LMFDB - Embedded newform 770.2.i.j.221.1

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			221.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	770.221
Dual form			770.2.i.j.331.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.939693 + 1.62760i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.87939 q^{6} +(1.35844 + 2.27038i) q^{7} -1.00000 q^{8} +(-0.266044 - 0.460802i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.939693 + 1.62760i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.87939 q^{6} +(1.35844 + 2.27038i) q^{7} -1.00000 q^{8} +(-0.266044 - 0.460802i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.939693 - 1.62760i) q^{12} -4.82295 q^{13} +(-1.28699 + 2.31164i) q^{14} +1.87939 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.76604 + 4.79093i) q^{17} +(0.266044 - 0.460802i) q^{18} +(3.40033 + 5.88954i) q^{19} +1.00000 q^{20} +(-4.97178 + 0.0775297i) q^{21} +1.00000 q^{22} +(-3.71688 - 6.43783i) q^{23} +(0.939693 - 1.62760i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.41147 - 4.17680i) q^{26} -4.63816 q^{27} +(-2.64543 + 0.0412527i) q^{28} -3.73648 q^{29} +(0.939693 + 1.62760i) q^{30} +(1.01114 - 1.75135i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.939693 + 1.62760i) q^{33} -5.53209 q^{34} +(1.28699 - 2.31164i) q^{35} +0.532089 q^{36} +(-2.58125 - 4.47086i) q^{37} +(-3.40033 + 5.88954i) q^{38} +(4.53209 - 7.84981i) q^{39} +(0.500000 + 0.866025i) q^{40} +11.0642 q^{41} +(-2.55303 - 4.26692i) q^{42} +4.08378 q^{43} +(0.500000 + 0.866025i) q^{44} +(-0.266044 + 0.460802i) q^{45} +(3.71688 - 6.43783i) q^{46} +(-5.17024 - 8.95513i) q^{47} +1.87939 q^{48} +(-3.30928 + 6.16836i) q^{49} -1.00000 q^{50} +(-5.19846 - 9.00400i) q^{51} +(2.41147 - 4.17680i) q^{52} +(-0.592396 + 1.02606i) q^{53} +(-2.31908 - 4.01676i) q^{54} -1.00000 q^{55} +(-1.35844 - 2.27038i) q^{56} -12.7811 q^{57} +(-1.86824 - 3.23589i) q^{58} +(-5.06418 + 8.77141i) q^{59} +(-0.939693 + 1.62760i) q^{60} +(2.95084 + 5.11100i) q^{61} +2.02229 q^{62} +(0.684793 - 1.23000i) q^{63} +1.00000 q^{64} +(2.41147 + 4.17680i) q^{65} +(-0.939693 + 1.62760i) q^{66} +(-3.68479 + 6.38225i) q^{67} +(-2.76604 - 4.79093i) q^{68} +13.9709 q^{69} +(2.64543 - 0.0412527i) q^{70} +3.41147 q^{71} +(0.266044 + 0.460802i) q^{72} +(-4.25877 + 7.37641i) q^{73} +(2.58125 - 4.47086i) q^{74} +(-0.939693 - 1.62760i) q^{75} -6.80066 q^{76} +(2.64543 - 0.0412527i) q^{77} +9.06418 q^{78} +(-0.120615 - 0.208911i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.15657 - 8.93145i) q^{81} +(5.53209 + 9.58186i) q^{82} -6.61081 q^{83} +(2.41875 - 4.34445i) q^{84} +5.53209 q^{85} +(2.04189 + 3.53666i) q^{86} +(3.51114 - 6.08148i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(3.42989 + 5.94075i) q^{89} -0.532089 q^{90} +(-6.55169 - 10.9499i) q^{91} +7.43376 q^{92} +(1.90033 + 3.29147i) q^{93} +(5.17024 - 8.95513i) q^{94} +(3.40033 - 5.88954i) q^{95} +(0.939693 + 1.62760i) q^{96} +9.75877 q^{97} +(-6.99660 + 0.218262i) q^{98} -0.532089 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
$3$	−0.939693	+	1.62760i	−0.542532	+	0.939693i	0.456226	+	0.889864i	$0.349201\pi$
$3$	−0.939693	+	1.62760i	−0.542532	+	0.939693i	−0.998758	+	0.0498287i	$0.984132\pi$
$4$	−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
$6$	−1.87939			−0.767256
$7$	1.35844	+	2.27038i	0.513442	+	0.858124i
$7$	1.35844	+	2.27038i	0.513442	+	0.858124i
$8$	−1.00000			−0.353553
$9$	−0.266044	−	0.460802i	−0.0886815	−	0.153601i
$10$	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
$12$	−0.939693	−	1.62760i	−0.271266	−	0.469846i
$13$	−4.82295			−1.33765			−0.668823	−	0.743422i	$-0.733201\pi$
$13$	−4.82295			−1.33765			−0.668823	+	0.743422i	$0.733201\pi$
$14$	−1.28699	+	2.31164i	−0.343962	+	0.617811i
$15$	1.87939			0.485255
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.76604	+	4.79093i	−0.670864	+	1.16197i	0.306795	+	0.951776i	$0.400743\pi$
$17$	−2.76604	+	4.79093i	−0.670864	+	1.16197i	−0.977659	+	0.210195i	$0.932590\pi$
$18$	0.266044	−	0.460802i	0.0627073	−	0.108612i
$19$	3.40033	+	5.88954i	0.780089	+	1.35115i	0.931889	+	0.362743i	$0.118160\pi$
$19$	3.40033	+	5.88954i	0.780089	+	1.35115i	−0.151800	+	0.988411i	$0.548507\pi$
$20$	1.00000			0.223607
$21$	−4.97178	+	0.0775297i	−1.08493	+	0.0169184i
$22$	1.00000			0.213201
$23$	−3.71688	−	6.43783i	−0.775023	−	1.34238i	−0.934781	−	0.355224i	$-0.884405\pi$
$23$	−3.71688	−	6.43783i	−0.775023	−	1.34238i	0.159758	−	0.987156i	$-0.448929\pi$
$24$	0.939693	−	1.62760i	0.191814	−	0.332232i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.41147	−	4.17680i	−0.472929	−	0.819137i
$27$	−4.63816			−0.892613
$28$	−2.64543	+	0.0412527i	−0.499939	+	0.00779602i
$29$	−3.73648			−0.693847			−0.346924	−	0.937893i	$-0.612774\pi$
$29$	−3.73648			−0.693847			−0.346924	+	0.937893i	$0.612774\pi$
$30$	0.939693	+	1.62760i	0.171564	+	0.297157i
$31$	1.01114	−	1.75135i	0.181607	−	0.314552i	−0.760821	−	0.648962i	$-0.775203\pi$
$31$	1.01114	−	1.75135i	0.181607	−	0.314552i	0.942428	+	0.334409i	$0.108537\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.939693	+	1.62760i	0.163579	+	0.283328i
$34$	−5.53209			−0.948745
$35$	1.28699	−	2.31164i	0.217541	−	0.390738i
$36$	0.532089			0.0886815
$37$	−2.58125	−	4.47086i	−0.424355	−	0.735005i	0.572005	−	0.820250i	$-0.306166\pi$
$37$	−2.58125	−	4.47086i	−0.424355	−	0.735005i	−0.996360	+	0.0852455i	$0.972833\pi$
$38$	−3.40033	+	5.88954i	−0.551606	+	0.955410i
$39$	4.53209	−	7.84981i	0.725715	−	1.25698i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	11.0642			1.72793			0.863967	−	0.503548i	$-0.167972\pi$
$41$	11.0642			1.72793			0.863967	+	0.503548i	$0.167972\pi$
$42$	−2.55303	−	4.26692i	−0.393942	−	0.658401i
$43$	4.08378			0.622770			0.311385	−	0.950284i	$-0.399207\pi$
$43$	4.08378			0.622770			0.311385	+	0.950284i	$0.399207\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	−0.266044	+	0.460802i	−0.0396596	+	0.0686924i
$46$	3.71688	−	6.43783i	0.548024	−	0.949206i
$47$	−5.17024	−	8.95513i	−0.754158	−	1.30624i	−0.945792	−	0.324773i	$-0.894712\pi$
$47$	−5.17024	−	8.95513i	−0.754158	−	1.30624i	0.191634	−	0.981466i	$-0.438621\pi$
$48$	1.87939			0.271266
$49$	−3.30928	+	6.16836i	−0.472754	+	0.881194i
$50$	−1.00000			−0.141421
$51$	−5.19846	−	9.00400i	−0.727930	−	1.26081i
$52$	2.41147	−	4.17680i	0.334411	−	0.579217i
$53$	−0.592396	+	1.02606i	−0.0813719	+	0.140940i	−0.903839	−	0.427872i	$-0.859263\pi$
$53$	−0.592396	+	1.02606i	−0.0813719	+	0.140940i	0.822468	+	0.568812i	$0.192597\pi$
$54$	−2.31908	−	4.01676i	−0.315587	−	0.546612i
$55$	−1.00000			−0.134840
$56$	−1.35844	−	2.27038i	−0.181529	−	0.303393i
$57$	−12.7811			−1.69289
$58$	−1.86824	−	3.23589i	−0.245312	−	0.424893i
$59$	−5.06418	+	8.77141i	−0.659300	+	1.14194i	0.321497	+	0.946910i	$0.395814\pi$
$59$	−5.06418	+	8.77141i	−0.659300	+	1.14194i	−0.980797	+	0.195030i	$0.937519\pi$
$60$	−0.939693	+	1.62760i	−0.121314	+	0.210122i
$61$	2.95084	+	5.11100i	0.377816	+	0.654396i	0.990744	−	0.135742i	$-0.0433419\pi$
$61$	2.95084	+	5.11100i	0.377816	+	0.654396i	−0.612928	+	0.790139i	$0.710009\pi$
$62$	2.02229			0.256831
$63$	0.684793	−	1.23000i	0.0862757	−	0.154965i
$64$	1.00000			0.125000
$65$	2.41147	+	4.17680i	0.299107	+	0.518068i
$66$	−0.939693	+	1.62760i	−0.115668	+	0.200343i
$67$	−3.68479	+	6.38225i	−0.450169	+	0.779716i	−0.998396	−	0.0566138i	$-0.981970\pi$
$67$	−3.68479	+	6.38225i	−0.450169	+	0.779716i	0.548227	+	0.836330i	$0.315303\pi$
$68$	−2.76604	−	4.79093i	−0.335432	−	0.580986i
$69$	13.9709			1.68190
$70$	2.64543	−	0.0412527i	0.316189	−	0.00493064i
$71$	3.41147			0.404867			0.202434	−	0.979296i	$-0.435115\pi$
$71$	3.41147			0.404867			0.202434	+	0.979296i	$0.435115\pi$
$72$	0.266044	+	0.460802i	0.0313536	+	0.0543061i
$73$	−4.25877	+	7.37641i	−0.498451	+	0.863343i	−0.999998	−	0.00178727i	$-0.999431\pi$
$73$	−4.25877	+	7.37641i	−0.498451	+	0.863343i	0.501547	+	0.865130i	$0.332764\pi$
$74$	2.58125	−	4.47086i	0.300064	−	0.519727i
$75$	−0.939693	−	1.62760i	−0.108506	−	0.187939i
$76$	−6.80066			−0.780089
$77$	2.64543	−	0.0412527i	0.301475	−	0.00470118i
$78$	9.06418			1.02632
$79$	−0.120615	−	0.208911i	−0.0135702	−	0.0235043i	0.859161	−	0.511706i	$-0.170986\pi$
$79$	−0.120615	−	0.208911i	−0.0135702	−	0.0235043i	−0.872731	+	0.488202i	$0.837653\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	5.15657	−	8.93145i	0.572953	−	0.992383i
$82$	5.53209	+	9.58186i	0.610917	+	1.05814i
$83$	−6.61081			−0.725631			−0.362816	−	0.931861i	$-0.618185\pi$
$83$	−6.61081			−0.725631			−0.362816	+	0.931861i	$0.618185\pi$
$84$	2.41875	−	4.34445i	0.263907	−	0.474019i
$85$	5.53209			0.600039
$86$	2.04189	+	3.53666i	0.220183	+	0.381367i
$87$	3.51114	−	6.08148i	0.376434	−	0.652003i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	3.42989	+	5.94075i	0.363568	+	0.629718i	0.988545	−	0.150925i	$-0.0482251\pi$
$89$	3.42989	+	5.94075i	0.363568	+	0.629718i	−0.624977	+	0.780643i	$0.714892\pi$
$90$	−0.532089			−0.0560871
$91$	−6.55169	−	10.9499i	−0.686804	−	1.14787i
$92$	7.43376			0.775023
$93$	1.90033	+	3.29147i	0.197055	+	0.341309i
$94$	5.17024	−	8.95513i	0.533270	−	0.923651i
$95$	3.40033	−	5.88954i	0.348866	−	0.604254i
$96$	0.939693	+	1.62760i	0.0959070	+	0.166116i
$97$	9.75877			0.990853			0.495427	−	0.868650i	$-0.335012\pi$
$97$	9.75877			0.990853			0.495427	+	0.868650i	$0.335012\pi$
$98$	−6.99660	+	0.218262i	−0.706763	+	0.0220478i
$99$	−0.532089			−0.0534769
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−5.68479	+	9.84635i	−0.565658	+	0.979748i	0.431330	+	0.902194i	$0.358044\pi$
$101$	−5.68479	+	9.84635i	−0.565658	+	0.979748i	−0.996988	+	0.0775542i	$0.975289\pi$
$102$	5.19846	−	9.00400i	0.514725	−	0.891529i
$103$	2.46791	+	4.27455i	0.243171	+	0.421184i	0.961616	−	0.274400i	$-0.0884792\pi$
$103$	2.46791	+	4.27455i	0.243171	+	0.421184i	−0.718445	+	0.695584i	$0.755146\pi$
$104$	4.82295			0.472929
$105$	2.55303	+	4.26692i	0.249151	+	0.416409i
$106$	−1.18479			−0.115077
$107$	1.59627	+	2.76481i	0.154317	+	0.267285i	0.932810	−	0.360368i	$-0.117349\pi$
$107$	1.59627	+	2.76481i	0.154317	+	0.267285i	−0.778493	+	0.627653i	$0.784016\pi$
$108$	2.31908	−	4.01676i	0.223153	−	0.386513i
$109$	−3.99020	+	6.91123i	−0.382192	+	0.661976i	−0.991375	−	0.131054i	$-0.958164\pi$
$109$	−3.99020	+	6.91123i	−0.382192	+	0.661976i	0.609183	+	0.793029i	$0.291497\pi$
$110$	−0.500000	−	0.866025i	−0.0476731	−	0.0825723i
$111$	9.70233			0.920905
$112$	1.28699	−	2.31164i	0.121609	−	0.218429i
$113$	20.5817			1.93617			0.968083	−	0.250631i	$-0.0806382\pi$
$113$	20.5817			1.93617			0.968083	+	0.250631i	$0.0806382\pi$
$114$	−6.39053	−	11.0687i	−0.598528	−	1.03668i
$115$	−3.71688	+	6.43783i	−0.346601	+	0.600331i
$116$	1.86824	−	3.23589i	0.173462	−	0.300445i
$117$	1.28312	+	2.22243i	0.118624	+	0.205463i
$118$	−10.1284			−0.932391
$119$	−14.6348	+	0.228213i	−1.34157	+	0.0209203i
$120$	−1.87939			−0.171564
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−2.95084	+	5.11100i	−0.267156	+	0.462728i
$123$	−10.3969	+	18.0080i	−0.937459	+	1.62373i
$124$	1.01114	+	1.75135i	0.0908034	+	0.157276i
$125$	1.00000			0.0894427
$126$	1.40760	−	0.0219501i	0.125399	−	0.00195547i
$127$	−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
$129$	−3.83750	+	6.64674i	−0.337873	+	0.585213i
$130$	−2.41147	+	4.17680i	−0.211500	+	0.366329i
$131$	−7.52481	−	13.0334i	−0.657446	−	1.13873i	−0.981275	−	0.192614i	$-0.938303\pi$
$131$	−7.52481	−	13.0334i	−0.657446	−	1.13873i	0.323828	−	0.946116i	$-0.395030\pi$
$132$	−1.87939			−0.163579
$133$	−8.75237	+	15.7206i	−0.758927	+	1.36315i
$134$	−7.36959			−0.636635
$135$	2.31908	+	4.01676i	0.199594	+	0.345708i
$136$	2.76604	−	4.79093i	0.237186	−	0.410819i
$137$	−5.80066	+	10.0470i	−0.495584	+	0.858376i	−0.999987	−	0.00509191i	$-0.998379\pi$
$137$	−5.80066	+	10.0470i	−0.495584	+	0.858376i	0.504403	+	0.863468i	$0.331713\pi$
$138$	6.98545	+	12.0992i	0.594641	+	1.02995i
$139$	21.0155			1.78251			0.891255	−	0.453503i	$-0.149826\pi$
$139$	21.0155			1.78251			0.891255	+	0.453503i	$0.149826\pi$
$140$	1.35844	+	2.27038i	0.114809	+	0.191882i
$141$	19.4338			1.63662
$142$	1.70574	+	2.95442i	0.143142	+	0.247930i
$143$	−2.41147	+	4.17680i	−0.201658	+	0.349281i
$144$	−0.266044	+	0.460802i	−0.0221704	+	0.0384002i
$145$	1.86824	+	3.23589i	0.155149	+	0.268726i
$146$	−8.51754			−0.704917
$147$	−6.92989	−	11.1825i	−0.571568	−	0.922319i
$148$	5.16250			0.424355
$149$	−2.10220	−	3.64111i	−0.172219	−	0.298291i	0.766977	−	0.641675i	$-0.221760\pi$
$149$	−2.10220	−	3.64111i	−0.172219	−	0.298291i	−0.939195	+	0.343384i	$0.888427\pi$
$150$	0.939693	−	1.62760i	0.0767256	−	0.132893i
$151$	0.453363	−	0.785248i	0.0368942	−	0.0639026i	−0.846989	−	0.531611i	$-0.821587\pi$
$151$	0.453363	−	0.785248i	0.0368942	−	0.0639026i	0.883883	+	0.467708i	$0.154920\pi$
$152$	−3.40033	−	5.88954i	−0.275803	−	0.477705i
$153$	2.94356			0.237973
$154$	1.35844	+	2.27038i	0.109466	+	0.182953i
$155$	−2.02229			−0.162434
$156$	4.53209	+	7.84981i	0.362858	+	0.628488i
$157$	−6.58512	+	11.4058i	−0.525550	+	0.910279i	0.474007	+	0.880521i	$0.342807\pi$
$157$	−6.58512	+	11.4058i	−0.525550	+	0.910279i	−0.999557	+	0.0297583i	$0.990526\pi$
$158$	0.120615	−	0.208911i	0.00959559	−	0.0166201i
$159$	−1.11334	−	1.92836i	−0.0882937	−	0.152929i
$160$	−1.00000			−0.0790569
$161$	9.56717	−	17.1842i	0.753999	−	1.35430i
$162$	10.3131			0.810277
$163$	11.6420	+	20.1646i	0.911874	+	1.57941i	0.811415	+	0.584471i	$0.198698\pi$
$163$	11.6420	+	20.1646i	0.911874	+	1.57941i	0.100459	+	0.994941i	$0.467969\pi$
$164$	−5.53209	+	9.58186i	−0.431984	+	0.748217i
$165$	0.939693	−	1.62760i	0.0731550	−	0.126708i
$166$	−3.30541	−	5.72513i	−0.256549	−	0.444357i
$167$	−7.07192			−0.547241			−0.273621	−	0.961838i	$-0.588221\pi$
$167$	−7.07192			−0.547241			−0.273621	+	0.961838i	$0.588221\pi$
$168$	4.97178	−	0.0775297i	0.383581	−	0.00598154i
$169$	10.2608			0.789295
$170$	2.76604	+	4.79093i	0.212146	+	0.367448i
$171$	1.80928	−	3.13376i	0.138359	−	0.239645i
$172$	−2.04189	+	3.53666i	−0.155693	+	0.269667i
$173$	12.8229	+	22.2100i	0.974911	+	1.68859i	0.680229	+	0.732999i	$0.261880\pi$
$173$	12.8229	+	22.2100i	0.974911	+	1.68859i	0.294681	+	0.955596i	$0.404787\pi$
$174$	7.02229			0.532358
$175$	−2.64543	+	0.0412527i	−0.199976	+	0.00311841i
$176$	−1.00000			−0.0753778
$177$	−9.51754	−	16.4849i	−0.715382	−	1.23908i
$178$	−3.42989	+	5.94075i	−0.257081	+	0.445278i
$179$	2.36959	−	4.10424i	0.177111	−	0.306765i	−0.763779	−	0.645478i	$-0.776658\pi$
$179$	2.36959	−	4.10424i	0.177111	−	0.306765i	0.940890	+	0.338713i	$0.109991\pi$
$180$	−0.266044	−	0.460802i	−0.0198298	−	0.0343462i
$181$	−20.0155			−1.48774			−0.743870	−	0.668325i	$-0.767012\pi$
$181$	−20.0155			−1.48774			−0.743870	+	0.668325i	$0.767012\pi$
$182$	6.20708	−	11.1489i	0.460099	−	0.826411i
$183$	−11.0915			−0.819909
$184$	3.71688	+	6.43783i	0.274012	+	0.474603i
$185$	−2.58125	+	4.47086i	−0.189777	+	0.328704i
$186$	−1.90033	+	3.29147i	−0.139339	+	0.241342i
$187$	2.76604	+	4.79093i	0.202273	+	0.350347i
$188$	10.3405			0.754158
$189$	−6.30066	−	10.5304i	−0.458306	−	0.765973i
$190$	6.80066			0.493372
$191$	6.56418	+	11.3695i	0.474967	+	0.822667i	0.999589	−	0.0286680i	$-0.00912657\pi$
$191$	6.56418	+	11.3695i	0.474967	+	0.822667i	−0.524622	+	0.851335i	$0.675793\pi$
$192$	−0.939693	+	1.62760i	−0.0678165	+	0.117462i
$193$	6.32888	−	10.9619i	0.455563	−	0.789058i	−0.543158	−	0.839631i	$-0.682771\pi$
$193$	6.32888	−	10.9619i	0.455563	−	0.789058i	0.998720	+	0.0505731i	$0.0161048\pi$
$194$	4.87939	+	8.45134i	0.350319	+	0.606771i
$195$	−9.06418			−0.649099
$196$	−3.68732	−	5.95010i	−0.263380	−	0.425007i
$197$	19.8580			1.41483			0.707413	−	0.706800i	$-0.249862\pi$
$197$	19.8580			1.41483			0.707413	+	0.706800i	$0.249862\pi$
$198$	−0.266044	−	0.460802i	−0.0189070	−	0.0327478i
$199$	−8.68392	+	15.0410i	−0.615586	+	1.06623i	0.374695	+	0.927148i	$0.377747\pi$
$199$	−8.68392	+	15.0410i	−0.615586	+	1.06623i	−0.990281	+	0.139079i	$0.955586\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−6.92514	−	11.9947i	−0.488462	−	0.846041i
$202$	−11.3696			−0.799961
$203$	−5.07579	−	8.48324i	−0.356251	−	0.595407i
$204$	10.3969			0.727930
$205$	−5.53209	−	9.58186i	−0.386378	−	0.669226i
$206$	−2.46791	+	4.27455i	−0.171948	+	0.297822i
$207$	−1.97771	+	3.42550i	−0.137460	+	0.238088i
$208$	2.41147	+	4.17680i	0.167206	+	0.289609i
$209$	6.80066			0.470411
$210$	−2.41875	+	4.34445i	−0.166909	+	0.299796i
$211$	1.68180			0.115780			0.0578899	−	0.998323i	$-0.481563\pi$
$211$	1.68180			0.115780			0.0578899	+	0.998323i	$0.481563\pi$
$212$	−0.592396	−	1.02606i	−0.0406859	−	0.0704701i
$213$	−3.20574	+	5.55250i	−0.219653	+	0.380451i
$214$	−1.59627	+	2.76481i	−0.109119	+	0.188999i
$215$	−2.04189	−	3.53666i	−0.139256	−	0.241198i
$216$	4.63816			0.315587
$217$	5.34982	−	0.0834248i	0.363170	−	0.00566325i
$218$	−7.98040			−0.540501
$219$	−8.00387	−	13.8631i	−0.540851	−	0.936782i
$220$	0.500000	−	0.866025i	0.0337100	−	0.0583874i
$221$	13.3405	−	23.1064i	0.897378	−	1.55431i
$222$	4.85117	+	8.40247i	0.325589	+	0.563937i
$223$	0.128356			0.00859532			0.00429766	−	0.999991i	$-0.498632\pi$
$223$	0.128356			0.00859532			0.00429766	+	0.999991i	$0.498632\pi$
$224$	2.64543	−	0.0412527i	0.176755	−	0.00275631i
$225$	0.532089			0.0354726
$226$	10.2909	+	17.8243i	0.684538	+	1.18565i
$227$	12.2121	−	21.1520i	0.810548	−	1.40391i	−0.101933	−	0.994791i	$-0.532503\pi$
$227$	12.2121	−	21.1520i	0.810548	−	1.40391i	0.912481	−	0.409119i	$-0.134164\pi$
$228$	6.39053	−	11.0687i	0.423223	−	0.733044i
$229$	−1.36184	−	2.35878i	−0.0899932	−	0.155873i	0.817515	−	0.575908i	$-0.195351\pi$
$229$	−1.36184	−	2.35878i	−0.0899932	−	0.155873i	−0.907508	+	0.420035i	$0.862018\pi$
$230$	−7.43376			−0.490168
$231$	−2.41875	+	4.34445i	−0.159142	+	0.285844i
$232$	3.73648			0.245312
$233$	−1.06031	−	1.83651i	−0.0694630	−	0.120314i	0.829202	−	0.558949i	$-0.188795\pi$
$233$	−1.06031	−	1.83651i	−0.0694630	−	0.120314i	−0.898665	+	0.438636i	$0.855462\pi$
$234$	−1.28312	+	2.22243i	−0.0838801	+	0.145285i
$235$	−5.17024	+	8.95513i	−0.337270	+	0.584168i
$236$	−5.06418	−	8.77141i	−0.329650	−	0.570970i
$237$	0.453363			0.0294491
$238$	−7.51501	−	12.5600i	−0.487126	−	0.814141i
$239$	24.3114			1.57257			0.786287	−	0.617862i	$-0.212001\pi$
$239$	24.3114			1.57257			0.786287	+	0.617862i	$0.212001\pi$
$240$	−0.939693	−	1.62760i	−0.0606569	−	0.105061i
$241$	−2.54664	+	4.41090i	−0.164043	+	0.284131i	−0.936315	−	0.351161i	$-0.885787\pi$
$241$	−2.54664	+	4.41090i	−0.164043	+	0.284131i	0.772272	+	0.635292i	$0.219120\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$	2.73396	+	4.73535i	0.175383	+	0.303773i
$244$	−5.90167			−0.377816
$245$	6.99660	−	0.218262i	0.446996	−	0.0139443i
$246$	−20.7939			−1.32577
$247$	−16.3996	−	28.4050i	−1.04348	−	1.80736i
$248$	−1.01114	+	1.75135i	−0.0642077	+	0.111211i
$249$	6.21213	−	10.7597i	0.393678	−	0.681870i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	11.3500			0.716405			0.358202	−	0.933644i	$-0.383390\pi$
$251$	11.3500			0.716405			0.358202	+	0.933644i	$0.383390\pi$
$252$	0.722811	+	1.20805i	0.0455328	+	0.0760997i
$253$	−7.43376			−0.467357
$254$	−0.500000	−	0.866025i	−0.0313728	−	0.0543393i
$255$	−5.19846	+	9.00400i	−0.325540	+	0.563852i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.78106	+	15.2092i	0.547747	+	0.948726i	0.998428	+	0.0560413i	$0.0178479\pi$
$257$	8.78106	+	15.2092i	0.547747	+	0.948726i	−0.450681	+	0.892685i	$0.648819\pi$
$258$	−7.67499			−0.477824
$259$	6.64409	−	11.9338i	0.412843	−	0.741532i
$260$	−4.82295			−0.299107
$261$	0.994070	+	1.72178i	0.0615314	+	0.106576i
$262$	7.52481	−	13.0334i	0.464885	−	0.805204i
$263$	6.80453	−	11.7858i	0.419585	−	0.726743i	−0.576312	−	0.817229i	$-0.695509\pi$
$263$	6.80453	−	11.7858i	0.419585	−	0.726743i	0.995898	+	0.0904864i	$0.0288422\pi$
$264$	−0.939693	−	1.62760i	−0.0578341	−	0.100172i
$265$	1.18479			0.0727812
$266$	−17.9907	+	0.280545i	−1.10308	+	0.0172013i
$267$	−12.8922			−0.788989
$268$	−3.68479	−	6.38225i	−0.225085	−	0.389858i
$269$	9.49794	−	16.4509i	0.579100	−	1.00303i	−0.416483	−	0.909143i	$-0.636738\pi$
$269$	9.49794	−	16.4509i	0.579100	−	1.00303i	0.995583	−	0.0938866i	$-0.0299291\pi$
$270$	−2.31908	+	4.01676i	−0.141135	+	0.244452i
$271$	−7.68004	−	13.3022i	−0.466529	−	0.808053i	0.532740	−	0.846279i	$-0.321163\pi$
$271$	−7.68004	−	13.3022i	−0.466529	−	0.808053i	−0.999269	+	0.0382264i	$0.987829\pi$
$272$	5.53209			0.335432
$273$	23.9786	−	0.373922i	1.45125	−	0.0226308i
$274$	−11.6013			−0.700861
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	−6.98545	+	12.0992i	−0.420475	+	0.728284i
$277$	−7.29860	+	12.6415i	−0.438530	+	0.759557i	−0.997576	−	0.0695797i	$-0.977834\pi$
$277$	−7.29860	+	12.6415i	−0.438530	+	0.759557i	0.559046	+	0.829137i	$0.311168\pi$
$278$	10.5077	+	18.1999i	0.630212	+	1.09156i
$279$	−1.07604			−0.0644207
$280$	−1.28699	+	2.31164i	−0.0769123	+	0.138147i
$281$	−16.9905			−1.01357			−0.506784	−	0.862073i	$-0.669166\pi$
$281$	−16.9905			−1.01357			−0.506784	+	0.862073i	$0.669166\pi$
$282$	9.71688	+	16.8301i	0.578632	+	1.00222i
$283$	5.16250	−	8.94172i	0.306879	−	0.531530i	−0.670799	−	0.741639i	$-0.734049\pi$
$283$	5.16250	−	8.94172i	0.306879	−	0.531530i	0.977678	+	0.210109i	$0.0673820\pi$
$284$	−1.70574	+	2.95442i	−0.101217	+	0.175313i
$285$	6.39053	+	11.0687i	0.378542	+	0.655655i
$286$	−4.82295			−0.285187
$287$	15.0300	+	25.1199i	0.887195	+	1.48278i
$288$	−0.532089			−0.0313536
$289$	−6.80200	−	11.7814i	−0.400118	−	0.693024i
$290$	−1.86824	+	3.23589i	−0.109707	+	0.190018i
$291$	−9.17024	+	15.8833i	−0.537569	+	0.931097i
$292$	−4.25877	−	7.37641i	−0.249226	−	0.431672i
$293$	1.47296			0.0860514			0.0430257	−	0.999074i	$-0.486300\pi$
$293$	1.47296			0.0860514			0.0430257	+	0.999074i	$0.486300\pi$
$294$	6.21941	−	11.5927i	0.362723	−	0.676102i
$295$	10.1284			0.589696
$296$	2.58125	+	4.47086i	0.150032	+	0.259863i
$297$	−2.31908	+	4.01676i	−0.134567	+	0.233076i
$298$	2.10220	−	3.64111i	0.121777	−	0.210924i
$299$	17.9263	+	31.0493i	1.03671	+	1.79563i
$300$	1.87939			0.108506
$301$	5.54757	+	9.27174i	0.319757	+	0.534414i
$302$	0.906726			0.0521762
$303$	−10.6839	−	18.5051i	−0.613775	−	1.06309i
$304$	3.40033	−	5.88954i	0.195022	−	0.337789i
$305$	2.95084	−	5.11100i	0.168964	−	0.292655i
$306$	1.47178	+	2.54920i	0.0841361	+	0.145728i
$307$	−25.3655			−1.44768			−0.723842	−	0.689966i	$-0.757625\pi$
$307$	−25.3655			−1.44768			−0.723842	+	0.689966i	$0.757625\pi$
$308$	−1.28699	+	2.31164i	−0.0733330	+	0.131718i
$309$	−9.27631			−0.527711
$310$	−1.01114	−	1.75135i	−0.0574291	−	0.0994702i
$311$	11.9217	−	20.6491i	0.676020	−	1.17090i	−0.300150	−	0.953892i	$-0.597037\pi$
$311$	11.9217	−	20.6491i	0.676020	−	1.17090i	0.976170	−	0.217009i	$-0.0696300\pi$
$312$	−4.53209	+	7.84981i	−0.256579	+	0.444408i
$313$	8.53714	+	14.7868i	0.482548	+	0.835797i	0.999799	−	0.0200362i	$-0.00637815\pi$
$313$	8.53714	+	14.7868i	0.482548	+	0.835797i	−0.517251	+	0.855833i	$0.673045\pi$
$314$	−13.1702			−0.743240
$315$	−1.40760	+	0.0219501i	−0.0793095	+	0.00123675i
$316$	0.241230			0.0135702
$317$	−11.3858	−	19.7208i	−0.639489	−	1.10763i	−0.985545	−	0.169414i	$-0.945813\pi$
$317$	−11.3858	−	19.7208i	−0.639489	−	1.10763i	0.346056	−	0.938214i	$-0.387521\pi$
$318$	1.11334	−	1.92836i	0.0624331	−	0.108137i
$319$	−1.86824	+	3.23589i	−0.104601	+	0.181175i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−6.00000			−0.334887
$322$	19.6655	−	0.306663i	1.09592	−	0.0170896i
$323$	−37.6219			−2.09334
$324$	5.15657	+	8.93145i	0.286476	+	0.496192i
$325$	2.41147	−	4.17680i	0.133765	−	0.231687i
$326$	−11.6420	+	20.1646i	−0.644792	+	1.11681i
$327$	−7.49912	−	12.9889i	−0.414702	−	0.718286i
$328$	−11.0642			−0.610917
$329$	13.3081	−	23.9034i	0.733699	−	1.31784i
$330$	1.87939			0.103457
$331$	−9.94356	−	17.2228i	−0.546548	−	0.946648i	−0.998508	−	0.0546101i	$-0.982608\pi$
$331$	−9.94356	−	17.2228i	−0.546548	−	0.946648i	0.451960	−	0.892038i	$-0.350725\pi$
$332$	3.30541	−	5.72513i	0.181408	−	0.314208i
$333$	−1.37346	+	2.37889i	−0.0752649	+	0.130363i
$334$	−3.53596	−	6.12446i	−0.193479	−	0.335116i
$335$	7.36959			0.402643
$336$	2.55303	+	4.26692i	0.139279	+	0.232780i
$337$	7.85710			0.428003			0.214002	−	0.976833i	$-0.431350\pi$
$337$	7.85710			0.428003			0.214002	+	0.976833i	$0.431350\pi$
$338$	5.13041	+	8.88614i	0.279058	+	0.483342i
$339$	−19.3405	+	33.4987i	−1.05043	+	1.81940i
$340$	−2.76604	+	4.79093i	−0.150010	+	0.259825i
$341$	−1.01114	−	1.75135i	−0.0547565	−	0.0948411i
$342$	3.61856			0.195669
$343$	−18.5000	+	0.866025i	−0.998906	+	0.0467610i
$344$	−4.08378			−0.220183
$345$	−6.98545	−	12.0992i	−0.376084	−	0.651397i
$346$	−12.8229	+	22.2100i	−0.689366	+	1.19402i
$347$	6.55438	−	11.3525i	0.351857	−	0.609435i	−0.634717	−	0.772744i	$-0.718884\pi$
$347$	6.55438	−	11.3525i	0.351857	−	0.609435i	0.986575	+	0.163309i	$0.0522169\pi$
$348$	3.51114	+	6.08148i	0.188217	+	0.326002i
$349$	−11.0547			−0.591744			−0.295872	−	0.955228i	$-0.595610\pi$
$349$	−11.0547			−0.591744			−0.295872	+	0.955228i	$0.595610\pi$
$350$	−1.35844	−	2.27038i	−0.0726117	−	0.121357i
$351$	22.3696			1.19400
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	9.98545	−	17.2953i	0.531472	−	0.920536i	−0.467853	−	0.883806i	$-0.654972\pi$
$353$	9.98545	−	17.2953i	0.531472	−	0.920536i	0.999325	−	0.0367303i	$-0.0116943\pi$
$354$	9.51754	−	16.4849i	0.505852	−	0.876161i
$355$	−1.70574	−	2.95442i	−0.0905311	−	0.156805i
$356$	−6.85978			−0.363568
$357$	13.3807	−	24.0339i	0.708183	−	1.27201i
$358$	4.73917			0.250473
$359$	1.73917	+	3.01233i	0.0917899	+	0.158985i	0.908264	−	0.418397i	$-0.137408\pi$
$359$	1.73917	+	3.01233i	0.0917899	+	0.158985i	−0.816474	+	0.577382i	$0.804075\pi$
$360$	0.266044	−	0.460802i	0.0140218	−	0.0242864i
$361$	−13.6245	+	23.5983i	−0.717078	+	1.24202i
$362$	−10.0077	−	17.3339i	−0.525995	−	0.911050i
$363$	1.87939			0.0986421
$364$	12.7588	−	0.198960i	0.668741	−	0.0104283i
$365$	8.51754			0.445828
$366$	−5.54576	−	9.60554i	−0.289881	−	0.502089i
$367$	−4.26857	+	7.39338i	−0.222818	+	0.385931i	−0.955662	−	0.294464i	$-0.904859\pi$
$367$	−4.26857	+	7.39338i	−0.222818	+	0.385931i	0.732845	+	0.680396i	$0.238192\pi$
$368$	−3.71688	+	6.43783i	−0.193756	+	0.335595i
$369$	−2.94356	−	5.09840i	−0.153236	−	0.265412i
$370$	−5.16250			−0.268386
$371$	−3.13429	+	0.0488759i	−0.162724	+	0.00253751i
$372$	−3.80066			−0.197055
$373$	4.99319	+	8.64846i	0.258538	+	0.447800i	0.965850	−	0.259100i	$-0.0834260\pi$
$373$	4.99319	+	8.64846i	0.258538	+	0.447800i	−0.707313	+	0.706901i	$0.750093\pi$
$374$	−2.76604	+	4.79093i	−0.143029	+	0.247733i
$375$	−0.939693	+	1.62760i	−0.0485255	+	0.0840487i
$376$	5.17024	+	8.95513i	0.266635	+	0.461825i
$377$	18.0209			0.928121
$378$	5.96926	−	10.7217i	0.307025	−	0.551466i
$379$	−19.2918			−0.990953			−0.495476	−	0.868621i	$-0.665007\pi$
$379$	−19.2918			−0.990953			−0.495476	+	0.868621i	$0.665007\pi$
$380$	3.40033	+	5.88954i	0.174433	+	0.302127i
$381$	0.939693	−	1.62760i	0.0481419	−	0.0833842i
$382$	−6.56418	+	11.3695i	−0.335853	+	0.581714i
$383$	−13.0915	−	22.6752i	−0.668945	−	1.15865i	−0.978199	−	0.207668i	$-0.933413\pi$
$383$	−13.0915	−	22.6752i	−0.668945	−	1.15865i	0.309254	−	0.950979i	$-0.399921\pi$
$384$	−1.87939			−0.0959070
$385$	−1.35844	−	2.27038i	−0.0692325	−	0.115709i
$386$	12.6578			0.644263
$387$	−1.08647	−	1.88182i	−0.0552282	−	0.0956580i
$388$	−4.87939	+	8.45134i	−0.247713	+	0.429052i
$389$	−8.49525	+	14.7142i	−0.430726	+	0.746040i	−0.996936	−	0.0782213i	$-0.975076\pi$
$389$	−8.49525	+	14.7142i	−0.430726	+	0.746040i	0.566210	+	0.824261i	$0.308409\pi$
$390$	−4.53209	−	7.84981i	−0.229491	−	0.397490i
$391$	41.1242			2.07974
$392$	3.30928	−	6.16836i	0.167144	−	0.311549i
$393$	28.2841			1.42674
$394$	9.92902	+	17.1976i	0.500217	+	0.866400i
$395$	−0.120615	+	0.208911i	−0.00606879	+	0.0105114i
$396$	0.266044	−	0.460802i	0.0133692	−	0.0231562i
$397$	9.46316	+	16.3907i	0.474943	+	0.822625i	0.999588	−	0.0286961i	$-0.00913550\pi$
$397$	9.46316	+	16.3907i	0.474943	+	0.822625i	−0.524646	+	0.851321i	$0.675802\pi$
$398$	−17.3678			−0.870571
$399$	−17.3623	−	29.0179i	−0.869203	−	1.45271i
$400$	1.00000			0.0500000
$401$	4.93969	+	8.55580i	0.246676	+	0.427256i	0.962602	−	0.270921i	$-0.0873282\pi$
$401$	4.93969	+	8.55580i	0.246676	+	0.427256i	−0.715925	+	0.698177i	$0.753995\pi$
$402$	6.92514	−	11.9947i	0.345395	−	0.598241i
$403$	−4.87670	+	8.44669i	−0.242926	+	0.420759i
$404$	−5.68479	−	9.84635i	−0.282829	−	0.489874i
$405$	−10.3131			−0.512464
$406$	4.80881	−	8.63738i	0.238657	−	0.428666i
$407$	−5.16250			−0.255896
$408$	5.19846	+	9.00400i	0.257362	+	0.445765i
$409$	8.19253	−	14.1899i	0.405095	−	0.701645i	−0.589238	−	0.807960i	$-0.700572\pi$
$409$	8.19253	−	14.1899i	0.405095	−	0.701645i	0.994332	+	0.106315i	$0.0339052\pi$
$410$	5.53209	−	9.58186i	0.273210	−	0.473214i
$411$	−10.9017	−	18.8823i	−0.537740	−	0.931393i
$412$	−4.93582			−0.243171
$413$	−26.7939	+	0.417822i	−1.31844	+	0.0205597i
$414$	−3.95542			−0.194398
$415$	3.30541	+	5.72513i	0.162256	+	0.281036i
$416$	−2.41147	+	4.17680i	−0.118232	+	0.204784i
$417$	−19.7481	+	34.2047i	−0.967068	+	1.67501i
$418$	3.40033	+	5.88954i	0.166316	+	0.288067i
$419$	−32.5681			−1.59106			−0.795528	−	0.605917i	$-0.792806\pi$
$419$	−32.5681			−1.59106			−0.795528	+	0.605917i	$0.792806\pi$
$420$	−4.97178	+	0.0775297i	−0.242598	+	0.00378306i
$421$	−4.38507			−0.213715			−0.106858	−	0.994274i	$-0.534079\pi$
$421$	−4.38507			−0.213715			−0.106858	+	0.994274i	$0.534079\pi$
$422$	0.840900	+	1.45648i	0.0409344	+	0.0709004i
$423$	−2.75103	+	4.76492i	−0.133760	+	0.231678i
$424$	0.592396	−	1.02606i	0.0287693	−	0.0498299i
$425$	−2.76604	−	4.79093i	−0.134173	−	0.232394i
$426$	−6.41147			−0.310637
$427$	−7.59539	+	13.6425i	−0.367567	+	0.660208i
$428$	−3.19253			−0.154317
$429$	−4.53209	−	7.84981i	−0.218811	−	0.378992i
$430$	2.04189	−	3.53666i	0.0984686	−	0.170553i
$431$	5.38919	−	9.33434i	0.259588	−	0.449619i	−0.706544	−	0.707669i	$-0.749747\pi$
$431$	5.38919	−	9.33434i	0.259588	−	0.449619i	0.966132	+	0.258050i	$0.0830799\pi$
$432$	2.31908	+	4.01676i	0.111577	+	0.193256i
$433$	26.7493			1.28549			0.642744	−	0.766081i	$-0.277796\pi$
$433$	26.7493			1.28549			0.642744	+	0.766081i	$0.277796\pi$
$434$	2.74716	+	4.59137i	0.131868	+	0.220393i
$435$	−7.02229			−0.336693
$436$	−3.99020	−	6.91123i	−0.191096	−	0.330988i
$437$	25.2772	−	43.7815i	1.20917	−	2.09435i
$438$	8.00387	−	13.8631i	0.382440	−	0.662405i
$439$	10.8871	+	18.8571i	0.519614	+	0.899998i	0.999740	+	0.0227986i	$0.00725764\pi$
$439$	10.8871	+	18.8571i	0.519614	+	0.899998i	−0.480126	+	0.877200i	$0.659409\pi$
$440$	1.00000			0.0476731
$441$	3.72281	−	0.116135i	0.177277	−	0.00553023i
$442$	26.6810			1.26908
$443$	6.49794	+	11.2548i	0.308726	+	0.534730i	0.978084	−	0.208210i	$-0.0667639\pi$
$443$	6.49794	+	11.2548i	0.308726	+	0.534730i	−0.669358	+	0.742940i	$0.733431\pi$
$444$	−4.85117	+	8.40247i	−0.230226	+	0.398763i
$445$	3.42989	−	5.94075i	0.162592	−	0.281618i
$446$	0.0641778	+	0.111159i	0.00303891	+	0.00526354i
$447$	7.90167			0.373736
$448$	1.35844	+	2.27038i	0.0641803	+	0.107266i
$449$	−23.6810			−1.11757			−0.558787	−	0.829311i	$-0.688733\pi$
$449$	−23.6810			−1.11757			−0.558787	+	0.829311i	$0.688733\pi$
$450$	0.266044	+	0.460802i	0.0125415	+	0.0217224i
$451$	5.53209	−	9.58186i	0.260496	−	0.451192i
$452$	−10.2909	+	17.8243i	−0.484041	+	0.838384i
$453$	0.852044	+	1.47578i	0.0400325	+	0.0693384i
$454$	24.4243			1.14629
$455$	−6.20708	+	11.1489i	−0.290992	+	0.522668i
$456$	12.7811			0.598528
$457$	−0.0675813	−	0.117054i	−0.00316132	−	0.00547557i	0.864440	−	0.502735i	$-0.167673\pi$
$457$	−0.0675813	−	0.117054i	−0.00316132	−	0.00547557i	−0.867602	+	0.497260i	$0.834340\pi$
$458$	1.36184	−	2.35878i	0.0636348	−	0.110219i
$459$	12.8293	−	22.2211i	0.598823	−	1.03719i
$460$	−3.71688	−	6.43783i	−0.173300	−	0.300165i
$461$	−39.9718			−1.86167			−0.930837	−	0.365435i	$-0.880920\pi$
$461$	−39.9718			−1.86167			−0.930837	+	0.365435i	$0.880920\pi$
$462$	−4.97178	+	0.0775297i	−0.231308	+	0.00360701i
$463$	35.1925			1.63554			0.817768	−	0.575548i	$-0.195211\pi$
$463$	35.1925			1.63554			0.817768	+	0.575548i	$0.195211\pi$
$464$	1.86824	+	3.23589i	0.0867309	+	0.150222i
$465$	1.90033	−	3.29147i	0.0881257	−	0.152638i
$466$	1.06031	−	1.83651i	0.0491178	−	0.0850745i
$467$	−10.8302	−	18.7585i	−0.501163	−	0.868040i	−0.999999	−	0.00134334i	$-0.999572\pi$
$467$	−10.8302	−	18.7585i	−0.501163	−	0.868040i	0.498836	−	0.866696i	$-0.333761\pi$
$468$	−2.56624			−0.118624
$469$	−19.4957	+	0.304015i	−0.900229	+	0.0140381i
$470$	−10.3405			−0.476971
$471$	−12.3760	−	21.4358i	−0.570255	−	0.987711i
$472$	5.06418	−	8.77141i	0.233098	−	0.403737i
$473$	2.04189	−	3.53666i	0.0938862	−	0.162616i
$474$	0.226682	+	0.392624i	0.0104118	+	0.0180338i
$475$	−6.80066			−0.312036
$476$	7.11974	−	12.7882i	0.326333	−	0.586145i
$477$	0.630415			0.0288647
$478$	12.1557	+	21.0543i	0.555989	+	0.963001i
$479$	4.07873	−	7.06456i	0.186362	−	0.322788i	−0.757673	−	0.652635i	$-0.773664\pi$
$479$	4.07873	−	7.06456i	0.186362	−	0.322788i	0.944035	+	0.329847i	$0.106997\pi$
$480$	0.939693	−	1.62760i	0.0428909	−	0.0742892i
$481$	12.4492	+	21.5627i	0.567637	+	0.983176i
$482$	−5.09327			−0.231992
$483$	18.9786	+	31.7193i	0.863558	+	1.44328i
$484$	1.00000			0.0454545
$485$	−4.87939	−	8.45134i	−0.221561	−	0.383756i
$486$	−2.73396	+	4.73535i	−0.124015	+	0.214800i
$487$	−12.6382	+	21.8899i	−0.572690	+	0.991927i	0.423599	+	0.905850i	$0.360767\pi$
$487$	−12.6382	+	21.8899i	−0.572690	+	0.991927i	−0.996288	+	0.0860775i	$0.972567\pi$
$488$	−2.95084	−	5.11100i	−0.133578	−	0.231364i
$489$	−43.7597			−1.97888
$490$	3.68732	+	5.95010i	0.166576	+	0.268798i
$491$	42.9846			1.93987			0.969935	−	0.243366i	$-0.0782515\pi$
$491$	42.9846			1.93987			0.969935	+	0.243366i	$0.0782515\pi$
$492$	−10.3969	−	18.0080i	−0.468730	−	0.811864i
$493$	10.3353	−	17.9012i	0.465477	−	0.806230i
$494$	16.3996	−	28.4050i	0.737854	−	1.27800i
$495$	0.266044	+	0.460802i	0.0119578	+	0.0207115i
$496$	−2.02229			−0.0908034
$497$	4.63429	+	7.74535i	0.207876	+	0.347427i
$498$	12.4243			0.556745
$499$	−6.67499	−	11.5614i	−0.298814	−	0.517561i	0.677051	−	0.735936i	$-0.263258\pi$
$499$	−6.67499	−	11.5614i	−0.298814	−	0.517561i	−0.975865	+	0.218375i	$0.929924\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	6.64543	−	11.5102i	0.296896	−	0.514239i
$502$	5.67499	+	9.82938i	0.253287	+	0.438706i
$503$	−25.7784			−1.14940			−0.574700	−	0.818364i	$-0.694881\pi$
$503$	−25.7784			−1.14940			−0.574700	+	0.818364i	$0.694881\pi$
$504$	−0.684793	+	1.23000i	−0.0305031	+	0.0547884i
$505$	11.3696			0.505940
$506$	−3.71688	−	6.43783i	−0.165236	−	0.286196i
$507$	−9.64203	+	16.7005i	−0.428217	+	0.741694i
$508$	0.500000	−	0.866025i	0.0221839	−	0.0384237i
$509$	4.59627	+	7.96097i	0.203726	+	0.352864i	0.949726	−	0.313082i	$-0.101362\pi$
$509$	4.59627	+	7.96097i	0.203726	+	0.352864i	−0.746000	+	0.665946i	$0.768028\pi$
$510$	−10.3969			−0.460384
$511$	−22.5326	+	0.351371i	−0.996782	+	0.0155438i
$512$	−1.00000			−0.0441942
$513$	−15.7713	−	27.3166i	−0.696318	−	1.20606i
$514$	−8.78106	+	15.2092i	−0.387316	+	0.670851i
$515$	2.46791	−	4.27455i	0.108749	−	0.188359i
$516$	−3.83750	−	6.64674i	−0.168936	−	0.292606i
$517$	−10.3405			−0.454774
$518$	13.6570	−	0.212967i	0.600056	−	0.00935724i
$519$	−48.1985			−2.11568
$520$	−2.41147	−	4.17680i	−0.105750	−	0.183165i
$521$	−12.4513	+	21.5663i	−0.545502	+	0.944836i	0.453074	+	0.891473i	$0.350327\pi$
$521$	−12.4513	+	21.5663i	−0.545502	+	0.944836i	−0.998575	+	0.0533633i	$0.983006\pi$
$522$	−0.994070	+	1.72178i	−0.0435093	+	0.0753603i
$523$	−5.39693	−	9.34775i	−0.235991	−	0.408749i	0.723569	−	0.690252i	$-0.242500\pi$
$523$	−5.39693	−	9.34775i	−0.235991	−	0.408749i	−0.959560	+	0.281503i	$0.909167\pi$
$524$	15.0496			0.657446
$525$	2.41875	−	4.34445i	0.105563	−	0.189608i
$526$	13.6091			0.593383
$527$	5.59374	+	9.68864i	0.243667	+	0.422044i
$528$	0.939693	−	1.62760i	0.0408949	−	0.0708320i
$529$	−16.1304	+	27.9387i	−0.701322	+	1.21473i
$530$	0.592396	+	1.02606i	0.0257320	+	0.0445692i
$531$	5.38919			0.233871
$532$	−9.23829	−	15.4401i	−0.400531	−	0.669413i
$533$	−53.3620			−2.31136
$534$	−6.44609	−	11.1650i	−0.278950	−	0.483155i
$535$	1.59627	−	2.76481i	0.0690126	−	0.119533i
$536$	3.68479	−	6.38225i	0.159159	−	0.275671i
$537$	4.45336	+	7.71345i	0.192177	+	0.332860i
$538$	18.9959			0.818971
$539$	3.68732	+	5.95010i	0.158824	+	0.256289i
$540$	−4.63816			−0.199594
$541$	6.68392	+	11.5769i	0.287364	+	0.497729i	0.973180	−	0.230046i	$-0.0738877\pi$
$541$	6.68392	+	11.5769i	0.287364	+	0.497729i	−0.685816	+	0.727775i	$0.740554\pi$
$542$	7.68004	−	13.3022i	0.329886	−	0.571380i
$543$	18.8084	−	32.5771i	0.807146	−	1.39802i
$544$	2.76604	+	4.79093i	0.118593	+	0.205409i
$545$	7.98040			0.341843
$546$	12.3131	+	20.5792i	0.526954	+	0.880707i
$547$	−23.6459			−1.01103			−0.505513	−	0.862819i	$-0.668697\pi$
$547$	−23.6459			−1.01103			−0.505513	+	0.862819i	$0.668697\pi$
$548$	−5.80066	−	10.0470i	−0.247792	−	0.429188i
$549$	1.57011	−	2.71951i	0.0670106	−	0.116066i
$550$	−0.500000	+	0.866025i	−0.0213201	+	0.0369274i
$551$	−12.7053	−	22.0062i	−0.541263	−	0.937495i
$552$	−13.9709			−0.594641
$553$	0.310460	−	0.557635i	0.0132021	−	0.0237130i
$554$	−14.5972			−0.620176
$555$	−4.85117	−	8.40247i	−0.205921	−	0.356665i
$556$	−10.5077	+	18.1999i	−0.445627	+	0.771849i
$557$	−19.6827	+	34.0915i	−0.833984	+	1.44450i	0.0608707	+	0.998146i	$0.480612\pi$
$557$	−19.6827	+	34.0915i	−0.833984	+	1.44450i	−0.894855	+	0.446357i	$0.852721\pi$
$558$	−0.538019	−	0.931876i	−0.0227761	−	0.0394494i
$559$	−19.6959			−0.833046
$560$	−2.64543	+	0.0412527i	−0.111790	+	0.00174324i
$561$	−10.3969			−0.438959
$562$	−8.49525	−	14.7142i	−0.358351	−	0.620681i
$563$	5.51249	−	9.54791i	0.232324	−	0.402396i	−0.726168	−	0.687517i	$-0.758700\pi$
$563$	5.51249	−	9.54791i	0.232324	−	0.402396i	0.958492	+	0.285121i	$0.0920338\pi$
$564$	−9.71688	+	16.8301i	−0.409155	+	0.708676i
$565$	−10.2909	−	17.8243i	−0.432940	−	0.749874i
$566$	10.3250			0.433992
$567$	27.2827	−	0.425445i	1.14577	−	0.0178670i
$568$	−3.41147			−0.143142
$569$	−21.1361	−	36.6088i	−0.886071	−	1.53472i	−0.844481	−	0.535586i	$-0.820091\pi$
$569$	−21.1361	−	36.6088i	−0.886071	−	1.53472i	−0.0415904	−	0.999135i	$-0.513242\pi$
$570$	−6.39053	+	11.0687i	−0.267670	+	0.463618i
$571$	4.74644	−	8.22108i	0.198633	−	0.344042i	−0.749453	−	0.662058i	$-0.769683\pi$
$571$	4.74644	−	8.22108i	0.198633	−	0.344042i	0.948085	+	0.318016i	$0.103017\pi$
$572$	−2.41147	−	4.17680i	−0.100829	−	0.174641i
$573$	−24.6732			−1.03074
$574$	−14.2395	+	25.5763i	−0.594344	+	1.06754i
$575$	7.43376			0.310009
$576$	−0.266044	−	0.460802i	−0.0110852	−	0.0192001i
$577$	−12.7743	+	22.1257i	−0.531799	+	0.921103i	0.467512	+	0.883987i	$0.345151\pi$
$577$	−12.7743	+	22.1257i	−0.531799	+	0.921103i	−0.999311	+	0.0371162i	$0.988183\pi$
$578$	6.80200	−	11.7814i	0.282926	−	0.490042i
$579$	11.8944	+	20.6017i	0.494314	+	0.856178i
$580$	−3.73648			−0.155149
$581$	−8.98040	−	15.0091i	−0.372570	−	0.622682i
$582$	−18.3405			−0.760238
$583$	0.592396	+	1.02606i	0.0245345	+	0.0424951i
$584$	4.25877	−	7.37641i	0.176229	−	0.305238i
$585$	1.28312	−	2.22243i	0.0530504	−	0.0918860i
$586$	0.736482	+	1.27562i	0.0304238	+	0.0526955i
$587$	42.2814			1.74514			0.872569	−	0.488490i	$-0.162452\pi$
$587$	42.2814			1.74514			0.872569	+	0.488490i	$0.162452\pi$
$588$	13.1493	−	0.410199i	0.542268	−	0.0169163i
$589$	13.7529			0.566678
$590$	5.06418	+	8.77141i	0.208489	+	0.361113i
$591$	−18.6604	+	32.3208i	−0.767588	+	1.32950i
$592$	−2.58125	+	4.47086i	−0.106089	+	0.183751i
$593$	13.6655	+	23.6693i	0.561175	+	0.971983i	0.997394	+	0.0721429i	$0.0229837\pi$
$593$	13.6655	+	23.6693i	0.561175	+	0.971983i	−0.436220	+	0.899840i	$0.643683\pi$
$594$	−4.63816			−0.190306
$595$	7.51501	+	12.5600i	0.308086	+	0.514908i
$596$	4.20439			0.172219
$597$	−16.3204	−	28.2678i	−0.667950	−	1.15692i
$598$	−17.9263	+	31.0493i	−0.733062	+	1.26970i
$599$	−5.96538	+	10.3323i	−0.243739	+	0.422168i	−0.961776	−	0.273836i	$-0.911707\pi$
$599$	−5.96538	+	10.3323i	−0.243739	+	0.422168i	0.718037	+	0.696005i	$0.245041\pi$
$600$	0.939693	+	1.62760i	0.0383628	+	0.0664463i
$601$	36.6655			1.49562			0.747808	−	0.663915i	$-0.231106\pi$
$601$	36.6655			1.49562			0.747808	+	0.663915i	$0.231106\pi$
$602$	−5.25578	+	9.44021i	−0.214209	+	0.384754i
$603$	3.92127			0.159687
$604$	0.453363	+	0.785248i	0.0184471	+	0.0319513i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$	10.6839	−	18.5051i	0.434004	−	0.751718i
$607$	15.4153	+	26.7002i	0.625690	+	1.08373i	0.988407	+	0.151827i	$0.0485156\pi$
$607$	15.4153	+	26.7002i	0.625690	+	1.08373i	−0.362718	+	0.931899i	$0.618151\pi$
$608$	6.80066			0.275803
$609$	18.5770	−	0.289688i	0.752777	−	0.0117388i
$610$	5.90167			0.238952
$611$	24.9358	+	43.1901i	1.00880	+	1.74728i
$612$	−1.47178	+	2.54920i	−0.0594932	+	0.103045i
$613$	8.51754	−	14.7528i	0.344020	−	0.595861i	−0.641155	−	0.767411i	$-0.721544\pi$
$613$	8.51754	−	14.7528i	0.344020	−	0.595861i	0.985175	+	0.171551i	$0.0548778\pi$
$614$	−12.6827	−	21.9671i	−0.511833	−	0.886522i
$615$	20.7939			0.838489
$616$	−2.64543	+	0.0412527i	−0.106587	+	0.00166212i
$617$	37.2080			1.49794			0.748969	−	0.662605i	$-0.230549\pi$
$617$	37.2080			1.49794			0.748969	+	0.662605i	$0.230549\pi$
$618$	−4.63816	−	8.03352i	−0.186574	−	0.323156i
$619$	3.13516	−	5.43026i	0.126013	−	0.218261i	−0.796116	−	0.605145i	$-0.793115\pi$
$619$	3.13516	−	5.43026i	0.126013	−	0.218261i	0.922128	+	0.386884i	$0.126449\pi$
$620$	1.01114	−	1.75135i	0.0406085	−	0.0703360i
$621$	17.2395	+	29.8596i	0.691796	+	1.19823i
$622$	23.8435			0.956037
$623$	−8.82847	+	15.8573i	−0.353705	+	0.635310i
$624$	−9.06418			−0.362858
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−8.53714	+	14.7868i	−0.341213	+	0.590998i
$627$	−6.39053	+	11.0687i	−0.255213	+	0.442042i
$628$	−6.58512	−	11.4058i	−0.262775	−	0.455140i
$629$	28.5594			1.13874
$630$	−0.722811	−	1.20805i	−0.0287975	−	0.0481297i
$631$	37.2327			1.48221			0.741105	−	0.671390i	$-0.234302\pi$
$631$	37.2327			1.48221			0.741105	+	0.671390i	$0.234302\pi$
$632$	0.120615	+	0.208911i	0.00479780	+	0.00831003i
$633$	−1.58037	+	2.73729i	−0.0628142	+	0.108797i
$634$	11.3858	−	19.7208i	0.452187	−	0.783211i
$635$	0.500000	+	0.866025i	0.0198419	+	0.0343672i
$636$	2.22668			0.0882937
$637$	15.9605	−	29.7497i	0.632377	−	1.17873i
$638$	−3.73648			−0.147929
$639$	−0.907604	−	1.57202i	−0.0359042	−	0.0621880i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−12.3366	+	21.3677i	−0.487267	+	0.843971i	−0.999893	−	0.0146408i	$-0.995340\pi$
$641$	−12.3366	+	21.3677i	−0.487267	+	0.843971i	0.512626	+	0.858612i	$0.328673\pi$
$642$	−3.00000	−	5.19615i	−0.118401	−	0.205076i
$643$	−39.0574			−1.54027			−0.770136	−	0.637880i	$-0.779812\pi$
$643$	−39.0574			−1.54027			−0.770136	+	0.637880i	$0.779812\pi$
$644$	10.0983	+	16.8775i	0.397930	+	0.665066i
$645$	7.67499			0.302203
$646$	−18.8109	−	32.5815i	−0.740106	−	1.28190i
$647$	17.0642	−	29.5560i	0.670862	−	1.16197i	−0.306798	−	0.951775i	$-0.599258\pi$
$647$	17.0642	−	29.5560i	0.670862	−	1.16197i	0.977660	−	0.210192i	$-0.0674091\pi$
$648$	−5.15657	+	8.93145i	−0.202569	+	0.350860i
$649$	5.06418	+	8.77141i	0.198786	+	0.344308i
$650$	4.82295			0.189172
$651$	−4.89141	+	8.78574i	−0.191709	+	0.344340i
$652$	−23.2841			−0.911874
$653$	3.85756	+	6.68150i	0.150958	+	0.261467i	0.931580	−	0.363537i	$-0.118431\pi$
$653$	3.85756	+	6.68150i	0.150958	+	0.261467i	−0.780622	+	0.625004i	$0.785097\pi$
$654$	7.49912	−	12.9889i	0.293239	−	0.507905i
$655$	−7.52481	+	13.0334i	−0.294019	+	0.509256i
$656$	−5.53209	−	9.58186i	−0.215992	−	0.374109i
$657$	4.53209			0.176814
$658$	27.3550	−	0.426573i	1.06641	−	0.0166295i
$659$	−2.62536			−0.102270			−0.0511348	−	0.998692i	$-0.516284\pi$
$659$	−2.62536			−0.102270			−0.0511348	+	0.998692i	$0.516284\pi$
$660$	0.939693	+	1.62760i	0.0365775	+	0.0633541i
$661$	15.3405	−	26.5705i	0.596676	−	1.03347i	−0.396632	−	0.917978i	$-0.629821\pi$
$661$	15.3405	−	26.5705i	0.596676	−	1.03347i	0.993308	−	0.115495i	$-0.0368455\pi$
$662$	9.94356	−	17.2228i	0.386468	−	0.669381i
$663$	25.0719	+	43.4258i	0.973713	+	1.68652i
$664$	6.61081			0.256549
$665$	17.9907	−	0.280545i	0.697648	−	0.0108791i
$666$	−2.74691			−0.106441
$667$	13.8881	+	24.0548i	0.537748	+	0.931407i
$668$	3.53596	−	6.12446i	0.136810	−	0.236963i
$669$	−0.120615	+	0.208911i	−0.00466324	+	0.00807696i
$670$	3.68479	+	6.38225i	0.142356	+	0.246568i
$671$	5.90167			0.227832
$672$	−2.41875	+	4.34445i	−0.0933052	+	0.167591i
$673$	27.8280			1.07269			0.536345	−	0.843999i	$-0.319804\pi$
$673$	27.8280			1.07269			0.536345	+	0.843999i	$0.319804\pi$
$674$	3.92855	+	6.80445i	0.151322	+	0.262097i
$675$	2.31908	−	4.01676i	0.0892613	−	0.154605i
$676$	−5.13041	+	8.88614i	−0.197324	+	0.341775i
$677$	−13.0719	−	22.6412i	−0.502395	−	0.870173i	−0.999996	−	0.00276731i	$-0.999119\pi$
$677$	−13.0719	−	22.6412i	−0.502395	−	0.870173i	0.497602	−	0.867406i	$-0.334214\pi$
$678$	−38.6810			−1.48553
$679$	13.2567	+	22.1561i	0.508746	+	0.850275i
$680$	−5.53209			−0.212146
$681$	22.9513	+	39.7528i	0.879496	+	1.52333i
$682$	1.01114	−	1.75135i	0.0387187	−	0.0670628i
$683$	−1.89347	+	3.27958i	−0.0724515	+	0.125490i	−0.899975	−	0.435941i	$-0.856416\pi$
$683$	−1.89347	+	3.27958i	−0.0724515	+	0.125490i	0.827524	+	0.561431i	$0.189749\pi$
$684$	1.80928	+	3.13376i	0.0691795	+	0.119822i
$685$	11.6013			0.443264
$686$	−10.0000	−	15.5885i	−0.381802	−	0.595170i
$687$	5.11886			0.195297
$688$	−2.04189	−	3.53666i	−0.0778463	−	0.134834i
$689$	2.85710	−	4.94864i	0.108847	−	0.188528i
$690$	6.98545	−	12.0992i	0.265932	−	0.460607i
$691$	−21.0077	−	36.3865i	−0.799172	−	1.38421i	−0.920156	−	0.391552i	$-0.871938\pi$
$691$	−21.0077	−	36.3865i	−0.799172	−	1.38421i	0.120984	−	0.992654i	$-0.461395\pi$
$692$	−25.6459			−0.974911
$693$	−0.722811	−	1.20805i	−0.0274573	−	0.0458899i
$694$	13.1088			0.497602
$695$	−10.5077	−	18.1999i	−0.398581	−	0.690363i
$696$	−3.51114	+	6.08148i	−0.133090	+	0.230518i
$697$	−30.6040	+	53.0077i	−1.15921	+	2.00781i
$698$	−5.52734	−	9.57364i	−0.209213	−	0.362367i
$699$	3.98545			0.150744
$700$	1.28699	−	2.31164i	0.0486436	−	0.0873716i
$701$	34.2968			1.29537			0.647687	−	0.761907i	$-0.275736\pi$
$701$	34.2968			1.29537			0.647687	+	0.761907i	$0.275736\pi$
$702$	11.1848	+	19.3726i	0.422143	+	0.731173i
$703$	17.5542	−	30.4048i	0.662070	−	1.14674i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$	−9.71688	−	16.8301i	−0.365959	−	0.633859i
$706$	19.9709			0.751615
$707$	−30.0774	+	0.469026i	−1.13118	+	0.0176395i
$708$	19.0351			0.715382
$709$	−0.445622	−	0.771841i	−0.0167357	−	0.0289871i	0.857536	−	0.514424i	$-0.171994\pi$
$709$	−0.445622	−	0.771841i	−0.0167357	−	0.0289871i	−0.874272	+	0.485436i	$0.838661\pi$
$710$	1.70574	−	2.95442i	0.0640152	−	0.110878i
$711$	−0.0641778	+	0.111159i	−0.00240685	+	0.00416879i
$712$	−3.42989	−	5.94075i	−0.128541	−	0.222639i
$713$	−15.0332			−0.562998
$714$	27.5043	−	0.428901i	1.02932	−	0.0160512i
$715$	4.82295			0.180368
$716$	2.36959	+	4.10424i	0.0885556	+	0.153383i
$717$	−22.8452	+	39.5691i	−0.853171	+	1.47774i
$718$	−1.73917	+	3.01233i	−0.0649053	+	0.112419i
$719$	−7.20099	−	12.4725i	−0.268552	−	0.465145i	0.699936	−	0.714205i	$-0.253212\pi$
$719$	−7.20099	−	12.4725i	−0.268552	−	0.465145i	−0.968488	+	0.249060i	$0.919878\pi$
$720$	0.532089			0.0198298
$721$	−6.35235	+	11.4098i	−0.236574	+	0.424924i
$722$	−27.2490			−1.01410
$723$	−4.78611	−	8.28979i	−0.177997	−	0.308301i
$724$	10.0077	−	17.3339i	0.371935	−	0.644210i
$725$	1.86824	−	3.23589i	0.0693847	−	0.120178i
$726$	0.939693	+	1.62760i	0.0348753	+	0.0604057i
$727$	−4.63640			−0.171955			−0.0859773	−	0.996297i	$-0.527401\pi$
$727$	−4.63640			−0.171955			−0.0859773	+	0.996297i	$0.527401\pi$
$728$	6.55169	+	10.9499i	0.242822	+	0.405832i
$729$	20.6631			0.765301
$730$	4.25877	+	7.37641i	0.157624	+	0.273013i
$731$	−11.2959	+	19.5651i	−0.417794	+	0.723641i
$732$	5.54576	−	9.60554i	0.204977	−	0.355031i
$733$	−16.0993	−	27.8847i	−0.594640	−	1.02995i	−0.993598	−	0.112977i	$-0.963961\pi$
$733$	−16.0993	−	27.8847i	−0.594640	−	1.02995i	0.398958	−	0.916969i	$-0.369372\pi$
$734$	−8.53714			−0.315112
$735$	−6.21941	+	11.5927i	−0.229406	+	0.427604i
$736$	−7.43376			−0.274012
$737$	3.68479	+	6.38225i	0.135731	+	0.235093i
$738$	2.94356	−	5.09840i	0.108354	−	0.187675i
$739$	5.94562	−	10.2981i	0.218713	−	0.378822i	−0.735702	−	0.677306i	$-0.763147\pi$
$739$	5.94562	−	10.2981i	0.218713	−	0.378822i	0.954415	+	0.298483i	$0.0964807\pi$
$740$	−2.58125	−	4.47086i	−0.0948887	−	0.164352i
$741$	61.6424			2.26449
$742$	−1.60947	−	2.68993i	−0.0590855	−	0.0987505i
$743$	−0.686852			−0.0251982			−0.0125991	−	0.999921i	$-0.504011\pi$
$743$	−0.686852			−0.0251982			−0.0125991	+	0.999921i	$0.504011\pi$
$744$	−1.90033	−	3.29147i	−0.0696695	−	0.120671i
$745$	−2.10220	+	3.64111i	−0.0770185	+	0.133400i
$746$	−4.99319	+	8.64846i	−0.182814	+	0.316643i
$747$	1.75877	+	3.04628i	0.0643500	+	0.111458i
$748$	−5.53209			−0.202273
$749$	−4.10876	+	7.37997i	−0.150131	+	0.269658i
$750$	−1.87939			−0.0686254
$751$	−8.41875	−	14.5817i	−0.307204	−	0.532094i	0.670545	−	0.741869i	$-0.266060\pi$
$751$	−8.41875	−	14.5817i	−0.307204	−	0.532094i	−0.977750	+	0.209775i	$0.932727\pi$
$752$	−5.17024	+	8.95513i	−0.188539	+	0.326560i
$753$	−10.6655	+	18.4732i	−0.388672	+	0.673200i
$754$	9.01043	+	15.6065i	0.328140	+	0.568356i
$755$	−0.906726			−0.0329992
$756$	12.2699	−	0.191336i	0.446252	−	0.00695884i
$757$	−15.9804			−0.580818			−0.290409	−	0.956903i	$-0.593791\pi$
$757$	−15.9804			−0.580818			−0.290409	+	0.956903i	$0.593791\pi$
$758$	−9.64590	−	16.7072i	−0.350355	−	0.606832i
$759$	6.98545	−	12.0992i	0.253556	−	0.439172i
$760$	−3.40033	+	5.88954i	−0.123343	+	0.213636i
$761$	−12.8425	−	22.2439i	−0.465542	−	0.806342i	0.533684	−	0.845684i	$-0.320807\pi$
$761$	−12.8425	−	22.2439i	−0.465542	−	0.806342i	−0.999226	+	0.0393417i	$0.987474\pi$
$762$	1.87939			0.0680829
$763$	−21.1116	+	0.329213i	−0.764291	+	0.0119183i
$764$	−13.1284			−0.474967
$765$	−1.47178	−	2.54920i	−0.0532124	−	0.0921665i
$766$	13.0915	−	22.6752i	0.473016	−	0.819287i
$767$	24.4243	−	42.3041i	0.881909	−	1.52751i
$768$	−0.939693	−	1.62760i	−0.0339082	−	0.0587308i
$769$	28.8539			1.04050			0.520249	−	0.854014i	$-0.325839\pi$
$769$	28.8539			1.04050			0.520249	+	0.854014i	$0.325839\pi$
$770$	1.28699	−	2.31164i	0.0463799	−	0.0833056i
$771$	−33.0060			−1.18868
$772$	6.32888	+	10.9619i	0.227781	+	0.394529i
$773$	15.7147	−	27.2186i	0.565217	−	0.978985i	−0.431812	−	0.901963i	$-0.642126\pi$
$773$	15.7147	−	27.2186i	0.565217	−	0.978985i	0.997029	−	0.0770212i	$-0.0245409\pi$
$774$	1.08647	−	1.88182i	0.0390522	−	0.0676404i
$775$	1.01114	+	1.75135i	0.0363214	+	0.0629105i
$776$	−9.75877			−0.350319
$777$	13.1800	+	22.0280i	0.472831	+	0.790251i
$778$	−16.9905			−0.609139
$779$	37.6219	+	65.1630i	1.34794	+	2.33471i
$780$	4.53209	−	7.84981i	0.162275	−	0.281068i
$781$	1.70574	−	2.95442i	0.0610361	−	0.105718i
$782$	20.5621	+	35.6146i	0.735300	+	1.27358i
$783$	17.3304			0.619337
$784$	6.99660	−	0.218262i	0.249878	−	0.00779508i
$785$	13.1702			0.470066
$786$	14.1420	+	24.4947i	0.504429	+	0.873697i
$787$	−12.5621	+	21.7582i	−0.447791	+	0.775597i	−0.998242	−	0.0592706i	$-0.981123\pi$
$787$	−12.5621	+	21.7582i	−0.447791	+	0.775597i	0.550451	+	0.834868i	$0.314456\pi$
$788$	−9.92902	+	17.1976i	−0.353707	+	0.612638i
$789$	12.7883	+	22.1500i	0.455277	+	0.788562i
$790$	−0.241230			−0.00858256
$791$	27.9590	+	46.7284i	0.994109	+	1.66147i
$792$	0.532089			0.0189070
$793$	−14.2317	−	24.6501i	−0.505384	−	0.875350i
$794$	−9.46316	+	16.3907i	−0.335835	+	0.581683i
$795$	−1.11334	+	1.92836i	−0.0394861	+	0.0683920i
$796$	−8.68392	−	15.0410i	−0.307793	−	0.533113i
$797$	−34.5330			−1.22322			−0.611611	−	0.791158i	$-0.709478\pi$
$797$	−34.5330			−1.22322			−0.611611	+	0.791158i	$0.709478\pi$
$798$	16.4491	−	29.5452i	0.582291	−	1.04589i
$799$	57.2045			2.02375
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	1.82501	−	3.16101i	0.0644835	−	0.111689i
$802$	−4.93969	+	8.55580i	−0.174427	+	0.302116i
$803$	4.25877	+	7.37641i	0.150289	+	0.260308i
$804$	13.8503			0.488462
$805$	−19.6655	+	0.306663i	−0.693118	+	0.0108084i
$806$	−9.75339			−0.343549
$807$	17.8503	+	30.9176i	0.628360	+	1.08835i
$808$	5.68479	−	9.84635i	0.199990	−	0.346393i
$809$	−15.8726	+	27.4921i	−0.558050	+	0.966571i	0.439609	+	0.898189i	$0.355117\pi$
$809$	−15.8726	+	27.4921i	−0.558050	+	0.966571i	−0.997659	+	0.0683820i	$0.978216\pi$
$810$	−5.15657	−	8.93145i	−0.181184	−	0.313819i
$811$	33.5422			1.17783			0.588913	−	0.808197i	$-0.299556\pi$
$811$	33.5422			1.17783			0.588913	+	0.808197i	$0.299556\pi$
$812$	9.88460	−	0.154140i	0.346881	−	0.00540925i
$813$	28.8675			1.01243
$814$	−2.58125	−	4.47086i	−0.0904728	−	0.156704i
$815$	11.6420	−	20.1646i	0.407802	−	0.706334i
$816$	−5.19846	+	9.00400i	−0.181983	+	0.315203i
$817$	13.8862	+	24.0516i	0.485816	+	0.841459i
$818$	16.3851			0.572890
$819$	−3.30272	+	5.93221i	−0.115406	+	0.207288i
$820$	11.0642			0.386378
$821$	14.8037	+	25.6407i	0.516651	+	0.894866i	0.999813	+	0.0193349i	$0.00615487\pi$
$821$	14.8037	+	25.6407i	0.516651	+	0.894866i	−0.483162	+	0.875531i	$0.660512\pi$
$822$	10.9017	−	18.8823i	0.380240	−	0.658594i
$823$	−7.14290	+	12.3719i	−0.248986	+	0.431256i	−0.963245	−	0.268625i	$-0.913431\pi$
$823$	−7.14290	+	12.3719i	−0.248986	+	0.431256i	0.714259	+	0.699882i	$0.246764\pi$
$824$	−2.46791	−	4.27455i	−0.0859738	−	0.148911i
$825$	−1.87939			−0.0654318
$826$	−13.7588	−	22.9952i	−0.478729	−	0.800107i
$827$	6.80933			0.236784			0.118392	−	0.992967i	$-0.462226\pi$
$827$	6.80933			0.236784			0.118392	+	0.992967i	$0.462226\pi$
$828$	−1.97771	−	3.42550i	−0.0687302	−	0.119044i
$829$	−15.3996	+	26.6729i	−0.534851	+	0.926389i	0.464320	+	0.885668i	$0.346299\pi$
$829$	−15.3996	+	26.6729i	−0.534851	+	0.926389i	−0.999171	+	0.0407210i	$0.987035\pi$
$830$	−3.30541	+	5.72513i	−0.114732	+	0.198722i
$831$	−13.7169	−	23.7583i	−0.475833	−	0.824168i
$832$	−4.82295			−0.167206
$833$	−20.3986	−	32.9165i	−0.706769	−	1.14049i
$834$	−39.4962			−1.36764
$835$	3.53596	+	6.12446i	0.122367	+	0.211946i
$836$	−3.40033	+	5.88954i	−0.117603	+	0.203694i
$837$	−4.68984	+	8.12305i	−0.162105	+	0.280774i
$838$	−16.2841	−	28.2048i	−0.562523	−	0.974319i
$839$	−18.9026			−0.652590			−0.326295	−	0.945268i	$-0.605800\pi$
$839$	−18.9026			−0.652590			−0.326295	+	0.945268i	$0.605800\pi$
$840$	−2.55303	−	4.26692i	−0.0880880	−	0.147223i
$841$	−15.0387			−0.518576
$842$	−2.19253	−	3.79758i	−0.0755597	−	0.130873i
$843$	15.9659	−	27.6537i	0.549893	−	0.952443i
$844$	−0.840900	+	1.45648i	−0.0289450	+	0.0501341i
$845$	−5.13041	−	8.88614i	−0.176492	−	0.305692i
$846$	−5.50206			−0.189165
$847$	1.28699	−	2.31164i	0.0442215	−	0.0794287i
$848$	1.18479			0.0406859
$849$	9.70233	+	16.8049i	0.332983	+	0.576744i
$850$	2.76604	−	4.79093i	0.0948745	−	0.164328i
$851$	−19.1884	+	33.2353i	−0.657770	+	1.13929i
$852$	−3.20574	−	5.55250i	−0.109827	−	0.190225i
$853$	26.9222			0.921799			0.460899	−	0.887452i	$-0.347527\pi$
$853$	26.9222			0.921799			0.460899	+	0.887452i	$0.347527\pi$
$854$	−15.6125	+	0.243460i	−0.534248	+	0.00833102i
$855$	−3.61856			−0.123752
$856$	−1.59627	−	2.76481i	−0.0545593	−	0.0944994i
$857$	14.8905	−	25.7912i	0.508651	−	0.881009i	−0.491299	−	0.870991i	$-0.663478\pi$
$857$	14.8905	−	25.7912i	0.508651	−	0.881009i	0.999950	−	0.0100181i	$-0.00318890\pi$
$858$	4.53209	−	7.84981i	0.154723	−	0.267988i
$859$	−2.70233	−	4.68058i	−0.0922024	−	0.159699i	0.816235	−	0.577720i	$-0.196057\pi$
$859$	−2.70233	−	4.68058i	−0.0922024	−	0.159699i	−0.908438	+	0.418020i	$0.862724\pi$
$860$	4.08378			0.139256
$861$	−55.0087	+	0.857802i	−1.87469	+	0.0292338i
$862$	10.7784			0.367113
$863$	−15.9290	−	27.5899i	−0.542230	−	0.939170i	−0.998776	−	0.0494699i	$-0.984247\pi$
$863$	−15.9290	−	27.5899i	−0.542230	−	0.939170i	0.456546	−	0.889700i	$-0.349087\pi$
$864$	−2.31908	+	4.01676i	−0.0788966	+	0.136653i
$865$	12.8229	−	22.2100i	0.435993	−	0.755163i
$866$	13.3746	+	23.1656i	0.454489	+	0.787197i
$867$	25.5672			0.868307
$868$	−2.60266	+	4.67479i	−0.0883401	+	0.158673i
$869$	−0.241230			−0.00818315
$870$	−3.51114	−	6.08148i	−0.119039	−	0.206181i
$871$	17.7716	−	30.7813i	0.602166	−	1.04298i
$872$	3.99020	−	6.91123i	0.135125	−	0.234044i
$873$	−2.59627	−	4.49687i	−0.0878703	−	0.152196i
$874$	50.5545			1.71003
$875$	1.35844	+	2.27038i	0.0459237	+	0.0767530i
$876$	16.0077			0.540851
$877$	9.34049	+	16.1782i	0.315406	+	0.546299i	0.979524	−	0.201329i	$-0.0645260\pi$
$877$	9.34049	+	16.1782i	0.315406	+	0.546299i	−0.664118	+	0.747628i	$0.731193\pi$
$878$	−10.8871	+	18.8571i	−0.367423	+	0.636395i
$879$	−1.38413	+	2.39739i	−0.0466856	+	0.0808619i
$880$	0.500000	+	0.866025i	0.0168550	+	0.0291937i
$881$	−0.385067			−0.0129732			−0.00648661	−	0.999979i	$-0.502065\pi$
$881$	−0.385067			−0.0129732			−0.00648661	+	0.999979i	$0.502065\pi$
$882$	1.96198	+	3.16598i	0.0660633	+	0.106604i
$883$	6.83162			0.229902			0.114951	−	0.993371i	$-0.463329\pi$
$883$	6.83162			0.229902			0.114951	+	0.993371i	$0.463329\pi$
$884$	13.3405	+	23.1064i	0.448689	+	0.777153i
$885$	−9.51754	+	16.4849i	−0.319929	+	0.554133i
$886$	−6.49794	+	11.2548i	−0.218303	+	0.378111i
$887$	3.59121	+	6.22017i	0.120581	+	0.208853i	0.919997	−	0.391925i	$-0.128191\pi$
$887$	3.59121	+	6.22017i	0.120581	+	0.208853i	−0.799416	+	0.600778i	$0.794858\pi$
$888$	−9.70233			−0.325589
$889$	−1.35844	−	2.27038i	−0.0455606	−	0.0761462i
$890$	6.85978			0.229941
$891$	−5.15657	−	8.93145i	−0.172752	−	0.299215i
$892$	−0.0641778	+	0.111159i	−0.00214883	+	0.00372188i
$893$	35.1611	−	60.9008i	1.17662	−	2.03797i
$894$	3.95084	+	6.84305i	0.132136	+	0.228866i
$895$	−4.73917			−0.158413
$896$	−1.28699	+	2.31164i	−0.0429953	+	0.0772263i
$897$	−67.3809			−2.24978
$898$	−11.8405	−	20.5083i	−0.395122	−	0.684372i
$899$	−3.77812	+	6.54390i	−0.126007	+	0.218251i
$900$	−0.266044	+	0.460802i	−0.00886815	+	0.0153601i
$901$	−3.27719	−	5.67626i	−0.109179	−	0.189104i
$902$	11.0642			0.368397
$903$	−20.3037	+	0.316614i	−0.675663	+	0.0105363i
$904$	−20.5817			−0.684538
$905$	10.0077	+	17.3339i	0.332669	+	0.576199i
$906$	−0.852044	+	1.47578i	−0.0283073	+	0.0490296i
$907$	5.65704	−	9.79828i	0.187839	−	0.325347i	−0.756691	−	0.653773i	$-0.773185\pi$
$907$	5.65704	−	9.79828i	0.187839	−	0.325347i	0.944529	+	0.328427i	$0.106518\pi$
$908$	12.2121	+	21.1520i	0.405274	+	0.701955i
$909$	6.04963			0.200654
$910$	−12.7588	+	0.198960i	−0.422949	+	0.00659544i
$911$	−1.57667			−0.0522373			−0.0261186	−	0.999659i	$-0.508315\pi$
$911$	−1.57667			−0.0522373			−0.0261186	+	0.999659i	$0.508315\pi$
$912$	6.39053	+	11.0687i	0.211612	+	0.366522i
$913$	−3.30541	+	5.72513i	−0.109393	+	0.189474i
$914$	0.0675813	−	0.117054i	0.00223539	−	0.00387181i
$915$	5.54576	+	9.60554i	0.183337	+	0.317549i
$916$	2.72369			0.0899932
$917$	19.3687	−	34.7893i	0.639611	−	1.14884i
$918$	25.6587			0.846863
$919$	19.6186	+	33.9803i	0.647156	+	1.12091i	0.983799	+	0.179275i	$0.0573753\pi$
$919$	19.6186	+	33.9803i	0.647156	+	1.12091i	−0.336643	+	0.941633i	$0.609291\pi$
$920$	3.71688	−	6.43783i	0.122542	−	0.212249i
$921$	23.8357	−	41.2847i	0.785414	−	1.36038i
$922$	−19.9859	−	34.6166i	−0.658201	−	1.14004i
$923$	−16.4534			−0.541569
$924$	−2.55303	−	4.26692i	−0.0839886	−	0.140372i
$925$	5.16250			0.169742
$926$	17.5963	+	30.4776i	0.578249	+	1.00156i
$927$	1.31315	−	2.27444i	0.0431294	−	0.0747024i
$928$	−1.86824	+	3.23589i	−0.0613280	+	0.106223i
$929$	−6.30200	−	10.9154i	−0.206762	−	0.358122i	0.743931	−	0.668257i	$-0.232959\pi$
$929$	−6.30200	−	10.9154i	−0.206762	−	0.358122i	−0.950693	+	0.310134i	$0.899626\pi$
$930$	3.80066			0.124629
$931$	−47.5815	+	1.48433i	−1.55942	+	0.0486468i
$932$	2.12061			0.0694630
$933$	22.4055	+	38.8075i	0.733525	+	1.27050i
$934$	10.8302	−	18.7585i	0.354376	−	0.613797i
$935$	2.76604	−	4.79093i	0.0904593	−	0.156680i
$936$	−1.28312	−	2.22243i	−0.0419400	−	0.0726423i
$937$	−27.1634			−0.887391			−0.443695	−	0.896178i	$-0.646333\pi$
$937$	−27.1634			−0.887391			−0.443695	+	0.896178i	$0.646333\pi$
$938$	−10.0111	−	16.7318i	−0.326875	−	0.546312i
$939$	−32.0892			−1.04719
$940$	−5.17024	−	8.95513i	−0.168635	−	0.292084i
$941$	−16.1099	+	27.9032i	−0.525169	+	0.909619i	0.474401	+	0.880309i	$0.342665\pi$
$941$	−16.1099	+	27.9032i	−0.525169	+	0.909619i	−0.999570	+	0.0293107i	$0.990669\pi$
$942$	12.3760	−	21.4358i	0.403231	−	0.698417i
$943$	−41.1242	−	71.2293i	−1.33919	−	2.31954i
$944$	10.1284			0.329650
$945$	−5.96926	+	10.7217i	−0.194180	+	0.348778i
$946$	4.08378			0.132775
$947$	11.1518	+	19.3155i	0.362386	+	0.627670i	0.988353	−	0.152179i	$-0.0486290\pi$
$947$	11.1518	+	19.3155i	0.362386	+	0.627670i	−0.625967	+	0.779849i	$0.715296\pi$
$948$	−0.226682	+	0.392624i	−0.00736228	+	0.0127518i
$949$	20.5398	−	35.5760i	0.666751	−	1.15485i
$950$	−3.40033	−	5.88954i	−0.110321	−	0.191082i
$951$	42.7965			1.38777
$952$	14.6348	−	0.228213i	0.474315	−	0.00739644i
$953$	−51.8958			−1.68107			−0.840535	−	0.541757i	$-0.817759\pi$
$953$	−51.8958			−1.68107			−0.840535	+	0.541757i	$0.817759\pi$
$954$	0.315207	+	0.545955i	0.0102052	+	0.0176760i
$955$	6.56418	−	11.3695i	0.212412	−	0.367908i
$956$	−12.1557	+	21.0543i	−0.393143	+	0.680944i
$957$	−3.51114	−	6.08148i	−0.113499	−	0.196586i
$958$	8.15745			0.263555
$959$	−30.6905	+	0.478585i	−0.991047	+	0.0154543i
$960$	1.87939			0.0606569
$961$	13.4552	+	23.3050i	0.434038	+	0.751776i
$962$	−12.4492	+	21.5627i	−0.401380	+	0.695210i
$963$	0.849356	−	1.47113i	0.0273701	−	0.0474064i
$964$	−2.54664	−	4.41090i	−0.0820216	−	0.142066i
$965$	−12.6578			−0.407468
$966$	−17.9804	+	32.2956i	−0.578510	+	1.03910i
$967$	11.1857			0.359709			0.179854	−	0.983693i	$-0.442437\pi$
$967$	11.1857			0.359709			0.179854	+	0.983693i	$0.442437\pi$
$968$	0.500000	+	0.866025i	0.0160706	+	0.0278351i
$969$	35.3530	−	61.2332i	1.13570	−	1.96709i
$970$	4.87939	−	8.45134i	0.156668	−	0.271356i
$971$	−24.6905	−	42.7652i	−0.792355	−	1.37240i	−0.924505	−	0.381169i	$-0.875521\pi$
$971$	−24.6905	−	42.7652i	−0.792355	−	1.37240i	0.132150	−	0.991230i	$-0.457812\pi$
$972$	−5.46791			−0.175383
$973$	28.5483	+	47.7132i	0.915216	+	1.52961i
$974$	−25.2763			−0.809905
$975$	4.53209	+	7.84981i	0.145143	+	0.251395i
$976$	2.95084	−	5.11100i	0.0944540	−	0.163599i
$977$	−15.3182	+	26.5319i	−0.490073	+	0.848831i	−0.999935	−	0.0114254i	$-0.996363\pi$
$977$	−15.3182	+	26.5319i	−0.490073	+	0.848831i	0.509862	+	0.860256i	$0.329696\pi$
$978$	−21.8799	−	37.8970i	−0.699641	−	1.21181i
$979$	6.85978			0.219240
$980$	−3.30928	+	6.16836i	−0.105711	+	0.197041i
$981$	4.24628			0.135573
$982$	21.4923	+	37.2258i	0.685847	+	1.18792i
$983$	13.2909	−	23.0204i	0.423913	−	0.734238i	−0.572406	−	0.819971i	$-0.693990\pi$
$983$	13.2909	−	23.0204i	0.423913	−	0.734238i	0.996318	+	0.0857325i	$0.0273230\pi$
$984$	10.3969	−	18.0080i	0.331442	−	0.574074i
$985$	−9.92902	−	17.1976i	−0.316365	−	0.547960i
$986$	20.6705			0.658284
$987$	26.3996	+	44.1221i	0.840309	+	1.40442i
$988$	32.7992			1.04348
$989$	−15.1789	−	26.2907i	−0.482662	−	0.835994i
$990$	−0.266044	+	0.460802i	−0.00845545	+	0.0146453i
$991$	−1.67705	+	2.90474i	−0.0532733	+	0.0922721i	−0.891432	−	0.453154i	$-0.850299\pi$
$991$	−1.67705	+	2.90474i	−0.0532733	+	0.0922721i	0.838159	+	0.545426i	$0.183632\pi$
$992$	−1.01114	−	1.75135i	−0.0321039	−	0.0556055i
$993$	37.3756			1.18608
$994$	−4.39053	+	7.88609i	−0.139259	+	0.250131i
$995$	17.3678			0.550597
$996$	6.21213	+	10.7597i	0.196839	+	0.340935i
$997$	−21.8135	+	37.7820i	−0.690839	+	1.19657i	0.280724	+	0.959788i	$0.409425\pi$
$997$	−21.8135	+	37.7820i	−0.690839	+	1.19657i	−0.971563	+	0.236780i	$0.923908\pi$
$998$	6.67499	−	11.5614i	0.211293	−	0.365971i
$999$	11.9722	+	20.7365i	0.378785	+	0.656075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.i.j.221.1	✓	6
7.2	even	3	inner	770.2.i.j.331.1	yes	6
7.3	odd	6		5390.2.a.bv.1.1		3
7.4	even	3		5390.2.a.bx.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.i.j.221.1	✓	6	1.1	even	1	trivial
770.2.i.j.331.1	yes	6	7.2	even	3	inner
5390.2.a.bv.1.1		3	7.3	odd	6
5390.2.a.bx.1.3		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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.939693 + 1.62760i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.87939 q^{6} +(1.35844 + 2.27038i) q^{7} -1.00000 q^{8} +(-0.266044 - 0.460802i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.939693 + 1.62760i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.87939 q^{6} +(1.35844 + 2.27038i) q^{7} -1.00000 q^{8} +(-0.266044 - 0.460802i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.939693 - 1.62760i) q^{12} -4.82295 q^{13} +(-1.28699 + 2.31164i) q^{14} +1.87939 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.76604 + 4.79093i) q^{17} +(0.266044 - 0.460802i) q^{18} +(3.40033 + 5.88954i) q^{19} +1.00000 q^{20} +(-4.97178 + 0.0775297i) q^{21} +1.00000 q^{22} +(-3.71688 - 6.43783i) q^{23} +(0.939693 - 1.62760i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.41147 - 4.17680i) q^{26} -4.63816 q^{27} +(-2.64543 + 0.0412527i) q^{28} -3.73648 q^{29} +(0.939693 + 1.62760i) q^{30} +(1.01114 - 1.75135i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.939693 + 1.62760i) q^{33} -5.53209 q^{34} +(1.28699 - 2.31164i) q^{35} +0.532089 q^{36} +(-2.58125 - 4.47086i) q^{37} +(-3.40033 + 5.88954i) q^{38} +(4.53209 - 7.84981i) q^{39} +(0.500000 + 0.866025i) q^{40} +11.0642 q^{41} +(-2.55303 - 4.26692i) q^{42} +4.08378 q^{43} +(0.500000 + 0.866025i) q^{44} +(-0.266044 + 0.460802i) q^{45} +(3.71688 - 6.43783i) q^{46} +(-5.17024 - 8.95513i) q^{47} +1.87939 q^{48} +(-3.30928 + 6.16836i) q^{49} -1.00000 q^{50} +(-5.19846 - 9.00400i) q^{51} +(2.41147 - 4.17680i) q^{52} +(-0.592396 + 1.02606i) q^{53} +(-2.31908 - 4.01676i) q^{54} -1.00000 q^{55} +(-1.35844 - 2.27038i) q^{56} -12.7811 q^{57} +(-1.86824 - 3.23589i) q^{58} +(-5.06418 + 8.77141i) q^{59} +(-0.939693 + 1.62760i) q^{60} +(2.95084 + 5.11100i) q^{61} +2.02229 q^{62} +(0.684793 - 1.23000i) q^{63} +1.00000 q^{64} +(2.41147 + 4.17680i) q^{65} +(-0.939693 + 1.62760i) q^{66} +(-3.68479 + 6.38225i) q^{67} +(-2.76604 - 4.79093i) q^{68} +13.9709 q^{69} +(2.64543 - 0.0412527i) q^{70} +3.41147 q^{71} +(0.266044 + 0.460802i) q^{72} +(-4.25877 + 7.37641i) q^{73} +(2.58125 - 4.47086i) q^{74} +(-0.939693 - 1.62760i) q^{75} -6.80066 q^{76} +(2.64543 - 0.0412527i) q^{77} +9.06418 q^{78} +(-0.120615 - 0.208911i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.15657 - 8.93145i) q^{81} +(5.53209 + 9.58186i) q^{82} -6.61081 q^{83} +(2.41875 - 4.34445i) q^{84} +5.53209 q^{85} +(2.04189 + 3.53666i) q^{86} +(3.51114 - 6.08148i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(3.42989 + 5.94075i) q^{89} -0.532089 q^{90} +(-6.55169 - 10.9499i) q^{91} +7.43376 q^{92} +(1.90033 + 3.29147i) q^{93} +(5.17024 - 8.95513i) q^{94} +(3.40033 - 5.88954i) q^{95} +(0.939693 + 1.62760i) q^{96} +9.75877 q^{97} +(-6.99660 + 0.218262i) q^{98} -0.532089 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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