LMFDB - Embedded newform 240.2.bf.a.77.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(53,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2, 3]))

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

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

chi := DirichletCharacter("240.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bf (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.10
Character	$\chi$	$=$	240.77
Dual form			240.2.bf.a.53.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09247 + 0.898057i) q^{2} +(-0.296326 - 1.70651i) q^{3} +(0.386989 - 1.96220i) q^{4} +(0.503115 + 2.17873i) q^{5} +(1.85627 + 1.59820i) q^{6} +(2.12944 - 2.12944i) q^{7} +(1.33939 + 2.49119i) q^{8} +(-2.82438 + 1.01137i) q^{9} +O(q^{10})$	\(q+(-1.09247 + 0.898057i) q^{2} +(-0.296326 - 1.70651i) q^{3} +(0.386989 - 1.96220i) q^{4} +(0.503115 + 2.17873i) q^{5} +(1.85627 + 1.59820i) q^{6} +(2.12944 - 2.12944i) q^{7} +(1.33939 + 2.49119i) q^{8} +(-2.82438 + 1.01137i) q^{9} +(-2.50626 - 1.92838i) q^{10} +(-2.92724 - 2.92724i) q^{11} +(-3.46320 - 0.0789503i) q^{12} +3.82476 q^{13} +(-0.413995 + 4.23870i) q^{14} +(3.56895 - 1.50419i) q^{15} +(-3.70048 - 1.51870i) q^{16} +(4.54825 - 4.54825i) q^{17} +(2.17729 - 3.64135i) q^{18} +(2.02084 - 2.02084i) q^{19} +(4.46981 - 0.144068i) q^{20} +(-4.26492 - 3.00290i) q^{21} +(5.82676 + 0.569101i) q^{22} +(2.64430 - 2.64430i) q^{23} +(3.85435 - 3.02390i) q^{24} +(-4.49375 + 2.19231i) q^{25} +(-4.17844 + 3.43485i) q^{26} +(2.56285 + 4.52015i) q^{27} +(-3.35432 - 5.00245i) q^{28} +(-0.843557 - 0.843557i) q^{29} +(-2.54813 + 4.84840i) q^{30} +1.38749 q^{31} +(5.40655 - 1.66410i) q^{32} +(-4.12797 + 5.86280i) q^{33} +(-0.884248 + 9.05341i) q^{34} +(5.71082 + 3.56812i) q^{35} +(0.891507 + 5.93340i) q^{36} -6.69746 q^{37} +(-0.392882 + 4.02254i) q^{38} +(-1.13338 - 6.52701i) q^{39} +(-4.75377 + 4.17154i) q^{40} +2.65508 q^{41} +(7.35608 - 0.549550i) q^{42} +6.23355i q^{43} +(-6.87666 + 4.61104i) q^{44} +(-3.62449 - 5.64474i) q^{45} +(-0.514093 + 5.26356i) q^{46} +(3.32248 - 3.32248i) q^{47} +(-1.49514 + 6.76495i) q^{48} -2.06899i q^{49} +(2.94048 - 6.43067i) q^{50} +(-9.10941 - 6.41388i) q^{51} +(1.48014 - 7.50495i) q^{52} -3.88396 q^{53} +(-6.85920 - 2.63655i) q^{54} +(4.90494 - 7.85042i) q^{55} +(8.15698 + 2.45267i) q^{56} +(-4.04742 - 2.84976i) q^{57} +(1.67912 + 0.164000i) q^{58} +(-10.3658 + 10.3658i) q^{59} +(-1.57038 - 7.58511i) q^{60} +(3.84345 + 3.84345i) q^{61} +(-1.51579 + 1.24604i) q^{62} +(-3.86069 + 8.16798i) q^{63} +(-4.41204 + 6.67337i) q^{64} +(1.92429 + 8.33313i) q^{65} +(-0.755443 - 10.1121i) q^{66} +10.0836i q^{67} +(-7.16446 - 10.6847i) q^{68} +(-5.29612 - 3.72897i) q^{69} +(-9.44328 + 1.23057i) q^{70} -5.37152 q^{71} +(-6.30247 - 5.68145i) q^{72} +(2.68667 + 2.68667i) q^{73} +(7.31679 - 6.01470i) q^{74} +(5.07282 + 7.01901i) q^{75} +(-3.18325 - 4.74734i) q^{76} -12.4668 q^{77} +(7.09980 + 6.11273i) q^{78} -5.55500i q^{79} +(1.44708 - 8.82644i) q^{80} +(6.95426 - 5.71299i) q^{81} +(-2.90060 + 2.38441i) q^{82} -1.35478i q^{83} +(-7.54278 + 7.20654i) q^{84} +(12.1977 + 7.62112i) q^{85} +(-5.59808 - 6.80998i) q^{86} +(-1.18957 + 1.68951i) q^{87} +(3.37158 - 11.2131i) q^{88} +5.23963i q^{89} +(9.02895 + 2.91172i) q^{90} +(8.14458 - 8.14458i) q^{91} +(-4.16534 - 6.21198i) q^{92} +(-0.411150 - 2.36777i) q^{93} +(-0.645941 + 6.61349i) q^{94} +(5.41958 + 3.38615i) q^{95} +(-4.44191 - 8.73324i) q^{96} +(-6.28272 - 6.28272i) q^{97} +(1.85807 + 2.26031i) q^{98} +(11.2282 + 5.30713i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{3} + 4 q^{4} - 4 q^{6}+O(q^{10}) $ 88 * q - 4 * q^3 + 4 * q^4 - 4 * q^6	$ 88 q - 4 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{10} - 8 q^{12} - 8 q^{13} - 4 q^{15} - 12 q^{16} - 12 q^{18} + 8 q^{19} - 4 q^{21} - 4 q^{22} + 12 q^{24} - 4 q^{27} - 4 q^{28} - 28 q^{30} - 16 q^{31} - 4 q^{33} - 28 q^{34} - 20 q^{36} - 8 q^{37} - 24 q^{39} - 44 q^{40} + 40 q^{42} + 8 q^{45} - 36 q^{46} + 32 q^{48} - 4 q^{51} - 48 q^{52} + 24 q^{54} - 12 q^{57} - 20 q^{58} + 28 q^{60} - 24 q^{61} - 32 q^{63} + 28 q^{64} + 12 q^{66} + 12 q^{69} - 76 q^{70} + 24 q^{72} - 36 q^{75} - 36 q^{76} + 60 q^{78} - 8 q^{81} + 64 q^{82} - 48 q^{84} + 16 q^{85} + 12 q^{87} + 44 q^{88} - 56 q^{90} - 8 q^{91} - 16 q^{93} + 20 q^{94} + 48 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) $ 88 * q - 4 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^10 - 8 * q^12 - 8 * q^13 - 4 * q^15 - 12 * q^16 - 12 * q^18 + 8 * q^19 - 4 * q^21 - 4 * q^22 + 12 * q^24 - 4 * q^27 - 4 * q^28 - 28 * q^30 - 16 * q^31 - 4 * q^33 - 28 * q^34 - 20 * q^36 - 8 * q^37 - 24 * q^39 - 44 * q^40 + 40 * q^42 + 8 * q^45 - 36 * q^46 + 32 * q^48 - 4 * q^51 - 48 * q^52 + 24 * q^54 - 12 * q^57 - 20 * q^58 + 28 * q^60 - 24 * q^61 - 32 * q^63 + 28 * q^64 + 12 * q^66 + 12 * q^69 - 76 * q^70 + 24 * q^72 - 36 * q^75 - 36 * q^76 + 60 * q^78 - 8 * q^81 + 64 * q^82 - 48 * q^84 + 16 * q^85 + 12 * q^87 + 44 * q^88 - 56 * q^90 - 8 * q^91 - 16 * q^93 + 20 * q^94 + 48 * q^96 - 8 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.09247	+	0.898057i	−0.772494	+	0.635022i
$2$	−1.09247	+	0.898057i	−0.772494	+	0.635022i
$3$	−0.296326	−	1.70651i	−0.171084	−	0.985256i
$3$	−0.296326	−	1.70651i	−0.171084	−	0.985256i
$4$	0.386989	−	1.96220i	0.193494	−	0.981101i
$5$	0.503115	+	2.17873i	0.225000	+	0.974359i
$5$	0.503115	+	2.17873i	0.225000	+	0.974359i
$6$	1.85627	+	1.59820i	0.757821	+	0.652463i
$7$	2.12944	−	2.12944i	0.804851	−	0.804851i	−0.178999	−	0.983849i	$-0.557286\pi$
$7$	2.12944	−	2.12944i	0.804851	−	0.804851i	0.983849	+	0.178999i	$0.0572857\pi$
$8$	1.33939	+	2.49119i	0.473547	+	0.880768i
$9$	−2.82438	+	1.01137i	−0.941461	+	0.337123i
$10$	−2.50626	−	1.92838i	−0.792550	−	0.609807i
$11$	−2.92724	−	2.92724i	−0.882597	−	0.882597i	0.111201	−	0.993798i	$-0.464530\pi$
$11$	−2.92724	−	2.92724i	−0.882597	−	0.882597i	−0.993798	+	0.111201i	$0.964530\pi$
$12$	−3.46320	−	0.0789503i	−0.999740	−	0.0227910i
$13$	3.82476			1.06080			0.530399	−	0.847748i	$-0.322042\pi$
$13$	3.82476			1.06080			0.530399	+	0.847748i	$0.322042\pi$
$14$	−0.413995	+	4.23870i	−0.110645	+	1.13284i
$15$	3.56895	−	1.50419i	0.921499	−	0.388380i
$16$	−3.70048	−	1.51870i	−0.925120	−	0.379675i
$17$	4.54825	−	4.54825i	1.10311	−	1.10311i	0.109079	−	0.994033i	$-0.465210\pi$
$17$	4.54825	−	4.54825i	1.10311	−	1.10311i	0.994033	−	0.109079i	$-0.0347901\pi$
$18$	2.17729	−	3.64135i	0.513192	−	0.858274i
$19$	2.02084	−	2.02084i	0.463612	−	0.463612i	−0.436225	−	0.899837i	$-0.643685\pi$
$19$	2.02084	−	2.02084i	0.463612	−	0.463612i	0.899837	+	0.436225i	$0.143685\pi$
$20$	4.46981	−	0.144068i	0.999481	−	0.0322145i
$21$	−4.26492	−	3.00290i	−0.930682	−	0.655287i
$22$	5.82676	+	0.569101i	1.24227	+	0.121333i
$23$	2.64430	−	2.64430i	0.551376	−	0.551376i	−0.375462	−	0.926838i	$-0.622516\pi$
$23$	2.64430	−	2.64430i	0.551376	−	0.551376i	0.926838	+	0.375462i	$0.122516\pi$
$24$	3.85435	−	3.02390i	0.786766	−	0.617251i
$25$	−4.49375	+	2.19231i	−0.898750	+	0.438461i
$26$	−4.17844	+	3.43485i	−0.819460	+	0.673630i
$27$	2.56285	+	4.52015i	0.493222	+	0.869904i
$28$	−3.35432	−	5.00245i	−0.633906	−	0.945374i
$29$	−0.843557	−	0.843557i	−0.156645	−	0.156645i	0.624433	−	0.781078i	$-0.285330\pi$
$29$	−0.843557	−	0.843557i	−0.156645	−	0.156645i	−0.781078	+	0.624433i	$0.785330\pi$
$30$	−2.54813	+	4.84840i	−0.465223	+	0.885193i
$31$	1.38749			0.249201			0.124600	−	0.992207i	$-0.460235\pi$
$31$	1.38749			0.249201			0.124600	+	0.992207i	$0.460235\pi$
$32$	5.40655	−	1.66410i	0.955752	−	0.294174i
$33$	−4.12797	+	5.86280i	−0.718587	+	1.02058i
$34$	−0.884248	+	9.05341i	−0.151647	+	1.55265i
$35$	5.71082	+	3.56812i	0.965305	+	0.603122i
$36$	0.891507	+	5.93340i	0.148585	+	0.988900i
$37$	−6.69746			−1.10106			−0.550528	−	0.834817i	$-0.685574\pi$
$37$	−6.69746			−1.10106			−0.550528	+	0.834817i	$0.685574\pi$
$38$	−0.392882	+	4.02254i	−0.0637338	+	0.652542i
$39$	−1.13338	−	6.52701i	−0.181485	−	1.04516i
$40$	−4.75377	+	4.17154i	−0.751636	+	0.659578i
$41$	2.65508			0.414654			0.207327	−	0.978272i	$-0.433524\pi$
$41$	2.65508			0.414654			0.207327	+	0.978272i	$0.433524\pi$
$42$	7.35608	−	0.549550i	1.13507	−	0.0847974i
$43$			6.23355i			0.950607i	0.879822	+	0.475304i	$0.157662\pi$
$43$			6.23355i			0.950607i	−0.879822	+	0.475304i	$0.842338\pi$
$44$	−6.87666	+	4.61104i	−1.03670	+	0.695140i
$45$	−3.62449	−	5.64474i	−0.540307	−	0.841468i
$46$	−0.514093	+	5.26356i	−0.0757989	+	0.776070i
$47$	3.32248	−	3.32248i	0.484634	−	0.484634i	−0.421974	−	0.906608i	$-0.638663\pi$
$47$	3.32248	−	3.32248i	0.484634	−	0.484634i	0.906608	+	0.421974i	$0.138663\pi$
$48$	−1.49514	+	6.76495i	−0.215804	+	0.976437i
$49$		−	2.06899i		−	0.295570i
$50$	2.94048	−	6.43067i	0.415847	−	0.909435i
$51$	−9.10941	−	6.41388i	−1.27557	−	0.898123i
$52$	1.48014	−	7.50495i	0.205258	−	1.04075i
$53$	−3.88396			−0.533503			−0.266751	−	0.963765i	$-0.585950\pi$
$53$	−3.88396			−0.533503			−0.266751	+	0.963765i	$0.585950\pi$
$54$	−6.85920	−	2.63655i	−0.933419	−	0.358789i
$55$	4.90494	−	7.85042i	0.661382	−	1.05855i
$56$	8.15698	+	2.45267i	1.09002	+	0.327752i
$57$	−4.04742	−	2.84976i	−0.536094	−	0.377460i
$58$	1.67912	+	0.164000i	0.220480	+	0.0215343i
$59$	−10.3658	+	10.3658i	−1.34951	+	1.34951i	−0.463316	+	0.886193i	$0.653340\pi$
$59$	−10.3658	+	10.3658i	−1.34951	+	1.34951i	−0.886193	+	0.463316i	$0.846660\pi$
$60$	−1.57038	−	7.58511i	−0.202735	−	0.979234i
$61$	3.84345	+	3.84345i	0.492104	+	0.492104i	0.908968	−	0.416865i	$-0.136871\pi$
$61$	3.84345	+	3.84345i	0.492104	+	0.492104i	−0.416865	+	0.908968i	$0.636871\pi$
$62$	−1.51579	+	1.24604i	−0.192506	+	0.158248i
$63$	−3.86069	+	8.16798i	−0.486401	+	1.02907i
$64$	−4.41204	+	6.67337i	−0.551506	+	0.834171i
$65$	1.92429	+	8.33313i	0.238679	+	1.03360i
$66$	−0.755443	−	10.1121i	−0.0929886	−	1.24471i
$67$			10.0836i			1.23191i	0.787781	+	0.615955i	$0.211230\pi$
$67$			10.0836i			1.23191i	−0.787781	+	0.615955i	$0.788770\pi$
$68$	−7.16446	−	10.6847i	−0.868819	−	1.29571i
$69$	−5.29612	−	3.72897i	−0.637578	−	0.448915i
$70$	−9.44328	+	1.23057i	−1.12869	+	0.147081i
$71$	−5.37152			−0.637482			−0.318741	−	0.947842i	$-0.603260\pi$
$71$	−5.37152			−0.637482			−0.318741	+	0.947842i	$0.603260\pi$
$72$	−6.30247	−	5.68145i	−0.742754	−	0.669565i
$73$	2.68667	+	2.68667i	0.314451	+	0.314451i	0.846631	−	0.532180i	$-0.178627\pi$
$73$	2.68667	+	2.68667i	0.314451	+	0.314451i	−0.532180	+	0.846631i	$0.678627\pi$
$74$	7.31679	−	6.01470i	0.850560	−	0.699195i
$75$	5.07282	+	7.01901i	0.585758	+	0.810486i
$76$	−3.18325	−	4.74734i	−0.365144	−	0.544557i
$77$	−12.4668			−1.42072
$78$	7.09980	+	6.11273i	0.803894	+	0.692131i
$79$		−	5.55500i		−	0.624986i	−0.949920	−	0.312493i	$-0.898836\pi$
$79$		−	5.55500i		−	0.624986i	0.949920	−	0.312493i	$-0.101164\pi$
$80$	1.44708	−	8.82644i	0.161788	−	0.986825i
$81$	6.95426	−	5.71299i	0.772696	−	0.634776i
$82$	−2.90060	+	2.38441i	−0.320318	+	0.263314i
$83$		−	1.35478i		−	0.148706i	−0.997232	−	0.0743530i	$-0.976311\pi$
$83$		−	1.35478i		−	0.148706i	0.997232	−	0.0743530i	$-0.0236892\pi$
$84$	−7.54278	+	7.20654i	−0.822985	+	0.786298i
$85$	12.1977	+	7.62112i	1.32303	+	0.826627i
$86$	−5.59808	−	6.80998i	−0.603657	−	0.734339i
$87$	−1.18957	+	1.68951i	−0.127536	+	0.181135i
$88$	3.37158	−	11.2131i	0.359412	−	1.19532i
$89$			5.23963i			0.555400i	0.960668	+	0.277700i	$0.0895721\pi$
$89$			5.23963i			0.555400i	−0.960668	+	0.277700i	$0.910428\pi$
$90$	9.02895	+	2.91172i	0.951735	+	0.306922i
$91$	8.14458	−	8.14458i	0.853784	−	0.853784i
$92$	−4.16534	−	6.21198i	−0.434267	−	0.647643i
$93$	−0.411150	−	2.36777i	−0.0426342	−	0.245527i
$94$	−0.645941	+	6.61349i	−0.0666237	+	0.682130i
$95$	5.41958	+	3.38615i	0.556037	+	0.347412i
$96$	−4.44191	−	8.73324i	−0.453351	−	0.891332i
$97$	−6.28272	−	6.28272i	−0.637913	−	0.637913i	0.312127	−	0.950040i	$-0.398959\pi$
$97$	−6.28272	−	6.28272i	−0.637913	−	0.637913i	−0.950040	+	0.312127i	$0.898959\pi$
$98$	1.85807	+	2.26031i	0.187693	+	0.228326i
$99$	11.2282	+	5.30713i	1.12847	+	0.533387i
$100$	2.56272	+	9.66605i	0.256272	+	0.966605i
$101$	11.7523	+	11.7523i	1.16939	+	1.16939i	0.982352	+	0.187040i	$0.0598895\pi$
$101$	11.7523	+	11.7523i	1.16939	+	1.16939i	0.187040	+	0.982352i	$0.440110\pi$
$102$	15.7118	−	1.17378i	1.55570	−	0.116222i
$103$	7.99433	+	7.99433i	0.787705	+	0.787705i	0.981117	−	0.193413i	$-0.0619557\pi$
$103$	7.99433	+	7.99433i	0.787705	+	0.787705i	−0.193413	+	0.981117i	$0.561956\pi$
$104$	5.12286	+	9.52820i	0.502338	+	0.934317i
$105$	4.39678	−	10.8029i	0.429082	−	1.05426i
$106$	4.24312	−	3.48802i	0.412128	−	0.338786i
$107$		−	9.47431i		−	0.915916i	−0.888974	−	0.457958i	$-0.848581\pi$
$107$		−	9.47431i		−	0.915916i	0.888974	−	0.457958i	$-0.151419\pi$
$108$	9.86125	−	3.27959i	0.948899	−	0.315579i
$109$	−7.26909	+	7.26909i	−0.696253	+	0.696253i	−0.963600	−	0.267347i	$-0.913853\pi$
$109$	−7.26909	+	7.26909i	−0.696253	+	0.696253i	0.267347	+	0.963600i	$0.413853\pi$
$110$	1.69161	+	12.9813i	0.161289	+	1.23772i
$111$	1.98463	+	11.4293i	0.188373	+	1.08482i
$112$	−11.1139	+	4.64595i	−1.05017	+	0.439001i
$113$	12.9233	+	12.9233i	1.21572	+	1.21572i	0.969117	+	0.246601i	$0.0793138\pi$
$113$	12.9233	+	12.9233i	1.21572	+	1.21572i	0.246601	+	0.969117i	$0.420686\pi$
$114$	6.98094	−	0.521524i	0.653825	−	0.0488452i
$115$	7.09162	+	4.43084i	0.661297	+	0.413178i
$116$	−1.98168	+	1.32878i	−0.183994	+	0.123374i
$117$	−10.8026	+	3.86824i	−0.998699	+	0.357619i
$118$	2.01526	−	20.6334i	0.185520	−	1.89946i
$119$		−	19.3704i		−	1.77568i
$120$	8.52745	+	6.87623i	0.778446	+	0.627711i
$121$			6.13752i			0.557956i
$122$	−7.65050	−	0.747225i	−0.692644	−	0.0676506i
$123$	−0.786770	−	4.53093i	−0.0709406	−	0.408541i
$124$	0.536943	−	2.72254i	0.0482189	−	0.244491i
$125$	−7.03732	−	8.68770i	−0.629437	−	0.777052i
$126$	−3.11761	−	12.3904i	−0.277739	−	1.10383i
$127$	−5.95234	−	5.95234i	−0.528185	−	0.528185i	0.391846	−	0.920031i	$-0.371837\pi$
$127$	−5.95234	−	5.95234i	−0.528185	−	0.528185i	−0.920031	+	0.391846i	$0.871837\pi$
$128$	−1.17303	−	11.2527i	−0.103682	−	0.994610i
$129$	10.6376	−	1.84716i	0.936592	−	0.162634i
$130$	−9.58586	−	7.37558i	−0.840735	−	0.646881i
$131$	−6.51499	+	6.51499i	−0.569217	+	0.569217i	−0.931909	−	0.362692i	$-0.881858\pi$
$131$	−6.51499	+	6.51499i	−0.569217	+	0.569217i	0.362692	+	0.931909i	$0.381858\pi$
$132$	9.90653	+	10.3687i	0.862253	+	0.902483i
$133$		−	8.60649i		−	0.746277i
$134$	−9.05566	−	11.0161i	−0.782290	−	0.951644i
$135$	−8.55879	+	7.85793i	−0.736624	+	0.676303i
$136$	17.4224	+	5.23865i	1.49396	+	0.449210i
$137$	7.87520	+	7.87520i	0.672824	+	0.672824i	0.958366	−	0.285542i	$-0.0921736\pi$
$137$	7.87520	+	7.87520i	0.672824	+	0.672824i	−0.285542	+	0.958366i	$0.592174\pi$
$138$	9.13468	−	0.682424i	0.777596	−	0.0580918i
$139$	−9.10718	−	9.10718i	−0.772461	−	0.772461i	0.206075	−	0.978536i	$-0.433931\pi$
$139$	−9.10718	−	9.10718i	−0.772461	−	0.772461i	−0.978536	+	0.206075i	$0.933931\pi$
$140$	9.21140	−	9.82496i	0.778505	−	0.830361i
$141$	−6.65440	−	4.68533i	−0.560402	−	0.394576i
$142$	5.86823	−	4.82392i	0.492451	−	0.404815i
$143$	−11.1960	−	11.1960i	−0.936257	−	0.936257i
$144$	11.9875	+	0.546841i	0.998961	+	0.0455701i
$145$	1.41348	−	2.26229i	0.117383	−	0.187873i
$146$	−5.34790	−	0.522330i	−0.442595	−	0.0432283i
$147$	−3.53076	+	0.613095i	−0.291212	+	0.0505672i
$148$	−2.59184	+	13.1418i	−0.213048	+	1.08025i
$149$	−4.17118	+	4.17118i	−0.341717	+	0.341717i	−0.857012	−	0.515296i	$-0.827682\pi$
$149$	−4.17118	+	4.17118i	−0.341717	+	0.341717i	0.515296	+	0.857012i	$0.327682\pi$
$150$	−11.8454	−	3.11240i	−0.967171	−	0.254126i
$151$			4.13255i			0.336302i	0.985761	+	0.168151i	$0.0537796\pi$
$151$			4.13255i			0.336302i	−0.985761	+	0.168151i	$0.946220\pi$
$152$	7.74099	+	2.32759i	0.627877	+	0.188793i
$153$	−8.24603	+	17.4459i	−0.666652	+	1.41042i
$154$	13.6196	−	11.1958i	1.09750	−	0.902187i
$155$	0.698067	+	3.02297i	0.0560701	+	0.242811i
$156$	−13.2459	−	0.301966i	−1.06052	−	0.0241766i
$157$		−	20.1683i		−	1.60961i	−0.593542	−	0.804803i	$-0.702271\pi$
$157$		−	20.1683i		−	1.60961i	0.593542	−	0.804803i	$-0.297729\pi$
$158$	4.98870	+	6.06868i	0.396880	+	0.482798i
$159$	1.15092	+	6.62803i	0.0912738	+	0.525637i
$160$	6.34575	+	10.9422i	0.501675	+	0.865056i
$161$		−	11.2617i		−	0.887550i
$162$	−2.46675	+	12.4866i	−0.193806	+	0.981040i
$163$	−5.54371			−0.434217			−0.217108	−	0.976147i	$-0.569663\pi$
$163$	−5.54371			−0.434217			−0.217108	+	0.976147i	$0.569663\pi$
$164$	1.02749	−	5.20981i	0.0802333	−	0.406818i
$165$	−14.8503	−	6.04407i	−1.15610	−	0.470530i
$166$	1.21667	+	1.48005i	0.0944316	+	0.114875i
$167$	3.75517	+	3.75517i	0.290584	+	0.290584i	0.837311	−	0.546727i	$-0.184127\pi$
$167$	3.75517	+	3.75517i	0.290584	+	0.290584i	−0.546727	+	0.837311i	$0.684127\pi$
$168$	1.76839	−	14.6468i	0.136434	−	1.13002i
$169$	1.62879			0.125291
$170$	−20.1698	+	2.62837i	−1.54696	+	0.201586i
$171$	−3.66381	+	7.75143i	−0.280178	+	0.592767i
$172$	12.2315	+	2.41231i	0.932642	+	0.183937i
$173$			4.82930i			0.367165i	0.983004	+	0.183582i	$0.0587694\pi$
$173$			4.82930i			0.367165i	−0.983004	+	0.183582i	$0.941231\pi$
$174$	−0.217699	−	2.91405i	−0.0165038	−	0.220913i
$175$	−4.90078	+	14.2375i	−0.370464	+	1.07626i
$176$	6.38660	+	15.2778i	0.481408	+	1.15161i
$177$	20.7610	+	14.6177i	1.56049	+	1.09873i
$178$	−4.70548	−	5.72415i	−0.352691	−	0.429043i
$179$	−11.2085	−	11.2085i	−0.837761	−	0.837761i	0.150803	−	0.988564i	$-0.451814\pi$
$179$	−11.2085	−	11.2085i	−0.837761	−	0.837761i	−0.988564	+	0.150803i	$0.951814\pi$
$180$	−12.4788	+	4.92754i	−0.930112	+	0.367277i
$181$	17.3401	−	17.3401i	1.28888	−	1.28888i	0.353411	−	0.935468i	$-0.385022\pi$
$181$	17.3401	−	17.3401i	1.28888	−	1.28888i	0.935468	−	0.353411i	$-0.114978\pi$
$182$	−1.58343	+	16.2120i	−0.117372	+	1.20171i
$183$	5.41999	−	7.69782i	0.400657	−	0.569039i
$184$	10.1292	+	3.04569i	0.746737	+	0.224532i
$185$	−3.36959	−	14.5920i	−0.247737	−	1.07282i
$186$	2.57556	+	2.21749i	0.188849	+	0.162594i
$187$	−26.6277			−1.94721
$188$	−5.23362	−	7.80515i	−0.381701	−	0.569249i
$189$	15.0828	+	4.16794i	1.09711	+	0.303173i
$190$	−8.96170	+	1.16781i	−0.650150	+	0.0847221i
$191$		−	5.45453i		−	0.394676i	−0.980336	−	0.197338i	$-0.936770\pi$
$191$		−	5.45453i		−	0.394676i	0.980336	−	0.197338i	$-0.0632296\pi$
$192$	12.6956	+	5.55172i	0.916226	+	0.400661i
$193$	−6.53795	+	6.53795i	−0.470612	+	0.470612i	−0.902113	−	0.431501i	$-0.857984\pi$
$193$	−6.53795	+	6.53795i	−0.470612	+	0.470612i	0.431501	+	0.902113i	$0.357984\pi$
$194$	12.5059	+	1.22146i	0.897873	+	0.0876954i
$195$	13.6504	−	5.75316i	0.977524	−	0.411992i
$196$	−4.05977	−	0.800675i	−0.289984	−	0.0571911i
$197$		−	6.76577i		−	0.482041i	−0.970520	−	0.241021i	$-0.922518\pi$
$197$		−	6.76577i		−	0.482041i	0.970520	−	0.241021i	$-0.0774822\pi$
$198$	−17.0326	+	4.28565i	−1.21045	+	0.304568i
$199$	−2.72711			−0.193319			−0.0966597	−	0.995317i	$-0.530816\pi$
$199$	−2.72711			−0.193319			−0.0966597	+	0.995317i	$0.530816\pi$
$200$	−11.4804	−	8.25842i	−0.811783	−	0.583959i
$201$	17.2078	−	2.98804i	1.21375	−	0.210760i
$202$	−23.3932	−	2.28482i	−1.64594	−	0.160759i
$203$	−3.59260			−0.252151
$204$	−16.1106	+	15.3924i	−1.12797	+	1.07768i
$205$	1.33581	+	5.78471i	0.0932971	+	0.404022i
$206$	−15.9129	−	1.55422i	−1.10871	−	0.108288i
$207$	−4.79416	+	10.1429i	−0.333217	+	0.704980i
$208$	−14.1534	−	5.80867i	−0.981365	−	0.402759i
$209$	−11.8310			−0.818366
$210$	4.89828	+	15.7504i	0.338013	+	1.08688i
$211$	−1.60522	−	1.60522i	−0.110508	−	0.110508i	0.649691	−	0.760198i	$-0.274898\pi$
$211$	−1.60522	−	1.60522i	−0.110508	−	0.110508i	−0.760198	+	0.649691i	$0.774898\pi$
$212$	−1.50305	+	7.62112i	−0.103230	+	0.523420i
$213$	1.59172	+	9.16657i	0.109063	+	0.628083i
$214$	8.50847	+	10.3504i	0.581627	+	0.707540i
$215$	−13.5812	+	3.13619i	−0.926233	+	0.213886i
$216$	−7.82788	+	12.4388i	−0.532620	+	0.846355i
$217$	2.95457	−	2.95457i	0.200569	−	0.200569i
$218$	1.41322	−	14.4693i	0.0957155	−	0.979987i
$219$	3.78871	−	5.38098i	0.256018	−	0.363613i
$220$	−13.5060	−	12.6625i	−0.910572	−	0.853707i
$221$	17.3960	−	17.3960i	1.17018	−	1.17018i
$222$	−12.4323	−	10.7039i	−0.834403	−	0.718398i
$223$	6.16926	−	6.16926i	0.413124	−	0.413124i	−0.469701	−	0.882825i	$-0.655638\pi$
$223$	6.16926	−	6.16926i	0.413124	−	0.413124i	0.882825	+	0.469701i	$0.155638\pi$
$224$	7.96930	−	15.0565i	0.532471	−	1.00600i
$225$	10.4748	−	10.7367i	0.698323	−	0.715783i
$226$	−25.7241	−	2.51248i	−1.71114	−	0.167128i
$227$	15.9373			1.05779			0.528897	−	0.848686i	$-0.322606\pi$
$227$	15.9373			1.05779			0.528897	+	0.848686i	$0.322606\pi$
$228$	−7.15812	+	6.83903i	−0.474058	+	0.452926i
$229$	18.0573	+	18.0573i	1.19326	+	1.19326i	0.976146	+	0.217115i	$0.0696646\pi$
$229$	18.0573	+	18.0573i	1.19326	+	1.19326i	0.217115	+	0.976146i	$0.430335\pi$
$230$	−11.7265	+	1.52810i	−0.773225	+	0.100760i
$231$	3.69422	+	21.2747i	0.243062	+	1.39977i
$232$	0.971604	−	3.23132i	0.0637890	−	0.212146i
$233$	−2.38354	+	2.38354i	−0.156151	+	0.156151i	−0.780859	−	0.624708i	$-0.785218\pi$
$233$	−2.38354	+	2.38354i	−0.156151	+	0.156151i	0.624708	+	0.780859i	$0.285218\pi$
$234$	8.32761	−	13.9273i	0.544393	−	0.910455i
$235$	8.91039	+	5.56721i	0.581250	+	0.363165i
$236$	16.3283	+	24.3512i	1.06288	+	1.58513i
$237$	−9.47968	+	1.64609i	−0.615771	+	0.106925i
$238$	17.3957	+	21.1616i	1.12760	+	1.37170i
$239$	4.65924			0.301381			0.150691	−	0.988581i	$-0.451850\pi$
$239$	4.65924			0.301381			0.150691	+	0.988581i	$0.451850\pi$
$240$	−15.4912	+	0.146043i	−0.999956	+	0.00942703i
$241$	−21.7499			−1.40104			−0.700518	−	0.713635i	$-0.747048\pi$
$241$	−21.7499			−1.40104			−0.700518	+	0.713635i	$0.747048\pi$
$242$	−5.51184	−	6.70506i	−0.354314	−	0.431018i
$243$	−11.8100	−	10.1746i	−0.757613	−	0.652704i
$244$	9.02900	−	6.05426i	0.578023	−	0.387584i
$245$	4.50777	−	1.04094i	0.287991	−	0.0665031i
$246$	4.92856	+	4.24335i	0.314233	+	0.270546i
$247$	7.72922	−	7.72922i	0.491799	−	0.491799i
$248$	1.85840	+	3.45650i	0.118008	+	0.219488i
$249$	−2.31194	+	0.401456i	−0.146514	+	0.0254412i
$250$	15.4901	+	3.17116i	0.979681	+	0.200562i
$251$	−3.41489	−	3.41489i	−0.215546	−	0.215546i	0.591073	−	0.806618i	$-0.298705\pi$
$251$	−3.41489	−	3.41489i	−0.215546	−	0.215546i	−0.806618	+	0.591073i	$0.798705\pi$
$252$	14.5332	+	10.7364i	0.915505	+	0.676328i
$253$	−15.4810			−0.973285
$254$	11.8483	+	1.15723i	0.743428	+	0.0726108i
$255$	9.39106	−	23.0739i	0.588091	−	1.44494i
$256$	11.3871	+	11.2398i	0.711693	+	0.702490i
$257$	−10.2183	+	10.2183i	−0.637399	+	0.637399i	−0.949913	−	0.312514i	$-0.898829\pi$
$257$	−10.2183	+	10.2183i	−0.637399	+	0.637399i	0.312514	+	0.949913i	$0.398829\pi$
$258$	−9.96247	+	11.5712i	−0.620236	+	0.720390i
$259$	−14.2618	+	14.2618i	−0.886186	+	0.886186i
$260$	17.0960	−	0.551025i	1.06025	−	0.0341731i
$261$	3.23568	+	1.52938i	0.200283	+	0.0946662i
$262$	1.26661	−	12.9683i	0.0782516	−	0.801182i
$263$	−10.1554	+	10.1554i	−0.626208	+	0.626208i	−0.947112	−	0.320904i	$-0.896013\pi$
$263$	−10.1554	+	10.1554i	−0.626208	+	0.626208i	0.320904	+	0.947112i	$0.396013\pi$
$264$	−20.1343	−	2.43094i	−1.23918	−	0.149614i
$265$	−1.95408	−	8.46211i	−0.120038	−	0.519823i
$266$	7.72911	+	9.40235i	0.473902	+	0.576495i
$267$	8.94150	−	1.55264i	0.547211	−	0.0950200i
$268$	19.7861	+	3.90225i	1.20863	+	0.238368i
$269$	13.4591	+	13.4591i	0.820618	+	0.820618i	0.986197	−	0.165579i	$-0.0529492\pi$
$269$	13.4591	+	13.4591i	0.820618	+	0.820618i	−0.165579	+	0.986197i	$0.552949\pi$
$270$	2.29338	−	16.2708i	0.139570	−	0.990212i
$271$	−2.61645			−0.158938			−0.0794689	−	0.996837i	$-0.525322\pi$
$271$	−2.61645			−0.158938			−0.0794689	+	0.996837i	$0.525322\pi$
$272$	−23.7381	+	9.92326i	−1.43934	+	0.601686i
$273$	−16.3123	−	11.4854i	−0.987265	−	0.695127i
$274$	−15.6758	−	1.53106i	−0.947011	−	0.0924947i
$275$	19.5717	+	6.73689i	1.18022	+	0.406250i
$276$	−9.36653	+	8.94899i	−0.563799	+	0.538666i
$277$	12.0608			0.724664			0.362332	−	0.932049i	$-0.381981\pi$
$277$	12.0608			0.724664			0.362332	+	0.932049i	$0.381981\pi$
$278$	18.1281	+	1.77057i	1.08725	+	0.106192i
$279$	−3.91880	+	1.40327i	−0.234613	+	0.0840113i
$280$	−1.23982	+	19.0059i	−0.0740933	+	1.13582i
$281$	2.60207			0.155227			0.0776134	−	0.996984i	$-0.475270\pi$
$281$	2.60207			0.155227			0.0776134	+	0.996984i	$0.475270\pi$
$282$	11.4774	−	0.857443i	0.683471	−	0.0510600i
$283$			7.11274i			0.422809i	0.977399	+	0.211404i	$0.0678037\pi$
$283$			7.11274i			0.422809i	−0.977399	+	0.211404i	$0.932196\pi$
$284$	−2.07872	+	10.5400i	−0.123349	+	0.625434i
$285$	4.17256	−	10.2520i	0.247161	−	0.607276i
$286$	22.2860	+	2.17667i	1.31780	+	0.128709i
$287$	5.65382	−	5.65382i	0.333735	−	0.333735i
$288$	−13.5871	+	10.1681i	−0.800630	+	0.599160i
$289$		−	24.3731i		−	1.43371i
$290$	0.487479	+	3.74087i	0.0286258	+	0.219672i
$291$	−8.85982	+	12.5833i	−0.519372	+	0.737645i
$292$	6.31151	−	4.23208i	0.369353	−	0.247664i
$293$	−4.42114			−0.258286			−0.129143	−	0.991626i	$-0.541223\pi$
$293$	−4.42114			−0.258286			−0.129143	+	0.991626i	$0.541223\pi$
$294$	3.30666	−	3.84061i	0.192848	−	0.223989i
$295$	−27.7994	−	17.3691i	−1.61855	−	1.01127i
$296$	−8.97055	−	16.6846i	−0.521402	−	0.969776i
$297$	5.72949	−	20.7337i	0.332459	−	1.20309i
$298$	0.810941	−	8.30286i	0.0469766	−	0.480972i
$299$	10.1138	−	10.1138i	0.584898	−	0.584898i
$300$	15.7358	−	7.23761i	0.908510	−	0.417864i
$301$	13.2739	+	13.2739i	0.765097	+	0.765097i
$302$	−3.71126	−	4.51469i	−0.213559	−	0.259791i
$303$	16.5729	−	23.5379i	0.952087	−	1.35222i
$304$	−10.5471	+	4.40902i	−0.604919	+	0.252875i
$305$	−6.44016	+	10.3076i	−0.368762	+	0.590209i
$306$	−6.65889	−	26.4646i	−0.380663	−	1.51288i
$307$			29.9499i			1.70933i	0.519179	+	0.854665i	$0.326238\pi$
$307$			29.9499i			1.70933i	−0.519179	+	0.854665i	$0.673762\pi$
$308$	−4.82450	+	24.4623i	−0.274901	+	1.39387i
$309$	11.2735	−	16.0114i	0.641327	−	0.910855i
$310$	−3.47742	−	2.67561i	−0.197504	−	0.151964i
$311$	−4.45934			−0.252866			−0.126433	−	0.991975i	$-0.540353\pi$
$311$	−4.45934			−0.252866			−0.126433	+	0.991975i	$0.540353\pi$
$312$	14.7420	−	11.5657i	0.834600	−	0.654778i
$313$	−10.2148	−	10.2148i	−0.577374	−	0.577374i	0.356805	−	0.934179i	$-0.383866\pi$
$313$	−10.2148	−	10.2148i	−0.577374	−	0.577374i	−0.934179	+	0.356805i	$0.883866\pi$
$314$	18.1123	+	22.0333i	1.02214	+	1.24341i
$315$	−19.7382	−	4.30198i	−1.11212	−	0.242389i
$316$	−10.9000	−	2.14972i	−0.613175	−	0.120931i
$317$	12.3959			0.696222			0.348111	−	0.937453i	$-0.386823\pi$
$317$	12.3959			0.696222			0.348111	+	0.937453i	$0.386823\pi$
$318$	−7.20969	−	6.20735i	−0.404300	−	0.348091i
$319$			4.93860i			0.276508i
$320$	−16.7593	−	6.25519i	−0.936871	−	0.349676i
$321$	−16.1680	+	2.80749i	−0.902412	+	0.156699i
$322$	10.1137	+	12.3031i	0.563614	+	0.685627i
$323$		−	18.3825i		−	1.02283i
$324$	−8.51881	−	15.8565i	−0.473267	−	0.880919i
$325$	−17.1875	+	8.38504i	−0.953392	+	0.465118i
$326$	6.05635	−	4.97856i	0.335430	−	0.275737i
$327$	14.5588	+	10.2508i	0.805105	+	0.566870i
$328$	3.55620	+	6.61431i	0.196358	+	0.365214i
$329$		−	14.1500i		−	0.780116i
$330$	21.6515	−	6.73345i	1.19187	−	0.370664i
$331$	−3.32345	+	3.32345i	−0.182673	+	0.182673i	−0.792520	−	0.609846i	$-0.791231\pi$
$331$	−3.32345	+	3.32345i	−0.182673	+	0.182673i	0.609846	+	0.792520i	$0.291231\pi$
$332$	−2.65835	−	0.524283i	−0.145896	−	0.0287738i
$333$	18.9162	−	6.77361i	1.03660	−	0.371192i
$334$	−7.47477	−	0.730061i	−0.409001	−	0.0399472i
$335$	−21.9695	+	5.07322i	−1.20032	+	0.277180i
$336$	11.2217	+	17.5893i	0.612195	+	0.959576i
$337$	23.8025	+	23.8025i	1.29660	+	1.29660i	0.930623	+	0.365980i	$0.119266\pi$
$337$	23.8025	+	23.8025i	1.29660	+	1.29660i	0.365980	+	0.930623i	$0.380734\pi$
$338$	−1.77940	+	1.46274i	−0.0967868	+	0.0795627i
$339$	18.2242	−	25.8832i	0.989804	−	1.40578i
$340$	19.6746	−	20.9851i	1.06700	−	1.13808i
$341$	−4.06152	−	4.06152i	−0.219944	−	0.219944i
$342$	−2.95862	−	11.7585i	−0.159984	−	0.635828i
$343$	10.5003	+	10.5003i	0.566961	+	0.566961i
$344$	−15.5290	+	8.34918i	−0.837265	+	0.450158i
$345$	5.45986	−	13.4149i	0.293949	−	0.722235i
$346$	−4.33698	−	5.27587i	−0.233158	−	0.283633i
$347$			0.669706i			0.0359517i	0.999838	+	0.0179758i	$0.00572220\pi$
$347$			0.669706i			0.0359517i	−0.999838	+	0.0179758i	$0.994278\pi$
$348$	2.85481	+	2.98801i	0.153034	+	0.160174i
$349$	7.86448	−	7.86448i	0.420976	−	0.420976i	−0.464564	−	0.885540i	$-0.653789\pi$
$349$	7.86448	−	7.86448i	0.420976	−	0.420976i	0.885540	+	0.464564i	$0.153789\pi$
$350$	−7.43214	−	19.9553i	−0.397264	−	1.06665i
$351$	9.80230	+	17.2885i	0.523208	+	0.922792i
$352$	−20.6975	−	10.9551i	−1.10318	−	0.583907i
$353$	−6.77427	−	6.77427i	−0.360558	−	0.360558i	0.503460	−	0.864018i	$-0.332060\pi$
$353$	−6.77427	−	6.77427i	−0.360558	−	0.360558i	−0.864018	+	0.503460i	$0.832060\pi$
$354$	−35.8083	+	2.67513i	−1.90319	+	0.142181i
$355$	−2.70249	−	11.7031i	−0.143433	−	0.621136i
$356$	10.2812	+	2.02768i	0.544903	+	0.107467i
$357$	−33.0559	+	5.73995i	−1.74950	+	0.303791i
$358$	22.3108	+	2.17910i	1.17916	+	0.115169i
$359$			13.6099i			0.718301i	0.933280	+	0.359151i	$0.116934\pi$
$359$			13.6099i			0.718301i	−0.933280	+	0.359151i	$0.883066\pi$
$360$	9.20748	−	16.5898i	0.485277	−	0.874360i
$361$			10.8324i			0.570127i
$362$	−3.37118	+	34.5159i	−0.177185	+	1.81412i
$363$	10.4738	−	1.81871i	0.549730	−	0.0954573i
$364$	−12.8295	−	19.1332i	−0.672446	−	1.00285i
$365$	−4.50184	+	7.20524i	−0.235637	+	0.377140i
$366$	0.991892	+	13.2771i	0.0518470	+	0.694006i
$367$	−25.1103	−	25.1103i	−1.31075	−	1.31075i	−0.920863	−	0.389886i	$-0.872514\pi$
$367$	−25.1103	−	25.1103i	−1.31075	−	1.31075i	−0.389886	−	0.920863i	$-0.627486\pi$
$368$	−13.8011	+	5.76928i	−0.719432	+	0.300745i
$369$	−7.49896	+	2.68527i	−0.390380	+	0.139789i
$370$	16.7856	+	12.9152i	0.872642	+	0.671432i
$371$	−8.27064	+	8.27064i	−0.429390	+	0.429390i
$372$	−4.80516	−	0.109543i	−0.249136	−	0.00567953i
$373$		−	24.1055i		−	1.24814i	−0.781370	−	0.624068i	$-0.785479\pi$
$373$		−	24.1055i		−	1.24814i	0.781370	−	0.624068i	$-0.214521\pi$
$374$	29.0900	−	23.9131i	1.50421	−	1.23652i
$375$	−12.7403	+	14.5837i	−0.657909	+	0.753098i
$376$	12.7270	+	3.82682i	0.656347	+	0.197353i
$377$	−3.22640	−	3.22640i	−0.166168	−	0.166168i
$378$	−20.2206	+	8.99185i	−1.04003	+	0.462491i
$379$	13.7770	+	13.7770i	0.707677	+	0.707677i	0.966046	−	0.258369i	$-0.0831850\pi$
$379$	13.7770	+	13.7770i	0.707677	+	0.707677i	−0.258369	+	0.966046i	$0.583185\pi$
$380$	8.74164	−	9.32391i	0.448437	−	0.478307i
$381$	−8.39392	+	11.9216i	−0.430033	+	0.610761i
$382$	4.89847	+	5.95892i	0.250628	+	0.304885i
$383$	24.2856	+	24.2856i	1.24093	+	1.24093i	0.959614	+	0.281319i	$0.0907721\pi$
$383$	24.2856	+	24.2856i	1.24093	+	1.24093i	0.281319	+	0.959614i	$0.409228\pi$
$384$	−18.8554	+	5.33627i	−0.962208	+	0.272315i
$385$	−6.27221	−	27.1617i	−0.319661	−	1.38429i
$386$	1.27108	−	13.0140i	0.0646961	−	0.662394i
$387$	−6.30442	−	17.6059i	−0.320472	−	0.894959i
$388$	−14.7593	+	9.89663i	−0.749290	+	0.502425i
$389$	4.67054	−	4.67054i	0.236806	−	0.236806i	−0.578720	−	0.815526i	$-0.696448\pi$
$389$	4.67054	−	4.67054i	0.236806	−	0.236806i	0.815526	+	0.578720i	$0.196448\pi$
$390$	−9.74600	+	18.5440i	−0.493508	+	0.939011i
$391$		−	24.0539i		−	1.21646i
$392$	5.15424	−	2.77119i	0.260328	−	0.139966i
$393$	13.0485	+	9.18736i	0.658209	+	0.463441i
$394$	6.07605	+	7.39142i	0.306107	+	0.372374i
$395$	12.1029	−	2.79480i	0.608961	−	0.140622i
$396$	14.7588	−	19.9782i	0.741660	−	1.00394i
$397$			26.1442i			1.31214i	0.754699	+	0.656071i	$0.227783\pi$
$397$			26.1442i			1.31214i	−0.754699	+	0.656071i	$0.772217\pi$
$398$	2.97929	−	2.44910i	0.149338	−	0.122762i
$399$	−14.6871	+	2.55033i	−0.735275	+	0.127676i
$400$	19.9585	−	1.28791i	0.997924	−	0.0643956i
$401$		−	18.1955i		−	0.908642i	−0.890838	−	0.454321i	$-0.849882\pi$
$401$		−	18.1955i		−	0.908642i	0.890838	−	0.454321i	$-0.150118\pi$
$402$	−16.1157	+	18.7180i	−0.803776	+	0.933567i
$403$	5.30682			0.264351
$404$	27.6083	−	18.5123i	1.37356	−	0.921022i
$405$	15.9459	+	12.2772i	0.792356	+	0.610059i
$406$	3.92481	−	3.22636i	0.194785	−	0.160121i
$407$	19.6051	+	19.6051i	0.971789	+	0.971789i
$408$	3.77710	−	31.2840i	0.186994	−	1.54879i
$409$	−24.5643			−1.21463			−0.607314	−	0.794462i	$-0.707753\pi$
$409$	−24.5643			−1.21463			−0.607314	+	0.794462i	$0.707753\pi$
$410$	−6.65433	−	5.12000i	−0.328634	−	0.252859i
$411$	11.1055	−	15.7728i	0.547795	−	0.778014i
$412$	18.7802	−	12.5928i	0.925235	−	0.620402i
$413$			44.1465i			2.17231i
$414$	−3.87141	−	15.3862i	−0.190269	−	0.756193i
$415$	2.95169	−	0.681608i	0.144893	−	0.0334588i
$416$	20.6787	−	6.36479i	1.01386	−	0.312059i
$417$	−12.8428	+	18.2402i	−0.628917	+	0.893228i
$418$	12.9250	−	10.6249i	0.632183	−	0.519680i
$419$	−10.9549	−	10.9549i	−0.535182	−	0.535182i	0.386928	−	0.922110i	$-0.373536\pi$
$419$	−10.9549	−	10.9549i	−0.535182	−	0.535182i	−0.922110	+	0.386928i	$0.873536\pi$
$420$	−19.4960	−	12.8080i	−0.951308	−	0.624966i
$421$	−8.82488	+	8.82488i	−0.430098	+	0.430098i	−0.888662	−	0.458564i	$-0.848364\pi$
$421$	−8.82488	+	8.82488i	−0.430098	+	0.430098i	0.458564	+	0.888662i	$0.348364\pi$
$422$	3.19523	+	0.312078i	0.155541	+	0.0151917i
$423$	−6.02370	+	12.7442i	−0.292882	+	0.619645i
$424$	−5.20216	−	9.67568i	−0.252639	−	0.469892i
$425$	−10.4675	+	30.4098i	−0.507750	+	1.47509i
$426$	−9.97101	−	8.58476i	−0.483097	−	0.415933i
$427$	16.3688			0.792140
$428$	−18.5905	−	3.66645i	−0.898607	−	0.177225i
$429$	−15.7885	+	22.4238i	−0.762275	+	1.08263i
$430$	12.0206	−	15.6229i	0.579687	−	0.753404i
$431$		−	0.399838i		−	0.0192595i	−0.999954	−	0.00962976i	$-0.996935\pi$
$431$		−	0.399838i		−	0.0192595i	0.999954	−	0.00962976i	$-0.00306530\pi$
$432$	−2.61903	−	20.6189i	−0.126008	−	0.992029i
$433$	−2.81479	+	2.81479i	−0.135270	+	0.135270i	−0.771500	−	0.636230i	$-0.780493\pi$
$433$	−2.81479	+	2.81479i	−0.135270	+	0.135270i	0.636230	+	0.771500i	$0.280493\pi$
$434$	−0.574414	+	5.88116i	−0.0275727	+	0.282305i
$435$	−4.27948	−	1.74175i	−0.205186	−	0.0835104i
$436$	11.4504	+	17.0765i	0.548374	+	0.817816i
$437$		−	10.6874i		−	0.511249i
$438$	0.693358	+	9.28104i	0.0331299	+	0.443465i
$439$	−4.64758			−0.221817			−0.110909	−	0.993831i	$-0.535376\pi$
$439$	−4.64758			−0.221817			−0.110909	+	0.993831i	$0.535376\pi$
$440$	26.1265	+	1.70433i	1.24553	+	0.0812506i
$441$	2.09251	+	5.84361i	0.0996434	+	0.278267i
$442$	−3.38204	+	34.6271i	−0.160867	+	1.64704i
$443$	33.7852			1.60518			0.802591	−	0.596529i	$-0.203454\pi$
$443$	33.7852			1.60518			0.802591	+	0.596529i	$0.203454\pi$
$444$	23.1947	+	0.528767i	1.10077	+	0.0250942i
$445$	−11.4158	+	2.63614i	−0.541159	+	0.124965i
$446$	−1.19940	+	12.2801i	−0.0567931	+	0.581479i
$447$	8.35421	+	5.88215i	0.395141	+	0.278216i
$448$	4.81535	+	23.6057i	0.227504	+	1.11526i
$449$	9.64441			0.455148			0.227574	−	0.973761i	$-0.426921\pi$
$449$	9.64441			0.455148			0.227574	+	0.973761i	$0.426921\pi$
$450$	−1.80126	+	21.1366i	−0.0849121	+	0.996388i
$451$	−7.77207	−	7.77207i	−0.365973	−	0.365973i
$452$	30.3592	−	20.3569i	1.42798	−	0.957508i
$453$	7.05225	−	1.22458i	0.331344	−	0.0575358i
$454$	−17.4110	+	14.3126i	−0.817139	+	0.671722i
$455$	21.8425	+	13.6472i	1.02399	+	0.639791i
$456$	1.67821	−	13.8998i	0.0785893	−	0.650920i
$457$	12.1950	−	12.1950i	0.570460	−	0.570460i	−0.361797	−	0.932257i	$-0.617837\pi$
$457$	12.1950	−	12.1950i	0.570460	−	0.570460i	0.932257	+	0.361797i	$0.117837\pi$
$458$	−35.9436	−	3.51062i	−1.67953	−	0.164040i
$459$	32.2153	+	8.90228i	1.50368	+	0.415523i
$460$	11.4386	−	12.2005i	0.533327	−	0.568852i
$461$	−3.33005	+	3.33005i	−0.155096	+	0.155096i	−0.780390	−	0.625294i	$-0.784979\pi$
$461$	−3.33005	+	3.33005i	−0.155096	+	0.155096i	0.625294	+	0.780390i	$0.284979\pi$
$462$	−23.1417	−	19.9244i	−1.07665	−	0.926966i
$463$	3.26673	−	3.26673i	0.151818	−	0.151818i	−0.627112	−	0.778929i	$-0.715763\pi$
$463$	3.26673	−	3.26673i	0.151818	−	0.151818i	0.778929	+	0.627112i	$0.215763\pi$
$464$	1.84045	+	4.40268i	0.0854409	+	0.204389i
$465$	4.95189	−	2.08705i	0.229638	−	0.0967845i
$466$	0.463396	−	4.74450i	0.0214664	−	0.219785i
$467$	−33.0741			−1.53048			−0.765242	−	0.643742i	$-0.777381\pi$
$467$	−33.0741			−1.53048			−0.765242	+	0.643742i	$0.777381\pi$
$468$	3.40980	+	22.6938i	0.157618	+	1.04902i
$469$	21.4724	+	21.4724i	0.991504	+	0.991504i
$470$	−14.7340	+	1.92001i	−0.679630	+	0.0885637i
$471$	−34.4175	+	5.97640i	−1.58587	+	0.275378i
$472$	−39.7070	−	11.9392i	−1.82766	−	0.549548i
$473$	18.2471	−	18.2471i	0.839004	−	0.839004i
$474$	8.87800	−	10.3116i	0.407780	−	0.473627i
$475$	−4.65085	+	13.5114i	−0.213396	+	0.619947i
$476$	−38.0086	−	7.49613i	−1.74212	−	0.343584i
$477$	10.9698	−	3.92812i	0.502272	−	0.179856i
$478$	−5.09009	+	4.18426i	−0.232815	+	0.191384i
$479$	−27.6867			−1.26504			−0.632518	−	0.774546i	$-0.717979\pi$
$479$	−27.6867			−1.26504			−0.632518	+	0.774546i	$0.717979\pi$
$480$	16.7926	−	14.0716i	0.766473	−	0.642276i
$481$	−25.6162			−1.16800
$482$	23.7612	−	19.5327i	1.08229	−	0.889688i
$483$	−19.2183	+	3.33715i	−0.874464	+	0.151846i
$484$	12.0431	+	2.37515i	0.547412	+	0.107961i
$485$	10.5274	−	16.8493i	0.478026	−	0.765087i
$486$	22.0395	+	0.509443i	0.999733	+	0.0231088i
$487$	28.8225	−	28.8225i	1.30607	−	1.30607i	0.381843	−	0.924227i	$-0.375289\pi$
$487$	28.8225	−	28.8225i	1.30607	−	1.30607i	0.924227	−	0.381843i	$-0.124711\pi$
$488$	−4.42687	+	14.7227i	−0.200395	+	0.666464i
$489$	1.64275	+	9.46042i	0.0742875	+	0.427815i
$490$	−3.98979	+	5.18543i	−0.180240	+	0.234254i
$491$	2.93822	+	2.93822i	0.132600	+	0.132600i	0.770292	−	0.637692i	$-0.220111\pi$
$491$	2.93822	+	2.93822i	0.132600	+	0.132600i	−0.637692	+	0.770292i	$0.720111\pi$
$492$	−9.19508	−	0.209619i	−0.414546	−	0.00945037i
$493$	−7.67341			−0.345593
$494$	−1.50268	+	15.3852i	−0.0676087	+	0.692214i
$495$	−5.91375	+	27.1333i	−0.265803	+	1.21955i
$496$	−5.13438	−	2.10718i	−0.230540	−	0.0946154i
$497$	−11.4383	+	11.4383i	−0.513078	+	0.513078i
$498$	2.16520	−	2.51484i	0.0970251	−	0.112692i
$499$	4.06607	−	4.06607i	0.182022	−	0.182022i	−0.610214	−	0.792237i	$-0.708917\pi$
$499$	4.06607	−	4.06607i	0.182022	−	0.182022i	0.792237	+	0.610214i	$0.208917\pi$
$500$	−19.7704	+	10.4466i	−0.884159	+	0.467186i
$501$	5.29549	−	7.52100i	0.236585	−	0.336013i
$502$	6.79743	+	0.663906i	0.303384	+	0.0296316i
$503$	15.4387	−	15.4387i	0.688376	−	0.688376i	−0.273497	−	0.961873i	$-0.588180\pi$
$503$	15.4387	−	15.4387i	0.688376	−	0.688376i	0.961873	+	0.273497i	$0.0881804\pi$
$504$	−25.5190	+	1.32244i	−1.13671	+	0.0589061i
$505$	−19.6923	+	31.5177i	−0.876295	+	1.40252i
$506$	16.9126	−	13.9029i	0.751857	−	0.618057i
$507$	−0.482652	−	2.77955i	−0.0214353	−	0.123444i
$508$	−13.9832	+	9.37621i	−0.620403	+	0.416002i
$509$	−11.3533	−	11.3533i	−0.503227	−	0.503227i	0.409212	−	0.912439i	$-0.365804\pi$
$509$	−11.3533	−	11.3533i	−0.503227	−	0.503227i	−0.912439	+	0.409212i	$0.865804\pi$
$510$	10.4622	+	33.6413i	0.463274	+	1.48966i
$511$	11.4422			0.506173
$512$	−22.5341	−	2.05296i	−0.995876	−	0.0907290i
$513$	14.3136	+	3.95538i	0.631961	+	0.174634i
$514$	1.98659	−	20.3398i	0.0876246	−	0.897149i
$515$	−13.3954	+	21.4396i	−0.590274	+	0.944740i
$516$	0.492140	−	21.5880i	0.0216653	−	0.950361i
$517$	−19.4514			−0.855473
$518$	2.77271	−	28.3885i	0.121826	−	1.24732i
$519$	8.24126	−	1.43105i	0.361751	−	0.0628160i
$520$	−18.1820	+	15.9551i	−0.797334	+	0.699679i
$521$	−20.3718			−0.892506			−0.446253	−	0.894907i	$-0.647242\pi$
$521$	−20.3718			−0.892506			−0.446253	+	0.894907i	$0.647242\pi$
$522$	−4.90835	+	1.23502i	−0.214833	+	0.0540552i
$523$		−	41.7664i		−	1.82632i	−0.407604	−	0.913159i	$-0.633636\pi$
$523$		−	41.7664i		−	1.82632i	0.407604	−	0.913159i	$-0.366364\pi$
$524$	10.2625	+	15.3050i	0.448319	+	0.668600i
$525$	25.7488	+	4.14430i	1.12377	+	0.180872i
$526$	1.97436	−	20.2146i	0.0860863	−	0.881398i
$527$	6.31065	−	6.31065i	0.274896	−	0.274896i
$528$	24.1793	−	15.4260i	1.05227	−	0.671332i
$529$			9.01531i			0.391970i
$530$	9.73423	+	7.48974i	0.422828	+	0.325334i
$531$	18.7933	−	39.7605i	0.815559	−	1.72546i
$532$	−16.8877	−	3.33062i	−0.732174	−	0.144401i
$533$	10.1550			0.439864
$534$	−8.37398	+	9.72619i	−0.362378	+	0.420893i
$535$	20.6420	−	4.76667i	0.892431	−	0.206081i
$536$	−25.1202	+	13.5059i	−1.08503	+	0.583368i
$537$	−15.8061	+	22.4488i	−0.682082	+	0.968737i
$538$	−26.7908	−	2.61666i	−1.15503	−	0.112812i
$539$	−6.05643	+	6.05643i	−0.260869	+	0.260869i
$540$	12.1067	+	19.8350i	0.520989	+	0.853563i
$541$	−20.4942	−	20.4942i	−0.881113	−	0.881113i	0.112535	−	0.993648i	$-0.464103\pi$
$541$	−20.4942	−	20.4942i	−0.881113	−	0.881113i	−0.993648	+	0.112535i	$0.964103\pi$
$542$	2.85839	−	2.34972i	0.122778	−	0.100929i
$543$	−34.7294	−	24.4528i	−1.49038	−	1.04937i
$544$	17.0216	−	32.1591i	0.729794	−	1.37881i
$545$	−19.4946	−	12.1802i	−0.835057	−	0.521743i
$546$	28.1352	−	2.10190i	1.20408	−	0.0899529i
$547$			10.5384i			0.450588i	0.974291	+	0.225294i	$0.0723342\pi$
$547$			10.5384i			0.450588i	−0.974291	+	0.225294i	$0.927666\pi$
$548$	18.5004	−	12.4051i	0.790296	−	0.529921i
$549$	−14.7425	−	6.96823i	−0.629196	−	0.297397i
$550$	−27.4317	+	10.2166i	−1.16969	+	0.435639i
$551$	−3.40939			−0.145245
$552$	2.19597	−	18.1882i	0.0934666	−	0.774141i
$553$	−11.8290	−	11.8290i	−0.503020	−	0.503020i
$554$	−13.1761	+	10.8313i	−0.559798	+	0.460177i
$555$	−23.9029	+	10.0742i	−1.01462	+	0.427628i
$556$	−21.3945	+	14.3458i	−0.907330	+	0.608396i
$557$	23.7749			1.00737			0.503687	−	0.863886i	$-0.331976\pi$
$557$	23.7749			1.00737			0.503687	+	0.863886i	$0.331976\pi$
$558$	3.02097	−	5.05233i	0.127888	−	0.213882i
$559$			23.8418i			1.00840i
$560$	−15.7139	−	21.8768i	−0.664032	−	0.924463i
$561$	7.89047	+	45.4405i	0.333136	+	1.91850i
$562$	−2.84269	+	2.33681i	−0.119912	+	0.0985724i
$563$			5.63612i			0.237534i	0.992922	+	0.118767i	$0.0378942\pi$
$563$			5.63612i			0.237534i	−0.992922	+	0.118767i	$0.962106\pi$
$564$	−11.7687	+	11.2441i	−0.495553	+	0.473463i
$565$	−21.6544	+	34.6582i	−0.911009	+	1.45808i
$566$	−6.38765	−	7.77047i	−0.268493	−	0.326617i
$567$	2.64322	−	26.9741i	0.111005	−	1.13281i
$568$	−7.19458	−	13.3815i	−0.301878	−	0.561474i
$569$			8.82620i			0.370014i	0.982737	+	0.185007i	$0.0592307\pi$
$569$			8.82620i			0.370014i	−0.982737	+	0.185007i	$0.940769\pi$
$570$	4.64847	+	14.9472i	0.194703	+	0.626070i
$571$	−1.54350	+	1.54350i	−0.0645936	+	0.0645936i	−0.738666	−	0.674072i	$-0.764544\pi$
$571$	−1.54350	+	1.54350i	−0.0645936	+	0.0645936i	0.674072	+	0.738666i	$0.264544\pi$
$572$	−26.3016	+	17.6361i	−1.09972	+	0.737403i
$573$	−9.30823	+	1.61632i	−0.388857	+	0.0675227i
$574$	−1.09919	+	11.2541i	−0.0458793	+	0.469737i
$575$	−6.08572	+	17.6800i	−0.253792	+	0.737306i
$576$	5.71206	−	23.3103i	0.238002	−	0.971265i
$577$	−0.768842	−	0.768842i	−0.0320073	−	0.0320073i	0.690922	−	0.722929i	$-0.257205\pi$
$577$	−0.768842	−	0.768842i	−0.0320073	−	0.0320073i	−0.722929	+	0.690922i	$0.757205\pi$
$578$	21.8884	+	26.6269i	0.910438	+	1.10753i
$579$	13.0945	+	9.21974i	0.544188	+	0.383159i
$580$	−3.89207	−	3.64901i	−0.161610	−	0.151517i
$581$	−2.88491	−	2.88491i	−0.119686	−	0.119686i
$582$	−1.62140	−	21.7035i	−0.0672092	−	0.899639i
$583$	11.3693	+	11.3693i	0.470868	+	0.470868i
$584$	−3.09449	+	10.2915i	−0.128051	+	0.425866i
$585$	−13.8628	−	21.5898i	−0.573157	−	0.892627i
$586$	4.82997	−	3.97043i	0.199524	−	0.164017i
$587$			0.262771i			0.0108457i	0.999985	+	0.00542286i	$0.00172616\pi$
$587$			0.262771i			0.0108457i	−0.999985	+	0.00542286i	$0.998274\pi$
$588$	−0.163347	+	7.16532i	−0.00673632	+	0.295493i
$589$	2.80389	−	2.80389i	0.115532	−	0.115532i
$590$	45.9685	−	5.99023i	1.89249	−	0.246614i
$591$	−11.5459	+	2.00488i	−0.474934	+	0.0824696i
$592$	24.7838	+	10.1714i	1.01861	+	0.418044i
$593$	−10.9183	−	10.9183i	−0.448362	−	0.448362i	0.446448	−	0.894810i	$-0.352689\pi$
$593$	−10.9183	−	10.9183i	−0.448362	−	0.448362i	−0.894810	+	0.446448i	$0.852689\pi$
$594$	12.3607	+	27.7964i	0.507166	+	1.14050i
$595$	42.2029	−	9.74553i	1.73015	−	0.399528i
$596$	6.57050	+	9.79891i	0.269138	+	0.401379i
$597$	0.808113	+	4.65385i	0.0330739	+	0.190469i
$598$	−1.96628	+	20.1319i	−0.0804072	+	0.823253i
$599$			48.0234i			1.96218i	0.193545	+	0.981091i	$0.438001\pi$
$599$			48.0234i			1.96218i	−0.193545	+	0.981091i	$0.561999\pi$
$600$	−10.6912	+	22.0386i	−0.436466	+	0.899721i
$601$			42.1359i			1.71876i	0.511337	+	0.859380i	$0.329150\pi$
$601$			42.1359i			1.71876i	−0.511337	+	0.859380i	$0.670850\pi$
$602$	−26.4222	−	2.58066i	−1.07689	−	0.105180i
$603$	−10.1983	−	28.4800i	−0.415305	−	1.15979i
$604$	8.10889	+	1.59925i	0.329946	+	0.0650725i
$605$	−13.3720	+	3.08788i	−0.543650	+	0.125540i
$606$	3.03294	+	40.5979i	0.123205	+	1.64918i
$607$	14.3583	+	14.3583i	0.582787	+	0.582787i	0.935668	−	0.352881i	$-0.114798\pi$
$607$	14.3583	+	14.3583i	0.582787	+	0.582787i	−0.352881	+	0.935668i	$0.614798\pi$
$608$	7.56288	−	14.2886i	0.306715	−	0.579481i
$609$	1.06458	+	6.13082i	0.0431390	+	0.248434i
$610$	−2.22107	−	17.0443i	−0.0899287	−	0.690105i
$611$	12.7077	−	12.7077i	0.514098	−	0.514098i
$612$	31.0414	+	22.9318i	1.25477	+	0.926962i
$613$		−	35.1551i		−	1.41990i	−0.704251	−	0.709951i	$-0.748717\pi$
$613$		−	35.1551i		−	1.41990i	0.704251	−	0.709951i	$-0.251283\pi$
$614$	−26.8967	−	32.7194i	−1.08546	−	1.32045i
$615$	9.47586	−	3.99374i	0.382103	−	0.161043i
$616$	−16.6979	−	31.0570i	−0.672778	−	1.25132i
$617$	−14.6639	−	14.6639i	−0.590344	−	0.590344i	0.347380	−	0.937724i	$-0.387071\pi$
$617$	−14.6639	−	14.6639i	−0.590344	−	0.590344i	−0.937724	+	0.347380i	$0.887071\pi$
$618$	2.06312	+	27.6162i	0.0829909	+	1.11089i
$619$	−3.72169	−	3.72169i	−0.149587	−	0.149587i	0.628346	−	0.777934i	$-0.283732\pi$
$619$	−3.72169	−	3.72169i	−0.149587	−	0.149587i	−0.777934	+	0.628346i	$0.783732\pi$
$620$	6.20183	−	0.199893i	0.249071	−	0.00802789i
$621$	18.7296	+	5.17569i	0.751594	+	0.207693i
$622$	4.87171	−	4.00474i	0.195338	−	0.160576i
$623$	11.1575	+	11.1575i	0.447014	+	0.447014i
$624$	−5.71854	+	25.8743i	−0.228925	+	1.03580i
$625$	15.3876	−	19.7033i	0.615504	−	0.788134i
$626$	20.3328	+	1.98591i	0.812663	+	0.0793729i
$627$	3.50583	+	20.1897i	0.140009	+	0.806300i
$628$	−39.5743	−	7.80491i	−1.57919	−	0.311450i
$629$	−30.4617	+	30.4617i	−1.21459	+	1.21459i
$630$	25.4269	−	13.0262i	1.01303	−	0.518978i
$631$			31.9724i			1.27280i	0.771359	+	0.636400i	$0.219577\pi$
$631$			31.9724i			1.27280i	−0.771359	+	0.636400i	$0.780423\pi$
$632$	13.8385	−	7.44033i	0.550468	−	0.295961i
$633$	−2.26366	+	3.21499i	−0.0899723	+	0.127784i
$634$	−13.5422	+	11.1322i	−0.537828	+	0.442116i
$635$	9.97384	−	15.9633i	0.395800	−	0.633483i
$636$	13.4509	+	0.306640i	0.533364	+	0.0121591i
$637$		−	7.91338i		−	0.313540i
$638$	−4.43514	−	5.39528i	−0.175589	−	0.213601i
$639$	15.1712	−	5.43259i	0.600164	−	0.214910i
$640$	23.9265	−	8.21713i	0.945779	−	0.324811i
$641$		−	22.6325i		−	0.893930i	−0.894551	−	0.446965i	$-0.852505\pi$
$641$		−	22.6325i		−	0.893930i	0.894551	−	0.446965i	$-0.147495\pi$
$642$	15.1419	−	17.5869i	0.597601	−	0.694100i
$643$	13.0421			0.514329			0.257165	−	0.966368i	$-0.417212\pi$
$643$	13.0421			0.514329			0.257165	+	0.966368i	$0.417212\pi$
$644$	−22.0978	−	4.35817i	−0.870777	−	0.171736i
$645$	9.37643	+	22.2472i	0.369197	+	0.875984i
$646$	16.5086	+	20.0824i	0.649521	+	0.790132i
$647$	−29.6121	−	29.6121i	−1.16417	−	1.16417i	−0.983553	−	0.180621i	$-0.942189\pi$
$647$	−29.6121	−	29.6121i	−1.16417	−	1.16417i	−0.180621	−	0.983553i	$-0.557811\pi$
$648$	23.5466	+	9.67244i	0.924999	+	0.379969i
$649$	60.6863			2.38215
$650$	11.2466	−	24.5958i	0.441129	−	0.964726i
$651$	−5.91753	−	4.16650i	−0.231926	−	0.163298i
$652$	−2.14535	+	10.8779i	−0.0840186	+	0.426011i
$653$		−	28.5044i		−	1.11546i	−0.830021	−	0.557732i	$-0.811672\pi$
$653$		−	28.5044i		−	1.11546i	0.830021	−	0.557732i	$-0.188328\pi$
$654$	−25.1109	+	1.87596i	−0.981914	+	0.0733558i
$655$	−17.4722	−	10.9166i	−0.682695	−	0.426548i
$656$	−9.82507	−	4.03228i	−0.383605	−	0.157434i
$657$	−10.3054	−	4.87097i	−0.402052	−	0.190035i
$658$	12.7075	+	15.4585i	0.495391	+	0.602635i
$659$	−1.45554	−	1.45554i	−0.0566997	−	0.0566997i	0.678188	−	0.734888i	$-0.262765\pi$
$659$	−1.45554	−	1.45554i	−0.0566997	−	0.0566997i	−0.734888	+	0.678188i	$0.762765\pi$
$660$	−17.6066	+	26.8003i	−0.685336	+	1.04320i
$661$	15.7799	−	15.7799i	0.613765	−	0.613765i	−0.330160	−	0.943925i	$-0.607103\pi$
$661$	15.7799	−	15.7799i	0.613765	−	0.613765i	0.943925	+	0.330160i	$0.107103\pi$
$662$	0.646128	−	6.61541i	0.0251125	−	0.257115i
$663$	−34.8413	−	24.5316i	−1.35312	−	0.952727i
$664$	3.37500	−	1.81458i	0.130976	−	0.0704194i
$665$	18.7512	−	4.33005i	0.727142	−	0.167912i
$666$	−14.5823	+	24.3878i	−0.565054	+	0.945008i
$667$	−4.46124			−0.172740
$668$	8.82161	−	5.91519i	0.341318	−	0.228866i
$669$	−12.3560	−	8.69982i	−0.477712	−	0.336354i
$670$	19.4450	−	25.2722i	0.751227	−	0.976351i
$671$		−	22.5014i		−	0.868659i
$672$	−28.0556	−	9.13809i	−1.08227	−	0.352510i
$673$	−0.659734	+	0.659734i	−0.0254309	+	0.0254309i	−0.719708	−	0.694277i	$-0.755724\pi$
$673$	−0.659734	+	0.659734i	−0.0254309	+	0.0254309i	0.694277	+	0.719708i	$0.255724\pi$
$674$	−47.3795	−	4.62756i	−1.82499	−	0.178247i
$675$	−21.4264	−	14.6939i	−0.824702	−	0.565568i
$676$	0.630323	−	3.19601i	0.0242432	−	0.122923i
$677$		−	41.0728i		−	1.57856i	−0.614036	−	0.789278i	$-0.710455\pi$
$677$		−	41.0728i		−	1.57856i	0.614036	−	0.789278i	$-0.289545\pi$
$678$	3.33515	+	44.6431i	0.128086	+	1.71451i
$679$	−26.7573			−1.02685
$680$	−2.64812	+	40.5945i	−0.101551	+	1.55673i
$681$	−4.72263	−	27.1972i	−0.180971	−	1.04220i
$682$	8.08458	+	0.789622i	0.309574	+	0.0302362i
$683$	−37.5396			−1.43641			−0.718207	−	0.695830i	$-0.755037\pi$
$683$	−37.5396			−1.43641			−0.718207	+	0.695830i	$0.755037\pi$
$684$	13.7920	+	10.1888i	0.527352	+	0.389580i
$685$	−13.1958	+	21.1201i	−0.504187	+	0.806957i
$686$	−20.9011	−	2.04141i	−0.798007	−	0.0779415i
$687$	25.4642	−	36.1659i	0.971520	−	1.37982i
$688$	9.46690	−	23.0671i	0.360922	−	0.879426i
$689$	−14.8552			−0.565939
$690$	6.08261	+	19.5587i	0.231561	+	0.744587i
$691$	−29.6548	−	29.6548i	−1.12812	−	1.12812i	−0.990483	−	0.137638i	$-0.956049\pi$
$691$	−29.6548	−	29.6548i	−1.12812	−	1.12812i	−0.137638	−	0.990483i	$-0.543951\pi$
$692$	9.47606	+	1.86888i	0.360226	+	0.0710443i
$693$	35.2109	−	12.6085i	1.33755	−	0.478957i
$694$	−0.601433	−	0.731634i	−0.0228301	−	0.0277725i
$695$	15.2602	−	24.4241i	0.578851	−	0.926458i
$696$	−5.80220	−	0.700533i	−0.219932	−	0.0265537i
$697$	12.0760	−	12.0760i	0.457410	−	0.457410i
$698$	−1.52897	+	15.6545i	−0.0578725	+	0.592530i
$699$	4.77385	+	3.36124i	0.180564	+	0.127134i
$700$	26.0404	+	15.1261i	0.984233	+	0.571712i
$701$	16.0824	−	16.0824i	0.607422	−	0.607422i	−0.334849	−	0.942272i	$-0.608685\pi$
$701$	16.0824	−	16.0824i	0.607422	−	0.607422i	0.942272	+	0.334849i	$0.108685\pi$
$702$	−26.2348	−	10.0842i	−0.990168	−	0.380603i
$703$	−13.5345	+	13.5345i	−0.510463	+	0.510463i
$704$	32.4497	−	6.61945i	1.22299	−	0.249480i
$705$	6.86014	−	16.8554i	0.258368	−	0.634812i
$706$	13.4844	+	1.31702i	0.507492	+	0.0495668i
$707$	50.0513			1.88237
$708$	36.7172	−	35.0804i	1.37992	−	1.31840i
$709$	−24.7407	−	24.7407i	−0.929157	−	0.929157i	0.0684944	−	0.997651i	$-0.478180\pi$
$709$	−24.7407	−	24.7407i	−0.929157	−	0.929157i	−0.997651	+	0.0684944i	$0.978180\pi$
$710$	13.4624	+	10.3583i	0.505236	+	0.388741i
$711$	5.61815	+	15.6894i	0.210697	+	0.588400i
$712$	−13.0529	+	7.01793i	−0.489179	+	0.263008i
$713$	3.66895	−	3.66895i	0.137403	−	0.137403i
$714$	30.9578	−	35.9568i	1.15857	−	1.34565i
$715$	18.7602	−	30.0260i	0.701593	−	1.12291i
$716$	−26.3309	+	17.6558i	−0.984031	+	0.659826i
$717$	−1.38066	−	7.95107i	−0.0515615	−	0.296938i
$718$	−12.2224	−	14.8684i	−0.456137	−	0.554884i
$719$	13.4644			0.502137			0.251068	−	0.967969i	$-0.419218\pi$
$719$	13.4644			0.502137			0.251068	+	0.967969i	$0.419218\pi$
$720$	4.83968	+	26.3928i	0.180364	+	0.983600i
$721$	34.0468			1.26797
$722$	−9.72813	−	11.8341i	−0.362043	−	0.440420i
$723$	6.44507	+	37.1165i	0.239695	+	1.38038i
$724$	−27.3144	−	40.7352i	−1.01513	−	1.51391i
$725$	5.64007	+	1.94140i	0.209467	+	0.0721018i
$726$	−9.80899	+	11.3929i	−0.364046	+	0.422831i
$727$	−16.7234	+	16.7234i	−0.620235	+	0.620235i	−0.945592	−	0.325356i	$-0.894516\pi$
$727$	−16.7234	+	16.7234i	−0.620235	+	0.620235i	0.325356	+	0.945592i	$0.394516\pi$
$728$	31.1985	+	9.38088i	1.15629	+	0.347679i
$729$	−13.8636	+	23.1690i	−0.513465	+	0.858110i
$730$	−1.55259	−	11.9144i	−0.0574639	−	0.440973i
$731$	28.3517	+	28.3517i	1.04863	+	1.04863i
$732$	−13.0072	−	13.6141i	−0.480760	−	0.503191i
$733$	48.3320			1.78518			0.892591	−	0.450867i	$-0.148885\pi$
$733$	48.3320			1.78518			0.892591	+	0.450867i	$0.148885\pi$
$734$	49.9828	+	4.88183i	1.84490	+	0.180192i
$735$	−3.11215	−	7.38412i	−0.114793	−	0.272367i
$736$	9.89617	−	18.6969i	0.364778	−	0.689179i
$737$	29.5172	−	29.5172i	1.08728	−	1.08728i
$738$	5.78088	−	9.66807i	0.212797	−	0.355887i
$739$	21.0974	−	21.0974i	0.776080	−	0.776080i	−0.203081	−	0.979162i	$-0.565096\pi$
$739$	21.0974	−	21.0974i	0.776080	−	0.776080i	0.979162	+	0.203081i	$0.0650956\pi$
$740$	−29.9364	+	0.964889i	−1.10048	+	0.0354700i
$741$	−15.4804	−	10.8997i	−0.568687	−	0.400409i
$742$	1.60794	−	16.4629i	0.0590293	−	0.604374i
$743$	−12.2403	+	12.2403i	−0.449053	+	0.449053i	−0.895040	−	0.445986i	$-0.852853\pi$
$743$	−12.2403	+	12.2403i	−0.449053	+	0.449053i	0.445986	+	0.895040i	$0.352853\pi$
$744$	5.34788	−	4.19563i	0.196063	−	0.153819i
$745$	−11.1865	−	6.98931i	−0.409841	−	0.256068i
$746$	21.6481	+	26.3346i	0.792594	+	0.964178i
$747$	1.37018	+	3.82641i	0.0501322	+	0.140001i
$748$	−10.3046	+	52.2489i	−0.376774	+	1.91041i
$749$	−20.1749	−	20.1749i	−0.737176	−	0.737176i
$750$	0.821498	−	27.3738i	0.0299969	−	0.999550i
$751$	29.0583			1.06035			0.530177	−	0.847887i	$-0.322126\pi$
$751$	29.0583			1.06035			0.530177	+	0.847887i	$0.322126\pi$
$752$	−17.3406	+	7.24892i	−0.632348	+	0.264341i
$753$	−4.81563	+	6.83948i	−0.175491	+	0.249244i
$754$	6.42225	+	0.627262i	0.233884	+	0.0228435i
$755$	−9.00371	+	2.07914i	−0.327679	+	0.0756678i
$756$	14.0152	−	27.9826i	0.509729	−	1.01772i
$757$	25.6342			0.931691			0.465846	−	0.884866i	$-0.345750\pi$
$757$	25.6342			0.931691			0.465846	+	0.884866i	$0.345750\pi$
$758$	−27.4235	−	2.67846i	−0.996067	−	0.0972860i
$759$	4.58744	+	26.4186i	0.166513	+	0.958935i
$760$	−1.17659	+	18.0366i	−0.0426794	+	0.654256i
$761$	−34.7046			−1.25804			−0.629020	−	0.777389i	$-0.716544\pi$
$761$	−34.7046			−1.25804			−0.629020	+	0.777389i	$0.716544\pi$
$762$	−1.53614	−	20.5622i	−0.0556484	−	0.744890i
$763$			30.9581i			1.12076i
$764$	−10.7029	−	2.11084i	−0.387217	−	0.0763676i
$765$	−42.1587	−	9.18858i	−1.52425	−	0.332214i
$766$	−48.3411	−	4.72148i	−1.74663	−	0.170594i
$767$	−39.6466	+	39.6466i	−1.43156	+	1.43156i
$768$	15.8067	−	22.7629i	0.570374	−	0.821385i
$769$			5.49454i			0.198138i	0.995081	+	0.0990691i	$0.0315865\pi$
$769$			5.49454i			0.198138i	−0.995081	+	0.0990691i	$0.968414\pi$
$770$	31.2450	+	24.0406i	1.12599	+	0.866364i
$771$	20.4656	+	14.4097i	0.737050	+	0.518952i
$772$	10.2987	+	15.3589i	0.370657	+	0.552779i
$773$	−27.3609			−0.984103			−0.492051	−	0.870566i	$-0.663753\pi$
$773$	−27.3609			−0.984103			−0.492051	+	0.870566i	$0.663753\pi$
$774$	22.6985	+	13.5722i	0.815881	+	0.487844i
$775$	−6.23504	+	3.04180i	−0.223969	+	0.109265i
$776$	7.23640	−	24.0665i	0.259772	−	0.863936i
$777$	28.5641	+	20.1118i	1.02473	+	0.721508i
$778$	−0.908024	+	9.29684i	−0.0325542	+	0.333308i
$779$	5.36549	−	5.36549i	0.192239	−	0.192239i
$780$	−6.00631	−	29.0112i	−0.215061	−	1.03877i
$781$	15.7237	+	15.7237i	0.562640	+	0.562640i
$782$	21.6018	+	26.2782i	0.772477	+	0.939707i
$783$	1.65109	−	5.97492i	0.0590052	−	0.213526i
$784$	−3.14218	+	7.65625i	−0.112221	+	0.273437i
$785$	43.9413	−	10.1470i	1.56833	−	0.362161i
$786$	−22.5059	+	1.68134i	−0.802758	+	0.0599715i
$787$			38.9292i			1.38768i	0.720131	+	0.693838i	$0.244082\pi$
$787$			38.9292i			1.38768i	−0.720131	+	0.693838i	$0.755918\pi$
$788$	−13.2758	−	2.61828i	−0.472932	−	0.0932724i
$789$	20.3396	+	14.3210i	0.724110	+	0.509841i
$790$	−10.7121	+	13.9223i	−0.381121	+	0.495333i
$791$	55.0385			1.95694
$792$	1.81790	+	35.0799i	0.0645963	+	1.24651i
$793$	14.7003	+	14.7003i	0.522022	+	0.522022i
$794$	−23.4790	−	28.5618i	−0.833238	−	1.01362i
$795$	−13.8617	+	5.84221i	−0.491623	+	0.207202i
$796$	−1.05536	+	5.35114i	−0.0374062	+	0.189666i
$797$	−23.1152			−0.818784			−0.409392	−	0.912359i	$-0.634259\pi$
$797$	−23.1152			−0.818784			−0.409392	+	0.912359i	$0.634259\pi$
$798$	13.7549	−	15.9760i	0.486918	−	0.565544i
$799$		−	30.2229i		−	1.06921i
$800$	−20.6475	+	19.3309i	−0.729998	+	0.683449i
$801$	−5.29920	−	14.7987i	−0.187238	−	0.522887i
$802$	16.3406	+	19.8781i	0.577007	+	0.701921i
$803$		−	15.7291i		−	0.555068i
$804$	0.796104	−	34.9216i	0.0280764	−	1.23159i
$805$	24.5363	−	5.66595i	0.864792	−	0.199699i
$806$	−5.79755	+	4.76582i	−0.204210	+	0.167869i
$807$	18.9799	−	26.9565i	0.668124	−	0.948913i
$808$	−13.5362	+	45.0180i	−0.476201	+	1.58373i
$809$		−	22.0206i		−	0.774203i	−0.922037	−	0.387102i	$-0.873476\pi$
$809$		−	22.0206i		−	0.774203i	0.922037	−	0.387102i	$-0.126524\pi$
$810$	−28.4460	+	0.907799i	−0.999491	+	0.0318968i
$811$	−13.5094	+	13.5094i	−0.474381	+	0.474381i	−0.903329	−	0.428948i	$-0.858884\pi$
$811$	−13.5094	+	13.5094i	−0.474381	+	0.474381i	0.428948	+	0.903329i	$0.358884\pi$
$812$	−1.39030	+	7.04941i	−0.0487898	+	0.247386i
$813$	0.775321	+	4.46500i	0.0271917	+	0.156594i
$814$	−39.0245	−	3.81153i	−1.36781	−	0.133594i
$815$	−2.78912	−	12.0783i	−0.0976987	−	0.423083i
$816$	23.9684	+	37.5689i	0.839062	+	1.31518i
$817$	12.5970	+	12.5970i	0.440713	+	0.440713i
$818$	26.8358	−	22.0602i	0.938293	−	0.771316i
$819$	−14.7662	+	31.2406i	−0.515973	+	1.09163i
$820$	11.8677	−	0.382512i	0.414439	−	0.0133579i
$821$	1.40441	+	1.40441i	0.0490142	+	0.0490142i	0.731189	−	0.682175i	$-0.238966\pi$
$821$	1.40441	+	1.40441i	0.0490142	+	0.0490142i	−0.682175	+	0.731189i	$0.738966\pi$
$822$	2.03238	+	27.2047i	0.0708874	+	0.948873i
$823$	13.2359	+	13.2359i	0.461373	+	0.461373i	0.899105	−	0.437732i	$-0.144218\pi$
$823$	13.2359	+	13.2359i	0.461373	+	0.461373i	−0.437732	+	0.899105i	$0.644218\pi$
$824$	−9.20782	+	30.6229i	−0.320770	+	1.06680i
$825$	5.69700	−	35.3957i	0.198344	−	1.23232i
$826$	−39.6460	−	48.2288i	−1.37946	−	1.67809i
$827$			8.66513i			0.301316i	0.988586	+	0.150658i	$0.0481392\pi$
$827$			8.66513i			0.301316i	−0.988586	+	0.150658i	$0.951861\pi$
$828$	18.0471	+	13.3323i	0.627181	+	0.463329i
$829$	13.0794	−	13.0794i	0.454266	−	0.454266i	−0.442501	−	0.896768i	$-0.645909\pi$
$829$	13.0794	−	13.0794i	0.454266	−	0.454266i	0.896768	+	0.442501i	$0.145909\pi$
$830$	−2.61252	+	3.39543i	−0.0906819	+	0.117857i
$831$	−3.57393	−	20.5819i	−0.123978	−	0.713980i
$832$	−16.8750	+	25.5240i	−0.585036	+	0.884887i
$833$	−9.41027	−	9.41027i	−0.326046	−	0.326046i
$834$	−2.35032	−	31.4605i	−0.0813849	−	1.08939i
$835$	−6.29222	+	10.0708i	−0.217751	+	0.348514i
$836$	−4.57846	+	23.2148i	−0.158349	+	0.802900i
$837$	3.55594	+	6.27167i	0.122911	+	0.216781i
$838$	21.8060	+	2.12980i	0.753277	+	0.0735726i
$839$		−	32.7312i		−	1.13001i	−0.825088	−	0.565004i	$-0.808875\pi$
$839$		−	32.7312i		−	1.13001i	0.825088	−	0.565004i	$-0.191125\pi$
$840$	32.8011	−	3.51616i	1.13175	−	0.121319i
$841$		−	27.5768i		−	0.950925i
$842$	1.71569	−	17.5662i	0.0591266	−	0.605370i
$843$	−0.771063	−	4.44048i	−0.0265568	−	0.152938i
$844$	−3.77096	+	2.52856i	−0.129802	+	0.0870366i
$845$	0.819467	+	3.54869i	0.0281905	+	0.122079i
$846$	−4.86430	−	19.3323i	−0.167238	−	0.664659i
$847$	13.0694	+	13.0694i	0.449071	+	0.449071i
$848$	14.3725	+	5.89858i	0.493554	+	0.202558i
$849$	12.1380	−	2.10769i	0.416575	−	0.0723358i
$850$	−15.8743	−	42.6223i	−0.544482	−	1.46193i
$851$	−17.7101	+	17.7101i	−0.607096	+	0.607096i
$852$	18.6026	+	0.424083i	0.637316	+	0.0145288i
$853$			14.6057i			0.500089i	0.968234	+	0.250045i	$0.0804453\pi$
$853$			14.6057i			0.500089i	−0.968234	+	0.250045i	$0.919555\pi$
$854$	−17.8824	+	14.7001i	−0.611923	+	0.503026i
$855$	−18.7316	−	4.08259i	−0.640608	−	0.139622i
$856$	23.6023	−	12.6898i	0.806710	−	0.433730i
$857$	15.0381	+	15.0381i	0.513692	+	0.513692i	0.915656	−	0.401964i	$-0.131672\pi$
$857$	15.0381	+	15.0381i	0.513692	+	0.513692i	−0.401964	+	0.915656i	$0.631672\pi$
$858$	−2.88939	−	38.6763i	−0.0986421	−	1.32039i
$859$	−10.2451	−	10.2451i	−0.349557	−	0.349557i	0.510387	−	0.859945i	$-0.329502\pi$
$859$	−10.2451	−	10.2451i	−0.349557	−	0.349557i	−0.859945	+	0.510387i	$0.829502\pi$
$860$	0.898054	+	27.8628i	0.0306234	+	0.950114i
$861$	−11.3237	−	7.97295i	−0.385911	−	0.271718i
$862$	0.359077	+	0.436812i	0.0122302	+	0.0148779i
$863$	20.5930	+	20.5930i	0.700995	+	0.700995i	0.964624	−	0.263629i	$-0.0849196\pi$
$863$	20.5930	+	20.5930i	0.700995	+	0.700995i	−0.263629	+	0.964624i	$0.584920\pi$
$864$	21.3782	+	20.1736i	0.727301	+	0.686319i
$865$	−10.5217	+	2.42969i	−0.357750	+	0.0826119i
$866$	0.547237	−	5.60291i	0.0185959	−	0.190395i
$867$	−41.5930	+	7.22238i	−1.41257	+	0.245285i
$868$	−4.65408	−	6.94085i	−0.157970	−	0.235588i
$869$	−16.2608	+	16.2608i	−0.551611	+	0.551611i
$870$	6.23940	−	1.94041i	0.211536	−	0.0657860i
$871$			38.5674i			1.30681i
$872$	−27.8449	−	8.37250i	−0.942946	−	0.283529i
$873$	24.0989	+	11.3906i	0.815626	+	0.385515i
$874$	9.59791	+	11.6757i	0.324654	+	0.394937i
$875$	−33.4854	−	3.51438i	−1.13201	−	0.118808i
$876$	−9.09237	−	9.51660i	−0.307203	−	0.321536i
$877$		−	12.6122i		−	0.425883i	−0.977065	−	0.212941i	$-0.931696\pi$
$877$		−	12.6122i		−	0.425883i	0.977065	−	0.212941i	$-0.0683043\pi$
$878$	5.07735	−	4.17379i	0.171352	−	0.140859i
$879$	1.31010	+	7.54474i	0.0441885	+	0.254478i
$880$	−30.0731	+	21.6012i	−1.01376	+	0.728176i
$881$			54.9606i			1.85167i	0.377929	+	0.925835i	$0.376636\pi$
$881$			54.9606i			1.85167i	−0.377929	+	0.925835i	$0.623364\pi$
$882$	−7.53390	−	4.50479i	−0.253680	−	0.151684i
$883$	−53.0273			−1.78451			−0.892255	−	0.451532i	$-0.850878\pi$
$883$	−53.0273			−1.78451			−0.892255	+	0.451532i	$0.850878\pi$
$884$	−27.4023	−	40.8664i	−0.921641	−	1.37449i
$885$	−21.4029	+	52.5870i	−0.719450	+	1.76769i
$886$	−36.9094	+	30.3410i	−1.23999	+	1.01933i
$887$	−12.4037	−	12.4037i	−0.416476	−	0.416476i	0.467511	−	0.883987i	$-0.345151\pi$
$887$	−12.4037	−	12.4037i	−0.416476	−	0.416476i	−0.883987	+	0.467511i	$0.845151\pi$
$888$	−25.8144	+	20.2525i	−0.866274	+	0.679628i
$889$	−25.3502			−0.850220
$890$	10.1040	−	13.1319i	0.338687	−	0.440182i
$891$	−37.0801	−	3.63352i	−1.24223	−	0.121728i
$892$	−9.71791	−	14.4928i	−0.325380	−	0.485254i
$893$		−	13.4284i		−	0.449364i
$894$	−14.4092	+	1.07647i	−0.481917	+	0.0360025i
$895$	18.7811	−	30.0594i	0.627784	−	1.00478i
$896$	−26.4599	−	21.4641i	−0.883962	−	0.717064i
$897$	−20.2564	−	14.2624i	−0.676341	−	0.476208i
$898$	−10.5362	+	8.66122i	−0.351599	+	0.289029i
$899$	−1.17043	−	1.17043i	−0.0390359	−	0.0390359i
$900$	−17.0140	−	24.7088i	−0.567134	−	0.823625i
$901$	−17.6652	+	17.6652i	−0.588513	+	0.588513i
$902$	15.4705	+	1.51101i	0.515112	+	0.0503111i
$903$	18.7188	−	26.5856i	0.622921	−	0.884713i
$904$	−14.8849	+	49.5036i	−0.495066	+	1.64647i
$905$	46.5035	+	29.0554i	1.54583	+	0.965833i
$906$	−6.60464	+	7.67114i	−0.219424	+	0.254856i
$907$	−13.2167			−0.438853			−0.219426	−	0.975629i	$-0.570419\pi$
$907$	−13.2167			−0.438853			−0.219426	+	0.975629i	$0.570419\pi$
$908$	6.16754	−	31.2721i	0.204677	−	1.03780i
$909$	−45.0787	−	21.3070i	−1.49517	−	0.706708i
$910$	−36.1183	+	4.70663i	−1.19731	+	0.156023i
$911$		−	38.6519i		−	1.28059i	−0.768127	−	0.640297i	$-0.778811\pi$
$911$		−	38.6519i		−	1.28059i	0.768127	−	0.640297i	$-0.221189\pi$
$912$	10.6494	+	16.6923i	0.352638	+	0.552737i
$913$	−3.96576	+	3.96576i	−0.131248	+	0.131248i
$914$	−2.37090	+	24.2746i	−0.0784224	+	0.802932i
$915$	19.4984	+	7.93582i	0.644596	+	0.262350i
$916$	42.4201	−	28.4441i	1.40160	−	0.939820i
$917$			27.7465i			0.916270i
$918$	−43.1890	+	19.2056i	−1.42545	+	0.633881i
$919$	−28.3921			−0.936568			−0.468284	−	0.883578i	$-0.655128\pi$
$919$	−28.3921			−0.936568			−0.468284	+	0.883578i	$0.655128\pi$
$920$	−1.53959	+	23.6012i	−0.0507588	+	0.778109i
$921$	51.1099	−	8.87493i	1.68413	−	0.292439i
$922$	0.647413	−	6.62856i	0.0213214	−	0.218300i
$923$	−20.5448			−0.676239
$924$	43.1749	+	0.984253i	1.42035	+	0.0323796i
$925$	30.0967	−	14.6829i	0.989575	−	0.482770i
$926$	−0.635103	+	6.50253i	−0.0208708	+	0.213686i
$927$	−30.6643	−	14.4938i	−1.00715	−	0.476039i
$928$	−5.96450	−	3.15697i	−0.195794	−	0.103633i
$929$	54.4255			1.78564			0.892822	−	0.450410i	$-0.148722\pi$
$929$	54.4255			1.78564			0.892822	+	0.450410i	$0.148722\pi$
$930$	−3.53551	+	6.72711i	−0.115934	+	0.220591i
$931$	−4.18109	−	4.18109i	−0.137030	−	0.137030i
$932$	3.75458	+	5.59939i	0.122985	+	0.183414i
$933$	1.32142	+	7.60993i	0.0432613	+	0.249138i
$934$	36.1325	−	29.7024i	1.18229	−	0.971891i
$935$	−13.3968	−	58.0145i	−0.438121	−	1.89728i
$936$	−24.1054	−	21.7302i	−0.787911	−	0.710273i
$937$	30.3898	−	30.3898i	0.992791	−	0.992791i	−0.00718307	−	0.999974i	$-0.502286\pi$
$937$	30.3898	−	30.3898i	0.992791	−	0.992791i	0.999974	+	0.00718307i	$0.00228646\pi$
$938$	−42.7414	−	4.17456i	−1.39556	−	0.136304i
$939$	−14.4048	+	20.4586i	−0.470082	+	0.667641i
$940$	14.3722	−	15.3295i	0.468770	−	0.499995i
$941$	−33.7798	+	33.7798i	−1.10119	+	1.10119i	−0.106922	+	0.994267i	$0.534100\pi$
$941$	−33.7798	+	33.7798i	−1.10119	+	1.10119i	−0.994267	+	0.106922i	$0.965900\pi$
$942$	32.2330	−	37.4379i	1.05021	−	1.21979i
$943$	7.02084	−	7.02084i	0.228630	−	0.228630i
$944$	54.1009	−	22.6158i	1.76083	−	0.736082i
$945$	−1.49244	+	34.9583i	−0.0485492	+	1.13720i
$946$	−3.54752	+	36.3214i	−0.115340	+	1.18091i
$947$	0.231368			0.00751845			0.00375923	−	0.999993i	$-0.498803\pi$
$947$	0.231368			0.00751845			0.00375923	+	0.999993i	$0.498803\pi$
$948$	−0.438568	+	19.2381i	−0.0142440	+	0.624824i
$949$	10.2759	+	10.2759i	0.333569	+	0.333569i
$950$	−7.05311	−	18.9376i	−0.228833	−	0.614417i
$951$	−3.67322	−	21.1538i	−0.119112	−	0.685958i
$952$	48.2553	−	25.9446i	1.56396	−	0.840869i
$953$	−28.2451	+	28.2451i	−0.914950	+	0.914950i	−0.996656	−	0.0817066i	$-0.973963\pi$
$953$	−28.2451	+	28.2451i	−0.914950	+	0.914950i	0.0817066	+	0.996656i	$0.473963\pi$
$954$	−8.45651	+	14.1428i	−0.273790	+	0.457892i
$955$	11.8840	−	2.74425i	0.384556	−	0.0888020i
$956$	1.80308	−	9.14238i	0.0583156	−	0.295686i
$957$	8.42778	−	1.46343i	0.272432	−	0.0473061i
$958$	30.2469	−	24.8642i	0.977233	−	0.803326i
$959$	33.5395			1.08305
$960$	−5.70837	+	30.4535i	−0.184237	+	0.982882i
$961$	−29.0749			−0.937899
$962$	27.9850	−	23.0048i	0.902272	−	0.741704i
$963$	9.58203	+	26.7591i	0.308777	+	0.862299i
$964$	−8.41698	+	42.6777i	−0.271093	+	1.37456i
$965$	−17.5338	−	10.9551i	−0.564433	−	0.352657i
$966$	17.9985	−	20.9049i	0.579093	−	0.672604i
$967$	−24.2968	+	24.2968i	−0.781332	+	0.781332i	−0.980056	−	0.198723i	$-0.936320\pi$
$967$	−24.2968	+	24.2968i	−0.781332	+	0.781332i	0.198723	+	0.980056i	$0.436320\pi$
$968$	−15.2897	+	8.22056i	−0.491430	+	0.264219i
$969$	−31.3701	+	5.44723i	−1.00775	+	0.174990i
$970$	3.63069	+	27.8616i	0.116574	+	0.894582i
$971$	19.7408	+	19.7408i	0.633512	+	0.633512i	0.948947	−	0.315435i	$-0.102150\pi$
$971$	19.7408	+	19.7408i	0.633512	+	0.633512i	−0.315435	+	0.948947i	$0.602150\pi$
$972$	−24.5351	+	19.2362i	−0.786962	+	0.617001i
$973$	−38.7863			−1.24343
$974$	−5.60352	+	57.3719i	−0.179548	+	1.83831i
$975$	19.4023	+	26.8460i	0.621371	+	0.859761i
$976$	−8.38556	−	20.0597i	−0.268415	−	0.642094i
$977$	−0.855791	+	0.855791i	−0.0273792	+	0.0273792i	−0.720664	−	0.693285i	$-0.756163\pi$
$977$	−0.855791	+	0.855791i	−0.0273792	+	0.0273792i	0.693285	+	0.720664i	$0.256163\pi$
$978$	−10.2906	−	8.85996i	−0.329059	−	0.283310i
$979$	15.3377	−	15.3377i	0.490194	−	0.490194i
$980$	−0.298075	−	9.24799i	−0.00952164	−	0.295416i
$981$	13.1790	−	27.8824i	0.420772	−	0.890218i
$982$	−5.84860	−	0.571234i	−0.186636	−	0.0182288i
$983$	−2.64752	+	2.64752i	−0.0844427	+	0.0844427i	−0.748066	−	0.663624i	$-0.769018\pi$
$983$	−2.64752	+	2.64752i	−0.0844427	+	0.0844427i	0.663624	+	0.748066i	$0.269018\pi$
$984$	10.2336	−	8.02870i	0.326236	−	0.255946i
$985$	14.7408	−	3.40396i	0.469681	−	0.108459i
$986$	8.38299	−	6.89116i	0.266969	−	0.219459i
$987$	−24.1472	+	4.19302i	−0.768614	+	0.133465i
$988$	−12.1752	−	18.1574i	−0.387344	−	0.577665i
$989$	16.4834	+	16.4834i	0.524142	+	0.524142i
$990$	−17.9066	−	34.9532i	−0.569110	−	1.11089i
$991$	−56.4625			−1.79359			−0.896794	−	0.442447i	$-0.854110\pi$
$991$	−56.4625			−1.79359			−0.896794	+	0.442447i	$0.854110\pi$
$992$	7.50154	−	2.30892i	0.238174	−	0.0733084i
$993$	6.65633	+	4.68668i	0.211232	+	0.148727i
$994$	2.22378	−	22.7682i	0.0705340	−	0.722165i
$995$	−1.37205	−	5.94163i	−0.0434968	−	0.188362i
$996$	−0.106960	+	4.69186i	−0.00338916	+	0.148667i
$997$	−30.4515			−0.964408			−0.482204	−	0.876059i	$-0.660164\pi$
$997$	−30.4515			−0.964408			−0.482204	+	0.876059i	$0.660164\pi$
$998$	−0.790507	+	8.09364i	−0.0250231	+	0.256200i
$999$	−17.1646	−	30.2736i	−0.543065	−	0.957813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bf.a.77.10	yes	88
3.2	odd	2	inner	240.2.bf.a.77.35	yes	88
4.3	odd	2		960.2.bf.a.17.24		88
5.3	odd	4		240.2.bb.a.173.32	yes	88
12.11	even	2		960.2.bf.a.17.23		88
15.8	even	4		240.2.bb.a.173.13	✓	88
16.5	even	4		240.2.bb.a.197.13	yes	88
16.11	odd	4		960.2.bb.a.497.43		88
20.3	even	4		960.2.bb.a.593.2		88
48.5	odd	4		240.2.bb.a.197.32	yes	88
48.11	even	4		960.2.bb.a.497.2		88
60.23	odd	4		960.2.bb.a.593.43		88
80.43	even	4		960.2.bf.a.113.24		88
80.53	odd	4	inner	240.2.bf.a.53.35	yes	88
240.53	even	4	inner	240.2.bf.a.53.10	yes	88
240.203	odd	4		960.2.bf.a.113.23		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bb.a.173.13	✓	88	15.8	even	4
240.2.bb.a.173.32	yes	88	5.3	odd	4
240.2.bb.a.197.13	yes	88	16.5	even	4
240.2.bb.a.197.32	yes	88	48.5	odd	4
240.2.bf.a.53.10	yes	88	240.53	even	4	inner
240.2.bf.a.53.35	yes	88	80.53	odd	4	inner
240.2.bf.a.77.10	yes	88	1.1	even	1	trivial
240.2.bf.a.77.35	yes	88	3.2	odd	2	inner
960.2.bb.a.497.2		88	48.11	even	4
960.2.bb.a.497.43		88	16.11	odd	4
960.2.bb.a.593.2		88	20.3	even	4
960.2.bb.a.593.43		88	60.23	odd	4
960.2.bf.a.17.23		88	12.11	even	2
960.2.bf.a.17.24		88	4.3	odd	2
960.2.bf.a.113.23		88	240.203	odd	4
960.2.bf.a.113.24		88	80.43	even	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bf (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09247 + 0.898057i) q^{2} +(-0.296326 - 1.70651i) q^{3} +(0.386989 - 1.96220i) q^{4} +(0.503115 + 2.17873i) q^{5} +(1.85627 + 1.59820i) q^{6} +(2.12944 - 2.12944i) q^{7} +(1.33939 + 2.49119i) q^{8} +(-2.82438 + 1.01137i) q^{9} +O(q^{10})\)	\(q+(-1.09247 + 0.898057i) q^{2} +(-0.296326 - 1.70651i) q^{3} +(0.386989 - 1.96220i) q^{4} +(0.503115 + 2.17873i) q^{5} +(1.85627 + 1.59820i) q^{6} +(2.12944 - 2.12944i) q^{7} +(1.33939 + 2.49119i) q^{8} +(-2.82438 + 1.01137i) q^{9} +(-2.50626 - 1.92838i) q^{10} +(-2.92724 - 2.92724i) q^{11} +(-3.46320 - 0.0789503i) q^{12} +3.82476 q^{13} +(-0.413995 + 4.23870i) q^{14} +(3.56895 - 1.50419i) q^{15} +(-3.70048 - 1.51870i) q^{16} +(4.54825 - 4.54825i) q^{17} +(2.17729 - 3.64135i) q^{18} +(2.02084 - 2.02084i) q^{19} +(4.46981 - 0.144068i) q^{20} +(-4.26492 - 3.00290i) q^{21} +(5.82676 + 0.569101i) q^{22} +(2.64430 - 2.64430i) q^{23} +(3.85435 - 3.02390i) q^{24} +(-4.49375 + 2.19231i) q^{25} +(-4.17844 + 3.43485i) q^{26} +(2.56285 + 4.52015i) q^{27} +(-3.35432 - 5.00245i) q^{28} +(-0.843557 - 0.843557i) q^{29} +(-2.54813 + 4.84840i) q^{30} +1.38749 q^{31} +(5.40655 - 1.66410i) q^{32} +(-4.12797 + 5.86280i) q^{33} +(-0.884248 + 9.05341i) q^{34} +(5.71082 + 3.56812i) q^{35} +(0.891507 + 5.93340i) q^{36} -6.69746 q^{37} +(-0.392882 + 4.02254i) q^{38} +(-1.13338 - 6.52701i) q^{39} +(-4.75377 + 4.17154i) q^{40} +2.65508 q^{41} +(7.35608 - 0.549550i) q^{42} +6.23355i q^{43} +(-6.87666 + 4.61104i) q^{44} +(-3.62449 - 5.64474i) q^{45} +(-0.514093 + 5.26356i) q^{46} +(3.32248 - 3.32248i) q^{47} +(-1.49514 + 6.76495i) q^{48} -2.06899i q^{49} +(2.94048 - 6.43067i) q^{50} +(-9.10941 - 6.41388i) q^{51} +(1.48014 - 7.50495i) q^{52} -3.88396 q^{53} +(-6.85920 - 2.63655i) q^{54} +(4.90494 - 7.85042i) q^{55} +(8.15698 + 2.45267i) q^{56} +(-4.04742 - 2.84976i) q^{57} +(1.67912 + 0.164000i) q^{58} +(-10.3658 + 10.3658i) q^{59} +(-1.57038 - 7.58511i) q^{60} +(3.84345 + 3.84345i) q^{61} +(-1.51579 + 1.24604i) q^{62} +(-3.86069 + 8.16798i) q^{63} +(-4.41204 + 6.67337i) q^{64} +(1.92429 + 8.33313i) q^{65} +(-0.755443 - 10.1121i) q^{66} +10.0836i q^{67} +(-7.16446 - 10.6847i) q^{68} +(-5.29612 - 3.72897i) q^{69} +(-9.44328 + 1.23057i) q^{70} -5.37152 q^{71} +(-6.30247 - 5.68145i) q^{72} +(2.68667 + 2.68667i) q^{73} +(7.31679 - 6.01470i) q^{74} +(5.07282 + 7.01901i) q^{75} +(-3.18325 - 4.74734i) q^{76} -12.4668 q^{77} +(7.09980 + 6.11273i) q^{78} -5.55500i q^{79} +(1.44708 - 8.82644i) q^{80} +(6.95426 - 5.71299i) q^{81} +(-2.90060 + 2.38441i) q^{82} -1.35478i q^{83} +(-7.54278 + 7.20654i) q^{84} +(12.1977 + 7.62112i) q^{85} +(-5.59808 - 6.80998i) q^{86} +(-1.18957 + 1.68951i) q^{87} +(3.37158 - 11.2131i) q^{88} +5.23963i q^{89} +(9.02895 + 2.91172i) q^{90} +(8.14458 - 8.14458i) q^{91} +(-4.16534 - 6.21198i) q^{92} +(-0.411150 - 2.36777i) q^{93} +(-0.645941 + 6.61349i) q^{94} +(5.41958 + 3.38615i) q^{95} +(-4.44191 - 8.73324i) q^{96} +(-6.28272 - 6.28272i) q^{97} +(1.85807 + 2.26031i) q^{98} +(11.2282 + 5.30713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{3} + 4 q^{4} - 4 q^{6}+O(q^{10}) \) 88 * q - 4 * q^3 + 4 * q^4 - 4 * q^6	\( 88 q - 4 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{10} - 8 q^{12} - 8 q^{13} - 4 q^{15} - 12 q^{16} - 12 q^{18} + 8 q^{19} - 4 q^{21} - 4 q^{22} + 12 q^{24} - 4 q^{27} - 4 q^{28} - 28 q^{30} - 16 q^{31} - 4 q^{33} - 28 q^{34} - 20 q^{36} - 8 q^{37} - 24 q^{39} - 44 q^{40} + 40 q^{42} + 8 q^{45} - 36 q^{46} + 32 q^{48} - 4 q^{51} - 48 q^{52} + 24 q^{54} - 12 q^{57} - 20 q^{58} + 28 q^{60} - 24 q^{61} - 32 q^{63} + 28 q^{64} + 12 q^{66} + 12 q^{69} - 76 q^{70} + 24 q^{72} - 36 q^{75} - 36 q^{76} + 60 q^{78} - 8 q^{81} + 64 q^{82} - 48 q^{84} + 16 q^{85} + 12 q^{87} + 44 q^{88} - 56 q^{90} - 8 q^{91} - 16 q^{93} + 20 q^{94} + 48 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) \) 88 * q - 4 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^10 - 8 * q^12 - 8 * q^13 - 4 * q^15 - 12 * q^16 - 12 * q^18 + 8 * q^19 - 4 * q^21 - 4 * q^22 + 12 * q^24 - 4 * q^27 - 4 * q^28 - 28 * q^30 - 16 * q^31 - 4 * q^33 - 28 * q^34 - 20 * q^36 - 8 * q^37 - 24 * q^39 - 44 * q^40 + 40 * q^42 + 8 * q^45 - 36 * q^46 + 32 * q^48 - 4 * q^51 - 48 * q^52 + 24 * q^54 - 12 * q^57 - 20 * q^58 + 28 * q^60 - 24 * q^61 - 32 * q^63 + 28 * q^64 + 12 * q^66 + 12 * q^69 - 76 * q^70 + 24 * q^72 - 36 * q^75 - 36 * q^76 + 60 * q^78 - 8 * q^81 + 64 * q^82 - 48 * q^84 + 16 * q^85 + 12 * q^87 + 44 * q^88 - 56 * q^90 - 8 * q^91 - 16 * q^93 + 20 * q^94 + 48 * q^96 - 8 * q^97 + 32 * q^99

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