LMFDB - Embedded newform 252.2.i.b.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(25,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 4]))

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

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.2
Root			$-0.473632 + 1.66604i$ of defining polynomial
Character	$\chi$	$=$	252.121
Dual form			252.2.i.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20601 - 1.24319i) q^{3} +(0.951504 + 1.64805i) q^{5} +(2.11495 - 1.58965i) q^{7} +(-0.0910656 + 2.99862i) q^{9} +O(q^{10})$	\(q+(-1.20601 - 1.24319i) q^{3} +(0.951504 + 1.64805i) q^{5} +(2.11495 - 1.58965i) q^{7} +(-0.0910656 + 2.99862i) q^{9} +(1.53293 - 2.65512i) q^{11} +(1.13161 - 1.96000i) q^{13} +(0.901324 - 3.17048i) q^{15} +(-0.713726 - 1.23621i) q^{17} +(2.98444 - 5.16919i) q^{19} +(-4.52690 - 0.712149i) q^{21} +(3.57771 + 6.19678i) q^{23} +(0.689282 - 1.19387i) q^{25} +(3.83769 - 3.50316i) q^{27} +(0.468164 + 0.810884i) q^{29} -8.22129 q^{31} +(-5.14956 + 1.29637i) q^{33} +(4.63221 + 1.97298i) q^{35} +(-1.41550 + 2.45171i) q^{37} +(-3.80140 + 0.956979i) q^{39} +(-5.31672 + 9.20883i) q^{41} +(2.98444 + 5.16919i) q^{43} +(-5.02853 + 2.70311i) q^{45} -0.966679 q^{47} +(1.94600 - 6.72407i) q^{49} +(-0.676086 + 2.37818i) q^{51} +(5.45142 + 9.44213i) q^{53} +5.83436 q^{55} +(-10.0256 + 2.52388i) q^{57} -11.3636 q^{59} +0.899436 q^{61} +(4.57416 + 6.48668i) q^{63} +4.30692 q^{65} +1.62762 q^{67} +(3.38904 - 11.9212i) q^{69} -2.36378 q^{71} +(-0.996286 - 1.72562i) q^{73} +(-2.31550 + 0.582912i) q^{75} +(-0.978644 - 8.05226i) q^{77} -8.33889 q^{79} +(-8.98341 - 0.546142i) q^{81} +(-7.98203 - 13.8253i) q^{83} +(1.35822 - 2.35251i) q^{85} +(0.443475 - 1.55996i) q^{87} +(-2.58992 + 4.48587i) q^{89} +(-0.722433 - 5.94416i) q^{91} +(9.91499 + 10.2207i) q^{93} +11.3588 q^{95} +(0.922890 + 1.59849i) q^{97} +(7.82208 + 4.83847i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9}+O(q^{10}) $ 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9	$ 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 11 q^{21} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 4 q^{33} - 19 q^{35} + 10 q^{37} - 2 q^{39} - 33 q^{41} + 7 q^{43} - 10 q^{45} + 6 q^{47} - 4 q^{49} - 13 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} + 28 q^{59} + 20 q^{61} + 33 q^{63} - 30 q^{65} - 12 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} - 44 q^{75} - 47 q^{77} + 20 q^{79} - 29 q^{81} - 25 q^{83} + 8 q^{85} + 28 q^{87} - 6 q^{89} + 2 q^{91} + 22 q^{93} + 56 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) $ 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 11 * q^21 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 4 * q^33 - 19 * q^35 + 10 * q^37 - 2 * q^39 - 33 * q^41 + 7 * q^43 - 10 * q^45 + 6 * q^47 - 4 * q^49 - 13 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 + 28 * q^59 + 20 * q^61 + 33 * q^63 - 30 * q^65 - 12 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 - 44 * q^75 - 47 * q^77 + 20 * q^79 - 29 * q^81 - 25 * q^83 + 8 * q^85 + 28 * q^87 - 6 * q^89 + 2 * q^91 + 22 * q^93 + 56 * q^95 - 18 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.20601	−	1.24319i	−0.696292	−	0.717759i
$3$	−1.20601	−	1.24319i	−0.696292	−	0.717759i
$4$		0			0
$5$	0.951504	+	1.64805i	0.425525	+	0.737032i	0.996469	−	0.0839575i	$-0.0267560\pi$
$5$	0.951504	+	1.64805i	0.425525	+	0.737032i	−0.570944	+	0.820989i	$0.693423\pi$
$6$		0			0
$7$	2.11495	−	1.58965i	0.799375	−	0.600833i
$7$	2.11495	−	1.58965i	0.799375	−	0.600833i
$8$		0			0
$9$	−0.0910656	+	2.99862i	−0.0303552	+	0.999539i
$10$		0			0
$11$	1.53293	−	2.65512i	0.462196	−	0.800548i	−0.536874	−	0.843663i	$-0.680395\pi$
$11$	1.53293	−	2.65512i	0.462196	−	0.800548i	0.999070	+	0.0431149i	$0.0137282\pi$
$12$		0			0
$13$	1.13161	−	1.96000i	0.313851	−	0.543607i	−0.665341	−	0.746539i	$-0.731714\pi$
$13$	1.13161	−	1.96000i	0.313851	−	0.543607i	0.979193	+	0.202933i	$0.0650473\pi$
$14$		0			0
$15$	0.901324	−	3.17048i	0.232721	−	0.818614i
$16$		0			0
$17$	−0.713726	−	1.23621i	−0.173104	−	0.299825i	0.766400	−	0.642364i	$-0.222046\pi$
$17$	−0.713726	−	1.23621i	−0.173104	−	0.299825i	−0.939503	+	0.342539i	$0.888713\pi$
$18$		0			0
$19$	2.98444	−	5.16919i	0.684677	−	1.18589i	−0.288862	−	0.957371i	$-0.593277\pi$
$19$	2.98444	−	5.16919i	0.684677	−	1.18589i	0.973538	−	0.228524i	$-0.0733898\pi$
$20$		0			0
$21$	−4.52690	−	0.712149i	−0.987851	−	0.155404i
$22$		0			0
$23$	3.57771	+	6.19678i	0.746005	+	1.29212i	0.949724	+	0.313089i	$0.101364\pi$
$23$	3.57771	+	6.19678i	0.746005	+	1.29212i	−0.203719	+	0.979029i	$0.565303\pi$
$24$		0			0
$25$	0.689282	−	1.19387i	0.137856	−	0.238774i
$26$		0			0
$27$	3.83769	−	3.50316i	0.738564	−	0.674183i
$28$		0			0
$29$	0.468164	+	0.810884i	0.0869359	+	0.150577i	0.906214	−	0.422818i	$-0.138959\pi$
$29$	0.468164	+	0.810884i	0.0869359	+	0.150577i	−0.819279	+	0.573396i	$0.805626\pi$
$30$		0			0
$31$	−8.22129			−1.47659			−0.738294	−	0.674479i	$-0.764368\pi$
$31$	−8.22129			−1.47659			−0.738294	+	0.674479i	$0.764368\pi$
$32$		0			0
$33$	−5.14956	+	1.29637i	−0.896424	+	0.225669i
$34$		0			0
$35$	4.63221	+	1.97298i	0.782987	+	0.333495i
$36$		0			0
$37$	−1.41550	+	2.45171i	−0.232706	+	0.403059i	−0.958604	−	0.284744i	$-0.908091\pi$
$37$	−1.41550	+	2.45171i	−0.232706	+	0.403059i	0.725897	+	0.687803i	$0.241425\pi$
$38$		0			0
$39$	−3.80140	+	0.956979i	−0.608711	+	0.153239i
$40$		0			0
$41$	−5.31672	+	9.20883i	−0.830332	+	1.43818i	0.0674429	+	0.997723i	$0.478516\pi$
$41$	−5.31672	+	9.20883i	−0.830332	+	1.43818i	−0.897775	+	0.440454i	$0.854817\pi$
$42$		0			0
$43$	2.98444	+	5.16919i	0.455122	+	0.788295i	0.998695	−	0.0510671i	$-0.0162622\pi$
$43$	2.98444	+	5.16919i	0.455122	+	0.788295i	−0.543573	+	0.839362i	$0.682929\pi$
$44$		0			0
$45$	−5.02853	+	2.70311i	−0.749609	+	0.402957i
$46$		0			0
$47$	−0.966679			−0.141005			−0.0705023	−	0.997512i	$-0.522460\pi$
$47$	−0.966679			−0.141005			−0.0705023	+	0.997512i	$0.522460\pi$
$48$		0			0
$49$	1.94600	−	6.72407i	0.278001	−	0.960581i
$50$		0			0
$51$	−0.676086	+	2.37818i	−0.0946710	+	0.333012i
$52$		0			0
$53$	5.45142	+	9.44213i	0.748810	+	1.29698i	0.948393	+	0.317096i	$0.102708\pi$
$53$	5.45142	+	9.44213i	0.748810	+	1.29698i	−0.199583	+	0.979881i	$0.563959\pi$
$54$		0			0
$55$	5.83436			0.786705
$56$		0			0
$57$	−10.0256	+	2.52388i	−1.32792	+	0.334296i
$58$		0			0
$59$	−11.3636			−1.47942			−0.739708	−	0.672928i	$-0.765036\pi$
$59$	−11.3636			−1.47942			−0.739708	+	0.672928i	$0.765036\pi$
$60$		0			0
$61$	0.899436			0.115161			0.0575805	−	0.998341i	$-0.481661\pi$
$61$	0.899436			0.115161			0.0575805	+	0.998341i	$0.481661\pi$
$62$		0			0
$63$	4.57416	+	6.48668i	0.576290	+	0.817245i
$64$		0			0
$65$	4.30692			0.534207
$66$		0			0
$67$	1.62762			0.198845			0.0994227	−	0.995045i	$-0.468300\pi$
$67$	1.62762			0.198845			0.0994227	+	0.995045i	$0.468300\pi$
$68$		0			0
$69$	3.38904	−	11.9212i	0.407992	−	1.43514i
$70$		0			0
$71$	−2.36378			−0.280529			−0.140264	−	0.990114i	$-0.544795\pi$
$71$	−2.36378			−0.280529			−0.140264	+	0.990114i	$0.544795\pi$
$72$		0			0
$73$	−0.996286	−	1.72562i	−0.116606	−	0.201968i	0.801814	−	0.597573i	$-0.203868\pi$
$73$	−0.996286	−	1.72562i	−0.116606	−	0.201968i	−0.918421	+	0.395605i	$0.870535\pi$
$74$		0			0
$75$	−2.31550	+	0.582912i	−0.267371	+	0.0673089i
$76$		0			0
$77$	−0.978644	−	8.05226i	−0.111527	−	0.917640i
$78$		0			0
$79$	−8.33889			−0.938198			−0.469099	−	0.883145i	$-0.655421\pi$
$79$	−8.33889			−0.938198			−0.469099	+	0.883145i	$0.655421\pi$
$80$		0			0
$81$	−8.98341	−	0.546142i	−0.998157	−	0.0606824i
$82$		0			0
$83$	−7.98203	−	13.8253i	−0.876141	−	1.51752i	−0.855542	−	0.517734i	$-0.826776\pi$
$83$	−7.98203	−	13.8253i	−0.876141	−	1.51752i	−0.0205995	−	0.999788i	$-0.506557\pi$
$84$		0			0
$85$	1.35822	−	2.35251i	0.147320	−	0.255166i
$86$		0			0
$87$	0.443475	−	1.55996i	0.0475455	−	0.167245i
$88$		0			0
$89$	−2.58992	+	4.48587i	−0.274531	+	0.475501i	−0.970017	−	0.243039i	$-0.921856\pi$
$89$	−2.58992	+	4.48587i	−0.274531	+	0.475501i	0.695486	+	0.718540i	$0.255189\pi$
$90$		0			0
$91$	−0.722433	−	5.94416i	−0.0757316	−	0.623118i
$92$		0			0
$93$	9.91499	+	10.2207i	1.02814	+	1.05983i
$94$		0			0
$95$	11.3588			1.16539
$96$		0			0
$97$	0.922890	+	1.59849i	0.0937053	+	0.162302i	0.909068	−	0.416649i	$-0.136796\pi$
$97$	0.922890	+	1.59849i	0.0937053	+	0.162302i	−0.815362	+	0.578951i	$0.803462\pi$
$98$		0			0
$99$	7.82208	+	4.83847i	0.786149	+	0.486284i
$100$		0			0
$101$	4.03175	−	6.98320i	0.401174	−	0.694854i	−0.592694	−	0.805428i	$-0.701936\pi$
$101$	4.03175	−	6.98320i	0.401174	−	0.694854i	0.993868	+	0.110574i	$0.0352688\pi$
$102$		0			0
$103$	8.89931	+	15.4141i	0.876875	+	1.51879i	0.854752	+	0.519037i	$0.173709\pi$
$103$	8.89931	+	15.4141i	0.876875	+	1.51879i	0.0221235	+	0.999755i	$0.492957\pi$
$104$		0			0
$105$	−3.13371	−	8.13819i	−0.305818	−	0.794206i
$106$		0			0
$107$	8.76005	−	15.1729i	0.846866	−	1.46682i	−0.0371245	−	0.999311i	$-0.511820\pi$
$107$	8.76005	−	15.1729i	0.846866	−	1.46682i	0.883991	−	0.467505i	$-0.154847\pi$
$108$		0			0
$109$	1.11441	+	1.93021i	0.106741	+	0.184881i	0.914448	−	0.404703i	$-0.132625\pi$
$109$	1.11441	+	1.93021i	0.106741	+	0.184881i	−0.807707	+	0.589584i	$0.799292\pi$
$110$		0			0
$111$	4.75507	−	1.19706i	0.451331	−	0.113620i
$112$		0			0
$113$	−7.59999	+	13.1636i	−0.714947	+	1.23832i	0.248033	+	0.968751i	$0.420216\pi$
$113$	−7.59999	+	13.1636i	−0.714947	+	1.23832i	−0.962980	+	0.269573i	$0.913118\pi$
$114$		0			0
$115$	−6.80842	+	11.7925i	−0.634888	+	1.09966i
$116$		0			0
$117$	5.77425	+	3.57175i	0.533829	+	0.330208i
$118$		0			0
$119$	−3.47464	−	1.47994i	−0.318519	−	0.135666i
$120$		0			0
$121$	0.800238	+	1.38605i	0.0727489	+	0.126005i
$122$		0			0
$123$	17.8604	−	4.49625i	1.61042	−	0.405413i
$124$		0			0
$125$	12.1385			1.08570
$126$		0			0
$127$	−16.9303			−1.50232			−0.751161	−	0.660119i	$-0.770506\pi$
$127$	−16.9303			−1.50232			−0.751161	+	0.660119i	$0.770506\pi$
$128$		0			0
$129$	2.82705	−	9.94435i	0.248908	−	0.875551i
$130$		0			0
$131$	−1.19177	−	2.06420i	−0.104125	−	0.180350i	0.809255	−	0.587457i	$-0.199871\pi$
$131$	−1.19177	−	2.06420i	−0.104125	−	0.180350i	−0.913380	+	0.407107i	$0.866538\pi$
$132$		0			0
$133$	−1.90530	−	15.6768i	−0.165211	−	1.35935i
$134$		0			0
$135$	9.42497	+	2.99145i	0.811172	+	0.257463i
$136$		0			0
$137$	−5.49099	+	9.51068i	−0.469127	+	0.812552i	−0.999377	−	0.0352893i	$-0.988765\pi$
$137$	−5.49099	+	9.51068i	−0.469127	+	0.812552i	0.530250	+	0.847841i	$0.322098\pi$
$138$		0			0
$139$	−3.70422	+	6.41590i	−0.314188	+	0.544190i	−0.979265	−	0.202585i	$-0.935066\pi$
$139$	−3.70422	+	6.41590i	−0.314188	+	0.544190i	0.665076	+	0.746775i	$0.268399\pi$
$140$		0			0
$141$	1.16583	+	1.20177i	0.0981804	+	0.101207i
$142$		0			0
$143$	−3.46936	−	6.00910i	−0.290122	−	0.502506i
$144$		0			0
$145$	−0.890919	+	1.54312i	−0.0739868	+	0.128149i
$146$		0			0
$147$	−10.7062	+	5.69005i	−0.883035	+	0.469307i
$148$		0			0
$149$	−8.81197	−	15.2628i	−0.721904	−	1.25038i	−0.960236	−	0.279191i	$-0.909934\pi$
$149$	−8.81197	−	15.2628i	−0.721904	−	1.25038i	0.238331	−	0.971184i	$-0.423400\pi$
$150$		0			0
$151$	10.1832	−	17.6378i	0.828697	−	1.43535i	−0.0703634	−	0.997521i	$-0.522416\pi$
$151$	10.1832	−	17.6378i	0.828697	−	1.43535i	0.899061	−	0.437824i	$-0.144251\pi$
$152$		0			0
$153$	3.77191	−	2.02761i	0.304941	−	0.163923i
$154$		0			0
$155$	−7.82259	−	13.5491i	−0.628326	−	1.08829i
$156$		0			0
$157$	9.28235			0.740812			0.370406	−	0.928870i	$-0.379218\pi$
$157$	9.28235			0.740812			0.370406	+	0.928870i	$0.379218\pi$
$158$		0			0
$159$	5.16393	−	18.1645i	0.409526	−	1.44054i
$160$		0			0
$161$	17.4174	+	7.41854i	1.37268	+	0.584663i
$162$		0			0
$163$	−11.9069	+	20.6234i	−0.932623	+	1.61535i	−0.153803	+	0.988101i	$0.549152\pi$
$163$	−11.9069	+	20.6234i	−0.932623	+	1.61535i	−0.778819	+	0.627248i	$0.784181\pi$
$164$		0			0
$165$	−7.03632	−	7.25325i	−0.547776	−	0.564665i
$166$		0			0
$167$	−0.883505	+	1.53028i	−0.0683676	+	0.118416i	−0.898183	−	0.439622i	$-0.855112\pi$
$167$	−0.883505	+	1.53028i	−0.0683676	+	0.118416i	0.829815	+	0.558038i	$0.188446\pi$
$168$		0			0
$169$	3.93893	+	6.82242i	0.302994	+	0.524802i
$170$		0			0
$171$	15.2287	+	9.41992i	1.16456	+	0.720359i
$172$		0			0
$173$	0.360099			0.0273778			0.0136889	−	0.999906i	$-0.495643\pi$
$173$	0.360099			0.0273778			0.0136889	+	0.999906i	$0.495643\pi$
$174$		0			0
$175$	−0.440047	−	3.62069i	−0.0332644	−	0.273699i
$176$		0			0
$177$	13.7047	+	14.1272i	1.03011	+	1.06186i
$178$		0			0
$179$	−3.57701	−	6.19556i	−0.267358	−	0.463078i	0.700821	−	0.713337i	$-0.252817\pi$
$179$	−3.57701	−	6.19556i	−0.267358	−	0.463078i	−0.968179	+	0.250260i	$0.919484\pi$
$180$		0			0
$181$	11.0542			0.821650			0.410825	−	0.911714i	$-0.365241\pi$
$181$	11.0542			0.821650			0.410825	+	0.911714i	$0.365241\pi$
$182$		0			0
$183$	−1.08473	−	1.11817i	−0.0801857	−	0.0826578i
$184$		0			0
$185$	−5.38741			−0.396090
$186$		0			0
$187$	−4.37637			−0.320032
$188$		0			0
$189$	2.54771	−	13.5096i	0.185318	−	0.982679i
$190$		0			0
$191$	−8.70167			−0.629630			−0.314815	−	0.949153i	$-0.601943\pi$
$191$	−8.70167			−0.629630			−0.314815	+	0.949153i	$0.601943\pi$
$192$		0			0
$193$	−1.41929			−0.102163			−0.0510813	−	0.998694i	$-0.516267\pi$
$193$	−1.41929			−0.102163			−0.0510813	+	0.998694i	$0.516267\pi$
$194$		0			0
$195$	−5.19420	−	5.35433i	−0.371964	−	0.383432i
$196$		0			0
$197$	5.69424			0.405698			0.202849	−	0.979210i	$-0.434980\pi$
$197$	5.69424			0.405698			0.202849	+	0.979210i	$0.434980\pi$
$198$		0			0
$199$	2.61327	+	4.52631i	0.185250	+	0.320862i	0.943661	−	0.330915i	$-0.107357\pi$
$199$	2.61327	+	4.52631i	0.185250	+	0.320862i	−0.758411	+	0.651777i	$0.774024\pi$
$200$		0			0
$201$	−1.96293	−	2.02345i	−0.138454	−	0.142723i
$202$		0			0
$203$	2.27917	+	0.970758i	0.159966	+	0.0681339i
$204$		0			0
$205$	−20.2355			−1.41331
$206$		0			0
$207$	−18.9076	+	10.1639i	−1.31417	+	0.706439i
$208$		0			0
$209$	−9.14987	−	15.8480i	−0.632910	−	1.09623i
$210$		0			0
$211$	−5.93079	+	10.2724i	−0.408293	+	0.707183i	−0.994699	−	0.102834i	$-0.967209\pi$
$211$	−5.93079	+	10.2724i	−0.408293	+	0.707183i	0.586406	+	0.810017i	$0.300542\pi$
$212$		0			0
$213$	2.85075	+	2.93864i	0.195330	+	0.201352i
$214$		0			0
$215$	−5.67940	+	9.83701i	−0.387332	+	0.670879i
$216$		0			0
$217$	−17.3876	+	13.0690i	−1.18035	+	0.887182i
$218$		0			0
$219$	−0.943745	+	3.31969i	−0.0637724	+	0.224324i
$220$		0			0
$221$	−3.23063			−0.217316
$222$		0			0
$223$	12.2950	+	21.2955i	0.823333	+	1.42605i	0.903187	+	0.429248i	$0.141221\pi$
$223$	12.2950	+	21.2955i	0.823333	+	1.42605i	−0.0798535	+	0.996807i	$0.525445\pi$
$224$		0			0
$225$	3.51719	+	2.17561i	0.234479	+	0.145041i
$226$		0			0
$227$	−7.65898	+	13.2657i	−0.508344	+	0.880478i	0.491609	+	0.870816i	$0.336409\pi$
$227$	−7.65898	+	13.2657i	−0.508344	+	0.880478i	−0.999953	+	0.00966216i	$0.996924\pi$
$228$		0			0
$229$	−8.52297	−	14.7622i	−0.563214	−	0.975515i	−0.997213	−	0.0746016i	$-0.976231\pi$
$229$	−8.52297	−	14.7622i	−0.563214	−	0.975515i	0.434000	−	0.900913i	$-0.357102\pi$
$230$		0			0
$231$	−8.83027	+	10.9278i	−0.580989	+	0.718995i
$232$		0			0
$233$	9.88255	−	17.1171i	0.647427	−	1.12138i	−0.336308	−	0.941752i	$-0.609178\pi$
$233$	9.88255	−	17.1171i	0.647427	−	1.12138i	0.983735	−	0.179625i	$-0.0574884\pi$
$234$		0			0
$235$	−0.919799	−	1.59314i	−0.0600011	−	0.103925i
$236$		0			0
$237$	10.0568	+	10.3669i	0.653260	+	0.673400i
$238$		0			0
$239$	8.35041	−	14.4633i	0.540143	−	0.935555i	−0.458752	−	0.888564i	$-0.651703\pi$
$239$	8.35041	−	14.4633i	0.540143	−	0.935555i	0.998895	−	0.0469909i	$-0.0149632\pi$
$240$		0			0
$241$	−3.19998	+	5.54252i	−0.206129	+	0.357025i	−0.950492	−	0.310750i	$-0.899420\pi$
$241$	−3.19998	+	5.54252i	−0.206129	+	0.357025i	0.744363	+	0.667775i	$0.232753\pi$
$242$		0			0
$243$	10.1552	+	11.8268i	0.651453	+	0.758689i
$244$		0			0
$245$	12.9332	−	3.19086i	0.826275	−	0.203856i
$246$		0			0
$247$	−6.75442	−	11.6990i	−0.429774	−	0.744390i
$248$		0			0
$249$	−7.56108	+	26.5967i	−0.479164	+	1.68550i
$250$		0			0
$251$	−26.8346			−1.69378			−0.846891	−	0.531766i	$-0.821529\pi$
$251$	−26.8346			−1.69378			−0.846891	+	0.531766i	$0.821529\pi$
$252$		0			0
$253$	21.9376			1.37920
$254$		0			0
$255$	−4.56267	+	1.14863i	−0.285725	+	0.0719297i
$256$		0			0
$257$	−3.58798	−	6.21457i	−0.223812	−	0.387654i	0.732150	−	0.681143i	$-0.238517\pi$
$257$	−3.58798	−	6.21457i	−0.223812	−	0.387654i	−0.955962	+	0.293489i	$0.905184\pi$
$258$		0			0
$259$	0.903673	+	7.43540i	0.0561515	+	0.462013i
$260$		0			0
$261$	−2.47416	+	1.33000i	−0.153147	+	0.0823250i
$262$		0			0
$263$	−10.2069	+	17.6788i	−0.629382	+	1.09012i	0.358294	+	0.933609i	$0.383359\pi$
$263$	−10.2069	+	17.6788i	−0.629382	+	1.09012i	−0.987676	+	0.156513i	$0.949975\pi$
$264$		0			0
$265$	−10.3741	+	17.9685i	−0.637275	+	1.10379i
$266$		0			0
$267$	8.70028	−	2.19024i	0.532448	−	0.134041i
$268$		0			0
$269$	−3.37251	−	5.84136i	−0.205626	−	0.356154i	0.744706	−	0.667392i	$-0.232590\pi$
$269$	−3.37251	−	5.84136i	−0.205626	−	0.356154i	−0.950332	+	0.311238i	$0.899256\pi$
$270$		0			0
$271$	−1.04632	+	1.81228i	−0.0635596	+	0.110088i	−0.896054	−	0.443945i	$-0.853579\pi$
$271$	−1.04632	+	1.81228i	−0.0635596	+	0.110088i	0.832495	+	0.554033i	$0.186912\pi$
$272$		0			0
$273$	−6.51849	+	8.06686i	−0.394517	+	0.488229i
$274$		0			0
$275$	−2.11324	−	3.66025i	−0.127433	−	0.220721i
$276$		0			0
$277$	11.7705	−	20.3871i	0.707221	−	1.22494i	−0.258662	−	0.965968i	$-0.583282\pi$
$277$	11.7705	−	20.3871i	0.707221	−	1.22494i	0.965884	−	0.258976i	$-0.0833850\pi$
$278$		0			0
$279$	0.748677	−	24.6525i	0.0448221	−	1.47591i
$280$		0			0
$281$	9.66048	+	16.7324i	0.576296	+	0.998173i	0.995900	+	0.0904661i	$0.0288357\pi$
$281$	9.66048	+	16.7324i	0.576296	+	0.998173i	−0.419604	+	0.907707i	$0.637831\pi$
$282$		0			0
$283$	−4.45316			−0.264713			−0.132356	−	0.991202i	$-0.542254\pi$
$283$	−4.45316			−0.264713			−0.132356	+	0.991202i	$0.542254\pi$
$284$		0			0
$285$	−13.6989	−	14.1212i	−0.811451	−	0.836468i
$286$		0			0
$287$	3.39426	+	27.9279i	0.200357	+	1.64853i
$288$		0			0
$289$	7.48119	−	12.9578i	0.440070	−	0.762224i
$290$		0			0
$291$	0.874220	−	3.07514i	0.0512477	−	0.180268i
$292$		0			0
$293$	−11.7314	+	20.3193i	−0.685354	+	1.18707i	0.287972	+	0.957639i	$0.407019\pi$
$293$	−11.7314	+	20.3193i	−0.685354	+	1.18707i	−0.973325	+	0.229429i	$0.926314\pi$
$294$		0			0
$295$	−10.8125	−	18.7278i	−0.629529	−	1.09038i
$296$		0			0
$297$	−3.41837	−	15.5596i	−0.198354	−	0.902861i
$298$		0			0
$299$	16.1943			0.936539
$300$		0			0
$301$	14.5292	+	6.18836i	0.837446	+	0.356691i
$302$		0			0
$303$	−13.5438	+	3.40958i	−0.778072	+	0.195875i
$304$		0			0
$305$	0.855817	+	1.48232i	0.0490039	+	0.0848773i
$306$		0			0
$307$	7.79955			0.445144			0.222572	−	0.974916i	$-0.428555\pi$
$307$	7.79955			0.445144			0.222572	+	0.974916i	$0.428555\pi$
$308$		0			0
$309$	8.42999	−	29.6531i	0.479565	−	1.68691i
$310$		0			0
$311$	14.9890			0.849947			0.424974	−	0.905206i	$-0.360283\pi$
$311$	14.9890			0.849947			0.424974	+	0.905206i	$0.360283\pi$
$312$		0			0
$313$	6.92663			0.391517			0.195758	−	0.980652i	$-0.437283\pi$
$313$	6.92663			0.391517			0.195758	+	0.980652i	$0.437283\pi$
$314$		0			0
$315$	−6.33806	+	13.7106i	−0.357109	+	0.772503i
$316$		0			0
$317$	10.8574			0.609815			0.304907	−	0.952382i	$-0.401374\pi$
$317$	10.8574			0.609815			0.304907	+	0.952382i	$0.401374\pi$
$318$		0			0
$319$	2.87065			0.160726
$320$		0			0
$321$	−29.4275	+	7.40821i	−1.64249	+	0.413486i
$322$		0			0
$323$	−8.52027			−0.474081
$324$		0			0
$325$	−1.55999	−	2.70199i	−0.0865328	−	0.149879i
$326$		0			0
$327$	1.05564	−	3.71329i	0.0583770	−	0.205345i
$328$		0			0
$329$	−2.04448	+	1.53668i	−0.112716	+	0.0847202i
$330$		0			0
$331$	−8.05169			−0.442561			−0.221280	−	0.975210i	$-0.571024\pi$
$331$	−8.05169			−0.442561			−0.221280	+	0.975210i	$0.571024\pi$
$332$		0			0
$333$	−7.22285	−	4.46780i	−0.395810	−	0.244834i
$334$		0			0
$335$	1.54869	+	2.68240i	0.0846138	+	0.146555i
$336$		0			0
$337$	11.4293	−	19.7961i	0.622594	−	1.07836i	−0.366407	−	0.930455i	$-0.619412\pi$
$337$	11.4293	−	19.7961i	0.622594	−	1.07836i	0.989001	−	0.147909i	$-0.0472543\pi$
$338$		0			0
$339$	25.5306	−	6.42717i	1.38663	−	0.349076i
$340$		0			0
$341$	−12.6027	+	21.8285i	−0.682474	+	1.18208i
$342$		0			0
$343$	−6.57324	−	17.3145i	−0.354922	−	0.934896i
$344$		0			0
$345$	22.8714	−	5.75775i	1.23136	−	0.309987i
$346$		0			0
$347$	25.7784			1.38386			0.691928	−	0.721967i	$-0.256762\pi$
$347$	25.7784			1.38386			0.691928	+	0.721967i	$0.256762\pi$
$348$		0			0
$349$	6.90108	+	11.9530i	0.369406	+	0.639830i	0.989473	−	0.144719i	$-0.0462277\pi$
$349$	6.90108	+	11.9530i	0.369406	+	0.639830i	−0.620067	+	0.784549i	$0.712894\pi$
$350$		0			0
$351$	−2.52344	−	11.4861i	−0.134691	−	0.613082i
$352$		0			0
$353$	12.4514	−	21.5665i	0.662721	−	1.14787i	−0.317177	−	0.948366i	$-0.602735\pi$
$353$	12.4514	−	21.5665i	0.662721	−	1.14787i	0.979898	−	0.199500i	$-0.0639318\pi$
$354$		0			0
$355$	−2.24914	−	3.89563i	−0.119372	−	0.206759i
$356$		0			0
$357$	2.35060	+	6.10448i	0.124407	+	0.323083i
$358$		0			0
$359$	10.6980	−	18.5295i	0.564620	−	0.977951i	−0.432465	−	0.901651i	$-0.642356\pi$
$359$	10.6980	−	18.5295i	0.564620	−	0.977951i	0.997085	−	0.0763002i	$-0.0243107\pi$
$360$		0			0
$361$	−8.31371	−	14.3998i	−0.437564	−	0.757883i
$362$		0			0
$363$	0.758036	−	2.66645i	0.0397866	−	0.139952i
$364$		0			0
$365$	1.89594	−	3.28386i	0.0992380	−	0.171885i
$366$		0			0
$367$	5.75791	−	9.97299i	0.300560	−	0.520586i	−0.675703	−	0.737174i	$-0.736160\pi$
$367$	5.75791	−	9.97299i	0.300560	−	0.520586i	0.976263	+	0.216589i	$0.0694930\pi$
$368$		0			0
$369$	−27.1296	−	16.7814i	−1.41231	−	0.873606i
$370$		0			0
$371$	26.5392	+	11.3038i	1.37785	+	0.586861i
$372$		0			0
$373$	0.846990	+	1.46703i	0.0438555	+	0.0759599i	0.887120	−	0.461539i	$-0.152703\pi$
$373$	0.846990	+	1.46703i	0.0438555	+	0.0759599i	−0.843264	+	0.537499i	$0.819369\pi$
$374$		0			0
$375$	−14.6391	−	15.0905i	−0.755961	−	0.779268i
$376$		0			0
$377$	2.11911			0.109140
$378$		0			0
$379$	8.50319			0.436780			0.218390	−	0.975862i	$-0.429920\pi$
$379$	8.50319			0.436780			0.218390	+	0.975862i	$0.429920\pi$
$380$		0			0
$381$	20.4182	+	21.0477i	1.04605	+	1.07831i
$382$		0			0
$383$	6.39094	+	11.0694i	0.326562	+	0.565622i	0.981827	−	0.189777i	$-0.0607765\pi$
$383$	6.39094	+	11.0694i	0.326562	+	0.565622i	−0.655265	+	0.755399i	$0.727443\pi$
$384$		0			0
$385$	12.3394	−	9.27461i	0.628872	−	0.472678i
$386$		0			0
$387$	−15.7722	+	8.47845i	−0.801747	+	0.430984i
$388$		0			0
$389$	−1.77980	+	3.08270i	−0.0902393	+	0.156299i	−0.907612	−	0.419811i	$-0.862097\pi$
$389$	−1.77980	+	3.08270i	−0.0902393	+	0.156299i	0.817372	+	0.576110i	$0.195430\pi$
$390$		0			0
$391$	5.10701	−	8.84560i	0.258273	−	0.447341i
$392$		0			0
$393$	−1.12892	+	3.97106i	−0.0569464	+	0.200313i
$394$		0			0
$395$	−7.93448	−	13.7429i	−0.399227	−	0.691482i
$396$		0			0
$397$	11.0411	−	19.1238i	0.554138	−	0.959795i	−0.443832	−	0.896110i	$-0.646381\pi$
$397$	11.0411	−	19.1238i	0.554138	−	0.959795i	0.997970	−	0.0636848i	$-0.0202852\pi$
$398$		0			0
$399$	−17.1915	+	21.2751i	−0.860651	+	1.06509i
$400$		0			0
$401$	−1.29927	−	2.25040i	−0.0648823	−	0.112379i	0.831759	−	0.555136i	$-0.187334\pi$
$401$	−1.29927	−	2.25040i	−0.0648823	−	0.112379i	−0.896642	+	0.442757i	$0.854001\pi$
$402$		0			0
$403$	−9.30328	+	16.1138i	−0.463429	+	0.802683i
$404$		0			0
$405$	−7.64768	−	15.3248i	−0.380016	−	0.761495i
$406$		0			0
$407$	4.33973	+	7.51662i	0.215112	+	0.372585i
$408$		0			0
$409$	3.03208			0.149926			0.0749632	−	0.997186i	$-0.476116\pi$
$409$	3.03208			0.149926			0.0749632	+	0.997186i	$0.476116\pi$
$410$		0			0
$411$	18.4458	−	4.64363i	0.909866	−	0.229053i
$412$		0			0
$413$	−24.0334	+	18.0642i	−1.18261	+	0.888881i
$414$		0			0
$415$	15.1899	−	26.3096i	0.745641	−	1.29149i
$416$		0			0
$417$	12.4436	−	3.13259i	0.609364	−	0.153404i
$418$		0			0
$419$	−17.4979	+	30.3073i	−0.854829	+	1.48061i	0.0219749	+	0.999759i	$0.493005\pi$
$419$	−17.4979	+	30.3073i	−0.854829	+	1.48061i	−0.876804	+	0.480848i	$0.840329\pi$
$420$		0			0
$421$	13.3264	+	23.0820i	0.649488	+	1.12495i	0.983245	+	0.182288i	$0.0583502\pi$
$421$	13.3264	+	23.0820i	0.649488	+	1.12495i	−0.333757	+	0.942659i	$0.608316\pi$
$422$		0			0
$423$	0.0880313	−	2.89870i	0.00428023	−	0.140940i
$424$		0			0
$425$	−1.96783			−0.0954539
$426$		0			0
$427$	1.90226	−	1.42979i	0.0920568	−	0.0691925i
$428$		0			0
$429$	−3.28639	+	11.5601i	−0.158669	+	0.558129i
$430$		0			0
$431$	−8.77241	−	15.1943i	−0.422552	−	0.731882i	0.573636	−	0.819110i	$-0.305532\pi$
$431$	−8.77241	−	15.1943i	−0.422552	−	0.731882i	−0.996188	+	0.0872286i	$0.972199\pi$
$432$		0			0
$433$	−18.0202			−0.865997			−0.432998	−	0.901395i	$-0.642544\pi$
$433$	−18.0202			−0.865997			−0.432998	+	0.901395i	$0.642544\pi$
$434$		0			0
$435$	2.99286	−	0.753434i	0.143496	−	0.0361244i
$436$		0			0
$437$	42.7098			2.04309
$438$		0			0
$439$	37.4319			1.78653			0.893263	−	0.449535i	$-0.148410\pi$
$439$	37.4319			1.78653			0.893263	+	0.449535i	$0.148410\pi$
$440$		0			0
$441$	19.9857	+	6.44765i	0.951699	+	0.307031i
$442$		0			0
$443$	7.34324			0.348888			0.174444	−	0.984667i	$-0.444187\pi$
$443$	7.34324			0.348888			0.174444	+	0.984667i	$0.444187\pi$
$444$		0			0
$445$	−9.85726			−0.467279
$446$		0			0
$447$	−8.34725	+	29.3621i	−0.394812	+	1.38878i
$448$		0			0
$449$	−40.3618			−1.90479			−0.952395	−	0.304866i	$-0.901388\pi$
$449$	−40.3618			−1.90479			−0.952395	+	0.304866i	$0.901388\pi$
$450$		0			0
$451$	16.3003	+	28.2330i	0.767553	+	1.32944i
$452$		0			0
$453$	−34.2083	+	8.61174i	−1.60725	+	0.404615i
$454$		0			0
$455$	9.10890	−	6.84650i	0.427032	−	0.320969i
$456$		0			0
$457$	−27.4720			−1.28509			−0.642543	−	0.766250i	$-0.722120\pi$
$457$	−27.4720			−1.28509			−0.642543	+	0.766250i	$0.722120\pi$
$458$		0			0
$459$	−7.06969	−	2.24389i	−0.329985	−	0.104736i
$460$		0			0
$461$	−3.36325	−	5.82532i	−0.156642	−	0.271312i	0.777014	−	0.629484i	$-0.216734\pi$
$461$	−3.36325	−	5.82532i	−0.156642	−	0.271312i	−0.933656	+	0.358172i	$0.883400\pi$
$462$		0			0
$463$	1.89569	−	3.28344i	0.0881004	−	0.152594i	−0.818608	−	0.574353i	$-0.805254\pi$
$463$	1.89569	−	3.28344i	0.0881004	−	0.152594i	0.906708	+	0.421759i	$0.138587\pi$
$464$		0			0
$465$	−7.41005	+	26.0654i	−0.343633	+	1.20875i
$466$		0			0
$467$	10.2166	−	17.6957i	0.472769	−	0.818860i	−0.526746	−	0.850023i	$-0.676588\pi$
$467$	10.2166	−	17.6957i	0.472769	−	0.818860i	0.999514	+	0.0311635i	$0.00992126\pi$
$468$		0			0
$469$	3.44233	−	2.58735i	0.158952	−	0.119473i
$470$		0			0
$471$	−11.1946	−	11.5398i	−0.515822	−	0.531725i
$472$		0			0
$473$	18.2997			0.841423
$474$		0			0
$475$	−4.11423	−	7.12606i	−0.188774	−	0.326966i
$476$		0			0
$477$	−28.8098	+	15.4869i	−1.31911	+	0.709095i
$478$		0			0
$479$	−13.9539	+	24.1689i	−0.637572	+	1.10431i	0.348392	+	0.937349i	$0.386728\pi$
$479$	−13.9539	+	24.1689i	−0.637572	+	1.10431i	−0.985964	+	0.166958i	$0.946606\pi$
$480$		0			0
$481$	3.20358	+	5.54876i	0.146071	+	0.253002i
$482$		0			0
$483$	−11.7829	−	30.6001i	−0.536142	−	1.39235i
$484$		0			0
$485$	−1.75627	+	3.04194i	−0.0797480	+	0.138128i
$486$		0			0
$487$	−5.89480	−	10.2101i	−0.267119	−	0.462663i	0.700998	−	0.713163i	$-0.252738\pi$
$487$	−5.89480	−	10.2101i	−0.267119	−	0.462663i	−0.968117	+	0.250500i	$0.919405\pi$
$488$		0			0
$489$	39.9988	−	10.0695i	1.80881	−	0.455357i
$490$		0			0
$491$	13.2596	−	22.9662i	0.598396	−	1.03645i	−0.394662	−	0.918826i	$-0.629138\pi$
$491$	13.2596	−	22.9662i	0.598396	−	1.03645i	0.993058	−	0.117626i	$-0.0375283\pi$
$492$		0			0
$493$	0.668281	−	1.15750i	0.0300979	−	0.0521310i
$494$		0			0
$495$	−0.531310	+	17.4950i	−0.0238806	+	0.786343i
$496$		0			0
$497$	−4.99927	+	3.75759i	−0.224248	+	0.168551i
$498$		0			0
$499$	−21.1664	−	36.6614i	−0.947540	−	1.64119i	−0.750584	−	0.660776i	$-0.770227\pi$
$499$	−21.1664	−	36.6614i	−0.947540	−	1.64119i	−0.196957	−	0.980412i	$-0.563106\pi$
$500$		0			0
$501$	2.96795	−	0.747163i	0.132598	−	0.0333808i
$502$		0			0
$503$	11.0768			0.493890			0.246945	−	0.969029i	$-0.420573\pi$
$503$	11.0768			0.493890			0.246945	+	0.969029i	$0.420573\pi$
$504$		0			0
$505$	15.3449			0.682839
$506$		0			0
$507$	3.73120	−	13.1248i	0.165708	−	0.582892i
$508$		0			0
$509$	−12.3631	−	21.4135i	−0.547984	−	0.949136i	−0.998413	−	0.0563236i	$-0.982062\pi$
$509$	−12.3631	−	21.4135i	−0.547984	−	0.949136i	0.450429	−	0.892812i	$-0.351271\pi$
$510$		0			0
$511$	−4.85023	−	2.06584i	−0.214561	−	0.0913875i
$512$		0			0
$513$	−6.65517	−	30.2927i	−0.293833	−	1.33746i
$514$		0			0
$515$	−16.9355	+	29.3331i	−0.746265	+	1.29257i
$516$		0			0
$517$	−1.48185	+	2.56665i	−0.0651719	+	0.112881i
$518$		0			0
$519$	−0.434284	−	0.447673i	−0.0190629	−	0.0196507i
$520$		0			0
$521$	6.42298	+	11.1249i	0.281396	+	0.487392i	0.971729	−	0.236100i	$-0.0758693\pi$
$521$	6.42298	+	11.1249i	0.281396	+	0.487392i	−0.690333	+	0.723492i	$0.742536\pi$
$522$		0			0
$523$	−1.70453	+	2.95234i	−0.0745340	+	0.129097i	−0.900884	−	0.434061i	$-0.857080\pi$
$523$	−1.70453	+	2.95234i	−0.0745340	+	0.129097i	0.826350	+	0.563158i	$0.190414\pi$
$524$		0			0
$525$	−3.97052	+	4.91367i	−0.173288	+	0.214450i
$526$		0			0
$527$	5.86775	+	10.1632i	0.255603	+	0.442718i
$528$		0			0
$529$	−14.1001	+	24.4221i	−0.613047	+	1.06183i
$530$		0			0
$531$	1.03483	−	34.0751i	0.0449080	−	1.47873i
$532$		0			0
$533$	12.0329	+	20.8416i	0.521202	+	0.902748i
$534$		0			0
$535$	33.3409			1.44145
$536$		0			0
$537$	−3.38837	+	11.9188i	−0.146219	+	0.514336i
$538$		0			0
$539$	−14.8701	−	15.4744i	−0.640500	−	0.666530i
$540$		0			0
$541$	−22.9553	+	39.7598i	−0.986926	+	1.70941i	−0.353884	+	0.935289i	$0.615139\pi$
$541$	−22.9553	+	39.7598i	−0.986926	+	1.70941i	−0.633043	+	0.774117i	$0.718194\pi$
$542$		0			0
$543$	−13.3315	−	13.7425i	−0.572108	−	0.589746i
$544$		0			0
$545$	−2.12073	+	3.67321i	−0.0908421	+	0.157343i
$546$		0			0
$547$	−12.5502	−	21.7376i	−0.536608	−	0.929432i	−0.999084	−	0.0428004i	$-0.986372\pi$
$547$	−12.5502	−	21.7376i	−0.536608	−	0.929432i	0.462476	−	0.886632i	$-0.346961\pi$
$548$		0			0
$549$	−0.0819077	+	2.69707i	−0.00349574	+	0.115108i
$550$		0			0
$551$	5.58882			0.238092
$552$		0			0
$553$	−17.6363	+	13.2559i	−0.749972	+	0.563700i
$554$		0			0
$555$	6.49728	+	6.69759i	0.275794	+	0.284297i
$556$		0			0
$557$	0.836144	+	1.44824i	0.0354285	+	0.0613640i	0.883196	−	0.469004i	$-0.155387\pi$
$557$	0.836144	+	1.44824i	0.0354285	+	0.0613640i	−0.847767	+	0.530368i	$0.822054\pi$
$558$		0			0
$559$	13.5088			0.571363
$560$		0			0
$561$	5.27796	+	5.44068i	0.222836	+	0.229706i
$562$		0			0
$563$	−22.7529			−0.958920			−0.479460	−	0.877564i	$-0.659167\pi$
$563$	−22.7529			−0.958920			−0.479460	+	0.877564i	$0.659167\pi$
$564$		0			0
$565$	−28.9257			−1.21691
$566$		0			0
$567$	−19.8676	+	13.1255i	−0.834362	+	0.551217i
$568$		0			0
$569$	−26.0585			−1.09243			−0.546214	−	0.837646i	$-0.683932\pi$
$569$	−26.0585			−1.09243			−0.546214	+	0.837646i	$0.683932\pi$
$570$		0			0
$571$	12.4835			0.522418			0.261209	−	0.965282i	$-0.415879\pi$
$571$	12.4835			0.522418			0.261209	+	0.965282i	$0.415879\pi$
$572$		0			0
$573$	10.4943	+	10.8179i	0.438407	+	0.451923i
$574$		0			0
$575$	9.86421			0.411366
$576$		0			0
$577$	−10.3756	−	17.9710i	−0.431941	−	0.748143i	0.565100	−	0.825023i	$-0.308838\pi$
$577$	−10.3756	−	17.9710i	−0.431941	−	0.748143i	−0.997040	+	0.0768793i	$0.975504\pi$
$578$		0			0
$579$	1.71168	+	1.76445i	0.0711350	+	0.0733281i
$580$		0			0
$581$	−38.8590	−	16.5511i	−1.61214	−	0.686654i
$582$		0			0
$583$	33.4266			1.38439
$584$		0			0
$585$	−0.392212	+	12.9148i	−0.0162160	+	0.533961i
$586$		0			0
$587$	8.67294	+	15.0220i	0.357971	+	0.620023i	0.987622	−	0.156855i	$-0.0501355\pi$
$587$	8.67294	+	15.0220i	0.357971	+	0.620023i	−0.629651	+	0.776878i	$0.716802\pi$
$588$		0			0
$589$	−24.5359	+	42.4975i	−1.01099	+	1.75108i
$590$		0			0
$591$	−6.86732	−	7.07905i	−0.282484	−	0.291193i
$592$		0			0
$593$	−14.0203	+	24.2839i	−0.575745	+	0.997220i	0.420215	+	0.907425i	$0.361955\pi$
$593$	−14.0203	+	24.2839i	−0.575745	+	0.997220i	−0.995960	+	0.0897956i	$0.971379\pi$
$594$		0			0
$595$	−0.867109	−	7.13455i	−0.0355480	−	0.292488i
$596$		0			0
$597$	2.47545	−	8.70759i	0.101314	−	0.356378i
$598$		0			0
$599$	23.2094			0.948310			0.474155	−	0.880441i	$-0.342754\pi$
$599$	23.2094			0.948310			0.474155	+	0.880441i	$0.342754\pi$
$600$		0			0
$601$	−0.348014	−	0.602779i	−0.0141958	−	0.0245878i	0.858840	−	0.512244i	$-0.171185\pi$
$601$	−0.348014	−	0.602779i	−0.0141958	−	0.0245878i	−0.873036	+	0.487656i	$0.837852\pi$
$602$		0			0
$603$	−0.148220	+	4.88061i	−0.00603599	+	0.198754i
$604$		0			0
$605$	−1.52286	+	2.63767i	−0.0619130	+	0.107237i
$606$		0			0
$607$	0.855327	+	1.48147i	0.0347166	+	0.0601310i	0.882862	−	0.469633i	$-0.155614\pi$
$607$	0.855327	+	1.48147i	0.0347166	+	0.0601310i	−0.848145	+	0.529764i	$0.822280\pi$
$608$		0			0
$609$	−1.54186	−	4.00419i	−0.0624794	−	0.162258i
$610$		0			0
$611$	−1.09390	+	1.89469i	−0.0442545	+	0.0766511i
$612$		0			0
$613$	1.77253	+	3.07010i	0.0715916	+	0.124000i	0.899599	−	0.436717i	$-0.143859\pi$
$613$	1.77253	+	3.07010i	0.0715916	+	0.124000i	−0.828007	+	0.560717i	$0.810525\pi$
$614$		0			0
$615$	24.4043	+	25.1567i	0.984076	+	1.01442i
$616$		0			0
$617$	5.58526	−	9.67395i	0.224854	−	0.389458i	−0.731422	−	0.681925i	$-0.761143\pi$
$617$	5.58526	−	9.67395i	0.224854	−	0.389458i	0.956276	+	0.292467i	$0.0944762\pi$
$618$		0			0
$619$	−9.60858	+	16.6425i	−0.386201	+	0.668920i	−0.991935	−	0.126747i	$-0.959546\pi$
$619$	−9.60858	+	16.6425i	−0.386201	+	0.668920i	0.605734	+	0.795667i	$0.292880\pi$
$620$		0			0
$621$	35.4385	+	11.2480i	1.42210	+	0.451368i
$622$		0			0
$623$	1.65344	+	13.6044i	0.0662436	+	0.545051i
$624$		0			0
$625$	8.10337	+	14.0355i	0.324135	+	0.561418i
$626$		0			0
$627$	−8.66734	+	30.4880i	−0.346140	+	1.21757i
$628$		0			0
$629$	4.04111			0.161130
$630$		0			0
$631$	−23.1101			−0.920000			−0.460000	−	0.887919i	$-0.652151\pi$
$631$	−23.1101			−0.920000			−0.460000	+	0.887919i	$0.652151\pi$
$632$		0			0
$633$	19.9232	−	5.01556i	0.791878	−	0.199351i
$634$		0			0
$635$	−16.1093	−	27.9020i	−0.639276	−	1.10726i
$636$		0			0
$637$	−10.9771	−	11.4232i	−0.434927	−	0.452603i
$638$		0			0
$639$	0.215259	−	7.08807i	0.00851552	−	0.280400i
$640$		0			0
$641$	10.1969	−	17.6615i	0.402753	−	0.697589i	−0.591304	−	0.806449i	$-0.701387\pi$
$641$	10.1969	−	17.6615i	0.402753	−	0.697589i	0.994057	+	0.108860i	$0.0347200\pi$
$642$		0			0
$643$	−1.31644	+	2.28015i	−0.0519154	+	0.0899202i	−0.890815	−	0.454366i	$-0.849866\pi$
$643$	−1.31644	+	2.28015i	−0.0519154	+	0.0899202i	0.838900	+	0.544286i	$0.183199\pi$
$644$		0			0
$645$	19.0788	−	4.80296i	0.751225	−	0.189117i
$646$		0			0
$647$	3.63856	+	6.30217i	0.143047	+	0.247764i	0.928642	−	0.370976i	$-0.120977\pi$
$647$	3.63856	+	6.30217i	0.143047	+	0.247764i	−0.785596	+	0.618740i	$0.787643\pi$
$648$		0			0
$649$	−17.4196	+	30.1717i	−0.683781	+	1.18434i
$650$		0			0
$651$	37.2170	+	5.85478i	1.45865	+	0.229467i
$652$		0			0
$653$	−11.4335	−	19.8035i	−0.447429	−	0.774970i	0.550789	−	0.834645i	$-0.314327\pi$
$653$	−11.4335	−	19.8035i	−0.447429	−	0.774970i	−0.998218	+	0.0596747i	$0.980994\pi$
$654$		0			0
$655$	2.26794	−	3.92819i	0.0886159	−	0.153487i
$656$		0			0
$657$	5.26520	−	2.83034i	0.205415	−	0.110422i
$658$		0			0
$659$	−3.59545	−	6.22750i	−0.140059	−	0.242589i	0.787460	−	0.616366i	$-0.211396\pi$
$659$	−3.59545	−	6.22750i	−0.140059	−	0.242589i	−0.927519	+	0.373777i	$0.878062\pi$
$660$		0			0
$661$	−34.4127			−1.33850			−0.669250	−	0.743037i	$-0.733385\pi$
$661$	−34.4127			−1.33850			−0.669250	+	0.743037i	$0.733385\pi$
$662$		0			0
$663$	3.89618	+	4.01630i	0.151315	+	0.155980i
$664$		0			0
$665$	24.0233	−	18.0566i	0.931583	−	0.700204i
$666$		0			0
$667$	−3.34991	+	5.80222i	−0.129709	+	0.224663i
$668$		0			0
$669$	11.6466	−	40.9678i	0.450283	−	1.58390i
$670$		0			0
$671$	1.37877	−	2.38811i	0.0532270	−	0.0921919i
$672$		0			0
$673$	3.46705	+	6.00511i	0.133645	+	0.231480i	0.925079	−	0.379775i	$-0.123998\pi$
$673$	3.46705	+	6.00511i	0.133645	+	0.231480i	−0.791434	+	0.611255i	$0.790665\pi$
$674$		0			0
$675$	−1.53707	−	6.99637i	−0.0591618	−	0.269290i
$676$		0			0
$677$	34.6027			1.32989			0.664945	−	0.746892i	$-0.268455\pi$
$677$	34.6027			1.32989			0.664945	+	0.746892i	$0.268455\pi$
$678$		0			0
$679$	4.49291	+	1.91365i	0.172422	+	0.0734392i
$680$		0			0
$681$	25.7287	−	6.47705i	0.985927	−	0.248201i
$682$		0			0
$683$	−19.1618	−	33.1892i	−0.733206	−	1.26995i	−0.955506	−	0.294971i	$-0.904690\pi$
$683$	−19.1618	−	33.1892i	−0.733206	−	1.26995i	0.222300	−	0.974978i	$-0.428643\pi$
$684$		0			0
$685$	−20.8988			−0.798502
$686$		0			0
$687$	−8.07350	+	28.3991i	−0.308023	+	1.08349i
$688$		0			0
$689$	24.6755			0.940061
$690$		0			0
$691$	−7.89906			−0.300495			−0.150247	−	0.988648i	$-0.548007\pi$
$691$	−7.89906			−0.300495			−0.150247	+	0.988648i	$0.548007\pi$
$692$		0			0
$693$	24.2348	−	2.20129i	0.920603	−	0.0836203i
$694$		0			0
$695$	−14.0983			−0.534780
$696$		0			0
$697$	15.1787			0.574935
$698$		0			0
$699$	−33.1983	+	8.35748i	−1.25568	+	0.316109i
$700$		0			0
$701$	−25.9291			−0.979329			−0.489664	−	0.871911i	$-0.662881\pi$
$701$	−25.9291			−0.979329			−0.489664	+	0.871911i	$0.662881\pi$
$702$		0			0
$703$	8.44893	+	14.6340i	0.318657	+	0.551931i
$704$		0			0
$705$	−0.871292	+	3.06483i	−0.0328147	+	0.115428i
$706$		0			0
$707$	−2.57392	−	21.1782i	−0.0968023	−	0.796488i
$708$		0			0
$709$	28.1047			1.05549			0.527746	−	0.849402i	$-0.323037\pi$
$709$	28.1047			1.05549			0.527746	+	0.849402i	$0.323037\pi$
$710$		0			0
$711$	0.759386	−	25.0051i	0.0284792	−	0.937766i
$712$		0			0
$713$	−29.4134	−	50.9456i	−1.10154	−	1.90793i
$714$		0			0
$715$	6.60221	−	11.4354i	0.246909	−	0.427658i
$716$		0			0
$717$	−28.0514	+	7.06178i	−1.04760	+	0.263727i
$718$		0			0
$719$	−5.89461	+	10.2098i	−0.219832	+	0.380760i	−0.954756	−	0.297389i	$-0.903884\pi$
$719$	−5.89461	+	10.2098i	−0.219832	+	0.380760i	0.734924	+	0.678149i	$0.237218\pi$
$720$		0			0
$721$	43.3246	+	18.4531i	1.61349	+	0.687229i
$722$		0			0
$723$	10.7496	−	2.70616i	0.399783	−	0.100643i
$724$		0			0
$725$	1.29079			0.0479386
$726$		0			0
$727$	−24.5207	−	42.4711i	−0.909423	−	1.57517i	−0.814868	−	0.579647i	$-0.803191\pi$
$727$	−24.5207	−	42.4711i	−0.909423	−	1.57517i	−0.0945549	−	0.995520i	$-0.530143\pi$
$728$		0			0
$729$	2.45575	−	26.8881i	0.0909537	−	0.995855i
$730$		0			0
$731$	4.26014	−	7.37877i	0.157567	−	0.272914i
$732$		0			0
$733$	−7.54634	−	13.0706i	−0.278731	−	0.482775i	0.692339	−	0.721572i	$-0.256580\pi$
$733$	−7.54634	−	13.0706i	−0.278731	−	0.482775i	−0.971070	+	0.238797i	$0.923247\pi$
$734$		0			0
$735$	−19.5645	−	12.2303i	−0.721648	−	0.451122i
$736$		0			0
$737$	2.49503	−	4.32152i	0.0919056	−	0.159185i
$738$		0			0
$739$	15.9556	+	27.6359i	0.586937	+	1.01660i	0.994631	+	0.103486i	$0.0329996\pi$
$739$	15.9556	+	27.6359i	0.586937	+	1.01660i	−0.407694	+	0.913119i	$0.633667\pi$
$740$		0			0
$741$	−6.39821	+	22.5062i	−0.235044	+	0.826786i
$742$		0			0
$743$	12.1582	−	21.0586i	0.446041	−	0.772565i	−0.552083	−	0.833789i	$-0.686167\pi$
$743$	12.1582	−	21.0586i	0.446041	−	0.772565i	0.998124	+	0.0612238i	$0.0195003\pi$
$744$		0			0
$745$	16.7692	−	29.0452i	0.614377	−	1.06413i
$746$		0			0
$747$	42.1836	−	22.6760i	1.54342	−	0.829673i
$748$		0			0
$749$	−5.59253	−	46.0152i	−0.204347	−	1.68136i
$750$		0			0
$751$	16.7232	+	28.9654i	0.610237	+	1.05696i	0.991200	+	0.132371i	$0.0422591\pi$
$751$	16.7232	+	28.9654i	0.610237	+	1.05696i	−0.380963	+	0.924590i	$0.624408\pi$
$752$		0			0
$753$	32.3628	+	33.3606i	1.17937	+	1.21573i
$754$		0			0
$755$	38.7574			1.41053
$756$		0			0
$757$	−32.1248			−1.16759			−0.583797	−	0.811899i	$-0.698434\pi$
$757$	−32.1248			−1.16759			−0.583797	+	0.811899i	$0.698434\pi$
$758$		0			0
$759$	−26.4570	−	27.2727i	−0.960328	−	0.989935i
$760$		0			0
$761$	−16.8978	−	29.2679i	−0.612547	−	1.06096i	−0.990810	−	0.135264i	$-0.956812\pi$
$761$	−16.8978	−	29.2679i	−0.612547	−	1.06096i	0.378263	−	0.925698i	$-0.376521\pi$
$762$		0			0
$763$	5.42529	+	2.31078i	0.196409	+	0.0836557i
$764$		0			0
$765$	6.93060	+	4.28703i	0.250576	+	0.154998i
$766$		0			0
$767$	−12.8591	+	22.2727i	−0.464317	+	0.804221i
$768$		0			0
$769$	16.8957	−	29.2643i	0.609276	−	1.05530i	−0.382084	−	0.924128i	$-0.624793\pi$
$769$	16.8957	−	29.2643i	0.609276	−	1.05530i	0.991360	−	0.131170i	$-0.0418733\pi$
$770$		0			0
$771$	−3.39877	+	11.9554i	−0.122404	+	0.430564i
$772$		0			0
$773$	−12.0231	−	20.8247i	−0.432443	−	0.749012i	0.564640	−	0.825337i	$-0.309015\pi$
$773$	−12.0231	−	20.8247i	−0.432443	−	0.749012i	−0.997083	+	0.0763245i	$0.975682\pi$
$774$		0			0
$775$	−5.66679	+	9.81516i	−0.203557	+	0.352571i
$776$		0			0
$777$	8.15381	−	10.0906i	0.292516	−	0.361999i
$778$		0			0
$779$	31.7348	+	54.9663i	1.13702	+	1.96937i
$780$		0			0
$781$	−3.62351	+	6.27611i	−0.129659	+	0.224577i
$782$		0			0
$783$	4.63732	+	1.47187i	0.165724	+	0.0526003i
$784$		0			0
$785$	8.83219	+	15.2978i	0.315234	+	0.546002i
$786$		0			0
$787$	−6.45794			−0.230201			−0.115100	−	0.993354i	$-0.536719\pi$
$787$	−6.45794			−0.230201			−0.115100	+	0.993354i	$0.536719\pi$
$788$		0			0
$789$	34.2878	−	8.63175i	1.22068	−	0.307298i
$790$		0			0
$791$	4.85193	+	39.9216i	0.172515	+	1.41945i
$792$		0			0
$793$	1.01781	−	1.76290i	0.0361435	−	0.0626023i
$794$		0			0
$795$	34.8496	−	8.77317i	1.23599	−	0.311152i
$796$		0			0
$797$	18.6987	−	32.3871i	0.662341	−	1.14721i	−0.317658	−	0.948205i	$-0.602896\pi$
$797$	18.6987	−	32.3871i	0.662341	−	1.14721i	0.979999	−	0.199003i	$-0.0637704\pi$
$798$		0			0
$799$	0.689944	+	1.19502i	0.0244085	+	0.0422767i
$800$		0			0
$801$	−13.2155	−	8.17468i	−0.466948	−	0.288838i
$802$		0			0
$803$	−6.10896			−0.215580
$804$		0			0
$805$	4.34658	+	35.7636i	0.153197	+	1.26050i
$806$		0			0
$807$	−3.19466	+	11.2375i	−0.112457	+	0.395577i
$808$		0			0
$809$	−20.0048	−	34.6493i	−0.703331	−	1.21821i	−0.967290	−	0.253672i	$-0.918362\pi$
$809$	−20.0048	−	34.6493i	−0.703331	−	1.21821i	0.263959	−	0.964534i	$-0.414972\pi$
$810$		0			0
$811$	−27.6946			−0.972489			−0.486245	−	0.873823i	$-0.661634\pi$
$811$	−27.6946			−0.972489			−0.486245	+	0.873823i	$0.661634\pi$
$812$		0			0
$813$	3.51490	−	0.884855i	0.123273	−	0.0310332i
$814$		0			0
$815$	−45.3179			−1.58742
$816$		0			0
$817$	35.6274			1.24645
$818$		0			0
$819$	17.8901	−	1.62499i	0.625129	−	0.0567818i
$820$		0			0
$821$	−0.377464			−0.0131736			−0.00658679	−	0.999978i	$-0.502097\pi$
$821$	−0.377464			−0.0131736			−0.00658679	+	0.999978i	$0.502097\pi$
$822$		0			0
$823$	11.0063			0.383654			0.191827	−	0.981429i	$-0.438559\pi$
$823$	11.0063			0.383654			0.191827	+	0.981429i	$0.438559\pi$
$824$		0			0
$825$	−2.00180	+	7.04148i	−0.0696937	+	0.245153i
$826$		0			0
$827$	28.2473			0.982254			0.491127	−	0.871088i	$-0.336585\pi$
$827$	28.2473			0.982254			0.491127	+	0.871088i	$0.336585\pi$
$828$		0			0
$829$	−14.7833	−	25.6054i	−0.513445	−	0.889313i	−0.999878	−	0.0155953i	$-0.995036\pi$
$829$	−14.7833	−	25.6054i	−0.513445	−	0.889313i	0.486433	−	0.873718i	$-0.338298\pi$
$830$		0			0
$831$	−39.5406	+	9.95410i	−1.37165	+	0.345304i
$832$		0			0
$833$	−9.70126	+	2.39347i	−0.336129	+	0.0829288i
$834$		0			0
$835$	−3.36263			−0.116369
$836$		0			0
$837$	−31.5508	+	28.8005i	−1.09055	+	0.995491i
$838$		0			0
$839$	6.91508	+	11.9773i	0.238735	+	0.413501i	0.960352	−	0.278792i	$-0.0899339\pi$
$839$	6.91508	+	11.9773i	0.238735	+	0.413501i	−0.721617	+	0.692293i	$0.756601\pi$
$840$		0			0
$841$	14.0616	−	24.3555i	0.484884	−	0.839844i
$842$		0			0
$843$	9.15101	−	32.1894i	0.315178	−	1.10866i
$844$		0			0
$845$	−7.49581	+	12.9831i	−0.257864	+	0.446633i
$846$		0			0
$847$	3.89581	+	1.65933i	0.133861	+	0.0570152i
$848$		0			0
$849$	5.37056	+	5.53614i	0.184317	+	0.190000i
$850$		0			0
$851$	−20.2570			−0.694401
$852$		0			0
$853$	4.59367	+	7.95647i	0.157284	+	0.272424i	0.933888	−	0.357565i	$-0.116393\pi$
$853$	4.59367	+	7.95647i	0.157284	+	0.272424i	−0.776604	+	0.629989i	$0.783059\pi$
$854$		0			0
$855$	−1.03440	+	34.0607i	−0.0353756	+	1.16485i
$856$		0			0
$857$	−20.2230	+	35.0273i	−0.690805	+	1.19651i	0.280770	+	0.959775i	$0.409410\pi$
$857$	−20.2230	+	35.0273i	−0.690805	+	1.19651i	−0.971575	+	0.236734i	$0.923923\pi$
$858$		0			0
$859$	6.25642	+	10.8364i	0.213466	+	0.369735i	0.952797	−	0.303608i	$-0.0981913\pi$
$859$	6.25642	+	10.8364i	0.213466	+	0.369735i	−0.739331	+	0.673343i	$0.764858\pi$
$860$		0			0
$861$	30.6263	−	37.9012i	1.04374	−	1.29167i
$862$		0			0
$863$	−11.8005	+	20.4391i	−0.401694	+	0.695755i	−0.993931	−	0.110010i	$-0.964912\pi$
$863$	−11.8005	+	20.4391i	−0.401694	+	0.695755i	0.592236	+	0.805764i	$0.298245\pi$
$864$		0			0
$865$	0.342635	+	0.593462i	0.0116499	+	0.0201783i
$866$		0			0
$867$	−25.1315	+	6.32670i	−0.853510	+	0.214866i
$868$		0			0
$869$	−12.7830	+	22.1407i	−0.433632	+	0.751073i
$870$		0			0
$871$	1.84183	−	3.19014i	0.0624079	−	0.108094i
$872$		0			0
$873$	−4.87731	+	2.62183i	−0.165072	+	0.0887354i
$874$		0			0
$875$	25.6722	−	19.2959i	0.867878	−	0.652322i
$876$		0			0
$877$	13.7733	+	23.8561i	0.465092	+	0.805564i	0.999206	−	0.0398493i	$-0.0126878\pi$
$877$	13.7733	+	23.8561i	0.465092	+	0.805564i	−0.534113	+	0.845413i	$0.679354\pi$
$878$		0			0
$879$	39.4091	−	9.92100i	1.32923	−	0.334627i
$880$		0			0
$881$	42.0894			1.41803			0.709014	−	0.705194i	$-0.249140\pi$
$881$	42.0894			1.41803			0.709014	+	0.705194i	$0.249140\pi$
$882$		0			0
$883$	8.58158			0.288793			0.144397	−	0.989520i	$-0.453876\pi$
$883$	8.58158			0.288793			0.144397	+	0.989520i	$0.453876\pi$
$884$		0			0
$885$	−10.2423	+	36.0281i	−0.344291	+	1.21107i
$886$		0			0
$887$	−1.75954	−	3.04761i	−0.0590795	−	0.102329i	0.834973	−	0.550291i	$-0.185483\pi$
$887$	−1.75954	−	3.04761i	−0.0590795	−	0.102329i	−0.894052	+	0.447962i	$0.852150\pi$
$888$		0			0
$889$	−35.8067	+	26.9133i	−1.20092	+	0.902644i
$890$		0			0
$891$	−15.2210	+	23.0148i	−0.509924	+	0.771025i
$892$		0			0
$893$	−2.88499	+	4.99695i	−0.0965426	+	0.167217i
$894$		0			0
$895$	6.80707	−	11.7902i	0.227535	−	0.394103i
$896$		0			0
$897$	−19.5305	−	20.1326i	−0.652105	−	0.672209i
$898$		0			0
$899$	−3.84891	−	6.66651i	−0.128368	−	0.222341i
$900$		0			0
$901$	7.78163	−	13.4782i	0.259244	−	0.449023i
$902$		0			0
$903$	−9.82902	−	25.5258i	−0.327089	−	0.849445i
$904$		0			0
$905$	10.5181	+	18.2178i	0.349633	+	0.605582i
$906$		0			0
$907$	−18.6413	+	32.2876i	−0.618974	+	1.07209i	0.370700	+	0.928753i	$0.379118\pi$
$907$	−18.6413	+	32.2876i	−0.618974	+	1.07209i	−0.989673	+	0.143341i	$0.954215\pi$
$908$		0			0
$909$	20.5728	+	12.7256i	0.682356	+	0.422082i
$910$		0			0
$911$	−10.6458	−	18.4391i	−0.352711	−	0.610914i	0.634012	−	0.773323i	$-0.281407\pi$
$911$	−10.6458	−	18.4391i	−0.352711	−	0.610914i	−0.986723	+	0.162409i	$0.948074\pi$
$912$		0			0
$913$	−48.9436			−1.61980
$914$		0			0
$915$	0.810684	−	2.85164i	0.0268004	−	0.0942724i
$916$		0			0
$917$	−5.80190	−	2.47118i	−0.191595	−	0.0816056i
$918$		0			0
$919$	6.00453	−	10.4001i	0.198071	−	0.343069i	−0.749832	−	0.661628i	$-0.769866\pi$
$919$	6.00453	−	10.4001i	0.198071	−	0.343069i	0.947903	+	0.318559i	$0.103199\pi$
$920$		0			0
$921$	−9.40636	−	9.69636i	−0.309950	−	0.319506i
$922$		0			0
$923$	−2.67487	+	4.63301i	−0.0880444	+	0.152497i
$924$		0			0
$925$	1.95135	+	3.37984i	0.0641601	+	0.111129i
$926$		0			0
$927$	−47.0313	+	25.2819i	−1.54471	+	0.830368i
$928$		0			0
$929$	20.5204			0.673253			0.336626	−	0.941638i	$-0.390714\pi$
$929$	20.5204			0.673253			0.336626	+	0.941638i	$0.390714\pi$
$930$		0			0
$931$	−28.9503	−	30.1268i	−0.948807	−	0.987367i
$932$		0			0
$933$	−18.0769	−	18.6342i	−0.591811	−	0.610057i
$934$		0			0
$935$	−4.16413	−	7.21249i	−0.136182	−	0.235874i
$936$		0			0
$937$	−10.9040			−0.356217			−0.178109	−	0.984011i	$-0.556998\pi$
$937$	−10.9040			−0.356217			−0.178109	+	0.984011i	$0.556998\pi$
$938$		0			0
$939$	−8.35361	−	8.61115i	−0.272610	−	0.281014i
$940$		0			0
$941$	−30.9614			−1.00931			−0.504656	−	0.863320i	$-0.668381\pi$
$941$	−30.9614			−1.00931			−0.504656	+	0.863320i	$0.668381\pi$
$942$		0			0
$943$	−76.0868			−2.47773
$944$		0			0
$945$	24.6887	−	8.65568i	0.803123	−	0.281569i
$946$		0			0
$947$	−32.1818			−1.04577			−0.522884	−	0.852404i	$-0.675144\pi$
$947$	−32.1818			−1.04577			−0.522884	+	0.852404i	$0.675144\pi$
$948$		0			0
$949$	−4.50962			−0.146388
$950$		0			0
$951$	−13.0942	−	13.4979i	−0.424609	−	0.437700i
$952$		0			0
$953$	39.0934			1.26636			0.633179	−	0.774005i	$-0.281750\pi$
$953$	39.0934			1.26636			0.633179	+	0.774005i	$0.281750\pi$
$954$		0			0
$955$	−8.27967	−	14.3408i	−0.267924	−	0.464057i
$956$		0			0
$957$	−3.46205	−	3.56878i	−0.111912	−	0.115362i
$958$		0			0
$959$	3.50552	+	28.8434i	0.113199	+	0.931400i
$960$		0			0
$961$	36.5897			1.18031
$962$		0			0
$963$	44.6998	+	27.6498i	1.44043	+	0.891001i
$964$		0			0
$965$	−1.35046	−	2.33906i	−0.0434728	−	0.0752971i
$966$		0			0
$967$	−12.7235	+	22.0377i	−0.409159	+	0.708684i	−0.994796	−	0.101889i	$-0.967511\pi$
$967$	−12.7235	+	22.0377i	−0.409159	+	0.708684i	0.585637	+	0.810574i	$0.300845\pi$
$968$		0			0
$969$	10.2756	+	10.5924i	0.330098	+	0.340276i
$970$		0			0
$971$	8.81455	−	15.2673i	0.282872	−	0.489949i	−0.689219	−	0.724553i	$-0.742046\pi$
$971$	8.81455	−	15.2673i	0.282872	−	0.489949i	0.972091	+	0.234604i	$0.0753794\pi$
$972$		0			0
$973$	2.36482	+	19.4577i	0.0758128	+	0.623786i
$974$		0			0
$975$	−1.47772	+	5.19801i	−0.0473250	+	0.166469i
$976$		0			0
$977$	27.2538			0.871925			0.435963	−	0.899965i	$-0.356408\pi$
$977$	27.2538			0.871925			0.435963	+	0.899965i	$0.356408\pi$
$978$		0			0
$979$	7.94033	+	13.7531i	0.253774	+	0.439550i
$980$		0			0
$981$	−5.88946	+	3.16591i	−0.188036	+	0.101080i
$982$		0			0
$983$	10.3371	−	17.9043i	0.329701	−	0.571059i	−0.652751	−	0.757572i	$-0.726385\pi$
$983$	10.3371	−	17.9043i	0.329701	−	0.571059i	0.982452	+	0.186513i	$0.0597187\pi$
$984$		0			0
$985$	5.41809	+	9.38440i	0.172635	+	0.299012i
$986$		0			0
$987$	4.37606	+	0.688419i	0.139292	+	0.0219126i
$988$		0			0
$989$	−21.3549	+	36.9878i	−0.679047	+	1.17614i
$990$		0			0
$991$	−26.0081	−	45.0474i	−0.826175	−	1.43098i	−0.901018	−	0.433782i	$-0.857179\pi$
$991$	−26.0081	−	45.0474i	−0.826175	−	1.43098i	0.0748425	−	0.997195i	$-0.476155\pi$
$992$		0			0
$993$	9.71044	+	10.0098i	0.308151	+	0.317652i
$994$		0			0
$995$	−4.97307	+	8.61361i	−0.157657	+	0.273070i
$996$		0			0
$997$	4.64269	−	8.04137i	0.147035	−	0.254673i	−0.783095	−	0.621902i	$-0.786360\pi$
$997$	4.64269	−	8.04137i	0.147035	−	0.254673i	0.930130	+	0.367229i	$0.119694\pi$
$998$		0			0
$999$	3.15650	+	14.3676i	0.0998673	+	0.454572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.i.b.121.2	yes	14
3.2	odd	2		756.2.i.b.37.2		14
4.3	odd	2		1008.2.q.j.625.6		14
7.2	even	3		1764.2.j.g.589.7		14
7.3	odd	6		1764.2.l.i.949.4		14
7.4	even	3		252.2.l.b.193.4	yes	14
7.5	odd	6		1764.2.j.h.589.1		14
7.6	odd	2		1764.2.i.i.373.6		14
9.2	odd	6		756.2.l.b.289.6		14
9.4	even	3		2268.2.k.e.1297.6		14
9.5	odd	6		2268.2.k.f.1297.2		14
9.7	even	3		252.2.l.b.205.4	yes	14
12.11	even	2		3024.2.q.j.2305.2		14
21.2	odd	6		5292.2.j.h.1765.2		14
21.5	even	6		5292.2.j.g.1765.6		14
21.11	odd	6		756.2.l.b.361.6		14
21.17	even	6		5292.2.l.i.361.2		14
21.20	even	2		5292.2.i.i.1549.6		14
28.11	odd	6		1008.2.t.j.193.4		14
36.7	odd	6		1008.2.t.j.961.4		14
36.11	even	6		3024.2.t.j.289.6		14
63.2	odd	6		5292.2.j.h.3529.2		14
63.4	even	3		2268.2.k.e.1621.6		14
63.11	odd	6		756.2.i.b.613.2		14
63.16	even	3		1764.2.j.g.1177.7		14
63.20	even	6		5292.2.l.i.3313.2		14
63.25	even	3	inner	252.2.i.b.25.2	✓	14
63.32	odd	6		2268.2.k.f.1621.2		14
63.34	odd	6		1764.2.l.i.961.4		14
63.38	even	6		5292.2.i.i.2125.6		14
63.47	even	6		5292.2.j.g.3529.6		14
63.52	odd	6		1764.2.i.i.1537.6		14
63.61	odd	6		1764.2.j.h.1177.1		14
84.11	even	6		3024.2.t.j.1873.6		14
252.11	even	6		3024.2.q.j.2881.2		14
252.151	odd	6		1008.2.q.j.529.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.2	✓	14	63.25	even	3	inner
252.2.i.b.121.2	yes	14	1.1	even	1	trivial
252.2.l.b.193.4	yes	14	7.4	even	3
252.2.l.b.205.4	yes	14	9.7	even	3
756.2.i.b.37.2		14	3.2	odd	2
756.2.i.b.613.2		14	63.11	odd	6
756.2.l.b.289.6		14	9.2	odd	6
756.2.l.b.361.6		14	21.11	odd	6
1008.2.q.j.529.6		14	252.151	odd	6
1008.2.q.j.625.6		14	4.3	odd	2
1008.2.t.j.193.4		14	28.11	odd	6
1008.2.t.j.961.4		14	36.7	odd	6
1764.2.i.i.373.6		14	7.6	odd	2
1764.2.i.i.1537.6		14	63.52	odd	6
1764.2.j.g.589.7		14	7.2	even	3
1764.2.j.g.1177.7		14	63.16	even	3
1764.2.j.h.589.1		14	7.5	odd	6
1764.2.j.h.1177.1		14	63.61	odd	6
1764.2.l.i.949.4		14	7.3	odd	6
1764.2.l.i.961.4		14	63.34	odd	6
2268.2.k.e.1297.6		14	9.4	even	3
2268.2.k.e.1621.6		14	63.4	even	3
2268.2.k.f.1297.2		14	9.5	odd	6
2268.2.k.f.1621.2		14	63.32	odd	6
3024.2.q.j.2305.2		14	12.11	even	2
3024.2.q.j.2881.2		14	252.11	even	6
3024.2.t.j.289.6		14	36.11	even	6
3024.2.t.j.1873.6		14	84.11	even	6
5292.2.i.i.1549.6		14	21.20	even	2
5292.2.i.i.2125.6		14	63.38	even	6
5292.2.j.g.1765.6		14	21.5	even	6
5292.2.j.g.3529.6		14	63.47	even	6
5292.2.j.h.1765.2		14	21.2	odd	6
5292.2.j.h.3529.2		14	63.2	odd	6
5292.2.l.i.361.2		14	21.17	even	6
5292.2.l.i.3313.2		14	63.20	even	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20601 - 1.24319i) q^{3} +(0.951504 + 1.64805i) q^{5} +(2.11495 - 1.58965i) q^{7} +(-0.0910656 + 2.99862i) q^{9} +O(q^{10})\)	\(q+(-1.20601 - 1.24319i) q^{3} +(0.951504 + 1.64805i) q^{5} +(2.11495 - 1.58965i) q^{7} +(-0.0910656 + 2.99862i) q^{9} +(1.53293 - 2.65512i) q^{11} +(1.13161 - 1.96000i) q^{13} +(0.901324 - 3.17048i) q^{15} +(-0.713726 - 1.23621i) q^{17} +(2.98444 - 5.16919i) q^{19} +(-4.52690 - 0.712149i) q^{21} +(3.57771 + 6.19678i) q^{23} +(0.689282 - 1.19387i) q^{25} +(3.83769 - 3.50316i) q^{27} +(0.468164 + 0.810884i) q^{29} -8.22129 q^{31} +(-5.14956 + 1.29637i) q^{33} +(4.63221 + 1.97298i) q^{35} +(-1.41550 + 2.45171i) q^{37} +(-3.80140 + 0.956979i) q^{39} +(-5.31672 + 9.20883i) q^{41} +(2.98444 + 5.16919i) q^{43} +(-5.02853 + 2.70311i) q^{45} -0.966679 q^{47} +(1.94600 - 6.72407i) q^{49} +(-0.676086 + 2.37818i) q^{51} +(5.45142 + 9.44213i) q^{53} +5.83436 q^{55} +(-10.0256 + 2.52388i) q^{57} -11.3636 q^{59} +0.899436 q^{61} +(4.57416 + 6.48668i) q^{63} +4.30692 q^{65} +1.62762 q^{67} +(3.38904 - 11.9212i) q^{69} -2.36378 q^{71} +(-0.996286 - 1.72562i) q^{73} +(-2.31550 + 0.582912i) q^{75} +(-0.978644 - 8.05226i) q^{77} -8.33889 q^{79} +(-8.98341 - 0.546142i) q^{81} +(-7.98203 - 13.8253i) q^{83} +(1.35822 - 2.35251i) q^{85} +(0.443475 - 1.55996i) q^{87} +(-2.58992 + 4.48587i) q^{89} +(-0.722433 - 5.94416i) q^{91} +(9.91499 + 10.2207i) q^{93} +11.3588 q^{95} +(0.922890 + 1.59849i) q^{97} +(7.82208 + 4.83847i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9	\( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 11 q^{21} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 4 q^{33} - 19 q^{35} + 10 q^{37} - 2 q^{39} - 33 q^{41} + 7 q^{43} - 10 q^{45} + 6 q^{47} - 4 q^{49} - 13 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} + 28 q^{59} + 20 q^{61} + 33 q^{63} - 30 q^{65} - 12 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} - 44 q^{75} - 47 q^{77} + 20 q^{79} - 29 q^{81} - 25 q^{83} + 8 q^{85} + 28 q^{87} - 6 q^{89} + 2 q^{91} + 22 q^{93} + 56 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) \) 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 11 * q^21 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 4 * q^33 - 19 * q^35 + 10 * q^37 - 2 * q^39 - 33 * q^41 + 7 * q^43 - 10 * q^45 + 6 * q^47 - 4 * q^49 - 13 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 + 28 * q^59 + 20 * q^61 + 33 * q^63 - 30 * q^65 - 12 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 - 44 * q^75 - 47 * q^77 + 20 * q^79 - 29 * q^81 - 25 * q^83 + 8 * q^85 + 28 * q^87 - 6 * q^89 + 2 * q^91 + 22 * q^93 + 56 * q^95 - 18 * q^97 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more