LMFDB - Embedded newform 370.2.h.e.253.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(117,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("370.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.h (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 $ x^20 - 4x^19 + 8x^18 + 4x^17 + 103x^16 - 394x^15 + 760x^14 + 278x^13 + 2009x^12 - 7362x^11 + 13826x^10 + 4848x^9 + 13544x^8 - 44248x^7 + 76384x^6 + 24512x^5 + 28432x^4 - 61952x^3 + 61952x^2 - 5632*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.4
Root			$-0.794932 - 0.794932i$ of defining polynomial
Character	$\chi$	$=$	370.253
Dual form			370.2.h.e.117.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.794932 + 0.794932i) q^{3} +1.00000 q^{4} +(2.22550 - 0.217179i) q^{5} +(0.794932 - 0.794932i) q^{6} +(2.93770 - 2.93770i) q^{7} -1.00000 q^{8} +1.73617i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.794932 + 0.794932i) q^{3} +1.00000 q^{4} +(2.22550 - 0.217179i) q^{5} +(0.794932 - 0.794932i) q^{6} +(2.93770 - 2.93770i) q^{7} -1.00000 q^{8} +1.73617i q^{9} +(-2.22550 + 0.217179i) q^{10} -3.55539i q^{11} +(-0.794932 + 0.794932i) q^{12} -4.41538 q^{13} +(-2.93770 + 2.93770i) q^{14} +(-1.59648 + 1.94176i) q^{15} +1.00000 q^{16} -5.37801i q^{17} -1.73617i q^{18} +(1.98590 + 1.98590i) q^{19} +(2.22550 - 0.217179i) q^{20} +4.67054i q^{21} +3.55539i q^{22} +5.90774 q^{23} +(0.794932 - 0.794932i) q^{24} +(4.90567 - 0.966660i) q^{25} +4.41538 q^{26} +(-3.76493 - 3.76493i) q^{27} +(2.93770 - 2.93770i) q^{28} +(2.18437 - 2.18437i) q^{29} +(1.59648 - 1.94176i) q^{30} +(5.42197 + 5.42197i) q^{31} -1.00000 q^{32} +(2.82629 + 2.82629i) q^{33} +5.37801i q^{34} +(5.89983 - 7.17584i) q^{35} +1.73617i q^{36} +(-3.88900 + 4.67714i) q^{37} +(-1.98590 - 1.98590i) q^{38} +(3.50993 - 3.50993i) q^{39} +(-2.22550 + 0.217179i) q^{40} +6.34477i q^{41} -4.67054i q^{42} +1.78544 q^{43} -3.55539i q^{44} +(0.377058 + 3.86383i) q^{45} -5.90774 q^{46} +(1.82646 - 1.82646i) q^{47} +(-0.794932 + 0.794932i) q^{48} -10.2601i q^{49} +(-4.90567 + 0.966660i) q^{50} +(4.27515 + 4.27515i) q^{51} -4.41538 q^{52} +(-9.57437 - 9.57437i) q^{53} +(3.76493 + 3.76493i) q^{54} +(-0.772154 - 7.91250i) q^{55} +(-2.93770 + 2.93770i) q^{56} -3.15731 q^{57} +(-2.18437 + 2.18437i) q^{58} +(4.44588 + 4.44588i) q^{59} +(-1.59648 + 1.94176i) q^{60} +(1.44033 + 1.44033i) q^{61} +(-5.42197 - 5.42197i) q^{62} +(5.10033 + 5.10033i) q^{63} +1.00000 q^{64} +(-9.82642 + 0.958927i) q^{65} +(-2.82629 - 2.82629i) q^{66} +(7.88856 + 7.88856i) q^{67} -5.37801i q^{68} +(-4.69625 + 4.69625i) q^{69} +(-5.89983 + 7.17584i) q^{70} -11.2579 q^{71} -1.73617i q^{72} +(-4.02333 + 4.02333i) q^{73} +(3.88900 - 4.67714i) q^{74} +(-3.13124 + 4.66810i) q^{75} +(1.98590 + 1.98590i) q^{76} +(-10.4447 - 10.4447i) q^{77} +(-3.50993 + 3.50993i) q^{78} +(2.03059 + 2.03059i) q^{79} +(2.22550 - 0.217179i) q^{80} +0.777232 q^{81} -6.34477i q^{82} +(-4.51281 - 4.51281i) q^{83} +4.67054i q^{84} +(-1.16799 - 11.9687i) q^{85} -1.78544 q^{86} +3.47285i q^{87} +3.55539i q^{88} +(2.13937 - 2.13937i) q^{89} +(-0.377058 - 3.86383i) q^{90} +(-12.9711 + 12.9711i) q^{91} +5.90774 q^{92} -8.62020 q^{93} +(-1.82646 + 1.82646i) q^{94} +(4.85091 + 3.98832i) q^{95} +(0.794932 - 0.794932i) q^{96} +5.91995i q^{97} +10.2601i q^{98} +6.17274 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8} + 4 q^{10} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 6 q^{19} - 4 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} - 20 q^{27} - 2 q^{28} + 18 q^{29} + 4 q^{30} + 12 q^{31} - 20 q^{32} + 4 q^{33} - 12 q^{35} - 32 q^{37} - 6 q^{38} + 6 q^{39} + 4 q^{40} + 16 q^{43} + 22 q^{45} + 4 q^{46} - 22 q^{47} + 4 q^{48} - 10 q^{50} + 8 q^{51} - 4 q^{53} + 20 q^{54} + 16 q^{55} + 2 q^{56} + 24 q^{57} - 18 q^{58} - 10 q^{59} - 4 q^{60} + 10 q^{61} - 12 q^{62} - 2 q^{63} + 20 q^{64} + 20 q^{65} - 4 q^{66} + 8 q^{67} - 34 q^{69} + 12 q^{70} + 16 q^{71} - 6 q^{73} + 32 q^{74} - 26 q^{75} + 6 q^{76} - 4 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} - 28 q^{81} + 6 q^{83} + 10 q^{85} - 16 q^{86} - 44 q^{89} - 22 q^{90} - 40 q^{91} - 4 q^{92} - 40 q^{93} + 22 q^{94} + 50 q^{95} - 4 q^{96} - 20 q^{99}+O(q^{100}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8 + 4 * q^10 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 6 * q^19 - 4 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 - 20 * q^27 - 2 * q^28 + 18 * q^29 + 4 * q^30 + 12 * q^31 - 20 * q^32 + 4 * q^33 - 12 * q^35 - 32 * q^37 - 6 * q^38 + 6 * q^39 + 4 * q^40 + 16 * q^43 + 22 * q^45 + 4 * q^46 - 22 * q^47 + 4 * q^48 - 10 * q^50 + 8 * q^51 - 4 * q^53 + 20 * q^54 + 16 * q^55 + 2 * q^56 + 24 * q^57 - 18 * q^58 - 10 * q^59 - 4 * q^60 + 10 * q^61 - 12 * q^62 - 2 * q^63 + 20 * q^64 + 20 * q^65 - 4 * q^66 + 8 * q^67 - 34 * q^69 + 12 * q^70 + 16 * q^71 - 6 * q^73 + 32 * q^74 - 26 * q^75 + 6 * q^76 - 4 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 - 28 * q^81 + 6 * q^83 + 10 * q^85 - 16 * q^86 - 44 * q^89 - 22 * q^90 - 40 * q^91 - 4 * q^92 - 40 * q^93 + 22 * q^94 + 50 * q^95 - 4 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.794932	+	0.794932i	−0.458954	+	0.458954i	−0.898312	−	0.439358i	$-0.855206\pi$
$3$	−0.794932	+	0.794932i	−0.458954	+	0.458954i	0.439358	+	0.898312i	$0.355206\pi$
$4$	1.00000			0.500000
$5$	2.22550	−	0.217179i	0.995272	−	0.0971252i
$5$	2.22550	−	0.217179i	0.995272	−	0.0971252i
$6$	0.794932	−	0.794932i	0.324530	−	0.324530i
$7$	2.93770	−	2.93770i	1.11035	−	1.11035i	0.117242	−	0.993103i	$-0.462595\pi$
$7$	2.93770	−	2.93770i	1.11035	−	1.11035i	0.993103	−	0.117242i	$-0.0374053\pi$
$8$	−1.00000			−0.353553
$9$			1.73617i			0.578722i
$10$	−2.22550	+	0.217179i	−0.703764	+	0.0686779i
$11$		−	3.55539i		−	1.07199i	−0.844221	−	0.535995i	$-0.819937\pi$
$11$		−	3.55539i		−	1.07199i	0.844221	−	0.535995i	$-0.180063\pi$
$12$	−0.794932	+	0.794932i	−0.229477	+	0.229477i
$13$	−4.41538			−1.22461			−0.612303	−	0.790623i	$-0.709757\pi$
$13$	−4.41538			−1.22461			−0.612303	+	0.790623i	$0.709757\pi$
$14$	−2.93770	+	2.93770i	−0.785133	+	0.785133i
$15$	−1.59648	+	1.94176i	−0.412208	+	0.501360i
$16$	1.00000			0.250000
$17$		−	5.37801i		−	1.30436i	−0.758065	−	0.652179i	$-0.773855\pi$
$17$		−	5.37801i		−	1.30436i	0.758065	−	0.652179i	$-0.226145\pi$
$18$		−	1.73617i		−	0.409218i
$19$	1.98590	+	1.98590i	0.455597	+	0.455597i	0.897207	−	0.441610i	$-0.145592\pi$
$19$	1.98590	+	1.98590i	0.455597	+	0.455597i	−0.441610	+	0.897207i	$0.645592\pi$
$20$	2.22550	−	0.217179i	0.497636	−	0.0485626i
$21$			4.67054i			1.01920i
$22$			3.55539i			0.758011i
$23$	5.90774			1.23185			0.615925	−	0.787805i	$-0.288783\pi$
$23$	5.90774			1.23185			0.615925	+	0.787805i	$0.288783\pi$
$24$	0.794932	−	0.794932i	0.162265	−	0.162265i
$25$	4.90567	−	0.966660i	0.981133	−	0.193332i
$26$	4.41538			0.865928
$27$	−3.76493	−	3.76493i	−0.724561	−	0.724561i
$28$	2.93770	−	2.93770i	0.555173	−	0.555173i
$29$	2.18437	−	2.18437i	0.405627	−	0.405627i	−0.474584	−	0.880210i	$-0.657401\pi$
$29$	2.18437	−	2.18437i	0.405627	−	0.405627i	0.880210	+	0.474584i	$0.157401\pi$
$30$	1.59648	−	1.94176i	0.291475	−	0.354515i
$31$	5.42197	+	5.42197i	0.973815	+	0.973815i	0.999666	−	0.0258507i	$-0.00822946\pi$
$31$	5.42197	+	5.42197i	0.973815	+	0.973815i	−0.0258507	+	0.999666i	$0.508229\pi$
$32$	−1.00000			−0.176777
$33$	2.82629	+	2.82629i	0.491994	+	0.491994i
$34$			5.37801i			0.922321i
$35$	5.89983	−	7.17584i	0.997253	−	1.21294i
$36$			1.73617i			0.289361i
$37$	−3.88900	+	4.67714i	−0.639348	+	0.768918i
$37$	−3.88900	+	4.67714i	−0.639348	+	0.768918i
$38$	−1.98590	−	1.98590i	−0.322156	−	0.322156i
$39$	3.50993	−	3.50993i	0.562039	−	0.562039i
$40$	−2.22550	+	0.217179i	−0.351882	+	0.0343389i
$41$			6.34477i			0.990886i	0.868640	+	0.495443i	$0.164994\pi$
$41$			6.34477i			0.990886i	−0.868640	+	0.495443i	$0.835006\pi$
$42$		−	4.67054i		−	0.720680i
$43$	1.78544			0.272277			0.136139	−	0.990690i	$-0.456531\pi$
$43$	1.78544			0.272277			0.136139	+	0.990690i	$0.456531\pi$
$44$		−	3.55539i		−	0.535995i
$45$	0.377058	+	3.86383i	0.0562085	+	0.575986i
$46$	−5.90774			−0.871049
$47$	1.82646	−	1.82646i	0.266417	−	0.266417i	−0.561238	−	0.827655i	$-0.689675\pi$
$47$	1.82646	−	1.82646i	0.266417	−	0.266417i	0.827655	+	0.561238i	$0.189675\pi$
$48$	−0.794932	+	0.794932i	−0.114739	+	0.114739i
$49$		−	10.2601i		−	1.46573i
$50$	−4.90567	+	0.966660i	−0.693766	+	0.136706i
$51$	4.27515	+	4.27515i	0.598641	+	0.598641i
$52$	−4.41538			−0.612303
$53$	−9.57437	−	9.57437i	−1.31514	−	1.31514i	−0.917573	−	0.397567i	$-0.869855\pi$
$53$	−9.57437	−	9.57437i	−1.31514	−	1.31514i	−0.397567	−	0.917573i	$-0.630145\pi$
$54$	3.76493	+	3.76493i	0.512342	+	0.512342i
$55$	−0.772154	−	7.91250i	−0.104117	−	1.06692i
$56$	−2.93770	+	2.93770i	−0.392566	+	0.392566i
$57$	−3.15731			−0.418197
$58$	−2.18437	+	2.18437i	−0.286821	+	0.286821i
$59$	4.44588	+	4.44588i	0.578805	+	0.578805i	0.934574	−	0.355769i	$-0.115781\pi$
$59$	4.44588	+	4.44588i	0.578805	+	0.578805i	−0.355769	+	0.934574i	$0.615781\pi$
$60$	−1.59648	+	1.94176i	−0.206104	+	0.250680i
$61$	1.44033	+	1.44033i	0.184416	+	0.184416i	0.793277	−	0.608861i	$-0.208373\pi$
$61$	1.44033	+	1.44033i	0.184416	+	0.184416i	−0.608861	+	0.793277i	$0.708373\pi$
$62$	−5.42197	−	5.42197i	−0.688591	−	0.688591i
$63$	5.10033	+	5.10033i	0.642581	+	0.642581i
$64$	1.00000			0.125000
$65$	−9.82642	+	0.958927i	−1.21882	+	0.118940i
$66$	−2.82629	−	2.82629i	−0.347893	−	0.347893i
$67$	7.88856	+	7.88856i	0.963741	+	0.963741i	0.999365	−	0.0356245i	$-0.0113420\pi$
$67$	7.88856	+	7.88856i	0.963741	+	0.963741i	−0.0356245	+	0.999365i	$0.511342\pi$
$68$		−	5.37801i		−	0.652179i
$69$	−4.69625	+	4.69625i	−0.565363	+	0.565363i
$70$	−5.89983	+	7.17584i	−0.705165	+	0.857677i
$71$	−11.2579			−1.33606			−0.668032	−	0.744132i	$-0.732863\pi$
$71$	−11.2579			−1.33606			−0.668032	+	0.744132i	$0.732863\pi$
$72$		−	1.73617i		−	0.204609i
$73$	−4.02333	+	4.02333i	−0.470896	+	0.470896i	−0.902204	−	0.431309i	$-0.858052\pi$
$73$	−4.02333	+	4.02333i	−0.470896	+	0.470896i	0.431309	+	0.902204i	$0.358052\pi$
$74$	3.88900	−	4.67714i	0.452087	−	0.543707i
$75$	−3.13124	+	4.66810i	−0.361565	+	0.539026i
$76$	1.98590	+	1.98590i	0.227799	+	0.227799i
$77$	−10.4447	−	10.4447i	−1.19028	−	1.19028i
$78$	−3.50993	+	3.50993i	−0.397421	+	0.397421i
$79$	2.03059	+	2.03059i	0.228459	+	0.228459i	0.812049	−	0.583590i	$-0.198352\pi$
$79$	2.03059	+	2.03059i	0.228459	+	0.228459i	−0.583590	+	0.812049i	$0.698352\pi$
$80$	2.22550	−	0.217179i	0.248818	−	0.0242813i
$81$	0.777232			0.0863591
$82$		−	6.34477i		−	0.700662i
$83$	−4.51281	−	4.51281i	−0.495345	−	0.495345i	0.414640	−	0.909985i	$-0.363907\pi$
$83$	−4.51281	−	4.51281i	−0.495345	−	0.495345i	−0.909985	+	0.414640i	$0.863907\pi$
$84$			4.67054i			0.509598i
$85$	−1.16799	−	11.9687i	−0.126686	−	1.29819i
$86$	−1.78544			−0.192529
$87$			3.47285i			0.372328i
$88$			3.55539i			0.379006i
$89$	2.13937	−	2.13937i	0.226773	−	0.226773i	−0.584570	−	0.811343i	$-0.698737\pi$
$89$	2.13937	−	2.13937i	0.226773	−	0.226773i	0.811343	+	0.584570i	$0.198737\pi$
$90$	−0.377058	−	3.86383i	−0.0397454	−	0.407283i
$91$	−12.9711	+	12.9711i	−1.35974	+	1.35974i
$92$	5.90774			0.615925
$93$	−8.62020			−0.893873
$94$	−1.82646	+	1.82646i	−0.188385	+	0.188385i
$95$	4.85091	+	3.98832i	0.497693	+	0.409193i
$96$	0.794932	−	0.794932i	0.0811324	−	0.0811324i
$97$			5.91995i			0.601080i	0.953769	+	0.300540i	$0.0971669\pi$
$97$			5.91995i			0.601080i	−0.953769	+	0.300540i	$0.902833\pi$
$98$			10.2601i			1.03643i
$99$	6.17274			0.620384
$100$	4.90567	−	0.966660i	0.490567	−	0.0966660i
$101$			9.23382i			0.918799i	0.888230	+	0.459399i	$0.151935\pi$
$101$			9.23382i			0.918799i	−0.888230	+	0.459399i	$0.848065\pi$
$102$	−4.27515	−	4.27515i	−0.423303	−	0.423303i
$103$			8.03931i			0.792137i	0.918221	+	0.396068i	$0.129626\pi$
$103$			8.03931i			0.792137i	−0.918221	+	0.396068i	$0.870374\pi$
$104$	4.41538			0.432964
$105$	1.01434	+	10.3943i	0.0989896	+	1.01438i
$106$	9.57437	+	9.57437i	0.929945	+	0.929945i
$107$	4.60753	−	4.60753i	0.445427	−	0.445427i	−0.448404	−	0.893831i	$-0.648007\pi$
$107$	4.60753	−	4.60753i	0.445427	−	0.445427i	0.893831	+	0.448404i	$0.148007\pi$
$108$	−3.76493	−	3.76493i	−0.362281	−	0.362281i
$109$	−14.6123	−	14.6123i	−1.39961	−	1.39961i	−0.801166	−	0.598443i	$-0.795786\pi$
$109$	−14.6123	−	14.6123i	−1.39961	−	1.39961i	−0.598443	−	0.801166i	$-0.704214\pi$
$110$	0.772154	+	7.91250i	0.0736220	+	0.754428i
$111$	−0.626522	−	6.80950i	−0.0594668	−	0.646329i
$112$	2.93770	−	2.93770i	0.277586	−	0.277586i
$113$			8.61849i			0.810759i	0.914148	+	0.405380i	$0.132861\pi$
$113$			8.61849i			0.810759i	−0.914148	+	0.405380i	$0.867139\pi$
$114$	3.15731			0.295710
$115$	13.1477	−	1.28304i	1.22603	−	0.119644i
$116$	2.18437	−	2.18437i	0.202813	−	0.202813i
$117$		−	7.66584i		−	0.708707i
$118$	−4.44588	−	4.44588i	−0.409277	−	0.409277i
$119$	−15.7990	−	15.7990i	−1.44829	−	1.44829i
$120$	1.59648	−	1.94176i	0.145738	−	0.177258i
$121$	−1.64079			−0.149163
$122$	−1.44033	−	1.44033i	−0.130402	−	0.130402i
$123$	−5.04366	−	5.04366i	−0.454772	−	0.454772i
$124$	5.42197	+	5.42197i	0.486908	+	0.486908i
$125$	10.7076	−	3.21670i	0.957717	−	0.287711i
$126$	−5.10033	−	5.10033i	−0.454373	−	0.454373i
$127$	−4.22966	+	4.22966i	−0.375322	+	0.375322i	−0.869411	−	0.494089i	$-0.835502\pi$
$127$	−4.22966	+	4.22966i	−0.375322	+	0.375322i	0.494089	+	0.869411i	$0.335502\pi$
$128$	−1.00000			−0.0883883
$129$	−1.41931	+	1.41931i	−0.124963	+	0.124963i
$130$	9.82642	−	0.958927i	0.861834	−	0.0841034i
$131$	−15.2680	−	15.2680i	−1.33397	−	1.33397i	−0.901783	−	0.432188i	$-0.857742\pi$
$131$	−15.2680	−	15.2680i	−1.33397	−	1.33397i	−0.432188	−	0.901783i	$-0.642258\pi$
$132$	2.82629	+	2.82629i	0.245997	+	0.245997i
$133$	11.6680			1.01174
$134$	−7.88856	−	7.88856i	−0.681468	−	0.681468i
$135$	−9.19650	−	7.56118i	−0.791509	−	0.650762i
$136$			5.37801i			0.461160i
$137$	−14.4220	+	14.4220i	−1.23215	+	1.23215i	−0.269015	+	0.963136i	$0.586698\pi$
$137$	−14.4220	+	14.4220i	−1.23215	+	1.23215i	−0.963136	+	0.269015i	$0.913302\pi$
$138$	4.69625	−	4.69625i	0.399772	−	0.399772i
$139$	1.56244			0.132525			0.0662624	−	0.997802i	$-0.478893\pi$
$139$	1.56244			0.132525			0.0662624	+	0.997802i	$0.478893\pi$
$140$	5.89983	−	7.17584i	0.498627	−	0.606469i
$141$			2.90383i			0.244547i
$142$	11.2579			0.944740
$143$			15.6984i			1.31277i
$144$			1.73617i			0.144680i
$145$	4.38690	−	5.33570i	0.364312	−	0.443105i
$146$	4.02333	−	4.02333i	0.332973	−	0.332973i
$147$	8.15611	+	8.15611i	0.672705	+	0.672705i
$148$	−3.88900	+	4.67714i	−0.319674	+	0.384459i
$149$			8.42600i			0.690285i	0.938550	+	0.345142i	$0.112169\pi$
$149$			8.42600i			0.690285i	−0.938550	+	0.345142i	$0.887831\pi$
$150$	3.13124	−	4.66810i	0.255665	−	0.381149i
$151$		−	9.65715i		−	0.785887i	−0.919563	−	0.392944i	$-0.871457\pi$
$151$		−	9.65715i		−	0.785887i	0.919563	−	0.392944i	$-0.128543\pi$
$152$	−1.98590	−	1.98590i	−0.161078	−	0.161078i
$153$	9.33711			0.754861
$154$	10.4447	+	10.4447i	0.841654	+	0.841654i
$155$	13.2441	+	10.8890i	1.06379	+	0.874629i
$156$	3.50993	−	3.50993i	0.281019	−	0.281019i
$157$	−13.7789	+	13.7789i	−1.09968	+	1.09968i	−0.105231	+	0.994448i	$0.533558\pi$
$157$	−13.7789	+	13.7789i	−1.09968	+	1.09968i	−0.994448	+	0.105231i	$0.966442\pi$
$158$	−2.03059	−	2.03059i	−0.161545	−	0.161545i
$159$	15.2219			1.20718
$160$	−2.22550	+	0.217179i	−0.175941	+	0.0171695i
$161$	17.3552	−	17.3552i	1.36778	−	1.36778i
$162$	−0.777232			−0.0610651
$163$			9.92434i			0.777334i	0.921378	+	0.388667i	$0.127064\pi$
$163$			9.92434i			0.777334i	−0.921378	+	0.388667i	$0.872936\pi$
$164$			6.34477i			0.495443i
$165$	6.90371	+	5.67609i	0.537453	+	0.441883i
$166$	4.51281	+	4.51281i	0.350262	+	0.350262i
$167$		−	17.7622i		−	1.37448i	−0.726431	−	0.687239i	$-0.758822\pi$
$167$		−	17.7622i		−	1.37448i	0.726431	−	0.687239i	$-0.241178\pi$
$168$		−	4.67054i		−	0.360340i
$169$	6.49561			0.499662
$170$	1.16799	+	11.9687i	0.0895806	+	0.917960i
$171$	−3.44786	+	3.44786i	−0.263664	+	0.263664i
$172$	1.78544			0.136139
$173$	−4.93605	+	4.93605i	−0.375281	+	0.375281i	−0.869396	−	0.494116i	$-0.835492\pi$
$173$	−4.93605	+	4.93605i	−0.375281	+	0.375281i	0.494116	+	0.869396i	$0.335492\pi$
$174$		−	3.47285i		−	0.263276i
$175$	11.5716	−	17.2511i	0.874732	−	1.30406i
$176$		−	3.55539i		−	0.267998i
$177$	−7.06835			−0.531290
$178$	−2.13937	+	2.13937i	−0.160353	+	0.160353i
$179$	3.68868	−	3.68868i	0.275705	−	0.275705i	−0.555687	−	0.831392i	$-0.687545\pi$
$179$	3.68868	−	3.68868i	0.275705	−	0.275705i	0.831392	+	0.555687i	$0.187545\pi$
$180$	0.377058	+	3.86383i	0.0281042	+	0.287993i
$181$	−5.35458			−0.398002			−0.199001	−	0.979999i	$-0.563770\pi$
$181$	−5.35458			−0.398002			−0.199001	+	0.979999i	$0.563770\pi$
$182$	12.9711	−	12.9711i	0.961479	−	0.961479i
$183$	−2.28994			−0.169277
$184$	−5.90774			−0.435525
$185$	−7.63918	+	11.2536i	−0.561644	+	0.827379i
$186$	8.62020			0.632064
$187$	−19.1209			−1.39826
$188$	1.82646	−	1.82646i	0.133209	−	0.133209i
$189$	−22.1205			−1.60903
$190$	−4.85091	−	3.98832i	−0.351922	−	0.289343i
$191$	10.0773	−	10.0773i	0.729166	−	0.729166i	−0.241288	−	0.970454i	$-0.577570\pi$
$191$	10.0773	−	10.0773i	0.729166	−	0.729166i	0.970454	+	0.241288i	$0.0775698\pi$
$192$	−0.794932	+	0.794932i	−0.0573693	+	0.0573693i
$193$	24.7844			1.78402			0.892011	−	0.452014i	$-0.149294\pi$
$193$	24.7844			1.78402			0.892011	+	0.452014i	$0.149294\pi$
$194$		−	5.91995i		−	0.425028i
$195$	7.04905	−	8.57362i	0.504793	−	0.613970i
$196$		−	10.2601i		−	0.732867i
$197$	11.3006	−	11.3006i	0.805132	−	0.805132i	−0.178760	−	0.983893i	$-0.557209\pi$
$197$	11.3006	−	11.3006i	0.805132	−	0.805132i	0.983893	+	0.178760i	$0.0572087\pi$
$198$	−6.17274			−0.438678
$199$	−6.90680	+	6.90680i	−0.489610	+	0.489610i	−0.908183	−	0.418573i	$-0.862530\pi$
$199$	−6.90680	+	6.90680i	−0.489610	+	0.489610i	0.418573	+	0.908183i	$0.362530\pi$
$200$	−4.90567	+	0.966660i	−0.346883	+	0.0683532i
$201$	−12.5417			−0.884626
$202$		−	9.23382i		−	0.649689i
$203$		−	12.8340i		−	0.900771i
$204$	4.27515	+	4.27515i	0.299321	+	0.299321i
$205$	1.37795	+	14.1203i	0.0962400	+	0.986202i
$206$		−	8.03931i		−	0.560125i
$207$			10.2568i			0.712898i
$208$	−4.41538			−0.306152
$209$	7.06065	−	7.06065i	0.488396	−	0.488396i
$210$	−1.01434	−	10.3943i	−0.0699962	−	0.717273i
$211$	−22.7919			−1.56906			−0.784531	−	0.620090i	$-0.787096\pi$
$211$	−22.7919			−1.56906			−0.784531	+	0.620090i	$0.787096\pi$
$212$	−9.57437	−	9.57437i	−0.657570	−	0.657570i
$213$	8.94925	−	8.94925i	0.613193	−	0.613193i
$214$	−4.60753	+	4.60753i	−0.314964	+	0.314964i
$215$	3.97349	−	0.387760i	0.270990	−	0.0264450i
$216$	3.76493	+	3.76493i	0.256171	+	0.256171i
$217$	31.8562			2.16254
$218$	14.6123	+	14.6123i	0.989673	+	0.989673i
$219$		−	6.39655i		−	0.432239i
$220$	−0.772154	−	7.91250i	−0.0520586	−	0.533461i
$221$			23.7460i			1.59733i
$222$	0.626522	+	6.80950i	0.0420494	+	0.457024i
$223$	−7.23324	−	7.23324i	−0.484373	−	0.484373i	0.422152	−	0.906525i	$-0.361275\pi$
$223$	−7.23324	−	7.23324i	−0.484373	−	0.484373i	−0.906525	+	0.422152i	$0.861275\pi$
$224$	−2.93770	+	2.93770i	−0.196283	+	0.196283i
$225$	1.67828	+	8.51705i	0.111885	+	0.567803i
$226$		−	8.61849i		−	0.573293i
$227$		−	3.53828i		−	0.234844i	−0.993082	−	0.117422i	$-0.962537\pi$
$227$		−	3.53828i		−	0.234844i	0.993082	−	0.117422i	$-0.0374630\pi$
$228$	−3.15731			−0.209098
$229$			10.2694i			0.678622i	0.940674	+	0.339311i	$0.110194\pi$
$229$			10.2694i			0.678622i	−0.940674	+	0.339311i	$0.889806\pi$
$230$	−13.1477	+	1.28304i	−0.866931	+	0.0846008i
$231$	16.6056			1.09257
$232$	−2.18437	+	2.18437i	−0.143411	+	0.143411i
$233$	−0.731820	+	0.731820i	−0.0479431	+	0.0479431i	−0.730672	−	0.682729i	$-0.760793\pi$
$233$	−0.731820	+	0.731820i	−0.0479431	+	0.0479431i	0.682729	+	0.730672i	$0.260793\pi$
$234$			7.66584i			0.501131i
$235$	3.66812	−	4.46146i	0.239282	−	0.291033i
$236$	4.44588	+	4.44588i	0.289402	+	0.289402i
$237$	−3.22836			−0.209704
$238$	15.7990	+	15.7990i	1.02409	+	1.02409i
$239$	6.25677	+	6.25677i	0.404717	+	0.404717i	0.879892	−	0.475175i	$-0.157615\pi$
$239$	6.25677	+	6.25677i	0.404717	+	0.404717i	−0.475175	+	0.879892i	$0.657615\pi$
$240$	−1.59648	+	1.94176i	−0.103052	+	0.125340i
$241$	−6.31560	+	6.31560i	−0.406823	+	0.406823i	−0.880629	−	0.473806i	$-0.842880\pi$
$241$	−6.31560	+	6.31560i	−0.406823	+	0.406823i	0.473806	+	0.880629i	$0.342880\pi$
$242$	1.64079			0.105474
$243$	10.6769	−	10.6769i	0.684926	−	0.684926i
$244$	1.44033	+	1.44033i	0.0922079	+	0.0922079i
$245$	−2.22828	−	22.8339i	−0.142360	−	1.45880i
$246$	5.04366	+	5.04366i	0.321572	+	0.321572i
$247$	−8.76852	−	8.76852i	−0.557927	−	0.557927i
$248$	−5.42197	−	5.42197i	−0.344296	−	0.344296i
$249$	7.17475			0.454681
$250$	−10.7076	+	3.21670i	−0.677208	+	0.203442i
$251$	3.90237	+	3.90237i	0.246315	+	0.246315i	0.819457	−	0.573141i	$-0.194275\pi$
$251$	3.90237	+	3.90237i	0.246315	+	0.246315i	−0.573141	+	0.819457i	$0.694275\pi$
$252$	5.10033	+	5.10033i	0.321291	+	0.321291i
$253$		−	21.0043i		−	1.32053i
$254$	4.22966	−	4.22966i	0.265393	−	0.265393i
$255$	10.4428	+	8.58586i	0.653954	+	0.537668i
$256$	1.00000			0.0625000
$257$			2.21902i			0.138419i	0.997602	+	0.0692095i	$0.0220477\pi$
$257$			2.21902i			0.138419i	−0.997602	+	0.0692095i	$0.977952\pi$
$258$	1.41931	−	1.41931i	0.0883621	−	0.0883621i
$259$	2.31533	+	25.1647i	0.143868	+	1.56366i
$260$	−9.82642	+	0.958927i	−0.609409	+	0.0594701i
$261$	3.79242	+	3.79242i	0.234745	+	0.234745i
$262$	15.2680	+	15.2680i	0.943260	+	0.943260i
$263$	−11.1111	+	11.1111i	−0.685141	+	0.685141i	−0.961154	−	0.276013i	$-0.910987\pi$
$263$	−11.1111	+	11.1111i	−0.685141	+	0.685141i	0.276013	+	0.961154i	$0.410987\pi$
$264$	−2.82629	−	2.82629i	−0.173946	−	0.173946i
$265$	−23.3871	−	19.2284i	−1.43666	−	1.18119i
$266$	−11.6680			−0.715408
$267$			3.40131i			0.208157i
$268$	7.88856	+	7.88856i	0.481870	+	0.481870i
$269$			5.86174i			0.357396i	0.983904	+	0.178698i	$0.0571886\pi$
$269$			5.86174i			0.357396i	−0.983904	+	0.178698i	$0.942811\pi$
$270$	9.19650	+	7.56118i	0.559681	+	0.460159i
$271$	−4.91311			−0.298450			−0.149225	−	0.988803i	$-0.547678\pi$
$271$	−4.91311			−0.298450			−0.149225	+	0.988803i	$0.547678\pi$
$272$		−	5.37801i		−	0.326090i
$273$		−	20.6222i		−	1.24811i
$274$	14.4220	−	14.4220i	0.871262	−	0.871262i
$275$	−3.43685	−	17.4416i	−0.207250	−	1.05177i
$276$	−4.69625	+	4.69625i	−0.282681	+	0.282681i
$277$	8.21627			0.493668			0.246834	−	0.969058i	$-0.420610\pi$
$277$	8.21627			0.493668			0.246834	+	0.969058i	$0.420610\pi$
$278$	−1.56244			−0.0937092
$279$	−9.41344	+	9.41344i	−0.563568	+	0.563568i
$280$	−5.89983	+	7.17584i	−0.352582	+	0.428838i
$281$	−7.17894	+	7.17894i	−0.428259	+	0.428259i	−0.888035	−	0.459776i	$-0.847930\pi$
$281$	−7.17894	+	7.17894i	−0.428259	+	0.428259i	0.459776	+	0.888035i	$0.347930\pi$
$282$		−	2.90383i		−	0.172921i
$283$			21.1149i			1.25515i	0.778557	+	0.627574i	$0.215952\pi$
$283$			21.1149i			1.25515i	−0.778557	+	0.627574i	$0.784048\pi$
$284$	−11.2579			−0.668032
$285$	−7.02659	+	0.685701i	−0.416219	+	0.0406174i
$286$		−	15.6984i		−	0.928266i
$287$	18.6390	+	18.6390i	1.10023	+	1.10023i
$288$		−	1.73617i		−	0.102305i
$289$	−11.9230			−0.701352
$290$	−4.38690	+	5.33570i	−0.257608	+	0.313323i
$291$	−4.70596	−	4.70596i	−0.275868	−	0.275868i
$292$	−4.02333	+	4.02333i	−0.235448	+	0.235448i
$293$	8.03410	+	8.03410i	0.469357	+	0.469357i	0.901706	−	0.432349i	$-0.142315\pi$
$293$	8.03410	+	8.03410i	0.469357	+	0.469357i	−0.432349	+	0.901706i	$0.642315\pi$
$294$	−8.15611	−	8.15611i	−0.475674	−	0.475674i
$295$	10.8598	+	8.92875i	0.632285	+	0.519852i
$296$	3.88900	−	4.67714i	0.226044	−	0.271854i
$297$	−13.3858	+	13.3858i	−0.776722	+	0.776722i
$298$		−	8.42600i		−	0.488105i
$299$	−26.0849			−1.50853
$300$	−3.13124	+	4.66810i	−0.180782	+	0.269513i
$301$	5.24509	−	5.24509i	0.302322	−	0.302322i
$302$			9.65715i			0.555706i
$303$	−7.34026	−	7.34026i	−0.421687	−	0.421687i
$304$	1.98590	+	1.98590i	0.113899	+	0.113899i
$305$	3.51827	+	2.89265i	0.201455	+	0.165633i
$306$	−9.33711			−0.533767
$307$	3.81755	+	3.81755i	0.217879	+	0.217879i	0.807604	−	0.589725i	$-0.200764\pi$
$307$	3.81755	+	3.81755i	0.217879	+	0.217879i	−0.589725	+	0.807604i	$0.700764\pi$
$308$	−10.4447	−	10.4447i	−0.595140	−	0.595140i
$309$	−6.39071	−	6.39071i	−0.363555	−	0.363555i
$310$	−13.2441	−	10.8890i	−0.752215	−	0.618456i
$311$	8.92270	+	8.92270i	0.505960	+	0.505960i	0.913284	−	0.407324i	$-0.133538\pi$
$311$	8.92270	+	8.92270i	0.505960	+	0.505960i	−0.407324	+	0.913284i	$0.633538\pi$
$312$	−3.50993	+	3.50993i	−0.198711	+	0.198711i
$313$	−29.7794			−1.68323			−0.841616	−	0.540076i	$-0.818395\pi$
$313$	−29.7794			−1.68323			−0.841616	+	0.540076i	$0.818395\pi$
$314$	13.7789	−	13.7789i	0.777591	−	0.777591i
$315$	12.4584	+	10.2431i	0.701954	+	0.577132i
$316$	2.03059	+	2.03059i	0.114229	+	0.114229i
$317$	−16.2699	−	16.2699i	−0.913808	−	0.913808i	0.0827610	−	0.996569i	$-0.473626\pi$
$317$	−16.2699	−	16.2699i	−0.913808	−	0.913808i	−0.996569	+	0.0827610i	$0.973626\pi$
$318$	−15.2219			−0.853604
$319$	−7.76627	−	7.76627i	−0.434828	−	0.434828i
$320$	2.22550	−	0.217179i	0.124409	−	0.0121407i
$321$			7.32535i			0.408861i
$322$	−17.3552	+	17.3552i	−0.967165	+	0.967165i
$323$	10.6802	−	10.6802i	0.594262	−	0.594262i
$324$	0.777232			0.0431795
$325$	−21.6604	+	4.26818i	−1.20150	+	0.236756i
$326$		−	9.92434i		−	0.549658i
$327$	23.2316			1.28471
$328$		−	6.34477i		−	0.350331i
$329$		−	10.7312i		−	0.591630i
$330$	−6.90371	−	5.67609i	−0.380037	−	0.312459i
$331$	15.6327	−	15.6327i	0.859250	−	0.859250i	−0.132000	−	0.991250i	$-0.542140\pi$
$331$	15.6327	−	15.6327i	0.859250	−	0.859250i	0.991250	+	0.132000i	$0.0421399\pi$
$332$	−4.51281	−	4.51281i	−0.247672	−	0.247672i
$333$	−8.12030	−	6.75195i	−0.444990	−	0.370004i
$334$			17.7622i			0.971903i
$335$	19.2692	+	15.8427i	1.05279	+	0.865581i
$336$			4.67054i			0.254799i
$337$	22.0252	+	22.0252i	1.19979	+	1.19979i	0.974230	+	0.225558i	$0.0724204\pi$
$337$	22.0252	+	22.0252i	1.19979	+	1.19979i	0.225558	+	0.974230i	$0.427580\pi$
$338$	−6.49561			−0.353315
$339$	−6.85111	−	6.85111i	−0.372101	−	0.372101i
$340$	−1.16799	−	11.9687i	−0.0633431	−	0.649096i
$341$	19.2772	−	19.2772i	1.04392	−	1.04392i
$342$	3.44786	−	3.44786i	0.186439	−	0.186439i
$343$	−9.57729	−	9.57729i	−0.517125	−	0.517125i
$344$	−1.78544			−0.0962646
$345$	−9.43157	+	11.4714i	−0.507779	+	0.617601i
$346$	4.93605	−	4.93605i	0.265364	−	0.265364i
$347$	−35.2079			−1.89006			−0.945029	−	0.326987i	$-0.893967\pi$
$347$	−35.2079			−1.89006			−0.945029	+	0.326987i	$0.893967\pi$
$348$			3.47285i			0.186164i
$349$		−	7.00272i		−	0.374847i	−0.982279	−	0.187423i	$-0.939986\pi$
$349$		−	7.00272i		−	0.374847i	0.982279	−	0.187423i	$-0.0600137\pi$
$350$	−11.5716	+	17.2511i	−0.618529	+	0.922111i
$351$	16.6236	+	16.6236i	0.887303	+	0.887303i
$352$			3.55539i			0.189503i
$353$			24.1991i			1.28799i	0.765030	+	0.643995i	$0.222724\pi$
$353$			24.1991i			1.28799i	−0.765030	+	0.643995i	$0.777276\pi$
$354$	7.06835			0.375679
$355$	−25.0544	+	2.44497i	−1.32975	+	0.129766i
$356$	2.13937	−	2.13937i	0.113387	−	0.113387i
$357$	25.1182			1.32940
$358$	−3.68868	+	3.68868i	−0.194953	+	0.194953i
$359$		−	5.19872i		−	0.274378i	−0.990545	−	0.137189i	$-0.956193\pi$
$359$		−	5.19872i		−	0.274378i	0.990545	−	0.137189i	$-0.0438067\pi$
$360$	−0.377058	−	3.86383i	−0.0198727	−	0.203642i
$361$		−	11.1124i		−	0.584862i
$362$	5.35458			0.281430
$363$	1.30432	−	1.30432i	0.0684588	−	0.0684588i
$364$	−12.9711	+	12.9711i	−0.679868	+	0.679868i
$365$	−8.08013	+	9.82769i	−0.422933	+	0.514405i
$366$	2.28994			0.119697
$367$	22.4335	−	22.4335i	1.17102	−	1.17102i	0.189049	−	0.981968i	$-0.439460\pi$
$367$	22.4335	−	22.4335i	1.17102	−	1.17102i	0.981968	−	0.189049i	$-0.0605405\pi$
$368$	5.90774			0.307962
$369$	−11.0156			−0.573448
$370$	7.63918	−	11.2536i	0.397142	−	0.585045i
$371$	−56.2532			−2.92052
$372$	−8.62020			−0.446937
$373$	−10.4263	+	10.4263i	−0.539852	+	0.539852i	−0.923486	−	0.383633i	$-0.874673\pi$
$373$	−10.4263	+	10.4263i	−0.539852	+	0.539852i	0.383633	+	0.923486i	$0.374673\pi$
$374$	19.1209			0.988719
$375$	−5.95476	+	11.0689i	−0.307502	+	0.571595i
$376$	−1.82646	+	1.82646i	−0.0941927	+	0.0941927i
$377$	−9.64481	+	9.64481i	−0.496733	+	0.496733i
$378$	22.1205			1.13775
$379$		−	15.9233i		−	0.817925i	−0.912551	−	0.408963i	$-0.865891\pi$
$379$		−	15.9233i		−	0.817925i	0.912551	−	0.408963i	$-0.134109\pi$
$380$	4.85091	+	3.98832i	0.248847	+	0.204597i
$381$		−	6.72459i		−	0.344511i
$382$	−10.0773	+	10.0773i	−0.515598	+	0.515598i
$383$	24.2531			1.23928			0.619638	−	0.784888i	$-0.287279\pi$
$383$	24.2531			1.23928			0.619638	+	0.784888i	$0.287279\pi$
$384$	0.794932	−	0.794932i	0.0405662	−	0.0405662i
$385$	−25.5129	−	20.9762i	−1.30026	−	1.06905i
$386$	−24.7844			−1.26149
$387$			3.09982i			0.157573i
$388$			5.91995i			0.300540i
$389$	19.7499	+	19.7499i	1.00136	+	1.00136i	0.999999	+	0.00136297i	$0.000433846\pi$
$389$	19.7499	+	19.7499i	1.00136	+	1.00136i	0.00136297	+	0.999999i	$0.499566\pi$
$390$	−7.04905	+	8.57362i	−0.356943	+	0.434142i
$391$		−	31.7719i		−	1.60677i
$392$			10.2601i			0.518215i
$393$	24.2741			1.22446
$394$	−11.3006	+	11.3006i	−0.569314	+	0.569314i
$395$	4.96006	+	4.07806i	0.249568	+	0.205190i
$396$	6.17274			0.310192
$397$	−1.71599	−	1.71599i	−0.0861232	−	0.0861232i	0.662733	−	0.748856i	$-0.269397\pi$
$397$	−1.71599	−	1.71599i	−0.0861232	−	0.0861232i	−0.748856	+	0.662733i	$0.769397\pi$
$398$	6.90680	−	6.90680i	0.346206	−	0.346206i
$399$	−9.27524	+	9.27524i	−0.464343	+	0.464343i
$400$	4.90567	−	0.966660i	0.245283	−	0.0483330i
$401$	9.29247	+	9.29247i	0.464044	+	0.464044i	0.899978	−	0.435934i	$-0.143582\pi$
$401$	9.29247	+	9.29247i	0.464044	+	0.464044i	−0.435934	+	0.899978i	$0.643582\pi$
$402$	12.5417			0.625525
$403$	−23.9401	−	23.9401i	−1.19254	−	1.19254i
$404$			9.23382i			0.459399i
$405$	1.72973	−	0.168798i	0.0859508	−	0.00838764i
$406$			12.8340i			0.636941i
$407$	16.6291	+	13.8269i	0.824272	+	0.685374i
$408$	−4.27515	−	4.27515i	−0.211652	−	0.211652i
$409$	18.3866	−	18.3866i	0.909160	−	0.909160i	−0.0870446	−	0.996204i	$-0.527742\pi$
$409$	18.3866	−	18.3866i	0.909160	−	0.909160i	0.996204	+	0.0870446i	$0.0277423\pi$
$410$	−1.37795	−	14.1203i	−0.0680520	−	0.697350i
$411$		−	22.9290i		−	1.13100i
$412$			8.03931i			0.396068i
$413$	26.1213			1.28535
$414$		−	10.2568i		−	0.504095i
$415$	−11.0233	−	9.06315i	−0.541113	−	0.444892i
$416$	4.41538			0.216482
$417$	−1.24204	+	1.24204i	−0.0608228	+	0.0608228i
$418$	−7.06065	+	7.06065i	−0.345348	+	0.345348i
$419$			8.04256i			0.392905i	0.980513	+	0.196452i	$0.0629421\pi$
$419$			8.04256i			0.392905i	−0.980513	+	0.196452i	$0.937058\pi$
$420$	1.01434	+	10.3943i	0.0494948	+	0.507188i
$421$	11.0268	+	11.0268i	0.537416	+	0.537416i	0.922769	−	0.385353i	$-0.125920\pi$
$421$	11.0268	+	11.0268i	0.537416	+	0.537416i	−0.385353	+	0.922769i	$0.625920\pi$
$422$	22.7919			1.10949
$423$	3.17104	+	3.17104i	0.154181	+	0.154181i
$424$	9.57437	+	9.57437i	0.464972	+	0.464972i
$425$	−5.19871	−	26.3827i	−0.252174	−	1.27975i
$426$	−8.94925	+	8.94925i	−0.433593	+	0.433593i
$427$	8.46253			0.409530
$428$	4.60753	−	4.60753i	0.222713	−	0.222713i
$429$	−12.4792	−	12.4792i	−0.602500	−	0.602500i
$430$	−3.97349	+	0.387760i	−0.191619	+	0.0186994i
$431$	9.69563	+	9.69563i	0.467022	+	0.467022i	0.900948	−	0.433926i	$-0.142872\pi$
$431$	9.69563	+	9.69563i	0.467022	+	0.467022i	−0.433926	+	0.900948i	$0.642872\pi$
$432$	−3.76493	−	3.76493i	−0.181140	−	0.181140i
$433$	−7.39679	−	7.39679i	−0.355467	−	0.355467i	0.506672	−	0.862139i	$-0.330876\pi$
$433$	−7.39679	−	7.39679i	−0.355467	−	0.355467i	−0.862139	+	0.506672i	$0.830876\pi$
$434$	−31.8562			−1.52915
$435$	0.754228	+	7.72880i	0.0361624	+	0.370568i
$436$	−14.6123	−	14.6123i	−0.699804	−	0.699804i
$437$	11.7322	+	11.7322i	0.561227	+	0.561227i
$438$			6.39655i			0.305639i
$439$	21.3840	−	21.3840i	1.02060	−	1.02060i	0.0208186	−	0.999783i	$-0.493373\pi$
$439$	21.3840	−	21.3840i	1.02060	−	1.02060i	0.999783	−	0.0208186i	$-0.00662725\pi$
$440$	0.772154	+	7.91250i	0.0368110	+	0.377214i
$441$	17.8133			0.848252
$442$		−	23.7460i		−	1.12948i
$443$	−0.537851	+	0.537851i	−0.0255541	+	0.0255541i	−0.719768	−	0.694214i	$-0.755752\pi$
$443$	−0.537851	+	0.537851i	−0.0255541	+	0.0255541i	0.694214	+	0.719768i	$0.255752\pi$
$444$	−0.626522	−	6.80950i	−0.0297334	−	0.323165i
$445$	4.29654	−	5.22579i	0.203676	−	0.247726i
$446$	7.23324	+	7.23324i	0.342504	+	0.342504i
$447$	−6.69810	−	6.69810i	−0.316809	−	0.316809i
$448$	2.93770	−	2.93770i	0.138793	−	0.138793i
$449$	−17.9014	−	17.9014i	−0.844820	−	0.844820i	0.144661	−	0.989481i	$-0.453791\pi$
$449$	−17.9014	−	17.9014i	−0.844820	−	0.844820i	−0.989481	+	0.144661i	$0.953791\pi$
$450$	−1.67828	−	8.51705i	−0.0791150	−	0.401498i
$451$	22.5581			1.06222
$452$			8.61849i			0.405380i
$453$	7.67678	+	7.67678i	0.360686	+	0.360686i
$454$			3.53828i			0.166060i
$455$	−26.0500	+	31.6841i	−1.22124	+	1.48537i
$456$	3.15731			0.147855
$457$		−	10.3305i		−	0.483240i	−0.970371	−	0.241620i	$-0.922321\pi$
$457$		−	10.3305i		−	0.483240i	0.970371	−	0.241620i	$-0.0776787\pi$
$458$		−	10.2694i		−	0.479858i
$459$	−20.2478	+	20.2478i	−0.945088	+	0.945088i
$460$	13.1477	−	1.28304i	0.613013	−	0.0598218i
$461$	−19.5325	+	19.5325i	−0.909718	+	0.909718i	−0.996249	−	0.0865312i	$-0.972422\pi$
$461$	−19.5325	+	19.5325i	−0.909718	+	0.909718i	0.0865312	+	0.996249i	$0.472422\pi$
$462$	−16.6056			−0.772562
$463$	13.2709			0.616752			0.308376	−	0.951265i	$-0.400214\pi$
$463$	13.2709			0.616752			0.308376	+	0.951265i	$0.400214\pi$
$464$	2.18437	−	2.18437i	0.101407	−	0.101407i
$465$	−19.1842	+	1.87212i	−0.889647	+	0.0868176i
$466$	0.731820	−	0.731820i	0.0339009	−	0.0339009i
$467$			40.7473i			1.88556i	0.333414	+	0.942780i	$0.391799\pi$
$467$			40.7473i			1.88556i	−0.333414	+	0.942780i	$0.608201\pi$
$468$		−	7.66584i		−	0.354353i
$469$	46.3484			2.14017
$470$	−3.66812	+	4.46146i	−0.169198	+	0.205792i
$471$		−	21.9066i		−	1.00941i
$472$	−4.44588	−	4.44588i	−0.204638	−	0.204638i
$473$		−	6.34794i		−	0.291879i
$474$	3.22836			0.148283
$475$	11.6619	+	7.82248i	0.535083	+	0.358920i
$476$	−15.7990	−	15.7990i	−0.724144	−	0.724144i
$477$	16.6227	−	16.6227i	0.761100	−	0.761100i
$478$	−6.25677	−	6.25677i	−0.286178	−	0.286178i
$479$	8.91382	+	8.91382i	0.407283	+	0.407283i	0.880790	−	0.473507i	$-0.157012\pi$
$479$	8.91382	+	8.91382i	0.407283	+	0.407283i	−0.473507	+	0.880790i	$0.657012\pi$
$480$	1.59648	−	1.94176i	0.0728688	−	0.0886288i
$481$	17.1714	−	20.6514i	0.782950	−	0.941622i
$482$	6.31560	−	6.31560i	0.287667	−	0.287667i
$483$			27.5924i			1.25550i
$484$	−1.64079			−0.0745813
$485$	1.28569	+	13.1748i	0.0583800	+	0.598238i
$486$	−10.6769	+	10.6769i	−0.484316	+	0.484316i
$487$		−	27.7847i		−	1.25904i	−0.776983	−	0.629522i	$-0.783251\pi$
$487$		−	27.7847i		−	1.25904i	0.776983	−	0.629522i	$-0.216749\pi$
$488$	−1.44033	−	1.44033i	−0.0652008	−	0.0652008i
$489$	−7.88918	−	7.88918i	−0.356761	−	0.356761i
$490$	2.22828	+	22.8339i	0.100663	+	1.03153i
$491$	−7.19820			−0.324850			−0.162425	−	0.986721i	$-0.551932\pi$
$491$	−7.19820			−0.324850			−0.162425	+	0.986721i	$0.551932\pi$
$492$	−5.04366	−	5.04366i	−0.227386	−	0.227386i
$493$	−11.7475	−	11.7475i	−0.529083	−	0.529083i
$494$	8.76852	+	8.76852i	0.394514	+	0.394514i
$495$	13.7374	−	1.34059i	0.617451	−	0.0602549i
$496$	5.42197	+	5.42197i	0.243454	+	0.243454i
$497$	−33.0722	+	33.0722i	−1.48349	+	1.48349i
$498$	−7.17475			−0.321508
$499$	−0.378337	+	0.378337i	−0.0169367	+	0.0169367i	−0.715524	−	0.698588i	$-0.753812\pi$
$499$	−0.378337	+	0.378337i	−0.0169367	+	0.0169367i	0.698588	+	0.715524i	$0.253812\pi$
$500$	10.7076	−	3.21670i	0.478859	−	0.143855i
$501$	14.1197	+	14.1197i	0.630823	+	0.630823i
$502$	−3.90237	−	3.90237i	−0.174171	−	0.174171i
$503$	22.0885			0.984876			0.492438	−	0.870348i	$-0.336106\pi$
$503$	22.0885			0.984876			0.492438	+	0.870348i	$0.336106\pi$
$504$	−5.10033	−	5.10033i	−0.227187	−	0.227187i
$505$	2.00539	+	20.5498i	0.0892385	+	0.914455i
$506$			21.0043i			0.933756i
$507$	−5.16357	+	5.16357i	−0.229322	+	0.229322i
$508$	−4.22966	+	4.22966i	−0.187661	+	0.187661i
$509$	24.8176			1.10002			0.550011	−	0.835157i	$-0.314624\pi$
$509$	24.8176			1.10002			0.550011	+	0.835157i	$0.314624\pi$
$510$	−10.4428	−	8.58586i	−0.462415	−	0.380188i
$511$			23.6387i			1.04571i
$512$	−1.00000			−0.0441942
$513$		−	14.9536i		−	0.660216i
$514$		−	2.21902i		−	0.0978769i
$515$	1.74597	+	17.8915i	0.0769364	+	0.788392i
$516$	−1.41931	+	1.41931i	−0.0624814	+	0.0624814i
$517$	−6.49379	−	6.49379i	−0.285597	−	0.285597i
$518$	−2.31533	−	25.1647i	−0.101730	−	1.10568i
$519$		−	7.84764i		−	0.344473i
$520$	9.82642	−	0.958927i	0.430917	−	0.0420517i
$521$		−	2.41522i		−	0.105813i	−0.998599	−	0.0529064i	$-0.983151\pi$
$521$		−	2.41522i		−	0.105813i	0.998599	−	0.0529064i	$-0.0168485\pi$
$522$	−3.79242	−	3.79242i	−0.165990	−	0.165990i
$523$	24.1447			1.05577			0.527887	−	0.849315i	$-0.322985\pi$
$523$	24.1447			1.05577			0.527887	+	0.849315i	$0.322985\pi$
$524$	−15.2680	−	15.2680i	−0.666986	−	0.666986i
$525$	4.51483	+	22.9121i	0.197043	+	0.999967i
$526$	11.1111	−	11.1111i	0.484468	−	0.484468i
$527$	29.1594	−	29.1594i	1.27020	−	1.27020i
$528$	2.82629	+	2.82629i	0.122999	+	0.122999i
$529$	11.9014			0.517453
$530$	23.3871	+	19.2284i	1.01587	+	0.835227i
$531$	−7.71879	+	7.71879i	−0.334967	+	0.334967i
$532$	11.6680			0.505870
$533$		−	28.0146i		−	1.21345i
$534$		−	3.40131i		−	0.147189i
$535$	9.25339	−	11.2547i	0.400059	−	0.486583i
$536$	−7.88856	−	7.88856i	−0.340734	−	0.340734i
$537$			5.86451i			0.253072i
$538$		−	5.86174i		−	0.252717i
$539$	−36.4788			−1.57125
$540$	−9.19650	−	7.56118i	−0.395754	−	0.325381i
$541$	12.3532	−	12.3532i	0.531107	−	0.531107i	−0.389795	−	0.920902i	$-0.627454\pi$
$541$	12.3532	−	12.3532i	0.531107	−	0.531107i	0.920902	+	0.389795i	$0.127454\pi$
$542$	4.91311			0.211036
$543$	4.25652	−	4.25652i	0.182665	−	0.182665i
$544$			5.37801i			0.230580i
$545$	−35.6932	−	29.3462i	−1.52893	−	1.25705i
$546$			20.6222i			0.882550i
$547$	−34.8143			−1.48855			−0.744277	−	0.667871i	$-0.767206\pi$
$547$	−34.8143			−1.48855			−0.744277	+	0.667871i	$0.767206\pi$
$548$	−14.4220	+	14.4220i	−0.616075	+	0.616075i
$549$	−2.50066	+	2.50066i	−0.106725	+	0.106725i
$550$	3.43685	+	17.4416i	0.146548	+	0.743710i
$551$	8.67587			0.369605
$552$	4.69625	−	4.69625i	0.199886	−	0.199886i
$553$	11.9305			0.507336
$554$	−8.21627			−0.349076
$555$	−2.87320	−	15.0185i	−0.121961	−	0.637498i
$556$	1.56244			0.0662624
$557$	31.3271			1.32737			0.663685	−	0.748012i	$-0.268992\pi$
$557$	31.3271			1.32737			0.663685	+	0.748012i	$0.268992\pi$
$558$	9.41344	−	9.41344i	0.398503	−	0.398503i
$559$	−7.88341			−0.333433
$560$	5.89983	−	7.17584i	0.249313	−	0.303235i
$561$	15.1998	−	15.1998i	0.641737	−	0.641737i
$562$	7.17894	−	7.17894i	0.302825	−	0.302825i
$563$	22.9644			0.967836			0.483918	−	0.875113i	$-0.339213\pi$
$563$	22.9644			0.967836			0.483918	+	0.875113i	$0.339213\pi$
$564$			2.90383i			0.122273i
$565$	1.87175	+	19.1804i	0.0787452	+	0.806926i
$566$		−	21.1149i		−	0.887524i
$567$	2.28327	−	2.28327i	0.0958884	−	0.0958884i
$568$	11.2579			0.472370
$569$	30.2581	−	30.2581i	1.26849	−	1.26849i	0.321616	−	0.946870i	$-0.395774\pi$
$569$	30.2581	−	30.2581i	1.26849	−	1.26849i	0.946870	−	0.321616i	$-0.104226\pi$
$570$	7.02659	−	0.685701i	0.294312	−	0.0287209i
$571$	25.3502			1.06087			0.530436	−	0.847725i	$-0.322028\pi$
$571$	25.3502			1.06087			0.530436	+	0.847725i	$0.322028\pi$
$572$			15.6984i			0.656383i
$573$			16.0215i			0.669307i
$574$	−18.6390	−	18.6390i	−0.777977	−	0.777977i
$575$	28.9814	−	5.71078i	1.20861	−	0.238156i
$576$			1.73617i			0.0723402i
$577$			29.6723i			1.23527i	0.786464	+	0.617637i	$0.211910\pi$
$577$			29.6723i			1.23527i	−0.786464	+	0.617637i	$0.788090\pi$
$578$	11.9230			0.495931
$579$	−19.7019	+	19.7019i	−0.818784	+	0.818784i
$580$	4.38690	−	5.33570i	0.182156	−	0.221553i
$581$	−26.5145			−1.10001
$582$	4.70596	+	4.70596i	0.195068	+	0.195068i
$583$	−34.0406	+	34.0406i	−1.40982	+	1.40982i
$584$	4.02333	−	4.02333i	0.166487	−	0.166487i
$585$	−1.66486	−	17.0603i	−0.0688333	−	0.705356i
$586$	−8.03410	−	8.03410i	−0.331886	−	0.331886i
$587$	−16.9046			−0.697726			−0.348863	−	0.937174i	$-0.613432\pi$
$587$	−16.9046			−0.697726			−0.348863	+	0.937174i	$0.613432\pi$
$588$	8.15611	+	8.15611i	0.336352	+	0.336352i
$589$			21.5350i			0.887335i
$590$	−10.8598	−	8.92875i	−0.447093	−	0.367591i
$591$			17.9664i			0.739038i
$592$	−3.88900	+	4.67714i	−0.159837	+	0.192229i
$593$	13.2570	+	13.2570i	0.544398	+	0.544398i	0.924815	−	0.380417i	$-0.124220\pi$
$593$	13.2570	+	13.2570i	0.544398	+	0.544398i	−0.380417	+	0.924815i	$0.624220\pi$
$594$	13.3858	−	13.3858i	0.549226	−	0.549226i
$595$	−38.5917	−	31.7293i	−1.58211	−	1.30078i
$596$			8.42600i			0.345142i
$597$		−	10.9809i		−	0.449417i
$598$	26.0849			1.06669
$599$			9.47521i			0.387147i	0.981086	+	0.193573i	$0.0620077\pi$
$599$			9.47521i			0.387147i	−0.981086	+	0.193573i	$0.937992\pi$
$600$	3.13124	−	4.66810i	0.127832	−	0.190574i
$601$	−0.0866615			−0.00353500			−0.00176750	−	0.999998i	$-0.500563\pi$
$601$	−0.0866615			−0.00353500			−0.00176750	+	0.999998i	$0.500563\pi$
$602$	−5.24509	+	5.24509i	−0.213774	+	0.213774i
$603$	−13.6958	+	13.6958i	−0.557738	+	0.557738i
$604$		−	9.65715i		−	0.392944i
$605$	−3.65157	+	0.356344i	−0.148457	+	0.0144875i
$606$	7.34026	+	7.34026i	0.298178	+	0.298178i
$607$	−24.7793			−1.00576			−0.502880	−	0.864356i	$-0.667726\pi$
$607$	−24.7793			−1.00576			−0.502880	+	0.864356i	$0.667726\pi$
$608$	−1.98590	−	1.98590i	−0.0805390	−	0.0805390i
$609$	10.2022	+	10.2022i	0.413413	+	0.413413i
$610$	−3.51827	−	2.89265i	−0.142450	−	0.117120i
$611$	−8.06454	+	8.06454i	−0.326256	+	0.326256i
$612$	9.33711			0.377430
$613$	−3.88165	+	3.88165i	−0.156779	+	0.156779i	−0.781138	−	0.624359i	$-0.785360\pi$
$613$	−3.88165	+	3.88165i	−0.156779	+	0.156779i	0.624359	+	0.781138i	$0.285360\pi$
$614$	−3.81755	−	3.81755i	−0.154064	−	0.154064i
$615$	−12.3200	−	10.1293i	−0.496791	−	0.408452i
$616$	10.4447	+	10.4447i	0.420827	+	0.420827i
$617$	−34.7871	−	34.7871i	−1.40047	−	1.40047i	−0.798563	−	0.601911i	$-0.794406\pi$
$617$	−34.7871	−	34.7871i	−1.40047	−	1.40047i	−0.601911	−	0.798563i	$-0.705594\pi$
$618$	6.39071	+	6.39071i	0.257072	+	0.257072i
$619$	−14.8991			−0.598845			−0.299422	−	0.954121i	$-0.596794\pi$
$619$	−14.8991			−0.598845			−0.299422	+	0.954121i	$0.596794\pi$
$620$	13.2441	+	10.8890i	0.531897	+	0.437315i
$621$	−22.2422	−	22.2422i	−0.892550	−	0.892550i
$622$	−8.92270	−	8.92270i	−0.357768	−	0.357768i
$623$		−	12.5697i		−	0.503593i
$624$	3.50993	−	3.50993i	0.140510	−	0.140510i
$625$	23.1311	−	9.48423i	0.925245	−	0.379369i
$626$	29.7794			1.19022
$627$			11.2255i			0.448303i
$628$	−13.7789	+	13.7789i	−0.549840	+	0.549840i
$629$	25.1537	+	20.9151i	1.00294	+	0.833939i
$630$	−12.4584	−	10.2431i	−0.496356	−	0.408094i
$631$	−26.9215	−	26.9215i	−1.07173	−	1.07173i	−0.997220	−	0.0745080i	$-0.976261\pi$
$631$	−26.9215	−	26.9215i	−1.07173	−	1.07173i	−0.0745080	−	0.997220i	$-0.523739\pi$
$632$	−2.03059	−	2.03059i	−0.0807724	−	0.0807724i
$633$	18.1180	−	18.1180i	0.720128	−	0.720128i
$634$	16.2699	+	16.2699i	0.646160	+	0.646160i
$635$	−8.49450	+	10.3317i	−0.337094	+	0.410000i
$636$	15.2219			0.603589
$637$			45.3024i			1.79495i
$638$	7.76627	+	7.76627i	0.307470	+	0.307470i
$639$		−	19.5455i		−	0.773210i
$640$	−2.22550	+	0.217179i	−0.0879705	+	0.00858474i
$641$	−13.9581			−0.551314			−0.275657	−	0.961256i	$-0.588895\pi$
$641$	−13.9581			−0.551314			−0.275657	+	0.961256i	$0.588895\pi$
$642$		−	7.32535i		−	0.289109i
$643$			32.7954i			1.29332i	0.762777	+	0.646662i	$0.223836\pi$
$643$			32.7954i			1.29332i	−0.762777	+	0.646662i	$0.776164\pi$
$644$	17.3552	−	17.3552i	0.683889	−	0.683889i
$645$	−2.85042	+	3.46690i	−0.112235	+	0.136509i
$646$	−10.6802	+	10.6802i	−0.420207	+	0.420207i
$647$	0.428355			0.0168404			0.00842020	−	0.999965i	$-0.497320\pi$
$647$	0.428355			0.0168404			0.00842020	+	0.999965i	$0.497320\pi$
$648$	−0.777232			−0.0305325
$649$	15.8068	−	15.8068i	0.620473	−	0.620473i
$650$	21.6604	−	4.26818i	0.849591	−	0.167412i
$651$	−25.3235	+	25.3235i	−0.992508	+	0.992508i
$652$			9.92434i			0.388667i
$653$		−	35.6290i		−	1.39427i	−0.716939	−	0.697136i	$-0.754457\pi$
$653$		−	35.6290i		−	1.39427i	0.716939	−	0.697136i	$-0.245543\pi$
$654$	−23.2316			−0.908429
$655$	−37.2948	−	30.6630i	−1.45723	−	1.19810i
$656$			6.34477i			0.247722i
$657$	−6.98517	−	6.98517i	−0.272518	−	0.272518i
$658$			10.7312i			0.418346i
$659$	−23.0667			−0.898552			−0.449276	−	0.893393i	$-0.648318\pi$
$659$	−23.0667			−0.898552			−0.449276	+	0.893393i	$0.648318\pi$
$660$	6.90371	+	5.67609i	0.268727	+	0.220942i
$661$	2.71363	+	2.71363i	0.105548	+	0.105548i	0.757909	−	0.652361i	$-0.226221\pi$
$661$	2.71363	+	2.71363i	0.105548	+	0.105548i	−0.652361	+	0.757909i	$0.726221\pi$
$662$	−15.6327	+	15.6327i	−0.607581	+	0.607581i
$663$	−18.8764	−	18.8764i	−0.733100	−	0.733100i
$664$	4.51281	+	4.51281i	0.175131	+	0.175131i
$665$	25.9670	−	2.53403i	1.00696	−	0.0982655i
$666$	8.12030	+	6.75195i	0.314655	+	0.261633i
$667$	12.9047	−	12.9047i	0.499671	−	0.499671i
$668$		−	17.7622i		−	0.687239i
$669$	11.4999			0.444610
$670$	−19.2692	−	15.8427i	−0.744433	−	0.612058i
$671$	5.12095	−	5.12095i	0.197692	−	0.197692i
$672$		−	4.67054i		−	0.180170i
$673$	−19.5626	−	19.5626i	−0.754083	−	0.754083i	0.221156	−	0.975238i	$-0.429017\pi$
$673$	−19.5626	−	19.5626i	−0.754083	−	0.754083i	−0.975238	+	0.221156i	$0.929017\pi$
$674$	−22.0252	−	22.0252i	−0.848378	−	0.848378i
$675$	−22.1089	−	14.8301i	−0.850972	−	0.570810i
$676$	6.49561			0.249831
$677$	−23.4376	−	23.4376i	−0.900781	−	0.900781i	0.0947229	−	0.995504i	$-0.469803\pi$
$677$	−23.4376	−	23.4376i	−0.900781	−	0.900781i	−0.995504	+	0.0947229i	$0.969803\pi$
$678$	6.85111	+	6.85111i	0.263115	+	0.263115i
$679$	17.3910	+	17.3910i	0.667406	+	0.667406i
$680$	1.16799	+	11.9687i	0.0447903	+	0.458980i
$681$	2.81269	+	2.81269i	0.107783	+	0.107783i
$682$	−19.2772	+	19.2772i	−0.738163	+	0.738163i
$683$	−15.8368			−0.605977			−0.302988	−	0.952994i	$-0.597984\pi$
$683$	−15.8368			−0.605977			−0.302988	+	0.952994i	$0.597984\pi$
$684$	−3.44786	+	3.44786i	−0.131832	+	0.131832i
$685$	−28.9639	+	35.2281i	−1.10665	+	1.34600i
$686$	9.57729	+	9.57729i	0.365663	+	0.365663i
$687$	−8.16348	−	8.16348i	−0.311456	−	0.311456i
$688$	1.78544			0.0680693
$689$	42.2745	+	42.2745i	1.61053	+	1.61053i
$690$	9.43157	−	11.4714i	0.359054	−	0.436710i
$691$		−	25.5077i		−	0.970358i	−0.874415	−	0.485179i	$-0.838754\pi$
$691$		−	25.5077i		−	0.970358i	0.874415	−	0.485179i	$-0.161246\pi$
$692$	−4.93605	+	4.93605i	−0.187640	+	0.187640i
$693$	18.1337	−	18.1337i	0.688841	−	0.688841i
$694$	35.2079			1.33647
$695$	3.47721	−	0.339330i	0.131898	−	0.0128715i
$696$		−	3.47285i		−	0.131638i
$697$	34.1222			1.29247
$698$			7.00272i			0.265057i
$699$		−	1.16349i		−	0.0440074i
$700$	11.5716	−	17.2511i	0.437366	−	0.652031i
$701$	6.69201	−	6.69201i	0.252754	−	0.252754i	−0.569345	−	0.822099i	$-0.692803\pi$
$701$	6.69201	−	6.69201i	0.252754	−	0.252754i	0.822099	+	0.569345i	$0.192803\pi$
$702$	−16.6236	−	16.6236i	−0.627418	−	0.627418i
$703$	−17.0115	+	1.56518i	−0.641602	+	0.0590318i
$704$		−	3.55539i		−	0.133999i
$705$	0.630650	+	6.46246i	0.0237516	+	0.243390i
$706$		−	24.1991i		−	0.910746i
$707$	27.1262	+	27.1262i	1.02018	+	1.02018i
$708$	−7.06835			−0.265645
$709$	−9.99501	−	9.99501i	−0.375370	−	0.375370i	0.494058	−	0.869429i	$-0.335513\pi$
$709$	−9.99501	−	9.99501i	−0.375370	−	0.375370i	−0.869429	+	0.494058i	$0.835513\pi$
$710$	25.0544	−	2.44497i	0.940274	−	0.0917581i
$711$	−3.52544	+	3.52544i	−0.132214	+	0.132214i
$712$	−2.13937	+	2.13937i	−0.0801764	+	0.0801764i
$713$	32.0316	+	32.0316i	1.19959	+	1.19959i
$714$	−25.1182			−0.940025
$715$	3.40936	+	34.9367i	0.127503	+	1.30656i
$716$	3.68868	−	3.68868i	0.137853	−	0.137853i
$717$	−9.94742			−0.371493
$718$			5.19872i			0.194014i
$719$			19.0225i			0.709421i	0.934976	+	0.354711i	$0.115421\pi$
$719$			19.0225i			0.709421i	−0.934976	+	0.354711i	$0.884579\pi$
$720$	0.377058	+	3.86383i	0.0140521	+	0.143996i
$721$	23.6171	+	23.6171i	0.879545	+	0.879545i
$722$			11.1124i			0.413560i
$723$		−	10.0409i		−	0.373427i
$724$	−5.35458			−0.199001
$725$	8.60423	−	12.8273i	0.319553	−	0.476394i
$726$	−1.30432	+	1.30432i	−0.0484077	+	0.0484077i
$727$	32.8141			1.21701			0.608504	−	0.793551i	$-0.291770\pi$
$727$	32.8141			1.21701			0.608504	+	0.793551i	$0.291770\pi$
$728$	12.9711	−	12.9711i	0.480739	−	0.480739i
$729$			19.3066i			0.715059i
$730$	8.08013	−	9.82769i	0.299059	−	0.363739i
$731$		−	9.60212i		−	0.355147i
$732$	−2.28994			−0.0846384
$733$	−30.2477	+	30.2477i	−1.11722	+	1.11722i	−0.125077	+	0.992147i	$0.539918\pi$
$733$	−30.2477	+	30.2477i	−1.11722	+	1.11722i	−0.992147	+	0.125077i	$0.960082\pi$
$734$	−22.4335	+	22.4335i	−0.828034	+	0.828034i
$735$	19.9227	+	16.3801i	0.734861	+	0.604188i
$736$	−5.90774			−0.217762
$737$	28.0469	−	28.0469i	1.03312	−	1.03312i
$738$	11.0156			0.405489
$739$	27.9037			1.02646			0.513228	−	0.858253i	$-0.328450\pi$
$739$	27.9037			1.02646			0.513228	+	0.858253i	$0.328450\pi$
$740$	−7.63918	+	11.2536i	−0.280822	+	0.413690i
$741$	13.9408			0.512126
$742$	56.2532			2.06512
$743$	−10.9502	+	10.9502i	−0.401723	+	0.401723i	−0.878840	−	0.477117i	$-0.841682\pi$
$743$	−10.9502	+	10.9502i	−0.401723	+	0.401723i	0.477117	+	0.878840i	$0.341682\pi$
$744$	8.62020			0.316032
$745$	1.82995	+	18.7520i	0.0670440	+	0.687021i
$746$	10.4263	−	10.4263i	0.381733	−	0.381733i
$747$	7.83498	−	7.83498i	0.286667	−	0.286667i
$748$	−19.1209			−0.699130
$749$		−	27.0711i		−	0.989155i
$750$	5.95476	−	11.0689i	0.217437	−	0.404178i
$751$		−	44.1738i		−	1.61193i	−0.591966	−	0.805963i	$-0.701648\pi$
$751$		−	44.1738i		−	1.61193i	0.591966	−	0.805963i	$-0.298352\pi$
$752$	1.82646	−	1.82646i	0.0666043	−	0.0666043i
$753$	−6.20423			−0.226095
$754$	9.64481	−	9.64481i	0.351243	−	0.351243i
$755$	−2.09733	−	21.4919i	−0.0763295	−	0.782172i
$756$	−22.1205			−0.804513
$757$			3.52885i			0.128258i	0.997942	+	0.0641291i	$0.0204269\pi$
$757$			3.52885i			0.128258i	−0.997942	+	0.0641291i	$0.979573\pi$
$758$			15.9233i			0.578361i
$759$	16.6970	+	16.6970i	0.606063	+	0.606063i
$760$	−4.85091	−	3.98832i	−0.175961	−	0.144672i
$761$		−	15.9891i		−	0.579605i	−0.957086	−	0.289803i	$-0.906410\pi$
$761$		−	15.9891i		−	0.579605i	0.957086	−	0.289803i	$-0.0935896\pi$
$762$			6.72459i			0.243606i
$763$	−85.8533			−3.10810
$764$	10.0773	−	10.0773i	0.364583	−	0.364583i
$765$	20.7797	−	2.02782i	0.751292	−	0.0733160i
$766$	−24.2531			−0.876301
$767$	−19.6303	−	19.6303i	−0.708808	−	0.708808i
$768$	−0.794932	+	0.794932i	−0.0286846	+	0.0286846i
$769$	−10.5741	+	10.5741i	−0.381313	+	0.381313i	−0.871575	−	0.490262i	$-0.836901\pi$
$769$	−10.5741	+	10.5741i	−0.381313	+	0.381313i	0.490262	+	0.871575i	$0.336901\pi$
$770$	25.5129	+	20.9762i	0.919421	+	0.755929i
$771$	−1.76397	−	1.76397i	−0.0635280	−	0.0635280i
$772$	24.7844			0.892011
$773$	−5.39429	−	5.39429i	−0.194019	−	0.194019i	0.603411	−	0.797430i	$-0.293808\pi$
$773$	−5.39429	−	5.39429i	−0.194019	−	0.194019i	−0.797430	+	0.603411i	$0.793808\pi$
$774$		−	3.09982i		−	0.111421i
$775$	31.8396	+	21.3572i	1.14371	+	0.767173i
$776$		−	5.91995i		−	0.212514i
$777$	−21.8448	−	18.1637i	−0.783678	−	0.651620i
$778$	−19.7499	−	19.7499i	−0.708070	−	0.708070i
$779$	−12.6001	+	12.6001i	−0.451445	+	0.451445i
$780$	7.04905	−	8.57362i	0.252397	−	0.306985i
$781$			40.0261i			1.43225i
$782$			31.7719i			1.13616i
$783$	−16.4480			−0.587803
$784$		−	10.2601i		−	0.366433i
$785$	−27.6725	+	33.6575i	−0.987674	+	1.20129i
$786$	−24.2741			−0.865827
$787$	−20.2260	+	20.2260i	−0.720978	+	0.720978i	−0.968804	−	0.247827i	$-0.920284\pi$
$787$	−20.2260	+	20.2260i	−0.720978	+	0.720978i	0.247827	+	0.968804i	$0.420284\pi$
$788$	11.3006	−	11.3006i	0.402566	−	0.402566i
$789$		−	17.6652i		−	0.628897i
$790$	−4.96006	−	4.07806i	−0.176471	−	0.145091i
$791$	25.3185	+	25.3185i	0.900223	+	0.900223i
$792$	−6.17274			−0.219339
$793$	−6.35962	−	6.35962i	−0.225837	−	0.225837i
$794$	1.71599	+	1.71599i	0.0608983	+	0.0608983i
$795$	33.8764	−	3.30588i	1.20147	−	0.117247i
$796$	−6.90680	+	6.90680i	−0.244805	+	0.244805i
$797$	−40.0646			−1.41916			−0.709580	−	0.704625i	$-0.751115\pi$
$797$	−40.0646			−1.41916			−0.709580	+	0.704625i	$0.751115\pi$
$798$	9.27524	−	9.27524i	0.328340	−	0.328340i
$799$	−9.82274	−	9.82274i	−0.347504	−	0.347504i
$800$	−4.90567	+	0.966660i	−0.173442	+	0.0341766i
$801$	3.71431	+	3.71431i	0.131239	+	0.131239i
$802$	−9.29247	−	9.29247i	−0.328129	−	0.328129i
$803$	14.3045	+	14.3045i	0.504795	+	0.504795i
$804$	−12.5417			−0.442313
$805$	34.8547	−	42.3930i	1.22847	−	1.49416i
$806$	23.9401	+	23.9401i	0.843254	+	0.843254i
$807$	−4.65968	−	4.65968i	−0.164029	−	0.164029i
$808$		−	9.23382i		−	0.324844i
$809$	−33.6427	+	33.6427i	−1.18282	+	1.18282i	−0.203803	+	0.979012i	$0.565330\pi$
$809$	−33.6427	+	33.6427i	−1.18282	+	1.18282i	−0.979012	+	0.203803i	$0.934670\pi$
$810$	−1.72973	+	0.168798i	−0.0607764	+	0.00593096i
$811$	−11.9502			−0.419628			−0.209814	−	0.977741i	$-0.567286\pi$
$811$	−11.9502			−0.419628			−0.209814	+	0.977741i	$0.567286\pi$
$812$		−	12.8340i		−	0.450386i
$813$	3.90559	−	3.90559i	0.136975	−	0.136975i
$814$	−16.6291	−	13.8269i	−0.582848	−	0.484633i
$815$	2.15535	+	22.0866i	0.0754988	+	0.773659i
$816$	4.27515	+	4.27515i	0.149660	+	0.149660i
$817$	3.54571	+	3.54571i	0.124049	+	0.124049i
$818$	−18.3866	+	18.3866i	−0.642873	+	0.642873i
$819$	−22.5199	−	22.5199i	−0.786909	−	0.786909i
$820$	1.37795	+	14.1203i	0.0481200	+	0.493101i
$821$	−23.5565			−0.822126			−0.411063	−	0.911607i	$-0.634842\pi$
$821$	−23.5565			−0.822126			−0.411063	+	0.911607i	$0.634842\pi$
$822$			22.9290i			0.799739i
$823$	12.5168	+	12.5168i	0.436309	+	0.436309i	0.890768	−	0.454459i	$-0.150167\pi$
$823$	12.5168	+	12.5168i	0.436309	+	0.436309i	−0.454459	+	0.890768i	$0.650167\pi$
$824$		−	8.03931i		−	0.280063i
$825$	16.5969	+	11.1328i	0.577830	+	0.387594i
$826$	−26.1213			−0.908877
$827$			2.77988i			0.0966659i	0.998831	+	0.0483329i	$0.0153908\pi$
$827$			2.77988i			0.0966659i	−0.998831	+	0.0483329i	$0.984609\pi$
$828$			10.2568i			0.356449i
$829$	−20.9695	+	20.9695i	−0.728301	+	0.728301i	−0.970281	−	0.241980i	$-0.922203\pi$
$829$	−20.9695	+	20.9695i	−0.728301	+	0.728301i	0.241980	+	0.970281i	$0.422203\pi$
$830$	11.0233	+	9.06315i	0.382625	+	0.314586i
$831$	−6.53137	+	6.53137i	−0.226571	+	0.226571i
$832$	−4.41538			−0.153076
$833$	−55.1791			−1.91184
$834$	1.24204	−	1.24204i	0.0430082	−	0.0430082i
$835$	−3.85756	−	39.5297i	−0.133496	−	1.36798i
$836$	7.06065	−	7.06065i	0.244198	−	0.244198i
$837$		−	40.8267i		−	1.41118i
$838$		−	8.04256i		−	0.277825i
$839$	−28.7182			−0.991464			−0.495732	−	0.868476i	$-0.665100\pi$
$839$	−28.7182			−0.991464			−0.495732	+	0.868476i	$0.665100\pi$
$840$	−1.01434	−	10.3943i	−0.0349981	−	0.358636i
$841$			19.4571i			0.670934i
$842$	−11.0268	−	11.0268i	−0.380010	−	0.380010i
$843$		−	11.4135i		−	0.393103i
$844$	−22.7919			−0.784531
$845$	14.4560	−	1.41071i	0.497300	−	0.0485298i
$846$	−3.17104	−	3.17104i	−0.109023	−	0.109023i
$847$	−4.82014	+	4.82014i	−0.165622	+	0.165622i
$848$	−9.57437	−	9.57437i	−0.328785	−	0.328785i
$849$	−16.7849	−	16.7849i	−0.576056	−	0.576056i
$850$	5.19871	+	26.3827i	0.178314	+	0.904920i
$851$	−22.9752	+	27.6314i	−0.787580	+	0.947191i
$852$	8.94925	−	8.94925i	0.306596	−	0.306596i
$853$		−	11.9189i		−	0.408097i	−0.978961	−	0.204048i	$-0.934590\pi$
$853$		−	11.9189i		−	0.408097i	0.978961	−	0.204048i	$-0.0654100\pi$
$854$	−8.46253			−0.289582
$855$	−6.92439	+	8.42199i	−0.236809	+	0.288026i
$856$	−4.60753	+	4.60753i	−0.157482	+	0.157482i
$857$		−	17.5942i		−	0.601008i	−0.953781	−	0.300504i	$-0.902845\pi$
$857$		−	17.5942i		−	0.601008i	0.953781	−	0.300504i	$-0.0971548\pi$
$858$	12.4792	+	12.4792i	0.426032	+	0.426032i
$859$	15.4861	+	15.4861i	0.528379	+	0.528379i	0.920089	−	0.391710i	$-0.128116\pi$
$859$	15.4861	+	15.4861i	0.528379	+	0.528379i	−0.391710	+	0.920089i	$0.628116\pi$
$860$	3.97349	−	0.387760i	0.135495	−	0.0132225i
$861$	−29.6335			−1.00991
$862$	−9.69563	−	9.69563i	−0.330234	−	0.330234i
$863$	−22.0613	−	22.0613i	−0.750974	−	0.750974i	0.223687	−	0.974661i	$-0.428191\pi$
$863$	−22.0613	−	22.0613i	−0.750974	−	0.750974i	−0.974661	+	0.223687i	$0.928191\pi$
$864$	3.76493	+	3.76493i	0.128086	+	0.128086i
$865$	−9.91315	+	12.0572i	−0.337057	+	0.409956i
$866$	7.39679	+	7.39679i	0.251353	+	0.251353i
$867$	9.47796	−	9.47796i	0.321888	−	0.321888i
$868$	31.8562			1.08127
$869$	7.21953	−	7.21953i	0.244906	−	0.244906i
$870$	−0.754228	−	7.72880i	−0.0255707	−	0.262031i
$871$	−34.8310	−	34.8310i	−1.18020	−	1.18020i
$872$	14.6123	+	14.6123i	0.494836	+	0.494836i
$873$	−10.2780			−0.347858
$874$	−11.7322	−	11.7322i	−0.396848	−	0.396848i
$875$	22.0060	−	40.9054i	0.743939	−	1.38286i
$876$		−	6.39655i		−	0.216120i
$877$	23.3891	−	23.3891i	0.789793	−	0.789793i	−0.191667	−	0.981460i	$-0.561389\pi$
$877$	23.3891	−	23.3891i	0.789793	−	0.789793i	0.981460	+	0.191667i	$0.0613893\pi$
$878$	−21.3840	+	21.3840i	−0.721675	+	0.721675i
$879$	−12.7731			−0.430827
$880$	−0.772154	−	7.91250i	−0.0260293	−	0.266730i
$881$		−	16.5058i		−	0.556094i	−0.960567	−	0.278047i	$-0.910313\pi$
$881$		−	16.5058i		−	0.556094i	0.960567	−	0.278047i	$-0.0896871\pi$
$882$	−17.8133			−0.599805
$883$			33.7230i			1.13487i	0.823418	+	0.567435i	$0.192064\pi$
$883$			33.7230i			1.13487i	−0.823418	+	0.567435i	$0.807936\pi$
$884$			23.7460i			0.798663i
$885$	−15.7306	+	1.53509i	−0.528778	+	0.0516016i
$886$	0.537851	−	0.537851i	0.0180695	−	0.0180695i
$887$	39.4709	+	39.4709i	1.32530	+	1.32530i	0.909417	+	0.415885i	$0.136528\pi$
$887$	39.4709	+	39.4709i	1.32530	+	1.32530i	0.415885	+	0.909417i	$0.363472\pi$
$888$	0.626522	+	6.80950i	0.0210247	+	0.228512i
$889$			24.8509i			0.833473i
$890$	−4.29654	+	5.22579i	−0.144020	+	0.175169i
$891$		−	2.76336i		−	0.0925761i
$892$	−7.23324	−	7.23324i	−0.242187	−	0.242187i
$893$	7.25436			0.242758
$894$	6.69810	+	6.69810i	0.224018	+	0.224018i
$895$	7.40805	−	9.01025i	0.247624	−	0.301180i
$896$	−2.93770	+	2.93770i	−0.0981416	+	0.0981416i
$897$	20.7358	−	20.7358i	0.692347	−	0.692347i
$898$	17.9014	+	17.9014i	0.597378	+	0.597378i
$899$	23.6871			0.790011
$900$	1.67828	+	8.51705i	0.0559427	+	0.283902i
$901$	−51.4910	+	51.4910i	−1.71541	+	1.71541i
$902$	−22.5581			−0.751103
$903$			8.33898i			0.277504i
$904$		−	8.61849i		−	0.286647i
$905$	−11.9166	+	1.16290i	−0.396121	+	0.0386561i
$906$	−7.67678	−	7.67678i	−0.255044	−	0.255044i
$907$		−	2.85857i		−	0.0949173i	−0.998873	−	0.0474587i	$-0.984888\pi$
$907$		−	2.85857i		−	0.0949173i	0.998873	−	0.0474587i	$-0.0151122\pi$
$908$		−	3.53828i		−	0.117422i
$909$	−16.0314			−0.531729
$910$	26.0500	−	31.6841i	0.863549	−	1.05032i
$911$	7.44807	−	7.44807i	0.246765	−	0.246765i	−0.572876	−	0.819642i	$-0.694172\pi$
$911$	7.44807	−	7.44807i	0.246765	−	0.246765i	0.819642	+	0.572876i	$0.194172\pi$
$912$	−3.15731			−0.104549
$913$	−16.0448	+	16.0448i	−0.531005	+	0.531005i
$914$			10.3305i			0.341702i
$915$	−5.09624	+	0.497325i	−0.168477	+	0.0164411i
$916$			10.2694i			0.339311i
$917$	−89.7056			−2.96234
$918$	20.2478	−	20.2478i	0.668278	−	0.668278i
$919$	7.70512	−	7.70512i	0.254168	−	0.254168i	−0.568509	−	0.822677i	$-0.692479\pi$
$919$	7.70512	−	7.70512i	0.254168	−	0.254168i	0.822677	+	0.568509i	$0.192479\pi$
$920$	−13.1477	+	1.28304i	−0.433466	+	0.0423004i
$921$	−6.06939			−0.199993
$922$	19.5325	−	19.5325i	0.643268	−	0.643268i
$923$	49.7079			1.63615
$924$	16.6056			0.546284
$925$	−14.5569	+	26.7039i	−0.478629	+	0.878017i
$926$	−13.2709			−0.436110
$927$	−13.9576			−0.458427
$928$	−2.18437	+	2.18437i	−0.0717053	+	0.0717053i
$929$	29.3928			0.964346			0.482173	−	0.876076i	$-0.339848\pi$
$929$	29.3928			0.964346			0.482173	+	0.876076i	$0.339848\pi$
$930$	19.1842	−	1.87212i	0.629076	−	0.0613893i
$931$	20.3756	−	20.3756i	0.667784	−	0.667784i
$932$	−0.731820	+	0.731820i	−0.0239716	+	0.0239716i
$933$	−14.1859			−0.464425
$934$		−	40.7473i		−	1.33329i
$935$	−42.5535	+	4.15265i	−1.39165	+	0.135806i
$936$			7.66584i			0.250566i
$937$	10.7698	−	10.7698i	0.351834	−	0.351834i	−0.508958	−	0.860791i	$-0.669969\pi$
$937$	10.7698	−	10.7698i	0.351834	−	0.351834i	0.860791	+	0.508958i	$0.169969\pi$
$938$	−46.3484			−1.51333
$939$	23.6726	−	23.6726i	0.772527	−	0.772527i
$940$	3.66812	−	4.46146i	0.119641	−	0.145517i
$941$	29.3530			0.956880			0.478440	−	0.878120i	$-0.341202\pi$
$941$	29.3530			0.956880			0.478440	+	0.878120i	$0.341202\pi$
$942$			21.9066i			0.713757i
$943$			37.4833i			1.22062i
$944$	4.44588	+	4.44588i	0.144701	+	0.144701i
$945$	−49.2290	+	4.80409i	−1.60142	+	0.156277i
$946$			6.34794i			0.206389i
$947$		−	14.6562i		−	0.476262i	−0.971233	−	0.238131i	$-0.923465\pi$
$947$		−	14.6562i		−	0.476262i	0.971233	−	0.238131i	$-0.0765347\pi$
$948$	−3.22836			−0.104852
$949$	17.7646	−	17.7646i	0.576662	−	0.576662i
$950$	−11.6619	−	7.82248i	−0.378361	−	0.253795i
$951$	25.8669			0.838793
$952$	15.7990	+	15.7990i	0.512047	+	0.512047i
$953$	7.12766	−	7.12766i	0.230887	−	0.230887i	−0.582176	−	0.813063i	$-0.697798\pi$
$953$	7.12766	−	7.12766i	0.230887	−	0.230887i	0.813063	+	0.582176i	$0.197798\pi$
$954$	−16.6227	+	16.6227i	−0.538179	+	0.538179i
$955$	20.2384	−	24.6155i	0.654898	−	0.796539i
$956$	6.25677	+	6.25677i	0.202358	+	0.202358i
$957$	12.3473			0.399132
$958$	−8.91382	−	8.91382i	−0.287992	−	0.287992i
$959$			84.7347i			2.73623i
$960$	−1.59648	+	1.94176i	−0.0515261	+	0.0626701i
$961$			27.7956i			0.896632i
$962$	−17.1714	+	20.6514i	−0.553629	+	0.665827i
$963$	7.99944	+	7.99944i	0.257778	+	0.257778i
$964$	−6.31560	+	6.31560i	−0.203412	+	0.203412i
$965$	55.1576	−	5.38264i	1.77559	−	0.173273i
$966$		−	27.5924i		−	0.887769i
$967$		−	38.4439i		−	1.23627i	−0.786071	−	0.618136i	$-0.787888\pi$
$967$		−	38.4439i		−	1.23627i	0.786071	−	0.618136i	$-0.212112\pi$
$968$	1.64079			0.0527370
$969$			16.9801i			0.545478i
$970$	−1.28569	−	13.1748i	−0.0412809	−	0.423018i
$971$	−45.1188			−1.44793			−0.723965	−	0.689837i	$-0.757682\pi$
$971$	−45.1188			−1.44793			−0.723965	+	0.689837i	$0.757682\pi$
$972$	10.6769	−	10.6769i	0.342463	−	0.342463i
$973$	4.58999	−	4.58999i	0.147148	−	0.147148i
$974$			27.7847i			0.890278i
$975$	13.8256	−	20.6115i	0.442775	−	0.660095i
$976$	1.44033	+	1.44033i	0.0461040	+	0.0461040i
$977$	34.3176			1.09792			0.548959	−	0.835850i	$-0.315024\pi$
$977$	34.3176			1.09792			0.548959	+	0.835850i	$0.315024\pi$
$978$	7.88918	+	7.88918i	0.252268	+	0.252268i
$979$	−7.60630	−	7.60630i	−0.243099	−	0.243099i
$980$	−2.22828	−	22.8339i	−0.0711798	−	0.729402i
$981$	25.3694	−	25.3694i	0.809984	−	0.809984i
$982$	7.19820			0.229704
$983$	−35.5214	+	35.5214i	−1.13296	+	1.13296i	−0.143272	+	0.989683i	$0.545762\pi$
$983$	−35.5214	+	35.5214i	−1.13296	+	1.13296i	−0.989683	+	0.143272i	$0.954238\pi$
$984$	5.04366	+	5.04366i	0.160786	+	0.160786i
$985$	22.6951	−	27.6036i	0.723127	−	0.879524i
$986$	11.7475	+	11.7475i	0.374118	+	0.374118i
$987$	8.53057	+	8.53057i	0.271531	+	0.271531i
$988$	−8.76852	−	8.76852i	−0.278964	−	0.278964i
$989$	10.5479			0.335405
$990$	−13.7374	+	1.34059i	−0.436604	+	0.0426067i
$991$	32.2431	+	32.2431i	1.02424	+	1.02424i	0.999699	+	0.0245377i	$0.00781138\pi$
$991$	32.2431	+	32.2431i	1.02424	+	1.02424i	0.0245377	+	0.999699i	$0.492189\pi$
$992$	−5.42197	−	5.42197i	−0.172148	−	0.172148i
$993$			24.8538i			0.788713i
$994$	33.0722	−	33.0722i	1.04899	−	1.04899i
$995$	−13.8710	+	16.8711i	−0.439742	+	0.534849i
$996$	7.17475			0.227341
$997$		−	2.02170i		−	0.0640278i	−0.999487	−	0.0320139i	$-0.989808\pi$
$997$		−	2.02170i		−	0.0640278i	0.999487	−	0.0320139i	$-0.0101921\pi$
$998$	0.378337	−	0.378337i	0.0119761	−	0.0119761i
$999$	32.2509	−	2.96731i	1.02037	−	0.0938815i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.h.e.253.4	yes	20
5.2	odd	4		370.2.g.e.327.7	yes	20
37.6	odd	4		370.2.g.e.43.7	✓	20
185.117	even	4	inner	370.2.h.e.117.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.7	✓	20	37.6	odd	4
370.2.g.e.327.7	yes	20	5.2	odd	4
370.2.h.e.117.4	yes	20	185.117	even	4	inner
370.2.h.e.253.4	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.794932 + 0.794932i) q^{3} +1.00000 q^{4} +(2.22550 - 0.217179i) q^{5} +(0.794932 - 0.794932i) q^{6} +(2.93770 - 2.93770i) q^{7} -1.00000 q^{8} +1.73617i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.794932 + 0.794932i) q^{3} +1.00000 q^{4} +(2.22550 - 0.217179i) q^{5} +(0.794932 - 0.794932i) q^{6} +(2.93770 - 2.93770i) q^{7} -1.00000 q^{8} +1.73617i q^{9} +(-2.22550 + 0.217179i) q^{10} -3.55539i q^{11} +(-0.794932 + 0.794932i) q^{12} -4.41538 q^{13} +(-2.93770 + 2.93770i) q^{14} +(-1.59648 + 1.94176i) q^{15} +1.00000 q^{16} -5.37801i q^{17} -1.73617i q^{18} +(1.98590 + 1.98590i) q^{19} +(2.22550 - 0.217179i) q^{20} +4.67054i q^{21} +3.55539i q^{22} +5.90774 q^{23} +(0.794932 - 0.794932i) q^{24} +(4.90567 - 0.966660i) q^{25} +4.41538 q^{26} +(-3.76493 - 3.76493i) q^{27} +(2.93770 - 2.93770i) q^{28} +(2.18437 - 2.18437i) q^{29} +(1.59648 - 1.94176i) q^{30} +(5.42197 + 5.42197i) q^{31} -1.00000 q^{32} +(2.82629 + 2.82629i) q^{33} +5.37801i q^{34} +(5.89983 - 7.17584i) q^{35} +1.73617i q^{36} +(-3.88900 + 4.67714i) q^{37} +(-1.98590 - 1.98590i) q^{38} +(3.50993 - 3.50993i) q^{39} +(-2.22550 + 0.217179i) q^{40} +6.34477i q^{41} -4.67054i q^{42} +1.78544 q^{43} -3.55539i q^{44} +(0.377058 + 3.86383i) q^{45} -5.90774 q^{46} +(1.82646 - 1.82646i) q^{47} +(-0.794932 + 0.794932i) q^{48} -10.2601i q^{49} +(-4.90567 + 0.966660i) q^{50} +(4.27515 + 4.27515i) q^{51} -4.41538 q^{52} +(-9.57437 - 9.57437i) q^{53} +(3.76493 + 3.76493i) q^{54} +(-0.772154 - 7.91250i) q^{55} +(-2.93770 + 2.93770i) q^{56} -3.15731 q^{57} +(-2.18437 + 2.18437i) q^{58} +(4.44588 + 4.44588i) q^{59} +(-1.59648 + 1.94176i) q^{60} +(1.44033 + 1.44033i) q^{61} +(-5.42197 - 5.42197i) q^{62} +(5.10033 + 5.10033i) q^{63} +1.00000 q^{64} +(-9.82642 + 0.958927i) q^{65} +(-2.82629 - 2.82629i) q^{66} +(7.88856 + 7.88856i) q^{67} -5.37801i q^{68} +(-4.69625 + 4.69625i) q^{69} +(-5.89983 + 7.17584i) q^{70} -11.2579 q^{71} -1.73617i q^{72} +(-4.02333 + 4.02333i) q^{73} +(3.88900 - 4.67714i) q^{74} +(-3.13124 + 4.66810i) q^{75} +(1.98590 + 1.98590i) q^{76} +(-10.4447 - 10.4447i) q^{77} +(-3.50993 + 3.50993i) q^{78} +(2.03059 + 2.03059i) q^{79} +(2.22550 - 0.217179i) q^{80} +0.777232 q^{81} -6.34477i q^{82} +(-4.51281 - 4.51281i) q^{83} +4.67054i q^{84} +(-1.16799 - 11.9687i) q^{85} -1.78544 q^{86} +3.47285i q^{87} +3.55539i q^{88} +(2.13937 - 2.13937i) q^{89} +(-0.377058 - 3.86383i) q^{90} +(-12.9711 + 12.9711i) q^{91} +5.90774 q^{92} -8.62020 q^{93} +(-1.82646 + 1.82646i) q^{94} +(4.85091 + 3.98832i) q^{95} +(0.794932 - 0.794932i) q^{96} +5.91995i q^{97} +10.2601i q^{98} +6.17274 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8} + 4 q^{10} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 6 q^{19} - 4 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} - 20 q^{27} - 2 q^{28} + 18 q^{29} + 4 q^{30} + 12 q^{31} - 20 q^{32} + 4 q^{33} - 12 q^{35} - 32 q^{37} - 6 q^{38} + 6 q^{39} + 4 q^{40} + 16 q^{43} + 22 q^{45} + 4 q^{46} - 22 q^{47} + 4 q^{48} - 10 q^{50} + 8 q^{51} - 4 q^{53} + 20 q^{54} + 16 q^{55} + 2 q^{56} + 24 q^{57} - 18 q^{58} - 10 q^{59} - 4 q^{60} + 10 q^{61} - 12 q^{62} - 2 q^{63} + 20 q^{64} + 20 q^{65} - 4 q^{66} + 8 q^{67} - 34 q^{69} + 12 q^{70} + 16 q^{71} - 6 q^{73} + 32 q^{74} - 26 q^{75} + 6 q^{76} - 4 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} - 28 q^{81} + 6 q^{83} + 10 q^{85} - 16 q^{86} - 44 q^{89} - 22 q^{90} - 40 q^{91} - 4 q^{92} - 40 q^{93} + 22 q^{94} + 50 q^{95} - 4 q^{96} - 20 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8 + 4 * q^10 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 6 * q^19 - 4 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 - 20 * q^27 - 2 * q^28 + 18 * q^29 + 4 * q^30 + 12 * q^31 - 20 * q^32 + 4 * q^33 - 12 * q^35 - 32 * q^37 - 6 * q^38 + 6 * q^39 + 4 * q^40 + 16 * q^43 + 22 * q^45 + 4 * q^46 - 22 * q^47 + 4 * q^48 - 10 * q^50 + 8 * q^51 - 4 * q^53 + 20 * q^54 + 16 * q^55 + 2 * q^56 + 24 * q^57 - 18 * q^58 - 10 * q^59 - 4 * q^60 + 10 * q^61 - 12 * q^62 - 2 * q^63 + 20 * q^64 + 20 * q^65 - 4 * q^66 + 8 * q^67 - 34 * q^69 + 12 * q^70 + 16 * q^71 - 6 * q^73 + 32 * q^74 - 26 * q^75 + 6 * q^76 - 4 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 - 28 * q^81 + 6 * q^83 + 10 * q^85 - 16 * q^86 - 44 * q^89 - 22 * q^90 - 40 * q^91 - 4 * q^92 - 40 * q^93 + 22 * q^94 + 50 * q^95 - 4 * q^96 - 20 * q^99

Introduction

L-functions

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Database

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