LMFDB - Embedded newform 125.2.g.a.106.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(6,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

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

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

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

chi := DirichletCharacter("125.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.g (of order $25$, degree $20$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$11$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			106.2
Character	$\chi$	$=$	125.106
Dual form			125.2.g.a.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27891 + 2.01523i) q^{2} +(0.512565 - 0.481331i) q^{3} +(-1.57401 - 3.34494i) q^{4} +(0.847185 + 2.06937i) q^{5} +(0.314471 + 1.64852i) q^{6} +(-3.30265 + 2.39951i) q^{7} +(4.01791 + 0.507580i) q^{8} +(-0.157328 + 2.50065i) q^{9} +O(q^{10})$	\(q+(-1.27891 + 2.01523i) q^{2} +(0.512565 - 0.481331i) q^{3} +(-1.57401 - 3.34494i) q^{4} +(0.847185 + 2.06937i) q^{5} +(0.314471 + 1.64852i) q^{6} +(-3.30265 + 2.39951i) q^{7} +(4.01791 + 0.507580i) q^{8} +(-0.157328 + 2.50065i) q^{9} +(-5.25373 - 0.939249i) q^{10} +(1.32763 - 2.09201i) q^{11} +(-2.41681 - 0.956881i) q^{12} +(-0.238672 + 3.79358i) q^{13} +(-0.611805 - 9.72436i) q^{14} +(1.43029 + 0.652909i) q^{15} +(-1.44860 + 1.75106i) q^{16} +(1.73221 - 3.68113i) q^{17} +(-4.83820 - 3.51515i) q^{18} +(-2.17821 - 2.04548i) q^{19} +(5.58843 - 6.09099i) q^{20} +(-0.537862 + 2.81957i) q^{21} +(2.51798 + 5.35098i) q^{22} +(4.33365 + 1.11269i) q^{23} +(2.30376 - 1.67378i) q^{24} +(-3.56455 + 3.50627i) q^{25} +(-7.33972 - 5.33262i) q^{26} +(2.46759 + 2.98281i) q^{27} +(13.2246 + 7.27030i) q^{28} +(8.15030 + 4.48067i) q^{29} +(-3.14497 + 2.04736i) q^{30} +(1.91555 - 4.07076i) q^{31} +(0.826773 + 2.54454i) q^{32} +(-0.326452 - 1.71132i) q^{33} +(5.20300 + 8.19862i) q^{34} +(-7.76342 - 4.80155i) q^{35} +(8.61217 - 3.40980i) q^{36} +(2.22918 - 2.69462i) q^{37} +(6.90785 - 1.77363i) q^{38} +(1.70363 + 2.05934i) q^{39} +(2.35355 + 8.74455i) q^{40} +(-6.11953 + 1.57123i) q^{41} +(-4.99422 - 4.68989i) q^{42} +(1.85131 - 5.69773i) q^{43} +(-9.08736 - 1.14800i) q^{44} +(-5.30805 + 1.79295i) q^{45} +(-7.78468 + 7.31030i) q^{46} +(-0.290407 + 0.0366869i) q^{47} +(0.100336 + 1.59479i) q^{48} +(2.98669 - 9.19209i) q^{49} +(-2.50723 - 11.6676i) q^{50} +(-0.883971 - 2.72058i) q^{51} +(13.0650 - 5.17279i) q^{52} +(1.67953 - 8.80442i) q^{53} +(-9.16687 + 1.15805i) q^{54} +(5.45389 + 0.975033i) q^{55} +(-14.4877 + 7.96467i) q^{56} -2.10103 q^{57} +(-19.4531 + 10.6944i) q^{58} +(7.25227 + 2.87137i) q^{59} +(-0.0673450 - 5.81191i) q^{60} +(8.23754 + 2.11504i) q^{61} +(5.75372 + 9.06641i) q^{62} +(-5.48075 - 8.63628i) q^{63} +(-10.5876 - 2.71844i) q^{64} +(-8.05251 + 2.71997i) q^{65} +(3.86622 + 1.53074i) q^{66} +(-6.62813 + 3.64385i) q^{67} -15.0397 q^{68} +(2.75685 - 1.51559i) q^{69} +(19.6050 - 9.50438i) q^{70} +(2.13763 - 0.270046i) q^{71} +(-1.90141 + 9.96755i) q^{72} +(-10.8377 + 4.29095i) q^{73} +(2.57937 + 7.93849i) q^{74} +(-0.139389 + 3.51292i) q^{75} +(-3.41347 + 10.5056i) q^{76} +(0.635114 + 10.0948i) q^{77} +(-6.32884 + 0.799518i) q^{78} +(-4.18155 + 3.92674i) q^{79} +(-4.85082 - 1.51422i) q^{80} +(-4.75700 - 0.600949i) q^{81} +(4.65992 - 14.3417i) q^{82} +(2.16010 + 2.02847i) q^{83} +(10.2779 - 2.63892i) q^{84} +(9.08510 + 0.465973i) q^{85} +(9.11462 + 11.0177i) q^{86} +(6.33425 - 1.62636i) q^{87} +(6.39617 - 7.73164i) q^{88} +(10.5684 - 4.18434i) q^{89} +(3.17529 - 12.9900i) q^{90} +(-8.31450 - 13.1016i) q^{91} +(-3.09932 - 16.2472i) q^{92} +(-0.977535 - 3.00854i) q^{93} +(0.297470 - 0.632157i) q^{94} +(2.38749 - 6.24042i) q^{95} +(1.64854 + 0.906294i) q^{96} +(3.15396 + 1.73390i) q^{97} +(14.7045 + 17.7747i) q^{98} +(5.02252 + 3.64908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) $ 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{25}\right)$

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 $

$2$	−1.27891	+	2.01523i	−0.904324	+	1.42499i	0.000875931		1.00000i	$0.499721\pi$
$2$	−1.27891	+	2.01523i	−0.904324	+	1.42499i	−0.905200	+	0.424987i	$0.860279\pi$
$3$	0.512565	−	0.481331i	0.295930	−	0.277897i	−0.522332	−	0.852742i	$-0.674938\pi$
$3$	0.512565	−	0.481331i	0.295930	−	0.277897i	0.818262	+	0.574846i	$0.194938\pi$
$4$	−1.57401	−	3.34494i	−0.787005	−	1.67247i
$5$	0.847185	+	2.06937i	0.378873	+	0.925449i
$5$	0.847185	+	2.06937i	0.378873	+	0.925449i
$6$	0.314471	+	1.64852i	0.128382	+	0.673004i
$7$	−3.30265	+	2.39951i	−1.24828	+	0.906931i	−0.998121	−	0.0612735i	$-0.980484\pi$
$7$	−3.30265	+	2.39951i	−1.24828	+	0.906931i	−0.250162	+	0.968204i	$0.580484\pi$
$8$	4.01791	+	0.507580i	1.42055	+	0.179457i
$9$	−0.157328	+	2.50065i	−0.0524426	+	0.833551i
$10$	−5.25373	−	0.939249i	−1.66138	−	0.297017i
$11$	1.32763	−	2.09201i	0.400296	−	0.630765i	−0.583066	−	0.812425i	$-0.698147\pi$
$11$	1.32763	−	2.09201i	0.400296	−	0.630765i	0.983361	+	0.181660i	$0.0581470\pi$
$12$	−2.41681	−	0.956881i	−0.697672	−	0.276228i
$13$	−0.238672	+	3.79358i	−0.0661957	+	1.05215i	0.815019	+	0.579434i	$0.196726\pi$
$13$	−0.238672	+	3.79358i	−0.0661957	+	1.05215i	−0.881215	+	0.472716i	$0.843274\pi$
$14$	−0.611805	−	9.72436i	−0.163512	−	2.59894i
$15$	1.43029	+	0.652909i	0.369299	+	0.168580i
$16$	−1.44860	+	1.75106i	−0.362151	+	0.437765i
$17$	1.73221	−	3.68113i	0.420122	−	0.892804i	−0.576982	−	0.816757i	$-0.695770\pi$
$17$	1.73221	−	3.68113i	0.420122	−	0.892804i	0.997104	−	0.0760476i	$-0.0242301\pi$
$18$	−4.83820	−	3.51515i	−1.14037	−	0.828530i
$19$	−2.17821	−	2.04548i	−0.499716	−	0.469265i	0.393222	−	0.919443i	$-0.371360\pi$
$19$	−2.17821	−	2.04548i	−0.499716	−	0.469265i	−0.892938	+	0.450179i	$0.851360\pi$
$20$	5.58843	−	6.09099i	1.24961	−	1.36199i
$21$	−0.537862	+	2.81957i	−0.117371	+	0.615281i
$22$	2.51798	+	5.35098i	0.536835	+	1.14083i
$23$	4.33365	+	1.11269i	0.903629	+	0.232013i	0.671790	−	0.740742i	$-0.265526\pi$
$23$	4.33365	+	1.11269i	0.903629	+	0.232013i	0.231839	+	0.972754i	$0.425526\pi$
$24$	2.30376	−	1.67378i	0.470252	−	0.341658i
$25$	−3.56455	+	3.50627i	−0.712911	+	0.701255i
$26$	−7.33972	−	5.33262i	−1.43944	−	1.04581i
$27$	2.46759	+	2.98281i	0.474888	+	0.574041i
$28$	13.2246	+	7.27030i	2.49922	+	1.37396i
$29$	8.15030	+	4.48067i	1.51347	+	0.832039i	0.999665	−	0.0258661i	$-0.00823436\pi$
$29$	8.15030	+	4.48067i	1.51347	+	0.832039i	0.513808	+	0.857905i	$0.328234\pi$
$30$	−3.14497	+	2.04736i	−0.574190	+	0.373794i
$31$	1.91555	−	4.07076i	0.344044	−	0.731130i	−0.655670	−	0.755047i	$-0.727614\pi$
$31$	1.91555	−	4.07076i	0.344044	−	0.731130i	0.999714	+	0.0239174i	$0.00761388\pi$
$32$	0.826773	+	2.54454i	0.146154	+	0.449816i
$33$	−0.326452	−	1.71132i	−0.0568280	−	0.297903i
$34$	5.20300	+	8.19862i	0.892308	+	1.40605i
$35$	−7.76342	−	4.80155i	−1.31226	−	0.811610i
$36$	8.61217	−	3.40980i	1.43536	−	0.568300i
$37$	2.22918	−	2.69462i	0.366475	−	0.442992i	−0.554753	−	0.832015i	$-0.687187\pi$
$37$	2.22918	−	2.69462i	0.366475	−	0.442992i	0.921228	+	0.389023i	$0.127187\pi$
$38$	6.90785	−	1.77363i	1.12060	−	0.287721i
$39$	1.70363	+	2.05934i	0.272800	+	0.329758i
$40$	2.35355	+	8.74455i	0.372128	+	1.38263i
$41$	−6.11953	+	1.57123i	−0.955710	+	0.245385i	−0.694172	−	0.719809i	$-0.744230\pi$
$41$	−6.11953	+	1.57123i	−0.955710	+	0.245385i	−0.261538	+	0.965193i	$0.584230\pi$
$42$	−4.99422	−	4.68989i	−0.770626	−	0.723666i
$43$	1.85131	−	5.69773i	0.282321	−	0.868896i	−0.704867	−	0.709339i	$-0.748993\pi$
$43$	1.85131	−	5.69773i	0.282321	−	0.868896i	0.987189	−	0.159557i	$-0.0510065\pi$
$44$	−9.08736	−	1.14800i	−1.36997	−	0.173068i
$45$	−5.30805	+	1.79295i	−0.791278	+	0.267277i
$46$	−7.78468	+	7.31030i	−1.14779	+	1.07784i
$47$	−0.290407	+	0.0366869i	−0.0423602	+	0.00535133i	−0.146485	−	0.989213i	$-0.546796\pi$
$47$	−0.290407	+	0.0366869i	−0.0423602	+	0.00535133i	0.104125	+	0.994564i	$0.466796\pi$
$48$	0.100336	+	1.59479i	0.0144822	+	0.230188i
$49$	2.98669	−	9.19209i	0.426670	−	1.31316i
$50$	−2.50723	−	11.6676i	−0.354576	−	1.65005i
$51$	−0.883971	−	2.72058i	−0.123781	−	0.380958i
$52$	13.0650	−	5.17279i	1.81179	−	0.717337i
$53$	1.67953	−	8.80442i	0.230702	−	1.20938i	−0.658754	−	0.752358i	$-0.728916\pi$
$53$	1.67953	−	8.80442i	0.230702	−	1.20938i	0.889456	−	0.457022i	$-0.151084\pi$
$54$	−9.16687	+	1.15805i	−1.24745	+	0.157590i
$55$	5.45389	+	0.975033i	0.735402	+	0.131473i
$56$	−14.4877	+	7.96467i	−1.93600	+	1.06432i
$57$	−2.10103			−0.278288
$58$	−19.4531	+	10.6944i	−2.55431	+	1.40425i
$59$	7.25227	+	2.87137i	0.944165	+	0.373821i	0.789226	−	0.614103i	$-0.210482\pi$
$59$	7.25227	+	2.87137i	0.944165	+	0.373821i	0.154939	+	0.987924i	$0.450482\pi$
$60$	−0.0673450	−	5.81191i	−0.00869421	−	0.750315i
$61$	8.23754	+	2.11504i	1.05471	+	0.270803i	0.735953	−	0.677033i	$-0.236735\pi$
$61$	8.23754	+	2.11504i	1.05471	+	0.270803i	0.318757	+	0.947837i	$0.396735\pi$
$62$	5.75372	+	9.06641i	0.730723	+	1.15144i
$63$	−5.48075	−	8.63628i	−0.690510	−	1.08807i
$64$	−10.5876	−	2.71844i	−1.32345	−	0.339804i
$65$	−8.05251	+	2.71997i	−0.998791	+	0.337370i
$66$	3.86622	+	1.53074i	0.475899	+	0.188422i
$67$	−6.62813	+	3.64385i	−0.809755	+	0.445167i	−0.832128	−	0.554583i	$-0.812878\pi$
$67$	−6.62813	+	3.64385i	−0.809755	+	0.445167i	0.0223732	+	0.999750i	$0.492878\pi$
$68$	−15.0397			−1.82383
$69$	2.75685	−	1.51559i	0.331886	−	0.182456i
$70$	19.6050	−	9.50438i	2.34324	−	1.13599i
$71$	2.13763	−	0.270046i	0.253690	−	0.0320485i	0.00254055	−	0.999997i	$-0.499191\pi$
$71$	2.13763	−	0.270046i	0.253690	−	0.0320485i	0.251150	+	0.967948i	$0.419191\pi$
$72$	−1.90141	+	9.96755i	−0.224083	+	1.17469i
$73$	−10.8377	+	4.29095i	−1.26846	+	0.502217i	−0.903412	−	0.428773i	$-0.858946\pi$
$73$	−10.8377	+	4.29095i	−1.26846	+	0.502217i	−0.365044	+	0.930990i	$0.618946\pi$
$74$	2.57937	+	7.93849i	0.299846	+	0.922830i
$75$	−0.139389	+	3.51292i	−0.0160952	+	0.405638i
$76$	−3.41347	+	10.5056i	−0.391552	+	1.20507i
$77$	0.635114	+	10.0948i	0.0723779	+	1.15041i
$78$	−6.32884	+	0.799518i	−0.716600	+	0.0905276i
$79$	−4.18155	+	3.92674i	−0.470461	+	0.441793i	−0.883158	−	0.469076i	$-0.844587\pi$
$79$	−4.18155	+	3.92674i	−0.470461	+	0.441793i	0.412696	+	0.910869i	$0.364587\pi$
$80$	−4.85082	−	1.51422i	−0.542338	−	0.169295i
$81$	−4.75700	−	0.600949i	−0.528556	−	0.0667721i
$82$	4.65992	−	14.3417i	0.514602	−	1.58378i
$83$	2.16010	+	2.02847i	0.237102	+	0.222653i	0.793985	−	0.607937i	$-0.208003\pi$
$83$	2.16010	+	2.02847i	0.237102	+	0.222653i	−0.556883	+	0.830591i	$0.688003\pi$
$84$	10.2779	−	2.63892i	1.12141	−	0.287929i
$85$	9.08510	+	0.465973i	0.985417	+	0.0505419i
$86$	9.11462	+	11.0177i	0.982855	+	1.18807i
$87$	6.33425	−	1.62636i	0.679103	−	0.174364i
$88$	6.39617	−	7.73164i	0.681834	−	0.824195i
$89$	10.5684	−	4.18434i	1.12025	−	0.443539i	0.266300	−	0.963890i	$-0.414199\pi$
$89$	10.5684	−	4.18434i	1.12025	−	0.443539i	0.853952	+	0.520351i	$0.174199\pi$
$90$	3.17529	−	12.9900i	0.334705	−	1.36926i
$91$	−8.31450	−	13.1016i	−0.871596	−	1.37342i
$92$	−3.09932	−	16.2472i	−0.323126	−	1.69389i
$93$	−0.977535	−	3.00854i	−0.101366	−	0.311972i
$94$	0.297470	−	0.632157i	0.0306817	−	0.0652020i
$95$	2.38749	−	6.24042i	0.244951	−	0.640253i
$96$	1.64854	+	0.906294i	0.168254	+	0.0924983i
$97$	3.15396	+	1.73390i	0.320236	+	0.176051i	0.633761	−	0.773529i	$-0.281510\pi$
$97$	3.15396	+	1.73390i	0.320236	+	0.176051i	−0.313525	+	0.949580i	$0.601510\pi$
$98$	14.7045	+	17.7747i	1.48538	+	1.79552i
$99$	5.02252	+	3.64908i	0.504782	+	0.366746i
$100$	17.3389	+	6.40431i	1.73389	+	0.640431i
$101$	−1.80213	+	1.30932i	−0.179318	+	0.130282i	−0.673824	−	0.738892i	$-0.735349\pi$
$101$	−1.80213	+	1.30932i	−0.179318	+	0.130282i	0.494505	+	0.869175i	$0.335349\pi$
$102$	6.61313	+	1.69796i	0.654797	+	0.168123i
$103$	−4.77576	−	10.1490i	−0.470570	−	1.00001i	−0.989411	−	0.145141i	$-0.953636\pi$
$103$	−4.77576	−	10.1490i	−0.470570	−	1.00001i	0.518841	−	0.854871i	$-0.326364\pi$
$104$	−2.88451	+	15.1211i	−0.282849	+	1.48275i
$105$	−6.29040	+	1.27567i	−0.613880	+	0.124492i
$106$	15.5950	+	14.6447i	1.51472	+	1.42242i
$107$	−11.7027	−	8.50250i	−1.13134	−	0.821967i	−0.145452	−	0.989365i	$-0.546464\pi$
$107$	−11.7027	−	8.50250i	−1.13134	−	0.821967i	−0.985889	+	0.167398i	$0.946464\pi$
$108$	6.09330	−	12.9489i	0.586328	−	1.24601i
$109$	−9.92761	+	12.0004i	−0.950892	+	1.14943i	0.0377715	+	0.999286i	$0.487974\pi$
$109$	−9.92761	+	12.0004i	−0.950892	+	1.14943i	−0.988664	+	0.150145i	$0.952026\pi$
$110$	−8.93994	+	9.74389i	−0.852389	+	0.929043i
$111$	−0.154401	−	2.45414i	−0.0146551	−	0.232937i
$112$	0.582532	−	9.25908i	0.0550441	−	0.874900i
$113$	−3.88189	−	1.53695i	−0.365178	−	0.144584i	0.178368	−	0.983964i	$-0.442918\pi$
$113$	−3.88189	−	1.53695i	−0.365178	−	0.144584i	−0.543545	+	0.839380i	$0.682918\pi$
$114$	2.68702	−	4.23406i	0.251662	−	0.396556i
$115$	1.36884	+	9.91057i	0.127645	+	0.924166i
$116$	2.15891	−	34.3149i	0.200450	−	3.18606i
$117$	−9.44888	−	1.19367i	−0.873550	−	0.110355i
$118$	−15.0615	+	10.9428i	−1.38652	+	1.00737i
$119$	3.11204	+	16.3139i	0.285281	+	1.49549i
$120$	5.41537	+	3.34932i	0.494353	+	0.305749i
$121$	2.06966	+	4.39826i	0.188151	+	0.399842i
$122$	−14.7974	+	13.8956i	−1.33969	+	1.25805i
$123$	−2.38038	+	3.75088i	−0.214631	+	0.338205i
$124$	−16.6315			−1.49356
$125$	−10.2756	−	4.40590i	−0.919078	−	0.394076i
$126$	24.4135			2.17493
$127$	6.84406	−	10.7845i	0.607312	−	0.956971i	−0.392003	−	0.919964i	$-0.628218\pi$
$127$	6.84406	−	10.7845i	0.607312	−	0.956971i	0.999315	−	0.0370068i	$-0.0117823\pi$
$128$	15.1181	−	14.1969i	1.33627	−	1.25484i
$129$	−1.79358	−	3.81155i	−0.157916	−	0.335588i
$130$	4.81704	−	19.7063i	0.422482	−	1.72836i
$131$	1.07131	+	5.61598i	0.0936004	+	0.490671i	0.997957	+	0.0638924i	$0.0203515\pi$
$131$	1.07131	+	5.61598i	0.0936004	+	0.490671i	−0.904356	+	0.426778i	$0.859649\pi$
$132$	−5.21043	+	3.78560i	−0.453510	+	0.329494i
$133$	12.1020	+	1.52884i	1.04938	+	0.132567i
$134$	1.13356	−	18.0174i	0.0979245	−	1.55646i
$135$	−4.08201	+	7.63334i	−0.351323	+	0.656973i
$136$	8.82832	−	13.9112i	0.757022	−	1.19288i
$137$	2.16679	+	0.857892i	0.185121	+	0.0732947i	0.458856	−	0.888510i	$-0.348259\pi$
$137$	2.16679	+	0.857892i	0.185121	+	0.0732947i	−0.273735	+	0.961805i	$0.588259\pi$
$138$	−0.471483	+	7.49401i	−0.0401353	+	0.637932i
$139$	−0.771977	−	12.2702i	−0.0654782	−	1.04075i	−0.884366	−	0.466794i	$-0.845409\pi$
$139$	−0.771977	−	12.2702i	−0.0654782	−	1.04075i	0.818888	−	0.573953i	$-0.194591\pi$
$140$	−3.84120	+	33.5259i	−0.324641	+	2.83345i
$141$	−0.131194	+	0.158586i	−0.0110485	+	0.0133554i
$142$	−2.18963	+	4.65320i	−0.183749	+	0.390488i
$143$	7.61935	+	5.53578i	0.637162	+	0.462925i
$144$	−4.15089	−	3.89795i	−0.345908	−	0.324829i
$145$	−2.36732	+	20.6619i	−0.196596	+	1.71588i
$146$	5.21314	−	27.3282i	0.431442	−	2.26170i
$147$	−2.89356	−	6.14913i	−0.238657	−	0.507172i
$148$	−12.5221	−	3.21513i	−1.02931	−	0.264282i
$149$	−8.41736	+	6.11557i	−0.689577	+	0.501007i	−0.876521	−	0.481364i	$-0.840142\pi$
$149$	−8.41736	+	6.11557i	−0.689577	+	0.501007i	0.186944	+	0.982371i	$0.440142\pi$
$150$	−6.90110	−	4.77360i	−0.563473	−	0.389763i
$151$	−9.12056	−	6.62647i	−0.742220	−	0.539255i	0.151185	−	0.988505i	$-0.451691\pi$
$151$	−9.12056	−	6.62647i	−0.742220	−	0.539255i	−0.893406	+	0.449251i	$0.851691\pi$
$152$	−7.71362	−	9.32416i	−0.625657	−	0.756289i
$153$	8.93270	+	4.91079i	0.722166	+	0.397014i
$154$	−21.1557	−	11.6305i	−1.70478	−	0.937209i
$155$	10.0467	+	0.515295i	0.806972	+	0.0413895i
$156$	4.20683	−	8.93997i	0.336816	−	0.715771i
$157$	−2.40783	−	7.41052i	−0.192165	−	0.591424i	−0.999998	−	0.00201222i	$-0.999359\pi$
$157$	−2.40783	−	7.41052i	−0.192165	−	0.591424i	0.807833	−	0.589412i	$-0.200641\pi$
$158$	−2.56549	−	13.4487i	−0.204099	−	1.06992i
$159$	−3.37697	−	5.32125i	−0.267811	−	0.422003i
$160$	−4.56517	+	3.86660i	−0.360908	+	0.305681i
$161$	−16.9824	+	6.72382i	−1.33840	+	0.529912i
$162$	7.29482	−	8.81792i	0.573135	−	0.692801i
$163$	13.5197	−	3.47126i	1.05894	−	0.271890i	0.321228	−	0.947002i	$-0.395905\pi$
$163$	13.5197	−	3.47126i	1.05894	−	0.271890i	0.737716	+	0.675112i	$0.235905\pi$
$164$	14.8879	+	17.9963i	1.16255	+	1.40528i
$165$	3.26479	−	2.12536i	0.254163	−	0.165459i
$166$	−6.85041	+	1.75889i	−0.531695	+	0.136516i
$167$	4.05500	+	3.80790i	0.313785	+	0.294664i	0.825397	−	0.564553i	$-0.190951\pi$
$167$	4.05500	+	3.80790i	0.313785	+	0.294664i	−0.511612	+	0.859217i	$0.670951\pi$
$168$	−3.59224	+	11.0558i	−0.277148	+	0.852972i
$169$	−1.43681	−	0.181511i	−0.110524	−	0.0139624i
$170$	−12.5580	+	17.7127i	−0.963158	+	1.35850i
$171$	5.45772	−	5.12514i	0.417362	−	0.391929i
$172$	−21.9725	+	2.77578i	−1.67539	+	0.211651i
$173$	0.555317	+	8.82651i	0.0422200	+	0.671067i	0.961043	+	0.276398i	$0.0891408\pi$
$173$	0.555317	+	8.82651i	0.0422200	+	0.671067i	−0.918823	+	0.394669i	$0.870859\pi$
$174$	−4.82342	+	14.8450i	−0.365662	+	1.12539i
$175$	3.35911	−	20.1332i	0.253925	−	1.52192i
$176$	1.74003	+	5.35526i	0.131160	+	0.403668i
$177$	5.09934	−	2.01897i	0.383290	−	0.151755i
$178$	−5.08362	+	26.6493i	−0.381033	+	1.99745i
$179$	19.3574	−	2.44541i	1.44684	−	0.182779i	0.637652	−	0.770324i	$-0.279906\pi$
$179$	19.3574	−	2.44541i	1.44684	−	0.182779i	0.809191	+	0.587546i	$0.199906\pi$
$180$	14.3522	+	14.9330i	1.06975	+	1.11304i
$181$	−10.7169	+	5.89167i	−0.796582	+	0.437925i	−0.827409	−	0.561600i	$-0.810186\pi$
$181$	−10.7169	+	5.89167i	−0.796582	+	0.437925i	0.0308270	+	0.999525i	$0.490186\pi$
$182$	37.0362			2.74530
$183$	5.24031	−	2.88089i	0.387375	−	0.212961i
$184$	16.8475	+	6.67038i	1.24201	+	0.491747i
$185$	7.46468	+	2.33015i	0.548814	+	0.171316i
$186$	7.31310	+	1.87769i	0.536223	+	0.137679i
$187$	−5.40123	−	8.51097i	−0.394977	−	0.622384i
$188$	0.579819	+	0.913648i	0.0422876	+	0.0666346i
$189$	−15.3069	−	3.93013i	−1.11341	−	0.285875i
$190$	9.52252	+	12.7923i	0.690836	+	0.928049i
$191$	18.4737	+	7.31424i	1.33671	+	0.529240i	0.924268	−	0.381745i	$-0.124677\pi$
$191$	18.4737	+	7.31424i	1.33671	+	0.529240i	0.412439	+	0.910985i	$0.364677\pi$
$192$	−6.73531	+	3.70277i	−0.486079	+	0.267224i
$193$	23.6672			1.70360			0.851800	−	0.523868i	$-0.175511\pi$
$193$	23.6672			1.70360			0.851800	+	0.523868i	$0.175511\pi$
$194$	−7.52784	+	4.13847i	−0.540468	+	0.297125i
$195$	−2.81823	+	5.27008i	−0.201818	+	0.377398i
$196$	−35.4481	+	4.47813i	−2.53200	+	0.319867i
$197$	1.26229	−	6.61714i	0.0899342	−	0.471451i	−0.908616	−	0.417632i	$-0.862860\pi$
$197$	1.26229	−	6.61714i	0.0899342	−	0.471451i	0.998551	−	0.0538199i	$-0.0171397\pi$
$198$	−13.7771	+	5.45473i	−0.979095	+	0.387651i
$199$	−4.07787	−	12.5504i	−0.289073	−	0.889674i	−0.985148	−	0.171705i	$-0.945072\pi$
$199$	−4.07787	−	12.5504i	−0.289073	−	0.889674i	0.696076	−	0.717968i	$-0.254928\pi$
$200$	−16.1018	+	12.2786i	−1.13857	+	0.868228i
$201$	−1.64345	+	5.05803i	−0.115920	+	0.356766i
$202$	−0.333838	−	5.30620i	−0.0234888	−	0.373343i
$203$	−37.6690	+	4.75870i	−2.64384	+	0.333995i
$204$	−7.70881	+	7.23905i	−0.539725	+	0.506835i
$205$	−8.43582	−	11.3324i	−0.589183	−	0.791491i
$206$	26.5604	+	3.35536i	1.85055	+	0.233779i
$207$	−3.46426	+	10.6619i	−0.240783	+	0.741054i
$208$	−6.29705	−	5.91332i	−0.436622	−	0.410015i
$209$	−7.17102	+	1.84121i	−0.496030	+	0.127359i
$210$	5.47406	−	14.3081i	0.377746	−	0.987352i
$211$	−3.95042	−	4.77524i	−0.271958	−	0.328741i	0.616798	−	0.787122i	$-0.288430\pi$
$211$	−3.95042	−	4.77524i	−0.271958	−	0.328741i	−0.888756	+	0.458381i	$0.848430\pi$
$212$	−32.0939	+	8.24030i	−2.20422	+	0.565946i
$213$	0.965695	−	1.16732i	0.0661683	−	0.0799838i
$214$	32.1012	−	12.7098i	2.19439	−	0.868821i
$215$	13.3591	−	0.996006i	0.911083	−	0.0679271i
$216$	8.40055	+	13.2371i	0.571585	+	0.900674i
$217$	3.44144	+	18.0407i	0.233620	+	1.22468i
$218$	−11.4872	−	35.3539i	−0.778009	−	2.39447i
$219$	−3.48966	+	7.41591i	−0.235809	+	0.501121i
$220$	−5.32304	−	19.7776i	−0.358880	−	1.33341i
$221$	13.5512	+	7.44985i	0.911554	+	0.501131i
$222$	5.14314	+	2.82746i	0.345185	+	0.189767i
$223$	9.63811	+	11.6505i	0.645416	+	0.780174i	0.987180	−	0.159612i	$-0.0510244\pi$
$223$	9.63811	+	11.6505i	0.645416	+	0.780174i	−0.341764	+	0.939786i	$0.611024\pi$
$224$	−8.83621	−	6.41988i	−0.590394	−	0.428946i
$225$	−8.20717	−	9.46535i	−0.547145	−	0.631023i
$226$	8.06190	−	5.85731i	0.536269	−	0.389623i
$227$	−24.9776	−	6.41316i	−1.65782	−	0.425656i	−0.700260	−	0.713888i	$-0.746933\pi$
$227$	−24.9776	−	6.41316i	−1.65782	−	0.425656i	−0.957561	+	0.288231i	$0.906933\pi$
$228$	3.30704	+	7.02781i	0.219014	+	0.465428i
$229$	3.49925	−	18.3437i	0.231237	−	1.21219i	−0.657388	−	0.753552i	$-0.728339\pi$
$229$	3.49925	−	18.3437i	0.231237	−	1.21219i	0.888625	−	0.458634i	$-0.151661\pi$
$230$	−21.7227	−	9.91617i	−1.43236	−	0.653853i
$231$	5.18450	+	4.86857i	0.341115	+	0.320328i
$232$	30.4729	+	22.1399i	2.00064	+	1.45355i
$233$	6.49669	−	13.8062i	0.425612	−	0.904472i	−0.570900	−	0.821020i	$-0.693405\pi$
$233$	6.49669	−	13.8062i	0.425612	−	0.904472i	0.996512	−	0.0834520i	$-0.0265945\pi$
$234$	14.4898	−	17.5151i	0.947226	−	1.14500i
$235$	−0.321947	−	0.569877i	−0.0210015	−	0.0371747i
$236$	−1.81056	−	28.7780i	−0.117857	−	1.87329i
$237$	−0.253258	+	4.02542i	−0.0164509	+	0.261479i
$238$	−36.8564	−	14.5925i	−2.38904	−	0.945889i
$239$	−7.50256	+	11.8221i	−0.485300	+	0.764711i	−0.995441	−	0.0953801i	$-0.969593\pi$
$239$	−7.50256	+	11.8221i	−0.485300	+	0.764711i	0.510141	+	0.860091i	$0.329593\pi$
$240$	−3.21520	+	1.55871i	−0.207540	+	0.100615i
$241$	0.763102	−	12.1292i	0.0491557	−	0.781308i	−0.893816	−	0.448434i	$-0.851982\pi$
$241$	0.763102	−	12.1292i	0.0491557	−	0.781308i	0.942971	−	0.332874i	$-0.108018\pi$
$242$	−11.5104	−	1.45411i	−0.739919	−	0.0934734i
$243$	−12.1231	+	8.80796i	−0.777698	+	0.565031i
$244$	−5.89128	−	30.8832i	−0.377151	−	1.97709i
$245$	21.5521	−	1.60685i	1.37691	−	0.102658i
$246$	−4.51461	−	9.59404i	−0.287841	−	0.611694i
$247$	8.27956	−	7.77503i	0.526816	−	0.494713i
$248$	9.76276	−	15.3837i	0.619936	−	0.976863i
$249$	2.08356			0.132040
$250$	22.0205	−	15.0730i	1.39270	−	0.953301i
$251$	−22.2071			−1.40170			−0.700851	−	0.713308i	$-0.747196\pi$
$251$	−22.2071			−1.40170			−0.700851	+	0.713308i	$0.747196\pi$
$252$	−20.2611	+	31.9264i	−1.27633	+	2.01117i
$253$	8.08126	−	7.58881i	0.508064	−	0.477104i
$254$	12.9804	+	27.5848i	0.814463	+	1.73082i
$255$	4.88099	−	4.13410i	0.305660	−	0.258887i
$256$	5.17881	+	27.1483i	0.323676	+	1.69677i
$257$	25.4852	−	18.5161i	1.58973	−	1.15500i	0.685395	−	0.728172i	$-0.259630\pi$
$257$	25.4852	−	18.5161i	1.58973	−	1.15500i	0.904331	−	0.426832i	$-0.140370\pi$
$258$	9.97499	+	1.26013i	0.621016	+	0.0784525i
$259$	−0.896428	+	14.2483i	−0.0557013	+	0.885347i
$260$	21.7729	+	22.6539i	1.35030	+	1.40494i
$261$	−12.4869	+	19.6761i	−0.772917	+	1.21792i
$262$	−12.6876	−	5.02338i	−0.783844	−	0.310346i
$263$	−0.274828	+	4.36827i	−0.0169466	+	0.269359i	0.980424	+	0.196896i	$0.0630860\pi$
$263$	−0.274828	+	4.36827i	−0.0169466	+	0.269359i	−0.997371	+	0.0724633i	$0.976914\pi$
$264$	−0.443023	−	7.04164i	−0.0272662	−	0.433383i
$265$	19.6424	−	3.98341i	1.20663	−	0.244699i
$266$	−18.5583	+	22.4331i	−1.13788	+	1.37546i
$267$	3.40296	−	7.23166i	0.208258	−	0.442571i
$268$	22.6212	+	16.4353i	1.38181	+	1.00394i
$269$	−6.97260	−	6.54770i	−0.425127	−	0.399221i	0.442235	−	0.896899i	$-0.354186\pi$
$269$	−6.97260	−	6.54770i	−0.425127	−	0.399221i	−0.867361	+	0.497679i	$0.834186\pi$
$270$	−10.1625	−	17.9885i	−0.618468	−	1.09475i
$271$	−0.851867	+	4.46564i	−0.0517472	+	0.271269i	−0.998752	−	0.0499521i	$-0.984093\pi$
$271$	−0.851867	+	4.46564i	−0.0517472	+	0.271269i	0.947004	+	0.321221i	$0.104093\pi$
$272$	3.93660	+	8.36569i	0.238691	+	0.507245i
$273$	−10.5679	−	2.71338i	−0.639599	−	0.164221i
$274$	−4.49997	+	3.26942i	−0.271853	+	0.197513i
$275$	2.60275	+	12.1121i	0.156952	+	0.730389i
$276$	−9.40888	−	6.83595i	−0.566348	−	0.411476i
$277$	8.97977	+	10.8547i	0.539542	+	0.652194i	0.967876	−	0.251426i	$-0.0808996\pi$
$277$	8.97977	+	10.8547i	0.539542	+	0.652194i	−0.428335	+	0.903620i	$0.640900\pi$
$278$	25.7147	+	14.1368i	1.54226	+	0.847866i
$279$	9.87819	+	5.43058i	0.591392	+	0.325120i
$280$	−28.7556	−	23.2328i	−1.71847	−	1.38842i
$281$	10.1295	−	21.5262i	0.604274	−	1.28415i	−0.335399	−	0.942076i	$-0.608871\pi$
$281$	10.1295	−	21.5262i	0.604274	−	1.28415i	0.939674	−	0.342072i	$-0.111129\pi$
$282$	−0.151804	−	0.467203i	−0.00903977	−	0.0278216i
$283$	0.917543	+	4.80993i	0.0545423	+	0.285921i	0.999100	−	0.0424258i	$-0.0135086\pi$
$283$	0.917543	+	4.80993i	0.0545423	+	0.285921i	−0.944557	+	0.328347i	$0.893509\pi$
$284$	−4.26794	−	6.72520i	−0.253256	−	0.399067i
$285$	−1.77996	−	4.34779i	−0.105436	−	0.257541i
$286$	−20.9003	+	8.27503i	−1.23586	+	0.489313i
$287$	16.4405	−	19.8731i	0.970450	−	1.17307i
$288$	−6.49310	+	1.66714i	−0.382610	+	0.0982374i
$289$	0.286058	+	0.345785i	0.0168269	+	0.0203403i
$290$	−38.6110	−	31.1954i	−2.26732	−	1.83186i
$291$	2.45119	−	0.629359i	0.143691	−	0.0368937i
$292$	31.4116	+	29.4975i	1.83822	+	1.72621i
$293$	0.104040	−	0.320203i	0.00607810	−	0.0187065i	−0.947971	−	0.318355i	$-0.896870\pi$
$293$	0.104040	−	0.320203i	0.00607810	−	0.0187065i	0.954050	+	0.299649i	$0.0968695\pi$
$294$	16.0925	+	2.03296i	0.938536	+	0.118565i
$295$	0.202087	+	17.4402i	0.0117659	+	1.01541i
$296$	10.3244	−	9.69525i	0.600093	−	0.563525i
$297$	9.51611	−	1.20216i	0.552181	−	0.0697567i
$298$	−1.55929	−	24.7842i	−0.0903272	−	1.43571i
$299$	−5.25541	+	16.1745i	−0.303928	+	0.935395i
$300$	11.9699	−	5.06313i	0.691084	−	0.292320i
$301$	7.55757	+	23.2598i	0.435611	+	1.34067i
$302$	25.0182	−	9.90542i	1.43964	−	0.569993i
$303$	−0.293490	+	1.53853i	−0.0168606	+	0.0883863i
$304$	6.73712	−	0.851096i	0.386400	−	0.0488137i
$305$	2.60193	+	18.8383i	0.148986	+	1.07868i
$306$	−21.3205	+	11.7210i	−1.21881	+	0.670047i
$307$	−31.7425			−1.81164			−0.905821	−	0.423661i	$-0.860745\pi$
$307$	−31.7425			−1.81164			−0.905821	+	0.423661i	$0.860745\pi$
$308$	32.7670	−	18.0138i	1.86707	−	1.02643i
$309$	−7.33292	−	2.90331i	−0.417155	−	0.165163i
$310$	−13.8873	+	19.5875i	−0.788743	+	1.11249i
$311$	−0.0756057	−	0.0194122i	−0.00428721	−	0.00110077i	0.246546	−	0.969131i	$-0.420704\pi$
$311$	−0.0756057	−	0.0194122i	−0.00428721	−	0.00110077i	−0.250833	+	0.968030i	$0.580704\pi$
$312$	5.79977	+	9.13897i	0.328347	+	0.517392i
$313$	2.85151	+	4.49326i	0.161177	+	0.253974i	0.915312	−	0.402745i	$-0.131944\pi$
$313$	2.85151	+	4.49326i	0.161177	+	0.253974i	−0.754135	+	0.656719i	$0.771944\pi$
$314$	18.0133	+	4.62504i	1.01655	+	0.261006i
$315$	13.2284	−	18.6582i	0.745337	−	1.05127i
$316$	19.7165	+	7.80632i	1.10914	+	0.439140i
$317$	8.65638	−	4.75888i	0.486191	−	0.267286i	−0.219750	−	0.975556i	$-0.570524\pi$
$317$	8.65638	−	4.75888i	0.486191	−	0.267286i	0.705941	+	0.708271i	$0.250524\pi$
$318$	15.0424			0.843536
$319$	20.1942	−	11.1019i	1.13066	−	0.621585i
$320$	−3.34423	−	24.2127i	−0.186948	−	1.35353i
$321$	−10.0909	+	1.27478i	−0.563219	+	0.0711511i
$322$	8.16888	−	42.8228i	0.455234	−	2.38642i
$323$	−11.3028	+	4.47508i	−0.628903	+	0.249000i
$324$	5.47743	+	16.8578i	0.304302	+	0.936544i
$325$	−12.4506	−	14.3593i	−0.690634	−	0.796509i
$326$	−10.2950	+	31.6848i	−0.570187	+	1.75486i
$327$	0.687624	+	10.9295i	0.0380257	+	0.604401i
$328$	−25.3853	+	3.20690i	−1.40167	+	0.177072i
$329$	0.871080	−	0.817998i	0.0480242	−	0.0450977i
$330$	0.107733	+	9.29745i	0.00593052	+	0.511808i
$331$	−4.85629	−	0.613492i	−0.266926	−	0.0337206i	−0.00926894	−	0.999957i	$-0.502950\pi$
$331$	−4.85629	−	0.613492i	−0.266926	−	0.0337206i	−0.257657	+	0.966236i	$0.582950\pi$
$332$	3.38509	−	10.4182i	0.185781	−	0.571775i
$333$	6.38759	+	5.99835i	0.350038	+	0.328707i
$334$	−12.8598	+	3.30183i	−0.703656	+	0.180668i
$335$	−13.1557	−	10.6290i	−0.718773	−	0.580725i
$336$	−4.15809	−	5.02627i	−0.226843	−	0.274206i
$337$	−0.925519	+	0.237633i	−0.0504163	+	0.0129447i	−0.273814	−	0.961783i	$-0.588285\pi$
$337$	−0.925519	+	0.237633i	−0.0504163	+	0.0129447i	0.223398	+	0.974727i	$0.428285\pi$
$338$	2.20333	−	2.66337i	0.119845	−	0.144868i
$339$	−2.72951	+	1.08069i	−0.148246	+	0.0586949i
$340$	−12.7414	−	31.1226i	−0.690998	−	1.68786i
$341$	−5.97293	−	9.41183i	−0.323452	−	0.509679i
$342$	3.34845	+	17.5532i	0.181063	+	0.949167i
$343$	3.36206	+	10.3474i	0.181534	+	0.558705i
$344$	10.3304	−	21.9533i	0.556980	−	1.18364i
$345$	5.47188	+	4.42095i	0.294596	+	0.238016i
$346$	−18.4977	−	10.1692i	−0.994442	−	0.546699i
$347$	14.0288	+	7.71241i	0.753107	+	0.414024i	0.811562	−	0.584266i	$-0.198618\pi$
$347$	14.0288	+	7.71241i	0.753107	+	0.414024i	−0.0584553	+	0.998290i	$0.518618\pi$
$348$	−15.4102	−	18.6278i	−0.826076	−	0.998554i
$349$	−9.13188	−	6.63470i	−0.488818	−	0.355147i	0.315911	−	0.948789i	$-0.397690\pi$
$349$	−9.13188	−	6.63470i	−0.488818	−	0.355147i	−0.804730	+	0.593641i	$0.797690\pi$
$350$	36.2771	+	32.5179i	1.93909	+	1.73815i
$351$	−11.9045	+	8.64910i	−0.635413	+	0.461655i
$352$	6.42087	+	1.64860i	0.342233	+	0.0878706i
$353$	−1.55658	−	3.30790i	−0.0828483	−	0.176062i	0.859110	−	0.511790i	$-0.171017\pi$
$353$	−1.55658	−	3.30790i	−0.0828483	−	0.176062i	−0.941959	+	0.335729i	$0.891017\pi$
$354$	−2.45288	+	12.8584i	−0.130369	+	0.683419i
$355$	2.36980	+	4.19477i	0.125776	+	0.222635i
$356$	−30.6312	−	28.7646i	−1.62345	−	1.52452i
$357$	9.44751	+	6.86402i	0.500015	+	0.363282i
$358$	−19.8283	+	42.1372i	−1.04796	+	2.22702i
$359$	−3.65979	+	4.42392i	−0.193156	+	0.233486i	−0.858196	−	0.513322i	$-0.828415\pi$
$359$	−3.65979	+	4.42392i	−0.193156	+	0.233486i	0.665040	+	0.746808i	$0.268415\pi$
$360$	−22.2374	+	4.50964i	−1.17201	+	0.237679i
$361$	−0.632390	−	10.0515i	−0.0332837	−	0.529029i
$362$	1.83283	−	29.1320i	0.0963314	−	1.53114i
$363$	3.17786	+	1.25820i	0.166794	+	0.0660385i
$364$	−30.7368	+	48.4335i	−1.61105	+	2.53860i
$365$	−18.0611	−	18.7919i	−0.945360	−	0.983615i
$366$	−0.896210	+	14.2449i	−0.0468456	+	0.744590i
$367$	−11.7674	−	1.48657i	−0.614252	−	0.0775981i	−0.187949	−	0.982179i	$-0.560184\pi$
$367$	−11.7674	−	1.48657i	−0.614252	−	0.0775981i	−0.426303	+	0.904581i	$0.640184\pi$
$368$	−8.22614	+	5.97664i	−0.428817	+	0.311554i
$369$	−2.96632	−	15.5500i	−0.154421	−	0.809502i
$370$	−14.2424	+	12.0630i	−0.740429	+	0.627127i
$371$	15.5794	+	33.1079i	0.808843	+	1.71888i
$372$	−8.52476	+	8.00528i	−0.441988	+	0.415054i
$373$	11.0788	−	17.4574i	0.573639	−	0.903910i	−0.426361	−	0.904553i	$-0.640205\pi$
$373$	11.0788	−	17.4574i	0.573639	−	0.903910i	1.00000		0.000643282i	$0.000204763\pi$
$374$	24.0593			1.24408
$375$	−7.38762	+	2.68765i	−0.381495	+	0.138790i
$376$	−1.18545			−0.0611349
$377$	−18.9430	+	29.8494i	−0.975616	+	1.53732i
$378$	27.4962	−	25.8206i	1.41425	−	1.32807i
$379$	10.8535	+	23.0648i	0.557505	+	1.18476i	0.962711	+	0.270533i	$0.0871999\pi$
$379$	10.8535	+	23.0648i	0.557505	+	1.18476i	−0.405206	+	0.914226i	$0.632800\pi$
$380$	−24.6318	+	1.83646i	−1.26358	+	0.0942082i
$381$	−1.68289	−	8.82203i	−0.0862171	−	0.451966i
$382$	−38.3660	+	27.8745i	−1.96297	+	1.42618i
$383$	10.7954	+	1.36378i	0.551621	+	0.0696859i	0.396203	−	0.918163i	$-0.370328\pi$
$383$	10.7954	+	1.36378i	0.551621	+	0.0696859i	0.155418	+	0.987849i	$0.450328\pi$
$384$	0.915639	−	14.5537i	0.0467260	−	0.742688i
$385$	−20.3519	+	9.86648i	−1.03723	+	0.502843i
$386$	−30.2681	+	47.6949i	−1.54061	+	2.42761i
$387$	13.9568	+	5.52588i	0.709463	+	0.280896i
$388$	0.835443	−	13.2790i	0.0424132	−	0.674139i
$389$	0.326971	+	5.19706i	0.0165781	+	0.263501i	0.997581	+	0.0695096i	$0.0221434\pi$
$389$	0.326971	+	5.19706i	0.0165781	+	0.263501i	−0.981003	+	0.193992i	$0.937857\pi$
$390$	−7.01620	−	12.4193i	−0.355279	−	0.628878i
$391$	11.6027	−	14.0253i	0.586776	−	0.709290i
$392$	16.6660	−	35.4170i	0.841759	−	1.78883i
$393$	3.25226	+	2.36290i	0.164055	+	0.119193i
$394$	11.7207	+	11.0065i	0.590482	+	0.554500i
$395$	−11.6684	−	5.32649i	−0.587102	−	0.268005i
$396$	4.30045	−	22.5437i	0.216105	−	1.13286i
$397$	−2.74151	−	5.82601i	−0.137593	−	0.292399i	0.824141	−	0.566384i	$-0.191658\pi$
$397$	−2.74151	−	5.82601i	−0.137593	−	0.292399i	−0.961734	+	0.273985i	$0.911658\pi$
$398$	30.5072	+	7.83292i	1.52919	+	0.392629i
$399$	6.93895	−	5.04144i	0.347382	−	0.252388i
$400$	−0.976073	−	11.3210i	−0.0488037	−	0.566048i
$401$	−10.9941	−	7.98769i	−0.549019	−	0.398886i	0.278404	−	0.960464i	$-0.410194\pi$
$401$	−10.9941	−	7.98769i	−0.549019	−	0.398886i	−0.827424	+	0.561578i	$0.810194\pi$
$402$	−8.09130	−	9.78070i	−0.403557	−	0.487817i
$403$	14.9856	+	8.23839i	0.746484	+	0.410383i
$404$	7.21616	+	3.96712i	0.359018	+	0.197372i
$405$	−2.78648	−	10.3531i	−0.138461	−	0.514449i
$406$	38.5852	−	81.9978i	1.91495	−	4.06948i
$407$	−2.67764	−	8.24093i	−0.132726	−	0.408488i
$408$	−2.17080	−	11.3797i	−0.107471	−	0.563381i
$409$	−9.05941	−	14.2754i	−0.447959	−	0.705871i	0.543045	−	0.839704i	$-0.317271\pi$
$409$	−9.05941	−	14.2754i	−0.447959	−	0.705871i	−0.991004	+	0.133833i	$0.957271\pi$
$410$	33.6261	−	2.50704i	1.66068	−	0.123814i
$411$	1.52355	−	0.603216i	0.0751512	−	0.0297545i
$412$	−26.4307	+	31.9493i	−1.30215	+	1.57403i
$413$	−30.8416	+	7.91877i	−1.51761	+	0.389657i
$414$	−17.0558	−	20.6169i	−0.838246	−	1.01326i
$415$	−2.36764	+	6.18853i	−0.116223	+	0.303783i
$416$	−9.85027	+	2.52912i	−0.482949	+	0.124000i
$417$	−6.30173	−	5.91772i	−0.308597	−	0.289792i
$418$	5.46061	−	16.8060i	0.267087	−	0.822010i
$419$	−21.7419	−	2.74663i	−1.06216	−	0.134182i	−0.425215	−	0.905092i	$-0.639802\pi$
$419$	−21.7419	−	2.74663i	−1.06216	−	0.134182i	−0.636944	+	0.770910i	$0.719802\pi$
$420$	14.1682	+	19.0331i	0.691336	+	0.928720i
$421$	−0.705443	+	0.662455i	−0.0343812	+	0.0322861i	−0.701547	−	0.712623i	$-0.747507\pi$
$421$	−0.705443	+	0.662455i	−0.0343812	+	0.0322861i	0.667166	+	0.744909i	$0.267507\pi$
$422$	14.6754	−	1.85394i	0.714390	−	0.0902484i
$423$	−0.0460522	−	0.731978i	−0.00223913	−	0.0355900i
$424$	11.2172	−	34.5229i	0.544754	−	1.67658i
$425$	6.73249	+	19.1952i	0.326574	+	0.931102i
$426$	1.11740	+	3.43900i	0.0541382	+	0.166620i
$427$	−32.2808	+	12.7809i	−1.56218	+	0.618509i
$428$	−10.0202	+	52.5278i	−0.484345	+	2.53903i
$429$	6.56996	−	0.829979i	0.317200	−	0.0400717i
$430$	−15.0778	+	28.1955i	−0.727118	+	1.35971i
$431$	26.6487	−	14.6503i	1.28362	−	0.705678i	0.313800	−	0.949489i	$-0.398398\pi$
$431$	26.6487	−	14.6503i	1.28362	−	0.705678i	0.969823	+	0.243811i	$0.0783977\pi$
$432$	−8.79764			−0.423276
$433$	−10.6132	+	5.83464i	−0.510036	+	0.280395i	−0.715921	−	0.698182i	$-0.753993\pi$
$433$	−10.6132	+	5.83464i	−0.510036	+	0.280395i	0.205885	+	0.978576i	$0.433993\pi$
$434$	−40.7575	−	16.1370i	−1.95642	−	0.774602i
$435$	8.73181	+	11.7300i	0.418658	+	0.562413i
$436$	55.7668	+	14.3185i	2.67075	+	0.685731i
$437$	−7.16363	−	11.2881i	−0.342683	−	0.539982i
$438$	−10.4818	−	16.5167i	−0.500842	−	0.789200i
$439$	−15.8037	−	4.05770i	−0.754270	−	0.193664i	−0.148071	−	0.988977i	$-0.547306\pi$
$439$	−15.8037	−	4.05770i	−0.754270	−	0.193664i	−0.606199	+	0.795313i	$0.707306\pi$
$440$	21.4183	+	6.68588i	1.02108	+	0.318737i
$441$	22.5163	+	8.91485i	1.07221	+	0.424516i
$442$	−32.3439	+	17.7812i	−1.53844	+	0.845767i
$443$	−23.0660			−1.09590			−0.547948	−	0.836512i	$-0.684591\pi$
$443$	−23.0660			−1.09590			−0.547948	+	0.836512i	$0.684591\pi$
$444$	−7.96593	+	4.37931i	−0.378046	+	0.207833i
$445$	17.6124	+	18.3251i	0.834906	+	0.868691i
$446$	−35.8047	+	4.52318i	−1.69540	+	0.214179i
$447$	−1.37083	+	7.18616i	−0.0648382	+	0.339894i
$448$	41.4900	−	16.4271i	1.96022	−	0.776106i
$449$	−10.1244	−	31.1596i	−0.477799	−	1.47051i	−0.842146	−	0.539250i	$-0.818708\pi$
$449$	−10.1244	−	31.1596i	−0.477799	−	1.47051i	0.364347	−	0.931263i	$-0.381292\pi$
$450$	29.5711	−	4.43408i	1.39400	−	0.209025i
$451$	−4.83745	+	14.8881i	−0.227787	+	0.701055i
$452$	0.969130	+	15.4039i	0.0455840	+	0.724538i
$453$	−7.86441	+	0.993505i	−0.369502	+	0.0466790i
$454$	44.8680	−	42.1339i	2.10576	−	1.97744i
$455$	20.0680	−	28.3052i	0.940802	−	1.32697i
$456$	−8.44174	−	1.06644i	−0.395321	−	0.0499406i
$457$	−1.23568	+	3.80303i	−0.0578026	+	0.177898i	−0.975789	−	0.218713i	$-0.929814\pi$
$457$	−1.23568	+	3.80303i	−0.0578026	+	0.177898i	0.917987	+	0.396612i	$0.129814\pi$
$458$	32.4917	+	30.5117i	1.51824	+	1.42572i
$459$	15.2545	−	3.91668i	0.712017	−	0.182815i
$460$	30.9957	−	20.1780i	1.44518	−	0.940805i
$461$	5.64706	+	6.82612i	0.263010	+	0.317924i	0.885442	−	0.464749i	$-0.153856\pi$
$461$	5.64706	+	6.82612i	0.263010	+	0.317924i	−0.622433	+	0.782673i	$0.713856\pi$
$462$	−16.4418	+	4.22153i	−0.764941	+	0.196404i
$463$	−23.1169	+	27.9436i	−1.07434	+	1.29865i	−0.122356	+	0.992486i	$0.539045\pi$
$463$	−23.1169	+	27.9436i	−1.07434	+	1.29865i	−0.951979	+	0.306163i	$0.900955\pi$
$464$	−19.6525	+	7.78097i	−0.912343	+	0.361222i
$465$	5.39763	−	4.57167i	0.250309	−	0.212006i
$466$	19.5140	+	30.7491i	0.903969	+	1.42443i
$467$	−1.57128	−	8.23696i	−0.0727104	−	0.381161i	−0.999977	−	0.00675979i	$-0.997848\pi$
$467$	−1.57128	−	8.23696i	−0.0727104	−	0.381161i	0.927267	−	0.374401i	$-0.122152\pi$
$468$	10.8799	+	33.4848i	0.502922	+	1.54784i
$469$	13.1469	−	27.9386i	0.607068	−	1.29009i
$470$	1.56018	+	0.0800212i	0.0719656	+	0.00369110i
$471$	−4.80108	−	2.63942i	−0.221222	−	0.121618i
$472$	27.6815	+	15.2180i	1.27414	+	0.700467i
$473$	−9.46187	−	11.4374i	−0.435057	−	0.525894i
$474$	−7.78828	−	5.65851i	−0.357727	−	0.259904i
$475$	14.9364	−	0.346194i	0.685327	−	0.0158845i
$476$	49.6707	−	36.0879i	2.27665	−	1.65408i
$477$	21.7526	+	5.58511i	0.995981	+	0.255725i
$478$	−14.2293	−	30.2388i	−0.650834	−	1.38309i
$479$	1.65168	−	8.65841i	0.0754672	−	0.395613i	−0.924431	−	0.381349i	$-0.875460\pi$
$479$	1.65168	−	8.65841i	0.0754672	−	0.395613i	0.999898	−	0.0142638i	$-0.00454046\pi$
$480$	−0.478833	+	4.17924i	−0.0218556	+	0.190755i
$481$	9.69021	+	9.09971i	0.441835	+	0.414911i
$482$	23.4672	+	17.0499i	1.06890	+	0.776602i
$483$	−5.46823	+	11.6206i	−0.248813	+	0.528754i
$484$	11.4542	−	13.8458i	0.520648	−	0.629355i
$485$	−0.916094	+	7.99564i	−0.0415977	+	0.363063i
$486$	−2.24577	−	35.6955i	−0.101870	−	1.61918i
$487$	−0.769655	+	12.2333i	−0.0348764	+	0.554344i	0.941328	+	0.337493i	$0.109579\pi$
$487$	−0.769655	+	12.2333i	−0.0348764	+	0.554344i	−0.976205	+	0.216852i	$0.930421\pi$
$488$	32.0242	+	12.6793i	1.44967	+	0.573963i
$489$	5.25889	−	8.28669i	0.237815	−	0.374737i
$490$	−24.3249	+	45.4875i	−1.09889	+	2.05492i
$491$	0.388318	−	6.17214i	0.0175245	−	0.278545i	−0.979499	−	0.201448i	$-0.935435\pi$
$491$	0.388318	−	6.17214i	0.0175245	−	0.278545i	0.997024	−	0.0770962i	$-0.0245648\pi$
$492$	16.2932	+	2.05831i	0.734554	+	0.0927958i
$493$	30.6119	−	22.2409i	1.37869	−	1.00168i
$494$	5.07971	+	26.6288i	0.228547	+	1.19809i
$495$	−3.29627	+	13.4849i	−0.148156	+	0.606100i
$496$	4.35327	+	9.25117i	0.195468	+	0.415390i
$497$	−6.41187	+	6.02114i	−0.287612	+	0.270085i
$498$	−2.66468	+	4.19886i	−0.119407	+	0.188155i
$499$	−28.9868			−1.29763			−0.648814	−	0.760947i	$-0.724735\pi$
$499$	−28.9868			−1.29763			−0.648814	+	0.760947i	$0.724735\pi$
$500$	1.43641	+	41.3062i	0.0642382	+	1.84727i
$501$	3.91131			0.174745
$502$	28.4009	−	44.7526i	1.26759	−	1.99741i
$503$	−3.87909	+	3.64271i	−0.172960	+	0.162420i	−0.766193	−	0.642611i	$-0.777851\pi$
$503$	−3.87909	+	3.64271i	−0.172960	+	0.162420i	0.593233	+	0.805031i	$0.297851\pi$
$504$	−17.6376	−	37.4817i	−0.785640	−	1.66957i
$505$	−4.23620	−	2.62002i	−0.188508	−	0.116589i
$506$	4.95805	+	25.9910i	0.220412	+	1.15544i
$507$	−0.823825	+	0.598544i	−0.0365873	+	0.0265823i
$508$	−46.8462	−	5.91805i	−2.07846	−	0.262571i
$509$	−1.80957	+	28.7623i	−0.0802077	+	1.27487i	0.727840	+	0.685748i	$0.240525\pi$
$509$	−1.80957	+	28.7623i	−0.0802077	+	1.27487i	−0.808047	+	0.589118i	$0.799475\pi$
$510$	2.08884	+	15.1235i	0.0924953	+	0.669679i
$511$	25.4969	−	40.1767i	1.12792	−	1.77731i
$512$	−22.7680	−	9.01448i	−1.00621	−	0.398387i
$513$	0.726324	−	11.5446i	0.0320680	−	0.509706i
$514$	4.72106	+	75.0391i	0.208237	+	3.30983i
$515$	16.9561	−	18.4809i	0.747173	−	0.814365i
$516$	−9.92630	+	11.9988i	−0.436981	+	0.528219i
$517$	−0.308804	+	0.656241i	−0.0135812	+	0.0288614i
$518$	−27.5673	−	20.0288i	−1.21124	−	0.880014i
$519$	4.53311	+	4.25687i	0.198981	+	0.186856i
$520$	−33.7349	+	6.84129i	−1.47937	+	0.300011i
$521$	0.826635	−	4.33337i	0.0362155	−	0.189848i	−0.959582	−	0.281429i	$-0.909192\pi$
$521$	0.826635	−	4.33337i	0.0362155	−	0.189848i	0.995798	+	0.0915801i	$0.0291918\pi$
$522$	−23.6825	−	50.3279i	−1.03656	−	2.20279i
$523$	−1.09462	−	0.281050i	−0.0478642	−	0.0122894i	0.224682	−	0.974432i	$-0.427866\pi$
$523$	−1.09462	−	0.281050i	−0.0478642	−	0.0122894i	−0.272546	+	0.962143i	$0.587866\pi$
$524$	17.0989	−	12.4231i	0.746968	−	0.542704i
$525$	−7.96895	−	11.9364i	−0.347794	−	0.520948i
$526$	−8.45161	−	6.14045i	−0.368508	−	0.267736i
$527$	−11.6668	−	14.1028i	−0.508216	−	0.614327i
$528$	3.46953	+	1.90739i	0.150992	+	0.0830085i
$529$	−2.61259	−	1.43628i	−0.113591	−	0.0624471i
$530$	−17.0934	+	44.6785i	−0.742488	+	1.94071i
$531$	−8.32130	+	17.6837i	−0.361113	+	0.767405i
$532$	−13.9348	−	42.8869i	−0.604150	−	1.85938i
$533$	−4.50002	−	23.5899i	−0.194918	−	1.02179i
$534$	10.2214	+	16.1064i	0.442324	+	0.696992i
$535$	7.68044	−	31.4203i	0.332054	−	1.35842i
$536$	−28.4808	+	11.2763i	−1.23018	+	0.487064i
$537$	8.74490	−	10.5708i	0.377370	−	0.456162i
$538$	22.1125	−	5.67752i	0.953336	−	0.244775i
$539$	−15.2647	−	18.4519i	−0.657498	−	0.794779i
$540$	31.9582	+	1.63913i	1.37526	+	0.0705370i
$541$	15.4718	−	3.97249i	0.665186	−	0.170791i	0.0990244	−	0.995085i	$-0.468428\pi$
$541$	15.4718	−	3.97249i	0.665186	−	0.170791i	0.566162	+	0.824294i	$0.308428\pi$
$542$	−7.90986	−	7.42785i	−0.339758	−	0.319054i
$543$	−2.65727	+	8.17825i	−0.114035	+	0.350962i
$544$	10.7989	+	1.36422i	0.463000	+	0.0584906i
$545$	−33.2438	−	10.3773i	−1.42401	−	0.444514i
$546$	18.9835	−	17.8267i	0.812417	−	0.762910i
$547$	3.26170	−	0.412049i	0.139460	−	0.0176179i	−0.0552931	−	0.998470i	$-0.517609\pi$
$547$	3.26170	−	0.412049i	0.139460	−	0.0176179i	0.194753	+	0.980852i	$0.437609\pi$
$548$	−0.540947	−	8.59811i	−0.0231081	−	0.367293i
$549$	−6.58498	+	20.2665i	−0.281040	+	0.864953i
$550$	−27.7375	−	10.2451i	−1.18273	−	0.436853i
$551$	−8.58798	−	26.4311i	−0.365860	−	1.12600i
$552$	11.8461	−	4.69019i	0.504203	−	0.199628i
$553$	4.38793	−	23.0023i	0.186594	−	0.978158i
$554$	−33.3590	+	4.21422i	−1.41729	+	0.179045i
$555$	4.94771	−	2.39863i	0.210019	−	0.101816i
$556$	−39.8281	+	21.8957i	−1.68909	+	0.928583i
$557$	−20.6772			−0.876121			−0.438061	−	0.898945i	$-0.644335\pi$
$557$	−20.6772			−0.876121			−0.438061	+	0.898945i	$0.644335\pi$
$558$	−23.5772	+	12.9617i	−0.998101	+	0.548711i
$559$	21.1730	+	8.38297i	0.895521	+	0.354562i
$560$	19.6539	−	6.63868i	0.830530	−	0.280536i
$561$	−6.86508	−	1.76265i	−0.289844	−	0.0744192i
$562$	30.4258	+	47.9433i	1.28343	+	2.02237i
$563$	4.87918	+	7.68835i	0.205633	+	0.324025i	0.931455	−	0.363857i	$-0.118540\pi$
$563$	4.87918	+	7.68835i	0.205633	+	0.324025i	−0.725822	+	0.687883i	$0.758540\pi$
$564$	0.736962	+	0.189220i	0.0310317	+	0.00796758i
$565$	−0.108170	−	9.33514i	−0.00455075	−	0.392732i
$566$	−10.8666	−	4.30239i	−0.456757	−	0.180843i
$567$	17.1527	−	9.42976i	0.720345	−	0.396013i
$568$	8.72589			0.366130
$569$	−7.04694	+	3.87409i	−0.295423	+	0.162410i	−0.622572	−	0.782563i	$-0.713912\pi$
$569$	−7.04694	+	3.87409i	−0.295423	+	0.162410i	0.327149	+	0.944973i	$0.393912\pi$
$570$	11.0382	+	1.97339i	0.462341	+	0.0826561i
$571$	0.968401	−	0.122337i	0.0405263	−	0.00511966i	−0.105044	−	0.994468i	$-0.533498\pi$
$571$	0.968401	−	0.122337i	0.0405263	−	0.00511966i	0.145570	+	0.989348i	$0.453498\pi$
$572$	6.52393	−	34.1996i	0.272779	−	1.42996i
$573$	12.9895	−	5.14292i	0.542645	−	0.214848i
$574$	19.0231	+	58.5472i	0.794011	+	2.44371i
$575$	−19.3489	+	11.2287i	−0.806907	+	0.468270i
$576$	8.46359	−	26.0482i	0.352649	−	1.08534i
$577$	0.728970	+	11.5866i	0.0303474	+	0.482358i	0.983621	+	0.180250i	$0.0576905\pi$
$577$	0.728970	+	11.5866i	0.0303474	+	0.482358i	−0.953274	+	0.302109i	$0.902309\pi$
$578$	−1.06268	+	0.134248i	−0.0442016	+	0.00558396i
$579$	12.1310	−	11.3917i	0.504146	−	0.473424i
$580$	72.8391	−	24.6035i	3.02448	−	1.02160i
$581$	−12.0014	−	1.51613i	−0.497901	−	0.0628996i
$582$	−1.86654	+	5.74462i	−0.0773706	+	0.238122i
$583$	−16.1891	−	15.2026i	−0.670486	−	0.629628i
$584$	−45.7229	+	11.7396i	−1.89203	+	0.485790i
$585$	−5.53481	−	20.5645i	−0.228836	−	0.850236i
$586$	0.512227	+	0.619176i	0.0211599	+	0.0255779i
$587$	−32.1886	+	8.26463i	−1.32857	+	0.341118i	−0.845270	−	0.534340i	$-0.820560\pi$
$587$	−32.1886	+	8.26463i	−1.32857	+	0.341118i	−0.483296	+	0.875457i	$0.660560\pi$
$588$	−16.0140	+	19.3576i	−0.660406	+	0.798293i
$589$	−12.4991	+	4.94875i	−0.515017	+	0.203910i
$590$	−35.4045	−	21.8971i	−1.45758	−	0.901490i
$591$	−2.53803	−	3.99929i	−0.104401	−	0.164509i
$592$	1.48924	+	7.80686i	0.0612073	+	0.320860i
$593$	10.1298	+	31.1762i	0.415979	+	1.28025i	0.911372	+	0.411583i	$0.135024\pi$
$593$	10.1298	+	31.1762i	0.415979	+	1.28025i	−0.495393	+	0.868669i	$0.664976\pi$
$594$	−9.74758	+	20.7147i	−0.399948	+	0.849933i
$595$	−31.1230	+	20.2609i	−1.27592	+	0.830614i
$596$	33.7052	+	18.5296i	1.38062	+	0.759002i
$597$	−8.13107	−	4.47009i	−0.332782	−	0.182949i
$598$	−25.8742	−	31.2766i	−1.05808	−	1.27899i
$599$	4.54522	+	3.30230i	0.185713	+	0.134928i	0.676757	−	0.736206i	$-0.263385\pi$
$599$	4.54522	+	3.30230i	0.185713	+	0.134928i	−0.491044	+	0.871135i	$0.663385\pi$
$600$	−2.34314	+	14.0439i	−0.0956584	+	0.573339i
$601$	30.0932	−	21.8640i	1.22753	−	0.891851i	0.230825	−	0.972995i	$-0.425857\pi$
$601$	30.0932	−	21.8640i	1.22753	−	0.891851i	0.996702	+	0.0811442i	$0.0258574\pi$
$602$	−56.5394	−	14.5169i	−2.30438	−	0.591663i
$603$	−8.06921	−	17.1479i	−0.328604	−	0.698318i
$604$	−7.80931	+	40.9379i	−0.317756	+	1.66574i
$605$	−7.34822	+	8.00903i	−0.298748	+	0.325613i
$606$	−2.72515	−	2.55909i	−0.110702	−	0.103956i
$607$	17.0957	+	12.4208i	0.693894	+	0.504144i	0.877938	−	0.478774i	$-0.158919\pi$
$607$	17.0957	+	12.4208i	0.693894	+	0.504144i	−0.184044	+	0.982918i	$0.558919\pi$
$608$	3.40392	−	7.23370i	0.138047	−	0.293365i
$609$	−17.0173	+	20.5704i	−0.689576	+	0.833554i
$610$	−41.2913	−	18.8490i	−1.67184	−	0.763172i
$611$	−0.0698628	−	1.11044i	−0.00282635	−	0.0449235i
$612$	2.36616	−	37.6090i	0.0956462	−	1.52025i
$613$	28.1807	+	11.1575i	1.13821	+	0.450648i	0.860213	−	0.509934i	$-0.170330\pi$
$613$	28.1807	+	11.1575i	1.13821	+	0.450648i	0.277995	+	0.960583i	$0.410330\pi$
$614$	40.5957	−	63.9686i	1.63831	−	2.58156i
$615$	−9.77856	−	1.74819i	−0.394310	−	0.0704937i
$616$	−2.57211	+	40.8826i	−0.103633	+	1.64720i
$617$	25.8771	+	3.26904i	1.04177	+	0.131606i	0.627556	−	0.778572i	$-0.284055\pi$
$617$	25.8771	+	3.26904i	1.04177	+	0.131606i	0.414217	+	0.910178i	$0.364055\pi$
$618$	15.2290	−	11.0645i	0.612599	−	0.445079i
$619$	7.46328	+	39.1239i	0.299975	+	1.57252i	0.738784	+	0.673942i	$0.235400\pi$
$619$	7.46328	+	39.1239i	0.299975	+	1.57252i	−0.438809	+	0.898580i	$0.644600\pi$
$620$	−14.0900	−	34.4168i	−0.565868	−	1.38221i
$621$	7.37474	+	15.6721i	0.295938	+	0.628900i
$622$	0.135813	−	0.127537i	0.00544560	−	0.00511376i
$623$	−24.8634	+	39.1785i	−0.996132	+	1.56965i
$624$	−6.07392			−0.243151
$625$	0.412088	−	24.9966i	0.0164835	−	0.999864i
$626$	−12.7018			−0.507665
$627$	−2.78939	+	4.39537i	−0.111397	+	0.175534i
$628$	−20.9978	+	19.7183i	−0.837904	+	0.786845i
$629$	−6.05782	−	12.8735i	−0.241541	−	0.513301i
$630$	20.6828	+	50.5205i	0.824021	+	2.01278i
$631$	0.863577	+	4.52703i	0.0343785	+	0.180218i	0.995335	−	0.0964821i	$-0.0307591\pi$
$631$	0.863577	+	4.52703i	0.0343785	+	0.180218i	−0.960956	+	0.276700i	$0.910759\pi$
$632$	−18.7942	+	13.6548i	−0.747595	+	0.543160i
$633$	−4.32332	−	0.546162i	−0.171836	−	0.0217080i
$634$	−1.48043	+	23.5308i	−0.0587955	+	0.934528i
$635$	28.1153	+	5.02639i	1.11572	+	0.199466i
$636$	−12.4839	+	19.6715i	−0.495018	+	0.780024i
$637$	34.1581	+	13.5241i	1.35339	+	0.535846i
$638$	−3.45366	+	54.8943i	−0.136732	+	2.17329i
$639$	0.338982	+	5.38796i	0.0134099	+	0.213145i
$640$	42.1864	+	19.2576i	1.66756	+	0.761223i
$641$	0.825662	−	0.998054i	0.0326117	−	0.0394208i	−0.753955	−	0.656926i	$-0.771856\pi$
$641$	0.825662	−	0.998054i	0.0326117	−	0.0394208i	0.786567	+	0.617505i	$0.211856\pi$
$642$	10.3363	−	21.9659i	0.407943	−	0.866923i
$643$	−19.0066	−	13.8091i	−0.749547	−	0.544578i	0.146140	−	0.989264i	$-0.453315\pi$
$643$	−19.0066	−	13.8091i	−0.749547	−	0.544578i	−0.895686	+	0.444686i	$0.853315\pi$
$644$	49.2213	+	46.2219i	1.93959	+	1.82140i
$645$	6.36800	−	6.94066i	0.250740	−	0.273288i
$646$	5.43685	−	28.5010i	0.213910	−	1.12135i
$647$	19.7636	+	41.9999i	0.776989	+	1.65119i	0.758776	+	0.651351i	$0.225798\pi$
$647$	19.7636	+	41.9999i	0.776989	+	1.65119i	0.0182126	+	0.999834i	$0.494202\pi$
$648$	−18.8082	−	4.82912i	−0.738855	−	0.189706i
$649$	15.6353	−	11.3597i	0.613738	−	0.445907i
$650$	44.8604	−	6.72666i	1.75957	−	0.263841i
$651$	10.4475	+	7.59055i	0.409470	+	0.297497i
$652$	−32.8913	−	39.7587i	−1.28812	−	1.55707i
$653$	−20.5654	−	11.3059i	−0.804786	−	0.442435i	0.0255668	−	0.999673i	$-0.491861\pi$
$653$	−20.5654	−	11.3059i	−0.804786	−	0.442435i	−0.830353	+	0.557238i	$0.811861\pi$
$654$	−22.9048	−	12.5920i	−0.895650	−	0.492388i
$655$	−10.7139	+	6.97470i	−0.418628	+	0.272524i
$656$	6.11346	−	12.9918i	0.238690	−	0.507243i
$657$	−9.02510	−	27.7764i	−0.352103	−	1.08366i
$658$	0.534429	+	2.80157i	0.0208342	+	0.109217i
$659$	−4.14340	−	6.52895i	−0.161404	−	0.254332i	0.753995	−	0.656880i	$-0.228124\pi$
$659$	−4.14340	−	6.52895i	−0.161404	−	0.254332i	−0.915399	+	0.402549i	$0.868124\pi$
$660$	−12.2480	−	7.57519i	−0.476753	−	0.294864i
$661$	−12.8029	+	5.06903i	−0.497976	+	0.197162i	−0.603667	−	0.797237i	$-0.706294\pi$
$661$	−12.8029	+	5.06903i	−0.497976	+	0.197162i	0.105692	+	0.994399i	$0.466294\pi$
$662$	7.44707	−	9.00197i	0.289439	−	0.349871i
$663$	10.5317	−	2.70409i	0.409018	−	0.105018i
$664$	7.64948	+	9.24664i	0.296858	+	0.358839i
$665$	7.08892	+	26.3387i	0.274896	+	1.02137i
$666$	−20.2572	+	5.20117i	−0.784951	+	0.201541i
$667$	30.3350	+	28.4864i	1.17458	+	1.10300i
$668$	6.35459	−	19.5574i	0.245866	−	0.756699i
$669$	10.5479	+	1.33251i	0.407805	+	0.0515178i
$670$	38.2449	−	12.9183i	1.47753	−	0.499078i
$671$	15.3611	−	14.4250i	0.593009	−	0.556873i
$672$	−7.61922	+	0.962531i	−0.293918	+	0.0371304i
$673$	0.658471	+	10.4661i	0.0253822	+	0.403438i	0.990120	+	0.140225i	$0.0447824\pi$
$673$	0.658471	+	10.4661i	0.0253822	+	0.403438i	−0.964738	+	0.263214i	$0.915218\pi$
$674$	0.704767	−	2.16905i	0.0271466	−	0.0835487i
$675$	−19.2544	−	1.98032i	−0.741102	−	0.0762226i
$676$	1.65441	+	5.09174i	0.0636310	+	0.195836i
$677$	23.9430	−	9.47971i	0.920204	−	0.364335i	0.140210	−	0.990122i	$-0.455222\pi$
$677$	23.9430	−	9.47971i	0.920204	−	0.364335i	0.779994	+	0.625787i	$0.215222\pi$
$678$	1.31294	−	6.88269i	0.0504233	−	0.264328i
$679$	−14.5769	+	1.84150i	−0.559411	+	0.0706701i
$680$	36.2666	+	6.48366i	1.39076	+	0.248637i
$681$	−15.8895	+	8.73533i	−0.608887	+	0.334738i
$682$	26.6059			1.01879
$683$	26.3887	−	14.5073i	1.00973	−	0.555106i	0.111102	−	0.993809i	$-0.464562\pi$
$683$	26.3887	−	14.5073i	1.00973	−	0.555106i	0.898632	+	0.438703i	$0.144562\pi$
$684$	−25.7338	−	10.1887i	−0.983957	−	0.389576i
$685$	0.0603782	+	5.21067i	0.00230693	+	0.199090i
$686$	−25.1521	−	6.45796i	−0.960312	−	0.246566i
$687$	−7.03580	−	11.0866i	−0.268432	−	0.422982i
$688$	7.29527	+	11.4955i	0.278129	+	0.438262i
$689$	32.9994	+	8.47281i	1.25718	+	0.322788i
$690$	−15.9073	+	5.37314i	−0.605580	+	0.204552i
$691$	−42.5397	−	16.8426i	−1.61828	−	0.640724i	−0.627803	−	0.778372i	$-0.716046\pi$
$691$	−42.5397	−	16.8426i	−1.61828	−	0.640724i	−0.990481	+	0.137648i	$0.956046\pi$
$692$	28.6501	−	15.7505i	1.08911	−	0.598745i
$693$	−25.3436			−0.962724
$694$	−33.4839	+	18.4079i	−1.27103	+	0.698755i
$695$	24.7376	−	11.9927i	0.938350	−	0.454907i
$696$	26.2760	−	3.31942i	0.995987	−	0.125822i
$697$	−4.81640	+	25.2485i	−0.182434	+	0.956353i
$698$	25.0493	−	9.91772i	0.948130	−	0.375391i
$699$	−3.31536	−	10.2036i	−0.125398	−	0.385936i
$700$	−72.6316	+	20.4538i	−2.74521	+	0.773080i
$701$	−8.79128	+	27.0568i	−0.332042	+	1.02192i	0.636118	+	0.771591i	$0.280539\pi$
$701$	−8.79128	+	27.0568i	−0.332042	+	1.02192i	−0.968161	+	0.250329i	$0.919461\pi$
$702$	−2.20526	−	35.0517i	−0.0832323	−	1.32294i
$703$	−10.3674	+	1.30971i	−0.391014	+	0.0493966i
$704$	−19.7434	+	18.5403i	−0.744109	+	0.698764i
$705$	−0.439318	−	0.137136i	−0.0165457	−	0.00516485i
$706$	8.65691	+	1.09362i	0.325807	+	0.0411590i
$707$	2.81005	−	8.64844i	0.105683	−	0.325258i
$708$	−14.7798	−	13.8791i	−0.555457	−	0.521609i
$709$	30.8951	−	7.93252i	1.16029	−	0.297912i	0.381001	−	0.924575i	$-0.375580\pi$
$709$	30.8951	−	7.93252i	1.16029	−	0.297912i	0.779291	+	0.626663i	$0.215580\pi$
$710$	−11.4842	−	0.589022i	−0.430994	−	0.0221056i
$711$	−9.16154	−	11.0744i	−0.343585	−	0.415322i
$712$	44.5869	−	11.4480i	1.67097	−	0.429031i
$713$	12.8308	−	15.5098i	0.480519	−	0.580848i
$714$	−25.9151	+	10.2605i	−0.969848	+	0.383990i
$715$	−5.00056	+	20.4571i	−0.187010	+	0.765051i
$716$	−38.6486	−	60.9004i	−1.44436	−	2.27595i
$717$	1.84481	+	9.67083i	0.0688957	+	0.361164i
$718$	−4.23471	−	13.0331i	−0.158038	−	0.486391i
$719$	−19.5802	+	41.6100i	−0.730217	+	1.55179i	0.100401	+	0.994947i	$0.467987\pi$
$719$	−19.5802	+	41.6100i	−0.730217	+	1.55179i	−0.830618	+	0.556843i	$0.812013\pi$
$720$	4.54970	−	11.8920i	0.169557	−	0.443188i
$721$	40.1253	+	22.0591i	1.49434	+	0.821523i
$722$	21.0650	+	11.5806i	0.783958	+	0.430984i
$723$	−5.44700	−	6.58429i	−0.202576	−	0.244873i
$724$	36.5758	+	26.5739i	1.35933	+	0.987611i
$725$	−44.7626	+	12.6056i	−1.66244	+	0.468161i
$726$	−6.59975	+	4.79500i	−0.244940	+	0.177959i
$727$	25.6843	+	6.59460i	0.952577	+	0.244580i	0.692834	−	0.721097i	$-0.256362\pi$
$727$	25.6843	+	6.59460i	0.952577	+	0.244580i	0.259744	+	0.965678i	$0.416362\pi$
$728$	−26.7568	−	56.8612i	−0.991674	−	2.10741i
$729$	0.721028	−	3.77976i	0.0267047	−	0.139991i
$730$	60.9686	−	12.3642i	2.25655	−	0.457619i
$731$	−17.7672	−	16.6845i	−0.657145	−	0.617100i
$732$	−17.8847	−	12.9940i	−0.661038	−	0.480272i
$733$	−1.63329	+	3.47092i	−0.0603269	+	0.128201i	−0.932717	−	0.360609i	$-0.882569\pi$
$733$	−1.63329	+	3.47092i	−0.0603269	+	0.128201i	0.872390	+	0.488810i	$0.162569\pi$
$734$	18.0452	−	21.8128i	0.666059	−	0.805127i
$735$	10.2734	−	11.1973i	0.378941	−	0.413018i
$736$	0.751649	+	11.9471i	0.0277062	+	0.440377i
$737$	−1.17674	+	18.7038i	−0.0433459	+	0.688964i
$738$	35.1306	+	13.9092i	1.29318	+	0.512004i
$739$	10.0107	−	15.7743i	0.368249	−	0.580267i	−0.608789	−	0.793332i	$-0.708344\pi$
$739$	10.0107	−	15.7743i	0.368249	−	0.580267i	0.977038	+	0.213065i	$0.0683445\pi$
$740$	−3.95526	−	28.6366i	−0.145398	−	1.05270i
$741$	0.501456	−	7.97042i	0.0184215	−	0.292801i
$742$	−86.6449	−	10.9458i	−3.18083	−	0.401833i
$743$	16.7088	−	12.1396i	0.612985	−	0.445359i	−0.237479	−	0.971393i	$-0.576321\pi$
$743$	16.7088	−	12.1396i	0.612985	−	0.445359i	0.850464	+	0.526033i	$0.176321\pi$
$744$	−2.40057	−	12.5842i	−0.0880093	−	0.461361i
$745$	−19.7864	−	12.2376i	−0.724918	−	0.448350i
$746$	21.0120	+	44.6528i	0.769304	+	1.63485i
$747$	−5.41234	+	5.08253i	−0.198027	+	0.185960i
$748$	−19.9671	+	31.4631i	−0.730070	+	1.15041i
$749$	59.0517			2.15770
$750$	4.03182	−	18.3250i	0.147221	−	0.669136i
$751$	30.9173			1.12819			0.564093	−	0.825711i	$-0.309226\pi$
$751$	30.9173			1.12819			0.564093	+	0.825711i	$0.309226\pi$
$752$	0.356443	−	0.561665i	0.0129981	−	0.0204818i
$753$	−11.3826	+	10.6890i	−0.414805	+	0.389528i
$754$	−35.9273	−	76.3493i	−1.30839	−	2.78048i
$755$	5.98580	−	24.4876i	0.217845	−	0.891196i
$756$	10.9471	+	57.3866i	0.398142	+	2.08713i
$757$	−30.0096	+	21.8032i	−1.09072	+	0.792452i	−0.979520	−	0.201347i	$-0.935468\pi$
$757$	−30.0096	+	21.8032i	−1.09072	+	0.792452i	−0.111196	+	0.993798i	$0.535468\pi$
$758$	−60.3615	−	7.62544i	−2.19243	−	0.276968i
$759$	0.489446	−	7.77952i	0.0177658	−	0.282379i
$760$	12.7602	−	23.8616i	0.462863	−	0.865551i
$761$	−10.0599	+	15.8518i	−0.364671	+	0.574629i	−0.976275	−	0.216535i	$-0.930524\pi$
$761$	−10.0599	+	15.8518i	−0.364671	+	0.574629i	0.611604	+	0.791164i	$0.290524\pi$
$762$	19.9307	+	7.89113i	0.722014	+	0.285865i
$763$	3.99222	−	63.4546i	0.144528	−	2.29721i
$764$	−4.61202	−	73.3060i	−0.166857	−	2.65212i
$765$	−2.59458	+	22.6454i	−0.0938071	+	0.818745i
$766$	−16.5547	+	20.0112i	−0.598145	+	0.723033i
$767$	−12.6237	+	26.8267i	−0.455816	+	0.968658i
$768$	15.7218	+	11.4226i	0.567311	+	0.412176i
$769$	−32.2297	−	30.2657i	−1.16223	−	1.09141i	−0.994409	−	0.105593i	$-0.966326\pi$
$769$	−32.2297	−	30.2657i	−1.16223	−	1.09141i	−0.167824	−	0.985817i	$-0.553674\pi$
$770$	6.14486	−	53.6321i	0.221445	−	1.93277i
$771$	4.15048	−	21.7576i	0.149476	−	0.783579i
$772$	−37.2523	−	79.1653i	−1.34074	−	2.84922i
$773$	−12.4204	−	3.18903i	−0.446732	−	0.114701i	0.0186206	−	0.999827i	$-0.494073\pi$
$773$	−12.4204	−	3.18903i	−0.446732	−	0.114701i	−0.465353	+	0.885125i	$0.654073\pi$
$774$	−28.9854	+	21.0591i	−1.04186	+	0.756954i
$775$	7.44510	+	21.2269i	0.267436	+	0.762493i
$776$	11.7922	+	8.56756i	0.423317	+	0.307558i
$777$	6.39868	+	7.73467i	0.229551	+	0.277480i
$778$	−10.8915	−	5.98763i	−0.390477	−	0.214667i
$779$	16.5435	+	9.09489i	0.592734	+	0.325858i
$780$	22.0640	+	1.13166i	0.790019	+	0.0405200i
$781$	2.27305	−	4.83047i	0.0813361	−	0.172848i
$782$	13.4255	+	41.3193i	0.480093	+	1.47758i
$783$	6.74666	+	35.3672i	0.241106	+	1.26392i
$784$	11.7694	+	18.5456i	0.420335	+	0.662342i
$785$	13.2952	−	11.2608i	0.474527	−	0.401914i
$786$	−8.92114	+	3.53213i	−0.318207	+	0.125987i
$787$	−5.60677	+	6.77742i	−0.199860	+	0.241589i	−0.860916	−	0.508748i	$-0.830109\pi$
$787$	−5.60677	+	6.77742i	−0.199860	+	0.241589i	0.661056	+	0.750337i	$0.270109\pi$
$788$	−24.1208	+	6.19316i	−0.859267	+	0.220622i
$789$	1.96171	+	2.37131i	0.0698389	+	0.0844207i
$790$	25.6569	−	16.7025i	0.912833	−	0.594249i
$791$	16.5085	−	4.23865i	0.586973	−	0.150709i
$792$	18.3279	+	17.2110i	0.651252	+	0.611566i
$793$	−9.98965	+	30.7450i	−0.354743	+	1.09179i
$794$	15.2469	+	1.92613i	0.541093	+	0.0683559i
$795$	8.15070	−	11.4963i	0.289075	−	0.407731i
$796$	−35.5617	+	33.3947i	−1.26045	+	1.18364i
$797$	−0.880709	+	0.111259i	−0.0311963	+	0.00394101i	−0.140916	−	0.990022i	$-0.545005\pi$
$797$	−0.880709	+	0.111259i	−0.0311963	+	0.00394101i	0.109720	+	0.993963i	$0.465005\pi$
$798$	1.28542	+	20.4311i	0.0455033	+	0.723255i
$799$	−0.367995	+	1.13257i	−0.0130187	+	0.0400676i
$800$	−11.8689	−	6.17128i	−0.419631	−	0.218188i
$801$	8.80088	+	27.0863i	0.310964	+	0.957048i
$802$	30.1575	−	11.9402i	1.06490	−	0.421623i
$803$	−5.41175	+	28.3694i	−0.190976	+	1.00113i
$804$	19.5056	−	2.46414i	0.687911	−	0.0869034i
$805$	−28.3013	−	29.4466i	−0.997491	−	1.03786i
$806$	−35.7674	+	19.6633i	−1.25985	+	0.692611i
$807$	−6.72552			−0.236750
$808$	−7.90537	+	4.34601i	−0.278110	+	0.152892i
$809$	6.99296	+	2.76871i	0.245859	+	0.0973426i	0.487823	−	0.872943i	$-0.337791\pi$
$809$	6.99296	+	2.76871i	0.245859	+	0.0973426i	−0.241963	+	0.970285i	$0.577791\pi$
$810$	24.4276	+	7.62524i	0.858297	+	0.267923i
$811$	7.70064	+	1.97719i	0.270406	+	0.0694284i	0.381458	−	0.924386i	$-0.375422\pi$
$811$	7.70064	+	1.97719i	0.270406	+	0.0694284i	−0.111052	+	0.993815i	$0.535422\pi$
$812$	75.2089	+	118.510i	2.63932	+	4.15890i
$813$	1.71281	+	2.69896i	0.0600710	+	0.0946568i
$814$	20.0319	+	5.14331i	0.702116	+	0.180273i
$815$	18.6370	+	25.0364i	0.652825	+	0.876986i
$816$	6.04443	+	2.39316i	0.211597	+	0.0837773i
$817$	−15.6871	+	8.62406i	−0.548823	+	0.301718i
$818$	40.3543			1.41096
$819$	34.0705	−	18.7304i	1.19052	−	0.654495i
$820$	−24.6282	+	46.0547i	−0.860055	+	1.60830i
$821$	32.2128	−	4.06943i	1.12424	−	0.142024i	0.458843	−	0.888517i	$-0.348264\pi$
$821$	32.2128	−	4.06943i	1.12424	−	0.142024i	0.665393	+	0.746493i	$0.268264\pi$
$822$	−0.732857	+	3.84177i	−0.0255613	+	0.133997i
$823$	−36.9349	+	14.6236i	−1.28747	+	0.509745i	−0.909358	−	0.416015i	$-0.863426\pi$
$823$	−36.9349	+	14.6236i	−1.28747	+	0.509745i	−0.378112	+	0.925760i	$0.623426\pi$
$824$	−14.0371	−	43.2019i	−0.489007	−	1.50501i
$825$	7.16402	+	4.95547i	0.249419	+	0.172527i
$826$	23.4853	−	72.2804i	0.817159	−	2.51496i
$827$	−1.63990	−	26.0655i	−0.0570250	−	0.906386i	−0.917711	−	0.397250i	$-0.869965\pi$
$827$	−1.63990	−	26.0655i	−0.0570250	−	0.906386i	0.860686	−	0.509137i	$-0.170035\pi$
$828$	41.1162	−	5.19419i	1.42889	−	0.180511i
$829$	−33.9931	+	31.9216i	−1.18063	+	1.10868i	−0.188680	+	0.982039i	$0.560421\pi$
$829$	−33.9931	+	31.9216i	−1.18063	+	1.10868i	−0.991948	+	0.126645i	$0.959579\pi$
$830$	−9.44335	−	12.6859i	−0.327783	−	0.440334i
$831$	9.82741	+	1.24149i	0.340909	+	0.0430668i
$832$	12.8396	−	39.5161i	0.445132	−	1.36998i
$833$	−28.6637	−	26.9170i	−0.993137	−	0.932618i
$834$	19.9849	−	5.13125i	0.692021	−	0.177681i
$835$	−4.44460	+	11.6173i	−0.153812	+	0.402032i
$836$	17.4460	+	21.0886i	0.603382	+	0.729364i
$837$	16.8691	−	4.33124i	0.583081	−	0.149710i
$838$	33.3409	−	40.3022i	1.15174	−	1.39222i
$839$	−21.8890	+	8.66647i	−0.755692	+	0.299200i	−0.714202	−	0.699939i	$-0.753210\pi$
$839$	−21.8890	+	8.66647i	−0.755692	+	0.299200i	−0.0414897	+	0.999139i	$0.513210\pi$
$840$	−25.9218	+	1.93263i	−0.894386	+	0.0666822i
$841$	30.8121	+	48.5521i	1.06249	+	1.67421i
$842$	−0.432806	−	2.26885i	−0.0149155	−	0.0781897i
$843$	−5.16923	−	15.9092i	−0.178038	−	0.547943i
$844$	−9.75489	+	20.7302i	−0.335777	+	0.713563i
$845$	−0.841630	−	3.12706i	−0.0289529	−	0.107574i
$846$	1.53400	+	0.843326i	0.0527402	+	0.0289942i
$847$	−17.3890	−	9.55971i	−0.597495	−	0.328475i
$848$	12.9841	+	15.6951i	0.445876	+	0.538971i
$849$	2.78547	+	2.02376i	0.0955971	+	0.0694553i
$850$	−47.2930	−	10.9813i	−1.62214	−	0.376655i
$851$	12.6588	−	9.19714i	0.433937	−	0.315274i
$852$	−5.42465	−	1.39281i	−0.185845	−	0.0477170i
$853$	−12.7319	−	27.0567i	−0.435932	−	0.926403i	−0.995241	−	0.0974434i	$-0.968934\pi$
$853$	−12.7319	−	27.0567i	−0.435932	−	0.926403i	0.559309	−	0.828959i	$-0.311066\pi$
$854$	15.5277	−	81.3988i	0.531346	−	2.78541i
$855$	15.2295	+	6.95208i	0.520838	+	0.237756i
$856$	−42.7046	−	40.1023i	−1.45961	−	1.37067i
$857$	−6.33786	−	4.60472i	−0.216497	−	0.157294i	0.474251	−	0.880389i	$-0.342719\pi$
$857$	−6.33786	−	4.60472i	−0.216497	−	0.157294i	−0.690748	+	0.723095i	$0.742719\pi$
$858$	−6.72976	+	14.3015i	−0.229750	+	0.488244i
$859$	−13.7900	+	16.6693i	−0.470509	+	0.568748i	−0.951371	−	0.308049i	$-0.900324\pi$
$859$	−13.7900	+	16.6693i	−0.470509	+	0.568748i	0.480861	+	0.876797i	$0.340324\pi$
$860$	−24.3589	−	43.1177i	−0.830632	−	1.47030i
$861$	−1.13873	−	18.0996i	−0.0388077	−	0.616831i
$862$	−4.55752	+	72.4397i	−0.155230	+	2.46731i
$863$	23.2744	+	9.21497i	0.792268	+	0.313681i	0.729176	−	0.684327i	$-0.239904\pi$
$863$	23.2744	+	9.21497i	0.792268	+	0.313681i	0.0630925	+	0.998008i	$0.479904\pi$
$864$	−5.54975	+	8.74500i	−0.188806	+	0.297511i
$865$	−17.7948	+	8.62685i	−0.605042	+	0.293322i
$866$	1.81509	−	28.8500i	0.0616791	−	0.980362i
$867$	0.313060	+	0.0395487i	0.0106321	+	0.00134314i
$868$	54.9281	−	39.9076i	1.86438	−	1.35455i
$869$	2.66323	+	13.9611i	0.0903437	+	0.473599i
$870$	−34.8060	+	2.59501i	−1.18003	+	0.0879791i
$871$	−12.2413	−	26.0140i	−0.414780	−	0.881452i
$872$	−45.9794	+	43.1776i	−1.55706	+	1.46218i
$873$	−4.83210	+	7.61417i	−0.163542	+	0.257701i
$874$	31.9097			1.07936
$875$	44.5087	−	10.1053i	1.50467	−	0.341621i
$876$	30.2985			1.02369
$877$	−5.30017	+	8.35174i	−0.178974	+	0.282018i	−0.921957	−	0.387292i	$-0.873410\pi$
$877$	−5.30017	+	8.35174i	−0.178974	+	0.282018i	0.742983	+	0.669311i	$0.233410\pi$
$878$	28.3887	−	26.6588i	0.958072	−	0.899689i
$879$	−0.100796	−	0.214203i	−0.00339977	−	0.00722489i
$880$	−9.60786	+	8.13765i	−0.323881	+	0.274320i
$881$	−3.15545	−	16.5414i	−0.106310	−	0.557295i	−0.995091	−	0.0989637i	$-0.968447\pi$
$881$	−3.15545	−	16.5414i	−0.106310	−	0.557295i	0.888781	−	0.458332i	$-0.151553\pi$
$882$	−46.7618	+	33.9744i	−1.57455	+	1.14398i
$883$	5.97956	+	0.755394i	0.201228	+	0.0254210i	0.225301	−	0.974289i	$-0.427663\pi$
$883$	5.97956	+	0.755394i	0.201228	+	0.0254210i	−0.0240730	+	0.999710i	$0.507663\pi$
$884$	3.58954	−	57.0542i	0.120729	−	1.91894i
$885$	8.49808	+	8.84196i	0.285660	+	0.297219i
$886$	29.4992	−	46.4833i	0.991045	−	1.56164i
$887$	0.805093	+	0.318759i	0.0270324	+	0.0107029i	0.381602	−	0.924327i	$-0.375373\pi$
$887$	0.805093	+	0.318759i	0.0270324	+	0.0107029i	−0.354569	+	0.935030i	$0.615373\pi$
$888$	0.625302	−	9.93889i	0.0209838	−	0.333527i
$889$	3.27407	+	52.0398i	0.109809	+	1.74536i
$890$	−59.4539	+	12.0570i	−1.99290	+	0.404151i
$891$	−7.57274	+	9.15386i	−0.253696	+	0.306666i
$892$	23.7997	−	50.5769i	0.796872	−	1.69344i
$893$	0.707609	+	0.514108i	0.0236792	+	0.0172040i
$894$	−12.7286	−	11.9530i	−0.425709	−	0.399768i
$895$	21.4598	+	37.9859i	0.717322	+	1.26973i
$896$	−15.8643	+	83.1635i	−0.529988	+	2.77830i
$897$	5.09154	+	10.8201i	0.170002	+	0.361272i
$898$	75.7421	+	19.4473i	2.52755	+	0.648964i
$899$	33.8521	−	24.5950i	1.12903	−	0.820288i
$900$	−18.7429	+	42.3511i	−0.624762	+	1.41170i
$901$	−29.5009	−	21.4336i	−0.982817	−	0.714058i
$902$	−23.8164	−	28.7891i	−0.793001	−	0.958574i
$903$	15.0694	+	8.28448i	0.501479	+	0.275690i
$904$	−14.8170	−	8.14570i	−0.492805	−	0.270922i
$905$	−21.2712	−	17.1859i	−0.707080	−	0.571278i
$906$	8.05570	−	17.1192i	0.267633	−	0.568748i
$907$	1.50500	+	4.63193i	0.0499729	+	0.153801i	0.972929	−	0.231105i	$-0.0742340\pi$
$907$	1.50500	+	4.63193i	0.0499729	+	0.153801i	−0.922956	+	0.384905i	$0.874234\pi$
$908$	17.8633	+	93.6429i	0.592816	+	3.10765i
$909$	−2.99063	−	4.71248i	−0.0991930	−	0.156303i
$910$	31.3765	+	76.6414i	1.04012	+	2.54064i
$911$	12.0968	−	4.78948i	0.400786	−	0.158682i	−0.159080	−	0.987266i	$-0.550853\pi$
$911$	12.0968	−	4.78948i	0.400786	−	0.158682i	0.559866	+	0.828583i	$0.310853\pi$
$912$	3.04355	−	3.67903i	0.100782	−	0.121825i
$913$	7.11140	−	1.82590i	0.235353	−	0.0604284i
$914$	−6.08368	−	7.35390i	−0.201230	−	0.243246i
$915$	10.4011	+	8.40348i	0.343851	+	0.277811i
$916$	−66.8665	+	17.1684i	−2.20933	+	0.567260i
$917$	−17.0138	−	15.9770i	−0.561844	−	0.527606i
$918$	−11.6160	+	35.7504i	−0.383385	+	1.17994i
$919$	−35.3731	−	4.46867i	−1.16685	−	0.147408i	−0.482055	−	0.876141i	$-0.660109\pi$
$919$	−35.3731	−	4.46867i	−1.16685	−	0.147408i	−0.684797	+	0.728734i	$0.740109\pi$
$920$	0.469459	+	40.5146i	0.0154776	+	1.33573i
$921$	−16.2701	+	15.2787i	−0.536119	+	0.503449i
$922$	−20.9783	+	2.65017i	−0.690883	+	0.0872789i
$923$	0.514248	+	8.17374i	0.0169267	+	0.269042i
$924$	8.12462	−	25.0050i	0.267280	−	0.822604i
$925$	1.50203	+	17.4212i	0.0493864	+	0.572806i
$926$	−26.7485	−	82.3233i	−0.879009	−	2.70531i
$927$	26.1305	−	10.3458i	0.858238	−	0.339801i
$928$	−4.66281	+	24.4433i	−0.153064	+	0.802391i
$929$	−25.8543	+	3.26616i	−0.848253	+	0.107159i	−0.537430	−	0.843309i	$-0.680605\pi$
$929$	−25.8543	+	3.26616i	−0.848253	+	0.107159i	−0.310823	+	0.950468i	$0.600605\pi$
$930$	2.30993	+	16.7242i	0.0757457	+	0.548409i
$931$	−25.3078	+	13.9131i	−0.829431	+	0.455984i
$932$	−56.4066			−1.84766
$933$	−0.0480966	+	0.0264413i	−0.00157461	+	0.000865650i
$934$	18.6089	+	7.36780i	0.608903	+	0.241082i
$935$	13.0365	−	18.3875i	0.426338	−	0.601335i
$936$	−37.3589	−	9.59213i	−1.22111	−	0.313529i
$937$	−20.2980	−	31.9846i	−0.663108	−	1.04489i	−0.994834	−	0.101515i	$-0.967631\pi$
$937$	−20.2980	−	31.9846i	−0.663108	−	1.04489i	0.331726	−	0.943376i	$-0.392369\pi$
$938$	39.4892	+	62.2250i	1.28937	+	2.03172i
$939$	3.62433	+	0.930569i	0.118275	+	0.0303680i
$940$	−1.39946	+	1.97389i	−0.0456453	+	0.0643811i
$941$	−17.8089	−	7.05105i	−0.580554	−	0.229858i	0.0594474	−	0.998231i	$-0.481066\pi$
$941$	−17.8089	−	7.05105i	−0.580554	−	0.229858i	−0.640001	+	0.768374i	$0.721066\pi$
$942$	11.4592	−	6.29974i	0.373360	−	0.205257i
$943$	−28.2682			−0.920540
$944$	−15.5336	+	8.53967i	−0.505576	+	0.277943i
$945$	−4.83486	−	35.0051i	−0.157278	−	1.13871i
$946$	35.1500	−	4.44047i	1.14282	−	0.144372i
$947$	7.90792	−	41.4548i	0.256973	−	1.34710i	−0.586510	−	0.809942i	$-0.699498\pi$
$947$	7.90792	−	41.4548i	0.256973	−	1.34710i	0.843482	−	0.537157i	$-0.180502\pi$
$948$	13.8634	−	5.48892i	0.450263	−	0.178272i
$949$	−13.6914	−	42.1378i	−0.444442	−	1.36785i
$950$	−18.4045	+	30.5430i	−0.597122	+	0.990946i
$951$	2.14636	−	6.60582i	0.0696005	−	0.214208i
$952$	4.22330	+	67.1275i	0.136878	+	2.17561i
$953$	57.3425	−	7.24404i	1.85751	−	0.234658i	0.884680	−	0.466198i	$-0.154377\pi$
$953$	57.3425	−	7.24404i	1.85751	−	0.234658i	0.972825	+	0.231541i	$0.0743767\pi$
$954$	−39.0748	+	36.6937i	−1.26509	+	1.18800i
$955$	0.514774	+	44.4253i	0.0166577	+	1.43757i
$956$	51.3535	+	6.48745i	1.66089	+	0.209819i
$957$	5.00718	−	15.4105i	0.161859	−	0.498151i
$958$	15.3364	+	14.4018i	0.495496	+	0.465302i
$959$	−9.21466	+	2.36592i	−0.297557	+	0.0763996i
$960$	−13.3684	−	10.8009i	−0.431464	−	0.348597i
$961$	6.85841	+	8.29040i	0.221239	+	0.267432i
$962$	−30.7309	+	7.89036i	−0.990805	+	0.254395i
$963$	23.1030	−	27.9267i	0.744482	−	0.899924i
$964$	−41.7725	+	16.5389i	−1.34540	+	0.532682i
$965$	20.0505	+	48.9760i	0.645448	+	1.57659i
$966$	−16.4248	−	25.8814i	−0.528460	−	0.832720i
$967$	−7.58040	−	39.7379i	−0.243769	−	1.27788i	−0.867969	−	0.496619i	$-0.834575\pi$
$967$	−7.58040	−	39.7379i	−0.243769	−	1.27788i	0.624200	−	0.781265i	$-0.285425\pi$
$968$	6.08326	+	18.7223i	0.195523	+	0.601759i
$969$	−3.63941	+	7.73414i	−0.116915	+	0.248457i
$970$	−14.9415	−	12.0718i	−0.479742	−	0.387603i
$971$	−43.0145	−	23.6474i	−1.38040	−	0.758881i	−0.393364	−	0.919383i	$-0.628689\pi$
$971$	−43.0145	−	23.6474i	−1.38040	−	0.758881i	−0.987036	+	0.160502i	$0.948689\pi$
$972$	48.5440	+	26.6873i	1.55705	+	0.855995i
$973$	31.9921	+	38.6718i	1.02562	+	1.23976i
$974$	−23.6687	−	17.1963i	−0.758393	−	0.551005i
$975$	−13.2933	−	1.36722i	−0.425726	−	0.0437861i
$976$	−15.6365	+	11.3606i	−0.500512	+	0.363643i
$977$	−22.7347	−	5.83728i	−0.727347	−	0.186751i	−0.133179	−	0.991092i	$-0.542519\pi$
$977$	−22.7347	−	5.83728i	−0.727347	−	0.186751i	−0.594168	+	0.804341i	$0.702519\pi$
$978$	9.97399	+	21.1958i	0.318933	+	0.677767i
$979$	5.27730	−	27.6646i	0.168663	−	0.884163i
$980$	−39.2980	−	69.5612i	−1.25533	−	2.22205i
$981$	−28.4470	−	26.7135i	−0.908243	−	0.852897i
$982$	11.9417	+	8.67614i	0.381074	+	0.276867i
$983$	6.12090	−	13.0076i	0.195226	−	0.414877i	−0.783114	−	0.621878i	$-0.786370\pi$
$983$	6.12090	−	13.0076i	0.195226	−	0.414877i	0.978341	+	0.207000i	$0.0663701\pi$
$984$	−11.4680	+	13.8625i	−0.365587	+	0.441919i
$985$	14.7627	−	2.99381i	0.470378	−	0.0953907i
$986$	5.67076	+	90.1342i	0.180594	+	2.87046i
$987$	0.0527574	−	0.838555i	0.00167929	−	0.0266915i
$988$	−39.0391	−	15.4567i	−1.24200	−	0.491742i
$989$	14.3627	−	22.6321i	0.456709	−	0.719658i
$990$	−22.9596	−	23.8887i	−0.729703	−	0.759232i
$991$	0.661730	−	10.5179i	0.0210205	−	0.334112i	−0.973436	−	0.228961i	$-0.926467\pi$
$991$	0.661730	−	10.5179i	0.0210205	−	0.334112i	0.994456	−	0.105151i	$-0.0335327\pi$
$992$	11.9420	+	1.50862i	0.379157	+	0.0478987i
$993$	−2.78446	+	2.02303i	−0.0883621	+	0.0641989i
$994$	−3.93384	−	20.6219i	−0.124774	−	0.654087i
$995$	22.5166	−	19.0711i	0.713826	−	0.604595i
$996$	−3.27954	−	6.96938i	−0.103916	−	0.220833i
$997$	−15.9843	+	15.0102i	−0.506227	+	0.475379i	−0.895070	−	0.445925i	$-0.852875\pi$
$997$	−15.9843	+	15.0102i	−0.506227	+	0.475379i	0.388843	+	0.921304i	$0.372875\pi$
$998$	37.0715	−	58.4153i	1.17348	−	1.84910i
$999$	13.5382			0.428331

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.g.a.106.2	yes	220
5.2	odd	4		625.2.h.b.474.2		440
5.3	odd	4		625.2.h.b.474.21		440
5.4	even	2		625.2.g.a.151.10		220
125.3	odd	100		625.2.h.b.149.2		440
125.46	even	25	inner	125.2.g.a.46.2	✓	220
125.79	even	50		625.2.g.a.476.10		220
125.122	odd	100		625.2.h.b.149.21		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.46.2	✓	220	125.46	even	25	inner
125.2.g.a.106.2	yes	220	1.1	even	1	trivial
625.2.g.a.151.10		220	5.4	even	2
625.2.g.a.476.10		220	125.79	even	50
625.2.h.b.149.2		440	125.3	odd	100
625.2.h.b.149.21		440	125.122	odd	100
625.2.h.b.474.2		440	5.2	odd	4
625.2.h.b.474.21		440	5.3	odd	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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.g (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27891 + 2.01523i) q^{2} +(0.512565 - 0.481331i) q^{3} +(-1.57401 - 3.34494i) q^{4} +(0.847185 + 2.06937i) q^{5} +(0.314471 + 1.64852i) q^{6} +(-3.30265 + 2.39951i) q^{7} +(4.01791 + 0.507580i) q^{8} +(-0.157328 + 2.50065i) q^{9} +O(q^{10})\)	\(q+(-1.27891 + 2.01523i) q^{2} +(0.512565 - 0.481331i) q^{3} +(-1.57401 - 3.34494i) q^{4} +(0.847185 + 2.06937i) q^{5} +(0.314471 + 1.64852i) q^{6} +(-3.30265 + 2.39951i) q^{7} +(4.01791 + 0.507580i) q^{8} +(-0.157328 + 2.50065i) q^{9} +(-5.25373 - 0.939249i) q^{10} +(1.32763 - 2.09201i) q^{11} +(-2.41681 - 0.956881i) q^{12} +(-0.238672 + 3.79358i) q^{13} +(-0.611805 - 9.72436i) q^{14} +(1.43029 + 0.652909i) q^{15} +(-1.44860 + 1.75106i) q^{16} +(1.73221 - 3.68113i) q^{17} +(-4.83820 - 3.51515i) q^{18} +(-2.17821 - 2.04548i) q^{19} +(5.58843 - 6.09099i) q^{20} +(-0.537862 + 2.81957i) q^{21} +(2.51798 + 5.35098i) q^{22} +(4.33365 + 1.11269i) q^{23} +(2.30376 - 1.67378i) q^{24} +(-3.56455 + 3.50627i) q^{25} +(-7.33972 - 5.33262i) q^{26} +(2.46759 + 2.98281i) q^{27} +(13.2246 + 7.27030i) q^{28} +(8.15030 + 4.48067i) q^{29} +(-3.14497 + 2.04736i) q^{30} +(1.91555 - 4.07076i) q^{31} +(0.826773 + 2.54454i) q^{32} +(-0.326452 - 1.71132i) q^{33} +(5.20300 + 8.19862i) q^{34} +(-7.76342 - 4.80155i) q^{35} +(8.61217 - 3.40980i) q^{36} +(2.22918 - 2.69462i) q^{37} +(6.90785 - 1.77363i) q^{38} +(1.70363 + 2.05934i) q^{39} +(2.35355 + 8.74455i) q^{40} +(-6.11953 + 1.57123i) q^{41} +(-4.99422 - 4.68989i) q^{42} +(1.85131 - 5.69773i) q^{43} +(-9.08736 - 1.14800i) q^{44} +(-5.30805 + 1.79295i) q^{45} +(-7.78468 + 7.31030i) q^{46} +(-0.290407 + 0.0366869i) q^{47} +(0.100336 + 1.59479i) q^{48} +(2.98669 - 9.19209i) q^{49} +(-2.50723 - 11.6676i) q^{50} +(-0.883971 - 2.72058i) q^{51} +(13.0650 - 5.17279i) q^{52} +(1.67953 - 8.80442i) q^{53} +(-9.16687 + 1.15805i) q^{54} +(5.45389 + 0.975033i) q^{55} +(-14.4877 + 7.96467i) q^{56} -2.10103 q^{57} +(-19.4531 + 10.6944i) q^{58} +(7.25227 + 2.87137i) q^{59} +(-0.0673450 - 5.81191i) q^{60} +(8.23754 + 2.11504i) q^{61} +(5.75372 + 9.06641i) q^{62} +(-5.48075 - 8.63628i) q^{63} +(-10.5876 - 2.71844i) q^{64} +(-8.05251 + 2.71997i) q^{65} +(3.86622 + 1.53074i) q^{66} +(-6.62813 + 3.64385i) q^{67} -15.0397 q^{68} +(2.75685 - 1.51559i) q^{69} +(19.6050 - 9.50438i) q^{70} +(2.13763 - 0.270046i) q^{71} +(-1.90141 + 9.96755i) q^{72} +(-10.8377 + 4.29095i) q^{73} +(2.57937 + 7.93849i) q^{74} +(-0.139389 + 3.51292i) q^{75} +(-3.41347 + 10.5056i) q^{76} +(0.635114 + 10.0948i) q^{77} +(-6.32884 + 0.799518i) q^{78} +(-4.18155 + 3.92674i) q^{79} +(-4.85082 - 1.51422i) q^{80} +(-4.75700 - 0.600949i) q^{81} +(4.65992 - 14.3417i) q^{82} +(2.16010 + 2.02847i) q^{83} +(10.2779 - 2.63892i) q^{84} +(9.08510 + 0.465973i) q^{85} +(9.11462 + 11.0177i) q^{86} +(6.33425 - 1.62636i) q^{87} +(6.39617 - 7.73164i) q^{88} +(10.5684 - 4.18434i) q^{89} +(3.17529 - 12.9900i) q^{90} +(-8.31450 - 13.1016i) q^{91} +(-3.09932 - 16.2472i) q^{92} +(-0.977535 - 3.00854i) q^{93} +(0.297470 - 0.632157i) q^{94} +(2.38749 - 6.24042i) q^{95} +(1.64854 + 0.906294i) q^{96} +(3.15396 + 1.73390i) q^{97} +(14.7045 + 17.7747i) q^{98} +(5.02252 + 3.64908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Introduction

L-functions

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