LMFDB - Embedded newform 75.3.k.a.58.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(13,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, 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:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			58.2
Character	$\chi$	$=$	75.58
Dual form			75.3.k.a.22.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.18220 - 1.62141i) q^{2} +(1.71073 + 0.270952i) q^{3} +(5.14628 + 7.08325i) q^{4} +(-4.97907 - 0.457044i) q^{5} +(-5.00455 - 3.63602i) q^{6} +(-6.93420 + 6.93420i) q^{7} +(-2.65683 - 16.7746i) q^{8} +(2.85317 + 0.927051i) q^{9} +O(q^{10})$	\(q+(-3.18220 - 1.62141i) q^{2} +(1.71073 + 0.270952i) q^{3} +(5.14628 + 7.08325i) q^{4} +(-4.97907 - 0.457044i) q^{5} +(-5.00455 - 3.63602i) q^{6} +(-6.93420 + 6.93420i) q^{7} +(-2.65683 - 16.7746i) q^{8} +(2.85317 + 0.927051i) q^{9} +(15.1033 + 9.52752i) q^{10} +(6.28289 + 19.3367i) q^{11} +(6.88465 + 13.5119i) q^{12} +(5.19789 - 2.64846i) q^{13} +(33.3092 - 10.8228i) q^{14} +(-8.39398 - 2.13097i) q^{15} +(-7.92167 + 24.3804i) q^{16} +(-14.9517 + 2.36812i) q^{17} +(-7.57622 - 7.57622i) q^{18} +(-8.05018 + 11.0801i) q^{19} +(-22.3863 - 37.6200i) q^{20} +(-13.7414 + 9.98368i) q^{21} +(11.3594 - 71.7205i) q^{22} +(-2.45285 + 4.81399i) q^{23} -29.4166i q^{24} +(24.5822 + 4.55131i) q^{25} -20.8350 q^{26} +(4.62981 + 2.35900i) q^{27} +(-84.8019 - 13.4313i) q^{28} +(-4.66296 - 6.41802i) q^{29} +(23.2562 + 20.3913i) q^{30} +(-32.0251 - 23.2676i) q^{31} +(16.7020 - 16.7020i) q^{32} +(5.50896 + 34.7822i) q^{33} +(51.4191 + 16.7071i) q^{34} +(37.6951 - 31.3566i) q^{35} +(8.11668 + 24.9806i) q^{36} +(-3.70986 - 7.28100i) q^{37} +(43.5827 - 22.2065i) q^{38} +(9.60978 - 3.12241i) q^{39} +(5.56182 + 84.7360i) q^{40} +(2.26706 - 6.97730i) q^{41} +(59.9154 - 9.48966i) q^{42} +(7.11814 + 7.11814i) q^{43} +(-104.633 + 144.015i) q^{44} +(-13.7824 - 5.91987i) q^{45} +(15.6109 - 11.3420i) q^{46} +(-5.34190 + 33.7274i) q^{47} +(-20.1577 + 39.5618i) q^{48} -47.1662i q^{49} +(-70.8460 - 54.3411i) q^{50} -26.2200 q^{51} +(45.5095 + 23.1883i) q^{52} +(35.8736 + 5.68183i) q^{53} +(-10.9081 - 15.0136i) q^{54} +(-22.4452 - 99.1505i) q^{55} +(134.741 + 97.8951i) q^{56} +(-16.7738 + 16.7738i) q^{57} +(4.43223 + 27.9840i) q^{58} +(11.0469 + 3.58934i) q^{59} +(-28.1036 - 70.4232i) q^{60} +(-4.08403 - 12.5694i) q^{61} +(64.1839 + 125.968i) q^{62} +(-26.2128 + 13.3561i) q^{63} +(17.2918 - 5.61843i) q^{64} +(-27.0911 + 10.8112i) q^{65} +(38.8657 - 119.616i) q^{66} +(46.8716 - 7.42374i) q^{67} +(-93.7198 - 93.7198i) q^{68} +(-5.50052 + 7.57082i) q^{69} +(-170.795 + 38.6637i) q^{70} +(105.361 - 76.5490i) q^{71} +(7.97049 - 50.3237i) q^{72} +(-20.8347 + 40.8904i) q^{73} +29.1848i q^{74} +(40.8203 + 14.4467i) q^{75} -119.912 q^{76} +(-177.651 - 90.5180i) q^{77} +(-35.6430 - 5.64529i) q^{78} +(50.4913 + 69.4954i) q^{79} +(50.5855 - 117.771i) q^{80} +(7.28115 + 5.29007i) q^{81} +(-18.5273 + 18.5273i) q^{82} +(24.4251 + 154.214i) q^{83} +(-141.434 - 45.9546i) q^{84} +(75.5280 - 4.95744i) q^{85} +(-11.1099 - 34.1928i) q^{86} +(-6.23807 - 12.2429i) q^{87} +(307.673 - 156.767i) q^{88} +(29.2261 - 9.49613i) q^{89} +(34.2599 + 41.1852i) q^{90} +(-17.6783 + 54.4082i) q^{91} +(-46.7218 + 7.40000i) q^{92} +(-48.4817 - 48.4817i) q^{93} +(71.6851 - 98.6660i) q^{94} +(45.1465 - 51.4894i) q^{95} +(33.0980 - 24.0471i) q^{96} +(-22.3189 + 140.916i) q^{97} +(-76.4758 + 150.092i) q^{98} +60.9955i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{3}{20}\right)$

Coefficient data

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

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

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

$2$	−3.18220	−	1.62141i	−1.59110	−	0.810706i	−0.999992	−	0.00411388i	$-0.998691\pi$
$2$	−3.18220	−	1.62141i	−1.59110	−	0.810706i	−0.591108	−	0.806592i	$-0.701309\pi$
$3$	1.71073	+	0.270952i	0.570242	+	0.0903175i
$3$	1.71073	+	0.270952i	0.570242	+	0.0903175i
$4$	5.14628	+	7.08325i	1.28657	+	1.77081i
$5$	−4.97907	−	0.457044i	−0.995813	−	0.0914088i
$5$	−4.97907	−	0.457044i	−0.995813	−	0.0914088i
$6$	−5.00455	−	3.63602i	−0.834091	−	0.606003i
$7$	−6.93420	+	6.93420i	−0.990600	+	0.990600i	−0.999956	−	0.00935663i	$-0.997022\pi$
$7$	−6.93420	+	6.93420i	−0.990600	+	0.990600i	0.00935663	+	0.999956i	$0.497022\pi$
$8$	−2.65683	−	16.7746i	−0.332104	−	2.09682i
$9$	2.85317	+	0.927051i	0.317019	+	0.103006i
$10$	15.1033	+	9.52752i	1.51033	+	0.952752i
$11$	6.28289	+	19.3367i	0.571171	+	1.75788i	0.648861	+	0.760907i	$0.275246\pi$
$11$	6.28289	+	19.3367i	0.571171	+	1.75788i	−0.0776891	+	0.996978i	$0.524754\pi$
$12$	6.88465	+	13.5119i	0.573721	+	1.12599i
$13$	5.19789	−	2.64846i	0.399838	−	0.203728i	−0.242496	−	0.970152i	$-0.577966\pi$
$13$	5.19789	−	2.64846i	0.399838	−	0.203728i	0.642334	+	0.766425i	$0.277966\pi$
$14$	33.3092	−	10.8228i	2.37923	−	0.773058i
$15$	−8.39398	−	2.13097i	−0.559599	−	0.142065i
$16$	−7.92167	+	24.3804i	−0.495105	+	1.52378i
$17$	−14.9517	+	2.36812i	−0.879514	+	0.139301i	−0.579830	−	0.814737i	$-0.696881\pi$
$17$	−14.9517	+	2.36812i	−0.879514	+	0.139301i	−0.299684	+	0.954039i	$0.596881\pi$
$18$	−7.57622	−	7.57622i	−0.420901	−	0.420901i
$19$	−8.05018	+	11.0801i	−0.423694	+	0.583165i	−0.966491	−	0.256699i	$-0.917365\pi$
$19$	−8.05018	+	11.0801i	−0.423694	+	0.583165i	0.542798	+	0.839864i	$0.317365\pi$
$20$	−22.3863	−	37.6200i	−1.11932	−	1.88100i
$21$	−13.7414	+	9.98368i	−0.654350	+	0.475413i
$22$	11.3594	−	71.7205i	0.516337	−	3.26002i
$23$	−2.45285	+	4.81399i	−0.106646	+	0.209304i	−0.938162	−	0.346196i	$-0.887473\pi$
$23$	−2.45285	+	4.81399i	−0.106646	+	0.209304i	0.831516	+	0.555500i	$0.187473\pi$
$24$		−	29.4166i		−	1.22569i
$25$	24.5822	+	4.55131i	0.983289	+	0.182052i
$26$	−20.8350			−0.801346
$27$	4.62981	+	2.35900i	0.171474	+	0.0873705i
$28$	−84.8019	−	13.4313i	−3.02864	−	0.479690i
$29$	−4.66296	−	6.41802i	−0.160792	−	0.221311i	0.721018	−	0.692917i	$-0.243675\pi$
$29$	−4.66296	−	6.41802i	−0.160792	−	0.221311i	−0.881810	+	0.471606i	$0.843675\pi$
$30$	23.2562	+	20.3913i	0.775205	+	0.679709i
$31$	−32.0251	−	23.2676i	−1.03307	−	0.750567i	−0.0641467	−	0.997940i	$-0.520433\pi$
$31$	−32.0251	−	23.2676i	−1.03307	−	0.750567i	−0.968920	+	0.247373i	$0.920433\pi$
$32$	16.7020	−	16.7020i	0.521937	−	0.521937i
$33$	5.50896	+	34.7822i	0.166938	+	1.05401i
$34$	51.4191	+	16.7071i	1.51233	+	0.491385i
$35$	37.6951	−	31.3566i	1.07700	−	0.895903i
$36$	8.11668	+	24.9806i	0.225463	+	0.693905i
$37$	−3.70986	−	7.28100i	−0.100266	−	0.196784i	0.835424	−	0.549606i	$-0.185222\pi$
$37$	−3.70986	−	7.28100i	−0.100266	−	0.196784i	−0.935690	+	0.352822i	$0.885222\pi$
$38$	43.5827	−	22.2065i	1.14691	−	0.584382i
$39$	9.60978	−	3.12241i	0.246405	−	0.0800617i
$40$	5.56182	+	84.7360i	0.139045	+	2.11840i
$41$	2.26706	−	6.97730i	0.0552942	−	0.170178i	−0.919595	−	0.392867i	$-0.871483\pi$
$41$	2.26706	−	6.97730i	0.0552942	−	0.170178i	0.974890	+	0.222689i	$0.0714834\pi$
$42$	59.9154	−	9.48966i	1.42656	−	0.225944i
$43$	7.11814	+	7.11814i	0.165538	+	0.165538i	0.785015	−	0.619477i	$-0.212655\pi$
$43$	7.11814	+	7.11814i	0.165538	+	0.165538i	−0.619477	+	0.785015i	$0.712655\pi$
$44$	−104.633	+	144.015i	−2.37803	+	3.27308i
$45$	−13.7824	−	5.91987i	−0.306276	−	0.131553i
$46$	15.6109	−	11.3420i	0.339368	−	0.246565i
$47$	−5.34190	+	33.7274i	−0.113657	+	0.717605i	0.863383	+	0.504550i	$0.168341\pi$
$47$	−5.34190	+	33.7274i	−0.113657	+	0.717605i	−0.977040	+	0.213055i	$0.931659\pi$
$48$	−20.1577	+	39.5618i	−0.419953	+	0.824204i
$49$		−	47.1662i		−	0.962575i
$50$	−70.8460	−	54.3411i	−1.41692	−	1.08682i
$51$	−26.2200			−0.514117
$52$	45.5095	+	23.1883i	0.875183	+	0.445928i
$53$	35.8736	+	5.68183i	0.676861	+	0.107204i	0.485395	−	0.874295i	$-0.338676\pi$
$53$	35.8736	+	5.68183i	0.676861	+	0.107204i	0.191466	+	0.981499i	$0.438676\pi$
$54$	−10.9081	−	15.0136i	−0.202001	−	0.278030i
$55$	−22.4452	−	99.1505i	−0.408094	−	1.80274i
$56$	134.741	+	97.8951i	2.40609	+	1.74813i
$57$	−16.7738	+	16.7738i	−0.294278	+	0.294278i
$58$	4.43223	+	27.9840i	0.0764177	+	0.482483i
$59$	11.0469	+	3.58934i	0.187235	+	0.0608363i	0.401134	−	0.916019i	$-0.368616\pi$
$59$	11.0469	+	3.58934i	0.187235	+	0.0608363i	−0.213899	+	0.976856i	$0.568616\pi$
$60$	−28.1036	−	70.4232i	−0.468394	−	1.17372i
$61$	−4.08403	−	12.5694i	−0.0669514	−	0.206055i	0.911984	−	0.410226i	$-0.134550\pi$
$61$	−4.08403	−	12.5694i	−0.0669514	−	0.206055i	−0.978935	+	0.204171i	$0.934550\pi$
$62$	64.1839	+	125.968i	1.03522	+	2.03174i
$63$	−26.2128	+	13.3561i	−0.416076	+	0.212001i
$64$	17.2918	−	5.61843i	0.270184	−	0.0877880i
$65$	−27.0911	+	10.8112i	−0.416787	+	0.166326i
$66$	38.8657	−	119.616i	0.588874	−	1.81237i
$67$	46.8716	−	7.42374i	0.699577	−	0.110802i	0.203493	−	0.979076i	$-0.434771\pi$
$67$	46.8716	−	7.42374i	0.699577	−	0.110802i	0.496084	+	0.868274i	$0.334771\pi$
$68$	−93.7198	−	93.7198i	−1.37823	−	1.37823i
$69$	−5.50052	+	7.57082i	−0.0797177	+	0.109722i
$70$	−170.795	+	38.6637i	−2.43993	+	0.552339i
$71$	105.361	−	76.5490i	1.48395	−	1.07815i	0.507697	−	0.861536i	$-0.330497\pi$
$71$	105.361	−	76.5490i	1.48395	−	1.07815i	0.976256	−	0.216619i	$-0.0695030\pi$
$72$	7.97049	−	50.3237i	0.110701	−	0.698940i
$73$	−20.8347	+	40.8904i	−0.285407	+	0.560143i	−0.988548	−	0.150908i	$-0.951780\pi$
$73$	−20.8347	+	40.8904i	−0.285407	+	0.560143i	0.703141	+	0.711051i	$0.251780\pi$
$74$			29.1848i			0.394389i
$75$	40.8203	+	14.4467i	0.544270	+	0.192622i
$76$	−119.912			−1.57779
$77$	−177.651	−	90.5180i	−2.30716	−	1.17556i
$78$	−35.6430	−	5.64529i	−0.456961	−	0.0723755i
$79$	50.4913	+	69.4954i	0.639131	+	0.879688i	0.998569	−	0.0534808i	$-0.0170316\pi$
$79$	50.4913	+	69.4954i	0.639131	+	0.879688i	−0.359438	+	0.933169i	$0.617032\pi$
$80$	50.5855	−	117.771i	0.632318	−	1.47214i
$81$	7.28115	+	5.29007i	0.0898908	+	0.0653095i
$82$	−18.5273	+	18.5273i	−0.225943	+	0.225943i
$83$	24.4251	+	154.214i	0.294278	+	1.85800i	0.482530	+	0.875880i	$0.339718\pi$
$83$	24.4251	+	154.214i	0.294278	+	1.85800i	−0.188251	+	0.982121i	$0.560282\pi$
$84$	−141.434	−	45.9546i	−1.68373	−	0.547078i
$85$	75.5280	−	4.95744i	0.888565	−	0.0583228i
$86$	−11.1099	−	34.1928i	−0.129185	−	0.397591i
$87$	−6.23807	−	12.2429i	−0.0717020	−	0.140723i
$88$	307.673	−	156.767i	3.49628	−	1.78144i
$89$	29.2261	−	9.49613i	0.328383	−	0.106698i	−0.140186	−	0.990125i	$-0.544770\pi$
$89$	29.2261	−	9.49613i	0.328383	−	0.106698i	0.468568	+	0.883427i	$0.344770\pi$
$90$	34.2599	+	41.1852i	0.380665	+	0.457613i
$91$	−17.6783	+	54.4082i	−0.194267	+	0.597892i
$92$	−46.7218	+	7.40000i	−0.507845	+	0.0804348i
$93$	−48.4817	−	48.4817i	−0.521309	−	0.521309i
$94$	71.6851	−	98.6660i	0.762607	−	1.04964i
$95$	45.1465	−	51.4894i	0.475226	−	0.541994i
$96$	33.0980	−	24.0471i	0.344771	−	0.250490i
$97$	−22.3189	+	140.916i	−0.230092	+	1.45274i	0.554218	+	0.832372i	$0.313017\pi$
$97$	−22.3189	+	140.916i	−0.230092	+	1.45274i	−0.784310	+	0.620370i	$0.786983\pi$
$98$	−76.4758	+	150.092i	−0.780365	+	1.53155i
$99$			60.9955i			0.616117i
$100$	94.2690	+	197.544i	0.942690	+	1.97544i
$101$	−104.983			−1.03944			−0.519719	−	0.854337i	$-0.673963\pi$
$101$	−104.983			−1.03944			−0.519719	+	0.854337i	$0.673963\pi$
$102$	83.4372	+	42.5134i	0.818012	+	0.416798i
$103$	77.3925	+	12.2578i	0.751384	+	0.119007i	0.520368	−	0.853942i	$-0.325795\pi$
$103$	77.3925	+	12.2578i	0.751384	+	0.119007i	0.231016	+	0.972950i	$0.425795\pi$
$104$	−58.2367	−	80.1559i	−0.559968	−	0.770730i
$105$	72.9821	−	43.4290i	0.695068	−	0.413609i
$106$	−104.945	−	76.2467i	−0.990043	−	0.719308i
$107$	101.221	−	101.221i	0.945994	−	0.945994i	−0.0526201	−	0.998615i	$-0.516757\pi$
$107$	101.221	−	101.221i	0.945994	−	0.945994i	0.998615	+	0.0526201i	$0.0167572\pi$
$108$	7.11687	+	44.9341i	0.0658969	+	0.416057i
$109$	−112.084	−	36.4183i	−1.02829	−	0.334113i	−0.254179	−	0.967157i	$-0.581805\pi$
$109$	−112.084	−	36.4183i	−1.02829	−	0.334113i	−0.774116	+	0.633044i	$0.781805\pi$
$110$	−89.3387	+	351.909i	−0.812170	+	3.19918i
$111$	−4.37374	−	13.4610i	−0.0394031	−	0.121270i
$112$	−114.128	−	223.989i	−1.01900	−	1.99990i
$113$	165.164	−	84.1554i	1.46163	−	0.744738i	0.471107	−	0.882076i	$-0.343855\pi$
$113$	165.164	−	84.1554i	1.46163	−	0.744738i	0.990524	+	0.137338i	$0.0438547\pi$
$114$	80.5751	−	26.1804i	0.706799	−	0.229653i
$115$	14.4131	−	22.8481i	0.125332	−	0.198679i
$116$	21.4635	−	66.0578i	0.185030	−	0.569464i
$117$	17.2857	−	2.73779i	0.147741	−	0.0233999i
$118$	−29.3335	−	29.3335i	−0.248589	−	0.248589i
$119$	87.2572	−	120.099i	0.733254	−	1.00924i
$120$	−13.4447	+	146.467i	−0.112039	+	1.22056i
$121$	−236.544	+	171.859i	−1.95491	+	1.42032i
$122$	−7.38390	+	46.6201i	−0.0605238	+	0.382132i
$123$	5.76884	−	11.3220i	0.0469011	−	0.0920487i
$124$		−	346.583i		−	2.79502i
$125$	−120.316	−	33.8964i	−0.962531	−	0.271171i
$126$	105.070			0.833889
$127$	−45.8146	−	23.3437i	−0.360745	−	0.183809i	0.264219	−	0.964463i	$-0.414886\pi$
$127$	−45.8146	−	23.3437i	−0.360745	−	0.183809i	−0.624963	+	0.780654i	$0.714886\pi$
$128$	−157.453	−	24.9381i	−1.23010	−	0.194829i
$129$	10.2485	+	14.1059i	0.0794459	+	0.109348i
$130$	103.739	+	9.52251i	0.797991	+	0.0732501i
$131$	28.4366	+	20.6604i	0.217073	+	0.157713i	0.691008	−	0.722847i	$-0.257167\pi$
$131$	28.4366	+	20.6604i	0.217073	+	0.157713i	−0.473935	+	0.880560i	$0.657167\pi$
$132$	−218.020	+	218.020i	−1.65167	+	1.65167i
$133$	−21.0102	−	132.653i	−0.157972	−	0.997394i
$134$	−161.192	−	52.3744i	−1.20292	−	0.390854i
$135$	−21.9739	−	13.8617i	−0.162770	−	0.102679i
$136$	79.4484	+	244.517i	0.584180	+	1.79792i
$137$	17.7846	+	34.9042i	0.129815	+	0.254775i	0.946760	−	0.321939i	$-0.104335\pi$
$137$	17.7846	+	34.9042i	0.129815	+	0.254775i	−0.816946	+	0.576714i	$0.804335\pi$
$138$	29.7792	−	15.1733i	0.215791	−	0.109951i
$139$	−87.3089	+	28.3684i	−0.628121	+	0.204089i	−0.605743	−	0.795661i	$-0.707124\pi$
$139$	−87.3089	+	28.3684i	−0.628121	+	0.204089i	−0.0223787	+	0.999750i	$0.507124\pi$
$140$	416.096	+	105.634i	2.97211	+	0.754526i
$141$	−18.2771	+	56.2510i	−0.129625	+	0.398943i
$142$	−459.396	+	72.7612i	−3.23518	+	0.512403i
$143$	83.8703	+	83.8703i	0.586506	+	0.586506i
$144$	−45.2038	+	62.2176i	−0.313915	+	0.432067i
$145$	20.2839	+	34.0869i	0.139889	+	0.235082i
$146$	132.600	−	96.3398i	0.908222	−	0.659862i
$147$	12.7798	−	80.6884i	0.0869374	−	0.548901i
$148$	32.4812	−	63.7479i	0.219467	−	0.430729i
$149$			65.2768i			0.438100i	0.975714	+	0.219050i	$0.0702957\pi$
$149$			65.2768i			0.438100i	−0.975714	+	0.219050i	$0.929704\pi$
$150$	−106.474	−	112.159i	−0.709829	−	0.747724i
$151$	209.173			1.38525			0.692627	−	0.721296i	$-0.256453\pi$
$151$	209.173			1.38525			0.692627	+	0.721296i	$0.256453\pi$
$152$	207.252	+	105.600i	1.36350	+	0.694739i
$153$	−44.8552	−	7.10437i	−0.293171	−	0.0464338i
$154$	418.556	+	576.093i	2.71789	+	3.74086i
$155$	148.821	+	130.488i	0.960134	+	0.841856i
$156$	71.5714	+	51.9997i	0.458791	+	0.333331i
$157$	119.424	−	119.424i	0.760664	−	0.760664i	−0.215779	−	0.976442i	$-0.569229\pi$
$157$	119.424	−	119.424i	0.760664	−	0.760664i	0.976442	+	0.215779i	$0.0692290\pi$
$158$	−47.9929	−	303.015i	−0.303753	−	1.91782i
$159$	59.8305	+	19.4401i	0.376292	+	0.122265i
$160$	−90.7939	+	75.5268i	−0.567462	+	0.472042i
$161$	−16.3726	−	50.3897i	−0.101693	−	0.312980i
$162$	−14.5927	−	28.6398i	−0.0900784	−	0.176789i
$163$	5.04028	−	2.56815i	0.0309219	−	0.0157555i	−0.438461	−	0.898750i	$-0.644476\pi$
$163$	5.04028	−	2.56815i	0.0309219	−	0.0157555i	0.469383	+	0.882995i	$0.344476\pi$
$164$	61.0889	−	19.8490i	0.372493	−	0.121030i
$165$	−11.5325	−	175.701i	−0.0698938	−	1.06485i
$166$	172.319	−	530.343i	1.03807	−	3.19484i
$167$	−153.388	+	24.2942i	−0.918489	+	0.145474i	−0.597740	−	0.801690i	$-0.703934\pi$
$167$	−153.388	+	24.2942i	−0.918489	+	0.145474i	−0.320749	+	0.947164i	$0.603934\pi$
$168$	203.980	+	203.980i	1.21417	+	1.21417i
$169$	−79.3319	+	109.191i	−0.469420	+	0.646101i
$170$	−248.383	−	106.686i	−1.46108	−	0.627568i
$171$	−33.2404	+	24.1505i	−0.194388	+	0.141231i
$172$	−13.7876	+	87.0515i	−0.0801605	+	0.506113i
$173$	−6.78775	+	13.3217i	−0.0392355	+	0.0770041i	−0.909792	−	0.415064i	$-0.863759\pi$
$173$	−6.78775	+	13.3217i	−0.0392355	+	0.0770041i	0.870556	+	0.492068i	$0.163759\pi$
$174$			49.0739i			0.282034i
$175$	−202.018	+	138.898i	−1.15439	+	0.793705i
$176$	−521.208			−2.96141
$177$	17.9256	+	9.13356i	0.101275	+	0.0516020i
$178$	−108.400	−	17.1689i	−0.608991	−	0.0964547i
$179$	−174.964	−	240.817i	−0.977453	−	1.34535i	−0.938190	−	0.346120i	$-0.887499\pi$
$179$	−174.964	−	240.817i	−0.977453	−	1.34535i	−0.0392626	−	0.999229i	$-0.512501\pi$
$180$	−28.9963	−	128.090i	−0.161090	−	0.711609i
$181$	113.916	+	82.7651i	0.629372	+	0.457266i	0.856183	−	0.516673i	$-0.172830\pi$
$181$	113.916	+	82.7651i	0.629372	+	0.457266i	−0.226811	+	0.973939i	$0.572830\pi$
$182$	144.474	−	144.474i	0.793813	−	0.793813i
$183$	−3.58096	−	22.6093i	−0.0195681	−	0.123548i
$184$	87.2694	+	28.3556i	0.474290	+	0.154106i
$185$	15.1439	+	37.9482i	0.0818588	+	0.205125i
$186$	75.6697	+	232.887i	0.406826	+	1.25208i
$187$	−139.732	−	274.239i	−0.747229	−	1.46652i
$188$	−266.391	+	135.733i	−1.41697	+	0.721983i
$189$	−48.4618	+	15.7462i	−0.256412	+	0.0833132i
$190$	−227.151	+	90.6485i	−1.19553	+	0.477097i
$191$	5.54743	−	17.0732i	0.0290441	−	0.0893886i	−0.935484	−	0.353370i	$-0.885036\pi$
$191$	5.54743	−	17.0732i	0.0290441	−	0.0893886i	0.964528	+	0.263981i	$0.0850357\pi$
$192$	31.1038	−	4.92636i	0.161999	−	0.0256581i
$193$	−38.8419	−	38.8419i	−0.201253	−	0.201253i	0.599284	−	0.800537i	$-0.295452\pi$
$193$	−38.8419	−	38.8419i	−0.201253	−	0.201253i	−0.800537	+	0.599284i	$0.795452\pi$
$194$	299.506	−	412.234i	1.54384	−	2.12492i
$195$	−49.2748	+	11.1546i	−0.252691	+	0.0572030i
$196$	334.090	−	242.730i	1.70454	−	1.23842i
$197$	−7.75822	+	48.9835i	−0.0393818	+	0.248647i	−0.999524	−	0.0308666i	$-0.990173\pi$
$197$	−7.75822	+	48.9835i	−0.0393818	+	0.248647i	0.960142	+	0.279514i	$0.0901733\pi$
$198$	98.8989	−	194.100i	0.499489	−	0.980303i
$199$			181.948i			0.914311i	0.889387	+	0.457155i	$0.151132\pi$
$199$			181.948i			0.914311i	−0.889387	+	0.457155i	$0.848868\pi$
$200$	11.0354	−	424.448i	0.0551771	−	2.12224i
$201$	82.1960			0.408935
$202$	334.078	+	170.221i	1.65385	+	0.842679i
$203$	76.8377	+	12.1699i	0.378511	+	0.0599502i
$204$	−134.935	−	185.723i	−0.661448	−	0.910405i
$205$	−14.4768	+	33.7043i	−0.0706185	+	0.164411i
$206$	−226.404	−	164.492i	−1.09905	−	0.798504i
$207$	−11.4612	+	11.4612i	−0.0553682	+	0.0553682i
$208$	23.3945	+	147.707i	0.112474	+	0.710130i
$209$	−264.832	−	86.0491i	−1.26714	−	0.411718i
$210$	−302.660	+	19.8657i	−1.44124	+	0.0945986i
$211$	117.528	+	361.713i	0.557003	+	1.71428i	0.690594	+	0.723243i	$0.257349\pi$
$211$	117.528	+	361.713i	0.557003	+	1.71428i	−0.133591	+	0.991037i	$0.542651\pi$
$212$	144.370	+	283.342i	0.680991	+	1.33652i
$213$	200.984	−	102.407i	0.943589	−	0.480782i
$214$	−486.228	+	157.985i	−2.27210	+	0.738248i
$215$	−32.1884	−	38.6950i	−0.149714	−	0.179977i
$216$	27.2706	−	83.9304i	0.126253	−	0.388567i
$217$	383.410	−	60.7262i	1.76687	−	0.279844i
$218$	297.625	+	297.625i	1.36525	+	1.36525i
$219$	−46.7218	+	64.3071i	−0.213342	+	0.293640i
$220$	586.798	−	669.241i	2.66726	−	3.04200i
$221$	−71.4457	+	51.9083i	−0.323284	+	0.234879i
$222$	−7.90770	+	49.9272i	−0.0356203	+	0.224897i
$223$	−20.0418	+	39.3343i	−0.0898737	+	0.176387i	−0.931568	−	0.363568i	$-0.881559\pi$
$223$	−20.0418	+	39.3343i	−0.0898737	+	0.176387i	0.841694	+	0.539955i	$0.181559\pi$
$224$			231.630i			1.03406i
$225$	65.9180	+	35.7746i	0.292969	+	0.158998i
$226$	−662.036			−2.92936
$227$	−234.291	−	119.377i	−1.03212	−	0.525891i	−0.145969	−	0.989289i	$-0.546630\pi$
$227$	−234.291	−	119.377i	−1.03212	−	0.525891i	−0.886150	+	0.463398i	$0.846630\pi$
$228$	−205.136	−	32.4904i	−0.899720	−	0.142502i
$229$	−90.7715	−	124.936i	−0.396382	−	0.545573i	0.563449	−	0.826151i	$-0.309474\pi$
$229$	−90.7715	−	124.936i	−0.396382	−	0.545573i	−0.959831	+	0.280578i	$0.909474\pi$
$230$	−82.9117	+	49.3377i	−0.360486	+	0.214512i
$231$	−279.387	−	202.987i	−1.20947	−	0.878730i
$232$	−95.2707	+	95.2707i	−0.410650	+	0.410650i
$233$	19.0432	+	120.234i	0.0817305	+	0.516026i	0.994258	+	0.107010i	$0.0341278\pi$
$233$	19.0432	+	120.234i	0.0817305	+	0.516026i	−0.912527	+	0.409015i	$0.865872\pi$
$234$	−59.4457	−	19.3151i	−0.254042	−	0.0825431i
$235$	42.0126	−	165.490i	0.178777	−	0.704211i
$236$	31.4261	+	96.7194i	0.133161	+	0.409828i
$237$	67.5469	+	132.568i	0.285008	+	0.559360i
$238$	−472.400	+	240.700i	−1.98488	+	1.01134i
$239$	102.512	−	33.3083i	0.428922	−	0.139365i	−0.0865970	−	0.996243i	$-0.527599\pi$
$239$	102.512	−	33.3083i	0.428922	−	0.139365i	0.515519	+	0.856878i	$0.327599\pi$
$240$	118.448	−	187.768i	0.493534	−	0.782366i
$241$	66.0569	−	203.302i	0.274095	−	0.843578i	−0.715362	−	0.698754i	$-0.753738\pi$
$241$	66.0569	−	203.302i	0.274095	−	0.843578i	0.989457	−	0.144824i	$-0.0462616\pi$
$242$	1031.38	−	163.355i	4.26191	−	0.675021i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$	68.0143	−	93.6137i	0.278747	−	0.383663i
$245$	−21.5570	+	234.844i	−0.0879879	+	0.958545i
$246$	−36.7152	+	26.6752i	−0.149249	+	0.108436i
$247$	−12.4987	+	78.9139i	−0.0506022	+	0.319490i
$248$	−305.218	+	599.025i	−1.23072	+	2.41542i
$249$			270.436i			1.08609i
$250$	327.911	+	302.948i	1.31164	+	1.21179i
$251$	456.072			1.81702			0.908510	−	0.417864i	$-0.137221\pi$
$251$	456.072			1.81702			0.908510	+	0.417864i	$0.137221\pi$
$252$	−229.503	−	116.938i	−0.910725	−	0.464038i
$253$	−108.498	−	17.1844i	−0.428846	−	0.0679225i
$254$	107.941	+	148.569i	0.424966	+	0.584916i
$255$	130.551	+	11.9837i	0.511965	+	0.0469948i
$256$	401.775	+	291.907i	1.56943	+	1.14026i
$257$	11.1944	−	11.1944i	0.0435579	−	0.0435579i	−0.684992	−	0.728550i	$-0.740194\pi$
$257$	11.1944	−	11.1944i	0.0435579	−	0.0435579i	0.728550	+	0.684992i	$0.240194\pi$
$258$	−9.74140	−	61.5048i	−0.0377574	−	0.238391i
$259$	76.2128	+	24.7630i	0.294258	+	0.0956102i
$260$	−215.997	−	136.256i	−0.830757	−	0.524061i
$261$	−7.35439	−	22.6345i	−0.0281777	−	0.0867222i
$262$	−56.9918	−	111.853i	−0.217526	−	0.426919i
$263$	−415.603	+	211.760i	−1.58024	+	0.805173i	−0.999957	−	0.00924184i	$-0.997058\pi$
$263$	−415.603	+	211.760i	−1.58024	+	0.805173i	−0.580283	+	0.814415i	$0.697058\pi$
$264$	568.820	−	184.821i	2.15462	−	0.700079i
$265$	−176.020	−	44.6860i	−0.664228	−	0.168627i
$266$	−148.227	+	456.196i	−0.557244	+	1.71502i
$267$	52.5708	−	8.32640i	0.196894	−	0.0311850i
$268$	293.799	+	293.799i	1.09626	+	1.09626i
$269$	−250.616	+	344.944i	−0.931659	+	1.28232i	0.0275506	+	0.999620i	$0.491229\pi$
$269$	−250.616	+	344.944i	−0.931659	+	1.28232i	−0.959209	+	0.282698i	$0.908771\pi$
$270$	47.4500	+	79.7394i	0.175741	+	0.295331i
$271$	−92.2543	+	67.0267i	−0.340422	+	0.247331i	−0.744840	−	0.667243i	$-0.767474\pi$
$271$	−92.2543	+	67.0267i	−0.340422	+	0.247331i	0.404418	+	0.914574i	$0.367474\pi$
$272$	60.7070	−	383.289i	0.223187	−	1.40915i
$273$	−44.9847	+	88.2875i	−0.164779	+	0.323397i
$274$		−	139.908i		−	0.510614i
$275$	66.4399	+	503.935i	0.241600	+	1.83249i
$276$	−81.9332			−0.296859
$277$	132.280	+	67.4002i	0.477546	+	0.243322i	0.676158	−	0.736756i	$-0.263643\pi$
$277$	132.280	+	67.4002i	0.477546	+	0.243322i	−0.198612	+	0.980078i	$0.563643\pi$
$278$	323.831	+	51.2898i	1.16486	+	0.184496i
$279$	−69.8027	−	96.0752i	−0.250189	−	0.344356i
$280$	−626.143	−	549.009i	−2.23622	−	1.96075i
$281$	47.4375	+	34.4653i	0.168817	+	0.122652i	0.668986	−	0.743275i	$-0.266729\pi$
$281$	47.4375	+	34.4653i	0.168817	+	0.122652i	−0.500169	+	0.865928i	$0.666729\pi$
$282$	149.367	−	149.367i	0.529671	−	0.529671i
$283$	−71.0927	−	448.862i	−0.251211	−	1.58608i	−0.714344	−	0.699795i	$-0.753275\pi$
$283$	−71.0927	−	448.862i	−0.251211	−	1.58608i	0.463133	−	0.886289i	$-0.346725\pi$
$284$	1084.43	+	352.353i	3.81842	+	1.24068i
$285$	91.1845	−	75.8517i	0.319946	−	0.266146i
$286$	−130.904	−	402.881i	−0.457706	−	1.40867i
$287$	32.6617	+	64.1022i	0.113804	+	0.223353i
$288$	63.1372	−	32.1700i	0.219226	−	0.111701i
$289$	−56.9090	+	18.4909i	−0.196917	+	0.0639822i
$290$	−9.27845	−	141.360i	−0.0319946	−	0.487448i
$291$	−76.3630	+	235.021i	−0.262416	+	0.807633i
$292$	−396.858	+	62.8561i	−1.35910	+	0.215261i
$293$	−170.270	−	170.270i	−0.581128	−	0.581128i	0.354085	−	0.935213i	$-0.384792\pi$
$293$	−170.270	−	170.270i	−0.581128	−	0.581128i	−0.935213	+	0.354085i	$0.884792\pi$
$294$	−171.497	+	236.045i	−0.583323	+	0.802876i
$295$	−53.3626	−	22.9205i	−0.180890	−	0.0776966i
$296$	−112.279	+	81.5756i	−0.379321	+	0.275593i
$297$	−16.5269	+	104.347i	−0.0556461	+	0.351336i
$298$	105.841	−	207.724i	0.355170	−	0.697060i
$299$			31.5189i			0.105414i
$300$	107.743	+	363.487i	0.359144	+	1.21162i
$301$	−98.7172			−0.327964
$302$	−665.632	−	339.156i	−2.20408	−	1.12303i
$303$	−179.598	−	28.4455i	−0.592732	−	0.0938795i
$304$	−206.367	−	284.040i	−0.678839	−	0.934342i
$305$	14.5899	+	64.4503i	0.0478358	+	0.211312i
$306$	131.219	+	95.3363i	0.428821	+	0.311556i
$307$	334.311	−	334.311i	1.08896	−	1.08896i	0.0933264	−	0.995636i	$-0.470250\pi$
$307$	334.311	−	334.311i	1.08896	−	1.08896i	0.995636	−	0.0933264i	$-0.0297500\pi$
$308$	−273.083	−	1724.18i	−0.886634	−	5.59799i
$309$	129.076	+	41.9394i	0.417722	+	0.135726i
$310$	−262.003	−	656.538i	−0.845171	−	2.11786i
$311$	84.3045	+	259.463i	0.271076	+	0.834285i	0.990231	+	0.139436i	$0.0445289\pi$
$311$	84.3045	+	259.463i	0.271076	+	0.834285i	−0.719155	+	0.694849i	$0.755471\pi$
$312$	−77.9086	−	152.904i	−0.249707	−	0.490077i
$313$	301.198	−	153.468i	0.962293	−	0.490313i	0.0990392	−	0.995084i	$-0.468423\pi$
$313$	301.198	−	153.468i	0.962293	−	0.490313i	0.863253	+	0.504771i	$0.168423\pi$
$314$	−573.667	+	186.396i	−1.82697	+	0.593617i
$315$	136.620	−	54.5204i	0.433713	−	0.173081i
$316$	−232.410	+	715.285i	−0.735475	+	2.26356i
$317$	−189.680	+	30.0424i	−0.598360	+	0.0947709i	−0.448265	−	0.893901i	$-0.647958\pi$
$317$	−189.680	+	30.0424i	−0.598360	+	0.0947709i	−0.150095	+	0.988672i	$0.547958\pi$
$318$	−158.872	−	158.872i	−0.499598	−	0.499598i
$319$	94.8066	−	130.490i	0.297199	−	0.409060i
$320$	−88.6647	+	20.0715i	−0.277077	+	0.0627233i
$321$	200.588	−	145.736i	0.624886	−	0.454006i
$322$	−29.6016	+	186.897i	−0.0919304	+	0.580426i
$323$	94.1251	−	184.731i	0.291409	−	0.571922i
$324$			78.7984i			0.243205i
$325$	139.830	−	41.4478i	0.430245	−	0.127532i
$326$	−20.2032			−0.0619730
$327$	−181.878	−	92.6713i	−0.556201	−	0.283398i
$328$	−123.064	−	19.4915i	−0.375196	−	0.0594252i
$329$	−196.831	−	270.915i	−0.598270	−	0.823448i
$330$	−248.185	+	577.814i	−0.752075	+	1.75095i
$331$	−93.5042	−	67.9348i	−0.282490	−	0.205241i	0.437513	−	0.899212i	$-0.355860\pi$
$331$	−93.5042	−	67.9348i	−0.282490	−	0.205241i	−0.720003	+	0.693971i	$0.755860\pi$
$332$	−966.638	+	966.638i	−2.91156	+	2.91156i
$333$	−3.83499	−	24.2132i	−0.0115165	−	0.0727122i
$334$	527.501	+	171.395i	1.57934	+	0.513160i
$335$	−236.770	+	15.5409i	−0.706776	+	0.0463907i
$336$	−134.552	−	414.107i	−0.400451	−	1.23246i
$337$	195.958	+	384.590i	0.581479	+	1.14122i	0.975063	+	0.221928i	$0.0712351\pi$
$337$	195.958	+	384.590i	0.581479	+	1.14122i	−0.393584	+	0.919289i	$0.628765\pi$
$338$	429.494	−	218.838i	1.27069	−	0.647450i
$339$	305.353	−	99.2152i	0.900746	−	0.292670i
$340$	423.803	+	509.471i	1.24648	+	1.49844i
$341$	248.709	−	765.448i	0.729352	−	2.24472i
$342$	144.936	−	22.9555i	0.423788	−	0.0671214i
$343$	−12.7161	−	12.7161i	−0.0370731	−	0.0370731i
$344$	100.492	−	138.315i	0.292128	−	0.402080i
$345$	30.8477	−	35.1816i	0.0894135	−	0.101976i
$346$	43.1999	−	31.3866i	0.124855	−	0.0907127i
$347$	7.27173	−	45.9119i	0.0209560	−	0.132311i	−0.974992	−	0.222239i	$-0.928664\pi$
$347$	7.27173	−	45.9119i	0.0209560	−	0.132311i	0.995948	+	0.0899277i	$0.0286636\pi$
$348$	54.6167	−	107.191i	0.156944	−	0.308021i
$349$		−	683.170i		−	1.95751i	−0.205042	−	0.978753i	$-0.565733\pi$
$349$		−	683.170i		−	1.95751i	0.205042	−	0.978753i	$-0.434267\pi$
$350$	868.072	−	114.448i	2.48021	−	0.326995i
$351$	30.3130			0.0863617
$352$	427.899	+	218.025i	1.21562	+	0.619390i
$353$	311.111	+	49.2751i	0.881333	+	0.139589i	0.580668	−	0.814140i	$-0.302791\pi$
$353$	311.111	+	49.2751i	0.881333	+	0.139589i	0.300665	+	0.953730i	$0.402791\pi$
$354$	−42.2337	−	58.1296i	−0.119304	−	0.164208i
$355$	−559.584	+	332.988i	−1.57629	+	0.937995i
$356$	217.669	+	158.146i	0.611430	+	0.444230i
$357$	181.814	−	181.814i	0.509284	−	0.509284i
$358$	166.307	+	1050.02i	0.464543	+	2.93301i
$359$	656.333	+	213.256i	1.82823	+	0.594027i	0.999404	+	0.0345132i	$0.0109881\pi$
$359$	656.333	+	213.256i	1.82823	+	0.594027i	0.828821	+	0.559513i	$0.189012\pi$
$360$	−62.6857	+	246.922i	−0.174127	+	0.685895i
$361$	53.5914	+	164.937i	0.148453	+	0.456890i
$362$	−228.308	−	448.080i	−0.630686	−	1.23779i
$363$	−451.227	+	229.912i	−1.24305	+	0.633365i
$364$	−476.364	+	154.780i	−1.30869	+	0.425220i
$365$	122.426	−	194.074i	0.335414	−	0.531709i
$366$	−25.2637	+	77.7536i	−0.0690264	+	0.212442i
$367$	−52.9422	+	8.38522i	−0.144257	+	0.0228480i	−0.228145	−	0.973627i	$-0.573266\pi$
$367$	−52.9422	+	8.38522i	−0.144257	+	0.0228480i	0.0838884	+	0.996475i	$0.473266\pi$
$368$	−97.9364	−	97.9364i	−0.266132	−	0.266132i
$369$	12.9366	−	17.8057i	0.0350586	−	0.0482540i
$370$	13.3387	−	145.313i	0.0360507	−	0.392738i
$371$	−288.154	+	209.356i	−0.776695	+	0.564302i
$372$	93.9075	−	592.909i	0.252440	−	1.59384i
$373$	179.228	−	351.754i	0.480503	−	0.943040i	−0.515766	−	0.856730i	$-0.672492\pi$
$373$	179.228	−	351.754i	0.480503	−	0.943040i	0.996268	−	0.0863101i	$-0.0275076\pi$
$374$			1099.25i			2.93916i
$375$	−196.644	−	90.5875i	−0.524384	−	0.241567i
$376$	579.955			1.54243
$377$	−41.2354	−	21.0105i	−0.109378	−	0.0557308i
$378$	179.746	+	28.4690i	0.475519	+	0.0753148i
$379$	−335.709	−	462.064i	−0.885776	−	1.21917i	−0.974787	−	0.223135i	$-0.928371\pi$
$379$	−335.709	−	462.064i	−0.885776	−	1.21917i	0.0890116	−	0.996031i	$-0.471629\pi$
$380$	597.049	+	54.8050i	1.57118	+	0.144224i
$381$	−72.0511	−	52.3482i	−0.189111	−	0.137397i
$382$	−45.3357	+	45.3357i	−0.118680	+	0.118680i
$383$	56.0307	+	353.764i	0.146294	+	0.923666i	0.946210	+	0.323553i	$0.104878\pi$
$383$	56.0307	+	353.764i	0.146294	+	0.923666i	−0.799916	+	0.600112i	$0.795122\pi$
$384$	−262.602	−	85.3246i	−0.683860	−	0.222199i
$385$	843.168	+	531.890i	2.19005	+	1.38153i
$386$	60.6239	+	186.581i	0.157057	+	0.483371i
$387$	13.7104	+	26.9082i	0.0354274	+	0.0695301i
$388$	−1113.00	+	567.102i	−2.86856	+	1.46160i
$389$	58.8421	−	19.1190i	0.151265	−	0.0491490i	−0.232406	−	0.972619i	$-0.574660\pi$
$389$	58.8421	−	19.1190i	0.151265	−	0.0491490i	0.383671	+	0.923470i	$0.374660\pi$
$390$	174.889	+	44.3987i	0.448432	+	0.113843i
$391$	25.2743	−	77.7862i	0.0646401	−	0.198942i
$392$	−791.192	+	125.312i	−2.01835	+	0.319675i
$393$	43.0492	+	43.0492i	0.109540	+	0.109540i
$394$	104.111	−	143.296i	0.264240	−	0.363695i
$395$	−219.637	−	369.099i	−0.556044	−	0.934428i
$396$	−432.046	+	313.900i	−1.09103	+	0.792677i
$397$	−77.4450	+	488.968i	−0.195076	+	1.23166i	0.674656	+	0.738133i	$0.264292\pi$
$397$	−77.4450	+	488.968i	−0.195076	+	1.23166i	−0.869731	+	0.493526i	$0.835708\pi$
$398$	295.012	−	578.994i	0.741237	−	1.45476i
$399$		−	232.626i		−	0.583023i
$400$	−305.695	+	563.270i	−0.764238	+	1.40818i
$401$	−92.8824			−0.231627			−0.115813	−	0.993271i	$-0.536947\pi$
$401$	−92.8824			−0.231627			−0.115813	+	0.993271i	$0.536947\pi$
$402$	−261.564	−	133.274i	−0.650657	−	0.331526i
$403$	−228.086	−	36.1253i	−0.565971	−	0.0896410i
$404$	−540.273	−	743.622i	−1.33731	−	1.84065i
$405$	−33.8356	−	29.6674i	−0.0835446	−	0.0732529i
$406$	−224.780	−	163.313i	−0.553646	−	0.402248i
$407$	117.482	−	117.482i	0.288654	−	0.288654i
$408$	69.6620	+	439.829i	0.170740	+	1.07801i
$409$	423.115	+	137.478i	1.03451	+	0.336133i	0.776572	−	0.630028i	$-0.216957\pi$
$409$	423.115	+	137.478i	1.03451	+	0.336133i	0.257939	+	0.966161i	$0.416957\pi$
$410$	100.717	−	83.7810i	0.245650	−	0.204344i
$411$	20.9672	+	64.5303i	0.0510150	+	0.157008i
$412$	311.459	+	611.272i	0.755968	+	1.48367i
$413$	−101.490	+	51.7119i	−0.245739	+	0.125210i
$414$	55.0553	−	17.8885i	0.132984	−	0.0432090i
$415$	−51.1316	−	779.005i	−0.123209	−	1.87712i
$416$	42.5806	−	131.050i	0.102357	−	0.315023i
$417$	−157.048	+	24.8740i	−0.376614	+	0.0596498i
$418$	703.227	+	703.227i	1.68236	+	1.68236i
$419$	47.2500	−	65.0340i	0.112768	−	0.155212i	−0.748902	−	0.662681i	$-0.769419\pi$
$419$	47.2500	−	65.0340i	0.112768	−	0.155212i	0.861670	+	0.507468i	$0.169419\pi$
$420$	683.204	+	293.452i	1.62668	+	0.698696i
$421$	40.1238	−	29.1517i	0.0953060	−	0.0692438i	−0.539112	−	0.842234i	$-0.681240\pi$
$421$	40.1238	−	29.1517i	0.0953060	−	0.0692438i	0.634418	+	0.772990i	$0.281240\pi$
$422$	212.489	−	1341.60i	0.503529	−	3.17916i
$423$	−46.5084	+	91.2779i	−0.109949	+	0.215787i
$424$		−	616.860i		−	1.45486i
$425$	−378.325	−	9.83624i	−0.890176	−	0.0231441i
$426$	−805.616			−1.89112
$427$	115.478	+	58.8389i	0.270440	+	0.137796i
$428$	1237.89	+	196.062i	2.89227	+	0.458090i
$429$	120.754	+	166.204i	0.281479	+	0.387422i
$430$	39.6894	+	175.326i	0.0923009	+	0.407735i
$431$	−290.737	−	211.233i	−0.674565	−	0.490100i	0.196985	−	0.980406i	$-0.436885\pi$
$431$	−290.737	−	211.233i	−0.674565	−	0.490100i	−0.871550	+	0.490306i	$0.836885\pi$
$432$	−94.1893	+	94.1893i	−0.218031	+	0.218031i
$433$	−19.2423	−	121.491i	−0.0444396	−	0.280581i	0.955454	−	0.295139i	$-0.0953659\pi$
$433$	−19.2423	−	121.491i	−0.0444396	−	0.280581i	−0.999894	+	0.0145581i	$0.995366\pi$
$434$	−1318.55	−	428.423i	−3.03813	−	0.987150i
$435$	25.4642	+	63.8093i	0.0585385	+	0.146688i
$436$	−318.856	−	981.339i	−0.731322	−	2.25078i
$437$	−33.5938	−	65.9315i	−0.0768736	−	0.150873i
$438$	252.947	−	128.883i	0.577503	−	0.294253i
$439$	−316.188	+	102.736i	−0.720246	+	0.234022i	−0.646130	−	0.763227i	$-0.723614\pi$
$439$	−316.188	+	102.736i	−0.720246	+	0.234022i	−0.0741162	+	0.997250i	$0.523614\pi$
$440$	−1603.57	+	639.934i	−3.64448	+	1.45439i
$441$	43.7255	−	134.573i	0.0991507	−	0.305154i
$442$	311.519	−	49.3398i	0.704794	−	0.111628i
$443$	−75.4358	−	75.4358i	−0.170284	−	0.170284i	0.616820	−	0.787104i	$-0.288421\pi$
$443$	−75.4358	−	75.4358i	−0.170284	−	0.170284i	−0.787104	+	0.616820i	$0.788421\pi$
$444$	72.8391	−	100.254i	0.164052	−	0.225798i
$445$	−149.859	+	33.9243i	−0.336761	+	0.0762343i
$446$	127.554	−	92.6736i	0.285996	−	0.207788i
$447$	−17.6869	+	111.671i	−0.0395681	+	0.249823i
$448$	−80.9451	+	158.864i	−0.180681	+	0.354607i
$449$			123.901i			0.275948i	0.990436	+	0.137974i	$0.0440591\pi$
$449$			123.901i			0.275948i	−0.990436	+	0.137974i	$0.955941\pi$
$450$	−151.759	−	220.722i	−0.337242	−	0.490494i
$451$	149.162			0.330736
$452$	1446.08	+	736.812i	3.19928	+	1.63012i
$453$	357.839	+	56.6761i	0.789931	+	0.125113i
$454$	552.002	+	759.765i	1.21586	+	1.67349i
$455$	112.888	−	262.822i	0.248106	−	0.577631i
$456$	325.939	+	236.809i	0.714779	+	0.519317i
$457$	278.089	−	278.089i	0.608510	−	0.608510i	−0.334047	−	0.942557i	$-0.608414\pi$
$457$	278.089	−	278.089i	0.608510	−	0.608510i	0.942557	+	0.334047i	$0.108414\pi$
$458$	86.2799	+	544.750i	0.188384	+	1.18941i
$459$	−74.8100	−	24.3073i	−0.162985	−	0.0529570i
$460$	236.013	−	15.4912i	0.513072	−	0.0336765i
$461$	31.4099	+	96.6697i	0.0681342	+	0.209696i	0.979327	−	0.202286i	$-0.0648369\pi$
$461$	31.4099	+	96.6697i	0.0681342	+	0.209696i	−0.911192	+	0.411981i	$0.864837\pi$
$462$	559.941	+	1098.95i	1.21199	+	2.37867i
$463$	58.1198	−	29.6135i	0.125529	−	0.0639600i	−0.390098	−	0.920773i	$-0.627559\pi$
$463$	58.1198	−	29.6135i	0.125529	−	0.0639600i	0.515627	+	0.856813i	$0.327559\pi$
$464$	193.412	−	62.8435i	0.416837	−	0.135438i
$465$	219.236	+	263.552i	0.471474	+	0.566779i
$466$	134.350	−	413.486i	0.288304	−	0.887308i
$467$	−430.191	+	68.1356i	−0.921181	+	0.145901i	−0.598974	−	0.800769i	$-0.704425\pi$
$467$	−430.191	+	68.1356i	−0.921181	+	0.145901i	−0.322207	+	0.946669i	$0.604425\pi$
$468$	108.350	+	108.350i	0.231516	+	0.231516i
$469$	−273.540	+	376.495i	−0.583240	+	0.802761i
$470$	−402.020	+	458.502i	−0.855361	+	0.975535i
$471$	236.660	−	171.944i	0.502464	−	0.365061i
$472$	30.8600	−	194.843i	0.0653814	−	0.412802i
$473$	−92.9192	+	182.364i	−0.196446	+	0.385548i
$474$		−	531.380i		−	1.12106i
$475$	−248.320	+	235.735i	−0.522780	+	0.496285i
$476$	1299.74			2.73055
$477$	97.0862	+	49.4679i	0.203535	+	0.103706i
$478$	−380.221	−	60.2211i	−0.795442	−	0.125986i
$479$	413.844	+	569.608i	0.863976	+	1.18916i	0.980607	+	0.195986i	$0.0627906\pi$
$479$	413.844	+	569.608i	0.863976	+	1.18916i	−0.116631	+	0.993175i	$0.537209\pi$
$480$	−175.788	+	104.605i	−0.366224	+	0.217927i
$481$	−38.5669	−	28.0205i	−0.0801806	−	0.0582546i
$482$	−539.843	+	539.843i	−1.12001	+	1.12001i
$483$	−14.3559	−	90.6393i	−0.0297223	−	0.187659i
$484$	−2434.64	−	791.062i	−5.03025	−	1.63443i
$485$	175.532	−	691.429i	0.361922	−	1.42563i
$486$	−17.2041	−	52.9488i	−0.0353994	−	0.108948i
$487$	−0.165347	−	0.324513i	−0.000339522	−	0.000666350i	0.890837	−	0.454324i	$-0.150119\pi$
$487$	−0.165347	−	0.324513i	−0.000339522	−	0.000666350i	−0.891176	+	0.453657i	$0.850119\pi$
$488$	−199.995	+	101.903i	−0.409826	+	0.208817i
$489$	9.31838	−	3.02773i	0.0190560	−	0.00619167i
$490$	449.377	−	712.366i	0.917096	−	1.45381i
$491$	91.2616	−	280.874i	0.185869	−	0.572046i	−0.814093	−	0.580734i	$-0.802766\pi$
$491$	91.2616	−	280.874i	0.185869	−	0.572046i	0.999962	+	0.00868841i	$0.00276564\pi$
$492$	109.884	−	17.4040i	0.223342	−	0.0353740i
$493$	84.9180	+	84.9180i	0.172247	+	0.172247i
$494$	167.725	−	230.854i	0.339525	−	0.467316i
$495$	27.8777	−	303.701i	0.0563185	−	0.613537i
$496$	820.965	−	596.466i	1.65517	−	1.20255i
$497$	−199.786	+	1261.40i	−0.401983	+	2.53802i
$498$	438.488	−	860.582i	0.880499	−	1.72808i
$499$			640.547i			1.28366i	0.766847	+	0.641830i	$0.221825\pi$
$499$			640.547i			1.28366i	−0.766847	+	0.641830i	$0.778175\pi$
$500$	−379.085	−	1026.67i	−0.758170	−	2.05334i
$501$	−268.987			−0.536900
$502$	−1451.31	−	739.480i	−2.89106	−	1.47307i
$503$	302.873	+	47.9703i	0.602133	+	0.0953685i	0.450056	−	0.893000i	$-0.351404\pi$
$503$	302.873	+	47.9703i	0.602133	+	0.0953685i	0.152077	+	0.988369i	$0.451404\pi$
$504$	293.685	+	404.223i	0.582709	+	0.802030i
$505$	522.719	+	47.9820i	1.03509	+	0.0950139i
$506$	317.399	+	230.604i	0.627271	+	0.455739i
$507$	−165.301	+	165.301i	−0.326037	+	0.326037i
$508$	−70.4255	−	444.649i	−0.138633	−	0.875293i
$509$	137.294	+	44.6097i	0.269734	+	0.0876418i	0.440761	−	0.897625i	$-0.354709\pi$
$509$	137.294	+	44.6097i	0.269734	+	0.0876418i	−0.171027	+	0.985266i	$0.554709\pi$
$510$	−396.009	−	249.811i	−0.776488	−	0.489826i
$511$	−139.070	−	428.014i	−0.272153	−	0.837601i
$512$	−515.735	−	1012.19i	−1.00730	−	1.97693i
$513$	−63.4088	+	32.3084i	−0.123604	+	0.0629794i
$514$	−53.7735	+	17.4721i	−0.104618	+	0.0339923i
$515$	−379.740	−	96.4041i	−0.737360	−	0.187192i
$516$	−47.1736	+	145.186i	−0.0914218	+	0.281367i
$517$	−685.741	+	108.611i	−1.32639	+	0.210079i
$518$	−202.373	−	202.373i	−0.390682	−	0.390682i
$519$	−15.2215	+	20.9506i	−0.0293286	+	0.0403673i
$520$	253.329	+	425.718i	0.487172	+	0.818689i
$521$	−207.263	+	150.586i	−0.397818	+	0.289032i	−0.768652	−	0.639667i	$-0.779072\pi$
$521$	−207.263	+	150.586i	−0.397818	+	0.289032i	0.370833	+	0.928699i	$0.379072\pi$
$522$	−13.2967	+	83.9520i	−0.0254726	+	0.160828i
$523$	−405.426	+	795.692i	−0.775192	+	1.52140i	0.0763305	+	0.997083i	$0.475680\pi$
$523$	−405.426	+	795.692i	−0.775192	+	1.52140i	−0.851523	+	0.524318i	$0.824320\pi$
$524$			307.747i			0.587304i
$525$	−383.232	+	182.880i	−0.729965	+	0.348343i
$526$	1665.88			3.16708
$527$	533.931	+	272.051i	1.01315	+	0.516227i
$528$	−891.645	−	141.223i	−1.68872	−	0.267467i
$529$	293.780	+	404.354i	0.555350	+	0.764374i
$530$	487.678	+	427.602i	0.920147	+	0.806795i
$531$	28.1911	+	20.4820i	0.0530905	+	0.0385725i
$532$	831.492	−	831.492i	1.56295	−	1.56295i
$533$	−6.69515	−	42.2715i	−0.0125613	−	0.0793086i
$534$	−180.791	−	58.7427i	−0.338561	−	0.110005i
$535$	−550.251	+	457.726i	−1.02851	+	0.855562i
$536$	−249.060	−	766.528i	−0.464664	−	1.43009i
$537$	−234.066	−	459.380i	−0.435876	−	0.855456i
$538$	1356.81	−	691.327i	2.52194	−	1.28499i
$539$	912.040	−	296.340i	1.69210	−	0.549795i
$540$	−14.8985	−	226.983i	−0.0275898	−	0.420339i
$541$	−54.2103	+	166.842i	−0.100204	+	0.308396i	−0.988575	−	0.150730i	$-0.951837\pi$
$541$	−54.2103	+	166.842i	−0.100204	+	0.308396i	0.888371	+	0.459126i	$0.151837\pi$
$542$	402.249	−	63.7101i	0.742158	−	0.117546i
$543$	172.454	+	172.454i	0.317595	+	0.317595i
$544$	−210.171	+	289.276i	−0.386344	+	0.531757i
$545$	541.430	+	232.557i	0.993449	+	0.426710i
$546$	286.301	−	208.010i	0.524361	−	0.380970i
$547$	−87.1049	+	549.959i	−0.159241	+	1.00541i	0.770566	+	0.637361i	$0.219974\pi$
$547$	−87.1049	+	549.959i	−0.159241	+	1.00541i	−0.929807	+	0.368048i	$0.880026\pi$
$548$	−155.711	+	305.599i	−0.284144	+	0.557663i
$549$		−	39.6486i		−	0.0722197i
$550$	605.662	−	1711.35i	1.10120	−	3.11154i
$551$	108.650			0.197187
$552$	141.611	+	72.1545i	0.256542	+	0.130715i
$553$	−832.011	−	131.778i	−1.50454	−	0.238296i
$554$	−311.659	−	428.962i	−0.562561	−	0.774299i
$555$	15.6249	+	69.0222i	0.0281530	+	0.124364i
$556$	−650.256	−	472.439i	−1.16953	−	0.849710i
$557$	−111.419	+	111.419i	−0.200035	+	0.200035i	−0.800015	−	0.599980i	$-0.795175\pi$
$557$	−111.419	+	111.419i	−0.200035	+	0.200035i	0.599980	+	0.800015i	$0.295175\pi$
$558$	66.3488	+	418.910i	0.118905	+	0.750734i
$559$	55.8515	+	18.1472i	0.0999132	+	0.0324638i
$560$	465.879	+	1167.42i	0.831926	+	2.08467i
$561$	−164.737	−	507.009i	−0.293649	−	0.903759i
$562$	−95.0730	−	186.591i	−0.169169	−	0.332013i
$563$	−198.620	+	101.202i	−0.352789	+	0.179755i	−0.621399	−	0.783494i	$-0.713435\pi$
$563$	−198.620	+	101.202i	−0.352789	+	0.179755i	0.268611	+	0.963249i	$0.413435\pi$
$564$	−492.499	+	160.023i	−0.873225	+	0.283728i
$565$	−860.827	+	343.528i	−1.52359	+	0.608014i
$566$	−501.558	+	1543.64i	−0.886145	+	2.72728i
$567$	−87.1713	+	13.8066i	−0.153741	+	0.0243502i
$568$	−1564.00	−	1564.00i	−2.75352	−	2.75352i
$569$	45.7946	−	63.0309i	0.0804826	−	0.110775i	−0.766877	−	0.641794i	$-0.778191\pi$
$569$	45.7946	−	63.0309i	0.0804826	−	0.110775i	0.847360	+	0.531019i	$0.178191\pi$
$570$	−413.154	+	93.5277i	−0.724832	+	0.164084i
$571$	−164.439	+	119.472i	−0.287984	+	0.209233i	−0.722392	−	0.691483i	$-0.756958\pi$
$571$	−164.439	+	119.472i	−0.287984	+	0.209233i	0.434408	+	0.900716i	$0.356958\pi$
$572$	−162.454	+	1025.69i	−0.284011	+	1.79317i
$573$	14.1162	−	27.7045i	0.0246355	−	0.0483500i
$574$		−	256.944i		−	0.447638i
$575$	−82.2065	+	107.175i	−0.142968	+	0.186391i
$576$	54.5449			0.0946960
$577$	−40.4069	−	20.5884i	−0.0700293	−	0.0356817i	0.418625	−	0.908159i	$-0.362512\pi$
$577$	−40.4069	−	20.5884i	−0.0700293	−	0.0356817i	−0.488654	+	0.872477i	$0.662512\pi$
$578$	211.077	+	33.4313i	0.365185	+	0.0578397i
$579$	−55.9235	−	76.9721i	−0.0965863	−	0.132940i
$580$	−137.059	+	319.097i	−0.236309	+	0.550166i
$581$	−1238.72	−	899.982i	−2.13205	−	1.54902i
$582$	624.068	−	624.068i	1.07228	−	1.07228i
$583$	115.522	+	729.377i	0.198151	+	1.25108i
$584$	741.273	+	240.854i	1.26930	+	0.412422i
$585$	−87.3181	+	5.73130i	−0.149262	+	0.00979710i
$586$	265.756	+	817.913i	0.453509	+	1.39576i
$587$	−246.279	−	483.350i	−0.419556	−	0.823425i	−0.999959	−	0.00909505i	$-0.997105\pi$
$587$	−246.279	−	483.350i	−0.419556	−	0.823425i	0.580403	−	0.814329i	$-0.302895\pi$
$588$	637.304	−	324.723i	1.08385	−	0.552250i
$589$	515.615	−	167.534i	0.875408	−	0.284437i
$590$	132.647	+	159.460i	0.224825	+	0.270272i
$591$	−26.5444	+	81.6953i	−0.0449144	+	0.138232i
$592$	206.902	−	32.7701i	0.349497	−	0.0553548i
$593$	−393.037	−	393.037i	−0.662794	−	0.662794i	0.293243	−	0.956038i	$-0.405265\pi$
$593$	−393.037	−	393.037i	−0.662794	−	0.662794i	−0.956038	+	0.293243i	$0.905265\pi$
$594$	221.781	−	305.255i	0.373368	−	0.513897i
$595$	−489.350	+	558.102i	−0.822438	+	0.937987i
$596$	−462.372	+	335.933i	−0.775792	+	0.563646i
$597$	−49.2992	+	311.263i	−0.0825782	+	0.521378i
$598$	51.1051	−	100.299i	0.0854601	−	0.167725i
$599$		−	881.586i		−	1.47176i	−0.677110	−	0.735881i	$-0.736768\pi$
$599$		−	881.586i		−	1.47176i	0.677110	−	0.735881i	$-0.263232\pi$
$600$	133.884	−	723.124i	0.223140	−	1.20521i
$601$	−495.138			−0.823857			−0.411929	−	0.911216i	$-0.635145\pi$
$601$	−495.138			−0.823857			−0.411929	+	0.911216i	$0.635145\pi$
$602$	314.138	+	160.061i	0.521824	+	0.265882i
$603$	140.615	+	22.2712i	0.233192	+	0.0369340i
$604$	1076.47	+	1481.63i	1.78223	+	2.45303i
$605$	1256.31	−	747.587i	2.07655	−	1.23568i
$606$	525.394	+	381.721i	0.866987	+	0.629903i
$607$	160.186	−	160.186i	0.263899	−	0.263899i	−0.562737	−	0.826636i	$-0.690252\pi$
$607$	160.186	−	160.186i	0.263899	−	0.263899i	0.826636	+	0.562737i	$0.190252\pi$
$608$	50.6061	+	319.514i	0.0832337	+	0.525517i
$609$	128.151	+	41.6387i	0.210428	+	0.0683723i
$610$	58.0724	−	228.750i	0.0952007	−	0.375000i
$611$	61.5591	+	189.459i	0.100751	+	0.310081i
$612$	−180.515	−	354.281i	−0.294960	−	0.578891i
$613$	769.440	−	392.049i	1.25520	−	0.639558i	0.305347	−	0.952241i	$-0.401228\pi$
$613$	769.440	−	392.049i	1.25520	−	0.639558i	0.949858	+	0.312683i	$0.101228\pi$
$614$	−1605.90	+	521.789i	−2.61548	+	0.849819i
$615$	−33.8981	+	53.7363i	−0.0551188	+	0.0873761i
$616$	−1046.41	+	3220.52i	−1.69872	+	5.22811i
$617$	1038.77	−	164.525i	1.68358	−	0.266653i	0.759961	−	0.649969i	$-0.225218\pi$
$617$	1038.77	−	164.525i	1.68358	−	0.266653i	0.923617	+	0.383316i	$0.125218\pi$
$618$	−342.745	−	342.745i	−0.554604	−	0.554604i
$619$	404.382	−	556.584i	0.653283	−	0.899167i	−0.345953	−	0.938252i	$-0.612444\pi$
$619$	404.382	−	556.584i	0.653283	−	0.899167i	0.999236	+	0.0390848i	$0.0124443\pi$
$620$	−158.404	+	1725.66i	−0.255490	+	2.78332i
$621$	−22.7125	+	16.5016i	−0.0365740	+	0.0265726i
$622$	152.422	−	962.354i	0.245051	−	1.54719i
$623$	−136.811	+	268.507i	−0.219601	+	0.430991i
$624$			259.025i			0.415104i
$625$	583.571	+	223.762i	0.933714	+	0.358020i
$626$	−1207.31			−1.92860
$627$	−429.740	−	218.963i	−0.685390	−	0.349224i
$628$	1460.50	+	231.321i	2.32564	+	0.368345i
$629$	72.7111	+	100.078i	0.115598	+	0.159107i
$630$	−523.151	−	48.0217i	−0.830398	−	0.0762249i
$631$	863.730	+	627.537i	1.36883	+	0.994511i	0.997828	+	0.0658784i	$0.0209849\pi$
$631$	863.730	+	627.537i	1.36883	+	0.994511i	0.371000	+	0.928633i	$0.379015\pi$
$632$	1031.61	−	1031.61i	1.63229	−	1.63229i
$633$	103.051	+	650.636i	0.162797	+	1.02786i
$634$	652.311	+	211.949i	1.02888	+	0.334304i
$635$	217.445	+	137.169i	0.342433	+	0.216014i
$636$	170.205	+	523.838i	0.267618	+	0.823645i
$637$	−124.918	−	245.165i	−0.196103	−	0.384874i
$638$	−513.272	+	261.525i	−0.804501	+	0.409914i
$639$	371.577	−	120.733i	0.581497	−	0.188940i
$640$	772.572	+	196.132i	1.20714	+	0.306456i
$641$	−81.7940	+	251.736i	−0.127604	+	0.392724i	−0.994366	−	0.105997i	$-0.966197\pi$
$641$	−81.7940	+	251.736i	−0.127604	+	0.392724i	0.866763	+	0.498721i	$0.166197\pi$
$642$	−874.610	+	138.525i	−1.36232	+	0.215770i
$643$	330.534	+	330.534i	0.514050	+	0.514050i	0.915765	−	0.401715i	$-0.131586\pi$
$643$	330.534	+	330.534i	0.514050	+	0.514050i	−0.401715	+	0.915765i	$0.631586\pi$
$644$	272.665	−	375.291i	0.423393	−	0.582750i
$645$	−44.5810	−	74.9181i	−0.0691179	−	0.116152i
$646$	−599.050	+	435.235i	−0.927322	+	0.673739i
$647$	79.6577	−	502.939i	0.123119	−	0.777340i	−0.846441	−	0.532483i	$-0.821259\pi$
$647$	79.6577	−	502.939i	0.123119	−	0.777340i	0.969559	−	0.244857i	$-0.0787411\pi$
$648$	69.3938	−	136.193i	0.107089	−	0.210174i
$649$			236.162i			0.363886i
$650$	−512.170	−	94.8264i	−0.787954	−	0.145887i
$651$	672.364			1.03282
$652$	44.1295	+	22.4851i	0.0676833	+	0.0344864i
$653$	−1064.21	−	168.554i	−1.62973	−	0.258123i	−0.726461	−	0.687207i	$-0.758836\pi$
$653$	−1064.21	−	168.554i	−1.62973	−	0.258123i	−0.903264	+	0.429084i	$0.858836\pi$
$654$	428.513	+	589.797i	0.655218	+	0.901831i
$655$	−132.145	−	115.866i	−0.201748	−	0.176895i
$656$	152.150	+	110.544i	0.231937	+	0.168512i
$657$	−97.3524	+	97.3524i	−0.148177	+	0.148177i
$658$	187.091	+	1181.25i	0.284333	+	1.79521i
$659$	−5.24490	−	1.70417i	−0.00795887	−	0.00258599i	0.305035	−	0.952341i	$-0.401332\pi$
$659$	−5.24490	−	1.70417i	−0.00795887	−	0.00258599i	−0.312994	+	0.949755i	$0.601332\pi$
$660$	1185.18	−	985.893i	1.79573	−	1.49378i
$661$	−260.381	−	801.372i	−0.393920	−	1.21236i	−0.929799	−	0.368067i	$-0.880020\pi$
$661$	−260.381	−	801.372i	−0.393920	−	1.21236i	0.535879	−	0.844295i	$-0.319980\pi$
$662$	187.399	+	367.791i	0.283080	+	0.555575i
$663$	−136.289	+	69.4425i	−0.205564	+	0.104740i
$664$	2521.98	−	819.441i	3.79816	−	1.23410i
$665$	43.9829	+	670.092i	0.0661397	+	1.00766i
$666$	−27.0558	+	83.2692i	−0.0406243	+	0.125029i
$667$	42.3338	−	6.70502i	0.0634690	−	0.0100525i
$668$	−961.457	−	961.457i	−1.43931	−	1.43931i
$669$	−44.9438	+	61.8599i	−0.0671806	+	0.0924662i
$670$	778.648	+	334.448i	1.16216	+	0.499175i
$671$	217.391	−	157.944i	0.323981	−	0.235386i
$672$	−62.7606	+	396.255i	−0.0933938	+	0.589665i
$673$	388.393	−	762.263i	0.577106	−	1.13263i	−0.399326	−	0.916809i	$-0.630756\pi$
$673$	388.393	−	762.263i	0.577106	−	1.13263i	0.976432	−	0.215826i	$-0.0692443\pi$
$674$		−	1541.57i		−	2.28720i
$675$	103.074	+	79.0612i	0.152703	+	0.117128i
$676$	−1181.69			−1.74806
$677$	−131.082	−	66.7895i	−0.193622	−	0.0986551i	0.354492	−	0.935059i	$-0.384654\pi$
$677$	−131.082	−	66.7895i	−0.193622	−	0.0986551i	−0.548114	+	0.836404i	$0.684654\pi$
$678$	−1132.56	−	179.380i	−1.67045	−	0.264573i
$679$	−822.375	−	1131.90i	−1.21116	−	1.66701i
$680$	−283.824	−	1253.78i	−0.417388	−	1.84379i
$681$	−368.462	−	267.704i	−0.541061	−	0.393104i
$682$	−2032.55	+	2032.55i	−2.98028	+	2.98028i
$683$	−177.605	−	1121.35i	−0.260036	−	1.64180i	−0.679244	−	0.733912i	$-0.737692\pi$
$683$	−177.605	−	1121.35i	−0.260036	−	1.64180i	0.419209	−	0.907890i	$-0.362308\pi$
$684$	−342.129	−	111.164i	−0.500188	−	0.162521i
$685$	−72.5979	−	181.919i	−0.105982	−	0.265575i
$686$	19.8471	+	61.0831i	0.0289316	+	0.0890424i
$687$	−121.433	−	238.326i	−0.176759	−	0.346909i
$688$	−229.931	+	117.156i	−0.334202	+	0.170284i
$689$	201.515	−	65.4764i	0.292475	−	0.0950310i
$690$	−155.207	+	61.9382i	−0.224938	+	0.0897656i
$691$	254.902	−	784.506i	0.368888	−	1.13532i	−0.578622	−	0.815596i	$-0.696409\pi$
$691$	254.902	−	784.506i	0.368888	−	1.13532i	0.947510	−	0.319725i	$-0.103591\pi$
$692$	−129.293	+	20.4779i	−0.186839	+	0.0295924i
$693$	−422.955	−	422.955i	−0.610325	−	0.610325i
$694$	−97.5822	+	134.310i	−0.140608	+	0.193531i
$695$	447.682	−	101.344i	0.644147	−	0.145819i
$696$	−188.796	+	137.168i	−0.271259	+	0.197081i
$697$	−17.3734	+	109.691i	−0.0249260	+	0.157376i
$698$	−1107.70	+	2173.98i	−1.58696	+	3.11459i
$699$			210.847i			0.301641i
$700$	−2023.49	−	716.131i	−2.89070	−	1.02304i
$701$	126.969			0.181125			0.0905627	−	0.995891i	$-0.471133\pi$
$701$	126.969			0.181125			0.0905627	+	0.995891i	$0.471133\pi$
$702$	−96.4619	−	49.1498i	−0.137410	−	0.0700140i
$703$	110.539	+	17.5077i	0.157240	+	0.0249043i
$704$	217.284	+	299.066i	0.308642	+	0.424810i
$705$	116.712	−	271.724i	0.165549	−	0.385424i
$706$	−910.121	−	661.242i	−1.28912	−	0.936603i
$707$	727.975	−	727.975i	1.02967	−	1.02967i
$708$	27.5550	+	173.975i	0.0389195	+	0.245728i
$709$	−941.792	−	306.007i	−1.32834	−	0.431603i	−0.442988	−	0.896528i	$-0.646082\pi$
$709$	−941.792	−	306.007i	−1.32834	−	0.431603i	−0.885350	+	0.464924i	$0.846082\pi$
$710$	2320.62	−	152.319i	3.26848	−	0.214533i
$711$	79.6346	+	245.090i	0.112004	+	0.344712i
$712$	−236.942	−	465.025i	−0.332784	−	0.653125i
$713$	190.563	−	97.0966i	0.267269	−	0.136180i
$714$	−873.366	+	283.774i	−1.22320	+	0.397442i
$715$	−379.264	−	455.929i	−0.530439	−	0.637662i
$716$	805.355	−	2478.63i	1.12480	−	3.46177i
$717$	184.395	−	29.2054i	0.257176	−	0.0407327i
$718$	−1742.81	−	1742.81i	−2.42731	−	2.42731i
$719$	−547.789	+	753.967i	−0.761876	+	1.04863i	0.235180	+	0.971952i	$0.424432\pi$
$719$	−547.789	+	753.967i	−0.761876	+	1.04863i	−0.997056	+	0.0766803i	$0.975568\pi$
$720$	253.509	−	289.126i	0.352095	−	0.401563i
$721$	−621.653	+	451.657i	−0.862209	+	0.626432i
$722$	96.8928	−	611.757i	0.134201	−	0.847309i
$723$	168.090	−	329.896i	0.232490	−	0.456288i
$724$			1232.83i			1.70280i
$725$	−85.4156	−	178.992i	−0.117815	−	0.246885i
$726$	1808.68			2.49129
$727$	463.047	+	235.934i	0.636929	+	0.324531i	0.742466	−	0.669884i	$-0.233656\pi$
$727$	463.047	+	235.934i	0.636929	+	0.324531i	−0.105537	+	0.994415i	$0.533656\pi$
$728$	959.641	+	151.992i	1.31819	+	0.208781i
$729$	15.8702	+	21.8435i	0.0217698	+	0.0299636i
$730$	−704.258	+	419.078i	−0.964737	+	0.574080i
$731$	−123.285	−	89.5719i	−0.168653	−	0.122533i
$732$	141.719	−	141.719i	0.193605	−	0.193605i
$733$	−109.823	−	693.392i	−0.149826	−	0.945965i	−0.941986	−	0.335651i	$-0.891044\pi$
$733$	−109.823	−	693.392i	−0.149826	−	0.945965i	0.792160	−	0.610313i	$-0.208956\pi$
$734$	182.069	+	59.1577i	0.248050	+	0.0805963i
$735$	−100.510	+	395.912i	−0.136748	+	0.538656i
$736$	39.4358	+	121.371i	0.0535812	+	0.164906i
$737$	438.040	+	859.702i	0.594356	+	1.16649i
$738$	−70.0374	+	35.6858i	−0.0949016	+	0.0483548i
$739$	1132.84	−	368.081i	1.53293	−	0.498080i	0.583517	−	0.812101i	$-0.301676\pi$
$739$	1132.84	−	368.081i	1.53293	−	0.498080i	0.949416	+	0.314021i	$0.101676\pi$
$740$	−190.862	+	302.560i	−0.257921	+	0.408864i
$741$	−42.7638	+	131.614i	−0.0577110	+	0.177616i
$742$	1256.42	−	198.997i	1.69328	−	0.268190i
$743$	645.690	+	645.690i	0.869031	+	0.869031i	0.992365	−	0.123335i	$-0.0393588\pi$
$743$	645.690	+	645.690i	0.869031	+	0.869031i	−0.123335	+	0.992365i	$0.539359\pi$
$744$	−684.452	+	942.068i	−0.919963	+	1.26622i
$745$	29.8344	−	325.018i	0.0400462	−	0.436266i
$746$	−1140.68	+	828.749i	−1.52906	+	1.11092i
$747$	−73.2753	+	462.642i	−0.0980928	+	0.619334i
$748$	1223.40	−	2401.07i	1.63557	−	3.20998i
$749$			1403.78i			1.87420i
$750$	478.881	+	607.109i	0.638508	+	0.809478i
$751$	−65.3157			−0.0869716			−0.0434858	−	0.999054i	$-0.513846\pi$
$751$	−65.3157			−0.0869716			−0.0434858	+	0.999054i	$0.513846\pi$
$752$	−779.972	−	397.415i	−1.03720	−	0.528478i
$753$	780.214	+	123.574i	1.03614	+	0.164109i
$754$	97.1527	+	133.719i	0.128850	+	0.177347i
$755$	−1041.49	−	95.6015i	−1.37946	−	0.126625i
$756$	−360.932	−	262.232i	−0.477423	−	0.346868i
$757$	−718.130	+	718.130i	−0.948653	+	0.948653i	−0.998745	−	0.0500915i	$-0.984049\pi$
$757$	−718.130	+	718.130i	−0.948653	+	0.948653i	0.0500915	+	0.998745i	$0.484049\pi$
$758$	319.098	+	2014.70i	0.420973	+	2.65792i
$759$	−180.954	−	58.7956i	−0.238411	−	0.0774645i
$760$	−983.659	−	620.514i	−1.29429	−	0.816466i
$761$	1.70066	+	5.23410i	0.00223477	+	0.00687793i	0.952168	−	0.305576i	$-0.0988490\pi$
$761$	1.70066	+	5.23410i	0.00223477	+	0.00687793i	−0.949933	+	0.312454i	$0.898849\pi$
$762$	144.403	+	283.407i	0.189505	+	0.371925i
$763$	1029.75	−	524.682i	1.34960	−	0.687656i
$764$	149.482	−	48.5698i	0.195658	−	0.0635730i
$765$	220.090	+	55.8739i	0.287699	+	0.0730378i
$766$	395.296	−	1216.60i	0.516053	−	1.58825i
$767$	66.9267	−	10.6001i	0.0872577	−	0.0138203i
$768$	608.235	+	608.235i	0.791972	+	0.791972i
$769$	−331.303	+	456.000i	−0.430824	+	0.592978i	−0.968142	−	0.250402i	$-0.919437\pi$
$769$	−331.303	+	456.000i	−0.430824	+	0.592978i	0.537318	+	0.843379i	$0.319437\pi$
$770$	−1820.72	−	3059.70i	−2.36457	−	3.97364i
$771$	22.1837	−	16.1174i	0.0287726	−	0.0209045i
$772$	75.2354	−	475.017i	0.0974551	−	0.615308i
$773$	431.709	−	847.276i	0.558485	−	1.09609i	−0.423282	−	0.905998i	$-0.639122\pi$
$773$	431.709	−	847.276i	0.558485	−	1.09609i	0.981767	−	0.190090i	$-0.0608780\pi$
$774$		−	107.857i		−	0.139351i
$775$	−681.350	−	717.725i	−0.879161	−	0.926096i
$776$	2423.10			3.12255
$777$	123.670	+	63.0128i	0.159163	+	0.0810976i
$778$	−218.247	−	34.5669i	−0.280523	−	0.0444305i
$779$	59.0591	+	81.2879i	0.0758140	+	0.104349i
$780$	−332.593	−	291.621i	−0.426401	−	0.373873i
$781$	2142.18	+	1556.38i	2.74286	+	1.99281i
$782$	−206.551	+	206.551i	−0.264132	+	0.264132i
$783$	−6.44848	−	40.7141i	−0.00823561	−	0.0519976i
$784$	1149.93	+	373.635i	1.46675	+	0.476575i
$785$	−649.203	+	540.039i	−0.827010	+	0.687948i
$786$	−67.1907	−	206.792i	−0.0854843	−	0.263094i
$787$	305.878	+	600.319i	0.388663	+	0.762794i	0.999582	−	0.0288988i	$-0.00920006\pi$
$787$	305.878	+	600.319i	0.388663	+	0.762794i	−0.610919	+	0.791693i	$0.709200\pi$
$788$	−386.888	+	197.129i	−0.490975	+	0.250164i
$789$	−768.361	+	249.655i	−0.973841	+	0.316420i
$790$	100.469	+	1530.67i	0.127175	+	1.93756i
$791$	−561.732	+	1728.83i	−0.710154	+	2.18563i
$792$	1023.17	−	162.055i	1.29189	−	0.204615i
$793$	−54.5178	−	54.5178i	−0.0687488	−	0.0687488i
$794$	1039.26	−	1430.43i	1.30890	−	1.80154i
$795$	−289.015	−	124.139i	−0.363541	−	0.156149i
$796$	−1288.78	+	936.354i	−1.61907	+	1.17632i
$797$	101.573	−	641.310i	0.127445	−	0.804655i	−0.838309	−	0.545195i	$-0.816456\pi$
$797$	101.573	−	641.310i	0.127445	−	0.804655i	0.965754	−	0.259459i	$-0.0835444\pi$
$798$	−377.183	+	740.264i	−0.472661	+	0.927649i
$799$		−	516.934i		−	0.646976i
$800$	486.588	−	334.556i	0.608235	−	0.418195i
$801$	92.1903			0.115094
$802$	295.570	+	150.601i	0.368542	+	0.187781i
$803$	−921.589	−	145.965i	−1.14768	−	0.181775i
$804$	423.004	+	582.215i	0.526124	+	0.724148i
$805$	58.4900	+	258.377i	0.0726584	+	0.320965i
$806$	667.242	+	484.780i	0.827844	+	0.601464i
$807$	−522.199	+	522.199i	−0.647087	+	0.647087i
$808$	278.923	+	1761.05i	0.345201	+	2.17952i
$809$	−53.9555	−	17.5312i	−0.0666940	−	0.0216702i	0.275480	−	0.961307i	$-0.411163\pi$
$809$	−53.9555	−	17.5312i	−0.0666940	−	0.0216702i	−0.342174	+	0.939637i	$0.611163\pi$
$810$	59.5684	+	149.269i	0.0735413	+	0.184283i
$811$	81.0206	+	249.356i	0.0999021	+	0.307467i	0.988500	−	0.151220i	$-0.0483201\pi$
$811$	81.0206	+	249.356i	0.0999021	+	0.307467i	−0.888598	+	0.458687i	$0.848320\pi$
$812$	309.226	+	606.890i	0.380820	+	0.747401i
$813$	−175.983	+	89.6678i	−0.216461	+	0.110292i
$814$	−564.339	+	183.365i	−0.693291	+	0.225264i
$815$	−26.2696	+	10.4834i	−0.0322327	+	0.0128630i
$816$	207.706	−	639.254i	0.254542	−	0.783399i
$817$	−136.172	+	21.5676i	−0.166674	+	0.0263985i
$818$	−1123.53	−	1123.53i	−1.37350	−	1.37350i
$819$	−100.878	+	138.847i	−0.123173	+	0.169532i
$820$	−313.237	+	70.9091i	−0.381997	+	0.0864745i
$821$	1127.16	−	818.930i	1.37291	−	0.997479i	0.375409	−	0.926859i	$-0.377502\pi$
$821$	1127.16	−	818.930i	1.37291	−	0.997479i	0.997503	−	0.0706197i	$-0.0224977\pi$
$822$	37.9085	−	239.345i	0.0461174	−	0.291174i
$823$	−561.736	+	1102.47i	−0.682546	+	1.33957i	0.246331	+	0.969186i	$0.420775\pi$
$823$	−561.736	+	1102.47i	−0.682546	+	1.33957i	−0.928878	+	0.370387i	$0.879225\pi$
$824$		−	1330.79i		−	1.61504i
$825$	−22.8820	+	880.097i	−0.0277358	+	1.06678i
$826$	406.809			0.492505
$827$	−50.2652	−	25.6114i	−0.0607801	−	0.0309690i	0.423336	−	0.905973i	$-0.360859\pi$
$827$	−50.2652	−	25.6114i	−0.0607801	−	0.0309690i	−0.484116	+	0.875004i	$0.660859\pi$
$828$	−140.165	−	22.2000i	−0.169282	−	0.0268116i
$829$	−690.720	−	950.695i	−0.833197	−	1.14680i	−0.987320	−	0.158746i	$-0.949255\pi$
$829$	−690.720	−	950.695i	−0.833197	−	1.14680i	0.154122	−	0.988052i	$-0.450745\pi$
$830$	−1100.38	+	2561.86i	−1.32576	+	3.08657i
$831$	208.033	+	151.145i	0.250341	+	0.181883i
$832$	75.0005	−	75.0005i	0.0901449	−	0.0901449i
$833$	111.695	+	705.216i	0.134088	+	0.846598i
$834$	540.089	+	175.486i	0.647589	+	0.210414i
$835$	774.831	−	50.8576i	0.927941	−	0.0609073i
$836$	−753.392	−	2318.70i	−0.901186	−	2.77357i
$837$	−93.3816	−	183.272i	−0.111567	−	0.218963i
$838$	−255.806	+	130.340i	−0.305257	+	0.155536i
$839$	−728.784	+	236.796i	−0.868634	+	0.282236i	−0.709230	−	0.704977i	$-0.750957\pi$
$839$	−728.784	+	236.796i	−0.868634	+	0.282236i	−0.159404	+	0.987213i	$0.550957\pi$
$840$	−922.403	−	1108.86i	−1.09810	−	1.32007i
$841$	240.436	−	739.985i	0.285892	−	0.879887i
$842$	−174.949	+	27.7092i	−0.207778	+	0.0329088i
$843$	71.8141	+	71.8141i	0.0851887	+	0.0851887i
$844$	−1957.27	+	2693.95i	−2.31904	+	3.19189i
$845$	444.904	−	507.411i	0.526514	−	0.600487i
$846$	295.998	−	215.055i	0.349880	−	0.254202i
$847$	448.536	−	2831.94i	0.529558	−	3.34350i
$848$	−422.704	+	829.604i	−0.498472	+	0.978307i
$849$		−	787.142i		−	0.927140i
$850$	1187.96	+	644.721i	1.39760	+	0.758496i
$851$	44.1504			0.0518806
$852$	1759.69	+	896.609i	2.06537	+	1.05236i
$853$	675.444	+	106.980i	0.791845	+	0.125416i	0.539238	−	0.842153i	$-0.318712\pi$
$853$	675.444	+	106.980i	0.791845	+	0.125416i	0.252606	+	0.967569i	$0.418712\pi$
$854$	−272.072	−	374.475i	−0.318585	−	0.438495i
$855$	176.544	−	105.055i	0.206484	−	0.122871i
$856$	−1966.87	−	1429.02i	−2.29775	−	1.66941i
$857$	836.314	−	836.314i	0.975863	−	0.975863i	−0.0238527	−	0.999715i	$-0.507593\pi$
$857$	836.314	−	836.314i	0.975863	−	0.975863i	0.999715	+	0.0238527i	$0.00759326\pi$
$858$	−114.779	−	724.687i	−0.133775	−	0.844624i
$859$	368.694	+	119.796i	0.429213	+	0.139460i	0.515654	−	0.856797i	$-0.327549\pi$
$859$	368.694	+	119.796i	0.429213	+	0.139460i	−0.0864402	+	0.996257i	$0.527549\pi$
$860$	108.436	−	427.134i	0.126088	−	0.496667i
$861$	38.5066	+	118.511i	0.0447231	+	0.137644i
$862$	582.689	+	1143.59i	0.675973	+	1.32667i
$863$	−119.909	+	61.0966i	−0.138944	+	0.0707956i	−0.522080	−	0.852896i	$-0.674844\pi$
$863$	−119.909	+	61.0966i	−0.138944	+	0.0707956i	0.383136	+	0.923692i	$0.374844\pi$
$864$	116.727	−	37.9269i	0.135101	−	0.0438969i
$865$	39.8853	−	63.2274i	0.0461101	−	0.0730952i
$866$	−135.755	+	417.810i	−0.156761	+	0.482459i
$867$	−102.366	+	16.2132i	−0.118069	+	0.0187003i
$868$	2403.27	+	2403.27i	2.76875	+	2.76875i
$869$	−1026.58	+	1412.97i	−1.18134	+	1.62597i
$870$	22.4289	−	244.342i	0.0257804	−	0.280853i
$871$	223.972	−	162.725i	0.257144	−	0.186826i
$872$	−313.113	+	1976.92i	−0.359075	+	2.26711i
$873$	−194.316	+	381.366i	−0.222584	+	0.436846i
$874$			264.276i			0.302376i
$875$	1069.34	−	599.253i	1.22211	−	0.684861i
$876$	−695.947			−0.794460
$877$	−1106.19	−	563.634i	−1.26134	−	0.642684i	−0.309972	−	0.950746i	$-0.600320\pi$
$877$	−1106.19	−	563.634i	−1.26134	−	0.642684i	−0.951366	+	0.308061i	$0.900320\pi$
$878$	1172.75	+	185.745i	1.33571	+	0.211555i
$879$	−245.151	−	337.421i	−0.278898	−	0.383870i
$880$	2595.13	+	238.215i	2.94901	+	0.270699i
$881$	−471.283	−	342.407i	−0.534941	−	0.388658i	0.287262	−	0.957852i	$-0.407255\pi$
$881$	−471.283	−	342.407i	−0.534941	−	0.388658i	−0.822203	+	0.569195i	$0.807255\pi$
$882$	−357.342	+	357.342i	−0.405149	+	0.405149i
$883$	29.3825	+	185.514i	0.0332758	+	0.210095i	0.998724	−	0.0504997i	$-0.0160814\pi$
$883$	29.3825	+	185.514i	0.0332758	+	0.210095i	−0.965448	+	0.260595i	$0.916081\pi$
$884$	−735.359	−	238.933i	−0.831854	−	0.270286i
$885$	−85.0784	−	53.6694i	−0.0961338	−	0.0606434i
$886$	117.739	+	362.365i	0.132889	+	0.408989i
$887$	289.432	+	568.042i	0.326304	+	0.640409i	0.994634	−	0.103457i	$-0.0329904\pi$
$887$	289.432	+	568.042i	0.326304	+	0.640409i	−0.668329	+	0.743865i	$0.732990\pi$
$888$	−214.182	+	109.131i	−0.241196	+	0.122895i
$889$	479.557	−	155.817i	0.539434	−	0.175273i
$890$	531.886	+	135.029i	0.597624	+	0.151718i
$891$	−56.5460	+	174.031i	−0.0634635	+	0.195321i
$892$	−381.756	+	60.4641i	−0.427977	+	0.0677849i
$893$	−330.701	−	330.701i	−0.370326	−	0.370326i
$894$	237.348	−	326.681i	0.265490	−	0.365415i
$895$	761.094	+	1279.01i	0.850384	+	1.42906i
$896$	1264.74	−	918.885i	1.41154	−	1.02554i
$897$	−8.54013	+	53.9202i	−0.00952077	+	0.0601118i
$898$	200.894	−	394.277i	0.223713	−	0.439061i
$899$			314.033i			0.349314i
$900$	85.8317	+	651.019i	0.0953686	+	0.723355i
$901$	−549.828			−0.610242
$902$	−474.663	−	241.853i	−0.526234	−	0.268130i
$903$	−168.878	−	26.7477i	−0.187019	−	0.0296209i
$904$	−1850.48	−	2546.97i	−2.04700	−	2.81745i
$905$	−529.370	−	464.158i	−0.584939	−	0.512881i
$906$	−1046.82	−	760.558i	−1.15543	−	0.839468i
$907$	473.380	−	473.380i	0.521918	−	0.521918i	−0.396232	−	0.918150i	$-0.629683\pi$
$907$	473.380	−	473.380i	0.521918	−	0.521918i	0.918150	+	0.396232i	$0.129683\pi$
$908$	−360.149	−	2273.89i	−0.396640	−	2.50429i
$909$	−299.535	−	97.3249i	−0.329522	−	0.107068i
$910$	−785.376	+	653.314i	−0.863051	+	0.717928i
$911$	171.003	+	526.292i	0.187709	+	0.577708i	0.999985	−	0.00556528i	$-0.00177149\pi$
$911$	171.003	+	526.292i	0.187709	+	0.577708i	−0.812276	+	0.583274i	$0.801771\pi$
$912$	−276.076	−	541.830i	−0.302715	−	0.594112i
$913$	−2828.54	+	1441.21i	−3.09807	+	1.57854i
$914$	−1335.83	+	434.038i	−1.46152	+	0.474878i
$915$	7.49641	+	114.210i	0.00819279	+	0.124820i
$916$	417.819	−	1285.91i	0.456134	−	1.40384i
$917$	−340.448	+	53.9216i	−0.371263	+	0.0588022i
$918$	198.648	+	198.648i	0.216393	+	0.216393i
$919$	−808.309	+	1112.54i	−0.879553	+	1.21060i	0.0969921	+	0.995285i	$0.469078\pi$
$919$	−808.309	+	1112.54i	−0.879553	+	1.21060i	−0.976545	+	0.215315i	$0.930922\pi$
$920$	−421.561	−	181.070i	−0.458218	−	0.196815i
$921$	662.498	−	481.333i	0.719324	−	0.522620i
$922$	56.7888	−	358.551i	0.0615931	−	0.388884i
$923$	344.917	−	676.937i	0.373691	−	0.733410i
$924$		−	3023.59i		−	3.27229i
$925$	−58.0584	−	195.868i	−0.0627659	−	0.211749i
$926$	−232.964			−0.251581
$927$	209.450	+	106.720i	0.225944	+	0.115124i
$928$	−185.074	−	29.3129i	−0.199434	−	0.0315872i
$929$	−993.428	−	1367.34i	−1.06935	−	1.47184i	−0.870730	−	0.491761i	$-0.836353\pi$
$929$	−993.428	−	1367.34i	−1.06935	−	1.47184i	−0.198622	−	0.980076i	$-0.563647\pi$
$930$	−270.325	−	1194.15i	−0.290672	−	1.28403i
$931$	522.607	+	379.696i	0.561340	+	0.407837i
$932$	−753.646	+	753.646i	−0.808633	+	0.808633i
$933$	73.9199	+	466.712i	0.0792282	+	0.500227i
$934$	1479.43	+	480.696i	1.58397	+	0.514664i
$935$	570.395	+	1429.32i	0.610048	+	1.52868i
$936$	−91.8505	−	282.687i	−0.0981309	−	0.302016i
$937$	−624.632	−	1225.91i	−0.666630	−	1.30834i	−0.938259	−	0.345933i	$-0.887562\pi$
$937$	−624.632	−	1225.91i	−0.666630	−	1.30834i	0.271629	−	0.962402i	$-0.412438\pi$
$938$	1480.91	−	754.562i	1.57880	−	0.804437i
$939$	556.849	−	180.931i	0.593024	−	0.192685i
$940$	1388.41	−	554.071i	1.47704	−	0.589437i
$941$	−355.388	+	1093.77i	−0.377670	+	1.16235i	0.563989	+	0.825782i	$0.309266\pi$
$941$	−355.388	+	1093.77i	−0.377670	+	1.16235i	−0.941659	+	0.336568i	$0.890734\pi$
$942$	−1031.89	+	163.436i	−1.09543	+	0.173499i
$943$	28.0279	+	28.0279i	0.0297221	+	0.0297221i
$944$	−175.019	+	240.893i	−0.185402	+	0.255184i
$945$	248.491	−	56.2522i	0.262954	−	0.0595261i
$946$	591.375	−	429.659i	0.625132	−	0.454185i
$947$	−149.844	+	946.080i	−0.158231	+	0.999029i	0.772949	+	0.634468i	$0.218781\pi$
$947$	−149.844	+	946.080i	−0.158231	+	0.999029i	−0.931180	+	0.364561i	$0.881219\pi$
$948$	−591.399	+	1160.69i	−0.623838	+	1.22435i
$949$			267.724i			0.282112i
$950$	1172.43	−	347.527i	1.23414	−	0.365818i
$951$	−332.631			−0.349769
$952$	−2246.44	−	1144.62i	−2.35971	−	1.20233i
$953$	1150.08	+	182.155i	1.20680	+	0.191138i	0.727247	−	0.686376i	$-0.240799\pi$
$953$	1150.08	+	182.155i	1.20680	+	0.191138i	0.479551	+	0.877514i	$0.340799\pi$
$954$	−228.740	−	314.834i	−0.239769	−	0.330014i
$955$	−35.4242	+	82.4733i	−0.0370934	+	0.0863595i
$956$	763.488	+	554.706i	0.798627	+	0.580237i
$957$	197.545	−	197.545i	0.206421	−	0.206421i
$958$	−393.367	−	2483.62i	−0.410612	−	2.59250i
$959$	−365.355	−	118.711i	−0.380975	−	0.123786i
$960$	−157.119	+	10.3129i	−0.163666	+	0.0107426i
$961$	187.260	+	576.327i	0.194859	+	0.599716i
$962$	77.2948	+	151.700i	0.0803480	+	0.157692i
$963$	382.639	−	194.964i	0.397341	−	0.202455i
$964$	1779.99	−	578.353i	1.84646	−	0.599951i
$965$	175.644	+	211.149i	0.182014	+	0.218807i
$966$	−101.280	+	311.709i	−0.104845	+	0.322680i
$967$	1607.54	−	254.609i	1.66240	−	0.263298i	0.746698	−	0.665163i	$-0.231638\pi$
$967$	1607.54	−	254.609i	1.66240	−	0.263298i	0.915699	+	0.401865i	$0.131638\pi$
$968$	3511.31	+	3511.31i	3.62739	+	3.62739i
$969$	211.076	−	290.521i	0.217828	−	0.299815i
$970$	−1679.67	+	1915.66i	−1.73162	+	1.97490i
$971$	−484.385	+	351.927i	−0.498852	+	0.362437i	−0.808578	−	0.588388i	$-0.799763\pi$
$971$	−484.385	+	351.927i	−0.498852	+	0.362437i	0.309726	+	0.950826i	$0.399763\pi$
$972$	−21.3506	+	134.802i	−0.0219656	+	0.138686i
$973$	408.705	−	802.129i	0.420046	−	0.824387i
$974$			1.30076i			0.00133548i
$975$	250.441	−	33.0186i	0.256862	−	0.0338653i
$976$	338.799			0.347130
$977$	290.230	+	147.879i	0.297062	+	0.151361i	0.596169	−	0.802859i	$-0.296689\pi$
$977$	290.230	+	147.879i	0.297062	+	0.151361i	−0.299107	+	0.954220i	$0.596689\pi$
$978$	−34.5621	−	5.47411i	−0.0353396	−	0.00559725i
$979$	367.248	+	505.474i	0.375126	+	0.516316i
$980$	−1774.39	+	1055.88i	−1.81061	+	1.07743i
$981$	−286.033	−	207.815i	−0.291573	−	0.211840i
$982$	−745.826	+	745.826i	−0.759497	+	0.759497i
$983$	−128.821	−	813.342i	−0.131048	−	0.827408i	−0.962395	−	0.271653i	$-0.912430\pi$
$983$	−128.821	−	813.342i	−0.131048	−	0.827408i	0.831347	−	0.555754i	$-0.187570\pi$
$984$	−205.248	−	66.6892i	−0.208586	−	0.0677735i
$985$	61.0163	−	240.346i	0.0619455	−	0.244006i
$986$	−132.539	−	407.913i	−0.134421	−	0.413705i
$987$	−263.319	−	516.792i	−0.266787	−	0.523599i
$988$	−623.289	+	317.581i	−0.630859	+	0.321439i
$989$	−51.7265	+	16.8069i	−0.0523018	+	0.0169939i
$990$	−581.136	+	921.236i	−0.587007	+	0.930541i
$991$	55.3319	−	170.294i	0.0558344	−	0.171841i	−0.919250	−	0.393674i	$-0.871204\pi$
$991$	55.3319	−	170.294i	0.0558344	−	0.171841i	0.975085	+	0.221833i	$0.0712040\pi$
$992$	−923.497	+	146.268i	−0.930945	+	0.147447i
$993$	−141.553	−	141.553i	−0.142551	−	0.142551i
$994$	2681.00	−	3690.08i	2.69719	−	3.71236i
$995$	83.1582	−	905.930i	0.0835761	−	0.910483i
$996$	−1915.57	+	1391.74i	−1.92326	+	1.39733i
$997$	−181.153	+	1143.76i	−0.181698	+	1.14720i	0.713211	+	0.700949i	$0.247240\pi$
$997$	−181.153	+	1143.76i	−0.181698	+	1.14720i	−0.894910	+	0.446248i	$0.852760\pi$
$998$	1038.59	−	2038.35i	1.04067	−	2.04243i
$999$		−	42.4612i		−	0.0425037i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.58.2	yes	80
3.2	odd	2		225.3.r.b.208.9		80
5.2	odd	4		375.3.k.c.232.9		80
5.3	odd	4		375.3.k.b.232.2		80
5.4	even	2		375.3.k.a.268.9		80
25.3	odd	20		375.3.k.a.7.9		80
25.4	even	10		375.3.k.b.118.2		80
25.21	even	5		375.3.k.c.118.9		80
25.22	odd	20	inner	75.3.k.a.22.2	✓	80
75.47	even	20		225.3.r.b.172.9		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.22.2	✓	80	25.22	odd	20	inner
75.3.k.a.58.2	yes	80	1.1	even	1	trivial
225.3.r.b.172.9		80	75.47	even	20
225.3.r.b.208.9		80	3.2	odd	2
375.3.k.a.7.9		80	25.3	odd	20
375.3.k.a.268.9		80	5.4	even	2
375.3.k.b.118.2		80	25.4	even	10
375.3.k.b.232.2		80	5.3	odd	4
375.3.k.c.118.9		80	25.21	even	5
375.3.k.c.232.9		80	5.2	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.18220 - 1.62141i) q^{2} +(1.71073 + 0.270952i) q^{3} +(5.14628 + 7.08325i) q^{4} +(-4.97907 - 0.457044i) q^{5} +(-5.00455 - 3.63602i) q^{6} +(-6.93420 + 6.93420i) q^{7} +(-2.65683 - 16.7746i) q^{8} +(2.85317 + 0.927051i) q^{9} +O(q^{10})\)	\(q+(-3.18220 - 1.62141i) q^{2} +(1.71073 + 0.270952i) q^{3} +(5.14628 + 7.08325i) q^{4} +(-4.97907 - 0.457044i) q^{5} +(-5.00455 - 3.63602i) q^{6} +(-6.93420 + 6.93420i) q^{7} +(-2.65683 - 16.7746i) q^{8} +(2.85317 + 0.927051i) q^{9} +(15.1033 + 9.52752i) q^{10} +(6.28289 + 19.3367i) q^{11} +(6.88465 + 13.5119i) q^{12} +(5.19789 - 2.64846i) q^{13} +(33.3092 - 10.8228i) q^{14} +(-8.39398 - 2.13097i) q^{15} +(-7.92167 + 24.3804i) q^{16} +(-14.9517 + 2.36812i) q^{17} +(-7.57622 - 7.57622i) q^{18} +(-8.05018 + 11.0801i) q^{19} +(-22.3863 - 37.6200i) q^{20} +(-13.7414 + 9.98368i) q^{21} +(11.3594 - 71.7205i) q^{22} +(-2.45285 + 4.81399i) q^{23} -29.4166i q^{24} +(24.5822 + 4.55131i) q^{25} -20.8350 q^{26} +(4.62981 + 2.35900i) q^{27} +(-84.8019 - 13.4313i) q^{28} +(-4.66296 - 6.41802i) q^{29} +(23.2562 + 20.3913i) q^{30} +(-32.0251 - 23.2676i) q^{31} +(16.7020 - 16.7020i) q^{32} +(5.50896 + 34.7822i) q^{33} +(51.4191 + 16.7071i) q^{34} +(37.6951 - 31.3566i) q^{35} +(8.11668 + 24.9806i) q^{36} +(-3.70986 - 7.28100i) q^{37} +(43.5827 - 22.2065i) q^{38} +(9.60978 - 3.12241i) q^{39} +(5.56182 + 84.7360i) q^{40} +(2.26706 - 6.97730i) q^{41} +(59.9154 - 9.48966i) q^{42} +(7.11814 + 7.11814i) q^{43} +(-104.633 + 144.015i) q^{44} +(-13.7824 - 5.91987i) q^{45} +(15.6109 - 11.3420i) q^{46} +(-5.34190 + 33.7274i) q^{47} +(-20.1577 + 39.5618i) q^{48} -47.1662i q^{49} +(-70.8460 - 54.3411i) q^{50} -26.2200 q^{51} +(45.5095 + 23.1883i) q^{52} +(35.8736 + 5.68183i) q^{53} +(-10.9081 - 15.0136i) q^{54} +(-22.4452 - 99.1505i) q^{55} +(134.741 + 97.8951i) q^{56} +(-16.7738 + 16.7738i) q^{57} +(4.43223 + 27.9840i) q^{58} +(11.0469 + 3.58934i) q^{59} +(-28.1036 - 70.4232i) q^{60} +(-4.08403 - 12.5694i) q^{61} +(64.1839 + 125.968i) q^{62} +(-26.2128 + 13.3561i) q^{63} +(17.2918 - 5.61843i) q^{64} +(-27.0911 + 10.8112i) q^{65} +(38.8657 - 119.616i) q^{66} +(46.8716 - 7.42374i) q^{67} +(-93.7198 - 93.7198i) q^{68} +(-5.50052 + 7.57082i) q^{69} +(-170.795 + 38.6637i) q^{70} +(105.361 - 76.5490i) q^{71} +(7.97049 - 50.3237i) q^{72} +(-20.8347 + 40.8904i) q^{73} +29.1848i q^{74} +(40.8203 + 14.4467i) q^{75} -119.912 q^{76} +(-177.651 - 90.5180i) q^{77} +(-35.6430 - 5.64529i) q^{78} +(50.4913 + 69.4954i) q^{79} +(50.5855 - 117.771i) q^{80} +(7.28115 + 5.29007i) q^{81} +(-18.5273 + 18.5273i) q^{82} +(24.4251 + 154.214i) q^{83} +(-141.434 - 45.9546i) q^{84} +(75.5280 - 4.95744i) q^{85} +(-11.1099 - 34.1928i) q^{86} +(-6.23807 - 12.2429i) q^{87} +(307.673 - 156.767i) q^{88} +(29.2261 - 9.49613i) q^{89} +(34.2599 + 41.1852i) q^{90} +(-17.6783 + 54.4082i) q^{91} +(-46.7218 + 7.40000i) q^{92} +(-48.4817 - 48.4817i) q^{93} +(71.6851 - 98.6660i) q^{94} +(45.1465 - 51.4894i) q^{95} +(33.0980 - 24.0471i) q^{96} +(-22.3189 + 140.916i) q^{97} +(-76.4758 + 150.092i) q^{98} +60.9955i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Introduction

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