LMFDB - Embedded newform 525.2.bc.c.157.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(82,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.3
Character	$\chi$	$=$	525.157
Dual form			525.2.bc.c.418.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.124466 + 0.464515i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.53177 + 0.884367i) q^{4} +0.480901i q^{6} +(1.13788 + 2.38856i) q^{7} +(-1.28155 + 1.28155i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.124466 + 0.464515i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.53177 + 0.884367i) q^{4} +0.480901i q^{6} +(1.13788 + 2.38856i) q^{7} +(-1.28155 + 1.28155i) q^{8} +(0.866025 - 0.500000i) q^{9} +(1.38437 - 2.39779i) q^{11} +(1.70847 + 0.457782i) q^{12} +(-0.707107 - 0.707107i) q^{13} +(-1.25115 + 0.231266i) q^{14} +(1.33294 + 2.30873i) q^{16} +(1.14777 + 4.28352i) q^{17} +(0.124466 + 0.464515i) q^{18} +(-0.280619 - 0.486046i) q^{19} +(1.71731 + 2.01267i) q^{21} +(0.941503 + 0.941503i) q^{22} +(-7.77636 - 2.08367i) q^{23} +(-0.906194 + 1.56957i) q^{24} +(0.416472 - 0.240450i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.369399 + 4.66503i) q^{28} -5.53747i q^{29} +(6.97209 + 4.02534i) q^{31} +(-4.73961 + 1.26997i) q^{32} +(0.716601 - 2.67439i) q^{33} -2.13261 q^{34} +1.76873 q^{36} +(1.09593 - 4.09007i) q^{37} +(0.260703 - 0.0698552i) q^{38} +(-0.866025 - 0.500000i) q^{39} -4.21689i q^{41} +(-1.14866 + 0.547207i) q^{42} +(-1.08930 + 1.08930i) q^{43} +(4.24106 - 2.44858i) q^{44} +(1.93579 - 3.35289i) q^{46} +(8.46995 + 2.26952i) q^{47} +(1.88507 + 1.88507i) q^{48} +(-4.41046 + 5.43579i) q^{49} +(2.21731 + 3.84050i) q^{51} +(-0.457782 - 1.70847i) q^{52} +(-0.194837 - 0.727140i) q^{53} +(0.240450 + 0.416472i) q^{54} +(-4.51932 - 1.60282i) q^{56} +(-0.396855 - 0.396855i) q^{57} +(2.57224 + 0.689228i) q^{58} +(5.09165 - 8.81899i) q^{59} +(-7.50000 + 4.33013i) q^{61} +(-2.73762 + 2.73762i) q^{62} +(2.17971 + 1.49962i) q^{63} +2.97209i q^{64} +(1.15310 + 0.665743i) q^{66} +(-9.65128 + 2.58605i) q^{67} +(-2.03009 + 7.57640i) q^{68} -8.05068 q^{69} -14.4067 q^{71} +(-0.469080 + 1.75063i) q^{72} +(7.60111 - 2.03671i) q^{73} +(1.76349 + 1.01815i) q^{74} -0.992681i q^{76} +(7.30252 + 0.578249i) q^{77} +(0.340048 - 0.340048i) q^{78} +(8.05941 - 4.65310i) q^{79} +(0.500000 - 0.866025i) q^{81} +(1.95881 + 0.524861i) q^{82} +(-6.20043 - 6.20043i) q^{83} +(0.850586 + 4.60168i) q^{84} +(-0.370413 - 0.641575i) q^{86} +(-1.43320 - 5.34878i) q^{87} +(1.29876 + 4.84704i) q^{88} +(7.67428 + 13.2922i) q^{89} +(0.884367 - 2.49357i) q^{91} +(-10.0689 - 10.0689i) q^{92} +(7.77636 + 2.08367i) q^{93} +(-2.10845 + 3.65194i) q^{94} +(-4.24942 + 2.45340i) q^{96} +(6.41530 - 6.41530i) q^{97} +(-1.97605 - 2.72530i) q^{98} -2.76873i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 36 q^{16} + 12 q^{21} + 12 q^{26} - 24 q^{31} - 24 q^{36} - 24 q^{46} + 24 q^{51} - 36 q^{56} - 180 q^{61} - 72 q^{66} - 96 q^{71} + 12 q^{81} + 120 q^{86} - 12 q^{91} - 108 q^{96}+O(q^{100}) $ 24 * q + 36 * q^16 + 12 * q^21 + 12 * q^26 - 24 * q^31 - 24 * q^36 - 24 * q^46 + 24 * q^51 - 36 * q^56 - 180 * q^61 - 72 * q^66 - 96 * q^71 + 12 * q^81 + 120 * q^86 - 12 * q^91 - 108 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.124466	+	0.464515i	−0.0880110	+	0.328461i	−0.995867	−	0.0908199i	$-0.971051\pi$
$2$	−0.124466	+	0.464515i	−0.0880110	+	0.328461i	0.907856	+	0.419281i	$0.137718\pi$
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	1.53177	+	0.884367i	0.765884	+	0.442184i
$5$		0			0
$5$		0			0
$6$			0.480901i			0.196327i
$7$	1.13788	+	2.38856i	0.430078	+	0.902792i
$7$	1.13788	+	2.38856i	0.430078	+	0.902792i
$8$	−1.28155	+	1.28155i	−0.453097	+	0.453097i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	1.38437	−	2.39779i	0.417402	−	0.722962i	−0.578275	−	0.815842i	$-0.696274\pi$
$11$	1.38437	−	2.39779i	0.417402	−	0.722962i	0.995677	+	0.0928798i	$0.0296072\pi$
$12$	1.70847	+	0.457782i	0.493192	+	0.132150i
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i	0.602217	−	0.798333i	$-0.294284\pi$
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i	−0.798333	+	0.602217i	$0.794284\pi$
$14$	−1.25115	+	0.231266i	−0.334384	+	0.0618084i
$15$		0			0
$16$	1.33294	+	2.30873i	0.333236	+	0.577182i
$17$	1.14777	+	4.28352i	0.278374	+	1.03891i	0.953547	+	0.301246i	$0.0974025\pi$
$17$	1.14777	+	4.28352i	0.278374	+	1.03891i	−0.675173	+	0.737660i	$0.735931\pi$
$18$	0.124466	+	0.464515i	0.0293370	+	0.109487i
$19$	−0.280619	−	0.486046i	−0.0643784	−	0.111507i	0.832040	−	0.554716i	$-0.187173\pi$
$19$	−0.280619	−	0.486046i	−0.0643784	−	0.111507i	−0.896418	+	0.443209i	$0.853840\pi$
$20$		0			0
$21$	1.71731	+	2.01267i	0.374748	+	0.439201i
$22$	0.941503	+	0.941503i	0.200729	+	0.200729i
$23$	−7.77636	−	2.08367i	−1.62148	−	0.434475i	−0.670046	−	0.742319i	$-0.733726\pi$
$23$	−7.77636	−	2.08367i	−1.62148	−	0.434475i	−0.951437	+	0.307844i	$0.900392\pi$
$24$	−0.906194	+	1.56957i	−0.184976	+	0.320388i
$25$		0			0
$26$	0.416472	−	0.240450i	0.0816770	−	0.0471562i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−0.369399	+	4.66503i	−0.0698099	+	0.881608i
$29$		−	5.53747i		−	1.02828i	−0.857706	−	0.514141i	$-0.828111\pi$
$29$		−	5.53747i		−	1.02828i	0.857706	−	0.514141i	$-0.171889\pi$
$30$		0			0
$31$	6.97209	+	4.02534i	1.25222	+	0.722972i	0.971551	−	0.236831i	$-0.0761087\pi$
$31$	6.97209	+	4.02534i	1.25222	+	0.722972i	0.280674	+	0.959803i	$0.409442\pi$
$32$	−4.73961	+	1.26997i	−0.837852	+	0.224502i
$33$	0.716601	−	2.67439i	0.124744	−	0.465552i
$34$	−2.13261			−0.365740
$35$		0			0
$36$	1.76873			0.294789
$37$	1.09593	−	4.09007i	0.180170	−	0.672403i	−0.815443	−	0.578837i	$-0.803507\pi$
$37$	1.09593	−	4.09007i	0.180170	−	0.672403i	0.995613	−	0.0935660i	$-0.0298266\pi$
$38$	0.260703	−	0.0698552i	0.0422916	−	0.0113320i
$39$	−0.866025	−	0.500000i	−0.138675	−	0.0800641i
$40$		0			0
$41$		−	4.21689i		−	0.658568i	−0.944231	−	0.329284i	$-0.893193\pi$
$41$		−	4.21689i		−	0.658568i	0.944231	−	0.329284i	$-0.106807\pi$
$42$	−1.14866	+	0.547207i	−0.177242	+	0.0844359i
$43$	−1.08930	+	1.08930i	−0.166116	+	0.166116i	−0.785270	−	0.619154i	$-0.787476\pi$
$43$	−1.08930	+	1.08930i	−0.166116	+	0.166116i	0.619154	+	0.785270i	$0.287476\pi$
$44$	4.24106	−	2.44858i	0.639364	−	0.369137i
$45$		0			0
$46$	1.93579	−	3.35289i	0.285417	−	0.494356i
$47$	8.46995	+	2.26952i	1.23547	+	0.331043i	0.816707	−	0.577053i	$-0.195797\pi$
$47$	8.46995	+	2.26952i	1.23547	+	0.331043i	0.418762	+	0.908096i	$0.362464\pi$
$48$	1.88507	+	1.88507i	0.272086	+	0.272086i
$49$	−4.41046	+	5.43579i	−0.630066	+	0.776541i
$50$		0			0
$51$	2.21731	+	3.84050i	0.310486	+	0.537777i
$52$	−0.457782	−	1.70847i	−0.0634830	−	0.236922i
$53$	−0.194837	−	0.727140i	−0.0267629	−	0.0998804i	0.951253	−	0.308413i	$-0.0997979\pi$
$53$	−0.194837	−	0.727140i	−0.0267629	−	0.0998804i	−0.978015	+	0.208533i	$0.933131\pi$
$54$	0.240450	+	0.416472i	0.0327212	+	0.0566747i
$55$		0			0
$56$	−4.51932	−	1.60282i	−0.603919	−	0.214185i
$57$	−0.396855	−	0.396855i	−0.0525647	−	0.0525647i
$58$	2.57224	+	0.689228i	0.337751	+	0.0905001i
$59$	5.09165	−	8.81899i	0.662876	−	1.14813i	−0.316981	−	0.948432i	$-0.602669\pi$
$59$	5.09165	−	8.81899i	0.662876	−	1.14813i	0.979857	−	0.199703i	$-0.0639977\pi$
$60$		0			0
$61$	−7.50000	+	4.33013i	−0.960277	+	0.554416i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−7.50000	+	4.33013i	−0.960277	+	0.554416i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	−2.73762	+	2.73762i	−0.347678	+	0.347678i
$63$	2.17971	+	1.49962i	0.274618	+	0.188934i
$64$			2.97209i			0.371512i
$65$		0			0
$66$	1.15310	+	0.665743i	0.141937	+	0.0819474i
$67$	−9.65128	+	2.58605i	−1.17909	+	0.315937i	−0.794566	−	0.607178i	$-0.792302\pi$
$67$	−9.65128	+	2.58605i	−1.17909	+	0.315937i	−0.384526	+	0.923114i	$0.625635\pi$
$68$	−2.03009	+	7.57640i	−0.246185	+	0.918774i
$69$	−8.05068			−0.969188
$70$		0			0
$71$	−14.4067			−1.70976			−0.854881	−	0.518824i	$-0.826370\pi$
$71$	−14.4067			−1.70976			−0.854881	+	0.518824i	$0.826370\pi$
$72$	−0.469080	+	1.75063i	−0.0552817	+	0.206314i
$73$	7.60111	−	2.03671i	0.889643	−	0.238379i	0.215080	−	0.976596i	$-0.430999\pi$
$73$	7.60111	−	2.03671i	0.889643	−	0.238379i	0.674563	+	0.738217i	$0.264332\pi$
$74$	1.76349	+	1.01815i	0.205002	+	0.118358i
$75$		0			0
$76$		−	0.992681i		−	0.113868i
$77$	7.30252	+	0.578249i	0.832200	+	0.0658976i
$78$	0.340048	−	0.340048i	0.0385029	−	0.0385029i
$79$	8.05941	−	4.65310i	0.906754	−	0.523515i	0.0273688	−	0.999625i	$-0.491287\pi$
$79$	8.05941	−	4.65310i	0.906754	−	0.523515i	0.879385	+	0.476111i	$0.157954\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	1.95881	+	0.524861i	0.216314	+	0.0579612i
$83$	−6.20043	−	6.20043i	−0.680586	−	0.680586i	0.279546	−	0.960132i	$-0.409816\pi$
$83$	−6.20043	−	6.20043i	−0.680586	−	0.680586i	−0.960132	+	0.279546i	$0.909816\pi$
$84$	0.850586	+	4.60168i	0.0928065	+	0.502084i
$85$		0			0
$86$	−0.370413	−	0.641575i	−0.0399427	−	0.0691828i
$87$	−1.43320	−	5.34878i	−0.153655	−	0.573450i
$88$	1.29876	+	4.84704i	0.138448	+	0.516696i
$89$	7.67428	+	13.2922i	0.813472	+	1.40898i	0.910420	+	0.413686i	$0.135759\pi$
$89$	7.67428	+	13.2922i	0.813472	+	1.40898i	−0.0969472	+	0.995290i	$0.530908\pi$
$90$		0			0
$91$	0.884367	−	2.49357i	0.0927069	−	0.261397i
$92$	−10.0689	−	10.0689i	−1.04975	−	1.04975i
$93$	7.77636	+	2.08367i	0.806371	+	0.216066i
$94$	−2.10845	+	3.65194i	−0.217470	+	0.376668i
$95$		0			0
$96$	−4.24942	+	2.45340i	−0.433704	+	0.250399i
$97$	6.41530	−	6.41530i	0.651375	−	0.651375i	−0.301949	−	0.953324i	$-0.597637\pi$
$97$	6.41530	−	6.41530i	0.651375	−	0.651375i	0.953324	+	0.301949i	$0.0976372\pi$
$98$	−1.97605	−	2.72530i	−0.199611	−	0.275297i
$99$		−	2.76873i		−	0.278268i
$100$		0			0
$101$	−7.62403	−	4.40173i	−0.758619	−	0.437989i	0.0701806	−	0.997534i	$-0.477642\pi$
$101$	−7.62403	−	4.40173i	−0.758619	−	0.437989i	−0.828800	+	0.559545i	$0.810976\pi$
$102$	−2.05995	+	0.551961i	−0.203965	+	0.0546523i
$103$	3.87506	−	14.4619i	0.381821	−	1.42498i	−0.461296	−	0.887246i	$-0.652615\pi$
$103$	3.87506	−	14.4619i	0.381821	−	1.42498i	0.843117	−	0.537730i	$-0.180718\pi$
$104$	1.81239			0.177719
$105$		0			0
$106$	0.362018			0.0351623
$107$	3.43305	−	12.8123i	0.331886	−	1.23861i	−0.575321	−	0.817928i	$-0.695123\pi$
$107$	3.43305	−	12.8123i	0.331886	−	1.23861i	0.907206	−	0.420686i	$-0.138211\pi$
$108$	1.70847	−	0.457782i	0.164397	−	0.0440501i
$109$	−17.8488	−	10.3050i	−1.70961	−	0.987044i	−0.935031	−	0.354566i	$-0.884629\pi$
$109$	−17.8488	−	10.3050i	−1.70961	−	0.987044i	−0.774579	−	0.632478i	$-0.782038\pi$
$110$		0			0
$111$		−	4.23435i		−	0.401907i
$112$	−3.99781	+	5.81088i	−0.377758	+	0.549076i
$113$	5.69269	−	5.69269i	0.535523	−	0.535523i	−0.386688	−	0.922211i	$-0.626381\pi$
$113$	5.69269	−	5.69269i	0.535523	−	0.535523i	0.922211	+	0.386688i	$0.126381\pi$
$114$	0.233740	−	0.134950i	0.0218918	−	0.0126392i
$115$		0			0
$116$	4.89716	−	8.48212i	0.454689	−	0.787545i
$117$	−0.965926	−	0.258819i	−0.0892999	−	0.0239278i
$118$	3.46281	+	3.46281i	0.318778	+	0.318778i
$119$	−8.92543	+	7.61563i	−0.818193	+	0.698124i
$120$		0			0
$121$	1.66706	+	2.88742i	0.151550	+	0.262493i
$122$	−1.07791	−	4.02281i	−0.0975894	−	0.364209i
$123$	−1.09141	−	4.07321i	−0.0984093	−	0.367269i
$124$	7.11976	+	12.3318i	0.639373	+	1.10743i
$125$		0			0
$126$	−0.967895	+	0.825857i	−0.0862269	+	0.0735732i
$127$	−5.56673	−	5.56673i	−0.493968	−	0.493968i	0.415586	−	0.909554i	$-0.363576\pi$
$127$	−5.56673	−	5.56673i	−0.493968	−	0.493968i	−0.909554	+	0.415586i	$0.863576\pi$
$128$	−10.8598	−	2.90987i	−0.959880	−	0.257199i
$129$	−0.770249	+	1.33411i	−0.0678166	+	0.117462i
$130$		0			0
$131$	−8.63798	+	4.98714i	−0.754704	+	0.435729i	−0.827391	−	0.561626i	$-0.810176\pi$
$131$	−8.63798	+	4.98714i	−0.754704	+	0.435729i	0.0726871	+	0.997355i	$0.476843\pi$
$132$	3.46281	−	3.46281i	0.301399	−	0.301399i
$133$	0.841642	−	1.22334i	0.0729796	−	0.106077i
$134$		−	4.80504i		−	0.415092i
$135$		0			0
$136$	−6.96047	−	4.01863i	−0.596855	−	0.344595i
$137$	−1.48801	+	0.398710i	−0.127129	+	0.0340641i	−0.321823	−	0.946800i	$-0.604295\pi$
$137$	−1.48801	+	0.398710i	−0.127129	+	0.0340641i	0.194694	+	0.980864i	$0.437629\pi$
$138$	1.00204	−	3.73966i	0.0852992	−	0.318341i
$139$	−1.13993			−0.0966879			−0.0483440	−	0.998831i	$-0.515394\pi$
$139$	−1.13993			−0.0966879			−0.0483440	+	0.998831i	$0.515394\pi$
$140$		0			0
$141$	8.76873			0.738461
$142$	1.79315	−	6.69213i	0.150478	−	0.561591i
$143$	−2.67439	+	0.716601i	−0.223644	+	0.0599252i
$144$	2.30873	+	1.33294i	0.192394	+	0.111079i
$145$		0			0
$146$			3.78433i			0.313193i
$147$	−2.85330	+	6.39208i	−0.235336	+	0.527210i
$148$	5.29583	−	5.29583i	0.435315	−	0.435315i
$149$	1.35566	−	0.782688i	0.111060	−	0.0641203i	−0.443441	−	0.896303i	$-0.646243\pi$
$149$	1.35566	−	0.782688i	0.111060	−	0.0641203i	0.554501	+	0.832183i	$0.312909\pi$
$150$		0			0
$151$	−6.75362	+	11.6976i	−0.549601	+	0.951938i	0.448700	+	0.893682i	$0.351887\pi$
$151$	−6.75362	+	11.6976i	−0.549601	+	0.951938i	−0.998302	+	0.0582553i	$0.981446\pi$
$152$	0.982521	+	0.263266i	0.0796930	+	0.0213537i
$153$	3.13575	+	3.13575i	0.253511	+	0.253511i
$154$	−1.17752	+	3.32016i	−0.0948875	+	0.267546i
$155$		0			0
$156$	−0.884367	−	1.53177i	−0.0708060	−	0.122640i
$157$	−2.12319	−	7.92384i	−0.169449	−	0.632391i	−0.997431	−	0.0716365i	$-0.977178\pi$
$157$	−2.12319	−	7.92384i	−0.169449	−	0.632391i	0.827982	−	0.560754i	$-0.189489\pi$
$158$	1.15831	+	4.32287i	0.0921501	+	0.343909i
$159$	−0.376395	−	0.651936i	−0.0298501	−	0.0517019i
$160$		0			0
$161$	−3.87158	−	20.9453i	−0.305123	−	1.65072i
$162$	0.340048	+	0.340048i	0.0267167	+	0.0267167i
$163$	1.87492	+	0.502384i	0.146855	+	0.0393497i	0.331498	−	0.943456i	$-0.392446\pi$
$163$	1.87492	+	0.502384i	0.146855	+	0.0393497i	−0.184643	+	0.982806i	$0.559113\pi$
$164$	3.72928	−	6.45930i	0.291208	−	0.504387i
$165$		0			0
$166$	3.65194	−	2.10845i	0.283445	−	0.163647i
$167$	−14.6857	+	14.6857i	−1.13641	+	1.13641i	−0.147327	+	0.989088i	$0.547067\pi$
$167$	−14.6857	+	14.6857i	−1.13641	+	1.13641i	−0.989088	+	0.147327i	$0.952933\pi$
$168$	−4.78016	−	0.378516i	−0.368798	−	0.0292032i
$169$		−	12.0000i		−	0.923077i
$170$		0			0
$171$	−0.486046	−	0.280619i	−0.0371689	−	0.0214595i
$172$	−2.63189	+	0.705212i	−0.200680	+	0.0537719i
$173$	−1.55291	+	5.79555i	−0.118066	+	0.440628i	−0.999498	−	0.0316829i	$-0.989913\pi$
$173$	−1.55291	+	5.79555i	−0.118066	+	0.440628i	0.881432	+	0.472311i	$0.156580\pi$
$174$	2.66297			0.201880
$175$		0			0
$176$	7.38114			0.556374
$177$	2.63563	−	9.83631i	0.198106	−	0.739342i
$178$	−7.12963	+	1.91038i	−0.534389	+	0.143189i
$179$	−10.3923	−	6.00000i	−0.776757	−	0.448461i	0.0585225	−	0.998286i	$-0.481361\pi$
$179$	−10.3923	−	6.00000i	−0.776757	−	0.448461i	−0.835280	+	0.549825i	$0.814694\pi$
$180$		0			0
$181$		−	17.8643i		−	1.32784i	−0.747803	−	0.663921i	$-0.768891\pi$
$181$		−	17.8643i		−	1.32784i	0.747803	−	0.663921i	$-0.231109\pi$
$182$	1.04823	+	0.721167i	0.0776997	+	0.0534565i
$183$	−6.12372	+	6.12372i	−0.452679	+	0.452679i
$184$	12.6361	−	7.29548i	0.931548	−	0.537830i
$185$		0			0
$186$	−1.93579	+	3.35289i	−0.141939	+	0.245846i
$187$	11.8599	+	3.17786i	0.867283	+	0.232388i
$188$	10.9669	+	10.9669i	0.799845	+	0.799845i
$189$	2.49357	+	0.884367i	0.181381	+	0.0643282i
$190$		0			0
$191$	11.3565	+	19.6700i	0.821725	+	1.42327i	0.904397	+	0.426692i	$0.140321\pi$
$191$	11.3565	+	19.6700i	0.821725	+	1.42327i	−0.0826724	+	0.996577i	$0.526346\pi$
$192$	0.769234	+	2.87082i	0.0555147	+	0.207184i
$193$	0.539451	+	2.01326i	0.0388305	+	0.144917i	0.982620	−	0.185631i	$-0.0594329\pi$
$193$	0.539451	+	2.01326i	0.0388305	+	0.144917i	−0.943789	+	0.330549i	$0.892766\pi$
$194$	2.18151	+	3.77849i	0.156623	+	0.271280i
$195$		0			0
$196$	−11.5630	+	4.42590i	−0.825932	+	0.316136i
$197$	−7.07757	−	7.07757i	−0.504256	−	0.504256i	0.408501	−	0.912758i	$-0.366051\pi$
$197$	−7.07757	−	7.07757i	−0.504256	−	0.504256i	−0.912758	+	0.408501i	$0.866051\pi$
$198$	1.28612	+	0.344614i	0.0914004	+	0.0244907i
$199$	1.16208	−	2.01279i	0.0823779	−	0.142683i	−0.821893	−	0.569642i	$-0.807082\pi$
$199$	1.16208	−	2.01279i	0.0823779	−	0.142683i	0.904271	+	0.426959i	$0.140415\pi$
$200$		0			0
$201$	−8.65310	+	4.99587i	−0.610343	+	0.352382i
$202$	2.99360	−	2.99360i	0.210629	−	0.210629i
$203$	13.2266	−	6.30097i	0.928325	−	0.442241i
$204$			7.84367i			0.549167i
$205$		0			0
$206$	6.23546	+	3.60005i	0.434445	+	0.250827i
$207$	−7.77636	+	2.08367i	−0.540494	+	0.144825i
$208$	0.689983	−	2.57505i	0.0478417	−	0.178548i
$209$	−1.55392			−0.107487
$210$		0			0
$211$	18.9163			1.30225			0.651125	−	0.758970i	$-0.274297\pi$
$211$	18.9163			1.30225			0.651125	+	0.758970i	$0.274297\pi$
$212$	0.344614	−	1.28612i	0.0236682	−	0.0883309i
$213$	−13.9158	+	3.72873i	−0.953496	+	0.255489i
$214$	5.52421	+	3.18940i	0.377627	+	0.218023i
$215$		0			0
$216$			1.81239i			0.123317i
$217$	−1.68138	+	21.2336i	−0.114140	+	1.44143i
$218$	7.00842	−	7.00842i	0.474670	−	0.474670i
$219$	6.81497	−	3.93462i	0.460513	−	0.265877i
$220$		0			0
$221$	2.21731	−	3.84050i	0.149153	−	0.258340i
$222$	1.96692	+	0.527034i	0.132011	+	0.0353722i
$223$	−1.71989	−	1.71989i	−0.115172	−	0.115172i	0.647172	−	0.762344i	$-0.275952\pi$
$223$	−1.71989	−	1.71989i	−0.115172	−	0.115172i	−0.762344	+	0.647172i	$0.775952\pi$
$224$	−8.42651	−	9.87578i	−0.563020	−	0.659853i
$225$		0			0
$226$	1.93579	+	3.35289i	0.128767	+	0.223031i
$227$	6.02426	+	22.4829i	0.399844	+	1.49224i	0.813370	+	0.581747i	$0.197631\pi$
$227$	6.02426	+	22.4829i	0.399844	+	1.49224i	−0.413525	+	0.910493i	$0.635703\pi$
$228$	−0.256925	−	0.958856i	−0.0170153	−	0.0635018i
$229$	3.07898	+	5.33294i	0.203465	+	0.352411i	0.949642	−	0.313336i	$-0.101447\pi$
$229$	3.07898	+	5.33294i	0.203465	+	0.352411i	−0.746178	+	0.665747i	$0.768113\pi$
$230$		0			0
$231$	7.20336	−	1.33149i	0.473946	−	0.0876054i
$232$	7.09655	+	7.09655i	0.465911	+	0.465911i
$233$	8.90728	+	2.38670i	0.583535	+	0.156358i	0.538497	−	0.842627i	$-0.318992\pi$
$233$	8.90728	+	2.38670i	0.583535	+	0.156358i	0.0450382	+	0.998985i	$0.485659\pi$
$234$	0.240450	−	0.416472i	0.0157187	−	0.0272257i
$235$		0			0
$236$	15.5985	−	9.00577i	1.01537	−	0.586226i
$237$	6.58048	−	6.58048i	0.427448	−	0.427448i
$238$	−2.42666	−	5.09388i	−0.157297	−	0.330187i
$239$			16.8134i			1.08757i	0.839224	+	0.543785i	$0.183009\pi$
$239$			16.8134i			1.08757i	−0.839224	+	0.543785i	$0.816991\pi$
$240$		0			0
$241$	2.66472	+	1.53848i	0.171650	+	0.0991022i	0.583364	−	0.812211i	$-0.301736\pi$
$241$	2.66472	+	1.53848i	0.171650	+	0.0991022i	−0.411714	+	0.911313i	$0.635070\pi$
$242$	−1.54874	+	0.414984i	−0.0995570	+	0.0266762i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−15.3177			−0.980615
$245$		0			0
$246$	2.02791			0.129295
$247$	−0.145259	+	0.542114i	−0.00924261	+	0.0344939i
$248$	−14.0938	+	3.77642i	−0.894956	+	0.239803i
$249$	−7.59395	−	4.38437i	−0.481247	−	0.277848i
$250$		0			0
$251$			29.3307i			1.85134i	0.378333	+	0.925670i	$0.376498\pi$
$251$			29.3307i			1.85134i	−0.378333	+	0.925670i	$0.623502\pi$
$252$	2.01261	+	4.22473i	0.126782	+	0.266133i
$253$	−15.7615	+	15.7615i	−0.990920	+	0.990920i
$254$	3.27870	−	1.89296i	0.205724	−	0.118775i
$255$		0			0
$256$	−0.268734	+	0.465461i	−0.0167959	+	0.0290913i
$257$	26.1254	+	7.00029i	1.62966	+	0.436666i	0.953819	−	0.300382i	$-0.0971142\pi$
$257$	26.1254	+	7.00029i	1.62966	+	0.436666i	0.675840	+	0.737048i	$0.263781\pi$
$258$	−0.523844	−	0.523844i	−0.0326131	−	0.0326131i
$259$	11.0164	−	2.03630i	0.684527	−	0.126530i
$260$		0			0
$261$	−2.76873	−	4.79559i	−0.171380	−	0.296839i
$262$	−1.24146	−	4.63320i	−0.0766978	−	0.286240i
$263$	3.77766	+	14.0984i	0.232941	+	0.869347i	0.979066	+	0.203542i	$0.0652452\pi$
$263$	3.77766	+	14.0984i	0.232941	+	0.869347i	−0.746126	+	0.665805i	$0.768088\pi$
$264$	2.50901	+	4.34573i	0.154419	+	0.267461i
$265$		0			0
$266$	0.463502	+	0.543219i	0.0284191	+	0.0333069i
$267$	10.8531	+	10.8531i	0.664197	+	0.664197i
$268$	−17.0706	−	4.57404i	−1.04275	−	0.279404i
$269$	−4.61075	+	7.98605i	−0.281122	+	0.486918i	−0.971661	−	0.236377i	$-0.924040\pi$
$269$	−4.61075	+	7.98605i	−0.281122	+	0.486918i	0.690539	+	0.723295i	$0.257373\pi$
$270$		0			0
$271$	−9.50117	+	5.48550i	−0.577155	+	0.333220i	−0.760002	−	0.649921i	$-0.774802\pi$
$271$	−9.50117	+	5.48550i	−0.577155	+	0.333220i	0.182847	+	0.983141i	$0.441469\pi$
$272$	−8.35957	+	8.35957i	−0.506873	+	0.506873i
$273$	0.208849	−	2.63750i	0.0126401	−	0.159628i
$274$		−	0.740827i		−	0.0447550i
$275$		0			0
$276$	−12.3318	−	7.11976i	−0.742286	−	0.428559i
$277$	10.7485	−	2.88004i	0.645813	−	0.173045i	0.0789780	−	0.996876i	$-0.474834\pi$
$277$	10.7485	−	2.88004i	0.645813	−	0.173045i	0.566835	+	0.823831i	$0.308168\pi$
$278$	0.141883	−	0.529516i	0.00850960	−	0.0317583i
$279$	8.05068			0.481982
$280$		0			0
$281$	−9.77107			−0.582893			−0.291446	−	0.956587i	$-0.594137\pi$
$281$	−9.77107			−0.582893			−0.291446	+	0.956587i	$0.594137\pi$
$282$	−1.09141	+	4.07321i	−0.0649926	+	0.242556i
$283$	−9.63455	+	2.58157i	−0.572715	+	0.153458i	−0.533541	−	0.845774i	$-0.679139\pi$
$283$	−9.63455	+	2.58157i	−0.572715	+	0.153458i	−0.0391734	+	0.999232i	$0.512472\pi$
$284$	−22.0678	−	12.7408i	−1.30948	−	0.756029i
$285$		0			0
$286$		−	1.33149i		−	0.0787325i
$287$	10.0723	−	4.79831i	0.594550	−	0.283235i
$288$	−3.46963	+	3.46963i	−0.204450	+	0.204450i
$289$	−2.30873	+	1.33294i	−0.135808	+	0.0784085i
$290$		0			0
$291$	4.53630	−	7.85711i	0.265923	−	0.460592i
$292$	13.4443	+	3.60240i	0.786771	+	0.210815i
$293$	−10.6991	−	10.6991i	−0.625046	−	0.625046i	0.321772	−	0.946817i	$-0.395722\pi$
$293$	−10.6991	−	10.6991i	−0.625046	−	0.625046i	−0.946817	+	0.321772i	$0.895722\pi$
$294$	−2.61408	−	2.12100i	−0.152456	−	0.123699i
$295$		0			0
$296$	3.83714	+	6.64613i	0.223029	+	0.386298i
$297$	−0.716601	−	2.67439i	−0.0415814	−	0.155184i
$298$	0.194837	+	0.727140i	0.0112866	+	0.0421221i
$299$	4.02534	+	6.97209i	0.232791	+	0.403207i
$300$		0			0
$301$	−3.84134	−	1.36237i	−0.221411	−	0.0785255i
$302$	−4.59311	−	4.59311i	−0.264304	−	0.264304i
$303$	−8.50350	−	2.27851i	−0.488513	−	0.130897i
$304$	0.748099	−	1.29575i	0.0429064	−	0.0743161i
$305$		0			0
$306$	−1.84690	+	1.06631i	−0.105580	+	0.0609567i
$307$	−23.1631	+	23.1631i	−1.32199	+	1.32199i	−0.409826	+	0.912164i	$0.634411\pi$
$307$	−23.1631	+	23.1631i	−1.32199	+	1.32199i	−0.912164	+	0.409826i	$0.865589\pi$
$308$	10.6744	+	7.34386i	0.608230	+	0.418455i
$309$		−	14.9721i		−	0.851733i
$310$		0			0
$311$	29.5845	+	17.0806i	1.67758	+	0.968553i	0.963195	+	0.268803i	$0.0866281\pi$
$311$	29.5845	+	17.0806i	1.67758	+	0.968553i	0.714388	+	0.699750i	$0.246705\pi$
$312$	1.75063	−	0.469080i	0.0991100	−	0.0265565i
$313$	−2.50172	+	9.33653i	−0.141405	+	0.527732i	0.858484	+	0.512841i	$0.171407\pi$
$313$	−2.50172	+	9.33653i	−0.141405	+	0.527732i	−0.999889	+	0.0148913i	$0.995260\pi$
$314$	3.94500			0.222629
$315$		0			0
$316$	16.4602			0.925959
$317$	3.07940	−	11.4925i	0.172956	−	0.645482i	−0.823934	−	0.566685i	$-0.808226\pi$
$317$	3.07940	−	11.4925i	0.172956	−	0.645482i	0.996891	−	0.0787966i	$-0.0251078\pi$
$318$	0.349682	−	0.0936971i	0.0196092	−	0.00525427i
$319$	−13.2777	−	7.66589i	−0.743409	−	0.429207i
$320$		0			0
$321$		−	13.2643i		−	0.740340i
$322$	10.2113	+	0.808577i	0.569052	+	0.0450603i
$323$	1.75990	−	1.75990i	0.0979236	−	0.0979236i
$324$	1.53177	−	0.884367i	0.0850983	−	0.0491315i
$325$		0			0
$326$	−0.466729	+	0.808399i	−0.0258497	+	0.0447731i
$327$	−19.9078	−	5.33428i	−1.10090	−	0.294986i
$328$	5.40417	+	5.40417i	0.298395	+	0.298395i
$329$	4.21689	+	22.8134i	0.232485	+	1.25775i
$330$		0			0
$331$	3.05142	+	5.28522i	0.167721	+	0.290502i	0.937618	−	0.347666i	$-0.113026\pi$
$331$	3.05142	+	5.28522i	0.167721	+	0.290502i	−0.769897	+	0.638168i	$0.779692\pi$
$332$	−4.01417	−	14.9811i	−0.220306	−	0.822194i
$333$	−1.09593	−	4.09007i	−0.0600566	−	0.224134i
$334$	−4.99385	−	8.64960i	−0.273251	−	0.473285i
$335$		0			0
$336$	−2.35763	+	6.64758i	−0.128619	+	0.362655i
$337$	3.12959	+	3.12959i	0.170479	+	0.170479i	0.787190	−	0.616711i	$-0.211535\pi$
$337$	3.12959	+	3.12959i	0.170479	+	0.170479i	−0.616711	+	0.787190i	$0.711535\pi$
$338$	5.57418	+	1.49360i	0.303195	+	0.0812409i
$339$	4.02534	−	6.97209i	0.218626	−	0.378672i
$340$		0			0
$341$	19.3039	−	11.1451i	1.04536	−	0.603541i
$342$	0.190848	−	0.190848i	0.0103199	−	0.0103199i
$343$	−18.0023	−	4.34940i	−0.972033	−	0.234846i
$344$		−	2.79198i		−	0.150533i
$345$		0			0
$346$	−2.49883	−	1.44270i	−0.134338	−	0.0775602i
$347$	3.85835	−	1.03384i	0.207127	−	0.0554996i	−0.153764	−	0.988108i	$-0.549139\pi$
$347$	3.85835	−	1.03384i	0.207127	−	0.0554996i	0.360891	+	0.932608i	$0.382473\pi$
$348$	2.53495	−	9.46058i	0.135888	−	0.507140i
$349$	27.4555			1.46966			0.734829	−	0.678253i	$-0.237263\pi$
$349$	27.4555			1.46966			0.734829	+	0.678253i	$0.237263\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$	−3.51622	+	13.1227i	−0.187415	+	0.699443i
$353$	13.2973	−	3.56301i	0.707745	−	0.189640i	0.113048	−	0.993590i	$-0.463939\pi$
$353$	13.2973	−	3.56301i	0.707745	−	0.189640i	0.594697	+	0.803950i	$0.297272\pi$
$354$	4.24106	+	2.44858i	0.225410	+	0.130140i
$355$		0			0
$356$			27.1475i			1.43882i
$357$	−6.65024	+	9.66621i	−0.351968	+	0.511590i
$358$	4.08058	−	4.08058i	0.215665	−	0.215665i
$359$	−5.68376	+	3.28152i	−0.299978	+	0.173192i	−0.642433	−	0.766342i	$-0.722075\pi$
$359$	−5.68376	+	3.28152i	−0.299978	+	0.173192i	0.342455	+	0.939534i	$0.388741\pi$
$360$		0			0
$361$	9.34251	−	16.1817i	0.491711	−	0.851668i
$362$	8.29822	+	2.22350i	0.436145	+	0.116865i
$363$	2.35757	+	2.35757i	0.123740	+	0.123740i
$364$	3.55988	−	3.03747i	0.186588	−	0.159207i
$365$		0			0
$366$	−2.08236	−	3.60676i	−0.108847	−	0.188528i
$367$	−1.58615	−	5.91960i	−0.0827965	−	0.309001i	0.912091	−	0.409987i	$-0.134467\pi$
$367$	−1.58615	−	5.91960i	−0.0827965	−	0.309001i	−0.994888	+	0.100986i	$0.967800\pi$
$368$	−5.55483	−	20.7309i	−0.289566	−	1.08067i
$369$	−2.10845	−	3.65194i	−0.109761	−	0.190112i
$370$		0			0
$371$	1.51512	−	1.29278i	0.0786611	−	0.0671176i
$372$	10.0689	+	10.0689i	0.522046	+	0.522046i
$373$	15.2125	+	4.07618i	0.787673	+	0.211056i	0.630165	−	0.776461i	$-0.282987\pi$
$373$	15.2125	+	4.07618i	0.787673	+	0.211056i	0.157508	+	0.987518i	$0.449654\pi$
$374$	−2.95232	+	5.11357i	−0.152661	+	0.264416i
$375$		0			0
$376$	−13.7632	+	7.94617i	−0.709782	+	0.409793i
$377$	−3.91558	+	3.91558i	−0.201663	+	0.201663i
$378$	−0.721167	+	1.04823i	−0.0370928	+	0.0539149i
$379$		−	9.25039i		−	0.475161i	−0.971368	−	0.237580i	$-0.923646\pi$
$379$		−	9.25039i		−	0.475161i	0.971368	−	0.237580i	$-0.0763543\pi$
$380$		0			0
$381$	−6.81783	−	3.93627i	−0.349288	−	0.201661i
$382$	−10.5505	+	2.82699i	−0.539810	+	0.144642i
$383$	−4.23192	+	15.7938i	−0.216241	+	0.807023i	0.769485	+	0.638665i	$0.220513\pi$
$383$	−4.23192	+	15.7938i	−0.216241	+	0.807023i	−0.985726	+	0.168358i	$0.946154\pi$
$384$	−11.2429			−0.573736
$385$		0			0
$386$	−1.00233			−0.0510173
$387$	−0.398710	+	1.48801i	−0.0202676	+	0.0756396i
$388$	15.5002	−	4.15328i	0.786905	−	0.210851i
$389$	23.4234	+	13.5235i	1.18761	+	0.685669i	0.957764	−	0.287557i	$-0.0928429\pi$
$389$	23.4234	+	13.5235i	1.18761	+	0.685669i	0.229851	+	0.973226i	$0.426176\pi$
$390$		0			0
$391$		−	35.7017i		−	1.80551i
$392$	−1.31401	−	12.6185i	−0.0663674	−	0.637330i
$393$	−7.05288	+	7.05288i	−0.355771	+	0.355771i
$394$	4.16856	−	2.40672i	0.210009	−	0.121249i
$395$		0			0
$396$	2.44858	−	4.24106i	0.123046	−	0.213121i
$397$	−37.5655	−	10.0657i	−1.88536	−	0.505181i	−0.999119	−	0.0419554i	$-0.986641\pi$
$397$	−37.5655	−	10.0657i	−1.88536	−	0.505181i	−0.886241	−	0.463225i	$-0.846692\pi$
$398$	0.790329	+	0.790329i	0.0396156	+	0.0396156i
$399$	0.496340	−	1.39949i	0.0248481	−	0.0700620i
$400$		0			0
$401$	0.0418611	+	0.0725056i	0.00209045	+	0.00362076i	0.867069	−	0.498189i	$-0.166001\pi$
$401$	0.0418611	+	0.0725056i	0.00209045	+	0.00362076i	−0.864978	+	0.501809i	$0.832668\pi$
$402$	−1.24364	−	4.64131i	−0.0620269	−	0.231487i
$403$	−2.08367	−	7.77636i	−0.103795	−	0.387368i
$404$	−7.78550	−	13.4849i	−0.387343	−	0.670898i
$405$		0			0
$406$	1.28063	+	6.92820i	0.0635564	+	0.343841i
$407$	−8.28997	−	8.28997i	−0.410919	−	0.410919i
$408$	−7.76340	−	2.08020i	−0.384345	−	0.102985i
$409$	−7.60268	+	13.1682i	−0.375928	+	0.651127i	−0.990465	−	0.137761i	$-0.956009\pi$
$409$	−7.60268	+	13.1682i	−0.375928	+	0.651127i	0.614537	+	0.788888i	$0.289343\pi$
$410$		0			0
$411$	−1.33411	+	0.770249i	−0.0658068	+	0.0379936i
$412$	18.7254	−	18.7254i	0.922532	−	0.922532i
$413$	26.8584	+	2.12678i	1.32161	+	0.104652i
$414$		−	3.87158i		−	0.190278i
$415$		0			0
$416$	4.24942	+	2.45340i	0.208345	+	0.120288i
$417$	−1.10109	+	0.295037i	−0.0539207	+	0.0144480i
$418$	0.193411	−	0.721818i	0.00946002	−	0.0353053i
$419$	2.55064			0.124607			0.0623034	−	0.998057i	$-0.480155\pi$
$419$	2.55064			0.124607			0.0623034	+	0.998057i	$0.480155\pi$
$420$		0			0
$421$	−11.7408			−0.572213			−0.286106	−	0.958198i	$-0.592361\pi$
$421$	−11.7408			−0.572213			−0.286106	+	0.958198i	$0.592361\pi$
$422$	−2.35444	+	8.78689i	−0.114612	+	0.427739i
$423$	8.46995	−	2.26952i	0.411823	−	0.110348i
$424$	1.18156	+	0.682174i	0.0573817	+	0.0331293i
$425$		0			0
$426$		−	6.92820i		−	0.335673i
$427$	−18.8769	−	12.9871i	−0.913516	−	0.628488i
$428$	16.5894	−	16.5894i	0.801881	−	0.801881i
$429$	−2.39779	+	1.38437i	−0.115767	+	0.0668379i
$430$		0			0
$431$	−1.43462	+	2.48484i	−0.0691034	+	0.119691i	−0.898507	−	0.438959i	$-0.855347\pi$
$431$	−1.43462	+	2.48484i	−0.0691034	+	0.119691i	0.829403	+	0.558650i	$0.188681\pi$
$432$	2.57505	+	0.689983i	0.123892	+	0.0331968i
$433$	−6.83482	−	6.83482i	−0.328460	−	0.328460i	0.523540	−	0.852001i	$-0.324611\pi$
$433$	−6.83482	−	6.83482i	−0.328460	−	0.328460i	−0.852001	+	0.523540i	$0.824611\pi$
$434$	−9.65406	−	3.42390i	−0.463410	−	0.164352i
$435$		0			0
$436$	−18.2269	−	31.5699i	−0.872909	−	1.51192i
$437$	1.16943	+	4.36439i	0.0559416	+	0.208777i
$438$	0.979456	+	3.65538i	0.0468002	+	0.174661i
$439$	17.9359	+	31.0659i	0.856034	+	1.48269i	0.875683	+	0.482887i	$0.160412\pi$
$439$	17.9359	+	31.0659i	0.856034	+	1.48269i	−0.0196492	+	0.999807i	$0.506255\pi$
$440$		0			0
$441$	−1.10168	+	6.91276i	−0.0524609	+	0.329179i
$442$	1.50799	+	1.50799i	0.0717276	+	0.0717276i
$443$	27.7594	+	7.43810i	1.31889	+	0.353395i	0.848561	−	0.529098i	$-0.177469\pi$
$443$	27.7594	+	7.43810i	1.31889	+	0.353395i	0.470327	+	0.882492i	$0.344136\pi$
$444$	3.74472	−	6.48605i	0.177717	−	0.307814i
$445$		0			0
$446$	1.01298	−	0.584846i	0.0479661	−	0.0276933i
$447$	1.10689	−	1.10689i	0.0523540	−	0.0523540i
$448$	−7.09903	+	3.38188i	−0.335398	+	0.159779i
$449$			4.63565i			0.218770i	0.993999	+	0.109385i	$0.0348881\pi$
$449$			4.63565i			0.218770i	−0.993999	+	0.109385i	$0.965112\pi$
$450$		0			0
$451$	−10.1112	−	5.83773i	−0.476120	−	0.274888i
$452$	13.7543	−	3.68546i	0.646948	−	0.173349i
$453$	−3.49593	+	13.0470i	−0.164253	+	0.613001i
$454$	−11.1934			−0.525334
$455$		0			0
$456$	1.01718			0.0476339
$457$	10.5345	−	39.3154i	0.492785	−	1.83910i	−0.0493161	−	0.998783i	$-0.515704\pi$
$457$	10.5345	−	39.3154i	0.492785	−	1.83910i	0.542101	−	0.840314i	$-0.317629\pi$
$458$	−2.86046	+	0.766458i	−0.133661	+	0.0358142i
$459$	3.84050	+	2.21731i	0.179259	+	0.103495i
$460$		0			0
$461$			8.46870i			0.394427i	0.980361	+	0.197213i	$0.0631892\pi$
$461$			8.46870i			0.394427i	−0.980361	+	0.197213i	$0.936811\pi$
$462$	−0.278080	+	3.51179i	−0.0129375	+	0.163383i
$463$	−26.3656	+	26.3656i	−1.22531	+	1.22531i	−0.259593	+	0.965718i	$0.583589\pi$
$463$	−26.3656	+	26.3656i	−1.22531	+	1.22531i	−0.965718	+	0.259593i	$0.916411\pi$
$464$	12.7845	−	7.38114i	0.593506	−	0.342661i
$465$		0			0
$466$	−2.21731	+	3.84050i	−0.102715	+	0.177908i
$467$	7.92609	+	2.12379i	0.366776	+	0.0982772i	0.437499	−	0.899219i	$-0.355864\pi$
$467$	7.92609	+	2.12379i	0.366776	+	0.0982772i	−0.0707238	+	0.997496i	$0.522531\pi$
$468$	−1.25068	−	1.25068i	−0.0578129	−	0.0578129i
$469$	−17.1589	−	20.1101i	−0.792326	−	0.928597i
$470$		0			0
$471$	−4.10168	−	7.10432i	−0.188995	−	0.327350i
$472$	4.77678	+	17.8272i	0.219869	+	0.820563i
$473$	1.10392	+	4.11990i	0.0507584	+	0.189433i
$474$	2.23768	+	3.87578i	0.102780	+	0.178020i
$475$		0			0
$476$	−20.4067	+	3.77203i	−0.935340	+	0.172891i
$477$	−0.532303	−	0.532303i	−0.0243725	−	0.0243725i
$478$	−7.81009	−	2.09271i	−0.357225	−	0.0957181i
$479$	−2.38034	+	4.12286i	−0.108760	+	0.188378i	−0.915268	−	0.402845i	$-0.868021\pi$
$479$	−2.38034	+	4.12286i	−0.108760	+	0.188378i	0.806508	+	0.591223i	$0.201355\pi$
$480$		0			0
$481$	−3.66706	+	2.11718i	−0.167203	+	0.0965349i
$482$	−1.04631	+	1.04631i	−0.0476583	+	0.0476583i
$483$	−9.16070	−	19.2296i	−0.416826	−	0.874975i
$484$			5.89716i			0.268053i
$485$		0			0
$486$	0.416472	+	0.240450i	0.0188916	+	0.0109071i
$487$	−12.2067	+	3.27076i	−0.553136	+	0.148212i	−0.524551	−	0.851379i	$-0.675767\pi$
$487$	−12.2067	+	3.27076i	−0.553136	+	0.148212i	−0.0285851	+	0.999591i	$0.509100\pi$
$488$	4.06236	−	15.1609i	0.183894	−	0.686303i
$489$	1.94106			0.0877779
$490$		0			0
$491$	−38.8692			−1.75414			−0.877072	−	0.480358i	$-0.840507\pi$
$491$	−38.8692			−1.75414			−0.877072	+	0.480358i	$0.840507\pi$
$492$	1.93042	−	7.20442i	0.0870300	−	0.324800i
$493$	23.7198	−	6.35571i	1.06829	−	0.286247i
$494$	−0.233740	−	0.134950i	−0.0105165	−	0.00607168i
$495$		0			0
$496$			21.4622i			0.963682i
$497$	−16.3931	−	34.4113i	−0.735331	−	1.54356i
$498$	2.98179	−	2.98179i	0.133617	−	0.133617i
$499$	−12.7881	+	7.38320i	−0.572473	+	0.330517i	−0.758136	−	0.652096i	$-0.773890\pi$
$499$	−12.7881	+	7.38320i	−0.572473	+	0.330517i	0.185663	+	0.982613i	$0.440557\pi$
$500$		0			0
$501$	−10.3844	+	17.9863i	−0.463939	+	0.803566i
$502$	−13.6246	−	3.65069i	−0.608094	−	0.162938i
$503$	−16.3164	−	16.3164i	−0.727514	−	0.727514i	0.242610	−	0.970124i	$-0.421997\pi$
$503$	−16.3164	−	16.3164i	−0.727514	−	0.727514i	−0.970124	+	0.242610i	$0.921997\pi$
$504$	−4.71525	+	0.871579i	−0.210034	+	0.0388232i
$505$		0			0
$506$	−5.35969	−	9.28325i	−0.238267	−	0.412691i
$507$	−3.10583	−	11.5911i	−0.137935	−	0.514779i
$508$	−3.60391	−	13.4500i	−0.159898	−	0.596746i
$509$	−16.8891	−	29.2527i	−0.748595	−	1.29660i	−0.948496	−	0.316788i	$-0.897396\pi$
$509$	−16.8891	−	29.2527i	−0.748595	−	1.29660i	0.199902	−	0.979816i	$-0.435938\pi$
$510$		0			0
$511$	13.5140	+	15.8382i	0.597822	+	0.700641i
$512$	−16.0826	−	16.0826i	−0.710758	−	0.710758i
$513$	−0.542114	−	0.145259i	−0.0239349	−	0.00641334i
$514$	−6.50347	+	11.2643i	−0.286856	+	0.496849i
$515$		0			0
$516$	−2.35969	+	1.36237i	−0.103879	+	0.0599748i
$517$	17.1673	−	17.1673i	0.755019	−	0.755019i
$518$	−0.425281	+	5.37074i	−0.0186858	+	0.235977i
$519$			6.00000i			0.263371i
$520$		0			0
$521$	−6.33178	−	3.65565i	−0.277400	−	0.160157i	0.354846	−	0.934925i	$-0.384533\pi$
$521$	−6.33178	−	3.65565i	−0.277400	−	0.160157i	−0.632246	+	0.774768i	$0.717867\pi$
$522$	2.57224	−	0.689228i	0.112584	−	0.0301667i
$523$	1.26025	−	4.70333i	0.0551071	−	0.205662i	−0.932883	−	0.360179i	$-0.882715\pi$
$523$	1.26025	−	4.70333i	0.0551071	−	0.205662i	0.987990	+	0.154517i	$0.0493821\pi$
$524$	−17.6419			−0.770688
$525$		0			0
$526$	−7.01912			−0.306048
$527$	−9.24029	+	34.4852i	−0.402513	+	1.50220i
$528$	7.12963	−	1.91038i	0.310277	−	0.0831386i
$529$	36.2115	+	20.9067i	1.57441	+	0.908988i
$530$		0			0
$531$		−	10.1833i		−	0.441917i
$532$	2.37108	−	1.12955i	0.102799	−	0.0489722i
$533$	−2.98179	+	2.98179i	−0.129156	+	0.129156i
$534$	−6.39225	+	3.69057i	−0.276620	+	0.159707i
$535$		0			0
$536$	9.05445	−	15.6828i	0.391093	−	0.677393i
$537$	−11.5911	−	3.10583i	−0.500193	−	0.134026i
$538$	−3.13575	−	3.13575i	−0.135192	−	0.135192i
$539$	6.92820	+	18.1005i	0.298419	+	0.779644i
$540$		0			0
$541$	−8.13798	−	14.0954i	−0.349879	−	0.606009i	0.636349	−	0.771402i	$-0.280444\pi$
$541$	−8.13798	−	14.0954i	−0.349879	−	0.606009i	−0.986228	+	0.165393i	$0.947111\pi$
$542$	−1.36552	−	5.09619i	−0.0586541	−	0.218900i
$543$	−4.62362	−	17.2556i	−0.198418	−	0.740508i
$544$	−10.8799	−	18.8446i	−0.466473	−	0.807954i
$545$		0			0
$546$	1.19916	+	0.425293i	0.0513193	+	0.0182009i
$547$	25.4022	+	25.4022i	1.08612	+	1.08612i	0.995924	+	0.0901966i	$0.0287495\pi$
$547$	25.4022	+	25.4022i	1.08612	+	1.08612i	0.0901966	+	0.995924i	$0.471250\pi$
$548$	−2.63189	−	0.705212i	−0.112429	−	0.0301252i
$549$	−4.33013	+	7.50000i	−0.184805	+	0.320092i
$550$		0			0
$551$	−2.69147	+	1.55392i	−0.114660	+	0.0661992i
$552$	10.3174	−	10.3174i	0.439136	−	0.439136i
$553$	20.2849	+	13.9557i	0.862600	+	0.593458i
$554$			5.35129i			0.227355i
$555$		0			0
$556$	−1.74612	−	1.00812i	−0.0740518	−	0.0427538i
$557$	21.9344	−	5.87732i	0.929392	−	0.249030i	0.237797	−	0.971315i	$-0.423575\pi$
$557$	21.9344	−	5.87732i	0.929392	−	0.249030i	0.691596	+	0.722285i	$0.256908\pi$
$558$	−1.00204	+	3.73966i	−0.0424197	+	0.158312i
$559$	1.54050			0.0651561
$560$		0			0
$561$	12.2783			0.518390
$562$	1.21617	−	4.53880i	0.0513010	−	0.191458i
$563$	17.4838	−	4.68476i	0.736852	−	0.197439i	0.129174	−	0.991622i	$-0.458768\pi$
$563$	17.4838	−	4.68476i	0.736852	−	0.197439i	0.607679	+	0.794183i	$0.292101\pi$
$564$	13.4317	+	7.75478i	0.565576	+	0.326535i
$565$		0			0
$566$		−	4.79671i		−	0.201621i
$567$	2.63750	+	0.208849i	0.110764	+	0.00877085i
$568$	18.4630	−	18.4630i	0.774688	−	0.774688i
$569$	−14.6334	+	8.44858i	−0.613463	+	0.354183i	−0.774319	−	0.632795i	$-0.781908\pi$
$569$	−14.6334	+	8.44858i	−0.613463	+	0.354183i	0.160857	+	0.986978i	$0.448574\pi$
$570$		0			0
$571$	−16.8565	+	29.1962i	−0.705421	+	1.22182i	0.261119	+	0.965307i	$0.415909\pi$
$571$	−16.8565	+	29.1962i	−0.705421	+	1.22182i	−0.966539	+	0.256518i	$0.917425\pi$
$572$	−4.73029	−	1.26748i	−0.197783	−	0.0529959i
$573$	16.0605	+	16.0605i	0.670935	+	0.670935i
$574$	0.975223	+	5.27596i	0.0407050	+	0.220215i
$575$		0			0
$576$	1.48605	+	2.57391i	0.0619186	+	0.107246i
$577$	−4.62985	−	17.2788i	−0.192743	−	0.719327i	−0.992840	−	0.119456i	$-0.961885\pi$
$577$	−4.62985	−	17.2788i	−0.192743	−	0.719327i	0.800096	−	0.599872i	$-0.204782\pi$
$578$	−0.331813	−	1.23834i	−0.0138016	−	0.0515083i
$579$	1.04214	+	1.80504i	0.0433098	+	0.0750148i
$580$		0			0
$581$	7.75478	−	21.8655i	0.321723	−	0.907132i
$582$	3.08512	+	3.08512i	0.127883	+	0.127883i
$583$	−2.01326	−	0.539451i	−0.0833806	−	0.0223418i
$584$	−7.13106	+	12.3514i	−0.295086	+	0.511103i
$585$		0			0
$586$	6.30154	−	3.63820i	0.260314	−	0.150293i
$587$	−16.1315	+	16.1315i	−0.665820	+	0.665820i	−0.956746	−	0.290926i	$-0.906037\pi$
$587$	−16.1315	+	16.1315i	−0.665820	+	0.665820i	0.290926	+	0.956746i	$0.406037\pi$
$588$	−10.0235	+	7.26783i	−0.413364	+	0.299720i
$589$		−	4.51835i		−	0.186175i
$590$		0			0
$591$	−8.66822	−	5.00460i	−0.356563	−	0.205862i
$592$	10.9037	−	2.92163i	0.448138	−	0.120078i
$593$	−0.930010	+	3.47085i	−0.0381909	+	0.142531i	−0.982389	−	0.186848i	$-0.940173\pi$
$593$	−0.930010	+	3.47085i	−0.0381909	+	0.142531i	0.944198	+	0.329379i	$0.106839\pi$
$594$	1.33149			0.0546316
$595$		0			0
$596$	2.76873			0.113412
$597$	0.601539	−	2.24497i	0.0246193	−	0.0918806i
$598$	−3.73966	+	1.00204i	−0.152926	+	0.0409764i
$599$	9.50413	+	5.48721i	0.388328	+	0.224201i	0.681436	−	0.731878i	$-0.261356\pi$
$599$	9.50413	+	5.48721i	0.388328	+	0.224201i	−0.293107	+	0.956080i	$0.594689\pi$
$600$		0			0
$601$			12.4108i			0.506247i	0.967434	+	0.253123i	$0.0814578\pi$
$601$			12.4108i			0.506247i	−0.967434	+	0.253123i	$0.918542\pi$
$602$	1.11096	−	1.61479i	0.0452792	−	0.0658139i
$603$	−7.06523	+	7.06523i	−0.287718	+	0.287718i
$604$	−20.6900	+	11.9454i	−0.841862	+	0.486049i
$605$		0			0
$606$	2.11680	−	3.66640i	0.0859891	−	0.148937i
$607$	−16.2158	−	4.34502i	−0.658180	−	0.176359i	−0.0857555	−	0.996316i	$-0.527330\pi$
$607$	−16.2158	−	4.34502i	−0.658180	−	0.176359i	−0.572425	+	0.819957i	$0.693997\pi$
$608$	1.94729	+	1.94729i	0.0789731	+	0.0789731i
$609$	11.1451	−	9.50956i	0.451622	−	0.385347i
$610$		0			0
$611$	−4.38437	−	7.59395i	−0.177373	−	0.307218i
$612$	2.03009	+	7.57640i	0.0820616	+	0.306258i
$613$	7.98659	+	29.8064i	0.322575	+	1.20387i	0.916727	+	0.399514i	$0.130821\pi$
$613$	7.98659	+	29.8064i	0.322575	+	1.20387i	−0.594152	+	0.804353i	$0.702512\pi$
$614$	−7.87658	−	13.6426i	−0.317873	−	0.550572i
$615$		0			0
$616$	−10.0996	+	8.61751i	−0.406925	+	0.347209i
$617$	−16.2844	−	16.2844i	−0.655584	−	0.655584i	0.298748	−	0.954332i	$-0.403431\pi$
$617$	−16.2844	−	16.2844i	−0.655584	−	0.655584i	−0.954332	+	0.298748i	$0.903431\pi$
$618$	6.95476	+	1.86352i	0.279761	+	0.0749618i
$619$	17.6727	−	30.6101i	0.710327	−	1.23032i	−0.254407	−	0.967097i	$-0.581880\pi$
$619$	17.6727	−	30.6101i	0.710327	−	1.23032i	0.964734	−	0.263226i	$-0.0847863\pi$
$620$		0			0
$621$	−6.97209	+	4.02534i	−0.279780	+	0.161531i
$622$	−11.6165	+	11.6165i	−0.465778	+	0.465778i
$623$	−23.0170	+	33.4555i	−0.922155	+	1.34037i
$624$		−	2.66589i		−	0.106721i
$625$		0			0
$626$	−4.02558	−	2.32417i	−0.160894	−	0.0928924i
$627$	−1.50097	+	0.402184i	−0.0599430	+	0.0160617i
$628$	3.75535	−	14.0152i	0.149855	−	0.559266i
$629$	18.7778			0.748718
$630$		0			0
$631$	−5.97442			−0.237838			−0.118919	−	0.992904i	$-0.537943\pi$
$631$	−5.97442			−0.237838			−0.118919	+	0.992904i	$0.537943\pi$
$632$	−4.36536	+	16.2917i	−0.173645	+	0.648051i
$633$	18.2717	−	4.89589i	0.726236	−	0.194594i
$634$	4.95514	+	2.86085i	0.196794	+	0.113619i
$635$		0			0
$636$		−	1.33149i		−	0.0527969i
$637$	6.96235	−	0.725015i	0.275858	−	0.0287261i
$638$	5.21355	−	5.21355i	0.206406	−	0.206406i
$639$	−12.4766	+	7.20336i	−0.493566	+	0.284960i
$640$		0			0
$641$	7.30387	−	12.6507i	0.288486	−	0.499672i	−0.684963	−	0.728578i	$-0.740182\pi$
$641$	7.30387	−	12.6507i	0.288486	−	0.499672i	0.973448	+	0.228906i	$0.0735149\pi$
$642$	6.16146	+	1.65096i	0.243173	+	0.0651581i
$643$	7.37675	+	7.37675i	0.290910	+	0.290910i	0.837440	−	0.546529i	$-0.184051\pi$
$643$	7.37675	+	7.37675i	0.290910	+	0.290910i	−0.546529	+	0.837440i	$0.684051\pi$
$644$	12.5930	−	35.5072i	0.496232	−	1.39918i
$645$		0			0
$646$	0.598452	+	1.03655i	0.0235458	+	0.0407825i
$647$	0.716601	+	2.67439i	0.0281725	+	0.105141i	0.978580	−	0.205865i	$-0.0660007\pi$
$647$	0.716601	+	2.67439i	0.0281725	+	0.105141i	−0.950408	+	0.311006i	$0.899334\pi$
$648$	0.469080	+	1.75063i	0.0184272	+	0.0687713i
$649$	−14.0974	−	24.4174i	−0.553372	−	0.958468i
$650$		0			0
$651$	3.87158	+	20.9453i	0.151739	+	0.820910i
$652$	2.42766	+	2.42766i	0.0950743	+	0.0950743i
$653$	−22.1982	−	5.94798i	−0.868681	−	0.232762i	−0.203164	−	0.979145i	$-0.565122\pi$
$653$	−22.1982	−	5.94798i	−0.868681	−	0.232762i	−0.665517	+	0.746382i	$0.731789\pi$
$654$	4.95570	−	8.58353i	0.193783	−	0.335642i
$655$		0			0
$656$	9.73566	−	5.62088i	0.380114	−	0.219459i
$657$	5.56440	−	5.56440i	0.217088	−	0.217088i
$658$	−11.1220	−	0.880696i	−0.433582	−	0.0343331i
$659$			0.160991i			0.00627130i	0.999995	+	0.00313565i	$0.000998110\pi$
$659$			0.160991i			0.00627130i	−0.999995	+	0.00313565i	$0.999002\pi$
$660$		0			0
$661$	16.6089	+	9.58916i	0.646012	+	0.372975i	0.786927	−	0.617047i	$-0.211671\pi$
$661$	16.6089	+	9.58916i	0.646012	+	0.372975i	−0.140915	+	0.990022i	$0.545004\pi$
$662$	−2.83486	+	0.759599i	−0.110180	+	0.0295226i
$663$	1.14777	−	4.28352i	0.0445755	−	0.166358i
$664$	15.8923			0.616743
$665$		0			0
$666$	2.03630			0.0789051
$667$	−11.5383	+	43.0613i	−0.446763	+	1.66734i
$668$	−35.4827	+	9.50756i	−1.37287	+	0.367858i
$669$	−2.10643	−	1.21615i	−0.0814392	−	0.0470189i
$670$		0			0
$671$			23.9779i			0.925658i
$672$	−10.6954	−	7.35833i	−0.412585	−	0.283854i
$673$	9.09603	−	9.09603i	0.350626	−	0.350626i	−0.509716	−	0.860342i	$-0.670250\pi$
$673$	9.09603	−	9.09603i	0.350626	−	0.350626i	0.860342	+	0.509716i	$0.170250\pi$
$674$	−1.84327	+	1.06421i	−0.0710000	+	0.0409919i
$675$		0			0
$676$	10.6124	−	18.3812i	0.408169	−	0.706970i
$677$	15.7938	+	4.23192i	0.607003	+	0.162646i	0.549213	−	0.835683i	$-0.314928\pi$
$677$	15.7938	+	4.23192i	0.607003	+	0.162646i	0.0577908	+	0.998329i	$0.481594\pi$
$678$	2.73762	+	2.73762i	0.105138	+	0.105138i
$679$	22.6232	+	8.02351i	0.868198	+	0.307914i
$680$		0			0
$681$	11.6380	+	20.1576i	0.445968	+	0.772440i
$682$	2.77438	+	10.3541i	0.106236	+	0.396480i
$683$	7.80774	+	29.1389i	0.298755	+	1.11497i	0.938189	+	0.346122i	$0.112502\pi$
$683$	7.80774	+	29.1389i	0.298755	+	1.11497i	−0.639435	+	0.768845i	$0.720832\pi$
$684$	−0.496340	−	0.859687i	−0.0189780	−	0.0328709i
$685$		0			0
$686$	4.26104	−	7.82098i	0.162687	−	0.298606i
$687$	4.35433	+	4.35433i	0.166128	+	0.166128i
$688$	−3.96686	−	1.06292i	−0.151235	−	0.0405233i
$689$	−0.376395	+	0.651936i	−0.0143395	+	0.0248368i
$690$		0			0
$691$	24.7946	−	14.3152i	0.943230	−	0.544574i	0.0522588	−	0.998634i	$-0.483358\pi$
$691$	24.7946	−	14.3152i	0.943230	−	0.544574i	0.890971	+	0.454059i	$0.150025\pi$
$692$	−7.50410	+	7.50410i	−0.285263	+	0.285263i
$693$	6.61330	−	3.15048i	0.251218	−	0.119677i
$694$			1.92094i			0.0729179i
$695$		0			0
$696$	8.69147	+	5.01802i	0.329449	+	0.190208i
$697$	18.0631	−	4.84000i	0.684190	−	0.183328i
$698$	−3.41728	+	12.7535i	−0.129346	+	0.482726i
$699$	9.22149			0.348789
$700$		0			0
$701$	−33.9721			−1.28311			−0.641554	−	0.767078i	$-0.721710\pi$
$701$	−33.9721			−1.28311			−0.641554	+	0.767078i	$0.721710\pi$
$702$	0.124466	−	0.464515i	0.00469768	−	0.0175320i
$703$	−2.29550	+	0.615078i	−0.0865765	+	0.0231981i
$704$	7.12647	+	4.11447i	0.268589	+	0.155070i
$705$		0			0
$706$			6.62028i			0.249157i
$707$	1.83860	−	23.2191i	0.0691477	−	0.873245i
$708$	12.7361	−	12.7361i	0.478651	−	0.478651i
$709$	−25.3557	+	14.6391i	−0.952255	+	0.549785i	−0.893781	−	0.448504i	$-0.851957\pi$
$709$	−25.3557	+	14.6391i	−0.952255	+	0.549785i	−0.0584744	+	0.998289i	$0.518624\pi$
$710$		0			0
$711$	4.65310	−	8.05941i	0.174505	−	0.302251i
$712$	−26.8697	−	7.19971i	−1.00698	−	0.269821i
$713$	−45.8300	−	45.8300i	−1.71635	−	1.71635i
$714$	−3.66236	−	4.29225i	−0.137061	−	0.160633i
$715$		0			0
$716$	−10.6124	−	18.3812i	−0.396604	−	0.686939i
$717$	4.35164	+	16.2405i	0.162515	+	0.606514i
$718$	−0.816878	−	3.04863i	−0.0304856	−	0.113774i
$719$	−21.2239	−	36.7608i	−0.791517	−	1.37095i	−0.925027	−	0.379901i	$-0.875958\pi$
$719$	−21.2239	−	36.7608i	−0.791517	−	1.37095i	0.133510	−	0.991047i	$-0.457375\pi$
$720$		0			0
$721$	38.9526	−	7.20009i	1.45067	−	0.268145i
$722$	6.35381	+	6.35381i	0.236464	+	0.236464i
$723$	2.97211	+	0.796375i	0.110534	+	0.0296175i
$724$	15.7986	−	27.3640i	0.587150	−	1.01697i
$725$		0			0
$726$	−1.38856	+	0.801688i	−0.0515345	+	0.0297534i
$727$	31.0670	−	31.0670i	1.15221	−	1.15221i	0.166104	−	0.986108i	$-0.446881\pi$
$727$	31.0670	−	31.0670i	1.15221	−	1.15221i	0.986108	−	0.166104i	$-0.0531186\pi$
$728$	2.06228	+	4.32900i	0.0764331	+	0.160443i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−5.91628	−	3.41576i	−0.218821	−	0.126337i
$732$	−14.7958	+	3.96451i	−0.546867	+	0.146532i
$733$	−2.65962	+	9.92582i	−0.0982351	+	0.366619i	−0.997490	−	0.0708064i	$-0.977443\pi$
$733$	−2.65962	+	9.92582i	−0.0982351	+	0.366619i	0.899255	+	0.437425i	$0.144109\pi$
$734$	2.94716			0.108782
$735$		0			0
$736$	39.5031			1.45610
$737$	−7.16009	+	26.7218i	−0.263745	+	0.984311i
$738$	1.95881	−	0.524861i	0.0721047	−	0.0193204i
$739$	−10.4814	−	6.05142i	−0.385563	−	0.222605i	0.294673	−	0.955598i	$-0.404789\pi$
$739$	−10.4814	−	6.05142i	−0.385563	−	0.222605i	−0.680236	+	0.732993i	$0.738123\pi$
$740$		0			0
$741$			0.561238i			0.0206176i
$742$	0.411932	+	0.864702i	0.0151225	+	0.0317442i
$743$	−15.1951	+	15.1951i	−0.557453	+	0.557453i	−0.928581	−	0.371129i	$-0.878971\pi$
$743$	−15.1951	+	15.1951i	−0.557453	+	0.557453i	0.371129	+	0.928581i	$0.378971\pi$
$744$	−12.6361	+	7.29548i	−0.463263	+	0.267465i
$745$		0			0
$746$	−3.78689	+	6.55908i	−0.138648	+	0.240145i
$747$	−8.46995	−	2.26952i	−0.309899	−	0.0830372i
$748$	15.3563	+	15.3563i	0.561481	+	0.561481i
$749$	34.5094	−	6.37881i	1.26095	−	0.233077i
$750$		0			0
$751$	4.48372	+	7.76602i	0.163613	+	0.283386i	0.936162	−	0.351569i	$-0.114352\pi$
$751$	4.48372	+	7.76602i	0.163613	+	0.283386i	−0.772549	+	0.634955i	$0.781018\pi$
$752$	6.05028	+	22.5799i	0.220631	+	0.823406i
$753$	7.59135	+	28.3313i	0.276644	+	1.03245i
$754$	−1.33149	−	2.30620i	−0.0484899	−	0.0839870i
$755$		0			0
$756$	3.03747	+	3.55988i	0.110472	+	0.129472i
$757$	18.2139	+	18.2139i	0.661995	+	0.661995i	0.955850	−	0.293855i	$-0.0949383\pi$
$757$	18.2139	+	18.2139i	0.661995	+	0.661995i	−0.293855	+	0.955850i	$0.594938\pi$
$758$	4.29694	+	1.15136i	0.156072	+	0.0418193i
$759$	−11.1451	+	19.3039i	−0.404541	+	0.700686i
$760$		0			0
$761$	40.2620	−	23.2453i	1.45950	−	0.842641i	0.460510	−	0.887654i	$-0.347666\pi$
$761$	40.2620	−	23.2453i	1.45950	−	0.842641i	0.998986	+	0.0450135i	$0.0143331\pi$
$762$	2.67705	−	2.67705i	0.0969792	−	0.0969792i
$763$	4.30440	−	54.3590i	0.155830	−	1.96793i
$764$			40.1731i			1.45341i
$765$		0			0
$766$	−6.80970	−	3.93158i	−0.246044	−	0.142054i
$767$	−9.83631	+	2.63563i	−0.355168	+	0.0951671i
$768$	−0.139107	+	0.519155i	−0.00501960	+	0.0187334i
$769$	−25.1138			−0.905628			−0.452814	−	0.891605i	$-0.649580\pi$
$769$	−25.1138			−0.905628			−0.452814	+	0.891605i	$0.649580\pi$
$770$		0			0
$771$	27.0470			0.974075
$772$	−0.954145	+	3.56092i	−0.0343404	+	0.128160i
$773$	−34.6116	+	9.27415i	−1.24489	+	0.333568i	−0.820361	−	0.571845i	$-0.806228\pi$
$773$	−34.6116	+	9.27415i	−1.24489	+	0.333568i	−0.424531	+	0.905413i	$0.639561\pi$
$774$	−0.641575	−	0.370413i	−0.0230609	−	0.0133142i
$775$		0			0
$776$			16.4431i			0.590272i
$777$	10.1140	−	4.81818i	0.362838	−	0.172851i
$778$	−9.19730	+	9.19730i	−0.329739	+	0.329739i
$779$	−2.04960	+	1.18334i	−0.0734347	+	0.0423976i
$780$		0			0
$781$	−19.9442	+	34.5443i	−0.713659	+	1.23609i
$782$	16.5840	+	4.44366i	0.593042	+	0.158905i
$783$	−3.91558	−	3.91558i	−0.139931	−	0.139931i
$784$	−18.4287	−	2.93695i	−0.658167	−	0.104891i
$785$		0			0
$786$	−2.39832	−	4.15401i	−0.0855453	−	0.148169i
$787$	3.10355	+	11.5826i	0.110630	+	0.412876i	0.998923	−	0.0464010i	$-0.0147752\pi$
$787$	3.10355	+	11.5826i	0.110630	+	0.412876i	−0.888293	+	0.459277i	$0.848109\pi$
$788$	−4.58203	−	17.1004i	−0.163228	−	0.609176i
$789$	7.29789	+	12.6403i	0.259812	+	0.450007i
$790$		0			0
$791$	20.0749	+	7.11976i	0.713783	+	0.253149i
$792$	3.54828	+	3.54828i	0.126083	+	0.126083i
$793$	8.36516	+	2.24144i	0.297056	+	0.0795958i
$794$	9.35129	−	16.1969i	0.331865	−	0.574807i
$795$		0			0
$796$	3.56009	−	2.05542i	0.126184	−	0.0728523i
$797$	2.68298	−	2.68298i	0.0950361	−	0.0950361i	−0.657990	−	0.753026i	$-0.728593\pi$
$797$	2.68298	−	2.68298i	0.0950361	−	0.0950361i	0.753026	+	0.657990i	$0.228593\pi$
$798$	0.588304	+	0.404746i	0.0208257	+	0.0143279i
$799$			38.8860i			1.37569i
$800$		0			0
$801$	13.2922	+	7.67428i	0.469659	+	0.271157i
$802$	−0.0388902	+	0.0104206i	−0.00137326	+	0.000367964i
$803$	5.63911	−	21.0455i	0.199000	−	0.742678i
$804$	−17.6727			−0.623269
$805$		0			0
$806$	3.87158			0.136371
$807$	−2.38670	+	8.90728i	−0.0840157	+	0.313551i
$808$	15.4116	−	4.12954i	0.542180	−	0.145277i
$809$	19.1009	+	11.0279i	0.671552	+	0.387721i	0.796664	−	0.604422i	$-0.206596\pi$
$809$	19.1009	+	11.0279i	0.671552	+	0.387721i	−0.125113	+	0.992143i	$0.539929\pi$
$810$		0			0
$811$		−	25.6111i		−	0.899327i	−0.893198	−	0.449663i	$-0.851544\pi$
$811$		−	25.6111i		−	0.899327i	0.893198	−	0.449663i	$-0.148456\pi$
$812$	25.8324	+	2.04554i	0.906541	+	0.0717843i
$813$	−7.75767	+	7.75767i	−0.272073	+	0.272073i
$814$	4.88264	−	2.81899i	0.171136	−	0.0988056i
$815$		0			0
$816$	−5.91111	+	10.2383i	−0.206930	+	0.358414i
$817$	0.835126	+	0.223771i	0.0292174	+	0.00782877i
$818$	−5.17055	−	5.17055i	−0.180784	−	0.180784i
$819$	−0.480901	−	2.60168i	−0.0168040	−	0.0909100i
$820$		0			0
$821$	−0.320157	−	0.554528i	−0.0111735	−	0.0193531i	0.860385	−	0.509645i	$-0.170223\pi$
$821$	−0.320157	−	0.554528i	−0.0111735	−	0.0193531i	−0.871558	+	0.490292i	$0.836890\pi$
$822$	−0.191740	−	0.715584i	−0.00668770	−	0.0249589i
$823$	−6.10575	−	22.7870i	−0.212833	−	0.794304i	−0.986918	−	0.161222i	$-0.948456\pi$
$823$	−6.10575	−	22.7870i	−0.212833	−	0.794304i	0.774085	−	0.633081i	$-0.218210\pi$
$824$	13.5676	+	23.4998i	0.472650	+	0.818655i
$825$		0			0
$826$	−4.33088	+	12.2114i	−0.150691	+	0.424889i
$827$	10.8626	+	10.8626i	0.377728	+	0.377728i	0.870282	−	0.492554i	$-0.163936\pi$
$827$	10.8626	+	10.8626i	0.377728	+	0.377728i	−0.492554	+	0.870282i	$0.663936\pi$
$828$	−13.7543	−	3.68546i	−0.477995	−	0.128078i
$829$	−13.8410	+	23.9733i	−0.480717	+	0.832626i	−0.999755	−	0.0221252i	$-0.992957\pi$
$829$	−13.8410	+	23.9733i	−0.480717	+	0.832626i	0.519039	+	0.854751i	$0.326290\pi$
$830$		0			0
$831$	9.63682	−	5.56382i	0.334297	−	0.193007i
$832$	2.10159	−	2.10159i	0.0728594	−	0.0728594i
$833$	−28.3465	−	12.6533i	−0.982147	−	0.438411i
$834$		−	0.548195i		−	0.0189825i
$835$		0			0
$836$	−2.38024	−	1.37423i	−0.0823225	−	0.0475289i
$837$	7.77636	−	2.08367i	0.268790	−	0.0720221i
$838$	−0.317468	+	1.18481i	−0.0109668	+	0.0409285i
$839$	5.36086			0.185078			0.0925388	−	0.995709i	$-0.470502\pi$
$839$	5.36086			0.185078			0.0925388	+	0.995709i	$0.470502\pi$
$840$		0			0
$841$	−1.66356			−0.0573641
$842$	1.46134	−	5.45379i	0.0503610	−	0.187950i
$843$	−9.43812	+	2.52894i	−0.325066	+	0.0871012i
$844$	28.9754	+	16.7289i	0.997373	+	0.575834i
$845$		0			0
$846$			4.21689i			0.144980i
$847$	−4.99989	+	7.26740i	−0.171798	+	0.249711i
$848$	1.41906	−	1.41906i	0.0487308	−	0.0487308i
$849$	−8.63810	+	4.98721i	−0.296459	+	0.171161i
$850$		0			0
$851$	−17.0447	+	29.5223i	−0.584285	+	1.01201i
$852$	−24.6134	−	6.59514i	−0.843241	−	0.225946i
$853$	13.3031	+	13.3031i	0.455490	+	0.455490i	0.897172	−	0.441682i	$-0.145618\pi$
$853$	13.3031	+	13.3031i	0.455490	+	0.455490i	−0.441682	+	0.897172i	$0.645618\pi$
$854$	8.38221	−	7.15213i	0.286833	−	0.244741i
$855$		0			0
$856$	12.0200	+	20.8193i	0.410836	+	0.711588i
$857$	10.8271	+	40.4071i	0.369845	+	1.38028i	0.860732	+	0.509058i	$0.170006\pi$
$857$	10.8271	+	40.4071i	0.369845	+	1.38028i	−0.490887	+	0.871223i	$0.663327\pi$
$858$	−0.344614	−	1.28612i	−0.0117649	−	0.0439073i
$859$	−27.4729	−	47.5845i	−0.937364	−	1.62356i	−0.770363	−	0.637605i	$-0.779925\pi$
$859$	−27.4729	−	47.5845i	−0.937364	−	1.62356i	−0.167001	−	0.985957i	$-0.553408\pi$
$860$		0			0
$861$	8.48721	−	7.24172i	0.289243	−	0.246797i
$862$	−0.975683	−	0.975683i	−0.0332319	−	0.0332319i
$863$	−2.02622	−	0.542924i	−0.0689734	−	0.0184814i	0.224167	−	0.974551i	$-0.428034\pi$
$863$	−2.02622	−	0.542924i	−0.0689734	−	0.0184814i	−0.293141	+	0.956069i	$0.594700\pi$
$864$	−2.45340	+	4.24942i	−0.0834664	+	0.144568i
$865$		0			0
$866$	4.02558	−	2.32417i	0.136795	−	0.0789784i
$867$	−1.88507	+	1.88507i	−0.0640203	+	0.0640203i
$868$	−21.3538	+	31.0381i	−0.724796	+	1.05350i
$869$		−	25.7664i		−	0.874065i
$870$		0			0
$871$	8.65310	+	4.99587i	0.293199	+	0.169279i
$872$	36.0807	−	9.66778i	1.22185	−	0.327392i
$873$	2.34816	−	8.76346i	0.0794733	−	0.296598i
$874$	−2.17288			−0.0734987
$875$		0			0
$876$	13.9186			0.470266
$877$	−11.8874	+	44.3643i	−0.401408	+	1.49808i	0.409176	+	0.912455i	$0.365816\pi$
$877$	−11.8874	+	44.3643i	−0.401408	+	1.49808i	−0.810585	+	0.585621i	$0.800851\pi$
$878$	−16.6630	+	4.46483i	−0.562348	+	0.150681i
$879$	−13.1036	−	7.56538i	−0.441974	−	0.255174i
$880$		0			0
$881$		−	47.5647i		−	1.60250i	−0.598333	−	0.801248i	$-0.704170\pi$
$881$		−	47.5647i		−	1.60250i	0.598333	−	0.801248i	$-0.295830\pi$
$882$	−3.07396	−	1.37215i	−0.103506	−	0.0462028i
$883$	16.0900	−	16.0900i	0.541473	−	0.541473i	−0.382488	−	0.923961i	$-0.624933\pi$
$883$	16.0900	−	16.0900i	0.541473	−	0.541473i	0.923961	+	0.382488i	$0.124933\pi$
$884$	6.79282	−	3.92184i	0.228467	−	0.131906i
$885$		0			0
$886$	−6.91021	+	11.9688i	−0.232153	+	0.402101i
$887$	−11.3385	−	3.03815i	−0.380710	−	0.102011i	0.0633884	−	0.997989i	$-0.479809\pi$
$887$	−11.3385	−	3.03815i	−0.380710	−	0.102011i	−0.444099	+	0.895978i	$0.646476\pi$
$888$	5.42654	+	5.42654i	0.182103	+	0.182103i
$889$	6.96222	−	19.6308i	0.233505	−	0.658394i
$890$		0			0
$891$	−1.38437	−	2.39779i	−0.0463780	−	0.0803291i
$892$	−1.11346	−	4.15549i	−0.0372814	−	0.139136i
$893$	−1.27374	−	4.75366i	−0.0426240	−	0.159075i
$894$	0.376395	+	0.651936i	0.0125885	+	0.0218040i
$895$		0			0
$896$	−5.40672	−	29.2504i	−0.180626	−	0.977187i
$897$	5.69269	+	5.69269i	0.190073	+	0.190073i
$898$	−2.15333	−	0.576982i	−0.0718575	−	0.0192542i
$899$	22.2902	−	38.6077i	0.743420	−	1.28764i
$900$		0			0
$901$	2.89109	−	1.66917i	0.0963162	−	0.0556082i
$902$	3.97022	−	3.97022i	0.132194	−	0.132194i
$903$	−4.06306	−	0.321732i	−0.135210	−	0.0107066i
$904$			14.5910i			0.485288i
$905$		0			0
$906$	−5.62539	−	3.24782i	−0.186891	−	0.107902i
$907$	22.7870	−	6.10575i	0.756629	−	0.202738i	0.140172	−	0.990127i	$-0.455234\pi$
$907$	22.7870	−	6.10575i	0.756629	−	0.202738i	0.616456	+	0.787389i	$0.288568\pi$
$908$	−10.6553	+	39.7662i	−0.353609	+	1.31969i
$909$	−8.80347			−0.291993
$910$		0			0
$911$	−32.4067			−1.07368			−0.536841	−	0.843683i	$-0.680383\pi$
$911$	−32.4067			−1.07368			−0.536841	+	0.843683i	$0.680383\pi$
$912$	0.387245	−	1.44522i	0.0128230	−	0.0478559i
$913$	−23.4510	+	6.28369i	−0.776116	+	0.207960i
$914$	16.9514	+	9.78689i	0.560702	+	0.323721i
$915$		0			0
$916$			10.8918i			0.359875i
$917$	−21.7411	−	14.9576i	−0.717954	−	0.493943i
$918$	−1.50799	+	1.50799i	−0.0497710	+	0.0497710i
$919$	−39.3883	+	22.7408i	−1.29930	+	0.750151i	−0.980283	−	0.197599i	$-0.936686\pi$
$919$	−39.3883	+	22.7408i	−1.29930	+	0.750151i	−0.319016	+	0.947749i	$0.603352\pi$
$920$		0			0
$921$	−16.3788	+	28.3689i	−0.539700	+	0.934788i
$922$	−3.93384	−	1.05407i	−0.129554	−	0.0347139i
$923$	10.1871	+	10.1871i	0.335312	+	0.335312i
$924$	12.2114	+	4.33088i	0.401726	+	0.142476i
$925$		0			0
$926$	−8.96556	−	15.5288i	−0.294627	−	0.510308i
$927$	−3.87506	−	14.4619i	−0.127274	−	0.474992i
$928$	7.03244	+	26.2454i	0.230851	+	0.861549i
$929$	−8.12318	−	14.0698i	−0.266513	−	0.461614i	0.701446	−	0.712723i	$-0.252538\pi$
$929$	−8.12318	−	14.0698i	−0.266513	−	0.461614i	−0.967959	+	0.251109i	$0.919205\pi$
$930$		0			0
$931$	3.87971	+	0.618304i	0.127152	+	0.0202641i
$932$	11.5332	+	11.5332i	0.377782	+	0.377782i
$933$	32.9972	+	8.84158i	1.08028	+	0.289460i
$934$	−1.97306	+	3.41744i	−0.0645606	+	0.111822i
$935$		0			0
$936$	1.56957	−	0.906194i	0.0513031	−	0.0296199i
$937$	2.91923	−	2.91923i	0.0953672	−	0.0953672i	−0.657814	−	0.753181i	$-0.728519\pi$
$937$	2.91923	−	2.91923i	0.0953672	−	0.0953672i	0.753181	+	0.657814i	$0.228519\pi$
$938$	11.4771	−	5.46755i	0.374742	−	0.178522i
$939$			9.66589i			0.315434i
$940$		0			0
$941$	−18.6706	−	10.7794i	−0.608643	−	0.351400i	0.163791	−	0.986495i	$-0.447628\pi$
$941$	−18.6706	−	10.7794i	−0.608643	−	0.351400i	−0.772434	+	0.635095i	$0.780961\pi$
$942$	3.81058	−	1.02104i	0.124155	−	0.0332673i
$943$	−8.78661	+	32.7921i	−0.286131	+	1.06786i
$944$	27.1475			0.883577
$945$		0			0
$946$	−2.05115			−0.0666887
$947$	−2.27503	+	8.49054i	−0.0739286	+	0.275905i	−0.992988	−	0.118213i	$-0.962283\pi$
$947$	−2.27503	+	8.49054i	−0.0739286	+	0.275905i	0.919060	+	0.394119i	$0.128950\pi$
$948$	15.8993	−	4.26021i	0.516386	−	0.138365i
$949$	−6.81497	−	3.93462i	−0.221223	−	0.127723i
$950$		0			0
$951$		−	11.8979i		−	0.385815i
$952$	1.67858	−	21.1982i	0.0544030	−	0.687039i
$953$	27.9501	−	27.9501i	0.905393	−	0.905393i	−0.0905028	−	0.995896i	$-0.528847\pi$
$953$	27.9501	−	27.9501i	0.905393	−	0.905393i	0.995896	+	0.0905028i	$0.0288474\pi$
$954$	0.313517	−	0.181009i	0.0101505	−	0.00586038i
$955$		0			0
$956$	−14.8692	+	25.7543i	−0.480906	+	0.832953i
$957$	−14.8094	−	3.96816i	−0.478719	−	0.128272i
$958$	−1.61886	−	1.61886i	−0.0523029	−	0.0523029i
$959$	−2.64552	−	3.10051i	−0.0854282	−	0.100121i
$960$		0			0
$961$	16.9067	+	29.2833i	0.545378	+	0.944622i
$962$	−0.527034	−	1.96692i	−0.0169923	−	0.0634160i
$963$	−3.43305	−	12.8123i	−0.110629	−	0.412871i
$964$	2.72116	+	4.71319i	0.0876427	+	0.151802i
$965$		0			0
$966$	10.0726	−	1.86185i	0.324081	−	0.0599039i
$967$	1.10164	+	1.10164i	0.0354264	+	0.0354264i	0.724598	−	0.689172i	$-0.242025\pi$
$967$	1.10164	+	1.10164i	0.0354264	+	0.0354264i	−0.689172	+	0.724598i	$0.742025\pi$
$968$	−5.83680	−	1.56397i	−0.187602	−	0.0502678i
$969$	1.24444	−	2.15543i	0.0399772	−	0.0692425i
$970$		0			0
$971$	−8.48721	+	4.90009i	−0.272368	+	0.157252i	−0.629963	−	0.776625i	$-0.716930\pi$
$971$	−8.48721	+	4.90009i	−0.272368	+	0.157252i	0.357596	+	0.933877i	$0.383597\pi$
$972$	1.25068	−	1.25068i	0.0401157	−	0.0401157i
$973$	−1.29711	−	2.72280i	−0.0415833	−	0.0872891i
$974$		−	6.07727i		−	0.194728i
$975$		0			0
$976$	−19.9942	−	11.5436i	−0.639998	−	0.369503i
$977$	28.1502	−	7.54282i	0.900604	−	0.241316i	0.221328	−	0.975199i	$-0.428961\pi$
$977$	28.1502	−	7.54282i	0.900604	−	0.241316i	0.679276	+	0.733883i	$0.262294\pi$
$978$	−0.241597	+	0.901652i	−0.00772541	+	0.0288316i
$979$	42.4961			1.35818
$980$		0			0
$981$	−20.6101			−0.658029
$982$	4.83791	−	18.0553i	0.154384	−	0.576169i
$983$	2.03344	−	0.544860i	0.0648568	−	0.0173783i	−0.226245	−	0.974070i	$-0.572645\pi$
$983$	2.03344	−	0.544860i	0.0648568	−	0.0173783i	0.291102	+	0.956692i	$0.405978\pi$
$984$	6.61872	+	3.82132i	0.210997	+	0.121819i
$985$		0			0
$986$			11.8093i			0.376084i
$987$	9.97776	+	20.9447i	0.317595	+	0.666676i
$988$	−0.701931	+	0.701931i	−0.0223314	+	0.0223314i
$989$	10.7405	−	6.20103i	0.341528	−	0.197181i
$990$		0			0
$991$	23.5435	−	40.7786i	0.747885	−	1.29537i	−0.200950	−	0.979602i	$-0.564403\pi$
$991$	23.5435	−	40.7786i	0.747885	−	1.29537i	0.948835	−	0.315773i	$-0.102264\pi$
$992$	−38.1571	−	10.2242i	−1.21149	−	0.324617i
$993$	4.31536	+	4.31536i	0.136944	+	0.136944i
$994$	18.0250	−	3.33178i	0.571717	−	0.105678i
$995$		0			0
$996$	−7.75478	−	13.4317i	−0.245720	−	0.425599i
$997$	1.60555	+	5.99198i	0.0508482	+	0.189768i	0.986678	−	0.162683i	$-0.0520149\pi$
$997$	1.60555	+	5.99198i	0.0508482	+	0.189768i	−0.935830	+	0.352451i	$0.885348\pi$
$998$	−1.83792	−	6.85921i	−0.0581783	−	0.217125i
$999$	−2.11718	−	3.66706i	−0.0669845	−	0.116020i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bc.c.157.3	yes	24
5.2	odd	4	inner	525.2.bc.c.493.3	yes	24
5.3	odd	4	inner	525.2.bc.c.493.4	yes	24
5.4	even	2	inner	525.2.bc.c.157.4	yes	24
7.5	odd	6	inner	525.2.bc.c.82.4	yes	24
35.12	even	12	inner	525.2.bc.c.418.4	yes	24
35.19	odd	6	inner	525.2.bc.c.82.3	✓	24
35.33	even	12	inner	525.2.bc.c.418.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bc.c.82.3	✓	24	35.19	odd	6	inner
525.2.bc.c.82.4	yes	24	7.5	odd	6	inner
525.2.bc.c.157.3	yes	24	1.1	even	1	trivial
525.2.bc.c.157.4	yes	24	5.4	even	2	inner
525.2.bc.c.418.3	yes	24	35.33	even	12	inner
525.2.bc.c.418.4	yes	24	35.12	even	12	inner
525.2.bc.c.493.3	yes	24	5.2	odd	4	inner
525.2.bc.c.493.4	yes	24	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.124466 + 0.464515i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.53177 + 0.884367i) q^{4} +0.480901i q^{6} +(1.13788 + 2.38856i) q^{7} +(-1.28155 + 1.28155i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.124466 + 0.464515i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.53177 + 0.884367i) q^{4} +0.480901i q^{6} +(1.13788 + 2.38856i) q^{7} +(-1.28155 + 1.28155i) q^{8} +(0.866025 - 0.500000i) q^{9} +(1.38437 - 2.39779i) q^{11} +(1.70847 + 0.457782i) q^{12} +(-0.707107 - 0.707107i) q^{13} +(-1.25115 + 0.231266i) q^{14} +(1.33294 + 2.30873i) q^{16} +(1.14777 + 4.28352i) q^{17} +(0.124466 + 0.464515i) q^{18} +(-0.280619 - 0.486046i) q^{19} +(1.71731 + 2.01267i) q^{21} +(0.941503 + 0.941503i) q^{22} +(-7.77636 - 2.08367i) q^{23} +(-0.906194 + 1.56957i) q^{24} +(0.416472 - 0.240450i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.369399 + 4.66503i) q^{28} -5.53747i q^{29} +(6.97209 + 4.02534i) q^{31} +(-4.73961 + 1.26997i) q^{32} +(0.716601 - 2.67439i) q^{33} -2.13261 q^{34} +1.76873 q^{36} +(1.09593 - 4.09007i) q^{37} +(0.260703 - 0.0698552i) q^{38} +(-0.866025 - 0.500000i) q^{39} -4.21689i q^{41} +(-1.14866 + 0.547207i) q^{42} +(-1.08930 + 1.08930i) q^{43} +(4.24106 - 2.44858i) q^{44} +(1.93579 - 3.35289i) q^{46} +(8.46995 + 2.26952i) q^{47} +(1.88507 + 1.88507i) q^{48} +(-4.41046 + 5.43579i) q^{49} +(2.21731 + 3.84050i) q^{51} +(-0.457782 - 1.70847i) q^{52} +(-0.194837 - 0.727140i) q^{53} +(0.240450 + 0.416472i) q^{54} +(-4.51932 - 1.60282i) q^{56} +(-0.396855 - 0.396855i) q^{57} +(2.57224 + 0.689228i) q^{58} +(5.09165 - 8.81899i) q^{59} +(-7.50000 + 4.33013i) q^{61} +(-2.73762 + 2.73762i) q^{62} +(2.17971 + 1.49962i) q^{63} +2.97209i q^{64} +(1.15310 + 0.665743i) q^{66} +(-9.65128 + 2.58605i) q^{67} +(-2.03009 + 7.57640i) q^{68} -8.05068 q^{69} -14.4067 q^{71} +(-0.469080 + 1.75063i) q^{72} +(7.60111 - 2.03671i) q^{73} +(1.76349 + 1.01815i) q^{74} -0.992681i q^{76} +(7.30252 + 0.578249i) q^{77} +(0.340048 - 0.340048i) q^{78} +(8.05941 - 4.65310i) q^{79} +(0.500000 - 0.866025i) q^{81} +(1.95881 + 0.524861i) q^{82} +(-6.20043 - 6.20043i) q^{83} +(0.850586 + 4.60168i) q^{84} +(-0.370413 - 0.641575i) q^{86} +(-1.43320 - 5.34878i) q^{87} +(1.29876 + 4.84704i) q^{88} +(7.67428 + 13.2922i) q^{89} +(0.884367 - 2.49357i) q^{91} +(-10.0689 - 10.0689i) q^{92} +(7.77636 + 2.08367i) q^{93} +(-2.10845 + 3.65194i) q^{94} +(-4.24942 + 2.45340i) q^{96} +(6.41530 - 6.41530i) q^{97} +(-1.97605 - 2.72530i) q^{98} -2.76873i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 36 q^{16} + 12 q^{21} + 12 q^{26} - 24 q^{31} - 24 q^{36} - 24 q^{46} + 24 q^{51} - 36 q^{56} - 180 q^{61} - 72 q^{66} - 96 q^{71} + 12 q^{81} + 120 q^{86} - 12 q^{91} - 108 q^{96}+O(q^{100}) \) 24 * q + 36 * q^16 + 12 * q^21 + 12 * q^26 - 24 * q^31 - 24 * q^36 - 24 * q^46 + 24 * q^51 - 36 * q^56 - 180 * q^61 - 72 * q^66 - 96 * q^71 + 12 * q^81 + 120 * q^86 - 12 * q^91 - 108 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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