LMFDB - Embedded newform 78.3.l.c.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,3,Mod(7,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("78.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	78.l (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.12534606201$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 82x^{5} + 5053x^{4} - 6736x^{3} + 6728x^{2} + 275384x + 5635876 $ x^8 - 2x^7 + 2x^6 + 82x^5 + 5053x^4 - 6736x^3 + 6728x^2 + 275384*x + 5635876
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.1
Root			$-5.39181 - 5.39181i$ of defining polynomial
Character	$\chi$	$=$	78.67
Dual form			78.3.l.c.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-6.39181 + 6.39181i) q^{5} +(0.633975 + 2.36603i) q^{6} +(9.23137 - 2.47354i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-6.39181 + 6.39181i) q^{5} +(0.633975 + 2.36603i) q^{6} +(9.23137 - 2.47354i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(-11.0709 + 6.39181i) q^{10} +(4.21503 - 15.7307i) q^{11} +3.46410i q^{12} +(-3.81310 - 12.4282i) q^{13} +13.5157 q^{14} +(-15.1232 - 4.05225i) q^{15} +(2.00000 + 3.46410i) q^{16} +(8.31934 + 4.80317i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(2.56168 + 9.56033i) q^{19} +(-17.4627 + 4.67913i) q^{20} +(11.7049 + 11.7049i) q^{21} +(11.5157 - 19.9457i) q^{22} +(-23.6929 + 13.6791i) q^{23} +(-1.26795 + 4.73205i) q^{24} -56.7105i q^{25} +(-0.659759 - 18.3729i) q^{26} -5.19615 q^{27} +(18.4627 + 4.94708i) q^{28} +(-13.8023 - 23.9063i) q^{29} +(-19.1754 - 11.0709i) q^{30} +(11.5613 - 11.5613i) q^{31} +(1.46410 + 5.46410i) q^{32} +(27.2464 - 7.30064i) q^{33} +(9.60634 + 9.60634i) q^{34} +(-43.1948 + 74.8156i) q^{35} +(-5.19615 + 3.00000i) q^{36} +(-5.45615 + 20.3626i) q^{37} +13.9973i q^{38} +(15.3401 - 16.4828i) q^{39} -25.5672 q^{40} +(39.1030 + 10.4776i) q^{41} +(11.7049 + 20.2735i) q^{42} +(-30.9095 - 17.8456i) q^{43} +(23.0313 - 23.0313i) q^{44} +(-7.01869 - 26.1941i) q^{45} +(-37.3721 + 10.0138i) q^{46} +(25.5184 + 25.5184i) q^{47} +(-3.46410 + 6.00000i) q^{48} +(36.6646 - 21.1683i) q^{49} +(20.7575 - 77.4679i) q^{50} +16.6387i q^{51} +(5.82371 - 25.3394i) q^{52} -39.0697 q^{53} +(-7.09808 - 1.90192i) q^{54} +(73.6060 + 127.489i) q^{55} +(23.4098 + 13.5157i) q^{56} +(-12.1220 + 12.1220i) q^{57} +(-10.1040 - 37.7086i) q^{58} +(-46.0300 + 12.3337i) q^{59} +(-22.1419 - 22.1419i) q^{60} +(-35.2717 + 61.0923i) q^{61} +(20.0248 - 11.5613i) q^{62} +(-7.42062 + 27.6941i) q^{63} +8.00000i q^{64} +(103.811 + 55.0661i) q^{65} +39.8915 q^{66} +(38.7250 + 10.3763i) q^{67} +(9.60634 + 16.6387i) q^{68} +(-41.0374 - 23.6929i) q^{69} +(-86.3896 + 86.3896i) q^{70} +(-8.28114 - 30.9056i) q^{71} +(-8.19615 + 2.19615i) q^{72} +(-9.68320 - 9.68320i) q^{73} +(-14.9065 + 25.8188i) q^{74} +(85.0657 - 49.1127i) q^{75} +(-5.12337 + 19.1207i) q^{76} -155.642i q^{77} +(26.9880 - 16.9011i) q^{78} -56.1543 q^{79} +(-34.9255 - 9.35826i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(49.5806 + 28.6254i) q^{82} +(4.59931 - 4.59931i) q^{83} +(8.56859 + 31.9784i) q^{84} +(-83.8766 + 22.4747i) q^{85} +(-35.6912 - 35.6912i) q^{86} +(23.9063 - 41.4069i) q^{87} +(39.8915 - 23.0313i) q^{88} +(29.9479 - 111.767i) q^{89} -38.3509i q^{90} +(-65.9418 - 105.298i) q^{91} -54.7165 q^{92} +(27.3544 + 7.32958i) q^{93} +(25.5184 + 44.1991i) q^{94} +(-77.4816 - 44.7340i) q^{95} +(-6.92820 + 6.92820i) q^{96} +(-9.04249 - 33.7470i) q^{97} +(57.8330 - 15.4963i) q^{98} +(34.5470 + 34.5470i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 6 q^{5} + 12 q^{6} + 10 q^{7} + 16 q^{8} - 12 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - 6 * q^5 + 12 * q^6 + 10 * q^7 + 16 * q^8 - 12 * q^9	$ 8 q + 4 q^{2} - 6 q^{5} + 12 q^{6} + 10 q^{7} + 16 q^{8} - 12 q^{9} - 6 q^{10} + 24 q^{11} + 4 q^{14} - 12 q^{15} + 16 q^{16} - 84 q^{17} - 24 q^{18} + 10 q^{19} - 12 q^{20} + 18 q^{21} - 12 q^{22} - 12 q^{23} - 24 q^{24} + 26 q^{26} + 20 q^{28} + 36 q^{29} - 18 q^{30} - 94 q^{31} - 16 q^{32} + 60 q^{34} - 204 q^{35} + 140 q^{37} + 66 q^{39} - 24 q^{40} + 72 q^{41} + 18 q^{42} - 222 q^{43} - 24 q^{44} - 84 q^{46} + 300 q^{47} + 42 q^{49} - 62 q^{50} + 44 q^{52} + 84 q^{53} - 36 q^{54} + 396 q^{55} + 36 q^{56} + 24 q^{57} - 66 q^{58} - 60 q^{59} - 12 q^{60} - 90 q^{61} + 198 q^{62} - 24 q^{63} - 108 q^{65} + 72 q^{66} + 304 q^{67} + 60 q^{68} - 216 q^{69} - 408 q^{70} - 192 q^{71} - 24 q^{72} + 16 q^{73} - 46 q^{74} + 312 q^{75} - 20 q^{76} + 114 q^{78} - 96 q^{79} - 24 q^{80} - 36 q^{81} + 114 q^{82} - 12 q^{84} - 390 q^{85} + 168 q^{86} + 30 q^{87} + 72 q^{88} + 354 q^{89} - 218 q^{91} - 288 q^{92} - 42 q^{93} + 300 q^{94} - 576 q^{95} - 460 q^{97} + 58 q^{98} - 36 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 6 * q^5 + 12 * q^6 + 10 * q^7 + 16 * q^8 - 12 * q^9 - 6 * q^10 + 24 * q^11 + 4 * q^14 - 12 * q^15 + 16 * q^16 - 84 * q^17 - 24 * q^18 + 10 * q^19 - 12 * q^20 + 18 * q^21 - 12 * q^22 - 12 * q^23 - 24 * q^24 + 26 * q^26 + 20 * q^28 + 36 * q^29 - 18 * q^30 - 94 * q^31 - 16 * q^32 + 60 * q^34 - 204 * q^35 + 140 * q^37 + 66 * q^39 - 24 * q^40 + 72 * q^41 + 18 * q^42 - 222 * q^43 - 24 * q^44 - 84 * q^46 + 300 * q^47 + 42 * q^49 - 62 * q^50 + 44 * q^52 + 84 * q^53 - 36 * q^54 + 396 * q^55 + 36 * q^56 + 24 * q^57 - 66 * q^58 - 60 * q^59 - 12 * q^60 - 90 * q^61 + 198 * q^62 - 24 * q^63 - 108 * q^65 + 72 * q^66 + 304 * q^67 + 60 * q^68 - 216 * q^69 - 408 * q^70 - 192 * q^71 - 24 * q^72 + 16 * q^73 - 46 * q^74 + 312 * q^75 - 20 * q^76 + 114 * q^78 - 96 * q^79 - 24 * q^80 - 36 * q^81 + 114 * q^82 - 12 * q^84 - 390 * q^85 + 168 * q^86 + 30 * q^87 + 72 * q^88 + 354 * q^89 - 218 * q^91 - 288 * q^92 - 42 * q^93 + 300 * q^94 - 576 * q^95 - 460 * q^97 + 58 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$	−6.39181	+	6.39181i	−1.27836	+	1.27836i	−0.336778	+	0.941584i	$0.609337\pi$
$5$	−6.39181	+	6.39181i	−1.27836	+	1.27836i	−0.941584	+	0.336778i	$0.890663\pi$
$6$	0.633975	+	2.36603i	0.105662	+	0.394338i
$7$	9.23137	−	2.47354i	1.31877	−	0.353363i	0.470252	−	0.882532i	$-0.344163\pi$
$7$	9.23137	−	2.47354i	1.31877	−	0.353363i	0.848516	+	0.529170i	$0.177496\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$	−11.0709	+	6.39181i	−1.10709	+	0.639181i
$11$	4.21503	−	15.7307i	0.383184	−	1.43006i	−0.457825	−	0.889042i	$-0.651371\pi$
$11$	4.21503	−	15.7307i	0.383184	−	1.43006i	0.841009	−	0.541021i	$-0.181962\pi$
$12$			3.46410i			0.288675i
$13$	−3.81310	−	12.4282i	−0.293316	−	0.956016i
$13$	−3.81310	−	12.4282i	−0.293316	−	0.956016i
$14$	13.5157			0.965405
$15$	−15.1232	−	4.05225i	−1.00821	−	0.270150i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	8.31934	+	4.80317i	0.489373	+	0.282540i	0.724314	−	0.689470i	$-0.242157\pi$
$17$	8.31934	+	4.80317i	0.489373	+	0.282540i	−0.234941	+	0.972010i	$0.575490\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$	2.56168	+	9.56033i	0.134825	+	0.503175i	0.999999	+	0.00170204i	$0.000541777\pi$
$19$	2.56168	+	9.56033i	0.134825	+	0.503175i	−0.865173	+	0.501473i	$0.832792\pi$
$20$	−17.4627	+	4.67913i	−0.873137	+	0.233956i
$21$	11.7049	+	11.7049i	0.557377	+	0.557377i
$22$	11.5157	−	19.9457i	0.523440	−	0.906624i
$23$	−23.6929	+	13.6791i	−1.03013	+	0.594745i	−0.917021	−	0.398838i	$-0.869414\pi$
$23$	−23.6929	+	13.6791i	−1.03013	+	0.594745i	−0.113107	+	0.993583i	$0.536080\pi$
$24$	−1.26795	+	4.73205i	−0.0528312	+	0.197169i
$25$		−	56.7105i		−	2.26842i
$26$	−0.659759	−	18.3729i	−0.0253754	−	0.706651i
$27$	−5.19615			−0.192450
$28$	18.4627	+	4.94708i	0.659384	+	0.176681i
$29$	−13.8023	−	23.9063i	−0.475942	−	0.824356i	0.523678	−	0.851916i	$-0.324559\pi$
$29$	−13.8023	−	23.9063i	−0.475942	−	0.824356i	−0.999620	+	0.0275606i	$0.991226\pi$
$30$	−19.1754	−	11.0709i	−0.639181	−	0.369031i
$31$	11.5613	−	11.5613i	0.372946	−	0.372946i	−0.495603	−	0.868549i	$-0.665053\pi$
$31$	11.5613	−	11.5613i	0.372946	−	0.372946i	0.868549	+	0.495603i	$0.165053\pi$
$32$	1.46410	+	5.46410i	0.0457532	+	0.170753i
$33$	27.2464	−	7.30064i	0.825648	−	0.221232i
$34$	9.60634	+	9.60634i	0.282540	+	0.282540i
$35$	−43.1948	+	74.8156i	−1.23414	+	2.13759i
$36$	−5.19615	+	3.00000i	−0.144338	+	0.0833333i
$37$	−5.45615	+	20.3626i	−0.147464	+	0.550342i	0.852170	+	0.523265i	$0.175286\pi$
$37$	−5.45615	+	20.3626i	−0.147464	+	0.550342i	−0.999633	+	0.0270763i	$0.991380\pi$
$38$			13.9973i			0.368350i
$39$	15.3401	−	16.4828i	0.393335	−	0.422636i
$40$	−25.5672			−0.639181
$41$	39.1030	+	10.4776i	0.953731	+	0.255551i	0.701945	−	0.712232i	$-0.252315\pi$
$41$	39.1030	+	10.4776i	0.953731	+	0.255551i	0.251786	+	0.967783i	$0.418982\pi$
$42$	11.7049	+	20.2735i	0.278688	+	0.482703i
$43$	−30.9095	−	17.8456i	−0.718826	−	0.415014i	0.0954945	−	0.995430i	$-0.469557\pi$
$43$	−30.9095	−	17.8456i	−0.718826	−	0.415014i	−0.814320	+	0.580416i	$0.802890\pi$
$44$	23.0313	−	23.0313i	0.523440	−	0.523440i
$45$	−7.01869	−	26.1941i	−0.155971	−	0.582092i
$46$	−37.3721	+	10.0138i	−0.812436	+	0.217692i
$47$	25.5184	+	25.5184i	0.542944	+	0.542944i	0.924391	−	0.381447i	$-0.124574\pi$
$47$	25.5184	+	25.5184i	0.542944	+	0.542944i	−0.381447	+	0.924391i	$0.624574\pi$
$48$	−3.46410	+	6.00000i	−0.0721688	+	0.125000i
$49$	36.6646	−	21.1683i	0.748258	−	0.432007i
$50$	20.7575	−	77.4679i	0.415149	−	1.54936i
$51$			16.6387i			0.326249i
$52$	5.82371	−	25.3394i	0.111994	−	0.487296i
$53$	−39.0697			−0.737165			−0.368582	−	0.929595i	$-0.620157\pi$
$53$	−39.0697			−0.737165			−0.368582	+	0.929595i	$0.620157\pi$
$54$	−7.09808	−	1.90192i	−0.131446	−	0.0352208i
$55$	73.6060	+	127.489i	1.33829	+	2.31799i
$56$	23.4098	+	13.5157i	0.418033	+	0.241351i
$57$	−12.1220	+	12.1220i	−0.212667	+	0.212667i
$58$	−10.1040	−	37.7086i	−0.174207	−	0.650149i
$59$	−46.0300	+	12.3337i	−0.780169	+	0.209046i	−0.626859	−	0.779132i	$-0.715660\pi$
$59$	−46.0300	+	12.3337i	−0.780169	+	0.209046i	−0.153310	+	0.988178i	$0.548993\pi$
$60$	−22.1419	−	22.1419i	−0.369031	−	0.369031i
$61$	−35.2717	+	61.0923i	−0.578224	+	1.00151i	0.417459	+	0.908696i	$0.362921\pi$
$61$	−35.2717	+	61.0923i	−0.578224	+	1.00151i	−0.995683	+	0.0928174i	$0.970413\pi$
$62$	20.0248	−	11.5613i	0.322981	−	0.186473i
$63$	−7.42062	+	27.6941i	−0.117788	+	0.439589i
$64$			8.00000i			0.125000i
$65$	103.811	+	55.0661i	1.59710	+	0.847170i
$66$	39.8915			0.604416
$67$	38.7250	+	10.3763i	0.577984	+	0.154870i	0.535956	−	0.844246i	$-0.319951\pi$
$67$	38.7250	+	10.3763i	0.577984	+	0.154870i	0.0420285	+	0.999116i	$0.486618\pi$
$68$	9.60634	+	16.6387i	0.141270	+	0.244686i
$69$	−41.0374	−	23.6929i	−0.594745	−	0.343376i
$70$	−86.3896	+	86.3896i	−1.23414	+	1.23414i
$71$	−8.28114	−	30.9056i	−0.116636	−	0.435291i	0.882768	−	0.469809i	$-0.155677\pi$
$71$	−8.28114	−	30.9056i	−0.116636	−	0.435291i	−0.999404	+	0.0345180i	$0.989010\pi$
$72$	−8.19615	+	2.19615i	−0.113835	+	0.0305021i
$73$	−9.68320	−	9.68320i	−0.132647	−	0.132647i	0.637666	−	0.770313i	$-0.279900\pi$
$73$	−9.68320	−	9.68320i	−0.132647	−	0.132647i	−0.770313	+	0.637666i	$0.779900\pi$
$74$	−14.9065	+	25.8188i	−0.201439	+	0.348903i
$75$	85.0657	−	49.1127i	1.13421	−	0.654836i
$76$	−5.12337	+	19.1207i	−0.0674127	+	0.251588i
$77$		−	155.642i		−	2.02132i
$78$	26.9880	−	16.9011i	0.346000	−	0.216680i
$79$	−56.1543			−0.710814			−0.355407	−	0.934712i	$-0.615658\pi$
$79$	−56.1543			−0.710814			−0.355407	+	0.934712i	$0.615658\pi$
$80$	−34.9255	−	9.35826i	−0.436569	−	0.116978i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	49.5806	+	28.6254i	0.604641	+	0.349090i
$83$	4.59931	−	4.59931i	0.0554133	−	0.0554133i	−0.678857	−	0.734270i	$-0.737524\pi$
$83$	4.59931	−	4.59931i	0.0554133	−	0.0554133i	0.734270	+	0.678857i	$0.237524\pi$
$84$	8.56859	+	31.9784i	0.102007	+	0.380695i
$85$	−83.8766	+	22.4747i	−0.986783	+	0.264408i
$86$	−35.6912	−	35.6912i	−0.415014	−	0.415014i
$87$	23.9063	−	41.4069i	0.274785	−	0.475942i
$88$	39.8915	−	23.0313i	0.453312	−	0.261720i
$89$	29.9479	−	111.767i	0.336494	−	1.25581i	−0.565747	−	0.824579i	$-0.691412\pi$
$89$	29.9479	−	111.767i	0.336494	−	1.25581i	0.902241	−	0.431233i	$-0.141921\pi$
$90$		−	38.3509i		−	0.426121i
$91$	−65.9418	−	105.298i	−0.724636	−	1.15712i
$92$	−54.7165			−0.594745
$93$	27.3544	+	7.32958i	0.294133	+	0.0788127i
$94$	25.5184	+	44.1991i	0.271472	+	0.470203i
$95$	−77.4816	−	44.7340i	−0.815596	−	0.470885i
$96$	−6.92820	+	6.92820i	−0.0721688	+	0.0721688i
$97$	−9.04249	−	33.7470i	−0.0932215	−	0.347908i	0.903522	−	0.428541i	$-0.140972\pi$
$97$	−9.04249	−	33.7470i	−0.0932215	−	0.347908i	−0.996744	+	0.0806336i	$0.974306\pi$
$98$	57.8330	−	15.4963i	0.590132	−	0.158126i
$99$	34.5470	+	34.5470i	0.348960	+	0.348960i
$100$	56.7105	−	98.2254i	0.567105	−	0.982254i
$101$	−101.471	+	58.5846i	−1.00467	+	0.580045i	−0.909626	−	0.415428i	$-0.863632\pi$
$101$	−101.471	+	58.5846i	−1.00467	+	0.580045i	−0.0950419	+	0.995473i	$0.530299\pi$
$102$	−6.09018	+	22.7289i	−0.0597076	+	0.222832i
$103$			184.178i			1.78813i	0.447933	+	0.894067i	$0.352160\pi$
$103$			184.178i			1.78813i	−0.447933	+	0.894067i	$0.647840\pi$
$104$	17.2302	−	32.4826i	0.165675	−	0.312333i
$105$	−149.631			−1.42506
$106$	−53.3702	−	14.3005i	−0.503493	−	0.134910i
$107$	−3.57599	−	6.19380i	−0.0334205	−	0.0578860i	0.848831	−	0.528664i	$-0.177307\pi$
$107$	−3.57599	−	6.19380i	−0.0334205	−	0.0578860i	−0.882252	+	0.470778i	$0.843973\pi$
$108$	−9.00000	−	5.19615i	−0.0833333	−	0.0481125i
$109$	8.07627	−	8.07627i	0.0740942	−	0.0740942i	−0.669089	−	0.743183i	$-0.733315\pi$
$109$	8.07627	−	8.07627i	0.0740942	−	0.0740942i	0.743183	+	0.669089i	$0.233315\pi$
$110$	53.8833	+	201.095i	0.489848	+	1.82814i
$111$	−35.2691	+	9.45034i	−0.317740	+	0.0851382i
$112$	27.0313	+	27.0313i	0.241351	+	0.241351i
$113$	58.2038	−	100.812i	0.515077	−	0.892140i	−0.484769	−	0.874642i	$-0.661096\pi$
$113$	58.2038	−	100.812i	0.515077	−	0.892140i	0.999847	−	0.0174984i	$-0.00557019\pi$
$114$	−20.9959	+	12.1220i	−0.184175	+	0.106333i
$115$	64.0064	−	238.875i	0.556578	−	2.07718i
$116$		−	55.2093i		−	0.475942i
$117$	38.0091	+	8.73557i	0.324864	+	0.0746630i
$118$	−67.3926			−0.571124
$119$	88.6798	+	23.7617i	0.745208	+	0.199678i
$120$	−22.1419	−	38.3509i	−0.184516	−	0.319591i
$121$	−124.899	−	72.1107i	−1.03223	−	0.595956i
$122$	−70.5433	+	70.5433i	−0.578224	+	0.578224i
$123$	18.1477	+	67.7283i	0.147543	+	0.550637i
$124$	31.5861	−	8.46347i	0.254727	−	0.0682538i
$125$	202.687	+	202.687i	1.62150	+	1.62150i
$126$	−20.2735	+	35.1147i	−0.160901	+	0.278688i
$127$	−23.3984	+	13.5091i	−0.184240	+	0.106371i	−0.589283	−	0.807927i	$-0.700590\pi$
$127$	−23.3984	+	13.5091i	−0.184240	+	0.106371i	0.405043	+	0.914297i	$0.367256\pi$
$128$	−2.92820	+	10.9282i	−0.0228766	+	0.0853766i
$129$		−	61.8190i		−	0.479217i
$130$	121.653	+	113.219i	0.935795	+	0.870917i
$131$	−64.5682			−0.492887			−0.246444	−	0.969157i	$-0.579262\pi$
$131$	−64.5682			−0.492887			−0.246444	+	0.969157i	$0.579262\pi$
$132$	54.4927	+	14.6013i	0.412824	+	0.110616i
$133$	47.2957	+	81.9186i	0.355607	+	0.615929i
$134$	49.1013	+	28.3486i	0.366427	+	0.211557i
$135$	33.2128	−	33.2128i	0.246021	−	0.246021i
$136$	7.03233	+	26.2450i	0.0517083	+	0.192978i
$137$	197.212	−	52.8428i	1.43950	−	0.385714i	0.547143	−	0.837039i	$-0.315715\pi$
$137$	197.212	−	52.8428i	1.43950	−	0.385714i	0.892360	+	0.451325i	$0.149049\pi$
$138$	−47.3859	−	47.3859i	−0.343376	−	0.343376i
$139$	−31.8057	+	55.0890i	−0.228818	+	0.396324i	−0.957458	−	0.288573i	$-0.906819\pi$
$139$	−31.8057	+	55.0890i	−0.228818	+	0.396324i	0.728640	+	0.684897i	$0.240153\pi$
$140$	−149.631	+	86.3896i	−1.06879	+	0.617069i
$141$	−16.1780	+	60.3771i	−0.114738	+	0.428207i
$142$		−	45.2490i		−	0.318655i
$143$	−211.577	+	7.59757i	−1.47956	+	0.0531299i
$144$	−12.0000			−0.0833333
$145$	241.026	+	64.5828i	1.66225	+	0.445399i
$146$	−9.68320	−	16.7718i	−0.0663233	−	0.114875i
$147$	63.5050	+	36.6646i	0.432007	+	0.249419i
$148$	−29.8130	+	29.8130i	−0.201439	+	0.201439i
$149$	7.51093	+	28.0312i	0.0504089	+	0.188129i	0.986539	−	0.163525i	$-0.0522863\pi$
$149$	7.51093	+	28.0312i	0.0504089	+	0.188129i	−0.936130	+	0.351653i	$0.885620\pi$
$150$	134.178	−	35.9530i	0.894523	−	0.239687i
$151$	31.6350	+	31.6350i	0.209503	+	0.209503i	0.804056	−	0.594553i	$-0.202671\pi$
$151$	31.6350	+	31.6350i	0.209503	+	0.209503i	−0.594553	+	0.804056i	$0.702671\pi$
$152$	−13.9973	+	24.2440i	−0.0920875	+	0.159500i
$153$	−24.9580	+	14.4095i	−0.163124	+	0.0941798i
$154$	56.9689	−	212.611i	0.369928	−	1.38059i
$155$			147.796i			0.953520i
$156$	43.0526	−	13.2090i	0.275978	−	0.0846730i
$157$	242.423			1.54409			0.772047	−	0.635566i	$-0.219233\pi$
$157$	242.423			1.54409			0.772047	+	0.635566i	$0.219233\pi$
$158$	−76.7082	−	20.5539i	−0.485495	−	0.130088i
$159$	−33.8354	−	58.6046i	−0.212801	−	0.368582i
$160$	−44.2838	−	25.5672i	−0.276773	−	0.159795i
$161$	−184.883	+	184.883i	−1.14834	+	1.14834i
$162$	−3.29423	−	12.2942i	−0.0203347	−	0.0758903i
$163$	−15.0812	+	4.04100i	−0.0925228	+	0.0247914i	−0.304783	−	0.952422i	$-0.598584\pi$
$163$	−15.0812	+	4.04100i	−0.0925228	+	0.0247914i	0.212261	+	0.977213i	$0.431917\pi$
$164$	57.2507	+	57.2507i	0.349090	+	0.349090i
$165$	−127.489	+	220.818i	−0.772662	+	1.33829i
$166$	7.96623	−	4.59931i	0.0479894	−	0.0277067i
$167$	12.8137	−	47.8214i	0.0767287	−	0.286355i	−0.916891	−	0.399138i	$-0.869310\pi$
$167$	12.8137	−	47.8214i	0.0767287	−	0.286355i	0.993620	+	0.112782i	$0.0359762\pi$
$168$			46.8197i			0.278688i
$169$	−139.920	+	94.7801i	−0.827932	+	0.560829i
$170$	−122.804			−0.722376
$171$	−28.6810	−	7.68505i	−0.167725	−	0.0449418i
$172$	−35.6912	−	61.8190i	−0.207507	−	0.359413i
$173$	−145.860	−	84.2123i	−0.843122	−	0.486776i	0.0152025	−	0.999884i	$-0.495161\pi$
$173$	−145.860	−	84.2123i	−0.843122	−	0.486776i	−0.858324	+	0.513108i	$0.828494\pi$
$174$	47.8126	−	47.8126i	0.274785	−	0.274785i
$175$	−140.276	−	523.516i	−0.801575	−	2.99152i
$176$	62.9228	−	16.8601i	0.357516	−	0.0957961i
$177$	−58.3637	−	58.3637i	−0.329738	−	0.329738i
$178$	81.8193	−	141.715i	0.459659	−	0.796153i
$179$	271.106	−	156.523i	1.51456	−	0.874432i	0.514707	−	0.857366i	$-0.327901\pi$
$179$	271.106	−	156.523i	1.51456	−	0.874432i	0.999854	−	0.0170659i	$-0.00543251\pi$
$180$	14.0374	−	52.3882i	0.0779855	−	0.291046i
$181$			19.4795i			0.107622i	0.998551	+	0.0538108i	$0.0171368\pi$
$181$			19.4795i			0.107622i	−0.998551	+	0.0538108i	$0.982863\pi$
$182$	−51.5367	−	167.976i	−0.283168	−	0.922942i
$183$	−122.185			−0.667675
$184$	−74.7442	−	20.0276i	−0.406218	−	0.108846i
$185$	−95.2795	−	165.029i	−0.515024	−	0.892048i
$186$	34.6840	+	20.0248i	0.186473	+	0.107660i
$187$	110.623	−	110.623i	0.591569	−	0.591569i
$188$	18.6807	+	69.7175i	0.0993657	+	0.370838i
$189$	−47.9676	+	12.8529i	−0.253797	+	0.0680047i
$190$	−89.4681	−	89.4681i	−0.470885	−	0.470885i
$191$	−71.4756	+	123.799i	−0.374218	+	0.648164i	−0.990210	−	0.139588i	$-0.955422\pi$
$191$	−71.4756	+	123.799i	−0.374218	+	0.648164i	0.615992	+	0.787752i	$0.288755\pi$
$192$	−12.0000	+	6.92820i	−0.0625000	+	0.0360844i
$193$	−43.4334	+	162.096i	−0.225044	+	0.839874i	0.757344	+	0.653017i	$0.226497\pi$
$193$	−43.4334	+	162.096i	−0.225044	+	0.839874i	−0.982387	+	0.186857i	$0.940170\pi$
$194$		−	49.4091i		−	0.254686i
$195$	7.30415	+	203.406i	0.0374572	+	1.04311i
$196$	84.6734			0.432007
$197$	164.580	+	44.0992i	0.835434	+	0.223854i	0.651083	−	0.759007i	$-0.274315\pi$
$197$	164.580	+	44.0992i	0.835434	+	0.223854i	0.184351	+	0.982860i	$0.440982\pi$
$198$	34.5470	+	59.8372i	0.174480	+	0.302208i
$199$	140.059	+	80.8629i	0.703813	+	0.406346i	0.808766	−	0.588131i	$-0.200136\pi$
$199$	140.059	+	80.8629i	0.703813	+	0.406346i	−0.104953	+	0.994477i	$0.533469\pi$
$200$	113.421	−	113.421i	0.567105	−	0.567105i
$201$	17.9723	+	67.0736i	0.0894145	+	0.333699i
$202$	−160.056	+	42.8869i	−0.792357	+	0.212311i
$203$	−186.548	−	186.548i	−0.918953	−	0.918953i
$204$	−16.6387	+	28.8190i	−0.0815621	+	0.141270i
$205$	−316.910	+	182.968i	−1.54590	+	0.892526i
$206$	−67.4138	+	251.592i	−0.327251	+	1.22132i
$207$		−	82.0748i		−	0.396497i
$208$	35.4264	−	38.0654i	0.170319	−	0.183007i
$209$	161.188			0.771236
$210$	−204.400	−	54.7688i	−0.973333	−	0.260804i
$211$	89.9377	+	155.777i	0.426245	+	0.738278i	0.996536	−	0.0831651i	$-0.0265029\pi$
$211$	89.9377	+	155.777i	0.426245	+	0.738278i	−0.570291	+	0.821443i	$0.693170\pi$
$212$	−67.6707	−	39.0697i	−0.319202	−	0.184291i
$213$	39.1868	−	39.1868i	0.183975	−	0.183975i
$214$	−2.61781	−	9.76979i	−0.0122327	−	0.0456532i
$215$	311.634	−	83.5020i	1.44946	−	0.388381i
$216$	−10.3923	−	10.3923i	−0.0481125	−	0.0481125i
$217$	78.1295	−	135.324i	0.360044	−	0.623614i
$218$	13.9885	−	8.07627i	0.0641675	−	0.0370471i
$219$	6.13890	−	22.9107i	0.0280315	−	0.104615i
$220$			294.424i			1.33829i
$221$	27.9723	−	121.709i	0.126571	−	0.550721i
$222$	−51.6376			−0.232602
$223$	376.519	+	100.888i	1.68843	+	0.452413i	0.969983	−	0.243171i	$-0.0781877\pi$
$223$	376.519	+	100.888i	1.68843	+	0.452413i	0.718445	+	0.695584i	$0.244854\pi$
$224$	27.0313	+	46.8197i	0.120676	+	0.209016i
$225$	147.338	+	85.0657i	0.654836	+	0.378070i
$226$	116.408	−	116.408i	0.515077	−	0.515077i
$227$	34.5070	+	128.782i	0.152013	+	0.567321i	0.999343	+	0.0362535i	$0.0115424\pi$
$227$	34.5070	+	128.782i	0.152013	+	0.567321i	−0.847329	+	0.531068i	$0.821791\pi$
$228$	−33.1180	+	8.87393i	−0.145254	+	0.0389207i
$229$	−304.866	−	304.866i	−1.33129	−	1.33129i	−0.904215	−	0.427077i	$-0.859543\pi$
$229$	−304.866	−	304.866i	−1.33129	−	1.33129i	−0.427077	−	0.904215i	$-0.640457\pi$
$230$	174.869	−	302.882i	0.760299	−	1.31688i
$231$	233.463	−	134.790i	1.01066	−	0.583506i
$232$	20.2080	−	75.4172i	0.0871034	−	0.325074i
$233$		−	44.1414i		−	0.189448i	−0.995504	−	0.0947240i	$-0.969803\pi$
$233$		−	44.1414i		−	0.189448i	0.995504	−	0.0947240i	$-0.0301969\pi$
$234$	48.7239	+	25.8453i	0.208222	+	0.110450i
$235$	−326.217			−1.38816
$236$	−92.0600	−	24.6674i	−0.390085	−	0.104523i
$237$	−48.6311	−	84.2315i	−0.205194	−	0.355407i
$238$	112.441	+	64.9181i	0.472443	+	0.272765i
$239$	−15.8448	+	15.8448i	−0.0662964	+	0.0662964i	−0.739478	−	0.673181i	$-0.764927\pi$
$239$	−15.8448	+	15.8448i	−0.0662964	+	0.0662964i	0.673181	+	0.739478i	$0.264927\pi$
$240$	−16.2090	−	60.4927i	−0.0675374	−	0.252053i
$241$	−464.593	+	124.487i	−1.92777	+	0.516545i	−0.947076	+	0.321010i	$0.895978\pi$
$241$	−464.593	+	124.487i	−1.92777	+	0.516545i	−0.980697	+	0.195535i	$0.937356\pi$
$242$	−144.221	−	144.221i	−0.595956	−	0.595956i
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$	−122.185	+	70.5433i	−0.500757	+	0.289112i
$245$	−99.0494	+	369.657i	−0.404283	+	1.50881i
$246$			99.1611i			0.403094i
$247$	109.050	−	68.2917i	0.441497	−	0.276484i
$248$	46.2453			0.186473
$249$	10.8821	+	2.91584i	0.0437031	+	0.0117102i
$250$	202.687	+	351.065i	0.810749	+	1.40426i
$251$	−183.403	−	105.888i	−0.730691	−	0.421865i	0.0879839	−	0.996122i	$-0.471958\pi$
$251$	−183.403	−	105.888i	−0.730691	−	0.421865i	−0.818675	+	0.574257i	$0.805291\pi$
$252$	−40.5470	+	40.5470i	−0.160901	+	0.160901i
$253$	115.316	+	430.365i	0.455794	+	1.70105i
$254$	−36.9075	+	9.88934i	−0.145305	+	0.0389344i
$255$	−106.351	−	106.351i	−0.417064	−	0.417064i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	235.923	−	136.210i	0.917990	−	0.530002i	0.0349966	−	0.999387i	$-0.488858\pi$
$257$	235.923	−	136.210i	0.917990	−	0.530002i	0.882993	+	0.469386i	$0.155525\pi$
$258$	22.6273	−	84.4464i	0.0877029	−	0.327311i
$259$			201.471i			0.777881i
$260$	124.740	+	199.189i	0.479771	+	0.766110i
$261$	82.8139			0.317295
$262$	−88.2018	−	23.6336i	−0.336648	−	0.0902046i
$263$	−118.171	−	204.679i	−0.449321	−	0.778247i	0.549021	−	0.835809i	$-0.315001\pi$
$263$	−118.171	−	204.679i	−0.449321	−	0.778247i	−0.998342	+	0.0575615i	$0.981667\pi$
$264$	69.0940	+	39.8915i	0.261720	+	0.151104i
$265$	249.726	−	249.726i	0.942363	−	0.942363i
$266$	34.6229	+	129.214i	0.130161	+	0.485768i
$267$	193.587	−	51.8713i	0.725043	−	0.194275i
$268$	56.6973	+	56.6973i	0.211557	+	0.211557i
$269$	−233.180	+	403.880i	−0.866842	+	1.50141i	−0.00163514	+	0.999999i	$0.500520\pi$
$269$	−233.180	+	403.880i	−0.866842	+	1.50141i	−0.865207	+	0.501415i	$0.832813\pi$
$270$	57.5263	−	33.2128i	0.213060	−	0.123010i
$271$	−119.372	+	445.502i	−0.440486	+	1.64392i	0.287099	+	0.957901i	$0.407309\pi$
$271$	−119.372	+	445.502i	−0.440486	+	1.64392i	−0.727586	+	0.686017i	$0.759358\pi$
$272$			38.4254i			0.141270i
$273$	100.839	−	190.103i	0.369374	−	0.696348i
$274$	288.738			1.05379
$275$	−892.095	−	239.036i	−3.24398	−	0.869223i
$276$	−47.3859	−	82.0748i	−0.171688	−	0.297372i
$277$	−21.2638	−	12.2766i	−0.0767645	−	0.0443200i	0.461126	−	0.887334i	$-0.347445\pi$
$277$	−21.2638	−	12.2766i	−0.0767645	−	0.0443200i	−0.537891	+	0.843014i	$0.680779\pi$
$278$	−63.6113	+	63.6113i	−0.228818	+	0.228818i
$279$	12.6952	+	47.3792i	0.0455025	+	0.169818i
$280$	−236.021	+	63.2416i	−0.842931	+	0.225863i
$281$	276.591	+	276.591i	0.984311	+	0.984311i	0.999879	−	0.0155674i	$-0.00495547\pi$
$281$	276.591	+	276.591i	0.984311	+	0.984311i	−0.0155674	+	0.999879i	$0.504955\pi$
$282$	−44.1991	+	76.5551i	−0.156734	+	0.271472i
$283$	339.231	−	195.855i	1.19870	−	0.692068i	0.238432	−	0.971159i	$-0.423366\pi$
$283$	339.231	−	195.855i	1.19870	−	0.692068i	0.960265	+	0.279091i	$0.0900331\pi$
$284$	16.5623	−	61.8113i	0.0583179	−	0.217645i
$285$		−	154.963i		−	0.543731i
$286$	−291.800	−	67.0640i	−1.02028	−	0.234489i
$287$	386.891			1.34805
$288$	−16.3923	−	4.39230i	−0.0569177	−	0.0152511i
$289$	−98.3591	−	170.363i	−0.340343	−	0.589491i
$290$	305.609	+	176.444i	1.05382	+	0.608426i
$291$	42.7895	−	42.7895i	0.147043	−	0.147043i
$292$	−7.08860	−	26.4550i	−0.0242760	−	0.0905993i
$293$	286.280	−	76.7084i	0.977064	−	0.261804i	0.265256	−	0.964178i	$-0.414543\pi$
$293$	286.280	−	76.7084i	0.977064	−	0.261804i	0.711808	+	0.702374i	$0.247877\pi$
$294$	73.3293	+	73.3293i	0.249419	+	0.249419i
$295$	215.380	−	373.050i	0.730103	−	1.26457i
$296$	−51.6376	+	29.8130i	−0.174451	+	0.100720i
$297$	−21.9019	+	81.7391i	−0.0737439	+	0.275216i
$298$			41.0405i			0.137720i
$299$	260.351	+	242.301i	0.870738	+	0.810371i
$300$	196.451			0.654836
$301$	−329.479	−	88.2837i	−1.09462	−	0.293301i
$302$	31.6350	+	54.7934i	0.104752	+	0.181435i
$303$	−175.754	−	101.471i	−0.580045	−	0.334889i
$304$	−27.9946	+	27.9946i	−0.0920875	+	0.0920875i
$305$	−165.041	−	615.940i	−0.541117	−	2.01948i
$306$	−39.3675	+	10.5485i	−0.128652	+	0.0344722i
$307$	221.215	+	221.215i	0.720571	+	0.720571i	0.968722	−	0.248150i	$-0.0798227\pi$
$307$	221.215	+	221.215i	0.720571	+	0.720571i	−0.248150	+	0.968722i	$0.579823\pi$
$308$	155.642	−	269.580i	0.505331	−	0.875259i
$309$	−276.267	+	159.503i	−0.894067	+	0.516190i
$310$	−54.0969	+	201.892i	−0.174506	+	0.651266i
$311$			12.5556i			0.0403716i	0.999796	+	0.0201858i	$0.00642578\pi$
$311$			12.5556i			0.0403716i	−0.999796	+	0.0201858i	$0.993574\pi$
$312$	63.6457	−	2.28547i	0.203993	−	0.00732523i
$313$	590.956			1.88804			0.944018	−	0.329893i	$-0.107013\pi$
$313$	590.956			1.88804			0.944018	+	0.329893i	$0.107013\pi$
$314$	331.156	+	88.7329i	1.05464	+	0.282589i
$315$	−129.584	−	224.447i	−0.411379	−	0.712529i
$316$	−97.2622	−	56.1543i	−0.307792	−	0.177704i
$317$	54.7137	−	54.7137i	0.172598	−	0.172598i	−0.615522	−	0.788120i	$-0.711055\pi$
$317$	54.7137	−	54.7137i	0.172598	−	0.172598i	0.788120	+	0.615522i	$0.211055\pi$
$318$	−24.7692	−	92.4400i	−0.0778906	−	0.290692i
$319$	−434.240	+	116.354i	−1.36125	+	0.364747i
$320$	−51.1345	−	51.1345i	−0.159795	−	0.159795i
$321$	6.19380	−	10.7280i	0.0192953	−	0.0334205i
$322$	−320.226	+	184.883i	−0.994491	+	0.574170i
$323$	−24.6084	+	91.8398i	−0.0761870	+	0.284334i
$324$		−	18.0000i		−	0.0555556i
$325$	−704.809	+	216.243i	−2.16864	+	0.665363i
$326$	−22.0804			−0.0677314
$327$	19.1087	+	5.12015i	0.0584362	+	0.0156579i
$328$	57.2507	+	99.1611i	0.174545	+	0.302321i
$329$	298.690	+	172.449i	0.907874	+	0.524161i
$330$	−254.979	+	254.979i	−0.772662	+	0.772662i
$331$	−5.29073	−	19.7453i	−0.0159841	−	0.0596534i	0.957473	−	0.288522i	$-0.0931640\pi$
$331$	−5.29073	−	19.7453i	−0.0159841	−	0.0596534i	−0.973457	+	0.228869i	$0.926497\pi$
$332$	12.5655	−	3.36693i	0.0378480	−	0.0101413i
$333$	−44.7195	−	44.7195i	−0.134293	−	0.134293i
$334$	35.0077	−	60.6351i	0.104813	−	0.181542i
$335$	−313.846	+	181.199i	−0.936854	+	0.540893i
$336$	−17.1372	+	63.9568i	−0.0510035	+	0.190348i
$337$		−	202.326i		−	0.600375i	−0.953880	−	0.300188i	$-0.902951\pi$
$337$		−	202.326i		−	0.600375i	0.953880	−	0.300188i	$-0.0970493\pi$
$338$	−225.827	+	78.2575i	−0.668127	+	0.231531i
$339$	201.624			0.594760
$340$	−167.753	−	44.9493i	−0.493392	−	0.132204i
$341$	−133.136	−	230.599i	−0.390429	−	0.676243i
$342$	−36.3660	−	20.9959i	−0.106333	−	0.0613917i
$343$	−45.0296	+	45.0296i	−0.131282	+	0.131282i
$344$	−26.1278	−	97.5103i	−0.0759529	−	0.283460i
$345$	413.744	−	110.862i	1.19926	−	0.321340i
$346$	−168.425	−	168.425i	−0.486776	−	0.486776i
$347$	−278.263	+	481.966i	−0.801911	+	1.38895i	0.116446	+	0.993197i	$0.462850\pi$
$347$	−278.263	+	481.966i	−0.801911	+	1.38895i	−0.918357	+	0.395753i	$0.870483\pi$
$348$	82.8139	−	47.8126i	0.237971	−	0.137393i
$349$	119.978	−	447.764i	0.343777	−	1.28299i	−0.550258	−	0.834995i	$-0.685471\pi$
$349$	119.978	−	447.764i	0.343777	−	1.28299i	0.894035	−	0.447998i	$-0.147863\pi$
$350$		−	766.480i		−	2.18994i
$351$	19.8135	+	64.5788i	0.0564486	+	0.183985i
$352$	92.1254			0.261720
$353$	−272.941	−	73.1344i	−0.773205	−	0.207180i	−0.149418	−	0.988774i	$-0.547740\pi$
$353$	−272.941	−	73.1344i	−0.773205	−	0.207180i	−0.623787	+	0.781595i	$0.714407\pi$
$354$	−58.3637	−	101.089i	−0.164869	−	0.285562i
$355$	250.474	+	144.611i	0.705562	+	0.407356i
$356$	163.639	−	163.639i	0.459659	−	0.459659i
$357$	41.1564	+	153.598i	0.115284	+	0.430246i
$358$	427.630	−	114.583i	1.19450	−	0.320064i
$359$	−280.398	−	280.398i	−0.781054	−	0.781054i	0.198955	−	0.980009i	$-0.436245\pi$
$359$	−280.398	−	280.398i	−0.781054	−	0.781054i	−0.980009	+	0.198955i	$0.936245\pi$
$360$	38.3509	−	66.4256i	0.106530	−	0.184516i
$361$	227.797	−	131.519i	0.631018	−	0.364318i
$362$	−7.12999	+	26.6095i	−0.0196961	+	0.0735069i
$363$		−	249.799i		−	0.688151i
$364$	−8.91709	−	248.323i	−0.0244975	−	0.682205i
$365$	123.786			0.339141
$366$	−166.907	−	44.7227i	−0.456031	−	0.122193i
$367$	−295.943	−	512.588i	−0.806384	−	1.39670i	−0.915353	−	0.402653i	$-0.868088\pi$
$367$	−295.943	−	512.588i	−0.806384	−	1.39670i	0.108968	−	0.994045i	$-0.465245\pi$
$368$	−94.7718	−	54.7165i	−0.257532	−	0.148686i
$369$	−85.8761	+	85.8761i	−0.232726	+	0.232726i
$370$	−69.7494	−	260.308i	−0.188512	−	0.703536i
$371$	−360.667	+	96.6405i	−0.972149	+	0.260487i
$372$	40.0496	+	40.0496i	0.107660	+	0.107660i
$373$	255.943	−	443.306i	0.686174	−	1.18849i	−0.286892	−	0.957963i	$-0.592622\pi$
$373$	255.943	−	443.306i	0.686174	−	1.18849i	0.973066	−	0.230525i	$-0.0740445\pi$
$374$	191.606	−	110.623i	0.512314	−	0.295785i
$375$	−128.499	+	479.563i	−0.342663	+	1.27884i
$376$			102.073i			0.271472i
$377$	−244.483	+	262.695i	−0.648496	+	0.696804i
$378$	−70.2295			−0.185792
$379$	197.686	+	52.9699i	0.521600	+	0.139762i	0.510006	−	0.860171i	$-0.329643\pi$
$379$	197.686	+	52.9699i	0.521600	+	0.139762i	0.0115932	+	0.999933i	$0.496310\pi$
$380$	−89.4681	−	154.963i	−0.235442	−	0.407798i
$381$	−40.5273	−	23.3984i	−0.106371	−	0.0614132i
$382$	−142.951	+	142.951i	−0.374218	+	0.374218i
$383$	84.9951	+	317.206i	0.221919	+	0.828214i	0.983615	+	0.180280i	$0.0577002\pi$
$383$	84.9951	+	317.206i	0.221919	+	0.828214i	−0.761696	+	0.647934i	$0.775633\pi$
$384$	−18.9282	+	5.07180i	−0.0492922	+	0.0132078i
$385$	994.834	+	994.834i	2.58398	+	2.58398i
$386$	−118.662	+	205.529i	−0.307415	+	0.532459i
$387$	92.7285	−	53.5369i	0.239609	−	0.138338i
$388$	18.0850	−	67.4941i	0.0466108	−	0.173954i
$389$			393.984i			1.01281i	0.862295	+	0.506406i	$0.169026\pi$
$389$			393.984i			1.01281i	−0.862295	+	0.506406i	$0.830974\pi$
$390$	−64.4740	+	280.531i	−0.165318	+	0.719310i
$391$	−262.813			−0.672156
$392$	115.666	+	30.9926i	0.295066	+	0.0790628i
$393$	−55.9177	−	96.8523i	−0.142284	−	0.246444i
$394$	208.680	+	120.481i	0.529644	+	0.305790i
$395$	358.928	−	358.928i	0.908678	−	0.908678i
$396$	25.2902	+	94.3842i	0.0638641	+	0.238344i
$397$	−115.976	+	31.0756i	−0.292130	+	0.0782760i	−0.401908	−	0.915680i	$-0.631653\pi$
$397$	−115.976	+	31.0756i	−0.292130	+	0.0782760i	0.109778	+	0.993956i	$0.464986\pi$
$398$	161.726	+	161.726i	0.406346	+	0.406346i
$399$	−81.9186	+	141.887i	−0.205310	+	0.355607i
$400$	196.451	−	113.421i	0.491127	−	0.283552i
$401$	85.9977	−	320.948i	0.214458	−	0.800368i	−0.771899	−	0.635746i	$-0.780693\pi$
$401$	85.9977	−	320.948i	0.214458	−	0.800368i	0.986357	−	0.164623i	$-0.0526407\pi$
$402$			98.2025i			0.244285i
$403$	−187.771	−	99.6019i	−0.465933	−	0.247151i
$404$	−234.338			−0.580045
$405$	78.5824	+	21.0561i	0.194031	+	0.0519903i
$406$	−186.548	−	323.110i	−0.459477	−	0.795837i
$407$	297.321	+	171.658i	0.730518	+	0.421765i
$408$	−33.2773	+	33.2773i	−0.0815621	+	0.0815621i
$409$	−113.840	−	424.856i	−0.278337	−	1.03877i	−0.953572	−	0.301165i	$-0.902625\pi$
$409$	−113.840	−	424.856i	−0.278337	−	1.03877i	0.675235	−	0.737603i	$-0.264042\pi$
$410$	−499.877	+	133.942i	−1.21921	+	0.326687i
$411$	250.055	+	250.055i	0.608406	+	0.608406i
$412$	−184.178	+	319.005i	−0.447034	+	0.774285i
$413$	−394.412	+	227.714i	−0.954993	+	0.551366i
$414$	30.0415	−	112.116i	0.0725639	−	0.270812i
$415$			58.7958i			0.141677i
$416$	62.3262	−	39.0313i	0.149823	−	0.0938253i
$417$	−110.178			−0.264216
$418$	220.187	+	58.9990i	0.526764	+	0.141146i
$419$	62.4764	+	108.212i	0.149108	+	0.258263i	0.930898	−	0.365279i	$-0.119026\pi$
$419$	62.4764	+	108.212i	0.149108	+	0.258263i	−0.781790	+	0.623542i	$0.785693\pi$
$420$	−259.169	−	149.631i	−0.617069	−	0.356265i
$421$	9.46318	−	9.46318i	0.0224779	−	0.0224779i	−0.695779	−	0.718256i	$-0.744940\pi$
$421$	9.46318	−	9.46318i	0.0224779	−	0.0224779i	0.718256	+	0.695779i	$0.244940\pi$
$422$	65.8389	+	245.714i	0.156016	+	0.582261i
$423$	−104.576	+	28.0211i	−0.247225	+	0.0662438i
$424$	−78.1394	−	78.1394i	−0.184291	−	0.184291i
$425$	272.390	−	471.794i	0.640918	−	1.11010i
$426$	67.8735	−	39.1868i	0.159327	−	0.0919877i
$427$	−174.492	+	651.212i	−0.408646	+	1.52509i
$428$		−	14.3040i		−	0.0334205i
$429$	−194.627	−	310.785i	−0.453676	−	0.724441i
$430$	456.263			1.06108
$431$	698.341	+	187.120i	1.62028	+	0.434153i	0.951084	−	0.308932i	$-0.0999715\pi$
$431$	698.341	+	187.120i	1.62028	+	0.434153i	0.669197	+	0.743085i	$0.266638\pi$
$432$	−10.3923	−	18.0000i	−0.0240563	−	0.0416667i
$433$	35.4730	+	20.4803i	0.0819237	+	0.0472987i	0.540402	−	0.841407i	$-0.318272\pi$
$433$	35.4730	+	20.4803i	0.0819237	+	0.0472987i	−0.458479	+	0.888705i	$0.651605\pi$
$434$	156.259	−	156.259i	0.360044	−	0.360044i
$435$	111.861	+	417.470i	0.257151	+	0.959701i
$436$	22.0648	−	5.91224i	0.0506073	−	0.0135602i
$437$	−191.471	−	191.471i	−0.438148	−	0.438148i
$438$	16.7718	−	29.0496i	0.0382918	−	0.0663233i
$439$	−576.214	+	332.678i	−1.31256	+	0.757808i	−0.982520	−	0.186159i	$-0.940396\pi$
$439$	−576.214	+	332.678i	−1.31256	+	0.757808i	−0.330042	+	0.943966i	$0.607063\pi$
$440$	−107.767	+	402.191i	−0.244924	+	0.914069i
$441$			127.010i			0.288005i
$442$	82.7596	−	156.020i	0.187239	−	0.352985i
$443$	267.578			0.604013			0.302006	−	0.953306i	$-0.402344\pi$
$443$	267.578			0.604013			0.302006	+	0.953306i	$0.402344\pi$
$444$	−70.5383	−	18.9007i	−0.158870	−	0.0425691i
$445$	522.973	+	905.816i	1.17522	+	2.03554i
$446$	477.408	+	275.631i	1.07042	+	0.618008i
$447$	−35.5421	+	35.5421i	−0.0795125	+	0.0795125i
$448$	19.7883	+	73.8510i	0.0441703	+	0.164846i
$449$	−543.945	+	145.750i	−1.21146	+	0.324610i	−0.807335	−	0.590094i	$-0.799091\pi$
$449$	−543.945	+	145.750i	−1.21146	+	0.324610i	−0.404125	+	0.914704i	$0.632424\pi$
$450$	170.131	+	170.131i	0.378070	+	0.378070i
$451$	329.640	−	570.953i	0.730909	−	1.26597i
$452$	201.624	−	116.408i	0.446070	−	0.257539i
$453$	−20.0558	+	74.8492i	−0.0442732	+	0.165230i
$454$			188.550i			0.415308i
$455$	1094.53	+	251.554i	2.40556	+	0.552866i
$456$	−48.4881			−0.106333
$457$	−643.576	−	172.446i	−1.40826	−	0.377343i	−0.526958	−	0.849891i	$-0.676668\pi$
$457$	−643.576	−	172.446i	−1.40826	−	0.377343i	−0.881305	+	0.472548i	$0.843334\pi$
$458$	−304.866	−	528.043i	−0.665646	−	1.15293i
$459$	−43.2285	−	24.9580i	−0.0941798	−	0.0543748i
$460$	349.738	−	349.738i	0.760299	−	0.760299i
$461$	−92.7172	−	346.025i	−0.201122	−	0.750597i	−0.990597	−	0.136814i	$-0.956314\pi$
$461$	−92.7172	−	346.025i	−0.201122	−	0.750597i	0.789475	−	0.613783i	$-0.210353\pi$
$462$	368.253	−	98.6731i	0.797084	−	0.213578i
$463$	−630.292	−	630.292i	−1.36132	−	1.36132i	−0.872236	−	0.489084i	$-0.837331\pi$
$463$	−630.292	−	630.292i	−1.36132	−	1.36132i	−0.489084	−	0.872236i	$-0.662669\pi$
$464$	55.2093	−	95.6252i	0.118985	−	0.206089i
$465$	−221.693	+	127.995i	−0.476760	+	0.275257i
$466$	16.1569	−	60.2983i	0.0346714	−	0.129395i
$467$			425.264i			0.910630i	0.890331	+	0.455315i	$0.150473\pi$
$467$			425.264i			0.910630i	−0.890331	+	0.455315i	$0.849527\pi$
$468$	57.0981	+	53.1395i	0.122004	+	0.113546i
$469$	383.151			0.816953
$470$	−445.621	−	119.404i	−0.948130	−	0.254051i
$471$	209.944	+	363.634i	0.445741	+	0.772047i
$472$	−116.727	−	67.3926i	−0.247304	−	0.142781i
$473$	−411.009	+	411.009i	−0.868940	+	0.868940i
$474$	−35.6004	−	132.863i	−0.0751064	−	0.280301i
$475$	542.171	−	145.274i	1.14141	−	0.305841i
$476$	129.836	+	129.836i	0.272765	+	0.272765i
$477$	58.6046	−	101.506i	0.122861	−	0.212801i
$478$	−27.4441	+	15.8448i	−0.0574144	+	0.0331482i
$479$	−71.3059	+	266.117i	−0.148864	+	0.555568i	0.850689	+	0.525670i	$0.176185\pi$
$479$	−71.3059	+	266.117i	−0.148864	+	0.555568i	−0.999553	+	0.0298988i	$0.990481\pi$
$480$		−	88.5675i		−	0.184516i
$481$	273.876	−	9.83470i	0.569389	−	0.0204464i
$482$	−680.212			−1.41123
$483$	−437.437	−	117.211i	−0.905667	−	0.242673i
$484$	−144.221	−	249.799i	−0.297978	−	0.516113i
$485$	273.502	+	157.907i	0.563923	+	0.325581i
$486$	15.5885	−	15.5885i	0.0320750	−	0.0320750i
$487$	−165.703	−	618.410i	−0.340252	−	1.26984i	−0.898062	−	0.439868i	$-0.855025\pi$
$487$	−165.703	−	618.410i	−0.340252	−	1.26984i	0.557811	−	0.829968i	$-0.311641\pi$
$488$	−192.728	+	51.6413i	−0.394934	+	0.105822i
$489$	−19.1222	−	19.1222i	−0.0391048	−	0.0391048i
$490$	−270.608	+	468.707i	−0.552261	+	0.956545i
$491$	490.748	−	283.333i	0.999486	−	0.577053i	0.0913898	−	0.995815i	$-0.470869\pi$
$491$	490.748	−	283.333i	0.999486	−	0.577053i	0.908096	+	0.418762i	$0.137536\pi$
$492$	−36.2955	+	135.457i	−0.0737713	+	0.275318i
$493$		−	265.180i		−	0.537890i
$494$	173.961	−	53.3732i	0.352148	−	0.108043i
$495$	−441.636			−0.892194
$496$	63.1722	+	16.9269i	0.127363	+	0.0341269i
$497$	−152.893	−	264.818i	−0.307631	−	0.532833i
$498$	13.7979	+	7.96623i	0.0277067	+	0.0159965i
$499$	−409.292	+	409.292i	−0.820224	+	0.820224i	−0.986140	−	0.165916i	$-0.946942\pi$
$499$	−409.292	+	409.292i	−0.820224	+	0.820224i	0.165916	+	0.986140i	$0.446942\pi$
$500$	148.377	+	553.752i	0.296755	+	1.10750i
$501$	82.8290	−	22.1940i	0.165327	−	0.0442993i
$502$	−211.776	−	211.776i	−0.421865	−	0.421865i
$503$	−111.621	+	193.333i	−0.221910	+	0.384360i	−0.955388	−	0.295354i	$-0.904563\pi$
$503$	−111.621	+	193.333i	−0.221910	+	0.384360i	0.733478	+	0.679714i	$0.237896\pi$
$504$	−70.2295	+	40.5470i	−0.139344	+	0.0804504i
$505$	274.125	−	1023.05i	0.542822	−	2.02584i
$506$			630.097i			1.24525i
$507$	−263.345	−	127.799i	−0.519418	−	0.252069i
$508$	−54.0363			−0.106371
$509$	−414.332	−	111.020i	−0.814012	−	0.218114i	−0.172285	−	0.985047i	$-0.555115\pi$
$509$	−414.332	−	111.020i	−0.814012	−	0.218114i	−0.641727	+	0.766933i	$0.721782\pi$
$510$	−106.351	−	184.206i	−0.208532	−	0.361188i
$511$	−113.341	−	65.4375i	−0.221802	−	0.128058i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−13.3109	−	49.6769i	−0.0259472	−	0.0968361i
$514$	372.134	−	99.7130i	0.723996	−	0.193994i
$515$	−1177.23	−	1177.23i	−2.28588	−	2.28588i
$516$	61.8190	−	107.074i	0.119804	−	0.207507i
$517$	508.983	−	293.861i	0.984492	−	0.568397i
$518$	−73.7436	+	275.215i	−0.142362	+	0.531303i
$519$		−	291.720i		−	0.562081i
$520$	97.4906	+	317.755i	0.187482	+	0.611067i
$521$	−470.908			−0.903854			−0.451927	−	0.892055i	$-0.649263\pi$
$521$	−470.908			−0.903854			−0.451927	+	0.892055i	$0.649263\pi$
$522$	113.126	+	30.3120i	0.216716	+	0.0580689i
$523$	455.785	+	789.442i	0.871481	+	1.50945i	0.860464	+	0.509511i	$0.170174\pi$
$523$	455.785	+	789.442i	0.871481	+	1.50945i	0.0110172	+	0.999939i	$0.496493\pi$
$524$	−111.835	−	64.5682i	−0.213426	−	0.123222i
$525$	663.791	−	663.791i	1.26436	−	1.26436i
$526$	−86.5075	−	322.851i	−0.164463	−	0.613784i
$527$	151.714	−	40.6515i	0.287881	−	0.0771376i
$528$	79.7829	+	79.7829i	0.151104	+	0.151104i
$529$	109.737	−	190.070i	0.207443	−	0.359301i
$530$	432.539	−	249.726i	0.816110	−	0.471182i
$531$	37.0011	−	138.090i	0.0696819	−	0.260056i
$532$			189.183i			0.355607i
$533$	−18.8858	−	525.932i	−0.0354331	−	0.986739i
$534$	283.430			0.530768
$535$	62.4466	+	16.7325i	0.116723	+	0.0312758i
$536$	56.6973	+	98.2025i	0.105778	+	0.183214i
$537$	469.570	+	271.106i	0.874432	+	0.504854i
$538$	−466.361	+	466.361i	−0.866842	+	0.866842i
$539$	−178.450	−	665.986i	−0.331077	−	1.23559i
$540$	90.7391	−	24.3135i	0.168035	−	0.0450249i
$541$	−393.572	−	393.572i	−0.727490	−	0.727490i	0.242629	−	0.970119i	$-0.421990\pi$
$541$	−393.572	−	393.572i	−0.727490	−	0.727490i	−0.970119	+	0.242629i	$0.921990\pi$
$542$	−326.130	+	564.873i	−0.601716	+	1.04220i
$543$	−29.2193	+	16.8697i	−0.0538108	+	0.0310677i
$544$	−14.0647	+	52.4900i	−0.0258542	+	0.0964890i
$545$			103.244i			0.189438i
$546$	207.331	−	222.776i	0.379727	−	0.408015i
$547$	−388.679			−0.710565			−0.355283	−	0.934759i	$-0.615615\pi$
$547$	−388.679			−0.710565			−0.355283	+	0.934759i	$0.615615\pi$
$548$	394.424	+	105.686i	0.719751	+	0.192857i
$549$	−105.815	−	183.277i	−0.192741	−	0.333838i
$550$	−1131.13	−	653.059i	−2.05660	−	1.18738i
$551$	193.195	−	193.195i	0.350626	−	0.350626i
$552$	−34.6889	−	129.461i	−0.0628422	−	0.234530i
$553$	−518.382	+	138.900i	−0.937399	+	0.251175i
$554$	−24.5533	−	24.5533i	−0.0443200	−	0.0443200i
$555$	165.029	−	285.838i	0.297349	−	0.515024i
$556$	−110.178	+	63.6113i	−0.198162	+	0.114409i
$557$	183.042	−	683.123i	0.328622	−	1.22643i	−0.581999	−	0.813190i	$-0.697729\pi$
$557$	183.042	−	683.123i	0.328622	−	1.22643i	0.910621	−	0.413244i	$-0.135604\pi$
$558$			69.3679i			0.124315i
$559$	−103.928	+	452.197i	−0.185917	+	0.808939i
$560$	−345.558			−0.617069
$561$	261.738	+	70.1325i	0.466556	+	0.125013i
$562$	276.591	+	479.071i	0.492156	+	0.852439i
$563$	−514.657	−	297.138i	−0.914134	−	0.527776i	−0.0323751	−	0.999476i	$-0.510307\pi$
$563$	−514.657	−	297.138i	−0.914134	−	0.527776i	−0.881759	+	0.471700i	$0.843640\pi$
$564$	−88.3982	+	88.3982i	−0.156734	+	0.156734i
$565$	272.343	+	1016.40i	0.482023	+	1.79893i
$566$	535.087	−	143.376i	0.945383	−	0.253314i
$567$	−60.8205	−	60.8205i	−0.107267	−	0.107267i
$568$	45.2490	−	78.3735i	0.0796637	−	0.137982i
$569$	101.268	−	58.4673i	0.177976	−	0.102754i	−0.408365	−	0.912819i	$-0.633901\pi$
$569$	101.268	−	58.4673i	0.177976	−	0.102754i	0.586341	+	0.810064i	$0.300568\pi$
$570$	56.7205	−	211.684i	0.0995096	−	0.371375i
$571$			137.505i			0.240815i	0.992725	+	0.120408i	$0.0384201\pi$
$571$			137.505i			0.240815i	−0.992725	+	0.120408i	$0.961580\pi$
$572$	−374.059	−	198.417i	−0.653949	−	0.346883i
$573$	−247.599			−0.432109
$574$	528.503	+	141.612i	0.920736	+	0.246711i
$575$	775.750	+	1343.64i	1.34913	+	2.33676i
$576$	−20.7846	−	12.0000i	−0.0360844	−	0.0208333i
$577$	−617.016	+	617.016i	−1.06935	+	1.06935i	−0.0719422	+	0.997409i	$0.522920\pi$
$577$	−617.016	+	617.016i	−1.06935	+	1.06935i	−0.997409	+	0.0719422i	$0.977080\pi$
$578$	−72.0038	−	268.722i	−0.124574	−	0.464917i
$579$	−280.758	+	75.2289i	−0.484901	+	0.129929i
$580$	352.887	+	352.887i	0.608426	+	0.608426i
$581$	31.0814	−	53.8345i	0.0534963	−	0.0926583i
$582$	74.1136	−	42.7895i	0.127343	−	0.0735215i
$583$	−164.680	+	614.594i	−0.282470	+	1.05419i
$584$		−	38.7328i		−	0.0663233i
$585$	−298.783	+	187.111i	−0.510740	+	0.319847i
$586$	419.143			0.715261
$587$	373.261	+	100.015i	0.635878	+	0.170383i	0.562336	−	0.826909i	$-0.309903\pi$
$587$	373.261	+	100.015i	0.635878	+	0.170383i	0.0735425	+	0.997292i	$0.476570\pi$
$588$	73.3293	+	127.010i	0.124710	+	0.216003i
$589$	140.146	+	80.9136i	0.237940	+	0.137375i
$590$	430.761	−	430.761i	0.730103	−	0.730103i
$591$	76.3821	+	285.062i	0.129242	+	0.482338i
$592$	−81.4506	+	21.8246i	−0.137585	+	0.0368659i
$593$	536.353	+	536.353i	0.904473	+	0.904473i	0.995819	−	0.0913459i	$-0.0291169\pi$
$593$	536.353	+	536.353i	0.904473	+	0.904473i	−0.0913459	+	0.995819i	$0.529117\pi$
$594$	−59.8372	+	103.641i	−0.100736	+	0.174480i
$595$	−718.704	+	414.944i	−1.20791	+	0.697385i
$596$	−15.0219	+	56.0623i	−0.0252045	+	0.0940643i
$597$			280.117i			0.469208i
$598$	266.957	+	426.284i	0.446417	+	0.712850i
$599$	344.623			0.575331			0.287666	−	0.957731i	$-0.407121\pi$
$599$	344.623			0.575331			0.287666	+	0.957731i	$0.407121\pi$
$600$	268.357	+	71.9060i	0.447261	+	0.119843i
$601$	−445.870	−	772.269i	−0.741879	−	1.28497i	−0.951639	−	0.307220i	$-0.900601\pi$
$601$	−445.870	−	772.269i	−0.741879	−	1.28497i	0.209759	−	0.977753i	$-0.432732\pi$
$602$	−417.763	−	241.195i	−0.693958	−	0.400657i
$603$	−85.0459	+	85.0459i	−0.141038	+	0.141038i
$604$	23.1584	+	86.4284i	0.0383417	+	0.143093i
$605$	1259.25	−	337.415i	2.08141	−	0.557711i
$606$	−202.943	−	202.943i	−0.334889	−	0.334889i
$607$	−232.733	+	403.106i	−0.383416	+	0.664096i	−0.991548	−	0.129740i	$-0.958586\pi$
$607$	−232.733	+	403.106i	−0.383416	+	0.664096i	0.608132	+	0.793836i	$0.291919\pi$
$608$	−48.4881	+	27.9946i	−0.0797501	+	0.0460437i
$609$	118.266	−	441.376i	0.194198	−	0.724756i
$610$		−	901.799i		−	1.47836i
$611$	219.843	−	414.452i	0.359809	−	0.678317i
$612$	−57.6381			−0.0941798
$613$	851.290	+	228.103i	1.38873	+	0.372109i	0.874284	−	0.485415i	$-0.161332\pi$
$613$	851.290	+	228.103i	1.38873	+	0.372109i	0.514444	+	0.857524i	$0.327998\pi$
$614$	221.215	+	383.156i	0.360286	+	0.624033i
$615$	−548.903	−	316.910i	−0.892526	−	0.515300i
$616$	311.284	−	311.284i	0.505331	−	0.505331i
$617$	293.787	+	1096.43i	0.476154	+	1.77703i	0.616960	+	0.786995i	$0.288364\pi$
$617$	293.787	+	1096.43i	0.476154	+	1.77703i	−0.140805	+	0.990037i	$0.544969\pi$
$618$	−435.769	+	116.764i	−0.705129	+	0.188939i
$619$	69.6384	+	69.6384i	0.112501	+	0.112501i	0.761117	−	0.648615i	$-0.224651\pi$
$619$	69.6384	+	69.6384i	0.112501	+	0.112501i	−0.648615	+	0.761117i	$0.724651\pi$
$620$	−147.796	+	255.989i	−0.238380	+	0.412886i
$621$	123.112	−	71.0788i	0.198248	−	0.114459i
$622$	−4.59566	+	17.1512i	−0.00738852	+	0.0275743i
$623$		−	1105.84i		−	1.77503i
$624$	87.7782	+	20.1739i	0.140670	+	0.0323300i
$625$	−1173.32			−1.87731
$626$	807.260	+	216.305i	1.28955	+	0.345535i
$627$	139.593	+	241.782i	0.222637	+	0.385618i
$628$	419.888	+	242.423i	0.668612	+	0.386023i
$629$	−143.197	+	143.197i	−0.227658	+	0.227658i
$630$	−94.8624	−	354.031i	−0.150575	−	0.561954i
$631$	616.962	−	165.314i	0.977752	−	0.261988i	0.265655	−	0.964068i	$-0.414412\pi$
$631$	616.962	−	165.314i	0.977752	−	0.261988i	0.712098	+	0.702080i	$0.247745\pi$
$632$	−112.309	−	112.309i	−0.177704	−	0.177704i
$633$	−155.777	+	269.813i	−0.246093	+	0.426245i
$634$	94.7669	−	54.7137i	0.149475	−	0.0862992i
$635$	63.2108	−	235.906i	0.0995445	−	0.371505i
$636$		−	135.341i		−	0.212801i
$637$	−402.891	−	374.959i	−0.632481	−	0.588632i
$638$	−635.772			−0.996507
$639$	92.7169	+	24.8434i	0.145097	+	0.0388786i
$640$	−51.1345	−	88.5675i	−0.0798976	−	0.138387i
$641$	−792.951	−	457.811i	−1.23705	−	0.714213i	−0.268563	−	0.963262i	$-0.586549\pi$
$641$	−792.951	−	457.811i	−1.23705	−	0.714213i	−0.968491	+	0.249049i	$0.919882\pi$
$642$	12.3876	−	12.3876i	0.0192953	−	0.0192953i
$643$	109.397	+	408.276i	0.170136	+	0.634955i	0.997329	+	0.0730378i	$0.0232694\pi$
$643$	109.397	+	408.276i	0.170136	+	0.634955i	−0.827194	+	0.561917i	$0.810064\pi$
$644$	−505.109	+	135.343i	−0.784330	+	0.210161i
$645$	395.135	+	395.135i	0.612613	+	0.612613i
$646$	−67.2314	+	116.448i	−0.104073	+	0.180260i
$647$	557.382	−	321.805i	0.861487	−	0.497380i	−0.00302290	−	0.999995i	$-0.500962\pi$
$647$	557.382	−	321.805i	0.861487	−	0.497380i	0.864510	+	0.502616i	$0.167629\pi$
$648$	6.58846	−	24.5885i	0.0101674	−	0.0379452i
$649$			776.071i			1.19579i
$650$	−1041.94	+	37.4153i	−1.60298	+	0.0575619i
$651$	270.649			0.415743
$652$	−30.1624	−	8.08200i	−0.0462614	−	0.0123957i
$653$	149.123	+	258.289i	0.228366	+	0.395542i	0.957324	−	0.289016i	$-0.0933282\pi$
$653$	149.123	+	258.289i	0.228366	+	0.395542i	−0.728958	+	0.684559i	$0.759995\pi$
$654$	24.2288	+	13.9885i	0.0370471	+	0.0213892i
$655$	412.708	−	412.708i	0.630088	−	0.630088i
$656$	41.9104	+	156.412i	0.0638878	+	0.238433i
$657$	39.6825	−	10.6329i	0.0603995	−	0.0161840i
$658$	344.898	+	344.898i	0.524161	+	0.524161i
$659$	322.944	−	559.356i	0.490052	−	0.848794i	−0.509883	−	0.860244i	$-0.670311\pi$
$659$	322.944	−	559.356i	0.490052	−	0.848794i	0.999934	+	0.0114495i	$0.00364456\pi$
$660$	−441.636	+	254.979i	−0.669145	+	0.386331i
$661$	251.425	−	938.332i	0.380371	−	1.41956i	−0.464965	−	0.885329i	$-0.653933\pi$
$661$	251.425	−	938.332i	0.380371	−	1.41956i	0.845336	−	0.534235i	$-0.179400\pi$
$662$		−	28.9091i		−	0.0436693i
$663$	206.789	−	63.4450i	0.311899	−	0.0956938i
$664$	18.3972			0.0277067
$665$	−825.913	−	221.303i	−1.24197	−	0.332786i
$666$	−44.7195	−	77.4564i	−0.0671464	−	0.116301i
$667$	654.035	+	377.607i	0.980562	+	0.566128i
$668$	70.0153	−	70.0153i	0.104813	−	0.104813i
$669$	174.743	+	652.151i	0.261201	+	0.974814i
$670$	−495.045	+	132.647i	−0.738873	+	0.197981i
$671$	812.354	+	812.354i	1.21066	+	1.21066i
$672$	−46.8197	+	81.0940i	−0.0696721	+	0.120676i
$673$	−712.407	+	411.308i	−1.05855	+	0.611156i	−0.925032	−	0.379890i	$-0.875962\pi$
$673$	−712.407	+	411.308i	−1.05855	+	0.611156i	−0.133522	+	0.991046i	$0.542629\pi$
$674$	74.0566	−	276.383i	0.109876	−	0.410064i
$675$			294.676i			0.436557i
$676$	−337.129	+	24.2434i	−0.498712	+	0.0358631i
$677$	195.713			0.289089			0.144544	−	0.989498i	$-0.453828\pi$
$677$	195.713			0.289089			0.144544	+	0.989498i	$0.453828\pi$
$678$	275.423	+	73.7994i	0.406229	+	0.108849i
$679$	−166.949	−	289.165i	−0.245875	−	0.425868i
$680$	−212.702	−	122.804i	−0.312798	−	0.180594i
$681$	−163.289	+	163.289i	−0.239778	+	0.239778i
$682$	−97.4626	−	363.735i	−0.142907	−	0.533336i
$683$	−628.395	+	168.378i	−0.920052	+	0.246527i	−0.687607	−	0.726083i	$-0.741339\pi$
$683$	−628.395	+	168.378i	−0.920052	+	0.246527i	−0.232444	+	0.972610i	$0.574672\pi$
$684$	−41.9919	−	41.9919i	−0.0613917	−	0.0613917i
$685$	−922.780	+	1598.30i	−1.34712	+	2.33329i
$686$	−77.9936	+	45.0296i	−0.113693	+	0.0656408i
$687$	193.277	−	721.320i	0.281335	−	1.04996i
$688$		−	142.765i		−	0.207507i
$689$	148.977	+	485.566i	0.216222	+	0.704741i
$690$	605.763			0.877918
$691$	−303.752	−	81.3900i	−0.439583	−	0.117786i	0.0322384	−	0.999480i	$-0.489736\pi$
$691$	−303.752	−	81.3900i	−0.439583	−	0.117786i	−0.471821	+	0.881694i	$0.656403\pi$
$692$	−168.425	−	291.720i	−0.243388	−	0.421561i
$693$	404.370	+	233.463i	0.583506	+	0.336887i
$694$	−556.526	+	556.526i	−0.801911	+	0.801911i
$695$	−148.823	−	555.414i	−0.214134	−	0.799157i
$696$	130.627	−	35.0013i	0.187682	−	0.0502892i
$697$	274.985	+	274.985i	0.394526	+	0.394526i
$698$	327.786	−	567.742i	0.469608	−	0.813385i
$699$	66.2121	−	38.2276i	0.0947240	−	0.0546889i
$700$	280.551	−	1047.03i	0.400787	−	1.49576i
$701$			769.901i			1.09829i	0.835727	+	0.549145i	$0.185046\pi$
$701$			769.901i			1.09829i	−0.835727	+	0.549145i	$0.814954\pi$
$702$	3.42821	+	95.4686i	0.00488349	+	0.135995i
$703$	−208.651			−0.296800
$704$	125.846	+	33.7202i	0.178758	+	0.0478980i
$705$	−282.512	−	489.326i	−0.400727	−	0.694079i
$706$	−346.076	−	199.807i	−0.490192	−	0.283013i
$707$	−791.810	+	791.810i	−1.11996	+	1.11996i
$708$	−42.7252	−	159.453i	−0.0603463	−	0.225215i
$709$	918.547	−	246.124i	1.29555	−	0.347142i	0.455786	−	0.890089i	$-0.349358\pi$
$709$	918.547	−	246.124i	1.29555	−	0.347142i	0.839767	+	0.542947i	$0.182692\pi$
$710$	289.223	+	289.223i	0.407356	+	0.407356i
$711$	84.2315	−	145.893i	0.118469	−	0.205194i
$712$	283.430	−	163.639i	0.398076	−	0.229829i
$713$	−115.773	+	432.071i	−0.162374	+	0.605990i
$714$			224.883i			0.314962i
$715$	1303.80	−	1400.92i	1.82349	−	1.95933i
$716$	626.093			0.874432
$717$	−37.4893	−	10.0452i	−0.0522863	−	0.0140101i
$718$	−280.398	−	485.664i	−0.390527	−	0.676412i
$719$	−1165.21	−	672.733i	−1.62060	−	0.935651i	−0.986761	−	0.162183i	$-0.948146\pi$
$719$	−1165.21	−	672.733i	−1.62060	−	0.935651i	−0.633835	−	0.773468i	$-0.718520\pi$
$720$	76.7017	−	76.7017i	0.106530	−	0.106530i
$721$	455.571	+	1700.21i	0.631860	+	2.35813i
$722$	359.316	−	96.2785i	0.497668	−	0.133350i
$723$	−589.081	−	589.081i	−0.814773	−	0.814773i
$724$	−19.4795	+	33.7395i	−0.0269054	+	0.0466015i
$725$	−1355.74	+	782.736i	−1.86998	+	1.07964i
$726$	91.4327	−	341.231i	0.125940	−	0.470016i
$727$		−	681.807i		−	0.937837i	−0.883241	−	0.468918i	$-0.844644\pi$
$727$		−	681.807i		−	0.937837i	0.883241	−	0.468918i	$-0.155356\pi$
$728$	78.7114	−	342.479i	0.108120	−	0.470438i
$729$	27.0000			0.0370370
$730$	169.095	+	45.3090i	0.231637	+	0.0620671i
$731$	−171.431	−	296.927i	−0.234516	−	0.406193i
$732$	−211.630	−	122.185i	−0.289112	−	0.166919i
$733$	760.545	−	760.545i	1.03758	−	1.03758i	0.0383126	−	0.999266i	$-0.487802\pi$
$733$	760.545	−	760.545i	1.03758	−	1.03758i	0.999266	−	0.0383126i	$-0.0121983\pi$
$734$	−216.645	−	808.531i	−0.295157	−	1.10154i
$735$	−640.265	+	171.559i	−0.871109	+	0.233413i
$736$	−109.433	−	109.433i	−0.148686	−	0.148686i
$737$	326.454	−	565.434i	0.442949	−	0.767210i
$738$	−148.742	+	85.8761i	−0.201547	+	0.116363i
$739$	202.762	−	756.716i	0.274373	−	1.02397i	−0.681888	−	0.731457i	$-0.738841\pi$
$739$	202.762	−	756.716i	0.274373	−	1.02397i	0.956260	−	0.292517i	$-0.0944927\pi$
$740$		−	381.118i		−	0.515024i
$741$	196.877	+	104.432i	0.265691	+	0.140934i
$742$	−528.053			−0.711662
$743$	779.633	+	208.902i	1.04930	+	0.281160i	0.741964	−	0.670440i	$-0.233894\pi$
$743$	779.633	+	208.902i	1.04930	+	0.281160i	0.307340	+	0.951600i	$0.400561\pi$
$744$	40.0496	+	69.3679i	0.0538301	+	0.0932365i
$745$	−227.178	−	131.161i	−0.304937	−	0.176056i
$746$	511.886	−	511.886i	0.686174	−	0.686174i
$747$	5.05039	+	18.8483i	0.00676090	+	0.0252320i
$748$	302.229	−	80.9820i	0.404049	−	0.108265i
$749$	−48.3319	−	48.3319i	−0.0645286	−	0.0645286i
$750$	−351.065	+	608.062i	−0.468086	+	0.810749i
$751$	858.524	−	495.669i	1.14317	−	0.660012i	0.195959	−	0.980612i	$-0.437218\pi$
$751$	858.524	−	495.669i	1.14317	−	0.660012i	0.947215	+	0.320600i	$0.103885\pi$
$752$	−37.3615	+	139.435i	−0.0496828	+	0.185419i
$753$		−	366.807i		−	0.487127i
$754$	−430.123	+	269.361i	−0.570455	+	0.357243i
$755$	−404.410			−0.535642
$756$	−95.9353	−	25.7058i	−0.126898	−	0.0340023i
$757$	−370.164	−	641.143i	−0.488988	−	0.846952i	0.510932	−	0.859621i	$-0.329301\pi$
$757$	−370.164	−	641.143i	−0.488988	−	0.846952i	−0.999920	+	0.0126691i	$0.995967\pi$
$758$	250.656	+	144.716i	0.330681	+	0.190919i
$759$	−545.680	+	545.680i	−0.718946	+	0.718946i
$760$	−65.4952	−	244.431i	−0.0861778	−	0.321620i
$761$	762.920	−	204.424i	1.00252	−	0.268625i	0.280021	−	0.959994i	$-0.409659\pi$
$761$	762.920	−	204.424i	1.00252	−	0.268625i	0.722502	+	0.691368i	$0.242992\pi$
$762$	−46.7968	−	46.7968i	−0.0614132	−	0.0614132i
$763$	54.5781	−	94.5320i	0.0715309	−	0.123895i
$764$	−247.599	+	142.951i	−0.324082	+	0.187109i
$765$	67.4240	−	251.630i	0.0881359	−	0.328928i
$766$			464.422i			0.606295i
$767$	328.803	+	525.040i	0.428687	+	0.684538i
$768$	−27.7128			−0.0360844
$769$	12.3641	+	3.31296i	0.0160782	+	0.00430814i	0.266849	−	0.963738i	$-0.414017\pi$
$769$	12.3641	+	3.31296i	0.0160782	+	0.00430814i	−0.250771	+	0.968046i	$0.580684\pi$
$770$	994.834	+	1723.10i	1.29199	+	2.23780i
$771$	408.631	+	235.923i	0.530002	+	0.305997i
$772$	−237.325	+	237.325i	−0.307415	+	0.307415i
$773$	24.6452	+	91.9770i	0.0318825	+	0.118987i	0.980033	−	0.198834i	$-0.0637155\pi$
$773$	24.6452	+	91.9770i	0.0318825	+	0.118987i	−0.948151	+	0.317821i	$0.897049\pi$
$774$	146.265	−	39.1917i	0.188973	−	0.0506353i
$775$	−655.648	−	655.648i	−0.845997	−	0.845997i
$776$	49.4091	−	85.5790i	0.0636715	−	0.110282i
$777$	−302.207	+	174.479i	−0.388941	+	0.224555i
$778$	−144.208	+	538.192i	−0.185358	+	0.691764i
$779$			400.678i			0.514349i
$780$	−190.754	+	359.613i	−0.244557	+	0.461042i
$781$	−521.072			−0.667186
$782$	−359.009	−	96.1962i	−0.459091	−	0.123013i
$783$	71.7189	+	124.221i	0.0915951	+	0.158647i
$784$	146.659	+	84.6734i	0.187064	+	0.108002i
$785$	−1549.52	+	1549.52i	−1.97391	+	1.97391i
$786$	−40.9346	−	152.770i	−0.0520797	−	0.194364i
$787$	−869.425	+	232.962i	−1.10473	+	0.296012i	−0.764690	−	0.644398i	$-0.777108\pi$
$787$	−869.425	+	232.962i	−1.10473	+	0.296012i	−0.340042	+	0.940410i	$0.610441\pi$
$788$	240.963	+	240.963i	0.305790	+	0.305790i
$789$	204.679	−	354.514i	0.259416	−	0.449321i
$790$	621.681	−	358.928i	0.786938	−	0.454339i
$791$	287.939	−	1074.60i	0.364018	−	1.35854i
$792$			138.188i			0.174480i
$793$	893.762	+	205.412i	1.12706	+	0.259032i
$794$	−169.800			−0.213854
$795$	590.859	+	158.320i	0.743218	+	0.199145i
$796$	161.726	+	280.117i	0.203173	+	0.351906i
$797$	−559.840	−	323.224i	−0.702435	−	0.405551i	0.105819	−	0.994385i	$-0.466254\pi$
$797$	−559.840	−	323.224i	−0.702435	−	0.405551i	−0.808254	+	0.588835i	$0.799587\pi$
$798$	−163.837	+	163.837i	−0.205310	+	0.205310i
$799$	89.7268	+	334.865i	0.112299	+	0.419105i
$800$	309.872	−	83.0299i	0.387340	−	0.103787i
$801$	245.458	+	245.458i	0.306439	+	0.306439i
$802$	234.950	−	406.945i	0.292955	−	0.507413i
$803$	−193.139	+	111.509i	−0.240521	+	0.138865i
$804$	−35.9446	+	134.147i	−0.0447072	+	0.166850i
$805$		−	2363.47i		−	2.93599i
$806$	−220.043	−	204.788i	−0.273006	−	0.254079i
$807$	−807.761			−1.00094
$808$	−320.112	−	85.7738i	−0.396178	−	0.106156i
$809$	572.693	+	991.934i	0.707903	+	1.22612i	0.965634	+	0.259907i	$0.0836918\pi$
$809$	572.693	+	991.934i	0.707903	+	1.22612i	−0.257731	+	0.966217i	$0.582975\pi$
$810$	99.6385	+	57.5263i	0.123010	+	0.0710201i
$811$	394.302	−	394.302i	0.486192	−	0.486192i	−0.420910	−	0.907102i	$-0.638289\pi$
$811$	394.302	−	394.302i	0.486192	−	0.486192i	0.907102	+	0.420910i	$0.138289\pi$
$812$	−136.562	−	509.657i	−0.168180	−	0.627657i
$813$	−771.631	+	206.758i	−0.949116	+	0.254315i
$814$	343.316	+	343.316i	0.421765	+	0.421765i
$815$	70.5670	−	122.226i	0.0865853	−	0.149970i
$816$	−57.6381	+	33.2773i	−0.0706349	+	0.0407811i
$817$	91.4296	−	341.220i	0.111909	−	0.417650i
$818$		−	622.032i		−	0.760431i
$819$	372.484	−	13.3756i	0.454803	−	0.0163317i
$820$	−731.871			−0.892526
$821$	−684.846	−	183.504i	−0.834161	−	0.223513i	−0.183633	−	0.982995i	$-0.558786\pi$
$821$	−684.846	−	183.504i	−0.834161	−	0.223513i	−0.650528	+	0.759482i	$0.725452\pi$
$822$	250.055	+	433.107i	0.304203	+	0.526895i
$823$	479.938	+	277.093i	0.583157	+	0.336686i	0.762387	−	0.647121i	$-0.224027\pi$
$823$	479.938	+	277.093i	0.583157	+	0.336686i	−0.179230	+	0.983807i	$0.557361\pi$
$824$	−368.356	+	368.356i	−0.447034	+	0.447034i
$825$	−414.023	−	1545.15i	−0.501846	−	1.87291i
$826$	−622.126	+	166.698i	−0.753179	+	0.201814i
$827$	140.395	+	140.395i	0.169764	+	0.169764i	0.786876	−	0.617112i	$-0.211697\pi$
$827$	140.395	+	140.395i	0.169764	+	0.169764i	−0.617112	+	0.786876i	$0.711697\pi$
$828$	82.0748	−	142.158i	0.0991241	−	0.171688i
$829$	446.523	−	257.800i	0.538628	−	0.310977i	−0.205894	−	0.978574i	$-0.566010\pi$
$829$	446.523	−	257.800i	0.538628	−	0.310977i	0.744523	+	0.667597i	$0.232677\pi$
$830$	−21.5208	+	80.3165i	−0.0259286	+	0.0967669i
$831$		−	42.5275i		−	0.0511763i
$832$	99.4256	−	30.5048i	0.119502	−	0.0366645i
$833$	406.701			0.488236
$834$	−150.506	−	40.3280i	−0.180463	−	0.0483549i
$835$	223.762	+	387.568i	0.267979	+	0.464153i
$836$	279.186	+	161.188i	0.333955	+	0.192809i
$837$	−60.0744	+	60.0744i	−0.0717735	+	0.0717735i
$838$	45.7359	+	170.689i	0.0545775	+	0.203686i
$839$	−840.624	+	225.244i	−1.00194	+	0.268468i	−0.722256	−	0.691626i	$-0.756895\pi$
$839$	−840.624	+	225.244i	−1.00194	+	0.268468i	−0.279679	+	0.960094i	$0.590228\pi$
$840$	−299.262	−	299.262i	−0.356265	−	0.356265i
$841$	39.4922	−	68.4025i	0.0469586	−	0.0813348i
$842$	16.3907	−	9.46318i	0.0194664	−	0.0112389i
$843$	−175.352	+	654.423i	−0.208009	+	0.776302i
$844$			359.751i			0.426245i
$845$	288.529	−	1500.16i	0.341454	−	1.77534i
$846$	−153.110			−0.180981
$847$	−1331.36	−	356.737i	−1.57186	−	0.421177i
$848$	−78.1394	−	135.341i	−0.0921456	−	0.159601i
$849$	587.566	+	339.231i	0.692068	+	0.399566i
$850$	544.780	−	544.780i	0.640918	−	0.640918i
$851$	−149.271	−	557.087i	−0.175406	−	0.654626i
$852$	107.060	−	28.6867i	0.125658	−	0.0336698i
$853$	−42.9256	−	42.9256i	−0.0503230	−	0.0503230i	0.681497	−	0.731820i	$-0.261329\pi$
$853$	−42.9256	−	42.9256i	−0.0503230	−	0.0503230i	−0.731820	+	0.681497i	$0.761329\pi$
$854$	−476.720	+	825.703i	−0.558220	+	0.966866i
$855$	232.445	−	134.202i	0.271865	−	0.156962i
$856$	5.23561	−	19.5396i	0.00611637	−	0.0228266i
$857$			236.541i			0.276011i	0.990431	+	0.138005i	$0.0440692\pi$
$857$			236.541i			0.276011i	−0.990431	+	0.138005i	$0.955931\pi$
$858$	−152.110	−	495.779i	−0.177285	−	0.577831i
$859$	−646.957			−0.753151			−0.376575	−	0.926386i	$-0.622898\pi$
$859$	−646.957			−0.753151			−0.376575	+	0.926386i	$0.622898\pi$
$860$	623.267	+	167.004i	0.724729	+	0.194191i
$861$	335.057	+	580.336i	0.389149	+	0.674026i
$862$	885.461	+	511.221i	1.02722	+	0.593064i
$863$	−344.605	+	344.605i	−0.399310	+	0.399310i	−0.877990	−	0.478680i	$-0.841116\pi$
$863$	−344.605	+	344.605i	−0.399310	+	0.399310i	0.478680	+	0.877990i	$0.341116\pi$
$864$	−7.60770	−	28.3923i	−0.00880520	−	0.0328615i
$865$	1470.58	−	394.040i	1.70009	−	0.455538i
$866$	40.9607	+	40.9607i	0.0472987	+	0.0472987i
$867$	170.363	−	295.077i	0.196497	−	0.340343i
$868$	270.649	−	156.259i	0.311807	−	0.180022i
$869$	−236.692	+	883.347i	−0.272373	+	1.01651i
$870$			611.218i			0.702550i
$871$	−18.7033	−	520.848i	−0.0214733	−	0.597988i
$872$	32.3051			0.0370471
$873$	101.241	+	27.1275i	0.115969	+	0.0310738i
$874$	−191.471	−	331.637i	−0.219074	−	0.379448i
$875$	2372.44	+	1369.73i	2.71136	+	1.56540i
$876$	33.5436	−	33.5436i	0.0382918	−	0.0382918i
$877$	227.669	+	849.673i	0.259600	+	0.968840i	0.965473	+	0.260502i	$0.0838881\pi$
$877$	227.669	+	849.673i	0.259600	+	0.968840i	−0.705873	+	0.708338i	$0.749445\pi$
$878$	−908.892	+	243.537i	−1.03518	+	0.277377i
$879$	362.988	+	362.988i	0.412956	+	0.412956i
$880$	−294.424	+	509.957i	−0.334573	+	0.579497i
$881$	35.9052	−	20.7299i	0.0407551	−	0.0235299i	−0.479484	−	0.877551i	$-0.659176\pi$
$881$	35.9052	−	20.7299i	0.0407551	−	0.0235299i	0.520239	+	0.854021i	$0.325843\pi$
$882$	−46.4889	+	173.499i	−0.0527085	+	0.196711i
$883$		−	28.0736i		−	0.0317934i	−0.999874	−	0.0158967i	$-0.994940\pi$
$883$		−	28.0736i		−	0.0317934i	0.999874	−	0.0158967i	$-0.00506029\pi$
$884$	170.159	−	182.835i	0.192487	−	0.206826i
$885$	746.099			0.843050
$886$	365.518	+	97.9402i	0.412548	+	0.110542i
$887$	−68.9319	−	119.393i	−0.0777135	−	0.134604i	0.824550	−	0.565790i	$-0.191429\pi$
$887$	−68.9319	−	119.393i	−0.0777135	−	0.134604i	−0.902263	+	0.431186i	$0.858095\pi$
$888$	−89.4389	−	51.6376i	−0.100720	−	0.0581505i
$889$	−182.584	+	182.584i	−0.205382	+	0.205382i
$890$	382.843	+	1428.79i	0.430161	+	1.60538i
$891$	−141.576	+	37.9353i	−0.158896	+	0.0425760i
$892$	551.263	+	551.263i	0.618008	+	0.618008i
$893$	−178.594	+	309.334i	−0.199993	+	0.346399i
$894$	−61.5607	+	35.5421i	−0.0688598	+	0.0397563i
$895$	−732.393	+	2733.33i	−0.818316	+	3.05400i
$896$			108.125i			0.120676i
$897$	−137.981	+	600.365i	−0.153825	+	0.669303i
$898$	−796.391			−0.886850
$899$	−435.962	−	116.816i	−0.484941	−	0.129939i
$900$	170.131	+	294.676i	0.189035	+	0.327418i
$901$	−325.034	−	187.659i	−0.360748	−	0.208278i
$902$	659.280	−	659.280i	0.730909	−	0.730909i
$903$	−152.912	−	570.675i	−0.169338	−	0.631976i
$904$	318.031	−	85.2162i	0.351804	−	0.0942657i
$905$	−124.509	−	124.509i	−0.137579	−	0.137579i
$906$	−54.7934	+	94.9049i	−0.0604784	+	0.104752i
$907$	776.354	−	448.228i	0.855958	−	0.494187i	−0.00669893	−	0.999978i	$-0.502132\pi$
$907$	776.354	−	448.228i	0.855958	−	0.494187i	0.862657	+	0.505790i	$0.168799\pi$
$908$	−69.0140	+	257.564i	−0.0760066	+	0.283661i
$909$		−	351.507i		−	0.386697i
$910$	1403.08	+	744.255i	1.54185	+	0.817863i
$911$	−318.659			−0.349791			−0.174895	−	0.984587i	$-0.555959\pi$
$911$	−318.659			−0.349791			−0.174895	+	0.984587i	$0.555959\pi$
$912$	−66.2359	−	17.7479i	−0.0726271	−	0.0194604i
$913$	−52.9641	−	91.7365i	−0.0580111	−	0.100478i
$914$	−816.022	−	471.131i	−0.892803	−	0.515460i
$915$	780.981	−	780.981i	0.853531	−	0.853531i
$916$	−223.177	−	832.909i	−0.243643	−	0.909289i
$917$	−596.053	+	159.712i	−0.650004	+	0.174168i
$918$	−49.9160	−	49.9160i	−0.0543748	−	0.0543748i
$919$	50.2641	−	87.0600i	0.0546944	−	0.0947334i	−0.837382	−	0.546618i	$-0.815915\pi$
$919$	50.2641	−	87.0600i	0.0546944	−	0.0947334i	0.892076	+	0.451885i	$0.149248\pi$
$920$	605.763	−	349.738i	0.658438	−	0.380150i
$921$	−140.245	+	523.401i	−0.152275	+	0.568297i
$922$		−	506.616i		−	0.549475i
$923$	−352.525	+	220.766i	−0.381934	+	0.239183i
$924$	539.160			0.583506
$925$	1154.78	+	309.421i	1.24841	+	0.334509i
$926$	−630.292	−	1091.70i	−0.680660	−	1.17894i
$927$	−478.508	−	276.267i	−0.516190	−	0.298022i
$928$	110.419	−	110.419i	0.118985	−	0.118985i
$929$	−287.719	−	1073.78i	−0.309709	−	1.15585i	−0.928816	−	0.370542i	$-0.879172\pi$
$929$	−287.719	−	1073.78i	−0.309709	−	1.15585i	0.619107	−	0.785306i	$-0.287495\pi$
$930$	−349.688	+	93.6986i	−0.376009	+	0.100751i
$931$	296.300	+	296.300i	0.318259	+	0.318259i
$932$	44.1414	−	76.4552i	0.0473620	−	0.0820334i
$933$	−18.8334	+	10.8734i	−0.0201858	+	0.0116543i
$934$	−155.657	+	580.921i	−0.166657	+	0.621972i
$935$			1414.17i			1.51248i
$936$	58.5470	+	93.4893i	0.0625502	+	0.0998817i
$937$	−99.5793			−0.106275			−0.0531373	−	0.998587i	$-0.516922\pi$
$937$	−99.5793			−0.106275			−0.0531373	+	0.998587i	$0.516922\pi$
$938$	523.394	+	140.243i	0.557989	+	0.149513i
$939$	511.783	+	886.433i	0.545029	+	0.944018i
$940$	−565.025	−	326.217i	−0.601090	−	0.347040i
$941$	795.092	−	795.092i	0.844943	−	0.844943i	−0.144554	−	0.989497i	$-0.546175\pi$
$941$	795.092	−	795.092i	0.844943	−	0.844943i	0.989497	+	0.144554i	$0.0461746\pi$
$942$	153.690	+	573.578i	0.163153	+	0.608894i
$943$	−1069.79	+	286.649i	−1.13445	+	0.303976i
$944$	−134.785	−	134.785i	−0.142781	−	0.142781i
$945$	224.447	−	388.753i	0.237510	−	0.411379i
$946$	−711.888	+	411.009i	−0.752524	+	0.434470i
$947$	94.5423	−	352.837i	0.0998335	−	0.372584i	−0.897874	−	0.440252i	$-0.854889\pi$
$947$	94.5423	−	352.837i	0.0998335	−	0.372584i	0.997708	+	0.0676681i	$0.0215559\pi$
$948$		−	194.524i		−	0.205194i
$949$	−83.4217	+	157.268i	−0.0879049	+	0.165720i
$950$	793.793			0.835572
$951$	129.454	+	34.6871i	0.136124	+	0.0364743i
$952$	129.836	+	224.883i	0.136383	+	0.236221i
$953$	−262.250	−	151.410i	−0.275184	−	0.158877i	0.356057	−	0.934464i	$-0.384121\pi$
$953$	−262.250	−	151.410i	−0.275184	−	0.158877i	−0.631241	+	0.775587i	$0.717454\pi$
$954$	117.209	−	117.209i	0.122861	−	0.122861i
$955$	−334.443	−	1248.16i	−0.350203	−	1.30697i
$956$	−43.2889	+	11.5992i	−0.0452813	+	0.0121331i
$957$	−550.594	−	550.594i	−0.575334	−	0.575334i
$958$	−194.811	+	337.423i	−0.203352	+	0.352216i
$959$	1689.83	−	975.623i	1.76207	−	1.01733i
$960$	32.4180	−	120.985i	0.0337687	−	0.126027i
$961$			693.672i			0.721823i
$962$	377.721	+	86.8111i	0.392642	+	0.0902403i
$963$	21.4559			0.0222803
$964$	−929.186	−	248.975i	−0.963886	−	0.258273i
$965$	−758.467	−	1313.70i	−0.785976	−	1.36135i
$966$	−554.648	−	320.226i	−0.574170	−	0.331497i
$967$	228.726	−	228.726i	0.236532	−	0.236532i	−0.578881	−	0.815412i	$-0.696510\pi$
$967$	228.726	−	228.726i	0.236532	−	0.236532i	0.815412	+	0.578881i	$0.196510\pi$
$968$	−105.577	−	394.020i	−0.109068	−	0.407046i
$969$	−159.071	+	42.6230i	−0.164160	+	0.0439866i
$970$	315.813	+	315.813i	0.325581	+	0.325581i
$971$	297.774	−	515.760i	0.306668	−	0.531164i	−0.670964	−	0.741490i	$-0.734119\pi$
$971$	297.774	−	515.760i	0.306668	−	0.531164i	0.977631	+	0.210326i	$0.0674526\pi$
$972$	27.0000	−	15.5885i	0.0277778	−	0.0160375i
$973$	−157.345	+	587.220i	−0.161711	+	0.603515i
$974$		−	905.415i		−	0.929585i
$975$	−934.747	−	869.942i	−0.958715	−	0.892248i
$976$	−282.173			−0.289112
$977$	922.516	+	247.187i	0.944233	+	0.253007i	0.697914	−	0.716182i	$-0.254112\pi$
$977$	922.516	+	247.187i	0.944233	+	0.253007i	0.246320	+	0.969189i	$0.420779\pi$
$978$	−19.1222	−	33.1207i	−0.0195524	−	0.0338657i
$979$	−1631.95	−	942.204i	−1.66695	−	0.962415i
$980$	−541.216	+	541.216i	−0.552261	+	0.552261i
$981$	8.86836	+	33.0972i	0.00904012	+	0.0337382i
$982$	774.081	−	207.414i	0.788270	−	0.211216i
$983$	265.546	+	265.546i	0.270138	+	0.270138i	0.829156	−	0.559018i	$-0.188822\pi$
$983$	265.546	+	265.546i	0.270138	+	0.270138i	−0.559018	+	0.829156i	$0.688822\pi$
$984$	−99.1611	+	171.752i	−0.100774	+	0.174545i
$985$	−1333.84	+	770.093i	−1.35415	+	0.781821i
$986$	97.0625	−	362.242i	0.0984406	−	0.367385i
$987$			597.381i			0.605249i
$988$	257.171	−	9.23485i	0.260295	−	0.00934701i
$989$	976.450			0.987310
$990$	−603.286	−	161.650i	−0.609380	−	0.163283i
$991$	−72.5775	−	125.708i	−0.0732366	−	0.126850i	0.827081	−	0.562082i	$-0.189999\pi$
$991$	−72.5775	−	125.708i	−0.0732366	−	0.126850i	−0.900318	+	0.435233i	$0.856666\pi$
$992$	80.0992	+	46.2453i	0.0807451	+	0.0466182i
$993$	25.0360	−	25.0360i	0.0252125	−	0.0252125i
$994$	−111.925	−	417.710i	−0.112601	−	0.420232i
$995$	−1412.09	+	378.368i	−1.41919	+	0.380269i
$996$	15.9325	+	15.9325i	0.0159965	+	0.0159965i
$997$	−292.161	+	506.038i	−0.293040	+	0.507561i	−0.974527	−	0.224270i	$-0.928000\pi$
$997$	−292.161	+	506.038i	−0.293040	+	0.507561i	0.681487	+	0.731830i	$0.261334\pi$
$998$	−708.914	+	409.292i	−0.710335	+	0.410112i
$999$	28.3510	−	105.807i	0.0283794	−	0.105913i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.3.l.c.67.1	yes	8
3.2	odd	2		234.3.bb.d.145.2		8
13.2	odd	12		1014.3.f.j.775.2		8
13.3	even	3		1014.3.f.h.577.1		8
13.7	odd	12	inner	78.3.l.c.7.1	✓	8
13.10	even	6		1014.3.f.j.577.2		8
13.11	odd	12		1014.3.f.h.775.1		8
39.20	even	12		234.3.bb.d.163.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.c.7.1	✓	8	13.7	odd	12	inner
78.3.l.c.67.1	yes	8	1.1	even	1	trivial
234.3.bb.d.145.2		8	3.2	odd	2
234.3.bb.d.163.2		8	39.20	even	12
1014.3.f.h.577.1		8	13.3	even	3
1014.3.f.h.775.1		8	13.11	odd	12
1014.3.f.j.577.2		8	13.10	even	6
1014.3.f.j.775.2		8	13.2	odd	12

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	78.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-6.39181 + 6.39181i) q^{5} +(0.633975 + 2.36603i) q^{6} +(9.23137 - 2.47354i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.36603 + 0.366025i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-6.39181 + 6.39181i) q^{5} +(0.633975 + 2.36603i) q^{6} +(9.23137 - 2.47354i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(-11.0709 + 6.39181i) q^{10} +(4.21503 - 15.7307i) q^{11} +3.46410i q^{12} +(-3.81310 - 12.4282i) q^{13} +13.5157 q^{14} +(-15.1232 - 4.05225i) q^{15} +(2.00000 + 3.46410i) q^{16} +(8.31934 + 4.80317i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(2.56168 + 9.56033i) q^{19} +(-17.4627 + 4.67913i) q^{20} +(11.7049 + 11.7049i) q^{21} +(11.5157 - 19.9457i) q^{22} +(-23.6929 + 13.6791i) q^{23} +(-1.26795 + 4.73205i) q^{24} -56.7105i q^{25} +(-0.659759 - 18.3729i) q^{26} -5.19615 q^{27} +(18.4627 + 4.94708i) q^{28} +(-13.8023 - 23.9063i) q^{29} +(-19.1754 - 11.0709i) q^{30} +(11.5613 - 11.5613i) q^{31} +(1.46410 + 5.46410i) q^{32} +(27.2464 - 7.30064i) q^{33} +(9.60634 + 9.60634i) q^{34} +(-43.1948 + 74.8156i) q^{35} +(-5.19615 + 3.00000i) q^{36} +(-5.45615 + 20.3626i) q^{37} +13.9973i q^{38} +(15.3401 - 16.4828i) q^{39} -25.5672 q^{40} +(39.1030 + 10.4776i) q^{41} +(11.7049 + 20.2735i) q^{42} +(-30.9095 - 17.8456i) q^{43} +(23.0313 - 23.0313i) q^{44} +(-7.01869 - 26.1941i) q^{45} +(-37.3721 + 10.0138i) q^{46} +(25.5184 + 25.5184i) q^{47} +(-3.46410 + 6.00000i) q^{48} +(36.6646 - 21.1683i) q^{49} +(20.7575 - 77.4679i) q^{50} +16.6387i q^{51} +(5.82371 - 25.3394i) q^{52} -39.0697 q^{53} +(-7.09808 - 1.90192i) q^{54} +(73.6060 + 127.489i) q^{55} +(23.4098 + 13.5157i) q^{56} +(-12.1220 + 12.1220i) q^{57} +(-10.1040 - 37.7086i) q^{58} +(-46.0300 + 12.3337i) q^{59} +(-22.1419 - 22.1419i) q^{60} +(-35.2717 + 61.0923i) q^{61} +(20.0248 - 11.5613i) q^{62} +(-7.42062 + 27.6941i) q^{63} +8.00000i q^{64} +(103.811 + 55.0661i) q^{65} +39.8915 q^{66} +(38.7250 + 10.3763i) q^{67} +(9.60634 + 16.6387i) q^{68} +(-41.0374 - 23.6929i) q^{69} +(-86.3896 + 86.3896i) q^{70} +(-8.28114 - 30.9056i) q^{71} +(-8.19615 + 2.19615i) q^{72} +(-9.68320 - 9.68320i) q^{73} +(-14.9065 + 25.8188i) q^{74} +(85.0657 - 49.1127i) q^{75} +(-5.12337 + 19.1207i) q^{76} -155.642i q^{77} +(26.9880 - 16.9011i) q^{78} -56.1543 q^{79} +(-34.9255 - 9.35826i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(49.5806 + 28.6254i) q^{82} +(4.59931 - 4.59931i) q^{83} +(8.56859 + 31.9784i) q^{84} +(-83.8766 + 22.4747i) q^{85} +(-35.6912 - 35.6912i) q^{86} +(23.9063 - 41.4069i) q^{87} +(39.8915 - 23.0313i) q^{88} +(29.9479 - 111.767i) q^{89} -38.3509i q^{90} +(-65.9418 - 105.298i) q^{91} -54.7165 q^{92} +(27.3544 + 7.32958i) q^{93} +(25.5184 + 44.1991i) q^{94} +(-77.4816 - 44.7340i) q^{95} +(-6.92820 + 6.92820i) q^{96} +(-9.04249 - 33.7470i) q^{97} +(57.8330 - 15.4963i) q^{98} +(34.5470 + 34.5470i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 6 q^{5} + 12 q^{6} + 10 q^{7} + 16 q^{8} - 12 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - 6 * q^5 + 12 * q^6 + 10 * q^7 + 16 * q^8 - 12 * q^9	\( 8 q + 4 q^{2} - 6 q^{5} + 12 q^{6} + 10 q^{7} + 16 q^{8} - 12 q^{9} - 6 q^{10} + 24 q^{11} + 4 q^{14} - 12 q^{15} + 16 q^{16} - 84 q^{17} - 24 q^{18} + 10 q^{19} - 12 q^{20} + 18 q^{21} - 12 q^{22} - 12 q^{23} - 24 q^{24} + 26 q^{26} + 20 q^{28} + 36 q^{29} - 18 q^{30} - 94 q^{31} - 16 q^{32} + 60 q^{34} - 204 q^{35} + 140 q^{37} + 66 q^{39} - 24 q^{40} + 72 q^{41} + 18 q^{42} - 222 q^{43} - 24 q^{44} - 84 q^{46} + 300 q^{47} + 42 q^{49} - 62 q^{50} + 44 q^{52} + 84 q^{53} - 36 q^{54} + 396 q^{55} + 36 q^{56} + 24 q^{57} - 66 q^{58} - 60 q^{59} - 12 q^{60} - 90 q^{61} + 198 q^{62} - 24 q^{63} - 108 q^{65} + 72 q^{66} + 304 q^{67} + 60 q^{68} - 216 q^{69} - 408 q^{70} - 192 q^{71} - 24 q^{72} + 16 q^{73} - 46 q^{74} + 312 q^{75} - 20 q^{76} + 114 q^{78} - 96 q^{79} - 24 q^{80} - 36 q^{81} + 114 q^{82} - 12 q^{84} - 390 q^{85} + 168 q^{86} + 30 q^{87} + 72 q^{88} + 354 q^{89} - 218 q^{91} - 288 q^{92} - 42 q^{93} + 300 q^{94} - 576 q^{95} - 460 q^{97} + 58 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 6 * q^5 + 12 * q^6 + 10 * q^7 + 16 * q^8 - 12 * q^9 - 6 * q^10 + 24 * q^11 + 4 * q^14 - 12 * q^15 + 16 * q^16 - 84 * q^17 - 24 * q^18 + 10 * q^19 - 12 * q^20 + 18 * q^21 - 12 * q^22 - 12 * q^23 - 24 * q^24 + 26 * q^26 + 20 * q^28 + 36 * q^29 - 18 * q^30 - 94 * q^31 - 16 * q^32 + 60 * q^34 - 204 * q^35 + 140 * q^37 + 66 * q^39 - 24 * q^40 + 72 * q^41 + 18 * q^42 - 222 * q^43 - 24 * q^44 - 84 * q^46 + 300 * q^47 + 42 * q^49 - 62 * q^50 + 44 * q^52 + 84 * q^53 - 36 * q^54 + 396 * q^55 + 36 * q^56 + 24 * q^57 - 66 * q^58 - 60 * q^59 - 12 * q^60 - 90 * q^61 + 198 * q^62 - 24 * q^63 - 108 * q^65 + 72 * q^66 + 304 * q^67 + 60 * q^68 - 216 * q^69 - 408 * q^70 - 192 * q^71 - 24 * q^72 + 16 * q^73 - 46 * q^74 + 312 * q^75 - 20 * q^76 + 114 * q^78 - 96 * q^79 - 24 * q^80 - 36 * q^81 + 114 * q^82 - 12 * q^84 - 390 * q^85 + 168 * q^86 + 30 * q^87 + 72 * q^88 + 354 * q^89 - 218 * q^91 - 288 * q^92 - 42 * q^93 + 300 * q^94 - 576 * q^95 - 460 * q^97 + 58 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more