LMFDB - Embedded newform 510.2.bi.b.97.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [510,2,Mod(37,510)] 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("510.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(510, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 4, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.bi (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] 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:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			97.1
Character	$\chi$	$=$	510.97
Dual form			510.2.bi.b.163.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.382683 + 0.923880i) q^{2} +(-0.195090 + 0.980785i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(-2.18813 + 0.460513i) q^{5} +(-0.831470 - 0.555570i) q^{6} +(-2.55505 - 1.70723i) q^{7} +(0.923880 - 0.382683i) q^{8} +(-0.923880 - 0.382683i) q^{9} +(0.411904 - 2.19780i) q^{10} +(0.585805 - 0.876719i) q^{11} +(0.831470 - 0.555570i) q^{12} +4.53366 q^{13} +(2.55505 - 1.70723i) q^{14} +(-0.0247808 - 2.23593i) q^{15} +1.00000i q^{16} +(-3.63928 - 1.93795i) q^{17} +(0.707107 - 0.707107i) q^{18} +(6.96826 - 2.88635i) q^{19} +(1.87288 + 1.22161i) q^{20} +(2.17289 - 2.17289i) q^{21} +(0.585805 + 0.876719i) q^{22} +(0.742586 - 0.147710i) q^{23} +(0.195090 + 0.980785i) q^{24} +(4.57586 - 2.01533i) q^{25} +(-1.73496 + 4.18856i) q^{26} +(0.555570 - 0.831470i) q^{27} +(0.599500 + 3.01389i) q^{28} +(0.755194 + 0.150218i) q^{29} +(2.07521 + 0.832759i) q^{30} +(-4.84216 - 7.24681i) q^{31} +(-0.923880 - 0.382683i) q^{32} +(0.745588 + 0.745588i) q^{33} +(3.18313 - 2.62063i) q^{34} +(6.37699 + 2.55901i) q^{35} +(0.382683 + 0.923880i) q^{36} +(-6.63629 - 1.32004i) q^{37} +7.54239i q^{38} +(-0.884474 + 4.44655i) q^{39} +(-1.84534 + 1.26282i) q^{40} +(3.12038 - 0.620681i) q^{41} +(1.17596 + 2.83902i) q^{42} +(-2.73138 - 6.59414i) q^{43} +(-1.03416 + 0.205707i) q^{44} +(2.19780 + 0.411904i) q^{45} +(-0.147710 + 0.742586i) q^{46} +9.85778i q^{47} +(-0.980785 - 0.195090i) q^{48} +(0.934865 + 2.25696i) q^{49} +(0.110816 + 4.99877i) q^{50} +(2.61070 - 3.19127i) q^{51} +(-3.20578 - 3.20578i) q^{52} +(-5.64339 - 2.33757i) q^{53} +(0.555570 + 0.831470i) q^{54} +(-0.878079 + 2.18815i) q^{55} +(-3.01389 - 0.599500i) q^{56} +(1.47145 + 7.39747i) q^{57} +(-0.427783 + 0.640223i) q^{58} +(4.98271 - 12.0293i) q^{59} +(-1.56352 + 1.59856i) q^{60} +(-1.06436 - 5.35091i) q^{61} +(8.54820 - 1.70034i) q^{62} +(1.70723 + 2.55505i) q^{63} +(0.707107 - 0.707107i) q^{64} +(-9.92026 + 2.08781i) q^{65} +(-0.974158 + 0.403510i) q^{66} +(6.14334 - 6.14334i) q^{67} +(1.20302 + 3.94370i) q^{68} +0.757134i q^{69} +(-4.80459 + 4.91228i) q^{70} +(5.05916 - 3.38042i) q^{71} -1.00000 q^{72} +(0.183532 - 0.122632i) q^{73} +(3.75916 - 5.62598i) q^{74} +(1.08390 + 4.88110i) q^{75} +(-6.96826 - 2.88635i) q^{76} +(-2.99352 + 1.23996i) q^{77} +(-3.76960 - 2.51877i) q^{78} +(5.87290 + 3.92414i) q^{79} +(-0.460513 - 2.18813i) q^{80} +(0.707107 + 0.707107i) q^{81} +(-0.620681 + 3.12038i) q^{82} +(-5.67006 + 13.6887i) q^{83} -3.07293 q^{84} +(8.85568 + 2.56457i) q^{85} +7.13745 q^{86} +(-0.294662 + 0.711378i) q^{87} +(0.205707 - 1.03416i) q^{88} +(-7.15149 - 7.15149i) q^{89} +(-1.22161 + 1.87288i) q^{90} +(-11.5837 - 7.74001i) q^{91} +(-0.629534 - 0.420641i) q^{92} +(8.05223 - 3.33534i) q^{93} +(-9.10740 - 3.77241i) q^{94} +(-13.9183 + 9.52469i) q^{95} +(0.555570 - 0.831470i) q^{96} +(-10.9149 + 7.29309i) q^{97} -2.44292 q^{98} +(-0.876719 + 0.585805i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 48 q^{25} + 16 q^{28} + 32 q^{29} + 16 q^{30} + 16 q^{31} - 16 q^{33} - 32 q^{34} - 32 q^{35} + 48 q^{37} + 32 q^{41} + 32 q^{43} + 16 q^{44} - 64 q^{49} + 48 q^{50} - 32 q^{51} + 16 q^{52} - 32 q^{53}+ \cdots - 144 q^{98}+O(q^{100}) $ 80 * q + 48 * q^25 + 16 * q^28 + 32 * q^29 + 16 * q^30 + 16 * q^31 - 16 * q^33 - 32 * q^34 - 32 * q^35 + 48 * q^37 + 32 * q^41 + 32 * q^43 + 16 * q^44 - 64 * q^49 + 48 * q^50 - 32 * q^51 + 16 * q^52 - 32 * q^53 + 16 * q^55 - 16 * q^56 + 32 * q^57 + 32 * q^58 - 16 * q^60 + 48 * q^61 + 32 * q^62 - 32 * q^65 - 16 * q^67 - 16 * q^70 - 80 * q^72 - 80 * q^73 - 32 * q^74 - 48 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 32 * q^82 - 32 * q^83 - 32 * q^85 - 48 * q^87 - 16 * q^88 - 32 * q^89 - 32 * q^92 - 48 * q^93 - 16 * q^94 - 96 * q^95 + 80 * q^97 - 144 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−0.382683	+	0.923880i	−0.270598	+	0.653281i
$2$	−0.382683	+	0.923880i	−0.270598	+	0.653281i
$3$	−0.195090	+	0.980785i	−0.112635	+	0.566257i
$3$	−0.195090	+	0.980785i	−0.112635	+	0.566257i
$4$	−0.707107	−	0.707107i	−0.353553	−	0.353553i
$5$	−2.18813	+	0.460513i	−0.978563	+	0.205948i
$5$	−2.18813	+	0.460513i	−0.978563	+	0.205948i
$6$	−0.831470	−	0.555570i	−0.339446	−	0.226811i
$7$	−2.55505	−	1.70723i	−0.965718	−	0.645272i	−0.0305715	−	0.999533i	$-0.509733\pi$
$7$	−2.55505	−	1.70723i	−0.965718	−	0.645272i	−0.935147	+	0.354260i	$0.884733\pi$
$8$	0.923880	−	0.382683i	0.326641	−	0.135299i
$9$	−0.923880	−	0.382683i	−0.307960	−	0.127561i
$10$	0.411904	−	2.19780i	0.130255	−	0.695006i
$11$	0.585805	−	0.876719i	0.176627	−	0.264341i	−0.732584	−	0.680677i	$-0.761686\pi$
$11$	0.585805	−	0.876719i	0.176627	−	0.264341i	0.909211	+	0.416336i	$0.136686\pi$
$12$	0.831470	−	0.555570i	0.240025	−	0.160379i
$13$	4.53366			1.25741			0.628706	−	0.777643i	$-0.283585\pi$
$13$	4.53366			1.25741			0.628706	+	0.777643i	$0.283585\pi$
$14$	2.55505	−	1.70723i	0.682866	−	0.456277i
$15$	−0.0247808	−	2.23593i	−0.00639838	−	0.577315i
$16$			1.00000i			0.250000i
$17$	−3.63928	−	1.93795i	−0.882654	−	0.470023i
$17$	−3.63928	−	1.93795i	−0.882654	−	0.470023i
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	6.96826	−	2.88635i	1.59863	−	0.662174i	0.607408	−	0.794390i	$-0.292209\pi$
$19$	6.96826	−	2.88635i	1.59863	−	0.662174i	0.991221	+	0.132216i	$0.0422093\pi$
$20$	1.87288	+	1.22161i	0.418788	+	0.273161i
$21$	2.17289	−	2.17289i	0.474164	−	0.474164i
$22$	0.585805	+	0.876719i	0.124894	+	0.186917i
$23$	0.742586	−	0.147710i	0.154840	−	0.0307996i	−0.117062	−	0.993125i	$-0.537347\pi$
$23$	0.742586	−	0.147710i	0.154840	−	0.0307996i	0.271902	+	0.962325i	$0.412347\pi$
$24$	0.195090	+	0.980785i	0.0398226	+	0.200202i
$25$	4.57586	−	2.01533i	0.915171	−	0.403066i
$26$	−1.73496	+	4.18856i	−0.340253	+	0.821444i
$27$	0.555570	−	0.831470i	0.106920	−	0.160016i
$28$	0.599500	+	3.01389i	0.113295	+	0.569571i
$29$	0.755194	+	0.150218i	0.140236	+	0.0278947i	0.264709	−	0.964328i	$-0.414724\pi$
$29$	0.755194	+	0.150218i	0.140236	+	0.0278947i	−0.124473	+	0.992223i	$0.539724\pi$
$30$	2.07521	+	0.832759i	0.378880	+	0.152040i
$31$	−4.84216	−	7.24681i	−0.869679	−	1.30157i	−0.952356	−	0.304989i	$-0.901347\pi$
$31$	−4.84216	−	7.24681i	−0.869679	−	1.30157i	0.0826772	−	0.996576i	$-0.473653\pi$
$32$	−0.923880	−	0.382683i	−0.163320	−	0.0676495i
$33$	0.745588	+	0.745588i	0.129790	+	0.129790i
$34$	3.18313	−	2.62063i	0.545902	−	0.449434i
$35$	6.37699	+	2.55901i	1.07791	+	0.432552i
$36$	0.382683	+	0.923880i	0.0637806	+	0.153980i
$37$	−6.63629	−	1.32004i	−1.09100	−	0.217013i	−0.383369	−	0.923595i	$-0.625236\pi$
$37$	−6.63629	−	1.32004i	−1.09100	−	0.217013i	−0.707631	+	0.706582i	$0.750236\pi$
$38$			7.54239i			1.22354i
$39$	−0.884474	+	4.44655i	−0.141629	+	0.712018i
$40$	−1.84534	+	1.26282i	−0.291774	+	0.199670i
$41$	3.12038	−	0.620681i	0.487321	−	0.0969341i	0.0546864	−	0.998504i	$-0.482584\pi$
$41$	3.12038	−	0.620681i	0.487321	−	0.0969341i	0.432634	+	0.901569i	$0.357584\pi$
$42$	1.17596	+	2.83902i	0.181455	+	0.438070i
$43$	−2.73138	−	6.59414i	−0.416532	−	1.00560i	−0.983345	−	0.181751i	$-0.941824\pi$
$43$	−2.73138	−	6.59414i	−0.416532	−	1.00560i	0.566813	−	0.823847i	$-0.308176\pi$
$44$	−1.03416	+	0.205707i	−0.155906	+	0.0310116i
$45$	2.19780	+	0.411904i	0.327629	+	0.0614030i
$46$	−0.147710	+	0.742586i	−0.0217786	+	0.109488i
$47$			9.85778i			1.43790i	0.695060	+	0.718952i	$0.255378\pi$
$47$			9.85778i			1.43790i	−0.695060	+	0.718952i	$0.744622\pi$
$48$	−0.980785	−	0.195090i	−0.141564	−	0.0281589i
$49$	0.934865	+	2.25696i	0.133552	+	0.322423i
$50$	0.110816	+	4.99877i	0.0156718	+	0.706933i
$51$	2.61070	−	3.19127i	0.365572	−	0.446868i
$52$	−3.20578	−	3.20578i	−0.444562	−	0.444562i
$53$	−5.64339	−	2.33757i	−0.775179	−	0.321090i	−0.0402109	−	0.999191i	$-0.512803\pi$
$53$	−5.64339	−	2.33757i	−0.775179	−	0.321090i	−0.734968	+	0.678101i	$0.762803\pi$
$54$	0.555570	+	0.831470i	0.0756035	+	0.113149i
$55$	−0.878079	+	2.18815i	−0.118400	+	0.295050i
$56$	−3.01389	−	0.599500i	−0.402748	−	0.0801115i
$57$	1.47145	+	7.39747i	0.194898	+	0.979818i
$58$	−0.427783	+	0.640223i	−0.0561707	+	0.0840654i
$59$	4.98271	−	12.0293i	0.648693	−	1.56608i	−0.165958	−	0.986133i	$-0.553071\pi$
$59$	4.98271	−	12.0293i	0.648693	−	1.56608i	0.814651	−	0.579952i	$-0.196929\pi$
$60$	−1.56352	+	1.59856i	−0.201849	+	0.206374i
$61$	−1.06436	−	5.35091i	−0.136278	−	0.685114i	−0.987157	−	0.159753i	$-0.948930\pi$
$61$	−1.06436	−	5.35091i	−0.136278	−	0.685114i	0.850879	−	0.525361i	$-0.176070\pi$
$62$	8.54820	−	1.70034i	1.08562	−	0.215944i
$63$	1.70723	+	2.55505i	0.215091	+	0.321906i
$64$	0.707107	−	0.707107i	0.0883883	−	0.0883883i
$65$	−9.92026	+	2.08781i	−1.23046	+	0.258961i
$66$	−0.974158	+	0.403510i	−0.119911	+	0.0496686i
$67$	6.14334	−	6.14334i	0.750528	−	0.750528i	−0.224049	−	0.974578i	$-0.571928\pi$
$67$	6.14334	−	6.14334i	0.750528	−	0.750528i	0.974578	+	0.224049i	$0.0719277\pi$
$68$	1.20302	+	3.94370i	0.145887	+	0.478244i
$69$			0.757134i			0.0911483i
$70$	−4.80459	+	4.91228i	−0.574258	+	0.587130i
$71$	5.05916	−	3.38042i	0.600412	−	0.401182i	−0.217888	−	0.975974i	$-0.569917\pi$
$71$	5.05916	−	3.38042i	0.600412	−	0.401182i	0.818300	+	0.574792i	$0.194917\pi$
$72$	−1.00000			−0.117851
$73$	0.183532	−	0.122632i	0.0214808	−	0.0143530i	−0.544783	−	0.838577i	$-0.683388\pi$
$73$	0.183532	−	0.122632i	0.0214808	−	0.0143530i	0.566264	+	0.824224i	$0.308388\pi$
$74$	3.75916	−	5.62598i	0.436993	−	0.654006i
$75$	1.08390	+	4.88110i	0.125158	+	0.563621i
$76$	−6.96826	−	2.88635i	−0.799314	−	0.331087i
$77$	−2.99352	+	1.23996i	−0.341144	+	0.141306i
$78$	−3.76960	−	2.51877i	−0.426823	−	0.285194i
$79$	5.87290	+	3.92414i	0.660753	+	0.441501i	0.840207	−	0.542265i	$-0.182433\pi$
$79$	5.87290	+	3.92414i	0.660753	+	0.441501i	−0.179455	+	0.983766i	$0.557433\pi$
$80$	−0.460513	−	2.18813i	−0.0514869	−	0.244641i
$81$	0.707107	+	0.707107i	0.0785674	+	0.0785674i
$82$	−0.620681	+	3.12038i	−0.0685428	+	0.344588i
$83$	−5.67006	+	13.6887i	−0.622370	+	1.50254i	0.226542	+	0.974001i	$0.427258\pi$
$83$	−5.67006	+	13.6887i	−0.622370	+	1.50254i	−0.848912	+	0.528534i	$0.822742\pi$
$84$	−3.07293			−0.335285
$85$	8.85568	+	2.56457i	0.960533	+	0.278166i
$86$	7.13745			0.769651
$87$	−0.294662	+	0.711378i	−0.0315911	+	0.0762677i
$88$	0.205707	−	1.03416i	0.0219285	−	0.110242i
$89$	−7.15149	−	7.15149i	−0.758056	−	0.758056i	0.217912	−	0.975968i	$-0.430075\pi$
$89$	−7.15149	−	7.15149i	−0.758056	−	0.758056i	−0.975968	+	0.217912i	$0.930075\pi$
$90$	−1.22161	+	1.87288i	−0.128769	+	0.197418i
$91$	−11.5837	−	7.74001i	−1.21431	−	0.811373i
$92$	−0.629534	−	0.420641i	−0.0656335	−	0.0438549i
$93$	8.05223	−	3.33534i	0.834977	−	0.345859i
$94$	−9.10740	−	3.77241i	−0.939356	−	0.389094i
$95$	−13.9183	+	9.52469i	−1.42799	+	0.977213i
$96$	0.555570	−	0.831470i	0.0567026	−	0.0848615i
$97$	−10.9149	+	7.29309i	−1.10824	+	0.740501i	−0.968333	−	0.249663i	$-0.919680\pi$
$97$	−10.9149	+	7.29309i	−1.10824	+	0.740501i	−0.139906	+	0.990165i	$0.544680\pi$
$98$	−2.44292			−0.246772
$99$	−0.876719	+	0.585805i	−0.0881136	+	0.0588756i
$100$	−4.66067	−	1.81057i	−0.466067	−	0.181057i
$101$			0.669611i			0.0666288i	0.999445	+	0.0333144i	$0.0106063\pi$
$101$			0.669611i			0.0666288i	−0.999445	+	0.0333144i	$0.989394\pi$
$102$	1.94928	+	3.63322i	0.193007	+	0.359743i
$103$	7.91526	−	7.91526i	0.779914	−	0.779914i	−0.199902	−	0.979816i	$-0.564062\pi$
$103$	7.91526	−	7.91526i	0.779914	−	0.779914i	0.979816	+	0.199902i	$0.0640623\pi$
$104$	4.18856	−	1.73496i	0.410722	−	0.170127i
$105$	−3.75393	+	5.75522i	−0.366346	+	0.561652i
$106$	4.31926	−	4.31926i	0.419524	−	0.419524i
$107$	−2.07124	−	3.09982i	−0.200234	−	0.299671i	0.717741	−	0.696311i	$-0.245176\pi$
$107$	−2.07124	−	3.09982i	−0.200234	−	0.299671i	−0.917975	+	0.396639i	$0.870176\pi$
$108$	−0.980785	+	0.195090i	−0.0943761	+	0.0187726i
$109$	0.475047	+	2.38822i	0.0455012	+	0.228750i	0.996844	−	0.0793842i	$-0.0252954\pi$
$109$	0.475047	+	2.38822i	0.0455012	+	0.228750i	−0.951343	+	0.308134i	$0.900295\pi$
$110$	−1.68556	−	1.64861i	−0.160712	−	0.157189i
$111$	2.58935	−	6.25125i	0.245770	−	0.593342i
$112$	1.70723	−	2.55505i	0.161318	−	0.241430i
$113$	−2.91435	−	14.6514i	−0.274159	−	1.37829i	−0.834946	−	0.550331i	$-0.814501\pi$
$113$	−2.91435	−	14.6514i	−0.274159	−	1.37829i	0.560787	−	0.827960i	$-0.310499\pi$
$114$	−7.39747	−	1.47145i	−0.692836	−	0.137814i
$115$	−1.55686	+	0.665179i	−0.145178	+	0.0620283i
$116$	−0.427783	−	0.640223i	−0.0397187	−	0.0594432i
$117$	−4.18856	−	1.73496i	−0.387232	−	0.160397i
$118$	9.20685	+	9.20685i	0.847559	+	0.847559i
$119$	5.99000	+	11.1647i	0.549103	+	1.02346i
$120$	−0.878548	−	2.05625i	−0.0802001	−	0.187709i
$121$	3.78405	+	9.13550i	0.344004	+	0.830500i
$122$	5.35091	+	1.06436i	0.484449	+	0.0963629i
$123$			3.18151i			0.286867i
$124$	−1.70034	+	8.54820i	−0.152695	+	0.767651i
$125$	−9.08450	+	6.51705i	−0.812542	+	0.582902i
$126$	−3.01389	+	0.599500i	−0.268498	+	0.0534077i
$127$	−1.50513	−	3.63370i	−0.133559	−	0.322439i	0.842925	−	0.538031i	$-0.180832\pi$
$127$	−1.50513	−	3.63370i	−0.133559	−	0.322439i	−0.976483	+	0.215592i	$0.930832\pi$
$128$	0.382683	+	0.923880i	0.0338248	+	0.0816602i
$129$	7.00031	−	1.39245i	0.616343	−	0.122598i
$130$	1.86743	−	9.96409i	0.163785	−	0.873909i
$131$	1.74443	−	8.76985i	0.152412	−	0.766225i	−0.826659	−	0.562704i	$-0.809761\pi$
$131$	1.74443	−	8.76985i	0.152412	−	0.766225i	0.979070	−	0.203522i	$-0.0652387\pi$
$132$		−	1.05442i		−	0.0917756i
$133$	−22.7319	−	4.52166i	−1.97111	−	0.392078i
$134$	3.32475	+	8.02666i	0.287215	+	0.693398i
$135$	−0.832759	+	2.07521i	−0.0716725	+	0.178606i
$136$	−4.10388	−	0.397745i	−0.351904	−	0.0341063i
$137$	−1.73165	−	1.73165i	−0.147945	−	0.147945i	0.629254	−	0.777199i	$-0.283360\pi$
$137$	−1.73165	−	1.73165i	−0.147945	−	0.147945i	−0.777199	+	0.629254i	$0.783360\pi$
$138$	−0.699501	−	0.289743i	−0.0595455	−	0.0246645i
$139$	−6.62619	−	9.91679i	−0.562026	−	0.841132i	0.436250	−	0.899826i	$-0.356306\pi$
$139$	−6.62619	−	9.91679i	−0.562026	−	0.841132i	−0.998276	+	0.0586940i	$0.981306\pi$
$140$	−2.69972	−	6.31871i	−0.228168	−	0.534029i
$141$	−9.66836	−	1.92316i	−0.814223	−	0.161959i
$142$	1.18705	+	5.96768i	0.0996147	+	0.500797i
$143$	2.65584	−	3.97475i	0.222093	−	0.332385i
$144$	0.382683	−	0.923880i	0.0318903	−	0.0769900i
$145$	−1.72164	+	0.0190810i	−0.142975	+	0.00158459i
$146$	0.0430627	+	0.216491i	0.00356390	+	0.0179169i
$147$	−2.39598	+	0.476590i	−0.197617	+	0.0393085i
$148$	3.75916	+	5.62598i	0.309001	+	0.462452i
$149$	−12.4348	+	12.4348i	−1.01870	+	1.01870i	−0.0188740	+	0.999822i	$0.506008\pi$
$149$	−12.4348	+	12.4348i	−1.01870	+	1.01870i	−0.999822	+	0.0188740i	$0.993992\pi$
$150$	−4.92434	−	0.866525i	−0.402071	−	0.0707515i
$151$	−15.5610	+	6.44557i	−1.26634	+	0.524533i	−0.911848	−	0.410528i	$-0.865345\pi$
$151$	−15.5610	+	6.44557i	−1.26634	+	0.524533i	−0.354487	+	0.935061i	$0.615345\pi$
$152$	5.33328	−	5.33328i	0.432586	−	0.432586i
$153$	2.62063	+	3.18313i	0.211865	+	0.257341i
$154$		−	3.24017i		−	0.261100i
$155$	13.9326	+	13.6271i	1.11909	+	1.09456i
$156$	3.76960	−	2.51877i	0.301810	−	0.201663i
$157$	−4.93690			−0.394007			−0.197004	−	0.980403i	$-0.563121\pi$
$157$	−4.93690			−0.394007			−0.197004	+	0.980403i	$0.563121\pi$
$158$	−5.87290	+	3.92414i	−0.467223	+	0.312188i
$159$	3.39362	−	5.07892i	0.269132	−	0.402784i
$160$	2.19780	+	0.411904i	0.173752	+	0.0325639i
$161$	−2.14952	−	0.890360i	−0.169406	−	0.0701702i
$162$	−0.923880	+	0.382683i	−0.0725868	+	0.0300665i
$163$	19.4447	+	12.9925i	1.52303	+	1.01765i	0.984568	+	0.175003i	$0.0559935\pi$
$163$	19.4447	+	12.9925i	1.52303	+	1.01765i	0.538459	+	0.842651i	$0.319006\pi$
$164$	−2.64533	−	1.76755i	−0.206565	−	0.138023i
$165$	−1.97480	−	1.28809i	−0.153738	−	0.100278i
$166$	−10.4769	−	10.4769i	−0.813166	−	0.813166i
$167$	1.52950	−	7.68930i	0.118356	−	0.595016i	−0.875396	−	0.483406i	$-0.839399\pi$
$167$	1.52950	−	7.68930i	0.118356	−	0.595016i	0.993752	−	0.111610i	$-0.0356006\pi$
$168$	1.17596	−	2.83902i	0.0907273	−	0.219035i
$169$	7.55409			0.581084
$170$	−5.75827	+	7.20016i	−0.441639	+	0.552227i
$171$	−7.54239			−0.576781
$172$	−2.73138	+	6.59414i	−0.208266	+	0.502799i
$173$	−3.18423	+	16.0082i	−0.242092	+	1.21708i	0.648122	+	0.761537i	$0.275555\pi$
$173$	−3.18423	+	16.0082i	−0.242092	+	1.21708i	−0.890214	+	0.455543i	$0.849445\pi$
$174$	−0.544465	−	0.544465i	−0.0412758	−	0.0412758i
$175$	−15.1322	−	2.66277i	−1.14388	−	0.201287i
$176$	0.876719	+	0.585805i	0.0660852	+	0.0441567i
$177$	10.8261	+	7.23377i	0.813740	+	0.543724i
$178$	9.34387	−	3.87036i	0.700353	−	0.290096i
$179$	−2.83872	−	1.17584i	−0.212176	−	0.0878862i	0.274064	−	0.961711i	$-0.411632\pi$
$179$	−2.83872	−	1.17584i	−0.212176	−	0.0878862i	−0.486240	+	0.873825i	$0.661632\pi$
$180$	−1.26282	−	1.84534i	−0.0941251	−	0.137544i
$181$	−3.41954	+	5.11770i	−0.254172	+	0.380396i	−0.936510	−	0.350642i	$-0.885964\pi$
$181$	−3.41954	+	5.11770i	−0.254172	+	0.380396i	0.682337	+	0.731037i	$0.260964\pi$
$182$	11.5837	−	7.74001i	0.858644	−	0.573727i
$183$	5.45575			0.403300
$184$	0.629534	−	0.420641i	0.0464099	−	0.0310101i
$185$	15.1290	−	0.167674i	1.11231	−	0.0123277i
$186$			8.71567i			0.639064i
$187$	−3.83095	+	2.05536i	−0.280147	+	0.150303i
$188$	6.97050	−	6.97050i	0.508376	−	0.508376i
$189$	−2.83902	+	1.17596i	−0.206508	+	0.0855386i
$190$	−3.47337	−	16.5038i	−0.251985	−	1.19731i
$191$	17.0283	−	17.0283i	1.23212	−	1.23212i	0.268976	−	0.963147i	$-0.413315\pi$
$191$	17.0283	−	17.0283i	1.23212	−	1.23212i	0.963147	−	0.268976i	$-0.0866853\pi$
$192$	0.555570	+	0.831470i	0.0400948	+	0.0600062i
$193$	23.9178	−	4.75755i	1.72164	−	0.342456i	0.767328	−	0.641255i	$-0.221586\pi$
$193$	23.9178	−	4.75755i	1.72164	−	0.342456i	0.954316	+	0.298799i	$0.0965859\pi$
$194$	−2.56099	−	12.8750i	−0.183869	−	0.924370i
$195$	−0.112348	−	10.1370i	−0.00804539	−	0.725922i
$196$	0.934865	−	2.25696i	0.0667761	−	0.161212i
$197$	−5.21379	+	7.80299i	−0.371467	+	0.555940i	−0.969363	−	0.245634i	$-0.921004\pi$
$197$	−5.21379	+	7.80299i	−0.371467	+	0.555940i	0.597895	+	0.801574i	$0.296004\pi$
$198$	−0.205707	−	1.03416i	−0.0146190	−	0.0734946i
$199$	8.94253	+	1.77878i	0.633919	+	0.126094i	0.501582	−	0.865110i	$-0.332752\pi$
$199$	8.94253	+	1.77878i	0.633919	+	0.126094i	0.132338	+	0.991205i	$0.457752\pi$
$200$	3.45631	−	3.61302i	0.244398	−	0.255479i
$201$	4.82679	+	7.22380i	0.340456	+	0.509528i
$202$	−0.618640	−	0.256249i	−0.0435274	−	0.0180296i
$203$	−1.67310	−	1.67310i	−0.117429	−	0.117429i
$204$	−4.10262	+	0.410524i	−0.287241	+	0.0287425i
$205$	−6.54197	+	2.79511i	−0.456911	+	0.195219i
$206$	4.28371	+	10.3418i	0.298460	+	0.720547i
$207$	−0.742586	−	0.147710i	−0.0516133	−	0.0102665i
$208$			4.53366i			0.314353i
$209$	1.55153	−	7.80005i	0.107321	−	0.539541i
$210$	−3.88056	−	5.67061i	−0.267784	−	0.391309i
$211$	14.8485	−	2.95356i	1.02222	−	0.203331i	0.344602	−	0.938749i	$-0.388014\pi$
$211$	14.8485	−	2.95356i	1.02222	−	0.203331i	0.677614	+	0.735417i	$0.263014\pi$
$212$	2.33757	+	5.64339i	0.160545	+	0.387590i
$213$	2.32847	+	5.62143i	0.159544	+	0.385174i
$214$	3.65649	−	0.727321i	0.249953	−	0.0497187i
$215$	9.01332	+	13.1710i	0.614703	+	0.898257i
$216$	0.195090	−	0.980785i	0.0132742	−	0.0667340i
$217$			26.7827i			1.81813i
$218$	−2.38822	−	0.475047i	−0.161751	−	0.0321742i
$219$	0.0844706	+	0.203930i	0.00570799	+	0.0137803i
$220$	2.16815	−	0.926360i	0.146177	−	0.0624552i
$221$	−16.4993	−	8.78603i	−1.10986	−	0.591012i
$222$	4.78450	+	4.78450i	0.321115	+	0.321115i
$223$	4.03185	+	1.67005i	0.269993	+	0.111835i	0.513572	−	0.858046i	$-0.328322\pi$
$223$	4.03185	+	1.67005i	0.269993	+	0.111835i	−0.243580	+	0.969881i	$0.578322\pi$
$224$	1.70723	+	2.55505i	0.114069	+	0.170717i
$225$	−4.99877	+	0.110816i	−0.333251	+	0.00738775i
$226$	14.6514	+	2.91435i	0.974599	+	0.193860i
$227$	−3.02457	−	15.2056i	−0.200748	−	1.00923i	−0.941388	−	0.337326i	$-0.890477\pi$
$227$	−3.02457	−	15.2056i	−0.200748	−	1.00923i	0.740640	−	0.671902i	$-0.234523\pi$
$228$	4.19033	−	6.27127i	0.277511	−	0.415325i
$229$	−8.47427	+	20.4587i	−0.559995	+	1.35195i	0.349774	+	0.936834i	$0.386258\pi$
$229$	−8.47427	+	20.4587i	−0.559995	+	1.35195i	−0.909769	+	0.415114i	$0.863742\pi$
$230$	−0.0187624	−	1.69290i	−0.00123716	−	0.111627i
$231$	−0.632125	−	3.17791i	−0.0415908	−	0.209091i
$232$	0.755194	−	0.150218i	0.0495809	−	0.00986226i
$233$	13.3550	+	19.9872i	0.874916	+	1.30940i	0.950007	+	0.312227i	$0.101075\pi$
$233$	13.3550	+	19.9872i	0.874916	+	1.30940i	−0.0750918	+	0.997177i	$0.523925\pi$
$234$	3.20578	−	3.20578i	0.209569	−	0.209569i
$235$	−4.53963	−	21.5701i	−0.296133	−	1.40708i
$236$	−12.0293	+	4.98271i	−0.783042	+	0.324347i
$237$	−4.99449	+	4.99449i	−0.324427	+	0.324427i
$238$	−12.6071	+	1.26151i	−0.817195	+	0.0817718i
$239$		−	9.34353i		−	0.604383i	−0.953247	−	0.302191i	$-0.902282\pi$
$239$		−	9.34353i		−	0.604383i	0.953247	−	0.302191i	$-0.0977181\pi$
$240$	2.23593	−	0.0247808i	0.144329	−	0.00159959i
$241$	0.515487	−	0.344437i	0.0332054	−	0.0221872i	−0.538857	−	0.842397i	$-0.681144\pi$
$241$	0.515487	−	0.344437i	0.0332054	−	0.0221872i	0.572062	+	0.820210i	$0.306144\pi$
$242$	−9.88820			−0.635637
$243$	−0.831470	+	0.555570i	−0.0533388	+	0.0356398i
$244$	−3.03105	+	4.53629i	−0.194043	+	0.290406i
$245$	−3.08497	−	4.50802i	−0.197092	−	0.288007i
$246$	−2.93933	−	1.21751i	−0.187405	−	0.0776256i
$247$	31.5917	−	13.0857i	2.01013	−	0.832625i
$248$	−7.24681	−	4.84216i	−0.460173	−	0.307478i
$249$	−12.3195	−	8.23166i	−0.780720	−	0.521660i
$250$	−2.54448	−	10.8869i	−0.160927	−	0.688551i
$251$	6.69768	+	6.69768i	0.422754	+	0.422754i	0.886151	−	0.463397i	$-0.153370\pi$
$251$	6.69768	+	6.69768i	0.422754	+	0.422754i	−0.463397	+	0.886151i	$0.653370\pi$
$252$	0.599500	−	3.01389i	0.0377649	−	0.189857i
$253$	0.305511	−	0.737569i	0.0192073	−	0.0463705i
$254$	3.93309			0.246784
$255$	−4.24295	+	8.18519i	−0.265704	+	0.512577i
$256$	−1.00000			−0.0625000
$257$	4.00430	−	9.66724i	0.249781	−	0.603026i	−0.748404	−	0.663243i	$-0.769179\pi$
$257$	4.00430	−	9.66724i	0.249781	−	0.603026i	0.998185	+	0.0602175i	$0.0191794\pi$
$258$	−1.39245	+	7.00031i	−0.0866900	+	0.435820i
$259$	14.7024	+	14.7024i	0.913566	+	0.913566i
$260$	8.49099	+	5.53838i	0.526589	+	0.343476i
$261$	−0.640223	−	0.427783i	−0.0396288	−	0.0264791i
$262$	7.43472	+	4.96772i	0.459318	+	0.306907i
$263$	8.14160	−	3.37236i	0.502032	−	0.207949i	−0.117272	−	0.993100i	$-0.537415\pi$
$263$	8.14160	−	3.37236i	0.502032	−	0.207949i	0.619304	+	0.785151i	$0.287415\pi$
$264$	0.974158	+	0.403510i	0.0599553	+	0.0248343i
$265$	13.4250	+	2.51606i	0.824689	+	0.154560i
$266$	12.8766	−	19.2712i	0.789515	−	1.18159i
$267$	8.40926	−	5.61889i	0.514638	−	0.343870i
$268$	−8.68799			−0.530704
$269$	12.9958	−	8.68354i	0.792370	−	0.529445i	−0.0922619	−	0.995735i	$-0.529410\pi$
$269$	12.9958	−	8.68354i	0.792370	−	0.529445i	0.884632	+	0.466290i	$0.154410\pi$
$270$	−1.59856	−	1.56352i	−0.0972855	−	0.0951527i
$271$			21.7686i			1.32235i	0.750232	+	0.661175i	$0.229942\pi$
$271$			21.7686i			1.32235i	−0.750232	+	0.661175i	$0.770058\pi$
$272$	1.93795	−	3.63928i	0.117506	−	0.220664i
$273$	9.85116	−	9.85116i	0.596219	−	0.596219i
$274$	2.26251	−	0.937162i	0.136683	−	0.0566160i
$275$	0.913682	−	5.19233i	0.0550971	−	0.313109i
$276$	0.535375	−	0.535375i	0.0322258	−	0.0322258i
$277$	0.693732	+	1.03824i	0.0416823	+	0.0623820i	0.851726	−	0.523988i	$-0.175556\pi$
$277$	0.693732	+	1.03824i	0.0416823	+	0.0623820i	−0.810043	+	0.586370i	$0.800556\pi$
$278$	11.6977	−	2.32681i	0.701579	−	0.139553i
$279$	1.70034	+	8.54820i	0.101797	+	0.511767i
$280$	6.87087	−	0.0761498i	0.410613	−	0.00455082i
$281$	0.122056	−	0.294670i	0.00728128	−	0.0175786i	−0.920197	−	0.391455i	$-0.871972\pi$
$281$	0.122056	−	0.294670i	0.00728128	−	0.0175786i	0.927478	+	0.373877i	$0.121972\pi$
$282$	5.47669	−	8.19644i	0.326132	−	0.488091i
$283$	−4.93712	−	24.8206i	−0.293482	−	1.47543i	−0.793050	−	0.609157i	$-0.791508\pi$
$283$	−4.93712	−	24.8206i	−0.293482	−	1.47543i	0.499568	−	0.866275i	$-0.333492\pi$
$284$	−5.96768	−	1.18705i	−0.354117	−	0.0704382i
$285$	−6.62635	−	15.5090i	−0.392511	−	0.918675i
$286$	2.65584	+	3.97475i	0.157043	+	0.235032i
$287$	−9.03237	−	3.74133i	−0.533164	−	0.220844i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	9.48867	+	14.1055i	0.558157	+	0.829735i
$290$	0.641216	−	1.59789i	0.0376535	−	0.0938315i
$291$	−5.02357	−	12.1280i	−0.294487	−	0.710954i
$292$	−0.216491	−	0.0430627i	−0.0126692	−	0.00252006i
$293$		−	24.4558i		−	1.42872i	−0.699778	−	0.714360i	$-0.746718\pi$
$293$		−	24.4558i		−	1.42872i	0.699778	−	0.714360i	$-0.253282\pi$
$294$	0.476590	−	2.39598i	0.0277953	−	0.139736i
$295$	−5.36317	+	28.6164i	−0.312256	+	1.66611i
$296$	−6.63629	+	1.32004i	−0.385727	+	0.0767258i
$297$	−0.403510	−	0.974158i	−0.0234140	−	0.0565264i
$298$	−6.72965	−	16.2468i	−0.389838	−	0.941152i
$299$	3.36663	−	0.669665i	0.194698	−	0.0387277i
$300$	2.68503	−	4.21789i	0.155020	−	0.243520i
$301$	−4.27890	+	21.5115i	−0.246632	+	1.23990i
$302$		−	16.8431i		−	0.969211i
$303$	−0.656745	−	0.130635i	−0.0377290	−	0.00750477i
$304$	2.88635	+	6.96826i	0.165543	+	0.399657i
$305$	4.79313	+	11.2184i	0.274454	+	0.642362i
$306$	−3.94370	+	1.20302i	−0.225446	+	0.0687719i
$307$	−11.7717	−	11.7717i	−0.671847	−	0.671847i	0.286295	−	0.958142i	$-0.407576\pi$
$307$	−11.7717	−	11.7717i	−0.671847	−	0.671847i	−0.958142	+	0.286295i	$0.907576\pi$
$308$	2.99352	+	1.23996i	0.170572	+	0.0706532i
$309$	6.21898	+	9.30737i	0.353786	+	0.529478i
$310$	−17.9216	+	7.65713i	−1.01788	+	0.434896i
$311$	−12.7812	−	2.54233i	−0.724753	−	0.144162i	−0.181091	−	0.983466i	$-0.557963\pi$
$311$	−12.7812	−	2.54233i	−0.724753	−	0.144162i	−0.543662	+	0.839304i	$0.682963\pi$
$312$	0.884474	+	4.44655i	0.0500735	+	0.251736i
$313$	5.99826	−	8.97703i	0.339042	−	0.507412i	−0.622297	−	0.782781i	$-0.713800\pi$
$313$	5.99826	−	8.97703i	0.339042	−	0.507412i	0.961338	+	0.275370i	$0.0888002\pi$
$314$	1.88927	−	4.56110i	0.106618	−	0.257398i
$315$	−4.91228	−	4.80459i	−0.276776	−	0.270708i
$316$	−1.37798	−	6.92756i	−0.0775172	−	0.389705i
$317$	−13.0320	+	2.59224i	−0.731953	+	0.145594i	−0.546976	−	0.837148i	$-0.684221\pi$
$317$	−13.0320	+	2.59224i	−0.731953	+	0.145594i	−0.184977	+	0.982743i	$0.559221\pi$
$318$	3.39362	+	5.07892i	0.190305	+	0.284811i
$319$	0.574095	−	0.574095i	0.0321432	−	0.0321432i
$320$	−1.22161	+	1.87288i	−0.0682902	+	0.104697i
$321$	3.44434	−	1.42669i	0.192244	−	0.0796302i
$322$	1.64517	−	1.64517i	0.0916818	−	0.0916818i
$323$	−30.9530	−	2.99995i	−1.72227	−	0.166922i
$324$		−	1.00000i		−	0.0555556i
$325$	20.7454	−	9.13682i	1.15075	−	0.506819i
$326$	−19.4447	+	12.9925i	−1.07694	+	0.719590i
$327$	−2.43501			−0.134656
$328$	2.64533	−	1.76755i	0.146064	−	0.0975967i
$329$	16.8295	−	25.1871i	0.927840	−	1.38861i
$330$	1.94577	−	1.33155i	0.107111	−	0.0732992i
$331$	23.3281	+	9.66280i	1.28223	+	0.531116i	0.916659	−	0.399669i	$-0.130875\pi$
$331$	23.3281	+	9.66280i	1.28223	+	0.531116i	0.365567	+	0.930785i	$0.380875\pi$
$332$	13.6887	−	5.67006i	0.751268	−	0.311185i
$333$	5.62598	+	3.75916i	0.308302	+	0.206001i
$334$	6.51867	+	4.35564i	0.356686	+	0.238330i
$335$	−10.6134	+	16.2715i	−0.579870	+	0.889009i
$336$	2.17289	+	2.17289i	0.118541	+	0.118541i
$337$	−6.68664	+	33.6160i	−0.364245	+	1.83118i	0.169492	+	0.985532i	$0.445787\pi$
$337$	−6.68664	+	33.6160i	−0.364245	+	1.83118i	−0.533737	+	0.845651i	$0.679213\pi$
$338$	−2.89083	+	6.97907i	−0.157240	+	0.379611i
$339$	14.9385			0.811347
$340$	−4.44849	−	8.07533i	−0.241253	−	0.437946i
$341$	−9.18998			−0.497666
$342$	2.88635	−	6.96826i	0.156076	−	0.376800i
$343$	−2.73197	+	13.7345i	−0.147512	+	0.741595i
$344$	−5.04694	−	5.04694i	−0.272113	−	0.272113i
$345$	−0.348670	−	1.65671i	−0.0187718	−	0.0891943i
$346$	−13.5711	−	9.06791i	−0.729586	−	0.487494i
$347$	−2.88422	−	1.92717i	−0.154833	−	0.103456i	0.475740	−	0.879586i	$-0.342180\pi$
$347$	−2.88422	−	1.92717i	−0.154833	−	0.103456i	−0.630573	+	0.776130i	$0.717180\pi$
$348$	0.711378	−	0.294662i	0.0381338	−	0.0157956i
$349$	−23.5196	−	9.74215i	−1.25898	−	0.521486i	−0.349382	−	0.936980i	$-0.613608\pi$
$349$	−23.5196	−	9.74215i	−1.25898	−	0.521486i	−0.909596	+	0.415495i	$0.863608\pi$
$350$	8.25091	−	12.9613i	0.441030	−	0.692811i
$351$	2.51877	−	3.76960i	0.134442	−	0.201206i
$352$	−0.876719	+	0.585805i	−0.0467293	+	0.0312235i
$353$	−0.275496			−0.0146632			−0.00733158	−	0.999973i	$-0.502334\pi$
$353$	−0.275496			−0.0146632			−0.00733158	+	0.999973i	$0.502334\pi$
$354$	−10.8261	+	7.23377i	−0.575401	+	0.384471i
$355$	−9.51338	+	9.72662i	−0.504918	+	0.516235i
$356$			10.1137i			0.536027i
$357$	−12.1187	+	3.69679i	−0.641391	+	0.195655i
$358$	2.17266	−	2.17266i	0.114829	−	0.114829i
$359$	10.2500	−	4.24571i	0.540977	−	0.224080i	−0.0954264	−	0.995436i	$-0.530421\pi$
$359$	10.2500	−	4.24571i	0.540977	−	0.224080i	0.636403	+	0.771357i	$0.280421\pi$
$360$	2.18813	−	0.460513i	0.115325	−	0.0242712i
$361$	26.7906	−	26.7906i	1.41003	−	1.41003i
$362$	−3.41954	−	5.11770i	−0.179727	−	0.268980i
$363$	−9.69820	+	1.92909i	−0.509023	+	0.101251i
$364$	2.71793	+	13.6639i	0.142458	+	0.716186i
$365$	−0.345119	+	0.352855i	−0.0180644	+	0.0184693i
$366$	−2.08782	+	5.04045i	−0.109132	+	0.263469i
$367$	−2.38417	+	3.56817i	−0.124453	+	0.186257i	−0.888464	−	0.458946i	$-0.848227\pi$
$367$	−2.38417	+	3.56817i	−0.124453	+	0.186257i	0.764011	+	0.645203i	$0.223227\pi$
$368$	0.147710	+	0.742586i	0.00769989	+	0.0387100i
$369$	−3.12038	−	0.620681i	−0.162440	−	0.0323114i
$370$	−5.63470	+	14.0415i	−0.292934	+	0.729984i
$371$	10.4284	+	15.6072i	0.541414	+	0.810284i
$372$	−8.05223	−	3.33534i	−0.417488	−	0.172929i
$373$	14.3443	+	14.3443i	0.742720	+	0.742720i	0.973101	−	0.230381i	$-0.0739972\pi$
$373$	14.3443	+	14.3443i	0.742720	+	0.742720i	−0.230381	+	0.973101i	$0.573997\pi$
$374$	−0.432866	−	4.32589i	−0.0223829	−	0.223686i
$375$	−4.61953	−	10.1814i	−0.238551	−	0.525763i
$376$	3.77241	+	9.10740i	0.194547	+	0.469678i
$377$	3.42380	+	0.681035i	0.176334	+	0.0350751i
$378$		−	3.07293i		−	0.158055i
$379$	−4.60315	+	23.1416i	−0.236448	+	1.18870i	0.661959	+	0.749540i	$0.269725\pi$
$379$	−4.60315	+	23.1416i	−0.236448	+	1.18870i	−0.898407	+	0.439164i	$0.855275\pi$
$380$	16.5767	+	3.10674i	0.850366	+	0.159372i
$381$	3.85752	−	0.767308i	0.197627	−	0.0393104i
$382$	9.21564	+	22.2485i	0.471513	+	1.13833i
$383$	−9.10119	−	21.9722i	−0.465049	−	1.12273i	−0.966298	−	0.257425i	$-0.917126\pi$
$383$	−9.10119	−	21.9722i	−0.465049	−	1.12273i	0.501249	−	0.865303i	$-0.332874\pi$
$384$	−0.980785	+	0.195090i	−0.0500505	+	0.00995566i
$385$	5.97921	−	4.09175i	0.304729	−	0.208535i
$386$	−4.75755	+	23.9178i	−0.242153	+	1.21739i
$387$			7.13745i			0.362817i
$388$	12.8750	+	2.56099i	0.653628	+	0.130015i
$389$	10.2006	+	24.6265i	0.517192	+	1.24861i	0.939621	+	0.342216i	$0.111178\pi$
$389$	10.2006	+	24.6265i	0.517192	+	1.24861i	−0.422429	+	0.906396i	$0.638822\pi$
$390$	9.40832	+	3.77545i	0.476409	+	0.191177i
$391$	−2.98873	−	0.901542i	−0.151147	−	0.0455929i
$392$	1.72741	+	1.72741i	0.0872471	+	0.0872471i
$393$	8.26102	+	3.42182i	0.416713	+	0.172608i
$394$	−5.21379	−	7.80299i	−0.262667	−	0.393109i
$395$	−14.6578	−	5.88201i	−0.737514	−	0.295956i
$396$	1.03416	+	0.205707i	0.0519685	+	0.0103372i
$397$	−5.73771	−	28.8454i	−0.287968	−	1.44771i	−0.805779	−	0.592216i	$-0.798253\pi$
$397$	−5.73771	−	28.8454i	−0.287968	−	1.44771i	0.517812	−	0.855495i	$-0.326747\pi$
$398$	−5.06554	+	7.58111i	−0.253913	+	0.380007i
$399$	8.86956	−	21.4130i	0.444033	−	1.07199i
$400$	2.01533	+	4.57586i	0.100766	+	0.228793i
$401$	2.76863	+	13.9189i	0.138259	+	0.695075i	0.986276	+	0.165106i	$0.0527965\pi$
$401$	2.76863	+	13.9189i	0.138259	+	0.695075i	−0.848017	+	0.529969i	$0.822203\pi$
$402$	−8.52106	+	1.69494i	−0.424992	+	0.0845361i
$403$	−21.9527	−	32.8546i	−1.09354	−	1.63660i
$404$	0.473487	−	0.473487i	0.0235568	−	0.0235568i
$405$	−1.87288	−	1.22161i	−0.0930640	−	0.0607024i
$406$	2.18602	−	0.905477i	0.108490	−	0.0449381i
$407$	−5.04488	+	5.04488i	−0.250065	+	0.250065i
$408$	1.19073	−	3.94743i	0.0589499	−	0.195427i
$409$		−	16.0113i		−	0.791710i	−0.918313	−	0.395855i	$-0.870448\pi$
$409$		−	16.0113i		−	0.791710i	0.918313	−	0.395855i	$-0.129552\pi$
$410$	−0.0788403	−	7.11363i	−0.00389365	−	0.351317i
$411$	2.03621	−	1.36055i	0.100439	−	0.0671109i
$412$	−11.1939			−0.551483
$413$	−33.2679	+	22.2289i	−1.63701	+	1.09381i
$414$	0.420641	−	0.629534i	0.0206734	−	0.0309399i
$415$	6.10301	−	32.5639i	0.299585	−	1.59850i
$416$	−4.18856	−	1.73496i	−0.205361	−	0.0850633i
$417$	11.0190	−	4.56420i	0.539600	−	0.223510i
$418$	6.61256	+	4.41837i	0.323431	+	0.216110i
$419$	9.74552	+	6.51175i	0.476100	+	0.318120i	0.770364	−	0.637604i	$-0.220075\pi$
$419$	9.74552	+	6.51175i	0.476100	+	0.318120i	−0.294264	+	0.955724i	$0.595075\pi$
$420$	6.72399	−	1.41513i	0.328097	−	0.0690511i
$421$	−8.14478	−	8.14478i	−0.396952	−	0.396952i	0.480204	−	0.877157i	$-0.340562\pi$
$421$	−8.14478	−	8.14478i	−0.396952	−	0.396952i	−0.877157	+	0.480204i	$0.840562\pi$
$422$	−2.95356	+	14.8485i	−0.143777	+	0.722816i
$423$	3.77241	−	9.10740i	0.183421	−	0.442817i
$424$	−6.10836			−0.296648
$425$	−20.5584	−	1.53346i	−0.997230	−	0.0743837i
$426$	−6.08460			−0.294800
$427$	−6.41574	+	15.4890i	−0.310480	+	0.749564i
$428$	−0.727321	+	3.65649i	−0.0351564	+	0.176743i
$429$	3.38025	+	3.38025i	0.163200	+	0.163200i
$430$	−15.6177	+	3.28689i	−0.753152	+	0.158508i
$431$	0.671420	+	0.448629i	0.0323412	+	0.0216097i	0.571636	−	0.820508i	$-0.306309\pi$
$431$	0.671420	+	0.448629i	0.0323412	+	0.0216097i	−0.539295	+	0.842117i	$0.681309\pi$
$432$	0.831470	+	0.555570i	0.0400041	+	0.0267299i
$433$	−15.2871	+	6.33212i	−0.734651	+	0.304302i	−0.718462	−	0.695567i	$-0.755153\pi$
$433$	−15.2871	+	6.33212i	−0.734651	+	0.304302i	−0.0161893	+	0.999869i	$0.505153\pi$
$434$	−24.7440	−	10.2493i	−1.18775	−	0.491981i
$435$	0.317162	−	1.69228i	0.0152067	−	0.0811389i
$436$	1.35282	−	2.02464i	0.0647883	−	0.0969625i
$437$	4.74819	−	3.17264i	0.227137	−	0.151768i
$438$	−0.220732			−0.0105470
$439$	−21.8285	+	14.5854i	−1.04182	+	0.696121i	−0.953936	−	0.300010i	$-0.903010\pi$
$439$	−21.8285	+	14.5854i	−1.04182	+	0.696121i	−0.0878828	+	0.996131i	$0.528010\pi$
$440$	0.0261294	+	2.35761i	0.00124567	+	0.112395i
$441$		−	2.44292i		−	0.116330i
$442$	14.4312	−	11.8811i	0.686423	−	0.565124i
$443$	−14.5716	+	14.5716i	−0.692319	+	0.692319i	−0.962742	−	0.270423i	$-0.912837\pi$
$443$	−14.5716	+	14.5716i	−0.692319	+	0.692319i	0.270423	+	0.962742i	$0.412837\pi$
$444$	−6.25125	+	2.58935i	−0.296671	+	0.122885i
$445$	18.9418	+	12.3551i	0.897926	+	0.585686i
$446$	−3.08584	+	3.08584i	−0.146119	+	0.146119i
$447$	−9.76993	−	14.6217i	−0.462102	−	0.691585i
$448$	−3.01389	+	0.599500i	−0.142393	+	0.0283237i
$449$	−2.60161	−	13.0792i	−0.122778	−	0.617244i	−0.992352	−	0.123442i	$-0.960607\pi$
$449$	−2.60161	−	13.0792i	−0.122778	−	0.617244i	0.869574	−	0.493802i	$-0.164393\pi$
$450$	1.81057	−	4.66067i	0.0853509	−	0.219706i
$451$	1.28377	−	3.09929i	0.0604503	−	0.145940i
$452$	−8.29937	+	12.4209i	−0.390370	+	0.584229i
$453$	−3.28592	−	16.5195i	−0.154386	−	0.776152i
$454$	15.2056	+	3.02457i	0.713632	+	0.141950i
$455$	28.9111	+	11.6017i	1.35537	+	0.543896i
$456$	4.19033	+	6.27127i	0.196230	+	0.293679i
$457$	13.6497	+	5.65388i	0.638505	+	0.264477i	0.678362	−	0.734728i	$-0.262690\pi$
$457$	13.6497	+	5.65388i	0.638505	+	0.264477i	−0.0398570	+	0.999205i	$0.512690\pi$
$458$	−15.6584	−	15.6584i	−0.731669	−	0.731669i
$459$	−3.63322	+	1.94928i	−0.169584	+	0.0909845i
$460$	1.57122	+	0.630511i	0.0732583	+	0.0293977i
$461$	6.43573	+	15.5372i	0.299742	+	0.723640i	0.999953	+	0.00970460i	$0.00308912\pi$
$461$	6.43573	+	15.5372i	0.299742	+	0.723640i	−0.700211	+	0.713936i	$0.746911\pi$
$462$	3.17791	+	0.632125i	0.147850	+	0.0294091i
$463$		−	2.77334i		−	0.128888i	−0.997921	−	0.0644439i	$-0.979473\pi$
$463$		−	2.77334i		−	0.128888i	0.997921	−	0.0644439i	$-0.0205274\pi$
$464$	−0.150218	+	0.755194i	−0.00697367	+	0.0350590i
$465$	−16.0834	+	11.0063i	−0.745849	+	0.510406i
$466$	−23.5765	+	4.68966i	−1.09216	+	0.217244i
$467$	0.227890	+	0.550175i	0.0105455	+	0.0254591i	0.929065	−	0.369918i	$-0.120614\pi$
$467$	0.227890	+	0.550175i	0.0105455	+	0.0254591i	−0.918519	+	0.395377i	$0.870614\pi$
$468$	1.73496	+	4.18856i	0.0801984	+	0.193616i
$469$	−26.1846	+	5.20845i	−1.20909	+	0.240504i
$470$	21.6654	+	4.06046i	0.999352	+	0.187295i
$471$	0.963141	−	4.84204i	0.0443792	−	0.223109i
$472$		−	13.0204i		−	0.599315i
$473$	−7.38127	−	1.46823i	−0.339391	−	0.0675091i
$474$	−2.70300	−	6.52561i	−0.124153	−	0.299731i
$475$	26.0688	−	27.2508i	1.19612	−	1.25035i
$476$	3.65903	−	12.1302i	0.167711	−	0.555986i
$477$	4.31926	+	4.31926i	0.197765	+	0.197765i
$478$	8.63229	+	3.57561i	0.394832	+	0.163545i
$479$	−7.05143	−	10.5532i	−0.322188	−	0.482188i	0.634654	−	0.772796i	$-0.281143\pi$
$479$	−7.05143	−	10.5532i	−0.322188	−	0.482188i	−0.956842	+	0.290608i	$0.906143\pi$
$480$	−0.832759	+	2.07521i	−0.0380101	+	0.0947201i
$481$	−30.0867	−	5.98462i	−1.37184	−	0.272875i
$482$	0.120950	+	0.608058i	0.00550914	+	0.0276963i
$483$	1.29260	−	1.93452i	0.0588155	−	0.0880236i
$484$	3.78405	−	9.13550i	0.172002	−	0.415250i
$485$	20.5247	−	20.9847i	0.931977	−	0.952866i
$486$	−0.195090	−	0.980785i	−0.00884948	−	0.0444893i
$487$	6.20234	−	1.23372i	0.281055	−	0.0559052i	−0.0525501	−	0.998618i	$-0.516735\pi$
$487$	6.20234	−	1.23372i	0.281055	−	0.0559052i	0.333605	+	0.942713i	$0.391735\pi$
$488$	−3.03105	−	4.53629i	−0.137209	−	0.205348i
$489$	−16.5364	+	16.5364i	−0.747800	+	0.747800i
$490$	5.34543	−	1.12500i	0.241482	−	0.0508222i
$491$	27.6777	−	11.4645i	1.24908	−	0.517386i	0.342538	−	0.939504i	$-0.388713\pi$
$491$	27.6777	−	11.4645i	1.24908	−	0.517386i	0.906541	+	0.422118i	$0.138713\pi$
$492$	2.24967	−	2.24967i	0.101423	−	0.101423i
$493$	−2.45725	−	2.01021i	−0.110669	−	0.0905355i
$494$			34.1947i			1.53849i
$495$	1.64861	−	1.68556i	0.0740994	−	0.0757603i
$496$	7.24681	−	4.84216i	0.325391	−	0.217420i
$497$	−18.6976			−0.838700
$498$	12.3195	−	8.23166i	0.552052	−	0.368869i
$499$	−19.0580	+	28.5223i	−0.853152	+	1.27683i	0.106122	+	0.994353i	$0.466157\pi$
$499$	−19.0580	+	28.5223i	−0.853152	+	1.27683i	−0.959274	+	0.282478i	$0.908843\pi$
$500$	11.0320	+	1.81546i	0.493364	+	0.0811899i
$501$	7.24316	+	3.00022i	0.323601	+	0.134040i
$502$	−8.75094	+	3.62476i	−0.390573	+	0.161781i
$503$	−10.8977	−	7.28160i	−0.485904	−	0.324670i	0.288373	−	0.957518i	$-0.406886\pi$
$503$	−10.8977	−	7.28160i	−0.485904	−	0.324670i	−0.774276	+	0.632848i	$0.781886\pi$
$504$	2.55505	+	1.70723i	0.113811	+	0.0760461i
$505$	−0.308365	−	1.46520i	−0.0137221	−	0.0652005i
$506$	0.564511	+	0.564511i	0.0250956	+	0.0250956i
$507$	−1.47373	+	7.40894i	−0.0654507	+	0.329043i
$508$	−1.50513	+	3.63370i	−0.0667793	+	0.161219i
$509$	−30.3220			−1.34400			−0.672000	−	0.740552i	$-0.734564\pi$
$509$	−30.3220			−1.34400			−0.672000	+	0.740552i	$0.734564\pi$
$510$	−5.93843	−	7.05231i	−0.262958	−	0.312281i
$511$	−0.678296			−0.0300060
$512$	0.382683	−	0.923880i	0.0169124	−	0.0408301i
$513$	1.47145	−	7.39747i	0.0649660	−	0.326606i
$514$	7.39899	+	7.39899i	0.326355	+	0.326355i
$515$	−13.6746	+	20.9647i	−0.602574	+	0.923817i
$516$	−5.93457	−	3.96535i	−0.261255	−	0.174565i
$517$	8.64250	+	5.77474i	0.380097	+	0.253973i
$518$	−19.2097	+	7.95691i	−0.844025	+	0.349606i
$519$	−15.0794	−	6.24608i	−0.661911	−	0.274173i
$520$	−8.36615	+	5.72520i	−0.366880	+	0.251067i
$521$	10.7682	−	16.1157i	0.471763	−	0.706043i	−0.516925	−	0.856031i	$-0.672923\pi$
$521$	10.7682	−	16.1157i	0.471763	−	0.706043i	0.988688	+	0.149987i	$0.0479233\pi$
$522$	0.640223	−	0.427783i	0.0280218	−	0.0187236i
$523$	−11.2182			−0.490538			−0.245269	−	0.969455i	$-0.578876\pi$
$523$	−11.2182			−0.490538			−0.245269	+	0.969455i	$0.578876\pi$
$524$	−7.43472	+	4.96772i	−0.324787	+	0.217016i
$525$	5.56375	−	14.3219i	0.242822	−	0.625060i
$526$			8.81240i			0.384239i
$527$	3.57799	+	35.7570i	0.155860	+	1.55760i
$528$	−0.745588	+	0.745588i	−0.0324476	+	0.0324476i
$529$	−20.7196	+	8.58234i	−0.900853	+	0.373145i
$530$	−7.46205	+	11.4402i	−0.324131	+	0.496931i
$531$	−9.20685	+	9.20685i	−0.399543	+	0.399543i
$532$	12.8766	+	19.2712i	0.558271	+	0.835512i
$533$	14.1467	−	2.81396i	0.612763	−	0.121886i
$534$	1.97309	+	9.91940i	0.0853840	+	0.429254i
$535$	5.95965	+	5.82900i	0.257658	+	0.252010i
$536$	3.32475	−	8.02666i	0.143607	−	0.346699i
$537$	1.70705	−	2.55478i	0.0736647	−	0.110247i
$538$	3.04925	+	15.3296i	0.131463	+	0.660907i
$539$	2.52637	+	0.502527i	0.108819	+	0.0216454i
$540$	2.05625	−	0.878548i	0.0884868	−	0.0378067i
$541$	−9.18323	−	13.7437i	−0.394818	−	0.590887i	0.579801	−	0.814758i	$-0.303130\pi$
$541$	−9.18323	−	13.7437i	−0.394818	−	0.590887i	−0.974619	+	0.223871i	$0.928130\pi$
$542$	−20.1116	−	8.33049i	−0.863867	−	0.357825i
$543$	−4.35225	−	4.35225i	−0.186773	−	0.186773i
$544$	2.62063	+	3.18313i	0.112359	+	0.136475i
$545$	−2.13927	−	5.00698i	−0.0916364	−	0.214475i
$546$	5.33141	+	12.8712i	0.228163	+	0.550835i
$547$	−10.3263	−	2.05403i	−0.441521	−	0.0878239i	−0.0306762	−	0.999529i	$-0.509766\pi$
$547$	−10.3263	−	2.05403i	−0.441521	−	0.0878239i	−0.410844	+	0.911705i	$0.634766\pi$
$548$			2.44892i			0.104613i
$549$	−1.06436	+	5.35091i	−0.0454259	+	0.228371i
$550$	4.44744	+	2.83115i	0.189639	+	0.120721i
$551$	5.69597	−	1.13300i	0.242657	−	0.0482674i
$552$	0.289743	+	0.699501i	0.0123323	+	0.0297727i
$553$	−8.30613	−	20.0528i	−0.353213	−	0.852731i
$554$	−1.22469	+	0.243606i	−0.0520322	+	0.0103498i
$555$	−2.78707	+	14.8710i	−0.118304	+	0.631239i
$556$	−2.32681	+	11.6977i	−0.0986787	+	0.496091i
$557$		−	40.9701i		−	1.73596i	−0.496598	−	0.867980i	$-0.665418\pi$
$557$		−	40.9701i		−	1.73596i	0.496598	−	0.867980i	$-0.334582\pi$
$558$	−8.54820	−	1.70034i	−0.361874	−	0.0719812i
$559$	−12.3832	−	29.8956i	−0.523752	−	1.26445i
$560$	−2.55901	+	6.37699i	−0.108138	+	0.269477i
$561$	−1.26849	−	4.15832i	−0.0535556	−	0.175564i
$562$	0.225531	+	0.225531i	0.00951345	+	0.00951345i
$563$	−15.7612	−	6.52850i	−0.664256	−	0.275144i	0.0249725	−	0.999688i	$-0.492050\pi$
$563$	−15.7612	−	6.52850i	−0.664256	−	0.275144i	−0.689228	+	0.724544i	$0.742050\pi$
$564$	5.47669	+	8.19644i	0.230610	+	0.345132i
$565$	13.1242	+	30.7172i	0.552138	+	1.29228i
$566$	24.8206	+	4.93712i	1.04329	+	0.207523i
$567$	−0.599500	−	3.01389i	−0.0251766	−	0.126571i
$568$	3.38042	−	5.05916i	0.141839	−	0.212278i
$569$	7.08982	−	17.1163i	0.297221	−	0.717555i	−0.702760	−	0.711427i	$-0.748049\pi$
$569$	7.08982	−	17.1163i	0.297221	−	0.717555i	0.999981	−	0.00612801i	$-0.00195062\pi$
$570$	16.8643	−	0.186907i	0.706366	−	0.00782865i
$571$	7.29886	+	36.6939i	0.305448	+	1.53559i	0.762995	+	0.646405i	$0.223728\pi$
$571$	7.29886	+	36.6939i	0.305448	+	1.53559i	−0.457547	+	0.889185i	$0.651272\pi$
$572$	−4.68854	+	0.932608i	−0.196038	+	0.0389943i
$573$	13.3790	+	20.0231i	0.558917	+	0.836479i
$574$	6.91307	−	6.91307i	0.288546	−	0.288546i
$575$	3.10028	−	2.17245i	0.129291	−	0.0905975i
$576$	−0.923880	+	0.382683i	−0.0384950	+	0.0159451i
$577$	24.8533	−	24.8533i	1.03466	−	1.03466i	0.0352793	−	0.999377i	$-0.488768\pi$
$577$	24.8533	−	24.8533i	1.03466	−	1.03466i	0.999377	−	0.0352793i	$-0.0112321\pi$
$578$	−16.6629	+	3.36845i	−0.693087	+	0.140109i
$579$			24.3864i			1.01347i
$580$	1.23088	+	1.20389i	0.0511094	+	0.0499890i
$581$	37.8571	−	25.2953i	1.57058	−	1.04943i
$582$	13.1272			0.544141
$583$	−5.35532	+	3.57831i	−0.221795	+	0.148198i
$584$	0.122632	−	0.183532i	0.00507456	−	0.00759462i
$585$	9.96409	+	1.86743i	0.411965	+	0.0772088i
$586$	22.5942	+	9.35881i	0.933357	+	0.386609i
$587$	5.54262	−	2.29583i	0.228768	−	0.0947589i	−0.265355	−	0.964151i	$-0.585489\pi$
$587$	5.54262	−	2.29583i	0.228768	−	0.0947589i	0.494123	+	0.869392i	$0.335489\pi$
$588$	2.03121	+	1.35721i	0.0837658	+	0.0559705i
$589$	−54.6583	−	36.5215i	−2.25216	−	1.50484i
$590$	−24.3857	−	15.9059i	−1.00394	−	0.654837i
$591$	−6.63590	−	6.63590i	−0.272964	−	0.272964i
$592$	1.32004	−	6.63629i	0.0542533	−	0.272750i
$593$	−13.9893	+	33.7731i	−0.574471	+	1.38690i	0.323242	+	0.946316i	$0.395227\pi$
$593$	−13.9893	+	33.7731i	−0.574471	+	1.38690i	−0.897713	+	0.440580i	$0.854773\pi$
$594$	1.05442			0.0432634
$595$	−18.2484	−	21.6713i	−0.748111	−	0.888436i
$596$	17.5854			0.720327
$597$	−3.48920	+	8.42368i	−0.142804	+	0.344758i
$598$	−0.669665	+	3.36663i	−0.0273847	+	0.137672i
$599$	25.8200	+	25.8200i	1.05498	+	1.05498i	0.998398	+	0.0565797i	$0.0180195\pi$
$599$	25.8200	+	25.8200i	1.05498	+	1.05498i	0.0565797	+	0.998398i	$0.481980\pi$
$600$	2.86931	+	4.09476i	0.117139	+	0.167168i
$601$	29.3675	+	19.6227i	1.19792	+	0.800427i	0.984302	−	0.176490i	$-0.0564742\pi$
$601$	29.3675	+	19.6227i	1.19792	+	0.800427i	0.213621	+	0.976917i	$0.431474\pi$
$602$	−18.2365	−	12.1853i	−0.743266	−	0.496635i
$603$	−8.02666	+	3.32475i	−0.326871	+	0.135394i
$604$	15.5610	+	6.44557i	0.633168	+	0.262267i
$605$	−12.4870	−	18.2471i	−0.507670	−	0.741850i
$606$	0.372016	−	0.556761i	0.0151121	−	0.0226169i
$607$	3.71467	−	2.48206i	0.150774	−	0.100744i	−0.477895	−	0.878417i	$-0.658600\pi$
$607$	3.71467	−	2.48206i	0.150774	−	0.100744i	0.628669	+	0.777673i	$0.283600\pi$
$608$	−7.54239			−0.305884
$609$	1.96736	−	1.31455i	0.0797216	−	0.0532682i
$610$	−12.1987	+	0.135198i	−0.493910	+	0.00547400i
$611$			44.6918i			1.80804i
$612$	0.397745	−	4.10388i	0.0160779	−	0.165889i
$613$	−2.82437	+	2.82437i	−0.114075	+	0.114075i	−0.761840	−	0.647765i	$-0.775704\pi$
$613$	−2.82437	+	2.82437i	−0.114075	+	0.114075i	0.647765	+	0.761840i	$0.275704\pi$
$614$	15.3805	−	6.37080i	0.620706	−	0.257105i
$615$	−1.46513	−	6.96156i	−0.0590796	−	0.280717i
$616$	−2.29114	+	2.29114i	−0.0923128	+	0.0923128i
$617$	−13.2351	−	19.8078i	−0.532827	−	0.797432i	0.463222	−	0.886242i	$-0.346693\pi$
$617$	−13.2351	−	19.8078i	−0.532827	−	0.797432i	−0.996049	+	0.0888107i	$0.971693\pi$
$618$	−10.9788	+	2.18382i	−0.441632	+	0.0878460i
$619$	−3.02261	−	15.1957i	−0.121489	−	0.610766i	−0.992775	−	0.119991i	$-0.961713\pi$
$619$	−3.02261	−	15.1957i	−0.121489	−	0.610766i	0.871286	−	0.490776i	$-0.163287\pi$
$620$	−0.215981	−	19.4876i	−0.00867401	−	0.782642i
$621$	0.289743	−	0.699501i	0.0116270	−	0.0280700i
$622$	7.23995	−	10.8353i	0.290295	−	0.434458i
$623$	6.06318	+	30.4816i	0.242916	+	1.22122i
$624$	−4.44655	−	0.884474i	−0.178004	−	0.0354073i
$625$	16.8769	−	18.4437i	0.675076	−	0.737748i
$626$	5.99826	+	8.97703i	0.239739	+	0.358794i
$627$	7.34748	+	3.04343i	0.293430	+	0.121543i
$628$	3.49091	+	3.49091i	0.139303	+	0.139303i
$629$	21.5931	+	17.6648i	0.860974	+	0.704342i
$630$	6.31871	−	2.69972i	0.251743	−	0.107559i
$631$	6.65501	+	16.0666i	0.264932	+	0.639601i	0.999230	−	0.0392249i	$-0.0124889\pi$
$631$	6.65501	+	16.0666i	0.264932	+	0.639601i	−0.734299	+	0.678826i	$0.762489\pi$
$632$	6.92756	+	1.37798i	0.275563	+	0.0548130i
$633$			15.1394i			0.601739i
$634$	2.59224	−	13.0320i	0.102951	−	0.517569i
$635$	4.96679	+	7.25789i	0.197101	+	0.288021i
$636$	−5.99099	+	1.19168i	−0.237558	+	0.0472533i
$637$	4.23836	+	10.2323i	0.167930	+	0.405419i
$638$	0.310698	+	0.750092i	0.0123007	+	0.0296964i
$639$	−5.96768	+	1.18705i	−0.236078	+	0.0469588i
$640$	−1.26282	−	1.84534i	−0.0499174	−	0.0729435i
$641$	−1.11786	+	5.61985i	−0.0441527	+	0.221971i	−0.996562	−	0.0828519i	$-0.973597\pi$
$641$	−1.11786	+	5.61985i	−0.0441527	+	0.221971i	0.952409	+	0.304823i	$0.0985971\pi$
$642$			3.72813i			0.147137i
$643$	−0.488439	−	0.0971565i	−0.0192621	−	0.00383148i	0.185450	−	0.982654i	$-0.440626\pi$
$643$	−0.488439	−	0.0971565i	−0.0192621	−	0.00383148i	−0.204712	+	0.978822i	$0.565626\pi$
$644$	0.890360	+	2.14952i	0.0350851	+	0.0847029i
$645$	−14.6764	+	6.27059i	−0.577881	+	0.246904i
$646$	14.6168	−	27.4489i	0.575091	−	1.07996i
$647$	18.0530	+	18.0530i	0.709738	+	0.709738i	0.966480	−	0.256742i	$-0.0826490\pi$
$647$	18.0530	+	18.0530i	0.709738	+	0.709738i	−0.256742	+	0.966480i	$0.582649\pi$
$648$	0.923880	+	0.382683i	0.0362934	+	0.0150332i
$649$	−7.62744	−	11.4153i	−0.299403	−	0.448089i
$650$	0.502404	+	22.6627i	0.0197059	+	0.888906i
$651$	−26.2680	−	5.22504i	−1.02953	−	0.204785i
$652$	−4.56237	−	22.9366i	−0.178676	−	0.898267i
$653$	19.1447	−	28.6521i	0.749191	−	1.12124i	−0.239445	−	0.970910i	$-0.576965\pi$
$653$	19.1447	−	28.6521i	0.749191	−	1.12124i	0.988635	−	0.150333i	$-0.0480346\pi$
$654$	0.931838	−	2.24965i	0.0364377	−	0.0879685i
$655$	0.221582	+	19.9929i	0.00865791	+	0.781188i
$656$	0.620681	+	3.12038i	0.0242335	+	0.121830i
$657$	−0.216491	+	0.0430627i	−0.00844612	+	0.00168004i
$658$	16.8295	+	25.1871i	0.656082	+	0.981896i
$659$	23.5017	−	23.5017i	0.915497	−	0.915497i	−0.0812010	−	0.996698i	$-0.525876\pi$
$659$	23.5017	−	23.5017i	0.915497	−	0.915497i	0.996698	+	0.0812010i	$0.0258756\pi$
$660$	0.485575	+	2.30721i	0.0189010	+	0.0898082i
$661$	2.15143	−	0.891152i	0.0836810	−	0.0346618i	−0.340450	−	0.940263i	$-0.610579\pi$
$661$	2.15143	−	0.891152i	0.0836810	−	0.0346618i	0.424131	+	0.905601i	$0.360579\pi$
$662$	−17.8545	+	17.8545i	−0.693936	+	0.693936i
$663$	11.8361	−	14.4682i	0.459674	−	0.561897i
$664$			14.8166i			0.574995i
$665$	51.8228	−	0.574351i	2.00960	−	0.0222724i
$666$	−5.62598	+	3.75916i	−0.218002	+	0.145664i
$667$	0.582986			0.0225733
$668$	−6.51867	+	4.35564i	−0.252215	+	0.168525i
$669$	−2.42453	+	3.62857i	−0.0937378	+	0.140289i
$670$	−10.9714	−	16.0323i	−0.423861	−	0.619382i
$671$	−5.31476	−	2.20145i	−0.205174	−	0.0849859i
$672$	−2.83902	+	1.17596i	−0.109518	+	0.0453637i
$673$	37.2430	+	24.8850i	1.43561	+	0.959246i	0.998199	+	0.0599861i	$0.0191056\pi$
$673$	37.2430	+	24.8850i	1.43561	+	0.959246i	0.437414	+	0.899260i	$0.355894\pi$
$674$	−28.4983	−	19.0420i	−1.09771	−	0.733469i
$675$	0.866525	−	4.92434i	0.0333526	−	0.189538i
$676$	−5.34155	−	5.34155i	−0.205444	−	0.205444i
$677$	6.98614	−	35.1217i	0.268499	−	1.34984i	−0.577385	−	0.816472i	$-0.695927\pi$
$677$	6.98614	−	35.1217i	0.268499	−	1.34984i	0.845885	−	0.533366i	$-0.179073\pi$
$678$	−5.71671	+	13.8014i	−0.219549	+	0.530038i
$679$	40.3391			1.54807
$680$	9.16299	−	1.01957i	0.351385	−	0.0390987i
$681$	15.5035			0.594094
$682$	3.51685	−	8.49044i	0.134667	−	0.325116i
$683$	9.13210	−	45.9102i	0.349430	−	1.75670i	−0.261676	−	0.965156i	$-0.584275\pi$
$683$	9.13210	−	45.9102i	0.349430	−	1.75670i	0.611106	−	0.791549i	$-0.290725\pi$
$684$	5.33328	+	5.33328i	0.203923	+	0.203923i
$685$	4.58653	+	2.99163i	0.175242	+	0.114304i
$686$	−11.6436	−	7.77999i	−0.444554	−	0.297041i
$687$	−18.4123	−	12.3027i	−0.702474	−	0.469378i
$688$	6.59414	−	2.73138i	0.251399	−	0.104133i
$689$	−25.5852	−	10.5977i	−0.974719	−	0.403742i
$690$	1.66403	+	0.311866i	0.0633486	+	0.0118726i
$691$	3.91102	−	5.85326i	0.148782	−	0.222668i	−0.749591	−	0.661901i	$-0.769750\pi$
$691$	3.91102	−	5.85326i	0.148782	−	0.222668i	0.898373	+	0.439233i	$0.144750\pi$
$692$	13.5711	−	9.06791i	0.515895	−	0.344710i
$693$	3.24017			0.123084
$694$	2.88422	−	1.92717i	0.109483	−	0.0731545i
$695$	19.0658	+	18.6478i	0.723207	+	0.707352i
$696$			0.769990i			0.0291864i
$697$	−12.5588	−	3.78831i	−0.475697	−	0.143493i
$698$	18.0012	−	18.0012i	0.681354	−	0.681354i
$699$	−22.2086	+	9.19909i	−0.840005	+	0.347942i
$700$	8.81720	+	12.5829i	0.333259	+	0.475590i
$701$	16.9500	−	16.9500i	0.640193	−	0.640193i	−0.310410	−	0.950603i	$-0.600466\pi$
$701$	16.9500	−	16.9500i	0.640193	−	0.640193i	0.950603	+	0.310410i	$0.100466\pi$
$702$	2.51877	+	3.76960i	0.0950648	+	0.142274i
$703$	−50.0535	+	9.95626i	−1.88780	+	0.375508i
$704$	−0.205707	−	1.03416i	−0.00775289	−	0.0389764i
$705$	22.0413	−	0.244284i	0.830123	−	0.00920025i
$706$	0.105428	−	0.254525i	0.00396782	−	0.00957917i
$707$	1.14318	−	1.71089i	0.0429937	−	0.0643447i
$708$	−2.54016	−	12.7703i	−0.0954652	−	0.479936i
$709$	−18.8669	−	3.75286i	−0.708561	−	0.140941i	−0.172363	−	0.985034i	$-0.555140\pi$
$709$	−18.8669	−	3.75286i	−0.708561	−	0.140941i	−0.536198	+	0.844092i	$0.680140\pi$
$710$	−5.34561	−	12.5114i	−0.200617	−	0.469546i
$711$	−3.92414	−	5.87290i	−0.147167	−	0.220251i
$712$	−9.34387	−	3.87036i	−0.350176	−	0.145048i
$713$	−4.66615	−	4.66615i	−0.174749	−	0.174749i
$714$	1.22224	−	12.6109i	0.0457413	−	0.471952i
$715$	−3.98091	+	9.92033i	−0.148878	+	0.370999i
$716$	1.17584	+	2.83872i	0.0439431	+	0.106088i
$717$	9.16399	+	1.82283i	0.342236	+	0.0680749i
$718$			11.0946i			0.414046i
$719$	1.51331	−	7.60794i	0.0564371	−	0.283728i	−0.942253	−	0.334903i	$-0.891296\pi$
$719$	1.51331	−	7.60794i	0.0564371	−	0.283728i	0.998690	+	0.0511745i	$0.0162965\pi$
$720$	−0.411904	+	2.19780i	−0.0153507	+	0.0819073i
$721$	−33.7371	+	6.71072i	−1.25643	+	0.249920i
$722$	14.4990	+	35.0037i	0.539596	+	1.30270i
$723$	0.237253	+	0.572778i	0.00882352	+	0.0213019i
$724$	6.03674	−	1.20078i	0.224354	−	0.0446267i
$725$	3.75840	−	0.834591i	0.139583	−	0.0309959i
$726$	1.92909	−	9.69820i	0.0715953	−	0.359934i
$727$			19.3598i			0.718015i	0.933335	+	0.359007i	$0.116885\pi$
$727$			19.3598i			0.718015i	−0.933335	+	0.359007i	$0.883115\pi$
$728$	−13.6639	−	2.71793i	−0.506420	−	0.100733i
$729$	−0.382683	−	0.923880i	−0.0141735	−	0.0342178i
$730$	−0.193924	−	0.453880i	−0.00717745	−	0.0167989i
$731$	−2.83888	+	29.2912i	−0.105000	+	1.08337i
$732$	−3.85779	−	3.85779i	−0.142588	−	0.142588i
$733$	−0.141656	−	0.0586759i	−0.00523219	−	0.00216725i	0.380066	−	0.924959i	$-0.375901\pi$
$733$	−0.141656	−	0.0586759i	−0.00523219	−	0.00216725i	−0.385298	+	0.922792i	$0.625901\pi$
$734$	−2.38417	−	3.56817i	−0.0880014	−	0.131703i
$735$	5.02325	−	2.14622i	0.185285	−	0.0791646i
$736$	−0.742586	−	0.147710i	−0.0273721	−	0.00544465i
$737$	−1.78718	−	8.98478i	−0.0658318	−	0.330959i
$738$	1.76755	−	2.64533i	0.0650645	−	0.0973758i
$739$	14.7577	−	35.6283i	0.542872	−	1.31061i	−0.379816	−	0.925062i	$-0.624013\pi$
$739$	14.7577	−	35.6283i	0.542872	−	1.31061i	0.922688	−	0.385548i	$-0.125987\pi$
$740$	−10.8164	−	10.5792i	−0.397618	−	0.388901i
$741$	6.67105	+	33.5376i	0.245067	+	1.23204i
$742$	−18.4099	+	3.66196i	−0.675849	+	0.134435i
$743$	22.1515	+	33.1521i	0.812660	+	1.21623i	0.973372	+	0.229231i	$0.0736211\pi$
$743$	22.1515	+	33.1521i	0.812660	+	1.21623i	−0.160712	+	0.987001i	$0.551379\pi$
$744$	6.16291	−	6.16291i	0.225943	−	0.225943i
$745$	21.4826	−	32.9353i	0.787060	−	1.20666i
$746$	−18.7417	+	7.76308i	−0.686184	+	0.284227i
$747$	10.4769	−	10.4769i	0.383330	−	0.383330i
$748$	4.16225	+	1.25553i	0.152187	+	0.0459067i
$749$			11.4563i			0.418604i
$750$	11.1742	−	0.371651i	0.408023	−	0.0135708i
$751$	−15.1600	+	10.1296i	−0.553198	+	0.369635i	−0.800527	−	0.599296i	$-0.795447\pi$
$751$	−15.1600	+	10.1296i	−0.553198	+	0.369635i	0.247329	+	0.968932i	$0.420447\pi$
$752$	−9.85778			−0.359476
$753$	−7.87564	+	5.26233i	−0.287004	+	0.191770i
$754$	−1.93942	+	2.90255i	−0.0706297	+	0.105705i
$755$	31.0813	−	21.2698i	1.13116	−	0.774088i
$756$	2.83902	+	1.17596i	0.103254	+	0.0427693i
$757$	29.3380	−	12.1522i	1.06631	−	0.441679i	0.220621	−	0.975360i	$-0.429192\pi$
$757$	29.3380	−	12.1522i	1.06631	−	0.441679i	0.845686	+	0.533681i	$0.179192\pi$
$758$	−19.6185	−	13.1087i	−0.712576	−	0.476128i
$759$	0.663794	+	0.443533i	0.0240942	+	0.0160992i
$760$	−9.21388	+	14.1260i	−0.334222	+	0.512403i
$761$	−14.6281	−	14.6281i	−0.530268	−	0.530268i	0.390384	−	0.920652i	$-0.372342\pi$
$761$	−14.6281	−	14.6281i	−0.530268	−	0.530268i	−0.920652	+	0.390384i	$0.872342\pi$
$762$	−0.767308	+	3.85752i	−0.0277966	+	0.139743i
$763$	2.86347	−	6.91304i	0.103665	−	0.250269i
$764$	−24.0816			−0.871243
$765$	−7.20016	−	5.75827i	−0.260322	−	0.208191i
$766$	23.7826			0.859299
$767$	22.5899	−	54.5369i	0.815675	−	1.96921i
$768$	0.195090	−	0.980785i	0.00703972	−	0.0353910i
$769$	3.55397	+	3.55397i	0.128160	+	0.128160i	0.768277	−	0.640117i	$-0.221114\pi$
$769$	3.55397	+	3.55397i	0.128160	+	0.128160i	−0.640117	+	0.768277i	$0.721114\pi$
$770$	1.49214	+	7.08992i	0.0537730	+	0.255503i
$771$	8.70029	+	5.81335i	0.313333	+	0.209363i
$772$	−20.2766	−	13.5484i	−0.729770	−	0.487616i
$773$	−32.4264	+	13.4315i	−1.16630	+	0.483096i	−0.879967	−	0.475035i	$-0.842435\pi$
$773$	−32.4264	+	13.4315i	−1.16630	+	0.483096i	−0.286330	+	0.958131i	$0.592435\pi$
$774$	−6.59414	−	2.73138i	−0.237022	−	0.0981776i
$775$	−36.7618	−	23.4018i	−1.32052	−	0.840618i
$776$	−7.29309	+	10.9149i	−0.261807	+	0.391821i
$777$	−17.2883	+	11.5516i	−0.620213	+	0.414413i
$778$	−26.6555			−0.955646
$779$	19.9521	−	13.3316i	0.714858	−	0.477653i
$780$	−7.08847	+	7.24735i	−0.253808	+	0.259497i
$781$		−	6.41573i		−	0.229573i
$782$	1.97665	−	2.41622i	0.0706850	−	0.0864039i
$783$	0.544465	−	0.544465i	0.0194576	−	0.0194576i
$784$	−2.25696	+	0.934865i	−0.0806058	+	0.0333880i
$785$	10.8026	−	2.27351i	0.385561	−	0.0811449i
$786$	−6.32271	+	6.32271i	−0.225524	+	0.225524i
$787$	−6.52355	−	9.76318i	−0.232539	−	0.348020i	0.696788	−	0.717277i	$-0.254612\pi$
$787$	−6.52355	−	9.76318i	−0.232539	−	0.348020i	−0.929327	+	0.369258i	$0.879612\pi$
$788$	9.20425	−	1.83084i	0.327888	−	0.0652210i
$789$	1.71921	+	8.64307i	0.0612056	+	0.307702i
$790$	11.0436	−	11.2911i	0.392912	−	0.401719i
$791$	−17.5671	+	42.4106i	−0.624613	+	1.50795i
$792$	−0.585805	+	0.876719i	−0.0208157	+	0.0311529i
$793$	−4.82546	−	24.2592i	−0.171357	−	0.861471i
$794$	28.8454	+	5.73771i	1.02369	+	0.203624i
$795$	−5.08679	+	12.6762i	−0.180410	+	0.449577i
$796$	−5.06554	−	7.58111i	−0.179543	−	0.268705i
$797$	27.3826	+	11.3422i	0.969942	+	0.401763i	0.810690	−	0.585475i	$-0.199092\pi$
$797$	27.3826	+	11.3422i	0.969942	+	0.401763i	0.159251	+	0.987238i	$0.449092\pi$
$798$	16.3888	+	16.3888i	0.580157	+	0.580157i
$799$	19.1039	−	35.8752i	0.675848	−	1.26917i
$800$	−4.99877	+	0.110816i	−0.176733	+	0.00391795i
$801$	3.87036	+	9.34387i	0.136752	+	0.330149i
$802$	−13.9189	−	2.76863i	−0.491492	−	0.0977639i
$803$		−	0.232745i		−	0.00821339i
$804$	1.69494	−	8.52106i	0.0597761	−	0.300515i
$805$	5.11346	+	0.958345i	0.180226	+	0.0337772i
$806$	38.7546	−	7.70878i	1.36507	−	0.271530i
$807$	5.98132	+	14.4402i	0.210553	+	0.508319i
$808$	0.256249	+	0.618640i	0.00901481	+	0.0217637i
$809$	−15.4151	+	3.06625i	−0.541965	+	0.107803i	−0.458479	−	0.888705i	$-0.651605\pi$
$809$	−15.4151	+	3.06625i	−0.541965	+	0.107803i	−0.0834861	+	0.996509i	$0.526605\pi$
$810$	1.84534	−	1.26282i	0.0648387	−	0.0443710i
$811$	−4.74183	+	23.8388i	−0.166508	+	0.837093i	0.803740	+	0.594980i	$0.202840\pi$
$811$	−4.74183	+	23.8388i	−0.166508	+	0.837093i	−0.970248	+	0.242112i	$0.922160\pi$
$812$			2.36613i			0.0830348i
$813$	−21.3504	−	4.24685i	−0.748789	−	0.148943i
$814$	−2.73027	−	6.59145i	−0.0956959	−	0.231030i
$815$	−48.5309	−	19.4749i	−1.69996	−	0.682175i
$816$	3.19127	+	2.61070i	0.111717	+	0.0913929i
$817$	−38.0660	−	38.0660i	−1.33176	−	1.33176i
$818$	14.7926	+	6.12728i	0.517210	+	0.214235i
$819$	7.74001	+	11.5837i	0.270458	+	0.404769i
$820$	6.60231	+	2.64943i	0.230563	+	0.0925221i
$821$	−37.3770	−	7.43474i	−1.30447	−	0.259474i	−0.506533	−	0.862221i	$-0.669073\pi$
$821$	−37.3770	−	7.43474i	−1.30447	−	0.259474i	−0.797933	+	0.602747i	$0.794073\pi$
$822$	0.477761	+	2.40187i	0.0166638	+	0.0837748i
$823$	1.57767	−	2.36115i	0.0549940	−	0.0823043i	−0.802954	−	0.596042i	$-0.796739\pi$
$823$	1.57767	−	2.36115i	0.0549940	−	0.0823043i	0.857948	+	0.513737i	$0.171739\pi$
$824$	4.28371	−	10.3418i	0.149230	−	0.360273i
$825$	4.91431	+	1.90910i	0.171094	+	0.0664663i
$826$	−7.80575	−	39.2422i	−0.271597	−	1.36541i
$827$	6.70236	−	1.33318i	0.233064	−	0.0463593i	−0.0771765	−	0.997017i	$-0.524590\pi$
$827$	6.70236	−	1.33318i	0.233064	−	0.0463593i	0.310240	+	0.950658i	$0.399590\pi$
$828$	0.420641	+	0.629534i	0.0146183	+	0.0218778i
$829$	18.3950	−	18.3950i	0.638885	−	0.638885i	−0.311396	−	0.950280i	$-0.600796\pi$
$829$	18.3950	−	18.3950i	0.638885	−	0.638885i	0.950280	+	0.311396i	$0.100796\pi$
$830$	27.7496	+	18.1001i	0.963204	+	0.628265i
$831$	−1.15363	+	0.477851i	−0.0400191	+	0.0165765i
$832$	3.20578	−	3.20578i	0.111141	−	0.111141i
$833$	0.971659	−	10.0254i	0.0336660	−	0.347361i
$834$			11.9268i			0.412992i
$835$	0.194280	+	17.5296i	0.00672334	+	0.606636i
$836$	−6.61256	+	4.41837i	−0.228700	+	0.152813i
$837$	−8.71567			−0.301258
$838$	−9.74552	+	6.51175i	−0.336654	+	0.224945i
$839$	−25.4529	+	38.0929i	−0.878731	+	1.31511i	0.0695157	+	0.997581i	$0.477855\pi$
$839$	−25.4529	+	38.0929i	−0.878731	+	1.31511i	−0.948247	+	0.317533i	$0.897145\pi$
$840$	−1.26575	+	6.75370i	−0.0436726	+	0.233025i
$841$	−26.2448	−	10.8709i	−0.904991	−	0.374860i
$842$	10.6417	−	4.40792i	0.366736	−	0.151907i
$843$	0.265196	+	0.177199i	0.00913385	+	0.00610304i
$844$	−12.5880	−	8.41103i	−0.433297	−	0.289519i
$845$	−16.5294	+	3.47876i	−0.568627	+	0.119673i
$846$	6.97050	+	6.97050i	0.239651	+	0.239651i
$847$	5.92797	−	29.8019i	0.203687	−	1.02401i
$848$	2.33757	−	5.64339i	0.0802724	−	0.193795i
$849$	25.3069			0.868529
$850$	9.28410	−	18.4067i	0.318442	−	0.631344i
$851$	−5.12300			−0.175614
$852$	2.32847	−	5.62143i	0.0797722	−	0.192587i
$853$	−0.228264	+	1.14756i	−0.00781560	+	0.0392917i	−0.984496	−	0.175405i	$-0.943876\pi$
$853$	−0.228264	+	1.14756i	−0.00781560	+	0.0392917i	0.976681	+	0.214697i	$0.0688764\pi$
$854$	−11.8547	−	11.8547i	−0.405661	−	0.405661i
$855$	16.5038	−	3.47337i	0.564417	−	0.118787i
$856$	−3.09982	−	2.07124i	−0.105950	−	0.0707934i
$857$	40.8318	+	27.2829i	1.39479	+	0.931968i	0.999912	+	0.0132331i	$0.00421235\pi$
$857$	40.8318	+	27.2829i	1.39479	+	0.931968i	0.394876	+	0.918735i	$0.370788\pi$
$858$	−4.41650	+	1.82938i	−0.150777	+	0.0624539i
$859$	23.9249	+	9.91002i	0.816307	+	0.338125i	0.751467	−	0.659770i	$-0.229346\pi$
$859$	23.9249	+	9.91002i	0.816307	+	0.338125i	0.0648397	+	0.997896i	$0.479346\pi$
$860$	2.93994	−	15.6867i	0.100251	−	0.534912i
$861$	5.43157	−	8.12891i	0.185107	−	0.277033i
$862$	−0.671420	+	0.448629i	−0.0228687	+	0.0152804i
$863$	29.0419			0.988596			0.494298	−	0.869292i	$-0.335425\pi$
$863$	29.0419			0.988596			0.494298	+	0.869292i	$0.335425\pi$
$864$	−0.831470	+	0.555570i	−0.0282872	+	0.0189009i
$865$	−0.404467	−	36.4944i	−0.0137523	−	1.24085i
$866$		−	16.5466i		−	0.562278i
$867$	−15.6856	+	6.55450i	−0.532711	+	0.222603i
$868$	18.9382	−	18.9382i	0.642804	−	0.642804i
$869$	6.88075	−	2.85010i	0.233413	−	0.0966830i
$870$	1.44209	+	0.940629i	0.0488916	+	0.0318903i
$871$	27.8518	−	27.8518i	0.943723	−	0.943723i
$872$	1.35282	+	2.02464i	0.0458122	+	0.0685628i
$873$	12.8750	−	2.56099i	0.435752	−	0.0866765i
$874$	1.11408	+	5.60088i	0.0376844	+	0.189452i
$875$	34.3375	−	1.14206i	1.16082	−	0.0386087i
$876$	0.0844706	−	0.203930i	0.00285400	−	0.00689016i
$877$	15.5795	−	23.3164i	0.526083	−	0.787339i	−0.469329	−	0.883024i	$-0.655504\pi$
$877$	15.5795	−	23.3164i	0.526083	−	0.787339i	0.995412	+	0.0956845i	$0.0305040\pi$
$878$	−5.12170	−	25.7485i	−0.172849	−	0.868970i
$879$	23.9858	+	4.77108i	0.809022	+	0.160925i
$880$	−2.18815	−	0.878079i	−0.0737625	−	0.0296000i
$881$	16.5262	+	24.7333i	0.556783	+	0.833285i	0.997941	−	0.0641445i	$-0.0204319\pi$
$881$	16.5262	+	24.7333i	0.556783	+	0.833285i	−0.441157	+	0.897430i	$0.645432\pi$
$882$	2.25696	+	0.934865i	0.0759959	+	0.0314785i
$883$	−15.3748	−	15.3748i	−0.517405	−	0.517405i	0.399380	−	0.916785i	$-0.369225\pi$
$883$	−15.3748	−	15.3748i	−0.517405	−	0.517405i	−0.916785	+	0.399380i	$0.869225\pi$
$884$	5.45407	+	17.8794i	0.183440	+	0.601349i
$885$	−27.0202	−	10.8429i	−0.908274	−	0.364480i
$886$	−7.88611	−	19.0388i	−0.264939	−	0.639619i
$887$	13.9846	+	2.78172i	0.469559	+	0.0934010i	0.424198	−	0.905570i	$-0.360556\pi$
$887$	13.9846	+	2.78172i	0.469559	+	0.0934010i	0.0453610	+	0.998971i	$0.485556\pi$
$888$		−	6.76630i		−	0.227062i
$889$	−2.35789	+	11.8539i	−0.0790809	+	0.397567i
$890$	−18.6633	+	12.7718i	−0.625595	+	0.428113i
$891$	1.03416	−	0.205707i	0.0346457	−	0.00689146i
$892$	−1.67005	−	4.03185i	−0.0559173	−	0.134996i
$893$	28.4530	+	68.6916i	0.952143	+	2.29868i
$894$	17.2475	−	3.43074i	0.576843	−	0.114741i
$895$	6.75299	+	1.26562i	0.225728	+	0.0423050i
$896$	0.599500	−	3.01389i	0.0200279	−	0.100687i
$897$			3.43259i			0.114611i
$898$	13.0792	+	2.60161i	0.436458	+	0.0868168i
$899$	−2.56818	−	6.20013i	−0.0856535	−	0.206786i
$900$	3.61302	+	3.45631i	0.120434	+	0.115210i
$901$	16.0078	+	19.4437i	0.533296	+	0.647763i
$902$	2.37210	+	2.37210i	0.0789821	+	0.0789821i
$903$	−20.2634	−	8.39336i	−0.674323	−	0.279314i
$904$	−8.29937	−	12.4209i	−0.276033	−	0.413113i
$905$	5.12564	−	12.7730i	0.170382	−	0.424587i
$906$	16.5195	+	3.28592i	0.548822	+	0.109168i
$907$	−6.81990	−	34.2860i	−0.226451	−	1.13845i	−0.911927	−	0.410352i	$-0.865406\pi$
$907$	−6.81990	−	34.2860i	−0.226451	−	1.13845i	0.685476	−	0.728095i	$-0.259594\pi$
$908$	−8.61326	+	12.8906i	−0.285841	+	0.427791i
$909$	0.256249	−	0.618640i	0.00849925	−	0.0205190i
$910$	−21.7824	+	22.2706i	−0.722079	+	0.738264i
$911$	4.71562	+	23.7070i	0.156236	+	0.785449i	0.976843	+	0.213957i	$0.0686352\pi$
$911$	4.71562	+	23.7070i	0.156236	+	0.785449i	−0.820608	+	0.571492i	$0.806365\pi$
$912$	−7.39747	+	1.47145i	−0.244955	+	0.0487245i
$913$	8.67964	+	12.9900i	0.287254	+	0.429906i
$914$	−10.4470	+	10.4470i	−0.345556	+	0.345556i
$915$	−11.9379	+	2.51244i	−0.394655	+	0.0830588i
$916$	20.4587	−	8.47427i	0.675974	−	0.279998i
$917$	−19.4293	+	19.4293i	−0.641611	+	0.641611i
$918$	−0.410524	−	4.10262i	−0.0135493	−	0.135407i
$919$		−	21.3804i		−	0.705276i	−0.935760	−	0.352638i	$-0.885285\pi$
$919$		−	21.3804i		−	0.705276i	0.935760	−	0.352638i	$-0.114715\pi$
$920$	−1.18379	+	1.21033i	−0.0390285	+	0.0399033i
$921$	13.8421	−	9.24897i	0.456112	−	0.304764i
$922$	−16.8174			−0.553850
$923$	22.9365	−	15.3257i	0.754964	−	0.504451i
$924$	−1.80014	+	2.69410i	−0.0592203	+	0.0886294i
$925$	−33.0270	+	7.33399i	−1.08592	+	0.241140i
$926$	2.56223	+	1.06131i	0.0842000	+	0.0348768i
$927$	−10.3418	+	4.28371i	−0.339669	+	0.140695i
$928$	−0.640223	−	0.427783i	−0.0210163	−	0.0140427i
$929$	32.6504	+	21.8163i	1.07122	+	0.715769i	0.960555	−	0.278088i	$-0.0897008\pi$
$929$	32.6504	+	21.8163i	1.07122	+	0.715769i	0.110668	+	0.993857i	$0.464701\pi$
$930$	−4.01368	−	19.0710i	−0.131614	−	0.625364i
$931$	13.0288	+	13.0288i	0.427001	+	0.427001i
$932$	4.68966	−	23.5765i	0.153615	−	0.772274i
$933$	4.98696	−	12.0396i	0.163266	−	0.394159i
$934$	−0.595505			−0.0194855
$935$	7.43611	−	6.26161i	0.243187	−	0.204776i
$936$	−4.53366			−0.148187
$937$	−13.5693	+	32.7593i	−0.443291	+	1.07020i	0.531496	+	0.847061i	$0.321630\pi$
$937$	−13.5693	+	32.7593i	−0.443291	+	1.07020i	−0.974787	+	0.223138i	$0.928370\pi$
$938$	5.20845	−	26.1846i	0.170062	−	0.854959i
$939$	7.63434	+	7.63434i	0.249137	+	0.249137i
$940$	−12.0424	+	18.4624i	−0.392779	+	0.602177i
$941$	−17.2957	−	11.5566i	−0.563825	−	0.376736i	0.240750	−	0.970587i	$-0.422607\pi$
$941$	−17.2957	−	11.5566i	−0.563825	−	0.376736i	−0.804575	+	0.593851i	$0.797607\pi$
$942$	4.10488	+	2.74279i	0.133744	+	0.0893651i
$943$	2.22547	−	0.921819i	0.0724712	−	0.0300186i
$944$	12.0293	+	4.98271i	0.391521	+	0.162173i
$945$	5.67061	−	3.88056i	0.184465	−	0.126235i
$946$	4.18115	−	6.25754i	0.135941	−	0.203450i
$947$	−27.4648	+	18.3514i	−0.892488	+	0.596341i	−0.915022	−	0.403405i	$-0.867827\pi$
$947$	−27.4648	+	18.3514i	−0.892488	+	0.596341i	0.0225339	+	0.999746i	$0.492827\pi$
$948$	7.06327			0.229404
$949$	0.832073	−	0.555973i	0.0270102	−	0.0180477i
$950$	15.2004	+	34.5129i	0.493166	+	1.11975i
$951$		−	13.2874i		−	0.430872i
$952$	9.80657	+	8.02252i	0.317833	+	0.260011i
$953$	−7.85712	+	7.85712i	−0.254517	+	0.254517i	−0.822820	−	0.568303i	$-0.807600\pi$
$953$	−7.85712	+	7.85712i	−0.254517	+	0.254517i	0.568303	+	0.822820i	$0.307600\pi$
$954$	−5.64339	+	2.33757i	−0.182711	+	0.0756816i
$955$	−29.4184	+	45.1019i	−0.951957	+	1.45946i
$956$	−6.60687	+	6.60687i	−0.213682	+	0.213682i
$957$	0.451064	+	0.675065i	0.0145808	+	0.0218217i
$958$	12.4484	−	2.47613i	0.402188	−	0.0800002i
$959$	1.46813	+	7.38078i	0.0474083	+	0.238338i
$960$	−1.59856	−	1.56352i	−0.0515934	−	0.0504624i
$961$	−17.2065	+	41.5403i	−0.555050	+	1.34001i
$962$	17.0427	−	25.5063i	0.549480	−	0.822355i
$963$	0.727321	+	3.65649i	0.0234376	+	0.117829i
$964$	−0.608058	−	0.120950i	−0.0195842	−	0.00389555i
$965$	−50.1445	+	21.4246i	−1.61421	+	0.689684i
$966$	1.29260	+	1.93452i	0.0415888	+	0.0622421i
$967$	15.7538	+	6.52542i	0.506607	+	0.209843i	0.621322	−	0.783555i	$-0.286596\pi$
$967$	15.7538	+	6.52542i	0.506607	+	0.209843i	−0.114716	+	0.993398i	$0.536596\pi$
$968$	6.99201	+	6.99201i	0.224732	+	0.224732i
$969$	8.98094	−	29.7730i	0.288509	−	0.956447i
$970$	11.5329	+	26.9928i	0.370299	+	0.866687i
$971$	−8.87245	−	21.4200i	−0.284731	−	0.687400i	0.715203	−	0.698917i	$-0.246334\pi$
$971$	−8.87245	−	21.4200i	−0.284731	−	0.687400i	−0.999934	+	0.0115163i	$0.996334\pi$
$972$	0.980785	+	0.195090i	0.0314587	+	0.00625752i
$973$			36.6503i			1.17496i
$974$	−1.23372	+	6.20234i	−0.0395310	+	0.198736i
$975$	4.91403	+	22.1293i	0.157375	+	0.708704i
$976$	5.35091	−	1.06436i	0.171279	−	0.0340694i
$977$	16.9995	+	41.0404i	0.543862	+	1.31300i	0.921978	+	0.387241i	$0.126572\pi$
$977$	16.9995	+	41.0404i	0.543862	+	1.31300i	−0.378116	+	0.925758i	$0.623428\pi$
$978$	−8.94942	−	21.6058i	−0.286171	−	0.690878i
$979$	−10.4592	+	2.08047i	−0.334278	+	0.0664921i
$980$	−1.00625	+	5.36906i	−0.0321434	+	0.171508i
$981$	0.475047	−	2.38822i	0.0151671	−	0.0762500i
$982$			29.9582i			0.956004i
$983$	4.28876	+	0.853087i	0.136790	+	0.0272092i	0.263010	−	0.964793i	$-0.415285\pi$
$983$	4.28876	+	0.853087i	0.136790	+	0.0272092i	−0.126220	+	0.992002i	$0.540285\pi$
$984$	1.21751	+	2.93933i	0.0388128	+	0.0937024i
$985$	7.81509	−	19.4750i	0.249010	−	0.620525i
$986$	2.79754	−	1.50092i	0.0890920	−	0.0477992i
$987$	21.4199	+	21.4199i	0.681802	+	0.681802i
$988$	−31.5917	−	13.0857i	−1.00507	−	0.416313i
$989$	−3.00231	−	4.49327i	−0.0954678	−	0.142878i
$990$	0.926360	+	2.16815i	0.0294416	+	0.0689084i
$991$	−25.6204	−	5.09622i	−0.813859	−	0.161887i	−0.229423	−	0.973327i	$-0.573684\pi$
$991$	−25.6204	−	5.09622i	−0.813859	−	0.161887i	−0.584436	+	0.811440i	$0.698684\pi$
$992$	1.70034	+	8.54820i	0.0539859	+	0.271406i
$993$	−14.0282	+	20.9947i	−0.445172	+	0.666247i
$994$	7.15525	−	17.2743i	0.226951	−	0.547907i
$995$	−20.3866	+	0.225945i	−0.646299	+	0.00716293i
$996$	2.89057	+	14.5319i	0.0915913	+	0.460461i
$997$	−27.2489	+	5.42014i	−0.862981	+	0.171658i	−0.606686	−	0.794941i	$-0.707502\pi$
$997$	−27.2489	+	5.42014i	−0.862981	+	0.171658i	−0.256294	+	0.966599i	$0.582502\pi$
$998$	−19.0580	−	28.5223i	−0.603269	−	0.902856i
$999$	−4.78450	+	4.78450i	−0.151375	+	0.151375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.bi.b.97.1	yes	80
5.3	odd	4		510.2.bd.b.403.2	yes	80
17.10	odd	16		510.2.bd.b.367.2	✓	80
85.78	even	16	inner	510.2.bi.b.163.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.bd.b.367.2	✓	80	17.10	odd	16
510.2.bd.b.403.2	yes	80	5.3	odd	4
510.2.bi.b.97.1	yes	80	1.1	even	1	trivial
510.2.bi.b.163.1	yes	80	85.78	even	16	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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.bi (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 + 0.923880i) q^{2} +(-0.195090 + 0.980785i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(-2.18813 + 0.460513i) q^{5} +(-0.831470 - 0.555570i) q^{6} +(-2.55505 - 1.70723i) q^{7} +(0.923880 - 0.382683i) q^{8} +(-0.923880 - 0.382683i) q^{9} +(0.411904 - 2.19780i) q^{10} +(0.585805 - 0.876719i) q^{11} +(0.831470 - 0.555570i) q^{12} +4.53366 q^{13} +(2.55505 - 1.70723i) q^{14} +(-0.0247808 - 2.23593i) q^{15} +1.00000i q^{16} +(-3.63928 - 1.93795i) q^{17} +(0.707107 - 0.707107i) q^{18} +(6.96826 - 2.88635i) q^{19} +(1.87288 + 1.22161i) q^{20} +(2.17289 - 2.17289i) q^{21} +(0.585805 + 0.876719i) q^{22} +(0.742586 - 0.147710i) q^{23} +(0.195090 + 0.980785i) q^{24} +(4.57586 - 2.01533i) q^{25} +(-1.73496 + 4.18856i) q^{26} +(0.555570 - 0.831470i) q^{27} +(0.599500 + 3.01389i) q^{28} +(0.755194 + 0.150218i) q^{29} +(2.07521 + 0.832759i) q^{30} +(-4.84216 - 7.24681i) q^{31} +(-0.923880 - 0.382683i) q^{32} +(0.745588 + 0.745588i) q^{33} +(3.18313 - 2.62063i) q^{34} +(6.37699 + 2.55901i) q^{35} +(0.382683 + 0.923880i) q^{36} +(-6.63629 - 1.32004i) q^{37} +7.54239i q^{38} +(-0.884474 + 4.44655i) q^{39} +(-1.84534 + 1.26282i) q^{40} +(3.12038 - 0.620681i) q^{41} +(1.17596 + 2.83902i) q^{42} +(-2.73138 - 6.59414i) q^{43} +(-1.03416 + 0.205707i) q^{44} +(2.19780 + 0.411904i) q^{45} +(-0.147710 + 0.742586i) q^{46} +9.85778i q^{47} +(-0.980785 - 0.195090i) q^{48} +(0.934865 + 2.25696i) q^{49} +(0.110816 + 4.99877i) q^{50} +(2.61070 - 3.19127i) q^{51} +(-3.20578 - 3.20578i) q^{52} +(-5.64339 - 2.33757i) q^{53} +(0.555570 + 0.831470i) q^{54} +(-0.878079 + 2.18815i) q^{55} +(-3.01389 - 0.599500i) q^{56} +(1.47145 + 7.39747i) q^{57} +(-0.427783 + 0.640223i) q^{58} +(4.98271 - 12.0293i) q^{59} +(-1.56352 + 1.59856i) q^{60} +(-1.06436 - 5.35091i) q^{61} +(8.54820 - 1.70034i) q^{62} +(1.70723 + 2.55505i) q^{63} +(0.707107 - 0.707107i) q^{64} +(-9.92026 + 2.08781i) q^{65} +(-0.974158 + 0.403510i) q^{66} +(6.14334 - 6.14334i) q^{67} +(1.20302 + 3.94370i) q^{68} +0.757134i q^{69} +(-4.80459 + 4.91228i) q^{70} +(5.05916 - 3.38042i) q^{71} -1.00000 q^{72} +(0.183532 - 0.122632i) q^{73} +(3.75916 - 5.62598i) q^{74} +(1.08390 + 4.88110i) q^{75} +(-6.96826 - 2.88635i) q^{76} +(-2.99352 + 1.23996i) q^{77} +(-3.76960 - 2.51877i) q^{78} +(5.87290 + 3.92414i) q^{79} +(-0.460513 - 2.18813i) q^{80} +(0.707107 + 0.707107i) q^{81} +(-0.620681 + 3.12038i) q^{82} +(-5.67006 + 13.6887i) q^{83} -3.07293 q^{84} +(8.85568 + 2.56457i) q^{85} +7.13745 q^{86} +(-0.294662 + 0.711378i) q^{87} +(0.205707 - 1.03416i) q^{88} +(-7.15149 - 7.15149i) q^{89} +(-1.22161 + 1.87288i) q^{90} +(-11.5837 - 7.74001i) q^{91} +(-0.629534 - 0.420641i) q^{92} +(8.05223 - 3.33534i) q^{93} +(-9.10740 - 3.77241i) q^{94} +(-13.9183 + 9.52469i) q^{95} +(0.555570 - 0.831470i) q^{96} +(-10.9149 + 7.29309i) q^{97} -2.44292 q^{98} +(-0.876719 + 0.585805i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 48 q^{25} + 16 q^{28} + 32 q^{29} + 16 q^{30} + 16 q^{31} - 16 q^{33} - 32 q^{34} - 32 q^{35} + 48 q^{37} + 32 q^{41} + 32 q^{43} + 16 q^{44} - 64 q^{49} + 48 q^{50} - 32 q^{51} + 16 q^{52} - 32 q^{53}+ \cdots - 144 q^{98}+O(q^{100}) \) 80 * q + 48 * q^25 + 16 * q^28 + 32 * q^29 + 16 * q^30 + 16 * q^31 - 16 * q^33 - 32 * q^34 - 32 * q^35 + 48 * q^37 + 32 * q^41 + 32 * q^43 + 16 * q^44 - 64 * q^49 + 48 * q^50 - 32 * q^51 + 16 * q^52 - 32 * q^53 + 16 * q^55 - 16 * q^56 + 32 * q^57 + 32 * q^58 - 16 * q^60 + 48 * q^61 + 32 * q^62 - 32 * q^65 - 16 * q^67 - 16 * q^70 - 80 * q^72 - 80 * q^73 - 32 * q^74 - 48 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 32 * q^82 - 32 * q^83 - 32 * q^85 - 48 * q^87 - 16 * q^88 - 32 * q^89 - 32 * q^92 - 48 * q^93 - 16 * q^94 - 96 * q^95 + 80 * q^97 - 144 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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