LMFDB - Embedded newform 425.2.k.b.86.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.1
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.26173 + 1.64324i) q^{2} +(0.672306 - 2.06914i) q^{3} +(1.79714 - 5.53104i) q^{4} +(-2.15401 + 0.600183i) q^{5} +(1.87953 + 5.78461i) q^{6} +2.13787 q^{7} +(3.29638 + 10.1452i) q^{8} +(-1.40231 - 1.01884i) q^{9} +(3.88556 - 4.89702i) q^{10} +(-1.30839 + 0.950598i) q^{11} +(-10.2363 - 7.43709i) q^{12} +(4.30178 + 3.12543i) q^{13} +(-4.83530 + 3.51305i) q^{14} +(-0.206292 + 4.86047i) q^{15} +(-14.7166 - 10.6922i) q^{16} +(0.309017 + 0.951057i) q^{17} +4.84585 q^{18} +(-0.0523214 - 0.161029i) q^{19} +(-0.551439 + 12.9926i) q^{20} +(1.43731 - 4.42357i) q^{21} +(1.39715 - 4.29999i) q^{22} +(4.64126 - 3.37208i) q^{23} +23.2081 q^{24} +(4.27956 - 2.58561i) q^{25} -14.8653 q^{26} +(2.22945 - 1.61979i) q^{27} +(3.84207 - 11.8247i) q^{28} +(2.62934 - 8.09228i) q^{29} +(-7.52037 - 11.3321i) q^{30} +(-0.0866369 - 0.266641i) q^{31} +29.5204 q^{32} +(1.08729 + 3.34633i) q^{33} +(-2.26173 - 1.64324i) q^{34} +(-4.60501 + 1.28312i) q^{35} +(-8.15539 + 5.92523i) q^{36} +(-1.79934 - 1.30729i) q^{37} +(0.382947 + 0.278227i) q^{38} +(9.35908 - 6.79977i) q^{39} +(-13.1894 - 19.8745i) q^{40} +(0.458723 + 0.333282i) q^{41} +(4.01821 + 12.3668i) q^{42} +2.13707 q^{43} +(2.90644 + 8.94509i) q^{44} +(3.63209 + 1.35295i) q^{45} +(-4.95615 + 15.2535i) q^{46} +(-1.98852 + 6.12005i) q^{47} +(-32.0179 + 23.2623i) q^{48} -2.42949 q^{49} +(-5.43044 + 12.8803i) q^{50} +2.17563 q^{51} +(25.0178 - 18.1765i) q^{52} +(2.00087 - 6.15806i) q^{53} +(-2.38071 + 7.32707i) q^{54} +(2.24775 - 2.83287i) q^{55} +(7.04725 + 21.6892i) q^{56} -0.368368 q^{57} +(7.35073 + 22.6232i) q^{58} +(-2.57454 - 1.87052i) q^{59} +(26.5127 + 9.87597i) q^{60} +(10.3529 - 7.52183i) q^{61} +(0.634105 + 0.460704i) q^{62} +(-2.99797 - 2.17815i) q^{63} +(-37.3339 + 27.1247i) q^{64} +(-11.1419 - 4.15036i) q^{65} +(-7.95799 - 5.78182i) q^{66} +(4.20141 + 12.9306i) q^{67} +5.81568 q^{68} +(-3.85696 - 11.8705i) q^{69} +(8.30683 - 10.4692i) q^{70} +(-1.64618 + 5.06643i) q^{71} +(5.71378 - 17.5852i) q^{72} +(-2.96839 + 2.15666i) q^{73} +6.21781 q^{74} +(-2.47282 - 10.5933i) q^{75} -0.984685 q^{76} +(-2.79716 + 2.03226i) q^{77} +(-9.99404 + 30.7585i) q^{78} +(-2.19437 + 6.75358i) q^{79} +(38.1171 + 14.1986i) q^{80} +(-3.45961 - 10.6476i) q^{81} -1.58517 q^{82} +(-3.05870 - 9.41370i) q^{83} +(-21.8839 - 15.8996i) q^{84} +(-1.23643 - 1.86312i) q^{85} +(-4.83347 + 3.51172i) q^{86} +(-14.9764 - 10.8810i) q^{87} +(-13.9570 - 10.1403i) q^{88} +(11.7548 - 8.54039i) q^{89} +(-10.4380 + 2.90840i) q^{90} +(9.19668 + 6.68178i) q^{91} +(-10.3101 - 31.7311i) q^{92} -0.609965 q^{93} +(-5.55922 - 17.1095i) q^{94} +(0.209348 + 0.315456i) q^{95} +(19.8467 - 61.0819i) q^{96} +(2.11429 - 6.50710i) q^{97} +(5.49486 - 3.99225i) q^{98} +2.80327 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−2.26173	+	1.64324i	−1.59929	+	1.16195i	−0.710422	+	0.703776i	$0.751496\pi$
$2$	−2.26173	+	1.64324i	−1.59929	+	1.16195i	−0.888863	+	0.458173i	$0.848504\pi$
$3$	0.672306	−	2.06914i	0.388156	−	1.19462i	−0.546009	−	0.837779i	$-0.683854\pi$
$3$	0.672306	−	2.06914i	0.388156	−	1.19462i	0.934165	−	0.356842i	$-0.116146\pi$
$4$	1.79714	−	5.53104i	0.898571	−	2.76552i
$5$	−2.15401	+	0.600183i	−0.963305	+	0.268410i
$5$	−2.15401	+	0.600183i	−0.963305	+	0.268410i
$6$	1.87953	+	5.78461i	0.767316	+	2.36156i
$7$	2.13787			0.808041			0.404020	−	0.914750i	$-0.367612\pi$
$7$	2.13787			0.808041			0.404020	+	0.914750i	$0.367612\pi$
$8$	3.29638	+	10.1452i	1.16545	+	3.58687i
$9$	−1.40231	−	1.01884i	−0.467437	−	0.339613i
$10$	3.88556	−	4.89702i	1.22872	−	1.54857i
$11$	−1.30839	+	0.950598i	−0.394493	+	0.286616i	−0.767294	−	0.641295i	$-0.778397\pi$
$11$	−1.30839	+	0.950598i	−0.394493	+	0.286616i	0.372801	+	0.927911i	$0.378397\pi$
$12$	−10.2363	−	7.43709i	−2.95496	−	2.14690i
$13$	4.30178	+	3.12543i	1.19310	+	0.866838i	0.993588	−	0.113057i	$-0.0360644\pi$
$13$	4.30178	+	3.12543i	1.19310	+	0.866838i	0.199512	+	0.979895i	$0.436064\pi$
$14$	−4.83530	+	3.51305i	−1.29229	+	0.938902i
$15$	−0.206292	+	4.86047i	−0.0532643	+	1.25497i
$16$	−14.7166	−	10.6922i	−3.67915	−	2.67306i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	4.84585			1.14218
$19$	−0.0523214	−	0.161029i	−0.0120034	−	0.0369425i	0.944875	−	0.327430i	$-0.106183\pi$
$19$	−0.0523214	−	0.161029i	−0.0120034	−	0.0369425i	−0.956879	+	0.290487i	$0.906183\pi$
$20$	−0.551439	+	12.9926i	−0.123306	+	2.90522i
$21$	1.43731	−	4.42357i	0.313646	−	0.965302i
$22$	1.39715	−	4.29999i	0.297874	−	0.916762i
$23$	4.64126	−	3.37208i	0.967770	−	0.703126i	0.0128281	−	0.999918i	$-0.495917\pi$
$23$	4.64126	−	3.37208i	0.967770	−	0.703126i	0.954942	+	0.296791i	$0.0959166\pi$
$24$	23.2081			4.73733
$25$	4.27956	−	2.58561i	0.855912	−	0.517121i
$26$	−14.8653			−2.91533
$27$	2.22945	−	1.61979i	0.429058	−	0.311729i
$28$	3.84207	−	11.8247i	0.726082	−	2.23465i
$29$	2.62934	−	8.09228i	0.488257	−	1.50270i	−0.338952	−	0.940804i	$-0.610072\pi$
$29$	2.62934	−	8.09228i	0.488257	−	1.50270i	0.827208	−	0.561896i	$-0.189928\pi$
$30$	−7.52037	−	11.3321i	−1.37302	−	2.06894i
$31$	−0.0866369	−	0.266641i	−0.0155604	−	0.0478901i	0.942975	−	0.332864i	$-0.108015\pi$
$31$	−0.0866369	−	0.266641i	−0.0155604	−	0.0478901i	−0.958535	+	0.284974i	$0.908015\pi$
$32$	29.5204			5.21852
$33$	1.08729	+	3.34633i	0.189273	+	0.582521i
$34$	−2.26173	−	1.64324i	−0.387884	−	0.281814i
$35$	−4.60501	+	1.28312i	−0.778390	+	0.216886i
$36$	−8.15539	+	5.92523i	−1.35923	+	0.987539i
$37$	−1.79934	−	1.30729i	−0.295809	−	0.214918i	0.429975	−	0.902841i	$-0.358523\pi$
$37$	−1.79934	−	1.30729i	−0.295809	−	0.214918i	−0.725783	+	0.687923i	$0.758523\pi$
$38$	0.382947	+	0.278227i	0.0621221	+	0.0451344i
$39$	9.35908	−	6.79977i	1.49865	−	1.08883i
$40$	−13.1894	−	19.8745i	−2.08543	−	3.14244i
$41$	0.458723	+	0.333282i	0.0716405	+	0.0520498i	0.623029	−	0.782199i	$-0.285902\pi$
$41$	0.458723	+	0.333282i	0.0716405	+	0.0520498i	−0.551389	+	0.834249i	$0.685902\pi$
$42$	4.01821	+	12.3668i	0.620023	+	1.90823i
$43$	2.13707			0.325900			0.162950	−	0.986634i	$-0.447899\pi$
$43$	2.13707			0.325900			0.162950	+	0.986634i	$0.447899\pi$
$44$	2.90644	+	8.94509i	0.438162	+	1.34852i
$45$	3.63209	+	1.35295i	0.541440	+	0.201686i
$46$	−4.95615	+	15.2535i	−0.730744	+	2.24900i
$47$	−1.98852	+	6.12005i	−0.290056	+	0.892701i	0.694781	+	0.719221i	$0.255501\pi$
$47$	−1.98852	+	6.12005i	−0.290056	+	0.892701i	−0.984837	+	0.173480i	$0.944499\pi$
$48$	−32.0179	+	23.2623i	−4.62138	+	3.35763i
$49$	−2.42949			−0.347070
$50$	−5.43044	+	12.8803i	−0.767980	+	1.82155i
$51$	2.17563			0.304649
$52$	25.0178	−	18.1765i	3.46934	−	2.52063i
$53$	2.00087	−	6.15806i	0.274841	−	0.845874i	−0.714420	−	0.699717i	$-0.753309\pi$
$53$	2.00087	−	6.15806i	0.274841	−	0.845874i	0.989261	−	0.146157i	$-0.0466906\pi$
$54$	−2.38071	+	7.32707i	−0.323973	+	0.997087i
$55$	2.24775	−	2.83287i	0.303087	−	0.381984i
$56$	7.04725	+	21.6892i	0.941728	+	2.89834i
$57$	−0.368368			−0.0487915
$58$	7.35073	+	22.6232i	0.965198	+	2.97057i
$59$	−2.57454	−	1.87052i	−0.335177	−	0.243520i	0.407447	−	0.913229i	$-0.366419\pi$
$59$	−2.57454	−	1.87052i	−0.335177	−	0.243520i	−0.742624	+	0.669708i	$0.766419\pi$
$60$	26.5127	+	9.87597i	3.42278	+	1.27498i
$61$	10.3529	−	7.52183i	1.32555	−	0.963071i	0.325709	−	0.945470i	$-0.394397\pi$
$61$	10.3529	−	7.52183i	1.32555	−	0.963071i	0.999845	−	0.0176012i	$-0.00560291\pi$
$62$	0.634105	+	0.460704i	0.0805314	+	0.0585095i
$63$	−2.99797	−	2.17815i	−0.377708	−	0.274421i
$64$	−37.3339	+	27.1247i	−4.66674	+	3.39059i
$65$	−11.1419	−	4.15036i	−1.38199	−	0.514789i
$66$	−7.95799	−	5.78182i	−0.979561	−	0.711693i
$67$	4.20141	+	12.9306i	0.513284	+	1.57972i	0.786383	+	0.617739i	$0.211951\pi$
$67$	4.20141	+	12.9306i	0.513284	+	1.57972i	−0.273100	+	0.961986i	$0.588049\pi$
$68$	5.81568			0.705254
$69$	−3.85696	−	11.8705i	−0.464324	−	1.42904i
$70$	8.30683	−	10.4692i	0.992856	−	1.25131i
$71$	−1.64618	+	5.06643i	−0.195366	+	0.601275i	0.804606	+	0.593809i	$0.202376\pi$
$71$	−1.64618	+	5.06643i	−0.195366	+	0.601275i	−0.999972	+	0.00746575i	$0.997624\pi$
$72$	5.71378	−	17.5852i	0.673376	−	2.07244i
$73$	−2.96839	+	2.15666i	−0.347423	+	0.252418i	−0.747787	−	0.663938i	$-0.768884\pi$
$73$	−2.96839	+	2.15666i	−0.347423	+	0.252418i	0.400364	+	0.916356i	$0.368884\pi$
$74$	6.21781			0.722806
$75$	−2.47282	−	10.5933i	−0.285536	−	1.22321i
$76$	−0.984685			−0.112951
$77$	−2.79716	+	2.03226i	−0.318766	+	0.231597i
$78$	−9.99404	+	30.7585i	−1.13160	+	3.48271i
$79$	−2.19437	+	6.75358i	−0.246886	+	0.759837i	0.748435	+	0.663208i	$0.230806\pi$
$79$	−2.19437	+	6.75358i	−0.246886	+	0.759837i	−0.995321	+	0.0966281i	$0.969194\pi$
$80$	38.1171	+	14.1986i	4.26162	+	1.58745i
$81$	−3.45961	−	10.6476i	−0.384402	−	1.18307i
$82$	−1.58517			−0.175053
$83$	−3.05870	−	9.41370i	−0.335736	−	1.03329i	−0.966359	−	0.257199i	$-0.917201\pi$
$83$	−3.05870	−	9.41370i	−0.335736	−	1.03329i	0.630623	−	0.776089i	$-0.282799\pi$
$84$	−21.8839	−	15.8996i	−2.38773	−	1.73479i
$85$	−1.23643	−	1.86312i	−0.134110	−	0.202084i
$86$	−4.83347	+	3.51172i	−0.521207	+	0.378679i
$87$	−14.9764	−	10.8810i	−1.60564	−	1.16656i
$88$	−13.9570	−	10.1403i	−1.48782	−	1.08096i
$89$	11.7548	−	8.54039i	1.24601	−	0.905280i	0.248027	−	0.968753i	$-0.420218\pi$
$89$	11.7548	−	8.54039i	1.24601	−	0.905280i	0.997984	+	0.0634733i	$0.0202178\pi$
$90$	−10.4380	+	2.90840i	−1.10027	+	0.306572i
$91$	9.19668	+	6.68178i	0.964074	+	0.700441i
$92$	−10.3101	−	31.7311i	−1.07490	−	3.30820i
$93$	−0.609965			−0.0632504
$94$	−5.55922	−	17.1095i	−0.573390	−	1.76471i
$95$	0.209348	+	0.315456i	0.0214786	+	0.0323651i
$96$	19.8467	−	61.0819i	2.02560	−	6.23415i
$97$	2.11429	−	6.50710i	0.214673	−	0.660696i	−0.784503	−	0.620124i	$-0.787082\pi$
$97$	2.11429	−	6.50710i	0.214673	−	0.660696i	0.999177	−	0.0405716i	$-0.0129179\pi$
$98$	5.49486	−	3.99225i	0.555064	−	0.403278i
$99$	2.80327			0.281739
$100$	−6.61010	−	28.3171i	−0.661010	−	2.83171i
$101$	11.8257			1.17670			0.588352	−	0.808605i	$-0.299777\pi$
$101$	11.8257			1.17670			0.588352	+	0.808605i	$0.299777\pi$
$102$	−4.92068	+	3.57508i	−0.487220	+	0.353986i
$103$	−2.14471	+	6.60074i	−0.211324	+	0.650390i	0.788070	+	0.615586i	$0.211081\pi$
$103$	−2.14471	+	6.60074i	−0.211324	+	0.650390i	−0.999394	+	0.0348038i	$0.988919\pi$
$104$	−17.5278	+	53.9451i	−1.71875	+	5.28975i
$105$	−0.441026	+	10.3911i	−0.0430397	+	1.01407i
$106$	5.59375	+	17.2158i	0.543313	+	1.67215i
$107$	8.14884			0.787778			0.393889	−	0.919158i	$-0.371129\pi$
$107$	8.14884			0.787778			0.393889	+	0.919158i	$0.371129\pi$
$108$	−4.95248	−	15.2422i	−0.476553	−	1.46668i
$109$	−8.14444	−	5.91728i	−0.780096	−	0.566773i	0.124912	−	0.992168i	$-0.460135\pi$
$109$	−8.14444	−	5.91728i	−0.780096	−	0.566773i	−0.905008	+	0.425395i	$0.860135\pi$
$110$	−0.428705	+	10.1008i	−0.0408755	+	0.963073i
$111$	−3.91468	+	2.84418i	−0.371565	+	0.269958i
$112$	−31.4623	−	22.8587i	−2.97291	−	2.15994i
$113$	11.1807	+	8.12323i	1.05179	+	0.764170i	0.972552	−	0.232686i	$-0.0747515\pi$
$113$	11.1807	+	8.12323i	1.05179	+	0.764170i	0.0792372	+	0.996856i	$0.474752\pi$
$114$	0.833149	−	0.605318i	0.0780315	−	0.0566932i
$115$	−7.97349	+	10.0491i	−0.743532	+	0.937084i
$116$	−40.0334	−	29.0860i	−3.71701	−	2.70057i
$117$	−2.84813	−	8.76565i	−0.263310	−	0.810384i
$118$	8.89664			0.819002
$119$	0.660640	+	2.03324i	0.0605607	+	0.186387i
$120$	−49.9905	+	13.9291i	−4.56349	+	1.27155i
$121$	−2.59095	+	7.97412i	−0.235541	+	0.724920i
$122$	−11.0553	+	34.0247i	−1.00090	+	3.08045i
$123$	0.998009	−	0.725096i	0.0899875	−	0.0653797i
$124$	−1.63050			−0.146423
$125$	−7.66640	+	8.13795i	−0.685704	+	0.727881i
$126$	10.3598			0.922926
$127$	−5.02574	+	3.65142i	−0.445962	+	0.324011i	−0.788000	−	0.615676i	$-0.788883\pi$
$127$	−5.02574	+	3.65142i	−0.445962	+	0.324011i	0.342037	+	0.939686i	$0.388883\pi$
$128$	21.6222	−	66.5464i	1.91115	−	5.88192i
$129$	1.43676	−	4.42190i	0.126500	−	0.389327i
$130$	32.0201	−	8.92191i	2.80835	−	0.782503i
$131$	1.87935	+	5.78403i	0.164199	+	0.505353i	0.998976	−	0.0452347i	$-0.0144036\pi$
$131$	1.87935	+	5.78403i	0.164199	+	0.505353i	−0.834777	+	0.550588i	$0.814404\pi$
$132$	20.4627			1.78105
$133$	−0.111857	−	0.344259i	−0.00969920	−	0.0298511i
$134$	−30.7506	−	22.3416i	−2.65645	−	1.93002i
$135$	−3.83010	+	4.82713i	−0.329643	+	0.415454i
$136$	−8.63003	+	6.27009i	−0.740019	+	0.537655i
$137$	6.31427	+	4.58758i	0.539464	+	0.391944i	0.823886	−	0.566756i	$-0.191802\pi$
$137$	6.31427	+	4.58758i	0.539464	+	0.391944i	−0.284422	+	0.958699i	$0.591802\pi$
$138$	28.2295	+	20.5100i	2.40306	+	1.74592i
$139$	3.80093	−	2.76154i	0.322391	−	0.234231i	−0.414804	−	0.909911i	$-0.636150\pi$
$139$	3.80093	−	2.76154i	0.322391	−	0.234231i	0.737195	+	0.675680i	$0.236150\pi$
$140$	−1.17891	+	27.7764i	−0.0996359	+	2.34754i
$141$	11.3264	+	8.22909i	0.953852	+	0.693014i
$142$	−4.60216	−	14.1640i	−0.386204	−	1.18861i
$143$	−8.59942			−0.719120
$144$	9.74360	+	29.9877i	0.811966	+	2.49898i
$145$	−0.806793	+	19.0090i	−0.0670005	+	1.57861i
$146$	3.16977	−	9.75556i	0.262332	−	0.807376i
$147$	−1.63336	+	5.02697i	−0.134717	+	0.414617i
$148$	−10.4644	+	7.60280i	−0.860164	+	0.624946i
$149$	−2.95746			−0.242284			−0.121142	−	0.992635i	$-0.538656\pi$
$149$	−2.95746			−0.242284			−0.121142	+	0.992635i	$0.538656\pi$
$150$	23.0003	+	19.8959i	1.87797	+	1.62449i
$151$	10.1738			0.827929			0.413964	−	0.910293i	$-0.364144\pi$
$151$	10.1738			0.827929			0.413964	+	0.910293i	$0.364144\pi$
$152$	1.46120	−	1.06162i	0.118519	−	0.0861091i
$153$	0.535635	−	1.64852i	0.0433035	−	0.133275i
$154$	2.98694	−	9.19285i	0.240694	−	0.740781i
$155$	0.346650	+	0.522350i	0.0278436	+	0.0419562i
$156$	−20.7902	−	63.9856i	−1.66455	−	5.12294i
$157$	−9.73912			−0.777267			−0.388633	−	0.921393i	$-0.627053\pi$
$157$	−9.73912			−0.777267			−0.388633	+	0.921393i	$0.627053\pi$
$158$	−6.13470	−	18.8807i	−0.488050	−	1.50206i
$159$	−11.3967	−	8.28019i	−0.903818	−	0.656662i
$160$	−63.5873	+	17.7176i	−5.02702	+	1.40070i
$161$	9.92244	−	7.20908i	0.781998	−	0.568155i
$162$	25.3213	+	18.3970i	1.98943	+	1.44541i
$163$	−3.74244	−	2.71904i	−0.293131	−	0.212972i	0.431494	−	0.902116i	$-0.357987\pi$
$163$	−3.74244	−	2.71904i	−0.293131	−	0.212972i	−0.724624	+	0.689144i	$0.757987\pi$
$164$	2.66778	−	1.93826i	0.208319	−	0.151353i
$165$	−4.35045	−	6.55547i	−0.338682	−	0.510343i
$166$	22.3870	+	16.2651i	1.73756	+	1.26241i
$167$	−3.36801	−	10.3657i	−0.260625	−	0.802120i	−0.992669	−	0.120863i	$-0.961434\pi$
$167$	−3.36801	−	10.3657i	−0.260625	−	0.802120i	0.732044	−	0.681257i	$-0.238566\pi$
$168$	49.6160			3.82796
$169$	4.71982	+	14.5261i	0.363063	+	1.11739i
$170$	5.85805	+	2.18212i	0.449292	+	0.167361i
$171$	−0.0906914	+	0.279120i	−0.00693535	+	0.0213448i
$172$	3.84062	−	11.8202i	0.292844	−	0.901282i
$173$	−15.3525	+	11.1542i	−1.16723	+	0.848040i	−0.990674	−	0.136251i	$-0.956495\pi$
$173$	−15.3525	+	11.1542i	−1.16723	+	0.848040i	−0.176553	+	0.984291i	$0.556495\pi$
$174$	51.7526			3.92336
$175$	9.14917	−	5.52770i	0.691612	−	0.417855i
$176$	29.4190			2.21754
$177$	−5.60125	+	4.06954i	−0.421015	+	0.305886i
$178$	−12.5523	+	38.6321i	−0.940838	+	2.89560i
$179$	−3.91865	+	12.0604i	−0.292894	+	0.901434i	0.691027	+	0.722829i	$0.257158\pi$
$179$	−3.91865	+	12.0604i	−0.292894	+	0.901434i	−0.983921	+	0.178605i	$0.942842\pi$
$180$	14.0106	−	17.6578i	1.04429	−	1.31613i
$181$	−3.14564	−	9.68130i	−0.233814	−	0.719605i	−0.997277	−	0.0737532i	$-0.976502\pi$
$181$	−3.14564	−	9.68130i	−0.233814	−	0.719605i	0.763463	−	0.645852i	$-0.223498\pi$
$182$	−31.7802			−2.35570
$183$	−8.60343	−	26.4786i	−0.635984	−	1.95736i
$184$	49.5098	+	35.9710i	3.64991	+	2.65182i
$185$	4.66041	+	1.73600i	0.342640	+	0.127633i
$186$	1.37958	−	1.00232i	0.101155	−	0.0734937i
$187$	−1.30839	−	0.950598i	−0.0956786	−	0.0695146i
$188$	30.2766	+	21.9972i	2.20814	+	1.60431i
$189$	4.76629	−	3.46291i	0.346697	−	0.251890i
$190$	−0.991860	−	0.369467i	−0.0719571	−	0.0268040i
$191$	−4.92243	−	3.57635i	−0.356174	−	0.258776i	0.395280	−	0.918561i	$-0.370647\pi$
$191$	−4.92243	−	3.57635i	−0.356174	−	0.258776i	−0.751455	+	0.659785i	$0.770647\pi$
$192$	31.0251	+	95.4853i	2.23904	+	6.89106i
$193$	−5.48155			−0.394570			−0.197285	−	0.980346i	$-0.563212\pi$
$193$	−5.48155			−0.394570			−0.197285	+	0.980346i	$0.563212\pi$
$194$	5.91081	+	18.1916i	0.424371	+	1.30608i
$195$	−16.0785	+	20.2640i	−1.15140	+	1.45113i
$196$	−4.36614	+	13.4376i	−0.311867	+	0.959829i
$197$	−1.02977	+	3.16931i	−0.0733683	+	0.225804i	−0.981015	−	0.193930i	$-0.937877\pi$
$197$	−1.02977	+	3.16931i	−0.0733683	+	0.225804i	0.907647	+	0.419734i	$0.137877\pi$
$198$	−6.34024	+	4.60645i	−0.450581	+	0.327366i
$199$	−17.2260			−1.22112			−0.610559	−	0.791971i	$-0.709055\pi$
$199$	−17.2260			−1.22112			−0.610559	+	0.791971i	$0.709055\pi$
$200$	40.3386	+	34.8939i	2.85237	+	2.46737i
$201$	29.5799			2.08641
$202$	−26.7466	+	19.4325i	−1.88188	+	1.36727i
$203$	5.62120	−	17.3003i	0.394531	−	1.21424i
$204$	3.90991	−	12.0335i	0.273749	−	0.842512i
$205$	−1.18813	−	0.442576i	−0.0829823	−	0.0309108i
$206$	−5.99586	−	18.4534i	−0.417752	−	1.28571i
$207$	−9.94410			−0.691162
$208$	−29.8898	−	91.9915i	−2.07249	−	6.37846i
$209$	0.221530	+	0.160951i	0.0153236	+	0.0111332i
$210$	−16.0776	−	24.2265i	−1.10946	−	1.67179i
$211$	9.48515	−	6.89136i	0.652984	−	0.474421i	−0.211302	−	0.977421i	$-0.567770\pi$
$211$	9.48515	−	6.89136i	0.652984	−	0.474421i	0.864286	+	0.503000i	$0.167770\pi$
$212$	−30.4646	−	22.1338i	−2.09232	−	1.52016i
$213$	9.37643	+	6.81238i	0.642463	+	0.466776i
$214$	−18.4305	+	13.3905i	−1.25988	+	0.915358i
$215$	−4.60328	+	1.28263i	−0.313941	+	0.0874748i
$216$	23.7823	+	17.2788i	1.61818	+	1.17567i
$217$	−0.185219	−	0.570045i	−0.0125735	−	0.0386972i
$218$	28.1441			1.90616
$219$	2.46677	+	7.59195i	0.166689	+	0.513017i
$220$	−11.6292	−	17.5235i	−0.784040	−	1.18143i
$221$	−1.64314	+	5.05705i	−0.110529	+	0.340174i
$222$	4.18027	−	12.8656i	0.280561	−	0.863479i
$223$	−13.0920	+	9.51187i	−0.876703	+	0.636962i	−0.932377	−	0.361487i	$-0.882269\pi$
$223$	−13.0920	+	9.51187i	−0.876703	+	0.636962i	0.0556741	+	0.998449i	$0.482269\pi$
$224$	63.1109			4.21677
$225$	−8.63559	−	0.734359i	−0.575706	−	0.0489573i
$226$	−38.6361			−2.57004
$227$	−3.17133	+	2.30410i	−0.210488	+	0.152929i	−0.688035	−	0.725678i	$-0.741526\pi$
$227$	−3.17133	+	2.30410i	−0.210488	+	0.152929i	0.477546	+	0.878607i	$0.341526\pi$
$228$	−0.662010	+	2.03746i	−0.0438427	+	0.134934i
$229$	1.34519	−	4.14007i	0.0888927	−	0.273584i	−0.896721	−	0.442596i	$-0.854058\pi$
$229$	1.34519	−	4.14007i	0.0888927	−	0.273584i	0.985614	+	0.169012i	$0.0540577\pi$
$230$	1.52076	−	35.8308i	0.100276	−	2.36261i
$231$	2.32449	+	7.15404i	0.152940	+	0.470701i
$232$	90.7652			5.95903
$233$	3.97822	+	12.2437i	0.260622	+	0.802112i	0.992670	+	0.120858i	$0.0385647\pi$
$233$	3.97822	+	12.2437i	0.260622	+	0.802112i	−0.732048	+	0.681253i	$0.761435\pi$
$234$	20.8458	+	15.1454i	1.36273	+	0.990083i
$235$	0.610163	−	14.3762i	0.0398027	−	0.937797i
$236$	−14.9727	+	10.8783i	−0.974641	+	0.708118i
$237$	12.4988	+	9.08093i	0.811886	+	0.589870i
$238$	−4.83530	−	3.51305i	−0.313426	−	0.227717i
$239$	−2.98967	+	2.17212i	−0.193386	+	0.140503i	−0.680265	−	0.732966i	$-0.738135\pi$
$239$	−2.98967	+	2.17212i	−0.193386	+	0.140503i	0.486879	+	0.873469i	$0.338135\pi$
$240$	55.0053	−	69.3240i	3.55058	−	4.47484i
$241$	0.139708	+	0.101504i	0.00899939	+	0.00653844i	0.592276	−	0.805735i	$-0.298230\pi$
$241$	0.139708	+	0.101504i	0.00899939	+	0.00653844i	−0.583276	+	0.812274i	$0.698230\pi$
$242$	−7.24340	−	22.2929i	−0.465623	−	1.43304i
$243$	−16.0901			−1.03218
$244$	−22.9979	−	70.7801i	−1.47229	−	4.53123i
$245$	5.23316	−	1.45814i	0.334334	−	0.0931571i
$246$	−1.06572	+	3.27995i	−0.0679478	+	0.209122i
$247$	0.278209	−	0.856238i	0.0177020	−	0.0544811i
$248$	2.41954	−	1.75790i	0.153641	−	0.111627i
$249$	−21.5347			−1.36471
$250$	3.96670	−	31.0036i	0.250876	−	1.96084i
$251$	−23.9210			−1.50988			−0.754939	−	0.655795i	$-0.772333\pi$
$251$	−23.9210			−1.50988			−0.754939	+	0.655795i	$0.772333\pi$
$252$	−17.4352	+	12.6674i	−1.09831	+	0.797972i
$253$	−2.86708	+	8.82395i	−0.180251	+	0.554757i
$254$	5.36671	−	16.5170i	0.336737	−	1.03637i
$255$	−4.68633	+	1.30577i	−0.293470	+	0.0817707i
$256$	31.9277	+	98.2632i	1.99548	+	6.14145i
$257$	−3.35633			−0.209362			−0.104681	−	0.994506i	$-0.533382\pi$
$257$	−3.35633			−0.209362			−0.104681	+	0.994506i	$0.533382\pi$
$258$	4.01669	+	12.3621i	0.250068	+	0.769631i
$259$	−3.84675	−	2.79483i	−0.239026	−	0.173662i
$260$	−42.9795	+	54.1677i	−2.66547	+	3.35934i
$261$	−11.9319	+	8.66902i	−0.738565	+	0.536599i
$262$	−13.7552	−	9.99370i	−0.849796	−	0.617413i
$263$	−15.5602	−	11.3051i	−0.959483	−	0.697105i	−0.00645236	−	0.999979i	$-0.502054\pi$
$263$	−15.5602	−	11.3051i	−0.959483	−	0.697105i	−0.953031	+	0.302874i	$0.902054\pi$
$264$	−30.3651	+	22.0615i	−1.86884	+	1.35779i
$265$	−0.613953	+	14.4654i	−0.0377148	+	0.888605i
$266$	0.818692	+	0.594814i	0.0501972	+	0.0364704i
$267$	−9.76846	−	30.0642i	−0.597820	−	1.83990i
$268$	79.0702			4.82998
$269$	4.92596	+	15.1605i	0.300341	+	0.924354i	0.981375	+	0.192102i	$0.0615305\pi$
$269$	4.92596	+	15.1605i	0.300341	+	0.924354i	−0.681034	+	0.732252i	$0.738469\pi$
$270$	0.730502	−	17.2115i	0.0444569	−	1.04746i
$271$	−8.79720	+	27.0750i	−0.534392	+	1.64469i	0.210568	+	0.977579i	$0.432469\pi$
$271$	−8.79720	+	27.0750i	−0.534392	+	1.64469i	−0.744960	+	0.667109i	$0.767531\pi$
$272$	5.62125	−	17.3004i	0.340838	−	1.04899i
$273$	20.0085	−	14.5371i	1.21097	−	0.879822i
$274$	−21.8197			−1.31818
$275$	−3.14145	+	7.45111i	−0.189436	+	0.449319i
$276$	−72.5877			−4.36927
$277$	5.85395	−	4.25315i	0.351730	−	0.255547i	−0.397864	−	0.917444i	$-0.630249\pi$
$277$	5.85395	−	4.25315i	0.351730	−	0.255547i	0.749594	+	0.661897i	$0.230249\pi$
$278$	−4.05880	+	12.4917i	−0.243431	+	0.749203i
$279$	−0.150172	+	0.462182i	−0.00899057	+	0.0276701i
$280$	−28.1974	−	42.4892i	−1.68511	−	2.53922i
$281$	3.16508	+	9.74112i	0.188813	+	0.581107i	0.999993	−	0.00368970i	$-0.00117447\pi$
$281$	3.16508	+	9.74112i	0.188813	+	0.581107i	−0.811180	+	0.584796i	$0.801174\pi$
$282$	−39.1396			−2.33073
$283$	7.16796	+	22.0607i	0.426091	+	1.31137i	0.901946	+	0.431849i	$0.142139\pi$
$283$	7.16796	+	22.0607i	0.426091	+	1.31137i	−0.475855	+	0.879524i	$0.657861\pi$
$284$	25.0642	+	18.2102i	1.48729	+	1.08058i
$285$	0.793470	−	0.221088i	0.0470011	−	0.0130961i
$286$	19.4496	−	14.1309i	1.15008	−	0.835580i
$287$	0.980692	+	0.712514i	0.0578884	+	0.0420584i
$288$	−41.3967	−	30.0765i	−2.43933	−	1.77227i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−29.4116	−	44.3190i	−1.72711	−	2.60250i
$291$	−12.0427	−	8.74952i	−0.705955	−	0.512906i
$292$	6.59395	+	20.2941i	0.385881	+	1.18762i
$293$	−7.30701			−0.426880			−0.213440	−	0.976956i	$-0.568467\pi$
$293$	−7.30701			−0.426880			−0.213440	+	0.976956i	$0.568467\pi$
$294$	−4.56631	−	14.0537i	−0.266313	−	0.819626i
$295$	6.66826	+	2.48392i	0.388241	+	0.144620i
$296$	7.33148	−	22.5640i	0.426134	−	1.31150i
$297$	−1.37721	+	4.23862i	−0.0799140	+	0.245950i
$298$	6.68897	−	4.85982i	0.387482	−	0.281522i
$299$	30.5049			1.76414
$300$	−63.0362	−	5.36051i	−3.63940	−	0.309489i
$301$	4.56879			0.263340
$302$	−23.0103	+	16.7180i	−1.32409	+	0.962011i
$303$	7.95050	−	24.4691i	0.456744	−	1.40571i
$304$	−0.951765	+	2.92923i	−0.0545875	+	0.168003i
$305$	−17.7858	+	22.4158i	−1.01841	+	1.28352i
$306$	1.49745	+	4.60868i	0.0856035	+	0.263461i
$307$	8.92968			0.509644			0.254822	−	0.966988i	$-0.417983\pi$
$307$	8.92968			0.509644			0.254822	+	0.966988i	$0.417983\pi$
$308$	6.21360	+	19.1235i	0.354052	+	1.08966i
$309$	12.2160	+	8.87542i	0.694942	+	0.504905i
$310$	−1.64238	−	0.611785i	−0.0932809	−	0.0347471i
$311$	20.8878	−	15.1759i	1.18444	−	0.860544i	0.191772	−	0.981439i	$-0.438577\pi$
$311$	20.8878	−	15.1759i	1.18444	−	0.860544i	0.992665	+	0.120895i	$0.0385765\pi$
$312$	99.8362	+	72.5352i	5.65211	+	4.10650i
$313$	22.9650	+	16.6851i	1.29806	+	0.943096i	0.999935	−	0.0114300i	$-0.00363837\pi$
$313$	22.9650	+	16.6851i	1.29806	+	0.943096i	0.298126	+	0.954526i	$0.403638\pi$
$314$	22.0273	−	16.0038i	1.24307	−	0.903144i
$315$	7.76495	+	2.89244i	0.437505	+	0.162970i
$316$	33.4107	+	24.2743i	1.87950	+	1.36553i
$317$	−10.1069	−	31.1058i	−0.567660	−	1.74708i	−0.659914	−	0.751341i	$-0.729407\pi$
$317$	−10.1069	−	31.1058i	−0.567660	−	1.74708i	0.0922546	−	0.995735i	$-0.470593\pi$
$318$	39.3827			2.20847
$319$	4.25231	+	13.0873i	0.238084	+	0.732747i
$320$	64.1381	−	80.8341i	3.58543	−	4.51877i
$321$	5.47851	−	16.8611i	0.305781	−	0.941096i
$322$	−10.5956	+	32.6100i	−0.590471	+	1.81728i
$323$	0.136979	−	0.0995213i	0.00762173	−	0.00553751i
$324$	−65.1097			−3.61720
$325$	26.4909	+	2.25275i	1.46945	+	0.124960i
$326$	12.9324			0.716262
$327$	−17.7193	+	12.8738i	−0.979878	+	0.711923i
$328$	−1.86909	+	5.75246i	−0.103203	+	0.317627i
$329$	−4.25122	+	13.0839i	−0.234377	+	0.721339i
$330$	20.6118	+	7.67787i	1.13464	+	0.422653i
$331$	−9.69330	−	29.8329i	−0.532792	−	1.63976i	−0.748373	−	0.663278i	$-0.769165\pi$
$331$	−9.69330	−	29.8329i	−0.532792	−	1.63976i	0.215581	−	0.976486i	$-0.430835\pi$
$332$	−57.5645			−3.15926
$333$	1.19131	+	3.66646i	0.0652832	+	0.200921i
$334$	24.6509	+	17.9099i	1.34884	+	0.979987i
$335$	−16.8106	−	25.3311i	−0.918462	−	1.38399i
$336$	−68.4502	+	49.7320i	−3.73426	+	2.71310i
$337$	1.42569	+	1.03582i	0.0776620	+	0.0564248i	0.625939	−	0.779872i	$-0.284716\pi$
$337$	1.42569	+	1.03582i	0.0776620	+	0.0564248i	−0.548277	+	0.836297i	$0.684716\pi$
$338$	−34.5449	−	25.0983i	−1.87900	−	1.36517i
$339$	24.3250	−	17.6731i	1.32115	−	0.959872i
$340$	−12.5271	+	3.49047i	−0.679375	+	0.189297i
$341$	0.366823	+	0.266512i	0.0198646	+	0.0144324i
$342$	−0.253542	−	0.780321i	−0.0137100	−	0.0421949i
$343$	−20.1591			−1.08849
$344$	7.04459	+	21.6810i	0.379819	+	1.16896i
$345$	15.4324	+	23.2544i	0.830854	+	1.25197i
$346$	16.3941	−	50.4557i	0.881350	−	2.71252i
$347$	0.697559	−	2.14686i	0.0374469	−	0.115250i	−0.930586	−	0.366074i	$-0.880702\pi$
$347$	0.697559	−	2.14686i	0.0374469	−	0.115250i	0.968033	+	0.250824i	$0.0807017\pi$
$348$	−87.0978	+	63.2802i	−4.66893	+	3.39218i
$349$	5.27167			0.282186			0.141093	−	0.989996i	$-0.454938\pi$
$349$	5.27167			0.282186			0.141093	+	0.989996i	$0.454938\pi$
$350$	−11.6096	+	27.5365i	−0.620559	+	1.47189i
$351$	14.6532			0.782128
$352$	−38.6240	+	28.0620i	−2.05867	+	1.49571i
$353$	−9.05678	+	27.8739i	−0.482044	+	1.48358i	0.354173	+	0.935180i	$0.384762\pi$
$353$	−9.05678	+	27.8739i	−0.482044	+	1.48358i	−0.836217	+	0.548398i	$0.815238\pi$
$354$	5.98126	−	18.4084i	0.317900	−	0.978397i
$355$	0.505118	−	11.9012i	0.0268089	−	0.631649i
$356$	−26.1121	−	80.3648i	−1.38394	−	4.25932i
$357$	4.65122			0.246169
$358$	−10.9552	−	33.7166i	−0.579000	−	1.78198i
$359$	−27.5304	−	20.0020i	−1.45300	−	1.05567i	−0.985119	−	0.171876i	$-0.945017\pi$
$359$	−27.5304	−	20.0020i	−1.45300	−	1.05567i	−0.467883	−	0.883791i	$-0.654983\pi$
$360$	−1.75323	+	41.3081i	−0.0924034	+	2.17713i
$361$	15.3481	−	11.1511i	0.807796	−	0.586898i
$362$	23.0233	+	16.7274i	1.21008	+	0.879174i
$363$	14.7577	+	10.7221i	0.774578	+	0.562764i
$364$	53.4849	−	38.8591i	2.80337	−	2.03677i
$365$	5.09956	−	6.42705i	0.266923	−	0.336407i
$366$	62.9695	+	45.7500i	3.29147	+	2.39139i
$367$	−3.14542	−	9.68062i	−0.164190	−	0.505324i	0.834786	−	0.550575i	$-0.185591\pi$
$367$	−3.14542	−	9.68062i	−0.164190	−	0.505324i	−0.998976	+	0.0452505i	$0.985591\pi$
$368$	−104.359			−5.44008
$369$	−0.303712	−	0.934729i	−0.0158106	−	0.0486600i
$370$	−13.3933	+	3.73183i	−0.696283	+	0.194008i
$371$	4.27762	−	13.1652i	0.222083	−	0.683501i
$372$	−1.09619	+	3.37374i	−0.0568350	+	0.174920i
$373$	1.36548	−	0.992077i	0.0707017	−	0.0513678i	−0.551873	−	0.833928i	$-0.686087\pi$
$373$	1.36548	−	0.992077i	0.0707017	−	0.0513678i	0.622575	+	0.782560i	$0.286087\pi$
$374$	4.52128			0.233790
$375$	11.6844	+	21.3341i	0.603381	+	1.10169i
$376$	−68.6441			−3.54005
$377$	36.6027	−	26.5934i	1.88514	−	1.36963i
$378$	−5.08966	+	15.6643i	−0.261784	+	0.805687i
$379$	9.49291	−	29.2162i	0.487618	−	1.50073i	−0.340535	−	0.940232i	$-0.610608\pi$
$379$	9.49291	−	29.2162i	0.487618	−	1.50073i	0.828153	−	0.560502i	$-0.189392\pi$
$380$	2.12103	−	0.590991i	0.108806	−	0.0303172i
$381$	4.17647	+	12.8539i	0.213967	+	0.658523i
$382$	17.0100			0.870308
$383$	7.86034	+	24.1916i	0.401645	+	1.23613i	0.923665	+	0.383202i	$0.125179\pi$
$383$	7.86034	+	24.1916i	0.401645	+	1.23613i	−0.522020	+	0.852933i	$0.674821\pi$
$384$	−123.157	−	89.4790i	−6.28484	−	4.56621i
$385$	4.80541	−	6.05633i	0.244906	−	0.308659i
$386$	12.3978	−	9.00752i	0.631031	−	0.458471i
$387$	−2.99683	−	2.17733i	−0.152338	−	0.110680i
$388$	−32.1913	−	23.3884i	−1.63427	−	1.18737i
$389$	−26.7259	+	19.4175i	−1.35506	+	0.984506i	−0.356315	+	0.934366i	$0.615967\pi$
$389$	−26.7259	+	19.4175i	−1.35506	+	0.984506i	−0.998742	+	0.0501404i	$0.984033\pi$
$390$	3.06659	−	72.2525i	0.155283	−	3.65865i
$391$	4.64126	+	3.37208i	0.234719	+	0.170533i
$392$	−8.00852	−	24.6477i	−0.404492	−	1.24490i
$393$	13.2315			0.667440
$394$	−2.87889	−	8.86030i	−0.145036	−	0.446376i
$395$	0.673325	−	15.8643i	0.0338787	−	0.798221i
$396$	5.03787	−	15.5050i	0.253163	−	0.779155i
$397$	3.68229	−	11.3329i	0.184809	−	0.568784i	−0.815136	−	0.579270i	$-0.803338\pi$
$397$	3.68229	−	11.3329i	0.184809	−	0.568784i	0.999945	+	0.0104859i	$0.00333782\pi$
$398$	38.9606	−	28.3065i	1.95292	−	1.41888i
$399$	−0.787524			−0.0394255
$400$	−90.6266	−	7.70676i	−4.53133	−	0.385338i
$401$	−5.22387			−0.260868			−0.130434	−	0.991457i	$-0.541637\pi$
$401$	−5.22387			−0.260868			−0.130434	+	0.991457i	$0.541637\pi$
$402$	−66.9018	+	48.6070i	−3.33676	+	2.42430i
$403$	0.460674	−	1.41781i	0.0229478	−	0.0706261i
$404$	21.2525	−	65.4085i	1.05735	−	3.25420i
$405$	13.8426	+	20.8587i	0.687843	+	1.03648i
$406$	15.7149	+	48.3656i	0.779919	+	2.40034i
$407$	3.59693			0.178293
$408$	7.17169	+	22.0722i	0.355052	+	1.09274i
$409$	−7.67521	−	5.57637i	−0.379515	−	0.275734i	0.381631	−	0.924315i	$-0.375363\pi$
$409$	−7.67521	−	5.57637i	−0.379515	−	0.275734i	−0.761145	+	0.648581i	$0.775363\pi$
$410$	3.41448	−	0.951392i	0.168629	−	0.0469859i
$411$	13.7375	−	9.98087i	0.677620	−	0.492320i
$412$	32.6546	+	23.7249i	1.60877	+	1.16884i
$413$	−5.50405	−	3.99893i	−0.270837	−	0.196774i
$414$	22.4909	−	16.3406i	1.10537	−	0.803095i
$415$	12.2384	+	18.4415i	0.600761	+	0.905257i
$416$	126.990	+	92.2639i	6.22621	+	4.52361i
$417$	−3.15863	−	9.72127i	−0.154679	−	0.476053i
$418$	−0.765524			−0.0374430
$419$	−0.882013	−	2.71456i	−0.0430892	−	0.132615i	0.927198	−	0.374572i	$-0.122210\pi$
$419$	−0.882013	−	2.71456i	−0.0430892	−	0.132615i	−0.970287	+	0.241958i	$0.922210\pi$
$420$	56.6809	+	21.1136i	2.76574	+	1.03024i
$421$	5.35282	−	16.4743i	0.260880	−	0.802907i	−0.731734	−	0.681591i	$-0.761288\pi$
$421$	5.35282	−	16.4743i	0.260880	−	0.802907i	0.992614	−	0.121316i	$-0.0387115\pi$
$422$	−10.1287	+	31.1728i	−0.493055	+	1.51747i
$423$	9.02387	−	6.55623i	0.438756	−	0.318775i
$424$	69.0705			3.35436
$425$	3.78151	+	3.27111i	0.183430	+	0.158672i
$426$	−32.4014			−1.56985
$427$	22.1332	−	16.0807i	1.07110	−	0.778201i
$428$	14.6446	−	45.0715i	0.707875	−	2.17861i
$429$	−5.78144	+	17.7934i	−0.279130	+	0.859075i
$430$	8.30370	−	10.4653i	0.400440	−	0.504680i
$431$	3.20387	+	9.86050i	0.154325	+	0.474964i	0.998092	−	0.0617462i	$-0.0196669\pi$
$431$	3.20387	+	9.86050i	0.154325	+	0.474964i	−0.843767	+	0.536710i	$0.819667\pi$
$432$	−50.1292			−2.41184
$433$	−0.217213	−	0.668514i	−0.0104386	−	0.0321267i	0.945702	−	0.325036i	$-0.105377\pi$
$433$	−0.217213	−	0.668514i	−0.0104386	−	0.0321267i	−0.956140	+	0.292910i	$0.905377\pi$
$434$	1.35564	+	0.984928i	0.0650727	+	0.0472781i
$435$	38.7899	+	14.4492i	1.85983	+	0.692787i
$436$	−47.3654	+	34.4130i	−2.26839	+	1.64808i
$437$	−0.785839	−	0.570945i	−0.0375918	−	0.0273120i
$438$	−18.0546	−	13.1174i	−0.862683	−	0.626776i
$439$	−26.7062	+	19.4032i	−1.27462	+	0.926065i	−0.999376	−	0.0353102i	$-0.988758\pi$
$439$	−26.7062	+	19.4032i	−1.27462	+	0.926065i	−0.275242	+	0.961375i	$0.588758\pi$
$440$	36.1495	+	13.4657i	1.72336	+	0.641951i
$441$	3.40690	+	2.47526i	0.162233	+	0.117869i
$442$	−4.59364	−	14.1378i	−0.218497	−	0.672465i
$443$	−0.0155633			−0.000739433			−0.000369717	−	1.00000i	$-0.500118\pi$
$443$	−0.0155633			−0.000739433			−0.000369717		1.00000i	$0.500118\pi$
$444$	8.69604	+	26.7637i	0.412696	+	1.27015i
$445$	−20.1943	+	25.4512i	−0.957302	+	1.20650i
$446$	13.9802	−	43.0266i	0.661981	−	2.03737i
$447$	−1.98831	+	6.11940i	−0.0940440	+	0.289438i
$448$	−79.8153	+	57.9892i	−3.77092	+	2.73973i
$449$	−6.44978			−0.304384			−0.152192	−	0.988351i	$-0.548633\pi$
$449$	−6.44978			−0.304384			−0.152192	+	0.988351i	$0.548633\pi$
$450$	20.7381	−	12.5295i	0.977604	−	0.590644i
$451$	−0.917003			−0.0431800
$452$	65.0232	−	47.2421i	3.05843	−	2.22208i
$453$	6.83987	−	21.0510i	0.321365	−	0.989061i
$454$	3.38649	−	10.4225i	0.158936	−	0.489154i
$455$	−23.8201	−	8.87296i	−1.11670	−	0.415971i
$456$	−1.21428	−	3.73717i	−0.0568639	−	0.175009i
$457$	−28.1634			−1.31743			−0.658715	−	0.752392i	$-0.728900\pi$
$457$	−28.1634			−1.31743			−0.658715	+	0.752392i	$0.728900\pi$
$458$	3.76069	+	11.5742i	0.175725	+	0.540827i
$459$	2.22945	+	1.61979i	0.104062	+	0.0756054i
$460$	41.2525	+	62.1614i	1.92341	+	2.89829i
$461$	11.8230	−	8.58992i	0.550653	−	0.400073i	−0.277373	−	0.960762i	$-0.589464\pi$
$461$	11.8230	−	8.58992i	0.550653	−	0.400073i	0.828026	+	0.560690i	$0.189464\pi$
$462$	−17.0132	−	12.3608i	−0.791525	−	0.575077i
$463$	−6.70420	−	4.87088i	−0.311570	−	0.226369i	0.421000	−	0.907061i	$-0.361679\pi$
$463$	−6.70420	−	4.87088i	−0.311570	−	0.226369i	−0.732570	+	0.680692i	$0.761679\pi$
$464$	−125.220	+	90.9775i	−5.81318	+	4.22352i
$465$	1.31387	−	0.366090i	0.0609294	−	0.0169770i
$466$	−29.1170	−	21.1548i	−1.34882	−	0.979976i
$467$	7.11165	+	21.8874i	0.329088	+	1.01283i	0.969562	+	0.244848i	$0.0787380\pi$
$467$	7.11165	+	21.8874i	0.329088	+	1.01283i	−0.640474	+	0.767980i	$0.721262\pi$
$468$	−53.6016			−2.47774
$469$	8.98208	+	27.6440i	0.414754	+	1.27648i
$470$	22.2435	+	33.5176i	1.02602	+	1.54605i
$471$	−6.54767	+	20.1516i	−0.301701	+	0.928539i
$472$	10.4901	−	32.2852i	0.482846	−	1.48605i
$473$	−2.79611	+	2.03149i	−0.128565	+	0.0934081i
$474$	−43.1912			−1.98384
$475$	−0.640270	−	0.553850i	−0.0293776	−	0.0254124i
$476$	12.4332			0.569874
$477$	−9.07991	+	6.59694i	−0.415741	+	0.302053i
$478$	3.19251	−	9.82552i	0.146022	−	0.449409i
$479$	3.93983	−	12.1255i	0.180015	−	0.554030i	−0.819812	−	0.572633i	$-0.805922\pi$
$479$	3.93983	−	12.1255i	0.180015	−	0.554030i	0.999827	+	0.0186033i	$0.00592195\pi$
$480$	−6.08981	+	143.483i	−0.277961	+	6.54907i
$481$	−3.65450	−	11.2474i	−0.166631	−	0.512837i
$482$	−0.482778			−0.0219899
$483$	−8.24570	−	25.3777i	−0.375192	−	1.15472i
$484$	39.4489	+	28.6613i	1.79313	+	1.30279i
$485$	−0.648752	+	15.2854i	−0.0294583	+	0.694072i
$486$	36.3914	−	26.4399i	1.65075	−	1.19934i
$487$	6.44893	+	4.68542i	0.292229	+	0.212317i	0.724234	−	0.689555i	$-0.242194\pi$
$487$	6.44893	+	4.68542i	0.292229	+	0.212317i	−0.432005	+	0.901871i	$0.642194\pi$
$488$	110.438	+	80.2376i	4.99928	+	3.63219i
$489$	−8.14216	+	5.91562i	−0.368201	+	0.267514i
$490$	−9.43992	+	11.8973i	−0.426452	+	0.537464i
$491$	22.5945	+	16.4158i	1.01967	+	0.740837i	0.966216	−	0.257733i	$-0.0829756\pi$
$491$	22.5945	+	16.4158i	1.01967	+	0.740837i	0.0534584	+	0.998570i	$0.482976\pi$
$492$	−2.21697	−	6.82313i	−0.0999487	−	0.307610i
$493$	8.50873			0.383214
$494$	0.777775	+	2.39374i	0.0349937	+	0.107700i
$495$	−6.03828	+	1.68247i	−0.271401	+	0.0756216i
$496$	−1.57599	+	4.85039i	−0.0707640	+	0.217789i
$497$	−3.51933	+	10.8314i	−0.157864	+	0.485854i
$498$	48.7057	−	35.3867i	2.18255	−	1.58572i
$499$	−0.237952			−0.0106522			−0.00532609	−	0.999986i	$-0.501695\pi$
$499$	−0.237952			−0.0106522			−0.00532609	+	0.999986i	$0.501695\pi$
$500$	31.2337	+	57.0282i	1.39681	+	2.55038i
$501$	−23.7124			−1.05939
$502$	54.1028	−	39.3080i	2.41472	−	1.75440i
$503$	−4.93018	+	15.1735i	−0.219826	+	0.676554i	0.778950	+	0.627086i	$0.215753\pi$
$503$	−4.93018	+	15.1735i	−0.219826	+	0.676554i	−0.998776	+	0.0494679i	$0.984247\pi$
$504$	12.2154	−	37.5950i	0.544115	−	1.67461i
$505$	−25.4728	+	7.09760i	−1.13352	+	0.315839i
$506$	−8.01535	−	24.6687i	−0.356326	−	1.09666i
$507$	33.2298			1.47579
$508$	11.1641	+	34.3597i	0.495328	+	1.52446i
$509$	−23.3014	−	16.9295i	−1.03282	−	0.750385i	−0.0639458	−	0.997953i	$-0.520368\pi$
$509$	−23.3014	−	16.9295i	−1.03282	−	0.750385i	−0.968870	+	0.247569i	$0.920368\pi$
$510$	8.45352	−	10.6541i	0.374328	−	0.471771i
$511$	−6.34604	+	4.61067i	−0.280732	+	0.203964i
$512$	−120.467	−	87.5242i	−5.32393	−	3.86806i
$513$	−0.377481	−	0.274256i	−0.0166662	−	0.0121087i
$514$	7.59112	−	5.51527i	0.334830	−	0.243268i
$515$	0.658087	−	15.5053i	0.0289988	−	0.683245i
$516$	−21.8756	−	15.8936i	−0.963021	−	0.699676i
$517$	−3.21595	−	9.89767i	−0.141437	−	0.435299i
$518$	13.2929			0.584057
$519$	12.7581	+	39.2655i	0.560020	+	1.72357i
$520$	5.37828	−	126.718i	0.235853	−	5.55697i
$521$	−8.81257	+	27.1223i	−0.386086	+	1.18825i	0.549604	+	0.835425i	$0.314779\pi$
$521$	−8.81257	+	27.1223i	−0.386086	+	1.18825i	−0.935690	+	0.352824i	$0.885221\pi$
$522$	12.7414	−	39.2140i	0.557676	−	1.71635i
$523$	−14.6567	+	10.6487i	−0.640891	+	0.465635i	−0.860156	−	0.510031i	$-0.829634\pi$
$523$	−14.6567	+	10.6487i	−0.640891	+	0.465635i	0.219265	+	0.975665i	$0.429634\pi$
$524$	35.3692			1.54511
$525$	−5.28657	−	22.6472i	−0.230725	−	0.988407i
$526$	53.7701			2.34449
$527$	0.226818	−	0.164793i	0.00988036	−	0.00717850i
$528$	19.7786	−	60.8722i	0.860752	−	2.64912i
$529$	3.06305	−	9.42709i	0.133176	−	0.409873i
$530$	−22.3816	−	33.7258i	−0.972197	−	1.46496i
$531$	1.70456	+	5.24609i	0.0739715	+	0.227661i
$532$	−2.10513			−0.0912691
$533$	0.931678	+	2.86741i	0.0403555	+	0.124201i
$534$	71.4964	+	51.9452i	3.09395	+	2.24789i
$535$	−17.5527	+	4.89079i	−0.758870	+	0.211447i
$536$	−117.334	+	85.2483i	−5.06807	+	3.68217i
$537$	22.3201	+	16.2165i	0.963183	+	0.699794i
$538$	−36.0536	−	26.1945i	−1.55438	−	1.12933i
$539$	3.17871	−	2.30947i	0.136917	−	0.0994759i
$540$	19.8158	+	29.8595i	0.852737	+	1.28495i
$541$	−12.7659	−	9.27499i	−0.548850	−	0.398763i	0.278511	−	0.960433i	$-0.410159\pi$
$541$	−12.7659	−	9.27499i	−0.548850	−	0.398763i	−0.827361	+	0.561670i	$0.810159\pi$
$542$	−24.5939	−	75.6923i	−1.05640	−	3.25126i
$543$	−22.1468			−0.950412
$544$	9.12230	+	28.0755i	0.391115	+	1.20373i
$545$	21.0947	+	7.85776i	0.903598	+	0.336590i
$546$	−21.3660	+	65.7578i	−0.914381	+	2.81417i
$547$	9.48091	−	29.1793i	0.405375	−	1.24761i	−0.515207	−	0.857066i	$-0.672285\pi$
$547$	9.48091	−	29.1793i	0.405375	−	1.24761i	0.920582	−	0.390549i	$-0.127715\pi$
$548$	36.7217	−	26.6799i	1.56867	−	1.13971i
$549$	−22.1815			−0.946684
$550$	−5.13889	−	22.0146i	−0.219123	−	0.938704i
$551$	−1.44066			−0.0613743
$552$	107.715	−	78.2594i	4.58465	−	3.33094i
$553$	−4.69129	+	14.4383i	−0.199494	+	0.613979i
$554$	−6.25111	+	19.2389i	−0.265584	+	0.817384i
$555$	6.72525	−	8.47594i	0.285471	−	0.359784i
$556$	−8.44335	−	25.9860i	−0.358078	−	1.10205i
$557$	15.6609			0.663576			0.331788	−	0.943354i	$-0.392348\pi$
$557$	15.6609			0.663576			0.331788	+	0.943354i	$0.392348\pi$
$558$	−0.419829	−	1.29210i	−0.0177728	−	0.0546990i
$559$	9.19321	+	6.67926i	0.388831	+	0.282502i
$560$	81.4896	+	30.3548i	3.44357	+	1.28273i
$561$	−2.84656	+	2.06815i	−0.120182	+	0.0873172i
$562$	−23.1656	−	16.8308i	−0.977182	−	0.709964i
$563$	−20.6285	−	14.9875i	−0.869388	−	0.631647i	0.0610350	−	0.998136i	$-0.480560\pi$
$563$	−20.6285	−	14.9875i	−0.869388	−	0.631647i	−0.930423	+	0.366489i	$0.880560\pi$
$564$	65.8705	−	47.8577i	2.77365	−	2.01517i
$565$	−28.9588	−	10.7871i	−1.21830	−	0.453818i
$566$	−52.4631	−	38.1167i	−2.20519	−	1.60216i
$567$	−7.39622	−	22.7632i	−0.310612	−	0.955966i
$568$	−56.8264			−2.38438
$569$	−10.3095	−	31.7295i	−0.432198	−	1.33017i	−0.895931	−	0.444193i	$-0.853490\pi$
$569$	−10.3095	−	31.7295i	−0.432198	−	1.33017i	0.463733	−	0.885975i	$-0.346510\pi$
$570$	−1.43131	+	1.80391i	−0.0599511	+	0.0755573i
$571$	−8.58612	+	26.4254i	−0.359318	+	1.10587i	0.594145	+	0.804358i	$0.297490\pi$
$571$	−8.58612	+	26.4254i	−0.359318	+	1.10587i	−0.953463	+	0.301509i	$0.902510\pi$
$572$	−15.4544	+	47.5637i	−0.646180	+	1.98874i
$573$	−10.7094	+	7.78081i	−0.447390	+	0.325048i
$574$	−3.38890			−0.141450
$575$	11.1437	−	26.4315i	0.464725	−	1.10227i
$576$	79.9894			3.33289
$577$	10.7421	−	7.80463i	0.447201	−	0.324911i	−0.341288	−	0.939959i	$-0.610863\pi$
$577$	10.7421	−	7.80463i	0.447201	−	0.324911i	0.788490	+	0.615048i	$0.210863\pi$
$578$	0.863904	−	2.65882i	0.0359337	−	0.110593i
$579$	−3.68527	+	11.3421i	−0.153155	+	0.471362i
$580$	103.689	+	38.6243i	4.30547	+	1.60379i
$581$	−6.53911	−	20.1253i	−0.271288	−	0.834939i
$582$	41.6149			1.72499
$583$	3.23592	+	9.95914i	0.134018	+	0.412466i
$584$	−31.6647	−	23.0057i	−1.31029	−	0.951984i
$585$	11.3959	+	17.1719i	0.471163	+	0.709972i
$586$	16.5265	−	12.0072i	0.682703	−	0.496013i
$587$	−26.8542	−	19.5107i	−1.10839	−	0.805293i	−0.125982	−	0.992033i	$-0.540208\pi$
$587$	−26.8542	−	19.5107i	−1.10839	−	0.805293i	−0.982410	+	0.186739i	$0.940208\pi$
$588$	24.8690	+	18.0684i	1.02558	+	0.745126i
$589$	−0.0384039	+	0.0279021i	−0.00158241	+	0.00114968i
$590$	−19.1635	+	5.33961i	−0.788948	+	0.219828i
$591$	5.86545	+	4.26150i	0.241272	+	0.175295i
$592$	12.5022	+	38.4779i	0.513838	+	1.58143i
$593$	14.4000			0.591337			0.295668	−	0.955291i	$-0.404458\pi$
$593$	14.4000			0.591337			0.295668	+	0.955291i	$0.404458\pi$
$594$	−3.85021	−	11.8497i	−0.157976	−	0.486200i
$595$	−2.64334	−	3.98312i	−0.108367	−	0.163292i
$596$	−5.31497	+	16.3578i	−0.217710	+	0.670041i
$597$	−11.5811	+	35.6431i	−0.473984	+	1.45877i
$598$	−68.9939	+	50.1270i	−2.82137	+	2.04985i
$599$	−43.9162			−1.79437			−0.897184	−	0.441656i	$-0.854391\pi$
$599$	−43.9162			−1.79437			−0.897184	+	0.441656i	$0.854391\pi$
$600$	99.3204	−	60.0069i	4.05474	−	2.44977i
$601$	14.6904			0.599232			0.299616	−	0.954060i	$-0.403141\pi$
$601$	14.6904			0.599232			0.299616	+	0.954060i	$0.403141\pi$
$602$	−10.3334	+	7.50763i	−0.421156	+	0.305988i
$603$	7.28252	−	22.4133i	0.296567	−	0.912739i
$604$	18.2837	−	56.2714i	0.743953	−	2.28965i
$605$	0.795013	−	18.7314i	0.0323219	−	0.761541i
$606$	22.2268	+	68.4072i	0.902904	+	2.77885i
$607$	34.8966			1.41641			0.708204	−	0.706008i	$-0.249506\pi$
$607$	34.8966			1.41641			0.708204	+	0.706008i	$0.249506\pi$
$608$	−1.54455	−	4.75363i	−0.0626397	−	0.192785i
$609$	−32.0176	−	23.2622i	−1.29742	−	0.942630i
$610$	3.39223	−	79.9249i	0.137347	−	3.23606i
$611$	−27.6820	+	20.1121i	−1.11989	+	0.813650i
$612$	−8.15539	−	5.92523i	−0.329662	−	0.239513i
$613$	15.2106	+	11.0512i	0.614352	+	0.446353i	0.850944	−	0.525256i	$-0.176031\pi$
$613$	15.2106	+	11.0512i	0.614352	+	0.446353i	−0.236592	+	0.971609i	$0.576031\pi$
$614$	−20.1965	+	14.6736i	−0.815066	+	0.592180i
$615$	−1.71454	+	2.16086i	−0.0691368	+	0.0871341i
$616$	−29.8382	−	21.6787i	−1.20222	−	0.873461i
$617$	13.6133	+	41.8974i	0.548051	+	1.68673i	0.713624	+	0.700529i	$0.247053\pi$
$617$	13.6133	+	41.8974i	0.548051	+	1.68673i	−0.165573	+	0.986198i	$0.552947\pi$
$618$	−42.2137			−1.69808
$619$	−1.85908	−	5.72165i	−0.0747226	−	0.229973i	0.906718	−	0.421736i	$-0.138579\pi$
$619$	−1.85908	−	5.72165i	−0.0747226	−	0.229973i	−0.981441	+	0.191764i	$0.938579\pi$
$620$	3.51212	−	0.978598i	0.141050	−	0.0393014i
$621$	4.88542	−	15.0358i	0.196045	−	0.603364i
$622$	−22.3049	+	68.6474i	−0.894345	+	2.75251i
$623$	25.1304	−	18.2583i	1.00683	−	0.731503i
$624$	−210.439			−8.42429
$625$	11.6293	−	22.1305i	0.465172	−	0.885221i
$626$	−79.3584			−3.17180
$627$	0.481967	−	0.350170i	0.0192479	−	0.0139844i
$628$	−17.5026	+	53.8674i	−0.698429	+	2.14954i
$629$	0.687285	−	2.11525i	0.0274038	−	0.0843404i
$630$	−22.3152	+	6.21779i	−0.889059	+	0.247723i
$631$	5.43117	+	16.7154i	0.216211	+	0.665430i	0.999065	+	0.0432248i	$0.0137632\pi$
$631$	5.43117	+	16.7154i	0.216211	+	0.665430i	−0.782854	+	0.622205i	$0.786237\pi$
$632$	−75.7499			−3.01317
$633$	−7.88230	−	24.2592i	−0.313293	−	0.964218i
$634$	73.9735	+	53.7449i	2.93786	+	2.13448i
$635$	8.63401	−	10.8816i	0.342630	−	0.431822i
$636$	−66.2796	+	48.1549i	−2.62816	+	1.90947i
$637$	−10.4511	−	7.59320i	−0.414090	−	0.300854i
$638$	−31.1232	−	22.6123i	−1.23218	−	0.895230i
$639$	7.47033	−	5.42751i	0.295522	−	0.214709i
$640$	−6.63461	+	156.319i	−0.262256	+	6.17906i
$641$	−8.43360	−	6.12737i	−0.333107	−	0.242017i	0.408641	−	0.912695i	$-0.366003\pi$
$641$	−8.43360	−	6.12737i	−0.333107	−	0.242017i	−0.741748	+	0.670679i	$0.766003\pi$
$642$	15.3160	+	47.1378i	0.604475	+	1.86038i
$643$	−14.1297			−0.557220			−0.278610	−	0.960404i	$-0.589874\pi$
$643$	−14.1297			−0.557220			−0.278610	+	0.960404i	$0.589874\pi$
$644$	−22.0416	−	67.8371i	−0.868562	−	2.67316i
$645$	−0.440860	+	10.3872i	−0.0173588	+	0.408994i
$646$	−0.146273	+	0.450181i	−0.00575502	+	0.0177121i
$647$	−6.43028	+	19.7904i	−0.252800	+	0.778040i	0.741455	+	0.671003i	$0.234136\pi$
$647$	−6.43028	+	19.7904i	−0.252800	+	0.778040i	−0.994255	+	0.107037i	$0.965864\pi$
$648$	96.6179	−	70.1970i	3.79551	−	2.75760i
$649$	5.14660			0.202022
$650$	−63.6171	+	38.4359i	−2.49527	+	1.50758i
$651$	−1.30403			−0.0511089
$652$	−21.7648	+	15.8131i	−0.852377	+	0.619288i
$653$	9.35031	−	28.7773i	0.365906	−	1.12614i	−0.583506	−	0.812109i	$-0.698319\pi$
$653$	9.35031	−	28.7773i	0.365906	−	1.12614i	0.949412	−	0.314034i	$-0.101681\pi$
$654$	18.9214	−	58.2341i	0.739886	−	2.27714i
$655$	−7.51962	−	11.3309i	−0.293816	−	0.442737i
$656$	−3.18732	−	9.80955i	−0.124444	−	0.382999i
$657$	6.35989			0.248123
$658$	−11.8849	−	36.5780i	−0.463323	−	1.42596i
$659$	−16.1667	−	11.7458i	−0.629764	−	0.457550i	0.226554	−	0.973999i	$-0.427254\pi$
$659$	−16.1667	−	11.7458i	−0.629764	−	0.457550i	−0.856318	+	0.516448i	$0.827254\pi$
$660$	−44.0769	+	12.2814i	−1.71569	+	0.478051i
$661$	−19.8535	+	14.4244i	−0.772213	+	0.561046i	−0.902632	−	0.430413i	$-0.858368\pi$
$661$	−19.8535	+	14.4244i	−0.772213	+	0.561046i	0.130419	+	0.991459i	$0.458368\pi$
$662$	70.9463	+	51.5455i	2.75741	+	2.00337i
$663$	9.35908	+	6.79977i	0.363476	+	0.264081i
$664$	85.4214	−	62.0623i	3.31499	−	2.40848i
$665$	0.447560	+	0.674406i	0.0173556	+	0.0261523i
$666$	−8.71931	−	6.33495i	−0.337866	−	0.245474i
$667$	−15.0843	−	46.4248i	−0.584067	−	1.79757i
$668$	−63.3858			−2.45247
$669$	10.8796	+	33.4841i	0.420631	+	1.29457i
$670$	79.6463	+	29.6682i	3.07700	+	1.14618i
$671$	−6.39536	+	19.6829i	−0.246890	+	0.759850i
$672$	42.4298	−	130.585i	1.63676	−	5.03744i
$673$	15.3489	−	11.1516i	0.591657	−	0.429864i	−0.251251	−	0.967922i	$-0.580842\pi$
$673$	15.3489	−	11.1516i	0.591657	−	0.429864i	0.842908	+	0.538058i	$0.180842\pi$
$674$	−4.92662			−0.189766
$675$	5.35293	−	12.6965i	0.206035	−	0.488688i
$676$	88.8267			3.41641
$677$	−13.6110	+	9.88898i	−0.523114	+	0.380064i	−0.817776	−	0.575537i	$-0.804793\pi$
$677$	−13.6110	+	9.88898i	−0.523114	+	0.380064i	0.294662	+	0.955602i	$0.404793\pi$
$678$	−25.9753	+	79.9437i	−0.997575	+	3.07022i
$679$	4.52008	−	13.9114i	0.173465	−	0.533869i
$680$	14.8260	−	18.6855i	0.568552	−	0.716555i
$681$	2.63542	+	8.11100i	0.100990	+	0.310814i
$682$	−1.26760			−0.0485389
$683$	−7.99810	−	24.6156i	−0.306039	−	0.941891i	−0.979287	−	0.202475i	$-0.935102\pi$
$683$	−7.99810	−	24.6156i	−0.306039	−	0.941891i	0.673249	−	0.739416i	$-0.264898\pi$
$684$	1.38083	+	1.00324i	0.0527975	+	0.0383597i
$685$	−16.3544	−	6.09201i	−0.624870	−	0.232764i
$686$	45.5944	−	33.1263i	1.74080	−	1.26477i
$687$	−7.66202	−	5.56678i	−0.292324	−	0.212386i
$688$	−31.4504	−	22.8501i	−1.19904	−	0.871151i
$689$	27.8539	−	20.2370i	1.06115	−	0.770970i
$690$	−73.1166	−	27.2359i	−2.78350	−	1.03685i
$691$	0.555342	+	0.403480i	0.0211262	+	0.0153491i	0.598298	−	0.801273i	$-0.295844\pi$
$691$	0.555342	+	0.403480i	0.0211262	+	0.0153491i	−0.577172	+	0.816623i	$0.695844\pi$
$692$	34.1038	+	104.961i	1.29643	+	3.99001i
$693$	5.99304			0.227657
$694$	1.95013	+	6.00189i	0.0740260	+	0.227829i
$695$	−6.52984	+	8.22965i	−0.247691	+	0.312168i
$696$	61.0220	−	187.806i	2.31303	−	7.11878i
$697$	−0.175216	+	0.539261i	−0.00663680	+	0.0204260i
$698$	−11.9231	+	8.66264i	−0.451296	+	0.327886i
$699$	28.0086			1.05938
$700$	−14.1316	−	60.5384i	−0.534123	−	2.28814i
$701$	0.640166			0.0241787			0.0120894	−	0.999927i	$-0.496152\pi$
$701$	0.640166			0.0241787			0.0120894	+	0.999927i	$0.496152\pi$
$702$	−33.1415	+	24.0787i	−1.25085	+	0.908793i
$703$	−0.116368	+	0.358144i	−0.00438891	+	0.0135077i
$704$	23.0625	−	70.9791i	0.869201	−	2.67512i
$705$	−29.3361	−	10.9277i	−1.10486	−	0.411560i
$706$	−25.3196	−	77.9258i	−0.952916	−	2.93277i
$707$	25.2819			0.950824
$708$	12.4426	+	38.2943i	0.467620	+	1.43919i
$709$	−24.1262	−	17.5287i	−0.906079	−	0.658305i	0.0339409	−	0.999424i	$-0.489194\pi$
$709$	−24.1262	−	17.5287i	−0.906079	−	0.658305i	−0.940020	+	0.341119i	$0.889194\pi$
$710$	18.4141	+	27.7473i	0.691068	+	1.04134i
$711$	9.95799	−	7.23490i	0.373454	−	0.271330i
$712$	125.393	+	91.1030i	4.69928	+	3.41423i
$713$	−1.30124	−	0.945405i	−0.0487317	−	0.0354057i
$714$	−10.5198	+	7.64308i	−0.393694	+	0.286035i
$715$	18.5233	−	5.16122i	0.692731	−	0.193019i
$716$	59.6640	+	43.3484i	2.22975	+	1.62001i
$717$	2.48446	+	7.64640i	0.0927840	+	0.285560i
$718$	95.1347			3.55039
$719$	8.23941	+	25.3583i	0.307278	+	0.945705i	0.978817	+	0.204736i	$0.0656336\pi$
$719$	8.23941	+	25.3583i	0.307278	+	0.945705i	−0.671539	+	0.740969i	$0.734366\pi$
$720$	−38.9860	−	58.7460i	−1.45292	−	2.18934i
$721$	−4.58512	+	14.1115i	−0.170759	+	0.525541i
$722$	−16.3894	+	50.4414i	−0.609951	+	1.87724i
$723$	0.303953	−	0.220835i	0.0113041	−	0.00821293i
$724$	−59.2008			−2.20018
$725$	−9.67102	−	41.4299i	−0.359173	−	1.53867i
$726$	−50.9970			−1.89268
$727$	−6.28879	+	4.56907i	−0.233238	+	0.169458i	−0.698266	−	0.715839i	$-0.746045\pi$
$727$	−6.28879	+	4.56907i	−0.233238	+	0.169458i	0.465027	+	0.885296i	$0.346045\pi$
$728$	−37.4723	+	115.328i	−1.38882	+	4.27434i
$729$	−0.438600	+	1.34987i	−0.0162445	+	0.0499953i
$730$	−0.972621	+	22.9161i	−0.0359983	+	0.848162i
$731$	0.660391	+	2.03247i	0.0244254	+	0.0751737i
$732$	−161.916			−5.98458
$733$	−0.146010	−	0.449372i	−0.00539299	−	0.0165979i	0.948324	−	0.317304i	$-0.102778\pi$
$733$	−0.146010	−	0.449372i	−0.00539299	−	0.0165979i	−0.953717	+	0.300706i	$0.902778\pi$
$734$	23.0217	+	16.7263i	0.849747	+	0.617378i
$735$	0.501184	−	11.8085i	0.0184865	−	0.435562i
$736$	137.012	−	99.5450i	5.05032	−	3.66928i
$737$	−17.7889	−	12.9244i	−0.655261	−	0.476075i
$738$	2.22290	+	1.61503i	0.0818261	+	0.0594502i
$739$	14.4251	−	10.4804i	0.530635	−	0.385529i	−0.289960	−	0.957039i	$-0.593642\pi$
$739$	14.4251	−	10.4804i	0.530635	−	0.385529i	0.820595	+	0.571510i	$0.193642\pi$
$740$	17.9773	−	22.6571i	0.660859	−	0.832890i
$741$	−1.58464	−	1.15131i	−0.0582132	−	0.0422943i
$742$	11.9587	+	36.8052i	0.439019	+	1.35116i
$743$	−0.932633			−0.0342150			−0.0171075	−	0.999854i	$-0.505446\pi$
$743$	−0.932633			−0.0342150			−0.0171075	+	0.999854i	$0.505446\pi$
$744$	−2.01068	−	6.18822i	−0.0737149	−	0.226871i
$745$	6.37040	−	1.77501i	0.233394	−	0.0650315i
$746$	−1.45812	+	4.48762i	−0.0533854	+	0.164303i
$747$	−5.30180	+	16.3173i	−0.193983	+	0.597017i
$748$	−7.60915	+	5.52837i	−0.278218	+	0.202137i
$749$	17.4212			0.636557
$750$	−61.4841	−	29.0516i	−2.24508	−	1.06081i
$751$	−49.4816			−1.80561			−0.902805	−	0.430050i	$-0.858496\pi$
$751$	−49.4816			−1.80561			−0.902805	+	0.430050i	$0.858496\pi$
$752$	94.7014	−	68.8046i	3.45341	−	2.50905i
$753$	−16.0822	+	49.4959i	−0.586068	+	1.80373i
$754$	−39.0860	+	120.294i	−1.42343	+	4.38086i
$755$	−21.9144	+	6.10611i	−0.797548	+	0.222224i
$756$	−10.5878	−	32.5859i	−0.385074	−	1.18514i
$757$	34.4410			1.25178			0.625889	−	0.779912i	$-0.284736\pi$
$757$	34.4410			1.25178			0.625889	+	0.779912i	$0.284736\pi$
$758$	26.5389	+	81.6783i	0.963936	+	2.96669i
$759$	16.3305	+	11.8648i	0.592759	+	0.430664i
$760$	−2.51028	+	3.16374i	−0.0910574	+	0.114761i
$761$	−6.69081	+	4.86116i	−0.242542	+	0.176217i	−0.702415	−	0.711768i	$-0.747895\pi$
$761$	−6.69081	+	4.86116i	−0.242542	+	0.176217i	0.459873	+	0.887985i	$0.347895\pi$
$762$	−30.5681	−	22.2090i	−1.10736	−	0.804547i
$763$	−17.4118	−	12.6504i	−0.630349	−	0.457976i
$764$	−28.6272	+	20.7989i	−1.03570	+	0.752478i
$765$	−0.164355	+	3.87241i	−0.00594229	+	0.140007i
$766$	−57.5307	−	41.7985i	−2.07867	−	1.51024i
$767$	−5.22897	−	16.0931i	−0.188807	−	0.581089i
$768$	224.786			8.11126
$769$	2.52734	+	7.77834i	0.0911381	+	0.280494i	0.986228	−	0.165391i	$-0.0528888\pi$
$769$	2.52734	+	7.77834i	0.0911381	+	0.280494i	−0.895090	+	0.445886i	$0.852889\pi$
$770$	−0.916519	+	21.5942i	−0.0330290	+	0.778202i
$771$	−2.25648	+	6.94473i	−0.0812652	+	0.250108i
$772$	−9.85112	+	30.3186i	−0.354550	+	1.09119i
$773$	1.95957	−	1.42371i	0.0704808	−	0.0512073i	−0.551987	−	0.833853i	$-0.686130\pi$
$773$	1.95957	−	1.42371i	0.0704808	−	0.0512073i	0.622468	+	0.782645i	$0.286130\pi$
$774$	10.3559			0.372236
$775$	−1.06020	−	0.917097i	−0.0380834	−	0.0329431i
$776$	72.9854			2.62002
$777$	−8.36910	+	6.08051i	−0.300240	+	0.218137i
$778$	28.5391	−	87.8343i	1.02318	−	3.14901i
$779$	0.0296669	−	0.0913053i	0.00106293	−	0.00327135i
$780$	83.1854	+	125.348i	2.97851	+	4.48818i
$781$	−2.66229	−	8.19370i	−0.0952644	−	0.293194i
$782$	−16.0384			−0.573533
$783$	−7.24582	−	22.3003i	−0.258945	−	0.796949i
$784$	35.7539	+	25.9767i	1.27692	+	0.927740i
$785$	20.9782	−	5.84525i	0.748745	−	0.208626i
$786$	−29.9261	+	21.7426i	−1.06743	+	0.775532i
$787$	14.8265	+	10.7721i	0.528507	+	0.383983i	0.819799	−	0.572651i	$-0.194085\pi$
$787$	14.8265	+	10.7721i	0.528507	+	0.383983i	−0.291292	+	0.956634i	$0.594085\pi$
$788$	15.6789	+	11.3914i	0.558539	+	0.405803i
$789$	−33.8532	+	24.5958i	−1.20521	+	0.875633i
$790$	24.5461	+	36.9873i	0.873310	+	1.31595i
$791$	23.9029	+	17.3665i	0.849888	+	0.617480i
$792$	9.24064	+	28.4398i	0.328352	+	1.01056i
$793$	68.0449			2.41635
$794$	10.2944	+	31.6830i	0.365335	+	1.12439i
$795$	29.5183	+	10.9956i	1.04691	+	0.389972i
$796$	−30.9576	+	95.2776i	−1.09726	+	3.37702i
$797$	−12.0969	+	37.2303i	−0.428492	+	1.31876i	0.471118	+	0.882070i	$0.343851\pi$
$797$	−12.0969	+	37.2303i	−0.428492	+	1.31876i	−0.899610	+	0.436694i	$0.856149\pi$
$798$	1.78117	−	1.29409i	0.0630527	−	0.0458104i
$799$	−6.43500			−0.227654
$800$	126.334	−	76.3281i	4.46659	−	2.69860i
$801$	−25.1852			−0.889876
$802$	11.8150	−	8.58410i	0.417202	−	0.303115i
$803$	1.83368	−	5.64348i	0.0647091	−	0.199154i
$804$	53.1593	−	163.608i	1.87478	−	5.76999i
$805$	−17.0463	+	21.4837i	−0.600804	+	0.757202i
$806$	1.28788	+	3.96370i	0.0453638	+	0.139615i
$807$	34.6811			1.22083
$808$	38.9821	+	119.974i	1.37138	+	4.22069i
$809$	−29.4903	−	21.4260i	−1.03682	−	0.753297i	−0.0671615	−	0.997742i	$-0.521394\pi$
$809$	−29.4903	−	21.4260i	−1.03682	−	0.753297i	−0.969663	+	0.244445i	$0.921394\pi$
$810$	−65.5841	−	24.4300i	−2.30439	−	0.858383i
$811$	−25.2812	+	18.3679i	−0.887742	+	0.644982i	−0.935288	−	0.353887i	$-0.884860\pi$
$811$	−25.2812	+	18.3679i	−0.887742	+	0.644982i	0.0475461	+	0.998869i	$0.484860\pi$
$812$	−85.5864	−	62.1822i	−3.00350	−	2.18217i
$813$	50.1076	+	36.4053i	1.75735	+	1.27679i
$814$	−8.13530	+	5.91064i	−0.285142	+	0.207168i
$815$	9.69320	+	3.61071i	0.339538	+	0.126478i
$816$	−32.0179	−	23.2623i	−1.12085	−	0.814345i
$817$	−0.111814	−	0.344130i	−0.00391189	−	0.0120396i
$818$	26.5226			0.927341
$819$	−6.08895	−	18.7399i	−0.212765	−	0.654824i
$820$	−4.58314	+	5.77619i	−0.160050	+	0.201713i
$821$	10.8598	−	33.4231i	0.379010	−	1.16647i	−0.561723	−	0.827325i	$-0.689861\pi$
$821$	10.8598	−	33.4231i	0.379010	−	1.16647i	0.940733	−	0.339147i	$-0.110139\pi$
$822$	−14.6695	+	45.1481i	−0.511658	+	1.57472i
$823$	−13.7943	+	10.0221i	−0.480838	+	0.349349i	−0.801650	−	0.597794i	$-0.796044\pi$
$823$	−13.7943	+	10.0221i	−0.480838	+	0.349349i	0.320812	+	0.947143i	$0.396044\pi$
$824$	−74.0356			−2.57915
$825$	13.3054	+	11.5095i	0.463235	+	0.400710i
$826$	19.0199			0.661787
$827$	−36.6054	+	26.5954i	−1.27289	+	0.924812i	−0.999314	−	0.0370373i	$-0.988208\pi$
$827$	−36.6054	+	26.5954i	−1.27289	+	0.924812i	−0.273580	+	0.961849i	$0.588208\pi$
$828$	−17.8710	+	55.0012i	−0.621059	+	1.91142i
$829$	−8.50663	+	26.1807i	−0.295447	+	0.909294i	0.687623	+	0.726068i	$0.258654\pi$
$829$	−8.50663	+	26.1807i	−0.295447	+	0.909294i	−0.983071	+	0.183226i	$0.941346\pi$
$830$	−57.9839	−	21.5990i	−2.01265	−	0.749711i
$831$	−4.86473	−	14.9721i	−0.168755	−	0.519376i
$832$	−245.379			−8.50698
$833$	−0.750754	−	2.31058i	−0.0260121	−	0.0800570i
$834$	23.1184	+	16.7965i	0.800525	+	0.581615i
$835$	13.4761	+	20.3064i	0.466358	+	0.702732i
$836$	1.28835	−	0.936040i	0.0445585	−	0.0323736i
$837$	−0.625055	−	0.454129i	−0.0216051	−	0.0156970i
$838$	6.45556	+	4.69024i	0.223003	+	0.162021i
$839$	−10.0278	+	7.28565i	−0.346200	+	0.251529i	−0.747273	−	0.664517i	$-0.768637\pi$
$839$	−10.0278	+	7.28565i	−0.346200	+	0.251529i	0.401073	+	0.916046i	$0.368637\pi$
$840$	−106.874	+	29.7787i	−3.68749	+	1.02746i
$841$	−35.1101	−	25.5090i	−1.21069	−	0.879621i
$842$	14.9646	+	46.0564i	0.515715	+	1.58721i
$843$	22.2837			0.767491
$844$	−21.0702	−	64.8475i	−0.725267	−	2.23214i
$845$	−18.8849	−	28.4567i	−0.649660	−	0.978941i
$846$	−9.63609	+	29.6568i	−0.331296	+	1.01962i
$847$	−5.53913	+	17.0477i	−0.190327	+	0.585765i
$848$	−95.2896	+	69.2319i	−3.27226	+	2.37743i
$849$	50.4658			1.73198
$850$	−13.9280	−	1.18442i	−0.477726	−	0.0406252i
$851$	−12.7595			−0.437389
$852$	54.5303	−	39.6186i	1.86818	−	1.35731i
$853$	14.0547	−	43.2559i	0.481223	−	1.48105i	−0.356154	−	0.934427i	$-0.615912\pi$
$853$	14.0547	−	43.2559i	0.481223	−	1.48105i	0.837377	−	0.546625i	$-0.184088\pi$
$854$	−23.6348	+	72.7405i	−0.808767	+	2.48913i
$855$	0.0278280	−	0.655659i	0.000951696	−	0.0224231i
$856$	26.8617	+	82.6717i	0.918113	+	2.82566i
$857$	40.7609			1.39237			0.696183	−	0.717865i	$-0.254880\pi$
$857$	40.7609			1.39237			0.696183	+	0.717865i	$0.254880\pi$
$858$	−16.1629	−	49.7443i	−0.551792	−	1.69824i
$859$	8.62729	+	6.26809i	0.294359	+	0.213865i	0.725156	−	0.688584i	$-0.241767\pi$
$859$	8.62729	+	6.26809i	0.294359	+	0.213865i	−0.430797	+	0.902449i	$0.641767\pi$
$860$	−1.17846	+	27.7660i	−0.0401853	+	0.946812i
$861$	2.13362	−	1.55017i	0.0727135	−	0.0528295i
$862$	−23.4495	−	17.0371i	−0.798693	−	0.580285i
$863$	−14.2666	−	10.3653i	−0.485639	−	0.352838i	0.317866	−	0.948136i	$-0.397034\pi$
$863$	−14.2666	−	10.3653i	−0.485639	−	0.352838i	−0.803505	+	0.595298i	$0.797034\pi$
$864$	65.8143	−	47.8169i	2.23905	−	1.62676i
$865$	26.3749	−	33.2407i	0.896773	−	1.13022i
$866$	1.58981	+	1.15506i	0.0540239	+	0.0392507i
$867$	0.672306	+	2.06914i	0.0228327	+	0.0702718i
$868$	−3.48580			−0.118316
$869$	−3.54885	−	10.9222i	−0.120387	−	0.370512i
$870$	−111.476	+	31.0610i	−3.77939	+	1.05307i
$871$	−22.3401	+	68.7559i	−0.756967	+	2.32970i
$872$	33.1849	−	102.133i	1.12378	−	3.45865i
$873$	−9.59457	+	6.97086i	−0.324727	+	0.235928i
$874$	2.71556			0.0918551
$875$	−16.3898	+	17.3979i	−0.554077	+	0.588157i
$876$	46.4245			1.56854
$877$	0.509952	−	0.370502i	0.0172199	−	0.0125110i	−0.579142	−	0.815227i	$-0.696612\pi$
$877$	0.509952	−	0.370502i	0.0172199	−	0.0125110i	0.596362	+	0.802716i	$0.296612\pi$
$878$	28.5181	−	87.7697i	0.962439	−	2.96208i
$879$	−4.91254	+	15.1193i	−0.165696	+	0.509960i
$880$	−63.3690	+	17.6568i	−2.13617	+	0.595211i
$881$	15.7292	+	48.4094i	0.529929	+	1.63095i	0.754358	+	0.656463i	$0.227948\pi$
$881$	15.7292	+	48.4094i	0.529929	+	1.63095i	−0.224430	+	0.974490i	$0.572052\pi$
$882$	−11.7729			−0.396416
$883$	10.5943	+	32.6060i	0.356528	+	1.09728i	0.955118	+	0.296225i	$0.0957278\pi$
$883$	10.5943	+	32.6060i	0.356528	+	1.09728i	−0.598590	+	0.801055i	$0.704272\pi$
$884$	25.0178	+	18.1765i	0.841439	+	0.611341i
$885$	9.62270	−	12.1276i	0.323463	−	0.407666i
$886$	0.0351999	−	0.0255743i	0.00118256	−	0.000859184i
$887$	9.38593	+	6.81928i	0.315149	+	0.228969i	0.734103	−	0.679039i	$-0.237603\pi$
$887$	9.38593	+	6.81928i	0.315149	+	0.228969i	−0.418954	+	0.908007i	$0.637603\pi$
$888$	−41.7591	−	30.3398i	−1.40134	−	1.01814i
$889$	−10.7444	+	7.80627i	−0.360356	+	0.261814i
$890$	3.85159	−	90.7479i	0.129106	−	3.04188i
$891$	14.6481	+	10.6425i	0.490730	+	0.356536i
$892$	29.0824	+	89.5064i	0.973750	+	2.99689i
$893$	1.08955			0.0364603
$894$	−5.55864	−	17.1077i	−0.185909	−	0.572168i
$895$	1.20241	−	28.3301i	0.0401921	−	0.946971i
$896$	46.2256	−	142.268i	1.54429	−	4.75283i
$897$	20.5086	−	63.1190i	0.684763	−	2.10748i
$898$	14.5877	−	10.5986i	0.486797	−	0.353679i
$899$	−2.38553			−0.0795619
$900$	−19.5812	+	46.4440i	−0.652705	+	1.54813i
$901$	6.47497			0.215712
$902$	2.07401	−	1.50686i	0.0690571	−	0.0501729i
$903$	3.07162	−	9.45347i	0.102217	−	0.314592i
$904$	−45.5562	+	140.208i	−1.51518	+	4.66323i
$905$	12.5863	+	18.9657i	0.418383	+	0.630441i
$906$	19.1219	+	58.8512i	0.635283	+	1.95520i
$907$	−11.6095			−0.385486			−0.192743	−	0.981249i	$-0.561738\pi$
$907$	−11.6095			−0.385486			−0.192743	+	0.981249i	$0.561738\pi$
$908$	7.04476	+	21.6815i	0.233789	+	0.719527i
$909$	−16.5833	−	12.0485i	−0.550035	−	0.399624i
$910$	68.4550	−	19.0739i	2.26926	−	0.632295i
$911$	16.9805	−	12.3370i	0.562589	−	0.408745i	−0.269817	−	0.962912i	$-0.586963\pi$
$911$	16.9805	−	12.3370i	0.562589	−	0.408745i	0.832405	+	0.554167i	$0.186963\pi$
$912$	5.42113	+	3.93868i	0.179511	+	0.130423i
$913$	12.9506	+	9.40916i	0.428602	+	0.311398i
$914$	63.6981	−	46.2794i	2.10695	−	1.53079i
$915$	34.4239	+	51.8717i	1.13802	+	1.71483i
$916$	−20.4814	−	14.8806i	−0.676724	−	0.491669i
$917$	4.01781	+	12.3655i	0.132680	+	0.408346i
$918$	−7.70413			−0.254274
$919$	−5.75344	−	17.7073i	−0.189788	−	0.584109i	0.810209	−	0.586140i	$-0.199353\pi$
$919$	−5.75344	−	17.7073i	−0.189788	−	0.584109i	−0.999998	+	0.00203162i	$0.999353\pi$
$920$	−128.234	−	47.7671i	−4.22775	−	1.57483i
$921$	6.00348	−	18.4768i	0.197821	−	0.608831i
$922$	−12.6251	+	38.8562i	−0.415787	+	1.27966i
$923$	−22.9163	+	16.6497i	−0.754299	+	0.548030i
$924$	43.7467			1.43916
$925$	−11.0805	−	0.942272i	−0.364325	−	0.0309817i
$926$	23.1671			0.761319
$927$	9.73263	−	7.07117i	0.319662	−	0.232248i
$928$	77.6192	−	238.887i	2.54797	−	7.84186i
$929$	−2.38062	+	7.32681i	−0.0781058	+	0.240385i	−0.982484	−	0.186347i	$-0.940335\pi$
$929$	−2.38062	+	7.32681i	−0.0781058	+	0.240385i	0.904378	+	0.426732i	$0.140335\pi$
$930$	−2.37005	+	2.98701i	−0.0777171	+	0.0979480i
$931$	0.127114	+	0.391218i	0.00416601	+	0.0128217i
$932$	74.8698			2.45244
$933$	−17.3581	−	53.4226i	−0.568278	−	1.74898i
$934$	−52.0510	−	37.8172i	−1.70316	−	1.23742i
$935$	3.38881	+	1.26233i	0.110826	+	0.0412826i
$936$	79.5408	−	57.7898i	2.59987	−	1.88892i
$937$	32.3744	+	23.5214i	1.05763	+	0.768411i	0.973648	−	0.228056i	$-0.0732371\pi$
$937$	32.3744	+	23.5214i	1.05763	+	0.768411i	0.0839792	+	0.996468i	$0.473237\pi$
$938$	−65.7409	−	47.7636i	−2.14652	−	1.55954i
$939$	49.9634	−	36.3005i	1.63049	−	1.18462i
$940$	−78.4185	−	29.2108i	−2.55773	−	0.952753i
$941$	−11.4597	−	8.32593i	−0.373574	−	0.271418i	0.385117	−	0.922868i	$-0.374161\pi$
$941$	−11.4597	−	8.32593i	−0.373574	−	0.271418i	−0.758692	+	0.651450i	$0.774161\pi$
$942$	−18.3050	−	56.3370i	−0.596409	−	1.83556i
$943$	3.25290			0.105929
$944$	17.8886	+	55.0553i	0.582223	+	1.79190i
$945$	−8.18828	+	10.3198i	−0.266365	+	0.335703i
$946$	2.98581	−	9.18938i	0.0970771	−	0.298773i
$947$	0.483455	−	1.48792i	0.0157102	−	0.0483509i	−0.942894	−	0.333093i	$-0.891908\pi$
$947$	0.483455	−	1.48792i	0.0157102	−	0.0483509i	0.958604	+	0.284742i	$0.0919078\pi$
$948$	72.6892	−	52.8118i	2.36083	−	1.71525i
$949$	−19.5098			−0.633316
$950$	2.35823	+	0.200541i	0.0765110	+	0.00650640i
$951$	−71.1573			−2.30743
$952$	−18.4499	+	13.4047i	−0.597966	+	0.434447i
$953$	−6.22563	+	19.1605i	−0.201668	+	0.620670i	0.798166	+	0.602438i	$0.205804\pi$
$953$	−6.22563	+	19.1605i	−0.201668	+	0.620670i	−0.999834	+	0.0182320i	$0.994196\pi$
$954$	9.69594	−	29.8410i	0.313918	−	0.966139i
$955$	12.7494	+	4.74916i	0.412562	+	0.153679i
$956$	6.64123	+	20.4396i	0.214793	+	0.661064i
$957$	29.9383			0.967768
$958$	11.0144	+	33.8988i	0.355859	+	1.09522i
$959$	13.4991	+	9.80768i	0.435909	+	0.316706i
$960$	−124.137	−	187.056i	−4.00651	−	6.03721i
$961$	25.0159	−	18.1751i	0.806966	−	0.586295i
$962$	26.7477	+	19.4333i	0.862380	+	0.626556i
$963$	−11.4272	−	8.30235i	−0.368237	−	0.267540i
$964$	0.812497	−	0.590314i	0.0261688	−	0.0190127i
$965$	11.8073	−	3.28993i	0.380092	−	0.105907i
$966$	60.3512	+	43.8477i	1.94177	+	1.41078i
$967$	−15.9145	−	48.9797i	−0.511774	−	1.57508i	−0.789075	−	0.614297i	$-0.789440\pi$
$967$	−15.9145	−	48.9797i	−0.511774	−	1.57508i	0.277301	−	0.960783i	$-0.410560\pi$
$968$	−89.4399			−2.87471
$969$	−0.113832	−	0.350339i	−0.00365681	−	0.0112545i
$970$	−23.6503	−	35.6374i	−0.759364	−	1.14425i
$971$	7.65864	−	23.5709i	0.245777	−	0.756425i	−0.749730	−	0.661743i	$-0.769817\pi$
$971$	7.65864	−	23.5709i	0.245777	−	0.756425i	0.995508	−	0.0946813i	$-0.0301832\pi$
$972$	−28.9162	+	88.9948i	−0.927486	+	2.85451i
$973$	8.12592	−	5.90382i	0.260505	−	0.189268i
$974$	−22.2850			−0.714058
$975$	22.4712	−	53.2989i	0.719655	−	1.70693i
$976$	−232.785			−7.45127
$977$	18.5974	−	13.5118i	0.594983	−	0.432281i	−0.249111	−	0.968475i	$-0.580139\pi$
$977$	18.5974	−	13.5118i	0.594983	−	0.432281i	0.844095	+	0.536194i	$0.180139\pi$
$978$	8.69456	−	26.7591i	0.278021	−	0.855661i
$979$	−7.26139	+	22.3483i	−0.232075	+	0.714253i
$980$	1.33972	−	31.5653i	0.0427957	−	1.00832i
$981$	5.39228	+	16.5957i	0.172162	+	0.529861i
$982$	−78.0779			−2.49156
$983$	2.57215	+	7.91625i	0.0820387	+	0.252489i	0.983660	−	0.180038i	$-0.0576220\pi$
$983$	2.57215	+	7.91625i	0.0820387	+	0.252489i	−0.901621	+	0.432527i	$0.857622\pi$
$984$	10.6461	+	7.73482i	0.339384	+	0.246577i
$985$	0.315978	−	7.44480i	0.0100679	−	0.237211i
$986$	−19.2445	+	13.9819i	−0.612868	+	0.445275i
$987$	24.2144	+	17.5928i	0.770751	+	0.559984i
$988$	−4.23590	−	3.07756i	−0.134762	−	0.0979104i
$989$	9.91870	−	7.20636i	0.315396	−	0.229149i
$990$	10.8923	−	13.7277i	0.346179	−	0.436294i
$991$	12.0126	+	8.72766i	0.381593	+	0.277243i	0.762002	−	0.647575i	$-0.224217\pi$
$991$	12.0126	+	8.72766i	0.381593	+	0.277243i	−0.380409	+	0.924818i	$0.624217\pi$
$992$	−2.55755	−	7.87134i	−0.0812024	−	0.249915i
$993$	−68.2454			−2.16570
$994$	−9.83883	−	30.2808i	−0.312069	−	0.960449i
$995$	37.1050	−	10.3387i	1.17631	−	0.327760i
$996$	−38.7009	+	119.109i	−1.22629	+	3.77412i
$997$	8.07800	−	24.8615i	0.255833	−	0.787372i	−0.737832	−	0.674985i	$-0.764150\pi$
$997$	8.07800	−	24.8615i	0.255833	−	0.787372i	0.993664	−	0.112388i	$-0.0358498\pi$
$998$	0.538182	−	0.391012i	0.0170359	−	0.0123773i
$999$	−6.12908			−0.193915

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.86.1	✓	76
25.16	even	5	inner	425.2.k.b.341.1	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.1	✓	76	1.1	even	1	trivial
425.2.k.b.341.1	yes	76	25.16	even	5	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.26173 + 1.64324i) q^{2} +(0.672306 - 2.06914i) q^{3} +(1.79714 - 5.53104i) q^{4} +(-2.15401 + 0.600183i) q^{5} +(1.87953 + 5.78461i) q^{6} +2.13787 q^{7} +(3.29638 + 10.1452i) q^{8} +(-1.40231 - 1.01884i) q^{9} +(3.88556 - 4.89702i) q^{10} +(-1.30839 + 0.950598i) q^{11} +(-10.2363 - 7.43709i) q^{12} +(4.30178 + 3.12543i) q^{13} +(-4.83530 + 3.51305i) q^{14} +(-0.206292 + 4.86047i) q^{15} +(-14.7166 - 10.6922i) q^{16} +(0.309017 + 0.951057i) q^{17} +4.84585 q^{18} +(-0.0523214 - 0.161029i) q^{19} +(-0.551439 + 12.9926i) q^{20} +(1.43731 - 4.42357i) q^{21} +(1.39715 - 4.29999i) q^{22} +(4.64126 - 3.37208i) q^{23} +23.2081 q^{24} +(4.27956 - 2.58561i) q^{25} -14.8653 q^{26} +(2.22945 - 1.61979i) q^{27} +(3.84207 - 11.8247i) q^{28} +(2.62934 - 8.09228i) q^{29} +(-7.52037 - 11.3321i) q^{30} +(-0.0866369 - 0.266641i) q^{31} +29.5204 q^{32} +(1.08729 + 3.34633i) q^{33} +(-2.26173 - 1.64324i) q^{34} +(-4.60501 + 1.28312i) q^{35} +(-8.15539 + 5.92523i) q^{36} +(-1.79934 - 1.30729i) q^{37} +(0.382947 + 0.278227i) q^{38} +(9.35908 - 6.79977i) q^{39} +(-13.1894 - 19.8745i) q^{40} +(0.458723 + 0.333282i) q^{41} +(4.01821 + 12.3668i) q^{42} +2.13707 q^{43} +(2.90644 + 8.94509i) q^{44} +(3.63209 + 1.35295i) q^{45} +(-4.95615 + 15.2535i) q^{46} +(-1.98852 + 6.12005i) q^{47} +(-32.0179 + 23.2623i) q^{48} -2.42949 q^{49} +(-5.43044 + 12.8803i) q^{50} +2.17563 q^{51} +(25.0178 - 18.1765i) q^{52} +(2.00087 - 6.15806i) q^{53} +(-2.38071 + 7.32707i) q^{54} +(2.24775 - 2.83287i) q^{55} +(7.04725 + 21.6892i) q^{56} -0.368368 q^{57} +(7.35073 + 22.6232i) q^{58} +(-2.57454 - 1.87052i) q^{59} +(26.5127 + 9.87597i) q^{60} +(10.3529 - 7.52183i) q^{61} +(0.634105 + 0.460704i) q^{62} +(-2.99797 - 2.17815i) q^{63} +(-37.3339 + 27.1247i) q^{64} +(-11.1419 - 4.15036i) q^{65} +(-7.95799 - 5.78182i) q^{66} +(4.20141 + 12.9306i) q^{67} +5.81568 q^{68} +(-3.85696 - 11.8705i) q^{69} +(8.30683 - 10.4692i) q^{70} +(-1.64618 + 5.06643i) q^{71} +(5.71378 - 17.5852i) q^{72} +(-2.96839 + 2.15666i) q^{73} +6.21781 q^{74} +(-2.47282 - 10.5933i) q^{75} -0.984685 q^{76} +(-2.79716 + 2.03226i) q^{77} +(-9.99404 + 30.7585i) q^{78} +(-2.19437 + 6.75358i) q^{79} +(38.1171 + 14.1986i) q^{80} +(-3.45961 - 10.6476i) q^{81} -1.58517 q^{82} +(-3.05870 - 9.41370i) q^{83} +(-21.8839 - 15.8996i) q^{84} +(-1.23643 - 1.86312i) q^{85} +(-4.83347 + 3.51172i) q^{86} +(-14.9764 - 10.8810i) q^{87} +(-13.9570 - 10.1403i) q^{88} +(11.7548 - 8.54039i) q^{89} +(-10.4380 + 2.90840i) q^{90} +(9.19668 + 6.68178i) q^{91} +(-10.3101 - 31.7311i) q^{92} -0.609965 q^{93} +(-5.55922 - 17.1095i) q^{94} +(0.209348 + 0.315456i) q^{95} +(19.8467 - 61.0819i) q^{96} +(2.11429 - 6.50710i) q^{97} +(5.49486 - 3.99225i) q^{98} +2.80327 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

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