LMFDB - Embedded newform 368.2.m.b.225.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(49,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("368.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.m (of order $11$, degree $10$, not 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:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 46)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			225.1
Root			$0.654861 + 0.755750i$ of defining polynomial
Character	$\chi$	$=$	368.225
Dual form			368.2.m.b.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.712591 + 0.822373i) q^{3} +(0.174863 - 1.21620i) q^{5} +(-0.260554 - 0.570534i) q^{7} +(0.258432 + 1.79743i) q^{9} +(5.65177 - 1.65951i) q^{11} +(-0.977031 + 2.13940i) q^{13} +(0.875565 + 1.01046i) q^{15} +(4.49223 - 2.88698i) q^{17} +(0.227916 + 0.146473i) q^{19} +(0.654861 + 0.192284i) q^{21} +(2.50079 + 4.09219i) q^{23} +(3.34890 + 0.983325i) q^{25} +(-4.40856 - 2.83321i) q^{27} +(-1.66810 + 1.07202i) q^{29} +(4.32439 + 4.99061i) q^{31} +(-2.66266 + 5.83041i) q^{33} +(-0.739446 + 0.217121i) q^{35} +(-1.43317 - 9.96790i) q^{37} +(-1.06316 - 2.32800i) q^{39} +(-1.53880 + 10.7026i) q^{41} +(3.01056 - 3.47437i) q^{43} +2.23123 q^{45} -6.97259 q^{47} +(4.32640 - 4.99294i) q^{49} +(-0.826944 + 5.75152i) q^{51} +(-1.09543 - 2.39865i) q^{53} +(-1.03001 - 7.16387i) q^{55} +(-0.282866 + 0.0830570i) q^{57} +(-0.685131 + 1.50023i) q^{59} +(-5.98206 - 6.90366i) q^{61} +(0.958162 - 0.615773i) q^{63} +(2.43109 + 1.56237i) q^{65} +(-5.94311 - 1.74505i) q^{67} +(-5.14735 - 0.859474i) q^{69} +(-8.69524 - 2.55315i) q^{71} +(-4.99580 - 3.21061i) q^{73} +(-3.19505 + 2.05334i) q^{75} +(-2.41940 - 2.79213i) q^{77} +(2.49546 - 5.46429i) q^{79} +(0.244379 - 0.0717563i) q^{81} +(-0.277948 - 1.93317i) q^{83} +(-2.72562 - 5.96828i) q^{85} +(0.307069 - 2.13571i) q^{87} +(-3.00611 + 3.46923i) q^{89} +1.47517 q^{91} -7.18567 q^{93} +(0.217995 - 0.251579i) q^{95} +(-1.44938 + 10.0807i) q^{97} +(4.44345 + 9.72980i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{3} - 6 q^{5} - 3 q^{7} + 9 q^{9} + 12 q^{11} - 14 q^{13} + 13 q^{15} + 15 q^{17} - 2 q^{19} + q^{21} + q^{23} + 13 q^{25} - 26 q^{27} - 8 q^{29} + 21 q^{31} - 15 q^{33} - 7 q^{35} + 28 q^{37}+ \cdots - 20 q^{99}+O(q^{100}) $ 10 * q + 4 * q^3 - 6 * q^5 - 3 * q^7 + 9 * q^9 + 12 * q^11 - 14 * q^13 + 13 * q^15 + 15 * q^17 - 2 * q^19 + q^21 + q^23 + 13 * q^25 - 26 * q^27 - 8 * q^29 + 21 * q^31 - 15 * q^33 - 7 * q^35 + 28 * q^37 + 12 * q^39 - 31 * q^41 - 11 * q^43 + 10 * q^45 - 18 * q^47 - 24 * q^49 + 17 * q^51 - 21 * q^53 - 5 * q^55 + 19 * q^57 + 5 * q^59 + 37 * q^61 - 17 * q^63 + 37 * q^65 + 13 * q^67 - 15 * q^69 - 49 * q^71 - 8 * q^73 - 8 * q^75 - 8 * q^77 - 8 * q^79 - 11 * q^81 + 7 * q^83 - 42 * q^85 + 21 * q^87 - 13 * q^89 + 24 * q^91 - 40 * q^93 + 10 * q^95 - 32 * q^97 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.712591	+	0.822373i	−0.411414	+	0.474797i	−0.923202	−	0.384314i	$-0.874438\pi$
$3$	−0.712591	+	0.822373i	−0.411414	+	0.474797i	0.511788	+	0.859112i	$0.328983\pi$
$4$		0			0
$5$	0.174863	−	1.21620i	0.0782012	−	0.543902i	−0.912629	−	0.408789i	$-0.865951\pi$
$5$	0.174863	−	1.21620i	0.0782012	−	0.543902i	0.990830	−	0.135113i	$-0.0431397\pi$
$6$		0			0
$7$	−0.260554	−	0.570534i	−0.0984803	−	0.215642i	0.853979	−	0.520307i	$-0.174183\pi$
$7$	−0.260554	−	0.570534i	−0.0984803	−	0.215642i	−0.952459	+	0.304666i	$0.901455\pi$
$8$		0			0
$9$	0.258432	+	1.79743i	0.0861440	+	0.599144i
$10$		0			0
$11$	5.65177	−	1.65951i	1.70407	−	0.500361i	0.722486	−	0.691385i	$-0.242999\pi$
$11$	5.65177	−	1.65951i	1.70407	−	0.500361i	0.981585	+	0.191025i	$0.0611810\pi$
$12$		0			0
$13$	−0.977031	+	2.13940i	−0.270980	+	0.593362i	−0.995380	−	0.0960174i	$-0.969390\pi$
$13$	−0.977031	+	2.13940i	−0.270980	+	0.593362i	0.724400	+	0.689380i	$0.242117\pi$
$14$		0			0
$15$	0.875565	+	1.01046i	0.226070	+	0.260899i
$16$		0			0
$17$	4.49223	−	2.88698i	1.08953	−	0.700195i	0.132787	−	0.991145i	$-0.457607\pi$
$17$	4.49223	−	2.88698i	1.08953	−	0.700195i	0.956739	+	0.290949i	$0.0939710\pi$
$18$		0			0
$19$	0.227916	+	0.146473i	0.0522876	+	0.0336032i	0.566523	−	0.824046i	$-0.308288\pi$
$19$	0.227916	+	0.146473i	0.0522876	+	0.0336032i	−0.514236	+	0.857649i	$0.671924\pi$
$20$		0			0
$21$	0.654861	+	0.192284i	0.142902	+	0.0419599i
$22$		0			0
$23$	2.50079	+	4.09219i	0.521451	+	0.853281i
$23$	2.50079	+	4.09219i	0.521451	+	0.853281i
$24$		0			0
$25$	3.34890	+	0.983325i	0.669779	+	0.196665i
$26$		0			0
$27$	−4.40856	−	2.83321i	−0.848428	−	0.545252i
$28$		0			0
$29$	−1.66810	+	1.07202i	−0.309758	+	0.199070i	−0.686279	−	0.727339i	$-0.740757\pi$
$29$	−1.66810	+	1.07202i	−0.309758	+	0.199070i	0.376520	+	0.926408i	$0.377121\pi$
$30$		0			0
$31$	4.32439	+	4.99061i	0.776683	+	0.896340i	0.996865	−	0.0791185i	$-0.0252105\pi$
$31$	4.32439	+	4.99061i	0.776683	+	0.896340i	−0.220182	+	0.975459i	$0.570665\pi$
$32$		0			0
$33$	−2.66266	+	5.83041i	−0.463510	+	1.01494i
$34$		0			0
$35$	−0.739446	+	0.217121i	−0.124989	+	0.0367001i
$36$		0			0
$37$	−1.43317	−	9.96790i	−0.235611	−	1.63871i	−0.673145	−	0.739510i	$-0.735057\pi$
$37$	−1.43317	−	9.96790i	−0.235611	−	1.63871i	0.437534	−	0.899202i	$-0.355852\pi$
$38$		0			0
$39$	−1.06316	−	2.32800i	−0.170242	−	0.372778i
$40$		0			0
$41$	−1.53880	+	10.7026i	−0.240320	+	1.67146i	0.410219	+	0.911987i	$0.365452\pi$
$41$	−1.53880	+	10.7026i	−0.240320	+	1.67146i	−0.650539	+	0.759473i	$0.725457\pi$
$42$		0			0
$43$	3.01056	−	3.47437i	0.459106	−	0.529836i	−0.478244	−	0.878227i	$-0.658726\pi$
$43$	3.01056	−	3.47437i	0.459106	−	0.529836i	0.937349	+	0.348391i	$0.113272\pi$
$44$		0			0
$45$	2.23123			0.332612
$46$		0			0
$47$	−6.97259			−1.01706			−0.508528	−	0.861045i	$-0.669810\pi$
$47$	−6.97259			−1.01706			−0.508528	+	0.861045i	$0.669810\pi$
$48$		0			0
$49$	4.32640	−	4.99294i	0.618058	−	0.713277i
$50$		0			0
$51$	−0.826944	+	5.75152i	−0.115795	+	0.805374i
$52$		0			0
$53$	−1.09543	−	2.39865i	−0.150468	−	0.329480i	0.819356	−	0.573285i	$-0.194331\pi$
$53$	−1.09543	−	2.39865i	−0.150468	−	0.329480i	−0.969824	+	0.243806i	$0.921604\pi$
$54$		0			0
$55$	−1.03001	−	7.16387i	−0.138886	−	0.965976i
$56$		0			0
$57$	−0.282866	+	0.0830570i	−0.0374666	+	0.0110012i
$58$		0			0
$59$	−0.685131	+	1.50023i	−0.0891965	+	0.195313i	−0.948973	−	0.315358i	$-0.897876\pi$
$59$	−0.685131	+	1.50023i	−0.0891965	+	0.195313i	0.859776	+	0.510671i	$0.170603\pi$
$60$		0			0
$61$	−5.98206	−	6.90366i	−0.765924	−	0.883923i	0.230086	−	0.973170i	$-0.426099\pi$
$61$	−5.98206	−	6.90366i	−0.765924	−	0.883923i	−0.996010	+	0.0892472i	$0.971554\pi$
$62$		0			0
$63$	0.958162	−	0.615773i	0.120717	−	0.0775801i
$64$		0			0
$65$	2.43109	+	1.56237i	0.301540	+	0.193788i
$66$		0			0
$67$	−5.94311	−	1.74505i	−0.726066	−	0.213192i	−0.102245	−	0.994759i	$-0.532602\pi$
$67$	−5.94311	−	1.74505i	−0.726066	−	0.213192i	−0.623821	+	0.781567i	$0.714421\pi$
$68$		0			0
$69$	−5.14735	−	0.859474i	−0.619668	−	0.103469i
$70$		0			0
$71$	−8.69524	−	2.55315i	−1.03194	−	0.303003i	−0.278438	−	0.960454i	$-0.589817\pi$
$71$	−8.69524	−	2.55315i	−1.03194	−	0.303003i	−0.753497	+	0.657451i	$0.771635\pi$
$72$		0			0
$73$	−4.99580	−	3.21061i	−0.584714	−	0.375773i	0.214586	−	0.976705i	$-0.431160\pi$
$73$	−4.99580	−	3.21061i	−0.584714	−	0.375773i	−0.799300	+	0.600932i	$0.794796\pi$
$74$		0			0
$75$	−3.19505	+	2.05334i	−0.368933	+	0.237099i
$76$		0			0
$77$	−2.41940	−	2.79213i	−0.275716	−	0.318193i
$78$		0			0
$79$	2.49546	−	5.46429i	0.280761	−	0.614780i	−0.715740	−	0.698367i	$-0.753910\pi$
$79$	2.49546	−	5.46429i	0.280761	−	0.614780i	0.996501	+	0.0835867i	$0.0266376\pi$
$80$		0			0
$81$	0.244379	−	0.0717563i	0.0271533	−	0.00797292i
$82$		0			0
$83$	−0.277948	−	1.93317i	−0.0305087	−	0.212193i	0.968865	−	0.247591i	$-0.0796390\pi$
$83$	−0.277948	−	1.93317i	−0.0305087	−	0.212193i	−0.999373	+	0.0353985i	$0.988730\pi$
$84$		0			0
$85$	−2.72562	−	5.96828i	−0.295635	−	0.647351i
$86$		0			0
$87$	0.307069	−	2.13571i	0.0329213	−	0.228973i
$88$		0			0
$89$	−3.00611	+	3.46923i	−0.318647	+	0.367738i	−0.892365	−	0.451315i	$-0.850955\pi$
$89$	−3.00611	+	3.46923i	−0.318647	+	0.367738i	0.573718	+	0.819053i	$0.305501\pi$
$90$		0			0
$91$	1.47517			0.154640
$92$		0			0
$93$	−7.18567			−0.745119
$94$		0			0
$95$	0.217995	−	0.251579i	0.0223658	−	0.0258115i
$96$		0			0
$97$	−1.44938	+	10.0807i	−0.147163	+	1.02354i	0.773672	+	0.633586i	$0.218418\pi$
$97$	−1.44938	+	10.0807i	−0.147163	+	1.02354i	−0.920835	+	0.389953i	$0.872491\pi$
$98$		0			0
$99$	4.44345	+	9.72980i	0.446584	+	0.977882i
$100$		0			0
$101$	2.02588	+	14.0903i	0.201583	+	1.40204i	0.799589	+	0.600548i	$0.205051\pi$
$101$	2.02588	+	14.0903i	0.201583	+	1.40204i	−0.598006	+	0.801492i	$0.704040\pi$
$102$		0			0
$103$	−0.723186	+	0.212347i	−0.0712576	+	0.0209231i	−0.317167	−	0.948370i	$-0.602732\pi$
$103$	−0.723186	+	0.212347i	−0.0712576	+	0.0209231i	0.245909	+	0.969293i	$0.420913\pi$
$104$		0			0
$105$	0.348368	−	0.762819i	0.0339972	−	0.0744435i
$106$		0			0
$107$	0.388356	+	0.448187i	0.0375438	+	0.0433279i	0.774211	−	0.632928i	$-0.218147\pi$
$107$	0.388356	+	0.448187i	0.0375438	+	0.0433279i	−0.736667	+	0.676256i	$0.763602\pi$
$108$		0			0
$109$	−5.77288	+	3.71001i	−0.552942	+	0.355354i	−0.787082	−	0.616849i	$-0.788409\pi$
$109$	−5.77288	+	3.71001i	−0.552942	+	0.355354i	0.234140	+	0.972203i	$0.424773\pi$
$110$		0			0
$111$	9.21860	+	5.92443i	0.874990	+	0.562322i
$112$		0			0
$113$	1.19580	+	0.351119i	0.112491	+	0.0330305i	0.337494	−	0.941328i	$-0.390421\pi$
$113$	1.19580	+	0.351119i	0.112491	+	0.0330305i	−0.225002	+	0.974358i	$0.572239\pi$
$114$		0			0
$115$	5.41423	−	2.32589i	0.504879	−	0.216890i
$116$		0			0
$117$	−4.09792	−	1.20326i	−0.378853	−	0.111241i
$118$		0			0
$119$	−2.81759	−	1.81076i	−0.258288	−	0.165992i
$120$		0			0
$121$	19.9347	−	12.8113i	1.81225	−	1.16466i
$122$		0			0
$123$	−7.70497	−	8.89201i	−0.694734	−	0.801766i
$124$		0			0
$125$	4.33364	−	9.48934i	0.387612	−	0.848753i
$126$		0			0
$127$	−6.89460	+	2.02444i	−0.611796	+	0.179640i	−0.572929	−	0.819605i	$-0.694193\pi$
$127$	−6.89460	+	2.02444i	−0.611796	+	0.179640i	−0.0388671	+	0.999244i	$0.512375\pi$
$128$		0			0
$129$	0.711933	+	4.95160i	0.0626822	+	0.435964i
$130$		0			0
$131$	0.273443	+	0.598756i	0.0238908	+	0.0523136i	0.921201	−	0.389086i	$-0.127209\pi$
$131$	0.273443	+	0.598756i	0.0238908	+	0.0523136i	−0.897310	+	0.441400i	$0.854482\pi$
$132$		0			0
$133$	0.0241832	−	0.168198i	0.00209695	−	0.0145846i
$134$		0			0
$135$	−4.21665	+	4.86627i	−0.362911	+	0.418822i
$136$		0			0
$137$	−12.5241			−1.07001			−0.535003	−	0.844850i	$-0.679689\pi$
$137$	−12.5241			−1.07001			−0.535003	+	0.844850i	$0.679689\pi$
$138$		0			0
$139$	−17.0602			−1.44703			−0.723515	−	0.690309i	$-0.757475\pi$
$139$	−17.0602			−1.44703			−0.723515	+	0.690309i	$0.757475\pi$
$140$		0			0
$141$	4.96860	−	5.73407i	0.418432	−	0.482896i
$142$		0			0
$143$	−1.97160	+	13.7128i	−0.164873	+	1.14672i
$144$		0			0
$145$	1.01211	+	2.21620i	0.0840508	+	0.184046i
$146$		0			0
$147$	1.02310	+	7.11584i	0.0843841	+	0.586905i
$148$		0			0
$149$	17.6680	−	5.18781i	1.44742	−	0.425002i	0.538734	−	0.842476i	$-0.318903\pi$
$149$	17.6680	−	5.18781i	1.44742	−	0.425002i	0.908689	+	0.417474i	$0.137085\pi$
$150$		0			0
$151$	4.77740	−	10.4611i	0.388780	−	0.851309i	−0.609506	−	0.792781i	$-0.708632\pi$
$151$	4.77740	−	10.4611i	0.388780	−	0.851309i	0.998286	−	0.0585274i	$-0.0186405\pi$
$152$		0			0
$153$	6.35009	+	7.32839i	0.513374	+	0.592465i
$154$		0			0
$155$	6.82576	−	4.38665i	0.548259	−	0.352344i
$156$		0			0
$157$	2.71568	+	1.74526i	0.216735	+	0.139287i	0.644504	−	0.764601i	$-0.277064\pi$
$157$	2.71568	+	1.74526i	0.216735	+	0.139287i	−0.427769	+	0.903888i	$0.640700\pi$
$158$		0			0
$159$	2.75317	+	0.808405i	0.218341	+	0.0641107i
$160$		0			0
$161$	1.68314	−	2.49303i	0.132650	−	0.196478i
$162$		0			0
$163$	10.6155	+	3.11700i	0.831473	+	0.244143i	0.669650	−	0.742677i	$-0.266444\pi$
$163$	10.6155	+	3.11700i	0.831473	+	0.244143i	0.161824	+	0.986820i	$0.448262\pi$
$164$		0			0
$165$	6.62535	+	4.25785i	0.515783	+	0.331474i
$166$		0			0
$167$	18.4501	−	11.8572i	1.42771	−	0.917536i	0.427807	−	0.903870i	$-0.359286\pi$
$167$	18.4501	−	11.8572i	1.42771	−	0.917536i	0.999907	−	0.0136652i	$-0.00434990\pi$
$168$		0			0
$169$	4.89075	+	5.64423i	0.376212	+	0.434171i
$170$		0			0
$171$	−0.204374	+	0.447517i	−0.0156289	+	0.0342225i
$172$		0			0
$173$	−10.6459	+	3.12591i	−0.809391	+	0.237659i	−0.660142	−	0.751141i	$-0.729504\pi$
$173$	−10.6459	+	3.12591i	−0.809391	+	0.237659i	−0.149249	+	0.988800i	$0.547686\pi$
$174$		0			0
$175$	−0.311549	−	2.16687i	−0.0235509	−	0.163800i
$176$		0			0
$177$	−0.745530	−	1.63248i	−0.0560374	−	0.122705i
$178$		0			0
$179$	−2.49587	+	17.3592i	−0.186550	+	1.29749i	0.654307	+	0.756229i	$0.272961\pi$
$179$	−2.49587	+	17.3592i	−0.186550	+	1.29749i	−0.840857	+	0.541257i	$0.817949\pi$
$180$		0			0
$181$	−13.3631	+	15.4218i	−0.993269	+	1.14629i	−0.00402916	+	0.999992i	$0.501283\pi$
$181$	−13.3631	+	15.4218i	−0.993269	+	1.14629i	−0.989240	+	0.146302i	$0.953263\pi$
$182$		0			0
$183$	9.94014			0.734797
$184$		0			0
$185$	−12.3736			−0.909723
$186$		0			0
$187$	20.5981	−	23.7714i	1.50628	−	1.73834i
$188$		0			0
$189$	−0.467774	+	3.25344i	−0.0340256	+	0.236653i
$190$		0			0
$191$	3.93085	+	8.60736i	0.284426	+	0.622807i	0.996882	−	0.0789105i	$-0.0251441\pi$
$191$	3.93085	+	8.60736i	0.284426	+	0.622807i	−0.712455	+	0.701718i	$0.752417\pi$
$192$		0			0
$193$	−3.63769	−	25.3007i	−0.261847	−	1.82118i	−0.518955	−	0.854801i	$-0.673679\pi$
$193$	−3.63769	−	25.3007i	−0.261847	−	1.82118i	0.257108	−	0.966383i	$-0.417230\pi$
$194$		0			0
$195$	−3.01722	+	0.885937i	−0.216068	+	0.0634432i
$196$		0			0
$197$	2.18904	−	4.79334i	0.155963	−	0.341511i	−0.815480	−	0.578786i	$-0.803527\pi$
$197$	2.18904	−	4.79334i	0.155963	−	0.341511i	0.971443	+	0.237274i	$0.0762540\pi$
$198$		0			0
$199$	−16.3820	−	18.9058i	−1.16129	−	1.34020i	−0.930108	−	0.367285i	$-0.880287\pi$
$199$	−16.3820	−	18.9058i	−1.16129	−	1.34020i	−0.231178	−	0.972911i	$-0.574258\pi$
$200$		0			0
$201$	5.67009	−	3.64394i	0.399937	−	0.257024i
$202$		0			0
$203$	1.04626	+	0.672388i	0.0734328	+	0.0471924i
$204$		0			0
$205$	12.7474	+	3.74297i	0.890317	+	0.261421i
$206$		0			0
$207$	−6.70916	+	5.55256i	−0.466319	+	0.385929i
$208$		0			0
$209$	1.53120	+	0.449602i	0.105915	+	0.0310996i
$210$		0			0
$211$	7.45882	+	4.79349i	0.513487	+	0.329998i	0.771591	−	0.636119i	$-0.219461\pi$
$211$	7.45882	+	4.79349i	0.513487	+	0.329998i	−0.258104	+	0.966117i	$0.583098\pi$
$212$		0			0
$213$	8.29579	−	5.33138i	0.568418	−	0.365300i
$214$		0			0
$215$	−3.69909	−	4.26898i	−0.252276	−	0.291142i
$216$		0			0
$217$	1.72058	−	3.76754i	0.116800	−	0.255757i
$218$		0			0
$219$	6.20028	−	1.82057i	0.418976	−	0.123022i
$220$		0			0
$221$	1.78736	+	12.4313i	0.120231	+	0.836222i
$222$		0			0
$223$	7.05499	+	15.4483i	0.472437	+	1.03449i	0.984474	+	0.175530i	$0.0561638\pi$
$223$	7.05499	+	15.4483i	0.472437	+	1.03449i	−0.512037	+	0.858963i	$0.671109\pi$
$224$		0			0
$225$	−0.901999	+	6.27354i	−0.0601333	+	0.418236i
$226$		0			0
$227$	−11.7844	+	13.5999i	−0.782155	+	0.902655i	−0.997263	−	0.0739349i	$-0.976444\pi$
$227$	−11.7844	+	13.5999i	−0.782155	+	0.902655i	0.215108	+	0.976590i	$0.430990\pi$
$228$		0			0
$229$	7.49653			0.495385			0.247692	−	0.968839i	$-0.420328\pi$
$229$	7.49653			0.495385			0.247692	+	0.968839i	$0.420328\pi$
$230$		0			0
$231$	4.02022			0.264511
$232$		0			0
$233$	−3.61684	+	4.17406i	−0.236947	+	0.273452i	−0.861753	−	0.507329i	$-0.830633\pi$
$233$	−3.61684	+	4.17406i	−0.236947	+	0.273452i	0.624805	+	0.780781i	$0.285178\pi$
$234$		0			0
$235$	−1.21925	+	8.48007i	−0.0795351	+	0.553179i
$236$		0			0
$237$	2.71545	+	5.94600i	0.176387	+	0.386234i
$238$		0			0
$239$	0.742743	+	5.16589i	0.0480440	+	0.334153i	0.999641	+	0.0268040i	$0.00853299\pi$
$239$	0.742743	+	5.16589i	0.0480440	+	0.334153i	−0.951597	+	0.307350i	$0.900558\pi$
$240$		0			0
$241$	1.49095	−	0.437783i	0.0960407	−	0.0282001i	−0.233359	−	0.972391i	$-0.574972\pi$
$241$	1.49095	−	0.437783i	0.0960407	−	0.0282001i	0.329400	+	0.944191i	$0.393154\pi$
$242$		0			0
$243$	6.41578	−	14.0486i	0.411572	−	0.901217i
$244$		0			0
$245$	−5.31589	−	6.13486i	−0.339619	−	0.391942i
$246$		0			0
$247$	−0.536045	+	0.344495i	−0.0341077	+	0.0219197i
$248$		0			0
$249$	1.78785	+	1.14898i	0.113300	+	0.0728137i
$250$		0			0
$251$	−8.56499	−	2.51491i	−0.540617	−	0.158740i	1.28787e−5	−	1.00000i	$-0.499996\pi$
$251$	−8.56499	−	2.51491i	−0.540617	−	0.158740i	−0.540630	+	0.841260i	$0.681814\pi$
$252$		0			0
$253$	20.9249	+	18.9780i	1.31554	+	1.19314i
$254$		0			0
$255$	6.85041	+	2.01146i	0.428989	+	0.125963i
$256$		0			0
$257$	−3.06431	−	1.96932i	−0.191147	−	0.122843i	0.441567	−	0.897228i	$-0.354423\pi$
$257$	−3.06431	−	1.96932i	−0.191147	−	0.122843i	−0.632714	+	0.774386i	$0.718059\pi$
$258$		0			0
$259$	−5.31361	+	3.41485i	−0.330172	+	0.212188i
$260$		0			0
$261$	−2.35798	−	2.72125i	−0.145955	−	0.168441i
$262$		0			0
$263$	−6.70351	+	14.6786i	−0.413356	+	0.905124i	0.582384	+	0.812914i	$0.302120\pi$
$263$	−6.70351	+	14.6786i	−0.413356	+	0.905124i	−0.995740	+	0.0922095i	$0.970607\pi$
$264$		0			0
$265$	−3.10879	+	0.912822i	−0.190971	+	0.0560742i
$266$		0			0
$267$	−0.710880	−	4.94428i	−0.0435052	−	0.302585i
$268$		0			0
$269$	−1.86684	−	4.08782i	−0.113823	−	0.249239i	0.844143	−	0.536117i	$-0.180110\pi$
$269$	−1.86684	−	4.08782i	−0.113823	−	0.249239i	−0.957967	+	0.286879i	$0.907382\pi$
$270$		0			0
$271$	−0.498456	+	3.46684i	−0.0302791	+	0.210595i	−0.999344	−	0.0362095i	$-0.988472\pi$
$271$	−0.498456	+	3.46684i	−0.0302791	+	0.210595i	0.969065	+	0.246805i	$0.0793807\pi$
$272$		0			0
$273$	−1.05119	+	1.21314i	−0.0636210	+	0.0734226i
$274$		0			0
$275$	20.5590			1.23976
$276$		0			0
$277$	−12.0692			−0.725166			−0.362583	−	0.931951i	$-0.618105\pi$
$277$	−12.0692			−0.725166			−0.362583	+	0.931951i	$0.618105\pi$
$278$		0			0
$279$	−7.85273	+	9.06254i	−0.470131	+	0.542560i
$280$		0			0
$281$	0.891748	−	6.20224i	0.0531972	−	0.369995i	−0.945781	−	0.324804i	$-0.894702\pi$
$281$	0.891748	−	6.20224i	0.0531972	−	0.369995i	0.998978	−	0.0451902i	$-0.0143894\pi$
$282$		0			0
$283$	−13.1398	−	28.7722i	−0.781080	−	1.71033i	−0.700581	−	0.713573i	$-0.747076\pi$
$283$	−13.1398	−	28.7722i	−0.781080	−	1.71033i	−0.0804995	−	0.996755i	$-0.525652\pi$
$284$		0			0
$285$	0.0515511	+	0.358546i	0.00305362	+	0.0212384i
$286$		0			0
$287$	6.50712	−	1.91066i	0.384103	−	0.112783i
$288$		0			0
$289$	4.78341	−	10.4742i	0.281377	−	0.616130i
$290$		0			0
$291$	−7.25727	−	8.37534i	−0.425429	−	0.490971i
$292$		0			0
$293$	5.70182	−	3.66434i	0.333104	−	0.214073i	−0.363387	−	0.931638i	$-0.618380\pi$
$293$	5.70182	−	3.66434i	0.333104	−	0.214073i	0.696491	+	0.717565i	$0.254744\pi$
$294$		0			0
$295$	1.70477	+	1.09559i	0.0992558	+	0.0637878i
$296$		0			0
$297$	−29.6179	−	8.69660i	−1.71860	−	0.504628i
$298$		0			0
$299$	−11.1982	+	1.35199i	−0.647608	+	0.0781877i
$300$		0			0
$301$	−2.76666	−	0.812365i	−0.159468	−	0.0468239i
$302$		0			0
$303$	−13.0311	−	8.37460i	−0.748619	−	0.481108i
$304$		0			0
$305$	−9.44228	+	6.06819i	−0.540663	+	0.347463i
$306$		0			0
$307$	−3.97728	−	4.59002i	−0.226995	−	0.261966i	0.630815	−	0.775933i	$-0.282721\pi$
$307$	−3.97728	−	4.59002i	−0.226995	−	0.261966i	−0.857810	+	0.513967i	$0.828175\pi$
$308$		0			0
$309$	0.340707	−	0.746045i	0.0193822	−	0.0424410i
$310$		0			0
$311$	9.81498	−	2.88194i	0.556556	−	0.163420i	0.00865482	−	0.999963i	$-0.497245\pi$
$311$	9.81498	−	2.88194i	0.556556	−	0.163420i	0.547901	+	0.836543i	$0.315427\pi$
$312$		0			0
$313$	−0.572129	−	3.97924i	−0.0323386	−	0.224920i	0.967243	−	0.253853i	$-0.0816981\pi$
$313$	−0.572129	−	3.97924i	−0.0323386	−	0.224920i	−0.999581	+	0.0289333i	$0.990789\pi$
$314$		0			0
$315$	−0.581357	−	1.27299i	−0.0327557	−	0.0717251i
$316$		0			0
$317$	−0.710583	+	4.94221i	−0.0399103	+	0.277582i	−0.999998	−	0.00211768i	$-0.999326\pi$
$317$	−0.710583	+	4.94221i	−0.0399103	+	0.277582i	0.960087	+	0.279700i	$0.0902350\pi$
$318$		0			0
$319$	−7.64868	+	8.82705i	−0.428244	+	0.494220i
$320$		0			0
$321$	−0.645316			−0.0360180
$322$		0			0
$323$	1.44672			0.0804974
$324$		0			0
$325$	−5.37570	+	6.20389i	−0.298190	+	0.344130i
$326$		0			0
$327$	1.06269	−	7.39118i	0.0587670	−	0.408733i
$328$		0			0
$329$	1.81674	+	3.97810i	0.100160	+	0.219320i
$330$		0			0
$331$	0.698720	+	4.85970i	0.0384051	+	0.267113i	0.999972	−	0.00745672i	$-0.00237357\pi$
$331$	0.698720	+	4.85970i	0.0384051	+	0.267113i	−0.961567	+	0.274570i	$0.911464\pi$
$332$		0			0
$333$	17.5463	−	5.15205i	0.961529	−	0.282330i
$334$		0			0
$335$	−3.16157	+	6.92286i	−0.172735	+	0.378237i
$336$		0			0
$337$	−19.4055	−	22.3951i	−1.05708	−	1.21994i	−0.974742	−	0.223334i	$-0.928306\pi$
$337$	−19.4055	−	22.3951i	−1.05708	−	1.21994i	−0.0823405	−	0.996604i	$-0.526239\pi$
$338$		0			0
$339$	−1.14087	+	0.733190i	−0.0619634	+	0.0398214i
$340$		0			0
$341$	32.7224	+	21.0294i	1.77202	+	1.13881i
$342$		0			0
$343$	−8.18856	−	2.40438i	−0.442141	−	0.129824i
$344$		0			0
$345$	−1.94538	+	6.10992i	−0.104736	+	0.328947i
$346$		0			0
$347$	−12.3371	−	3.62249i	−0.662288	−	0.194465i	−0.0667221	−	0.997772i	$-0.521254\pi$
$347$	−12.3371	−	3.62249i	−0.662288	−	0.194465i	−0.595566	+	0.803306i	$0.703072\pi$
$348$		0			0
$349$	−19.8005	−	12.7250i	−1.05990	−	0.681156i	−0.110070	−	0.993924i	$-0.535107\pi$
$349$	−19.8005	−	12.7250i	−1.05990	−	0.681156i	−0.949830	+	0.312768i	$0.898744\pi$
$350$		0			0
$351$	10.3687	−	6.66354i	0.553439	−	0.355673i
$352$		0			0
$353$	−5.44378	−	6.28246i	−0.289743	−	0.334382i	0.592153	−	0.805826i	$-0.298278\pi$
$353$	−5.44378	−	6.28246i	−0.289743	−	0.334382i	−0.881896	+	0.471444i	$0.843733\pi$
$354$		0			0
$355$	−4.62563	+	10.1287i	−0.245503	+	0.537576i
$356$		0			0
$357$	3.49691	−	1.02678i	0.185076	−	0.0543432i
$358$		0			0
$359$	−2.75167	−	19.1383i	−0.145228	−	1.01008i	−0.923896	−	0.382645i	$-0.875013\pi$
$359$	−2.75167	−	19.1383i	−0.145228	−	1.01008i	0.778668	−	0.627436i	$-0.215896\pi$
$360$		0			0
$361$	−7.86239	−	17.2162i	−0.413810	−	0.906118i
$362$		0			0
$363$	−3.66965	+	25.5230i	−0.192606	+	1.33961i
$364$		0			0
$365$	−4.77832	+	5.51448i	−0.250109	+	0.288641i
$366$		0			0
$367$	−30.4419			−1.58906			−0.794528	−	0.607228i	$-0.792282\pi$
$367$	−30.4419			−1.58906			−0.794528	+	0.607228i	$0.792282\pi$
$368$		0			0
$369$	−19.6348			−1.02215
$370$		0			0
$371$	−1.08309	+	1.24996i	−0.0562314	+	0.0648945i
$372$		0			0
$373$	−2.74614	+	19.0998i	−0.142190	+	0.988951i	0.786367	+	0.617760i	$0.211960\pi$
$373$	−2.74614	+	19.0998i	−0.142190	+	0.988951i	−0.928557	+	0.371191i	$0.878949\pi$
$374$		0			0
$375$	4.71567	+	10.3259i	0.243516	+	0.533226i
$376$		0			0
$377$	−0.663699	−	4.61613i	−0.0341823	−	0.237743i
$378$		0			0
$379$	31.0238	−	9.10940i	1.59358	−	0.467918i	0.639832	−	0.768515i	$-0.279004\pi$
$379$	31.0238	−	9.10940i	1.59358	−	0.467918i	0.953751	+	0.300596i	$0.0971857\pi$
$380$		0			0
$381$	3.24818	−	7.11253i	0.166409	−	0.364386i
$382$		0			0
$383$	−4.70842	−	5.43380i	−0.240589	−	0.277654i	0.622595	−	0.782544i	$-0.286078\pi$
$383$	−4.70842	−	5.43380i	−0.240589	−	0.277654i	−0.863184	+	0.504890i	$0.831533\pi$
$384$		0			0
$385$	−3.81886	+	2.45423i	−0.194627	+	0.125079i
$386$		0			0
$387$	7.02297	+	4.51339i	0.356998	+	0.229428i
$388$		0			0
$389$	−25.2205	−	7.40541i	−1.27873	−	0.375469i	−0.429296	−	0.903164i	$-0.641238\pi$
$389$	−25.2205	−	7.40541i	−1.27873	−	0.375469i	−0.849434	+	0.527695i	$0.823056\pi$
$390$		0			0
$391$	23.0482	+	11.1633i	1.16560	+	0.564554i
$392$		0			0
$393$	−0.687254	−	0.201796i	−0.0346674	−	0.0101793i
$394$		0			0
$395$	−6.20931	−	3.99048i	−0.312424	−	0.200783i
$396$		0			0
$397$	−7.79986	+	5.01267i	−0.391464	+	0.251579i	−0.721536	−	0.692377i	$-0.756563\pi$
$397$	−7.79986	+	5.01267i	−0.391464	+	0.251579i	0.330072	+	0.943956i	$0.392927\pi$
$398$		0			0
$399$	0.121089	+	0.139744i	0.00606203	+	0.00699595i
$400$		0			0
$401$	−11.6450	+	25.4989i	−0.581522	+	1.27336i	0.358910	+	0.933372i	$0.383149\pi$
$401$	−11.6450	+	25.4989i	−0.581522	+	1.27336i	−0.940432	+	0.339983i	$0.889579\pi$
$402$		0			0
$403$	−14.9020	+	4.37561i	−0.742320	+	0.217965i
$404$		0			0
$405$	−0.0445371	−	0.309762i	−0.00221306	−	0.0153922i
$406$		0			0
$407$	−24.6417	−	53.9579i	−1.22145	−	2.67459i
$408$		0			0
$409$	−0.00630601	+	0.0438593i	−0.000311812	+	0.00216870i	−0.989977	−	0.141230i	$-0.954894\pi$
$409$	−0.00630601	+	0.0438593i	−0.000311812	+	0.00216870i	0.989665	+	0.143399i	$0.0458033\pi$
$410$		0			0
$411$	8.92455	−	10.2995i	0.440216	−	0.508036i
$412$		0			0
$413$	1.03445			0.0509017
$414$		0			0
$415$	−2.39972			−0.117798
$416$		0			0
$417$	12.1570	−	14.0299i	0.595329	−	0.687046i
$418$		0			0
$419$	1.75577	−	12.2117i	0.0857752	−	0.596579i	−0.900918	−	0.433989i	$-0.857106\pi$
$419$	1.75577	−	12.2117i	0.0857752	−	0.596579i	0.986694	−	0.162591i	$-0.0519851\pi$
$420$		0			0
$421$	1.15963	+	2.53923i	0.0565167	+	0.123754i	0.935783	−	0.352576i	$-0.114694\pi$
$421$	1.15963	+	2.53923i	0.0565167	+	0.123754i	−0.879267	+	0.476330i	$0.841967\pi$
$422$		0			0
$423$	−1.80194	−	12.5328i	−0.0876133	−	0.609364i
$424$		0			0
$425$	17.8829	−	5.25088i	0.867446	−	0.254705i
$426$		0			0
$427$	−2.38012	+	5.21175i	−0.115182	+	0.252214i
$428$		0			0
$429$	−9.87207	−	11.3930i	−0.476628	−	0.550058i
$430$		0			0
$431$	−2.94160	+	1.89045i	−0.141692	+	0.0910597i	−0.609566	−	0.792735i	$-0.708656\pi$
$431$	−2.94160	+	1.89045i	−0.141692	+	0.0910597i	0.467874	+	0.883795i	$0.345020\pi$
$432$		0			0
$433$	−7.93237	−	5.09782i	−0.381205	−	0.244986i	0.335979	−	0.941870i	$-0.390933\pi$
$433$	−7.93237	−	5.09782i	−0.381205	−	0.244986i	−0.717184	+	0.696884i	$0.754569\pi$
$434$		0			0
$435$	−2.54376	−	0.746916i	−0.121964	−	0.0358119i
$436$		0			0
$437$	−0.0294243	+	1.29898i	−0.00140756	+	0.0621384i
$438$		0			0
$439$	21.6681	+	6.36232i	1.03416	+	0.303657i	0.754402	−	0.656413i	$-0.227927\pi$
$439$	21.6681	+	6.36232i	1.03416	+	0.303657i	0.279759	+	0.960070i	$0.409745\pi$
$440$		0			0
$441$	10.0926	+	6.48609i	0.480598	+	0.308861i
$442$		0			0
$443$	5.11530	−	3.28740i	0.243035	−	0.156189i	−0.413453	−	0.910525i	$-0.635677\pi$
$443$	5.11530	−	3.28740i	0.243035	−	0.156189i	0.656488	+	0.754336i	$0.272041\pi$
$444$		0			0
$445$	3.69362	+	4.26267i	0.175095	+	0.202070i
$446$		0			0
$447$	−8.32377	+	18.2265i	−0.393701	+	0.862084i
$448$		0			0
$449$	11.5754	−	3.39884i	0.546276	−	0.160401i	0.00306173	−	0.999995i	$-0.499025\pi$
$449$	11.5754	−	3.39884i	0.546276	−	0.160401i	0.543214	+	0.839594i	$0.317207\pi$
$450$		0			0
$451$	9.06408	+	63.0421i	0.426811	+	2.96853i
$452$		0			0
$453$	5.19856	+	11.3833i	0.244250	+	0.534832i
$454$		0			0
$455$	0.257953	−	1.79410i	0.0120930	−	0.0841088i
$456$		0			0
$457$	13.2021	−	15.2360i	0.617566	−	0.712709i	−0.357677	−	0.933845i	$-0.616431\pi$
$457$	13.2021	−	15.2360i	0.617566	−	0.712709i	0.975243	+	0.221136i	$0.0709765\pi$
$458$		0			0
$459$	−27.9837			−1.30617
$460$		0			0
$461$	34.1368			1.58991			0.794954	−	0.606670i	$-0.207495\pi$
$461$	34.1368			1.58991			0.794954	+	0.606670i	$0.207495\pi$
$462$		0			0
$463$	7.64326	−	8.82079i	0.355212	−	0.409937i	−0.549818	−	0.835285i	$-0.685303\pi$
$463$	7.64326	−	8.82079i	0.355212	−	0.409937i	0.905030	+	0.425348i	$0.139848\pi$
$464$		0			0
$465$	−1.25651	+	8.73921i	−0.0582692	+	0.405271i
$466$		0			0
$467$	−1.97120	−	4.31632i	−0.0912162	−	0.199736i	0.858525	−	0.512772i	$-0.171381\pi$
$467$	−1.97120	−	4.31632i	−0.0912162	−	0.199736i	−0.949741	+	0.313036i	$0.898654\pi$
$468$		0			0
$469$	0.552889	+	3.84543i	0.0255300	+	0.177565i
$470$		0			0
$471$	−3.37043	+	0.989647i	−0.155301	+	0.0456005i
$472$		0			0
$473$	11.2492	−	24.6324i	0.517240	−	1.13260i
$474$		0			0
$475$	0.619238	+	0.714638i	0.0284126	+	0.0327899i
$476$		0			0
$477$	4.02832	−	2.58884i	0.184444	−	0.118535i
$478$		0			0
$479$	25.0307	+	16.0862i	1.14368	+	0.734999i	0.968371	−	0.249514i	$-0.0802708\pi$
$479$	25.0307	+	16.0862i	1.14368	+	0.734999i	0.175310	+	0.984513i	$0.443907\pi$
$480$		0			0
$481$	22.7256	+	6.67283i	1.03620	+	0.304255i
$482$		0			0
$483$	0.850805	+	3.16068i	0.0387130	+	0.143816i
$484$		0			0
$485$	12.0067	+	3.52549i	0.545196	+	0.160084i
$486$		0			0
$487$	7.33075	+	4.71119i	0.332188	+	0.213484i	0.696093	−	0.717952i	$-0.254920\pi$
$487$	7.33075	+	4.71119i	0.332188	+	0.213484i	−0.363905	+	0.931436i	$0.618557\pi$
$488$		0			0
$489$	−10.1279	+	6.50879i	−0.457998	+	0.294338i
$490$		0			0
$491$	9.86350	+	11.3831i	0.445134	+	0.513712i	0.933329	−	0.359023i	$-0.116890\pi$
$491$	9.86350	+	11.3831i	0.445134	+	0.513712i	−0.488195	+	0.872735i	$0.662345\pi$
$492$		0			0
$493$	−4.39858	+	9.63154i	−0.198102	+	0.433783i
$494$		0			0
$495$	12.6104	−	3.70275i	0.566795	−	0.166426i
$496$		0			0
$497$	0.808921	+	5.62617i	0.0362851	+	0.252368i
$498$		0			0
$499$	−13.1268	−	28.7438i	−0.587638	−	1.28675i	−0.936859	−	0.349707i	$-0.886281\pi$
$499$	−13.1268	−	28.7438i	−0.587638	−	1.28675i	0.349221	−	0.937040i	$-0.386446\pi$
$500$		0			0
$501$	−3.39636	+	23.6222i	−0.151738	+	1.05536i
$502$		0			0
$503$	−21.8882	+	25.2604i	−0.975947	+	1.12630i	0.0160278	+	0.999872i	$0.494898\pi$
$503$	−21.8882	+	25.2604i	−0.975947	+	1.12630i	−0.991975	+	0.126432i	$0.959647\pi$
$504$		0			0
$505$	17.4909			0.778336
$506$		0			0
$507$	−8.12677			−0.360922
$508$		0			0
$509$	11.7336	−	13.5414i	0.520085	−	0.600210i	−0.433567	−	0.901121i	$-0.642745\pi$
$509$	11.7336	−	13.5414i	0.520085	−	0.600210i	0.953652	+	0.300911i	$0.0972908\pi$
$510$		0			0
$511$	−0.530084	+	3.68681i	−0.0234495	+	0.163095i
$512$		0			0
$513$	−0.589794	−	1.29147i	−0.0260401	−	0.0570198i
$514$		0			0
$515$	0.131797	+	0.916671i	0.00580769	+	0.0403934i
$516$		0			0
$517$	−39.4074	+	11.5711i	−1.73314	+	0.508895i
$518$		0			0
$519$	5.01548	−	10.9824i	0.220155	−	0.482073i
$520$		0			0
$521$	−5.37419	−	6.20215i	−0.235448	−	0.271721i	0.625714	−	0.780053i	$-0.284808\pi$
$521$	−5.37419	−	6.20215i	−0.235448	−	0.271721i	−0.861161	+	0.508332i	$0.830262\pi$
$522$		0			0
$523$	5.46786	−	3.51398i	0.239093	−	0.153656i	−0.415608	−	0.909544i	$-0.636431\pi$
$523$	5.46786	−	3.51398i	0.239093	−	0.153656i	0.654701	+	0.755888i	$0.272795\pi$
$524$		0			0
$525$	2.00398	+	1.28788i	0.0874610	+	0.0562078i
$526$		0			0
$527$	33.8339	+	9.93454i	1.47383	+	0.432755i
$528$		0			0
$529$	−10.4921	+	20.4674i	−0.456178	+	0.889889i
$530$		0			0
$531$	−2.87362	−	0.843771i	−0.124704	−	0.0366165i
$532$		0			0
$533$	−21.3936	−	13.7488i	−0.926660	−	0.595528i
$534$		0			0
$535$	0.612995	−	0.393948i	0.0265021	−	0.0170318i
$536$		0			0
$537$	−12.4972	−	14.4225i	−0.539294	−	0.622378i
$538$		0			0
$539$	16.1660	−	35.3986i	0.696319	−	1.52473i
$540$		0			0
$541$	25.2892	−	7.42559i	1.08727	−	0.319251i	0.311486	−	0.950251i	$-0.399173\pi$
$541$	25.2892	−	7.42559i	1.08727	−	0.319251i	0.775783	+	0.631000i	$0.217355\pi$
$542$		0			0
$543$	−3.16008	−	21.9789i	−0.135612	−	0.943203i
$544$		0			0
$545$	3.50265	+	7.66973i	0.150037	+	0.328535i
$546$		0			0
$547$	−2.88152	+	20.0414i	−0.123205	+	0.856910i	0.830683	+	0.556746i	$0.187950\pi$
$547$	−2.88152	+	20.0414i	−0.123205	+	0.856910i	−0.953888	+	0.300164i	$0.902959\pi$
$548$		0			0
$549$	10.8629	−	12.5365i	0.463618	−	0.535044i
$550$		0			0
$551$	−0.537209			−0.0228859
$552$		0			0
$553$	−3.76777			−0.160222
$554$		0			0
$555$	8.81729	−	10.1757i	0.374273	−	0.431934i
$556$		0			0
$557$	−1.16082	+	8.07369i	−0.0491856	+	0.342093i	0.950338	+	0.311220i	$0.100738\pi$
$557$	−1.16082	+	8.07369i	−0.0491856	+	0.342093i	−0.999523	+	0.0308728i	$0.990171\pi$
$558$		0			0
$559$	4.49165	+	9.83535i	0.189977	+	0.415991i
$560$		0			0
$561$	4.87101	+	33.8786i	0.205654	+	1.43036i
$562$		0			0
$563$	30.1773	−	8.86085i	1.27182	−	0.373440i	0.424940	−	0.905222i	$-0.360295\pi$
$563$	30.1773	−	8.86085i	1.27182	−	0.373440i	0.846882	+	0.531781i	$0.178477\pi$
$564$		0			0
$565$	0.636132	−	1.39294i	0.0267623	−	0.0586012i
$566$		0			0
$567$	−0.104614	−	0.120730i	−0.00439336	−	0.00507020i
$568$		0			0
$569$	−22.4600	+	14.4342i	−0.941573	+	0.605112i	−0.918840	−	0.394629i	$-0.870873\pi$
$569$	−22.4600	+	14.4342i	−0.941573	+	0.605112i	−0.0227328	+	0.999742i	$0.507237\pi$
$570$		0			0
$571$	24.2752	+	15.6007i	1.01589	+	0.652870i	0.938910	−	0.344163i	$-0.111837\pi$
$571$	24.2752	+	15.6007i	1.01589	+	0.652870i	0.0769759	+	0.997033i	$0.475474\pi$
$572$		0			0
$573$	−9.87955	−	2.90090i	−0.412724	−	0.121187i
$574$		0			0
$575$	4.35094	+	16.1634i	0.181447	+	0.674061i
$576$		0			0
$577$	26.9449	+	7.91174i	1.12173	+	0.329370i	0.789453	−	0.613811i	$-0.210364\pi$
$577$	26.9449	+	7.91174i	1.12173	+	0.329370i	0.332278	+	0.943181i	$0.392183\pi$
$578$		0			0
$579$	23.3988	+	15.0375i	0.972421	+	0.624937i
$580$		0			0
$581$	−1.03052	+	0.662274i	−0.0427531	+	0.0274758i
$582$		0			0
$583$	−10.1717	−	11.7387i	−0.421267	−	0.486168i
$584$		0			0
$585$	−2.17998	+	4.77349i	−0.0901311	+	0.197360i
$586$		0			0
$587$	−26.9043	+	7.89980i	−1.11046	+	0.326060i	−0.784999	−	0.619497i	$-0.787337\pi$
$587$	−26.9043	+	7.89980i	−1.11046	+	0.326060i	−0.325458	+	0.945556i	$0.605519\pi$
$588$		0			0
$589$	0.254609	+	1.77085i	0.0104910	+	0.0729665i
$590$		0			0
$591$	2.38202	+	5.21590i	0.0979833	+	0.214553i
$592$		0			0
$593$	1.07775	−	7.49592i	0.0442579	−	0.307821i	−0.955653	−	0.294494i	$-0.904849\pi$
$593$	1.07775	−	7.49592i	0.0442579	−	0.307821i	0.999911	−	0.0133265i	$-0.00424207\pi$
$594$		0			0
$595$	−2.69494	+	3.11012i	−0.110482	+	0.127503i
$596$		0			0
$597$	27.2213			1.11409
$598$		0			0
$599$	12.5238			0.511708			0.255854	−	0.966715i	$-0.417643\pi$
$599$	12.5238			0.511708			0.255854	+	0.966715i	$0.417643\pi$
$600$		0			0
$601$	11.9356	−	13.7745i	0.486865	−	0.561872i	−0.458160	−	0.888870i	$-0.651491\pi$
$601$	11.9356	−	13.7745i	0.486865	−	0.561872i	0.945025	+	0.326997i	$0.106037\pi$
$602$		0			0
$603$	1.60073	−	11.1333i	0.0651867	−	0.453384i
$604$		0			0
$605$	−12.0952	−	26.4848i	−0.491740	−	1.07676i
$606$		0			0
$607$	−1.26113	−	8.77135i	−0.0511877	−	0.356018i	−0.999277	−	0.0380146i	$-0.987897\pi$
$607$	−1.26113	−	8.77135i	−0.0511877	−	0.356018i	0.948089	−	0.318004i	$-0.103012\pi$
$608$		0			0
$609$	−1.29851	+	0.381276i	−0.0526181	+	0.0154501i
$610$		0			0
$611$	6.81243	−	14.9171i	0.275602	−	0.603483i
$612$		0			0
$613$	13.9575	+	16.1078i	0.563736	+	0.650586i	0.964028	−	0.265802i	$-0.0856366\pi$
$613$	13.9575	+	16.1078i	0.563736	+	0.650586i	−0.400292	+	0.916388i	$0.631091\pi$
$614$		0			0
$615$	−12.1618	+	7.81591i	−0.490411	+	0.315168i
$616$		0			0
$617$	30.0653	+	19.3218i	1.21038	+	0.777866i	0.980723	−	0.195404i	$-0.0626020\pi$
$617$	30.0653	+	19.3218i	1.21038	+	0.777866i	0.229661	+	0.973271i	$0.426238\pi$
$618$		0			0
$619$	−7.07491	−	2.07738i	−0.284365	−	0.0834970i	0.136440	−	0.990648i	$-0.456434\pi$
$619$	−7.07491	−	2.07738i	−0.284365	−	0.0834970i	−0.420804	+	0.907151i	$0.638252\pi$
$620$		0			0
$621$	0.569152	−	25.1260i	0.0228393	−	1.00827i
$622$		0			0
$623$	2.76257	+	0.811163i	0.110680	+	0.0324986i
$624$		0			0
$625$	3.89789	+	2.50502i	0.155916	+	0.100201i
$626$		0			0
$627$	−1.46086	+	0.938838i	−0.0583411	+	0.0374936i
$628$		0			0
$629$	−35.2152	−	40.6406i	−1.40412	−	1.62044i
$630$		0			0
$631$	7.98638	−	17.4877i	0.317933	−	0.696176i	−0.681429	−	0.731884i	$-0.738641\pi$
$631$	7.98638	−	17.4877i	0.317933	−	0.696176i	0.999362	+	0.0357081i	$0.0113687\pi$
$632$		0			0
$633$	−9.25713	+	2.71814i	−0.367938	+	0.108036i
$634$		0			0
$635$	1.25651	+	8.73921i	0.0498630	+	0.346805i
$636$		0			0
$637$	6.45485	+	14.1342i	0.255751	+	0.560016i
$638$		0			0
$639$	2.34199	−	16.2889i	0.0926479	−	0.644380i
$640$		0			0
$641$	−10.1695	+	11.7363i	−0.401673	+	0.463555i	−0.920167	−	0.391526i	$-0.871947\pi$
$641$	−10.1695	+	11.7363i	−0.401673	+	0.463555i	0.518494	+	0.855081i	$0.326493\pi$
$642$		0			0
$643$	−12.8573			−0.507043			−0.253522	−	0.967330i	$-0.581589\pi$
$643$	−12.8573			−0.507043			−0.253522	+	0.967330i	$0.581589\pi$
$644$		0			0
$645$	6.14664			0.242024
$646$		0			0
$647$	−23.0648	+	26.6182i	−0.906771	+	1.04647i	0.0919425	+	0.995764i	$0.470692\pi$
$647$	−23.0648	+	26.6182i	−0.906771	+	1.04647i	−0.998714	+	0.0507053i	$0.983853\pi$
$648$		0			0
$649$	−1.38256	+	9.61592i	−0.0542703	+	0.377458i
$650$		0			0
$651$	1.87226	+	4.09967i	0.0733795	+	0.160679i
$652$		0			0
$653$	−4.09454	−	28.4782i	−0.160232	−	1.11444i	−0.898196	−	0.439596i	$-0.855122\pi$
$653$	−4.09454	−	28.4782i	−0.160232	−	1.11444i	0.737964	−	0.674840i	$-0.235787\pi$
$654$		0			0
$655$	0.776023	−	0.227861i	0.0303217	−	0.00890326i
$656$		0			0
$657$	4.47978	−	9.80934i	0.174773	−	0.382699i
$658$		0			0
$659$	1.97220	+	2.27605i	0.0768262	+	0.0886621i	0.792861	−	0.609402i	$-0.208590\pi$
$659$	1.97220	+	2.27605i	0.0768262	+	0.0886621i	−0.716035	+	0.698064i	$0.754045\pi$
$660$		0			0
$661$	8.06392	−	5.18236i	0.313650	−	0.201571i	−0.374339	−	0.927292i	$-0.622130\pi$
$661$	8.06392	−	5.18236i	0.313650	−	0.201571i	0.687989	+	0.725721i	$0.258494\pi$
$662$		0			0
$663$	−11.4969	−	7.38858i	−0.446501	−	0.286949i
$664$		0			0
$665$	−0.200334	−	0.0588234i	−0.00776862	−	0.00228107i
$666$		0			0
$667$	−8.55850	−	4.14528i	−0.331386	−	0.160506i
$668$		0			0
$669$	−17.7316	−	5.20646i	−0.685542	−	0.201293i
$670$		0			0
$671$	−45.2659	−	29.0906i	−1.74747	−	1.12303i
$672$		0			0
$673$	13.4283	−	8.62986i	0.517624	−	0.332657i	−0.255607	−	0.966781i	$-0.582275\pi$
$673$	13.4283	−	8.62986i	0.517624	−	0.332657i	0.773231	+	0.634124i	$0.218639\pi$
$674$		0			0
$675$	−11.9779	−	13.8232i	−0.461028	−	0.532055i
$676$		0			0
$677$	10.8453	−	23.7479i	0.416819	−	0.912706i	−0.578466	−	0.815707i	$-0.696348\pi$
$677$	10.8453	−	23.7479i	0.416819	−	0.912706i	0.995284	−	0.0969993i	$-0.0309244\pi$
$678$		0			0
$679$	6.12902	−	1.79964i	0.235210	−	0.0690640i
$680$		0			0
$681$	−2.78675	−	19.3823i	−0.106789	−	0.742731i
$682$		0			0
$683$	17.1908	+	37.6427i	0.657789	+	1.44036i	0.884568	+	0.466411i	$0.154453\pi$
$683$	17.1908	+	37.6427i	0.657789	+	1.44036i	−0.226779	+	0.973946i	$0.572819\pi$
$684$		0			0
$685$	−2.19000	+	15.2318i	−0.0836758	+	0.581978i
$686$		0			0
$687$	−5.34196	+	6.16495i	−0.203808	+	0.235207i
$688$		0			0
$689$	6.20193			0.236275
$690$		0			0
$691$	−40.6203			−1.54527			−0.772635	−	0.634850i	$-0.781062\pi$
$691$	−40.6203			−1.54527			−0.772635	+	0.634850i	$0.781062\pi$
$692$		0			0
$693$	4.39343	−	5.07028i	0.166892	−	0.192604i
$694$		0			0
$695$	−2.98321	+	20.7487i	−0.113160	+	0.787042i
$696$		0			0
$697$	23.9855	+	52.5209i	0.908515	+	1.98937i
$698$		0			0
$699$	−0.855307	−	5.94879i	−0.0323507	−	0.225004i
$700$		0			0
$701$	−1.52463	+	0.447673i	−0.0575846	+	0.0169084i	−0.310398	−	0.950607i	$-0.600462\pi$
$701$	−1.52463	+	0.447673i	−0.0575846	+	0.0169084i	0.252813	+	0.967515i	$0.418644\pi$
$702$		0			0
$703$	1.13338	−	2.48177i	0.0427464	−	0.0936016i
$704$		0			0
$705$	−6.10496	−	7.04550i	−0.229926	−	0.265349i
$706$		0			0
$707$	7.51116	−	4.82713i	0.282486	−	0.181543i
$708$		0			0
$709$	−3.64246	−	2.34087i	−0.136796	−	0.0879131i	0.470453	−	0.882425i	$-0.344090\pi$
$709$	−3.64246	−	2.34087i	−0.136796	−	0.0879131i	−0.607249	+	0.794512i	$0.707727\pi$
$710$		0			0
$711$	10.4666	+	3.07327i	0.392528	+	0.115257i
$712$		0			0
$713$	−9.60815	+	30.1767i	−0.359828	+	1.13013i
$714$		0			0
$715$	16.3327	+	4.79572i	0.610809	+	0.179350i
$716$		0			0
$717$	−4.77756	−	3.07035i	−0.178421	−	0.114664i
$718$		0			0
$719$	21.8293	−	14.0289i	0.814096	−	0.523188i	−0.0660915	−	0.997814i	$-0.521053\pi$
$719$	21.8293	−	14.0289i	0.814096	−	0.523188i	0.880188	+	0.474626i	$0.157417\pi$
$720$		0			0
$721$	0.309580	+	0.357275i	0.0115294	+	0.0133056i
$722$		0			0
$723$	−0.702417	+	1.53808i	−0.0261232	+	0.0572018i
$724$		0			0
$725$	−6.64044	+	1.94981i	−0.246620	+	0.0724141i
$726$		0			0
$727$	2.47161	+	17.1904i	0.0916670	+	0.637558i	0.982918	+	0.184047i	$0.0589198\pi$
$727$	2.47161	+	17.1904i	0.0916670	+	0.637558i	−0.891251	+	0.453511i	$0.850171\pi$
$728$		0			0
$729$	7.29878	+	15.9821i	0.270325	+	0.591929i
$730$		0			0
$731$	3.49368	−	24.2991i	0.129218	−	0.898734i
$732$		0			0
$733$	−30.9021	+	35.6630i	−1.14140	+	1.31724i	−0.200055	+	0.979785i	$0.564112\pi$
$733$	−30.9021	+	35.6630i	−1.14140	+	1.31724i	−0.941341	+	0.337457i	$0.890433\pi$
$734$		0			0
$735$	8.83319			0.325817
$736$		0			0
$737$	−36.4850			−1.34394
$738$		0			0
$739$	9.88757	−	11.4109i	0.363720	−	0.419755i	−0.544163	−	0.838980i	$-0.683153\pi$
$739$	9.88757	−	11.4109i	0.363720	−	0.419755i	0.907883	+	0.419224i	$0.137698\pi$
$740$		0			0
$741$	0.0986769	−	0.686313i	0.00362499	−	0.0252123i
$742$		0			0
$743$	4.94255	+	10.8227i	0.181324	+	0.397045i	0.978367	−	0.206878i	$-0.0663304\pi$
$743$	4.94255	+	10.8227i	0.181324	+	0.397045i	−0.797042	+	0.603924i	$0.793603\pi$
$744$		0			0
$745$	−3.21992	−	22.3950i	−0.117969	−	0.820491i
$746$		0			0
$747$	3.40291	−	0.999185i	0.124506	−	0.0365583i
$748$		0			0
$749$	0.154518	−	0.338348i	0.00564597	−	0.0123630i
$750$		0			0
$751$	5.20597	+	6.00801i	0.189969	+	0.219235i	0.842742	−	0.538318i	$-0.180940\pi$
$751$	5.20597	+	6.00801i	0.189969	+	0.219235i	−0.652773	+	0.757553i	$0.726395\pi$
$752$		0			0
$753$	8.17152	−	5.25152i	0.297787	−	0.191376i
$754$		0			0
$755$	−11.8874	−	7.63954i	−0.432625	−	0.278031i
$756$		0			0
$757$	−21.3067	−	6.25622i	−0.774406	−	0.227386i	−0.129430	−	0.991589i	$-0.541315\pi$
$757$	−21.3067	−	6.25622i	−0.774406	−	0.227386i	−0.644977	+	0.764202i	$0.723133\pi$
$758$		0			0
$759$	−30.5179	+	3.68452i	−1.10773	+	0.133740i
$760$		0			0
$761$	−3.25541	−	0.955875i	−0.118009	−	0.0346504i	0.222195	−	0.975002i	$-0.428678\pi$
$761$	−3.25541	−	0.955875i	−0.118009	−	0.0346504i	−0.340204	+	0.940352i	$0.610496\pi$
$762$		0			0
$763$	3.62084	+	2.32697i	0.131083	+	0.0842420i
$764$		0			0
$765$	10.0232	−	6.44152i	0.362389	−	0.232894i
$766$		0			0
$767$	−2.54019	−	2.93154i	−0.0917210	−	0.105852i
$768$		0			0
$769$	1.72530	−	3.77789i	0.0622160	−	0.136234i	−0.875970	−	0.482366i	$-0.839778\pi$
$769$	1.72530	−	3.77789i	0.0622160	−	0.136234i	0.938186	+	0.346132i	$0.112505\pi$
$770$		0			0
$771$	3.80311	−	1.11670i	0.136966	−	0.0402168i
$772$		0			0
$773$	4.01918	+	27.9540i	0.144560	+	1.00544i	0.924935	+	0.380125i	$0.124119\pi$
$773$	4.01918	+	27.9540i	0.144560	+	1.00544i	−0.780375	+	0.625311i	$0.784972\pi$
$774$		0			0
$775$	9.57454	+	20.9653i	0.343928	+	0.753097i
$776$		0			0
$777$	0.978147	−	6.80316i	0.0350908	−	0.244062i
$778$		0			0
$779$	−1.91835	+	2.21390i	−0.0687321	+	0.0793211i
$780$		0			0
$781$	−53.3804			−1.91010
$782$		0			0
$783$	10.3912			0.371351
$784$		0			0
$785$	2.59746	−	2.99763i	0.0927075	−	0.106990i
$786$		0			0
$787$	3.11544	−	21.6684i	0.111053	−	0.772393i	−0.855845	−	0.517232i	$-0.826962\pi$
$787$	3.11544	−	21.6684i	0.111053	−	0.772393i	0.966899	−	0.255161i	$-0.0821285\pi$
$788$		0			0
$789$	−7.29446	−	15.9726i	−0.259690	−	0.568641i
$790$		0			0
$791$	−0.111246	−	0.773730i	−0.00395544	−	0.0275107i
$792$		0			0
$793$	20.6143	−	6.05291i	0.732036	−	0.214945i
$794$		0			0
$795$	1.46461	−	3.20705i	0.0519444	−	0.113742i
$796$		0			0
$797$	7.02444	+	8.10663i	0.248818	+	0.287152i	0.866395	−	0.499359i	$-0.166431\pi$
$797$	7.02444	+	8.10663i	0.248818	+	0.287152i	−0.617577	+	0.786510i	$0.711886\pi$
$798$		0			0
$799$	−31.3225	+	20.1297i	−1.10811	+	0.712139i
$800$		0			0
$801$	−7.01258	−	4.50671i	−0.247777	−	0.159237i
$802$		0			0
$803$	−33.5631	−	9.85502i	−1.18442	−	0.347776i
$804$		0			0
$805$	−2.73770	−	2.48298i	−0.0964912	−	0.0875136i
$806$		0			0
$807$	4.69201	+	1.37770i	0.165166	+	0.0484972i
$808$		0			0
$809$	28.3453	+	18.2164i	0.996568	+	0.640456i	0.933883	−	0.357578i	$-0.116397\pi$
$809$	28.3453	+	18.2164i	0.996568	+	0.640456i	0.0626850	+	0.998033i	$0.480034\pi$
$810$		0			0
$811$	−29.2735	+	18.8129i	−1.02793	+	0.660611i	−0.941973	−	0.335688i	$-0.891031\pi$
$811$	−29.2735	+	18.8129i	−1.02793	+	0.660611i	−0.0859572	+	0.996299i	$0.527395\pi$
$812$		0			0
$813$	−2.49584	−	2.88035i	−0.0875330	−	0.101018i
$814$		0			0
$815$	5.64717	−	12.3656i	0.197812	−	0.433147i
$816$		0			0
$817$	1.19506	−	0.350900i	0.0418097	−	0.0122764i
$818$		0			0
$819$	0.381231	+	2.65152i	0.0133213	+	0.0926516i
$820$		0			0
$821$	−9.90154	−	21.6813i	−0.345566	−	0.756684i	−1.00000		0.000564668i	$-0.999820\pi$
$821$	−9.90154	−	21.6813i	−0.345566	−	0.756684i	0.654434	−	0.756119i	$-0.272907\pi$
$822$		0			0
$823$	−3.38486	+	23.5422i	−0.117989	+	0.820630i	0.841776	+	0.539826i	$0.181510\pi$
$823$	−3.38486	+	23.5422i	−0.117989	+	0.820630i	−0.959765	+	0.280804i	$0.909399\pi$
$824$		0			0
$825$	−14.6502	+	16.9072i	−0.510053	+	0.588633i
$826$		0			0
$827$	−30.8236			−1.07184			−0.535921	−	0.844268i	$-0.680035\pi$
$827$	−30.8236			−1.07184			−0.535921	+	0.844268i	$0.680035\pi$
$828$		0			0
$829$	−30.9416			−1.07465			−0.537324	−	0.843376i	$-0.680565\pi$
$829$	−30.9416			−1.07465			−0.537324	+	0.843376i	$0.680565\pi$
$830$		0			0
$831$	8.60038	−	9.92537i	0.298344	−	0.344307i
$832$		0			0
$833$	5.02069	−	34.9197i	0.173957	−	1.20989i
$834$		0			0
$835$	−11.1945	−	24.5124i	−0.387400	−	0.848288i
$836$		0			0
$837$	−4.92489	−	34.2533i	−0.170229	−	1.18397i
$838$		0			0
$839$	−37.7321	+	11.0791i	−1.30266	+	0.382494i	−0.858204	−	0.513308i	$-0.828420\pi$
$839$	−37.7321	+	11.0791i	−1.30266	+	0.382494i	−0.444452	+	0.895803i	$0.646602\pi$
$840$		0			0
$841$	−10.4137	+	22.8028i	−0.359093	+	0.786305i
$842$		0			0
$843$	4.46511	+	5.15301i	0.153786	+	0.177479i
$844$		0			0
$845$	7.71973	−	4.96117i	0.265567	−	0.170669i
$846$		0			0
$847$	−12.5033	−	8.03540i	−0.429620	−	0.276100i
$848$		0			0
$849$	33.0248	+	9.69695i	1.13341	+	0.332798i
$850$		0			0
$851$	37.2065	−	30.7924i	1.27542	−	1.05555i
$852$		0			0
$853$	5.57235	+	1.63619i	0.190794	+	0.0560220i	0.375733	−	0.926728i	$-0.377391\pi$
$853$	5.57235	+	1.63619i	0.190794	+	0.0560220i	−0.184940	+	0.982750i	$0.559209\pi$
$854$		0			0
$855$	0.508534	+	0.326815i	0.0173915	+	0.0111768i
$856$		0			0
$857$	−17.8082	+	11.4446i	−0.608316	+	0.390941i	−0.808225	−	0.588873i	$-0.799572\pi$
$857$	−17.8082	+	11.4446i	−0.608316	+	0.390941i	0.199909	+	0.979814i	$0.435935\pi$
$858$		0			0
$859$	1.76327	+	2.03492i	0.0601620	+	0.0694306i	0.785033	−	0.619454i	$-0.212646\pi$
$859$	1.76327	+	2.03492i	0.0601620	+	0.0694306i	−0.724871	+	0.688885i	$0.758101\pi$
$860$		0			0
$861$	−3.06564	+	6.71280i	−0.104477	+	0.228772i
$862$		0			0
$863$	19.3770	−	5.68960i	0.659601	−	0.193676i	0.0652336	−	0.997870i	$-0.479221\pi$
$863$	19.3770	−	5.68960i	0.659601	−	0.193676i	0.594367	+	0.804194i	$0.297403\pi$
$864$		0			0
$865$	1.94016	+	13.4941i	0.0659675	+	0.458814i
$866$		0			0
$867$	5.20509	+	11.3976i	0.176774	+	0.387082i
$868$		0			0
$869$	5.03571	−	35.0241i	0.170825	−	1.18811i
$870$		0			0
$871$	9.53996	−	11.0097i	0.323249	−	0.373049i
$872$		0			0
$873$	−18.4939			−0.625925
$874$		0			0
$875$	−6.54314			−0.221199
$876$		0			0
$877$	−13.7744	+	15.8966i	−0.465130	+	0.536789i	−0.939051	−	0.343779i	$-0.888293\pi$
$877$	−13.7744	+	15.8966i	−0.465130	+	0.536789i	0.473921	+	0.880568i	$0.342838\pi$
$878$		0			0
$879$	−1.04961	+	7.30020i	−0.0354025	+	0.246229i
$880$		0			0
$881$	−10.2339	−	22.4090i	−0.344787	−	0.754979i	0.655212	−	0.755445i	$-0.272579\pi$
$881$	−10.2339	−	22.4090i	−0.344787	−	0.754979i	−1.00000		0.000465480i	$0.999852\pi$
$882$		0			0
$883$	−0.165923	−	1.15402i	−0.00558376	−	0.0388359i	0.986839	−	0.161705i	$-0.0516994\pi$
$883$	−0.165923	−	1.15402i	−0.00558376	−	0.0388359i	−0.992423	+	0.122870i	$0.960790\pi$
$884$		0			0
$885$	−2.11579	+	0.621253i	−0.0711216	+	0.0208832i
$886$		0			0
$887$	4.22870	−	9.25957i	0.141986	−	0.310906i	−0.825257	−	0.564757i	$-0.808970\pi$
$887$	4.22870	−	9.25957i	0.141986	−	0.310906i	0.967243	+	0.253851i	$0.0816973\pi$
$888$		0			0
$889$	2.95143	+	3.40613i	0.0989877	+	0.114238i
$890$		0			0
$891$	1.26210	−	0.811100i	0.0422818	−	0.0271729i
$892$		0			0
$893$	−1.58917	−	1.02130i	−0.0531794	−	0.0341763i
$894$		0			0
$895$	20.6758	+	6.07097i	0.691116	+	0.202930i
$896$		0			0
$897$	6.86788	−	10.1725i	0.229312	−	0.339650i
$898$		0			0
$899$	−12.5636	−	3.68900i	−0.419018	−	0.123035i
$900$		0			0
$901$	−11.8457	−	7.61280i	−0.394639	−	0.253619i
$902$		0			0
$903$	2.63956	−	1.69634i	0.0878392	−	0.0564508i
$904$		0			0
$905$	16.4193	+	18.9489i	0.545796	+	0.629882i
$906$		0			0
$907$	−8.16401	+	17.8767i	−0.271082	+	0.593586i	−0.995392	−	0.0958881i	$-0.969431\pi$
$907$	−8.16401	+	17.8767i	−0.271082	+	0.593586i	0.724311	+	0.689474i	$0.242158\pi$
$908$		0			0
$909$	−24.8029	+	7.28278i	−0.822659	+	0.241555i
$910$		0			0
$911$	−6.81180	−	47.3771i	−0.225685	−	1.56967i	−0.715983	−	0.698118i	$-0.754021\pi$
$911$	−6.81180	−	47.3771i	−0.225685	−	1.56967i	0.490298	−	0.871555i	$-0.336888\pi$
$912$		0			0
$913$	−4.77901	−	10.4646i	−0.158162	−	0.346326i
$914$		0			0
$915$	1.73817	−	12.0892i	0.0574620	−	0.399657i
$916$		0			0
$917$	0.270364	−	0.312017i	0.00892821	−	0.0103037i
$918$		0			0
$919$	35.7413			1.17900			0.589499	−	0.807769i	$-0.299325\pi$
$919$	35.7413			1.17900			0.589499	+	0.807769i	$0.299325\pi$
$920$		0			0
$921$	6.60888			0.217770
$922$		0			0
$923$	13.9577	−	16.1081i	0.459424	−	0.530204i
$924$		0			0
$925$	5.00215	−	34.7907i	0.164470	−	1.14391i
$926$		0			0
$927$	−0.568573	−	1.24500i	−0.0186744	−	0.0408912i
$928$		0			0
$929$	3.26383	+	22.7004i	0.107083	+	0.744777i	0.970642	+	0.240529i	$0.0773210\pi$
$929$	3.26383	+	22.7004i	0.107083	+	0.744777i	−0.863559	+	0.504247i	$0.831770\pi$
$930$		0			0
$931$	1.71739	−	0.504270i	0.0562851	−	0.0165268i
$932$		0			0
$933$	−4.62403	+	10.1252i	−0.151384	+	0.331485i
$934$		0			0
$935$	−25.3090	−	29.2081i	−0.827692	−	0.955208i
$936$		0			0
$937$	−16.5521	+	10.6374i	−0.540735	+	0.347509i	−0.782326	−	0.622869i	$-0.785967\pi$
$937$	−16.5521	+	10.6374i	−0.540735	+	0.347509i	0.241591	+	0.970378i	$0.422331\pi$
$938$		0			0
$939$	3.68012	+	2.36507i	0.120096	+	0.0771811i
$940$		0			0
$941$	50.1716	+	14.7317i	1.63555	+	0.480240i	0.965136	−	0.261748i	$-0.0842989\pi$
$941$	50.1716	+	14.7317i	1.63555	+	0.480240i	0.670413	+	0.741989i	$0.266117\pi$
$942$		0			0
$943$	−47.6452	+	20.4678i	−1.55154	+	0.666524i
$944$		0			0
$945$	3.87504	+	1.13781i	0.126055	+	0.0370131i
$946$		0			0
$947$	22.1851	+	14.2575i	0.720917	+	0.463305i	0.848956	−	0.528464i	$-0.177232\pi$
$947$	22.1851	+	14.2575i	0.720917	+	0.463305i	−0.128038	+	0.991769i	$0.540868\pi$
$948$		0			0
$949$	11.7498	−	7.55115i	0.381415	−	0.245121i
$950$		0			0
$951$	−3.55799	−	4.10614i	−0.115376	−	0.133151i
$952$		0			0
$953$	17.2026	−	37.6685i	0.557247	−	1.22020i	−0.396067	−	0.918222i	$-0.629625\pi$
$953$	17.2026	−	37.6685i	0.557247	−	1.22020i	0.953314	−	0.301980i	$-0.0976474\pi$
$954$		0			0
$955$	11.1556	−	3.27559i	0.360988	−	0.105996i
$956$		0			0
$957$	−1.80875	−	12.5801i	−0.0584686	−	0.406658i
$958$		0			0
$959$	3.26321	+	7.14543i	0.105374	+	0.230738i
$960$		0			0
$961$	−1.79410	+	12.4782i	−0.0578742	+	0.402524i
$962$		0			0
$963$	−0.705223	+	0.813870i	−0.0227255	+	0.0262266i
$964$		0			0
$965$	−31.4068			−1.01102
$966$		0			0
$967$	24.8632			0.799546			0.399773	−	0.916614i	$-0.369089\pi$
$967$	24.8632			0.799546			0.399773	+	0.916614i	$0.369089\pi$
$968$		0			0
$969$	−1.03092	+	1.18974i	−0.0331178	+	0.0382200i
$970$		0			0
$971$	−7.51378	+	52.2595i	−0.241129	+	1.67709i	0.405355	+	0.914159i	$0.367148\pi$
$971$	−7.51378	+	52.2595i	−0.241129	+	1.67709i	−0.646484	+	0.762928i	$0.723761\pi$
$972$		0			0
$973$	4.44512	+	9.73345i	0.142504	+	0.312040i
$974$		0			0
$975$	−1.27124	−	8.84166i	−0.0407122	−	0.283160i
$976$		0			0
$977$	12.6033	−	3.70065i	0.403214	−	0.118394i	−0.0738363	−	0.997270i	$-0.523524\pi$
$977$	12.6033	−	3.70065i	0.403214	−	0.118394i	0.477050	+	0.878876i	$0.341706\pi$
$978$		0			0
$979$	−11.2326	+	24.5959i	−0.358995	+	0.786090i
$980$		0			0
$981$	−8.16039	−	9.41759i	−0.260541	−	0.300680i
$982$		0			0
$983$	45.2576	−	29.0853i	1.44349	−	0.927677i	0.443995	−	0.896029i	$-0.353561\pi$
$983$	45.2576	−	29.0853i	1.44349	−	0.927677i	0.999499	−	0.0316476i	$-0.0100754\pi$
$984$		0			0
$985$	−5.44688	−	3.50050i	−0.173552	−	0.111535i
$986$		0			0
$987$	−4.56608	−	1.34072i	−0.145340	−	0.0426756i
$988$		0			0
$989$	21.7466	+	3.63111i	0.691500	+	0.115463i
$990$		0			0
$991$	−41.8902	−	12.3001i	−1.33069	−	0.390725i	−0.462348	−	0.886698i	$-0.652993\pi$
$991$	−41.8902	−	12.3001i	−1.33069	−	0.390725i	−0.868337	+	0.495974i	$0.834811\pi$
$992$		0			0
$993$	−4.49439	−	2.88837i	−0.142625	−	0.0916596i
$994$		0			0
$995$	−25.8579	+	16.6178i	−0.819749	+	0.526821i
$996$		0			0
$997$	34.9557	+	40.3411i	1.10706	+	1.27761i	0.957365	+	0.288882i	$0.0932836\pi$
$997$	34.9557	+	40.3411i	1.10706	+	1.27761i	0.149695	+	0.988732i	$0.452171\pi$
$998$		0			0
$999$	−21.9230	+	48.0046i	−0.693612	+	1.51880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.m.b.225.1		10
4.3	odd	2		46.2.c.a.41.1	yes	10
12.11	even	2		414.2.i.f.271.1		10
23.3	even	11		8464.2.a.bx.1.4		5
23.9	even	11	inner	368.2.m.b.193.1		10
23.20	odd	22		8464.2.a.bw.1.4		5
92.3	odd	22		1058.2.a.m.1.2		5
92.43	even	22		1058.2.a.l.1.2		5
92.55	odd	22		46.2.c.a.9.1	✓	10
276.95	even	22		9522.2.a.bp.1.5		5
276.227	odd	22		9522.2.a.bu.1.1		5
276.239	even	22		414.2.i.f.55.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.a.9.1	✓	10	92.55	odd	22
46.2.c.a.41.1	yes	10	4.3	odd	2
368.2.m.b.193.1		10	23.9	even	11	inner
368.2.m.b.225.1		10	1.1	even	1	trivial
414.2.i.f.55.1		10	276.239	even	22
414.2.i.f.271.1		10	12.11	even	2
1058.2.a.l.1.2		5	92.43	even	22
1058.2.a.m.1.2		5	92.3	odd	22
8464.2.a.bw.1.4		5	23.20	odd	22
8464.2.a.bx.1.4		5	23.3	even	11
9522.2.a.bp.1.5		5	276.95	even	22
9522.2.a.bu.1.1		5	276.227	odd	22

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.m (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.712591 + 0.822373i) q^{3} +(0.174863 - 1.21620i) q^{5} +(-0.260554 - 0.570534i) q^{7} +(0.258432 + 1.79743i) q^{9} +(5.65177 - 1.65951i) q^{11} +(-0.977031 + 2.13940i) q^{13} +(0.875565 + 1.01046i) q^{15} +(4.49223 - 2.88698i) q^{17} +(0.227916 + 0.146473i) q^{19} +(0.654861 + 0.192284i) q^{21} +(2.50079 + 4.09219i) q^{23} +(3.34890 + 0.983325i) q^{25} +(-4.40856 - 2.83321i) q^{27} +(-1.66810 + 1.07202i) q^{29} +(4.32439 + 4.99061i) q^{31} +(-2.66266 + 5.83041i) q^{33} +(-0.739446 + 0.217121i) q^{35} +(-1.43317 - 9.96790i) q^{37} +(-1.06316 - 2.32800i) q^{39} +(-1.53880 + 10.7026i) q^{41} +(3.01056 - 3.47437i) q^{43} +2.23123 q^{45} -6.97259 q^{47} +(4.32640 - 4.99294i) q^{49} +(-0.826944 + 5.75152i) q^{51} +(-1.09543 - 2.39865i) q^{53} +(-1.03001 - 7.16387i) q^{55} +(-0.282866 + 0.0830570i) q^{57} +(-0.685131 + 1.50023i) q^{59} +(-5.98206 - 6.90366i) q^{61} +(0.958162 - 0.615773i) q^{63} +(2.43109 + 1.56237i) q^{65} +(-5.94311 - 1.74505i) q^{67} +(-5.14735 - 0.859474i) q^{69} +(-8.69524 - 2.55315i) q^{71} +(-4.99580 - 3.21061i) q^{73} +(-3.19505 + 2.05334i) q^{75} +(-2.41940 - 2.79213i) q^{77} +(2.49546 - 5.46429i) q^{79} +(0.244379 - 0.0717563i) q^{81} +(-0.277948 - 1.93317i) q^{83} +(-2.72562 - 5.96828i) q^{85} +(0.307069 - 2.13571i) q^{87} +(-3.00611 + 3.46923i) q^{89} +1.47517 q^{91} -7.18567 q^{93} +(0.217995 - 0.251579i) q^{95} +(-1.44938 + 10.0807i) q^{97} +(4.44345 + 9.72980i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{3} - 6 q^{5} - 3 q^{7} + 9 q^{9} + 12 q^{11} - 14 q^{13} + 13 q^{15} + 15 q^{17} - 2 q^{19} + q^{21} + q^{23} + 13 q^{25} - 26 q^{27} - 8 q^{29} + 21 q^{31} - 15 q^{33} - 7 q^{35} + 28 q^{37}+ \cdots - 20 q^{99}+O(q^{100}) \) 10 * q + 4 * q^3 - 6 * q^5 - 3 * q^7 + 9 * q^9 + 12 * q^11 - 14 * q^13 + 13 * q^15 + 15 * q^17 - 2 * q^19 + q^21 + q^23 + 13 * q^25 - 26 * q^27 - 8 * q^29 + 21 * q^31 - 15 * q^33 - 7 * q^35 + 28 * q^37 + 12 * q^39 - 31 * q^41 - 11 * q^43 + 10 * q^45 - 18 * q^47 - 24 * q^49 + 17 * q^51 - 21 * q^53 - 5 * q^55 + 19 * q^57 + 5 * q^59 + 37 * q^61 - 17 * q^63 + 37 * q^65 + 13 * q^67 - 15 * q^69 - 49 * q^71 - 8 * q^73 - 8 * q^75 - 8 * q^77 - 8 * q^79 - 11 * q^81 + 7 * q^83 - 42 * q^85 + 21 * q^87 - 13 * q^89 + 24 * q^91 - 40 * q^93 + 10 * q^95 - 32 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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