$	−26.8451	+	1.14600i	−0.285586	+	0.0121915i
$95$	19.5054	+	44.4728i	0.205320	+	0.468135i
$96$	−78.0646	+	121.236i	−0.813173	+	1.26287i
$97$	11.6094	−	11.6094i	0.119685	−	0.119685i	−0.644728	−	0.764412i	$-0.723029\pi$
$97$	11.6094	−	11.6094i	0.119685	−	0.119685i	0.764412	+	0.644728i	$0.223029\pi$
$98$	59.9763	−	65.3253i	0.612003	−	0.666585i
$99$	−115.999	+	115.999i	−1.17170	+	1.17170i
$100$	61.2181	−	79.0718i	0.612181	−	0.790718i
$101$	−16.5754	+	16.5754i	−0.164113	+	0.164113i	−0.784386	−	0.620273i	$-0.787022\pi$
$101$	−16.5754	+	16.5754i	−0.164113	+	0.164113i	0.620273	+	0.784386i	$0.287022\pi$
$102$	10.0821	+	236.174i	0.0988445	+	2.31543i
$103$	−99.5646	+	99.5646i	−0.966647	+	0.966647i	−0.999461	−	0.0328145i	$-0.989553\pi$
$103$	−99.5646	+	99.5646i	−0.966647	+	0.966647i	0.0328145	+	0.999461i	$0.489553\pi$
$104$	−135.851	−	104.872i	−1.30626	−	1.00838i
$105$	−19.5329	−	44.5353i	−0.186027	−	0.424146i
$106$	119.379	+	109.604i	1.12622	+	1.03400i
$107$		−	157.800i		−	1.47477i	−0.675474	−	0.737384i	$-0.736061\pi$
$107$		−	157.800i		−	1.47477i	0.675474	−	0.737384i	$-0.263939\pi$
$108$	−41.3920	+	3.54045i	−0.383260	+	0.0327820i
$109$	38.8130	−	38.8130i	0.356083	−	0.356083i	−0.506284	−	0.862367i	$-0.668981\pi$
$109$	38.8130	−	38.8130i	0.356083	−	0.356083i	0.862367	+	0.506284i	$0.168981\pi$
$110$	46.9412	−	137.310i	0.426738	−	1.24827i
$111$	−3.68877			−0.0332322
$112$	−28.2124	−	19.9180i	−0.251896	−	0.177840i
$113$	−131.857	−	131.857i	−1.16688	−	1.16688i	−0.982938	−	0.183938i	$-0.941116\pi$
$113$	−131.857	−	131.857i	−1.16688	−	1.16688i	−0.183938	−	0.982938i	$-0.558884\pi$
$114$	3.73321	+	87.4507i	0.0327475	+	0.767111i
$115$	−13.6625	−	31.1508i	−0.118805	−	0.270877i
$116$	31.6062	+	26.6254i	0.272467	+	0.229529i
$117$		−	242.518i		−	2.07280i
$118$	1.04397	+	24.4551i	0.00884722	+	0.207246i
$119$	−56.6158			−0.475763
$120$	154.474	−	92.8733i	1.28729	−	0.773944i
$121$		−	89.5750i		−	0.740290i
$122$	−1.97483	−	46.2605i	−0.0161872	−	0.379185i
$123$	163.087			1.32591
$124$	8.48605	+	99.2119i	0.0684359	+	0.800096i
$125$	−112.306	+	54.8859i	−0.898444	+	0.439087i
$126$	−2.08141	−	48.7571i	−0.0165191	−	0.386961i
$127$	−154.162	+	154.162i	−1.21388	+	1.21388i	−0.244136	+	0.969741i	$0.578504\pi$
$127$	−154.162	+	154.162i	−1.21388	+	1.21388i	−0.969741	+	0.244136i	$0.921496\pi$
$128$	59.8732	−	113.134i	0.467759	−	0.883856i
$129$			159.004i			1.23259i
$130$	94.4667	+	192.606i	0.726667	+	1.48159i
$131$	128.318	+	128.318i	0.979530	+	0.979530i	0.999795	−	0.0202649i	$-0.00645095\pi$
$131$	128.318	+	128.318i	0.979530	+	0.979530i	−0.0202649	+	0.999795i	$0.506451\pi$
$132$	168.513	−	200.036i	1.27661	−	1.51543i
$133$	−20.9637			−0.157622
$134$	−68.7689	−	63.1379i	−0.513201	−	0.471178i
$135$	48.3758	+	18.8786i	0.358339	+	0.139841i
$136$	−26.7842	−	208.124i	−0.196943	−	1.53032i
$137$	98.3855	+	98.3855i	0.718142	+	0.718142i	0.968225	−	0.250082i	$-0.0804576\pi$
$137$	98.3855	+	98.3855i	0.718142	+	0.718142i	−0.250082	+	0.968225i	$0.580458\pi$
$138$	−2.61492	−	61.2546i	−0.0189487	−	0.443874i
$139$	−89.3606	−	89.3606i	−0.642882	−	0.642882i	0.308381	−	0.951263i	$-0.400213\pi$
$139$	−89.3606	−	89.3606i	−0.642882	−	0.642882i	−0.951263	+	0.308381i	$0.900213\pi$
$140$	20.6452	+	37.9119i	0.147466	+	0.270800i
$141$	42.8070	+	42.8070i	0.303596	+	0.303596i
$142$	109.372	−	119.126i	0.770224	−	0.838917i
$143$	220.124	+	220.124i	1.53933	+	1.53933i
$144$	178.250	−	30.7178i	1.23785	−	0.213318i
$145$	−20.7488	−	47.3077i	−0.143095	−	0.326260i
$146$	−77.6937	+	3.31669i	−0.532149	+	0.0227171i
$147$	−199.805			−1.35922
$148$	3.26256	−	0.279062i	0.0220443	−	0.00188555i
$149$	135.878	+	135.878i	0.911932	+	0.911932i	0.996424	−	0.0844918i	$-0.0269267\pi$
$149$	135.878	+	135.878i	0.911932	+	0.911932i	−0.0844918	+	0.996424i	$0.526927\pi$
$150$	−224.512	+	18.8852i	−1.49674	+	0.125901i
$151$			174.395i			1.15493i	0.816415	+	0.577466i	$0.195958\pi$
$151$			174.395i			1.15493i	−0.816415	+	0.577466i	$0.804042\pi$
$152$	−9.91768	−	77.0641i	−0.0652479	−	0.507000i
$153$	209.675	−	209.675i	1.37043	−	1.37043i
$154$	46.1442	+	42.3658i	0.299638	+	0.275102i
$155$	45.2497	−	115.951i	0.291934	−	0.748072i
$156$	32.9532	+	385.262i	0.211239	+	2.46963i
$157$	230.146			1.46590			0.732948	−	0.680285i	$-0.238144\pi$
$157$	230.146			1.46590			0.732948	+	0.680285i	$0.238144\pi$
$158$	107.704	−	117.309i	0.681669	−	0.742464i
$159$		−	365.135i		−	2.29645i
$160$	−129.600	+	93.8288i	−0.810000	+	0.586430i
$161$	14.6840			0.0912047
$162$	−80.9462	−	74.3181i	−0.499668	−	0.458754i
$163$		−	205.854i		−	1.26291i	−0.775414	−	0.631453i	$-0.782459\pi$
$163$		−	205.854i		−	1.26291i	0.775414	−	0.631453i	$-0.217541\pi$
$164$	−144.243	+	12.3378i	−0.879533	+	0.0752305i
$165$	−299.412	+	131.320i	−1.81462	+	0.795877i
$166$	39.9018	−	43.4604i	0.240372	−	0.261810i
$167$	52.8722	+	52.8722i	0.316600	+	0.316600i	0.847460	−	0.530860i	$-0.178131\pi$
$167$	52.8722	+	52.8722i	0.316600	+	0.316600i	−0.530860	+	0.847460i	$0.678131\pi$
$168$	9.93162	+	77.1724i	0.0591168	+	0.459360i
$169$	−291.212			−1.72315
$170$	−84.8495	+	248.197i	−0.499115	+	1.45998i
$171$	77.6387	−	77.6387i	0.454027	−	0.454027i
$172$	−12.0289	−	140.632i	−0.0699356	−	0.817629i
$173$			138.325i			0.799567i	0.916610	+	0.399783i	$0.130915\pi$
$173$			138.325i			0.799567i	−0.916610	+	0.399783i	$0.869085\pi$
$174$	−3.97119	−	93.0252i	−0.0228229	−	0.534628i
$175$	−2.22557	−	53.9150i	−0.0127175	−	0.308086i
$176$	−133.909	+	189.672i	−0.760848	+	1.07768i
$177$	38.9959	−	38.9959i	0.220316	−	0.220316i
$178$	43.4618	+	39.9030i	0.244168	+	0.224174i
$179$	103.785	−	103.785i	0.579802	−	0.579802i	−0.355047	−	0.934849i	$-0.615535\pi$
$179$	103.785	−	103.785i	0.579802	−	0.579802i	0.934849	+	0.355047i	$0.115535\pi$
$180$	−216.865	−	63.9471i	−1.20481	−	0.355262i
$181$	79.6876	−	79.6876i	0.440263	−	0.440263i	−0.451837	−	0.892100i	$-0.649231\pi$
$181$	79.6876	−	79.6876i	0.440263	−	0.440263i	0.892100	+	0.451837i	$0.149231\pi$
$182$	−92.5237	+	3.94978i	−0.508372	+	0.0217021i
$183$	−73.7668	+	73.7668i	−0.403097	+	0.403097i
$184$	6.94680	+	53.9793i	0.0377544	+	0.293366i
$185$	−3.81303	−	1.48803i	−0.0206110	−	0.00804339i
$186$	151.726	−	165.257i	0.815729	−	0.888481i
$187$			380.629i			2.03545i
$188$	−41.0994	−	34.6226i	−0.218614	−	0.184163i
$189$	−15.8513	+	15.8513i	−0.0838691	+	0.0838691i
$190$	−31.4181	+	91.9025i	−0.165358	+	0.483698i
$191$	−113.437			−0.593911			−0.296956	−	0.954891i	$-0.595971\pi$
$191$	−113.437			−0.593911			−0.296956	+	0.954891i	$0.595971\pi$
$192$	−278.993	+	73.0186i	−1.45309	+	0.380305i
$193$	207.468	+	207.468i	1.07496	+	1.07496i	0.996953	+	0.0780092i	$0.0248564\pi$
$193$	207.468	+	207.468i	1.07496	+	1.07496i	0.0780092	+	0.996953i	$0.475144\pi$
$194$	32.8065	−	1.40049i	0.169106	−	0.00721902i
$195$	175.715	−	450.264i	0.901100	−	2.30905i
$196$	176.719	−	15.1156i	0.901629	−	0.0771205i
$197$		−	30.4535i		−	0.154586i	−0.997008	−	0.0772932i	$-0.975372\pi$
$197$		−	30.4535i		−	0.154586i	0.997008	−	0.0772932i	$-0.0246278\pi$
$198$	−327.795	+	13.9934i	−1.65553	+	0.0706735i
$199$	227.899			1.14522			0.572611	−	0.819827i	$-0.305931\pi$
$199$	227.899			1.14522			0.572611	+	0.819827i	$0.305931\pi$
$200$	197.142	−	33.6879i	0.985712	−	0.168439i
$201$			210.338i			1.04646i
$202$	−46.8397	+	1.99956i	−0.231880	+	0.00989881i
$203$	22.3000			0.109852
$204$	−304.598	+	361.580i	−1.49313	+	1.77245i
$205$	168.580	+	65.7882i	0.822344	+	0.320918i
$206$	−281.355	+	12.0109i	−1.36580	+	0.0583052i
$207$	−54.3818	+	54.3818i	−0.262714	+	0.262714i
$208$	−58.2915	−	338.255i	−0.280248	−	1.62623i
$209$			140.939i			0.674351i
$210$	31.4623	−	92.0317i	0.149820	−	0.438246i
$211$	−162.639	−	162.639i	−0.770801	−	0.770801i	0.207445	−	0.978247i	$-0.433485\pi$
$211$	−162.639	−	162.639i	−0.770801	−	0.770801i	−0.978247	+	0.207445i	$0.933485\pi$
$212$	27.6231	+	322.947i	0.130298	+	1.52333i
$213$	−364.361			−1.71062
$214$	213.442	−	232.478i	0.997393	−	1.08635i
$215$	−64.1412	+	164.360i	−0.298331	+	0.764465i
$216$	−65.7694	−	50.7713i	−0.304488	−	0.235052i
$217$	37.9937	+	37.9937i	0.175086	+	0.175086i
$218$	109.680	−	4.68216i	0.503119	−	0.0214778i
$219$	123.890	+	123.890i	0.565707	+	0.565707i
$220$	254.883	−	138.798i	1.15856	−	0.630899i
$221$	−397.889	−	397.889i	−1.80040	−	1.80040i
$222$	−5.43446	−	4.98947i	−0.0244795	−	0.0224751i
$223$	14.2230	+	14.2230i	0.0637803	+	0.0637803i	0.738277	−	0.674497i	$-0.235640\pi$
$223$	14.2230	+	14.2230i	0.0637803	+	0.0637803i	−0.674497	+	0.738277i	$0.735640\pi$
$224$	−14.6223	−	67.5044i	−0.0652783	−	0.301359i
$225$	207.915	+	191.431i	0.924069	+	0.850803i
$226$	−15.9064	−	372.608i	−0.0703824	−	1.64871i
$227$	284.554			1.25354			0.626771	−	0.779203i	$-0.284376\pi$
$227$	284.554			1.25354			0.626771	+	0.779203i	$0.284376\pi$
$228$	−112.787	+	133.886i	−0.494679	+	0.587218i
$229$	20.0023	+	20.0023i	0.0873464	+	0.0873464i	0.749430	−	0.662084i	$-0.230328\pi$
$229$	20.0023	+	20.0023i	0.0873464	+	0.0873464i	−0.662084	+	0.749430i	$0.730328\pi$
$230$	22.0067	−	64.3728i	0.0956813	−	0.279882i
$231$		−	141.138i		−	0.610985i
$232$	10.5499	+	81.9765i	0.0454736	+	0.353347i
$233$	−147.800	+	147.800i	−0.634336	+	0.634336i	−0.949153	−	0.314817i	$-0.898057\pi$
$233$	−147.800	+	147.800i	−0.634336	+	0.634336i	0.314817	+	0.949153i	$0.398057\pi$
$234$	328.032	−	357.288i	1.40184	−	1.52687i
$235$	26.9809	+	61.5171i	0.114812	+	0.261775i
$236$	−31.5401	+	37.4404i	−0.133645	+	0.158646i
$237$	−358.805			−1.51394
$238$	−83.4089	−	76.5791i	−0.350457	−	0.321761i
$239$			230.738i			0.965433i	0.875777	+	0.482716i	$0.160350\pi$
$239$			230.738i			0.965433i	−0.875777	+	0.482716i	$0.839650\pi$
$240$	353.199	+	72.1184i	1.47166	+	0.300493i
$241$	165.848			0.688167			0.344083	−	0.938939i	$-0.388190\pi$
$241$	165.848			0.688167			0.344083	+	0.938939i	$0.388190\pi$
$242$	121.160	−	131.966i	0.500662	−	0.545314i
$243$			341.056i			1.40352i
$244$	59.6631	−	70.8242i	0.244521	−	0.290263i
$245$	−206.536	−	80.6002i	−0.843003	−	0.328980i
$246$	240.266	+	220.593i	0.976693	+	0.896718i
$247$	−147.331	−	147.331i	−0.596480	−	0.596480i
$248$	−121.693	+	157.642i	−0.490698	+	0.635652i
$249$	−132.929			−0.533851
$250$	−239.693	−	71.0452i	−0.958771	−	0.284181i
$251$	74.6924	−	74.6924i	0.297579	−	0.297579i	−0.542486	−	0.840065i	$-0.682517\pi$
$251$	74.6924	−	74.6924i	0.297579	−	0.297579i	0.840065	+	0.542486i	$0.182517\pi$
$252$	62.8829	−	74.6465i	0.249536	−	0.296216i
$253$		−	98.7205i		−	0.390200i
$254$	−435.640	+	18.5972i	−1.71512	+	0.0732174i
$255$	541.208	−	237.369i	2.12238	−	0.930861i
$256$	241.233	−	85.6882i	0.942318	−	0.334720i
$257$	136.830	−	136.830i	0.532413	−	0.532413i	−0.388876	−	0.921290i	$-0.627137\pi$
$257$	136.830	−	136.830i	0.532413	−	0.532413i	0.921290	+	0.388876i	$0.127137\pi$
$258$	−215.070	+	234.251i	−0.833605	+	0.907951i
$259$	1.24941	−	1.24941i	0.00482399	−	0.00482399i
$260$	−121.349	+	411.533i	−0.466727	+	1.58282i
$261$	−82.5877	+	82.5877i	−0.316428	+	0.316428i
$262$	15.4795	+	362.609i	0.0590823	+	1.38400i
$263$	20.0534	−	20.0534i	0.0762487	−	0.0762487i	−0.667954	−	0.744203i	$-0.732830\pi$
$263$	20.0534	−	20.0534i	0.0762487	−	0.0762487i	0.744203	+	0.667954i	$0.232830\pi$
$264$	518.831	−	66.7704i	1.96527	−	0.252918i
$265$	147.293	−	377.435i	0.555823	−	1.42428i
$266$	−30.8847	−	28.3557i	−0.116108	−	0.106600i
$267$		−	132.933i		−	0.497877i
$268$	−15.9124	−	186.035i	−0.0593748	−	0.694161i
$269$	−104.051	+	104.051i	−0.386807	+	0.386807i	−0.873547	−	0.486740i	$-0.838186\pi$
$269$	−104.051	+	104.051i	−0.386807	+	0.386807i	0.486740	+	0.873547i	$0.338186\pi$
$270$	45.7340	+	93.2463i	0.169385	+	0.345357i
$271$	−91.2232			−0.336617			−0.168308	−	0.985734i	$-0.553830\pi$
$271$	−91.2232			−0.336617			−0.168308	+	0.985734i	$0.553830\pi$
$272$	242.050	−	342.845i	0.889891	−	1.26046i
$273$	147.538	+	147.538i	0.540431	+	0.540431i
$274$	11.8686	+	278.023i	0.0433162	+	1.01468i
$275$	−362.471	+	14.9625i	−1.31808	+	0.0544092i
$276$	79.0011	−	93.7798i	0.286236	−	0.339782i
$277$		−	87.2400i		−	0.314946i	−0.987523	−	0.157473i	$-0.949665\pi$
$277$		−	87.2400i		−	0.314946i	0.987523	−	0.157473i	$-0.0503347\pi$
$278$	−10.7799	−	252.520i	−0.0387767	−	0.908345i
$279$	−281.417			−1.00866
$280$	−20.8647	+	83.7784i	−0.0745168	+	0.299209i
$281$		−	163.799i		−	0.582915i	−0.956584	−	0.291458i	$-0.905860\pi$
$281$		−	163.799i		−	0.582915i	0.956584	−	0.291458i	$-0.0941402\pi$
$282$	5.16398	+	120.966i	0.0183120	+	0.428959i
$283$	−234.667			−0.829213			−0.414607	−	0.910001i	$-0.636081\pi$
$283$	−234.667			−0.829213			−0.414607	+	0.910001i	$0.636081\pi$
$284$	322.262	−	27.5646i	1.13473	−	0.0970584i
$285$	200.398	−	87.8932i	0.703152	−	0.308397i
$286$	26.5544	+	622.038i	0.0928476	+	2.17496i
$287$	−55.2387	+	55.2387i	−0.192469	+	0.192469i
$288$	304.155	+	195.848i	1.05609	+	0.680027i
$289$		−	399.013i		−	1.38067i
$290$	33.4208	−	97.7608i	0.115244	−	0.337106i
$291$	−52.3131	−	52.3131i	−0.179770	−	0.179770i
$292$	−118.948	−	100.203i	−0.407356	−	0.343161i
$293$	−305.403			−1.04233			−0.521166	−	0.853455i	$-0.674503\pi$
$293$	−305.403			−1.04233			−0.521166	+	0.853455i	$0.674503\pi$
$294$	−294.362	−	270.258i	−1.00123	−	0.919246i
$295$	56.0402	−	24.5788i	0.189967	−	0.0833180i
$296$	5.18401	+	4.00185i	0.0175136	+	0.0135198i
$297$	106.568	+	106.568i	0.358816	+	0.358816i
$298$	16.3915	+	383.971i	0.0550050	+	1.28849i
$299$	103.197	+	103.197i	0.345141	+	0.345141i
$300$	−356.305	−	275.854i	−1.18768	−	0.919513i
$301$	−53.8557	−	53.8557i	−0.178923	−	0.178923i
$302$	−235.888	+	256.926i	−0.781086	+	0.850748i
$303$	74.6904	+	74.6904i	0.246503	+	0.246503i
$304$	89.6264	−	126.949i	0.294824	−	0.417595i
$305$	−106.009	+	46.4946i	−0.347570	+	0.152441i
$306$	592.512	−	25.2940i	1.93631	−	0.0826600i
$307$	495.760			1.61485			0.807427	−	0.589967i	$-0.200859\pi$
$307$	495.760			1.61485			0.807427	+	0.589967i	$0.200859\pi$
$308$	10.6773	+	124.830i	0.0346666	+	0.405293i
$309$	448.647	+	448.647i	1.45193	+	1.45193i
$310$	223.501	−	109.619i	0.720970	−	0.353610i
$311$			38.1349i			0.122620i	0.998119	+	0.0613101i	$0.0195279\pi$
$311$			38.1349i			0.122620i	−0.998119	+	0.0613101i	$0.980472\pi$
$312$	−472.561	+	612.157i	−1.51462	+	1.96204i
$313$	−30.8202	+	30.8202i	−0.0984671	+	0.0984671i	−0.754624	−	0.656157i	$-0.772181\pi$
$313$	−30.8202	+	30.8202i	−0.0984671	+	0.0984671i	0.656157	+	0.754624i	$0.272181\pi$
$314$	339.060	+	311.297i	1.07981	+	0.991392i
$315$	−111.730	+	49.0039i	−0.354698	+	0.155568i
$316$	317.348	−	27.1442i	1.00426	−	0.0858994i
$317$	194.056			0.612164			0.306082	−	0.952005i	$-0.400982\pi$
$317$	194.056			0.612164			0.306082	+	0.952005i	$0.400982\pi$
$318$	493.885	−	537.933i	1.55310	−	1.69161i
$319$		−	149.924i		−	0.469980i
$320$	−317.846	−	37.0655i	−0.993269	−	0.115830i
$321$	−711.062			−2.21515
$322$	21.6331	+	19.8617i	0.0671834	+	0.0616822i
$323$		−	254.758i		−	0.788723i
$324$	−18.7301	−	218.977i	−0.0578091	−	0.675856i
$325$	363.267	−	394.550i	1.11775	−	1.21400i
$326$	278.440	−	303.273i	0.854110	−	0.930285i
$327$	−174.895	−	174.895i	−0.534847	−	0.534847i
$328$	−229.194	−	176.928i	−0.698762	−	0.539416i
$329$	−28.9981			−0.0881401
$330$	−618.731	−	211.521i	−1.87494	−	0.640974i
$331$	−109.097	+	109.097i	−0.329598	+	0.329598i	−0.852434	−	0.522836i	$-0.824874\pi$
$331$	−109.097	+	109.097i	−0.329598	+	0.329598i	0.522836	+	0.852434i	$0.324874\pi$
$332$	117.570	−	10.0563i	0.354127	−	0.0302901i
$333$			9.25435i			0.0277909i
$334$	6.37818	+	149.409i	0.0190964	+	0.447333i
$335$	−84.8490	+	217.423i	−0.253281	+	0.649025i
$336$	−89.7525	+	127.127i	−0.267120	+	0.378355i
$337$	−73.7614	+	73.7614i	−0.218877	+	0.218877i	−0.808025	−	0.589148i	$-0.799463\pi$
$337$	−73.7614	+	73.7614i	−0.218877	+	0.218877i	0.589148	+	0.808025i	$0.299463\pi$
$338$	−429.026	−	393.896i	−1.26931	−	1.16537i
$339$	−594.159	+	594.159i	−1.75268	+	1.75268i
$340$	−460.718	+	250.887i	−1.35505	+	0.737902i
$341$	255.432	−	255.432i	0.749067	−	0.749067i
$342$	219.396	−	9.36586i	0.641507	−	0.0273855i
$343$	142.461	−	142.461i	0.415340	−	0.415340i
$344$	172.499	−	223.456i	0.501451	−	0.649581i
$345$	−140.368	+	61.5645i	−0.406865	+	0.178448i
$346$	−187.100	+	203.787i	−0.540751	+	0.588978i
$347$		−	644.536i		−	1.85745i	−0.370767	−	0.928726i	$-0.620905\pi$
$347$		−	644.536i		−	1.85745i	0.370767	−	0.928726i	$-0.379095\pi$
$348$	119.976	−	142.420i	0.344759	−	0.409254i
$349$	−161.816	+	161.816i	−0.463657	+	0.463657i	−0.899852	−	0.436195i	$-0.856326\pi$
$349$	−161.816	+	161.816i	−0.463657	+	0.463657i	0.436195	+	0.899852i	$0.356326\pi$
$350$	69.6471	−	82.4402i	0.198992	−	0.235544i
$351$	−222.802			−0.634763
$352$	−453.833	+	98.3062i	−1.28930	+	0.279279i
$353$	91.5785	+	91.5785i	0.259429	+	0.259429i	0.824822	−	0.565393i	$-0.191275\pi$
$353$	91.5785	+	91.5785i	0.259429	+	0.259429i	−0.565393	+	0.824822i	$0.691275\pi$
$354$	110.197	−	4.70423i	0.311290	−	0.0132888i
$355$	−376.635	−	146.981i	−1.06094	−	0.414031i
$356$	10.0566	+	117.574i	0.0282490	+	0.330263i
$357$			255.116i			0.714610i
$358$	293.280	−	12.5199i	0.819217	−	0.0349719i
$359$	218.109			0.607545			0.303772	−	0.952745i	$-0.401754\pi$
$359$	218.109			0.607545			0.303772	+	0.952745i	$0.401754\pi$
$360$	−233.000	−	387.544i	−0.647221	−	1.07651i
$361$			266.668i			0.738693i
$362$	225.185	−	9.61302i	0.622059	−	0.0265553i
$363$	−403.633			−1.11194
$364$	−141.652	−	119.329i	−0.389155	−	0.327828i
$365$	78.0869	+	178.040i	0.213937	+	0.487780i
$366$	−208.454	+	8.89878i	−0.569547	+	0.0243136i
$367$	−232.108	+	232.108i	−0.632446	+	0.632446i	−0.948681	−	0.316235i	$-0.897581\pi$
$367$	−232.108	+	232.108i	−0.632446	+	0.632446i	0.316235	+	0.948681i	$0.397581\pi$
$368$	−62.7786	+	88.9209i	−0.170594	+	0.241633i
$369$		−	409.150i		−	1.10881i
$370$	−3.60480	−	7.34977i	−0.00974271	−	0.0198642i
$371$	123.674	+	123.674i	0.333353	+	0.333353i
$372$	447.058	−	38.2389i	1.20177	−	0.102793i
$373$	71.3315			0.191237			0.0956187	−	0.995418i	$-0.469517\pi$
$373$	71.3315			0.191237			0.0956187	+	0.995418i	$0.469517\pi$
$374$	−514.842	+	560.759i	−1.37658	+	1.49936i
$375$	247.321	+	506.059i	0.659522	+	1.34949i
$376$	−13.7186	−	106.599i	−0.0364857	−	0.283508i
$377$	156.722	+	156.722i	0.415709	+	0.415709i
$378$	−44.7934	+	1.91220i	−0.118501	+	0.00505873i
$379$	449.527	+	449.527i	1.18609	+	1.18609i	0.978140	+	0.207946i	$0.0666779\pi$
$379$	449.527	+	449.527i	1.18609	+	1.18609i	0.207946	+	0.978140i	$0.433322\pi$
$380$	−170.595	+	92.8984i	−0.448934	+	0.244469i
$381$	694.669	+	694.669i	1.82328	+	1.82328i
$382$	−167.120	−	153.436i	−0.437488	−	0.401665i
$383$	−392.032	−	392.032i	−1.02358	−	1.02358i	−0.999715	−	0.0238677i	$-0.992402\pi$
$383$	−392.032	−	392.032i	−1.02358	−	1.02358i	−0.0238677	−	0.999715i	$-0.507598\pi$
$384$	−509.790	−	269.794i	−1.32758	−	0.702588i
$385$	56.9340	−	145.892i	0.147881	−	0.378940i
$386$	25.0276	+	586.273i	0.0648384	+	1.51884i
$387$	398.907			1.03077
$388$	50.2263	+	42.3112i	0.129449	+	0.109049i
$389$	0.333140	+	0.333140i	0.000856400	+	0.000856400i	0.707535	−	0.706678i	$-0.249807\pi$
$389$	0.333140	+	0.333140i	0.000856400	+	0.000856400i	−0.706678	+	0.707535i	$0.749807\pi$
$390$	867.902	−	425.675i	2.22539	−	1.09148i
$391$			178.444i			0.456379i
$392$	280.796	+	216.763i	0.716317	+	0.552968i
$393$	578.214	−	578.214i	1.47128	−	1.47128i
$394$	41.1917	−	44.8655i	0.104548	−	0.113872i
$395$	−370.891	−	144.740i	−0.938965	−	0.366429i
$396$	−501.849	−	422.763i	−1.26730	−	1.06758i
$397$	−3.73338			−0.00940399			−0.00470199	−	0.999989i	$-0.501497\pi$
$397$	−3.73338			−0.00940399			−0.00470199	+	0.999989i	$0.501497\pi$
$398$	335.751	+	308.259i	0.843595	+	0.774519i
$399$			94.4643i			0.236753i
$400$	336.005	+	217.026i	0.840013	+	0.542566i
$401$	−327.705			−0.817219			−0.408609	−	0.912709i	$-0.633986\pi$
$401$	−327.705			−0.817219			−0.408609	+	0.912709i	$0.633986\pi$
$402$	−284.505	+	309.879i	−0.707724	+	0.770843i
$403$			534.030i			1.32514i
$404$	−71.7110	−	60.4101i	−0.177502	−	0.149530i
$405$	−99.8737	+	255.924i	−0.246602	+	0.631910i
$406$	32.8534	+	30.1632i	0.0809197	+	0.0742937i
$407$	−8.39983	−	8.39983i	−0.0206384	−	0.0206384i
$408$	−937.824	+	120.692i	−2.29859	+	0.295814i
$409$	−192.834			−0.471478			−0.235739	−	0.971816i	$-0.575751\pi$
$409$	−192.834			−0.471478			−0.235739	+	0.971816i	$0.575751\pi$
$410$	159.374	+	324.946i	0.388718	+	0.792550i
$411$	443.334	−	443.334i	1.07867	−	1.07867i
$412$	−430.751	−	362.869i	−1.04551	−	0.880749i
$413$			26.4164i			0.0639622i
$414$	−153.675	+	6.56028i	−0.371195	+	0.0158461i
$415$	−137.407	−	53.6227i	−0.331101	−	0.129211i
$416$	371.649	−	577.178i	0.893388	−	1.38745i
$417$	−402.667	+	402.667i	−0.965628	+	0.965628i
$418$	−190.636	+	207.638i	−0.456067	+	0.496742i
$419$	100.155	−	100.155i	0.239034	−	0.239034i	−0.577416	−	0.816450i	$-0.695939\pi$
$419$	100.155	−	100.155i	0.239034	−	0.239034i	0.816450	+	0.577416i	$0.195939\pi$
$420$	170.835	−	93.0290i	0.406749	−	0.221498i
$421$	281.009	−	281.009i	0.667479	−	0.667479i	−0.289653	−	0.957132i	$-0.593540\pi$
$421$	281.009	−	281.009i	0.667479	−	0.667479i	0.957132	+	0.289653i	$0.0935399\pi$
$422$	−19.6198	−	459.594i	−0.0464924	−	1.08909i
$423$	107.394	−	107.394i	0.253886	−	0.253886i
$424$	−396.125	+	513.142i	−0.934257	+	1.21024i
$425$	655.192	−	27.0458i	1.54163	−	0.0636371i
$426$	−536.793	−	492.839i	−1.26008	−	1.15690i
$427$		−	49.9707i		−	0.117027i
$428$	628.904	−	53.7931i	1.46940	−	0.125685i
$429$	991.898	−	991.898i	2.31212	−	2.31212i
$430$	−316.811	+	155.384i	−0.736769	+	0.361359i
$431$	33.2755			0.0772054			0.0386027	−	0.999255i	$-0.487709\pi$
$431$	33.2755			0.0772054			0.0386027	+	0.999255i	$0.487709\pi$
$432$	−28.2206	−	163.759i	−0.0653254	−	0.379071i
$433$	210.976	+	210.976i	0.487243	+	0.487243i	0.907435	−	0.420192i	$-0.138037\pi$
$433$	210.976	+	210.976i	0.487243	+	0.487243i	−0.420192	+	0.907435i	$0.638037\pi$
$434$	4.58332	+	107.365i	0.0105607	+	0.247384i
$435$	−213.173	+	93.4960i	−0.490052	+	0.214933i
$436$	167.918	+	141.456i	0.385134	+	0.324441i
$437$			66.0743i			0.151200i
$438$	14.9453	+	350.095i	0.0341217	+	0.799303i
$439$	−533.725			−1.21577			−0.607887	−	0.794023i	$-0.707983\pi$
$439$	−533.725			−1.21577			−0.607887	+	0.794023i	$0.707983\pi$
$440$	563.244	+	140.274i	1.28010	+	0.318804i
$441$			501.269i			1.13667i
$442$	−47.9990	−	1124.38i	−0.108595	−	2.54384i
$443$	79.6496			0.179796			0.0898979	−	0.995951i	$-0.471346\pi$
$443$	79.6496			0.179796			0.0898979	+	0.995951i	$0.471346\pi$
$444$	−1.25748	−	14.7014i	−0.00283216	−	0.0331113i
$445$	53.6244	−	137.411i	0.120504	−	0.308789i
$446$	1.71578	+	40.1922i	0.00384704	+	0.0901170i
$447$	612.278	−	612.278i	1.36975	−	1.36975i
$448$	69.7649	−	119.229i	0.155725	−	0.266136i
$449$		−	816.938i		−	1.81946i	−0.415200	−	0.909730i	$-0.636288\pi$
$449$		−	816.938i		−	1.81946i	0.415200	−	0.909730i	$-0.363712\pi$
$450$	47.3790	+	563.253i	0.105287	+	1.25167i
$451$	371.370	+	371.370i	0.823438	+	0.823438i
$452$	480.560	−	570.458i	1.06319	−	1.26208i
$453$	785.838			1.73474
$454$	419.218	+	384.891i	0.923387	+	0.847777i
$455$	92.9919	+	212.024i	0.204378	+	0.465986i
$456$	−347.257	+	44.6899i	−0.761530	+	0.0980042i
$457$	−238.754	−	238.754i	−0.522437	−	0.522437i	0.395870	−	0.918307i	$-0.370443\pi$
$457$	−238.754	−	238.754i	−0.522437	−	0.522437i	−0.918307	+	0.395870i	$0.870443\pi$
$458$	2.41296	+	56.5236i	0.00526847	+	0.123414i
$459$	−192.630	−	192.630i	−0.419672	−	0.419672i
$460$	119.493	−	65.0704i	0.259766	−	0.141457i
$461$	−243.794	−	243.794i	−0.528837	−	0.528837i	0.391389	−	0.920225i	$-0.371995\pi$
$461$	−243.794	−	243.794i	−0.528837	−	0.528837i	−0.920225	+	0.391389i	$0.871995\pi$
$462$	190.904	−	207.930i	0.413212	−	0.450065i
$463$	195.645	+	195.645i	0.422559	+	0.422559i	0.886084	−	0.463525i	$-0.153415\pi$
$463$	195.645	+	195.645i	0.422559	+	0.422559i	−0.463525	+	0.886084i	$0.653415\pi$
$464$	−95.3397	+	135.041i	−0.205473	+	0.291037i
$465$	−522.486	−	203.899i	−1.12363	−	0.438493i
$466$	−417.662	+	17.8297i	−0.896270	+	0.0382612i
$467$	108.782			0.232938			0.116469	−	0.993194i	$-0.462842\pi$
$467$	108.782			0.232938			0.116469	+	0.993194i	$0.462842\pi$
$468$	966.541	−	82.6727i	2.06526	−	0.176651i
$469$	−71.2430	−	71.2430i	−0.151904	−	0.151904i
$470$	−43.4591	+	127.124i	−0.0924663	+	0.270477i
$471$		−	1037.06i		−	2.20182i
$472$	−97.1085	+	12.4973i	−0.205738	+	0.0264773i
$473$	−362.073	+	362.073i	−0.765482	+	0.765482i
$474$	−528.606	−	485.322i	−1.11520	−	1.02389i
$475$	242.605	−	10.0145i	0.510747	−	0.0210832i
$476$	−19.3000	−	225.639i	−0.0405462	−	0.474032i
$477$	−916.047			−1.92043
$478$	−312.099	+	339.934i	−0.652927	+	0.711159i
$479$		−	186.555i		−	0.389467i	−0.980856	−	0.194733i	$-0.937616\pi$
$479$		−	186.555i		−	0.389467i	0.980856	−	0.194733i	$-0.0623842\pi$
$480$	422.801	+	583.989i	0.880835	+	1.21664i
$481$	17.5615			0.0365103
$482$	244.335	+	224.328i	0.506919	+	0.465411i
$483$		−	66.1672i		−	0.136992i
$484$	356.997	−	30.5356i	0.737596	−	0.0630900i
$485$	−32.9725	−	75.1781i	−0.0679846	−	0.155006i
$486$	−461.315	+	502.458i	−0.949208	+	1.03386i
$487$	87.5337	+	87.5337i	0.179741	+	0.179741i	0.791243	−	0.611502i	$-0.209434\pi$
$487$	87.5337	+	87.5337i	0.179741	+	0.179741i	−0.611502	+	0.791243i	$0.709434\pi$
$488$	183.696	−	23.6405i	0.376426	−	0.0484437i
$489$	−927.595			−1.89692
$490$	−195.257	−	398.106i	−0.398484	−	0.812461i
$491$	−481.445	+	481.445i	−0.980540	+	0.980540i	−0.999814	−	0.0192739i	$-0.993865\pi$
$491$	−481.445	+	481.445i	−0.980540	+	0.980540i	0.0192739	+	0.999814i	$0.493865\pi$
$492$	55.5952	+	649.973i	0.112998	+	1.32108i
$493$			270.997i			0.549690i
$494$	−17.7731	−	416.335i	−0.0359779	−	0.842783i
$495$	329.454	+	751.162i	0.665563	+	1.51750i
$496$	−392.511	+	67.6415i	−0.791353	+	0.136374i
$497$	123.412	−	123.412i	0.248314	−	0.248314i
$498$	−195.837	−	179.801i	−0.393246	−	0.361046i
$499$	−263.132	+	263.132i	−0.527319	+	0.527319i	−0.919772	−	0.392453i	$-0.871627\pi$
$499$	−263.132	+	263.132i	−0.527319	+	0.527319i	0.392453	+	0.919772i	$0.371627\pi$
$500$	−257.029	−	428.878i	−0.514058	−	0.857755i
$501$	238.247	−	238.247i	0.475543	−	0.475543i
$502$	211.070	−	9.01043i	0.420458	−	0.0179491i
$503$	433.805	−	433.805i	0.862435	−	0.862435i	−0.129186	−	0.991620i	$-0.541236\pi$
$503$	433.805	−	433.805i	0.862435	−	0.862435i	0.991620	+	0.129186i	$0.0412363\pi$
$504$	193.609	−	24.9164i	0.384146	−	0.0494372i
$505$	47.0768	+	107.336i	0.0932213	+	0.212547i
$506$	133.530	−	145.439i	0.263894	−	0.287430i
$507$			1312.23i			2.58822i
$508$	−666.959	−	561.853i	−1.31291	−	1.10601i
$509$	−513.368	+	513.368i	−1.00858	+	1.00858i	−0.00861858	+	0.999963i	$0.502743\pi$
$509$	−513.368	+	513.368i	−1.00858	+	1.00858i	−0.999963	+	0.00861858i	$0.997257\pi$
$510$	1118.40	+	382.339i	2.19294	+	0.749685i
$511$	−83.9248			−0.164236
$512$	471.298	+	200.055i	0.920504	+	0.390732i
$513$	−71.3269	−	71.3269i	−0.139039	−	0.139039i
$514$	386.662	−	16.5064i	0.752261	−	0.0321136i
$515$	282.779	+	644.742i	0.549085	+	1.25193i
$516$	−633.701	+	54.2034i	−1.22810	+	0.105045i
$517$			194.955i			0.377088i
$518$	3.53066	−	0.150722i	0.00681594	−	0.000290968i
$519$	623.305			1.20097
$520$	−735.420	+	442.150i	−1.41427	+	0.850289i
$521$			228.528i			0.438633i	0.975654	+	0.219316i	$0.0703827\pi$
$521$			228.528i			0.438633i	−0.975654	+	0.219316i	$0.929617\pi$
$522$	−233.381	+	9.96288i	−0.447090	+	0.0190860i
$523$	−42.0347			−0.0803723			−0.0401862	−	0.999192i	$-0.512795\pi$
$523$	−42.0347			−0.0803723			−0.0401862	+	0.999192i	$0.512795\pi$
$524$	−467.663	+	555.149i	−0.892487	+	1.05945i
$525$	−242.946	+	10.0286i	−0.462754	+	0.0191021i
$526$	56.6680	−	2.41912i	0.107734	−	0.00459909i
$527$	−461.711	+	461.711i	−0.876112	+	0.876112i
$528$	854.679	+	603.407i	1.61871	+	1.14282i
$529$			482.718i			0.912511i
$530$	727.521	−	356.823i	1.37268	−	0.673252i
$531$	−97.8326	−	97.8326i	−0.184242	−	0.184242i
$532$	−7.14640	−	83.5498i	−0.0134331	−	0.157048i
$533$	−776.422			−1.45670
$534$	179.807	−	195.843i	0.336716	−	0.366747i
$535$	−735.015	−	286.838i	−1.37386	−	0.536146i
$536$	228.190	−	295.598i	0.425727	−	0.551489i
$537$	−467.662	−	467.662i	−0.870879	−	0.870879i
$538$	−294.033	+	12.5521i	−0.546530	+	0.0233310i
$539$	−454.983	−	454.983i	−0.844125	−	0.844125i
$540$	−58.7485	+	199.235i	−0.108793	+	0.368953i
$541$	300.583	+	300.583i	0.555607	+	0.555607i	0.928054	−	0.372446i	$-0.121481\pi$
$541$	300.583	+	300.583i	0.555607	+	0.555607i	−0.372446	+	0.928054i	$0.621481\pi$
$542$	−134.394	−	123.389i	−0.247959	−	0.227656i
$543$	−359.079	−	359.079i	−0.661288	−	0.661288i
$544$	820.335	−	177.695i	1.50797	−	0.326646i
$545$	−110.235	−	251.338i	−0.202266	−	0.461170i
$546$	17.7981	+	416.920i	0.0325972	+	0.763590i
$547$	−565.276			−1.03341			−0.516706	−	0.856163i	$-0.672842\pi$
$547$	−565.276			−1.03341			−0.516706	+	0.856163i	$0.672842\pi$
$548$	−358.571	+	425.649i	−0.654327	+	0.776732i
$549$	185.065	+	185.065i	0.337096	+	0.337096i
$550$	−554.247	−	468.239i	−1.00772	−	0.851344i
$551$			100.345i			0.182114i
$552$	243.235	−	31.3029i	0.440644	−	0.0567082i
$553$	121.530	−	121.530i	0.219764	−	0.219764i
$554$	118.002	−	128.526i	0.212999	−	0.231996i
$555$	−6.70518	+	17.1819i	−0.0120814	+	0.0309583i
$556$	325.680	−	386.604i	0.585755	−	0.695332i
$557$	−972.870			−1.74662			−0.873312	−	0.487161i	$-0.838032\pi$
$557$	−972.870			−1.74662			−0.873312	+	0.487161i	$0.838032\pi$
$558$	−414.597	−	380.648i	−0.743005	−	0.682165i
$559$		−	756.984i		−	1.35418i
$560$	−144.058	+	95.2042i	−0.257247	+	0.170008i
$561$	1715.15			3.05730
$562$	221.556	−	241.316i	0.394228	−	0.429388i
$563$		−	827.358i		−	1.46955i	−0.678310	−	0.734776i	$-0.737287\pi$
$563$		−	827.358i		−	1.46955i	0.678310	−	0.734776i	$-0.262713\pi$
$564$	−156.012	+	185.198i	−0.276618	+	0.328365i
$565$	−853.854	+	374.494i	−1.51125	+	0.662821i
$566$	−345.722	−	317.413i	−0.610817	−	0.560801i
$567$	−83.8583	−	83.8583i	−0.147898	−	0.147898i
$568$	512.055	+	395.286i	0.901506	+	0.695926i
$569$	1016.20			1.78594			0.892970	−	0.450115i	$-0.148617\pi$
$569$	1016.20			1.78594			0.892970	+	0.450115i	$0.148617\pi$
$570$	414.121	+	141.573i	0.726528	+	0.248373i
$571$	−381.530	+	381.530i	−0.668178	+	0.668178i	−0.957294	−	0.289116i	$-0.906639\pi$
$571$	−381.530	+	381.530i	−0.668178	+	0.668178i	0.289116	+	0.957294i	$0.406639\pi$
$572$	−802.254	+	952.332i	−1.40254	+	1.66492i
$573$			511.157i			0.892072i
$574$	−156.096	+	6.66365i	−0.271945	+	0.0116092i
$575$	−169.932	+	7.01464i	−0.295533	+	0.0121994i
$576$	183.189	+	699.934i	0.318036	+	1.21516i
$577$	−494.447	+	494.447i	−0.856928	+	0.856928i	−0.990975	−	0.134047i	$-0.957203\pi$
$577$	−494.447	+	494.447i	−0.856928	+	0.856928i	0.134047	+	0.990975i	$0.457203\pi$
$578$	539.709	−	587.844i	0.933753	−	1.01703i
$579$	934.868	−	934.868i	1.61462	−	1.61462i
$580$	181.469	−	98.8202i	0.312878	−	0.170380i
$581$	45.0240	−	45.0240i	0.0774939	−	0.0774939i
$582$	−6.31073	−	147.829i	−0.0108432	−	0.254002i
$583$	831.461	−	831.461i	1.42618	−	1.42618i
$584$	−39.7038	−	308.513i	−0.0679860	−	0.528277i
$585$	−1129.62	−	440.831i	−1.93097	−	0.753558i
$586$	−449.934	−	413.092i	−0.767805	−	0.704935i
$587$		−	1106.40i		−	1.88485i	−0.334423	−	0.942423i	$-0.608541\pi$
$587$		−	1106.40i		−	1.88485i	0.334423	−	0.942423i	$-0.391459\pi$
$588$	−68.1123	−	796.313i	−0.115837	−	1.35427i
$589$	−170.962	+	170.962i	−0.290259	+	0.290259i
$590$	115.806	+	39.5900i	0.196282	+	0.0671017i
$591$	−137.226			−0.232193
$592$	2.22437	+	12.9076i	0.00375739	+	0.0218035i
$593$	−312.835	−	312.835i	−0.527546	−	0.527546i	0.392294	−	0.919840i	$-0.371682\pi$
$593$	−312.835	−	312.835i	−0.527546	−	0.527546i	−0.919840	+	0.392294i	$0.871682\pi$
$594$	12.8558	+	301.146i	0.0216427	+	0.506981i
$595$	−102.912	+	263.710i	−0.172962	+	0.443210i
$596$	−495.214	+	587.854i	−0.830897	+	0.986333i
$597$		−	1026.93i		−	1.72016i
$598$	12.4491	+	291.620i	0.0208179	+	0.487659i
$599$	406.395			0.678457			0.339228	−	0.940704i	$-0.389834\pi$
$599$	406.395			0.678457			0.339228	+	0.940704i	$0.389834\pi$
$600$	−151.800	−	888.341i	−0.253001	−	1.48057i
$601$			172.522i			0.287058i	0.989646	+	0.143529i	$0.0458451\pi$
$601$			172.522i			0.287058i	−0.989646	+	0.143529i	$0.954155\pi$
$602$	−6.49683	−	152.188i	−0.0107921	−	0.252805i
$603$	527.694			0.875114
$604$	−695.041	+	59.4500i	−1.15073	+	0.0984272i
$605$	−417.230	−	162.823i	−0.689636	−	0.269129i
$606$	9.01019	+	211.064i	0.0148683	+	0.348291i
$607$	434.724	−	434.724i	0.716185	−	0.716185i	−0.251636	−	0.967822i	$-0.580969\pi$
$607$	434.724	−	434.724i	0.716185	−	0.716185i	0.967822	+	0.251636i	$0.0809687\pi$
$608$	303.754	−	65.7970i	0.499595	−	0.108219i
$609$		−	100.486i		−	0.165002i
$610$	−219.066	−	74.8906i	−0.359124	−	0.122771i
$611$	−203.795	−	203.795i	−0.333544	−	0.333544i
$612$	907.128	+	764.174i	1.48223	+	1.24865i
$613$	540.620			0.881925			0.440963	−	0.897525i	$-0.354637\pi$
$613$	540.620			0.881925			0.440963	+	0.897525i	$0.354637\pi$
$614$	730.376	+	670.570i	1.18954	+	1.09213i
$615$	296.447	−	759.639i	0.482028	−	1.23518i
$616$	−153.116	+	198.348i	−0.248565	+	0.321993i
$617$	840.793	+	840.793i	1.36271	+	1.36271i	0.870445	+	0.492266i	$0.163831\pi$
$617$	840.793	+	840.793i	1.36271	+	1.36271i	0.492266	+	0.870445i	$0.336169\pi$
$618$	54.1221	+	1267.81i	0.0875761	+	2.05147i
$619$	−379.330	−	379.330i	−0.612810	−	0.612810i	0.330867	−	0.943677i	$-0.392659\pi$
$619$	−379.330	−	379.330i	−0.612810	−	0.612810i	−0.943677	+	0.330867i	$0.892659\pi$
$620$	477.543	+	140.813i	0.770230	+	0.227118i
$621$	49.9607	+	49.9607i	0.0804520	+	0.0804520i
$622$	−51.5816	+	56.1820i	−0.0829287	+	0.0903247i
$623$	45.0254	+	45.0254i	0.0722719	+	0.0722719i
$624$	−1524.21	+	262.667i	−2.44264	+	0.420940i
$625$	51.5112	+	622.874i	0.0824179	+	0.996598i
$626$	−87.0934	+	3.71796i	−0.139127	+	0.00593924i
$627$	635.085			1.01290
$628$	78.4552	+	917.233i	0.124929	+	1.46056i
$629$	15.1833	+	15.1833i	0.0241387	+	0.0241387i
$630$	−230.888	−	78.9323i	−0.366490	−	0.125289i
$631$			685.081i			1.08571i	0.839827	+	0.542853i	$0.182656\pi$
$631$			685.081i			1.08571i	−0.839827	+	0.542853i	$0.817344\pi$
$632$	504.246	+	389.257i	0.797857	+	0.615914i
$633$	−732.866	+	732.866i	−1.15777	+	1.15777i
$634$	285.892	+	262.482i	0.450933	+	0.414010i
$635$	437.845	+	998.296i	0.689519	+	1.57212i
$636$	1455.23	−	124.472i	2.28809	−	0.195711i
$637$	951.231			1.49330
$638$	202.788	−	220.874i	0.317850	−	0.346197i
$639$			914.107i			1.43053i
$640$	−418.130	−	484.528i	−0.653327	−	0.757075i
$641$	510.792			0.796868			0.398434	−	0.917197i	$-0.369554\pi$
$641$	510.792			0.796868			0.398434	+	0.917197i	$0.369554\pi$
$642$	−1047.57	−	961.789i	−1.63172	−	1.49811i
$643$		−	566.933i		−	0.881700i	−0.897581	−	0.440850i	$-0.854677\pi$
$643$		−	566.933i		−	0.881700i	0.897581	−	0.440850i	$-0.145323\pi$
$644$	5.00567	+	58.5222i	0.00777278	+	0.0908729i
$645$	740.621	+	289.026i	1.14825	+	0.448102i
$646$	344.588	−	375.320i	0.533417	−	0.580991i
$647$	270.517	+	270.517i	0.418109	+	0.418109i	0.884552	−	0.466442i	$-0.154464\pi$
$647$	270.517	+	270.517i	0.418109	+	0.418109i	−0.466442	+	0.884552i	$0.654464\pi$
$648$	268.597	−	347.941i	0.414501	−	0.536947i
$649$	177.598			0.273648
$650$	1068.85	−	89.9085i	1.64439	−	0.138321i
$651$	171.203	−	171.203i	0.262984	−	0.262984i
$652$	820.419	−	70.1743i	1.25831	−	0.107629i
$653$		−	724.152i		−	1.10896i	−0.832197	−	0.554481i	$-0.812917\pi$
$653$		−	724.152i		−	1.10896i	0.832197	−	0.554481i	$-0.187083\pi$
$654$	−21.0982	−	494.227i	−0.0322603	−	0.755699i
$655$	830.940	−	364.444i	1.26861	−	0.556403i
$656$	−98.3433	−	570.669i	−0.149914	−	0.869922i
$657$	310.814	−	310.814i	0.473080	−	0.473080i
$658$	−42.7213	−	39.2231i	−0.0649259	−	0.0596096i
$659$	−641.423	+	641.423i	−0.973328	+	0.973328i	−0.999653	−	0.0263257i	$-0.991619\pi$
$659$	−641.423	+	641.423i	−0.973328	+	0.973328i	0.0263257	+	0.999653i	$0.491619\pi$
$660$	−625.435	−	1148.52i	−0.947630	−	1.74019i
$661$	−699.865	+	699.865i	−1.05880	+	1.05880i	−0.0606382	+	0.998160i	$0.519314\pi$
$661$	−699.865	+	699.865i	−1.05880	+	1.05880i	−0.998160	+	0.0606382i	$0.980686\pi$
$662$	−308.292	+	13.1608i	−0.465698	+	0.0198803i
$663$	−1792.93	+	1792.93i	−2.70426	+	2.70426i
$664$	186.812	+	144.211i	0.281343	+	0.217185i
$665$	−38.1063	+	97.6465i	−0.0573028	+	0.146837i
$666$	−12.5175	+	13.6339i	−0.0187951	+	0.0204713i
$667$		−	70.2862i		−	0.105377i
$668$	−192.696	+	228.743i	−0.288466	+	0.342430i
$669$	64.0902	−	64.0902i	0.0958000	−	0.0958000i
$670$	−419.092	+	205.550i	−0.625511	+	0.306791i
$671$	−335.954			−0.500676
$672$	−304.181	+	65.8895i	−0.452650	+	0.0980499i
$673$	−439.226	−	439.226i	−0.652639	−	0.652639i	0.300989	−	0.953628i	$-0.402683\pi$
$673$	−439.226	−	439.226i	−0.652639	−	0.652639i	−0.953628	+	0.300989i	$0.902683\pi$
$674$	−208.439	+	8.89813i	−0.309257	+	0.0132020i
$675$	175.868	−	191.013i	0.260545	−	0.282982i
$676$	−99.2724	−	1160.61i	−0.146853	−	1.71688i
$677$		−	372.736i		−	0.550570i	−0.961363	−	0.275285i	$-0.911228\pi$
$677$		−	372.736i		−	0.550570i	0.961363	−	0.275285i	$-0.0887722\pi$
$678$	−1679.01	+	71.6757i	−2.47641	+	0.105716i
$679$	35.4376			0.0521909
$680$	−1018.10	−	253.554i	−1.49721	−	0.372874i
$681$		−	1282.23i		−	1.88286i
$682$	721.813	−	30.8138i	1.05838	−	0.0451815i
$683$	−2.98479			−0.00437012			−0.00218506	−	0.999998i	$-0.500696\pi$
$683$	−2.98479			−0.00437012			−0.00218506	+	0.999998i	$0.500696\pi$
$684$	335.891	+	282.958i	0.491069	+	0.413682i
$685$	637.106	−	279.430i	0.930082	−	0.407927i
$686$	402.575	−	17.1857i	0.586844	−	0.0250520i
$687$	90.1323	−	90.1323i	0.131197	−	0.131197i
$688$	556.382	−	95.8813i	0.808694	−	0.139362i
$689$			1738.33i			2.52298i
$690$	−290.070	−	99.1642i	−0.420391	−	0.143716i
$691$	−153.000	−	153.000i	−0.221418	−	0.221418i	0.587678	−	0.809095i	$-0.300042\pi$
$691$	−153.000	−	153.000i	−0.221418	−	0.221418i	−0.809095	+	0.587678i	$0.800042\pi$
$692$	−551.287	+	47.1542i	−0.796658	+	0.0681418i
$693$	−354.085			−0.510945
$694$	871.806	−	949.558i	1.25620	−	1.36824i
$695$	−578.664	+	253.798i	−0.832611	+	0.365177i
$696$	369.393	−	47.5387i	0.530738	−	0.0683027i
$697$	−671.278	−	671.278i	−0.963096	−	0.963096i
$698$	−457.269	+	19.5205i	−0.655114	+	0.0279664i
$699$	666.001	+	666.001i	0.952791	+	0.952791i
$700$	214.117	−	27.2492i	0.305881	−	0.0389274i
$701$	374.594	+	374.594i	0.534371	+	0.534371i	0.921870	−	0.387499i	$-0.126661\pi$
$701$	374.594	+	374.594i	0.534371	+	0.534371i	−0.387499	+	0.921870i	$0.626661\pi$
$702$	−328.241	−	301.364i	−0.467580	−	0.429293i
$703$	5.62206	+	5.62206i	0.00799724	+	0.00799724i
$704$	−801.577	−	469.030i	−1.13860	−	0.666236i
$705$	277.201	−	121.578i	0.393194	−	0.172452i
$706$	11.0475	+	258.788i	0.0156480	+	0.366555i
$707$	−50.5964			−0.0715649
$708$	168.710	+	142.123i	0.238290	+	0.200738i
$709$	−841.096	−	841.096i	−1.18631	−	1.18631i	−0.978079	−	0.208233i	$-0.933229\pi$
$709$	−841.096	−	841.096i	−1.18631	−	1.18631i	−0.208233	−	0.978079i	$-0.566771\pi$
$710$	−356.067	−	725.980i	−0.501504	−	1.02251i
$711$			900.166i			1.26606i
$712$	−144.216	+	186.818i	−0.202550	+	0.262384i
$713$	119.750	−	119.750i	0.167952	−	0.167952i
$714$	−345.072	+	375.848i	−0.483294	+	0.526397i
$715$	1425.44	−	625.186i	1.99362	−	0.874386i
$716$	449.007	+	378.248i	0.627105	+	0.528280i
$717$	1039.73			1.45011
$718$	321.327	+	295.016i	0.447531	+	0.410886i
$719$		−	28.8722i		−	0.0401560i	−0.999798	−	0.0200780i	$-0.993609\pi$
$719$		−	28.8722i		−	0.0401560i	0.999798	−	0.0200780i	$-0.00639146\pi$
$720$	180.930	−	886.104i	0.251292	−	1.23070i
$721$	−303.920			−0.421526
$722$	−360.698	+	392.867i	−0.499582	+	0.544138i
$723$		−	747.327i		−	1.03365i
$724$	344.756	+	290.426i	0.476182	+	0.401140i
$725$	−258.069	+	10.6529i	−0.355958	+	0.0146936i
$726$	−594.650	−	545.958i	−0.819077	−	0.752008i
$727$	896.554	+	896.554i	1.23322	+	1.23322i	0.962718	+	0.270506i	$0.0871909\pi$
$727$	896.554	+	896.554i	1.23322	+	1.23322i	0.270506	+	0.962718i	$0.412809\pi$
$728$	−47.2824	−	367.402i	−0.0649483	−	0.504673i
$729$	1042.33			1.42981
$730$	−125.777	+	367.917i	−0.172298	+	0.503996i
$731$	654.472	−	654.472i	0.895311	−	0.895311i
$732$	−319.140	−	268.847i	−0.435984	−	0.367277i
$733$			83.0751i			0.113336i	0.998393	+	0.0566678i	$0.0180476\pi$
$733$			83.0751i			0.113336i	−0.998393	+	0.0566678i	$0.981952\pi$
$734$	−655.903	+	28.0001i	−0.893600	+	0.0381472i
$735$	−363.192	+	930.669i	−0.494138	+	1.26622i
$736$	−212.763	+	46.0873i	−0.289081	+	0.0626186i
$737$	−478.968	+	478.968i	−0.649888	+	0.649888i
$738$	553.421	−	602.778i	0.749893	−	0.816773i
$739$	−148.263	+	148.263i	−0.200626	+	0.200626i	−0.800268	−	0.599642i	$-0.795310\pi$
$739$	−148.263	+	148.263i	−0.200626	+	0.200626i	0.599642	+	0.800268i	$0.295310\pi$
$740$	4.63062	−	15.7039i	0.00625759	−	0.0212215i
$741$	−663.885	+	663.885i	−0.895931	+	0.895931i
$742$	14.9193	+	349.484i	0.0201068	+	0.471003i
$743$	−613.895	+	613.895i	−0.826238	+	0.826238i	−0.986994	−	0.160756i	$-0.948607\pi$
$743$	−613.895	+	613.895i	−0.826238	+	0.826238i	0.160756	+	0.986994i	$0.448607\pi$
$744$	710.347	+	548.359i	0.954768	+	0.737042i
$745$	879.893	−	385.914i	1.18106	−	0.518006i
$746$	105.089	+	96.4837i	0.140870	+	0.129335i
$747$			333.491i			0.446440i
$748$	−1516.98	+	129.754i	−2.02804	+	0.173468i
$749$	240.842	−	240.842i	0.321551	−	0.321551i
$750$	−320.136	+	1080.08i	−0.426848	+	1.44010i
$751$	516.621			0.687911			0.343956	−	0.938986i	$-0.388233\pi$
$751$	516.621			0.687911			0.343956	+	0.938986i	$0.388233\pi$
$752$	123.976	−	175.602i	0.164862	−	0.233514i
$753$	−336.570	−	336.570i	−0.446973	−	0.446973i
$754$	18.9060	+	442.874i	0.0250743	+	0.587366i
$755$	812.310	+	317.002i	1.07591	+	0.419870i
$756$	−68.5780	−	57.7708i	−0.0907116	−	0.0764164i
$757$			1230.47i			1.62545i	0.582644	+	0.812727i	$0.302018\pi$
$757$			1230.47i			1.62545i	−0.582644	+	0.812727i	$0.697982\pi$
$758$	54.2282	+	1270.30i	0.0715411	+	1.67585i
$759$	−444.843			−0.586091
$760$	−376.983	−	93.8862i	−0.496030	−	0.123534i
$761$		−	129.224i		−	0.169808i	−0.996389	−	0.0849040i	$-0.972942\pi$
$761$		−	129.224i		−	0.169808i	0.996389	−	0.0849040i	$-0.0270584\pi$
$762$	83.8007	+	1963.03i	0.109975	+	2.57616i
$763$	118.476			0.155277
$764$	−38.6700	−	452.097i	−0.0506151	−	0.591750i
$765$	−595.510	−	1357.78i	−0.778445	−	1.77487i
$766$	−47.2924	−	1107.83i	−0.0617394	−	1.44625i
$767$	−185.651	+	185.651i	−0.242049	+	0.242049i
$768$	−386.119	−	1087.02i	−0.502759	−	1.41539i
$769$		−	247.035i		−	0.321242i	−0.987016	−	0.160621i	$-0.948650\pi$
$769$		−	247.035i		−	0.321242i	0.987016	−	0.160621i	$-0.0513496\pi$
$770$	281.212	−	137.925i	0.365211	−	0.179123i
$771$	−616.569	−	616.569i	−0.799701	−	0.799701i
$772$	−756.127	+	897.576i	−0.979439	+	1.16266i
$773$	−149.770			−0.193751			−0.0968756	−	0.995296i	$-0.530885\pi$
$773$	−149.770			−0.193751			−0.0968756	+	0.995296i	$0.530885\pi$
$774$	587.688	+	539.566i	0.759286	+	0.697114i
$775$	−457.835	−	421.536i	−0.590755	−	0.543917i
$776$	16.7651	+	130.271i	0.0216045	+	0.167875i
$777$	−5.62997	−	5.62997i	−0.00724577	−	0.00724577i
$778$	0.0401879	+	0.941404i	5.16555e−5	+	0.00121003i
$779$	−248.561	−	248.561i	−0.319077	−	0.319077i
$780$	1854.40	+	546.809i	2.37744	+	0.701037i
$781$	−829.700	−	829.700i	−1.06236	−	1.06236i
$782$	−241.365	+	262.892i	−0.308651	+	0.336179i
$783$	75.8737	+	75.8737i	0.0969012	+	0.0969012i
$784$	120.485	+	699.153i	0.153680	+	0.891777i
$785$	418.342	−	1071.99i	0.532920	−	1.36559i
$786$	1633.95	−	69.7522i	2.07881	−	0.0887433i
$787$	−1010.58			−1.28409			−0.642044	−	0.766668i	$-0.721913\pi$
$787$	−1010.58			−1.28409			−0.642044	+	0.766668i	$0.721913\pi$
$788$	121.371	−	10.3814i	0.154024	−	0.0131744i
$789$	−90.3624	−	90.3624i	−0.114528	−	0.114528i
$790$	−350.637	−	714.908i	−0.443844	−	0.904947i
$791$		−	402.492i		−	0.508839i
$792$	−167.513	−	1301.64i	−0.211506	−	1.64348i
$793$	351.188	−	351.188i	0.442861	−	0.442861i
$794$	−5.50018	−	5.04981i	−0.00692718	−	0.00635996i
$795$	−1700.75	−	663.716i	−2.13931	−	0.834863i
$796$	77.6894	+	908.280i	0.0975997	+	1.14106i
$797$	627.322			0.787105			0.393552	−	0.919302i	$-0.371246\pi$
$797$	627.322			0.787105			0.393552	+	0.919302i	$0.371246\pi$
$798$	−127.773	+	139.169i	−0.160117	+	0.174397i
$799$		−	352.394i		−	0.441044i
$800$	201.466	+	774.217i	0.251832	+	0.967771i
$801$	−333.501			−0.416356
$802$	−482.789	−	443.257i	−0.601981	−	0.552689i
$803$			564.228i			0.702650i
$804$	−838.290	+	71.7029i	−1.04265	+	0.0891827i
$805$	26.6915	−	68.3962i	0.0331571	−	0.0849642i
$806$	−722.335	+	786.757i	−0.896197	+	0.976125i
$807$	468.864	+	468.864i	0.580996	+	0.580996i
$808$	−23.9365	−	185.996i	−0.0296244	−	0.230193i
$809$	1040.62			1.28631			0.643155	−	0.765736i	$-0.277625\pi$
$809$	1040.62			1.28631			0.643155	+	0.765736i	$0.277625\pi$
$810$	−493.303	+	241.948i	−0.609016	+	0.298701i
$811$	51.2843	−	51.2843i	0.0632359	−	0.0632359i	−0.674782	−	0.738018i	$-0.735762\pi$
$811$	51.2843	−	51.2843i	0.0632359	−	0.0632359i	0.738018	+	0.674782i	$0.235762\pi$
$812$	7.60194	+	88.8756i	0.00936200	+	0.109453i
$813$			411.060i			0.505609i
$814$	−1.01330	−	23.7367i	−0.00124485	−	0.0291605i
$815$	−958.843	−	374.186i	−1.17649	−	0.459124i
$816$	−1544.89	−	1090.70i	−1.89325	−	1.33664i
$817$	242.338	−	242.338i	0.296619	−	0.296619i
$818$	−284.092	−	260.830i	−0.347301	−	0.318863i
$819$	370.141	−	370.141i	0.451943	−	0.451943i
$820$	−204.727	+	694.295i	−0.249667	+	0.846702i
$821$	981.049	−	981.049i	1.19494	−	1.19494i	0.219282	−	0.975661i	$-0.429628\pi$
$821$	981.049	−	981.049i	1.19494	−	1.19494i	0.975661	−	0.219282i	$-0.0703715\pi$
$822$	1252.80	−	53.4811i	1.52408	−	0.0650622i
$823$	−175.154	+	175.154i	−0.212823	+	0.212823i	−0.805466	−	0.592642i	$-0.798085\pi$
$823$	−175.154	+	175.154i	−0.212823	+	0.212823i	0.592642	+	0.805466i	$0.298085\pi$
$824$	−143.781	−	1117.23i	−0.174491	−	1.35586i
$825$	67.4224	+	1633.33i	0.0817242	+	1.97979i
$826$	−35.7311	+	38.9178i	−0.0432580	+	0.0471160i
$827$		−	386.856i		−	0.467782i	−0.972263	−	0.233891i	$-0.924854\pi$
$827$		−	386.856i		−	0.467782i	0.972263	−	0.233891i	$-0.0751459\pi$
$828$	−235.274	−	198.197i	−0.284147	−	0.239369i
$829$	94.0409	−	94.0409i	0.113439	−	0.113439i	−0.648109	−	0.761548i	$-0.724440\pi$
$829$	94.0409	−	94.0409i	0.113439	−	0.113439i	0.761548	+	0.648109i	$0.224440\pi$
$830$	−129.903	−	264.857i	−0.156510	−	0.319105i
$831$	−393.111			−0.473058
$832$	1328.23	−	347.627i	1.59643	−	0.417820i
$833$	822.414	+	822.414i	0.987291	+	0.987291i
$834$	−1137.88	+	48.5753i	−1.36436	+	0.0582437i
$835$	342.380	−	150.165i	0.410036	−	0.179839i
$836$	−561.706	+	48.0453i	−0.671898	+	0.0574705i
$837$			258.539i			0.308888i
$838$	283.024	−	12.0821i	0.337738	−	0.0144178i
$839$	−1049.59			−1.25100			−0.625499	−	0.780225i	$-0.715105\pi$
$839$	−1049.59			−1.25100			−0.625499	+	0.780225i	$0.715105\pi$
$840$	377.513	+	94.0182i	0.449420	+	0.111926i
$841$			734.259i			0.873078i
$842$	794.089	−	33.8992i	0.943099	−	0.0402603i
$843$	−738.093			−0.875556
$844$	592.747	−	703.632i	0.702307	−	0.833687i
$845$	−529.345	+	1356.43i	−0.626443	+	1.60524i
$846$	303.479	−	12.9553i	0.358723	−	0.0153136i
$847$	136.713	−	136.713i	0.161409	−	0.161409i
$848$	−1277.67	+	220.181i	−1.50669	+	0.259647i
$849$			1057.43i			1.24550i
$850$	1001.84	+	846.374i	1.17864	+	0.995734i
$851$	−3.93796	−	3.93796i	−0.00462745	−	0.00462745i
$852$	−124.209	−	1452.14i	−0.145785	−	1.70439i
$853$	1697.19			1.98967			0.994835	−	0.101505i	$-0.0323659\pi$
$853$	1697.19			1.98967			0.994835	+	0.101505i	$0.0323659\pi$
$854$	67.5908	−	73.6190i	0.0791462	−	0.0862049i
$855$	−220.506	−	502.758i	−0.257901	−	0.588021i
$856$	999.290	+	771.412i	1.16740	+	0.901182i
$857$	−835.829	−	835.829i	−0.975296	−	0.975296i	0.0244059	−	0.999702i	$-0.492231\pi$
$857$	−835.829	−	835.829i	−0.975296	−	0.975296i	−0.999702	+	0.0244059i	$0.992231\pi$
$858$	2802.96	−	119.657i	3.26685	−	0.139460i
$859$	−101.258	−	101.258i	−0.117879	−	0.117879i	0.645707	−	0.763586i	$-0.276563\pi$
$859$	−101.258	−	101.258i	−0.117879	−	0.117879i	−0.763586	+	0.645707i	$0.776563\pi$
$860$	−676.914	−	199.602i	−0.787109	−	0.232095i
$861$	248.910	+	248.910i	0.289094	+	0.289094i
$862$	49.0229	+	45.0088i	0.0568712	+	0.0522144i
$863$	866.298	+	866.298i	1.00382	+	1.00382i	0.999993	+	0.00382915i	$0.00121886\pi$
$863$	866.298	+	866.298i	1.00382	+	1.00382i	0.00382915	+	0.999993i	$0.498781\pi$
$864$	179.926	−	279.428i	0.208248	−	0.323412i
$865$	644.302	+	251.437i	0.744858	+	0.290679i
$866$	25.4509	+	596.187i	0.0293890	+	0.688438i
$867$	−1797.99			−2.07380
$868$	−138.470	+	164.374i	−0.159528	+	0.189370i
$869$	−817.046	−	817.046i	−0.940214	−	0.940214i
$870$	−440.519	−	150.597i	−0.506344	−	0.173100i
$871$		−	1001.37i		−	1.14968i
$872$	56.0497	+	435.527i	0.0642772	+	0.499458i
$873$	−131.243	+	131.243i	−0.150335	+	0.150335i
$874$	−89.3728	+	97.3436i	−0.102257	+	0.111377i
$875$	−255.175	−	87.6364i	−0.291629	−	0.100156i
$876$	−451.523	+	535.990i	−0.515438	+	0.611861i
$877$	−708.097			−0.807408			−0.403704	−	0.914890i	$-0.632277\pi$
$877$	−708.097			−0.807408			−0.403704	+	0.914890i	$0.632277\pi$
$878$	−786.307	−	721.922i	−0.895566	−	0.822235i
$879$			1376.17i			1.56561i
$880$	640.059	+	968.506i	0.727340	+	1.10058i
$881$	678.953			0.770662			0.385331	−	0.922778i	$-0.374087\pi$
$881$	678.953			0.770662			0.385331	+	0.922778i	$0.374087\pi$
$882$	−678.022	+	738.492i	−0.768732	+	0.837293i
$883$		−	302.033i		−	0.342053i	−0.985266	−	0.171027i	$-0.945292\pi$
$883$		−	302.033i		−	0.342053i	0.985266	−	0.171027i	$-0.0547085\pi$
$884$	1450.13	−	1721.41i	1.64042	−	1.94729i
$885$	−110.754	−	252.522i	−0.125146	−	0.285336i
$886$	117.343	+	107.735i	0.132442	+	0.121597i
$887$	−961.511	−	961.511i	−1.08400	−	1.08400i	−0.996132	−	0.0878714i	$-0.971994\pi$
$887$	−961.511	−	961.511i	−1.08400	−	1.08400i	−0.0878714	−	0.996132i	$-0.528006\pi$
$888$	18.0327	−	23.3596i	0.0203071	−	0.0263059i
$889$	−470.579			−0.529335
$890$	264.865	−	129.907i	0.297602	−	0.145963i
$891$	−563.781	+	563.781i	−0.632751	+	0.632751i
$892$	−51.8366	+	61.5336i	−0.0581127	+	0.0689839i
$893$		−	130.485i		−	0.146119i
$894$	1730.21	−	73.8615i	1.93536	−	0.0826191i
$895$	−294.764	−	672.068i	−0.329345	−	0.750914i
$896$	264.051	−	81.2884i	0.294699	−	0.0907236i
$897$	465.016	−	465.016i	0.518412	−	0.518412i
$898$	1105.00	−	1203.55i	1.23051	−	1.34025i
$899$	181.860	−	181.860i	0.202292	−	0.202292i
$900$	−692.060	+	893.894i	−0.768956	+	0.993215i
$901$	−1502.92	+	1502.92i	−1.66806	+	1.66806i
$902$	44.7999	+	1049.44i	0.0496672	+	1.16346i
$903$	−242.679	+	242.679i	−0.268747	+	0.268747i
$904$	1479.59	−	190.414i	1.63671	−	0.210635i
$905$	−226.325	−	516.026i	−0.250083	−	0.570194i
$906$	1157.73	+	1062.93i	1.27785	+	1.17321i
$907$			504.237i			0.555940i	0.960590	+	0.277970i	$0.0896615\pi$
$907$			504.237i			0.555940i	−0.960590	+	0.277970i	$0.910338\pi$
$908$	97.0027	+	1134.08i	0.106831	+	1.24898i
$909$	187.383	−	187.383i	0.206141	−	0.206141i
$910$	−149.785	+	438.144i	−0.164599	+	0.481477i
$911$	1061.71			1.16544			0.582718	−	0.812675i	$-0.301989\pi$
$911$	1061.71			1.16544			0.582718	+	0.812675i	$0.301989\pi$
$912$	−572.043	−	403.865i	−0.627240	−	0.442834i
$913$	−302.697	−	302.697i	−0.331541	−	0.331541i
$914$	−28.8018	−	674.683i	−0.0315118	−	0.738165i
$915$	209.509	+	477.685i	0.228972	+	0.522060i
$916$	−72.8996	+	86.5369i	−0.0795847	+	0.0944726i
$917$			391.691i			0.427144i
$918$	−23.2377	−	544.343i	−0.0253134	−	0.592966i
$919$	216.839			0.235951			0.117975	−	0.993017i	$-0.462360\pi$
$919$	216.839			0.235951			0.117975	+	0.993017i	$0.462360\pi$
$920$	264.056	+	65.7623i	0.287018	+	0.0714807i
$921$		−	2233.94i		−	2.42556i
$922$	−29.4098	−	688.925i	−0.0318978	−	0.747207i
$923$	1734.65			1.87936
$924$	562.496	−	48.1129i	0.608762	−	0.0520702i
$925$	−13.8621	+	15.0558i	−0.0149861	+	0.0162766i
$926$	23.6014	+	552.864i	0.0254875	+	0.597045i
$927$	1125.56	−	1125.56i	1.21420	−	1.21420i
$928$	−323.117	+	69.9912i	−0.348186	+	0.0754216i
$929$		−	173.225i		−	0.186464i	−0.995644	−	0.0932321i	$-0.970280\pi$
$929$		−	173.225i		−	0.186464i	0.995644	−	0.0932321i	$-0.0297198\pi$
$930$	−493.954	−	1007.11i	−0.531133	−	1.08292i
$931$	304.524	+	304.524i	0.327093	+	0.327093i
$932$	−639.435	−	538.666i	−0.686089	−	0.577968i
$933$	171.839			0.184179
$934$	160.263	+	147.140i	0.171587	+	0.157537i
$935$	1772.92	+	691.880i	1.89618	+	0.739979i
$936$	1535.77	+	1185.56i	1.64078	+	1.26662i
$937$	681.081	+	681.081i	0.726874	+	0.726874i	0.969996	−	0.243122i	$-0.0781715\pi$
$937$	681.081	+	681.081i	0.726874	+	0.726874i	−0.243122	+	0.969996i	$0.578171\pi$
$938$	−8.59432	−	201.322i	−0.00916238	−	0.214629i
$939$	138.879	+	138.879i	0.147900	+	0.147900i
$940$	−235.976	+	128.502i	−0.251038	+	0.136704i
$941$	−622.205	−	622.205i	−0.661217	−	0.661217i	0.294450	−	0.955667i	$-0.404864\pi$
$941$	−622.205	−	622.205i	−0.661217	−	0.661217i	−0.955667	+	0.294450i	$0.904864\pi$
$942$	1402.73	−	1527.84i	1.48910	−	1.62191i
$943$	174.104	+	174.104i	0.184627	+	0.184627i
$944$	−159.968	−	112.938i	−0.169458	−	0.119638i
$945$	45.0200	+	102.647i	0.0476402	+	0.108621i
$946$	−1023.17	+	43.6783i	−1.08157	+	0.0461716i
$947$	−334.816			−0.353555			−0.176777	−	0.984251i	$-0.556567\pi$
$947$	−334.816			−0.353555			−0.176777	+	0.984251i	$0.556567\pi$
$948$	−122.314	−	1430.00i	−0.129023	−	1.50844i
$949$	−589.814	−	589.814i	−0.621511	−	0.621511i
$950$	370.962	+	313.396i	0.390486	+	0.329890i
$951$		−	874.434i		−	0.919489i
$952$	276.768	−	358.527i	0.290723	−	0.376604i
$953$	−503.098	+	503.098i	−0.527909	+	0.527909i	−0.919949	−	0.392039i	$-0.871770\pi$
$953$	−503.098	+	503.098i	−0.527909	+	0.527909i	0.392039	+	0.919949i	$0.371770\pi$
$954$	−1349.56	−	1239.05i	−1.41463	−	1.29880i
$955$	−206.198	+	528.376i	−0.215914	+	0.553274i
$956$	−919.596	+	78.6573i	−0.961920	+	0.0822775i
$957$	−675.569			−0.705923
$958$	252.336	−	274.840i	0.263398	−	0.286890i
$959$			300.321i			0.313160i
$960$	−167.021	+	1432.24i	−0.173980	+	1.49192i
$961$	−341.311			−0.355163
$962$	25.8723	+	23.7538i	0.0268943	+	0.0246921i
$963$			1783.91i			1.85245i
$964$	56.5366	+	660.979i	0.0586479	+	0.685663i
$965$	1343.48	−	589.240i	1.39221	−	0.610611i
$966$	89.4984	−	97.4805i	0.0926485	−	0.100911i
$967$	−855.714	−	855.714i	−0.884916	−	0.884916i	0.109113	−	0.994029i	$-0.465199\pi$
$967$	−855.714	−	855.714i	−0.884916	−	0.884916i	−0.994029	+	0.109113i	$0.965199\pi$
$968$	567.246	+	437.891i	0.585998	+	0.452367i
$969$	−1147.96			−1.18469
$970$	53.1100	−	155.355i	0.0547526	−	0.160159i
$971$	−1101.75	+	1101.75i	−1.13466	+	1.13466i	−0.145267	+	0.989392i	$0.546404\pi$
$971$	−1101.75	+	1101.75i	−1.13466	+	1.13466i	−0.989392	+	0.145267i	$0.953596\pi$
$972$	−1359.26	+	116.264i	−1.39841	+	0.119613i
$973$		−	272.772i		−	0.280342i
$974$	10.5595	+	247.357i	0.0108414	+	0.253960i
$975$	−1777.88	−	1636.92i	−1.82346	−	1.67889i
$976$	302.605	+	213.640i	0.310046	+	0.218894i
$977$	287.755	−	287.755i	0.294530	−	0.294530i	−0.544337	−	0.838867i	$-0.683219\pi$
$977$	287.755	−	287.755i	0.294530	−	0.294530i	0.838867	+	0.544337i	$0.183219\pi$
$978$	−1366.57	−	1254.67i	−1.39731	−	1.28290i
$979$	302.707	−	302.707i	0.309200	−	0.309200i
$980$	250.821	−	850.614i	0.255940	−	0.867973i
$981$	−438.775	+	438.775i	−0.447273	+	0.447273i
$982$	−1360.49	+	58.0786i	−1.38543	+	0.0591432i
$983$	1237.43	−	1237.43i	1.25883	−	1.25883i	0.307176	−	0.951653i	$-0.400616\pi$
$983$	1237.43	−	1237.43i	1.25883	−	1.25883i	0.951653	−	0.307176i	$-0.0993842\pi$
$984$	−797.255	+	1032.77i	−0.810219	+	1.04956i
$985$	−141.849	−	55.3563i	−0.144009	−	0.0561992i
$986$	−366.553	+	399.245i	−0.371758	+	0.404914i
$987$			130.668i			0.132389i
$988$	536.954	−	637.402i	0.543476	−	0.645144i
$989$	−169.745	+	169.745i	−0.171633	+	0.171633i
$990$	−530.663	+	1552.27i	−0.536023	+	1.56795i
$991$	1513.43			1.52717			0.763586	−	0.645706i	$-0.223437\pi$
$991$	1513.43			1.52717			0.763586	+	0.645706i	$0.223437\pi$
$992$	−669.757	−	431.262i	−0.675158	−	0.434740i
$993$	491.600	+	491.600i	0.495066	+	0.495066i
$994$	348.744	−	14.8877i	0.350849	−	0.0149775i
$995$	414.259	−	1061.53i	0.416341	−	1.06686i
$996$	−45.3146	−	529.781i	−0.0454966	−	0.531909i
$997$			764.377i			0.766677i	0.923608	+	0.383339i	$0.125226\pi$
$997$			764.377i			0.766677i	−0.923608	+	0.383339i	$0.874774\pi$
$998$	−743.573	+	31.7427i	−0.745063	+	0.0318063i
$999$	8.50201			0.00851052

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.3.i.a.13.18	✓	44
4.3	odd	2		320.3.i.a.273.19		44
5.2	odd	4		80.3.t.a.77.6	yes	44
5.3	odd	4		400.3.t.b.157.17		44
5.4	even	2		400.3.i.b.93.5		44
8.3	odd	2		640.3.i.a.33.4		44
8.5	even	2		640.3.i.b.33.19		44
16.3	odd	4		640.3.t.a.353.4		44
16.5	even	4		80.3.t.a.53.6	yes	44
16.11	odd	4		320.3.t.a.113.19		44
16.13	even	4		640.3.t.b.353.19		44
20.7	even	4		320.3.t.a.17.19		44
40.27	even	4		640.3.t.a.417.4		44
40.37	odd	4		640.3.t.b.417.19		44
80.27	even	4		320.3.i.a.177.4		44
80.37	odd	4	inner	80.3.i.a.37.18	yes	44
80.53	odd	4		400.3.i.b.357.5		44
80.67	even	4		640.3.i.a.97.19		44
80.69	even	4		400.3.t.b.293.17		44
80.77	odd	4		640.3.i.b.97.4		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.18	✓	44	1.1	even	1	trivial
80.3.i.a.37.18	yes	44	80.37	odd	4	inner
80.3.t.a.53.6	yes	44	16.5	even	4
80.3.t.a.77.6	yes	44	5.2	odd	4
320.3.i.a.177.4		44	80.27	even	4
320.3.i.a.273.19		44	4.3	odd	2
320.3.t.a.17.19		44	20.7	even	4
320.3.t.a.113.19		44	16.11	odd	4
400.3.i.b.93.5		44	5.4	even	2
400.3.i.b.357.5		44	80.53	odd	4
400.3.t.b.157.17		44	5.3	odd	4
400.3.t.b.293.17		44	80.69	even	4
640.3.i.a.33.4		44	8.3	odd	2
640.3.i.a.97.19		44	80.67	even	4
640.3.i.b.33.19		44	8.5	even	2
640.3.i.b.97.4		44	80.77	odd	4
640.3.t.a.353.4		44	16.3	odd	4
640.3.t.a.417.4		44	40.27	even	4
640.3.t.b.353.19		44	16.13	even	4
640.3.t.b.417.19		44	40.37	odd	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	80.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.47324 + 1.35261i) q^{2} -4.50609i q^{3} +(0.340894 + 3.98545i) q^{4} +(1.81773 - 4.65788i) q^{5} +(6.09498 - 6.63857i) q^{6} +(1.52625 + 1.52625i) q^{7} +(-4.88854 + 6.33263i) q^{8} -11.3048 q^{9} +O(q^{10})\)	\(q+(1.47324 + 1.35261i) q^{2} -4.50609i q^{3} +(0.340894 + 3.98545i) q^{4} +(1.81773 - 4.65788i) q^{5} +(6.09498 - 6.63857i) q^{6} +(1.52625 + 1.52625i) q^{7} +(-4.88854 + 6.33263i) q^{8} -11.3048 q^{9} +(8.97825 - 4.40352i) q^{10} +(10.2610 - 10.2610i) q^{11} +(17.9588 - 1.53610i) q^{12} +21.4526i q^{13} +(0.184117 + 4.31294i) q^{14} +(-20.9888 - 8.19085i) q^{15} +(-15.7676 + 2.71723i) q^{16} +(-18.5474 + 18.5474i) q^{17} +(-16.6548 - 15.2910i) q^{18} +(-6.86774 + 6.86774i) q^{19} +(19.1834 + 5.65662i) q^{20} +(6.87740 - 6.87740i) q^{21} +(28.9960 - 1.23782i) q^{22} +(4.81049 - 4.81049i) q^{23} +(28.5354 + 22.0282i) q^{24} +(-18.3917 - 16.9335i) q^{25} +(-29.0169 + 31.6048i) q^{26} +10.3858i q^{27} +(-5.56248 + 6.60306i) q^{28} +(7.30552 - 7.30552i) q^{29} +(-19.8426 - 40.4568i) q^{30} +24.8935 q^{31} +(-26.9048 - 17.3242i) q^{32} +(-46.2368 - 46.2368i) q^{33} +(-52.4123 + 2.23745i) q^{34} +(9.88337 - 4.33477i) q^{35} +(-3.85375 - 45.0548i) q^{36} -0.818619i q^{37} +(-19.4072 + 0.828482i) q^{38} +96.6671 q^{39} +(20.6106 + 34.2812i) q^{40} +36.1925i q^{41} +(19.4345 - 0.829647i) q^{42} -35.2864 q^{43} +(44.3925 + 37.3967i) q^{44} +(-20.5491 + 52.6566i) q^{45} +(13.5937 - 0.580308i) q^{46} +(-9.49981 + 9.49981i) q^{47} +(12.2441 + 71.0501i) q^{48} -44.3412i q^{49} +(-4.19104 - 49.8240i) q^{50} +(83.5763 + 83.5763i) q^{51} +(-85.4980 + 7.31304i) q^{52} +81.0314 q^{53} +(-14.0479 + 15.3008i) q^{54} +(-29.1427 - 66.4460i) q^{55} +(-17.1263 + 2.20404i) q^{56} +(30.9466 + 30.9466i) q^{57} +(20.6443 - 0.881294i) q^{58} +(8.65405 + 8.65405i) q^{59} +(25.4892 - 86.4421i) q^{60} +(-16.3705 - 16.3705i) q^{61} +(36.6743 + 33.6713i) q^{62} +(-17.2539 - 17.2539i) q^{63} +(-16.2044 - 61.9146i) q^{64} +(99.9235 + 38.9949i) q^{65} +(-5.57773 - 130.659i) q^{66} -46.6786 q^{67} +(-80.2424 - 67.5970i) q^{68} +(-21.6765 - 21.6765i) q^{69} +(20.4239 + 6.98217i) q^{70} -80.8598i q^{71} +(55.2641 - 71.5894i) q^{72} +(-27.4939 + 27.4939i) q^{73} +(1.10727 - 1.20603i) q^{74} +(-76.3040 + 82.8748i) q^{75} +(-29.7122 - 25.0298i) q^{76} +31.3215 q^{77} +(142.414 + 130.753i) q^{78} -79.6266i q^{79} +(-16.0047 + 78.3827i) q^{80} -54.9442 q^{81} +(-48.9544 + 53.3204i) q^{82} -29.4998i q^{83} +(29.7540 + 25.0650i) q^{84} +(52.6775 + 120.106i) q^{85} +(-51.9855 - 47.7288i) q^{86} +(-32.9193 - 32.9193i) q^{87} +(14.8178 + 115.140i) q^{88} +29.5008 q^{89} +(-101.498 + 49.7810i) q^{90} +(-32.7419 + 32.7419i) q^{91} +(20.8118 + 17.5321i) q^{92} -112.173i q^{93} +(-26.8451 + 1.14600i) q^{94} +(19.5054 + 44.4728i) q^{95} +(-78.0646 + 121.236i) q^{96} +(11.6094 - 11.6094i) q^{97} +(59.9763 - 65.3253i) q^{98} +(-115.999 + 115.999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9	\( 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9} + 6 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{15} + 24 q^{16} - 4 q^{17} + 22 q^{18} + 32 q^{19} + 40 q^{20} - 4 q^{21} + 92 q^{22} + 36 q^{24} - 52 q^{26} + 36 q^{28} - 28 q^{30} - 8 q^{31} - 132 q^{32} - 4 q^{33} - 88 q^{34} + 96 q^{35} - 116 q^{36} - 216 q^{38} + 72 q^{39} + 16 q^{40} + 16 q^{42} + 124 q^{43} - 168 q^{44} - 34 q^{45} + 108 q^{46} - 4 q^{47} + 340 q^{48} + 10 q^{50} - 100 q^{51} + 48 q^{52} - 4 q^{53} + 228 q^{54} - 172 q^{56} + 36 q^{57} + 16 q^{58} + 64 q^{59} + 136 q^{60} - 36 q^{61} - 356 q^{62} - 200 q^{63} - 176 q^{64} - 4 q^{65} + 276 q^{66} - 292 q^{67} - 72 q^{68} - 60 q^{69} - 92 q^{70} + 448 q^{72} + 48 q^{73} + 284 q^{74} + 96 q^{75} + 252 q^{76} + 192 q^{77} + 620 q^{78} + 4 q^{80} + 100 q^{81} - 240 q^{82} + 288 q^{84} + 48 q^{85} + 20 q^{86} + 36 q^{87} - 624 q^{88} - 578 q^{90} + 188 q^{91} - 412 q^{92} - 340 q^{94} + 380 q^{95} - 24 q^{96} - 4 q^{97} - 78 q^{98} - 92 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9 + 6 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^15 + 24 * q^16 - 4 * q^17 + 22 * q^18 + 32 * q^19 + 40 * q^20 - 4 * q^21 + 92 * q^22 + 36 * q^24 - 52 * q^26 + 36 * q^28 - 28 * q^30 - 8 * q^31 - 132 * q^32 - 4 * q^33 - 88 * q^34 + 96 * q^35 - 116 * q^36 - 216 * q^38 + 72 * q^39 + 16 * q^40 + 16 * q^42 + 124 * q^43 - 168 * q^44 - 34 * q^45 + 108 * q^46 - 4 * q^47 + 340 * q^48 + 10 * q^50 - 100 * q^51 + 48 * q^52 - 4 * q^53 + 228 * q^54 - 172 * q^56 + 36 * q^57 + 16 * q^58 + 64 * q^59 + 136 * q^60 - 36 * q^61 - 356 * q^62 - 200 * q^63 - 176 * q^64 - 4 * q^65 + 276 * q^66 - 292 * q^67 - 72 * q^68 - 60 * q^69 - 92 * q^70 + 448 * q^72 + 48 * q^73 + 284 * q^74 + 96 * q^75 + 252 * q^76 + 192 * q^77 + 620 * q^78 + 4 * q^80 + 100 * q^81 - 240 * q^82 + 288 * q^84 + 48 * q^85 + 20 * q^86 + 36 * q^87 - 624 * q^88 - 578 * q^90 + 188 * q^91 - 412 * q^92 - 340 * q^94 + 380 * q^95 - 24 * q^96 - 4 * q^97 - 78 * q^98 - 92 * q^99

Introduction

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