LMFDB - Embedded newform 775.2.ck.c.49.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(49,775)] 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("775.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 26])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.ck (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [80,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	775.49
Dual form			775.2.ck.c.174.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866342 - 1.19242i) q^{2} +(-1.18190 - 2.65459i) q^{3} +(-0.0532763 + 0.163968i) q^{4} +(-2.14145 + 3.70910i) q^{6} +(2.57003 - 2.31407i) q^{7} +(-2.56187 + 0.832401i) q^{8} +(-3.64256 + 4.04548i) q^{9} +(-2.60914 + 0.554589i) q^{11} +(0.498233 - 0.0523664i) q^{12} +(1.40170 + 0.147324i) q^{13} +(-4.98586 - 1.05978i) q^{14} +(3.49098 + 2.53634i) q^{16} +(-0.554253 + 2.60755i) q^{17} +(7.97960 + 0.838689i) q^{18} +(0.482893 + 4.59442i) q^{19} +(-9.18042 - 4.08739i) q^{21} +(2.92170 + 2.63071i) q^{22} +(-7.56957 + 2.45950i) q^{23} +(5.23755 + 5.81689i) q^{24} +(-1.03868 - 1.79904i) q^{26} +(6.75345 + 2.19433i) q^{27} +(0.242510 + 0.544687i) q^{28} +(-7.61531 + 5.53285i) q^{29} +(1.63570 - 5.32207i) q^{31} -0.972630i q^{32} +(4.55594 + 6.27071i) q^{33} +(3.58946 - 1.59813i) q^{34} +(-0.469264 - 0.812790i) q^{36} +(-8.26300 - 4.77065i) q^{37} +(5.06012 - 4.55615i) q^{38} +(-1.26558 - 3.89505i) q^{39} +(-0.186553 - 0.0830590i) q^{41} +(3.07951 + 14.4880i) q^{42} +(-3.20308 + 0.336657i) q^{43} +(0.0480705 - 0.457360i) q^{44} +(9.49058 + 6.89531i) q^{46} +(3.29049 - 4.52897i) q^{47} +(2.60697 - 12.2648i) q^{48} +(0.518459 - 4.93281i) q^{49} +(7.57705 - 1.61055i) q^{51} +(-0.0988335 + 0.221984i) q^{52} +(-2.88732 - 2.59976i) q^{53} +(-3.23424 - 9.95396i) q^{54} +(-4.65785 + 8.06763i) q^{56} +(11.6256 - 6.71202i) q^{57} +(13.1949 + 4.28729i) q^{58} +(9.59361 - 4.27135i) q^{59} -1.40790 q^{61} +(-7.76321 + 2.66030i) q^{62} +18.8261i q^{63} +(5.82218 - 4.23006i) q^{64} +(3.53030 - 10.8652i) q^{66} +(-4.06251 + 2.34549i) q^{67} +(-0.398025 - 0.229800i) q^{68} +(15.4754 + 17.1872i) q^{69} +(6.37569 - 7.08092i) q^{71} +(5.96430 - 13.3960i) q^{72} +(0.318386 + 1.49789i) q^{73} +(1.46998 + 13.9860i) q^{74} +(-0.779063 - 0.165595i) q^{76} +(-5.42221 + 7.46303i) q^{77} +(-3.54810 + 4.88354i) q^{78} +(-9.67493 - 2.05647i) q^{79} +(-0.449782 - 4.27939i) q^{81} +(0.0625781 + 0.294407i) q^{82} +(2.84228 - 6.38388i) q^{83} +(1.15930 - 1.28753i) q^{84} +(3.17639 + 3.52774i) q^{86} +(23.6880 + 13.6763i) q^{87} +(6.22262 - 3.59263i) q^{88} +(4.05038 - 12.4658i) q^{89} +(3.94332 - 2.86499i) q^{91} -1.37220i q^{92} +(-16.0612 + 1.94804i) q^{93} -8.25112 q^{94} +(-2.58193 + 1.14955i) q^{96} +(-14.1521 - 4.59828i) q^{97} +(-6.33113 + 3.65528i) q^{98} +(7.26037 - 12.5753i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 8 q^{6} - 4 q^{9} - 56 q^{11} + 12 q^{14} + 16 q^{16} + 26 q^{19} - 16 q^{21} + 164 q^{24} + 64 q^{26} - 84 q^{29} - 20 q^{31} - 64 q^{34} - 26 q^{36} - 74 q^{39} + 72 q^{41} + 112 q^{44}+ \cdots - 106 q^{99}+O(q^{100}) $ 80 * q + 20 * q^4 + 8 * q^6 - 4 * q^9 - 56 * q^11 + 12 * q^14 + 16 * q^16 + 26 * q^19 - 16 * q^21 + 164 * q^24 + 64 * q^26 - 84 * q^29 - 20 * q^31 - 64 * q^34 - 26 * q^36 - 74 * q^39 + 72 * q^41 + 112 * q^44 + 36 * q^46 + 62 * q^49 - 4 * q^51 - 44 * q^54 + 18 * q^56 + 2 * q^59 - 200 * q^61 - 34 * q^64 - 80 * q^66 - 16 * q^69 - 4 * q^71 + 4 * q^74 + 4 * q^76 + 134 * q^79 - 166 * q^81 - 52 * q^84 - 10 * q^86 - 40 * q^89 + 38 * q^91 - 260 * q^94 + 92 * q^96 - 106 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{13}{15}\right)$	$-1$

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 $

$2$	−0.866342	−	1.19242i	−0.612596	−	0.843166i	0.384192	−	0.923253i	$-0.374480\pi$
$2$	−0.866342	−	1.19242i	−0.612596	−	0.843166i	−0.996788	+	0.0800872i	$0.974480\pi$
$3$	−1.18190	−	2.65459i	−0.682370	−	1.53263i	−0.838506	−	0.544892i	$-0.816571\pi$
$3$	−1.18190	−	2.65459i	−0.682370	−	1.53263i	0.156137	−	0.987735i	$-0.450096\pi$
$4$	−0.0532763	+	0.163968i	−0.0266381	+	0.0819838i
$5$		0			0
$5$		0			0
$6$	−2.14145	+	3.70910i	−0.874242	+	1.51423i
$7$	2.57003	−	2.31407i	0.971381	−	0.874636i	−0.0207568	−	0.999785i	$-0.506608\pi$
$7$	2.57003	−	2.31407i	0.971381	−	0.874636i	0.992138	+	0.125149i	$0.0399409\pi$
$8$	−2.56187	+	0.832401i	−0.905757	+	0.294298i
$9$	−3.64256	+	4.04548i	−1.21419	+	1.34849i
$10$		0			0
$11$	−2.60914	+	0.554589i	−0.786684	+	0.167215i	−0.583702	−	0.811968i	$-0.698397\pi$
$11$	−2.60914	+	0.554589i	−0.786684	+	0.167215i	−0.202982	+	0.979183i	$0.565063\pi$
$12$	0.498233	−	0.0523664i	0.143828	−	0.0151169i
$13$	1.40170	+	0.147324i	0.388760	+	0.0408604i	0.296893	−	0.954911i	$-0.404050\pi$
$13$	1.40170	+	0.147324i	0.388760	+	0.0408604i	0.0918678	+	0.995771i	$0.470716\pi$
$14$	−4.98586	−	1.05978i	−1.33253	−	0.283237i
$15$		0			0
$16$	3.49098	+	2.53634i	0.872745	+	0.634086i
$17$	−0.554253	+	2.60755i	−0.134426	+	0.632425i	0.858412	+	0.512960i	$0.171451\pi$
$17$	−0.554253	+	2.60755i	−0.134426	+	0.632425i	−0.992838	+	0.119464i	$0.961882\pi$
$18$	7.97960	+	0.838689i	1.88081	+	0.197681i
$19$	0.482893	+	4.59442i	0.110783	+	1.05403i	0.898794	+	0.438371i	$0.144444\pi$
$19$	0.482893	+	4.59442i	0.110783	+	1.05403i	−0.788011	+	0.615661i	$0.788889\pi$
$20$		0			0
$21$	−9.18042	−	4.08739i	−2.00333	−	0.891941i
$22$	2.92170	+	2.63071i	0.622909	+	0.560870i
$23$	−7.56957	+	2.45950i	−1.57836	+	0.512842i	−0.961635	−	0.274333i	$-0.911543\pi$
$23$	−7.56957	+	2.45950i	−1.57836	+	0.512842i	−0.616730	+	0.787175i	$0.711543\pi$
$24$	5.23755	+	5.81689i	1.06911	+	1.18737i
$25$		0			0
$26$	−1.03868	−	1.79904i	−0.203701	−	0.352821i
$27$	6.75345	+	2.19433i	1.29970	+	0.422299i
$28$	0.242510	+	0.544687i	0.0458301	+	0.102936i
$29$	−7.61531	+	5.53285i	−1.41413	+	1.02742i	−0.421422	+	0.906865i	$0.638469\pi$
$29$	−7.61531	+	5.53285i	−1.41413	+	1.02742i	−0.992706	+	0.120560i	$0.961531\pi$
$30$		0			0
$31$	1.63570	−	5.32207i	0.293781	−	0.955873i
$31$	1.63570	−	5.32207i	0.293781	−	0.955873i
$32$		−	0.972630i		−	0.171938i
$33$	4.55594	+	6.27071i	0.793087	+	1.09159i
$34$	3.58946	−	1.59813i	0.615588	−	0.274077i
$35$		0			0
$36$	−0.469264	−	0.812790i	−0.0782107	−	0.135465i
$37$	−8.26300	−	4.77065i	−1.35843	−	0.784290i	−0.369017	−	0.929423i	$-0.620306\pi$
$37$	−8.26300	−	4.77065i	−1.35843	−	0.784290i	−0.989412	+	0.145133i	$0.953639\pi$
$38$	5.06012	−	4.55615i	0.820859	−	0.739105i
$39$	−1.26558	−	3.89505i	−0.202655	−	0.623707i
$40$		0			0
$41$	−0.186553	−	0.0830590i	−0.0291348	−	0.0129716i	0.392118	−	0.919915i	$-0.371743\pi$
$41$	−0.186553	−	0.0830590i	−0.0291348	−	0.0129716i	−0.421252	+	0.906943i	$0.638409\pi$
$42$	3.07951	+	14.4880i	0.475179	+	2.23554i
$43$	−3.20308	+	0.336657i	−0.488465	+	0.0513397i	−0.345560	−	0.938397i	$-0.612311\pi$
$43$	−3.20308	+	0.336657i	−0.488465	+	0.0513397i	−0.142905	+	0.989736i	$0.545644\pi$
$44$	0.0480705	−	0.457360i	0.00724690	−	0.0689496i
$45$		0			0
$46$	9.49058	+	6.89531i	1.39931	+	1.01666i
$47$	3.29049	−	4.52897i	0.479968	−	0.660619i	−0.498531	−	0.866872i	$-0.666127\pi$
$47$	3.29049	−	4.52897i	0.479968	−	0.660619i	0.978499	+	0.206253i	$0.0661270\pi$
$48$	2.60697	−	12.2648i	0.376283	−	1.77027i
$49$	0.518459	−	4.93281i	0.0740656	−	0.704687i
$50$		0			0
$51$	7.57705	−	1.61055i	1.06100	−	0.225522i
$52$	−0.0988335	+	0.221984i	−0.0137057	+	0.0307836i
$53$	−2.88732	−	2.59976i	−0.396604	−	0.357104i	0.446566	−	0.894751i	$-0.352647\pi$
$53$	−2.88732	−	2.59976i	−0.396604	−	0.357104i	−0.843170	+	0.537647i	$0.819313\pi$
$54$	−3.23424	−	9.95396i	−0.440124	−	1.35456i
$55$		0			0
$56$	−4.65785	+	8.06763i	−0.622431	+	1.07808i
$57$	11.6256	−	6.71202i	1.53984	−	0.889029i
$58$	13.1949	+	4.28729i	1.73258	+	0.562949i
$59$	9.59361	−	4.27135i	1.24898	−	0.556083i	0.327628	−	0.944807i	$-0.393751\pi$
$59$	9.59361	−	4.27135i	1.24898	−	0.556083i	0.921354	+	0.388724i	$0.127084\pi$
$60$		0			0
$61$	−1.40790			−0.180264			−0.0901318	−	0.995930i	$-0.528729\pi$
$61$	−1.40790			−0.180264			−0.0901318	+	0.995930i	$0.528729\pi$
$62$	−7.76321	+	2.66030i	−0.985928	+	0.337858i
$63$			18.8261i			2.37187i
$64$	5.82218	−	4.23006i	0.727772	−	0.528757i
$65$		0			0
$66$	3.53030	−	10.8652i	0.434550	−	1.33741i
$67$	−4.06251	+	2.34549i	−0.496314	+	0.286547i	−0.727190	−	0.686436i	$-0.759174\pi$
$67$	−4.06251	+	2.34549i	−0.496314	+	0.286547i	0.230876	+	0.972983i	$0.425841\pi$
$68$	−0.398025	−	0.229800i	−0.0482677	−	0.0278674i
$69$	15.4754	+	17.1872i	1.86302	+	2.06910i
$70$		0			0
$71$	6.37569	−	7.08092i	0.756655	−	0.840350i	−0.234630	−	0.972085i	$-0.575388\pi$
$71$	6.37569	−	7.08092i	0.756655	−	0.840350i	0.991285	+	0.131735i	$0.0420546\pi$
$72$	5.96430	−	13.3960i	0.702900	−	1.57874i
$73$	0.318386	+	1.49789i	0.0372643	+	0.175315i	0.992844	−	0.119418i	$-0.0381028\pi$
$73$	0.318386	+	1.49789i	0.0372643	+	0.175315i	−0.955580	+	0.294732i	$0.904769\pi$
$74$	1.46998	+	13.9860i	0.170882	+	1.62583i
$75$		0			0
$76$	−0.779063	−	0.165595i	−0.0893646	−	0.0189950i
$77$	−5.42221	+	7.46303i	−0.617918	+	0.850491i
$78$	−3.54810	+	4.88354i	−0.401743	+	0.552952i
$79$	−9.67493	−	2.05647i	−1.08851	−	0.231371i	−0.371503	−	0.928432i	$-0.621157\pi$
$79$	−9.67493	−	2.05647i	−1.08851	−	0.231371i	−0.717012	+	0.697061i	$0.754491\pi$
$80$		0			0
$81$	−0.449782	−	4.27939i	−0.0499758	−	0.475488i
$82$	0.0625781	+	0.294407i	0.00691060	+	0.0325118i
$83$	2.84228	−	6.38388i	0.311981	−	0.700721i	−0.687699	−	0.725996i	$-0.741379\pi$
$83$	2.84228	−	6.38388i	0.311981	−	0.700721i	0.999681	+	0.0252743i	$0.00804591\pi$
$84$	1.15930	−	1.28753i	0.126490	−	0.140481i
$85$		0			0
$86$	3.17639	+	3.52774i	0.342519	+	0.380406i
$87$	23.6880	+	13.6763i	2.53962	+	1.46625i
$88$	6.22262	−	3.59263i	0.663333	−	0.382976i
$89$	4.05038	−	12.4658i	0.429339	−	1.32137i	−0.469438	−	0.882965i	$-0.655543\pi$
$89$	4.05038	−	12.4658i	0.429339	−	1.32137i	0.898777	−	0.438405i	$-0.144457\pi$
$90$		0			0
$91$	3.94332	−	2.86499i	0.413373	−	0.300333i
$92$		−	1.37220i		−	0.143061i
$93$	−16.0612	+	1.94804i	−1.66546	+	0.202002i
$94$	−8.25112			−0.851038
$95$		0			0
$96$	−2.58193	+	1.14955i	−0.263517	+	0.117326i
$97$	−14.1521	−	4.59828i	−1.43692	−	0.466885i	−0.515987	−	0.856596i	$-0.672575\pi$
$97$	−14.1521	−	4.59828i	−1.43692	−	0.466885i	−0.920937	+	0.389712i	$0.872575\pi$
$98$	−6.33113	+	3.65528i	−0.639540	+	0.369239i
$99$	7.26037	−	12.5753i	0.729694	−	1.26387i
$100$		0			0
$101$	−2.78162	−	8.56095i	−0.276782	−	0.851847i	−0.988742	−	0.149627i	$-0.952193\pi$
$101$	−2.78162	−	8.56095i	−0.276782	−	0.851847i	0.711961	−	0.702219i	$-0.247807\pi$
$102$	−8.48476	−	7.63971i	−0.840117	−	0.756444i
$103$	−0.871417	+	1.95724i	−0.0858633	+	0.192852i	−0.951374	−	0.308038i	$-0.900327\pi$
$103$	−0.871417	+	1.95724i	−0.0858633	+	0.192852i	0.865511	+	0.500891i	$0.166994\pi$
$104$	−3.71359	+	0.789348i	−0.364148	+	0.0774020i
$105$		0			0
$106$	−0.598587	+	5.69517i	−0.0581399	+	0.553164i
$107$	−1.29355	+	6.08566i	−0.125052	+	0.588323i	0.870342	+	0.492449i	$0.163898\pi$
$107$	−1.29355	+	6.08566i	−0.125052	+	0.588323i	−0.995393	+	0.0958743i	$0.969435\pi$
$108$	−0.719597	+	0.990441i	−0.0692433	+	0.0953052i
$109$	−11.8039	−	8.57606i	−1.13061	−	0.821437i	−0.144828	−	0.989457i	$-0.546263\pi$
$109$	−11.8039	−	8.57606i	−1.13061	−	0.821437i	−0.985784	+	0.168020i	$0.946263\pi$
$110$		0			0
$111$	−2.89807	+	27.5733i	−0.275073	+	2.61714i
$112$	14.8412	−	1.55987i	1.40236	−	0.147394i
$113$	−2.35359	−	11.0728i	−0.221407	−	1.04164i	−0.938665	−	0.344831i	$-0.887936\pi$
$113$	−2.35359	−	11.0728i	−0.221407	−	1.04164i	0.717258	−	0.696808i	$-0.245397\pi$
$114$	−18.0752	−	8.04762i	−1.69290	−	0.753728i
$115$		0			0
$116$	−0.501492	−	1.54343i	−0.0465624	−	0.143304i
$117$	−5.70176	+	5.13389i	−0.527128	+	0.474628i
$118$	−13.4046	−	7.73914i	−1.23399	−	0.712445i
$119$	4.60961	+	7.98408i	0.422562	+	0.731899i
$120$		0			0
$121$	−3.54898	+	1.58011i	−0.322634	+	0.143646i
$122$	1.21973	+	1.67881i	0.110429	+	0.151992i
$123$			0.593390i			0.0535042i
$124$	0.785503	+	0.551742i	0.0705403	+	0.0495479i
$125$		0			0
$126$	22.4486	−	16.3099i	1.99988	−	1.45300i
$127$	2.66374	+	5.98285i	0.236368	+	0.530892i	0.992314	−	0.123742i	$-0.0394895\pi$
$127$	2.66374	+	5.98285i	0.236368	+	0.530892i	−0.755946	+	0.654634i	$0.772823\pi$
$128$	−11.9380	−	3.87890i	−1.05518	−	0.342850i
$129$	4.67940	+	8.10495i	0.411998	+	0.713601i
$130$		0			0
$131$	−0.867294	−	0.963228i	−0.0757759	−	0.0841576i	0.704065	−	0.710136i	$-0.251367\pi$
$131$	−0.867294	−	0.963228i	−0.0757759	−	0.0841576i	−0.779840	+	0.625978i	$0.784700\pi$
$132$	−1.27092	+	0.412946i	−0.110619	+	0.0359423i
$133$	11.8729	+	10.6904i	1.02951	+	0.926972i
$134$	6.31632	+	2.81221i	0.545647	+	0.242938i
$135$		0			0
$136$	−0.750609	−	7.14156i	−0.0643642	−	0.612384i
$137$	1.01699	+	0.106890i	0.0868875	+	0.00913224i	0.147872	−	0.989006i	$-0.452758\pi$
$137$	1.01699	+	0.106890i	0.0868875	+	0.00913224i	−0.0609850	+	0.998139i	$0.519424\pi$
$138$	7.08731	−	33.3432i	0.603312	−	2.83836i
$139$	5.63093	+	4.09111i	0.477609	+	0.347004i	0.800399	−	0.599467i	$-0.204621\pi$
$139$	5.63093	+	4.09111i	0.477609	+	0.347004i	−0.322790	+	0.946471i	$0.604621\pi$
$140$		0			0
$141$	−15.9116	−	3.38211i	−1.34000	−	0.284825i
$142$	−13.9669	−	1.46798i	−1.17208	−	0.123190i
$143$	−3.73892	+	0.392976i	−0.312664	+	0.0328623i
$144$	−22.9768	+	4.88388i	−1.91474	+	0.406990i
$145$		0			0
$146$	1.51028	−	1.67733i	0.124991	−	0.138817i
$147$	−13.7073	+	4.45379i	−1.13056	+	0.367342i
$148$	1.22245	−	1.10070i	0.100485	−	0.0904771i
$149$	−10.3942	+	18.0033i	−0.851527	+	1.47489i	0.0283025	+	0.999599i	$0.490990\pi$
$149$	−10.3942	+	18.0033i	−0.851527	+	1.47489i	−0.879830	+	0.475289i	$0.842344\pi$
$150$		0			0
$151$	0.0452157	−	0.139160i	0.00367960	−	0.0113246i	−0.949200	−	0.314674i	$-0.898105\pi$
$151$	0.0452157	−	0.139160i	0.00367960	−	0.0113246i	0.952879	+	0.303349i	$0.0981049\pi$
$152$	−5.06151	−	11.3683i	−0.410543	−	0.922094i
$153$	−8.52989	−	11.7404i	−0.689601	−	0.949154i
$154$	13.5965			1.09564
$155$		0			0
$156$	0.706087			0.0565322
$157$	0.244039	+	0.335891i	0.0194764	+	0.0268070i	0.818644	−	0.574301i	$-0.194726\pi$
$157$	0.244039	+	0.335891i	0.0194764	+	0.0268070i	−0.799168	+	0.601108i	$0.794726\pi$
$158$	5.92963	+	13.3182i	0.471736	+	1.05954i
$159$	−3.48876	+	10.7373i	−0.276677	+	0.851524i
$160$		0			0
$161$	−13.7626	+	23.8375i	−1.08464	+	1.87866i
$162$	−4.71315	+	4.24374i	−0.370300	+	0.333420i
$163$	10.0246	−	3.25720i	0.785191	−	0.255124i	0.111136	−	0.993805i	$-0.464551\pi$
$163$	10.0246	−	3.25720i	0.785191	−	0.255124i	0.674055	+	0.738681i	$0.264551\pi$
$164$	0.0235578	−	0.0261636i	0.00183956	−	0.00204304i
$165$		0			0
$166$	−10.0746	+	2.14143i	−0.781943	+	0.166207i
$167$	−14.6169	+	1.53630i	−1.13109	+	0.118882i	−0.651527	−	0.758625i	$-0.725871\pi$
$167$	−14.6169	+	1.53630i	−1.13109	+	0.118882i	−0.479563	+	0.877508i	$0.659205\pi$
$168$	26.9214	+	2.82955i	2.07703	+	0.218304i
$169$	−10.7729	−	2.28984i	−0.828682	−	0.176142i
$170$		0			0
$171$	−20.3456	−	14.7819i	−1.55587	−	1.13040i
$172$	0.115447	−	0.543136i	0.00880276	−	0.0414137i
$173$	−17.4044	−	1.82928i	−1.32323	−	0.139078i	−0.583575	−	0.812059i	$-0.698347\pi$
$173$	−17.4044	−	1.82928i	−1.32323	−	0.139078i	−0.739659	+	0.672981i	$0.765013\pi$
$174$	−4.21407	−	40.0942i	−0.319468	−	3.03954i
$175$		0			0
$176$	−10.5151	−	4.68161i	−0.792603	−	0.352890i
$177$	−22.6774	−	20.4188i	−1.70453	−	1.53477i
$178$	−18.3734	+	5.96989i	−1.37715	+	0.447462i
$179$	9.50956	+	10.5614i	0.710778	+	0.789399i	0.985053	−	0.172252i	$-0.0551044\pi$
$179$	9.50956	+	10.5614i	0.710778	+	0.789399i	−0.274275	+	0.961651i	$0.588438\pi$
$180$		0			0
$181$	10.6424	+	18.4332i	0.791044	+	1.37013i	0.925321	+	0.379185i	$0.123796\pi$
$181$	10.6424	+	18.4332i	0.791044	+	1.37013i	−0.134277	+	0.990944i	$0.542871\pi$
$182$	−6.83253	−	2.22002i	−0.506461	−	0.164559i
$183$	1.66400	+	3.73741i	0.123006	+	0.276277i
$184$	17.3449	−	12.6018i	1.27869	−	0.929020i
$185$		0			0
$186$	16.2373	+	17.4639i	1.19058	+	1.28052i
$187$		−	7.11084i		−	0.519996i
$188$	0.567299	+	0.780821i	0.0413746	+	0.0569472i
$189$	22.4344	−	9.98844i	1.63186	−	0.726552i
$190$		0			0
$191$	−6.87683	−	11.9110i	−0.497590	−	0.861851i	0.502406	−	0.864632i	$-0.332448\pi$
$191$	−6.87683	−	11.9110i	−0.497590	−	0.861851i	−0.999996	+	0.00278081i	$0.999115\pi$
$192$	−18.1103	−	10.4560i	−1.30700	−	0.754596i
$193$	15.1633	−	13.6531i	1.09148	−	0.982773i	0.0915648	−	0.995799i	$-0.470813\pi$
$193$	15.1633	−	13.6531i	1.09148	−	0.982773i	0.999915	+	0.0130261i	$0.00414646\pi$
$194$	6.77745	+	20.8588i	0.486592	+	1.49758i
$195$		0			0
$196$	0.781199	+	0.347812i	0.0557999	+	0.0248437i
$197$	3.19085	+	15.0118i	0.227338	+	1.06954i	0.932688	+	0.360684i	$0.117457\pi$
$197$	3.19085	+	15.0118i	0.227338	+	1.06954i	−0.705350	+	0.708859i	$0.749210\pi$
$198$	−21.2850	+	2.23714i	−1.51266	+	0.158987i
$199$	1.55425	−	14.7877i	0.110178	−	1.04827i	−0.790106	−	0.612971i	$-0.789974\pi$
$199$	1.55425	−	14.7877i	0.110178	−	1.04827i	0.900284	−	0.435304i	$-0.143359\pi$
$200$		0			0
$201$	11.0278	+	8.01215i	0.777839	+	0.565133i
$202$	−7.79839	+	10.7336i	−0.548693	+	0.755211i
$203$	−6.76822	+	31.8420i	−0.475036	+	2.23487i
$204$	−0.139599	+	1.32819i	−0.00977387	+	0.0929922i
$205$		0			0
$206$	3.08879	−	0.656542i	0.215206	−	0.0457434i
$207$	17.6228	−	39.5814i	1.22487	−	2.75110i
$208$	4.51963	+	4.06949i	0.313380	+	0.282168i
$209$	−3.80795	−	11.7197i	−0.263401	−	0.810666i
$210$		0			0
$211$	−4.43407	+	7.68004i	−0.305254	+	0.528716i	−0.977318	−	0.211777i	$-0.932075\pi$
$211$	−4.43407	+	7.68004i	−0.305254	+	0.528716i	0.672064	+	0.740493i	$0.265408\pi$
$212$	0.580102	−	0.334922i	0.0398415	−	0.0230025i
$213$	−26.3323	−	8.55589i	−1.80426	−	0.586240i
$214$	8.37730	−	3.72981i	0.572660	−	0.254965i
$215$		0			0
$216$	−19.1280			−1.30150
$217$	−8.11183	−	17.4630i	−0.550667	−	1.18547i
$218$			21.5050i			1.45650i
$219$	3.59998	−	2.61554i	0.243264	−	0.176742i
$220$		0			0
$221$	−1.16105	+	3.57334i	−0.0781006	+	0.240369i
$222$	35.3896	−	20.4322i	2.37519	−	1.37132i
$223$	18.7719	+	10.8379i	1.25706	+	0.725762i	0.972501	−	0.232897i	$-0.0748205\pi$
$223$	18.7719	+	10.8379i	1.25706	+	0.725762i	0.284556	+	0.958659i	$0.408154\pi$
$224$	−2.25073	−	2.49969i	−0.150383	−	0.167018i
$225$		0			0
$226$	−11.1643	+	12.3993i	−0.742641	+	0.824787i
$227$	−1.29900	+	2.91760i	−0.0862176	+	0.193648i	−0.951509	−	0.307622i	$-0.900467\pi$
$227$	−1.29900	+	2.91760i	−0.0862176	+	0.193648i	0.865291	+	0.501270i	$0.167134\pi$
$228$	0.481187	+	2.26381i	0.0318674	+	0.149924i
$229$	−0.902887	−	8.59039i	−0.0596644	−	0.567669i	−0.982991	−	0.183653i	$-0.941208\pi$
$229$	−0.902887	−	8.59039i	−0.0596644	−	0.567669i	0.923327	−	0.384016i	$-0.125459\pi$
$230$		0			0
$231$	26.2198	+	5.57319i	1.72513	+	0.366689i
$232$	14.9039	−	20.5134i	0.978487	−	1.34677i
$233$	4.37248	−	6.01820i	0.286451	−	0.394265i	−0.641407	−	0.767201i	$-0.721649\pi$
$233$	4.37248	−	6.01820i	0.286451	−	0.394265i	0.927857	+	0.372936i	$0.121649\pi$
$234$	11.0614	+	2.35118i	0.723107	+	0.153701i
$235$		0			0
$236$	0.189251	+	1.80060i	0.0123192	+	0.117209i
$237$	5.97571	+	28.1135i	0.388164	+	1.82617i
$238$	5.52685	−	12.4135i	0.358253	−	0.804648i
$239$	16.4005	−	18.2146i	1.06086	−	1.17820i	0.0774117	−	0.996999i	$-0.475334\pi$
$239$	16.4005	−	18.2146i	1.06086	−	1.17820i	0.983446	−	0.181202i	$-0.0579989\pi$
$240$		0			0
$241$	−5.04341	−	5.60127i	−0.324874	−	0.360810i	0.558478	−	0.829519i	$-0.311386\pi$
$241$	−5.04341	−	5.60127i	−0.324874	−	0.360810i	−0.883352	+	0.468710i	$0.844719\pi$
$242$	4.95877	+	2.86295i	0.318762	+	0.184037i
$243$	7.62050	−	4.39970i	0.488855	−	0.282241i
$244$	0.0750079	−	0.230851i	0.00480189	−	0.0147787i
$245$		0			0
$246$	0.707568	−	0.514078i	0.0451129	−	0.0327764i
$247$			6.51112i			0.414293i
$248$	0.239648	+	14.9960i	0.0152177	+	0.952247i
$249$	−20.3059			−1.28683
$250$		0			0
$251$	8.88229	−	3.95465i	0.560645	−	0.249615i	−0.106792	−	0.994281i	$-0.534058\pi$
$251$	8.88229	−	3.95465i	0.560645	−	0.249615i	0.667437	+	0.744666i	$0.267391\pi$
$252$	−3.08688	−	1.00299i	−0.194455	−	0.0631822i
$253$	18.3860	−	10.6152i	1.15592	−	0.667370i
$254$	4.82634	−	8.35947i	0.302832	−	0.524520i
$255$		0			0
$256$	1.26940	+	3.90682i	0.0793376	+	0.244176i
$257$	1.92310	+	1.73157i	0.119960	+	0.108012i	0.726928	−	0.686714i	$-0.240948\pi$
$257$	1.92310	+	1.73157i	0.119960	+	0.108012i	−0.606968	+	0.794727i	$0.707614\pi$
$258$	5.61053	−	12.6015i	0.349296	−	0.784532i
$259$	−32.2758	+	6.86043i	−2.00552	+	0.426286i
$260$		0			0
$261$	5.35625	−	50.9613i	0.331544	−	3.15443i
$262$	−0.397196	+	1.86866i	−0.0245389	+	0.115446i
$263$	−8.05344	+	11.0846i	−0.496596	+	0.683506i	−0.981588	−	0.191013i	$-0.938823\pi$
$263$	−8.05344	+	11.0846i	−0.496596	+	0.683506i	0.484991	+	0.874519i	$0.338823\pi$
$264$	−16.8915	−	12.2724i	−1.03960	−	0.755312i
$265$		0			0
$266$	2.46143	−	23.4189i	0.150920	−	1.43591i
$267$	−37.8787	+	3.98121i	−2.31814	+	0.243646i
$268$	−0.168149	−	0.791078i	−0.0102713	−	0.0483228i
$269$	−18.5821	−	8.27330i	−1.13297	−	0.504432i	−0.247391	−	0.968916i	$-0.579573\pi$
$269$	−18.5821	−	8.27330i	−1.13297	−	0.504432i	−0.885582	+	0.464484i	$0.846240\pi$
$270$		0			0
$271$	−8.58819	−	26.4317i	−0.521696	−	1.60561i	−0.770759	−	0.637127i	$-0.780123\pi$
$271$	−8.58819	−	26.4317i	−0.521696	−	1.60561i	0.249064	−	0.968487i	$-0.419877\pi$
$272$	−8.54854	+	7.69714i	−0.518331	+	0.466708i
$273$	−12.2660	−	7.08177i	−0.742371	−	0.428608i
$274$	−0.753605	−	1.30528i	−0.0455269	−	0.0788549i
$275$		0			0
$276$	−3.64262	+	1.62180i	−0.219260	+	0.0976207i
$277$	2.99878	+	4.12746i	0.180179	+	0.247995i	0.889548	−	0.456843i	$-0.151020\pi$
$277$	2.99878	+	4.12746i	0.180179	+	0.247995i	−0.709368	+	0.704838i	$0.751020\pi$
$278$		−	10.2587i		−	0.615277i
$279$	15.5722	+	26.0032i	0.932282	+	1.55677i
$280$		0			0
$281$	3.96958	−	2.88407i	0.236805	−	0.172049i	−0.463053	−	0.886330i	$-0.653246\pi$
$281$	3.96958	−	2.88407i	0.236805	−	0.172049i	0.699859	+	0.714281i	$0.253246\pi$
$282$	9.75198	+	21.9033i	0.580722	+	1.30432i
$283$	−14.6470	−	4.75911i	−0.870675	−	0.282899i	−0.160595	−	0.987020i	$-0.551341\pi$
$283$	−14.6470	−	4.75911i	−0.870675	−	0.282899i	−0.710080	+	0.704121i	$0.751341\pi$
$284$	0.821367	+	1.42265i	0.0487392	+	0.0844188i
$285$		0			0
$286$	3.70777	+	4.11790i	0.219245	+	0.243496i
$287$	−0.671653	+	0.218233i	−0.0396464	+	0.0128819i
$288$	3.93475	+	3.54287i	0.231858	+	0.208765i
$289$	9.03814	+	4.02404i	0.531655	+	0.236708i
$290$		0			0
$291$	4.51976	+	43.0026i	0.264953	+	2.52086i
$292$	−0.262568	−	0.0275970i	−0.0153656	−	0.00161499i
$293$	−3.08839	+	14.5297i	−0.180426	+	0.848835i	0.791060	+	0.611738i	$0.209529\pi$
$293$	−3.08839	+	14.5297i	−0.180426	+	0.848835i	−0.971486	+	0.237097i	$0.923804\pi$
$294$	17.1860	+	12.4864i	1.00231	+	0.728220i
$295$		0			0
$296$	25.1398	+	5.34363i	1.46122	+	0.310592i
$297$	−18.8376	−	1.97991i	−1.09307	−	0.114886i
$298$	30.4724	−	3.20278i	1.76522	−	0.185532i
$299$	−10.9726	+	2.33229i	−0.634561	+	0.134880i
$300$		0			0
$301$	−7.45296	+	8.27735i	−0.429582	+	0.477099i
$302$	−0.205108	+	0.0666438i	−0.0118027	+	0.00383492i
$303$	−19.4382	+	17.5022i	−1.11670	+	1.00548i
$304$	−9.96727	+	17.2638i	−0.571662	+	0.990148i
$305$		0			0
$306$	−6.60964	+	20.3424i	−0.377848	+	1.16290i
$307$	9.15872	+	20.5708i	0.522716	+	1.17404i	0.961339	+	0.275368i	$0.0887997\pi$
$307$	9.15872	+	20.5708i	0.522716	+	1.17404i	−0.438623	+	0.898671i	$0.644534\pi$
$308$	−0.934819	−	1.28667i	−0.0532663	−	0.0733147i
$309$	6.22558			0.354161
$310$		0			0
$311$	9.55538			0.541836			0.270918	−	0.962602i	$-0.412673\pi$
$311$	9.55538			0.541836			0.270918	+	0.962602i	$0.412673\pi$
$312$	6.48448	+	8.92513i	0.367112	+	0.505286i
$313$	5.58387	+	12.5416i	0.315619	+	0.708892i	0.999791	−	0.0204285i	$-0.00650305\pi$
$313$	5.58387	+	12.5416i	0.315619	+	0.708892i	−0.684172	+	0.729320i	$0.739836\pi$
$314$	0.189101	−	0.581992i	0.0106716	−	0.0328437i
$315$		0			0
$316$	0.852639	−	1.47681i	0.0479647	−	0.0830772i
$317$	22.2105	−	19.9984i	1.24746	−	1.12322i	0.259961	−	0.965619i	$-0.416290\pi$
$317$	22.2105	−	19.9984i	1.24746	−	1.12322i	0.987503	−	0.157602i	$-0.0503764\pi$
$318$	15.8258	−	5.14212i	0.887467	−	0.288356i
$319$	16.8009	−	18.6593i	0.940672	−	1.04472i
$320$		0			0
$321$	17.6838	−	3.75880i	0.987011	−	0.209796i
$322$	40.3473	−	4.24068i	2.24847	−	0.236324i
$323$	−12.2478	−	1.28730i	−0.681488	−	0.0716273i
$324$	0.725644	+	0.154240i	0.0403136	+	0.00856891i
$325$		0			0
$326$	−12.5687	−	9.13170i	−0.696116	−	0.505758i
$327$	−8.81485	+	41.4706i	−0.487462	+	2.29333i
$328$	0.547064	+	0.0574987i	0.0302065	+	0.00317483i
$329$	−2.02368	−	19.2540i	−0.111569	−	1.06151i
$330$		0			0
$331$	−12.5135	−	5.57139i	−0.687807	−	0.306231i	0.0329126	−	0.999458i	$-0.489522\pi$
$331$	−12.5135	−	5.57139i	−0.687807	−	0.306231i	−0.720719	+	0.693227i	$0.756188\pi$
$332$	0.895322	+	0.806151i	0.0491372	+	0.0442433i
$333$	49.3980	−	16.0504i	2.70700	−	0.879556i
$334$	14.4951	+	16.0985i	0.793139	+	0.880870i
$335$		0			0
$336$	−21.6816	−	37.5537i	−1.18283	−	2.04872i
$337$	9.41650	+	3.05961i	0.512950	+	0.166667i	0.554043	−	0.832488i	$-0.313084\pi$
$337$	9.41650	+	3.05961i	0.512950	+	0.166667i	−0.0410937	+	0.999155i	$0.513084\pi$
$338$	6.60254	+	14.8295i	0.359131	+	0.806621i
$339$	−26.6119	+	19.3347i	−1.44536	+	1.05012i
$340$		0			0
$341$	−1.31621	+	14.7932i	−0.0712766	+	0.801094i
$342$			37.0666i			2.00433i
$343$	4.14685	+	5.70765i	0.223909	+	0.308184i
$344$	7.92562	−	3.52871i	0.427321	−	0.190256i
$345$		0			0
$346$	12.8969	+	22.3381i	0.693343	+	1.20090i
$347$	−19.0913	−	11.0224i	−1.02487	−	0.591711i	−0.109362	−	0.994002i	$-0.534881\pi$
$347$	−19.0913	−	11.0224i	−1.02487	−	0.591711i	−0.915512	+	0.402291i	$0.868214\pi$
$348$	−3.50447	+	3.15544i	−0.187859	+	0.169149i
$349$	5.14640	+	15.8390i	0.275480	+	0.847842i	0.989092	+	0.147300i	$0.0470582\pi$
$349$	5.14640	+	15.8390i	0.275480	+	0.847842i	−0.713611	+	0.700542i	$0.752942\pi$
$350$		0			0
$351$	9.14300	+	4.07073i	0.488017	+	0.217279i
$352$	0.539410	+	2.53772i	0.0287507	+	0.135261i
$353$	−8.66048	+	0.910253i	−0.460951	+	0.0484479i	−0.332158	−	0.943224i	$-0.607777\pi$
$353$	−8.66048	+	0.910253i	−0.460951	+	0.0484479i	−0.128793	+	0.991672i	$0.541110\pi$
$354$	−4.70137	+	44.7305i	−0.249875	+	2.37740i
$355$		0			0
$356$	1.82819	+	1.32826i	0.0968941	+	0.0703977i
$357$	15.7463	−	21.6730i	0.833385	−	1.14706i
$358$	4.35511	−	20.4892i	0.230175	−	1.08289i
$359$	−1.51620	+	14.4256i	−0.0800218	+	0.761357i	0.878770	+	0.477246i	$0.158365\pi$
$359$	−1.51620	+	14.4256i	−0.0800218	+	0.761357i	−0.958792	+	0.284111i	$0.908302\pi$
$360$		0			0
$361$	−2.29072	+	0.486908i	−0.120564	+	0.0256267i
$362$	12.7601	−	28.6596i	0.670656	−	1.50632i
$363$	8.38907	+	7.55355i	0.440312	+	0.396459i
$364$	0.259680	+	0.799213i	0.0136109	+	0.0418901i
$365$		0			0
$366$	3.01495	−	5.22205i	0.157594	−	0.272961i
$367$	−12.4593	+	7.19340i	−0.650372	+	0.375493i	−0.788599	−	0.614908i	$-0.789193\pi$
$367$	−12.4593	+	7.19340i	−0.650372	+	0.375493i	0.138227	+	0.990401i	$0.455860\pi$
$368$	−32.6634	−	10.6130i	−1.70270	−	0.553239i
$369$	1.01555	−	0.452150i	0.0528672	−	0.0235380i
$370$		0			0
$371$	−13.4365			−0.697590
$372$	0.536264	−	2.73729i	0.0278040	−	0.141922i
$373$		−	18.6605i		−	0.966203i	−0.875564	−	0.483102i	$-0.839510\pi$
$373$		−	18.6605i		−	0.966203i	0.875564	−	0.483102i	$-0.160490\pi$
$374$	−8.47909	+	6.16042i	−0.438443	+	0.318548i
$375$		0			0
$376$	−4.65988	+	14.3416i	−0.240315	+	0.739614i
$377$	−11.4895	+	6.63345i	−0.591738	+	0.341640i
$378$	−31.3463	−	18.0978i	−1.61228	−	0.930849i
$379$	−8.57853	−	9.52743i	−0.440650	−	0.489391i	0.481379	−	0.876513i	$-0.340136\pi$
$379$	−8.57853	−	9.52743i	−0.440650	−	0.489391i	−0.922029	+	0.387121i	$0.873469\pi$
$380$		0			0
$381$	12.7337	−	14.1422i	0.652369	−	0.724529i
$382$	−8.24521	+	18.5191i	−0.421862	+	0.947517i
$383$	−5.80583	−	27.3143i	−0.296664	−	1.39570i	−0.833738	−	0.552160i	$-0.813804\pi$
$383$	−5.80583	−	27.3143i	−0.296664	−	1.39570i	0.537074	−	0.843535i	$-0.319530\pi$
$384$	3.81266	+	36.2751i	0.194564	+	1.85115i
$385$		0			0
$386$	−29.4168	−	6.25274i	−1.49728	−	0.318256i
$387$	10.3055	−	14.1843i	0.523856	−	0.721026i
$388$	1.50794	−	2.07550i	0.0765540	−	0.105367i
$389$	3.79125	+	0.805855i	0.192224	+	0.0408585i	0.303018	−	0.952985i	$-0.402006\pi$
$389$	3.79125	+	0.805855i	0.192224	+	0.0408585i	−0.110794	+	0.993843i	$0.535339\pi$
$390$		0			0
$391$	−2.21783	−	21.1012i	−0.112160	−	1.06714i
$392$	2.77785	+	13.0688i	0.140303	+	0.660072i
$393$	−1.53192	+	3.44075i	−0.0772751	+	0.173563i
$394$	15.1359	−	16.8101i	0.762536	−	0.846882i
$395$		0			0
$396$	1.67514	+	1.86043i	0.0841789	+	0.0934901i
$397$	23.8574	+	13.7741i	1.19737	+	0.691300i	0.959967	−	0.280112i	$-0.0903716\pi$
$397$	23.8574	+	13.7741i	1.19737	+	0.691300i	0.237399	+	0.971412i	$0.423705\pi$
$398$	−18.9797	+	10.9579i	−0.951364	+	0.549270i
$399$	14.3460	−	44.1525i	0.718199	−	2.21039i
$400$		0			0
$401$	9.00271	−	6.54085i	0.449574	−	0.326635i	−0.339854	−	0.940478i	$-0.610378\pi$
$401$	9.00271	−	6.54085i	0.449574	−	0.326635i	0.789427	+	0.613844i	$0.210378\pi$
$402$		−	20.0910i		−	1.00205i
$403$	3.07683	−	7.21895i	0.153268	−	0.359602i
$404$	1.55191			0.0772105
$405$		0			0
$406$	43.8325	−	19.5155i	2.17537	−	0.968537i
$407$	24.2050	+	7.86470i	1.19980	+	0.389839i
$408$	−18.0708	+	10.4332i	−0.894636	+	0.516519i
$409$	−1.26897	+	2.19793i	−0.0627468	+	0.108681i	−0.895692	−	0.444674i	$-0.853319\pi$
$409$	−1.26897	+	2.19793i	−0.0627468	+	0.108681i	0.832946	+	0.553355i	$0.186653\pi$
$410$		0			0
$411$	−0.918232	−	2.82603i	−0.0452930	−	0.139398i
$412$	−0.274497	−	0.247158i	−0.0135235	−	0.0121766i
$413$	14.7717	−	33.1778i	0.726868	−	1.63257i
$414$	−62.4649	+	13.2773i	−3.06998	+	0.652545i
$415$		0			0
$416$	0.143292	−	1.36333i	0.00702547	−	0.0668429i
$417$	4.20502	−	19.7831i	0.205921	−	0.968782i
$418$	−10.6757	+	14.6939i	−0.522167	+	0.718702i
$419$	14.6114	+	10.6158i	0.713812	+	0.518615i	0.884401	−	0.466727i	$-0.154567\pi$
$419$	14.6114	+	10.6158i	0.713812	+	0.518615i	−0.170589	+	0.985342i	$0.554567\pi$
$420$		0			0
$421$	0.184868	−	1.75890i	0.00900991	−	0.0857236i	−0.989093	−	0.147293i	$-0.952944\pi$
$421$	0.184868	−	1.75890i	0.00900991	−	0.0857236i	0.998103	+	0.0615695i	$0.0196106\pi$
$422$	12.9992	−	1.36627i	0.632793	−	0.0665092i
$423$	6.33603	+	29.8087i	0.308068	+	1.44935i
$424$	9.56098	+	4.25682i	0.464322	+	0.206730i
$425$		0			0
$426$	12.6106	+	38.8114i	0.610986	+	1.88042i
$427$	−3.61836	+	3.25799i	−0.175105	+	0.157665i
$428$	−0.928935	−	0.536321i	−0.0449018	−	0.0259240i
$429$	5.46221	+	9.46083i	0.263718	+	0.456773i
$430$		0			0
$431$	0.267400	−	0.119054i	0.0128802	−	0.00573463i	−0.400286	−	0.916390i	$-0.631089\pi$
$431$	0.267400	−	0.119054i	0.0128802	−	0.00573463i	0.413167	+	0.910655i	$0.364423\pi$
$432$	18.0106	+	24.7894i	0.866534	+	1.19268i
$433$			4.00282i			0.192363i	0.995364	+	0.0961816i	$0.0306630\pi$
$433$			4.00282i			0.192363i	−0.995364	+	0.0961816i	$0.969337\pi$
$434$	−13.7956	+	24.8016i	−0.662210	+	1.19052i
$435$		0			0
$436$	2.03506	−	1.47856i	0.0974619	−	0.0708102i
$437$	−14.9553	−	33.5901i	−0.715408	−	1.60683i
$438$	−6.23762	−	2.02673i	−0.298045	−	0.0968407i
$439$	−2.03306	−	3.52136i	−0.0970325	−	0.168065i	0.813423	−	0.581673i	$-0.197602\pi$
$439$	−2.03306	−	3.52136i	−0.0970325	−	0.168065i	−0.910455	+	0.413608i	$0.864268\pi$
$440$		0			0
$441$	18.0670	+	20.0655i	0.860335	+	0.955499i
$442$	5.26678	−	1.71128i	0.250515	−	0.0813973i
$443$	6.76020	+	6.08691i	0.321187	+	0.289198i	0.813913	−	0.580986i	$-0.197333\pi$
$443$	6.76020	+	6.08691i	0.321187	+	0.289198i	−0.492726	+	0.870184i	$0.664000\pi$
$444$	−4.36673	−	1.94419i	−0.207236	−	0.0922673i
$445$		0			0
$446$	−3.33950	−	31.7733i	−0.158130	−	1.50451i
$447$	60.0763	+	6.31427i	2.84151	+	0.298655i
$448$	5.17454	−	24.3443i	0.244474	−	1.15016i
$449$	−4.30026	−	3.12433i	−0.202942	−	0.147446i	0.481673	−	0.876351i	$-0.340029\pi$
$449$	−4.30026	−	3.12433i	−0.202942	−	0.147446i	−0.684615	+	0.728905i	$0.740029\pi$
$450$		0			0
$451$	0.532807	+	0.113252i	0.0250889	+	0.00533281i
$452$	1.94097	+	0.204004i	0.0912953	+	0.00959553i
$453$	−0.422852	+	0.0444435i	−0.0198673	+	0.00208814i
$454$	4.60437	−	0.978690i	0.216094	−	0.0459322i
$455$		0			0
$456$	−24.1961	+	26.8725i	−1.13308	+	1.25842i
$457$	−5.93396	+	1.92806i	−0.277579	+	0.0901909i	−0.444498	−	0.895780i	$-0.646618\pi$
$457$	−5.93396	+	1.92806i	−0.277579	+	0.0901909i	0.166919	+	0.985971i	$0.446618\pi$
$458$	−9.46112	+	8.51883i	−0.442089	+	0.398059i
$459$	−9.46494	+	16.3938i	−0.441786	+	0.765195i
$460$		0			0
$461$	8.34338	−	25.6783i	0.388590	−	1.19596i	−0.545252	−	0.838272i	$-0.683566\pi$
$461$	8.34338	−	25.6783i	0.388590	−	1.19596i	0.933842	−	0.357685i	$-0.116434\pi$
$462$	−16.0697	−	36.0932i	−0.747631	−	1.67921i
$463$	8.64731	+	11.9020i	0.401875	+	0.553133i	0.961213	−	0.275806i	$-0.0889448\pi$
$463$	8.64731	+	11.9020i	0.401875	+	0.553133i	−0.559339	+	0.828939i	$0.688945\pi$
$464$	−40.6181			−1.88565
$465$		0			0
$466$	−10.9643			−0.507910
$467$	16.6548	+	22.9234i	0.770694	+	1.06077i	0.996249	+	0.0865383i	$0.0275805\pi$
$467$	16.6548	+	22.9234i	0.770694	+	1.06077i	−0.225555	+	0.974230i	$0.572419\pi$
$468$	−0.538022	−	1.20842i	−0.0248701	−	0.0558591i
$469$	−5.01315	+	15.4289i	−0.231486	+	0.712440i
$470$		0			0
$471$	0.603222	−	1.04481i	0.0277950	−	0.0481424i
$472$	−21.0221	+	18.9284i	−0.967620	+	0.871249i
$473$	8.17055	−	2.65477i	0.375682	−	0.122067i
$474$	28.3460	−	31.4814i	1.30198	−	1.44599i
$475$		0			0
$476$	−1.55471	+	0.330464i	−0.0712601	+	0.0151468i
$477$	21.0345	−	2.21082i	0.963104	−	0.101226i
$478$	−35.9277	−	3.77616i	−1.64330	−	0.172717i
$479$	−5.96591	−	1.26809i	−0.272589	−	0.0579407i	0.0695887	−	0.997576i	$-0.477831\pi$
$479$	−5.96591	−	1.26809i	−0.272589	−	0.0579407i	−0.342178	+	0.939635i	$0.611165\pi$
$480$		0			0
$481$	−10.8794	−	7.90434i	−0.496057	−	0.360407i
$482$	−2.30974	+	10.8665i	−0.105206	+	0.494953i
$483$	79.5447	+	8.36049i	3.61941	+	0.380415i
$484$	−0.0700099	−	0.666099i	−0.00318227	−	0.0302772i
$485$		0			0
$486$	−11.8482	−	5.27517i	−0.537447	−	0.239287i
$487$	16.0771	+	14.4759i	0.728524	+	0.655966i	0.947497	−	0.319765i	$-0.103604\pi$
$487$	16.0771	+	14.4759i	0.728524	+	0.655966i	−0.218973	+	0.975731i	$0.570271\pi$
$488$	3.60686	−	1.17194i	0.163275	−	0.0530513i
$489$	−20.4947	−	22.7616i	−0.926800	−	1.02932i
$490$		0			0
$491$	0.338579	+	0.586436i	0.0152798	+	0.0264655i	0.873564	−	0.486709i	$-0.161803\pi$
$491$	0.338579	+	0.586436i	0.0152798	+	0.0264655i	−0.858284	+	0.513174i	$0.828469\pi$
$492$	−0.0972967	−	0.0316136i	−0.00438647	−	0.00142525i
$493$	−10.2064	−	22.9239i	−0.459673	−	1.03244i
$494$	7.76397	−	5.64086i	0.349318	−	0.253794i
$495$		0			0
$496$	19.2088	−	14.4305i	0.862501	−	0.647951i
$497$		−	32.9520i		−	1.47810i
$498$	17.5918	+	24.2130i	0.788308	+	1.08501i
$499$	−28.0667	+	12.4961i	−1.25644	+	0.559402i	−0.923519	−	0.383553i	$-0.874700\pi$
$499$	−28.0667	+	12.4961i	−1.25644	+	0.559402i	−0.332919	+	0.942955i	$0.608034\pi$
$500$		0			0
$501$	21.3539	+	36.9861i	0.954024	+	1.65242i
$502$	−12.4107	−	7.16532i	−0.553916	−	0.319804i
$503$	−10.9479	+	9.85750i	−0.488141	+	0.439524i	−0.876083	−	0.482159i	$-0.839853\pi$
$503$	−10.9479	+	9.85750i	−0.488141	+	0.439524i	0.387942	+	0.921684i	$0.373186\pi$
$504$	−15.6709	−	48.2301i	−0.698037	−	2.14834i
$505$		0			0
$506$	−28.5863	−	12.7274i	−1.27082	−	0.565804i
$507$	6.65385	+	31.3039i	0.295508	+	1.39026i
$508$	−1.12291	+	0.118022i	−0.0498209	+	0.00523639i
$509$	2.93549	−	27.9294i	0.130114	−	1.23795i	−0.713368	−	0.700789i	$-0.752831\pi$
$509$	2.93549	−	27.9294i	0.130114	−	1.23795i	0.843482	−	0.537158i	$-0.180502\pi$
$510$		0			0
$511$	4.28448	+	3.11286i	0.189534	+	0.137705i
$512$	−11.1974	+	15.4119i	−0.494860	+	0.681117i
$513$	−6.82048	+	32.0878i	−0.301131	+	1.41671i
$514$	0.398689	−	3.79327i	0.0175854	−	0.167314i
$515$		0			0
$516$	−1.57825	+	0.335467i	−0.0694786	+	0.0147681i
$517$	−6.07362	+	13.6416i	−0.267118	+	0.599956i
$518$	36.1424	+	32.5427i	1.58800	+	1.42985i
$519$	15.7143	+	48.3636i	0.689781	+	2.12293i
$520$		0			0
$521$	−0.658209	+	1.14005i	−0.0288366	+	0.0499465i	−0.880084	−	0.474819i	$-0.842514\pi$
$521$	−0.658209	+	1.14005i	−0.0288366	+	0.0499465i	0.851247	+	0.524765i	$0.175847\pi$
$522$	−65.4075	+	37.7630i	−2.86281	+	1.65284i
$523$	−19.6489	−	6.38431i	−0.859186	−	0.279167i	−0.153898	−	0.988087i	$-0.549183\pi$
$523$	−19.6489	−	6.38431i	−0.859186	−	0.279167i	−0.705289	+	0.708920i	$0.749183\pi$
$524$	0.204144	−	0.0908909i	0.00891809	−	0.00397059i
$525$		0			0
$526$	20.1945			0.880522
$527$	12.9710	+	7.21495i	0.565026	+	0.314288i
$528$			33.4464i			1.45557i
$529$	32.6418	−	23.7157i	1.41921	−	1.03112i
$530$		0			0
$531$	−17.6657	+	54.3694i	−0.766625	+	2.35943i
$532$	−2.38541	+	1.37722i	−0.103421	+	0.0597100i
$533$	−0.249255	−	0.143907i	−0.0107964	−	0.00623331i
$534$	37.5631	+	41.7181i	1.62552	+	1.80532i
$535$		0			0
$536$	8.45521	−	9.39046i	0.365210	−	0.405606i
$537$	16.7969	−	37.7265i	0.724841	−	1.62802i
$538$	6.23326	+	29.3252i	0.268735	+	1.26430i
$539$	1.38295	+	13.1579i	0.0595679	+	0.566751i
$540$		0			0
$541$	−44.1743	−	9.38953i	−1.89920	−	0.403688i	−0.899737	−	0.436432i	$-0.856242\pi$
$541$	−44.1743	−	9.38953i	−1.89920	−	0.403688i	−0.999464	+	0.0327444i	$0.989575\pi$
$542$	−24.0773	+	33.1396i	−1.03421	+	1.42347i
$543$	36.3543	−	50.0374i	1.56011	−	2.14731i
$544$	2.53619	+	0.539083i	0.108738	+	0.0231130i
$545$		0			0
$546$	2.18211	+	20.7614i	0.0933857	+	0.888506i
$547$	−8.28680	−	38.9863i	−0.354318	−	1.66694i	−0.689120	−	0.724647i	$-0.742003\pi$
$547$	−8.28680	−	38.9863i	−0.354318	−	1.66694i	0.334802	−	0.942288i	$-0.391330\pi$
$548$	−0.0717080	+	0.161059i	−0.00306322	+	0.00688009i
$549$	5.12838	−	5.69564i	0.218874	−	0.243084i
$550$		0			0
$551$	−29.0976	−	32.3162i	−1.23960	−	1.37672i
$552$	−53.9526	−	31.1496i	−2.29638	−	1.32581i
$553$	−29.6237	+	17.1033i	−1.25973	+	0.727304i
$554$	2.32369	−	7.15159i	0.0987242	−	0.303842i
$555$		0			0
$556$	−0.970804	+	0.705331i	−0.0411713	+	0.0299127i
$557$			19.9182i			0.843963i	0.906604	+	0.421982i	$0.138665\pi$
$557$			19.9182i			0.843963i	−0.906604	+	0.421982i	$0.861335\pi$
$558$	17.5158	−	41.0962i	0.741504	−	1.73974i
$559$	−4.53934			−0.191993
$560$		0			0
$561$	−18.8764	+	8.40430i	−0.796961	+	0.354830i
$562$	−6.87803	−	2.23481i	−0.290132	−	0.0942697i
$563$	28.1963	−	16.2792i	1.18833	−	0.686085i	0.230406	−	0.973095i	$-0.425994\pi$
$563$	28.1963	−	16.2792i	1.18833	−	0.686085i	0.957928	+	0.287010i	$0.0926611\pi$
$564$	1.40227	−	2.42880i	0.0590461	−	0.102271i
$565$		0			0
$566$	7.01449	+	21.5884i	0.294841	+	0.907427i
$567$	−11.0588	−	9.95735i	−0.464424	−	0.418170i
$568$	−10.4395	+	23.4475i	−0.438032	+	0.983835i
$569$	3.17999	−	0.675928i	0.133312	−	0.0283364i	−0.140772	−	0.990042i	$-0.544959\pi$
$569$	3.17999	−	0.675928i	0.133312	−	0.0283364i	0.274084	+	0.961706i	$0.411625\pi$
$570$		0			0
$571$	−0.840471	+	7.99655i	−0.0351726	+	0.334645i	0.962759	+	0.270361i	$0.0871431\pi$
$571$	−0.840471	+	7.99655i	−0.0351726	+	0.334645i	−0.997932	+	0.0642841i	$0.979524\pi$
$572$	0.134760	−	0.633998i	0.00563461	−	0.0265088i
$573$	−23.4911	+	32.3328i	−0.981356	+	1.35072i
$574$	0.842106	+	0.611826i	0.0351488	+	0.0255371i
$575$		0			0
$576$	−4.09504	+	38.9617i	−0.170627	+	1.62341i
$577$	25.6525	−	2.69618i	1.06793	−	0.112244i	0.445779	−	0.895143i	$-0.352927\pi$
$577$	25.6525	−	2.69618i	1.06793	−	0.112244i	0.622148	+	0.782900i	$0.286260\pi$
$578$	−3.03178	−	14.2634i	−0.126106	−	0.593280i
$579$	−54.1649	−	24.1158i	−2.25102	−	1.00222i
$580$		0			0
$581$	−7.46796	−	22.9840i	−0.309823	−	0.953537i
$582$	47.3614	−	42.6444i	1.96319	−	1.76767i
$583$	8.97522	+	5.18184i	0.371715	+	0.214610i
$584$	−2.06251	−	3.57237i	−0.0853472	−	0.147826i
$585$		0			0
$586$	20.0011	−	8.90506i	0.826237	−	0.367864i
$587$	1.12831	+	1.55298i	0.0465701	+	0.0640983i	0.831667	−	0.555275i	$-0.187387\pi$
$587$	1.12831	+	1.55298i	0.0465701	+	0.0640983i	−0.785097	+	0.619373i	$0.787387\pi$
$588$		−	2.48484i		−	0.102473i
$589$	25.2417	+	4.94511i	1.04007	+	0.203760i
$590$		0			0
$591$	36.0788	−	26.2128i	1.48408	−	1.07825i
$592$	−16.7460	−	37.6121i	−0.688255	−	1.54585i
$593$	−11.6701	−	3.79186i	−0.479235	−	0.155713i	0.0594306	−	0.998232i	$-0.481071\pi$
$593$	−11.6701	−	3.79186i	−0.479235	−	0.155713i	−0.538666	+	0.842519i	$0.681071\pi$
$594$	13.9589	+	24.1776i	0.572742	+	0.992018i
$595$		0			0
$596$	−2.39819	−	2.66346i	−0.0982338	−	0.109100i
$597$	−41.0923	+	13.3517i	−1.68180	+	0.546449i
$598$	12.2871	+	11.0633i	0.502456	+	0.452413i
$599$	1.61046	+	0.717023i	0.0658016	+	0.0292968i	0.439374	−	0.898304i	$-0.355200\pi$
$599$	1.61046	+	0.717023i	0.0658016	+	0.0292968i	−0.373572	+	0.927601i	$0.621867\pi$
$600$		0			0
$601$	0.814152	+	7.74614i	0.0332099	+	0.315971i	0.998498	+	0.0547846i	$0.0174472\pi$
$601$	0.814152	+	7.74614i	0.0332099	+	0.315971i	−0.965288	+	0.261187i	$0.915886\pi$
$602$	16.3269	+	1.71602i	0.665434	+	0.0699399i
$603$	5.30931	−	24.9784i	0.216212	−	1.01720i
$604$	0.0204087	+	0.0148278i	0.000830419	+	0.000603335i
$605$		0			0
$606$	37.7101	+	8.01553i	1.53187	+	0.325609i
$607$	1.70943	+	0.179668i	0.0693837	+	0.00729252i	0.139157	−	0.990270i	$-0.455561\pi$
$607$	1.70943	+	0.179668i	0.0693837	+	0.00729252i	−0.0697730	+	0.997563i	$0.522228\pi$
$608$	4.46867	−	0.469677i	0.181229	−	0.0190479i
$609$	92.5266	−	19.6671i	3.74937	−	0.796953i
$610$		0			0
$611$	5.27950	−	5.86348i	0.213586	−	0.237211i
$612$	2.37948	−	0.773141i	0.0961849	−	0.0312524i
$613$	−15.8323	+	14.2554i	−0.639459	+	0.575772i	−0.923764	−	0.382962i	$-0.874904\pi$
$613$	−15.8323	+	14.2554i	−0.639459	+	0.575772i	0.284305	+	0.958734i	$0.408237\pi$
$614$	16.5944	−	28.7424i	0.669696	−	1.15995i
$615$		0			0
$616$	7.67874	−	23.6327i	0.309385	−	0.952190i
$617$	−5.82757	−	13.0889i	−0.234609	−	0.526941i	0.757423	−	0.652924i	$-0.226458\pi$
$617$	−5.82757	−	13.0889i	−0.234609	−	0.526941i	−0.992032	+	0.125984i	$0.959791\pi$
$618$	−5.39348	−	7.42349i	−0.216958	−	0.298617i
$619$	9.19099			0.369417			0.184709	−	0.982793i	$-0.440866\pi$
$619$	9.19099			0.369417			0.184709	+	0.982793i	$0.440866\pi$
$620$		0			0
$621$	−56.5177			−2.26798
$622$	−8.27822	−	11.3940i	−0.331926	−	0.456857i
$623$	−18.4371	−	41.4103i	−0.738666	−	1.65907i
$624$	5.46108	−	16.8075i	0.218618	−	0.672837i
$625$		0			0
$626$	10.1172	−	17.5236i	0.404367	−	0.700384i
$627$	−26.6103	+	23.9600i	−1.06271	+	0.956870i
$628$	−0.0680766	+	0.0221194i	−0.00271655	+	0.000882661i
$629$	17.0195	−	18.9021i	0.678612	−	0.753675i
$630$		0			0
$631$	16.6459	−	3.53821i	0.662665	−	0.140854i	0.135712	−	0.990748i	$-0.456668\pi$
$631$	16.6459	−	3.53821i	0.662665	−	0.140854i	0.526953	+	0.849895i	$0.323334\pi$
$632$	26.4977	−	2.78502i	1.05402	−	0.110782i
$633$	25.6280	+	2.69361i	1.01862	+	0.107061i
$634$	−43.0883	−	9.15869i	−1.71125	−	0.363738i
$635$		0			0
$636$	−1.57470	−	1.14409i	−0.0624410	−	0.0453660i
$637$	1.45344	−	6.83792i	0.0575875	−	0.270928i
$638$	−36.8050	−	3.86837i	−1.45713	−	0.153150i
$639$	5.42184	+	51.5854i	0.214485	+	2.04069i
$640$		0			0
$641$	3.54414	+	1.57795i	0.139985	+	0.0623254i	0.475534	−	0.879698i	$-0.342255\pi$
$641$	3.54414	+	1.57795i	0.139985	+	0.0623254i	−0.335549	+	0.942023i	$0.608922\pi$
$642$	−19.8022	−	17.8300i	−0.781532	−	0.703694i
$643$	−21.0244	+	6.83125i	−0.829123	+	0.269398i	−0.692676	−	0.721249i	$-0.743568\pi$
$643$	−21.0244	+	6.83125i	−0.829123	+	0.269398i	−0.136447	+	0.990647i	$0.543568\pi$
$644$	−3.17536	−	3.52659i	−0.125127	−	0.138967i
$645$		0			0
$646$	9.07582	+	15.7198i	0.357083	+	0.618486i
$647$	−36.0479	−	11.7127i	−1.41719	−	0.460472i	−0.502480	−	0.864589i	$-0.667579\pi$
$647$	−36.0479	−	11.7127i	−1.41719	−	0.460472i	−0.914707	+	0.404117i	$0.867579\pi$
$648$	4.71445	+	10.5888i	0.185201	+	0.415969i
$649$	−22.6622	+	16.4650i	−0.889569	+	0.646310i
$650$		0			0
$651$	−36.7698	+	42.1731i	−1.44112	+	1.65289i
$652$			1.81725i			0.0711689i
$653$	−3.76912	−	5.18775i	−0.147497	−	0.203012i	0.728875	−	0.684647i	$-0.240043\pi$
$653$	−3.76912	−	5.18775i	−0.147497	−	0.203012i	−0.876372	+	0.481634i	$0.840043\pi$
$654$	57.0869	−	25.4167i	2.23228	−	0.993873i
$655$		0			0
$656$	−0.440588	−	0.763121i	−0.0172021	−	0.0297949i
$657$	−7.21941	−	4.16813i	−0.281656	−	0.162614i
$658$	−21.2056	+	19.0936i	−0.826682	+	0.744348i
$659$	−3.69830	−	11.3822i	−0.144065	−	0.443387i	0.852824	−	0.522198i	$-0.174888\pi$
$659$	−3.69830	−	11.3822i	−0.144065	−	0.443387i	−0.996890	+	0.0788106i	$0.974888\pi$
$660$		0			0
$661$	9.01893	+	4.01548i	0.350796	+	0.156184i	0.574567	−	0.818457i	$-0.305170\pi$
$661$	9.01893	+	4.01548i	0.350796	+	0.156184i	−0.223772	+	0.974642i	$0.571837\pi$
$662$	4.19759	+	19.7481i	0.163144	+	0.767531i
$663$	10.8580	−	1.14122i	0.421690	−	0.0443214i
$664$	−1.96761	+	18.7206i	−0.0763581	+	0.726499i
$665$		0			0
$666$	−61.9343	−	44.9979i	−2.39991	−	1.74363i
$667$	44.0366	−	60.6112i	1.70510	−	2.34687i
$668$	0.526831	−	2.47855i	0.0203837	−	0.0958978i
$669$	6.58383	−	62.6409i	0.254545	−	2.42184i
$670$		0			0
$671$	3.67341	−	0.780808i	0.141811	−	0.0301428i
$672$	−3.97552	+	8.92915i	−0.153359	+	0.344450i
$673$	−7.57833	−	6.82356i	−0.292123	−	0.263029i	0.510018	−	0.860164i	$-0.329639\pi$
$673$	−7.57833	−	6.82356i	−0.292123	−	0.263029i	−0.802141	+	0.597135i	$0.796306\pi$
$674$	−4.50958	−	13.8791i	−0.173703	−	0.534601i
$675$		0			0
$676$	0.949399	−	1.64441i	0.0365153	−	0.0632464i
$677$	−21.4806	+	12.4018i	−0.825566	+	0.476641i	−0.852332	−	0.523001i	$-0.824812\pi$
$677$	−21.4806	+	12.4018i	−0.825566	+	0.476641i	0.0267663	+	0.999642i	$0.491479\pi$
$678$	46.1101	+	14.9821i	1.77085	+	0.575383i
$679$	−47.0120	+	20.9311i	−1.80415	+	0.803262i
$680$		0			0
$681$	9.28031			0.355622
$682$	18.7799	−	11.2465i	0.719119	−	0.430649i
$683$		−	27.4082i		−	1.04875i	−0.851489	−	0.524373i	$-0.824300\pi$
$683$		−	27.4082i		−	1.04875i	0.851489	−	0.524373i	$-0.175700\pi$
$684$	3.50769	−	2.54849i	0.134120	−	0.0974439i
$685$		0			0
$686$	3.21331	−	9.88955i	0.122685	−	0.377585i
$687$	−21.7368	+	12.5498i	−0.829312	+	0.478803i
$688$	−12.0357	−	6.94884i	−0.458859	−	0.264922i
$689$	−3.66414	−	4.06944i	−0.139593	−	0.155033i
$690$		0			0
$691$	10.0242	−	11.1330i	0.381339	−	0.423520i	−0.521666	−	0.853150i	$-0.674689\pi$
$691$	10.0242	−	11.1330i	0.381339	−	0.423520i	0.903005	+	0.429630i	$0.141356\pi$
$692$	1.22719	−	2.75630i	0.0466506	−	0.104779i
$693$	−10.4408	−	49.1200i	−0.396612	−	1.86591i
$694$	3.39633	+	32.3139i	0.128923	+	1.22662i
$695$		0			0
$696$	−72.0696	−	15.3189i	−2.73179	−	0.580660i
$697$	0.319978	−	0.440412i	0.0121200	−	0.0166818i
$698$	14.4281	−	19.8586i	0.546113	−	0.751660i
$699$	−21.1437	−	4.49423i	−0.799727	−	0.169987i
$700$		0			0
$701$	4.23920	+	40.3333i	0.160113	+	1.52337i	0.719517	+	0.694474i	$0.244363\pi$
$701$	4.23920	+	40.3333i	0.160113	+	1.52337i	−0.559405	+	0.828895i	$0.688970\pi$
$702$	−3.06696	−	14.4289i	−0.115755	−	0.544584i
$703$	17.9282	−	40.2674i	0.676176	−	1.51872i
$704$	−12.8449	+	14.2657i	−0.484111	+	0.537659i
$705$		0			0
$706$	8.58834	+	9.53832i	0.323226	+	0.358979i
$707$	−26.9595	−	15.5651i	−1.01392	−	0.585385i
$708$	4.55618	−	2.63051i	0.171232	−	0.0988607i
$709$	−12.6179	+	38.8338i	−0.473874	+	1.45844i	0.373595	+	0.927592i	$0.378125\pi$
$709$	−12.6179	+	38.8338i	−0.473874	+	1.45844i	−0.847470	+	0.530844i	$0.821875\pi$
$710$		0			0
$711$	43.5609	−	31.6489i	1.63366	−	1.18693i
$712$			35.3072i			1.32319i
$713$	0.708091	+	44.3088i	0.0265182	+	1.65938i
$714$	−39.4849			−1.47769
$715$		0			0
$716$	−2.23837	+	0.996585i	−0.0836517	+	0.0372441i
$717$	−67.7358	−	22.0087i	−2.52964	−	0.821930i
$718$	18.5149	−	10.6896i	0.690971	−	0.398932i
$719$	3.15103	−	5.45775i	0.117514	−	0.203540i	−0.801268	−	0.598305i	$-0.795841\pi$
$719$	3.15103	−	5.45775i	0.117514	−	0.203540i	0.918782	+	0.394766i	$0.129174\pi$
$720$		0			0
$721$	2.28960	+	7.04668i	0.0852693	+	0.262432i
$722$	2.56514	+	2.30967i	0.0954648	+	0.0859569i
$723$	−8.90827	+	20.0083i	−0.331302	+	0.744117i
$724$	−3.58943	+	0.762958i	−0.133400	+	0.0283551i
$725$		0			0
$726$	1.73918	−	16.5472i	0.0645471	−	0.614125i
$727$	6.72695	−	31.6478i	0.249489	−	1.17375i	−0.657783	−	0.753208i	$-0.728506\pi$
$727$	6.72695	−	31.6478i	0.249489	−	1.17375i	0.907272	−	0.420545i	$-0.138161\pi$
$728$	−7.71745	+	10.6222i	−0.286028	+	0.393683i
$729$	−31.1296	−	22.6170i	−1.15295	−	0.837665i
$730$		0			0
$731$	0.897462	−	8.53878i	0.0331938	−	0.315818i
$732$	−0.701465	+	0.0737269i	−0.0259269	+	0.00272503i
$733$	−4.28094	−	20.1402i	−0.158120	−	0.743897i	−0.983730	−	0.179655i	$-0.942502\pi$
$733$	−4.28094	−	20.1402i	−0.158120	−	0.743897i	0.825610	−	0.564242i	$-0.190831\pi$
$734$	19.3716	+	8.62478i	0.715018	+	0.318346i
$735$		0			0
$736$	2.39219	+	7.36239i	0.0881772	+	0.271381i
$737$	9.29885	−	8.37272i	0.342527	−	0.308413i
$738$	−1.41896	−	0.819238i	−0.0522327	−	0.0301566i
$739$	−18.6769	−	32.3494i	−0.687041	−	1.18999i	−0.972791	−	0.231686i	$-0.925576\pi$
$739$	−18.6769	−	32.3494i	−0.687041	−	1.18999i	0.285749	−	0.958304i	$-0.407758\pi$
$740$		0			0
$741$	17.2844	−	7.69549i	0.634957	−	0.282701i
$742$	11.6406	+	16.0219i	0.427341	+	0.588184i
$743$			6.28553i			0.230594i	0.993331	+	0.115297i	$0.0367819\pi$
$743$			6.28553i			0.230594i	−0.993331	+	0.115297i	$0.963218\pi$
$744$	39.5250	−	18.3599i	1.44906	−	0.673108i
$745$		0			0
$746$	−22.2511	+	16.1664i	−0.814670	+	0.591892i
$747$	15.4726	+	34.7521i	0.566113	+	1.27151i
$748$	1.16595	+	0.378839i	0.0426313	+	0.0138517i
$749$	10.7582	+	18.6337i	0.393095	+	0.680860i
$750$		0			0
$751$	2.94353	+	3.26912i	0.107411	+	0.119292i	0.794453	−	0.607326i	$-0.207758\pi$
$751$	2.94353	+	3.26912i	0.107411	+	0.119292i	−0.687042	+	0.726618i	$0.741091\pi$
$752$	22.9741	−	7.46473i	0.837779	−	0.272211i
$753$	−20.9959	−	18.9048i	−0.765135	−	0.688930i
$754$	17.8637	+	7.95341i	0.650556	+	0.289646i
$755$		0			0
$756$	0.442558	+	4.21066i	0.0160957	+	0.153140i
$757$	−1.81984	−	0.191273i	−0.0661431	−	0.00695192i	0.0713991	−	0.997448i	$-0.477254\pi$
$757$	−1.81984	−	0.191273i	−0.0661431	−	0.00695192i	−0.137542	+	0.990496i	$0.543920\pi$
$758$	−3.92872	+	18.4832i	−0.142698	+	0.671340i
$759$	−49.9093	−	36.2613i	−1.81159	−	1.31620i
$760$		0			0
$761$	17.5931	+	3.73953i	0.637750	+	0.135558i	0.515429	−	0.856933i	$-0.327633\pi$
$761$	17.5931	+	3.73953i	0.637750	+	0.135558i	0.122322	+	0.992491i	$0.460966\pi$
$762$	−27.8952	−	2.93190i	−1.01054	−	0.106212i
$763$	−50.1821	+	5.27435i	−1.81671	+	0.190944i
$764$	2.31939	−	0.493002i	0.0839126	−	0.0178362i
$765$		0			0
$766$	−27.5402	+	30.5865i	−0.995067	+	1.10513i
$767$	14.0766	−	4.57376i	0.508277	−	0.165149i
$768$	8.87069	−	7.98720i	0.320093	−	0.288213i
$769$	−9.46486	+	16.3936i	−0.341311	+	0.591169i	−0.984677	−	0.174391i	$-0.944204\pi$
$769$	−9.46486	+	16.3936i	−0.341311	+	0.591169i	0.643365	+	0.765560i	$0.277538\pi$
$770$		0			0
$771$	2.32369	−	7.15159i	0.0836857	−	0.257558i
$772$	1.43082	+	3.21368i	0.0514964	+	0.115663i
$773$	12.3488	+	16.9967i	0.444156	+	0.611328i	0.971129	−	0.238554i	$-0.0766732\pi$
$773$	12.3488	+	16.9967i	0.444156	+	0.611328i	−0.526973	+	0.849882i	$0.676673\pi$
$774$	−25.8416			−0.928857
$775$		0			0
$776$	40.0833			1.43891
$777$	56.3583	+	77.5706i	2.02184	+	2.78283i
$778$	−2.32360	−	5.21889i	−0.0833051	−	0.187106i
$779$	0.291523	−	0.897214i	0.0104449	−	0.0321460i
$780$		0			0
$781$	−12.7080	+	22.0110i	−0.454729	+	0.787614i
$782$	−23.2401	+	20.9255i	−0.831063	+	0.748293i
$783$	−63.5705	+	20.6553i	−2.27183	+	0.738161i
$784$	14.3212	−	15.9053i	0.511473	−	0.568048i
$785$		0			0
$786$	5.42997	−	1.15418i	0.193681	−	0.0411681i
$787$	23.4700	−	2.46680i	0.836615	−	0.0879318i	0.323475	−	0.946237i	$-0.395149\pi$
$787$	23.4700	−	2.46680i	0.836615	−	0.0879318i	0.513140	+	0.858305i	$0.328482\pi$
$788$	−2.63144	−	0.276575i	−0.0937410	−	0.00985258i
$789$	38.9434	+	8.27768i	1.38642	+	0.294693i
$790$		0			0
$791$	−31.6719	−	23.0110i	−1.12612	−	0.818178i
$792$	−8.13238	+	38.2598i	−0.288972	+	1.35950i
$793$	−1.97345	−	0.207418i	−0.0700794	−	0.00736564i
$794$	−4.24421	−	40.3810i	−0.150621	−	1.43307i
$795$		0			0
$796$	2.34190	+	1.04268i	0.0830065	+	0.0369569i
$797$	−18.3363	−	16.5101i	−0.649506	−	0.584818i	0.277105	−	0.960840i	$-0.410625\pi$
$797$	−18.3363	−	16.5101i	−0.649506	−	0.584818i	−0.926611	+	0.376022i	$0.877292\pi$
$798$	−65.0767	+	21.1447i	−2.30369	+	0.748514i
$799$	9.98578	+	11.0903i	0.353271	+	0.392348i
$800$		0			0
$801$	35.6763	+	61.7931i	1.26056	+	2.18335i
$802$	−15.5988	−	5.06837i	−0.550814	−	0.178970i
$803$	−1.66143	−	3.73162i	−0.0586304	−	0.131686i
$804$	−1.90125	+	1.38134i	−0.0670520	+	0.0487161i
$805$		0			0
$806$	−11.2736	+	2.58522i	−0.397095	+	0.0910604i
$807$			59.1061i			2.08063i
$808$	14.2523	+	19.6166i	0.501394	+	0.690110i
$809$	11.3204	−	5.04018i	0.398005	−	0.177203i	−0.197966	−	0.980209i	$-0.563434\pi$
$809$	11.3204	−	5.04018i	0.398005	−	0.177203i	0.595972	+	0.803005i	$0.296767\pi$
$810$		0			0
$811$	27.1897	+	47.0939i	0.954758	+	1.65369i	0.734921	+	0.678153i	$0.237219\pi$
$811$	27.1897	+	47.0939i	0.954758	+	1.65369i	0.219837	+	0.975537i	$0.429447\pi$
$812$	−4.86046	−	2.80619i	−0.170569	−	0.0984779i
$813$	−60.0150	+	54.0378i	−2.10482	+	1.89519i
$814$	−11.5918	−	35.6760i	−0.406294	−	1.25044i
$815$		0			0
$816$	30.5362	+	13.5956i	1.06898	+	0.475942i
$817$	−3.09349	−	14.5537i	−0.108227	−	0.509170i
$818$	3.72021	−	0.391010i	0.130074	−	0.0136713i
$819$	−2.77355	+	26.3885i	−0.0969155	+	0.922090i
$820$		0			0
$821$	−19.9227	−	14.4747i	−0.695306	−	0.505169i	0.183094	−	0.983095i	$-0.441389\pi$
$821$	−19.9227	−	14.4747i	−0.695306	−	0.505169i	−0.878400	+	0.477926i	$0.841389\pi$
$822$	−2.57430	+	3.54322i	−0.0897890	+	0.123584i
$823$	1.98941	−	9.35942i	0.0693463	−	0.326249i	−0.929777	−	0.368124i	$-0.880000\pi$
$823$	1.98941	−	9.35942i	0.0693463	−	0.326249i	0.999123	+	0.0418757i	$0.0133334\pi$
$824$	0.603251	−	5.73955i	0.0210152	−	0.199947i
$825$		0			0
$826$	−52.3591	+	11.1293i	−1.82181	+	0.387237i
$827$	−16.1498	+	36.2730i	−0.561583	+	1.26134i	0.380135	+	0.924931i	$0.375878\pi$
$827$	−16.1498	+	36.2730i	−0.561583	+	1.26134i	−0.941718	+	0.336405i	$0.890789\pi$
$828$	5.55119	+	4.99831i	0.192917	+	0.173703i
$829$	−13.6971	−	42.1553i	−0.475720	−	1.46411i	−0.844985	−	0.534790i	$-0.820391\pi$
$829$	−13.6971	−	42.1553i	−0.475720	−	1.46411i	0.369265	−	0.929324i	$-0.379609\pi$
$830$		0			0
$831$	7.41246	−	12.8388i	0.257136	−	0.445372i
$832$	8.78411	−	5.07151i	0.304534	−	0.175823i
$833$	12.5752	+	4.08593i	0.435705	+	0.141569i
$834$	−27.2327	+	12.1248i	−0.942990	+	0.419846i
$835$		0			0
$836$	2.12452			0.0734780
$837$	22.7250	−	32.3531i	0.785491	−	1.11829i
$838$		−	26.6197i		−	0.919564i
$839$	−40.2618	+	29.2519i	−1.38999	+	1.00989i	−0.394124	+	0.919057i	$0.628952\pi$
$839$	−40.2618	+	29.2519i	−1.38999	+	1.00989i	−0.995866	+	0.0908299i	$0.971048\pi$
$840$		0			0
$841$	18.4191	−	56.6881i	0.635141	−	1.95476i
$842$	−2.25750	+	1.30337i	−0.0777986	+	0.0449171i
$843$	−12.3477	−	7.12893i	−0.425276	−	0.245533i
$844$	−1.02305	−	1.13621i	−0.0352147	−	0.0391099i
$845$		0			0
$846$	30.0552	−	33.3797i	1.03332	−	1.14762i
$847$	−5.46452	+	12.2735i	−0.187763	+	0.421723i
$848$	−3.48570	−	16.3989i	−0.119700	−	0.563142i
$849$	4.67783	+	44.5066i	0.160543	+	1.52746i
$850$		0			0
$851$	74.2808	+	15.7889i	2.54631	+	0.541235i
$852$	2.80578	−	3.86182i	0.0961243	−	0.132304i
$853$	−13.8055	+	19.0016i	−0.472690	+	0.650602i	−0.977080	−	0.212874i	$-0.931718\pi$
$853$	−13.8055	+	19.0016i	−0.472690	+	0.650602i	0.504390	+	0.863476i	$0.331718\pi$
$854$	7.01961	+	1.49206i	0.240206	+	0.0510574i
$855$		0			0
$856$	−1.75181	−	16.6674i	−0.0598758	−	0.569680i
$857$	−5.40517	−	25.4293i	−0.184637	−	0.868649i	−0.968752	−	0.248033i	$-0.920216\pi$
$857$	−5.40517	−	25.4293i	−0.184637	−	0.868649i	0.784114	−	0.620616i	$-0.213117\pi$
$858$	6.54911	−	14.7096i	0.223583	−	0.502176i
$859$	−9.55279	+	10.6095i	−0.325937	+	0.361990i	−0.883736	−	0.467987i	$-0.844980\pi$
$859$	−9.55279	+	10.6095i	−0.325937	+	0.361990i	0.557798	+	0.829976i	$0.311646\pi$
$860$		0			0
$861$	1.37314	+	1.52503i	0.0467967	+	0.0519730i
$862$	−0.373622	−	0.215711i	−0.0127256	−	0.00734713i
$863$	34.5317	−	19.9369i	1.17547	−	0.678659i	0.220509	−	0.975385i	$-0.429228\pi$
$863$	34.5317	−	19.9369i	1.17547	−	0.678659i	0.954963	+	0.296726i	$0.0958947\pi$
$864$	2.13427	−	6.56861i	0.0726094	−	0.223469i
$865$		0			0
$866$	4.77303	−	3.46781i	0.162194	−	0.117841i
$867$		−	28.7485i		−	0.976351i
$868$	3.29554	−	0.399712i	0.111858	−	0.0135671i
$869$	26.3837			0.895006
$870$		0			0
$871$	−6.03994	+	2.68916i	−0.204656	+	0.0911186i
$872$	37.3788	+	12.1451i	1.26581	+	0.411285i
$873$	70.1520	−	40.5023i	2.37429	−	1.37079i
$874$	−27.0970	+	46.9334i	−0.916571	+	1.58755i
$875$		0			0
$876$	0.237070	+	0.729626i	0.00800984	+	0.0246518i
$877$	−10.4152	−	9.37786i	−0.351695	−	0.316668i	0.474280	−	0.880374i	$-0.342708\pi$
$877$	−10.4152	−	9.37786i	−0.351695	−	0.316668i	−0.825975	+	0.563706i	$0.809375\pi$
$878$	−2.43761	+	5.47495i	−0.0822652	+	0.184771i
$879$	42.2206	−	8.97426i	1.42407	−	0.302694i
$880$		0			0
$881$	−5.27580	+	50.1959i	−0.177746	+	1.69114i	0.434656	+	0.900597i	$0.356870\pi$
$881$	−5.27580	+	50.1959i	−0.177746	+	1.69114i	−0.612402	+	0.790546i	$0.709797\pi$
$882$	8.27419	−	38.9270i	0.278606	−	1.31074i
$883$	9.49725	−	13.0718i	0.319608	−	0.439903i	−0.618739	−	0.785596i	$-0.712356\pi$
$883$	9.49725	−	13.0718i	0.319608	−	0.439903i	0.938347	+	0.345694i	$0.112356\pi$
$884$	−0.524056	−	0.380749i	−0.0176259	−	0.0128060i
$885$		0			0
$886$	1.40149	−	13.3343i	0.0470841	−	0.447975i
$887$	−3.18229	+	0.334472i	−0.106851	+	0.0112305i	−0.157803	−	0.987471i	$-0.550441\pi$
$887$	−3.18229	+	0.334472i	−0.106851	+	0.0112305i	0.0509521	+	0.998701i	$0.483774\pi$
$888$	−15.5276	−	73.0515i	−0.521071	−	2.45145i
$889$	20.6906	+	9.21205i	0.693941	+	0.308962i
$890$		0			0
$891$	3.54685	+	10.9161i	0.118824	+	0.365702i
$892$	−2.77717	+	2.50057i	−0.0929864	+	0.0837253i
$893$	22.3970	+	12.9309i	0.749486	+	0.432716i
$894$	−44.5173	−	77.1063i	−1.48888	−	2.57882i
$895$		0			0
$896$	−39.6572	+	17.6565i	−1.32485	+	0.589863i
$897$	19.1598	+	26.3711i	0.639726	+	0.880507i
$898$			7.83444i			0.261439i
$899$	16.9898	+	49.5794i	0.566643	+	1.65356i
$900$		0			0
$901$	8.37931	−	6.08793i	0.279155	−	0.202818i
$902$	−0.326550	−	0.733443i	−0.0108729	−	0.0244210i
$903$	30.7816	+	10.0016i	1.02435	+	0.332831i
$904$	15.2466	+	26.4078i	0.507093	+	0.878312i
$905$		0			0
$906$	0.419329	+	0.465712i	0.0139313	+	0.0154723i
$907$	−32.2453	+	10.4771i	−1.07069	+	0.347887i	−0.790755	−	0.612132i	$-0.790312\pi$
$907$	−32.2453	+	10.4771i	−1.07069	+	0.347887i	−0.279932	+	0.960020i	$0.590312\pi$
$908$	−0.409186	−	0.368433i	−0.0135793	−	0.0122269i
$909$	44.7654	+	19.9308i	1.48477	+	0.661064i
$910$		0			0
$911$	−1.46263	−	13.9160i	−0.0484592	−	0.461058i	−0.991664	−	0.128848i	$-0.958872\pi$
$911$	−1.46263	−	13.9160i	−0.0484592	−	0.461058i	0.943205	−	0.332211i	$-0.107794\pi$
$912$	57.6086	+	6.05491i	1.90761	+	0.200498i
$913$	−3.87548	+	18.2327i	−0.128260	+	0.603414i
$914$	7.43989	+	5.40540i	0.246090	+	0.178795i
$915$		0			0
$916$	1.45665	+	0.309620i	0.0481290	+	0.0102301i
$917$	−4.45795	−	0.468549i	−0.147214	−	0.0154729i
$918$	27.7481	−	2.91644i	0.915823	−	0.0962569i
$919$	38.5472	−	8.19345i	1.27155	−	0.270277i	0.477774	−	0.878483i	$-0.341444\pi$
$919$	38.5472	−	8.19345i	1.27155	−	0.270277i	0.793779	+	0.608206i	$0.208110\pi$
$920$		0			0
$921$	43.7824	−	48.6253i	1.44268	−	1.60226i
$922$	−37.8475	+	12.2974i	−1.24644	+	0.404993i
$923$	9.97996	−	8.98600i	0.328494	−	0.295778i
$924$	−2.31071	+	4.00227i	−0.0760169	+	0.131665i
$925$		0			0
$926$	6.70062	−	20.6224i	0.220196	−	0.677694i
$927$	−4.74376	−	10.6547i	−0.155805	−	0.349945i
$928$	5.38142	+	7.40689i	0.176654	+	0.243143i
$929$	12.8728			0.422342			0.211171	−	0.977449i	$-0.432272\pi$
$929$	12.8728			0.422342			0.211171	+	0.977449i	$0.432272\pi$
$930$		0			0
$931$	22.9138			0.750968
$932$	0.753840	+	1.03757i	0.0246929	+	0.0339868i
$933$	−11.2935	−	25.3656i	−0.369732	−	0.830432i
$934$	12.9055	−	39.7190i	0.422280	−	1.29965i
$935$		0			0
$936$	10.3337	−	17.8985i	0.337768	−	0.585031i
$937$	−21.2751	+	19.1562i	−0.695026	+	0.625805i	−0.938976	−	0.343983i	$-0.888224\pi$
$937$	−21.2751	+	19.1562i	−0.695026	+	0.625805i	0.243949	+	0.969788i	$0.421557\pi$
$938$	22.7408	−	7.38893i	0.742513	−	0.241257i
$939$	26.6932	−	29.6458i	0.871098	−	0.967453i
$940$		0			0
$941$	19.8694	−	4.22338i	0.647725	−	0.137678i	0.127678	−	0.991816i	$-0.459248\pi$
$941$	19.8694	−	4.22338i	0.647725	−	0.137678i	0.520047	+	0.854137i	$0.325914\pi$
$942$	−1.76845	+	0.185871i	−0.0576191	+	0.00605601i
$943$	1.61641	+	0.169892i	0.0526377	+	0.00553244i
$944$	44.3247	+	9.42151i	1.44265	+	0.306644i
$945$		0			0
$946$	−10.2441	−	7.44277i	−0.333064	−	0.241985i
$947$	9.92432	−	46.6903i	0.322497	−	1.51723i	−0.456227	−	0.889864i	$-0.650799\pi$
$947$	9.92432	−	46.6903i	0.322497	−	1.51723i	0.778724	−	0.627367i	$-0.215867\pi$
$948$	−4.92806	−	0.517960i	−0.160056	−	0.0168226i
$949$	0.225605	+	2.14649i	0.00732346	+	0.0696780i
$950$		0			0
$951$	−79.3380	−	35.3236i	−2.57271	−	1.14544i
$952$	−18.4552	−	16.6171i	−0.598135	−	0.538563i
$953$	9.28292	−	3.01620i	0.300703	−	0.0977044i	−0.154779	−	0.987949i	$-0.549467\pi$
$953$	9.28292	−	3.01620i	0.300703	−	0.0977044i	0.455483	+	0.890245i	$0.349467\pi$
$954$	−20.8593	−	23.1666i	−0.675344	−	0.750046i
$955$		0			0
$956$	2.11284	+	3.65955i	0.0683341	+	0.118358i
$957$	−69.3898	−	22.5461i	−2.24305	−	0.728813i
$958$	3.65642	+	8.21246i	0.118134	+	0.265332i
$959$	2.86105	−	2.07868i	0.0923882	−	0.0671240i
$960$		0			0
$961$	−25.6490	−	17.4107i	−0.827386	−	0.561634i
$962$			19.8206i			0.639042i
$963$	−19.9076	−	27.4004i	−0.641512	−	0.882966i
$964$	1.18712	−	0.528540i	0.0382346	−	0.0170231i
$965$		0			0
$966$	−58.9437	−	102.094i	−1.89648	−	3.28481i
$967$	37.1923	+	21.4730i	1.19602	+	0.690525i	0.959666	−	0.281141i	$-0.0907128\pi$
$967$	37.1923	+	21.4730i	1.19602	+	0.690525i	0.236358	+	0.971666i	$0.424046\pi$
$968$	7.77673	−	7.00220i	0.249954	−	0.225059i
$969$	11.0585	+	34.0344i	0.355249	+	1.09334i
$970$		0			0
$971$	17.8152	+	7.93183i	0.571717	+	0.254545i	0.672170	−	0.740397i	$-0.265363\pi$
$971$	17.8152	+	7.93183i	0.571717	+	0.254545i	−0.100453	+	0.994942i	$0.532029\pi$
$972$	0.315416	+	1.48391i	0.0101170	+	0.0475966i
$973$	23.9388	−	2.51607i	0.767442	−	0.0806614i
$974$	3.33304	−	31.7117i	0.106797	−	1.01611i
$975$		0			0
$976$	−4.91496	−	3.57093i	−0.157324	−	0.114303i
$977$	6.48067	−	8.91987i	0.207335	−	0.285372i	−0.692667	−	0.721257i	$-0.743565\pi$
$977$	6.48067	−	8.91987i	0.207335	−	0.285372i	0.900002	+	0.435885i	$0.143565\pi$
$978$	−9.38597	+	44.1575i	−0.300130	+	1.41200i
$979$	−3.65460	+	34.7712i	−0.116802	+	1.11129i
$980$		0			0
$981$	77.6908	−	16.5137i	2.48048	−	0.527241i
$982$	0.405951	−	0.911781i	0.0129544	−	0.0290961i
$983$	−30.6958	−	27.6386i	−0.979044	−	0.881535i	0.0139261	−	0.999903i	$-0.495567\pi$
$983$	−30.6958	−	27.6386i	−0.979044	−	0.881535i	−0.992970	+	0.118368i	$0.962234\pi$
$984$	−0.493939	−	1.52019i	−0.0157462	−	0.0484618i
$985$		0			0
$986$	−18.4927	+	32.0302i	−0.588926	+	1.02005i
$987$	−48.7198	+	28.1284i	−1.55077	+	0.895336i
$988$	−1.06761	−	0.346888i	−0.0339653	−	0.0110360i
$989$	23.4179	−	10.4263i	0.744646	−	0.331538i
$990$		0			0
$991$	−19.5359			−0.620579			−0.310290	−	0.950642i	$-0.600426\pi$
$991$	−19.5359			−0.620579			−0.310290	+	0.950642i	$0.600426\pi$
$992$	−5.17641	−	1.59093i	−0.164351	−	0.0505122i
$993$			39.8031i			1.26311i
$994$	−39.2925	+	28.5477i	−1.24628	+	0.905477i
$995$		0			0
$996$	1.08182	−	3.32950i	0.0342788	−	0.105499i
$997$	−4.56114	+	2.63337i	−0.144453	+	0.0833998i	−0.570484	−	0.821308i	$-0.693245\pi$
$997$	−4.56114	+	2.63337i	−0.144453	+	0.0833998i	0.426032	+	0.904708i	$0.359911\pi$
$998$	39.2159	+	22.6413i	1.24136	+	0.716698i
$999$	−45.3354	−	50.3501i	−1.43435	−	1.59301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.ck.c.49.3		80
5.2	odd	4		155.2.q.a.111.4	yes	40
5.3	odd	4		775.2.bl.c.576.2		40
5.4	even	2	inner	775.2.ck.c.49.8		80
31.19	even	15	inner	775.2.ck.c.174.8		80
155.19	even	30	inner	775.2.ck.c.174.3		80
155.22	even	60		4805.2.a.y.1.6		20
155.102	odd	60		4805.2.a.x.1.6		20
155.112	odd	60		155.2.q.a.81.4	✓	40
155.143	odd	60		775.2.bl.c.701.2		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.a.81.4	✓	40	155.112	odd	60
155.2.q.a.111.4	yes	40	5.2	odd	4
775.2.bl.c.576.2		40	5.3	odd	4
775.2.bl.c.701.2		40	155.143	odd	60
775.2.ck.c.49.3		80	1.1	even	1	trivial
775.2.ck.c.49.8		80	5.4	even	2	inner
775.2.ck.c.174.3		80	155.19	even	30	inner
775.2.ck.c.174.8		80	31.19	even	15	inner
4805.2.a.x.1.6		20	155.102	odd	60
4805.2.a.y.1.6		20	155.22	even	60

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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.ck (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866342 - 1.19242i) q^{2} +(-1.18190 - 2.65459i) q^{3} +(-0.0532763 + 0.163968i) q^{4} +(-2.14145 + 3.70910i) q^{6} +(2.57003 - 2.31407i) q^{7} +(-2.56187 + 0.832401i) q^{8} +(-3.64256 + 4.04548i) q^{9} +(-2.60914 + 0.554589i) q^{11} +(0.498233 - 0.0523664i) q^{12} +(1.40170 + 0.147324i) q^{13} +(-4.98586 - 1.05978i) q^{14} +(3.49098 + 2.53634i) q^{16} +(-0.554253 + 2.60755i) q^{17} +(7.97960 + 0.838689i) q^{18} +(0.482893 + 4.59442i) q^{19} +(-9.18042 - 4.08739i) q^{21} +(2.92170 + 2.63071i) q^{22} +(-7.56957 + 2.45950i) q^{23} +(5.23755 + 5.81689i) q^{24} +(-1.03868 - 1.79904i) q^{26} +(6.75345 + 2.19433i) q^{27} +(0.242510 + 0.544687i) q^{28} +(-7.61531 + 5.53285i) q^{29} +(1.63570 - 5.32207i) q^{31} -0.972630i q^{32} +(4.55594 + 6.27071i) q^{33} +(3.58946 - 1.59813i) q^{34} +(-0.469264 - 0.812790i) q^{36} +(-8.26300 - 4.77065i) q^{37} +(5.06012 - 4.55615i) q^{38} +(-1.26558 - 3.89505i) q^{39} +(-0.186553 - 0.0830590i) q^{41} +(3.07951 + 14.4880i) q^{42} +(-3.20308 + 0.336657i) q^{43} +(0.0480705 - 0.457360i) q^{44} +(9.49058 + 6.89531i) q^{46} +(3.29049 - 4.52897i) q^{47} +(2.60697 - 12.2648i) q^{48} +(0.518459 - 4.93281i) q^{49} +(7.57705 - 1.61055i) q^{51} +(-0.0988335 + 0.221984i) q^{52} +(-2.88732 - 2.59976i) q^{53} +(-3.23424 - 9.95396i) q^{54} +(-4.65785 + 8.06763i) q^{56} +(11.6256 - 6.71202i) q^{57} +(13.1949 + 4.28729i) q^{58} +(9.59361 - 4.27135i) q^{59} -1.40790 q^{61} +(-7.76321 + 2.66030i) q^{62} +18.8261i q^{63} +(5.82218 - 4.23006i) q^{64} +(3.53030 - 10.8652i) q^{66} +(-4.06251 + 2.34549i) q^{67} +(-0.398025 - 0.229800i) q^{68} +(15.4754 + 17.1872i) q^{69} +(6.37569 - 7.08092i) q^{71} +(5.96430 - 13.3960i) q^{72} +(0.318386 + 1.49789i) q^{73} +(1.46998 + 13.9860i) q^{74} +(-0.779063 - 0.165595i) q^{76} +(-5.42221 + 7.46303i) q^{77} +(-3.54810 + 4.88354i) q^{78} +(-9.67493 - 2.05647i) q^{79} +(-0.449782 - 4.27939i) q^{81} +(0.0625781 + 0.294407i) q^{82} +(2.84228 - 6.38388i) q^{83} +(1.15930 - 1.28753i) q^{84} +(3.17639 + 3.52774i) q^{86} +(23.6880 + 13.6763i) q^{87} +(6.22262 - 3.59263i) q^{88} +(4.05038 - 12.4658i) q^{89} +(3.94332 - 2.86499i) q^{91} -1.37220i q^{92} +(-16.0612 + 1.94804i) q^{93} -8.25112 q^{94} +(-2.58193 + 1.14955i) q^{96} +(-14.1521 - 4.59828i) q^{97} +(-6.33113 + 3.65528i) q^{98} +(7.26037 - 12.5753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 8 q^{6} - 4 q^{9} - 56 q^{11} + 12 q^{14} + 16 q^{16} + 26 q^{19} - 16 q^{21} + 164 q^{24} + 64 q^{26} - 84 q^{29} - 20 q^{31} - 64 q^{34} - 26 q^{36} - 74 q^{39} + 72 q^{41} + 112 q^{44}+ \cdots - 106 q^{99}+O(q^{100}) \) 80 * q + 20 * q^4 + 8 * q^6 - 4 * q^9 - 56 * q^11 + 12 * q^14 + 16 * q^16 + 26 * q^19 - 16 * q^21 + 164 * q^24 + 64 * q^26 - 84 * q^29 - 20 * q^31 - 64 * q^34 - 26 * q^36 - 74 * q^39 + 72 * q^41 + 112 * q^44 + 36 * q^46 + 62 * q^49 - 4 * q^51 - 44 * q^54 + 18 * q^56 + 2 * q^59 - 200 * q^61 - 34 * q^64 - 80 * q^66 - 16 * q^69 - 4 * q^71 + 4 * q^74 + 4 * q^76 + 134 * q^79 - 166 * q^81 - 52 * q^84 - 10 * q^86 - 40 * q^89 + 38 * q^91 - 260 * q^94 + 92 * q^96 - 106 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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