LMFDB - Embedded newform 625.2.g.b.451.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(26,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([14]))

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

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

chi := DirichletCharacter("625.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.g (of order $25$, degree $20$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$24$ over $\Q(\zeta_{25})$
Twist minimal:	no (minimal twist has level 125)
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			451.17
Character	$\chi$	$=$	625.451
Dual form			625.2.g.b.176.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28126 + 0.161861i) q^{2} +(1.41863 + 1.71483i) q^{3} +(-0.321728 - 0.0826056i) q^{4} +(1.54008 + 2.42678i) q^{6} +(0.740638 + 2.27945i) q^{7} +(-2.80036 - 1.10874i) q^{8} +(-0.365988 + 1.91858i) q^{9} +O(q^{10})$	\(q+(1.28126 + 0.161861i) q^{2} +(1.41863 + 1.71483i) q^{3} +(-0.321728 - 0.0826056i) q^{4} +(1.54008 + 2.42678i) q^{6} +(0.740638 + 2.27945i) q^{7} +(-2.80036 - 1.10874i) q^{8} +(-0.365988 + 1.91858i) q^{9} +(4.57197 + 0.577574i) q^{11} +(-0.314759 - 0.668897i) q^{12} +(-1.08143 + 5.66906i) q^{13} +(0.579998 + 3.04046i) q^{14} +(-2.82639 - 1.55382i) q^{16} +(-4.20471 + 1.07959i) q^{17} +(-0.779471 + 2.39897i) q^{18} +(3.02560 - 3.65732i) q^{19} +(-2.85818 + 4.50378i) q^{21} +(5.76442 + 1.48005i) q^{22} +(0.587001 + 0.551231i) q^{23} +(-2.07138 - 6.37505i) q^{24} +(-2.30320 + 7.08852i) q^{26} +(2.04161 - 1.12238i) q^{27} +(-0.0499884 - 0.794543i) q^{28} +(-0.0122026 - 0.193954i) q^{29} +(0.935449 - 0.240183i) q^{31} +(1.50346 + 1.09233i) q^{32} +(5.49551 + 8.65953i) q^{33} +(-5.56208 + 0.702655i) q^{34} +(0.276234 - 0.587027i) q^{36} +(-7.25681 - 3.98946i) q^{37} +(4.46857 - 4.19627i) q^{38} +(-11.2556 + 6.18784i) q^{39} +(0.442053 - 0.415115i) q^{41} +(-4.39107 + 5.30790i) q^{42} +(9.09003 - 6.60429i) q^{43} +(-1.42322 - 0.563492i) q^{44} +(0.662880 + 0.801285i) q^{46} +(3.71428 - 1.47059i) q^{47} +(-1.34507 - 7.05108i) q^{48} +(1.01577 - 0.738000i) q^{49} +(-7.81625 - 5.67884i) q^{51} +(0.816222 - 1.73456i) q^{52} +(-4.41327 + 6.95421i) q^{53} +(2.79751 - 1.10761i) q^{54} +(0.453266 - 7.20446i) q^{56} +10.5639 q^{57} +(0.0157590 - 0.250482i) q^{58} +(-2.33894 - 4.97049i) q^{59} +(-8.65640 - 8.12890i) q^{61} +(1.23743 - 0.156324i) q^{62} +(-4.64437 + 0.586720i) q^{63} +(6.45186 + 6.05870i) q^{64} +(5.63955 + 11.9847i) q^{66} +(0.0683896 - 1.08702i) q^{67} +1.44195 q^{68} +(-0.112529 + 1.78860i) q^{69} +(0.401350 - 0.158906i) q^{71} +(3.15211 - 4.96693i) q^{72} +(6.24516 - 13.2717i) q^{73} +(-8.65215 - 6.28615i) q^{74} +(-1.27554 + 0.926731i) q^{76} +(2.06963 + 10.8494i) q^{77} +(-15.4230 + 6.10641i) q^{78} +(-0.594972 - 0.719197i) q^{79} +(10.2690 + 4.06580i) q^{81} +(0.633577 - 0.460321i) q^{82} +(-1.16915 + 1.41326i) q^{83} +(1.29159 - 1.21289i) q^{84} +(12.7157 - 6.99052i) q^{86} +(0.315288 - 0.296076i) q^{87} +(-12.1628 - 6.68655i) q^{88} +(1.00941 - 2.14511i) q^{89} +(-13.7233 + 1.73365i) q^{91} +(-0.143320 - 0.225836i) q^{92} +(1.73893 + 1.26341i) q^{93} +(4.99700 - 1.28301i) q^{94} +(0.259698 + 4.12779i) q^{96} +(0.464575 + 7.38421i) q^{97} +(1.42092 - 0.781159i) q^{98} +(-2.78141 + 8.56030i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 40 q^{4} - 40 q^{6} + 40 q^{9}+O(q^{10}) $ 480 * q + 40 * q^4 - 40 * q^6 + 40 * q^9	$ 480 q + 40 q^{4} - 40 q^{6} + 40 q^{9} - 50 q^{11} + 60 q^{14} - 80 q^{16} + 20 q^{19} - 70 q^{21} - 30 q^{24} - 90 q^{26} + 20 q^{29} - 60 q^{31} + 40 q^{34} + 340 q^{36} - 70 q^{41} - 30 q^{44} - 80 q^{46} - 70 q^{49} - 110 q^{51} - 60 q^{54} + 130 q^{56} - 10 q^{59} - 80 q^{61} - 50 q^{64} - 190 q^{66} + 20 q^{69} + 90 q^{71} - 70 q^{74} - 130 q^{76} - 190 q^{81} - 90 q^{84} - 160 q^{86} - 60 q^{89} + 130 q^{91} - 120 q^{94} - 270 q^{96} - 90 q^{99}+O(q^{100}) $ 480 * q + 40 * q^4 - 40 * q^6 + 40 * q^9 - 50 * q^11 + 60 * q^14 - 80 * q^16 + 20 * q^19 - 70 * q^21 - 30 * q^24 - 90 * q^26 + 20 * q^29 - 60 * q^31 + 40 * q^34 + 340 * q^36 - 70 * q^41 - 30 * q^44 - 80 * q^46 - 70 * q^49 - 110 * q^51 - 60 * q^54 + 130 * q^56 - 10 * q^59 - 80 * q^61 - 50 * q^64 - 190 * q^66 + 20 * q^69 + 90 * q^71 - 70 * q^74 - 130 * q^76 - 190 * q^81 - 90 * q^84 - 160 * q^86 - 60 * q^89 + 130 * q^91 - 120 * q^94 - 270 * q^96 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{25}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.28126	+	0.161861i	0.905991	+	0.114453i	0.564501	−	0.825432i	$-0.309069\pi$
$2$	1.28126	+	0.161861i	0.905991	+	0.114453i	0.341489	+	0.939886i	$0.389069\pi$
$3$	1.41863	+	1.71483i	0.819048	+	0.990059i	0.999978	+	0.00656345i	$0.00208923\pi$
$3$	1.41863	+	1.71483i	0.819048	+	0.990059i	−0.180930	+	0.983496i	$0.557911\pi$
$4$	−0.321728	−	0.0826056i	−0.160864	−	0.0413028i
$5$		0			0
$5$		0			0
$6$	1.54008	+	2.42678i	0.628735	+	0.990727i
$7$	0.740638	+	2.27945i	0.279935	+	0.861551i	0.987871	+	0.155275i	$0.0496264\pi$
$7$	0.740638	+	2.27945i	0.279935	+	0.861551i	−0.707936	+	0.706276i	$0.750374\pi$
$8$	−2.80036	−	1.10874i	−0.990078	−	0.391999i
$9$	−0.365988	+	1.91858i	−0.121996	+	0.639526i
$10$		0			0
$11$	4.57197	+	0.577574i	1.37850	+	0.174145i	0.779399	−	0.626528i	$-0.215524\pi$
$11$	4.57197	+	0.577574i	1.37850	+	0.174145i	0.599102	+	0.800673i	$0.295524\pi$
$12$	−0.314759	−	0.668897i	−0.0908631	−	0.193094i
$13$	−1.08143	+	5.66906i	−0.299935	+	1.57231i	0.438969	+	0.898502i	$0.355344\pi$
$13$	−1.08143	+	5.66906i	−0.299935	+	1.57231i	−0.738903	+	0.673811i	$0.764656\pi$
$14$	0.579998	+	3.04046i	0.155011	+	0.812597i
$15$		0			0
$16$	−2.82639	−	1.55382i	−0.706597	−	0.388455i
$17$	−4.20471	+	1.07959i	−1.01979	+	0.261838i	−0.721336	−	0.692586i	$-0.756472\pi$
$17$	−4.20471	+	1.07959i	−1.01979	+	0.261838i	−0.298456	+	0.954423i	$0.596472\pi$
$18$	−0.779471	+	2.39897i	−0.183723	+	0.565442i
$19$	3.02560	−	3.65732i	0.694120	−	0.839048i	−0.299230	−	0.954181i	$-0.596730\pi$
$19$	3.02560	−	3.65732i	0.694120	−	0.839048i	0.993350	+	0.115134i	$0.0367296\pi$
$20$		0			0
$21$	−2.85818	+	4.50378i	−0.623707	+	0.982804i
$22$	5.76442	+	1.48005i	1.22898	+	0.315548i
$23$	0.587001	+	0.551231i	0.122398	+	0.114940i	0.743330	−	0.668925i	$-0.233245\pi$
$23$	0.587001	+	0.551231i	0.122398	+	0.114940i	−0.620931	+	0.783865i	$0.713245\pi$
$24$	−2.07138	−	6.37505i	−0.422819	−	1.30130i
$25$		0			0
$26$	−2.30320	+	7.08852i	−0.451695	+	1.39017i
$27$	2.04161	−	1.12238i	0.392908	−	0.216003i
$28$	−0.0499884	−	0.794543i	−0.00944693	−	0.150155i
$29$	−0.0122026	−	0.193954i	−0.00226596	−	0.0360164i	0.996731	−	0.0807885i	$-0.0257438\pi$
$29$	−0.0122026	−	0.193954i	−0.00226596	−	0.0360164i	−0.998997	+	0.0447721i	$0.985744\pi$
$30$		0			0
$31$	0.935449	−	0.240183i	0.168012	−	0.0431381i	−0.163747	−	0.986502i	$-0.552358\pi$
$31$	0.935449	−	0.240183i	0.168012	−	0.0431381i	0.331759	+	0.943364i	$0.392358\pi$
$32$	1.50346	+	1.09233i	0.265776	+	0.193098i
$33$	5.49551	+	8.65953i	0.956645	+	1.50743i
$34$	−5.56208	+	0.702655i	−0.953890	+	0.120504i
$35$		0			0
$36$	0.276234	−	0.587027i	0.0460390	−	0.0978378i
$37$	−7.25681	−	3.98946i	−1.19301	−	0.655864i	−0.243593	−	0.969877i	$-0.578326\pi$
$37$	−7.25681	−	3.98946i	−1.19301	−	0.655864i	−0.949418	+	0.314014i	$0.898326\pi$
$38$	4.46857	−	4.19627i	0.724898	−	0.680725i
$39$	−11.2556	+	6.18784i	−1.80235	+	0.990848i
$40$		0			0
$41$	0.442053	−	0.415115i	0.0690370	−	0.0648301i	−0.649261	−	0.760566i	$-0.724922\pi$
$41$	0.442053	−	0.415115i	0.0690370	−	0.0648301i	0.718298	+	0.695736i	$0.244922\pi$
$42$	−4.39107	+	5.30790i	−0.677557	+	0.819026i
$43$	9.09003	−	6.60429i	1.38622	−	1.00715i	0.389948	−	0.920837i	$-0.372493\pi$
$43$	9.09003	−	6.60429i	1.38622	−	1.00715i	0.996268	−	0.0863081i	$-0.0275069\pi$
$44$	−1.42322	−	0.563492i	−0.214558	−	0.0849497i
$45$		0			0
$46$	0.662880	+	0.801285i	0.0977364	+	0.118143i
$47$	3.71428	−	1.47059i	0.541783	−	0.214507i	−0.0812622	−	0.996693i	$-0.525895\pi$
$47$	3.71428	−	1.47059i	0.541783	−	0.214507i	0.623046	+	0.782186i	$0.285895\pi$
$48$	−1.34507	−	7.05108i	−0.194144	−	1.01774i
$49$	1.01577	−	0.738000i	0.145110	−	0.105429i
$50$		0			0
$51$	−7.81625	−	5.67884i	−1.09449	−	0.795196i
$52$	0.816222	−	1.73456i	0.113190	−	0.240540i
$53$	−4.41327	+	6.95421i	−0.606210	+	0.955234i	0.393151	+	0.919474i	$0.371385\pi$
$53$	−4.41327	+	6.95421i	−0.606210	+	0.955234i	−0.999360	+	0.0357596i	$0.988615\pi$
$54$	2.79751	−	1.10761i	0.380693	−	0.150727i
$55$		0			0
$56$	0.453266	−	7.20446i	0.0605703	−	0.962737i
$57$	10.5639			1.39923
$58$	0.0157590	−	0.250482i	0.00206926	−	0.0328899i
$59$	−2.33894	−	4.97049i	−0.304504	−	0.647103i	0.692749	−	0.721179i	$-0.256399\pi$
$59$	−2.33894	−	4.97049i	−0.304504	−	0.647103i	−0.997253	+	0.0740756i	$0.976399\pi$
$60$		0			0
$61$	−8.65640	−	8.12890i	−1.10834	−	1.04080i	−0.998904	−	0.0468051i	$-0.985096\pi$
$61$	−8.65640	−	8.12890i	−1.10834	−	1.04080i	−0.109434	−	0.993994i	$-0.534904\pi$
$62$	1.23743	−	0.156324i	0.157154	−	0.0198532i
$63$	−4.64437	+	0.586720i	−0.585135	+	0.0739198i
$64$	6.45186	+	6.05870i	0.806483	+	0.757338i
$65$		0			0
$66$	5.63955	+	11.9847i	0.694181	+	1.47521i
$67$	0.0683896	−	1.08702i	0.00835511	−	0.132801i	−0.991638	−	0.129052i	$-0.958807\pi$
$67$	0.0683896	−	1.08702i	0.00835511	−	0.132801i	0.999993	−	0.00374898i	$-0.00119334\pi$
$68$	1.44195			0.174862
$69$	−0.112529	+	1.78860i	−0.0135469	+	0.215322i
$70$		0			0
$71$	0.401350	−	0.158906i	0.0476315	−	0.0188587i	−0.344188	−	0.938901i	$-0.611846\pi$
$71$	0.401350	−	0.158906i	0.0476315	−	0.0188587i	0.391820	+	0.920042i	$0.371846\pi$
$72$	3.15211	−	4.96693i	0.371479	−	0.585358i
$73$	6.24516	−	13.2717i	0.730941	−	1.55333i	−0.0987536	−	0.995112i	$-0.531486\pi$
$73$	6.24516	−	13.2717i	0.730941	−	1.55333i	0.829695	−	0.558217i	$-0.188514\pi$
$74$	−8.65215	−	6.28615i	−1.00579	−	0.730750i
$75$		0			0
$76$	−1.27554	+	0.926731i	−0.146314	+	0.106303i
$77$	2.06963	+	10.8494i	0.235856	+	1.23640i
$78$	−15.4230	+	6.10641i	−1.74631	+	0.691414i
$79$	−0.594972	−	0.719197i	−0.0669396	−	0.0809160i	0.735981	−	0.677003i	$-0.236721\pi$
$79$	−0.594972	−	0.719197i	−0.0669396	−	0.0809160i	−0.802920	+	0.596087i	$0.796721\pi$
$80$		0			0
$81$	10.2690	+	4.06580i	1.14100	+	0.451756i
$82$	0.633577	−	0.460321i	0.0699669	−	0.0508339i
$83$	−1.16915	+	1.41326i	−0.128331	+	0.155125i	−0.830765	−	0.556624i	$-0.812097\pi$
$83$	−1.16915	+	1.41326i	−0.128331	+	0.155125i	0.702434	+	0.711749i	$0.252097\pi$
$84$	1.29159	−	1.21289i	0.140924	−	0.132337i
$85$		0			0
$86$	12.7157	−	6.99052i	1.37117	−	0.753807i
$87$	0.315288	−	0.296076i	0.0338025	−	0.0317426i
$88$	−12.1628	−	6.68655i	−1.29656	−	0.712789i
$89$	1.00941	−	2.14511i	0.106998	−	0.227381i	−0.844157	−	0.536096i	$-0.819899\pi$
$89$	1.00941	−	2.14511i	0.106998	−	0.227381i	0.951155	+	0.308714i	$0.0998987\pi$
$90$		0			0
$91$	−13.7233	+	1.73365i	−1.43859	+	0.181736i
$92$	−0.143320	−	0.225836i	−0.0149421	−	0.0235450i
$93$	1.73893	+	1.26341i	0.180319	+	0.131009i
$94$	4.99700	−	1.28301i	0.515402	−	0.132333i
$95$		0			0
$96$	0.259698	+	4.12779i	0.0265053	+	0.421290i
$97$	0.464575	+	7.38421i	0.0471705	+	0.749753i	0.948531	+	0.316684i	$0.102569\pi$
$97$	0.464575	+	7.38421i	0.0471705	+	0.749753i	−0.901361	+	0.433069i	$0.857431\pi$
$98$	1.42092	−	0.781159i	0.143535	−	0.0789090i
$99$	−2.78141	+	8.56030i	−0.279542	+	0.860342i
$100$		0			0
$101$	−3.00233	−	9.24022i	−0.298743	−	0.919436i	−0.981938	−	0.189201i	$-0.939410\pi$
$101$	−3.00233	−	9.24022i	−0.298743	−	0.919436i	0.683195	−	0.730236i	$-0.260590\pi$
$102$	−9.09549	−	8.54124i	−0.900588	−	0.845708i
$103$	6.59022	+	1.69208i	0.649353	+	0.166726i	0.558978	−	0.829182i	$-0.311193\pi$
$103$	6.59022	+	1.69208i	0.649353	+	0.166726i	0.0903749	+	0.995908i	$0.471193\pi$
$104$	9.31392	−	14.6764i	0.913305	−	1.43914i
$105$		0			0
$106$	−6.78019	+	8.19584i	−0.658550	+	0.796050i
$107$	−3.45898	+	10.6456i	−0.334392	+	1.02915i	0.632629	+	0.774455i	$0.281976\pi$
$107$	−3.45898	+	10.6456i	−0.334392	+	1.02915i	−0.967021	+	0.254697i	$0.918024\pi$
$108$	−0.749557	+	0.192454i	−0.0721262	+	0.0185189i
$109$	10.8208	+	5.94880i	1.03645	+	0.569791i	0.906709	−	0.421757i	$-0.138586\pi$
$109$	10.8208	+	5.94880i	1.03645	+	0.569791i	0.129738	+	0.991548i	$0.458586\pi$
$110$		0			0
$111$	−3.45348	−	18.1038i	−0.327790	−	1.71834i
$112$	1.44852	−	7.59343i	0.136873	−	0.717512i
$113$	−6.34083	−	13.4749i	−0.596495	−	1.26762i	−0.944002	−	0.329939i	$-0.892972\pi$
$113$	−6.34083	−	13.4749i	−0.596495	−	1.26762i	0.347507	−	0.937677i	$-0.387028\pi$
$114$	13.5352	+	1.70989i	1.26768	+	0.160146i
$115$		0			0
$116$	−0.0120958	+	0.0634085i	−0.00112307	+	0.00588733i
$117$	−10.4807	−	4.14962i	−0.968944	−	0.383632i
$118$	−2.19227	−	6.74710i	−0.201814	−	0.621121i
$119$	−5.57503	−	8.78484i	−0.511062	−	0.805305i
$120$		0			0
$121$	9.91492	+	2.54572i	0.901356	+	0.231429i
$122$	−9.77538	−	11.8164i	−0.885021	−	1.06981i
$123$	1.33896	+	0.169150i	0.120730	+	0.0152518i
$124$	−0.320800			−0.0288087
$125$		0			0
$126$	−6.04563			−0.538587
$127$	1.54903	+	0.195688i	0.137454	+	0.0173645i	0.193759	−	0.981049i	$-0.437932\pi$
$127$	1.54903	+	0.195688i	0.137454	+	0.0173645i	−0.0563052	+	0.998414i	$0.517932\pi$
$128$	4.91673	+	5.94330i	0.434581	+	0.525319i
$129$	24.2207	+	6.21881i	2.13251	+	0.547536i
$130$		0			0
$131$	−1.25967	−	1.98492i	−0.110058	−	0.173423i	0.784835	−	0.619705i	$-0.212748\pi$
$131$	−1.25967	−	1.98492i	−0.110058	−	0.173423i	−0.894892	+	0.446282i	$0.852748\pi$
$132$	−1.05273	−	3.23997i	−0.0916285	−	0.282003i
$133$	10.5776	+	4.18795i	0.917191	+	0.363142i
$134$	0.263572	−	1.38169i	0.0227691	−	0.119360i
$135$		0			0
$136$	12.9717	+	1.63871i	1.11231	+	0.140518i
$137$	−3.16951	−	6.73554i	−0.270789	−	0.575456i	0.722466	−	0.691407i	$-0.243009\pi$
$137$	−3.16951	−	6.73554i	−0.270789	−	0.575456i	−0.993255	+	0.115950i	$0.963009\pi$
$138$	−0.433685	+	2.27346i	−0.0369177	+	0.193530i
$139$	1.36337	+	7.14706i	0.115640	+	0.606206i	0.992174	+	0.124865i	$0.0398499\pi$
$139$	1.36337	+	7.14706i	0.115640	+	0.606206i	−0.876534	+	0.481340i	$0.840150\pi$
$140$		0			0
$141$	7.79101	+	4.28315i	0.656122	+	0.360706i
$142$	0.539957	−	0.138637i	0.0453121	−	0.0116342i
$143$	−8.21857	+	25.2942i	−0.687272	+	2.11520i
$144$	4.01555	−	4.85396i	0.334629	−	0.404497i
$145$		0			0
$146$	10.1499	−	15.9936i	0.840009	−	1.32364i
$147$	2.70655	+	0.694925i	0.223233	+	0.0573164i
$148$	2.00516	+	1.88297i	0.164823	+	0.154780i
$149$	6.51667	+	20.0563i	0.533867	+	1.64307i	0.746085	+	0.665850i	$0.231931\pi$
$149$	6.51667	+	20.0563i	0.533867	+	1.64307i	−0.212219	+	0.977222i	$0.568069\pi$
$150$		0			0
$151$	−1.38145	+	4.25168i	−0.112421	+	0.345997i	−0.991400	−	0.130863i	$-0.958225\pi$
$151$	−1.38145	+	4.25168i	−0.112421	+	0.345997i	0.878979	+	0.476860i	$0.158225\pi$
$152$	−12.5278	+	6.88722i	−1.01614	+	0.558627i
$153$	−0.532395	−	8.46217i	−0.0430416	−	0.684126i
$154$	0.895646	+	14.2359i	0.0721732	+	1.14716i
$155$		0			0
$156$	4.13240	−	1.06102i	0.330857	−	0.0849497i
$157$	4.06955	+	2.95670i	0.324786	+	0.235971i	0.738215	−	0.674566i	$-0.235669\pi$
$157$	4.06955	+	2.95670i	0.324786	+	0.235971i	−0.413429	+	0.910536i	$0.635669\pi$
$158$	−0.645906	−	1.01778i	−0.0513855	−	0.0809706i
$159$	−18.1861	+	2.29744i	−1.44225	+	0.182199i
$160$		0			0
$161$	−0.821747	+	1.74630i	−0.0647628	+	0.137628i
$162$	12.4993	+	6.87152i	0.982034	+	0.539878i
$163$	−3.62971	+	3.40852i	−0.284301	+	0.266976i	−0.813556	−	0.581486i	$-0.802471\pi$
$163$	−3.62971	+	3.40852i	−0.284301	+	0.266976i	0.529255	+	0.848463i	$0.322471\pi$
$164$	−0.176511	+	0.0970380i	−0.0137832	+	0.00757739i
$165$		0			0
$166$	−1.72674	+	1.62152i	−0.134021	+	0.125854i
$167$	4.88355	−	5.90320i	0.377901	−	0.456803i	−0.546932	−	0.837177i	$-0.684205\pi$
$167$	4.88355	−	5.90320i	0.377901	−	0.456803i	0.924833	+	0.380373i	$0.124205\pi$
$168$	12.9975	−	9.44322i	1.00278	−	0.728560i
$169$	−18.8816	−	7.47577i	−1.45243	−	0.575059i
$170$		0			0
$171$	5.90952	+	7.14339i	0.451913	+	0.546269i
$172$	−3.47007	+	1.37390i	−0.264590	+	0.104759i
$173$	−0.250079	−	1.31096i	−0.0190132	−	0.0996704i	0.971516	−	0.236975i	$-0.0761560\pi$
$173$	−0.250079	−	1.31096i	−0.0190132	−	0.0996704i	−0.990529	+	0.137305i	$0.956156\pi$
$174$	0.451891	−	0.328318i	0.0342578	−	0.0248897i
$175$		0			0
$176$	−12.0247	−	8.73647i	−0.906397	−	0.658536i
$177$	5.20547	−	11.0622i	0.391267	−	0.831485i
$178$	1.64053	−	2.58507i	0.122963	−	0.193759i
$179$	−13.7021	+	5.42503i	−1.02414	+	0.405486i	−0.819334	−	0.573317i	$-0.805656\pi$
$179$	−13.7021	+	5.42503i	−1.02414	+	0.405486i	−0.204806	+	0.978803i	$0.565656\pi$
$180$		0			0
$181$	−0.0768556	+	1.22159i	−0.00571263	+	0.0907997i	−0.999850	−	0.0173257i	$-0.994485\pi$
$181$	−0.0768556	+	1.22159i	−0.00571263	+	0.0907997i	0.994137	+	0.108125i	$0.0344848\pi$
$182$	−17.8638			−1.32415
$183$	1.65945	−	26.3762i	0.122670	−	1.94979i
$184$	−1.03264	−	2.19448i	−0.0761274	−	0.161779i
$185$		0			0
$186$	2.02354	+	1.90023i	0.148373	+	0.139331i
$187$	−19.8473	+	2.50730i	−1.45138	+	0.183352i
$188$	−1.31647	+	0.166308i	−0.0960131	+	0.0121293i
$189$	4.07051	+	3.82247i	0.296086	+	0.278043i
$190$		0			0
$191$	−2.92625	−	6.21860i	−0.211736	−	0.449962i	0.770542	−	0.637389i	$-0.219985\pi$
$191$	−2.92625	−	6.21860i	−0.211736	−	0.449962i	−0.982279	+	0.187426i	$0.939985\pi$
$192$	−1.23684	+	19.6590i	−0.0892610	+	1.41876i
$193$	−22.1313			−1.59304			−0.796522	−	0.604609i	$-0.793329\pi$
$193$	−22.1313			−1.59304			−0.796522	+	0.604609i	$0.793329\pi$
$194$	−0.599975	+	9.53632i	−0.0430757	+	0.684668i
$195$		0			0
$196$	−0.387764	+	0.153527i	−0.0276975	+	0.0109662i
$197$	5.76869	−	9.09001i	0.411002	−	0.647636i	−0.574263	−	0.818671i	$-0.694711\pi$
$197$	5.76869	−	9.09001i	0.411002	−	0.647636i	0.985265	+	0.171035i	$0.0547111\pi$
$198$	−4.94930	+	10.5178i	−0.351731	+	0.747467i
$199$	−5.76789	−	4.19062i	−0.408875	−	0.297065i	0.364271	−	0.931293i	$-0.381318\pi$
$199$	−5.76789	−	4.19062i	−0.408875	−	0.297065i	−0.773146	+	0.634228i	$0.781318\pi$
$200$		0			0
$201$	1.96108	−	1.42481i	0.138324	−	0.100498i
$202$	−2.35114	−	12.3251i	−0.165426	−	0.867193i
$203$	0.433072	−	0.171465i	0.0303957	−	0.0120345i
$204$	2.04560	+	2.47271i	0.143221	+	0.173124i
$205$		0			0
$206$	8.16992	+	3.23470i	0.569226	+	0.225372i
$207$	−1.27241	+	0.924463i	−0.0884389	+	0.0642546i
$208$	11.8652	−	14.3426i	0.822706	−	0.994481i
$209$	15.9453	−	14.9737i	1.10296	−	1.03575i
$210$		0			0
$211$	−23.5752	+	12.9606i	−1.62298	+	0.892243i	−0.629662	+	0.776869i	$0.716807\pi$
$211$	−23.5752	+	12.9606i	−1.62298	+	0.892243i	−0.993322	+	0.115374i	$0.963193\pi$
$212$	1.99433	−	1.87280i	0.136971	−	0.128624i
$213$	0.841866	+	0.462820i	0.0576837	+	0.0317119i
$214$	−6.15498	+	13.0800i	−0.420746	+	0.894130i
$215$		0			0
$216$	−6.96168	+	0.879465i	−0.473682	+	0.0598400i
$217$	1.24031	+	1.95442i	0.0841980	+	0.132675i
$218$	12.9014	+	9.37345i	0.873796	+	0.634850i
$219$	31.6183	−	8.11819i	2.13656	−	0.548577i
$220$		0			0
$221$	−1.57313	−	25.0042i	−0.105820	−	1.68197i
$222$	−1.49452	−	23.7547i	−0.100306	−	1.59431i
$223$	11.3649	−	6.24793i	0.761053	−	0.418393i	−0.0534360	−	0.998571i	$-0.517017\pi$
$223$	11.3649	−	6.24793i	0.761053	−	0.418393i	0.814489	+	0.580179i	$0.197017\pi$
$224$	−1.37638	+	4.23607i	−0.0919635	+	0.283034i
$225$		0			0
$226$	−5.94320	−	18.2913i	−0.395336	−	1.21672i
$227$	−16.2278	−	15.2390i	−1.07708	−	1.01144i	−0.999896	−	0.0144279i	$-0.995407\pi$
$227$	−16.2278	−	15.2390i	−1.07708	−	1.01144i	−0.0771834	−	0.997017i	$-0.524593\pi$
$228$	−3.39871	−	0.872639i	−0.225085	−	0.0577920i
$229$	−0.467076	+	0.735995i	−0.0308653	+	0.0486359i	−0.859410	−	0.511287i	$-0.829169\pi$
$229$	−0.467076	+	0.735995i	−0.0308653	+	0.0486359i	0.828545	+	0.559922i	$0.189169\pi$
$230$		0			0
$231$	−15.6688	+	18.9403i	−1.03093	+	1.24618i
$232$	−0.180874	+	0.556672i	−0.0118749	+	0.0365473i
$233$	−16.6353	+	4.27122i	−1.08981	+	0.279817i	−0.750509	−	0.660860i	$-0.770192\pi$
$233$	−16.6353	+	4.27122i	−1.08981	+	0.279817i	−0.339305	+	0.940677i	$0.610192\pi$
$234$	−12.7569	−	7.01318i	−0.833947	−	0.458466i
$235$		0			0
$236$	0.341910	+	1.79236i	0.0222564	+	0.116672i
$237$	0.389257	−	2.04055i	0.0252849	−	0.132548i
$238$	−5.72116	−	12.1581i	−0.370848	−	0.788091i
$239$	−26.2269	−	3.31323i	−1.69648	−	0.214315i	−0.783234	−	0.621727i	$-0.786431\pi$
$239$	−26.2269	−	3.31323i	−1.69648	−	0.214315i	−0.913244	+	0.407412i	$0.866431\pi$
$240$		0			0
$241$	−0.0299061	+	0.156773i	−0.00192642	+	0.0100987i	−0.983237	−	0.182330i	$-0.941636\pi$
$241$	−0.0299061	+	0.156773i	−0.00192642	+	0.0100987i	0.981311	+	0.192428i	$0.0616362\pi$
$242$	12.2916	+	4.86658i	0.790132	+	0.312835i
$243$	5.43600	+	16.7303i	0.348720	+	1.07325i
$244$	2.11351	+	3.33036i	0.135304	+	0.213204i
$245$		0			0
$246$	1.68819	+	0.433453i	0.107635	+	0.0276359i
$247$	17.4616	+	21.1074i	1.11106	+	1.34303i
$248$	−2.88590	−	0.364574i	−0.183255	−	0.0231505i
$249$	−4.08210			−0.258692
$250$		0			0
$251$	23.7462			1.49885			0.749423	−	0.662091i	$-0.230331\pi$
$251$	23.7462			1.49885			0.749423	+	0.662091i	$0.230331\pi$
$252$	1.54269	+	0.194887i	0.0971802	+	0.0122767i
$253$	2.36537	+	2.85925i	0.148710	+	0.179759i
$254$	1.95304	+	0.501455i	0.122545	+	0.0314641i
$255$		0			0
$256$	−4.14722	−	6.53498i	−0.259201	−	0.408436i
$257$	8.26780	+	25.4457i	0.515731	+	1.58726i	0.781947	+	0.623345i	$0.214227\pi$
$257$	8.26780	+	25.4457i	0.515731	+	1.58726i	−0.266216	+	0.963913i	$0.585773\pi$
$258$	30.0265	+	11.8883i	1.86937	+	0.740135i
$259$	3.71911	−	19.4963i	0.231095	−	1.21144i
$260$		0			0
$261$	0.376582	+	0.0475734i	0.0233099	+	0.00294472i
$262$	−1.29269	−	2.74710i	−0.0798624	−	0.169716i
$263$	−4.46169	+	23.3890i	−0.275120	+	1.44223i	0.529435	+	0.848350i	$0.322404\pi$
$263$	−4.46169	+	23.3890i	−0.275120	+	1.44223i	−0.804555	+	0.593878i	$0.797596\pi$
$264$	−5.78822	−	30.3429i	−0.356241	−	1.86748i
$265$		0			0
$266$	12.8748	+	7.07797i	0.789404	+	0.433978i
$267$	5.11049	−	1.31215i	0.312757	−	0.0803024i
$268$	−0.111797	+	0.344075i	−0.00682908	+	0.0210178i
$269$	−1.43803	+	1.73828i	−0.0876782	+	0.105985i	−0.812528	−	0.582922i	$-0.801909\pi$
$269$	−1.43803	+	1.73828i	−0.0876782	+	0.105985i	0.724850	+	0.688907i	$0.241909\pi$
$270$		0			0
$271$	7.43111	−	11.7096i	0.451408	−	0.711305i	−0.540064	−	0.841624i	$-0.681600\pi$
$271$	7.43111	−	11.7096i	0.451408	−	0.711305i	0.991472	+	0.130319i	$0.0416001\pi$
$272$	13.5616	+	3.48203i	0.822294	+	0.211129i
$273$	−22.4412	−	21.0737i	−1.35821	−	1.27544i
$274$	−2.97075	−	9.14303i	−0.179470	−	0.552351i
$275$		0			0
$276$	0.183952	−	0.566148i	0.0110726	−	0.0340781i
$277$	−23.5279	+	12.9346i	−1.41366	+	0.777164i	−0.991592	−	0.129403i	$-0.958694\pi$
$277$	−23.5279	+	12.9346i	−1.41366	+	0.777164i	−0.422063	+	0.906566i	$0.638694\pi$
$278$	0.590010	+	9.37795i	0.0353865	+	0.562452i
$279$	0.118445	+	1.88264i	0.00709114	+	0.112710i
$280$		0			0
$281$	−19.9870	+	5.13179i	−1.19232	+	0.306137i	−0.792164	−	0.610309i	$-0.791045\pi$
$281$	−19.9870	+	5.13179i	−1.19232	+	0.306137i	−0.400160	+	0.916445i	$0.631045\pi$
$282$	9.28907	+	6.74890i	0.553156	+	0.401891i
$283$	−1.47686	−	2.32715i	−0.0877900	−	0.138335i	0.797595	−	0.603193i	$-0.206105\pi$
$283$	−1.47686	−	2.32715i	−0.0877900	−	0.138335i	−0.885385	+	0.464858i	$0.846105\pi$
$284$	−0.142252	+	0.0179706i	−0.00844111	+	0.00106636i
$285$		0			0
$286$	−14.6243	+	31.0782i	−0.864753	+	1.83769i
$287$	1.27364	+	0.700187i	0.0751803	+	0.0413307i
$288$	−2.64596	+	2.48472i	−0.155915	+	0.146414i
$289$	1.61685	−	0.888870i	0.0951087	−	0.0522864i
$290$		0			0
$291$	−12.0036	+	11.2722i	−0.703665	+	0.660786i
$292$	−3.10556	+	3.75397i	−0.181739	+	0.219685i
$293$	−1.91207	+	1.38920i	−0.111704	+	0.0811581i	−0.642235	−	0.766508i	$-0.721993\pi$
$293$	−1.91207	+	1.38920i	−0.111704	+	0.0811581i	0.530531	+	0.847666i	$0.321993\pi$
$294$	3.35533	+	1.32847i	0.195687	+	0.0774778i
$295$		0			0
$296$	15.8984	+	19.2179i	0.924076	+	1.11702i
$297$	9.98244	−	3.95233i	0.579240	−	0.229337i
$298$	5.10325	+	26.7522i	0.295623	+	1.54971i
$299$	−3.75976	+	2.73162i	−0.217432	+	0.157974i
$300$		0			0
$301$	21.7866	+	15.8289i	1.25576	+	0.912361i
$302$	−2.45819	+	5.22392i	−0.141453	+	0.300603i
$303$	11.5862	−	18.2570i	0.665612	−	1.04884i
$304$	−14.2343	+	5.63578i	−0.816396	+	0.323234i
$305$		0			0
$306$	0.687560	−	10.9285i	0.0393052	−	0.624738i
$307$	15.4005			0.878950			0.439475	−	0.898255i	$-0.355164\pi$
$307$	15.4005			0.878950			0.439475	+	0.898255i	$0.355164\pi$
$308$	0.230362	−	3.66150i	0.0131261	−	0.208633i
$309$	6.44746	+	13.7016i	0.366783	+	0.779455i
$310$		0			0
$311$	1.28486	+	1.20657i	0.0728579	+	0.0684182i	0.720121	−	0.693849i	$-0.244086\pi$
$311$	1.28486	+	1.20657i	0.0728579	+	0.0684182i	−0.647263	+	0.762267i	$0.724086\pi$
$312$	38.3806	−	4.84860i	2.17287	−	0.274498i
$313$	29.5069	−	3.72758i	1.66783	−	0.210695i	0.766014	−	0.642824i	$-0.222237\pi$
$313$	29.5069	−	3.72758i	1.66783	−	0.210695i	0.901812	+	0.432129i	$0.142237\pi$
$314$	4.73560	+	4.44702i	0.267245	+	0.250960i
$315$		0			0
$316$	0.132009	+	0.280534i	0.00742610	+	0.0157813i
$317$	0.388273	−	6.17143i	0.0218076	−	0.346622i	−0.971960	−	0.235147i	$-0.924443\pi$
$317$	0.388273	−	6.17143i	0.0218076	−	0.346622i	0.993767	−	0.111474i	$-0.0355573\pi$
$318$	−23.6731			−1.32752
$319$	0.0562332	−	0.893802i	0.00314846	−	0.0500433i
$320$		0			0
$321$	−23.1625	+	9.17069i	−1.29281	+	0.511858i
$322$	−1.33553	+	2.10446i	−0.0744264	+	0.117277i
$323$	−8.77337	+	18.6444i	−0.488164	+	1.03740i
$324$	−2.96798	−	2.15636i	−0.164888	−	0.119798i
$325$		0			0
$326$	−5.20232	+	3.77971i	−0.288130	+	0.209339i
$327$	5.14958	+	26.9951i	0.284773	+	1.49283i
$328$	−1.69816	+	0.672350i	−0.0937654	+	0.0371243i
$329$	6.10307	+	7.37734i	0.336473	+	0.406726i
$330$		0			0
$331$	27.4519	+	10.8690i	1.50889	+	0.597413i	0.969598	−	0.244704i	$-0.0786907\pi$
$331$	27.4519	+	10.8690i	1.50889	+	0.597413i	0.539295	+	0.842117i	$0.318691\pi$
$332$	0.492891	−	0.358106i	0.0270509	−	0.0196536i
$333$	10.3100	−	12.4627i	0.564985	−	0.682949i
$334$	7.21262	−	6.77310i	0.394657	−	0.370608i
$335$		0			0
$336$	15.0764	−	8.28832i	0.822484	−	0.452165i
$337$	14.6391	−	13.7470i	0.797442	−	0.748848i	−0.174351	−	0.984684i	$-0.555783\pi$
$337$	14.6391	−	13.7470i	0.797442	−	0.748848i	0.971793	+	0.235836i	$0.0757827\pi$
$338$	−22.9823	−	12.6346i	−1.25007	−	0.687234i
$339$	14.1120	−	29.9895i	0.766457	−	1.62880i
$340$		0			0
$341$	4.41557	−	0.557816i	0.239117	−	0.0302074i
$342$	6.41542	+	10.1091i	0.346906	+	0.546637i
$343$	16.0077	+	11.6303i	0.864333	+	0.627975i
$344$	−32.7778	+	8.41592i	−1.76726	+	0.453756i
$345$		0			0
$346$	−0.108224	−	1.72016i	−0.00581813	−	0.0924766i
$347$	0.696960	+	11.0779i	0.0374148	+	0.594690i	0.971410	+	0.237406i	$0.0762973\pi$
$347$	0.696960	+	11.0779i	0.0374148	+	0.594690i	−0.933996	+	0.357284i	$0.883703\pi$
$348$	−0.125895	+	0.0692111i	−0.00674866	+	0.00371010i
$349$	−4.53597	+	13.9603i	−0.242805	+	0.747276i	0.753185	+	0.657809i	$0.228517\pi$
$349$	−4.53597	+	13.9603i	−0.242805	+	0.747276i	−0.995990	+	0.0894676i	$0.971483\pi$
$350$		0			0
$351$	4.15500	+	12.7878i	0.221778	+	0.682561i
$352$	6.24286	+	5.86244i	0.332746	+	0.312469i
$353$	−8.24304	−	2.11645i	−0.438733	−	0.112647i	0.0228614	−	0.999739i	$-0.492722\pi$
$353$	−8.24304	−	2.11645i	−0.438733	−	0.112647i	−0.461594	+	0.887091i	$0.652722\pi$
$354$	8.46013	−	13.3310i	0.449651	−	0.708536i
$355$		0			0
$356$	−0.501954	+	0.606759i	−0.0266035	+	0.0321581i
$357$	7.15561	−	22.0227i	0.378715	−	1.16557i
$358$	−18.4341	+	4.73306i	−0.974270	+	0.250150i
$359$	−23.5213	−	12.9310i	−1.24141	−	0.682469i	−0.280637	−	0.959814i	$-0.590546\pi$
$359$	−23.5213	−	12.9310i	−1.24141	−	0.682469i	−0.960771	+	0.277345i	$0.910546\pi$
$360$		0			0
$361$	−0.661508	−	3.46774i	−0.0348162	−	0.182513i
$362$	−0.296200	+	1.55273i	−0.0155679	+	0.0816099i
$363$	9.70015	+	20.6139i	0.509126	+	1.08195i
$364$	4.55837	+	0.575856i	0.238924	+	0.0301831i
$365$		0			0
$366$	6.39548	−	33.5263i	0.334297	−	1.75245i
$367$	13.9716	+	5.53176i	0.729313	+	0.288755i	0.703287	−	0.710906i	$-0.251715\pi$
$367$	13.9716	+	5.53176i	0.729313	+	0.288755i	0.0260258	+	0.999661i	$0.491715\pi$
$368$	−0.802579	−	2.47008i	−0.0418373	−	0.128762i
$369$	0.634644	+	1.00004i	0.0330383	+	0.0520600i
$370$		0			0
$371$	−19.1204	−	4.90929i	−0.992682	−	0.254877i
$372$	−0.455098	−	0.550119i	−0.0235957	−	0.0285224i
$373$	−4.34579	−	0.549001i	−0.225017	−	0.0284262i	0.0120164	−	0.999928i	$-0.496175\pi$
$373$	−4.34579	−	0.549001i	−0.225017	−	0.0284262i	−0.237033	+	0.971502i	$0.576175\pi$
$374$	−25.8355			−1.33592
$375$		0			0
$376$	−12.0318			−0.620494
$377$	1.11273	+	0.140571i	0.0573088	+	0.00723978i
$378$	4.59669	+	5.55645i	0.236428	+	0.285793i
$379$	4.75810	+	1.22167i	0.244407	+	0.0627531i	0.368906	−	0.929467i	$-0.379732\pi$
$379$	4.75810	+	1.22167i	0.244407	+	0.0627531i	−0.124499	+	0.992220i	$0.539732\pi$
$380$		0			0
$381$	1.86193	+	2.93393i	0.0953896	+	0.150310i
$382$	−2.74275	−	8.44132i	−0.140331	−	0.431896i
$383$	−25.0307	−	9.91036i	−1.27901	−	0.506396i	−0.372285	−	0.928119i	$-0.621426\pi$
$383$	−25.0307	−	9.91036i	−1.27901	−	0.506396i	−0.906725	+	0.421723i	$0.861426\pi$
$384$	−3.21674	+	16.8627i	−0.164154	+	0.860523i
$385$		0			0
$386$	−28.3560	−	3.58220i	−1.44328	−	0.182329i
$387$	9.34400	+	19.8570i	0.474982	+	1.00939i
$388$	0.460511	−	2.41408i	0.0233789	−	0.122557i
$389$	−2.32366	−	12.1810i	−0.117814	−	0.617603i	−0.991393	−	0.130920i	$-0.958207\pi$
$389$	−2.32366	−	12.1810i	−0.117814	−	0.617603i	0.873579	−	0.486683i	$-0.161793\pi$
$390$		0			0
$391$	−3.06327	−	1.68405i	−0.154916	−	0.0851658i
$392$	−3.66278	+	0.940441i	−0.184998	+	0.0474995i
$393$	1.61680	−	4.97599i	0.0815567	−	0.251006i
$394$	8.86254	−	10.7130i	0.446488	−	0.539712i
$395$		0			0
$396$	1.60199	−	2.52432i	0.0805028	−	0.126852i
$397$	−31.9058	−	8.19202i	−1.60131	−	0.411146i	−0.660701	−	0.750649i	$-0.729741\pi$
$397$	−31.9058	−	8.19202i	−1.60131	−	0.411146i	−0.940605	+	0.339503i	$0.889741\pi$
$398$	−6.71189	−	6.30288i	−0.336437	−	0.315935i
$399$	7.82404	+	24.0799i	0.391692	+	1.20550i
$400$		0			0
$401$	2.45252	−	7.54808i	0.122473	−	0.376933i	−0.870959	−	0.491355i	$-0.836502\pi$
$401$	2.45252	−	7.54808i	0.122473	−	0.376933i	0.993432	+	0.114422i	$0.0365016\pi$
$402$	2.74328	−	1.50813i	0.136822	−	0.0752188i
$403$	0.349985	+	5.56286i	0.0174340	+	0.277106i
$404$	0.202638	+	3.22084i	0.0100816	+	0.160243i
$405$		0			0
$406$	0.582633	−	0.149595i	0.0289156	−	0.00742426i
$407$	−30.8737	−	22.4311i	−1.53035	−	1.11187i
$408$	15.5920	+	24.5690i	0.771917	+	1.21635i
$409$	3.01037	−	0.380298i	0.148853	−	0.0188045i	−0.0505535	−	0.998721i	$-0.516099\pi$
$409$	3.01037	−	0.380298i	0.148853	−	0.0188045i	0.199407	+	0.979917i	$0.436099\pi$
$410$		0			0
$411$	7.05397	−	14.9904i	0.347946	−	0.739424i
$412$	−1.98048	−	1.08878i	−0.0975712	−	0.0536402i
$413$	9.59769	−	9.01283i	0.472271	−	0.443492i
$414$	−1.77993	+	0.978526i	−0.0874789	+	0.0480920i
$415$		0			0
$416$	−7.81834	+	7.34191i	−0.383326	+	0.359967i
$417$	−10.3219	+	12.4770i	−0.505465	+	0.611002i
$418$	22.8538	−	16.6043i	1.11782	−	0.812142i
$419$	7.19409	+	2.84834i	0.351454	+	0.139151i	0.537217	−	0.843444i	$-0.319476\pi$
$419$	7.19409	+	2.84834i	0.351454	+	0.139151i	−0.185763	+	0.982595i	$0.559476\pi$
$420$		0			0
$421$	16.1357	+	19.5047i	0.786405	+	0.950600i	0.999651	−	0.0263985i	$-0.00840387\pi$
$421$	16.1357	+	19.5047i	0.786405	+	0.950600i	−0.213247	+	0.976998i	$0.568404\pi$
$422$	−32.3039	+	12.7900i	−1.57253	+	0.622608i
$423$	1.46205	+	7.66435i	0.0710875	+	0.372654i
$424$	20.0692	−	14.5811i	0.974646	−	0.708122i
$425$		0			0
$426$	1.00374	+	0.729260i	0.0486314	+	0.0353328i
$427$	12.1182	−	25.7524i	0.586439	−	1.24625i
$428$	1.99224	−	3.13927i	0.0962985	−	0.151742i
$429$	−55.0344	+	21.7897i	−2.65709	+	1.05201i
$430$		0			0
$431$	−1.77100	+	28.1492i	−0.0853061	+	1.35590i	0.689768	+	0.724031i	$0.257713\pi$
$431$	−1.77100	+	28.1492i	−0.0853061	+	1.35590i	−0.775074	+	0.631871i	$0.782287\pi$
$432$	−7.51436			−0.361535
$433$	−0.599701	+	9.53198i	−0.0288198	+	0.458078i	0.956980	+	0.290153i	$0.0937063\pi$
$433$	−0.599701	+	9.53198i	−0.0288198	+	0.458078i	−0.985800	+	0.167924i	$0.946294\pi$
$434$	1.27282	+	2.70489i	0.0610975	+	0.129839i
$435$		0			0
$436$	−2.98995	−	2.80775i	−0.143193	−	0.134467i
$437$	3.79206	−	0.479048i	0.181399	−	0.0229160i
$438$	41.8254	−	5.28377i	1.99849	−	0.252468i
$439$	22.0611	+	20.7167i	1.05292	+	0.988756i	0.999952	−	0.00984037i	$-0.00313234\pi$
$439$	22.0611	+	20.7167i	1.05292	+	0.988756i	0.0529665	+	0.998596i	$0.483132\pi$
$440$		0			0
$441$	1.04415	+	2.21893i	0.0497215	+	0.105663i
$442$	2.03162	−	32.2916i	0.0966342	−	1.53596i
$443$	−19.6665			−0.934382			−0.467191	−	0.884156i	$-0.654734\pi$
$443$	−19.6665			−0.934382			−0.467191	+	0.884156i	$0.654734\pi$
$444$	−0.384394	+	6.10977i	−0.0182425	+	0.289957i
$445$		0			0
$446$	15.5728	−	6.16571i	0.737393	−	0.291955i
$447$	−25.1484	+	39.6275i	−1.18948	+	1.87432i
$448$	−9.03202	+	19.1940i	−0.426723	+	0.906832i
$449$	10.1828	+	7.39826i	0.480558	+	0.349146i	0.801542	−	0.597939i	$-0.204014\pi$
$449$	10.1828	+	7.39826i	0.480558	+	0.349146i	−0.320984	+	0.947085i	$0.604014\pi$
$450$		0			0
$451$	2.26081	−	1.64258i	0.106457	−	0.0773459i
$452$	0.926914	+	4.85905i	0.0435984	+	0.228551i
$453$	−9.25070	+	3.66261i	−0.434636	+	0.172084i
$454$	−18.3255	−	22.1518i	−0.860061	−	1.03963i
$455$		0			0
$456$	−29.5828	−	11.7127i	−1.38534	−	0.548496i
$457$	13.6982	−	9.95236i	0.640777	−	0.465552i	−0.219340	−	0.975648i	$-0.570390\pi$
$457$	13.6982	−	9.95236i	0.640777	−	0.465552i	0.860117	+	0.510097i	$0.170390\pi$
$458$	−0.717577	+	0.867402i	−0.0335302	+	0.0405310i
$459$	−7.37266	+	6.92339i	−0.344126	+	0.323156i
$460$		0			0
$461$	7.03750	−	3.86890i	0.327769	−	0.180193i	−0.309369	−	0.950942i	$-0.600118\pi$
$461$	7.03750	−	3.86890i	0.327769	−	0.180193i	0.637138	+	0.770749i	$0.280118\pi$
$462$	−23.1416	+	21.7314i	−1.07664	+	1.01104i
$463$	−1.19737	−	0.658259i	−0.0556464	−	0.0305919i	0.453688	−	0.891161i	$-0.350108\pi$
$463$	−1.19737	−	0.658259i	−0.0556464	−	0.0305919i	−0.509334	+	0.860569i	$0.670108\pi$
$464$	−0.266881	+	0.567151i	−0.0123896	+	0.0263293i
$465$		0			0
$466$	−22.0055	+	2.77995i	−1.01939	+	0.128779i
$467$	−15.1304	−	23.8417i	−0.700152	−	1.10326i	−0.989288	−	0.145975i	$-0.953368\pi$
$467$	−15.1304	−	23.8417i	−0.700152	−	1.10326i	0.289136	−	0.957288i	$-0.406632\pi$
$468$	3.02916	+	2.20082i	0.140023	+	0.101733i
$469$	2.52846	−	0.649199i	0.116754	−	0.0299772i
$470$		0			0
$471$	0.702951	+	11.1731i	0.0323903	+	0.514829i
$472$	1.03888	+	16.5125i	0.0478181	+	0.760048i
$473$	45.3738	−	24.9445i	2.08629	−	1.14695i
$474$	0.829027	−	2.55148i	0.0380785	−	0.117194i
$475$		0			0
$476$	1.06796	+	3.28686i	0.0489501	+	0.150653i
$477$	−11.7270	−	11.0124i	−0.536941	−	0.504222i
$478$	−33.0673	−	8.49025i	−1.51246	−	0.388335i
$479$	21.3622	−	33.6614i	0.976062	−	1.53803i	0.139452	−	0.990229i	$-0.455466\pi$
$479$	21.3622	−	33.6614i	0.976062	−	1.53803i	0.836610	−	0.547799i	$-0.184534\pi$
$480$		0			0
$481$	30.4642	−	36.8249i	1.38905	−	1.67907i
$482$	−0.0636932	+	0.196027i	−0.00290115	+	0.00892881i
$483$	−4.16037	+	1.06820i	−0.189304	+	0.0486049i
$484$	−2.97961	−	1.63806i	−0.135437	−	0.0744571i
$485$		0			0
$486$	4.25697	+	22.3158i	0.193100	+	1.01227i
$487$	−1.91076	+	10.0166i	−0.0865848	+	0.453893i	0.912419	+	0.409258i	$0.134212\pi$
$487$	−1.91076	+	10.0166i	−0.0865848	+	0.453893i	−0.999003	+	0.0446350i	$0.985788\pi$
$488$	15.2282	+	32.3616i	0.689349	+	1.46494i
$489$	−10.9943	−	1.38890i	−0.497178	−	0.0628082i
$490$		0			0
$491$	0.157079	−	0.823439i	0.00708889	−	0.0371613i	−0.978567	−	0.205928i	$-0.933979\pi$
$491$	0.157079	−	0.823439i	0.00708889	−	0.0371613i	0.985656	+	0.168767i	$0.0539786\pi$
$492$	−0.416809	−	0.165026i	−0.0187912	−	0.00743996i
$493$	0.260699	+	0.802348i	0.0117413	+	0.0361359i
$494$	18.9564	+	29.8706i	0.852891	+	1.34394i
$495$		0			0
$496$	−3.01714	−	0.774671i	−0.135474	−	0.0347837i
$497$	0.659473	+	0.797166i	0.0295814	+	0.0357578i
$498$	−5.23024	−	0.660733i	−0.234373	−	0.0296082i
$499$	21.9417			0.982246			0.491123	−	0.871090i	$-0.336586\pi$
$499$	21.9417			0.982246			0.491123	+	0.871090i	$0.336586\pi$
$500$		0			0
$501$	17.0510			0.761781
$502$	30.4252	+	3.84359i	1.35794	+	0.171548i
$503$	8.87103	+	10.7232i	0.395540	+	0.478125i	0.930259	−	0.366905i	$-0.119583\pi$
$503$	8.87103	+	10.7232i	0.395540	+	0.478125i	−0.534719	+	0.845030i	$0.679583\pi$
$504$	13.6564	+	3.50638i	0.608306	+	0.156186i
$505$		0			0
$506$	2.56787	+	4.04631i	0.114156	+	0.179881i
$507$	−13.9664	−	42.9842i	−0.620270	−	1.90900i
$508$	−0.482200	−	0.190917i	−0.0213942	−	0.00847055i
$509$	1.37195	−	7.19204i	0.0608108	−	0.318782i	−0.938864	−	0.344289i	$-0.888120\pi$
$509$	1.37195	−	7.19204i	0.0608108	−	0.318782i	0.999675	+	0.0255072i	$0.00812008\pi$
$510$		0			0
$511$	34.8775	+	4.40605i	1.54289	+	0.194912i
$512$	−10.8244	−	23.0030i	−0.478374	−	1.01660i
$513$	2.07217	−	10.8627i	0.0914887	−	0.479600i
$514$	6.47457	+	33.9409i	0.285581	+	1.49707i
$515$		0			0
$516$	−7.27875	−	4.00153i	−0.320429	−	0.176158i
$517$	17.8310	−	4.57821i	0.784204	−	0.201349i
$518$	7.92086	−	24.3779i	0.348023	−	1.07110i
$519$	1.89331	−	2.28862i	0.0831070	−	0.100459i
$520$		0			0
$521$	2.92542	−	4.60972i	0.128165	−	0.201956i	−0.774185	−	0.632959i	$-0.781840\pi$
$521$	2.92542	−	4.60972i	0.128165	−	0.201956i	0.902350	+	0.431003i	$0.141840\pi$
$522$	0.474801	+	0.121908i	0.0207815	+	0.00533578i
$523$	−15.0102	−	14.0955i	−0.656349	−	0.616353i	0.283080	−	0.959096i	$-0.408644\pi$
$523$	−15.0102	−	14.0955i	−0.656349	−	0.616353i	−0.939429	+	0.342743i	$0.888644\pi$
$524$	0.241305	+	0.742659i	0.0105414	+	0.0324432i
$525$		0			0
$526$	−9.50238	+	29.2453i	−0.414324	+	1.27516i
$527$	−3.67399	+	2.01979i	−0.160042	+	0.0879836i
$528$	−2.07708	−	33.0142i	−0.0903933	−	1.43676i
$529$	−1.40347	−	22.3075i	−0.0610203	−	0.969890i
$530$		0			0
$531$	10.3923	−	2.66829i	0.450987	−	0.115794i
$532$	−3.05715	−	2.22115i	−0.132544	−	0.0962990i
$533$	1.87526	+	2.95494i	0.0812266	+	0.127993i
$534$	6.76028	−	0.854022i	0.292546	−	0.0369571i
$535$		0			0
$536$	−1.39674	+	2.96823i	−0.0603300	+	0.128208i
$537$	−28.7412	−	15.8006i	−1.24027	−	0.681847i
$538$	−2.12386	+	1.99443i	−0.0915659	+	0.0859861i
$539$	5.07032	−	2.78743i	0.218394	−	0.120063i
$540$		0			0
$541$	17.5737	−	16.5028i	0.755553	−	0.709511i	−0.207675	−	0.978198i	$-0.566590\pi$
$541$	17.5737	−	16.5028i	0.755553	−	0.709511i	0.963228	+	0.268687i	$0.0865896\pi$
$542$	11.4165	−	13.8002i	0.490382	−	0.592770i
$543$	−2.20385	+	1.60119i	−0.0945761	+	0.0687135i
$544$	−7.50085	−	2.96980i	−0.321596	−	0.127329i
$545$		0			0
$546$	−25.3421	−	30.6334i	−1.08454	−	1.31099i
$547$	38.2616	−	15.1488i	1.63595	−	0.647717i	0.642955	−	0.765904i	$-0.277708\pi$
$547$	38.2616	−	15.1488i	1.63595	−	0.647717i	0.992991	+	0.118186i	$0.0377080\pi$
$548$	0.463324	+	2.42883i	0.0197922	+	0.103754i
$549$	18.7641	−	13.6329i	0.800831	−	0.581838i
$550$		0			0
$551$	−0.746274	−	0.542200i	−0.0317923	−	0.0230985i
$552$	2.29822	−	4.88397i	0.0978188	−	0.207876i
$553$	1.19872	−	1.88887i	0.0509746	−	0.0803231i
$554$	−32.2391	+	12.7644i	−1.36971	+	0.542306i
$555$		0			0
$556$	0.151752	−	2.41203i	0.00643572	−	0.102293i
$557$	−11.6966			−0.495599			−0.247799	−	0.968811i	$-0.579707\pi$
$557$	−11.6966			−0.495599			−0.247799	+	0.968811i	$0.579707\pi$
$558$	−0.152966	+	2.43133i	−0.00647557	+	0.102926i
$559$	27.6099	+	58.6740i	1.16777	+	2.48164i
$560$		0			0
$561$	−32.4557	−	30.4779i	−1.37028	−	1.28678i
$562$	−26.4392	+	3.34005i	−1.11527	+	0.140892i
$563$	−25.6113	+	3.23546i	−1.07939	+	0.136359i	−0.644861	−	0.764300i	$-0.723085\pi$
$563$	−25.6113	+	3.23546i	−1.07939	+	0.136359i	−0.434528	+	0.900658i	$0.643085\pi$
$564$	−2.15277	−	2.02159i	−0.0906481	−	0.0851242i
$565$		0			0
$566$	−1.51557	−	3.22074i	−0.0637040	−	0.135378i
$567$	−1.66215	+	26.4191i	−0.0698036	+	1.10950i
$568$	−1.30011			−0.0545515
$569$	−1.08886	+	17.3070i	−0.0456476	+	0.725548i	0.906936	+	0.421269i	$0.138415\pi$
$569$	−1.08886	+	17.3070i	−0.0456476	+	0.725548i	−0.952583	+	0.304278i	$0.901585\pi$
$570$		0			0
$571$	−36.6876	+	14.5256i	−1.53533	+	0.607879i	−0.975357	−	0.220634i	$-0.929188\pi$
$571$	−36.6876	+	14.5256i	−1.53533	+	0.607879i	−0.559970	+	0.828513i	$0.689188\pi$
$572$	4.73358	−	7.45893i	0.197921	−	0.311874i
$573$	6.51259	−	13.8400i	0.272067	−	0.578172i
$574$	1.51853	+	1.10328i	0.0633822	+	0.0460499i
$575$		0			0
$576$	−13.9854	+	10.1610i	−0.582725	+	0.423375i
$577$	−0.727434	−	3.81334i	−0.0302835	−	0.158751i	0.963933	−	0.266144i	$-0.0857498\pi$
$577$	−0.727434	−	3.81334i	−0.0302835	−	0.158751i	−0.994217	+	0.107393i	$0.965750\pi$
$578$	2.21548	−	0.877172i	0.0921519	−	0.0364855i
$579$	−31.3962	−	37.9515i	−1.30478	−	1.57721i
$580$		0			0
$581$	−4.08737	−	1.61830i	−0.169573	−	0.0671385i
$582$	−17.2044	+	12.4997i	−0.713143	+	0.518129i
$583$	−24.1939	+	29.2454i	−1.00201	+	1.21122i
$584$	−32.2036	+	30.2412i	−1.33259	+	1.25139i
$585$		0			0
$586$	−2.67473	+	1.47044i	−0.110492	+	0.0607435i
$587$	−9.27951	+	8.71404i	−0.383006	+	0.359667i	−0.852007	−	0.523531i	$-0.824614\pi$
$587$	−9.27951	+	8.71404i	−0.383006	+	0.359667i	0.469000	+	0.883198i	$0.344614\pi$
$588$	−0.813368	−	0.447153i	−0.0335427	−	0.0184403i
$589$	1.95187	−	4.14794i	0.0804254	−	0.170913i
$590$		0			0
$591$	23.7715	−	3.00304i	0.977829	−	0.123529i
$592$	14.3116	+	22.5515i	0.588205	+	0.926863i
$593$	−24.0634	−	17.4831i	−0.988166	−	0.717945i	−0.0286475	−	0.999590i	$-0.509120\pi$
$593$	−24.0634	−	17.4831i	−0.988166	−	0.717945i	−0.959519	+	0.281645i	$0.909120\pi$
$594$	13.4299	−	3.44820i	0.551034	−	0.141482i
$595$		0			0
$596$	−0.439834	−	6.99097i	−0.0180163	−	0.286361i
$597$	−0.996311	−	15.8359i	−0.0407763	−	0.648121i
$598$	−5.25939	+	2.89137i	−0.215072	+	0.118237i
$599$	12.5249	−	38.5477i	0.511754	−	1.57502i	−0.277358	−	0.960767i	$-0.589459\pi$
$599$	12.5249	−	38.5477i	0.511754	−	1.57502i	0.789112	−	0.614250i	$-0.210541\pi$
$600$		0			0
$601$	−4.17440	−	12.8475i	−0.170277	−	0.524059i	0.829109	−	0.559087i	$-0.188848\pi$
$601$	−4.17440	−	12.8475i	−0.170277	−	0.524059i	−0.999386	+	0.0350274i	$0.988848\pi$
$602$	25.3523	+	23.8074i	1.03328	+	0.970316i
$603$	2.06050	+	0.529048i	0.0839102	+	0.0215445i
$604$	0.795665	−	1.25377i	0.0323751	−	0.0510151i
$605$		0			0
$606$	17.8001	−	21.5166i	0.723080	−	0.874054i
$607$	2.54307	−	7.82677i	0.103220	−	0.317679i	−0.886089	−	0.463516i	$-0.846588\pi$
$607$	2.54307	−	7.82677i	0.103220	−	0.317679i	0.989309	+	0.145837i	$0.0465876\pi$
$608$	8.54385	−	2.19369i	0.346499	−	0.0889657i
$609$	0.908404	+	0.499399i	0.0368104	+	0.0202367i
$610$		0			0
$611$	4.32011	+	22.6468i	0.174773	+	0.916192i
$612$	−0.527737	+	2.76649i	−0.0213325	+	0.111829i
$613$	5.52546	+	11.7422i	0.223171	+	0.474263i	0.984787	−	0.173766i	$-0.0555937\pi$
$613$	5.52546	+	11.7422i	0.223171	+	0.474263i	−0.761616	+	0.648029i	$0.775594\pi$
$614$	19.7320	+	2.49274i	0.796320	+	0.100599i
$615$		0			0
$616$	6.23343	−	32.6768i	0.251152	−	1.31659i
$617$	−12.4029	−	4.91066i	−0.499322	−	0.197696i	0.104944	−	0.994478i	$-0.466534\pi$
$617$	−12.4029	−	4.91066i	−0.499322	−	0.197696i	−0.604266	+	0.796782i	$0.706534\pi$
$618$	6.04315	+	18.5989i	0.243091	+	0.748158i
$619$	−12.2030	−	19.2288i	−0.490480	−	0.772872i	0.505464	−	0.862847i	$-0.331321\pi$
$619$	−12.2030	−	19.2288i	−0.490480	−	0.772872i	−0.995944	+	0.0899752i	$0.971321\pi$
$620$		0			0
$621$	1.81712	+	0.466557i	0.0729185	+	0.0187223i
$622$	1.45095	+	1.75390i	0.0581779	+	0.0703250i
$623$	5.63728	+	0.712155i	0.225853	+	0.0285319i
$624$	41.4276			1.65843
$625$		0			0
$626$	38.4094			1.53515
$627$	48.2979	+	6.10145i	1.92883	+	0.243668i
$628$	−1.06505	−	1.28742i	−0.0425000	−	0.0513737i
$629$	34.8197	+	8.94018i	1.38835	+	0.356468i
$630$		0			0
$631$	3.01367	+	4.74878i	0.119972	+	0.189046i	0.899006	−	0.437936i	$-0.144290\pi$
$631$	3.01367	+	4.74878i	0.119972	+	0.189046i	−0.779034	+	0.626981i	$0.784290\pi$
$632$	0.868732	+	2.67368i	0.0345563	+	0.106353i
$633$	−55.6698	−	22.0412i	−2.21268	−	0.876060i
$634$	1.49640	−	7.84438i	0.0594295	−	0.311540i
$635$		0			0
$636$	6.04076	+	0.763126i	0.239532	+	0.0302599i
$637$	3.08528	+	6.55656i	0.122243	+	0.259780i
$638$	0.216722	−	1.13609i	0.00858009	−	0.0449784i
$639$	0.157984	+	0.828180i	0.00624974	+	0.0327623i
$640$		0			0
$641$	7.06472	+	3.88386i	0.279040	+	0.153403i	0.615128	−	0.788427i	$-0.289104\pi$
$641$	7.06472	+	3.88386i	0.279040	+	0.153403i	−0.336089	+	0.941830i	$0.609104\pi$
$642$	−31.1617	+	8.00096i	−1.22985	+	0.315773i
$643$	10.1454	−	31.2243i	0.400095	−	1.23137i	−0.524827	−	0.851209i	$-0.675870\pi$
$643$	10.1454	−	31.2243i	0.400095	−	1.23137i	0.924922	−	0.380157i	$-0.124130\pi$
$644$	0.408633	−	0.493953i	0.0161024	−	0.0194645i
$645$		0			0
$646$	−14.2588	+	22.4683i	−0.561005	+	0.884003i
$647$	−26.8836	−	6.90254i	−1.05690	−	0.271367i	−0.320037	−	0.947405i	$-0.603695\pi$
$647$	−26.8836	−	6.90254i	−1.05690	−	0.271367i	−0.736866	+	0.676038i	$0.763695\pi$
$648$	−24.2491	−	22.7714i	−0.952595	−	0.894546i
$649$	−7.82272	−	24.0759i	−0.307069	−	0.945060i
$650$		0			0
$651$	−1.59196	+	4.89954i	−0.0623937	+	0.192028i
$652$	1.44934	−	0.796782i	0.0567606	−	0.0312044i
$653$	−1.02010	−	16.2141i	−0.0399198	−	0.634507i	−0.966220	−	0.257720i	$-0.917029\pi$
$653$	−1.02010	−	16.2141i	−0.0399198	−	0.634507i	0.926300	−	0.376787i	$-0.122971\pi$
$654$	2.22852	+	35.4213i	0.0871421	+	1.38508i
$655$		0			0
$656$	−1.89443	+	0.486406i	−0.0739649	+	0.0189910i
$657$	23.1770	+	16.8391i	0.904222	+	0.656956i
$658$	6.62554	+	10.4402i	0.258290	+	0.407000i
$659$	15.2615	−	1.92797i	0.594503	−	0.0751032i	0.177676	−	0.984089i	$-0.443142\pi$
$659$	15.2615	−	1.92797i	0.594503	−	0.0751032i	0.416827	+	0.908986i	$0.363142\pi$
$660$		0			0
$661$	8.75412	−	18.6034i	0.340496	−	0.723590i	−0.659099	−	0.752056i	$-0.729062\pi$
$661$	8.75412	−	18.6034i	0.340496	−	0.723590i	0.999595	+	0.0284660i	$0.00906223\pi$
$662$	33.4139	+	18.3694i	1.29867	+	0.713948i
$663$	40.6464	−	38.1695i	1.57857	−	1.48238i
$664$	4.84098	−	2.66135i	0.187866	−	0.103280i
$665$		0			0
$666$	15.2271	−	14.2992i	0.590036	−	0.554081i
$667$	0.0997506	−	0.120578i	0.00386236	−	0.00466879i
$668$	−2.05881	+	1.49581i	−0.0796578	+	0.0578748i
$669$	26.8369	+	10.6255i	1.03757	+	0.410804i
$670$		0			0
$671$	−34.8818	−	42.1648i	−1.34660	−	1.62775i
$672$	−9.21674	+	3.64917i	−0.355543	+	0.140770i
$673$	4.07318	+	21.3524i	0.157010	+	0.823073i	0.970427	+	0.241393i	$0.0776044\pi$
$673$	4.07318	+	21.3524i	0.157010	+	0.823073i	−0.813418	+	0.581680i	$0.802396\pi$
$674$	20.9816	−	15.2441i	0.808183	−	0.587179i
$675$		0			0
$676$	5.45720	+	3.96489i	0.209892	+	0.152496i
$677$	−3.07517	+	6.53506i	−0.118188	+	0.251163i	−0.955164	−	0.296077i	$-0.904321\pi$
$677$	−3.07517	+	6.53506i	−0.118188	+	0.251163i	0.836976	+	0.547240i	$0.184321\pi$
$678$	22.9353	−	36.1403i	0.880825	−	1.38796i
$679$	−16.4879	+	6.52801i	−0.632746	+	0.250522i
$680$		0			0
$681$	3.11091	−	49.4465i	0.119210	−	1.89479i
$682$	5.74780			0.220095
$683$	1.63344	−	25.9627i	0.0625017	−	0.993436i	−0.834387	−	0.551179i	$-0.814178\pi$
$683$	1.63344	−	25.9627i	0.0625017	−	0.993436i	0.896888	−	0.442257i	$-0.145822\pi$
$684$	−1.31117	−	2.78639i	−0.0501340	−	0.106540i
$685$		0			0
$686$	18.6276	+	17.4924i	0.711204	+	0.667865i
$687$	−1.92472	+	0.243148i	−0.0734326	+	0.00927669i
$688$	−35.9538	+	4.54202i	−1.37073	+	0.173163i
$689$	−34.6511	−	32.5396i	−1.32010	−	1.23966i
$690$		0			0
$691$	−12.4999	−	26.5637i	−0.475520	−	1.01053i	−0.988372	−	0.152054i	$-0.951411\pi$
$691$	−12.4999	−	26.5637i	−0.475520	−	1.01053i	0.512853	−	0.858477i	$-0.328589\pi$
$692$	−0.0278353	+	0.442430i	−0.00105814	+	0.0168187i
$693$	−21.5728			−0.819482
$694$	−0.900087	+	14.3065i	−0.0341668	+	0.543066i
$695$		0			0
$696$	−1.21119	+	0.479545i	−0.0459102	+	0.0181771i
$697$	−1.41055	+	2.22267i	−0.0534284	+	0.0841897i
$698$	−8.07140	+	17.1526i	−0.305507	+	0.649236i
$699$	−30.9238	−	22.4675i	−1.16965	−	0.849797i
$700$		0			0
$701$	8.21119	−	5.96578i	0.310132	−	0.225324i	−0.421821	−	0.906679i	$-0.638609\pi$
$701$	8.21119	−	5.96578i	0.310132	−	0.225324i	0.731953	+	0.681355i	$0.238609\pi$
$702$	3.25381	+	17.0571i	0.122807	+	0.643777i
$703$	−36.5470	+	14.4700i	−1.37839	+	0.545745i
$704$	25.9984	+	31.4267i	0.979851	+	1.18444i
$705$		0			0
$706$	−10.2189	−	4.04596i	−0.384595	−	0.152272i
$707$	18.8390	−	13.6873i	0.708513	−	0.514765i
$708$	−2.58855	+	3.12901i	−0.0972835	+	0.117596i
$709$	34.1604	−	32.0788i	1.28292	−	1.20474i	0.316264	−	0.948671i	$-0.397571\pi$
$709$	34.1604	−	32.0788i	1.28292	−	1.20474i	0.966658	−	0.256072i	$-0.0824286\pi$
$710$		0			0
$711$	1.59759	−	0.878282i	0.0599142	−	0.0329381i
$712$	−5.20510	+	4.88791i	−0.195069	+	0.183182i
$713$	0.681506	+	0.374661i	0.0255226	+	0.0140312i
$714$	12.7329	−	27.0587i	0.476515	−	1.01265i
$715$		0			0
$716$	4.85647	−	0.613515i	0.181495	−	0.0229281i
$717$	−31.5247	−	49.6751i	−1.17731	−	1.85515i
$718$	−28.0440	−	20.3752i	−1.04659	−	0.760394i
$719$	−22.1441	+	5.68564i	−0.825835	+	0.212038i	−0.637877	−	0.770138i	$-0.720187\pi$
$719$	−22.1441	+	5.68564i	−0.825835	+	0.212038i	−0.187959	+	0.982177i	$0.560187\pi$
$720$		0			0
$721$	1.02395	+	16.2753i	0.0381341	+	0.606123i
$722$	−0.286272	−	4.55017i	−0.0106540	−	0.169340i
$723$	−0.311266	+	0.171120i	−0.0115761	+	0.00636402i
$724$	0.125636	−	0.386669i	0.00466924	−	0.0143704i
$725$		0			0
$726$	9.09187	+	27.9819i	0.337431	+	1.03851i
$727$	−8.51386	−	7.99505i	−0.315762	−	0.296520i	0.510418	−	0.859926i	$-0.329491\pi$
$727$	−8.51386	−	7.99505i	−0.315762	−	0.296520i	−0.826180	+	0.563406i	$0.809491\pi$
$728$	40.3524	+	10.3607i	1.49556	+	0.383994i
$729$	−3.22394	+	5.08011i	−0.119405	+	0.188152i
$730$		0			0
$731$	−31.0910	+	37.5826i	−1.14994	+	1.39004i
$732$	−2.71272	+	8.34888i	−0.100265	+	0.308583i
$733$	16.9311	−	4.34718i	0.625366	−	0.160567i	0.0773083	−	0.997007i	$-0.475367\pi$
$733$	16.9311	−	4.34718i	0.625366	−	0.160567i	0.548058	+	0.836441i	$0.315367\pi$
$734$	17.0060	+	9.34911i	0.627702	+	0.345082i
$735$		0			0
$736$	0.280407	+	1.46995i	0.0103360	+	0.0541830i
$737$	0.940510	−	4.93033i	0.0346441	−	0.181611i
$738$	0.651279	+	1.38404i	0.0239739	+	0.0509472i
$739$	−11.5925	−	1.46448i	−0.426439	−	0.0538717i	−0.0908148	−	0.995868i	$-0.528947\pi$
$739$	−11.5925	−	1.46448i	−0.426439	−	0.0538717i	−0.335624	+	0.941996i	$0.608947\pi$
$740$		0			0
$741$	−11.4241	+	59.8875i	−0.419676	+	2.20002i
$742$	−23.7037	−	9.38495i	−0.870189	−	0.344532i
$743$	6.81750	+	20.9821i	0.250110	+	0.769759i	0.994754	+	0.102297i	$0.0326192\pi$
$743$	6.81750	+	20.9821i	0.250110	+	0.769759i	−0.744644	+	0.667462i	$0.767381\pi$
$744$	−3.46885	−	5.46603i	−0.127174	−	0.200394i
$745$		0			0
$746$	−5.47925	−	1.40683i	−0.200609	−	0.0515078i
$747$	−2.28355	−	2.76034i	−0.0835508	−	0.100996i
$748$	6.59256	+	0.832834i	0.241048	+	0.0304514i
$749$	−26.8281			−0.980276
$750$		0			0
$751$	−21.3393			−0.778684			−0.389342	−	0.921093i	$-0.627298\pi$
$751$	−21.3393			−0.778684			−0.389342	+	0.921093i	$0.627298\pi$
$752$	−12.7830	−	1.61487i	−0.466149	−	0.0588883i
$753$	33.6872	+	40.7208i	1.22763	+	1.48395i
$754$	1.40295	+	0.360217i	0.0510926	+	0.0131183i
$755$		0			0
$756$	−0.993840	−	1.56604i	−0.0361456	−	0.0569563i
$757$	−0.725104	−	2.23164i	−0.0263544	−	0.0811104i	0.937014	−	0.349291i	$-0.113578\pi$
$757$	−0.725104	−	2.23164i	−0.0263544	−	0.0811104i	−0.963369	+	0.268181i	$0.913578\pi$
$758$	5.89864	+	2.33544i	0.214248	+	0.0848269i
$759$	−1.54753	+	8.11245i	−0.0561718	+	0.294463i
$760$		0			0
$761$	−37.4792	−	4.73473i	−1.35862	−	0.171634i	−0.587966	−	0.808886i	$-0.700071\pi$
$761$	−37.4792	−	4.73473i	−1.35862	−	0.171634i	−0.770656	+	0.637252i	$0.780071\pi$
$762$	1.91073	+	4.06052i	0.0692186	+	0.147097i
$763$	−5.54567	+	29.0714i	−0.200767	+	1.05246i
$764$	0.427765	+	2.24242i	0.0154760	+	0.0811280i
$765$		0			0
$766$	−30.4668	−	16.7493i	−1.10081	−	0.605176i
$767$	30.7074	−	7.88432i	1.10878	−	0.284686i
$768$	5.32301	−	16.3825i	0.192077	−	0.591154i
$769$	−14.5843	+	17.6294i	−0.525924	+	0.635732i	−0.964853	−	0.262789i	$-0.915358\pi$
$769$	−14.5843	+	17.6294i	−0.525924	+	0.635732i	0.438930	+	0.898521i	$0.355358\pi$
$770$		0			0
$771$	−31.9061	+	50.2760i	−1.14907	+	1.81065i
$772$	7.12025	+	1.82817i	0.256263	+	0.0657972i
$773$	17.2344	+	16.1842i	0.619880	+	0.582106i	0.929531	−	0.368744i	$-0.120212\pi$
$773$	17.2344	+	16.1842i	0.619880	+	0.582106i	−0.309651	+	0.950850i	$0.600212\pi$
$774$	8.75805	+	26.9545i	0.314802	+	0.968860i
$775$		0			0
$776$	6.88621	−	21.1936i	0.247200	−	0.760805i
$777$	38.7089	−	21.2804i	1.38868	−	0.763431i
$778$	−1.00558	−	15.9832i	−0.0360518	−	0.573027i
$779$	−0.180735	−	2.87270i	−0.00647551	−	0.102925i
$780$		0			0
$781$	1.92674	−	0.494703i	0.0689443	−	0.0177019i
$782$	−3.65227	−	2.65353i	−0.130605	−	0.0948901i
$783$	−0.242604	−	0.382283i	−0.00866996	−	0.0136617i
$784$	−4.01768	+	0.507551i	−0.143489	+	0.0181268i
$785$		0			0
$786$	2.87697	−	6.11387i	0.102618	−	0.218074i
$787$	7.27172	+	3.99766i	0.259209	+	0.142501i	0.606060	−	0.795419i	$-0.292749\pi$
$787$	7.27172	+	3.99766i	0.259209	+	0.142501i	−0.346851	+	0.937920i	$0.612749\pi$
$788$	−2.60683	+	2.44798i	−0.0928646	+	0.0872057i
$789$	−46.4378	+	25.5294i	−1.65323	+	0.908870i
$790$		0			0
$791$	26.0192	−	24.4337i	0.925137	−	0.868761i
$792$	17.2801	−	20.8881i	0.614022	−	0.742225i
$793$	55.4445	−	40.2828i	1.96889	−	1.43048i
$794$	−39.5538	−	15.6604i	−1.40371	−	0.555769i
$795$		0			0
$796$	1.50952	+	1.82470i	0.0535036	+	0.0646747i
$797$	−12.2094	+	4.83404i	−0.432479	+	0.171231i	−0.574270	−	0.818666i	$-0.694714\pi$
$797$	−12.2094	+	4.83404i	−0.432479	+	0.171231i	0.141791	+	0.989897i	$0.454714\pi$
$798$	6.12706	+	32.1192i	0.216895	+	1.13701i
$799$	−14.0298	+	10.1933i	−0.496340	+	0.360612i
$800$		0			0
$801$	3.74613	+	2.72172i	0.132363	+	0.0961673i
$802$	4.36407	−	9.27412i	0.154101	−	0.327481i
$803$	36.2181	−	57.0706i	1.27811	−	2.01398i
$804$	−0.748631	+	0.296404i	−0.0264022	+	0.0104534i
$805$		0			0
$806$	−0.451988	+	7.18414i	−0.0159206	+	0.253050i
$807$	−5.02090			−0.176744
$808$	−1.83741	+	29.2048i	−0.0646398	+	1.02742i
$809$	12.0325	+	25.5705i	0.423042	+	0.899009i	0.996796	+	0.0799821i	$0.0254863\pi$
$809$	12.0325	+	25.5705i	0.423042	+	0.899009i	−0.573755	+	0.819027i	$0.694514\pi$
$810$		0			0
$811$	40.0019	+	37.5643i	1.40466	+	1.31906i	0.885700	+	0.464259i	$0.153679\pi$
$811$	40.0019	+	37.5643i	1.40466	+	1.31906i	0.518956	+	0.854801i	$0.326321\pi$
$812$	−0.153495	+	0.0193909i	−0.00538662	+	0.000680489i
$813$	30.6220	−	3.86845i	1.07396	−	0.135673i
$814$	−35.9266	−	33.7374i	−1.25923	−	1.18249i
$815$		0			0
$816$	13.2679	+	28.1956i	0.464468	+	0.987045i
$817$	3.34877	−	53.2271i	0.117159	−	1.86218i
$818$	3.91863			0.137012
$819$	1.69641	−	26.9637i	0.0592774	−	0.942187i
$820$		0			0
$821$	8.58760	−	3.40007i	0.299709	−	0.118663i	−0.213457	−	0.976952i	$-0.568472\pi$
$821$	8.58760	−	3.40007i	0.299709	−	0.118663i	0.513166	+	0.858289i	$0.328472\pi$
$822$	11.4644	−	18.0649i	0.399866	−	0.630087i
$823$	−14.6404	+	31.1123i	−0.510331	+	1.08451i	0.469178	+	0.883104i	$0.344550\pi$
$823$	−14.6404	+	31.1123i	−0.510331	+	1.08451i	−0.979508	+	0.201404i	$0.935450\pi$
$824$	−16.5789	−	12.0453i	−0.577554	−	0.419617i
$825$		0			0
$826$	13.7560	−	9.99432i	0.478632	−	0.347747i
$827$	1.22971	+	6.44636i	0.0427612	+	0.224162i	0.997253	−	0.0740766i	$-0.0236009\pi$
$827$	1.22971	+	6.44636i	0.0427612	+	0.224162i	−0.954491	+	0.298238i	$0.903601\pi$
$828$	0.485737	−	0.192317i	0.0168805	−	0.00668347i
$829$	−28.4362	−	34.3734i	−0.987629	−	1.19384i	−0.981029	−	0.193860i	$-0.937899\pi$
$829$	−28.4362	−	34.3734i	−0.987629	−	1.19384i	−0.00659956	−	0.999978i	$-0.502101\pi$
$830$		0			0
$831$	−55.5581	−	21.9970i	−1.92729	−	0.763068i
$832$	−41.3244	+	30.0239i	−1.43267	+	1.04089i
$833$	−3.47428	+	4.19969i	−0.120377	+	0.145510i
$834$	−15.2446	+	14.3156i	−0.527877	+	0.495710i
$835$		0			0
$836$	−6.36697	+	3.50027i	−0.220206	+	0.121059i
$837$	1.64024	−	1.54029i	0.0566951	−	0.0532403i
$838$	8.75649	+	4.81392i	0.302488	+	0.166294i
$839$	−6.30331	+	13.3952i	−0.217615	+	0.462454i	−0.983591	−	0.180415i	$-0.942256\pi$
$839$	−6.30331	+	13.3952i	−0.217615	+	0.462454i	0.765976	+	0.642869i	$0.222256\pi$
$840$		0			0
$841$	28.7339	−	3.62993i	0.990823	−	0.125170i
$842$	17.5170	+	27.6024i	0.603676	+	0.951241i
$843$	−37.1544	−	26.9942i	−1.27966	−	0.929731i
$844$	8.65541	−	2.22233i	0.297932	−	0.0764958i
$845$		0			0
$846$	0.632714	+	10.0567i	0.0217532	+	0.345757i
$847$	1.54053	+	24.4860i	0.0529332	+	0.841349i
$848$	23.2792	−	12.7979i	0.799411	−	0.439480i
$849$	1.89556	−	5.83394i	0.0650555	−	0.200220i
$850$		0			0
$851$	−2.06064	−	6.34199i	−0.0706378	−	0.217401i
$852$	−0.232620	−	0.218445i	−0.00796944	−	0.00748380i
$853$	−4.73615	−	1.21604i	−0.162163	−	0.0416363i	0.166736	−	0.986002i	$-0.446677\pi$
$853$	−4.73615	−	1.21604i	−0.162163	−	0.0416363i	−0.328898	+	0.944365i	$0.606677\pi$
$854$	19.6949	−	31.0342i	0.673945	−	1.06197i
$855$		0			0
$856$	21.4897	−	25.9765i	0.734501	−	0.887860i
$857$	−7.31615	+	22.5168i	−0.249915	+	0.769159i	0.744874	+	0.667205i	$0.232510\pi$
$857$	−7.31615	+	22.5168i	−0.249915	+	0.769159i	−0.994789	+	0.101954i	$0.967490\pi$
$858$	−74.0405	+	19.0104i	−2.52770	+	0.649003i
$859$	12.2950	+	6.75925i	0.419501	+	0.230623i	0.677500	−	0.735522i	$-0.263063\pi$
$859$	12.2950	+	6.75925i	0.419501	+	0.230623i	−0.257999	+	0.966145i	$0.583063\pi$
$860$		0			0
$861$	0.606118	+	3.17738i	0.0206564	+	0.108285i
$862$	−6.82539	+	35.7800i	−0.232474	+	1.21867i
$863$	−10.4325	−	22.1702i	−0.355127	−	0.754683i	0.644827	−	0.764329i	$-0.276930\pi$
$863$	−10.4325	−	22.1702i	−0.355127	−	0.754683i	−0.999953	+	0.00964574i	$0.996930\pi$
$864$	4.29548	+	0.542645i	0.146135	+	0.0184612i
$865$		0			0
$866$	−2.31123	+	12.1159i	−0.0785389	+	0.411715i
$867$	3.81798	+	1.51164i	0.129665	+	0.0513381i
$868$	−0.237597	−	0.731249i	−0.00806457	−	0.0248202i
$869$	−2.30480	−	3.63179i	−0.0781851	−	0.123200i
$870$		0			0
$871$	6.08843	+	1.56324i	0.206298	+	0.0529684i
$872$	−23.7065	−	28.6563i	−0.802805	−	0.970424i
$873$	−14.3372	−	1.81121i	−0.485241	−	0.0613002i
$874$	4.93617			0.166968
$875$		0			0
$876$	−10.8431			−0.366354
$877$	−54.9784	−	6.94538i	−1.85649	−	0.234529i	−0.884001	−	0.467485i	$-0.845160\pi$
$877$	−54.9784	−	6.94538i	−1.85649	−	0.234529i	−0.972487	+	0.232956i	$0.925160\pi$
$878$	24.9128	+	30.1144i	0.840768	+	1.01631i
$879$	−5.09478	−	1.30812i	−0.171843	−	0.0441217i
$880$		0			0
$881$	−29.0306	−	45.7449i	−0.978065	−	1.54118i	−0.834109	−	0.551600i	$-0.814018\pi$
$881$	−29.0306	−	45.7449i	−0.978065	−	1.54118i	−0.143956	−	0.989584i	$-0.545982\pi$
$882$	0.978673	+	3.01205i	0.0329536	+	0.101421i
$883$	9.86984	+	3.90775i	0.332147	+	0.131506i	0.528278	−	0.849071i	$-0.322838\pi$
$883$	9.86984	+	3.90775i	0.332147	+	0.131506i	−0.196131	+	0.980578i	$0.562838\pi$
$884$	−1.55937	+	8.17450i	−0.0524473	+	0.274938i
$885$		0			0
$886$	−25.1979	−	3.18324i	−0.846542	−	0.106943i
$887$	20.1688	+	42.8609i	0.677202	+	1.43913i	0.887181	+	0.461422i	$0.152661\pi$
$887$	20.1688	+	42.8609i	0.677202	+	1.43913i	−0.209978	+	0.977706i	$0.567339\pi$
$888$	−10.4014	+	54.5262i	−0.349049	+	1.82978i
$889$	0.701209	+	3.67587i	0.0235178	+	0.123285i
$890$		0			0
$891$	44.6015	+	24.5199i	1.49421	+	0.821446i
$892$	−4.17253	+	1.07132i	−0.139707	+	0.0358706i
$893$	5.85951	−	18.0337i	0.196081	−	0.603476i
$894$	−38.6358	+	46.7027i	−1.29218	+	1.56197i
$895$		0			0
$896$	−9.90595	+	15.6093i	−0.330934	+	0.521469i
$897$	−10.0180	−	2.57218i	−0.334491	−	0.0858828i
$898$	11.8494	+	11.1273i	0.395420	+	0.371324i
$899$	−0.0579993	−	0.178504i	−0.00193439	−	0.00595343i
$900$		0			0
$901$	11.0489	−	34.0049i	0.368091	−	1.13287i
$902$	3.16257	−	1.73864i	0.105302	−	0.0578902i
$903$	3.76329	+	59.8157i	0.125234	+	1.99054i
$904$	2.81638	+	44.7651i	0.0936714	+	1.48886i
$905$		0			0
$906$	−12.4454	+	3.19544i	−0.413471	+	0.106161i
$907$	24.0545	+	17.4766i	0.798715	+	0.580300i	0.910537	−	0.413428i	$-0.135669\pi$
$907$	24.0545	+	17.4766i	0.798715	+	0.580300i	−0.111822	+	0.993728i	$0.535669\pi$
$908$	3.96212	+	6.24330i	0.131488	+	0.207191i
$909$	18.8269	−	2.37839i	0.624449	−	0.0788862i
$910$		0			0
$911$	−11.0778	+	23.5416i	−0.367025	+	0.779968i	0.632958	+	0.774186i	$0.281841\pi$
$911$	−11.0778	+	23.5416i	−0.367025	+	0.779968i	−0.999983	+	0.00578219i	$0.998159\pi$
$912$	−29.8577	−	16.4144i	−0.988688	−	0.543536i
$913$	−6.16158	+	5.78611i	−0.203918	+	0.191492i
$914$	19.1620	−	10.5344i	0.633822	−	0.348446i
$915$		0			0
$916$	0.211069	−	0.198207i	0.00697391	−	0.00654893i
$917$	3.59157	−	4.34146i	0.118604	−	0.143368i
$918$	−10.5670	+	7.67734i	−0.348761	+	0.253390i
$919$	−25.5410	−	10.1124i	−0.842521	−	0.333577i	−0.0930878	−	0.995658i	$-0.529674\pi$
$919$	−25.5410	−	10.1124i	−0.842521	−	0.333577i	−0.749433	+	0.662080i	$0.769674\pi$
$920$		0			0
$921$	21.8476	+	26.4092i	0.719903	+	0.870213i
$922$	9.64312	−	3.81798i	0.317579	−	0.125739i
$923$	0.466814	+	2.44712i	0.0153654	+	0.0805481i
$924$	6.60566	−	4.79930i	0.217310	−	0.157885i
$925$		0			0
$926$	−1.42760	−	1.03721i	−0.0469138	−	0.0340849i
$927$	−5.65833	+	12.0246i	−0.185844	+	0.394938i
$928$	0.193515	−	0.304931i	0.00635245	−	0.0100099i
$929$	39.3131	−	15.5652i	1.28982	−	0.510677i	0.379735	−	0.925095i	$-0.376015\pi$
$929$	39.3131	−	15.5652i	1.28982	−	0.510677i	0.910086	+	0.414419i	$0.136015\pi$
$930$		0			0
$931$	0.374210	−	5.94789i	0.0122642	−	0.194934i
$932$	5.70486			0.186869
$933$	−0.246311	+	3.91500i	−0.00806386	+	0.128171i
$934$	−15.5270	−	32.9966i	−0.508059	−	1.07968i
$935$		0			0
$936$	24.7490	+	23.2409i	0.808947	+	0.759651i
$937$	−24.5658	+	3.10338i	−0.802528	+	0.101383i	−0.515889	−	0.856656i	$-0.672538\pi$
$937$	−24.5658	+	3.10338i	−0.802528	+	0.101383i	−0.286640	+	0.958038i	$0.592538\pi$
$938$	3.34471	−	0.422535i	0.109209	−	0.0137963i
$939$	48.2516	+	45.3113i	1.57463	+	1.47868i
$940$		0			0
$941$	7.92949	+	16.8510i	0.258494	+	0.549328i	0.991379	−	0.131025i	$-0.0418267\pi$
$941$	7.92949	+	16.8510i	0.258494	+	0.549328i	−0.732885	+	0.680353i	$0.761827\pi$
$942$	−0.907824	+	14.4295i	−0.0295785	+	0.470137i
$943$	0.488309			0.0159015
$944$	−1.11251	+	17.6828i	−0.0362091	+	0.575527i
$945$		0			0
$946$	62.1734	−	24.6162i	2.02143	−	0.800341i
$947$	8.54599	−	13.4663i	0.277707	−	0.437597i	−0.676632	−	0.736321i	$-0.736561\pi$
$947$	8.54599	−	13.4663i	0.277707	−	0.437597i	0.954339	+	0.298725i	$0.0965612\pi$
$948$	−0.293796	+	0.624348i	−0.00954205	+	0.0202779i
$949$	68.4840	+	49.7566i	2.22309	+	1.61517i
$950$		0			0
$951$	11.1338	−	8.08917i	0.361038	−	0.262309i
$952$	5.87198	+	30.7820i	0.190312	+	0.997651i
$953$	−8.10213	+	3.20786i	−0.262454	+	0.103913i	−0.495667	−	0.868513i	$-0.665076\pi$
$953$	−8.10213	+	3.20786i	−0.262454	+	0.103913i	0.233213	+	0.972426i	$0.425076\pi$
$954$	−13.2429	−	16.0079i	−0.428754	−	0.518275i
$955$		0			0
$956$	8.16424	+	3.23245i	0.264050	+	0.104545i
$957$	1.61250	−	1.17155i	0.0521246	−	0.0378707i
$958$	32.8191	−	39.6714i	1.06034	−	1.28173i
$959$	13.0059	−	12.2133i	0.419982	−	0.394389i
$960$		0			0
$961$	−26.3481	+	14.4850i	−0.849940	+	0.467258i
$962$	44.9933	−	42.2515i	1.45064	−	1.36224i
$963$	−19.1585	−	10.5325i	−0.617375	−	0.339405i
$964$	0.0225720	−	0.0479679i	0.000726995	−	0.00154494i
$965$		0			0
$966$	−5.50344	+	0.695246i	−0.177070	+	0.0223692i
$967$	15.5325	+	24.4753i	0.499491	+	0.787072i	0.996752	−	0.0805287i	$-0.0256609\pi$
$967$	15.5325	+	24.4753i	0.499491	+	0.787072i	−0.497261	+	0.867601i	$0.665661\pi$
$968$	−24.9428	−	18.1220i	−0.801692	−	0.582464i
$969$	−44.4182	+	11.4047i	−1.42692	+	0.366370i
$970$		0			0
$971$	2.08524	+	33.1440i	0.0669187	+	1.06364i	0.877985	+	0.478688i	$0.158887\pi$
$971$	2.08524	+	33.1440i	0.0669187	+	1.06364i	−0.811067	+	0.584954i	$0.801113\pi$
$972$	−0.366896	−	5.83164i	−0.0117682	−	0.187050i
$973$	−15.2816	+	8.40113i	−0.489905	+	0.269328i
$974$	−4.06948	+	12.5246i	−0.130395	+	0.401313i
$975$		0			0
$976$	11.8355	+	36.4259i	0.378845	+	1.16597i
$977$	11.1057	+	10.4289i	0.355303	+	0.333651i	0.841559	−	0.540165i	$-0.181638\pi$
$977$	11.1057	+	10.4289i	0.355303	+	0.333651i	−0.486257	+	0.873816i	$0.661638\pi$
$978$	−13.8618	−	3.55909i	−0.443250	−	0.113807i
$979$	5.85397	−	9.22437i	0.187094	−	0.294812i
$980$		0			0
$981$	−15.3735	+	18.5834i	−0.490839	+	0.593322i
$982$	0.334543	−	1.02962i	0.0106757	−	0.0328564i
$983$	−45.9413	+	11.7957i	−1.46530	+	0.376225i	−0.895316	−	0.445431i	$-0.853050\pi$
$983$	−45.9413	+	11.7957i	−1.46530	+	0.376225i	−0.569984	+	0.821656i	$0.693050\pi$
$984$	−3.56204	−	1.95825i	−0.113554	−	0.0624267i
$985$		0			0
$986$	0.204155	+	1.07022i	0.00650161	+	0.0340826i
$987$	−3.99290	+	20.9315i	−0.127095	+	0.666257i
$988$	−3.87429	−	8.23328i	−0.123257	−	0.261936i
$989$	8.97634	+	1.13398i	0.285431	+	0.0360583i
$990$		0			0
$991$	−4.14836	+	21.7465i	−0.131777	+	0.690800i	0.853670	+	0.520815i	$0.174372\pi$
$991$	−4.14836	+	21.7465i	−0.131777	+	0.690800i	−0.985447	+	0.169985i	$0.945628\pi$
$992$	1.66876	+	0.660711i	0.0529833	+	0.0209776i
$993$	20.3057	+	62.4945i	0.644382	+	1.98320i
$994$	0.715929	+	1.12812i	0.0227079	+	0.0357819i
$995$		0			0
$996$	1.31332	+	0.337204i	0.0416142	+	0.0106847i
$997$	21.1642	+	25.5832i	0.670278	+	0.810227i	0.990558	−	0.137096i	$-0.0437768\pi$
$997$	21.1642	+	25.5832i	0.670278	+	0.810227i	−0.320279	+	0.947323i	$0.603777\pi$
$998$	28.1131	+	3.55152i	0.889906	+	0.112421i
$999$	−19.2933			−0.610412

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.g.b.451.17		480
5.2	odd	4		625.2.h.a.174.5		240
5.3	odd	4		125.2.h.a.109.8	yes	240
5.4	even	2	inner	625.2.g.b.451.8		480
125.27	odd	100		125.2.h.a.39.8	✓	240
125.39	even	50	inner	625.2.g.b.176.8		480
125.86	even	25	inner	625.2.g.b.176.17		480
125.98	odd	100		625.2.h.a.449.5		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.39.8	✓	240	125.27	odd	100
125.2.h.a.109.8	yes	240	5.3	odd	4
625.2.g.b.176.8		480	125.39	even	50	inner
625.2.g.b.176.17		480	125.86	even	25	inner
625.2.g.b.451.8		480	5.4	even	2	inner
625.2.g.b.451.17		480	1.1	even	1	trivial
625.2.h.a.174.5		240	5.2	odd	4
625.2.h.a.449.5		240	125.98	odd	100

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.g (of order \(25\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.28126 + 0.161861i) q^{2} +(1.41863 + 1.71483i) q^{3} +(-0.321728 - 0.0826056i) q^{4} +(1.54008 + 2.42678i) q^{6} +(0.740638 + 2.27945i) q^{7} +(-2.80036 - 1.10874i) q^{8} +(-0.365988 + 1.91858i) q^{9} +O(q^{10})\)	\(q+(1.28126 + 0.161861i) q^{2} +(1.41863 + 1.71483i) q^{3} +(-0.321728 - 0.0826056i) q^{4} +(1.54008 + 2.42678i) q^{6} +(0.740638 + 2.27945i) q^{7} +(-2.80036 - 1.10874i) q^{8} +(-0.365988 + 1.91858i) q^{9} +(4.57197 + 0.577574i) q^{11} +(-0.314759 - 0.668897i) q^{12} +(-1.08143 + 5.66906i) q^{13} +(0.579998 + 3.04046i) q^{14} +(-2.82639 - 1.55382i) q^{16} +(-4.20471 + 1.07959i) q^{17} +(-0.779471 + 2.39897i) q^{18} +(3.02560 - 3.65732i) q^{19} +(-2.85818 + 4.50378i) q^{21} +(5.76442 + 1.48005i) q^{22} +(0.587001 + 0.551231i) q^{23} +(-2.07138 - 6.37505i) q^{24} +(-2.30320 + 7.08852i) q^{26} +(2.04161 - 1.12238i) q^{27} +(-0.0499884 - 0.794543i) q^{28} +(-0.0122026 - 0.193954i) q^{29} +(0.935449 - 0.240183i) q^{31} +(1.50346 + 1.09233i) q^{32} +(5.49551 + 8.65953i) q^{33} +(-5.56208 + 0.702655i) q^{34} +(0.276234 - 0.587027i) q^{36} +(-7.25681 - 3.98946i) q^{37} +(4.46857 - 4.19627i) q^{38} +(-11.2556 + 6.18784i) q^{39} +(0.442053 - 0.415115i) q^{41} +(-4.39107 + 5.30790i) q^{42} +(9.09003 - 6.60429i) q^{43} +(-1.42322 - 0.563492i) q^{44} +(0.662880 + 0.801285i) q^{46} +(3.71428 - 1.47059i) q^{47} +(-1.34507 - 7.05108i) q^{48} +(1.01577 - 0.738000i) q^{49} +(-7.81625 - 5.67884i) q^{51} +(0.816222 - 1.73456i) q^{52} +(-4.41327 + 6.95421i) q^{53} +(2.79751 - 1.10761i) q^{54} +(0.453266 - 7.20446i) q^{56} +10.5639 q^{57} +(0.0157590 - 0.250482i) q^{58} +(-2.33894 - 4.97049i) q^{59} +(-8.65640 - 8.12890i) q^{61} +(1.23743 - 0.156324i) q^{62} +(-4.64437 + 0.586720i) q^{63} +(6.45186 + 6.05870i) q^{64} +(5.63955 + 11.9847i) q^{66} +(0.0683896 - 1.08702i) q^{67} +1.44195 q^{68} +(-0.112529 + 1.78860i) q^{69} +(0.401350 - 0.158906i) q^{71} +(3.15211 - 4.96693i) q^{72} +(6.24516 - 13.2717i) q^{73} +(-8.65215 - 6.28615i) q^{74} +(-1.27554 + 0.926731i) q^{76} +(2.06963 + 10.8494i) q^{77} +(-15.4230 + 6.10641i) q^{78} +(-0.594972 - 0.719197i) q^{79} +(10.2690 + 4.06580i) q^{81} +(0.633577 - 0.460321i) q^{82} +(-1.16915 + 1.41326i) q^{83} +(1.29159 - 1.21289i) q^{84} +(12.7157 - 6.99052i) q^{86} +(0.315288 - 0.296076i) q^{87} +(-12.1628 - 6.68655i) q^{88} +(1.00941 - 2.14511i) q^{89} +(-13.7233 + 1.73365i) q^{91} +(-0.143320 - 0.225836i) q^{92} +(1.73893 + 1.26341i) q^{93} +(4.99700 - 1.28301i) q^{94} +(0.259698 + 4.12779i) q^{96} +(0.464575 + 7.38421i) q^{97} +(1.42092 - 0.781159i) q^{98} +(-2.78141 + 8.56030i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 40 q^{4} - 40 q^{6} + 40 q^{9}+O(q^{10}) \) 480 * q + 40 * q^4 - 40 * q^6 + 40 * q^9	\( 480 q + 40 q^{4} - 40 q^{6} + 40 q^{9} - 50 q^{11} + 60 q^{14} - 80 q^{16} + 20 q^{19} - 70 q^{21} - 30 q^{24} - 90 q^{26} + 20 q^{29} - 60 q^{31} + 40 q^{34} + 340 q^{36} - 70 q^{41} - 30 q^{44} - 80 q^{46} - 70 q^{49} - 110 q^{51} - 60 q^{54} + 130 q^{56} - 10 q^{59} - 80 q^{61} - 50 q^{64} - 190 q^{66} + 20 q^{69} + 90 q^{71} - 70 q^{74} - 130 q^{76} - 190 q^{81} - 90 q^{84} - 160 q^{86} - 60 q^{89} + 130 q^{91} - 120 q^{94} - 270 q^{96} - 90 q^{99}+O(q^{100}) \) 480 * q + 40 * q^4 - 40 * q^6 + 40 * q^9 - 50 * q^11 + 60 * q^14 - 80 * q^16 + 20 * q^19 - 70 * q^21 - 30 * q^24 - 90 * q^26 + 20 * q^29 - 60 * q^31 + 40 * q^34 + 340 * q^36 - 70 * q^41 - 30 * q^44 - 80 * q^46 - 70 * q^49 - 110 * q^51 - 60 * q^54 + 130 * q^56 - 10 * q^59 - 80 * q^61 - 50 * q^64 - 190 * q^66 + 20 * q^69 + 90 * q^71 - 70 * q^74 - 130 * q^76 - 190 * q^81 - 90 * q^84 - 160 * q^86 - 60 * q^89 + 130 * q^91 - 120 * q^94 - 270 * q^96 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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