LMFDB - Embedded newform 170.3.e.b.157.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,3,Mod(13,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("170.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	170.e (of order $4$, 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:	$4.63216449413$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 80 x^{14} + 2532 x^{12} + 40532 x^{10} + 346464 x^{8} + 1518752 x^{6} + 2895224 x^{4} + \cdots + 148996 $ x^16 + 80x^14 + 2532x^12 + 40532x^10 + 346464x^8 + 1518752x^6 + 2895224x^4 + 1253728*x^2 + 148996
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			157.8
Root			$-4.26845i$ of defining polynomial
Character	$\chi$	$=$	170.157
Dual form			170.3.e.b.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +4.26845i q^{3} -2.00000i q^{4} +(-4.54937 + 2.07442i) q^{5} +(4.26845 + 4.26845i) q^{6} +3.42439i q^{7} +(-2.00000 - 2.00000i) q^{8} -9.21970 q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +4.26845i q^{3} -2.00000i q^{4} +(-4.54937 + 2.07442i) q^{5} +(4.26845 + 4.26845i) q^{6} +3.42439i q^{7} +(-2.00000 - 2.00000i) q^{8} -9.21970 q^{9} +(-2.47495 + 6.62379i) q^{10} +(2.24732 + 2.24732i) q^{11} +8.53691 q^{12} +(-15.8980 + 15.8980i) q^{13} +(3.42439 + 3.42439i) q^{14} +(-8.85457 - 19.4188i) q^{15} -4.00000 q^{16} +(14.7881 + 8.38518i) q^{17} +(-9.21970 + 9.21970i) q^{18} -9.07667 q^{19} +(4.14884 + 9.09874i) q^{20} -14.6169 q^{21} +4.49463 q^{22} -3.13728 q^{23} +(8.53691 - 8.53691i) q^{24} +(16.3935 - 18.8746i) q^{25} +31.7959i q^{26} -0.937764i q^{27} +6.84878 q^{28} +(1.52106 + 1.52106i) q^{29} +(-28.2734 - 10.5642i) q^{30} +(41.5231 - 41.5231i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-9.59256 + 9.59256i) q^{33} +(23.1733 - 6.40295i) q^{34} +(-7.10364 - 15.5788i) q^{35} +18.4394i q^{36} +39.7435 q^{37} +(-9.07667 + 9.07667i) q^{38} +(-67.8597 - 67.8597i) q^{39} +(13.2476 + 4.94990i) q^{40} +(35.4105 + 35.4105i) q^{41} +(-14.6169 + 14.6169i) q^{42} +(7.50319 + 7.50319i) q^{43} +(4.49463 - 4.49463i) q^{44} +(41.9438 - 19.1255i) q^{45} +(-3.13728 + 3.13728i) q^{46} +(28.1845 + 28.1845i) q^{47} -17.0738i q^{48} +37.2735 q^{49} +(-2.48109 - 35.2682i) q^{50} +(-35.7917 + 63.1224i) q^{51} +(31.7959 + 31.7959i) q^{52} +(0.379900 + 0.379900i) q^{53} +(-0.937764 - 0.937764i) q^{54} +(-14.8858 - 5.56199i) q^{55} +(6.84878 - 6.84878i) q^{56} -38.7433i q^{57} +3.04212 q^{58} -58.3149 q^{59} +(-38.8376 + 17.7091i) q^{60} +(-59.4346 - 59.4346i) q^{61} -83.0461i q^{62} -31.5719i q^{63} +8.00000i q^{64} +(39.3466 - 105.305i) q^{65} +19.1851i q^{66} +(-63.7959 - 63.7959i) q^{67} +(16.7704 - 29.5763i) q^{68} -13.3913i q^{69} +(-22.6825 - 8.47519i) q^{70} +(-39.7153 + 39.7153i) q^{71} +(18.4394 + 18.4394i) q^{72} -3.56790i q^{73} +(39.7435 - 39.7435i) q^{74} +(80.5655 + 69.9751i) q^{75} +18.1533i q^{76} +(-7.69569 + 7.69569i) q^{77} -135.719 q^{78} +(-42.6309 + 42.6309i) q^{79} +(18.1975 - 8.29769i) q^{80} -78.9745 q^{81} +70.8210 q^{82} +(42.2940 + 42.2940i) q^{83} +29.2337i q^{84} +(-84.6711 - 7.47045i) q^{85} +15.0064 q^{86} +(-6.49257 + 6.49257i) q^{87} -8.98926i q^{88} +167.220i q^{89} +(22.8183 - 61.0694i) q^{90} +(-54.4408 - 54.4408i) q^{91} +6.27457i q^{92} +(177.239 + 177.239i) q^{93} +56.3689 q^{94} +(41.2931 - 18.8288i) q^{95} +(-17.0738 - 17.0738i) q^{96} +158.089 q^{97} +(37.2735 - 37.2735i) q^{98} +(-20.7196 - 20.7196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9	$ 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9} - 4 q^{10} + 20 q^{11} + 4 q^{13} - 12 q^{14} + 12 q^{15} - 64 q^{16} + 36 q^{17} - 16 q^{18} - 16 q^{19} - 4 q^{20} + 40 q^{22} + 16 q^{23} + 44 q^{25} - 24 q^{28} - 20 q^{29} + 12 q^{30} + 92 q^{31} - 64 q^{32} - 60 q^{33} + 24 q^{34} - 124 q^{35} + 32 q^{37} - 16 q^{38} - 140 q^{39} - 60 q^{41} + 52 q^{43} + 40 q^{44} + 198 q^{45} + 16 q^{46} + 112 q^{47} + 136 q^{49} - 4 q^{50} - 140 q^{51} - 8 q^{52} + 48 q^{53} + 108 q^{54} + 40 q^{55} - 24 q^{56} - 40 q^{58} + 76 q^{61} - 40 q^{65} + 116 q^{67} - 24 q^{68} - 124 q^{70} - 268 q^{71} + 32 q^{72} + 32 q^{74} + 136 q^{75} - 116 q^{77} - 280 q^{78} - 88 q^{79} + 8 q^{80} - 352 q^{81} - 120 q^{82} - 160 q^{83} + 310 q^{85} + 104 q^{86} + 236 q^{87} + 260 q^{90} - 168 q^{91} + 48 q^{93} + 224 q^{94} + 264 q^{95} - 256 q^{97} + 136 q^{98} - 348 q^{99}+O(q^{100}) $ 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9 - 4 * q^10 + 20 * q^11 + 4 * q^13 - 12 * q^14 + 12 * q^15 - 64 * q^16 + 36 * q^17 - 16 * q^18 - 16 * q^19 - 4 * q^20 + 40 * q^22 + 16 * q^23 + 44 * q^25 - 24 * q^28 - 20 * q^29 + 12 * q^30 + 92 * q^31 - 64 * q^32 - 60 * q^33 + 24 * q^34 - 124 * q^35 + 32 * q^37 - 16 * q^38 - 140 * q^39 - 60 * q^41 + 52 * q^43 + 40 * q^44 + 198 * q^45 + 16 * q^46 + 112 * q^47 + 136 * q^49 - 4 * q^50 - 140 * q^51 - 8 * q^52 + 48 * q^53 + 108 * q^54 + 40 * q^55 - 24 * q^56 - 40 * q^58 + 76 * q^61 - 40 * q^65 + 116 * q^67 - 24 * q^68 - 124 * q^70 - 268 * q^71 + 32 * q^72 + 32 * q^74 + 136 * q^75 - 116 * q^77 - 280 * q^78 - 88 * q^79 + 8 * q^80 - 352 * q^81 - 120 * q^82 - 160 * q^83 + 310 * q^85 + 104 * q^86 + 236 * q^87 + 260 * q^90 - 168 * q^91 + 48 * q^93 + 224 * q^94 + 264 * q^95 - 256 * q^97 + 136 * q^98 - 348 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$			4.26845i			1.42282i	0.702778	+	0.711409i	$0.251943\pi$
$3$			4.26845i			1.42282i	−0.702778	+	0.711409i	$0.748057\pi$
$4$		−	2.00000i		−	0.500000i
$5$	−4.54937	+	2.07442i	−0.909874	+	0.414884i
$5$	−4.54937	+	2.07442i	−0.909874	+	0.414884i
$6$	4.26845	+	4.26845i	0.711409	+	0.711409i
$7$			3.42439i			0.489199i	0.969624	+	0.244599i	$0.0786565\pi$
$7$			3.42439i			0.489199i	−0.969624	+	0.244599i	$0.921344\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	−9.21970			−1.02441
$10$	−2.47495	+	6.62379i	−0.247495	+	0.662379i
$11$	2.24732	+	2.24732i	0.204301	+	0.204301i	0.801840	−	0.597539i	$-0.203855\pi$
$11$	2.24732	+	2.24732i	0.204301	+	0.204301i	−0.597539	+	0.801840i	$0.703855\pi$
$12$	8.53691			0.711409
$13$	−15.8980	+	15.8980i	−1.22292	+	1.22292i	−0.256331	+	0.966589i	$0.582514\pi$
$13$	−15.8980	+	15.8980i	−1.22292	+	1.22292i	−0.966589	+	0.256331i	$0.917486\pi$
$14$	3.42439	+	3.42439i	0.244599	+	0.244599i
$15$	−8.85457	−	19.4188i	−0.590305	−	1.29459i
$16$	−4.00000			−0.250000
$17$	14.7881	+	8.38518i	0.869890	+	0.493246i
$17$	14.7881	+	8.38518i	0.869890	+	0.493246i
$18$	−9.21970	+	9.21970i	−0.512205	+	0.512205i
$19$	−9.07667			−0.477719			−0.238860	−	0.971054i	$-0.576774\pi$
$19$	−9.07667			−0.477719			−0.238860	+	0.971054i	$0.576774\pi$
$20$	4.14884	+	9.09874i	0.207442	+	0.454937i
$21$	−14.6169			−0.696041
$22$	4.49463			0.204301
$23$	−3.13728			−0.136404			−0.0682018	−	0.997672i	$-0.521726\pi$
$23$	−3.13728			−0.136404			−0.0682018	+	0.997672i	$0.521726\pi$
$24$	8.53691	−	8.53691i	0.355704	−	0.355704i
$25$	16.3935	−	18.8746i	0.655742	−	0.754985i
$26$			31.7959i			1.22292i
$27$		−	0.937764i		−	0.0347320i
$28$	6.84878			0.244599
$29$	1.52106	+	1.52106i	0.0524503	+	0.0524503i	0.732845	−	0.680395i	$-0.238192\pi$
$29$	1.52106	+	1.52106i	0.0524503	+	0.0524503i	−0.680395	+	0.732845i	$0.738192\pi$
$30$	−28.2734	−	10.5642i	−0.942445	−	0.352140i
$31$	41.5231	−	41.5231i	1.33945	−	1.33945i	0.442866	−	0.896588i	$-0.353962\pi$
$31$	41.5231	−	41.5231i	1.33945	−	1.33945i	0.896588	−	0.442866i	$-0.146038\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	−9.59256	+	9.59256i	−0.290684	+	0.290684i
$34$	23.1733	−	6.40295i	0.681568	−	0.188322i
$35$	−7.10364	−	15.5788i	−0.202961	−	0.445109i
$36$			18.4394i			0.512205i
$37$	39.7435			1.07415			0.537075	−	0.843535i	$-0.319529\pi$
$37$	39.7435			1.07415			0.537075	+	0.843535i	$0.319529\pi$
$38$	−9.07667	+	9.07667i	−0.238860	+	0.238860i
$39$	−67.8597	−	67.8597i	−1.73999	−	1.73999i
$40$	13.2476	+	4.94990i	0.331190	+	0.123747i
$41$	35.4105	+	35.4105i	0.863671	+	0.863671i	0.991762	−	0.128091i	$-0.0408850\pi$
$41$	35.4105	+	35.4105i	0.863671	+	0.863671i	−0.128091	+	0.991762i	$0.540885\pi$
$42$	−14.6169	+	14.6169i	−0.348020	+	0.348020i
$43$	7.50319	+	7.50319i	0.174493	+	0.174493i	0.788950	−	0.614457i	$-0.210625\pi$
$43$	7.50319	+	7.50319i	0.174493	+	0.174493i	−0.614457	+	0.788950i	$0.710625\pi$
$44$	4.49463	−	4.49463i	0.102151	−	0.102151i
$45$	41.9438	−	19.1255i	0.932085	−	0.425012i
$46$	−3.13728	+	3.13728i	−0.0682018	+	0.0682018i
$47$	28.1845	+	28.1845i	0.599670	+	0.599670i	0.940225	−	0.340555i	$-0.110615\pi$
$47$	28.1845	+	28.1845i	0.599670	+	0.599670i	−0.340555	+	0.940225i	$0.610615\pi$
$48$		−	17.0738i		−	0.355704i
$49$	37.2735			0.760684
$50$	−2.48109	−	35.2682i	−0.0496217	−	0.705364i
$51$	−35.7917	+	63.1224i	−0.701799	+	1.23770i
$52$	31.7959	+	31.7959i	0.611460	+	0.611460i
$53$	0.379900	+	0.379900i	0.00716792	+	0.00716792i	0.710682	−	0.703514i	$-0.248387\pi$
$53$	0.379900	+	0.379900i	0.00716792	+	0.00716792i	−0.703514	+	0.710682i	$0.748387\pi$
$54$	−0.937764	−	0.937764i	−0.0173660	−	0.0173660i
$55$	−14.8858	−	5.56199i	−0.270650	−	0.101127i
$56$	6.84878	−	6.84878i	0.122300	−	0.122300i
$57$		−	38.7433i		−	0.679707i
$58$	3.04212			0.0524503
$59$	−58.3149			−0.988388			−0.494194	−	0.869352i	$-0.664537\pi$
$59$	−58.3149			−0.988388			−0.494194	+	0.869352i	$0.664537\pi$
$60$	−38.8376	+	17.7091i	−0.647293	+	0.295152i
$61$	−59.4346	−	59.4346i	−0.974337	−	0.974337i	0.0253419	−	0.999679i	$-0.491933\pi$
$61$	−59.4346	−	59.4346i	−0.974337	−	0.974337i	−0.999679	+	0.0253419i	$0.991933\pi$
$62$		−	83.0461i		−	1.33945i
$63$		−	31.5719i		−	0.501141i
$64$			8.00000i			0.125000i
$65$	39.3466	−	105.305i	0.605333	−	1.62007i
$66$			19.1851i			0.290684i
$67$	−63.7959	−	63.7959i	−0.952178	−	0.952178i	0.0467296	−	0.998908i	$-0.485120\pi$
$67$	−63.7959	−	63.7959i	−0.952178	−	0.952178i	−0.998908	+	0.0467296i	$0.985120\pi$
$68$	16.7704	−	29.5763i	0.246623	−	0.434945i
$69$		−	13.3913i		−	0.194077i
$70$	−22.6825	−	8.47519i	−0.324035	−	0.121074i
$71$	−39.7153	+	39.7153i	−0.559371	+	0.559371i	−0.929128	−	0.369757i	$-0.879441\pi$
$71$	−39.7153	+	39.7153i	−0.559371	+	0.559371i	0.369757	+	0.929128i	$0.379441\pi$
$72$	18.4394	+	18.4394i	0.256103	+	0.256103i
$73$		−	3.56790i		−	0.0488754i	−0.999701	−	0.0244377i	$-0.992220\pi$
$73$		−	3.56790i		−	0.0488754i	0.999701	−	0.0244377i	$-0.00777953\pi$
$74$	39.7435	−	39.7435i	0.537075	−	0.537075i
$75$	80.5655	+	69.9751i	1.07421	+	0.933001i
$76$			18.1533i			0.238860i
$77$	−7.69569	+	7.69569i	−0.0999440	+	0.0999440i
$78$	−135.719			−1.73999
$79$	−42.6309	+	42.6309i	−0.539631	+	0.539631i	−0.923421	−	0.383789i	$-0.874619\pi$
$79$	−42.6309	+	42.6309i	−0.539631	+	0.539631i	0.383789	+	0.923421i	$0.374619\pi$
$80$	18.1975	−	8.29769i	0.227469	−	0.103721i
$81$	−78.9745			−0.974993
$82$	70.8210			0.863671
$83$	42.2940	+	42.2940i	0.509566	+	0.509566i	0.914393	−	0.404827i	$-0.132668\pi$
$83$	42.2940	+	42.2940i	0.509566	+	0.509566i	−0.404827	+	0.914393i	$0.632668\pi$
$84$			29.2337i			0.348020i
$85$	−84.6711	−	7.47045i	−0.996130	−	0.0878877i
$86$	15.0064			0.174493
$87$	−6.49257	+	6.49257i	−0.0746273	+	0.0746273i
$88$		−	8.98926i		−	0.102151i
$89$			167.220i			1.87887i	0.342724	+	0.939436i	$0.388650\pi$
$89$			167.220i			1.87887i	−0.342724	+	0.939436i	$0.611350\pi$
$90$	22.8183	−	61.0694i	0.253536	−	0.678548i
$91$	−54.4408	−	54.4408i	−0.598251	−	0.598251i
$92$			6.27457i			0.0682018i
$93$	177.239	+	177.239i	1.90580	+	1.90580i
$94$	56.3689			0.599670
$95$	41.2931	−	18.8288i	0.434664	−	0.198198i
$96$	−17.0738	−	17.0738i	−0.177852	−	0.177852i
$97$	158.089			1.62979			0.814894	−	0.579610i	$-0.196795\pi$
$97$	158.089			1.62979			0.814894	+	0.579610i	$0.196795\pi$
$98$	37.2735	−	37.2735i	0.380342	−	0.380342i
$99$	−20.7196	−	20.7196i	−0.209289	−	0.209289i
$100$	−37.7493	−	32.7871i	−0.377493	−	0.327871i
$101$	−54.6804			−0.541390			−0.270695	−	0.962665i	$-0.587253\pi$
$101$	−54.6804			−0.541390			−0.270695	+	0.962665i	$0.587253\pi$
$102$	27.3307	+	98.9142i	0.267948	+	0.969747i
$103$	15.0256	−	15.0256i	0.145879	−	0.145879i	−0.630395	−	0.776274i	$-0.717107\pi$
$103$	15.0256	−	15.0256i	0.145879	−	0.145879i	0.776274	+	0.630395i	$0.217107\pi$
$104$	63.5918			0.611460
$105$	66.4975	−	30.3215i	0.633310	−	0.288777i
$106$	0.759800			0.00716792
$107$	19.2375			0.179790			0.0898949	−	0.995951i	$-0.471347\pi$
$107$	19.2375			0.179790			0.0898949	+	0.995951i	$0.471347\pi$
$108$	−1.87553			−0.0173660
$109$	−30.6515	+	30.6515i	−0.281206	+	0.281206i	−0.833590	−	0.552384i	$-0.813718\pi$
$109$	−30.6515	+	30.6515i	−0.281206	+	0.281206i	0.552384	+	0.833590i	$0.313718\pi$
$110$	−20.4477	+	9.32376i	−0.185889	+	0.0847615i
$111$			169.643i			1.52832i
$112$		−	13.6976i		−	0.122300i
$113$	146.103			1.29295			0.646474	−	0.762936i	$-0.276243\pi$
$113$	146.103			1.29295			0.646474	+	0.762936i	$0.276243\pi$
$114$	−38.7433	−	38.7433i	−0.339854	−	0.339854i
$115$	14.2727	−	6.50805i	0.124110	−	0.0565917i
$116$	3.04212	−	3.04212i	0.0262252	−	0.0262252i
$117$	146.574	−	146.574i	1.25277	−	1.25277i
$118$	−58.3149	+	58.3149i	−0.494194	+	0.494194i
$119$	−28.7141	+	50.6404i	−0.241295	+	0.425549i
$120$	−21.1284	+	56.5467i	−0.176070	+	0.471223i
$121$		−	110.899i		−	0.916522i
$122$	−118.869			−0.974337
$123$	−151.148	+	151.148i	−1.22885	+	1.22885i
$124$	−83.0461	−	83.0461i	−0.669727	−	0.669727i
$125$	−35.4264	+	119.875i	−0.283411	+	0.958999i
$126$	−31.5719	−	31.5719i	−0.250570	−	0.250570i
$127$	−80.2658	+	80.2658i	−0.632014	+	0.632014i	−0.948573	−	0.316559i	$-0.897473\pi$
$127$	−80.2658	+	80.2658i	−0.632014	+	0.632014i	0.316559	+	0.948573i	$0.397473\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$	−32.0270	+	32.0270i	−0.248271	+	0.248271i
$130$	−65.9582	−	144.651i	−0.507370	−	1.11270i
$131$	58.8060	−	58.8060i	0.448901	−	0.448901i	−0.446088	−	0.894989i	$-0.647183\pi$
$131$	58.8060	−	58.8060i	0.448901	−	0.448901i	0.894989	+	0.446088i	$0.147183\pi$
$132$	19.1851	+	19.1851i	0.145342	+	0.145342i
$133$		−	31.0821i		−	0.233700i
$134$	−127.592			−0.952178
$135$	1.94532	+	4.26624i	0.0144098	+	0.0316017i
$136$	−12.8059	−	46.3466i	−0.0941611	−	0.340784i
$137$	14.3489	+	14.3489i	0.104736	+	0.104736i	0.757533	−	0.652797i	$-0.226404\pi$
$137$	14.3489	+	14.3489i	0.104736	+	0.104736i	−0.652797	+	0.757533i	$0.726404\pi$
$138$	−13.3913	−	13.3913i	−0.0970387	−	0.0970387i
$139$	131.110	+	131.110i	0.943236	+	0.943236i	0.998473	−	0.0552371i	$-0.0175915\pi$
$139$	131.110	+	131.110i	0.943236	+	0.943236i	−0.0552371	+	0.998473i	$0.517591\pi$
$140$	−31.1577	+	14.2073i	−0.222555	+	0.101481i
$141$	−120.304	+	120.304i	−0.853220	+	0.853220i
$142$			79.4307i			0.559371i
$143$	−71.4554			−0.499688
$144$	36.8788			0.256103
$145$	−10.0752	−	3.76454i	−0.0694840	−	0.0259624i
$146$	−3.56790	−	3.56790i	−0.0244377	−	0.0244377i
$147$			159.100i			1.08232i
$148$		−	79.4871i		−	0.537075i
$149$		−	118.596i		−	0.795946i	−0.917397	−	0.397973i	$-0.869714\pi$
$149$		−	118.596i		−	0.795946i	0.917397	−	0.397973i	$-0.130286\pi$
$150$	150.541	−	10.5904i	1.00360	−	0.0706027i
$151$		−	262.580i		−	1.73894i	−0.493986	−	0.869470i	$-0.664461\pi$
$151$		−	262.580i		−	1.73894i	0.493986	−	0.869470i	$-0.335539\pi$
$152$	18.1533	+	18.1533i	0.119430	+	0.119430i
$153$	−136.342	−	77.3088i	−0.891125	−	0.505286i
$154$			15.3914i			0.0999440i
$155$	−102.767	+	275.040i	−0.663016	+	1.77445i
$156$	−135.719	+	135.719i	−0.869996	+	0.869996i
$157$	−54.8608	−	54.8608i	−0.349432	−	0.349432i	0.510466	−	0.859898i	$-0.329473\pi$
$157$	−54.8608	−	54.8608i	−0.349432	−	0.349432i	−0.859898	+	0.510466i	$0.829473\pi$
$158$			85.2617i			0.539631i
$159$	−1.62159	+	1.62159i	−0.0101987	+	0.0101987i
$160$	9.89979	−	26.4952i	0.0618737	−	0.165595i
$161$		−	10.7433i		−	0.0667285i
$162$	−78.9745	+	78.9745i	−0.487497	+	0.487497i
$163$	−261.591			−1.60485			−0.802427	−	0.596750i	$-0.796459\pi$
$163$	−261.591			−1.60485			−0.802427	+	0.596750i	$0.796459\pi$
$164$	70.8210	−	70.8210i	0.431836	−	0.431836i
$165$	23.7411	−	63.5391i	0.143885	−	0.385086i
$166$	84.5880			0.509566
$167$	−136.137			−0.815192			−0.407596	−	0.913162i	$-0.633633\pi$
$167$	−136.137			−0.815192			−0.407596	+	0.913162i	$0.633633\pi$
$168$	29.2337	+	29.2337i	0.174010	+	0.174010i
$169$		−	336.490i		−	1.99107i
$170$	−92.1415	+	77.2006i	−0.542009	+	0.454121i
$171$	83.6841			0.489381
$172$	15.0064	−	15.0064i	0.0872464	−	0.0872464i
$173$		−	74.4455i		−	0.430321i	−0.976579	−	0.215161i	$-0.930973\pi$
$173$		−	74.4455i		−	0.430321i	0.976579	−	0.215161i	$-0.0690275\pi$
$174$			12.9851i			0.0746273i
$175$	64.6341	+	56.1379i	0.369338	+	0.320788i
$176$	−8.98926	−	8.98926i	−0.0510753	−	0.0510753i
$177$		−	248.915i		−	1.40630i
$178$	167.220	+	167.220i	0.939436	+	0.939436i
$179$	255.927			1.42976			0.714881	−	0.699246i	$-0.246481\pi$
$179$	255.927			1.42976			0.714881	+	0.699246i	$0.246481\pi$
$180$	−38.2511	−	83.8876i	−0.212506	−	0.466042i
$181$	184.276	+	184.276i	1.01810	+	1.01810i	0.999833	+	0.0182673i	$0.00581499\pi$
$181$	184.276	+	184.276i	1.01810	+	1.01810i	0.0182673	+	0.999833i	$0.494185\pi$
$182$	−108.882			−0.598251
$183$	253.694	−	253.694i	1.38630	−	1.38630i
$184$	6.27457	+	6.27457i	0.0341009	+	0.0341009i
$185$	−180.808	+	82.4449i	−0.977341	+	0.445648i
$186$	354.479			1.90580
$187$	14.3895	+	52.0777i	0.0769490	+	0.278491i
$188$	56.3689	−	56.3689i	0.299835	−	0.299835i
$189$	3.21127			0.0169909
$190$	22.4643	−	60.1219i	0.118233	−	0.316431i
$191$	−148.464			−0.777301			−0.388650	−	0.921385i	$-0.627059\pi$
$191$	−148.464			−0.777301			−0.388650	+	0.921385i	$0.627059\pi$
$192$	−34.1476			−0.177852
$193$	369.174			1.91282			0.956409	−	0.292031i	$-0.0943310\pi$
$193$	369.174			1.91282			0.956409	+	0.292031i	$0.0943310\pi$
$194$	158.089	−	158.089i	0.814894	−	0.814894i
$195$	449.489	+	167.949i	2.30507	+	0.861278i
$196$		−	74.5471i		−	0.380342i
$197$			17.2775i			0.0877029i	0.999038	+	0.0438515i	$0.0139628\pi$
$197$			17.2775i			0.0877029i	−0.999038	+	0.0438515i	$0.986037\pi$
$198$	−41.4391			−0.209289
$199$	−216.111	−	216.111i	−1.08598	−	1.08598i	−0.995938	−	0.0900451i	$-0.971299\pi$
$199$	−216.111	−	216.111i	−1.08598	−	1.08598i	−0.0900451	−	0.995938i	$-0.528701\pi$
$200$	−70.5364	+	4.96217i	−0.352682	+	0.0248109i
$201$	272.310	−	272.310i	1.35478	−	1.35478i
$202$	−54.6804	+	54.6804i	−0.270695	+	0.270695i
$203$	−5.20871	+	5.20871i	−0.0256586	+	0.0256586i
$204$	126.245	+	71.5835i	0.618848	+	0.350899i
$205$	−234.552	−	87.6392i	−1.14416	−	0.427508i
$206$		−	30.0512i		−	0.145879i
$207$	28.9248			0.139733
$208$	63.5918	−	63.5918i	0.305730	−	0.305730i
$209$	−20.3981	−	20.3981i	−0.0975987	−	0.0975987i
$210$	36.1760	−	96.8190i	0.172267	−	0.461043i
$211$	−44.6333	−	44.6333i	−0.211532	−	0.211532i	0.593386	−	0.804918i	$-0.297791\pi$
$211$	−44.6333	−	44.6333i	−0.211532	−	0.211532i	−0.804918	+	0.593386i	$0.797791\pi$
$212$	0.759800	−	0.759800i	0.00358396	−	0.00358396i
$213$	−169.523	−	169.523i	−0.795883	−	0.795883i
$214$	19.2375	−	19.2375i	0.0898949	−	0.0898949i
$215$	−49.6996	−	18.5700i	−0.231161	−	0.0863721i
$216$	−1.87553	+	1.87553i	−0.00868300	+	0.00868300i
$217$	142.191	+	142.191i	0.655259	+	0.655259i
$218$			61.3030i			0.281206i
$219$	15.2294			0.0695408
$220$	−11.1240	+	29.7715i	−0.0505635	+	0.135325i
$221$	−368.408	+	101.794i	−1.66701	+	0.460606i
$222$	169.643	+	169.643i	0.764159	+	0.764159i
$223$	−88.5056	−	88.5056i	−0.396886	−	0.396886i	0.480247	−	0.877133i	$-0.340547\pi$
$223$	−88.5056	−	88.5056i	−0.396886	−	0.396886i	−0.877133	+	0.480247i	$0.840547\pi$
$224$	−13.6976	−	13.6976i	−0.0611499	−	0.0611499i
$225$	−151.144	+	174.018i	−0.671749	+	0.773415i
$226$	146.103	−	146.103i	0.646474	−	0.646474i
$227$		−	29.8311i		−	0.131414i	−0.997839	−	0.0657072i	$-0.979070\pi$
$227$		−	29.8311i		−	0.131414i	0.997839	−	0.0657072i	$-0.0209303\pi$
$228$	−77.4866			−0.339854
$229$	34.7033			0.151543			0.0757714	−	0.997125i	$-0.475858\pi$
$229$	34.7033			0.151543			0.0757714	+	0.997125i	$0.475858\pi$
$230$	7.76461	−	20.7807i	0.0337592	−	0.0903509i
$231$	−32.8487	−	32.8487i	−0.142202	−	0.142202i
$232$		−	6.08424i		−	0.0262252i
$233$			392.306i			1.68371i	0.539700	+	0.841857i	$0.318538\pi$
$233$			392.306i			1.68371i	−0.539700	+	0.841857i	$0.681462\pi$
$234$		−	293.149i		−	1.25277i
$235$	−186.688	−	69.7551i	−0.794417	−	0.296830i
$236$			116.630i			0.494194i
$237$	−181.968	−	181.968i	−0.767797	−	0.767797i
$238$	21.9262	+	79.3545i	0.0921270	+	0.333422i
$239$			180.766i			0.756343i	0.925736	+	0.378172i	$0.123447\pi$
$239$			180.766i			0.756343i	−0.925736	+	0.378172i	$0.876553\pi$
$240$	35.4183	+	77.6751i	0.147576	+	0.323646i
$241$	154.216	−	154.216i	0.639901	−	0.639901i	−0.310630	−	0.950531i	$-0.600540\pi$
$241$	154.216	−	154.216i	0.639901	−	0.639901i	0.950531	+	0.310630i	$0.100540\pi$
$242$	−110.899	−	110.899i	−0.458261	−	0.458261i
$243$		−	345.539i		−	1.42197i
$244$	−118.869	+	118.869i	−0.487168	+	0.487168i
$245$	−169.571	+	77.3211i	−0.692127	+	0.315596i
$246$			302.296i			1.22885i
$247$	144.300	−	144.300i	0.584212	−	0.584212i
$248$	−166.092			−0.669727
$249$	−180.530	+	180.530i	−0.725020	+	0.725020i
$250$	84.4485	+	155.301i	0.337794	+	0.621205i
$251$	472.857			1.88389			0.941946	−	0.335765i	$-0.108995\pi$
$251$	472.857			1.88389			0.941946	+	0.335765i	$0.108995\pi$
$252$	−63.1437			−0.250570
$253$	−7.05046	−	7.05046i	−0.0278674	−	0.0278674i
$254$			160.532i			0.632014i
$255$	31.8873	−	361.415i	0.125048	−	1.41731i
$256$	16.0000			0.0625000
$257$	173.073	−	173.073i	0.673434	−	0.673434i	−0.285072	−	0.958506i	$-0.592018\pi$
$257$	173.073	−	173.073i	0.673434	−	0.673434i	0.958506	+	0.285072i	$0.0920175\pi$
$258$			64.0540i			0.248271i
$259$			136.097i			0.525473i
$260$	−210.610	−	78.6932i	−0.810037	−	0.302666i
$261$	−14.0237	−	14.0237i	−0.0537307	−	0.0537307i
$262$		−	117.612i		−	0.448901i
$263$	−258.005	−	258.005i	−0.981006	−	0.981006i	0.0188169	−	0.999823i	$-0.494010\pi$
$263$	−258.005	−	258.005i	−0.981006	−	0.981006i	−0.999823	+	0.0188169i	$0.994010\pi$
$264$	38.3702			0.145342
$265$	−2.51638	−	0.940233i	−0.00949577	−	0.00354805i
$266$	−31.0821	−	31.0821i	−0.116850	−	0.116850i
$267$	−713.769			−2.67329
$268$	−127.592	+	127.592i	−0.476089	+	0.476089i
$269$	8.95236	+	8.95236i	0.0332801	+	0.0332801i	0.723551	−	0.690271i	$-0.242509\pi$
$269$	8.95236	+	8.95236i	0.0332801	+	0.0332801i	−0.690271	+	0.723551i	$0.742509\pi$
$270$	6.21155	+	2.32092i	0.0230058	+	0.00859599i
$271$	−34.3025			−0.126577			−0.0632887	−	0.997995i	$-0.520159\pi$
$271$	−34.3025			−0.126577			−0.0632887	+	0.997995i	$0.520159\pi$
$272$	−59.1525	−	33.5407i	−0.217473	−	0.123311i
$273$	232.378	−	232.378i	0.851202	−	0.851202i
$274$	28.6978			0.104736
$275$	79.2587	−	5.57578i	0.288213	−	0.0202756i
$276$	−26.7827			−0.0970387
$277$	353.035			1.27449			0.637247	−	0.770659i	$-0.280073\pi$
$277$	353.035			1.27449			0.637247	+	0.770659i	$0.280073\pi$
$278$	262.220			0.943236
$279$	−382.830	+	382.830i	−1.37215	+	1.37215i
$280$	−16.9504	+	45.3649i	−0.0605371	+	0.162018i
$281$		−	169.438i		−	0.602984i	−0.953469	−	0.301492i	$-0.902515\pi$
$281$		−	169.438i		−	0.602984i	0.953469	−	0.301492i	$-0.0974846\pi$
$282$			240.608i			0.853220i
$283$	80.6930			0.285134			0.142567	−	0.989785i	$-0.454464\pi$
$283$	80.6930			0.285134			0.142567	+	0.989785i	$0.454464\pi$
$284$	79.4307	+	79.4307i	0.279686	+	0.279686i
$285$	80.3700	+	176.258i	0.282000	+	0.618448i
$286$	−71.4554	+	71.4554i	−0.249844	+	0.249844i
$287$	−121.259	+	121.259i	−0.422507	+	0.422507i
$288$	36.8788	−	36.8788i	0.128051	−	0.128051i
$289$	148.378	+	248.002i	0.513417	+	0.858139i
$290$	−13.8397	+	6.31064i	−0.0477232	+	0.0217608i
$291$			674.798i			2.31889i
$292$	−7.13581			−0.0244377
$293$	−235.170	+	235.170i	−0.802627	+	0.802627i	−0.983505	−	0.180878i	$-0.942106\pi$
$293$	−235.170	+	235.170i	−0.802627	+	0.802627i	0.180878	+	0.983505i	$0.442106\pi$
$294$	159.100	+	159.100i	0.541158	+	0.541158i
$295$	265.296	−	120.970i	0.899309	−	0.410067i
$296$	−79.4871	−	79.4871i	−0.268537	−	0.268537i
$297$	2.10745	−	2.10745i	0.00709579	−	0.00709579i
$298$	−118.596	−	118.596i	−0.397973	−	0.397973i
$299$	49.8764	−	49.8764i	0.166811	−	0.166811i
$300$	139.950	−	161.131i	0.466501	−	0.537103i
$301$	−25.6939	+	25.6939i	−0.0853617	+	0.0853617i
$302$	−262.580	−	262.580i	−0.869470	−	0.869470i
$303$		−	233.401i		−	0.770299i
$304$	36.3067			0.119430
$305$	393.682	+	147.097i	1.29076	+	0.482287i
$306$	−213.651	+	59.0333i	−0.698205	+	0.192919i
$307$	−140.454	−	140.454i	−0.457505	−	0.457505i	0.440331	−	0.897836i	$-0.354861\pi$
$307$	−140.454	−	140.454i	−0.457505	−	0.457505i	−0.897836	+	0.440331i	$0.854861\pi$
$308$	15.3914	+	15.3914i	0.0499720	+	0.0499720i
$309$	64.1360	+	64.1360i	0.207560	+	0.207560i
$310$	172.273	+	377.808i	0.555718	+	1.21873i
$311$	239.244	−	239.244i	0.769274	−	0.769274i	−0.208704	−	0.977979i	$-0.566925\pi$
$311$	239.244	−	239.244i	0.769274	−	0.769274i	0.977979	+	0.208704i	$0.0669246\pi$
$312$			271.439i			0.869996i
$313$	171.184			0.546913			0.273456	−	0.961884i	$-0.411833\pi$
$313$	171.184			0.546913			0.273456	+	0.961884i	$0.411833\pi$
$314$	−109.722			−0.349432
$315$	65.4934	+	143.632i	0.207915	+	0.455975i
$316$	85.2617	+	85.2617i	0.269816	+	0.269816i
$317$			334.893i			1.05645i	0.849106	+	0.528223i	$0.177142\pi$
$317$			334.893i			1.05645i	−0.849106	+	0.528223i	$0.822858\pi$
$318$			3.24317i			0.0101987i
$319$			6.83660i			0.0214314i
$320$	−16.5954	−	36.3950i	−0.0518606	−	0.113734i
$321$			82.1144i			0.255808i
$322$	−10.7433	−	10.7433i	−0.0333642	−	0.0333642i
$323$	−134.227	−	76.1094i	−0.415563	−	0.235633i
$324$			157.949i			0.487497i
$325$	39.4442	+	560.692i	0.121367	+	1.72521i
$326$	−261.591	+	261.591i	−0.802427	+	0.802427i
$327$	−130.834	−	130.834i	−0.400105	−	0.400105i
$328$		−	141.642i		−	0.431836i
$329$	−96.5147	+	96.5147i	−0.293358	+	0.293358i
$330$	−39.7980	−	87.2802i	−0.120600	−	0.264486i
$331$		−	420.984i		−	1.27185i	−0.771749	−	0.635927i	$-0.780618\pi$
$331$		−	420.984i		−	1.27185i	0.771749	−	0.635927i	$-0.219382\pi$
$332$	84.5880	−	84.5880i	0.254783	−	0.254783i
$333$	−366.423			−1.10037
$334$	−136.137	+	136.137i	−0.407596	+	0.407596i
$335$	422.571	+	157.892i	1.26141	+	0.471318i
$336$	58.4674			0.174010
$337$	−579.939			−1.72089			−0.860443	−	0.509547i	$-0.829813\pi$
$337$	−579.939			−1.72089			−0.860443	+	0.509547i	$0.829813\pi$
$338$	−336.490	−	336.490i	−0.995533	−	0.995533i
$339$			623.634i			1.83963i
$340$	−14.9409	+	169.342i	−0.0439438	+	0.498065i
$341$	186.631			0.547304
$342$	83.6841	−	83.6841i	0.244690	−	0.244690i
$343$			295.434i			0.861325i
$344$		−	30.0128i		−	0.0872464i
$345$	27.7793	+	60.9222i	0.0805197	+	0.176586i
$346$	−74.4455	−	74.4455i	−0.215161	−	0.215161i
$347$		−	367.067i		−	1.05783i	−0.848675	−	0.528914i	$-0.822599\pi$
$347$		−	367.067i		−	1.05783i	0.848675	−	0.528914i	$-0.177401\pi$
$348$	12.9851	+	12.9851i	0.0373136	+	0.0373136i
$349$	329.371			0.943755			0.471878	−	0.881664i	$-0.343576\pi$
$349$	329.371			0.943755			0.471878	+	0.881664i	$0.343576\pi$
$350$	120.772	−	8.49621i	0.345063	−	0.0242749i
$351$	14.9085	+	14.9085i	0.0424744	+	0.0424744i
$352$	−17.9785			−0.0510753
$353$	−230.053	+	230.053i	−0.651709	+	0.651709i	−0.953404	−	0.301695i	$-0.902447\pi$
$353$	−230.053	+	230.053i	−0.651709	+	0.651709i	0.301695	+	0.953404i	$0.402447\pi$
$354$	−248.915	−	248.915i	−0.703148	−	0.703148i
$355$	98.2934	−	263.066i	0.276883	−	0.741032i
$356$	334.439			0.939436
$357$	−216.156	−	122.565i	−0.605479	−	0.343319i
$358$	255.927	−	255.927i	0.714881	−	0.714881i
$359$	471.776			1.31414			0.657069	−	0.753830i	$-0.271796\pi$
$359$	471.776			1.31414			0.657069	+	0.753830i	$0.271796\pi$
$360$	−122.139	−	45.6365i	−0.339274	−	0.126768i
$361$	−278.614			−0.771784
$362$	368.552			1.01810
$363$	473.368			1.30404
$364$	−108.882	+	108.882i	−0.299126	+	0.299126i
$365$	7.40134	+	16.2317i	0.0202776	+	0.0444704i
$366$		−	507.387i		−	1.38630i
$367$		−	103.342i		−	0.281585i	−0.990039	−	0.140792i	$-0.955035\pi$
$367$		−	103.342i		−	0.281585i	0.990039	−	0.140792i	$-0.0449650\pi$
$368$	12.5491			0.0341009
$369$	−326.474	−	326.474i	−0.884754	−	0.884754i
$370$	−98.3632	+	263.253i	−0.265846	+	0.711494i
$371$	−1.30093	+	1.30093i	−0.00350654	+	0.00350654i
$372$	354.479	−	354.479i	0.952899	−	0.952899i
$373$	185.868	−	185.868i	0.498306	−	0.498306i	−0.412605	−	0.910910i	$-0.635381\pi$
$373$	185.868	−	185.868i	0.498306	−	0.498306i	0.910910	+	0.412605i	$0.135381\pi$
$374$	66.4672	+	37.6883i	0.177720	+	0.100771i
$375$	−511.680	−	151.216i	−1.36448	−	0.403242i
$376$		−	112.738i		−	0.299835i
$377$	−48.3635			−0.128285
$378$	3.21127	−	3.21127i	0.00849543	−	0.00849543i
$379$	−450.138	−	450.138i	−1.18770	−	1.18770i	−0.977702	−	0.209997i	$-0.932655\pi$
$379$	−450.138	−	450.138i	−1.18770	−	1.18770i	−0.209997	−	0.977702i	$-0.567345\pi$
$380$	−37.6577	−	82.5862i	−0.0990991	−	0.217332i
$381$	−342.611	−	342.611i	−0.899241	−	0.899241i
$382$	−148.464	+	148.464i	−0.388650	+	0.388650i
$383$	−31.9999	−	31.9999i	−0.0835507	−	0.0835507i	0.664096	−	0.747647i	$-0.268816\pi$
$383$	−31.9999	−	31.9999i	−0.0835507	−	0.0835507i	−0.747647	+	0.664096i	$0.768816\pi$
$384$	−34.1476	+	34.1476i	−0.0889261	+	0.0889261i
$385$	19.0464	−	50.9746i	0.0494713	−	0.132402i
$386$	369.174	−	369.174i	0.956409	−	0.956409i
$387$	−69.1771	−	69.1771i	−0.178752	−	0.178752i
$388$		−	316.179i		−	0.814894i
$389$	95.9249			0.246594			0.123297	−	0.992370i	$-0.460653\pi$
$389$	95.9249			0.246594			0.123297	+	0.992370i	$0.460653\pi$
$390$	617.438	−	281.539i	1.58317	−	0.721896i
$391$	−46.3946	−	26.3067i	−0.118656	−	0.0672805i
$392$	−74.5471	−	74.5471i	−0.190171	−	0.190171i
$393$	251.011	+	251.011i	0.638704	+	0.638704i
$394$	17.2775	+	17.2775i	0.0438515	+	0.0438515i
$395$	105.509	−	282.378i	0.267112	−	0.714881i
$396$	−41.4391	+	41.4391i	−0.104644	+	0.104644i
$397$			648.692i			1.63398i	0.576649	+	0.816992i	$0.304360\pi$
$397$			648.692i			1.63398i	−0.576649	+	0.816992i	$0.695640\pi$
$398$	−432.221			−1.08598
$399$	132.672			0.332512
$400$	−65.5742	+	75.4985i	−0.163935	+	0.188746i
$401$	180.926	+	180.926i	0.451186	+	0.451186i	0.895748	−	0.444562i	$-0.146641\pi$
$401$	180.926	+	180.926i	0.451186	+	0.451186i	−0.444562	+	0.895748i	$0.646641\pi$
$402$		−	544.620i		−	1.35478i
$403$			1320.26i			3.27609i
$404$			109.361i			0.270695i
$405$	359.284	−	163.826i	0.887121	−	0.404510i
$406$			10.4174i			0.0256586i
$407$	89.3162	+	89.3162i	0.219450	+	0.219450i
$408$	197.828	−	54.6614i	0.484873	−	0.133974i
$409$			237.078i			0.579653i	0.957079	+	0.289827i	$0.0935977\pi$
$409$			237.078i			0.579653i	−0.957079	+	0.289827i	$0.906402\pi$
$410$	−322.191	+	146.913i	−0.785832	+	0.358324i
$411$	−61.2475	+	61.2475i	−0.149021	+	0.149021i
$412$	−30.0512	−	30.0512i	−0.0729397	−	0.0729397i
$413$		−	199.693i		−	0.483519i
$414$	28.9248	−	28.9248i	0.0698667	−	0.0698667i
$415$	−280.147	−	104.675i	−0.675052	−	0.252230i
$416$		−	127.184i		−	0.305730i
$417$	−559.636	+	559.636i	−1.34205	+	1.34205i
$418$	−40.7963			−0.0975987
$419$	266.966	−	266.966i	0.637151	−	0.637151i	−0.312701	−	0.949852i	$-0.601234\pi$
$419$	266.966	−	266.966i	0.637151	−	0.637151i	0.949852	+	0.312701i	$0.101234\pi$
$420$	−60.6431	−	132.995i	−0.144388	−	0.316655i
$421$	280.120			0.665368			0.332684	−	0.943038i	$-0.392046\pi$
$421$	280.120			0.665368			0.332684	+	0.943038i	$0.392046\pi$
$422$	−89.2667			−0.211532
$423$	−259.852	−	259.852i	−0.614308	−	0.614308i
$424$		−	1.51960i		−	0.00358396i
$425$	400.697	−	141.658i	0.942816	−	0.333312i
$426$	−339.046			−0.795883
$427$	203.527	−	203.527i	0.476645	−	0.476645i
$428$		−	38.4750i		−	0.0898949i
$429$		−	305.004i		−	0.710966i
$430$	−68.2696	+	31.1296i	−0.158766	+	0.0723943i
$431$	304.363	+	304.363i	0.706178	+	0.706178i	0.965729	−	0.259552i	$-0.0835748\pi$
$431$	304.363	+	304.363i	0.706178	+	0.706178i	−0.259552	+	0.965729i	$0.583575\pi$
$432$			3.75106i			0.00868300i
$433$	220.505	+	220.505i	0.509250	+	0.509250i	0.914296	−	0.405046i	$-0.132745\pi$
$433$	220.505	+	220.505i	0.509250	+	0.509250i	−0.405046	+	0.914296i	$0.632745\pi$
$434$	284.382			0.655259
$435$	16.0688	−	43.0055i	0.0369397	−	0.0988631i
$436$	61.3030	+	61.3030i	0.140603	+	0.140603i
$437$	28.4761			0.0651626
$438$	15.2294	−	15.2294i	0.0347704	−	0.0347704i
$439$	−336.631	−	336.631i	−0.766814	−	0.766814i	0.210731	−	0.977544i	$-0.432416\pi$
$439$	−336.631	−	336.631i	−0.766814	−	0.766814i	−0.977544	+	0.210731i	$0.932416\pi$
$440$	18.6475	+	40.8955i	0.0423807	+	0.0929443i
$441$	−343.651			−0.779253
$442$	−266.614	+	470.202i	−0.603200	+	1.06381i
$443$	547.360	−	547.360i	1.23557	−	1.23557i	0.273784	−	0.961791i	$-0.411725\pi$
$443$	547.360	−	547.360i	1.23557	−	1.23557i	0.961791	−	0.273784i	$-0.0882752\pi$
$444$	339.287			0.764159
$445$	−346.884	−	760.744i	−0.779515	−	1.70954i
$446$	−177.011			−0.396886
$447$	506.221			1.13249
$448$	−27.3951			−0.0611499
$449$	29.3642	−	29.3642i	0.0653990	−	0.0653990i	−0.673651	−	0.739050i	$-0.735275\pi$
$449$	29.3642	−	29.3642i	0.0653990	−	0.0653990i	0.739050	+	0.673651i	$0.235275\pi$
$450$	22.8749	+	325.162i	0.0508330	+	0.722582i
$451$			159.157i			0.352898i
$452$		−	292.206i		−	0.646474i
$453$	1120.81			2.47419
$454$	−29.8311	−	29.8311i	−0.0657072	−	0.0657072i
$455$	360.605	+	134.738i	0.792538	+	0.296128i
$456$	−77.4866	+	77.4866i	−0.169927	+	0.169927i
$457$	−217.775	+	217.775i	−0.476531	+	0.476531i	−0.904020	−	0.427490i	$-0.859398\pi$
$457$	−217.775	+	217.775i	−0.476531	+	0.476531i	0.427490	+	0.904020i	$0.359398\pi$
$458$	34.7033	−	34.7033i	0.0757714	−	0.0757714i
$459$	7.86332	−	13.8678i	0.0171314	−	0.0302130i
$460$	−13.0161	−	28.5453i	−0.0282959	−	0.0620551i
$461$			199.177i			0.432054i	0.976387	+	0.216027i	$0.0693099\pi$
$461$			199.177i			0.432054i	−0.976387	+	0.216027i	$0.930690\pi$
$462$	−65.6974			−0.142202
$463$	114.645	−	114.645i	0.247614	−	0.247614i	−0.572377	−	0.819991i	$-0.693979\pi$
$463$	114.645	−	114.645i	0.247614	−	0.247614i	0.819991	+	0.572377i	$0.193979\pi$
$464$	−6.08424	−	6.08424i	−0.0131126	−	0.0131126i
$465$	−1174.00	−	438.658i	−2.52472	−	0.943351i
$466$	392.306	+	392.306i	0.841857	+	0.841857i
$467$	138.667	−	138.667i	0.296932	−	0.296932i	−0.542879	−	0.839811i	$-0.682666\pi$
$467$	138.667	−	138.667i	0.296932	−	0.296932i	0.839811	+	0.542879i	$0.182666\pi$
$468$	−293.149	−	293.149i	−0.626386	−	0.626386i
$469$	218.462	−	218.462i	0.465804	−	0.465804i
$470$	−256.443	+	116.933i	−0.545624	+	0.248794i
$471$	234.171	−	234.171i	0.497178	−	0.497178i
$472$	116.630	+	116.630i	0.247097	+	0.247097i
$473$			33.7241i			0.0712982i
$474$	−363.936			−0.767797
$475$	−148.799	+	171.319i	−0.313260	+	0.360671i
$476$	101.281	+	57.4283i	0.212775	+	0.120648i
$477$	−3.50256	−	3.50256i	−0.00734290	−	0.00734290i
$478$	180.766	+	180.766i	0.378172	+	0.378172i
$479$	24.1275	+	24.1275i	0.0503707	+	0.0503707i	0.731843	−	0.681473i	$-0.238660\pi$
$479$	24.1275	+	24.1275i	0.0503707	+	0.0503707i	−0.681473	+	0.731843i	$0.738660\pi$
$480$	113.093	+	42.2568i	0.235611	+	0.0880350i
$481$	−631.841	+	631.841i	−1.31360	+	1.31360i
$482$		−	308.432i		−	0.639901i
$483$	45.8572			0.0949425
$484$	−221.798			−0.458261
$485$	−719.208	+	327.944i	−1.48290	+	0.676174i
$486$	−345.539	−	345.539i	−0.710985	−	0.710985i
$487$			746.620i			1.53310i	0.642184	+	0.766550i	$0.278028\pi$
$487$			746.620i			1.53310i	−0.642184	+	0.766550i	$0.721972\pi$
$488$			237.738i			0.487168i
$489$		−	1116.59i		−	2.28342i
$490$	−92.2501	+	246.892i	−0.188265	+	0.503862i
$491$			679.078i			1.38305i	0.722352	+	0.691526i	$0.243061\pi$
$491$			679.078i			1.38305i	−0.722352	+	0.691526i	$0.756939\pi$
$492$	302.296	+	302.296i	0.614423	+	0.614423i
$493$	9.73928	+	35.2480i	0.0197551	+	0.0714969i
$494$		−	288.601i		−	0.584212i
$495$	137.242	+	51.2799i	0.277257	+	0.103596i
$496$	−166.092	+	166.092i	−0.334863	+	0.334863i
$497$	−136.001	−	136.001i	−0.273644	−	0.273644i
$498$			361.060i			0.725020i
$499$	445.536	−	445.536i	0.892857	−	0.892857i	−0.101934	−	0.994791i	$-0.532503\pi$
$499$	445.536	−	445.536i	0.892857	−	0.892857i	0.994791	+	0.101934i	$0.0325031\pi$
$500$	239.750	+	70.8527i	0.479499	+	0.141705i
$501$		−	581.095i		−	1.15987i
$502$	472.857	−	472.857i	0.941946	−	0.941946i
$503$	−843.862			−1.67766			−0.838829	−	0.544395i	$-0.816759\pi$
$503$	−843.862			−1.67766			−0.838829	+	0.544395i	$0.816759\pi$
$504$	−63.1437	+	63.1437i	−0.125285	+	0.125285i
$505$	248.761	−	113.430i	0.492597	−	0.224614i
$506$	−14.1009			−0.0278674
$507$	1436.29			2.83292
$508$	160.532	+	160.532i	0.316007	+	0.316007i
$509$		−	600.694i		−	1.18014i	−0.807350	−	0.590072i	$-0.799099\pi$
$509$		−	600.694i		−	1.18014i	0.807350	−	0.590072i	$-0.200901\pi$
$510$	−329.527	−	393.302i	−0.646132	−	0.771180i
$511$	12.2179			0.0239098
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$			8.51177i			0.0165921i
$514$		−	346.145i		−	0.673434i
$515$	−37.1875	+	99.5263i	−0.0722088	+	0.193255i
$516$	64.0540	+	64.0540i	0.124136	+	0.124136i
$517$			126.679i			0.245027i
$518$	136.097	+	136.097i	0.262736	+	0.262736i
$519$	317.767			0.612269
$520$	−289.303	+	131.916i	−0.556352	+	0.253685i
$521$	−359.131	−	359.131i	−0.689311	−	0.689311i	0.272769	−	0.962080i	$-0.412061\pi$
$521$	−359.131	−	359.131i	−0.689311	−	0.689311i	−0.962080	+	0.272769i	$0.912061\pi$
$522$	−28.0474			−0.0537307
$523$	−373.569	+	373.569i	−0.714281	+	0.714281i	−0.967428	−	0.253147i	$-0.918534\pi$
$523$	−373.569	+	373.569i	−0.714281	+	0.714281i	0.253147	+	0.967428i	$0.418534\pi$
$524$	−117.612	−	117.612i	−0.224450	−	0.224450i
$525$	−239.622	+	275.888i	−0.456423	+	0.525501i
$526$	−516.009			−0.981006
$527$	962.227	−	265.870i	1.82586	−	0.504498i
$528$	38.3702	−	38.3702i	0.0726709	−	0.0726709i
$529$	−519.157			−0.981394
$530$	−3.45661	+	1.57615i	−0.00652191	+	0.00297386i
$531$	537.646			1.01252
$532$	−62.1641			−0.116850
$533$	−1125.91			−2.11240
$534$	−713.769	+	713.769i	−1.33665	+	1.33665i
$535$	−87.5186	+	39.9067i	−0.163586	+	0.0745920i
$536$			255.184i			0.476089i
$537$			1092.41i			2.03429i
$538$	17.9047			0.0332801
$539$	83.7654	+	83.7654i	0.155409	+	0.155409i
$540$	8.53247	−	3.89064i	0.0158009	−	0.00720488i
$541$	361.770	−	361.770i	0.668707	−	0.668707i	−0.288710	−	0.957417i	$-0.593226\pi$
$541$	361.770	−	361.770i	0.668707	−	0.668707i	0.957417	+	0.288710i	$0.0932264\pi$
$542$	−34.3025	+	34.3025i	−0.0632887	+	0.0632887i
$543$	−786.574	+	786.574i	−1.44857	+	1.44857i
$544$	−92.6932	+	25.6118i	−0.170392	+	0.0470805i
$545$	75.8608	−	203.029i	0.139194	−	0.372530i
$546$		−	464.756i		−	0.851202i
$547$	666.808			1.21903			0.609514	−	0.792775i	$-0.291365\pi$
$547$	666.808			1.21903			0.609514	+	0.792775i	$0.291365\pi$
$548$	28.6978	−	28.6978i	0.0523682	−	0.0523682i
$549$	547.969	+	547.969i	0.998121	+	0.998121i
$550$	73.6829	−	84.8345i	0.133969	−	0.154245i
$551$	−13.8062	−	13.8062i	−0.0250565	−	0.0250565i
$552$	−26.7827	+	26.7827i	−0.0485194	+	0.0485194i
$553$	−145.985	−	145.985i	−0.263987	−	0.263987i
$554$	353.035	−	353.035i	0.637247	−	0.637247i
$555$	−351.912	−	771.771i	−0.634076	−	1.39058i
$556$	262.220	−	262.220i	0.471618	−	0.471618i
$557$	324.863	+	324.863i	0.583237	+	0.583237i	0.935791	−	0.352554i	$-0.114687\pi$
$557$	324.863	+	324.863i	0.583237	+	0.583237i	−0.352554	+	0.935791i	$0.614687\pi$
$558$			765.660i			1.37215i
$559$	−238.571			−0.426781
$560$	28.4145	+	62.3153i	0.0507403	+	0.111277i
$561$	−222.291	+	61.4207i	−0.396241	+	0.109484i
$562$	−169.438	−	169.438i	−0.301492	−	0.301492i
$563$	−273.266	−	273.266i	−0.485375	−	0.485375i	0.421468	−	0.906843i	$-0.361515\pi$
$563$	−273.266	−	273.266i	−0.485375	−	0.485375i	−0.906843	+	0.421468i	$0.861515\pi$
$564$	240.608	+	240.608i	0.426610	+	0.426610i
$565$	−664.677	+	303.079i	−1.17642	+	0.536424i
$566$	80.6930	−	80.6930i	0.142567	−	0.142567i
$567$		−	270.440i		−	0.476966i
$568$	158.861			0.279686
$569$	115.091			0.202269			0.101135	−	0.994873i	$-0.467753\pi$
$569$	115.091			0.202269			0.101135	+	0.994873i	$0.467753\pi$
$570$	256.628	+	95.8877i	0.450224	+	0.168224i
$571$	131.481	+	131.481i	0.230265	+	0.230265i	0.812803	−	0.582538i	$-0.197940\pi$
$571$	131.481	+	131.481i	0.230265	+	0.230265i	−0.582538	+	0.812803i	$0.697940\pi$
$572$			142.911i			0.249844i
$573$		−	633.713i		−	1.10596i
$574$			242.519i			0.422507i
$575$	−51.4312	+	59.2151i	−0.0894455	+	0.102983i
$576$		−	73.7576i		−	0.128051i
$577$	−442.212	−	442.212i	−0.766399	−	0.766399i	0.211072	−	0.977471i	$-0.432305\pi$
$577$	−442.212	−	442.212i	−0.766399	−	0.766399i	−0.977471	+	0.211072i	$0.932305\pi$
$578$	396.380	+	99.6246i	0.685778	+	0.172361i
$579$			1575.80i			2.72159i
$580$	−7.52909	+	20.1504i	−0.0129812	+	0.0347420i
$581$	−144.831	+	144.831i	−0.249279	+	0.249279i
$582$	674.798	+	674.798i	1.15945	+	1.15945i
$583$			1.70751i			0.00292883i
$584$	−7.13581	+	7.13581i	−0.0122188	+	0.0122188i
$585$	−362.764	+	970.878i	−0.620109	+	1.65962i
$586$			470.339i			0.802627i
$587$	−622.551	+	622.551i	−1.06056	+	1.06056i	−0.0625206	+	0.998044i	$0.519914\pi$
$587$	−622.551	+	622.551i	−1.06056	+	1.06056i	−0.998044	+	0.0625206i	$0.980086\pi$
$588$	318.201			0.541158
$589$	−376.891	+	376.891i	−0.639883	+	0.639883i
$590$	144.326	−	386.266i	0.244621	−	0.654688i
$591$	−73.7481			−0.124785
$592$	−158.974			−0.268537
$593$	−170.876	−	170.876i	−0.288154	−	0.288154i	0.548196	−	0.836350i	$-0.315315\pi$
$593$	−170.876	−	170.876i	−0.288154	−	0.288154i	−0.836350	+	0.548196i	$0.815315\pi$
$594$		−	4.21490i		−	0.00709579i
$595$	25.5818	−	289.947i	0.0429945	−	0.487306i
$596$	−237.192			−0.397973
$597$	922.458	−	922.458i	1.54516	−	1.54516i
$598$		−	99.7528i		−	0.166811i
$599$		−	1118.96i		−	1.86804i	−0.357218	−	0.934021i	$-0.616275\pi$
$599$		−	1118.96i		−	1.86804i	0.357218	−	0.934021i	$-0.383725\pi$
$600$	−21.1808	−	301.081i	−0.0353013	−	0.501802i
$601$	68.8243	+	68.8243i	0.114516	+	0.114516i	0.762043	−	0.647527i	$-0.224197\pi$
$601$	68.8243	+	68.8243i	0.114516	+	0.114516i	−0.647527	+	0.762043i	$0.724197\pi$
$602$			51.3877i			0.0853617i
$603$	588.179	+	588.179i	0.975421	+	0.975421i
$604$	−525.160			−0.869470
$605$	230.052	+	504.521i	0.380251	+	0.833920i
$606$	−233.401	−	233.401i	−0.385150	−	0.385150i
$607$	−237.917			−0.391955			−0.195977	−	0.980608i	$-0.562788\pi$
$607$	−237.917			−0.391955			−0.195977	+	0.980608i	$0.562788\pi$
$608$	36.3067	−	36.3067i	0.0597149	−	0.0597149i
$609$	−22.2331	−	22.2331i	−0.0365076	−	0.0365076i
$610$	540.780	−	246.585i	0.886524	−	0.404237i
$611$	−896.151			−1.46670
$612$	−154.618	+	272.684i	−0.252643	+	0.445562i
$613$	159.005	−	159.005i	0.259389	−	0.259389i	−0.565417	−	0.824805i	$-0.691285\pi$
$613$	159.005	−	159.005i	0.259389	−	0.259389i	0.824805	+	0.565417i	$0.191285\pi$
$614$	−280.908			−0.457505
$615$	374.084	−	1001.17i	0.608266	−	1.62793i
$616$	30.7828			0.0499720
$617$	−348.516			−0.564856			−0.282428	−	0.959288i	$-0.591140\pi$
$617$	−348.516			−0.564856			−0.282428	+	0.959288i	$0.591140\pi$
$618$	128.272			0.207560
$619$	314.746	−	314.746i	0.508475	−	0.508475i	−0.405583	−	0.914058i	$-0.632932\pi$
$619$	314.746	−	314.746i	0.508475	−	0.508475i	0.914058	+	0.405583i	$0.132932\pi$
$620$	550.080	+	205.535i	0.887226	+	0.331508i
$621$			2.94203i			0.00473757i
$622$		−	478.489i		−	0.769274i
$623$	−572.626			−0.919142
$624$	271.439	+	271.439i	0.434998	+	0.434998i
$625$	−87.5034	−	618.844i	−0.140005	−	0.990151i
$626$	171.184	−	171.184i	0.273456	−	0.273456i
$627$	87.0685	−	87.0685i	0.138865	−	0.138865i
$628$	−109.722	+	109.722i	−0.174716	+	0.174716i
$629$	587.732	+	333.257i	0.934392	+	0.529820i
$630$	209.125	+	78.1387i	0.331945	+	0.124030i
$631$			758.862i			1.20263i	0.799011	+	0.601317i	$0.205357\pi$
$631$			758.862i			1.20263i	−0.799011	+	0.601317i	$0.794643\pi$
$632$	170.523			0.269816
$633$	190.515	−	190.515i	0.300972	−	0.300972i
$634$	334.893	+	334.893i	0.528223	+	0.528223i
$635$	198.654	−	531.664i	0.312840	−	0.837266i
$636$	3.24317	+	3.24317i	0.00509933	+	0.00509933i
$637$	−592.573	+	592.573i	−0.930256	+	0.930256i
$638$	6.83660	+	6.83660i	0.0107157	+	0.0107157i
$639$	366.163	−	366.163i	0.573026	−	0.573026i
$640$	−52.9903	−	19.7996i	−0.0827974	−	0.0309369i
$641$	267.894	−	267.894i	0.417931	−	0.417931i	−0.466559	−	0.884490i	$-0.654506\pi$
$641$	267.894	−	267.894i	0.417931	−	0.417931i	0.884490	+	0.466559i	$0.154506\pi$
$642$	82.1144	+	82.1144i	0.127904	+	0.127904i
$643$			950.654i			1.47847i	0.673449	+	0.739233i	$0.264812\pi$
$643$			950.654i			1.47847i	−0.673449	+	0.739233i	$0.735188\pi$
$644$	−21.4866			−0.0333642
$645$	79.2652	−	212.140i	0.122892	−	0.328900i
$646$	−210.336	+	58.1175i	−0.325598	+	0.0899651i
$647$	−382.956	−	382.956i	−0.591895	−	0.591895i	0.346248	−	0.938143i	$-0.387456\pi$
$647$	−382.956	−	382.956i	−0.591895	−	0.591895i	−0.938143	+	0.346248i	$0.887456\pi$
$648$	157.949	+	157.949i	0.243748	+	0.243748i
$649$	−131.052	−	131.052i	−0.201929	−	0.201929i
$650$	600.136	+	521.248i	0.923286	+	0.801920i
$651$	−606.937	+	606.937i	−0.932315	+	0.932315i
$652$			523.183i			0.802427i
$653$	660.333			1.01123			0.505615	−	0.862759i	$-0.331266\pi$
$653$	660.333			1.01123			0.505615	+	0.862759i	$0.331266\pi$
$654$	−261.669			−0.400105
$655$	−145.542	+	389.519i	−0.222201	+	0.594685i
$656$	−141.642	−	141.642i	−0.215918	−	0.215918i
$657$			32.8950i			0.0500685i
$658$			193.029i			0.293358i
$659$			330.355i			0.501298i	0.968078	+	0.250649i	$0.0806440\pi$
$659$			330.355i			0.501298i	−0.968078	+	0.250649i	$0.919356\pi$
$660$	−127.078	−	47.4822i	−0.192543	−	0.0719427i
$661$		−	421.496i		−	0.637665i	−0.947811	−	0.318832i	$-0.896709\pi$
$661$		−	421.496i		−	0.637665i	0.947811	−	0.318832i	$-0.103291\pi$
$662$	−420.984	−	420.984i	−0.635927	−	0.635927i
$663$	−434.502	−	1572.53i	−0.655358	−	2.37185i
$664$		−	169.176i		−	0.254783i
$665$	64.4773	+	141.404i	0.0969584	+	0.212637i
$666$	−366.423	+	366.423i	−0.550185	+	0.550185i
$667$	−4.77200	−	4.77200i	−0.00715442	−	0.00715442i
$668$			272.274i			0.407596i
$669$	377.782	−	377.782i	0.564697	−	0.564697i
$670$	580.463	−	264.679i	0.866362	−	0.395044i
$671$		−	267.136i		−	0.398117i
$672$	58.4674	−	58.4674i	0.0870051	−	0.0870051i
$673$	299.975			0.445728			0.222864	−	0.974850i	$-0.428459\pi$
$673$	299.975			0.445728			0.222864	+	0.974850i	$0.428459\pi$
$674$	−579.939	+	579.939i	−0.860443	+	0.860443i
$675$	−17.6999	−	15.3733i	−0.0262221	−	0.0227752i
$676$	−672.980			−0.995533
$677$	1131.00			1.67060			0.835301	−	0.549794i	$-0.185294\pi$
$677$	1131.00			1.67060			0.835301	+	0.549794i	$0.185294\pi$
$678$	623.634	+	623.634i	0.919814	+	0.919814i
$679$			541.360i			0.797291i
$680$	154.401	+	184.283i	0.227061	+	0.271005i
$681$	127.333			0.186979
$682$	186.631	−	186.631i	0.273652	−	0.273652i
$683$			93.6215i			0.137074i	0.997649	+	0.0685370i	$0.0218331\pi$
$683$			93.6215i			0.137074i	−0.997649	+	0.0685370i	$0.978167\pi$
$684$		−	167.368i		−	0.244690i
$685$	−95.0440	−	35.5127i	−0.138750	−	0.0518434i
$686$	295.434	+	295.434i	0.430662	+	0.430662i
$687$			148.130i			0.215618i
$688$	−30.0128	−	30.0128i	−0.0436232	−	0.0436232i
$689$	−12.0793			−0.0175316
$690$	88.7015	+	33.1429i	0.128553	+	0.0480332i
$691$	326.031	+	326.031i	0.471825	+	0.471825i	0.902505	−	0.430680i	$-0.141726\pi$
$691$	326.031	+	326.031i	0.471825	+	0.471825i	−0.430680	+	0.902505i	$0.641726\pi$
$692$	−148.891			−0.215161
$693$	70.9519	−	70.9519i	0.102384	−	0.102384i
$694$	−367.067	−	367.067i	−0.528914	−	0.528914i
$695$	−868.444	−	324.490i	−1.24956	−	0.466892i
$696$	25.9703			0.0373136
$697$	226.732	+	820.579i	0.325297	+	1.17730i
$698$	329.371	−	329.371i	0.471878	−	0.471878i
$699$	−1674.54			−2.39562
$700$	112.276	−	129.268i	0.160394	−	0.184669i
$701$	−448.957			−0.640453			−0.320226	−	0.947341i	$-0.603759\pi$
$701$	−448.957			−0.640453			−0.320226	+	0.947341i	$0.603759\pi$
$702$	29.8171			0.0424744
$703$	−360.739			−0.513142
$704$	−17.9785	+	17.9785i	−0.0255377	+	0.0255377i
$705$	297.746	−	796.869i	0.422335	−	1.13031i
$706$			460.107i			0.651709i
$707$		−	187.247i		−	0.264847i
$708$	−497.829			−0.703148
$709$	173.601	+	173.601i	0.244854	+	0.244854i	0.818855	−	0.574001i	$-0.194609\pi$
$709$	173.601	+	173.601i	0.244854	+	0.244854i	−0.574001	+	0.818855i	$0.694609\pi$
$710$	−164.773	−	361.360i	−0.232074	−	0.508957i
$711$	393.044	−	393.044i	0.552804	−	0.552804i
$712$	334.439	−	334.439i	0.469718	−	0.469718i
$713$	−130.270	+	130.270i	−0.182706	+	0.182706i
$714$	−338.721	+	93.5911i	−0.474399	+	0.131080i
$715$	325.077	−	148.229i	0.454654	−	0.207313i
$716$		−	511.855i		−	0.714881i
$717$	−771.591			−1.07614
$718$	471.776	−	471.776i	0.657069	−	0.657069i
$719$	−442.246	−	442.246i	−0.615086	−	0.615086i	0.329181	−	0.944267i	$-0.393227\pi$
$719$	−442.246	−	442.246i	−0.615086	−	0.615086i	−0.944267	+	0.329181i	$0.893227\pi$
$720$	−167.775	+	76.5022i	−0.233021	+	0.106253i
$721$	51.4535	+	51.4535i	0.0713640	+	0.0713640i
$722$	−278.614	+	278.614i	−0.385892	+	0.385892i
$723$	658.265	+	658.265i	0.910463	+	0.910463i
$724$	368.552	−	368.552i	0.509050	−	0.509050i
$725$	53.6450	−	3.77388i	0.0739931	−	0.00520535i
$726$	473.368	−	473.368i	0.652022	−	0.652022i
$727$	−495.287	−	495.287i	−0.681275	−	0.681275i	0.279013	−	0.960287i	$-0.409993\pi$
$727$	−495.287	−	495.287i	−0.681275	−	0.681275i	−0.960287	+	0.279013i	$0.909993\pi$
$728$			217.763i			0.299126i
$729$	764.146			1.04821
$730$	23.6330	+	8.83038i	0.0323740	+	0.0120964i
$731$	48.0426	+	173.874i	0.0657217	+	0.237857i
$732$	−507.387	−	507.387i	−0.693152	−	0.693152i
$733$	−1005.84	−	1005.84i	−1.37222	−	1.37222i	−0.857145	−	0.515076i	$-0.827764\pi$
$733$	−1005.84	−	1005.84i	−1.37222	−	1.37222i	−0.515076	−	0.857145i	$-0.672236\pi$
$734$	−103.342	−	103.342i	−0.140792	−	0.140792i
$735$	−330.041	−	723.807i	−0.449036	−	0.984771i
$736$	12.5491	−	12.5491i	0.0170505	−	0.0170505i
$737$		−	286.739i		−	0.389063i
$738$	−652.948			−0.884754
$739$	−933.317			−1.26295			−0.631473	−	0.775398i	$-0.717549\pi$
$739$	−933.317			−1.26295			−0.631473	+	0.775398i	$0.717549\pi$
$740$	164.890	+	361.616i	0.222824	+	0.488670i
$741$	615.940	+	615.940i	0.831228	+	0.831228i
$742$			2.60185i			0.00350654i
$743$		−	960.655i		−	1.29294i	−0.762939	−	0.646470i	$-0.776244\pi$
$743$		−	960.655i		−	1.29294i	0.762939	−	0.646470i	$-0.223756\pi$
$744$		−	708.957i		−	0.952899i
$745$	246.018	+	539.537i	0.330225	+	0.724210i
$746$		−	371.736i		−	0.498306i
$747$	−389.938	−	389.938i	−0.522005	−	0.522005i
$748$	104.155	−	28.7789i	0.139245	−	0.0384745i
$749$			65.8768i			0.0879530i
$750$	−662.896	+	360.464i	−0.883861	+	0.480619i
$751$	158.161	−	158.161i	0.210601	−	0.210601i	−0.593922	−	0.804523i	$-0.702421\pi$
$751$	158.161	−	158.161i	0.210601	−	0.210601i	0.804523	+	0.593922i	$0.202421\pi$
$752$	−112.738	−	112.738i	−0.149917	−	0.149917i
$753$			2018.37i			2.68043i
$754$	−48.3635	+	48.3635i	−0.0641426	+	0.0641426i
$755$	544.701	+	1194.57i	0.721459	+	1.58222i
$756$		−	6.42254i		−	0.00849543i
$757$	984.105	−	984.105i	1.30001	−	1.30001i	0.371622	−	0.928384i	$-0.378802\pi$
$757$	984.105	−	984.105i	1.30001	−	1.30001i	0.928384	−	0.371622i	$-0.121198\pi$
$758$	−900.276			−1.18770
$759$	30.0946	−	30.0946i	0.0396503	−	0.0396503i
$760$	−120.244	−	44.9286i	−0.158216	−	0.0591165i
$761$	−337.120			−0.442997			−0.221498	−	0.975161i	$-0.571095\pi$
$761$	−337.120			−0.442997			−0.221498	+	0.975161i	$0.571095\pi$
$762$	−685.222			−0.899241
$763$	−104.963	−	104.963i	−0.137566	−	0.137566i
$764$			296.929i			0.388650i
$765$	780.642	+	68.8753i	1.02045	+	0.0900331i
$766$	−63.9998			−0.0835507
$767$	927.088	−	927.088i	1.20872	−	1.20872i
$768$			68.2953i			0.0889261i
$769$			992.104i			1.29012i	0.764131	+	0.645061i	$0.223168\pi$
$769$			992.104i			1.29012i	−0.764131	+	0.645061i	$0.776832\pi$
$770$	−31.9282	−	70.0211i	−0.0414652	−	0.0909365i
$771$	738.752	+	738.752i	0.958174	+	0.958174i
$772$		−	738.348i		−	0.956409i
$773$	−983.734	−	983.734i	−1.27262	−	1.27262i	−0.944709	−	0.327909i	$-0.893656\pi$
$773$	−983.734	−	983.734i	−1.27262	−	1.27262i	−0.327909	−	0.944709i	$-0.606344\pi$
$774$	−138.354			−0.178752
$775$	−103.022	−	1464.44i	−0.132932	−	1.88960i
$776$	−316.179	−	316.179i	−0.407447	−	0.407447i
$777$	−580.926			−0.747652
$778$	95.9249	−	95.9249i	0.123297	−	0.123297i
$779$	−321.409	−	321.409i	−0.412592	−	0.412592i
$780$	335.898	−	898.977i	0.430639	−	1.15253i
$781$	−178.506			−0.228561
$782$	−72.7012	+	20.0879i	−0.0929683	+	0.0256878i
$783$	1.42639	−	1.42639i	0.00182170	−	0.00182170i
$784$	−149.094			−0.190171
$785$	363.387	+	135.778i	0.462913	+	0.172965i
$786$	502.022			0.638704
$787$	210.433			0.267387			0.133693	−	0.991023i	$-0.457316\pi$
$787$	210.433			0.267387			0.133693	+	0.991023i	$0.457316\pi$
$788$	34.5550			0.0438515
$789$	1101.28	−	1101.28i	1.39579	−	1.39579i
$790$	−176.869	−	387.887i	−0.223885	−	0.490996i
$791$			500.314i			0.632508i
$792$			82.8783i			0.104644i
$793$	1889.78			2.38307
$794$	648.692	+	648.692i	0.816992	+	0.816992i
$795$	4.01334	−	10.7410i	0.00504823	−	0.0135107i
$796$	−432.221	+	432.221i	−0.542991	+	0.542991i
$797$	−90.7770	+	90.7770i	−0.113898	+	0.113898i	−0.761759	−	0.647861i	$-0.775664\pi$
$797$	−90.7770	+	90.7770i	−0.113898	+	0.113898i	0.647861	+	0.761759i	$0.275664\pi$
$798$	132.672	−	132.672i	0.166256	−	0.166256i
$799$	180.464	+	653.127i	0.225862	+	0.817431i
$800$	9.92434	+	141.073i	0.0124054	+	0.176341i
$801$		−	1541.71i		−	1.92474i
$802$	361.851			0.451186
$803$	8.01820	−	8.01820i	0.00998531	−	0.00998531i
$804$	−544.620	−	544.620i	−0.677388	−	0.677388i
$805$	22.2861	+	48.8752i	0.0276846	+	0.0607145i
$806$	1320.26	+	1320.26i	1.63804	+	1.63804i
$807$	−38.2127	+	38.2127i	−0.0473516	+	0.0473516i
$808$	109.361	+	109.361i	0.135347	+	0.135347i
$809$	761.890	−	761.890i	0.941767	−	0.941767i	−0.0566283	−	0.998395i	$-0.518035\pi$
$809$	761.890	−	761.890i	0.941767	−	0.941767i	0.998395	+	0.0566283i	$0.0180350\pi$
$810$	195.458	−	523.110i	0.241306	−	0.645815i
$811$	−714.555	+	714.555i	−0.881079	+	0.881079i	−0.993644	−	0.112565i	$-0.964093\pi$
$811$	−714.555	+	714.555i	−0.881079	+	0.881079i	0.112565	+	0.993644i	$0.464093\pi$
$812$	10.4174	+	10.4174i	0.0128293	+	0.0128293i
$813$		−	146.418i		−	0.180096i
$814$	178.632			0.219450
$815$	1190.08	−	542.651i	1.46022	−	0.665829i
$816$	143.167	−	252.490i	0.175450	−	0.309424i
$817$	−68.1039	−	68.1039i	−0.0833585	−	0.0833585i
$818$	237.078	+	237.078i	0.289827	+	0.289827i
$819$	501.928	+	501.928i	0.612855	+	0.612855i
$820$	−175.278	+	469.104i	−0.213754	+	0.572078i
$821$	−494.373	+	494.373i	−0.602160	+	0.602160i	−0.940885	−	0.338726i	$-0.890004\pi$
$821$	−494.373	+	494.373i	−0.602160	+	0.602160i	0.338726	+	0.940885i	$0.390004\pi$
$822$			122.495i			0.149021i
$823$	239.718			0.291274			0.145637	−	0.989338i	$-0.453477\pi$
$823$	239.718			0.291274			0.145637	+	0.989338i	$0.453477\pi$
$824$	−60.1023			−0.0729397
$825$	23.8000	+	338.312i	0.0288484	+	0.410075i
$826$	−199.693	−	199.693i	−0.241759	−	0.241759i
$827$		−	658.211i		−	0.795902i	−0.917407	−	0.397951i	$-0.869721\pi$
$827$		−	658.211i		−	0.795902i	0.917407	−	0.397951i	$-0.130279\pi$
$828$		−	57.8496i		−	0.0698667i
$829$			1183.66i			1.42782i	0.700240	+	0.713908i	$0.253076\pi$
$829$			1183.66i			1.42782i	−0.700240	+	0.713908i	$0.746924\pi$
$830$	−384.822	+	175.471i	−0.463641	+	0.211411i
$831$			1506.91i			1.81337i
$832$	−127.184	−	127.184i	−0.152865	−	0.152865i
$833$	551.206	+	312.545i	0.661712	+	0.375204i
$834$			1119.27i			1.34205i
$835$	619.338	−	282.406i	0.741722	−	0.338211i
$836$	−40.7963	+	40.7963i	−0.0487993	+	0.0487993i
$837$	−38.9388	−	38.9388i	−0.0465219	−	0.0465219i
$838$		−	533.932i		−	0.637151i
$839$	396.357	−	396.357i	0.472416	−	0.472416i	−0.430279	−	0.902696i	$-0.641585\pi$
$839$	396.357	−	396.357i	0.472416	−	0.472416i	0.902696	+	0.430279i	$0.141585\pi$
$840$	−193.638	−	72.3519i	−0.230522	−	0.0861333i
$841$		−	836.373i		−	0.994498i
$842$	280.120	−	280.120i	0.332684	−	0.332684i
$843$	723.240			0.857936
$844$	−89.2667	+	89.2667i	−0.105766	+	0.105766i
$845$	698.023	+	1530.82i	0.826062	+	1.81162i
$846$	−519.704			−0.614308
$847$	379.762			0.448361
$848$	−1.51960	−	1.51960i	−0.00179198	−	0.00179198i
$849$			344.434i			0.405694i
$850$	259.039	−	542.355i	0.304752	−	0.638064i
$851$	−124.687			−0.146518
$852$	−339.046	+	339.046i	−0.397942	+	0.397942i
$853$		−	133.730i		−	0.156776i	−0.996923	−	0.0783879i	$-0.975023\pi$
$853$		−	133.730i		−	0.156776i	0.996923	−	0.0783879i	$-0.0249773\pi$
$854$		−	407.054i		−	0.476645i
$855$	−380.710	+	173.596i	−0.445275	+	0.203036i
$856$	−38.4750	−	38.4750i	−0.0449475	−	0.0449475i
$857$			352.596i			0.411431i	0.978612	+	0.205715i	$0.0659521\pi$
$857$			352.596i			0.411431i	−0.978612	+	0.205715i	$0.934048\pi$
$858$	−305.004	−	305.004i	−0.355483	−	0.355483i
$859$	−685.813			−0.798385			−0.399192	−	0.916867i	$-0.630709\pi$
$859$	−685.813			−0.798385			−0.399192	+	0.916867i	$0.630709\pi$
$860$	−37.1400	+	99.3991i	−0.0431861	+	0.115580i
$861$	−517.591	−	517.591i	−0.601150	−	0.601150i
$862$	608.725			0.706178
$863$	−604.548	+	604.548i	−0.700519	+	0.700519i	−0.964522	−	0.264003i	$-0.914957\pi$
$863$	−604.548	+	604.548i	−0.700519	+	0.700519i	0.264003	+	0.964522i	$0.414957\pi$
$864$	3.75106	+	3.75106i	0.00434150	+	0.00434150i
$865$	154.431	+	338.680i	0.178534	+	0.391538i
$866$	441.011			0.509250
$867$	−1058.59	+	633.343i	−1.22098	+	0.730499i
$868$	284.382	−	284.382i	0.327630	−	0.327630i
$869$	−191.610			−0.220495
$870$	−26.9367	−	59.0742i	−0.0309617	−	0.0679014i
$871$	2028.45			2.32887
$872$	122.606			0.140603
$873$	−1457.54			−1.66957
$874$	28.4761	−	28.4761i	0.0325813	−	0.0325813i
$875$	−410.498	−	121.314i	−0.469141	−	0.138644i
$876$		−	30.4589i		−	0.0347704i
$877$			932.785i			1.06361i	0.846867	+	0.531805i	$0.178486\pi$
$877$			932.785i			1.06361i	−0.846867	+	0.531805i	$0.821514\pi$
$878$	−673.262			−0.766814
$879$	−1003.81	−	1003.81i	−1.14199	−	1.14199i
$880$	59.5430	+	22.2480i	0.0676625	+	0.0252818i
$881$	−615.396	+	615.396i	−0.698520	+	0.698520i	−0.964091	−	0.265571i	$-0.914439\pi$
$881$	−615.396	+	615.396i	−0.698520	+	0.698520i	0.265571	+	0.964091i	$0.414439\pi$
$882$	−343.651	+	343.651i	−0.389627	+	0.389627i
$883$	359.169	−	359.169i	0.406759	−	0.406759i	−0.473847	−	0.880607i	$-0.657135\pi$
$883$	359.169	−	359.169i	0.406759	−	0.406759i	0.880607	+	0.473847i	$0.157135\pi$
$884$	203.588	+	736.817i	0.230303	+	0.833503i
$885$	516.354	+	1132.40i	0.583451	+	1.27955i
$886$		−	1094.72i		−	1.23557i
$887$	−799.364			−0.901200			−0.450600	−	0.892726i	$-0.648790\pi$
$887$	−799.364			−0.901200			−0.450600	+	0.892726i	$0.648790\pi$
$888$	339.287	−	339.287i	0.382080	−	0.382080i
$889$	−274.862	−	274.862i	−0.309181	−	0.309181i
$890$	−1107.63	−	413.860i	−1.24453	−	0.465011i
$891$	−177.481	−	177.481i	−0.199193	−	0.199193i
$892$	−177.011	+	177.011i	−0.198443	+	0.198443i
$893$	−255.821	−	255.821i	−0.286474	−	0.286474i
$894$	506.221	−	506.221i	0.566243	−	0.566243i
$895$	−1164.31	+	530.901i	−1.30090	+	0.593186i
$896$	−27.3951	+	27.3951i	−0.0305749	+	0.0305749i
$897$	212.895	+	212.895i	0.237341	+	0.237341i
$898$		−	58.7283i		−	0.0653990i
$899$	126.318			0.140510
$900$	348.037	+	302.287i	0.386707	+	0.335874i
$901$	2.43248	+	8.80354i	0.00269976	+	0.00977085i
$902$	159.157	+	159.157i	0.176449	+	0.176449i
$903$	−109.673	−	109.673i	−0.121454	−	0.121454i
$904$	−292.206	−	292.206i	−0.323237	−	0.323237i
$905$	−1220.61	−	456.074i	−1.34874	−	0.503949i
$906$	1120.81	−	1120.81i	1.23710	−	1.23710i
$907$			333.394i			0.367579i	0.982966	+	0.183789i	$0.0588365\pi$
$907$			333.394i			0.367579i	−0.982966	+	0.183789i	$0.941164\pi$
$908$	−59.6622			−0.0657072
$909$	504.137			0.554606
$910$	495.343	−	225.867i	0.544333	−	0.248205i
$911$	907.939	+	907.939i	0.996640	+	0.996640i	0.999994	−	0.00335487i	$-0.00106789\pi$
$911$	907.939	+	907.939i	0.996640	+	0.996640i	−0.00335487	+	0.999994i	$0.501068\pi$
$912$			154.973i			0.169927i
$913$			190.096i			0.208210i
$914$			435.549i			0.476531i
$915$	−627.879	+	1680.41i	−0.686206	+	1.83652i
$916$		−	69.4066i		−	0.0757714i
$917$	201.375	+	201.375i	0.219602	+	0.219602i
$918$	−6.00446	−	21.7311i	−0.00654080	−	0.0236722i
$919$			926.040i			1.00766i	0.863803	+	0.503830i	$0.168076\pi$
$919$			926.040i			1.00766i	−0.863803	+	0.503830i	$0.831924\pi$
$920$	−41.5614	−	15.5292i	−0.0451755	−	0.0168796i
$921$	599.522	−	599.522i	0.650946	−	0.650946i
$922$	199.177	+	199.177i	0.216027	+	0.216027i
$923$		−	1262.79i		−	1.36813i
$924$	−65.6974	+	65.6974i	−0.0711011	+	0.0711011i
$925$	651.537	−	750.144i	0.704365	−	0.810967i
$926$		−	229.290i		−	0.247614i
$927$	−138.531	+	138.531i	−0.149440	+	0.149440i
$928$	−12.1685			−0.0131126
$929$	−523.269	+	523.269i	−0.563260	+	0.563260i	−0.930232	−	0.366972i	$-0.880395\pi$
$929$	−523.269	+	523.269i	−0.563260	+	0.563260i	0.366972	+	0.930232i	$0.380395\pi$
$930$	−1612.65	+	735.338i	−1.73404	+	0.790686i
$931$	−338.319			−0.363394
$932$	784.611			0.841857
$933$	1021.20	+	1021.20i	1.09454	+	1.09454i
$934$		−	277.335i		−	0.296932i
$935$	−173.494	−	207.071i	−0.185555	−	0.221466i
$936$	−586.297			−0.626386
$937$	−656.378	+	656.378i	−0.700510	+	0.700510i	−0.964520	−	0.264010i	$-0.914955\pi$
$937$	−656.378	+	656.378i	−0.700510	+	0.700510i	0.264010	+	0.964520i	$0.414955\pi$
$938$		−	436.925i		−	0.465804i
$939$			730.689i			0.778157i
$940$	−139.510	+	373.376i	−0.148415	+	0.397209i
$941$	−164.577	−	164.577i	−0.174895	−	0.174895i	0.614231	−	0.789126i	$-0.289466\pi$
$941$	−164.577	−	164.577i	−0.174895	−	0.174895i	−0.789126	+	0.614231i	$0.789466\pi$
$942$		−	468.342i		−	0.497178i
$943$	−111.093	−	111.093i	−0.117808	−	0.117808i
$944$	233.260			0.247097
$945$	−14.6093	+	6.66153i	−0.0154595	+	0.00704924i
$946$	33.7241	+	33.7241i	0.0356491	+	0.0356491i
$947$	82.4386			0.0870524			0.0435262	−	0.999052i	$-0.486141\pi$
$947$	82.4386			0.0870524			0.0435262	+	0.999052i	$0.486141\pi$
$948$	−363.936	+	363.936i	−0.383898	+	0.383898i
$949$	56.7224	+	56.7224i	0.0597707	+	0.0597707i
$950$	22.5200	+	320.117i	0.0237052	+	0.336966i
$951$	−1429.48			−1.50313
$952$	158.709	−	43.8525i	0.166711	−	0.0460635i
$953$	−937.183	+	937.183i	−0.983403	+	0.983403i	−0.999864	−	0.0164619i	$-0.994760\pi$
$953$	−937.183	+	937.183i	−0.983403	+	0.983403i	0.0164619	+	0.999864i	$0.494760\pi$
$954$	−7.00513			−0.00734290
$955$	675.420	−	307.978i	0.707246	−	0.322490i
$956$	361.532			0.378172
$957$	−29.1817			−0.0304929
$958$	48.2551			0.0503707
$959$	−49.1362	+	49.1362i	−0.0512369	+	0.0512369i
$960$	155.350	−	70.8366i	0.161823	−	0.0737881i
$961$		−	2487.33i		−	2.58827i
$962$			1263.68i			1.31360i
$963$	−177.364			−0.184179
$964$	−308.432	−	308.432i	−0.319951	−	0.319951i
$965$	−1679.51	+	765.822i	−1.74042	+	0.793598i
$966$	45.8572	−	45.8572i	0.0474712	−	0.0474712i
$967$	−812.158	+	812.158i	−0.839873	+	0.839873i	−0.988842	−	0.148969i	$-0.952405\pi$
$967$	−812.158	+	812.158i	−0.839873	+	0.839873i	0.148969	+	0.988842i	$0.452405\pi$
$968$	−221.798	+	221.798i	−0.229130	+	0.229130i
$969$	324.870	−	572.941i	0.335263	−	0.591271i
$970$	−391.263	+	1047.15i	−0.403364	+	1.07954i
$971$			485.915i			0.500427i	0.968191	+	0.250213i	$0.0805008\pi$
$971$			485.915i			0.500427i	−0.968191	+	0.250213i	$0.919499\pi$
$972$	−691.077			−0.710985
$973$	−448.971	+	448.971i	−0.461430	+	0.461430i
$974$	746.620	+	746.620i	0.766550	+	0.766550i
$975$	−2393.29	+	168.366i	−2.45465	+	0.172683i
$976$	237.738	+	237.738i	0.243584	+	0.243584i
$977$	−317.093	+	317.093i	−0.324558	+	0.324558i	−0.850513	−	0.525955i	$-0.823708\pi$
$977$	−317.093	+	317.093i	−0.324558	+	0.324558i	0.525955	+	0.850513i	$0.323708\pi$
$978$	−1116.59	−	1116.59i	−1.14171	−	1.14171i
$979$	−375.795	+	375.795i	−0.383856	+	0.383856i
$980$	154.642	+	339.142i	0.157798	+	0.346064i
$981$	282.597	−	282.597i	0.288071	−	0.288071i
$982$	679.078	+	679.078i	0.691526	+	0.691526i
$983$			1363.97i			1.38756i	0.720188	+	0.693779i	$0.244056\pi$
$983$			1363.97i			1.38756i	−0.720188	+	0.693779i	$0.755944\pi$
$984$	604.593			0.614423
$985$	−35.8408	−	78.6016i	−0.0363866	−	0.0797986i
$986$	44.9873	+	25.5087i	0.0456260	+	0.0258709i
$987$	−411.968	−	411.968i	−0.417395	−	0.417395i
$988$	−288.601	−	288.601i	−0.292106	−	0.292106i
$989$	−23.5396	−	23.5396i	−0.0238014	−	0.0238014i
$990$	188.522	−	85.9622i	0.190426	−	0.0868306i
$991$	713.952	−	713.952i	0.720436	−	0.720436i	−0.248258	−	0.968694i	$-0.579858\pi$
$991$	713.952	−	713.952i	0.720436	−	0.720436i	0.968694	+	0.248258i	$0.0798581\pi$
$992$			332.184i			0.334863i
$993$	1796.95			1.80962
$994$	−272.002			−0.273644
$995$	1431.47	+	534.862i	1.43866	+	0.537550i
$996$	361.060	+	361.060i	0.362510	+	0.362510i
$997$		−	218.369i		−	0.219026i	−0.993985	−	0.109513i	$-0.965071\pi$
$997$		−	218.369i		−	0.219026i	0.993985	−	0.109513i	$-0.0349291\pi$
$998$		−	891.071i		−	0.892857i
$999$		−	37.2700i		−	0.0373073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.3.e.b.157.8	yes	16
5.3	odd	4		170.3.j.b.123.1	yes	16
17.13	even	4		170.3.j.b.47.1	yes	16
85.13	odd	4	inner	170.3.e.b.13.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.3.e.b.13.1	✓	16	85.13	odd	4	inner
170.3.e.b.157.8	yes	16	1.1	even	1	trivial
170.3.j.b.47.1	yes	16	17.13	even	4
170.3.j.b.123.1	yes	16	5.3	odd	4

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	170.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +4.26845i q^{3} -2.00000i q^{4} +(-4.54937 + 2.07442i) q^{5} +(4.26845 + 4.26845i) q^{6} +3.42439i q^{7} +(-2.00000 - 2.00000i) q^{8} -9.21970 q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +4.26845i q^{3} -2.00000i q^{4} +(-4.54937 + 2.07442i) q^{5} +(4.26845 + 4.26845i) q^{6} +3.42439i q^{7} +(-2.00000 - 2.00000i) q^{8} -9.21970 q^{9} +(-2.47495 + 6.62379i) q^{10} +(2.24732 + 2.24732i) q^{11} +8.53691 q^{12} +(-15.8980 + 15.8980i) q^{13} +(3.42439 + 3.42439i) q^{14} +(-8.85457 - 19.4188i) q^{15} -4.00000 q^{16} +(14.7881 + 8.38518i) q^{17} +(-9.21970 + 9.21970i) q^{18} -9.07667 q^{19} +(4.14884 + 9.09874i) q^{20} -14.6169 q^{21} +4.49463 q^{22} -3.13728 q^{23} +(8.53691 - 8.53691i) q^{24} +(16.3935 - 18.8746i) q^{25} +31.7959i q^{26} -0.937764i q^{27} +6.84878 q^{28} +(1.52106 + 1.52106i) q^{29} +(-28.2734 - 10.5642i) q^{30} +(41.5231 - 41.5231i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-9.59256 + 9.59256i) q^{33} +(23.1733 - 6.40295i) q^{34} +(-7.10364 - 15.5788i) q^{35} +18.4394i q^{36} +39.7435 q^{37} +(-9.07667 + 9.07667i) q^{38} +(-67.8597 - 67.8597i) q^{39} +(13.2476 + 4.94990i) q^{40} +(35.4105 + 35.4105i) q^{41} +(-14.6169 + 14.6169i) q^{42} +(7.50319 + 7.50319i) q^{43} +(4.49463 - 4.49463i) q^{44} +(41.9438 - 19.1255i) q^{45} +(-3.13728 + 3.13728i) q^{46} +(28.1845 + 28.1845i) q^{47} -17.0738i q^{48} +37.2735 q^{49} +(-2.48109 - 35.2682i) q^{50} +(-35.7917 + 63.1224i) q^{51} +(31.7959 + 31.7959i) q^{52} +(0.379900 + 0.379900i) q^{53} +(-0.937764 - 0.937764i) q^{54} +(-14.8858 - 5.56199i) q^{55} +(6.84878 - 6.84878i) q^{56} -38.7433i q^{57} +3.04212 q^{58} -58.3149 q^{59} +(-38.8376 + 17.7091i) q^{60} +(-59.4346 - 59.4346i) q^{61} -83.0461i q^{62} -31.5719i q^{63} +8.00000i q^{64} +(39.3466 - 105.305i) q^{65} +19.1851i q^{66} +(-63.7959 - 63.7959i) q^{67} +(16.7704 - 29.5763i) q^{68} -13.3913i q^{69} +(-22.6825 - 8.47519i) q^{70} +(-39.7153 + 39.7153i) q^{71} +(18.4394 + 18.4394i) q^{72} -3.56790i q^{73} +(39.7435 - 39.7435i) q^{74} +(80.5655 + 69.9751i) q^{75} +18.1533i q^{76} +(-7.69569 + 7.69569i) q^{77} -135.719 q^{78} +(-42.6309 + 42.6309i) q^{79} +(18.1975 - 8.29769i) q^{80} -78.9745 q^{81} +70.8210 q^{82} +(42.2940 + 42.2940i) q^{83} +29.2337i q^{84} +(-84.6711 - 7.47045i) q^{85} +15.0064 q^{86} +(-6.49257 + 6.49257i) q^{87} -8.98926i q^{88} +167.220i q^{89} +(22.8183 - 61.0694i) q^{90} +(-54.4408 - 54.4408i) q^{91} +6.27457i q^{92} +(177.239 + 177.239i) q^{93} +56.3689 q^{94} +(41.2931 - 18.8288i) q^{95} +(-17.0738 - 17.0738i) q^{96} +158.089 q^{97} +(37.2735 - 37.2735i) q^{98} +(-20.7196 - 20.7196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9	\( 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9} - 4 q^{10} + 20 q^{11} + 4 q^{13} - 12 q^{14} + 12 q^{15} - 64 q^{16} + 36 q^{17} - 16 q^{18} - 16 q^{19} - 4 q^{20} + 40 q^{22} + 16 q^{23} + 44 q^{25} - 24 q^{28} - 20 q^{29} + 12 q^{30} + 92 q^{31} - 64 q^{32} - 60 q^{33} + 24 q^{34} - 124 q^{35} + 32 q^{37} - 16 q^{38} - 140 q^{39} - 60 q^{41} + 52 q^{43} + 40 q^{44} + 198 q^{45} + 16 q^{46} + 112 q^{47} + 136 q^{49} - 4 q^{50} - 140 q^{51} - 8 q^{52} + 48 q^{53} + 108 q^{54} + 40 q^{55} - 24 q^{56} - 40 q^{58} + 76 q^{61} - 40 q^{65} + 116 q^{67} - 24 q^{68} - 124 q^{70} - 268 q^{71} + 32 q^{72} + 32 q^{74} + 136 q^{75} - 116 q^{77} - 280 q^{78} - 88 q^{79} + 8 q^{80} - 352 q^{81} - 120 q^{82} - 160 q^{83} + 310 q^{85} + 104 q^{86} + 236 q^{87} + 260 q^{90} - 168 q^{91} + 48 q^{93} + 224 q^{94} + 264 q^{95} - 256 q^{97} + 136 q^{98} - 348 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9 - 4 * q^10 + 20 * q^11 + 4 * q^13 - 12 * q^14 + 12 * q^15 - 64 * q^16 + 36 * q^17 - 16 * q^18 - 16 * q^19 - 4 * q^20 + 40 * q^22 + 16 * q^23 + 44 * q^25 - 24 * q^28 - 20 * q^29 + 12 * q^30 + 92 * q^31 - 64 * q^32 - 60 * q^33 + 24 * q^34 - 124 * q^35 + 32 * q^37 - 16 * q^38 - 140 * q^39 - 60 * q^41 + 52 * q^43 + 40 * q^44 + 198 * q^45 + 16 * q^46 + 112 * q^47 + 136 * q^49 - 4 * q^50 - 140 * q^51 - 8 * q^52 + 48 * q^53 + 108 * q^54 + 40 * q^55 - 24 * q^56 - 40 * q^58 + 76 * q^61 - 40 * q^65 + 116 * q^67 - 24 * q^68 - 124 * q^70 - 268 * q^71 + 32 * q^72 + 32 * q^74 + 136 * q^75 - 116 * q^77 - 280 * q^78 - 88 * q^79 + 8 * q^80 - 352 * q^81 - 120 * q^82 - 160 * q^83 + 310 * q^85 + 104 * q^86 + 236 * q^87 + 260 * q^90 - 168 * q^91 + 48 * q^93 + 224 * q^94 + 264 * q^95 - 256 * q^97 + 136 * q^98 - 348 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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