LMFDB - Embedded newform 504.2.cz.b.187.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(187,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4, 5]))

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

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

chi := DirichletCharacter("504.187");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$90$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			187.8
Character	$\chi$	$=$	504.187
Dual form			504.2.cz.b.283.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37231 + 0.341717i) q^{2} +(1.71120 + 0.267930i) q^{3} +(1.76646 - 0.937883i) q^{4} -1.57990 q^{5} +(-2.43985 + 0.217065i) q^{6} +(-2.61033 - 0.431470i) q^{7} +(-2.10363 + 1.89069i) q^{8} +(2.85643 + 0.916964i) q^{9} +O(q^{10})$	\(q+(-1.37231 + 0.341717i) q^{2} +(1.71120 + 0.267930i) q^{3} +(1.76646 - 0.937883i) q^{4} -1.57990 q^{5} +(-2.43985 + 0.217065i) q^{6} +(-2.61033 - 0.431470i) q^{7} +(-2.10363 + 1.89069i) q^{8} +(2.85643 + 0.916964i) q^{9} +(2.16811 - 0.539878i) q^{10} -6.43974 q^{11} +(3.27405 - 1.13162i) q^{12} +(-1.62213 - 2.80961i) q^{13} +(3.72962 - 0.299886i) q^{14} +(-2.70352 - 0.423301i) q^{15} +(2.24075 - 3.31346i) q^{16} +(-1.83488 + 1.05937i) q^{17} +(-4.23324 - 0.282267i) q^{18} +(-2.20317 - 1.27200i) q^{19} +(-2.79082 + 1.48176i) q^{20} +(-4.35120 - 1.43772i) q^{21} +(8.83731 - 2.20057i) q^{22} -2.86553i q^{23} +(-4.10632 + 2.67173i) q^{24} -2.50393 q^{25} +(3.18616 + 3.30135i) q^{26} +(4.64224 + 2.33443i) q^{27} +(-5.01571 + 1.68601i) q^{28} +(0.163813 + 0.0945775i) q^{29} +(3.85472 - 0.342941i) q^{30} +(-2.14571 + 3.71647i) q^{31} +(-1.94273 + 5.31279i) q^{32} +(-11.0197 - 1.72540i) q^{33} +(2.15602 - 2.08079i) q^{34} +(4.12406 + 0.681678i) q^{35} +(5.90577 - 1.05921i) q^{36} +(5.83709 + 3.37004i) q^{37} +(3.45810 + 0.992717i) q^{38} +(-2.02302 - 5.24244i) q^{39} +(3.32353 - 2.98710i) q^{40} +(-0.0248856 + 0.0143677i) q^{41} +(6.46248 + 0.486111i) q^{42} +(3.24547 - 5.62132i) q^{43} +(-11.3755 + 6.03972i) q^{44} +(-4.51286 - 1.44871i) q^{45} +(0.979200 + 3.93239i) q^{46} +(2.98964 + 5.17821i) q^{47} +(4.72216 - 5.06964i) q^{48} +(6.62767 + 2.25256i) q^{49} +(3.43616 - 0.855635i) q^{50} +(-3.42369 + 1.32118i) q^{51} +(-5.50052 - 3.44170i) q^{52} +(-6.16601 + 3.55995i) q^{53} +(-7.16830 - 1.61723i) q^{54} +10.1741 q^{55} +(6.30696 - 4.02768i) q^{56} +(-3.42927 - 2.76695i) q^{57} +(-0.257121 - 0.0738117i) q^{58} +(-10.2662 - 5.92720i) q^{59} +(-5.17267 + 1.78784i) q^{60} +(-7.03219 - 12.1801i) q^{61} +(1.67459 - 5.83337i) q^{62} +(-7.06058 - 3.62604i) q^{63} +(0.850557 - 7.95466i) q^{64} +(2.56280 + 4.43890i) q^{65} +(15.7120 - 1.39784i) q^{66} +(-5.06203 + 8.76769i) q^{67} +(-2.24768 + 3.59224i) q^{68} +(0.767760 - 4.90350i) q^{69} +(-5.89242 + 0.473789i) q^{70} -10.1268i q^{71} +(-7.74258 + 3.47167i) q^{72} +(4.57757 - 2.64286i) q^{73} +(-9.16188 - 2.63010i) q^{74} +(-4.28472 - 0.670876i) q^{75} +(-5.08481 - 0.180622i) q^{76} +(16.8099 + 2.77855i) q^{77} +(4.56763 + 6.50294i) q^{78} +(-9.11569 + 5.26295i) q^{79} +(-3.54016 + 5.23493i) q^{80} +(7.31835 + 5.23848i) q^{81} +(0.0292410 - 0.0282208i) q^{82} +(-4.95055 - 2.85820i) q^{83} +(-9.03463 + 1.54125i) q^{84} +(2.89893 - 1.67370i) q^{85} +(-2.53288 + 8.82322i) q^{86} +(0.254977 + 0.205732i) q^{87} +(13.5469 - 12.1756i) q^{88} +(4.15406 + 2.39835i) q^{89} +(6.68808 + 0.445952i) q^{90} +(3.02204 + 8.03393i) q^{91} +(-2.68753 - 5.06184i) q^{92} +(-4.66749 + 5.78474i) q^{93} +(-5.87220 - 6.08449i) q^{94} +(3.48079 + 2.00963i) q^{95} +(-4.74787 + 8.57075i) q^{96} +(4.11170 + 2.37389i) q^{97} +(-9.86494 - 0.826417i) q^{98} +(-18.3947 - 5.90501i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) $ 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9	$ 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9} + 16 q^{11} - 3 q^{12} + 7 q^{14} - 7 q^{16} - 18 q^{17} - 13 q^{18} - 6 q^{19} - 36 q^{20} - 16 q^{22} - 24 q^{24} + 156 q^{25} - 6 q^{26} + 16 q^{28} - 8 q^{30} + 13 q^{32} - 36 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 42 q^{41} + 31 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} + 9 q^{48} + 20 q^{49} + 15 q^{50} - 42 q^{51} - 12 q^{54} - 40 q^{56} - 26 q^{57} - 38 q^{58} + 18 q^{59} - 38 q^{60} - 8 q^{64} - 12 q^{65} - 21 q^{66} - 14 q^{67} - 42 q^{70} + 5 q^{72} + 18 q^{73} - 98 q^{74} - 48 q^{75} + 12 q^{76} - 33 q^{78} - 63 q^{80} + 8 q^{81} - 54 q^{82} - 6 q^{83} - 77 q^{84} + 26 q^{86} - 58 q^{88} - 66 q^{89} + 51 q^{90} + 2 q^{91} - 60 q^{92} + 9 q^{94} - 30 q^{96} + 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) $ 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9 + 16 * q^11 - 3 * q^12 + 7 * q^14 - 7 * q^16 - 18 * q^17 - 13 * q^18 - 6 * q^19 - 36 * q^20 - 16 * q^22 - 24 * q^24 + 156 * q^25 - 6 * q^26 + 16 * q^28 - 8 * q^30 + 13 * q^32 - 36 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 42 * q^41 + 31 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 + 9 * q^48 + 20 * q^49 + 15 * q^50 - 42 * q^51 - 12 * q^54 - 40 * q^56 - 26 * q^57 - 38 * q^58 + 18 * q^59 - 38 * q^60 - 8 * q^64 - 12 * q^65 - 21 * q^66 - 14 * q^67 - 42 * q^70 + 5 * q^72 + 18 * q^73 - 98 * q^74 - 48 * q^75 + 12 * q^76 - 33 * q^78 - 63 * q^80 + 8 * q^81 - 54 * q^82 - 6 * q^83 - 77 * q^84 + 26 * q^86 - 58 * q^88 - 66 * q^89 + 51 * q^90 + 2 * q^91 - 60 * q^92 + 9 * q^94 - 30 * q^96 + 6 * q^97 + 31 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.37231	+	0.341717i	−0.970368	+	0.241631i
$2$	−1.37231	+	0.341717i	−0.970368	+	0.241631i
$3$	1.71120	+	0.267930i	0.987963	+	0.154689i
$3$	1.71120	+	0.267930i	0.987963	+	0.154689i
$4$	1.76646	−	0.937883i	0.883229	−	0.468941i
$5$	−1.57990			−0.706551			−0.353276	−	0.935519i	$-0.614932\pi$
$5$	−1.57990			−0.706551			−0.353276	+	0.935519i	$0.614932\pi$
$6$	−2.43985	+	0.217065i	−0.996066	+	0.0886165i
$7$	−2.61033	−	0.431470i	−0.986613	−	0.163080i
$7$	−2.61033	−	0.431470i	−0.986613	−	0.163080i
$8$	−2.10363	+	1.89069i	−0.743747	+	0.668461i
$9$	2.85643	+	0.916964i	0.952142	+	0.305655i
$10$	2.16811	−	0.539878i	0.685615	−	0.170724i
$11$	−6.43974			−1.94165			−0.970827	−	0.239779i	$-0.922925\pi$
$11$	−6.43974			−1.94165			−0.970827	+	0.239779i	$0.922925\pi$
$12$	3.27405	−	1.13162i	0.945138	−	0.326671i
$13$	−1.62213	−	2.80961i	−0.449898	−	0.779247i	0.548481	−	0.836163i	$-0.315206\pi$
$13$	−1.62213	−	2.80961i	−0.449898	−	0.779247i	−0.998379	+	0.0569164i	$0.981873\pi$
$14$	3.72962	−	0.299886i	0.996783	−	0.0801479i
$15$	−2.70352	−	0.423301i	−0.698047	−	0.109296i
$16$	2.24075	−	3.31346i	0.560188	−	0.828365i
$17$	−1.83488	+	1.05937i	−0.445025	+	0.256935i	−0.705727	−	0.708484i	$-0.749379\pi$
$17$	−1.83488	+	1.05937i	−0.445025	+	0.256935i	0.260702	+	0.965419i	$0.416046\pi$
$18$	−4.23324	−	0.282267i	−0.997784	−	0.0665309i
$19$	−2.20317	−	1.27200i	−0.505443	−	0.291818i	0.225516	−	0.974240i	$-0.427593\pi$
$19$	−2.20317	−	1.27200i	−0.505443	−	0.291818i	−0.730958	+	0.682422i	$0.760927\pi$
$20$	−2.79082	+	1.48176i	−0.624047	+	0.331331i
$21$	−4.35120	−	1.43772i	−0.949510	−	0.313736i
$22$	8.83731	−	2.20057i	1.88412	−	0.469163i
$23$		−	2.86553i		−	0.597504i	−0.954331	−	0.298752i	$-0.903430\pi$
$23$		−	2.86553i		−	0.597504i	0.954331	−	0.298752i	$-0.0965703\pi$
$24$	−4.10632	+	2.67173i	−0.838199	+	0.545365i
$25$	−2.50393			−0.500785
$26$	3.18616	+	3.30135i	0.624857	+	0.647447i
$27$	4.64224	+	2.33443i	0.893400	+	0.449262i
$28$	−5.01571	+	1.68601i	−0.947880	+	0.318626i
$29$	0.163813	+	0.0945775i	0.0304193	+	0.0175626i	0.515133	−	0.857111i	$-0.327743\pi$
$29$	0.163813	+	0.0945775i	0.0304193	+	0.0175626i	−0.484713	+	0.874673i	$0.661076\pi$
$30$	3.85472	−	0.342941i	0.703772	−	0.0626121i
$31$	−2.14571	+	3.71647i	−0.385380	+	0.667498i	−0.991822	−	0.127630i	$-0.959263\pi$
$31$	−2.14571	+	3.71647i	−0.385380	+	0.667498i	0.606441	+	0.795128i	$0.292596\pi$
$32$	−1.94273	+	5.31279i	−0.343430	+	0.939178i
$33$	−11.0197	−	1.72540i	−1.91828	−	0.300353i
$34$	2.15602	−	2.08079i	0.369754	−	0.356853i
$35$	4.12406	+	0.681678i	0.697093	+	0.115225i
$36$	5.90577	−	1.05921i	0.984294	−	0.176536i
$37$	5.83709	+	3.37004i	0.959611	+	0.554032i	0.896053	−	0.443946i	$-0.146422\pi$
$37$	5.83709	+	3.37004i	0.959611	+	0.554032i	0.0635578	+	0.997978i	$0.479755\pi$
$38$	3.45810	+	0.992717i	0.560978	+	0.161040i
$39$	−2.02302	−	5.24244i	−0.323942	−	0.839462i
$40$	3.32353	−	2.98710i	0.525496	−	0.472302i
$41$	−0.0248856	+	0.0143677i	−0.00388648	+	0.00224386i	−0.501942	−	0.864901i	$-0.667381\pi$
$41$	−0.0248856	+	0.0143677i	−0.00388648	+	0.00224386i	0.498056	+	0.867145i	$0.334048\pi$
$42$	6.46248	+	0.486111i	0.997183	+	0.0750085i
$43$	3.24547	−	5.62132i	0.494930	−	0.857243i	−0.505053	−	0.863088i	$-0.668527\pi$
$43$	3.24547	−	5.62132i	0.494930	−	0.857243i	0.999983	+	0.00584491i	$0.00186050\pi$
$44$	−11.3755	+	6.03972i	−1.71493	+	0.910522i
$45$	−4.51286	−	1.44871i	−0.672738	−	0.215961i
$46$	0.979200	+	3.93239i	0.144375	+	0.579799i
$47$	2.98964	+	5.17821i	0.436084	+	0.755320i	0.997383	−	0.0722928i	$-0.0230316\pi$
$47$	2.98964	+	5.17821i	0.436084	+	0.755320i	−0.561299	+	0.827613i	$0.689698\pi$
$48$	4.72216	−	5.06964i	0.681584	−	0.731739i
$49$	6.62767	+	2.25256i	0.946810	+	0.321794i
$50$	3.43616	−	0.855635i	0.485946	−	0.121005i
$51$	−3.42369	+	1.32118i	−0.479413	+	0.185002i
$52$	−5.50052	−	3.44170i	−0.762785	−	0.477278i
$53$	−6.16601	+	3.55995i	−0.846967	+	0.488997i	−0.859626	−	0.510923i	$-0.829304\pi$
$53$	−6.16601	+	3.55995i	−0.846967	+	0.488997i	0.0126594	+	0.999920i	$0.495970\pi$
$54$	−7.16830	−	1.61723i	−0.975483	−	0.220077i
$55$	10.1741			1.37188
$56$	6.30696	−	4.02768i	0.842803	−	0.538222i
$57$	−3.42927	−	2.76695i	−0.454218	−	0.366492i
$58$	−0.257121	−	0.0738117i	−0.0337616	−	0.00969195i
$59$	−10.2662	−	5.92720i	−1.33655	−	0.771656i	−0.350254	−	0.936655i	$-0.613905\pi$
$59$	−10.2662	−	5.92720i	−1.33655	−	0.771656i	−0.986294	+	0.164999i	$0.947238\pi$
$60$	−5.17267	+	1.78784i	−0.667789	+	0.230810i
$61$	−7.03219	−	12.1801i	−0.900380	−	1.55950i	−0.827001	−	0.562200i	$-0.809955\pi$
$61$	−7.03219	−	12.1801i	−0.900380	−	1.55950i	−0.0733790	−	0.997304i	$-0.523378\pi$
$62$	1.67459	−	5.83337i	0.212673	−	0.740839i
$63$	−7.06058	−	3.62604i	−0.889550	−	0.456838i
$64$	0.850557	−	7.95466i	0.106320	−	0.994332i
$65$	2.56280	+	4.43890i	0.317876	+	0.550578i
$66$	15.7120	−	1.39784i	1.93402	−	0.172063i
$67$	−5.06203	+	8.76769i	−0.618425	+	1.07114i	0.371348	+	0.928494i	$0.378896\pi$
$67$	−5.06203	+	8.76769i	−0.618425	+	1.07114i	−0.989773	+	0.142650i	$0.954438\pi$
$68$	−2.24768	+	3.59224i	−0.272571	+	0.435623i
$69$	0.767760	−	4.90350i	0.0924275	−	0.590312i
$70$	−5.89242	+	0.473789i	−0.704278	+	0.0566286i
$71$		−	10.1268i		−	1.20183i	−0.799313	−	0.600915i	$-0.794803\pi$
$71$		−	10.1268i		−	1.20183i	0.799313	−	0.600915i	$-0.205197\pi$
$72$	−7.74258	+	3.47167i	−0.912471	+	0.409140i
$73$	4.57757	−	2.64286i	0.535764	−	0.309323i	−0.207597	−	0.978215i	$-0.566564\pi$
$73$	4.57757	−	2.64286i	0.535764	−	0.309323i	0.743360	+	0.668891i	$0.233231\pi$
$74$	−9.16188	−	2.63010i	−1.06505	−	0.305743i
$75$	−4.28472	−	0.670876i	−0.494757	−	0.0774661i
$76$	−5.08481	−	0.180622i	−0.583267	−	0.0207188i
$77$	16.8099	+	2.77855i	1.91566	+	0.316646i
$78$	4.56763	+	6.50294i	0.517183	+	0.736313i
$79$	−9.11569	+	5.26295i	−1.02560	+	0.592128i	−0.915720	−	0.401817i	$-0.868379\pi$
$79$	−9.11569	+	5.26295i	−1.02560	+	0.592128i	−0.109876	+	0.993945i	$0.535045\pi$
$80$	−3.54016	+	5.23493i	−0.395802	+	0.585283i
$81$	7.31835	+	5.23848i	0.813150	+	0.582054i
$82$	0.0292410	−	0.0282208i	0.00322913	−	0.00311646i
$83$	−4.95055	−	2.85820i	−0.543393	−	0.313728i	0.203060	−	0.979166i	$-0.434911\pi$
$83$	−4.95055	−	2.85820i	−0.543393	−	0.313728i	−0.746453	+	0.665438i	$0.768245\pi$
$84$	−9.03463	+	1.54125i	−0.985759	+	0.168164i
$85$	2.89893	−	1.67370i	0.314433	−	0.181538i
$86$	−2.53288	+	8.82322i	−0.273128	+	0.951432i
$87$	0.254977	+	0.205732i	0.0273364	+	0.0220567i
$88$	13.5469	−	12.1756i	1.44410	−	1.29792i
$89$	4.15406	+	2.39835i	0.440330	+	0.254224i	0.703737	−	0.710460i	$-0.251513\pi$
$89$	4.15406	+	2.39835i	0.440330	+	0.254224i	−0.263408	+	0.964685i	$0.584846\pi$
$90$	6.68808	+	0.445952i	0.704986	+	0.0470075i
$91$	3.02204	+	8.03393i	0.316796	+	0.842185i
$92$	−2.68753	−	5.06184i	−0.280194	−	0.527733i
$93$	−4.66749	+	5.78474i	−0.483997	+	0.599850i
$94$	−5.87220	−	6.08449i	−0.605671	−	0.627567i
$95$	3.48079	+	2.00963i	0.357121	+	0.206184i
$96$	−4.74787	+	8.57075i	−0.484577	+	0.874748i
$97$	4.11170	+	2.37389i	0.417480	+	0.241032i	0.693999	−	0.719976i	$-0.255847\pi$
$97$	4.11170	+	2.37389i	0.417480	+	0.241032i	−0.276518	+	0.961009i	$0.589181\pi$
$98$	−9.86494	−	0.826417i	−0.996509	−	0.0834807i
$99$	−18.3947	−	5.90501i	−1.84873	−	0.593476i
$100$	−4.42308	+	2.34839i	−0.442308	+	0.234839i
$101$	9.14375			0.909837			0.454918	−	0.890533i	$-0.349668\pi$
$101$	9.14375			0.909837			0.454918	+	0.890533i	$0.349668\pi$
$102$	4.24689	−	2.98300i	0.420505	−	0.295361i
$103$	−1.38834			−0.136797			−0.0683986	−	0.997658i	$-0.521789\pi$
$103$	−1.38834			−0.136797			−0.0683986	+	0.997658i	$0.521789\pi$
$104$	8.72449	+	2.84345i	0.855507	+	0.278823i
$105$	6.87445	+	2.27145i	0.670878	+	0.221670i
$106$	7.24517	−	6.99238i	0.703713	−	0.679160i
$107$	3.67455	−	6.36450i	0.355232	−	0.615279i	−0.631926	−	0.775029i	$-0.717735\pi$
$107$	3.67455	−	6.36450i	0.355232	−	0.615279i	0.987158	+	0.159749i	$0.0510686\pi$
$108$	10.3898	−	0.230201i	0.999755	−	0.0221511i
$109$	−2.54040	+	1.46670i	−0.243326	+	0.140485i	−0.616705	−	0.787195i	$-0.711533\pi$
$109$	−2.54040	+	1.46670i	−0.243326	+	0.140485i	0.373378	+	0.927679i	$0.378199\pi$
$110$	−13.9620	+	3.47667i	−1.33123	+	0.331488i
$111$	9.08550	+	7.33076i	0.862358	+	0.695805i
$112$	−7.27877	+	7.68242i	−0.687779	+	0.725920i
$113$	6.06291	+	10.5013i	0.570351	+	0.987876i	0.996530	+	0.0832375i	$0.0265260\pi$
$113$	6.06291	+	10.5013i	0.570351	+	0.987876i	−0.426179	+	0.904639i	$0.640141\pi$
$114$	5.65153	+	2.62527i	0.529314	+	0.245879i
$115$			4.52724i			0.422167i
$116$	0.378071	+	0.0134298i	0.0351031	+	0.00124693i
$117$	−2.05719	−	9.51290i	−0.190187	−	0.879468i
$118$	16.1138	+	4.62580i	1.48340	+	0.425840i
$119$	5.24674	−	1.97361i	0.480968	−	0.180921i
$120$	6.48756	−	4.22106i	0.592230	−	0.385328i
$121$	30.4703			2.77002
$122$	13.8125	+	14.3119i	1.25052	+	1.29573i
$123$	−0.0464338	+	0.0179185i	−0.00418680	+	0.00161565i
$124$	−0.304686	+	8.57742i	−0.0273617	+	0.770275i
$125$	11.8554			1.06038
$126$	10.9284	+	2.56333i	0.973577	+	0.228359i
$127$			13.3381i			1.18356i	0.806098	+	0.591782i	$0.201576\pi$
$127$			13.3381i			1.18356i	−0.806098	+	0.591782i	$0.798424\pi$
$128$	1.55102	+	11.2069i	0.137092	+	0.990558i
$129$	7.05978	−	8.74966i	0.621579	−	0.770364i
$130$	−5.03380	−	5.21579i	−0.441494	−	0.457455i
$131$		−	7.68223i		−	0.671200i	−0.942005	−	0.335600i	$-0.891061\pi$
$131$		−	7.68223i		−	0.671200i	0.942005	−	0.335600i	$-0.108939\pi$
$132$	−21.0841	+	7.28734i	−1.83513	+	0.634282i
$133$	5.20218	+	4.27095i	0.451087	+	0.370339i
$134$	3.95059	−	13.7618i	0.341279	−	1.18883i
$135$	−7.33427	−	3.68816i	−0.631233	−	0.317427i
$136$	1.85698	−	5.69773i	0.159235	−	0.488576i
$137$	−0.971559			−0.0830059			−0.0415029	−	0.999138i	$-0.513215\pi$
$137$	−0.971559			−0.0830059			−0.0415029	+	0.999138i	$0.513215\pi$
$138$	0.622007	+	6.99147i	0.0529487	+	0.595153i
$139$	−16.2508	+	9.38242i	−1.37838	+	0.795806i	−0.991964	−	0.126520i	$-0.959619\pi$
$139$	−16.2508	+	9.38242i	−1.37838	+	0.795806i	−0.386413	+	0.922326i	$0.626286\pi$
$140$	7.92431	−	2.66372i	0.669726	−	0.225126i
$141$	3.72849	+	9.66199i	0.313995	+	0.813686i
$142$	3.46050	+	13.8971i	0.290399	+	1.16622i
$143$	10.4461	+	18.0932i	0.873547	+	1.51303i
$144$	9.43887	−	7.40997i	0.786573	−	0.617498i
$145$	−0.258808	−	0.149423i	−0.0214928	−	0.0124089i
$146$	−5.37872	+	5.19105i	−0.445146	+	0.429615i
$147$	10.7378	+	5.63033i	0.885635	+	0.464382i
$148$	13.4717	+	0.478540i	1.10737	+	0.0393357i
$149$		−	23.0638i		−	1.88946i	−0.327849	−	0.944730i	$-0.606324\pi$
$149$		−	23.0638i		−	1.88946i	0.327849	−	0.944730i	$-0.393676\pi$
$150$	6.10921	−	0.543515i	0.498815	−	0.0443778i
$151$		−	2.59747i		−	0.211379i	−0.994399	−	0.105690i	$-0.966295\pi$
$151$		−	2.59747i		−	0.211379i	0.994399	−	0.105690i	$-0.0337050\pi$
$152$	7.03964	−	1.48970i	0.570990	−	0.120830i
$153$	−6.21262	+	1.34349i	−0.502260	+	0.108615i
$154$	−24.0178	+	1.93119i	−1.93541	+	0.155620i
$155$	3.39000	−	5.87165i	0.272291	−	0.471622i
$156$	−8.49037	−	7.36320i	−0.679773	−	0.589527i
$157$	−6.28385	+	10.8839i	−0.501506	+	0.868634i	0.498493	+	0.866894i	$0.333887\pi$
$157$	−6.28385	+	10.8839i	−0.501506	+	0.868634i	−0.999998	+	0.00173962i	$0.999446\pi$
$158$	10.7111	−	10.3374i	0.852129	−	0.822397i
$159$	−11.5051	+	4.43973i	−0.912415	+	0.352094i
$160$	3.06932	−	8.39367i	0.242651	−	0.663578i
$161$	−1.23639	+	7.47998i	−0.0974411	+	0.589505i
$162$	−11.8331	−	4.68800i	−0.929697	−	0.368324i
$163$	−7.58651	+	13.1402i	−0.594221	+	1.02922i	0.399435	+	0.916761i	$0.369206\pi$
$163$	−7.58651	+	13.1402i	−0.594221	+	1.02922i	−0.993656	+	0.112460i	$0.964127\pi$
$164$	−0.0304842	+	0.0487197i	−0.00238041	+	0.00380437i
$165$	17.4100	+	2.72595i	1.35537	+	0.212215i
$166$	7.77038	+	2.23064i	0.603098	+	0.173132i
$167$	−2.90273	−	5.02767i	−0.224620	−	0.389053i	0.731585	−	0.681750i	$-0.238781\pi$
$167$	−2.90273	−	5.02767i	−0.224620	−	0.389053i	−0.956205	+	0.292697i	$0.905447\pi$
$168$	11.8716	−	5.20236i	0.915916	−	0.401371i
$169$	1.23738	−	2.14320i	0.0951828	−	0.164861i
$170$	−3.40629	+	3.28744i	−0.261250	+	0.252135i
$171$	−5.12683	−	5.65362i	−0.392058	−	0.432343i
$172$	0.460851	−	12.9737i	0.0351395	−	0.989235i
$173$	−1.80858	−	3.13255i	−0.137504	−	0.238163i	0.789047	−	0.614332i	$-0.210575\pi$
$173$	−1.80858	−	3.13255i	−0.137504	−	0.238163i	−0.926551	+	0.376169i	$0.877241\pi$
$174$	−0.420209	−	0.195197i	−0.0318560	−	0.0147979i
$175$	6.53608	+	1.08037i	0.494081	+	0.0816682i
$176$	−14.4299	+	21.3378i	−1.08769	+	1.60840i
$177$	−15.9795	−	12.8933i	−1.20109	−	0.969117i
$178$	−6.52021	−	1.87176i	−0.488710	−	0.140294i
$179$	−1.68514	−	2.91875i	−0.125953	−	0.218157i	0.796152	−	0.605097i	$-0.206866\pi$
$179$	−1.68514	−	2.91875i	−0.125953	−	0.218157i	−0.922105	+	0.386939i	$0.873532\pi$
$180$	−9.33050	+	1.67345i	−0.695454	+	0.124732i
$181$	−22.6963			−1.68700			−0.843501	−	0.537128i	$-0.819509\pi$
$181$	−22.6963			−1.68700			−0.843501	+	0.537128i	$0.819509\pi$
$182$	−6.89250	−	9.99234i	−0.510906	−	0.740682i
$183$	−8.77009	−	22.7268i	−0.648304	−	1.68001i
$184$	5.41783	+	6.02802i	0.399408	+	0.444392i
$185$	−9.22199	−	5.32432i	−0.678015	−	0.391452i
$186$	4.42849	−	9.53341i	0.324713	−	0.699023i
$187$	11.8162	−	6.82207i	0.864084	−	0.498879i
$188$	10.1376	+	6.34317i	0.739363	+	0.462623i
$189$	−11.1106	−	8.09663i	−0.808174	−	0.588943i
$190$	−5.46344	−	1.56839i	−0.396360	−	0.113783i
$191$	−10.5634	+	6.09877i	−0.764339	+	0.441292i	−0.830852	−	0.556494i	$-0.812146\pi$
$191$	−10.5634	+	6.09877i	−0.764339	+	0.441292i	0.0665122	+	0.997786i	$0.478813\pi$
$192$	3.58676	−	13.3841i	0.258852	−	0.965917i
$193$	0.864535	−	1.49742i	0.0622306	−	0.107786i	−0.833232	−	0.552924i	$-0.813512\pi$
$193$	0.864535	−	1.49742i	0.0622306	−	0.107786i	0.895462	+	0.445138i	$0.146845\pi$
$194$	−6.45373	−	1.85267i	−0.463351	−	0.133014i
$195$	3.19616	+	8.28251i	0.228882	+	0.593123i
$196$	13.8201	−	2.23692i	0.987153	−	0.159780i
$197$			22.7268i			1.61922i	0.586971	+	0.809608i	$0.300320\pi$
$197$			22.7268i			1.61922i	−0.586971	+	0.809608i	$0.699680\pi$
$198$	27.2610	+	1.81772i	1.93735	+	0.129180i
$199$	0.0536797	+	0.0929760i	0.00380526	+	0.00659090i	0.867922	−	0.496701i	$-0.165455\pi$
$199$	0.0536797	+	0.0929760i	0.00380526	+	0.00659090i	−0.864117	+	0.503292i	$0.832122\pi$
$200$	5.26735	−	4.73416i	0.372458	−	0.334755i
$201$	−11.0113	+	13.6470i	−0.776676	+	0.962587i
$202$	−12.5480	+	3.12458i	−0.882877	+	0.219844i
$203$	−0.386799	−	0.317559i	−0.0271480	−	0.0222883i
$204$	−4.80870	+	5.54483i	−0.336677	+	0.388216i
$205$	0.0393167	−	0.0226995i	0.00274600	−	0.00158540i
$206$	1.90523	−	0.474420i	0.132744	−	0.0330544i
$207$	2.62759	−	8.18517i	0.182630	−	0.568909i
$208$	−12.9443	−	0.920778i	−0.897529	−	0.0638445i
$209$	14.1879	+	8.19137i	0.981395	+	0.566609i
$210$	−10.2101	−	0.768005i	−0.704561	−	0.0529974i
$211$	0.665635	+	1.15291i	0.0458242	+	0.0793699i	0.888028	−	0.459790i	$-0.152075\pi$
$211$	0.665635	+	1.15291i	0.0458242	+	0.0793699i	−0.842204	+	0.539160i	$0.818742\pi$
$212$	−7.55319	+	12.0715i	−0.518755	+	0.829074i
$213$	2.71327	−	17.3290i	0.185910	−	1.18736i
$214$	−2.86775	+	9.98971i	−0.196035	+	0.682883i
$215$	−5.12751	+	8.88111i	−0.349693	+	0.605686i
$216$	−14.1793	+	3.86626i	−0.964778	+	0.263066i
$217$	7.20456	−	8.77542i	0.489077	−	0.595715i
$218$	2.98502	−	2.88087i	0.202171	−	0.195117i
$219$	8.54125	−	3.29600i	0.577164	−	0.222723i
$220$	17.9722	−	9.54214i	1.21168	−	0.643331i
$221$	5.95285	+	3.43688i	0.400432	+	0.231189i
$222$	−14.9732	−	6.95538i	−1.00493	−	0.466815i
$223$	11.4772	−	19.8790i	0.768568	−	1.33120i	−0.169772	−	0.985483i	$-0.554303\pi$
$223$	11.4772	−	19.8790i	0.768568	−	1.33120i	0.938340	−	0.345715i	$-0.112364\pi$
$224$	7.36349	−	13.0299i	0.491994	−	0.870599i
$225$	−7.15228	−	2.29601i	−0.476819	−	0.153067i
$226$	−11.9086	−	12.3392i	−0.792151	−	0.820790i
$227$		−	13.8904i		−	0.921938i	−0.887416	−	0.460969i	$-0.847502\pi$
$227$		−	13.8904i		−	0.921938i	0.887416	−	0.460969i	$-0.152498\pi$
$228$	−8.65274	−	1.67145i	−0.573041	−	0.110695i
$229$	15.2683			1.00896			0.504478	−	0.863425i	$-0.331685\pi$
$229$	15.2683			1.00896			0.504478	+	0.863425i	$0.331685\pi$
$230$	−1.54704	−	6.21277i	−0.102009	−	0.409658i
$231$	28.0206	+	9.25853i	1.84362	+	0.609167i
$232$	−0.523420	+	0.110764i	−0.0343642	+	0.00727199i
$233$	−1.62112	+	2.80786i	−0.106203	+	0.183949i	−0.914229	−	0.405198i	$-0.867203\pi$
$233$	−1.62112	+	2.80786i	−0.106203	+	0.183949i	0.808026	+	0.589147i	$0.200536\pi$
$234$	6.07381	+	12.3516i	0.397058	+	0.807453i
$235$	−4.72333	−	8.18104i	−0.308116	−	0.533673i
$236$	−23.6939	−	0.841652i	−1.54234	−	0.0547869i
$237$	−17.0089	+	6.56360i	−1.10485	+	0.426352i
$238$	−6.52573	+	4.50131i	−0.423000	+	0.291776i
$239$	4.93370	−	2.84847i	0.319134	−	0.184252i	−0.331872	−	0.943324i	$-0.607680\pi$
$239$	4.93370	−	2.84847i	0.319134	−	0.184252i	0.651007	+	0.759072i	$0.274347\pi$
$240$	−7.46052	+	8.00951i	−0.481574	+	0.517012i
$241$		−	8.30028i		−	0.534668i	−0.963604	−	0.267334i	$-0.913857\pi$
$241$		−	8.30028i		−	0.534668i	0.963604	−	0.267334i	$-0.0861427\pi$
$242$	−41.8146	+	10.4122i	−2.68794	+	0.669322i
$243$	11.1196	+	10.9249i	0.713325	+	0.700833i
$244$	−23.8456	−	14.9203i	−1.52656	−	0.955174i
$245$	−10.4710	−	3.55881i	−0.668970	−	0.227364i
$246$	0.0575985	−	0.0404569i	0.00367234	−	0.00257944i
$247$			8.25343i			0.525153i
$248$	−2.51293	−	11.8750i	−0.159571	−	0.754062i
$249$	−7.70559	−	6.21736i	−0.488322	−	0.394009i
$250$	−16.2693	+	4.05120i	−1.02896	+	0.256221i
$251$		−	29.4543i		−	1.85914i	−0.368644	−	0.929571i	$-0.620178\pi$
$251$		−	29.4543i		−	1.85914i	0.368644	−	0.929571i	$-0.379822\pi$
$252$	−15.8730	+	0.216742i	−0.999907	+	0.0136535i
$253$			18.4533i			1.16015i
$254$	−4.55786	−	18.3040i	−0.285985	−	1.14849i
$255$	5.40908	−	2.08732i	0.338730	−	0.130713i
$256$	−5.95806	−	14.8493i	−0.372379	−	0.928081i
$257$		−	26.2140i		−	1.63518i	−0.575800	−	0.817591i	$-0.695309\pi$
$257$		−	26.2140i		−	1.63518i	0.575800	−	0.817591i	$-0.304691\pi$
$258$	−6.69828	+	14.4197i	−0.417017	+	0.897730i
$259$	−13.7827	−	11.3155i	−0.856413	−	0.703108i
$260$	8.69025	+	5.43753i	0.538946	+	0.337221i
$261$	0.381196	+	0.420364i	0.0235954	+	0.0260199i
$262$	2.62515	+	10.5424i	0.162182	+	0.651311i
$263$			28.3308i			1.74695i	0.486866	+	0.873477i	$0.338140\pi$
$263$			28.3308i			1.74695i	−0.486866	+	0.873477i	$0.661860\pi$
$264$	26.4436	−	17.2053i	1.62749	−	1.05891i
$265$	9.74166	−	5.62435i	0.598426	−	0.345501i
$266$	−8.59846	−	4.08339i	−0.527205	−	0.250369i
$267$	6.46585	+	5.21706i	0.395704	+	0.319279i
$268$	−0.718799	+	20.2354i	−0.0439076	+	1.23607i
$269$	−0.109451	−	0.189575i	−0.00667337	−	0.0115586i	0.862669	−	0.505768i	$-0.168791\pi$
$269$	−0.109451	−	0.189575i	−0.00667337	−	0.0115586i	−0.869343	+	0.494210i	$0.835458\pi$
$270$	11.3252	+	2.55505i	0.689229	+	0.155495i
$271$	−11.0321	+	19.1082i	−0.670155	+	1.16074i	0.307705	+	0.951482i	$0.400439\pi$
$271$	−11.0321	+	19.1082i	−0.670155	+	1.16074i	−0.977860	+	0.209261i	$0.932894\pi$
$272$	−0.601335	+	8.45360i	−0.0364613	+	0.512575i
$273$	3.01879	+	14.5574i	0.182706	+	0.881052i
$274$	1.33328	−	0.331998i	0.0805463	−	0.0200568i
$275$	16.1246			0.972352
$276$	−3.24269	−	9.38190i	−0.195187	−	0.564724i
$277$			9.92542i			0.596361i	0.954510	+	0.298180i	$0.0963797\pi$
$277$			9.92542i			0.596361i	−0.954510	+	0.298180i	$0.903620\pi$
$278$	19.0950	−	18.4288i	1.14524	−	1.10528i
$279$	−9.53693	+	8.64830i	−0.570961	+	0.517760i
$280$	−9.96435	+	6.36332i	−0.595484	+	0.380281i
$281$	4.58068	−	7.93397i	0.273260	−	0.473301i	−0.696434	−	0.717620i	$-0.745231\pi$
$281$	4.58068	−	7.93397i	0.273260	−	0.473301i	0.969695	+	0.244320i	$0.0785646\pi$
$282$	−8.41830	−	11.9851i	−0.501303	−	0.713704i
$283$	−16.3835	−	9.45902i	−0.973898	−	0.562280i	−0.0734758	−	0.997297i	$-0.523409\pi$
$283$	−16.3835	−	9.45902i	−0.973898	−	0.562280i	−0.900422	+	0.435017i	$0.856742\pi$
$284$	−9.49776	−	17.8886i	−0.563588	−	1.06149i
$285$	5.41789	+	4.37150i	0.320928	+	0.258945i
$286$	−20.5180	−	21.2598i	−1.21326	−	1.25712i
$287$	0.0711589	−	0.0267671i	0.00420038	−	0.00158001i
$288$	−10.4209	+	13.3942i	−0.614059	+	0.789260i
$289$	−6.25547	+	10.8348i	−0.367969	+	0.637341i
$290$	0.406224	+	0.116615i	0.0238543	+	0.00684786i
$291$	6.39992	+	5.16386i	0.375170	+	0.302711i
$292$	5.60739	−	8.96173i	0.328148	−	0.524445i
$293$	−4.55962	−	7.89749i	−0.266376	−	0.461376i	0.701547	−	0.712623i	$-0.252493\pi$
$293$	−4.55962	−	7.89749i	−0.266376	−	0.461376i	−0.967923	+	0.251246i	$0.919160\pi$
$294$	−16.6595	−	4.05728i	−0.971601	−	0.236625i
$295$	16.2196	+	9.36437i	0.944340	+	0.545215i
$296$	−18.6508	+	3.94680i	−1.08406	+	0.229403i
$297$	−29.8948	−	15.0331i	−1.73467	−	0.872311i
$298$	7.88130	+	31.6506i	0.456551	+	1.83347i
$299$	−8.05103	+	4.64826i	−0.465603	+	0.268816i
$300$	−8.19799	+	2.83349i	−0.473311	+	0.163592i
$301$	−10.8972	+	13.2732i	−0.628103	+	0.765054i
$302$	0.887602	+	3.56454i	0.0510757	+	0.205116i
$303$	15.6468	+	2.44988i	0.898885	+	0.140742i
$304$	−9.15150	+	4.44989i	−0.524875	+	0.255219i
$305$	11.1101	+	19.2433i	0.636165	+	1.10187i
$306$	8.06653	−	3.96664i	0.461133	−	0.226758i
$307$		−	30.0655i		−	1.71593i	−0.513707	−	0.857966i	$-0.671728\pi$
$307$		−	30.0655i		−	1.71593i	0.513707	−	0.857966i	$-0.328272\pi$
$308$	32.2999	−	10.8575i	1.84046	−	0.618662i
$309$	−2.37573	−	0.371978i	−0.135151	−	0.0211611i
$310$	−2.64568	+	9.21613i	−0.150264	+	0.523441i
$311$	15.0047	−	25.9888i	0.850836	−	1.47369i	−0.0296181	−	0.999561i	$-0.509429\pi$
$311$	15.0047	−	25.9888i	0.850836	−	1.47369i	0.880455	−	0.474131i	$-0.157238\pi$
$312$	14.1675	+	7.20327i	0.802078	+	0.407805i
$313$	−5.52085	+	3.18747i	−0.312057	+	0.180166i	−0.647847	−	0.761771i	$-0.724330\pi$
$313$	−5.52085	+	3.18747i	−0.312057	+	0.180166i	0.335790	+	0.941937i	$0.390997\pi$
$314$	4.90414	−	17.0834i	0.276757	−	0.964074i
$315$	11.1550	+	5.72877i	0.628513	+	0.322780i
$316$	−11.1665	+	17.8462i	−0.628163	+	1.00393i
$317$	0.305703	−	0.176498i	0.0171700	−	0.00991310i	−0.491390	−	0.870939i	$-0.663511\pi$
$317$	0.305703	−	0.176498i	0.0171700	−	0.00991310i	0.508560	+	0.861026i	$0.330178\pi$
$318$	14.2714	−	10.0242i	0.800302	−	0.562128i
$319$	−1.05491	−	0.609054i	−0.0590638	−	0.0341005i
$320$	−1.34379	+	12.5675i	−0.0751203	+	0.702547i
$321$	7.99313	−	9.90643i	0.446133	−	0.552923i
$322$	−0.859331	−	10.6873i	−0.0478887	−	0.595582i
$323$	5.39009			0.299913
$324$	17.8407	+	2.38980i	0.991147	+	0.132767i
$325$	4.06170	+	7.03507i	0.225302	+	0.390235i
$326$	5.92079	−	20.6249i	0.327922	−	1.14231i
$327$	−4.74011	+	1.82917i	−0.262129	+	0.101154i
$328$	0.0251853	−	0.0772754i	0.00139062	−	0.00426682i
$329$	−5.56972	−	14.8068i	−0.307069	−	0.816325i
$330$	−24.8234	+	2.20845i	−1.36648	+	0.121571i
$331$	13.3257	+	23.0807i	0.732445	+	1.26863i	0.955835	+	0.293902i	$0.0949540\pi$
$331$	13.3257	+	23.0807i	0.732445	+	1.26863i	−0.223391	+	0.974729i	$0.571713\pi$
$332$	−11.4256	−	0.405859i	−0.627061	−	0.0222744i
$333$	13.5830	+	14.9787i	0.744344	+	0.820827i
$334$	5.70148	+	5.90760i	0.311971	+	0.323250i
$335$	7.99748	−	13.8521i	0.436949	−	0.756818i
$336$	−14.5138	+	11.1960i	−0.791792	+	0.610791i
$337$	−0.598894	−	1.03731i	−0.0326238	−	0.0565061i	0.849253	−	0.527987i	$-0.177053\pi$
$337$	−0.598894	−	1.03731i	−0.0326238	−	0.0565061i	−0.881876	+	0.471481i	$0.843720\pi$
$338$	−0.965694	+	3.36396i	−0.0525268	+	0.182975i
$339$	7.56127	+	19.5942i	0.410672	+	1.06421i
$340$	3.55110	−	5.67537i	0.192586	−	0.307790i
$341$	13.8178	−	23.9331i	0.748276	−	1.29605i
$342$	8.96752	+	6.00658i	0.484908	+	0.324798i
$343$	−16.3285	−	8.73957i	−0.881656	−	0.471892i
$344$	3.80091	+	17.9614i	0.204931	+	0.968413i
$345$	−1.21298	+	7.74702i	−0.0653047	+	0.417086i
$346$	3.55237	+	3.68080i	0.190977	+	0.197881i
$347$	−15.2800	+	26.4657i	−0.820271	+	1.42075i	0.0852099	+	0.996363i	$0.472844\pi$
$347$	−15.2800	+	26.4657i	−0.820271	+	1.42075i	−0.905481	+	0.424388i	$0.860489\pi$
$348$	0.643359	+	0.124278i	0.0344876	+	0.00666199i
$349$	−4.29724	+	7.44303i	−0.230026	+	0.398416i	−0.957815	−	0.287384i	$-0.907214\pi$
$349$	−4.29724	+	7.44303i	−0.230026	+	0.398416i	0.727790	+	0.685800i	$0.240548\pi$
$350$	−9.33869	+	0.750892i	−0.499174	+	0.0401369i
$351$	−0.971474	−	16.8297i	−0.0518534	−	0.898301i
$352$	12.5107	−	34.2130i	0.666823	−	1.82356i
$353$			16.9245i			0.900799i	0.892827	+	0.450399i	$0.148718\pi$
$353$			16.9245i			0.900799i	−0.892827	+	0.450399i	$0.851282\pi$
$354$	26.3347	+	12.2331i	1.39967	+	0.650180i
$355$			15.9993i			0.849155i
$356$	9.58735	+	0.340561i	0.508128	+	0.0180497i
$357$	9.50703	−	1.97149i	0.503165	−	0.104342i
$358$	3.30992	+	3.42958i	0.174935	+	0.181259i
$359$	−17.3940	−	10.0424i	−0.918020	−	0.530019i	−0.0350169	−	0.999387i	$-0.511149\pi$
$359$	−17.3940	−	10.0424i	−0.918020	−	0.530019i	−0.883003	+	0.469368i	$0.844482\pi$
$360$	12.2325	−	5.48488i	0.644708	−	0.289079i
$361$	−6.26402	−	10.8496i	−0.329685	−	0.571031i
$362$	31.1463	−	7.75571i	1.63701	−	0.407631i
$363$	52.1408	+	8.16389i	2.73668	+	0.428493i
$364$	12.8732	+	11.3573i	0.674738	+	0.595283i
$365$	−7.23209	+	4.17545i	−0.378545	+	0.218553i
$366$	19.8014	+	28.1913i	1.03504	+	1.47358i
$367$	−31.9516			−1.66786			−0.833931	−	0.551869i	$-0.813915\pi$
$367$	−31.9516			−1.66786			−0.833931	+	0.551869i	$0.813915\pi$
$368$	−9.49482	−	6.42094i	−0.494952	−	0.334715i
$369$	−0.0842586	+	0.0182211i	−0.00438633	+	0.000948553i
$370$	14.4748	+	4.15529i	0.752511	+	0.216023i
$371$	17.6314	−	6.63220i	0.915374	−	0.344327i
$372$	−2.81953	+	14.5961i	−0.146186	+	0.756771i
$373$		−	21.9618i		−	1.13714i	−0.822636	−	0.568569i	$-0.807497\pi$
$373$		−	21.9618i		−	1.13714i	0.822636	−	0.568569i	$-0.192503\pi$
$374$	−13.8842	+	13.3998i	−0.717935	+	0.692886i
$375$	20.2870	+	3.17642i	1.04762	+	0.164030i
$376$	−16.0795	−	5.24057i	−0.829239	−	0.270262i
$377$		−	0.613669i		−	0.0316055i
$378$	18.0139	+	7.31441i	0.926533	+	0.376212i
$379$	−8.88209			−0.456243			−0.228121	−	0.973633i	$-0.573258\pi$
$379$	−8.88209			−0.456243			−0.228121	+	0.973633i	$0.573258\pi$
$380$	8.03347	+	0.285364i	0.412108	+	0.0146389i
$381$	−3.57367	+	22.8242i	−0.183085	+	1.16932i
$382$	12.4122	−	11.9791i	0.635061	−	0.612903i
$383$	−27.6820			−1.41448			−0.707241	−	0.706972i	$-0.750061\pi$
$383$	−27.6820			−1.41448			−0.707241	+	0.706972i	$0.750061\pi$
$384$	−0.348555	+	19.5928i	−0.0177871	+	0.999842i
$385$	−26.5578	−	4.38983i	−1.35351	−	0.223726i
$386$	−0.674714	+	2.35034i	−0.0343421	+	0.119629i
$387$	14.4250	−	13.0809i	0.733264	−	0.664940i
$388$	9.48959	+	0.337089i	0.481761	+	0.0171131i
$389$		−	19.6465i		−	0.996116i	−0.867144	−	0.498058i	$-0.834047\pi$
$389$		−	19.6465i		−	0.996116i	0.867144	−	0.498058i	$-0.165953\pi$
$390$	−7.21639	−	10.2740i	−0.365416	−	0.520243i
$391$	3.03566	+	5.25791i	0.153520	+	0.265904i
$392$	−18.2011	+	7.79232i	−0.919294	+	0.393572i
$393$	2.05830	−	13.1458i	0.103827	−	0.663120i
$394$	−7.76613	−	31.1881i	−0.391252	−	1.57124i
$395$	14.4019	−	8.31491i	0.724636	−	0.418369i
$396$	−38.0316	+	6.82107i	−1.91116	+	0.342772i
$397$	10.9555	−	18.9756i	0.549843	−	0.952356i	−0.448442	−	0.893812i	$-0.648021\pi$
$397$	10.9555	−	18.9756i	0.549843	−	0.952356i	0.998285	−	0.0585438i	$-0.0186457\pi$
$398$	−0.105437	−	0.109248i	−0.00528506	−	0.00547613i
$399$	7.75768	+	8.70229i	0.388370	+	0.435659i
$400$	−5.61068	+	8.29666i	−0.280534	+	0.414833i
$401$	−31.7377			−1.58490			−0.792452	−	0.609934i	$-0.791196\pi$
$401$	−31.7377			−1.58490			−0.792452	+	0.609934i	$0.791196\pi$
$402$	10.4474	−	22.4907i	0.521071	−	1.12173i
$403$	13.9225			0.693528
$404$	16.1520	−	8.57576i	0.803595	−	0.426660i
$405$	−11.5622	−	8.27626i	−0.574533	−	0.411251i
$406$	0.639323	+	0.303613i	0.0317291	+	0.0150681i
$407$	−37.5893	−	21.7022i	−1.86323	−	1.07574i
$408$	4.70426	−	9.25243i	0.232896	−	0.458064i
$409$	−20.1056	−	11.6080i	−0.994157	−	0.573977i	−0.0876429	−	0.996152i	$-0.527933\pi$
$409$	−20.1056	−	11.6080i	−0.994157	−	0.573977i	−0.906514	+	0.422175i	$0.861267\pi$
$410$	−0.0461978	+	0.0445859i	−0.00228155	+	0.00220194i
$411$	−1.66253	−	0.260310i	−0.0820068	−	0.0128401i
$412$	−2.45245	+	1.30210i	−0.120823	+	0.0641499i
$413$	24.2408	+	19.9015i	1.19281	+	0.979290i
$414$	−0.808843	+	12.1305i	−0.0397525	+	0.596180i
$415$	7.82136	+	4.51566i	0.383935	+	0.221665i
$416$	18.0783	−	3.15972i	0.886360	−	0.154918i
$417$	−30.3223	+	11.7011i	−1.48489	+	0.573007i
$418$	−22.2693	−	6.39284i	−1.08923	−	0.312684i
$419$	10.9299	−	6.31037i	0.533960	−	0.308282i	−0.208668	−	0.977987i	$-0.566913\pi$
$419$	10.9299	−	6.31037i	0.533960	−	0.308282i	0.742627	+	0.669705i	$0.233579\pi$
$420$	14.2738	−	2.43501i	0.696489	−	0.118817i
$421$	12.3281	+	7.11761i	0.600833	+	0.346891i	0.769369	−	0.638804i	$-0.220571\pi$
$421$	12.3281	+	7.11761i	0.600833	+	0.346891i	−0.168536	+	0.985695i	$0.553904\pi$
$422$	−1.30743	−	1.35469i	−0.0636446	−	0.0659455i
$423$	3.79146	+	17.5326i	0.184347	+	0.852464i
$424$	6.24027	−	19.1469i	0.303054	−	0.929854i
$425$	4.59441	−	2.65259i	0.222862	−	0.128669i
$426$	2.19818	+	24.7079i	0.106502	+	1.19710i
$427$	13.1010	+	34.8283i	0.634002	+	1.68546i
$428$	0.521779	−	14.6889i	0.0252211	−	0.710016i
$429$	13.0277	+	33.7599i	0.628983	+	1.62994i
$430$	4.00169	−	13.9398i	0.192979	−	0.672235i
$431$	15.7997	−	9.12197i	0.761045	−	0.439390i	−0.0686256	−	0.997642i	$-0.521861\pi$
$431$	15.7997	−	9.12197i	0.761045	−	0.439390i	0.829671	+	0.558253i	$0.188528\pi$
$432$	18.1372	−	10.1510i	0.872625	−	0.488391i
$433$		−	9.24491i		−	0.444282i	−0.975015	−	0.222141i	$-0.928696\pi$
$433$		−	9.24491i		−	0.444282i	0.975015	−	0.222141i	$-0.0713045\pi$
$434$	−6.88816	+	14.5045i	−0.330642	+	0.696239i
$435$	−0.402838	−	0.325035i	−0.0193146	−	0.0155842i
$436$	−3.11192	+	4.97347i	−0.149034	+	0.238186i
$437$	−3.64496	+	6.31326i	−0.174362	+	0.302004i
$438$	−10.5949	+	7.44182i	−0.506245	+	0.355584i
$439$	−0.829288	−	1.43637i	−0.0395797	−	0.0685541i	0.845557	−	0.533885i	$-0.179269\pi$
$439$	−0.829288	−	1.43637i	−0.0395797	−	0.0685541i	−0.885137	+	0.465331i	$0.845935\pi$
$440$	−21.4026	+	19.2362i	−1.02033	+	0.917048i
$441$	16.8659	+	12.5116i	0.803140	+	0.595791i
$442$	−9.34358	−	2.68226i	−0.444429	−	0.127582i
$443$	6.92473	+	11.9940i	0.329004	+	0.569851i	0.982314	−	0.187239i	$-0.0599538\pi$
$443$	6.92473	+	11.9940i	0.329004	+	0.569851i	−0.653311	+	0.757090i	$0.726620\pi$
$444$	22.9246	+	4.42834i	1.08795	+	0.210160i
$445$	−6.56299	−	3.78914i	−0.311116	−	0.179623i
$446$	−8.95720	+	31.2021i	−0.424135	+	1.47746i
$447$	6.17948	−	39.4668i	0.292279	−	1.86672i
$448$	−5.65243	+	20.3973i	−0.267052	+	0.963682i
$449$	6.58369			0.310704			0.155352	−	0.987859i	$-0.450349\pi$
$449$	6.58369			0.310704			0.155352	+	0.987859i	$0.450349\pi$
$450$	10.5997	+	0.706775i	0.499676	+	0.0333177i
$451$	0.160257	−	0.0925243i	0.00754620	−	0.00435680i
$452$	20.5588	+	12.8638i	0.967007	+	0.605060i
$453$	0.695941	−	4.44480i	0.0326981	−	0.208835i
$454$	4.74659	+	19.0619i	0.222769	+	0.894620i
$455$	−4.77451	−	12.6928i	−0.223832	−	0.595047i
$456$	12.4454	−	0.663043i	0.582809	−	0.0310498i
$457$	3.58343	+	6.20668i	0.167626	+	0.290336i	0.937585	−	0.347757i	$-0.113057\pi$
$457$	3.58343	+	6.20668i	0.167626	+	0.290336i	−0.769959	+	0.638093i	$0.779723\pi$
$458$	−20.9528	+	5.21743i	−0.979059	+	0.243795i
$459$	−10.9910	+	0.634443i	−0.513016	+	0.0296133i
$460$	4.24602	+	7.99718i	0.197972	+	0.372870i
$461$	−14.5335	+	25.1728i	−0.676894	+	1.17241i	0.299018	+	0.954248i	$0.403341\pi$
$461$	−14.5335	+	25.1728i	−0.676894	+	1.17241i	−0.975911	+	0.218167i	$0.929992\pi$
$462$	−41.6167	−	3.13043i	−1.93618	−	0.145641i
$463$	24.6921	−	14.2560i	1.14754	−	0.662533i	0.199253	−	0.979948i	$-0.436148\pi$
$463$	24.6921	−	14.2560i	1.14754	−	0.662533i	0.948287	+	0.317415i	$0.102815\pi$
$464$	0.680443	−	0.330863i	0.0315888	−	0.0153600i
$465$	7.37416	−	9.13929i	0.341968	−	0.423825i
$466$	1.26518	−	4.40721i	0.0586083	−	0.204160i
$467$	−0.742356	−	0.428599i	−0.0343521	−	0.0198332i	0.482726	−	0.875772i	$-0.339647\pi$
$467$	−0.742356	−	0.428599i	−0.0343521	−	0.0198332i	−0.517078	+	0.855938i	$0.672980\pi$
$468$	−12.5559	−	14.8747i	−0.580397	−	0.687585i
$469$	16.9966	−	20.7025i	0.784829	−	0.955952i
$470$	9.27747	+	9.61287i	0.427938	+	0.443409i
$471$	−13.6691	+	16.9410i	−0.629838	+	0.780600i
$472$	32.8029	−	6.94160i	1.50988	−	0.319513i
$473$	−20.9000	+	36.1998i	−0.960982	+	1.66447i
$474$	21.0985	−	14.8195i	0.969088	−	0.680683i
$475$	5.51658	+	3.18500i	0.253118	+	0.146138i
$476$	7.41714	−	8.40713i	0.339964	−	0.385340i
$477$	−20.8771	+	4.51472i	−0.955897	+	0.206715i
$478$	−5.79718	+	5.59491i	−0.265157	+	0.255905i
$479$	−21.0909			−0.963668			−0.481834	−	0.876263i	$-0.660029\pi$
$479$	−21.0909			−0.963668			−0.481834	+	0.876263i	$0.660029\pi$
$480$	7.50114	−	13.5409i	0.342379	−	0.618055i
$481$		−	21.8666i		−	0.997032i
$482$	2.83635	+	11.3905i	0.129192	+	0.518825i
$483$	−4.11982	+	12.4685i	−0.187458	+	0.567336i
$484$	53.8244	−	28.5775i	2.44657	−	1.29898i
$485$	−6.49607	−	3.75051i	−0.294971	−	0.170302i
$486$	−18.9928	−	11.1926i	−0.861531	−	0.507705i
$487$	19.2411	−	11.1088i	0.871897	−	0.503390i	0.00391861	−	0.999992i	$-0.498753\pi$
$487$	19.2411	−	11.1088i	0.871897	−	0.503390i	0.867978	+	0.496603i	$0.165419\pi$
$488$	37.8220	+	12.3268i	1.71212	+	0.558008i
$489$	−16.5027	+	20.4529i	−0.746278	+	0.924913i
$490$	15.5856	+	1.30565i	0.704085	+	0.0589834i
$491$	9.70907	+	16.8166i	0.438164	+	0.758923i	0.997548	−	0.0699860i	$-0.0222955\pi$
$491$	9.70907	+	16.8166i	0.438164	+	0.758923i	−0.559384	+	0.828909i	$0.688962\pi$
$492$	−0.0652180	+	0.0752017i	−0.00294026	+	0.00339035i
$493$	−0.400770			−0.0180498
$494$	−2.82034	−	11.3262i	−0.126893	−	0.509592i
$495$	29.0617	+	9.32931i	1.30622	+	0.419321i
$496$	7.50640	+	15.4374i	0.337047	+	0.693160i
$497$	−4.36941	+	26.4343i	−0.195995	+	1.18574i
$498$	12.6990	+	5.89900i	0.569057	+	0.264340i
$499$	−34.7324			−1.55483			−0.777417	−	0.628986i	$-0.783470\pi$
$499$	−34.7324			−1.55483			−0.777417	+	0.628986i	$0.783470\pi$
$500$	20.9421	−	11.1190i	0.936560	−	0.497257i
$501$	−3.62009	−	9.38109i	−0.161734	−	0.419116i
$502$	10.0651	+	40.4204i	0.449225	+	1.80405i
$503$	13.1738			0.587389			0.293695	−	0.955899i	$-0.405115\pi$
$503$	13.1738			0.587389			0.293695	+	0.955899i	$0.405115\pi$
$504$	21.7086	−	5.72152i	0.966979	−	0.254857i
$505$	−14.4462			−0.642846
$506$	−6.30580	−	25.3236i	−0.280327	−	1.12577i
$507$	2.69163	−	3.33592i	0.119539	−	0.148153i
$508$	12.5096	+	23.5612i	0.555022	+	1.04536i
$509$	−31.7274			−1.40629			−0.703146	−	0.711046i	$-0.748222\pi$
$509$	−31.7274			−1.40629			−0.703146	+	0.711046i	$0.748222\pi$
$510$	−6.70965	+	4.71283i	−0.297108	+	0.208688i
$511$	−13.0893	+	4.92366i	−0.579036	+	0.217810i
$512$	13.2506	+	18.3418i	0.585597	+	0.810602i
$513$	−7.25826	−	11.0481i	−0.320460	−	0.487786i
$514$	8.95776	+	35.9736i	0.395110	+	1.58673i
$515$	2.19343			0.0966543
$516$	4.26465	−	22.0772i	0.187741	−	0.971892i
$517$	−19.2525	−	33.3464i	−0.846725	−	1.46657i
$518$	22.7807	+	10.8185i	1.00093	+	0.475339i
$519$	−2.25554	−	5.84500i	−0.0990073	−	0.256567i
$520$	−13.7838	−	4.49236i	−0.604460	−	0.197003i
$521$	−15.8002	+	9.12228i	−0.692221	+	0.399654i	−0.804444	−	0.594029i	$-0.797536\pi$
$521$	−15.8002	+	9.12228i	−0.692221	+	0.399654i	0.112222	+	0.993683i	$0.464203\pi$
$522$	−0.666764	−	0.446608i	−0.0291835	−	0.0195475i
$523$	2.29531	+	1.32520i	0.100367	+	0.0579469i	0.549343	−	0.835597i	$-0.314878\pi$
$523$	2.29531	+	1.32520i	0.100367	+	0.0579469i	−0.448976	+	0.893544i	$0.648211\pi$
$524$	−7.20503	−	13.5703i	−0.314753	−	0.592823i
$525$	10.8951	+	3.59994i	0.475501	+	0.157114i
$526$	−9.68113	−	38.8786i	−0.422117	−	1.69519i
$527$		−	9.09240i		−	0.396071i
$528$	−30.4095	+	32.6472i	−1.32340	+	1.42079i
$529$	14.7888			0.642989
$530$	−11.4466	+	11.0472i	−0.497210	+	0.479861i
$531$	−23.8897	−	26.3444i	−1.03672	−	1.14325i
$532$	13.1951	+	2.66542i	0.572080	+	0.115561i
$533$	0.0807354	+	0.0466126i	0.00349704	+	0.00201902i
$534$	−10.6559	−	4.94992i	−0.461126	−	0.214204i
$535$	−5.80540	+	10.0553i	−0.250989	+	0.434727i
$536$	−5.92836	−	28.0148i	−0.256066	−	1.21005i
$537$	−2.10160	−	5.44607i	−0.0906905	−	0.235015i
$538$	0.214982	+	0.222754i	0.00926854	+	0.00960362i
$539$	−42.6805	−	14.5059i	−1.83838	−	0.624813i
$540$	−16.4147	+	0.363693i	−0.706378	+	0.0156509i
$541$	−0.353156	−	0.203894i	−0.0151833	−	0.00876611i	0.492389	−	0.870375i	$-0.336124\pi$
$541$	−0.353156	−	0.203894i	−0.0151833	−	0.00876611i	−0.507572	+	0.861609i	$0.669457\pi$
$542$	8.60989	−	29.9923i	0.369826	−	1.28828i
$543$	−38.8379	−	6.08101i	−1.66670	−	0.260961i
$544$	−2.06352	−	11.8064i	−0.0884729	−	0.506197i
$545$	4.01357	−	2.31724i	0.171923	−	0.0992595i
$546$	−9.11722	−	18.9456i	−0.390181	−	0.810798i
$547$	−5.83895	+	10.1134i	−0.249656	+	0.432416i	−0.963430	−	0.267959i	$-0.913651\pi$
$547$	−5.83895	+	10.1134i	−0.249656	+	0.432416i	0.713775	+	0.700375i	$0.246984\pi$
$548$	−1.71622	+	0.911208i	−0.0733132	+	0.0389249i
$549$	−8.91822	−	41.2399i	−0.380620	−	1.76008i
$550$	−22.1280	+	5.51007i	−0.943540	+	0.234950i
$551$	−0.240606	−	0.416741i	−0.0102501	−	0.0177538i
$552$	7.65592	+	11.7668i	0.325858	+	0.500827i
$553$	26.0658	−	9.80489i	1.10843	−	0.416947i
$554$	−3.39169	−	13.6207i	−0.144099	−	0.578690i
$555$	−14.3542	−	11.5818i	−0.609300	−	0.491622i
$556$	−19.9068	+	31.8150i	−0.844236	+	1.34926i
$557$	12.9292	−	7.46469i	0.547829	−	0.316289i	−0.200417	−	0.979711i	$-0.564230\pi$
$557$	12.9292	−	7.46469i	0.547829	−	0.316289i	0.748246	+	0.663422i	$0.230896\pi$
$558$	10.1323	−	15.1271i	0.428936	−	0.640380i
$559$	−21.0583			−0.890672
$560$	11.4997	−	12.1374i	0.485951	−	0.512900i
$561$	22.0477	−	8.50804i	0.930855	−	0.359210i
$562$	−3.57493	+	12.4531i	−0.150799	+	0.525304i
$563$	4.29182	+	2.47789i	0.180879	+	0.104430i	0.587706	−	0.809075i	$-0.300031\pi$
$563$	4.29182	+	2.47789i	0.180879	+	0.104430i	−0.406827	+	0.913505i	$0.633365\pi$
$564$	15.6480	+	13.5706i	0.658901	+	0.571426i
$565$	−9.57877	−	16.5909i	−0.402982	−	0.697985i
$566$	25.7155	+	7.38216i	1.08090	+	0.310295i
$567$	−16.8431	−	16.8318i	−0.707343	−	0.706870i
$568$	19.1467	+	21.3031i	0.803377	+	0.893858i
$569$	6.08386	+	10.5375i	0.255048	+	0.441757i	0.964909	−	0.262586i	$-0.0845752\pi$
$569$	6.08386	+	10.5375i	0.255048	+	0.441757i	−0.709860	+	0.704343i	$0.751242\pi$
$570$	−8.92883	−	4.14765i	−0.373988	−	0.173726i
$571$	−6.47017	+	11.2067i	−0.270768	+	0.468985i	−0.969059	−	0.246830i	$-0.920611\pi$
$571$	−6.47017	+	11.2067i	−0.270768	+	0.468985i	0.698290	+	0.715815i	$0.253944\pi$
$572$	35.4219	+	22.1636i	1.48106	+	0.926709i
$573$	−19.7101	+	7.60599i	−0.823402	+	0.317745i
$574$	−0.0885052	+	0.0610489i	−0.00369413	+	0.00254813i
$575$			7.17507i			0.299221i
$576$	9.72369	−	21.9420i	0.405154	−	0.914249i
$577$	−18.3981	+	10.6222i	−0.765924	+	0.442206i	−0.831419	−	0.555647i	$-0.812471\pi$
$577$	−18.3981	+	10.6222i	−0.765924	+	0.442206i	0.0654948	+	0.997853i	$0.479137\pi$
$578$	4.88200	−	17.0063i	0.203064	−	0.707368i
$579$	1.88060	−	2.33075i	0.0781549	−	0.0968627i
$580$	−0.597314	−	0.0212177i	−0.0248021	−	0.000881019i
$581$	11.6894	+	9.59687i	0.484956	+	0.398145i
$582$	−10.5472	−	4.89944i	−0.437197	−	0.203088i
$583$	39.7075	−	22.9251i	1.64452	−	0.949463i
$584$	−4.63269	+	14.2144i	−0.191702	+	0.588196i
$585$	3.25014	+	15.0294i	0.134377	+	0.621389i
$586$	8.95591	+	9.27969i	0.369965	+	0.383341i
$587$	9.71740	+	5.61034i	0.401080	+	0.231564i	0.686950	−	0.726705i	$-0.258949\pi$
$587$	9.71740	+	5.61034i	0.401080	+	0.231564i	−0.285870	+	0.958268i	$0.592283\pi$
$588$	24.2484	−	0.125000i	0.999987	−	0.00515490i
$589$	9.45473	−	5.45869i	0.389575	−	0.224922i
$590$	−25.4582	−	7.30829i	−1.04810	−	0.300878i
$591$	−6.08918	+	38.8901i	−0.250475	+	1.59973i
$592$	24.2460	−	11.7895i	0.996503	−	0.484547i
$593$	−17.1728	−	9.91473i	−0.705203	−	0.407149i	0.104079	−	0.994569i	$-0.466810\pi$
$593$	−17.1728	−	9.91473i	−0.705203	−	0.407149i	−0.809282	+	0.587420i	$0.800144\pi$
$594$	46.1620	+	10.4145i	1.89405	+	0.427313i
$595$	−8.28931	+	3.11810i	−0.339829	+	0.127830i
$596$	−21.6311	−	40.7413i	−0.886046	−	1.66883i
$597$	0.0669458	+	0.173483i	0.00273991	+	0.00710019i
$598$	9.46010	−	9.13003i	0.386852	−	0.373355i
$599$	−15.6899	−	9.05856i	−0.641071	−	0.370123i	0.143956	−	0.989584i	$-0.454018\pi$
$599$	−15.6899	−	9.05856i	−0.641071	−	0.370123i	−0.785027	+	0.619461i	$0.787351\pi$
$600$	10.2819	−	6.68982i	0.419757	−	0.273111i
$601$	−38.6103	−	22.2917i	−1.57495	−	0.909297i	−0.995548	−	0.0942541i	$-0.969953\pi$
$601$	−38.6103	−	22.2917i	−1.57495	−	0.909297i	−0.579401	−	0.815043i	$-0.696713\pi$
$602$	10.4186	−	21.9387i	0.424631	−	0.894153i
$603$	−22.4990	+	20.4026i	−0.916229	+	0.830857i
$604$	−2.43613	−	4.58833i	−0.0991246	−	0.186697i
$605$	−48.1399			−1.95716
$606$	−22.3094	+	1.98479i	−0.906257	+	0.0806266i
$607$	17.7638			0.721009			0.360504	−	0.932758i	$-0.382605\pi$
$607$	17.7638			0.721009			0.360504	+	0.932758i	$0.382605\pi$
$608$	11.0381	−	9.23384i	0.447653	−	0.374482i
$609$	−0.576808	−	0.647043i	−0.0233734	−	0.0262195i
$610$	−21.8223	−	22.6112i	−0.883560	−	0.915503i
$611$	9.69919	−	16.7995i	0.392387	−	0.679635i
$612$	−9.71429	+	8.19993i	−0.392677	+	0.331462i
$613$	1.42165	−	0.820787i	0.0574197	−	0.0331513i	−0.471015	−	0.882125i	$-0.656112\pi$
$613$	1.42165	−	0.820787i	0.0574197	−	0.0331513i	0.528435	+	0.848974i	$0.322779\pi$
$614$	10.2739	+	41.2592i	0.414622	+	1.66509i
$615$	0.0733607	−	0.0283093i	0.00295819	−	0.00114154i
$616$	−40.6152	+	25.9372i	−1.63643	+	1.04504i
$617$	12.3248	+	21.3472i	0.496178	+	0.859406i	0.999990	−	0.00440750i	$-0.00140296\pi$
$617$	12.3248	+	21.3472i	0.496178	+	0.859406i	−0.503812	+	0.863813i	$0.668070\pi$
$618$	3.38735	−	0.301360i	0.136259	−	0.0121225i
$619$			13.2905i			0.534191i	0.963670	+	0.267095i	$0.0860638\pi$
$619$			13.2905i			0.534191i	−0.963670	+	0.267095i	$0.913936\pi$
$620$	0.481373	−	13.5514i	0.0193324	−	0.544239i
$621$	6.68938	−	13.3025i	0.268436	−	0.533810i
$622$	−11.7102	+	40.7920i	−0.469536	+	1.63561i
$623$	−9.80867	−	8.05284i	−0.392976	−	0.322630i
$624$	−21.9037	−	5.04381i	−0.876849	−	0.201914i
$625$	−6.21073			−0.248429
$626$	6.48710	−	6.26075i	0.259277	−	0.250230i
$627$	22.0836	+	17.8184i	0.881934	+	0.711600i
$628$	−0.892295	+	25.1196i	−0.0356064	+	1.00238i
$629$	−14.2805			−0.569401
$630$	−17.2657	−	4.04979i	−0.687882	−	0.161347i
$631$		−	30.5024i		−	1.21428i	−0.794594	−	0.607142i	$-0.792316\pi$
$631$		−	30.5024i		−	1.21428i	0.794594	−	0.607142i	$-0.207684\pi$
$632$	9.22547	−	28.3063i	0.366969	−	1.12596i
$633$	0.830137	+	2.15121i	0.0329950	+	0.0855030i
$634$	−0.359207	+	0.346673i	−0.0142659	+	0.0137682i
$635$		−	21.0728i		−	0.836249i
$636$	−16.1594	+	18.6331i	−0.640760	+	0.738849i
$637$	−4.42213	−	22.2751i	−0.175211	−	0.882573i
$638$	1.65579	+	0.475328i	0.0655534	+	0.0188184i
$639$	9.28592	−	28.9265i	0.367345	−	1.14431i
$640$	−2.45045	−	17.7057i	−0.0968624	−	0.699880i
$641$	−10.5101			−0.415126			−0.207563	−	0.978222i	$-0.566553\pi$
$641$	−10.5101			−0.415126			−0.207563	+	0.978222i	$0.566553\pi$
$642$	−7.58384	+	16.3261i	−0.299310	+	0.644338i
$643$	22.6783	−	13.0933i	0.894345	−	0.516350i	0.0189836	−	0.999820i	$-0.493957\pi$
$643$	22.6783	−	13.0933i	0.894345	−	0.516350i	0.875361	+	0.483470i	$0.160624\pi$
$644$	4.83131	+	14.3727i	0.190380	+	0.566362i
$645$	−11.1537	+	13.8236i	−0.439177	+	0.544302i
$646$	−7.39686	+	1.84189i	−0.291026	+	0.0724681i
$647$	13.3960	+	23.2026i	0.526652	+	0.912188i	0.999518	+	0.0310532i	$0.00988612\pi$
$647$	13.3960	+	23.2026i	0.526652	+	0.912188i	−0.472866	+	0.881134i	$0.656781\pi$
$648$	−25.2995	+	2.81691i	−0.993858	+	0.110659i
$649$	66.1118	+	38.1697i	2.59511	+	1.49829i
$650$	−7.97790	−	8.26633i	−0.312919	−	0.324232i
$651$	14.6796	−	13.0862i	0.575341	−	0.512889i
$652$	−1.07727	+	30.3269i	−0.0421891	+	1.18769i
$653$			7.32809i			0.286770i	0.989667	+	0.143385i	$0.0457988\pi$
$653$			7.32809i			0.286770i	−0.989667	+	0.143385i	$0.954201\pi$
$654$	5.87984	−	4.12997i	0.229920	−	0.161495i
$655$			12.1371i			0.474237i
$656$	−0.00815561	+	0.114652i	−0.000318423	+	0.00447641i
$657$	15.4989	−	3.35167i	0.604670	−	0.130761i
$658$	12.7031	+	18.4162i	0.495219	+	0.717939i
$659$	−23.5560	+	40.8002i	−0.917612	+	1.58935i	−0.114580	+	0.993414i	$0.536552\pi$
$659$	−23.5560	+	40.8002i	−0.917612	+	1.58935i	−0.803032	+	0.595937i	$0.796781\pi$
$660$	33.3106	−	11.5132i	1.29662	−	0.448153i
$661$	6.20958	−	10.7553i	0.241525	−	0.418333i	−0.719624	−	0.694364i	$-0.755686\pi$
$661$	6.20958	−	10.7553i	0.241525	−	0.418333i	0.961149	+	0.276031i	$0.0890192\pi$
$662$	−26.1740	−	27.1203i	−1.01728	−	1.05406i
$663$	9.26568	+	7.47614i	0.359849	+	0.290349i
$664$	15.8181	−	3.34736i	0.613862	−	0.129903i
$665$	−8.21891	−	6.74767i	−0.318716	−	0.261663i
$666$	−23.7585	−	15.9138i	−0.920625	−	0.616648i
$667$	0.271014	−	0.469411i	0.0104937	−	0.0181757i
$668$	−9.84292	−	6.15876i	−0.380834	−	0.238289i
$669$	24.9659	−	30.9420i	0.965239	−	1.19629i
$670$	−6.24153	+	21.7422i	−0.241131	+	0.839973i
$671$	45.2855	+	78.4368i	1.74823	+	3.02802i
$672$	16.0915	−	20.3239i	0.620744	−	0.784013i
$673$	5.72927	−	9.92339i	0.220847	−	0.382519i	−0.734218	−	0.678913i	$-0.762451\pi$
$673$	5.72927	−	9.92339i	0.220847	−	0.382519i	0.955065	+	0.296395i	$0.0957845\pi$
$674$	1.17634	+	1.21886i	0.0453107	+	0.0469488i
$675$	−11.6238	−	5.84525i	−0.447402	−	0.224984i
$676$	0.175705	−	4.94639i	0.00675789	−	0.190246i
$677$	13.0327	+	22.5733i	0.500887	+	0.867562i	0.999999	+	0.00102497i	$0.000326258\pi$
$677$	13.0327	+	22.5733i	0.500887	+	0.867562i	−0.499112	+	0.866537i	$0.666340\pi$
$678$	−17.0721	−	24.3055i	−0.655649	−	0.933447i
$679$	−9.70865	−	7.97073i	−0.372584	−	0.305888i
$680$	−2.93384	+	9.00183i	−0.112507	+	0.345204i
$681$	3.72165	−	23.7693i	0.142614	−	0.910841i
$682$	−10.7839	+	37.5654i	−0.412937	+	1.43845i
$683$	12.2243	+	21.1731i	0.467750	+	0.810167i	0.999321	−	0.0368469i	$-0.0117314\pi$
$683$	12.2243	+	21.1731i	0.467750	+	0.810167i	−0.531571	+	0.847014i	$0.678398\pi$
$684$	−14.3588	−	5.17852i	−0.549021	−	0.198006i
$685$	1.53496			0.0586479
$686$	25.3942	+	6.41365i	0.969555	+	0.244874i
$687$	26.1271	+	4.09082i	0.996811	+	0.156075i
$688$	−11.3537	−	23.3497i	−0.432857	−	0.890200i
$689$	20.0042	+	11.5494i	0.762098	+	0.439998i
$690$	−0.982706	−	11.0458i	−0.0374110	−	0.420506i
$691$	41.1548	−	23.7607i	1.56560	−	0.903901i	0.568930	−	0.822386i	$-0.307358\pi$
$691$	41.1548	−	23.7607i	1.56560	−	0.903901i	0.996672	−	0.0815143i	$-0.0259756\pi$
$692$	−6.13274	−	3.83729i	−0.233132	−	0.145872i
$693$	45.4683	+	23.3508i	1.72720	+	0.887023i
$694$	11.9250	−	41.5404i	0.452668	−	1.57685i
$695$	25.6746	−	14.8233i	0.973894	−	0.562278i
$696$	−0.925354	+	0.0492994i	−0.0350755	+	0.00186869i
$697$	0.0304414	−	0.0527261i	0.00115305	−	0.00199714i
$698$	3.35372	−	11.6826i	0.126940	−	0.442192i
$699$	−3.52637	+	4.37047i	−0.133380	+	0.165306i
$700$	12.5590	−	4.22165i	0.474684	−	0.159563i
$701$			20.9749i			0.792212i	0.918205	+	0.396106i	$0.129639\pi$
$701$			20.9749i			0.792212i	−0.918205	+	0.396106i	$0.870361\pi$
$702$	7.08415	+	22.7635i	0.267374	+	0.859154i
$703$	−8.57341	−	14.8496i	−0.323352	−	0.560063i
$704$	−5.47737	+	51.2259i	−0.206436	+	1.93065i
$705$	−5.89063	−	15.2649i	−0.221854	−	0.574911i
$706$	−5.78338	−	23.2256i	−0.217661	−	0.874107i
$707$	−23.8682	−	3.94525i	−0.897657	−	0.148376i
$708$	−40.3195	−	7.78853i	−1.51530	−	0.292711i
$709$	−31.4955	+	18.1839i	−1.18284	+	0.682911i	−0.956669	−	0.291177i	$-0.905953\pi$
$709$	−31.4955	+	18.1839i	−1.18284	+	0.682911i	−0.226168	+	0.974088i	$0.572620\pi$
$710$	−5.46724	−	21.9560i	−0.205182	−	0.823993i
$711$	−30.8642	+	6.67447i	−1.15750	+	0.250312i
$712$	−13.2732	+	2.80881i	−0.497433	+	0.105265i
$713$	10.6497	+	6.14858i	0.398833	+	0.230266i
$714$	−12.3729	+	5.95421i	−0.463043	+	0.222831i
$715$	−16.5038	−	28.5854i	−0.617206	−	1.06903i
$716$	−5.71417	−	3.57538i	−0.213549	−	0.133618i
$717$	9.20574	−	3.55243i	0.343795	−	0.132668i
$718$	27.3016	+	7.83747i	1.01889	+	0.292492i
$719$	−4.91668	+	8.51594i	−0.183361	+	0.317591i	−0.943023	−	0.332727i	$-0.892031\pi$
$719$	−4.91668	+	8.51594i	−0.183361	+	0.317591i	0.759662	+	0.650318i	$0.225364\pi$
$720$	−14.9124	+	11.7070i	−0.555754	+	0.436294i
$721$	3.62403	+	0.599027i	0.134966	+	0.0223089i
$722$	12.3037	+	12.7485i	0.457895	+	0.474449i
$723$	2.22389	−	14.2035i	0.0827074	−	0.528232i
$724$	−40.0921	+	21.2865i	−1.49001	+	0.791105i
$725$	−0.410176	−	0.236815i	−0.0152335	−	0.00879509i
$726$	−74.3429	+	6.61403i	−2.75913	+	0.245470i
$727$	4.04274	−	7.00222i	0.149937	−	0.259698i	−0.781267	−	0.624197i	$-0.785426\pi$
$727$	4.04274	−	7.00222i	0.149937	−	0.259698i	0.931204	+	0.364499i	$0.118760\pi$
$728$	−21.5470	−	11.1867i	−0.798583	−	0.414607i
$729$	16.1008	+	21.6740i	0.596328	+	0.802741i
$730$	8.49783	−	8.20133i	0.314519	−	0.303545i
$731$			13.7526i			0.508659i
$732$	−36.8071	−	31.9206i	−1.36043	−	1.17982i
$733$	15.3893			0.568416			0.284208	−	0.958763i	$-0.408269\pi$
$733$	15.3893			0.568416			0.284208	+	0.958763i	$0.408269\pi$
$734$	43.8475	−	10.9184i	1.61844	−	0.403006i
$735$	−16.9645	−	8.89535i	−0.625747	−	0.328110i
$736$	15.2240	+	5.56696i	0.561163	+	0.205201i
$737$	32.5982	−	56.4617i	1.20077	−	2.07979i
$738$	0.109402	−	0.0537976i	0.00402715	−	0.00198032i
$739$	−18.3244	−	31.7388i	−0.674074	−	1.16753i	−0.976739	−	0.214434i	$-0.931209\pi$
$739$	−18.3244	−	31.7388i	−0.674074	−	1.16753i	0.302664	−	0.953097i	$-0.402124\pi$
$740$	−21.2839	−	0.756044i	−0.782410	−	0.0277927i
$741$	−2.21134	+	14.1233i	−0.0812355	+	0.518832i
$742$	−21.9293	+	15.1264i	−0.805050	+	0.555306i
$743$	−5.25418	+	3.03350i	−0.192757	+	0.111288i	−0.593273	−	0.805002i	$-0.702164\pi$
$743$	−5.25418	+	3.03350i	−0.192757	+	0.111288i	0.400515	+	0.916290i	$0.368831\pi$
$744$	−1.11847	−	20.9938i	−0.0410051	−	0.769669i
$745$			36.4384i			1.33500i
$746$	7.50471	+	30.1383i	0.274767	+	1.10344i
$747$	−11.5200	−	12.7037i	−0.421495	−	0.464805i
$748$	14.4745	−	23.1331i	0.529239	−	0.845830i
$749$	−12.3379	+	15.0280i	−0.450816	+	0.549111i
$750$	−28.9255	+	2.57340i	−1.05621	+	0.0939674i
$751$			19.0418i			0.694845i	0.937709	+	0.347423i	$0.112943\pi$
$751$			19.0418i			0.694845i	−0.937709	+	0.347423i	$0.887057\pi$
$752$	23.8569	+	1.69703i	0.869970	+	0.0618841i
$753$	7.89169	−	50.4023i	0.287589	−	1.83676i
$754$	0.209701	+	0.842142i	0.00763687	+	0.0306690i
$755$			4.10374i			0.149350i
$756$	−27.2200	−	3.88197i	−0.989983	−	0.141186i
$757$		−	13.2191i		−	0.480456i	−0.970717	−	0.240228i	$-0.922778\pi$
$757$		−	13.2191i		−	0.480456i	0.970717	−	0.240228i	$-0.0772222\pi$
$758$	12.1890	−	3.03517i	0.442723	−	0.110242i
$759$	−4.94418	+	31.5773i	−0.179462	+	1.14618i
$760$	−11.1219	+	2.35357i	−0.403434	+	0.0853728i
$761$		−	14.4986i		−	0.525575i	−0.964854	−	0.262787i	$-0.915358\pi$
$761$		−	14.4986i		−	0.525575i	0.964854	−	0.262787i	$-0.0846418\pi$
$762$	−2.89524	−	32.5430i	−0.104883	−	1.17891i
$763$	7.26413	−	2.73247i	0.262979	−	0.0989221i
$764$	−12.9398	+	20.6804i	−0.468147	+	0.748192i
$765$	9.81529	−	2.12258i	0.354873	−	0.0767420i
$766$	37.9882	−	9.45941i	1.37257	−	0.341782i
$767$			38.4588i			1.38867i
$768$	−6.21688	−	27.0065i	−0.224332	−	0.974513i
$769$	−7.45590	+	4.30467i	−0.268867	+	0.155230i	−0.628373	−	0.777913i	$-0.716279\pi$
$769$	−7.45590	+	4.30467i	−0.268867	+	0.155230i	0.359506	+	0.933143i	$0.382945\pi$
$770$	37.9456	−	3.05108i	1.36747	−	0.109953i
$771$	7.02350	−	44.8574i	0.252945	−	1.61550i
$772$	0.122762	−	3.45596i	0.00441831	−	0.124383i
$773$	−16.8787	−	29.2348i	−0.607085	−	1.05150i	−0.991718	−	0.128433i	$-0.959005\pi$
$773$	−16.8787	−	29.2348i	−0.607085	−	1.05150i	0.384633	−	0.923070i	$-0.374328\pi$
$774$	−15.3256	+	22.8803i	−0.550866	+	0.822416i
$775$	5.37269	−	9.30578i	0.192993	−	0.334273i
$776$	−13.1378	+	2.78017i	−0.471621	+	0.0998022i
$777$	−20.5532	−	23.0558i	−0.737341	−	0.827123i
$778$	6.71354	+	26.9610i	0.240692	+	0.966599i
$779$	0.0731031			0.00261919
$780$	13.4139	+	11.6331i	0.480295	+	0.416531i
$781$			65.2140i			2.33354i
$782$	−5.96257	−	6.17814i	−0.213221	−	0.220930i
$783$	0.539675	+	0.821462i	0.0192864	+	0.0293567i
$784$	22.3147	−	16.9131i	0.796955	−	0.604039i
$785$	9.92783	−	17.1955i	0.354340	−	0.613734i
$786$	1.66755	+	18.7435i	0.0594794	+	0.668559i
$787$	−9.12433	−	5.26793i	−0.325247	−	0.187782i	0.328482	−	0.944510i	$-0.393463\pi$
$787$	−9.12433	−	5.26793i	−0.325247	−	0.187782i	−0.653729	+	0.756729i	$0.726796\pi$
$788$	21.3150	+	40.1459i	0.759317	+	1.43014i
$789$	−7.59067	+	48.4798i	−0.270235	+	1.72593i
$790$	−16.9224	+	16.3320i	−0.602073	+	0.581066i
$791$	−11.2952	−	30.0278i	−0.401612	−	1.06766i
$792$	49.8602	−	22.3567i	1.77170	−	0.794409i
$793$	−22.8143	+	39.5155i	−0.810159	+	1.40324i
$794$	−8.55010	+	29.7840i	−0.303432	+	1.05699i
$795$	18.1769	−	7.01432i	0.644668	−	0.248772i
$796$	0.182024	+	0.113893i	0.00645166	+	0.00403683i
$797$	−20.2076	−	35.0006i	−0.715790	−	1.23978i	−0.962654	−	0.270734i	$-0.912734\pi$
$797$	−20.2076	−	35.0006i	−0.715790	−	1.23978i	0.246864	−	0.969050i	$-0.420600\pi$
$798$	−13.6196	−	9.29129i	−0.482130	−	0.328908i
$799$	−10.9713	−	6.33428i	−0.388137	−	0.224091i
$800$	4.86446	−	13.3028i	0.171985	−	0.470327i
$801$	9.66658	+	10.6598i	0.341552	+	0.376647i
$802$	43.5539	−	10.8453i	1.53794	−	0.382961i
$803$	−29.4784	+	17.0193i	−1.04027	+	0.600599i
$804$	−6.65166	+	34.4342i	−0.234586	+	1.21440i
$805$	1.95337	−	11.8176i	0.0688471	−	0.416516i
$806$	−19.1059	+	4.75755i	−0.672978	+	0.167578i
$807$	−0.136501	−	0.353727i	−0.00480505	−	0.0124518i
$808$	−19.2351	+	17.2880i	−0.676689	+	0.608190i
$809$	0.375981	+	0.651218i	0.0132188	+	0.0228956i	0.872559	−	0.488509i	$-0.162459\pi$
$809$	0.375981	+	0.651218i	0.0132188	+	0.0228956i	−0.859340	+	0.511404i	$0.829126\pi$
$810$	18.6951	+	7.40656i	0.656879	+	0.260240i
$811$			22.4964i			0.789955i	0.918691	+	0.394977i	$0.129248\pi$
$811$			22.4964i			0.789955i	−0.918691	+	0.394977i	$0.870752\pi$
$812$	−0.981098	−	0.198183i	−0.0344298	−	0.00695485i
$813$	−23.9979	+	29.7422i	−0.841643	+	1.04311i
$814$	59.0001	+	16.9372i	2.06795	+	0.593648i
$815$	11.9859	−	20.7602i	0.419848	−	0.727198i
$816$	−3.29398	+	14.3047i	−0.115312	+	0.500765i
$817$	−14.3007	+	8.25650i	−0.500317	+	0.288858i
$818$	31.5577	+	9.05928i	1.10339	+	0.316750i
$819$	1.26541	+	25.7194i	0.0442170	+	0.898710i
$820$	0.0481618	−	0.0769721i	0.00168188	−	0.00268798i
$821$	15.5745	−	8.99192i	0.543552	−	0.313820i	−0.202965	−	0.979186i	$-0.565058\pi$
$821$	15.5745	−	8.99192i	0.543552	−	0.313820i	0.746517	+	0.665366i	$0.231724\pi$
$822$	2.37046	−	0.210892i	0.0826793	−	0.00735569i
$823$	0.937715	+	0.541390i	0.0326867	+	0.0188717i	0.516254	−	0.856435i	$-0.327326\pi$
$823$	0.937715	+	0.541390i	0.0326867	+	0.0188717i	−0.483568	+	0.875307i	$0.660659\pi$
$824$	2.92056	−	2.62493i	0.101743	−	0.0914436i
$825$	27.5925	+	4.32027i	0.960648	+	0.150412i
$826$	−40.0666	−	19.0275i	−1.39409	−	0.662052i
$827$	48.2472			1.67772			0.838860	−	0.544347i	$-0.183222\pi$
$827$	48.2472			1.67772			0.838860	+	0.544347i	$0.183222\pi$
$828$	−3.03521	−	16.9231i	−0.105481	−	0.588120i
$829$	3.40060	+	5.89002i	0.118108	+	0.204569i	0.919018	−	0.394216i	$-0.128984\pi$
$829$	3.40060	+	5.89002i	0.118108	+	0.204569i	−0.800910	+	0.598785i	$0.795650\pi$
$830$	−12.2764	−	3.52419i	−0.426120	−	0.122326i
$831$	−2.65932	+	16.9844i	−0.0922507	+	0.589183i
$832$	−23.7292	+	10.5138i	−0.822663	+	0.364499i
$833$	−14.5473	+	2.88797i	−0.504034	+	0.100062i
$834$	37.6130	−	26.4192i	1.30243	−	0.914822i
$835$	4.58601	+	7.94320i	0.158705	+	0.274886i
$836$	32.7448	+	1.16316i	1.13250	+	0.0402287i
$837$	−18.6368	+	12.2438i	−0.644180	+	0.423207i
$838$	−12.8428	+	12.3947i	−0.443647	+	0.428168i
$839$	−8.14424	+	14.1062i	−0.281170	+	0.487001i	−0.971673	−	0.236328i	$-0.924056\pi$
$839$	−8.14424	+	14.1062i	−0.281170	+	0.487001i	0.690503	+	0.723330i	$0.257389\pi$
$840$	−18.7559	+	8.21919i	−0.647142	+	0.283589i
$841$	−14.4821	−	25.0838i	−0.499383	−	0.864957i
$842$	−19.3501	−	5.55484i	−0.666849	−	0.191432i
$843$	9.96421	−	12.3493i	0.343186	−	0.425333i
$844$	2.25712	+	1.41229i	0.0776931	+	0.0486129i
$845$	−1.95493	+	3.38603i	−0.0672516	+	0.116483i
$846$	−11.1942	−	22.7645i	−0.384866	−	0.782660i
$847$	−79.5375	−	13.1470i	−2.73294	−	0.451736i
$848$	−2.02075	+	28.4078i	−0.0693928	+	0.975528i
$849$	−25.5011	−	20.5759i	−0.875197	−	0.706164i
$850$	−5.39851	+	5.21015i	−0.185168	+	0.178707i
$851$	9.65695	−	16.7263i	0.331036	−	0.573371i
$852$	−11.4597	−	33.1557i	−0.392603	−	1.13590i
$853$	17.7650	−	30.7700i	0.608264	−	1.05354i	−0.383263	−	0.923639i	$-0.625200\pi$
$853$	17.7650	−	30.7700i	0.608264	−	1.05354i	0.991527	−	0.129904i	$-0.0414670\pi$
$854$	−29.8801	−	43.3184i	−1.02247	−	1.48232i
$855$	8.09985	+	8.93213i	0.277009	+	0.305472i
$856$	4.30342	+	20.3360i	0.147088	+	0.695071i
$857$			8.63641i			0.295014i	0.989061	+	0.147507i	$0.0471249\pi$
$857$			8.63641i			0.295014i	−0.989061	+	0.147507i	$0.952875\pi$
$858$	−29.4144	−	41.8772i	−1.00419	−	1.42967i
$859$		−	9.66511i		−	0.329769i	−0.986313	−	0.164885i	$-0.947275\pi$
$859$		−	9.66511i		−	0.329769i	0.986313	−	0.164885i	$-0.0527252\pi$
$860$	−0.728097	+	20.4971i	−0.0248279	+	0.698946i
$861$	0.128939	−	0.0267383i	0.00439423	−	0.000911240i
$862$	−18.5649	+	17.9172i	−0.632324	+	0.610262i
$863$	2.43125	+	1.40368i	0.0827608	+	0.0477820i	0.540809	−	0.841145i	$-0.318118\pi$
$863$	2.43125	+	1.40368i	0.0827608	+	0.0477820i	−0.458049	+	0.888927i	$0.651451\pi$
$864$	−21.4210	+	20.1281i	−0.728758	+	0.684772i
$865$	2.85737	+	4.94911i	0.0971534	+	0.168275i
$866$	3.15914	+	12.6869i	0.107352	+	0.431117i
$867$	−13.6073	+	16.8645i	−0.462129	+	0.572748i
$868$	4.49623	−	22.2585i	0.152612	−	0.755501i
$869$	58.7027	−	33.8920i	1.99135	−	1.14971i
$870$	0.663887	+	0.308391i	0.0225079	+	0.0104554i
$871$	32.8451			1.11291
$872$	2.57099	−	7.88852i	0.0870648	−	0.267139i
$873$	9.56801	+	10.5511i	0.323828	+	0.357102i
$874$	2.84466	−	9.90928i	0.0962220	−	0.335186i
$875$	−30.9466	−	5.11526i	−1.04619	−	0.172927i
$876$	11.9965	−	13.8329i	0.405324	−	0.467372i
$877$			16.3187i			0.551042i	0.961295	+	0.275521i	$0.0888504\pi$
$877$			16.3187i			0.551042i	−0.961295	+	0.275521i	$0.911150\pi$
$878$	1.62887	+	1.68776i	0.0549717	+	0.0569591i
$879$	−5.68646	−	14.7359i	−0.191799	−	0.497028i
$880$	22.7977	−	33.7116i	0.768510	−	1.13642i
$881$			2.00105i			0.0674171i	0.999432	+	0.0337086i	$0.0107318\pi$
$881$			2.00105i			0.0674171i	−0.999432	+	0.0337086i	$0.989268\pi$
$882$	−27.4207	−	11.4064i	−0.923303	−	0.384073i
$883$	−0.275603			−0.00927479			−0.00463739	−	0.999989i	$-0.501476\pi$
$883$	−0.275603			−0.00927479			−0.00463739	+	0.999989i	$0.501476\pi$
$884$	13.7388	+	0.488030i	0.462087	+	0.0164142i
$885$	25.2460	+	20.3700i	0.848634	+	0.684731i
$886$	−13.6014	−	14.0931i	−0.456948	−	0.473468i
$887$	−25.4528			−0.854623			−0.427311	−	0.904104i	$-0.640539\pi$
$887$	−25.4528			−0.854623			−0.427311	+	0.904104i	$0.640539\pi$
$888$	−32.9728	+	1.75667i	−1.10649	+	0.0589499i
$889$	5.75499	−	34.8169i	0.193016	−	1.16772i
$890$	10.3013	+	2.95719i	0.345299	+	0.0991251i
$891$	−47.1283	−	33.7345i	−1.57886	−	1.13015i
$892$	1.62974	−	45.8797i	0.0545676	−	1.53617i
$893$		−	15.2113i		−	0.509028i
$894$	5.00635	+	56.2723i	0.167437	+	1.88203i
$895$	2.66235	+	4.61132i	0.0889924	+	0.154139i
$896$	0.786766	−	29.9229i	0.0262840	−	0.999655i
$897$	−15.0223	+	5.79701i	−0.501582	+	0.193557i
$898$	−9.03485	+	2.24976i	−0.301497	+	0.0750755i
$899$	−0.702990	+	0.405871i	−0.0234460	+	0.0135366i
$900$	−14.7876	+	2.65220i	−0.492920	+	0.0884065i
$901$	7.54261	−	13.0642i	0.251281	−	0.435231i
$902$	−0.188305	+	0.181734i	−0.00626985	+	0.00605109i
$903$	−22.2036	+	19.7934i	−0.738889	+	0.658684i
$904$	−32.6088	−	10.6277i	−1.08455	−	0.353473i
$905$	35.8578			1.19195
$906$	0.563822	+	6.33746i	0.0187317	+	0.210548i
$907$	−13.3379			−0.442877			−0.221439	−	0.975174i	$-0.571075\pi$
$907$	−13.3379			−0.442877			−0.221439	+	0.975174i	$0.571075\pi$
$908$	−13.0276	−	24.5368i	−0.432335	−	0.814283i
$909$	26.1184	+	8.38449i	0.866294	+	0.278096i
$910$	10.8894	+	15.7869i	0.360981	+	0.523330i
$911$	−24.2678	−	14.0110i	−0.804028	−	0.464206i	0.0408499	−	0.999165i	$-0.486993\pi$
$911$	−24.2678	−	14.0110i	−0.804028	−	0.464206i	−0.844878	+	0.534960i	$0.820327\pi$
$912$	−16.8523	+	5.16270i	−0.558036	+	0.170954i
$913$	31.8803	+	18.4061i	1.05508	+	0.609152i
$914$	−7.03850	−	7.29296i	−0.232813	−	0.241230i
$915$	13.8558	+	35.9060i	0.458060	+	1.18701i
$916$	26.9708	−	14.3198i	0.891139	−	0.473141i
$917$	−3.31465	+	20.0532i	−0.109459	+	0.662214i
$918$	14.8662	−	4.62647i	0.490659	−	0.152696i
$919$	34.5432	+	19.9435i	1.13948	+	0.657877i	0.946301	−	0.323288i	$-0.104788\pi$
$919$	34.5432	+	19.9435i	1.13948	+	0.657877i	0.193175	+	0.981164i	$0.438121\pi$
$920$	−8.55962	−	9.52366i	−0.282202	−	0.313986i
$921$	8.05545	−	51.4482i	0.265436	−	1.69528i
$922$	11.3425	−	39.5112i	0.373545	−	1.30123i
$923$	−28.4524	+	16.4270i	−0.936523	+	0.540702i
$924$	58.1807	−	9.92524i	1.91400	−	0.326516i
$925$	−14.6156	−	8.43834i	−0.480559	−	0.277451i
$926$	−29.0137	+	28.0013i	−0.953448	+	0.920181i
$927$	−3.96569	−	1.27306i	−0.130250	−	0.0418127i
$928$	−0.820716	+	0.686566i	−0.0269413	+	0.0225376i
$929$	−3.18838	+	1.84081i	−0.104607	+	0.0603951i	−0.551391	−	0.834247i	$-0.685903\pi$
$929$	−3.18838	+	1.84081i	−0.104607	+	0.0603951i	0.446784	+	0.894642i	$0.352569\pi$
$930$	−6.99656	+	15.0618i	−0.229426	+	0.493896i
$931$	−11.7366	−	13.3932i	−0.384653	−	0.438944i
$932$	−0.230196	+	6.48038i	−0.00754031	+	0.212272i
$933$	32.6392	−	40.4520i	1.06856	−	1.32434i
$934$	1.16520	+	0.334495i	0.0381265	+	0.0109450i
$935$	−18.6683	+	10.7782i	−0.610520	+	0.352484i
$936$	22.3135	+	16.1222i	0.729341	+	0.526969i
$937$			45.8566i			1.49807i	0.662530	+	0.749035i	$0.269483\pi$
$937$			45.8566i			1.49807i	−0.662530	+	0.749035i	$0.730517\pi$
$938$	−16.2501	+	34.2182i	−0.530586	+	1.11726i
$939$	−10.3013	+	3.97520i	−0.336171	+	0.129726i
$940$	−16.0164	−	10.0215i	−0.522398	−	0.326867i
$941$	−23.1484	+	40.0942i	−0.754616	+	1.30703i	0.190949	+	0.981600i	$0.438843\pi$
$941$	−23.1484	+	40.0942i	−0.754616	+	1.30703i	−0.945565	+	0.325433i	$0.894490\pi$
$942$	12.9691	−	27.9192i	0.422557	−	0.909658i
$943$	0.0411711	+	0.0713104i	0.00134071	+	0.00232219i
$944$	−42.6436	+	20.7353i	−1.38793	+	0.674877i
$945$	17.5535	+	12.7918i	0.571017	+	0.416119i
$946$	16.3111	−	56.8192i	0.530320	−	1.84735i
$947$	−9.04477	−	15.6660i	−0.293915	−	0.509077i	0.680817	−	0.732454i	$-0.261625\pi$
$947$	−9.04477	−	15.6660i	−0.293915	−	0.509077i	−0.974732	+	0.223377i	$0.928292\pi$
$948$	−23.8896	+	27.5467i	−0.775899	+	0.894675i
$949$	−14.8508	−	8.57414i	−0.482079	−	0.278328i
$950$	−8.65882	−	2.48569i	−0.280929	−	0.0806465i
$951$	0.570409	−	0.220116i	0.0184968	−	0.00713777i
$952$	−7.30573	+	14.0717i	−0.236780	+	0.456068i
$953$	−5.06379			−0.164032			−0.0820161	−	0.996631i	$-0.526136\pi$
$953$	−5.06379			−0.164032			−0.0820161	+	0.996631i	$0.526136\pi$
$954$	27.1071	−	13.3297i	0.877624	−	0.431564i
$955$	16.6891	−	9.63543i	0.540045	−	0.311795i
$956$	6.04364	−	9.65893i	0.195465	−	0.312392i
$957$	−1.64199	−	1.32486i	−0.0530779	−	0.0428266i
$958$	28.9432	−	7.20713i	0.935113	−	0.232852i
$959$	2.53609	+	0.419198i	0.0818947	+	0.0135366i
$960$	−5.66672	+	21.1456i	−0.182893	+	0.682470i
$961$	6.29188	+	10.8979i	0.202964	+	0.351544i
$962$	7.47220	+	30.0077i	0.240913	+	0.967488i
$963$	16.3321	−	14.8103i	0.526294	−	0.477255i
$964$	−7.78469	−	14.6621i	−0.250728	−	0.472234i
$965$	−1.36588	+	2.36577i	−0.0439691	+	0.0761567i
$966$	1.39296	−	18.5184i	0.0448179	−	0.595821i
$967$	−3.42105	+	1.97514i	−0.110013	+	0.0635163i	−0.553997	−	0.832519i	$-0.686898\pi$
$967$	−3.42105	+	1.97514i	−0.110013	+	0.0635163i	0.443984	+	0.896035i	$0.353565\pi$
$968$	−64.0983	+	57.6099i	−2.06020	+	1.85165i
$969$	9.22353	+	1.44417i	0.296303	+	0.0463933i
$970$	10.1962	+	2.92703i	0.327381	+	0.0939813i
$971$	8.39411	+	4.84634i	0.269380	+	0.155526i	0.628606	−	0.777724i	$-0.283626\pi$
$971$	8.39411	+	4.84634i	0.269380	+	0.155526i	−0.359226	+	0.933251i	$0.616959\pi$
$972$	29.8887	+	8.86948i	0.958679	+	0.284489i
$973$	46.4683	−	17.4795i	1.48970	−	0.560367i
$974$	−22.6086	+	21.8198i	−0.724427	+	0.699150i
$975$	5.06548	+	13.1267i	0.162225	+	0.420390i
$976$	−56.1158	−	3.99172i	−1.79622	−	0.127772i
$977$	2.89229	−	5.00960i	0.0925327	−	0.160271i	−0.816043	−	0.577990i	$-0.803837\pi$
$977$	2.89229	−	5.00960i	0.0925327	−	0.160271i	0.908576	+	0.417719i	$0.137170\pi$
$978$	15.6577	−	33.7070i	0.500677	−	1.07783i
$979$	−26.7511	−	15.4447i	−0.854968	−	0.493616i
$980$	−21.8344	+	3.53411i	−0.697474	+	0.112893i
$981$	−8.60139	+	1.86007i	−0.274621	+	0.0593874i
$982$	−19.0704	−	19.7598i	−0.608560	−	0.630561i
$983$	17.1658			0.547503			0.273752	−	0.961800i	$-0.411735\pi$
$983$	17.1658			0.547503			0.273752	+	0.961800i	$0.411735\pi$
$984$	0.0638015	−	0.125486i	0.00203392	−	0.00400035i
$985$		−	35.9060i		−	1.14406i
$986$	0.549980	−	0.136950i	0.0175149	−	0.00436138i
$987$	−5.56373	−	26.8297i	−0.177096	−	0.854000i
$988$	7.74075	+	14.5793i	0.246266	+	0.463830i
$989$	−16.1080	−	9.29999i	−0.512206	−	0.295722i
$990$	−43.0695	−	2.87182i	−1.36884	−	0.0912723i
$991$	10.2645	−	5.92623i	0.326064	−	0.188253i	−0.328029	−	0.944668i	$-0.606384\pi$
$991$	10.2645	−	5.92623i	0.326064	−	0.188253i	0.654092	+	0.756415i	$0.273051\pi$
$992$	−15.5763	−	18.6198i	−0.494549	−	0.591180i
$993$	16.6189	+	43.0661i	0.527385	+	1.36666i
$994$	−3.03689	−	37.7691i	−0.0963242	−	1.19796i
$995$	−0.0848084	−	0.146893i	−0.00268861	−	0.00465681i
$996$	−19.4428	−	3.75576i	−0.616068	−	0.119006i
$997$	43.1479			1.36651			0.683254	−	0.730181i	$-0.260564\pi$
$997$	43.1479			1.36651			0.683254	+	0.730181i	$0.260564\pi$
$998$	47.6635	−	11.8686i	1.50876	−	0.375695i
$999$	19.2300	+	29.2708i	0.608411	+	0.926089i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cz.b.187.8	yes	180
7.3	odd	6		504.2.bf.b.115.53	✓	180
8.3	odd	2	inner	504.2.cz.b.187.69	yes	180
9.4	even	3		504.2.bf.b.355.53	yes	180
56.3	even	6		504.2.bf.b.115.54	yes	180
63.31	odd	6	inner	504.2.cz.b.283.69	yes	180
72.67	odd	6		504.2.bf.b.355.54	yes	180
504.283	even	6	inner	504.2.cz.b.283.8	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.b.115.53	✓	180	7.3	odd	6
504.2.bf.b.115.54	yes	180	56.3	even	6
504.2.bf.b.355.53	yes	180	9.4	even	3
504.2.bf.b.355.54	yes	180	72.67	odd	6
504.2.cz.b.187.8	yes	180	1.1	even	1	trivial
504.2.cz.b.187.69	yes	180	8.3	odd	2	inner
504.2.cz.b.283.8	yes	180	504.283	even	6	inner
504.2.cz.b.283.69	yes	180	63.31	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37231 + 0.341717i) q^{2} +(1.71120 + 0.267930i) q^{3} +(1.76646 - 0.937883i) q^{4} -1.57990 q^{5} +(-2.43985 + 0.217065i) q^{6} +(-2.61033 - 0.431470i) q^{7} +(-2.10363 + 1.89069i) q^{8} +(2.85643 + 0.916964i) q^{9} +O(q^{10})\)	\(q+(-1.37231 + 0.341717i) q^{2} +(1.71120 + 0.267930i) q^{3} +(1.76646 - 0.937883i) q^{4} -1.57990 q^{5} +(-2.43985 + 0.217065i) q^{6} +(-2.61033 - 0.431470i) q^{7} +(-2.10363 + 1.89069i) q^{8} +(2.85643 + 0.916964i) q^{9} +(2.16811 - 0.539878i) q^{10} -6.43974 q^{11} +(3.27405 - 1.13162i) q^{12} +(-1.62213 - 2.80961i) q^{13} +(3.72962 - 0.299886i) q^{14} +(-2.70352 - 0.423301i) q^{15} +(2.24075 - 3.31346i) q^{16} +(-1.83488 + 1.05937i) q^{17} +(-4.23324 - 0.282267i) q^{18} +(-2.20317 - 1.27200i) q^{19} +(-2.79082 + 1.48176i) q^{20} +(-4.35120 - 1.43772i) q^{21} +(8.83731 - 2.20057i) q^{22} -2.86553i q^{23} +(-4.10632 + 2.67173i) q^{24} -2.50393 q^{25} +(3.18616 + 3.30135i) q^{26} +(4.64224 + 2.33443i) q^{27} +(-5.01571 + 1.68601i) q^{28} +(0.163813 + 0.0945775i) q^{29} +(3.85472 - 0.342941i) q^{30} +(-2.14571 + 3.71647i) q^{31} +(-1.94273 + 5.31279i) q^{32} +(-11.0197 - 1.72540i) q^{33} +(2.15602 - 2.08079i) q^{34} +(4.12406 + 0.681678i) q^{35} +(5.90577 - 1.05921i) q^{36} +(5.83709 + 3.37004i) q^{37} +(3.45810 + 0.992717i) q^{38} +(-2.02302 - 5.24244i) q^{39} +(3.32353 - 2.98710i) q^{40} +(-0.0248856 + 0.0143677i) q^{41} +(6.46248 + 0.486111i) q^{42} +(3.24547 - 5.62132i) q^{43} +(-11.3755 + 6.03972i) q^{44} +(-4.51286 - 1.44871i) q^{45} +(0.979200 + 3.93239i) q^{46} +(2.98964 + 5.17821i) q^{47} +(4.72216 - 5.06964i) q^{48} +(6.62767 + 2.25256i) q^{49} +(3.43616 - 0.855635i) q^{50} +(-3.42369 + 1.32118i) q^{51} +(-5.50052 - 3.44170i) q^{52} +(-6.16601 + 3.55995i) q^{53} +(-7.16830 - 1.61723i) q^{54} +10.1741 q^{55} +(6.30696 - 4.02768i) q^{56} +(-3.42927 - 2.76695i) q^{57} +(-0.257121 - 0.0738117i) q^{58} +(-10.2662 - 5.92720i) q^{59} +(-5.17267 + 1.78784i) q^{60} +(-7.03219 - 12.1801i) q^{61} +(1.67459 - 5.83337i) q^{62} +(-7.06058 - 3.62604i) q^{63} +(0.850557 - 7.95466i) q^{64} +(2.56280 + 4.43890i) q^{65} +(15.7120 - 1.39784i) q^{66} +(-5.06203 + 8.76769i) q^{67} +(-2.24768 + 3.59224i) q^{68} +(0.767760 - 4.90350i) q^{69} +(-5.89242 + 0.473789i) q^{70} -10.1268i q^{71} +(-7.74258 + 3.47167i) q^{72} +(4.57757 - 2.64286i) q^{73} +(-9.16188 - 2.63010i) q^{74} +(-4.28472 - 0.670876i) q^{75} +(-5.08481 - 0.180622i) q^{76} +(16.8099 + 2.77855i) q^{77} +(4.56763 + 6.50294i) q^{78} +(-9.11569 + 5.26295i) q^{79} +(-3.54016 + 5.23493i) q^{80} +(7.31835 + 5.23848i) q^{81} +(0.0292410 - 0.0282208i) q^{82} +(-4.95055 - 2.85820i) q^{83} +(-9.03463 + 1.54125i) q^{84} +(2.89893 - 1.67370i) q^{85} +(-2.53288 + 8.82322i) q^{86} +(0.254977 + 0.205732i) q^{87} +(13.5469 - 12.1756i) q^{88} +(4.15406 + 2.39835i) q^{89} +(6.68808 + 0.445952i) q^{90} +(3.02204 + 8.03393i) q^{91} +(-2.68753 - 5.06184i) q^{92} +(-4.66749 + 5.78474i) q^{93} +(-5.87220 - 6.08449i) q^{94} +(3.48079 + 2.00963i) q^{95} +(-4.74787 + 8.57075i) q^{96} +(4.11170 + 2.37389i) q^{97} +(-9.86494 - 0.826417i) q^{98} +(-18.3947 - 5.90501i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) \) 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9	\( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9} + 16 q^{11} - 3 q^{12} + 7 q^{14} - 7 q^{16} - 18 q^{17} - 13 q^{18} - 6 q^{19} - 36 q^{20} - 16 q^{22} - 24 q^{24} + 156 q^{25} - 6 q^{26} + 16 q^{28} - 8 q^{30} + 13 q^{32} - 36 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 42 q^{41} + 31 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} + 9 q^{48} + 20 q^{49} + 15 q^{50} - 42 q^{51} - 12 q^{54} - 40 q^{56} - 26 q^{57} - 38 q^{58} + 18 q^{59} - 38 q^{60} - 8 q^{64} - 12 q^{65} - 21 q^{66} - 14 q^{67} - 42 q^{70} + 5 q^{72} + 18 q^{73} - 98 q^{74} - 48 q^{75} + 12 q^{76} - 33 q^{78} - 63 q^{80} + 8 q^{81} - 54 q^{82} - 6 q^{83} - 77 q^{84} + 26 q^{86} - 58 q^{88} - 66 q^{89} + 51 q^{90} + 2 q^{91} - 60 q^{92} + 9 q^{94} - 30 q^{96} + 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9 + 16 * q^11 - 3 * q^12 + 7 * q^14 - 7 * q^16 - 18 * q^17 - 13 * q^18 - 6 * q^19 - 36 * q^20 - 16 * q^22 - 24 * q^24 + 156 * q^25 - 6 * q^26 + 16 * q^28 - 8 * q^30 + 13 * q^32 - 36 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 42 * q^41 + 31 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 + 9 * q^48 + 20 * q^49 + 15 * q^50 - 42 * q^51 - 12 * q^54 - 40 * q^56 - 26 * q^57 - 38 * q^58 + 18 * q^59 - 38 * q^60 - 8 * q^64 - 12 * q^65 - 21 * q^66 - 14 * q^67 - 42 * q^70 + 5 * q^72 + 18 * q^73 - 98 * q^74 - 48 * q^75 + 12 * q^76 - 33 * q^78 - 63 * q^80 + 8 * q^81 - 54 * q^82 - 6 * q^83 - 77 * q^84 + 26 * q^86 - 58 * q^88 - 66 * q^89 + 51 * q^90 + 2 * q^91 - 60 * q^92 + 9 * q^94 - 30 * q^96 + 6 * q^97 + 31 * q^98 + 4 * q^99

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