LMFDB - Embedded newform 725.2.bd.c.43.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [725,2,Mod(43,725)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("725.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(725, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([21, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.bd (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [240] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$20$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			43.1
Character	$\chi$	$=$	725.43
Dual form			725.2.bd.c.607.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.16243 - 1.72448i) q^{2} +(-0.539817 + 2.36509i) q^{3} +(1.25723 + 5.50829i) q^{4} +(5.24588 - 4.18345i) q^{6} +(-1.28727 - 2.04868i) q^{7} +(4.38015 - 9.09547i) q^{8} +(-2.59936 - 1.25179i) q^{9} +(-1.48429 + 4.24186i) q^{11} -13.7063 q^{12} +(-0.424646 + 1.21357i) q^{13} +(-0.749276 + 6.65001i) q^{14} +(-14.9759 + 7.21201i) q^{16} +2.59131i q^{17} +(3.46226 + 7.18946i) q^{18} +(3.74108 - 5.95389i) q^{19} +(5.54022 - 1.93861i) q^{21} +(10.5247 - 6.61310i) q^{22} +(-0.717256 + 6.36582i) q^{23} +(19.1472 + 15.2694i) q^{24} +(3.01105 - 1.89197i) q^{26} +(-0.173827 + 0.217972i) q^{27} +(9.66633 - 9.66633i) q^{28} +(-4.87407 + 2.28985i) q^{29} +(0.0230497 + 0.204572i) q^{31} +(25.1371 + 5.73738i) q^{32} +(-9.23115 - 5.80032i) q^{33} +(4.46867 - 5.60353i) q^{34} +(3.62721 - 15.8918i) q^{36} +(-6.28087 - 3.02471i) q^{37} +(-18.3572 + 6.42346i) q^{38} +(-2.64097 - 1.65943i) q^{39} +(-1.86960 - 1.86960i) q^{41} +(-15.3234 - 5.36190i) q^{42} +(-3.80880 - 4.77608i) q^{43} +(-25.2315 - 2.84291i) q^{44} +(12.5288 - 12.5288i) q^{46} +(2.10136 - 1.01196i) q^{47} +(-8.97283 - 39.3126i) q^{48} +(0.497158 - 1.03236i) q^{49} +(-6.12869 - 1.39883i) q^{51} +(-7.21857 - 0.813337i) q^{52} +(-0.0406512 + 0.00458029i) q^{53} +(0.751778 - 0.171589i) q^{54} +(-24.2722 + 2.73482i) q^{56} +(12.0620 + 12.0620i) q^{57} +(14.4886 + 3.45362i) q^{58} -1.45069i q^{59} +(-7.05216 - 11.2234i) q^{61} +(0.302937 - 0.482121i) q^{62} +(0.781574 + 6.93666i) q^{63} +(-23.7360 - 29.7640i) q^{64} +(9.95920 + 28.4617i) q^{66} +(1.03194 + 2.94912i) q^{67} +(-14.2737 + 3.25787i) q^{68} +(-14.6686 - 5.13276i) q^{69} +(-2.18859 - 4.54465i) q^{71} +(-22.7712 + 18.1594i) q^{72} +(-0.171187 + 0.136517i) q^{73} +(8.36590 + 17.3720i) q^{74} +(37.4992 + 13.1215i) q^{76} +(10.6009 - 2.41959i) q^{77} +(2.84926 + 8.14272i) q^{78} +(0.726507 + 2.07624i) q^{79} +(-5.81814 - 7.29571i) q^{81} +(0.818793 + 7.26699i) q^{82} +(2.55579 - 4.06752i) q^{83} +(17.6437 + 28.0798i) q^{84} +16.8961i q^{86} +(-2.78459 - 12.7637i) q^{87} +(32.0803 + 32.0803i) q^{88} +(-11.5205 + 1.29805i) q^{89} +(3.03285 - 0.692229i) q^{91} +(-35.9665 + 4.05246i) q^{92} +(-0.496274 - 0.0559167i) q^{93} +(-6.28917 - 1.43546i) q^{94} +(-27.1389 + 56.3545i) q^{96} +(-2.56898 - 11.2555i) q^{97} +(-2.85536 + 1.37507i) q^{98} +(9.16812 - 9.16812i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 40 q^{4} - 56 q^{9} - 12 q^{14} - 80 q^{16} + 4 q^{19} - 28 q^{21} + 12 q^{29} - 16 q^{31} + 8 q^{34} - 104 q^{36} - 100 q^{39} + 28 q^{41} - 264 q^{44} - 100 q^{46} + 168 q^{49} - 112 q^{51} + 168 q^{54}+ \cdots + 56 q^{99}+O(q^{100}) $ 240 * q + 40 * q^4 - 56 * q^9 - 12 * q^14 - 80 * q^16 + 4 * q^19 - 28 * q^21 + 12 * q^29 - 16 * q^31 + 8 * q^34 - 104 * q^36 - 100 * q^39 + 28 * q^41 - 264 * q^44 - 100 * q^46 + 168 * q^49 - 112 * q^51 + 168 * q^54 - 156 * q^56 - 88 * q^61 - 280 * q^64 - 144 * q^66 - 184 * q^69 - 56 * q^71 + 224 * q^74 + 108 * q^76 + 208 * q^79 - 200 * q^81 + 4 * q^84 - 100 * q^89 - 168 * q^94 + 84 * q^96 + 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−2.16243	−	1.72448i	−1.52907	−	1.21939i	−0.894958	−	0.446151i	$-0.852794\pi$
$2$	−2.16243	−	1.72448i	−1.52907	−	1.21939i	−0.634112	−	0.773241i	$-0.718634\pi$
$3$	−0.539817	+	2.36509i	−0.311664	+	1.36549i	0.540117	+	0.841590i	$0.318380\pi$
$3$	−0.539817	+	2.36509i	−0.311664	+	1.36549i	−0.851781	+	0.523898i	$0.824477\pi$
$4$	1.25723	+	5.50829i	0.628615	+	2.75414i
$5$		0			0
$5$		0			0
$6$	5.24588	−	4.18345i	2.14162	−	1.70789i
$7$	−1.28727	−	2.04868i	−0.486543	−	0.774329i	0.509753	−	0.860321i	$-0.329737\pi$
$7$	−1.28727	−	2.04868i	−0.486543	−	0.774329i	−0.996296	+	0.0859920i	$0.972594\pi$
$8$	4.38015	−	9.09547i	1.54862	−	3.21573i
$9$	−2.59936	−	1.25179i	−0.866454	−	0.417262i
$10$		0			0
$11$	−1.48429	+	4.24186i	−0.447531	+	1.27897i	0.470479	+	0.882411i	$0.344081\pi$
$11$	−1.48429	+	4.24186i	−0.447531	+	1.27897i	−0.918010	+	0.396558i	$0.870205\pi$
$12$	−13.7063			−3.95667
$13$	−0.424646	+	1.21357i	−0.117776	+	0.336584i	−0.987647	−	0.156695i	$-0.949916\pi$
$13$	−0.424646	+	1.21357i	−0.117776	+	0.336584i	0.869871	+	0.493279i	$0.164202\pi$
$14$	−0.749276	+	6.65001i	−0.200252	+	1.77729i
$15$		0			0
$16$	−14.9759	+	7.21201i	−3.74397	+	1.80300i
$17$			2.59131i			0.628485i	0.949343	+	0.314242i	$0.101750\pi$
$17$			2.59131i			0.628485i	−0.949343	+	0.314242i	$0.898250\pi$
$18$	3.46226	+	7.18946i	0.816063	+	1.69457i
$19$	3.74108	−	5.95389i	0.858263	−	1.36592i	−0.0713781	−	0.997449i	$-0.522740\pi$
$19$	3.74108	−	5.95389i	0.858263	−	1.36592i	0.929641	−	0.368468i	$-0.120117\pi$
$20$		0			0
$21$	5.54022	−	1.93861i	1.20897	−	0.423039i
$22$	10.5247	−	6.61310i	2.24387	−	1.40992i
$23$	−0.717256	+	6.36582i	−0.149558	+	1.32737i	0.664808	+	0.747014i	$0.268513\pi$
$23$	−0.717256	+	6.36582i	−0.149558	+	1.32737i	−0.814366	+	0.580352i	$0.802915\pi$
$24$	19.1472	+	15.2694i	3.90840	+	3.11684i
$25$		0			0
$26$	3.01105	−	1.89197i	0.590515	−	0.371045i
$27$	−0.173827	+	0.217972i	−0.0334530	+	0.0419488i
$28$	9.66633	−	9.66633i	1.82677	−	1.82677i
$29$	−4.87407	+	2.28985i	−0.905093	+	0.425214i
$29$	−4.87407	+	2.28985i	−0.905093	+	0.425214i
$30$		0			0
$31$	0.0230497	+	0.204572i	0.00413985	+	0.0367422i	0.995612	−	0.0935743i	$-0.0298293\pi$
$31$	0.0230497	+	0.204572i	0.00413985	+	0.0367422i	−0.991472	+	0.130316i	$0.958401\pi$
$32$	25.1371	+	5.73738i	4.44365	+	1.01423i
$33$	−9.23115	−	5.80032i	−1.60694	−	1.00971i
$34$	4.46867	−	5.60353i	0.766370	−	0.960997i
$35$		0			0
$36$	3.62721	−	15.8918i	0.604534	−	2.64864i
$37$	−6.28087	−	3.02471i	−1.03257	−	0.497259i	−0.160703	−	0.987003i	$-0.551376\pi$
$37$	−6.28087	−	3.02471i	−1.03257	−	0.497259i	−0.871866	+	0.489744i	$0.837090\pi$
$38$	−18.3572	+	6.42346i	−2.97793	+	1.04202i
$39$	−2.64097	−	1.65943i	−0.422894	−	0.265722i
$40$		0			0
$41$	−1.86960	−	1.86960i	−0.291983	−	0.291983i	0.545880	−	0.837863i	$-0.316195\pi$
$41$	−1.86960	−	1.86960i	−0.291983	−	0.291983i	−0.837863	+	0.545880i	$0.816195\pi$
$42$	−15.3234	−	5.36190i	−2.36446	−	0.827359i
$43$	−3.80880	−	4.77608i	−0.580836	−	0.728345i	0.401419	−	0.915894i	$-0.368517\pi$
$43$	−3.80880	−	4.77608i	−0.580836	−	0.728345i	−0.982255	+	0.187549i	$0.939946\pi$
$44$	−25.2315	−	2.84291i	−3.80379	−	0.428584i
$45$		0			0
$46$	12.5288	−	12.5288i	1.84726	−	1.84726i
$47$	2.10136	−	1.01196i	0.306515	−	0.147610i	−0.274303	−	0.961643i	$-0.588447\pi$
$47$	2.10136	−	1.01196i	0.306515	−	0.147610i	0.580818	+	0.814033i	$0.302733\pi$
$48$	−8.97283	−	39.3126i	−1.29512	−	5.67428i
$49$	0.497158	−	1.03236i	0.0710226	−	0.147480i
$50$		0			0
$51$	−6.12869	−	1.39883i	−0.858189	−	0.195876i
$52$	−7.21857	−	0.813337i	−1.00104	−	0.112790i
$53$	−0.0406512	+	0.00458029i	−0.00558387	+	0.000629151i	−0.114756	−	0.993394i	$-0.536609\pi$
$53$	−0.0406512	+	0.00458029i	−0.00558387	+	0.000629151i	0.109172	+	0.994023i	$0.465180\pi$
$54$	0.751778	−	0.171589i	0.102304	−	0.0233502i
$55$		0			0
$56$	−24.2722	+	2.73482i	−3.24350	+	0.365455i
$57$	12.0620	+	12.0620i	1.59765	+	1.59765i
$58$	14.4886	+	3.45362i	1.90245	+	0.453482i
$59$		−	1.45069i		−	0.188864i	−0.995531	−	0.0944322i	$-0.969896\pi$
$59$		−	1.45069i		−	0.188864i	0.995531	−	0.0944322i	$-0.0301036\pi$
$60$		0			0
$61$	−7.05216	−	11.2234i	−0.902936	−	1.43702i	−0.899451	−	0.437021i	$-0.856033\pi$
$61$	−7.05216	−	11.2234i	−0.902936	−	1.43702i	−0.00348523	−	0.999994i	$-0.501109\pi$
$62$	0.302937	−	0.482121i	0.0384730	−	0.0612294i
$63$	0.781574	+	6.93666i	0.0984690	+	0.873937i
$64$	−23.7360	−	29.7640i	−2.96700	−	3.72049i
$65$		0			0
$66$	9.95920	+	28.4617i	1.22589	+	3.50340i
$67$	1.03194	+	2.94912i	0.126072	+	0.360292i	0.989569	−	0.144062i	$-0.0460165\pi$
$67$	1.03194	+	2.94912i	0.126072	+	0.360292i	−0.863497	+	0.504354i	$0.831731\pi$
$68$	−14.2737	+	3.25787i	−1.73094	+	0.395075i
$69$	−14.6686	−	5.13276i	−1.76589	−	0.617912i
$70$		0			0
$71$	−2.18859	−	4.54465i	−0.259738	−	0.539351i	0.729794	−	0.683667i	$-0.239616\pi$
$71$	−2.18859	−	4.54465i	−0.259738	−	0.539351i	−0.989532	+	0.144316i	$0.953902\pi$
$72$	−22.7712	+	18.1594i	−2.68361	+	2.14011i
$73$	−0.171187	+	0.136517i	−0.0200359	+	0.0159781i	−0.633457	−	0.773778i	$-0.718364\pi$
$73$	−0.171187	+	0.136517i	−0.0200359	+	0.0159781i	0.613421	+	0.789756i	$0.289793\pi$
$74$	8.36590	+	17.3720i	0.972516	+	2.01945i
$75$		0			0
$76$	37.4992	+	13.1215i	4.30145	+	1.50514i
$77$	10.6009	−	2.41959i	1.20809	−	0.275738i
$78$	2.84926	+	8.14272i	0.322615	+	0.921982i
$79$	0.726507	+	2.07624i	0.0817385	+	0.233595i	0.977498	−	0.210943i	$-0.0676535\pi$
$79$	0.726507	+	2.07624i	0.0817385	+	0.233595i	−0.895760	+	0.444538i	$0.853368\pi$
$80$		0			0
$81$	−5.81814	−	7.29571i	−0.646460	−	0.810635i
$82$	0.818793	+	7.26699i	0.0904206	+	0.802505i
$83$	2.55579	−	4.06752i	0.280535	−	0.446469i	−0.676500	−	0.736443i	$-0.736504\pi$
$83$	2.55579	−	4.06752i	0.280535	−	0.446469i	0.957034	+	0.289974i	$0.0936468\pi$
$84$	17.6437	+	28.0798i	1.92509	+	3.06376i
$85$		0			0
$86$			16.8961i			1.82196i
$87$	−2.78459	−	12.7637i	−0.298540	−	1.36842i
$88$	32.0803	+	32.0803i	3.41977	+	3.41977i
$89$	−11.5205	+	1.29805i	−1.22117	+	0.137593i	−0.698920	−	0.715200i	$-0.746336\pi$
$89$	−11.5205	+	1.29805i	−1.22117	+	0.137593i	−0.522249	+	0.852793i	$0.674907\pi$
$90$		0			0
$91$	3.03285	−	0.692229i	0.317929	−	0.0725653i
$92$	−35.9665	+	4.05246i	−3.74977	+	0.422498i
$93$	−0.496274	−	0.0559167i	−0.0514612	−	0.00579829i
$94$	−6.28917	−	1.43546i	−0.648678	−	0.148057i
$95$		0			0
$96$	−27.1389	+	56.3545i	−2.76985	+	5.75165i
$97$	−2.56898	−	11.2555i	−0.260841	−	1.14282i	−0.920342	−	0.391115i	$-0.872090\pi$
$97$	−2.56898	−	11.2555i	−0.260841	−	1.14282i	0.659501	−	0.751703i	$-0.270768\pi$
$98$	−2.85536	+	1.37507i	−0.288434	+	0.138903i
$99$	9.16812	−	9.16812i	0.921431	−	0.921431i
$100$		0			0
$101$	0.756450	+	0.0852314i	0.0752696	+	0.00848084i	0.149519	−	0.988759i	$-0.452228\pi$
$101$	0.756450	+	0.0852314i	0.0752696	+	0.00848084i	−0.0742494	+	0.997240i	$0.523656\pi$
$102$	10.8406	+	13.5937i	1.07338	+	1.34598i
$103$	0.0238399	+	0.00834193i	0.00234901	+	0.000821955i	0.331453	−	0.943472i	$-0.392461\pi$
$103$	0.0238399	+	0.00834193i	0.00234901	+	0.000821955i	−0.329104	+	0.944294i	$0.606747\pi$
$104$	9.17797	+	9.17797i	0.899974	+	0.899974i
$105$		0			0
$106$	0.0958040	+	0.0601977i	0.00930531	+	0.00584691i
$107$	5.95852	−	2.08498i	0.576032	−	0.201562i	−0.0265111	−	0.999649i	$-0.508440\pi$
$107$	5.95852	−	2.08498i	0.576032	−	0.201562i	0.602543	+	0.798086i	$0.294154\pi$
$108$	−1.41920	−	0.683448i	−0.136562	−	0.0657649i
$109$	−0.642704	+	2.81587i	−0.0615599	+	0.269712i	−0.996336	−	0.0855260i	$-0.972743\pi$
$109$	−0.642704	+	2.81587i	−0.0615599	+	0.269712i	0.934776	+	0.355238i	$0.115600\pi$
$110$		0			0
$111$	10.5442	−	13.2221i	1.00082	−	1.25498i
$112$	34.0532	+	21.3970i	3.21772	+	2.02183i
$113$	−18.1862	−	4.15088i	−1.71081	−	0.390482i	−0.748652	−	0.662964i	$-0.769298\pi$
$113$	−18.1862	−	4.15088i	−1.71081	−	0.390482i	−0.962161	+	0.272482i	$0.912155\pi$
$114$	−5.28256	−	46.8840i	−0.494757	−	4.39109i
$115$		0			0
$116$	−18.7410	−	23.9689i	−1.74006	−	2.22546i
$117$	2.62294	−	2.62294i	0.242491	−	0.242491i
$118$	−2.50170	+	3.13703i	−0.230300	+	0.288787i
$119$	5.30877	−	3.33572i	0.486654	−	0.305785i
$120$		0			0
$121$	−7.19011	−	5.73392i	−0.653647	−	0.521266i
$122$	−4.10482	+	36.4312i	−0.371633	+	3.29833i
$123$	5.43104	−	3.41255i	0.489700	−	0.307699i
$124$	−1.09786	+	0.384158i	−0.0985909	+	0.0344984i
$125$		0			0
$126$	10.2720	−	16.3479i	0.915106	−	1.45638i
$127$	7.06698	+	14.6747i	0.627094	+	1.30217i	0.936308	+	0.351181i	$0.114220\pi$
$127$	7.06698	+	14.6747i	0.627094	+	1.30217i	−0.309214	+	0.950992i	$0.600066\pi$
$128$			53.7276i			4.74890i
$129$	13.3519	−	6.42995i	1.17557	−	0.566126i
$130$		0			0
$131$	0.542423	−	4.81414i	0.0473917	−	0.420613i	−0.947507	−	0.319735i	$-0.896406\pi$
$131$	0.542423	−	4.81414i	0.0473917	−	0.420613i	0.994899	−	0.100878i	$-0.0321653\pi$
$132$	20.3441	−	58.1402i	1.77073	−	5.06046i
$133$	−17.0134			−1.47525
$134$	2.85419	−	8.15682i	0.246565	−	0.704642i
$135$		0			0
$136$	23.5692	+	11.3503i	2.02104	+	0.973282i
$137$	3.71460	−	7.71345i	0.317360	−	0.659005i	−0.679874	−	0.733329i	$-0.737966\pi$
$137$	3.71460	−	7.71345i	0.317360	−	0.659005i	0.997234	+	0.0743240i	$0.0236799\pi$
$138$	22.8685	+	36.3949i	1.94669	+	3.09814i
$139$	−12.0545	+	9.61316i	−1.02245	+	0.815377i	−0.982956	−	0.183843i	$-0.941146\pi$
$139$	−12.0545	+	9.61316i	−1.02245	+	0.815377i	−0.0394950	+	0.999220i	$0.512575\pi$
$140$		0			0
$141$	1.25904	+	5.51620i	0.106030	+	0.464548i
$142$	−3.10449	+	13.6017i	−0.260523	+	1.14143i
$143$	−4.51749	−	3.60258i	−0.377772	−	0.301263i
$144$	47.9557			3.99631
$145$		0			0
$146$	0.605601			0.0501199
$147$	2.17325	+	1.73311i	0.179247	+	0.142945i
$148$	8.76446	−	38.3996i	0.720434	−	3.15643i
$149$	−0.146224	−	0.640650i	−0.0119792	−	0.0524841i	0.968585	−	0.248682i	$-0.0799975\pi$
$149$	−0.146224	−	0.640650i	−0.0119792	−	0.0524841i	−0.980564	+	0.196198i	$0.937140\pi$
$150$		0			0
$151$	−14.1614	+	11.2933i	−1.15244	+	0.919037i	−0.997623	−	0.0689064i	$-0.978049\pi$
$151$	−14.1614	+	11.2933i	−1.15244	+	0.919037i	−0.154813	+	0.987944i	$0.549478\pi$
$152$	−37.7670	−	60.1058i	−3.06331	−	4.87523i
$153$	3.24377	−	6.73576i	0.262243	−	0.544554i
$154$	−27.0963	−	13.0489i	−2.18348	−	1.05151i
$155$		0			0
$156$	5.82033	−	16.6335i	0.465999	−	1.33175i
$157$	−7.15385			−0.570940			−0.285470	−	0.958388i	$-0.592150\pi$
$157$	−7.15385			−0.570940			−0.285470	+	0.958388i	$0.592150\pi$
$158$	2.00941	−	5.74257i	0.159860	−	0.456855i
$159$	0.0111114	−	0.0986164i	0.000881192	−	0.00782079i
$160$		0			0
$161$	13.9649	−	6.72512i	1.10058	−	0.530014i
$162$			25.8097i			2.02780i
$163$	−3.82325	−	7.93906i	−0.299460	−	0.621835i	0.695891	−	0.718147i	$-0.255010\pi$
$163$	−3.82325	−	7.93906i	−0.299460	−	0.621835i	−0.995351	+	0.0963122i	$0.969295\pi$
$164$	7.94780	−	12.6488i	0.620619	−	0.987709i
$165$		0			0
$166$	−12.5411	+	4.38832i	−0.973378	+	0.340600i
$167$	4.84962	−	3.04722i	0.375275	−	0.235801i	−0.331167	−	0.943572i	$-0.607442\pi$
$167$	4.84962	−	3.04722i	0.375275	−	0.235801i	0.706441	+	0.707772i	$0.250299\pi$
$168$	6.63444	−	58.8823i	0.511858	−	4.54287i
$169$	8.87138	+	7.07469i	0.682414	+	0.544207i
$170$		0			0
$171$	−17.1774	+	10.7933i	−1.31359	+	0.825384i
$172$	21.5195	−	26.9846i	1.64085	−	2.05756i
$173$	−9.81582	+	9.81582i	−0.746283	+	0.746283i	−0.973779	−	0.227496i	$-0.926946\pi$
$173$	−9.81582	+	9.81582i	−0.746283	+	0.746283i	0.227496	+	0.973779i	$0.426946\pi$
$174$	−15.9894	+	32.4027i	−1.21215	+	2.45644i
$175$		0			0
$176$	−8.36375	−	74.2303i	−0.630441	−	5.59532i
$177$	3.43103	+	0.783110i	0.257892	+	0.0588622i
$178$	27.1507	+	17.0599i	2.03503	+	1.27870i
$179$	−10.7420	+	13.4701i	−0.802897	+	1.00680i	0.196756	+	0.980453i	$0.436959\pi$
$179$	−10.7420	+	13.4701i	−0.802897	+	1.00680i	−0.999653	+	0.0263486i	$0.991612\pi$
$180$		0			0
$181$	−0.350572	+	1.53596i	−0.0260578	+	0.114167i	−0.986284	−	0.165056i	$-0.947220\pi$
$181$	−0.350572	+	1.53596i	−0.0260578	+	0.114167i	0.960226	+	0.279223i	$0.0900767\pi$
$182$	−7.75207	−	3.73320i	−0.574622	−	0.276723i
$183$	30.3514	−	10.6204i	2.24364	−	0.785083i
$184$	54.7585	+	34.4070i	4.03685	+	2.53652i
$185$		0			0
$186$	0.976732	+	0.976732i	0.0716174	+	0.0716174i
$187$	−10.9920	−	3.84626i	−0.803813	−	0.281266i
$188$	8.21608	+	10.3026i	0.599220	+	0.751398i
$189$	0.670319	+	0.0755268i	0.0487585	+	0.00549377i
$190$		0			0
$191$	−3.04842	+	3.04842i	−0.220576	+	0.220576i	−0.808741	−	0.588165i	$-0.799851\pi$
$191$	−3.04842	+	3.04842i	−0.220576	+	0.220576i	0.588165	+	0.808741i	$0.299851\pi$
$192$	83.2077	−	40.0707i	6.00500	−	2.89185i
$193$	−3.30295	−	14.4712i	−0.237752	−	1.04166i	−0.943025	−	0.332722i	$-0.892033\pi$
$193$	−3.30295	−	14.4712i	−0.237752	−	1.04166i	0.705273	−	0.708936i	$-0.250824\pi$
$194$	−13.8546	+	28.7693i	−0.994700	+	2.06552i
$195$		0			0
$196$	6.31158	+	1.44058i	0.450827	+	0.102898i
$197$	−11.5926	−	1.30618i	−0.825941	−	0.0930612i	−0.311133	−	0.950366i	$-0.600708\pi$
$197$	−11.5926	−	1.30618i	−0.825941	−	0.0930612i	−0.514809	+	0.857305i	$0.672137\pi$
$198$	−35.6357	+	4.01518i	−2.53252	+	0.285346i
$199$	20.5453	−	4.68933i	1.45642	−	0.332418i	0.580255	−	0.814435i	$-0.302953\pi$
$199$	20.5453	−	4.68933i	1.45642	−	0.332418i	0.876162	+	0.482017i	$0.160096\pi$
$200$		0			0
$201$	−7.53200	+	0.848652i	−0.531266	+	0.0598593i
$202$	−1.48879	−	1.48879i	−0.104751	−	0.104751i
$203$	10.9654	+	7.03777i	0.769622	+	0.493955i
$204$		−	35.5173i		−	2.48671i
$205$		0			0
$206$	−0.0371666	−	0.0591503i	−0.00258952	−	0.00412119i
$207$	9.83307	−	15.6492i	0.683445	−	1.08770i
$208$	−2.39282	−	21.2368i	−0.165912	−	1.47251i
$209$	19.7027	+	24.7064i	1.36287	+	1.70898i
$210$		0			0
$211$	−0.730107	−	2.08653i	−0.0502626	−	0.143642i	0.916016	−	0.401143i	$-0.131387\pi$
$211$	−0.730107	−	2.08653i	−0.0502626	−	0.143642i	−0.966278	+	0.257500i	$0.917101\pi$
$212$	−0.0763375	−	0.218160i	−0.00524288	−	0.0149833i
$213$	11.9300	−	2.72294i	0.817428	−	0.186573i
$214$	−16.4804	−	5.76674i	−1.12658	−	0.394206i
$215$		0			0
$216$	1.22117	+	2.53579i	0.0830903	+	0.172539i
$217$	0.389431	−	0.310561i	0.0264363	−	0.0210823i
$218$	6.24572	−	4.98080i	0.423014	−	0.337342i
$219$	−0.230466	−	0.478568i	−0.0155735	−	0.0323386i
$220$		0			0
$221$	−3.14473	−	1.10039i	−0.211538	−	0.0740202i
$222$	−45.6024	+	10.4085i	−3.06063	+	0.698570i
$223$	8.71100	+	24.8946i	0.583332	+	1.66707i	0.734541	+	0.678564i	$0.237397\pi$
$223$	8.71100	+	24.8946i	0.583332	+	1.66707i	−0.151210	+	0.988502i	$0.548317\pi$
$224$	−20.6042	−	58.8835i	−1.37668	−	3.93432i
$225$		0			0
$226$	32.1683	+	40.3377i	2.13980	+	2.68323i
$227$	0.163159	+	1.44808i	0.0108293	+	0.0961125i	0.997964	−	0.0637772i	$-0.0203147\pi$
$227$	0.163159	+	1.44808i	0.0108293	+	0.0961125i	−0.987135	+	0.159890i	$0.948886\pi$
$228$	−51.2764	+	81.6058i	−3.39586	+	5.40448i
$229$	−8.82639	−	14.0471i	−0.583265	−	0.928260i	−0.999817	−	0.0191483i	$-0.993905\pi$
$229$	−8.82639	−	14.0471i	−0.583265	−	0.928260i	0.416552	−	0.909112i	$-0.363238\pi$
$230$		0			0
$231$			26.3783i			1.73556i
$232$	−0.521944	+	54.3619i	−0.0342673	+	3.56903i
$233$	3.31134	+	3.31134i	0.216933	+	0.216933i	0.807205	−	0.590272i	$-0.200979\pi$
$233$	3.31134	+	3.31134i	0.216933	+	0.216933i	−0.590272	+	0.807205i	$0.700979\pi$
$234$	−10.1951	+	1.14872i	−0.666477	+	0.0750939i
$235$		0			0
$236$	7.99084	−	1.82386i	0.520160	−	0.118723i
$237$	−5.30268	+	0.597469i	−0.344446	+	0.0388098i
$238$	−17.2322	−	1.94161i	−1.11700	−	0.125856i
$239$	15.8235	+	3.61161i	1.02354	+	0.233616i	0.701167	−	0.712997i	$-0.252663\pi$
$239$	15.8235	+	3.61161i	1.02354	+	0.233616i	0.322372	+	0.946613i	$0.395520\pi$
$240$		0			0
$241$	5.45103	−	11.3192i	0.351132	−	0.729133i	−0.648349	−	0.761343i	$-0.724540\pi$
$241$	5.45103	−	11.3192i	0.351132	−	0.729133i	0.999481	+	0.0322104i	$0.0102547\pi$
$242$	5.66008	+	24.7984i	0.363844	+	1.59410i
$243$	19.6422	−	9.45919i	1.26005	−	0.606808i
$244$	52.9558	−	52.9558i	3.39015	−	3.39015i
$245$		0			0
$246$	−17.6291	−	1.98632i	−1.12399	−	0.126643i
$247$	5.63683	+	7.06836i	0.358663	+	0.449749i
$248$	1.96164	+	0.686407i	0.124564	+	0.0435869i
$249$	8.24041	+	8.24041i	0.522215	+	0.522215i
$250$		0			0
$251$	2.80992	+	1.76559i	0.177361	+	0.111443i	0.617786	−	0.786346i	$-0.288030\pi$
$251$	2.80992	+	1.76559i	0.177361	+	0.111443i	−0.440426	+	0.897789i	$0.645172\pi$
$252$	−37.2265	+	13.0261i	−2.34505	+	0.820568i
$253$	−25.9383	−	12.4912i	−1.63073	−	0.785317i
$254$	10.0245	−	43.9200i	0.628990	−	2.75579i
$255$		0			0
$256$	45.1804	−	56.6544i	2.82377	−	3.54090i
$257$	−6.48264	−	4.07331i	−0.404376	−	0.254086i	0.314453	−	0.949273i	$-0.398179\pi$
$257$	−6.48264	−	4.07331i	−0.404376	−	0.254086i	−0.718829	+	0.695187i	$0.755322\pi$
$258$	−39.9610	−	9.12083i	−2.48786	−	0.567838i
$259$	1.88853	+	16.7611i	0.117347	+	1.04149i
$260$		0			0
$261$	15.5359	+	0.149165i	0.961648	+	0.00923306i
$262$	−9.47484	+	9.47484i	−0.585358	+	0.585358i
$263$	13.7383	−	17.2272i	0.847137	−	1.06228i	−0.150150	−	0.988663i	$-0.547976\pi$
$263$	13.7383	−	17.2272i	0.847137	−	1.06228i	0.997287	−	0.0736130i	$-0.0234530\pi$
$264$	−93.1904	+	58.5554i	−5.73548	+	3.60384i
$265$		0			0
$266$	36.7904	+	29.3393i	2.25576	+	1.79891i
$267$	3.14896	−	27.9478i	0.192713	−	1.71037i
$268$	−14.9472	+	9.39194i	−0.913045	+	0.573704i
$269$	−18.6461	+	6.52455i	−1.13687	+	0.397809i	−0.832105	−	0.554618i	$-0.812864\pi$
$269$	−18.6461	+	6.52455i	−1.13687	+	0.397809i	−0.304767	+	0.952427i	$0.598579\pi$
$270$		0			0
$271$	−10.2651	+	16.3367i	−0.623558	+	0.992386i	0.374322	+	0.927299i	$0.377875\pi$
$271$	−10.2651	+	16.3367i	−0.623558	+	0.992386i	−0.997880	+	0.0650874i	$0.979267\pi$
$272$	−18.6885	−	38.8072i	−1.13316	−	2.35303i
$273$			7.54666i			0.456745i
$274$	−21.3343	+	10.2740i	−1.28885	+	0.620678i
$275$		0			0
$276$	9.83093	−	87.2519i	0.591752	−	5.25195i
$277$	−1.71407	+	4.89853i	−0.102988	+	0.294324i	−0.983835	−	0.179078i	$-0.942689\pi$
$277$	−1.71407	+	4.89853i	−0.102988	+	0.294324i	0.880846	+	0.473402i	$0.156974\pi$
$278$	42.6448			2.55766
$279$	0.196166	−	0.560610i	0.0117441	−	0.0335628i
$280$		0			0
$281$	24.9150	+	11.9984i	1.48630	+	0.715767i	0.988458	−	0.151498i	$-0.0484098\pi$
$281$	24.9150	+	11.9984i	1.48630	+	0.715767i	0.497847	+	0.867265i	$0.334124\pi$
$282$	6.79000	−	14.0996i	0.404339	−	0.839618i
$283$	8.00713	+	12.7433i	0.475974	+	0.757509i	0.995276	−	0.0970819i	$-0.0309509\pi$
$283$	8.00713	+	12.7433i	0.475974	+	0.757509i	−0.519302	+	0.854591i	$0.673808\pi$
$284$	22.2817	−	17.7690i	1.32217	−	1.05440i
$285$		0			0
$286$	3.55618	+	15.5807i	0.210282	+	0.921304i
$287$	−1.42354	+	6.23692i	−0.0840286	+	0.368154i
$288$	−58.1585	−	46.3798i	−3.42702	−	2.73296i
$289$	10.2851			0.605007
$290$		0			0
$291$	28.0070			1.64180
$292$	−0.967197	−	0.771314i	−0.0566009	−	0.0451377i
$293$	−6.33455	+	27.7535i	−0.370068	+	1.62138i	0.356510	+	0.934292i	$0.383967\pi$
$293$	−6.33455	+	27.7535i	−0.370068	+	1.62138i	−0.726578	+	0.687084i	$0.758891\pi$
$294$	−1.71079	−	7.49547i	−0.0997754	−	0.437145i
$295$		0			0
$296$	−55.0223	+	43.8788i	−3.19811	+	2.55040i
$297$	−0.666598	−	1.06088i	−0.0386799	−	0.0615588i
$298$	−0.788589	+	1.63752i	−0.0456818	+	0.0948591i
$299$	−7.42079	−	3.57366i	−0.429155	−	0.206670i
$300$		0			0
$301$	−4.88171	+	13.9511i	−0.281377	+	0.804130i
$302$	50.0981			2.88282
$303$	−0.609925	+	1.74307i	−0.0350393	+	0.100137i
$304$	−13.0865	+	116.146i	−0.750560	+	6.66140i
$305$		0			0
$306$	−18.6301	+	8.97179i	−1.06501	+	0.512883i
$307$		−	3.60465i		−	0.205728i	−0.994695	−	0.102864i	$-0.967199\pi$
$307$		−	3.60465i		−	0.205728i	0.994695	−	0.102864i	$-0.0328007\pi$
$308$	26.6556	+	55.3509i	1.51884	+	3.15391i
$309$	−0.0325986	+	0.0518804i	−0.00185447	+	0.00295137i
$310$		0			0
$311$	−20.1629	+	7.05529i	−1.14333	+	0.400069i	−0.834478	−	0.551041i	$-0.814231\pi$
$311$	−20.1629	+	7.05529i	−1.14333	+	0.400069i	−0.308853	+	0.951110i	$0.599945\pi$
$312$	−26.6612	+	16.7523i	−1.50939	+	0.948414i
$313$	3.38338	−	30.0283i	0.191240	−	1.69730i	−0.421348	−	0.906899i	$-0.638443\pi$
$313$	3.38338	−	30.0283i	0.191240	−	1.69730i	0.612588	−	0.790402i	$-0.290128\pi$
$314$	15.4697	+	12.3367i	0.873007	+	0.696200i
$315$		0			0
$316$	−10.5231	+	6.61212i	−0.591973	+	0.371961i
$317$	−14.6018	+	18.3101i	−0.820119	+	1.02840i	0.178889	+	0.983869i	$0.442750\pi$
$317$	−14.6018	+	18.3101i	−0.820119	+	1.02840i	−0.999008	+	0.0445274i	$0.985822\pi$
$318$	−0.194090	+	0.194090i	−0.0108840	+	0.0108840i
$319$	−2.47866	−	24.0739i	−0.138778	−	1.34788i
$320$		0			0
$321$	1.71465	+	15.2180i	0.0957027	+	0.849385i
$322$	−41.7954	−	9.53952i	−2.32916	−	0.531617i
$323$	15.4284	+	9.69430i	0.858458	+	0.539405i
$324$	32.8721	−	41.2204i	1.82623	−	2.29002i
$325$		0			0
$326$	−5.42324	+	23.7608i	−0.300366	+	1.31599i
$327$	−6.31286	−	3.04011i	−0.349102	−	0.168119i
$328$	−25.1941	+	8.81579i	−1.39111	+	0.486771i
$329$	−4.77822	−	3.00235i	−0.263432	−	0.165525i
$330$		0			0
$331$	−0.312454	−	0.312454i	−0.0171740	−	0.0171740i	0.698468	−	0.715642i	$-0.253866\pi$
$331$	−0.312454	−	0.312454i	−0.0171740	−	0.0171740i	−0.715642	+	0.698468i	$0.753866\pi$
$332$	25.6183	+	8.96423i	1.40599	+	0.491976i
$333$	12.5400	+	15.7246i	0.687186	+	0.861705i
$334$	−15.7418	−	1.77368i	−0.861354	−	0.0970513i
$335$		0			0
$336$	−68.9884	+	68.9884i	−3.76363	+	3.76363i
$337$	−15.9267	+	7.66991i	−0.867584	+	0.417806i	−0.814074	−	0.580761i	$-0.802755\pi$
$337$	−15.9267	+	7.66991i	−0.867584	+	0.417806i	−0.0535098	+	0.998567i	$0.517041\pi$
$338$	−6.98358	−	30.5971i	−0.379857	−	1.66426i
$339$	19.6344	−	40.7713i	1.06640	−	2.21439i
$340$		0			0
$341$	−0.901977	−	0.205870i	−0.0488448	−	0.0111485i
$342$	55.7579	+	6.28240i	3.01504	+	0.339713i
$343$	−19.5852	+	2.20673i	−1.05750	+	0.119152i
$344$	−60.1238	+	13.7229i	−3.24166	+	0.739887i
$345$		0			0
$346$	38.1532	−	4.29884i	2.05113	−	0.231107i
$347$	13.2334	+	13.2334i	0.710405	+	0.710405i	0.966620	−	0.256215i	$-0.0824755\pi$
$347$	13.2334	+	13.2334i	0.710405	+	0.710405i	−0.256215	+	0.966620i	$0.582476\pi$
$348$	66.8055	−	31.3853i	3.58115	−	1.68243i
$349$			21.7404i			1.16374i	0.813283	+	0.581868i	$0.197678\pi$
$349$			21.7404i			1.16374i	−0.813283	+	0.581868i	$0.802322\pi$
$350$		0			0
$351$	−0.190709	−	0.303512i	−0.0101793	−	0.0162003i
$352$	−61.6479	+	98.1121i	−3.28585	+	5.22939i
$353$	−2.23395	−	19.8269i	−0.118901	−	1.05528i	−0.901508	−	0.432762i	$-0.857539\pi$
$353$	−2.23395	−	19.8269i	−0.118901	−	1.05528i	0.782607	−	0.622516i	$-0.213889\pi$
$354$	−6.06891	−	7.61017i	−0.322559	−	0.404476i
$355$		0			0
$356$	−21.6339	−	61.8262i	−1.14660	−	3.27678i
$357$	5.02353	+	14.3564i	0.265873	+	0.759823i
$358$	46.4578	−	10.6037i	2.45537	−	0.560422i
$359$	−4.87076	−	1.70435i	−0.257069	−	0.0899523i	0.198668	−	0.980067i	$-0.436338\pi$
$359$	−4.87076	−	1.70435i	−0.257069	−	0.0899523i	−0.455737	+	0.890115i	$0.650624\pi$
$360$		0			0
$361$	−13.2094	−	27.4296i	−0.695231	−	1.44366i
$362$	3.40682	−	2.71685i	0.179058	−	0.142794i
$363$	17.4426	−	13.9100i	0.915500	−	0.730087i
$364$	7.62599	+	15.8355i	0.399711	+	0.830008i
$365$		0			0
$366$	−83.9475	−	29.3745i	−4.38801	−	1.53543i
$367$	17.1084	−	3.90489i	0.893054	−	0.203834i	0.248718	−	0.968576i	$-0.419991\pi$
$367$	17.1084	−	3.90489i	0.893054	−	0.203834i	0.644336	+	0.764742i	$0.277134\pi$
$368$	−35.1688	−	100.507i	−1.83330	−	5.23927i
$369$	2.51943	+	7.20013i	0.131157	+	0.374824i
$370$		0			0
$371$	0.0617127	+	0.0773853i	0.00320396	+	0.00401764i
$372$	−0.315926	−	2.80392i	−0.0163800	−	0.145377i
$373$	−3.28881	+	5.23411i	−0.170288	+	0.271012i	−0.920955	−	0.389669i	$-0.872589\pi$
$373$	−3.28881	+	5.23411i	−0.170288	+	0.271012i	0.750667	+	0.660681i	$0.229732\pi$
$374$	17.1366	+	27.2727i	0.886112	+	1.41024i
$375$		0			0
$376$		−	23.5454i		−	1.21426i
$377$	−0.709129	−	6.88740i	−0.0365220	−	0.354719i
$378$	−1.31927	−	1.31927i	−0.0678561	−	0.0678561i
$379$	−2.05931	+	0.232028i	−0.105779	+	0.0119185i	−0.164696	−	0.986344i	$-0.552664\pi$
$379$	−2.05931	+	0.232028i	−0.105779	+	0.0119185i	0.0589160	+	0.998263i	$0.481236\pi$
$380$		0			0
$381$	−38.5220	+	8.79241i	−1.97354	+	0.450449i
$382$	11.8490	−	1.33506i	0.606245	−	0.0683074i
$383$	1.36274	+	0.153544i	0.0696328	+	0.00784573i	0.146712	−	0.989179i	$-0.453131\pi$
$383$	1.36274	+	0.153544i	0.0696328	+	0.00784573i	−0.0770793	+	0.997025i	$0.524559\pi$
$384$	−127.071	−	29.0031i	−6.48456	−	1.48006i
$385$		0			0
$386$	−17.8129	+	36.9888i	−0.906651	+	1.88268i
$387$	3.92181	+	17.1826i	0.199357	+	0.873439i
$388$	58.7685	−	28.3014i	2.98352	−	1.43679i
$389$	−22.8737	+	22.8737i	−1.15974	+	1.15974i	−0.175212	+	0.984531i	$0.556061\pi$
$389$	−22.8737	+	22.8737i	−1.15974	+	1.15974i	−0.984531	+	0.175212i	$0.943939\pi$
$390$		0			0
$391$	−16.4958	−	1.85863i	−0.834230	−	0.0939951i
$392$	−7.21217	−	9.04377i	−0.364270	−	0.456780i
$393$	11.0931	+	3.88164i	0.559572	+	0.195803i
$394$	22.8158	+	22.8158i	1.14944	+	1.14944i
$395$		0			0
$396$	62.0271	+	38.9742i	3.11698	+	1.95853i
$397$	−14.5701	+	5.09828i	−0.731250	+	0.255876i	−0.670118	−	0.742254i	$-0.733757\pi$
$397$	−14.5701	+	5.09828i	−0.731250	+	0.255876i	−0.0611318	+	0.998130i	$0.519471\pi$
$398$	−52.5144	−	25.2896i	−2.63231	−	1.26765i
$399$	9.18414	−	40.2384i	0.459782	−	2.01444i
$400$		0			0
$401$	−7.00151	+	8.77961i	−0.349639	+	0.438433i	−0.925289	−	0.379263i	$-0.876178\pi$
$401$	−7.00151	+	8.77961i	−0.349639	+	0.438433i	0.575650	+	0.817696i	$0.304749\pi$
$402$	17.7509	+	11.1536i	0.885335	+	0.556293i
$403$	−0.258050	−	0.0588982i	−0.0128544	−	0.00293393i
$404$	0.481553	+	4.27390i	0.0239581	+	0.212634i
$405$		0			0
$406$	−11.5755	−	34.1284i	−0.574481	−	1.69376i
$407$	22.1530	−	22.1530i	1.09809	−	1.09809i
$408$	−39.5676	+	49.6162i	−1.95889	+	2.45637i
$409$	33.2362	−	20.8837i	1.64342	−	1.03263i	0.693349	−	0.720602i	$-0.256134\pi$
$409$	33.2362	−	20.8837i	1.64342	−	1.03263i	0.950073	−	0.312029i	$-0.101009\pi$
$410$		0			0
$411$	16.2378	+	12.9492i	0.800954	+	0.638739i
$412$	−0.0159775	+	0.141805i	−0.000787157	+	0.00698621i
$413$	−2.97201	+	1.86744i	−0.146243	+	0.0918907i
$414$	−48.2501	+	16.8835i	−2.37137	+	0.829777i
$415$		0			0
$416$	−17.6371	+	28.0692i	−0.864729	+	1.37621i
$417$	−16.2288	−	33.6994i	−0.794727	−	1.65027i
$418$		−	87.4030i		−	4.27502i
$419$	−26.5325	+	12.7774i	−1.29620	+	0.624215i	−0.949501	−	0.313763i	$-0.898410\pi$
$419$	−26.5325	+	12.7774i	−1.29620	+	0.624215i	−0.346694	+	0.937978i	$0.612696\pi$
$420$		0			0
$421$	−1.27158	+	11.2856i	−0.0619732	+	0.550027i	0.923912	+	0.382605i	$0.124973\pi$
$421$	−1.27158	+	11.2856i	−0.0619732	+	0.550027i	−0.985885	+	0.167423i	$0.946456\pi$
$422$	−2.01937	+	5.77102i	−0.0983013	+	0.280929i
$423$	−6.72897			−0.327174
$424$	−0.136398	+	0.389804i	−0.00662409	+	0.0189306i
$425$		0			0
$426$	−30.4934	−	14.6848i	−1.47741	−	0.711483i
$427$	−13.9152	+	28.8953i	−0.673405	+	1.39834i
$428$	18.9759	+	30.2000i	0.917235	+	1.45977i
$429$	10.9591	−	8.73956i	0.529109	−	0.421950i
$430$		0			0
$431$	−5.32174	−	23.3161i	−0.256339	−	1.12310i	−0.925132	−	0.379646i	$-0.876046\pi$
$431$	−5.32174	−	23.3161i	−0.256339	−	1.12310i	0.668793	−	0.743449i	$-0.266811\pi$
$432$	1.03120	−	4.51797i	0.0496135	−	0.217371i
$433$	10.9653	+	8.74453i	0.526958	+	0.420235i	0.850497	−	0.525980i	$-0.176301\pi$
$433$	10.9653	+	8.74453i	0.526958	+	0.420235i	−0.323539	+	0.946215i	$0.604873\pi$
$434$	−1.37767			−0.0661305
$435$		0			0
$436$	−16.3187			−0.781522
$437$	35.2181	+	28.0855i	1.68471	+	1.34351i
$438$	−0.326914	+	1.43230i	−0.0156206	+	0.0684382i
$439$	5.45843	+	23.9149i	0.260517	+	1.14140i	0.920693	+	0.390287i	$0.127624\pi$
$439$	5.45843	+	23.9149i	0.260517	+	1.14140i	−0.660176	+	0.751111i	$0.729518\pi$
$440$		0			0
$441$	−2.58459	+	2.06114i	−0.123076	+	0.0981496i
$442$	4.90267	+	7.80255i	0.233196	+	0.371130i
$443$	0.0803463	−	0.166841i	0.00381737	−	0.00792685i	−0.899051	−	0.437843i	$-0.855743\pi$
$443$	0.0803463	−	0.166841i	0.00381737	−	0.00792685i	0.902869	+	0.429916i	$0.141457\pi$
$444$	86.0875	+	41.4576i	4.08553	+	1.96749i
$445$		0			0
$446$	24.0933	−	68.8548i	1.14085	−	3.26037i
$447$	1.59413			0.0753999
$448$	−30.4222	+	86.9417i	−1.43732	+	4.10761i
$449$	−3.44221	+	30.5504i	−0.162448	+	1.44176i	0.602730	+	0.797945i	$0.294079\pi$
$449$	−3.44221	+	30.5504i	−0.162448	+	1.44176i	−0.765178	+	0.643819i	$0.777349\pi$
$450$		0			0
$451$	10.7056	−	5.15556i	0.504109	−	0.242766i
$452$		−	105.393i		−	4.95729i
$453$	−19.0652	−	39.5893i	−0.895762	−	1.86007i
$454$	2.14437	−	3.41274i	0.100640	−	0.160168i
$455$		0			0
$456$	162.543	−	56.8763i	7.61178	−	2.66348i
$457$	11.5608	−	7.26413i	0.540791	−	0.339802i	−0.233779	−	0.972290i	$-0.575109\pi$
$457$	11.5608	−	7.26413i	0.540791	−	0.339802i	0.774570	+	0.632488i	$0.217966\pi$
$458$	−5.13754	+	45.5969i	−0.240061	+	2.13060i
$459$	−0.564834	−	0.450440i	−0.0263642	−	0.0210247i
$460$		0			0
$461$	5.27808	−	3.31644i	0.245825	−	0.154462i	−0.403484	−	0.914987i	$-0.632201\pi$
$461$	5.27808	−	3.31644i	0.245825	−	0.154462i	0.649309	+	0.760525i	$0.275058\pi$
$462$	45.4889	−	57.0412i	2.11633	−	2.65380i
$463$	−23.8054	+	23.8054i	−1.10633	+	1.10633i	−0.112703	+	0.993629i	$0.535951\pi$
$463$	−23.8054	+	23.8054i	−1.10633	+	1.10633i	−0.993629	+	0.112703i	$0.964049\pi$
$464$	56.4792	−	69.4443i	2.62198	−	3.22387i
$465$		0			0
$466$	−1.45020	−	12.8709i	−0.0671793	−	0.596232i
$467$	40.3312	+	9.20534i	1.86631	+	0.425972i	0.997593	−	0.0693438i	$-0.0220906\pi$
$467$	40.3312	+	9.20534i	1.86631	+	0.425972i	0.868713	+	0.495316i	$0.164948\pi$
$468$	17.7456	+	11.1503i	0.820288	+	0.515421i
$469$	4.71341	−	5.91043i	0.217645	−	0.272918i
$470$		0			0
$471$	3.86177	−	16.9195i	0.177941	−	0.779611i
$472$	−13.1948	−	6.35426i	−0.607338	−	0.292478i
$473$	25.9128	−	9.06729i	1.19147	−	0.416914i
$474$	12.4970	+	7.85239i	0.574007	+	0.360672i
$475$		0			0
$476$	25.0485	+	25.0485i	1.14809	+	1.14809i
$477$	0.111401	+	0.0389808i	0.00510069	+	0.00178481i
$478$	−27.9891	−	35.0972i	−1.28019	−	1.60531i
$479$	−34.5747	−	3.89563i	−1.57976	−	0.177996i	−0.721942	−	0.691954i	$-0.756750\pi$
$479$	−34.5747	−	3.89563i	−1.57976	−	0.177996i	−0.857815	+	0.513958i	$0.828179\pi$
$480$		0			0
$481$	6.33784	−	6.33784i	0.288981	−	0.288981i
$482$	−31.3072	+	15.0767i	−1.42600	+	0.686727i
$483$	8.36707	+	36.6585i	0.380715	+	1.66802i
$484$	22.5445	−	46.8141i	1.02475	−	2.12791i
$485$		0			0
$486$	−58.7871	−	13.4178i	−2.66664	−	0.608643i
$487$	0.462666	+	0.0521300i	0.0209654	+	0.00236223i	0.122441	−	0.992476i	$-0.460928\pi$
$487$	0.462666	+	0.0521300i	0.0209654	+	0.00236223i	−0.101476	+	0.994838i	$0.532356\pi$
$488$	−132.972	+	14.9823i	−6.01936	+	0.678219i
$489$	20.8405	−	4.75670i	0.942439	−	0.215106i
$490$		0			0
$491$	29.0433	−	3.27239i	1.31071	−	0.147681i	0.571188	−	0.820819i	$-0.306483\pi$
$491$	29.0433	−	3.27239i	1.31071	−	0.147681i	0.739517	+	0.673138i	$0.235054\pi$
$492$	25.6254	+	25.6254i	1.15528	+	1.15528i
$493$	−5.93370	−	12.6302i	−0.267240	−	0.568837i
$494$		−	25.0054i		−	1.12505i
$495$		0			0
$496$	−1.82056	−	2.89741i	−0.0817457	−	0.130098i
$497$	−6.49323	+	10.3339i	−0.291261	+	0.463540i
$498$	−3.60889	−	32.0298i	−0.161718	−	1.43529i
$499$	11.9806	+	15.0232i	0.536325	+	0.672531i	0.973986	−	0.226610i	$-0.0727642\pi$
$499$	11.9806	+	15.0232i	0.536325	+	0.672531i	−0.437660	+	0.899140i	$0.644193\pi$
$500$		0			0
$501$	4.58905	+	13.1147i	0.205023	+	0.585923i
$502$	−3.03153	−	8.66362i	−0.135304	−	0.386676i
$503$	−7.02208	+	1.60274i	−0.313099	+	0.0714628i	−0.376183	−	0.926545i	$-0.622764\pi$
$503$	−7.02208	+	1.60274i	−0.313099	+	0.0714628i	0.0630839	+	0.998008i	$0.479906\pi$
$504$	66.5156	+	23.2748i	2.96284	+	1.03674i
$505$		0			0
$506$	34.5489	+	71.7416i	1.53589	+	3.18930i
$507$	−21.5212	+	17.1626i	−0.955792	+	0.762219i
$508$	−71.9479	+	57.3765i	−3.19217	+	2.54567i
$509$	−11.0289	−	22.9018i	−0.488849	−	1.01510i	−0.988827	−	0.149067i	$-0.952373\pi$
$509$	−11.0289	−	22.9018i	−0.488849	−	1.01510i	0.499979	−	0.866038i	$-0.333341\pi$
$510$		0			0
$511$	0.500044	+	0.174973i	0.0221207	+	0.00774035i
$512$	−90.6378	+	20.6875i	−4.00566	+	0.914267i
$513$	0.647483	+	1.85040i	0.0285871	+	0.0816972i
$514$	6.99391	+	19.9874i	0.308488	+	0.881608i
$515$		0			0
$516$	52.2045	+	65.4624i	2.29817	+	2.88182i
$517$	1.17357	+	10.4157i	0.0516136	+	0.458084i
$518$	24.8204	−	39.5015i	1.09055	−	1.73560i
$519$	−17.9166	−	28.5141i	−0.786451	−	1.25163i
$520$		0			0
$521$		−	7.08506i		−	0.310402i	−0.987883	−	0.155201i	$-0.950397\pi$
$521$		−	7.08506i		−	0.310402i	0.987883	−	0.155201i	$-0.0496025\pi$
$522$	−33.3381	−	27.1139i	−1.45917	−	1.18674i
$523$	3.22436	+	3.22436i	0.140991	+	0.140991i	0.774080	−	0.633088i	$-0.218213\pi$
$523$	3.22436	+	3.22436i	0.140991	+	0.140991i	−0.633088	+	0.774080i	$0.718213\pi$
$524$	27.1996	−	3.06466i	1.18822	−	0.133880i
$525$		0			0
$526$	−59.4161	+	13.5613i	−2.59066	+	0.591302i
$527$	−0.530109	+	0.0597289i	−0.0230919	+	0.00260183i
$528$	180.077	+	20.2898i	7.83683	+	0.882999i
$529$	−17.5859	−	4.01387i	−0.764605	−	0.174516i
$530$		0			0
$531$	−1.81596	+	3.77088i	−0.0788060	+	0.163642i
$532$	−21.3898	−	93.7148i	−0.927365	−	4.06305i
$533$	3.06282	−	1.47497i	0.132665	−	0.0638882i
$534$	−55.0048	+	55.0048i	−2.38029	+	2.38029i
$535$		0			0
$536$	31.3436	+	3.53158i	1.35384	+	0.152541i
$537$	−26.0593	−	32.6773i	−1.12454	−	1.41013i
$538$	51.5724	+	18.0459i	2.22344	+	0.778016i
$539$	3.64120	+	3.64120i	0.156837	+	0.156837i
$540$		0			0
$541$	2.41801	+	1.51934i	0.103959	+	0.0653215i	0.583008	−	0.812466i	$-0.301876\pi$
$541$	2.41801	+	1.51934i	0.103959	+	0.0653215i	−0.479049	+	0.877788i	$0.659019\pi$
$542$	50.3699	−	17.6252i	2.16357	−	0.757066i
$543$	−3.44344	−	1.65827i	−0.147772	−	0.0711633i
$544$	−14.8673	+	65.1380i	−0.637431	+	2.79277i
$545$		0			0
$546$	13.0141	−	16.3191i	0.556951	−	0.698394i
$547$	−24.6088	−	15.4627i	−1.05219	−	0.661138i	−0.109225	−	0.994017i	$-0.534837\pi$
$547$	−24.6088	−	15.4627i	−1.05219	−	0.661138i	−0.942969	+	0.332879i	$0.891980\pi$
$548$	47.1580	+	10.7635i	2.01449	+	0.459795i
$549$	4.28175	+	38.0016i	0.182741	+	1.62187i
$550$		0			0
$551$	−4.60080	+	37.5862i	−0.196001	+	1.60123i
$552$	−110.935	+	110.935i	−4.72173	+	4.72173i
$553$	3.31834	−	4.16107i	0.141110	−	0.176947i
$554$	12.1540	−	7.63685i	0.516373	−	0.324459i
$555$		0			0
$556$	−68.1073	−	54.3138i	−2.88839	−	2.30342i
$557$	−2.57079	+	22.8164i	−0.108928	+	0.966763i	0.813756	+	0.581206i	$0.197419\pi$
$557$	−2.57079	+	22.8164i	−0.108928	+	0.966763i	−0.922684	+	0.385556i	$0.874009\pi$
$558$	−1.39096	+	0.873996i	−0.0588839	+	0.0369992i
$559$	7.41349	−	2.59409i	0.313557	−	0.109718i
$560$		0			0
$561$	15.0304	−	23.9208i	0.634585	−	1.00994i
$562$	−33.1859	−	68.9112i	−1.39986	−	2.90685i
$563$			20.9289i			0.882047i	0.897496	+	0.441023i	$0.145384\pi$
$563$			20.9289i			0.882047i	−0.897496	+	0.441023i	$0.854616\pi$
$564$	−28.8019	+	13.8703i	−1.21278	+	0.584044i
$565$		0			0
$566$	4.66067	−	41.3646i	0.195903	−	1.73868i
$567$	−7.45707	+	21.3111i	−0.313167	+	0.894981i
$568$	−50.9221			−2.13664
$569$	5.68051	−	16.2340i	0.238139	−	0.680563i	−0.761342	−	0.648351i	$-0.775459\pi$
$569$	5.68051	−	16.2340i	0.238139	−	0.680563i	0.999481	−	0.0322125i	$-0.0102553\pi$
$570$		0			0
$571$	−8.63331	−	4.15758i	−0.361293	−	0.173989i	0.244427	−	0.969668i	$-0.421400\pi$
$571$	−8.63331	−	4.15758i	−0.361293	−	0.173989i	−0.605719	+	0.795678i	$0.707115\pi$
$572$	14.1645	−	29.4129i	0.592248	−	1.22982i
$573$	−5.56422	−	8.85540i	−0.232448	−	0.369940i
$574$	13.8337	−	11.0320i	0.577409	−	0.460469i
$575$		0			0
$576$	24.4402	+	107.080i	1.01834	+	4.46165i
$577$	−2.58216	+	11.3132i	−0.107497	+	0.470973i	0.892312	+	0.451419i	$0.149082\pi$
$577$	−2.58216	+	11.3132i	−0.107497	+	0.470973i	−0.999809	+	0.0195544i	$0.993775\pi$
$578$	−22.2408	−	17.7365i	−0.925097	−	0.737740i
$579$	36.0087			1.49647
$580$		0			0
$581$	−11.6231			−0.482206
$582$	−60.5632	−	48.2975i	−2.51042	−	2.00200i
$583$	0.0409093	−	0.179235i	0.00169429	−	0.00742316i
$584$	0.491863	+	2.15499i	0.0203534	+	0.0891742i
$585$		0			0
$586$	61.5584	−	49.0912i	2.54295	−	2.02794i
$587$	2.74128	+	4.36272i	0.113145	+	0.180069i	0.898496	−	0.438981i	$-0.144661\pi$
$587$	2.74128	+	4.36272i	0.113145	+	0.180069i	−0.785352	+	0.619050i	$0.787518\pi$
$588$	−6.81420	+	14.1498i	−0.281013	+	0.583529i
$589$	1.30423	+	0.628084i	0.0537398	+	0.0258797i
$590$		0			0
$591$	9.34714	−	26.7126i	0.384490	−	1.09881i
$592$	115.876			4.76247
$593$	2.30898	−	6.59867i	0.0948183	−	0.270975i	−0.886699	−	0.462346i	$-0.847008\pi$
$593$	2.30898	−	6.59867i	0.0948183	−	0.270975i	0.981518	+	0.191371i	$0.0612934\pi$
$594$	−0.388004	+	3.44363i	−0.0159200	+	0.141294i
$595$		0			0
$596$	3.34505	−	1.61089i	0.137018	−	0.0659846i
$597$			51.1229i			2.09232i
$598$	9.88423	+	20.5248i	0.404196	+	0.839322i
$599$	7.08530	−	11.2762i	0.289498	−	0.460733i	−0.670035	−	0.742329i	$-0.733721\pi$
$599$	7.08530	−	11.2762i	0.289498	−	0.460733i	0.959533	+	0.281596i	$0.0908639\pi$
$600$		0			0
$601$	−31.4439	+	11.0027i	−1.28262	+	0.448809i	−0.883648	−	0.468152i	$-0.844920\pi$
$601$	−31.4439	+	11.0027i	−1.28262	+	0.448809i	−0.398976	+	0.916961i	$0.630634\pi$
$602$	34.6148	−	21.7499i	1.41079	−	0.886461i
$603$	1.00928	−	8.95759i	0.0411010	−	0.364781i
$604$	−80.0110	−	63.8066i	−3.25560	−	2.59625i
$605$		0			0
$606$	4.32481	−	2.71746i	0.175683	−	0.110389i
$607$	21.3881	−	26.8199i	0.868117	−	1.08858i	−0.127196	−	0.991878i	$-0.540598\pi$
$607$	21.3881	−	26.8199i	0.868117	−	1.08858i	0.995313	−	0.0967067i	$-0.0308309\pi$
$608$	128.200	−	128.200i	5.19918	−	5.19918i
$609$	−22.5643	+	22.1352i	−0.914353	+	0.896962i
$610$		0			0
$611$	0.335751	+	2.97988i	0.0135830	+	0.120553i
$612$	41.1807	+	9.39922i	1.66463	+	0.379941i
$613$	−0.216474	−	0.136019i	−0.00874329	−	0.00549377i	0.527653	−	0.849460i	$-0.323072\pi$
$613$	−0.216474	−	0.136019i	−0.00874329	−	0.00549377i	−0.536397	+	0.843966i	$0.680215\pi$
$614$	−6.21615	+	7.79480i	−0.250863	+	0.314573i
$615$		0			0
$616$	24.4263	−	107.018i	0.984162	−	4.31189i
$617$	−7.86435	−	3.78727i	−0.316607	−	0.152470i	0.268830	−	0.963188i	$-0.413363\pi$
$617$	−7.86435	−	3.78727i	−0.316607	−	0.152470i	−0.585437	+	0.810718i	$0.699077\pi$
$618$	0.159959	−	0.0559721i	0.00643450	−	0.00225153i
$619$	−25.5090	−	16.0283i	−1.02529	−	0.644233i	−0.0892086	−	0.996013i	$-0.528434\pi$
$619$	−25.5090	−	16.0283i	−1.02529	−	0.644233i	−0.936083	+	0.351780i	$0.885577\pi$
$620$		0			0
$621$	−1.26289	−	1.26289i	−0.0506782	−	0.0506782i
$622$	55.7676	+	19.5139i	2.23608	+	0.782437i
$623$	17.4893	+	21.9309i	0.700694	+	0.878642i
$624$	51.5188	+	5.80477i	2.06240	+	0.232377i
$625$		0			0
$626$	−59.0996	+	59.0996i	−2.36210	+	2.36210i
$627$	−69.0690	+	33.2619i	−2.75835	+	1.32835i
$628$	−8.99405	−	39.4055i	−0.358901	−	1.57245i
$629$	7.83796	−	16.2757i	0.312520	−	0.648954i
$630$		0			0
$631$	10.4586	+	2.38710i	0.416349	+	0.0950288i	0.425563	−	0.904929i	$-0.360076\pi$
$631$	10.4586	+	2.38710i	0.416349	+	0.0950288i	−0.00921466	+	0.999958i	$0.502933\pi$
$632$	22.0666	+	2.48631i	0.877761	+	0.0989000i
$633$	5.32895	−	0.600429i	0.211807	−	0.0238649i
$634$	63.1508	−	14.4138i	2.50804	−	0.572443i
$635$		0			0
$636$	0.557177	−	0.0627788i	0.0220935	−	0.00248934i
$637$	1.04172	+	1.04172i	0.0412746	+	0.0412746i
$638$	−36.1551	+	56.3326i	−1.43140	+	2.23023i
$639$			14.5528i			0.575701i
$640$		0			0
$641$	21.3302	+	33.9468i	0.842491	+	1.34082i	0.938444	+	0.345431i	$0.112267\pi$
$641$	21.3302	+	33.9468i	0.842491	+	1.34082i	−0.0959532	+	0.995386i	$0.530590\pi$
$642$	22.5353	−	35.8647i	0.889397	−	1.41547i
$643$	4.96299	+	44.0477i	0.195721	+	1.73707i	0.580673	+	0.814137i	$0.302789\pi$
$643$	4.96299	+	44.0477i	0.195721	+	1.73707i	−0.384952	+	0.922937i	$0.625782\pi$
$644$	54.6009	+	68.4674i	2.15158	+	2.69799i
$645$		0			0
$646$	−16.6452	−	47.5692i	−0.654896	−	1.87159i
$647$	−1.18603	−	3.38949i	−0.0466278	−	0.133255i	0.918215	−	0.396082i	$-0.129631\pi$
$647$	−1.18603	−	3.38949i	−0.0466278	−	0.133255i	−0.964843	+	0.262828i	$0.915345\pi$
$648$	−91.8422	+	20.9624i	−3.60790	+	0.823480i
$649$	6.15364	+	2.15325i	0.241552	+	0.0845226i
$650$		0			0
$651$	0.524284	+	1.08869i	0.0205483	+	0.0426690i
$652$	38.9239	−	31.0408i	1.52438	−	1.21565i
$653$	17.9581	−	14.3211i	0.702753	−	0.560427i	−0.205597	−	0.978637i	$-0.565914\pi$
$653$	17.9581	−	14.3211i	0.702753	−	0.560427i	0.908351	+	0.418210i	$0.137342\pi$
$654$	8.40851	+	17.4604i	0.328799	+	0.682758i
$655$		0			0
$656$	41.4826	+	14.5154i	1.61962	+	0.566731i
$657$	0.615868	−	0.140568i	0.0240273	−	0.00548407i
$658$	5.15506	+	14.7323i	0.200965	+	0.574326i
$659$	−10.1868	−	29.1121i	−0.396820	−	1.13405i	−0.952996	−	0.302981i	$-0.902018\pi$
$659$	−10.1868	−	29.1121i	−0.396820	−	1.13405i	0.556177	−	0.831064i	$-0.312268\pi$
$660$		0			0
$661$	7.73328	+	9.69722i	0.300790	+	0.377178i	0.909140	−	0.416490i	$-0.136740\pi$
$661$	7.73328	+	9.69722i	0.300790	+	0.377178i	−0.608351	+	0.793668i	$0.708169\pi$
$662$	0.136839	+	1.21448i	0.00531840	+	0.0472021i
$663$	4.30011	−	6.84358i	0.167002	−	0.265783i
$664$	−25.8013	−	41.0625i	−1.00128	−	1.59353i
$665$		0			0
$666$		−	55.6284i		−	2.15556i
$667$	−11.0808	−	32.6699i	−0.429050	−	1.26498i
$668$	22.8820	+	22.8820i	0.885332	+	0.885332i
$669$	−63.5804	+	7.16380i	−2.45816	+	0.276968i
$670$		0			0
$671$	58.0758	−	13.2554i	2.24199	−	0.511719i
$672$	150.388	−	16.9446i	5.80132	−	0.653652i
$673$	−31.2873	−	3.52523i	−1.20604	−	0.135888i	−0.514025	−	0.857775i	$-0.671846\pi$
$673$	−31.2873	−	3.52523i	−1.20604	−	0.135888i	−0.692011	+	0.721887i	$0.743275\pi$
$674$	47.6671	+	10.8797i	1.83607	+	0.419070i
$675$		0			0
$676$	−27.8161	+	57.7607i	−1.06985	+	2.22156i
$677$	−6.44115	−	28.2205i	−0.247553	−	1.08460i	−0.933958	−	0.357383i	$-0.883669\pi$
$677$	−6.44115	−	28.2205i	−0.247553	−	1.08460i	0.686405	−	0.727220i	$-0.259188\pi$
$678$	−112.768	+	54.3060i	−4.33081	+	2.08561i
$679$	−19.7519	+	19.7519i	−0.758007	+	0.758007i
$680$		0			0
$681$	−3.51292	−	0.395811i	−0.134616	−	0.0151675i
$682$	1.59544	+	2.00062i	0.0610927	+	0.0766078i
$683$	−43.1707	−	15.1061i	−1.65188	−	0.578018i	−0.666071	−	0.745889i	$-0.732025\pi$
$683$	−43.1707	−	15.1061i	−1.65188	−	0.578018i	−0.985809	+	0.167871i	$0.946311\pi$
$684$	−81.0486	−	81.0486i	−3.09897	−	3.09897i
$685$		0			0
$686$	46.1572	+	29.0025i	1.76229	+	1.10732i
$687$	37.9874	−	13.2924i	1.44931	−	0.507136i
$688$	91.4852	+	44.0570i	3.48784	+	1.67966i
$689$	0.0117039	−	0.0512780i	0.000445882	−	0.00195354i
$690$		0			0
$691$	22.5163	−	28.2345i	0.856559	−	1.07409i	−0.139913	−	0.990164i	$-0.544682\pi$
$691$	22.5163	−	28.2345i	0.856559	−	1.07409i	0.996472	−	0.0839273i	$-0.0267463\pi$
$692$	−66.4091	−	41.7276i	−2.52450	−	1.58625i
$693$	−30.5844	−	6.98070i	−1.16181	−	0.265175i
$694$	−5.79555	−	51.4370i	−0.219996	−	1.95252i
$695$		0			0
$696$	−128.289	−	30.5799i	−4.86279	−	1.15913i
$697$	4.84473	−	4.84473i	0.183507	−	0.183507i
$698$	37.4909	−	47.0121i	1.41905	−	1.77943i
$699$	−9.61915	+	6.04411i	−0.363830	+	0.228609i
$700$		0			0
$701$	−16.7502	−	13.3578i	−0.632646	−	0.504519i	0.253856	−	0.967242i	$-0.418301\pi$
$701$	−16.7502	−	13.3578i	−0.632646	−	0.504519i	−0.886503	+	0.462723i	$0.846872\pi$
$702$	−0.111005	+	0.985200i	−0.00418963	+	0.0371840i
$703$	−41.5060	+	26.0800i	−1.56543	+	0.983625i
$704$	161.486	−	56.5063i	6.08622	−	2.12966i
$705$		0			0
$706$	−29.3603	+	46.7266i	−1.10499	+	1.75858i
$707$	−0.799145	−	1.65944i	−0.0300549	−	0.0624097i
$708$			19.8837i			0.747274i
$709$	−33.9635	+	16.3560i	−1.27553	+	0.614261i	−0.944236	−	0.329268i	$-0.893198\pi$
$709$	−33.9635	+	16.3560i	−1.27553	+	0.614261i	−0.331289	+	0.943529i	$0.607484\pi$
$710$		0			0
$711$	0.710553	−	6.30633i	0.0266478	−	0.236506i
$712$	−38.6551	+	110.470i	−1.44866	+	4.14003i
$713$	−1.31880			−0.0493895
$714$	13.8943	−	39.7078i	0.519983	−	1.48603i
$715$		0			0
$716$	−87.7023	−	42.2352i	−3.27759	−	1.57840i
$717$	−17.0836	+	35.4745i	−0.638000	+	1.32482i
$718$	7.59356	+	12.0851i	0.283389	+	0.451011i
$719$	−23.5403	+	18.7727i	−0.877904	+	0.700105i	−0.954900	−	0.296926i	$-0.904038\pi$
$719$	−23.5403	+	18.7727i	−0.877904	+	0.700105i	0.0769965	+	0.997031i	$0.475467\pi$
$720$		0			0
$721$	−0.0135984	−	0.0595786i	−0.000506432	−	0.00221882i
$722$	−18.7374	+	82.0939i	−0.697334	+	3.05522i
$723$	23.8284	+	19.0025i	0.886187	+	0.706710i
$724$	−8.90125			−0.330812
$725$		0			0
$726$	−61.7060			−2.29013
$727$	−33.5972	−	26.7929i	−1.24605	−	0.993693i	−0.999700	−	0.0245122i	$-0.992197\pi$
$727$	−33.5972	−	26.7929i	−1.24605	−	0.993693i	−0.246352	−	0.969180i	$-0.579232\pi$
$728$	6.98819	−	30.6173i	0.259000	−	1.13475i
$729$	5.53927	+	24.2691i	0.205158	+	0.898857i
$730$		0			0
$731$	12.3763	−	9.86977i	0.457754	−	0.365047i
$732$	96.6590	+	153.832i	3.57262	+	5.68579i
$733$	−1.59159	+	3.30497i	−0.0587867	+	0.122072i	−0.928292	−	0.371851i	$-0.878723\pi$
$733$	−1.59159	+	3.30497i	−0.0587867	+	0.122072i	0.869506	+	0.493923i	$0.164438\pi$
$734$	−43.7298	−	21.0591i	−1.61409	−	0.777307i
$735$		0			0
$736$	−54.5529	+	155.903i	−2.01085	+	5.74667i
$737$	−14.0414			−0.517223
$738$	6.96839	−	19.9145i	0.256510	−	0.733063i
$739$	5.30059	−	47.0440i	0.194985	−	1.73054i	−0.391147	−	0.920328i	$-0.627922\pi$
$739$	5.30059	−	47.0440i	0.194985	−	1.73054i	0.586133	−	0.810215i	$-0.300650\pi$
$740$		0			0
$741$	−19.7602	+	9.51601i	−0.725909	+	0.349579i
$742$		−	0.273763i		−	0.0100501i
$743$	−11.3279	−	23.5225i	−0.415579	−	0.862959i	−0.998720	−	0.0505874i	$-0.983891\pi$
$743$	−11.3279	−	23.5225i	−0.415579	−	0.862959i	0.583141	−	0.812371i	$-0.301824\pi$
$744$	−2.68234	+	4.26892i	−0.0983395	+	0.156506i
$745$		0			0
$746$	16.1379	−	5.64691i	0.590852	−	0.206748i
$747$	−11.7351	+	7.37366i	−0.429365	+	0.269788i
$748$	7.36685	−	65.3826i	0.269359	−	2.39062i
$749$	−11.9417	−	9.52319i	−0.436340	−	0.347970i
$750$		0			0
$751$	13.9633	−	8.77370i	0.509527	−	0.320157i	−0.252615	−	0.967567i	$-0.581291\pi$
$751$	13.9633	−	8.77370i	0.509527	−	0.320157i	0.762142	+	0.647410i	$0.224148\pi$
$752$	−24.1715	+	30.3101i	−0.881444	+	1.10530i
$753$	−5.69263	+	5.69263i	−0.207451	+	0.207451i
$754$	−10.3438	+	16.1164i	−0.376697	+	0.586925i
$755$		0			0
$756$	0.426722	+	3.78726i	0.0155197	+	0.137741i
$757$	17.6103	+	4.01944i	0.640058	+	0.146089i	0.530219	−	0.847860i	$-0.322110\pi$
$757$	17.6103	+	4.01944i	0.640058	+	0.146089i	0.109838	+	0.993949i	$0.464967\pi$
$758$	4.85324	+	3.04949i	0.176277	+	0.110762i
$759$	43.5449	−	54.6036i	1.58058	−	1.98198i
$760$		0			0
$761$	10.3524	−	45.3570i	0.375275	−	1.64419i	−0.336429	−	0.941709i	$-0.609219\pi$
$761$	10.3524	−	45.3570i	0.375275	−	1.64419i	0.711704	−	0.702479i	$-0.247924\pi$
$762$	98.4636	+	47.4176i	3.56696	+	1.71776i
$763$	6.59616	−	2.30810i	0.238797	−	0.0835587i
$764$	−20.6242	−	12.9590i	−0.746156	−	0.468841i
$765$		0			0
$766$	−2.68205	−	2.68205i	−0.0969064	−	0.0969064i
$767$	1.76052	+	0.616032i	0.0635686	+	0.0222436i
$768$	109.604	+	137.439i	3.95499	+	4.95940i
$769$	36.0123	+	4.05761i	1.29864	+	0.146321i	0.734074	−	0.679069i	$-0.237617\pi$
$769$	36.0123	+	4.05761i	1.29864	+	0.146321i	0.564562	+	0.825391i	$0.309045\pi$
$770$		0			0
$771$	13.1332	−	13.1332i	0.472981	−	0.472981i
$772$	75.5588	−	36.3872i	2.71942	−	1.30960i
$773$	10.6864	+	46.8201i	0.384363	+	1.68400i	0.683627	+	0.729832i	$0.260402\pi$
$773$	10.6864	+	46.8201i	0.384363	+	1.68400i	−0.299264	+	0.954170i	$0.596741\pi$
$774$	21.1504	−	43.9192i	0.760235	−	1.57864i
$775$		0			0
$776$	−113.626	−	25.9344i	−4.07894	−	0.930992i
$777$	−40.6611	−	4.58141i	−1.45871	−	0.164357i
$778$	88.9081	−	10.0175i	3.18751	−	0.359146i
$779$	−18.1258	+	4.13709i	−0.649423	+	0.148227i
$780$		0			0
$781$	22.5263	−	2.53810i	0.806053	−	0.0908204i
$782$	32.4659	+	32.4659i	1.16098	+	1.16098i
$783$	0.348123	−	1.46045i	0.0124409	−	0.0521923i
$784$			19.0460i			0.680215i
$785$		0			0
$786$	−17.2942	−	27.5236i	−0.616864	−	0.981734i
$787$	0.776468	−	1.23574i	0.0276781	−	0.0440494i	−0.832599	−	0.553877i	$-0.813148\pi$
$787$	0.776468	−	1.23574i	0.0276781	−	0.0440494i	0.860277	+	0.509827i	$0.170291\pi$
$788$	−7.37983	−	65.4978i	−0.262895	−	2.33326i
$789$	33.3279	+	41.7918i	1.18650	+	1.48783i
$790$		0			0
$791$	14.9067	+	42.6010i	0.530023	+	1.51472i
$792$	−43.2306	−	123.546i	−1.53613	−	4.39002i
$793$	16.6151	−	3.79229i	0.590020	−	0.134668i
$794$	40.2986	+	14.1011i	1.43015	+	0.500429i
$795$		0			0
$796$	51.6603	+	107.274i	1.83105	+	3.80222i
$797$	13.7519	−	10.9668i	0.487118	−	0.388464i	−0.348905	−	0.937158i	$-0.613446\pi$
$797$	13.7519	−	10.9668i	0.487118	−	0.388464i	0.836023	+	0.548695i	$0.184875\pi$
$798$	−89.2504	+	71.1748i	−3.15943	+	2.51956i
$799$	2.62231	+	5.44528i	0.0927707	+	0.192640i
$800$		0			0
$801$	31.5708	+	11.0471i	1.11550	+	0.390330i
$802$	30.2806	−	6.91134i	1.06924	−	0.244048i
$803$	−0.324995	−	0.928783i	−0.0114688	−	0.0327760i
$804$	−14.1441	−	40.4215i	−0.498823	−	1.42555i
$805$		0			0
$806$	0.456446	+	0.572366i	0.0160776	+	0.0201607i
$807$	−5.36569	−	47.6218i	−0.188881	−	1.67637i
$808$	4.08858	−	6.50694i	0.143836	−	0.228913i
$809$	19.3227	+	30.7518i	0.679349	+	1.08118i	0.991369	+	0.131102i	$0.0418515\pi$
$809$	19.3227	+	30.7518i	0.679349	+	1.08118i	−0.312020	+	0.950075i	$0.601006\pi$
$810$		0			0
$811$			37.3564i			1.31176i	0.754866	+	0.655879i	$0.227702\pi$
$811$			37.3564i			1.31176i	−0.754866	+	0.655879i	$0.772298\pi$
$812$	−24.9800	+	69.2488i	−0.876627	+	2.43016i
$813$	−33.0967	−	33.0967i	−1.16075	−	1.16075i
$814$	−86.1069	+	9.70192i	−3.01805	+	0.340052i
$815$		0			0
$816$	101.871	−	23.2514i	3.56620	−	0.813962i
$817$	−42.6853	+	4.80948i	−1.49337	+	0.168262i
$818$	−107.884	−	12.1556i	−3.77209	−	0.425012i
$819$	−8.75001	−	1.99713i	−0.305750	−	0.0697855i
$820$		0			0
$821$	−4.54252	+	9.43263i	−0.158535	+	0.329201i	−0.965073	−	0.261981i	$-0.915624\pi$
$821$	−4.54252	+	9.43263i	−0.158535	+	0.329201i	0.806538	+	0.591182i	$0.201339\pi$
$822$	−12.7825	−	56.0037i	−0.445840	−	1.95335i
$823$	31.9636	−	15.3928i	1.11418	−	0.536561i	0.216091	−	0.976373i	$-0.430669\pi$
$823$	31.9636	−	15.3928i	1.11418	−	0.536561i	0.898090	+	0.439812i	$0.144955\pi$
$824$	0.180296	−	0.180296i	0.00628091	−	0.00628091i
$825$		0			0
$826$	9.64714	+	1.08697i	0.335667	+	0.0378206i
$827$	−31.7255	−	39.7825i	−1.10320	−	1.38337i	−0.916060	−	0.401040i	$-0.868649\pi$
$827$	−31.7255	−	39.7825i	−1.10320	−	1.38337i	−0.187143	−	0.982333i	$-0.559923\pi$
$828$	98.5629	+	34.4887i	3.42530	+	1.19856i
$829$	5.07005	+	5.07005i	0.176090	+	0.176090i	0.789649	−	0.613559i	$-0.210263\pi$
$829$	5.07005	+	5.07005i	0.176090	+	0.176090i	−0.613559	+	0.789649i	$0.710263\pi$
$830$		0			0
$831$	−10.6602	−	6.69825i	−0.369798	−	0.232360i
$832$	46.2000	−	16.1661i	1.60170	−	0.560458i
$833$	2.67516	+	1.28829i	0.0926889	+	0.0446366i
$834$	−23.0204	+	100.859i	−0.797131	+	3.49246i
$835$		0			0
$836$	−111.319	+	139.590i	−3.85006	+	4.82782i
$837$	−0.0485976	−	0.0305359i	−0.00167978	−	0.00105548i
$838$	79.4089	+	18.1246i	2.74314	+	0.626103i
$839$	4.04028	+	35.8585i	0.139486	+	1.23797i	0.847123	+	0.531397i	$0.178333\pi$
$839$	4.04028	+	35.8585i	0.139486	+	1.23797i	−0.707637	+	0.706576i	$0.750239\pi$
$840$		0			0
$841$	18.5132	−	22.3218i	0.638387	−	0.769716i
$842$	22.2116	−	22.2116i	0.765461	−	0.765461i
$843$	−41.8270	+	52.4494i	−1.44060	+	1.80645i
$844$	10.5753	−	6.64488i	0.364016	−	0.228726i
$845$		0			0
$846$	14.5509	+	11.6040i	0.500271	+	0.398953i
$847$	−2.49135	+	22.1114i	−0.0856039	+	0.759756i
$848$	0.575755	−	0.361771i	0.0197715	−	0.0124233i
$849$	−34.4614	+	12.0586i	−1.18271	+	0.413849i
$850$		0			0
$851$	23.7598	−	37.8134i	0.814474	−	1.29623i
$852$	29.9974	+	62.2903i	1.02770	+	2.13403i
$853$			23.6930i			0.811232i	0.914043	+	0.405616i	$0.132943\pi$
$853$			23.6930i			0.811232i	−0.914043	+	0.405616i	$0.867057\pi$
$854$	79.9201	−	38.4875i	2.73481	−	1.31701i
$855$		0			0
$856$	7.13536	−	63.3281i	0.243882	−	2.16451i
$857$	1.87737	−	5.36521i	0.0641297	−	0.183272i	−0.907360	−	0.420355i	$-0.861906\pi$
$857$	1.87737	−	5.36521i	0.0641297	−	0.183272i	0.971489	+	0.237083i	$0.0761913\pi$
$858$	−38.7694			−1.32357
$859$	−14.6187	+	41.7779i	−0.498785	+	1.42544i	0.369431	+	0.929258i	$0.379552\pi$
$859$	−14.6187	+	41.7779i	−0.498785	+	1.42544i	−0.868216	+	0.496187i	$0.834733\pi$
$860$		0			0
$861$	−13.9824	−	6.73359i	−0.476521	−	0.229480i
$862$	−28.7002	+	59.5966i	−0.977533	+	2.02987i
$863$	−4.09440	−	6.51620i	−0.139375	−	0.221814i	0.769742	−	0.638355i	$-0.220385\pi$
$863$	−4.09440	−	6.51620i	−0.139375	−	0.221814i	−0.909117	+	0.416541i	$0.863242\pi$
$864$	−5.62010	+	4.48188i	−0.191200	+	0.152477i
$865$		0			0
$866$	−8.63191	−	37.8189i	−0.293324	−	1.28514i
$867$	−5.55208	+	24.3253i	−0.188559	+	0.826129i
$868$	2.20026	+	1.75465i	0.0746818	+	0.0595568i
$869$	−9.88546			−0.335341
$870$		0			0
$871$	−4.01716			−0.136116
$872$	22.7965	+	18.1796i	0.771988	+	0.615640i
$873$	−7.41171	+	32.4728i	−0.250848	+	1.09904i
$874$	−27.7238	−	121.466i	−0.937772	−	4.10865i
$875$		0			0
$876$	2.34634	−	1.87114i	0.0792755	−	0.0632201i
$877$	−0.977789	−	1.55614i	−0.0330176	−	0.0525472i	0.829808	−	0.558049i	$-0.188450\pi$
$877$	−0.977789	−	1.55614i	−0.0330176	−	0.0525472i	−0.862825	+	0.505502i	$0.831307\pi$
$878$	29.4374	−	61.1274i	0.993464	−	2.06295i
$879$	−62.2201	−	29.9636i	−2.09863	−	1.01065i
$880$		0			0
$881$	−14.7729	+	42.2185i	−0.497712	+	1.42238i	0.371729	+	0.928341i	$0.378765\pi$
$881$	−14.7729	+	42.2185i	−0.497712	+	1.42238i	−0.869441	+	0.494037i	$0.835521\pi$
$882$	9.14340			0.307874
$883$	−9.38103	+	26.8094i	−0.315697	+	0.902210i	0.671260	+	0.741222i	$0.265754\pi$
$883$	−9.38103	+	26.8094i	−0.315697	+	0.902210i	−0.986956	+	0.160987i	$0.948532\pi$
$884$	2.10761	−	18.7055i	0.0708866	−	0.629136i
$885$		0			0
$886$	−0.461457	+	0.222226i	−0.0155030	+	0.00746583i
$887$		−	26.1020i		−	0.876418i	−0.898873	−	0.438209i	$-0.855613\pi$
$887$		−	26.1020i		−	0.876418i	0.898873	−	0.438209i	$-0.144387\pi$
$888$	−74.0755	−	153.819i	−2.48581	−	5.16184i
$889$	20.9668	−	33.3684i	0.703202	−	1.11914i
$890$		0			0
$891$	39.5832	−	13.8508i	1.32609	−	0.464018i
$892$	−126.175	+	79.2810i	−4.22465	+	2.65452i
$893$	1.83625	−	16.2971i	0.0614476	−	0.545363i
$894$	−3.44720	−	2.74905i	−0.115292	−	0.0919420i
$895$		0			0
$896$	110.071	−	69.1621i	3.67721	−	2.31054i
$897$	12.4579	−	15.6217i	0.415958	−	0.521595i
$898$	60.1272	−	60.1272i	2.00647	−	2.00647i
$899$	−0.580784	−	0.944318i	−0.0193702	−	0.0314948i
$900$		0			0
$901$	−0.0118689	−	0.105340i	−0.000395412	−	0.00350938i
$902$	−32.0409	−	7.31312i	−1.06684	−	0.243500i
$903$	−30.3605	−	19.0768i	−1.01033	−	0.634835i
$904$	−117.412	+	147.230i	−3.90508	+	4.89681i
$905$		0			0
$906$	−27.0438	+	118.487i	−0.898471	+	3.93646i
$907$	22.4627	+	10.8175i	0.745862	+	0.359188i	0.767901	−	0.640569i	$-0.221301\pi$
$907$	22.4627	+	10.8175i	0.745862	+	0.359188i	−0.0220388	+	0.999757i	$0.507016\pi$
$908$	−7.77132	+	2.71930i	−0.257900	+	0.0902432i
$909$	−1.85960	−	1.16846i	−0.0616789	−	0.0387554i
$910$		0			0
$911$	−11.1579	−	11.1579i	−0.369677	−	0.369677i	0.497683	−	0.867359i	$-0.334184\pi$
$911$	−11.1579	−	11.1579i	−0.369677	−	0.369677i	−0.867359	+	0.497683i	$0.834184\pi$
$912$	−267.631	−	93.6481i	−8.86214	−	3.10100i
$913$	13.4603	+	16.8787i	0.445472	+	0.558604i
$914$	−37.5263	−	4.22820i	−1.24126	−	0.139856i
$915$		0			0
$916$	66.2788	−	66.2788i	2.18991	−	2.18991i
$917$	−10.5609	+	5.08585i	−0.348751	+	0.167950i
$918$	0.444639	+	1.94809i	0.0146753	+	0.0642966i
$919$	9.34582	−	19.4068i	0.308290	−	0.640171i	−0.688049	−	0.725665i	$-0.741532\pi$
$919$	9.34582	−	19.4068i	0.308290	−	0.640171i	0.996339	+	0.0854937i	$0.0272468\pi$
$920$		0			0
$921$	8.52533	+	1.94585i	0.280919	+	0.0641180i
$922$	−17.1326	−	1.93038i	−0.564233	−	0.0635738i
$923$	6.44462	−	0.726134i	0.212127	−	0.0239010i
$924$	−145.299	+	33.1636i	−4.77999	+	1.09100i
$925$		0			0
$926$	92.5296	−	10.4256i	3.04071	−	0.342606i
$927$	−0.0515262	−	0.0515262i	−0.00169234	−	0.00169234i
$928$	−135.658	+	29.5957i	−4.45318	+	0.971525i
$929$			39.4861i			1.29550i	0.761854	+	0.647749i	$0.224289\pi$
$929$			39.4861i			1.29550i	−0.761854	+	0.647749i	$0.775711\pi$
$930$		0			0
$931$	−4.28665	−	6.82217i	−0.140489	−	0.223587i
$932$	−14.0767	+	22.4029i	−0.461098	+	0.733833i
$933$	−5.80217	−	51.4957i	−0.189954	−	1.68589i
$934$	−71.3390	−	89.4563i	−2.33428	−	2.92710i
$935$		0			0
$936$	−12.3680	−	35.3457i	−0.404261	−	1.15531i
$937$	5.78013	+	16.5186i	0.188828	+	0.539641i	0.998910	−	0.0466764i	$-0.0148630\pi$
$937$	5.78013	+	16.5186i	0.188828	+	0.539641i	−0.810082	+	0.586317i	$0.800577\pi$
$938$	−20.3849	+	4.65271i	−0.665589	+	0.151916i
$939$	69.1934	+	24.2118i	2.25804	+	0.790123i
$940$		0			0
$941$	−13.2247	−	27.4614i	−0.431114	−	0.895217i	−0.997472	−	0.0710580i	$-0.977362\pi$
$941$	−13.2247	−	27.4614i	−0.431114	−	0.895217i	0.566358	−	0.824159i	$-0.308352\pi$
$942$	−37.5283	+	29.9278i	−1.22274	+	0.975100i
$943$	13.2426	−	10.5606i	0.431237	−	0.343900i
$944$	10.4624	+	21.7254i	0.340523	+	0.707103i
$945$		0			0
$946$	−71.6711	−	25.0788i	−2.33023	−	0.815382i
$947$	39.1375	−	8.93289i	1.27180	−	0.290280i	0.467229	−	0.884137i	$-0.345253\pi$
$947$	39.1375	−	8.93289i	1.27180	−	0.290280i	0.804571	+	0.593857i	$0.202395\pi$
$948$	−9.95773	−	28.4576i	−0.323412	−	0.924258i
$949$	−0.0929790	−	0.265719i	−0.00301823	−	0.00862560i
$950$		0			0
$951$	−35.4228	−	44.4187i	−1.14866	−	1.44038i
$952$	−7.08676	−	62.8967i	−0.229683	−	2.03849i
$953$	−19.5922	+	31.1808i	−0.634654	+	1.01005i	0.362301	+	0.932061i	$0.381991\pi$
$953$	−19.5922	+	31.1808i	−0.634654	+	1.01005i	−0.996955	+	0.0779844i	$0.975152\pi$
$954$	−0.173675	−	0.276402i	−0.00562293	−	0.00894884i
$955$		0			0
$956$			91.7011i			2.96583i
$957$	58.2752	+	7.13327i	1.88377	+	0.230586i
$958$	68.0474	+	68.0474i	2.19851	+	2.19851i
$959$	−20.5841	+	2.31927i	−0.664696	+	0.0748932i
$960$		0			0
$961$	30.1814	−	6.88872i	0.973595	−	0.222217i
$962$	−24.6346	+	2.77566i	−0.794252	+	0.0894908i
$963$	−18.0983	−	2.03919i	−0.583210	−	0.0657120i
$964$	69.2025	+	15.7950i	2.22886	+	0.508723i
$965$		0			0
$966$	45.1237	−	93.7004i	1.45183	−	3.01476i
$967$	2.51341	+	11.0120i	0.0808257	+	0.354121i	0.999128	−	0.0417600i	$-0.0132965\pi$
$967$	2.51341	+	11.0120i	0.0808257	+	0.354121i	−0.918302	+	0.395881i	$0.870439\pi$
$968$	−83.6465	+	40.2820i	−2.68850	+	1.29471i
$969$	−31.2564	+	31.2564i	−1.00410	+	1.00410i
$970$		0			0
$971$	−26.4125	−	2.97597i	−0.847617	−	0.0955036i	−0.322538	−	0.946557i	$-0.604536\pi$
$971$	−26.4125	−	2.97597i	−0.847617	−	0.0955036i	−0.525080	+	0.851053i	$0.675964\pi$
$972$	76.7988	+	96.3026i	2.46332	+	3.08891i
$973$	35.2117	+	12.3211i	1.12884	+	0.394997i
$974$	−0.910587	−	0.910587i	−0.0291771	−	0.0291771i
$975$		0			0
$976$	186.556	+	117.221i	5.97151	+	3.75215i
$977$	−23.6478	+	8.27471i	−0.756559	+	0.264731i	−0.680874	−	0.732400i	$-0.738400\pi$
$977$	−23.6478	+	8.27471i	−0.756559	+	0.264731i	−0.0756846	+	0.997132i	$0.524114\pi$
$978$	−53.2689	−	25.6530i	−1.70335	−	0.820292i
$979$	11.5936	−	50.7950i	0.370534	−	1.62341i
$980$		0			0
$981$	5.19550	−	6.51495i	0.165879	−	0.208006i
$982$	−68.4473	−	43.0083i	−2.18424	−	1.37245i
$983$	3.04259	+	0.694451i	0.0970435	+	0.0221496i	0.270767	−	0.962645i	$-0.412723\pi$
$983$	3.04259	+	0.694451i	0.0970435	+	0.0221496i	−0.173723	+	0.984794i	$0.555580\pi$
$984$	−7.24997	−	64.3453i	−0.231121	−	2.05125i
$985$		0			0
$986$	−8.94939	+	37.5446i	−0.285007	+	1.19566i
$987$	9.68021	−	9.68021i	0.308125	−	0.308125i
$988$	−31.8478	+	39.9358i	−1.01321	+	1.27053i
$989$	33.1356	−	20.8205i	1.05365	−	0.662052i
$990$		0			0
$991$	−44.8944	−	35.8021i	−1.42612	−	1.13729i	−0.968757	−	0.248011i	$-0.920223\pi$
$991$	−44.8944	−	35.8021i	−1.42612	−	1.13729i	−0.457362	−	0.889281i	$-0.651206\pi$
$992$	−0.594303	+	5.27458i	−0.0188691	+	0.167468i
$993$	0.907650	−	0.570314i	0.0288034	−	0.0180984i
$994$	31.8618	−	11.1489i	1.01060	−	0.353623i
$995$		0			0
$996$	−35.0305	+	55.7507i	−1.10998	+	1.76653i
$997$	6.80003	+	14.1204i	0.215359	+	0.447198i	0.980462	−	0.196711i	$-0.0630260\pi$
$997$	6.80003	+	14.1204i	0.215359	+	0.447198i	−0.765102	+	0.643909i	$0.777312\pi$
$998$		−	53.1470i		−	1.68234i
$999$	1.75109	−	0.843280i	0.0554020	−	0.0266802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.bd.c.43.1	yes	240
5.2	odd	4		725.2.y.c.507.20	yes	240
5.3	odd	4		725.2.y.c.507.1	yes	240
5.4	even	2	inner	725.2.bd.c.43.20	yes	240
29.27	odd	28		725.2.y.c.143.20	yes	240
145.27	even	28	inner	725.2.bd.c.607.1	yes	240
145.114	odd	28		725.2.y.c.143.1	✓	240
145.143	even	28	inner	725.2.bd.c.607.20	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.y.c.143.1	✓	240	145.114	odd	28
725.2.y.c.143.20	yes	240	29.27	odd	28
725.2.y.c.507.1	yes	240	5.3	odd	4
725.2.y.c.507.20	yes	240	5.2	odd	4
725.2.bd.c.43.1	yes	240	1.1	even	1	trivial
725.2.bd.c.43.20	yes	240	5.4	even	2	inner
725.2.bd.c.607.1	yes	240	145.27	even	28	inner
725.2.bd.c.607.20	yes	240	145.143	even	28	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.bd (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.16243 - 1.72448i) q^{2} +(-0.539817 + 2.36509i) q^{3} +(1.25723 + 5.50829i) q^{4} +(5.24588 - 4.18345i) q^{6} +(-1.28727 - 2.04868i) q^{7} +(4.38015 - 9.09547i) q^{8} +(-2.59936 - 1.25179i) q^{9} +(-1.48429 + 4.24186i) q^{11} -13.7063 q^{12} +(-0.424646 + 1.21357i) q^{13} +(-0.749276 + 6.65001i) q^{14} +(-14.9759 + 7.21201i) q^{16} +2.59131i q^{17} +(3.46226 + 7.18946i) q^{18} +(3.74108 - 5.95389i) q^{19} +(5.54022 - 1.93861i) q^{21} +(10.5247 - 6.61310i) q^{22} +(-0.717256 + 6.36582i) q^{23} +(19.1472 + 15.2694i) q^{24} +(3.01105 - 1.89197i) q^{26} +(-0.173827 + 0.217972i) q^{27} +(9.66633 - 9.66633i) q^{28} +(-4.87407 + 2.28985i) q^{29} +(0.0230497 + 0.204572i) q^{31} +(25.1371 + 5.73738i) q^{32} +(-9.23115 - 5.80032i) q^{33} +(4.46867 - 5.60353i) q^{34} +(3.62721 - 15.8918i) q^{36} +(-6.28087 - 3.02471i) q^{37} +(-18.3572 + 6.42346i) q^{38} +(-2.64097 - 1.65943i) q^{39} +(-1.86960 - 1.86960i) q^{41} +(-15.3234 - 5.36190i) q^{42} +(-3.80880 - 4.77608i) q^{43} +(-25.2315 - 2.84291i) q^{44} +(12.5288 - 12.5288i) q^{46} +(2.10136 - 1.01196i) q^{47} +(-8.97283 - 39.3126i) q^{48} +(0.497158 - 1.03236i) q^{49} +(-6.12869 - 1.39883i) q^{51} +(-7.21857 - 0.813337i) q^{52} +(-0.0406512 + 0.00458029i) q^{53} +(0.751778 - 0.171589i) q^{54} +(-24.2722 + 2.73482i) q^{56} +(12.0620 + 12.0620i) q^{57} +(14.4886 + 3.45362i) q^{58} -1.45069i q^{59} +(-7.05216 - 11.2234i) q^{61} +(0.302937 - 0.482121i) q^{62} +(0.781574 + 6.93666i) q^{63} +(-23.7360 - 29.7640i) q^{64} +(9.95920 + 28.4617i) q^{66} +(1.03194 + 2.94912i) q^{67} +(-14.2737 + 3.25787i) q^{68} +(-14.6686 - 5.13276i) q^{69} +(-2.18859 - 4.54465i) q^{71} +(-22.7712 + 18.1594i) q^{72} +(-0.171187 + 0.136517i) q^{73} +(8.36590 + 17.3720i) q^{74} +(37.4992 + 13.1215i) q^{76} +(10.6009 - 2.41959i) q^{77} +(2.84926 + 8.14272i) q^{78} +(0.726507 + 2.07624i) q^{79} +(-5.81814 - 7.29571i) q^{81} +(0.818793 + 7.26699i) q^{82} +(2.55579 - 4.06752i) q^{83} +(17.6437 + 28.0798i) q^{84} +16.8961i q^{86} +(-2.78459 - 12.7637i) q^{87} +(32.0803 + 32.0803i) q^{88} +(-11.5205 + 1.29805i) q^{89} +(3.03285 - 0.692229i) q^{91} +(-35.9665 + 4.05246i) q^{92} +(-0.496274 - 0.0559167i) q^{93} +(-6.28917 - 1.43546i) q^{94} +(-27.1389 + 56.3545i) q^{96} +(-2.56898 - 11.2555i) q^{97} +(-2.85536 + 1.37507i) q^{98} +(9.16812 - 9.16812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 40 q^{4} - 56 q^{9} - 12 q^{14} - 80 q^{16} + 4 q^{19} - 28 q^{21} + 12 q^{29} - 16 q^{31} + 8 q^{34} - 104 q^{36} - 100 q^{39} + 28 q^{41} - 264 q^{44} - 100 q^{46} + 168 q^{49} - 112 q^{51} + 168 q^{54}+ \cdots + 56 q^{99}+O(q^{100}) \) 240 * q + 40 * q^4 - 56 * q^9 - 12 * q^14 - 80 * q^16 + 4 * q^19 - 28 * q^21 + 12 * q^29 - 16 * q^31 + 8 * q^34 - 104 * q^36 - 100 * q^39 + 28 * q^41 - 264 * q^44 - 100 * q^46 + 168 * q^49 - 112 * q^51 + 168 * q^54 - 156 * q^56 - 88 * q^61 - 280 * q^64 - 144 * q^66 - 184 * q^69 - 56 * q^71 + 224 * q^74 + 108 * q^76 + 208 * q^79 - 200 * q^81 + 4 * q^84 - 100 * q^89 - 168 * q^94 + 84 * q^96 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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