LMFDB - Embedded newform 840.2.dj.a.403.48

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(67,840)] 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("840.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 3, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.dj (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			403.48
Character	$\chi$	$=$	840.403
Dual form			840.2.dj.a.667.48

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0812078 + 1.41188i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.98681 - 0.229311i) q^{4} +(-0.422435 - 2.19580i) q^{5} +(0.286981 + 1.38479i) q^{6} +(-1.48397 - 2.19039i) q^{7} +(0.485105 - 2.78652i) q^{8} +(0.866025 - 0.500000i) q^{9} +(3.13451 - 0.418111i) q^{10} +(-2.78550 + 4.82463i) q^{11} +(-1.97846 + 0.292727i) q^{12} +(-4.22999 + 4.22999i) q^{13} +(3.21308 - 1.91732i) q^{14} +(-0.976356 - 2.01165i) q^{15} +(3.89483 + 0.911196i) q^{16} +(-0.0957741 - 0.357434i) q^{17} +(0.635612 + 1.26333i) q^{18} +(3.88557 - 2.24334i) q^{19} +(0.335775 + 4.45951i) q^{20} +(-2.00032 - 1.73168i) q^{21} +(-6.58559 - 4.32459i) q^{22} +(-5.12067 - 1.37208i) q^{23} +(-0.252628 - 2.81712i) q^{24} +(-4.64310 + 1.85517i) q^{25} +(-5.62873 - 6.31574i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.44609 + 4.69219i) q^{28} -2.15497 q^{29} +(2.91949 - 1.21514i) q^{30} +(-7.57009 - 4.37059i) q^{31} +(-1.60279 + 5.42504i) q^{32} +(-1.44188 + 5.38117i) q^{33} +(0.512431 - 0.106195i) q^{34} +(-4.18279 + 4.18381i) q^{35} +(-1.83528 + 0.794816i) q^{36} +(-0.398738 + 1.48811i) q^{37} +(2.85178 + 5.66814i) q^{38} +(-2.99105 + 5.18066i) q^{39} +(-6.32356 + 0.111927i) q^{40} -6.48184 q^{41} +(2.60736 - 2.68359i) q^{42} +(-4.80750 - 4.80750i) q^{43} +(6.64060 - 8.94687i) q^{44} +(-1.46374 - 1.69040i) q^{45} +(2.35305 - 7.11835i) q^{46} +(0.335928 - 1.25370i) q^{47} +(3.99795 - 0.127909i) q^{48} +(-2.59564 + 6.50097i) q^{49} +(-2.24222 - 6.70615i) q^{50} +(-0.185021 - 0.320466i) q^{51} +(9.37417 - 7.43420i) q^{52} +(0.463759 + 1.73077i) q^{53} +(0.940927 + 1.05577i) q^{54} +(11.7706 + 4.07832i) q^{55} +(-6.82345 + 3.07255i) q^{56} +(3.17256 - 3.17256i) q^{57} +(0.175001 - 3.04256i) q^{58} +(2.91223 + 1.68137i) q^{59} +(1.47854 + 4.22065i) q^{60} +(9.74986 - 5.62909i) q^{61} +(6.78550 - 10.3331i) q^{62} +(-2.38036 - 1.15495i) q^{63} +(-7.52935 - 2.70350i) q^{64} +(11.0751 + 7.50133i) q^{65} +(-7.48048 - 2.47276i) q^{66} +(-3.73855 - 13.9525i) q^{67} +(0.108321 + 0.732115i) q^{68} -5.30131 q^{69} +(-5.56736 - 6.24535i) q^{70} +10.8638i q^{71} +(-0.973145 - 2.65575i) q^{72} +(-7.09104 + 1.90004i) q^{73} +(-2.06866 - 0.683817i) q^{74} +(-4.00474 + 2.99368i) q^{75} +(-8.23432 + 3.56608i) q^{76} +(14.7014 - 1.05828i) q^{77} +(-7.07157 - 4.64372i) q^{78} +(0.655100 + 1.13467i) q^{79} +(0.355495 - 8.93720i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.526376 - 9.15159i) q^{82} +(6.80401 + 6.80401i) q^{83} +(3.57717 + 3.89921i) q^{84} +(-0.744396 + 0.361294i) q^{85} +(7.17802 - 6.39721i) q^{86} +(-2.08154 + 0.557748i) q^{87} +(12.0926 + 10.1023i) q^{88} +(-3.23303 + 1.86659i) q^{89} +(2.50551 - 1.92935i) q^{90} +(15.5425 + 2.98815i) q^{91} +(9.85917 + 3.90029i) q^{92} +(-8.44333 - 2.26238i) q^{93} +(1.74279 + 0.576100i) q^{94} +(-6.56733 - 7.58429i) q^{95} +(-0.144073 + 5.65502i) q^{96} +(5.31523 - 5.31523i) q^{97} +(-8.96781 - 4.19267i) q^{98} +5.57100i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + 24 q^{8} - 16 q^{16} + 32 q^{26} + 44 q^{28} + 48 q^{35} + 12 q^{38} + 20 q^{40} - 20 q^{42} - 48 q^{46} - 32 q^{48} - 72 q^{50} + 4 q^{52} + 32 q^{56} + 8 q^{58} + 20 q^{60} - 144 q^{62} - 24 q^{66}+ \cdots - 80 q^{98}+O(q^{100}) $ 384 * q + 24 * q^8 - 16 * q^16 + 32 * q^26 + 44 * q^28 + 48 * q^35 + 12 * q^38 + 20 * q^40 - 20 * q^42 - 48 * q^46 - 32 * q^48 - 72 * q^50 + 4 * q^52 + 32 * q^56 + 8 * q^58 + 20 * q^60 - 144 * q^62 - 24 * q^66 + 48 * q^67 + 44 * q^68 - 40 * q^70 + 12 * q^72 + 96 * q^76 - 48 * q^78 + 36 * q^80 + 192 * q^81 - 44 * q^82 + 32 * q^86 + 68 * q^88 + 24 * q^90 - 64 * q^91 - 72 * q^92 + 32 * q^97 - 80 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.0812078	+	1.41188i	−0.0574226	+	0.998350i
$2$	−0.0812078	+	1.41188i	−0.0574226	+	0.998350i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−1.98681	−	0.229311i	−0.993405	−	0.114656i
$5$	−0.422435	−	2.19580i	−0.188919	−	0.981993i
$5$	−0.422435	−	2.19580i	−0.188919	−	0.981993i
$6$	0.286981	+	1.38479i	0.117159	+	0.565338i
$7$	−1.48397	−	2.19039i	−0.560889	−	0.827891i
$7$	−1.48397	−	2.19039i	−0.560889	−	0.827891i
$8$	0.485105	−	2.78652i	0.171510	−	0.985182i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	3.13451	−	0.418111i	0.991221	−	0.132218i
$11$	−2.78550	+	4.82463i	−0.839860	+	1.45468i	0.0501521	+	0.998742i	$0.484029\pi$
$11$	−2.78550	+	4.82463i	−0.839860	+	1.45468i	−0.890012	+	0.455938i	$0.849304\pi$
$12$	−1.97846	+	0.292727i	−0.571133	+	0.0845029i
$13$	−4.22999	+	4.22999i	−1.17319	+	1.17319i	−0.191742	+	0.981445i	$0.561414\pi$
$13$	−4.22999	+	4.22999i	−1.17319	+	1.17319i	−0.981445	+	0.191742i	$0.938586\pi$
$14$	3.21308	−	1.91732i	0.858732	−	0.512424i
$15$	−0.976356	−	2.01165i	−0.252094	−	0.519405i
$16$	3.89483	+	0.911196i	0.973708	+	0.227799i
$17$	−0.0957741	−	0.357434i	−0.0232286	−	0.0866904i	0.953338	−	0.301904i	$-0.0976221\pi$
$17$	−0.0957741	−	0.357434i	−0.0232286	−	0.0866904i	−0.976567	+	0.215213i	$0.930955\pi$
$18$	0.635612	+	1.26333i	0.149815	+	0.297769i
$19$	3.88557	−	2.24334i	0.891412	−	0.514657i	0.0170079	−	0.999855i	$-0.494586\pi$
$19$	3.88557	−	2.24334i	0.891412	−	0.514657i	0.874404	+	0.485198i	$0.161253\pi$
$20$	0.335775	+	4.45951i	0.0750817	+	0.997177i
$21$	−2.00032	−	1.73168i	−0.436506	−	0.377883i
$22$	−6.58559	−	4.32459i	−1.40405	−	0.922005i
$23$	−5.12067	−	1.37208i	−1.06773	−	0.286098i	−0.318172	−	0.948033i	$-0.603069\pi$
$23$	−5.12067	−	1.37208i	−1.06773	−	0.286098i	−0.749562	+	0.661934i	$0.769736\pi$
$24$	−0.252628	−	2.81712i	−0.0515676	−	0.575043i
$25$	−4.64310	+	1.85517i	−0.928620	+	0.371033i
$26$	−5.62873	−	6.31574i	−1.10388	−	1.23862i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.44609	+	4.69219i	0.462268	+	0.886740i
$29$	−2.15497			−0.400168			−0.200084	−	0.979779i	$-0.564122\pi$
$29$	−2.15497			−0.400168			−0.200084	+	0.979779i	$0.564122\pi$
$30$	2.91949	−	1.21514i	0.533024	−	0.221853i
$31$	−7.57009	−	4.37059i	−1.35963	−	0.784981i	−0.370054	−	0.929010i	$-0.620661\pi$
$31$	−7.57009	−	4.37059i	−1.35963	−	0.784981i	−0.989574	+	0.144029i	$0.953994\pi$
$32$	−1.60279	+	5.42504i	−0.283336	+	0.959021i
$33$	−1.44188	+	5.38117i	−0.250999	+	0.936742i
$34$	0.512431	−	0.106195i	0.0878813	−	0.0182123i
$35$	−4.18279	+	4.18381i	−0.707020	+	0.707193i
$36$	−1.83528	+	0.794816i	−0.305881	+	0.132469i
$37$	−0.398738	+	1.48811i	−0.0655522	+	0.244644i	−0.990925	−	0.134413i	$-0.957085\pi$
$37$	−0.398738	+	1.48811i	−0.0655522	+	0.244644i	0.925373	+	0.379057i	$0.123752\pi$
$38$	2.85178	+	5.66814i	0.462621	+	0.919494i
$39$	−2.99105	+	5.18066i	−0.478952	+	0.829569i
$40$	−6.32356	+	0.111927i	−0.999843	+	0.0176973i
$41$	−6.48184			−1.01229			−0.506147	−	0.862447i	$-0.668931\pi$
$41$	−6.48184			−1.01229			−0.506147	+	0.862447i	$0.668931\pi$
$42$	2.60736	−	2.68359i	0.402325	−	0.414087i
$43$	−4.80750	−	4.80750i	−0.733137	−	0.733137i	0.238103	−	0.971240i	$-0.423474\pi$
$43$	−4.80750	−	4.80750i	−0.733137	−	0.733137i	−0.971240	+	0.238103i	$0.923474\pi$
$44$	6.64060	−	8.94687i	1.00111	−	1.34879i
$45$	−1.46374	−	1.69040i	−0.218202	−	0.251990i
$46$	2.35305	−	7.11835i	0.346938	−	1.04954i
$47$	0.335928	−	1.25370i	0.0490001	−	0.182871i	−0.937088	−	0.349092i	$-0.886490\pi$
$47$	0.335928	−	1.25370i	0.0490001	−	0.182871i	0.986088	+	0.166221i	$0.0531567\pi$
$48$	3.99795	−	0.127909i	0.577055	−	0.0184620i
$49$	−2.59564	+	6.50097i	−0.370806	+	0.928710i
$50$	−2.24222	−	6.70615i	−0.317097	−	0.948393i
$51$	−0.185021	−	0.320466i	−0.0259082	−	0.0448743i
$52$	9.37417	−	7.43420i	1.29996	−	1.03094i
$53$	0.463759	+	1.73077i	0.0637022	+	0.237740i	0.990435	−	0.137982i	$-0.0440616\pi$
$53$	0.463759	+	1.73077i	0.0637022	+	0.237740i	−0.926733	+	0.375722i	$0.877395\pi$
$54$	0.940927	+	1.05577i	0.128044	+	0.143672i
$55$	11.7706	+	4.07832i	1.58715	+	0.549920i
$56$	−6.82345	+	3.07255i	−0.911822	+	0.410586i
$57$	3.17256	−	3.17256i	0.420216	−	0.420216i
$58$	0.175001	−	3.04256i	0.0229787	−	0.399508i
$59$	2.91223	+	1.68137i	0.379140	+	0.218896i	0.677444	−	0.735574i	$-0.263088\pi$
$59$	2.91223	+	1.68137i	0.379140	+	0.218896i	−0.298304	+	0.954471i	$0.596421\pi$
$60$	1.47854	+	4.22065i	0.190879	+	0.544884i
$61$	9.74986	−	5.62909i	1.24834	−	0.720731i	0.277563	−	0.960707i	$-0.410473\pi$
$61$	9.74986	−	5.62909i	1.24834	−	0.720731i	0.970779	+	0.239977i	$0.0771398\pi$
$62$	6.78550	−	10.3331i	0.861760	−	1.31231i
$63$	−2.38036	−	1.15495i	−0.299897	−	0.145510i
$64$	−7.52935	−	2.70350i	−0.941168	−	0.337938i
$65$	11.0751	+	7.50133i	1.37370	+	0.930425i
$66$	−7.48048	−	2.47276i	−0.920783	−	0.304375i
$67$	−3.73855	−	13.9525i	−0.456736	−	1.70456i	−0.682933	−	0.730481i	$-0.739296\pi$
$67$	−3.73855	−	13.9525i	−0.456736	−	1.70456i	0.226196	−	0.974082i	$-0.427371\pi$
$68$	0.108321	+	0.732115i	0.0131359	+	0.0887820i
$69$	−5.30131			−0.638203
$70$	−5.56736	−	6.24535i	−0.665427	−	0.746463i
$71$			10.8638i			1.28929i	0.764481	+	0.644646i	$0.222995\pi$
$71$			10.8638i			1.28929i	−0.764481	+	0.644646i	$0.777005\pi$
$72$	−0.973145	−	2.65575i	−0.114686	−	0.312983i
$73$	−7.09104	+	1.90004i	−0.829944	+	0.222383i	−0.648689	−	0.761053i	$-0.724682\pi$
$73$	−7.09104	+	1.90004i	−0.829944	+	0.222383i	−0.181255	+	0.983436i	$0.558016\pi$
$74$	−2.06866	−	0.683817i	−0.240476	−	0.0794921i
$75$	−4.00474	+	2.99368i	−0.462427	+	0.345680i
$76$	−8.23432	+	3.56608i	−0.944542	+	0.409057i
$77$	14.7014	−	1.05828i	1.67538	−	0.120602i
$78$	−7.07157	−	4.64372i	−0.800698	−	0.525798i
$79$	0.655100	+	1.13467i	0.0737045	+	0.127660i	0.900522	−	0.434810i	$-0.143184\pi$
$79$	0.655100	+	1.13467i	0.0737045	+	0.127660i	−0.826818	+	0.562470i	$0.809851\pi$
$80$	0.355495	−	8.93720i	0.0397455	−	0.999210i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	0.526376	−	9.15159i	0.0581285	−	1.01062i
$83$	6.80401	+	6.80401i	0.746837	+	0.746837i	0.973884	−	0.227047i	$-0.0729070\pi$
$83$	6.80401	+	6.80401i	0.746837	+	0.746837i	−0.227047	+	0.973884i	$0.572907\pi$
$84$	3.57717	+	3.89921i	0.390301	+	0.425439i
$85$	−0.744396	+	0.361294i	−0.0807411	+	0.0391878i
$86$	7.17802	−	6.39721i	0.774026	−	0.689829i
$87$	−2.08154	+	0.557748i	−0.223165	+	0.0597968i
$88$	12.0926	+	10.1023i	1.28908	+	1.07691i
$89$	−3.23303	+	1.86659i	−0.342700	+	0.197858i	−0.661465	−	0.749976i	$-0.730065\pi$
$89$	−3.23303	+	1.86659i	−0.342700	+	0.197858i	0.318765	+	0.947834i	$0.396732\pi$
$90$	2.50551	−	1.92935i	0.264104	−	0.203372i
$91$	15.5425	+	2.98815i	1.62930	+	0.313243i
$92$	9.85917	+	3.90029i	1.02789	+	0.406633i
$93$	−8.44333	−	2.26238i	−0.875533	−	0.234598i
$94$	1.74279	+	0.576100i	0.179755	+	0.0594201i
$95$	−6.56733	−	7.58429i	−0.673794	−	0.778132i
$96$	−0.144073	+	5.65502i	−0.0147044	+	0.577163i
$97$	5.31523	−	5.31523i	0.539679	−	0.539679i	−0.383755	−	0.923435i	$-0.625369\pi$
$97$	5.31523	−	5.31523i	0.539679	−	0.539679i	0.923435	+	0.383755i	$0.125369\pi$
$98$	−8.96781	−	4.19267i	−0.905885	−	0.423523i
$99$			5.57100i			0.559906i
$100$	9.65037	−	2.62115i	0.965037	−	0.262115i
$101$	12.1989	+	7.04305i	1.21384	+	0.700810i	0.963593	−	0.267373i	$-0.0861556\pi$
$101$	12.1989	+	7.04305i	1.21384	+	0.700810i	0.250245	+	0.968183i	$0.419489\pi$
$102$	0.467485	−	0.235204i	0.0462879	−	0.0232886i
$103$	8.90017	+	2.38479i	0.876960	+	0.234981i	0.669095	−	0.743177i	$-0.266682\pi$
$103$	8.90017	+	2.38479i	0.876960	+	0.234981i	0.207865	+	0.978158i	$0.433349\pi$
$104$	9.73495	+	13.8389i	0.954590	+	1.35702i
$105$	−2.95741	+	5.12384i	−0.288614	+	0.500035i
$106$	−2.48130	+	0.514220i	−0.241005	+	0.0499454i
$107$	−7.47856	−	2.00387i	−0.722979	−	0.193722i	−0.121479	−	0.992594i	$-0.538764\pi$
$107$	−7.47856	−	2.00387i	−0.722979	−	0.193722i	−0.601501	+	0.798872i	$0.705430\pi$
$108$	−1.56703	+	1.24274i	−0.150788	+	0.119583i
$109$	2.51427	−	4.35484i	0.240823	−	0.417118i	−0.720126	−	0.693844i	$-0.755916\pi$
$109$	2.51427	−	4.35484i	0.240823	−	0.417118i	0.960949	+	0.276725i	$0.0892492\pi$
$110$	−6.71396	+	16.2875i	−0.640151	+	1.55295i
$111$			1.54061i			0.146228i
$112$	−3.78395	−	9.88341i	−0.357550	−	0.933894i
$113$	1.95011	+	1.95011i	0.183451	+	0.183451i	0.792858	−	0.609407i	$-0.208592\pi$
$113$	1.95011	+	1.95011i	0.183451	+	0.183451i	−0.609407	+	0.792858i	$0.708592\pi$
$114$	4.22164	+	4.73691i	0.395392	+	0.443652i
$115$	−0.849667	+	11.8236i	−0.0792318	+	1.10256i
$116$	4.28152	+	0.494159i	0.397529	+	0.0458816i
$117$	−1.54828	+	5.77827i	−0.143139	+	0.534201i
$118$	−2.61040	+	3.97517i	−0.240306	+	0.365944i
$119$	−0.640794	+	0.740205i	−0.0587415	+	0.0678545i
$120$	−6.07913	+	1.74477i	−0.554946	+	0.159275i
$121$	−10.0180	−	17.3517i	−0.910728	−	1.57743i
$122$	7.15583	+	14.2228i	0.647858	+	1.28767i
$123$	−6.26098	+	1.67762i	−0.564534	+	0.151266i
$124$	14.0381	+	10.4194i	1.26066	+	0.935694i
$125$	6.03499	+	9.41164i	0.539786	+	0.841803i
$126$	1.82395	−	3.26699i	0.162491	−	0.291046i
$127$	−14.2525	−	14.2525i	−1.26471	−	1.26471i	−0.948786	−	0.315919i	$-0.897687\pi$
$127$	−14.2525	−	14.2525i	−1.26471	−	1.26471i	−0.315919	−	0.948786i	$-0.602313\pi$
$128$	4.42846	−	10.4110i	0.391425	−	0.920210i
$129$	−5.88796	−	3.39942i	−0.518406	−	0.299302i
$130$	−11.4904	+	15.0276i	−1.00777	+	1.31800i
$131$	1.17297	+	2.03165i	0.102483	+	0.177506i	0.912707	−	0.408614i	$-0.133988\pi$
$131$	1.17297	+	2.03165i	0.102483	+	0.177506i	−0.810224	+	0.586120i	$0.800655\pi$
$132$	4.09871	−	10.3607i	0.356747	−	0.901786i
$133$	−10.6799	−	5.18188i	−0.926063	−	0.449326i
$134$	20.0028	−	4.14533i	1.72798	−	0.358102i
$135$	−1.85137	−	1.25396i	−0.159341	−	0.107924i
$136$	−1.04246	+	0.0934833i	−0.0893898	+	0.00801613i
$137$	1.12053	+	4.18186i	0.0957331	+	0.357281i	0.997130	−	0.0757139i	$-0.0241236\pi$
$137$	1.12053	+	4.18186i	0.0957331	+	0.357281i	−0.901396	+	0.432995i	$0.857457\pi$
$138$	0.430508	−	7.48481i	0.0366472	−	0.637150i
$139$		−	19.6140i		−	1.66364i	−0.555046	−	0.831819i	$-0.687300\pi$
$139$		−	19.6140i		−	1.66364i	0.555046	−	0.831819i	$-0.312700\pi$
$140$	9.26980	−	7.35328i	0.783441	−	0.621466i
$141$		−	1.29792i		−	0.109305i
$142$	−15.3383	−	0.882223i	−1.28716	−	0.0740345i
$143$	−8.62548	−	32.1907i	−0.721299	−	2.69192i
$144$	3.82862	−	1.15830i	0.319052	−	0.0965248i
$145$	0.910335	+	4.73189i	0.0755992	+	0.392962i
$146$	−2.10678	−	10.1660i	−0.174358	−	0.841344i
$147$	−0.824624	+	6.95126i	−0.0680139	+	0.573330i
$148$	1.13346	−	2.86516i	0.0931697	−	0.235515i
$149$	9.37590	+	16.2395i	0.768103	+	1.33039i	0.938590	+	0.345034i	$0.112133\pi$
$149$	9.37590	+	16.2395i	0.768103	+	1.33039i	−0.170487	+	0.985360i	$0.554534\pi$
$150$	−3.90150	−	5.89732i	−0.318556	−	0.481514i
$151$	−11.9413	−	6.89433i	−0.971771	−	0.561052i	−0.0719956	−	0.997405i	$-0.522937\pi$
$151$	−11.9413	−	6.89433i	−0.971771	−	0.561052i	−0.899776	+	0.436352i	$0.856270\pi$
$152$	−4.36619	−	11.9155i	−0.354145	−	0.966472i
$153$	−0.261660	−	0.261660i	−0.0211539	−	0.0211539i
$154$	0.300293	+	20.8426i	0.0241983	+	1.67954i
$155$	−6.39909	+	18.4687i	−0.513987	+	1.48344i
$156$	7.13064	−	9.60710i	0.570908	−	0.769184i
$157$	4.68010	−	1.25403i	0.373512	−	0.100082i	−0.0671792	−	0.997741i	$-0.521400\pi$
$157$	4.68010	−	1.25403i	0.373512	−	0.100082i	0.440692	+	0.897659i	$0.354733\pi$
$158$	−1.65521	+	0.832779i	−0.131682	+	0.0662524i
$159$	0.895913	+	1.55177i	0.0710506	+	0.123063i
$160$	12.5894	+	1.22769i	0.995279	+	0.0970571i
$161$	4.59355	+	13.2524i	0.362022	+	1.04444i
$162$	1.18212	+	0.776268i	0.0928761	+	0.0609894i
$163$	0.692231	−	2.58344i	0.0542197	−	0.202351i	−0.933503	−	0.358571i	$-0.883264\pi$
$163$	0.692231	−	2.58344i	0.0542197	−	0.202351i	0.987722	+	0.156220i	$0.0499309\pi$
$164$	12.8782	+	1.48636i	1.00562	+	0.116065i
$165$	12.4251	+	0.892891i	0.967292	+	0.0695115i
$166$	−10.1590	+	9.05391i	−0.788490	+	0.702720i
$167$	−13.5322	−	13.5322i	−1.04715	−	1.04715i	−0.998832	−	0.0483210i	$-0.984613\pi$
$167$	−13.5322	−	13.5322i	−1.04715	−	1.04715i	−0.0483210	−	0.998832i	$-0.515387\pi$
$168$	−5.79571	+	4.73389i	−0.447149	+	0.365228i
$169$		−	22.7856i		−	1.75274i
$170$	−0.449652	−	1.08034i	−0.0344868	−	0.0828581i
$171$	2.24334	−	3.88557i	0.171552	−	0.297137i
$172$	8.44918	+	10.6540i	0.644244	+	0.812361i
$173$	6.51581	+	1.74590i	0.495388	+	0.132739i	0.497859	−	0.867258i	$-0.334120\pi$
$173$	6.51581	+	1.74590i	0.495388	+	0.132739i	−0.00247098	+	0.999997i	$0.500787\pi$
$174$	−0.618435	−	2.98418i	−0.0468835	−	0.226230i
$175$	10.9538	+	7.41719i	0.828028	+	0.560687i
$176$	−15.2452	+	16.2530i	−1.14915	+	1.22511i
$177$	3.24817	+	0.870344i	0.244147	+	0.0654190i
$178$	−2.37285	−	4.71623i	−0.177853	−	0.353496i
$179$	−1.10843	−	0.639953i	−0.0828481	−	0.0478324i	0.458004	−	0.888950i	$-0.348565\pi$
$179$	−1.10843	−	0.639953i	−0.0828481	−	0.0478324i	−0.540852	+	0.841118i	$0.681898\pi$
$180$	2.52055	+	3.69416i	0.187870	+	0.275347i
$181$			19.3108i			1.43536i	0.696374	+	0.717679i	$0.254795\pi$
$181$			19.3108i			1.43536i	−0.696374	+	0.717679i	$0.745205\pi$
$182$	−5.48108	+	21.7015i	−0.406285	+	1.60862i
$183$	7.96073	−	7.96073i	0.588474	−	0.588474i
$184$	−6.30739	+	13.6032i	−0.464987	+	1.00284i
$185$	3.43604	+	0.246921i	0.252623	+	0.0181540i
$186$	3.87988	−	11.7373i	0.284487	−	0.860617i
$187$	1.99126	+	0.533557i	0.145616	+	0.0390176i
$188$	−0.954912	+	2.41383i	−0.0696441	+	0.176047i
$189$	−2.59817	−	0.499514i	−0.188989	−	0.0363343i
$190$	11.2414	−	8.65638i	0.815539	−	0.628000i
$191$	11.9792	−	6.91618i	0.866783	−	0.500437i	0.000505095	−	1.00000i	$-0.499839\pi$
$191$	11.9792	−	6.91618i	0.866783	−	0.500437i	0.866278	+	0.499563i	$0.166506\pi$
$192$	−7.97251	−	0.662646i	−0.575366	−	0.0478223i
$193$	18.6186	−	4.98883i	1.34019	−	0.359104i	0.483688	−	0.875241i	$-0.339297\pi$
$193$	18.6186	−	4.98883i	1.34019	−	0.359104i	0.856506	+	0.516137i	$0.172630\pi$
$194$	7.07282	+	7.93610i	0.507799	+	0.569779i
$195$	12.6392	+	4.37927i	0.905114	+	0.313606i
$196$	6.64780	−	12.3210i	0.474843	−	0.880071i
$197$	−8.87857	−	8.87857i	−0.632572	−	0.632572i	0.316140	−	0.948712i	$-0.397613\pi$
$197$	−8.87857	−	8.87857i	−0.632572	−	0.632572i	−0.948712	+	0.316140i	$0.897613\pi$
$198$	−7.86558	−	0.452408i	−0.558982	−	0.0321513i
$199$	−6.58171	+	11.3999i	−0.466565	+	0.808115i	−0.999271	−	0.0381859i	$-0.987842\pi$
$199$	−6.58171	+	11.3999i	−0.466565	+	0.808115i	0.532705	+	0.846301i	$0.321175\pi$
$200$	2.91706	+	13.8380i	0.206268	+	0.978496i
$201$	−7.22232	−	12.5094i	−0.509423	−	0.882347i
$202$	−10.9346	+	16.6515i	−0.769355	+	1.17159i
$203$	3.19792	+	4.72024i	0.224450	+	0.331296i
$204$	0.294116	+	0.679134i	0.0205922	+	0.0475489i
$205$	2.73816	+	14.2328i	0.191241	+	0.994065i
$206$	−4.08981	+	12.3723i	−0.284950	+	0.862020i
$207$	−5.12067	+	1.37208i	−0.355911	+	0.0953662i
$208$	−20.3294	+	12.6207i	−1.40959	+	0.875091i
$209$			24.9953i			1.72896i
$210$	−6.99408	−	4.59161i	−0.482637	−	0.316851i
$211$	−0.281828			−0.0194019			−0.00970093	−	0.999953i	$-0.503088\pi$
$211$	−0.281828			−0.0194019			−0.00970093	+	0.999953i	$0.503088\pi$
$212$	−0.524516	−	3.54506i	−0.0360239	−	0.243476i
$213$	2.81175	+	10.4936i	0.192658	+	0.719009i
$214$	3.43655	−	10.3961i	0.234917	−	0.710662i
$215$	−8.52547	+	12.5872i	−0.581432	+	0.858439i
$216$	−1.62734	−	2.31339i	−0.110727	−	0.157406i
$217$	1.66050	+	23.0673i	0.112722	+	1.56591i
$218$	5.94434	+	3.90349i	0.402601	+	0.264378i
$219$	−6.35766	+	3.67059i	−0.429611	+	0.248036i
$220$	−22.4508	−	10.8020i	−1.51363	−	0.728269i
$221$	1.91706	+	1.10682i	0.128956	+	0.0744526i
$222$	−2.17515	−	0.125109i	−0.145987	−	0.00839679i
$223$	−0.661316	+	0.661316i	−0.0442850	+	0.0442850i	−0.728902	−	0.684618i	$-0.759969\pi$
$223$	−0.661316	+	0.661316i	−0.0442850	+	0.0442850i	0.684618	+	0.728902i	$0.259969\pi$
$224$	14.2615	−	4.53988i	0.952885	−	0.303333i
$225$	−3.09346	+	3.92817i	−0.206230	+	0.261878i
$226$	−2.91169	+	2.59496i	−0.193682	+	0.172614i
$227$	−5.73653	−	21.4090i	−0.380747	−	1.42097i	−0.844763	−	0.535140i	$-0.820259\pi$
$227$	−5.73653	−	21.4090i	−0.380747	−	1.42097i	0.464016	−	0.885827i	$-0.346408\pi$
$228$	−7.03078	+	5.57577i	−0.465625	+	0.369264i
$229$	2.38356	+	4.12844i	0.157510	+	0.272815i	0.933970	−	0.357351i	$-0.116320\pi$
$229$	2.38356	+	4.12844i	0.157510	+	0.272815i	−0.776460	+	0.630166i	$0.782987\pi$
$230$	−16.6245	−	2.15980i	−1.09619	−	0.142413i
$231$	13.9266	−	4.82723i	0.916302	−	0.317608i
$232$	−1.04539	+	6.00486i	−0.0686330	+	0.394239i
$233$	−0.00292416	+	0.0109131i	−0.000191568	+	0.000714941i	−0.966022	−	0.258462i	$-0.916784\pi$
$233$	−0.00292416	+	0.0109131i	−0.000191568	+	0.000714941i	0.965830	+	0.259176i	$0.0834511\pi$
$234$	−8.03249	−	2.65523i	−0.525101	−	0.173578i
$235$	−2.89478	−	0.208025i	−0.188835	−	0.0135700i
$236$	−5.40048	−	4.00838i	−0.351542	−	0.260923i
$237$	0.926452	+	0.926452i	0.0601795	+	0.0601795i
$238$	−0.993044	−	0.964835i	−0.0643695	−	0.0625410i
$239$	−10.3228			−0.667723			−0.333862	−	0.942622i	$-0.608352\pi$
$239$	−10.3228			−0.667723			−0.333862	+	0.942622i	$0.608352\pi$
$240$	−1.96974	−	8.72469i	−0.127146	−	0.563176i
$241$	−5.14413	+	8.90990i	−0.331363	+	0.573937i	−0.982779	−	0.184783i	$-0.940842\pi$
$241$	−5.14413	+	8.90990i	−0.331363	+	0.573937i	0.651417	+	0.758720i	$0.274175\pi$
$242$	25.3121	−	12.7351i	1.62712	−	0.818645i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−20.6619	+	8.94817i	−1.32275	+	0.572848i
$245$	15.3713	+	2.95329i	0.982039	+	0.188678i
$246$	−1.86016	−	8.97599i	−0.118600	−	0.572288i
$247$	−6.94664	+	25.9252i	−0.442004	+	1.64958i
$248$	−15.8510	+	18.9740i	−1.00654	+	1.20485i
$249$	8.33318	+	4.81116i	0.528094	+	0.304895i
$250$	−13.7782	+	7.75638i	−0.871409	+	0.490556i
$251$	−1.10630			−0.0698290			−0.0349145	−	0.999390i	$-0.511116\pi$
$251$	−1.10630			−0.0698290			−0.0349145	+	0.999390i	$0.511116\pi$
$252$	4.46447	+	2.84051i	0.281235	+	0.178935i
$253$	20.8834	−	20.8834i	1.31293	−	1.31293i
$254$	21.2802	−	18.9654i	1.33524	−	1.19000i
$255$	−0.625522	+	0.541647i	−0.0391717	+	0.0339192i
$256$	14.3394	+	7.09791i	0.896215	+	0.443620i
$257$	−19.6781	−	5.27272i	−1.22748	−	0.328903i	−0.413884	−	0.910329i	$-0.635828\pi$
$257$	−19.6781	−	5.27272i	−1.22748	−	0.328903i	−0.813599	+	0.581426i	$0.802495\pi$
$258$	5.27772	−	8.03704i	0.328576	−	0.500364i
$259$	3.85127	−	1.33493i	0.239306	−	0.0829482i
$260$	−20.2840	−	17.4434i	−1.25796	−	1.08179i
$261$	−1.86626	+	1.07749i	−0.115519	+	0.0666947i
$262$	−2.96370	+	1.49111i	−0.183098	+	0.0921211i
$263$	−4.20813	−	15.7050i	−0.259485	−	0.968410i	−0.965540	−	0.260254i	$-0.916194\pi$
$263$	−4.20813	−	15.7050i	−0.259485	−	0.968410i	0.706056	−	0.708156i	$-0.250473\pi$
$264$	14.2953	+	6.62825i	0.879812	+	0.407941i
$265$	3.60453	−	1.74946i	0.221424	−	0.107469i
$266$	8.18349	−	14.6579i	0.501762	−	0.898734i
$267$	−2.63976	+	2.63976i	−0.161550	+	0.161550i
$268$	4.22833	+	28.5782i	0.258286	+	1.74569i
$269$	−2.46307	+	4.26616i	−0.150176	+	0.260112i	−0.931292	−	0.364274i	$-0.881317\pi$
$269$	−2.46307	+	4.26616i	−0.150176	+	0.260112i	0.781116	+	0.624386i	$0.214651\pi$
$270$	1.92079	−	2.51209i	0.116895	−	0.152881i
$271$	9.47009	−	5.46756i	0.575267	−	0.332130i	−0.183983	−	0.982929i	$-0.558899\pi$
$271$	9.47009	−	5.46756i	0.575267	−	0.332130i	0.759250	+	0.650799i	$0.225566\pi$
$272$	−0.0473317	−	1.47941i	−0.00286991	−	0.0897027i
$273$	15.7863	−	1.13638i	0.955432	−	0.0687766i
$274$	−5.99529	+	1.24245i	−0.362188	+	0.0750591i
$275$	3.98286	−	27.5688i	0.240175	−	1.66246i
$276$	10.5327	+	1.21565i	0.633994	+	0.0731736i
$277$	−10.8608	+	2.91014i	−0.652562	+	0.174854i	−0.569887	−	0.821723i	$-0.693013\pi$
$277$	−10.8608	+	2.91014i	−0.652562	+	0.174854i	−0.0826752	+	0.996577i	$0.526346\pi$
$278$	27.6926	+	1.59281i	1.66089	+	0.0955304i
$279$	−8.74118			−0.523321
$280$	9.62917	+	13.6850i	0.575453	+	0.817835i
$281$	−12.9485			−0.772444			−0.386222	−	0.922406i	$-0.626220\pi$
$281$	−12.9485			−0.772444			−0.386222	+	0.922406i	$0.626220\pi$
$282$	1.83251	+	0.105402i	0.109125	+	0.00627657i
$283$	−22.2576	+	5.96390i	−1.32308	+	0.354517i	−0.850129	−	0.526574i	$-0.823476\pi$
$283$	−22.2576	+	5.96390i	−1.32308	+	0.354517i	−0.472947	+	0.881091i	$0.656810\pi$
$284$	2.49118	−	21.5842i	0.147825	−	1.28079i
$285$	−8.30651	−	5.62611i	−0.492035	−	0.333262i
$286$	46.1499	−	9.56401i	2.72890	−	0.565532i
$287$	9.61888	+	14.1978i	0.567785	+	0.838069i
$288$	1.32446	+	5.49962i	0.0780447	+	0.324068i
$289$	14.6038	−	8.43153i	0.859050	−	0.495973i
$290$	−6.75479	+	0.901017i	−0.396655	+	0.0529096i
$291$	3.75843	−	6.50980i	0.220323	−	0.381611i
$292$	14.5243	−	2.14896i	0.849968	−	0.125758i
$293$	−7.48370	+	7.48370i	−0.437203	+	0.437203i	−0.891070	−	0.453867i	$-0.850044\pi$
$293$	−7.48370	+	7.48370i	−0.437203	+	0.437203i	0.453867	+	0.891070i	$0.350044\pi$
$294$	−9.74738	−	1.72877i	−0.568479	−	0.100824i
$295$	2.46174	−	7.10495i	0.143328	−	0.413666i
$296$	3.95322	+	1.83298i	0.229776	+	0.106540i
$297$	1.44188	+	5.38117i	0.0836664	+	0.312247i
$298$	−23.6897	+	11.9189i	−1.37231	+	0.690441i
$299$	27.4643	−	15.8565i	1.58830	−	0.917005i
$300$	8.64313	−	5.02954i	0.499012	−	0.290380i
$301$	−3.39611	+	17.6645i	−0.195749	+	1.01817i
$302$	10.7037	−	16.2998i	0.615928	−	0.937951i
$303$	13.6061	+	3.64575i	0.781652	+	0.209443i
$304$	17.1778	−	5.19690i	0.985213	−	0.298063i
$305$	−16.4790	−	19.0309i	−0.943587	−	1.08970i
$306$	0.390681	−	0.348183i	0.0223337	−	0.0199043i
$307$	−20.7138	+	20.7138i	−1.18220	+	1.18220i	−0.203028	+	0.979173i	$0.565078\pi$
$307$	−20.7138	+	20.7138i	−1.18220	+	1.18220i	−0.979173	+	0.203028i	$0.934922\pi$
$308$	−29.4516	−	1.26860i	−1.67816	−	0.0722854i
$309$	9.21414			0.524174
$310$	−25.5559	−	10.5345i	−1.45148	−	0.598322i
$311$	−9.94499	−	5.74174i	−0.563928	−	0.325584i	0.190792	−	0.981630i	$-0.438894\pi$
$311$	−9.94499	−	5.74174i	−0.563928	−	0.325584i	−0.754721	+	0.656046i	$0.772228\pi$
$312$	12.9850	+	10.8478i	0.735131	+	0.614135i
$313$	−2.95266	+	11.0195i	−0.166894	+	0.622857i	0.830897	+	0.556426i	$0.187828\pi$
$313$	−2.95266	+	11.0195i	−0.166894	+	0.622857i	−0.997791	+	0.0664309i	$0.978839\pi$
$314$	1.39048	+	6.70957i	0.0784692	+	0.378643i
$315$	−1.53050	+	5.71468i	−0.0862337	+	0.321986i
$316$	−1.04137	−	2.40459i	−0.0585815	−	0.135269i
$317$	1.27621	−	4.76290i	0.0716794	−	0.267511i	−0.920780	−	0.390081i	$-0.872447\pi$
$317$	1.27621	−	4.76290i	0.0716794	−	0.267511i	0.992460	+	0.122570i	$0.0391136\pi$
$318$	−2.26366	+	1.13891i	−0.126940	+	0.0638667i
$319$	6.00267	−	10.3969i	0.336085	−	0.582116i
$320$	−2.75570	+	17.6750i	−0.154048	+	0.988063i
$321$	−7.74237			−0.432137
$322$	−19.0839	+	5.40934i	−1.06350	+	0.301451i
$323$	−1.17398	−	1.17398i	−0.0653221	−	0.0653221i
$324$	−1.19199	+	1.60597i	−0.0662219	+	0.0892207i
$325$	11.7929	−	27.4876i	0.654153	−	1.52474i
$326$	3.59129	+	1.18714i	0.198903	+	0.0657497i
$327$	1.30148	−	4.85720i	0.0719721	−	0.268604i
$328$	−3.14437	+	18.0618i	−0.173619	+	0.997294i
$329$	−3.24460	+	1.12464i	−0.178881	+	0.0620035i
$330$	−2.26967	+	17.4702i	−0.124941	+	0.961704i
$331$	2.95564	+	5.11931i	0.162456	+	0.281383i	0.935749	−	0.352666i	$-0.114725\pi$
$331$	2.95564	+	5.11931i	0.162456	+	0.281383i	−0.773293	+	0.634049i	$0.781392\pi$
$332$	−11.9580	−	15.0785i	−0.656283	−	0.827541i
$333$	0.398738	+	1.48811i	0.0218507	+	0.0815480i
$334$	20.2048	−	18.0069i	1.10556	−	0.985295i
$335$	−29.0575	+	14.1031i	−1.58758	+	0.770535i
$336$	−6.21303	−	8.56728i	−0.338949	−	0.467383i
$337$	22.1222	−	22.1222i	1.20507	−	1.20507i	0.232469	−	0.972604i	$-0.425320\pi$
$337$	22.1222	−	22.1222i	1.20507	−	1.20507i	0.972604	−	0.232469i	$-0.0746804\pi$
$338$	32.1705	+	1.85037i	1.74985	+	0.100647i
$339$	2.38839	+	1.37894i	0.129719	+	0.0748935i
$340$	1.56182	−	0.547123i	0.0847017	−	0.0296719i
$341$	42.1729	−	24.3486i	2.28379	−	1.31855i
$342$	5.30379	+	3.48286i	0.286796	+	0.188332i
$343$	18.0916	−	3.96179i	0.976852	−	0.213917i
$344$	−15.7283	+	11.0640i	−0.848014	+	0.596533i
$345$	2.23946	+	11.6406i	0.120568	+	0.626710i
$346$	−2.99414	+	9.05776i	−0.160966	+	0.486948i
$347$	4.35285	+	16.2451i	0.233673	+	0.872081i	0.978742	+	0.205094i	$0.0657499\pi$
$347$	4.35285	+	16.2451i	0.233673	+	0.872081i	−0.745069	+	0.666988i	$0.767583\pi$
$348$	4.26353	−	0.630818i	0.228549	−	0.0338154i
$349$	−0.714880			−0.0382667			−0.0191333	−	0.999817i	$-0.506091\pi$
$349$	−0.714880			−0.0382667			−0.0191333	+	0.999817i	$0.506091\pi$
$350$	−11.3617	+	14.8631i	−0.607309	+	0.794466i
$351$			5.98211i			0.319301i
$352$	−21.7092	−	22.8443i	−1.15711	−	1.21761i
$353$	−1.47233	+	0.394510i	−0.0783643	+	0.0209977i	−0.297788	−	0.954632i	$-0.596249\pi$
$353$	−1.47233	+	0.394510i	−0.0783643	+	0.0209977i	0.219424	+	0.975630i	$0.429582\pi$
$354$	−1.49260	+	4.51534i	−0.0793307	+	0.239988i
$355$	23.8547	−	4.58923i	1.26608	−	0.243571i
$356$	6.85144	−	2.96719i	0.363126	−	0.157261i
$357$	−0.427381	+	0.880833i	−0.0226194	+	0.0466186i
$358$	0.993551	−	1.51300i	0.0525108	−	0.0799647i
$359$	8.03539	+	13.9177i	0.424092	+	0.734548i	0.996335	−	0.0855354i	$-0.0272601\pi$
$359$	8.03539	+	13.9177i	0.424092	+	0.734548i	−0.572243	+	0.820084i	$0.693927\pi$
$360$	−5.42040	+	3.25871i	−0.285680	+	0.171749i
$361$	0.565127	−	0.978828i	0.0297435	−	0.0515173i
$362$	−27.2645	−	1.56818i	−1.43299	−	0.0824220i
$363$	−14.1676	−	14.1676i	−0.743606	−	0.743606i
$364$	−30.1948	−	9.50096i	−1.58264	−	0.497986i
$365$	7.16761	+	14.7679i	0.375170	+	0.772987i
$366$	10.5931	+	11.8861i	0.553711	+	0.621295i
$367$	17.6035	−	4.71685i	0.918897	−	0.246218i	0.231783	−	0.972767i	$-0.425544\pi$
$367$	17.6035	−	4.71685i	0.918897	−	0.246218i	0.687114	+	0.726550i	$0.258877\pi$
$368$	−18.6939	−	10.0100i	−0.974488	−	0.521805i
$369$	−5.61344	+	3.24092i	−0.292224	+	0.168716i
$370$	−0.627656	+	4.83123i	−0.0326303	+	0.251163i
$371$	3.10286	−	3.58423i	0.161093	−	0.186084i
$372$	16.2565	+	6.43108i	0.842861	+	0.333436i
$373$	−14.3013	−	3.83202i	−0.740493	−	0.198414i	−0.131196	−	0.991356i	$-0.541882\pi$
$373$	−14.3013	−	3.83202i	−0.740493	−	0.198414i	−0.609297	+	0.792942i	$0.708548\pi$
$374$	−0.915025	+	2.76810i	−0.0473148	+	0.143135i
$375$	8.26526	+	7.52898i	0.426816	+	0.388795i
$376$	−3.33049	−	1.54424i	−0.171757	−	0.0796382i
$377$	9.11551	−	9.11551i	0.469472	−	0.469472i
$378$	0.916245	−	3.62774i	0.0471266	−	0.186591i
$379$		−	21.4047i		−	1.09949i	−0.835334	−	0.549743i	$-0.814726\pi$
$379$		−	21.4047i		−	1.09949i	0.835334	−	0.549743i	$-0.185274\pi$
$380$	11.3089	+	16.5745i	0.580133	+	0.850255i
$381$	−17.4557	−	10.0780i	−0.894282	−	0.516314i
$382$	8.79202	+	17.4748i	0.449839	+	0.894089i
$383$	−17.8415	−	4.78061i	−0.911658	−	0.244278i	−0.227642	−	0.973745i	$-0.573101\pi$
$383$	−17.8415	−	4.78061i	−0.911658	−	0.244278i	−0.684016	+	0.729467i	$0.739768\pi$
$384$	1.58301	−	11.2024i	0.0807824	−	0.571671i
$385$	−8.53417	−	31.8344i	−0.434942	−	1.62243i
$386$	5.53166	+	26.6923i	0.281554	+	1.35860i
$387$	−6.56717	−	1.75967i	−0.333828	−	0.0894489i
$388$	−11.7792	+	9.34151i	−0.597998	+	0.474243i
$389$	−12.1014	+	20.9602i	−0.613563	+	1.06272i	0.377072	+	0.926184i	$0.376931\pi$
$389$	−12.1014	+	20.9602i	−0.613563	+	1.06272i	−0.990635	+	0.136538i	$0.956402\pi$
$390$	−7.20941	+	17.4894i	−0.365063	+	0.885612i
$391$			1.96171i			0.0992080i
$392$	16.8559	+	10.3865i	0.851352	+	0.524595i
$393$	1.65883	+	1.65883i	0.0836771	+	0.0836771i
$394$	13.2565	−	11.8145i	0.667852	−	0.595205i
$395$	2.21477	−	1.91779i	0.111437	−	0.0964947i
$396$	1.27749	−	11.0685i	0.0641964	−	0.556214i
$397$	1.12078	−	4.18281i	0.0562504	−	0.209929i	−0.932081	−	0.362251i	$-0.882008\pi$
$397$	1.12078	−	4.18281i	0.0562504	−	0.209929i	0.988331	+	0.152322i	$0.0486750\pi$
$398$	−15.5608	−	10.2183i	−0.779990	−	0.512200i
$399$	−11.6571	−	2.24116i	−0.583587	−	0.112198i
$400$	−19.7745	+	2.99479i	−0.988725	+	0.149740i
$401$	−13.4159	−	23.2370i	−0.669958	−	1.16040i	−0.977915	−	0.209001i	$-0.932979\pi$
$401$	−13.4159	−	23.2370i	−0.669958	−	1.16040i	0.307958	−	0.951400i	$-0.400355\pi$
$402$	18.2483	−	9.18119i	0.910143	−	0.457916i
$403$	50.5089	−	13.5338i	2.51603	−	0.674168i
$404$	−22.6219	−	16.7906i	−1.12548	−	0.835361i
$405$	−2.11284	−	0.732062i	−0.104988	−	0.0363765i
$406$	−6.92410	+	4.13176i	−0.343637	+	0.205056i
$407$	−6.06890	−	6.06890i	−0.300824	−	0.300824i
$408$	−0.982740	+	0.360105i	−0.0486529	+	0.0178279i
$409$	12.0607	+	6.96325i	0.596364	+	0.344311i	0.767610	−	0.640918i	$-0.221446\pi$
$409$	12.0607	+	6.96325i	0.596364	+	0.344311i	−0.171246	+	0.985228i	$0.554779\pi$
$410$	−20.3174	+	2.71013i	−1.00341	+	0.133844i
$411$	2.16469	+	3.74936i	0.106776	+	0.184942i
$412$	−17.1361	−	6.77904i	−0.844235	−	0.333980i
$413$	−0.638796	−	8.87404i	−0.0314331	−	0.436663i
$414$	−1.52137	−	7.34120i	−0.0747715	−	0.360800i
$415$	12.0660	−	17.8145i	0.592297	−	0.874480i
$416$	−16.1681	−	29.7276i	−0.792705	−	1.45752i
$417$	−5.07648	−	18.9457i	−0.248596	−	0.927774i
$418$	−35.2903	−	2.02981i	−1.72611	−	0.0992812i
$419$		−	1.69659i		−	0.0828841i	−0.999141	−	0.0414420i	$-0.986805\pi$
$419$		−	1.69659i		−	0.0828841i	0.999141	−	0.0414420i	$-0.0131952\pi$
$420$	7.05077	−	9.50193i	0.344043	−	0.463646i
$421$			10.8090i			0.526800i	0.964687	+	0.263400i	$0.0848439\pi$
$421$			10.8090i			0.526800i	−0.964687	+	0.263400i	$0.915156\pi$
$422$	0.0228867	−	0.397908i	0.00111411	−	0.0193699i
$423$	−0.335928	−	1.25370i	−0.0163334	−	0.0609569i
$424$	5.04780	−	0.452666i	0.245143	−	0.0219834i
$425$	1.10779	+	1.48192i	0.0537356	+	0.0718838i
$426$	−15.0440	+	3.11769i	−0.728886	+	0.151053i
$427$	−26.7985	−	13.0026i	−1.29687	−	0.629241i
$428$	14.3990	+	5.69623i	0.696000	+	0.275338i
$429$	−16.6632	−	28.8614i	−0.804505	−	1.39344i
$430$	−17.0793	−	13.0591i	−0.823635	−	0.629767i
$431$	2.61429	+	1.50936i	0.125926	+	0.0727034i	0.561640	−	0.827382i	$-0.310171\pi$
$431$	2.61429	+	1.50936i	0.125926	+	0.0727034i	−0.435714	+	0.900085i	$0.643504\pi$
$432$	3.39838	−	2.10975i	0.163504	−	0.101505i
$433$	−8.45880	−	8.45880i	−0.406504	−	0.406504i	0.474014	−	0.880518i	$-0.342805\pi$
$433$	−8.45880	−	8.45880i	−0.406504	−	0.406504i	−0.880518	+	0.474014i	$0.842805\pi$
$434$	−32.7031	+	0.471176i	−1.56980	+	0.0226172i
$435$	2.10402	+	4.33505i	0.100880	+	0.207850i
$436$	−5.99399	+	8.07570i	−0.287060	+	0.386756i
$437$	−22.9748	+	6.15608i	−1.09903	+	0.294485i
$438$	−4.66615	−	9.27433i	−0.222957	−	0.443145i
$439$	5.28278	+	9.15005i	0.252133	+	0.436708i	0.964113	−	0.265492i	$-0.0855345\pi$
$439$	5.28278	+	9.15005i	0.252133	+	0.436708i	−0.711980	+	0.702200i	$0.752201\pi$
$440$	17.0743	−	30.8206i	0.813984	−	1.46931i
$441$	1.00259	+	6.92783i	0.0477425	+	0.329897i
$442$	−1.71837	+	2.61678i	−0.0817347	+	0.124468i
$443$	7.74694	−	28.9120i	0.368068	−	1.37365i	−0.495145	−	0.868810i	$-0.664885\pi$
$443$	7.74694	−	28.9120i	0.368068	−	1.37365i	0.863213	−	0.504839i	$-0.168448\pi$
$444$	0.353279	−	3.06089i	0.0167659	−	0.145264i
$445$	5.46440	+	6.31058i	0.259038	+	0.299150i
$446$	−0.879995	−	0.987403i	−0.0416689	−	0.0467549i
$447$	13.2595	+	13.2595i	0.627154	+	0.627154i
$448$	5.25162	+	20.5042i	0.248116	+	0.968730i
$449$			4.41290i			0.208257i	0.994564	+	0.104129i	$0.0332054\pi$
$449$			4.41290i			0.208257i	−0.994564	+	0.104129i	$0.966795\pi$
$450$	−5.29489	−	4.68659i	−0.249604	−	0.220928i
$451$	18.0552	−	31.2725i	0.850185	−	1.47256i
$452$	−3.42732	−	4.32168i	−0.161207	−	0.203275i
$453$	−13.3188	−	3.56877i	−0.625773	−	0.167675i
$454$	30.6928	−	6.36071i	1.44049	−	0.298523i
$455$	−0.00432617	−	35.3906i	−0.000202814	−	1.65914i
$456$	−7.30136	−	10.3794i	−0.341918	−	0.486060i
$457$	−35.8936	−	9.61767i	−1.67903	−	0.449896i	−0.711510	−	0.702676i	$-0.751988\pi$
$457$	−35.8936	−	9.61767i	−1.67903	−	0.449896i	−0.967524	+	0.252780i	$0.918655\pi$
$458$	−6.02242	+	3.03003i	−0.281409	+	0.141584i
$459$	−0.320466	−	0.185021i	−0.0149581	−	0.00863606i
$460$	4.39941	−	23.2964i	0.205124	−	1.08620i
$461$			15.8272i			0.737148i	0.929598	+	0.368574i	$0.120154\pi$
$461$			15.8272i			0.737148i	−0.929598	+	0.368574i	$0.879846\pi$
$462$	5.68452	+	20.0547i	0.264468	+	0.933028i
$463$	−8.81202	+	8.81202i	−0.409529	+	0.409529i	−0.881574	−	0.472045i	$-0.843516\pi$
$463$	−8.81202	+	8.81202i	−0.409529	+	0.409529i	0.472045	+	0.881574i	$0.343516\pi$
$464$	−8.39325	−	1.96360i	−0.389647	−	0.0911580i
$465$	−1.40099	+	19.4956i	−0.0649694	+	0.904087i
$466$	−0.0151705	−	0.00501479i	−0.000702761	−	0.000232305i
$467$	32.7580	+	8.77747i	1.51586	+	0.406173i	0.918376	−	0.395709i	$-0.129501\pi$
$467$	32.7580	+	8.77747i	1.51586	+	0.406173i	0.597482	+	0.801882i	$0.296168\pi$
$468$	4.40117	−	11.1253i	0.203444	−	0.514267i
$469$	−25.0134	+	28.8940i	−1.15501	+	1.33420i
$470$	0.528785	−	4.07019i	0.0243910	−	0.187744i
$471$	4.19606	−	2.42260i	0.193344	−	0.111627i
$472$	6.09791	−	7.29932i	0.280679	−	0.335979i
$473$	36.5857	−	9.80311i	1.68221	−	0.450747i
$474$	−1.38327	+	1.23280i	−0.0635359	+	0.0566245i
$475$	−13.8793	+	17.6244i	−0.636828	+	0.808664i
$476$	1.44287	−	1.32371i	0.0661340	−	0.0606720i
$477$	1.26701	+	1.26701i	0.0580125	+	0.0580125i
$478$	0.838288	−	14.5745i	0.0383424	−	0.666621i
$479$	−9.32972	+	16.1595i	−0.426286	+	0.738348i	−0.996540	−	0.0831201i	$-0.973511\pi$
$479$	−9.32972	+	16.1595i	−0.426286	+	0.738348i	0.570254	+	0.821468i	$0.306845\pi$
$480$	12.4782	−	2.07252i	0.569548	−	0.0945972i
$481$	−4.60804	−	7.98136i	−0.210108	−	0.363918i
$482$	−12.1620	−	7.98645i	−0.553962	−	0.363773i
$483$	7.86700	+	11.6120i	0.357961	+	0.528362i
$484$	15.9249	+	36.7718i	0.723861	+	1.67144i
$485$	−13.9165	−	9.42585i	−0.631917	−	0.428006i
$486$	1.34275	+	0.443862i	0.0609085	+	0.0201340i
$487$	−17.4237	+	4.66866i	−0.789542	+	0.211557i	−0.630987	−	0.775793i	$-0.717350\pi$
$487$	−17.4237	+	4.66866i	−0.789542	+	0.211557i	−0.158554	+	0.987350i	$0.550683\pi$
$488$	−10.9558	−	29.8988i	−0.495947	−	1.35346i
$489$		−	2.67457i		−	0.120948i
$490$	−5.41796	+	21.4627i	−0.244758	+	0.969584i
$491$	20.1191			0.907962			0.453981	−	0.891011i	$-0.350003\pi$
$491$	20.1191			0.907962			0.453981	+	0.891011i	$0.350003\pi$
$492$	12.8241	−	1.89741i	0.578154	−	0.0855418i
$493$	0.206391	+	0.770260i	0.00929536	+	0.0346908i
$494$	−36.0392	−	11.9132i	−1.62148	−	0.535998i
$495$	12.2328	−	2.35338i	0.549824	−	0.105777i
$496$	−25.5018	−	23.9206i	−1.14506	−	1.07406i
$497$	23.7959	−	16.1215i	1.06739	−	0.723150i
$498$	−7.46950	+	11.3747i	−0.334716	+	0.509714i
$499$	−8.51618	+	4.91682i	−0.381237	+	0.220107i	−0.678356	−	0.734733i	$-0.737307\pi$
$499$	−8.51618	+	4.91682i	−0.381237	+	0.220107i	0.297119	+	0.954840i	$0.403974\pi$
$500$	−9.83218	−	20.0830i	−0.439708	−	0.898141i
$501$	−16.5735	−	9.56871i	−0.740449	−	0.427498i
$502$	0.0898401	−	1.56196i	0.00400976	−	0.0697138i
$503$	−11.2005	+	11.2005i	−0.499406	+	0.499406i	−0.911253	−	0.411847i	$-0.864884\pi$
$503$	−11.2005	+	11.2005i	−0.499406	+	0.499406i	0.411847	+	0.911253i	$0.364884\pi$
$504$	−4.37301	+	6.07263i	−0.194789	+	0.270496i
$505$	10.3119	−	29.7616i	0.458873	−	1.32438i
$506$	27.7890	+	31.1808i	1.23537	+	1.38615i
$507$	−5.89735	−	22.0092i	−0.261910	−	0.977463i
$508$	25.0488	+	31.5853i	1.11136	+	1.40137i
$509$	−2.28874	−	3.96422i	−0.101447	−	0.175711i	0.810834	−	0.585276i	$-0.199014\pi$
$509$	−2.28874	−	3.96422i	−0.101447	−	0.175711i	−0.912281	+	0.409565i	$0.865680\pi$
$510$	−0.713943	−	0.927147i	−0.0316139	−	0.0410548i
$511$	14.6848	+	12.7126i	0.649615	+	0.562371i
$512$	−11.1859	+	19.6692i	−0.494351	+	0.869263i
$513$	1.16124	−	4.33380i	0.0512699	−	0.191342i
$514$	9.04246	−	27.3549i	0.398846	−	1.20657i
$515$	1.47679	−	20.5504i	0.0650753	−	0.905561i
$516$	10.9187	+	8.10418i	0.480671	+	0.356766i
$517$	5.11290	+	5.11290i	0.224865	+	0.224865i
$518$	1.57200	+	5.54593i	0.0690698	+	0.243674i
$519$	6.74566			0.296102
$520$	26.2752	−	27.2221i	1.15224	−	1.19377i
$521$	−10.5312	+	18.2406i	−0.461382	+	0.799137i	−0.999030	−	0.0440323i	$-0.985980\pi$
$521$	−10.5312	+	18.2406i	−0.461382	+	0.799137i	0.537648	+	0.843169i	$0.319313\pi$
$522$	−1.36973	−	2.72244i	−0.0599513	−	0.119158i
$523$	0.144603	−	0.539666i	0.00632305	−	0.0235980i	−0.962692	−	0.270599i	$-0.912778\pi$
$523$	0.144603	−	0.539666i	0.00632305	−	0.0235980i	0.969015	+	0.247001i	$0.0794450\pi$
$524$	−1.86459	−	4.30548i	−0.0814552	−	0.188086i
$525$	12.5002	+	4.32941i	0.545556	+	0.188951i
$526$	22.5153	−	4.66601i	0.981712	−	0.203448i
$527$	−0.837179	+	3.12439i	−0.0364681	+	0.136101i
$528$	−10.5192	+	19.6449i	−0.457789	+	0.854936i
$529$	4.42010	+	2.55195i	0.192178	+	0.110954i
$530$	2.17731	+	5.23123i	0.0945765	+	0.227230i
$531$	3.36275			0.145931
$532$	20.0306	+	12.7444i	0.868438	+	0.552541i
$533$	27.4181	−	27.4181i	1.18761	−	1.18761i
$534$	−3.51265	−	3.94139i	−0.152007	−	0.170561i
$535$	−1.24091	+	17.2679i	−0.0536491	+	0.746558i
$536$	−40.6923	+	3.64913i	−1.75764	+	0.157618i
$537$	−1.23630	−	0.331264i	−0.0533501	−	0.0142951i
$538$	−5.82328	−	3.82400i	−0.251060	−	0.164864i
$539$	−24.1346	−	30.6315i	−1.03955	−	1.31939i
$540$	3.39078	+	2.91592i	0.145916	+	0.125481i
$541$	11.9490	−	6.89877i	0.513728	−	0.296601i	−0.220637	−	0.975356i	$-0.570813\pi$
$541$	11.9490	−	6.89877i	0.513728	−	0.296601i	0.734365	+	0.678755i	$0.237480\pi$
$542$	6.95049	+	13.8146i	0.298549	+	0.593389i
$543$	4.99799	+	18.6528i	0.214484	+	0.800467i
$544$	2.09260	+	0.0533133i	0.0897194	+	0.00228579i
$545$	−10.6245	−	3.68120i	−0.455103	−	0.157685i
$546$	0.322453	+	22.3807i	0.0137997	+	0.957804i
$547$	−2.63775	+	2.63775i	−0.112782	+	0.112782i	−0.761246	−	0.648464i	$-0.775412\pi$
$547$	−2.63775	+	2.63775i	−0.112782	+	0.112782i	0.648464	+	0.761246i	$0.275412\pi$
$548$	−1.26733	−	8.56552i	−0.0541375	−	0.365901i
$549$	5.62909	−	9.74986i	0.240244	−	0.416114i
$550$	38.6004	+	7.86212i	1.64592	+	0.335242i
$551$	−8.37330	+	4.83433i	−0.356715	+	0.205949i
$552$	−2.57169	+	14.7722i	−0.109458	+	0.628746i
$553$	1.51322	−	3.11874i	0.0643485	−	0.132622i
$554$	−3.22679	−	15.5705i	−0.137093	−	0.661526i
$555$	3.38287	−	0.650806i	0.143595	−	0.0276252i
$556$	−4.49772	+	38.9693i	−0.190746	+	1.65267i
$557$	−17.5592	+	4.70498i	−0.744008	+	0.199356i	−0.610859	−	0.791740i	$-0.709176\pi$
$557$	−17.5592	+	4.70498i	−0.744008	+	0.199356i	−0.133149	+	0.991096i	$0.542509\pi$
$558$	0.709852	−	12.3415i	0.0300504	−	0.522457i
$559$	40.6714			1.72022
$560$	−20.1035	+	12.4839i	−0.849529	+	0.527541i
$561$	2.06151			0.0870369
$562$	1.05152	−	18.2818i	0.0443557	−	0.771170i
$563$	−24.3030	+	6.51198i	−1.02425	+	0.274447i	−0.731572	−	0.681764i	$-0.761213\pi$
$563$	−24.3030	+	6.51198i	−1.02425	+	0.274447i	−0.292678	+	0.956211i	$0.594547\pi$
$564$	−0.297629	+	2.57873i	−0.0125324	+	0.108584i
$565$	3.45826	−	5.10585i	0.145490	−	0.214805i
$566$	−6.61283	−	31.9094i	−0.277958	−	1.34125i
$567$	−2.63892	+	0.189962i	−0.110824	+	0.00797767i
$568$	30.2721	+	5.27006i	1.27019	+	0.221127i
$569$	−13.9329	+	8.04416i	−0.584097	+	0.337229i	−0.762760	−	0.646682i	$-0.776156\pi$
$569$	−13.9329	+	8.04416i	−0.584097	+	0.337229i	0.178663	+	0.983910i	$0.442823\pi$
$570$	8.61795	−	11.2709i	0.360966	−	0.472087i
$571$	−20.7948	+	36.0177i	−0.870236	+	1.50729i	−0.00848298	+	0.999964i	$0.502700\pi$
$571$	−20.7948	+	36.0177i	−0.870236	+	1.50729i	−0.861753	+	0.507328i	$0.830633\pi$
$572$	9.75550	+	65.9348i	0.407898	+	2.75687i
$573$	9.78096	−	9.78096i	0.408605	−	0.408605i
$574$	−20.8267	+	12.4277i	−0.869290	+	0.518724i
$575$	26.3212	−	3.12900i	1.09767	−	0.130488i
$576$	−7.87236	+	1.42337i	−0.328015	+	0.0593071i
$577$	8.56429	+	31.9623i	0.356536	+	1.33061i	0.878541	+	0.477667i	$0.158518\pi$
$577$	8.56429	+	31.9623i	0.356536	+	1.33061i	−0.522005	+	0.852943i	$0.674816\pi$
$578$	10.7184	+	21.3036i	0.445825	+	0.886112i
$579$	16.6929	−	9.63768i	0.693735	−	0.400528i
$580$	−0.723587	−	9.61012i	−0.0300453	−	0.399039i
$581$	4.80649	−	25.0004i	0.199407	−	1.03719i
$582$	8.88584	+	5.83510i	0.368330	+	0.241873i
$583$	−9.64213	−	2.58360i	−0.399336	−	0.107002i
$584$	1.85459	+	20.6810i	0.0767436	+	0.855787i
$585$	13.3420	+	0.958781i	0.551623	+	0.0396407i
$586$	−9.95836	−	11.1738i	−0.411376	−	0.461587i
$587$	−22.3262	+	22.3262i	−0.921501	+	0.921501i	−0.997136	−	0.0756346i	$-0.975902\pi$
$587$	−22.3262	+	22.3262i	−0.921501	+	0.921501i	0.0756346	+	0.997136i	$0.475902\pi$
$588$	3.23237	−	13.6217i	0.133301	−	0.561751i
$589$	−39.2188			−1.61598
$590$	9.83142	+	4.05266i	0.404753	+	0.166845i
$591$	−10.8740	−	6.27810i	−0.447296	−	0.258247i
$592$	−2.90898	+	5.43262i	−0.119558	+	0.223279i
$593$	−4.18981	+	15.6366i	−0.172055	+	0.642117i	0.824980	+	0.565162i	$0.191186\pi$
$593$	−4.18981	+	15.6366i	−0.172055	+	0.642117i	−0.997035	+	0.0769548i	$0.975480\pi$
$594$	−7.71466	+	1.59877i	−0.316536	+	0.0655983i
$595$	1.89604	+	1.09437i	0.0777300	+	0.0448648i
$596$	−14.9042	−	34.4149i	−0.610501	−	1.40969i
$597$	−3.40695	+	12.7149i	−0.139437	+	0.520386i
$598$	20.1572	+	40.0639i	0.824288	+	1.63834i
$599$	−1.79982	+	3.11738i	−0.0735386	+	0.127373i	−0.900450	−	0.434960i	$-0.856763\pi$
$599$	−1.79982	+	3.11738i	−0.0735386	+	0.127373i	0.826911	+	0.562332i	$0.190096\pi$
$600$	6.39921	+	12.6115i	0.261247	+	0.514863i
$601$	17.5729			0.716814			0.358407	−	0.933565i	$-0.383320\pi$
$601$	17.5729			0.716814			0.358407	+	0.933565i	$0.383320\pi$
$602$	−24.6644	−	6.22940i	−1.00525	−	0.253891i
$603$	−10.2139	−	10.2139i	−0.415942	−	0.415942i
$604$	22.1442	+	16.4360i	0.901035	+	0.668772i
$605$	−33.8690	+	29.3275i	−1.37697	+	1.19233i
$606$	−6.25229	+	18.9142i	−0.253982	+	0.768335i
$607$	11.5490	−	43.1013i	0.468758	−	1.74943i	−0.175362	−	0.984504i	$-0.556110\pi$
$607$	11.5490	−	43.1013i	0.468758	−	1.74943i	0.644120	−	0.764924i	$-0.277224\pi$
$608$	5.94243	+	24.6750i	0.240998	+	1.00070i
$609$	4.31064	+	3.73171i	0.174676	+	0.151217i
$610$	28.2075	−	21.7210i	1.14209	−	0.879457i
$611$	3.88216	+	6.72410i	0.157055	+	0.272028i
$612$	0.459867	+	0.579870i	0.0185890	+	0.0234399i
$613$	−10.4904	−	39.1507i	−0.423703	−	1.58128i	−0.766738	−	0.641960i	$-0.778121\pi$
$613$	−10.4904	−	39.1507i	−0.423703	−	1.58128i	0.343035	−	0.939323i	$-0.388545\pi$
$614$	−27.5633	−	30.9276i	−1.11236	−	1.24813i
$615$	6.32859	+	13.0392i	0.255193	+	0.525791i
$616$	4.18282	−	41.4792i	0.168531	−	1.67124i
$617$	6.80159	−	6.80159i	0.273822	−	0.273822i	−0.556815	−	0.830637i	$-0.687977\pi$
$617$	6.80159	−	6.80159i	0.273822	−	0.273822i	0.830637	+	0.556815i	$0.187977\pi$
$618$	−0.748260	+	13.0093i	−0.0300994	+	0.523309i
$619$	−17.8113	−	10.2834i	−0.715898	−	0.413324i	0.0973433	−	0.995251i	$-0.468966\pi$
$619$	−17.8113	−	10.2834i	−0.715898	−	0.413324i	−0.813241	+	0.581927i	$0.802299\pi$
$620$	16.9489	−	35.2264i	0.680683	−	1.41473i
$621$	−4.59107	+	2.65066i	−0.184233	+	0.106367i
$622$	8.91426	−	13.5749i	0.357429	−	0.544302i
$623$	8.88629	+	4.31163i	0.356022	+	0.172742i
$624$	−16.3702	+	17.4524i	−0.655334	+	0.698653i
$625$	18.1167	−	17.2274i	0.724669	−	0.689098i
$626$	−15.3184	−	5.06367i	−0.612246	−	0.202385i
$627$	6.46925	+	24.1436i	0.258357	+	0.964201i
$628$	−9.58603	+	1.41832i	−0.382524	+	0.0565970i
$629$	0.570090			0.0227310
$630$	−7.94416	−	2.62495i	−0.316503	−	0.104581i
$631$			39.2014i			1.56058i	0.625416	+	0.780291i	$0.284929\pi$
$631$			39.2014i			1.56058i	−0.625416	+	0.780291i	$0.715071\pi$
$632$	3.47956	−	1.27502i	0.138409	−	0.0507174i
$633$	−0.272225	+	0.0729425i	−0.0108200	+	0.00289921i
$634$	6.62100	+	2.18865i	0.262954	+	0.0869223i
$635$	−25.2749	+	37.3164i	−1.00301	+	1.48086i
$636$	−1.42417	−	3.28851i	−0.0564721	−	0.130398i
$637$	−16.5195	−	38.4786i	−0.654526	−	1.52458i
$638$	14.1918	+	9.31936i	0.561857	+	0.368957i
$639$	5.43188	+	9.40830i	0.214882	+	0.372187i
$640$	−24.7312	−	5.32607i	−0.977587	−	0.210531i
$641$	−1.84164	+	3.18982i	−0.0727406	+	0.125990i	−0.900101	−	0.435680i	$-0.856508\pi$
$641$	−1.84164	+	3.18982i	−0.0727406	+	0.125990i	0.827361	+	0.561671i	$0.189841\pi$
$642$	0.628741	−	10.9313i	0.0248144	−	0.431424i
$643$	−1.34191	−	1.34191i	−0.0529196	−	0.0529196i	0.680152	−	0.733071i	$-0.261914\pi$
$643$	−1.34191	−	1.34191i	−0.0529196	−	0.0529196i	−0.733071	+	0.680152i	$0.761914\pi$
$644$	−6.08758	−	27.3834i	−0.239884	−	1.07906i
$645$	−4.97717	+	14.3648i	−0.195976	+	0.565615i
$646$	1.75286	−	1.56219i	0.0689653	−	0.0614634i
$647$	28.6343	−	7.67253i	1.12573	−	0.301638i	0.352530	−	0.935801i	$-0.385322\pi$
$647$	28.6343	−	7.67253i	1.12573	−	0.301638i	0.773200	+	0.634162i	$0.218655\pi$
$648$	−2.17064	−	1.81337i	−0.0852709	−	0.0712359i
$649$	−16.2240	+	9.36694i	−0.636848	+	0.367684i
$650$	37.8515	+	18.8824i	1.48466	+	0.740628i
$651$	7.57417	+	21.8515i	0.296855	+	0.856429i
$652$	−1.96774	+	4.97407i	−0.0770628	+	0.194800i
$653$	31.0796	+	8.32776i	1.21624	+	0.325890i	0.809207	−	0.587523i	$-0.199897\pi$
$653$	31.0796	+	8.32776i	1.21624	+	0.325890i	0.407032	+	0.913414i	$0.366564\pi$
$654$	6.75209	+	2.23198i	0.264027	+	0.0872772i
$655$	3.96559	−	3.43385i	0.154949	−	0.134172i
$656$	−25.2457	−	5.90623i	−0.985679	−	0.230600i
$657$	−5.19100	+	5.19100i	−0.202520	+	0.202520i
$658$	−1.32437	−	4.67232i	−0.0516295	−	0.182146i
$659$			45.5239i			1.77336i	0.462382	+	0.886681i	$0.346995\pi$
$659$			45.5239i			1.77336i	−0.462382	+	0.886681i	$0.653005\pi$
$660$	−24.4815	−	4.62322i	−0.952943	−	0.179959i
$661$	−27.4916	−	15.8723i	−1.06930	−	0.617360i	−0.141309	−	0.989966i	$-0.545131\pi$
$661$	−27.4916	−	15.8723i	−1.06930	−	0.617360i	−0.927990	+	0.372606i	$0.878464\pi$
$662$	−7.46788	+	3.75728i	−0.290247	+	0.146031i
$663$	2.13821	+	0.572931i	0.0830411	+	0.0222508i
$664$	22.2601	−	15.6588i	0.863861	−	0.607680i
$665$	−6.86684	+	25.6399i	−0.266284	+	0.994273i
$666$	−2.13342	+	0.442125i	−0.0826682	+	0.0171320i
$667$	11.0349	+	2.95679i	0.427273	+	0.114488i
$668$	23.7828	+	29.9890i	0.920185	+	1.16031i
$669$	−0.467621	+	0.809943i	−0.0180793	+	0.0313142i
$670$	−17.5522	−	42.1710i	−0.678101	−	1.62921i
$671$			62.7193i			2.42125i
$672$	12.6005	−	8.07632i	0.486075	−	0.311551i
$673$	26.2642	+	26.2642i	1.01241	+	1.01241i	0.999922	+	0.0124869i	$0.00397481\pi$
$673$	26.2642	+	26.2642i	1.01241	+	1.01241i	0.0124869	+	0.999922i	$0.496025\pi$
$674$	29.4374	+	33.0304i	1.13389	+	1.27228i
$675$	−1.97136	+	4.59497i	−0.0758779	+	0.176860i
$676$	−5.22500	+	45.2707i	−0.200961	+	1.74118i
$677$	1.90486	−	7.10904i	0.0732098	−	0.273223i	−0.919612	−	0.392829i	$-0.871496\pi$
$677$	1.90486	−	7.10904i	0.0732098	−	0.273223i	0.992821	+	0.119606i	$0.0381632\pi$
$678$	−2.14085	+	3.26014i	−0.0822188	+	0.125205i
$679$	−19.5301	−	3.75478i	−0.749496	−	0.144095i
$680$	0.645641	+	2.24954i	0.0247592	+	0.0862658i
$681$	−11.0821	−	19.1948i	−0.424668	−	0.735546i
$682$	30.9525	+	61.5204i	1.18523	+	2.35574i
$683$	−14.5409	+	3.89621i	−0.556391	+	0.149084i	−0.526048	−	0.850455i	$-0.676327\pi$
$683$	−14.5409	+	3.89621i	−0.556391	+	0.149084i	−0.0303430	+	0.999540i	$0.509660\pi$
$684$	−5.34809	+	7.20548i	−0.204489	+	0.275508i
$685$	8.70920	−	4.22702i	0.332761	−	0.161506i
$686$	4.12440	+	25.8648i	0.157470	+	0.987524i
$687$	3.37086	+	3.37086i	0.128606	+	0.128606i
$688$	−14.3438	−	23.1050i	−0.546854	−	0.880870i
$689$	−9.28284	−	5.35945i	−0.353648	−	0.204179i
$690$	−16.6170	+	2.21654i	−0.632600	+	0.0843821i
$691$	20.5402	+	35.5766i	0.781385	+	1.35340i	0.931135	+	0.364674i	$0.118820\pi$
$691$	20.5402	+	35.5766i	0.781385	+	1.35340i	−0.149750	+	0.988724i	$0.547847\pi$
$692$	−12.5453	−	4.96293i	−0.476901	−	0.188662i
$693$	12.2027	−	8.26721i	0.463541	−	0.314046i
$694$	−23.2896	+	4.82648i	−0.884061	+	0.183211i
$695$	−43.0685	+	8.28564i	−1.63368	+	0.314292i
$696$	0.544407	+	6.07082i	0.0206357	+	0.230114i
$697$	0.620793	+	2.31683i	0.0235142	+	0.0877562i
$698$	0.0580538	−	1.00933i	0.00219737	−	0.0382035i
$699$			0.0112981i			0.000427332i
$700$	−20.0622	−	17.2484i	−0.758281	−	0.651927i
$701$		−	34.1172i		−	1.28859i	−0.764777	−	0.644295i	$-0.777151\pi$
$701$		−	34.1172i		−	1.28859i	0.764777	−	0.644295i	$-0.222849\pi$
$702$	−8.44602	−	0.485794i	−0.318774	−	0.0183351i
$703$	1.78901	+	6.67668i	0.0674738	+	0.251816i
$704$	34.0164	−	28.7957i	1.28204	−	1.08528i
$705$	−2.84999	+	0.548288i	−0.107337	+	0.0206497i
$706$	−0.437436	−	2.11079i	−0.0164631	−	0.0794408i
$707$	−2.67583	−	37.1721i	−0.100635	−	1.39800i
$708$	−6.25391	−	2.47405i	−0.235036	−	0.0929805i
$709$	0.746144	+	1.29236i	0.0280220	+	0.0485356i	0.879696	−	0.475536i	$-0.157746\pi$
$709$	0.746144	+	1.29236i	0.0280220	+	0.0485356i	−0.851674	+	0.524071i	$0.824412\pi$
$710$	4.54226	+	34.0526i	0.170468	+	1.27797i
$711$	1.13467	+	0.655100i	0.0425533	+	0.0245682i
$712$	3.63293	+	9.91437i	0.136150	+	0.371557i
$713$	32.7671	+	32.7671i	1.22714	+	1.22714i
$714$	−1.20892	−	0.674941i	−0.0452429	−	0.0252590i
$715$	−67.0408	+	32.5383i	−2.50718	+	1.21687i
$716$	2.05550	+	1.52564i	0.0768175	+	0.0570159i
$717$	−9.97101	+	2.67172i	−0.372374	+	0.0997774i
$718$	−20.3027	+	10.2148i	−0.757689	+	0.381212i
$719$	−4.78565	−	8.28900i	−0.178475	−	0.309127i	0.762884	−	0.646536i	$-0.223783\pi$
$719$	−4.78565	−	8.28900i	−0.178475	−	0.309127i	−0.941358	+	0.337409i	$0.890450\pi$
$720$	−4.16073	−	7.91759i	−0.155061	−	0.295071i
$721$	−7.98398	−	23.0338i	−0.297339	−	0.857825i
$722$	1.33610	+	0.877380i	0.0497243	+	0.0326527i
$723$	−2.66280	+	9.93770i	−0.0990305	+	0.369587i
$724$	4.42818	−	38.3668i	0.164572	−	1.42589i
$725$	10.0057	−	3.99783i	0.371604	−	0.148476i
$726$	21.1535	−	18.8524i	0.785079	−	0.699680i
$727$	5.91197	+	5.91197i	0.219263	+	0.219263i	0.808188	−	0.588925i	$-0.200449\pi$
$727$	5.91197	+	5.91197i	0.219263	+	0.219263i	−0.588925	+	0.808188i	$0.700449\pi$
$728$	15.8663	−	41.8599i	0.588043	−	1.55143i
$729$		−	1.00000i		−	0.0370370i
$730$	−21.4326	+	8.92054i	−0.793254	+	0.330164i
$731$	−1.25793	+	2.17880i	−0.0465262	+	0.0805858i
$732$	−17.6419	+	13.9910i	−0.652065	+	0.517121i
$733$	11.6657	+	3.12580i	0.430881	+	0.115454i	0.467740	−	0.883866i	$-0.345068\pi$
$733$	11.6657	+	3.12580i	0.430881	+	0.115454i	−0.0368587	+	0.999320i	$0.511735\pi$
$734$	5.23009	+	25.2371i	0.193046	+	0.931519i
$735$	15.6119	−	1.12574i	0.575855	−	0.0415236i
$736$	15.6510	−	25.5807i	0.576902	−	0.942917i
$737$	77.7291	+	20.8274i	2.86319	+	0.767189i
$738$	−4.11994	−	8.18869i	−0.151657	−	0.301430i
$739$	0.587739	+	0.339331i	0.0216203	+	0.0124825i	0.510771	−	0.859717i	$-0.329360\pi$
$739$	0.587739	+	0.339331i	0.0216203	+	0.0124825i	−0.489151	+	0.872199i	$0.662693\pi$
$740$	−6.77014	−	1.27851i	−0.248875	−	0.0469989i
$741$			26.8398i			0.985984i
$742$	4.80853	+	4.67194i	0.176527	+	0.171512i
$743$	24.0328	−	24.0328i	0.881679	−	0.881679i	−0.112026	−	0.993705i	$-0.535734\pi$
$743$	24.0328	−	24.0328i	0.881679	−	0.881679i	0.993705	+	0.112026i	$0.0357339\pi$
$744$	−10.4001	+	22.4300i	−0.381285	+	0.822324i
$745$	31.6981	−	27.4478i	1.16133	−	1.00561i
$746$	6.57173	−	19.8805i	0.240608	−	0.727877i
$747$	9.29445	+	2.49044i	0.340066	+	0.0911205i
$748$	−3.83391	−	1.51670i	−0.140182	−	0.0554559i
$749$	6.70871	+	19.3547i	0.245131	+	0.707204i
$750$	−11.3012	+	11.0581i	−0.412662	+	0.403786i
$751$	−2.78825	+	1.60979i	−0.101745	+	0.0587422i	−0.550009	−	0.835159i	$-0.685376\pi$
$751$	−2.78825	+	1.60979i	−0.101745	+	0.0587422i	0.448264	+	0.893901i	$0.352042\pi$
$752$	2.45075	−	4.57685i	0.0893696	−	0.166901i
$753$	−1.06860	+	0.286331i	−0.0389420	+	0.0104345i
$754$	12.1298	+	13.6103i	0.441739	+	0.495656i
$755$	−10.0942	+	29.1332i	−0.367364	+	1.06027i
$756$	5.04753	+	1.58823i	0.183577	+	0.0577633i
$757$	15.5635	+	15.5635i	0.565666	+	0.565666i	0.930911	−	0.365245i	$-0.119015\pi$
$757$	15.5635	+	15.5635i	0.565666	+	0.565666i	−0.365245	+	0.930911i	$0.619015\pi$
$758$	30.2209	+	1.73823i	1.09767	+	0.0631353i
$759$	14.7668	−	25.5768i	0.536001	−	0.928380i
$760$	−24.3196	+	14.6208i	−0.882164	+	0.530352i
$761$	−20.2867	−	35.1375i	−0.735391	−	1.27373i	−0.954552	−	0.298046i	$-0.903665\pi$
$761$	−20.2867	−	35.1375i	−0.735391	−	1.27373i	0.219161	−	0.975689i	$-0.429668\pi$
$762$	15.6465	−	23.8269i	0.566814	−	0.863158i
$763$	−13.2699	+	0.955233i	−0.480404	+	0.0345818i
$764$	−25.3863	+	10.9942i	−0.918445	+	0.397756i
$765$	−0.464019	+	0.685087i	−0.0167766	+	0.0247694i
$766$	8.19852	−	24.8018i	0.296225	−	0.896126i
$767$	−19.4309	+	5.20649i	−0.701608	+	0.187995i
$768$	15.6879	+	3.14474i	0.566089	+	0.113476i
$769$			7.68776i			0.277228i	0.990347	+	0.138614i	$0.0442647\pi$
$769$			7.68776i			0.277228i	−0.990347	+	0.138614i	$0.955735\pi$
$770$	45.6394	−	9.46402i	1.64473	−	0.341060i
$771$	−20.3722			−0.733688
$772$	−38.1356	+	5.64241i	−1.37253	+	0.203075i
$773$	−3.15384	−	11.7703i	−0.113436	−	0.423348i	0.885729	−	0.464202i	$-0.153659\pi$
$773$	−3.15384	−	11.7703i	−0.113436	−	0.423348i	−0.999165	+	0.0408542i	$0.986992\pi$
$774$	3.01775	−	9.12916i	0.108471	−	0.328141i
$775$	43.2568	+	6.24931i	1.55383	+	0.224482i
$776$	−12.2325	−	17.3894i	−0.439122	−	0.624243i
$777$	3.37453	−	2.28622i	0.121061	−	0.0820177i
$778$	−28.6105	−	18.7878i	−1.02574	−	0.673575i
$779$	−25.1857	+	14.5410i	−0.902371	+	0.520984i
$780$	−24.1075	−	11.5991i	−0.863188	−	0.415315i
$781$	−52.4136	−	30.2610i	−1.87551	−	1.08282i
$782$	−2.76970	−	0.159306i	−0.0990443	−	0.00569678i
$783$	−1.52380	+	1.52380i	−0.0544560	+	0.0544560i
$784$	−16.0333	+	22.9551i	−0.572616	+	0.819823i
$785$	−4.73063	−	9.74682i	−0.168844	−	0.347879i
$786$	−2.47678	+	2.20736i	−0.0883440	+	0.0787341i
$787$	−1.00173	−	3.73852i	−0.0357079	−	0.133264i	0.945771	−	0.324834i	$-0.105309\pi$
$787$	−1.00173	−	3.73852i	−0.0357079	−	0.133264i	−0.981479	+	0.191571i	$0.938642\pi$
$788$	15.6041	+	19.6760i	0.555873	+	0.700929i
$789$	−8.12949	−	14.0807i	−0.289418	−	0.501286i
$790$	2.52784	+	3.28273i	0.0899365	+	0.116794i
$791$	1.37760	−	7.16542i	0.0489817	−	0.254773i
$792$	15.5237	+	2.70252i	0.551610	+	0.0960297i
$793$	−17.4308	+	65.0528i	−0.618987	+	2.31009i
$794$	5.81461	+	1.92209i	0.206353	+	0.0682123i
$795$	3.02891	−	2.62277i	0.107424	−	0.0930200i
$796$	15.6907	−	21.1401i	0.556143	−	0.749291i
$797$	13.1189	+	13.1189i	0.464694	+	0.464694i	0.900191	−	0.435496i	$-0.143427\pi$
$797$	13.1189	+	13.1189i	0.464694	+	0.464694i	−0.435496	+	0.900191i	$0.643427\pi$
$798$	4.11090	−	16.2765i	0.145524	−	0.576181i
$799$	−0.480288			−0.0169914
$800$	−2.62244	−	28.1624i	−0.0927173	−	0.995692i
$801$	−1.86659	+	3.23303i	−0.0659527	+	0.114233i
$802$	33.8973	−	17.0546i	1.19696	−	0.602219i
$803$	10.5851	−	39.5042i	0.373541	−	1.39407i
$804$	11.4808	+	26.5100i	0.404898	+	0.934936i
$805$	27.1592	−	15.6848i	0.957237	−	0.552817i
$806$	15.0064	+	72.4116i	0.528579	+	2.55059i
$807$	−1.27498	+	4.75828i	−0.0448813	+	0.167499i
$808$	25.5433	−	30.5759i	0.898611	−	1.07566i
$809$	−37.5240	−	21.6645i	−1.31927	−	0.761683i	−0.335662	−	0.941983i	$-0.608960\pi$
$809$	−37.5240	−	21.6645i	−1.31927	−	0.761683i	−0.983612	+	0.180300i	$0.942293\pi$
$810$	1.20516	−	2.92362i	0.0423451	−	0.102726i
$811$	37.8178			1.32796			0.663981	−	0.747749i	$-0.268865\pi$
$811$	37.8178			1.32796			0.663981	+	0.747749i	$0.268865\pi$
$812$	−5.27126	−	10.1115i	−0.184985	−	0.354845i
$813$	7.73229	−	7.73229i	0.271183	−	0.271183i
$814$	9.06140	−	8.07571i	0.317602	−	0.283054i
$815$	−5.96515	−	0.428667i	−0.208950	−	0.0150156i
$816$	−0.428619	−	1.41675i	−0.0150047	−	0.0495963i
$817$	−29.4648	−	7.89506i	−1.03084	−	0.276213i
$818$	−10.8107	+	16.4628i	−0.377987	+	0.575608i
$819$	14.9543	−	5.18345i	0.522545	−	0.181125i
$820$	−2.17644	−	28.9059i	−0.0760047	−	1.00944i
$821$	−32.9300	+	19.0121i	−1.14926	+	0.663528i	−0.948708	−	0.316154i	$-0.897608\pi$
$821$	−32.9300	+	19.0121i	−1.14926	+	0.663528i	−0.200557	+	0.979682i	$0.564275\pi$
$822$	−5.46943	+	2.75181i	−0.190768	+	0.0959804i
$823$	−1.70018	−	6.34518i	−0.0592647	−	0.221179i	0.929942	−	0.367707i	$-0.119857\pi$
$823$	−1.70018	−	6.34518i	−0.0592647	−	0.221179i	−0.989207	+	0.146528i	$0.953190\pi$
$824$	10.9628	−	23.6436i	0.381907	−	0.823664i
$825$	−3.28818	−	27.6602i	−0.114480	−	0.963006i
$826$	12.5810	−	0.181262i	0.437747	−	0.00630692i
$827$	−7.93806	+	7.93806i	−0.276033	+	0.276033i	−0.831523	−	0.555490i	$-0.812531\pi$
$827$	−7.93806	+	7.93806i	−0.276033	+	0.276033i	0.555490	+	0.831523i	$0.312531\pi$
$828$	10.4884	−	1.55183i	0.364498	−	0.0539300i
$829$	14.2927	−	24.7556i	0.496405	−	0.859798i	−0.503587	−	0.863945i	$-0.667987\pi$
$829$	14.2927	−	24.7556i	0.496405	−	0.859798i	0.999991	+	0.00414644i	$0.00131986\pi$
$830$	24.1721	+	18.4824i	0.839026	+	0.641535i
$831$	−9.73753	+	5.62196i	−0.337791	+	0.195024i
$832$	43.2848	−	20.4133i	1.50063	−	0.707702i
$833$	2.57226	+	0.305146i	0.0891236	+	0.0105727i
$834$	27.1613	−	5.62884i	0.940518	−	0.194911i
$835$	−23.9976	+	35.4305i	−0.830470	+	1.22612i
$836$	5.73170	−	49.6608i	0.198235	−	1.71756i
$837$	−8.44333	+	2.26238i	−0.291844	+	0.0781995i
$838$	2.39539	+	0.137777i	0.0827473	+	0.00475942i
$839$	38.6351			1.33383			0.666916	−	0.745133i	$-0.267614\pi$
$839$	38.6351			1.33383			0.666916	+	0.745133i	$0.267614\pi$
$840$	12.8430	+	10.7265i	0.443126	+	0.370099i
$841$	−24.3561			−0.839865
$842$	−15.2611	−	0.877778i	−0.525931	−	0.0302502i
$843$	−12.5073	+	3.35132i	−0.430775	+	0.115426i
$844$	0.559940	+	0.0646264i	0.0192739	+	0.00222453i
$845$	−50.0327	+	9.62543i	−1.72118	+	0.331125i
$846$	1.79735	−	0.372479i	0.0617942	−	0.0128061i
$847$	−23.1406	+	47.6928i	−0.795120	+	1.63875i
$848$	0.229190	+	7.16364i	0.00787043	+	0.246000i
$849$	−19.9556	+	11.5214i	−0.684875	+	0.395413i
$850$	−2.18226	+	1.44372i	−0.0748509	+	0.0495192i
$851$	4.08362	−	7.07303i	0.139985	−	0.242460i
$852$	−3.18011	−	21.4935i	−0.108949	−	0.736357i
$853$	4.38108	−	4.38108i	0.150005	−	0.150005i	−0.628115	−	0.778120i	$-0.716173\pi$
$853$	4.38108	−	4.38108i	0.150005	−	0.150005i	0.778120	+	0.628115i	$0.216173\pi$
$854$	20.5344	−	36.7803i	0.702672	−	1.25860i
$855$	−9.47962	−	3.28452i	−0.324196	−	0.112328i
$856$	−9.21171	+	19.8670i	−0.314850	+	0.679041i
$857$	−6.87991	−	25.6762i	−0.235013	−	0.877082i	−0.978143	−	0.207934i	$-0.933326\pi$
$857$	−6.87991	−	25.6762i	−0.235013	−	0.877082i	0.743129	−	0.669148i	$-0.233341\pi$
$858$	42.1021	−	21.1826i	1.43734	−	0.723162i
$859$	24.4080	−	14.0920i	0.832791	−	0.480812i	−0.0220160	−	0.999758i	$-0.507008\pi$
$859$	24.4080	−	14.0920i	0.832791	−	0.480812i	0.854807	+	0.518945i	$0.173675\pi$
$860$	19.8249	−	23.0534i	0.676023	−	0.786113i
$861$	12.9658	+	11.2245i	0.441873	+	0.382528i
$862$	−2.34334	+	3.56849i	−0.0798145	+	0.121543i
$863$	−30.6688	−	8.21769i	−1.04398	−	0.279733i	−0.304218	−	0.952603i	$-0.598395\pi$
$863$	−30.6688	−	8.21769i	−1.04398	−	0.279733i	−0.739761	+	0.672869i	$0.765062\pi$
$864$	2.70274	+	4.96943i	0.0919490	+	0.169063i
$865$	1.08116	−	15.0450i	0.0367605	−	0.511544i
$866$	12.6297	−	11.2559i	0.429176	−	0.382491i
$867$	11.9240	−	11.9240i	0.404960	−	0.404960i
$868$	1.99050	−	46.2111i	0.0675621	−	1.56851i
$869$	−7.29913			−0.247606
$870$	−6.29143	+	2.61858i	−0.213299	+	0.0887783i
$871$	74.8327	+	43.2047i	2.53561	+	1.46394i
$872$	−10.9152	−	9.11861i	−0.369634	−	0.308795i
$873$	1.94551	−	7.26073i	0.0658455	−	0.245739i
$874$	−6.82591	−	32.9376i	−0.230890	−	1.11413i
$875$	11.6594	−	27.1856i	0.394161	−	0.919042i
$876$	13.4732	−	5.83489i	0.455216	−	0.197143i
$877$	−10.4889	+	39.1450i	−0.354184	+	1.32183i	0.527324	+	0.849664i	$0.323195\pi$
$877$	−10.4889	+	39.1450i	−0.354184	+	1.32183i	−0.881508	+	0.472169i	$0.843471\pi$
$878$	−13.3478	+	6.71560i	−0.450465	+	0.226640i
$879$	−5.29178	+	9.16563i	−0.178487	+	0.309149i
$880$	42.1284	+	26.6097i	1.42015	+	0.897013i
$881$	−4.02287			−0.135534			−0.0677669	−	0.997701i	$-0.521587\pi$
$881$	−4.02287			−0.135534			−0.0677669	+	0.997701i	$0.521587\pi$
$882$	−9.86268	+	0.852946i	−0.332094	+	0.0287202i
$883$	40.5197	+	40.5197i	1.36360	+	1.36360i	0.869283	+	0.494314i	$0.164581\pi$
$883$	40.5197	+	40.5197i	1.36360	+	1.36360i	0.494314	+	0.869283i	$0.335419\pi$
$884$	−3.55504	−	2.63864i	−0.119569	−	0.0887471i
$885$	0.538964	−	7.50000i	0.0181171	−	0.252110i
$886$	40.1911	+	13.2856i	1.35025	+	0.446339i
$887$	4.77718	−	17.8287i	0.160402	−	0.598628i	−0.838180	−	0.545394i	$-0.816380\pi$
$887$	4.77718	−	17.8287i	0.160402	−	0.598628i	0.998582	−	0.0532347i	$-0.0169532\pi$
$888$	4.29293	+	0.747356i	0.144061	+	0.0250796i
$889$	−10.0682	+	52.3689i	−0.337678	+	1.75640i
$890$	−9.35353	+	7.20262i	−0.313531	+	0.241432i
$891$	2.78550	+	4.82463i	0.0933177	+	0.161631i
$892$	1.46556	−	1.16226i	0.0490705	−	0.0389154i
$893$	−1.50720	−	5.62494i	−0.0504365	−	0.188231i
$894$	−19.7976	+	17.6441i	−0.662132	+	0.590106i
$895$	−0.936971	+	2.70424i	−0.0313195	+	0.0903926i
$896$	−29.3759	+	5.74956i	−0.981379	+	0.192079i
$897$	22.4245	−	22.4245i	0.748732	−	0.748732i
$898$	−6.23048	−	0.358362i	−0.207914	−	0.0119587i
$899$	16.3133	+	9.41850i	0.544080	+	0.314125i
$900$	7.04689	−	7.09517i	0.234896	−	0.236506i
$901$	0.574220	−	0.331526i	0.0191301	−	0.0110447i
$902$	42.6868	+	28.0313i	1.42131	+	0.933340i
$903$	1.29152	+	17.9416i	0.0429792	+	0.597059i
$904$	6.38002	−	4.48801i	0.212196	−	0.149269i
$905$	42.4026	−	8.15754i	1.40951	−	0.271166i
$906$	6.12026	−	18.5148i	0.203332	−	0.615112i
$907$	0.679115	+	2.53449i	0.0225496	+	0.0841564i	0.976284	−	0.216495i	$-0.0694626\pi$
$907$	0.679115	+	2.53449i	0.0225496	+	0.0841564i	−0.953734	+	0.300652i	$0.902796\pi$
$908$	6.48807	+	43.8511i	0.215314	+	1.45525i
$909$	14.0861			0.467206
$910$	49.9677	+	2.86789i	1.65641	+	0.0950695i
$911$		−	38.3707i		−	1.27128i	−0.771986	−	0.635639i	$-0.780737\pi$
$911$		−	38.3707i		−	1.27128i	0.771986	−	0.635639i	$-0.219263\pi$
$912$	15.2474	−	9.46576i	0.504892	−	0.313443i
$913$	−51.7794	+	13.8742i	−1.71365	+	0.459170i
$914$	16.4938	−	49.8965i	0.545568	−	1.65043i
$915$	−20.8431	−	14.1173i	−0.689051	−	0.466704i
$916$	−3.78898	−	8.74900i	−0.125191	−	0.289075i
$917$	2.70945	−	5.58418i	0.0894738	−	0.184406i
$918$	0.287252	−	0.437435i	0.00948074	−	0.0144375i
$919$	−27.3963	−	47.4518i	−0.903722	−	1.56529i	−0.822624	−	0.568586i	$-0.807491\pi$
$919$	−27.3963	−	47.4518i	−0.903722	−	1.56529i	−0.0810976	−	0.996706i	$-0.525843\pi$
$920$	32.5345	+	8.10329i	1.07263	+	0.267158i
$921$	−14.6469	+	25.3692i	−0.482631	+	0.835942i
$922$	−22.3462	−	1.28530i	−0.735932	−	0.0423289i
$923$	−45.9536	−	45.9536i	−1.51258	−	1.51258i
$924$	−28.7764	+	6.39727i	−0.946675	+	0.210455i
$925$	−0.909314	−	7.64918i	−0.0298981	−	0.251503i
$926$	−11.7259	−	13.1571i	−0.385337	−	0.432370i
$927$	8.90017	−	2.38479i	0.292320	−	0.0783269i
$928$	3.45397	−	11.6908i	0.113382	−	0.383770i
$929$	−33.4605	+	19.3184i	−1.09780	+	0.633817i	−0.935643	−	0.352948i	$-0.885179\pi$
$929$	−33.4605	+	19.3184i	−1.09780	+	0.633817i	−0.162160	+	0.986764i	$0.551846\pi$
$930$	−27.4117	−	3.56123i	−0.898865	−	0.116777i
$931$	4.49830	+	31.0829i	0.147426	+	1.01870i
$932$	0.00831224	−	0.0210117i	0.000272276	−	0.000688262i
$933$	−11.0922	−	2.97214i	−0.363142	−	0.0973036i
$934$	−15.0529	+	45.5375i	−0.492547	+	1.49003i
$935$	0.330408	−	4.59781i	0.0108055	−	0.150365i
$936$	15.3502	+	7.11738i	0.501736	+	0.232639i
$937$	−30.8098	+	30.8098i	−1.00651	+	1.00651i	−0.00653468	+	0.999979i	$0.502080\pi$
$937$	−30.8098	+	30.8098i	−1.00651	+	1.00651i	−0.999979	+	0.00653468i	$0.997920\pi$
$938$	−38.7635	−	37.6624i	−1.26567	−	1.22972i
$939$			11.4082i			0.372292i
$940$	5.70368	+	1.07711i	0.186034	+	0.0351315i
$941$	44.6989	+	25.8069i	1.45714	+	0.841282i	0.998870	−	0.0475297i	$-0.0151349\pi$
$941$	44.6989	+	25.8069i	1.45714	+	0.841282i	0.458273	+	0.888812i	$0.348468\pi$
$942$	3.07966	+	6.12107i	0.100341	+	0.199435i
$943$	33.1914	+	8.89361i	1.08086	+	0.289616i
$944$	9.81057	+	9.20228i	0.319307	+	0.299509i
$945$	0.000723185		5.91608i	2.35252e−5		0.192450i
$946$	10.8698	+	52.4507i	0.353407	+	1.70532i
$947$	−1.63709	−	0.438657i	−0.0531983	−	0.0142544i	0.232122	−	0.972687i	$-0.425433\pi$
$947$	−1.63709	−	0.438657i	−0.0531983	−	0.0142544i	−0.285320	+	0.958432i	$0.592100\pi$
$948$	−1.62824	−	2.05313i	−0.0528827	−	0.0666826i
$949$	21.9579	−	38.0322i	0.712783	−	1.23458i
$950$	−23.7565	−	21.0272i	−0.770761	−	0.682212i
$951$		−	4.93092i		−	0.159896i
$952$	1.75174	+	2.14466i	0.0567743	+	0.0695089i
$953$	−4.60430	−	4.60430i	−0.149148	−	0.149148i	0.628589	−	0.777737i	$-0.283633\pi$
$953$	−4.60430	−	4.60430i	−0.149148	−	0.149148i	−0.777737	+	0.628589i	$0.783633\pi$
$954$	−1.89176	+	1.68598i	−0.0612480	+	0.0545856i
$955$	−20.2470	−	23.3823i	−0.655177	−	0.756633i
$956$	20.5093	+	2.36712i	0.663320	+	0.0765582i
$957$	3.10721	−	11.5963i	0.100442	−	0.374854i
$958$	−22.0577	−	14.4847i	−0.712652	−	0.467980i
$959$	7.49709	−	8.66017i	0.242094	−	0.279652i
$960$	1.91283	+	17.7860i	0.0617362	+	0.574040i
$961$	22.7041	+	39.3247i	0.732392	+	1.26854i
$962$	11.6429	−	5.85785i	0.375383	−	0.188865i
$963$	−7.47856	+	2.00387i	−0.240993	+	0.0645739i
$964$	12.2636	−	16.5227i	0.394982	−	0.532159i
$965$	−18.8196	−	38.7752i	−0.605825	−	1.24822i
$966$	−17.0335	+	10.1643i	−0.548045	+	0.327031i
$967$	−11.1120	−	11.1120i	−0.357336	−	0.357336i	0.505494	−	0.862830i	$-0.331310\pi$
$967$	−11.1120	−	11.1120i	−0.357336	−	0.357336i	−0.862830	+	0.505494i	$0.831310\pi$
$968$	−53.2106	+	19.4980i	−1.71025	+	0.626688i
$969$	−1.43783	−	0.830131i	−0.0461897	−	0.0266676i
$970$	14.4383	−	18.8830i	0.463586	−	0.606297i
$971$	30.9372	+	53.5848i	0.992822	+	1.71962i	0.599986	+	0.800011i	$0.295173\pi$
$971$	30.9372	+	53.5848i	0.992822	+	1.71962i	0.392837	+	0.919608i	$0.371494\pi$
$972$	−0.735722	+	1.85976i	−0.0235983	+	0.0596519i
$973$	−42.9624	+	29.1067i	−1.37731	+	0.933117i
$974$	−5.17665	−	24.9793i	−0.165870	−	0.800387i
$975$	4.27677	−	29.6032i	0.136966	−	0.948061i
$976$	43.1033	−	13.0403i	1.37970	−	0.417410i
$977$	−5.42070	−	20.2303i	−0.173424	−	0.647226i	−0.996815	−	0.0797515i	$-0.974587\pi$
$977$	−5.42070	−	20.2303i	−0.173424	−	0.647226i	0.823391	−	0.567474i	$-0.192079\pi$
$978$	3.77618	+	0.217196i	0.120749	+	0.00694517i
$979$		−	20.7975i		−	0.664692i
$980$	−29.8627	−	9.39244i	−0.953930	−	0.300031i
$981$		−	5.02854i		−	0.160549i
$982$	−1.63383	+	28.4057i	−0.0521375	+	0.906464i
$983$	8.59852	+	32.0901i	0.274250	+	1.02352i	0.956342	+	0.292249i	$0.0944036\pi$
$983$	8.59852	+	32.0901i	0.274250	+	1.02352i	−0.682092	+	0.731266i	$0.738930\pi$
$984$	1.63750	+	18.2601i	0.0522015	+	0.582112i
$985$	−15.7450	+	23.2462i	−0.501677	+	0.740686i
$986$	−1.10428	+	0.228848i	−0.0351673	+	0.00728799i
$987$	−2.84296	+	1.92609i	−0.0904926	+	0.0613080i
$988$	19.7466	−	49.9156i	0.628223	−	1.58803i
$989$	18.0214	+	31.2139i	0.573046	+	0.992545i
$990$	2.32930	+	17.4624i	0.0740299	+	0.554991i
$991$	−23.8565	−	13.7735i	−0.757826	−	0.437531i	0.0706886	−	0.997498i	$-0.477480\pi$
$991$	−23.8565	−	13.7735i	−0.757826	−	0.437531i	−0.828515	+	0.559967i	$0.810814\pi$
$992$	35.8439	−	34.0629i	1.13804	−	1.08150i
$993$	4.17990	+	4.17990i	0.132645	+	0.132645i
$994$	20.8293	+	34.9062i	0.660664	+	1.10716i
$995$	27.8122	+	9.63645i	0.881706	+	0.305496i
$996$	−15.4532	−	11.4698i	−0.489653	−	0.363433i
$997$	−44.3628	+	11.8870i	−1.40498	+	0.376464i	−0.880132	−	0.474730i	$-0.842546\pi$
$997$	−44.3628	+	11.8870i	−1.40498	+	0.376464i	−0.524852	+	0.851194i	$0.675879\pi$
$998$	−6.25038	−	12.4231i	−0.197852	−	0.393247i
$999$	0.770303	+	1.33420i	0.0243713	+	0.0422124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.dj.a.403.48	yes	384
5.2	odd	4	inner	840.2.dj.a.67.3	✓	384
7.2	even	3	inner	840.2.dj.a.163.82	yes	384
8.3	odd	2	inner	840.2.dj.a.403.64	yes	384
35.2	odd	12	inner	840.2.dj.a.667.64	yes	384
40.27	even	4	inner	840.2.dj.a.67.82	yes	384
56.51	odd	6	inner	840.2.dj.a.163.3	yes	384
280.107	even	12	inner	840.2.dj.a.667.48	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dj.a.67.3	✓	384	5.2	odd	4	inner
840.2.dj.a.67.82	yes	384	40.27	even	4	inner
840.2.dj.a.163.3	yes	384	56.51	odd	6	inner
840.2.dj.a.163.82	yes	384	7.2	even	3	inner
840.2.dj.a.403.48	yes	384	1.1	even	1	trivial
840.2.dj.a.403.64	yes	384	8.3	odd	2	inner
840.2.dj.a.667.48	yes	384	280.107	even	12	inner
840.2.dj.a.667.64	yes	384	35.2	odd	12	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.dj (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0812078 + 1.41188i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.98681 - 0.229311i) q^{4} +(-0.422435 - 2.19580i) q^{5} +(0.286981 + 1.38479i) q^{6} +(-1.48397 - 2.19039i) q^{7} +(0.485105 - 2.78652i) q^{8} +(0.866025 - 0.500000i) q^{9} +(3.13451 - 0.418111i) q^{10} +(-2.78550 + 4.82463i) q^{11} +(-1.97846 + 0.292727i) q^{12} +(-4.22999 + 4.22999i) q^{13} +(3.21308 - 1.91732i) q^{14} +(-0.976356 - 2.01165i) q^{15} +(3.89483 + 0.911196i) q^{16} +(-0.0957741 - 0.357434i) q^{17} +(0.635612 + 1.26333i) q^{18} +(3.88557 - 2.24334i) q^{19} +(0.335775 + 4.45951i) q^{20} +(-2.00032 - 1.73168i) q^{21} +(-6.58559 - 4.32459i) q^{22} +(-5.12067 - 1.37208i) q^{23} +(-0.252628 - 2.81712i) q^{24} +(-4.64310 + 1.85517i) q^{25} +(-5.62873 - 6.31574i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.44609 + 4.69219i) q^{28} -2.15497 q^{29} +(2.91949 - 1.21514i) q^{30} +(-7.57009 - 4.37059i) q^{31} +(-1.60279 + 5.42504i) q^{32} +(-1.44188 + 5.38117i) q^{33} +(0.512431 - 0.106195i) q^{34} +(-4.18279 + 4.18381i) q^{35} +(-1.83528 + 0.794816i) q^{36} +(-0.398738 + 1.48811i) q^{37} +(2.85178 + 5.66814i) q^{38} +(-2.99105 + 5.18066i) q^{39} +(-6.32356 + 0.111927i) q^{40} -6.48184 q^{41} +(2.60736 - 2.68359i) q^{42} +(-4.80750 - 4.80750i) q^{43} +(6.64060 - 8.94687i) q^{44} +(-1.46374 - 1.69040i) q^{45} +(2.35305 - 7.11835i) q^{46} +(0.335928 - 1.25370i) q^{47} +(3.99795 - 0.127909i) q^{48} +(-2.59564 + 6.50097i) q^{49} +(-2.24222 - 6.70615i) q^{50} +(-0.185021 - 0.320466i) q^{51} +(9.37417 - 7.43420i) q^{52} +(0.463759 + 1.73077i) q^{53} +(0.940927 + 1.05577i) q^{54} +(11.7706 + 4.07832i) q^{55} +(-6.82345 + 3.07255i) q^{56} +(3.17256 - 3.17256i) q^{57} +(0.175001 - 3.04256i) q^{58} +(2.91223 + 1.68137i) q^{59} +(1.47854 + 4.22065i) q^{60} +(9.74986 - 5.62909i) q^{61} +(6.78550 - 10.3331i) q^{62} +(-2.38036 - 1.15495i) q^{63} +(-7.52935 - 2.70350i) q^{64} +(11.0751 + 7.50133i) q^{65} +(-7.48048 - 2.47276i) q^{66} +(-3.73855 - 13.9525i) q^{67} +(0.108321 + 0.732115i) q^{68} -5.30131 q^{69} +(-5.56736 - 6.24535i) q^{70} +10.8638i q^{71} +(-0.973145 - 2.65575i) q^{72} +(-7.09104 + 1.90004i) q^{73} +(-2.06866 - 0.683817i) q^{74} +(-4.00474 + 2.99368i) q^{75} +(-8.23432 + 3.56608i) q^{76} +(14.7014 - 1.05828i) q^{77} +(-7.07157 - 4.64372i) q^{78} +(0.655100 + 1.13467i) q^{79} +(0.355495 - 8.93720i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.526376 - 9.15159i) q^{82} +(6.80401 + 6.80401i) q^{83} +(3.57717 + 3.89921i) q^{84} +(-0.744396 + 0.361294i) q^{85} +(7.17802 - 6.39721i) q^{86} +(-2.08154 + 0.557748i) q^{87} +(12.0926 + 10.1023i) q^{88} +(-3.23303 + 1.86659i) q^{89} +(2.50551 - 1.92935i) q^{90} +(15.5425 + 2.98815i) q^{91} +(9.85917 + 3.90029i) q^{92} +(-8.44333 - 2.26238i) q^{93} +(1.74279 + 0.576100i) q^{94} +(-6.56733 - 7.58429i) q^{95} +(-0.144073 + 5.65502i) q^{96} +(5.31523 - 5.31523i) q^{97} +(-8.96781 - 4.19267i) q^{98} +5.57100i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + 24 q^{8} - 16 q^{16} + 32 q^{26} + 44 q^{28} + 48 q^{35} + 12 q^{38} + 20 q^{40} - 20 q^{42} - 48 q^{46} - 32 q^{48} - 72 q^{50} + 4 q^{52} + 32 q^{56} + 8 q^{58} + 20 q^{60} - 144 q^{62} - 24 q^{66}+ \cdots - 80 q^{98}+O(q^{100}) \) 384 * q + 24 * q^8 - 16 * q^16 + 32 * q^26 + 44 * q^28 + 48 * q^35 + 12 * q^38 + 20 * q^40 - 20 * q^42 - 48 * q^46 - 32 * q^48 - 72 * q^50 + 4 * q^52 + 32 * q^56 + 8 * q^58 + 20 * q^60 - 144 * q^62 - 24 * q^66 + 48 * q^67 + 44 * q^68 - 40 * q^70 + 12 * q^72 + 96 * q^76 - 48 * q^78 + 36 * q^80 + 192 * q^81 - 44 * q^82 + 32 * q^86 + 68 * q^88 + 24 * q^90 - 64 * q^91 - 72 * q^92 + 32 * q^97 - 80 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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