LMFDB - Embedded newform 770.2.n.h.421.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.n (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 9 x^{9} + 55 x^{8} - 32 x^{7} + 287 x^{6} - 302 x^{5} + 1175 x^{4} + \cdots + 361 $ x^12 - 3x^11 + 7x^10 - 9x^9 + 55x^8 - 32x^7 + 287x^6 - 302x^5 + 1175x^4 - 1639x^3 + 1692x^2 - 988*x + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.3
Root			$-0.666872 + 2.05242i$ of defining polynomial
Character	$\chi$	$=$	770.421
Dual form			770.2.n.h.631.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.357855 + 1.10136i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.936877 - 0.680681i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.34211 - 0.975098i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.357855 + 1.10136i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.936877 - 0.680681i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.34211 - 0.975098i) q^{9} -1.00000 q^{10} +(2.83465 + 1.72185i) q^{11} +1.15804 q^{12} +(2.90157 - 2.10811i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-0.357855 + 1.10136i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-3.47089 - 2.52175i) q^{17} +(-0.512639 + 1.57774i) q^{18} +(-1.51209 - 4.65373i) q^{19} +(0.809017 - 0.587785i) q^{20} +1.15804 q^{21} +(-3.30536 + 0.273157i) q^{22} +2.85699 q^{23} +(-0.936877 + 0.680681i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-1.10830 + 3.41100i) q^{26} +(4.36485 + 3.17125i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-0.233254 + 0.717882i) q^{29} +(-0.357855 - 1.10136i) q^{30} +(7.56718 - 5.49788i) q^{31} +1.00000 q^{32} +(-0.881993 + 3.73815i) q^{33} +4.29025 q^{34} +(0.809017 - 0.587785i) q^{35} +(-0.512639 - 1.57774i) q^{36} +(-1.31048 + 4.03324i) q^{37} +(3.95870 + 2.87616i) q^{38} +(3.36014 + 2.44129i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(0.626966 + 1.92960i) q^{41} +(-0.936877 + 0.680681i) q^{42} -0.0689189 q^{43} +(2.51353 - 2.16383i) q^{44} +1.65894 q^{45} +(-2.31136 + 1.67930i) q^{46} +(0.691535 + 2.12833i) q^{47} +(0.357855 - 1.10136i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(1.53529 - 4.72513i) q^{51} +(-1.10830 - 3.41100i) q^{52} +(-10.6002 + 7.70149i) q^{53} -5.39525 q^{54} +(1.28120 + 3.05917i) q^{55} +1.00000 q^{56} +(4.58434 - 3.33072i) q^{57} +(-0.233254 - 0.717882i) q^{58} +(0.378583 - 1.16516i) q^{59} +(0.936877 + 0.680681i) q^{60} +(3.26063 + 2.36898i) q^{61} +(-2.89040 + 8.89575i) q^{62} +(-0.512639 - 1.57774i) q^{63} +(-0.809017 + 0.587785i) q^{64} +3.58654 q^{65} +(-1.48368 - 3.54265i) q^{66} -14.3059 q^{67} +(-3.47089 + 2.52175i) q^{68} +(1.02239 + 3.14659i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(4.69029 + 3.40769i) q^{71} +(1.34211 + 0.975098i) q^{72} +(-2.80171 + 8.62277i) q^{73} +(-1.31048 - 4.03324i) q^{74} +(-0.936877 + 0.680681i) q^{75} -4.89322 q^{76} +(2.51353 - 2.16383i) q^{77} -4.15337 q^{78} +(4.07153 - 2.95814i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(-0.392798 + 1.20891i) q^{81} +(-1.64142 - 1.19256i) q^{82} +(13.4506 + 9.77240i) q^{83} +(0.357855 - 1.10136i) q^{84} +(-1.32576 - 4.08027i) q^{85} +(0.0557565 - 0.0405095i) q^{86} -0.874121 q^{87} +(-0.761624 + 3.22799i) q^{88} +9.92243 q^{89} +(-1.34211 + 0.975098i) q^{90} +(-1.10830 - 3.41100i) q^{91} +(0.882859 - 2.71716i) q^{92} +(8.76312 + 6.36678i) q^{93} +(-1.81046 - 1.31538i) q^{94} +(1.51209 - 4.65373i) q^{95} +(0.357855 + 1.10136i) q^{96} +(5.43443 - 3.94835i) q^{97} +1.00000 q^{98} +(5.48338 - 0.453150i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9	$ 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9} - 12 q^{10} - q^{11} - 10 q^{12} - 3 q^{14} - 3 q^{16} - 8 q^{18} - q^{19} + 3 q^{20} - 10 q^{21} - q^{22} - 4 q^{23} + 5 q^{24} - 3 q^{25} + 3 q^{27} - 3 q^{28} + 22 q^{29} + 6 q^{31} + 12 q^{32} - 29 q^{33} - 30 q^{34} + 3 q^{35} - 8 q^{36} - 10 q^{37} + 14 q^{38} + 20 q^{39} + 3 q^{40} + 16 q^{41} + 5 q^{42} + 30 q^{43} + 14 q^{44} - 22 q^{45} - 4 q^{46} + 34 q^{47} - 3 q^{49} - 3 q^{50} + 37 q^{51} - 26 q^{53} - 52 q^{54} + 11 q^{55} + 12 q^{56} - 19 q^{57} + 22 q^{58} + q^{59} - 5 q^{60} + 40 q^{61} - 4 q^{62} - 8 q^{63} - 3 q^{64} + 16 q^{66} - 58 q^{67} + 14 q^{69} + 3 q^{70} - 14 q^{71} - 3 q^{72} + 32 q^{73} - 10 q^{74} + 5 q^{75} - 26 q^{76} + 14 q^{77} - 60 q^{78} + 16 q^{79} + 3 q^{80} - 46 q^{81} + q^{82} + 35 q^{83} - 15 q^{85} + 5 q^{86} - q^{88} - 58 q^{89} + 3 q^{90} + 6 q^{92} + 46 q^{93} - 16 q^{94} + q^{95} + 57 q^{97} + 12 q^{98} + 69 q^{99}+O(q^{100}) $ 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9 - 12 * q^10 - q^11 - 10 * q^12 - 3 * q^14 - 3 * q^16 - 8 * q^18 - q^19 + 3 * q^20 - 10 * q^21 - q^22 - 4 * q^23 + 5 * q^24 - 3 * q^25 + 3 * q^27 - 3 * q^28 + 22 * q^29 + 6 * q^31 + 12 * q^32 - 29 * q^33 - 30 * q^34 + 3 * q^35 - 8 * q^36 - 10 * q^37 + 14 * q^38 + 20 * q^39 + 3 * q^40 + 16 * q^41 + 5 * q^42 + 30 * q^43 + 14 * q^44 - 22 * q^45 - 4 * q^46 + 34 * q^47 - 3 * q^49 - 3 * q^50 + 37 * q^51 - 26 * q^53 - 52 * q^54 + 11 * q^55 + 12 * q^56 - 19 * q^57 + 22 * q^58 + q^59 - 5 * q^60 + 40 * q^61 - 4 * q^62 - 8 * q^63 - 3 * q^64 + 16 * q^66 - 58 * q^67 + 14 * q^69 + 3 * q^70 - 14 * q^71 - 3 * q^72 + 32 * q^73 - 10 * q^74 + 5 * q^75 - 26 * q^76 + 14 * q^77 - 60 * q^78 + 16 * q^79 + 3 * q^80 - 46 * q^81 + q^82 + 35 * q^83 - 15 * q^85 + 5 * q^86 - q^88 - 58 * q^89 + 3 * q^90 + 6 * q^92 + 46 * q^93 - 16 * q^94 + q^95 + 57 * q^97 + 12 * q^98 + 69 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.357855	+	1.10136i	0.206608	+	0.635873i	0.999644	+	0.0266981i	$0.00849928\pi$
$3$	0.357855	+	1.10136i	0.206608	+	0.635873i	−0.793036	+	0.609175i	$0.791501\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	−0.936877	−	0.680681i	−0.382478	−	0.277887i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	1.34211	−	0.975098i	0.447369	−	0.325033i
$10$	−1.00000			−0.316228
$11$	2.83465	+	1.72185i	0.854678	+	0.519158i
$11$	2.83465	+	1.72185i	0.854678	+	0.519158i
$12$	1.15804			0.334298
$13$	2.90157	−	2.10811i	0.804751	−	0.584686i	−0.107553	−	0.994199i	$-0.534302\pi$
$13$	2.90157	−	2.10811i	0.804751	−	0.584686i	0.912304	+	0.409514i	$0.134302\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	−0.357855	+	1.10136i	−0.0923978	+	0.284371i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−3.47089	−	2.52175i	−0.841814	−	0.611614i	0.0810629	−	0.996709i	$-0.474169\pi$
$17$	−3.47089	−	2.52175i	−0.841814	−	0.611614i	−0.922877	+	0.385095i	$0.874169\pi$
$18$	−0.512639	+	1.57774i	−0.120830	+	0.371877i
$19$	−1.51209	−	4.65373i	−0.346897	−	1.06764i	−0.960561	−	0.278071i	$-0.910305\pi$
$19$	−1.51209	−	4.65373i	−0.346897	−	1.06764i	0.613664	−	0.789567i	$-0.289695\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$	1.15804			0.252706
$22$	−3.30536	+	0.273157i	−0.704704	+	0.0582372i
$23$	2.85699			0.595724			0.297862	−	0.954609i	$-0.403726\pi$
$23$	2.85699			0.595724			0.297862	+	0.954609i	$0.403726\pi$
$24$	−0.936877	+	0.680681i	−0.191239	+	0.138943i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−1.10830	+	3.41100i	−0.217356	+	0.668952i
$27$	4.36485	+	3.17125i	0.840015	+	0.610307i
$28$	−0.809017	−	0.587785i	−0.152890	−	0.111081i
$29$	−0.233254	+	0.717882i	−0.0433142	+	0.133307i	−0.970375	−	0.241603i	$-0.922327\pi$
$29$	−0.233254	+	0.717882i	−0.0433142	+	0.133307i	0.927061	+	0.374911i	$0.122327\pi$
$30$	−0.357855	−	1.10136i	−0.0653351	−	0.201081i
$31$	7.56718	−	5.49788i	1.35910	−	0.987448i	0.360604	−	0.932719i	$-0.382571\pi$
$31$	7.56718	−	5.49788i	1.35910	−	0.987448i	0.998501	−	0.0547284i	$-0.0174293\pi$
$32$	1.00000			0.176777
$33$	−0.881993	+	3.73815i	−0.153535	+	0.650729i
$34$	4.29025			0.735772
$35$	0.809017	−	0.587785i	0.136749	−	0.0993538i
$36$	−0.512639	−	1.57774i	−0.0854399	−	0.262957i
$37$	−1.31048	+	4.03324i	−0.215441	+	0.663061i	0.783681	+	0.621164i	$0.213340\pi$
$37$	−1.31048	+	4.03324i	−0.215441	+	0.663061i	−0.999122	+	0.0418964i	$0.986660\pi$
$38$	3.95870	+	2.87616i	0.642185	+	0.466575i
$39$	3.36014	+	2.44129i	0.538054	+	0.390919i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	0.626966	+	1.92960i	0.0979157	+	0.301354i	0.988003	−	0.154437i	$-0.0493565\pi$
$41$	0.626966	+	1.92960i	0.0979157	+	0.301354i	−0.890087	+	0.455791i	$0.849356\pi$
$42$	−0.936877	+	0.680681i	−0.144563	+	0.105031i
$43$	−0.0689189			−0.0105100			−0.00525502	−	0.999986i	$-0.501673\pi$
$43$	−0.0689189			−0.0105100			−0.00525502	+	0.999986i	$0.501673\pi$
$44$	2.51353	−	2.16383i	0.378929	−	0.326209i
$45$	1.65894			0.247300
$46$	−2.31136	+	1.67930i	−0.340791	+	0.247599i
$47$	0.691535	+	2.12833i	0.100871	+	0.310448i	0.988739	−	0.149649i	$-0.0478145\pi$
$47$	0.691535	+	2.12833i	0.100871	+	0.310448i	−0.887868	+	0.460097i	$0.847814\pi$
$48$	0.357855	−	1.10136i	0.0516519	−	0.158968i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	1.53529	−	4.72513i	0.214983	−	0.661651i
$52$	−1.10830	−	3.41100i	−0.153694	−	0.473021i
$53$	−10.6002	+	7.70149i	−1.45605	+	1.05788i	−0.471678	+	0.881771i	$0.656351\pi$
$53$	−10.6002	+	7.70149i	−1.45605	+	1.05788i	−0.984371	+	0.176110i	$0.943649\pi$
$54$	−5.39525			−0.734200
$55$	1.28120	+	3.05917i	0.172757	+	0.412499i
$56$	1.00000			0.133631
$57$	4.58434	−	3.33072i	0.607211	−	0.441164i
$58$	−0.233254	−	0.717882i	−0.0306278	−	0.0942626i
$59$	0.378583	−	1.16516i	0.0492873	−	0.151691i	−0.923384	−	0.383878i	$-0.874588\pi$
$59$	0.378583	−	1.16516i	0.0492873	−	0.151691i	0.972671	+	0.232187i	$0.0745883\pi$
$60$	0.936877	+	0.680681i	0.120950	+	0.0878755i
$61$	3.26063	+	2.36898i	0.417481	+	0.303317i	0.776623	−	0.629965i	$-0.216931\pi$
$61$	3.26063	+	2.36898i	0.417481	+	0.303317i	−0.359143	+	0.933283i	$0.616931\pi$
$62$	−2.89040	+	8.89575i	−0.367082	+	1.12976i
$63$	−0.512639	−	1.57774i	−0.0645865	−	0.198777i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	3.58654			0.444855
$66$	−1.48368	−	3.54265i	−0.182629	−	0.436070i
$67$	−14.3059			−1.74774			−0.873870	−	0.486159i	$-0.838398\pi$
$67$	−14.3059			−1.74774			−0.873870	+	0.486159i	$0.838398\pi$
$68$	−3.47089	+	2.52175i	−0.420907	+	0.305807i
$69$	1.02239	+	3.14659i	0.123081	+	0.378805i
$70$	−0.309017	+	0.951057i	−0.0369346	+	0.113673i
$71$	4.69029	+	3.40769i	0.556635	+	0.404419i	0.830226	−	0.557427i	$-0.188211\pi$
$71$	4.69029	+	3.40769i	0.556635	+	0.404419i	−0.273591	+	0.961846i	$0.588211\pi$
$72$	1.34211	+	0.975098i	0.158169	+	0.114916i
$73$	−2.80171	+	8.62277i	−0.327915	+	1.00922i	0.642192	+	0.766543i	$0.278025\pi$
$73$	−2.80171	+	8.62277i	−0.327915	+	1.00922i	−0.970108	+	0.242675i	$0.921975\pi$
$74$	−1.31048	−	4.03324i	−0.152340	−	0.468855i
$75$	−0.936877	+	0.680681i	−0.108181	+	0.0785982i
$76$	−4.89322			−0.561291
$77$	2.51353	−	2.16383i	0.286444	−	0.246591i
$78$	−4.15337			−0.470276
$79$	4.07153	−	2.95814i	0.458083	−	0.332817i	−0.334696	−	0.942326i	$-0.608633\pi$
$79$	4.07153	−	2.95814i	0.458083	−	0.332817i	0.792779	+	0.609509i	$0.208633\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	−0.392798	+	1.20891i	−0.0436443	+	0.134323i
$82$	−1.64142	−	1.19256i	−0.181264	−	0.131696i
$83$	13.4506	+	9.77240i	1.47639	+	1.07266i	0.978698	+	0.205307i	$0.0658194\pi$
$83$	13.4506	+	9.77240i	1.47639	+	1.07266i	0.497693	+	0.867353i	$0.334181\pi$
$84$	0.357855	−	1.10136i	0.0390452	−	0.120169i
$85$	−1.32576	−	4.08027i	−0.143799	−	0.442568i
$86$	0.0557565	−	0.0405095i	0.00601238	−	0.00436825i
$87$	−0.874121			−0.0937156
$88$	−0.761624	+	3.22799i	−0.0811894	+	0.344105i
$89$	9.92243			1.05177			0.525887	−	0.850554i	$-0.323733\pi$
$89$	9.92243			1.05177			0.525887	+	0.850554i	$0.323733\pi$
$90$	−1.34211	+	0.975098i	−0.141471	+	0.102784i
$91$	−1.10830	−	3.41100i	−0.116182	−	0.357570i
$92$	0.882859	−	2.71716i	0.0920444	−	0.283284i
$93$	8.76312	+	6.36678i	0.908693	+	0.660204i
$94$	−1.81046	−	1.31538i	−0.186735	−	0.135671i
$95$	1.51209	−	4.65373i	0.155137	−	0.477462i
$96$	0.357855	+	1.10136i	0.0365234	+	0.112408i
$97$	5.43443	−	3.94835i	0.551783	−	0.400894i	−0.276659	−	0.960968i	$-0.589227\pi$
$97$	5.43443	−	3.94835i	0.551783	−	0.400894i	0.828443	+	0.560074i	$0.189227\pi$
$98$	1.00000			0.101015
$99$	5.48338	−	0.453150i	0.551100	−	0.0455432i
$100$	1.00000			0.100000
$101$	−2.55591	+	1.85698i	−0.254322	+	0.184776i	−0.707640	−	0.706573i	$-0.750240\pi$
$101$	−2.55591	+	1.85698i	−0.254322	+	0.184776i	0.453318	+	0.891349i	$0.350240\pi$
$102$	1.53529	+	4.72513i	0.152016	+	0.467858i
$103$	−4.47448	+	13.7710i	−0.440884	+	1.35690i	0.446051	+	0.895008i	$0.352830\pi$
$103$	−4.47448	+	13.7710i	−0.440884	+	1.35690i	−0.886935	+	0.461894i	$0.847170\pi$
$104$	2.90157	+	2.10811i	0.284522	+	0.206718i
$105$	0.936877	+	0.680681i	0.0914298	+	0.0664276i
$106$	4.04891	−	12.4613i	0.393265	−	1.21035i
$107$	−2.19761	−	6.76354i	−0.212451	−	0.653856i	−0.999325	−	0.0367425i	$-0.988302\pi$
$107$	−2.19761	−	6.76354i	−0.212451	−	0.653856i	0.786874	−	0.617114i	$-0.211698\pi$
$108$	4.36485	−	3.17125i	0.420008	−	0.305153i
$109$	−15.0710			−1.44354			−0.721770	−	0.692133i	$-0.756671\pi$
$109$	−15.0710			−1.44354			−0.721770	+	0.692133i	$0.756671\pi$
$110$	−2.83465	−	1.72185i	−0.270273	−	0.164172i
$111$	−4.91103			−0.466134
$112$	−0.809017	+	0.587785i	−0.0764449	+	0.0555405i
$113$	0.174057	+	0.535693i	0.0163739	+	0.0503937i	0.958910	−	0.283712i	$-0.0915659\pi$
$113$	0.174057	+	0.535693i	0.0163739	+	0.0503937i	−0.942536	+	0.334105i	$0.891566\pi$
$114$	−1.75106	+	5.38922i	−0.164002	+	0.504746i
$115$	2.31136	+	1.67930i	0.215535	+	0.156595i
$116$	0.610667	+	0.443676i	0.0566990	+	0.0411942i
$117$	1.83860	−	5.65863i	0.169979	−	0.523141i
$118$	0.378583	+	1.16516i	0.0348514	+	0.107262i
$119$	−3.47089	+	2.52175i	−0.318176	+	0.231168i
$120$	−1.15804			−0.105714
$121$	5.07045	+	9.76169i	0.460950	+	0.887426i
$122$	−4.03036			−0.364891
$123$	−1.90083	+	1.38104i	−0.171392	+	0.124524i
$124$	−2.89040	−	8.89575i	−0.259566	−	0.798862i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	1.34211	+	0.975098i	0.119564	+	0.0868687i
$127$	−9.95873	−	7.23544i	−0.883694	−	0.642041i	0.0505321	−	0.998722i	$-0.483908\pi$
$127$	−9.95873	−	7.23544i	−0.883694	−	0.642041i	−0.934226	+	0.356681i	$0.883908\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−0.0246630	−	0.0759048i	−0.00217145	−	0.00668305i
$130$	−2.90157	+	2.10811i	−0.254485	+	0.184894i
$131$	−14.9957			−1.31018			−0.655090	−	0.755551i	$-0.727369\pi$
$131$	−14.9957			−1.31018			−0.655090	+	0.755551i	$0.727369\pi$
$132$	3.28264	+	1.99398i	0.285717	+	0.173554i
$133$	−4.89322			−0.424296
$134$	11.5737	−	8.40878i	0.999815	−	0.726408i
$135$	1.66722	+	5.13119i	0.143492	+	0.441622i
$136$	1.32576	−	4.08027i	0.113683	−	0.349881i
$137$	0.342984	+	0.249192i	0.0293031	+	0.0212899i	0.602340	−	0.798239i	$-0.294235\pi$
$137$	0.342984	+	0.249192i	0.0293031	+	0.0212899i	−0.573037	+	0.819529i	$0.694235\pi$
$138$	−2.67665	−	1.94470i	−0.227851	−	0.165544i
$139$	5.99462	−	18.4495i	0.508457	−	1.56487i	−0.286424	−	0.958103i	$-0.592466\pi$
$139$	5.99462	−	18.4495i	0.508457	−	1.56487i	0.794880	−	0.606766i	$-0.207534\pi$
$140$	−0.309017	−	0.951057i	−0.0261167	−	0.0803789i
$141$	−2.09659	+	1.52326i	−0.176565	+	0.128282i
$142$	−5.79751			−0.486517
$143$	11.8548	−	0.979687i	0.991348	−	0.0819256i
$144$	−1.65894			−0.138245
$145$	−0.610667	+	0.443676i	−0.0507131	+	0.0368453i
$146$	−2.80171	−	8.62277i	−0.231871	−	0.713625i
$147$	0.357855	−	1.10136i	0.0295154	−	0.0908390i
$148$	3.43088	+	2.49268i	0.282016	+	0.204897i
$149$	−16.3583	−	11.8850i	−1.34012	−	0.973656i	−0.999439	−	0.0334774i	$-0.989342\pi$
$149$	−16.3583	−	11.8850i	−1.34012	−	0.973656i	−0.340683	−	0.940178i	$-0.610658\pi$
$150$	0.357855	−	1.10136i	0.0292187	−	0.0899260i
$151$	−4.75400	−	14.6313i	−0.386875	−	1.19068i	−0.935111	−	0.354355i	$-0.884701\pi$
$151$	−4.75400	−	14.6313i	−0.386875	−	1.19068i	0.548236	−	0.836323i	$-0.315299\pi$
$152$	3.95870	−	2.87616i	0.321093	−	0.233287i
$153$	−7.11726			−0.575396
$154$	−0.761624	+	3.22799i	−0.0613734	+	0.260119i
$155$	9.35354			0.751295
$156$	3.36014	−	2.44129i	0.269027	−	0.195459i
$157$	−1.49516	−	4.60164i	−0.119327	−	0.367251i	0.873498	−	0.486828i	$-0.161846\pi$
$157$	−1.49516	−	4.60164i	−0.119327	−	0.367251i	−0.992825	+	0.119577i	$0.961846\pi$
$158$	−1.55519	+	4.78638i	−0.123724	+	0.380784i
$159$	−12.2755	−	8.91866i	−0.973509	−	0.707295i
$160$	0.809017	+	0.587785i	0.0639584	+	0.0464685i
$161$	0.882859	−	2.71716i	0.0695790	−	0.214142i
$162$	−0.392798	−	1.20891i	−0.0308612	−	0.0949809i
$163$	−3.22178	+	2.34076i	−0.252349	+	0.183343i	−0.706767	−	0.707446i	$-0.749847\pi$
$163$	−3.22178	+	2.34076i	−0.252349	+	0.183343i	0.454418	+	0.890789i	$0.349847\pi$
$164$	2.02891			0.158431
$165$	−2.91078	+	2.50581i	−0.226604	+	0.195077i
$166$	−16.6258			−1.29041
$167$	19.3789	−	14.0796i	1.49958	−	1.08951i	0.529037	−	0.848599i	$-0.322553\pi$
$167$	19.3789	−	14.0796i	1.49958	−	1.08951i	0.970547	−	0.240913i	$-0.0774469\pi$
$168$	0.357855	+	1.10136i	0.0276091	+	0.0849721i
$169$	−0.0422541	+	0.130045i	−0.00325032	+	0.0100034i
$170$	3.47089	+	2.52175i	0.266205	+	0.193409i
$171$	−6.56722	−	4.77137i	−0.502208	−	0.364876i
$172$	−0.0212971	+	0.0655458i	−0.00162389	+	0.00499782i
$173$	2.88213	+	8.87028i	0.219124	+	0.674395i	0.998835	+	0.0482550i	$0.0153660\pi$
$173$	2.88213	+	8.87028i	0.219124	+	0.674395i	−0.779711	+	0.626140i	$0.784634\pi$
$174$	0.707179	−	0.513795i	0.0536111	−	0.0389507i
$175$	1.00000			0.0755929
$176$	−1.28120	−	3.05917i	−0.0965740	−	0.230594i
$177$	1.41874			0.106639
$178$	−8.02741	+	5.83226i	−0.601680	+	0.437146i
$179$	6.49431	+	19.9874i	0.485407	+	1.49393i	0.831390	+	0.555689i	$0.187546\pi$
$179$	6.49431	+	19.9874i	0.485407	+	1.49393i	−0.345983	+	0.938241i	$0.612454\pi$
$180$	0.512639	−	1.57774i	0.0382099	−	0.117598i
$181$	1.79022	+	1.30067i	0.133066	+	0.0966783i	0.652327	−	0.757937i	$-0.273793\pi$
$181$	1.79022	+	1.30067i	0.133066	+	0.0966783i	−0.519261	+	0.854616i	$0.673793\pi$
$182$	2.90157	+	2.10811i	0.215079	+	0.156264i
$183$	−1.44228	+	4.43889i	−0.106617	+	0.328132i
$184$	0.882859	+	2.71716i	0.0650852	+	0.200312i
$185$	−3.43088	+	2.49268i	−0.252243	+	0.183265i
$186$	−10.8318			−0.794227
$187$	−5.49667	−	13.1246i	−0.401956	−	0.959767i
$188$	2.23785			0.163212
$189$	4.36485	−	3.17125i	0.317496	−	0.230674i
$190$	1.51209	+	4.65373i	0.109698	+	0.337617i
$191$	5.92237	−	18.2272i	0.428527	−	1.31887i	−0.471049	−	0.882107i	$-0.656124\pi$
$191$	5.92237	−	18.2272i	0.428527	−	1.31887i	0.899576	−	0.436764i	$-0.143876\pi$
$192$	−0.936877	−	0.680681i	−0.0676132	−	0.0491239i
$193$	−6.83340	−	4.96475i	−0.491879	−	0.357371i	0.314028	−	0.949414i	$-0.398322\pi$
$193$	−6.83340	−	4.96475i	−0.491879	−	0.357371i	−0.805906	+	0.592043i	$0.798322\pi$
$194$	−2.07577	+	6.38856i	−0.149032	+	0.458672i
$195$	1.28346	+	3.95009i	0.0919105	+	0.282872i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	−11.1821			−0.796693			−0.398347	−	0.917235i	$-0.630416\pi$
$197$	−11.1821			−0.796693			−0.398347	+	0.917235i	$0.630416\pi$
$198$	−4.16979	+	3.58965i	−0.296334	+	0.255106i
$199$	−4.23045			−0.299888			−0.149944	−	0.988694i	$-0.547909\pi$
$199$	−4.23045			−0.299888			−0.149944	+	0.988694i	$0.547909\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$	−5.11943	−	15.7560i	−0.361097	−	1.11134i
$202$	0.976270	−	3.00465i	0.0686901	−	0.211406i
$203$	0.610667	+	0.443676i	0.0428604	+	0.0311399i
$204$	−4.01944	−	2.92029i	−0.281417	−	0.204461i
$205$	−0.626966	+	1.92960i	−0.0437892	+	0.134769i
$206$	−4.47448	−	13.7710i	−0.311752	−	0.959474i
$207$	3.83439	−	2.78585i	0.266509	−	0.193630i
$208$	−3.58654			−0.248682
$209$	3.72679	−	15.7953i	0.257788	−	1.09258i
$210$	−1.15804			−0.0799126
$211$	2.25309	−	1.63697i	0.155109	−	0.112694i	−0.507524	−	0.861638i	$-0.669439\pi$
$211$	2.25309	−	1.63697i	0.155109	−	0.112694i	0.662633	+	0.748944i	$0.269439\pi$
$212$	4.04891	+	12.4613i	0.278080	+	0.855844i
$213$	−2.07467	+	6.38518i	−0.142154	+	0.437505i
$214$	5.75341	+	4.18010i	0.393295	+	0.285746i
$215$	−0.0557565	−	0.0405095i	−0.00380256	−	0.00276273i
$216$	−1.66722	+	5.13119i	−0.113440	+	0.349133i
$217$	−2.89040	−	8.89575i	−0.196213	−	0.603883i
$218$	12.1927	−	8.85852i	0.825794	−	0.599974i
$219$	−10.4994			−0.709485
$220$	3.30536	−	0.273157i	0.222847	−	0.0184162i
$221$	−15.3872			−1.03505
$222$	3.97311	−	2.88663i	0.266657	−	0.193738i
$223$	−3.47965	−	10.7093i	−0.233015	−	0.717146i	−0.997379	−	0.0723607i	$-0.976947\pi$
$223$	−3.47965	−	10.7093i	−0.233015	−	0.717146i	0.764364	−	0.644785i	$-0.223053\pi$
$224$	0.309017	−	0.951057i	0.0206471	−	0.0635451i
$225$	1.34211	+	0.975098i	0.0894738	+	0.0650065i
$226$	−0.455688	−	0.331076i	−0.0303119	−	0.0220229i
$227$	1.28917	−	3.96765i	0.0855650	−	0.263342i	−0.899115	−	0.437712i	$-0.855789\pi$
$227$	1.28917	−	3.96765i	0.0855650	−	0.263342i	0.984680	+	0.174370i	$0.0557889\pi$
$228$	−1.75106	−	5.38922i	−0.115967	−	0.356910i
$229$	−11.4699	+	8.33335i	−0.757951	+	0.550683i	−0.898281	−	0.439421i	$-0.855184\pi$
$229$	−11.4699	+	8.33335i	−0.757951	+	0.550683i	0.140330	+	0.990105i	$0.455184\pi$
$230$	−2.85699			−0.188384
$231$	3.28264	+	1.99398i	0.215982	+	0.131194i
$232$	−0.754826			−0.0495568
$233$	7.68390	−	5.58268i	0.503389	−	0.365733i	−0.306921	−	0.951735i	$-0.599299\pi$
$233$	7.68390	−	5.58268i	0.503389	−	0.365733i	0.810310	+	0.586002i	$0.199299\pi$
$234$	1.83860	+	5.65863i	0.120193	+	0.369916i
$235$	−0.691535	+	2.12833i	−0.0451108	+	0.138837i
$236$	−0.991144	−	0.720108i	−0.0645180	−	0.0468750i
$237$	4.71501	+	3.42566i	0.306273	+	0.222520i
$238$	1.32576	−	4.08027i	0.0859363	−	0.264485i
$239$	0.627860	+	1.93235i	0.0406129	+	0.124994i	0.969307	−	0.245852i	$-0.0790678\pi$
$239$	0.627860	+	1.93235i	0.0406129	+	0.124994i	−0.928694	+	0.370846i	$0.879068\pi$
$240$	0.936877	−	0.680681i	0.0604751	−	0.0439377i
$241$	−18.6496			−1.20133			−0.600663	−	0.799502i	$-0.705097\pi$
$241$	−18.6496			−1.20133			−0.600663	+	0.799502i	$0.705097\pi$
$242$	−9.83986	−	4.91703i	−0.632530	−	0.316079i
$243$	14.7137			0.943886
$244$	3.26063	−	2.36898i	0.208740	−	0.151659i
$245$	−0.309017	−	0.951057i	−0.0197424	−	0.0607608i
$246$	0.726054	−	2.23457i	0.0462915	−	0.142471i
$247$	−14.1980	−	10.3155i	−0.903398	−	0.656357i
$248$	7.56718	+	5.49788i	0.480516	+	0.349115i
$249$	−5.94963	+	18.3111i	−0.377042	+	1.16042i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	11.7363	−	8.52690i	0.740787	−	0.538213i	−0.152170	−	0.988354i	$-0.548626\pi$
$251$	11.7363	−	8.52690i	0.740787	−	0.538213i	0.892958	+	0.450141i	$0.148626\pi$
$252$	−1.65894			−0.104503
$253$	8.09857	+	4.91932i	0.509152	+	0.309275i
$254$	12.3097			0.772377
$255$	4.01944	−	2.92029i	0.251707	−	0.182876i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−4.58714	+	14.1178i	−0.286138	+	0.880642i	0.699917	+	0.714224i	$0.253220\pi$
$257$	−4.58714	+	14.1178i	−0.286138	+	0.880642i	−0.986055	+	0.166418i	$0.946780\pi$
$258$	0.0645685	+	0.0469118i	0.00401986	+	0.00292060i
$259$	3.43088	+	2.49268i	0.213184	+	0.154888i
$260$	1.10830	−	3.41100i	0.0687339	−	0.211541i
$261$	0.386954	+	1.19092i	0.0239518	+	0.0737161i
$262$	12.1318	−	8.81425i	0.749504	−	0.544546i
$263$	−31.6286			−1.95030			−0.975152	−	0.221539i	$-0.928892\pi$
$263$	−31.6286			−1.95030			−0.975152	+	0.221539i	$0.928892\pi$
$264$	−3.82775	+	0.316327i	−0.235581	+	0.0194686i
$265$	−13.1026			−0.804884
$266$	3.95870	−	2.87616i	0.242723	−	0.176349i
$267$	3.55079	+	10.9282i	0.217305	+	0.668795i
$268$	−4.42076	+	13.6057i	−0.270041	+	0.831100i
$269$	−8.98185	−	6.52569i	−0.547633	−	0.397879i	0.279279	−	0.960210i	$-0.409905\pi$
$269$	−8.98185	−	6.52569i	−0.547633	−	0.397879i	−0.826912	+	0.562331i	$0.809905\pi$
$270$	−4.36485	−	3.17125i	−0.265636	−	0.192996i
$271$	−4.42291	+	13.6123i	−0.268672	+	0.826889i	0.722152	+	0.691734i	$0.243153\pi$
$271$	−4.42291	+	13.6123i	−0.268672	+	0.826889i	−0.990825	+	0.135155i	$0.956847\pi$
$272$	1.32576	+	4.08027i	0.0803861	+	0.247403i
$273$	3.36014	−	2.44129i	0.203365	−	0.147753i
$274$	−0.423951			−0.0256118
$275$	−0.761624	+	3.22799i	−0.0459277	+	0.194655i
$276$	3.30852			0.199149
$277$	−3.14189	+	2.28272i	−0.188778	+	0.137155i	−0.678160	−	0.734914i	$-0.737222\pi$
$277$	−3.14189	+	2.28272i	−0.188778	+	0.137155i	0.489382	+	0.872069i	$0.337222\pi$
$278$	5.99462	+	18.4495i	0.359533	+	1.10653i
$279$	4.79500	−	14.7575i	0.287069	−	0.883507i
$280$	0.809017	+	0.587785i	0.0483480	+	0.0351269i
$281$	19.1609	+	13.9212i	1.14305	+	0.830471i	0.987541	−	0.157364i	$-0.0502996\pi$
$281$	19.1609	+	13.9212i	1.14305	+	0.830471i	0.155505	+	0.987835i	$0.450300\pi$
$282$	0.800827	−	2.46469i	0.0476886	−	0.146770i
$283$	2.76857	+	8.52079i	0.164574	+	0.506508i	0.999005	−	0.0446055i	$-0.0142031\pi$
$283$	2.76857	+	8.52079i	0.164574	+	0.506508i	−0.834430	+	0.551114i	$0.814203\pi$
$284$	4.69029	−	3.40769i	0.278317	−	0.202209i
$285$	5.66656			0.335658
$286$	−9.01488	+	7.76066i	−0.533061	+	0.458897i
$287$	2.02891			0.119763
$288$	1.34211	−	0.975098i	0.0790844	−	0.0574582i
$289$	0.434562	+	1.33744i	0.0255625	+	0.0786731i
$290$	0.233254	−	0.717882i	0.0136972	−	0.0421555i
$291$	6.29331	+	4.57236i	0.368920	+	0.268036i
$292$	7.33497	+	5.32916i	0.429246	+	0.311866i
$293$	3.93783	−	12.1194i	0.230051	−	0.708023i	−0.767689	−	0.640823i	$-0.778593\pi$
$293$	3.93783	−	12.1194i	0.230051	−	0.708023i	0.997739	−	0.0672005i	$-0.0214067\pi$
$294$	0.357855	+	1.10136i	0.0208705	+	0.0642329i
$295$	0.991144	−	0.720108i	0.0577066	−	0.0419263i
$296$	−4.24080			−0.246491
$297$	6.91239	+	16.5050i	0.401097	+	0.957717i
$298$	20.2199			1.17131
$299$	8.28977	−	6.02287i	0.479410	−	0.348311i
$300$	0.357855	+	1.10136i	0.0206608	+	0.0635873i
$301$	−0.0212971	+	0.0655458i	−0.00122754	+	0.00377799i
$302$	12.4461	+	9.04264i	0.716194	+	0.520345i
$303$	−2.95985	−	2.15046i	−0.170039	−	0.123541i
$304$	−1.51209	+	4.65373i	−0.0867242	+	0.266910i
$305$	1.24545	+	3.83310i	0.0713142	+	0.219483i
$306$	5.75798	−	4.18342i	0.329162	−	0.239150i
$307$	−5.75775			−0.328612			−0.164306	−	0.986409i	$-0.552538\pi$
$307$	−5.75775			−0.328612			−0.164306	+	0.986409i	$0.552538\pi$
$308$	−1.28120	−	3.05917i	−0.0730031	−	0.174312i
$309$	−16.7682			−0.953907
$310$	−7.56718	+	5.49788i	−0.429787	+	0.312258i
$311$	3.77168	+	11.6080i	0.213872	+	0.658232i	0.999232	+	0.0391914i	$0.0124782\pi$
$311$	3.77168	+	11.6080i	0.213872	+	0.658232i	−0.785359	+	0.619040i	$0.787522\pi$
$312$	−1.28346	+	3.95009i	−0.0726617	+	0.223630i
$313$	−16.4362	−	11.9416i	−0.929026	−	0.674977i	0.0167279	−	0.999860i	$-0.494675\pi$
$313$	−16.4362	−	11.9416i	−0.929026	−	0.674977i	−0.945754	+	0.324883i	$0.894675\pi$
$314$	3.91439	+	2.84397i	0.220902	+	0.160495i
$315$	0.512639	−	1.57774i	0.0288840	−	0.0888957i
$316$	−1.55519	−	4.78638i	−0.0874861	−	0.269255i
$317$	−21.4627	+	15.5936i	−1.20547	+	0.875823i	−0.994811	−	0.101737i	$-0.967560\pi$
$317$	−21.4627	+	15.5936i	−1.20547	+	0.875823i	−0.210656	+	0.977560i	$0.567560\pi$
$318$	15.1733			0.850878
$319$	−1.89728	+	1.63331i	−0.106227	+	0.0914480i
$320$	−1.00000			−0.0559017
$321$	6.66270	−	4.84073i	0.371876	−	0.270183i
$322$	0.882859	+	2.71716i	0.0491998	+	0.151421i
$323$	−6.48724	+	19.9657i	−0.360960	+	1.11092i
$324$	1.02836	+	0.747147i	0.0571311	+	0.0415082i
$325$	2.90157	+	2.10811i	0.160950	+	0.116937i
$326$	1.23061	−	3.78743i	0.0681573	−	0.209766i
$327$	−5.39323	−	16.5987i	−0.298247	−	0.917909i
$328$	−1.64142	+	1.19256i	−0.0906322	+	0.0658482i
$329$	2.23785			0.123377
$330$	0.881993	−	3.73815i	0.0485521	−	0.205779i
$331$	0.393891			0.0216502			0.0108251	−	0.999941i	$-0.496554\pi$
$331$	0.393891			0.0216502			0.0108251	+	0.999941i	$0.496554\pi$
$332$	13.4506	−	9.77240i	0.738195	−	0.536330i
$333$	2.17400	+	6.69089i	0.119135	+	0.366658i
$334$	−7.40208	+	22.7813i	−0.405024	+	1.24654i
$335$	−11.5737	−	8.40878i	−0.632339	−	0.459421i
$336$	−0.936877	−	0.680681i	−0.0511108	−	0.0371342i
$337$	−0.384350	+	1.18291i	−0.0209369	+	0.0644371i	−0.960979	−	0.276621i	$-0.910785\pi$
$337$	−0.384350	+	1.18291i	−0.0209369	+	0.0644371i	0.940042	+	0.341058i	$0.110785\pi$
$338$	−0.0422541	−	0.130045i	−0.00229832	−	0.00707350i
$339$	−0.527706	+	0.383401i	−0.0286610	+	0.0208235i
$340$	−4.29025			−0.232672
$341$	30.9168	−	2.55498i	1.67424	−	0.138360i
$342$	8.11754			0.438946
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−0.0212971	−	0.0655458i	−0.00114826	−	0.00353399i
$345$	−1.02239	+	3.14659i	−0.0550436	+	0.169407i
$346$	−7.54551	−	5.48213i	−0.405649	−	0.294721i
$347$	12.7096	+	9.23407i	0.682287	+	0.495711i	0.874116	−	0.485718i	$-0.161442\pi$
$347$	12.7096	+	9.23407i	0.682287	+	0.495711i	−0.191828	+	0.981428i	$0.561442\pi$
$348$	−0.270118	+	0.831339i	−0.0144799	+	0.0445644i
$349$	5.07147	+	15.6084i	0.271469	+	0.835497i	0.990132	+	0.140138i	$0.0447546\pi$
$349$	5.07147	+	15.6084i	0.271469	+	0.835497i	−0.718663	+	0.695359i	$0.755245\pi$
$350$	−0.809017	+	0.587785i	−0.0432438	+	0.0314184i
$351$	19.3503			1.03284
$352$	2.83465	+	1.72185i	0.151087	+	0.0917750i
$353$	22.8233			1.21476			0.607382	−	0.794410i	$-0.292220\pi$
$353$	22.8233			1.21476			0.607382	+	0.794410i	$0.292220\pi$
$354$	−1.14779	+	0.833916i	−0.0610042	+	0.0443221i
$355$	1.79153	+	5.51376i	0.0950846	+	0.292640i
$356$	3.06620	−	9.43679i	0.162508	−	0.500149i
$357$	−4.01944	−	2.92029i	−0.212731	−	0.154558i
$358$	−17.0023	−	12.3529i	−0.898600	−	0.652871i
$359$	−3.35431	+	10.3235i	−0.177034	+	0.544854i	−0.999721	−	0.0236409i	$-0.992474\pi$
$359$	−3.35431	+	10.3235i	−0.177034	+	0.544854i	0.822687	+	0.568495i	$0.192474\pi$
$360$	0.512639	+	1.57774i	0.0270185	+	0.0831543i
$361$	−3.99944	+	2.90576i	−0.210497	+	0.152935i
$362$	−2.21284			−0.116304
$363$	−8.93669	+	9.07768i	−0.469054	+	0.476455i
$364$	−3.58654			−0.187986
$365$	−7.33497	+	5.32916i	−0.383930	+	0.278941i
$366$	−1.44228	−	4.43889i	−0.0753894	−	0.232025i
$367$	6.60984	−	20.3430i	0.345031	−	1.06190i	−0.616537	−	0.787326i	$-0.711465\pi$
$367$	6.60984	−	20.3430i	0.345031	−	1.06190i	0.961567	−	0.274569i	$-0.0885352\pi$
$368$	−2.31136	−	1.67930i	−0.120488	−	0.0875394i
$369$	2.72301	+	1.97838i	0.141754	+	0.102990i
$370$	1.31048	−	4.03324i	0.0681286	−	0.209678i
$371$	4.04891	+	12.4613i	0.210209	+	0.646957i
$372$	8.76312	−	6.36678i	0.454346	−	0.330102i
$373$	2.90463			0.150396			0.0751981	−	0.997169i	$-0.476041\pi$
$373$	2.90463			0.150396			0.0751981	+	0.997169i	$0.476041\pi$
$374$	12.1614	+	7.38718i	0.628849	+	0.381982i
$375$	−1.15804			−0.0598011
$376$	−1.81046	+	1.31538i	−0.0933675	+	0.0678354i
$377$	0.836575	+	2.57471i	0.0430858	+	0.132604i
$378$	−1.66722	+	5.13119i	−0.0857527	+	0.263920i
$379$	−0.0507588	−	0.0368784i	−0.00260731	−	0.00189432i	0.586481	−	0.809963i	$-0.300513\pi$
$379$	−0.0507588	−	0.0368784i	−0.00260731	−	0.00189432i	−0.589088	+	0.808069i	$0.700513\pi$
$380$	−3.95870	−	2.87616i	−0.203077	−	0.147544i
$381$	4.40507	−	13.5574i	0.225679	−	0.694568i
$382$	5.92237	+	18.2272i	0.303015	+	0.932583i
$383$	6.82320	−	4.95735i	0.348649	−	0.253309i	−0.399653	−	0.916667i	$-0.630869\pi$
$383$	6.82320	−	4.95735i	0.348649	−	0.253309i	0.748302	+	0.663358i	$0.230869\pi$
$384$	1.15804			0.0590961
$385$	3.30536	−	0.273157i	0.168457	−	0.0139214i
$386$	8.44654			0.429918
$387$	−0.0924966	+	0.0672027i	−0.00470186	+	0.00341610i
$388$	−2.07577	−	6.38856i	−0.105381	−	0.324330i
$389$	−11.3311	+	34.8734i	−0.574508	+	1.76815i	0.0633405	+	0.997992i	$0.479825\pi$
$389$	−11.3311	+	34.8734i	−0.574508	+	1.76815i	−0.637848	+	0.770162i	$0.720175\pi$
$390$	−3.36014	−	2.44129i	−0.170148	−	0.123619i
$391$	−9.91630	−	7.20461i	−0.501489	−	0.364353i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$	−5.36629	−	16.5157i	−0.270693	−	0.833108i
$394$	9.04653	−	6.57269i	0.455758	−	0.331127i
$395$	5.03269			0.253222
$396$	1.26349	−	5.35503i	0.0634925	−	0.269100i
$397$	−2.91177			−0.146137			−0.0730687	−	0.997327i	$-0.523279\pi$
$397$	−2.91177			−0.146137			−0.0730687	+	0.997327i	$0.523279\pi$
$398$	3.42250	−	2.48659i	0.171555	−	0.124642i
$399$	−1.75106	−	5.38922i	−0.0876628	−	0.269798i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	−12.4204	−	9.02397i	−0.620247	−	0.450636i	0.232761	−	0.972534i	$-0.425224\pi$
$401$	−12.4204	−	9.02397i	−0.620247	−	0.450636i	−0.853008	+	0.521898i	$0.825224\pi$
$402$	13.4028	+	9.73773i	0.668473	+	0.485674i
$403$	10.3665	−	31.9050i	0.516395	−	1.58930i
$404$	0.976270	+	3.00465i	0.0485712	+	0.149487i
$405$	−1.02836	+	0.747147i	−0.0510996	+	0.0371260i
$406$	−0.754826			−0.0374614
$407$	−10.6594	+	9.17636i	−0.528366	+	0.454855i
$408$	4.96830			0.245967
$409$	12.1303	−	8.81315i	0.599803	−	0.435782i	−0.246006	−	0.969268i	$-0.579118\pi$
$409$	12.1303	−	8.81315i	0.599803	−	0.435782i	0.845809	+	0.533486i	$0.179118\pi$
$410$	−0.626966	−	1.92960i	−0.0309637	−	0.0952964i
$411$	−0.151713	+	0.466925i	−0.00748345	+	0.0230317i
$412$	11.7144	+	8.51098i	0.577125	+	0.419306i
$413$	−0.991144	−	0.720108i	−0.0487710	−	0.0354342i
$414$	−1.46461	+	4.50760i	−0.0719815	+	0.221536i
$415$	5.13766	+	15.8121i	0.252198	+	0.776184i
$416$	2.90157	−	2.10811i	0.142261	−	0.103359i
$417$	22.4649			1.10011
$418$	6.26919	+	14.9692i	0.306636	+	0.732167i
$419$	26.8166			1.31008			0.655038	−	0.755596i	$-0.272653\pi$
$419$	26.8166			1.31008			0.655038	+	0.755596i	$0.272653\pi$
$420$	0.936877	−	0.680681i	0.0457149	−	0.0332138i
$421$	12.0721	+	37.1541i	0.588358	+	1.81078i	0.585343	+	0.810786i	$0.300960\pi$
$421$	12.0721	+	37.1541i	0.588358	+	1.81078i	0.00301552	+	0.999995i	$0.499040\pi$
$422$	−0.860605	+	2.64867i	−0.0418936	+	0.128935i
$423$	3.00344	+	2.18213i	0.146032	+	0.106099i
$424$	−10.6002	−	7.70149i	−0.514791	−	0.374017i
$425$	1.32576	−	4.08027i	0.0643089	−	0.197922i
$426$	−2.07467	−	6.38518i	−0.100518	−	0.309363i
$427$	3.26063	−	2.36898i	0.157793	−	0.114643i
$428$	−7.11161			−0.343753
$429$	5.32129	+	12.7059i	0.256914	+	0.613445i
$430$	0.0689189			0.00332356
$431$	−29.8622	+	21.6962i	−1.43841	+	1.04507i	−0.450041	+	0.893008i	$0.648590\pi$
$431$	−29.8622	+	21.6962i	−1.43841	+	1.04507i	−0.988371	+	0.152059i	$0.951410\pi$
$432$	−1.66722	−	5.13119i	−0.0802143	−	0.246874i
$433$	−3.85368	+	11.8604i	−0.185196	+	0.569975i	−0.999952	−	0.00982950i	$-0.996871\pi$
$433$	−3.85368	+	11.8604i	−0.185196	+	0.569975i	0.814756	+	0.579805i	$0.196871\pi$
$434$	7.56718	+	5.49788i	0.363236	+	0.263906i
$435$	−0.707179	−	0.513795i	−0.0339066	−	0.0246346i
$436$	−4.65720	+	14.3334i	−0.223039	+	0.686444i
$437$	−4.32002	−	13.2957i	−0.206655	−	0.636018i
$438$	8.49421	−	6.17140i	0.405869	−	0.294881i
$439$	−5.79416			−0.276540			−0.138270	−	0.990395i	$-0.544154\pi$
$439$	−5.79416			−0.276540			−0.138270	+	0.990395i	$0.544154\pi$
$440$	−2.51353	+	2.16383i	−0.119828	+	0.103156i
$441$	−1.65894			−0.0789970
$442$	12.4485	−	9.04435i	0.592114	−	0.430196i
$443$	3.66425	+	11.2774i	0.174094	+	0.535806i	0.999591	−	0.0286006i	$-0.00910510\pi$
$443$	3.66425	+	11.2774i	0.174094	+	0.535806i	−0.825497	+	0.564406i	$0.809105\pi$
$444$	−1.51759	+	4.67067i	−0.0720217	+	0.221660i
$445$	8.02741	+	5.83226i	0.380536	+	0.276475i
$446$	9.10985	+	6.61870i	0.431364	+	0.313404i
$447$	7.23581	−	22.2695i	0.342242	−	1.05331i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	5.07184	−	3.68491i	0.239355	−	0.173902i	−0.461641	−	0.887067i	$-0.652739\pi$
$449$	5.07184	−	3.68491i	0.239355	−	0.173902i	0.700996	+	0.713165i	$0.252739\pi$
$450$	−1.65894			−0.0782030
$451$	−1.54526	+	6.54929i	−0.0727636	+	0.308394i
$452$	0.563261			0.0264936
$453$	14.4131	−	10.4718i	0.677189	−	0.492007i
$454$	1.28917	+	3.96765i	0.0605036	+	0.186211i
$455$	1.10830	−	3.41100i	0.0519580	−	0.159910i
$456$	4.58434	+	3.33072i	0.214681	+	0.155975i
$457$	24.3010	+	17.6557i	1.13675	+	0.825900i	0.986664	−	0.162772i	$-0.0520436\pi$
$457$	24.3010	+	17.6557i	1.13675	+	0.825900i	0.150090	+	0.988672i	$0.452044\pi$
$458$	4.38110	−	13.4836i	0.204716	−	0.630050i
$459$	−7.15281	−	22.0141i	−0.333865	−	1.02753i
$460$	2.31136	−	1.67930i	0.107767	−	0.0782977i
$461$	−37.8904			−1.76473			−0.882365	−	0.470566i	$-0.844050\pi$
$461$	−37.8904			−1.76473			−0.882365	+	0.470566i	$0.844050\pi$
$462$	−3.82775	+	0.316327i	−0.178083	+	0.0147169i
$463$	2.23043			0.103657			0.0518285	−	0.998656i	$-0.483495\pi$
$463$	2.23043			0.103657			0.0518285	+	0.998656i	$0.483495\pi$
$464$	0.610667	−	0.443676i	0.0283495	−	0.0205971i
$465$	3.34721	+	10.3017i	0.155223	+	0.477728i
$466$	−2.93499	+	9.03296i	−0.135961	+	0.418444i
$467$	−32.4981	−	23.6113i	−1.50383	−	1.09260i	−0.968823	−	0.247753i	$-0.920308\pi$
$467$	−32.4981	−	23.6113i	−1.50383	−	1.09260i	−0.535010	−	0.844846i	$-0.679692\pi$
$468$	−4.81352	−	3.49723i	−0.222505	−	0.161659i
$469$	−4.42076	+	13.6057i	−0.204132	+	0.628253i
$470$	−0.691535	−	2.12833i	−0.0318981	−	0.0981723i
$471$	4.53303	−	3.29344i	0.208871	−	0.151754i
$472$	1.22512			0.0563908
$473$	−0.195361	−	0.118668i	−0.00898270	−	0.00545636i
$474$	−5.82808			−0.267692
$475$	3.95870	−	2.87616i	0.181637	−	0.131967i
$476$	1.32576	+	4.08027i	0.0607662	+	0.187019i
$477$	−6.71689	+	20.6725i	−0.307545	+	0.946527i
$478$	−1.64376	−	1.19426i	−0.0751837	−	0.0546242i
$479$	12.5114	+	9.09003i	0.571658	+	0.415334i	0.835707	−	0.549175i	$-0.185058\pi$
$479$	12.5114	+	9.09003i	0.571658	+	0.415334i	−0.264049	+	0.964509i	$0.585058\pi$
$480$	−0.357855	+	1.10136i	−0.0163338	+	0.0502702i
$481$	4.70008	+	14.4654i	0.214305	+	0.659564i
$482$	15.0879	−	10.9620i	0.687233	−	0.499304i
$483$	3.30852			0.150543
$484$	10.8508	−	1.80576i	0.493217	−	0.0820800i
$485$	6.71733			0.305018
$486$	−11.9037	+	8.64851i	−0.539961	+	0.392305i
$487$	−5.53709	−	17.0414i	−0.250910	−	0.772220i	−0.994608	−	0.103705i	$-0.966930\pi$
$487$	−5.53709	−	17.0414i	−0.250910	−	0.772220i	0.743699	−	0.668515i	$-0.233070\pi$
$488$	−1.24545	+	3.83310i	−0.0563788	+	0.173516i
$489$	−3.73096	−	2.71070i	−0.168720	−	0.122582i
$490$	0.809017	+	0.587785i	0.0365477	+	0.0265534i
$491$	8.23260	−	25.3373i	0.371532	−	1.14346i	−0.574256	−	0.818675i	$-0.694709\pi$
$491$	8.23260	−	25.3373i	0.371532	−	1.14346i	0.945789	−	0.324783i	$-0.105291\pi$
$492$	0.726054	+	2.23457i	0.0327331	+	0.100742i
$493$	2.61992	−	1.90348i	0.117995	−	0.0857285i
$494$	17.5497			0.789599
$495$	4.70250	+	2.85644i	0.211362	+	0.128388i
$496$	−9.35354			−0.419987
$497$	4.69029	−	3.40769i	0.210388	−	0.152856i
$498$	−5.94963	−	18.3111i	−0.266609	−	0.820539i
$499$	9.09434	−	27.9895i	0.407119	−	1.25298i	−0.511994	−	0.858989i	$-0.671093\pi$
$499$	9.09434	−	27.9895i	0.407119	−	1.25298i	0.919113	−	0.393994i	$-0.128907\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	22.4416	+	16.3048i	1.00262	+	0.728444i
$502$	−4.48286	+	13.7968i	−0.200080	+	0.615782i
$503$	−7.78005	−	23.9445i	−0.346895	−	1.06763i	−0.960561	−	0.278068i	$-0.910306\pi$
$503$	−7.78005	−	23.9445i	−0.346895	−	1.06763i	0.613666	−	0.789566i	$-0.289694\pi$
$504$	1.34211	−	0.975098i	0.0597822	−	0.0434343i
$505$	−3.15928			−0.140586
$506$	−9.44338	+	0.780407i	−0.419809	+	0.0346933i
$507$	−0.158348			−0.00703246
$508$	−9.95873	+	7.23544i	−0.441847	+	0.321021i
$509$	8.91049	+	27.4237i	0.394951	+	1.21553i	0.929000	+	0.370080i	$0.120670\pi$
$509$	8.91049	+	27.4237i	0.394951	+	1.21553i	−0.534049	+	0.845453i	$0.679330\pi$
$510$	−1.53529	+	4.72513i	−0.0679837	+	0.209232i
$511$	7.33497	+	5.32916i	0.324480	+	0.235748i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	8.15809	−	25.1080i	0.360188	−	1.10855i
$514$	−4.58714	−	14.1178i	−0.202330	−	0.622708i
$515$	−11.7144	+	8.51098i	−0.516196	+	0.375038i
$516$	−0.0798110			−0.00351348
$517$	−1.70440	+	7.22377i	−0.0749596	+	0.317701i
$518$	−4.24080			−0.186330
$519$	−8.73802	+	6.34854i	−0.383557	+	0.278670i
$520$	1.10830	+	3.41100i	0.0486022	+	0.149582i
$521$	2.73874	−	8.42896i	0.119986	−	0.369280i	−0.872968	−	0.487777i	$-0.837808\pi$
$521$	2.73874	−	8.42896i	0.119986	−	0.369280i	0.992954	+	0.118498i	$0.0378078\pi$
$522$	−1.01306	−	0.736030i	−0.0443403	−	0.0322151i
$523$	18.7966	+	13.6565i	0.821918	+	0.597159i	0.917261	−	0.398286i	$-0.130395\pi$
$523$	18.7966	+	13.6565i	0.821918	+	0.597159i	−0.0953431	+	0.995444i	$0.530395\pi$
$524$	−4.63393	+	14.2618i	−0.202434	+	0.623028i
$525$	0.357855	+	1.10136i	0.0156181	+	0.0480675i
$526$	25.5881	−	18.5908i	1.11569	−	0.810599i
$527$	−40.1291			−1.74805
$528$	2.91078	−	2.50581i	0.126675	−	0.109051i
$529$	−14.8376			−0.645113
$530$	10.6002	−	7.70149i	0.460443	−	0.334531i
$531$	−0.628045	−	1.93292i	−0.0272548	−	0.0838818i
$532$	−1.51209	+	4.65373i	−0.0655573	+	0.201765i
$533$	5.88702	+	4.27717i	0.254995	+	0.185265i
$534$	−9.29609	−	6.75400i	−0.402281	−	0.292274i
$535$	2.19761	−	6.76354i	0.0950109	−	0.292413i
$536$	−4.42076	−	13.6057i	−0.190948	−	0.587677i
$537$	−19.6894	+	14.3052i	−0.849661	+	0.617315i
$538$	11.1022			0.478649
$539$	−1.28120	−	3.05917i	−0.0551851	−	0.131768i
$540$	5.39525			0.232175
$541$	17.1941	−	12.4922i	0.739231	−	0.537083i	−0.153239	−	0.988189i	$-0.548970\pi$
$541$	17.1941	−	12.4922i	0.739231	−	0.537083i	0.892470	+	0.451106i	$0.148970\pi$
$542$	−4.42291	−	13.6123i	−0.189980	−	0.584699i
$543$	−0.791875	+	2.43714i	−0.0339826	+	0.104588i
$544$	−3.47089	−	2.52175i	−0.148813	−	0.108119i
$545$	−12.1927	−	8.85852i	−0.522278	−	0.379457i
$546$	−1.28346	+	3.95009i	−0.0549271	+	0.169048i
$547$	12.3157	+	37.9038i	0.526581	+	1.62065i	0.761169	+	0.648554i	$0.224626\pi$
$547$	12.3157	+	37.9038i	0.526581	+	1.62065i	−0.234588	+	0.972095i	$0.575374\pi$
$548$	0.342984	−	0.249192i	0.0146515	−	0.0106450i
$549$	6.68611			0.285356
$550$	−1.28120	−	3.05917i	−0.0546305	−	0.130444i
$551$	3.69353			0.157350
$552$	−2.67665	+	1.94470i	−0.113926	+	0.0827719i
$553$	−1.55519	−	4.78638i	−0.0661333	−	0.203537i
$554$	1.20010	−	3.69351i	0.0509872	−	0.156922i
$555$	−3.97311	−	2.88663i	−0.168649	−	0.122531i
$556$	−15.6941	−	11.4024i	−0.665579	−	0.483571i
$557$	6.09550	−	18.7600i	0.258275	−	0.794888i	−0.734892	−	0.678184i	$-0.762767\pi$
$557$	6.09550	−	18.7600i	0.258275	−	0.794888i	0.993167	−	0.116704i	$-0.0372328\pi$
$558$	4.79500	+	14.7575i	0.202988	+	0.624734i
$559$	−0.199973	+	0.145289i	−0.00845796	+	0.00614507i
$560$	−1.00000			−0.0422577
$561$	12.4880	−	10.7505i	0.527243	−	0.453888i
$562$	−23.6842			−0.999058
$563$	−16.6358	+	12.0866i	−0.701116	+	0.509391i	−0.880296	−	0.474426i	$-0.842656\pi$
$563$	−16.6358	+	12.0866i	−0.701116	+	0.509391i	0.179179	+	0.983816i	$0.442656\pi$
$564$	0.800827	+	2.46469i	0.0337209	+	0.103782i
$565$	−0.174057	+	0.535693i	−0.00732264	+	0.0225368i
$566$	−7.24821	−	5.26614i	−0.304665	−	0.221352i
$567$	1.02836	+	0.747147i	0.0431870	+	0.0313772i
$568$	−1.79153	+	5.51376i	−0.0751709	+	0.231352i
$569$	6.77142	+	20.8403i	0.283873	+	0.873671i	0.986734	+	0.162344i	$0.0519054\pi$
$569$	6.77142	+	20.8403i	0.283873	+	0.873671i	−0.702861	+	0.711327i	$0.748095\pi$
$570$	−4.58434	+	3.33072i	−0.192017	+	0.139508i
$571$	−17.3899			−0.727745			−0.363872	−	0.931449i	$-0.618546\pi$
$571$	−17.3899			−0.727745			−0.363872	+	0.931449i	$0.618546\pi$
$572$	2.73159	−	11.5773i	0.114214	−	0.484072i
$573$	22.1941			0.927172
$574$	−1.64142	+	1.19256i	−0.0685115	+	0.0497765i
$575$	0.882859	+	2.71716i	0.0368178	+	0.113313i
$576$	−0.512639	+	1.57774i	−0.0213600	+	0.0657393i
$577$	−20.7119	−	15.0481i	−0.862249	−	0.626461i	0.0662468	−	0.997803i	$-0.478898\pi$
$577$	−20.7119	−	15.0481i	−0.862249	−	0.626461i	−0.928496	+	0.371343i	$0.878898\pi$
$578$	−1.13770	−	0.826585i	−0.0473220	−	0.0343814i
$579$	3.02264	−	9.30272i	0.125617	−	0.386608i
$580$	0.233254	+	0.717882i	0.00968535	+	0.0298084i
$581$	13.4506	−	9.77240i	0.558023	−	0.405428i
$582$	−7.77896			−0.322448
$583$	−43.3086	+	3.57905i	−1.79366	+	0.148229i
$584$	−9.06652			−0.375175
$585$	4.81352	−	3.49723i	0.199015	−	0.144593i
$586$	3.93783	+	12.1194i	0.162670	+	0.500648i
$587$	−11.8257	+	36.3958i	−0.488100	+	1.50222i	0.339341	+	0.940664i	$0.389796\pi$
$587$	−11.8257	+	36.3958i	−0.488100	+	1.50222i	−0.827441	+	0.561553i	$0.810204\pi$
$588$	−0.936877	−	0.680681i	−0.0386361	−	0.0280708i
$589$	−37.0278	−	26.9023i	−1.52571	−	1.10849i
$590$	−0.378583	+	1.16516i	−0.0155860	+	0.0479688i
$591$	−4.00158	−	12.3156i	−0.164603	−	0.506596i
$592$	3.43088	−	2.49268i	0.141008	−	0.102448i
$593$	−11.8855			−0.488078			−0.244039	−	0.969765i	$-0.578473\pi$
$593$	−11.8855			−0.488078			−0.244039	+	0.969765i	$0.578473\pi$
$594$	−15.2936	−	9.28982i	−0.627505	−	0.381166i
$595$	−4.29025			−0.175883
$596$	−16.3583	+	11.8850i	−0.670061	+	0.486828i
$597$	−1.51389	−	4.65926i	−0.0619593	−	0.190691i
$598$	−3.16641	+	9.74520i	−0.129484	+	0.398511i
$599$	3.76491	+	2.73537i	0.153830	+	0.111764i	0.662038	−	0.749470i	$-0.269692\pi$
$599$	3.76491	+	2.73537i	0.153830	+	0.111764i	−0.508208	+	0.861234i	$0.669692\pi$
$600$	−0.936877	−	0.680681i	−0.0382478	−	0.0277887i
$601$	−4.08848	+	12.5831i	−0.166773	+	0.513274i	−0.999163	−	0.0409168i	$-0.986972\pi$
$601$	−4.08848	+	12.5831i	−0.166773	+	0.513274i	0.832390	+	0.554191i	$0.186972\pi$
$602$	−0.0212971	−	0.0655458i	−0.000868005	−	0.00267145i
$603$	−19.2000	+	13.9496i	−0.781885	+	0.568073i
$604$	−15.3843			−0.625977
$605$	−1.63569	+	10.8777i	−0.0665003	+	0.442242i
$606$	3.65858			0.148620
$607$	−24.5243	+	17.8180i	−0.995412	+	0.723209i	−0.961100	−	0.276202i	$-0.910924\pi$
$607$	−24.5243	+	17.8180i	−0.995412	+	0.723209i	−0.0343124	+	0.999411i	$0.510924\pi$
$608$	−1.51209	−	4.65373i	−0.0613232	−	0.188734i
$609$	−0.270118	+	0.831339i	−0.0109457	+	0.0336875i
$610$	−3.26063	−	2.36898i	−0.132019	−	0.0959174i
$611$	6.49329	+	4.71765i	0.262691	+	0.190856i
$612$	−2.19935	+	6.76891i	−0.0889036	+	0.273617i
$613$	−3.90353	−	12.0138i	−0.157662	−	0.485235i	0.840759	−	0.541410i	$-0.182109\pi$
$613$	−3.90353	−	12.0138i	−0.157662	−	0.485235i	−0.998421	+	0.0561755i	$0.982109\pi$
$614$	4.65812	−	3.38432i	0.187986	−	0.136580i
$615$	−2.34956			−0.0947434
$616$	2.83465	+	1.72185i	0.114211	+	0.0693754i
$617$	−48.4310			−1.94976			−0.974880	−	0.222731i	$-0.928503\pi$
$617$	−48.4310			−1.94976			−0.974880	+	0.222731i	$0.928503\pi$
$618$	13.5657	−	9.85608i	0.545693	−	0.396470i
$619$	−0.855584	−	2.63322i	−0.0343888	−	0.105838i	0.932389	−	0.361457i	$-0.117721\pi$
$619$	−0.855584	−	2.63322i	−0.0343888	−	0.105838i	−0.966778	+	0.255619i	$0.917721\pi$
$620$	2.89040	−	8.89575i	0.116081	−	0.357262i
$621$	12.4703	+	9.06023i	0.500417	+	0.363574i
$622$	−9.87439	−	7.17416i	−0.395927	−	0.287658i
$623$	3.06620	−	9.43679i	0.122845	−	0.378077i
$624$	−1.28346	−	3.95009i	−0.0513796	−	0.158130i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	20.3162			0.811999
$627$	18.7300	−	1.54786i	0.748004	−	0.0618155i
$628$	−4.83845			−0.193075
$629$	14.7193	−	10.6942i	0.586898	−	0.426407i
$630$	0.512639	+	1.57774i	0.0204240	+	0.0628587i
$631$	6.51639	−	20.0554i	0.259413	−	0.798392i	−0.733515	−	0.679674i	$-0.762121\pi$
$631$	6.51639	−	20.0554i	0.259413	−	0.798392i	0.992928	−	0.118718i	$-0.0378786\pi$
$632$	4.07153	+	2.95814i	0.161957	+	0.117669i
$633$	2.60918	+	1.89568i	0.103706	+	0.0753465i
$634$	8.19804	−	25.2310i	0.325586	−	1.00205i
$635$	−3.80390	−	11.7072i	−0.150953	−	0.464585i
$636$	−12.2755	+	8.91866i	−0.486754	+	0.353648i
$637$	−3.58654			−0.142104
$638$	0.574894	−	2.43657i	0.0227603	−	0.0964648i
$639$	9.61771			0.380471
$640$	0.809017	−	0.587785i	0.0319792	−	0.0232343i
$641$	3.35890	+	10.3376i	0.132668	+	0.408311i	0.995220	−	0.0976576i	$-0.0311350\pi$
$641$	3.35890	+	10.3376i	0.132668	+	0.408311i	−0.862552	+	0.505969i	$0.831135\pi$
$642$	−2.54492	+	7.83247i	−0.100440	+	0.309123i
$643$	−3.00291	−	2.18174i	−0.118423	−	0.0860396i	0.526997	−	0.849867i	$-0.323318\pi$
$643$	−3.00291	−	2.18174i	−0.118423	−	0.0860396i	−0.645420	+	0.763827i	$0.723318\pi$
$644$	−2.31136	−	1.67930i	−0.0910802	−	0.0661736i
$645$	0.0246630	−	0.0759048i	0.000971103	−	0.00298875i
$646$	−6.48724	−	19.9657i	−0.255237	−	0.785539i
$647$	20.3304	−	14.7709i	0.799269	−	0.580703i	−0.111430	−	0.993772i	$-0.535543\pi$
$647$	20.3304	−	14.7709i	0.799269	−	0.580703i	0.910700	+	0.413069i	$0.135543\pi$
$648$	−1.27112			−0.0499344
$649$	3.07938	−	2.65095i	0.120876	−	0.104059i
$650$	−3.58654			−0.140676
$651$	8.76312	−	6.36678i	0.343454	−	0.249534i
$652$	1.23061	+	3.78743i	0.0481945	+	0.148327i
$653$	8.45069	−	26.0085i	0.330701	−	1.01779i	−0.638100	−	0.769953i	$-0.720279\pi$
$653$	8.45069	−	26.0085i	0.330701	−	1.01779i	0.968801	−	0.247839i	$-0.0797205\pi$
$654$	14.1197	+	10.2585i	0.552123	+	0.401141i
$655$	−12.1318	−	8.81425i	−0.474028	−	0.344401i
$656$	0.626966	−	1.92960i	0.0244789	−	0.0753384i
$657$	4.64785	+	14.3046i	0.181330	+	0.558077i
$658$	−1.81046	+	1.31538i	−0.0705792	+	0.0512788i
$659$	−6.74968			−0.262930			−0.131465	−	0.991321i	$-0.541968\pi$
$659$	−6.74968			−0.262930			−0.131465	+	0.991321i	$0.541968\pi$
$660$	1.48368	+	3.54265i	0.0577523	+	0.137898i
$661$	−34.5615			−1.34429			−0.672144	−	0.740421i	$-0.734626\pi$
$661$	−34.5615			−1.34429			−0.672144	+	0.740421i	$0.734626\pi$
$662$	−0.318664	+	0.231523i	−0.0123852	+	0.00899841i
$663$	−5.50637	−	16.9469i	−0.213850	−	0.658162i
$664$	−5.13766	+	15.8121i	−0.199380	+	0.613628i
$665$	−3.95870	−	2.87616i	−0.153512	−	0.111533i
$666$	−5.69161	−	4.13520i	−0.220545	−	0.160236i
$667$	−0.666405	+	2.05098i	−0.0258033	+	0.0794144i
$668$	−7.40208	−	22.7813i	−0.286395	−	0.881433i
$669$	10.5496	−	7.66474i	0.407871	−	0.296336i
$670$	14.3059			0.552684
$671$	5.16369	+	12.3296i	0.199342	+	0.475977i
$672$	1.15804			0.0446725
$673$	−2.41678	+	1.75590i	−0.0931602	+	0.0676848i	−0.633390	−	0.773833i	$-0.718337\pi$
$673$	−2.41678	+	1.75590i	−0.0931602	+	0.0676848i	0.540230	+	0.841517i	$0.318337\pi$
$674$	−0.384350	−	1.18291i	−0.0148046	−	0.0455639i
$675$	−1.66722	+	5.13119i	−0.0641715	+	0.197499i
$676$	0.110623	+	0.0803721i	0.00425472	+	0.00309123i
$677$	−4.36533	−	3.17160i	−0.167773	−	0.121894i	0.500730	−	0.865603i	$-0.333065\pi$
$677$	−4.36533	−	3.17160i	−0.167773	−	0.121894i	−0.668504	+	0.743709i	$0.733065\pi$
$678$	0.201566	−	0.620355i	0.00774108	−	0.0238246i
$679$	−2.07577	−	6.38856i	−0.0796607	−	0.245170i
$680$	3.47089	−	2.52175i	0.133102	−	0.0967046i
$681$	4.83116			0.185130
$682$	−23.5104	+	20.2395i	−0.900261	+	0.775009i
$683$	2.39397			0.0916028			0.0458014	−	0.998951i	$-0.485416\pi$
$683$	2.39397			0.0916028			0.0458014	+	0.998951i	$0.485416\pi$
$684$	−6.56722	+	4.77137i	−0.251104	+	0.182438i
$685$	0.131008	+	0.403202i	0.00500556	+	0.0154055i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	−13.2826	−	9.65038i	−0.506763	−	0.368185i
$688$	0.0557565	+	0.0405095i	0.00212570	+	0.00154441i
$689$	−14.5216	+	44.6928i	−0.553228	+	1.70266i
$690$	−1.02239	−	3.14659i	−0.0389217	−	0.119789i
$691$	22.8731	−	16.6183i	0.870132	−	0.632188i	−0.0604902	−	0.998169i	$-0.519266\pi$
$691$	22.8731	−	16.6183i	0.870132	−	0.632188i	0.930622	+	0.365981i	$0.119266\pi$
$692$	9.32676			0.354550
$693$	1.26349	−	5.35503i	0.0479959	−	0.203421i
$694$	−15.7099			−0.596341
$695$	15.6941	−	11.4024i	0.595312	−	0.432519i
$696$	−0.270118	−	0.831339i	−0.0102388	−	0.0315118i
$697$	2.68984	−	8.27849i	0.101885	−	0.313570i
$698$	−13.2773	−	9.64650i	−0.502552	−	0.365126i
$699$	8.89828	+	6.46498i	0.336564	+	0.244528i
$700$	0.309017	−	0.951057i	0.0116797	−	0.0359466i
$701$	13.1855	+	40.5808i	0.498009	+	1.53271i	0.812215	+	0.583359i	$0.198262\pi$
$701$	13.1855	+	40.5808i	0.498009	+	1.53271i	−0.314206	+	0.949355i	$0.601738\pi$
$702$	−15.6547	+	11.3738i	−0.590849	+	0.429277i
$703$	20.7512			0.782645
$704$	−3.30536	+	0.273157i	−0.124575	+	0.0102950i
$705$	−2.59153			−0.0976027
$706$	−18.4645	+	13.4152i	−0.694919	+	0.504888i
$707$	0.976270	+	3.00465i	0.0367164	+	0.113001i
$708$	0.438416	−	1.34930i	0.0164767	−	0.0507100i
$709$	−39.7414	−	28.8738i	−1.49252	−	1.08438i	−0.973245	−	0.229770i	$-0.926203\pi$
$709$	−39.7414	−	28.8738i	−1.49252	−	1.08438i	−0.519274	−	0.854608i	$-0.673797\pi$
$710$	−4.69029	−	3.40769i	−0.176023	−	0.127888i
$711$	2.57996	−	7.94029i	0.0967559	−	0.297784i
$712$	3.06620	+	9.43679i	0.114911	+	0.353659i
$713$	21.6194	−	15.7074i	0.809651	−	0.588246i
$714$	4.96830			0.185934
$715$	10.1666	+	6.17549i	0.380208	+	0.230950i
$716$	21.0160			0.785405
$717$	−1.90354	+	1.38300i	−0.0710891	+	0.0516492i
$718$	−3.35431	−	10.3235i	−0.125182	−	0.385270i
$719$	9.59918	−	29.5433i	0.357989	−	1.10178i	−0.596267	−	0.802786i	$-0.703350\pi$
$719$	9.59918	−	29.5433i	0.357989	−	1.10178i	0.954256	−	0.298991i	$-0.0966500\pi$
$720$	−1.34211	−	0.975098i	−0.0500174	−	0.0363398i
$721$	11.7144	+	8.51098i	0.436265	+	0.316965i
$722$	1.52765	−	4.70163i	0.0568533	−	0.174976i
$723$	−6.67386	−	20.5400i	−0.248203	−	0.763891i
$724$	1.79022	−	1.30067i	0.0665331	−	0.0483391i
$725$	−0.754826			−0.0280335
$726$	1.89420	−	12.5969i	0.0703004	−	0.467513i
$727$	41.2246			1.52894			0.764468	−	0.644662i	$-0.223002\pi$
$727$	41.2246			1.52894			0.764468	+	0.644662i	$0.223002\pi$
$728$	2.90157	−	2.10811i	0.107539	−	0.0781319i
$729$	6.44378	+	19.8319i	0.238658	+	0.734515i
$730$	2.80171	−	8.62277i	0.103696	−	0.319143i
$731$	0.239210	+	0.173796i	0.00884749	+	0.00642808i
$732$	3.77595	+	2.74339i	0.139563	+	0.101398i
$733$	13.9107	−	42.8128i	0.513804	−	1.58133i	−0.271643	−	0.962398i	$-0.587567\pi$
$733$	13.9107	−	42.8128i	0.513804	−	1.58133i	0.785447	−	0.618929i	$-0.212433\pi$
$734$	6.60984	+	20.3430i	0.243974	+	0.750873i
$735$	0.936877	−	0.680681i	0.0345572	−	0.0251073i
$736$	2.85699			0.105310
$737$	−40.5521	−	24.6326i	−1.49376	−	0.907353i
$738$	−3.36583			−0.123898
$739$	31.9117	−	23.1852i	1.17389	−	0.852881i	0.182420	−	0.983221i	$-0.441607\pi$
$739$	31.9117	−	23.1852i	1.17389	−	0.852881i	0.991469	+	0.130340i	$0.0416068\pi$
$740$	1.31048	+	4.03324i	0.0481742	+	0.148265i
$741$	6.28025	−	19.3286i	0.230711	−	0.710055i
$742$	−10.6002	−	7.70149i	−0.389145	−	0.282731i
$743$	−30.7337	−	22.3293i	−1.12751	−	0.819184i	−0.142180	−	0.989841i	$-0.545411\pi$
$743$	−30.7337	−	22.3293i	−1.12751	−	0.819184i	−0.985331	+	0.170657i	$0.945411\pi$
$744$	−3.34721	+	10.3017i	−0.122715	+	0.377677i
$745$	−6.24831	−	19.2303i	−0.228920	−	0.704544i
$746$	−2.34990	+	1.70730i	−0.0860358	+	0.0625087i
$747$	27.5811			1.00914
$748$	−14.1808	+	1.17191i	−0.518502	+	0.0428493i
$749$	−7.11161			−0.259852
$750$	0.936877	−	0.680681i	0.0342099	−	0.0248549i
$751$	13.8373	+	42.5867i	0.504929	+	1.55401i	0.800890	+	0.598812i	$0.204360\pi$
$751$	13.8373	+	42.5867i	0.504929	+	1.55401i	−0.295960	+	0.955200i	$0.595640\pi$
$752$	0.691535	−	2.12833i	0.0252177	−	0.0776121i
$753$	13.5911	+	9.87452i	0.495288	+	0.359848i
$754$	−2.19018	−	1.59126i	−0.0797617	−	0.0579503i
$755$	4.75400	−	14.6313i	0.173016	−	0.532487i
$756$	−1.66722	−	5.13119i	−0.0606363	−	0.186619i
$757$	36.9761	−	26.8647i	1.34392	−	0.976414i	0.344629	−	0.938739i	$-0.388005\pi$
$757$	36.9761	−	26.8647i	1.34392	−	0.976414i	0.999290	−	0.0376754i	$-0.0119953\pi$
$758$	0.0627414			0.00227887
$759$	−2.51985	+	10.6799i	−0.0914647	+	0.387655i
$760$	4.89322			0.177496
$761$	17.5122	−	12.7233i	0.634815	−	0.461220i	−0.223250	−	0.974761i	$-0.571667\pi$
$761$	17.5122	−	12.7233i	0.634815	−	0.461220i	0.858065	+	0.513541i	$0.171667\pi$
$762$	4.40507	+	13.5574i	0.159579	+	0.491134i
$763$	−4.65720	+	14.3334i	−0.168602	+	0.518903i
$764$	−15.5050	−	11.2650i	−0.560950	−	0.407554i
$765$	−5.75798	−	4.18342i	−0.208180	−	0.151252i
$766$	−2.60623	+	8.02116i	−0.0941670	+	0.289816i
$767$	−1.35780	−	4.17889i	−0.0490274	−	0.150891i
$768$	−0.936877	+	0.680681i	−0.0338066	+	0.0245619i
$769$	−38.7211			−1.39632			−0.698159	−	0.715942i	$-0.745997\pi$
$769$	−38.7211			−1.39632			−0.698159	+	0.715942i	$0.745997\pi$
$770$	−2.51353	+	2.16383i	−0.0905814	+	0.0779790i
$771$	−17.1903			−0.619095
$772$	−6.83340	+	4.96475i	−0.245939	+	0.178685i
$773$	−9.78512	−	30.1155i	−0.351946	−	1.08318i	−0.957759	−	0.287572i	$-0.907152\pi$
$773$	−9.78512	−	30.1155i	−0.351946	−	1.08318i	0.605813	−	0.795607i	$-0.292848\pi$
$774$	0.0353305	−	0.108736i	0.00126993	−	0.00390844i
$775$	7.56718	+	5.49788i	0.271821	+	0.197490i
$776$	5.43443	+	3.94835i	0.195085	+	0.141737i
$777$	−1.51759	+	4.67067i	−0.0544433	+	0.167559i
$778$	−11.3311	−	34.8734i	−0.406239	−	1.25027i
$779$	8.03182	−	5.83546i	0.287770	−	0.209077i
$780$	4.15337			0.148714
$781$	7.42777	+	17.7356i	0.265786	+	0.634629i
$782$	12.2572			0.438317
$783$	−3.29470	+	2.39374i	−0.117743	+	0.0855453i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	1.49516	−	4.60164i	0.0533647	−	0.164240i
$786$	14.0491	+	10.2073i	0.501115	+	0.364082i
$787$	34.3142	+	24.9307i	1.22317	+	0.888685i	0.996359	−	0.0852536i	$-0.0271700\pi$
$787$	34.3142	+	24.9307i	1.22317	+	0.888685i	0.226811	+	0.973939i	$0.427170\pi$
$788$	−3.45547	+	10.6348i	−0.123096	+	0.378850i
$789$	−11.3185	−	34.8346i	−0.402948	−	1.24015i
$790$	−4.07153	+	2.95814i	−0.144859	+	0.105246i
$791$	0.563261			0.0200272
$792$	2.12543	+	5.07497i	0.0755238	+	0.180331i
$793$	14.4550			0.513313
$794$	2.35567	−	1.71149i	0.0835995	−	0.0607386i
$795$	−4.68882	−	14.4307i	−0.166295	−	0.511804i
$796$	−1.30728	+	4.02339i	−0.0463353	+	0.142605i
$797$	−11.1036	−	8.06726i	−0.393311	−	0.285757i	0.373500	−	0.927630i	$-0.378158\pi$
$797$	−11.1036	−	8.06726i	−0.393311	−	0.285757i	−0.766811	+	0.641873i	$0.778158\pi$
$798$	4.58434	+	3.33072i	0.162284	+	0.117906i
$799$	2.96686	−	9.13106i	0.104960	−	0.323034i
$800$	0.309017	+	0.951057i	0.0109254	+	0.0336249i
$801$	13.3170	−	9.67534i	0.470532	−	0.341861i
$802$	15.3525			0.542116
$803$	−22.7890	+	19.6184i	−0.804206	+	0.692318i
$804$	−16.5668			−0.584267
$805$	2.31136	−	1.67930i	0.0814646	−	0.0591875i
$806$	10.3665	+	31.9050i	0.365146	+	1.12380i
$807$	3.97297	−	12.2275i	0.139855	−	0.430430i
$808$	−2.55591	−	1.85698i	−0.0899165	−	0.0653282i
$809$	25.9649	+	18.8646i	0.912876	+	0.663243i	0.941741	−	0.336340i	$-0.109189\pi$
$809$	25.9649	+	18.8646i	0.912876	+	0.663243i	−0.0288645	+	0.999583i	$0.509189\pi$
$810$	0.392798	−	1.20891i	0.0138015	−	0.0424767i
$811$	13.8739	+	42.6994i	0.487178	+	1.49938i	0.828801	+	0.559543i	$0.189023\pi$
$811$	13.8739	+	42.6994i	0.487178	+	1.49938i	−0.341623	+	0.939837i	$0.610977\pi$
$812$	0.610667	−	0.443676i	0.0214302	−	0.0155700i
$813$	−16.5749			−0.581306
$814$	3.22989	−	13.6893i	0.113208	−	0.479808i
$815$	−3.98234			−0.139495
$816$	−4.01944	+	2.92029i	−0.140708	+	0.102231i
$817$	0.104211	+	0.320730i	0.00364589	+	0.0112209i
$818$	−4.63335	+	14.2600i	−0.162001	+	0.498589i
$819$	−4.81352	−	3.49723i	−0.168198	−	0.122203i
$820$	1.64142	+	1.19256i	0.0573209	+	0.0416460i
$821$	−12.7555	+	39.2573i	−0.445169	+	1.37009i	0.437130	+	0.899398i	$0.355995\pi$
$821$	−12.7555	+	39.2573i	−0.445169	+	1.37009i	−0.882299	+	0.470690i	$0.844005\pi$
$822$	−0.151713	−	0.466925i	−0.00529160	−	0.0162859i
$823$	−11.9364	+	8.67228i	−0.416076	+	0.302297i	−0.776057	−	0.630663i	$-0.782783\pi$
$823$	−11.9364	+	8.67228i	−0.416076	+	0.302297i	0.359981	+	0.932960i	$0.382783\pi$
$824$	−14.4797			−0.504426
$825$	−3.82775	+	0.316327i	−0.133265	+	0.0110131i
$826$	1.22512			0.0426274
$827$	−41.7264	+	30.3160i	−1.45097	+	1.05419i	−0.465366	+	0.885118i	$0.654077\pi$
$827$	−41.7264	+	30.3160i	−1.45097	+	1.05419i	−0.985604	+	0.169073i	$0.945923\pi$
$828$	−1.46461	−	4.50760i	−0.0508986	−	0.156650i
$829$	3.30075	−	10.1587i	0.114640	−	0.352825i	−0.877232	−	0.480067i	$-0.840612\pi$
$829$	3.30075	−	10.1587i	0.114640	−	0.352825i	0.991872	+	0.127242i	$0.0406125\pi$
$830$	−13.4506	−	9.77240i	−0.466876	−	0.339205i
$831$	−3.63844	−	2.64348i	−0.126216	−	0.0917015i
$832$	−1.10830	+	3.41100i	−0.0384234	+	0.118255i
$833$	1.32576	+	4.08027i	0.0459349	+	0.141373i
$834$	−18.1745	+	13.2045i	−0.629330	+	0.457235i
$835$	23.9536			0.828950
$836$	−13.8705	−	8.42540i	−0.479723	−	0.291398i
$837$	50.4647			1.74432
$838$	−21.6951	+	15.7624i	−0.749444	+	0.544503i
$839$	−8.47516	−	26.0839i	−0.292595	−	0.900515i	−0.984019	−	0.178065i	$-0.943016\pi$
$839$	−8.47516	−	26.0839i	−0.292595	−	0.900515i	0.691424	−	0.722449i	$-0.256984\pi$
$840$	−0.357855	+	1.10136i	−0.0123472	+	0.0380007i
$841$	23.0005	+	16.7109i	0.793122	+	0.576237i
$842$	−31.6052	−	22.9625i	−1.08919	−	0.791340i
$843$	−8.47551	+	26.0850i	−0.291912	+	0.898413i
$844$	−0.860605	−	2.64867i	−0.0296232	−	0.0911710i
$845$	−0.110623	+	0.0803721i	−0.00380554	+	0.00276488i
$846$	−3.71246			−0.127637
$847$	10.8508	−	1.80576i	0.372837	−	0.0620467i
$848$	13.1026			0.449944
$849$	−8.39374	+	6.09841i	−0.288073	+	0.209297i
$850$	1.32576	+	4.08027i	0.0454732	+	0.139952i
$851$	−3.74403	+	11.5229i	−0.128344	+	0.395001i
$852$	5.43156	+	3.94626i	0.186082	+	0.135196i
$853$	−40.6324	−	29.5212i	−1.39123	−	1.01079i	−0.995729	−	0.0923196i	$-0.970572\pi$
$853$	−40.6324	−	29.5212i	−1.39123	−	1.01079i	−0.395498	−	0.918467i	$-0.629428\pi$
$854$	−1.24545	+	3.83310i	−0.0426184	+	0.131166i
$855$	−2.50846	−	7.72024i	−0.0857874	−	0.264026i
$856$	5.75341	−	4.18010i	0.196648	−	0.142873i
$857$	−2.69776			−0.0921539			−0.0460769	−	0.998938i	$-0.514672\pi$
$857$	−2.69776			−0.0921539			−0.0460769	+	0.998938i	$0.514672\pi$
$858$	−11.7733	−	7.15148i	−0.401935	−	0.244148i
$859$	19.0873			0.651252			0.325626	−	0.945499i	$-0.394425\pi$
$859$	19.0873			0.651252			0.325626	+	0.945499i	$0.394425\pi$
$860$	−0.0557565	+	0.0405095i	−0.00190128	+	0.00138136i
$861$	0.726054	+	2.23457i	0.0247439	+	0.0761538i
$862$	11.4063	−	35.1051i	0.388502	−	1.19569i
$863$	17.2195	+	12.5107i	0.586159	+	0.425869i	0.840939	−	0.541130i	$-0.182003\pi$
$863$	17.2195	+	12.5107i	0.586159	+	0.425869i	−0.254781	+	0.966999i	$0.582003\pi$
$864$	4.36485	+	3.17125i	0.148495	+	0.107888i
$865$	−2.88213	+	8.87028i	−0.0979953	+	0.301598i
$866$	−3.85368	−	11.8604i	−0.130953	−	0.403033i
$867$	−1.31750	+	0.957222i	−0.0447447	+	0.0325090i
$868$	−9.35354			−0.317480
$869$	16.6348	−	1.37471i	0.564299	−	0.0466340i
$870$	0.874121			0.0296355
$871$	−41.5095	+	30.1584i	−1.40650	+	1.02188i
$872$	−4.65720	−	14.3334i	−0.157713	−	0.485389i
$873$	3.44357	−	10.5982i	0.116547	−	0.358695i
$874$	11.3100	+	8.21717i	0.382565	+	0.277950i
$875$	0.809017	+	0.587785i	0.0273498	+	0.0198708i
$876$	−3.24450	+	9.98554i	−0.109621	+	0.337380i
$877$	4.57247	+	14.0726i	0.154401	+	0.475199i	0.998100	−	0.0616188i	$-0.0196263\pi$
$877$	4.57247	+	14.0726i	0.154401	+	0.475199i	−0.843698	+	0.536818i	$0.819626\pi$
$878$	4.68758	−	3.40572i	0.158198	−	0.114938i
$879$	14.7571			0.497743
$880$	0.761624	−	3.22799i	0.0256743	−	0.108816i
$881$	−38.9767			−1.31316			−0.656579	−	0.754257i	$-0.727997\pi$
$881$	−38.9767			−1.31316			−0.656579	+	0.754257i	$0.727997\pi$
$882$	1.34211	−	0.975098i	0.0451911	−	0.0328333i
$883$	−12.6374	−	38.8938i	−0.425281	−	1.30888i	−0.902725	−	0.430219i	$-0.858437\pi$
$883$	−12.6374	−	38.8938i	−0.425281	−	1.30888i	0.477444	−	0.878662i	$-0.341563\pi$
$884$	−4.75489	+	14.6341i	−0.159924	+	0.492197i
$885$	1.14779	+	0.833916i	0.0385824	+	0.0280318i
$886$	−9.59314	−	6.96982i	−0.322288	−	0.234156i
$887$	−9.57598	+	29.4718i	−0.321530	+	0.989568i	0.651453	+	0.758689i	$0.274160\pi$
$887$	−9.57598	+	29.4718i	−0.321530	+	0.989568i	−0.972983	+	0.230878i	$0.925840\pi$
$888$	−1.51759	−	4.67067i	−0.0509270	−	0.156737i
$889$	−9.95873	+	7.23544i	−0.334005	+	0.242669i
$890$	−9.92243			−0.332600
$891$	−3.19501	+	2.75049i	−0.107037	+	0.0921449i
$892$	−11.2604			−0.377026
$893$	8.85899	−	6.43643i	0.296455	−	0.215387i
$894$	7.23581	+	22.2695i	0.242002	+	0.744804i
$895$	−6.49431	+	19.9874i	−0.217081	+	0.668106i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	9.59991	+	6.97474i	0.320532	+	0.232880i
$898$	−1.93727	+	5.96230i	−0.0646475	+	0.198965i
$899$	2.18175	+	6.71474i	0.0727655	+	0.223949i
$900$	1.34211	−	0.975098i	0.0447369	−	0.0325033i
$901$	56.2133			1.87274
$902$	−2.59943	−	6.20677i	−0.0865516	−	0.206663i
$903$	−0.0798110			−0.00265594
$904$	−0.455688	+	0.331076i	−0.0151559	+	0.0110114i
$905$	0.683804	+	2.10453i	0.0227304	+	0.0699571i
$906$	−5.50533	+	16.9437i	−0.182902	+	0.562916i
$907$	6.40938	+	4.65669i	0.212820	+	0.154623i	0.689089	−	0.724677i	$-0.258011\pi$
$907$	6.40938	+	4.65669i	0.212820	+	0.154623i	−0.476269	+	0.879300i	$0.658011\pi$
$908$	−3.37508	−	2.45214i	−0.112006	−	0.0813771i
$909$	−1.61957	+	4.98452i	−0.0537177	+	0.165326i
$910$	1.10830	+	3.41100i	0.0367398	+	0.113074i
$911$	−24.6947	+	17.9418i	−0.818173	+	0.594437i	−0.916189	−	0.400747i	$-0.868750\pi$
$911$	−24.6947	+	17.9418i	−0.818173	+	0.594437i	0.0980157	+	0.995185i	$0.468750\pi$
$912$	−5.66656			−0.187638
$913$	21.3010	+	50.8612i	0.704959	+	1.68326i
$914$	−30.0377			−0.993559
$915$	−3.77595	+	2.74339i	−0.124829	+	0.0906935i
$916$	4.38110	+	13.4836i	0.144756	+	0.445512i
$917$	−4.63393	+	14.2618i	−0.153026	+	0.470965i
$918$	18.7263	+	13.6055i	0.618060	+	0.449047i
$919$	4.15926	+	3.02188i	0.137201	+	0.0996827i	0.654269	−	0.756262i	$-0.272976\pi$
$919$	4.15926	+	3.02188i	0.137201	+	0.0996827i	−0.517068	+	0.855945i	$0.672976\pi$
$920$	−0.882859	+	2.71716i	−0.0291070	+	0.0895821i
$921$	−2.06044	−	6.34138i	−0.0678938	−	0.208956i
$922$	30.6539	−	22.2714i	1.00953	−	0.733469i
$923$	20.7930			0.684410
$924$	2.91078	−	2.50581i	0.0957576	−	0.0824350i
$925$	−4.24080			−0.139437
$926$	−1.80446	+	1.31102i	−0.0592982	+	0.0430826i
$927$	7.42288	+	22.8453i	0.243800	+	0.750338i
$928$	−0.233254	+	0.717882i	−0.00765694	+	0.0235656i
$929$	−7.57718	−	5.50514i	−0.248599	−	0.180618i	0.456507	−	0.889720i	$-0.349101\pi$
$929$	−7.57718	−	5.50514i	−0.248599	−	0.180618i	−0.705106	+	0.709102i	$0.749101\pi$
$930$	−8.76312	−	6.36678i	−0.287354	−	0.208775i
$931$	−1.51209	+	4.65373i	−0.0495567	+	0.152520i
$932$	−2.93499	−	9.03296i	−0.0961387	−	0.295884i
$933$	−11.4350	+	8.30799i	−0.374364	+	0.271991i
$934$	40.1699			1.31440
$935$	3.26756	−	13.8489i	0.106861	−	0.452907i
$936$	5.94984			0.194477
$937$	26.2481	−	19.0704i	0.857489	−	0.623002i	−0.0697115	−	0.997567i	$-0.522208\pi$
$937$	26.2481	−	19.0704i	0.857489	−	0.623002i	0.927201	+	0.374565i	$0.122208\pi$
$938$	−4.42076	−	13.6057i	−0.144343	−	0.444242i
$939$	7.27025	−	22.3755i	0.237256	−	0.730198i
$940$	1.81046	+	1.31538i	0.0590508	+	0.0429029i
$941$	9.67998	+	7.03292i	0.315558	+	0.229267i	0.734278	−	0.678849i	$-0.237521\pi$
$941$	9.67998	+	7.03292i	0.315558	+	0.229267i	−0.418719	+	0.908116i	$0.637521\pi$
$942$	−1.73146	+	5.32890i	−0.0564141	+	0.173625i
$943$	1.79124	+	5.51286i	0.0583307	+	0.179524i
$944$	−0.991144	+	0.720108i	−0.0322590	+	0.0234375i
$945$	5.39525			0.175507
$946$	0.227802	−	0.0188257i	0.00740647	−	0.000612075i
$947$	5.99311			0.194750			0.0973749	−	0.995248i	$-0.468955\pi$
$947$	5.99311			0.194750			0.0973749	+	0.995248i	$0.468955\pi$
$948$	4.71501	−	3.42566i	0.153136	−	0.111260i
$949$	10.0484	+	30.9259i	0.326186	+	1.00390i
$950$	−1.51209	+	4.65373i	−0.0490586	+	0.150987i
$951$	−24.8548	−	18.0580i	−0.805971	−	0.585572i
$952$	−3.47089	−	2.52175i	−0.112492	−	0.0817303i
$953$	11.6471	−	35.8460i	0.377286	−	1.16117i	−0.564638	−	0.825339i	$-0.690984\pi$
$953$	11.6471	−	35.8460i	0.377286	−	1.16117i	0.941924	−	0.335827i	$-0.109016\pi$
$954$	−6.71689	−	20.6725i	−0.217467	−	0.669295i
$955$	15.5050	−	11.2650i	0.501728	−	0.364527i
$956$	2.03180			0.0657130
$957$	−2.47783	−	1.50511i	−0.0800967	−	0.0486532i
$958$	−15.4649			−0.499648
$959$	0.342984	−	0.249192i	0.0110755	−	0.00804684i
$960$	−0.357855	−	1.10136i	−0.0115497	−	0.0355464i
$961$	17.4560	−	53.7240i	0.563097	−	1.73303i
$962$	−12.3050	−	8.94009i	−0.396728	−	0.288240i
$963$	−9.54454	−	6.93452i	−0.307569	−	0.223462i
$964$	−5.76305	+	17.7368i	−0.185615	+	0.571265i
$965$	−2.61013	−	8.03314i	−0.0840229	−	0.258596i
$966$	−2.67665	+	1.94470i	−0.0861198	+	0.0625697i
$967$	−49.5830			−1.59448			−0.797241	−	0.603662i	$-0.793708\pi$
$967$	−49.5830			−1.59448			−0.797241	+	0.603662i	$0.793708\pi$
$968$	−7.71706	+	7.83881i	−0.248036	+	0.251949i
$969$	−24.3110			−0.780981
$970$	−5.43443	+	3.94835i	−0.174489	+	0.126774i
$971$	−11.8166	−	36.3678i	−0.379213	−	1.16710i	−0.940592	−	0.339538i	$-0.889729\pi$
$971$	−11.8166	−	36.3678i	−0.379213	−	1.16710i	0.561380	−	0.827558i	$-0.310271\pi$
$972$	4.54679	−	13.9936i	0.145838	−	0.448845i
$973$	−15.6941	−	11.4024i	−0.503130	−	0.365545i
$974$	14.4963	+	10.5322i	0.464491	+	0.337473i
$975$	−1.28346	+	3.95009i	−0.0411036	+	0.126504i
$976$	−1.24545	−	3.83310i	−0.0398658	−	0.122694i
$977$	5.68077	−	4.12732i	0.181744	−	0.132045i	−0.493194	−	0.869920i	$-0.664171\pi$
$977$	5.68077	−	4.12732i	0.181744	−	0.132045i	0.674938	+	0.737875i	$0.264171\pi$
$978$	4.61172			0.147467
$979$	28.1266	+	17.0849i	0.898929	+	0.546037i
$980$	−1.00000			−0.0319438
$981$	−20.2269	+	14.6957i	−0.645796	+	0.469198i
$982$	8.23260	+	25.3373i	0.262713	+	0.808547i
$983$	−9.59675	+	29.5358i	−0.306089	+	0.942045i	0.673180	+	0.739479i	$0.264928\pi$
$983$	−9.59675	+	29.5358i	−0.306089	+	0.942045i	−0.979269	+	0.202566i	$0.935072\pi$
$984$	−1.90083	−	1.38104i	−0.0605964	−	0.0440259i
$985$	−9.04653	−	6.57269i	−0.288246	−	0.209423i
$986$	−1.00072	+	3.07990i	−0.0318694	+	0.0980839i
$987$	0.800827	+	2.46469i	0.0254906	+	0.0784520i
$988$	−14.1980	+	10.3155i	−0.451699	+	0.328179i
$989$	−0.196901			−0.00626108
$990$	−5.48338	+	0.453150i	−0.174273	+	0.0144020i
$991$	20.2609			0.643608			0.321804	−	0.946806i	$-0.395711\pi$
$991$	20.2609			0.643608			0.321804	+	0.946806i	$0.395711\pi$
$992$	7.56718	−	5.49788i	0.240258	−	0.174558i
$993$	0.140956	+	0.433817i	0.00447310	+	0.0137668i
$994$	−1.79153	+	5.51376i	−0.0568239	+	0.174886i
$995$	−3.42250	−	2.48659i	−0.108501	−	0.0788303i
$996$	15.5763	+	11.3169i	0.493555	+	0.358589i
$997$	4.96877	−	15.2923i	0.157363	−	0.484312i	−0.841030	−	0.540988i	$-0.818050\pi$
$997$	4.96877	−	15.2923i	0.157363	−	0.484312i	0.998393	+	0.0566762i	$0.0180503\pi$
$998$	9.09434	+	27.9895i	0.287876	+	0.885992i
$999$	−18.5104	+	13.4486i	−0.585645	+	0.425496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.h.421.3	✓	12
11.2	odd	10		8470.2.a.cu.1.5		6
11.4	even	5	inner	770.2.n.h.631.3	yes	12
11.9	even	5		8470.2.a.da.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.h.421.3	✓	12	1.1	even	1	trivial
770.2.n.h.631.3	yes	12	11.4	even	5	inner
8470.2.a.cu.1.5		6	11.2	odd	10
8470.2.a.da.1.5		6	11.9	even	5

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.357855 + 1.10136i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.936877 - 0.680681i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.34211 - 0.975098i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.357855 + 1.10136i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.936877 - 0.680681i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.34211 - 0.975098i) q^{9} -1.00000 q^{10} +(2.83465 + 1.72185i) q^{11} +1.15804 q^{12} +(2.90157 - 2.10811i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-0.357855 + 1.10136i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-3.47089 - 2.52175i) q^{17} +(-0.512639 + 1.57774i) q^{18} +(-1.51209 - 4.65373i) q^{19} +(0.809017 - 0.587785i) q^{20} +1.15804 q^{21} +(-3.30536 + 0.273157i) q^{22} +2.85699 q^{23} +(-0.936877 + 0.680681i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-1.10830 + 3.41100i) q^{26} +(4.36485 + 3.17125i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-0.233254 + 0.717882i) q^{29} +(-0.357855 - 1.10136i) q^{30} +(7.56718 - 5.49788i) q^{31} +1.00000 q^{32} +(-0.881993 + 3.73815i) q^{33} +4.29025 q^{34} +(0.809017 - 0.587785i) q^{35} +(-0.512639 - 1.57774i) q^{36} +(-1.31048 + 4.03324i) q^{37} +(3.95870 + 2.87616i) q^{38} +(3.36014 + 2.44129i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(0.626966 + 1.92960i) q^{41} +(-0.936877 + 0.680681i) q^{42} -0.0689189 q^{43} +(2.51353 - 2.16383i) q^{44} +1.65894 q^{45} +(-2.31136 + 1.67930i) q^{46} +(0.691535 + 2.12833i) q^{47} +(0.357855 - 1.10136i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(1.53529 - 4.72513i) q^{51} +(-1.10830 - 3.41100i) q^{52} +(-10.6002 + 7.70149i) q^{53} -5.39525 q^{54} +(1.28120 + 3.05917i) q^{55} +1.00000 q^{56} +(4.58434 - 3.33072i) q^{57} +(-0.233254 - 0.717882i) q^{58} +(0.378583 - 1.16516i) q^{59} +(0.936877 + 0.680681i) q^{60} +(3.26063 + 2.36898i) q^{61} +(-2.89040 + 8.89575i) q^{62} +(-0.512639 - 1.57774i) q^{63} +(-0.809017 + 0.587785i) q^{64} +3.58654 q^{65} +(-1.48368 - 3.54265i) q^{66} -14.3059 q^{67} +(-3.47089 + 2.52175i) q^{68} +(1.02239 + 3.14659i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(4.69029 + 3.40769i) q^{71} +(1.34211 + 0.975098i) q^{72} +(-2.80171 + 8.62277i) q^{73} +(-1.31048 - 4.03324i) q^{74} +(-0.936877 + 0.680681i) q^{75} -4.89322 q^{76} +(2.51353 - 2.16383i) q^{77} -4.15337 q^{78} +(4.07153 - 2.95814i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(-0.392798 + 1.20891i) q^{81} +(-1.64142 - 1.19256i) q^{82} +(13.4506 + 9.77240i) q^{83} +(0.357855 - 1.10136i) q^{84} +(-1.32576 - 4.08027i) q^{85} +(0.0557565 - 0.0405095i) q^{86} -0.874121 q^{87} +(-0.761624 + 3.22799i) q^{88} +9.92243 q^{89} +(-1.34211 + 0.975098i) q^{90} +(-1.10830 - 3.41100i) q^{91} +(0.882859 - 2.71716i) q^{92} +(8.76312 + 6.36678i) q^{93} +(-1.81046 - 1.31538i) q^{94} +(1.51209 - 4.65373i) q^{95} +(0.357855 + 1.10136i) q^{96} +(5.43443 - 3.94835i) q^{97} +1.00000 q^{98} +(5.48338 - 0.453150i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9} - 12 q^{10} - q^{11} - 10 q^{12} - 3 q^{14} - 3 q^{16} - 8 q^{18} - q^{19} + 3 q^{20} - 10 q^{21} - q^{22} - 4 q^{23} + 5 q^{24} - 3 q^{25} + 3 q^{27} - 3 q^{28} + 22 q^{29} + 6 q^{31} + 12 q^{32} - 29 q^{33} - 30 q^{34} + 3 q^{35} - 8 q^{36} - 10 q^{37} + 14 q^{38} + 20 q^{39} + 3 q^{40} + 16 q^{41} + 5 q^{42} + 30 q^{43} + 14 q^{44} - 22 q^{45} - 4 q^{46} + 34 q^{47} - 3 q^{49} - 3 q^{50} + 37 q^{51} - 26 q^{53} - 52 q^{54} + 11 q^{55} + 12 q^{56} - 19 q^{57} + 22 q^{58} + q^{59} - 5 q^{60} + 40 q^{61} - 4 q^{62} - 8 q^{63} - 3 q^{64} + 16 q^{66} - 58 q^{67} + 14 q^{69} + 3 q^{70} - 14 q^{71} - 3 q^{72} + 32 q^{73} - 10 q^{74} + 5 q^{75} - 26 q^{76} + 14 q^{77} - 60 q^{78} + 16 q^{79} + 3 q^{80} - 46 q^{81} + q^{82} + 35 q^{83} - 15 q^{85} + 5 q^{86} - q^{88} - 58 q^{89} + 3 q^{90} + 6 q^{92} + 46 q^{93} - 16 q^{94} + q^{95} + 57 q^{97} + 12 q^{98} + 69 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9 - 12 * q^10 - q^11 - 10 * q^12 - 3 * q^14 - 3 * q^16 - 8 * q^18 - q^19 + 3 * q^20 - 10 * q^21 - q^22 - 4 * q^23 + 5 * q^24 - 3 * q^25 + 3 * q^27 - 3 * q^28 + 22 * q^29 + 6 * q^31 + 12 * q^32 - 29 * q^33 - 30 * q^34 + 3 * q^35 - 8 * q^36 - 10 * q^37 + 14 * q^38 + 20 * q^39 + 3 * q^40 + 16 * q^41 + 5 * q^42 + 30 * q^43 + 14 * q^44 - 22 * q^45 - 4 * q^46 + 34 * q^47 - 3 * q^49 - 3 * q^50 + 37 * q^51 - 26 * q^53 - 52 * q^54 + 11 * q^55 + 12 * q^56 - 19 * q^57 + 22 * q^58 + q^59 - 5 * q^60 + 40 * q^61 - 4 * q^62 - 8 * q^63 - 3 * q^64 + 16 * q^66 - 58 * q^67 + 14 * q^69 + 3 * q^70 - 14 * q^71 - 3 * q^72 + 32 * q^73 - 10 * q^74 + 5 * q^75 - 26 * q^76 + 14 * q^77 - 60 * q^78 + 16 * q^79 + 3 * q^80 - 46 * q^81 + q^82 + 35 * q^83 - 15 * q^85 + 5 * q^86 - q^88 - 58 * q^89 + 3 * q^90 + 6 * q^92 + 46 * q^93 - 16 * q^94 + q^95 + 57 * q^97 + 12 * q^98 + 69 * q^99

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