LMFDB - Embedded newform 770.2.m.f.43.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(43,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0, 2]))

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

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

chi := DirichletCharacter("770.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.7
Character	$\chi$	$=$	770.43
Dual form			770.2.m.f.197.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.47574 + 1.47574i) q^{3} +1.00000i q^{4} +(-2.23579 - 0.0355240i) q^{5} -2.08701i q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.35562i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.47574 + 1.47574i) q^{3} +1.00000i q^{4} +(-2.23579 - 0.0355240i) q^{5} -2.08701i q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.35562i q^{9} +(1.55582 + 1.60606i) q^{10} +(0.318348 - 3.30131i) q^{11} +(-1.47574 + 1.47574i) q^{12} +(2.95379 - 2.95379i) q^{13} +1.00000i q^{14} +(-3.24702 - 3.35187i) q^{15} -1.00000 q^{16} +(0.451150 + 0.451150i) q^{17} +(0.958571 - 0.958571i) q^{18} +4.23465 q^{19} +(0.0355240 - 2.23579i) q^{20} -2.08701i q^{21} +(-2.55949 + 2.10927i) q^{22} +(1.62422 + 1.62422i) q^{23} +2.08701 q^{24} +(4.99748 + 0.158848i) q^{25} -4.17729 q^{26} +(2.42667 - 2.42667i) q^{27} +(0.707107 - 0.707107i) q^{28} -2.38849 q^{29} +(-0.0741390 + 4.66611i) q^{30} +3.62644 q^{31} +(0.707107 + 0.707107i) q^{32} +(5.34168 - 4.40208i) q^{33} -0.638022i q^{34} +(1.55582 + 1.60606i) q^{35} -1.35562 q^{36} +(-0.785489 + 0.785489i) q^{37} +(-2.99435 - 2.99435i) q^{38} +8.71806 q^{39} +(-1.60606 + 1.55582i) q^{40} -5.52698i q^{41} +(-1.47574 + 1.47574i) q^{42} +(0.646902 - 0.646902i) q^{43} +(3.30131 + 0.318348i) q^{44} +(0.0481572 - 3.03089i) q^{45} -2.29699i q^{46} +(-0.355472 + 0.355472i) q^{47} +(-1.47574 - 1.47574i) q^{48} +1.00000i q^{49} +(-3.42143 - 3.64607i) q^{50} +1.33156i q^{51} +(2.95379 + 2.95379i) q^{52} +(7.85510 + 7.85510i) q^{53} -3.43183 q^{54} +(-0.829033 + 7.36972i) q^{55} -1.00000 q^{56} +(6.24925 + 6.24925i) q^{57} +(1.68891 + 1.68891i) q^{58} -3.53659i q^{59} +(3.35187 - 3.24702i) q^{60} +3.09739i q^{61} +(-2.56428 - 2.56428i) q^{62} +(0.958571 - 0.958571i) q^{63} -1.00000i q^{64} +(-6.70897 + 6.49911i) q^{65} +(-6.88988 - 0.664396i) q^{66} +(11.1243 - 11.1243i) q^{67} +(-0.451150 + 0.451150i) q^{68} +4.79386i q^{69} +(0.0355240 - 2.23579i) q^{70} -12.2919 q^{71} +(0.958571 + 0.958571i) q^{72} +(-1.42798 + 1.42798i) q^{73} +1.11085 q^{74} +(7.14056 + 7.60940i) q^{75} +4.23465i q^{76} +(-2.55949 + 2.10927i) q^{77} +(-6.16460 - 6.16460i) q^{78} -2.62585 q^{79} +(2.23579 + 0.0355240i) q^{80} +11.2292 q^{81} +(-3.90816 + 3.90816i) q^{82} +(-5.82143 + 5.82143i) q^{83} +2.08701 q^{84} +(-0.992648 - 1.02470i) q^{85} -0.914857 q^{86} +(-3.52479 - 3.52479i) q^{87} +(-2.10927 - 2.55949i) q^{88} -2.20970i q^{89} +(-2.17721 + 2.10911i) q^{90} -4.17729 q^{91} +(-1.62422 + 1.62422i) q^{92} +(5.35168 + 5.35168i) q^{93} +0.502713 q^{94} +(-9.46777 - 0.150432i) q^{95} +2.08701i q^{96} +(10.4915 - 10.4915i) q^{97} +(0.707107 - 0.707107i) q^{98} +(4.47534 + 0.431560i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{3}+O(q^{10}) $ 36 * q - 4 * q^3	$ 36 q - 4 q^{3} + 12 q^{11} + 4 q^{12} - 4 q^{15} - 36 q^{16} - 12 q^{20} - 12 q^{22} + 4 q^{23} + 12 q^{25} + 24 q^{26} + 56 q^{27} + 8 q^{31} - 44 q^{33} - 44 q^{36} - 28 q^{37} + 16 q^{38} + 4 q^{42} - 44 q^{45} + 12 q^{47} + 4 q^{48} + 28 q^{53} + 40 q^{55} - 36 q^{56} - 24 q^{58} + 12 q^{60} + 24 q^{66} + 12 q^{67} - 12 q^{70} - 112 q^{71} - 52 q^{75} - 12 q^{77} + 48 q^{78} + 4 q^{81} + 40 q^{82} + 32 q^{86} - 12 q^{88} + 24 q^{91} - 4 q^{92} - 80 q^{93} + 100 q^{97}+O(q^{100}) $ 36 * q - 4 * q^3 + 12 * q^11 + 4 * q^12 - 4 * q^15 - 36 * q^16 - 12 * q^20 - 12 * q^22 + 4 * q^23 + 12 * q^25 + 24 * q^26 + 56 * q^27 + 8 * q^31 - 44 * q^33 - 44 * q^36 - 28 * q^37 + 16 * q^38 + 4 * q^42 - 44 * q^45 + 12 * q^47 + 4 * q^48 + 28 * q^53 + 40 * q^55 - 36 * q^56 - 24 * q^58 + 12 * q^60 + 24 * q^66 + 12 * q^67 - 12 * q^70 - 112 * q^71 - 52 * q^75 - 12 * q^77 + 48 * q^78 + 4 * q^81 + 40 * q^82 + 32 * q^86 - 12 * q^88 + 24 * q^91 - 4 * q^92 - 80 * q^93 + 100 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	1.47574	+	1.47574i	0.852020	+	0.852020i	0.990382	−	0.138362i	$-0.0441838\pi$
$3$	1.47574	+	1.47574i	0.852020	+	0.852020i	−0.138362	+	0.990382i	$0.544184\pi$
$4$			1.00000i			0.500000i
$5$	−2.23579	−	0.0355240i	−0.999874	−	0.0158868i
$5$	−2.23579	−	0.0355240i	−0.999874	−	0.0158868i
$6$		−	2.08701i		−	0.852020i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			1.35562i			0.451875i
$10$	1.55582	+	1.60606i	0.491993	+	0.507880i
$11$	0.318348	−	3.30131i	0.0959854	−	0.995383i
$11$	0.318348	−	3.30131i	0.0959854	−	0.995383i
$12$	−1.47574	+	1.47574i	−0.426010	+	0.426010i
$13$	2.95379	−	2.95379i	0.819234	−	0.819234i	−0.166763	−	0.985997i	$-0.553332\pi$
$13$	2.95379	−	2.95379i	0.819234	−	0.819234i	0.985997	+	0.166763i	$0.0533315\pi$
$14$			1.00000i			0.267261i
$15$	−3.24702	−	3.35187i	−0.838376	−	0.865448i
$16$	−1.00000			−0.250000
$17$	0.451150	+	0.451150i	0.109420	+	0.109420i	0.759697	−	0.650277i	$-0.225347\pi$
$17$	0.451150	+	0.451150i	0.109420	+	0.109420i	−0.650277	+	0.759697i	$0.725347\pi$
$18$	0.958571	−	0.958571i	0.225937	−	0.225937i
$19$	4.23465			0.971496			0.485748	−	0.874099i	$-0.338547\pi$
$19$	4.23465			0.971496			0.485748	+	0.874099i	$0.338547\pi$
$20$	0.0355240	−	2.23579i	0.00794340	−	0.499937i
$21$		−	2.08701i		−	0.455424i
$22$	−2.55949	+	2.10927i	−0.545684	+	0.449699i
$23$	1.62422	+	1.62422i	0.338673	+	0.338673i	0.855868	−	0.517195i	$-0.173024\pi$
$23$	1.62422	+	1.62422i	0.338673	+	0.338673i	−0.517195	+	0.855868i	$0.673024\pi$
$24$	2.08701			0.426010
$25$	4.99748	+	0.158848i	0.999495	+	0.0317696i
$26$	−4.17729			−0.819234
$27$	2.42667	−	2.42667i	0.467013	−	0.467013i
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	−2.38849			−0.443531			−0.221765	−	0.975100i	$-0.571182\pi$
$29$	−2.38849			−0.443531			−0.221765	+	0.975100i	$0.571182\pi$
$30$	−0.0741390	+	4.66611i	−0.0135359	+	0.851912i
$31$	3.62644			0.651327			0.325663	−	0.945486i	$-0.394412\pi$
$31$	3.62644			0.651327			0.325663	+	0.945486i	$0.394412\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	5.34168	−	4.40208i	0.929867	−	0.766304i
$34$		−	0.638022i		−	0.109420i
$35$	1.55582	+	1.60606i	0.262982	+	0.271473i
$36$	−1.35562			−0.225937
$37$	−0.785489	+	0.785489i	−0.129134	+	0.129134i	−0.768720	−	0.639586i	$-0.779106\pi$
$37$	−0.785489	+	0.785489i	−0.129134	+	0.129134i	0.639586	+	0.768720i	$0.279106\pi$
$38$	−2.99435	−	2.99435i	−0.485748	−	0.485748i
$39$	8.71806			1.39601
$40$	−1.60606	+	1.55582i	−0.253940	+	0.245997i
$41$		−	5.52698i		−	0.863169i	−0.902073	−	0.431584i	$-0.857955\pi$
$41$		−	5.52698i		−	0.863169i	0.902073	−	0.431584i	$-0.142045\pi$
$42$	−1.47574	+	1.47574i	−0.227712	+	0.227712i
$43$	0.646902	−	0.646902i	0.0986516	−	0.0986516i	−0.656058	−	0.754710i	$-0.727778\pi$
$43$	0.646902	−	0.646902i	0.0986516	−	0.0986516i	0.754710	+	0.656058i	$0.227778\pi$
$44$	3.30131	+	0.318348i	0.497691	+	0.0479927i
$45$	0.0481572	−	3.03089i	0.00717885	−	0.451818i
$46$		−	2.29699i		−	0.338673i
$47$	−0.355472	+	0.355472i	−0.0518509	+	0.0518509i	−0.732557	−	0.680706i	$-0.761673\pi$
$47$	−0.355472	+	0.355472i	−0.0518509	+	0.0518509i	0.680706	+	0.732557i	$0.261673\pi$
$48$	−1.47574	−	1.47574i	−0.213005	−	0.213005i
$49$			1.00000i			0.142857i
$50$	−3.42143	−	3.64607i	−0.483863	−	0.515632i
$51$			1.33156i			0.186456i
$52$	2.95379	+	2.95379i	0.409617	+	0.409617i
$53$	7.85510	+	7.85510i	1.07898	+	1.07898i	0.996601	+	0.0823796i	$0.0262520\pi$
$53$	7.85510	+	7.85510i	1.07898	+	1.07898i	0.0823796	+	0.996601i	$0.473748\pi$
$54$	−3.43183			−0.467013
$55$	−0.829033	+	7.36972i	−0.111787	+	0.993732i
$56$	−1.00000			−0.133631
$57$	6.24925	+	6.24925i	0.827733	+	0.827733i
$58$	1.68891	+	1.68891i	0.221765	+	0.221765i
$59$		−	3.53659i		−	0.460425i	−0.973140	−	0.230213i	$-0.926058\pi$
$59$		−	3.53659i		−	0.460425i	0.973140	−	0.230213i	$-0.0739421\pi$
$60$	3.35187	−	3.24702i	0.432724	−	0.419188i
$61$			3.09739i			0.396580i	0.980143	+	0.198290i	$0.0635387\pi$
$61$			3.09739i			0.396580i	−0.980143	+	0.198290i	$0.936461\pi$
$62$	−2.56428	−	2.56428i	−0.325663	−	0.325663i
$63$	0.958571	−	0.958571i	0.120769	−	0.120769i
$64$		−	1.00000i		−	0.125000i
$65$	−6.70897	+	6.49911i	−0.832145	+	0.806115i
$66$	−6.88988	−	0.664396i	−0.848086	−	0.0817815i
$67$	11.1243	−	11.1243i	1.35905	−	1.35905i	0.483955	−	0.875093i	$-0.339200\pi$
$67$	11.1243	−	11.1243i	1.35905	−	1.35905i	0.875093	−	0.483955i	$-0.160800\pi$
$68$	−0.451150	+	0.451150i	−0.0547100	+	0.0547100i
$69$			4.79386i			0.577112i
$70$	0.0355240	−	2.23579i	0.00424593	−	0.267228i
$71$	−12.2919			−1.45878			−0.729391	−	0.684097i	$-0.760196\pi$
$71$	−12.2919			−1.45878			−0.729391	+	0.684097i	$0.760196\pi$
$72$	0.958571	+	0.958571i	0.112969	+	0.112969i
$73$	−1.42798	+	1.42798i	−0.167132	+	0.167132i	−0.785717	−	0.618586i	$-0.787706\pi$
$73$	−1.42798	+	1.42798i	−0.167132	+	0.167132i	0.618586	+	0.785717i	$0.287706\pi$
$74$	1.11085			0.129134
$75$	7.14056	+	7.60940i	0.824521	+	0.878658i
$76$			4.23465i			0.485748i
$77$	−2.55949	+	2.10927i	−0.291680	+	0.240374i
$78$	−6.16460	−	6.16460i	−0.698003	−	0.698003i
$79$	−2.62585			−0.295431			−0.147716	−	0.989030i	$-0.547192\pi$
$79$	−2.62585			−0.295431			−0.147716	+	0.989030i	$0.547192\pi$
$80$	2.23579	+	0.0355240i	0.249968	+	0.00397170i
$81$	11.2292			1.24768
$82$	−3.90816	+	3.90816i	−0.431584	+	0.431584i
$83$	−5.82143	+	5.82143i	−0.638985	+	0.638985i	−0.950305	−	0.311320i	$-0.899229\pi$
$83$	−5.82143	+	5.82143i	−0.638985	+	0.638985i	0.311320	+	0.950305i	$0.399229\pi$
$84$	2.08701			0.227712
$85$	−0.992648	−	1.02470i	−0.107668	−	0.111144i
$86$	−0.914857			−0.0986516
$87$	−3.52479	−	3.52479i	−0.377897	−	0.377897i
$88$	−2.10927	−	2.55949i	−0.224849	−	0.272842i
$89$		−	2.20970i		−	0.234227i	−0.993119	−	0.117114i	$-0.962636\pi$
$89$		−	2.20970i		−	0.234227i	0.993119	−	0.117114i	$-0.0373642\pi$
$90$	−2.17721	+	2.10911i	−0.229498	+	0.222320i
$91$	−4.17729			−0.437899
$92$	−1.62422	+	1.62422i	−0.169337	+	0.169337i
$93$	5.35168	+	5.35168i	0.554943	+	0.554943i
$94$	0.502713			0.0518509
$95$	−9.46777	−	0.150432i	−0.971373	−	0.0154340i
$96$			2.08701i			0.213005i
$97$	10.4915	−	10.4915i	1.06525	−	1.06525i	0.0675298	−	0.997717i	$-0.478488\pi$
$97$	10.4915	−	10.4915i	1.06525	−	1.06525i	0.997717	−	0.0675298i	$-0.0215118\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$	4.47534	+	0.431560i	0.449788	+	0.0433734i
$100$	−0.158848	+	4.99748i	−0.0158848	+	0.499748i
$101$		−	13.9455i		−	1.38763i	−0.720153	−	0.693815i	$-0.755928\pi$
$101$		−	13.9455i		−	1.38763i	0.720153	−	0.693815i	$-0.244072\pi$
$102$	0.941556	−	0.941556i	0.0932279	−	0.0932279i
$103$	−7.72807	−	7.72807i	−0.761469	−	0.761469i	0.215119	−	0.976588i	$-0.430986\pi$
$103$	−7.72807	−	7.72807i	−0.761469	−	0.761469i	−0.976588	+	0.215119i	$0.930986\pi$
$104$		−	4.17729i		−	0.409617i
$105$	−0.0741390	+	4.66611i	−0.00723522	+	0.455366i
$106$		−	11.1088i		−	1.07898i
$107$	−13.5470	−	13.5470i	−1.30964	−	1.30964i	−0.921673	−	0.387968i	$-0.873177\pi$
$107$	−13.5470	−	13.5470i	−1.30964	−	1.30964i	−0.387968	−	0.921673i	$-0.626823\pi$
$108$	2.42667	+	2.42667i	0.233507	+	0.233507i
$109$	−4.21601			−0.403821			−0.201910	−	0.979404i	$-0.564715\pi$
$109$	−4.21601			−0.403821			−0.201910	+	0.979404i	$0.564715\pi$
$110$	5.79739	−	4.62496i	0.552759	−	0.440973i
$111$	−2.31836			−0.220049
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	6.60224	+	6.60224i	0.621086	+	0.621086i	0.945809	−	0.324723i	$-0.105271\pi$
$113$	6.60224	+	6.60224i	0.621086	+	0.621086i	−0.324723	+	0.945809i	$0.605271\pi$
$114$		−	8.83777i		−	0.827733i
$115$	−3.57371	−	3.68911i	−0.333250	−	0.344011i
$116$		−	2.38849i		−	0.221765i
$117$	4.00423	+	4.00423i	0.370191	+	0.370191i
$118$	−2.50075	+	2.50075i	−0.230213	+	0.230213i
$119$		−	0.638022i		−	0.0584874i
$120$	−4.66611	−	0.0741390i	−0.425956	−	0.00676793i
$121$	−10.7973	−	2.10193i	−0.981574	−	0.191084i
$122$	2.19018	−	2.19018i	0.198290	−	0.198290i
$123$	8.15639	−	8.15639i	0.735437	−	0.735437i
$124$			3.62644i			0.325663i
$125$	−11.1676	−	0.532680i	−0.998864	−	0.0476444i
$126$	−1.35562			−0.120769
$127$	12.7004	+	12.7004i	1.12698	+	1.12698i	0.990666	+	0.136309i	$0.0435240\pi$
$127$	12.7004	+	12.7004i	1.12698	+	1.12698i	0.136309	+	0.990666i	$0.456476\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	1.90932			0.168106
$130$	9.33952	+	0.148394i	0.819130	+	0.0130150i
$131$		−	15.8131i		−	1.38160i	−0.723046	−	0.690799i	$-0.757259\pi$
$131$		−	15.8131i		−	1.38160i	0.723046	−	0.690799i	$-0.242741\pi$
$132$	4.40208	+	5.34168i	0.383152	+	0.464934i
$133$	−2.99435	−	2.99435i	−0.259643	−	0.259643i
$134$	−15.7321			−1.35905
$135$	−5.51173	+	5.33932i	−0.474374	+	0.459535i
$136$	0.638022			0.0547100
$137$	7.73685	−	7.73685i	0.661004	−	0.661004i	−0.294613	−	0.955617i	$-0.595191\pi$
$137$	7.73685	−	7.73685i	0.661004	−	0.661004i	0.955617	+	0.294613i	$0.0951908\pi$
$138$	3.38977	−	3.38977i	0.288556	−	0.288556i
$139$	−10.3861			−0.880941			−0.440470	−	0.897767i	$-0.645188\pi$
$139$	−10.3861			−0.880941			−0.440470	+	0.897767i	$0.645188\pi$
$140$	−1.60606	+	1.55582i	−0.135737	+	0.131491i
$141$	−1.04917			−0.0883560
$142$	8.69169	+	8.69169i	0.729391	+	0.729391i
$143$	−8.81105	−	10.6917i	−0.736817	−	0.894086i
$144$		−	1.35562i		−	0.112969i
$145$	5.34014	+	0.0848485i	0.443475	+	0.00704628i
$146$	2.01946			0.167132
$147$	−1.47574	+	1.47574i	−0.121717	+	0.121717i
$148$	−0.785489	−	0.785489i	−0.0645668	−	0.0645668i
$149$	−13.8478			−1.13446			−0.567228	−	0.823561i	$-0.691984\pi$
$149$	−13.8478			−1.13446			−0.567228	+	0.823561i	$0.691984\pi$
$150$	0.331518	−	10.4298i	0.0270683	−	0.851590i
$151$			4.71579i			0.383765i	0.981418	+	0.191883i	$0.0614593\pi$
$151$			4.71579i			0.383765i	−0.981418	+	0.191883i	$0.938541\pi$
$152$	2.99435	−	2.99435i	0.242874	−	0.242874i
$153$	−0.611590	+	0.611590i	−0.0494441	+	0.0494441i
$154$	3.30131	+	0.318348i	0.266027	+	0.0256532i
$155$	−8.10793	−	0.128825i	−0.651245	−	0.0103475i
$156$			8.71806i			0.698003i
$157$	−10.9043	+	10.9043i	−0.870259	+	0.870259i	−0.992500	−	0.122241i	$-0.960992\pi$
$157$	−10.9043	+	10.9043i	−0.870259	+	0.870259i	0.122241	+	0.992500i	$0.460992\pi$
$158$	1.85676	+	1.85676i	0.147716	+	0.147716i
$159$			23.1842i			1.83863i
$160$	−1.55582	−	1.60606i	−0.122998	−	0.126970i
$161$		−	2.29699i		−	0.181028i
$162$	−7.94021	−	7.94021i	−0.623842	−	0.623842i
$163$	15.3862	+	15.3862i	1.20514	+	1.20514i	0.972584	+	0.232554i	$0.0747081\pi$
$163$	15.3862	+	15.3862i	1.20514	+	1.20514i	0.232554	+	0.972584i	$0.425292\pi$
$164$	5.52698			0.431584
$165$	−12.0992	+	9.65236i	−0.941924	+	0.751435i
$166$	8.23275			0.638985
$167$	7.55138	+	7.55138i	0.584343	+	0.584343i	0.936094	−	0.351751i	$-0.114413\pi$
$167$	7.55138	+	7.55138i	0.584343	+	0.584343i	−0.351751	+	0.936094i	$0.614413\pi$
$168$	−1.47574	−	1.47574i	−0.113856	−	0.113856i
$169$		−	4.44974i		−	0.342288i
$170$	−0.0226651	+	1.42648i	−0.00173833	+	0.109406i
$171$			5.74060i			0.438994i
$172$	0.646902	+	0.646902i	0.0493258	+	0.0493258i
$173$	3.44316	−	3.44316i	0.261778	−	0.261778i	−0.563998	−	0.825776i	$-0.690737\pi$
$173$	3.44316	−	3.44316i	0.261778	−	0.261778i	0.825776	+	0.563998i	$0.190737\pi$
$174$			4.98480i			0.377897i
$175$	−3.42143	−	3.64607i	−0.258636	−	0.275617i
$176$	−0.318348	+	3.30131i	−0.0239964	+	0.248846i
$177$	5.21910	−	5.21910i	0.392291	−	0.392291i
$178$	−1.56249	+	1.56249i	−0.117114	+	0.117114i
$179$			26.0874i			1.94986i	0.222502	+	0.974932i	$0.428578\pi$
$179$			26.0874i			1.94986i	−0.222502	+	0.974932i	$0.571422\pi$
$180$	3.03089	+	0.0481572i	0.225909	+	0.00358942i
$181$	2.87265			0.213523			0.106761	−	0.994285i	$-0.465952\pi$
$181$	2.87265			0.213523			0.106761	+	0.994285i	$0.465952\pi$
$182$	2.95379	+	2.95379i	0.218949	+	0.218949i
$183$	−4.57094	+	4.57094i	−0.337894	+	0.337894i
$184$	2.29699			0.169337
$185$	1.78409	−	1.72828i	0.131169	−	0.127066i
$186$		−	7.56842i		−	0.554943i
$187$	1.63301	−	1.34576i	0.119417	−	0.0984120i
$188$	−0.355472	−	0.355472i	−0.0259255	−	0.0259255i
$189$	−3.43183			−0.249629
$190$	6.58836	+	6.80110i	0.477970	+	0.493404i
$191$	−14.6811			−1.06229			−0.531145	−	0.847281i	$-0.678238\pi$
$191$	−14.6811			−1.06229			−0.531145	+	0.847281i	$0.678238\pi$
$192$	1.47574	−	1.47574i	0.106502	−	0.106502i
$193$	−1.26793	+	1.26793i	−0.0912678	+	0.0912678i	−0.751267	−	0.659999i	$-0.770557\pi$
$193$	−1.26793	+	1.26793i	−0.0912678	+	0.0912678i	0.659999	+	0.751267i	$0.270557\pi$
$194$	−14.8372			−1.06525
$195$	−19.4917	−	0.309700i	−1.39583	−	0.0221781i
$196$	−1.00000			−0.0714286
$197$	15.7038	+	15.7038i	1.11885	+	1.11885i	0.991911	+	0.126938i	$0.0405150\pi$
$197$	15.7038	+	15.7038i	1.11885	+	1.11885i	0.126938	+	0.991911i	$0.459485\pi$
$198$	−2.85938	−	3.46970i	−0.203208	−	0.246581i
$199$			12.2135i			0.865792i	0.901444	+	0.432896i	$0.142508\pi$
$199$			12.2135i			0.865792i	−0.901444	+	0.432896i	$0.857492\pi$
$200$	3.64607	−	3.42143i	0.257816	−	0.241931i
$201$	32.8331			2.31587
$202$	−9.86097	+	9.86097i	−0.693815	+	0.693815i
$203$	1.68891	+	1.68891i	0.118539	+	0.118539i
$204$	−1.33156			−0.0932279
$205$	−0.196340	+	12.3571i	−0.0137130	+	0.863060i
$206$			10.9291i			0.761469i
$207$	−2.20183	+	2.20183i	−0.153038	+	0.153038i
$208$	−2.95379	+	2.95379i	−0.204808	+	0.204808i
$209$	1.34809	−	13.9799i	0.0932494	−	0.967010i
$210$	3.35187	−	3.24702i	0.231301	−	0.224065i
$211$			16.2608i			1.11944i	0.828681	+	0.559721i	$0.189092\pi$
$211$			16.2608i			1.11944i	−0.828681	+	0.559721i	$0.810908\pi$
$212$	−7.85510	+	7.85510i	−0.539490	+	0.539490i
$213$	−18.1397	−	18.1397i	−1.24291	−	1.24291i
$214$			19.1584i			1.30964i
$215$	−1.46931	+	1.42335i	−0.100206	+	0.0970719i
$216$		−	3.43183i		−	0.233507i
$217$	−2.56428	−	2.56428i	−0.174074	−	0.174074i
$218$	2.98117	+	2.98117i	0.201910	+	0.201910i
$219$	−4.21465			−0.284799
$220$	−7.36972	−	0.829033i	−0.496866	−	0.0558934i
$221$	2.66520			0.179281
$222$	1.63933	+	1.63933i	0.110024	+	0.110024i
$223$	4.94544	+	4.94544i	0.331171	+	0.331171i	0.853031	−	0.521860i	$-0.174762\pi$
$223$	4.94544	+	4.94544i	0.331171	+	0.331171i	−0.521860	+	0.853031i	$0.674762\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−0.215338	+	6.77470i	−0.0143559	+	0.451647i
$226$		−	9.33697i		−	0.621086i
$227$	14.8708	+	14.8708i	0.987007	+	0.987007i	0.999917	−	0.0129093i	$-0.00410927\pi$
$227$	14.8708	+	14.8708i	0.987007	+	0.987007i	−0.0129093	+	0.999917i	$0.504109\pi$
$228$	−6.24925	+	6.24925i	−0.413867	+	0.413867i
$229$		−	21.1809i		−	1.39967i	−0.714302	−	0.699837i	$-0.753256\pi$
$229$		−	21.1809i		−	1.39967i	0.714302	−	0.699837i	$-0.246744\pi$
$230$	−0.0815983	+	5.13559i	−0.00538043	+	0.338630i
$231$	−6.88988	−	0.664396i	−0.453321	−	0.0437140i
$232$	−1.68891	+	1.68891i	−0.110883	+	0.110883i
$233$	−12.9511	+	12.9511i	−0.848457	+	0.848457i	−0.989941	−	0.141483i	$-0.954813\pi$
$233$	−12.9511	+	12.9511i	−0.848457	+	0.848457i	0.141483	+	0.989941i	$0.454813\pi$
$234$		−	5.66284i		−	0.370191i
$235$	0.807387	−	0.782132i	0.0526681	−	0.0510206i
$236$	3.53659			0.230213
$237$	−3.87508	−	3.87508i	−0.251713	−	0.251713i
$238$	−0.451150	+	0.451150i	−0.0292437	+	0.0292437i
$239$	−23.2798			−1.50585			−0.752923	−	0.658108i	$-0.771357\pi$
$239$	−23.2798			−1.50585			−0.752923	+	0.658108i	$0.771357\pi$
$240$	3.24702	+	3.35187i	0.209594	+	0.216362i
$241$			2.12212i			0.136698i	0.997661	+	0.0683490i	$0.0217731\pi$
$241$			2.12212i			0.136698i	−0.997661	+	0.0683490i	$0.978227\pi$
$242$	6.14856	+	9.12114i	0.395245	+	0.586329i
$243$	9.29131	+	9.29131i	0.596038	+	0.596038i
$244$	−3.09739			−0.198290
$245$	0.0355240	−	2.23579i	0.00226954	−	0.142839i
$246$	−11.5349			−0.735437
$247$	12.5083	−	12.5083i	0.795882	−	0.795882i
$248$	2.56428	−	2.56428i	0.162832	−	0.162832i
$249$	−17.1819			−1.08886
$250$	7.52005	+	8.27338i	0.475610	+	0.523254i
$251$	−21.6471			−1.36635			−0.683177	−	0.730253i	$-0.739402\pi$
$251$	−21.6471			−1.36635			−0.683177	+	0.730253i	$0.739402\pi$
$252$	0.958571	+	0.958571i	0.0603843	+	0.0603843i
$253$	5.87912	−	4.84499i	0.369617	−	0.304602i
$254$		−	17.9610i		−	1.12698i
$255$	0.0473023	−	2.97709i	0.00296219	−	0.186432i
$256$	1.00000			0.0625000
$257$	−0.914758	+	0.914758i	−0.0570610	+	0.0570610i	−0.735061	−	0.678000i	$-0.762847\pi$
$257$	−0.914758	+	0.914758i	−0.0570610	+	0.0570610i	0.678000	+	0.735061i	$0.262847\pi$
$258$	−1.35009	−	1.35009i	−0.0840531	−	0.0840531i
$259$	1.11085			0.0690248
$260$	−6.49911	−	6.70897i	−0.403058	−	0.416073i
$261$		−	3.23789i		−	0.200420i
$262$	−11.1816	+	11.1816i	−0.690799	+	0.690799i
$263$	6.10328	−	6.10328i	0.376345	−	0.376345i	−0.493437	−	0.869782i	$-0.664260\pi$
$263$	6.10328	−	6.10328i	0.376345	−	0.376345i	0.869782	+	0.493437i	$0.164260\pi$
$264$	0.664396	−	6.88988i	0.0408907	−	0.424043i
$265$	−17.2833	−	17.8414i	−1.06170	−	1.09599i
$266$			4.23465i			0.259643i
$267$	3.26094	−	3.26094i	0.199566	−	0.199566i
$268$	11.1243	+	11.1243i	0.679524	+	0.679524i
$269$			12.9188i			0.787670i	0.919181	+	0.393835i	$0.128852\pi$
$269$			12.9188i			0.787670i	−0.919181	+	0.393835i	$0.871148\pi$
$270$	7.67284	+	0.121912i	0.466954	+	0.00741935i
$271$			7.09160i			0.430784i	0.976528	+	0.215392i	$0.0691029\pi$
$271$			7.09160i			0.430784i	−0.976528	+	0.215392i	$0.930897\pi$
$272$	−0.451150	−	0.451150i	−0.0273550	−	0.0273550i
$273$	−6.16460	−	6.16460i	−0.373098	−	0.373098i
$274$	−10.9416			−0.661004
$275$	2.11534	−	16.4477i	0.127560	−	0.991831i
$276$	−4.79386			−0.288556
$277$	9.52729	+	9.52729i	0.572440	+	0.572440i	0.932809	−	0.360370i	$-0.117350\pi$
$277$	9.52729	+	9.52729i	0.572440	+	0.572440i	−0.360370	+	0.932809i	$0.617350\pi$
$278$	7.34411	+	7.34411i	0.440470	+	0.440470i
$279$			4.91608i			0.294318i
$280$	2.23579	+	0.0355240i	0.133614	+	0.00212296i
$281$			14.5582i			0.868467i	0.900800	+	0.434233i	$0.142981\pi$
$281$			14.5582i			0.868467i	−0.900800	+	0.434233i	$0.857019\pi$
$282$	0.741875	+	0.741875i	0.0441780	+	0.0441780i
$283$	−8.22752	+	8.22752i	−0.489076	+	0.489076i	−0.908014	−	0.418939i	$-0.862402\pi$
$283$	−8.22752	+	8.22752i	−0.489076	+	0.489076i	0.418939	+	0.908014i	$0.362402\pi$
$284$		−	12.2919i		−	0.729391i
$285$	−13.7500	−	14.1940i	−0.814479	−	0.840779i
$286$	−1.32983	+	13.7905i	−0.0786345	+	0.815451i
$287$	−3.90816	+	3.90816i	−0.230692	+	0.230692i
$288$	−0.958571	+	0.958571i	−0.0564844	+	0.0564844i
$289$		−	16.5929i		−	0.976055i
$290$	−3.71605	−	3.83605i	−0.218214	−	0.225260i
$291$	30.9654			1.81522
$292$	−1.42798	−	1.42798i	−0.0835660	−	0.0835660i
$293$	11.7454	−	11.7454i	0.686174	−	0.686174i	−0.275210	−	0.961384i	$-0.588747\pi$
$293$	11.7454	−	11.7454i	0.686174	−	0.686174i	0.961384	+	0.275210i	$0.0887474\pi$
$294$	2.08701			0.121717
$295$	−0.125634	+	7.90706i	−0.00731468	+	0.460367i
$296$			1.11085i			0.0645668i
$297$	−7.23868	−	8.78373i	−0.420031	−	0.509684i
$298$	9.79187	+	9.79187i	0.567228	+	0.567228i
$299$	9.59521			0.554905
$300$	−7.60940	+	7.14056i	−0.439329	+	0.412261i
$301$	−0.914857			−0.0527315
$302$	3.33457	−	3.33457i	0.191883	−	0.191883i
$303$	20.5800	−	20.5800i	1.18229	−	1.18229i
$304$	−4.23465			−0.242874
$305$	0.110031	−	6.92509i	0.00630038	−	0.396530i
$306$	0.864919			0.0494441
$307$	15.2346	+	15.2346i	0.869486	+	0.869486i	0.992415	−	0.122929i	$-0.0392289\pi$
$307$	15.2346	+	15.2346i	0.869486	+	0.869486i	−0.122929	+	0.992415i	$0.539229\pi$
$308$	−2.10927	−	2.55949i	−0.120187	−	0.145840i
$309$		−	22.8093i		−	1.29757i
$310$	5.64208	+	5.82427i	0.320449	+	0.330796i
$311$	−0.783279			−0.0444157			−0.0222078	−	0.999753i	$-0.507070\pi$
$311$	−0.783279			−0.0444157			−0.0222078	+	0.999753i	$0.507070\pi$
$312$	6.16460	−	6.16460i	0.349002	−	0.349002i
$313$	−6.12181	−	6.12181i	−0.346025	−	0.346025i	0.512601	−	0.858627i	$-0.328682\pi$
$313$	−6.12181	−	6.12181i	−0.346025	−	0.346025i	−0.858627	+	0.512601i	$0.828682\pi$
$314$	15.4210			0.870259
$315$	−2.17721	+	2.10911i	−0.122672	+	0.118835i
$316$		−	2.62585i		−	0.147716i
$317$	8.70477	−	8.70477i	0.488909	−	0.488909i	−0.419053	−	0.907962i	$-0.637638\pi$
$317$	8.70477	−	8.70477i	0.488909	−	0.488909i	0.907962	+	0.419053i	$0.137638\pi$
$318$	16.3937	−	16.3937i	0.919313	−	0.919313i
$319$	−0.760369	+	7.88513i	−0.0425725	+	0.441483i
$320$	−0.0355240	+	2.23579i	−0.00198585	+	0.124984i
$321$		−	39.9838i		−	2.23168i
$322$	−1.62422	+	1.62422i	−0.0905142	+	0.0905142i
$323$	1.91046	+	1.91046i	0.106301	+	0.106301i
$324$			11.2292i			0.623842i
$325$	15.2307	−	14.2923i	0.844847	−	0.792794i
$326$		−	21.7593i		−	1.20514i
$327$	−6.22174	−	6.22174i	−0.344063	−	0.344063i
$328$	−3.90816	−	3.90816i	−0.215792	−	0.215792i
$329$	0.502713			0.0277155
$330$	15.3807	+	1.73020i	0.846679	+	0.0952445i
$331$	6.44423			0.354207			0.177104	−	0.984192i	$-0.443327\pi$
$331$	6.44423			0.354207			0.177104	+	0.984192i	$0.443327\pi$
$332$	−5.82143	−	5.82143i	−0.319493	−	0.319493i
$333$	−1.06483	−	1.06483i	−0.0583522	−	0.0583522i
$334$		−	10.6793i		−	0.584343i
$335$	−25.2667	+	24.4763i	−1.38047	+	1.33729i
$336$			2.08701i			0.113856i
$337$	5.75820	+	5.75820i	0.313669	+	0.313669i	0.846329	−	0.532660i	$-0.178808\pi$
$337$	5.75820	+	5.75820i	0.313669	+	0.313669i	−0.532660	+	0.846329i	$0.678808\pi$
$338$	−3.14644	+	3.14644i	−0.171144	+	0.171144i
$339$			19.4864i			1.05836i
$340$	1.02470	−	0.992648i	0.0555722	−	0.0538339i
$341$	1.15447	−	11.9720i	0.0625179	−	0.648320i
$342$	4.05922	−	4.05922i	0.219497	−	0.219497i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		−	0.914857i		−	0.0493258i
$345$	0.170297	−	10.7180i	0.00916847	−	0.577040i
$346$	−4.86936			−0.261778
$347$	20.0949	+	20.0949i	1.07875	+	1.07875i	0.996622	+	0.0821292i	$0.0261720\pi$
$347$	20.0949	+	20.0949i	1.07875	+	1.07875i	0.0821292	+	0.996622i	$0.473828\pi$
$348$	3.52479	−	3.52479i	0.188948	−	0.188948i
$349$	8.12638			0.434995			0.217498	−	0.976061i	$-0.430211\pi$
$349$	8.12638			0.434995			0.217498	+	0.976061i	$0.430211\pi$
$350$	−0.158848	+	4.99748i	−0.00849078	+	0.267126i
$351$		−	14.3358i		−	0.765186i
$352$	2.55949	−	2.10927i	0.136421	−	0.112425i
$353$	−22.3007	−	22.3007i	−1.18695	−	1.18695i	−0.977907	−	0.209040i	$-0.932966\pi$
$353$	−22.3007	−	22.3007i	−1.18695	−	1.18695i	−0.209040	−	0.977907i	$-0.567034\pi$
$354$	−7.38092			−0.392291
$355$	27.4821	+	0.436657i	1.45860	+	0.0231754i
$356$	2.20970			0.117114
$357$	0.941556	−	0.941556i	0.0498324	−	0.0498324i
$358$	18.4466	−	18.4466i	0.974932	−	0.974932i
$359$	11.6079			0.612644			0.306322	−	0.951928i	$-0.400902\pi$
$359$	11.6079			0.612644			0.306322	+	0.951928i	$0.400902\pi$
$360$	−2.10911	−	2.17721i	−0.111160	−	0.114749i
$361$	−1.06773			−0.0561961
$362$	−2.03127	−	2.03127i	−0.106761	−	0.106761i
$363$	−12.8321	−	19.0359i	−0.673512	−	0.999128i
$364$		−	4.17729i		−	0.218949i
$365$	3.24337	−	3.14192i	0.169766	−	0.164456i
$366$	6.46429			0.337894
$367$	−13.7724	+	13.7724i	−0.718912	+	0.718912i	−0.968382	−	0.249471i	$-0.919743\pi$
$367$	−13.7724	+	13.7724i	−0.718912	+	0.718912i	0.249471	+	0.968382i	$0.419743\pi$
$368$	−1.62422	−	1.62422i	−0.0846683	−	0.0846683i
$369$	7.49251			0.390044
$370$	−2.48362	−	0.0394618i	−0.129117	−	0.00205152i
$371$		−	11.1088i		−	0.576739i
$372$	−5.35168	+	5.35168i	−0.277472	+	0.277472i
$373$	−11.7098	+	11.7098i	−0.606310	+	0.606310i	−0.941980	−	0.335670i	$-0.891037\pi$
$373$	−11.7098	+	11.7098i	−0.606310	+	0.606310i	0.335670	+	0.941980i	$0.391037\pi$
$374$	−2.10631	−	0.203113i	−0.108915	−	0.0105027i
$375$	−15.6945	−	17.2666i	−0.810458	−	0.891646i
$376$			0.502713i			0.0259255i
$377$	−7.05508	+	7.05508i	−0.363355	+	0.363355i
$378$	2.42667	+	2.42667i	0.124815	+	0.124815i
$379$			8.67876i			0.445798i	0.974842	+	0.222899i	$0.0715520\pi$
$379$			8.67876i			0.445798i	−0.974842	+	0.222899i	$0.928448\pi$
$380$	0.150432	−	9.46777i	0.00771698	−	0.485687i
$381$			37.4849i			1.92041i
$382$	10.3811	+	10.3811i	0.531145	+	0.531145i
$383$	−19.8379	−	19.8379i	−1.01367	−	1.01367i	−0.999905	−	0.0137617i	$-0.995619\pi$
$383$	−19.8379	−	19.8379i	−1.01367	−	1.01367i	−0.0137617	−	0.999905i	$-0.504381\pi$
$384$	−2.08701			−0.106502
$385$	5.79739	−	4.62496i	0.295462	−	0.235710i
$386$	1.79313			0.0912678
$387$	0.876956	+	0.876956i	0.0445782	+	0.0445782i
$388$	10.4915	+	10.4915i	0.532624	+	0.532624i
$389$			8.60678i			0.436381i	0.975906	+	0.218190i	$0.0700154\pi$
$389$			8.60678i			0.436381i	−0.975906	+	0.218190i	$0.929985\pi$
$390$	13.5637	+	14.0017i	0.686826	+	0.709004i
$391$			1.46553i			0.0741152i
$392$	0.707107	+	0.707107i	0.0357143	+	0.0357143i
$393$	23.3361	−	23.3361i	1.17715	−	1.17715i
$394$		−	22.2085i		−	1.11885i
$395$	5.87084	+	0.0932807i	0.295394	+	0.00469346i
$396$	−0.431560	+	4.47534i	−0.0216867	+	0.224894i
$397$	2.62954	−	2.62954i	0.131973	−	0.131973i	−0.638035	−	0.770008i	$-0.720252\pi$
$397$	2.62954	−	2.62954i	0.131973	−	0.131973i	0.770008	+	0.638035i	$0.220252\pi$
$398$	8.63625	−	8.63625i	0.432896	−	0.432896i
$399$		−	8.83777i		−	0.442442i
$400$	−4.99748	−	0.158848i	−0.249874	−	0.00794240i
$401$	23.0172			1.14943			0.574713	−	0.818355i	$-0.305114\pi$
$401$	23.0172			1.14943			0.574713	+	0.818355i	$0.305114\pi$
$402$	−23.2165	−	23.2165i	−1.15794	−	1.15794i
$403$	10.7117	−	10.7117i	0.533589	−	0.533589i
$404$	13.9455			0.693815
$405$	−25.1060	−	0.398904i	−1.24753	−	0.0198217i
$406$		−	2.38849i		−	0.118539i
$407$	2.34309	+	2.84320i	0.116142	+	0.140932i
$408$	0.941556	+	0.941556i	0.0466140	+	0.0466140i
$409$	0.547602			0.0270772			0.0135386	−	0.999908i	$-0.495690\pi$
$409$	0.547602			0.0270772			0.0135386	+	0.999908i	$0.495690\pi$
$410$	8.87665	−	8.59898i	0.438386	−	0.424673i
$411$	22.8352			1.12638
$412$	7.72807	−	7.72807i	0.380735	−	0.380735i
$413$	−2.50075	+	2.50075i	−0.123054	+	0.123054i
$414$	3.11386			0.153038
$415$	13.2223	−	12.8087i	0.649056	−	0.628753i
$416$	4.17729			0.204808
$417$	−15.3273	−	15.3273i	−0.750579	−	0.750579i
$418$	−10.8385	+	8.93204i	−0.530130	+	0.436880i
$419$			31.6243i			1.54495i	0.635046	+	0.772474i	$0.280981\pi$
$419$			31.6243i			1.54495i	−0.635046	+	0.772474i	$0.719019\pi$
$420$	−4.66611	−	0.0741390i	−0.227683	−	0.00361761i
$421$	6.39666			0.311754			0.155877	−	0.987776i	$-0.450180\pi$
$421$	6.39666			0.311754			0.155877	+	0.987776i	$0.450180\pi$
$422$	11.4981	−	11.4981i	0.559721	−	0.559721i
$423$	−0.481887	−	0.481887i	−0.0234301	−	0.0234301i
$424$	11.1088			0.539490
$425$	2.18295	+	2.32627i	0.105888	+	0.112841i
$426$			25.6534i			1.24291i
$427$	2.19018	−	2.19018i	0.105990	−	0.105990i
$428$	13.5470	−	13.5470i	0.654820	−	0.654820i
$429$	2.77537	−	28.7810i	0.133996	−	1.38956i
$430$	2.04543	+	0.0324994i	0.0986392	+	0.00156726i
$431$		−	19.1600i		−	0.922906i	−0.887165	−	0.461453i	$-0.847328\pi$
$431$		−	19.1600i		−	0.922906i	0.887165	−	0.461453i	$-0.152672\pi$
$432$	−2.42667	+	2.42667i	−0.116753	+	0.116753i
$433$	−12.6808	−	12.6808i	−0.609402	−	0.609402i	0.333388	−	0.942790i	$-0.391808\pi$
$433$	−12.6808	−	12.6808i	−0.609402	−	0.609402i	−0.942790	+	0.333388i	$0.891808\pi$
$434$			3.62644i			0.174074i
$435$	7.75545	+	8.00588i	0.371846	+	0.383853i
$436$		−	4.21601i		−	0.201910i
$437$	6.87800	+	6.87800i	0.329020	+	0.329020i
$438$	2.98020	+	2.98020i	0.142400	+	0.142400i
$439$	13.1593			0.628058			0.314029	−	0.949413i	$-0.398321\pi$
$439$	13.1593			0.628058			0.314029	+	0.949413i	$0.398321\pi$
$440$	4.62496	+	5.79739i	0.220486	+	0.276380i
$441$	−1.35562			−0.0645536
$442$	−1.88458	−	1.88458i	−0.0896405	−	0.0896405i
$443$	16.6641	+	16.6641i	0.791734	+	0.791734i	0.981776	−	0.190042i	$-0.0608624\pi$
$443$	16.6641	+	16.6641i	0.791734	+	0.791734i	−0.190042	+	0.981776i	$0.560862\pi$
$444$		−	2.31836i		−	0.110024i
$445$	−0.0784972	+	4.94041i	−0.00372112	+	0.234198i
$446$		−	6.99391i		−	0.331171i
$447$	−20.4358	−	20.4358i	−0.966578	−	0.966578i
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$		−	22.3700i		−	1.05570i	−0.849336	−	0.527852i	$-0.822998\pi$
$449$		−	22.3700i		−	1.05570i	0.849336	−	0.527852i	$-0.177002\pi$
$450$	4.94270	−	4.63817i	0.233001	−	0.218645i
$451$	−18.2463	−	1.75950i	−0.859183	−	0.0828516i
$452$	−6.60224	+	6.60224i	−0.310543	+	0.310543i
$453$	−6.95928	+	6.95928i	−0.326976	+	0.326976i
$454$		−	21.0304i		−	0.987007i
$455$	9.33952	+	0.148394i	0.437844	+	0.00695681i
$456$	8.83777			0.413867
$457$	−8.45249	−	8.45249i	−0.395391	−	0.395391i	0.481213	−	0.876604i	$-0.340196\pi$
$457$	−8.45249	−	8.45249i	−0.395391	−	0.395391i	−0.876604	+	0.481213i	$0.840196\pi$
$458$	−14.9772	+	14.9772i	−0.699837	+	0.699837i
$459$	2.18959			0.102201
$460$	3.68911	−	3.57371i	0.172005	−	0.166625i
$461$		−	0.146501i		−	0.00682324i	−0.999994	−	0.00341162i	$-0.998914\pi$
$461$		−	0.146501i		−	0.00682324i	0.999994	−	0.00341162i	$-0.00108595\pi$
$462$	4.40208	+	5.34168i	0.204803	+	0.248517i
$463$	−14.7640	−	14.7640i	−0.686140	−	0.686140i	0.275236	−	0.961377i	$-0.411244\pi$
$463$	−14.7640	−	14.7640i	−0.686140	−	0.686140i	−0.961377	+	0.275236i	$0.911244\pi$
$464$	2.38849			0.110883
$465$	−11.7751	−	12.1553i	−0.546057	−	0.563690i
$466$	18.3157			0.848457
$467$	−2.19138	+	2.19138i	−0.101405	+	0.101405i	−0.755989	−	0.654584i	$-0.772844\pi$
$467$	−2.19138	+	2.19138i	−0.101405	+	0.101405i	0.654584	+	0.755989i	$0.272844\pi$
$468$	−4.00423	+	4.00423i	−0.185096	+	0.185096i
$469$	−15.7321			−0.726442
$470$	−1.12396	−	0.0178584i	−0.0518444	−	0.000823745i
$471$	−32.1839			−1.48296
$472$	−2.50075	−	2.50075i	−0.115106	−	0.115106i
$473$	−1.92968	−	2.34156i	−0.0887270	−	0.107665i
$474$			5.48019i			0.251713i
$475$	21.1626	+	0.672666i	0.971005	+	0.0308640i
$476$	0.638022			0.0292437
$477$	−10.6486	+	10.6486i	−0.487564	+	0.487564i
$478$	16.4613	+	16.4613i	0.752923	+	0.752923i
$479$	−20.9509			−0.957271			−0.478636	−	0.878014i	$-0.658869\pi$
$479$	−20.9509			−0.957271			−0.478636	+	0.878014i	$0.658869\pi$
$480$	0.0741390	−	4.66611i	0.00338397	−	0.212978i
$481$			4.64034i			0.211581i
$482$	1.50057	−	1.50057i	0.0683490	−	0.0683490i
$483$	3.38977	−	3.38977i	0.154240	−	0.154240i
$484$	2.10193	−	10.7973i	0.0955422	−	0.490787i
$485$	−23.8294	+	23.0840i	−1.08204	+	1.04819i
$486$		−	13.1399i		−	0.596038i
$487$	−17.6907	+	17.6907i	−0.801643	+	0.801643i	−0.983352	−	0.181709i	$-0.941837\pi$
$487$	−17.6907	+	17.6907i	−0.801643	+	0.801643i	0.181709	+	0.983352i	$0.441837\pi$
$488$	2.19018	+	2.19018i	0.0991449	+	0.0991449i
$489$			45.4120i			2.05360i
$490$	−1.60606	+	1.55582i	−0.0725543	+	0.0702848i
$491$		−	24.3169i		−	1.09741i	−0.836017	−	0.548703i	$-0.815122\pi$
$491$		−	24.3169i		−	1.09741i	0.836017	−	0.548703i	$-0.184878\pi$
$492$	8.15639	+	8.15639i	0.367718	+	0.367718i
$493$	−1.07757	−	1.07757i	−0.0485311	−	0.0485311i
$494$	−17.6894			−0.795882
$495$	−9.99057	−	1.12386i	−0.449043	−	0.0505136i
$496$	−3.62644			−0.162832
$497$	8.69169	+	8.69169i	0.389876	+	0.389876i
$498$	12.1494	+	12.1494i	0.544428	+	0.544428i
$499$			2.40488i			0.107657i	0.998550	+	0.0538285i	$0.0171424\pi$
$499$			2.40488i			0.107657i	−0.998550	+	0.0538285i	$0.982858\pi$
$500$	0.532680	−	11.1676i	0.0238222	−	0.499432i
$501$			22.2878i			0.995744i
$502$	15.3068	+	15.3068i	0.683177	+	0.683177i
$503$	−25.9760	+	25.9760i	−1.15821	+	1.15821i	−0.173355	+	0.984859i	$0.555461\pi$
$503$	−25.9760	+	25.9760i	−1.15821	+	1.15821i	−0.984859	+	0.173355i	$0.944539\pi$
$504$		−	1.35562i		−	0.0603843i
$505$	−0.495400	+	31.1792i	−0.0220450	+	1.38746i
$506$	−7.58309	−	0.731243i	−0.337109	−	0.0325077i
$507$	6.56667	−	6.56667i	0.291636	−	0.291636i
$508$	−12.7004	+	12.7004i	−0.563488	+	0.563488i
$509$		−	5.06074i		−	0.224314i	−0.993691	−	0.112157i	$-0.964224\pi$
$509$		−	5.06074i		−	0.224314i	0.993691	−	0.112157i	$-0.0357759\pi$
$510$	−2.13856	+	2.07167i	−0.0946972	+	0.0917351i
$511$	2.01946			0.0893358
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	10.2761	−	10.2761i	0.453701	−	0.453701i
$514$	1.29366			0.0570610
$515$	17.0038	+	17.5528i	0.749276	+	0.773470i
$516$			1.90932i			0.0840531i
$517$	1.06036	+	1.28669i	0.0466346	+	0.0565885i
$518$	−0.785489	−	0.785489i	−0.0345124	−	0.0345124i
$519$	10.1624			0.446081
$520$	−0.148394	+	9.33952i	−0.00650750	+	0.409565i
$521$	40.5987			1.77866			0.889330	−	0.457266i	$-0.151171\pi$
$521$	40.5987			1.77866			0.889330	+	0.457266i	$0.151171\pi$
$522$	−2.28953	+	2.28953i	−0.100210	+	0.100210i
$523$	−16.6613	+	16.6613i	−0.728547	+	0.728547i	−0.970330	−	0.241783i	$-0.922268\pi$
$523$	−16.6613	+	16.6613i	−0.728547	+	0.728547i	0.241783	+	0.970330i	$0.422268\pi$
$524$	15.8131			0.690799
$525$	0.331518	−	10.4298i	0.0144686	−	0.455194i
$526$	−8.63135			−0.376345
$527$	1.63607	+	1.63607i	0.0712681	+	0.0712681i
$528$	−5.34168	+	4.40208i	−0.232467	+	0.191576i
$529$		−	17.7238i		−	0.770601i
$530$	−0.394628	+	24.8369i	−0.0171415	+	1.07884i
$531$	4.79429			0.208055
$532$	2.99435	−	2.99435i	0.129822	−	0.129822i
$533$	−16.3255	−	16.3255i	−0.707137	−	0.707137i
$534$	−4.61167			−0.199566
$535$	29.8070	+	30.7695i	1.28867	+	1.33028i
$536$		−	15.7321i		−	0.679524i
$537$	−38.4983	+	38.4983i	−1.66132	+	1.66132i
$538$	9.13494	−	9.13494i	0.393835	−	0.393835i
$539$	3.30131	+	0.318348i	0.142198	+	0.0137122i
$540$	−5.33932	−	5.51173i	−0.229768	−	0.237187i
$541$			20.3179i			0.873536i	0.899574	+	0.436768i	$0.143877\pi$
$541$			20.3179i			0.873536i	−0.899574	+	0.436768i	$0.856123\pi$
$542$	5.01452	−	5.01452i	0.215392	−	0.215392i
$543$	4.23929	+	4.23929i	0.181925	+	0.181925i
$544$			0.638022i			0.0273550i
$545$	9.42610	+	0.149769i	0.403770	+	0.00641542i
$546$			8.71806i			0.373098i
$547$	−16.5699	−	16.5699i	−0.708477	−	0.708477i	0.257738	−	0.966215i	$-0.417023\pi$
$547$	−16.5699	−	16.5699i	−0.708477	−	0.708477i	−0.966215	+	0.257738i	$0.917023\pi$
$548$	7.73685	+	7.73685i	0.330502	+	0.330502i
$549$	−4.19889			−0.179204
$550$	−13.1260	+	10.1345i	−0.559695	+	0.432135i
$551$	−10.1144			−0.430888
$552$	3.38977	+	3.38977i	0.144278	+	0.144278i
$553$	1.85676	+	1.85676i	0.0789574	+	0.0789574i
$554$		−	13.4736i		−	0.572440i
$555$	5.18335	+	0.0823572i	0.220021	+	0.00349587i
$556$		−	10.3861i		−	0.440470i
$557$	−19.5253	−	19.5253i	−0.827314	−	0.827314i	0.159830	−	0.987145i	$-0.448905\pi$
$557$	−19.5253	−	19.5253i	−0.827314	−	0.827314i	−0.987145	+	0.159830i	$0.948905\pi$
$558$	3.47620	−	3.47620i	0.147159	−	0.147159i
$559$		−	3.82162i		−	0.161637i
$560$	−1.55582	−	1.60606i	−0.0657454	−	0.0678684i
$561$	4.39590	+	0.423899i	0.185595	+	0.0178970i
$562$	10.2942	−	10.2942i	0.434233	−	0.434233i
$563$	−5.73877	+	5.73877i	−0.241860	+	0.241860i	−0.817619	−	0.575759i	$-0.804707\pi$
$563$	−5.73877	+	5.73877i	−0.241860	+	0.241860i	0.575759	+	0.817619i	$0.304707\pi$
$564$		−	1.04917i		−	0.0441780i
$565$	−14.5266	−	14.9957i	−0.611141	−	0.630875i
$566$	11.6355			0.489076
$567$	−7.94021	−	7.94021i	−0.333458	−	0.333458i
$568$	−8.69169	+	8.69169i	−0.364695	+	0.364695i
$569$	42.3285			1.77450			0.887251	−	0.461286i	$-0.152612\pi$
$569$	42.3285			1.77450			0.887251	+	0.461286i	$0.152612\pi$
$570$	−0.313953	+	19.7594i	−0.0131500	+	0.827629i
$571$			27.0984i			1.13403i	0.823707	+	0.567015i	$0.191902\pi$
$571$			27.0984i			1.13403i	−0.823707	+	0.567015i	$0.808098\pi$
$572$	10.6917	−	8.81105i	0.447043	−	0.368408i
$573$	−21.6656	−	21.6656i	−0.905092	−	0.905092i
$574$	5.52698			0.230692
$575$	7.85900	+	8.37500i	0.327743	+	0.349262i
$576$	1.35562			0.0564844
$577$	9.69696	−	9.69696i	0.403690	−	0.403690i	−0.475841	−	0.879531i	$-0.657856\pi$
$577$	9.69696	−	9.69696i	0.403690	−	0.403690i	0.879531	+	0.475841i	$0.157856\pi$
$578$	−11.7330	+	11.7330i	−0.488027	+	0.488027i
$579$	−3.74228			−0.155524
$580$	−0.0848485	+	5.34014i	−0.00352314	+	0.221737i
$581$	8.23275			0.341552
$582$	−21.8958	−	21.8958i	−0.907611	−	0.907611i
$583$	28.4328	−	23.4315i	1.17757	−	0.970432i
$584$			2.01946i			0.0835660i
$585$	−8.81035	−	9.09485i	−0.364263	−	0.376026i
$586$	−16.6105			−0.686174
$587$	11.6110	−	11.6110i	0.479236	−	0.479236i	−0.425651	−	0.904887i	$-0.639955\pi$
$587$	11.6110	−	11.6110i	0.479236	−	0.479236i	0.904887	+	0.425651i	$0.139955\pi$
$588$	−1.47574	−	1.47574i	−0.0608585	−	0.0608585i
$589$	15.3567			0.632761
$590$	5.67997	−	5.50230i	0.233841	−	0.226526i
$591$			46.3495i			1.90656i
$592$	0.785489	−	0.785489i	0.0322834	−	0.0322834i
$593$	−18.4078	+	18.4078i	−0.755919	+	0.755919i	−0.975577	−	0.219658i	$-0.929506\pi$
$593$	−18.4078	+	18.4078i	−0.755919	+	0.755919i	0.219658	+	0.975577i	$0.429506\pi$
$594$	−1.09252	+	11.3295i	−0.0448265	+	0.464857i
$595$	−0.0226651	+	1.42648i	−0.000929178	+	0.0584800i
$596$		−	13.8478i		−	0.567228i
$597$	−18.0240	+	18.0240i	−0.737672	+	0.737672i
$598$	−6.78484	−	6.78484i	−0.277453	−	0.277453i
$599$			36.7222i			1.50043i	0.661195	+	0.750214i	$0.270050\pi$
$599$			36.7222i			1.50043i	−0.661195	+	0.750214i	$0.729950\pi$
$600$	10.4298	+	0.331518i	0.425795	+	0.0135342i
$601$		−	47.5649i		−	1.94021i	−0.242678	−	0.970107i	$-0.578026\pi$
$601$		−	47.5649i		−	1.94021i	0.242678	−	0.970107i	$-0.421974\pi$
$602$	0.646902	+	0.646902i	0.0263658	+	0.0263658i
$603$	15.0804	+	15.0804i	0.614120	+	0.614120i
$604$	−4.71579			−0.191883
$605$	24.0658	+	5.08303i	0.978414	+	0.206654i
$606$	−29.1045			−1.18229
$607$	−24.1570	−	24.1570i	−0.980504	−	0.980504i	0.0193095	−	0.999814i	$-0.493853\pi$
$607$	−24.1570	−	24.1570i	−0.980504	−	0.980504i	−0.999814	+	0.0193095i	$0.993853\pi$
$608$	2.99435	+	2.99435i	0.121437	+	0.121437i
$609$			4.98480i			0.201994i
$610$	−4.97458	+	4.81897i	−0.201415	+	0.195115i
$611$			2.09998i			0.0849561i
$612$	−0.611590	−	0.611590i	−0.0247221	−	0.0247221i
$613$	27.9101	−	27.9101i	1.12728	−	1.12728i	0.136661	−	0.990618i	$-0.456363\pi$
$613$	27.9101	−	27.9101i	1.12728	−	1.12728i	0.990618	−	0.136661i	$-0.0436371\pi$
$614$		−	21.5450i		−	0.869486i
$615$	−18.5257	+	17.9462i	−0.747028	+	0.723660i
$616$	−0.318348	+	3.30131i	−0.0128266	+	0.133014i
$617$	−10.0855	+	10.0855i	−0.406027	+	0.406027i	−0.880351	−	0.474324i	$-0.842693\pi$
$617$	−10.0855	+	10.0855i	−0.406027	+	0.406027i	0.474324	+	0.880351i	$0.342693\pi$
$618$	−16.1286	+	16.1286i	−0.648787	+	0.648787i
$619$			26.9422i			1.08290i	0.840734	+	0.541449i	$0.182124\pi$
$619$			26.9422i			1.08290i	−0.840734	+	0.541449i	$0.817876\pi$
$620$	0.128825	−	8.10793i	0.00517375	−	0.325622i
$621$	7.88290			0.316330
$622$	0.553862	+	0.553862i	0.0222078	+	0.0222078i
$623$	−1.56249	+	1.56249i	−0.0625999	+	0.0625999i
$624$	−8.71806			−0.349002
$625$	24.9495	+	1.58768i	0.997981	+	0.0635071i
$626$			8.65755i			0.346025i
$627$	22.6202	−	18.6413i	0.903362	−	0.744461i
$628$	−10.9043	−	10.9043i	−0.435130	−	0.435130i
$629$	−0.708747			−0.0282596
$630$	3.03089	+	0.0481572i	0.120753	+	0.00191863i
$631$	−9.30329			−0.370358			−0.185179	−	0.982705i	$-0.559286\pi$
$631$	−9.30329			−0.370358			−0.185179	+	0.982705i	$0.559286\pi$
$632$	−1.85676	+	1.85676i	−0.0738579	+	0.0738579i
$633$	−23.9968	+	23.9968i	−0.953786	+	0.953786i
$634$	−12.3104			−0.488909
$635$	−27.9441	−	28.8465i	−1.10893	−	1.14474i
$636$	−23.1842			−0.919313
$637$	2.95379	+	2.95379i	0.117033	+	0.117033i
$638$	6.11329	−	5.03797i	0.242028	−	0.199455i
$639$		−	16.6632i		−	0.659187i
$640$	1.60606	−	1.55582i	0.0634850	−	0.0614992i
$641$	35.8033			1.41414			0.707072	−	0.707141i	$-0.250015\pi$
$641$	35.8033			1.41414			0.707072	+	0.707141i	$0.250015\pi$
$642$	−28.2728	+	28.2728i	−1.11584	+	1.11584i
$643$	17.7953	+	17.7953i	0.701779	+	0.701779i	0.964792	−	0.263013i	$-0.0847162\pi$
$643$	17.7953	+	17.7953i	0.701779	+	0.701779i	−0.263013	+	0.964792i	$0.584716\pi$
$644$	2.29699			0.0905142
$645$	−4.26883	−	0.0678266i	−0.168085	−	0.00267067i
$646$		−	2.70180i		−	0.106301i
$647$	18.0279	−	18.0279i	0.708751	−	0.708751i	−0.257521	−	0.966273i	$-0.582906\pi$
$647$	18.0279	−	18.0279i	0.708751	−	0.708751i	0.966273	+	0.257521i	$0.0829058\pi$
$648$	7.94021	−	7.94021i	0.311921	−	0.311921i
$649$	−11.6754	−	1.12587i	−0.458299	−	0.0441941i
$650$	−20.8759	−	0.663554i	−0.818820	−	0.0260267i
$651$		−	7.56842i		−	0.296630i
$652$	−15.3862	+	15.3862i	−0.602569	+	0.602569i
$653$	25.7477	+	25.7477i	1.00758	+	1.00758i	0.999971	+	0.00761340i	$0.00242344\pi$
$653$	25.7477	+	25.7477i	1.00758	+	1.00758i	0.00761340	+	0.999971i	$0.497577\pi$
$654$			8.79887i			0.344063i
$655$	−0.561745	+	35.3548i	−0.0219492	+	1.38142i
$656$			5.52698i			0.215792i
$657$	−1.93580	−	1.93580i	−0.0755227	−	0.0755227i
$658$	−0.355472	−	0.355472i	−0.0138577	−	0.0138577i
$659$	23.8584			0.929390			0.464695	−	0.885471i	$-0.346164\pi$
$659$	23.8584			0.929390			0.464695	+	0.885471i	$0.346164\pi$
$660$	−9.65236	−	12.0992i	−0.375717	−	0.470962i
$661$	−1.47363			−0.0573177			−0.0286589	−	0.999589i	$-0.509124\pi$
$661$	−1.47363			−0.0573177			−0.0286589	+	0.999589i	$0.509124\pi$
$662$	−4.55676	−	4.55676i	−0.177104	−	0.177104i
$663$	3.93315	+	3.93315i	0.152751	+	0.152751i
$664$			8.23275i			0.319493i
$665$	6.58836	+	6.80110i	0.255485	+	0.263735i
$666$			1.50589i			0.0583522i
$667$	−3.87943	−	3.87943i	−0.150212	−	0.150212i
$668$	−7.55138	+	7.55138i	−0.292172	+	0.292172i
$669$			14.5964i			0.564329i
$670$	35.1736	+	0.558867i	1.35888	+	0.0215909i
$671$	10.2254	+	0.986046i	0.394748	+	0.0380659i
$672$	1.47574	−	1.47574i	0.0569280	−	0.0569280i
$673$	−32.8063	+	32.8063i	−1.26459	+	1.26459i	−0.315745	+	0.948844i	$0.602255\pi$
$673$	−32.8063	+	32.8063i	−1.26459	+	1.26459i	−0.948844	+	0.315745i	$0.897745\pi$
$674$		−	8.14333i		−	0.313669i
$675$	12.5127	−	11.7418i	0.481614	−	0.451941i
$676$	4.44974			0.171144
$677$	−16.3316	−	16.3316i	−0.627676	−	0.627676i	0.319807	−	0.947483i	$-0.396382\pi$
$677$	−16.3316	−	16.3316i	−0.627676	−	0.627676i	−0.947483	+	0.319807i	$0.896382\pi$
$678$	13.7790	−	13.7790i	0.529178	−	0.529178i
$679$	−14.8372			−0.569399
$680$	−1.42648	−	0.0226651i	−0.0547031	−	0.000869166i
$681$			43.8908i			1.68190i
$682$	−9.28181	+	7.64914i	−0.355419	+	0.292901i
$683$	−19.4623	−	19.4623i	−0.744704	−	0.744704i	0.228775	−	0.973479i	$-0.426528\pi$
$683$	−19.4623	−	19.4623i	−0.744704	−	0.744704i	−0.973479	+	0.228775i	$0.926528\pi$
$684$	−5.74060			−0.219497
$685$	−17.5728	+	17.0231i	−0.671421	+	0.650419i
$686$	−1.00000			−0.0381802
$687$	31.2576	−	31.2576i	1.19255	−	1.19255i
$688$	−0.646902	+	0.646902i	−0.0246629	+	0.0246629i
$689$	46.4046			1.76787
$690$	−7.69921	+	7.45838i	−0.293104	+	0.283936i
$691$	−38.1138			−1.44992			−0.724959	−	0.688792i	$-0.758141\pi$
$691$	−38.1138			−1.44992			−0.724959	+	0.688792i	$0.758141\pi$
$692$	3.44316	+	3.44316i	0.130889	+	0.130889i
$693$	−2.85938	−	3.46970i	−0.108619	−	0.131803i
$694$		−	28.4185i		−	1.07875i
$695$	23.2212	+	0.368957i	0.880830	+	0.0139953i
$696$	−4.98480			−0.188948
$697$	2.49349	−	2.49349i	0.0944478	−	0.0944478i
$698$	−5.74622	−	5.74622i	−0.217498	−	0.217498i
$699$	−38.2251			−1.44580
$700$	3.64607	−	3.42143i	0.137809	−	0.129318i
$701$			0.759781i			0.0286965i	0.999897	+	0.0143483i	$0.00456735\pi$
$701$			0.759781i			0.0286965i	−0.999897	+	0.0143483i	$0.995433\pi$
$702$	−10.1369	+	10.1369i	−0.382593	+	0.382593i
$703$	−3.32627	+	3.32627i	−0.125453	+	0.125453i
$704$	−3.30131	−	0.318348i	−0.124423	−	0.0119982i
$705$	2.34572	+	0.0372707i	0.0883449	+	0.00140369i
$706$			31.5380i			1.18695i
$707$	−9.86097	+	9.86097i	−0.370860	+	0.370860i
$708$	5.21910	+	5.21910i	0.196146	+	0.196146i
$709$			1.83601i			0.0689527i	0.999406	+	0.0344764i	$0.0109763\pi$
$709$			1.83601i			0.0689527i	−0.999406	+	0.0344764i	$0.989024\pi$
$710$	−19.1240	−	19.7415i	−0.717711	−	0.740886i
$711$		−	3.55967i		−	0.133498i
$712$	−1.56249	−	1.56249i	−0.0585568	−	0.0585568i
$713$	5.89013	+	5.89013i	0.220587	+	0.220587i
$714$	−1.33156			−0.0498324
$715$	19.3198	+	24.2174i	0.722519	+	0.905678i
$716$	−26.0874			−0.974932
$717$	−34.3550	−	34.3550i	−1.28301	−	1.28301i
$718$	−8.20805	−	8.20805i	−0.306322	−	0.306322i
$719$			2.38284i			0.0888650i	0.999012	+	0.0444325i	$0.0141480\pi$
$719$			2.38284i			0.0888650i	−0.999012	+	0.0444325i	$0.985852\pi$
$720$	−0.0481572	+	3.03089i	−0.00179471	+	0.112954i
$721$			10.9291i			0.407022i
$722$	0.754997	+	0.754997i	0.0280981	+	0.0280981i
$723$	−3.13170	+	3.13170i	−0.116469	+	0.116469i
$724$			2.87265i			0.106761i
$725$	−11.9364	−	0.379406i	−0.443307	−	0.0140908i
$726$	−4.38675	+	22.5341i	−0.162808	+	0.836320i
$727$	31.6519	−	31.6519i	1.17390	−	1.17390i	0.192631	−	0.981271i	$-0.438298\pi$
$727$	31.6519	−	31.6519i	1.17390	−	1.17390i	0.981271	−	0.192631i	$-0.0617020\pi$
$728$	−2.95379	+	2.95379i	−0.109475	+	0.109475i
$729$		−	6.26433i		−	0.232012i
$730$	−4.51509	−	0.0717393i	−0.167111	−	0.00265519i
$731$	0.583699			0.0215889
$732$	−4.57094	−	4.57094i	−0.168947	−	0.168947i
$733$	−25.9397	+	25.9397i	−0.958103	+	0.958103i	−0.999157	−	0.0410539i	$-0.986928\pi$
$733$	−25.9397	+	25.9397i	−0.958103	+	0.958103i	0.0410539	+	0.999157i	$0.486928\pi$
$734$	19.4771			0.718912
$735$	3.35187	−	3.24702i	0.123635	−	0.119768i
$736$			2.29699i			0.0846683i
$737$	−33.1833	−	40.2661i	−1.22232	−	1.48322i
$738$	−5.29800	−	5.29800i	−0.195022	−	0.195022i
$739$	36.4736			1.34170			0.670851	−	0.741592i	$-0.265929\pi$
$739$	36.4736			1.34170			0.670851	+	0.741592i	$0.265929\pi$
$740$	1.72828	+	1.78409i	0.0635329	+	0.0655844i
$741$	36.9179			1.35621
$742$	−7.85510	+	7.85510i	−0.288370	+	0.288370i
$743$	−37.4779	+	37.4779i	−1.37493	+	1.37493i	−0.521961	+	0.852970i	$0.674799\pi$
$743$	−37.4779	+	37.4779i	−1.37493	+	1.37493i	−0.852970	+	0.521961i	$0.825201\pi$
$744$	7.56842			0.277472
$745$	30.9607	+	0.491929i	1.13431	+	0.0180229i
$746$	16.5601			0.606310
$747$	−7.89167	−	7.89167i	−0.288741	−	0.288741i
$748$	1.34576	+	1.63301i	0.0492060	+	0.0597087i
$749$			19.1584i			0.700032i
$750$	−1.11171	+	23.3070i	−0.0405939	+	0.851052i
$751$	−2.51171			−0.0916534			−0.0458267	−	0.998949i	$-0.514592\pi$
$751$	−2.51171			−0.0916534			−0.0458267	+	0.998949i	$0.514592\pi$
$752$	0.355472	−	0.355472i	0.0129627	−	0.0129627i
$753$	−31.9455	−	31.9455i	−1.16416	−	1.16416i
$754$	9.97740			0.363355
$755$	0.167524	−	10.5435i	0.00609681	−	0.383717i
$756$		−	3.43183i		−	0.124815i
$757$	−14.0827	+	14.0827i	−0.511846	+	0.511846i	−0.915092	−	0.403246i	$-0.867882\pi$
$757$	−14.0827	+	14.0827i	−0.511846	+	0.511846i	0.403246	+	0.915092i	$0.367882\pi$
$758$	6.13681	−	6.13681i	0.222899	−	0.222899i
$759$	15.8260	+	1.52611i	0.574448	+	0.0553944i
$760$	−6.80110	+	6.58836i	−0.246702	+	0.238985i
$761$		−	34.1598i		−	1.23829i	−0.785276	−	0.619146i	$-0.787479\pi$
$761$		−	34.1598i		−	1.23829i	0.785276	−	0.619146i	$-0.212521\pi$
$762$	26.5058	−	26.5058i	0.960205	−	0.960205i
$763$	2.98117	+	2.98117i	0.107926	+	0.107926i
$764$		−	14.6811i		−	0.531145i
$765$	1.38911	−	1.34566i	0.0502234	−	0.0486524i
$766$			28.0550i			1.01367i
$767$	−10.4463	−	10.4463i	−0.377196	−	0.377196i
$768$	1.47574	+	1.47574i	0.0532512	+	0.0532512i
$769$	9.07276			0.327172			0.163586	−	0.986529i	$-0.447694\pi$
$769$	9.07276			0.327172			0.163586	+	0.986529i	$0.447694\pi$
$770$	−7.36972	−	0.829033i	−0.265586	−	0.0298763i
$771$	−2.69989			−0.0972342
$772$	−1.26793	−	1.26793i	−0.0456339	−	0.0456339i
$773$	29.5465	+	29.5465i	1.06271	+	1.06271i	0.997897	+	0.0648172i	$0.0206464\pi$
$773$	29.5465	+	29.5465i	1.06271	+	1.06271i	0.0648172	+	0.997897i	$0.479354\pi$
$774$		−	1.24020i		−	0.0445782i
$775$	18.1230	+	0.576052i	0.650998	+	0.0206924i
$776$		−	14.8372i		−	0.532624i
$777$	1.63933	+	1.63933i	0.0588105	+	0.0588105i
$778$	6.08591	−	6.08591i	0.218190	−	0.218190i
$779$		−	23.4048i		−	0.838565i
$780$	0.309700	−	19.4917i	0.0110890	−	0.697915i
$781$	−3.91310	+	40.5794i	−0.140022	+	1.45205i
$782$	1.03629	−	1.03629i	0.0370576	−	0.0370576i
$783$	−5.79607	+	5.79607i	−0.207135	+	0.207135i
$784$		−	1.00000i		−	0.0357143i
$785$	24.7671	−	23.9924i	0.883975	−	0.856324i
$786$	−33.0022			−1.17715
$787$	−37.6226	−	37.6226i	−1.34110	−	1.34110i	−0.894967	−	0.446133i	$-0.852801\pi$
$787$	−37.6226	−	37.6226i	−1.34110	−	1.34110i	−0.446133	−	0.894967i	$-0.647199\pi$
$788$	−15.7038	+	15.7038i	−0.559424	+	0.559424i
$789$	18.0137			0.641306
$790$	−4.08535	−	4.21727i	−0.145350	−	0.150044i
$791$		−	9.33697i		−	0.331984i
$792$	3.46970	−	2.85938i	0.123290	−	0.101604i
$793$	9.14903	+	9.14903i	0.324891	+	0.324891i
$794$	−3.71873			−0.131973
$795$	0.823594	−	51.8349i	0.0292099	−	1.83839i
$796$	−12.2135			−0.432896
$797$	21.9068	−	21.9068i	0.775978	−	0.775978i	−0.203166	−	0.979144i	$-0.565123\pi$
$797$	21.9068	−	21.9068i	0.775978	−	0.775978i	0.979144	+	0.203166i	$0.0651231\pi$
$798$	−6.24925	+	6.24925i	−0.221221	+	0.221221i
$799$	−0.320742			−0.0113470
$800$	3.42143	+	3.64607i	0.120966	+	0.128908i
$801$	2.99552			0.105841
$802$	−16.2756	−	16.2756i	−0.574713	−	0.574713i
$803$	4.25960	+	5.16878i	0.150318	+	0.182402i
$804$			32.8331i			1.15794i
$805$	−0.0815983	+	5.13559i	−0.00287596	+	0.181006i
$806$	−15.1487			−0.533589
$807$	−19.0647	+	19.0647i	−0.671111	+	0.671111i
$808$	−9.86097	−	9.86097i	−0.346908	−	0.346908i
$809$	−25.0567			−0.880946			−0.440473	−	0.897766i	$-0.645189\pi$
$809$	−25.0567			−0.880946			−0.440473	+	0.897766i	$0.645189\pi$
$810$	17.4705	+	18.0347i	0.613852	+	0.633674i
$811$			10.5291i			0.369728i	0.982764	+	0.184864i	$0.0591845\pi$
$811$			10.5291i			0.369728i	−0.982764	+	0.184864i	$0.940816\pi$
$812$	−1.68891	+	1.68891i	−0.0592693	+	0.0592693i
$813$	−10.4654	+	10.4654i	−0.367036	+	0.367036i
$814$	0.353636	−	3.66726i	0.0123949	−	0.128537i
$815$	−33.8536	−	34.9467i	−1.18584	−	1.22413i
$816$		−	1.33156i		−	0.0466140i
$817$	2.73940	−	2.73940i	0.0958396	−	0.0958396i
$818$	−0.387213	−	0.387213i	−0.0135386	−	0.0135386i
$819$		−	5.66284i		−	0.197876i
$820$	−12.3571	−	0.196340i	−0.431530	−	0.00685649i
$821$		−	28.0056i		−	0.977402i	−0.872451	−	0.488701i	$-0.837471\pi$
$821$		−	28.0056i		−	0.977402i	0.872451	−	0.488701i	$-0.162529\pi$
$822$	−16.1469	−	16.1469i	−0.563188	−	0.563188i
$823$	−7.64451	−	7.64451i	−0.266471	−	0.266471i	0.561206	−	0.827676i	$-0.310338\pi$
$823$	−7.64451	−	7.64451i	−0.266471	−	0.266471i	−0.827676	+	0.561206i	$0.810338\pi$
$824$	−10.9291			−0.380735
$825$	27.3942	−	21.1508i	0.953743	−	0.736376i
$826$	3.53659			0.123054
$827$	37.7125	+	37.7125i	1.31139	+	1.31139i	0.920389	+	0.391003i	$0.127872\pi$
$827$	37.7125	+	37.7125i	1.31139	+	1.31139i	0.391003	+	0.920389i	$0.372128\pi$
$828$	−2.20183	−	2.20183i	−0.0765190	−	0.0765190i
$829$			0.141044i			0.00489867i	0.999997	+	0.00244933i	$0.000779648\pi$
$829$			0.141044i			0.00489867i	−0.999997	+	0.00244933i	$0.999220\pi$
$830$	−18.4067	−	0.292460i	−0.638904	−	0.0101514i
$831$			28.1196i			0.975460i
$832$	−2.95379	−	2.95379i	−0.102404	−	0.102404i
$833$	−0.451150	+	0.451150i	−0.0156314	+	0.0156314i
$834$			21.6760i			0.750579i
$835$	−16.6150	−	17.1515i	−0.574986	−	0.593553i
$836$	13.9799	+	1.34809i	0.483505	+	0.0466247i
$837$	8.80017	−	8.80017i	0.304178	−	0.304178i
$838$	22.3618	−	22.3618i	0.772474	−	0.772474i
$839$			19.7090i			0.680430i	0.940348	+	0.340215i	$0.110500\pi$
$839$			19.7090i			0.680430i	−0.940348	+	0.340215i	$0.889500\pi$
$840$	3.24702	+	3.35187i	0.112033	+	0.115650i
$841$	−23.2951			−0.803281
$842$	−4.52312	−	4.52312i	−0.155877	−	0.155877i
$843$	−21.4841	+	21.4841i	−0.739951	+	0.739951i
$844$	−16.2608			−0.559721
$845$	−0.158073	+	9.94867i	−0.00543786	+	0.342245i
$846$			0.681491i			0.0234301i
$847$	6.14856	+	9.12114i	0.211267	+	0.313406i
$848$	−7.85510	−	7.85510i	−0.269745	−	0.269745i
$849$	−24.2834			−0.833404
$850$	0.101349	−	3.18850i	0.00347623	−	0.109365i
$851$	−2.55161			−0.0874682
$852$	18.1397	−	18.1397i	0.621455	−	0.621455i
$853$	24.4965	−	24.4965i	0.838743	−	0.838743i	−0.149950	−	0.988694i	$-0.547911\pi$
$853$	24.4965	−	24.4965i	0.838743	−	0.838743i	0.988694	+	0.149950i	$0.0479114\pi$
$854$	−3.09739			−0.105990
$855$	0.203929	−	12.8347i	0.00697422	−	0.438939i
$856$	−19.1584			−0.654820
$857$	13.4939	+	13.4939i	0.460944	+	0.460944i	0.898965	−	0.438021i	$-0.144320\pi$
$857$	13.4939	+	13.4939i	0.460944	+	0.460944i	−0.438021	+	0.898965i	$0.644320\pi$
$858$	−22.3137	+	18.3888i	−0.761779	+	0.627782i
$859$		−	29.9431i		−	1.02165i	−0.859686	−	0.510823i	$-0.829341\pi$
$859$		−	29.9431i		−	1.02165i	0.859686	−	0.510823i	$-0.170659\pi$
$860$	−1.42335	−	1.46931i	−0.0485360	−	0.0501032i
$861$	−11.5349			−0.393107
$862$	−13.5482	+	13.5482i	−0.461453	+	0.461453i
$863$	−26.0079	−	26.0079i	−0.885319	−	0.885319i	0.108750	−	0.994069i	$-0.465315\pi$
$863$	−26.0079	−	26.0079i	−0.885319	−	0.885319i	−0.994069	+	0.108750i	$0.965315\pi$
$864$	3.43183			0.116753
$865$	−7.82048	+	7.57585i	−0.265904	+	0.257587i
$866$			17.9334i			0.609402i
$867$	24.4869	−	24.4869i	0.831618	−	0.831618i
$868$	2.56428	−	2.56428i	0.0870372	−	0.0870372i
$869$	−0.835934	+	8.66876i	−0.0283571	+	0.294067i
$870$	0.177080	−	11.1449i	0.00600357	−	0.377849i
$871$		−	65.7176i		−	2.22676i
$872$	−2.98117	+	2.98117i	−0.100955	+	0.100955i
$873$	14.2225	+	14.2225i	0.481358	+	0.481358i
$874$		−	9.72697i		−	0.329020i
$875$	7.52005	+	8.27338i	0.254224	+	0.279691i
$876$		−	4.21465i		−	0.142400i
$877$	23.0521	+	23.0521i	0.778416	+	0.778416i	0.979561	−	0.201146i	$-0.0644665\pi$
$877$	23.0521	+	23.0521i	0.778416	+	0.778416i	−0.201146	+	0.979561i	$0.564467\pi$
$878$	−9.30502	−	9.30502i	−0.314029	−	0.314029i
$879$	34.6664			1.16927
$880$	0.829033	−	7.36972i	0.0279467	−	0.248433i
$881$	55.7383			1.87787			0.938936	−	0.344091i	$-0.111813\pi$
$881$	55.7383			1.87787			0.938936	+	0.344091i	$0.111813\pi$
$882$	0.958571	+	0.958571i	0.0322768	+	0.0322768i
$883$	31.9573	+	31.9573i	1.07545	+	1.07545i	0.996911	+	0.0785373i	$0.0250250\pi$
$883$	31.9573	+	31.9573i	1.07545	+	1.07545i	0.0785373	+	0.996911i	$0.474975\pi$
$884$			2.66520i			0.0896405i
$885$	−11.8542	+	11.4834i	−0.398474	+	0.386009i
$886$		−	23.5666i		−	0.791734i
$887$	−2.98403	−	2.98403i	−0.100194	−	0.100194i	0.655233	−	0.755427i	$-0.272570\pi$
$887$	−2.98403	−	2.98403i	−0.100194	−	0.100194i	−0.755427	+	0.655233i	$0.772570\pi$
$888$	−1.63933	+	1.63933i	−0.0550122	+	0.0550122i
$889$		−	17.9610i		−	0.602394i
$890$	3.54890	−	3.43789i	0.118959	−	0.115238i
$891$	3.57478	−	37.0709i	0.119759	−	1.24192i
$892$	−4.94544	+	4.94544i	−0.165586	+	0.165586i
$893$	−1.50530	+	1.50530i	−0.0503730	+	0.0503730i
$894$			28.9005i			0.966578i
$895$	0.926728	−	58.3259i	0.0309771	−	1.94962i
$896$	1.00000			0.0334077
$897$	14.1600	+	14.1600i	0.472790	+	0.472790i
$898$	−15.8180	+	15.8180i	−0.527852	+	0.527852i
$899$	−8.66169			−0.288884
$900$	−6.77470	−	0.215338i	−0.225823	−	0.00717794i
$901$			7.08765i			0.236124i
$902$	11.6579	+	14.1462i	0.388166	+	0.471017i
$903$	−1.35009	−	1.35009i	−0.0449283	−	0.0449283i
$904$	9.33697			0.310543
$905$	−6.42263	−	0.102048i	−0.213496	−	0.00339219i
$906$	9.84191			0.326976
$907$	10.1465	−	10.1465i	0.336908	−	0.336908i	−0.518295	−	0.855202i	$-0.673433\pi$
$907$	10.1465	−	10.1465i	0.336908	−	0.336908i	0.855202	+	0.518295i	$0.173433\pi$
$908$	−14.8708	+	14.8708i	−0.493504	+	0.493504i
$909$	18.9049			0.627035
$910$	−6.49911	−	6.70897i	−0.215443	−	0.222400i
$911$	−11.4249			−0.378522			−0.189261	−	0.981927i	$-0.560609\pi$
$911$	−11.4249			−0.378522			−0.189261	+	0.981927i	$0.560609\pi$
$912$	−6.24925	−	6.24925i	−0.206933	−	0.206933i
$913$	17.3651	+	21.0716i	0.574701	+	0.697368i
$914$			11.9536i			0.395391i
$915$	10.3820	−	10.0573i	0.343219	−	0.332483i
$916$	21.1809			0.699837
$917$	−11.1816	+	11.1816i	−0.369248	+	0.369248i
$918$	−1.54827	−	1.54827i	−0.0511006	−	0.0511006i
$919$	−15.0819			−0.497506			−0.248753	−	0.968567i	$-0.580021\pi$
$919$	−15.0819			−0.497506			−0.248753	+	0.968567i	$0.580021\pi$
$920$	−5.13559	−	0.0815983i	−0.169315	−	0.00269022i
$921$			44.9647i			1.48164i
$922$	−0.103592	+	0.103592i	−0.00341162	+	0.00341162i
$923$	−36.3077	+	36.3077i	−1.19508	+	1.19508i
$924$	0.664396	−	6.88988i	0.0218570	−	0.226660i
$925$	−4.05024	+	3.80069i	−0.133171	+	0.124966i
$926$			20.8794i			0.686140i
$927$	10.4764	−	10.4764i	0.344089	−	0.344089i
$928$	−1.68891	−	1.68891i	−0.0554413	−	0.0554413i
$929$			38.4146i			1.26034i	0.776456	+	0.630171i	$0.217015\pi$
$929$			38.4146i			1.26034i	−0.776456	+	0.630171i	$0.782985\pi$
$930$	−0.268860	+	16.9214i	−0.00881627	+	0.554873i
$931$			4.23465i			0.138785i
$932$	−12.9511	−	12.9511i	−0.424229	−	0.424229i
$933$	−1.15592	−	1.15592i	−0.0378430	−	0.0378430i
$934$	3.09908			0.101405
$935$	−3.69886	+	2.95083i	−0.120966	+	0.0965024i
$936$	5.66284			0.185096
$937$	−41.9861	−	41.9861i	−1.37163	−	1.37163i	−0.858034	−	0.513592i	$-0.828314\pi$
$937$	−41.9861	−	41.9861i	−1.37163	−	1.37163i	−0.513592	−	0.858034i	$-0.671686\pi$
$938$	11.1243	+	11.1243i	0.363221	+	0.363221i
$939$		−	18.0684i		−	0.589641i
$940$	0.782132	+	0.807387i	0.0255103	+	0.0263341i
$941$		−	22.7031i		−	0.740099i	−0.929012	−	0.370050i	$-0.879341\pi$
$941$		−	22.7031i		−	0.740099i	0.929012	−	0.370050i	$-0.120659\pi$
$942$	22.7575	+	22.7575i	0.741478	+	0.741478i
$943$	8.97702	−	8.97702i	0.292332	−	0.292332i
$944$			3.53659i			0.115106i
$945$	7.67284	+	0.121912i	0.249598	+	0.00396581i
$946$	−0.291243	+	3.02023i	−0.00946912	+	0.0981961i
$947$	−33.0622	+	33.0622i	−1.07438	+	1.07438i	−0.0773765	+	0.997002i	$0.524654\pi$
$947$	−33.0622	+	33.0622i	−1.07438	+	1.07438i	−0.997002	+	0.0773765i	$0.975346\pi$
$948$	3.87508	−	3.87508i	0.125857	−	0.125857i
$949$			8.43588i			0.273840i
$950$	−14.4885	−	15.4398i	−0.470071	−	0.500935i
$951$	25.6920			0.833120
$952$	−0.451150	−	0.451150i	−0.0146219	−	0.0146219i
$953$	−10.6655	+	10.6655i	−0.345491	+	0.345491i	−0.858427	−	0.512936i	$-0.828558\pi$
$953$	−10.6655	+	10.6655i	−0.345491	+	0.345491i	0.512936	+	0.858427i	$0.328558\pi$
$954$	15.0593			0.487564
$955$	32.8239	+	0.521532i	1.06216	+	0.0168764i
$956$		−	23.2798i		−	0.752923i
$957$	−12.7585	+	10.5143i	−0.412425	+	0.339879i
$958$	14.8145	+	14.8145i	0.478636	+	0.478636i
$959$	−10.9416			−0.353321
$960$	−3.35187	+	3.24702i	−0.108181	+	0.104797i
$961$	−17.8490			−0.575773
$962$	3.28121	−	3.28121i	0.105791	−	0.105791i
$963$	18.3647	−	18.3647i	0.591794	−	0.591794i
$964$	−2.12212			−0.0683490
$965$	2.87987	−	2.78978i	0.0927062	−	0.0898063i
$966$	−4.79386			−0.154240
$967$	−9.58221	−	9.58221i	−0.308143	−	0.308143i	0.536046	−	0.844189i	$-0.319917\pi$
$967$	−9.58221	−	9.58221i	−0.308143	−	0.308143i	−0.844189	+	0.536046i	$0.819917\pi$
$968$	−9.12114	+	6.14856i	−0.293165	+	0.197622i
$969$			5.63870i			0.181141i
$970$	33.1727	+	0.527075i	1.06511	+	0.0169234i
$971$	−42.1363			−1.35222			−0.676109	−	0.736802i	$-0.736335\pi$
$971$	−42.1363			−1.35222			−0.676109	+	0.736802i	$0.736335\pi$
$972$	−9.29131	+	9.29131i	−0.298019	+	0.298019i
$973$	7.34411	+	7.34411i	0.235441	+	0.235441i
$974$	25.0185			0.801643
$975$	43.5683	+	1.38485i	1.39530	+	0.0443506i
$976$		−	3.09739i		−	0.0991449i
$977$	−10.1045	+	10.1045i	−0.323273	+	0.323273i	−0.850021	−	0.526748i	$-0.823411\pi$
$977$	−10.1045	+	10.1045i	−0.323273	+	0.323273i	0.526748	+	0.850021i	$0.323411\pi$
$978$	32.1111	−	32.1111i	1.02680	−	1.02680i
$979$	−7.29490	−	0.703452i	−0.233146	−	0.0224824i
$980$	2.23579	+	0.0355240i	0.0714196	+	0.00113477i
$981$		−	5.71533i		−	0.182476i
$982$	−17.1946	+	17.1946i	−0.548703	+	0.548703i
$983$	13.0602	+	13.0602i	0.416556	+	0.416556i	0.884015	−	0.467459i	$-0.154830\pi$
$983$	13.0602	+	13.0602i	0.416556	+	0.416556i	−0.467459	+	0.884015i	$0.654830\pi$
$984$		−	11.5349i		−	0.367718i
$985$	−34.5524	−	35.6682i	−1.10093	−	1.13648i
$986$			1.52391i			0.0485311i
$987$	0.741875	+	0.741875i	0.0236141	+	0.0236141i
$988$	12.5083	+	12.5083i	0.397941	+	0.397941i
$989$	2.10142			0.0668213
$990$	6.26971	+	7.85909i	0.199264	+	0.249778i
$991$	−32.7518			−1.04040			−0.520198	−	0.854046i	$-0.674142\pi$
$991$	−32.7518			−1.04040			−0.520198	+	0.854046i	$0.674142\pi$
$992$	2.56428	+	2.56428i	0.0814159	+	0.0814159i
$993$	9.51002	+	9.51002i	0.301791	+	0.301791i
$994$		−	12.2919i		−	0.389876i
$995$	0.433872	−	27.3068i	0.0137547	−	0.865683i
$996$		−	17.1819i		−	0.544428i
$997$	26.6548	+	26.6548i	0.844167	+	0.844167i	0.989398	−	0.145231i	$-0.0463926\pi$
$997$	26.6548	+	26.6548i	0.844167	+	0.844167i	−0.145231	+	0.989398i	$0.546393\pi$
$998$	1.70050	−	1.70050i	0.0538285	−	0.0538285i
$999$			3.81225i			0.120614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.m.f.43.7	✓	36
5.2	odd	4	inner	770.2.m.f.197.16	yes	36
11.10	odd	2	inner	770.2.m.f.43.16	yes	36
55.32	even	4	inner	770.2.m.f.197.7	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.m.f.43.7	✓	36	1.1	even	1	trivial
770.2.m.f.43.16	yes	36	11.10	odd	2	inner
770.2.m.f.197.7	yes	36	55.32	even	4	inner
770.2.m.f.197.16	yes	36	5.2	odd	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.47574 + 1.47574i) q^{3} +1.00000i q^{4} +(-2.23579 - 0.0355240i) q^{5} -2.08701i q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.35562i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.47574 + 1.47574i) q^{3} +1.00000i q^{4} +(-2.23579 - 0.0355240i) q^{5} -2.08701i q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.35562i q^{9} +(1.55582 + 1.60606i) q^{10} +(0.318348 - 3.30131i) q^{11} +(-1.47574 + 1.47574i) q^{12} +(2.95379 - 2.95379i) q^{13} +1.00000i q^{14} +(-3.24702 - 3.35187i) q^{15} -1.00000 q^{16} +(0.451150 + 0.451150i) q^{17} +(0.958571 - 0.958571i) q^{18} +4.23465 q^{19} +(0.0355240 - 2.23579i) q^{20} -2.08701i q^{21} +(-2.55949 + 2.10927i) q^{22} +(1.62422 + 1.62422i) q^{23} +2.08701 q^{24} +(4.99748 + 0.158848i) q^{25} -4.17729 q^{26} +(2.42667 - 2.42667i) q^{27} +(0.707107 - 0.707107i) q^{28} -2.38849 q^{29} +(-0.0741390 + 4.66611i) q^{30} +3.62644 q^{31} +(0.707107 + 0.707107i) q^{32} +(5.34168 - 4.40208i) q^{33} -0.638022i q^{34} +(1.55582 + 1.60606i) q^{35} -1.35562 q^{36} +(-0.785489 + 0.785489i) q^{37} +(-2.99435 - 2.99435i) q^{38} +8.71806 q^{39} +(-1.60606 + 1.55582i) q^{40} -5.52698i q^{41} +(-1.47574 + 1.47574i) q^{42} +(0.646902 - 0.646902i) q^{43} +(3.30131 + 0.318348i) q^{44} +(0.0481572 - 3.03089i) q^{45} -2.29699i q^{46} +(-0.355472 + 0.355472i) q^{47} +(-1.47574 - 1.47574i) q^{48} +1.00000i q^{49} +(-3.42143 - 3.64607i) q^{50} +1.33156i q^{51} +(2.95379 + 2.95379i) q^{52} +(7.85510 + 7.85510i) q^{53} -3.43183 q^{54} +(-0.829033 + 7.36972i) q^{55} -1.00000 q^{56} +(6.24925 + 6.24925i) q^{57} +(1.68891 + 1.68891i) q^{58} -3.53659i q^{59} +(3.35187 - 3.24702i) q^{60} +3.09739i q^{61} +(-2.56428 - 2.56428i) q^{62} +(0.958571 - 0.958571i) q^{63} -1.00000i q^{64} +(-6.70897 + 6.49911i) q^{65} +(-6.88988 - 0.664396i) q^{66} +(11.1243 - 11.1243i) q^{67} +(-0.451150 + 0.451150i) q^{68} +4.79386i q^{69} +(0.0355240 - 2.23579i) q^{70} -12.2919 q^{71} +(0.958571 + 0.958571i) q^{72} +(-1.42798 + 1.42798i) q^{73} +1.11085 q^{74} +(7.14056 + 7.60940i) q^{75} +4.23465i q^{76} +(-2.55949 + 2.10927i) q^{77} +(-6.16460 - 6.16460i) q^{78} -2.62585 q^{79} +(2.23579 + 0.0355240i) q^{80} +11.2292 q^{81} +(-3.90816 + 3.90816i) q^{82} +(-5.82143 + 5.82143i) q^{83} +2.08701 q^{84} +(-0.992648 - 1.02470i) q^{85} -0.914857 q^{86} +(-3.52479 - 3.52479i) q^{87} +(-2.10927 - 2.55949i) q^{88} -2.20970i q^{89} +(-2.17721 + 2.10911i) q^{90} -4.17729 q^{91} +(-1.62422 + 1.62422i) q^{92} +(5.35168 + 5.35168i) q^{93} +0.502713 q^{94} +(-9.46777 - 0.150432i) q^{95} +2.08701i q^{96} +(10.4915 - 10.4915i) q^{97} +(0.707107 - 0.707107i) q^{98} +(4.47534 + 0.431560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{3}+O(q^{10}) \) 36 * q - 4 * q^3	\( 36 q - 4 q^{3} + 12 q^{11} + 4 q^{12} - 4 q^{15} - 36 q^{16} - 12 q^{20} - 12 q^{22} + 4 q^{23} + 12 q^{25} + 24 q^{26} + 56 q^{27} + 8 q^{31} - 44 q^{33} - 44 q^{36} - 28 q^{37} + 16 q^{38} + 4 q^{42} - 44 q^{45} + 12 q^{47} + 4 q^{48} + 28 q^{53} + 40 q^{55} - 36 q^{56} - 24 q^{58} + 12 q^{60} + 24 q^{66} + 12 q^{67} - 12 q^{70} - 112 q^{71} - 52 q^{75} - 12 q^{77} + 48 q^{78} + 4 q^{81} + 40 q^{82} + 32 q^{86} - 12 q^{88} + 24 q^{91} - 4 q^{92} - 80 q^{93} + 100 q^{97}+O(q^{100}) \) 36 * q - 4 * q^3 + 12 * q^11 + 4 * q^12 - 4 * q^15 - 36 * q^16 - 12 * q^20 - 12 * q^22 + 4 * q^23 + 12 * q^25 + 24 * q^26 + 56 * q^27 + 8 * q^31 - 44 * q^33 - 44 * q^36 - 28 * q^37 + 16 * q^38 + 4 * q^42 - 44 * q^45 + 12 * q^47 + 4 * q^48 + 28 * q^53 + 40 * q^55 - 36 * q^56 - 24 * q^58 + 12 * q^60 + 24 * q^66 + 12 * q^67 - 12 * q^70 - 112 * q^71 - 52 * q^75 - 12 * q^77 + 48 * q^78 + 4 * q^81 + 40 * q^82 + 32 * q^86 - 12 * q^88 + 24 * q^91 - 4 * q^92 - 80 * q^93 + 100 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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