LMFDB - Embedded newform 630.2.p.b.307.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(307,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.307"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.p (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.4
Root			$-3.16053i$ of defining polynomial
Character	$\chi$	$=$	630.307
Dual form			630.2.p.b.433.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(1.52773 + 1.63280i) q^{5} +(2.33991 - 1.23483i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.0743018 + 2.23483i) q^{10} +5.73528 q^{11} +(-3.41421 - 3.41421i) q^{13} +(2.52773 + 0.781409i) q^{14} -1.00000 q^{16} +(2.57474 - 2.57474i) q^{17} -1.85140 q^{19} +(-1.63280 + 1.52773i) q^{20} +(4.05545 + 4.05545i) q^{22} +(-6.46967 + 6.46967i) q^{23} +(-0.332104 + 4.98896i) q^{25} -4.82843i q^{26} +(1.23483 + 2.33991i) q^{28} +3.47577i q^{29} -0.469666i q^{31} +(-0.707107 - 0.707107i) q^{32} +3.64124 q^{34} +(5.59099 + 1.93413i) q^{35} +(0.574745 + 0.574745i) q^{37} +(-1.30913 - 1.30913i) q^{38} +(-2.23483 - 0.0743018i) q^{40} -1.03858i q^{41} +(6.17246 - 6.17246i) q^{43} +5.73528i q^{44} -9.14949 q^{46} +(-3.85140 + 3.85140i) q^{47} +(3.95037 - 5.77880i) q^{49} +(-3.76256 + 3.29289i) q^{50} +(3.41421 - 3.41421i) q^{52} +(1.85140 - 1.85140i) q^{53} +(8.76193 + 9.36459i) q^{55} +(-0.781409 + 2.52773i) q^{56} +(-2.45774 + 2.45774i) q^{58} -13.3306 q^{59} +8.53122i q^{61} +(0.332104 - 0.332104i) q^{62} -1.00000i q^{64} +(0.358761 - 10.7907i) q^{65} +(-4.46967 - 4.46967i) q^{67} +(2.57474 + 2.57474i) q^{68} +(2.58579 + 5.32106i) q^{70} -5.13387 q^{71} +(-7.80177 - 7.80177i) q^{73} +0.812812i q^{74} -1.85140i q^{76} +(13.4200 - 7.08211i) q^{77} -4.16422i q^{79} +(-1.52773 - 1.63280i) q^{80} +(0.734390 - 0.734390i) q^{82} +(1.77297 + 1.77297i) q^{83} +(8.13756 + 0.270551i) q^{85} +8.72918 q^{86} +(-4.05545 + 4.05545i) q^{88} +9.12563 q^{89} +(-12.2049 - 3.77297i) q^{91} +(-6.46967 - 6.46967i) q^{92} -5.44670 q^{94} +(-2.82843 - 3.02297i) q^{95} +(0.0119278 - 0.0119278i) q^{97} +(6.87957 - 1.29289i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7} - 4 q^{10} - 8 q^{11} - 16 q^{13} + 8 q^{14} - 8 q^{16} - 12 q^{17} - 8 q^{19} - 4 q^{20} + 8 q^{22} - 16 q^{23} - 4 q^{25} - 8 q^{28} + 16 q^{34} - 8 q^{35} - 28 q^{37} + 4 q^{38} - 8 q^{46}+ \cdots - 28 q^{97}+O(q^{100}) $ 8 * q + 4 * q^7 - 4 * q^10 - 8 * q^11 - 16 * q^13 + 8 * q^14 - 8 * q^16 - 12 * q^17 - 8 * q^19 - 4 * q^20 + 8 * q^22 - 16 * q^23 - 4 * q^25 - 8 * q^28 + 16 * q^34 - 8 * q^35 - 28 * q^37 + 4 * q^38 - 8 * q^46 - 24 * q^47 + 4 * q^49 + 16 * q^52 + 8 * q^53 + 28 * q^55 - 4 * q^56 - 12 * q^58 - 8 * q^59 + 4 * q^62 + 16 * q^65 - 12 * q^68 + 32 * q^70 - 8 * q^71 - 28 * q^73 + 44 * q^77 + 24 * q^82 + 16 * q^83 + 28 * q^85 - 8 * q^86 - 8 * q^88 + 64 * q^89 - 8 * q^91 - 16 * q^92 + 8 * q^94 - 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	1.52773	+	1.63280i	0.683220	+	0.730213i
$5$	1.52773	+	1.63280i	0.683220	+	0.730213i
$6$		0			0
$7$	2.33991	−	1.23483i	0.884404	−	0.466723i
$7$	2.33991	−	1.23483i	0.884404	−	0.466723i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−0.0743018	+	2.23483i	−0.0234963	+	0.706716i
$11$	5.73528			1.72925			0.864625	−	0.502417i	$-0.167556\pi$
$11$	5.73528			1.72925			0.864625	+	0.502417i	$0.167556\pi$
$12$		0			0
$13$	−3.41421	−	3.41421i	−0.946932	−	0.946932i	0.0517287	−	0.998661i	$-0.483527\pi$
$13$	−3.41421	−	3.41421i	−0.946932	−	0.946932i	−0.998661	+	0.0517287i	$0.983527\pi$
$14$	2.52773	+	0.781409i	0.675563	+	0.208840i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	2.57474	−	2.57474i	0.624467	−	0.624467i	−0.322203	−	0.946671i	$-0.604423\pi$
$17$	2.57474	−	2.57474i	0.624467	−	0.624467i	0.946671	+	0.322203i	$0.104423\pi$
$18$		0			0
$19$	−1.85140			−0.424739			−0.212370	−	0.977189i	$-0.568118\pi$
$19$	−1.85140			−0.424739			−0.212370	+	0.977189i	$0.568118\pi$
$20$	−1.63280	+	1.52773i	−0.365106	+	0.341610i
$21$		0			0
$22$	4.05545	+	4.05545i	0.864625	+	0.864625i
$23$	−6.46967	+	6.46967i	−1.34902	+	1.34902i	−0.462290	+	0.886729i	$0.652972\pi$
$23$	−6.46967	+	6.46967i	−1.34902	+	1.34902i	−0.886729	+	0.462290i	$0.847028\pi$
$24$		0			0
$25$	−0.332104	+	4.98896i	−0.0664208	+	0.997792i
$26$		−	4.82843i		−	0.946932i
$27$		0			0
$28$	1.23483	+	2.33991i	0.233362	+	0.442202i
$29$			3.47577i			0.645434i	0.946496	+	0.322717i	$0.104596\pi$
$29$			3.47577i			0.645434i	−0.946496	+	0.322717i	$0.895404\pi$
$30$		0			0
$31$		−	0.469666i		−	0.0843546i	−0.999110	−	0.0421773i	$-0.986571\pi$
$31$		−	0.469666i		−	0.0843546i	0.999110	−	0.0421773i	$-0.0134294\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	3.64124			0.624467
$35$	5.59099	+	1.93413i	0.945049	+	0.326928i
$36$		0			0
$37$	0.574745	+	0.574745i	0.0944875	+	0.0944875i	0.752771	−	0.658283i	$-0.228717\pi$
$37$	0.574745	+	0.574745i	0.0944875	+	0.0944875i	−0.658283	+	0.752771i	$0.728717\pi$
$38$	−1.30913	−	1.30913i	−0.212370	−	0.212370i
$39$		0			0
$40$	−2.23483	−	0.0743018i	−0.353358	−	0.0117481i
$41$		−	1.03858i		−	0.162200i	−0.996706	−	0.0810998i	$-0.974157\pi$
$41$		−	1.03858i		−	0.162200i	0.996706	−	0.0810998i	$-0.0258433\pi$
$42$		0			0
$43$	6.17246	−	6.17246i	0.941291	−	0.941291i	−0.0570785	−	0.998370i	$-0.518179\pi$
$43$	6.17246	−	6.17246i	0.941291	−	0.941291i	0.998370	+	0.0570785i	$0.0181785\pi$
$44$			5.73528i			0.864625i
$45$		0			0
$46$	−9.14949			−1.34902
$47$	−3.85140	+	3.85140i	−0.561784	+	0.561784i	−0.929814	−	0.368030i	$-0.880032\pi$
$47$	−3.85140	+	3.85140i	−0.561784	+	0.561784i	0.368030	+	0.929814i	$0.380032\pi$
$48$		0			0
$49$	3.95037	−	5.77880i	0.564339	−	0.825543i
$50$	−3.76256	+	3.29289i	−0.532106	+	0.465685i
$51$		0			0
$52$	3.41421	−	3.41421i	0.473466	−	0.473466i
$53$	1.85140	−	1.85140i	0.254309	−	0.254309i	−0.568426	−	0.822735i	$-0.692447\pi$
$53$	1.85140	−	1.85140i	0.254309	−	0.254309i	0.822735	+	0.568426i	$0.192447\pi$
$54$		0			0
$55$	8.76193	+	9.36459i	1.18146	+	1.26272i
$56$	−0.781409	+	2.52773i	−0.104420	+	0.337782i
$57$		0			0
$58$	−2.45774	+	2.45774i	−0.322717	+	0.322717i
$59$	−13.3306			−1.73549			−0.867747	−	0.497007i	$-0.834432\pi$
$59$	−13.3306			−1.73549			−0.867747	+	0.497007i	$0.834432\pi$
$60$		0			0
$61$			8.53122i			1.09231i	0.837684	+	0.546155i	$0.183909\pi$
$61$			8.53122i			1.09231i	−0.837684	+	0.546155i	$0.816091\pi$
$62$	0.332104	−	0.332104i	0.0421773	−	0.0421773i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	0.358761	−	10.7907i	0.0444988	−	1.33843i
$66$		0			0
$67$	−4.46967	−	4.46967i	−0.546057	−	0.546057i	0.379241	−	0.925298i	$-0.376185\pi$
$67$	−4.46967	−	4.46967i	−0.546057	−	0.546057i	−0.925298	+	0.379241i	$0.876185\pi$
$68$	2.57474	+	2.57474i	0.312234	+	0.312234i
$69$		0			0
$70$	2.58579	+	5.32106i	0.309061	+	0.635989i
$71$	−5.13387			−0.609279			−0.304639	−	0.952468i	$-0.598536\pi$
$71$	−5.13387			−0.609279			−0.304639	+	0.952468i	$0.598536\pi$
$72$		0			0
$73$	−7.80177	−	7.80177i	−0.913128	−	0.913128i	0.0833889	−	0.996517i	$-0.473426\pi$
$73$	−7.80177	−	7.80177i	−0.913128	−	0.913128i	−0.996517	+	0.0833889i	$0.973426\pi$
$74$			0.812812i			0.0944875i
$75$		0			0
$76$		−	1.85140i		−	0.212370i
$77$	13.4200	−	7.08211i	1.52936	−	0.807081i
$78$		0			0
$79$		−	4.16422i		−	0.468511i	−0.972175	−	0.234256i	$-0.924735\pi$
$79$		−	4.16422i		−	0.468511i	0.972175	−	0.234256i	$-0.0752653\pi$
$80$	−1.52773	−	1.63280i	−0.170805	−	0.182553i
$81$		0			0
$82$	0.734390	−	0.734390i	0.0810998	−	0.0810998i
$83$	1.77297	+	1.77297i	0.194609	+	0.194609i	0.797684	−	0.603075i	$-0.206058\pi$
$83$	1.77297	+	1.77297i	0.194609	+	0.194609i	−0.603075	+	0.797684i	$0.706058\pi$
$84$		0			0
$85$	8.13756	+	0.270551i	0.882643	+	0.0293453i
$86$	8.72918			0.941291
$87$		0			0
$88$	−4.05545	+	4.05545i	−0.432313	+	0.432313i
$89$	9.12563			0.967315			0.483658	−	0.875257i	$-0.339308\pi$
$89$	9.12563			0.967315			0.483658	+	0.875257i	$0.339308\pi$
$90$		0			0
$91$	−12.2049	−	3.77297i	−1.27943	−	0.395515i
$92$	−6.46967	−	6.46967i	−0.674509	−	0.674509i
$93$		0			0
$94$	−5.44670			−0.561784
$95$	−2.82843	−	3.02297i	−0.290191	−	0.310150i
$96$		0			0
$97$	0.0119278	−	0.0119278i	0.00121108	−	0.00121108i	−0.706501	−	0.707712i	$-0.749727\pi$
$97$	0.0119278	−	0.0119278i	0.00121108	−	0.00121108i	0.707712	+	0.706501i	$0.249727\pi$
$98$	6.87957	−	1.29289i	0.694941	−	0.130602i
$99$		0			0
$100$	−4.98896	−	0.332104i	−0.498896	−	0.0332104i
$101$		−	6.25088i		−	0.621986i	−0.950412	−	0.310993i	$-0.899338\pi$
$101$		−	6.25088i		−	0.621986i	0.950412	−	0.310993i	$-0.100662\pi$
$102$		0			0
$103$	−1.36459	−	1.36459i	−0.134457	−	0.134457i	0.636675	−	0.771132i	$-0.280309\pi$
$103$	−1.36459	−	1.36459i	−0.134457	−	0.134457i	−0.771132	+	0.636675i	$0.780309\pi$
$104$	4.82843			0.473466
$105$		0			0
$106$	2.61827			0.254309
$107$	−11.2981	−	11.2981i	−1.09223	−	1.09223i	−0.995290	−	0.0969374i	$-0.969095\pi$
$107$	−11.2981	−	11.2981i	−1.09223	−	1.09223i	−0.0969374	−	0.995290i	$-0.530905\pi$
$108$		0			0
$109$			1.91295i			0.183227i	0.995795	+	0.0916137i	$0.0292025\pi$
$109$			1.91295i			0.183227i	−0.995795	+	0.0916137i	$0.970798\pi$
$110$	−0.426141	+	12.8174i	−0.0406310	+	1.22209i
$111$		0			0
$112$	−2.33991	+	1.23483i	−0.221101	+	0.116681i
$113$	2.37563	−	2.37563i	0.223480	−	0.223480i	−0.586482	−	0.809962i	$-0.699488\pi$
$113$	2.37563	−	2.37563i	0.223480	−	0.223480i	0.809962	+	0.586482i	$0.199488\pi$
$114$		0			0
$115$	−20.4476	−	0.679824i	−1.90675	−	0.0633939i
$116$	−3.47577			−0.322717
$117$		0			0
$118$	−9.42614	−	9.42614i	−0.867747	−	0.867747i
$119$	2.84530	−	9.20406i	0.260828	−	0.843734i
$120$		0			0
$121$	21.8934			1.99031
$122$	−6.03248	+	6.03248i	−0.546155	+	0.546155i
$123$		0			0
$124$	0.469666			0.0421773
$125$	−8.65336	+	7.07950i	−0.773980	+	0.633210i
$126$		0			0
$127$	−13.3802	−	13.3802i	−1.18730	−	1.18730i	−0.977811	−	0.209490i	$-0.932820\pi$
$127$	−13.3802	−	13.3802i	−1.18730	−	1.18730i	−0.209490	−	0.977811i	$-0.567180\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	7.88388	−	7.37652i	0.691462	−	0.646963i
$131$			11.5646i			1.01040i	0.863001	+	0.505201i	$0.168582\pi$
$131$			11.5646i			1.01040i	−0.863001	+	0.505201i	$0.831418\pi$
$132$		0			0
$133$	−4.33210	+	2.28617i	−0.375641	+	0.198236i
$134$		−	6.32106i		−	0.546057i
$135$		0			0
$136$			3.64124i			0.312234i
$137$	8.03248	+	8.03248i	0.686261	+	0.686261i	0.961404	−	0.275142i	$-0.0887249\pi$
$137$	8.03248	+	8.03248i	0.686261	+	0.686261i	−0.275142	+	0.961404i	$0.588725\pi$
$138$		0			0
$139$	7.02297			0.595680			0.297840	−	0.954616i	$-0.403734\pi$
$139$	7.02297			0.595680			0.297840	+	0.954616i	$0.403734\pi$
$140$	−1.93413	+	5.59099i	−0.163464	+	0.472525i
$141$		0			0
$142$	−3.63020	−	3.63020i	−0.304639	−	0.304639i
$143$	−19.5815	−	19.5815i	−1.63748	−	1.63748i
$144$		0			0
$145$	−5.67525	+	5.31002i	−0.471304	+	0.440973i
$146$		−	11.0334i		−	0.913128i
$147$		0			0
$148$	−0.574745	+	0.574745i	−0.0472437	+	0.0472437i
$149$		−	1.88388i		−	0.154333i	−0.997018	−	0.0771667i	$-0.975413\pi$
$149$		−	1.88388i		−	0.154333i	0.997018	−	0.0771667i	$-0.0245874\pi$
$150$		0			0
$151$	3.28248			0.267124			0.133562	−	0.991040i	$-0.457358\pi$
$151$	3.28248			0.267124			0.133562	+	0.991040i	$0.457358\pi$
$152$	1.30913	−	1.30913i	0.106185	−	0.106185i
$153$		0			0
$154$	14.4972	+	4.48159i	1.16822	+	0.361137i
$155$	0.766874	−	0.717522i	0.0615968	−	0.0576327i
$156$		0			0
$157$	7.57106	−	7.57106i	0.604236	−	0.604236i	−0.337198	−	0.941434i	$-0.609479\pi$
$157$	7.57106	−	7.57106i	0.604236	−	0.604236i	0.941434	+	0.337198i	$0.109479\pi$
$158$	2.94455	−	2.94455i	0.234256	−	0.234256i
$159$		0			0
$160$	0.0743018	−	2.23483i	0.00587407	−	0.176679i
$161$	−7.14949	+	23.1274i	−0.563459	+	1.82269i
$162$		0			0
$163$	−10.3367	+	10.3367i	−0.809631	+	0.809631i	−0.984578	−	0.174947i	$-0.944025\pi$
$163$	−10.3367	+	10.3367i	−0.809631	+	0.809631i	0.174947	+	0.984578i	$0.444025\pi$
$164$	1.03858			0.0810998
$165$		0			0
$166$			2.50736i			0.194609i
$167$	9.85140	−	9.85140i	0.762324	−	0.762324i	−0.214418	−	0.976742i	$-0.568785\pi$
$167$	9.85140	−	9.85140i	0.762324	−	0.762324i	0.976742	+	0.214418i	$0.0687855\pi$
$168$		0			0
$169$			10.3137i			0.793362i
$170$	5.56282	+	5.94543i	0.426649	+	0.455994i
$171$		0			0
$172$	6.17246	+	6.17246i	0.470646	+	0.470646i
$173$	−8.83947	−	8.83947i	−0.672052	−	0.672052i	0.286137	−	0.958189i	$-0.407629\pi$
$173$	−8.83947	−	8.83947i	−0.672052	−	0.672052i	−0.958189	+	0.286137i	$0.907629\pi$
$174$		0			0
$175$	5.38344	+	12.0838i	0.406950	+	0.913451i
$176$	−5.73528			−0.432313
$177$		0			0
$178$	6.45280	+	6.45280i	0.483658	+	0.483658i
$179$		−	7.68934i		−	0.574728i	−0.957821	−	0.287364i	$-0.907221\pi$
$179$		−	7.68934i		−	0.574728i	0.957821	−	0.287364i	$-0.0927789\pi$
$180$		0			0
$181$			10.7071i			0.795852i	0.917418	+	0.397926i	$0.130270\pi$
$181$			10.7071i			0.795852i	−0.917418	+	0.397926i	$0.869730\pi$
$182$	−5.96230	−	11.2981i	−0.441955	−	0.837470i
$183$		0			0
$184$		−	9.14949i		−	0.674509i
$185$	−0.0603934	+	1.81650i	−0.00444021	+	0.133552i
$186$		0			0
$187$	14.7669	−	14.7669i	1.07986	−	1.07986i
$188$	−3.85140	−	3.85140i	−0.280892	−	0.280892i
$189$		0			0
$190$	0.137562	−	4.13756i	0.00997980	−	0.300170i
$191$	4.91206			0.355424			0.177712	−	0.984082i	$-0.443130\pi$
$191$	4.91206			0.355424			0.177712	+	0.984082i	$0.443130\pi$
$192$		0			0
$193$	16.4706	−	16.4706i	1.18558	−	1.18558i	0.207299	−	0.978278i	$-0.433533\pi$
$193$	16.4706	−	16.4706i	1.18558	−	1.18558i	0.978278	−	0.207299i	$-0.0664672\pi$
$194$	0.0168684			0.00121108
$195$		0			0
$196$	5.77880	+	3.95037i	0.412772	+	0.282170i
$197$	5.13387	+	5.13387i	0.365773	+	0.365773i	0.865933	−	0.500160i	$-0.166725\pi$
$197$	5.13387	+	5.13387i	0.365773	+	0.365773i	−0.500160	+	0.865933i	$0.666725\pi$
$198$		0			0
$199$	8.63388			0.612040			0.306020	−	0.952025i	$-0.401003\pi$
$199$	8.63388			0.612040			0.306020	+	0.952025i	$0.401003\pi$
$200$	−3.29289	−	3.76256i	−0.232843	−	0.266053i
$201$		0			0
$202$	4.42004	−	4.42004i	0.310993	−	0.310993i
$203$	4.29199	+	8.13299i	0.301239	+	0.570824i
$204$		0			0
$205$	1.69581	−	1.58667i	0.118440	−	0.110818i
$206$		−	1.92982i		−	0.134457i
$207$		0			0
$208$	3.41421	+	3.41421i	0.236733	+	0.236733i
$209$	−10.6183			−0.734481
$210$		0			0
$211$	7.73402			0.532432			0.266216	−	0.963913i	$-0.414227\pi$
$211$	7.73402			0.532432			0.266216	+	0.963913i	$0.414227\pi$
$212$	1.85140	+	1.85140i	0.127154	+	0.127154i
$213$		0			0
$214$		−	15.9779i		−	1.09223i
$215$	19.5083	+	0.648593i	1.33045	+	0.0442337i
$216$		0			0
$217$	−0.579960	−	1.09898i	−0.0393702	−	0.0746035i
$218$	−1.35266	+	1.35266i	−0.0916137	+	0.0916137i
$219$		0			0
$220$	−9.36459	+	8.76193i	−0.631360	+	0.590729i
$221$	−17.5815			−1.18266
$222$		0			0
$223$	−8.63883	−	8.63883i	−0.578499	−	0.578499i	0.355991	−	0.934489i	$-0.384143\pi$
$223$	−8.63883	−	8.63883i	−0.578499	−	0.578499i	−0.934489	+	0.355991i	$0.884143\pi$
$224$	−2.52773	−	0.781409i	−0.168891	−	0.0522101i
$225$		0			0
$226$	3.35965			0.223480
$227$	−4.08705	+	4.08705i	−0.271267	+	0.271267i	−0.829610	−	0.558343i	$-0.811437\pi$
$227$	−4.08705	+	4.08705i	−0.271267	+	0.271267i	0.558343	+	0.829610i	$0.311437\pi$
$228$		0			0
$229$	−9.31371			−0.615467			−0.307734	−	0.951473i	$-0.599571\pi$
$229$	−9.31371			−0.615467			−0.307734	+	0.951473i	$0.599571\pi$
$230$	−13.9779	−	14.9393i	−0.921677	−	0.985070i
$231$		0			0
$232$	−2.45774	−	2.45774i	−0.161358	−	0.161358i
$233$	5.22791	−	5.22791i	0.342492	−	0.342492i	−0.514812	−	0.857303i	$-0.672138\pi$
$233$	5.22791	−	5.22791i	0.342492	−	0.342492i	0.857303	+	0.514812i	$0.172138\pi$
$234$		0			0
$235$	−12.1725	−	0.404699i	−0.794044	−	0.0263997i
$236$		−	13.3306i		−	0.867747i
$237$		0			0
$238$	8.52018	−	4.49632i	0.552281	−	0.291453i
$239$			7.38514i			0.477705i	0.971056	+	0.238853i	$0.0767713\pi$
$239$			7.38514i			0.477705i	−0.971056	+	0.238853i	$0.923229\pi$
$240$		0			0
$241$		−	4.44417i		−	0.286274i	−0.989703	−	0.143137i	$-0.954281\pi$
$241$		−	4.44417i		−	0.286274i	0.989703	−	0.143137i	$-0.0457190\pi$
$242$	15.4810	+	15.4810i	0.995154	+	0.995154i
$243$		0			0
$244$	−8.53122			−0.546155
$245$	15.4707	−	2.37824i	0.988390	−	0.151940i
$246$		0			0
$247$	6.32106	+	6.32106i	0.402200	+	0.402200i
$248$	0.332104	+	0.332104i	0.0210886	+	0.0210886i
$249$		0			0
$250$	−11.1248	−	1.11289i	−0.703595	−	0.0703851i
$251$			14.1400i			0.892507i	0.894907	+	0.446254i	$0.147242\pi$
$251$			14.1400i			0.892507i	−0.894907	+	0.446254i	$0.852758\pi$
$252$		0			0
$253$	−37.1053	+	37.1053i	−2.33279	+	2.33279i
$254$		−	18.9225i		−	1.18730i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−6.67400	+	6.67400i	−0.416312	+	0.416312i	−0.883931	−	0.467618i	$-0.845112\pi$
$257$	−6.67400	+	6.67400i	−0.416312	+	0.416312i	0.467618	+	0.883931i	$0.345112\pi$
$258$		0			0
$259$	2.05457	+	0.635138i	0.127665	+	0.0394656i
$260$	10.7907	+	0.358761i	0.669213	+	0.0222494i
$261$		0			0
$262$	−8.17740	+	8.17740i	−0.505201	+	0.505201i
$263$	−2.21016	+	2.21016i	−0.136284	+	0.136284i	−0.771958	−	0.635674i	$-0.780722\pi$
$263$	−2.21016	+	2.21016i	−0.136284	+	0.136284i	0.635674	+	0.771958i	$0.280722\pi$
$264$		0			0
$265$	5.85140	+	0.194542i	0.359448	+	0.0119506i
$266$	−4.67982	−	1.44670i	−0.286938	−	0.0887027i
$267$		0			0
$268$	4.46967	−	4.46967i	0.273028	−	0.273028i
$269$	−16.2362			−0.989937			−0.494968	−	0.868911i	$-0.664820\pi$
$269$	−16.2362			−0.989937			−0.494968	+	0.868911i	$0.664820\pi$
$270$		0			0
$271$			30.1841i			1.83355i	0.399399	+	0.916777i	$0.369219\pi$
$271$			30.1841i			1.83355i	−0.399399	+	0.916777i	$0.630781\pi$
$272$	−2.57474	+	2.57474i	−0.156117	+	0.156117i
$273$		0			0
$274$			11.3596i			0.686261i
$275$	−1.90471	+	28.6131i	−0.114858	+	1.72543i
$276$		0			0
$277$	12.3646	+	12.3646i	0.742916	+	0.742916i	0.973138	−	0.230222i	$-0.0739453\pi$
$277$	12.3646	+	12.3646i	0.742916	+	0.742916i	−0.230222	+	0.973138i	$0.573945\pi$
$278$	4.96599	+	4.96599i	0.297840	+	0.297840i
$279$		0			0
$280$	−5.32106	+	2.58579i	−0.317994	+	0.154530i
$281$	22.1127			1.31913			0.659566	−	0.751647i	$-0.270740\pi$
$281$	22.1127			1.31913			0.659566	+	0.751647i	$0.270740\pi$
$282$		0			0
$283$	−14.9172	−	14.9172i	−0.886738	−	0.886738i	0.107470	−	0.994208i	$-0.465725\pi$
$283$	−14.9172	−	14.9172i	−0.886738	−	0.886738i	−0.994208	+	0.107470i	$0.965725\pi$
$284$		−	5.13387i		−	0.304639i
$285$		0			0
$286$		−	27.6924i		−	1.63748i
$287$	−1.28248	−	2.43020i	−0.0757023	−	0.143450i
$288$		0			0
$289$			3.74138i			0.220081i
$290$	−7.76776	−	0.258256i	−0.456139	−	0.0151653i
$291$		0			0
$292$	7.80177	−	7.80177i	0.456564	−	0.456564i
$293$	11.5977	+	11.5977i	0.677546	+	0.677546i	0.959444	−	0.281899i	$-0.0909642\pi$
$293$	11.5977	+	11.5977i	0.677546	+	0.677546i	−0.281899	+	0.959444i	$0.590964\pi$
$294$		0			0
$295$	−20.3655	−	21.7662i	−1.18572	−	1.26728i
$296$	−0.812812			−0.0472437
$297$		0			0
$298$	1.33210	−	1.33210i	0.0771667	−	0.0771667i
$299$	44.1776			2.55486
$300$		0			0
$301$	6.82105	−	22.0650i	0.393159	−	1.27180i
$302$	2.32106	+	2.32106i	0.133562	+	0.133562i
$303$		0			0
$304$	1.85140			0.106185
$305$	−13.9298	+	13.0334i	−0.797619	+	0.746289i
$306$		0			0
$307$	−12.4164	+	12.4164i	−0.708639	+	0.708639i	−0.966249	−	0.257610i	$-0.917065\pi$
$307$	−12.4164	+	12.4164i	−0.708639	+	0.708639i	0.257610	+	0.966249i	$0.417065\pi$
$308$	7.08211	+	13.4200i	0.403541	+	0.764678i
$309$		0			0
$310$	1.04963	+	0.0348971i	0.0596147	+	0.00198202i
$311$			9.81370i			0.556484i	0.960511	+	0.278242i	$0.0897517\pi$
$311$			9.81370i			0.556484i	−0.960511	+	0.278242i	$0.910248\pi$
$312$		0			0
$313$	13.4586	+	13.4586i	0.760726	+	0.760726i	0.976454	−	0.215727i	$-0.0692122\pi$
$313$	13.4586	+	13.4586i	0.760726	+	0.760726i	−0.215727	+	0.976454i	$0.569212\pi$
$314$	10.7071			0.604236
$315$		0			0
$316$	4.16422			0.234256
$317$	8.01040	+	8.01040i	0.449909	+	0.449909i	0.895324	−	0.445415i	$-0.146944\pi$
$317$	8.01040	+	8.01040i	0.449909	+	0.449909i	−0.445415	+	0.895324i	$0.646944\pi$
$318$		0			0
$319$			19.9345i			1.11612i
$320$	1.63280	−	1.52773i	0.0912766	−	0.0854025i
$321$		0			0
$322$	−21.4090	+	11.2981i	−1.19308	+	0.629618i
$323$	−4.76687	+	4.76687i	−0.265236	+	0.265236i
$324$		0			0
$325$	18.1672	−	15.8995i	1.00774	−	0.881945i
$326$	−14.6183			−0.809631
$327$		0			0
$328$	0.734390	+	0.734390i	0.0405499	+	0.0405499i
$329$	−4.25610	+	13.7678i	−0.234646	+	0.759041i
$330$		0			0
$331$	−13.6906			−0.752503			−0.376251	−	0.926518i	$-0.622787\pi$
$331$	−13.6906			−0.752503			−0.376251	+	0.926518i	$0.622787\pi$
$332$	−1.77297	+	1.77297i	−0.0973046	+	0.0973046i
$333$		0			0
$334$	13.9320			0.762324
$335$	0.469666	−	14.1265i	0.0256606	−	0.771814i
$336$		0			0
$337$	−4.47055	−	4.47055i	−0.243527	−	0.243527i	0.574781	−	0.818307i	$-0.305087\pi$
$337$	−4.47055	−	4.47055i	−0.243527	−	0.243527i	−0.818307	+	0.574781i	$0.805087\pi$
$338$	−7.29289	+	7.29289i	−0.396681	+	0.396681i
$339$		0			0
$340$	−0.270551	+	8.13756i	−0.0146727	+	0.441321i
$341$		−	2.69367i		−	0.145870i
$342$		0			0
$343$	2.10767	−	18.3999i	0.113804	−	0.993503i
$344$			8.72918i			0.470646i
$345$		0			0
$346$		−	12.5009i		−	0.672052i
$347$	−12.9103	−	12.9103i	−0.693059	−	0.693059i	0.269845	−	0.962904i	$-0.413028\pi$
$347$	−12.9103	−	12.9103i	−0.693059	−	0.693059i	−0.962904	+	0.269845i	$0.913028\pi$
$348$		0			0
$349$	13.5937			0.727652			0.363826	−	0.931467i	$-0.381470\pi$
$349$	13.5937			0.727652			0.363826	+	0.931467i	$0.381470\pi$
$350$	−4.73788	+	12.3512i	−0.253251	+	0.660200i
$351$		0			0
$352$	−4.05545	−	4.05545i	−0.216156	−	0.216156i
$353$	−17.4032	−	17.4032i	−0.926277	−	0.926277i	0.0711857	−	0.997463i	$-0.477322\pi$
$353$	−17.4032	−	17.4032i	−0.926277	−	0.926277i	−0.997463	+	0.0711857i	$0.977322\pi$
$354$		0			0
$355$	−7.84316	−	8.38262i	−0.416271	−	0.444903i
$356$			9.12563i			0.483658i
$357$		0			0
$358$	5.43718	−	5.43718i	0.287364	−	0.287364i
$359$		−	7.02297i		−	0.370658i	−0.982677	−	0.185329i	$-0.940665\pi$
$359$		−	7.02297i		−	0.370658i	0.982677	−	0.185329i	$-0.0593351\pi$
$360$		0			0
$361$	−15.5723			−0.819596
$362$	−7.57106	+	7.57106i	−0.397926	+	0.397926i
$363$		0			0
$364$	3.77297	−	12.2049i	0.197758	−	0.639713i
$365$	0.819799	−	24.6577i	0.0429103	−	1.29065i
$366$		0			0
$367$	−23.0609	+	23.0609i	−1.20377	+	1.20377i	−0.230759	+	0.973011i	$0.574121\pi$
$367$	−23.0609	+	23.0609i	−1.20377	+	1.20377i	−0.973011	+	0.230759i	$0.925879\pi$
$368$	6.46967	−	6.46967i	0.337255	−	0.337255i
$369$		0			0
$370$	−1.32716	+	1.24175i	−0.0689959	+	0.0645557i
$371$	2.04594	−	6.61827i	0.106220	−	0.343603i
$372$		0			0
$373$	−8.04352	+	8.04352i	−0.416478	+	0.416478i	−0.883988	−	0.467510i	$-0.845151\pi$
$373$	−8.04352	+	8.04352i	−0.416478	+	0.416478i	0.467510	+	0.883988i	$0.345151\pi$
$374$	20.8835			1.07986
$375$		0			0
$376$		−	5.44670i		−	0.280892i
$377$	11.8670	−	11.8670i	0.611182	−	0.611182i
$378$		0			0
$379$			11.4368i			0.587470i	0.955887	+	0.293735i	$0.0948983\pi$
$379$			11.4368i			0.587470i	−0.955887	+	0.293735i	$0.905102\pi$
$380$	3.02297	−	2.82843i	0.155075	−	0.145095i
$381$		0			0
$382$	3.47335	+	3.47335i	0.177712	+	0.177712i
$383$	−5.71841	−	5.71841i	−0.292197	−	0.292197i	0.545751	−	0.837948i	$-0.316245\pi$
$383$	−5.71841	−	5.71841i	−0.292197	−	0.292197i	−0.837948	+	0.545751i	$0.816245\pi$
$384$		0			0
$385$	32.0659	+	11.0928i	1.63423	+	0.565341i
$386$	23.2929			1.18558
$387$		0			0
$388$	0.0119278	+	0.0119278i	0.000605541	+	0.000605541i
$389$			32.4151i			1.64351i	0.569840	+	0.821755i	$0.307005\pi$
$389$			32.4151i			1.64351i	−0.569840	+	0.821755i	$0.692995\pi$
$390$		0			0
$391$			33.3155i			1.68484i
$392$	1.29289	+	6.87957i	0.0653010	+	0.347471i
$393$		0			0
$394$			7.26040i			0.365773i
$395$	6.79936	−	6.36179i	0.342113	−	0.320096i
$396$		0			0
$397$	25.6023	−	25.6023i	1.28494	−	1.28494i	0.347122	−	0.937820i	$-0.387159\pi$
$397$	25.6023	−	25.6023i	1.28494	−	1.28494i	0.937820	−	0.347122i	$-0.112841\pi$
$398$	6.10508	+	6.10508i	0.306020	+	0.306020i
$399$		0			0
$400$	0.332104	−	4.98896i	0.0166052	−	0.249448i
$401$	12.8597			0.642181			0.321090	−	0.947049i	$-0.395951\pi$
$401$	12.8597			0.642181			0.321090	+	0.947049i	$0.395951\pi$
$402$		0			0
$403$	−1.60354	+	1.60354i	−0.0798781	+	0.0798781i
$404$	6.25088			0.310993
$405$		0			0
$406$	−2.71599	+	8.78579i	−0.134793	+	0.436031i
$407$	3.29632	+	3.29632i	0.163393	+	0.163393i
$408$		0			0
$409$	−7.67894			−0.379699			−0.189850	−	0.981813i	$-0.560800\pi$
$409$	−7.67894			−0.379699			−0.189850	+	0.981813i	$0.560800\pi$
$410$	2.32106	+	0.0771687i	0.114629	+	0.00381109i
$411$		0			0
$412$	1.36459	−	1.36459i	0.0672284	−	0.0672284i
$413$	−31.1924	+	16.4610i	−1.53488	+	0.809995i
$414$		0			0
$415$	−0.186302	+	5.60354i	−0.00914519	+	0.275067i
$416$			4.82843i			0.236733i
$417$		0			0
$418$	−7.50825	−	7.50825i	−0.367241	−	0.367241i
$419$	−15.2534			−0.745178			−0.372589	−	0.927997i	$-0.621530\pi$
$419$	−15.2534			−0.745178			−0.372589	+	0.927997i	$0.621530\pi$
$420$		0			0
$421$	16.5264			0.805447			0.402724	−	0.915322i	$-0.368064\pi$
$421$	16.5264			0.805447			0.402724	+	0.915322i	$0.368064\pi$
$422$	5.46878	+	5.46878i	0.266216	+	0.266216i
$423$		0			0
$424$			2.61827i			0.127154i
$425$	11.9902	+	13.7004i	0.581611	+	0.664566i
$426$		0			0
$427$	10.5346	+	19.9623i	0.509807	+	0.966043i
$428$	11.2981	−	11.2981i	0.546114	−	0.546114i
$429$		0			0
$430$	13.3358	+	14.2530i	0.643109	+	0.687343i
$431$	−7.22830			−0.348175			−0.174087	−	0.984730i	$-0.555698\pi$
$431$	−7.22830			−0.348175			−0.174087	+	0.984730i	$0.555698\pi$
$432$		0			0
$433$	13.0916	+	13.0916i	0.629143	+	0.629143i	0.947853	−	0.318709i	$-0.103249\pi$
$433$	13.0916	+	13.0916i	0.629143	+	0.629143i	−0.318709	+	0.947853i	$0.603249\pi$
$434$	0.367001	−	1.18719i	0.0176166	−	0.0569868i
$435$		0			0
$436$	−1.91295			−0.0916137
$437$	11.9779	−	11.9779i	0.572981	−	0.572981i
$438$		0			0
$439$	24.9034			1.18857			0.594287	−	0.804253i	$-0.297434\pi$
$439$	24.9034			1.18857			0.594287	+	0.804253i	$0.297434\pi$
$440$	−12.8174	−	0.426141i	−0.611045	−	0.0203155i
$441$		0			0
$442$	−12.4320	−	12.4320i	−0.591328	−	0.591328i
$443$	−12.2821	+	12.2821i	−0.583541	+	0.583541i	−0.935874	−	0.352334i	$-0.885388\pi$
$443$	−12.2821	+	12.2821i	−0.583541	+	0.583541i	0.352334	+	0.935874i	$0.385388\pi$
$444$		0			0
$445$	13.9415	+	14.9004i	0.660889	+	0.706346i
$446$		−	12.2171i		−	0.578499i
$447$		0			0
$448$	−1.23483	−	2.33991i	−0.0583404	−	0.110550i
$449$			4.53122i			0.213841i	0.994268	+	0.106921i	$0.0340991\pi$
$449$			4.53122i			0.213841i	−0.994268	+	0.106921i	$0.965901\pi$
$450$		0			0
$451$		−	5.95657i		−	0.280484i
$452$	2.37563	+	2.37563i	0.111740	+	0.111740i
$453$		0			0
$454$	−5.77996			−0.271267
$455$	−12.4853	−	25.6924i	−0.585319	−	1.20448i
$456$		0			0
$457$	−5.34315	−	5.34315i	−0.249942	−	0.249942i	0.571005	−	0.820947i	$-0.306554\pi$
$457$	−5.34315	−	5.34315i	−0.249942	−	0.249942i	−0.820947	+	0.571005i	$0.806554\pi$
$458$	−6.58579	−	6.58579i	−0.307734	−	0.307734i
$459$		0			0
$460$	0.679824	−	20.4476i	0.0316969	−	0.953373i
$461$			12.9004i			0.600831i	0.953808	+	0.300415i	$0.0971253\pi$
$461$			12.9004i			0.600831i	−0.953808	+	0.300415i	$0.902875\pi$
$462$		0			0
$463$	11.9452	−	11.9452i	0.555139	−	0.555139i	−0.372781	−	0.927919i	$-0.621596\pi$
$463$	11.9452	−	11.9452i	0.555139	−	0.555139i	0.927919	+	0.372781i	$0.121596\pi$
$464$		−	3.47577i		−	0.161358i
$465$		0			0
$466$	7.39338			0.342492
$467$	−25.1204	+	25.1204i	−1.16243	+	1.16243i	−0.178493	+	0.983941i	$0.557122\pi$
$467$	−25.1204	+	25.1204i	−1.16243	+	1.16243i	−0.983941	+	0.178493i	$0.942878\pi$
$468$		0			0
$469$	−15.9779	−	4.93933i	−0.737792	−	0.228077i
$470$	−8.32106	−	8.89339i	−0.383822	−	0.410222i
$471$		0			0
$472$	9.42614	−	9.42614i	0.433873	−	0.433873i
$473$	35.4008	−	35.4008i	1.62773	−	1.62773i
$474$		0			0
$475$	0.614857	−	9.23654i	0.0282116	−	0.423802i
$476$	9.20406	+	2.84530i	0.421867	+	0.130414i
$477$		0			0
$478$	−5.22208	+	5.22208i	−0.238853	+	0.238853i
$479$	1.17157			0.0535305			0.0267653	−	0.999642i	$-0.491479\pi$
$479$	1.17157			0.0535305			0.0267653	+	0.999642i	$0.491479\pi$
$480$		0			0
$481$		−	3.92460i		−	0.178947i
$482$	3.14250	−	3.14250i	0.143137	−	0.143137i
$483$		0			0
$484$			21.8934i			0.995154i
$485$	0.0376981	+	0.00125335i	0.00171178	+	5.69118e-5i
$486$		0			0
$487$	5.67741	+	5.67741i	0.257268	+	0.257268i	0.823942	−	0.566674i	$-0.191770\pi$
$487$	5.67741	+	5.67741i	0.257268	+	0.257268i	−0.566674	+	0.823942i	$0.691770\pi$
$488$	−6.03248	−	6.03248i	−0.273078	−	0.273078i
$489$		0			0
$490$	12.6211	+	9.25780i	0.570165	+	0.418225i
$491$	21.3462			0.963340			0.481670	−	0.876353i	$-0.340030\pi$
$491$	21.3462			0.963340			0.481670	+	0.876353i	$0.340030\pi$
$492$		0			0
$493$	8.94921	+	8.94921i	0.403052	+	0.403052i
$494$			8.93933i			0.402200i
$495$		0			0
$496$			0.469666i			0.0210886i
$497$	−12.0128	+	6.33948i	−0.538848	+	0.284364i
$498$		0			0
$499$		−	33.4411i		−	1.49703i	−0.663118	−	0.748515i	$-0.730767\pi$
$499$		−	33.4411i		−	1.49703i	0.663118	−	0.748515i	$-0.269233\pi$
$500$	−7.07950	−	8.65336i	−0.316605	−	0.386990i
$501$		0			0
$502$	−9.99847	+	9.99847i	−0.446254	+	0.446254i
$503$	−9.00089	−	9.00089i	−0.401330	−	0.401330i	0.477372	−	0.878701i	$-0.341590\pi$
$503$	−9.00089	−	9.00089i	−0.401330	−	0.401330i	−0.878701	+	0.477372i	$0.841590\pi$
$504$		0			0
$505$	10.2065	−	9.54964i	0.454182	−	0.424953i
$506$	−52.4749			−2.33279
$507$		0			0
$508$	13.3802	−	13.3802i	0.593651	−	0.593651i
$509$	−24.7938			−1.09896			−0.549482	−	0.835506i	$-0.685175\pi$
$509$	−24.7938			−1.09896			−0.549482	+	0.835506i	$0.685175\pi$
$510$		0			0
$511$	−27.8893	−	8.62157i	−1.23375	−	0.381396i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−9.43846			−0.416312
$515$	0.143389	−	4.31282i	0.00631847	−	0.190046i
$516$		0			0
$517$	−22.0888	+	22.0888i	−0.971465	+	0.971465i
$518$	1.00369	+	1.90191i	0.0440995	+	0.0835651i
$519$		0			0
$520$	7.37652	+	7.88388i	0.323482	+	0.345731i
$521$		−	36.4871i		−	1.59853i	−0.600981	−	0.799263i	$-0.705223\pi$
$521$		−	36.4871i		−	1.59853i	0.600981	−	0.799263i	$-0.294777\pi$
$522$		0			0
$523$	22.9887	+	22.9887i	1.00522	+	1.00522i	0.999986	+	0.00523871i	$0.00166754\pi$
$523$	22.9887	+	22.9887i	1.00522	+	1.00522i	0.00523871	+	0.999986i	$0.498332\pi$
$524$	−11.5646			−0.505201
$525$		0			0
$526$	−3.12563			−0.136284
$527$	−1.20927	−	1.20927i	−0.0526767	−	0.0526767i
$528$		0			0
$529$		−	60.7132i		−	2.63970i
$530$	4.00000	+	4.27512i	0.173749	+	0.185700i
$531$		0			0
$532$	−2.28617	−	4.33210i	−0.0991179	−	0.187821i
$533$	−3.54595	+	3.54595i	−0.153592	+	0.153592i
$534$		0			0
$535$	1.18719	−	35.7080i	0.0513266	−	1.54379i
$536$	6.32106			0.273028
$537$		0			0
$538$	−11.4807	−	11.4807i	−0.494968	−	0.494968i
$539$	22.6565	−	33.1430i	0.975884	−	1.42757i
$540$		0			0
$541$	−17.9896			−0.773432			−0.386716	−	0.922199i	$-0.626391\pi$
$541$	−17.9896			−0.773432			−0.386716	+	0.922199i	$0.626391\pi$
$542$	−21.3434	+	21.3434i	−0.916777	+	0.916777i
$543$		0			0
$544$	−3.64124			−0.156117
$545$	−3.12347	+	2.92246i	−0.133795	+	0.125185i
$546$		0			0
$547$	22.6044	+	22.6044i	0.966496	+	0.966496i	0.999457	−	0.0329611i	$-0.0104937\pi$
$547$	22.6044	+	22.6044i	0.966496	+	0.966496i	−0.0329611	+	0.999457i	$0.510494\pi$
$548$	−8.03248	+	8.03248i	−0.343131	+	0.343131i
$549$		0			0
$550$	−21.5793	+	18.8857i	−0.920145	+	0.805287i
$551$		−	6.43502i		−	0.274141i
$552$		0			0
$553$	−5.14212	−	9.74390i	−0.218665	−	0.414353i
$554$			17.4862i			0.742916i
$555$		0			0
$556$			7.02297i			0.297840i
$557$	−11.1240	−	11.1240i	−0.471339	−	0.471339i	0.431009	−	0.902348i	$-0.358158\pi$
$557$	−11.1240	−	11.1240i	−0.471339	−	0.471339i	−0.902348	+	0.431009i	$0.858158\pi$
$558$		0			0
$559$	−42.1482			−1.78268
$560$	−5.59099	−	1.93413i	−0.236262	−	0.0817320i
$561$		0			0
$562$	15.6360	+	15.6360i	0.659566	+	0.659566i
$563$	29.1274	+	29.1274i	1.22757	+	1.22757i	0.964879	+	0.262695i	$0.0846113\pi$
$563$	29.1274	+	29.1274i	1.22757	+	1.22757i	0.262695	+	0.964879i	$0.415389\pi$
$564$		0			0
$565$	7.50825	+	0.249628i	0.315874	+	0.0105019i
$566$		−	21.0962i		−	0.886738i
$567$		0			0
$568$	3.63020	−	3.63020i	0.152320	−	0.152320i
$569$		−	8.70532i		−	0.364946i	−0.983211	−	0.182473i	$-0.941590\pi$
$569$		−	8.70532i		−	0.364946i	0.983211	−	0.182473i	$-0.0584102\pi$
$570$		0			0
$571$	−35.9454			−1.50427			−0.752134	−	0.659010i	$-0.770975\pi$
$571$	−35.9454			−1.50427			−0.752134	+	0.659010i	$0.770975\pi$
$572$	19.5815	−	19.5815i	0.818742	−	0.818742i
$573$		0			0
$574$	0.811559	−	2.62526i	0.0338738	−	0.109576i
$575$	−30.1283	−	34.4255i	−1.25644	−	1.43564i
$576$		0			0
$577$	22.5860	−	22.5860i	0.940269	−	0.940269i	−0.0580452	−	0.998314i	$-0.518487\pi$
$577$	22.5860	−	22.5860i	0.940269	−	0.940269i	0.998314	+	0.0580452i	$0.0184867\pi$
$578$	−2.64555	+	2.64555i	−0.110041	+	0.110041i
$579$		0			0
$580$	−5.31002	−	5.67525i	−0.220487	−	0.235652i
$581$	6.33793	+	1.95928i	0.262942	+	0.0812845i
$582$		0			0
$583$	10.6183	−	10.6183i	0.439764	−	0.439764i
$584$	11.0334			0.456564
$585$		0			0
$586$			16.4016i			0.677546i
$587$	−25.9727	+	25.9727i	−1.07201	+	1.07201i	−0.0748104	+	0.997198i	$0.523835\pi$
$587$	−25.9727	+	25.9727i	−1.07201	+	1.07201i	−0.997198	+	0.0748104i	$0.976165\pi$
$588$		0			0
$589$			0.869539i			0.0358287i
$590$	0.990486	−	29.7916i	0.0407777	−	1.22650i
$591$		0			0
$592$	−0.574745	−	0.574745i	−0.0236219	−	0.0236219i
$593$	24.4656	+	24.4656i	1.00468	+	1.00468i	0.999989	+	0.00469328i	$0.00149392\pi$
$593$	24.4656	+	24.4656i	1.00468	+	1.00468i	0.00469328	+	0.999989i	$0.498506\pi$
$594$		0			0
$595$	19.3753	−	9.41547i	0.794308	−	0.385997i
$596$	1.88388			0.0771667
$597$		0			0
$598$	31.2383	+	31.2383i	1.27743	+	1.27743i
$599$		−	6.72576i		−	0.274807i	−0.990515	−	0.137404i	$-0.956124\pi$
$599$		−	6.72576i		−	0.274807i	0.990515	−	0.137404i	$-0.0438757\pi$
$600$		0			0
$601$		−	44.3830i		−	1.81042i	−0.424965	−	0.905210i	$-0.639714\pi$
$601$		−	44.3830i		−	1.81042i	0.424965	−	0.905210i	$-0.360286\pi$
$602$	20.4255	−	10.7791i	0.832481	−	0.439322i
$603$		0			0
$604$			3.28248i			0.133562i
$605$	33.4471	+	35.7476i	1.35982	+	1.45335i
$606$		0			0
$607$	−7.20378	+	7.20378i	−0.292393	+	0.292393i	−0.838025	−	0.545632i	$-0.816290\pi$
$607$	−7.20378	+	7.20378i	−0.292393	+	0.292393i	0.545632	+	0.838025i	$0.316290\pi$
$608$	1.30913	+	1.30913i	0.0530924	+	0.0530924i
$609$		0			0
$610$	−19.0659	−	0.633885i	−0.771954	−	0.0256653i
$611$	26.2990			1.06394
$612$		0			0
$613$	21.6324	−	21.6324i	0.873723	−	0.873723i	−0.119153	−	0.992876i	$-0.538018\pi$
$613$	21.6324	−	21.6324i	0.873723	−	0.873723i	0.992876	+	0.119153i	$0.0380180\pi$
$614$	−17.5594			−0.708639
$615$		0			0
$616$	−4.48159	+	14.4972i	−0.180569	+	0.584109i
$617$	−29.8652	−	29.8652i	−1.20233	−	1.20233i	−0.973457	−	0.228871i	$-0.926496\pi$
$617$	−29.8652	−	29.8652i	−1.20233	−	1.20233i	−0.228871	−	0.973457i	$-0.573504\pi$
$618$		0			0
$619$	−12.6963			−0.510308			−0.255154	−	0.966900i	$-0.582126\pi$
$619$	−12.6963			−0.510308			−0.255154	+	0.966900i	$0.582126\pi$
$620$	0.717522	+	0.766874i	0.0288164	+	0.0307984i
$621$		0			0
$622$	−6.93933	+	6.93933i	−0.278242	+	0.278242i
$623$	21.3532	−	11.2686i	0.855497	−	0.451468i
$624$		0			0
$625$	−24.7794	−	3.31371i	−0.991177	−	0.132548i
$626$			19.0334i			0.760726i
$627$		0			0
$628$	7.57106	+	7.57106i	0.302118	+	0.302118i
$629$	2.95964			0.118009
$630$		0			0
$631$	36.4650			1.45165			0.725824	−	0.687881i	$-0.241459\pi$
$631$	36.4650			1.45165			0.725824	+	0.687881i	$0.241459\pi$
$632$	2.94455	+	2.94455i	0.117128	+	0.117128i
$633$		0			0
$634$			11.3284i			0.449909i
$635$	1.40597	−	42.2886i	0.0557943	−	1.67817i
$636$		0			0
$637$	−33.2175	+	6.24264i	−1.31612	+	0.247342i
$638$	−14.0958	+	14.0958i	−0.558058	+	0.558058i
$639$		0			0
$640$	2.23483	+	0.0743018i	0.0883395	+	0.00293704i
$641$	0.862164			0.0340534			0.0170267	−	0.999855i	$-0.494580\pi$
$641$	0.862164			0.0340534			0.0170267	+	0.999855i	$0.494580\pi$
$642$		0			0
$643$	8.58057	+	8.58057i	0.338385	+	0.338385i	0.855759	−	0.517374i	$-0.173091\pi$
$643$	8.58057	+	8.58057i	0.338385	+	0.338385i	−0.517374	+	0.855759i	$0.673091\pi$
$644$	−23.1274	−	7.14949i	−0.911347	−	0.281729i
$645$		0			0
$646$	−6.74138			−0.265236
$647$	−1.35623	+	1.35623i	−0.0533191	+	0.0533191i	−0.733264	−	0.679945i	$-0.762004\pi$
$647$	−1.35623	+	1.35623i	−0.0533191	+	0.0533191i	0.679945	+	0.733264i	$0.262004\pi$
$648$		0			0
$649$	−76.4545			−3.00110
$650$	24.0888	+	1.60354i	0.944841	+	0.0628961i
$651$		0			0
$652$	−10.3367	−	10.3367i	−0.404816	−	0.404816i
$653$	15.8873	−	15.8873i	0.621718	−	0.621718i	−0.324253	−	0.945971i	$-0.605113\pi$
$653$	15.8873	−	15.8873i	0.621718	−	0.621718i	0.945971	+	0.324253i	$0.105113\pi$
$654$		0			0
$655$	−18.8827	+	17.6675i	−0.737809	+	0.690327i
$656$			1.03858i			0.0405499i
$657$		0			0
$658$	−12.7448	+	6.72576i	−0.496844	+	0.262198i
$659$			25.8315i			1.00625i	0.864213	+	0.503126i	$0.167817\pi$
$659$			25.8315i			1.00625i	−0.864213	+	0.503126i	$0.832183\pi$
$660$		0			0
$661$			30.7383i			1.19558i	0.801652	+	0.597791i	$0.203955\pi$
$661$			30.7383i			1.19558i	−0.801652	+	0.597791i	$0.796045\pi$
$662$	−9.68071	−	9.68071i	−0.376251	−	0.376251i
$663$		0			0
$664$	−2.50736			−0.0973046
$665$	−10.3511	−	3.58085i	−0.401400	−	0.138859i
$666$		0			0
$667$	−22.4871	−	22.4871i	−0.870702	−	0.870702i
$668$	9.85140	+	9.85140i	0.381162	+	0.381162i
$669$		0			0
$670$	10.3211	−	9.65685i	0.398737	−	0.373077i
$671$			48.9289i			1.88888i
$672$		0			0
$673$	−4.05024	+	4.05024i	−0.156125	+	0.156125i	−0.780847	−	0.624722i	$-0.785212\pi$
$673$	−4.05024	+	4.05024i	−0.156125	+	0.156125i	0.624722	+	0.780847i	$0.285212\pi$
$674$		−	6.32232i		−	0.243527i
$675$		0			0
$676$	−10.3137			−0.396681
$677$	2.32222	−	2.32222i	0.0892503	−	0.0892503i	−0.661072	−	0.750322i	$-0.729898\pi$
$677$	2.32222	−	2.32222i	0.0892503	−	0.0892503i	0.750322	+	0.661072i	$0.229898\pi$
$678$		0			0
$679$	0.0131811	−	0.0426387i	0.000505845	−	0.00163632i
$680$	−5.94543	+	5.56282i	−0.227997	+	0.213324i
$681$		0			0
$682$	1.90471	−	1.90471i	0.0729351	−	0.0729351i
$683$	13.2028	−	13.2028i	0.505191	−	0.505191i	−0.407855	−	0.913047i	$-0.633723\pi$
$683$	13.2028	−	13.2028i	0.505191	−	0.505191i	0.913047	+	0.407855i	$0.133723\pi$
$684$		0			0
$685$	−0.844042	+	25.3869i	−0.0322492	+	0.969984i
$686$	14.5011	−	11.5204i	0.553653	−	0.439850i
$687$		0			0
$688$	−6.17246	+	6.17246i	−0.235323	+	0.235323i
$689$	−12.6421			−0.481627
$690$		0			0
$691$		−	49.4659i		−	1.88177i	−0.338726	−	0.940885i	$-0.609996\pi$
$691$		−	49.4659i		−	1.88177i	0.338726	−	0.940885i	$-0.390004\pi$
$692$	8.83947	−	8.83947i	0.336026	−	0.336026i
$693$		0			0
$694$		−	18.2579i		−	0.693059i
$695$	10.7292	+	11.4671i	0.406981	+	0.434973i
$696$		0			0
$697$	−2.67409	−	2.67409i	−0.101288	−	0.101288i
$698$	9.61217	+	9.61217i	0.363826	+	0.363826i
$699$		0			0
$700$	−12.0838	+	5.38344i	−0.456725	+	0.203475i
$701$	−31.2773			−1.18133			−0.590663	−	0.806918i	$-0.701134\pi$
$701$	−31.2773			−1.18133			−0.590663	+	0.806918i	$0.701134\pi$
$702$		0			0
$703$	−1.06408	−	1.06408i	−0.0401326	−	0.0401326i
$704$		−	5.73528i		−	0.216156i
$705$		0			0
$706$		−	24.6118i		−	0.926277i
$707$	−7.71880	−	14.6265i	−0.290295	−	0.550087i
$708$		0			0
$709$			42.4051i			1.59256i	0.604931	+	0.796278i	$0.293201\pi$
$709$			42.4051i			1.59256i	−0.604931	+	0.796278i	$0.706799\pi$
$710$	0.381456	−	11.4734i	0.0143158	−	0.430587i
$711$		0			0
$712$	−6.45280	+	6.45280i	−0.241829	+	0.241829i
$713$	3.03858	+	3.03858i	0.113796	+	0.113796i
$714$		0			0
$715$	2.05759	−	61.8878i	0.0769496	−	2.31447i
$716$	7.68934			0.287364
$717$		0			0
$718$	4.96599	−	4.96599i	0.185329	−	0.185329i
$719$	−31.0675			−1.15862			−0.579311	−	0.815107i	$-0.696678\pi$
$719$	−31.0675			−1.15862			−0.579311	+	0.815107i	$0.696678\pi$
$720$		0			0
$721$	−4.87805	−	1.50798i	−0.181668	−	0.0561600i
$722$	−11.0113	−	11.0113i	−0.409798	−	0.409798i
$723$		0			0
$724$	−10.7071			−0.397926
$725$	−17.3405	−	1.15432i	−0.644008	−	0.0428703i
$726$		0			0
$727$	6.60937	−	6.60937i	0.245128	−	0.245128i	−0.573840	−	0.818968i	$-0.694547\pi$
$727$	6.60937	−	6.60937i	0.245128	−	0.245128i	0.818968	+	0.573840i	$0.194547\pi$
$728$	11.2981	−	5.96230i	0.418735	−	0.220978i
$729$		0			0
$730$	18.0153	−	16.8560i	0.666778	−	0.623867i
$731$		−	31.7850i		−	1.17561i
$732$		0			0
$733$	3.30331	+	3.30331i	0.122010	+	0.122010i	0.765476	−	0.643465i	$-0.222504\pi$
$733$	3.30331	+	3.30331i	0.122010	+	0.122010i	−0.643465	+	0.765476i	$0.722504\pi$
$734$	−32.6131			−1.20377
$735$		0			0
$736$	9.14949			0.337255
$737$	−25.6348	−	25.6348i	−0.944269	−	0.944269i
$738$		0			0
$739$		−	8.70709i		−	0.320296i	−0.987093	−	0.160148i	$-0.948803\pi$
$739$		−	8.70709i		−	0.320296i	0.987093	−	0.160148i	$-0.0511971\pi$
$740$	−1.81650	−	0.0603934i	−0.0667758	−	0.00222011i
$741$		0			0
$742$	6.12652	−	3.23313i	0.224912	−	0.118692i
$743$	−33.9264	+	33.9264i	−1.24464	+	1.24464i	−0.286582	+	0.958056i	$0.592519\pi$
$743$	−33.9264	+	33.9264i	−1.24464	+	1.24464i	−0.958056	+	0.286582i	$0.907481\pi$
$744$		0			0
$745$	3.07601	−	2.87805i	0.112696	−	0.105444i
$746$	−11.3753			−0.416478
$747$		0			0
$748$	14.7669	+	14.7669i	0.539930	+	0.539930i
$749$	−40.3878	−	12.4853i	−1.47574	−	0.456202i
$750$		0			0
$751$	40.1365			1.46460			0.732301	−	0.680981i	$-0.238446\pi$
$751$	40.1365			1.46460			0.732301	+	0.680981i	$0.238446\pi$
$752$	3.85140	−	3.85140i	0.140446	−	0.140446i
$753$		0			0
$754$	16.7825			0.611182
$755$	5.01473	+	5.35965i	0.182505	+	0.195058i
$756$		0			0
$757$	7.01659	+	7.01659i	0.255022	+	0.255022i	0.823026	−	0.568004i	$-0.192284\pi$
$757$	7.01659	+	7.01659i	0.255022	+	0.255022i	−0.568004	+	0.823026i	$0.692284\pi$
$758$	−8.08705	+	8.08705i	−0.293735	+	0.293735i
$759$		0			0
$760$	4.13756	+	0.137562i	0.150085	+	0.00498990i
$761$		−	35.9693i		−	1.30388i	−0.758269	−	0.651942i	$-0.773954\pi$
$761$		−	35.9693i		−	1.30388i	0.758269	−	0.651942i	$-0.226046\pi$
$762$		0			0
$763$	2.36217	+	4.47613i	0.0855164	+	0.162047i
$764$			4.91206i			0.177712i
$765$		0			0
$766$		−	8.08705i		−	0.292197i
$767$	45.5134	+	45.5134i	1.64339	+	1.64339i
$768$		0			0
$769$	29.0018			1.04583			0.522916	−	0.852384i	$-0.324844\pi$
$769$	29.0018			1.04583			0.522916	+	0.852384i	$0.324844\pi$
$770$	14.8302	+	30.5178i	0.534443	+	1.09978i
$771$		0			0
$772$	16.4706	+	16.4706i	0.592788	+	0.592788i
$773$	33.1042	+	33.1042i	1.19067	+	1.19067i	0.976878	+	0.213796i	$0.0685826\pi$
$773$	33.1042	+	33.1042i	1.19067	+	1.19067i	0.213796	+	0.976878i	$0.431417\pi$
$774$		0			0
$775$	2.34315	+	0.155978i	0.0841683	+	0.00560290i
$776$			0.0168684i			0.000605541i
$777$		0			0
$778$	−22.9209	+	22.9209i	−0.821755	+	0.821755i
$779$			1.92283i			0.0688926i
$780$		0			0
$781$	−29.4442			−1.05360
$782$	−23.5576	+	23.5576i	−0.842418	+	0.842418i
$783$		0			0
$784$	−3.95037	+	5.77880i	−0.141085	+	0.206386i
$785$	23.9286	+	0.795556i	0.854047	+	0.0283946i
$786$		0			0
$787$	0.532861	−	0.532861i	0.0189944	−	0.0189944i	−0.697546	−	0.716540i	$-0.745725\pi$
$787$	0.532861	−	0.532861i	0.0189944	−	0.0189944i	0.716540	+	0.697546i	$0.245725\pi$
$788$	−5.13387	+	5.13387i	−0.182887	+	0.182887i
$789$		0			0
$790$	9.30633	+	0.309409i	0.331105	+	0.0110083i
$791$	2.62526	−	8.49227i	0.0933434	−	0.301950i
$792$		0			0
$793$	29.1274	−	29.1274i	1.03434	−	1.03434i
$794$	36.2071			1.28494
$795$		0			0
$796$			8.63388i			0.306020i
$797$	22.6961	−	22.6961i	0.803935	−	0.803935i	−0.179773	−	0.983708i	$-0.557536\pi$
$797$	22.6961	−	22.6961i	0.803935	−	0.803935i	0.983708	+	0.179773i	$0.0575363\pi$
$798$		0			0
$799$			19.8327i			0.701631i
$800$	3.76256	−	3.29289i	0.133027	−	0.116421i
$801$		0			0
$802$	9.09315	+	9.09315i	0.321090	+	0.321090i
$803$	−44.7453	−	44.7453i	−1.57903	−	1.57903i
$804$		0			0
$805$	−48.6850	+	23.6586i	−1.71592	+	0.833857i
$806$	−2.26775			−0.0798781
$807$		0			0
$808$	4.42004	+	4.42004i	0.155496	+	0.155496i
$809$			16.6404i			0.585044i	0.956259	+	0.292522i	$0.0944944\pi$
$809$			16.6404i			0.585044i	−0.956259	+	0.292522i	$0.905506\pi$
$810$		0			0
$811$			13.7933i			0.484347i	0.970233	+	0.242173i	$0.0778603\pi$
$811$			13.7933i			0.484347i	−0.970233	+	0.242173i	$0.922140\pi$
$812$	−8.13299	+	4.29199i	−0.285412	+	0.150619i
$813$		0			0
$814$			4.66170i			0.163393i
$815$	−32.6694	−	1.08616i	−1.14436	−	0.0380467i
$816$		0			0
$817$	−11.4277	+	11.4277i	−0.399804	+	0.399804i
$818$	−5.42983	−	5.42983i	−0.189850	−	0.189850i
$819$		0			0
$820$	1.58667	+	1.69581i	0.0554090	+	0.0592201i
$821$	25.2001			0.879489			0.439745	−	0.898123i	$-0.355069\pi$
$821$	25.2001			0.879489			0.439745	+	0.898123i	$0.355069\pi$
$822$		0			0
$823$	4.45075	−	4.45075i	0.155143	−	0.155143i	−0.625267	−	0.780411i	$-0.715010\pi$
$823$	4.45075	−	4.45075i	0.155143	−	0.155143i	0.780411	+	0.625267i	$0.215010\pi$
$824$	1.92982			0.0672284
$825$		0			0
$826$	−33.6961	−	10.4166i	−1.17244	−	0.362441i
$827$	21.7665	+	21.7665i	0.756896	+	0.756896i	0.975756	−	0.218861i	$-0.0702340\pi$
$827$	21.7665	+	21.7665i	0.756896	+	0.756896i	−0.218861	+	0.975756i	$0.570234\pi$
$828$		0			0
$829$	30.3787			1.05509			0.527547	−	0.849526i	$-0.323112\pi$
$829$	30.3787			1.05509			0.527547	+	0.849526i	$0.323112\pi$
$830$	−4.09404	+	3.83057i	−0.142106	+	0.132961i
$831$		0			0
$832$	−3.41421	+	3.41421i	−0.118367	+	0.118367i
$833$	−4.70773	−	25.0501i	−0.163113	−	0.867936i
$834$		0			0
$835$	31.1356	+	1.03517i	1.07749	+	0.0358236i
$836$		−	10.6183i		−	0.367241i
$837$		0			0
$838$	−10.7858	−	10.7858i	−0.372589	−	0.372589i
$839$	16.1464			0.557436			0.278718	−	0.960373i	$-0.410090\pi$
$839$	16.1464			0.557436			0.278718	+	0.960373i	$0.410090\pi$
$840$		0			0
$841$	16.9190			0.583415
$842$	11.6859	+	11.6859i	0.402724	+	0.402724i
$843$		0			0
$844$			7.73402i			0.266216i
$845$	−16.8403	+	15.7565i	−0.579323	+	0.542041i
$846$		0			0
$847$	51.2286	−	27.0347i	1.76024	−	0.928923i
$848$	−1.85140	+	1.85140i	−0.0635772	+	0.0635772i
$849$		0			0
$850$	−1.20927	+	18.1660i	−0.0414777	+	0.623088i
$851$	−7.43682			−0.254931
$852$		0			0
$853$	26.8216	+	26.8216i	0.918353	+	0.918353i	0.996910	−	0.0785565i	$-0.0250311\pi$
$853$	26.8216	+	26.8216i	0.918353	+	0.918353i	−0.0785565	+	0.996910i	$0.525031\pi$
$854$	−6.66637	+	21.5646i	−0.228118	+	0.737925i
$855$		0			0
$856$	15.9779			0.546114
$857$	18.6709	−	18.6709i	0.637787	−	0.637787i	−0.312222	−	0.950009i	$-0.601073\pi$
$857$	18.6709	−	18.6709i	0.637787	−	0.637787i	0.950009	+	0.312222i	$0.101073\pi$
$858$		0			0
$859$	8.11664			0.276936			0.138468	−	0.990367i	$-0.455782\pi$
$859$	8.11664			0.276936			0.138468	+	0.990367i	$0.455782\pi$
$860$	−0.648593	+	19.5083i	−0.0221169	+	0.665226i
$861$		0			0
$862$	−5.11118	−	5.11118i	−0.174087	−	0.174087i
$863$	−6.62651	+	6.62651i	−0.225569	+	0.225569i	−0.810839	−	0.585270i	$-0.800989\pi$
$863$	−6.62651	+	6.62651i	−0.225569	+	0.225569i	0.585270	+	0.810839i	$0.300989\pi$
$864$		0			0
$865$	0.928839	−	27.9374i	0.0315815	−	0.949901i
$866$			18.5144i			0.629143i
$867$		0			0
$868$	1.09898	−	0.579960i	0.0373017	−	0.0196851i
$869$		−	23.8829i		−	0.810173i
$870$		0			0
$871$			30.5208i			1.03416i
$872$	−1.35266	−	1.35266i	−0.0458068	−	0.0458068i
$873$		0			0
$874$	16.9393			0.572981
$875$	−11.5061	+	27.2509i	−0.388977	+	0.921247i
$876$		0			0
$877$	−27.9123	−	27.9123i	−0.942532	−	0.942532i	0.0559044	−	0.998436i	$-0.482196\pi$
$877$	−27.9123	−	27.9123i	−0.942532	−	0.942532i	−0.998436	+	0.0559044i	$0.982196\pi$
$878$	17.6094	+	17.6094i	0.594287	+	0.594287i
$879$		0			0
$880$	−8.76193	−	9.36459i	−0.295365	−	0.315680i
$881$		−	34.6317i		−	1.16677i	−0.812195	−	0.583386i	$-0.801728\pi$
$881$		−	34.6317i		−	1.16677i	0.812195	−	0.583386i	$-0.198272\pi$
$882$		0			0
$883$	5.61001	−	5.61001i	0.188792	−	0.188792i	−0.606382	−	0.795174i	$-0.707380\pi$
$883$	5.61001	−	5.61001i	0.188792	−	0.188792i	0.795174	+	0.606382i	$0.207380\pi$
$884$		−	17.5815i		−	0.591328i
$885$		0			0
$886$	−17.3695			−0.583541
$887$	24.0494	−	24.0494i	0.807498	−	0.807498i	−0.176756	−	0.984255i	$-0.556560\pi$
$887$	24.0494	−	24.0494i	0.807498	−	0.807498i	0.984255	+	0.176756i	$0.0565605\pi$
$888$		0			0
$889$	−47.8308	−	14.7862i	−1.60419	−	0.495912i
$890$	−0.678051	+	20.3943i	−0.0227283	+	0.683617i
$891$		0			0
$892$	8.63883	−	8.63883i	0.289249	−	0.289249i
$893$	7.13046	−	7.13046i	0.238612	−	0.238612i
$894$		0			0
$895$	12.5552	−	11.7472i	0.419674	−	0.392666i
$896$	0.781409	−	2.52773i	0.0261050	−	0.0844454i
$897$		0			0
$898$	−3.20406	+	3.20406i	−0.106921	+	0.106921i
$899$	1.63245			0.0544453
$900$		0			0
$901$		−	9.53375i		−	0.317615i
$902$	4.21193	−	4.21193i	0.140242	−	0.140242i
$903$		0			0
$904$			3.35965i			0.111740i
$905$	−17.4826	+	16.3575i	−0.581141	+	0.543742i
$906$		0			0
$907$	34.2153	+	34.2153i	1.13610	+	1.13610i	0.989143	+	0.146959i	$0.0469486\pi$
$907$	34.2153	+	34.2153i	1.13610	+	1.13610i	0.146959	+	0.989143i	$0.453051\pi$
$908$	−4.08705	−	4.08705i	−0.135634	−	0.135634i
$909$		0			0
$910$	9.33882	−	26.9957i	0.309579	−	0.894898i
$911$	−56.4059			−1.86881			−0.934406	−	0.356210i	$-0.884069\pi$
$911$	−56.4059			−1.86881			−0.934406	+	0.356210i	$0.884069\pi$
$912$		0			0
$913$	10.1685	+	10.1685i	0.336528	+	0.336528i
$914$		−	7.55635i		−	0.249942i
$915$		0			0
$916$		−	9.31371i		−	0.307734i
$917$	14.2803	+	27.0601i	0.471578	+	0.893604i
$918$		0			0
$919$			37.1036i			1.22393i	0.790884	+	0.611967i	$0.209621\pi$
$919$			37.1036i			1.22393i	−0.790884	+	0.611967i	$0.790379\pi$
$920$	14.9393	−	13.9779i	0.492535	−	0.460838i
$921$		0			0
$922$	−9.12195	+	9.12195i	−0.300415	+	0.300415i
$923$	17.5281	+	17.5281i	0.576946	+	0.576946i
$924$		0			0
$925$	−3.05825	+	2.67650i	−0.100555	+	0.0880029i
$926$	16.8930			0.555139
$927$		0			0
$928$	2.45774	−	2.45774i	0.0806792	−	0.0806792i
$929$	0.164219			0.00538784			0.00269392	−	0.999996i	$-0.499142\pi$
$929$	0.164219			0.00538784			0.00269392	+	0.999996i	$0.499142\pi$
$930$		0			0
$931$	−7.31371	+	10.6989i	−0.239697	+	0.350641i
$932$	5.22791	+	5.22791i	0.171246	+	0.171246i
$933$		0			0
$934$	−35.5256			−1.16243
$935$	46.6712	+	1.55168i	1.52631	+	0.0507454i
$936$		0			0
$937$	−25.1804	+	25.1804i	−0.822609	+	0.822609i	−0.986482	−	0.163872i	$-0.947602\pi$
$937$	−25.1804	+	25.1804i	−0.822609	+	0.822609i	0.163872	+	0.986482i	$0.447602\pi$
$938$	−7.80546	−	14.7907i	−0.254857	−	0.482934i
$939$		0			0
$940$	0.404699	−	12.1725i	0.0131998	−	0.397022i
$941$			46.5762i			1.51834i	0.650892	+	0.759171i	$0.274395\pi$
$941$			46.5762i			1.51834i	−0.650892	+	0.759171i	$0.725605\pi$
$942$		0			0
$943$	6.71929	+	6.71929i	0.218810	+	0.218810i
$944$	13.3306			0.433873
$945$		0			0
$946$	50.0642			1.62773
$947$	−15.2362	−	15.2362i	−0.495108	−	0.495108i	0.414803	−	0.909911i	$-0.363851\pi$
$947$	−15.2362	−	15.2362i	−0.495108	−	0.495108i	−0.909911	+	0.414803i	$0.863851\pi$
$948$		0			0
$949$			53.2738i			1.72934i
$950$	6.96599	−	6.09645i	0.226007	−	0.197795i
$951$		0			0
$952$	4.49632	+	8.52018i	0.145727	+	0.276141i
$953$	2.21318	−	2.21318i	0.0716920	−	0.0716920i	−0.670352	−	0.742044i	$-0.733857\pi$
$953$	2.21318	−	2.21318i	0.0716920	−	0.0716920i	0.742044	+	0.670352i	$0.233857\pi$
$954$		0			0
$955$	7.50429	+	8.02044i	0.242833	+	0.259535i
$956$	−7.38514			−0.238853
$957$		0			0
$958$	0.828427	+	0.828427i	0.0267653	+	0.0267653i
$959$	28.7141	+	8.87653i	0.927226	+	0.286638i
$960$		0			0
$961$	30.7794			0.992884
$962$	2.77511	−	2.77511i	0.0894733	−	0.0894733i
$963$		0			0
$964$	4.44417			0.143137
$965$	52.0557	+	1.73070i	1.67573	+	0.0557133i
$966$		0			0
$967$	4.58606	+	4.58606i	0.147478	+	0.147478i	0.776990	−	0.629513i	$-0.216745\pi$
$967$	4.58606	+	4.58606i	0.147478	+	0.147478i	−0.629513	+	0.776990i	$0.716745\pi$
$968$	−15.4810	+	15.4810i	−0.497577	+	0.497577i
$969$		0			0
$970$	0.0257703	+	0.0275428i	0.000827435	+	0.000884347i
$971$			37.1737i			1.19296i	0.802627	+	0.596481i	$0.203435\pi$
$971$			37.1737i			1.19296i	−0.802627	+	0.596481i	$0.796565\pi$
$972$		0			0
$973$	16.4331	−	8.67220i	0.526822	−	0.278018i
$974$			8.02907i			0.257268i
$975$		0			0
$976$		−	8.53122i		−	0.273078i
$977$	42.4680	+	42.4680i	1.35867	+	1.35867i	0.875557	+	0.483114i	$0.160494\pi$
$977$	42.4680	+	42.4680i	1.35867	+	1.35867i	0.483114	+	0.875557i	$0.339506\pi$
$978$		0			0
$979$	52.3380			1.67273
$980$	2.37824	+	15.4707i	0.0759700	+	0.494195i
$981$		0			0
$982$	15.0940	+	15.0940i	0.481670	+	0.481670i
$983$	31.8722	+	31.8722i	1.01657	+	1.01657i	0.999860	+	0.0167048i	$0.00531754\pi$
$983$	31.8722	+	31.8722i	1.01657	+	1.01657i	0.0167048	+	0.999860i	$0.494682\pi$
$984$		0			0
$985$	−0.539460	+	16.2258i	−0.0171886	+	0.516996i
$986$			12.6561i			0.403052i
$987$		0			0
$988$	−6.32106	+	6.32106i	−0.201100	+	0.201100i
$989$			79.8675i			2.53964i
$990$		0			0
$991$	12.2660			0.389642			0.194821	−	0.980839i	$-0.437587\pi$
$991$	12.2660			0.389642			0.194821	+	0.980839i	$0.437587\pi$
$992$	−0.332104	+	0.332104i	−0.0105443	+	0.0105443i
$993$		0			0
$994$	−12.9770	−	4.01165i	−0.411606	−	0.127242i
$995$	13.1902	+	14.0975i	0.418158	+	0.446919i
$996$		0			0
$997$	−18.0221	+	18.0221i	−0.570764	+	0.570764i	−0.932342	−	0.361578i	$-0.882238\pi$
$997$	−18.0221	+	18.0221i	−0.570764	+	0.570764i	0.361578	+	0.932342i	$0.382238\pi$
$998$	23.6464	−	23.6464i	0.748515	−	0.748515i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.p.b.307.4		8
3.2	odd	2		210.2.m.a.97.1	yes	8
5.3	odd	4		630.2.p.c.433.3		8
7.6	odd	2		630.2.p.c.307.3		8
12.11	even	2		1680.2.cz.b.97.3		8
15.2	even	4		1050.2.m.a.643.4		8
15.8	even	4		210.2.m.b.13.2	yes	8
15.14	odd	2		1050.2.m.b.307.3		8
21.20	even	2		210.2.m.b.97.2	yes	8
35.13	even	4	inner	630.2.p.b.433.4		8
60.23	odd	4		1680.2.cz.a.433.2		8
84.83	odd	2		1680.2.cz.a.97.2		8
105.62	odd	4		1050.2.m.b.643.3		8
105.83	odd	4		210.2.m.a.13.1	✓	8
105.104	even	2		1050.2.m.a.307.4		8
420.83	even	4		1680.2.cz.b.433.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.m.a.13.1	✓	8	105.83	odd	4
210.2.m.a.97.1	yes	8	3.2	odd	2
210.2.m.b.13.2	yes	8	15.8	even	4
210.2.m.b.97.2	yes	8	21.20	even	2
630.2.p.b.307.4		8	1.1	even	1	trivial
630.2.p.b.433.4		8	35.13	even	4	inner
630.2.p.c.307.3		8	7.6	odd	2
630.2.p.c.433.3		8	5.3	odd	4
1050.2.m.a.307.4		8	105.104	even	2
1050.2.m.a.643.4		8	15.2	even	4
1050.2.m.b.307.3		8	15.14	odd	2
1050.2.m.b.643.3		8	105.62	odd	4
1680.2.cz.a.97.2		8	84.83	odd	2
1680.2.cz.a.433.2		8	60.23	odd	4
1680.2.cz.b.97.3		8	12.11	even	2
1680.2.cz.b.433.3		8	420.83	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(1.52773 + 1.63280i) q^{5} +(2.33991 - 1.23483i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.0743018 + 2.23483i) q^{10} +5.73528 q^{11} +(-3.41421 - 3.41421i) q^{13} +(2.52773 + 0.781409i) q^{14} -1.00000 q^{16} +(2.57474 - 2.57474i) q^{17} -1.85140 q^{19} +(-1.63280 + 1.52773i) q^{20} +(4.05545 + 4.05545i) q^{22} +(-6.46967 + 6.46967i) q^{23} +(-0.332104 + 4.98896i) q^{25} -4.82843i q^{26} +(1.23483 + 2.33991i) q^{28} +3.47577i q^{29} -0.469666i q^{31} +(-0.707107 - 0.707107i) q^{32} +3.64124 q^{34} +(5.59099 + 1.93413i) q^{35} +(0.574745 + 0.574745i) q^{37} +(-1.30913 - 1.30913i) q^{38} +(-2.23483 - 0.0743018i) q^{40} -1.03858i q^{41} +(6.17246 - 6.17246i) q^{43} +5.73528i q^{44} -9.14949 q^{46} +(-3.85140 + 3.85140i) q^{47} +(3.95037 - 5.77880i) q^{49} +(-3.76256 + 3.29289i) q^{50} +(3.41421 - 3.41421i) q^{52} +(1.85140 - 1.85140i) q^{53} +(8.76193 + 9.36459i) q^{55} +(-0.781409 + 2.52773i) q^{56} +(-2.45774 + 2.45774i) q^{58} -13.3306 q^{59} +8.53122i q^{61} +(0.332104 - 0.332104i) q^{62} -1.00000i q^{64} +(0.358761 - 10.7907i) q^{65} +(-4.46967 - 4.46967i) q^{67} +(2.57474 + 2.57474i) q^{68} +(2.58579 + 5.32106i) q^{70} -5.13387 q^{71} +(-7.80177 - 7.80177i) q^{73} +0.812812i q^{74} -1.85140i q^{76} +(13.4200 - 7.08211i) q^{77} -4.16422i q^{79} +(-1.52773 - 1.63280i) q^{80} +(0.734390 - 0.734390i) q^{82} +(1.77297 + 1.77297i) q^{83} +(8.13756 + 0.270551i) q^{85} +8.72918 q^{86} +(-4.05545 + 4.05545i) q^{88} +9.12563 q^{89} +(-12.2049 - 3.77297i) q^{91} +(-6.46967 - 6.46967i) q^{92} -5.44670 q^{94} +(-2.82843 - 3.02297i) q^{95} +(0.0119278 - 0.0119278i) q^{97} +(6.87957 - 1.29289i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7} - 4 q^{10} - 8 q^{11} - 16 q^{13} + 8 q^{14} - 8 q^{16} - 12 q^{17} - 8 q^{19} - 4 q^{20} + 8 q^{22} - 16 q^{23} - 4 q^{25} - 8 q^{28} + 16 q^{34} - 8 q^{35} - 28 q^{37} + 4 q^{38} - 8 q^{46}+ \cdots - 28 q^{97}+O(q^{100}) \) 8 * q + 4 * q^7 - 4 * q^10 - 8 * q^11 - 16 * q^13 + 8 * q^14 - 8 * q^16 - 12 * q^17 - 8 * q^19 - 4 * q^20 + 8 * q^22 - 16 * q^23 - 4 * q^25 - 8 * q^28 + 16 * q^34 - 8 * q^35 - 28 * q^37 + 4 * q^38 - 8 * q^46 - 24 * q^47 + 4 * q^49 + 16 * q^52 + 8 * q^53 + 28 * q^55 - 4 * q^56 - 12 * q^58 - 8 * q^59 + 4 * q^62 + 16 * q^65 - 12 * q^68 + 32 * q^70 - 8 * q^71 - 28 * q^73 + 44 * q^77 + 24 * q^82 + 16 * q^83 + 28 * q^85 - 8 * q^86 - 8 * q^88 + 64 * q^89 - 8 * q^91 - 16 * q^92 + 8 * q^94 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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