LMFDB - Embedded newform 370.2.g.e.43.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(43,370)]

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([3, 3]))

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

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

chi := DirichletCharacter("370.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.g (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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.7
Root			$-0.794932 + 0.794932i$ of defining polynomial
Character	$\chi$	$=$	370.43
Dual form			370.2.g.e.327.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.794932	−	0.794932i	0.458954	−	0.458954i	−0.439358	−	0.898312i	$-0.644794\pi$
$3$	0.794932	−	0.794932i	0.458954	−	0.458954i	0.898312	+	0.439358i	$0.144794\pi$
$4$	−1.00000			−0.500000
$5$	0.217179	+	2.22550i	0.0971252	+	0.995272i
$5$	0.217179	+	2.22550i	0.0971252	+	0.995272i
$6$	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	$-0.0374053\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.73617i			0.578722i
$10$	−2.22550	+	0.217179i	−0.703764	+	0.0686779i
$11$			3.55539i			1.07199i	0.844221	+	0.535995i	$0.180063\pi$
$11$			3.55539i			1.07199i	−0.844221	+	0.535995i	$0.819937\pi$
$12$	−0.794932	+	0.794932i	−0.229477	+	0.229477i
$13$		−	4.41538i		−	1.22461i	−0.790623	−	0.612303i	$-0.790243\pi$
$13$		−	4.41538i		−	1.22461i	0.790623	−	0.612303i	$-0.209757\pi$
$14$	2.93770	+	2.93770i	0.785133	+	0.785133i
$15$	1.94176	+	1.59648i	0.501360	+	0.412208i
$16$	1.00000			0.250000
$17$	5.37801			1.30436			0.652179	−	0.758065i	$-0.273855\pi$
$17$	5.37801			1.30436			0.652179	+	0.758065i	$0.273855\pi$
$18$	−1.73617			−0.409218
$19$	−1.98590	+	1.98590i	−0.455597	+	0.455597i	−0.897207	−	0.441610i	$-0.854408\pi$
$19$	−1.98590	+	1.98590i	−0.455597	+	0.455597i	0.441610	+	0.897207i	$0.354408\pi$
$20$	−0.217179	−	2.22550i	−0.0485626	−	0.497636i
$21$		−	4.67054i		−	1.01920i
$22$	−3.55539			−0.758011
$23$			5.90774i			1.23185i	0.787805	+	0.615925i	$0.211217\pi$
$23$			5.90774i			1.23185i	−0.787805	+	0.615925i	$0.788783\pi$
$24$	−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	$-0.342599\pi$
$29$	−2.18437	−	2.18437i	−0.405627	−	0.405627i	−0.880210	+	0.474584i	$0.842599\pi$
$30$	−1.59648	+	1.94176i	−0.291475	+	0.354515i
$31$	5.42197	−	5.42197i	0.973815	−	0.973815i	−0.0258507	−	0.999666i	$-0.508229\pi$
$31$	5.42197	−	5.42197i	0.973815	−	0.973815i	0.999666	+	0.0258507i	$0.00822946\pi$
$32$			1.00000i			0.176777i
$33$	2.82629	+	2.82629i	0.491994	+	0.491994i
$34$			5.37801i			0.922321i
$35$	7.17584	+	5.89983i	1.21294	+	0.997253i
$36$		−	1.73617i		−	0.289361i
$37$	−4.67714	+	3.88900i	−0.768918	+	0.639348i
$37$	−4.67714	+	3.88900i	−0.768918	+	0.639348i
$38$	−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	$-0.835006\pi$
$41$		−	6.34477i		−	0.990886i	0.868640	−	0.495443i	$-0.164994\pi$
$42$	4.67054			0.720680
$43$			1.78544i			0.272277i	0.990690	+	0.136139i	$0.0434693\pi$
$43$			1.78544i			0.272277i	−0.990690	+	0.136139i	$0.956531\pi$
$44$		−	3.55539i		−	0.535995i
$45$	−3.86383	+	0.377058i	−0.575986	+	0.0562085i
$46$	−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
$50$	−0.966660	−	4.90567i	−0.136706	−	0.693766i
$51$	4.27515	−	4.27515i	0.598641	−	0.598641i
$52$			4.41538i			0.612303i
$53$	−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
$55$	−7.91250	+	0.772154i	−1.06692	+	0.104117i
$56$	−2.93770	−	2.93770i	−0.392566	−	0.392566i
$57$			3.15731i			0.418197i
$58$	2.18437	−	2.18437i	0.286821	−	0.286821i
$59$	−4.44588	+	4.44588i	−0.578805	+	0.578805i	−0.934574	−	0.355769i	$-0.884219\pi$
$59$	−4.44588	+	4.44588i	−0.578805	+	0.578805i	0.355769	+	0.934574i	$0.384219\pi$
$60$	−1.94176	−	1.59648i	−0.250680	−	0.206104i
$61$	1.44033	−	1.44033i	0.184416	−	0.184416i	−0.608861	−	0.793277i	$-0.708373\pi$
$61$	1.44033	−	1.44033i	0.184416	−	0.184416i	0.793277	+	0.608861i	$0.208373\pi$
$62$	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	0.0356245	−	0.999365i	$-0.488658\pi$
$67$	−7.88856	−	7.88856i	−0.963741	−	0.963741i	−0.999365	+	0.0356245i	$0.988658\pi$
$68$	−5.37801			−0.652179
$69$	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	$0.732863\pi$
$72$	1.73617			0.204609
$73$	4.02333	−	4.02333i	0.470896	−	0.470896i	−0.431309	−	0.902204i	$-0.641948\pi$
$73$	4.02333	−	4.02333i	0.470896	−	0.470896i	0.902204	+	0.431309i	$0.141948\pi$
$74$	−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	$-0.801648\pi$
$79$	−2.03059	+	2.03059i	−0.228459	+	0.228459i	0.583590	+	0.812049i	$0.301648\pi$
$80$	0.217179	+	2.22550i	0.0242813	+	0.248818i
$81$	0.777232			0.0863591
$82$	6.34477			0.700662
$83$	−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
$87$	−3.47285			−0.372328
$88$	3.55539			0.379006
$89$	−2.13937	−	2.13937i	−0.226773	−	0.226773i	0.584570	−	0.811343i	$-0.301263\pi$
$89$	−2.13937	−	2.13937i	−0.226773	−	0.226773i	−0.811343	+	0.584570i	$0.801263\pi$
$90$	−0.377058	−	3.86383i	−0.0397454	−	0.407283i
$91$	−12.9711	−	12.9711i	−1.35974	−	1.35974i
$92$		−	5.90774i		−	0.615925i
$93$		−	8.62020i		−	0.893873i
$94$	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
$97$	−5.91995			−0.601080			−0.300540	−	0.953769i	$-0.597167\pi$
$97$	−5.91995			−0.601080			−0.300540	+	0.953769i	$0.597167\pi$
$98$	10.2601			1.03643
$99$	−6.17274			−0.620384
$100$	4.90567	−	0.966660i	0.490567	−	0.0966660i
$101$		−	9.23382i		−	0.918799i	−0.888230	−	0.459399i	$-0.848065\pi$
$101$		−	9.23382i		−	0.918799i	0.888230	−	0.459399i	$-0.151935\pi$
$102$	4.27515	+	4.27515i	0.423303	+	0.423303i
$103$	8.03931			0.792137			0.396068	−	0.918221i	$-0.370374\pi$
$103$	8.03931			0.792137			0.396068	+	0.918221i	$0.370374\pi$
$104$	−4.41538			−0.432964
$105$	10.3943	−	1.01434i	1.01438	−	0.0989896i
$106$	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	0.598443	−	0.801166i	$-0.295786\pi$
$109$	14.6123	−	14.6123i	1.39961	−	1.39961i	0.801166	−	0.598443i	$-0.204214\pi$
$110$	−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
$113$	8.61849			0.810759			0.405380	−	0.914148i	$-0.367139\pi$
$113$	8.61849			0.810759			0.405380	+	0.914148i	$0.367139\pi$
$114$	−3.15731			−0.295710
$115$	−13.1477	+	1.28304i	−1.22603	+	0.119644i
$116$	2.18437	+	2.18437i	0.202813	+	0.202813i
$117$	7.66584			0.708707
$118$	−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
$125$	−3.21670	−	10.7076i	−0.287711	−	0.957717i
$126$	−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	$0.335502\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	1.41931	+	1.41931i	0.124963	+	0.124963i
$130$	0.958927	+	9.82642i	0.0841034	+	0.861834i
$131$	−15.2680	+	15.2680i	−1.33397	+	1.33397i	−0.432188	+	0.901783i	$0.642258\pi$
$131$	−15.2680	+	15.2680i	−1.33397	+	1.33397i	−0.901783	+	0.432188i	$0.857742\pi$
$132$	−2.82629	−	2.82629i	−0.245997	−	0.245997i
$133$			11.6680i			1.01174i
$134$	7.88856	−	7.88856i	0.681468	−	0.681468i
$135$	−7.56118	+	9.19650i	−0.650762	+	0.791509i
$136$		−	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	$-0.521107\pi$
$139$	−1.56244			−0.132525			−0.0662624	+	0.997802i	$0.521107\pi$
$140$	−7.17584	−	5.89983i	−0.606469	−	0.498627i
$141$		−	2.90383i		−	0.244547i
$142$		−	11.2579i		−	0.944740i
$143$	15.6984			1.31277
$144$			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
$148$	4.67714	−	3.88900i	0.384459	−	0.319674i
$149$			8.42600i			0.690285i	0.938550	+	0.345142i	$0.112169\pi$
$149$			8.42600i			0.690285i	−0.938550	+	0.345142i	$0.887831\pi$
$150$	−4.66810	−	3.13124i	−0.381149	−	0.255665i
$151$			9.65715i			0.785887i	0.919563	+	0.392944i	$0.128543\pi$
$151$			9.65715i			0.785887i	−0.919563	+	0.392944i	$0.871457\pi$
$152$	1.98590	+	1.98590i	0.161078	+	0.161078i
$153$			9.33711i			0.754861i
$154$	−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
$162$			0.777232i			0.0610651i
$163$	9.92434			0.777334			0.388667	−	0.921378i	$-0.372936\pi$
$163$	9.92434			0.777334			0.388667	+	0.921378i	$0.372936\pi$
$164$			6.34477i			0.495443i
$165$	−5.67609	+	6.90371i	−0.441883	+	0.537453i
$166$	4.51281	−	4.51281i	0.350262	−	0.350262i
$167$	17.7622			1.37448			0.687239	−	0.726431i	$-0.258822\pi$
$167$	17.7622			1.37448			0.687239	+	0.726431i	$0.258822\pi$
$168$	−4.67054			−0.360340
$169$	−6.49561			−0.499662
$170$	−11.9687	+	1.16799i	−0.917960	+	0.0895806i
$171$	−3.44786	−	3.44786i	−0.263664	−	0.263664i
$172$		−	1.78544i		−	0.136139i
$173$	4.93605	−	4.93605i	0.375281	−	0.375281i	−0.494116	−	0.869396i	$-0.664508\pi$
$173$	4.93605	−	4.93605i	0.375281	−	0.375281i	0.869396	+	0.494116i	$0.164508\pi$
$174$		−	3.47285i		−	0.263276i
$175$	−11.5716	+	17.2511i	−0.874732	+	1.30406i
$176$			3.55539i			0.267998i
$177$			7.06835i			0.531290i
$178$	2.13937	−	2.13937i	0.160353	−	0.160353i
$179$	−3.68868	−	3.68868i	−0.275705	−	0.275705i	0.555687	−	0.831392i	$-0.312455\pi$
$179$	−3.68868	−	3.68868i	−0.275705	−	0.275705i	−0.831392	+	0.555687i	$0.812455\pi$
$180$	3.86383	−	0.377058i	0.287993	−	0.0281042i
$181$	−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
$183$		−	2.28994i		−	0.169277i
$184$	5.90774			0.435525
$185$	−9.67073	−	9.56436i	−0.711006	−	0.703186i
$186$	8.62020			0.632064
$187$			19.1209i			1.39826i
$188$	−1.82646	+	1.82646i	−0.133209	+	0.133209i
$189$	22.1205			1.60903
$190$	3.98832	−	4.85091i	0.289343	−	0.351922i
$191$	10.0773	+	10.0773i	0.729166	+	0.729166i	0.970454	−	0.241288i	$-0.0775698\pi$
$191$	10.0773	+	10.0773i	0.729166	+	0.729166i	−0.241288	+	0.970454i	$0.577570\pi$
$192$	−0.794932	+	0.794932i	−0.0573693	+	0.0573693i
$193$			24.7844i			1.78402i	0.452014	+	0.892011i	$0.350706\pi$
$193$			24.7844i			1.78402i	−0.452014	+	0.892011i	$0.649294\pi$
$194$		−	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	$0.0572087\pi$
$198$		−	6.17274i		−	0.438678i
$199$	6.90680	+	6.90680i	0.489610	+	0.489610i	0.908183	−	0.418573i	$-0.137470\pi$
$199$	6.90680	+	6.90680i	0.489610	+	0.489610i	−0.418573	+	0.908183i	$0.637470\pi$
$200$	0.966660	+	4.90567i	0.0683532	+	0.346883i
$201$	−12.5417			−0.884626
$202$	9.23382			0.649689
$203$	−12.8340			−0.900771
$204$	−4.27515	+	4.27515i	−0.299321	+	0.299321i
$205$	14.1203	−	1.37795i	0.986202	−	0.0962400i
$206$			8.03931i			0.560125i
$207$	−10.2568			−0.712898
$208$		−	4.41538i		−	0.306152i
$209$	−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
$217$		−	31.8562i		−	2.16254i
$218$	14.6123	+	14.6123i	0.989673	+	0.989673i
$219$		−	6.39655i		−	0.432239i
$220$	7.91250	−	0.772154i	0.533461	−	0.0520586i
$221$		−	23.7460i		−	1.59733i
$222$	−6.80950	−	0.626522i	−0.457024	−	0.0420494i
$223$	−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
$227$	3.53828			0.234844			0.117422	−	0.993082i	$-0.462537\pi$
$227$	3.53828			0.234844			0.117422	+	0.993082i	$0.462537\pi$
$228$		−	3.15731i		−	0.209098i
$229$			10.2694i			0.678622i	0.940674	+	0.339311i	$0.110194\pi$
$229$			10.2694i			0.678622i	−0.940674	+	0.339311i	$0.889806\pi$
$230$	−1.28304	−	13.1477i	−0.0846008	−	0.866931i
$231$	16.6056			1.09257
$232$	−2.18437	+	2.18437i	−0.143411	+	0.143411i
$233$	0.731820	−	0.731820i	0.0479431	−	0.0479431i	−0.682729	−	0.730672i	$-0.739207\pi$
$233$	0.731820	−	0.731820i	0.0479431	−	0.0479431i	0.730672	+	0.682729i	$0.239207\pi$
$234$			7.66584i			0.501131i
$235$	4.46146	+	3.66812i	0.291033	+	0.239282i
$236$	4.44588	−	4.44588i	0.289402	−	0.289402i
$237$			3.22836i			0.209704i
$238$	15.7990	+	15.7990i	1.02409	+	1.02409i
$239$	−6.25677	+	6.25677i	−0.404717	+	0.404717i	−0.879892	−	0.475175i	$-0.842385\pi$
$239$	−6.25677	+	6.25677i	−0.404717	+	0.404717i	0.475175	+	0.879892i	$0.342385\pi$
$240$	1.94176	+	1.59648i	0.125340	+	0.103052i
$241$	−6.31560	−	6.31560i	−0.406823	−	0.406823i	0.473806	−	0.880629i	$-0.342880\pi$
$241$	−6.31560	−	6.31560i	−0.406823	−	0.406823i	−0.880629	+	0.473806i	$0.842880\pi$
$242$		−	1.64079i		−	0.105474i
$243$	−10.6769	+	10.6769i	−0.684926	+	0.684926i
$244$	−1.44033	+	1.44033i	−0.0922079	+	0.0922079i
$245$	22.8339	−	2.22828i	1.45880	−	0.142360i
$246$	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	−0.573141	−	0.819457i	$-0.694275\pi$
$251$	3.90237	−	3.90237i	0.246315	−	0.246315i	0.819457	+	0.573141i	$0.194275\pi$
$252$	−5.10033	−	5.10033i	−0.321291	−	0.321291i
$253$	−21.0043			−1.32053
$254$	−4.22966	−	4.22966i	−0.265393	−	0.265393i
$255$	10.4428	+	8.58586i	0.653954	+	0.537668i
$256$	1.00000			0.0625000
$257$	−2.21902			−0.138419			−0.0692095	−	0.997602i	$-0.522048\pi$
$257$	−2.21902			−0.138419			−0.0692095	+	0.997602i	$0.522048\pi$
$258$	−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	−0.276013	−	0.961154i	$-0.589013\pi$
$263$	11.1111	−	11.1111i	0.685141	−	0.685141i	0.961154	+	0.276013i	$0.0890131\pi$
$264$	2.82629	−	2.82629i	0.173946	−	0.173946i
$265$	19.2284	−	23.3871i	1.18119	−	1.43666i
$266$	−11.6680			−0.715408
$267$	−3.40131			−0.208157
$268$	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	$0.547678\pi$
$272$	5.37801			0.326090
$273$	−20.6222			−1.24811
$274$	−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
$277$		−	8.21627i		−	0.493668i	−0.969058	−	0.246834i	$-0.920610\pi$
$277$		−	8.21627i		−	0.493668i	0.969058	−	0.246834i	$-0.0793902\pi$
$278$		−	1.56244i		−	0.0937092i
$279$	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	0.459776	−	0.888035i	$-0.347930\pi$
$281$	−7.17894	−	7.17894i	−0.428259	−	0.428259i	−0.888035	+	0.459776i	$0.847930\pi$
$282$	2.90383			0.172921
$283$	21.1149			1.25515			0.627574	−	0.778557i	$-0.284048\pi$
$283$	21.1149			1.25515			0.627574	+	0.778557i	$0.284048\pi$
$284$	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
$288$	−1.73617			−0.102305
$289$	11.9230			0.701352
$290$	5.33570	+	4.38690i	0.313323	+	0.257608i
$291$	−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
$298$	−8.42600			−0.488105
$299$	26.0849			1.50853
$300$	3.13124	−	4.66810i	0.180782	−	0.269513i
$301$	5.24509	+	5.24509i	0.302322	+	0.302322i
$302$	−9.65715			−0.555706
$303$	−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	0.589725	−	0.807604i	$-0.299236\pi$
$307$	−3.81755	−	3.81755i	−0.217879	−	0.217879i	−0.807604	+	0.589725i	$0.799236\pi$
$308$	−10.4447	−	10.4447i	−0.595140	−	0.595140i
$309$	6.39071	−	6.39071i	0.363555	−	0.363555i
$310$	−10.8890	+	13.2441i	−0.618456	+	0.752215i
$311$	8.92270	−	8.92270i	0.505960	−	0.505960i	−0.407324	−	0.913284i	$-0.633538\pi$
$311$	8.92270	−	8.92270i	0.505960	−	0.505960i	0.913284	+	0.407324i	$0.133538\pi$
$312$	−3.50993	+	3.50993i	−0.198711	+	0.198711i
$313$		−	29.7794i		−	1.68323i	−0.540076	−	0.841616i	$-0.681605\pi$
$313$		−	29.7794i		−	1.68323i	0.540076	−	0.841616i	$-0.318395\pi$
$314$	−13.7789	−	13.7789i	−0.777591	−	0.777591i
$315$	−10.2431	+	12.4584i	−0.577132	+	0.701954i
$316$	2.03059	−	2.03059i	0.114229	−	0.114229i
$317$	16.2699	+	16.2699i	0.913808	+	0.913808i	0.996569	−	0.0827610i	$-0.0263738\pi$
$317$	16.2699	+	16.2699i	0.913808	+	0.913808i	−0.0827610	+	0.996569i	$0.526374\pi$
$318$		−	15.2219i		−	0.853604i
$319$	7.76627	−	7.76627i	0.434828	−	0.434828i
$320$	−0.217179	−	2.22550i	−0.0121407	−	0.124409i
$321$		−	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
$325$	4.26818	+	21.6604i	0.236756	+	1.20150i
$326$			9.92434i			0.549658i
$327$		−	23.2316i		−	1.28471i
$328$	−6.34477			−0.350331
$329$		−	10.7312i		−	0.591630i
$330$	−6.90371	−	5.67609i	−0.380037	−	0.312459i
$331$	15.6327	+	15.6327i	0.859250	+	0.859250i	0.991250	−	0.132000i	$-0.0421399\pi$
$331$	15.6327	+	15.6327i	0.859250	+	0.859250i	−0.132000	+	0.991250i	$0.542140\pi$
$332$	4.51281	+	4.51281i	0.247672	+	0.247672i
$333$	−6.75195	−	8.12030i	−0.370004	−	0.444990i
$334$			17.7622i			0.971903i
$335$	15.8427	−	19.2692i	0.865581	−	1.05279i
$336$		−	4.67054i		−	0.254799i
$337$	−22.0252	−	22.0252i	−1.19979	−	1.19979i	−0.974230	−	0.225558i	$-0.927580\pi$
$337$	−22.0252	−	22.0252i	−1.19979	−	1.19979i	−0.225558	−	0.974230i	$-0.572420\pi$
$338$		−	6.49561i		−	0.353315i
$339$	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
$347$			35.2079i			1.89006i	0.326987	+	0.945029i	$0.393967\pi$
$347$			35.2079i			1.89006i	−0.326987	+	0.945029i	$0.606033\pi$
$348$	3.47285			0.186164
$349$		−	7.00272i		−	0.374847i	−0.982279	−	0.187423i	$-0.939986\pi$
$349$		−	7.00272i		−	0.374847i	0.982279	−	0.187423i	$-0.0600137\pi$
$350$	−17.2511	−	11.5716i	−0.922111	−	0.618529i
$351$	16.6236	−	16.6236i	0.887303	−	0.887303i
$352$	−3.55539			−0.189503
$353$	24.1991			1.28799			0.643995	−	0.765030i	$-0.277276\pi$
$353$	24.1991			1.28799			0.643995	+	0.765030i	$0.277276\pi$
$354$	−7.06835			−0.375679
$355$	−2.44497	−	25.0544i	−0.129766	−	1.32975i
$356$	2.13937	+	2.13937i	0.113387	+	0.113387i
$357$		−	25.1182i		−	1.32940i
$358$	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
$362$		−	5.35458i		−	0.281430i
$363$	−1.30432	+	1.30432i	−0.0684588	+	0.0684588i
$364$	12.9711	+	12.9711i	0.679868	+	0.679868i
$365$	9.82769	+	8.08013i	0.514405	+	0.422933i
$366$	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	$-0.0605405\pi$
$368$			5.90774i			0.307962i
$369$	11.0156			0.573448
$370$	9.56436	−	9.67073i	0.497227	−	0.502757i
$371$	−56.2532			−2.92052
$372$			8.62020i			0.446937i
$373$	10.4263	−	10.4263i	0.539852	−	0.539852i	−0.383633	−	0.923486i	$-0.625327\pi$
$373$	10.4263	−	10.4263i	0.539852	−	0.539852i	0.923486	+	0.383633i	$0.125327\pi$
$374$	−19.1209			−0.988719
$375$	−11.0689	−	5.95476i	−0.571595	−	0.307502i
$376$	−1.82646	−	1.82646i	−0.0941927	−	0.0941927i
$377$	−9.64481	+	9.64481i	−0.496733	+	0.496733i
$378$			22.1205i			1.13775i
$379$		−	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
$383$			24.2531i			1.23928i	0.784888	+	0.619638i	$0.212721\pi$
$383$			24.2531i			1.23928i	−0.784888	+	0.619638i	$0.787279\pi$
$384$	−0.794932	−	0.794932i	−0.0405662	−	0.0405662i
$385$	−20.9762	+	25.5129i	−1.06905	+	1.30026i
$386$	−24.7844			−1.26149
$387$	−3.09982			−0.157573
$388$	5.91995			0.300540
$389$	−19.7499	+	19.7499i	−1.00136	+	1.00136i	−0.00136297	+	0.999999i	$0.500434\pi$
$389$	−19.7499	+	19.7499i	−1.00136	+	1.00136i	−0.999999	+	0.00136297i	$0.999566\pi$
$390$	8.57362	+	7.04905i	0.434142	+	0.356943i
$391$			31.7719i			1.60677i
$392$	−10.2601			−0.518215
$393$			24.2741i			1.22446i
$394$	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	0.748856	−	0.662733i	$-0.230603\pi$
$397$	1.71599	+	1.71599i	0.0861232	+	0.0861232i	−0.662733	+	0.748856i	$0.730603\pi$
$398$	−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	−0.435934	−	0.899978i	$-0.643582\pi$
$401$	9.29247	−	9.29247i	0.464044	−	0.464044i	0.899978	+	0.435934i	$0.143582\pi$
$402$		−	12.5417i		−	0.625525i
$403$	−23.9401	−	23.9401i	−1.19254	−	1.19254i
$404$			9.23382i			0.459399i
$405$	0.168798	+	1.72973i	0.00838764	+	0.0859508i
$406$		−	12.8340i		−	0.636941i
$407$	−13.8269	−	16.6291i	−0.685374	−	0.824272i
$408$	−4.27515	−	4.27515i	−0.211652	−	0.211652i
$409$	−18.3866	−	18.3866i	−0.909160	−	0.909160i	0.0870446	−	0.996204i	$-0.472258\pi$
$409$	−18.3866	−	18.3866i	−0.909160	−	0.909160i	−0.996204	+	0.0870446i	$0.972258\pi$
$410$	1.37795	+	14.1203i	0.0680520	+	0.697350i
$411$			22.9290i			1.13100i
$412$	−8.03931			−0.396068
$413$			26.1213i			1.28535i
$414$		−	10.2568i		−	0.504095i
$415$	9.06315	−	11.0233i	0.444892	−	0.541113i
$416$	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	$0.937058\pi$
$420$	−10.3943	+	1.01434i	−0.507188	+	0.0494948i
$421$	11.0268	−	11.0268i	0.537416	−	0.537416i	−0.385353	−	0.922769i	$-0.625920\pi$
$421$	11.0268	−	11.0268i	0.537416	−	0.537416i	0.922769	+	0.385353i	$0.125920\pi$
$422$		−	22.7919i		−	1.10949i
$423$	3.17104	+	3.17104i	0.154181	+	0.154181i
$424$	−9.57437	+	9.57437i	−0.464972	+	0.464972i
$425$	−26.3827	+	5.19871i	−1.27975	+	0.252174i
$426$	−8.94925	−	8.94925i	−0.433593	−	0.433593i
$427$		−	8.46253i		−	0.409530i
$428$	−4.60753	+	4.60753i	−0.222713	+	0.222713i
$429$	12.4792	−	12.4792i	0.602500	−	0.602500i
$430$	−0.387760	−	3.97349i	−0.0186994	−	0.191619i
$431$	9.69563	−	9.69563i	0.467022	−	0.467022i	−0.433926	−	0.900948i	$-0.642872\pi$
$431$	9.69563	−	9.69563i	0.467022	−	0.467022i	0.900948	+	0.433926i	$0.142872\pi$
$432$	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
$438$	6.39655			0.305639
$439$	−21.3840	−	21.3840i	−1.02060	−	1.02060i	−0.999783	−	0.0208186i	$-0.993373\pi$
$439$	−21.3840	−	21.3840i	−1.02060	−	1.02060i	−0.0208186	−	0.999783i	$-0.506627\pi$
$440$	0.772154	+	7.91250i	0.0368110	+	0.377214i
$441$	17.8133			0.848252
$442$	23.7460			1.12948
$443$	0.537851	−	0.537851i	0.0255541	−	0.0255541i	−0.694214	−	0.719768i	$-0.744248\pi$
$443$	0.537851	−	0.537851i	0.0255541	−	0.0255541i	0.719768	+	0.694214i	$0.244248\pi$
$444$	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	$-0.546209\pi$
$449$	17.9014	−	17.9014i	0.844820	−	0.844820i	0.989481	+	0.144661i	$0.0462091\pi$
$450$	8.51705	−	1.67828i	0.401498	−	0.0791150i
$451$	22.5581			1.06222
$452$	−8.61849			−0.405380
$453$	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
$457$	10.3305			0.483240			0.241620	−	0.970371i	$-0.422321\pi$
$457$	10.3305			0.483240			0.241620	+	0.970371i	$0.422321\pi$
$458$	−10.2694			−0.479858
$459$	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	0.0865312	−	0.996249i	$-0.472422\pi$
$461$	−19.5325	−	19.5325i	−0.909718	−	0.909718i	−0.996249	+	0.0865312i	$0.972422\pi$
$462$			16.6056i			0.772562i
$463$			13.2709i			0.616752i	0.951265	+	0.308376i	$0.0997855\pi$
$463$			13.2709i			0.616752i	−0.951265	+	0.308376i	$0.900214\pi$
$464$	−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
$467$	−40.7473			−1.88556			−0.942780	−	0.333414i	$-0.891799\pi$
$467$	−40.7473			−1.88556			−0.942780	+	0.333414i	$0.891799\pi$
$468$	−7.66584			−0.354353
$469$	−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
$473$	−6.34794			−0.291879
$474$	−3.22836			−0.148283
$475$	7.82248	−	11.6619i	0.358920	−	0.535083i
$476$	−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	$-0.842988\pi$
$479$	−8.91382	+	8.91382i	−0.407283	+	0.407283i	0.473507	+	0.880790i	$0.342988\pi$
$480$	−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
$483$	27.5924			1.25550
$484$	1.64079			0.0745813
$485$	−1.28569	−	13.1748i	−0.0583800	−	0.598238i
$486$	−10.6769	−	10.6769i	−0.484316	−	0.484316i
$487$	27.7847			1.25904			0.629522	−	0.776983i	$-0.283251\pi$
$487$	27.7847			1.25904			0.629522	+	0.776983i	$0.283251\pi$
$488$	−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
$495$	−1.34059	−	13.7374i	−0.0602549	−	0.617451i
$496$	5.42197	−	5.42197i	0.243454	−	0.243454i
$497$	−33.0722	+	33.0722i	−1.48349	+	1.48349i
$498$		−	7.17475i		−	0.321508i
$499$	0.378337	+	0.378337i	0.0169367	+	0.0169367i	0.715524	−	0.698588i	$-0.246188\pi$
$499$	0.378337	+	0.378337i	0.0169367	+	0.0169367i	−0.698588	+	0.715524i	$0.746188\pi$
$500$	3.21670	+	10.7076i	0.143855	+	0.478859i
$501$	14.1197	−	14.1197i	0.630823	−	0.630823i
$502$	3.90237	+	3.90237i	0.174171	+	0.174171i
$503$			22.0885i			0.984876i	0.870348	+	0.492438i	$0.163894\pi$
$503$			22.0885i			0.984876i	−0.870348	+	0.492438i	$0.836106\pi$
$504$	5.10033	−	5.10033i	0.227187	−	0.227187i
$505$	20.5498	−	2.00539i	0.914455	−	0.0892385i
$506$		−	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	$-0.685376\pi$
$509$	−24.8176			−1.10002			−0.550011	+	0.835157i	$0.685376\pi$
$510$	−8.58586	+	10.4428i	−0.380188	+	0.462415i
$511$		−	23.6387i		−	1.04571i
$512$			1.00000i			0.0441942i
$513$	−14.9536			−0.660216
$514$		−	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
$518$	−25.1647	−	2.31533i	−1.10568	−	0.101730i
$519$		−	7.84764i		−	0.344473i
$520$	−0.958927	−	9.82642i	−0.0420517	−	0.430917i
$521$			2.41522i			0.105813i	0.998599	+	0.0529064i	$0.0168485\pi$
$521$			2.41522i			0.105813i	−0.998599	+	0.0529064i	$0.983151\pi$
$522$	3.79242	+	3.79242i	0.165990	+	0.165990i
$523$			24.1447i			1.05577i	0.849315	+	0.527887i	$0.177015\pi$
$523$			24.1447i			1.05577i	−0.849315	+	0.527887i	$0.822985\pi$
$524$	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
$532$		−	11.6680i		−	0.505870i
$533$	−28.0146			−1.21345
$534$		−	3.40131i		−	0.147189i
$535$	11.2547	+	9.25339i	0.486583	+	0.400059i
$536$	−7.88856	+	7.88856i	−0.340734	+	0.340734i
$537$	−5.86451			−0.253072
$538$	−5.86174			−0.252717
$539$	36.4788			1.57125
$540$	7.56118	−	9.19650i	0.325381	−	0.395754i
$541$	12.3532	+	12.3532i	0.531107	+	0.531107i	0.920902	−	0.389795i	$-0.127454\pi$
$541$	12.3532	+	12.3532i	0.531107	+	0.531107i	−0.389795	+	0.920902i	$0.627454\pi$
$542$		−	4.91311i		−	0.211036i
$543$	−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
$547$			34.8143i			1.48855i	0.667871	+	0.744277i	$0.267206\pi$
$547$			34.8143i			1.48855i	−0.667871	+	0.744277i	$0.732794\pi$
$548$	14.4220	−	14.4220i	0.616075	−	0.616075i
$549$	2.50066	+	2.50066i	0.106725	+	0.106725i
$550$	17.4416	−	3.43685i	0.743710	−	0.146548i
$551$	8.67587			0.369605
$552$	4.69625	−	4.69625i	0.199886	−	0.199886i
$553$			11.9305i			0.507336i
$554$	8.21627			0.349076
$555$	−15.2906	+	0.0845569i	−0.649049	+	0.00358924i
$556$	1.56244			0.0662624
$557$		−	31.3271i		−	1.32737i	−0.748012	−	0.663685i	$-0.768992\pi$
$557$		−	31.3271i		−	1.32737i	0.748012	−	0.663685i	$-0.231008\pi$
$558$	−9.41344	+	9.41344i	−0.398503	+	0.398503i
$559$	7.88341			0.333433
$560$	7.17584	+	5.89983i	0.303235	+	0.249313i
$561$	15.1998	+	15.1998i	0.641737	+	0.641737i
$562$	7.17894	−	7.17894i	0.302825	−	0.302825i
$563$			22.9644i			0.967836i	0.875113	+	0.483918i	$0.160787\pi$
$563$			22.9644i			0.967836i	−0.875113	+	0.483918i	$0.839213\pi$
$564$			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
$568$			11.2579i			0.472370i
$569$	−30.2581	−	30.2581i	−1.26849	−	1.26849i	−0.946870	−	0.321616i	$-0.895774\pi$
$569$	−30.2581	−	30.2581i	−1.26849	−	1.26849i	−0.321616	−	0.946870i	$-0.604226\pi$
$570$	−0.685701	−	7.02659i	−0.0287209	−	0.294312i
$571$	25.3502			1.06087			0.530436	−	0.847725i	$-0.322028\pi$
$571$	25.3502			1.06087			0.530436	+	0.847725i	$0.322028\pi$
$572$	−15.6984			−0.656383
$573$	16.0215			0.669307
$574$	18.6390	−	18.6390i	0.777977	−	0.777977i
$575$	−5.71078	−	28.9814i	−0.238156	−	1.20861i
$576$		−	1.73617i		−	0.0723402i
$577$	−29.6723			−1.23527			−0.617637	−	0.786464i	$-0.711910\pi$
$577$	−29.6723			−1.23527			−0.617637	+	0.786464i	$0.711910\pi$
$578$			11.9230i			0.495931i
$579$	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
$587$			16.9046i			0.697726i	0.937174	+	0.348863i	$0.113432\pi$
$587$			16.9046i			0.697726i	−0.937174	+	0.348863i	$0.886568\pi$
$588$	8.15611	+	8.15611i	0.336352	+	0.336352i
$589$			21.5350i			0.887335i
$590$	8.92875	−	10.8598i	0.367591	−	0.447093i
$591$		−	17.9664i		−	0.739038i
$592$	−4.67714	+	3.88900i	−0.192229	+	0.159837i
$593$	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
$597$	10.9809			0.449417
$598$			26.0849i			1.06669i
$599$			9.47521i			0.387147i	0.981086	+	0.193573i	$0.0620077\pi$
$599$			9.47521i			0.387147i	−0.981086	+	0.193573i	$0.937992\pi$
$600$	4.66810	+	3.13124i	0.190574	+	0.127832i
$601$	−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
$605$	−0.356344	−	3.65157i	−0.0144875	−	0.148457i
$606$	7.34026	−	7.34026i	0.298178	−	0.298178i
$607$			24.7793i			1.00576i	0.864356	+	0.502880i	$0.167726\pi$
$607$			24.7793i			1.00576i	−0.864356	+	0.502880i	$0.832274\pi$
$608$	−1.98590	−	1.98590i	−0.0805390	−	0.0805390i
$609$	−10.2022	+	10.2022i	−0.413413	+	0.413413i
$610$	−2.89265	+	3.51827i	−0.117120	+	0.142450i
$611$	−8.06454	−	8.06454i	−0.326256	−	0.326256i
$612$		−	9.33711i		−	0.377430i
$613$	3.88165	−	3.88165i	0.156779	−	0.156779i	−0.624359	−	0.781138i	$-0.714640\pi$
$613$	3.88165	−	3.88165i	0.156779	−	0.156779i	0.781138	+	0.624359i	$0.214640\pi$
$614$	3.81755	−	3.81755i	0.154064	−	0.154064i
$615$	10.1293	−	12.3200i	0.408452	−	0.496791i
$616$	10.4447	−	10.4447i	0.420827	−	0.420827i
$617$	34.7871	+	34.7871i	1.40047	+	1.40047i	0.798563	+	0.601911i	$0.205594\pi$
$617$	34.7871	+	34.7871i	1.40047	+	1.40047i	0.601911	+	0.798563i	$0.294406\pi$
$618$	6.39071	+	6.39071i	0.257072	+	0.257072i
$619$	14.8991			0.598845			0.299422	−	0.954121i	$-0.403206\pi$
$619$	14.8991			0.598845			0.299422	+	0.954121i	$0.403206\pi$
$620$	−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
$623$	−12.5697			−0.503593
$624$	−3.50993	−	3.50993i	−0.140510	−	0.140510i
$625$	23.1311	−	9.48423i	0.925245	−	0.379369i
$626$	29.7794			1.19022
$627$	−11.2255			−0.448303
$628$	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	−0.0745080	+	0.997220i	$0.523739\pi$
$631$	−26.9215	+	26.9215i	−1.07173	+	1.07173i	−0.997220	+	0.0745080i	$0.976261\pi$
$632$	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
$635$	−10.3317	−	8.49450i	−0.410000	−	0.337094i
$636$	15.2219			0.603589
$637$	−45.3024			−1.79495
$638$	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	$0.588895\pi$
$642$	7.32535			0.289109
$643$	32.7954			1.29332			0.646662	−	0.762777i	$-0.276164\pi$
$643$	32.7954			1.29332			0.646662	+	0.762777i	$0.276164\pi$
$644$	−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
$647$		−	0.428355i		−	0.0168404i	−0.999965	−	0.00842020i	$-0.997320\pi$
$647$		−	0.428355i		−	0.0168404i	0.999965	−	0.00842020i	$-0.00268026\pi$
$648$		−	0.777232i		−	0.0305325i
$649$	−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
$652$	−9.92434			−0.388667
$653$	−35.6290			−1.39427			−0.697136	−	0.716939i	$-0.745543\pi$
$653$	−35.6290			−1.39427			−0.697136	+	0.716939i	$0.745543\pi$
$654$	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
$658$	10.7312			0.418346
$659$	23.0667			0.898552			0.449276	−	0.893393i	$-0.351682\pi$
$659$	23.0667			0.898552			0.449276	+	0.893393i	$0.351682\pi$
$660$	5.67609	−	6.90371i	0.220942	−	0.268727i
$661$	2.71363	−	2.71363i	0.105548	−	0.105548i	−0.652361	−	0.757909i	$-0.726221\pi$
$661$	2.71363	−	2.71363i	0.105548	−	0.105548i	0.757909	+	0.652361i	$0.226221\pi$
$662$	−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
$668$	−17.7622			−0.687239
$669$	−11.4999			−0.444610
$670$	19.2692	+	15.8427i	0.744433	+	0.612058i
$671$	5.12095	+	5.12095i	0.197692	+	0.197692i
$672$	4.67054			0.180170
$673$	−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	0.995504	−	0.0947229i	$-0.0301965\pi$
$677$	23.4376	+	23.4376i	0.900781	+	0.900781i	−0.0947229	+	0.995504i	$0.530197\pi$
$678$	6.85111	+	6.85111i	0.263115	+	0.263115i
$679$	−17.3910	+	17.3910i	−0.667406	+	0.667406i
$680$	11.9687	−	1.16799i	0.458980	−	0.0447903i
$681$	2.81269	−	2.81269i	0.107783	−	0.107783i
$682$	−19.2772	+	19.2772i	−0.738163	+	0.738163i
$683$		−	15.8368i		−	0.605977i	−0.952994	−	0.302988i	$-0.902016\pi$
$683$		−	15.8368i		−	0.605977i	0.952994	−	0.302988i	$-0.0979843\pi$
$684$	3.44786	+	3.44786i	0.131832	+	0.131832i
$685$	−35.2281	−	28.9639i	−1.34600	−	1.10665i
$686$	9.57729	−	9.57729i	0.365663	−	0.365663i
$687$	8.16348	+	8.16348i	0.311456	+	0.311456i
$688$			1.78544i			0.0680693i
$689$	−42.2745	+	42.2745i	−1.61053	+	1.61053i
$690$	−11.4714	−	9.43157i	−0.436710	−	0.359054i
$691$			25.5077i			0.970358i	0.874415	+	0.485179i	$0.161246\pi$
$691$			25.5077i			0.970358i	−0.874415	+	0.485179i	$0.838754\pi$
$692$	−4.93605	+	4.93605i	−0.187640	+	0.187640i
$693$	−18.1337	+	18.1337i	−0.688841	+	0.688841i
$694$	−35.2079			−1.33647
$695$	−0.339330	−	3.47721i	−0.0128715	−	0.131898i
$696$			3.47285i			0.131638i
$697$		−	34.1222i		−	1.29247i
$698$	7.00272			0.265057
$699$		−	1.16349i		−	0.0440074i
$700$	11.5716	−	17.2511i	0.437366	−	0.652031i
$701$	6.69201	+	6.69201i	0.252754	+	0.252754i	0.822099	−	0.569345i	$-0.192803\pi$
$701$	6.69201	+	6.69201i	0.252754	+	0.252754i	−0.569345	+	0.822099i	$0.692803\pi$
$702$	16.6236	+	16.6236i	0.627418	+	0.627418i
$703$	1.56518	−	17.0115i	0.0590318	−	0.641602i
$704$		−	3.55539i		−	0.133999i
$705$	6.46246	−	0.630650i	0.243390	−	0.0237516i
$706$			24.1991i			0.910746i
$707$	−27.1262	−	27.1262i	−1.02018	−	1.02018i
$708$		−	7.06835i		−	0.265645i
$709$	9.99501	−	9.99501i	0.375370	−	0.375370i	−0.494058	−	0.869429i	$-0.664487\pi$
$709$	9.99501	−	9.99501i	0.375370	−	0.375370i	0.869429	+	0.494058i	$0.164487\pi$
$710$	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
$717$			9.94742i			0.371493i
$718$	5.19872			0.194014
$719$			19.0225i			0.709421i	0.934976	+	0.354711i	$0.115421\pi$
$719$			19.0225i			0.709421i	−0.934976	+	0.354711i	$0.884579\pi$
$720$	−3.86383	+	0.377058i	−0.143996	+	0.0140521i
$721$	23.6171	−	23.6171i	0.879545	−	0.879545i
$722$	−11.1124			−0.413560
$723$	−10.0409			−0.373427
$724$	5.35458			0.199001
$725$	12.8273	+	8.60423i	0.476394	+	0.319553i
$726$	−1.30432	−	1.30432i	−0.0484077	−	0.0484077i
$727$		−	32.8141i		−	1.21701i	−0.793551	−	0.608504i	$-0.791770\pi$
$727$		−	32.8141i		−	1.21701i	0.793551	−	0.608504i	$-0.208230\pi$
$728$	−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
$732$			2.28994i			0.0846384i
$733$	30.2477	−	30.2477i	1.11722	−	1.11722i	0.125077	−	0.992147i	$-0.460082\pi$
$733$	30.2477	−	30.2477i	1.11722	−	1.11722i	0.992147	−	0.125077i	$-0.0399178\pi$
$734$	22.4335	+	22.4335i	0.828034	+	0.828034i
$735$	16.3801	−	19.9227i	0.604188	−	0.734861i
$736$	−5.90774			−0.217762
$737$	28.0469	−	28.0469i	1.03312	−	1.03312i
$738$			11.0156i			0.405489i
$739$	−27.9037			−1.02646			−0.513228	−	0.858253i	$-0.671550\pi$
$739$	−27.9037			−1.02646			−0.513228	+	0.858253i	$0.671550\pi$
$740$	9.67073	+	9.56436i	0.355503	+	0.351593i
$741$	13.9408			0.512126
$742$		−	56.2532i		−	2.06512i
$743$	10.9502	−	10.9502i	0.401723	−	0.401723i	−0.477117	−	0.878840i	$-0.658318\pi$
$743$	10.9502	−	10.9502i	0.401723	−	0.401723i	0.878840	+	0.477117i	$0.158318\pi$
$744$	−8.62020			−0.316032
$745$	−18.7520	+	1.82995i	−0.687021	+	0.0670440i
$746$	10.4263	+	10.4263i	0.381733	+	0.381733i
$747$	7.83498	−	7.83498i	0.286667	−	0.286667i
$748$		−	19.1209i		−	0.699130i
$749$		−	27.0711i		−	0.989155i
$750$	5.95476	−	11.0689i	0.217437	−	0.404178i
$751$			44.1738i			1.61193i	0.591966	+	0.805963i	$0.298352\pi$
$751$			44.1738i			1.61193i	−0.591966	+	0.805963i	$0.701648\pi$
$752$	1.82646	−	1.82646i	0.0666043	−	0.0666043i
$753$		−	6.20423i		−	0.226095i
$754$	−9.64481	−	9.64481i	−0.351243	−	0.351243i
$755$	−21.4919	+	2.09733i	−0.782172	+	0.0763295i
$756$	−22.1205			−0.804513
$757$	−3.52885			−0.128258			−0.0641291	−	0.997942i	$-0.520427\pi$
$757$	−3.52885			−0.128258			−0.0641291	+	0.997942i	$0.520427\pi$
$758$	15.9233			0.578361
$759$	−16.6970	+	16.6970i	−0.606063	+	0.606063i
$760$	−3.98832	+	4.85091i	−0.144672	+	0.175961i
$761$			15.9891i			0.579605i	0.957086	+	0.289803i	$0.0935896\pi$
$761$			15.9891i			0.579605i	−0.957086	+	0.289803i	$0.906410\pi$
$762$	−6.72459			−0.243606
$763$		−	85.8533i		−	3.10810i
$764$	−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	$-0.163099\pi$
$769$	10.5741	+	10.5741i	0.381313	+	0.381313i	−0.490262	+	0.871575i	$0.663099\pi$
$770$	−25.5129	−	20.9762i	−0.919421	−	0.755929i
$771$	−1.76397	+	1.76397i	−0.0635280	+	0.0635280i
$772$		−	24.7844i		−	0.892011i
$773$	−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
$775$	−21.3572	+	31.8396i	−0.767173	+	1.14371i
$776$			5.91995i			0.212514i
$777$	18.1637	+	21.8448i	0.651620	+	0.783678i
$778$	−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
$782$	−31.7719			−1.13616
$783$		−	16.4480i		−	0.587803i
$784$		−	10.2601i		−	0.366433i
$785$	−33.6575	−	27.6725i	−1.20129	−	0.987674i
$786$	−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
$790$	4.07806	−	4.96006i	0.145091	−	0.176471i
$791$	25.3185	−	25.3185i	0.900223	−	0.900223i
$792$			6.17274i			0.219339i
$793$	−6.35962	−	6.35962i	−0.225837	−	0.225837i
$794$	−1.71599	+	1.71599i	−0.0608983	+	0.0608983i
$795$	−3.30588	−	33.8764i	−0.117247	−	1.20147i
$796$	−6.90680	−	6.90680i	−0.244805	−	0.244805i
$797$			40.0646i			1.41916i	0.704625	+	0.709580i	$0.251115\pi$
$797$			40.0646i			1.41916i	−0.704625	+	0.709580i	$0.748885\pi$
$798$	−9.27524	+	9.27524i	−0.328340	+	0.328340i
$799$	9.82274	−	9.82274i	0.347504	−	0.347504i
$800$	−0.966660	−	4.90567i	−0.0341766	−	0.173442i
$801$	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
$808$	−9.23382			−0.324844
$809$	33.6427	+	33.6427i	1.18282	+	1.18282i	0.979012	+	0.203803i	$0.0653303\pi$
$809$	33.6427	+	33.6427i	1.18282	+	1.18282i	0.203803	+	0.979012i	$0.434670\pi$
$810$	−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	$0.567286\pi$
$812$	12.8340			0.450386
$813$	−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
$820$	−14.1203	+	1.37795i	−0.493101	+	0.0481200i
$821$	−23.5565			−0.822126			−0.411063	−	0.911607i	$-0.634842\pi$
$821$	−23.5565			−0.822126			−0.411063	+	0.911607i	$0.634842\pi$
$822$	−22.9290			−0.799739
$823$	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
$827$	−2.77988			−0.0966659			−0.0483329	−	0.998831i	$-0.515391\pi$
$827$	−2.77988			−0.0966659			−0.0483329	+	0.998831i	$0.515391\pi$
$828$	10.2568			0.356449
$829$	20.9695	+	20.9695i	0.728301	+	0.728301i	0.970281	−	0.241980i	$-0.0777968\pi$
$829$	20.9695	+	20.9695i	0.728301	+	0.728301i	−0.241980	+	0.970281i	$0.577797\pi$
$830$	11.0233	+	9.06315i	0.382625	+	0.314586i
$831$	−6.53137	−	6.53137i	−0.226571	−	0.226571i
$832$			4.41538i			0.153076i
$833$		−	55.1791i		−	1.91184i
$834$	−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
$837$	40.8267			1.41118
$838$	−8.04256			−0.277825
$839$	28.7182			0.991464			0.495732	−	0.868476i	$-0.334900\pi$
$839$	28.7182			0.991464			0.495732	+	0.868476i	$0.334900\pi$
$840$	−1.01434	−	10.3943i	−0.0349981	−	0.358636i
$841$		−	19.4571i		−	0.670934i
$842$	11.0268	+	11.0268i	0.380010	+	0.380010i
$843$	−11.4135			−0.393103
$844$	22.7919			0.784531
$845$	−1.41071	−	14.4560i	−0.0485298	−	0.497300i
$846$	−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
$853$	−11.9189			−0.408097			−0.204048	−	0.978961i	$-0.565410\pi$
$853$	−11.9189			−0.408097			−0.204048	+	0.978961i	$0.565410\pi$
$854$	8.46253			0.289582
$855$	6.92439	−	8.42199i	0.236809	−	0.288026i
$856$	−4.60753	−	4.60753i	−0.157482	−	0.157482i
$857$	17.5942			0.601008			0.300504	−	0.953781i	$-0.402845\pi$
$857$	17.5942			0.601008			0.300504	+	0.953781i	$0.402845\pi$
$858$	12.4792	+	12.4792i	0.426032	+	0.426032i
$859$	−15.4861	+	15.4861i	−0.528379	+	0.528379i	−0.920089	−	0.391710i	$-0.871884\pi$
$859$	−15.4861	+	15.4861i	−0.528379	+	0.528379i	0.391710	+	0.920089i	$0.371884\pi$
$860$	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
$865$	12.0572	+	9.91315i	0.409956	+	0.337057i
$866$	7.39679	−	7.39679i	0.251353	−	0.251353i
$867$	9.47796	−	9.47796i	0.321888	−	0.321888i
$868$			31.8562i			1.08127i
$869$	−7.21953	−	7.21953i	−0.244906	−	0.244906i
$870$	7.72880	−	0.754228i	0.262031	−	0.0255707i
$871$	−34.8310	+	34.8310i	−1.18020	+	1.18020i
$872$	−14.6123	−	14.6123i	−0.494836	−	0.494836i
$873$		−	10.2780i		−	0.347858i
$874$	11.7322	−	11.7322i	0.396848	−	0.396848i
$875$	−40.9054	−	22.0060i	−1.38286	−	0.743939i
$876$			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
$880$	−7.91250	+	0.772154i	−0.266730	+	0.0260293i
$881$			16.5058i			0.556094i	0.960567	+	0.278047i	$0.0896871\pi$
$881$			16.5058i			0.556094i	−0.960567	+	0.278047i	$0.910313\pi$
$882$			17.8133i			0.599805i
$883$	33.7230			1.13487			0.567435	−	0.823418i	$-0.307936\pi$
$883$	33.7230			1.13487			0.567435	+	0.823418i	$0.307936\pi$
$884$			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	$-0.863472\pi$
$887$	−39.4709	−	39.4709i	−1.32530	−	1.32530i	−0.415885	−	0.909417i	$-0.636528\pi$
$888$	6.80950	+	0.626522i	0.228512	+	0.0210247i
$889$			24.8509i			0.833473i
$890$	5.22579	+	4.29654i	0.175169	+	0.144020i
$891$			2.76336i			0.0925761i
$892$	7.23324	+	7.23324i	0.242187	+	0.242187i
$893$			7.25436i			0.242758i
$894$	−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
$902$			22.5581i			0.751103i
$903$	8.33898			0.277504
$904$		−	8.61849i		−	0.286647i
$905$	−1.16290	−	11.9166i	−0.0386561	−	0.396121i
$906$	−7.67678	+	7.67678i	−0.255044	+	0.255044i
$907$	2.85857			0.0949173			0.0474587	−	0.998873i	$-0.484888\pi$
$907$	2.85857			0.0949173			0.0474587	+	0.998873i	$0.484888\pi$
$908$	−3.53828			−0.117422
$909$	16.0314			0.531729
$910$	31.6841	+	26.0500i	1.05032	+	0.863549i
$911$	7.44807	+	7.44807i	0.246765	+	0.246765i	0.819642	−	0.572876i	$-0.194172\pi$
$911$	7.44807	+	7.44807i	0.246765	+	0.246765i	−0.572876	+	0.819642i	$0.694172\pi$
$912$			3.15731i			0.104549i
$913$	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
$917$			89.7056i			2.96234i
$918$	−20.2478	+	20.2478i	−0.668278	+	0.668278i
$919$	−7.70512	−	7.70512i	−0.254168	−	0.254168i	0.568509	−	0.822677i	$-0.307521\pi$
$919$	−7.70512	−	7.70512i	−0.254168	−	0.254168i	−0.822677	+	0.568509i	$0.807521\pi$
$920$	1.28304	+	13.1477i	0.0423004	+	0.433466i
$921$	−6.06939			−0.199993
$922$	19.5325	−	19.5325i	0.643268	−	0.643268i
$923$			49.7079i			1.63615i
$924$	−16.6056			−0.546284
$925$	19.1852	−	23.5993i	0.630805	−	0.775942i
$926$	−13.2709			−0.436110
$927$			13.9576i			0.458427i
$928$	2.18437	−	2.18437i	0.0717053	−	0.0717053i
$929$	−29.3928			−0.964346			−0.482173	−	0.876076i	$-0.660152\pi$
$929$	−29.3928			−0.964346			−0.482173	+	0.876076i	$0.660152\pi$
$930$	1.87212	+	19.1842i	0.0613893	+	0.629076i
$931$	20.3756	+	20.3756i	0.667784	+	0.667784i
$932$	−0.731820	+	0.731820i	−0.0239716	+	0.0239716i
$933$		−	14.1859i		−	0.464425i
$934$		−	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	$0.169969\pi$
$938$		−	46.3484i		−	1.51333i
$939$	−23.6726	−	23.6726i	−0.772527	−	0.772527i
$940$	−4.46146	−	3.66812i	−0.145517	−	0.119641i
$941$	29.3530			0.956880			0.478440	−	0.878120i	$-0.341202\pi$
$941$	29.3530			0.956880			0.478440	+	0.878120i	$0.341202\pi$
$942$	−21.9066			−0.713757
$943$	37.4833			1.22062
$944$	−4.44588	+	4.44588i	−0.144701	+	0.144701i
$945$	4.80409	+	49.2290i	0.156277	+	1.60142i
$946$		−	6.34794i		−	0.206389i
$947$	14.6562			0.476262			0.238131	−	0.971233i	$-0.423465\pi$
$947$	14.6562			0.476262			0.238131	+	0.971233i	$0.423465\pi$
$948$		−	3.22836i		−	0.104852i
$949$	−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	−0.813063	−	0.582176i	$-0.802202\pi$
$953$	−7.12766	+	7.12766i	−0.230887	+	0.230887i	0.582176	+	0.813063i	$0.302202\pi$
$954$	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
$957$		−	12.3473i		−	0.399132i
$958$	−8.91382	−	8.91382i	−0.287992	−	0.287992i
$959$			84.7347i			2.73623i
$960$	−1.94176	−	1.59648i	−0.0626701	−	0.0515261i
$961$		−	27.7956i		−	0.896632i
$962$	−20.6514	+	17.1714i	−0.665827	+	0.553629i
$963$	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
$967$	38.4439			1.23627			0.618136	−	0.786071i	$-0.287888\pi$
$967$	38.4439			1.23627			0.618136	+	0.786071i	$0.287888\pi$
$968$			1.64079i			0.0527370i
$969$			16.9801i			0.545478i
$970$	13.1748	−	1.28569i	0.423018	−	0.0412809i
$971$	−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
$975$	20.6115	+	13.8256i	0.660095	+	0.442775i
$976$	1.44033	−	1.44033i	0.0461040	−	0.0461040i
$977$		−	34.3176i		−	1.09792i	−0.835850	−	0.548959i	$-0.815024\pi$
$977$		−	34.3176i		−	1.09792i	0.835850	−	0.548959i	$-0.184976\pi$
$978$	7.88918	+	7.88918i	0.252268	+	0.252268i
$979$	7.60630	−	7.60630i	0.243099	−	0.243099i
$980$	−22.8339	+	2.22828i	−0.729402	+	0.0711798i
$981$	25.3694	+	25.3694i	0.809984	+	0.809984i
$982$		−	7.19820i		−	0.229704i
$983$	35.5214	−	35.5214i	1.13296	−	1.13296i	0.143272	−	0.989683i	$-0.454238\pi$
$983$	35.5214	−	35.5214i	1.13296	−	1.13296i	0.989683	−	0.143272i	$-0.0457623\pi$
$984$	−5.04366	+	5.04366i	−0.160786	+	0.160786i
$985$	27.6036	+	22.6951i	0.879524	+	0.723127i
$986$	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	0.0245377	−	0.999699i	$-0.492189\pi$
$991$	32.2431	−	32.2431i	1.02424	−	1.02424i	0.999699	−	0.0245377i	$-0.00781138\pi$
$992$	5.42197	+	5.42197i	0.172148	+	0.172148i
$993$	24.8538			0.788713
$994$	−33.0722	−	33.0722i	−1.04899	−	1.04899i
$995$	−13.8710	+	16.8711i	−0.439742	+	0.534849i
$996$	7.17475			0.227341
$997$	2.02170			0.0640278			0.0320139	−	0.999487i	$-0.489808\pi$
$997$	2.02170			0.0640278			0.0320139	+	0.999487i	$0.489808\pi$
$998$	−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.g.e.43.7	✓	20
5.2	odd	4		370.2.h.e.117.4	yes	20
37.31	odd	4		370.2.h.e.253.4	yes	20
185.142	even	4	inner	370.2.g.e.327.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.7	✓	20	1.1	even	1	trivial
370.2.g.e.327.7	yes	20	185.142	even	4	inner
370.2.h.e.117.4	yes	20	5.2	odd	4
370.2.h.e.253.4	yes	20	37.31	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.g (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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