LMFDB - Embedded newform 770.2.i.m.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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 12x^{8} - 6x^{7} + 113x^{6} - 43x^{5} + 381x^{4} - 75x^{3} + 982x^{2} - 217x + 49 $ x^10 + 12x^8 - 6x^7 + 113x^6 - 43x^5 + 381x^4 - 75x^3 + 982x^2 - 217x + 49
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			$1.08142 + 1.87308i$ of defining polynomial
Character	$\chi$	$=$	770.221
Dual form			770.2.i.m.331.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.08142 + 1.87308i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.16285 q^{6} +(-0.590793 + 2.57895i) q^{7} +1.00000 q^{8} +(-0.838952 - 1.45311i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.08142 + 1.87308i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.16285 q^{6} +(-0.590793 + 2.57895i) q^{7} +1.00000 q^{8} +(-0.838952 - 1.45311i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.08142 - 1.87308i) q^{12} +3.19817 q^{13} +(2.52883 - 0.777832i) q^{14} +2.16285 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.67222 + 2.89636i) q^{17} +(-0.838952 + 1.45311i) q^{18} +(-1.42038 - 2.46016i) q^{19} +1.00000 q^{20} +(-4.19168 - 3.89553i) q^{21} +1.00000 q^{22} +(2.61025 + 4.52109i) q^{23} +(-1.08142 + 1.87308i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.59908 - 2.76970i) q^{26} -2.85949 q^{27} +(-1.93804 - 1.80111i) q^{28} -6.93373 q^{29} +(-1.08142 - 1.87308i) q^{30} +(0.420375 - 0.728112i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.08142 - 1.87308i) q^{33} +3.34443 q^{34} +(2.52883 - 0.777832i) q^{35} +1.67790 q^{36} +(-4.38544 - 7.59581i) q^{37} +(-1.42038 + 2.46016i) q^{38} +(-3.45857 + 5.99043i) q^{39} +(-0.500000 - 0.866025i) q^{40} -9.29115 q^{41} +(-1.27779 + 5.57786i) q^{42} +9.22051 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-0.838952 + 1.45311i) q^{45} +(2.61025 - 4.52109i) q^{46} +(-2.84075 - 4.92032i) q^{47} +2.16285 q^{48} +(-6.30193 - 3.04724i) q^{49} +1.00000 q^{50} +(-3.61675 - 6.26439i) q^{51} +(-1.59908 + 2.76970i) q^{52} +(-4.45001 + 7.70764i) q^{53} +(1.42974 + 2.47639i) q^{54} +1.00000 q^{55} +(-0.590793 + 2.57895i) q^{56} +6.14411 q^{57} +(3.46687 + 6.00479i) q^{58} +(-3.78067 + 6.54831i) q^{59} +(-1.08142 + 1.87308i) q^{60} +(-5.69997 - 9.87263i) q^{61} -0.840751 q^{62} +(4.24313 - 1.30513i) q^{63} +1.00000 q^{64} +(-1.59908 - 2.76970i) q^{65} +(-1.08142 + 1.87308i) q^{66} +(-2.66285 + 4.61219i) q^{67} +(-1.67222 - 2.89636i) q^{68} -11.2912 q^{69} +(-1.93804 - 1.80111i) q^{70} -5.60026 q^{71} +(-0.838952 - 1.45311i) q^{72} +(-1.68700 + 2.92197i) q^{73} +(-4.38544 + 7.59581i) q^{74} +(-1.08142 - 1.87308i) q^{75} +2.84075 q^{76} +(-1.93804 - 1.80111i) q^{77} +6.91715 q^{78} +(3.60268 + 6.24003i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.60918 - 9.71538i) q^{81} +(4.64558 + 8.04637i) q^{82} -8.85733 q^{83} +(5.46947 - 1.68233i) q^{84} +3.34443 q^{85} +(-4.61025 - 7.98519i) q^{86} +(7.49830 - 12.9874i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(2.69925 + 4.67523i) q^{89} +1.67790 q^{90} +(-1.88945 + 8.24791i) q^{91} -5.22051 q^{92} +(0.909207 + 1.57479i) q^{93} +(-2.84075 + 4.92032i) q^{94} +(-1.42038 + 2.46016i) q^{95} +(-1.08142 - 1.87308i) q^{96} -8.09741 q^{97} +(0.511973 + 6.98125i) q^{98} +1.67790 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9	$ 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9} - 5 q^{10} - 5 q^{11} - 2 q^{13} + 3 q^{14} - 5 q^{16} - 9 q^{18} - 4 q^{19} + 10 q^{20} + 2 q^{21} + 10 q^{22} - 7 q^{23} - 5 q^{25} + q^{26} - 18 q^{27} - 3 q^{28} + 8 q^{29} - 6 q^{31} - 5 q^{32} + 3 q^{35} + 18 q^{36} - 16 q^{37} - 4 q^{38} - 7 q^{39} - 5 q^{40} - 2 q^{41} + 11 q^{42} + 26 q^{43} - 5 q^{44} - 9 q^{45} - 7 q^{46} - 8 q^{47} + 14 q^{49} + 10 q^{50} - 13 q^{51} + q^{52} - 4 q^{53} + 9 q^{54} + 10 q^{55} + 30 q^{57} - 4 q^{58} - 9 q^{59} - 2 q^{61} + 12 q^{62} + 25 q^{63} + 10 q^{64} + q^{65} - 5 q^{67} - 22 q^{69} - 3 q^{70} + 56 q^{71} - 9 q^{72} + q^{73} - 16 q^{74} + 8 q^{76} - 3 q^{77} + 14 q^{78} - 23 q^{79} - 5 q^{80} + 7 q^{81} + q^{82} - 46 q^{83} - 13 q^{84} - 13 q^{86} - 15 q^{87} - 5 q^{88} + 9 q^{89} + 18 q^{90} + 29 q^{91} + 14 q^{92} + 15 q^{93} - 8 q^{94} - 4 q^{95} - 26 q^{97} - 19 q^{98} + 18 q^{99}+O(q^{100}) $ 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9 - 5 * q^10 - 5 * q^11 - 2 * q^13 + 3 * q^14 - 5 * q^16 - 9 * q^18 - 4 * q^19 + 10 * q^20 + 2 * q^21 + 10 * q^22 - 7 * q^23 - 5 * q^25 + q^26 - 18 * q^27 - 3 * q^28 + 8 * q^29 - 6 * q^31 - 5 * q^32 + 3 * q^35 + 18 * q^36 - 16 * q^37 - 4 * q^38 - 7 * q^39 - 5 * q^40 - 2 * q^41 + 11 * q^42 + 26 * q^43 - 5 * q^44 - 9 * q^45 - 7 * q^46 - 8 * q^47 + 14 * q^49 + 10 * q^50 - 13 * q^51 + q^52 - 4 * q^53 + 9 * q^54 + 10 * q^55 + 30 * q^57 - 4 * q^58 - 9 * q^59 - 2 * q^61 + 12 * q^62 + 25 * q^63 + 10 * q^64 + q^65 - 5 * q^67 - 22 * q^69 - 3 * q^70 + 56 * q^71 - 9 * q^72 + q^73 - 16 * q^74 + 8 * q^76 - 3 * q^77 + 14 * q^78 - 23 * q^79 - 5 * q^80 + 7 * q^81 + q^82 - 46 * q^83 - 13 * q^84 - 13 * q^86 - 15 * q^87 - 5 * q^88 + 9 * q^89 + 18 * q^90 + 29 * q^91 + 14 * q^92 + 15 * q^93 - 8 * q^94 - 4 * q^95 - 26 * q^97 - 19 * q^98 + 18 * 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
$3$	−1.08142	+	1.87308i	−0.624360	+	1.08142i	0.364304	+	0.931280i	$0.381307\pi$
$3$	−1.08142	+	1.87308i	−0.624360	+	1.08142i	−0.988664	+	0.150143i	$0.952027\pi$
$4$	−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
$6$	2.16285			0.882978
$7$	−0.590793	+	2.57895i	−0.223299	+	0.974750i
$7$	−0.590793	+	2.57895i	−0.223299	+	0.974750i
$8$	1.00000			0.353553
$9$	−0.838952	−	1.45311i	−0.279651	−	0.484369i
$10$	−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
$12$	−1.08142	−	1.87308i	−0.312180	−	0.540712i
$13$	3.19817			0.887012			0.443506	−	0.896271i	$-0.353734\pi$
$13$	3.19817			0.887012			0.443506	+	0.896271i	$0.353734\pi$
$14$	2.52883	−	0.777832i	0.675858	−	0.207884i
$15$	2.16285			0.558445
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.67222	+	2.89636i	−0.405572	+	0.702471i	−0.994388	−	0.105796i	$-0.966261\pi$
$17$	−1.67222	+	2.89636i	−0.405572	+	0.702471i	0.588816	+	0.808267i	$0.299594\pi$
$18$	−0.838952	+	1.45311i	−0.197743	+	0.342501i
$19$	−1.42038	−	2.46016i	−0.325856	−	0.564400i	0.655829	−	0.754910i	$-0.272319\pi$
$19$	−1.42038	−	2.46016i	−0.325856	−	0.564400i	−0.981685	+	0.190510i	$0.938986\pi$
$20$	1.00000			0.223607
$21$	−4.19168	−	3.89553i	−0.914699	−	0.850075i
$22$	1.00000			0.213201
$23$	2.61025	+	4.52109i	0.544275	+	0.942712i	0.998652	+	0.0519029i	$0.0165286\pi$
$23$	2.61025	+	4.52109i	0.544275	+	0.942712i	−0.454377	+	0.890810i	$0.650138\pi$
$24$	−1.08142	+	1.87308i	−0.220745	+	0.382341i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.59908	−	2.76970i	−0.313606	−	0.543182i
$27$	−2.85949			−0.550309
$28$	−1.93804	−	1.80111i	−0.366255	−	0.340379i
$29$	−6.93373			−1.28756			−0.643781	−	0.765210i	$-0.722635\pi$
$29$	−6.93373			−1.28756			−0.643781	+	0.765210i	$0.722635\pi$
$30$	−1.08142	−	1.87308i	−0.197440	−	0.341976i
$31$	0.420375	−	0.728112i	0.0755016	−	0.130773i	−0.825803	−	0.563959i	$-0.809278\pi$
$31$	0.420375	−	0.728112i	0.0755016	−	0.130773i	0.901304	+	0.433186i	$0.142611\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.08142	−	1.87308i	−0.188252	−	0.326061i
$34$	3.34443			0.573565
$35$	2.52883	−	0.777832i	0.427450	−	0.131478i
$36$	1.67790			0.279651
$37$	−4.38544	−	7.59581i	−0.720962	−	1.24874i	−0.960614	−	0.277885i	$-0.910367\pi$
$37$	−4.38544	−	7.59581i	−0.720962	−	1.24874i	0.239652	−	0.970859i	$-0.422967\pi$
$38$	−1.42038	+	2.46016i	−0.230415	+	0.399091i
$39$	−3.45857	+	5.99043i	−0.553815	+	0.959236i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−9.29115			−1.45103			−0.725517	−	0.688204i	$-0.758399\pi$
$41$	−9.29115			−1.45103			−0.725517	+	0.688204i	$0.758399\pi$
$42$	−1.27779	+	5.57786i	−0.197168	+	0.860683i
$43$	9.22051			1.40611			0.703057	−	0.711134i	$-0.251818\pi$
$43$	9.22051			1.40611			0.703057	+	0.711134i	$0.251818\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	−0.838952	+	1.45311i	−0.125064	+	0.216617i
$46$	2.61025	−	4.52109i	0.384861	−	0.666598i
$47$	−2.84075	−	4.92032i	−0.414366	−	0.717703i	0.580996	−	0.813907i	$-0.302663\pi$
$47$	−2.84075	−	4.92032i	−0.414366	−	0.717703i	−0.995362	+	0.0962036i	$0.969330\pi$
$48$	2.16285			0.312180
$49$	−6.30193	−	3.04724i	−0.900275	−	0.435321i
$50$	1.00000			0.141421
$51$	−3.61675	−	6.26439i	−0.506446	−	0.877190i
$52$	−1.59908	+	2.76970i	−0.221753	+	0.384088i
$53$	−4.45001	+	7.70764i	−0.611256	+	1.05873i	0.379773	+	0.925080i	$0.376002\pi$
$53$	−4.45001	+	7.70764i	−0.611256	+	1.05873i	−0.991029	+	0.133647i	$0.957331\pi$
$54$	1.42974	+	2.47639i	0.194564	+	0.336994i
$55$	1.00000			0.134840
$56$	−0.590793	+	2.57895i	−0.0789480	+	0.344626i
$57$	6.14411			0.813807
$58$	3.46687	+	6.00479i	0.455222	+	0.788467i
$59$	−3.78067	+	6.54831i	−0.492201	+	0.852518i	−0.999960	−	0.00898191i	$-0.997141\pi$
$59$	−3.78067	+	6.54831i	−0.492201	+	0.852518i	0.507758	+	0.861500i	$0.330474\pi$
$60$	−1.08142	+	1.87308i	−0.139611	+	0.241814i
$61$	−5.69997	−	9.87263i	−0.729806	−	1.26406i	−0.956965	−	0.290203i	$-0.906277\pi$
$61$	−5.69997	−	9.87263i	−0.729806	−	1.26406i	0.227159	−	0.973858i	$-0.427056\pi$
$62$	−0.840751			−0.106775
$63$	4.24313	−	1.30513i	0.534585	−	0.164431i
$64$	1.00000			0.125000
$65$	−1.59908	−	2.76970i	−0.198342	−	0.343538i
$66$	−1.08142	+	1.87308i	−0.133114	+	0.230560i
$67$	−2.66285	+	4.61219i	−0.325318	+	0.563468i	−0.981577	−	0.191068i	$-0.938805\pi$
$67$	−2.66285	+	4.61219i	−0.325318	+	0.563468i	0.656258	+	0.754536i	$0.272138\pi$
$68$	−1.67222	−	2.89636i	−0.202786	−	0.351236i
$69$	−11.2912			−1.35929
$70$	−1.93804	−	1.80111i	−0.231640	−	0.215274i
$71$	−5.60026			−0.664628			−0.332314	−	0.943169i	$-0.607829\pi$
$71$	−5.60026			−0.664628			−0.332314	+	0.943169i	$0.607829\pi$
$72$	−0.838952	−	1.45311i	−0.0988715	−	0.171250i
$73$	−1.68700	+	2.92197i	−0.197449	+	0.341991i	−0.947700	−	0.319161i	$-0.896599\pi$
$73$	−1.68700	+	2.92197i	−0.197449	+	0.341991i	0.750252	+	0.661152i	$0.229932\pi$
$74$	−4.38544	+	7.59581i	−0.509797	+	0.882995i
$75$	−1.08142	−	1.87308i	−0.124872	−	0.216285i
$76$	2.84075			0.325856
$77$	−1.93804	−	1.80111i	−0.220860	−	0.205256i
$78$	6.91715			0.783213
$79$	3.60268	+	6.24003i	0.405333	+	0.702058i	0.994360	−	0.106055i	$-0.0338221\pi$
$79$	3.60268	+	6.24003i	0.405333	+	0.702058i	−0.589027	+	0.808113i	$0.700489\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	5.60918	−	9.71538i	0.623242	−	1.07949i
$82$	4.64558	+	8.04637i	0.513018	+	0.888573i
$83$	−8.85733			−0.972219			−0.486109	−	0.873898i	$-0.661584\pi$
$83$	−8.85733			−0.972219			−0.486109	+	0.873898i	$0.661584\pi$
$84$	5.46947	−	1.68233i	0.596768	−	0.183557i
$85$	3.34443			0.362755
$86$	−4.61025	−	7.98519i	−0.497136	−	0.861065i
$87$	7.49830	−	12.9874i	0.803902	−	1.39240i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	2.69925	+	4.67523i	0.286120	+	0.495574i	0.972880	−	0.231310i	$-0.0743012\pi$
$89$	2.69925	+	4.67523i	0.286120	+	0.495574i	−0.686761	+	0.726884i	$0.740968\pi$
$90$	1.67790			0.176867
$91$	−1.88945	+	8.24791i	−0.198069	+	0.864616i
$92$	−5.22051			−0.544275
$93$	0.909207	+	1.57479i	0.0942804	+	0.163298i
$94$	−2.84075	+	4.92032i	−0.293001	+	0.507493i
$95$	−1.42038	+	2.46016i	−0.145727	+	0.252407i
$96$	−1.08142	−	1.87308i	−0.110372	−	0.191170i
$97$	−8.09741			−0.822167			−0.411084	−	0.911598i	$-0.634850\pi$
$97$	−8.09741			−0.822167			−0.411084	+	0.911598i	$0.634850\pi$
$98$	0.511973	+	6.98125i	0.0517171	+	0.705213i
$99$	1.67790			0.168636
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	3.86102	−	6.68747i	0.384185	−	0.665429i	−0.607470	−	0.794342i	$-0.707816\pi$
$101$	3.86102	−	6.68747i	0.384185	−	0.665429i	0.991656	+	0.128914i	$0.0411490\pi$
$102$	−3.61675	+	6.26439i	−0.358111	+	0.620267i
$103$	3.10657	+	5.38074i	0.306100	+	0.530180i	0.977506	−	0.210910i	$-0.0676426\pi$
$103$	3.10657	+	5.38074i	0.306100	+	0.530180i	−0.671406	+	0.741090i	$0.734309\pi$
$104$	3.19817			0.313606
$105$	−1.27779	+	5.57786i	−0.124700	+	0.544344i
$106$	8.90002			0.864446
$107$	7.97127	+	13.8066i	0.770612	+	1.33474i	0.937228	+	0.348717i	$0.113382\pi$
$107$	7.97127	+	13.8066i	0.770612	+	1.33474i	−0.166617	+	0.986022i	$0.553284\pi$
$108$	1.42974	−	2.47639i	0.137577	−	0.238291i
$109$	6.64169	−	11.5037i	0.636158	−	1.10186i	−0.350110	−	0.936708i	$-0.613856\pi$
$109$	6.64169	−	11.5037i	0.636158	−	1.10186i	0.986269	−	0.165150i	$-0.0528107\pi$
$110$	−0.500000	−	0.866025i	−0.0476731	−	0.0825723i
$111$	18.9701			1.80056
$112$	2.52883	−	0.777832i	0.238952	−	0.0734982i
$113$	2.41591			0.227269			0.113635	−	0.993523i	$-0.463751\pi$
$113$	2.41591			0.227269			0.113635	+	0.993523i	$0.463751\pi$
$114$	−3.07205	−	5.32095i	−0.287724	−	0.498353i
$115$	2.61025	−	4.52109i	0.243407	−	0.421594i
$116$	3.46687	−	6.00479i	0.321890	−	0.557531i
$117$	−2.68311	−	4.64728i	−0.248054	−	0.429642i
$118$	7.56134			0.696078
$119$	−6.48163	−	6.02370i	−0.594170	−	0.552192i
$120$	2.16285			0.197440
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−5.69997	+	9.87263i	−0.516051	+	0.893826i
$123$	10.0477	−	17.4031i	0.905967	−	1.56918i
$124$	0.420375	+	0.728112i	0.0377508	+	0.0653863i
$125$	1.00000			0.0894427
$126$	−3.25184	−	3.02210i	−0.289697	−	0.269230i
$127$	21.5867			1.91551			0.957756	−	0.287582i	$-0.0928513\pi$
$127$	21.5867			1.91551			0.957756	+	0.287582i	$0.0928513\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−9.97127	+	17.2707i	−0.877921	+	1.52060i
$130$	−1.59908	+	2.76970i	−0.140249	+	0.242918i
$131$	1.65348	+	2.86391i	0.144465	+	0.250221i	0.929173	−	0.369645i	$-0.120521\pi$
$131$	1.65348	+	2.86391i	0.144465	+	0.250221i	−0.784708	+	0.619865i	$0.787187\pi$
$132$	2.16285			0.188252
$133$	7.18377	−	2.20963i	0.622912	−	0.191599i
$134$	5.32569			0.460070
$135$	1.42974	+	2.47639i	0.123053	+	0.213134i
$136$	−1.67222	+	2.89636i	−0.143391	+	0.248361i
$137$	2.95489	−	5.11803i	0.252454	−	0.437262i	−0.711747	−	0.702436i	$-0.752096\pi$
$137$	2.95489	−	5.11803i	0.252454	−	0.437262i	0.964201	+	0.265173i	$0.0854292\pi$
$138$	5.64558	+	9.77842i	0.480583	+	0.832395i
$139$	1.75993			0.149275			0.0746375	−	0.997211i	$-0.476220\pi$
$139$	1.75993			0.149275			0.0746375	+	0.997211i	$0.476220\pi$
$140$	−0.590793	+	2.57895i	−0.0499311	+	0.217961i
$141$	12.2882			1.03485
$142$	2.80013	+	4.84997i	0.234982	+	0.407000i
$143$	−1.59908	+	2.76970i	−0.133722	+	0.231614i
$144$	−0.838952	+	1.45311i	−0.0699127	+	0.121092i
$145$	3.46687	+	6.00479i	0.287908	+	0.498671i
$146$	3.37400			0.279234
$147$	12.5228	−	8.50865i	1.03286	−	0.701782i
$148$	8.77089			0.720962
$149$	3.54000	+	6.13146i	0.290008	+	0.502308i	0.973811	−	0.227358i	$-0.0730087\pi$
$149$	3.54000	+	6.13146i	0.290008	+	0.502308i	−0.683803	+	0.729666i	$0.739675\pi$
$150$	−1.08142	+	1.87308i	−0.0882978	+	0.152936i
$151$	−9.83617	+	17.0368i	−0.800456	+	1.38643i	0.118860	+	0.992911i	$0.462076\pi$
$151$	−9.83617	+	17.0368i	−0.800456	+	1.38643i	−0.919316	+	0.393520i	$0.871257\pi$
$152$	−1.42038	−	2.46016i	−0.115208	−	0.199546i
$153$	5.61164			0.453674
$154$	−0.590793	+	2.57895i	−0.0476074	+	0.207817i
$155$	−0.840751			−0.0675307
$156$	−3.45857	−	5.99043i	−0.276908	−	0.479618i
$157$	0.720135	−	1.24731i	0.0574730	−	0.0995462i	−0.835857	−	0.548947i	$-0.815029\pi$
$157$	0.720135	−	1.24731i	0.0574730	−	0.0995462i	0.893330	+	0.449400i	$0.148362\pi$
$158$	3.60268	−	6.24003i	0.286614	−	0.496430i
$159$	−9.62469	−	16.6704i	−0.763287	−	1.32205i
$160$	1.00000			0.0790569
$161$	−13.2018	+	4.06067i	−1.04044	+	0.320026i
$162$	−11.2184			−0.881397
$163$	−2.67509	−	4.63340i	−0.209529	−	0.362916i	0.742037	−	0.670359i	$-0.233860\pi$
$163$	−2.67509	−	4.63340i	−0.209529	−	0.362916i	−0.951566	+	0.307443i	$0.900527\pi$
$164$	4.64558	−	8.04637i	0.362758	−	0.628316i
$165$	−1.08142	+	1.87308i	−0.0841887	+	0.145819i
$166$	4.42867	+	7.67068i	0.343731	+	0.595360i
$167$	−10.7364			−0.830807			−0.415403	−	0.909637i	$-0.636360\pi$
$167$	−10.7364			−0.830807			−0.415403	+	0.909637i	$0.636360\pi$
$168$	−4.19168	−	3.89553i	−0.323395	−	0.300547i
$169$	−2.77171			−0.213209
$170$	−1.67222	−	2.89636i	−0.128253	−	0.222141i
$171$	−2.38325	+	4.12792i	−0.182252	+	0.315670i
$172$	−4.61025	+	7.98519i	−0.351528	+	0.608865i
$173$	6.33465	+	10.9719i	0.481614	+	0.834181i	0.999777	−	0.0211014i	$-0.00671728\pi$
$173$	6.33465	+	10.9719i	0.481614	+	0.834181i	−0.518163	+	0.855282i	$0.673384\pi$
$174$	−14.9966			−1.13689
$175$	−1.93804	−	1.80111i	−0.146502	−	0.136151i
$176$	1.00000			0.0753778
$177$	−8.17701	−	14.1630i	−0.614622	−	1.06456i
$178$	2.69925	−	4.67523i	0.202317	−	0.350423i
$179$	5.76553	−	9.98619i	0.430936	−	0.746403i	−0.566018	−	0.824393i	$-0.691517\pi$
$179$	5.76553	−	9.98619i	0.430936	−	0.746403i	0.996954	+	0.0779899i	$0.0248502\pi$
$180$	−0.838952	−	1.45311i	−0.0625318	−	0.108308i
$181$	−20.2610			−1.50599			−0.752995	−	0.658026i	$-0.771392\pi$
$181$	−20.2610			−1.50599			−0.752995	+	0.658026i	$0.771392\pi$
$182$	8.08762	−	2.48764i	0.599495	−	0.184396i
$183$	24.6563			1.82265
$184$	2.61025	+	4.52109i	0.192430	+	0.333299i
$185$	−4.38544	+	7.59581i	−0.322424	+	0.558455i
$186$	0.909207	−	1.57479i	0.0666663	−	0.115469i
$187$	−1.67222	−	2.89636i	−0.122285	−	0.211803i
$188$	5.68150			0.414366
$189$	1.68937	−	7.37447i	0.122883	−	0.536414i
$190$	2.84075			0.206090
$191$	−7.19267	−	12.4581i	−0.520443	−	0.901434i	−0.999717	−	0.0237690i	$-0.992433\pi$
$191$	−7.19267	−	12.4581i	−0.520443	−	0.901434i	0.479274	−	0.877665i	$-0.340900\pi$
$192$	−1.08142	+	1.87308i	−0.0780450	+	0.135178i
$193$	−6.16324	+	10.6750i	−0.443639	+	0.768406i	−0.997956	−	0.0638996i	$-0.979646\pi$
$193$	−6.16324	+	10.6750i	−0.443639	+	0.768406i	0.554317	+	0.832306i	$0.312980\pi$
$194$	4.04870	+	7.01256i	0.290680	+	0.503473i
$195$	6.91715			0.495347
$196$	5.78996	−	3.93401i	0.413568	−	0.281001i
$197$	24.9575			1.77815			0.889074	−	0.457763i	$-0.151349\pi$
$197$	24.9575			1.77815			0.889074	+	0.457763i	$0.151349\pi$
$198$	−0.838952	−	1.45311i	−0.0596217	−	0.103268i
$199$	1.27418	−	2.20694i	0.0903240	−	0.156446i	−0.817323	−	0.576179i	$-0.804543\pi$
$199$	1.27418	−	2.20694i	0.0903240	−	0.156446i	0.907647	+	0.419733i	$0.137876\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−5.75933	−	9.97545i	−0.406232	−	0.703614i
$202$	−7.72203			−0.543320
$203$	4.09640	−	17.8817i	0.287511	−	1.25505i
$204$	7.23349			0.506446
$205$	4.64558	+	8.04637i	0.324461	+	0.561983i
$206$	3.10657	−	5.38074i	0.216445	−	0.374894i
$207$	4.37975	−	7.58596i	0.304414	−	0.527260i
$208$	−1.59908	−	2.76970i	−0.110877	−	0.192044i
$209$	2.84075			0.196499
$210$	5.46947	−	1.68233i	0.377429	−	0.116092i
$211$	27.0267			1.86060			0.930298	−	0.366805i	$-0.119548\pi$
$211$	27.0267			1.86060			0.930298	+	0.366805i	$0.119548\pi$
$212$	−4.45001	−	7.70764i	−0.305628	−	0.529363i
$213$	6.05625	−	10.4897i	0.414967	−	0.718745i
$214$	7.97127	−	13.8066i	0.544905	−	0.943803i
$215$	−4.61025	−	7.98519i	−0.314417	−	0.544586i
$216$	−2.85949			−0.194564
$217$	1.62941	+	1.51429i	0.110611	+	0.102797i
$218$	−13.2834			−0.899663
$219$	−3.64872	−	6.31978i	−0.246558	−	0.427051i
$220$	−0.500000	+	0.866025i	−0.0337100	+	0.0583874i
$221$	−5.34803	+	9.26306i	−0.359747	+	0.623101i
$222$	−9.48504	−	16.4286i	−0.636594	−	1.10261i
$223$	−5.31833			−0.356142			−0.178071	−	0.984018i	$-0.556986\pi$
$223$	−5.31833			−0.356142			−0.178071	+	0.984018i	$0.556986\pi$
$224$	−1.93804	−	1.80111i	−0.129491	−	0.120342i
$225$	1.67790			0.111860
$226$	−1.20795	−	2.09224i	−0.0803518	−	0.139173i
$227$	6.00719	−	10.4048i	0.398711	−	0.690589i	−0.594856	−	0.803832i	$-0.702791\pi$
$227$	6.00719	−	10.4048i	0.398711	−	0.690589i	0.993567	+	0.113244i	$0.0361242\pi$
$228$	−3.07205	+	5.32095i	−0.203452	+	0.352389i
$229$	5.46620	+	9.46774i	0.361217	+	0.625646i	0.988161	−	0.153418i	$-0.0490281\pi$
$229$	5.46620	+	9.46774i	0.361217	+	0.625646i	−0.626945	+	0.779064i	$0.715695\pi$
$230$	−5.22051			−0.344230
$231$	5.46947	−	1.68233i	0.359865	−	0.110689i
$232$	−6.93373			−0.455222
$233$	2.23310	+	3.86785i	0.146295	+	0.253391i	0.929855	−	0.367925i	$-0.119932\pi$
$233$	2.23310	+	3.86785i	0.146295	+	0.253391i	−0.783560	+	0.621316i	$0.786598\pi$
$234$	−2.68311	+	4.64728i	−0.175400	+	0.303802i
$235$	−2.84075	+	4.92032i	−0.185310	+	0.320967i
$236$	−3.78067	−	6.54831i	−0.246101	−	0.426259i
$237$	−15.5841			−1.01230
$238$	−1.97587	+	8.62511i	−0.128076	+	0.559083i
$239$	−3.41574			−0.220946			−0.110473	−	0.993879i	$-0.535237\pi$
$239$	−3.41574			−0.220946			−0.110473	+	0.993879i	$0.535237\pi$
$240$	−1.08142	−	1.87308i	−0.0698056	−	0.120907i
$241$	−3.07065	+	5.31851i	−0.197798	+	0.342596i	−0.947814	−	0.318824i	$-0.896712\pi$
$241$	−3.07065	+	5.31851i	−0.197798	+	0.342596i	0.750016	+	0.661419i	$0.230046\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$	7.84255	+	13.5837i	0.503100	+	0.871394i
$244$	11.3999			0.729806
$245$	0.511973	+	6.98125i	0.0327087	+	0.446016i
$246$	−20.0953			−1.28123
$247$	−4.54260	−	7.86802i	−0.289039	−	0.500630i
$248$	0.420375	−	0.728112i	0.0266939	−	0.0462351i
$249$	9.57853	−	16.5905i	0.607014	−	1.05138i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−14.2997			−0.902590			−0.451295	−	0.892375i	$-0.649038\pi$
$251$	−14.2997			−0.902590			−0.451295	+	0.892375i	$0.649038\pi$
$252$	−0.991294	+	4.32723i	−0.0624456	+	0.272590i
$253$	−5.22051			−0.328210
$254$	−10.7934	−	18.6947i	−0.677236	−	1.17301i
$255$	−3.61675	+	6.26439i	−0.226489	+	0.392291i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.51623	−	7.82234i	−0.281715	−	0.487944i	0.690092	−	0.723721i	$-0.257570\pi$
$257$	−4.51623	−	7.82234i	−0.281715	−	0.487944i	−0.971807	+	0.235777i	$0.924237\pi$
$258$	19.9425			1.24157
$259$	22.1801	−	6.82227i	1.37820	−	0.423915i
$260$	3.19817			0.198342
$261$	5.81707	+	10.0755i	0.360068	+	0.623655i
$262$	1.65348	−	2.86391i	0.102152	−	0.176933i
$263$	−11.6743	+	20.2205i	−0.719869	+	1.24685i	0.241182	+	0.970480i	$0.422465\pi$
$263$	−11.6743	+	20.2205i	−0.719869	+	1.24685i	−0.961051	+	0.276371i	$0.910868\pi$
$264$	−1.08142	−	1.87308i	−0.0665570	−	0.115280i
$265$	8.90002			0.546724
$266$	−5.50548	−	5.11652i	−0.337563	−	0.313714i
$267$	−11.6761			−0.714566
$268$	−2.66285	−	4.61219i	−0.162659	−	0.281734i
$269$	7.84734	−	13.5920i	0.478461	−	0.828718i	−0.521234	−	0.853414i	$-0.674528\pi$
$269$	7.84734	−	13.5920i	0.478461	−	0.828718i	0.999695	+	0.0246952i	$0.00786152\pi$
$270$	1.42974	−	2.47639i	0.0870115	−	0.150708i
$271$	11.6490	+	20.1766i	0.707624	+	1.22564i	0.965736	+	0.259526i	$0.0835663\pi$
$271$	11.6490	+	20.1766i	0.707624	+	1.22564i	−0.258112	+	0.966115i	$0.583100\pi$
$272$	3.34443			0.202786
$273$	−13.4057	−	12.4586i	−0.811349	−	0.754027i
$274$	−5.90979			−0.357023
$275$	−0.500000	−	0.866025i	−0.0301511	−	0.0522233i
$276$	5.64558	−	9.77842i	0.339824	−	0.588592i
$277$	−9.74894	+	16.8857i	−0.585757	+	1.01456i	0.409023	+	0.912524i	$0.365869\pi$
$277$	−9.74894	+	16.8857i	−0.585757	+	1.01456i	−0.994781	+	0.102037i	$0.967464\pi$
$278$	−0.879964	−	1.52414i	−0.0527767	−	0.0914119i
$279$	−1.41070			−0.0844564
$280$	2.52883	−	0.777832i	0.151126	−	0.0464843i
$281$	−2.21913			−0.132382			−0.0661911	−	0.997807i	$-0.521085\pi$
$281$	−2.21913			−0.132382			−0.0661911	+	0.997807i	$0.521085\pi$
$282$	−6.14411	−	10.6419i	−0.365876	−	0.633716i
$283$	−3.20955	+	5.55910i	−0.190788	+	0.330454i	−0.945512	−	0.325589i	$-0.894438\pi$
$283$	−3.20955	+	5.55910i	−0.190788	+	0.330454i	0.754724	+	0.656043i	$0.227771\pi$
$284$	2.80013	−	4.84997i	0.166157	−	0.287793i
$285$	−3.07205	−	5.32095i	−0.181973	−	0.315186i
$286$	3.19817			0.189112
$287$	5.48914	−	23.9614i	0.324014	−	1.41440i
$288$	1.67790			0.0988715
$289$	2.90739	+	5.03575i	0.171023	+	0.296220i
$290$	3.46687	−	6.00479i	0.203581	−	0.352613i
$291$	8.75672	−	15.1671i	0.513328	−	0.889111i
$292$	−1.68700	−	2.92197i	−0.0987243	−	0.170995i
$293$	−23.8372			−1.39258			−0.696291	−	0.717759i	$-0.745168\pi$
$293$	−23.8372			−1.39258			−0.696291	+	0.717759i	$0.745168\pi$
$294$	−13.6301	−	6.59072i	−0.794924	−	0.384379i
$295$	7.56134			0.440238
$296$	−4.38544	−	7.59581i	−0.254899	−	0.441497i
$297$	1.42974	−	2.47639i	0.0829622	−	0.143695i
$298$	3.54000	−	6.13146i	0.205067	−	0.355186i
$299$	8.34803	+	14.4592i	0.482779	+	0.836198i
$300$	2.16285			0.124872
$301$	−5.44741	+	23.7792i	−0.313983	+	1.37061i
$302$	19.6723			1.13202
$303$	8.35078	+	14.4640i	0.479740	+	0.830934i
$304$	−1.42038	+	2.46016i	−0.0814641	+	0.141100i
$305$	−5.69997	+	9.87263i	−0.326379	+	0.565305i
$306$	−2.80582	−	4.85982i	−0.160398	−	0.277817i
$307$	−18.1197			−1.03415			−0.517074	−	0.855941i	$-0.672979\pi$
$307$	−18.1197			−1.03415			−0.517074	+	0.855941i	$0.672979\pi$
$308$	2.52883	−	0.777832i	0.144093	−	0.0443211i
$309$	−13.4381			−0.764465
$310$	0.420375	+	0.728112i	0.0238757	+	0.0413540i
$311$	−14.4597	+	25.0449i	−0.819934	+	1.42017i	0.0857970	+	0.996313i	$0.472656\pi$
$311$	−14.4597	+	25.0449i	−0.819934	+	1.42017i	−0.905731	+	0.423854i	$0.860677\pi$
$312$	−3.45857	+	5.99043i	−0.195803	+	0.339141i
$313$	8.12870	+	14.0793i	0.459461	+	0.795810i	0.998932	−	0.0461938i	$-0.0147092\pi$
$313$	8.12870	+	14.0793i	0.459461	+	0.795810i	−0.539471	+	0.842004i	$0.681376\pi$
$314$	−1.44027			−0.0812791
$315$	−3.25184	−	3.02210i	−0.183220	−	0.170276i
$316$	−7.20536			−0.405333
$317$	10.8037	+	18.7126i	0.606798	+	1.05100i	0.991765	+	0.128074i	$0.0408795\pi$
$317$	10.8037	+	18.7126i	0.606798	+	1.05100i	−0.384967	+	0.922930i	$0.625787\pi$
$318$	−9.62469	+	16.6704i	−0.539726	+	0.934832i
$319$	3.46687	−	6.00479i	0.194107	−	0.336204i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−34.4813			−1.92456
$322$	10.1175	+	9.40273i	0.563828	+	0.523994i
$323$	9.50070			0.528633
$324$	5.60918	+	9.71538i	0.311621	+	0.539743i
$325$	−1.59908	+	2.76970i	−0.0887012	+	0.153635i
$326$	−2.67509	+	4.63340i	−0.148160	+	0.256620i
$327$	14.3649	+	24.8808i	0.794383	+	1.37591i
$328$	−9.29115			−0.513018
$329$	14.3675	−	4.41925i	0.792109	−	0.243641i
$330$	2.16285			0.119061
$331$	11.5905	+	20.0753i	0.637070	+	1.10344i	0.986073	+	0.166316i	$0.0531872\pi$
$331$	11.5905	+	20.0753i	0.637070	+	1.10344i	−0.349002	+	0.937122i	$0.613479\pi$
$332$	4.42867	−	7.67068i	0.243055	−	0.420983i
$333$	−7.35835	+	12.7450i	−0.403235	+	0.698424i
$334$	5.36820	+	9.29799i	0.293735	+	0.508763i
$335$	5.32569			0.290974
$336$	−1.27779	+	5.57786i	−0.0697094	+	0.304297i
$337$	−18.9900			−1.03445			−0.517226	−	0.855849i	$-0.673035\pi$
$337$	−18.9900			−1.03445			−0.517226	+	0.855849i	$0.673035\pi$
$338$	1.38586	+	2.40038i	0.0753807	+	0.130563i
$339$	−2.61262	+	4.52519i	−0.141898	+	0.245774i
$340$	−1.67222	+	2.89636i	−0.0906886	+	0.157077i
$341$	0.420375	+	0.728112i	0.0227646	+	0.0394295i
$342$	4.76651			0.257743
$343$	11.5818	−	14.4520i	0.625359	−	0.780337i
$344$	9.22051			0.497136
$345$	5.64558	+	9.77842i	0.303948	+	0.526453i
$346$	6.33465	−	10.9719i	0.340553	−	0.589855i
$347$	−1.52087	+	2.63422i	−0.0816445	+	0.141412i	−0.903956	−	0.427625i	$-0.859351\pi$
$347$	−1.52087	+	2.63422i	−0.0816445	+	0.141412i	0.822312	+	0.569037i	$0.192684\pi$
$348$	7.49830	+	12.9874i	0.401951	+	0.696200i
$349$	31.9794			1.71182			0.855910	−	0.517125i	$-0.172998\pi$
$349$	31.9794			1.71182			0.855910	+	0.517125i	$0.172998\pi$
$350$	−0.590793	+	2.57895i	−0.0315792	+	0.137850i
$351$	−9.14513			−0.488131
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	−16.6579	+	28.8524i	−0.886612	+	1.53566i	−0.0427561	+	0.999086i	$0.513614\pi$
$353$	−16.6579	+	28.8524i	−0.886612	+	1.53566i	−0.843855	+	0.536571i	$0.819719\pi$
$354$	−8.17701	+	14.1630i	−0.434603	+	0.752755i
$355$	2.80013	+	4.84997i	0.148615	+	0.257410i
$356$	−5.39849			−0.286120
$357$	18.2923	−	5.62644i	0.968129	−	0.297783i
$358$	−11.5311			−0.609435
$359$	−12.2071	−	21.1434i	−0.644267	−	1.11590i	−0.984470	−	0.175552i	$-0.943829\pi$
$359$	−12.2071	−	21.1434i	−0.644267	−	1.11590i	0.340203	−	0.940352i	$-0.389504\pi$
$360$	−0.838952	+	1.45311i	−0.0442167	+	0.0765855i
$361$	5.46507	−	9.46577i	0.287635	−	0.498199i
$362$	10.1305	+	17.5466i	0.532448	+	0.922227i
$363$	2.16285			0.113520
$364$	−6.19817	−	5.76027i	−0.324872	−	0.301920i
$365$	3.37400			0.176603
$366$	−12.3282	−	21.3530i	−0.644403	−	1.11614i
$367$	0.891819	−	1.54468i	0.0465526	−	0.0806314i	−0.841810	−	0.539774i	$-0.818510\pi$
$367$	0.891819	−	1.54468i	0.0465526	−	0.0806314i	0.888363	+	0.459142i	$0.151843\pi$
$368$	2.61025	−	4.52109i	0.136069	−	0.235678i
$369$	7.79483	+	13.5010i	0.405783	+	0.702836i
$370$	8.77089			0.455977
$371$	−17.2486	−	16.0300i	−0.895501	−	0.832234i
$372$	−1.81841			−0.0942804
$373$	14.1526	+	24.5131i	0.732796	+	1.26924i	0.955684	+	0.294396i	$0.0951184\pi$
$373$	14.1526	+	24.5131i	0.732796	+	1.26924i	−0.222887	+	0.974844i	$0.571548\pi$
$374$	−1.67222	+	2.89636i	−0.0864682	+	0.149767i
$375$	−1.08142	+	1.87308i	−0.0558445	+	0.0967254i
$376$	−2.84075	−	4.92032i	−0.146501	−	0.253746i
$377$	−22.1752			−1.14208
$378$	−7.23116	+	2.22420i	−0.371931	+	0.114401i
$379$	−19.1494			−0.983641			−0.491820	−	0.870697i	$-0.663668\pi$
$379$	−19.1494			−0.983641			−0.491820	+	0.870697i	$0.663668\pi$
$380$	−1.42038	−	2.46016i	−0.0728637	−	0.126204i
$381$	−23.3444	+	40.4337i	−1.19597	+	2.07148i
$382$	−7.19267	+	12.4581i	−0.368009	+	0.637410i
$383$	11.0822	+	19.1949i	0.566274	+	0.980816i	0.996930	+	0.0782996i	$0.0249491\pi$
$383$	11.0822	+	19.1949i	0.566274	+	0.980816i	−0.430656	+	0.902516i	$0.641718\pi$
$384$	2.16285			0.110372
$385$	−0.590793	+	2.57895i	−0.0301096	+	0.131435i
$386$	12.3265			0.627401
$387$	−7.73556	−	13.3984i	−0.393221	−	0.681078i
$388$	4.04870	−	7.01256i	0.205542	−	0.356009i
$389$	4.25666	−	7.37275i	0.215821	−	0.373813i	−0.737705	−	0.675123i	$-0.764091\pi$
$389$	4.25666	−	7.37275i	0.215821	−	0.373813i	0.953526	+	0.301310i	$0.0974239\pi$
$390$	−3.45857	−	5.99043i	−0.175132	−	0.303337i
$391$	−17.4596			−0.882971
$392$	−6.30193	−	3.04724i	−0.318295	−	0.153909i
$393$	−7.15243			−0.360793
$394$	−12.4788	−	21.6138i	−0.628671	−	1.08889i
$395$	3.60268	−	6.24003i	0.181271	−	0.313970i
$396$	−0.838952	+	1.45311i	−0.0421589	+	0.0730214i
$397$	−14.9724	−	25.9329i	−0.751441	−	1.30153i	−0.947124	−	0.320867i	$-0.896026\pi$
$397$	−14.9724	−	25.9329i	−0.751441	−	1.30153i	0.195683	−	0.980667i	$-0.437308\pi$
$398$	−2.54835			−0.127737
$399$	−3.62989	+	15.8453i	−0.181722	+	0.793258i
$400$	1.00000			0.0500000
$401$	−0.464775	−	0.805013i	−0.0232097	−	0.0402004i	0.854187	−	0.519966i	$-0.174055\pi$
$401$	−0.464775	−	0.805013i	−0.0232097	−	0.0402004i	−0.877397	+	0.479765i	$0.840722\pi$
$402$	−5.75933	+	9.97545i	−0.287249	+	0.497530i
$403$	1.34443	−	2.32862i	0.0669709	−	0.115997i
$404$	3.86102	+	6.68747i	0.192093	+	0.332714i
$405$	−11.2184			−0.557444
$406$	−17.5342	+	5.39328i	−0.870209	+	0.267664i
$407$	8.77089			0.434757
$408$	−3.61675	−	6.26439i	−0.179056	−	0.310133i
$409$	14.5139	−	25.1388i	0.717665	−	1.24303i	−0.244258	−	0.969710i	$-0.578544\pi$
$409$	14.5139	−	25.1388i	0.717665	−	1.24303i	0.961923	−	0.273321i	$-0.0881222\pi$
$410$	4.64558	−	8.04637i	0.229429	−	0.397382i
$411$	6.39098	+	11.0695i	0.315244	+	0.546018i
$412$	−6.21314			−0.306100
$413$	−14.6542	−	13.6188i	−0.721084	−	0.670139i
$414$	−8.75951			−0.430506
$415$	4.42867	+	7.67068i	0.217395	+	0.376539i
$416$	−1.59908	+	2.76970i	−0.0784016	+	0.135796i
$417$	−1.90323	+	3.29648i	−0.0932014	+	0.161430i
$418$	−1.42038	−	2.46016i	−0.0694728	−	0.120330i
$419$	−6.96823			−0.340420			−0.170210	−	0.985408i	$-0.554445\pi$
$419$	−6.96823			−0.340420			−0.170210	+	0.985408i	$0.554445\pi$
$420$	−4.19168	−	3.89553i	−0.204533	−	0.190083i
$421$	35.9645			1.75280			0.876400	−	0.481584i	$-0.159938\pi$
$421$	35.9645			1.75280			0.876400	+	0.481584i	$0.159938\pi$
$422$	−13.5134	−	23.4058i	−0.657820	−	1.13938i
$423$	−4.76651	+	8.25583i	−0.231756	+	0.401412i
$424$	−4.45001	+	7.70764i	−0.216112	+	0.374316i
$425$	−1.67222	−	2.89636i	−0.0811144	−	0.140494i
$426$	−12.1125			−0.586853
$427$	28.8285	−	8.86723i	1.39511	−	0.429115i
$428$	−15.9425			−0.770612
$429$	−3.45857	−	5.99043i	−0.166982	−	0.289220i
$430$	−4.61025	+	7.98519i	−0.222326	+	0.385080i
$431$	−10.1287	+	17.5434i	−0.487882	+	0.845037i	−0.999903	−	0.0139363i	$-0.995564\pi$
$431$	−10.1287	+	17.5434i	−0.487882	+	0.845037i	0.512021	+	0.858973i	$0.328897\pi$
$432$	1.42974	+	2.47639i	0.0687886	+	0.119145i
$433$	24.8601			1.19470			0.597350	−	0.801981i	$-0.296220\pi$
$433$	24.8601			1.19470			0.597350	+	0.801981i	$0.296220\pi$
$434$	0.496709	−	2.16825i	0.0238428	−	0.104079i
$435$	−14.9966			−0.719032
$436$	6.64169	+	11.5037i	0.318079	+	0.550929i
$437$	7.41508	−	12.8433i	0.354711	−	0.614378i
$438$	−3.64872	+	6.31978i	−0.174343	+	0.301971i
$439$	15.3195	+	26.5342i	0.731160	+	1.26641i	0.956388	+	0.292100i	$0.0943541\pi$
$439$	15.3195	+	26.5342i	0.731160	+	1.26641i	−0.225228	+	0.974306i	$0.572313\pi$
$440$	1.00000			0.0476731
$441$	0.859041	+	11.7139i	0.0409067	+	0.557804i
$442$	10.6961			0.508760
$443$	−6.48417	−	11.2309i	−0.308072	−	0.533597i	0.669868	−	0.742480i	$-0.266351\pi$
$443$	−6.48417	−	11.2309i	−0.308072	−	0.533597i	−0.977941	+	0.208883i	$0.933017\pi$
$444$	−9.48504	+	16.4286i	−0.450140	+	0.779665i
$445$	2.69925	−	4.67523i	0.127957	−	0.221627i
$446$	2.65917	+	4.60581i	0.125915	+	0.218091i
$447$	−15.3129			−0.724277
$448$	−0.590793	+	2.57895i	−0.0279123	+	0.121844i
$449$	−25.1980			−1.18917			−0.594584	−	0.804034i	$-0.702683\pi$
$449$	−25.1980			−1.18917			−0.594584	+	0.804034i	$0.702683\pi$
$450$	−0.838952	−	1.45311i	−0.0395486	−	0.0685002i
$451$	4.64558	−	8.04637i	0.218752	−	0.378889i
$452$	−1.20795	+	2.09224i	−0.0568173	+	0.0984105i
$453$	−21.2741	−	36.8479i	−0.999546	−	1.73126i
$454$	−12.0144			−0.563863
$455$	8.08762	−	2.48764i	0.379154	−	0.116622i
$456$	6.14411			0.287724
$457$	1.77420	+	3.07300i	0.0829934	+	0.143749i	0.904534	−	0.426401i	$-0.140219\pi$
$457$	1.77420	+	3.07300i	0.0829934	+	0.143749i	−0.821541	+	0.570149i	$0.806885\pi$
$458$	5.46620	−	9.46774i	0.255419	−	0.442399i
$459$	4.78168	−	8.28212i	0.223190	−	0.386576i
$460$	2.61025	+	4.52109i	0.121704	+	0.210797i
$461$	21.3436			0.994069			0.497034	−	0.867731i	$-0.334422\pi$
$461$	21.3436			0.994069			0.497034	+	0.867731i	$0.334422\pi$
$462$	−4.19168	−	3.89553i	−0.195014	−	0.181237i
$463$	−38.9903			−1.81203			−0.906016	−	0.423244i	$-0.860891\pi$
$463$	−38.9903			−1.81203			−0.906016	+	0.423244i	$0.860891\pi$
$464$	3.46687	+	6.00479i	0.160945	+	0.278765i
$465$	0.909207	−	1.57479i	0.0421635	−	0.0730293i
$466$	2.23310	−	3.86785i	0.103446	−	0.179174i
$467$	−8.23494	−	14.2633i	−0.381068	−	0.660028i	0.610148	−	0.792288i	$-0.291110\pi$
$467$	−8.23494	−	14.2633i	−0.381068	−	0.660028i	−0.991215	+	0.132259i	$0.957777\pi$
$468$	5.36622			0.248054
$469$	−10.3214	−	9.59218i	−0.476597	−	0.442926i
$470$	5.68150			0.262068
$471$	1.55754	+	2.69774i	0.0717677	+	0.124305i
$472$	−3.78067	+	6.54831i	−0.174019	+	0.301410i
$473$	−4.61025	+	7.98519i	−0.211980	+	0.367160i
$474$	7.79205	+	13.4962i	0.357901	+	0.619902i
$475$	2.84075			0.130343
$476$	8.45750	−	2.60141i	0.387649	−	0.119235i
$477$	14.9334			0.683753
$478$	1.70787	+	2.95812i	0.0781161	+	0.135301i
$479$	−13.0954	+	22.6819i	−0.598344	+	1.03636i	0.394721	+	0.918801i	$0.370841\pi$
$479$	−13.0954	+	22.6819i	−0.598344	+	1.03636i	−0.993066	+	0.117562i	$0.962492\pi$
$480$	−1.08142	+	1.87308i	−0.0493600	+	0.0854940i
$481$	−14.0254	−	24.2927i	−0.639503	−	1.10765i
$482$	6.14129			0.279728
$483$	6.67073	−	29.1193i	0.303529	−	1.32497i
$484$	1.00000			0.0454545
$485$	4.04870	+	7.01256i	0.183842	+	0.318424i
$486$	7.84255	−	13.5837i	0.355745	−	0.616169i
$487$	−11.0052	+	19.0616i	−0.498694	+	0.863762i	−0.999999	−	0.00150795i	$-0.999520\pi$
$487$	−11.0052	+	19.0616i	−0.498694	+	0.863762i	0.501305	+	0.865270i	$0.332853\pi$
$488$	−5.69997	−	9.87263i	−0.258025	−	0.446913i
$489$	11.5716			0.523287
$490$	5.78996	−	3.93401i	0.261564	−	0.177720i
$491$	13.7546			0.620736			0.310368	−	0.950617i	$-0.399548\pi$
$491$	13.7546			0.620736			0.310368	+	0.950617i	$0.399548\pi$
$492$	10.0477	+	17.4031i	0.452984	+	0.784591i
$493$	11.5947	−	20.0826i	0.522199	−	0.904475i
$494$	−4.54260	+	7.86802i	−0.204381	+	0.353999i
$495$	−0.838952	−	1.45311i	−0.0377081	−	0.0653123i
$496$	−0.840751			−0.0377508
$497$	3.30859	−	14.4428i	0.148411	−	0.647847i
$498$	−19.1571			−0.858448
$499$	−14.3179	−	24.7994i	−0.640958	−	1.11017i	−0.985219	−	0.171298i	$-0.945204\pi$
$499$	−14.3179	−	24.7994i	−0.640958	−	1.11017i	0.344262	−	0.938874i	$-0.388129\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	11.6106	−	20.1101i	0.518723	−	0.898454i
$502$	7.14986	+	12.3839i	0.319114	+	0.552721i
$503$	35.7104			1.59225			0.796125	−	0.605132i	$-0.206880\pi$
$503$	35.7104			1.59225			0.796125	+	0.605132i	$0.206880\pi$
$504$	4.24313	−	1.30513i	0.189004	−	0.0581350i
$505$	−7.72203			−0.343626
$506$	2.61025	+	4.52109i	0.116040	+	0.200987i
$507$	2.99740	−	5.19164i	0.133119	−	0.230569i
$508$	−10.7934	+	18.6947i	−0.478878	+	0.829441i
$509$	15.7052	+	27.2022i	0.696122	+	1.20572i	0.969801	+	0.243897i	$0.0784259\pi$
$509$	15.7052	+	27.2022i	0.696122	+	1.20572i	−0.273679	+	0.961821i	$0.588241\pi$
$510$	7.23349			0.320304
$511$	−6.53894	−	6.07696i	−0.289266	−	0.268829i
$512$	1.00000			0.0441942
$513$	4.06155	+	7.03481i	0.179322	+	0.310594i
$514$	−4.51623	+	7.82234i	−0.199202	+	0.345029i
$515$	3.10657	−	5.38074i	0.136892	−	0.237104i
$516$	−9.97127	−	17.2707i	−0.438961	−	0.760302i
$517$	5.68150			0.249872
$518$	−16.9983	−	15.7974i	−0.746862	−	0.694097i
$519$	−27.4017			−1.20280
$520$	−1.59908	−	2.76970i	−0.0701245	−	0.121459i
$521$	5.60415	−	9.70667i	0.245522	−	0.425257i	−0.716756	−	0.697324i	$-0.754374\pi$
$521$	5.60415	−	9.70667i	0.245522	−	0.425257i	0.962278	+	0.272067i	$0.0877072\pi$
$522$	5.81707	−	10.0755i	0.254606	−	0.440991i
$523$	−2.73197	−	4.73190i	−0.119461	−	0.206912i	0.800093	−	0.599875i	$-0.204783\pi$
$523$	−2.73197	−	4.73190i	−0.119461	−	0.206912i	−0.919554	+	0.392964i	$0.871450\pi$
$524$	−3.30695			−0.144465
$525$	5.46947	−	1.68233i	0.238707	−	0.0734229i
$526$	23.3486			1.01805
$527$	1.40592	+	2.43512i	0.0612427	+	0.106075i
$528$	−1.08142	+	1.87308i	−0.0470629	+	0.0815153i
$529$	−2.12684	+	3.68379i	−0.0924711	+	0.160165i
$530$	−4.45001	−	7.70764i	−0.193296	−	0.334799i
$531$	12.6872			0.550578
$532$	−1.67829	+	7.32614i	−0.0727633	+	0.317629i
$533$	−29.7147			−1.28709
$534$	5.83806	+	10.1118i	0.252637	+	0.437581i
$535$	7.97127	−	13.8066i	0.344628	−	0.596913i
$536$	−2.66285	+	4.61219i	−0.115017	+	0.199216i
$537$	12.4700	+	21.5986i	0.538118	+	0.932048i
$538$	−15.6947			−0.676646
$539$	5.78996	−	3.93401i	0.249391	−	0.169450i
$540$	−2.85949			−0.123053
$541$	−11.3913	−	19.7303i	−0.489751	−	0.848273i	0.510180	−	0.860068i	$-0.329579\pi$
$541$	−11.3913	−	19.7303i	−0.489751	−	0.848273i	−0.999930	+	0.0117946i	$0.996246\pi$
$542$	11.6490	−	20.1766i	0.500366	−	0.866659i
$543$	21.9108	−	37.9505i	0.940280	−	1.62861i
$544$	−1.67222	−	2.89636i	−0.0716957	−	0.124181i
$545$	−13.2834			−0.568997
$546$	−4.08660	+	17.8390i	−0.174890	+	0.763437i
$547$	−18.8573			−0.806281			−0.403141	−	0.915138i	$-0.632081\pi$
$547$	−18.8573			−0.806281			−0.403141	+	0.915138i	$0.632081\pi$
$548$	2.95489	+	5.11803i	0.126227	+	0.218631i
$549$	−9.56400	+	16.5653i	−0.408182	+	0.706991i
$550$	−0.500000	+	0.866025i	−0.0213201	+	0.0369274i
$551$	9.84850	+	17.0581i	0.419560	+	0.726700i
$552$	−11.2912			−0.480583
$553$	−18.2211	+	5.60456i	−0.774841	+	0.238330i
$554$	19.4979			0.828386
$555$	−9.48504	−	16.4286i	−0.402617	−	0.697354i
$556$	−0.879964	+	1.52414i	−0.0373188	+	0.0646380i
$557$	−5.38335	+	9.32424i	−0.228100	+	0.395081i	−0.957245	−	0.289279i	$-0.906585\pi$
$557$	−5.38335	+	9.32424i	−0.228100	+	0.395081i	0.729145	+	0.684359i	$0.239918\pi$
$558$	0.705350	+	1.22170i	0.0298598	+	0.0517188i
$559$	29.4887			1.24724
$560$	−1.93804	−	1.80111i	−0.0818970	−	0.0761110i
$561$	7.23349			0.305398
$562$	1.10957	+	1.92182i	0.0468042	+	0.0810672i
$563$	12.5476	−	21.7330i	0.528818	−	0.915939i	−0.470618	−	0.882337i	$-0.655969\pi$
$563$	12.5476	−	21.7330i	0.528818	−	0.915939i	0.999435	−	0.0336016i	$-0.0106977\pi$
$564$	−6.14411	+	10.6419i	−0.258714	+	0.448105i
$565$	−1.20795	−	2.09224i	−0.0508190	−	0.0880210i
$566$	6.41909			0.269815
$567$	21.7416	+	20.2055i	0.913060	+	0.848553i
$568$	−5.60026			−0.234982
$569$	19.1924	+	33.2422i	0.804586	+	1.39358i	0.916570	+	0.399874i	$0.130946\pi$
$569$	19.1924	+	33.2422i	0.804586	+	1.39358i	−0.111984	+	0.993710i	$0.535720\pi$
$570$	−3.07205	+	5.32095i	−0.128674	+	0.222870i
$571$	12.1629	−	21.0668i	0.509002	−	0.881617i	−0.490944	−	0.871191i	$-0.663348\pi$
$571$	12.1629	−	21.0668i	0.509002	−	0.881617i	0.999946	−	0.0104259i	$-0.00331873\pi$
$572$	−1.59908	−	2.76970i	−0.0668611	−	0.115807i
$573$	31.1133			1.29978
$574$	−23.4957	+	7.22695i	−0.980693	+	0.301647i
$575$	−5.22051			−0.217710
$576$	−0.838952	−	1.45311i	−0.0349563	−	0.0605462i
$577$	−4.22946	+	7.32564i	−0.176075	+	0.304970i	−0.940533	−	0.339703i	$-0.889673\pi$
$577$	−4.22946	+	7.32564i	−0.176075	+	0.304970i	0.764458	+	0.644674i	$0.223007\pi$
$578$	2.90739	−	5.03575i	0.120931	−	0.209459i
$579$	−13.3301	−	23.0885i	−0.553981	−	0.959524i
$580$	−6.93373			−0.287908
$581$	5.23285	−	22.8426i	0.217095	−	0.947670i
$582$	−17.5134			−0.725956
$583$	−4.45001	−	7.70764i	−0.184301	−	0.319218i
$584$	−1.68700	+	2.92197i	−0.0698086	+	0.120912i
$585$	−2.68311	+	4.64728i	−0.110933	+	0.192142i
$586$	11.9186	+	20.6436i	0.492352	+	0.852779i
$587$	−35.2937			−1.45673			−0.728364	−	0.685190i	$-0.759719\pi$
$587$	−35.2937			−1.45673			−0.728364	+	0.685190i	$0.759719\pi$
$588$	1.10732	+	15.0994i	0.0456650	+	0.622688i
$589$	−2.38836			−0.0984108
$590$	−3.78067	−	6.54831i	−0.155648	−	0.269590i
$591$	−26.9896	+	46.7474i	−1.11021	+	1.92293i
$592$	−4.38544	+	7.59581i	−0.180241	+	0.312186i
$593$	−14.2277	−	24.6431i	−0.584262	−	1.01197i	−0.994967	−	0.100203i	$-0.968051\pi$
$593$	−14.2277	−	24.6431i	−0.584262	−	1.01197i	0.410705	−	0.911768i	$-0.365282\pi$
$594$	−2.85949			−0.117326
$595$	−1.97587	+	8.62511i	−0.0810026	+	0.353595i
$596$	−7.07999			−0.290008
$597$	2.75585	+	4.77327i	0.112789	+	0.195357i
$598$	8.34803	−	14.4592i	0.341376	−	0.591281i
$599$	12.7189	−	22.0298i	0.519681	−	0.900114i	−0.480057	−	0.877237i	$-0.659384\pi$
$599$	12.7189	−	22.0298i	0.519681	−	0.900114i	0.999738	−	0.0228765i	$-0.00728246\pi$
$600$	−1.08142	−	1.87308i	−0.0441489	−	0.0764682i
$601$	7.43398			0.303238			0.151619	−	0.988439i	$-0.451551\pi$
$601$	7.43398			0.303238			0.151619	+	0.988439i	$0.451551\pi$
$602$	23.3171	−	7.17200i	0.950333	−	0.292309i
$603$	8.93600			0.363902
$604$	−9.83617	−	17.0368i	−0.400228	−	0.693216i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$	8.35078	−	14.4640i	0.339227	−	0.587559i
$607$	10.5582	+	18.2873i	0.428544	+	0.742260i	0.996744	−	0.0806308i	$-0.0256935\pi$
$607$	10.5582	+	18.2873i	0.428544	+	0.742260i	−0.568200	+	0.822890i	$0.692360\pi$
$608$	2.84075			0.115208
$609$	29.0640	+	27.0106i	1.17773	+	1.09452i
$610$	11.3999			0.461570
$611$	−9.08520	−	15.7360i	−0.367548	−	0.636612i
$612$	−2.80582	+	4.85982i	−0.113418	+	0.196447i
$613$	2.49710	−	4.32510i	0.100857	−	0.174689i	−0.811181	−	0.584795i	$-0.801175\pi$
$613$	2.49710	−	4.32510i	0.100857	−	0.174689i	0.912038	+	0.410106i	$0.134508\pi$
$614$	9.05987	+	15.6922i	0.365627	+	0.633284i
$615$	−20.0953			−0.810322
$616$	−1.93804	−	1.80111i	−0.0780857	−	0.0725690i
$617$	−40.1469			−1.61625			−0.808126	−	0.589010i	$-0.799518\pi$
$617$	−40.1469			−1.61625			−0.808126	+	0.589010i	$0.799518\pi$
$618$	6.71904	+	11.6377i	0.270279	+	0.468138i
$619$	16.3947	−	28.3965i	0.658960	−	1.14135i	−0.321926	−	0.946765i	$-0.604330\pi$
$619$	16.3947	−	28.3965i	0.658960	−	1.14135i	0.980885	−	0.194587i	$-0.0623366\pi$
$620$	0.420375	−	0.728112i	0.0168827	−	0.0292417i
$621$	−7.46399	−	12.9280i	−0.299520	−	0.518783i
$622$	28.9194			1.15956
$623$	−13.6519	+	4.19912i	−0.546951	+	0.168234i
$624$	6.91715			0.276908
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	8.12870	−	14.0793i	0.324888	−	0.562723i
$627$	−3.07205	+	5.32095i	−0.122686	+	0.212498i
$628$	0.720135	+	1.24731i	0.0287365	+	0.0497731i
$629$	29.3336			1.16961
$630$	−0.991294	+	4.32723i	−0.0394941	+	0.172401i
$631$	−15.7365			−0.626459			−0.313229	−	0.949678i	$-0.601411\pi$
$631$	−15.7365			−0.626459			−0.313229	+	0.949678i	$0.601411\pi$
$632$	3.60268	+	6.24003i	0.143307	+	0.248215i
$633$	−29.2273	+	50.6232i	−1.16168	+	2.01209i
$634$	10.8037	−	18.7126i	0.429071	−	0.743172i
$635$	−10.7934	−	18.6947i	−0.428322	−	0.741875i
$636$	19.2494			0.763287
$637$	−20.1546	−	9.74560i	−0.798556	−	0.386135i
$638$	−6.93373			−0.274509
$639$	4.69835	+	8.13778i	0.185864	+	0.321926i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	6.96126	−	12.0573i	0.274953	−	0.476233i	−0.695170	−	0.718845i	$-0.744671\pi$
$641$	6.96126	−	12.0573i	0.274953	−	0.476233i	0.970123	+	0.242612i	$0.0780043\pi$
$642$	17.2406	+	29.8616i	0.680433	+	1.17855i
$643$	−7.23944			−0.285496			−0.142748	−	0.989759i	$-0.545594\pi$
$643$	−7.23944			−0.285496			−0.142748	+	0.989759i	$0.545594\pi$
$644$	3.08424	−	13.4634i	0.121536	−	0.530532i
$645$	19.9425			0.785237
$646$	−4.75035	−	8.22784i	−0.186900	−	0.323720i
$647$	10.6565	−	18.4577i	0.418952	−	0.725645i	−0.576883	−	0.816827i	$-0.695731\pi$
$647$	10.6565	−	18.4577i	0.418952	−	0.725645i	0.995834	+	0.0911816i	$0.0290644\pi$
$648$	5.60918	−	9.71538i	0.220349	−	0.381656i
$649$	−3.78067	−	6.54831i	−0.148404	−	0.257044i
$650$	3.19817			0.125443
$651$	−4.59846	+	1.41442i	−0.180228	+	0.0554355i
$652$	5.35018			0.209529
$653$	−15.9426	−	27.6134i	−0.623882	−	1.08060i	−0.988756	−	0.149539i	$-0.952221\pi$
$653$	−15.9426	−	27.6134i	−0.623882	−	1.08060i	0.364874	−	0.931057i	$-0.381112\pi$
$654$	14.3649	−	24.8808i	0.561714	−	0.972917i
$655$	1.65348	−	2.86391i	0.0646067	−	0.111902i
$656$	4.64558	+	8.04637i	0.181379	+	0.314158i
$657$	5.66125			0.220867
$658$	−11.0110	−	10.2330i	−0.429252	−	0.398925i
$659$	9.23787			0.359856			0.179928	−	0.983680i	$-0.442413\pi$
$659$	9.23787			0.359856			0.179928	+	0.983680i	$0.442413\pi$
$660$	−1.08142	−	1.87308i	−0.0420943	−	0.0729095i
$661$	2.33862	−	4.05061i	0.0909618	−	0.157551i	−0.816954	−	0.576702i	$-0.804339\pi$
$661$	2.33862	−	4.05061i	0.0909618	−	0.157551i	0.907916	+	0.419152i	$0.137673\pi$
$662$	11.5905	−	20.0753i	0.450477	−	0.780248i
$663$	−11.5670	−	20.0346i	−0.449224	−	0.778078i
$664$	−8.85733			−0.343731
$665$	−5.50548	−	5.11652i	−0.213493	−	0.198410i
$666$	14.7167			0.570261
$667$	−18.0988	−	31.3480i	−0.700788	−	1.21380i
$668$	5.36820	−	9.29799i	0.207702	−	0.359750i
$669$	5.75137	−	9.96166i	0.222361	−	0.385140i
$670$	−2.66285	−	4.61219i	−0.102875	−	0.178184i
$671$	11.3999			0.440090
$672$	5.46947	−	1.68233i	0.210989	−	0.0648973i
$673$	−1.92229			−0.0740987			−0.0370494	−	0.999313i	$-0.511796\pi$
$673$	−1.92229			−0.0740987			−0.0370494	+	0.999313i	$0.511796\pi$
$674$	9.49501	+	16.4458i	0.365734	+	0.633470i
$675$	1.42974	−	2.47639i	0.0550309	−	0.0953163i
$676$	1.38586	−	2.40038i	0.0533022	−	0.0923221i
$677$	19.5693	+	33.8950i	0.752110	+	1.30269i	0.946798	+	0.321827i	$0.104297\pi$
$677$	19.5693	+	33.8950i	0.752110	+	1.30269i	−0.194689	+	0.980865i	$0.562370\pi$
$678$	5.22523			0.200674
$679$	4.78389	−	20.8828i	0.183589	−	0.801408i
$680$	3.34443			0.128253
$681$	12.9926	+	22.5039i	0.497879	+	0.862352i
$682$	0.420375	−	0.728112i	0.0160970	−	0.0278808i
$683$	−6.42056	+	11.1207i	−0.245676	+	0.425523i	−0.962321	−	0.271915i	$-0.912343\pi$
$683$	−6.42056	+	11.1207i	−0.245676	+	0.425523i	0.716646	+	0.697437i	$0.245677\pi$
$684$	−2.38325	−	4.12792i	−0.0911260	−	0.157835i
$685$	−5.90979			−0.225801
$686$	−18.3067	−	2.80412i	−0.698955	−	0.107062i
$687$	−23.6451			−0.902117
$688$	−4.61025	−	7.98519i	−0.175764	−	0.304433i
$689$	−14.2319	+	24.6503i	−0.542192	+	0.939103i
$690$	5.64558	−	9.77842i	0.214923	−	0.372258i
$691$	15.1192	+	26.1872i	0.575161	+	0.996208i	0.996024	+	0.0890837i	$0.0283938\pi$
$691$	15.1192	+	26.1872i	0.575161	+	0.996208i	−0.420863	+	0.907124i	$0.638273\pi$
$692$	−12.6693			−0.481614
$693$	−0.991294	+	4.32723i	−0.0376561	+	0.164378i
$694$	3.04174			0.115463
$695$	−0.879964	−	1.52414i	−0.0333789	−	0.0578140i
$696$	7.49830	−	12.9874i	0.284222	−	0.492287i
$697$	15.5368	−	26.9105i	0.588499	−	1.01931i
$698$	−15.9897	−	27.6950i	−0.605220	−	1.04827i
$699$	−9.65971			−0.365364
$700$	2.52883	−	0.777832i	0.0955808	−	0.0293993i
$701$	14.6216			0.552252			0.276126	−	0.961121i	$-0.410949\pi$
$701$	14.6216			0.552252			0.276126	+	0.961121i	$0.410949\pi$
$702$	4.57257	+	7.91992i	0.172580	+	0.298918i
$703$	−12.4580	+	21.5778i	−0.469860	+	0.813822i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	−6.14411	−	10.6419i	−0.231400	−	0.400797i
$706$	33.3158			1.25386
$707$	14.9656	+	13.9083i	0.562839	+	0.523074i
$708$	16.3540			0.614622
$709$	9.71904	+	16.8339i	0.365006	+	0.632209i	0.988777	−	0.149398i	$-0.0477336\pi$
$709$	9.71904	+	16.8339i	0.365006	+	0.632209i	−0.623771	+	0.781607i	$0.714400\pi$
$710$	2.80013	−	4.84997i	0.105087	−	0.182016i
$711$	6.04496	−	10.4702i	0.226704	−	0.392662i
$712$	2.69925	+	4.67523i	0.101159	+	0.175212i
$713$	4.38914			0.164375
$714$	−14.0188	−	13.0283i	−0.524639	−	0.487574i
$715$	3.19817			0.119605
$716$	5.76553	+	9.98619i	0.215468	+	0.373201i
$717$	3.69386	−	6.39795i	0.137950	−	0.238936i
$718$	−12.2071	+	21.1434i	−0.455566	+	0.789063i
$719$	6.53292	+	11.3154i	0.243637	+	0.421992i	0.961748	−	0.273937i	$-0.0883261\pi$
$719$	6.53292	+	11.3154i	0.243637	+	0.421992i	−0.718111	+	0.695929i	$0.754993\pi$
$720$	1.67790			0.0625318
$721$	−15.7120	+	4.83278i	−0.585145	+	0.179982i
$722$	−10.9301			−0.406778
$723$	−6.64133	−	11.5031i	−0.246994	−	0.427806i
$724$	10.1305	−	17.5466i	0.376498	−	0.652113i
$725$	3.46687	−	6.00479i	0.128756	−	0.223012i
$726$	−1.08142	−	1.87308i	−0.0401354	−	0.0695165i
$727$	12.6829			0.470382			0.235191	−	0.971949i	$-0.424428\pi$
$727$	12.6829			0.470382			0.235191	+	0.971949i	$0.424428\pi$
$728$	−1.88945	+	8.24791i	−0.0700278	+	0.305688i
$729$	−0.269409			−0.00997811
$730$	−1.68700	−	2.92197i	−0.0624387	−	0.108147i
$731$	−15.4187	+	26.7059i	−0.570280	+	0.987754i
$732$	−12.3282	+	21.3530i	−0.455662	+	0.789229i
$733$	10.7310	+	18.5866i	0.396358	+	0.686512i	0.993273	−	0.115792i	$-0.0369406\pi$
$733$	10.7310	+	18.5866i	0.396358	+	0.686512i	−0.596915	+	0.802304i	$0.703607\pi$
$734$	−1.78364			−0.0658353
$735$	−13.6301	−	6.59072i	−0.502754	−	0.243102i
$736$	−5.22051			−0.192430
$737$	−2.66285	−	4.61219i	−0.0980872	−	0.169892i
$738$	7.79483	−	13.5010i	0.286932	−	0.496980i
$739$	−8.92187	+	15.4531i	−0.328196	+	0.568452i	−0.982154	−	0.188079i	$-0.939774\pi$
$739$	−8.92187	+	15.4531i	−0.328196	+	0.568452i	0.653958	+	0.756531i	$0.273107\pi$
$740$	−4.38544	−	7.59581i	−0.161212	−	0.279228i
$741$	19.6499			0.721857
$742$	−5.25807	+	22.9527i	−0.193030	+	0.842619i
$743$	25.4763			0.934636			0.467318	−	0.884089i	$-0.345220\pi$
$743$	25.4763			0.934636			0.467318	+	0.884089i	$0.345220\pi$
$744$	0.909207	+	1.57479i	0.0333332	+	0.0577347i
$745$	3.54000	−	6.13146i	0.129695	−	0.224639i
$746$	14.1526	−	24.5131i	0.518165	−	0.897488i
$747$	7.43088	+	12.8707i	0.271882	+	0.470913i
$748$	3.34443			0.122285
$749$	−40.3160	+	12.4006i	−1.47311	+	0.453108i
$750$	2.16285			0.0789760
$751$	16.4287	+	28.4554i	0.599493	+	1.03835i	0.992896	+	0.118986i	$0.0379645\pi$
$751$	16.4287	+	28.4554i	0.599493	+	1.03835i	−0.393403	+	0.919366i	$0.628702\pi$
$752$	−2.84075	+	4.92032i	−0.103592	+	0.179426i
$753$	15.4640	−	26.7845i	0.563541	−	0.976082i
$754$	11.0876	+	19.2043i	0.403787	+	0.699380i
$755$	19.6723			0.715950
$756$	5.54180	+	5.15027i	0.201553	+	0.187313i
$757$	22.9936			0.835717			0.417859	−	0.908512i	$-0.362781\pi$
$757$	22.9936			0.835717			0.417859	+	0.908512i	$0.362781\pi$
$758$	9.57472	+	16.5839i	0.347770	+	0.602354i
$759$	5.64558	−	9.77842i	0.204921	−	0.354934i
$760$	−1.42038	+	2.46016i	−0.0515224	+	0.0892395i
$761$	−15.3257	−	26.5449i	−0.555556	−	0.962251i	−0.997860	−	0.0653860i	$-0.979172\pi$
$761$	−15.3257	−	26.5449i	−0.555556	−	0.962251i	0.442304	−	0.896865i	$-0.354161\pi$
$762$	46.6888			1.69136
$763$	25.7437	+	23.9249i	0.931983	+	0.866139i
$764$	14.3853			0.520443
$765$	−2.80582	−	4.85982i	−0.101445	−	0.175707i
$766$	11.0822	−	19.1949i	0.400416	−	0.693542i
$767$	−12.0912	+	20.9426i	−0.436589	+	0.756194i
$768$	−1.08142	−	1.87308i	−0.0390225	−	0.0675889i
$769$	7.36622			0.265633			0.132816	−	0.991141i	$-0.457598\pi$
$769$	7.36622			0.265633			0.132816	+	0.991141i	$0.457598\pi$
$770$	2.52883	−	0.777832i	0.0911327	−	0.0280311i
$771$	19.5358			0.703566
$772$	−6.16324	−	10.6750i	−0.221820	−	0.384203i
$773$	3.98856	−	6.90839i	0.143459	−	0.248477i	−0.785338	−	0.619067i	$-0.787511\pi$
$773$	3.98856	−	6.90839i	0.143459	−	0.248477i	0.928797	+	0.370589i	$0.120844\pi$
$774$	−7.73556	+	13.3984i	−0.278049	+	0.481595i
$775$	0.420375	+	0.728112i	0.0151003	+	0.0261545i
$776$	−8.09741			−0.290680
$777$	−11.2074	+	48.9228i	−0.402063	+	1.75510i
$778$	−8.51331			−0.305217
$779$	13.1969	+	22.8577i	0.472829	+	0.818963i
$780$	−3.45857	+	5.99043i	−0.123837	+	0.214492i
$781$	2.80013	−	4.84997i	0.100197	−	0.173545i
$782$	8.72981	+	15.1205i	0.312177	+	0.540707i
$783$	19.8269			0.708557
$784$	0.511973	+	6.98125i	0.0182847	+	0.249330i
$785$	−1.44027			−0.0514054
$786$	3.57622	+	6.19419i	0.127559	+	0.220939i
$787$	−9.49568	+	16.4470i	−0.338484	+	0.586272i	−0.984148	−	0.177350i	$-0.943248\pi$
$787$	−9.49568	+	16.4470i	−0.338484	+	0.586272i	0.645664	+	0.763622i	$0.276581\pi$
$788$	−12.4788	+	21.6138i	−0.444537	+	0.769961i
$789$	−25.2498	−	43.7339i	−0.898915	−	1.55697i
$790$	−7.20536			−0.256355
$791$	−1.42730	+	6.23049i	−0.0507489	+	0.221531i
$792$	1.67790			0.0596217
$793$	−18.2295	−	31.5744i	−0.647347	−	1.12124i
$794$	−14.9724	+	25.9329i	−0.531349	+	0.920324i
$795$	−9.62469	+	16.6704i	−0.341352	+	0.591240i
$796$	1.27418	+	2.20694i	0.0451620	+	0.0782229i
$797$	31.6897			1.12251			0.561253	−	0.827644i	$-0.310320\pi$
$797$	31.6897			1.12251			0.561253	+	0.827644i	$0.310320\pi$
$798$	15.5374	−	4.77908i	0.550018	−	0.169178i
$799$	19.0014			0.672221
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	4.52908	−	7.84459i	0.160027	−	0.277175i
$802$	−0.464775	+	0.805013i	−0.0164118	+	0.0284260i
$803$	−1.68700	−	2.92197i	−0.0595330	−	0.103114i
$804$	11.5187			0.406232
$805$	10.1175	+	9.40273i	0.356596	+	0.331403i
$806$	−2.68886			−0.0947112
$807$	16.9726	+	29.3974i	0.597464	+	1.03484i
$808$	3.86102	−	6.68747i	0.135830	−	0.235265i
$809$	9.58229	−	16.5970i	0.336895	−	0.583520i	−0.646952	−	0.762531i	$-0.723956\pi$
$809$	9.58229	−	16.5970i	0.336895	−	0.583520i	0.983847	+	0.179011i	$0.0572898\pi$
$810$	5.60918	+	9.71538i	0.197086	+	0.341364i
$811$	19.3516			0.679527			0.339764	−	0.940511i	$-0.389653\pi$
$811$	19.3516			0.679527			0.339764	+	0.940511i	$0.389653\pi$
$812$	13.4378	+	12.4884i	0.471575	+	0.438259i
$813$	−50.3898			−1.76725
$814$	−4.38544	−	7.59581i	−0.153710	−	0.266233i
$815$	−2.67509	+	4.63340i	−0.0937044	+	0.162301i
$816$	−3.61675	+	6.26439i	−0.126611	+	0.219297i
$817$	−13.0966	−	22.6839i	−0.458191	−	0.793611i
$818$	−29.0277			−1.01493
$819$	13.5703	−	4.17402i	0.474183	−	0.145852i
$820$	−9.29115			−0.324461
$821$	24.4570	+	42.3608i	0.853556	+	1.47840i	0.877978	+	0.478701i	$0.158892\pi$
$821$	24.4570	+	42.3608i	0.853556	+	1.47840i	−0.0244215	+	0.999702i	$0.507774\pi$
$822$	6.39098	−	11.0695i	0.222911	−	0.386093i
$823$	6.01958	−	10.4262i	0.209829	−	0.363435i	−0.741831	−	0.670587i	$-0.766043\pi$
$823$	6.01958	−	10.4262i	0.209829	−	0.363435i	0.951661	+	0.307152i	$0.0993758\pi$
$824$	3.10657	+	5.38074i	0.108223	+	0.187447i
$825$	2.16285			0.0753006
$826$	−4.46718	+	19.5003i	−0.155433	+	0.678502i
$827$	3.84600			0.133738			0.0668692	−	0.997762i	$-0.478699\pi$
$827$	3.84600			0.133738			0.0668692	+	0.997762i	$0.478699\pi$
$828$	4.37975	+	7.58596i	0.152207	+	0.263630i
$829$	23.5426	−	40.7770i	0.817668	−	1.41624i	−0.0897277	−	0.995966i	$-0.528600\pi$
$829$	23.5426	−	40.7770i	0.817668	−	1.41624i	0.907396	−	0.420277i	$-0.138067\pi$
$830$	4.42867	−	7.67068i	0.153721	−	0.266253i
$831$	−21.0855	−	36.5211i	−0.731447	−	1.26690i
$832$	3.19817			0.110877
$833$	19.3641	−	13.1570i	0.670927	−	0.455864i
$834$	3.80645			0.131807
$835$	5.36820	+	9.29799i	0.185774	+	0.321770i
$836$	−1.42038	+	2.46016i	−0.0491247	+	0.0850865i
$837$	−1.20206	+	2.08203i	−0.0415492	+	0.0719654i
$838$	3.48411	+	6.03466i	0.120357	+	0.208464i
$839$	−48.7872			−1.68432			−0.842161	−	0.539226i	$-0.818717\pi$
$839$	−48.7872			−1.68432			−0.842161	+	0.539226i	$0.818717\pi$
$840$	−1.27779	+	5.57786i	−0.0440881	+	0.192455i
$841$	19.0766			0.657815
$842$	−17.9822	−	31.1461i	−0.619708	−	1.07337i
$843$	2.39982	−	4.15661i	0.0826542	−	0.143161i
$844$	−13.5134	+	23.4058i	−0.465149	+	0.805662i
$845$	1.38586	+	2.40038i	0.0476749	+	0.0825754i
$846$	9.53302			0.327752
$847$	2.52883	−	0.777832i	0.0868916	−	0.0267266i
$848$	8.90002			0.305628
$849$	−6.94176	−	12.0235i	−0.238240	−	0.412645i
$850$	−1.67222	+	2.89636i	−0.0573565	+	0.0993444i
$851$	22.8942	−	39.6540i	0.784804	−	1.35932i
$852$	6.05625	+	10.4897i	0.207484	+	0.359372i
$853$	−30.3160			−1.03800			−0.519000	−	0.854774i	$-0.673696\pi$
$853$	−30.3160			−1.03800			−0.519000	+	0.854774i	$0.673696\pi$
$854$	−22.0935	−	20.5326i	−0.756024	−	0.702611i
$855$	4.76651			0.163011
$856$	7.97127	+	13.8066i	0.272452	+	0.471901i
$857$	13.8953	−	24.0673i	0.474653	−	0.822124i	−0.524925	−	0.851148i	$-0.675907\pi$
$857$	13.8953	−	24.0673i	0.474653	−	0.822124i	0.999579	+	0.0290247i	$0.00924014\pi$
$858$	−3.45857	+	5.99043i	−0.118074	+	0.204510i
$859$	3.59549	+	6.22757i	0.122676	+	0.212482i	0.920822	−	0.389982i	$-0.127519\pi$
$859$	3.59549	+	6.22757i	0.122676	+	0.212482i	−0.798146	+	0.602464i	$0.794186\pi$
$860$	9.22051			0.314417
$861$	38.9455	+	36.1940i	1.32726	+	1.23349i
$862$	20.2574			0.689970
$863$	22.0695	+	38.2254i	0.751253	+	1.30121i	0.947216	+	0.320597i	$0.103884\pi$
$863$	22.0695	+	38.2254i	0.751253	+	1.30121i	−0.195963	+	0.980611i	$0.562783\pi$
$864$	1.42974	−	2.47639i	0.0486409	−	0.0842485i
$865$	6.33465	−	10.9719i	0.215384	−	0.373057i
$866$	−12.4301	−	21.5295i	−0.422390	−	0.731602i
$867$	−12.5765			−0.427119
$868$	−2.12612	+	0.653963i	−0.0721651	+	0.0221969i
$869$	−7.20536			−0.244425
$870$	7.49830	+	12.9874i	0.254216	+	0.440315i
$871$	−8.51623	+	14.7505i	−0.288562	+	0.499803i
$872$	6.64169	−	11.5037i	0.224916	−	0.389566i
$873$	6.79334	+	11.7664i	0.229920	+	0.398233i
$874$	−14.8302			−0.501637
$875$	−0.590793	+	2.57895i	−0.0199724	+	0.0871843i
$876$	7.29745			0.246558
$877$	6.80743	+	11.7908i	0.229871	+	0.398148i	0.957770	−	0.287537i	$-0.0928364\pi$
$877$	6.80743	+	11.7908i	0.229871	+	0.398148i	−0.727899	+	0.685684i	$0.759503\pi$
$878$	15.3195	−	26.5342i	0.517008	−	0.895485i
$879$	25.7781	−	44.6489i	0.869473	−	1.50597i
$880$	−0.500000	−	0.866025i	−0.0168550	−	0.0291937i
$881$	8.44309			0.284455			0.142227	−	0.989834i	$-0.454574\pi$
$881$	8.44309			0.284455			0.142227	+	0.989834i	$0.454574\pi$
$882$	9.71499	−	6.60089i	0.327121	−	0.222263i
$883$	−13.8197			−0.465070			−0.232535	−	0.972588i	$-0.574702\pi$
$883$	−13.8197			−0.465070			−0.232535	+	0.972588i	$0.574702\pi$
$884$	−5.34803	−	9.26306i	−0.179874	−	0.311550i
$885$	−8.17701	+	14.1630i	−0.274867	+	0.476084i
$886$	−6.48417	+	11.2309i	−0.217840	+	0.377310i
$887$	9.79066	+	16.9579i	0.328738	+	0.569391i	0.982262	−	0.187515i	$-0.0600433\pi$
$887$	9.79066	+	16.9579i	0.328738	+	0.569391i	−0.653523	+	0.756906i	$0.726710\pi$
$888$	18.9701			0.636594
$889$	−12.7533	+	55.6710i	−0.427731	+	1.86715i
$890$	−5.39849			−0.180958
$891$	5.60918	+	9.71538i	0.187914	+	0.325477i
$892$	2.65917	−	4.60581i	0.0890354	−	0.154214i
$893$	−8.06987	+	13.9774i	−0.270048	+	0.467736i
$894$	7.65647	+	13.2614i	0.256071	+	0.443527i
$895$	−11.5311			−0.385441
$896$	2.52883	−	0.777832i	0.0844823	−	0.0259855i
$897$	−36.1110			−1.20571
$898$	12.5990	+	21.8221i	0.420434	+	0.728213i
$899$	−2.91477	+	5.04853i	−0.0972130	+	0.168378i
$900$	−0.838952	+	1.45311i	−0.0279651	+	0.0484369i
$901$	−14.8828	−	25.7777i	−0.495816	−	0.858779i
$902$	−9.29115			−0.309361
$903$	−38.6494	−	35.9188i	−1.28617	−	1.19530i
$904$	2.41591			0.0803518
$905$	10.1305	+	17.5466i	0.336750	+	0.583268i
$906$	−21.2741	+	36.8479i	−0.706786	+	1.22419i
$907$	−24.0300	+	41.6213i	−0.797904	+	1.38201i	0.123074	+	0.992397i	$0.460725\pi$
$907$	−24.0300	+	41.6213i	−0.797904	+	1.38201i	−0.920978	+	0.389614i	$0.872609\pi$
$908$	6.00719	+	10.4048i	0.199356	+	0.345294i
$909$	−12.9568			−0.429751
$910$	−6.19817	−	5.76027i	−0.205467	−	0.190951i
$911$	13.2510			0.439026			0.219513	−	0.975610i	$-0.429553\pi$
$911$	13.2510			0.439026			0.219513	+	0.975610i	$0.429553\pi$
$912$	−3.07205	−	5.32095i	−0.101726	−	0.176194i
$913$	4.42867	−	7.67068i	0.146567	−	0.253862i
$914$	1.77420	−	3.07300i	0.0586852	−	0.101646i
$915$	−12.3282	−	21.3530i	−0.407556	−	0.705908i
$916$	−10.9324			−0.361217
$917$	−8.36272	+	2.57225i	−0.276161	+	0.0849433i
$918$	−9.56337			−0.315638
$919$	−25.8126	−	44.7087i	−0.851478	−	1.47480i	−0.879874	−	0.475207i	$-0.842373\pi$
$919$	−25.8126	−	44.7087i	−0.851478	−	1.47480i	0.0283959	−	0.999597i	$-0.490960\pi$
$920$	2.61025	−	4.52109i	0.0860575	−	0.149056i
$921$	19.5951	−	33.9397i	0.645681	−	1.11835i
$922$	−10.6718	−	18.4841i	−0.351456	−	0.608740i
$923$	−17.9106			−0.589534
$924$	−1.27779	+	5.57786i	−0.0420363	+	0.183498i
$925$	8.77089			0.288385
$926$	19.4951	+	33.7666i	0.640650	+	1.10964i
$927$	5.21253	−	9.02837i	0.171202	−	0.296530i
$928$	3.46687	−	6.00479i	0.113805	−	0.197117i
$929$	0.807700	+	1.39898i	0.0264998	+	0.0458990i	0.878971	−	0.476875i	$-0.158231\pi$
$929$	0.807700	+	1.39898i	0.0264998	+	0.0458990i	−0.852471	+	0.522774i	$0.824897\pi$
$930$	−1.81841			−0.0596282
$931$	1.45439	+	19.8320i	0.0476656	+	0.649967i
$932$	−4.46620			−0.146295
$933$	−31.2741	−	54.1683i	−1.02387	−	1.77339i
$934$	−8.23494	+	14.2633i	−0.269455	+	0.466711i
$935$	−1.67222	+	2.89636i	−0.0546873	+	0.0947212i
$936$	−2.68311	−	4.64728i	−0.0877002	−	0.151901i
$937$	−29.5490			−0.965323			−0.482661	−	0.875807i	$-0.660330\pi$
$937$	−29.5490			−0.965323			−0.482661	+	0.875807i	$0.660330\pi$
$938$	−3.14638	+	13.7347i	−0.102733	+	0.448453i
$939$	−35.1623			−1.14748
$940$	−2.84075	−	4.92032i	−0.0926551	−	0.160483i
$941$	−1.86552	+	3.23118i	−0.0608142	+	0.105333i	−0.894830	−	0.446408i	$-0.852703\pi$
$941$	−1.86552	+	3.23118i	−0.0608142	+	0.105333i	0.834015	+	0.551741i	$0.186036\pi$
$942$	1.55754	−	2.69774i	0.0507474	−	0.0878971i
$943$	−24.2522	−	42.0061i	−0.789762	−	1.36791i
$944$	7.56134			0.246101
$945$	−7.23116	+	2.22420i	−0.235230	+	0.0723533i
$946$	9.22051			0.299784
$947$	−13.9753	−	24.2059i	−0.454135	−	0.786585i	0.544503	−	0.838759i	$-0.316718\pi$
$947$	−13.9753	−	24.2059i	−0.454135	−	0.786585i	−0.998638	+	0.0521742i	$0.983385\pi$
$948$	7.79205	−	13.4962i	0.253074	−	0.438337i
$949$	−5.39531	+	9.34496i	−0.175139	+	0.303350i
$950$	−1.42038	−	2.46016i	−0.0460831	−	0.0798182i
$951$	−46.7336			−1.51544
$952$	−6.48163	−	6.02370i	−0.210071	−	0.195229i
$953$	45.5196			1.47452			0.737262	−	0.675607i	$-0.236118\pi$
$953$	45.5196			1.47452			0.737262	+	0.675607i	$0.236118\pi$
$954$	−7.46669	−	12.9327i	−0.241743	−	0.418711i
$955$	−7.19267	+	12.4581i	−0.232749	+	0.403134i
$956$	1.70787	−	2.95812i	0.0552364	−	0.0956723i
$957$	7.49830	+	12.9874i	0.242386	+	0.419824i
$958$	26.1908			0.846187
$959$	11.4534	+	10.6442i	0.369849	+	0.343719i
$960$	2.16285			0.0698056
$961$	15.1466	+	26.2346i	0.488599	+	0.846278i
$962$	−14.0254	+	24.2927i	−0.452197	+	0.783228i
$963$	13.3750	−	23.1662i	0.431004	−	0.746521i
$964$	−3.07065	−	5.31851i	−0.0988988	−	0.171298i
$965$	12.3265			0.396803
$966$	−28.5534	+	8.78262i	−0.918690	+	0.282576i
$967$	23.0124			0.740028			0.370014	−	0.929026i	$-0.379353\pi$
$967$	23.0124			0.740028			0.370014	+	0.929026i	$0.379353\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$	−10.2743	+	17.7956i	−0.330057	+	0.571676i
$970$	4.04870	−	7.01256i	0.129996	−	0.225160i
$971$	5.36782	+	9.29733i	0.172261	+	0.298365i	0.939210	−	0.343343i	$-0.111559\pi$
$971$	5.36782	+	9.29733i	0.172261	+	0.298365i	−0.766949	+	0.641708i	$0.778226\pi$
$972$	−15.6851			−0.503100
$973$	−1.03975	+	4.53876i	−0.0333329	+	0.145506i
$974$	22.0104			0.705259
$975$	−3.45857	−	5.99043i	−0.110763	−	0.191847i
$976$	−5.69997	+	9.87263i	−0.182452	+	0.316015i
$977$	28.6494	−	49.6221i	0.916574	−	1.58755i	0.111994	−	0.993709i	$-0.464276\pi$
$977$	28.6494	−	49.6221i	0.916574	−	1.58755i	0.804580	−	0.593844i	$-0.202390\pi$
$978$	−5.78581	−	10.0213i	−0.185010	−	0.320447i
$979$	−5.39849			−0.172537
$980$	−6.30193	−	3.04724i	−0.201308	−	0.0973407i
$981$	−22.2882			−0.711608
$982$	−6.87729	−	11.9118i	−0.219463	−	0.380121i
$983$	−14.5554	+	25.2106i	−0.464244	+	0.804094i	−0.999167	−	0.0408066i	$-0.987007\pi$
$983$	−14.5554	+	25.2106i	−0.464244	+	0.804094i	0.534923	+	0.844901i	$0.320341\pi$
$984$	10.0477	−	17.4031i	0.320308	−	0.554790i
$985$	−12.4788	−	21.6138i	−0.397606	−	0.688674i
$986$	−23.1894			−0.738501
$987$	−7.25979	+	31.6906i	−0.231082	+	1.00872i
$988$	9.08520			0.289039
$989$	24.0678	+	41.6867i	0.765313	+	1.32556i
$990$	−0.838952	+	1.45311i	−0.0266637	+	0.0461828i
$991$	−13.3080	+	23.0501i	−0.422742	+	0.732211i	−0.996207	−	0.0870196i	$-0.972266\pi$
$991$	−13.3080	+	23.0501i	−0.422742	+	0.732211i	0.573464	+	0.819230i	$0.305599\pi$
$992$	0.420375	+	0.728112i	0.0133469	+	0.0231176i
$993$	−50.1368			−1.59104
$994$	−14.1621	+	4.35606i	−0.449195	+	0.138166i
$995$	−2.54835			−0.0807882
$996$	9.57853	+	16.5905i	0.303507	+	0.525690i
$997$	17.8424	−	30.9039i	0.565073	−	0.978736i	−0.431970	−	0.901888i	$-0.642181\pi$
$997$	17.8424	−	30.9039i	0.565073	−	0.978736i	0.997043	−	0.0768474i	$-0.0244854\pi$
$998$	−14.3179	+	24.7994i	−0.453226	+	0.785010i
$999$	12.5401	+	21.7201i	0.396752	+	0.687195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.i.m.221.2	✓	10
7.2	even	3	inner	770.2.i.m.331.2	yes	10
7.3	odd	6		5390.2.a.ch.1.2		5
7.4	even	3		5390.2.a.ci.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.i.m.221.2	✓	10	1.1	even	1	trivial
770.2.i.m.331.2	yes	10	7.2	even	3	inner
5390.2.a.ch.1.2		5	7.3	odd	6
5390.2.a.ci.1.4		5	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.08142 + 1.87308i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.16285 q^{6} +(-0.590793 + 2.57895i) q^{7} +1.00000 q^{8} +(-0.838952 - 1.45311i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.08142 + 1.87308i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.16285 q^{6} +(-0.590793 + 2.57895i) q^{7} +1.00000 q^{8} +(-0.838952 - 1.45311i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.08142 - 1.87308i) q^{12} +3.19817 q^{13} +(2.52883 - 0.777832i) q^{14} +2.16285 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.67222 + 2.89636i) q^{17} +(-0.838952 + 1.45311i) q^{18} +(-1.42038 - 2.46016i) q^{19} +1.00000 q^{20} +(-4.19168 - 3.89553i) q^{21} +1.00000 q^{22} +(2.61025 + 4.52109i) q^{23} +(-1.08142 + 1.87308i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.59908 - 2.76970i) q^{26} -2.85949 q^{27} +(-1.93804 - 1.80111i) q^{28} -6.93373 q^{29} +(-1.08142 - 1.87308i) q^{30} +(0.420375 - 0.728112i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.08142 - 1.87308i) q^{33} +3.34443 q^{34} +(2.52883 - 0.777832i) q^{35} +1.67790 q^{36} +(-4.38544 - 7.59581i) q^{37} +(-1.42038 + 2.46016i) q^{38} +(-3.45857 + 5.99043i) q^{39} +(-0.500000 - 0.866025i) q^{40} -9.29115 q^{41} +(-1.27779 + 5.57786i) q^{42} +9.22051 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-0.838952 + 1.45311i) q^{45} +(2.61025 - 4.52109i) q^{46} +(-2.84075 - 4.92032i) q^{47} +2.16285 q^{48} +(-6.30193 - 3.04724i) q^{49} +1.00000 q^{50} +(-3.61675 - 6.26439i) q^{51} +(-1.59908 + 2.76970i) q^{52} +(-4.45001 + 7.70764i) q^{53} +(1.42974 + 2.47639i) q^{54} +1.00000 q^{55} +(-0.590793 + 2.57895i) q^{56} +6.14411 q^{57} +(3.46687 + 6.00479i) q^{58} +(-3.78067 + 6.54831i) q^{59} +(-1.08142 + 1.87308i) q^{60} +(-5.69997 - 9.87263i) q^{61} -0.840751 q^{62} +(4.24313 - 1.30513i) q^{63} +1.00000 q^{64} +(-1.59908 - 2.76970i) q^{65} +(-1.08142 + 1.87308i) q^{66} +(-2.66285 + 4.61219i) q^{67} +(-1.67222 - 2.89636i) q^{68} -11.2912 q^{69} +(-1.93804 - 1.80111i) q^{70} -5.60026 q^{71} +(-0.838952 - 1.45311i) q^{72} +(-1.68700 + 2.92197i) q^{73} +(-4.38544 + 7.59581i) q^{74} +(-1.08142 - 1.87308i) q^{75} +2.84075 q^{76} +(-1.93804 - 1.80111i) q^{77} +6.91715 q^{78} +(3.60268 + 6.24003i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.60918 - 9.71538i) q^{81} +(4.64558 + 8.04637i) q^{82} -8.85733 q^{83} +(5.46947 - 1.68233i) q^{84} +3.34443 q^{85} +(-4.61025 - 7.98519i) q^{86} +(7.49830 - 12.9874i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(2.69925 + 4.67523i) q^{89} +1.67790 q^{90} +(-1.88945 + 8.24791i) q^{91} -5.22051 q^{92} +(0.909207 + 1.57479i) q^{93} +(-2.84075 + 4.92032i) q^{94} +(-1.42038 + 2.46016i) q^{95} +(-1.08142 - 1.87308i) q^{96} -8.09741 q^{97} +(0.511973 + 6.98125i) q^{98} +1.67790 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9	\( 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9} - 5 q^{10} - 5 q^{11} - 2 q^{13} + 3 q^{14} - 5 q^{16} - 9 q^{18} - 4 q^{19} + 10 q^{20} + 2 q^{21} + 10 q^{22} - 7 q^{23} - 5 q^{25} + q^{26} - 18 q^{27} - 3 q^{28} + 8 q^{29} - 6 q^{31} - 5 q^{32} + 3 q^{35} + 18 q^{36} - 16 q^{37} - 4 q^{38} - 7 q^{39} - 5 q^{40} - 2 q^{41} + 11 q^{42} + 26 q^{43} - 5 q^{44} - 9 q^{45} - 7 q^{46} - 8 q^{47} + 14 q^{49} + 10 q^{50} - 13 q^{51} + q^{52} - 4 q^{53} + 9 q^{54} + 10 q^{55} + 30 q^{57} - 4 q^{58} - 9 q^{59} - 2 q^{61} + 12 q^{62} + 25 q^{63} + 10 q^{64} + q^{65} - 5 q^{67} - 22 q^{69} - 3 q^{70} + 56 q^{71} - 9 q^{72} + q^{73} - 16 q^{74} + 8 q^{76} - 3 q^{77} + 14 q^{78} - 23 q^{79} - 5 q^{80} + 7 q^{81} + q^{82} - 46 q^{83} - 13 q^{84} - 13 q^{86} - 15 q^{87} - 5 q^{88} + 9 q^{89} + 18 q^{90} + 29 q^{91} + 14 q^{92} + 15 q^{93} - 8 q^{94} - 4 q^{95} - 26 q^{97} - 19 q^{98} + 18 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9 - 5 * q^10 - 5 * q^11 - 2 * q^13 + 3 * q^14 - 5 * q^16 - 9 * q^18 - 4 * q^19 + 10 * q^20 + 2 * q^21 + 10 * q^22 - 7 * q^23 - 5 * q^25 + q^26 - 18 * q^27 - 3 * q^28 + 8 * q^29 - 6 * q^31 - 5 * q^32 + 3 * q^35 + 18 * q^36 - 16 * q^37 - 4 * q^38 - 7 * q^39 - 5 * q^40 - 2 * q^41 + 11 * q^42 + 26 * q^43 - 5 * q^44 - 9 * q^45 - 7 * q^46 - 8 * q^47 + 14 * q^49 + 10 * q^50 - 13 * q^51 + q^52 - 4 * q^53 + 9 * q^54 + 10 * q^55 + 30 * q^57 - 4 * q^58 - 9 * q^59 - 2 * q^61 + 12 * q^62 + 25 * q^63 + 10 * q^64 + q^65 - 5 * q^67 - 22 * q^69 - 3 * q^70 + 56 * q^71 - 9 * q^72 + q^73 - 16 * q^74 + 8 * q^76 - 3 * q^77 + 14 * q^78 - 23 * q^79 - 5 * q^80 + 7 * q^81 + q^82 - 46 * q^83 - 13 * q^84 - 13 * q^86 - 15 * q^87 - 5 * q^88 + 9 * q^89 + 18 * q^90 + 29 * q^91 + 14 * q^92 + 15 * q^93 - 8 * q^94 - 4 * q^95 - 26 * q^97 - 19 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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