LMFDB - Embedded newform 950.2.h.c.381.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			381.1
Character	$\chi$	$=$	950.381
Dual form			950.2.h.c.571.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-2.41843 + 1.75709i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.597004 - 2.15490i) q^{5} +(-2.41843 - 1.75709i) q^{6} +1.43148 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.83438 - 5.64563i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-2.41843 + 1.75709i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.597004 - 2.15490i) q^{5} +(-2.41843 - 1.75709i) q^{6} +1.43148 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.83438 - 5.64563i) q^{9} +(1.86495 - 1.23368i) q^{10} +(0.998632 + 3.07347i) q^{11} +(0.923758 - 2.84303i) q^{12} +(0.816476 - 2.51286i) q^{13} +(0.442352 + 1.36142i) q^{14} +(5.23016 + 4.16248i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.16059 + 0.843216i) q^{17} +5.93617 q^{18} +(0.809017 + 0.587785i) q^{19} +(1.74960 + 1.39244i) q^{20} +(-3.46194 + 2.51524i) q^{21} +(-2.61445 + 1.89951i) q^{22} +(2.18296 + 6.71847i) q^{23} +2.98934 q^{24} +(-4.28717 + 2.57296i) q^{25} +2.64217 q^{26} +(2.71231 + 8.34762i) q^{27} +(-1.15809 + 0.841404i) q^{28} +(7.77288 - 5.64733i) q^{29} +(-2.34254 + 6.26046i) q^{30} +(-0.326593 - 0.237284i) q^{31} +1.00000 q^{32} +(-7.81549 - 5.67829i) q^{33} +(-0.443305 + 1.36435i) q^{34} +(-0.854600 - 3.08470i) q^{35} +(1.83438 + 5.64563i) q^{36} +(-2.89846 + 8.92055i) q^{37} +(-0.309017 + 0.951057i) q^{38} +(2.44073 + 7.51179i) q^{39} +(-0.783631 + 2.09426i) q^{40} +(0.706140 - 2.17328i) q^{41} +(-3.46194 - 2.51524i) q^{42} +0.686773 q^{43} +(-2.61445 - 1.89951i) q^{44} +(-13.2609 - 0.582434i) q^{45} +(-5.71507 + 4.15224i) q^{46} +(-9.36376 + 6.80317i) q^{47} +(0.923758 + 2.84303i) q^{48} -4.95086 q^{49} +(-3.77184 - 3.28225i) q^{50} -4.28840 q^{51} +(0.816476 + 2.51286i) q^{52} +(5.21158 - 3.78643i) q^{53} +(-7.10091 + 5.15911i) q^{54} +(6.02683 - 3.98682i) q^{55} +(-1.15809 - 0.841404i) q^{56} -2.98934 q^{57} +(7.77288 + 5.64733i) q^{58} +(3.57476 - 11.0020i) q^{59} +(-6.67793 - 0.293303i) q^{60} +(2.46235 + 7.57834i) q^{61} +(0.124747 - 0.383933i) q^{62} +(2.62588 - 8.08161i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-5.90239 - 0.259240i) q^{65} +(2.98525 - 9.18766i) q^{66} +(10.8150 + 7.85756i) q^{67} -1.43456 q^{68} +(-17.0843 - 12.4125i) q^{69} +(2.66964 - 1.76600i) q^{70} +(-13.1823 + 9.57754i) q^{71} +(-4.80246 + 3.48919i) q^{72} +(3.81228 + 11.7330i) q^{73} -9.37962 q^{74} +(5.84729 - 13.7555i) q^{75} -1.00000 q^{76} +(1.42952 + 4.39962i) q^{77} +(-6.38991 + 4.64254i) q^{78} +(4.41789 - 3.20978i) q^{79} +(-2.23391 - 0.0981161i) q^{80} +(-6.81966 - 4.95478i) q^{81} +2.28512 q^{82} +(2.70486 + 1.96520i) q^{83} +(1.32234 - 4.06975i) q^{84} +(1.12417 - 3.00435i) q^{85} +(0.212225 + 0.653160i) q^{86} +(-8.87528 + 27.3153i) q^{87} +(0.998632 - 3.07347i) q^{88} +(-1.97815 - 6.08811i) q^{89} +(-3.54391 - 12.7918i) q^{90} +(1.16877 - 3.59711i) q^{91} +(-5.71507 - 4.15224i) q^{92} +1.20677 q^{93} +(-9.36376 - 6.80317i) q^{94} +(0.783631 - 2.09426i) q^{95} +(-2.41843 + 1.75709i) q^{96} +(-5.19172 + 3.77201i) q^{97} +(-1.52990 - 4.70855i) q^{98} +19.1836 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 11 q^{2} + q^{3} - 11 q^{4} - q^{5} + q^{6} + 18 q^{7} - 11 q^{8} - 8 q^{9}+O(q^{10}) $ 44 * q - 11 * q^2 + q^3 - 11 * q^4 - q^5 + q^6 + 18 * q^7 - 11 * q^8 - 8 * q^9	\( 44 q - 11 q^{2} + q^{3} - 11 q^{4} - q^{5} + q^{6} + 18 q^{7} - 11 q^{8} - 8 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} + 2 q^{13} + 3 q^{14} - 4 q^{15} - 11 q^{16} + 11 q^{17} + 42 q^{18} + 11 q^{19} - 6 q^{20} + 3 q^{21} - 6 q^{22} - 3 q^{23} + 6 q^{24} - 11 q^{25} + 22 q^{26} - 23 q^{27} - 12 q^{28} + 36 q^{29} - 4 q^{30} + 11 q^{31} + 44 q^{32} + 2 q^{33} - 19 q^{34} + 67 q^{35} - 8 q^{36} + 3 q^{37} + 11 q^{38} + 47 q^{39} + 4 q^{40} + 2 q^{41} + 3 q^{42} + 70 q^{43} - 6 q^{44} - 28 q^{45} - 8 q^{46} - 11 q^{47} - 4 q^{48} + 22 q^{49} + 14 q^{50} + 38 q^{51} + 2 q^{52} - 9 q^{53} + 32 q^{54} + 8 q^{55} - 12 q^{56} - 6 q^{57} + 36 q^{58} - 62 q^{59} + 11 q^{60} - 28 q^{61} - 29 q^{62} + 10 q^{63} - 11 q^{64} - 39 q^{65} - 8 q^{66} + 25 q^{67} + 16 q^{68} - 81 q^{69} - 43 q^{70} - 34 q^{71} - 13 q^{72} + 6 q^{73} + 8 q^{74} - 39 q^{75} - 44 q^{76} - 21 q^{77} - 58 q^{78} + 19 q^{79} - q^{80} - 22 q^{81} + 2 q^{82} - 50 q^{83} - 7 q^{84} + 102 q^{85} - 10 q^{86} + 47 q^{87} - q^{88} - 4 q^{89} - 38 q^{90} - 8 q^{91} - 8 q^{92} + 60 q^{93} - 11 q^{94} - 4 q^{95} + q^{96} + 8 q^{97} + 7 q^{98} - 12 q^{99}+O(q^{100}) \) 44 * q - 11 * q^2 + q^3 - 11 * q^4 - q^5 + q^6 + 18 * q^7 - 11 * q^8 - 8 * q^9 + 4 * q^10 - q^11 - 4 * q^12 + 2 * q^13 + 3 * q^14 - 4 * q^15 - 11 * q^16 + 11 * q^17 + 42 * q^18 + 11 * q^19 - 6 * q^20 + 3 * q^21 - 6 * q^22 - 3 * q^23 + 6 * q^24 - 11 * q^25 + 22 * q^26 - 23 * q^27 - 12 * q^28 + 36 * q^29 - 4 * q^30 + 11 * q^31 + 44 * q^32 + 2 * q^33 - 19 * q^34 + 67 * q^35 - 8 * q^36 + 3 * q^37 + 11 * q^38 + 47 * q^39 + 4 * q^40 + 2 * q^41 + 3 * q^42 + 70 * q^43 - 6 * q^44 - 28 * q^45 - 8 * q^46 - 11 * q^47 - 4 * q^48 + 22 * q^49 + 14 * q^50 + 38 * q^51 + 2 * q^52 - 9 * q^53 + 32 * q^54 + 8 * q^55 - 12 * q^56 - 6 * q^57 + 36 * q^58 - 62 * q^59 + 11 * q^60 - 28 * q^61 - 29 * q^62 + 10 * q^63 - 11 * q^64 - 39 * q^65 - 8 * q^66 + 25 * q^67 + 16 * q^68 - 81 * q^69 - 43 * q^70 - 34 * q^71 - 13 * q^72 + 6 * q^73 + 8 * q^74 - 39 * q^75 - 44 * q^76 - 21 * q^77 - 58 * q^78 + 19 * q^79 - q^80 - 22 * q^81 + 2 * q^82 - 50 * q^83 - 7 * q^84 + 102 * q^85 - 10 * q^86 + 47 * q^87 - q^88 - 4 * q^89 - 38 * q^90 - 8 * q^91 - 8 * q^92 + 60 * q^93 - 11 * q^94 - 4 * q^95 + q^96 + 8 * q^97 + 7 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−2.41843	+	1.75709i	−1.39628	+	1.01446i	−0.401137	+	0.916018i	$0.631385\pi$
$3$	−2.41843	+	1.75709i	−1.39628	+	1.01446i	−0.995143	+	0.0984391i	$0.968615\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.597004	−	2.15490i	−0.266988	−	0.963700i
$5$	−0.597004	−	2.15490i	−0.266988	−	0.963700i
$6$	−2.41843	−	1.75709i	−0.987319	−	0.717329i
$7$	1.43148			0.541049			0.270525	−	0.962713i	$-0.412803\pi$
$7$	1.43148			0.541049			0.270525	+	0.962713i	$0.412803\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	1.83438	−	5.64563i	0.611459	−	1.88188i
$10$	1.86495	−	1.23368i	0.589748	−	0.390125i
$11$	0.998632	+	3.07347i	0.301099	+	0.926687i	0.981104	+	0.193480i	$0.0619774\pi$
$11$	0.998632	+	3.07347i	0.301099	+	0.926687i	−0.680005	+	0.733207i	$0.738023\pi$
$12$	0.923758	−	2.84303i	0.266666	−	0.820713i
$13$	0.816476	−	2.51286i	0.226450	−	0.696941i	−0.771691	−	0.635997i	$-0.780589\pi$
$13$	0.816476	−	2.51286i	0.226450	−	0.696941i	0.998141	−	0.0609436i	$-0.0194110\pi$
$14$	0.442352	+	1.36142i	0.118224	+	0.363855i
$15$	5.23016	+	4.16248i	1.35042	+	1.07475i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	1.16059	+	0.843216i	0.281484	+	0.204510i	0.719564	−	0.694426i	$-0.244342\pi$
$17$	1.16059	+	0.843216i	0.281484	+	0.204510i	−0.438081	+	0.898936i	$0.644342\pi$
$18$	5.93617			1.39917
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$20$	1.74960	+	1.39244i	0.391223	+	0.311359i
$21$	−3.46194	+	2.51524i	−0.755456	+	0.548871i
$22$	−2.61445	+	1.89951i	−0.557403	+	0.404977i
$23$	2.18296	+	6.71847i	0.455179	+	1.40090i	0.870925	+	0.491416i	$0.163521\pi$
$23$	2.18296	+	6.71847i	0.455179	+	1.40090i	−0.415746	+	0.909481i	$0.636479\pi$
$24$	2.98934			0.610197
$25$	−4.28717	+	2.57296i	−0.857435	+	0.514593i
$26$	2.64217			0.518173
$27$	2.71231	+	8.34762i	0.521983	+	1.60650i
$28$	−1.15809	+	0.841404i	−0.218859	+	0.159010i
$29$	7.77288	−	5.64733i	1.44339	−	1.04868i	0.456066	−	0.889946i	$-0.349258\pi$
$29$	7.77288	−	5.64733i	1.44339	−	1.04868i	0.987321	−	0.158736i	$-0.0507420\pi$
$30$	−2.34254	+	6.26046i	−0.427688	+	1.14300i
$31$	−0.326593	−	0.237284i	−0.0586579	−	0.0426174i	0.558070	−	0.829794i	$-0.311542\pi$
$31$	−0.326593	−	0.237284i	−0.0586579	−	0.0426174i	−0.616728	+	0.787176i	$0.711542\pi$
$32$	1.00000			0.176777
$33$	−7.81549	−	5.67829i	−1.36050	−	0.988463i
$34$	−0.443305	+	1.36435i	−0.0760261	+	0.233984i
$35$	−0.854600	−	3.08470i	−0.144454	−	0.521409i
$36$	1.83438	+	5.64563i	0.305729	+	0.940938i
$37$	−2.89846	+	8.92055i	−0.476504	+	1.46653i	0.367414	+	0.930058i	$0.380243\pi$
$37$	−2.89846	+	8.92055i	−0.476504	+	1.46653i	−0.843918	+	0.536472i	$0.819757\pi$
$38$	−0.309017	+	0.951057i	−0.0501292	+	0.154282i
$39$	2.44073	+	7.51179i	0.390829	+	1.20285i
$40$	−0.783631	+	2.09426i	−0.123903	+	0.331131i
$41$	0.706140	−	2.17328i	0.110281	−	0.339409i	−0.880653	−	0.473762i	$-0.842896\pi$
$41$	0.706140	−	2.17328i	0.110281	−	0.339409i	0.990934	+	0.134353i	$0.0428957\pi$
$42$	−3.46194	−	2.51524i	−0.534188	−	0.388111i
$43$	0.686773			0.104732			0.0523660	−	0.998628i	$-0.483324\pi$
$43$	0.686773			0.104732			0.0523660	+	0.998628i	$0.483324\pi$
$44$	−2.61445	−	1.89951i	−0.394143	−	0.286362i
$45$	−13.2609	−	0.582434i	−1.97682	−	0.0868241i
$46$	−5.71507	+	4.15224i	−0.842641	+	0.612214i
$47$	−9.36376	+	6.80317i	−1.36585	+	0.992345i	−0.367796	+	0.929906i	$0.619888\pi$
$47$	−9.36376	+	6.80317i	−1.36585	+	0.992345i	−0.998049	+	0.0624382i	$0.980112\pi$
$48$	0.923758	+	2.84303i	0.133333	+	0.410357i
$49$	−4.95086			−0.707266
$50$	−3.77184	−	3.28225i	−0.533419	−	0.464181i
$51$	−4.28840			−0.600497
$52$	0.816476	+	2.51286i	0.113225	+	0.348470i
$53$	5.21158	−	3.78643i	0.715865	−	0.520107i	−0.169195	−	0.985583i	$-0.554117\pi$
$53$	5.21158	−	3.78643i	0.715865	−	0.520107i	0.885060	+	0.465476i	$0.154117\pi$
$54$	−7.10091	+	5.15911i	−0.966311	+	0.702066i
$55$	6.02683	−	3.98682i	0.812658	−	0.537583i
$56$	−1.15809	−	0.841404i	−0.154757	−	0.112437i
$57$	−2.98934			−0.395948
$58$	7.77288	+	5.64733i	1.02063	+	0.741530i
$59$	3.57476	−	11.0020i	0.465395	−	1.43234i	−0.393091	−	0.919500i	$-0.628594\pi$
$59$	3.57476	−	11.0020i	0.465395	−	1.43234i	0.858486	−	0.512838i	$-0.171406\pi$
$60$	−6.67793	−	0.293303i	−0.862118	−	0.0378652i
$61$	2.46235	+	7.57834i	0.315272	+	0.970308i	0.975642	+	0.219367i	$0.0703993\pi$
$61$	2.46235	+	7.57834i	0.315272	+	0.970308i	−0.660370	+	0.750940i	$0.729601\pi$
$62$	0.124747	−	0.383933i	0.0158429	−	0.0487596i
$63$	2.62588	−	8.08161i	0.330829	−	1.01819i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−5.90239	−	0.259240i	−0.732101	−	0.0321547i
$66$	2.98525	−	9.18766i	0.367459	−	1.13092i
$67$	10.8150	+	7.85756i	1.32126	+	0.959954i	0.999916	+	0.0129932i	$0.00413600\pi$
$67$	10.8150	+	7.85756i	1.32126	+	0.959954i	0.321348	+	0.946961i	$0.395864\pi$
$68$	−1.43456			−0.173966
$69$	−17.0843	−	12.4125i	−2.05671	−	1.49429i
$70$	2.66964	−	1.76600i	0.319082	−	0.211077i
$71$	−13.1823	+	9.57754i	−1.56446	+	1.13664i	−0.632224	+	0.774786i	$0.717858\pi$
$71$	−13.1823	+	9.57754i	−1.56446	+	1.13664i	−0.932233	+	0.361859i	$0.882142\pi$
$72$	−4.80246	+	3.48919i	−0.565975	+	0.411205i
$73$	3.81228	+	11.7330i	0.446193	+	1.37324i	0.881170	+	0.472800i	$0.156757\pi$
$73$	3.81228	+	11.7330i	0.446193	+	1.37324i	−0.434976	+	0.900442i	$0.643243\pi$
$74$	−9.37962			−1.09036
$75$	5.84729	−	13.7555i	0.675187	−	1.58835i
$76$	−1.00000			−0.114708
$77$	1.42952	+	4.39962i	0.162909	+	0.501383i
$78$	−6.38991	+	4.64254i	−0.723514	+	0.525664i
$79$	4.41789	−	3.20978i	0.497051	−	0.361129i	−0.310838	−	0.950463i	$-0.600610\pi$
$79$	4.41789	−	3.20978i	0.497051	−	0.361129i	0.807890	+	0.589334i	$0.200610\pi$
$80$	−2.23391	−	0.0981161i	−0.249759	−	0.0109697i
$81$	−6.81966	−	4.95478i	−0.757740	−	0.550531i
$82$	2.28512			0.252349
$83$	2.70486	+	1.96520i	0.296897	+	0.215708i	0.726254	−	0.687427i	$-0.241260\pi$
$83$	2.70486	+	1.96520i	0.296897	+	0.215708i	−0.429357	+	0.903135i	$0.641260\pi$
$84$	1.32234	−	4.06975i	0.144279	−	0.444046i
$85$	1.12417	−	3.00435i	0.121933	−	0.325867i
$86$	0.212225	+	0.653160i	0.0228848	+	0.0704321i
$87$	−8.87528	+	27.3153i	−0.951530	+	2.92851i
$88$	0.998632	−	3.07347i	0.106454	−	0.327633i
$89$	−1.97815	−	6.08811i	−0.209683	−	0.645338i	−0.999488	−	0.0319805i	$-0.989819\pi$
$89$	−1.97815	−	6.08811i	−0.209683	−	0.645338i	0.789806	−	0.613357i	$-0.210181\pi$
$90$	−3.54391	−	12.7918i	−0.373561	−	1.34838i
$91$	1.16877	−	3.59711i	0.122520	−	0.377079i
$92$	−5.71507	−	4.15224i	−0.595837	−	0.432901i
$93$	1.20677			0.125136
$94$	−9.36376	−	6.80317i	−0.965798	−	0.701694i
$95$	0.783631	−	2.09426i	0.0803989	−	0.214866i
$96$	−2.41843	+	1.75709i	−0.246830	+	0.179332i
$97$	−5.19172	+	3.77201i	−0.527140	+	0.382989i	−0.819287	−	0.573384i	$-0.805630\pi$
$97$	−5.19172	+	3.77201i	−0.527140	+	0.382989i	0.292147	+	0.956373i	$0.405630\pi$
$98$	−1.52990	−	4.70855i	−0.154543	−	0.475635i
$99$	19.1836			1.92802
$100$	1.95605	−	4.60151i	0.195605	−	0.460151i
$101$	11.5738			1.15164			0.575820	−	0.817576i	$-0.304683\pi$
$101$	11.5738			1.15164			0.575820	+	0.817576i	$0.304683\pi$
$102$	−1.32519	−	4.07851i	−0.131213	−	0.403833i
$103$	4.23428	−	3.07638i	0.417216	−	0.303125i	−0.359301	−	0.933222i	$-0.616985\pi$
$103$	4.23428	−	3.07638i	0.417216	−	0.303125i	0.776517	+	0.630097i	$0.216985\pi$
$104$	−2.13756	+	1.55303i	−0.209605	+	0.152287i
$105$	7.48688	+	5.95851i	0.730645	+	0.581491i
$106$	5.21158	+	3.78643i	0.506193	+	0.367771i
$107$	6.09293			0.589026			0.294513	−	0.955647i	$-0.404843\pi$
$107$	6.09293			0.589026			0.294513	+	0.955647i	$0.404843\pi$
$108$	−7.10091	−	5.15911i	−0.683285	−	0.496436i
$109$	−3.93399	+	12.1076i	−0.376808	+	1.15970i	0.565443	+	0.824788i	$0.308705\pi$
$109$	−3.93399	+	12.1076i	−0.376808	+	1.15970i	−0.942251	+	0.334908i	$0.891295\pi$
$110$	5.65409	+	4.49986i	0.539096	+	0.429045i
$111$	−8.66450	−	26.6666i	−0.822398	−	2.53108i
$112$	0.442352	−	1.36142i	0.0417983	−	0.128642i
$113$	−2.60819	+	8.02719i	−0.245358	+	0.755134i	0.750219	+	0.661189i	$0.229948\pi$
$113$	−2.60819	+	8.02719i	−0.245358	+	0.755134i	−0.995577	+	0.0939453i	$0.970052\pi$
$114$	−0.923758	−	2.84303i	−0.0865178	−	0.266274i
$115$	13.1744	−	8.71501i	1.22852	−	0.812679i
$116$	−2.96898	+	9.13757i	−0.275662	+	0.848402i
$117$	−12.6889	−	9.21904i	−1.17309	−	0.852301i
$118$	11.5682			1.06494
$119$	1.66136	+	1.20705i	0.152297	+	0.110650i
$120$	−1.78465	−	6.44173i	−0.162915	−	0.588047i
$121$	0.450220	−	0.327104i	0.0409291	−	0.0297367i
$122$	−6.44652	+	4.68367i	−0.583641	+	0.424040i
$123$	2.11090	+	6.49667i	0.190333	+	0.585785i
$124$	0.403691			0.0362526
$125$	8.10393	+	7.70235i	0.724838	+	0.688920i
$126$	8.49751			0.757019
$127$	2.99397	+	9.21448i	0.265671	+	0.817653i	0.991538	+	0.129817i	$0.0414390\pi$
$127$	2.99397	+	9.21448i	0.265671	+	0.817653i	−0.725866	+	0.687836i	$0.758561\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	−1.66091	+	1.20672i	−0.146235	+	0.106246i
$130$	−1.57739	−	5.69361i	−0.138346	−	0.499363i
$131$	0.831510	+	0.604127i	0.0726493	+	0.0527828i	0.623517	−	0.781810i	$-0.285703\pi$
$131$	0.831510	+	0.604127i	0.0726493	+	0.0527828i	−0.550868	+	0.834593i	$0.685703\pi$
$132$	9.66048			0.840837
$133$	1.15809	+	0.841404i	0.100419	+	0.0729590i
$134$	−4.13097	+	12.7138i	−0.356861	+	1.09831i
$135$	16.3690	−	10.8283i	1.40882	−	0.931952i
$136$	−0.443305	−	1.36435i	−0.0380131	−	0.116992i
$137$	−0.713774	+	2.19677i	−0.0609819	+	0.187683i	−0.976906	−	0.213668i	$-0.931459\pi$
$137$	−0.713774	+	2.19677i	−0.0609819	+	0.187683i	0.915925	+	0.401350i	$0.131459\pi$
$138$	6.52562	−	20.0838i	0.555498	−	1.70965i
$139$	3.76665	+	11.5926i	0.319483	+	0.983269i	0.973870	+	0.227108i	$0.0729271\pi$
$139$	3.76665	+	11.5926i	0.319483	+	0.983269i	−0.654386	+	0.756161i	$0.727073\pi$
$140$	2.50453	+	1.99325i	0.211671	+	0.168460i
$141$	10.6918	−	32.9060i	0.900412	−	2.77118i
$142$	−13.1823	−	9.57754i	−1.10624	−	0.803729i
$143$	8.53855			0.714030
$144$	−4.80246	−	3.48919i	−0.400205	−	0.290766i
$145$	−16.8099	−	13.3783i	−1.39598	−	1.11101i
$146$	−9.98068	+	7.25139i	−0.826007	+	0.600129i
$147$	11.9733	−	8.69911i	0.987541	−	0.717491i
$148$	−2.89846	−	8.92055i	−0.238252	−	0.733265i
$149$	−8.62186			−0.706331			−0.353165	−	0.935561i	$-0.614895\pi$
$149$	−8.62186			−0.706331			−0.353165	+	0.935561i	$0.614895\pi$
$150$	14.8892	+	1.31043i	1.21569	+	0.106996i
$151$	3.43023			0.279148			0.139574	−	0.990212i	$-0.455427\pi$
$151$	3.43023			0.279148			0.139574	+	0.990212i	$0.455427\pi$
$152$	−0.309017	−	0.951057i	−0.0250646	−	0.0771409i
$153$	6.88944	−	5.00547i	0.556978	−	0.404668i
$154$	−3.74254	+	2.71911i	−0.301582	+	0.219112i
$155$	−0.316345	+	0.845434i	−0.0254095	+	0.0679069i
$156$	−6.38991	−	4.64254i	−0.511602	−	0.371701i
$157$	8.47034			0.676007			0.338003	−	0.941145i	$-0.390248\pi$
$157$	8.47034			0.676007			0.338003	+	0.941145i	$0.390248\pi$
$158$	4.41789	+	3.20978i	0.351468	+	0.255357i
$159$	−5.95072	+	18.3144i	−0.471923	+	1.45243i
$160$	−0.597004	−	2.15490i	−0.0471973	−	0.170360i
$161$	3.12487	+	9.61736i	0.246274	+	0.757954i
$162$	2.60488	−	8.01700i	0.204659	−	0.629875i
$163$	−2.85273	+	8.77981i	−0.223443	+	0.687688i	0.775003	+	0.631958i	$0.217749\pi$
$163$	−2.85273	+	8.77981i	−0.223443	+	0.687688i	−0.998446	+	0.0557298i	$0.982251\pi$
$164$	0.706140	+	2.17328i	0.0551403	+	0.169704i
$165$	−7.57025	+	20.2315i	−0.589343	+	1.57502i
$166$	−1.03317	+	3.17976i	−0.0801892	+	0.246797i
$167$	−6.60829	−	4.80121i	−0.511365	−	0.371528i	0.301976	−	0.953315i	$-0.402354\pi$
$167$	−6.60829	−	4.80121i	−0.511365	−	0.371528i	−0.813341	+	0.581787i	$0.802354\pi$
$168$	4.27919			0.330147
$169$	4.86941	+	3.53783i	0.374570	+	0.272141i
$170$	3.20469	+	0.140754i	0.245789	+	0.0107953i
$171$	4.80246	−	3.48919i	0.367253	−	0.266825i
$172$	−0.555611	+	0.403675i	−0.0423650	+	0.0307799i
$173$	−1.08561	−	3.34118i	−0.0825378	−	0.254025i	0.901268	−	0.433261i	$-0.142637\pi$
$173$	−1.08561	−	3.34118i	−0.0825378	−	0.254025i	−0.983806	+	0.179236i	$0.942637\pi$
$174$	−28.7210			−2.17733
$175$	−6.13701	+	3.68315i	−0.463914	+	0.278420i
$176$	3.23164			0.243594
$177$	10.6862	+	32.8887i	0.803223	+	2.47207i
$178$	5.17885	−	3.76266i	0.388171	−	0.282023i
$179$	12.2059	−	8.86813i	0.912314	−	0.662835i	−0.0292851	−	0.999571i	$-0.509323\pi$
$179$	12.2059	−	8.86813i	0.912314	−	0.662835i	0.941599	+	0.336736i	$0.109323\pi$
$180$	11.0706	−	7.32335i	0.825156	−	0.545851i
$181$	12.0542	+	8.75787i	0.895980	+	0.650967i	0.937430	−	0.348173i	$-0.113198\pi$
$181$	12.0542	+	8.75787i	0.895980	+	0.650967i	−0.0414506	+	0.999141i	$0.513198\pi$
$182$	3.78222			0.280357
$183$	−19.2709	−	14.0011i	−1.42454	−	1.03499i
$184$	2.18296	−	6.71847i	0.160930	−	0.495292i
$185$	20.9533	+	0.920292i	1.54052	+	0.0676612i
$186$	0.372913	+	1.14771i	0.0273433	+	0.0841540i
$187$	−1.43260	+	4.40909i	−0.104762	+	0.322425i
$188$	3.57664	−	11.0078i	0.260853	−	0.802824i
$189$	3.88262	+	11.9495i	0.282419	+	0.869195i
$190$	2.23391	+	0.0981161i	0.162065	+	0.00711809i
$191$	1.66313	−	5.11858i	0.120340	−	0.370367i	−0.872684	−	0.488286i	$-0.837622\pi$
$191$	1.66313	−	5.11858i	0.120340	−	0.370367i	0.993023	+	0.117919i	$0.0376223\pi$
$192$	−2.41843	−	1.75709i	−0.174535	−	0.126807i
$193$	15.4879			1.11484			0.557421	−	0.830230i	$-0.311791\pi$
$193$	15.4879			1.11484			0.557421	+	0.830230i	$0.311791\pi$
$194$	−5.19172	−	3.77201i	−0.372744	−	0.270814i
$195$	14.7300	−	9.74408i	1.05484	−	0.697788i
$196$	4.00533	−	2.91004i	0.286095	−	0.207860i
$197$	2.37440	−	1.72510i	0.169169	−	0.122909i	−0.499979	−	0.866037i	$-0.666659\pi$
$197$	2.37440	−	1.72510i	0.169169	−	0.122909i	0.669148	+	0.743129i	$0.266659\pi$
$198$	5.92804	+	18.2446i	0.421288	+	1.29659i
$199$	14.7413			1.04499			0.522493	−	0.852644i	$-0.325002\pi$
$199$	14.7413			1.04499			0.522493	+	0.852644i	$0.325002\pi$
$200$	4.98075	+	0.438366i	0.352192	+	0.0309972i
$201$	−39.9618			−2.81869
$202$	3.57652	+	11.0074i	0.251643	+	0.774477i
$203$	11.1267	−	8.08404i	0.780943	−	0.567389i
$204$	3.46939	−	2.52066i	0.242906	−	0.176482i
$205$	−5.10476	−	0.224207i	−0.356532	−	0.0156593i
$206$	4.23428	+	3.07638i	0.295016	+	0.214342i
$207$	41.9343			2.91464
$208$	−2.13756	−	1.55303i	−0.148213	−	0.107683i
$209$	−0.998632	+	3.07347i	−0.0690768	+	0.212597i
$210$	−3.35331	+	8.96173i	−0.231400	+	0.618418i
$211$	−2.23772	−	6.88699i	−0.154051	−	0.474120i	0.844013	−	0.536323i	$-0.180187\pi$
$211$	−2.23772	−	6.88699i	−0.154051	−	0.474120i	−0.998063	+	0.0622033i	$0.980187\pi$
$212$	−1.99065	+	6.12658i	−0.136718	+	0.420775i
$213$	15.0520	−	46.3252i	1.03134	−	3.17415i
$214$	1.88282	+	5.79472i	0.128707	+	0.396119i
$215$	−0.410006	−	1.47993i	−0.0279622	−	0.100930i
$216$	2.71231	−	8.34762i	0.184549	−	0.567983i
$217$	−0.467512	−	0.339667i	−0.0317368	−	0.0230581i
$218$	−12.7307			−0.862229
$219$	−29.8357	−	21.6769i	−2.01611	−	1.46479i
$220$	−2.53241	+	6.76789i	−0.170735	+	0.456291i
$221$	3.06647	−	2.22792i	0.206273	−	0.149866i
$222$	22.6839	−	16.4809i	1.52245	−	1.10612i
$223$	−7.57198	−	23.3042i	−0.507057	−	1.56056i	−0.797284	−	0.603604i	$-0.793731\pi$
$223$	−7.57198	−	23.3042i	−0.507057	−	1.56056i	0.290226	−	0.956958i	$-0.406269\pi$
$224$	1.43148			0.0956449
$225$	6.66171	+	28.9236i	0.444114	+	1.92824i
$226$	−8.44028			−0.561439
$227$	−5.21246	−	16.0423i	−0.345963	−	1.06476i	−0.961066	−	0.276318i	$-0.910886\pi$
$227$	−5.21246	−	16.0423i	−0.345963	−	1.06476i	0.615103	−	0.788447i	$-0.289114\pi$
$228$	2.41843	−	1.75709i	0.160164	−	0.116366i
$229$	6.06507	−	4.40653i	0.400791	−	0.291192i	−0.369072	−	0.929401i	$-0.620324\pi$
$229$	6.06507	−	4.40653i	0.400791	−	0.291192i	0.769863	+	0.638209i	$0.220324\pi$
$230$	12.3596	+	9.83649i	0.814966	+	0.648599i
$231$	−11.1877	−	8.12836i	−0.736099	−	0.534807i
$232$	−9.60781			−0.630783
$233$	−17.0685	−	12.4010i	−1.11819	−	0.812416i	−0.134260	−	0.990946i	$-0.542866\pi$
$233$	−17.0685	−	12.4010i	−1.11819	−	0.812416i	−0.983934	+	0.178530i	$0.942866\pi$
$234$	4.84674	−	14.9167i	0.316841	−	0.975137i
$235$	20.2503	+	16.1164i	1.32099	+	1.05132i
$236$	3.57476	+	11.0020i	0.232697	+	0.716169i
$237$	−5.04446	+	15.5253i	−0.327673	+	1.00847i
$238$	−0.634583	+	1.95304i	−0.0411339	+	0.126597i
$239$	−0.914290	−	2.81389i	−0.0591405	−	0.182016i	0.917122	−	0.398607i	$-0.130506\pi$
$239$	−0.914290	−	2.81389i	−0.0591405	−	0.182016i	−0.976262	+	0.216591i	$0.930506\pi$
$240$	5.57496	−	3.68790i	0.359862	−	0.238053i
$241$	−1.46210	+	4.49989i	−0.0941822	+	0.289863i	−0.987040	−	0.160476i	$-0.948697\pi$
$241$	−1.46210	+	4.49989i	−0.0941822	+	0.289863i	0.892857	+	0.450339i	$0.148697\pi$
$242$	0.450220	+	0.327104i	0.0289412	+	0.0210270i
$243$	−1.13275			−0.0726659
$244$	−6.44652	−	4.68367i	−0.412696	−	0.299842i
$245$	2.95568	+	10.6686i	0.188832	+	0.681592i
$246$	−5.52640	+	4.01516i	−0.352350	+	0.255997i
$247$	2.13756	−	1.55303i	0.136010	−	0.0988169i
$248$	0.124747	+	0.383933i	0.00792147	+	0.0243798i
$249$	−9.99455			−0.633379
$250$	−4.82112	+	10.0875i	−0.304915	+	0.637987i
$251$	11.1575			0.704255			0.352128	−	0.935952i	$-0.385458\pi$
$251$	11.1575			0.704255			0.352128	+	0.935952i	$0.385458\pi$
$252$	2.62588	+	8.08161i	0.165415	+	0.509094i
$253$	−18.4690	+	13.4185i	−1.16114	+	0.843617i
$254$	−7.83830	+	5.69486i	−0.491819	+	0.357327i
$255$	2.56019	+	9.24107i	0.160325	+	0.578699i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	6.14754			0.383473			0.191737	−	0.981446i	$-0.438588\pi$
$257$	6.14754			0.383473			0.191737	+	0.981446i	$0.438588\pi$
$258$	−1.66091	−	1.20672i	−0.103404	−	0.0751273i
$259$	−4.14910	+	12.7696i	−0.257812	+	0.793465i
$260$	4.92751	−	3.25961i	0.305591	−	0.202152i
$261$	−17.6243	−	54.2421i	−1.09092	−	3.35750i
$262$	−0.317608	+	0.977498i	−0.0196219	+	0.0603900i
$263$	−6.99427	+	21.5261i	−0.431285	+	1.32736i	0.465561	+	0.885016i	$0.345853\pi$
$263$	−6.99427	+	21.5261i	−0.431285	+	1.32736i	−0.896846	+	0.442343i	$0.854147\pi$
$264$	2.98525	+	9.18766i	0.183730	+	0.565461i
$265$	−11.2707	−	8.96991i	−0.692354	−	0.551017i
$266$	−0.442352	+	1.36142i	−0.0271223	+	0.0834740i
$267$	15.4814	+	11.2479i	0.947444	+	0.688358i
$268$	−13.3681			−0.816586
$269$	−12.8458	−	9.33302i	−0.783222	−	0.569044i	0.122722	−	0.992441i	$-0.460838\pi$
$269$	−12.8458	−	9.33302i	−0.783222	−	0.569044i	−0.905944	+	0.423397i	$0.860838\pi$
$270$	15.3566	+	12.2217i	0.934575	+	0.743791i
$271$	−20.3093	+	14.7556i	−1.23370	+	0.896337i	−0.997162	−	0.0752849i	$-0.976013\pi$
$271$	−20.3093	+	14.7556i	−1.23370	+	0.896337i	−0.236540	+	0.971622i	$0.576013\pi$
$272$	1.16059	−	0.843216i	0.0703709	−	0.0511275i
$273$	3.49386	+	10.7530i	0.211458	+	0.650800i
$274$	−2.30982			−0.139541
$275$	−12.1892	−	10.6071i	−0.735039	−	0.639630i
$276$	21.1173			1.27111
$277$	−0.0560265	−	0.172432i	−0.00336631	−	0.0103604i	0.949359	−	0.314193i	$-0.101734\pi$
$277$	−0.0560265	−	0.172432i	−0.00336631	−	0.0103604i	−0.952726	+	0.303832i	$0.901734\pi$
$278$	−9.86123	+	7.16460i	−0.591437	+	0.429704i
$279$	−1.93871	+	1.40856i	−0.116068	+	0.0843280i
$280$	−1.12175	+	2.99789i	−0.0670376	+	0.179158i
$281$	−16.9129	−	12.2879i	−1.00894	−	0.733036i	−0.0449520	−	0.998989i	$-0.514314\pi$
$281$	−16.9129	−	12.2879i	−1.00894	−	0.733036i	−0.963986	+	0.265953i	$0.914314\pi$
$282$	34.5994			2.06036
$283$	0.411824	+	0.299208i	0.0244804	+	0.0177861i	0.599958	−	0.800031i	$-0.295184\pi$
$283$	0.411824	+	0.299208i	0.0244804	+	0.0177861i	−0.575478	+	0.817817i	$0.695184\pi$
$284$	5.03521	−	15.4968i	0.298785	−	0.919565i
$285$	1.78465	+	6.44173i	0.105713	+	0.381575i
$286$	2.63856	+	8.12064i	0.156021	+	0.480184i
$287$	1.01083	−	3.11101i	0.0596672	−	0.183637i
$288$	1.83438	−	5.64563i	0.108092	−	0.332672i
$289$	−4.61734	−	14.2107i	−0.271608	−	0.835924i
$290$	7.52898	−	20.1212i	0.442117	−	1.18156i
$291$	5.92805	−	18.2447i	0.347508	−	1.06952i
$292$	−9.98068	−	7.25139i	−0.584075	−	0.424355i
$293$	1.59058			0.0929229			0.0464615	−	0.998920i	$-0.485206\pi$
$293$	1.59058			0.0929229			0.0464615	+	0.998920i	$0.485206\pi$
$294$	11.9733	+	8.69911i	0.698297	+	0.507343i
$295$	−25.8423	−	1.13502i	−1.50460	−	0.0660837i
$296$	7.58827	−	5.51320i	0.441059	−	0.320448i
$297$	−22.9476	+	16.6724i	−1.33155	+	0.967430i
$298$	−2.66430	−	8.19988i	−0.154339	−	0.475006i
$299$	18.6649			1.07942
$300$	3.35471	+	14.5654i	0.193684	+	0.840932i
$301$	0.983103			0.0566651
$302$	1.06000	+	3.26234i	0.0609961	+	0.187727i
$303$	−27.9905	+	20.3363i	−1.60801	+	1.16829i
$304$	0.809017	−	0.587785i	0.0464003	−	0.0337118i
$305$	14.8605	−	9.83042i	0.850911	−	0.562888i
$306$	6.88944	+	5.00547i	0.393843	+	0.286144i
$307$	−22.3590			−1.27609			−0.638047	−	0.769998i	$-0.720257\pi$
$307$	−22.3590			−1.27609			−0.638047	+	0.769998i	$0.720257\pi$
$308$	−3.74254	−	2.71911i	−0.213251	−	0.154936i
$309$	−4.83481	+	14.8800i	−0.275043	+	0.846495i
$310$	−0.901812	−	0.0396086i	−0.0512195	−	0.00224962i
$311$	−9.32390	−	28.6960i	−0.528710	−	1.62720i	−0.756861	−	0.653576i	$-0.773268\pi$
$311$	−9.32390	−	28.6960i	−0.528710	−	1.62720i	0.228151	−	0.973626i	$-0.426732\pi$
$312$	2.44073	−	7.51179i	0.138179	−	0.425271i
$313$	0.178313	−	0.548791i	0.0100789	−	0.0310195i	−0.945891	−	0.324486i	$-0.894809\pi$
$313$	0.178313	−	0.548791i	0.0100789	−	0.0310195i	0.955969	+	0.293466i	$0.0948088\pi$
$314$	2.61748	+	8.05577i	0.147713	+	0.454613i
$315$	−18.9827	−	0.833743i	−1.06955	−	0.0469761i
$316$	−1.68748	+	5.19354i	−0.0949283	+	0.292159i
$317$	−24.3311	−	17.6776i	−1.36657	−	0.992872i	−0.997996	−	0.0632745i	$-0.979846\pi$
$317$	−24.3311	−	17.6776i	−1.36657	−	0.992872i	−0.368575	−	0.929598i	$-0.620154\pi$
$318$	−19.2569			−1.07988
$319$	25.1191	+	18.2501i	1.40640	+	1.02181i
$320$	1.86495	−	1.23368i	0.104254	−	0.0689650i
$321$	−14.7353	+	10.7058i	−0.822445	+	0.597542i
$322$	−8.18101	+	5.94386i	−0.455910	+	0.331238i
$323$	0.443305	+	1.36435i	0.0246661	+	0.0759146i
$324$	8.42957			0.468309
$325$	2.96511	+	12.8738i	0.164475	+	0.714111i
$326$	−9.23164			−0.511293
$327$	−11.7600	−	36.1937i	−0.650332	−	2.00152i
$328$	−1.84870	+	1.34316i	−0.102077	+	0.0741635i
$329$	−13.4041	+	9.73861i	−0.738989	+	0.536907i
$330$	−21.5807	−	0.947848i	−1.18798	−	0.0521773i
$331$	16.3305	+	11.8648i	0.897604	+	0.652147i	0.937849	−	0.347043i	$-0.112814\pi$
$331$	16.3305	+	11.8648i	0.897604	+	0.652147i	−0.0402457	+	0.999190i	$0.512814\pi$
$332$	−3.34339			−0.183493
$333$	45.0452	+	32.7273i	2.46846	+	1.79344i
$334$	2.52414	−	7.76851i	0.138115	−	0.425074i
$335$	10.4757	−	27.9962i	0.572346	−	1.52960i
$336$	1.32234	+	4.06975i	0.0721397	+	0.222023i
$337$	−1.36482	+	4.20048i	−0.0743464	+	0.228815i	−0.981323	−	0.192366i	$-0.938384\pi$
$337$	−1.36482	+	4.20048i	−0.0743464	+	0.228815i	0.906977	+	0.421180i	$0.138384\pi$
$338$	−1.85995	+	5.72434i	−0.101168	+	0.311363i
$339$	−7.79678	−	23.9960i	−0.423463	−	1.30328i
$340$	0.856440	+	3.09134i	0.0464470	+	0.167651i
$341$	0.403139	−	1.24073i	0.0218312	−	0.0671895i
$342$	4.80246	+	3.48919i	0.259687	+	0.188674i
$343$	−17.1074			−0.923715
$344$	−0.555611	−	0.403675i	−0.0299565	−	0.0217647i
$345$	−16.5482	+	44.2252i	−0.890926	+	2.38100i
$346$	2.84218	−	2.06496i	0.152796	−	0.111013i
$347$	17.3209	−	12.5844i	0.929836	−	0.675565i	−0.0161166	−	0.999870i	$-0.505130\pi$
$347$	17.3209	−	12.5844i	0.929836	−	0.675565i	0.945953	+	0.324305i	$0.105130\pi$
$348$	−8.87528	−	27.3153i	−0.475765	−	1.46425i
$349$	4.61288			0.246922			0.123461	−	0.992349i	$-0.460601\pi$
$349$	4.61288			0.246922			0.123461	+	0.992349i	$0.460601\pi$
$350$	−5.39932	−	4.69849i	−0.288606	−	0.251145i
$351$	23.1909			1.23784
$352$	0.998632	+	3.07347i	0.0532272	+	0.163817i
$353$	2.82544	−	2.05280i	0.150383	−	0.109260i	−0.510049	−	0.860145i	$-0.670373\pi$
$353$	2.82544	−	2.05280i	0.150383	−	0.109260i	0.660433	+	0.750885i	$0.270373\pi$
$354$	−27.9768	+	20.3263i	−1.48695	+	1.08033i
$355$	28.5085	+	22.6888i	1.51308	+	1.20420i
$356$	5.17885	+	3.76266i	0.274479	+	0.199420i
$357$	−6.13877			−0.324898
$358$	12.2059	+	8.86813i	0.645103	+	0.468695i
$359$	−7.87885	+	24.2486i	−0.415830	+	1.27979i	0.495677	+	0.868507i	$0.334920\pi$
$359$	−7.87885	+	24.2486i	−0.415830	+	1.27979i	−0.911506	+	0.411286i	$0.865080\pi$
$360$	10.3859	+	8.26575i	0.547387	+	0.435643i
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	−4.60428	+	14.1705i	−0.241996	+	0.744787i
$363$	−0.514073	+	1.58215i	−0.0269818	+	0.0830416i
$364$	1.16877	+	3.59711i	0.0612602	+	0.188540i
$365$	23.0075	−	15.2197i	1.20427	−	0.796636i
$366$	7.36082	−	22.6543i	0.384756	−	1.18416i
$367$	21.5338	+	15.6452i	1.12405	+	0.816673i	0.984819	−	0.173586i	$-0.0555355\pi$
$367$	21.5338	+	15.6452i	1.12405	+	0.816673i	0.139235	+	0.990259i	$0.455536\pi$
$368$	7.06421			0.368248
$369$	−10.9742	−	7.97321i	−0.571293	−	0.415069i
$370$	5.59967	+	20.2121i	0.291113	+	1.05078i
$371$	7.46028	−	5.42021i	0.387318	−	0.281403i
$372$	−0.976299	+	0.709322i	−0.0506187	+	0.0367767i
$373$	−9.86099	−	30.3490i	−0.510583	−	1.57141i	−0.791178	−	0.611585i	$-0.790532\pi$
$373$	−9.86099	−	30.3490i	−0.510583	−	1.57141i	0.280596	−	0.959826i	$-0.409468\pi$
$374$	−4.63600			−0.239722
$375$	−33.1325	−	4.38824i	−1.71096	−	0.226608i
$376$	11.5742			0.596896
$377$	−7.84455	−	24.1430i	−0.404015	−	1.24343i
$378$	−10.1648	+	7.38517i	−0.522822	+	0.379852i
$379$	−7.18738	+	5.22193i	−0.369191	+	0.268233i	−0.756875	−	0.653559i	$-0.773275\pi$
$379$	−7.18738	+	5.22193i	−0.369191	+	0.268233i	0.387685	+	0.921792i	$0.373275\pi$
$380$	0.597004	+	2.15490i	0.0306256	+	0.110544i
$381$	−23.4314	−	17.0239i	−1.20043	−	0.872160i
$382$	5.38199			0.275367
$383$	−16.0910	−	11.6908i	−0.822213	−	0.597373i	0.0951324	−	0.995465i	$-0.469673\pi$
$383$	−16.0910	−	11.6908i	−0.822213	−	0.597373i	−0.917346	+	0.398092i	$0.869673\pi$
$384$	0.923758	−	2.84303i	0.0471403	−	0.145083i
$385$	8.62730	−	5.70706i	0.439688	−	0.290859i
$386$	4.78602	+	14.7299i	0.243602	+	0.749730i
$387$	1.25980	−	3.87727i	0.0640393	−	0.197093i
$388$	1.98306	−	6.10324i	0.100675	−	0.309845i
$389$	−1.78444	−	5.49193i	−0.0904746	−	0.278452i	0.895573	−	0.444914i	$-0.146766\pi$
$389$	−1.78444	−	5.49193i	−0.0904746	−	0.278452i	−0.986048	+	0.166462i	$0.946766\pi$
$390$	13.8190	+	10.9980i	0.699752	+	0.556905i
$391$	−3.13160	+	9.63807i	−0.158372	+	0.487418i
$392$	4.00533	+	2.91004i	0.202300	+	0.146979i
$393$	−3.07245			−0.154985
$394$	2.37440	+	1.72510i	0.119621	+	0.0869094i
$395$	−9.55425	−	7.60385i	−0.480727	−	0.382591i
$396$	−15.5198	+	11.2758i	−0.779900	+	0.566631i
$397$	4.23920	−	3.07996i	0.212759	−	0.154579i	−0.476302	−	0.879282i	$-0.658023\pi$
$397$	4.23920	−	3.07996i	0.212759	−	0.154579i	0.689061	+	0.724703i	$0.258023\pi$
$398$	4.55532	+	14.0198i	0.228338	+	0.702751i
$399$	−4.27919			−0.214227
$400$	1.12222	+	4.87243i	0.0561112	+	0.243622i
$401$	37.3737			1.86635			0.933177	−	0.359417i	$-0.117024\pi$
$401$	37.3737			1.86635			0.933177	+	0.359417i	$0.117024\pi$
$402$	−12.3489	−	38.0059i	−0.615906	−	1.89556i
$403$	−0.862916	+	0.626945i	−0.0429849	+	0.0312303i
$404$	−9.36344	+	6.80294i	−0.465849	+	0.338459i
$405$	−6.60568	+	17.6537i	−0.328239	+	0.877220i
$406$	11.1267	+	8.08404i	0.552210	+	0.401204i
$407$	−30.3116			−1.50249
$408$	3.46939	+	2.52066i	0.171760	+	0.124791i
$409$	9.29268	−	28.5999i	0.459494	−	1.41418i	−0.406284	−	0.913747i	$-0.633176\pi$
$409$	9.29268	−	28.5999i	0.459494	−	1.41418i	0.865778	−	0.500429i	$-0.166824\pi$
$410$	−1.36422	−	4.92420i	−0.0673742	−	0.243189i
$411$	−2.13372	−	6.56690i	−0.105248	−	0.323921i
$412$	−1.61735	+	4.97769i	−0.0796811	+	0.245233i
$413$	5.11721	−	15.7491i	0.251801	−	0.774965i
$414$	12.9584	+	39.8819i	0.636872	+	1.96009i
$415$	2.61999	−	7.00193i	0.128610	−	0.343711i
$416$	0.816476	−	2.51286i	0.0400310	−	0.123203i
$417$	−29.4786	−	21.4174i	−1.44357	−	1.04882i
$418$	−3.23164			−0.158065
$419$	7.20660	+	5.23590i	0.352065	+	0.255790i	0.749735	−	0.661738i	$-0.230181\pi$
$419$	7.20660	+	5.23590i	0.352065	+	0.255790i	−0.397670	+	0.917529i	$0.630181\pi$
$420$	−9.55934	−	0.419857i	−0.466448	−	0.0204869i
$421$	−22.6916	+	16.4864i	−1.10592	+	0.803499i	−0.982017	−	0.188795i	$-0.939542\pi$
$421$	−22.6916	+	16.4864i	−1.10592	+	0.803499i	−0.123906	+	0.992294i	$0.539542\pi$
$422$	5.85843	−	4.25640i	0.285184	−	0.207198i
$423$	21.2315	+	65.3439i	1.03231	+	3.17713i
$424$	−6.44186			−0.312845
$425$	−7.14520	−	0.628864i	−0.346593	−	0.0305044i
$426$	48.7092			2.35997
$427$	3.52481	+	10.8483i	0.170578	+	0.524984i
$428$	−4.92929	+	3.58134i	−0.238266	+	0.173110i
$429$	−20.6499	+	15.0030i	−0.996985	+	0.724352i
$430$	1.28079	−	0.847261i	0.0617654	−	0.0408586i
$431$	14.1171	+	10.2567i	0.679997	+	0.494047i	0.873357	−	0.487081i	$-0.161938\pi$
$431$	14.1171	+	10.2567i	0.679997	+	0.494047i	−0.193360	+	0.981128i	$0.561938\pi$
$432$	8.77720			0.422293
$433$	7.83409	+	5.69180i	0.376482	+	0.273530i	0.759894	−	0.650047i	$-0.225251\pi$
$433$	7.83409	+	5.69180i	0.376482	+	0.273530i	−0.383411	+	0.923578i	$0.625251\pi$
$434$	0.178574	−	0.549593i	0.00857181	−	0.0263813i
$435$	64.1603	+	2.81799i	3.07625	+	0.135113i
$436$	−3.93399	−	12.1076i	−0.188404	−	0.579848i
$437$	−2.18296	+	6.71847i	−0.104425	+	0.321388i
$438$	11.3962	−	35.0739i	0.544532	−	1.67590i
$439$	−8.93830	−	27.5092i	−0.426602	−	1.31294i	−0.901452	−	0.432878i	$-0.857498\pi$
$439$	−8.93830	−	27.5092i	−0.426602	−	1.31294i	0.474851	−	0.880066i	$-0.342502\pi$
$440$	−7.21921	−	0.317076i	−0.344162	−	0.0151160i
$441$	−9.08174	+	27.9507i	−0.432464	+	1.33099i
$442$	3.06647	+	2.22792i	0.145857	+	0.105971i
$443$	17.0891			0.811930			0.405965	−	0.913889i	$-0.366936\pi$
$443$	17.0891			0.811930			0.405965	+	0.913889i	$0.366936\pi$
$444$	22.6839	+	16.4809i	1.07653	+	0.782147i
$445$	−11.9383	+	7.89732i	−0.565929	+	0.374369i
$446$	19.8237	−	14.4028i	0.938680	−	0.681991i
$447$	20.8514	−	15.1494i	0.986236	−	0.716542i
$448$	0.442352	+	1.36142i	0.0208992	+	0.0643210i
$449$	12.4293			0.586577			0.293288	−	0.956024i	$-0.405250\pi$
$449$	12.4293			0.586577			0.293288	+	0.956024i	$0.405250\pi$
$450$	−25.4494	+	15.2735i	−1.19969	+	0.720002i
$451$	7.38468			0.347731
$452$	−2.60819	−	8.02719i	−0.122679	−	0.377567i
$453$	−8.29576	+	6.02722i	−0.389769	+	0.283184i
$454$	13.6464	−	9.91468i	0.640457	−	0.465319i
$455$	−8.44916	−	0.371097i	−0.396103	−	0.0173973i
$456$	2.41843	+	1.75709i	0.113253	+	0.0822833i
$457$	−3.77197			−0.176445			−0.0882226	−	0.996101i	$-0.528119\pi$
$457$	−3.77197			−0.176445			−0.0882226	+	0.996101i	$0.528119\pi$
$458$	6.06507	+	4.40653i	0.283402	+	0.205904i
$459$	−3.89098	+	11.9752i	−0.181615	+	0.558954i
$460$	−5.53574	+	14.7943i	−0.258105	+	0.689787i
$461$	6.63404	+	20.4175i	0.308978	+	0.950936i	0.978163	+	0.207840i	$0.0666435\pi$
$461$	6.63404	+	20.4175i	0.308978	+	0.950936i	−0.669185	+	0.743096i	$0.733357\pi$
$462$	4.27333	−	13.1520i	0.198813	−	0.611885i
$463$	10.6372	−	32.7379i	0.494352	−	1.52146i	−0.323611	−	0.946190i	$-0.604897\pi$
$463$	10.6372	−	32.7379i	0.494352	−	1.52146i	0.817963	−	0.575270i	$-0.195103\pi$
$464$	−2.96898	−	9.13757i	−0.137831	−	0.424201i
$465$	−0.720447	−	2.60047i	−0.0334099	−	0.120594i
$466$	6.51959	−	20.0652i	0.302014	−	0.929504i
$467$	−2.18202	−	1.58533i	−0.100972	−	0.0733603i	0.536154	−	0.844120i	$-0.319877\pi$
$467$	−2.18202	−	1.58533i	−0.100972	−	0.0733603i	−0.637126	+	0.770760i	$0.719877\pi$
$468$	15.6844			0.725011
$469$	15.4815	+	11.2480i	0.714869	+	0.519382i
$470$	−9.06994	+	24.2395i	−0.418365	+	1.11808i
$471$	−20.4849	+	14.8832i	−0.943895	+	0.685780i
$472$	−9.35885	+	6.79961i	−0.430776	+	0.312977i
$473$	0.685833	+	2.11078i	0.0315347	+	0.0970537i
$474$	−16.3242			−0.749797
$475$	−4.98075	−	0.438366i	−0.228532	−	0.0201136i
$476$	−2.05355			−0.0941244
$477$	−11.8168	−	36.3684i	−0.541054	−	1.66519i
$478$	2.39364	−	1.73908i	0.109483	−	0.0795438i
$479$	3.37007	−	2.44850i	0.153983	−	0.111875i	−0.508126	−	0.861283i	$-0.669662\pi$
$479$	3.37007	−	2.44850i	0.153983	−	0.111875i	0.662109	+	0.749408i	$0.269662\pi$
$480$	5.23016	+	4.16248i	0.238723	+	0.189990i
$481$	20.0495	+	14.5668i	0.914180	+	0.664191i
$482$	−4.73146			−0.215512
$483$	−24.4559	−	17.7682i	−1.11278	−	0.808482i
$484$	−0.171969	+	0.529265i	−0.00781676	+	0.0240575i
$485$	11.2278	+	8.93573i	0.509827	+	0.405751i
$486$	−0.350039	−	1.07731i	−0.0158781	−	0.0488677i
$487$	−11.6856	+	35.9646i	−0.529525	+	1.62971i	0.225665	+	0.974205i	$0.427544\pi$
$487$	−11.6856	+	35.9646i	−0.529525	+	1.62971i	−0.755190	+	0.655506i	$0.772456\pi$
$488$	2.46235	−	7.57834i	0.111465	−	0.343056i
$489$	−8.52780	−	26.2459i	−0.385640	−	1.18688i
$490$	−9.23309	+	6.10780i	−0.417108	+	0.275922i
$491$	−3.73591	+	11.4980i	−0.168599	+	0.518896i	−0.999283	−	0.0378484i	$-0.987950\pi$
$491$	−3.73591	+	11.4980i	−0.168599	+	0.518896i	0.830684	+	0.556744i	$0.187950\pi$
$492$	−5.52640	−	4.01516i	−0.249149	−	0.181017i
$493$	13.7830			0.620756
$494$	2.13756	+	1.55303i	0.0961735	+	0.0698741i
$495$	−11.4526	−	41.3386i	−0.514758	−	1.85803i
$496$	−0.326593	+	0.237284i	−0.0146645	+	0.0106544i
$497$	−18.8703	+	13.7101i	−0.846448	+	0.614981i
$498$	−3.08849	−	9.50538i	−0.138398	−	0.425946i
$499$	−25.3498			−1.13481			−0.567407	−	0.823438i	$-0.692053\pi$
$499$	−25.3498			−1.13481			−0.567407	+	0.823438i	$0.692053\pi$
$500$	−11.0836	−	1.46796i	−0.495671	−	0.0656493i
$501$	24.4178			1.09091
$502$	3.44786	+	10.6114i	0.153885	+	0.473610i
$503$	23.4249	−	17.0192i	1.04446	−	0.758848i	0.0733124	−	0.997309i	$-0.476643\pi$
$503$	23.4249	−	17.0192i	1.04446	−	0.758848i	0.971152	+	0.238461i	$0.0766430\pi$
$504$	−6.87463	+	4.99471i	−0.306220	+	0.222482i
$505$	−6.90963	−	24.9405i	−0.307474	−	1.10984i
$506$	−18.4690	−	13.4185i	−0.821049	−	0.596527i
$507$	−17.9926			−0.799080
$508$	−7.83830	−	5.69486i	−0.347768	−	0.252669i
$509$	2.18039	−	6.71056i	0.0966443	−	0.297440i	−0.891034	−	0.453936i	$-0.850020\pi$
$509$	2.18039	−	6.71056i	0.0966443	−	0.297440i	0.987679	+	0.156495i	$0.0500196\pi$
$510$	−7.99764	+	5.29054i	−0.354141	+	0.234269i
$511$	5.45721	+	16.7956i	0.241413	+	0.742992i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−2.71231	+	8.34762i	−0.119751	+	0.368556i
$514$	1.89969	+	5.84666i	0.0837920	+	0.257885i
$515$	−9.15717	−	7.28782i	−0.403513	−	0.321140i
$516$	0.634412	−	1.95252i	0.0279284	−	0.0859549i
$517$	−30.2603	−	21.9854i	−1.33085	−	0.966917i
$518$	−13.4268			−0.589938
$519$	8.49624	+	6.17288i	0.372943	+	0.270959i
$520$	4.62275	+	3.67907i	0.202721	+	0.161338i
$521$	22.0443	−	16.0161i	0.965779	−	0.701679i	0.0112932	−	0.999936i	$-0.496405\pi$
$521$	22.0443	−	16.0161i	0.965779	−	0.701679i	0.954486	+	0.298257i	$0.0964052\pi$
$522$	46.1411	−	33.5235i	2.01954	−	1.46728i
$523$	11.2246	+	34.5457i	0.490817	+	1.51058i	0.823376	+	0.567496i	$0.192088\pi$
$523$	11.2246	+	34.5457i	0.490817	+	1.51058i	−0.332560	+	0.943082i	$0.607912\pi$
$524$	−1.02780			−0.0448998
$525$	8.37029	−	19.6907i	0.365309	−	0.859374i
$526$	−22.6339			−0.986886
$527$	−0.178958	−	0.550777i	−0.00779555	−	0.0239922i
$528$	−7.81549	+	5.67829i	−0.340126	+	0.247116i
$529$	−21.7651	+	15.8132i	−0.946307	+	0.687532i
$530$	5.04805	−	13.4909i	0.219273	−	0.586009i
$531$	−55.5557	−	40.3636i	−2.41091	−	1.75163i
$532$	−1.43148			−0.0620626
$533$	−4.88458	−	3.54886i	−0.211575	−	0.153718i
$534$	−5.91335	+	18.1994i	−0.255896	+	0.787566i
$535$	−3.63750	−	13.1296i	−0.157263	−	0.567644i
$536$	−4.13097	−	12.7138i	−0.178431	−	0.549153i
$537$	−13.9371	+	42.8939i	−0.601428	+	1.85101i
$538$	4.90666	−	15.1011i	0.211541	−	0.651056i
$539$	−4.94409	−	15.2163i	−0.212957	−	0.655414i
$540$	−6.87809	+	18.3817i	−0.295986	+	0.791024i
$541$	−5.57345	+	17.1533i	−0.239621	+	0.737478i	0.756853	+	0.653585i	$0.226736\pi$
$541$	−5.57345	+	17.1533i	−0.239621	+	0.737478i	−0.996475	+	0.0838937i	$0.973264\pi$
$542$	−20.3093	−	14.7556i	−0.872359	−	0.633806i
$543$	−44.5405			−1.91142
$544$	1.16059	+	0.843216i	0.0497598	+	0.0361526i
$545$	28.4392	+	1.24908i	1.21820	+	0.0535048i
$546$	−9.14703	+	6.64571i	−0.391457	+	0.284410i
$547$	26.8888	−	19.5359i	1.14968	−	0.835293i	0.161243	−	0.986915i	$-0.448450\pi$
$547$	26.8888	−	19.5359i	1.14968	−	0.835293i	0.988439	+	0.151622i	$0.0484496\pi$
$548$	−0.713774	−	2.19677i	−0.0304909	−	0.0938414i
$549$	47.3014			2.01877
$550$	6.32124	−	14.8704i	0.269538	−	0.634077i
$551$	9.60781			0.409306
$552$	6.52562	+	20.0838i	0.277749	+	0.854823i
$553$	6.32413	−	4.59475i	0.268929	−	0.195388i
$554$	0.146679	−	0.106569i	0.00623180	−	0.00452767i
$555$	−52.2910	+	34.5911i	−2.21963	+	1.46831i
$556$	−9.86123	−	7.16460i	−0.418209	−	0.303847i
$557$	−10.1173			−0.428686			−0.214343	−	0.976758i	$-0.568761\pi$
$557$	−10.1173			−0.428686			−0.214343	+	0.976758i	$0.568761\pi$
$558$	−1.93871	−	1.40856i	−0.0820722	−	0.0596289i
$559$	0.560734	−	1.72576i	0.0237165	−	0.0729919i
$560$	−3.19781	−	0.140451i	−0.135132	−	0.00593515i
$561$	−4.28254	−	13.1803i	−0.180809	−	0.556472i
$562$	6.46015	−	19.8823i	0.272505	−	0.838684i
$563$	−4.79149	+	14.7467i	−0.201937	+	0.621498i	0.797888	+	0.602805i	$0.205950\pi$
$563$	−4.79149	+	14.7467i	−0.201937	+	0.621498i	−0.999825	+	0.0186929i	$0.994050\pi$
$564$	10.6918	+	32.9060i	0.450206	+	1.38559i
$565$	18.8549	+	0.828128i	0.793230	+	0.0348396i
$566$	−0.157303	+	0.484129i	−0.00661193	+	0.0203494i
$567$	−9.76222	−	7.09267i	−0.409975	−	0.297864i
$568$	16.2943			0.683693
$569$	−14.8284	−	10.7735i	−0.621641	−	0.451648i	0.231854	−	0.972751i	$-0.425521\pi$
$569$	−14.8284	−	10.7735i	−0.621641	−	0.451648i	−0.853494	+	0.521102i	$0.825521\pi$
$570$	−5.57496	+	3.68790i	−0.233509	+	0.154469i
$571$	−25.7452	+	18.7050i	−1.07740	+	0.782780i	−0.977228	−	0.212190i	$-0.931940\pi$
$571$	−25.7452	+	18.7050i	−1.07740	+	0.782780i	−0.100176	+	0.994970i	$0.531940\pi$
$572$	−6.90783	+	5.01883i	−0.288831	+	0.209848i
$573$	4.97165	+	15.3012i	0.207694	+	0.639216i
$574$	3.27110			0.136533
$575$	−26.6451	−	23.1865i	−1.11118	−	0.966946i
$576$	5.93617			0.247340
$577$	5.87868	+	18.0927i	0.244733	+	0.753209i	0.995680	+	0.0928477i	$0.0295970\pi$
$577$	5.87868	+	18.0927i	0.244733	+	0.753209i	−0.750948	+	0.660362i	$0.770403\pi$
$578$	12.0884	−	8.78270i	0.502809	−	0.365312i
$579$	−37.4564	+	27.2136i	−1.55663	+	1.13096i
$580$	21.4630	+	0.942681i	0.891203	+	0.0391427i
$581$	3.87196	+	2.81314i	0.160636	+	0.116709i
$582$	19.1836			0.795185
$583$	16.8419	+	12.2364i	0.697522	+	0.506779i
$584$	3.81228	−	11.7330i	0.157753	−	0.485514i
$585$	−12.2908	+	32.8471i	−0.508161	+	1.35806i
$586$	0.491517	+	1.51274i	0.0203044	+	0.0624905i
$587$	12.6604	−	38.9646i	0.522549	−	1.60824i	−0.246562	−	0.969127i	$-0.579301\pi$
$587$	12.6604	−	38.9646i	0.522549	−	1.60824i	0.769111	−	0.639115i	$-0.220699\pi$
$588$	−4.57339	+	14.0755i	−0.188604	+	0.580462i
$589$	−0.124747	−	0.383933i	−0.00514013	−	0.0158197i
$590$	−6.90624	−	24.9282i	−0.284326	−	1.02628i
$591$	−2.71116	+	8.34408i	−0.111522	+	0.343230i
$592$	7.58827	+	5.51320i	0.311876	+	0.226591i
$593$	12.7517			0.523648			0.261824	−	0.965116i	$-0.415676\pi$
$593$	12.7517			0.523648			0.261824	+	0.965116i	$0.415676\pi$
$594$	−22.9476	−	16.6724i	−0.941551	−	0.684076i
$595$	1.60923	−	4.30067i	0.0659719	−	0.176310i
$596$	6.97523	−	5.06780i	0.285717	−	0.207585i
$597$	−35.6508	+	25.9019i	−1.45909	+	1.06009i
$598$	5.76776	+	17.7513i	0.235861	+	0.725907i
$599$	18.5533			0.758065			0.379033	−	0.925383i	$-0.376257\pi$
$599$	18.5533			0.758065			0.379033	+	0.925383i	$0.376257\pi$
$600$	−12.8158	+	7.69147i	−0.523204	+	0.314003i
$601$	39.2378			1.60054			0.800271	−	0.599638i	$-0.204689\pi$
$601$	39.2378			1.60054			0.800271	+	0.599638i	$0.204689\pi$
$602$	0.303796	+	0.934987i	0.0123818	+	0.0381072i
$603$	64.1997	−	46.6438i	2.61441	−	1.89948i
$604$	−2.77511	+	2.01624i	−0.112918	+	0.0820395i
$605$	−0.973658	−	0.774896i	−0.0395848	−	0.0315040i
$606$	−27.9905	−	20.3363i	−1.13704	−	0.826106i
$607$	−41.7289			−1.69372			−0.846861	−	0.531814i	$-0.821511\pi$
$607$	−41.7289			−1.69372			−0.846861	+	0.531814i	$0.821511\pi$
$608$	0.809017	+	0.587785i	0.0328100	+	0.0238378i
$609$	−12.7048	+	39.1014i	−0.514825	+	1.58447i
$610$	13.9414	+	11.0954i	0.564472	+	0.449241i
$611$	9.45010	+	29.0844i	0.382310	+	1.17663i
$612$	−2.63153	+	8.09902i	−0.106373	+	0.327383i
$613$	2.36486	−	7.27829i	0.0955158	−	0.293967i	−0.891872	−	0.452288i	$-0.850608\pi$
$613$	2.36486	−	7.27829i	0.0955158	−	0.293967i	0.987388	+	0.158321i	$0.0506080\pi$
$614$	−6.90930	−	21.2646i	−0.278837	−	0.858171i
$615$	12.7394	−	8.42730i	0.513704	−	0.339821i
$616$	1.42952	−	4.39962i	0.0575971	−	0.177266i
$617$	13.3809	+	9.72182i	0.538696	+	0.391386i	0.823601	−	0.567170i	$-0.191962\pi$
$617$	13.3809	+	9.72182i	0.538696	+	0.391386i	−0.284904	+	0.958556i	$0.591962\pi$
$618$	−15.6458			−0.629365
$619$	1.18554	+	0.861345i	0.0476508	+	0.0346204i	0.611356	−	0.791356i	$-0.290624\pi$
$619$	1.18554	+	0.861345i	0.0476508	+	0.0346204i	−0.563705	+	0.825976i	$0.690624\pi$
$620$	−0.241005	−	0.869914i	−0.00967900	−	0.0349366i
$621$	−50.1623	+	36.4451i	−2.01294	+	1.46249i
$622$	24.4103	−	17.7351i	0.978764	−	0.711113i
$623$	−2.83168	−	8.71501i	−0.113449	−	0.349160i
$624$	7.89836			0.316187
$625$	11.7597	−	22.0615i	0.470389	−	0.882459i
$626$	0.577033			0.0230629
$627$	−2.98525	−	9.18766i	−0.119219	−	0.366920i
$628$	−6.85265	+	4.97874i	−0.273450	+	0.198673i
$629$	−10.8859	+	7.90905i	−0.434048	+	0.315354i
$630$	−5.07304	−	18.3113i	−0.202115	−	0.729539i
$631$	−15.1306	−	10.9930i	−0.602338	−	0.437624i	0.244370	−	0.969682i	$-0.421419\pi$
$631$	−15.1306	−	10.9930i	−0.602338	−	0.437624i	−0.846708	+	0.532058i	$0.821419\pi$
$632$	−5.46081			−0.217219
$633$	17.5128	+	12.7238i	0.696073	+	0.505727i
$634$	9.29366	−	28.6029i	0.369098	−	1.13597i
$635$	18.0689	−	11.9528i	0.717041	−	0.474331i
$636$	−5.95072	−	18.3144i	−0.235961	−	0.726215i
$637$	−4.04226	+	12.4408i	−0.160160	+	0.492922i
$638$	−9.59466	+	29.5293i	−0.379856	+	1.16908i
$639$	29.8898	+	91.9915i	1.18242	+	3.63913i
$640$	1.74960	+	1.39244i	0.0691591	+	0.0550410i
$641$	−14.8589	+	45.7311i	−0.586893	+	1.80627i	0.00464007	+	0.999989i	$0.498523\pi$
$641$	−14.8589	+	45.7311i	−0.586893	+	1.80627i	−0.591533	+	0.806281i	$0.701477\pi$
$642$	−14.7353	−	10.7058i	−0.581557	−	0.422526i
$643$	−9.75085			−0.384536			−0.192268	−	0.981342i	$-0.561584\pi$
$643$	−9.75085			−0.384536			−0.192268	+	0.981342i	$0.561584\pi$
$644$	−8.18101	−	5.94386i	−0.322377	−	0.234221i
$645$	3.59194	+	2.85868i	0.141432	+	0.112560i
$646$	−1.16059	+	0.843216i	−0.0456627	+	0.0331759i
$647$	−20.3466	+	14.7827i	−0.799909	+	0.581168i	−0.910887	−	0.412655i	$-0.864601\pi$
$647$	−20.3466	+	14.7827i	−0.799909	+	0.581168i	0.110979	+	0.993823i	$0.464601\pi$
$648$	2.60488	+	8.01700i	0.102329	+	0.314937i
$649$	37.3842			1.46746
$650$	−11.3275	+	6.79821i	−0.444299	+	0.266648i
$651$	1.72747			0.0677049
$652$	−2.85273	−	8.77981i	−0.111722	−	0.343844i
$653$	0.0936469	−	0.0680384i	0.00366469	−	0.00266255i	−0.585951	−	0.810346i	$-0.699279\pi$
$653$	0.0936469	−	0.0680384i	0.00366469	−	0.00266255i	0.589616	+	0.807684i	$0.299279\pi$
$654$	30.7882	−	22.3689i	1.20391	−	0.874695i
$655$	0.805418	−	2.15248i	0.0314703	−	0.0841045i
$656$	−1.84870	−	1.34316i	−0.0721796	−	0.0524415i
$657$	73.2333			2.85710
$658$	−13.4041	−	9.73861i	−0.522544	−	0.379651i
$659$	−14.8818	+	45.8016i	−0.579714	+	1.78418i	0.0398209	+	0.999207i	$0.487321\pi$
$659$	−14.8818	+	45.8016i	−0.579714	+	1.78418i	−0.619535	+	0.784969i	$0.712679\pi$
$660$	−5.76734	−	20.8173i	−0.224493	−	0.810314i
$661$	−10.1786	−	31.3265i	−0.395901	−	1.21846i	−0.928257	−	0.371939i	$-0.878693\pi$
$661$	−10.1786	−	31.3265i	−0.395901	−	1.21846i	0.532356	−	0.846521i	$-0.321307\pi$
$662$	−6.23768	+	19.1976i	−0.242434	+	0.746137i
$663$	−3.50138	+	10.7761i	−0.135982	+	0.418511i
$664$	−1.03317	−	3.17976i	−0.0400946	−	0.123398i
$665$	1.12175	−	2.99789i	0.0434998	−	0.116253i
$666$	−17.2058	+	52.9539i	−0.666709	+	2.05192i
$667$	54.9093	+	39.8939i	2.12610	+	1.54470i
$668$	8.16830			0.316041
$669$	59.2598	+	43.0548i	2.29112	+	1.66459i
$670$	29.8632	+	1.31162i	1.15371	+	0.0506725i
$671$	−20.8328	+	15.1359i	−0.804243	+	0.584317i
$672$	−3.46194	+	2.51524i	−0.133547	+	0.0970276i
$673$	10.8225	+	33.3081i	0.417175	+	1.28393i	0.910291	+	0.413970i	$0.135858\pi$
$673$	10.8225	+	33.3081i	0.417175	+	1.28393i	−0.493115	+	0.869964i	$0.664142\pi$
$674$	−4.41665			−0.170123
$675$	−33.1062	−	28.8090i	−1.27426	−	1.10886i
$676$	−6.01892			−0.231497
$677$	−12.9826	−	39.9562i	−0.498960	−	1.53564i	−0.810693	−	0.585471i	$-0.800909\pi$
$677$	−12.9826	−	39.9562i	−0.498960	−	1.53564i	0.311733	−	0.950170i	$-0.399091\pi$
$678$	20.4122	−	14.8303i	0.783927	−	0.569556i
$679$	−7.43186	+	5.39956i	−0.285208	+	0.207216i
$680$	−2.67539	+	1.76980i	−0.102596	+	0.0678687i
$681$	40.7937	+	29.6384i	1.56322	+	1.13575i
$682$	1.30459			0.0499551
$683$	3.02696	+	2.19922i	0.115824	+	0.0841508i	0.644189	−	0.764866i	$-0.277195\pi$
$683$	3.02696	+	2.19922i	0.115824	+	0.0841508i	−0.528366	+	0.849017i	$0.677195\pi$
$684$	−1.83438	+	5.64563i	−0.0701391	+	0.215866i
$685$	5.15995	+	0.226631i	0.197151	+	0.00865912i
$686$	−5.28649	−	16.2701i	−0.201839	−	0.621197i
$687$	−6.92526	+	21.3138i	−0.264215	+	0.813171i
$688$	0.212225	−	0.653160i	0.00809099	−	0.0249015i
$689$	−5.25963	−	16.1875i	−0.200376	−	0.616694i
$690$	−47.1743	−	2.07195i	−1.79590	−	0.0788779i
$691$	−2.31081	+	7.11193i	−0.0879072	+	0.270550i	−0.985340	−	0.170600i	$-0.945429\pi$
$691$	−2.31081	+	7.11193i	−0.0879072	+	0.270550i	0.897433	+	0.441150i	$0.145429\pi$
$692$	2.84218	+	2.06496i	0.108043	+	0.0784981i
$693$	27.4609			1.04315
$694$	17.3209	+	12.5844i	0.657493	+	0.477697i
$695$	22.7321	−	15.0376i	0.862278	−	0.570407i
$696$	23.2358	−	16.8818i	0.880750	−	0.639903i
$697$	2.65208	−	1.92685i	0.100455	−	0.0729846i
$698$	1.42546	+	4.38711i	0.0539544	+	0.166055i
$699$	63.0686			2.38547
$700$	2.80004	−	6.58697i	0.105832	−	0.248964i
$701$	−28.7684			−1.08657			−0.543283	−	0.839549i	$-0.682819\pi$
$701$	−28.7684			−1.08657			−0.543283	+	0.839549i	$0.682819\pi$
$702$	7.16638	+	22.0558i	0.270478	+	0.832444i
$703$	−7.58827	+	5.51320i	−0.286197	+	0.207934i
$704$	−2.61445	+	1.89951i	−0.0985359	+	0.0715905i
$705$	−77.2921	−	3.39476i	−2.91099	−	0.127854i
$706$	2.82544	+	2.05280i	0.106337	+	0.0772583i
$707$	16.5677			0.623094
$708$	−27.9768	−	20.3263i	−1.05143	−	0.763911i
$709$	−5.48437	+	16.8791i	−0.205970	+	0.633909i	0.793703	+	0.608306i	$0.208151\pi$
$709$	−5.48437	+	16.8791i	−0.205970	+	0.633909i	−0.999672	+	0.0256033i	$0.991849\pi$
$710$	−12.7687	+	34.1244i	−0.479201	+	1.28067i
$711$	−10.0172	−	30.8297i	−0.375674	−	1.15620i
$712$	−1.97815	+	6.08811i	−0.0741341	+	0.228161i
$713$	0.881243	−	2.71219i	0.0330028	−	0.101572i
$714$	−1.89698	−	5.83832i	−0.0709929	−	0.218494i
$715$	−5.09755	−	18.3997i	−0.190637	−	0.688110i
$716$	−4.66225	+	14.3489i	−0.174236	+	0.536245i
$717$	7.15541	+	5.19871i	0.267224	+	0.194149i
$718$	−25.4965			−0.951521
$719$	−41.0266	−	29.8076i	−1.53003	−	1.11164i	−0.956219	−	0.292651i	$-0.905463\pi$
$719$	−41.0266	−	29.8076i	−1.53003	−	1.11164i	−0.573815	−	0.818985i	$-0.694537\pi$
$720$	−4.65177	+	12.4319i	−0.173361	+	0.463308i
$721$	6.06129	−	4.40378i	0.225734	−	0.164005i
$722$	−0.809017	+	0.587785i	−0.0301085	+	0.0218751i
$723$	−4.37072	−	13.4517i	−0.162549	−	0.500274i
$724$	−14.8998			−0.553746
$725$	−18.7933	+	44.2104i	−0.697966	+	1.64193i
$726$	−1.66358			−0.0617411
$727$	10.0290	+	30.8662i	0.371956	+	1.14476i	0.945509	+	0.325595i	$0.105565\pi$
$727$	10.0290	+	30.8662i	0.371956	+	1.14476i	−0.573553	+	0.819168i	$0.694435\pi$
$728$	−3.05988	+	2.22313i	−0.113407	+	0.0823948i
$729$	23.1985	−	16.8547i	0.859202	−	0.624247i
$730$	21.5845	+	17.1782i	0.798878	+	0.635795i
$731$	0.797060	+	0.579098i	0.0294803	+	0.0214187i
$732$	23.8201			0.880416
$733$	−15.6947	−	11.4029i	−0.579698	−	0.421175i	0.258917	−	0.965900i	$-0.416634\pi$
$733$	−15.6947	−	11.4029i	−0.579698	−	0.421175i	−0.838615	+	0.544724i	$0.816634\pi$
$734$	−8.22517	+	25.3145i	−0.303597	+	0.934374i
$735$	−25.8938	−	20.6078i	−0.955108	−	0.760132i
$736$	2.18296	+	6.71847i	0.0804650	+	0.247646i
$737$	−13.3498	+	41.0864i	−0.491746	+	1.51344i
$738$	4.19177	−	12.9009i	0.154301	−	0.474890i
$739$	−9.46481	−	29.1297i	−0.348169	−	1.07155i	−0.959865	−	0.280461i	$-0.909513\pi$
$739$	−9.46481	−	29.1297i	−0.348169	−	1.07155i	0.611697	−	0.791092i	$-0.290487\pi$
$740$	−17.4925	+	11.5715i	−0.643037	+	0.425376i
$741$	−2.44073	+	7.51179i	−0.0896623	+	0.275952i
$742$	7.46028	+	5.42021i	0.273875	+	0.198982i
$743$	−46.0385			−1.68899			−0.844495	−	0.535564i	$-0.820099\pi$
$743$	−46.0385			−1.68899			−0.844495	+	0.535564i	$0.820099\pi$
$744$	−0.976299	−	0.709322i	−0.0357928	−	0.0260050i
$745$	5.14728	+	18.5792i	0.188582	+	0.680691i
$746$	25.8164	−	18.7567i	0.945205	−	0.686732i
$747$	16.0565	−	11.6657i	0.587477	−	0.426827i
$748$	−1.43260	−	4.40909i	−0.0523811	−	0.161212i
$749$	8.72192			0.318692
$750$	−6.06504	−	32.8669i	−0.221464	−	1.20013i
$751$	11.4769			0.418797			0.209399	−	0.977830i	$-0.432849\pi$
$751$	11.4769			0.418797			0.209399	+	0.977830i	$0.432849\pi$
$752$	3.57664	+	11.0078i	0.130427	+	0.401412i
$753$	−26.9836	+	19.6047i	−0.983337	+	0.714436i
$754$	20.5373	−	14.9212i	0.747924	−	0.543399i
$755$	−2.04786	−	7.39179i	−0.0745292	−	0.269015i
$756$	−10.1648	−	7.38517i	−0.369691	−	0.268596i
$757$	−6.82134			−0.247926			−0.123963	−	0.992287i	$-0.539560\pi$
$757$	−6.82134			−0.247926			−0.123963	+	0.992287i	$0.539560\pi$
$758$	−7.18738	−	5.22193i	−0.261057	−	0.189669i
$759$	21.0885	−	64.9036i	0.765462	−	2.35585i
$760$	−1.86495	+	1.23368i	−0.0676487	+	0.0447504i
$761$	−0.277759	−	0.854854i	−0.0100688	−	0.0309884i	0.945896	−	0.324470i	$-0.105186\pi$
$761$	−0.277759	−	0.854854i	−0.0100688	−	0.0309884i	−0.955965	+	0.293482i	$0.905186\pi$
$762$	8.94999	−	27.5452i	0.324224	−	0.997858i
$763$	−5.63144	+	17.3318i	−0.203872	+	0.627453i
$764$	1.66313	+	5.11858i	0.0601698	+	0.185184i
$765$	−14.8993	−	11.8578i	−0.538685	−	0.428718i
$766$	6.14623	−	18.9161i	0.222072	−	0.683468i
$767$	−24.7277	−	17.9657i	−0.892866	−	0.648705i
$768$	2.98934			0.107869
$769$	6.19448	+	4.50055i	0.223379	+	0.162294i	0.693846	−	0.720123i	$-0.255915\pi$
$769$	6.19448	+	4.50055i	0.223379	+	0.162294i	−0.470468	+	0.882417i	$0.655915\pi$
$770$	8.09372	+	6.44147i	0.291678	+	0.232135i
$771$	−14.8674	+	10.8018i	−0.535436	+	0.389017i
$772$	−12.5300	+	9.10355i	−0.450963	+	0.327644i
$773$	−5.08241	−	15.6421i	−0.182802	−	0.562606i	0.817102	−	0.576493i	$-0.195579\pi$
$773$	−5.08241	−	15.6421i	−0.182802	−	0.562606i	−0.999904	+	0.0138877i	$0.995579\pi$
$774$	4.07680			0.146538
$775$	2.01068	+	0.176965i	0.0722259	+	0.00635675i
$776$	6.41732			0.230368
$777$	−12.4031	−	38.1727i	−0.444957	−	1.36944i
$778$	4.67172	−	3.39420i	0.167489	−	0.121688i
$779$	1.84870	−	1.34316i	0.0662365	−	0.0481237i
$780$	−6.18940	+	16.5412i	−0.221616	+	0.592270i
$781$	−42.6006	−	30.9511i	−1.52437	−	1.10752i
$782$	−10.1341			−0.362394
$783$	68.2241	+	49.5677i	2.43813	+	1.77141i
$784$	−1.52990	+	4.70855i	−0.0546393	+	0.168162i
$785$	−5.05682	−	18.2527i	−0.180486	−	0.651468i
$786$	−0.949440	−	2.92208i	−0.0338654	−	0.104227i
$787$	4.33015	−	13.3268i	0.154353	−	0.475051i	−0.843741	−	0.536750i	$-0.819652\pi$
$787$	4.33015	−	13.3268i	0.154353	−	0.475051i	0.998095	+	0.0616991i	$0.0196519\pi$
$788$	−0.906940	+	2.79128i	−0.0323084	+	0.0994351i
$789$	−20.9083	−	64.3490i	−0.744354	−	2.29088i
$790$	4.27926	−	11.4364i	0.152249	−	0.406887i
$791$	−3.73358	+	11.4908i	−0.132751	+	0.408565i
$792$	−15.5198	−	11.2758i	−0.551473	−	0.400668i
$793$	21.0537			0.747640
$794$	4.23920	+	3.07996i	0.150444	+	0.109304i
$795$	43.0183	+	1.88942i	1.52570	+	0.0670107i
$796$	−11.9260	+	8.66474i	−0.422705	+	0.307113i
$797$	44.6531	−	32.4424i	1.58169	−	1.14917i	0.666974	−	0.745081i	$-0.267589\pi$
$797$	44.6531	−	32.4424i	1.58169	−	1.14917i	0.914720	−	0.404087i	$-0.132411\pi$
$798$	−1.32234	−	4.06975i	−0.0468104	−	0.144068i
$799$	−16.6040			−0.587407
$800$	−4.28717	+	2.57296i	−0.151574	+	0.0909680i
$801$	−37.9998			−1.34266
$802$	11.5491	+	35.5445i	0.407813	+	1.25512i
$803$	−32.2540	+	23.4339i	−1.13822	+	0.826963i
$804$	32.3298	−	23.4889i	1.14018	−	0.828391i
$805$	18.8589	−	12.4754i	0.664688	−	0.439699i
$806$	−0.862916	−	0.626945i	−0.0303949	−	0.0220832i
$807$	47.4656			1.67087
$808$	−9.36344	−	6.80294i	−0.329405	−	0.239326i
$809$	10.7762	−	33.1659i	0.378873	−	1.16605i	−0.561956	−	0.827167i	$-0.689951\pi$
$809$	10.7762	−	33.1659i	0.378873	−	1.16605i	0.940829	−	0.338883i	$-0.110049\pi$
$810$	−18.8309	−	0.827076i	−0.661652	−	0.0290605i
$811$	1.82938	+	5.63026i	0.0642383	+	0.197705i	0.978024	−	0.208491i	$-0.0668551\pi$
$811$	1.82938	+	5.63026i	0.0642383	+	0.197705i	−0.913786	+	0.406196i	$0.866855\pi$
$812$	−4.25003	+	13.0803i	−0.149147	+	0.459027i
$813$	23.1897	−	71.3706i	0.813298	−	2.50308i
$814$	−9.36679	−	28.8280i	−0.328306	−	1.01042i
$815$	20.6227	+	0.905773i	0.722381	+	0.0317278i
$816$	−1.32519	+	4.07851i	−0.0463909	+	0.142777i
$817$	0.555611	+	0.403675i	0.0194384	+	0.0141228i
$818$	30.0718			1.05143
$819$	−18.1640	−	13.1969i	−0.634700	−	0.461137i
$820$	4.26162	−	2.81911i	0.148822	−	0.0984478i
$821$	36.7980	−	26.7353i	1.28426	−	0.933070i	0.284587	−	0.958650i	$-0.408143\pi$
$821$	36.7980	−	26.7353i	1.28426	−	0.933070i	0.999673	+	0.0255806i	$0.00814345\pi$
$822$	5.58614	−	4.05857i	0.194839	−	0.141559i
$823$	−3.73655	−	11.4999i	−0.130248	−	0.400862i	0.864573	−	0.502508i	$-0.167589\pi$
$823$	−3.73655	−	11.4999i	−0.130248	−	0.400862i	−0.994821	+	0.101646i	$0.967589\pi$
$824$	−5.23385			−0.182330
$825$	48.1164	+	4.23482i	1.67520	+	0.147438i
$826$	16.5596			0.576183
$827$	0.0332255	+	0.102258i	0.00115536	+	0.00355585i	0.951633	−	0.307239i	$-0.0994049\pi$
$827$	0.0332255	+	0.102258i	0.00115536	+	0.00355585i	−0.950477	+	0.310794i	$0.899405\pi$
$828$	−33.9256	+	24.6484i	−1.17900	+	0.856591i
$829$	33.2096	−	24.1282i	1.15342	−	0.838006i	0.164485	−	0.986380i	$-0.447404\pi$
$829$	33.2096	−	24.1282i	1.15342	−	0.838006i	0.988931	+	0.148373i	$0.0474037\pi$
$830$	7.46886	+	0.328041i	0.259248	+	0.0113865i
$831$	0.438474	+	0.318570i	0.0152105	+	0.0110511i
$832$	2.64217			0.0916009
$833$	−5.74590	−	4.17464i	−0.199084	−	0.144643i
$834$	11.2598	−	34.6541i	0.389896	−	1.19997i
$835$	−6.40094	+	17.1065i	−0.221514	+	0.591996i
$836$	−0.998632	−	3.07347i	−0.0345384	−	0.106298i
$837$	1.09493	−	3.36986i	0.0378465	−	0.116479i
$838$	−2.75268	+	8.47186i	−0.0950896	+	0.292656i
$839$	4.85887	+	14.9541i	0.167747	+	0.516272i	0.999228	−	0.0392809i	$-0.0125067\pi$
$839$	4.85887	+	14.9541i	0.167747	+	0.516272i	−0.831481	+	0.555553i	$0.812507\pi$
$840$	−2.55469	−	9.22122i	−0.0881452	−	0.318162i
$841$	19.5638	−	60.2113i	0.674615	−	2.07625i
$842$	−22.6916	−	16.4864i	−0.782005	−	0.568160i
$843$	62.4936			2.15239
$844$	5.85843	+	4.25640i	0.201655	+	0.146511i
$845$	4.71662	−	12.6052i	0.162257	−	0.433632i
$846$	−55.5848	+	40.3848i	−1.91105	+	1.38846i
$847$	0.644481	−	0.468243i	0.0221446	−	0.0160890i
$848$	−1.99065	−	6.12658i	−0.0683590	−	0.210388i
$849$	−1.52170			−0.0522247
$850$	−1.60990	−	6.98982i	−0.0552192	−	0.239749i
$851$	−66.2596			−2.27135
$852$	15.0520	+	46.3252i	0.515672	+	1.58707i
$853$	−29.6988	+	21.5774i	−1.01687	+	0.738797i	−0.965638	−	0.259890i	$-0.916314\pi$
$853$	−29.6988	+	21.5774i	−1.01687	+	0.738797i	−0.0512283	+	0.998687i	$0.516314\pi$
$854$	−9.22808	+	6.70459i	−0.315778	+	0.229426i
$855$	−10.3859	−	8.26575i	−0.355192	−	0.282683i
$856$	−4.92929	−	3.58134i	−0.168480	−	0.122408i
$857$	−13.0526			−0.445868			−0.222934	−	0.974834i	$-0.571563\pi$
$857$	−13.0526			−0.445868			−0.222934	+	0.974834i	$0.571563\pi$
$858$	−20.6499	−	15.0030i	−0.704975	−	0.512194i
$859$	12.8868	−	39.6614i	0.439690	−	1.35323i	−0.448513	−	0.893777i	$-0.648046\pi$
$859$	12.8868	−	39.6614i	0.439690	−	1.35323i	0.888203	−	0.459451i	$-0.151954\pi$
$860$	1.20158	+	0.956290i	0.0409736	+	0.0326092i
$861$	3.02171	+	9.29986i	0.102980	+	0.316938i
$862$	−5.39225	+	16.5957i	−0.183661	+	0.565250i
$863$	−5.65690	+	17.4101i	−0.192563	+	0.592648i	0.807433	+	0.589959i	$0.200856\pi$
$863$	−5.65690	+	17.4101i	−0.192563	+	0.592648i	−0.999996	+	0.00268926i	$0.999144\pi$
$864$	2.71231	+	8.34762i	0.0922745	+	0.283992i
$865$	−6.55179	+	4.33409i	−0.222767	+	0.147363i
$866$	−2.99236	+	9.20953i	−0.101684	+	0.312952i
$867$	36.1362	+	26.2545i	1.22725	+	0.891650i
$868$	0.577877			0.0196144
$869$	14.2770	+	10.3729i	0.484315	+	0.351875i
$870$	17.1465	+	61.8909i	0.581322	+	2.09830i
$871$	28.5751	−	20.7610i	0.968231	−	0.703461i
$872$	10.2993	−	7.48290i	0.348779	−	0.253403i
$873$	11.7718	+	36.2298i	0.398414	+	1.22619i
$874$	−7.06421			−0.238951
$875$	11.6006	+	11.0258i	0.392173	+	0.372739i
$876$	36.8789			1.24602
$877$	−11.0408	−	33.9802i	−0.372822	−	1.14743i	−0.944936	−	0.327255i	$-0.893876\pi$
$877$	−11.0408	−	33.9802i	−0.372822	−	1.14743i	0.572114	−	0.820174i	$-0.306124\pi$
$878$	23.4008	−	17.0017i	0.789738	−	0.573778i
$879$	−3.84671	+	2.79480i	−0.129746	+	0.0942663i
$880$	−1.92930	−	6.96386i	−0.0650367	−	0.234752i
$881$	−12.7511	−	9.26418i	−0.429594	−	0.312118i	0.351893	−	0.936040i	$-0.385538\pi$
$881$	−12.7511	−	9.26418i	−0.429594	−	0.312118i	−0.781487	+	0.623922i	$0.785538\pi$
$882$	−29.3891			−0.989583
$883$	−38.4343	−	27.9242i	−1.29342	−	0.939723i	−0.293550	−	0.955944i	$-0.594837\pi$
$883$	−38.4343	−	27.9242i	−1.29342	−	0.939723i	−0.999868	+	0.0162206i	$0.994837\pi$
$884$	−1.17129	+	3.60485i	−0.0393947	+	0.121244i
$885$	64.4921	−	42.6623i	2.16788	−	1.43408i
$886$	5.28083	+	16.2527i	0.177413	+	0.546021i
$887$	13.2625	−	40.8179i	0.445312	−	1.37053i	−0.436828	−	0.899545i	$-0.643898\pi$
$887$	13.2625	−	40.8179i	0.445312	−	1.37053i	0.882141	−	0.470986i	$-0.156102\pi$
$888$	−8.66450	+	26.6666i	−0.290761	+	0.894872i
$889$	4.28581	+	13.1904i	0.143741	+	0.442390i
$890$	−11.1999	−	8.91358i	−0.375423	−	0.298784i
$891$	8.41803	−	25.9080i	0.282015	−	0.867952i
$892$	19.8237	+	14.4028i	0.663747	+	0.482240i
$893$	−11.5742			−0.387317
$894$	20.8514	+	15.1494i	0.697374	+	0.506672i
$895$	−26.3969	−	21.0082i	−0.882351	−	0.702228i
$896$	−1.15809	+	0.841404i	−0.0386892	+	0.0281093i
$897$	−45.1397	+	32.7959i	−1.50717	+	1.09502i
$898$	3.84088	+	11.8210i	0.128172	+	0.394472i
$899$	−3.87859			−0.129358
$900$	−22.3903	−	19.4840i	−0.746343	−	0.649467i
$901$	9.24127			0.307871
$902$	2.28199	+	7.02325i	0.0759820	+	0.233849i
$903$	−2.37756	+	1.72740i	−0.0791204	+	0.0574843i
$904$	6.82833	−	4.96107i	0.227107	−	0.165003i
$905$	11.6759	−	31.2040i	0.388121	−	1.03726i
$906$	−8.29576	−	6.02722i	−0.275608	−	0.200241i
$907$	47.1470			1.56549			0.782746	−	0.622342i	$-0.213819\pi$
$907$	47.1470			1.56549			0.782746	+	0.622342i	$0.213819\pi$
$908$	13.6464	+	9.91468i	0.452871	+	0.329030i
$909$	21.2308	−	65.3417i	0.704181	−	2.16725i
$910$	−2.25800	−	8.15030i	−0.0748520	−	0.270180i
$911$	14.1799	+	43.6413i	0.469802	+	1.44590i	0.852842	+	0.522169i	$0.174877\pi$
$911$	14.1799	+	43.6413i	0.469802	+	1.44590i	−0.383040	+	0.923732i	$0.625123\pi$
$912$	−0.923758	+	2.84303i	−0.0305887	+	0.0941422i
$913$	−3.33882	+	10.2758i	−0.110499	+	0.340080i
$914$	−1.16560	−	3.58735i	−0.0385547	−	0.118659i
$915$	−18.6662	+	49.8855i	−0.617085	+	1.64916i
$916$	−2.31665	+	7.12992i	−0.0765443	+	0.235579i
$917$	1.19029	+	0.864797i	0.0393069	+	0.0285581i
$918$	−12.5915			−0.415580
$919$	18.5430	+	13.4722i	0.611676	+	0.444409i	0.850004	−	0.526776i	$-0.176599\pi$
$919$	18.5430	+	13.4722i	0.611676	+	0.444409i	−0.238328	+	0.971185i	$0.576599\pi$
$920$	−15.7808	−	0.693113i	−0.520279	−	0.0228513i
$921$	54.0736	−	39.2867i	1.78178	−	1.29454i
$922$	−17.3681	+	12.6187i	−0.571989	+	0.415574i
$923$	13.3039	+	40.9452i	0.437903	+	1.34773i
$924$	13.8288			0.454934
$925$	−10.5260	−	45.7016i	−0.346094	−	1.50266i
$926$	34.4227			1.13120
$927$	−9.60085	−	29.5484i	−0.315333	−	0.970496i
$928$	7.77288	−	5.64733i	0.255157	−	0.185383i
$929$	−2.80824	+	2.04031i	−0.0921354	+	0.0669403i	−0.632899	−	0.774234i	$-0.718135\pi$
$929$	−2.80824	+	2.04031i	−0.0921354	+	0.0669403i	0.540764	+	0.841174i	$0.318135\pi$
$930$	2.25056	−	1.48877i	0.0737989	−	0.0488189i
$931$	−4.00533	−	2.91004i	−0.131269	−	0.0953728i
$932$	21.0978			0.691082
$933$	72.9707	+	53.0163i	2.38895	+	1.73568i
$934$	0.833457	−	2.56512i	0.0272716	−	0.0839332i
$935$	10.3564	+	0.454866i	0.338691	+	0.0148757i
$936$	4.84674	+	14.9167i	0.158421	+	0.487569i
$937$	−17.3778	+	53.4834i	−0.567709	+	1.74723i	0.0920538	+	0.995754i	$0.470657\pi$
$937$	−17.3778	+	53.4834i	−0.567709	+	1.74723i	−0.659763	+	0.751474i	$0.729343\pi$
$938$	−5.91340	+	18.1996i	−0.193079	+	0.594237i
$939$	0.533039	+	1.64053i	0.0173951	+	0.0535365i
$940$	−25.8559	−	1.13562i	−0.843326	−	0.0370398i
$941$	−14.6498	+	45.0873i	−0.477568	+	1.46980i	0.364894	+	0.931049i	$0.381105\pi$
$941$	−14.6498	+	45.0873i	−0.477568	+	1.46980i	−0.842462	+	0.538755i	$0.818895\pi$
$942$	−20.4849	−	14.8832i	−0.667434	−	0.484920i
$943$	16.1426			0.525674
$944$	−9.35885	−	6.79961i	−0.304605	−	0.221308i
$945$	23.4319	−	15.5005i	0.762241	−	0.504232i
$946$	−1.79554	+	1.30453i	−0.0583779	+	0.0424140i
$947$	26.2033	−	19.0378i	0.851493	−	0.618646i	−0.0740642	−	0.997253i	$-0.523597\pi$
$947$	26.2033	−	19.0378i	0.851493	−	0.618646i	0.925557	+	0.378607i	$0.123597\pi$
$948$	−5.04446	−	15.5253i	−0.163837	−	0.504237i
$949$	32.5959			1.05811
$950$	−1.12222	−	4.87243i	−0.0364098	−	0.158083i
$951$	89.9042			2.91534
$952$	−0.634583	−	1.95304i	−0.0205669	−	0.0632985i
$953$	9.99983	−	7.26531i	0.323926	−	0.235346i	−0.413923	−	0.910312i	$-0.635842\pi$
$953$	9.99983	−	7.26531i	0.323926	−	0.235346i	0.737849	+	0.674966i	$0.235842\pi$
$954$	30.9368	−	22.4769i	1.00162	−	0.727716i
$955$	−12.0229	−	0.528060i	−0.389052	−	0.0170876i
$956$	2.39364	+	1.73908i	0.0774159	+	0.0562459i
$957$	−92.8160			−3.00032
$958$	3.37007	+	2.44850i	0.108882	+	0.0791075i
$959$	−1.02175	+	3.14464i	−0.0329942	+	0.101546i
$960$	−2.34254	+	6.26046i	−0.0756052	+	0.202055i
$961$	−9.52917	−	29.3278i	−0.307392	−	0.946057i
$962$	−7.65824	+	23.5696i	−0.246912	+	0.759916i
$963$	11.1767	−	34.3984i	0.360165	−	1.10847i
$964$	−1.46210	−	4.49989i	−0.0470911	−	0.144932i
$965$	−9.24633	−	33.3748i	−0.297650	−	1.07437i
$966$	9.34130	−	28.7496i	0.300552	−	0.925002i
$967$	4.15634	+	3.01976i	0.133659	+	0.0971089i	0.652606	−	0.757698i	$-0.273676\pi$
$967$	4.15634	+	3.01976i	0.133659	+	0.0971089i	−0.518947	+	0.854806i	$0.673676\pi$
$968$	−0.556502			−0.0178867
$969$	−3.46939	−	2.52066i	−0.111453	−	0.0809753i
$970$	−5.02882	+	13.4395i	−0.161466	+	0.431518i
$971$	−45.3579	+	32.9544i	−1.45560	+	1.05756i	−0.471123	+	0.882067i	$0.656151\pi$
$971$	−45.3579	+	32.9544i	−1.45560	+	1.05756i	−0.984481	+	0.175491i	$0.943849\pi$
$972$	0.916413	−	0.665813i	0.0293940	−	0.0213560i
$973$	5.39189	+	16.5945i	0.172856	+	0.531997i
$974$	−37.8154			−1.21168
$975$	−29.7914	−	25.9244i	−0.954087	−	0.830246i
$976$	7.96834			0.255060
$977$	1.84474	+	5.67752i	0.0590184	+	0.181640i	0.976219	−	0.216785i	$-0.0695570\pi$
$977$	1.84474	+	5.67752i	0.0590184	+	0.181640i	−0.917201	+	0.398425i	$0.869557\pi$
$978$	22.3261	−	16.2208i	0.713909	−	0.518685i
$979$	16.7362	−	12.1596i	0.534891	−	0.388621i
$980$	−8.66204	−	6.89377i	−0.276699	−	0.220214i
$981$	61.1385	+	44.4197i	1.95200	+	1.41821i
$982$	−12.0897			−0.385797
$983$	0.500626	+	0.363726i	0.0159675	+	0.0116011i	0.595740	−	0.803177i	$-0.296859\pi$
$983$	0.500626	+	0.363726i	0.0159675	+	0.0116011i	−0.579773	+	0.814778i	$0.696859\pi$
$984$	2.11090	−	6.49667i	0.0672929	−	0.207106i
$985$	−5.13495	−	4.08670i	−0.163613	−	0.130213i
$986$	4.25919	+	13.1084i	0.135640	+	0.417457i
$987$	15.3051	−	47.1043i	0.487167	−	1.49935i
$988$	−0.816476	+	2.51286i	−0.0259756	+	0.0799446i
$989$	1.49920	+	4.61406i	0.0476718	+	0.146719i
$990$	35.7763	−	23.6664i	1.13705	−	0.752169i
$991$	−13.3592	+	41.1153i	−0.424368	+	1.30607i	0.479230	+	0.877689i	$0.340916\pi$
$991$	−13.3592	+	41.1153i	−0.424368	+	1.30607i	−0.903598	+	0.428381i	$0.859084\pi$
$992$	−0.326593	−	0.237284i	−0.0103693	−	0.00753377i
$993$	−60.3416			−1.91488
$994$	−18.8703	−	13.7101i	−0.598529	−	0.434857i
$995$	−8.80062	−	31.7661i	−0.278999	−	1.00705i
$996$	8.08576	−	5.87465i	0.256207	−	0.186145i
$997$	−3.99238	+	2.90063i	−0.126440	+	0.0918640i	−0.649208	−	0.760611i	$-0.724899\pi$
$997$	−3.99238	+	2.90063i	−0.126440	+	0.0918640i	0.522768	+	0.852475i	$0.324899\pi$
$998$	−7.83352	−	24.1091i	−0.247966	−	0.763160i
$999$	−82.3269			−2.60471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.c.381.1	✓	44
25.21	even	5	inner	950.2.h.c.571.1	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.c.381.1	✓	44	1.1	even	1	trivial
950.2.h.c.571.1	yes	44	25.21	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-2.41843 + 1.75709i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.597004 - 2.15490i) q^{5} +(-2.41843 - 1.75709i) q^{6} +1.43148 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.83438 - 5.64563i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-2.41843 + 1.75709i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.597004 - 2.15490i) q^{5} +(-2.41843 - 1.75709i) q^{6} +1.43148 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.83438 - 5.64563i) q^{9} +(1.86495 - 1.23368i) q^{10} +(0.998632 + 3.07347i) q^{11} +(0.923758 - 2.84303i) q^{12} +(0.816476 - 2.51286i) q^{13} +(0.442352 + 1.36142i) q^{14} +(5.23016 + 4.16248i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.16059 + 0.843216i) q^{17} +5.93617 q^{18} +(0.809017 + 0.587785i) q^{19} +(1.74960 + 1.39244i) q^{20} +(-3.46194 + 2.51524i) q^{21} +(-2.61445 + 1.89951i) q^{22} +(2.18296 + 6.71847i) q^{23} +2.98934 q^{24} +(-4.28717 + 2.57296i) q^{25} +2.64217 q^{26} +(2.71231 + 8.34762i) q^{27} +(-1.15809 + 0.841404i) q^{28} +(7.77288 - 5.64733i) q^{29} +(-2.34254 + 6.26046i) q^{30} +(-0.326593 - 0.237284i) q^{31} +1.00000 q^{32} +(-7.81549 - 5.67829i) q^{33} +(-0.443305 + 1.36435i) q^{34} +(-0.854600 - 3.08470i) q^{35} +(1.83438 + 5.64563i) q^{36} +(-2.89846 + 8.92055i) q^{37} +(-0.309017 + 0.951057i) q^{38} +(2.44073 + 7.51179i) q^{39} +(-0.783631 + 2.09426i) q^{40} +(0.706140 - 2.17328i) q^{41} +(-3.46194 - 2.51524i) q^{42} +0.686773 q^{43} +(-2.61445 - 1.89951i) q^{44} +(-13.2609 - 0.582434i) q^{45} +(-5.71507 + 4.15224i) q^{46} +(-9.36376 + 6.80317i) q^{47} +(0.923758 + 2.84303i) q^{48} -4.95086 q^{49} +(-3.77184 - 3.28225i) q^{50} -4.28840 q^{51} +(0.816476 + 2.51286i) q^{52} +(5.21158 - 3.78643i) q^{53} +(-7.10091 + 5.15911i) q^{54} +(6.02683 - 3.98682i) q^{55} +(-1.15809 - 0.841404i) q^{56} -2.98934 q^{57} +(7.77288 + 5.64733i) q^{58} +(3.57476 - 11.0020i) q^{59} +(-6.67793 - 0.293303i) q^{60} +(2.46235 + 7.57834i) q^{61} +(0.124747 - 0.383933i) q^{62} +(2.62588 - 8.08161i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-5.90239 - 0.259240i) q^{65} +(2.98525 - 9.18766i) q^{66} +(10.8150 + 7.85756i) q^{67} -1.43456 q^{68} +(-17.0843 - 12.4125i) q^{69} +(2.66964 - 1.76600i) q^{70} +(-13.1823 + 9.57754i) q^{71} +(-4.80246 + 3.48919i) q^{72} +(3.81228 + 11.7330i) q^{73} -9.37962 q^{74} +(5.84729 - 13.7555i) q^{75} -1.00000 q^{76} +(1.42952 + 4.39962i) q^{77} +(-6.38991 + 4.64254i) q^{78} +(4.41789 - 3.20978i) q^{79} +(-2.23391 - 0.0981161i) q^{80} +(-6.81966 - 4.95478i) q^{81} +2.28512 q^{82} +(2.70486 + 1.96520i) q^{83} +(1.32234 - 4.06975i) q^{84} +(1.12417 - 3.00435i) q^{85} +(0.212225 + 0.653160i) q^{86} +(-8.87528 + 27.3153i) q^{87} +(0.998632 - 3.07347i) q^{88} +(-1.97815 - 6.08811i) q^{89} +(-3.54391 - 12.7918i) q^{90} +(1.16877 - 3.59711i) q^{91} +(-5.71507 - 4.15224i) q^{92} +1.20677 q^{93} +(-9.36376 - 6.80317i) q^{94} +(0.783631 - 2.09426i) q^{95} +(-2.41843 + 1.75709i) q^{96} +(-5.19172 + 3.77201i) q^{97} +(-1.52990 - 4.70855i) q^{98} +19.1836 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 11 q^{2} + q^{3} - 11 q^{4} - q^{5} + q^{6} + 18 q^{7} - 11 q^{8} - 8 q^{9}+O(q^{10}) \) 44 * q - 11 * q^2 + q^3 - 11 * q^4 - q^5 + q^6 + 18 * q^7 - 11 * q^8 - 8 * q^9	\( 44 q - 11 q^{2} + q^{3} - 11 q^{4} - q^{5} + q^{6} + 18 q^{7} - 11 q^{8} - 8 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} + 2 q^{13} + 3 q^{14} - 4 q^{15} - 11 q^{16} + 11 q^{17} + 42 q^{18} + 11 q^{19} - 6 q^{20} + 3 q^{21} - 6 q^{22} - 3 q^{23} + 6 q^{24} - 11 q^{25} + 22 q^{26} - 23 q^{27} - 12 q^{28} + 36 q^{29} - 4 q^{30} + 11 q^{31} + 44 q^{32} + 2 q^{33} - 19 q^{34} + 67 q^{35} - 8 q^{36} + 3 q^{37} + 11 q^{38} + 47 q^{39} + 4 q^{40} + 2 q^{41} + 3 q^{42} + 70 q^{43} - 6 q^{44} - 28 q^{45} - 8 q^{46} - 11 q^{47} - 4 q^{48} + 22 q^{49} + 14 q^{50} + 38 q^{51} + 2 q^{52} - 9 q^{53} + 32 q^{54} + 8 q^{55} - 12 q^{56} - 6 q^{57} + 36 q^{58} - 62 q^{59} + 11 q^{60} - 28 q^{61} - 29 q^{62} + 10 q^{63} - 11 q^{64} - 39 q^{65} - 8 q^{66} + 25 q^{67} + 16 q^{68} - 81 q^{69} - 43 q^{70} - 34 q^{71} - 13 q^{72} + 6 q^{73} + 8 q^{74} - 39 q^{75} - 44 q^{76} - 21 q^{77} - 58 q^{78} + 19 q^{79} - q^{80} - 22 q^{81} + 2 q^{82} - 50 q^{83} - 7 q^{84} + 102 q^{85} - 10 q^{86} + 47 q^{87} - q^{88} - 4 q^{89} - 38 q^{90} - 8 q^{91} - 8 q^{92} + 60 q^{93} - 11 q^{94} - 4 q^{95} + q^{96} + 8 q^{97} + 7 q^{98} - 12 q^{99}+O(q^{100}) \) 44 * q - 11 * q^2 + q^3 - 11 * q^4 - q^5 + q^6 + 18 * q^7 - 11 * q^8 - 8 * q^9 + 4 * q^10 - q^11 - 4 * q^12 + 2 * q^13 + 3 * q^14 - 4 * q^15 - 11 * q^16 + 11 * q^17 + 42 * q^18 + 11 * q^19 - 6 * q^20 + 3 * q^21 - 6 * q^22 - 3 * q^23 + 6 * q^24 - 11 * q^25 + 22 * q^26 - 23 * q^27 - 12 * q^28 + 36 * q^29 - 4 * q^30 + 11 * q^31 + 44 * q^32 + 2 * q^33 - 19 * q^34 + 67 * q^35 - 8 * q^36 + 3 * q^37 + 11 * q^38 + 47 * q^39 + 4 * q^40 + 2 * q^41 + 3 * q^42 + 70 * q^43 - 6 * q^44 - 28 * q^45 - 8 * q^46 - 11 * q^47 - 4 * q^48 + 22 * q^49 + 14 * q^50 + 38 * q^51 + 2 * q^52 - 9 * q^53 + 32 * q^54 + 8 * q^55 - 12 * q^56 - 6 * q^57 + 36 * q^58 - 62 * q^59 + 11 * q^60 - 28 * q^61 - 29 * q^62 + 10 * q^63 - 11 * q^64 - 39 * q^65 - 8 * q^66 + 25 * q^67 + 16 * q^68 - 81 * q^69 - 43 * q^70 - 34 * q^71 - 13 * q^72 + 6 * q^73 + 8 * q^74 - 39 * q^75 - 44 * q^76 - 21 * q^77 - 58 * q^78 + 19 * q^79 - q^80 - 22 * q^81 + 2 * q^82 - 50 * q^83 - 7 * q^84 + 102 * q^85 - 10 * q^86 + 47 * q^87 - q^88 - 4 * q^89 - 38 * q^90 - 8 * q^91 - 8 * q^92 + 60 * q^93 - 11 * q^94 - 4 * q^95 + q^96 + 8 * q^97 + 7 * q^98 - 12 * q^99

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