LMFDB - Embedded newform 770.2.i.j.221.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(221,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("770.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.i (of order $3$, degree $2$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.2
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	770.221
Dual form			770.2.i.j.331.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.173648 - 0.300767i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.347296 q^{6} +(-2.64543 + 0.0412527i) q^{7} -1.00000 q^{8} +(1.43969 + 2.49362i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.173648 - 0.300767i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.347296 q^{6} +(-2.64543 + 0.0412527i) q^{7} -1.00000 q^{8} +(1.43969 + 2.49362i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.173648 + 0.300767i) q^{12} +6.45336 q^{13} +(-1.35844 - 2.27038i) q^{14} -0.347296 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.06031 + 1.83651i) q^{17} +(-1.43969 + 2.49362i) q^{18} +(2.95084 + 5.11100i) q^{19} +1.00000 q^{20} +(-0.446967 + 0.802823i) q^{21} +1.00000 q^{22} +(4.29086 + 7.43199i) q^{23} +(-0.173648 + 0.300767i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.22668 + 5.58878i) q^{26} +2.04189 q^{27} +(1.28699 - 2.31164i) q^{28} -9.66044 q^{29} +(-0.173648 - 0.300767i) q^{30} +(-4.17752 + 7.23567i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.173648 - 0.300767i) q^{33} -2.12061 q^{34} +(1.35844 + 2.27038i) q^{35} -2.87939 q^{36} +(-5.47178 - 9.47740i) q^{37} +(-2.95084 + 5.11100i) q^{38} +(1.12061 - 1.94096i) q^{39} +(0.500000 + 0.866025i) q^{40} +4.24123 q^{41} +(-0.918748 + 0.0143269i) q^{42} +11.1925 q^{43} +(0.500000 + 0.866025i) q^{44} +(1.43969 - 2.49362i) q^{45} +(-4.29086 + 7.43199i) q^{46} +(4.92127 + 8.52390i) q^{47} -0.347296 q^{48} +(6.99660 - 0.218262i) q^{49} -1.00000 q^{50} +(0.368241 + 0.637812i) q^{51} +(-3.22668 + 5.58878i) q^{52} +(1.70574 - 2.95442i) q^{53} +(1.02094 + 1.76833i) q^{54} -1.00000 q^{55} +(2.64543 - 0.0412527i) q^{56} +2.04963 q^{57} +(-4.83022 - 8.36619i) q^{58} +(1.75877 - 3.04628i) q^{59} +(0.173648 - 0.300767i) q^{60} +(-3.35117 - 5.80439i) q^{61} -8.35504 q^{62} +(-3.91147 - 6.53731i) q^{63} +1.00000 q^{64} +(-3.22668 - 5.58878i) q^{65} +(0.173648 - 0.300767i) q^{66} +(0.911474 - 1.57872i) q^{67} +(-1.06031 - 1.83651i) q^{68} +2.98040 q^{69} +(-1.28699 + 2.31164i) q^{70} -2.22668 q^{71} +(-1.43969 - 2.49362i) q^{72} +(0.194593 - 0.337044i) q^{73} +(5.47178 - 9.47740i) q^{74} +(0.173648 + 0.300767i) q^{75} -5.90167 q^{76} +(-1.28699 + 2.31164i) q^{77} +2.24123 q^{78} +(-2.34730 - 4.06564i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-3.96451 + 6.86673i) q^{81} +(2.12061 + 3.67301i) q^{82} -1.87164 q^{83} +(-0.471782 - 0.788496i) q^{84} +2.12061 q^{85} +(5.59627 + 9.69302i) q^{86} +(-1.67752 + 2.90555i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-4.64930 - 8.05282i) q^{89} +2.87939 q^{90} +(-17.0719 + 0.266219i) q^{91} -8.58172 q^{92} +(1.45084 + 2.51292i) q^{93} +(-4.92127 + 8.52390i) q^{94} +(2.95084 - 5.11100i) q^{95} +(-0.173648 - 0.300767i) q^{96} +5.30541 q^{97} +(3.68732 + 5.95010i) q^{98} +2.87939 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^8 + 3 * q^9	$ 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 12 q^{13} - 3 q^{16} - 12 q^{17} - 3 q^{18} + 6 q^{19} + 6 q^{20} - 15 q^{21} + 6 q^{22} - 6 q^{23} - 3 q^{25} + 6 q^{26} + 6 q^{27} - 12 q^{29} + 3 q^{32} - 24 q^{34} - 6 q^{36} - 18 q^{37} - 6 q^{38} + 18 q^{39} + 3 q^{40} + 48 q^{41} - 3 q^{42} + 12 q^{43} + 3 q^{44} + 3 q^{45} + 6 q^{46} + 12 q^{47} - 6 q^{50} - 3 q^{51} - 6 q^{52} + 3 q^{54} - 6 q^{55} - 42 q^{57} - 6 q^{58} - 12 q^{59} + 6 q^{61} - 3 q^{63} + 6 q^{64} - 6 q^{65} - 15 q^{67} - 12 q^{68} + 12 q^{69} - 3 q^{72} - 3 q^{73} + 18 q^{74} - 12 q^{76} + 36 q^{78} - 12 q^{79} - 3 q^{80} + 9 q^{81} + 24 q^{82} - 48 q^{83} + 12 q^{84} + 24 q^{85} + 6 q^{86} + 15 q^{87} - 3 q^{88} + 12 q^{89} + 6 q^{90} - 36 q^{91} + 12 q^{92} - 3 q^{93} - 12 q^{94} + 6 q^{95} + 36 q^{97} + 6 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 12 * q^13 - 3 * q^16 - 12 * q^17 - 3 * q^18 + 6 * q^19 + 6 * q^20 - 15 * q^21 + 6 * q^22 - 6 * q^23 - 3 * q^25 + 6 * q^26 + 6 * q^27 - 12 * q^29 + 3 * q^32 - 24 * q^34 - 6 * q^36 - 18 * q^37 - 6 * q^38 + 18 * q^39 + 3 * q^40 + 48 * q^41 - 3 * q^42 + 12 * q^43 + 3 * q^44 + 3 * q^45 + 6 * q^46 + 12 * q^47 - 6 * q^50 - 3 * q^51 - 6 * q^52 + 3 * q^54 - 6 * q^55 - 42 * q^57 - 6 * q^58 - 12 * q^59 + 6 * q^61 - 3 * q^63 + 6 * q^64 - 6 * q^65 - 15 * q^67 - 12 * q^68 + 12 * q^69 - 3 * q^72 - 3 * q^73 + 18 * q^74 - 12 * q^76 + 36 * q^78 - 12 * q^79 - 3 * q^80 + 9 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^84 + 24 * q^85 + 6 * q^86 + 15 * q^87 - 3 * q^88 + 12 * q^89 + 6 * q^90 - 36 * q^91 + 12 * q^92 - 3 * q^93 - 12 * q^94 + 6 * q^95 + 36 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.173648	−	0.300767i	0.100256	−	0.173648i	−0.811534	−	0.584305i	$-0.801367\pi$
$3$	0.173648	−	0.300767i	0.100256	−	0.173648i	0.911790	+	0.410657i	$0.134701\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.347296			0.141783
$7$	−2.64543	+	0.0412527i	−0.999878	+	0.0155920i
$7$	−2.64543	+	0.0412527i	−0.999878	+	0.0155920i
$8$	−1.00000			−0.353553
$9$	1.43969	+	2.49362i	0.479898	+	0.831207i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	0.173648	+	0.300767i	0.0501279	+	0.0868241i
$13$	6.45336			1.78984			0.894920	−	0.446226i	$-0.147232\pi$
$13$	6.45336			1.78984			0.894920	+	0.446226i	$0.147232\pi$
$14$	−1.35844	−	2.27038i	−0.363059	−	0.606785i
$15$	−0.347296			−0.0896715
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.06031	+	1.83651i	−0.257162	+	0.445418i	−0.965481	−	0.260475i	$-0.916121\pi$
$17$	−1.06031	+	1.83651i	−0.257162	+	0.445418i	0.708318	+	0.705893i	$0.249454\pi$
$18$	−1.43969	+	2.49362i	−0.339339	+	0.587752i
$19$	2.95084	+	5.11100i	0.676968	+	1.17254i	0.975889	+	0.218266i	$0.0700400\pi$
$19$	2.95084	+	5.11100i	0.676968	+	1.17254i	−0.298921	+	0.954278i	$0.596627\pi$
$20$	1.00000			0.223607
$21$	−0.446967	+	0.802823i	−0.0975361	+	0.175190i
$22$	1.00000			0.213201
$23$	4.29086	+	7.43199i	0.894706	+	1.54968i	0.834168	+	0.551510i	$0.185948\pi$
$23$	4.29086	+	7.43199i	0.894706	+	1.54968i	0.0605380	+	0.998166i	$0.480718\pi$
$24$	−0.173648	+	0.300767i	−0.0354458	+	0.0613939i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.22668	+	5.58878i	0.632804	+	1.09605i
$27$	2.04189			0.392962
$28$	1.28699	−	2.31164i	0.243218	−	0.436858i
$29$	−9.66044			−1.79390			−0.896950	−	0.442133i	$-0.854222\pi$
$29$	−9.66044			−1.79390			−0.896950	+	0.442133i	$0.854222\pi$
$30$	−0.173648	−	0.300767i	−0.0317037	−	0.0549124i
$31$	−4.17752	+	7.23567i	−0.750304	+	1.29957i	0.197371	+	0.980329i	$0.436760\pi$
$31$	−4.17752	+	7.23567i	−0.750304	+	1.29957i	−0.947675	+	0.319237i	$0.896574\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.173648	−	0.300767i	−0.0302283	−	0.0523569i
$34$	−2.12061			−0.363682
$35$	1.35844	+	2.27038i	0.229618	+	0.383765i
$36$	−2.87939			−0.479898
$37$	−5.47178	−	9.47740i	−0.899555	−	1.55808i	−0.828063	−	0.560634i	$-0.810557\pi$
$37$	−5.47178	−	9.47740i	−0.899555	−	1.55808i	−0.0714919	−	0.997441i	$-0.522776\pi$
$38$	−2.95084	+	5.11100i	−0.478689	+	0.829114i
$39$	1.12061	−	1.94096i	0.179442	−	0.310803i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	4.24123			0.662369			0.331184	−	0.943566i	$-0.392552\pi$
$41$	4.24123			0.662369			0.331184	+	0.943566i	$0.392552\pi$
$42$	−0.918748	+	0.0143269i	−0.141766	+	0.00221069i
$43$	11.1925			1.70685			0.853423	−	0.521219i	$-0.174523\pi$
$43$	11.1925			1.70685			0.853423	+	0.521219i	$0.174523\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	1.43969	−	2.49362i	0.214617	−	0.371727i
$46$	−4.29086	+	7.43199i	−0.632653	+	1.09579i
$47$	4.92127	+	8.52390i	0.717842	+	1.24334i	0.961853	+	0.273566i	$0.0882032\pi$
$47$	4.92127	+	8.52390i	0.717842	+	1.24334i	−0.244012	+	0.969772i	$0.578464\pi$
$48$	−0.347296			−0.0501279
$49$	6.99660	−	0.218262i	0.999514	−	0.0311803i
$50$	−1.00000			−0.141421
$51$	0.368241	+	0.637812i	0.0515640	+	0.0893115i
$52$	−3.22668	+	5.58878i	−0.447460	+	0.775024i
$53$	1.70574	−	2.95442i	0.234301	−	0.405821i	−0.724768	−	0.688993i	$-0.758053\pi$
$53$	1.70574	−	2.95442i	0.234301	−	0.405821i	0.959069	+	0.283171i	$0.0913865\pi$
$54$	1.02094	+	1.76833i	0.138933	+	0.240639i
$55$	−1.00000			−0.134840
$56$	2.64543	−	0.0412527i	0.353510	−	0.00551262i
$57$	2.04963			0.271480
$58$	−4.83022	−	8.36619i	−0.634239	−	1.09853i
$59$	1.75877	−	3.04628i	0.228972	−	0.396592i	−0.728531	−	0.685012i	$-0.759797\pi$
$59$	1.75877	−	3.04628i	0.228972	−	0.396592i	0.957504	+	0.288421i	$0.0931301\pi$
$60$	0.173648	−	0.300767i	0.0224179	−	0.0388289i
$61$	−3.35117	−	5.80439i	−0.429073	−	0.743176i	0.567718	−	0.823223i	$-0.307826\pi$
$61$	−3.35117	−	5.80439i	−0.429073	−	0.743176i	−0.996791	+	0.0800469i	$0.974493\pi$
$62$	−8.35504			−1.06109
$63$	−3.91147	−	6.53731i	−0.492799	−	0.823623i
$64$	1.00000			0.125000
$65$	−3.22668	−	5.58878i	−0.400221	−	0.693202i
$66$	0.173648	−	0.300767i	0.0213746	−	0.0370219i
$67$	0.911474	−	1.57872i	0.111354	−	0.192871i	−0.804962	−	0.593326i	$-0.797814\pi$
$67$	0.911474	−	1.57872i	0.111354	−	0.192871i	0.916317	+	0.400455i	$0.131148\pi$
$68$	−1.06031	−	1.83651i	−0.128581	−	0.222709i
$69$	2.98040			0.358798
$70$	−1.28699	+	2.31164i	−0.153825	+	0.276293i
$71$	−2.22668			−0.264258			−0.132129	−	0.991232i	$-0.542181\pi$
$71$	−2.22668			−0.264258			−0.132129	+	0.991232i	$0.542181\pi$
$72$	−1.43969	−	2.49362i	−0.169669	−	0.293876i
$73$	0.194593	−	0.337044i	0.0227754	−	0.0394481i	−0.854413	−	0.519594i	$-0.826083\pi$
$73$	0.194593	−	0.337044i	0.0227754	−	0.0394481i	0.877188	+	0.480146i	$0.159416\pi$
$74$	5.47178	−	9.47740i	0.636082	−	1.10173i
$75$	0.173648	+	0.300767i	0.0200512	+	0.0347296i
$76$	−5.90167			−0.676968
$77$	−1.28699	+	2.31164i	−0.146666	+	0.263435i
$78$	2.24123			0.253769
$79$	−2.34730	−	4.06564i	−0.264091	−	0.457420i	0.703234	−	0.710959i	$-0.251739\pi$
$79$	−2.34730	−	4.06564i	−0.264091	−	0.457420i	−0.967325	+	0.253539i	$0.918405\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−3.96451	+	6.86673i	−0.440501	+	0.762970i
$82$	2.12061	+	3.67301i	0.234183	+	0.405616i
$83$	−1.87164			−0.205440			−0.102720	−	0.994710i	$-0.532755\pi$
$83$	−1.87164			−0.205440			−0.102720	+	0.994710i	$0.532755\pi$
$84$	−0.471782	−	0.788496i	−0.0514756	−	0.0860319i
$85$	2.12061			0.230013
$86$	5.59627	+	9.69302i	0.603461	+	1.04523i
$87$	−1.67752	+	2.90555i	−0.179849	+	0.311507i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−4.64930	−	8.05282i	−0.492825	−	0.853598i	0.507141	−	0.861863i	$-0.330702\pi$
$89$	−4.64930	−	8.05282i	−0.492825	−	0.853598i	−0.999966	+	0.00826546i	$0.997369\pi$
$90$	2.87939			0.303514
$91$	−17.0719	+	0.266219i	−1.78962	+	0.0279073i
$92$	−8.58172			−0.894706
$93$	1.45084	+	2.51292i	0.150445	+	0.260578i
$94$	−4.92127	+	8.52390i	−0.507591	+	0.879173i
$95$	2.95084	−	5.11100i	0.302749	−	0.524377i
$96$	−0.173648	−	0.300767i	−0.0177229	−	0.0306970i
$97$	5.30541			0.538682			0.269341	−	0.963045i	$-0.413194\pi$
$97$	5.30541			0.538682			0.269341	+	0.963045i	$0.413194\pi$
$98$	3.68732	+	5.95010i	0.372475	+	0.601051i
$99$	2.87939			0.289389
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−1.08853	+	1.88538i	−0.108312	+	0.187603i	−0.915087	−	0.403257i	$-0.867878\pi$
$101$	−1.08853	+	1.88538i	−0.108312	+	0.187603i	0.806774	+	0.590860i	$0.201211\pi$
$102$	−0.368241	+	0.637812i	−0.0364613	+	0.0631528i
$103$	5.87939	+	10.1834i	0.579313	+	1.00340i	0.995558	+	0.0941472i	$0.0300124\pi$
$103$	5.87939	+	10.1834i	0.579313	+	1.00340i	−0.416245	+	0.909252i	$0.636654\pi$
$104$	−6.45336			−0.632804
$105$	0.918748	−	0.0143269i	0.0896606	−	0.00139816i
$106$	3.41147			0.331352
$107$	−8.63816	−	14.9617i	−0.835082	−	1.44640i	−0.893964	−	0.448140i	$-0.852087\pi$
$107$	−8.63816	−	14.9617i	−0.835082	−	1.44640i	0.0588816	−	0.998265i	$-0.481247\pi$
$108$	−1.02094	+	1.76833i	−0.0982404	+	0.170157i
$109$	2.97565	−	5.15398i	0.285016	−	0.493662i	−0.687597	−	0.726092i	$-0.741334\pi$
$109$	2.97565	−	5.15398i	0.285016	−	0.493662i	0.972613	+	0.232431i	$0.0746678\pi$
$110$	−0.500000	−	0.866025i	−0.0476731	−	0.0825723i
$111$	−3.80066			−0.360743
$112$	1.35844	+	2.27038i	0.128361	+	0.214531i
$113$	4.85204			0.456442			0.228221	−	0.973609i	$-0.426709\pi$
$113$	4.85204			0.456442			0.228221	+	0.973609i	$0.426709\pi$
$114$	1.02481	+	1.77503i	0.0959827	+	0.166247i
$115$	4.29086	−	7.43199i	0.400125	−	0.693036i
$116$	4.83022	−	8.36619i	0.448475	−	0.776781i
$117$	9.29086	+	16.0922i	0.858940	+	1.48773i
$118$	3.51754			0.323816
$119$	2.72921	−	4.90209i	0.250186	−	0.449374i
$120$	0.347296			0.0317037
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	3.35117	−	5.80439i	0.303400	−	0.525505i
$123$	0.736482	−	1.27562i	0.0664063	−	0.115019i
$124$	−4.17752	−	7.23567i	−0.375152	−	0.649783i
$125$	1.00000			0.0894427
$126$	3.70574	−	6.65609i	0.330133	−	0.592972i
$127$	−1.00000			−0.0887357			−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000			−0.0887357			−0.0443678	+	0.999015i	$0.514127\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.94356	−	3.36635i	0.171121	−	0.296391i
$130$	3.22668	−	5.58878i	0.282999	−	0.490168i
$131$	−1.36571	−	2.36549i	−0.119323	−	0.206674i	0.800177	−	0.599765i	$-0.204739\pi$
$131$	−1.36571	−	2.36549i	−0.119323	−	0.206674i	−0.919500	+	0.393091i	$0.871406\pi$
$132$	0.347296			0.0302283
$133$	−8.01707	−	13.3991i	−0.695168	−	1.16185i
$134$	1.82295			0.157479
$135$	−1.02094	−	1.76833i	−0.0878689	−	0.152193i
$136$	1.06031	−	1.83651i	0.0909206	−	0.157479i
$137$	−4.90167	+	8.48995i	−0.418778	+	0.725345i	−0.995817	−	0.0913716i	$-0.970875\pi$
$137$	−4.90167	+	8.48995i	−0.418778	+	0.725345i	0.577039	+	0.816717i	$0.304208\pi$
$138$	1.49020	+	2.58110i	0.126854	+	0.219718i
$139$	−10.7297			−0.910079			−0.455040	−	0.890471i	$-0.650375\pi$
$139$	−10.7297			−0.910079			−0.455040	+	0.890471i	$0.650375\pi$
$140$	−2.64543	+	0.0412527i	−0.223580	+	0.00348649i
$141$	3.41828			0.287871
$142$	−1.11334	−	1.92836i	−0.0934295	−	0.161825i
$143$	3.22668	−	5.58878i	0.269829	−	0.467357i
$144$	1.43969	−	2.49362i	0.119974	−	0.207802i
$145$	4.83022	+	8.36619i	0.401128	+	0.694774i
$146$	0.389185			0.0322092
$147$	1.14930	−	2.14225i	0.0947927	−	0.176690i
$148$	10.9436			0.899555
$149$	−6.76991	−	11.7258i	−0.554613	−	0.960618i	−0.997934	−	0.0642548i	$-0.979533\pi$
$149$	−6.76991	−	11.7258i	−0.554613	−	0.960618i	0.443320	−	0.896363i	$-0.353800\pi$
$150$	−0.173648	+	0.300767i	−0.0141783	+	0.0245576i
$151$	−1.63041	+	2.82396i	−0.132681	+	0.229811i	−0.924709	−	0.380674i	$-0.875692\pi$
$151$	−1.63041	+	2.82396i	−0.132681	+	0.229811i	0.792028	+	0.610485i	$0.209025\pi$
$152$	−2.95084	−	5.11100i	−0.239344	−	0.414557i
$153$	−6.10607			−0.493646
$154$	−2.64543	+	0.0412527i	−0.213175	+	0.00332424i
$155$	8.35504			0.671093
$156$	1.12061	+	1.94096i	0.0897210	+	0.155401i
$157$	−1.53936	+	2.66625i	−0.122855	+	0.212790i	−0.920892	−	0.389817i	$-0.872538\pi$
$157$	−1.53936	+	2.66625i	−0.122855	+	0.212790i	0.798038	+	0.602607i	$0.205872\pi$
$158$	2.34730	−	4.06564i	0.186741	−	0.323445i
$159$	−0.592396	−	1.02606i	−0.0469801	−	0.0813719i
$160$	−1.00000			−0.0790569
$161$	−11.6578	−	19.4838i	−0.918760	−	1.53554i
$162$	−7.92902			−0.622962
$163$	−2.97431	−	5.15165i	−0.232966	−	0.403509i	0.725714	−	0.687997i	$-0.241510\pi$
$163$	−2.97431	−	5.15165i	−0.232966	−	0.403509i	−0.958680	+	0.284488i	$0.908176\pi$
$164$	−2.12061	+	3.67301i	−0.165592	+	0.286814i
$165$	−0.173648	+	0.300767i	−0.0135185	+	0.0234147i
$166$	−0.935822	−	1.62089i	−0.0726339	−	0.125806i
$167$	15.6236			1.20899			0.604496	−	0.796609i	$-0.293375\pi$
$167$	15.6236			1.20899			0.604496	+	0.796609i	$0.293375\pi$
$168$	0.446967	−	0.802823i	0.0344842	−	0.0619391i
$169$	28.6459			2.20353
$170$	1.06031	+	1.83651i	0.0813219	+	0.140854i
$171$	−8.49660	+	14.7165i	−0.649751	+	1.12540i
$172$	−5.59627	+	9.69302i	−0.426711	+	0.739086i
$173$	1.54664	+	2.67885i	0.117589	+	0.203669i	0.918812	−	0.394696i	$-0.129150\pi$
$173$	1.54664	+	2.67885i	0.117589	+	0.203669i	−0.801223	+	0.598366i	$0.795817\pi$
$174$	−3.35504			−0.254345
$175$	1.28699	−	2.31164i	0.0972872	−	0.174743i
$176$	−1.00000			−0.0753778
$177$	−0.610815	−	1.05796i	−0.0459116	−	0.0795213i
$178$	4.64930	−	8.05282i	0.348480	−	0.603585i
$179$	−6.82295	+	11.8177i	−0.509971	+	0.883296i	0.489962	+	0.871744i	$0.337011\pi$
$179$	−6.82295	+	11.8177i	−0.509971	+	0.883296i	−0.999933	+	0.0115522i	$0.996323\pi$
$180$	1.43969	+	2.49362i	0.107308	+	0.185864i
$181$	11.7297			0.871860			0.435930	−	0.899981i	$-0.356420\pi$
$181$	11.7297			0.871860			0.435930	+	0.899981i	$0.356420\pi$
$182$	−8.76651	−	14.6516i	−0.649817	−	1.08605i
$183$	−2.32770			−0.172068
$184$	−4.29086	−	7.43199i	−0.316326	−	0.547893i
$185$	−5.47178	+	9.47740i	−0.402293	+	0.696793i
$186$	−1.45084	+	2.51292i	−0.106381	+	0.184256i
$187$	1.06031	+	1.83651i	0.0775374	+	0.134299i
$188$	−9.84255			−0.717842
$189$	−5.40167	+	0.0842334i	−0.392914	+	0.00612708i
$190$	5.90167			0.428152
$191$	−0.258770	−	0.448204i	−0.0187240	−	0.0324309i	0.856512	−	0.516128i	$-0.172627\pi$
$191$	−0.258770	−	0.448204i	−0.0187240	−	0.0324309i	−0.875236	+	0.483697i	$0.839294\pi$
$192$	0.173648	−	0.300767i	0.0125320	−	0.0217060i
$193$	9.95471	−	17.2421i	0.716556	−	1.24111i	−0.245801	−	0.969320i	$-0.579051\pi$
$193$	9.95471	−	17.2421i	0.716556	−	1.24111i	0.962357	−	0.271790i	$-0.0876157\pi$
$194$	2.65270	+	4.59462i	0.190453	+	0.329874i
$195$	−2.24123			−0.160498
$196$	−3.30928	+	6.16836i	−0.236377	+	0.440597i
$197$	−9.23173			−0.657734			−0.328867	−	0.944376i	$-0.606667\pi$
$197$	−9.23173			−0.657734			−0.328867	+	0.944376i	$0.606667\pi$
$198$	1.43969	+	2.49362i	0.102314	+	0.177214i
$199$	2.37804	−	4.11889i	0.168575	−	0.291980i	−0.769344	−	0.638835i	$-0.779417\pi$
$199$	2.37804	−	4.11889i	0.168575	−	0.291980i	0.937919	+	0.346854i	$0.112750\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−0.316552	−	0.548284i	−0.0223278	−	0.0386729i
$202$	−2.17705			−0.153177
$203$	25.5560	−	0.398519i	1.79368	−	0.0279706i
$204$	−0.736482			−0.0515640
$205$	−2.12061	−	3.67301i	−0.148110	−	0.256534i
$206$	−5.87939	+	10.1834i	−0.409636	+	0.709511i
$207$	−12.3550	+	21.3996i	−0.858734	+	1.48737i
$208$	−3.22668	−	5.58878i	−0.223730	−	0.387512i
$209$	5.90167			0.408227
$210$	0.471782	+	0.788496i	0.0325560	+	0.0544114i
$211$	11.4875			0.790833			0.395416	−	0.918502i	$-0.370600\pi$
$211$	11.4875			0.790833			0.395416	+	0.918502i	$0.370600\pi$
$212$	1.70574	+	2.95442i	0.117151	+	0.202911i
$213$	−0.386659	+	0.669713i	−0.0264935	+	0.0458880i
$214$	8.63816	−	14.9617i	0.590492	−	1.02276i
$215$	−5.59627	−	9.69302i	−0.381662	−	0.661058i
$216$	−2.04189			−0.138933
$217$	10.7528	−	19.3138i	0.729950	−	1.31111i
$218$	5.95130			0.403073
$219$	−0.0675813	−	0.117054i	−0.00456672	−	0.00790980i
$220$	0.500000	−	0.866025i	0.0337100	−	0.0583874i
$221$	−6.84255	+	11.8516i	−0.460280	+	0.797228i
$222$	−1.90033	−	3.29147i	−0.127542	−	0.220909i
$223$	−13.5175			−0.905201			−0.452601	−	0.891713i	$-0.649504\pi$
$223$	−13.5175			−0.905201			−0.452601	+	0.891713i	$0.649504\pi$
$224$	−1.28699	+	2.31164i	−0.0859906	+	0.154453i
$225$	−2.87939			−0.191959
$226$	2.42602	+	4.20199i	0.161377	+	0.279512i
$227$	5.67499	−	9.82938i	0.376662	−	0.652399i	−0.613912	−	0.789375i	$-0.710405\pi$
$227$	5.67499	−	9.82938i	0.376662	−	0.652399i	0.990574	+	0.136976i	$0.0437383\pi$
$228$	−1.02481	+	1.77503i	−0.0678700	+	0.117554i
$229$	−8.04189	−	13.9290i	−0.531423	−	0.920452i	−0.999327	−	0.0366725i	$-0.988324\pi$
$229$	−8.04189	−	13.9290i	−0.531423	−	0.920452i	0.467904	−	0.883779i	$-0.345009\pi$
$230$	8.58172			0.565862
$231$	0.471782	+	0.788496i	0.0310409	+	0.0518792i
$232$	9.66044			0.634239
$233$	−2.17365	−	3.76487i	−0.142400	−	0.246645i	0.786000	−	0.618227i	$-0.212149\pi$
$233$	−2.17365	−	3.76487i	−0.142400	−	0.246645i	−0.928400	+	0.371582i	$0.878815\pi$
$234$	−9.29086	+	16.0922i	−0.607362	+	1.05198i
$235$	4.92127	−	8.52390i	0.321029	−	0.556038i
$236$	1.75877	+	3.04628i	0.114486	+	0.198296i
$237$	−1.63041			−0.105907
$238$	5.60994	−	0.0874810i	0.363638	−	0.00567055i
$239$	−6.86215			−0.443876			−0.221938	−	0.975061i	$-0.571238\pi$
$239$	−6.86215			−0.443876			−0.221938	+	0.975061i	$0.571238\pi$
$240$	0.173648	+	0.300767i	0.0112089	+	0.0194145i
$241$	−4.63041	+	8.02011i	−0.298271	+	0.516621i	−0.975741	−	0.218930i	$-0.929743\pi$
$241$	−4.63041	+	8.02011i	−0.298271	+	0.516621i	0.677469	+	0.735551i	$0.263077\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$	4.43969	+	7.68977i	0.284806	+	0.493299i
$244$	6.70233			0.429073
$245$	−3.68732	−	5.95010i	−0.235574	−	0.380138i
$246$	1.47296			0.0939127
$247$	19.0428	+	32.9831i	1.21167	+	2.09867i
$248$	4.17752	−	7.23567i	0.265273	−	0.459466i
$249$	−0.325008	+	0.562930i	−0.0205965	+	0.0356742i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−11.7743			−0.743184			−0.371592	−	0.928396i	$-0.621188\pi$
$251$	−11.7743			−0.743184			−0.371592	+	0.928396i	$0.621188\pi$
$252$	7.61721	−	0.118782i	0.479839	−	0.00748258i
$253$	8.58172			0.539528
$254$	−0.500000	−	0.866025i	−0.0313728	−	0.0543393i
$255$	0.368241	−	0.637812i	0.0230601	−	0.0399413i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.04963	−	10.4783i	−0.377366	−	0.653616i	0.613313	−	0.789840i	$-0.289837\pi$
$257$	−6.04963	−	10.4783i	−0.377366	−	0.653616i	−0.990678	+	0.136224i	$0.956503\pi$
$258$	3.88713			0.242002
$259$	14.8662	+	24.8461i	0.923740	+	1.54386i
$260$	6.45336			0.400221
$261$	−13.9081	−	24.0895i	−0.860888	−	1.49110i
$262$	1.36571	−	2.36549i	0.0843741	−	0.146140i
$263$	−2.03074	+	3.51735i	−0.125221	+	0.216889i	−0.921819	−	0.387620i	$-0.873297\pi$
$263$	−2.03074	+	3.51735i	−0.125221	+	0.216889i	0.796598	+	0.604509i	$0.206631\pi$
$264$	0.173648	+	0.300767i	0.0106873	+	0.0185110i
$265$	−3.41147			−0.209565
$266$	7.59539	−	13.6425i	0.465703	−	0.836477i
$267$	−3.22937			−0.197634
$268$	0.911474	+	1.57872i	0.0556771	+	0.0964356i
$269$	−13.3405	+	23.1064i	−0.813384	+	1.40882i	0.0970985	+	0.995275i	$0.469044\pi$
$269$	−13.3405	+	23.1064i	−0.813384	+	1.40882i	−0.910482	+	0.413548i	$0.864290\pi$
$270$	1.02094	−	1.76833i	0.0621327	−	0.107617i
$271$	−4.55438	−	7.88841i	−0.276659	−	0.479187i	0.693894	−	0.720078i	$-0.255894\pi$
$271$	−4.55438	−	7.88841i	−0.276659	−	0.479187i	−0.970552	+	0.240891i	$0.922560\pi$
$272$	2.12061			0.128581
$273$	−2.88444	+	5.18091i	−0.174574	+	0.313563i
$274$	−9.80335			−0.592242
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	−1.49020	+	2.58110i	−0.0896995	+	0.155364i
$277$	16.4388	−	28.4729i	0.987713	−	1.71077i	0.358513	−	0.933525i	$-0.383284\pi$
$277$	16.4388	−	28.4729i	0.987713	−	1.71077i	0.629199	−	0.777244i	$-0.283383\pi$
$278$	−5.36484	−	9.29217i	−0.321762	−	0.557307i
$279$	−24.0574			−1.44028
$280$	−1.35844	−	2.27038i	−0.0811824	−	0.135681i
$281$	−19.9317			−1.18903			−0.594513	−	0.804086i	$-0.702655\pi$
$281$	−19.9317			−1.18903			−0.594513	+	0.804086i	$0.702655\pi$
$282$	1.70914	+	2.96032i	0.101778	+	0.176284i
$283$	10.9436	−	18.9548i	0.650527	−	1.12675i	−0.332468	−	0.943115i	$-0.607881\pi$
$283$	10.9436	−	18.9548i	0.650527	−	1.12675i	0.982995	−	0.183632i	$-0.0587854\pi$
$284$	1.11334	−	1.92836i	0.0660646	−	0.114427i
$285$	−1.02481	−	1.77503i	−0.0607048	−	0.105144i
$286$	6.45336			0.381595
$287$	−11.2199	+	0.174962i	−0.662288	+	0.0103277i
$288$	2.87939			0.169669
$289$	6.25150	+	10.8279i	0.367735	+	0.636936i
$290$	−4.83022	+	8.36619i	−0.283640	+	0.491280i
$291$	0.921274	−	1.59569i	0.0540061	−	0.0935412i
$292$	0.194593	+	0.337044i	0.0113877	+	0.0197240i
$293$	13.3209			0.778215			0.389107	−	0.921192i	$-0.372784\pi$
$293$	13.3209			0.778215			0.389107	+	0.921192i	$0.372784\pi$
$294$	2.42989	−	0.0758016i	0.141714	−	0.00442084i
$295$	−3.51754			−0.204799
$296$	5.47178	+	9.47740i	0.318041	+	0.550863i
$297$	1.02094	−	1.76833i	0.0592412	−	0.102609i
$298$	6.76991	−	11.7258i	0.392171	−	0.679259i
$299$	27.6905	+	47.9613i	1.60138	+	2.77367i
$300$	−0.347296			−0.0200512
$301$	−29.6091	+	0.461722i	−1.70664	+	0.0266132i
$302$	−3.26083			−0.187640
$303$	0.378041	+	0.654786i	0.0217179	+	0.0376165i
$304$	2.95084	−	5.11100i	0.169242	−	0.293136i
$305$	−3.35117	+	5.80439i	−0.191887	+	0.332358i
$306$	−3.05303	−	5.28801i	−0.174530	−	0.302295i
$307$	29.5039			1.68388			0.841939	−	0.539573i	$-0.181414\pi$
$307$	29.5039			1.68388			0.841939	+	0.539573i	$0.181414\pi$
$308$	−1.35844	−	2.27038i	−0.0774043	−	0.129367i
$309$	4.08378			0.232318
$310$	4.17752	+	7.23567i	0.237267	+	0.410959i
$311$	−5.37077	+	9.30244i	−0.304548	+	0.527493i	−0.977161	−	0.212502i	$-0.931839\pi$
$311$	−5.37077	+	9.30244i	−0.304548	+	0.527493i	0.672612	+	0.739995i	$0.265172\pi$
$312$	−1.12061	+	1.94096i	−0.0634423	+	0.109885i
$313$	13.5621	+	23.4903i	0.766576	+	1.32775i	0.939409	+	0.342798i	$0.111375\pi$
$313$	13.5621	+	23.4903i	0.766576	+	1.32775i	−0.172833	+	0.984951i	$0.555292\pi$
$314$	−3.07873			−0.173743
$315$	−3.70574	+	6.65609i	−0.208795	+	0.375028i
$316$	4.69459			0.264091
$317$	−5.44104	−	9.42415i	−0.305599	−	0.529313i	0.671795	−	0.740737i	$-0.265523\pi$
$317$	−5.44104	−	9.42415i	−0.305599	−	0.529313i	−0.977395	+	0.211424i	$0.932190\pi$
$318$	0.592396	−	1.02606i	0.0332199	−	0.0575386i
$319$	−4.83022	+	8.36619i	−0.270441	+	0.468417i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−6.00000			−0.334887
$322$	11.0446	−	19.8378i	0.615490	−	1.10552i
$323$	−12.5152			−0.696363
$324$	−3.96451	−	6.86673i	−0.220250	−	0.381485i
$325$	−3.22668	+	5.58878i	−0.178984	+	0.310010i
$326$	2.97431	−	5.15165i	0.164732	−	0.285324i
$327$	−1.03343	−	1.78996i	−0.0571490	−	0.0989849i
$328$	−4.24123			−0.234183
$329$	−13.3705	−	22.3464i	−0.737141	−	1.23199i
$330$	−0.347296			−0.0191180
$331$	−0.893933	−	1.54834i	−0.0491350	−	0.0851043i	0.840412	−	0.541948i	$-0.182313\pi$
$331$	−0.893933	−	1.54834i	−0.0491350	−	0.0851043i	−0.889547	+	0.456844i	$0.848980\pi$
$332$	0.935822	−	1.62089i	0.0513599	−	0.0889580i
$333$	15.7554	−	27.2891i	0.863389	−	1.49543i
$334$	7.81180	+	13.5304i	0.427443	+	0.740353i
$335$	−1.82295			−0.0995983
$336$	0.918748	−	0.0143269i	0.0501218	−	0.000781597i
$337$	16.0077			0.871997			0.435999	−	0.899947i	$-0.356395\pi$
$337$	16.0077			0.871997			0.435999	+	0.899947i	$0.356395\pi$
$338$	14.3229	+	24.8081i	0.779066	+	1.34938i
$339$	0.842549	−	1.45934i	0.0457610	−	0.0792603i
$340$	−1.06031	+	1.83651i	−0.0575032	+	0.0995985i
$341$	4.17752	+	7.23567i	0.226225	+	0.391834i
$342$	−16.9932			−0.918887
$343$	−18.5000	+	0.866025i	−0.998906	+	0.0467610i
$344$	−11.1925			−0.603461
$345$	−1.49020	−	2.58110i	−0.0802297	−	0.138962i
$346$	−1.54664	+	2.67885i	−0.0831477	+	0.144016i
$347$	−7.23442	+	12.5304i	−0.388364	+	0.672666i	−0.992230	−	0.124420i	$-0.960293\pi$
$347$	−7.23442	+	12.5304i	−0.388364	+	0.672666i	0.603866	+	0.797086i	$0.293626\pi$
$348$	−1.67752	−	2.90555i	−0.0899244	−	0.155754i
$349$	−7.17293			−0.383958			−0.191979	−	0.981399i	$-0.561491\pi$
$349$	−7.17293			−0.383958			−0.191979	+	0.981399i	$0.561491\pi$
$350$	2.64543	−	0.0412527i	0.141404	−	0.00220505i
$351$	13.1771			0.703339
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	4.49020	−	7.77725i	0.238989	−	0.413941i	−0.721435	−	0.692482i	$-0.756517\pi$
$353$	4.49020	−	7.77725i	0.238989	−	0.413941i	0.960425	+	0.278540i	$0.0898506\pi$
$354$	0.610815	−	1.05796i	0.0324644	−	0.0562300i
$355$	1.11334	+	1.92836i	0.0590900	+	0.102347i
$356$	9.29860			0.492825
$357$	−1.00047	−	1.67210i	−0.0529503	−	0.0884967i
$358$	−13.6459			−0.721208
$359$	−16.6459	−	28.8315i	−0.878537	−	1.52167i	−0.852947	−	0.521998i	$-0.825187\pi$
$359$	−16.6459	−	28.8315i	−0.878537	−	1.52167i	−0.0255900	−	0.999673i	$-0.508146\pi$
$360$	−1.43969	+	2.49362i	−0.0758785	+	0.131425i
$361$	−7.91488	+	13.7090i	−0.416573	+	0.721525i
$362$	5.86484	+	10.1582i	0.308249	+	0.533903i
$363$	−0.347296			−0.0182283
$364$	8.30541	−	14.9178i	0.435322	−	0.781906i
$365$	−0.389185			−0.0203709
$366$	−1.16385	−	2.01584i	−0.0608353	−	0.105370i
$367$	−6.78106	+	11.7451i	−0.353968	+	0.613091i	−0.986941	−	0.161083i	$-0.948501\pi$
$367$	−6.78106	+	11.7451i	−0.353968	+	0.613091i	0.632972	+	0.774174i	$0.281835\pi$
$368$	4.29086	−	7.43199i	0.223677	−	0.387419i
$369$	6.10607	+	10.5760i	0.317869	+	0.550566i
$370$	−10.9436			−0.568929
$371$	−4.39053	+	7.88609i	−0.227945	+	0.409425i
$372$	−2.90167			−0.150445
$373$	−16.3746	−	28.3617i	−0.847847	−	1.46851i	−0.883126	−	0.469136i	$-0.844565\pi$
$373$	−16.3746	−	28.3617i	−0.847847	−	1.46851i	0.0352794	−	0.999377i	$-0.488768\pi$
$374$	−1.06031	+	1.83651i	−0.0548272	+	0.0949635i
$375$	0.173648	−	0.300767i	0.00896715	−	0.0155316i
$376$	−4.92127	−	8.52390i	−0.253795	−	0.439586i
$377$	−62.3424			−3.21079
$378$	−2.77379	−	4.63587i	−0.142668	−	0.238443i
$379$	25.8135			1.32595			0.662974	−	0.748642i	$-0.269294\pi$
$379$	25.8135			1.32595			0.662974	+	0.748642i	$0.269294\pi$
$380$	2.95084	+	5.11100i	0.151375	+	0.262189i
$381$	−0.173648	+	0.300767i	−0.00889627	+	0.0154088i
$382$	0.258770	−	0.448204i	0.0132398	−	0.0229321i
$383$	−4.32770	−	7.49579i	−0.221135	−	0.383017i	0.734018	−	0.679130i	$-0.237643\pi$
$383$	−4.32770	−	7.49579i	−0.221135	−	0.383017i	−0.955153	+	0.296113i	$0.904309\pi$
$384$	0.347296			0.0177229
$385$	2.64543	−	0.0412527i	0.134824	−	0.00210243i
$386$	19.9094			1.01336
$387$	16.1138	+	27.9099i	0.819111	+	1.41874i
$388$	−2.65270	+	4.59462i	−0.134671	+	0.233256i
$389$	−9.96585	+	17.2614i	−0.505289	+	0.875186i	0.494693	+	0.869068i	$0.335281\pi$
$389$	−9.96585	+	17.2614i	−0.505289	+	0.875186i	−0.999981	+	0.00611772i	$0.998053\pi$
$390$	−1.12061	−	1.94096i	−0.0567445	−	0.0982844i
$391$	−18.1985			−0.920339
$392$	−6.99660	+	0.218262i	−0.353381	+	0.0110239i
$393$	−0.948615			−0.0478513
$394$	−4.61587	−	7.99492i	−0.232544	−	0.402778i
$395$	−2.34730	+	4.06564i	−0.118105	+	0.204564i
$396$	−1.43969	+	2.49362i	−0.0723473	+	0.125309i
$397$	14.3452	+	24.8467i	0.719967	+	1.24702i	0.961012	+	0.276505i	$0.0891763\pi$
$397$	14.3452	+	24.8467i	0.719967	+	1.24702i	−0.241046	+	0.970514i	$0.577490\pi$
$398$	4.75608			0.238401
$399$	−5.42215	+	0.0845527i	−0.271447	+	0.00423293i
$400$	1.00000			0.0500000
$401$	3.82635	+	6.62744i	0.191079	+	0.330958i	0.945608	−	0.325308i	$-0.105468\pi$
$401$	3.82635	+	6.62744i	0.191079	+	0.330958i	−0.754529	+	0.656267i	$0.772135\pi$
$402$	0.316552	−	0.548284i	0.0157882	−	0.0273459i
$403$	−26.9590	+	46.6944i	−1.34293	+	2.32602i
$404$	−1.08853	−	1.88538i	−0.0541562	−	0.0938013i
$405$	7.92902			0.393996
$406$	13.1231	+	21.9329i	0.651291	+	1.08851i
$407$	−10.9436			−0.542452
$408$	−0.368241	−	0.637812i	−0.0182306	−	0.0315764i
$409$	−12.2763	+	21.2632i	−0.607025	+	1.05140i	0.384703	+	0.923040i	$0.374304\pi$
$409$	−12.2763	+	21.2632i	−0.607025	+	1.05140i	−0.991728	+	0.128357i	$0.959030\pi$
$410$	2.12061	−	3.67301i	0.104730	−	0.181397i
$411$	1.70233	+	2.94853i	0.0839699	+	0.145440i
$412$	−11.7588			−0.579313
$413$	−4.52704	+	8.13127i	−0.222761	+	0.400114i
$414$	−24.7101			−1.21443
$415$	0.935822	+	1.62089i	0.0459377	+	0.0795664i
$416$	3.22668	−	5.58878i	0.158201	−	0.274012i
$417$	−1.86319	+	3.22714i	−0.0912407	+	0.158034i
$418$	2.95084	+	5.11100i	0.144330	+	0.249987i
$419$	25.8972			1.26516			0.632581	−	0.774494i	$-0.281995\pi$
$419$	25.8972			1.26516			0.632581	+	0.774494i	$0.281995\pi$
$420$	−0.446967	+	0.802823i	−0.0218097	+	0.0391737i
$421$	36.5526			1.78147			0.890733	−	0.454527i	$-0.150192\pi$
$421$	36.5526			1.78147			0.890733	+	0.454527i	$0.150192\pi$
$422$	5.74376	+	9.94848i	0.279602	+	0.484284i
$423$	−14.1702	+	24.5436i	−0.688981	+	1.19335i
$424$	−1.70574	+	2.95442i	−0.0828379	+	0.143479i
$425$	−1.06031	−	1.83651i	−0.0514325	−	0.0890836i
$426$	−0.773318			−0.0374674
$427$	9.10472	+	15.2169i	0.440608	+	0.736396i
$428$	17.2763			0.835082
$429$	−1.12061	−	1.94096i	−0.0541038	−	0.0937105i
$430$	5.59627	−	9.69302i	0.269876	−	0.467439i
$431$	10.1284	−	17.5428i	0.487866	−	0.845008i	−0.512037	−	0.858963i	$-0.671109\pi$
$431$	10.1284	−	17.5428i	0.487866	−	0.845008i	0.999903	+	0.0139552i	$0.00444223\pi$
$432$	−1.02094	−	1.76833i	−0.0491202	−	0.0850787i
$433$	25.2371			1.21282			0.606409	−	0.795153i	$-0.292609\pi$
$433$	25.2371			1.21282			0.606409	+	0.795153i	$0.292609\pi$
$434$	22.1027	−	0.344668i	1.06096	−	0.0165446i
$435$	3.35504			0.160862
$436$	2.97565	+	5.15398i	0.142508	+	0.246831i
$437$	−25.3233	+	43.8612i	−1.21138	+	2.09816i
$438$	0.0675813	−	0.117054i	0.00322916	−	0.00559307i
$439$	−7.21213	−	12.4918i	−0.344216	−	0.596200i	0.640995	−	0.767545i	$-0.278522\pi$
$439$	−7.21213	−	12.4918i	−0.344216	−	0.596200i	−0.985211	+	0.171345i	$0.945189\pi$
$440$	1.00000			0.0476731
$441$	10.6172	+	17.1326i	0.505581	+	0.815839i
$442$	−13.6851			−0.650934
$443$	−16.3405	−	28.3026i	−0.776360	−	1.34470i	−0.934027	−	0.357203i	$-0.883731\pi$
$443$	−16.3405	−	28.3026i	−0.776360	−	1.34470i	0.157667	−	0.987492i	$-0.449603\pi$
$444$	1.90033	−	3.29147i	0.0901857	−	0.156206i
$445$	−4.64930	+	8.05282i	−0.220398	+	0.381740i
$446$	−6.75877	−	11.7065i	−0.320037	−	0.554320i
$447$	−4.70233			−0.222413
$448$	−2.64543	+	0.0412527i	−0.124985	+	0.00194901i
$449$	16.6851			0.787418			0.393709	−	0.919235i	$-0.371192\pi$
$449$	16.6851			0.787418			0.393709	+	0.919235i	$0.371192\pi$
$450$	−1.43969	−	2.49362i	−0.0678678	−	0.117550i
$451$	2.12061	−	3.67301i	0.0998558	−	0.172955i
$452$	−2.42602	+	4.20199i	−0.114110	+	0.197645i
$453$	0.566237	+	0.980752i	0.0266041	+	0.0460797i
$454$	11.3500			0.532681
$455$	8.76651	+	14.6516i	0.410980	+	0.686878i
$456$	−2.04963			−0.0959827
$457$	−3.92855	−	6.80445i	−0.183770	−	0.318299i	0.759392	−	0.650634i	$-0.225497\pi$
$457$	−3.92855	−	6.80445i	−0.183770	−	0.318299i	−0.943161	+	0.332335i	$0.892163\pi$
$458$	8.04189	−	13.9290i	0.375773	−	0.650858i
$459$	−2.16503	+	3.74994i	−0.101055	+	0.175032i
$460$	4.29086	+	7.43199i	0.200062	+	0.346518i
$461$	8.25908			0.384663			0.192332	−	0.981330i	$-0.438395\pi$
$461$	8.25908			0.384663			0.192332	+	0.981330i	$0.438395\pi$
$462$	−0.446967	+	0.802823i	−0.0207948	+	0.0373507i
$463$	14.7237			0.684268			0.342134	−	0.939651i	$-0.388850\pi$
$463$	14.7237			0.684268			0.342134	+	0.939651i	$0.388850\pi$
$464$	4.83022	+	8.36619i	0.224237	+	0.388391i
$465$	1.45084	−	2.51292i	0.0672810	−	0.116534i
$466$	2.17365	−	3.76487i	0.100692	−	0.174404i
$467$	−2.30154	−	3.98638i	−0.106502	−	0.184468i	0.807849	−	0.589390i	$-0.200632\pi$
$467$	−2.30154	−	3.98638i	−0.106502	−	0.184468i	−0.914351	+	0.404922i	$0.867299\pi$
$468$	−18.5817			−0.858940
$469$	−2.34611	+	4.21399i	−0.108333	+	0.194584i
$470$	9.84255			0.454003
$471$	0.534615	+	0.925981i	0.0246338	+	0.0426669i
$472$	−1.75877	+	3.04628i	−0.0809540	+	0.140216i
$473$	5.59627	−	9.69302i	0.257317	−	0.445685i
$474$	−0.815207	−	1.41198i	−0.0374437	−	0.0648544i
$475$	−5.90167			−0.270787
$476$	2.88073	+	4.81461i	0.132038	+	0.220677i
$477$	9.82295			0.449762
$478$	−3.43107	−	5.94280i	−0.156934	−	0.271817i
$479$	2.75103	−	4.76492i	0.125698	−	0.217715i	−0.796308	−	0.604892i	$-0.793216\pi$
$479$	2.75103	−	4.76492i	0.125698	−	0.217715i	0.922005	+	0.387177i	$0.126550\pi$
$480$	−0.173648	+	0.300767i	−0.00792592	+	0.0137281i
$481$	−35.3114	−	61.1611i	−1.61006	−	2.78871i
$482$	−9.26083			−0.421819
$483$	−7.88444	+	0.122949i	−0.358754	+	0.00559439i
$484$	1.00000			0.0454545
$485$	−2.65270	−	4.59462i	−0.120453	−	0.208631i
$486$	−4.43969	+	7.68977i	−0.201389	+	0.348815i
$487$	−5.95811	+	10.3198i	−0.269988	+	0.467633i	−0.968858	−	0.247616i	$-0.920353\pi$
$487$	−5.95811	+	10.3198i	−0.269988	+	0.467633i	0.698871	+	0.715248i	$0.253686\pi$
$488$	3.35117	+	5.80439i	0.151700	+	0.262752i
$489$	−2.06593			−0.0934247
$490$	3.30928	−	6.16836i	0.149498	−	0.278658i
$491$	−12.6824			−0.572349			−0.286175	−	0.958178i	$-0.592384\pi$
$491$	−12.6824			−0.572349			−0.286175	+	0.958178i	$0.592384\pi$
$492$	0.736482	+	1.27562i	0.0332032	+	0.0575096i
$493$	10.2430	−	17.7415i	0.461323	−	0.799035i
$494$	−19.0428	+	32.9831i	−0.856777	+	1.48398i
$495$	−1.43969	−	2.49362i	−0.0647094	−	0.112080i
$496$	8.35504			0.375152
$497$	5.89053	−	0.0918566i	0.264226	−	0.00412033i
$498$	−0.650015			−0.0291279
$499$	4.88713	+	8.46475i	0.218778	+	0.378934i	0.954435	−	0.298420i	$-0.0964597\pi$
$499$	4.88713	+	8.46475i	0.218778	+	0.378934i	−0.735657	+	0.677354i	$0.763126\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	2.71301	−	4.69907i	0.121208	−	0.209939i
$502$	−5.88713	−	10.1968i	−0.262755	−	0.455106i
$503$	−35.2567			−1.57202			−0.786010	−	0.618214i	$-0.787856\pi$
$503$	−35.2567			−1.57202			−0.786010	+	0.618214i	$0.787856\pi$
$504$	3.91147	+	6.53731i	0.174231	+	0.291195i
$505$	2.17705			0.0968775
$506$	4.29086	+	7.43199i	0.190752	+	0.330392i
$507$	4.97431	−	8.61575i	0.220917	−	0.382639i
$508$	0.500000	−	0.866025i	0.0221839	−	0.0384237i
$509$	−5.63816	−	9.76557i	−0.249907	−	0.432851i	0.713593	−	0.700561i	$-0.247067\pi$
$509$	−5.63816	−	9.76557i	−0.249907	−	0.432851i	−0.963500	+	0.267709i	$0.913733\pi$
$510$	0.736482			0.0326120
$511$	−0.500877	+	0.899655i	−0.0221575	+	0.0397984i
$512$	−1.00000			−0.0441942
$513$	6.02528	+	10.4361i	0.266023	+	0.460765i
$514$	6.04963	−	10.4783i	0.266838	−	0.462177i
$515$	5.87939	−	10.1834i	0.259077	−	0.448734i
$516$	1.94356	+	3.36635i	0.0855606	+	0.148195i
$517$	9.84255			0.432875
$518$	−14.0842	+	25.2975i	−0.618826	+	1.11151i
$519$	1.07428			0.0471558
$520$	3.22668	+	5.58878i	0.141499	+	0.245084i
$521$	12.4709	−	21.6002i	0.546360	−	0.946324i	−0.452160	−	0.891937i	$-0.649346\pi$
$521$	12.4709	−	21.6002i	0.546360	−	0.946324i	0.998520	−	0.0543867i	$-0.0173204\pi$
$522$	13.9081	−	24.0895i	0.608740	−	1.05437i
$523$	5.73648	+	9.93588i	0.250839	+	0.434466i	0.963757	−	0.266782i	$-0.0859602\pi$
$523$	5.73648	+	9.93588i	0.250839	+	0.434466i	−0.712918	+	0.701247i	$0.752627\pi$
$524$	2.73143			0.119323
$525$	−0.471782	−	0.788496i	−0.0205902	−	0.0344128i
$526$	−4.06149			−0.177089
$527$	−8.85891	−	15.3441i	−0.385900	−	0.668399i
$528$	−0.173648	+	0.300767i	−0.00755707	+	0.0130892i
$529$	−25.3229	+	43.8606i	−1.10100	+	1.90698i
$530$	−1.70574	−	2.95442i	−0.0740925	−	0.128332i
$531$	10.1284			0.439533
$532$	15.6125	−	0.243460i	0.676886	−	0.0105553i
$533$	27.3702			1.18553
$534$	−1.61468	−	2.79672i	−0.0698743	−	0.121026i
$535$	−8.63816	+	14.9617i	−0.373460	+	0.646852i
$536$	−0.911474	+	1.57872i	−0.0393697	+	0.0681903i
$537$	2.36959	+	4.10424i	0.102255	+	0.177111i
$538$	−26.6810			−1.15030
$539$	3.30928	−	6.16836i	0.142541	−	0.265690i
$540$	2.04189			0.0878689
$541$	−4.37804	−	7.58299i	−0.188227	−	0.326018i	0.756432	−	0.654072i	$-0.226941\pi$
$541$	−4.37804	−	7.58299i	−0.188227	−	0.326018i	−0.944659	+	0.328054i	$0.893607\pi$
$542$	4.55438	−	7.88841i	0.195627	−	0.338836i
$543$	2.03684	−	3.52790i	0.0874090	−	0.151397i
$544$	1.06031	+	1.83651i	0.0454603	+	0.0787396i
$545$	−5.95130			−0.254926
$546$	−5.92902	+	0.0924567i	−0.253738	+	0.00395678i
$547$	−1.09327			−0.0467450			−0.0233725	−	0.999727i	$-0.507440\pi$
$547$	−1.09327			−0.0467450			−0.0233725	+	0.999727i	$0.507440\pi$
$548$	−4.90167	−	8.48995i	−0.209389	−	0.362673i
$549$	9.64930	−	16.7131i	0.411822	−	0.713297i
$550$	−0.500000	+	0.866025i	−0.0213201	+	0.0369274i
$551$	−28.5064	−	49.3745i	−1.21441	−	2.10343i
$552$	−2.98040			−0.126854
$553$	6.37733	+	10.6585i	0.271191	+	0.453247i
$554$	32.8776			1.39684
$555$	1.90033	+	3.29147i	0.0806645	+	0.139715i
$556$	5.36484	−	9.29217i	0.227520	−	0.394076i
$557$	7.75196	−	13.4268i	0.328461	−	0.568912i	−0.653745	−	0.756714i	$-0.726803\pi$
$557$	7.75196	−	13.4268i	0.328461	−	0.568912i	0.982207	+	0.187803i	$0.0601366\pi$
$558$	−12.0287	−	20.8343i	−0.509215	−	0.881986i
$559$	72.2295			3.05498
$560$	1.28699	−	2.31164i	0.0543852	−	0.0976844i
$561$	0.736482			0.0310943
$562$	−9.96585	−	17.2614i	−0.420384	−	0.728127i
$563$	−11.8307	+	20.4914i	−0.498604	+	0.863608i	−0.999999	−	0.00161110i	$-0.999487\pi$
$563$	−11.8307	+	20.4914i	−0.498604	+	0.863608i	0.501395	+	0.865219i	$0.332821\pi$
$564$	−1.70914	+	2.96032i	−0.0719678	+	0.124652i
$565$	−2.42602	−	4.20199i	−0.102064	−	0.176779i
$566$	21.8871			0.919985
$567$	10.2046	−	18.3290i	0.428551	−	0.769745i
$568$	2.22668			0.0934295
$569$	8.38238	+	14.5187i	0.351408	+	0.608656i	0.986496	−	0.163783i	$-0.0523698\pi$
$569$	8.38238	+	14.5187i	0.351408	+	0.608656i	−0.635089	+	0.772439i	$0.719036\pi$
$570$	1.02481	−	1.77503i	0.0429248	−	0.0743479i
$571$	−10.8910	+	18.8638i	−0.455774	+	0.789424i	−0.998732	−	0.0503359i	$-0.983971\pi$
$571$	−10.8910	+	18.8638i	−0.455774	+	0.789424i	0.542958	+	0.839760i	$0.317304\pi$
$572$	3.22668	+	5.58878i	0.134914	+	0.233678i
$573$	−0.179740			−0.00750875
$574$	−5.76146	−	9.62922i	−0.240479	−	0.401916i
$575$	−8.58172			−0.357882
$576$	1.43969	+	2.49362i	0.0599872	+	0.103901i
$577$	23.4243	−	40.5720i	0.975165	−	1.68904i	0.295776	−	0.955257i	$-0.404422\pi$
$577$	23.4243	−	40.5720i	0.975165	−	1.68904i	0.679389	−	0.733778i	$-0.262245\pi$
$578$	−6.25150	+	10.8279i	−0.260028	+	0.450382i
$579$	−3.45723	−	5.98810i	−0.143678	−	0.248857i
$580$	−9.66044			−0.401128
$581$	4.95130	−	0.0772103i	0.205415	−	0.00320322i
$582$	1.84255			0.0763761
$583$	−1.70574	−	2.95442i	−0.0706444	−	0.122360i
$584$	−0.194593	+	0.337044i	−0.00805230	+	0.0139470i
$585$	9.29086	−	16.0922i	0.384130	−	0.665332i
$586$	6.66044	+	11.5362i	0.275140	+	0.476557i
$587$	37.3577			1.54192			0.770959	−	0.636885i	$-0.219777\pi$
$587$	37.3577			1.54192			0.770959	+	0.636885i	$0.219777\pi$
$588$	1.28059	+	2.06645i	0.0528107	+	0.0852189i
$589$	−49.3087			−2.03173
$590$	−1.75877	−	3.04628i	−0.0724074	−	0.125413i
$591$	−1.60307	+	2.77661i	−0.0659416	+	0.114214i
$592$	−5.47178	+	9.47740i	−0.224889	+	0.389519i
$593$	5.04458	+	8.73746i	0.207156	+	0.358805i	0.950818	−	0.309752i	$-0.100246\pi$
$593$	5.04458	+	8.73746i	0.207156	+	0.358805i	−0.743662	+	0.668556i	$0.766913\pi$
$594$	2.04189			0.0837797
$595$	−5.60994	+	0.0874810i	−0.229985	+	0.00358637i
$596$	13.5398			0.554613
$597$	−0.825885	−	1.43047i	−0.0338012	−	0.0585454i
$598$	−27.6905	+	47.9613i	−1.13235	+	1.96128i
$599$	−5.15863	+	8.93502i	−0.210776	+	0.365075i	−0.951958	−	0.306230i	$-0.900932\pi$
$599$	−5.15863	+	8.93502i	−0.210776	+	0.365075i	0.741182	+	0.671305i	$0.234266\pi$
$600$	−0.173648	−	0.300767i	−0.00708916	−	0.0122788i
$601$	28.0446			1.14396			0.571981	−	0.820267i	$-0.306175\pi$
$601$	28.0446			1.14396			0.571981	+	0.820267i	$0.306175\pi$
$602$	−15.2044	−	25.4113i	−0.619685	−	1.03569i
$603$	5.24897			0.213755
$604$	−1.63041	−	2.82396i	−0.0663406	−	0.114905i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$	−0.378041	+	0.654786i	−0.0153569	+	0.0265989i
$607$	1.84090	+	3.18853i	0.0747198	+	0.129419i	0.900964	−	0.433893i	$-0.142860\pi$
$607$	1.84090	+	3.18853i	0.0747198	+	0.129419i	−0.826245	+	0.563312i	$0.809527\pi$
$608$	5.90167			0.239344
$609$	4.31790	−	7.75562i	0.174970	−	0.314274i
$610$	−6.70233			−0.271370
$611$	31.7588	+	55.0078i	1.28482	+	2.22538i
$612$	3.05303	−	5.28801i	0.123412	−	0.213755i
$613$	−0.389185	+	0.674089i	−0.0157191	+	0.0272262i	−0.873778	−	0.486325i	$-0.838337\pi$
$613$	−0.389185	+	0.674089i	−0.0157191	+	0.0272262i	0.858059	+	0.513551i	$0.171670\pi$
$614$	14.7520	+	25.5512i	0.595341	+	1.03116i
$615$	−1.47296			−0.0593956
$616$	1.28699	−	2.31164i	0.0518543	−	0.0931385i
$617$	−15.0060			−0.604118			−0.302059	−	0.953289i	$-0.597674\pi$
$617$	−15.0060			−0.604118			−0.302059	+	0.953289i	$0.597674\pi$
$618$	2.04189	+	3.53666i	0.0821368	+	0.142265i
$619$	10.8571	−	18.8050i	0.436384	−	0.755838i	−0.561024	−	0.827800i	$-0.689592\pi$
$619$	10.8571	−	18.8050i	0.436384	−	0.755838i	0.997407	+	0.0719611i	$0.0229258\pi$
$620$	−4.17752	+	7.23567i	−0.167773	+	0.290592i
$621$	8.76146	+	15.1753i	0.351585	+	0.608963i
$622$	−10.7415			−0.430696
$623$	12.6316	+	21.1114i	0.506074	+	0.845810i
$624$	−2.24123			−0.0897210
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−13.5621	+	23.4903i	−0.542051	+	0.938860i
$627$	1.02481	−	1.77503i	0.0409272	−	0.0708879i
$628$	−1.53936	−	2.66625i	−0.0614273	−	0.106395i
$629$	23.2071			0.925327
$630$	−7.61721	+	0.118782i	−0.303477	+	0.00473240i
$631$	7.38682			0.294065			0.147032	−	0.989132i	$-0.453028\pi$
$631$	7.38682			0.294065			0.147032	+	0.989132i	$0.453028\pi$
$632$	2.34730	+	4.06564i	0.0933704	+	0.161722i
$633$	1.99479	−	3.45507i	0.0792856	−	0.137327i
$634$	5.44104	−	9.42415i	0.216091	−	0.374281i
$635$	0.500000	+	0.866025i	0.0198419	+	0.0343672i
$636$	1.18479			0.0469801
$637$	45.1516	−	1.40852i	1.78897	−	0.0558078i
$638$	−9.66044			−0.382461
$639$	−3.20574	−	5.55250i	−0.126817	−	0.219653i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−0.0898700	+	0.155659i	−0.00354965	+	0.00614818i	−0.867795	−	0.496923i	$-0.834463\pi$
$641$	−0.0898700	+	0.155659i	−0.00354965	+	0.00614818i	0.864245	+	0.503071i	$0.167797\pi$
$642$	−3.00000	−	5.19615i	−0.118401	−	0.205076i
$643$	−10.8666			−0.428537			−0.214268	−	0.976775i	$-0.568737\pi$
$643$	−10.8666			−0.428537			−0.214268	+	0.976775i	$0.568737\pi$
$644$	22.7023	−	0.354019i	0.894597	−	0.0139503i
$645$	−3.88713			−0.153055
$646$	−6.25759	−	10.8385i	−0.246202	−	0.426434i
$647$	10.2412	−	17.7383i	0.402624	−	0.697366i	−0.591417	−	0.806366i	$-0.701431\pi$
$647$	10.2412	−	17.7383i	0.402624	−	0.697366i	0.994042	+	0.109000i	$0.0347648\pi$
$648$	3.96451	−	6.86673i	0.155741	−	0.269751i
$649$	−1.75877	−	3.04628i	−0.0690378	−	0.119577i
$650$	−6.45336			−0.253122
$651$	−3.94175	−	6.58791i	−0.154489	−	0.258201i
$652$	5.94862			0.232966
$653$	−6.61200	−	11.4523i	−0.258747	−	0.448164i	0.707159	−	0.707054i	$-0.249976\pi$
$653$	−6.61200	−	11.4523i	−0.258747	−	0.448164i	−0.965907	+	0.258891i	$0.916643\pi$
$654$	1.03343	−	1.78996i	0.0404104	−	0.0699929i
$655$	−1.36571	+	2.36549i	−0.0533629	+	0.0924272i
$656$	−2.12061	−	3.67301i	−0.0827961	−	0.143407i
$657$	1.12061			0.0437193
$658$	12.6673	−	22.7524i	0.493821	−	0.886980i
$659$	−3.38144			−0.131722			−0.0658612	−	0.997829i	$-0.520979\pi$
$659$	−3.38144			−0.131722			−0.0658612	+	0.997829i	$0.520979\pi$
$660$	−0.173648	−	0.300767i	−0.00675925	−	0.0117074i
$661$	−4.84255	+	8.38754i	−0.188353	+	0.326238i	−0.944701	−	0.327932i	$-0.893648\pi$
$661$	−4.84255	+	8.38754i	−0.188353	+	0.326238i	0.756348	+	0.654169i	$0.226982\pi$
$662$	0.893933	−	1.54834i	0.0347437	−	0.0601779i
$663$	2.37639	+	4.11603i	0.0922914	+	0.159853i
$664$	1.87164			0.0726339
$665$	−7.59539	+	13.6425i	−0.294537	+	0.529034i
$666$	31.5107			1.22102
$667$	−41.4516	−	71.7963i	−1.60501	−	2.77996i
$668$	−7.81180	+	13.5304i	−0.302248	+	0.523508i
$669$	−2.34730	+	4.06564i	−0.0907517	+	0.157187i
$670$	−0.911474	−	1.57872i	−0.0352133	−	0.0609913i
$671$	−6.70233			−0.258741
$672$	0.471782	+	0.788496i	0.0181994	+	0.0304169i
$673$	24.9881			0.963222			0.481611	−	0.876385i	$-0.340052\pi$
$673$	24.9881			0.963222			0.481611	+	0.876385i	$0.340052\pi$
$674$	8.00387	+	13.8631i	0.308298	+	0.533987i
$675$	−1.02094	+	1.76833i	−0.0392962	+	0.0680630i
$676$	−14.3229	+	24.8081i	−0.550883	+	0.954157i
$677$	9.62361	+	16.6686i	0.369865	+	0.640625i	0.989544	−	0.144230i	$-0.0460705\pi$
$677$	9.62361	+	16.6686i	0.369865	+	0.640625i	−0.619679	+	0.784855i	$0.712737\pi$
$678$	1.68510			0.0647158
$679$	−14.0351	+	0.218862i	−0.538617	+	0.00839916i
$680$	−2.12061			−0.0813219
$681$	−1.97090	−	3.41371i	−0.0755252	−	0.130814i
$682$	−4.17752	+	7.23567i	−0.159965	+	0.277068i
$683$	−23.7822	+	41.1921i	−0.910002	+	1.57617i	−0.0959439	+	0.995387i	$0.530587\pi$
$683$	−23.7822	+	41.1921i	−0.910002	+	1.57617i	−0.814058	+	0.580783i	$0.802746\pi$
$684$	−8.49660	−	14.7165i	−0.324875	−	0.562701i
$685$	9.80335			0.374567
$686$	−10.0000	−	15.5885i	−0.381802	−	0.595170i
$687$	−5.58584			−0.213113
$688$	−5.59627	−	9.69302i	−0.213356	−	0.369543i
$689$	11.0077	−	19.0660i	0.419362	−	0.726355i
$690$	1.49020	−	2.58110i	0.0567309	−	0.0982609i
$691$	−5.13516	−	8.89436i	−0.195351	−	0.338358i	0.751665	−	0.659545i	$-0.229251\pi$
$691$	−5.13516	−	8.89436i	−0.195351	−	0.338358i	−0.947015	+	0.321188i	$0.895918\pi$
$692$	−3.09327			−0.117589
$693$	−7.61721	+	0.118782i	−0.289354	+	0.00451217i
$694$	−14.4688			−0.549230
$695$	5.36484	+	9.29217i	0.203500	+	0.352472i
$696$	1.67752	−	2.90555i	0.0635862	−	0.110134i
$697$	−4.49701	+	7.78904i	−0.170336	+	0.295031i
$698$	−3.58647	−	6.21194i	−0.135750	−	0.235125i
$699$	−1.50980			−0.0571059
$700$	1.35844	+	2.27038i	0.0513442	+	0.0858124i
$701$	−2.37195			−0.0895873			−0.0447936	−	0.998996i	$-0.514263\pi$
$701$	−2.37195			−0.0895873			−0.0447936	+	0.998996i	$0.514263\pi$
$702$	6.58853	+	11.4117i	0.248668	+	0.430705i
$703$	32.2927	−	55.9325i	1.21794	−	2.10954i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$	−1.70914	−	2.96032i	−0.0643700	−	0.111492i
$706$	8.98040			0.337982
$707$	2.80184	−	5.03255i	0.105374	−	0.189269i
$708$	1.22163			0.0459116
$709$	−14.2344	−	24.6547i	−0.534585	−	0.925928i	−0.999183	−	0.0404068i	$-0.987135\pi$
$709$	−14.2344	−	24.6547i	−0.534585	−	0.925928i	0.464598	−	0.885522i	$-0.346199\pi$
$710$	−1.11334	+	1.92836i	−0.0417829	+	0.0723702i
$711$	6.75877	−	11.7065i	0.253474	−	0.439029i
$712$	4.64930	+	8.05282i	0.174240	+	0.301792i
$713$	−71.7006			−2.68521
$714$	0.947844	−	1.70248i	0.0354722	−	0.0637136i
$715$	−6.45336			−0.241342
$716$	−6.82295	−	11.8177i	−0.254986	−	0.441648i
$717$	−1.19160	+	2.06391i	−0.0445011	+	0.0770782i
$718$	16.6459	−	28.8315i	0.621219	−	1.07598i
$719$	−5.85251	−	10.1368i	−0.218262	−	0.378041i	0.736015	−	0.676965i	$-0.236705\pi$
$719$	−5.85251	−	10.1368i	−0.218262	−	0.378041i	−0.954277	+	0.298925i	$0.903372\pi$
$720$	−2.87939			−0.107308
$721$	−15.9736	−	26.6969i	−0.594888	−	0.994245i
$722$	−15.8298			−0.589122
$723$	1.60813	+	2.78536i	0.0598069	+	0.103589i
$724$	−5.86484	+	10.1582i	−0.217965	+	0.377526i
$725$	4.83022	−	8.36619i	0.179390	−	0.310713i
$726$	−0.173648	−	0.300767i	−0.00644469	−	0.0111625i
$727$	14.9750			0.555393			0.277696	−	0.960669i	$-0.410429\pi$
$727$	14.9750			0.555393			0.277696	+	0.960669i	$0.410429\pi$
$728$	17.0719	−	0.266219i	0.632727	−	0.00986671i
$729$	−20.7033			−0.766788
$730$	−0.194593	−	0.337044i	−0.00720220	−	0.0124746i
$731$	−11.8675	+	20.5552i	−0.438936	+	0.760260i
$732$	1.16385	−	2.01584i	0.0430171	−	0.0745077i
$733$	8.53714	+	14.7868i	0.315327	+	0.546162i	0.979507	−	0.201411i	$-0.0645526\pi$
$733$	8.53714	+	14.7868i	0.315327	+	0.546162i	−0.664180	+	0.747572i	$0.731219\pi$
$734$	−13.5621			−0.500587
$735$	−2.42989	+	0.0758016i	−0.0896279	+	0.00279599i
$736$	8.58172			0.316326
$737$	−0.911474	−	1.57872i	−0.0335746	−	0.0581529i
$738$	−6.10607	+	10.5760i	−0.224767	+	0.389309i
$739$	19.7344	−	34.1810i	0.725942	−	1.25737i	−0.232642	−	0.972562i	$-0.574737\pi$
$739$	19.7344	−	34.1810i	0.725942	−	1.25737i	0.958585	−	0.284807i	$-0.0919295\pi$
$740$	−5.47178	−	9.47740i	−0.201147	−	0.348396i
$741$	13.2270			0.485906
$742$	−9.02481	+	0.140732i	−0.331311	+	0.00516645i
$743$	−18.9290			−0.694438			−0.347219	−	0.937784i	$-0.612874\pi$
$743$	−18.9290			−0.694438			−0.347219	+	0.937784i	$0.612874\pi$
$744$	−1.45084	−	2.51292i	−0.0531903	−	0.0921282i
$745$	−6.76991	+	11.7258i	−0.248030	+	0.429601i
$746$	16.3746	−	28.3617i	0.599518	−	1.03840i
$747$	−2.69459	−	4.66717i	−0.0985900	−	0.170763i
$748$	−2.12061			−0.0775374
$749$	23.4688	+	39.2238i	0.857533	+	1.43321i
$750$	0.347296			0.0126815
$751$	−5.52822	−	9.57516i	−0.201728	−	0.349402i	0.747358	−	0.664422i	$-0.231322\pi$
$751$	−5.52822	−	9.57516i	−0.201728	−	0.349402i	−0.949085	+	0.315020i	$0.897989\pi$
$752$	4.92127	−	8.52390i	0.179460	−	0.310835i
$753$	−2.04458	+	3.54131i	−0.0745085	+	0.129053i
$754$	−31.1712	−	53.9901i	−1.13519	−	1.96620i
$755$	3.26083			0.118674
$756$	2.62789	−	4.72010i	0.0955754	−	0.171669i
$757$	−2.04870			−0.0744611			−0.0372306	−	0.999307i	$-0.511854\pi$
$757$	−2.04870			−0.0744611			−0.0372306	+	0.999307i	$0.511854\pi$
$758$	12.9067	+	22.3551i	0.468793	+	0.811974i
$759$	1.49020	−	2.58110i	0.0540908	−	0.0936881i
$760$	−2.95084	+	5.11100i	−0.107038	+	0.185395i
$761$	−15.4979	−	26.8432i	−0.561800	−	0.973066i	−0.997340	−	0.0728964i	$-0.976776\pi$
$761$	−15.4979	−	26.8432i	−0.561800	−	0.973066i	0.435540	−	0.900170i	$-0.356558\pi$
$762$	−0.347296			−0.0125812
$763$	−7.65926	+	13.7572i	−0.277284	+	0.498046i
$764$	0.517541			0.0187240
$765$	3.05303	+	5.28801i	0.110383	+	0.191188i
$766$	4.32770	−	7.49579i	0.156366	−	0.270834i
$767$	11.3500	−	19.6588i	0.409824	−	0.709836i
$768$	0.173648	+	0.300767i	0.00626599	+	0.0108530i
$769$	−45.9127			−1.65565			−0.827827	−	0.560983i	$-0.810423\pi$
$769$	−45.9127			−1.65565			−0.827827	+	0.560983i	$0.810423\pi$
$770$	1.35844	+	2.27038i	0.0489548	+	0.0818189i
$771$	−4.20203			−0.151332
$772$	9.95471	+	17.2421i	0.358278	+	0.620555i
$773$	13.3957	−	23.2021i	0.481811	−	0.834522i	−0.517971	−	0.855398i	$-0.673312\pi$
$773$	13.3957	−	23.2021i	0.481811	−	0.834522i	0.999782	+	0.0208765i	$0.00664569\pi$
$774$	−16.1138	+	27.9099i	−0.579199	+	1.00320i
$775$	−4.17752	−	7.23567i	−0.150061	−	0.259913i
$776$	−5.30541			−0.190453
$777$	10.0544	−	0.156787i	0.360699	−	0.00562472i
$778$	−19.9317			−0.714586
$779$	12.5152	+	21.6769i	0.448403	+	0.776656i
$780$	1.12061	−	1.94096i	0.0401244	−	0.0694976i
$781$	−1.11334	+	1.92836i	−0.0398385	+	0.0690022i
$782$	−9.09926	−	15.7604i	−0.325389	−	0.563590i
$783$	−19.7256			−0.704934
$784$	−3.68732	−	5.95010i	−0.131690	−	0.212504i
$785$	3.07873			0.109884
$786$	−0.474308	−	0.821525i	−0.0169180	−	0.0293028i
$787$	17.0993	−	29.6168i	0.609523	−	1.05572i	−0.381796	−	0.924246i	$-0.624694\pi$
$787$	17.0993	−	29.6168i	0.609523	−	1.05572i	0.991319	−	0.131478i	$-0.0419722\pi$
$788$	4.61587	−	7.99492i	0.164433	−	0.284807i
$789$	0.705270	+	1.22156i	0.0251083	+	0.0434888i
$790$	−4.69459			−0.167026
$791$	−12.8357	+	0.200160i	−0.456386	+	0.00711686i
$792$	−2.87939			−0.102314
$793$	−21.6263	−	37.4578i	−0.767972	−	1.33017i
$794$	−14.3452	+	24.8467i	−0.509093	+	0.881776i
$795$	−0.592396	+	1.02606i	−0.0210101	+	0.0363906i
$796$	2.37804	+	4.11889i	0.0842874	+	0.145990i
$797$	6.11886			0.216741			0.108371	−	0.994111i	$-0.465437\pi$
$797$	6.11886			0.216741			0.108371	+	0.994111i	$0.465437\pi$
$798$	−2.78430	−	4.65344i	−0.0985632	−	0.164730i
$799$	−20.8723			−0.738407
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	13.3871	−	23.1872i	0.473011	−	0.819279i
$802$	−3.82635	+	6.62744i	−0.135113	+	0.234023i
$803$	−0.194593	−	0.337044i	−0.00686703	−	0.0118940i
$804$	0.633103			0.0223278
$805$	−11.0446	+	19.8378i	−0.389270	+	0.699191i
$806$	−53.9181			−1.89918
$807$	4.63310	+	8.02477i	0.163093	+	0.282485i
$808$	1.08853	−	1.88538i	0.0382942	−	0.0663275i
$809$	7.72193	−	13.3748i	0.271489	−	0.470232i	−0.697755	−	0.716337i	$-0.745817\pi$
$809$	7.72193	−	13.3748i	0.271489	−	0.470232i	0.969243	+	0.246105i	$0.0791507\pi$
$810$	3.96451	+	6.86673i	0.139299	+	0.241272i
$811$	47.0036			1.65052			0.825260	−	0.564753i	$-0.191028\pi$
$811$	47.0036			1.65052			0.825260	+	0.564753i	$0.191028\pi$
$812$	−12.4329	+	22.3314i	−0.436309	+	0.783679i
$813$	−3.16344			−0.110947
$814$	−5.47178	−	9.47740i	−0.191786	−	0.332183i
$815$	−2.97431	+	5.15165i	−0.104185	+	0.180455i
$816$	0.368241	−	0.637812i	0.0128910	−	0.0223279i
$817$	33.0273	+	57.2050i	1.15548	+	2.00135i
$818$	−24.5526			−0.858462
$819$	−25.2422	−	42.1876i	−0.882033	−	1.47415i
$820$	4.24123			0.148110
$821$	−0.497312	−	0.861369i	−0.0173563	−	0.0300620i	0.857217	−	0.514956i	$-0.172192\pi$
$821$	−0.497312	−	0.861369i	−0.0173563	−	0.0300620i	−0.874573	+	0.484894i	$0.838858\pi$
$822$	−1.70233	+	2.94853i	−0.0593757	+	0.102842i
$823$	1.00774	−	1.74546i	0.0351276	−	0.0608428i	−0.847927	−	0.530113i	$-0.822150\pi$
$823$	1.00774	−	1.74546i	0.0351276	−	0.0608428i	0.883055	+	0.469270i	$0.155483\pi$
$824$	−5.87939	−	10.1834i	−0.204818	−	0.354755i
$825$	0.347296			0.0120913
$826$	−9.30541	+	0.145108i	−0.323777	+	0.00504895i
$827$	−47.2026			−1.64140			−0.820698	−	0.571362i	$-0.806415\pi$
$827$	−47.2026			−1.64140			−0.820698	+	0.571362i	$0.806415\pi$
$828$	−12.3550	−	21.3996i	−0.429367	−	0.743686i
$829$	20.0428	−	34.7152i	0.696116	−	1.20571i	−0.273687	−	0.961819i	$-0.588243\pi$
$829$	20.0428	−	34.7152i	0.696116	−	1.20571i	0.969803	−	0.243889i	$-0.0784234\pi$
$830$	−0.935822	+	1.62089i	−0.0324829	+	0.0562620i
$831$	−5.70914	−	9.88852i	−0.198048	−	0.343029i
$832$	6.45336			0.223730
$833$	−7.01770	+	13.0807i	−0.243149	+	0.453220i
$834$	−3.72638			−0.129034
$835$	−7.81180	−	13.5304i	−0.270339	−	0.468240i
$836$	−2.95084	+	5.11100i	−0.102057	+	0.176768i
$837$	−8.53003	+	14.7744i	−0.294841	+	0.510680i
$838$	12.9486	+	22.4277i	0.447302	+	0.774751i
$839$	30.9418			1.06823			0.534115	−	0.845412i	$-0.320645\pi$
$839$	30.9418			1.06823			0.534115	+	0.845412i	$0.320645\pi$
$840$	−0.918748	+	0.0143269i	−0.0316998	+	0.000494325i
$841$	64.3242			2.21808
$842$	18.2763	+	31.6555i	0.629843	+	1.09092i
$843$	−3.46110	+	5.99481i	−0.119207	+	0.206472i
$844$	−5.74376	+	9.94848i	−0.197708	+	0.342441i
$845$	−14.3229	−	24.8081i	−0.492724	−	0.853424i
$846$	−28.3405			−0.974366
$847$	1.35844	+	2.27038i	0.0466766	+	0.0780113i
$848$	−3.41147			−0.117151
$849$	−3.80066	−	6.58294i	−0.130438	−	0.225926i
$850$	1.06031	−	1.83651i	0.0363682	−	0.0629916i
$851$	46.9573	−	81.3324i	1.60968	−	2.78804i
$852$	−0.386659	−	0.669713i	−0.0132467	−	0.0229440i
$853$	−8.99050			−0.307829			−0.153915	−	0.988084i	$-0.549188\pi$
$853$	−8.99050			−0.307829			−0.153915	+	0.988084i	$0.549188\pi$
$854$	−8.62583	+	15.4934i	−0.295170	+	0.530172i
$855$	16.9932			0.581155
$856$	8.63816	+	14.9617i	0.295246	+	0.511381i
$857$	7.47519	−	12.9474i	0.255347	−	0.442275i	−0.709642	−	0.704562i	$-0.751143\pi$
$857$	7.47519	−	12.9474i	0.255347	−	0.442275i	0.964990	+	0.262287i	$0.0844768\pi$
$858$	1.12061	−	1.94096i	0.0382572	−	0.0662633i
$859$	10.8007	+	18.7073i	0.368514	+	0.638285i	0.989333	−	0.145669i	$-0.0465334\pi$
$859$	10.8007	+	18.7073i	0.368514	+	0.638285i	−0.620820	+	0.783953i	$0.713200\pi$
$860$	11.1925			0.381662
$861$	−1.89569	+	3.40496i	−0.0646049	+	0.116041i
$862$	20.2567			0.689946
$863$	−1.38413	−	2.39739i	−0.0471164	−	0.0816081i	0.841505	−	0.540249i	$-0.181670\pi$
$863$	−1.38413	−	2.39739i	−0.0471164	−	0.0816081i	−0.888622	+	0.458641i	$0.848337\pi$
$864$	1.02094	−	1.76833i	0.0347332	−	0.0601597i
$865$	1.54664	−	2.67885i	0.0525872	−	0.0910838i
$866$	12.6186	+	21.8560i	0.428796	+	0.742696i
$867$	4.34224			0.147470
$868$	11.3498	+	18.9691i	0.385238	+	0.643854i
$869$	−4.69459			−0.159253
$870$	1.67752	+	2.90555i	0.0568732	+	0.0985073i
$871$	5.88207	−	10.1881i	0.199306	−	0.345209i
$872$	−2.97565	+	5.15398i	−0.100768	+	0.174536i
$873$	7.63816	+	13.2297i	0.258512	+	0.447757i
$874$	−50.6465			−1.71314
$875$	−2.64543	+	0.0412527i	−0.0894318	+	0.00139460i
$876$	0.135163			0.00456672
$877$	−10.8425	−	18.7798i	−0.366127	−	0.634150i	0.622829	−	0.782358i	$-0.285983\pi$
$877$	−10.8425	−	18.7798i	−0.366127	−	0.634150i	−0.988956	+	0.148207i	$0.952650\pi$
$878$	7.21213	−	12.4918i	0.243398	−	0.421577i
$879$	2.31315	−	4.00649i	0.0780205	−	0.135136i
$880$	0.500000	+	0.866025i	0.0168550	+	0.0291937i
$881$	40.5526			1.36625			0.683126	−	0.730300i	$-0.260620\pi$
$881$	40.5526			1.36625			0.683126	+	0.730300i	$0.260620\pi$
$882$	−9.52869	+	17.7611i	−0.320848	+	0.598047i
$883$	−57.5577			−1.93697			−0.968485	−	0.249072i	$-0.919874\pi$
$883$	−57.5577			−1.93697			−0.968485	+	0.249072i	$0.919874\pi$
$884$	−6.84255	−	11.8516i	−0.230140	−	0.398614i
$885$	−0.610815	+	1.05796i	−0.0205323	+	0.0355630i
$886$	16.3405	−	28.3026i	0.548969	−	0.950843i
$887$	−15.0797	−	26.1187i	−0.506325	−	0.876981i	−0.999973	−	0.00731942i	$-0.997670\pi$
$887$	−15.0797	−	26.1187i	−0.506325	−	0.876981i	0.493648	−	0.869662i	$-0.335663\pi$
$888$	3.80066			0.127542
$889$	2.64543	−	0.0412527i	0.0887249	−	0.00138357i
$890$	−9.29860			−0.311690
$891$	3.96451	+	6.86673i	0.132816	+	0.230044i
$892$	6.75877	−	11.7065i	0.226300	−	0.391964i
$893$	−29.0438	+	50.3053i	−0.971912	+	1.68340i
$894$	−2.35117	−	4.07234i	−0.0786348	−	0.136199i
$895$	13.6459			0.456132
$896$	−1.35844	−	2.27038i	−0.0453823	−	0.0758482i
$897$	19.2336			0.642191
$898$	8.34255	+	14.4497i	0.278394	+	0.482193i
$899$	40.3567	−	69.8998i	1.34597	−	2.33129i
$900$	1.43969	−	2.49362i	0.0479898	−	0.0831207i
$901$	3.61721	+	6.26519i	0.120507	+	0.208724i
$902$	4.24123			0.141217
$903$	−5.00269	+	8.98562i	−0.166479	+	0.299023i
$904$	−4.85204			−0.161377
$905$	−5.86484	−	10.1582i	−0.194954	−	0.337670i
$906$	−0.566237	+	0.980752i	−0.0188120	+	0.0325833i
$907$	−22.0842	+	38.2510i	−0.733295	+	1.27010i	0.222172	+	0.975008i	$0.428685\pi$
$907$	−22.0842	+	38.2510i	−0.733295	+	1.27010i	−0.955467	+	0.295097i	$0.904648\pi$
$908$	5.67499	+	9.82938i	0.188331	+	0.326199i
$909$	−6.26857			−0.207915
$910$	−8.30541	+	14.9178i	−0.275322	+	0.494521i
$911$	22.5895			0.748422			0.374211	−	0.927344i	$-0.377914\pi$
$911$	22.5895			0.748422			0.374211	+	0.927344i	$0.377914\pi$
$912$	−1.02481	−	1.77503i	−0.0339350	−	0.0587772i
$913$	−0.935822	+	1.62089i	−0.0309712	+	0.0536437i
$914$	3.92855	−	6.80445i	0.129945	−	0.225071i
$915$	1.16385	+	2.01584i	0.0384756	+	0.0666417i
$916$	16.0838			0.531423
$917$	3.71048	+	6.20139i	0.122531	+	0.204788i
$918$	−4.33006			−0.142913
$919$	−0.993193	−	1.72026i	−0.0327624	−	0.0567462i	0.849179	−	0.528105i	$-0.177097\pi$
$919$	−0.993193	−	1.72026i	−0.0327624	−	0.0567462i	−0.881942	+	0.471359i	$0.843764\pi$
$920$	−4.29086	+	7.43199i	−0.141465	+	0.245025i
$921$	5.12330	−	8.87382i	0.168819	−	0.292402i
$922$	4.12954	+	7.15257i	0.135999	+	0.235557i
$923$	−14.3696			−0.472981
$924$	−0.918748	+	0.0143269i	−0.0302246	+	0.000471321i
$925$	10.9436			0.359822
$926$	7.36184	+	12.7511i	0.241925	+	0.419027i
$927$	−16.9290	+	29.3219i	−0.556022	+	0.963058i
$928$	−4.83022	+	8.36619i	−0.158560	+	0.274634i
$929$	6.75150	+	11.6939i	0.221509	+	0.383666i	0.955267	−	0.295746i	$-0.0955683\pi$
$929$	6.75150	+	11.6939i	0.221509	+	0.383666i	−0.733757	+	0.679412i	$0.762235\pi$
$930$	2.90167			0.0951496
$931$	21.7614	+	35.1155i	0.713200	+	1.15087i
$932$	4.34730			0.142400
$933$	1.86525	+	3.23070i	0.0610655	+	0.105769i
$934$	2.30154	−	3.98638i	0.0753086	−	0.130438i
$935$	1.06031	−	1.83651i	0.0346758	−	0.0600602i
$936$	−9.29086	−	16.0922i	−0.303681	−	0.525991i
$937$	4.29591			0.140341			0.0701707	−	0.997535i	$-0.477646\pi$
$937$	4.29591			0.140341			0.0701707	+	0.997535i	$0.477646\pi$
$938$	−4.82248	+	0.0752015i	−0.157460	+	0.00245542i
$939$	9.42015			0.307415
$940$	4.92127	+	8.52390i	0.160514	+	0.278019i
$941$	−4.90508	+	8.49584i	−0.159901	+	0.276957i	−0.934833	−	0.355088i	$-0.884451\pi$
$941$	−4.90508	+	8.49584i	−0.159901	+	0.276957i	0.774932	+	0.632045i	$0.217784\pi$
$942$	−0.534615	+	0.925981i	−0.0174187	+	0.0301701i
$943$	18.1985	+	31.5208i	0.592625	+	1.02646i
$944$	−3.51754			−0.114486
$945$	2.77379	+	4.63587i	0.0902312	+	0.150805i
$946$	11.1925			0.363901
$947$	3.50134	+	6.06451i	0.113778	+	0.197070i	0.917291	−	0.398218i	$-0.130371\pi$
$947$	3.50134	+	6.06451i	0.113778	+	0.197070i	−0.803512	+	0.595288i	$0.797038\pi$
$948$	0.815207	−	1.41198i	0.0264767	−	0.0458590i
$949$	1.25578	−	2.17507i	0.0407643	−	0.0706058i
$950$	−2.95084	−	5.11100i	−0.0957378	−	0.165823i
$951$	−3.77930			−0.122552
$952$	−2.72921	+	4.90209i	−0.0884541	+	0.158878i
$953$	19.3164			0.625721			0.312861	−	0.949799i	$-0.398713\pi$
$953$	19.3164			0.625721			0.312861	+	0.949799i	$0.398713\pi$
$954$	4.91147	+	8.50692i	0.159015	+	0.275422i
$955$	−0.258770	+	0.448204i	−0.00837362	+	0.0145035i
$956$	3.43107	−	5.94280i	0.110969	−	0.192204i
$957$	1.67752	+	2.90555i	0.0542265	+	0.0939230i
$958$	5.50206			0.177763
$959$	12.6168	−	22.6618i	0.407418	−	0.731787i
$960$	−0.347296			−0.0112089
$961$	−19.4033	−	33.6075i	−0.625914	−	1.08411i
$962$	35.3114	−	61.1611i	1.13849	−	1.97191i
$963$	24.8726	−	43.0806i	0.801508	−	1.38825i
$964$	−4.63041	−	8.02011i	−0.149136	−	0.258310i
$965$	−19.9094			−0.640907
$966$	−4.04870	−	6.76665i	−0.130265	−	0.217713i
$967$	−30.6509			−0.985668			−0.492834	−	0.870123i	$-0.664039\pi$
$967$	−30.6509			−0.985668			−0.492834	+	0.870123i	$0.664039\pi$
$968$	0.500000	+	0.866025i	0.0160706	+	0.0278351i
$969$	−2.17324	+	3.76416i	−0.0698145	+	0.120922i
$970$	2.65270	−	4.59462i	0.0851732	−	0.147524i
$971$	18.6168	+	32.2452i	0.597442	+	1.03480i	0.993197	+	0.116443i	$0.0371493\pi$
$971$	18.6168	+	32.2452i	0.597442	+	1.03480i	−0.395756	+	0.918356i	$0.629517\pi$
$972$	−8.87939			−0.284806
$973$	28.3846	−	0.442628i	0.909968	−	0.0141900i
$974$	−11.9162			−0.381820
$975$	1.12061	+	1.94096i	0.0358884	+	0.0621605i
$976$	−3.35117	+	5.80439i	−0.107268	+	0.185794i
$977$	−5.51249	+	9.54791i	−0.176360	+	0.305465i	−0.940631	−	0.339431i	$-0.889766\pi$
$977$	−5.51249	+	9.54791i	−0.176360	+	0.305465i	0.764271	+	0.644895i	$0.223099\pi$
$978$	−1.03297	−	1.78915i	−0.0330306	−	0.0572107i
$979$	−9.29860			−0.297185
$980$	6.99660	−	0.218262i	0.223498	−	0.00697213i
$981$	17.1361			0.547113
$982$	−6.34120	−	10.9833i	−0.202356	−	0.350491i
$983$	5.42602	−	9.39815i	0.173063	−	0.299754i	−0.766426	−	0.642333i	$-0.777967\pi$
$983$	5.42602	−	9.39815i	0.173063	−	0.299754i	0.939489	+	0.342578i	$0.111300\pi$
$984$	−0.736482	+	1.27562i	−0.0234782	+	0.0406654i
$985$	4.61587	+	7.99492i	0.147074	+	0.254739i
$986$	20.4861			0.652410
$987$	−9.04282	+	0.141013i	−0.287836	+	0.00448850i
$988$	−38.0856			−1.21167
$989$	48.0256	+	83.1828i	1.52712	+	2.64506i
$990$	1.43969	−	2.49362i	0.0457564	−	0.0792525i
$991$	−12.9534	+	22.4359i	−0.411477	+	0.712699i	−0.995052	−	0.0993604i	$-0.968320\pi$
$991$	−12.9534	+	22.4359i	−0.411477	+	0.712699i	0.583574	+	0.812060i	$0.301654\pi$
$992$	4.17752	+	7.23567i	0.132636	+	0.229733i
$993$	−0.620919			−0.0197043
$994$	3.02481	+	5.05542i	0.0959413	+	0.160348i
$995$	−4.75608			−0.150778
$996$	−0.325008	−	0.562930i	−0.0102983	−	0.0178371i
$997$	−13.4783	+	23.3452i	−0.426863	+	0.739349i	−0.996592	−	0.0824836i	$-0.973715\pi$
$997$	−13.4783	+	23.3452i	−0.426863	+	0.739349i	0.569729	+	0.821833i	$0.307048\pi$
$998$	−4.88713	+	8.46475i	−0.154699	+	0.267947i
$999$	−11.1728	−	19.3518i	−0.353491	−	0.612264i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.i.j.221.2	✓	6
7.2	even	3	inner	770.2.i.j.331.2	yes	6
7.3	odd	6		5390.2.a.bv.1.2		3
7.4	even	3		5390.2.a.bx.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.i.j.221.2	✓	6	1.1	even	1	trivial
770.2.i.j.331.2	yes	6	7.2	even	3	inner
5390.2.a.bv.1.2		3	7.3	odd	6
5390.2.a.bx.1.2		3	7.4	even	3

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.173648 - 0.300767i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.347296 q^{6} +(-2.64543 + 0.0412527i) q^{7} -1.00000 q^{8} +(1.43969 + 2.49362i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.173648 - 0.300767i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.347296 q^{6} +(-2.64543 + 0.0412527i) q^{7} -1.00000 q^{8} +(1.43969 + 2.49362i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.173648 + 0.300767i) q^{12} +6.45336 q^{13} +(-1.35844 - 2.27038i) q^{14} -0.347296 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.06031 + 1.83651i) q^{17} +(-1.43969 + 2.49362i) q^{18} +(2.95084 + 5.11100i) q^{19} +1.00000 q^{20} +(-0.446967 + 0.802823i) q^{21} +1.00000 q^{22} +(4.29086 + 7.43199i) q^{23} +(-0.173648 + 0.300767i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.22668 + 5.58878i) q^{26} +2.04189 q^{27} +(1.28699 - 2.31164i) q^{28} -9.66044 q^{29} +(-0.173648 - 0.300767i) q^{30} +(-4.17752 + 7.23567i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.173648 - 0.300767i) q^{33} -2.12061 q^{34} +(1.35844 + 2.27038i) q^{35} -2.87939 q^{36} +(-5.47178 - 9.47740i) q^{37} +(-2.95084 + 5.11100i) q^{38} +(1.12061 - 1.94096i) q^{39} +(0.500000 + 0.866025i) q^{40} +4.24123 q^{41} +(-0.918748 + 0.0143269i) q^{42} +11.1925 q^{43} +(0.500000 + 0.866025i) q^{44} +(1.43969 - 2.49362i) q^{45} +(-4.29086 + 7.43199i) q^{46} +(4.92127 + 8.52390i) q^{47} -0.347296 q^{48} +(6.99660 - 0.218262i) q^{49} -1.00000 q^{50} +(0.368241 + 0.637812i) q^{51} +(-3.22668 + 5.58878i) q^{52} +(1.70574 - 2.95442i) q^{53} +(1.02094 + 1.76833i) q^{54} -1.00000 q^{55} +(2.64543 - 0.0412527i) q^{56} +2.04963 q^{57} +(-4.83022 - 8.36619i) q^{58} +(1.75877 - 3.04628i) q^{59} +(0.173648 - 0.300767i) q^{60} +(-3.35117 - 5.80439i) q^{61} -8.35504 q^{62} +(-3.91147 - 6.53731i) q^{63} +1.00000 q^{64} +(-3.22668 - 5.58878i) q^{65} +(0.173648 - 0.300767i) q^{66} +(0.911474 - 1.57872i) q^{67} +(-1.06031 - 1.83651i) q^{68} +2.98040 q^{69} +(-1.28699 + 2.31164i) q^{70} -2.22668 q^{71} +(-1.43969 - 2.49362i) q^{72} +(0.194593 - 0.337044i) q^{73} +(5.47178 - 9.47740i) q^{74} +(0.173648 + 0.300767i) q^{75} -5.90167 q^{76} +(-1.28699 + 2.31164i) q^{77} +2.24123 q^{78} +(-2.34730 - 4.06564i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-3.96451 + 6.86673i) q^{81} +(2.12061 + 3.67301i) q^{82} -1.87164 q^{83} +(-0.471782 - 0.788496i) q^{84} +2.12061 q^{85} +(5.59627 + 9.69302i) q^{86} +(-1.67752 + 2.90555i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-4.64930 - 8.05282i) q^{89} +2.87939 q^{90} +(-17.0719 + 0.266219i) q^{91} -8.58172 q^{92} +(1.45084 + 2.51292i) q^{93} +(-4.92127 + 8.52390i) q^{94} +(2.95084 - 5.11100i) q^{95} +(-0.173648 - 0.300767i) q^{96} +5.30541 q^{97} +(3.68732 + 5.95010i) q^{98} +2.87939 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^8 + 3 * q^9	\( 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 12 q^{13} - 3 q^{16} - 12 q^{17} - 3 q^{18} + 6 q^{19} + 6 q^{20} - 15 q^{21} + 6 q^{22} - 6 q^{23} - 3 q^{25} + 6 q^{26} + 6 q^{27} - 12 q^{29} + 3 q^{32} - 24 q^{34} - 6 q^{36} - 18 q^{37} - 6 q^{38} + 18 q^{39} + 3 q^{40} + 48 q^{41} - 3 q^{42} + 12 q^{43} + 3 q^{44} + 3 q^{45} + 6 q^{46} + 12 q^{47} - 6 q^{50} - 3 q^{51} - 6 q^{52} + 3 q^{54} - 6 q^{55} - 42 q^{57} - 6 q^{58} - 12 q^{59} + 6 q^{61} - 3 q^{63} + 6 q^{64} - 6 q^{65} - 15 q^{67} - 12 q^{68} + 12 q^{69} - 3 q^{72} - 3 q^{73} + 18 q^{74} - 12 q^{76} + 36 q^{78} - 12 q^{79} - 3 q^{80} + 9 q^{81} + 24 q^{82} - 48 q^{83} + 12 q^{84} + 24 q^{85} + 6 q^{86} + 15 q^{87} - 3 q^{88} + 12 q^{89} + 6 q^{90} - 36 q^{91} + 12 q^{92} - 3 q^{93} - 12 q^{94} + 6 q^{95} + 36 q^{97} + 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 12 * q^13 - 3 * q^16 - 12 * q^17 - 3 * q^18 + 6 * q^19 + 6 * q^20 - 15 * q^21 + 6 * q^22 - 6 * q^23 - 3 * q^25 + 6 * q^26 + 6 * q^27 - 12 * q^29 + 3 * q^32 - 24 * q^34 - 6 * q^36 - 18 * q^37 - 6 * q^38 + 18 * q^39 + 3 * q^40 + 48 * q^41 - 3 * q^42 + 12 * q^43 + 3 * q^44 + 3 * q^45 + 6 * q^46 + 12 * q^47 - 6 * q^50 - 3 * q^51 - 6 * q^52 + 3 * q^54 - 6 * q^55 - 42 * q^57 - 6 * q^58 - 12 * q^59 + 6 * q^61 - 3 * q^63 + 6 * q^64 - 6 * q^65 - 15 * q^67 - 12 * q^68 + 12 * q^69 - 3 * q^72 - 3 * q^73 + 18 * q^74 - 12 * q^76 + 36 * q^78 - 12 * q^79 - 3 * q^80 + 9 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^84 + 24 * q^85 + 6 * q^86 + 15 * q^87 - 3 * q^88 + 12 * q^89 + 6 * q^90 - 36 * q^91 + 12 * q^92 - 3 * q^93 - 12 * q^94 + 6 * q^95 + 36 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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