LMFDB - Embedded newform 770.2.n.j.71.2

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} - 2 x^{11} + 11 x^{10} - 11 x^{9} + 39 x^{8} - 43 x^{7} + 99 x^{6} + 36 x^{5} + 431 x^{4} + \cdots + 25 $ x^12 - 2x^11 + 11x^10 - 11x^9 + 39x^8 - 43x^7 + 99x^6 + 36x^5 + 431x^4 - 350x^3 + 510x^2 - 175*x + 25
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			71.2
Root			$0.289142 + 0.889888i$ of defining polynomial
Character	$\chi$	$=$	770.71
Dual form			770.2.n.j.141.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(0.756984 + 0.549981i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.289142 - 0.889888i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.656505 - 2.02052i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(0.756984 + 0.549981i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.289142 - 0.889888i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.656505 - 2.02052i) q^{9} -1.00000 q^{10} +(-3.09234 + 1.19893i) q^{11} -0.935683 q^{12} +(-0.776859 - 2.39093i) q^{13} +(0.809017 + 0.587785i) q^{14} +(0.756984 - 0.549981i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.44806 - 4.45667i) q^{17} +(-1.71875 + 1.24875i) q^{18} +(-3.28100 - 2.38379i) q^{19} +(0.309017 + 0.951057i) q^{20} -0.935683 q^{21} +(2.09584 + 2.57050i) q^{22} -3.46945 q^{23} +(0.289142 + 0.889888i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-2.03384 + 1.47767i) q^{26} +(1.48171 - 4.56023i) q^{27} +(0.309017 - 0.951057i) q^{28} +(6.03901 - 4.38760i) q^{29} +(-0.756984 - 0.549981i) q^{30} +(0.477714 + 1.47025i) q^{31} -1.00000 q^{32} +(-3.00024 - 0.793153i) q^{33} -4.68602 q^{34} +(0.309017 + 0.951057i) q^{35} +(1.71875 + 1.24875i) q^{36} +(3.98540 - 2.89556i) q^{37} +(-1.25323 + 3.85705i) q^{38} +(0.726894 - 2.23715i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-1.33552 - 0.970311i) q^{41} +(0.289142 + 0.889888i) q^{42} -7.97092 q^{43} +(1.79704 - 2.78759i) q^{44} -2.12450 q^{45} +(1.07212 + 3.29965i) q^{46} +(-1.43558 - 1.04301i) q^{47} +(0.756984 - 0.549981i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(3.54724 - 2.57722i) q^{51} +(2.03384 + 1.47767i) q^{52} +(2.20730 + 6.79337i) q^{53} -4.79491 q^{54} +(0.184670 + 3.31148i) q^{55} -1.00000 q^{56} +(-1.17263 - 3.60898i) q^{57} +(-6.03901 - 4.38760i) q^{58} +(0.345318 - 0.250889i) q^{59} +(-0.289142 + 0.889888i) q^{60} +(1.90107 - 5.85091i) q^{61} +(1.25067 - 0.908665i) q^{62} +(1.71875 + 1.24875i) q^{63} +(0.309017 + 0.951057i) q^{64} -2.51397 q^{65} +(0.172792 + 3.09850i) q^{66} -5.99409 q^{67} +(1.44806 + 4.45667i) q^{68} +(-2.62632 - 1.90813i) q^{69} +(0.809017 - 0.587785i) q^{70} +(2.02073 - 6.21917i) q^{71} +(0.656505 - 2.02052i) q^{72} +(0.692010 - 0.502775i) q^{73} +(-3.98540 - 2.89556i) q^{74} +(-0.289142 - 0.889888i) q^{75} +4.05554 q^{76} +(1.79704 - 2.78759i) q^{77} -2.35228 q^{78} +(-3.04746 - 9.37911i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(-1.52659 + 1.10914i) q^{81} +(-0.510123 + 1.57000i) q^{82} +(-2.52057 + 7.75752i) q^{83} +(0.756984 - 0.549981i) q^{84} +(-3.79107 - 2.75437i) q^{85} +(2.46315 + 7.58080i) q^{86} +6.98453 q^{87} +(-3.20647 - 0.847672i) q^{88} +1.00048 q^{89} +(0.656505 + 2.02052i) q^{90} +(2.03384 + 1.47767i) q^{91} +(2.80685 - 2.03929i) q^{92} +(-0.446989 + 1.37569i) q^{93} +(-0.548343 + 1.68763i) q^{94} +(-3.28100 + 2.38379i) q^{95} +(-0.756984 - 0.549981i) q^{96} +(3.50235 + 10.7791i) q^{97} -1.00000 q^{98} +(4.45260 + 5.46101i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 12 q^{10} - q^{11} - 2 q^{12} + 2 q^{13} + 3 q^{14} + 3 q^{15} - 3 q^{16} + 7 q^{17} + 9 q^{18} + 6 q^{19} - 3 q^{20} - 2 q^{21} + q^{22} + 8 q^{23} + 2 q^{24} - 3 q^{25} - 7 q^{26} - 3 q^{27} - 3 q^{28} + 20 q^{29} - 3 q^{30} + 6 q^{31} - 12 q^{32} - 12 q^{33} + 18 q^{34} - 3 q^{35} - 9 q^{36} + 22 q^{37} - 6 q^{38} + 23 q^{39} + 3 q^{40} + 2 q^{41} + 2 q^{42} - 60 q^{43} - 11 q^{44} + 6 q^{45} + 2 q^{46} - 4 q^{47} + 3 q^{48} - 3 q^{49} + 3 q^{50} + 13 q^{51} + 7 q^{52} + 18 q^{53} + 8 q^{54} + 14 q^{55} - 12 q^{56} + 8 q^{57} - 20 q^{58} - 32 q^{59} - 2 q^{60} + 8 q^{61} + 14 q^{62} - 9 q^{63} - 3 q^{64} - 18 q^{65} - 8 q^{66} + 36 q^{67} + 7 q^{68} + 50 q^{69} + 3 q^{70} - 34 q^{71} - 6 q^{72} + 14 q^{73} - 22 q^{74} - 2 q^{75} - 24 q^{76} - 11 q^{77} - 38 q^{78} - 12 q^{79} - 3 q^{80} + 4 q^{81} - 2 q^{82} + 30 q^{83} + 3 q^{84} + 2 q^{85} - 28 q^{87} + q^{88} - 36 q^{89} - 6 q^{90} + 7 q^{91} - 2 q^{92} + 12 q^{93} - 11 q^{94} + 6 q^{95} - 3 q^{96} + 39 q^{97} - 12 q^{98} - 15 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 - 12 * q^10 - q^11 - 2 * q^12 + 2 * q^13 + 3 * q^14 + 3 * q^15 - 3 * q^16 + 7 * q^17 + 9 * q^18 + 6 * q^19 - 3 * q^20 - 2 * q^21 + q^22 + 8 * q^23 + 2 * q^24 - 3 * q^25 - 7 * q^26 - 3 * q^27 - 3 * q^28 + 20 * q^29 - 3 * q^30 + 6 * q^31 - 12 * q^32 - 12 * q^33 + 18 * q^34 - 3 * q^35 - 9 * q^36 + 22 * q^37 - 6 * q^38 + 23 * q^39 + 3 * q^40 + 2 * q^41 + 2 * q^42 - 60 * q^43 - 11 * q^44 + 6 * q^45 + 2 * q^46 - 4 * q^47 + 3 * q^48 - 3 * q^49 + 3 * q^50 + 13 * q^51 + 7 * q^52 + 18 * q^53 + 8 * q^54 + 14 * q^55 - 12 * q^56 + 8 * q^57 - 20 * q^58 - 32 * q^59 - 2 * q^60 + 8 * q^61 + 14 * q^62 - 9 * q^63 - 3 * q^64 - 18 * q^65 - 8 * q^66 + 36 * q^67 + 7 * q^68 + 50 * q^69 + 3 * q^70 - 34 * q^71 - 6 * q^72 + 14 * q^73 - 22 * q^74 - 2 * q^75 - 24 * q^76 - 11 * q^77 - 38 * q^78 - 12 * q^79 - 3 * q^80 + 4 * q^81 - 2 * q^82 + 30 * q^83 + 3 * q^84 + 2 * q^85 - 28 * q^87 + q^88 - 36 * q^89 - 6 * q^90 + 7 * q^91 - 2 * q^92 + 12 * q^93 - 11 * q^94 + 6 * q^95 - 3 * q^96 + 39 * q^97 - 12 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	0.756984	+	0.549981i	0.437045	+	0.317532i	0.784460	−	0.620180i	$-0.212940\pi$
$3$	0.756984	+	0.549981i	0.437045	+	0.317532i	−0.347415	+	0.937712i	$0.612940\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$	0.289142	−	0.889888i	0.118042	−	0.363295i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.656505	−	2.02052i	−0.218835	−	0.673505i
$10$	−1.00000			−0.316228
$11$	−3.09234	+	1.19893i	−0.932375	+	0.361492i
$11$	−3.09234	+	1.19893i	−0.932375	+	0.361492i
$12$	−0.935683			−0.270109
$13$	−0.776859	−	2.39093i	−0.215462	−	0.663123i	−0.999120	−	0.0419317i	$-0.986649\pi$
$13$	−0.776859	−	2.39093i	−0.215462	−	0.663123i	0.783659	−	0.621192i	$-0.213351\pi$
$14$	0.809017	+	0.587785i	0.216219	+	0.157092i
$15$	0.756984	−	0.549981i	0.195452	−	0.142004i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	1.44806	−	4.45667i	0.351206	−	1.08090i	−0.606971	−	0.794724i	$-0.707616\pi$
$17$	1.44806	−	4.45667i	0.351206	−	1.08090i	0.958177	−	0.286177i	$-0.0923844\pi$
$18$	−1.71875	+	1.24875i	−0.405114	+	0.294333i
$19$	−3.28100	−	2.38379i	−0.752713	−	0.546878i	0.143953	−	0.989584i	$-0.454018\pi$
$19$	−3.28100	−	2.38379i	−0.752713	−	0.546878i	−0.896667	+	0.442706i	$0.854018\pi$
$20$	0.309017	+	0.951057i	0.0690983	+	0.212663i
$21$	−0.935683			−0.204183
$22$	2.09584	+	2.57050i	0.446835	+	0.548032i
$23$	−3.46945			−0.723431			−0.361716	−	0.932289i	$-0.617809\pi$
$23$	−3.46945			−0.723431			−0.361716	+	0.932289i	$0.617809\pi$
$24$	0.289142	+	0.889888i	0.0590209	+	0.181648i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−2.03384	+	1.47767i	−0.398869	+	0.289796i
$27$	1.48171	−	4.56023i	0.285155	−	0.877616i
$28$	0.309017	−	0.951057i	0.0583987	−	0.179733i
$29$	6.03901	−	4.38760i	1.12142	−	0.814757i	0.136993	−	0.990572i	$-0.456256\pi$
$29$	6.03901	−	4.38760i	1.12142	−	0.814757i	0.984423	+	0.175815i	$0.0562561\pi$
$30$	−0.756984	−	0.549981i	−0.138206	−	0.100412i
$31$	0.477714	+	1.47025i	0.0857999	+	0.264065i	0.984747	−	0.173992i	$-0.0556668\pi$
$31$	0.477714	+	1.47025i	0.0857999	+	0.264065i	−0.898947	+	0.438057i	$0.855667\pi$
$32$	−1.00000			−0.176777
$33$	−3.00024	−	0.793153i	−0.522275	−	0.138070i
$34$	−4.68602			−0.803645
$35$	0.309017	+	0.951057i	0.0522334	+	0.160758i
$36$	1.71875	+	1.24875i	0.286459	+	0.208125i
$37$	3.98540	−	2.89556i	0.655195	−	0.476027i	−0.209842	−	0.977735i	$-0.567295\pi$
$37$	3.98540	−	2.89556i	0.655195	−	0.476027i	0.865037	+	0.501708i	$0.167295\pi$
$38$	−1.25323	+	3.85705i	−0.203301	+	0.625696i
$39$	0.726894	−	2.23715i	0.116396	−	0.358231i
$40$	0.809017	−	0.587785i	0.127917	−	0.0929370i
$41$	−1.33552	−	0.970311i	−0.208573	−	0.151537i	0.478595	−	0.878036i	$-0.341146\pi$
$41$	−1.33552	−	0.970311i	−0.208573	−	0.151537i	−0.687168	+	0.726499i	$0.741146\pi$
$42$	0.289142	+	0.889888i	0.0446156	+	0.137313i
$43$	−7.97092			−1.21555			−0.607777	−	0.794108i	$-0.707939\pi$
$43$	−7.97092			−1.21555			−0.607777	+	0.794108i	$0.707939\pi$
$44$	1.79704	−	2.78759i	0.270914	−	0.420245i
$45$	−2.12450			−0.316701
$46$	1.07212	+	3.29965i	0.158075	+	0.486506i
$47$	−1.43558	−	1.04301i	−0.209401	−	0.152139i	0.478142	−	0.878283i	$-0.341311\pi$
$47$	−1.43558	−	1.04301i	−0.209401	−	0.152139i	−0.687543	+	0.726144i	$0.741311\pi$
$48$	0.756984	−	0.549981i	0.109261	−	0.0793829i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$	3.54724	−	2.57722i	0.496713	−	0.360883i
$52$	2.03384	+	1.47767i	0.282043	+	0.204916i
$53$	2.20730	+	6.79337i	0.303196	+	0.933141i	0.980344	+	0.197294i	$0.0632155\pi$
$53$	2.20730	+	6.79337i	0.303196	+	0.933141i	−0.677148	+	0.735846i	$0.736784\pi$
$54$	−4.79491			−0.652504
$55$	0.184670	+	3.31148i	0.0249009	+	0.446520i
$56$	−1.00000			−0.133631
$57$	−1.17263	−	3.60898i	−0.155318	−	0.478021i
$58$	−6.03901	−	4.38760i	−0.792961	−	0.576120i
$59$	0.345318	−	0.250889i	0.0449566	−	0.0326629i	−0.565080	−	0.825036i	$-0.691155\pi$
$59$	0.345318	−	0.250889i	0.0449566	−	0.0326629i	0.610037	+	0.792373i	$0.291155\pi$
$60$	−0.289142	+	0.889888i	−0.0373281	+	0.114884i
$61$	1.90107	−	5.85091i	0.243408	−	0.749132i	−0.752487	−	0.658608i	$-0.771146\pi$
$61$	1.90107	−	5.85091i	0.243408	−	0.749132i	0.995894	−	0.0905243i	$-0.0288543\pi$
$62$	1.25067	−	0.908665i	0.158835	−	0.115401i
$63$	1.71875	+	1.24875i	0.216543	+	0.157327i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−2.51397			−0.311819
$66$	0.172792	+	3.09850i	0.0212693	+	0.381399i
$67$	−5.99409			−0.732295			−0.366147	−	0.930557i	$-0.619323\pi$
$67$	−5.99409			−0.732295			−0.366147	+	0.930557i	$0.619323\pi$
$68$	1.44806	+	4.45667i	0.175603	+	0.540450i
$69$	−2.62632	−	1.90813i	−0.316172	−	0.229712i
$70$	0.809017	−	0.587785i	0.0966960	−	0.0702538i
$71$	2.02073	−	6.21917i	0.239817	−	0.738080i	−0.756629	−	0.653844i	$-0.773155\pi$
$71$	2.02073	−	6.21917i	0.239817	−	0.738080i	0.996446	−	0.0842354i	$-0.0268448\pi$
$72$	0.656505	−	2.02052i	0.0773699	−	0.238120i
$73$	0.692010	−	0.502775i	0.0809937	−	0.0588454i	−0.546552	−	0.837425i	$-0.684060\pi$
$73$	0.692010	−	0.502775i	0.0809937	−	0.0588454i	0.627545	+	0.778580i	$0.284060\pi$
$74$	−3.98540	−	2.89556i	−0.463293	−	0.336602i
$75$	−0.289142	−	0.889888i	−0.0333873	−	0.102755i
$76$	4.05554			0.465203
$77$	1.79704	−	2.78759i	0.204791	−	0.317675i
$78$	−2.35228			−0.266343
$79$	−3.04746	−	9.37911i	−0.342866	−	1.05523i	−0.962716	−	0.270513i	$-0.912807\pi$
$79$	−3.04746	−	9.37911i	−0.342866	−	1.05523i	0.619851	−	0.784720i	$-0.287193\pi$
$80$	−0.809017	−	0.587785i	−0.0904508	−	0.0657164i
$81$	−1.52659	+	1.10914i	−0.169622	+	0.123237i
$82$	−0.510123	+	1.57000i	−0.0563336	+	0.173377i
$83$	−2.52057	+	7.75752i	−0.276669	+	0.851499i	0.712104	+	0.702074i	$0.247742\pi$
$83$	−2.52057	+	7.75752i	−0.276669	+	0.851499i	−0.988773	+	0.149425i	$0.952258\pi$
$84$	0.756984	−	0.549981i	0.0825937	−	0.0600078i
$85$	−3.79107	−	2.75437i	−0.411199	−	0.298754i
$86$	2.46315	+	7.58080i	0.265608	+	0.817458i
$87$	6.98453			0.748820
$88$	−3.20647	−	0.847672i	−0.341811	−	0.0903621i
$89$	1.00048			0.106051			0.0530255	−	0.998593i	$-0.483114\pi$
$89$	1.00048			0.106051			0.0530255	+	0.998593i	$0.483114\pi$
$90$	0.656505	+	2.02052i	0.0692018	+	0.212981i
$91$	2.03384	+	1.47767i	0.213205	+	0.154902i
$92$	2.80685	−	2.03929i	0.292634	−	0.212611i
$93$	−0.446989	+	1.37569i	−0.0463506	+	0.142652i
$94$	−0.548343	+	1.68763i	−0.0565573	+	0.174065i
$95$	−3.28100	+	2.38379i	−0.336624	+	0.244571i
$96$	−0.756984	−	0.549981i	−0.0772593	−	0.0561322i
$97$	3.50235	+	10.7791i	0.355610	+	1.09445i	0.955655	+	0.294488i	$0.0951491\pi$
$97$	3.50235	+	10.7791i	0.355610	+	1.09445i	−0.600046	+	0.799966i	$0.704851\pi$
$98$	−1.00000			−0.101015
$99$	4.45260	+	5.46101i	0.447504	+	0.548852i
$100$	1.00000			0.100000
$101$	0.978533	+	3.01161i	0.0973677	+	0.299667i	0.987863	−	0.155325i	$-0.0496423\pi$
$101$	0.978533	+	3.01161i	0.0973677	+	0.299667i	−0.890496	+	0.454991i	$0.849642\pi$
$102$	−3.54724	−	2.57722i	−0.351229	−	0.255183i
$103$	−12.1736	+	8.84467i	−1.19950	+	0.871491i	−0.994236	−	0.107214i	$-0.965807\pi$
$103$	−12.1736	+	8.84467i	−1.19950	+	0.871491i	−0.205269	+	0.978706i	$0.565807\pi$
$104$	0.776859	−	2.39093i	0.0761773	−	0.234450i
$105$	−0.289142	+	0.889888i	−0.0282174	+	0.0868442i
$106$	5.77878	−	4.19853i	0.561285	−	0.407798i
$107$	11.6803	+	8.48626i	1.12918	+	0.820398i	0.985575	−	0.169237i	$-0.0541304\pi$
$107$	11.6803	+	8.48626i	1.12918	+	0.820398i	0.143606	+	0.989635i	$0.454130\pi$
$108$	1.48171	+	4.56023i	0.142577	+	0.438808i
$109$	−12.1869			−1.16729			−0.583646	−	0.812008i	$-0.698374\pi$
$109$	−12.1869			−1.16729			−0.583646	+	0.812008i	$0.698374\pi$
$110$	3.09234	−	1.19893i	0.294843	−	0.114314i
$111$	4.60938			0.437503
$112$	0.309017	+	0.951057i	0.0291994	+	0.0898664i
$113$	9.48931	+	6.89438i	0.892679	+	0.648569i	0.936575	−	0.350467i	$-0.113977\pi$
$113$	9.48931	+	6.89438i	0.892679	+	0.648569i	−0.0438963	+	0.999036i	$0.513977\pi$
$114$	−3.06998	+	2.23047i	−0.287530	+	0.208903i
$115$	−1.07212	+	3.29965i	−0.0999757	+	0.307694i
$116$	−2.30670	+	7.09929i	−0.214172	+	0.659152i
$117$	−4.32089	+	3.13931i	−0.399467	+	0.290229i
$118$	−0.345318	−	0.250889i	−0.0317891	−	0.0230962i
$119$	1.44806	+	4.45667i	0.132743	+	0.408542i
$120$	0.935683			0.0854158
$121$	8.12511	−	7.41502i	0.738646	−	0.674093i
$122$	−6.15201			−0.556977
$123$	−0.477314	−	1.46902i	−0.0430379	−	0.132457i
$124$	−1.25067	−	0.908665i	−0.112314	−	0.0816006i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$	0.656505	−	2.02052i	0.0584862	−	0.180002i
$127$	1.13816	−	3.50290i	0.100995	−	0.310832i	−0.887774	−	0.460279i	$-0.847749\pi$
$127$	1.13816	−	3.50290i	0.100995	−	0.310832i	0.988770	+	0.149447i	$0.0477494\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−6.03386	−	4.38385i	−0.531252	−	0.385977i
$130$	0.776859	+	2.39093i	0.0681350	+	0.209698i
$131$	8.57781			0.749447			0.374724	−	0.927137i	$-0.377738\pi$
$131$	8.57781			0.749447			0.374724	+	0.927137i	$0.377738\pi$
$132$	2.89345	−	1.12182i	0.251842	−	0.0976422i
$133$	4.05554			0.351660
$134$	1.85228	+	5.70072i	0.160012	+	0.492467i
$135$	−3.87916	−	2.81838i	−0.333865	−	0.242567i
$136$	3.79107	−	2.75437i	0.325081	−	0.236185i
$137$	0.503965	−	1.55104i	0.0430566	−	0.132515i	−0.927217	−	0.374523i	$-0.877806\pi$
$137$	0.503965	−	1.55104i	0.0430566	−	0.132515i	0.970274	+	0.242009i	$0.0778063\pi$
$138$	−1.00317	+	3.08742i	−0.0853951	+	0.262819i
$139$	18.7529	−	13.6248i	1.59060	−	1.15564i	0.687524	−	0.726161i	$-0.258697\pi$
$139$	18.7529	−	13.6248i	1.59060	−	1.15564i	0.903077	−	0.429478i	$-0.141303\pi$
$140$	−0.809017	−	0.587785i	−0.0683744	−	0.0496769i
$141$	−0.513076	−	1.57909i	−0.0432088	−	0.132983i
$142$	−6.53922			−0.548759
$143$	5.26887	+	6.46215i	0.440605	+	0.540392i
$144$	−2.12450			−0.177041
$145$	−2.30670	−	7.09929i	−0.191561	−	0.589564i
$146$	−0.692010	−	0.502775i	−0.0572712	−	0.0416100i
$147$	0.756984	−	0.549981i	0.0624350	−	0.0453617i
$148$	−1.52229	+	4.68512i	−0.125131	+	0.385114i
$149$	−0.443087	+	1.36368i	−0.0362991	+	0.111717i	−0.967564	−	0.252625i	$-0.918706\pi$
$149$	−0.443087	+	1.36368i	−0.0362991	+	0.111717i	0.931265	+	0.364342i	$0.118706\pi$
$150$	−0.756984	+	0.549981i	−0.0618075	+	0.0449058i
$151$	−14.3966	−	10.4597i	−1.17158	−	0.851201i	−0.180380	−	0.983597i	$-0.557733\pi$
$151$	−14.3966	−	10.4597i	−1.17158	−	0.851201i	−0.991197	+	0.132396i	$0.957733\pi$
$152$	−1.25323	−	3.85705i	−0.101650	−	0.312848i
$153$	−9.95543			−0.804849
$154$	−3.20647	−	0.847672i	−0.258385	−	0.0683074i
$155$	1.54591			0.124171
$156$	0.726894	+	2.23715i	0.0581981	+	0.179115i
$157$	5.89890	+	4.28580i	0.470783	+	0.342044i	0.797746	−	0.602993i	$-0.206025\pi$
$157$	5.89890	+	4.28580i	0.470783	+	0.342044i	−0.326963	+	0.945037i	$0.606025\pi$
$158$	−7.97835	+	5.79661i	−0.634723	+	0.461153i
$159$	−2.06533	+	6.35644i	−0.163792	+	0.504099i
$160$	−0.309017	+	0.951057i	−0.0244299	+	0.0751876i
$161$	2.80685	−	2.03929i	0.221211	−	0.160719i
$162$	1.52659	+	1.10914i	0.119941	+	0.0871419i
$163$	2.90879	+	8.95233i	0.227834	+	0.701201i	0.997992	+	0.0633471i	$0.0201775\pi$
$163$	2.90879	+	8.95233i	0.227834	+	0.701201i	−0.770158	+	0.637854i	$0.779822\pi$
$164$	1.65079			0.128905
$165$	−1.68146	+	2.60830i	−0.130901	+	0.203056i
$166$	8.15674			0.633086
$167$	−0.0895895	−	0.275728i	−0.00693264	−	0.0213365i	0.947530	−	0.319666i	$-0.103571\pi$
$167$	−0.0895895	−	0.275728i	−0.00693264	−	0.0213365i	−0.954463	+	0.298329i	$0.903571\pi$
$168$	−0.756984	−	0.549981i	−0.0584026	−	0.0424320i
$169$	5.40421	−	3.92639i	0.415708	−	0.302030i
$170$	−1.44806	+	4.45667i	−0.111061	+	0.341811i
$171$	−2.66249	+	8.19429i	−0.203605	+	0.626633i
$172$	6.44861	−	4.68519i	0.491702	−	0.357242i
$173$	8.42898	+	6.12401i	0.640844	+	0.465600i	0.860140	−	0.510058i	$-0.170376\pi$
$173$	8.42898	+	6.12401i	0.640844	+	0.465600i	−0.219296	+	0.975658i	$0.570376\pi$
$174$	−2.15834	−	6.64268i	−0.163623	−	0.503581i
$175$	1.00000			0.0755929
$176$	0.184670	+	3.31148i	0.0139200	+	0.249612i
$177$	0.399384			0.0300196
$178$	−0.309166	−	0.951516i	−0.0231730	−	0.0713191i
$179$	12.0637	+	8.76478i	0.901682	+	0.655111i	0.938898	−	0.344197i	$-0.111849\pi$
$179$	12.0637	+	8.76478i	0.901682	+	0.655111i	−0.0372152	+	0.999307i	$0.511849\pi$
$180$	1.71875	−	1.24875i	0.128108	−	0.0930762i
$181$	1.35143	−	4.15926i	0.100451	−	0.309155i	−0.888185	−	0.459486i	$-0.848034\pi$
$181$	1.35143	−	4.15926i	0.100451	−	0.309155i	0.988636	+	0.150330i	$0.0480337\pi$
$182$	0.776859	−	2.39093i	0.0575846	−	0.177227i
$183$	4.65697	−	3.38349i	0.344253	−	0.250115i
$184$	−2.80685	−	2.03929i	−0.206923	−	0.150339i
$185$	−1.52229	−	4.68512i	−0.111921	−	0.344457i
$186$	1.44649			0.106062
$187$	0.865366	+	15.5177i	0.0632818	+	1.13476i
$188$	1.77448			0.129417
$189$	1.48171	+	4.56023i	0.107778	+	0.331708i
$190$	3.28100	+	2.38379i	0.238029	+	0.172938i
$191$	8.59154	−	6.24212i	0.621662	−	0.451664i	−0.231840	−	0.972754i	$-0.574474\pi$
$191$	8.59154	−	6.24212i	0.621662	−	0.451664i	0.853502	+	0.521090i	$0.174474\pi$
$192$	−0.289142	+	0.889888i	−0.0208670	+	0.0642221i
$193$	2.46640	−	7.59081i	0.177536	−	0.546398i	−0.822205	−	0.569192i	$-0.807256\pi$
$193$	2.46640	−	7.59081i	0.177536	−	0.546398i	0.999740	+	0.0227938i	$0.00725612\pi$
$194$	9.16927	−	6.66186i	0.658315	−	0.478294i
$195$	−1.90303	−	1.38263i	−0.136279	−	0.0990125i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	−7.28621			−0.519121			−0.259560	−	0.965727i	$-0.583578\pi$
$197$	−7.28621			−0.519121			−0.259560	+	0.965727i	$0.583578\pi$
$198$	3.81780	−	5.92222i	0.271319	−	0.420874i
$199$	14.1853			1.00557			0.502783	−	0.864413i	$-0.332309\pi$
$199$	14.1853			1.00557			0.502783	+	0.864413i	$0.332309\pi$
$200$	−0.309017	−	0.951057i	−0.0218508	−	0.0672499i
$201$	−4.53743	−	3.29664i	−0.320046	−	0.232527i
$202$	2.56183	−	1.86128i	0.180250	−	0.130959i
$203$	−2.30670	+	7.09929i	−0.161898	+	0.498272i
$204$	−1.35492	+	4.17003i	−0.0948637	+	0.291961i
$205$	−1.33552	+	0.970311i	−0.0932767	+	0.0677695i
$206$	12.1736	+	8.84467i	0.848178	+	0.616237i
$207$	2.27772	+	7.01009i	0.158312	+	0.487235i
$208$	−2.51397			−0.174312
$209$	13.0040	+	3.43777i	0.899504	+	0.237795i
$210$	0.935683			0.0645683
$211$	−7.19300	−	22.1378i	−0.495187	−	1.52403i	−0.816665	−	0.577111i	$-0.804180\pi$
$211$	−7.19300	−	22.1378i	−0.495187	−	1.52403i	0.321479	−	0.946917i	$-0.395820\pi$
$212$	−5.77878	−	4.19853i	−0.396889	−	0.288356i
$213$	4.95008	−	3.59645i	0.339174	−	0.246424i
$214$	4.46149	−	13.7311i	0.304981	−	0.938636i
$215$	−2.46315	+	7.58080i	−0.167985	+	0.517006i
$216$	3.87916	−	2.81838i	0.263943	−	0.191766i
$217$	−1.25067	−	0.908665i	−0.0849011	−	0.0616842i
$218$	3.76595	+	11.5904i	0.255063	+	0.785002i
$219$	0.800357			0.0540831
$220$	−2.09584	−	2.57050i	−0.141301	−	0.173303i
$221$	−11.7805			−0.792442
$222$	−1.42438	−	4.38379i	−0.0955980	−	0.294220i
$223$	6.55100	+	4.75958i	0.438688	+	0.318725i	0.785113	−	0.619352i	$-0.212605\pi$
$223$	6.55100	+	4.75958i	0.438688	+	0.318725i	−0.346426	+	0.938077i	$0.612605\pi$
$224$	0.809017	−	0.587785i	0.0540547	−	0.0392731i
$225$	−0.656505	+	2.02052i	−0.0437670	+	0.134701i
$226$	3.62459	−	11.1553i	0.241104	−	0.742043i
$227$	15.2382	−	11.0712i	1.01139	−	0.734819i	0.0468911	−	0.998900i	$-0.485069\pi$
$227$	15.2382	−	11.0712i	1.01139	−	0.734819i	0.964501	+	0.264081i	$0.0850686\pi$
$228$	3.06998	+	2.23047i	0.203314	+	0.147717i
$229$	3.35967	+	10.3400i	0.222013	+	0.683287i	0.998581	+	0.0532533i	$0.0169591\pi$
$229$	3.35967	+	10.3400i	0.222013	+	0.683287i	−0.776568	+	0.630034i	$0.783041\pi$
$230$	3.46945			0.228769
$231$	2.89345	−	1.12182i	0.190375	−	0.0738106i
$232$	7.46463			0.490077
$233$	−2.77386	−	8.53705i	−0.181721	−	0.559281i	0.818155	−	0.574998i	$-0.194997\pi$
$233$	−2.77386	−	8.53705i	−0.181721	−	0.559281i	−0.999876	+	0.0157166i	$0.994997\pi$
$234$	4.32089	+	3.13931i	0.282465	+	0.205223i
$235$	−1.43558	+	1.04301i	−0.0936470	+	0.0680385i
$236$	−0.131900	+	0.405946i	−0.00858595	+	0.0264248i
$237$	2.85146	−	8.77588i	0.185222	−	0.570055i
$238$	3.79107	−	2.75437i	0.245738	−	0.178539i
$239$	7.91320	+	5.74927i	0.511862	+	0.371890i	0.813530	−	0.581524i	$-0.197543\pi$
$239$	7.91320	+	5.74927i	0.511862	+	0.371890i	−0.301667	+	0.953413i	$0.597543\pi$
$240$	−0.289142	−	0.889888i	−0.0186640	−	0.0574420i
$241$	23.3855			1.50639			0.753195	−	0.657797i	$-0.228512\pi$
$241$	23.3855			1.50639			0.753195	+	0.657797i	$0.228512\pi$
$242$	−9.56290	−	5.43607i	−0.614727	−	0.349444i
$243$	−16.1503			−1.03604
$244$	1.90107	+	5.85091i	0.121704	+	0.374566i
$245$	−0.809017	−	0.587785i	−0.0516862	−	0.0375522i
$246$	−1.24962	+	0.907904i	−0.0796731	+	0.0578859i
$247$	−3.15058	+	9.69650i	−0.200467	+	0.616973i
$248$	−0.477714	+	1.47025i	−0.0303348	+	0.0933611i
$249$	−6.17452	+	4.48605i	−0.391294	+	0.284292i
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	8.06347	+	24.8168i	0.508962	+	1.56642i	0.794007	+	0.607909i	$0.207991\pi$
$251$	8.06347	+	24.8168i	0.508962	+	1.56642i	−0.285045	+	0.958514i	$0.592009\pi$
$252$	−2.12450			−0.133831
$253$	10.7287	−	4.15965i	0.674509	−	0.261515i
$254$	−3.68316			−0.231102
$255$	−1.35492	−	4.17003i	−0.0848487	−	0.261137i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−4.46524	+	3.24419i	−0.278534	+	0.202367i	−0.718278	−	0.695756i	$-0.755069\pi$
$257$	−4.46524	+	3.24419i	−0.278534	+	0.202367i	0.439744	+	0.898123i	$0.355069\pi$
$258$	−2.30473	+	7.09323i	−0.143486	+	0.441605i
$259$	−1.52229	+	4.68512i	−0.0945903	+	0.291119i
$260$	2.03384	−	1.47767i	0.126134	−	0.0916414i
$261$	−12.8299	−	9.32144i	−0.794148	−	0.576983i
$262$	−2.65069	−	8.15799i	−0.163760	−	0.504002i
$263$	−27.1823			−1.67613			−0.838067	−	0.545568i	$-0.816314\pi$
$263$	−27.1823			−1.67613			−0.838067	+	0.545568i	$0.816314\pi$
$264$	−1.96104	−	2.40517i	−0.120694	−	0.148028i
$265$	7.14297			0.438789
$266$	−1.25323	−	3.85705i	−0.0768405	−	0.236491i
$267$	0.757349	+	0.550246i	0.0463490	+	0.0336745i
$268$	4.84932	−	3.52324i	0.296219	−	0.215216i
$269$	−2.51688	+	7.74617i	−0.153457	+	0.472292i	−0.998001	−	0.0631935i	$-0.979871\pi$
$269$	−2.51688	+	7.74617i	−0.153457	+	0.472292i	0.844544	+	0.535486i	$0.179871\pi$
$270$	−1.48171	+	4.56023i	−0.0901739	+	0.277527i
$271$	5.10158	−	3.70651i	0.309899	−	0.225155i	−0.421954	−	0.906617i	$-0.638656\pi$
$271$	5.10158	−	3.70651i	0.309899	−	0.225155i	0.731853	+	0.681463i	$0.238656\pi$
$272$	−3.79107	−	2.75437i	−0.229867	−	0.167008i
$273$	0.726894	+	2.23715i	0.0439936	+	0.135398i
$274$	−1.63086			−0.0985241
$275$	3.20647	+	0.847672i	0.193357	+	0.0511166i
$276$	3.24631			0.195405
$277$	−8.07757	−	24.8602i	−0.485334	−	1.49371i	−0.831496	−	0.555530i	$-0.812515\pi$
$277$	−8.07757	−	24.8602i	−0.485334	−	1.49371i	0.346162	−	0.938175i	$-0.387485\pi$
$278$	−18.7529	−	13.6248i	−1.12473	−	0.817161i
$279$	2.65705	−	1.93046i	0.159073	−	0.115573i
$280$	−0.309017	+	0.951057i	−0.0184673	+	0.0568365i
$281$	4.55356	−	14.0144i	0.271643	−	0.836031i	−0.718445	−	0.695584i	$-0.755146\pi$
$281$	4.55356	−	14.0144i	0.271643	−	0.836031i	0.990088	−	0.140447i	$-0.0448541\pi$
$282$	−1.34325	+	0.975928i	−0.0799894	+	0.0581157i
$283$	−17.3987	−	12.6409i	−1.03425	−	0.751424i	−0.0650920	−	0.997879i	$-0.520734\pi$
$283$	−17.3987	−	12.6409i	−1.03425	−	0.751424i	−0.969154	+	0.246456i	$0.920734\pi$
$284$	2.02073	+	6.21917i	0.119908	+	0.369040i
$285$	−3.79470			−0.224779
$286$	4.51770	−	7.00791i	0.267137	−	0.414386i
$287$	1.65079			0.0974432
$288$	0.656505	+	2.02052i	0.0386850	+	0.119060i
$289$	−4.01172	−	2.91469i	−0.235984	−	0.171452i
$290$	−6.03901	+	4.38760i	−0.354623	+	0.257649i
$291$	−3.27709	+	10.0858i	−0.192106	+	0.591243i
$292$	−0.264324	+	0.813507i	−0.0154684	+	0.0476069i
$293$	4.94798	−	3.59492i	0.289064	−	0.210017i	−0.433797	−	0.901011i	$-0.642827\pi$
$293$	4.94798	−	3.59492i	0.289064	−	0.210017i	0.722861	+	0.690993i	$0.242827\pi$
$294$	−0.756984	−	0.549981i	−0.0441482	−	0.0320755i
$295$	−0.131900	−	0.405946i	−0.00767951	−	0.0236351i
$296$	4.92622			0.286331
$297$	0.885474	+	15.8782i	0.0513804	+	0.921349i
$298$	1.43386			0.0830613
$299$	2.69528	+	8.29520i	0.155872	+	0.479724i
$300$	0.756984	+	0.549981i	0.0437045	+	0.0317532i
$301$	6.44861	−	4.68519i	0.371692	−	0.270050i
$302$	−5.49901	+	16.9242i	−0.316432	+	0.973878i
$303$	−0.915597	+	2.81792i	−0.0525997	+	0.161885i
$304$	−3.28100	+	2.38379i	−0.188178	+	0.136720i
$305$	−4.97708	−	3.61606i	−0.284987	−	0.207055i
$306$	3.07640	+	9.46817i	0.175866	+	0.541259i
$307$	24.8721			1.41952			0.709762	−	0.704441i	$-0.248802\pi$
$307$	24.8721			1.41952			0.709762	+	0.704441i	$0.248802\pi$
$308$	0.184670	+	3.31148i	0.0105225	+	0.188689i
$309$	−14.0797			−0.800963
$310$	−0.477714	−	1.47025i	−0.0271323	−	0.0835047i
$311$	−2.73404	−	1.98640i	−0.155033	−	0.112638i	0.507564	−	0.861614i	$-0.330546\pi$
$311$	−2.73404	−	1.98640i	−0.155033	−	0.112638i	−0.662598	+	0.748976i	$0.730546\pi$
$312$	1.90303	−	1.38263i	0.107738	−	0.0782763i
$313$	−6.40904	+	19.7250i	−0.362261	+	1.11492i	0.589418	+	0.807828i	$0.299357\pi$
$313$	−6.40904	+	19.7250i	−0.362261	+	1.11492i	−0.951679	+	0.307095i	$0.900643\pi$
$314$	2.25318	−	6.93457i	0.127154	−	0.391340i
$315$	1.71875	−	1.24875i	0.0968408	−	0.0703590i
$316$	7.97835	+	5.79661i	0.448817	+	0.326085i
$317$	2.30588	+	7.09678i	0.129511	+	0.398595i	0.994696	−	0.102858i	$-0.0327989\pi$
$317$	2.30588	+	7.09678i	0.129511	+	0.398595i	−0.865185	+	0.501453i	$0.832799\pi$
$318$	6.68356			0.374795
$319$	−13.4142	+	20.8083i	−0.751052	+	1.16504i
$320$	1.00000			0.0559017
$321$	4.17454	+	12.8479i	0.233000	+	0.717101i
$322$	−2.80685	−	2.03929i	−0.156419	−	0.113645i
$323$	−15.3748	+	11.1705i	−0.855479	+	0.621542i
$324$	0.583107	−	1.79462i	0.0323948	−	0.0997011i
$325$	−0.776859	+	2.39093i	−0.0430924	+	0.132625i
$326$	7.61531	−	5.53285i	0.421773	−	0.306436i
$327$	−9.22527	−	6.70255i	−0.510159	−	0.370652i
$328$	−0.510123	−	1.57000i	−0.0281668	−	0.0866886i
$329$	1.77448			0.0978301
$330$	3.00024	+	0.793153i	0.165158	+	0.0436616i
$331$	−8.26702			−0.454396			−0.227198	−	0.973849i	$-0.572956\pi$
$331$	−8.26702			−0.454396			−0.227198	+	0.973849i	$0.572956\pi$
$332$	−2.52057	−	7.75752i	−0.138334	−	0.425749i
$333$	−8.46696	−	6.15161i	−0.463987	−	0.337106i
$334$	−0.234548	+	0.170409i	−0.0128339	+	0.00932438i
$335$	−1.85228	+	5.70072i	−0.101201	+	0.311464i
$336$	−0.289142	+	0.889888i	−0.0157740	+	0.0485474i
$337$	−0.250073	+	0.181688i	−0.0136223	+	0.00989720i	−0.594576	−	0.804040i	$-0.702680\pi$
$337$	−0.250073	+	0.181688i	−0.0136223	+	0.00989720i	0.580953	+	0.813937i	$0.302680\pi$
$338$	−5.40421	−	3.92639i	−0.293950	−	0.213567i
$339$	3.39147	+	10.4379i	0.184199	+	0.566908i
$340$	4.68602			0.254135
$341$	−3.23999	−	3.97377i	−0.175455	−	0.215192i
$342$	8.61598			0.465899
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	−6.44861	−	4.68519i	−0.347686	−	0.252608i
$345$	−2.62632	+	1.90813i	−0.141396	+	0.102730i
$346$	3.21959	−	9.90886i	0.173086	−	0.532704i
$347$	−1.89215	+	5.82344i	−0.101576	+	0.312619i	−0.988912	−	0.148505i	$-0.952554\pi$
$347$	−1.89215	+	5.82344i	−0.101576	+	0.312619i	0.887336	+	0.461124i	$0.152554\pi$
$348$	−5.65060	+	4.10540i	−0.302904	+	0.220073i
$349$	−16.0054	−	11.6286i	−0.856751	−	0.622466i	0.0702484	−	0.997530i	$-0.477621\pi$
$349$	−16.0054	−	11.6286i	−0.856751	−	0.622466i	−0.926999	+	0.375064i	$0.877621\pi$
$350$	−0.309017	−	0.951057i	−0.0165177	−	0.0508361i
$351$	−12.0542			−0.643408
$352$	3.09234	−	1.19893i	0.164822	−	0.0639034i
$353$	−30.8256			−1.64068			−0.820340	−	0.571876i	$-0.806216\pi$
$353$	−30.8256			−1.64068			−0.820340	+	0.571876i	$0.806216\pi$
$354$	−0.123417	−	0.379837i	−0.00655952	−	0.0201881i
$355$	−5.29034	−	3.84366i	−0.280782	−	0.204000i
$356$	−0.809408	+	0.588069i	−0.0428985	+	0.0311676i
$357$	−1.35492	+	4.17003i	−0.0717102	+	0.220701i
$358$	4.60792	−	14.1817i	0.243536	−	0.749527i
$359$	−20.4221	+	14.8375i	−1.07784	+	0.783094i	−0.977304	−	0.211840i	$-0.932055\pi$
$359$	−20.4221	+	14.8375i	−1.07784	+	0.783094i	−0.100532	+	0.994934i	$0.532055\pi$
$360$	−1.71875	−	1.24875i	−0.0905863	−	0.0658148i
$361$	−0.788792	−	2.42765i	−0.0415154	−	0.127771i
$362$	−4.37330			−0.229856
$363$	10.2287	−	1.14440i	0.536867	−	0.0600653i
$364$	−2.51397			−0.131768
$365$	−0.264324	−	0.813507i	−0.0138354	−	0.0425809i
$366$	−4.65697	−	3.38349i	−0.243424	−	0.176858i
$367$	7.17619	−	5.21380i	0.374594	−	0.272158i	−0.384519	−	0.923117i	$-0.625633\pi$
$367$	7.17619	−	5.21380i	0.374594	−	0.272158i	0.759113	+	0.650959i	$0.225633\pi$
$368$	−1.07212	+	3.29965i	−0.0558881	+	0.172006i
$369$	−1.08375	+	3.33545i	−0.0564180	+	0.173637i
$370$	−3.98540	+	2.89556i	−0.207191	+	0.150533i
$371$	−5.77878	−	4.19853i	−0.300020	−	0.217977i
$372$	−0.446989	−	1.37569i	−0.0231753	−	0.0713262i
$373$	−23.0860			−1.19535			−0.597675	−	0.801739i	$-0.703909\pi$
$373$	−23.0860			−1.19535			−0.597675	+	0.801739i	$0.703909\pi$
$374$	14.4908	−	5.61823i	0.749299	−	0.290512i
$375$	−0.935683			−0.0483185
$376$	−0.548343	−	1.68763i	−0.0282787	−	0.0870327i
$377$	−15.1819	−	11.0303i	−0.781907	−	0.568089i
$378$	3.87916	−	2.81838i	0.199523	−	0.144962i
$379$	9.77466	−	30.0833i	0.502090	−	1.54528i	−0.303517	−	0.952826i	$-0.598161\pi$
$379$	9.77466	−	30.0833i	0.502090	−	1.54528i	0.805608	−	0.592450i	$-0.201839\pi$
$380$	1.25323	−	3.85705i	0.0642894	−	0.197862i
$381$	2.78809	−	2.02567i	0.142838	−	0.103778i
$382$	−8.59154	−	6.24212i	−0.439581	−	0.319375i
$383$	0.571635	+	1.75931i	0.0292092	+	0.0898966i	0.964598	−	0.263723i	$-0.0849506\pi$
$383$	0.571635	+	1.75931i	0.0292092	+	0.0898966i	−0.935389	+	0.353620i	$0.884951\pi$
$384$	0.935683			0.0477489
$385$	−2.09584	−	2.57050i	−0.106814	−	0.131005i
$386$	−7.98145			−0.406245
$387$	5.23295	+	16.1054i	0.266006	+	0.818682i
$388$	−9.16927	−	6.66186i	−0.465499	−	0.338205i
$389$	−12.6712	+	9.20614i	−0.642454	+	0.466770i	−0.860692	−	0.509126i	$-0.829969\pi$
$389$	−12.6712	+	9.20614i	−0.642454	+	0.466770i	0.218239	+	0.975895i	$0.429969\pi$
$390$	−0.726894	+	2.23715i	−0.0368077	+	0.113282i
$391$	−5.02397	+	15.4622i	−0.254073	+	0.781957i
$392$	0.809017	−	0.587785i	0.0408615	−	0.0296876i
$393$	6.49327	+	4.71763i	0.327542	+	0.237973i
$394$	2.25156	+	6.92959i	0.113432	+	0.349108i
$395$	−9.86178			−0.496200
$396$	−6.81213	−	1.80088i	−0.342323	−	0.0904974i
$397$	−14.8207			−0.743827			−0.371914	−	0.928267i	$-0.621298\pi$
$397$	−14.8207			−0.743827			−0.371914	+	0.928267i	$0.621298\pi$
$398$	−4.38349	−	13.4910i	−0.219724	−	0.676242i
$399$	3.06998	+	2.23047i	0.153691	+	0.111663i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	4.45980	−	13.7258i	0.222712	−	0.685436i	−0.775804	−	0.630974i	$-0.782656\pi$
$401$	4.45980	−	13.7258i	0.222712	−	0.685436i	0.998516	−	0.0544622i	$-0.0173444\pi$
$402$	−1.73314	+	5.33407i	−0.0864414	+	0.266039i
$403$	3.14415	−	2.28436i	0.156621	−	0.113792i
$404$	−2.56183	−	1.86128i	−0.127456	−	0.0926022i
$405$	0.583107	+	1.79462i	0.0289748	+	0.0891753i
$406$	7.46463			0.370463
$407$	−8.85261	+	13.7323i	−0.438807	+	0.680684i
$408$	4.38463			0.217071
$409$	−11.7531	−	36.1724i	−0.581155	−	1.78861i	−0.614193	−	0.789156i	$-0.710518\pi$
$409$	−11.7531	−	36.1724i	−0.581155	−	1.78861i	0.0330387	−	0.999454i	$-0.489482\pi$
$410$	1.33552	+	0.970311i	0.0659566	+	0.0479203i
$411$	1.23454	−	0.896944i	0.0608953	−	0.0442430i
$412$	4.64992	−	14.3110i	0.229085	−	0.705051i
$413$	−0.131900	+	0.405946i	−0.00649037	+	0.0199753i
$414$	5.96314	−	4.33247i	0.293072	−	0.212929i
$415$	6.59894	+	4.79441i	0.323929	+	0.235348i
$416$	0.776859	+	2.39093i	0.0380886	+	0.117225i
$417$	21.6890			1.06212
$418$	−0.748936	−	13.4298i	−0.0366316	−	0.656875i
$419$	24.2138			1.18292			0.591460	−	0.806334i	$-0.298552\pi$
$419$	24.2138			1.18292			0.591460	+	0.806334i	$0.298552\pi$
$420$	−0.289142	−	0.889888i	−0.0141087	−	0.0434221i
$421$	−31.2829	−	22.7284i	−1.52463	−	1.10771i	−0.959129	−	0.282968i	$-0.908681\pi$
$421$	−31.2829	−	22.7284i	−1.52463	−	1.10771i	−0.565505	−	0.824745i	$-0.691319\pi$
$422$	−18.8315	+	13.6819i	−0.916704	+	0.666025i
$423$	−1.16495	+	3.58536i	−0.0566420	+	0.174326i
$424$	−2.20730	+	6.79337i	−0.107196	+	0.329915i
$425$	−3.79107	+	2.75437i	−0.183894	+	0.133607i
$426$	−4.95008	−	3.59645i	−0.239832	−	0.174248i
$427$	1.90107	+	5.85091i	0.0919995	+	0.283145i
$428$	−14.4377			−0.697872
$429$	0.434395	+	7.78952i	0.0209728	+	0.376082i
$430$	7.97092			0.384392
$431$	−7.29369	−	22.4477i	−0.351325	−	1.08127i	−0.958110	−	0.286401i	$-0.907541\pi$
$431$	−7.29369	−	22.4477i	−0.351325	−	1.08127i	0.606785	−	0.794866i	$-0.292459\pi$
$432$	−3.87916	−	2.81838i	−0.186636	−	0.135599i
$433$	24.7990	−	18.0175i	1.19176	−	0.865866i	0.198313	−	0.980139i	$-0.436454\pi$
$433$	24.7990	−	18.0175i	1.19176	−	0.865866i	0.993449	+	0.114273i	$0.0364538\pi$
$434$	−0.477714	+	1.47025i	−0.0229310	+	0.0705743i
$435$	2.15834	−	6.64268i	0.103484	−	0.318492i
$436$	9.85939	−	7.16327i	0.472179	−	0.343058i
$437$	11.3833	+	8.27044i	0.544536	+	0.395629i
$438$	−0.247324	−	0.761185i	−0.0118176	−	0.0363708i
$439$	23.4152			1.11755			0.558774	−	0.829320i	$-0.311272\pi$
$439$	23.4152			1.11755			0.558774	+	0.829320i	$0.311272\pi$
$440$	−1.79704	+	2.78759i	−0.0856704	+	0.132893i
$441$	−2.12450			−0.101166
$442$	3.64037	+	11.2039i	0.173155	+	0.532916i
$443$	−0.674103	−	0.489764i	−0.0320276	−	0.0232694i	0.571656	−	0.820493i	$-0.306301\pi$
$443$	−0.674103	−	0.489764i	−0.0320276	−	0.0232694i	−0.603684	+	0.797224i	$0.706301\pi$
$444$	−3.72907	+	2.70933i	−0.176974	+	0.128579i
$445$	0.309166	−	0.951516i	0.0146559	−	0.0451062i
$446$	2.50226	−	7.70117i	0.118485	−	0.364661i
$447$	−1.08541	+	0.788595i	−0.0513381	+	0.0372993i
$448$	−0.809017	−	0.587785i	−0.0382225	−	0.0277702i
$449$	−1.84802	−	5.68761i	−0.0872133	−	0.268415i	0.897933	−	0.440132i	$-0.145068\pi$
$449$	−1.84802	−	5.68761i	−0.0872133	−	0.268415i	−0.985146	+	0.171717i	$0.945068\pi$
$450$	2.12450			0.100150
$451$	5.29322	+	1.39933i	0.249248	+	0.0658919i
$452$	−11.7294			−0.551706
$453$	−5.14533	−	15.8357i	−0.241749	−	0.744026i
$454$	−15.2382	−	11.0712i	−0.715162	−	0.519596i
$455$	2.03384	−	1.47767i	0.0953480	−	0.0692744i
$456$	1.17263	−	3.60898i	0.0549133	−	0.169006i
$457$	−12.9714	+	39.9218i	−0.606775	+	1.86746i	−0.122678	+	0.992447i	$0.539148\pi$
$457$	−12.9714	+	39.9218i	−0.606775	+	1.86746i	−0.484097	+	0.875014i	$0.660852\pi$
$458$	8.79574	−	6.39048i	0.410998	−	0.298607i
$459$	−18.1778	−	13.2070i	−0.848468	−	0.616448i
$460$	−1.07212	−	3.29965i	−0.0499879	−	0.153847i
$461$	−32.1474			−1.49725			−0.748626	−	0.662992i	$-0.769286\pi$
$461$	−32.1474			−1.49725			−0.748626	+	0.662992i	$0.769286\pi$
$462$	−1.96104	−	2.40517i	−0.0912360	−	0.111899i
$463$	−8.14625			−0.378588			−0.189294	−	0.981920i	$-0.560620\pi$
$463$	−8.14625			−0.378588			−0.189294	+	0.981920i	$0.560620\pi$
$464$	−2.30670	−	7.09929i	−0.107086	−	0.329576i
$465$	1.17023	+	0.850223i	0.0542682	+	0.0394282i
$466$	−7.26205	+	5.27619i	−0.336408	+	0.244415i
$467$	2.37323	−	7.30406i	0.109820	−	0.337992i	−0.881011	−	0.473095i	$-0.843137\pi$
$467$	2.37323	−	7.30406i	0.109820	−	0.337992i	0.990831	+	0.135103i	$0.0431367\pi$
$468$	1.65043	−	5.07951i	0.0762913	−	0.234801i
$469$	4.84932	−	3.52324i	0.223921	−	0.162688i
$470$	1.43558	+	1.04301i	0.0662184	+	0.0481105i
$471$	2.10826	+	6.48856i	0.0971436	+	0.298977i
$472$	0.426837			0.0196468
$473$	24.6488	−	9.55661i	1.13335	−	0.439414i
$474$	−9.22750			−0.423833
$475$	1.25323	+	3.85705i	0.0575022	+	0.176974i
$476$	−3.79107	−	2.75437i	−0.173763	−	0.126246i
$477$	12.2770	−	8.91977i	0.562126	−	0.408408i
$478$	3.02257	−	9.30252i	0.138249	−	0.425487i
$479$	−7.02164	+	21.6104i	−0.320827	+	0.987404i	0.652462	+	0.757821i	$0.273736\pi$
$479$	−7.02164	+	21.6104i	−0.320827	+	0.987404i	−0.973289	+	0.229583i	$0.926264\pi$
$480$	−0.756984	+	0.549981i	−0.0345514	+	0.0251031i
$481$	−10.0192	−	7.27935i	−0.456834	−	0.331910i
$482$	−7.22650	−	22.2409i	−0.329158	−	1.01304i
$483$	3.24631			0.147712
$484$	−2.21491	+	10.7747i	−0.100678	+	0.489759i
$485$	11.3338			0.514643
$486$	4.99073	+	15.3599i	0.226384	+	0.696738i
$487$	−27.0582	−	19.6589i	−1.22612	−	0.890831i	−0.229530	−	0.973302i	$-0.573719\pi$
$487$	−27.0582	−	19.6589i	−1.22612	−	0.890831i	−0.996593	+	0.0824707i	$0.973719\pi$
$488$	4.97708	−	3.61606i	0.225302	−	0.163691i
$489$	−2.72171	+	8.37655i	−0.123080	+	0.378801i
$490$	−0.309017	+	0.951057i	−0.0139600	+	0.0429644i
$491$	−4.94302	+	3.59132i	−0.223075	+	0.162074i	−0.693710	−	0.720254i	$-0.744025\pi$
$491$	−4.94302	+	3.59132i	−0.223075	+	0.162074i	0.470635	+	0.882328i	$0.344025\pi$
$492$	1.24962	+	0.907904i	0.0563374	+	0.0409315i
$493$	−10.8092	−	33.2674i	−0.486823	−	1.49829i
$494$	10.1955			0.458717
$495$	6.56966	−	2.54713i	0.295284	−	0.114485i
$496$	1.54591			0.0694136
$497$	2.02073	+	6.21917i	0.0906421	+	0.278968i
$498$	6.17452	+	4.48605i	0.276687	+	0.201025i
$499$	−17.0859	+	12.4136i	−0.764869	+	0.555710i	−0.900400	−	0.435063i	$-0.856726\pi$
$499$	−17.0859	+	12.4136i	−0.764869	+	0.555710i	0.135531	+	0.990773i	$0.456726\pi$
$500$	0.309017	−	0.951057i	0.0138197	−	0.0425325i
$501$	0.0838274	−	0.257994i	0.00374513	−	0.0115263i
$502$	21.1104	−	15.3376i	0.942205	−	0.684552i
$503$	20.6562	+	15.0076i	0.921016	+	0.669157i	0.943777	−	0.330584i	$-0.107246\pi$
$503$	20.6562	+	15.0076i	0.921016	+	0.669157i	−0.0227608	+	0.999741i	$0.507246\pi$
$504$	0.656505	+	2.02052i	0.0292431	+	0.0900009i
$505$	3.16660			0.140912
$506$	−7.27142	−	8.91822i	−0.323254	−	0.396463i
$507$	6.25033			0.277587
$508$	1.13816	+	3.50290i	0.0504977	+	0.155416i
$509$	17.7986	+	12.9314i	0.788908	+	0.573175i	0.907639	−	0.419751i	$-0.137883\pi$
$509$	17.7986	+	12.9314i	0.788908	+	0.573175i	−0.118731	+	0.992926i	$0.537883\pi$
$510$	−3.54724	+	2.57722i	−0.157074	+	0.114121i
$511$	−0.264324	+	0.813507i	−0.0116930	+	0.0359874i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−15.7321	+	11.4300i	−0.694589	+	0.504649i
$514$	4.46524	+	3.24419i	0.196953	+	0.143095i
$515$	4.64992	+	14.3110i	0.204900	+	0.630617i
$516$	7.45826			0.328332
$517$	5.68981	+	1.50417i	0.250237	+	0.0661535i
$518$	4.92622			0.216446
$519$	3.01251	+	9.27156i	0.132235	+	0.406976i
$520$	−2.03384	−	1.47767i	−0.0891899	−	0.0648003i
$521$	22.2845	−	16.1906i	0.976300	−	0.709323i	0.0194213	−	0.999811i	$-0.493818\pi$
$521$	22.2845	−	16.1906i	0.976300	−	0.709323i	0.956879	+	0.290488i	$0.0938176\pi$
$522$	−4.90057	+	15.0824i	−0.214492	+	0.660139i
$523$	0.799929	−	2.46193i	0.0349785	−	0.107653i	−0.932043	−	0.362348i	$-0.881975\pi$
$523$	0.799929	−	2.46193i	0.0349785	−	0.107653i	0.967021	+	0.254695i	$0.0819752\pi$
$524$	−6.93960	+	5.04191i	−0.303158	+	0.220257i
$525$	0.756984	+	0.549981i	0.0330375	+	0.0240031i
$526$	8.39980	+	25.8519i	0.366249	+	1.12720i
$527$	7.24418			0.315561
$528$	−1.68146	+	2.60830i	−0.0731761	+	0.113512i
$529$	−10.9629			−0.476647
$530$	−2.20730	−	6.79337i	−0.0958790	−	0.295085i
$531$	−0.733628	−	0.533012i	−0.0318367	−	0.0231307i
$532$	−3.28100	+	2.38379i	−0.142249	+	0.103350i
$533$	−1.28243	+	3.94692i	−0.0555483	+	0.170960i
$534$	0.289282	−	0.890317i	0.0125184	−	0.0385278i
$535$	11.6803	−	8.48626i	0.504985	−	0.366893i
$536$	−4.84932	−	3.52324i	−0.209459	−	0.152181i
$537$	4.31155	+	13.2696i	0.186057	+	0.572625i
$538$	8.14480			0.351147
$539$	0.184670	+	3.31148i	0.00795429	+	0.142636i
$540$	4.79491			0.206340
$541$	5.14492	+	15.8344i	0.221197	+	0.680775i	0.998655	+	0.0518404i	$0.0165087\pi$
$541$	5.14492	+	15.8344i	0.221197	+	0.680775i	−0.777458	+	0.628935i	$0.783491\pi$
$542$	−5.10158	−	3.70651i	−0.219131	−	0.159208i
$543$	3.31052	−	2.40523i	0.142068	−	0.103218i
$544$	−1.44806	+	4.45667i	−0.0620850	+	0.191078i
$545$	−3.76595	+	11.5904i	−0.161316	+	0.496479i
$546$	1.90303	−	1.38263i	0.0814423	−	0.0591713i
$547$	26.0712	+	18.9418i	1.11472	+	0.809895i	0.983401	−	0.181445i	$-0.0580774\pi$
$547$	26.0712	+	18.9418i	1.11472	+	0.809895i	0.131323	+	0.991340i	$0.458077\pi$
$548$	0.503965	+	1.55104i	0.0215283	+	0.0662573i
$549$	−13.0699			−0.557811
$550$	−0.184670	−	3.31148i	−0.00787434	−	0.141202i
$551$	−30.2731			−1.28968
$552$	−1.00317	−	3.08742i	−0.0426975	−	0.131410i
$553$	7.97835	+	5.79661i	0.339274	+	0.246497i
$554$	−21.1474	+	15.3645i	−0.898465	+	0.652773i
$555$	1.42438	−	4.38379i	0.0604615	−	0.186081i
$556$	−7.16298	+	22.0454i	−0.303778	+	0.934932i
$557$	35.1218	−	25.5175i	1.48816	−	1.08121i	0.513345	−	0.858183i	$-0.328406\pi$
$557$	35.1218	−	25.5175i	1.48816	−	1.08121i	0.974812	−	0.223027i	$-0.0715937\pi$
$558$	−2.65705	−	1.93046i	−0.112482	−	0.0817227i
$559$	6.19228	+	19.0579i	0.261906	+	0.806062i
$560$	1.00000			0.0422577
$561$	−7.87934	+	12.2225i	−0.332666	+	0.516036i
$562$	−14.7356			−0.621586
$563$	−3.72065	−	11.4510i	−0.156807	−	0.482601i	0.841533	−	0.540206i	$-0.181654\pi$
$563$	−3.72065	−	11.4510i	−0.156807	−	0.482601i	−0.998339	+	0.0576048i	$0.981654\pi$
$564$	1.34325	+	0.975928i	0.0565610	+	0.0410940i
$565$	9.48931	−	6.89438i	0.399218	−	0.290049i
$566$	−6.64572	+	20.4534i	−0.279340	+	0.859721i
$567$	0.583107	−	1.79462i	0.0244882	−	0.0753669i
$568$	5.29034	−	3.84366i	0.221978	−	0.161276i
$569$	21.3099	+	15.4826i	0.893358	+	0.649063i	0.936751	−	0.349995i	$-0.113817\pi$
$569$	21.3099	+	15.4826i	0.893358	+	0.649063i	−0.0433931	+	0.999058i	$0.513817\pi$
$570$	1.17263	+	3.60898i	0.0491160	+	0.151163i
$571$	22.2032			0.929176			0.464588	−	0.885527i	$-0.346203\pi$
$571$	22.2032			0.929176			0.464588	+	0.885527i	$0.346203\pi$
$572$	−8.06096	−	2.13102i	−0.337046	−	0.0891024i
$573$	9.93670			0.415112
$574$	−0.510123	−	1.57000i	−0.0212921	−	0.0655304i
$575$	2.80685	+	2.03929i	0.117054	+	0.0850444i
$576$	1.71875	−	1.24875i	0.0716147	−	0.0520312i
$577$	10.4888	−	32.2812i	0.436654	−	1.34388i	−0.454727	−	0.890631i	$-0.650263\pi$
$577$	10.4888	−	32.2812i	0.436654	−	1.34388i	0.891382	−	0.453254i	$-0.149737\pi$
$578$	−1.53234	+	4.71606i	−0.0637370	+	0.196162i
$579$	6.04183	−	4.38964i	0.251090	−	0.182427i
$580$	6.03901	+	4.38760i	0.250756	+	0.182185i
$581$	−2.52057	−	7.75752i	−0.104571	−	0.321836i
$582$	10.6049			0.439587
$583$	−14.9705	−	18.3610i	−0.620016	−	0.760434i
$584$	0.855372			0.0353955
$585$	1.65043	+	5.07951i	0.0682370	+	0.210012i
$586$	−4.94798	−	3.59492i	−0.204399	−	0.148505i
$587$	8.62007	−	6.26285i	0.355788	−	0.258495i	−0.395505	−	0.918464i	$-0.629430\pi$
$587$	8.62007	−	6.26285i	0.355788	−	0.258495i	0.751293	+	0.659968i	$0.229430\pi$
$588$	−0.289142	+	0.889888i	−0.0119240	+	0.0366984i
$589$	1.93739	−	5.96267i	0.0798287	−	0.245687i
$590$	−0.345318	+	0.250889i	−0.0142165	+	0.0103289i
$591$	−5.51554	−	4.00727i	−0.226879	−	0.164837i
$592$	−1.52229	−	4.68512i	−0.0625656	−	0.192557i
$593$	44.1567			1.81330			0.906649	−	0.421886i	$-0.138632\pi$
$593$	44.1567			1.81330			0.906649	+	0.421886i	$0.138632\pi$
$594$	14.8275	−	5.74878i	0.608379	−	0.235875i
$595$	4.68602			0.192108
$596$	−0.443087	−	1.36368i	−0.0181495	−	0.0558586i
$597$	10.7380	+	7.80162i	0.439478	+	0.319299i
$598$	7.05632	−	5.12672i	0.288554	−	0.209647i
$599$	7.96094	−	24.5012i	0.325275	−	1.00109i	−0.646041	−	0.763303i	$-0.723577\pi$
$599$	7.96094	−	24.5012i	0.325275	−	1.00109i	0.971316	−	0.237791i	$-0.0764234\pi$
$600$	0.289142	−	0.889888i	0.0118042	−	0.0363295i
$601$	−39.4938	+	28.6939i	−1.61099	+	1.17045i	−0.750694	+	0.660651i	$0.770281\pi$
$601$	−39.4938	+	28.6939i	−1.61099	+	1.17045i	−0.860293	+	0.509800i	$0.829719\pi$
$602$	−6.44861	−	4.68519i	−0.262826	−	0.190954i
$603$	3.93515	+	12.1112i	0.160252	+	0.493205i
$604$	17.7952			0.724075
$605$	−4.54131	−	10.0188i	−0.184630	−	0.407322i
$606$	2.96293			0.120361
$607$	−7.23450	−	22.2655i	−0.293639	−	0.903729i	−0.983675	−	0.179954i	$-0.942405\pi$
$607$	−7.23450	−	22.2655i	−0.293639	−	0.903729i	0.690036	−	0.723775i	$-0.257595\pi$
$608$	3.28100	+	2.38379i	0.133062	+	0.0966753i
$609$	−5.65060	+	4.10540i	−0.228974	+	0.166359i
$610$	−1.90107	+	5.85091i	−0.0769723	+	0.236896i
$611$	−1.37852	+	4.24264i	−0.0557689	+	0.171639i
$612$	8.05411	−	5.85165i	0.325568	−	0.236539i
$613$	27.8250	+	20.2160i	1.12384	+	0.816518i	0.984787	−	0.173767i	$-0.0555940\pi$
$613$	27.8250	+	20.2160i	1.12384	+	0.816518i	0.139054	+	0.990285i	$0.455594\pi$
$614$	−7.68589	−	23.6547i	−0.310177	−	0.954628i
$615$	−1.54462			−0.0622851
$616$	3.09234	−	1.19893i	0.124594	−	0.0483065i
$617$	−33.9149			−1.36536			−0.682681	−	0.730717i	$-0.739186\pi$
$617$	−33.9149			−1.36536			−0.682681	+	0.730717i	$0.739186\pi$
$618$	4.35085	+	13.3905i	0.175017	+	0.538647i
$619$	37.6422	+	27.3487i	1.51297	+	1.09924i	0.964839	+	0.262842i	$0.0846598\pi$
$619$	37.6422	+	27.3487i	1.51297	+	1.09924i	0.548129	+	0.836394i	$0.315340\pi$
$620$	−1.25067	+	0.908665i	−0.0502281	+	0.0364929i
$621$	−5.14072	+	15.8215i	−0.206290	+	0.634895i
$622$	−1.04431	+	3.21406i	−0.0418730	+	0.128872i
$623$	−0.809408	+	0.588069i	−0.0324282	+	0.0235605i
$624$	−1.90303	−	1.38263i	−0.0761823	−	0.0553497i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	20.7401			0.828941
$627$	7.95309	+	9.75427i	0.317616	+	0.389548i
$628$	−7.29144			−0.290960
$629$	−7.13346	−	21.9545i	−0.284430	−	0.875385i
$630$	−1.71875	−	1.24875i	−0.0684768	−	0.0497513i
$631$	39.7337	−	28.8683i	1.58178	−	1.14923i	0.667151	−	0.744923i	$-0.267514\pi$
$631$	39.7337	−	28.8683i	1.58178	−	1.14923i	0.914625	−	0.404304i	$-0.132486\pi$
$632$	3.04746	−	9.37911i	0.121221	−	0.373081i
$633$	6.73037	−	20.7140i	0.267508	−	0.823306i
$634$	6.03688	−	4.38605i	0.239755	−	0.174192i
$635$	−2.97974	−	2.16491i	−0.118247	−	0.0859118i
$636$	−2.06533	−	6.35644i	−0.0818958	−	0.252049i
$637$	−2.51397			−0.0996070
$638$	23.9351	+	6.32756i	0.947600	+	0.250510i
$639$	−13.8926			−0.549581
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	8.56092	+	6.21987i	0.338136	+	0.245670i	0.743875	−	0.668319i	$-0.232986\pi$
$641$	8.56092	+	6.21987i	0.338136	+	0.245670i	−0.405739	+	0.913989i	$0.632986\pi$
$642$	10.9291	−	7.94046i	0.431337	−	0.313385i
$643$	−8.40839	+	25.8784i	−0.331594	+	1.02054i	0.636781	+	0.771045i	$0.280266\pi$
$643$	−8.40839	+	25.8784i	−0.331594	+	1.02054i	−0.968375	+	0.249498i	$0.919734\pi$
$644$	−1.07212	+	3.29965i	−0.0422475	+	0.130024i
$645$	−6.03386	+	4.38385i	−0.237583	+	0.172614i
$646$	15.3748	+	11.1705i	0.604915	+	0.439496i
$647$	−10.0973	−	31.0763i	−0.396966	−	1.22174i	−0.927420	−	0.374022i	$-0.877979\pi$
$647$	−10.0973	−	31.0763i	−0.396966	−	1.22174i	0.530454	−	0.847714i	$-0.322021\pi$
$648$	−1.88697			−0.0741273
$649$	−0.767042	+	1.18985i	−0.0301090	+	0.0467056i
$650$	2.51397			0.0986059
$651$	−0.446989	−	1.37569i	−0.0175189	−	0.0539175i
$652$	−7.61531	−	5.53285i	−0.298239	−	0.216683i
$653$	29.0216	−	21.0854i	1.13570	−	0.825137i	0.149189	−	0.988809i	$-0.452334\pi$
$653$	29.0216	−	21.0854i	1.13570	−	0.825137i	0.986515	+	0.163671i	$0.0523336\pi$
$654$	−3.52374	+	10.8450i	−0.137789	+	0.424071i
$655$	2.65069	−	8.15799i	0.103571	−	0.318759i
$656$	−1.33552	+	0.970311i	−0.0521433	+	0.0378843i
$657$	−1.47017	−	1.06814i	−0.0573569	−	0.0416722i
$658$	−0.548343	−	1.68763i	−0.0213767	−	0.0657906i
$659$	−2.91875			−0.113698			−0.0568492	−	0.998383i	$-0.518105\pi$
$659$	−2.91875			−0.113698			−0.0568492	+	0.998383i	$0.518105\pi$
$660$	−0.172792	−	3.09850i	−0.00672594	−	0.120609i
$661$	−45.9224			−1.78617			−0.893087	−	0.449883i	$-0.851466\pi$
$661$	−45.9224			−1.78617			−0.893087	+	0.449883i	$0.851466\pi$
$662$	2.55465	+	7.86240i	0.0992892	+	0.305581i
$663$	−8.91765	−	6.47905i	−0.346333	−	0.251625i
$664$	−6.59894	+	4.79441i	−0.256089	+	0.186059i
$665$	1.25323	−	3.85705i	0.0485982	−	0.149570i
$666$	−3.23409	+	9.95351i	−0.125319	+	0.385691i
$667$	−20.9521	+	15.2226i	−0.811268	+	0.589420i
$668$	0.234548	+	0.170409i	0.00907495	+	0.00659334i
$669$	2.34132	+	7.20585i	0.0905208	+	0.278594i
$670$	5.99409			0.231572
$671$	1.13609	+	20.3722i	0.0438583	+	0.786462i
$672$	0.935683			0.0360948
$673$	−5.28949	−	16.2794i	−0.203895	−	0.627524i	−0.999757	−	0.0220461i	$-0.992982\pi$
$673$	−5.28949	−	16.2794i	−0.203895	−	0.627524i	0.795862	−	0.605478i	$-0.207018\pi$
$674$	0.250073	+	0.181688i	0.00963244	+	0.00699838i
$675$	−3.87916	+	2.81838i	−0.149309	+	0.108479i
$676$	−2.06422	+	6.35303i	−0.0793932	+	0.244347i
$677$	−0.0956622	+	0.294418i	−0.00367660	+	0.0113154i	−0.952878	−	0.303354i	$-0.901894\pi$
$677$	−0.0956622	+	0.294418i	−0.00367660	+	0.0113154i	0.949201	+	0.314669i	$0.101894\pi$
$678$	8.87899	−	6.45096i	0.340995	−	0.247748i
$679$	−9.16927	−	6.66186i	−0.351884	−	0.255659i
$680$	−1.44806	−	4.45667i	−0.0555305	−	0.170905i
$681$	17.6240			0.675352
$682$	−2.77807	+	4.30937i	−0.106378	+	0.165014i
$683$	44.6187			1.70729			0.853644	−	0.520856i	$-0.174387\pi$
$683$	44.6187			1.70729			0.853644	+	0.520856i	$0.174387\pi$
$684$	−2.66249	−	8.19429i	−0.101803	−	0.313316i
$685$	−1.31940	−	0.958598i	−0.0504116	−	0.0366261i
$686$	0.809017	−	0.587785i	0.0308884	−	0.0224417i
$687$	−3.14359	+	9.67498i	−0.119935	+	0.369123i
$688$	−2.46315	+	7.58080i	−0.0939067	+	0.289015i
$689$	14.5277	−	10.5550i	0.553460	−	0.402113i
$690$	2.62632	+	1.90813i	0.0999823	+	0.0726414i
$691$	0.570571	+	1.75604i	0.0217055	+	0.0668027i	0.961323	−	0.275425i	$-0.0888186\pi$
$691$	0.570571	+	1.75604i	0.0217055	+	0.0668027i	−0.939617	+	0.342228i	$0.888819\pi$
$692$	−10.4188			−0.396063
$693$	−6.81213	−	1.80088i	−0.258772	−	0.0684096i
$694$	6.12313			0.232431
$695$	−7.16298	−	22.0454i	−0.271707	−	0.836229i
$696$	5.65060	+	4.10540i	0.214186	+	0.155615i
$697$	−6.25827	+	4.54690i	−0.237049	+	0.172226i
$698$	−6.11353	+	18.8155i	−0.231400	+	0.712177i
$699$	2.59545	−	7.98798i	0.0981690	−	0.302133i
$700$	−0.809017	+	0.587785i	−0.0305780	+	0.0222162i
$701$	11.2934	+	8.20515i	0.426546	+	0.309904i	0.780266	−	0.625447i	$-0.215083\pi$
$701$	11.2934	+	8.20515i	0.426546	+	0.309904i	−0.353720	+	0.935351i	$0.615083\pi$
$702$	3.72497	+	11.4643i	0.140590	+	0.432691i
$703$	−19.9785			−0.753503
$704$	−2.09584	−	2.57050i	−0.0789899	−	0.0968793i
$705$	−1.66035			−0.0625323
$706$	9.52563	+	29.3169i	0.358502	+	1.10336i
$707$	−2.56183	−	1.86128i	−0.0963476	−	0.0700007i
$708$	−0.323109	+	0.234752i	−0.0121432	+	0.00882253i
$709$	−3.78408	+	11.6462i	−0.142114	+	0.437382i	−0.996629	−	0.0820453i	$-0.973855\pi$
$709$	−3.78408	+	11.6462i	−0.142114	+	0.437382i	0.854515	+	0.519428i	$0.173855\pi$
$710$	−2.02073	+	6.21917i	−0.0758367	+	0.233401i
$711$	−16.9500	+	12.3149i	−0.635674	+	0.461844i
$712$	0.809408	+	0.588069i	0.0303338	+	0.0220388i
$713$	−1.65741	−	5.10097i	−0.0620703	−	0.191033i
$714$	4.38463			0.164091
$715$	7.77404	−	3.01408i	0.290733	−	0.112720i
$716$	−14.9115			−0.557270
$717$	2.82817	+	8.70422i	0.105620	+	0.325065i
$718$	20.4221	+	14.8375i	0.762146	+	0.553731i
$719$	9.35473	−	6.79661i	0.348873	−	0.253471i	−0.399523	−	0.916723i	$-0.630824\pi$
$719$	9.35473	−	6.79661i	0.348873	−	0.253471i	0.748396	+	0.663252i	$0.230824\pi$
$720$	−0.656505	+	2.02052i	−0.0244665	+	0.0753002i
$721$	4.64992	−	14.3110i	0.173172	−	0.532969i
$722$	−2.06508	+	1.50037i	−0.0768545	+	0.0558380i
$723$	17.7024	+	12.8616i	0.658360	+	0.478326i
$724$	1.35143	+	4.15926i	0.0502253	+	0.154578i
$725$	−7.46463			−0.277229
$726$	−4.24923	−	9.37443i	−0.157704	−	0.347918i
$727$	−11.2457			−0.417080			−0.208540	−	0.978014i	$-0.566871\pi$
$727$	−11.2457			−0.417080			−0.208540	+	0.978014i	$0.566871\pi$
$728$	0.776859	+	2.39093i	0.0287923	+	0.0886136i
$729$	−7.64576	−	5.55497i	−0.283176	−	0.205740i
$730$	−0.692010	+	0.502775i	−0.0256125	+	0.0186085i
$731$	−11.5424	+	35.5237i	−0.426910	+	1.31389i
$732$	−1.77880	+	5.47460i	−0.0657465	+	0.202347i
$733$	10.7782	−	7.83082i	0.398102	−	0.289238i	−0.370665	−	0.928766i	$-0.620870\pi$
$733$	10.7782	−	7.83082i	0.398102	−	0.289238i	0.768767	+	0.639528i	$0.220870\pi$
$734$	−7.17619	−	5.21380i	−0.264878	−	0.192445i
$735$	−0.289142	−	0.889888i	−0.0106652	−	0.0328240i
$736$	3.46945			0.127886
$737$	18.5358	−	7.18653i	0.682773	−	0.264719i
$738$	3.50710			0.129098
$739$	−13.1336	−	40.4210i	−0.483127	−	1.48691i	−0.834675	−	0.550742i	$-0.814345\pi$
$739$	−13.1336	−	40.4210i	−0.483127	−	1.48691i	0.351548	−	0.936170i	$-0.385655\pi$
$740$	3.98540	+	2.89556i	0.146506	+	0.106443i
$741$	−7.71783	+	5.60733i	−0.283522	+	0.205990i
$742$	−2.20730	+	6.79337i	−0.0810325	+	0.249392i
$743$	6.82541	−	21.0064i	0.250400	−	0.770652i	−0.744301	−	0.667844i	$-0.767217\pi$
$743$	6.82541	−	21.0064i	0.250400	−	0.770652i	0.994701	−	0.102808i	$-0.0327827\pi$
$744$	−1.17023	+	0.850223i	−0.0429028	+	0.0311707i
$745$	1.16002	+	0.842802i	0.0424997	+	0.0308779i
$746$	7.13398	+	21.9561i	0.261193	+	0.803871i
$747$	17.3290			0.634034
$748$	−9.82114	−	12.0454i	−0.359097	−	0.440423i
$749$	−14.4377			−0.527542
$750$	0.289142	+	0.889888i	0.0105580	+	0.0324941i
$751$	−16.3987	−	11.9143i	−0.598395	−	0.434760i	0.246914	−	0.969037i	$-0.420584\pi$
$751$	−16.3987	−	11.9143i	−0.598395	−	0.434760i	−0.845309	+	0.534278i	$0.820584\pi$
$752$	−1.43558	+	1.04301i	−0.0523503	+	0.0380347i
$753$	−7.54486	+	23.2207i	−0.274950	+	0.846209i
$754$	−5.79896	+	17.8474i	−0.211186	+	0.649963i
$755$	−14.3966	+	10.4597i	−0.523945	+	0.380669i
$756$	−3.87916	−	2.81838i	−0.141084	−	0.102503i
$757$	−1.70285	−	5.24083i	−0.0618911	−	0.190481i	0.915330	−	0.402704i	$-0.131930\pi$
$757$	−1.70285	−	5.24083i	−0.0618911	−	0.190481i	−0.977221	+	0.212223i	$0.931930\pi$
$758$	−31.6315			−1.14891
$759$	10.4092	+	2.75181i	0.377830	+	0.0998843i
$760$	−4.05554			−0.147110
$761$	10.4972	+	32.3070i	0.380523	+	1.17113i	0.939676	+	0.342065i	$0.111126\pi$
$761$	10.4972	+	32.3070i	0.380523	+	1.17113i	−0.559153	+	0.829064i	$0.688874\pi$
$762$	−2.78809	−	2.02567i	−0.101002	−	0.0733823i
$763$	9.85939	−	7.16327i	0.356934	−	0.259328i
$764$	−3.28168	+	10.1000i	−0.118727	+	0.365404i
$765$	−3.07640	+	9.46817i	−0.111227	+	0.342323i
$766$	1.49656	−	1.08731i	0.0540729	−	0.0392862i
$767$	−0.868119	−	0.630726i	−0.0313460	−	0.0227742i
$768$	−0.289142	−	0.889888i	−0.0104335	−	0.0321111i
$769$	0.669422			0.0241400			0.0120700	−	0.999927i	$-0.496158\pi$
$769$	0.669422			0.0241400			0.0120700	+	0.999927i	$0.496158\pi$
$770$	−1.79704	+	2.78759i	−0.0647608	+	0.100458i
$771$	−5.16436			−0.185990
$772$	2.46640	+	7.59081i	0.0887678	+	0.273199i
$773$	26.4800	+	19.2388i	0.952419	+	0.691973i	0.951378	−	0.308027i	$-0.0996686\pi$
$773$	26.4800	+	19.2388i	0.952419	+	0.691973i	0.00104112	+	0.999999i	$0.499669\pi$
$774$	13.7000	−	9.95367i	0.492438	−	0.357777i
$775$	0.477714	−	1.47025i	0.0171600	−	0.0528130i
$776$	−3.50235	+	10.7791i	−0.125727	+	0.386948i
$777$	−3.72907	+	2.70933i	−0.133780	+	0.0971966i
$778$	12.6712	+	9.20614i	0.454283	+	0.330056i
$779$	2.06882	+	6.36719i	0.0741233	+	0.228128i
$780$	2.35228			0.0842251
$781$	1.20760	+	21.6545i	0.0432112	+	0.774859i
$782$	16.2579			0.581382
$783$	−11.0604	−	34.0404i	−0.395266	−	1.21651i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	5.89890	−	4.28580i	0.210541	−	0.152967i
$786$	2.48021	−	7.63329i	0.0884661	−	0.272271i
$787$	−5.25110	+	16.1612i	−0.187182	+	0.576086i	−0.999979	−	0.00646064i	$-0.997944\pi$
$787$	−5.25110	+	16.1612i	−0.187182	+	0.576086i	0.812798	+	0.582546i	$0.197944\pi$
$788$	5.89466	−	4.28272i	0.209989	−	0.152566i
$789$	−20.5766	−	14.9498i	−0.732546	−	0.532226i
$790$	3.04746	+	9.37911i	0.108424	+	0.333694i
$791$	−11.7294			−0.417050
$792$	0.392330	+	7.03523i	0.0139408	+	0.249986i
$793$	−15.4659			−0.549212
$794$	4.57983	+	14.0953i	0.162532	+	0.500223i
$795$	5.40711	+	3.92850i	0.191771	+	0.139329i
$796$	−11.4761	+	8.33789i	−0.406760	+	0.295529i
$797$	14.3562	−	44.1838i	0.508522	−	1.56507i	−0.286245	−	0.958156i	$-0.592407\pi$
$797$	14.3562	−	44.1838i	0.508522	−	1.56507i	0.794767	−	0.606914i	$-0.207593\pi$
$798$	1.17263	−	3.60898i	0.0415106	−	0.127756i
$799$	−6.72716	+	4.88757i	−0.237990	+	0.172910i
$800$	0.809017	+	0.587785i	0.0286031	+	0.0207813i
$801$	−0.656822	−	2.02149i	−0.0232077	−	0.0714259i
$802$	−14.4322			−0.509619
$803$	−1.53714	+	2.38443i	−0.0542443	+	0.0841445i
$804$	5.60857			0.197799
$805$	−1.07212	−	3.29965i	−0.0377873	−	0.116297i
$806$	−3.14415	−	2.28436i	−0.110748	−	0.0804630i
$807$	−6.16549	+	4.47949i	−0.217035	+	0.157685i
$808$	−0.978533	+	3.01161i	−0.0344247	+	0.105948i
$809$	0.879786	−	2.70770i	0.0309316	−	0.0951977i	−0.934399	−	0.356229i	$-0.884062\pi$
$809$	0.879786	−	2.70770i	0.0309316	−	0.0951977i	0.965330	+	0.261031i	$0.0840624\pi$
$810$	1.52659	−	1.10914i	0.0536391	−	0.0389711i
$811$	−1.18621	−	0.861833i	−0.0416535	−	0.0302630i	0.566764	−	0.823880i	$-0.308195\pi$
$811$	−1.18621	−	0.861833i	−0.0416535	−	0.0302630i	−0.608417	+	0.793617i	$0.708195\pi$
$812$	−2.30670	−	7.09929i	−0.0809492	−	0.249136i
$813$	5.90032			0.206933
$814$	15.7958	+	4.17582i	0.553642	+	0.146362i
$815$	9.41304			0.329724
$816$	−1.35492	−	4.17003i	−0.0474319	−	0.145980i
$817$	26.1526	+	19.0010i	0.914964	+	0.664760i
$818$	−30.7701	+	22.3558i	−1.07585	+	0.781651i
$819$	1.65043	−	5.07951i	0.0576708	−	0.177493i
$820$	0.510123	−	1.57000i	0.0178143	−	0.0548267i
$821$	15.8964	−	11.5494i	0.554789	−	0.403078i	−0.274759	−	0.961513i	$-0.588598\pi$
$821$	15.8964	−	11.5494i	0.554789	−	0.403078i	0.829548	+	0.558435i	$0.188598\pi$
$822$	−1.23454	−	0.896944i	−0.0430594	−	0.0312845i
$823$	−5.27652	−	16.2395i	−0.183928	−	0.566072i	0.816000	−	0.578051i	$-0.196187\pi$
$823$	−5.27652	−	16.2395i	−0.183928	−	0.566072i	−0.999928	+	0.0119797i	$0.996187\pi$
$824$	−15.0475			−0.524203
$825$	1.96104	+	2.40517i	0.0682747	+	0.0837373i
$826$	0.426837			0.0148516
$827$	4.93881	+	15.2001i	0.171739	+	0.528559i	0.999470	−	0.0325673i	$-0.0103683\pi$
$827$	4.93881	+	15.2001i	0.171739	+	0.528559i	−0.827730	+	0.561126i	$0.810368\pi$
$828$	−5.96314	−	4.33247i	−0.207233	−	0.150564i
$829$	−14.2757	+	10.3719i	−0.495817	+	0.360232i	−0.807417	−	0.589981i	$-0.799135\pi$
$829$	−14.2757	+	10.3719i	−0.495817	+	0.360232i	0.311600	+	0.950213i	$0.399135\pi$
$830$	2.52057	−	7.75752i	0.0874903	−	0.269268i
$831$	7.55805	−	23.2613i	0.262186	−	0.806925i
$832$	2.03384	−	1.47767i	0.0705108	−	0.0512291i
$833$	−3.79107	−	2.75437i	−0.131353	−	0.0954333i
$834$	−6.70228	−	20.6275i	−0.232081	−	0.714272i
$835$	−0.289918			−0.0100330
$836$	−12.5411	+	4.86233i	−0.433743	+	0.168167i
$837$	7.41251			0.256214
$838$	−7.48247	−	23.0287i	−0.258477	−	0.795512i
$839$	−6.44158	−	4.68008i	−0.222388	−	0.161574i	0.471013	−	0.882126i	$-0.343889\pi$
$839$	−6.44158	−	4.68008i	−0.222388	−	0.161574i	−0.693401	+	0.720552i	$0.743889\pi$
$840$	−0.756984	+	0.549981i	−0.0261184	+	0.0189761i
$841$	8.25715	−	25.4129i	0.284729	−	0.876307i
$842$	−11.9490	+	36.7752i	−0.411790	+	1.26736i
$843$	11.1546	−	8.10432i	0.384186	−	0.279128i
$844$	18.8315	+	13.6819i	0.648208	+	0.470951i
$845$	−2.06422	−	6.35303i	−0.0710114	−	0.218551i
$846$	3.76987			0.129611
$847$	−2.21491	+	10.7747i	−0.0761052	+	0.370223i
$848$	7.14297			0.245291
$849$	−6.21829	−	19.1379i	−0.213411	−	0.656812i
$850$	3.79107	+	2.75437i	0.130033	+	0.0944742i
$851$	−13.8272	+	10.0460i	−0.473989	+	0.344373i
$852$	−1.89076	+	5.81917i	−0.0647765	+	0.199362i
$853$	−12.1523	+	37.4009i	−0.416086	+	1.28058i	0.495189	+	0.868785i	$0.335099\pi$
$853$	−12.1523	+	37.4009i	−0.416086	+	1.28058i	−0.911276	+	0.411797i	$0.864901\pi$
$854$	4.97708	−	3.61606i	0.170312	−	0.123739i
$855$	6.97048	+	5.06435i	0.238385	+	0.173197i
$856$	4.46149	+	13.7311i	0.152491	+	0.469318i
$857$	−42.5288			−1.45276			−0.726379	−	0.687295i	$-0.758798\pi$
$857$	−42.5288			−1.45276			−0.726379	+	0.687295i	$0.758798\pi$
$858$	7.27404	−	2.82023i	0.248332	−	0.0962810i
$859$	36.8680			1.25792			0.628960	−	0.777438i	$-0.283481\pi$
$859$	36.8680			1.25792			0.628960	+	0.777438i	$0.283481\pi$
$860$	−2.46315	−	7.58080i	−0.0839927	−	0.258503i
$861$	1.24962	+	0.907904i	0.0425870	+	0.0309413i
$862$	−19.0951	+	13.8734i	−0.650383	+	0.472531i
$863$	7.75554	−	23.8691i	0.264002	−	0.812514i	−0.727920	−	0.685662i	$-0.759513\pi$
$863$	7.75554	−	23.8691i	0.264002	−	0.812514i	0.991922	−	0.126852i	$-0.0404872\pi$
$864$	−1.48171	+	4.56023i	−0.0504087	+	0.155142i
$865$	8.42898	−	6.12401i	0.286594	−	0.208223i
$866$	−24.7990	−	18.0175i	−0.842703	−	0.612260i
$867$	−1.43379	−	4.41274i	−0.0486939	−	0.149865i
$868$	1.54591			0.0524717
$869$	20.6687	+	25.3497i	0.701138	+	0.859929i
$870$	−6.98453			−0.236798
$871$	4.65656	+	14.3314i	0.157782	+	0.485602i
$872$	−9.85939	−	7.16327i	−0.333881	−	0.242579i
$873$	19.4801	−	14.1531i	0.659301	−	0.479010i
$874$	4.34803	−	13.3819i	0.147074	−	0.452648i
$875$	0.309017	−	0.951057i	0.0104467	−	0.0321516i
$876$	−0.647503	+	0.470438i	−0.0218771	+	0.0158946i
$877$	44.2073	+	32.1185i	1.49278	+	1.08456i	0.973150	+	0.230170i	$0.0739283\pi$
$877$	44.2073	+	32.1185i	1.49278	+	1.08456i	0.519625	+	0.854395i	$0.326072\pi$
$878$	−7.23571	−	22.2692i	−0.244193	−	0.751550i
$879$	5.72268			0.193021
$880$	3.20647	+	0.847672i	0.108090	+	0.0285750i
$881$	−49.1584			−1.65619			−0.828094	−	0.560590i	$-0.810575\pi$
$881$	−49.1584			−1.65619			−0.828094	+	0.560590i	$0.810575\pi$
$882$	0.656505	+	2.02052i	0.0221057	+	0.0680343i
$883$	21.7830	+	15.8262i	0.733055	+	0.532595i	0.890528	−	0.454928i	$-0.150335\pi$
$883$	21.7830	+	15.8262i	0.733055	+	0.532595i	−0.157474	+	0.987523i	$0.550335\pi$
$884$	9.53062	−	6.92440i	0.320550	−	0.232893i
$885$	0.123417	−	0.379837i	0.00414860	−	0.0127681i
$886$	−0.257484	+	0.792455i	−0.00865035	+	0.0266231i
$887$	−25.7369	+	18.6990i	−0.864162	+	0.627851i	−0.929014	−	0.370044i	$-0.879342\pi$
$887$	−25.7369	+	18.6990i	−0.864162	+	0.627851i	0.0648520	+	0.997895i	$0.479342\pi$
$888$	3.72907	+	2.70933i	0.125139	+	0.0909191i
$889$	1.13816	+	3.50290i	0.0381727	+	0.117483i
$890$	−1.00048			−0.0335363
$891$	3.39096	−	5.26011i	0.113602	−	0.176220i
$892$	−8.09748			−0.271124
$893$	2.22383	+	6.84424i	0.0744176	+	0.229034i
$894$	1.08541	+	0.788595i	0.0363015	+	0.0263746i
$895$	12.0637	−	8.76478i	0.403245	−	0.292974i
$896$	−0.309017	+	0.951057i	−0.0103235	+	0.0317726i
$897$	−2.52192	+	7.76169i	−0.0842046	+	0.259155i
$898$	−4.83817	+	3.51513i	−0.161452	+	0.117302i
$899$	9.33579	+	6.78285i	0.311366	+	0.226221i
$900$	−0.656505	−	2.02052i	−0.0218835	−	0.0673505i
$901$	33.4721			1.11512
$902$	−0.304851	−	5.46656i	−0.0101504	−	0.182017i
$903$	7.45826			0.248195
$904$	3.62459	+	11.1553i	0.120552	+	0.371021i
$905$	−3.53808	−	2.57056i	−0.117610	−	0.0854484i
$906$	−13.4706	+	9.78700i	−0.447532	+	0.325151i
$907$	8.60487	−	26.4831i	0.285720	−	0.879355i	−0.700462	−	0.713690i	$-0.747023\pi$
$907$	8.60487	−	26.4831i	0.285720	−	0.879355i	0.986182	−	0.165666i	$-0.0529773\pi$
$908$	−5.82046	+	17.9135i	−0.193159	+	0.594481i
$909$	5.44260	−	3.95428i	0.180520	−	0.131155i
$910$	−2.03384	−	1.47767i	−0.0674212	−	0.0489844i
$911$	−16.9951	−	52.3056i	−0.563074	−	1.73296i	−0.673607	−	0.739090i	$-0.735256\pi$
$911$	−16.9951	−	52.3056i	−0.563074	−	1.73296i	0.110533	−	0.993872i	$-0.464744\pi$
$912$	−3.79470			−0.125655
$913$	−1.50630	−	27.0109i	−0.0498514	−	0.893930i
$914$	41.9762			1.38845
$915$	−1.77880	−	5.47460i	−0.0588055	−	0.180985i
$916$	−8.79574	−	6.39048i	−0.290619	−	0.211147i
$917$	−6.93960	+	5.04191i	−0.229166	+	0.166499i
$918$	−6.94331	+	21.3693i	−0.229163	+	0.705292i
$919$	5.22285	−	16.0743i	0.172286	−	0.530241i	−0.827213	−	0.561888i	$-0.810075\pi$
$919$	5.22285	−	16.0743i	0.172286	−	0.530241i	0.999499	+	0.0316468i	$0.0100752\pi$
$920$	−2.80685	+	2.03929i	−0.0925390	+	0.0672335i
$921$	18.8278	+	13.6792i	0.620396	+	0.450744i
$922$	9.93408	+	30.5740i	0.327162	+	1.00690i
$923$	−16.4394			−0.541109
$924$	−1.68146	+	2.60830i	−0.0553159	+	0.0858068i
$925$	−4.92622			−0.161973
$926$	2.51733	+	7.74754i	0.0827246	+	0.254600i
$927$	25.8629	+	18.7905i	0.849448	+	0.617160i
$928$	−6.03901	+	4.38760i	−0.198240	+	0.144030i
$929$	−5.22802	+	16.0902i	−0.171526	+	0.527902i	−0.999458	−	0.0329263i	$-0.989517\pi$
$929$	−5.22802	+	16.0902i	−0.171526	+	0.527902i	0.827932	+	0.560829i	$0.189517\pi$
$930$	0.446989	−	1.37569i	0.0146573	−	0.0451107i
$931$	−3.28100	+	2.38379i	−0.107530	+	0.0781255i
$932$	7.26205	+	5.27619i	0.237876	+	0.172827i
$933$	−0.977144	−	3.00734i	−0.0319903	−	0.0984559i
$934$	−7.67994			−0.251295
$935$	15.0256	+	3.97221i	0.491389	+	0.129905i
$936$	−5.34092			−0.174573
$937$	−1.76425	−	5.42980i	−0.0576355	−	0.177384i	0.918094	−	0.396362i	$-0.129728\pi$
$937$	−1.76425	−	5.42980i	−0.0576355	−	0.177384i	−0.975730	+	0.218978i	$0.929728\pi$
$938$	−4.84932	−	3.52324i	−0.158336	−	0.115038i
$939$	−15.6999	+	11.4067i	−0.512348	+	0.372242i
$940$	0.548343	−	1.68763i	0.0178850	−	0.0550443i
$941$	−10.5900	+	32.5926i	−0.345224	+	1.06249i	0.616240	+	0.787558i	$0.288655\pi$
$941$	−10.5900	+	32.5926i	−0.345224	+	1.06249i	−0.961464	+	0.274931i	$0.911345\pi$
$942$	5.51950	−	4.01015i	0.179835	−	0.130658i
$943$	4.63352	+	3.36645i	0.150888	+	0.109627i
$944$	−0.131900	−	0.405946i	−0.00429298	−	0.0132124i
$945$	4.79491			0.155978
$946$	−16.7058	−	20.4892i	−0.543152	−	0.666162i
$947$	−29.4856			−0.958154			−0.479077	−	0.877773i	$-0.659029\pi$
$947$	−29.4856			−0.958154			−0.479077	+	0.877773i	$0.659029\pi$
$948$	2.85146	+	8.77588i	0.0926110	+	0.285027i
$949$	−1.73969	−	1.26396i	−0.0564728	−	0.0410299i
$950$	3.28100	−	2.38379i	0.106450	−	0.0773403i
$951$	−2.15758	+	6.64034i	−0.0699643	+	0.215328i
$952$	−1.44806	+	4.45667i	−0.0469319	+	0.144441i
$953$	35.4702	−	25.7706i	1.14899	−	0.834791i	0.160645	−	0.987012i	$-0.448643\pi$
$953$	35.4702	−	25.7706i	1.14899	−	0.834791i	0.988346	+	0.152221i	$0.0486427\pi$
$954$	−12.2770	−	8.91977i	−0.397483	−	0.288788i
$955$	−3.28168	−	10.1000i	−0.106193	−	0.326827i
$956$	−9.78125			−0.316348
$957$	−21.5985	+	8.37400i	−0.698181	+	0.270693i
$958$	22.7225			0.734131
$959$	0.503965	+	1.55104i	0.0162739	+	0.0500858i
$960$	0.756984	+	0.549981i	0.0244315	+	0.0177506i
$961$	23.1461	−	16.8166i	0.746648	−	0.542472i
$962$	−3.82698	+	11.7782i	−0.123387	+	0.379745i
$963$	9.47842	−	29.1716i	0.305438	−	0.940041i
$964$	−18.9192	+	13.7456i	−0.609347	+	0.442717i
$965$	−6.45713	−	4.69138i	−0.207862	−	0.151021i
$966$	−1.00317	−	3.08742i	−0.0322763	−	0.0993363i
$967$	−43.1164			−1.38653			−0.693265	−	0.720683i	$-0.743828\pi$
$967$	−43.1164			−1.38653			−0.693265	+	0.720683i	$0.743828\pi$
$968$	10.9318	−	1.22306i	0.351361	−	0.0393106i
$969$	−17.7820			−0.571242
$970$	−3.50235	−	10.7791i	−0.112454	−	0.346097i
$971$	45.0549	+	32.7343i	1.44588	+	1.05049i	0.986772	+	0.162115i	$0.0518315\pi$
$971$	45.0549	+	32.7343i	1.44588	+	1.05049i	0.459110	+	0.888380i	$0.348169\pi$
$972$	13.0659	−	9.49293i	0.419089	−	0.304486i
$973$	−7.16298	+	22.0454i	−0.229634	+	0.706742i
$974$	−10.3353	+	31.8088i	−0.331165	+	1.01922i
$975$	−1.90303	+	1.38263i	−0.0609458	+	0.0442797i
$976$	−4.97708	−	3.61606i	−0.159312	−	0.115747i
$977$	−2.97750	−	9.16381i	−0.0952588	−	0.293176i	0.892062	−	0.451913i	$-0.149258\pi$
$977$	−2.97750	−	9.16381i	−0.0952588	−	0.293176i	−0.987321	+	0.158736i	$0.949258\pi$
$978$	8.80763			0.281637
$979$	−3.09383	+	1.19951i	−0.0988793	+	0.0383366i
$980$	1.00000			0.0319438
$981$	8.00075	+	24.6238i	0.255444	+	0.786177i
$982$	4.94302	+	3.59132i	0.157738	+	0.114603i
$983$	−44.1493	+	32.0764i	−1.40814	+	1.02308i	−0.414556	+	0.910024i	$0.636063\pi$
$983$	−44.1493	+	32.0764i	−1.40814	+	1.02308i	−0.993589	+	0.113053i	$0.963937\pi$
$984$	0.477314	−	1.46902i	0.0152162	−	0.0468306i
$985$	−2.25156	+	6.92959i	−0.0717407	+	0.220795i
$986$	−28.2989	+	20.5604i	−0.901221	+	0.654776i
$987$	1.34325	+	0.975928i	0.0427561	+	0.0310641i
$988$	−3.15058	−	9.69650i	−0.100233	−	0.308487i
$989$	27.6547			0.879370
$990$	−4.45260	−	5.46101i	−0.141513	−	0.173562i
$991$	−50.0492			−1.58986			−0.794932	−	0.606699i	$-0.792494\pi$
$991$	−50.0492			−1.58986			−0.794932	+	0.606699i	$0.792494\pi$
$992$	−0.477714	−	1.47025i	−0.0151674	−	0.0466805i
$993$	−6.25800	−	4.54670i	−0.198592	−	0.144285i
$994$	5.29034	−	3.84366i	0.167799	−	0.121913i
$995$	4.38349	−	13.4910i	0.138966	−	0.427693i
$996$	2.35846	−	7.25858i	0.0747306	−	0.229997i
$997$	−18.5199	+	13.4555i	−0.586532	+	0.426141i	−0.841073	−	0.540921i	$-0.818076\pi$
$997$	−18.5199	+	13.4555i	−0.586532	+	0.426141i	0.254541	+	0.967062i	$0.418076\pi$
$998$	17.0859	+	12.4136i	0.540844	+	0.392946i
$999$	−7.29922	−	22.4647i	−0.230937	−	0.710751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.j.71.2	✓	12
11.3	even	5		8470.2.a.cw.1.3		6
11.8	odd	10		8470.2.a.dc.1.3		6
11.9	even	5	inner	770.2.n.j.141.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.j.71.2	✓	12	1.1	even	1	trivial
770.2.n.j.141.2	yes	12	11.9	even	5	inner
8470.2.a.cw.1.3		6	11.3	even	5
8470.2.a.dc.1.3		6	11.8	odd	10

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)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.756984 + 0.549981i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.289142 - 0.889888i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.656505 - 2.02052i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.756984 + 0.549981i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.289142 - 0.889888i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.656505 - 2.02052i) q^{9} -1.00000 q^{10} +(-3.09234 + 1.19893i) q^{11} -0.935683 q^{12} +(-0.776859 - 2.39093i) q^{13} +(0.809017 + 0.587785i) q^{14} +(0.756984 - 0.549981i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.44806 - 4.45667i) q^{17} +(-1.71875 + 1.24875i) q^{18} +(-3.28100 - 2.38379i) q^{19} +(0.309017 + 0.951057i) q^{20} -0.935683 q^{21} +(2.09584 + 2.57050i) q^{22} -3.46945 q^{23} +(0.289142 + 0.889888i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-2.03384 + 1.47767i) q^{26} +(1.48171 - 4.56023i) q^{27} +(0.309017 - 0.951057i) q^{28} +(6.03901 - 4.38760i) q^{29} +(-0.756984 - 0.549981i) q^{30} +(0.477714 + 1.47025i) q^{31} -1.00000 q^{32} +(-3.00024 - 0.793153i) q^{33} -4.68602 q^{34} +(0.309017 + 0.951057i) q^{35} +(1.71875 + 1.24875i) q^{36} +(3.98540 - 2.89556i) q^{37} +(-1.25323 + 3.85705i) q^{38} +(0.726894 - 2.23715i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-1.33552 - 0.970311i) q^{41} +(0.289142 + 0.889888i) q^{42} -7.97092 q^{43} +(1.79704 - 2.78759i) q^{44} -2.12450 q^{45} +(1.07212 + 3.29965i) q^{46} +(-1.43558 - 1.04301i) q^{47} +(0.756984 - 0.549981i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(3.54724 - 2.57722i) q^{51} +(2.03384 + 1.47767i) q^{52} +(2.20730 + 6.79337i) q^{53} -4.79491 q^{54} +(0.184670 + 3.31148i) q^{55} -1.00000 q^{56} +(-1.17263 - 3.60898i) q^{57} +(-6.03901 - 4.38760i) q^{58} +(0.345318 - 0.250889i) q^{59} +(-0.289142 + 0.889888i) q^{60} +(1.90107 - 5.85091i) q^{61} +(1.25067 - 0.908665i) q^{62} +(1.71875 + 1.24875i) q^{63} +(0.309017 + 0.951057i) q^{64} -2.51397 q^{65} +(0.172792 + 3.09850i) q^{66} -5.99409 q^{67} +(1.44806 + 4.45667i) q^{68} +(-2.62632 - 1.90813i) q^{69} +(0.809017 - 0.587785i) q^{70} +(2.02073 - 6.21917i) q^{71} +(0.656505 - 2.02052i) q^{72} +(0.692010 - 0.502775i) q^{73} +(-3.98540 - 2.89556i) q^{74} +(-0.289142 - 0.889888i) q^{75} +4.05554 q^{76} +(1.79704 - 2.78759i) q^{77} -2.35228 q^{78} +(-3.04746 - 9.37911i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(-1.52659 + 1.10914i) q^{81} +(-0.510123 + 1.57000i) q^{82} +(-2.52057 + 7.75752i) q^{83} +(0.756984 - 0.549981i) q^{84} +(-3.79107 - 2.75437i) q^{85} +(2.46315 + 7.58080i) q^{86} +6.98453 q^{87} +(-3.20647 - 0.847672i) q^{88} +1.00048 q^{89} +(0.656505 + 2.02052i) q^{90} +(2.03384 + 1.47767i) q^{91} +(2.80685 - 2.03929i) q^{92} +(-0.446989 + 1.37569i) q^{93} +(-0.548343 + 1.68763i) q^{94} +(-3.28100 + 2.38379i) q^{95} +(-0.756984 - 0.549981i) q^{96} +(3.50235 + 10.7791i) q^{97} -1.00000 q^{98} +(4.45260 + 5.46101i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 12 q^{10} - q^{11} - 2 q^{12} + 2 q^{13} + 3 q^{14} + 3 q^{15} - 3 q^{16} + 7 q^{17} + 9 q^{18} + 6 q^{19} - 3 q^{20} - 2 q^{21} + q^{22} + 8 q^{23} + 2 q^{24} - 3 q^{25} - 7 q^{26} - 3 q^{27} - 3 q^{28} + 20 q^{29} - 3 q^{30} + 6 q^{31} - 12 q^{32} - 12 q^{33} + 18 q^{34} - 3 q^{35} - 9 q^{36} + 22 q^{37} - 6 q^{38} + 23 q^{39} + 3 q^{40} + 2 q^{41} + 2 q^{42} - 60 q^{43} - 11 q^{44} + 6 q^{45} + 2 q^{46} - 4 q^{47} + 3 q^{48} - 3 q^{49} + 3 q^{50} + 13 q^{51} + 7 q^{52} + 18 q^{53} + 8 q^{54} + 14 q^{55} - 12 q^{56} + 8 q^{57} - 20 q^{58} - 32 q^{59} - 2 q^{60} + 8 q^{61} + 14 q^{62} - 9 q^{63} - 3 q^{64} - 18 q^{65} - 8 q^{66} + 36 q^{67} + 7 q^{68} + 50 q^{69} + 3 q^{70} - 34 q^{71} - 6 q^{72} + 14 q^{73} - 22 q^{74} - 2 q^{75} - 24 q^{76} - 11 q^{77} - 38 q^{78} - 12 q^{79} - 3 q^{80} + 4 q^{81} - 2 q^{82} + 30 q^{83} + 3 q^{84} + 2 q^{85} - 28 q^{87} + q^{88} - 36 q^{89} - 6 q^{90} + 7 q^{91} - 2 q^{92} + 12 q^{93} - 11 q^{94} + 6 q^{95} - 3 q^{96} + 39 q^{97} - 12 q^{98} - 15 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 - 12 * q^10 - q^11 - 2 * q^12 + 2 * q^13 + 3 * q^14 + 3 * q^15 - 3 * q^16 + 7 * q^17 + 9 * q^18 + 6 * q^19 - 3 * q^20 - 2 * q^21 + q^22 + 8 * q^23 + 2 * q^24 - 3 * q^25 - 7 * q^26 - 3 * q^27 - 3 * q^28 + 20 * q^29 - 3 * q^30 + 6 * q^31 - 12 * q^32 - 12 * q^33 + 18 * q^34 - 3 * q^35 - 9 * q^36 + 22 * q^37 - 6 * q^38 + 23 * q^39 + 3 * q^40 + 2 * q^41 + 2 * q^42 - 60 * q^43 - 11 * q^44 + 6 * q^45 + 2 * q^46 - 4 * q^47 + 3 * q^48 - 3 * q^49 + 3 * q^50 + 13 * q^51 + 7 * q^52 + 18 * q^53 + 8 * q^54 + 14 * q^55 - 12 * q^56 + 8 * q^57 - 20 * q^58 - 32 * q^59 - 2 * q^60 + 8 * q^61 + 14 * q^62 - 9 * q^63 - 3 * q^64 - 18 * q^65 - 8 * q^66 + 36 * q^67 + 7 * q^68 + 50 * q^69 + 3 * q^70 - 34 * q^71 - 6 * q^72 + 14 * q^73 - 22 * q^74 - 2 * q^75 - 24 * q^76 - 11 * q^77 - 38 * q^78 - 12 * q^79 - 3 * q^80 + 4 * q^81 - 2 * q^82 + 30 * q^83 + 3 * q^84 + 2 * q^85 - 28 * q^87 + q^88 - 36 * q^89 - 6 * q^90 + 7 * q^91 - 2 * q^92 + 12 * q^93 - 11 * q^94 + 6 * q^95 - 3 * q^96 + 39 * q^97 - 12 * q^98 - 15 * q^99

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