LMFDB - Embedded newform 675.2.l.h.151.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(76,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.76"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			151.11
Character	$\chi$	$=$	675.151
Dual form			675.2.l.h.76.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.948617 + 0.795984i) q^{2} +(-1.62630 - 0.595931i) q^{3} +(-0.0810128 - 0.459446i) q^{4} +(-1.06839 - 1.85982i) q^{6} +(0.395202 - 2.24130i) q^{7} +(1.52719 - 2.64518i) q^{8} +(2.28973 + 1.93833i) q^{9} +(-4.87230 + 1.77337i) q^{11} +(-0.142047 + 0.795478i) q^{12} +(-1.18441 + 0.993836i) q^{13} +(2.15894 - 1.81156i) q^{14} +(2.67745 - 0.974511i) q^{16} +(-2.66533 - 4.61649i) q^{17} +(0.629199 + 3.66133i) q^{18} +(-2.28767 + 3.96236i) q^{19} +(-1.97838 + 3.40953i) q^{21} +(-6.03353 - 2.19602i) q^{22} +(-0.892775 - 5.06318i) q^{23} +(-4.06003 + 3.39176i) q^{24} -1.91463 q^{26} +(-2.56869 - 4.51684i) q^{27} -1.06177 q^{28} +(-4.94693 - 4.15097i) q^{29} +(-0.228069 - 1.29344i) q^{31} +(-2.42480 - 0.882557i) q^{32} +(8.98066 + 0.0195113i) q^{33} +(1.14627 - 6.50084i) q^{34} +(0.705061 - 1.20904i) q^{36} +(1.84032 + 3.18754i) q^{37} +(-5.32410 + 1.93781i) q^{38} +(2.51847 - 0.910455i) q^{39} +(3.26644 - 2.74087i) q^{41} +(-4.59066 + 1.65958i) q^{42} +(-7.92956 + 2.88612i) q^{43} +(1.20949 + 2.09490i) q^{44} +(3.18331 - 5.51365i) q^{46} +(1.17913 - 6.68721i) q^{47} +(-4.93508 - 0.0107219i) q^{48} +(1.71059 + 0.622605i) q^{49} +(1.58353 + 9.09617i) q^{51} +(0.552567 + 0.463658i) q^{52} +6.64507 q^{53} +(1.15863 - 6.32939i) q^{54} +(-5.32509 - 4.46828i) q^{56} +(6.08174 - 5.08071i) q^{57} +(-1.38864 - 7.87536i) q^{58} +(-2.83430 - 1.03160i) q^{59} +(0.999796 - 5.67013i) q^{61} +(0.813210 - 1.40852i) q^{62} +(5.24929 - 4.36595i) q^{63} +(-4.44699 - 7.70241i) q^{64} +(8.50367 + 7.16697i) q^{66} +(-2.65278 + 2.22595i) q^{67} +(-1.90510 + 1.59857i) q^{68} +(-1.56538 + 8.76630i) q^{69} +(-0.0130487 - 0.0226011i) q^{71} +(8.62409 - 3.09654i) q^{72} +(2.89081 - 5.00704i) q^{73} +(-0.791465 + 4.48862i) q^{74} +(2.00582 + 0.730059i) q^{76} +(2.04912 + 11.6211i) q^{77} +(3.11377 + 1.14099i) q^{78} +(12.6845 + 10.6435i) q^{79} +(1.48575 + 8.87652i) q^{81} +5.28029 q^{82} +(-8.29793 - 6.96279i) q^{83} +(1.72677 + 0.632744i) q^{84} +(-9.81943 - 3.57398i) q^{86} +(5.57153 + 9.69877i) q^{87} +(-2.75006 + 15.5964i) q^{88} +(-2.32308 + 4.02369i) q^{89} +(1.75941 + 3.04738i) q^{91} +(-2.25393 + 0.820364i) q^{92} +(-0.399893 + 2.23944i) q^{93} +(6.44146 - 5.40503i) q^{94} +(3.41753 + 2.88032i) q^{96} +(-6.81695 + 2.48117i) q^{97} +(1.12712 + 1.95222i) q^{98} +(-14.5937 - 5.38358i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} - 6 q^{6} + 18 q^{9} - 6 q^{11} + 18 q^{14} - 24 q^{16} + 6 q^{19} + 24 q^{21} + 30 q^{24} + 48 q^{26} + 30 q^{29} - 30 q^{31} + 24 q^{34} + 54 q^{36} + 6 q^{39} - 12 q^{41} - 78 q^{44}+ \cdots - 36 q^{99}+O(q^{100}) $ 96 * q + 12 * q^4 - 6 * q^6 + 18 * q^9 - 6 * q^11 + 18 * q^14 - 24 * q^16 + 6 * q^19 + 24 * q^21 + 30 * q^24 + 48 * q^26 + 30 * q^29 - 30 * q^31 + 24 * q^34 + 54 * q^36 + 6 * q^39 - 12 * q^41 - 78 * q^44 - 6 * q^46 + 30 * q^49 - 90 * q^51 - 108 * q^54 - 96 * q^56 - 66 * q^59 + 6 * q^61 - 150 * q^66 - 24 * q^69 - 90 * q^71 - 66 * q^74 + 12 * q^76 - 24 * q^79 - 54 * q^81 - 198 * q^84 + 18 * q^86 - 96 * q^89 - 6 * q^91 - 24 * q^94 + 42 * q^96 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	0.948617	+	0.795984i	0.670774	+	0.562846i	0.913294	−	0.407300i	$-0.133530\pi$
$2$	0.948617	+	0.795984i	0.670774	+	0.562846i	−0.242521	+	0.970146i	$0.577974\pi$
$3$	−1.62630	−	0.595931i	−0.938947	−	0.344061i
$3$	−1.62630	−	0.595931i	−0.938947	−	0.344061i
$4$	−0.0810128	−	0.459446i	−0.0405064	−	0.229723i
$5$		0			0
$5$		0			0
$6$	−1.06839	−	1.85982i	−0.436168	−	0.759270i
$7$	0.395202	−	2.24130i	0.149372	−	0.847133i	−0.814379	−	0.580333i	$-0.802923\pi$
$7$	0.395202	−	2.24130i	0.149372	−	0.847133i	0.963752	−	0.266800i	$-0.0859664\pi$
$8$	1.52719	−	2.64518i	0.539945	−	0.935211i
$9$	2.28973	+	1.93833i	0.763244	+	0.646110i
$10$		0			0
$11$	−4.87230	+	1.77337i	−1.46905	+	0.534692i	−0.947844	−	0.318736i	$-0.896742\pi$
$11$	−4.87230	+	1.77337i	−1.46905	+	0.534692i	−0.521211	+	0.853428i	$0.674520\pi$
$12$	−0.142047	+	0.795478i	−0.0410054	+	0.229635i
$13$	−1.18441	+	0.993836i	−0.328496	+	0.275641i	−0.792087	−	0.610409i	$-0.791005\pi$
$13$	−1.18441	+	0.993836i	−0.328496	+	0.275641i	0.463591	+	0.886049i	$0.346561\pi$
$14$	2.15894	−	1.81156i	0.577000	−	0.484161i
$15$		0			0
$16$	2.67745	−	0.974511i	0.669361	−	0.243628i
$17$	−2.66533	−	4.61649i	−0.646438	−	1.11966i	−0.983967	−	0.178348i	$-0.942925\pi$
$17$	−2.66533	−	4.61649i	−0.646438	−	1.11966i	0.337530	−	0.941315i	$-0.390409\pi$
$18$	0.629199	+	3.66133i	0.148304	+	0.862983i
$19$	−2.28767	+	3.96236i	−0.524827	+	0.909027i	0.474755	+	0.880118i	$0.342537\pi$
$19$	−2.28767	+	3.96236i	−0.524827	+	0.909027i	−0.999582	+	0.0289093i	$0.990797\pi$
$20$		0			0
$21$	−1.97838	+	3.40953i	−0.431718	+	0.744020i
$22$	−6.03353	−	2.19602i	−1.28635	−	0.468194i
$23$	−0.892775	−	5.06318i	−0.186156	−	1.05575i	−0.924461	−	0.381278i	$-0.875484\pi$
$23$	−0.892775	−	5.06318i	−0.186156	−	1.05575i	0.738304	−	0.674468i	$-0.235627\pi$
$24$	−4.06003	+	3.39176i	−0.828749	+	0.692340i
$25$		0			0
$26$	−1.91463			−0.375490
$27$	−2.56869	−	4.51684i	−0.494345	−	0.869266i
$28$	−1.06177			−0.200657
$29$	−4.94693	−	4.15097i	−0.918622	−	0.770816i	0.0551173	−	0.998480i	$-0.482447\pi$
$29$	−4.94693	−	4.15097i	−0.918622	−	0.770816i	−0.973740	+	0.227664i	$0.926891\pi$
$30$		0			0
$31$	−0.228069	−	1.29344i	−0.0409624	−	0.232309i	0.957453	−	0.288591i	$-0.0931867\pi$
$31$	−0.228069	−	1.29344i	−0.0409624	−	0.232309i	−0.998415	+	0.0562816i	$0.982076\pi$
$32$	−2.42480	−	0.882557i	−0.428649	−	0.156015i
$33$	8.98066	+	0.0195113i	1.56333	+	0.00339649i
$34$	1.14627	−	6.50084i	0.196584	−	1.11489i
$35$		0			0
$36$	0.705061	−	1.20904i	0.117510	−	0.201506i
$37$	1.84032	+	3.18754i	0.302548	+	0.524028i	0.976712	−	0.214553i	$-0.0688296\pi$
$37$	1.84032	+	3.18754i	0.302548	+	0.524028i	−0.674165	+	0.738581i	$0.735496\pi$
$38$	−5.32410	+	1.93781i	−0.863683	+	0.314355i
$39$	2.51847	−	0.910455i	0.403277	−	0.145790i
$40$		0			0
$41$	3.26644	−	2.74087i	0.510132	−	0.428052i	−0.351044	−	0.936359i	$-0.614173\pi$
$41$	3.26644	−	2.74087i	0.510132	−	0.428052i	0.861176	+	0.508307i	$0.169729\pi$
$42$	−4.59066	+	1.65958i	−0.708354	+	0.256078i
$43$	−7.92956	+	2.88612i	−1.20925	+	0.440130i	−0.866442	−	0.499277i	$-0.833599\pi$
$43$	−7.92956	+	2.88612i	−1.20925	+	0.440130i	−0.342804	+	0.939407i	$0.611377\pi$
$44$	1.20949	+	2.09490i	0.182337	+	0.315817i
$45$		0			0
$46$	3.18331	−	5.51365i	0.469353	−	0.812944i
$47$	1.17913	−	6.68721i	0.171995	−	0.975429i	−0.769561	−	0.638573i	$-0.779525\pi$
$47$	1.17913	−	6.68721i	0.171995	−	0.975429i	0.941556	−	0.336857i	$-0.109364\pi$
$48$	−4.93508	−	0.0107219i	−0.712318	−	0.00154758i
$49$	1.71059	+	0.622605i	0.244371	+	0.0889436i
$50$		0			0
$51$	1.58353	+	9.09617i	0.221739	+	1.27372i
$52$	0.552567	+	0.463658i	0.0766272	+	0.0642979i
$53$	6.64507			0.912771			0.456385	−	0.889782i	$-0.349144\pi$
$53$	6.64507			0.912771			0.456385	+	0.889782i	$0.349144\pi$
$54$	1.15863	−	6.32939i	0.157669	−	0.861321i
$55$		0			0
$56$	−5.32509	−	4.46828i	−0.711596	−	0.597100i
$57$	6.08174	−	5.08071i	0.805546	−	0.672956i
$58$	−1.38864	−	7.87536i	−0.182337	−	1.03409i
$59$	−2.83430	−	1.03160i	−0.368995	−	0.134303i	0.150866	−	0.988554i	$-0.451794\pi$
$59$	−2.83430	−	1.03160i	−0.368995	−	0.134303i	−0.519861	+	0.854251i	$0.674016\pi$
$60$		0			0
$61$	0.999796	−	5.67013i	0.128011	−	0.725985i	−0.851463	−	0.524414i	$-0.824284\pi$
$61$	0.999796	−	5.67013i	0.128011	−	0.725985i	0.979474	−	0.201571i	$-0.0646046\pi$
$62$	0.813210	−	1.40852i	0.103278	−	0.178882i
$63$	5.24929	−	4.36595i	0.661349	−	0.550058i
$64$	−4.44699	−	7.70241i	−0.555874	−	0.962801i
$65$		0			0
$66$	8.50367	+	7.16697i	1.04673	+	0.882193i
$67$	−2.65278	+	2.22595i	−0.324089	+	0.271943i	−0.790286	−	0.612738i	$-0.790068\pi$
$67$	−2.65278	+	2.22595i	−0.324089	+	0.271943i	0.466197	+	0.884681i	$0.345624\pi$
$68$	−1.90510	+	1.59857i	−0.231028	+	0.193855i
$69$	−1.56538	+	8.76630i	−0.188450	+	1.05534i
$70$		0			0
$71$	−0.0130487	−	0.0226011i	−0.00154860	−	0.00268225i	0.865250	−	0.501341i	$-0.167160\pi$
$71$	−0.0130487	−	0.0226011i	−0.00154860	−	0.00268225i	−0.866799	+	0.498658i	$0.833826\pi$
$72$	8.62409	−	3.09654i	1.01636	−	0.364931i
$73$	2.89081	−	5.00704i	0.338344	−	0.586029i	−0.645777	−	0.763526i	$-0.723467\pi$
$73$	2.89081	−	5.00704i	0.338344	−	0.586029i	0.984121	+	0.177497i	$0.0567999\pi$
$74$	−0.791465	+	4.48862i	−0.0920059	+	0.521792i
$75$		0			0
$76$	2.00582	+	0.730059i	0.230083	+	0.0837435i
$77$	2.04912	+	11.6211i	0.233519	+	1.32435i
$78$	3.11377	+	1.14099i	0.352565	+	0.129191i
$79$	12.6845	+	10.6435i	1.42712	+	1.19749i	0.947393	+	0.320073i	$0.103708\pi$
$79$	12.6845	+	10.6435i	1.42712	+	1.19749i	0.479724	+	0.877420i	$0.340737\pi$
$80$		0			0
$81$	1.48575	+	8.87652i	0.165083	+	0.986280i
$82$	5.28029			0.583110
$83$	−8.29793	−	6.96279i	−0.910816	−	0.764265i	0.0614583	−	0.998110i	$-0.480425\pi$
$83$	−8.29793	−	6.96279i	−0.910816	−	0.764265i	−0.972274	+	0.233844i	$0.924869\pi$
$84$	1.72677	+	0.632744i	0.188406	+	0.0690381i
$85$		0			0
$86$	−9.81943	−	3.57398i	−1.05886	−	0.385392i
$87$	5.57153	+	9.69877i	0.597331	+	1.03982i
$88$	−2.75006	+	15.5964i	−0.293158	+	1.66258i
$89$	−2.32308	+	4.02369i	−0.246246	+	0.426510i	−0.962481	−	0.271349i	$-0.912530\pi$
$89$	−2.32308	+	4.02369i	−0.246246	+	0.426510i	0.716235	+	0.697859i	$0.245864\pi$
$90$		0			0
$91$	1.75941	+	3.04738i	0.184436	+	0.319453i
$92$	−2.25393	+	0.820364i	−0.234989	+	0.0855289i
$93$	−0.399893	+	2.23944i	−0.0414670	+	0.232220i
$94$	6.44146	−	5.40503i	0.664386	−	0.557486i
$95$		0			0
$96$	3.41753	+	2.88032i	0.348800	+	0.293972i
$97$	−6.81695	+	2.48117i	−0.692157	+	0.251924i	−0.664058	−	0.747681i	$-0.731167\pi$
$97$	−6.81695	+	2.48117i	−0.692157	+	0.251924i	−0.0280982	+	0.999605i	$0.508945\pi$
$98$	1.12712	+	1.95222i	0.113856	+	0.197204i
$99$	−14.5937	−	5.38358i	−1.46672	−	0.541070i
$100$		0			0
$101$	0.0757615	−	0.429665i	0.00753855	−	0.0427532i	−0.980806	−	0.194984i	$-0.937535\pi$
$101$	0.0757615	−	0.429665i	0.00753855	−	0.0427532i	0.988345	+	0.152231i	$0.0486457\pi$
$102$	−5.73824	+	9.88925i	−0.568171	+	0.979182i
$103$	2.13109	+	0.775652i	0.209982	+	0.0764273i	0.444870	−	0.895595i	$-0.353250\pi$
$103$	2.13109	+	0.775652i	0.209982	+	0.0764273i	−0.234888	+	0.972023i	$0.575472\pi$
$104$	0.820053	+	4.65075i	0.0804128	+	0.456044i
$105$		0			0
$106$	6.30363	+	5.28937i	0.612263	+	0.513749i
$107$	−4.36720			−0.422193			−0.211097	−	0.977465i	$-0.567703\pi$
$107$	−4.36720			−0.422193			−0.211097	+	0.977465i	$0.567703\pi$
$108$	−1.86715	+	1.54610i	−0.179666	+	0.148773i
$109$	7.95224			0.761686			0.380843	−	0.924640i	$-0.375634\pi$
$109$	7.95224			0.761686			0.380843	+	0.924640i	$0.375634\pi$
$110$		0			0
$111$	−1.09338	−	6.28061i	−0.103779	−	0.596129i
$112$	−1.12604	−	6.38610i	−0.106401	−	0.603429i
$113$	14.7879	+	5.38234i	1.39112	+	0.506328i	0.925531	−	0.378671i	$-0.123619\pi$
$113$	14.7879	+	5.38234i	1.39112	+	0.506328i	0.465593	+	0.884999i	$0.345841\pi$
$114$	9.81341	+	0.0213206i	0.919110	+	0.00199686i
$115$		0			0
$116$	−1.50638	+	2.60913i	−0.139864	+	0.242252i
$117$	−4.63836	−	0.0201547i	−0.428817	−	0.00186330i
$118$	−1.86753	−	3.23466i	−0.171920	−	0.297774i
$119$	−11.4003	+	4.14937i	−1.04506	+	0.380372i
$120$		0			0
$121$	12.1680	−	10.2102i	1.10618	−	0.928196i
$122$	5.46176	−	4.58296i	0.494484	−	0.414922i
$123$	−6.94559	+	2.51091i	−0.626263	+	0.226401i
$124$	−0.575791	+	0.209571i	−0.0517075	+	0.0188200i
$125$		0			0
$126$	8.45480	+	0.0367379i	0.753213	+	0.00327287i
$127$	1.67688	−	2.90443i	0.148799	−	0.257727i	−0.781985	−	0.623297i	$-0.785793\pi$
$127$	1.67688	−	2.90443i	0.148799	−	0.257727i	0.930784	+	0.365570i	$0.119126\pi$
$128$	1.01634	−	5.76393i	0.0898323	−	0.509464i
$129$	14.6158	+	0.0317543i	1.28685	+	0.00279581i
$130$		0			0
$131$	−0.958255	−	5.43454i	−0.0837231	−	0.474818i	−0.997625	−	0.0688819i	$-0.978057\pi$
$131$	−0.958255	−	5.43454i	−0.0837231	−	0.474818i	0.913902	−	0.405936i	$-0.133054\pi$
$132$	−0.718583	−	4.12771i	−0.0625447	−	0.359271i
$133$	7.97675	+	6.69329i	0.691672	+	0.580382i
$134$	−4.28829			−0.370452
$135$		0			0
$136$	−16.2819			−1.39616
$137$	4.55076	+	3.81854i	0.388798	+	0.326240i	0.816145	−	0.577848i	$-0.196107\pi$
$137$	4.55076	+	3.81854i	0.388798	+	0.326240i	−0.427347	+	0.904088i	$0.640552\pi$
$138$	−8.46279	+	7.06985i	−0.720400	+	0.601825i
$139$	−2.76633	−	15.6886i	−0.234637	−	1.33069i	−0.843377	−	0.537323i	$-0.819436\pi$
$139$	−2.76633	−	15.6886i	−0.234637	−	1.33069i	0.608740	−	0.793370i	$-0.291675\pi$
$140$		0			0
$141$	−5.90275	+	10.1728i	−0.497101	+	0.856700i
$142$	0.00561184	−	0.0318263i	0.000470935	−	0.00267081i
$143$	4.00835	−	6.94267i	0.335195	−	0.580575i
$144$	8.01956	+	2.95841i	0.668296	+	0.246534i
$145$		0			0
$146$	6.72780	−	2.44872i	0.556796	−	0.202657i
$147$	−2.41092	−	2.03194i	−0.198849	−	0.167592i
$148$	1.31541	−	1.10376i	0.108126	−	0.0907286i
$149$	15.5994	−	13.0894i	1.27795	−	1.07233i	0.284430	−	0.958697i	$-0.408196\pi$
$149$	15.5994	−	13.0894i	1.27795	−	1.07233i	0.993523	−	0.113632i	$-0.0362486\pi$
$150$		0			0
$151$	−1.80439	+	0.656743i	−0.146839	+	0.0534450i	−0.414394	−	0.910098i	$-0.636006\pi$
$151$	−1.80439	+	0.656743i	−0.146839	+	0.0534450i	0.267555	+	0.963543i	$0.413784\pi$
$152$	6.98743	+	12.1026i	0.566755	+	0.981649i
$153$	2.84539	−	15.7368i	0.230036	−	1.27225i
$154$	−7.30642	+	12.6551i	−0.588768	+	1.01978i
$155$		0			0
$156$	−0.622333	−	1.08334i	−0.0498265	−	0.0867367i
$157$	11.9904	+	4.36413i	0.956935	+	0.348296i	0.772832	−	0.634611i	$-0.218840\pi$
$157$	11.9904	+	4.36413i	0.956935	+	0.348296i	0.184103	+	0.982907i	$0.441062\pi$
$158$	3.56063	+	20.1933i	0.283268	+	1.60649i
$159$	−10.8069	−	3.96000i	−0.857044	−	0.314049i
$160$		0			0
$161$	−11.7009			−0.922163
$162$	−5.65616	+	9.60305i	−0.444390	+	0.754487i
$163$	24.6659			1.93198			0.965990	−	0.258578i	$-0.0832539\pi$
$163$	24.6659			1.93198			0.965990	+	0.258578i	$0.0832539\pi$
$164$	−1.52391	−	1.27871i	−0.118997	−	0.0998503i
$165$		0			0
$166$	−2.32929	−	13.2100i	−0.180788	−	1.02530i
$167$	5.03625	+	1.83304i	0.389716	+	0.141845i	0.529444	−	0.848345i	$-0.322401\pi$
$167$	5.03625	+	1.83304i	0.389716	+	0.141845i	−0.139728	+	0.990190i	$0.544623\pi$
$168$	5.99743	+	10.4402i	0.462712	+	0.805477i
$169$	−1.84231	+	10.4483i	−0.141717	+	0.803714i
$170$		0			0
$171$	−12.9185	+	4.63848i	−0.987903	+	0.354714i
$172$	1.96841	+	3.40939i	0.150090	+	0.259964i
$173$	−13.4581	+	4.89834i	−1.02320	+	0.372414i	−0.798487	−	0.602012i	$-0.794366\pi$
$173$	−13.4581	+	4.89834i	−1.02320	+	0.372414i	−0.224711	+	0.974426i	$0.572144\pi$
$174$	−2.43482	+	13.6353i	−0.184583	+	1.03369i
$175$		0			0
$176$	−11.3172	+	9.49622i	−0.853063	+	0.715805i
$177$	3.99468	+	3.36675i	0.300258	+	0.253060i
$178$	−5.40651	+	1.96781i	−0.405235	+	0.147493i
$179$	2.84521	+	4.92805i	0.212661	+	0.368340i	0.952547	−	0.304393i	$-0.0984536\pi$
$179$	2.84521	+	4.92805i	0.212661	+	0.368340i	−0.739885	+	0.672733i	$0.765120\pi$
$180$		0			0
$181$	5.07635	−	8.79249i	0.377322	−	0.653541i	−0.613350	−	0.789811i	$-0.710178\pi$
$181$	5.07635	−	8.79249i	0.377322	−	0.653541i	0.990672	+	0.136271i	$0.0435117\pi$
$182$	−0.756665	+	4.29126i	−0.0560878	+	0.318090i
$183$	−5.00498	+	8.62554i	−0.369979	+	0.637619i
$184$	−14.7564	−	5.37091i	−1.08786	−	0.395948i
$185$		0			0
$186$	−2.16191	+	1.80607i	−0.158519	+	0.132427i
$187$	21.1731	+	17.7663i	1.54833	+	1.29920i
$188$	−3.16794			−0.231046
$189$	−11.1388	+	3.97215i	−0.810225	+	0.288931i
$190$		0			0
$191$	−4.87022	−	4.08660i	−0.352397	−	0.295696i	0.449355	−	0.893353i	$-0.351654\pi$
$191$	−4.87022	−	4.08660i	−0.352397	−	0.295696i	−0.801752	+	0.597657i	$0.796098\pi$
$192$	2.64205	+	15.1766i	0.190674	+	1.09527i
$193$	−3.38673	−	19.2071i	−0.243782	−	1.38256i	−0.823304	−	0.567601i	$-0.807872\pi$
$193$	−3.38673	−	19.2071i	−0.243782	−	1.38256i	0.579521	−	0.814957i	$-0.303240\pi$
$194$	−8.44165	−	3.07251i	−0.606075	−	0.220593i
$195$		0			0
$196$	0.147474	−	0.836365i	0.0105338	−	0.0597404i
$197$	4.52311	−	7.83426i	0.322259	−	0.558168i	−0.658695	−	0.752410i	$-0.728891\pi$
$197$	4.52311	−	7.83426i	0.322259	−	0.558168i	0.980954	+	0.194242i	$0.0622246\pi$
$198$	−9.55854	−	16.7233i	−0.679296	−	1.18847i
$199$	−5.04715	−	8.74191i	−0.357783	−	0.619698i	0.629807	−	0.776751i	$-0.283134\pi$
$199$	−5.04715	−	8.74191i	−0.357783	−	0.619698i	−0.987590	+	0.157054i	$0.949800\pi$
$200$		0			0
$201$	5.64074	−	2.03919i	0.397867	−	0.143834i
$202$	0.413875	−	0.347282i	0.0291201	−	0.0244347i
$203$	−11.2586	+	9.44710i	−0.790200	+	0.663057i
$204$	4.05091	−	1.46445i	0.283621	−	0.102532i
$205$		0			0
$206$	1.40418	+	2.43211i	0.0978338	+	0.169453i
$207$	7.76990	−	13.3238i	0.540045	−	0.926069i
$208$	−2.20268	+	3.81516i	−0.152729	+	0.264534i
$209$	4.11947	−	23.3627i	0.284950	−	1.61603i
$210$		0			0
$211$	3.35281	+	1.22032i	0.230817	+	0.0840106i	0.454839	−	0.890573i	$-0.349697\pi$
$211$	3.35281	+	1.22032i	0.230817	+	0.0840106i	−0.224022	+	0.974584i	$0.571919\pi$
$212$	−0.538336	−	3.05305i	−0.0369730	−	0.209685i
$213$	0.00775253	+	0.0445323i	0.000531195	+	0.00305131i
$214$	−4.14280	−	3.47622i	−0.283196	−	0.237630i
$215$		0			0
$216$	−15.8707	−	0.103443i	−1.07987	−	0.00703843i
$217$	−2.98913			−0.202915
$218$	7.54363	+	6.32986i	0.510919	+	0.428712i
$219$	−7.68519	+	6.42024i	−0.519317	+	0.433840i
$220$		0			0
$221$	7.74487	+	2.81890i	0.520977	+	0.189620i
$222$	3.96207	−	6.82821i	0.265917	−	0.458279i
$223$	3.22320	−	18.2797i	0.215842	−	1.22410i	−0.663598	−	0.748089i	$-0.730971\pi$
$223$	3.22320	−	18.2797i	0.215842	−	1.22410i	0.879440	−	0.476010i	$-0.157917\pi$
$224$	−2.93637	+	5.08593i	−0.196194	+	0.339818i
$225$		0			0
$226$	9.74376	+	16.8767i	0.648145	+	1.12262i
$227$	−23.1217	+	8.41561i	−1.53464	+	0.558564i	−0.964753	−	0.263158i	$-0.915236\pi$
$227$	−23.1217	+	8.41561i	−1.53464	+	0.558564i	−0.569888	+	0.821722i	$0.693014\pi$
$228$	−2.82701	−	2.38263i	−0.187223	−	0.157793i
$229$	1.56307	−	1.31157i	0.103291	−	0.0866713i	−0.589680	−	0.807637i	$-0.700746\pi$
$229$	1.56307	−	1.31157i	0.103291	−	0.0866713i	0.692971	+	0.720966i	$0.256302\pi$
$230$		0			0
$231$	3.59291	−	20.1207i	0.236396	−	1.32384i
$232$	−18.5350	+	6.74618i	−1.21688	+	0.442908i
$233$	−4.33906	−	7.51547i	−0.284261	−	0.492355i	0.688169	−	0.725551i	$-0.258415\pi$
$233$	−4.33906	−	7.51547i	−0.284261	−	0.492355i	−0.972430	+	0.233196i	$0.925082\pi$
$234$	−4.38399	−	3.71118i	−0.286590	−	0.242608i
$235$		0			0
$236$	−0.244351	+	1.38578i	−0.0159059	+	0.0902068i
$237$	−14.2860	−	24.8687i	−0.927977	−	1.61540i
$238$	−14.1173	−	5.13829i	−0.915092	−	0.333066i
$239$	−0.654990	−	3.71463i	−0.0423678	−	0.240280i	0.956268	−	0.292491i	$-0.0944842\pi$
$239$	−0.654990	−	3.71463i	−0.0423678	−	0.240280i	−0.998636	+	0.0522114i	$0.983373\pi$
$240$		0			0
$241$	0.433776	+	0.363981i	0.0279420	+	0.0234461i	0.656652	−	0.754194i	$-0.271972\pi$
$241$	0.433776	+	0.363981i	0.0279420	+	0.0234461i	−0.628710	+	0.777640i	$0.716417\pi$
$242$	19.6699			1.26443
$243$	2.87351	−	15.3213i	0.184336	−	0.982863i
$244$	−2.68612			−0.171961
$245$		0			0
$246$	−8.58736	−	3.14669i	−0.547510	−	0.200626i
$247$	−1.22840	−	6.96662i	−0.0781614	−	0.443275i
$248$	−3.76969	−	1.37205i	−0.239375	−	0.0871256i
$249$	9.34561	+	16.2686i	0.592254	+	1.03098i
$250$		0			0
$251$	0.425928	−	0.737730i	0.0268844	−	0.0465651i	−0.852270	−	0.523102i	$-0.824775\pi$
$251$	0.425928	−	0.737730i	0.0268844	−	0.0465651i	0.879155	+	0.476537i	$0.158108\pi$
$252$	−2.43118	−	2.05807i	−0.153150	−	0.129646i
$253$	13.3288	+	23.0861i	0.837973	+	1.45141i
$254$	3.90260	−	1.42043i	0.244871	−	0.0891257i
$255$		0			0
$256$	−8.07425	+	6.77510i	−0.504641	+	0.423444i
$257$	−14.0912	+	11.8239i	−0.878982	+	0.737553i	−0.965970	−	0.258656i	$-0.916720\pi$
$257$	−14.0912	+	11.8239i	−0.878982	+	0.737553i	0.0869875	+	0.996209i	$0.472276\pi$
$258$	13.8395	+	11.6641i	0.861612	+	0.726174i
$259$	7.87153	−	2.86500i	0.489113	−	0.178023i
$260$		0			0
$261$	−3.28120	−	19.0934i	−0.203101	−	1.18185i
$262$	3.41679	−	5.91805i	0.211090	−	0.365618i
$263$	−1.21209	+	6.87408i	−0.0747404	+	0.423874i	0.924362	+	0.381516i	$0.124598\pi$
$263$	−1.21209	+	6.87408i	−0.0747404	+	0.423874i	−0.999103	+	0.0423576i	$0.986513\pi$
$264$	13.7668	−	23.7256i	0.847289	−	1.46021i
$265$		0			0
$266$	2.23913	+	12.6987i	0.137290	+	0.778610i
$267$	6.17587	−	5.15935i	0.377957	−	0.315747i
$268$	1.23761	+	1.03848i	0.0755992	+	0.0634352i
$269$	9.05450			0.552062			0.276031	−	0.961149i	$-0.410981\pi$
$269$	9.05450			0.552062			0.276031	+	0.961149i	$0.410981\pi$
$270$		0			0
$271$	−2.68123			−0.162873			−0.0814364	−	0.996679i	$-0.525951\pi$
$271$	−2.68123			−0.162873			−0.0814364	+	0.996679i	$0.525951\pi$
$272$	−11.6351	−	9.76300i	−0.705481	−	0.591969i
$273$	−1.04530	−	6.00446i	−0.0632646	−	0.363406i
$274$	1.27743	+	7.24467i	0.0771724	+	0.437667i
$275$		0			0
$276$	4.15446	+	0.00902597i	0.250069	+	0.000543299i
$277$	1.68116	−	9.53431i	0.101011	−	0.572861i	−0.891728	−	0.452572i	$-0.850507\pi$
$277$	1.68116	−	9.53431i	0.101011	−	0.572861i	0.992739	−	0.120289i	$-0.0383822\pi$
$278$	9.86372	−	17.0845i	0.591587	−	1.02466i
$279$	1.98490	−	3.40371i	0.118833	−	0.203775i
$280$		0			0
$281$	−12.4600	+	4.53506i	−0.743300	+	0.270539i	−0.685784	−	0.727806i	$-0.740540\pi$
$281$	−12.4600	+	4.53506i	−0.743300	+	0.270539i	−0.0575163	+	0.998345i	$0.518318\pi$
$282$	−13.6968	+	4.95155i	−0.815633	+	0.294861i
$283$	−14.9981	+	12.5849i	−0.891543	+	0.748094i	−0.968519	−	0.248939i	$-0.919918\pi$
$283$	−14.9981	+	12.5849i	−0.891543	+	0.748094i	0.0769758	+	0.997033i	$0.475474\pi$
$284$	−0.00932686	+	0.00782616i	−0.000553447	+	0.000464397i
$285$		0			0
$286$	9.32865	−	3.39535i	0.551615	−	0.200771i
$287$	−4.85221	−	8.40428i	−0.286417	−	0.496089i
$288$	−3.84147	−	6.72089i	−0.226361	−	0.396032i
$289$	−5.70798	+	9.88651i	−0.335763	+	0.581559i
$290$		0			0
$291$	12.5650	+	0.0272988i	0.736576	+	0.00160028i
$292$	−2.53466	−	0.922540i	−0.148330	−	0.0539875i
$293$	5.25257	+	29.7888i	0.306858	+	1.74028i	0.614625	+	0.788819i	$0.289307\pi$
$293$	5.25257	+	29.7888i	0.306858	+	1.74028i	−0.307767	+	0.951462i	$0.599582\pi$
$294$	−0.669644	−	3.84659i	−0.0390544	−	0.224338i
$295$		0			0
$296$	11.2421			0.653436
$297$	20.5255	+	17.4522i	1.19101	+	1.01268i
$298$	25.2169			1.46077
$299$	6.08938	+	5.10960i	0.352158	+	0.295496i
$300$		0			0
$301$	3.33490	+	18.9131i	0.192220	+	1.09014i
$302$	−2.23443	−	0.813265i	−0.128577	−	0.0467982i
$303$	−0.379262	+	0.653617i	−0.0217880	+	0.0375493i
$304$	−2.26375	+	12.8384i	−0.129835	+	0.736330i
$305$		0			0
$306$	15.2254	−	12.6633i	0.870381	−	0.723915i
$307$	−9.13533	−	15.8229i	−0.521381	−	0.903058i	−0.999691	−	0.0248672i	$-0.992084\pi$
$307$	−9.13533	−	15.8229i	−0.521381	−	0.903058i	0.478310	−	0.878191i	$-0.341250\pi$
$308$	5.17329	−	1.88292i	0.294775	−	0.107289i
$309$	−3.00356	−	2.53143i	−0.170867	−	0.144008i
$310$		0			0
$311$	25.8479	−	21.6890i	1.46570	−	1.22987i	0.545681	−	0.837993i	$-0.316271\pi$
$311$	25.8479	−	21.6890i	1.46570	−	1.22987i	0.920018	−	0.391875i	$-0.128174\pi$
$312$	1.43787	−	8.05223i	0.0814034	−	0.455868i
$313$	−2.62017	+	0.953665i	−0.148101	+	0.0539043i	−0.415007	−	0.909818i	$-0.636221\pi$
$313$	−2.62017	+	0.953665i	−0.148101	+	0.0539043i	0.266906	+	0.963723i	$0.413999\pi$
$314$	7.90048	+	13.6840i	0.445850	+	0.772235i
$315$		0			0
$316$	3.86253	−	6.69010i	0.217284	−	0.376348i
$317$	−0.479083	+	2.71702i	−0.0269080	+	0.152603i	−0.995301	−	0.0968248i	$-0.969131\pi$
$317$	−0.479083	+	2.71702i	−0.0269080	+	0.152603i	0.968393	+	0.249428i	$0.0802425\pi$
$318$	−7.09952	−	12.3587i	−0.398121	−	0.693039i
$319$	31.4642	+	11.4520i	1.76166	+	0.641190i
$320$		0			0
$321$	7.10240	+	2.60255i	0.396417	+	0.145260i
$322$	−11.0997	−	9.31377i	−0.618563	−	0.519036i
$323$	24.3896			1.35707
$324$	3.95792	−	1.40173i	0.219884	−	0.0778741i
$325$		0			0
$326$	23.3985	+	19.6337i	1.29592	+	1.08741i
$327$	−12.9328	−	4.73899i	−0.715183	−	0.262067i
$328$	−2.26160	−	12.8261i	−0.124876	−	0.708206i
$329$	−14.5221	−	5.28560i	−0.800627	−	0.291404i
$330$		0			0
$331$	−4.85007	+	27.5061i	−0.266584	+	1.51187i	0.497902	+	0.867233i	$0.334104\pi$
$331$	−4.85007	+	27.5061i	−0.266584	+	1.51187i	−0.764486	+	0.644640i	$0.777007\pi$
$332$	−2.52679	+	4.37653i	−0.138676	+	0.240193i
$333$	−1.96465	+	10.8658i	−0.107662	+	0.595440i
$334$	3.31840	+	5.74763i	0.181575	+	0.314496i
$335$		0			0
$336$	−1.97439	+	11.0568i	−0.107712	+	0.603197i
$337$	10.9318	−	9.17286i	0.595492	−	0.499677i	−0.294501	−	0.955651i	$-0.595153\pi$
$337$	10.9318	−	9.17286i	0.595492	−	0.499677i	0.889993	+	0.455974i	$0.150709\pi$
$338$	−10.0643	+	8.44497i	−0.547427	+	0.459346i
$339$	−20.8421	−	17.5659i	−1.13199	−	0.954047i
$340$		0			0
$341$	3.40498	+	5.89759i	0.184390	+	0.319372i
$342$	−15.9469	−	5.88279i	−0.862309	−	0.318105i
$343$	10.0371	−	17.3847i	0.541950	−	0.938685i
$344$	−4.47567	+	25.3828i	−0.241312	+	1.36855i
$345$		0			0
$346$	−16.6656	−	6.06577i	−0.895946	−	0.326098i
$347$	−3.06781	−	17.3984i	−0.164688	−	0.933994i	−0.949385	−	0.314114i	$-0.898292\pi$
$347$	−3.06781	−	17.3984i	−0.164688	−	0.933994i	0.784697	−	0.619880i	$-0.212819\pi$
$348$	4.00470	−	3.34554i	0.214674	−	0.179340i
$349$	−18.7439	−	15.7280i	−1.00334	−	0.841899i	−0.0158927	−	0.999874i	$-0.505059\pi$
$349$	−18.7439	−	15.7280i	−1.00334	−	0.841899i	−0.987443	+	0.157975i	$0.949503\pi$
$350$		0			0
$351$	7.53138	+	2.79692i	0.401995	+	0.149289i
$352$	13.3795			0.713129
$353$	−24.4328	−	20.5015i	−1.30043	−	1.09119i	−0.990071	−	0.140567i	$-0.955108\pi$
$353$	−24.4328	−	20.5015i	−1.30043	−	1.09119i	−0.310355	−	0.950621i	$-0.600448\pi$
$354$	1.10954	+	6.37346i	0.0589714	+	0.338745i
$355$		0			0
$356$	2.03687	+	0.741359i	0.107954	+	0.0392920i
$357$	21.0131	+	0.0456530i	1.11213	+	0.00241621i
$358$	−1.22364	+	6.93958i	−0.0646711	+	0.366768i
$359$	4.13080	−	7.15476i	0.218015	−	0.377614i	−0.736186	−	0.676780i	$-0.763375\pi$
$359$	4.13080	−	7.15476i	0.218015	−	0.377614i	0.954201	+	0.299166i	$0.0967083\pi$
$360$		0			0
$361$	−0.966856	−	1.67464i	−0.0508871	−	0.0881391i
$362$	11.8142	−	4.30002i	0.620941	−	0.226004i
$363$	−25.8734	+	9.35354i	−1.35800	+	0.490934i
$364$	1.25757	−	1.05523i	0.0659148	−	0.0553091i
$365$		0			0
$366$	−11.6136	+	4.19846i	−0.607053	+	0.219457i
$367$	−20.3480	+	7.40606i	−1.06216	+	0.386593i	−0.813238	−	0.581931i	$-0.802297\pi$
$367$	−20.3480	+	7.40606i	−1.06216	+	0.386593i	−0.248918	+	0.968525i	$0.580075\pi$
$368$	−7.32448	−	12.6864i	−0.381815	−	0.661323i
$369$	12.7920	+	0.0555839i	0.665924	+	0.00289358i
$370$		0			0
$371$	2.62615	−	14.8936i	0.136343	−	0.773238i
$372$	1.06130	+	0.00230578i	0.0550259	+	0.000119549i
$373$	−28.7136	−	10.4509i	−1.48673	−	0.541126i	−0.534145	−	0.845393i	$-0.679366\pi$
$373$	−28.7136	−	10.4509i	−1.48673	−	0.541126i	−0.952587	+	0.304267i	$0.901589\pi$
$374$	5.94343	+	33.7068i	0.307327	+	1.74294i
$375$		0			0
$376$	−15.8881	−	13.3317i	−0.819365	−	0.687529i
$377$	9.98457			0.514232
$378$	−13.7282	−	5.09822i	−0.706102	−	0.262224i
$379$	6.49045			0.333392			0.166696	−	0.986008i	$-0.446690\pi$
$379$	6.49045			0.333392			0.166696	+	0.986008i	$0.446690\pi$
$380$		0			0
$381$	−4.45795	+	3.72419i	−0.228388	+	0.190796i
$382$	−1.36711	−	7.75324i	−0.0699472	−	0.396690i
$383$	−7.08040	−	2.57705i	−0.361791	−	0.131681i	0.154727	−	0.987957i	$-0.450550\pi$
$383$	−7.08040	−	2.57705i	−0.361791	−	0.131681i	−0.516519	+	0.856276i	$0.672772\pi$
$384$	−5.08778	+	8.76824i	−0.259635	+	0.447452i
$385$		0			0
$386$	12.0758	−	20.9160i	0.614645	−	1.06460i
$387$	−23.7508	−	8.76165i	−1.20732	−	0.445380i
$388$	1.69222	+	2.93102i	0.0859096	+	0.148800i
$389$	7.42372	−	2.70201i	0.376398	−	0.136997i	−0.146892	−	0.989153i	$-0.546927\pi$
$389$	7.42372	−	2.70201i	0.376398	−	0.136997i	0.523289	+	0.852155i	$0.324705\pi$
$390$		0			0
$391$	−20.9946	+	17.6165i	−1.06174	+	0.890906i
$392$	4.25931	−	3.57399i	0.215128	−	0.180514i
$393$	−1.68019	+	9.40926i	−0.0847545	+	0.474635i
$394$	10.5267	−	3.83139i	0.530325	−	0.193023i
$395$		0			0
$396$	−1.29119	+	7.14114i	−0.0648850	+	0.358856i
$397$	0.808746	−	1.40079i	0.0405898	−	0.0703036i	−0.845017	−	0.534740i	$-0.820410\pi$
$397$	0.808746	−	1.40079i	0.0405898	−	0.0703036i	0.885607	+	0.464436i	$0.153743\pi$
$398$	2.17062	−	12.3102i	0.108803	−	0.617054i
$399$	−8.98389	−	15.6389i	−0.449757	−	0.782925i
$400$		0			0
$401$	2.06958	+	11.7372i	0.103350	+	0.586127i	0.991867	+	0.127282i	$0.0406254\pi$
$401$	2.06958	+	11.7372i	0.103350	+	0.586127i	−0.888517	+	0.458844i	$0.848264\pi$
$402$	6.97407	+	2.55553i	0.347835	+	0.127458i
$403$	1.55560	+	1.30530i	0.0774898	+	0.0650216i
$404$	−0.203545			−0.0101268
$405$		0			0
$406$	−18.1999			−0.903244
$407$	−14.6193	−	12.2671i	−0.724652	−	0.608055i
$408$	26.4793	+	9.70289i	1.31092	+	0.480365i
$409$	1.98160	+	11.2382i	0.0979836	+	0.555693i	0.993792	+	0.111253i	$0.0354863\pi$
$409$	1.98160	+	11.2382i	0.0979836	+	0.555693i	−0.895809	+	0.444440i	$0.853403\pi$
$410$		0			0
$411$	−5.12534	−	8.92205i	−0.252814	−	0.440092i
$412$	0.183725	−	1.04196i	0.00905149	−	0.0513336i
$413$	−3.43226	+	5.94484i	−0.168890	+	0.292527i
$414$	17.9762	−	6.45449i	0.883482	−	0.317221i
$415$		0			0
$416$	3.74908	−	1.36455i	0.183814	−	0.0669027i
$417$	−4.85045	+	27.1630i	−0.237528	+	1.33018i
$418$	22.5041	−	18.8832i	1.10071	−	0.923609i
$419$	24.7402	−	20.7595i	1.20864	−	1.01417i	0.209296	−	0.977852i	$-0.432883\pi$
$419$	24.7402	−	20.7595i	1.20864	−	1.01417i	0.999340	−	0.0363142i	$-0.0115617\pi$
$420$		0			0
$421$	−12.6800	+	4.61514i	−0.617986	+	0.224928i	−0.631994	−	0.774974i	$-0.717763\pi$
$421$	−12.6800	+	4.61514i	−0.617986	+	0.224928i	0.0140082	+	0.999902i	$0.495541\pi$
$422$	2.20918	+	3.82641i	0.107541	+	0.186267i
$423$	15.6619	−	13.0264i	0.761509	−	0.633363i
$424$	10.1483	−	17.5774i	0.492846	−	0.853634i
$425$		0			0
$426$	−0.0280929	+	0.0484150i	−0.00136110	+	0.00234572i
$427$	−12.3134	−	4.48169i	−0.595885	−	0.216884i
$428$	0.353799	+	2.00649i	0.0171015	+	0.0969875i
$429$	−10.6562	+	8.90219i	−0.514484	+	0.429802i
$430$		0			0
$431$	23.0480			1.11018			0.555092	−	0.831789i	$-0.312683\pi$
$431$	23.0480			1.11018			0.555092	+	0.831789i	$0.312683\pi$
$432$	−11.2792	−	9.59037i	−0.542673	−	0.461417i
$433$	−28.7044			−1.37944			−0.689722	−	0.724074i	$-0.742267\pi$
$433$	−28.7044			−1.37944			−0.689722	+	0.724074i	$0.742267\pi$
$434$	−2.83554	−	2.37930i	−0.136110	−	0.114210i
$435$		0			0
$436$	−0.644233	−	3.65363i	−0.0308532	−	0.174977i
$437$	22.1045	+	8.04538i	1.05740	+	0.384863i
$438$	−12.4007	−	0.0269418i	−0.592529	−	0.00128733i
$439$	0.464755	−	2.63576i	0.0221816	−	0.125798i	−0.971706	−	0.236193i	$-0.924100\pi$
$439$	0.464755	−	2.63576i	0.0221816	−	0.125798i	0.993888	+	0.110395i	$0.0352115\pi$
$440$		0			0
$441$	2.70999	+	4.74130i	0.129047	+	0.225776i
$442$	5.10312	+	8.83886i	0.242731	+	0.420422i
$443$	−2.62285	+	0.954638i	−0.124615	+	0.0453562i	−0.403575	−	0.914947i	$-0.632233\pi$
$443$	−2.62285	+	0.954638i	−0.124615	+	0.0453562i	0.278960	+	0.960303i	$0.410010\pi$
$444$	−2.79703	+	1.01116i	−0.132741	+	0.0479874i
$445$		0			0
$446$	17.6079	−	14.7748i	0.833760	−	0.699608i
$447$	−33.1698	+	11.9913i	−1.56888	+	0.567167i
$448$	−19.0209	+	6.92304i	−0.898653	+	0.327083i
$449$	−12.0160	−	20.8123i	−0.567069	−	0.982192i	−0.996854	−	0.0792608i	$-0.974744\pi$
$449$	−12.0160	−	20.8123i	−0.567069	−	0.982192i	0.429785	−	0.902931i	$-0.358589\pi$
$450$		0			0
$451$	−11.0545	+	19.1470i	−0.520536	+	0.901595i
$452$	1.27489	−	7.23026i	0.0599658	−	0.340083i
$453$	3.32585	+	0.00722574i	0.156262	+	0.000339495i
$454$	−28.6323	−	10.4213i	−1.34378	−	0.489097i
$455$		0			0
$456$	−4.15138	−	23.8465i	−0.194406	−	1.11671i
$457$	23.5193	+	19.7351i	1.10019	+	0.923167i	0.997438	−	0.0715399i	$-0.0227913\pi$
$457$	23.5193	+	19.7351i	1.10019	+	0.923167i	0.102750	+	0.994707i	$0.467236\pi$
$458$	2.52675			0.118067
$459$	−14.0055	+	23.8972i	−0.653722	+	1.11543i
$460$		0			0
$461$	−8.31123	−	6.97395i	−0.387093	−	0.324809i	0.428387	−	0.903595i	$-0.359082\pi$
$461$	−8.31123	−	6.97395i	−0.387093	−	0.324809i	−0.815479	+	0.578786i	$0.803527\pi$
$462$	19.4240	−	16.2269i	0.903687	−	0.754944i
$463$	5.65658	+	32.0801i	0.262884	+	1.49089i	0.774995	+	0.631968i	$0.217753\pi$
$463$	5.65658	+	32.0801i	0.262884	+	1.49089i	−0.512111	+	0.858919i	$0.671136\pi$
$464$	−17.2903	−	6.29316i	−0.802682	−	0.292153i
$465$		0			0
$466$	1.86609	−	10.5831i	0.0864450	−	0.490254i
$467$	6.85522	−	11.8736i	0.317222	−	0.549445i	−0.662685	−	0.748898i	$-0.730583\pi$
$467$	6.85522	−	11.8736i	0.317222	−	0.549445i	0.979907	+	0.199453i	$0.0639167\pi$
$468$	0.366507	+	2.13271i	0.0169418	+	0.0985846i
$469$	3.94064	+	6.82538i	0.181962	+	0.315167i
$470$		0			0
$471$	−16.8993	−	14.2428i	−0.778676	−	0.656275i
$472$	−7.05730	+	5.92178i	−0.324839	+	0.272572i
$473$	33.5170	−	28.1241i	1.54111	−	1.29315i
$474$	6.24316	−	34.9624i	0.286758	−	1.60587i
$475$		0			0
$476$	2.82998	+	4.90167i	0.129712	+	0.224668i
$477$	15.2154	+	12.8803i	0.696667	+	0.589750i
$478$	2.33545	−	4.04513i	0.106821	−	0.185020i
$479$	−2.05131	+	11.6335i	−0.0937266	+	0.531550i	0.901403	+	0.432980i	$0.142538\pi$
$479$	−2.05131	+	11.6335i	−0.0937266	+	0.531550i	−0.995130	+	0.0985701i	$0.968573\pi$
$480$		0			0
$481$	−5.34758	−	1.94636i	−0.243829	−	0.0887465i
$482$	0.121764	+	0.690558i	0.00554620	+	0.0314541i
$483$	19.0293	+	6.97295i	0.865863	+	0.317280i
$484$	−5.67678	−	4.76339i	−0.258036	−	0.216518i
$485$		0			0
$486$	14.9214	−	12.2468i	0.676848	−	0.555526i
$487$	−31.6087			−1.43233			−0.716163	−	0.697933i	$-0.754103\pi$
$487$	−31.6087			−1.43233			−0.716163	+	0.697933i	$0.754103\pi$
$488$	−13.4716	−	11.3040i	−0.609831	−	0.511709i
$489$	−40.1142	−	14.6992i	−1.81403	−	0.664719i
$490$		0			0
$491$	−15.3997	−	5.60502i	−0.694977	−	0.252951i	−0.0297121	−	0.999558i	$-0.509459\pi$
$491$	−15.3997	−	5.60502i	−0.694977	−	0.252951i	−0.665265	+	0.746608i	$0.731681\pi$
$492$	1.71631	+	2.98771i	0.0773773	+	0.134696i
$493$	−5.97769	+	33.9012i	−0.269222	+	1.52683i
$494$	4.38004	−	7.58644i	0.197067	−	0.341330i
$495$		0			0
$496$	−1.87111	−	3.24087i	−0.0840155	−	0.145519i
$497$	−0.0558127	+	0.0203142i	−0.00250354	+	0.000911215i
$498$	−4.08414	+	22.8716i	−0.183015	+	1.02490i
$499$	−30.4626	+	25.5612i	−1.36369	+	1.14427i	−0.388871	+	0.921292i	$0.627135\pi$
$499$	−30.4626	+	25.5612i	−1.36369	+	1.14427i	−0.974823	+	0.222982i	$0.928421\pi$
$500$		0			0
$501$	−7.09810	−	5.98234i	−0.317120	−	0.267271i
$502$	0.991264	−	0.360791i	0.0442423	−	0.0161029i
$503$	−2.96457	−	5.13479i	−0.132184	−	0.228949i	0.792334	−	0.610087i	$-0.208866\pi$
$503$	−2.96457	−	5.13479i	−0.132184	−	0.228949i	−0.924518	+	0.381138i	$0.875532\pi$
$504$	−3.53203	−	20.5530i	−0.157329	−	0.915502i
$505$		0			0
$506$	−5.73228	+	32.5094i	−0.254831	+	1.44522i
$507$	9.22262	−	15.8942i	0.409591	−	0.705886i
$508$	−1.47028	−	0.535138i	−0.0652331	−	0.0237429i
$509$	7.53016	+	42.7057i	0.333768	+	1.89290i	0.439067	+	0.898454i	$0.355309\pi$
$509$	7.53016	+	42.7057i	0.333768	+	1.89290i	−0.105298	+	0.994441i	$0.533580\pi$
$510$		0			0
$511$	−10.0798	−	8.45798i	−0.445905	−	0.374159i
$512$	−24.7579			−1.09416
$513$	23.7736	+	0.154954i	1.04963	+	0.00684137i
$514$	−22.7787			−1.00473
$515$		0			0
$516$	−1.16948	−	6.71775i	−0.0514834	−	0.295732i
$517$	6.11381	+	34.6731i	0.268885	+	1.52492i
$518$	9.74757	+	3.54783i	0.428284	+	0.155883i
$519$	24.8060	+	0.0538934i	1.08886	+	0.00236566i
$520$		0			0
$521$	−16.3247	+	28.2751i	−0.715196	+	1.23876i	0.247688	+	0.968840i	$0.420329\pi$
$521$	−16.3247	+	28.2751i	−0.715196	+	1.23876i	−0.962884	+	0.269916i	$0.913004\pi$
$522$	12.0854	−	20.7241i	0.528966	−	0.907070i
$523$	−8.80738	−	15.2548i	−0.385120	−	0.667047i	0.606666	−	0.794957i	$-0.292507\pi$
$523$	−8.80738	−	15.2548i	−0.385120	−	0.667047i	−0.991786	+	0.127910i	$0.959173\pi$
$524$	−2.41925	+	0.880534i	−0.105685	+	0.0384663i
$525$		0			0
$526$	−6.62147	+	5.55607i	−0.288710	+	0.242256i
$527$	−5.36328	+	4.50033i	−0.233628	+	0.196037i
$528$	24.0642	−	8.69950i	1.04726	−	0.378597i
$529$	−3.22579	+	1.17409i	−0.140252	+	0.0510475i
$530$		0			0
$531$	−4.49021	−	7.85591i	−0.194859	−	0.340917i
$532$	2.42899	−	4.20713i	0.105310	−	0.182402i
$533$	−1.14482	+	6.49261i	−0.0495878	+	0.281226i
$534$	9.96530	+	0.0216506i	0.431241	+	0.000936913i
$535$		0			0
$536$	1.83671	+	10.4165i	0.0793340	+	0.449925i
$537$	−1.69040	−	9.71006i	−0.0729463	−	0.419020i
$538$	8.58925	+	7.20724i	0.370309	+	0.310726i
$539$	−9.43865			−0.406551
$540$		0			0
$541$	40.8023			1.75423			0.877113	−	0.480284i	$-0.159466\pi$
$541$	40.8023			1.75423			0.877113	+	0.480284i	$0.159466\pi$
$542$	−2.54346	−	2.13421i	−0.109251	−	0.0916723i
$543$	−13.4954	+	11.2741i	−0.579143	+	0.483819i
$544$	2.38859	+	13.5464i	0.102410	+	0.580797i
$545$		0			0
$546$	3.78786	−	6.52798i	0.162106	−	0.279372i
$547$	5.26232	−	29.8441i	0.225000	−	1.27604i	−0.637684	−	0.770298i	$-0.720107\pi$
$547$	5.26232	−	29.8441i	0.225000	−	1.27604i	0.862684	−	0.505743i	$-0.168781\pi$
$548$	1.38575	−	2.40018i	0.0591961	−	0.102531i
$549$	13.2798	−	11.0451i	0.566770	−	0.471395i
$550$		0			0
$551$	27.7646	−	10.1055i	1.18281	−	0.430508i
$552$	20.7978	+	17.5286i	0.885212	+	0.746065i
$553$	28.8684	−	24.2234i	1.22761	−	1.03008i
$554$	9.18393	−	7.70623i	0.390188	−	0.327407i
$555$		0			0
$556$	−6.98398	+	2.54196i	−0.296187	+	0.107803i
$557$	−14.2033	−	24.6008i	−0.601812	−	1.04237i	−0.992547	−	0.121865i	$-0.961112\pi$
$557$	−14.2033	−	24.6008i	−0.601812	−	1.04237i	0.390735	−	0.920503i	$-0.372221\pi$
$558$	4.59221	−	1.64887i	0.194404	−	0.0698021i
$559$	6.52350	−	11.2990i	0.275915	−	0.477898i
$560$		0			0
$561$	−23.8463	−	41.5111i	−1.00679	−	1.75260i
$562$	−15.4296	−	5.61591i	−0.650858	−	0.236893i
$563$	−1.09651	−	6.21863i	−0.0462124	−	0.262084i	0.952944	−	0.303146i	$-0.0980370\pi$
$563$	−1.09651	−	6.21863i	−0.0462124	−	0.262084i	−0.999157	+	0.0410621i	$0.986926\pi$
$564$	5.15203	+	1.88787i	0.216940	+	0.0794937i
$565$		0			0
$566$	−24.2448			−1.01909
$567$	20.4821	+	0.178002i	0.860169	+	0.00747538i
$568$	−0.0797117			−0.00334463
$569$	−2.76710	−	2.32188i	−0.116003	−	0.0973381i	0.582941	−	0.812515i	$-0.301902\pi$
$569$	−2.76710	−	2.32188i	−0.116003	−	0.0973381i	−0.698944	+	0.715176i	$0.746346\pi$
$570$		0			0
$571$	6.03614	+	34.2327i	0.252605	+	1.43259i	0.802147	+	0.597127i	$0.203691\pi$
$571$	6.03614	+	34.2327i	0.252605	+	1.43259i	−0.549542	+	0.835466i	$0.685198\pi$
$572$	−3.51451	−	1.27918i	−0.146949	−	0.0534851i
$573$	5.48513	+	9.54837i	0.229145	+	0.398889i
$574$	2.08678	−	11.8347i	0.0871006	−	0.493972i
$575$		0			0
$576$	4.74740	−	26.2562i	0.197808	−	1.09401i
$577$	11.3377	+	19.6374i	0.471994	+	0.817517i	0.999487	−	0.0320424i	$-0.0102012\pi$
$577$	11.3377	+	19.6374i	0.471994	+	0.817517i	−0.527493	+	0.849559i	$0.676868\pi$
$578$	−13.2842	+	4.83505i	−0.552550	+	0.201112i
$579$	−5.93826	+	33.2549i	−0.246785	+	1.38203i
$580$		0			0
$581$	−18.8851	+	15.8465i	−0.783485	+	0.657422i
$582$	11.8977	+	10.0275i	0.493175	+	0.415652i
$583$	−32.3768	+	11.7842i	−1.34091	+	0.488051i
$584$	−8.82966	−	15.2934i	−0.365374	−	0.632847i
$585$		0			0
$586$	−18.7288	+	32.4391i	−0.773678	+	1.34005i
$587$	−3.28071	+	18.6058i	−0.135410	+	0.767946i	0.839164	+	0.543878i	$0.183045\pi$
$587$	−3.28071	+	18.6058i	−0.135410	+	0.767946i	−0.974574	+	0.224067i	$0.928066\pi$
$588$	−0.738253	+	1.27230i	−0.0304450	+	0.0524688i
$589$	5.64683	+	2.05528i	0.232673	+	0.0846862i
$590$		0			0
$591$	−12.0246	+	10.0454i	−0.494628	+	0.413214i
$592$	8.03366	+	6.74104i	0.330181	+	0.277055i
$593$	−8.73461			−0.358688			−0.179344	−	0.983786i	$-0.557397\pi$
$593$	−8.73461			−0.358688			−0.179344	+	0.983786i	$0.557397\pi$
$594$	5.57918	+	32.8934i	0.228917	+	1.34963i
$595$		0			0
$596$	−7.27765	−	6.10667i	−0.298104	−	0.250139i
$597$	2.99862	+	17.2248i	0.122725	+	0.704963i
$598$	1.70933	+	9.69410i	0.0698998	+	0.396421i
$599$	−6.00796	−	2.18672i	−0.245479	−	0.0893469i	0.216351	−	0.976316i	$-0.430585\pi$
$599$	−6.00796	−	2.18672i	−0.245479	−	0.0893469i	−0.461829	+	0.886969i	$0.652807\pi$
$600$		0			0
$601$	2.30763	−	13.0872i	0.0941304	−	0.533840i	−0.900880	−	0.434068i	$-0.857078\pi$
$601$	2.30763	−	13.0872i	0.0941304	−	0.533840i	0.995010	−	0.0997716i	$-0.0318112\pi$
$602$	−11.8910	+	20.5959i	−0.484642	+	0.839425i
$603$	−10.3888	−	0.0451415i	−0.423064	−	0.00183830i
$604$	0.447916	+	0.775814i	0.0182255	+	0.0315674i
$605$		0			0
$606$	−0.880043	+	0.318146i	−0.0357493	+	0.0129238i
$607$	3.43839	−	2.88515i	0.139560	−	0.117105i	−0.570335	−	0.821412i	$-0.693187\pi$
$607$	3.43839	−	2.88515i	0.139560	−	0.117105i	0.709895	+	0.704307i	$0.248742\pi$
$608$	9.04416	−	7.58895i	0.366789	−	0.307773i
$609$	23.9398	−	8.65451i	0.970088	−	0.350698i
$610$		0			0
$611$	5.24941	+	9.09225i	0.212369	+	0.367833i
$612$	−7.46073	−	0.0324185i	−0.301582	−	0.00131044i
$613$	−11.6086	+	20.1066i	−0.468866	+	0.812100i	−0.999367	−	0.0355848i	$-0.988671\pi$
$613$	−11.6086	+	20.1066i	−0.468866	+	0.812100i	0.530501	+	0.847685i	$0.322004\pi$
$614$	3.92882	−	22.2814i	0.158554	−	0.899205i
$615$		0			0
$616$	33.8694	+	12.3275i	1.36464	+	0.496687i
$617$	7.67572	+	43.5312i	0.309013	+	1.75250i	0.603988	+	0.796993i	$0.293577\pi$
$617$	7.67572	+	43.5312i	0.309013	+	1.75250i	−0.294975	+	0.955505i	$0.595311\pi$
$618$	−0.834253	−	4.79214i	−0.0335586	−	0.192768i
$619$	3.65944	+	3.07064i	0.147085	+	0.123419i	0.713361	−	0.700796i	$-0.247172\pi$
$619$	3.65944	+	3.07064i	0.147085	+	0.123419i	−0.566276	+	0.824216i	$0.691616\pi$
$620$		0			0
$621$	−20.5763	+	17.0383i	−0.825698	+	0.683722i
$622$	41.7838			1.67538
$623$	8.10022	+	6.79689i	0.324529	+	0.272312i
$624$	5.85581	−	4.89197i	0.234420	−	0.195835i
$625$		0			0
$626$	−3.24464	−	1.18095i	−0.129682	−	0.0472004i
$627$	−20.6221	+	35.5399i	−0.823566	+	1.41933i
$628$	1.03371	−	5.86248i	0.0412496	−	0.233938i
$629$	9.81015	−	16.9917i	0.391156	−	0.677502i
$630$		0			0
$631$	−18.1400	−	31.4193i	−0.722140	−	1.25078i	−0.960140	−	0.279518i	$-0.909825\pi$
$631$	−18.1400	−	31.4193i	−0.722140	−	1.25078i	0.238000	−	0.971265i	$-0.423508\pi$
$632$	47.5258	−	17.2980i	1.89047	−	0.688076i
$633$	−4.72546	−	3.98266i	−0.187820	−	0.158297i
$634$	−2.61717	+	2.19607i	−0.103941	+	0.0872169i
$635$		0			0
$636$	−0.943911	+	5.28600i	−0.0374285	+	0.209604i
$637$	−2.64481	+	0.962632i	−0.104791	+	0.0381409i
$638$	20.7318	+	35.9086i	0.820781	+	1.42163i
$639$	0.0139302	−	0.0770431i	0.000551071	−	0.00304778i
$640$		0			0
$641$	3.91713	−	22.2151i	0.154717	−	0.877445i	−0.804327	−	0.594187i	$-0.797474\pi$
$641$	3.91713	−	22.2151i	0.154717	−	0.877445i	0.959044	−	0.283258i	$-0.0914151\pi$
$642$	4.66587	+	8.12222i	0.184147	+	0.320558i
$643$	3.62196	+	1.31828i	0.142836	+	0.0519881i	0.412449	−	0.910981i	$-0.364674\pi$
$643$	3.62196	+	1.31828i	0.142836	+	0.0519881i	−0.269613	+	0.962969i	$0.586896\pi$
$644$	0.947926	+	5.37595i	0.0373535	+	0.211842i
$645$		0			0
$646$	23.1364	+	19.4137i	0.910288	+	0.763823i
$647$	16.5713			0.651486			0.325743	−	0.945458i	$-0.394386\pi$
$647$	16.5713			0.651486			0.325743	+	0.945458i	$0.394386\pi$
$648$	25.7490	+	9.62609i	1.01152	+	0.378148i
$649$	15.6390			0.613884
$650$		0			0
$651$	4.86123	+	1.78131i	0.190527	+	0.0698152i
$652$	−1.99825	−	11.3326i	−0.0782576	−	0.443821i
$653$	−4.85320	−	1.76642i	−0.189920	−	0.0691254i	0.245309	−	0.969445i	$-0.421111\pi$
$653$	−4.85320	−	1.76642i	−0.189920	−	0.0691254i	−0.435230	+	0.900320i	$0.643333\pi$
$654$	−8.49608	−	14.7898i	−0.332223	−	0.578325i
$655$		0			0
$656$	6.07471	−	10.5217i	0.237178	−	0.410804i
$657$	16.3245	−	5.86142i	0.636879	−	0.228676i
$658$	−9.56862	−	16.5733i	−0.373024	−	0.646096i
$659$	33.9146	−	12.3439i	1.32113	−	0.480850i	0.417307	−	0.908766i	$-0.362974\pi$
$659$	33.9146	−	12.3439i	1.32113	−	0.480850i	0.903819	+	0.427915i	$0.140752\pi$
$660$		0			0
$661$	29.5546	−	24.7993i	1.14954	−	0.964580i	0.149833	−	0.988711i	$-0.452127\pi$
$661$	29.5546	−	24.7993i	1.14954	−	0.964580i	0.999709	+	0.0241316i	$0.00768206\pi$
$662$	−26.4953	+	22.2322i	−1.02977	+	0.864079i
$663$	−10.9157	−	9.19981i	−0.423929	−	0.357291i
$664$	−31.0903	+	11.3160i	−1.20654	+	0.439144i
$665$		0			0
$666$	−10.5127	+	8.74362i	−0.407358	+	0.338808i
$667$	−16.6006	+	28.7531i	−0.642778	+	1.11332i
$668$	0.434185	−	2.46238i	0.0167991	−	0.0952725i
$669$	−16.1354	+	27.8076i	−0.623829	+	1.07510i
$670$		0			0
$671$	5.18394	+	29.3996i	0.200124	+	1.13496i
$672$	7.80629	−	6.52141i	0.301134	−	0.251569i
$673$	7.38532	+	6.19702i	0.284683	+	0.238878i	0.773935	−	0.633265i	$-0.218286\pi$
$673$	7.38532	+	6.19702i	0.284683	+	0.238878i	−0.489252	+	0.872143i	$0.662730\pi$
$674$	17.6715			0.680682
$675$		0			0
$676$	4.94968			0.190372
$677$	18.9204	+	15.8761i	0.727169	+	0.610167i	0.929358	−	0.369179i	$-0.120361\pi$
$677$	18.9204	+	15.8761i	0.727169	+	0.610167i	−0.202189	+	0.979346i	$0.564806\pi$
$678$	−5.78898	−	33.2532i	−0.222324	−	1.27708i
$679$	2.86697	+	16.2594i	0.110024	+	0.623979i
$680$		0			0
$681$	42.6180	+	0.0925918i	1.63313	+	0.00354813i
$682$	−1.46437	+	8.30486i	−0.0560737	+	0.318010i
$683$	10.3912	−	17.9981i	0.397609	−	0.688678i	−0.595822	−	0.803117i	$-0.703174\pi$
$683$	10.3912	−	17.9981i	0.397609	−	0.688678i	0.993430	+	0.114438i	$0.0365069\pi$
$684$	3.17770	+	5.55958i	0.121502	+	0.212576i
$685$		0			0
$686$	23.3593	−	8.50208i	0.891861	−	0.324611i
$687$	−3.32364	+	1.20154i	−0.126805	+	0.0458414i
$688$	−18.4184	+	15.4549i	−0.702195	+	0.589212i
$689$	−7.87048	+	6.60411i	−0.299841	+	0.251597i
$690$		0			0
$691$	−12.2565	+	4.46098i	−0.466257	+	0.169704i	−0.564456	−	0.825463i	$-0.690914\pi$
$691$	−12.2565	+	4.46098i	−0.466257	+	0.169704i	0.0981988	+	0.995167i	$0.468692\pi$
$692$	3.34080	+	5.78643i	0.126998	+	0.219967i
$693$	−17.8337	+	30.5812i	−0.677446	+	1.16168i
$694$	10.9387	−	18.9463i	0.415226	−	0.719193i
$695$		0			0
$696$	34.1638	+	0.0742241i	1.29497	+	0.00281346i
$697$	−21.3593	−	7.77416i	−0.809042	−	0.294467i
$698$	−5.26153	−	29.8396i	−0.199152	−	1.12945i
$699$	2.57793	+	14.8082i	0.0975062	+	0.560098i
$700$		0			0
$701$	25.6062			0.967135			0.483567	−	0.875307i	$-0.339341\pi$
$701$	25.6062			0.967135			0.483567	+	0.875307i	$0.339341\pi$
$702$	4.91809	+	8.64807i	0.185621	+	0.326400i
$703$	−16.8402			−0.635141
$704$	35.3263	+	29.6423i	1.33141	+	1.11719i
$705$		0			0
$706$	−6.85846	−	38.8962i	−0.258121	−	1.46388i
$707$	−0.933067	−	0.339609i	−0.0350916	−	0.0127723i
$708$	1.22322	−	2.10809i	0.0459714	−	0.0792268i
$709$	2.06567	−	11.7150i	0.0775777	−	0.439965i	−0.921135	−	0.389243i	$-0.872737\pi$
$709$	2.06567	−	11.7150i	0.0775777	−	0.439965i	0.998713	−	0.0507221i	$-0.0161523\pi$
$710$		0			0
$711$	8.41337	+	48.9576i	0.315526	+	1.83605i
$712$	7.09558	+	12.2899i	0.265918	+	0.460584i
$713$	−6.34531	+	2.30951i	−0.237634	+	0.0864917i
$714$	19.8970	+	16.7694i	0.744628	+	0.627579i
$715$		0			0
$716$	2.03368	−	1.70646i	0.0760021	−	0.0637733i
$717$	−1.14845	+	6.43145i	−0.0428897	+	0.240187i
$718$	9.61363	−	3.49908i	0.358777	−	0.130584i
$719$	−3.31070	−	5.73431i	−0.123468	−	0.213854i	0.797665	−	0.603101i	$-0.206068\pi$
$719$	−3.31070	−	5.73431i	−0.123468	−	0.213854i	−0.921133	+	0.389247i	$0.872735\pi$
$720$		0			0
$721$	2.58068	−	4.46987i	0.0961096	−	0.166467i
$722$	0.415814	−	2.35820i	0.0154750	−	0.0877630i
$723$	−0.488544	−	0.850445i	−0.0181692	−	0.0316284i
$724$	−4.45093	−	1.62000i	−0.165417	−	0.0602070i
$725$		0			0
$726$	−31.9892	−	11.7219i	−1.18723	−	0.435040i
$727$	−9.08463	−	7.62291i	−0.336930	−	0.282718i	0.458586	−	0.888650i	$-0.348356\pi$
$727$	−9.08463	−	7.62291i	−0.336930	−	0.282718i	−0.795517	+	0.605932i	$0.792800\pi$
$728$	10.7478			0.398341
$729$	−13.8037	+	23.2047i	−0.511246	+	0.859434i
$730$		0			0
$731$	34.4587	+	28.9142i	1.27450	+	1.06943i
$732$	4.36844	+	1.60074i	0.161462	+	0.0591650i
$733$	−2.23709	−	12.6872i	−0.0826289	−	0.468612i	−0.997843	−	0.0656441i	$-0.979090\pi$
$733$	−2.23709	−	12.6872i	−0.0826289	−	0.468612i	0.915214	−	0.402968i	$-0.132021\pi$
$734$	−25.1976	−	9.17116i	−0.930059	−	0.338514i
$735$		0			0
$736$	−2.30374	+	13.0651i	−0.0849169	+	0.481588i
$737$	8.97771	−	15.5499i	0.330698	−	0.572786i
$738$	12.0905	+	10.2349i	0.445056	+	0.376754i
$739$	12.2765	+	21.2636i	0.451600	+	0.782194i	0.998486	−	0.0550133i	$-0.0175201\pi$
$739$	12.2765	+	21.2636i	0.451600	+	0.782194i	−0.546886	+	0.837207i	$0.684187\pi$
$740$		0			0
$741$	−2.15387	+	12.0619i	−0.0791243	+	0.443104i
$742$	14.3463	−	12.0380i	0.526669	−	0.441928i
$743$	−31.5847	+	26.5027i	−1.15873	+	0.972291i	−0.999887	−	0.0150131i	$-0.995221\pi$
$743$	−31.5847	+	26.5027i	−1.15873	+	0.972291i	−0.158844	+	0.987304i	$0.550777\pi$
$744$	5.31301	+	4.47785i	0.194784	+	0.164166i
$745$		0			0
$746$	−18.9194	−	32.7694i	−0.692690	−	1.19977i
$747$	−5.50385	−	32.0270i	−0.201375	−	1.17181i
$748$	6.44737	−	11.1672i	0.235739	−	0.408313i
$749$	−1.72593	+	9.78822i	−0.0630640	+	0.357654i
$750$		0			0
$751$	−11.6980	−	4.25772i	−0.426866	−	0.155366i	0.119648	−	0.992816i	$-0.461823\pi$
$751$	−11.6980	−	4.25772i	−0.426866	−	0.155366i	−0.546514	+	0.837450i	$0.684045\pi$
$752$	−3.35968	−	19.0537i	−0.122515	−	0.694817i
$753$	−1.13233	+	0.945949i	−0.0412642	+	0.0344723i
$754$	9.47154	+	7.94756i	0.344933	+	0.289433i
$755$		0			0
$756$	2.72737	+	4.79586i	0.0991935	+	0.174424i
$757$	11.3137			0.411203			0.205602	−	0.978636i	$-0.434085\pi$
$757$	11.3137			0.411203			0.205602	+	0.978636i	$0.434085\pi$
$758$	6.15696	+	5.16630i	0.223631	+	0.187648i
$759$	−7.91891	−	45.4881i	−0.287438	−	1.65111i
$760$		0			0
$761$	−21.2994	−	7.75233i	−0.772101	−	0.281022i	−0.0742262	−	0.997241i	$-0.523649\pi$
$761$	−21.2994	−	7.75233i	−0.772101	−	0.281022i	−0.697875	+	0.716220i	$0.745871\pi$
$762$	−7.19329	−	0.0156281i	−0.260585	−	0.000566147i
$763$	3.14274	−	17.8234i	0.113775	−	0.645250i
$764$	−1.48302	+	2.56867i	−0.0536539	+	0.0929313i
$765$		0			0
$766$	−4.66529	−	8.08053i	−0.168564	−	0.291961i
$767$	4.38222	−	1.59500i	0.158233	−	0.0575920i
$768$	17.1687	−	6.20668i	0.619521	−	0.223964i
$769$	11.6191	−	9.74955i	0.418994	−	0.351578i	−0.408786	−	0.912630i	$-0.634048\pi$
$769$	11.6191	−	9.74955i	0.418994	−	0.351578i	0.827780	+	0.561052i	$0.189603\pi$
$770$		0			0
$771$	29.9627	−	10.8319i	1.07908	−	0.390101i
$772$	−8.55027	+	3.11204i	−0.307731	+	0.112005i
$773$	2.42962	+	4.20823i	0.0873874	+	0.151359i	0.906406	−	0.422407i	$-0.138815\pi$
$773$	2.42962	+	4.20823i	0.0873874	+	0.151359i	−0.819019	+	0.573767i	$0.805482\pi$
$774$	−15.5563	−	27.2167i	−0.559160	−	0.978286i
$775$		0			0
$776$	−3.84768	+	21.8213i	−0.138124	+	0.783338i
$777$	−14.5089	−	0.0315219i	−0.520502	−	0.00113084i
$778$	9.19303	+	3.34599i	0.329586	+	0.119960i
$779$	3.38777	+	19.2130i	0.121379	+	0.688377i
$780$		0			0
$781$	0.103657	+	0.0869789i	0.00370916	+	0.00311235i
$782$	−33.9383			−1.21363
$783$	−6.04211	+	33.0071i	−0.215928	+	1.17958i
$784$	5.18676			0.185241
$785$		0			0
$786$	−9.08349	+	7.58838i	−0.323997	+	0.270669i
$787$	0.851088	+	4.82676i	0.0303380	+	0.172055i	0.996212	−	0.0869567i	$-0.0277142\pi$
$787$	0.851088	+	4.82676i	0.0303380	+	0.172055i	−0.965874	+	0.259012i	$0.916603\pi$
$788$	−3.96585	−	1.44345i	−0.141278	−	0.0514209i
$789$	6.06770	−	10.4570i	0.216016	−	0.372280i
$790$		0			0
$791$	17.9076	−	31.0170i	0.636723	−	1.10284i
$792$	−36.5279	+	30.3810i	−1.29796	+	1.07954i
$793$	4.45101	+	7.70938i	0.158060	+	0.273768i
$794$	1.88220	−	0.685063i	0.0667966	−	0.0243120i
$795$		0			0
$796$	−3.60756	+	3.02710i	−0.127866	+	0.107293i
$797$	42.7450	−	35.8673i	1.51411	−	1.27049i	0.658855	−	0.752270i	$-0.271041\pi$
$797$	42.7450	−	35.8673i	1.51411	−	1.27049i	0.855250	−	0.518215i	$-0.173403\pi$
$798$	3.92607	−	21.9864i	0.138981	−	0.778310i
$799$	−34.0142	+	12.3802i	−1.20334	+	0.437978i
$800$		0			0
$801$	−13.1185	+	4.71028i	−0.463518	+	0.166430i
$802$	−7.37937	+	12.7814i	−0.260575	+	0.451328i
$803$	−5.20557	+	29.5223i	−0.183701	+	1.04182i
$804$	−1.39387	−	2.42641i	−0.0491581	−	0.0855731i
$805$		0			0
$806$	0.436667	+	2.47646i	0.0153809	+	0.0872296i
$807$	−14.7254	−	5.39585i	−0.518358	−	0.189943i
$808$	−1.02084	−	0.856584i	−0.0359129	−	0.0301345i
$809$	−25.0205			−0.879673			−0.439837	−	0.898078i	$-0.644964\pi$
$809$	−25.0205			−0.879673			−0.439837	+	0.898078i	$0.644964\pi$
$810$		0			0
$811$	22.4129			0.787024			0.393512	−	0.919320i	$-0.371260\pi$
$811$	22.4129			0.787024			0.393512	+	0.919320i	$0.371260\pi$
$812$	5.25253	+	4.40739i	0.184328	+	0.154669i
$813$	4.36049	+	1.59783i	0.152929	+	0.0560382i
$814$	−4.10374	−	23.2735i	−0.143836	−	0.815735i
$815$		0			0
$816$	13.1041	+	22.8113i	0.458736	+	0.798556i
$817$	6.70435	−	38.0222i	0.234555	−	1.33023i
$818$	−7.06565	+	12.2381i	−0.247045	+	0.427894i
$819$	−1.87826	+	10.3880i	−0.0656318	+	0.362986i
$820$		0			0
$821$	−37.8576	+	13.7790i	−1.32124	+	0.480892i	−0.903855	−	0.427838i	$-0.859275\pi$
$821$	−37.8576	+	13.7790i	−1.32124	+	0.480892i	−0.417384	+	0.908730i	$0.637053\pi$
$822$	2.23983	−	12.5433i	0.0781231	−	0.437498i
$823$	−10.6791	+	8.96086i	−0.372251	+	0.312356i	−0.809651	−	0.586911i	$-0.800344\pi$
$823$	−10.6791	+	8.96086i	−0.372251	+	0.312356i	0.437400	+	0.899267i	$0.355899\pi$
$824$	5.30632	−	4.45253i	0.184854	−	0.155111i
$825$		0			0
$826$	−7.98790	+	2.90736i	−0.277935	+	0.101160i
$827$	17.5386	+	30.3778i	0.609878	+	1.05634i	0.991260	+	0.131922i	$0.0421150\pi$
$827$	17.5386	+	30.3778i	0.609878	+	1.05634i	−0.381382	+	0.924418i	$0.624552\pi$
$828$	−6.75104	−	2.49045i	−0.234615	−	0.0865491i
$829$	16.3803	−	28.3716i	0.568912	−	0.985385i	−0.427762	−	0.903892i	$-0.640698\pi$
$829$	16.3803	−	28.3716i	0.568912	−	0.985385i	0.996674	−	0.0814933i	$-0.0259689\pi$
$830$		0			0
$831$	−8.41586	+	14.5038i	−0.291943	+	0.503132i
$832$	12.9220	+	4.70322i	0.447989	+	0.163055i
$833$	−1.68505	−	9.55639i	−0.0583835	−	0.331109i
$834$	−26.2226	+	21.9064i	−0.908014	+	0.758558i
$835$		0			0
$836$	−11.0676			−0.382782
$837$	−5.25643	+	4.35260i	−0.181689	+	0.150448i
$838$	39.9932			1.38154
$839$	13.1790	+	11.0585i	0.454991	+	0.381783i	0.841284	−	0.540593i	$-0.181800\pi$
$839$	13.1790	+	11.0585i	0.454991	+	0.381783i	−0.386293	+	0.922376i	$0.626245\pi$
$840$		0			0
$841$	2.20580	+	12.5097i	0.0760621	+	0.431370i
$842$	−15.7021	−	5.71508i	−0.541128	−	0.196955i
$843$	22.9663	+	0.0498965i	0.791001	+	0.00171853i
$844$	0.289053	−	1.63930i	0.00994960	−	0.0564270i
$845$		0			0
$846$	25.2259	+	0.109612i	0.867286	+	0.00376854i
$847$	−18.0752	−	31.3072i	−0.621073	−	1.07573i
$848$	17.7918	−	6.47569i	0.610973	−	0.222376i
$849$	31.8912	−	11.5290i	1.09450	−	0.395675i
$850$		0			0
$851$	14.4961	−	12.1636i	0.496919	−	0.416964i
$852$	0.0198322	−	0.00716956i	0.000679439	−	0.000245625i
$853$	45.7258	−	16.6428i	1.56562	−	0.569840i	0.593606	−	0.804756i	$-0.297704\pi$
$853$	45.7258	−	16.6428i	1.56562	−	0.569840i	0.972016	+	0.234916i	$0.0754815\pi$
$854$	−8.11330	−	14.0526i	−0.277631	−	0.480872i
$855$		0			0
$856$	−6.66956	+	11.5520i	−0.227961	+	0.394840i
$857$	−1.67160	+	9.48011i	−0.0571008	+	0.323835i	−0.999956	−	0.00936777i	$-0.997018\pi$
$857$	−1.67160	+	9.48011i	−0.0571008	+	0.323835i	0.942855	+	0.333202i	$0.108129\pi$
$858$	−17.1946	−	0.0373570i	−0.587015	−	0.00127535i
$859$	30.1158	+	10.9613i	1.02754	+	0.373993i	0.800143	−	0.599809i	$-0.204757\pi$
$859$	30.1158	+	10.9613i	1.02754	+	0.373993i	0.227395	+	0.973803i	$0.426979\pi$
$860$		0			0
$861$	2.88280	+	16.5595i	0.0982457	+	0.564346i
$862$	21.8638	+	18.3459i	0.744682	+	0.624863i
$863$	−11.1232			−0.378637			−0.189319	−	0.981916i	$-0.560628\pi$
$863$	−11.1232			−0.378637			−0.189319	+	0.981916i	$0.560628\pi$
$864$	2.24221	+	13.2195i	0.0762815	+	0.449735i
$865$		0			0
$866$	−27.2295	−	22.8482i	−0.925295	−	0.776415i
$867$	15.1746	−	12.6769i	0.515356	−	0.430531i
$868$	0.242158	+	1.37334i	0.00821936	+	0.0466143i
$869$	−80.6777	−	29.3643i	−2.73680	−	0.996114i
$870$		0			0
$871$	0.929747	−	5.27286i	0.0315033	−	0.178664i
$872$	12.1446	−	21.0351i	0.411268	−	0.712338i
$873$	−20.4183	−	7.53229i	−0.691055	−	0.254930i
$874$	14.5647	+	25.2268i	0.492659	+	0.853310i
$875$		0			0
$876$	3.57235	+	3.01081i	0.120699	+	0.101726i
$877$	−40.9704	+	34.3783i	−1.38347	+	1.16087i	−0.415567	+	0.909563i	$0.636417\pi$
$877$	−40.9704	+	34.3783i	−1.38347	+	1.16087i	−0.967907	+	0.251309i	$0.919139\pi$
$878$	2.53890	−	2.13039i	0.0856836	−	0.0718971i
$879$	9.20980	−	51.5758i	0.310639	−	1.73961i
$880$		0			0
$881$	−12.0656	−	20.8982i	−0.406500	−	0.704078i	0.587995	−	0.808864i	$-0.299917\pi$
$881$	−12.0656	−	20.8982i	−0.406500	−	0.704078i	−0.994495	+	0.104787i	$0.966584\pi$
$882$	−1.20326	+	6.65479i	−0.0405158	+	0.224078i
$883$	8.87464	−	15.3713i	0.298655	−	0.517286i	−0.677173	−	0.735824i	$-0.736795\pi$
$883$	8.87464	−	15.3713i	0.298655	−	0.517286i	0.975829	+	0.218537i	$0.0701286\pi$
$884$	0.667701	−	3.78672i	0.0224572	−	0.127361i
$885$		0			0
$886$	−3.24795	−	1.18216i	−0.109117	−	0.0397154i
$887$	0.364220	+	2.06559i	0.0122293	+	0.0693559i	0.990312	−	0.138863i	$-0.0443446\pi$
$887$	0.364220	+	2.06559i	0.0122293	+	0.0693559i	−0.978082	+	0.208218i	$0.933234\pi$
$888$	−18.2831	−	6.69953i	−0.613542	−	0.224822i
$889$	−5.84701	−	4.90623i	−0.196103	−	0.164550i
$890$		0			0
$891$	−22.9804	−	40.6143i	−0.769872	−	1.36063i
$892$	−8.65966			−0.289947
$893$	23.7996	+	19.9703i	0.796425	+	0.668280i
$894$	−41.0103	−	15.0275i	−1.37159	−	0.502595i
$895$		0			0
$896$	−12.5171	−	4.55584i	−0.418166	−	0.152200i
$897$	−6.85822	−	11.9386i	−0.228989	−	0.398619i
$898$	5.16769	−	29.3074i	0.172448	−	0.978001i
$899$	−4.24080	+	7.34528i	−0.141439	+	0.244979i
$900$		0			0
$901$	−17.7113	−	30.6769i	−0.590049	−	1.02200i
$902$	−25.7272	+	9.36392i	−0.856621	+	0.311785i
$903$	5.84737	−	32.7459i	0.194588	−	1.08972i
$904$	36.8212	−	30.8966i	1.22465	−	1.02761i
$905$		0			0
$906$	3.14921	+	2.65418i	0.104626	+	0.0881793i
$907$	40.1727	−	14.6217i	1.33391	−	0.485504i	0.426022	−	0.904713i	$-0.359915\pi$
$907$	40.1727	−	14.6217i	1.33391	−	0.485504i	0.907890	+	0.419208i	$0.137692\pi$
$908$	5.73967	+	9.94141i	0.190478	+	0.329917i
$909$	1.00631	−	0.836966i	0.0333770	−	0.0277604i
$910$		0			0
$911$	3.61639	−	20.5096i	0.119816	−	0.679513i	−0.864436	−	0.502743i	$-0.832324\pi$
$911$	3.61639	−	20.5096i	0.119816	−	0.679513i	0.984252	−	0.176770i	$-0.0565647\pi$
$912$	11.3323	−	19.5300i	0.375251	−	0.646704i
$913$	52.7776	+	19.2095i	1.74668	+	0.635741i
$914$	6.60204	+	37.4420i	0.218376	+	1.23847i
$915$		0			0
$916$	−0.729227	−	0.611894i	−0.0240943	−	0.0202175i
$917$	−12.5591			−0.414739
$918$	−32.3077	+	11.5211i	−1.06631	+	0.380254i
$919$	−14.9586			−0.493438			−0.246719	−	0.969087i	$-0.579352\pi$
$919$	−14.9586			−0.493438			−0.246719	+	0.969087i	$0.579352\pi$
$920$		0			0
$921$	5.42750	+	31.1768i	0.178842	+	1.02731i
$922$	−2.33302	−	13.2312i	−0.0768340	−	0.435747i
$923$	0.0379168	+	0.0138006i	0.00124805	+	0.000454252i
$924$	−9.53543	−	0.0207167i	−0.313693	−	0.000681528i
$925$		0			0
$926$	−20.1693	+	34.9343i	−0.662804	+	1.14801i
$927$	3.37615	+	5.90679i	0.110887	+	0.194004i
$928$	8.33188	+	14.4312i	0.273507	+	0.473729i
$929$	−25.6422	+	9.33300i	−0.841294	+	0.306206i	−0.726486	−	0.687182i	$-0.758848\pi$
$929$	−25.6422	+	9.33300i	−0.841294	+	0.306206i	−0.114808	+	0.993388i	$0.536625\pi$
$930$		0			0
$931$	−6.38026	+	5.35367i	−0.209105	+	0.175460i
$932$	−3.10144	+	2.60241i	−0.101591	+	0.0852449i
$933$	−54.9617	+	19.8693i	−1.79936	+	0.650491i
$934$	15.9542	−	5.80685i	0.522037	−	0.190006i
$935$		0			0
$936$	−7.13699	+	12.2385i	−0.233280	+	0.400028i
$937$	27.1913	−	47.0967i	0.888300	−	1.53858i	0.0464165	−	0.998922i	$-0.485220\pi$
$937$	27.1913	−	47.0967i	0.888300	−	1.53858i	0.841884	−	0.539659i	$-0.181447\pi$
$938$	−1.69474	+	9.61136i	−0.0553353	+	0.313822i
$939$	4.82952	+	0.0104926i	0.157605	+	0.000342413i
$940$		0			0
$941$	−8.21935	−	46.6142i	−0.267943	−	1.51958i	−0.760522	−	0.649313i	$-0.775057\pi$
$941$	−8.21935	−	46.6142i	−0.267943	−	1.51958i	0.492579	−	0.870268i	$-0.336054\pi$
$942$	−4.69385	−	26.9625i	−0.152934	−	0.878487i
$943$	−16.7937	−	14.0916i	−0.546878	−	0.458885i
$944$	−8.59400			−0.279711
$945$		0			0
$946$	54.1812			1.76158
$947$	−31.0617	−	26.0639i	−1.00937	−	0.846962i	−0.0211155	−	0.999777i	$-0.506722\pi$
$947$	−31.0617	−	26.0639i	−1.00937	−	0.846962i	−0.988255	+	0.152815i	$0.951166\pi$
$948$	−10.2685	+	8.57834i	−0.333505	+	0.278612i
$949$	1.55227	+	8.80337i	0.0503889	+	0.285769i
$950$		0			0
$951$	2.39829	−	4.13319i	0.0777699	−	0.134028i
$952$	−6.43465	+	36.4927i	−0.208548	+	1.18273i
$953$	−13.4443	+	23.2862i	−0.435504	+	0.754315i	−0.997337	−	0.0729359i	$-0.976763\pi$
$953$	−13.4443	+	23.2862i	−0.435504	+	0.754315i	0.561833	+	0.827251i	$0.310096\pi$
$954$	4.18107	+	24.3298i	0.135367	+	0.787705i
$955$		0			0
$956$	−1.65361	+	0.601865i	−0.0534816	+	0.0194657i
$957$	−44.3457	−	37.3750i	−1.43349	−	1.20816i
$958$	−11.2060	+	9.40297i	−0.362050	+	0.303796i
$959$	10.3570	−	8.69054i	0.334444	−	0.280632i
$960$		0			0
$961$	27.5095	−	10.0126i	0.887403	−	0.322988i
$962$	−3.52354	−	6.10295i	−0.113603	−	0.196767i
$963$	−9.99972	−	8.46508i	−0.322236	−	0.272783i
$964$	0.132088	−	0.228784i	0.00425428	−	0.00736864i
$965$		0			0
$966$	12.5012	+	21.7617i	0.402218	+	0.700171i
$967$	35.8418	+	13.0453i	1.15259	+	0.419510i	0.846446	−	0.532474i	$-0.178738\pi$
$967$	35.8418	+	13.0453i	1.15259	+	0.419510i	0.306147	+	0.951984i	$0.400960\pi$
$968$	−8.42480	−	47.7794i	−0.270783	−	1.53569i
$969$	−39.6649	−	14.5345i	−1.27422	−	0.466916i
$970$		0			0
$971$	−52.8853			−1.69717			−0.848585	−	0.529059i	$-0.822545\pi$
$971$	−52.8853			−1.69717			−0.848585	+	0.529059i	$0.822545\pi$
$972$	−7.27212	−	0.0789999i	−0.233253	−	0.00253392i
$973$	−36.2562			−1.16232
$974$	−29.9846	−	25.1600i	−0.960767	−	0.806179i
$975$		0			0
$976$	−2.84870	−	16.1558i	−0.0911846	−	0.517134i
$977$	−19.6744	−	7.16089i	−0.629439	−	0.229097i	0.00754795	−	0.999972i	$-0.497597\pi$
$977$	−19.6744	−	7.16089i	−0.629439	−	0.229097i	−0.636987	+	0.770874i	$0.719820\pi$
$978$	−26.3527	−	45.8742i	−0.842668	−	1.46689i
$979$	4.18324	−	23.7243i	0.133697	−	0.758233i
$980$		0			0
$981$	18.2085	+	15.4141i	0.581353	+	0.492133i
$982$	−10.1469	−	17.5749i	−0.323800	−	0.560838i
$983$	35.0835	−	12.7694i	1.11899	−	0.407279i	0.284707	−	0.958615i	$-0.408104\pi$
$983$	35.0835	−	12.7694i	1.11899	−	0.407279i	0.834284	+	0.551335i	$0.185881\pi$
$984$	−3.96546	+	22.2070i	−0.126414	+	0.707933i
$985$		0			0
$986$	−32.6553	+	27.4011i	−1.03996	+	0.872628i
$987$	20.4674	+	17.2501i	0.651486	+	0.549078i
$988$	−3.10127	+	1.12877i	−0.0986646	+	0.0359110i
$989$	21.6923	+	37.5721i	0.689774	+	1.19472i
$990$		0			0
$991$	17.5105	−	30.3291i	0.556240	−	0.963436i	−0.441566	−	0.897229i	$-0.645577\pi$
$991$	17.5105	−	30.3291i	0.556240	−	0.963436i	0.997806	−	0.0662071i	$-0.0210898\pi$
$992$	−0.588514	+	3.33763i	−0.0186853	+	0.105970i
$993$	24.2794	−	41.8430i	0.770485	−	1.32785i
$994$	−0.0691147	−	0.0251557i	−0.00219218	−	0.000797890i
$995$		0			0
$996$	6.71743	−	5.61177i	0.212850	−	0.177816i
$997$	−36.5143	−	30.6391i	−1.15642	−	0.970351i	−0.156569	−	0.987667i	$-0.550043\pi$
$997$	−36.5143	−	30.6391i	−1.15642	−	0.970351i	−0.999850	+	0.0173159i	$0.994488\pi$
$998$	−49.2436			−1.55878
$999$	9.67036	−	16.5002i	0.305957	−	0.522045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.h.151.11		96
5.2	odd	4		135.2.p.a.124.6	yes	96
5.3	odd	4		135.2.p.a.124.11	yes	96
5.4	even	2	inner	675.2.l.h.151.6		96
15.2	even	4		405.2.p.a.289.11		96
15.8	even	4		405.2.p.a.289.6		96
27.22	even	9	inner	675.2.l.h.76.11		96
135.22	odd	36		135.2.p.a.49.11	yes	96
135.32	even	36		405.2.p.a.199.6		96
135.49	even	18	inner	675.2.l.h.76.6		96
135.103	odd	36		135.2.p.a.49.6	✓	96
135.113	even	36		405.2.p.a.199.11		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.6	✓	96	135.103	odd	36
135.2.p.a.49.11	yes	96	135.22	odd	36
135.2.p.a.124.6	yes	96	5.2	odd	4
135.2.p.a.124.11	yes	96	5.3	odd	4
405.2.p.a.199.6		96	135.32	even	36
405.2.p.a.199.11		96	135.113	even	36
405.2.p.a.289.6		96	15.8	even	4
405.2.p.a.289.11		96	15.2	even	4
675.2.l.h.76.6		96	135.49	even	18	inner
675.2.l.h.76.11		96	27.22	even	9	inner
675.2.l.h.151.6		96	5.4	even	2	inner
675.2.l.h.151.11		96	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.948617 + 0.795984i) q^{2} +(-1.62630 - 0.595931i) q^{3} +(-0.0810128 - 0.459446i) q^{4} +(-1.06839 - 1.85982i) q^{6} +(0.395202 - 2.24130i) q^{7} +(1.52719 - 2.64518i) q^{8} +(2.28973 + 1.93833i) q^{9} +(-4.87230 + 1.77337i) q^{11} +(-0.142047 + 0.795478i) q^{12} +(-1.18441 + 0.993836i) q^{13} +(2.15894 - 1.81156i) q^{14} +(2.67745 - 0.974511i) q^{16} +(-2.66533 - 4.61649i) q^{17} +(0.629199 + 3.66133i) q^{18} +(-2.28767 + 3.96236i) q^{19} +(-1.97838 + 3.40953i) q^{21} +(-6.03353 - 2.19602i) q^{22} +(-0.892775 - 5.06318i) q^{23} +(-4.06003 + 3.39176i) q^{24} -1.91463 q^{26} +(-2.56869 - 4.51684i) q^{27} -1.06177 q^{28} +(-4.94693 - 4.15097i) q^{29} +(-0.228069 - 1.29344i) q^{31} +(-2.42480 - 0.882557i) q^{32} +(8.98066 + 0.0195113i) q^{33} +(1.14627 - 6.50084i) q^{34} +(0.705061 - 1.20904i) q^{36} +(1.84032 + 3.18754i) q^{37} +(-5.32410 + 1.93781i) q^{38} +(2.51847 - 0.910455i) q^{39} +(3.26644 - 2.74087i) q^{41} +(-4.59066 + 1.65958i) q^{42} +(-7.92956 + 2.88612i) q^{43} +(1.20949 + 2.09490i) q^{44} +(3.18331 - 5.51365i) q^{46} +(1.17913 - 6.68721i) q^{47} +(-4.93508 - 0.0107219i) q^{48} +(1.71059 + 0.622605i) q^{49} +(1.58353 + 9.09617i) q^{51} +(0.552567 + 0.463658i) q^{52} +6.64507 q^{53} +(1.15863 - 6.32939i) q^{54} +(-5.32509 - 4.46828i) q^{56} +(6.08174 - 5.08071i) q^{57} +(-1.38864 - 7.87536i) q^{58} +(-2.83430 - 1.03160i) q^{59} +(0.999796 - 5.67013i) q^{61} +(0.813210 - 1.40852i) q^{62} +(5.24929 - 4.36595i) q^{63} +(-4.44699 - 7.70241i) q^{64} +(8.50367 + 7.16697i) q^{66} +(-2.65278 + 2.22595i) q^{67} +(-1.90510 + 1.59857i) q^{68} +(-1.56538 + 8.76630i) q^{69} +(-0.0130487 - 0.0226011i) q^{71} +(8.62409 - 3.09654i) q^{72} +(2.89081 - 5.00704i) q^{73} +(-0.791465 + 4.48862i) q^{74} +(2.00582 + 0.730059i) q^{76} +(2.04912 + 11.6211i) q^{77} +(3.11377 + 1.14099i) q^{78} +(12.6845 + 10.6435i) q^{79} +(1.48575 + 8.87652i) q^{81} +5.28029 q^{82} +(-8.29793 - 6.96279i) q^{83} +(1.72677 + 0.632744i) q^{84} +(-9.81943 - 3.57398i) q^{86} +(5.57153 + 9.69877i) q^{87} +(-2.75006 + 15.5964i) q^{88} +(-2.32308 + 4.02369i) q^{89} +(1.75941 + 3.04738i) q^{91} +(-2.25393 + 0.820364i) q^{92} +(-0.399893 + 2.23944i) q^{93} +(6.44146 - 5.40503i) q^{94} +(3.41753 + 2.88032i) q^{96} +(-6.81695 + 2.48117i) q^{97} +(1.12712 + 1.95222i) q^{98} +(-14.5937 - 5.38358i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} - 6 q^{6} + 18 q^{9} - 6 q^{11} + 18 q^{14} - 24 q^{16} + 6 q^{19} + 24 q^{21} + 30 q^{24} + 48 q^{26} + 30 q^{29} - 30 q^{31} + 24 q^{34} + 54 q^{36} + 6 q^{39} - 12 q^{41} - 78 q^{44}+ \cdots - 36 q^{99}+O(q^{100}) \) 96 * q + 12 * q^4 - 6 * q^6 + 18 * q^9 - 6 * q^11 + 18 * q^14 - 24 * q^16 + 6 * q^19 + 24 * q^21 + 30 * q^24 + 48 * q^26 + 30 * q^29 - 30 * q^31 + 24 * q^34 + 54 * q^36 + 6 * q^39 - 12 * q^41 - 78 * q^44 - 6 * q^46 + 30 * q^49 - 90 * q^51 - 108 * q^54 - 96 * q^56 - 66 * q^59 + 6 * q^61 - 150 * q^66 - 24 * q^69 - 90 * q^71 - 66 * q^74 + 12 * q^76 - 24 * q^79 - 54 * q^81 - 198 * q^84 + 18 * q^86 - 96 * q^89 - 6 * q^91 - 24 * q^94 + 42 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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