LMFDB - Embedded newform 507.2.p.b.25.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [507,2,Mod(25,507)] 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("507.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(26)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.16
Character	$\chi$	$=$	507.25
Dual form			507.2.p.b.142.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.56554 + 0.972980i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(4.13827 + 3.66618i) q^{4} +(-1.46104 - 0.177402i) q^{5} +(-0.656644 - 2.66411i) q^{6} +(0.543789 + 1.03610i) q^{7} +(4.49950 + 8.57307i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-3.57574 - 1.87669i) q^{10} +(1.98271 - 0.751942i) q^{11} +(0.666407 - 5.48836i) q^{12} +(3.35466 - 1.32147i) q^{13} +(0.387003 + 3.18726i) q^{14} +(0.683965 + 1.30319i) q^{15} +(1.86938 + 15.3957i) q^{16} +(-1.92691 + 1.01132i) q^{17} +(-1.81950 + 2.05379i) q^{18} -1.87833i q^{19} +(-5.39577 - 6.09057i) q^{20} +(0.543789 - 1.03610i) q^{21} +5.81833 q^{22} -4.58644 q^{23} +(4.49950 - 8.57307i) q^{24} +(-2.75155 - 0.678196i) q^{25} +(9.89226 - 0.126264i) q^{26} +(0.970942 - 0.239316i) q^{27} +(-1.54820 + 6.28130i) q^{28} +(-1.62144 + 4.27539i) q^{29} +(0.486763 + 4.00885i) q^{30} +(-1.97240 - 8.00234i) q^{31} +(-5.54962 + 22.5157i) q^{32} +(-1.74514 - 1.20458i) q^{33} +(-5.92755 + 0.719735i) q^{34} +(-0.610689 - 1.61025i) q^{35} +(-4.89539 + 2.56930i) q^{36} +(-1.79313 - 7.27503i) q^{37} +(1.82757 - 4.81891i) q^{38} +(-2.99321 - 2.01015i) q^{39} +(-5.05305 - 13.3238i) q^{40} +(9.54492 - 6.58839i) q^{41} +(2.40322 - 2.12907i) q^{42} +(0.896123 + 0.220875i) q^{43} +(10.9617 + 4.15724i) q^{44} +(0.683965 - 1.30319i) q^{45} +(-11.7667 - 4.46251i) q^{46} +(-0.680969 - 0.768655i) q^{47} +(11.6085 - 10.2842i) q^{48} +(3.19865 - 4.63404i) q^{49} +(-6.39933 - 4.41714i) q^{50} +(1.92691 + 1.01132i) q^{51} +(18.7272 + 6.83020i) q^{52} +(-5.44679 + 2.85870i) q^{53} +(2.72384 + 0.330734i) q^{54} +(-3.03021 + 0.746879i) q^{55} +(-6.43581 + 9.32389i) q^{56} +(-1.54583 + 1.06701i) q^{57} +(-8.31974 + 9.39104i) q^{58} +(-10.0093 - 1.21535i) q^{59} +(-1.94729 + 7.90047i) q^{60} +(-0.346989 - 0.182114i) q^{61} +(2.72585 - 22.4494i) q^{62} +(-1.16160 + 0.141044i) q^{63} +(-18.5250 + 26.8381i) q^{64} +(-5.13571 + 1.33559i) q^{65} +(-3.30519 - 4.78839i) q^{66} +(7.77843 + 8.78003i) q^{67} +(-11.6818 - 2.87929i) q^{68} +(2.60540 + 3.77457i) q^{69} -4.72536i q^{70} +(-5.67368 + 3.91626i) q^{71} +(-9.61151 + 1.16705i) q^{72} +(-13.8104 + 5.23758i) q^{73} +(2.47811 - 20.4090i) q^{74} +(1.00491 + 2.64974i) q^{75} +(6.88629 - 7.77301i) q^{76} +(1.85726 + 1.64539i) q^{77} +(-5.72335 - 8.06944i) q^{78} +(7.46203 - 6.61078i) q^{79} -22.8254i q^{80} +(-0.748511 - 0.663123i) q^{81} +(30.8982 - 7.61573i) q^{82} +(2.12075 + 1.46385i) q^{83} +(6.04889 - 2.29404i) q^{84} +(2.99470 - 1.13574i) q^{85} +(2.08413 + 1.43857i) q^{86} +(4.43966 - 1.09428i) q^{87} +(15.3676 + 13.6145i) q^{88} +8.20740i q^{89} +(3.02271 - 2.67789i) q^{90} +(3.19340 + 2.75717i) q^{91} +(-18.9799 - 16.8147i) q^{92} +(-5.46534 + 6.16910i) q^{93} +(-0.999165 - 2.63458i) q^{94} +(-0.333219 + 2.74430i) q^{95} +(21.6826 - 8.22312i) q^{96} +(9.76489 - 1.18567i) q^{97} +(12.7151 - 8.77659i) q^{98} +2.12051i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34}+ \cdots + 104 q^{98}+O(q^{100}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

Coefficient data

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

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

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

$2$	2.56554	+	0.972980i	1.81411	+	0.688000i	0.993127	+	0.117046i	$0.0373424\pi$
$2$	2.56554	+	0.972980i	1.81411	+	0.688000i	0.820982	+	0.570955i	$0.193427\pi$
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$4$	4.13827	+	3.66618i	2.06913	+	1.83309i
$5$	−1.46104	−	0.177402i	−0.653396	−	0.0793366i	−0.212876	−	0.977079i	$-0.568283\pi$
$5$	−1.46104	−	0.177402i	−0.653396	−	0.0793366i	−0.440520	+	0.897743i	$0.645206\pi$
$6$	−0.656644	−	2.66411i	−0.268074	−	1.08762i
$7$	0.543789	+	1.03610i	0.205533	+	0.391610i	0.966301	−	0.257413i	$-0.0828701\pi$
$7$	0.543789	+	1.03610i	0.205533	+	0.391610i	−0.760769	+	0.649023i	$0.775178\pi$
$8$	4.49950	+	8.57307i	1.59081	+	3.03104i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	−3.57574	−	1.87669i	−1.13075	−	0.593462i
$11$	1.98271	−	0.751942i	0.597809	−	0.226719i	−0.0370929	−	0.999312i	$-0.511810\pi$
$11$	1.98271	−	0.751942i	0.597809	−	0.226719i	0.634902	+	0.772593i	$0.281041\pi$
$12$	0.666407	−	5.48836i	0.192375	−	1.58435i
$13$	3.35466	−	1.32147i	0.930414	−	0.366509i
$13$	3.35466	−	1.32147i	0.930414	−	0.366509i
$14$	0.387003	+	3.18726i	0.103431	+	0.851830i
$15$	0.683965	+	1.30319i	0.176599	+	0.336481i
$16$	1.86938	+	15.3957i	0.467345	+	3.84893i
$17$	−1.92691	+	1.01132i	−0.467344	+	0.245281i	−0.681921	−	0.731426i	$-0.738855\pi$
$17$	−1.92691	+	1.01132i	−0.467344	+	0.245281i	0.214576	+	0.976707i	$0.431163\pi$
$18$	−1.81950	+	2.05379i	−0.428861	+	0.484084i
$19$		−	1.87833i		−	0.430917i	−0.976513	−	0.215459i	$-0.930875\pi$
$19$		−	1.87833i		−	0.430917i	0.976513	−	0.215459i	$-0.0691247\pi$
$20$	−5.39577	−	6.09057i	−1.20653	−	1.36189i
$21$	0.543789	−	1.03610i	0.118665	−	0.226096i
$22$	5.81833			1.24047
$23$	−4.58644			−0.956339			−0.478169	−	0.878268i	$-0.658700\pi$
$23$	−4.58644			−0.956339			−0.478169	+	0.878268i	$0.658700\pi$
$24$	4.49950	−	8.57307i	0.918456	−	1.74997i
$25$	−2.75155	−	0.678196i	−0.550310	−	0.135639i
$26$	9.89226	−	0.126264i	1.94003	−	0.0247624i
$27$	0.970942	−	0.239316i	0.186858	−	0.0460563i
$28$	−1.54820	+	6.28130i	−0.292583	+	1.18705i
$29$	−1.62144	+	4.27539i	−0.301094	+	0.793920i	0.696021	+	0.718021i	$0.254952\pi$
$29$	−1.62144	+	4.27539i	−0.301094	+	0.793920i	−0.997116	+	0.0758991i	$0.975817\pi$
$30$	0.486763	+	4.00885i	0.0888704	+	0.731913i
$31$	−1.97240	−	8.00234i	−0.354253	−	1.43726i	−0.830041	−	0.557702i	$-0.811683\pi$
$31$	−1.97240	−	8.00234i	−0.354253	−	1.43726i	0.475788	−	0.879560i	$-0.342163\pi$
$32$	−5.54962	+	22.5157i	−0.981043	+	3.98025i
$33$	−1.74514	−	1.20458i	−0.303790	−	0.209691i
$34$	−5.92755	+	0.719735i	−1.01657	+	0.123434i
$35$	−0.610689	−	1.61025i	−0.103225	−	0.272183i
$36$	−4.89539	+	2.56930i	−0.815898	+	0.428217i
$37$	−1.79313	−	7.27503i	−0.294789	−	1.19601i	−0.912326	−	0.409465i	$-0.865715\pi$
$37$	−1.79313	−	7.27503i	−0.294789	−	1.19601i	0.617536	−	0.786542i	$-0.288131\pi$
$38$	1.82757	−	4.81891i	0.296471	−	0.781731i
$39$	−2.99321	−	2.01015i	−0.479297	−	0.321881i
$40$	−5.05305	−	13.3238i	−0.798957	−	2.10668i
$41$	9.54492	−	6.58839i	1.49067	−	1.02893i	0.504456	−	0.863437i	$-0.331693\pi$
$41$	9.54492	−	6.58839i	1.49067	−	1.02893i	0.986211	−	0.165496i	$-0.0529224\pi$
$42$	2.40322	−	2.12907i	0.370825	−	0.328522i
$43$	0.896123	+	0.220875i	0.136657	+	0.0336830i	0.307051	−	0.951693i	$-0.400658\pi$
$43$	0.896123	+	0.220875i	0.136657	+	0.0336830i	−0.170394	+	0.985376i	$0.554504\pi$
$44$	10.9617	+	4.15724i	1.65254	+	0.626727i
$45$	0.683965	−	1.30319i	0.101959	−	0.194267i
$46$	−11.7667	−	4.46251i	−1.73490	−	0.657962i
$47$	−0.680969	−	0.768655i	−0.0993295	−	0.112120i	0.696744	−	0.717320i	$-0.254631\pi$
$47$	−0.680969	−	0.768655i	−0.0993295	−	0.112120i	−0.796073	+	0.605200i	$0.793093\pi$
$48$	11.6085	−	10.2842i	1.67554	−	1.48440i
$49$	3.19865	−	4.63404i	0.456950	−	0.662006i
$50$	−6.39933	−	4.41714i	−0.905002	−	0.624678i
$51$	1.92691	+	1.01132i	0.269821	+	0.141613i
$52$	18.7272	+	6.83020i	2.59700	+	0.947178i
$53$	−5.44679	+	2.85870i	−0.748174	+	0.392672i	−0.795299	−	0.606217i	$-0.792686\pi$
$53$	−5.44679	+	2.85870i	−0.748174	+	0.392672i	0.0471251	+	0.998889i	$0.484994\pi$
$54$	2.72384	+	0.330734i	0.370667	+	0.0450071i
$55$	−3.03021	+	0.746879i	−0.408593	+	0.100709i
$56$	−6.43581	+	9.32389i	−0.860022	+	1.24596i
$57$	−1.54583	+	1.06701i	−0.204750	+	0.141329i
$58$	−8.31974	+	9.39104i	−1.09244	+	1.23310i
$59$	−10.0093	−	1.21535i	−1.30310	−	0.158225i	−0.560611	−	0.828079i	$-0.689434\pi$
$59$	−10.0093	−	1.21535i	−1.30310	−	0.158225i	−0.742493	+	0.669854i	$0.766357\pi$
$60$	−1.94729	+	7.90047i	−0.251394	+	1.01995i
$61$	−0.346989	−	0.182114i	−0.0444274	−	0.0233173i	0.442363	−	0.896836i	$-0.354140\pi$
$61$	−0.346989	−	0.182114i	−0.0444274	−	0.0233173i	−0.486791	+	0.873519i	$0.661833\pi$
$62$	2.72585	−	22.4494i	0.346183	−	2.85108i
$63$	−1.16160	+	0.141044i	−0.146348	+	0.0177699i
$64$	−18.5250	+	26.8381i	−2.31563	+	3.35477i
$65$	−5.13571	+	1.33559i	−0.637006	+	0.165660i
$66$	−3.30519	−	4.78839i	−0.406841	−	0.589411i
$67$	7.77843	+	8.78003i	0.950286	+	1.07265i	0.997276	+	0.0737559i	$0.0234986\pi$
$67$	7.77843	+	8.78003i	0.950286	+	1.07265i	−0.0469902	+	0.998895i	$0.514963\pi$
$68$	−11.6818	−	2.87929i	−1.41662	−	0.349166i
$69$	2.60540	+	3.77457i	0.313653	+	0.454404i
$70$		−	4.72536i		−	0.564788i
$71$	−5.67368	+	3.91626i	−0.673341	+	0.464774i	−0.855028	−	0.518583i	$-0.826460\pi$
$71$	−5.67368	+	3.91626i	−0.673341	+	0.464774i	0.181686	+	0.983357i	$0.441845\pi$
$72$	−9.61151	+	1.16705i	−1.13273	+	0.137538i
$73$	−13.8104	+	5.23758i	−1.61638	+	0.613012i	−0.986512	−	0.163690i	$-0.947660\pi$
$73$	−13.8104	+	5.23758i	−1.61638	+	0.613012i	−0.629868	+	0.776702i	$0.716891\pi$
$74$	2.47811	−	20.4090i	0.288074	−	2.37250i
$75$	1.00491	+	2.64974i	0.116038	+	0.305966i
$76$	6.88629	−	7.77301i	0.789911	−	0.891625i
$77$	1.85726	+	1.64539i	0.211655	+	0.187510i
$78$	−5.72335	−	8.06944i	−0.648042	−	0.913684i
$79$	7.46203	−	6.61078i	0.839544	−	0.743771i	−0.129257	−	0.991611i	$-0.541259\pi$
$79$	7.46203	−	6.61078i	0.839544	−	0.743771i	0.968801	+	0.247840i	$0.0797207\pi$
$80$		−	22.8254i		−	2.55195i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	30.8982	−	7.61573i	3.41214	−	0.841016i
$83$	2.12075	+	1.46385i	0.232783	+	0.160678i	0.678746	−	0.734373i	$-0.262524\pi$
$83$	2.12075	+	1.46385i	0.232783	+	0.160678i	−0.445964	+	0.895051i	$0.647139\pi$
$84$	6.04889	−	2.29404i	0.659988	−	0.250300i
$85$	2.99470	−	1.13574i	0.324821	−	0.123188i
$86$	2.08413	+	1.43857i	0.224738	+	0.155125i
$87$	4.43966	−	1.09428i	0.475982	−	0.117319i
$88$	15.3676	+	13.6145i	1.63820	+	1.45131i
$89$			8.20740i			0.869982i	0.900435	+	0.434991i	$0.143248\pi$
$89$			8.20740i			0.869982i	−0.900435	+	0.434991i	$0.856752\pi$
$90$	3.02271	−	2.67789i	0.318622	−	0.282274i
$91$	3.19340	+	2.75717i	0.334760	+	0.289030i
$92$	−18.9799	−	16.8147i	−1.97879	−	1.75306i
$93$	−5.46534	+	6.16910i	−0.566730	+	0.639706i
$94$	−0.999165	−	2.63458i	−0.103056	−	0.271736i
$95$	−0.333219	+	2.74430i	−0.0341875	+	0.281560i
$96$	21.6826	−	8.22312i	2.21297	−	0.839269i
$97$	9.76489	−	1.18567i	0.991475	−	0.120387i	0.391306	−	0.920261i	$-0.372023\pi$
$97$	9.76489	−	1.18567i	0.991475	−	0.120387i	0.600168	+	0.799874i	$0.295100\pi$
$98$	12.7151	−	8.77659i	1.28442	−	0.886569i
$99$			2.12051i			0.213119i
$100$	−8.90026	−	12.8942i	−0.890026	−	1.28942i
$101$	−8.49854	−	2.09470i	−0.845636	−	0.208431i	−0.207385	−	0.978259i	$-0.566495\pi$
$101$	−8.49854	−	2.09470i	−0.845636	−	0.208431i	−0.638250	+	0.769829i	$0.720342\pi$
$102$	3.95956	+	4.46942i	0.392055	+	0.442539i
$103$	4.75126	+	6.88338i	0.468155	+	0.678240i	0.983944	−	0.178476i	$-0.0571166\pi$
$103$	4.75126	+	6.88338i	0.468155	+	0.678240i	−0.515789	+	0.856716i	$0.672501\pi$
$104$	26.4233	+	22.8138i	2.59102	+	2.23707i
$105$	−0.978303	+	1.41732i	−0.0954726	+	0.138316i
$106$	−16.7554	+	2.03447i	−1.62743	+	0.197606i
$107$	1.94598	−	16.0266i	0.188125	−	1.54935i	−0.526701	−	0.850051i	$-0.676571\pi$
$107$	1.94598	−	16.0266i	0.188125	−	1.54935i	0.714826	−	0.699302i	$-0.246506\pi$
$108$	4.89539	+	2.56930i	0.471059	+	0.247231i
$109$	−2.30003	+	9.33160i	−0.220303	+	0.893805i	0.751826	+	0.659361i	$0.229173\pi$
$109$	−2.30003	+	9.33160i	−0.220303	+	0.893805i	−0.972130	+	0.234444i	$0.924673\pi$
$110$	−8.50080	−	1.03218i	−0.810520	−	0.0984149i
$111$	−4.96862	+	5.60841i	−0.471600	+	0.532327i
$112$	−14.9350	+	10.3089i	−1.41123	+	0.974100i
$113$	3.89040	−	5.63622i	0.365978	−	0.530211i	−0.596127	−	0.802890i	$-0.703294\pi$
$113$	3.89040	−	5.63622i	0.365978	−	0.530211i	0.962105	+	0.272679i	$0.0879098\pi$
$114$	−5.00407	+	1.23339i	−0.468674	+	0.115518i
$115$	6.70096	+	0.813644i	0.624868	+	0.0758727i
$116$	−22.3843	+	11.7482i	−2.07833	+	1.09079i
$117$	0.0460172	+	3.60526i	0.00425429	+	0.333306i
$118$	−24.4968	−	12.8569i	−2.25511	−	1.18357i
$119$	−2.09567	−	1.44653i	−0.192109	−	0.132604i
$120$	−8.09481	+	11.7274i	−0.738952	+	1.07056i
$121$	−4.86790	+	4.31259i	−0.442537	+	0.392053i
$122$	−0.713020	−	0.804833i	−0.0645538	−	0.0728661i
$123$	−10.8443	−	4.11269i	−0.977795	−	0.370829i
$124$	21.1757	−	40.3470i	1.90164	−	3.62327i
$125$	10.7804	+	4.08848i	0.964232	+	0.365685i
$126$	−3.11737	−	0.768363i	−0.277717	−	0.0684512i
$127$	8.51080	−	7.53991i	0.755211	−	0.669059i	−0.194952	−	0.980813i	$-0.562455\pi$
$127$	8.51080	−	7.53991i	0.755211	−	0.669059i	0.950163	+	0.311754i	$0.100917\pi$
$128$	−35.4704	+	24.4834i	−3.13517	+	2.16405i
$129$	−0.327280	−	0.862966i	−0.0288154	−	0.0759799i
$130$	−14.4754	−	1.57043i	−1.26957	−	0.137736i
$131$	−3.75570	+	9.90297i	−0.328137	+	0.865226i	0.664847	+	0.746979i	$0.268497\pi$
$131$	−3.75570	+	9.90297i	−0.328137	+	0.865226i	−0.992984	+	0.118247i	$0.962273\pi$
$132$	−2.80563	−	11.3829i	−0.244199	−	0.990755i
$133$	1.94614	−	1.02141i	0.168752	−	0.0885677i
$134$	11.4130	+	30.0937i	0.985937	+	2.59970i
$135$	−1.46104	+	0.177402i	−0.125746	+	0.0152683i
$136$	−17.3403	−	11.9691i	−1.48691	−	1.02634i
$137$	−4.49878	+	18.2523i	−0.384357	+	1.55940i	0.386439	+	0.922315i	$0.373705\pi$
$137$	−4.49878	+	18.2523i	−0.384357	+	1.55940i	−0.770796	+	0.637082i	$0.780141\pi$
$138$	3.01166	+	12.2188i	0.256369	+	1.04013i
$139$	1.60957	+	13.2560i	0.136522	+	1.12436i	0.886445	+	0.462834i	$0.153168\pi$
$139$	1.60957	+	13.2560i	0.136522	+	1.12436i	−0.749923	+	0.661525i	$0.769909\pi$
$140$	3.37630	−	8.90256i	0.285349	−	0.752404i
$141$	−0.245756	+	0.997072i	−0.0206964	+	0.0839686i
$142$	−18.3665	+	4.52693i	−1.54128	+	0.379891i
$143$	5.65764	−	5.14259i	0.473115	−	0.430045i
$144$	−15.0582	−	3.71150i	−1.25485	−	0.309292i
$145$	3.12745	−	5.95886i	0.259721	−	0.494856i
$146$	−40.5270			−3.35404
$147$	−5.63078			−0.464419
$148$	19.2511	−	36.6800i	1.58243	−	3.01507i
$149$	9.63167	+	10.8719i	0.789057	+	0.890661i	0.996150	−	0.0876599i	$-0.0279389\pi$
$149$	9.63167	+	10.8719i	0.789057	+	0.890661i	−0.207093	+	0.978321i	$0.566400\pi$
$150$			7.77577i			0.634889i
$151$	15.0509	−	16.9889i	1.22482	−	1.38254i	0.325330	−	0.945600i	$-0.394525\pi$
$151$	15.0509	−	16.9889i	1.22482	−	1.38254i	0.899492	−	0.436938i	$-0.143937\pi$
$152$	16.1030	−	8.45152i	1.30613	−	0.685509i
$153$	−0.262309	−	2.16031i	−0.0212065	−	0.174651i
$154$	3.16395	+	6.02840i	0.254958	+	0.485782i
$155$	1.46212	+	12.0416i	0.117440	+	0.967206i
$156$	−5.01712	−	19.2922i	−0.401691	−	1.54461i
$157$	−1.41370	+	11.6429i	−0.112826	+	0.929204i	0.820865	+	0.571123i	$0.193492\pi$
$157$	−1.41370	+	11.6429i	−0.112826	+	0.929204i	−0.933690	+	0.358081i	$0.883431\pi$
$158$	25.5763	−	9.69980i	2.03474	−	0.771675i
$159$	5.44679	+	2.85870i	0.431959	+	0.226709i
$160$	12.1025	−	31.9117i	0.956789	−	2.52284i
$161$	−2.49406	−	4.75203i	−0.196559	−	0.374512i
$162$	−1.27513	−	2.42955i	−0.100183	−	0.190884i
$163$	0.634772	+	2.57537i	0.0497192	+	0.201719i	0.990549	−	0.137162i	$-0.0437980\pi$
$163$	0.634772	+	2.57537i	0.0497192	+	0.201719i	−0.940829	+	0.338880i	$0.889952\pi$
$164$	63.6537	+	7.72895i	4.97052	+	0.603530i
$165$	2.33602	+	2.06953i	0.181859	+	0.161113i
$166$	4.01657	+	5.81901i	0.311747	+	0.451643i
$167$	−11.4419	−	4.33934i	−0.885400	−	0.335788i	−0.130360	−	0.991467i	$-0.541613\pi$
$167$	−11.4419	−	4.33934i	−0.885400	−	0.335788i	−0.755040	+	0.655679i	$0.772383\pi$
$168$	11.3294			0.874080
$169$	9.50744	−	8.86615i	0.731342	−	0.682011i
$170$	8.78806			0.674013
$171$	1.75626	+	0.666063i	0.134305	+	0.0509351i
$172$	2.89863	+	4.19939i	0.221018	+	0.320200i
$173$	−0.317986	−	0.281711i	−0.0241760	−	0.0214181i	0.650948	−	0.759122i	$-0.274372\pi$
$173$	−0.317986	−	0.281711i	−0.0241760	−	0.0214181i	−0.675124	+	0.737704i	$0.735910\pi$
$174$	12.4548	+	1.51229i	0.944198	+	0.114646i
$175$	−0.793582	−	3.21969i	−0.0599891	−	0.243386i
$176$	15.2831	+	29.1196i	1.15201	+	2.19497i
$177$	4.68573	+	8.92792i	0.352201	+	0.671063i
$178$	−7.98563	+	21.0564i	−0.598548	+	1.57824i
$179$	−0.877306	−	0.460446i	−0.0655729	−	0.0344153i	0.431618	−	0.902056i	$-0.357943\pi$
$179$	−0.877306	−	0.460446i	−0.0655729	−	0.0344153i	−0.497191	+	0.867641i	$0.665635\pi$
$180$	7.60815	−	2.88539i	0.567078	−	0.215064i
$181$	1.67895	−	13.8274i	0.124796	−	1.02778i	−0.786946	−	0.617022i	$-0.788339\pi$
$181$	1.67895	−	13.8274i	0.124796	−	1.02778i	0.911742	−	0.410763i	$-0.134738\pi$
$182$	5.51012	+	10.1807i	0.408437	+	0.754647i
$183$	0.0472354	+	0.389019i	0.00349174	+	0.0287571i
$184$	−20.6367	−	39.3199i	−1.52136	−	2.89870i
$185$	1.32923	+	10.9472i	0.0977269	+	0.804854i
$186$	−20.0239	+	10.5094i	−1.46823	+	0.770585i
$187$	−3.06005	+	3.45408i	−0.223773	+	0.252587i
$188$		−	5.67746i		−	0.414071i
$189$	0.775943	+	0.875859i	0.0564416	+	0.0637094i
$190$	−3.52504	+	6.71639i	−0.255733	+	0.487258i
$191$	6.88133			0.497916			0.248958	−	0.968514i	$-0.419912\pi$
$191$	6.88133			0.497916			0.248958	+	0.968514i	$0.419912\pi$
$192$	32.6108			2.35348
$193$	−9.34759	+	17.8103i	−0.672854	+	1.28202i	0.274426	+	0.961608i	$0.411512\pi$
$193$	−9.34759	+	17.8103i	−0.672854	+	1.28202i	−0.947280	+	0.320408i	$0.896180\pi$
$194$	26.2058	+	6.45916i	1.88147	+	0.463740i
$195$	4.01659	+	3.46790i	0.287634	+	0.248342i
$196$	30.2261	−	7.45007i	2.15901	−	0.532148i
$197$	−5.90668	+	23.9644i	−0.420834	+	1.70739i	0.252112	+	0.967698i	$0.418875\pi$
$197$	−5.90668	+	23.9644i	−0.420834	+	1.70739i	−0.672946	+	0.739692i	$0.734971\pi$
$198$	−2.06321	+	5.44024i	−0.146626	+	0.386621i
$199$	−1.71542	−	14.1277i	−0.121603	−	1.00149i	−0.917963	−	0.396666i	$-0.870167\pi$
$199$	−1.71542	−	14.1277i	−0.121603	−	1.00149i	0.796360	−	0.604822i	$-0.206756\pi$
$200$	−6.56637	−	26.6408i	−0.464312	−	1.88379i
$201$	2.80717	−	11.3891i	0.198003	−	0.803328i
$202$	−19.7652	−	13.6429i	−1.39067	−	0.959913i
$203$	−5.31147	+	0.644929i	−0.372792	+	0.0452652i
$204$	4.26638	+	11.2495i	0.298706	+	0.787624i
$205$	−15.1143	+	7.93259i	−1.05563	+	0.554036i
$206$	5.49213	+	22.2824i	0.382655	+	1.55249i
$207$	1.62637	−	4.28840i	0.113041	−	0.298064i
$208$	26.6161	+	49.1771i	1.84550	+	3.40982i
$209$	−1.41239	−	3.72417i	−0.0976972	−	0.257606i
$210$	−3.88889	+	2.68431i	−0.268359	+	0.185235i
$211$	2.25153	−	1.99468i	0.155002	−	0.137319i	−0.582058	−	0.813147i	$-0.697752\pi$
$211$	2.25153	−	1.99468i	0.155002	−	0.137319i	0.737059	+	0.675828i	$0.236214\pi$
$212$	−33.0208	−	8.13889i	−2.26788	−	0.558981i
$213$	6.44603	+	2.44466i	0.441675	+	0.167505i
$214$	20.5861	−	39.2235i	1.40724	−	2.68126i
$215$	−1.27009	−	0.481680i	−0.0866191	−	0.0328503i
$216$	6.42042	+	7.24716i	0.436854	+	0.493106i
$217$	7.21868	−	6.39519i	0.490036	−	0.434134i
$218$	−14.9803	+	21.7027i	−1.01459	+	1.46989i
$219$	12.1556	+	8.39042i	0.821401	+	0.566972i
$220$	−15.2780	−	8.01851i	−1.03004	−	0.540608i
$221$	−5.12769	+	5.93899i	−0.344926	+	0.399499i
$222$	−18.2040	+	9.55421i	−1.22177	+	0.641237i
$223$	14.2560	+	1.73099i	0.954649	+	0.115915i	0.583013	−	0.812463i	$-0.301874\pi$
$223$	14.2560	+	1.73099i	0.954649	+	0.115915i	0.371637	+	0.928378i	$0.378797\pi$
$224$	−26.3464	+	6.49380i	−1.76034	+	0.433886i
$225$	1.60984	−	2.33225i	0.107323	−	0.155484i
$226$	15.4649	−	10.6746i	1.02871	−	0.710067i
$227$	16.4853	−	18.6080i	1.09416	−	1.23506i	0.124085	−	0.992272i	$-0.460401\pi$
$227$	16.4853	−	18.6080i	1.09416	−	1.23506i	0.970080	−	0.242785i	$-0.0780610\pi$
$228$	−10.3089	−	1.25173i	−0.682725	−	0.0828978i
$229$	1.77093	−	7.18496i	0.117027	−	0.474795i	−0.882959	−	0.469450i	$-0.844452\pi$
$229$	1.77093	−	7.18496i	0.117027	−	0.474795i	0.999986	−	0.00534555i	$-0.00170155\pi$
$230$	16.3999	+	8.60733i	1.08138	+	0.567550i
$231$	0.299085	−	2.46319i	0.0196784	−	0.162066i
$232$	−43.9489	+	5.33637i	−2.88539	+	0.350350i
$233$	−4.56261	+	6.61008i	−0.298906	+	0.433041i	−0.943444	−	0.331532i	$-0.892435\pi$
$233$	−4.56261	+	6.61008i	−0.298906	+	0.433041i	0.644538	+	0.764573i	$0.277050\pi$
$234$	−3.38978	+	9.29419i	−0.221597	+	0.607580i
$235$	0.858560	+	1.24384i	0.0560063	+	0.0811391i
$236$	−36.9656	−	41.7255i	−2.40625	−	2.71610i
$237$	−9.67948	−	2.38578i	−0.628750	−	0.154973i
$238$	−3.96906	−	5.75017i	−0.257276	−	0.372728i
$239$			18.1608i			1.17473i	0.809323	+	0.587364i	$0.199834\pi$
$239$			18.1608i			1.17473i	−0.809323	+	0.587364i	$0.800166\pi$
$240$	−18.7849	+	12.9663i	−1.21256	+	0.836971i
$241$	−21.7669	+	2.64298i	−1.40213	+	0.170249i	−0.786404	−	0.617713i	$-0.788060\pi$
$241$	−21.7669	+	2.64298i	−1.40213	+	0.170249i	−0.615724	+	0.787962i	$0.711136\pi$
$242$	−16.6848	+	6.32773i	−1.07254	+	0.406762i
$243$	−0.120537	+	0.992709i	−0.00773243	+	0.0636823i
$244$	−0.768270	−	2.02576i	−0.0491834	−	0.129686i
$245$	−5.49543	+	6.20306i	−0.351090	+	0.396299i
$246$	−23.8198	−	21.1025i	−1.51870	−	1.34545i
$247$	−2.48215	−	6.30114i	−0.157935	−	0.400932i
$248$	59.7298	−	52.9160i	3.79285	−	3.36017i
$249$		−	2.57691i		−	0.163305i
$250$	23.6796	+	20.9783i	1.49763	+	1.32678i
$251$	−15.9563	+	3.93289i	−1.00716	+	0.248242i	−0.708190	−	0.706022i	$-0.750488\pi$
$251$	−15.9563	+	3.93289i	−1.00716	+	0.248242i	−0.298966	+	0.954264i	$0.596642\pi$
$252$	−5.32412	−	3.67497i	−0.335388	−	0.231502i
$253$	−9.09357	+	3.44874i	−0.571708	+	0.216820i
$254$	29.1709	−	11.0631i	1.83035	−	0.694159i
$255$	−2.63588	−	1.81941i	−0.165065	−	0.113936i
$256$	−51.4961	+	12.6926i	−3.21850	+	0.793290i
$257$	−1.28581	−	1.13913i	−0.0802068	−	0.0710571i	0.622067	−	0.782964i	$-0.286293\pi$
$257$	−1.28581	−	1.13913i	−0.0802068	−	0.0710571i	−0.702274	+	0.711907i	$0.747832\pi$
$258$		−	2.53241i		−	0.157661i
$259$	6.56260	−	5.81395i	0.407780	−	0.361262i
$260$	−26.1495	−	13.3014i	−1.62172	−	0.824919i
$261$	−3.42259	−	3.03215i	−0.211853	−	0.187685i
$262$	−19.2708	+	21.7522i	−1.19055	+	1.34386i
$263$	−6.70993	−	17.6926i	−0.413752	−	1.09097i	−0.966283	−	0.257482i	$-0.917107\pi$
$263$	−6.70993	−	17.6926i	−0.413752	−	1.09097i	0.552531	−	0.833492i	$-0.313662\pi$
$264$	2.47473	−	20.3813i	0.152309	−	1.25438i
$265$	8.46510	−	3.21039i	0.520007	−	0.197213i
$266$	5.98671	−	0.726918i	0.367069	−	0.0445702i
$267$	6.75455	−	4.66233i	0.413372	−	0.285330i
$268$			64.8512i			3.96142i
$269$	−12.8940	−	18.6802i	−0.786163	−	1.13895i	−0.987218	−	0.159374i	$-0.949052\pi$
$269$	−12.8940	−	18.6802i	−0.786163	−	1.13895i	0.201055	−	0.979580i	$-0.435563\pi$
$270$	−3.92095	−	0.966428i	−0.238622	−	0.0588149i
$271$	−1.73156	−	1.95453i	−0.105185	−	0.118729i	0.693560	−	0.720398i	$-0.256041\pi$
$271$	−1.73156	−	1.95453i	−0.105185	−	0.118729i	−0.798745	+	0.601669i	$0.794503\pi$
$272$	−19.1722	−	27.7757i	−1.16248	−	1.68415i
$273$	0.455047	−	4.19437i	0.0275407	−	0.253855i
$274$	−29.3009	+	42.4497i	−1.77013	+	2.56448i
$275$	−5.96549	+	0.724341i	−0.359732	+	0.0436794i
$276$	−3.05644	+	25.1720i	−0.183976	+	1.51518i
$277$	−7.41299	−	3.89064i	−0.445404	−	0.233766i	0.227083	−	0.973876i	$-0.427081\pi$
$277$	−7.41299	−	3.89064i	−0.445404	−	0.233766i	−0.672486	+	0.740110i	$0.734774\pi$
$278$	−8.76841	+	35.5748i	−0.525894	+	2.13364i
$279$	8.18174	+	0.993443i	0.489828	+	0.0594759i
$280$	11.0570	−	12.4808i	0.660785	−	0.745872i
$281$	−8.98476	+	6.20173i	−0.535986	+	0.369964i	−0.805096	−	0.593145i	$-0.797886\pi$
$281$	−8.98476	+	6.20173i	−0.535986	+	0.369964i	0.269109	+	0.963110i	$0.413271\pi$
$282$	−1.60063	+	2.31891i	−0.0953160	+	0.138089i
$283$	4.40387	−	1.08546i	0.261783	−	0.0645237i	−0.106240	−	0.994341i	$-0.533881\pi$
$283$	4.40387	−	1.08546i	0.261783	−	0.0645237i	0.368023	+	0.929817i	$0.380035\pi$
$284$	−37.8369	−	4.59423i	−2.24521	−	0.272617i
$285$	2.44781	−	1.28471i	0.144996	−	0.0760996i
$286$	19.5185	−	7.68875i	1.15415	−	0.454645i
$287$	12.0167	+	6.30684i	0.709322	+	0.372281i
$288$	−19.0846	−	13.1732i	−1.12457	−	0.776236i
$289$	−6.96689	+	10.0933i	−0.409817	+	0.593722i
$290$	13.8214	−	12.2447i	0.811623	−	0.719035i
$291$	−6.52288	−	7.36281i	−0.382378	−	0.431616i
$292$	−76.3528	−	28.9568i	−4.46821	−	1.69457i
$293$	−8.16058	+	15.5487i	−0.476746	+	0.908364i	0.521726	+	0.853113i	$0.325288\pi$
$293$	−8.16058	+	15.5487i	−0.476746	+	0.908364i	−0.998472	+	0.0552511i	$0.982404\pi$
$294$	−14.4460	−	5.47864i	−0.842507	−	0.319521i
$295$	14.4084	+	3.55135i	0.838889	+	0.206768i
$296$	54.3012	−	48.1066i	3.15619	−	2.79614i
$297$	1.74514	−	1.20458i	0.101263	−	0.0698971i
$298$	14.1323	+	37.2637i	0.818659	+	2.15863i
$299$	−15.3859	+	6.06084i	−0.889791	+	0.350507i
$300$	−5.55584	+	14.6495i	−0.320766	+	0.845791i
$301$	0.258453	+	1.04859i	0.0148970	+	0.0604395i
$302$	55.1434	−	28.9415i	3.17315	−	1.66540i
$303$	3.10381	+	8.18408i	0.178309	+	0.470163i
$304$	28.9182	−	3.51131i	1.65857	−	0.201387i
$305$	0.474656	+	0.327632i	0.0271787	+	0.0187601i
$306$	1.42898	−	5.79758i	0.0816891	−	0.331426i
$307$	−0.645091	−	2.61724i	−0.0368173	−	0.149374i	0.949656	−	0.313293i	$-0.101432\pi$
$307$	−0.645091	−	2.61724i	−0.0368173	−	0.149374i	−0.986474	+	0.163920i	$0.947586\pi$
$308$	1.65354	+	13.6181i	0.0942193	+	0.775966i
$309$	2.96589	−	7.82041i	0.168724	−	0.444888i
$310$	−7.96513	+	32.3158i	−0.452389	+	1.83542i
$311$	11.1353	−	2.74459i	0.631423	−	0.155632i	0.0894003	−	0.995996i	$-0.471505\pi$
$311$	11.1353	−	2.74459i	0.631423	−	0.155632i	0.542022	+	0.840364i	$0.317659\pi$
$312$	3.76521	−	34.7057i	0.213163	−	1.96482i
$313$	30.4496	+	7.50515i	1.72111	+	0.424216i	0.971381	−	0.237525i	$-0.0763362\pi$
$313$	30.4496	+	7.50515i	1.72111	+	0.424216i	0.749732	+	0.661742i	$0.230182\pi$
$314$	−14.9552	+	28.4948i	−0.843971	+	1.60805i
$315$	1.72217			0.0970332
$316$	55.1162			3.10053
$317$	−8.48800	+	16.1725i	−0.476734	+	0.908340i	0.521740	+	0.853105i	$0.325283\pi$
$317$	−8.48800	+	16.1725i	−0.476734	+	0.908340i	−0.998473	+	0.0552353i	$0.982409\pi$
$318$	11.1925	+	12.6337i	0.627644	+	0.708463i
$319$			9.69608i			0.542876i
$320$	31.8269	−	35.9251i	1.77918	−	2.00828i
$321$	−14.2951	+	7.50265i	−0.797875	+	0.418757i
$322$	−1.77497	−	14.6182i	−0.0989150	−	0.814638i
$323$	1.89959	+	3.61937i	0.105696	+	0.201387i
$324$	−0.666407	−	5.48836i	−0.0370226	−	0.304909i
$325$	−10.1267	+	1.36097i	−0.561730	+	0.0754932i
$326$	−0.877253	+	7.22483i	−0.0485866	+	0.400146i
$327$	8.98632	−	3.40806i	0.496945	−	0.188466i
$328$	99.4301	+	52.1849i	5.49011	+	2.88143i
$329$	0.426103	−	1.12354i	0.0234918	−	0.0619428i
$330$	3.97953	+	7.58237i	0.219066	+	0.417396i
$331$	−5.07136	−	9.66267i	−0.278747	−	0.531109i	0.705323	−	0.708886i	$-0.250802\pi$
$331$	−5.07136	−	9.66267i	−0.278747	−	0.531109i	−0.984071	+	0.177777i	$0.943109\pi$
$332$	3.40950	+	13.8329i	0.187120	+	0.759178i
$333$	7.43812	+	0.903152i	0.407607	+	0.0494924i
$334$	−25.1325	−	22.2655i	−1.37519	−	1.21831i
$335$	−9.80698	−	14.2079i	−0.535812	−	0.776258i
$336$	16.9681	+	6.43516i	0.925687	+	0.351067i
$337$	11.3659			0.619139			0.309570	−	0.950877i	$-0.399815\pi$
$337$	11.3659			0.619139			0.309570	+	0.950877i	$0.399815\pi$
$338$	33.0183	−	13.4959i	1.79596	−	0.734079i
$339$	−6.84852			−0.371961
$340$	16.5567	+	6.27912i	0.897912	+	0.340533i
$341$	−9.92798	−	14.3832i	−0.537630	−	0.778892i
$342$	3.85770	+	3.41762i	0.208600	+	0.184804i
$343$	14.6720	+	1.78150i	0.792212	+	0.0961919i
$344$	2.13853	+	8.67635i	0.115302	+	0.467798i
$345$	−3.13696	−	5.97698i	−0.168888	−	0.321790i
$346$	−0.541705	−	1.03213i	−0.0291223	−	0.0554878i
$347$	8.48168	−	22.3643i	0.455320	−	1.20058i	−0.489213	−	0.872164i	$-0.662716\pi$
$347$	8.48168	−	22.3643i	0.455320	−	1.20058i	0.944533	−	0.328416i	$-0.106515\pi$
$348$	22.3843	+	11.7482i	1.19993	+	0.629770i
$349$	−27.9815	+	10.6120i	−1.49781	+	0.568046i	−0.961217	−	0.275793i	$-0.911059\pi$
$349$	−27.9815	+	10.6120i	−1.49781	+	0.568046i	−0.536596	+	0.843839i	$0.680290\pi$
$350$	1.09673	−	9.03237i	0.0586226	−	0.482800i
$351$	2.94093	−	2.08589i	0.156975	−	0.111337i
$352$	5.92722	+	48.8150i	0.315922	+	2.60185i
$353$	−8.27820	−	15.7728i	−0.440604	−	0.839502i	−0.999944	−	0.0105631i	$-0.996638\pi$
$353$	−8.27820	−	15.7728i	−0.440604	−	0.839502i	0.559340	−	0.828938i	$-0.311055\pi$
$354$	3.33473	+	27.4640i	0.177239	+	1.45970i
$355$	8.98420	−	4.71527i	0.476832	−	0.250261i
$356$	−30.0898	+	33.9644i	−1.59476	+	1.80011i
$357$			2.54642i			0.134771i
$358$	−1.80276	−	2.03489i	−0.0952786	−	0.107547i
$359$	−3.66629	+	6.98554i	−0.193500	+	0.368683i	−0.962804	−	0.270199i	$-0.912910\pi$
$359$	−3.66629	+	6.98554i	−0.193500	+	0.368683i	0.769305	+	0.638882i	$0.220603\pi$
$360$	14.2498			0.751031
$361$	15.4719			0.814310
$362$	17.7612	−	33.8412i	0.933509	−	1.77865i
$363$	6.31447	+	1.55638i	0.331424	+	0.0816887i
$364$	3.10686	+	23.1175i	0.162844	+	1.21169i
$365$	21.1066	−	5.20231i	1.10477	−	0.272301i
$366$	−0.257323	+	1.04400i	−0.0134505	+	0.0545708i
$367$	−0.274861	+	0.724750i	−0.0143476	+	0.0378316i	−0.941999	−	0.335616i	$-0.891055\pi$
$367$	−0.274861	+	0.724750i	−0.0143476	+	0.0378316i	0.927651	+	0.373448i	$0.121825\pi$
$368$	−8.57380	−	70.6116i	−0.446940	−	3.68089i
$369$	2.77557	+	11.2609i	0.144490	+	0.586221i
$370$	−7.24121	+	29.3787i	−0.376452	+	1.52733i
$371$	−5.92381	−	4.08891i	−0.307549	−	0.212286i
$372$	−45.2341	+	5.49241i	−2.34528	+	0.284768i
$373$	−10.1757	−	26.8312i	−0.526880	−	1.38927i	−0.889330	−	0.457266i	$-0.848829\pi$
$373$	−10.1757	−	26.8312i	−0.526880	−	1.38927i	0.362450	−	0.932003i	$-0.381940\pi$
$374$	−11.2114	+	5.88420i	−0.579728	+	0.304265i
$375$	−2.75923	−	11.1946i	−0.142486	−	0.578089i
$376$	3.52572	−	9.29656i	0.181825	−	0.479433i
$377$	0.210415	+	16.4852i	0.0108369	+	0.849029i
$378$	1.13852	+	3.00203i	0.0585590	+	0.154408i
$379$	−1.10247	+	0.760979i	−0.0566300	+	0.0390889i	−0.596043	−	0.802952i	$-0.703261\pi$
$379$	−1.10247	+	0.760979i	−0.0566300	+	0.0390889i	0.539413	+	0.842041i	$0.318646\pi$
$380$	−11.4401	+	10.1350i	−0.586863	+	0.519915i
$381$	−11.0399	−	2.72109i	−0.565592	−	0.139406i
$382$	17.6543	+	6.69539i	0.903273	+	0.342566i
$383$	−2.91760	+	5.55901i	−0.149082	+	0.284052i	−0.948532	−	0.316680i	$-0.897432\pi$
$383$	−2.91760	+	5.55901i	−0.149082	+	0.284052i	0.799450	+	0.600732i	$0.205124\pi$
$384$	40.2989	+	15.2834i	2.05650	+	0.779926i
$385$	−2.42164	−	2.73346i	−0.123418	−	0.139310i
$386$	−41.3107	+	36.5981i	−2.10266	+	1.86279i
$387$	−0.524291	+	0.759567i	−0.0266512	+	0.0386109i
$388$	44.7566	+	30.8933i	2.27217	+	1.56837i
$389$	7.81946	+	4.10397i	0.396463	+	0.208080i	0.651159	−	0.758941i	$-0.274283\pi$
$389$	7.81946	+	4.10397i	0.396463	+	0.208080i	−0.254696	+	0.967021i	$0.581975\pi$
$390$	6.93050	+	12.8051i	0.350939	+	0.648411i
$391$	8.83766	−	4.63836i	0.446940	−	0.234572i
$392$	54.1203	+	6.57139i	2.73349	+	0.331906i
$393$	10.2835	−	2.53465i	0.518732	−	0.127856i
$394$	−38.4706	+	55.7343i	−1.93812	+	2.80786i
$395$	−12.0751	+	8.33482i	−0.607563	+	0.419370i
$396$	−7.77417	+	8.77522i	−0.390667	+	0.440971i
$397$	−31.5572	−	3.83174i	−1.58381	−	0.192310i	−0.719220	−	0.694783i	$-0.755500\pi$
$397$	−31.5572	−	3.83174i	−1.58381	−	0.192310i	−0.864593	+	0.502473i	$0.832424\pi$
$398$	9.34503	−	37.9143i	0.468424	−	1.90047i
$399$	−1.94614	−	1.02141i	−0.0974288	−	0.0511346i
$400$	5.29764	−	43.6300i	0.264882	−	2.18150i
$401$	30.0341	−	3.64681i	1.49983	−	0.182113i	0.670937	−	0.741514i	$-0.265892\pi$
$401$	30.0341	−	3.64681i	1.49983	−	0.182113i	0.828897	+	0.559402i	$0.188969\pi$
$402$	18.2833	−	26.4879i	0.911888	−	1.32110i
$403$	−17.1916	−	24.2386i	−0.856373	−	1.20741i
$404$	−27.4896	−	39.8256i	−1.36766	−	1.98140i
$405$	0.975963	+	1.10163i	0.0484960	+	0.0547406i
$406$	−14.2543	−	3.51336i	−0.707428	−	0.174365i
$407$	−9.02566	−	13.0759i	−0.447385	−	0.648150i
$408$			21.0700i			1.04312i
$409$	13.1070	−	9.04714i	0.648102	−	0.447352i	−0.198124	−	0.980177i	$-0.563485\pi$
$409$	13.1070	−	9.04714i	0.648102	−	0.447352i	0.846226	+	0.532825i	$0.178870\pi$
$410$	−46.4945	+	5.64545i	−2.29620	+	0.278809i
$411$	17.5769	−	6.66605i	0.867006	−	0.328812i
$412$	−5.57378	+	45.9042i	−0.274601	+	2.26154i
$413$	−4.18373	−	11.0316i	−0.205868	−	0.542829i
$414$	8.34504	−	9.41961i	0.410137	−	0.462948i
$415$	−2.83881	−	2.51497i	−0.139352	−	0.123455i
$416$	11.1367	+	82.8660i	0.546022	+	4.06284i
$417$	9.99514	−	8.85492i	0.489464	−	0.433627i
$418$		−	10.9287i		−	0.534541i
$419$	15.8584	+	14.0493i	0.774732	+	0.686353i	0.954783	−	0.297304i	$-0.0960876\pi$
$419$	15.8584	+	14.0493i	0.774732	+	0.686353i	−0.180050	+	0.983657i	$0.557626\pi$
$420$	−9.24462	+	2.27859i	−0.451091	+	0.111184i
$421$	−0.868922	−	0.599773i	−0.0423487	−	0.0292312i	0.546702	−	0.837327i	$-0.315883\pi$
$421$	−0.868922	−	0.599773i	−0.0423487	−	0.0292312i	−0.589051	+	0.808096i	$0.700498\pi$
$422$	7.71716	−	2.92673i	0.375666	−	0.142471i
$423$	0.960180	−	0.364148i	0.0466855	−	0.0177055i
$424$	−49.0156	−	33.8330i	−2.38041	−	1.64308i
$425$	5.98787	−	1.47588i	0.290454	−	0.0715905i
$426$	14.1589	+	12.5437i	0.686002	+	0.607745i
$427$		−	0.458548i		−	0.0221907i
$428$	66.8096	−	59.1881i	3.22936	−	2.86096i
$429$	−7.44617	−	1.73482i	−0.359505	−	0.0837578i
$430$	−2.78979	−	2.47153i	−0.134535	−	0.119188i
$431$	25.8188	−	29.1434i	1.24365	−	1.40379i	0.361801	−	0.932255i	$-0.382162\pi$
$431$	25.8188	−	29.1434i	1.24365	−	1.40379i	0.881848	−	0.471534i	$-0.156300\pi$
$432$	5.49950	+	14.5010i	0.264595	+	0.697679i
$433$	−4.56922	+	37.6309i	−0.219583	+	1.80843i	0.299927	+	0.953962i	$0.403038\pi$
$433$	−4.56922	+	37.6309i	−0.219583	+	1.80843i	−0.519509	+	0.854465i	$0.673885\pi$
$434$	24.7422	−	9.38347i	1.18766	−	0.450421i
$435$	−6.68064	+	0.811176i	−0.320312	+	0.0388929i
$436$	−43.7295	+	30.1843i	−2.09426	+	1.44557i
$437$			8.61483i			0.412103i
$438$	23.0220	+	33.3531i	1.10003	+	1.59367i
$439$	−35.6934	−	8.79763i	−1.70355	−	0.419888i	−0.736904	−	0.675997i	$-0.763713\pi$
$439$	−35.6934	−	8.79763i	−1.70355	−	0.419888i	−0.966648	+	0.256109i	$0.917559\pi$
$440$	−20.0374	−	22.6176i	−0.955248	−	1.07825i
$441$	3.19865	+	4.63404i	0.152317	+	0.220669i
$442$	−18.9338	+	10.2475i	−0.900589	+	0.487426i
$443$	−9.37509	+	13.5822i	−0.445424	+	0.645308i	−0.979810	−	0.199933i	$-0.935928\pi$
$443$	−9.37509	+	13.5822i	−0.445424	+	0.645308i	0.534386	+	0.845241i	$0.320543\pi$
$444$	−41.1229	+	4.99322i	−1.95161	+	0.236968i
$445$	1.45601	−	11.9913i	0.0690214	−	0.568443i
$446$	34.8900	+	18.3117i	1.65209	+	0.867082i
$447$	3.47599	−	14.1027i	0.164409	−	0.667033i
$448$	−37.8808	−	4.59956i	−1.78970	−	0.217309i
$449$	9.42948	−	10.6437i	0.445005	−	0.502306i	−0.482615	−	0.875833i	$-0.660313\pi$
$449$	9.42948	−	10.6437i	0.445005	−	0.502306i	0.927620	+	0.373526i	$0.121851\pi$
$450$	6.39933	−	4.41714i	0.301667	−	0.208226i
$451$	13.9707	−	20.2401i	0.657855	−	0.953068i
$452$	36.7629	−	9.06125i	1.72918	−	0.426205i
$453$	−22.5315	−	2.73582i	−1.05862	−	0.128540i
$454$	60.3987	−	31.6997i	2.83465	−	1.48774i
$455$	−4.17655	−	4.59485i	−0.195800	−	0.215410i
$456$	−16.1030	−	8.45152i	−0.754093	−	0.395779i
$457$	31.5858	+	21.8021i	1.47752	+	1.01986i	0.989099	+	0.147252i	$0.0470428\pi$
$457$	31.5858	+	21.8021i	1.47752	+	1.01986i	0.488422	+	0.872607i	$0.337573\pi$
$458$	11.5342	−	16.7102i	0.538958	−	0.780816i
$459$	−1.62889	+	1.44307i	−0.0760302	+	0.0673569i
$460$	24.7474	+	27.9340i	1.15385	+	1.30243i
$461$	−23.2801	−	8.82898i	−1.08426	−	0.411206i	−0.253216	−	0.967410i	$-0.581488\pi$
$461$	−23.2801	−	8.82898i	−1.08426	−	0.411206i	−0.831046	+	0.556203i	$0.812258\pi$
$462$	3.16395	−	6.02840i	0.147200	−	0.280466i
$463$	2.42268	+	0.918803i	0.112592	+	0.0427004i	0.410257	−	0.911970i	$-0.365439\pi$
$463$	2.42268	+	0.918803i	0.112592	+	0.0427004i	−0.297666	+	0.954670i	$0.596208\pi$
$464$	−68.8539	−	16.9710i	−3.19646	−	0.787857i
$465$	9.07948	−	8.04372i	0.421051	−	0.373018i
$466$	−18.1370	+	12.5191i	−0.840181	+	0.579935i
$467$	9.31688	+	24.5666i	0.431134	+	1.13681i	0.957977	+	0.286844i	$0.0926061\pi$
$467$	9.31688	+	24.5666i	0.431134	+	1.13681i	−0.526844	+	0.849962i	$0.676625\pi$
$468$	−13.0271	+	15.0882i	−0.602178	+	0.697453i
$469$	−4.86720	+	12.8337i	−0.224746	+	0.592607i
$470$	0.992437	+	4.02647i	0.0457777	+	0.185727i
$471$	10.3850	−	5.45046i	0.478515	−	0.251144i
$472$	−34.6176	−	91.2792i	−1.59341	−	4.20147i
$473$	1.94284	−	0.235903i	0.0893317	−	0.0108468i
$474$	−22.5118	−	15.5387i	−1.03400	−	0.713718i
$475$	−1.27387	+	5.16831i	−0.0584493	+	0.237138i
$476$	−3.36916	−	13.6692i	−0.154425	−	0.626528i
$477$	−0.741469	−	6.10655i	−0.0339495	−	0.279600i
$478$	−17.6701	+	46.5923i	−0.808213	+	2.13108i
$479$	1.96353	−	7.96634i	0.0897158	−	0.363991i	−0.908875	−	0.417070i	$-0.863057\pi$
$479$	1.96353	−	7.96634i	0.0897158	−	0.363991i	0.998590	+	0.0530783i	$0.0169033\pi$
$480$	−33.1379	+	8.16775i	−1.51253	+	0.372805i
$481$	−15.6291	−	22.0357i	−0.712624	−	1.00474i
$482$	−58.4153	−	14.3981i	−2.66074	−	0.655814i
$483$	−2.49406	+	4.75203i	−0.113483	+	0.216225i
$484$	−35.9554			−1.63434
$485$	−14.4772			−0.657376
$486$	−1.27513	+	2.42955i	−0.0578409	+	0.110207i
$487$	6.54047	+	7.38267i	0.296377	+	0.334541i	0.877770	−	0.479082i	$-0.159031\pi$
$487$	6.54047	+	7.38267i	0.296377	+	0.334541i	−0.581393	+	0.813623i	$0.697492\pi$
$488$		−	3.79418i		−	0.171755i
$489$	1.75890	−	1.98539i	0.0795401	−	0.0897822i
$490$	−20.1342	+	10.5672i	−0.909570	+	0.477379i
$491$	−2.49335	−	20.5346i	−0.112523	−	0.926713i	−0.934198	−	0.356756i	$-0.883883\pi$
$491$	−2.49335	−	20.5346i	−0.112523	−	0.926713i	0.821674	−	0.569957i	$-0.193040\pi$
$492$	−29.7986	−	56.7765i	−1.34342	−	2.55968i
$493$	−1.19942	−	9.87810i	−0.0540191	−	0.444887i
$494$	−0.237165	−	18.5809i	−0.0106705	−	0.835993i
$495$	0.376182	−	3.09814i	0.0169081	−	0.139251i
$496$	119.515	−	45.3260i	5.36637	−	2.03520i
$497$	−7.14293	−	3.74890i	−0.320404	−	0.168161i
$498$	2.50728	−	6.61115i	0.112354	−	0.296253i
$499$	13.5756	+	25.8662i	0.607728	+	1.15793i	0.973814	+	0.227348i	$0.0730053\pi$
$499$	13.5756	+	25.8662i	0.607728	+	1.15793i	−0.366086	+	0.930581i	$0.619302\pi$
$500$	29.6232	+	56.4423i	1.32479	+	2.52418i
$501$	2.92853	+	11.8815i	0.130837	+	0.530827i
$502$	−44.7632	−	5.43524i	−1.99788	−	0.242587i
$503$	6.56966	+	5.82021i	0.292927	+	0.259510i	0.796767	−	0.604286i	$-0.206542\pi$
$503$	6.56966	+	5.82021i	0.292927	+	0.259510i	−0.503841	+	0.863797i	$0.668080\pi$
$504$	−6.43581	−	9.32389i	−0.286674	−	0.415319i
$505$	12.0451	+	4.56809i	0.535999	+	0.203277i
$506$	−26.6854			−1.18631
$507$	−12.6975	−	2.78792i	−0.563917	−	0.123816i
$508$	62.8626			2.78908
$509$	−13.1108	−	4.97226i	−0.581125	−	0.220392i	0.0464857	−	0.998919i	$-0.485198\pi$
$509$	−13.1108	−	4.97226i	−0.581125	−	0.220392i	−0.627611	+	0.778527i	$0.715967\pi$
$510$	−4.99219	−	7.23243i	−0.221058	−	0.320257i
$511$	−12.9366	−	11.4608i	−0.572281	−	0.506997i
$512$	−58.8938	−	7.15100i	−2.60276	−	0.316033i
$513$	−0.449513	−	1.82374i	−0.0198465	−	0.0805203i
$514$	−2.19045	−	4.17355i	−0.0966166	−	0.184088i
$515$	−5.72063	−	10.8998i	−0.252081	−	0.480301i
$516$	1.80942	−	4.77105i	0.0796553	−	0.210034i
$517$	−1.92815	−	1.01197i	−0.0847998	−	0.0445064i
$518$	22.4934	−	8.53064i	0.988305	−	0.374815i
$519$	−0.0512070	+	0.421727i	−0.00224774	+	0.0185118i
$520$	−34.5582	−	38.0193i	−1.51548	−	1.66726i
$521$	0.894156	+	7.36403i	0.0391737	+	0.322624i	0.999102	+	0.0423774i	$0.0134932\pi$
$521$	0.894156	+	7.36403i	0.0391737	+	0.322624i	−0.959928	+	0.280247i	$0.909584\pi$
$522$	−5.83056	−	11.1092i	−0.255197	−	0.486236i
$523$	−4.80409	−	39.5652i	−0.210068	−	1.73007i	−0.592055	−	0.805898i	$-0.701683\pi$
$523$	−4.80409	−	39.5652i	−0.210068	−	1.73007i	0.381987	−	0.924168i	$-0.375240\pi$
$524$	−51.8482	+	27.2120i	−2.26500	+	1.18876i
$525$	−2.19895	+	2.48210i	−0.0959698	+	0.108328i
$526$		−	51.9197i		−	2.26381i
$527$	11.8936	+	13.4251i	0.518092	+	0.584805i
$528$	15.2831	−	29.1196i	0.665113	−	1.26727i
$529$	−1.96457			−0.0854159
$530$	24.8412			1.07903
$531$	4.68573	−	8.92792i	0.203343	−	0.387439i
$532$	11.7983	+	2.90803i	0.511523	+	0.126079i
$533$	23.3136	−	34.7151i	1.00982	−	1.50368i
$534$	21.8654	−	5.38934i	0.946209	−	0.233220i
$535$	−5.68631	+	23.0703i	−0.245841	+	0.997415i
$536$	−40.2728	+	106.191i	−1.73952	+	4.58674i
$537$	0.119427	+	0.983572i	0.00515366	+	0.0424442i
$538$	−14.9046	−	60.4705i	−0.642584	−	2.60707i
$539$	2.85746	−	11.5932i	0.123079	−	0.499352i
$540$	−6.69655	−	4.62229i	−0.288174	−	0.198912i
$541$	−17.1491	+	2.08228i	−0.737297	+	0.0895241i	−0.480566	−	0.876959i	$-0.659569\pi$
$541$	−17.1491	+	2.08228i	−0.737297	+	0.0895241i	−0.256731	+	0.966483i	$0.582646\pi$
$542$	−2.54067	−	6.69920i	−0.109131	−	0.287755i
$543$	−12.3335	+	6.47312i	−0.529282	+	0.277788i
$544$	−12.0770	−	48.9982i	−0.517795	−	2.10078i
$545$	5.01588	−	13.2258i	0.214857	−	0.566530i
$546$	5.24848	−	10.3181i	0.224614	−	0.441572i
$547$	9.21624	+	24.3012i	0.394058	+	1.03904i	0.974430	+	0.224693i	$0.0721380\pi$
$547$	9.21624	+	24.3012i	0.394058	+	1.03904i	−0.580372	+	0.814352i	$0.697093\pi$
$548$	−85.5333	+	59.0394i	−3.65380	+	2.52204i
$549$	0.293323	−	0.259862i	0.0125187	−	0.0110906i
$550$	−16.0094	−	3.94597i	−0.682645	−	0.168257i
$551$	8.03058	+	3.04560i	0.342114	+	0.129747i
$552$	−20.6367	+	39.3199i	−0.878355	+	1.67357i
$553$	10.9072	+	4.13657i	0.463822	+	0.175905i
$554$	−15.2328	−	17.1943i	−0.647179	−	0.730514i
$555$	8.25427	−	7.31265i	0.350374	−	0.310405i
$556$	−41.9381	+	60.7579i	−1.77857	+	2.57671i
$557$	−22.9649	−	15.8515i	−0.973053	−	0.671650i	−0.0283573	−	0.999598i	$-0.509028\pi$
$557$	−22.9649	−	15.8515i	−0.973053	−	0.671650i	−0.944696	+	0.327948i	$0.893643\pi$
$558$	20.0239	+	10.5094i	0.847681	+	0.444897i
$559$	3.29806	−	0.443241i	0.139493	−	0.0187471i
$560$	23.6495	−	12.4122i	0.999372	−	0.524511i
$561$	4.58096	+	0.556229i	0.193408	+	0.0234840i
$562$	−29.0849	+	7.16878i	−1.22687	+	0.302397i
$563$	−9.06320	+	13.1303i	−0.381968	+	0.553377i	−0.966062	−	0.258309i	$-0.916835\pi$
$563$	−9.06320	+	13.1303i	−0.381968	+	0.553377i	0.584094	+	0.811686i	$0.301450\pi$
$564$	−4.67245	+	3.22516i	−0.196746	+	0.135804i
$565$	−6.68390	+	7.54456i	−0.281194	+	0.317402i
$566$	12.3544	+	1.50010i	0.519295	+	0.0630539i
$567$	0.280032	−	1.13613i	0.0117602	−	0.0477131i
$568$	−59.1030	−	31.0197i	−2.47991	−	1.30156i
$569$	1.88615	−	15.5339i	0.0790716	−	0.651213i	−0.898255	−	0.439475i	$-0.855164\pi$
$569$	1.88615	−	15.5339i	0.0790716	−	0.651213i	0.977326	−	0.211738i	$-0.0679124\pi$
$570$	7.52993	−	0.914299i	0.315394	−	0.0382958i
$571$	−2.15976	+	3.12896i	−0.0903833	+	0.130943i	−0.865567	−	0.500793i	$-0.833042\pi$
$571$	−2.15976	+	3.12896i	−0.0903833	+	0.130943i	0.775184	+	0.631736i	$0.217657\pi$
$572$	42.2665	−	0.539486i	1.76725	−	0.0225570i
$573$	−3.90904	−	5.66322i	−0.163303	−	0.236585i
$574$	24.6928	+	27.8724i	1.03066	+	1.16337i
$575$	12.6198	+	3.11051i	0.526283	+	0.129717i
$576$	−18.5250	−	26.8381i	−0.771876	−	1.11826i
$577$			6.56709i			0.273392i	0.990613	+	0.136696i	$0.0436483\pi$
$577$			6.56709i			0.273392i	−0.990613	+	0.136696i	$0.956352\pi$
$578$	−27.6944	+	19.1160i	−1.15193	+	0.795122i
$579$	19.9677	−	2.42451i	0.829828	−	0.100759i
$580$	34.7885	−	13.1935i	1.44451	−	0.547832i
$581$	−0.363458	+	2.99335i	−0.0150788	+	0.124185i
$582$	−9.57082	−	25.2362i	−0.396723	−	1.04607i
$583$	−8.64982	+	9.76363i	−0.358239	+	0.404368i
$584$	−107.042	−	94.8307i	−4.42942	−	3.92412i
$585$	0.572347	−	5.27558i	0.0236636	−	0.218118i
$586$	−36.0648	+	31.9506i	−1.48982	+	1.31987i
$587$		−	33.2444i		−	1.37214i	−0.727534	−	0.686072i	$-0.759334\pi$
$587$		−	33.2444i		−	1.37214i	0.727534	−	0.686072i	$-0.240666\pi$
$588$	−23.3017	−	20.6435i	−0.960945	−	0.851323i
$589$	−15.0310	+	3.70481i	−0.619341	+	0.152654i
$590$	33.5099	+	23.1302i	1.37958	+	0.952255i
$591$	23.0777	−	8.75220i	0.949288	−	0.360017i
$592$	108.652	−	41.2064i	4.46559	−	1.69357i
$593$	30.3607	+	20.9565i	1.24677	+	0.860581i	0.994258	−	0.107014i	$-0.0341290\pi$
$593$	30.3607	+	20.9565i	1.24677	+	0.860581i	0.252509	+	0.967595i	$0.418744\pi$
$594$	5.64926	−	1.39242i	0.231792	−	0.0571316i
$595$	2.80523	+	2.48521i	0.115003	+	0.101884i
$596$			80.3023i			3.28931i
$597$	−10.6524	+	9.43722i	−0.435975	+	0.386240i
$598$	−45.3702	+	0.579101i	−1.85533	+	0.0236812i
$599$	−0.800358	−	0.709056i	−0.0327018	−	0.0289712i	0.646614	−	0.762818i	$-0.276185\pi$
$599$	−0.800358	−	0.709056i	−0.0327018	−	0.0289712i	−0.679315	+	0.733847i	$0.737723\pi$
$600$	−18.1948	+	20.5377i	−0.742801	+	0.838448i
$601$	−15.9816	−	42.1399i	−0.651901	−	1.71892i	−0.694164	−	0.719816i	$-0.744226\pi$
$601$	−15.9816	−	42.1399i	−0.651901	−	1.71892i	0.0422629	−	0.999107i	$-0.486543\pi$
$602$	−0.357181	+	2.94165i	−0.0145576	+	0.119893i
$603$	−10.9677	+	4.15951i	−0.446641	+	0.169389i
$604$	124.569	−	15.1254i	5.06864	−	0.615444i
$605$	7.87725	−	5.43727i	0.320256	−	0.221057i
$606$			24.0165i			0.975604i
$607$	6.60653	+	9.57121i	0.268151	+	0.388483i	0.933808	−	0.357774i	$-0.116464\pi$
$607$	6.60653	+	9.57121i	0.268151	+	0.388483i	−0.665657	+	0.746257i	$0.731849\pi$
$608$	42.2918	+	10.4240i	1.71516	+	0.422749i
$609$	3.54803	+	4.00489i	0.143773	+	0.162286i
$610$	0.898969	+	1.30238i	0.0363982	+	0.0527319i
$611$	−3.30017	−	1.67869i	−0.133511	−	0.0679127i
$612$	6.83459	−	9.90162i	0.276272	−	0.400249i
$613$	23.9912	−	2.91305i	0.968994	−	0.117657i	0.379291	−	0.925277i	$-0.376168\pi$
$613$	23.9912	−	2.91305i	0.968994	−	0.117657i	0.589703	+	0.807620i	$0.299245\pi$
$614$	0.891513	−	7.34227i	0.0359786	−	0.296310i
$615$	15.1143	+	7.93259i	0.609467	+	0.319873i
$616$	−5.74932	+	23.3259i	−0.231647	+	0.939827i
$617$	−21.9293	−	2.66270i	−0.882840	−	0.107196i	−0.333455	−	0.942766i	$-0.608215\pi$
$617$	−21.9293	−	2.66270i	−0.882840	−	0.107196i	−0.549384	+	0.835570i	$0.685138\pi$
$618$	15.2182	−	17.1778i	0.612166	−	0.690993i
$619$	14.5623	−	10.0516i	0.585307	−	0.404008i	−0.238281	−	0.971196i	$-0.576584\pi$
$619$	14.5623	−	10.0516i	0.585307	−	0.404008i	0.823588	+	0.567188i	$0.191969\pi$
$620$	−38.0962	+	55.1918i	−1.52998	+	2.21656i
$621$	−4.45317	+	1.09761i	−0.178699	+	0.0440455i
$622$	31.2383	+	3.79302i	1.25254	+	0.152086i
$623$	−8.50371	+	4.46309i	−0.340694	+	0.178810i
$624$	25.3523	−	49.8404i	1.01490	−	1.99521i
$625$	−2.47885	−	1.30100i	−0.0991540	−	0.0520400i
$626$	70.8172	+	48.8816i	2.83042	+	1.95370i
$627$	−2.26260	+	3.27795i	−0.0903596	+	0.130909i
$628$	−48.5353	+	42.9985i	−1.93677	+	1.71583i
$629$	10.8126	+	12.2049i	0.431126	+	0.486641i
$630$	4.41828	+	1.67563i	0.176029	+	0.0667589i
$631$	2.04453	−	3.89552i	0.0813914	−	0.155078i	−0.841359	−	0.540477i	$-0.818244\pi$
$631$	2.04453	−	3.89552i	0.0813914	−	0.155078i	0.922750	+	0.385399i	$0.125936\pi$
$632$	90.2501	+	34.2273i	3.58996	+	1.36149i
$633$	−2.92060	−	0.719864i	−0.116084	−	0.0286120i
$634$	−37.5118	+	33.2326i	−1.48978	+	1.31983i
$635$	−13.7722	+	9.50625i	−0.546532	+	0.377244i
$636$	12.0598	+	31.7990i	0.478201	+	1.26091i
$637$	4.60663	−	19.7725i	0.182521	−	0.783417i
$638$	−9.43409	+	24.8757i	−0.373499	+	0.984837i
$639$	−1.64985	−	6.69370i	−0.0652670	−	0.264799i
$640$	56.1669	−	29.4787i	2.22019	−	1.16525i
$641$	−13.7786	−	36.3313i	−0.544224	−	1.43500i	−0.871652	−	0.490124i	$-0.836951\pi$
$641$	−13.7786	−	36.3313i	−0.544224	−	1.43500i	0.327429	−	0.944876i	$-0.393818\pi$
$642$	−43.9745	+	5.33947i	−1.73554	+	0.210732i
$643$	22.1508	+	15.2896i	0.873544	+	0.602964i	0.918234	−	0.396037i	$-0.129615\pi$
$643$	22.1508	+	15.2896i	0.873544	+	0.602964i	−0.0446908	+	0.999001i	$0.514230\pi$
$644$	7.10074	−	28.8088i	0.279808	−	1.13523i
$645$	0.325076	+	1.31889i	0.0127999	+	0.0519311i
$646$	1.35190	+	11.1339i	0.0531897	+	0.438056i
$647$	−12.6504	+	33.3562i	−0.497337	+	1.31137i	0.417915	+	0.908486i	$0.362761\pi$
$647$	−12.6504	+	33.3562i	−0.497337	+	1.31137i	−0.915252	+	0.402883i	$0.868008\pi$
$648$	2.31708	−	9.40076i	0.0910234	−	0.369297i
$649$	−20.7594	+	5.11674i	−0.814880	+	0.200850i
$650$	−27.3047	−	6.36147i	−1.07098	−	0.249517i
$651$	−9.36382	−	2.30797i	−0.366997	−	0.0904566i
$652$	−6.81493	+	12.9848i	−0.266893	+	0.508523i
$653$	13.0441			0.510455			0.255228	−	0.966881i	$-0.417850\pi$
$653$	13.0441			0.510455			0.255228	+	0.966881i	$0.417850\pi$
$654$	26.3707			1.03118
$655$	7.24402	−	13.8023i	0.283047	−	0.539302i
$656$	119.276	+	134.635i	4.65695	+	5.25661i
$657$		−	14.7702i		−	0.576240i
$658$	2.18636	−	2.46789i	0.0852333	−	0.0962085i
$659$	32.1843	−	16.8916i	1.25372	−	0.658004i	0.298645	−	0.954364i	$-0.403465\pi$
$659$	32.1843	−	16.8916i	1.25372	−	0.658004i	0.955076	+	0.296360i	$0.0957730\pi$
$660$	2.07979	+	17.1286i	0.0809555	+	0.666729i
$661$	6.93308	+	13.2099i	0.269666	+	0.513805i	0.982201	−	0.187831i	$-0.0601457\pi$
$661$	6.93308	+	13.2099i	0.269666	+	0.513805i	−0.712536	+	0.701636i	$0.752453\pi$
$662$	−3.60918	−	29.7243i	−0.140275	−	1.15527i
$663$	7.80055	+	0.846281i	0.302948	+	0.0328668i
$664$	−3.00738	+	24.7680i	−0.116709	+	0.961183i
$665$	−3.02458	+	1.14707i	−0.117288	+	0.0444816i
$666$	18.2040	+	9.55421i	0.705392	+	0.370218i
$667$	7.43665	−	19.6088i	0.287948	−	0.759257i
$668$	−31.4408	−	59.9054i	−1.21648	−	2.31781i
$669$	−6.67373	−	12.7157i	−0.258021	−	0.491619i
$670$	−11.3362	−	45.9928i	−0.437955	−	1.77686i
$671$	−0.824917	−	0.100163i	−0.0318456	−	0.00386675i
$672$	20.3108	+	17.9938i	0.783505	+	0.694124i
$673$	−4.05565	−	5.87562i	−0.156334	−	0.226489i	0.736988	−	0.675905i	$-0.236247\pi$
$673$	−4.05565	−	5.87562i	−0.156334	−	0.226489i	−0.893322	+	0.449417i	$0.851632\pi$
$674$	29.1596	+	11.0588i	1.12319	+	0.425968i
$675$	−2.83390			−0.109077
$676$	71.8492	−	1.83445i	2.76343	−	0.0705559i
$677$	−11.0074			−0.423050			−0.211525	−	0.977373i	$-0.567843\pi$
$677$	−11.0074			−0.423050			−0.211525	+	0.977373i	$0.567843\pi$
$678$	−17.5701	−	6.66347i	−0.674777	−	0.255909i
$679$	6.53852	+	9.47268i	0.250925	+	0.363528i
$680$	23.2114	+	20.5635i	0.890117	+	0.788575i
$681$	−24.6788	−	2.99655i	−0.945693	−	0.114828i
$682$	−11.4761	−	46.5603i	−0.439442	−	1.78288i
$683$	−8.93938	−	17.0326i	−0.342056	−	0.651733i	0.652285	−	0.757974i	$-0.273811\pi$
$683$	−8.93938	−	17.0326i	−0.342056	−	0.651733i	−0.994340	+	0.106241i	$0.966118\pi$
$684$	4.82598	+	9.19514i	0.184526	+	0.351585i
$685$	9.81088	−	25.8692i	0.374854	−	0.988410i
$686$	35.9081	+	18.8460i	1.37098	+	0.719545i
$687$	−6.91911	+	2.62407i	−0.263980	+	0.100115i
$688$	−1.72533	+	14.2094i	−0.0657776	+	0.541727i
$689$	−14.4944	+	16.7877i	−0.552194	+	0.639561i
$690$	−2.23251	−	18.3864i	−0.0849902	−	0.699957i
$691$	−7.38606	−	14.0730i	−0.280979	−	0.535361i	0.703536	−	0.710659i	$-0.251603\pi$
$691$	−7.38606	−	14.0730i	−0.280979	−	0.535361i	−0.984515	+	0.175298i	$0.943911\pi$
$692$	−0.283106	−	2.33159i	−0.0107621	−	0.0886337i
$693$	−2.19706	+	1.15311i	−0.0834596	+	0.0438030i
$694$	43.5201	−	49.1240i	1.65200	−	1.86472i
$695$		−	19.6531i		−	0.745483i
$696$	29.3576	+	33.1379i	1.11280	+	1.25609i
$697$	−11.7292	+	22.3482i	−0.444277	+	0.846499i
$698$	−82.1127			−3.10801
$699$	8.03184			0.303792
$700$	8.51991	−	16.2333i	0.322023	−	0.613563i
$701$	47.3905	+	11.6807i	1.78992	+	0.441174i	0.987765	−	0.155948i	$-0.0498433\pi$
$701$	47.3905	+	11.6807i	1.78992	+	0.441174i	0.802150	+	0.597123i	$0.203689\pi$
$702$	9.57459	−	2.48997i	0.361370	−	0.0939777i
$703$	−13.6649	+	3.36809i	−0.515380	+	0.127030i
$704$	−16.5490	+	67.1419i	−0.623714	+	2.53051i
$705$	0.535942	−	1.41316i	0.0201847	−	0.0532227i
$706$	−5.89142	−	48.5202i	−0.221727	−	1.82608i
$707$	−2.45108	−	9.94444i	−0.0921825	−	0.373999i
$708$	−13.3406	+	54.1248i	−0.501369	+	2.03414i
$709$	5.72818	+	3.95387i	0.215126	+	0.148491i	0.670755	−	0.741679i	$-0.265970\pi$
$709$	5.72818	+	3.95387i	0.215126	+	0.148491i	−0.455629	+	0.890170i	$0.650586\pi$
$710$	27.6372	−	3.35576i	1.03720	−	0.125939i
$711$	3.53512	+	9.32134i	0.132577	+	0.349577i
$712$	−70.3626	+	36.9291i	−2.63695	+	1.38398i
$713$	9.04629	+	36.7022i	0.338786	+	1.37451i
$714$	−2.47762	+	6.53294i	−0.0927225	+	0.244489i
$715$	−9.17832	+	6.50984i	−0.343250	+	0.243454i
$716$	−1.94245	−	5.12181i	−0.0725926	−	0.191411i
$717$	14.9461	−	10.3165i	0.558172	−	0.385278i
$718$	−16.2028	+	14.3544i	−0.604683	+	0.535703i
$719$	−8.86601	−	2.18528i	−0.330646	−	0.0814970i	0.0704978	−	0.997512i	$-0.477541\pi$
$719$	−8.86601	−	2.18528i	−0.330646	−	0.0814970i	−0.401144	+	0.916015i	$0.631387\pi$
$720$	21.3421	+	8.09399i	0.795373	+	0.301645i
$721$	−4.54822	+	8.66590i	−0.169384	+	0.322735i
$722$	39.6937	+	15.0538i	1.47725	+	0.560246i
$723$	14.5401	+	16.4124i	0.540753	+	0.610384i
$724$	57.6419	−	51.0662i	2.14224	−	1.89786i
$725$	7.36104	−	10.6643i	0.273382	−	0.396062i
$726$	14.6857	+	10.1368i	0.545037	+	0.376212i
$727$	−5.02265	−	2.63609i	−0.186280	−	0.0977671i	0.369005	−	0.929427i	$-0.379698\pi$
$727$	−5.02265	−	2.63609i	−0.186280	−	0.0977671i	−0.555285	+	0.831660i	$0.687391\pi$
$728$	−9.26872	+	39.7832i	−0.343522	+	1.47446i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	59.2115	+	7.18958i	2.19152	+	0.266098i
$731$	−1.95012	+	0.480662i	−0.0721279	+	0.0177779i
$732$	−1.23074	+	1.78304i	−0.0454895	+	0.0659029i
$733$	−18.5414	+	12.7982i	−0.684844	+	0.472714i	−0.858981	−	0.512008i	$-0.828902\pi$
$733$	−18.5414	+	12.7982i	−0.684844	+	0.472714i	0.174137	+	0.984721i	$0.444286\pi$
$734$	−1.41033	+	1.59194i	−0.0520564	+	0.0587595i
$735$	8.22678	+	0.998912i	0.303449	+	0.0368454i
$736$	25.4530	−	103.267i	0.938210	−	3.80647i
$737$	22.0244	+	11.5593i	0.811280	+	0.425793i
$738$	−3.83583	+	31.5909i	−0.141199	+	1.16288i
$739$	−44.9937	+	5.46323i	−1.65512	+	0.200968i	−0.894134	−	0.447799i	$-0.852208\pi$
$739$	−44.9937	+	5.46323i	−1.65512	+	0.200968i	−0.760987	+	0.648767i	$0.775285\pi$
$740$	−34.6337	+	50.1756i	−1.27316	+	1.84449i
$741$	−3.77571	+	5.62222i	−0.138704	+	0.206537i
$742$	−11.2193	−	16.2540i	−0.411874	−	0.596703i
$743$	−19.9133	−	22.4775i	−0.730550	−	0.824620i	0.259440	−	0.965759i	$-0.416462\pi$
$743$	−19.9133	−	22.4775i	−0.730550	−	0.824620i	−0.989990	+	0.141139i	$0.954924\pi$
$744$	−77.4794	−	19.0970i	−2.84053	−	0.700129i
$745$	−12.1435	−	17.5929i	−0.444904	−	0.644555i
$746$		−	78.7373i		−	2.88278i
$747$	−2.12075	+	1.46385i	−0.0775943	+	0.0535595i
$748$	−25.3266	+	3.07520i	−0.926031	+	0.112441i
$749$	17.6634	−	6.69886i	0.645408	−	0.244771i
$750$	3.81325	−	31.4050i	0.139240	−	1.14675i
$751$	0.595359	+	1.56983i	0.0217249	+	0.0572840i	0.945440	−	0.325796i	$-0.105632\pi$
$751$	0.595359	+	1.56983i	0.0217249	+	0.0572840i	−0.923715	+	0.383080i	$0.874863\pi$
$752$	10.5610	−	11.9209i	0.385121	−	0.434711i
$753$	12.3009	+	10.8977i	0.448271	+	0.397134i
$754$	−15.4999	+	42.4980i	−0.564473	+	1.54769i
$755$	−25.0037	+	22.1514i	−0.909979	+	0.806171i
$756$			6.46929i			0.235286i
$757$	−34.0672	−	30.1809i	−1.23819	−	1.09694i	−0.991803	−	0.127774i	$-0.959217\pi$
$757$	−34.0672	−	30.1809i	−1.23819	−	1.09694i	−0.246391	−	0.969171i	$-0.579245\pi$
$758$	−3.56884	+	0.879640i	−0.129626	+	0.0319500i
$759$	8.00399	+	5.52476i	0.290526	+	0.200536i
$760$	−25.0264	+	9.49127i	−0.907804	+	0.344285i
$761$	30.1171	−	11.4219i	1.09174	−	0.414043i	0.257971	−	0.966153i	$-0.416946\pi$
$761$	30.1171	−	11.4219i	1.09174	−	0.414043i	0.833772	+	0.552109i	$0.186177\pi$
$762$	−25.6757	−	17.7227i	−0.930133	−	0.642024i
$763$	−10.9192	+	2.69135i	−0.395303	+	0.0974334i
$764$	28.4768	+	25.2282i	1.03025	+	0.912725i
$765$			3.20283i			0.115799i
$766$	−12.8940	+	11.4231i	−0.465879	+	0.412733i
$767$	−35.1839	+	9.14993i	−1.27042	+	0.330385i
$768$	39.6989	+	35.1702i	1.43251	+	1.26909i
$769$	−8.78211	+	9.91295i	−0.316691	+	0.357470i	−0.885203	−	0.465205i	$-0.845981\pi$
$769$	−8.78211	+	9.91295i	−0.316691	+	0.357470i	0.568512	+	0.822675i	$0.307519\pi$
$770$	−3.55319	−	9.36900i	−0.128048	−	0.337635i
$771$	−0.207061	+	1.70530i	−0.00745713	+	0.0614150i
$772$	−103.979	+	39.4340i	−3.74228	+	1.41926i
$773$	22.2091	−	2.69668i	0.798807	−	0.0969928i	0.289053	−	0.957313i	$-0.406659\pi$
$773$	22.2091	−	2.69668i	0.798807	−	0.0969928i	0.509754	+	0.860320i	$0.329736\pi$
$774$	−2.08413	+	1.43857i	−0.0749125	+	0.0517084i
$775$			23.3565i			0.838991i
$776$	54.1020	+	78.3802i	1.94215	+	2.81369i
$777$	−8.51277	−	2.09821i	−0.305394	−	0.0752728i
$778$	16.0680	+	18.1371i	0.576067	+	0.650245i
$779$	−12.3751	−	17.9285i	−0.443385	−	0.642354i
$780$	3.90773	+	29.0766i	0.139919	+	1.04111i
$781$	−8.30445	+	12.0311i	−0.297156	+	0.430505i
$782$	27.1864	−	3.30102i	0.972183	−	0.118044i
$783$	−0.551158	+	4.53919i	−0.0196968	+	0.162218i
$784$	77.3240	+	40.5828i	2.76157	+	1.44938i
$785$	4.13095	−	16.7599i	0.147440	−	0.598187i
$786$	28.8488	+	3.50287i	1.02900	+	0.124943i
$787$	−19.6233	+	22.1501i	−0.699496	+	0.789567i	−0.985684	−	0.168606i	$-0.946073\pi$
$787$	−19.6233	+	22.1501i	−0.699496	+	0.789567i	0.286188	+	0.958174i	$0.407612\pi$
$788$	−112.301	+	77.5159i	−4.00056	+	2.76139i
$789$	−10.7491	+	15.5727i	−0.382677	+	0.554403i
$790$	−39.0886	+	9.63448i	−1.39071	+	0.342780i
$791$	7.95527	+	0.965944i	0.282857	+	0.0343450i
$792$	−18.1793	+	9.54121i	−0.645972	+	0.339032i
$793$	−1.40469	−	0.152394i	−0.0498819	−	0.00541168i
$794$	−77.2330	−	40.5350i	−2.74090	−	1.43853i
$795$	−7.45083	−	5.14293i	−0.264254	−	0.182401i
$796$	44.6960	−	64.7533i	1.58421	−	2.29512i
$797$	−7.42047	+	6.57397i	−0.262847	+	0.232862i	−0.784245	−	0.620452i	$-0.786949\pi$
$797$	−7.42047	+	6.57397i	−0.262847	+	0.232862i	0.521398	+	0.853314i	$0.325411\pi$
$798$	−3.99908	−	4.51403i	−0.141566	−	0.159795i
$799$	2.08952	+	0.792451i	0.0739220	+	0.0280349i
$800$	30.5401	−	58.1893i	1.07976	−	2.05730i
$801$	−7.67405	−	2.91038i	−0.271149	−	0.102833i
$802$	80.6020	+	19.8666i	2.84615	+	0.701514i
$803$	−23.4435	+	20.7692i	−0.827305	+	0.732928i
$804$	53.3715	−	36.8397i	1.88227	−	1.29924i
$805$	2.80089	+	7.38534i	0.0987184	+	0.260299i
$806$	−20.5219	−	78.9121i	−0.722852	−	2.77956i
$807$	−8.04889	+	21.2232i	−0.283334	+	0.747091i
$808$	−20.2811	−	82.2837i	−0.713487	−	2.89473i
$809$	16.7724	−	8.80284i	0.589686	−	0.309491i	−0.143359	−	0.989671i	$-0.545790\pi$
$809$	16.7724	−	8.80284i	0.589686	−	0.309491i	0.733046	+	0.680179i	$0.238098\pi$
$810$	1.43200	+	3.77587i	0.0503154	+	0.132671i
$811$	34.9042	−	4.23813i	1.22565	−	0.148821i	0.517998	−	0.855382i	$-0.326677\pi$
$811$	34.9042	−	4.23813i	1.22565	−	0.148821i	0.707652	+	0.706561i	$0.249754\pi$
$812$	−24.3447	−	16.8039i	−0.854332	−	0.589703i
$813$	−0.624908	+	2.53535i	−0.0219165	+	0.0889186i
$814$	−10.4330	−	42.3285i	−0.365678	−	1.48361i
$815$	−0.470549	−	3.87532i	−0.0164826	−	0.135747i
$816$	−11.9679	+	31.5568i	−0.418960	+	1.10471i
$817$	0.414874	−	1.68321i	0.0145146	−	0.0588881i
$818$	42.4293	−	10.4579i	1.48350	−	0.365651i
$819$	−3.71040	+	2.00818i	−0.129652	+	0.0701714i
$820$	−91.6292	−	22.5846i	−3.19983	−	0.788688i
$821$	−2.24517	+	4.27781i	−0.0783568	+	0.149296i	−0.921482	−	0.388421i	$-0.873021\pi$
$821$	−2.24517	+	4.27781i	−0.0783568	+	0.149296i	0.843125	+	0.537717i	$0.180713\pi$
$822$	51.5802			1.79907
$823$	−12.5229			−0.436520			−0.218260	−	0.975891i	$-0.570038\pi$
$823$	−12.5229			−0.436520			−0.218260	+	0.975891i	$0.570038\pi$
$824$	−37.6335	+	71.7046i	−1.31102	+	2.49795i
$825$	3.98490	+	4.49803i	0.138737	+	0.156601i
$826$		−	32.3726i		−	1.12639i
$827$	3.45197	−	3.89647i	0.120037	−	0.135494i	−0.685420	−	0.728148i	$-0.740381\pi$
$827$	3.45197	−	3.89647i	0.120037	−	0.135494i	0.805457	+	0.592654i	$0.201920\pi$
$828$	22.4524	−	11.7839i	0.780275	−	0.409520i
$829$	0.796430	+	6.55919i	0.0276611	+	0.227810i	0.999983	−	0.00583555i	$-0.00185752\pi$
$829$	0.796430	+	6.55919i	0.0276611	+	0.227810i	−0.972322	+	0.233646i	$0.924934\pi$
$830$	−4.83606	−	9.21434i	−0.167862	−	0.319834i
$831$	1.00913	+	8.31091i	0.0350062	+	0.288302i
$832$	−26.6793	+	114.513i	−0.924940	+	3.97002i
$833$	−1.47701	+	12.1642i	−0.0511753	+	0.421466i
$834$	34.2585	−	12.9926i	1.18628	−	0.449895i
$835$	15.9472	+	8.36975i	0.551876	+	0.289647i
$836$	7.80864	−	20.5897i	0.270068	−	0.712110i
$837$	−3.83017	−	7.29778i	−0.132390	−	0.252248i
$838$	27.0156	+	51.4739i	0.933237	+	1.77814i
$839$	−10.1696	−	41.2599i	−0.351095	−	1.42445i	−0.835445	−	0.549574i	$-0.814790\pi$
$839$	−10.1696	−	41.2599i	−0.351095	−	1.42445i	0.484350	−	0.874874i	$-0.339056\pi$
$840$	−16.5526	−	2.00985i	−0.571120	−	0.0693465i
$841$	6.05691	+	5.36596i	0.208859	+	0.185033i
$842$	−1.64568	−	2.38418i	−0.0567140	−	0.0821644i
$843$	10.2079	+	3.87133i	0.351577	+	0.133336i
$844$	16.6303			0.572438
$845$	−15.4636	+	11.2671i	−0.531964	+	0.387601i
$846$	2.81768			0.0968740
$847$	−7.11540	−	2.69852i	−0.244488	−	0.0927221i
$848$	−54.1939	−	78.5134i	−1.86103	−	2.69616i
$849$	−3.39500	−	3.00771i	−0.116516	−	0.103224i
$850$	16.7981	+	2.03966i	0.576170	+	0.0699597i
$851$	8.22410	+	33.3665i	0.281919	+	1.14379i
$852$	17.7128	+	33.7490i	0.606831	+	1.15622i
$853$	11.6559	+	22.2085i	0.399092	+	0.760406i	0.999220	−	0.0394980i	$-0.0125759\pi$
$853$	11.6559	+	22.2085i	0.399092	+	0.760406i	−0.600128	+	0.799904i	$0.704884\pi$
$854$	0.446158	−	1.17642i	0.0152672	−	0.0402563i
$855$	−2.44781	−	1.28471i	−0.0837132	−	0.0439361i
$856$	146.153	−	55.4287i	4.99542	−	1.89451i
$857$	2.24148	−	18.4603i	0.0765676	−	0.630591i	−0.903024	−	0.429591i	$-0.858658\pi$
$857$	2.24148	−	18.4603i	0.0765676	−	0.630591i	0.979591	−	0.201000i	$-0.0644191\pi$
$858$	−17.4155	−	11.6957i	−0.594555	−	0.399285i
$859$	3.55233	+	29.2561i	0.121204	+	0.998204i	0.918721	+	0.394907i	$0.129223\pi$
$859$	3.55233	+	29.2561i	0.121204	+	0.998204i	−0.797517	+	0.603296i	$0.793854\pi$
$860$	−3.49002	−	6.64969i	−0.119009	−	0.226752i
$861$	−1.63582	−	13.4722i	−0.0557487	−	0.459132i
$862$	94.5951	−	49.6473i	3.22192	−	1.69100i
$863$	11.6913	−	13.1967i	0.397975	−	0.449221i	−0.515028	−	0.857173i	$-0.672218\pi$
$863$	11.6913	−	13.1967i	0.397975	−	0.449221i	0.913003	+	0.407952i	$0.133757\pi$
$864$			23.1895i			0.788924i
$865$	0.414613	+	0.468001i	0.0140973	+	0.0159125i
$866$	−48.3366	+	92.0978i	−1.64255	+	3.12961i
$867$	12.2642			0.416516
$868$	53.3188			1.80976
$869$	9.82410	−	18.7183i	0.333260	−	0.634974i
$870$	−17.9287	−	4.41902i	−0.607839	−	0.149819i
$871$	37.6965	+	19.1750i	1.27730	+	0.649721i
$872$	−90.3495	+	22.2691i	−3.05962	+	0.754129i
$873$	−2.35406	+	9.55078i	−0.0796727	+	0.323245i
$874$	−8.38205	+	22.1017i	−0.283527	+	0.747600i
$875$	1.62620	+	13.3929i	0.0549754	+	0.452763i
$876$	19.5424	+	79.2865i	0.660275	+	2.67884i
$877$	−4.24858	+	17.2372i	−0.143464	+	0.582058i	0.854567	+	0.519341i	$0.173823\pi$
$877$	−4.24858	+	17.2372i	−0.143464	+	0.582058i	−0.998031	+	0.0627169i	$0.980023\pi$
$878$	−83.0128	−	57.2996i	−2.80154	−	1.93377i
$879$	17.4321	−	2.11663i	0.587969	−	0.0713923i
$880$	−17.1634	−	45.2561i	−0.578577	−	1.52558i
$881$	2.47818	−	1.30065i	0.0834921	−	0.0438200i	−0.422460	−	0.906381i	$-0.638833\pi$
$881$	2.47818	−	1.30065i	0.0834921	−	0.0438200i	0.505952	+	0.862561i	$0.331141\pi$
$882$	3.69742	+	15.0010i	0.124499	+	0.505111i
$883$	−13.1291	+	34.6187i	−0.441830	+	1.16501i	0.510483	+	0.859888i	$0.329467\pi$
$883$	−13.1291	+	34.6187i	−0.441830	+	1.16501i	−0.952313	+	0.305123i	$0.901303\pi$
$884$	−42.9932	+	5.77803i	−1.44602	+	0.194336i
$885$	−5.26220	−	13.8753i	−0.176887	−	0.466412i
$886$	−37.2673	+	25.7238i	−1.25202	+	0.864206i
$887$	17.6043	−	15.5960i	0.591094	−	0.523664i	−0.313695	−	0.949524i	$-0.601567\pi$
$887$	17.6043	−	15.5960i	0.591094	−	0.523664i	0.904789	+	0.425860i	$0.140028\pi$
$888$	−70.4376	−	17.3613i	−2.36373	−	0.582607i
$889$	12.4402	+	4.71795i	0.417231	+	0.158235i
$890$	15.4027	−	29.3475i	0.516301	−	0.983730i
$891$	−1.98271	−	0.751942i	−0.0664232	−	0.0251910i
$892$	52.6488	+	59.4282i	1.76281	+	1.98980i
$893$	−1.44378	+	1.27908i	−0.0483144	+	0.0428028i
$894$	22.6394	−	32.7988i	0.757174	−	1.09696i
$895$	1.20009	+	0.828364i	0.0401147	+	0.0276892i
$896$	−44.6558	−	23.4371i	−1.49184	−	0.782980i
$897$	13.7282	+	9.21943i	0.458370	+	0.307828i
$898$	34.5477	−	18.1321i	1.15287	−	0.605075i
$899$	37.4113	+	4.54255i	1.24774	+	0.151502i
$900$	15.2124	−	3.74952i	0.507080	−	0.124984i
$901$	7.60442	−	11.0169i	0.253340	−	0.367026i
$902$	55.5356	−	38.3334i	1.84913	−	1.27636i
$903$	0.716151	−	0.808367i	0.0238320	−	0.0269008i
$904$	65.8246	+	7.99255i	2.18929	+	0.265828i
$905$	−4.90603	+	19.9045i	−0.163082	+	0.661649i
$906$	−55.1434	−	28.9415i	−1.83202	−	0.961517i
$907$	−3.61121	+	29.7410i	−0.119908	+	0.987533i	0.801246	+	0.598335i	$0.204171\pi$
$907$	−3.61121	+	29.7410i	−0.119908	+	0.987533i	−0.921154	+	0.389198i	$0.872752\pi$
$908$	136.441	−	16.5669i	4.52794	−	0.549792i
$909$	4.97220	−	7.20348i	0.164918	−	0.238924i
$910$	−6.24441	−	15.8519i	−0.207000	−	0.525487i
$911$	−12.3690	−	17.9196i	−0.409805	−	0.593704i	0.562679	−	0.826675i	$-0.309771\pi$
$911$	−12.3690	−	17.9196i	−0.409805	−	0.593704i	−0.972484	+	0.232971i	$0.925155\pi$
$912$	−19.3172	−	21.8046i	−0.639655	−	0.722021i
$913$	5.30556	+	1.30770i	0.175589	+	0.0432787i
$914$	59.8215	+	86.6664i	1.97872	+	2.86667i
$915$		−	0.576750i		−	0.0190668i
$916$	33.6700	−	23.2407i	1.11249	−	0.767894i
$917$	−12.3028	+	1.49383i	−0.406275	+	0.0493307i
$918$	−5.58307	+	2.11738i	−0.184269	+	0.0698839i
$919$	2.83909	−	23.3820i	0.0936530	−	0.771302i	−0.867911	−	0.496720i	$-0.834538\pi$
$919$	2.83909	−	23.3820i	0.0936530	−	0.771302i	0.961564	−	0.274582i	$-0.0885394\pi$
$920$	23.1755	+	61.1088i	0.764074	+	2.01470i
$921$	−1.78749	+	2.01766i	−0.0588998	+	0.0664841i
$922$	−51.1355	−	45.3021i	−1.68406	−	1.49195i
$923$	−13.8580	+	20.6353i	−0.456142	+	0.679218i
$924$	10.2682	−	9.09683i	0.337799	−	0.299264i
$925$			21.2337i			0.698160i
$926$	5.32151	+	4.71444i	0.174876	+	0.154926i
$927$	−8.12089	+	2.00162i	−0.266725	+	0.0657418i
$928$	−87.2650	−	60.2347i	−2.86461	−	1.97730i
$929$	27.7738	−	10.5332i	0.911228	−	0.345583i	0.145957	−	0.989291i	$-0.453374\pi$
$929$	27.7738	−	10.5332i	0.911228	−	0.345583i	0.765271	+	0.643708i	$0.222605\pi$
$930$	31.1201	−	11.8023i	1.02047	−	0.387013i
$931$	−8.70424	−	6.00810i	−0.285270	−	0.196908i
$932$	−43.1150	+	10.6269i	−1.41228	+	0.348096i
$933$	−8.58430	−	7.60503i	−0.281038	−	0.248978i
$934$			72.0916i			2.35891i
$935$	5.08360	−	4.50368i	0.166252	−	0.147286i
$936$	−30.7011	+	16.6164i	−1.00350	+	0.543122i
$937$	14.3763	+	12.7363i	0.469654	+	0.416077i	0.864471	−	0.502683i	$-0.167654\pi$
$937$	14.3763	+	12.7363i	0.469654	+	0.416077i	−0.394817	+	0.918760i	$0.629192\pi$
$938$	−24.9739	+	28.1897i	−0.815428	+	0.920428i
$939$	−11.1207	−	29.3229i	−0.362911	−	0.956918i
$940$	−1.00719	+	8.29497i	−0.0328510	+	0.270552i
$941$	−33.2534	+	12.6114i	−1.08403	+	0.411119i	−0.830962	−	0.556329i	$-0.812209\pi$
$941$	−33.2534	+	12.6114i	−1.08403	+	0.411119i	−0.253069	+	0.967448i	$0.581440\pi$
$942$	31.9463	−	3.87898i	1.04087	−	0.126384i
$943$	−43.7772	+	30.2172i	−1.42558	+	0.984009i
$944$		−	156.373i		−	5.08951i
$945$	−0.978303	−	1.41732i	−0.0318242	−	0.0461053i
$946$	5.21394	+	1.28512i	0.169520	+	0.0417829i
$947$	23.9127	+	26.9918i	0.777057	+	0.877116i	0.995105	−	0.0988217i	$-0.0315074\pi$
$947$	23.9127	+	26.9918i	0.777057	+	0.877116i	−0.218048	+	0.975938i	$0.569969\pi$
$948$	−31.3096	−	45.3598i	−1.01689	−	1.47322i
$949$	−39.4077	+	35.8202i	−1.27923	+	1.16277i
$950$	−8.29683	+	12.0200i	−0.269185	+	0.389981i
$951$	18.1315	−	2.20156i	0.587953	−	0.0713904i
$952$	2.97180	−	24.4750i	0.0963166	−	0.793238i
$953$	39.9073	+	20.9450i	1.29273	+	0.678475i	0.963988	−	0.265947i	$-0.0856845\pi$
$953$	39.9073	+	20.9450i	1.29273	+	0.678475i	0.328738	+	0.944421i	$0.393377\pi$
$954$	4.03928	−	16.3880i	0.130776	−	0.530581i
$955$	−10.0539	−	1.22076i	−0.325336	−	0.0395029i
$956$	−66.5810	+	75.1544i	−2.15338	+	2.43067i
$957$	7.97972	−	5.50800i	0.257948	−	0.178048i
$958$	12.7886	−	18.5275i	0.413180	−	0.598595i
$959$	−21.3576	+	5.26418i	−0.689674	+	0.169989i
$960$	−47.6455	−	5.78522i	−1.53775	−	0.186717i
$961$	−32.6979	+	17.1612i	−1.05477	+	0.553587i
$962$	−18.6567	−	71.7400i	−0.601516	−	2.31299i
$963$	14.2951	+	7.50265i	0.460653	+	0.241769i
$964$	−99.7668	−	68.8640i	−3.21327	−	2.21796i
$965$	16.8168	−	24.3633i	0.541351	−	0.784282i
$966$	−11.0222	+	9.76483i	−0.354634	+	0.314178i
$967$	−6.00135	−	6.77413i	−0.192991	−	0.217841i	0.644048	−	0.764985i	$-0.277254\pi$
$967$	−6.00135	−	6.77413i	−0.192991	−	0.217841i	−0.837039	+	0.547144i	$0.815715\pi$
$968$	−58.8752	−	22.3284i	−1.89232	−	0.717663i
$969$	1.89959	−	3.61937i	0.0610236	−	0.116271i
$970$	−37.1418	−	14.0860i	−1.19255	−	0.452275i
$971$	11.9064	+	2.93467i	0.382095	+	0.0941780i	0.425685	−	0.904872i	$-0.360033\pi$
$971$	11.9064	+	2.93467i	0.382095	+	0.0941780i	−0.0435896	+	0.999050i	$0.513879\pi$
$972$	−4.13827	+	3.66618i	−0.132735	+	0.117593i
$973$	−12.8593	+	8.87615i	−0.412251	+	0.284556i
$974$	9.59663	+	25.3042i	0.307496	+	0.810800i
$975$	6.87269	+	7.56101i	0.220102	+	0.242146i
$976$	2.15512	−	5.68259i	0.0689838	−	0.181895i
$977$	7.52052	+	30.5120i	0.240603	+	0.976164i	0.959649	+	0.281201i	$0.0907329\pi$
$977$	7.52052	+	30.5120i	0.240603	+	0.976164i	−0.719046	+	0.694963i	$0.755421\pi$
$978$	6.44425	−	3.38221i	0.206065	−	0.108151i
$979$	6.17149	+	16.2729i	0.197242	+	0.520083i
$980$	−45.4831	+	5.52265i	−1.45291	+	0.176415i
$981$	−7.90960	−	5.45960i	−0.252534	−	0.174312i
$982$	13.5830	−	55.1082i	0.433450	−	1.75857i
$983$	8.17401	+	33.1633i	0.260710	+	1.05774i	0.944617	+	0.328174i	$0.106433\pi$
$983$	8.17401	+	33.1633i	0.260710	+	1.05774i	−0.683907	+	0.729569i	$0.739721\pi$
$984$	−13.5354	−	111.474i	−0.431492	−	3.55365i
$985$	12.8812	−	33.9650i	0.410429	−	1.08221i
$986$	6.53403	−	26.5096i	0.208086	−	0.844238i
$987$	−1.16671	+	0.287568i	−0.0371368	+	0.00915339i
$988$	12.8293	−	35.1758i	0.408156	−	1.11909i
$989$	−4.11002	−	1.01303i	−0.130691	−	0.0322124i
$990$	3.97953	−	7.58237i	0.126478	−	0.240984i
$991$	32.5015			1.03244			0.516222	−	0.856455i	$-0.327338\pi$
$991$	32.5015			1.03244			0.516222	+	0.856455i	$0.327338\pi$
$992$	191.124			6.06820
$993$	−5.07136	+	9.66267i	−0.160935	+	0.306636i
$994$	−14.6778	−	16.5679i	−0.465553	−	0.525501i
$995$			20.9455i			0.664015i
$996$	9.44742	−	10.6639i	0.299353	−	0.337900i
$997$	−36.1403	+	18.9679i	−1.14457	+	0.600719i	−0.926902	−	0.375303i	$-0.877539\pi$
$997$	−36.1403	+	18.9679i	−1.14457	+	0.600719i	−0.217672	+	0.976022i	$0.569846\pi$
$998$	9.66147	+	79.5694i	0.305829	+	2.51872i
$999$	−3.48206	−	6.63451i	−0.110167	−	0.209906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.b.25.16	✓	192
169.142	even	26	inner	507.2.p.b.142.16	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.b.25.16	✓	192	1.1	even	1	trivial
507.2.p.b.142.16	yes	192	169.142	even	26	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.56554 + 0.972980i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(4.13827 + 3.66618i) q^{4} +(-1.46104 - 0.177402i) q^{5} +(-0.656644 - 2.66411i) q^{6} +(0.543789 + 1.03610i) q^{7} +(4.49950 + 8.57307i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-3.57574 - 1.87669i) q^{10} +(1.98271 - 0.751942i) q^{11} +(0.666407 - 5.48836i) q^{12} +(3.35466 - 1.32147i) q^{13} +(0.387003 + 3.18726i) q^{14} +(0.683965 + 1.30319i) q^{15} +(1.86938 + 15.3957i) q^{16} +(-1.92691 + 1.01132i) q^{17} +(-1.81950 + 2.05379i) q^{18} -1.87833i q^{19} +(-5.39577 - 6.09057i) q^{20} +(0.543789 - 1.03610i) q^{21} +5.81833 q^{22} -4.58644 q^{23} +(4.49950 - 8.57307i) q^{24} +(-2.75155 - 0.678196i) q^{25} +(9.89226 - 0.126264i) q^{26} +(0.970942 - 0.239316i) q^{27} +(-1.54820 + 6.28130i) q^{28} +(-1.62144 + 4.27539i) q^{29} +(0.486763 + 4.00885i) q^{30} +(-1.97240 - 8.00234i) q^{31} +(-5.54962 + 22.5157i) q^{32} +(-1.74514 - 1.20458i) q^{33} +(-5.92755 + 0.719735i) q^{34} +(-0.610689 - 1.61025i) q^{35} +(-4.89539 + 2.56930i) q^{36} +(-1.79313 - 7.27503i) q^{37} +(1.82757 - 4.81891i) q^{38} +(-2.99321 - 2.01015i) q^{39} +(-5.05305 - 13.3238i) q^{40} +(9.54492 - 6.58839i) q^{41} +(2.40322 - 2.12907i) q^{42} +(0.896123 + 0.220875i) q^{43} +(10.9617 + 4.15724i) q^{44} +(0.683965 - 1.30319i) q^{45} +(-11.7667 - 4.46251i) q^{46} +(-0.680969 - 0.768655i) q^{47} +(11.6085 - 10.2842i) q^{48} +(3.19865 - 4.63404i) q^{49} +(-6.39933 - 4.41714i) q^{50} +(1.92691 + 1.01132i) q^{51} +(18.7272 + 6.83020i) q^{52} +(-5.44679 + 2.85870i) q^{53} +(2.72384 + 0.330734i) q^{54} +(-3.03021 + 0.746879i) q^{55} +(-6.43581 + 9.32389i) q^{56} +(-1.54583 + 1.06701i) q^{57} +(-8.31974 + 9.39104i) q^{58} +(-10.0093 - 1.21535i) q^{59} +(-1.94729 + 7.90047i) q^{60} +(-0.346989 - 0.182114i) q^{61} +(2.72585 - 22.4494i) q^{62} +(-1.16160 + 0.141044i) q^{63} +(-18.5250 + 26.8381i) q^{64} +(-5.13571 + 1.33559i) q^{65} +(-3.30519 - 4.78839i) q^{66} +(7.77843 + 8.78003i) q^{67} +(-11.6818 - 2.87929i) q^{68} +(2.60540 + 3.77457i) q^{69} -4.72536i q^{70} +(-5.67368 + 3.91626i) q^{71} +(-9.61151 + 1.16705i) q^{72} +(-13.8104 + 5.23758i) q^{73} +(2.47811 - 20.4090i) q^{74} +(1.00491 + 2.64974i) q^{75} +(6.88629 - 7.77301i) q^{76} +(1.85726 + 1.64539i) q^{77} +(-5.72335 - 8.06944i) q^{78} +(7.46203 - 6.61078i) q^{79} -22.8254i q^{80} +(-0.748511 - 0.663123i) q^{81} +(30.8982 - 7.61573i) q^{82} +(2.12075 + 1.46385i) q^{83} +(6.04889 - 2.29404i) q^{84} +(2.99470 - 1.13574i) q^{85} +(2.08413 + 1.43857i) q^{86} +(4.43966 - 1.09428i) q^{87} +(15.3676 + 13.6145i) q^{88} +8.20740i q^{89} +(3.02271 - 2.67789i) q^{90} +(3.19340 + 2.75717i) q^{91} +(-18.9799 - 16.8147i) q^{92} +(-5.46534 + 6.16910i) q^{93} +(-0.999165 - 2.63458i) q^{94} +(-0.333219 + 2.74430i) q^{95} +(21.6826 - 8.22312i) q^{96} +(9.76489 - 1.18567i) q^{97} +(12.7151 - 8.77659i) q^{98} +2.12051i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34}+ \cdots + 104 q^{98}+O(q^{100}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more