LMFDB - Embedded newform 462.2.u.b.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(13,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("462.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.u (of order $10$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	462.13
Dual form			462.2.u.b.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-2.13481 + 0.693642i) q^{5} +(0.309017 + 0.951057i) q^{6} +(1.47539 - 2.19618i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-2.13481 + 0.693642i) q^{5} +(0.309017 + 0.951057i) q^{6} +(1.47539 - 2.19618i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +2.24467 q^{10} +(-1.12598 - 3.11964i) q^{11} -1.00000i q^{12} +(-1.40911 + 4.33678i) q^{13} +(-2.08184 + 1.63277i) q^{14} +(1.81598 + 1.31939i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.242618 - 0.746700i) q^{17} +(0.587785 - 0.809017i) q^{18} +(-0.320192 + 0.232633i) q^{19} +(-2.13481 - 0.693642i) q^{20} +(-2.64396 + 0.0972645i) q^{21} +(0.106848 + 3.31490i) q^{22} -6.90676 q^{23} +(-0.309017 + 0.951057i) q^{24} +(0.0311970 - 0.0226660i) q^{25} +(2.68028 - 3.68909i) q^{26} +(0.951057 - 0.309017i) q^{27} +(2.48450 - 0.909534i) q^{28} +(-2.38024 + 3.27613i) q^{29} +(-1.31939 - 1.81598i) q^{30} +(-8.84471 - 2.87382i) q^{31} -1.00000i q^{32} +(-1.86201 + 2.74462i) q^{33} +0.785127i q^{34} +(-1.62632 + 5.71183i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(5.16000 + 3.74896i) q^{37} +(0.376408 - 0.122303i) q^{38} +(4.33678 - 1.40911i) q^{39} +(1.81598 + 1.31939i) q^{40} +(-8.23363 + 5.98208i) q^{41} +(2.54461 + 0.724525i) q^{42} +0.783748i q^{43} +(0.922742 - 3.18568i) q^{44} -2.24467i q^{45} +(6.56871 + 2.13430i) q^{46} +(1.65844 + 2.28265i) q^{47} +(0.587785 - 0.809017i) q^{48} +(-2.64643 - 6.48046i) q^{49} +(-0.0366743 + 0.0119162i) q^{50} +(-0.461486 + 0.635181i) q^{51} +(-3.68909 + 2.68028i) q^{52} +(-2.77482 + 8.54001i) q^{53} -1.00000 q^{54} +(4.56767 + 5.87882i) q^{55} +(-2.64396 + 0.0972645i) q^{56} +(0.376408 + 0.122303i) q^{57} +(3.27613 - 2.38024i) q^{58} +(3.80725 - 5.24024i) q^{59} +(0.693642 + 2.13481i) q^{60} +(-1.57469 - 4.84639i) q^{61} +(7.52376 + 5.46633i) q^{62} +(1.63277 + 2.08184i) q^{63} +(-0.309017 + 0.951057i) q^{64} -10.2356i q^{65} +(2.61901 - 2.03489i) q^{66} +2.26255 q^{67} +(0.242618 - 0.746700i) q^{68} +(4.05969 + 5.58768i) q^{69} +(3.31178 - 4.92971i) q^{70} +(-0.360171 - 1.10849i) q^{71} +(0.951057 - 0.309017i) q^{72} +(-10.9407 - 7.94891i) q^{73} +(-3.74896 - 5.16000i) q^{74} +(-0.0366743 - 0.0119162i) q^{75} -0.395779 q^{76} +(-8.51257 - 2.12984i) q^{77} -4.55996 q^{78} +(-4.85962 - 1.57898i) q^{79} +(-1.31939 - 1.81598i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(9.67921 - 3.14497i) q^{82} +(2.78129 + 8.55992i) q^{83} +(-2.19618 - 1.47539i) q^{84} +(1.03589 + 1.42577i) q^{85} +(0.242192 - 0.745389i) q^{86} +4.04951 q^{87} +(-1.86201 + 2.74462i) q^{88} -18.2760i q^{89} +(-0.693642 + 2.13481i) q^{90} +(7.44537 + 9.49311i) q^{91} +(-5.58768 - 4.05969i) q^{92} +(2.87382 + 8.84471i) q^{93} +(-0.871894 - 2.68341i) q^{94} +(0.522186 - 0.718727i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(3.60967 + 1.17285i) q^{97} +(0.514328 + 6.98108i) q^{98} +(3.31490 - 0.106848i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9	$ 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} - 12 q^{17} - 16 q^{19} + 10 q^{20} - 8 q^{21} - 4 q^{22} + 8 q^{23} + 8 q^{24} + 6 q^{25} + 10 q^{28} + 20 q^{29} - 50 q^{31} - 16 q^{33} - 12 q^{35} - 8 q^{36} - 16 q^{37} + 6 q^{40} + 40 q^{41} + 12 q^{44} + 52 q^{49} + 40 q^{51} - 32 q^{54} - 40 q^{55} - 8 q^{56} + 10 q^{58} + 60 q^{59} + 4 q^{60} - 4 q^{61} + 20 q^{62} - 10 q^{63} + 8 q^{64} + 8 q^{66} - 16 q^{67} + 12 q^{68} + 30 q^{69} - 28 q^{70} - 48 q^{71} - 74 q^{73} - 40 q^{74} - 24 q^{76} + 6 q^{77} - 60 q^{79} - 8 q^{81} + 20 q^{82} + 4 q^{83} - 2 q^{84} - 10 q^{85} - 36 q^{86} + 20 q^{87} - 16 q^{88} - 4 q^{90} - 20 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} - 8 q^{96} + 60 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 - 12 * q^17 - 16 * q^19 + 10 * q^20 - 8 * q^21 - 4 * q^22 + 8 * q^23 + 8 * q^24 + 6 * q^25 + 10 * q^28 + 20 * q^29 - 50 * q^31 - 16 * q^33 - 12 * q^35 - 8 * q^36 - 16 * q^37 + 6 * q^40 + 40 * q^41 + 12 * q^44 + 52 * q^49 + 40 * q^51 - 32 * q^54 - 40 * q^55 - 8 * q^56 + 10 * q^58 + 60 * q^59 + 4 * q^60 - 4 * q^61 + 20 * q^62 - 10 * q^63 + 8 * q^64 + 8 * q^66 - 16 * q^67 + 12 * q^68 + 30 * q^69 - 28 * q^70 - 48 * q^71 - 74 * q^73 - 40 * q^74 - 24 * q^76 + 6 * q^77 - 60 * q^79 - 8 * q^81 + 20 * q^82 + 4 * q^83 - 2 * q^84 - 10 * q^85 - 36 * q^86 + 20 * q^87 - 16 * q^88 - 4 * q^90 - 20 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 - 8 * q^96 + 60 * q^97 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−2.13481	+	0.693642i	−0.954717	+	0.310206i	−0.744631	−	0.667477i	$-0.767374\pi$
$5$	−2.13481	+	0.693642i	−0.954717	+	0.310206i	−0.210086	+	0.977683i	$0.567374\pi$
$6$	0.309017	+	0.951057i	0.126156	+	0.388267i
$7$	1.47539	−	2.19618i	0.557646	−	0.830079i
$7$	1.47539	−	2.19618i	0.557646	−	0.830079i
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	2.24467			0.709828
$11$	−1.12598	−	3.11964i	−0.339496	−	0.940608i
$11$	−1.12598	−	3.11964i	−0.339496	−	0.940608i
$12$		−	1.00000i		−	0.288675i
$13$	−1.40911	+	4.33678i	−0.390816	+	1.20281i	0.541357	+	0.840793i	$0.317911\pi$
$13$	−1.40911	+	4.33678i	−0.390816	+	1.20281i	−0.932173	+	0.362014i	$0.882089\pi$
$14$	−2.08184	+	1.63277i	−0.556395	+	0.436376i
$15$	1.81598	+	1.31939i	0.468884	+	0.340664i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.242618	−	0.746700i	−0.0588434	−	0.181101i	0.917314	−	0.398164i	$-0.130352\pi$
$17$	−0.242618	−	0.746700i	−0.0588434	−	0.181101i	−0.976158	+	0.217062i	$0.930352\pi$
$18$	0.587785	−	0.809017i	0.138542	−	0.190687i
$19$	−0.320192	+	0.232633i	−0.0734571	+	0.0533697i	−0.623908	−	0.781498i	$-0.714456\pi$
$19$	−0.320192	+	0.232633i	−0.0734571	+	0.0533697i	0.550451	+	0.834868i	$0.314456\pi$
$20$	−2.13481	−	0.693642i	−0.477358	−	0.155103i
$21$	−2.64396	+	0.0972645i	−0.576960	+	0.0212249i
$22$	0.106848	+	3.31490i	0.0227802	+	0.706740i
$23$	−6.90676			−1.44016			−0.720079	−	0.693892i	$-0.755894\pi$
$23$	−6.90676			−1.44016			−0.720079	+	0.693892i	$0.755894\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	0.0311970	−	0.0226660i	0.00623940	−	0.00453319i
$26$	2.68028	−	3.68909i	0.525646	−	0.723489i
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	2.48450	−	0.909534i	0.469527	−	0.171886i
$29$	−2.38024	+	3.27613i	−0.442000	+	0.608361i	−0.970655	−	0.240476i	$-0.922697\pi$
$29$	−2.38024	+	3.27613i	−0.442000	+	0.608361i	0.528655	+	0.848837i	$0.322697\pi$
$30$	−1.31939	−	1.81598i	−0.240886	−	0.331551i
$31$	−8.84471	−	2.87382i	−1.58856	−	0.516154i	−0.624314	−	0.781173i	$-0.714622\pi$
$31$	−8.84471	−	2.87382i	−1.58856	−	0.516154i	−0.964243	+	0.265019i	$0.914622\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.86201	+	2.74462i	−0.324134	+	0.477776i
$34$			0.785127i			0.134648i
$35$	−1.62632	+	5.71183i	−0.274899	+	0.965476i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	5.16000	+	3.74896i	0.848298	+	0.616325i	0.924676	−	0.380754i	$-0.124336\pi$
$37$	5.16000	+	3.74896i	0.848298	+	0.616325i	−0.0763780	+	0.997079i	$0.524336\pi$
$38$	0.376408	−	0.122303i	0.0610615	−	0.0198401i
$39$	4.33678	−	1.40911i	0.694441	−	0.225637i
$40$	1.81598	+	1.31939i	0.287132	+	0.208613i
$41$	−8.23363	+	5.98208i	−1.28588	+	0.934244i	−0.999713	−	0.0239369i	$-0.992380\pi$
$41$	−8.23363	+	5.98208i	−1.28588	+	0.934244i	−0.286163	+	0.958181i	$0.592380\pi$
$42$	2.54461	+	0.724525i	0.392643	+	0.111797i
$43$			0.783748i			0.119521i	0.998213	+	0.0597603i	$0.0190336\pi$
$43$			0.783748i			0.119521i	−0.998213	+	0.0597603i	$0.980966\pi$
$44$	0.922742	−	3.18568i	0.139109	−	0.480259i
$45$		−	2.24467i		−	0.334616i
$46$	6.56871	+	2.13430i	0.968504	+	0.314686i
$47$	1.65844	+	2.28265i	0.241908	+	0.332958i	0.912657	−	0.408726i	$-0.134027\pi$
$47$	1.65844	+	2.28265i	0.241908	+	0.332958i	−0.670748	+	0.741685i	$0.734027\pi$
$48$	0.587785	−	0.809017i	0.0848395	−	0.116772i
$49$	−2.64643	−	6.48046i	−0.378061	−	0.925781i
$50$	−0.0366743	+	0.0119162i	−0.00518653	+	0.00168521i
$51$	−0.461486	+	0.635181i	−0.0646210	+	0.0889431i
$52$	−3.68909	+	2.68028i	−0.511584	+	0.371688i
$53$	−2.77482	+	8.54001i	−0.381151	+	1.17306i	0.558084	+	0.829785i	$0.311537\pi$
$53$	−2.77482	+	8.54001i	−0.381151	+	1.17306i	−0.939234	+	0.343276i	$0.888463\pi$
$54$	−1.00000			−0.136083
$55$	4.56767	+	5.87882i	0.615905	+	0.792700i
$56$	−2.64396	+	0.0972645i	−0.353314	+	0.0129975i
$57$	0.376408	+	0.122303i	0.0498565	+	0.0161994i
$58$	3.27613	−	2.38024i	0.430176	−	0.312541i
$59$	3.80725	−	5.24024i	0.495662	−	0.682221i	−0.485758	−	0.874094i	$-0.661456\pi$
$59$	3.80725	−	5.24024i	0.495662	−	0.682221i	0.981420	+	0.191873i	$0.0614562\pi$
$60$	0.693642	+	2.13481i	0.0895489	+	0.275603i
$61$	−1.57469	−	4.84639i	−0.201618	−	0.620517i	−0.999835	−	0.0181470i	$-0.994223\pi$
$61$	−1.57469	−	4.84639i	−0.201618	−	0.620517i	0.798217	−	0.602370i	$-0.205777\pi$
$62$	7.52376	+	5.46633i	0.955519	+	0.694225i
$63$	1.63277	+	2.08184i	0.205710	+	0.262287i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$		−	10.2356i		−	1.26957i
$66$	2.61901	−	2.03489i	0.322378	−	0.250478i
$67$	2.26255			0.276415			0.138208	−	0.990403i	$-0.455866\pi$
$67$	2.26255			0.276415			0.138208	+	0.990403i	$0.455866\pi$
$68$	0.242618	−	0.746700i	0.0294217	−	0.0905507i
$69$	4.05969	+	5.58768i	0.488729	+	0.672678i
$70$	3.31178	−	4.92971i	0.395833	−	0.589213i
$71$	−0.360171	−	1.10849i	−0.0427444	−	0.131554i	0.927407	−	0.374054i	$-0.122033\pi$
$71$	−0.360171	−	1.10849i	−0.0427444	−	0.131554i	−0.970151	+	0.242500i	$0.922033\pi$
$72$	0.951057	−	0.309017i	0.112083	−	0.0364180i
$73$	−10.9407	−	7.94891i	−1.28052	−	0.930350i	−0.280948	−	0.959723i	$-0.590649\pi$
$73$	−10.9407	−	7.94891i	−1.28052	−	0.930350i	−0.999569	+	0.0293735i	$0.990649\pi$
$74$	−3.74896	−	5.16000i	−0.435807	−	0.599838i
$75$	−0.0366743	−	0.0119162i	−0.00423478	−	0.00137596i
$76$	−0.395779			−0.0453990
$77$	−8.51257	−	2.12984i	−0.970097	−	0.242718i
$78$	−4.55996			−0.516314
$79$	−4.85962	−	1.57898i	−0.546749	−	0.177650i	0.0226010	−	0.999745i	$-0.492805\pi$
$79$	−4.85962	−	1.57898i	−0.546749	−	0.177650i	−0.569351	+	0.822095i	$0.692805\pi$
$80$	−1.31939	−	1.81598i	−0.147512	−	0.203033i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	9.67921	−	3.14497i	1.06889	−	0.347303i
$83$	2.78129	+	8.55992i	0.305286	+	0.939574i	0.979570	+	0.201102i	$0.0644522\pi$
$83$	2.78129	+	8.55992i	0.305286	+	0.939574i	−0.674284	+	0.738472i	$0.735548\pi$
$84$	−2.19618	−	1.47539i	−0.239623	−	0.160979i
$85$	1.03589	+	1.42577i	0.112358	+	0.154647i
$86$	0.242192	−	0.745389i	0.0261162	−	0.0803774i
$87$	4.04951			0.434154
$88$	−1.86201	+	2.74462i	−0.198491	+	0.292577i
$89$		−	18.2760i		−	1.93726i	−0.248513	−	0.968629i	$-0.579942\pi$
$89$		−	18.2760i		−	1.93726i	0.248513	−	0.968629i	$-0.420058\pi$
$90$	−0.693642	+	2.13481i	−0.0731163	+	0.225029i
$91$	7.44537	+	9.49311i	0.780487	+	0.995149i
$92$	−5.58768	−	4.05969i	−0.582556	−	0.423252i
$93$	2.87382	+	8.84471i	0.298001	+	0.917154i
$94$	−0.871894	−	2.68341i	−0.0899290	−	0.276773i
$95$	0.522186	−	0.718727i	0.0535751	−	0.0737398i
$96$	−0.809017	+	0.587785i	−0.0825700	+	0.0599906i
$97$	3.60967	+	1.17285i	0.366506	+	0.119085i	0.486480	−	0.873692i	$-0.338281\pi$
$97$	3.60967	+	1.17285i	0.366506	+	0.119085i	−0.119973	+	0.992777i	$0.538281\pi$
$98$	0.514328	+	6.98108i	0.0519549	+	0.705195i
$99$	3.31490	−	0.106848i	0.333160	−	0.0107387i
$100$	0.0385616			0.00385616
$101$	4.14385	−	12.7535i	0.412329	−	1.26902i	−0.502290	−	0.864699i	$-0.667509\pi$
$101$	4.14385	−	12.7535i	0.412329	−	1.26902i	0.914618	−	0.404318i	$-0.132491\pi$
$102$	0.635181	−	0.461486i	0.0628923	−	0.0456939i
$103$	6.38036	−	8.78182i	0.628676	−	0.865298i	−0.369273	−	0.929321i	$-0.620393\pi$
$103$	6.38036	−	8.78182i	0.628676	−	0.865298i	0.997948	+	0.0640230i	$0.0203931\pi$
$104$	4.33678	−	1.40911i	0.425256	−	0.138174i
$105$	5.57690	−	2.04161i	0.544249	−	0.199240i
$106$	5.27802	−	7.26457i	0.512646	−	0.705597i
$107$	2.79560	+	3.84781i	0.270261	+	0.371982i	0.922478	−	0.386050i	$-0.126161\pi$
$107$	2.79560	+	3.84781i	0.270261	+	0.371982i	−0.652217	+	0.758032i	$0.726161\pi$
$108$	0.951057	+	0.309017i	0.0915155	+	0.0297352i
$109$			3.29575i			0.315675i	0.987465	+	0.157838i	$0.0504523\pi$
$109$			3.29575i			0.315675i	−0.987465	+	0.157838i	$0.949548\pi$
$110$	−2.52746	−	7.00258i	−0.240984	−	0.667670i
$111$		−	6.37811i		−	0.605383i
$112$	2.54461	+	0.724525i	0.240443	+	0.0684612i
$113$	12.9329	−	9.39631i	1.21663	−	0.883930i	0.220810	−	0.975317i	$-0.429130\pi$
$113$	12.9329	−	9.39631i	1.21663	−	0.883930i	0.995816	+	0.0913863i	$0.0291298\pi$
$114$	−0.320192	−	0.232633i	−0.0299887	−	0.0217881i
$115$	14.7446	−	4.79082i	1.37494	−	0.446746i
$116$	−3.85132	+	1.25137i	−0.357586	+	0.116187i
$117$	−3.68909	−	2.68028i	−0.341056	−	0.247792i
$118$	−5.24024	+	3.80725i	−0.482403	+	0.350486i
$119$	−1.99785	−	0.568844i	−0.183142	−	0.0521459i
$120$		−	2.24467i		−	0.204910i
$121$	−8.46434	+	7.02531i	−0.769485	+	0.638665i
$122$			5.09580i			0.461352i
$123$	9.67921	+	3.14497i	0.872745	+	0.283572i
$124$	−5.46633	−	7.52376i	−0.490891	−	0.675654i
$125$	6.54605	−	9.00987i	0.585497	−	0.805867i
$126$	−0.909534	−	2.48450i	−0.0810277	−	0.221337i
$127$	−12.0380	+	3.91139i	−1.06820	+	0.347080i	−0.789787	−	0.613381i	$-0.789809\pi$
$127$	−12.0380	+	3.91139i	−1.06820	+	0.347080i	−0.278415	+	0.960461i	$0.589809\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	0.634066	−	0.460676i	0.0558264	−	0.0405602i
$130$	−3.16298	+	9.73466i	−0.277412	+	0.853786i
$131$	5.63170			0.492044			0.246022	−	0.969264i	$-0.420876\pi$
$131$	5.63170			0.492044			0.246022	+	0.969264i	$0.420876\pi$
$132$	−3.11964	+	1.12598i	−0.271530	+	0.0980040i
$133$	0.0384953	+	1.04643i	0.00333796	+	0.0907366i
$134$	−2.15182	−	0.699168i	−0.185889	−	0.0603989i
$135$	−1.81598	+	1.31939i	−0.156295	+	0.113555i
$136$	−0.461486	+	0.635181i	−0.0395721	+	0.0544663i
$137$	−1.23722	−	3.80777i	−0.105703	−	0.325319i	0.884192	−	0.467124i	$-0.154710\pi$
$137$	−1.23722	−	3.80777i	−0.105703	−	0.325319i	−0.989895	+	0.141804i	$0.954710\pi$
$138$	−2.13430	−	6.56871i	−0.181684	−	0.559166i
$139$	4.57297	+	3.32246i	0.387874	+	0.281807i	0.764584	−	0.644524i	$-0.222945\pi$
$139$	4.57297	+	3.32246i	0.387874	+	0.281807i	−0.376710	+	0.926331i	$0.622945\pi$
$140$	−4.67305	+	3.66504i	−0.394945	+	0.309752i
$141$	0.871894	−	2.68341i	0.0734267	−	0.225984i
$142$			1.16554i			0.0978098i
$143$	15.1158	−	0.487225i	1.26405	−	0.0407438i
$144$	−1.00000			−0.0833333
$145$	2.80892	−	8.64495i	0.233268	−	0.717924i
$146$	7.94891	+	10.9407i	0.657856	+	0.905462i
$147$	−3.68728	+	5.95013i	−0.304121	+	0.490758i
$148$	1.97094	+	6.06594i	0.162011	+	0.498617i
$149$	−1.98928	+	0.646356i	−0.162968	+	0.0529515i	−0.389365	−	0.921084i	$-0.627305\pi$
$149$	−1.98928	+	0.646356i	−0.162968	+	0.0529515i	0.226397	+	0.974035i	$0.427305\pi$
$150$	0.0311970	+	0.0226660i	0.00254723	+	0.00185067i
$151$	−5.43682	−	7.48314i	−0.442442	−	0.608969i	0.528311	−	0.849051i	$-0.322826\pi$
$151$	−5.43682	−	7.48314i	−0.442442	−	0.608969i	−0.970753	+	0.240082i	$0.922826\pi$
$152$	0.376408	+	0.122303i	0.0305308	+	0.00992004i
$153$	0.785127			0.0634738
$154$	7.43777	+	4.65613i	0.599353	+	0.375202i
$155$	20.8752			1.67674
$156$	4.33678	+	1.40911i	0.347220	+	0.112819i
$157$	11.5534	+	15.9019i	0.922060	+	1.26911i	0.962877	+	0.269941i	$0.0870041\pi$
$157$	11.5534	+	15.9019i	0.922060	+	1.26911i	−0.0408165	+	0.999167i	$0.512996\pi$
$158$	4.13384	+	3.00341i	0.328870	+	0.238938i
$159$	8.54001	−	2.77482i	0.677267	−	0.220057i
$160$	0.693642	+	2.13481i	0.0548372	+	0.168772i
$161$	−10.1902	+	15.1685i	−0.803099	+	1.19544i
$162$	0.587785	+	0.809017i	0.0461808	+	0.0635624i
$163$	5.94432	−	18.2947i	0.465595	−	1.43295i	−0.392637	−	0.919693i	$-0.628437\pi$
$163$	5.94432	−	18.2947i	0.465595	−	1.43295i	0.858232	−	0.513261i	$-0.171563\pi$
$164$	−10.1773			−0.794715
$165$	2.07126	−	7.15081i	0.161247	−	0.556690i
$166$		−	9.00044i		−	0.698569i
$167$	−2.93694	+	9.03896i	−0.227267	+	0.699456i	0.770787	+	0.637093i	$0.219863\pi$
$167$	−2.93694	+	9.03896i	−0.227267	+	0.699456i	−0.998054	+	0.0623623i	$0.980137\pi$
$168$	1.63277	+	2.08184i	0.125971	+	0.160617i
$169$	−6.30487	−	4.58076i	−0.484990	−	0.352366i
$170$	−0.544597	−	1.67610i	−0.0417687	−	0.128551i
$171$	−0.122303	−	0.376408i	−0.00935271	−	0.0287847i
$172$	−0.460676	+	0.634066i	−0.0351262	+	0.0483471i
$173$	−20.0875	+	14.5944i	−1.52722	+	1.10959i	−0.569468	+	0.822013i	$0.692851\pi$
$173$	−20.0875	+	14.5944i	−1.52722	+	1.10959i	−0.957756	+	0.287581i	$0.907149\pi$
$174$	−3.85132	−	1.25137i	−0.291968	−	0.0948660i
$175$	−0.00375068	−	0.101956i	−0.000283525	−	0.00770711i
$176$	2.61901	−	2.03489i	0.197415	−	0.153386i
$177$	−6.47729			−0.486863
$178$	−5.64761	+	17.3816i	−0.423306	+	1.30280i
$179$	−13.1862	+	9.58031i	−0.985580	+	0.716066i	−0.958949	−	0.283580i	$-0.908478\pi$
$179$	−13.1862	+	9.58031i	−0.985580	+	0.716066i	−0.0266313	+	0.999645i	$0.508478\pi$
$180$	1.31939	−	1.81598i	0.0983412	−	0.135355i
$181$	−12.0024	+	3.89982i	−0.892133	+	0.289872i	−0.718986	−	0.695024i	$-0.755394\pi$
$181$	−12.0024	+	3.89982i	−0.892133	+	0.289872i	−0.173147	+	0.984896i	$0.555394\pi$
$182$	−4.14744	−	11.3292i	−0.307429	−	0.839779i
$183$	−2.99523	+	4.12259i	−0.221414	+	0.304750i
$184$	4.05969	+	5.58768i	0.299284	+	0.411929i
$185$	−13.6161	−	4.42413i	−1.00107	−	0.325268i
$186$		−	9.29988i		−	0.681900i
$187$	−2.05625	+	1.59765i	−0.150368	+	0.116832i
$188$			2.82151i			0.205780i
$189$	0.724525	−	2.54461i	0.0527015	−	0.185093i
$190$	−0.718727	+	0.522186i	−0.0521419	+	0.0378833i
$191$	15.9536	+	11.5910i	1.15436	+	0.838695i	0.989055	−	0.147547i	$-0.0471378\pi$
$191$	15.9536	+	11.5910i	1.15436	+	0.838695i	0.165309	+	0.986242i	$0.447138\pi$
$192$	0.951057	−	0.309017i	0.0686366	−	0.0223014i
$193$	−16.8373	+	5.47078i	−1.21198	+	0.393795i	−0.844154	−	0.536101i	$-0.819897\pi$
$193$	−16.8373	+	5.47078i	−1.21198	+	0.393795i	−0.367823	+	0.929896i	$0.619897\pi$
$194$	−3.07057	−	2.23090i	−0.220454	−	0.160169i
$195$	−8.28080	+	6.01635i	−0.593000	+	0.430840i
$196$	1.66812	−	6.79834i	0.119151	−	0.485595i
$197$		−	11.1741i		−	0.796124i	−0.917359	−	0.398062i	$-0.869683\pi$
$197$		−	11.1741i		−	0.796124i	0.917359	−	0.398062i	$-0.130317\pi$
$198$	−3.18568	−	0.922742i	−0.226396	−	0.0655765i
$199$		−	24.8619i		−	1.76241i	−0.472734	−	0.881205i	$-0.656733\pi$
$199$		−	24.8619i		−	1.76241i	0.472734	−	0.881205i	$-0.343267\pi$
$200$	−0.0366743	−	0.0119162i	−0.00259326	−	0.000842603i
$201$	−1.32990	−	1.83045i	−0.0938037	−	0.129110i
$202$	−7.88208	+	10.8487i	−0.554581	+	0.763315i
$203$	3.68317	+	10.0610i	0.258508	+	0.706146i
$204$	−0.746700	+	0.242618i	−0.0522795	+	0.0169866i
$205$	13.4278	−	18.4818i	0.937840	−	1.29083i
$206$	−8.78182	+	6.38036i	−0.611858	+	0.444541i
$207$	2.13430	−	6.56871i	0.148344	−	0.456557i
$208$	−4.55996			−0.316176
$209$	1.08626	+	0.736945i	0.0751384	+	0.0509755i
$210$	−5.93483	+	0.218327i	−0.409543	+	0.0150660i
$211$	−27.1844	−	8.83275i	−1.87145	−	0.608072i	−0.990986	−	0.133963i	$-0.957230\pi$
$211$	−27.1844	−	8.83275i	−1.87145	−	0.608072i	−0.880466	−	0.474109i	$-0.842770\pi$
$212$	−7.26457	+	5.27802i	−0.498933	+	0.362496i
$213$	−0.685086	+	0.942940i	−0.0469413	+	0.0646092i
$214$	−1.46973	−	4.52337i	−0.100469	−	0.309211i
$215$	−0.543641	−	1.67316i	−0.0370760	−	0.114108i
$216$	−0.809017	−	0.587785i	−0.0550466	−	0.0399937i
$217$	−19.3609	+	15.1846i	−1.31430	+	1.03080i
$218$	1.01844	−	3.13444i	0.0689776	−	0.212291i
$219$			13.5235i			0.913833i
$220$	0.239840	+	7.44088i	0.0161700	+	0.501664i
$221$	3.58015			0.240827
$222$	−1.97094	+	6.06594i	−0.132281	+	0.407119i
$223$	6.98822	+	9.61846i	0.467966	+	0.644099i	0.976137	−	0.217157i	$-0.0696782\pi$
$223$	6.98822	+	9.61846i	0.467966	+	0.644099i	−0.508171	+	0.861256i	$0.669678\pi$
$224$	−2.19618	−	1.47539i	−0.146739	−	0.0985789i
$225$	0.0119162	+	0.0366743i	0.000794413	+	0.00244495i
$226$	−15.2035	+	4.93993i	−1.01133	+	0.328599i
$227$	6.91762	+	5.02595i	0.459139	+	0.333584i	0.793193	−	0.608970i	$-0.208417\pi$
$227$	6.91762	+	5.02595i	0.459139	+	0.333584i	−0.334055	+	0.942554i	$0.608417\pi$
$228$	0.232633	+	0.320192i	0.0154065	+	0.0212052i
$229$	−5.76569	−	1.87339i	−0.381007	−	0.123797i	0.112250	−	0.993680i	$-0.464194\pi$
$229$	−5.76569	−	1.87339i	−0.381007	−	0.123797i	−0.493258	+	0.869883i	$0.664194\pi$
$230$	−15.5034			−1.02226
$231$	3.28048	+	8.13870i	0.215840	+	0.535487i
$232$	4.04951			0.265864
$233$	8.55417	+	2.77942i	0.560402	+	0.182086i	0.575502	−	0.817800i	$-0.304807\pi$
$233$	8.55417	+	2.77942i	0.560402	+	0.182086i	−0.0150999	+	0.999886i	$0.504807\pi$
$234$	2.68028	+	3.68909i	0.175215	+	0.241163i
$235$	−5.12380	−	3.72266i	−0.334240	−	0.242840i
$236$	6.16027	−	2.00159i	0.400999	−	0.130293i
$237$	1.57898	+	4.85962i	0.102566	+	0.315666i
$238$	1.72428	+	1.15837i	0.111769	+	0.0750861i
$239$	3.19728	+	4.40068i	0.206815	+	0.284657i	0.899806	−	0.436289i	$-0.143708\pi$
$239$	3.19728	+	4.40068i	0.206815	+	0.284657i	−0.692991	+	0.720946i	$0.743708\pi$
$240$	−0.693642	+	2.13481i	−0.0447744	+	0.137802i
$241$	−6.33627			−0.408155			−0.204078	−	0.978955i	$-0.565420\pi$
$241$	−6.33627			−0.408155			−0.204078	+	0.978955i	$0.565420\pi$
$242$	10.2210	−	4.06585i	0.657031	−	0.261362i
$243$			1.00000i			0.0641500i
$244$	1.57469	−	4.84639i	0.100809	−	0.310258i
$245$	10.1447	+	11.9989i	0.648124	+	0.766582i
$246$	−8.23363	−	5.98208i	−0.524957	−	0.381404i
$247$	−0.557695	−	1.71641i	−0.0354853	−	0.109212i
$248$	2.87382	+	8.84471i	0.182488	+	0.561640i
$249$	5.29032	−	7.28151i	0.335261	−	0.461447i
$250$	−9.00987	+	6.54605i	−0.569834	+	0.414009i
$251$	−8.92087	−	2.89857i	−0.563080	−	0.182956i	0.0136264	−	0.999907i	$-0.495662\pi$
$251$	−8.92087	−	2.89857i	−0.563080	−	0.182956i	−0.576707	+	0.816951i	$0.695662\pi$
$252$	0.0972645	+	2.64396i	0.00612709	+	0.166554i
$253$	7.77687	+	21.5466i	0.488928	+	1.35462i
$254$	12.6575			0.794204
$255$	0.544597	−	1.67610i	0.0341040	−	0.104961i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	1.41175	−	1.94310i	0.0880623	−	0.121207i	−0.762713	−	0.646737i	$-0.776133\pi$
$257$	1.41175	−	1.94310i	0.0880623	−	0.121207i	0.850775	+	0.525530i	$0.176133\pi$
$258$	−0.745389	+	0.242192i	−0.0464059	+	0.0150782i
$259$	15.8464	−	5.80110i	0.984649	−	0.360463i
$260$	6.01635	−	8.28080i	0.373118	−	0.513553i
$261$	−2.38024	−	3.27613i	−0.147333	−	0.202787i
$262$	−5.35606	−	1.74029i	−0.330899	−	0.107516i
$263$		−	9.05435i		−	0.558315i	−0.960245	−	0.279158i	$-0.909945\pi$
$263$		−	9.05435i		−	0.558315i	0.960245	−	0.279158i	$-0.0900552\pi$
$264$	3.31490	−	0.106848i	0.204018	−	0.00657607i
$265$		−	20.1561i		−	1.23818i
$266$	0.286752	−	1.00711i	0.0175819	−	0.0617496i
$267$	−14.7856	+	10.7424i	−0.904866	+	0.657424i
$268$	1.83045	+	1.32990i	0.111812	+	0.0812364i
$269$	−3.13620	+	1.01901i	−0.191218	+	0.0621303i	−0.403060	−	0.915173i	$-0.632054\pi$
$269$	−3.13620	+	1.01901i	−0.191218	+	0.0621303i	0.211843	+	0.977304i	$0.432054\pi$
$270$	2.13481	−	0.693642i	0.129921	−	0.0422137i
$271$	15.2770	+	11.0994i	0.928015	+	0.674242i	0.945506	−	0.325605i	$-0.105568\pi$
$271$	15.2770	+	11.0994i	0.928015	+	0.674242i	−0.0174913	+	0.999847i	$0.505568\pi$
$272$	0.635181	−	0.461486i	0.0385135	−	0.0279817i
$273$	3.30381	−	11.6033i	0.199956	−	0.702266i
$274$			4.00372i			0.241874i
$275$	−0.105837	−	0.0718021i	−0.00638221	−	0.00432983i
$276$			6.90676i			0.415738i
$277$	−1.80187	−	0.585462i	−0.108264	−	0.0351770i	0.254384	−	0.967103i	$-0.418127\pi$
$277$	−1.80187	−	0.585462i	−0.108264	−	0.0351770i	−0.362648	+	0.931926i	$0.618127\pi$
$278$	−3.32246	−	4.57297i	−0.199268	−	0.274269i
$279$	5.46633	−	7.52376i	0.327261	−	0.450436i
$280$	5.57690	−	2.04161i	0.333283	−	0.122009i
$281$	14.9724	−	4.86484i	0.893181	−	0.290212i	0.173761	−	0.984788i	$-0.444408\pi$
$281$	14.9724	−	4.86484i	0.893181	−	0.290212i	0.719420	+	0.694576i	$0.244408\pi$
$282$	−1.65844	+	2.28265i	−0.0987587	+	0.135930i
$283$	−0.925886	+	0.672695i	−0.0550382	+	0.0399876i	−0.614964	−	0.788555i	$-0.710830\pi$
$283$	−0.925886	+	0.672695i	−0.0550382	+	0.0399876i	0.559926	+	0.828543i	$0.310830\pi$
$284$	0.360171	−	1.10849i	0.0213722	−	0.0657769i
$285$	−0.888395			−0.0526240
$286$	−14.5266	−	4.20767i	−0.858974	−	0.248805i
$287$	0.989893	+	26.9085i	0.0584315	+	1.58836i
$288$	0.951057	+	0.309017i	0.0560415	+	0.0182090i
$289$	13.2546	−	9.63002i	0.779682	−	0.566472i
$290$	−5.34287	+	7.35384i	−0.313744	+	0.431832i
$291$	−1.17285	−	3.60967i	−0.0687538	−	0.211603i
$292$	−4.17899	−	12.8616i	−0.244557	−	0.752669i
$293$	13.7365	+	9.98018i	0.802497	+	0.583048i	0.911646	−	0.410977i	$-0.134812\pi$
$293$	13.7365	+	9.98018i	0.802497	+	0.583048i	−0.109149	+	0.994025i	$0.534812\pi$
$294$	5.34550	−	4.51948i	0.311756	−	0.263581i
$295$	−4.49292	+	13.8278i	−0.261588	+	0.805085i
$296$		−	6.37811i		−	0.370720i
$297$	−2.03489	−	2.61901i	−0.118076	−	0.151970i
$298$	2.09165			0.121166
$299$	9.73235	−	29.9531i	0.562836	−	1.73223i
$300$	−0.0226660	−	0.0311970i	−0.00130862	−	0.00180116i
$301$	1.72125	+	1.15634i	0.0992114	+	0.0666502i
$302$	2.85831	+	8.79696i	0.164477	+	0.506208i
$303$	−12.7535	+	4.14385i	−0.732668	+	0.238058i
$304$	−0.320192	−	0.232633i	−0.0183643	−	0.0133424i
$305$	6.72332	+	9.25386i	0.384976	+	0.529875i
$306$	−0.746700	−	0.242618i	−0.0426860	−	0.0138695i
$307$	−24.1687			−1.37938			−0.689689	−	0.724106i	$-0.742253\pi$
$307$	−24.1687			−1.37938			−0.689689	+	0.724106i	$0.742253\pi$
$308$	−5.63492	−	6.72664i	−0.321079	−	0.383286i
$309$	−10.8549			−0.617515
$310$	−19.8535	−	6.45079i	−1.12760	−	0.366380i
$311$	1.18713	+	1.63394i	0.0673158	+	0.0926522i	0.841347	−	0.540495i	$-0.181763\pi$
$311$	1.18713	+	1.63394i	0.0673158	+	0.0926522i	−0.774032	+	0.633147i	$0.781763\pi$
$312$	−3.68909	−	2.68028i	−0.208853	−	0.151741i
$313$	−17.6594	+	5.73788i	−0.998168	+	0.324324i	−0.762133	−	0.647420i	$-0.775848\pi$
$313$	−17.6594	+	5.73788i	−0.998168	+	0.324324i	−0.236035	+	0.971745i	$0.575848\pi$
$314$	−6.07397	−	18.6938i	−0.342774	−	1.05495i
$315$	−4.92971	−	3.31178i	−0.277758	−	0.186598i
$316$	−3.00341	−	4.13384i	−0.168955	−	0.232546i
$317$	5.15908	−	15.8780i	0.289763	−	0.891798i	−0.695168	−	0.718847i	$-0.744670\pi$
$317$	5.15908	−	15.8780i	0.289763	−	0.891798i	0.984931	−	0.172950i	$-0.0553300\pi$
$318$	−8.97950			−0.503545
$319$	12.9005	+	3.73666i	0.722287	+	0.209213i
$320$		−	2.24467i		−	0.125481i
$321$	1.46973	−	4.52337i	0.0820325	−	0.252470i
$322$	14.3788	−	11.2771i	0.801297	−	0.628451i
$323$	0.251391	+	0.182647i	0.0139878	+	0.0101627i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	0.0543374	+	0.167233i	0.00301410	+	0.00927644i
$326$	−11.3068	+	15.5624i	−0.626224	+	0.861924i
$327$	2.66632	−	1.93719i	0.147448	−	0.107127i
$328$	9.67921	+	3.14497i	0.534445	+	0.173652i
$329$	7.45996	−	0.274433i	0.411281	−	0.0151300i
$330$	−4.17960	+	6.16077i	−0.230080	+	0.339139i
$331$	2.52200			0.138622			0.0693109	−	0.997595i	$-0.477920\pi$
$331$	2.52200			0.138622			0.0693109	+	0.997595i	$0.477920\pi$
$332$	−2.78129	+	8.55992i	−0.152643	+	0.469787i
$333$	−5.16000	+	3.74896i	−0.282766	+	0.205442i
$334$	5.58638	−	7.68900i	0.305673	−	0.420723i
$335$	−4.83013	+	1.56940i	−0.263898	+	0.0857457i
$336$	−0.909534	−	2.48450i	−0.0496191	−	0.135541i
$337$	−15.9819	+	21.9972i	−0.870590	+	1.19826i	0.108350	+	0.994113i	$0.465443\pi$
$337$	−15.9819	+	21.9972i	−0.870590	+	1.19826i	−0.978939	+	0.204151i	$0.934557\pi$
$338$	4.58076	+	6.30487i	0.249160	+	0.342940i
$339$	−15.2035	−	4.93993i	−0.825743	−	0.268300i
$340$			1.76235i			0.0955771i
$341$	0.993678	+	30.8282i	0.0538107	+	1.66944i
$342$			0.395779i			0.0214013i
$343$	−18.1368	−	3.74920i	−0.979295	−	0.202438i
$344$	0.634066	−	0.460676i	0.0341865	−	0.0248380i
$345$	−12.5425	−	9.11268i	−0.675267	−	0.490610i
$346$	23.6143	−	7.67274i	1.26951	−	0.412489i
$347$	3.30290	−	1.07318i	0.177309	−	0.0576111i	−0.219017	−	0.975721i	$-0.570285\pi$
$347$	3.30290	−	1.07318i	0.177309	−	0.0576111i	0.396326	+	0.918110i	$0.370285\pi$
$348$	3.27613	+	2.38024i	0.175619	+	0.127595i
$349$	26.8673	−	19.5202i	1.43817	−	1.04489i	0.449752	−	0.893153i	$-0.351512\pi$
$349$	26.8673	−	19.5202i	1.43817	−	1.04489i	0.988420	−	0.151740i	$-0.0484877\pi$
$350$	−0.0279389	+	0.0981245i	−0.00149340	+	0.00524497i
$351$			4.55996i			0.243393i
$352$	−3.11964	+	1.12598i	−0.166277	+	0.0600150i
$353$		−	19.2514i		−	1.02465i	−0.858792	−	0.512325i	$-0.828784\pi$
$353$		−	19.2514i		−	1.02465i	0.858792	−	0.512325i	$-0.171216\pi$
$354$	6.16027	+	2.00159i	0.327414	+	0.106383i
$355$	1.53779	+	2.11659i	0.0816177	+	0.112337i
$356$	10.7424	−	14.7856i	0.569346	−	0.783637i
$357$	0.714099	+	1.95065i	0.0377941	+	0.103239i
$358$	15.5013	−	5.03667i	0.819267	−	0.266196i
$359$	−14.9582	+	20.5882i	−0.789463	+	1.08660i	0.204712	+	0.978822i	$0.434374\pi$
$359$	−14.9582	+	20.5882i	−0.789463	+	1.08660i	−0.994175	+	0.107780i	$0.965626\pi$
$360$	−1.81598	+	1.31939i	−0.0957105	+	0.0695378i
$361$	−5.82292	+	17.9211i	−0.306469	+	0.943216i
$362$	12.6201			0.663297
$363$	10.6588	+	2.71842i	0.559442	+	0.142680i
$364$	0.443523	+	12.0564i	0.0232469	+	0.631925i
$365$	28.8701	+	9.38047i	1.51113	+	0.490996i
$366$	4.12259	−	2.99523i	0.215491	−	0.156563i
$367$	−1.59030	+	2.18886i	−0.0830131	+	0.114258i	−0.848504	−	0.529189i	$-0.822496\pi$
$367$	−1.59030	+	2.18886i	−0.0830131	+	0.114258i	0.765491	+	0.643447i	$0.222496\pi$
$368$	−2.13430	−	6.56871i	−0.111258	−	0.342418i
$369$	−3.14497	−	9.67921i	−0.163720	−	0.503880i
$370$	11.5825	+	8.41519i	0.602146	+	0.437485i
$371$	14.6615	+	18.6939i	0.761186	+	0.970538i
$372$	−2.87382	+	8.84471i	−0.149001	+	0.458577i
$373$			32.0171i			1.65778i	0.559412	+	0.828890i	$0.311027\pi$
$373$			32.0171i			1.65778i	−0.559412	+	0.828890i	$0.688973\pi$
$374$	2.44932	−	0.884038i	0.126651	−	0.0457125i
$375$	−11.1368			−0.575102
$376$	0.871894	−	2.68341i	0.0449645	−	0.138387i
$377$	−10.8538	−	14.9390i	−0.559000	−	0.769398i
$378$	−1.47539	+	2.19618i	−0.0758861	+	0.112959i
$379$	−6.68904	−	20.5867i	−0.343593	−	1.05747i	−0.962333	−	0.271874i	$-0.912357\pi$
$379$	−6.68904	−	20.5867i	−0.343593	−	1.05747i	0.618740	−	0.785596i	$-0.287643\pi$
$380$	0.844914	−	0.274529i	0.0433432	−	0.0140831i
$381$	10.2402	+	7.43991i	0.524619	+	0.381158i
$382$	−11.5910	−	15.9536i	−0.593047	−	0.816259i
$383$	−11.8622	−	3.85425i	−0.606128	−	0.196943i	−0.0101563	−	0.999948i	$-0.503233\pi$
$383$	−11.8622	−	3.85425i	−0.606128	−	0.196943i	−0.595972	+	0.803006i	$0.703233\pi$
$384$	−1.00000			−0.0510310
$385$	19.6501	−	1.35786i	1.00146	−	0.0692030i
$386$	17.7038			0.901100
$387$	−0.745389	−	0.242192i	−0.0378903	−	0.0123113i
$388$	2.23090	+	3.07057i	0.113257	+	0.155884i
$389$	−20.4448	−	14.8540i	−1.03659	−	0.753127i	−0.0669736	−	0.997755i	$-0.521334\pi$
$389$	−20.4448	−	14.8540i	−1.03659	−	0.753127i	−0.969617	+	0.244627i	$0.921334\pi$
$390$	9.73466	−	3.16298i	0.492934	−	0.160164i
$391$	1.67570	+	5.15727i	0.0847438	+	0.260815i
$392$	−3.68728	+	5.95013i	−0.186236	+	0.300527i
$393$	−3.31023	−	4.55614i	−0.166979	−	0.229827i
$394$	−3.45300	+	10.6272i	−0.173959	+	0.535392i
$395$	11.4696			0.577099
$396$	2.74462	+	1.86201i	0.137922	+	0.0935695i
$397$			13.7505i			0.690119i	0.938581	+	0.345059i	$0.112141\pi$
$397$			13.7505i			0.690119i	−0.938581	+	0.345059i	$0.887859\pi$
$398$	−7.68274	+	23.6450i	−0.385101	+	1.18522i
$399$	0.823949	−	0.646217i	0.0412491	−	0.0323513i
$400$	0.0311970	+	0.0226660i	0.00155985	+	0.00113330i
$401$	−1.63912	−	5.04469i	−0.0818537	−	0.251920i	0.901752	−	0.432255i	$-0.142282\pi$
$401$	−1.63912	−	5.04469i	−0.0818537	−	0.251920i	−0.983605	+	0.180335i	$0.942282\pi$
$402$	0.699168	+	2.15182i	0.0348713	+	0.107323i
$403$	24.9263	−	34.3081i	1.24167	−	1.70901i
$404$	10.8487	−	7.88208i	0.539745	−	0.392148i
$405$	2.13481	+	0.693642i	0.106080	+	0.0344674i
$406$	−0.393874	−	10.7068i	−0.0195476	−	0.531368i
$407$	5.88535	−	20.3186i	0.291726	−	1.00716i
$408$	0.785127			0.0388696
$409$	6.69458	−	20.6038i	0.331026	−	1.01879i	−0.637621	−	0.770350i	$-0.720081\pi$
$409$	6.69458	−	20.6038i	0.331026	−	1.01879i	0.968647	−	0.248442i	$-0.0799186\pi$
$410$	−18.4818	+	13.4278i	−0.912752	+	0.663153i
$411$	−2.35333	+	3.23908i	−0.116081	+	0.159772i
$412$	10.3236	−	3.35436i	0.508609	−	0.165257i
$413$	−5.89131	−	16.0928i	−0.289892	−	0.791876i
$414$	−4.05969	+	5.58768i	−0.199523	+	0.274620i
$415$	−11.8751	−	16.3446i	−0.582923	−	0.802325i
$416$	4.33678	+	1.40911i	0.212628	+	0.0690871i
$417$		−	5.65250i		−	0.276804i
$418$	−0.805369	−	1.03655i	−0.0393919	−	0.0506993i
$419$		−	38.5147i		−	1.88156i	−0.339011	−	0.940782i	$-0.610092\pi$
$419$		−	38.5147i		−	1.88156i	0.339011	−	0.940782i	$-0.389908\pi$
$420$	5.71183	+	1.62632i	0.278709	+	0.0793565i
$421$	16.4529	−	11.9537i	0.801866	−	0.582590i	−0.109595	−	0.993976i	$-0.534955\pi$
$421$	16.4529	−	11.9537i	0.801866	−	0.582590i	0.911461	+	0.411387i	$0.134955\pi$
$422$	23.1244	+	16.8009i	1.12568	+	0.817855i
$423$	−2.68341	+	0.871894i	−0.130472	+	0.0423929i
$424$	8.54001	−	2.77482i	0.414740	−	0.134757i
$425$	−0.0244936	−	0.0177957i	−0.00118811	−	0.000863216i
$426$	0.942940	−	0.685086i	0.0456856	−	0.0331925i
$427$	−12.9668	−	3.69203i	−0.627509	−	0.178670i
$428$			4.75615i			0.229897i
$429$	−9.27904	−	11.9426i	−0.447996	−	0.576593i
$430$			1.75926i			0.0848390i
$431$	3.29087	+	1.06927i	0.158516	+	0.0515048i	0.387200	−	0.921996i	$-0.373442\pi$
$431$	3.29087	+	1.06927i	0.158516	+	0.0515048i	−0.228684	+	0.973501i	$0.573442\pi$
$432$	0.587785	+	0.809017i	0.0282798	+	0.0389238i
$433$	11.2693	−	15.5108i	0.541567	−	0.745403i	−0.447271	−	0.894399i	$-0.647604\pi$
$433$	11.2693	−	15.5108i	0.541567	−	0.745403i	0.988838	+	0.148995i	$0.0476040\pi$
$434$	23.1056	−	8.45856i	1.10910	−	0.406024i
$435$	−8.64495	+	2.80892i	−0.414494	+	0.134677i
$436$	−1.93719	+	2.66632i	−0.0927747	+	0.127693i
$437$	2.21149	−	1.60674i	0.105790	−	0.0768608i
$438$	4.17899	−	12.8616i	0.199680	−	0.614551i
$439$	8.15274			0.389109			0.194555	−	0.980892i	$-0.437674\pi$
$439$	8.15274			0.389109			0.194555	+	0.980892i	$0.437674\pi$
$440$	2.07126	−	7.15081i	0.0987433	−	0.340901i
$441$	6.98108	−	0.514328i	0.332432	−	0.0244918i
$442$	−3.40492	−	1.10633i	−0.161956	−	0.0526226i
$443$	−6.79607	+	4.93763i	−0.322891	+	0.234594i	−0.737408	−	0.675448i	$-0.763950\pi$
$443$	−6.79607	+	4.93763i	−0.322891	+	0.234594i	0.414517	+	0.910042i	$0.363950\pi$
$444$	3.74896	−	5.16000i	0.177918	−	0.244883i
$445$	12.6770	+	39.0159i	0.600949	+	1.84953i
$446$	−3.67392	−	11.3072i	−0.173965	−	0.535410i
$447$	1.69218	+	1.22944i	0.0800375	+	0.0581506i
$448$	1.63277	+	2.08184i	0.0771412	+	0.0983577i
$449$	−1.21186	+	3.72971i	−0.0571911	+	0.176016i	−0.975571	−	0.219683i	$-0.929498\pi$
$449$	−1.21186	+	3.72971i	−0.0571911	+	0.176016i	0.918380	+	0.395699i	$0.129498\pi$
$450$		−	0.0385616i		−	0.00181781i
$451$	27.9329	+	18.9503i	1.31531	+	0.892333i
$452$	15.9860			0.751916
$453$	−2.85831	+	8.79696i	−0.134295	+	0.413317i
$454$	−5.02595	−	6.91762i	−0.235879	−	0.324660i
$455$	−22.4793	−	15.1016i	−1.05385	−	0.707973i
$456$	−0.122303	−	0.376408i	−0.00572734	−	0.0176269i
$457$	31.7927	−	10.3301i	1.48720	−	0.483221i	0.550945	−	0.834542i	$-0.314267\pi$
$457$	31.7927	−	10.3301i	1.48720	−	0.483221i	0.936255	+	0.351321i	$0.114267\pi$
$458$	4.90459	+	3.56339i	0.229176	+	0.166506i
$459$	−0.461486	−	0.635181i	−0.0215403	−	0.0296477i
$460$	14.7446	+	4.79082i	0.687472	+	0.223373i
$461$	−25.7199			−1.19789			−0.598947	−	0.800789i	$-0.704414\pi$
$461$	−25.7199			−1.19789			−0.598947	+	0.800789i	$0.704414\pi$
$462$	−0.604926	−	8.75409i	−0.0281437	−	0.407277i
$463$	−32.5936			−1.51475			−0.757377	−	0.652977i	$-0.773520\pi$
$463$	−32.5936			−1.51475			−0.757377	+	0.652977i	$0.773520\pi$
$464$	−3.85132	−	1.25137i	−0.178793	−	0.0580933i
$465$	−12.2701	−	16.8884i	−0.569014	−	0.783181i
$466$	−7.27661	−	5.28677i	−0.337083	−	0.244905i
$467$	−9.32088	+	3.02854i	−0.431319	+	0.140144i	−0.516627	−	0.856211i	$-0.672813\pi$
$467$	−9.32088	+	3.02854i	−0.431319	+	0.140144i	0.0853081	+	0.996355i	$0.472813\pi$
$468$	−1.40911	−	4.33678i	−0.0651359	−	0.200468i
$469$	3.33816	−	4.96898i	0.154142	−	0.229446i
$470$	3.72266	+	5.12380i	0.171713	+	0.236343i
$471$	6.07397	−	18.6938i	0.279874	−	0.861363i
$472$	−6.47729			−0.298141
$473$	2.44501	−	0.882485i	0.112422	−	0.0405767i
$474$		−	5.10970i		−	0.234696i
$475$	−0.00471618	+	0.0145149i	−0.000216393	+	0.000665990i
$476$	−1.28193	−	1.63451i	−0.0587573	−	0.0749176i
$477$	−7.26457	−	5.27802i	−0.332622	−	0.241664i
$478$	−1.68091	−	5.17331i	−0.0768831	−	0.236622i
$479$	1.91387	+	5.89029i	0.0874470	+	0.269134i	0.985212	−	0.171341i	$-0.0548100\pi$
$479$	1.91387	+	5.89029i	0.0874470	+	0.269134i	−0.897765	+	0.440475i	$0.854810\pi$
$480$	1.31939	−	1.81598i	0.0602215	−	0.0828877i
$481$	−23.5294	+	17.0951i	−1.07285	+	0.779470i
$482$	6.02616	+	1.95802i	0.274484	+	0.0891852i
$483$	18.2612	−	0.671782i	0.830914	−	0.0305672i
$484$	−10.9772	+	0.708385i	−0.498962	+	0.0321993i
$485$	−8.51951			−0.386851
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	21.4455	−	15.5810i	0.971786	−	0.706044i	0.0159283	−	0.999873i	$-0.494930\pi$
$487$	21.4455	−	15.5810i	0.971786	−	0.706044i	0.955858	+	0.293829i	$0.0949297\pi$
$488$	−2.99523	+	4.12259i	−0.135588	+	0.186621i
$489$	−18.2947	+	5.94432i	−0.827317	+	0.268812i
$490$	−5.94037	−	14.5465i	−0.268358	−	0.657145i
$491$	13.1421	−	18.0886i	0.593096	−	0.816326i	−0.401959	−	0.915658i	$-0.631670\pi$
$491$	13.1421	−	18.0886i	0.593096	−	0.816326i	0.995054	+	0.0993315i	$0.0316704\pi$
$492$	5.98208	+	8.23363i	0.269693	+	0.371201i
$493$	3.02377	+	0.982483i	0.136184	+	0.0442488i
$494$			1.80474i			0.0811990i
$495$	−7.00258	+	2.52746i	−0.314743	+	0.113601i
$496$		−	9.29988i		−	0.417577i
$497$	−2.96584	−	0.844462i	−0.133036	−	0.0378793i
$498$	−7.28151	+	5.29032i	−0.326292	+	0.237065i
$499$	26.3899	+	19.1734i	1.18137	+	0.858317i	0.992326	−	0.123651i	$-0.0394602\pi$
$499$	26.3899	+	19.1734i	1.18137	+	0.858317i	0.189047	+	0.981968i	$0.439460\pi$
$500$	10.5917	−	3.44146i	0.473677	−	0.153907i
$501$	9.03896	−	2.93694i	0.403831	−	0.131213i
$502$	7.58855	+	5.51340i	0.338693	+	0.246075i
$503$	10.7204	−	7.78880i	0.477998	−	0.347286i	−0.322552	−	0.946552i	$-0.604541\pi$
$503$	10.7204	−	7.78880i	0.477998	−	0.347286i	0.800550	+	0.599266i	$0.204541\pi$
$504$	0.724525	−	2.54461i	0.0322729	−	0.113346i
$505$			30.1006i			1.33946i
$506$	−0.737976	−	22.8952i	−0.0328071	−	1.01782i
$507$			7.79325i			0.346110i
$508$	−12.0380	−	3.91139i	−0.534101	−	0.173540i
$509$	24.4720	+	33.6828i	1.08470	+	1.49296i	0.854239	+	0.519881i	$0.174024\pi$
$509$	24.4720	+	33.6828i	1.08470	+	1.49296i	0.230462	+	0.973081i	$0.425976\pi$
$510$	−1.03589	+	1.42577i	−0.0458698	+	0.0631344i
$511$	−33.5991	+	12.3001i	−1.48634	+	0.544123i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−0.232633	+	0.320192i	−0.0102710	+	0.0141368i
$514$	−1.94310	+	1.41175i	−0.0857065	+	0.0622694i
$515$	−7.52943	+	23.1732i	−0.331787	+	1.02113i
$516$	0.783748			0.0345026
$517$	5.25367	−	7.74396i	0.231056	−	0.340579i
$518$	−16.8635	+	0.620364i	−0.740939	+	0.0272572i
$519$	23.6143	+	7.67274i	1.03655	+	0.336796i
$520$	−8.28080	+	6.01635i	−0.363137	+	0.263834i
$521$	−23.3981	+	32.2047i	−1.02509	+	1.41091i	−0.116516	+	0.993189i	$0.537173\pi$
$521$	−23.3981	+	32.2047i	−1.02509	+	1.41091i	−0.908573	+	0.417725i	$0.862827\pi$
$522$	1.25137	+	3.85132i	0.0547709	+	0.168568i
$523$	−1.62796	−	5.01034i	−0.0711856	−	0.219087i	0.909134	−	0.416504i	$-0.136745\pi$
$523$	−1.62796	−	5.01034i	−0.0711856	−	0.219087i	−0.980320	+	0.197417i	$0.936745\pi$
$524$	4.55614	+	3.31023i	0.199036	+	0.144608i
$525$	−0.0802792	+	0.0629623i	−0.00350367	+	0.00274790i
$526$	−2.79795	+	8.61120i	−0.121996	+	0.375466i
$527$			7.30159i			0.318062i
$528$	−3.18568	−	0.922742i	−0.138639	−	0.0401572i
$529$	24.7033			1.07406
$530$	−6.22856	+	19.1695i	−0.270551	+	0.832672i
$531$	3.80725	+	5.24024i	0.165221	+	0.227407i
$532$	−0.583930	+	0.869203i	−0.0253166	+	0.0376847i
$533$	−14.3409	−	44.1368i	−0.621174	−	1.91178i
$534$	17.3816	−	5.64761i	0.752173	−	0.244396i
$535$	−8.63708	−	6.27521i	−0.373413	−	0.271301i
$536$	−1.32990	−	1.83045i	−0.0574428	−	0.0790632i
$537$	15.5013	+	5.03667i	0.668929	+	0.217348i
$538$	3.29760			0.142169
$539$	−17.2369	+	15.5528i	−0.742446	+	0.669906i
$540$	−2.24467			−0.0965954
$541$	−29.9847	−	9.74260i	−1.28914	−	0.418867i	−0.417350	−	0.908746i	$-0.637041\pi$
$541$	−29.9847	−	9.74260i	−1.28914	−	0.418867i	−0.871791	+	0.489878i	$0.837041\pi$
$542$	−11.0994	−	15.2770i	−0.476761	−	0.656205i
$543$	10.2099	+	7.41791i	0.438147	+	0.318333i
$544$	−0.746700	+	0.242618i	−0.0320145	+	0.0104021i
$545$	−2.28607	−	7.03580i	−0.0979245	−	0.301381i
$546$	−6.72774	+	10.0145i	−0.287921	+	0.428581i
$547$	−15.5276	−	21.3719i	−0.663911	−	0.913796i	0.335692	−	0.941972i	$-0.391030\pi$
$547$	−15.5276	−	21.3719i	−0.663911	−	0.913796i	−0.999603	+	0.0281763i	$0.991030\pi$
$548$	1.23722	−	3.80777i	0.0528513	−	0.162660i
$549$	5.09580			0.217483
$550$	0.0784688	+	0.100993i	0.00334592	+	0.00430637i
$551$		−	1.60271i		−	0.0682779i
$552$	2.13430	−	6.56871i	0.0908420	−	0.279583i
$553$	−10.6376	+	8.34297i	−0.452356	+	0.354779i
$554$	1.53276	+	1.11362i	0.0651207	+	0.0473130i
$555$	4.42413	+	13.6161i	0.187794	+	0.577970i
$556$	1.74672	+	5.37585i	0.0740774	+	0.227987i
$557$	−14.6165	+	20.1179i	−0.619321	+	0.852422i	−0.997303	−	0.0733905i	$-0.976618\pi$
$557$	−14.6165	+	20.1179i	−0.619321	+	0.852422i	0.377982	+	0.925813i	$0.376618\pi$
$558$	−7.52376	+	5.46633i	−0.318506	+	0.231408i
$559$	−3.39895	−	1.10438i	−0.143760	−	0.0467105i
$560$	−5.93483	+	0.218327i	−0.250793	+	0.00922601i
$561$	2.50116	+	0.724470i	0.105599	+	0.0305871i
$562$	−15.7430			−0.664077
$563$	−2.26506	+	6.97114i	−0.0954610	+	0.293799i	−0.987374	−	0.158409i	$-0.949363\pi$
$563$	−2.26506	+	6.97114i	−0.0954610	+	0.293799i	0.891913	+	0.452208i	$0.149363\pi$
$564$	2.28265	−	1.65844i	0.0961168	−	0.0698330i
$565$	−21.0917	+	29.0302i	−0.887333	+	1.22131i
$566$	1.08844	−	0.353657i	0.0457507	−	0.0148653i
$567$	−2.48450	+	0.909534i	−0.104339	+	0.0381968i
$568$	−0.685086	+	0.942940i	−0.0287456	+	0.0395649i
$569$	−9.69569	−	13.3450i	−0.406464	−	0.559450i	0.555887	−	0.831258i	$-0.312379\pi$
$569$	−9.69569	−	13.3450i	−0.406464	−	0.559450i	−0.962352	+	0.271807i	$0.912379\pi$
$570$	0.844914	+	0.274529i	0.0353896	+	0.0114988i
$571$			15.9838i			0.668902i	0.942413	+	0.334451i	$0.108551\pi$
$571$			15.9838i			0.668902i	−0.942413	+	0.334451i	$0.891449\pi$
$572$	12.5153	+	8.49069i	0.523293	+	0.355014i
$573$		−	19.7198i		−	0.823805i
$574$	7.37373	−	25.8974i	0.307774	−	1.08094i
$575$	−0.215470	+	0.156548i	−0.00898573	+	0.00652851i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	26.4112	−	8.58153i	1.09951	−	0.357254i	0.297599	−	0.954691i	$-0.403814\pi$
$577$	26.4112	−	8.58153i	1.09951	−	0.357254i	0.801916	+	0.597437i	$0.203814\pi$
$578$	−15.5817	+	5.06280i	−0.648114	+	0.210585i
$579$	14.3227	+	10.4060i	0.595230	+	0.432460i
$580$	7.35384	−	5.34287i	0.305351	−	0.221851i
$581$	22.9026	+	6.52104i	0.950162	+	0.270538i
$582$			3.79543i			0.157326i
$583$	29.7662	−	0.959446i	1.23279	−	0.0397362i
$584$			13.5235i			0.559606i
$585$	9.73466	+	3.16298i	0.402479	+	0.130773i
$586$	−9.98018	−	13.7365i	−0.412277	−	0.567451i
$587$	−9.78830	+	13.4724i	−0.404006	+	0.556067i	−0.961744	−	0.273950i	$-0.911670\pi$
$587$	−9.78830	+	13.4724i	−0.404006	+	0.556067i	0.557738	+	0.830017i	$0.311670\pi$
$588$	−6.48046	+	2.64643i	−0.267250	+	0.109137i
$589$	3.50055	−	1.13740i	0.144238	−	0.0468657i
$590$	8.54604	−	11.7626i	0.351835	−	0.484259i
$591$	−9.04006	+	6.56799i	−0.371858	+	0.270171i
$592$	−1.97094	+	6.06594i	−0.0810053	+	0.249309i
$593$	−10.0260			−0.411719			−0.205859	−	0.978582i	$-0.565999\pi$
$593$	−10.0260			−0.411719			−0.205859	+	0.978582i	$0.565999\pi$
$594$	1.12598	+	3.11964i	0.0461995	+	0.128000i
$595$	4.65960	−	0.171415i	0.191025	−	0.00702731i
$596$	−1.98928	−	0.646356i	−0.0814841	−	0.0264758i
$597$	−20.1137	+	14.6134i	−0.823198	+	0.598088i
$598$	−18.5120	+	25.4796i	−0.757013	+	1.04194i
$599$	2.49585	+	7.68145i	0.101978	+	0.313855i	0.989009	−	0.147854i	$-0.0472364\pi$
$599$	2.49585	+	7.68145i	0.101978	+	0.313855i	−0.887031	+	0.461709i	$0.847236\pi$
$600$	0.0119162	+	0.0366743i	0.000486477	+	0.00149722i
$601$	−20.9629	−	15.2304i	−0.855093	−	0.621262i	0.0714525	−	0.997444i	$-0.477237\pi$
$601$	−20.9629	−	15.2304i	−0.855093	−	0.621262i	−0.926546	+	0.376182i	$0.877237\pi$
$602$	−1.27968	−	1.63164i	−0.0521559	−	0.0665006i
$603$	−0.699168	+	2.15182i	−0.0284723	+	0.0876288i
$604$		−	9.24967i		−	0.376364i
$605$	13.1967	−	20.8689i	0.536523	−	0.848443i
$606$	13.4098			0.544735
$607$	−4.73533	+	14.5738i	−0.192201	+	0.591534i	0.807797	+	0.589461i	$0.200660\pi$
$607$	−4.73533	+	14.5738i	−0.192201	+	0.591534i	−0.999998	+	0.00207281i	$0.999340\pi$
$608$	0.232633	+	0.320192i	0.00943452	+	0.0129855i
$609$	5.97463	−	8.89347i	0.242104	−	0.360382i
$610$	−3.53466	−	10.8786i	−0.143114	−	0.440460i
$611$	−12.2363	+	3.97580i	−0.495026	+	0.160844i
$612$	0.635181	+	0.461486i	0.0256757	+	0.0186545i
$613$	−11.4136	−	15.7095i	−0.460991	−	0.634500i	0.513723	−	0.857956i	$-0.328266\pi$
$613$	−11.4136	−	15.7095i	−0.460991	−	0.634500i	−0.974714	+	0.223456i	$0.928266\pi$
$614$	22.9858	+	7.46853i	0.927630	+	0.301405i
$615$	−22.8448			−0.921190
$616$	3.28048	+	8.13870i	0.132174	+	0.327918i
$617$	9.54578			0.384299			0.192149	−	0.981366i	$-0.438454\pi$
$617$	9.54578			0.384299			0.192149	+	0.981366i	$0.438454\pi$
$618$	10.3236	+	3.35436i	0.415278	+	0.134932i
$619$	−20.6405	−	28.4092i	−0.829612	−	1.14186i	−0.987995	−	0.154485i	$-0.950628\pi$
$619$	−20.6405	−	28.4092i	−0.829612	−	1.14186i	0.158383	−	0.987378i	$-0.449372\pi$
$620$	16.8884	+	12.2701i	0.678254	+	0.492781i
$621$	−6.56871	+	2.13430i	−0.263593	+	0.0856467i
$622$	−0.624109	−	1.92081i	−0.0250245	−	0.0770175i
$623$	−40.1375	−	26.9644i	−1.60808	−	1.08030i
$624$	2.68028	+	3.68909i	0.107297	+	0.147682i
$625$	−7.78455	+	23.9584i	−0.311382	+	0.958335i
$626$	18.5682			0.742134
$627$	−0.0422884	−	1.31197i	−0.00168884	−	0.0523950i
$628$			19.6558i			0.784351i
$629$	1.54744	−	4.76253i	0.0617005	−	0.189895i
$630$	3.66504	+	4.67305i	0.146019	+	0.186179i
$631$	36.1496	+	26.2643i	1.43909	+	1.04556i	0.988231	+	0.152971i	$0.0488840\pi$
$631$	36.1496	+	26.2643i	1.43909	+	1.04556i	0.450864	+	0.892593i	$0.351116\pi$
$632$	1.57898	+	4.85962i	0.0628086	+	0.193305i
$633$	8.83275	+	27.1844i	0.351070	+	1.08048i
$634$	−9.81315	+	13.5066i	−0.389730	+	0.536417i
$635$	22.9858	−	16.7002i	0.912164	−	0.662726i
$636$	8.54001	+	2.77482i	0.338634	+	0.110029i
$637$	31.8335	−	2.34531i	1.26129	−	0.0929247i
$638$	−11.1144	−	7.54023i	−0.440022	−	0.298521i
$639$	1.16554			0.0461080
$640$	−0.693642	+	2.13481i	−0.0274186	+	0.0843858i
$641$	−14.8683	+	10.8025i	−0.587264	+	0.426673i	−0.841336	−	0.540513i	$-0.818230\pi$
$641$	−14.8683	+	10.8025i	−0.587264	+	0.426673i	0.254071	+	0.967185i	$0.418230\pi$
$642$	−2.79560	+	3.84781i	−0.110333	+	0.151861i
$643$	−41.5308	+	13.4942i	−1.63781	+	0.532158i	−0.976049	−	0.217553i	$-0.930193\pi$
$643$	−41.5308	+	13.4942i	−1.63781	+	0.532158i	−0.661766	+	0.749711i	$0.730193\pi$
$644$	−17.1598	+	6.28193i	−0.676193	+	0.247543i
$645$	−1.03407	+	1.42327i	−0.0407163	+	0.0560412i
$646$	−0.182647	−	0.251391i	−0.00718613	−	0.00989087i
$647$	−31.0078	−	10.0750i	−1.21904	−	0.396091i	−0.372310	−	0.928109i	$-0.621434\pi$
$647$	−31.0078	−	10.0750i	−1.21904	−	0.396091i	−0.846733	+	0.532018i	$0.821434\pi$
$648$			1.00000i			0.0392837i
$649$	−20.6346	−	5.97687i	−0.809977	−	0.234613i
$650$		−	0.175840i		−	0.00689699i
$651$	23.6646	+	6.73800i	0.927489	+	0.264083i
$652$	15.5624	−	11.3068i	0.609472	−	0.442807i
$653$	−11.3338	−	8.23448i	−0.443526	−	0.322240i	0.343509	−	0.939150i	$-0.388385\pi$
$653$	−11.3338	−	8.23448i	−0.443526	−	0.322240i	−0.787034	+	0.616909i	$0.788385\pi$
$654$	−3.13444	+	1.01844i	−0.122566	+	0.0398242i
$655$	−12.0226	+	3.90638i	−0.469763	+	0.152635i
$656$	−8.23363	−	5.98208i	−0.321469	−	0.233561i
$657$	10.9407	−	7.94891i	0.426839	−	0.310117i
$658$	−7.17965	−	2.04425i	−0.279892	−	0.0796933i
$659$		−	30.8627i		−	1.20224i	−0.799158	−	0.601121i	$-0.794721\pi$
$659$		−	30.8627i		−	1.20224i	0.799158	−	0.601121i	$-0.205279\pi$
$660$	5.87882	−	4.56767i	0.228833	−	0.177796i
$661$			40.5396i			1.57681i	0.615159	+	0.788403i	$0.289092\pi$
$661$			40.5396i			1.57681i	−0.615159	+	0.788403i	$0.710908\pi$
$662$	−2.39857	−	0.779341i	−0.0932229	−	0.0302900i
$663$	−2.10436	−	2.89640i	−0.0817265	−	0.112487i
$664$	5.29032	−	7.28151i	0.205304	−	0.282577i
$665$	−0.808025	−	2.20722i	−0.0313339	−	0.0855923i
$666$	6.06594	−	1.97094i	0.235050	−	0.0763725i
$667$	16.4398	−	22.6274i	0.636550	−	0.876136i
$668$	−7.68900	+	5.58638i	−0.297496	+	0.216144i
$669$	3.67392	−	11.3072i	0.142042	−	0.437161i
$670$	5.07870			0.196207
$671$	−13.3459	+	10.3694i	−0.515214	+	0.400306i
$672$	0.0972645	+	2.64396i	0.00375206	+	0.101993i
$673$	0.351044	+	0.114061i	0.0135317	+	0.00439673i	0.315775	−	0.948834i	$-0.397736\pi$
$673$	0.351044	+	0.114061i	0.0135317	+	0.00439673i	−0.302243	+	0.953231i	$0.597736\pi$
$674$	21.9972	−	15.9819i	0.847300	−	0.615600i
$675$	0.0226660	−	0.0311970i	0.000872413	−	0.00120077i
$676$	−2.40825	−	7.41182i	−0.0926249	−	0.285070i
$677$	10.4050	+	32.0234i	0.399898	+	1.23076i	0.925081	+	0.379770i	$0.123997\pi$
$677$	10.4050	+	32.0234i	0.399898	+	1.23076i	−0.525183	+	0.850989i	$0.676003\pi$
$678$	12.9329	+	9.39631i	0.496685	+	0.360863i
$679$	7.90148	−	6.19707i	0.303231	−	0.237822i
$680$	0.544597	−	1.67610i	0.0208844	−	0.0642754i
$681$		−	8.55065i		−	0.327662i
$682$	8.58140	−	29.6264i	0.328599	−	1.13445i
$683$	−30.4603			−1.16553			−0.582766	−	0.812640i	$-0.698029\pi$
$683$	−30.4603			−1.16553			−0.582766	+	0.812640i	$0.698029\pi$
$684$	0.122303	−	0.376408i	0.00467635	−	0.0143923i
$685$	5.28246	+	7.27068i	0.201832	+	0.277798i
$686$	16.0906	+	9.17028i	0.614340	+	0.350123i
$687$	1.87339	+	5.76569i	0.0714741	+	0.219975i
$688$	−0.745389	+	0.242192i	−0.0284177	+	0.00923347i
$689$	−33.1262	−	24.0676i	−1.26201	−	0.916901i
$690$	9.11268	+	12.5425i	0.346914	+	0.477486i
$691$	16.8287	+	5.46799i	0.640195	+	0.208012i	0.611086	−	0.791564i	$-0.290733\pi$
$691$	16.8287	+	5.46799i	0.640195	+	0.208012i	0.0291093	+	0.999576i	$0.490733\pi$
$692$	−24.8295			−0.943877
$693$	4.65613	−	7.43777i	0.176872	−	0.282538i
$694$	−3.47287			−0.131828
$695$	−12.0670	−	3.92082i	−0.457729	−	0.148725i
$696$	−2.38024	−	3.27613i	−0.0902230	−	0.124181i
$697$	6.46444	+	4.69669i	0.244858	+	0.177900i
$698$	−31.5844	+	10.2624i	−1.19549	+	0.388437i
$699$	−2.77942	−	8.55417i	−0.105127	−	0.323548i
$700$	0.0568936	−	0.0846883i	0.00215038	−	0.00320092i
$701$	−3.83707	−	5.28127i	−0.144924	−	0.199471i	0.730384	−	0.683037i	$-0.239341\pi$
$701$	−3.83707	−	5.28127i	−0.144924	−	0.199471i	−0.875308	+	0.483566i	$0.839341\pi$
$702$	1.40911	−	4.33678i	0.0531833	−	0.163681i
$703$	−2.52432			−0.0952066
$704$	3.31490	−	0.106848i	0.124935	−	0.00402700i
$705$			6.33337i			0.238528i
$706$	−5.94902	+	18.3092i	−0.223894	+	0.689075i
$707$	−21.8951	−	27.9170i	−0.823451	−	1.04993i
$708$	−5.24024	−	3.80725i	−0.196940	−	0.143085i
$709$	−2.00674	−	6.17612i	−0.0753648	−	0.231949i	0.906276	−	0.422685i	$-0.138912\pi$
$709$	−2.00674	−	6.17612i	−0.0753648	−	0.231949i	−0.981641	+	0.190736i	$0.938912\pi$
$710$	−0.808466	−	2.48820i	−0.0303412	−	0.0933806i
$711$	3.00341	−	4.13384i	0.112637	−	0.155031i
$712$	−14.7856	+	10.7424i	−0.554115	+	0.402588i
$713$	61.0883	+	19.8488i	2.28777	+	0.743343i
$714$	−0.0763650	−	2.07585i	−0.00285789	−	0.0776866i
$715$	−31.9315	+	11.5251i	−1.19417	+	0.431015i
$716$	−16.2990			−0.609122
$717$	1.68091	−	5.17331i	0.0627748	−	0.193201i
$718$	20.5882	−	14.9582i	0.768344	−	0.558235i
$719$	−9.61014	+	13.2272i	−0.358398	+	0.493292i	−0.949701	−	0.313157i	$-0.898614\pi$
$719$	−9.61014	+	13.2272i	−0.358398	+	0.493292i	0.591304	+	0.806449i	$0.298614\pi$
$720$	2.13481	−	0.693642i	0.0795597	−	0.0258505i
$721$	−9.87292	−	26.9691i	−0.367687	−	1.00438i
$722$	11.0758	−	15.2446i	0.412200	−	0.567345i
$723$	3.72437	+	5.12615i	0.138511	+	0.190644i
$724$	−12.0024	−	3.89982i	−0.446067	−	0.144936i
$725$			0.156156i			0.00579948i
$726$	−9.29709	−	5.87912i	−0.345047	−	0.218195i
$727$		−	14.7213i		−	0.545985i	−0.962016	−	0.272992i	$-0.911987\pi$
$727$		−	14.7213i		−	0.545985i	0.962016	−	0.272992i	$-0.0880133\pi$
$728$	3.30381	−	11.6033i	0.122447	−	0.430049i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	−24.5584	−	17.8427i	−0.908947	−	0.660388i
$731$	0.585225	−	0.190151i	0.0216453	−	0.00703299i
$732$	−4.84639	+	1.57469i	−0.179128	+	0.0582021i
$733$	19.8659	+	14.4334i	0.733764	+	0.533110i	0.890752	−	0.454490i	$-0.150178\pi$
$733$	19.8659	+	14.4334i	0.733764	+	0.533110i	−0.156988	+	0.987600i	$0.550178\pi$
$734$	2.18886	−	1.59030i	0.0807924	−	0.0586991i
$735$	3.74438	−	15.2601i	0.138114	−	0.562875i
$736$			6.90676i			0.254586i
$737$	−2.54759	−	7.05836i	−0.0938418	−	0.259998i
$738$			10.1773i			0.374632i
$739$	11.2863	+	3.66713i	0.415172	+	0.134898i	0.509152	−	0.860676i	$-0.329959\pi$
$739$	11.2863	+	3.66713i	0.415172	+	0.134898i	−0.0939801	+	0.995574i	$0.529959\pi$
$740$	−8.41519	−	11.5825i	−0.309348	−	0.425782i
$741$	−1.06080	+	1.46006i	−0.0389694	+	0.0536368i
$742$	−8.16716	−	22.3096i	−0.299826	−	0.819011i
$743$	49.1255	−	15.9618i	1.80224	−	0.585583i	0.802305	−	0.596915i	$-0.203607\pi$
$743$	49.1255	−	15.9618i	1.80224	−	0.585583i	0.999936	+	0.0113313i	$0.00360695\pi$
$744$	5.46633	−	7.52376i	0.200406	−	0.275835i
$745$	3.79840	−	2.75970i	0.139162	−	0.101107i
$746$	9.89381	−	30.4500i	0.362238	−	1.11485i
$747$	−9.00044			−0.329309
$748$	−2.60262	+	0.0838896i	−0.0951612	+	0.00306731i
$749$	12.5751	−	0.462605i	0.459484	−	0.0169032i
$750$	10.5917	+	3.44146i	0.386756	+	0.125665i
$751$	−29.0677	+	21.1189i	−1.06070	+	0.770641i	−0.974217	−	0.225612i	$-0.927562\pi$
$751$	−29.0677	+	21.1189i	−1.06070	+	0.770641i	−0.0864796	+	0.996254i	$0.527562\pi$
$752$	−1.65844	+	2.28265i	−0.0604771	+	0.0832396i
$753$	2.89857	+	8.92087i	0.105630	+	0.325095i
$754$	5.70619	+	17.5619i	0.207807	+	0.639565i
$755$	16.7972	+	12.2039i	0.611313	+	0.444145i
$756$	2.08184	−	1.63277i	0.0757158	−	0.0593833i
$757$	−4.74981	+	14.6184i	−0.172635	+	0.531315i	−0.999518	−	0.0310592i	$-0.990112\pi$
$757$	−4.74981	+	14.6184i	−0.172635	+	0.531315i	0.826883	+	0.562374i	$0.190112\pi$
$758$			21.6462i			0.786225i
$759$	12.8604	−	18.9564i	0.466804	−	0.688074i
$760$	−0.888395			−0.0322255
$761$	2.40889	−	7.41379i	0.0873220	−	0.268750i	−0.897855	−	0.440292i	$-0.854875\pi$
$761$	2.40889	−	7.41379i	0.0873220	−	0.268750i	0.985177	+	0.171542i	$0.0548750\pi$
$762$	−7.43991	−	10.2402i	−0.269520	−	0.370962i
$763$	7.23806	+	4.86253i	0.262035	+	0.176035i
$764$	6.09374	+	18.7546i	0.220464	+	0.678518i
$765$	−1.67610	+	0.544597i	−0.0605995	+	0.0196900i
$766$	10.0906	+	7.33122i	0.364587	+	0.264888i
$767$	17.3609	+	23.8953i	0.626867	+	0.862808i
$768$	0.951057	+	0.309017i	0.0343183	+	0.0111507i
$769$	10.9936			0.396440			0.198220	−	0.980158i	$-0.436484\pi$
$769$	10.9936			0.396440			0.198220	+	0.980158i	$0.436484\pi$
$770$	−19.1079	−	4.78080i	−0.688602	−	0.172288i
$771$	−2.40181			−0.0864989
$772$	−16.8373	−	5.47078i	−0.605989	−	0.196898i
$773$	7.94403	+	10.9340i	0.285727	+	0.393269i	0.927620	−	0.373525i	$-0.121851\pi$
$773$	7.94403	+	10.9340i	0.285727	+	0.393269i	−0.641894	+	0.766794i	$0.721851\pi$
$774$	0.634066	+	0.460676i	0.0227910	+	0.0165586i
$775$	−0.341067	+	0.110819i	−0.0122515	+	0.00398075i
$776$	−1.17285	−	3.60967i	−0.0421030	−	0.129580i
$777$	−14.0075	−	9.41022i	−0.502516	−	0.337590i
$778$	14.8540	+	20.4448i	0.532541	+	0.732980i
$779$	1.24471	−	3.83083i	0.0445964	−	0.137254i
$780$	−10.2356			−0.366494
$781$	−3.05255	+	2.37175i	−0.109229	+	0.0848677i
$782$		−	5.42268i		−	0.193915i
$783$	−1.25137	+	3.85132i	−0.0447203	+	0.137635i
$784$	5.34550	−	4.51948i	0.190911	−	0.161410i
$785$	−35.6945	−	25.9336i	−1.27399	−	0.925609i
$786$	1.74029	+	5.35606i	0.0620741	+	0.191044i
$787$	2.40634	+	7.40595i	0.0857767	+	0.263994i	0.984740	−	0.174029i	$-0.0556788\pi$
$787$	2.40634	+	7.40595i	0.0857767	+	0.263994i	−0.898964	+	0.438023i	$0.855679\pi$
$788$	6.56799	−	9.04006i	0.233975	−	0.322039i
$789$	−7.32512	+	5.32201i	−0.260781	+	0.189469i
$790$	−10.9083	−	3.54431i	−0.388098	−	0.126101i
$791$	−1.55487	−	42.2663i	−0.0552847	−	1.50282i
$792$	−2.03489	−	2.61901i	−0.0723068	−	0.0930624i
$793$	23.2366			0.825157
$794$	4.24914	−	13.0775i	0.150797	−	0.464104i
$795$	−16.3066	+	11.8474i	−0.578335	+	0.420185i
$796$	14.6134	−	20.1137i	0.517959	−	0.712910i
$797$	28.9206	−	9.39688i	1.02442	−	0.332855i	0.251839	−	0.967769i	$-0.418965\pi$
$797$	28.9206	−	9.39688i	1.02442	−	0.332855i	0.772582	+	0.634915i	$0.218965\pi$
$798$	−0.983314	+	0.359975i	−0.0348089	+	0.0127430i
$799$	1.30209	−	1.79217i	0.0460645	−	0.0634024i
$800$	−0.0226660	−	0.0311970i	−0.000801363	−	0.00110298i
$801$	17.3816	+	5.64761i	0.614147	+	0.199548i
$802$			5.30430i			0.187301i
$803$	−12.4787	+	43.0815i	−0.440364	+	1.52031i
$804$		−	2.26255i		−	0.0797942i
$805$	11.2326	−	39.4502i	0.395898	−	1.39044i
$806$	−34.3081	+	24.9263i	−1.20845	+	0.877991i
$807$	2.66781	+	1.93828i	0.0939114	+	0.0682306i
$808$	−12.7535	+	4.14385i	−0.448665	+	0.145780i
$809$	−43.1208	+	14.0108i	−1.51605	+	0.492594i	−0.944650	−	0.328080i	$-0.893598\pi$
$809$	−43.1208	+	14.0108i	−1.51605	+	0.492594i	−0.571397	+	0.820674i	$0.693598\pi$
$810$	−1.81598	−	1.31939i	−0.0638070	−	0.0463585i
$811$	16.6729	−	12.1136i	0.585464	−	0.425364i	−0.255226	−	0.966881i	$-0.582150\pi$
$811$	16.6729	−	12.1136i	0.585464	−	0.425364i	0.840690	+	0.541517i	$0.182150\pi$
$812$	−2.93398	+	10.3045i	−0.102962	+	0.361615i
$813$		−	18.8835i		−	0.662272i
$814$	−11.8761	+	17.5055i	−0.416257	+	0.613566i
$815$			43.1791i			1.51250i
$816$	−0.746700	−	0.242618i	−0.0261397	−	0.00849331i
$817$	−0.182326	−	0.250950i	−0.00637878	−	0.00877963i
$818$	−12.7338	+	17.5266i	−0.445229	+	0.612805i
$819$	−11.3292	+	4.14744i	−0.395875	+	0.144923i
$820$	21.7267	−	7.05942i	0.758728	−	0.246526i
$821$	−26.2947	+	36.1916i	−0.917692	+	1.26309i	0.0467787	+	0.998905i	$0.485104\pi$
$821$	−26.2947	+	36.1916i	−0.917692	+	1.26309i	−0.964471	+	0.264190i	$0.914896\pi$
$822$	3.23908	−	2.35333i	0.112976	−	0.0820818i
$823$	−4.02012	+	12.3727i	−0.140133	+	0.431284i	−0.996353	−	0.0853268i	$-0.972807\pi$
$823$	−4.02012	+	12.3727i	−0.140133	+	0.431284i	0.856220	+	0.516611i	$0.172807\pi$
$824$	−10.8549			−0.378149
$825$	0.00412025	+	0.127828i	0.000143449	+	0.00445040i
$826$	0.630010	+	17.1257i	0.0219209	+	0.595880i
$827$	25.4018	+	8.25355i	0.883307	+	0.287004i	0.715330	−	0.698787i	$-0.246276\pi$
$827$	25.4018	+	8.25355i	0.883307	+	0.287004i	0.167977	+	0.985791i	$0.446276\pi$
$828$	5.58768	−	4.05969i	0.194185	−	0.141084i
$829$	−24.3996	+	33.5832i	−0.847434	+	1.16639i	0.136988	+	0.990573i	$0.456258\pi$
$829$	−24.3996	+	33.5832i	−0.847434	+	1.16639i	−0.984422	+	0.175820i	$0.943742\pi$
$830$	6.24308	+	19.2142i	0.216701	+	0.666936i
$831$	0.585462	+	1.80187i	0.0203095	+	0.0625061i
$832$	−3.68909	−	2.68028i	−0.127896	−	0.0929219i
$833$	−4.19689	+	3.54836i	−0.145414	+	0.122943i
$834$	−1.74672	+	5.37585i	−0.0604839	+	0.186150i
$835$		−	21.3337i		−	0.738282i
$836$	0.445640	+	1.23469i	0.0154128	+	0.0427026i
$837$	−9.29988			−0.321451
$838$	−11.9017	+	36.6296i	−0.411137	+	1.26535i
$839$	−1.09058	−	1.50105i	−0.0376509	−	0.0518221i	0.789776	−	0.613395i	$-0.210197\pi$
$839$	−1.09058	−	1.50105i	−0.0376509	−	0.0518221i	−0.827427	+	0.561573i	$0.810197\pi$
$840$	−4.92971	−	3.31178i	−0.170091	−	0.114267i
$841$	3.89406	+	11.9847i	0.134278	+	0.413265i
$842$	−19.3416	+	6.28445i	−0.666554	+	0.216577i
$843$	−12.7363	−	9.25348i	−0.438662	−	0.318707i
$844$	−16.8009	−	23.1244i	−0.578311	−	0.795976i
$845$	16.6371	+	5.40573i	0.572335	+	0.185963i
$846$	2.82151			0.0970055
$847$	2.94063	+	28.9543i	0.101041	+	0.994882i
$848$	−8.97950			−0.308357
$849$	1.08844	+	0.353657i	0.0373553	+	0.0121375i
$850$	0.0177957	+	0.0244936i	0.000610386	+	0.000840124i
$851$	−35.6388	−	25.8931i	−1.22168	−	0.887605i
$852$	−1.10849	+	0.360171i	−0.0379763	+	0.0123393i
$853$	16.3313	+	50.2625i	0.559172	+	1.72096i	0.684662	+	0.728861i	$0.259950\pi$
$853$	16.3313	+	50.2625i	0.559172	+	1.72096i	−0.125490	+	0.992095i	$0.540050\pi$
$854$	11.1913	+	7.51831i	0.382958	+	0.257271i
$855$	0.522186	+	0.718727i	0.0178584	+	0.0245799i
$856$	1.46973	−	4.52337i	0.0502344	−	0.154606i
$857$	20.6980			0.707031			0.353515	−	0.935429i	$-0.384986\pi$
$857$	20.6980			0.707031			0.353515	+	0.935429i	$0.384986\pi$
$858$	5.13443	+	14.2254i	0.175286	+	0.485649i
$859$		−	6.67811i		−	0.227854i	−0.993489	−	0.113927i	$-0.963657\pi$
$859$		−	6.67811i		−	0.227854i	0.993489	−	0.113927i	$-0.0363430\pi$
$860$	0.543641	−	1.67316i	0.0185380	−	0.0570541i
$861$	21.1876	−	16.6172i	0.722070	−	0.566314i
$862$	−2.79938	−	2.03387i	−0.0953473	−	0.0692739i
$863$	−3.02188	−	9.30039i	−0.102866	−	0.316589i	0.886358	−	0.463001i	$-0.153227\pi$
$863$	−3.02188	−	9.30039i	−0.102866	−	0.316589i	−0.989224	+	0.146412i	$0.953227\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	32.7597	−	45.0899i	1.11386	−	1.53310i
$866$	−15.5108	+	11.2693i	−0.527080	+	0.382946i
$867$	−15.5817	−	5.06280i	−0.529182	−	0.171942i
$868$	−24.5885	+	0.904549i	−0.834590	+	0.0307024i
$869$	0.545964	+	16.9382i	0.0185206	+	0.574588i
$870$	9.08984			0.308174
$871$	−3.18818	+	9.81221i	−0.108027	+	0.332474i
$872$	2.66632	−	1.93719i	0.0902928	−	0.0656016i
$873$	−2.23090	+	3.07057i	−0.0755045	+	0.103923i
$874$	−2.59976	+	0.844714i	−0.0879382	+	0.0285729i
$875$	−10.1293	−	27.6694i	−0.342433	−	0.935397i
$876$	−7.94891	+	10.9407i	−0.268569	+	0.369653i
$877$	16.0642	+	22.1104i	0.542448	+	0.746616i	0.988963	−	0.148160i	$-0.0473352\pi$
$877$	16.0642	+	22.1104i	0.542448	+	0.746616i	−0.446515	+	0.894776i	$0.647335\pi$
$878$	−7.75372	−	2.51934i	−0.261675	−	0.0850235i
$879$		−	16.9793i		−	0.572697i
$880$	−4.17960	+	6.16077i	−0.140894	+	0.207680i
$881$		−	27.1248i		−	0.913856i	−0.889504	−	0.456928i	$-0.848950\pi$
$881$		−	27.1248i		−	0.913856i	0.889504	−	0.456928i	$-0.151050\pi$
$882$	−6.79834	−	1.66812i	−0.228912	−	0.0561684i
$883$	21.1395	−	15.3587i	0.711400	−	0.516862i	−0.172225	−	0.985058i	$-0.555096\pi$
$883$	21.1395	−	15.3587i	0.711400	−	0.516862i	0.883625	+	0.468196i	$0.155096\pi$
$884$	2.89640	+	2.10436i	0.0974165	+	0.0707772i
$885$	13.8278	−	4.49292i	0.464816	−	0.151028i
$886$	7.98926	−	2.59587i	0.268404	−	0.0872099i
$887$	−4.67118	−	3.39381i	−0.156843	−	0.113953i	0.506596	−	0.862184i	$-0.330904\pi$
$887$	−4.67118	−	3.39381i	−0.156843	−	0.113953i	−0.663439	+	0.748231i	$0.730904\pi$
$888$	−5.16000	+	3.74896i	−0.173158	+	0.125807i
$889$	−9.17070	+	32.2085i	−0.307576	+	1.08024i
$890$		−	41.0238i		−	1.37512i
$891$	−0.922742	+	3.18568i	−0.0309130	+	0.106724i
$892$			11.8891i			0.398075i
$893$	−1.06204	−	0.345078i	−0.0355398	−	0.0115476i
$894$	−1.22944	−	1.69218i	−0.0411187	−	0.0565950i
$895$	21.5047	−	29.5986i	0.718822	−	0.989373i
$896$	−0.909534	−	2.48450i	−0.0303854	−	0.0830014i
$897$	−29.9531	+	9.73235i	−1.00010	+	0.324954i
$898$	2.30509	−	3.17268i	0.0769218	−	0.105874i
$899$	30.4676	−	22.1360i	1.01615	−	0.738277i
$900$	−0.0119162	+	0.0366743i	−0.000397207	+	0.00122248i
$901$	7.05005			0.234871
$902$	−20.7098	−	26.6545i	−0.689560	−	0.887498i
$903$	−0.0762309	−	2.07220i	−0.00253681	−	0.0689586i
$904$	−15.2035	−	4.93993i	−0.505663	−	0.164300i
$905$	22.9178	−	16.6508i	0.761815	−	0.553491i
$906$	5.43682	−	7.48314i	0.180626	−	0.248611i
$907$	−17.6932	−	54.4541i	−0.587493	−	1.80812i	−0.589018	−	0.808120i	$-0.700485\pi$
$907$	−17.6932	−	54.4541i	−0.587493	−	1.80812i	0.00152519	−	0.999999i	$-0.499515\pi$
$908$	2.64230	+	8.13215i	0.0876877	+	0.269875i
$909$	10.8487	+	7.88208i	0.359830	+	0.261432i
$910$	16.7124	+	21.3089i	0.554012	+	0.706385i
$911$	−3.74844	+	11.5365i	−0.124191	+	0.382222i	−0.993753	−	0.111603i	$-0.964402\pi$
$911$	−3.74844	+	11.5365i	−0.124191	+	0.382222i	0.869561	+	0.493825i	$0.164402\pi$
$912$			0.395779i			0.0131056i
$913$	23.5722	−	18.3149i	0.780127	−	0.606136i
$914$	−33.4288			−1.10573
$915$	3.53466	−	10.8786i	0.116852	−	0.359634i
$916$	−3.56339	−	4.90459i	−0.117738	−	0.162052i
$917$	8.30897	−	12.3682i	0.274386	−	0.408435i
$918$	0.242618	+	0.746700i	0.00800757	+	0.0246448i
$919$	−13.4812	+	4.38032i	−0.444705	+	0.144493i	−0.522805	−	0.852452i	$-0.675115\pi$
$919$	−13.4812	+	4.38032i	−0.444705	+	0.144493i	0.0781005	+	0.996945i	$0.475115\pi$
$920$	−12.5425	−	9.11268i	−0.413515	−	0.300436i
$921$	14.2060	+	19.5529i	0.468103	+	0.644288i
$922$	24.4610	+	7.94788i	0.805582	+	0.261749i
$923$	5.31481			0.174939
$924$	−2.12984	+	8.51257i	−0.0700667	+	0.280043i
$925$	0.245950			0.00808679
$926$	30.9984	+	10.0720i	1.01867	+	0.330986i
$927$	6.38036	+	8.78182i	0.209559	+	0.288433i
$928$	3.27613	+	2.38024i	0.107544	+	0.0781354i
$929$	−55.1169	+	17.9086i	−1.80833	+	0.587561i	−0.999999	−	0.00117446i	$-0.999626\pi$
$929$	−55.1169	+	17.9086i	−1.80833	+	0.587561i	−0.808326	+	0.588735i	$0.799626\pi$
$930$	6.45079	+	19.8535i	0.211530	+	0.651022i
$931$	2.35494	+	1.45935i	0.0771799	+	0.0478282i
$932$	5.28677	+	7.27661i	0.173174	+	0.238353i
$933$	0.624109	−	1.92081i	0.0204324	−	0.0628845i
$934$	9.80055			0.320684
$935$	3.28152	−	4.83699i	0.107317	−	0.158186i
$936$			4.55996i			0.149047i
$937$	−4.30684	+	13.2551i	−0.140698	+	0.433025i	−0.996433	−	0.0843903i	$-0.973106\pi$
$937$	−4.30684	+	13.2551i	−0.140698	+	0.433025i	0.855734	+	0.517415i	$0.173106\pi$
$938$	−4.71028	+	3.69423i	−0.153796	+	0.120621i
$939$	15.0220	+	10.9141i	0.490224	+	0.356168i
$940$	−1.95712	−	6.02339i	−0.0638341	−	0.196461i
$941$	11.6823	+	35.9545i	0.380833	+	1.17208i	0.939458	+	0.342663i	$0.111329\pi$
$941$	11.6823	+	35.9545i	0.380833	+	1.17208i	−0.558625	+	0.829420i	$0.688671\pi$
$942$	−11.5534	+	15.9019i	−0.376430	+	0.518111i
$943$	56.8676	−	41.3168i	1.85187	−	1.34546i
$944$	6.16027	+	2.00159i	0.200500	+	0.0651463i
$945$	0.218327	+	5.93483i	0.00710218	+	0.193060i
$946$	−2.59805	+	0.0837423i	−0.0844699	+	0.00272270i
$947$	36.9001			1.19909			0.599545	−	0.800341i	$-0.295348\pi$
$947$	36.9001			1.19909			0.599545	+	0.800341i	$0.295348\pi$
$948$	−1.57898	+	4.85962i	−0.0512830	+	0.157833i
$949$	49.8893	−	36.2467i	1.61948	−	1.17662i
$950$	0.00897072	−	0.0123471i	0.000291048	−	0.000400594i
$951$	−15.8780	+	5.15908i	−0.514880	+	0.167295i
$952$	0.714099	+	1.95065i	0.0231441	+	0.0632209i
$953$	−21.2338	+	29.2258i	−0.687829	+	0.946715i	−0.999995	−	0.00331226i	$-0.998946\pi$
$953$	−21.2338	+	29.2258i	−0.687829	+	0.946715i	0.312165	+	0.950028i	$0.398946\pi$
$954$	5.27802	+	7.26457i	0.170882	+	0.235199i
$955$	−42.0980	−	13.6785i	−1.36226	−	0.442625i
$956$			5.43954i			0.175927i
$957$	−4.55967	−	12.6330i	−0.147393	−	0.408368i
$958$		−	6.19342i		−	0.200100i
$959$	−10.1879	−	2.90080i	−0.328985	−	0.0936716i
$960$	−1.81598	+	1.31939i	−0.0586105	+	0.0425830i
$961$	44.8906	+	32.6149i	1.44808	+	1.05209i
$962$	27.6605	−	8.98743i	0.891809	−	0.289766i
$963$	−4.52337	+	1.46973i	−0.145764	+	0.0473615i
$964$	−5.12615	−	3.72437i	−0.165102	−	0.119954i
$965$	32.1498	−	23.3582i	1.03494	−	0.751926i
$966$	−17.5750	−	5.00412i	−0.565467	−	0.161005i
$967$			6.81124i			0.219035i	0.993985	+	0.109517i	$0.0349305\pi$
$967$			6.81124i			0.219035i	−0.993985	+	0.109517i	$0.965069\pi$
$968$	10.6588	+	2.71842i	0.342587	+	0.0873732i
$969$		−	0.310737i		−	0.00998231i
$970$	8.10253	+	2.63267i	0.260157	+	0.0845300i
$971$	−13.2092	−	18.1809i	−0.423903	−	0.583453i	0.542637	−	0.839967i	$-0.317426\pi$
$971$	−13.2092	−	18.1809i	−0.423903	−	0.583453i	−0.966540	+	0.256515i	$0.917426\pi$
$972$	−0.587785	+	0.809017i	−0.0188532	+	0.0259492i
$973$	14.0437	−	5.14114i	0.450219	−	0.164817i
$974$	−25.2106	+	8.19143i	−0.807801	+	0.262470i
$975$	0.103356	−	0.142257i	0.00331004	−	0.00455588i
$976$	4.12259	−	2.99523i	0.131961	−	0.0958751i
$977$	16.5579	−	50.9599i	0.529733	−	1.63035i	−0.225028	−	0.974352i	$-0.572247\pi$
$977$	16.5579	−	50.9599i	0.529733	−	1.63035i	0.754761	−	0.656000i	$-0.227753\pi$
$978$	19.2362			0.615107
$979$	−57.0147	+	20.5785i	−1.82220	+	0.657691i
$980$	1.15450	+	15.6702i	0.0368791	+	0.500568i
$981$	−3.13444	−	1.01844i	−0.100075	−	0.0325164i
$982$	−18.0886	+	13.1421i	−0.577230	+	0.419382i
$983$	14.2491	−	19.6122i	0.454476	−	0.625533i	−0.518876	−	0.854850i	$-0.673649\pi$
$983$	14.2491	−	19.6122i	0.454476	−	0.625533i	0.973352	+	0.229317i	$0.0736492\pi$
$984$	−3.14497	−	9.67921i	−0.100258	−	0.308562i
$985$	7.75085	+	23.8547i	0.246963	+	0.760073i
$986$	−2.57217	−	1.86879i	−0.0819147	−	0.0595145i
$987$	−4.60688	−	5.87393i	−0.146639	−	0.186969i
$988$	0.557695	−	1.71641i	0.0177426	−	0.0546062i
$989$		−	5.41316i		−	0.172128i
$990$	7.44088	−	0.239840i	0.236487	−	0.00762262i
$991$	40.3349			1.28128			0.640640	−	0.767841i	$-0.278669\pi$
$991$	40.3349			1.28128			0.640640	+	0.767841i	$0.278669\pi$
$992$	−2.87382	+	8.84471i	−0.0912439	+	0.280820i
$993$	−1.48240	−	2.04034i	−0.0470424	−	0.0647483i
$994$	2.55973	+	1.71963i	0.0811898	+	0.0545433i
$995$	17.2452	+	53.0754i	0.546711	+	1.68260i
$996$	8.55992	−	2.78129i	0.271232	−	0.0881285i
$997$	−16.7005	−	12.1336i	−0.528911	−	0.384276i	0.291039	−	0.956711i	$-0.405999\pi$
$997$	−16.7005	−	12.1336i	−0.528911	−	0.384276i	−0.819950	+	0.572435i	$0.805999\pi$
$998$	−19.1734	−	26.3899i	−0.606922	−	0.835357i
$999$	6.06594	+	1.97094i	0.191918	+	0.0623579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.u.b.13.1	yes	32
7.6	odd	2		462.2.u.a.13.4	✓	32
11.6	odd	10		462.2.u.a.391.4	yes	32
77.6	even	10	inner	462.2.u.b.391.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.u.a.13.4	✓	32	7.6	odd	2
462.2.u.a.391.4	yes	32	11.6	odd	10
462.2.u.b.13.1	yes	32	1.1	even	1	trivial
462.2.u.b.391.1	yes	32	77.6	even	10	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-2.13481 + 0.693642i) q^{5} +(0.309017 + 0.951057i) q^{6} +(1.47539 - 2.19618i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-2.13481 + 0.693642i) q^{5} +(0.309017 + 0.951057i) q^{6} +(1.47539 - 2.19618i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +2.24467 q^{10} +(-1.12598 - 3.11964i) q^{11} -1.00000i q^{12} +(-1.40911 + 4.33678i) q^{13} +(-2.08184 + 1.63277i) q^{14} +(1.81598 + 1.31939i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.242618 - 0.746700i) q^{17} +(0.587785 - 0.809017i) q^{18} +(-0.320192 + 0.232633i) q^{19} +(-2.13481 - 0.693642i) q^{20} +(-2.64396 + 0.0972645i) q^{21} +(0.106848 + 3.31490i) q^{22} -6.90676 q^{23} +(-0.309017 + 0.951057i) q^{24} +(0.0311970 - 0.0226660i) q^{25} +(2.68028 - 3.68909i) q^{26} +(0.951057 - 0.309017i) q^{27} +(2.48450 - 0.909534i) q^{28} +(-2.38024 + 3.27613i) q^{29} +(-1.31939 - 1.81598i) q^{30} +(-8.84471 - 2.87382i) q^{31} -1.00000i q^{32} +(-1.86201 + 2.74462i) q^{33} +0.785127i q^{34} +(-1.62632 + 5.71183i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(5.16000 + 3.74896i) q^{37} +(0.376408 - 0.122303i) q^{38} +(4.33678 - 1.40911i) q^{39} +(1.81598 + 1.31939i) q^{40} +(-8.23363 + 5.98208i) q^{41} +(2.54461 + 0.724525i) q^{42} +0.783748i q^{43} +(0.922742 - 3.18568i) q^{44} -2.24467i q^{45} +(6.56871 + 2.13430i) q^{46} +(1.65844 + 2.28265i) q^{47} +(0.587785 - 0.809017i) q^{48} +(-2.64643 - 6.48046i) q^{49} +(-0.0366743 + 0.0119162i) q^{50} +(-0.461486 + 0.635181i) q^{51} +(-3.68909 + 2.68028i) q^{52} +(-2.77482 + 8.54001i) q^{53} -1.00000 q^{54} +(4.56767 + 5.87882i) q^{55} +(-2.64396 + 0.0972645i) q^{56} +(0.376408 + 0.122303i) q^{57} +(3.27613 - 2.38024i) q^{58} +(3.80725 - 5.24024i) q^{59} +(0.693642 + 2.13481i) q^{60} +(-1.57469 - 4.84639i) q^{61} +(7.52376 + 5.46633i) q^{62} +(1.63277 + 2.08184i) q^{63} +(-0.309017 + 0.951057i) q^{64} -10.2356i q^{65} +(2.61901 - 2.03489i) q^{66} +2.26255 q^{67} +(0.242618 - 0.746700i) q^{68} +(4.05969 + 5.58768i) q^{69} +(3.31178 - 4.92971i) q^{70} +(-0.360171 - 1.10849i) q^{71} +(0.951057 - 0.309017i) q^{72} +(-10.9407 - 7.94891i) q^{73} +(-3.74896 - 5.16000i) q^{74} +(-0.0366743 - 0.0119162i) q^{75} -0.395779 q^{76} +(-8.51257 - 2.12984i) q^{77} -4.55996 q^{78} +(-4.85962 - 1.57898i) q^{79} +(-1.31939 - 1.81598i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(9.67921 - 3.14497i) q^{82} +(2.78129 + 8.55992i) q^{83} +(-2.19618 - 1.47539i) q^{84} +(1.03589 + 1.42577i) q^{85} +(0.242192 - 0.745389i) q^{86} +4.04951 q^{87} +(-1.86201 + 2.74462i) q^{88} -18.2760i q^{89} +(-0.693642 + 2.13481i) q^{90} +(7.44537 + 9.49311i) q^{91} +(-5.58768 - 4.05969i) q^{92} +(2.87382 + 8.84471i) q^{93} +(-0.871894 - 2.68341i) q^{94} +(0.522186 - 0.718727i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(3.60967 + 1.17285i) q^{97} +(0.514328 + 6.98108i) q^{98} +(3.31490 - 0.106848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9	\( 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} - 12 q^{17} - 16 q^{19} + 10 q^{20} - 8 q^{21} - 4 q^{22} + 8 q^{23} + 8 q^{24} + 6 q^{25} + 10 q^{28} + 20 q^{29} - 50 q^{31} - 16 q^{33} - 12 q^{35} - 8 q^{36} - 16 q^{37} + 6 q^{40} + 40 q^{41} + 12 q^{44} + 52 q^{49} + 40 q^{51} - 32 q^{54} - 40 q^{55} - 8 q^{56} + 10 q^{58} + 60 q^{59} + 4 q^{60} - 4 q^{61} + 20 q^{62} - 10 q^{63} + 8 q^{64} + 8 q^{66} - 16 q^{67} + 12 q^{68} + 30 q^{69} - 28 q^{70} - 48 q^{71} - 74 q^{73} - 40 q^{74} - 24 q^{76} + 6 q^{77} - 60 q^{79} - 8 q^{81} + 20 q^{82} + 4 q^{83} - 2 q^{84} - 10 q^{85} - 36 q^{86} + 20 q^{87} - 16 q^{88} - 4 q^{90} - 20 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} - 8 q^{96} + 60 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 - 12 * q^17 - 16 * q^19 + 10 * q^20 - 8 * q^21 - 4 * q^22 + 8 * q^23 + 8 * q^24 + 6 * q^25 + 10 * q^28 + 20 * q^29 - 50 * q^31 - 16 * q^33 - 12 * q^35 - 8 * q^36 - 16 * q^37 + 6 * q^40 + 40 * q^41 + 12 * q^44 + 52 * q^49 + 40 * q^51 - 32 * q^54 - 40 * q^55 - 8 * q^56 + 10 * q^58 + 60 * q^59 + 4 * q^60 - 4 * q^61 + 20 * q^62 - 10 * q^63 + 8 * q^64 + 8 * q^66 - 16 * q^67 + 12 * q^68 + 30 * q^69 - 28 * q^70 - 48 * q^71 - 74 * q^73 - 40 * q^74 - 24 * q^76 + 6 * q^77 - 60 * q^79 - 8 * q^81 + 20 * q^82 + 4 * q^83 - 2 * q^84 - 10 * q^85 - 36 * q^86 + 20 * q^87 - 16 * q^88 - 4 * q^90 - 20 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 - 8 * q^96 + 60 * q^97 - 40 * q^98 - 8 * q^99

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