LMFDB - Embedded newform 225.6.f.b.107.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,6,Mod(107,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("225.107");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	225.f (of order $4$, 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:	$36.0863594579$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 19978x^{16} + 11248353x^{12} + 1386043201x^{8} + 1477627450x^{4} + 332150625 $ x^20 + 19978x^16 + 11248353x^12 + 1386043201x^8 + 1477627450x^4 + 332150625
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{29}\cdot 3^{24}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.9
Root			$-0.658471 - 0.658471i$ of defining polynomial
Character	$\chi$	$=$	225.107
Dual form			225.6.f.b.143.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.73598 - 5.73598i) q^{2} -33.8030i q^{4} +(92.1304 + 92.1304i) q^{7} +(-10.3420 - 10.3420i) q^{8} +O(q^{10})$	\(q+(5.73598 - 5.73598i) q^{2} -33.8030i q^{4} +(92.1304 + 92.1304i) q^{7} +(-10.3420 - 10.3420i) q^{8} +126.118i q^{11} +(-415.539 + 415.539i) q^{13} +1056.92 q^{14} +963.053 q^{16} +(-1141.86 + 1141.86i) q^{17} +710.872i q^{19} +(723.410 + 723.410i) q^{22} +(3006.30 + 3006.30i) q^{23} +4767.05i q^{26} +(3114.29 - 3114.29i) q^{28} -7154.66 q^{29} +6943.51 q^{31} +(5855.00 - 5855.00i) q^{32} +13099.4i q^{34} +(6246.54 + 6246.54i) q^{37} +(4077.55 + 4077.55i) q^{38} -11335.2i q^{41} +(13033.3 - 13033.3i) q^{43} +4263.16 q^{44} +34488.1 q^{46} +(125.547 - 125.547i) q^{47} +169.034i q^{49} +(14046.5 + 14046.5i) q^{52} +(-1601.74 - 1601.74i) q^{53} -1905.63i q^{56} +(-41039.0 + 41039.0i) q^{58} +14819.1 q^{59} -42544.3 q^{61} +(39827.9 - 39827.9i) q^{62} -36350.7i q^{64} +(27389.5 + 27389.5i) q^{67} +(38598.3 + 38598.3i) q^{68} -29723.5i q^{71} +(-31397.3 + 31397.3i) q^{73} +71660.1 q^{74} +24029.6 q^{76} +(-11619.3 + 11619.3i) q^{77} +69868.2i q^{79} +(-65018.6 - 65018.6i) q^{82} +(-9923.69 - 9923.69i) q^{83} -149518. i q^{86} +(1304.31 - 1304.31i) q^{88} +3301.75 q^{89} -76567.6 q^{91} +(101622. - 101622. i) q^{92} -1440.27i q^{94} +(30659.8 + 30659.8i) q^{97} +(969.574 + 969.574i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 152 q^{7}+O(q^{10}) $ 20 * q - 152 * q^7	$ 20 q - 152 q^{7} - 1844 q^{13} - 6280 q^{16} + 6512 q^{22} - 29728 q^{28} + 43120 q^{31} + 37516 q^{37} - 5408 q^{43} + 118720 q^{46} + 285256 q^{52} - 274752 q^{58} + 163360 q^{61} + 302704 q^{67} - 146324 q^{73} + 760800 q^{76} + 305744 q^{82} - 355296 q^{88} + 499120 q^{91} + 362524 q^{97}+O(q^{100}) $ 20 * q - 152 * q^7 - 1844 * q^13 - 6280 * q^16 + 6512 * q^22 - 29728 * q^28 + 43120 * q^31 + 37516 * q^37 - 5408 * q^43 + 118720 * q^46 + 285256 * q^52 - 274752 * q^58 + 163360 * q^61 + 302704 * q^67 - 146324 * q^73 + 760800 * q^76 + 305744 * q^82 - 355296 * q^88 + 499120 * q^91 + 362524 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	5.73598	−	5.73598i	1.01399	−	1.01399i	0.0140874	−	0.999901i	$-0.495516\pi$
$2$	5.73598	−	5.73598i	1.01399	−	1.01399i	0.999901	−	0.0140874i	$-0.00448431\pi$
$3$		0			0
$3$		0			0
$4$		−	33.8030i		−	1.05634i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	92.1304	+	92.1304i	0.710654	+	0.710654i	0.966672	−	0.256018i	$-0.0824107\pi$
$7$	92.1304	+	92.1304i	0.710654	+	0.710654i	−0.256018	+	0.966672i	$0.582411\pi$
$8$	−10.3420	−	10.3420i	−0.0571321	−	0.0571321i
$9$		0			0
$10$		0			0
$11$			126.118i			0.314264i	0.987578	+	0.157132i	$0.0502248\pi$
$11$			126.118i			0.314264i	−0.987578	+	0.157132i	$0.949775\pi$
$12$		0			0
$13$	−415.539	+	415.539i	−0.681952	+	0.681952i	−0.960440	−	0.278488i	$-0.910167\pi$
$13$	−415.539	+	415.539i	−0.681952	+	0.681952i	0.278488	+	0.960440i	$0.410167\pi$
$14$	1056.92			1.44119
$15$		0			0
$16$	963.053			0.940481
$17$	−1141.86	+	1141.86i	−0.958277	+	0.958277i	−0.999164	−	0.0408872i	$-0.986982\pi$
$17$	−1141.86	+	1141.86i	−0.958277	+	0.958277i	0.0408872	+	0.999164i	$0.486982\pi$
$18$		0			0
$19$			710.872i			0.451760i	0.974155	+	0.225880i	$0.0725257\pi$
$19$			710.872i			0.451760i	−0.974155	+	0.225880i	$0.927474\pi$
$20$		0			0
$21$		0			0
$22$	723.410	+	723.410i	0.318660	+	0.318660i
$23$	3006.30	+	3006.30i	1.18498	+	1.18498i	0.978437	+	0.206546i	$0.0662224\pi$
$23$	3006.30	+	3006.30i	1.18498	+	1.18498i	0.206546	+	0.978437i	$0.433778\pi$
$24$		0			0
$25$		0			0
$26$			4767.05i			1.38298i
$27$		0			0
$28$	3114.29	−	3114.29i	0.750695	−	0.750695i
$29$	−7154.66			−1.57977			−0.789885	−	0.613255i	$-0.789860\pi$
$29$	−7154.66			−1.57977			−0.789885	+	0.613255i	$0.789860\pi$
$30$		0			0
$31$	6943.51			1.29770			0.648851	−	0.760915i	$-0.275250\pi$
$31$	6943.51			1.29770			0.648851	+	0.760915i	$0.275250\pi$
$32$	5855.00	−	5855.00i	1.01077	−	1.01077i
$33$		0			0
$34$			13099.4i			1.94336i
$35$		0			0
$36$		0			0
$37$	6246.54	+	6246.54i	0.750128	+	0.750128i	0.974503	−	0.224375i	$-0.0720341\pi$
$37$	6246.54	+	6246.54i	0.750128	+	0.750128i	−0.224375	+	0.974503i	$0.572034\pi$
$38$	4077.55	+	4077.55i	0.458079	+	0.458079i
$39$		0			0
$40$		0			0
$41$		−	11335.2i		−	1.05310i	−0.850144	−	0.526551i	$-0.823485\pi$
$41$		−	11335.2i		−	1.05310i	0.850144	−	0.526551i	$-0.176515\pi$
$42$		0			0
$43$	13033.3	−	13033.3i	1.07494	−	1.07494i	0.0779874	−	0.996954i	$-0.475151\pi$
$43$	13033.3	−	13033.3i	1.07494	−	1.07494i	0.996954	−	0.0779874i	$-0.0248494\pi$
$44$	4263.16			0.331971
$45$		0			0
$46$	34488.1			2.40312
$47$	125.547	−	125.547i	0.00829013	−	0.00829013i	−0.702950	−	0.711240i	$-0.748134\pi$
$47$	125.547	−	125.547i	0.00829013	−	0.00829013i	0.711240	+	0.702950i	$0.248134\pi$
$48$		0			0
$49$			169.034i			0.0100573i
$50$		0			0
$51$		0			0
$52$	14046.5	+	14046.5i	0.720376	+	0.720376i
$53$	−1601.74	−	1601.74i	−0.0783254	−	0.0783254i	0.666859	−	0.745184i	$-0.267638\pi$
$53$	−1601.74	−	1601.74i	−0.0783254	−	0.0783254i	−0.745184	+	0.666859i	$0.767638\pi$
$54$		0			0
$55$		0			0
$56$		−	1905.63i		−	0.0812023i
$57$		0			0
$58$	−41039.0	+	41039.0i	−1.60187	+	1.60187i
$59$	14819.1			0.554234			0.277117	−	0.960836i	$-0.410621\pi$
$59$	14819.1			0.554234			0.277117	+	0.960836i	$0.410621\pi$
$60$		0			0
$61$	−42544.3			−1.46392			−0.731959	−	0.681349i	$-0.761394\pi$
$61$	−42544.3			−1.46392			−0.731959	+	0.681349i	$0.761394\pi$
$62$	39827.9	−	39827.9i	1.31585	−	1.31585i
$63$		0			0
$64$		−	36350.7i		−	1.10933i
$65$		0			0
$66$		0			0
$67$	27389.5	+	27389.5i	0.745412	+	0.745412i	0.973614	−	0.228202i	$-0.0732846\pi$
$67$	27389.5	+	27389.5i	0.745412	+	0.745412i	−0.228202	+	0.973614i	$0.573285\pi$
$68$	38598.3	+	38598.3i	1.01227	+	1.01227i
$69$		0			0
$70$		0			0
$71$		−	29723.5i		−	0.699768i	−0.936793	−	0.349884i	$-0.886221\pi$
$71$		−	29723.5i		−	0.699768i	0.936793	−	0.349884i	$-0.113779\pi$
$72$		0			0
$73$	−31397.3	+	31397.3i	−0.689580	+	0.689580i	−0.962139	−	0.272559i	$-0.912130\pi$
$73$	−31397.3	+	31397.3i	−0.689580	+	0.689580i	0.272559	+	0.962139i	$0.412130\pi$
$74$	71660.1			1.52124
$75$		0			0
$76$	24029.6			0.477214
$77$	−11619.3	+	11619.3i	−0.223333	+	0.223333i
$78$		0			0
$79$			69868.2i			1.25954i	0.776782	+	0.629769i	$0.216851\pi$
$79$			69868.2i			1.25954i	−0.776782	+	0.629769i	$0.783149\pi$
$80$		0			0
$81$		0			0
$82$	−65018.6	−	65018.6i	−1.06783	−	1.06783i
$83$	−9923.69	−	9923.69i	−0.158117	−	0.158117i	0.623615	−	0.781732i	$-0.285663\pi$
$83$	−9923.69	−	9923.69i	−0.158117	−	0.158117i	−0.781732	+	0.623615i	$0.785663\pi$
$84$		0			0
$85$		0			0
$86$		−	149518.i		−	2.17996i
$87$		0			0
$88$	1304.31	−	1304.31i	0.0179546	−	0.0179546i
$89$	3301.75			0.0441845			0.0220922	−	0.999756i	$-0.492967\pi$
$89$	3301.75			0.0441845			0.0220922	+	0.999756i	$0.492967\pi$
$90$		0			0
$91$	−76567.6			−0.969263
$92$	101622.	−	101622.i	1.25175	−	1.25175i
$93$		0			0
$94$		−	1440.27i		−	0.0168122i
$95$		0			0
$96$		0			0
$97$	30659.8	+	30659.8i	0.330856	+	0.330856i	0.852912	−	0.522055i	$-0.174835\pi$
$97$	30659.8	+	30659.8i	0.330856	+	0.330856i	−0.522055	+	0.852912i	$0.674835\pi$
$98$	969.574	+	969.574i	0.0101980	+	0.0101980i
$99$		0			0
$100$		0			0
$101$		−	47113.7i		−	0.459561i	−0.973242	−	0.229781i	$-0.926199\pi$
$101$		−	47113.7i		−	0.459561i	0.973242	−	0.229781i	$-0.0738009\pi$
$102$		0			0
$103$	−38710.8	+	38710.8i	−0.359533	+	0.359533i	−0.863641	−	0.504108i	$-0.831822\pi$
$103$	−38710.8	+	38710.8i	−0.359533	+	0.359533i	0.504108	+	0.863641i	$0.331822\pi$
$104$	8595.03			0.0779227
$105$		0			0
$106$	−18375.1			−0.158842
$107$	103946.	−	103946.i	0.877703	−	0.877703i	−0.115594	−	0.993297i	$-0.536877\pi$
$107$	103946.	−	103946.i	0.877703	−	0.877703i	0.993297	+	0.115594i	$0.0368770\pi$
$108$		0			0
$109$		−	87300.2i		−	0.703800i	−0.936038	−	0.351900i	$-0.885536\pi$
$109$		−	87300.2i		−	0.703800i	0.936038	−	0.351900i	$-0.114464\pi$
$110$		0			0
$111$		0			0
$112$	88726.5	+	88726.5i	0.668357	+	0.668357i
$113$	−53948.1	−	53948.1i	−0.397447	−	0.397447i	0.479884	−	0.877332i	$-0.340679\pi$
$113$	−53948.1	−	53948.1i	−0.397447	−	0.397447i	−0.877332	+	0.479884i	$0.840679\pi$
$114$		0			0
$115$		0			0
$116$			241849.i			1.66878i
$117$		0			0
$118$	85002.3	−	85002.3i	0.561987	−	0.561987i
$119$	−210400.			−1.36201
$120$		0			0
$121$	145145.			0.901238
$122$	−244033.	+	244033.i	−1.48440	+	1.48440i
$123$		0			0
$124$		−	234712.i		−	1.37082i
$125$		0			0
$126$		0			0
$127$	−2755.24	−	2755.24i	−0.0151583	−	0.0151583i	0.699487	−	0.714645i	$-0.253412\pi$
$127$	−2755.24	−	2755.24i	−0.0151583	−	0.0151583i	−0.714645	+	0.699487i	$0.753412\pi$
$128$	−21146.8	−	21146.8i	−0.114083	−	0.114083i
$129$		0			0
$130$		0			0
$131$		−	120450.i		−	0.613239i	−0.951832	−	0.306620i	$-0.900802\pi$
$131$		−	120450.i		−	0.613239i	0.951832	−	0.306620i	$-0.0991980\pi$
$132$		0			0
$133$	−65493.0	+	65493.0i	−0.321045	+	0.321045i
$134$	314211.			1.51168
$135$		0			0
$136$	23618.3			0.109497
$137$	−181416.	+	181416.i	−0.825800	+	0.825800i	−0.986933	−	0.161133i	$-0.948485\pi$
$137$	−181416.	+	181416.i	−0.825800	+	0.825800i	0.161133	+	0.986933i	$0.448485\pi$
$138$		0			0
$139$			433587.i			1.90344i	0.306967	+	0.951720i	$0.400686\pi$
$139$			433587.i			1.90344i	−0.306967	+	0.951720i	$0.599314\pi$
$140$		0			0
$141$		0			0
$142$	−170494.	−	170494.i	−0.709557	−	0.709557i
$143$	−52406.9	−	52406.9i	−0.214313	−	0.214313i
$144$		0			0
$145$		0			0
$146$			360188.i			1.39845i
$147$		0			0
$148$	211152.	−	211152.i	0.792393	−	0.792393i
$149$	−308912.			−1.13991			−0.569953	−	0.821677i	$-0.693039\pi$
$149$	−308912.			−1.13991			−0.569953	+	0.821677i	$0.693039\pi$
$150$		0			0
$151$	224345.			0.800708			0.400354	−	0.916361i	$-0.368887\pi$
$151$	224345.			0.800708			0.400354	+	0.916361i	$0.368887\pi$
$152$	7351.86	−	7351.86i	0.0258100	−	0.0258100i
$153$		0			0
$154$			133296.i			0.452914i
$155$		0			0
$156$		0			0
$157$	172995.	+	172995.i	0.560125	+	0.560125i	0.929343	−	0.369218i	$-0.120374\pi$
$157$	172995.	+	172995.i	0.560125	+	0.560125i	−0.369218	+	0.929343i	$0.620374\pi$
$158$	400763.	+	400763.i	1.27716	+	1.27716i
$159$		0			0
$160$		0			0
$161$			553943.i			1.68423i
$162$		0			0
$163$	370703.	−	370703.i	1.09284	−	1.09284i	0.0976189	−	0.995224i	$-0.468877\pi$
$163$	370703.	−	370703.i	1.09284	−	1.09284i	0.995224	−	0.0976189i	$-0.0311226\pi$
$164$	−383164.			−1.11244
$165$		0			0
$166$	−113844.			−0.320657
$167$	−127540.	+	127540.i	−0.353880	+	0.353880i	−0.861551	−	0.507671i	$-0.830506\pi$
$167$	−127540.	+	127540.i	−0.353880	+	0.353880i	0.507671	+	0.861551i	$0.330506\pi$
$168$		0			0
$169$			25947.4i			0.0698838i
$170$		0			0
$171$		0			0
$172$	−440566.	−	440566.i	−1.13551	−	1.13551i
$173$	−307184.	−	307184.i	−0.780338	−	0.780338i	0.199550	−	0.979888i	$-0.436052\pi$
$173$	−307184.	−	307184.i	−0.780338	−	0.780338i	−0.979888	+	0.199550i	$0.936052\pi$
$174$		0			0
$175$		0			0
$176$			121458.i			0.295560i
$177$		0			0
$178$	18938.8	−	18938.8i	0.0448025	−	0.0448025i
$179$	−229555.			−0.535493			−0.267746	−	0.963489i	$-0.586279\pi$
$179$	−229555.			−0.535493			−0.267746	+	0.963489i	$0.586279\pi$
$180$		0			0
$181$	−463554.			−1.05173			−0.525865	−	0.850568i	$-0.676258\pi$
$181$	−463554.			−1.05173			−0.525865	+	0.850568i	$0.676258\pi$
$182$	−439191.	+	439191.i	−0.982821	+	0.982821i
$183$		0			0
$184$		−	62182.4i		−	0.135401i
$185$		0			0
$186$		0			0
$187$	−144009.	−	144009.i	−0.301152	−	0.301152i
$188$	−4243.86	−	4243.86i	−0.00875723	−	0.00875723i
$189$		0			0
$190$		0			0
$191$		−	515169.i		−	1.02180i	−0.859640	−	0.510901i	$-0.829312\pi$
$191$		−	515169.i		−	1.02180i	0.859640	−	0.510901i	$-0.170688\pi$
$192$		0			0
$193$	−257756.	+	257756.i	−0.498098	+	0.498098i	−0.910846	−	0.412747i	$-0.864569\pi$
$193$	−257756.	+	257756.i	−0.498098	+	0.498098i	0.412747	+	0.910846i	$0.364569\pi$
$194$	351728.			0.670969
$195$		0			0
$196$	5713.84			0.0106240
$197$	75887.2	−	75887.2i	0.139317	−	0.139317i	−0.634009	−	0.773326i	$-0.718592\pi$
$197$	75887.2	−	75887.2i	0.139317	−	0.139317i	0.773326	+	0.634009i	$0.218592\pi$
$198$		0			0
$199$		−	274337.i		−	0.491079i	−0.969387	−	0.245540i	$-0.921035\pi$
$199$		−	274337.i		−	0.491079i	0.969387	−	0.245540i	$-0.0789652\pi$
$200$		0			0
$201$		0			0
$202$	−270243.	−	270243.i	−0.465990	−	0.465990i
$203$	−659162.	−	659162.i	−1.12267	−	1.12267i
$204$		0			0
$205$		0			0
$206$			444089.i			0.729125i
$207$		0			0
$208$	−400186.	+	400186.i	−0.641363	+	0.641363i
$209$	−89653.7			−0.141972
$210$		0			0
$211$	−443976.			−0.686520			−0.343260	−	0.939240i	$-0.611531\pi$
$211$	−443976.			−0.686520			−0.343260	+	0.939240i	$0.611531\pi$
$212$	−54143.6	+	54143.6i	−0.0827385	+	0.0827385i
$213$		0			0
$214$		−	1.19246e6i		−	1.77996i
$215$		0			0
$216$		0			0
$217$	639709.	+	639709.i	0.922217	+	0.922217i
$218$	−500753.	−	500753.i	−0.713644	−	0.713644i
$219$		0			0
$220$		0			0
$221$		−	948976.i		−	1.30700i
$222$		0			0
$223$	587661.	−	587661.i	0.791343	−	0.791343i	−0.190370	−	0.981712i	$-0.560969\pi$
$223$	587661.	−	587661.i	0.791343	−	0.791343i	0.981712	+	0.190370i	$0.0609687\pi$
$224$	1.07885e6			1.43661
$225$		0			0
$226$	−618890.			−0.806014
$227$	388654.	−	388654.i	0.500609	−	0.500609i	−0.411018	−	0.911627i	$-0.634827\pi$
$227$	388654.	−	388654.i	0.500609	−	0.500609i	0.911627	+	0.411018i	$0.134827\pi$
$228$		0			0
$229$		−	1.27418e6i		−	1.60562i	−0.596235	−	0.802810i	$-0.703338\pi$
$229$		−	1.27418e6i		−	1.60562i	0.596235	−	0.802810i	$-0.296662\pi$
$230$		0			0
$231$		0			0
$232$	73993.7	+	73993.7i	0.0902557	+	0.0902557i
$233$	66255.4	+	66255.4i	0.0799523	+	0.0799523i	0.745952	−	0.666000i	$-0.231995\pi$
$233$	66255.4	+	66255.4i	0.0799523	+	0.0799523i	−0.666000	+	0.745952i	$0.731995\pi$
$234$		0			0
$235$		0			0
$236$		−	500932.i		−	0.585462i
$237$		0			0
$238$	−1.20685e6	+	1.20685e6i	−1.38106	+	1.38106i
$239$	−774388.			−0.876927			−0.438464	−	0.898749i	$-0.644477\pi$
$239$	−774388.			−0.876927			−0.438464	+	0.898749i	$0.644477\pi$
$240$		0			0
$241$	−403630.			−0.447653			−0.223826	−	0.974629i	$-0.571855\pi$
$241$	−403630.			−0.447653			−0.223826	+	0.974629i	$0.571855\pi$
$242$	832551.	−	832551.i	0.913845	−	0.913845i
$243$		0			0
$244$			1.43812e6i			1.54640i
$245$		0			0
$246$		0			0
$247$	−295395.	−	295395.i	−0.308078	−	0.308078i
$248$	−71810.0	−	71810.0i	−0.0741405	−	0.0741405i
$249$		0			0
$250$		0			0
$251$		−	692269.i		−	0.693571i	−0.937945	−	0.346785i	$-0.887273\pi$
$251$		−	692269.i		−	0.693571i	0.937945	−	0.346785i	$-0.112727\pi$
$252$		0			0
$253$	−379148.	+	379148.i	−0.372398	+	0.372398i
$254$	−31608.0			−0.0307406
$255$		0			0
$256$	920626.			0.877977
$257$	164414.	−	164414.i	0.155276	−	0.155276i	−0.625193	−	0.780470i	$-0.714980\pi$
$257$	164414.	−	164414.i	0.155276	−	0.155276i	0.780470	+	0.625193i	$0.214980\pi$
$258$		0			0
$259$			1.15099e6i			1.06616i
$260$		0			0
$261$		0			0
$262$	−690902.	−	690902.i	−0.621818	−	0.621818i
$263$	1.14375e6	+	1.14375e6i	1.01963	+	1.01963i	0.999803	+	0.0198244i	$0.00631073\pi$
$263$	1.14375e6	+	1.14375e6i	1.01963	+	1.01963i	0.0198244	+	0.999803i	$0.493689\pi$
$264$		0			0
$265$		0			0
$266$			751333.i			0.651071i
$267$		0			0
$268$	925846.	−	925846.i	0.787411	−	0.787411i
$269$	2.33596e6			1.96827			0.984137	−	0.177413i	$-0.0567727\pi$
$269$	2.33596e6			1.96827			0.984137	+	0.177413i	$0.0567727\pi$
$270$		0			0
$271$	516415.			0.427146			0.213573	−	0.976927i	$-0.431490\pi$
$271$	516415.			0.427146			0.213573	+	0.976927i	$0.431490\pi$
$272$	−1.09967e6	+	1.09967e6i	−0.901241	+	0.901241i
$273$		0			0
$274$			2.08120e6i			1.67470i
$275$		0			0
$276$		0			0
$277$	350664.	+	350664.i	0.274594	+	0.274594i	0.830947	−	0.556352i	$-0.187799\pi$
$277$	350664.	+	350664.i	0.274594	+	0.274594i	−0.556352	+	0.830947i	$0.687799\pi$
$278$	2.48705e6	+	2.48705e6i	1.93007	+	1.93007i
$279$		0			0
$280$		0			0
$281$		−	452829.i		−	0.342112i	−0.985261	−	0.171056i	$-0.945282\pi$
$281$		−	452829.i		−	0.342112i	0.985261	−	0.171056i	$-0.0547179\pi$
$282$		0			0
$283$	537627.	−	537627.i	0.399038	−	0.399038i	−0.478855	−	0.877894i	$-0.658948\pi$
$283$	537627.	−	537627.i	0.399038	−	0.399038i	0.877894	+	0.478855i	$0.158948\pi$
$284$	−1.00474e6			−0.739196
$285$		0			0
$286$	−601210.			−0.434622
$287$	1.04432e6	−	1.04432e6i	0.748390	−	0.748390i
$288$		0			0
$289$		−	1.18784e6i		−	0.836588i
$290$		0			0
$291$		0			0
$292$	1.06132e6	+	1.06132e6i	0.728434	+	0.728434i
$293$	−829564.	−	829564.i	−0.564522	−	0.564522i	0.366067	−	0.930589i	$-0.380704\pi$
$293$	−829564.	−	829564.i	−0.564522	−	0.564522i	−0.930589	+	0.366067i	$0.880704\pi$
$294$		0			0
$295$		0			0
$296$		−	129204.i		−	0.0857128i
$297$		0			0
$298$	−1.77191e6	+	1.77191e6i	−1.15585	+	1.15585i
$299$	−2.49847e6			−1.61620
$300$		0			0
$301$	2.40154e6			1.52782
$302$	1.28684e6	−	1.28684e6i	0.811908	−	0.811908i
$303$		0			0
$304$			684608.i			0.424872i
$305$		0			0
$306$		0			0
$307$	1.02729e6	+	1.02729e6i	0.622083	+	0.622083i	0.946064	−	0.323980i	$-0.105021\pi$
$307$	1.02729e6	+	1.02729e6i	0.622083	+	0.622083i	−0.323980	+	0.946064i	$0.605021\pi$
$308$	392767.	+	392767.i	0.235916	+	0.235916i
$309$		0			0
$310$		0			0
$311$			2.96171e6i			1.73637i	0.496244	+	0.868183i	$0.334712\pi$
$311$			2.96171e6i			1.73637i	−0.496244	+	0.868183i	$0.665288\pi$
$312$		0			0
$313$	1.36472e6	−	1.36472e6i	0.787378	−	0.787378i	−0.193686	−	0.981064i	$-0.562044\pi$
$313$	1.36472e6	−	1.36472e6i	0.787378	−	0.787378i	0.981064	+	0.193686i	$0.0620442\pi$
$314$	1.98460e6			1.13592
$315$		0			0
$316$	2.36175e6			1.33051
$317$	651823.	−	651823.i	0.364319	−	0.364319i	−0.501082	−	0.865400i	$-0.667064\pi$
$317$	651823.	−	651823.i	0.364319	−	0.364319i	0.865400	+	0.501082i	$0.167064\pi$
$318$		0			0
$319$		−	902330.i		−	0.496465i
$320$		0			0
$321$		0			0
$322$	3.17741e6	+	3.17741e6i	1.70778	+	1.70778i
$323$	−811717.	−	811717.i	−0.432911	−	0.432911i
$324$		0			0
$325$		0			0
$326$		−	4.25270e6i		−	2.21626i
$327$		0			0
$328$	−117229.	+	117229.i	−0.0601659	+	0.0601659i
$329$	23133.4			0.0117828
$330$		0			0
$331$	3.44640e6			1.72900			0.864501	−	0.502632i	$-0.167635\pi$
$331$	3.44640e6			1.72900			0.864501	+	0.502632i	$0.167635\pi$
$332$	−335451.	+	335451.i	−0.167026	+	0.167026i
$333$		0			0
$334$			1.46314e6i			0.717660i
$335$		0			0
$336$		0			0
$337$	−1.13322e6	−	1.13322e6i	−0.543551	−	0.543551i	0.381017	−	0.924568i	$-0.375574\pi$
$337$	−1.13322e6	−	1.13322e6i	−0.543551	−	0.543551i	−0.924568	+	0.381017i	$0.875574\pi$
$338$	148834.	+	148834.i	0.0708614	+	0.0708614i
$339$		0			0
$340$		0			0
$341$			875701.i			0.407821i
$342$		0			0
$343$	1.53286e6	−	1.53286e6i	0.703506	−	0.703506i
$344$	−269582.			−0.122827
$345$		0			0
$346$	−3.52400e6			−1.58251
$347$	−57438.3	+	57438.3i	−0.0256081	+	0.0256081i	−0.719795	−	0.694187i	$-0.755764\pi$
$347$	−57438.3	+	57438.3i	−0.0256081	+	0.0256081i	0.694187	+	0.719795i	$0.255764\pi$
$348$		0			0
$349$		−	1.87525e6i		−	0.824131i	−0.911154	−	0.412065i	$-0.864808\pi$
$349$		−	1.87525e6i		−	0.824131i	0.911154	−	0.412065i	$-0.135192\pi$
$350$		0			0
$351$		0			0
$352$	738420.	+	738420.i	0.317648	+	0.317648i
$353$	−1.81839e6	−	1.81839e6i	−0.776696	−	0.776696i	0.202571	−	0.979268i	$-0.435070\pi$
$353$	−1.81839e6	−	1.81839e6i	−0.776696	−	0.776696i	−0.979268	+	0.202571i	$0.935070\pi$
$354$		0			0
$355$		0			0
$356$		−	111609.i		−	0.0466740i
$357$		0			0
$358$	−1.31672e6	+	1.31672e6i	−0.542983	+	0.542983i
$359$	2.84933e6			1.16683			0.583414	−	0.812175i	$-0.301717\pi$
$359$	2.84933e6			1.16683			0.583414	+	0.812175i	$0.301717\pi$
$360$		0			0
$361$	1.97076e6			0.795913
$362$	−2.65894e6	+	2.65894e6i	−1.06644	+	1.06644i
$363$		0			0
$364$			2.58822e6i			1.02388i
$365$		0			0
$366$		0			0
$367$	−1.87816e6	−	1.87816e6i	−0.727895	−	0.727895i	0.242305	−	0.970200i	$-0.422096\pi$
$367$	−1.87816e6	−	1.87816e6i	−0.727895	−	0.727895i	−0.970200	+	0.242305i	$0.922096\pi$
$368$	2.89522e6	+	2.89522e6i	1.11445	+	1.11445i
$369$		0			0
$370$		0			0
$371$		−	295138.i		−	0.111324i
$372$		0			0
$373$	306598.	−	306598.i	0.114103	−	0.114103i	−0.647750	−	0.761853i	$-0.724290\pi$
$373$	306598.	−	306598.i	0.114103	−	0.114103i	0.761853	+	0.647750i	$0.224290\pi$
$374$	−1.65207e6			−0.610729
$375$		0			0
$376$	−2596.82			−0.000947265
$377$	2.97304e6	−	2.97304e6i	1.07733	−	1.07733i
$378$		0			0
$379$		−	1.69121e6i		−	0.604783i	−0.953184	−	0.302391i	$-0.902215\pi$
$379$		−	1.69121e6i		−	0.604783i	0.953184	−	0.302391i	$-0.0977850\pi$
$380$		0			0
$381$		0			0
$382$	−2.95500e6	−	2.95500e6i	−1.03609	−	1.03609i
$383$	−70174.9	−	70174.9i	−0.0244447	−	0.0244447i	0.694779	−	0.719223i	$-0.255502\pi$
$383$	−70174.9	−	70174.9i	−0.0244447	−	0.0244447i	−0.719223	+	0.694779i	$0.755502\pi$
$384$		0			0
$385$		0			0
$386$			2.95696e6i			1.01013i
$387$		0			0
$388$	1.03639e6	−	1.03639e6i	0.349498	−	0.349498i
$389$	−5.09621e6			−1.70755			−0.853774	−	0.520644i	$-0.825692\pi$
$389$	−5.09621e6			−1.70755			−0.853774	+	0.520644i	$0.825692\pi$
$390$		0			0
$391$	−6.86554e6			−2.27108
$392$	1748.15	−	1748.15i	0.000574597	−	0.000574597i
$393$		0			0
$394$		−	870576.i		−	0.282531i
$395$		0			0
$396$		0			0
$397$	−648381.	−	648381.i	−0.206469	−	0.206469i	0.596296	−	0.802765i	$-0.296638\pi$
$397$	−648381.	−	648381.i	−0.206469	−	0.206469i	−0.802765	+	0.596296i	$0.796638\pi$
$398$	−1.57359e6	−	1.57359e6i	−0.497949	−	0.497949i
$399$		0			0
$400$		0			0
$401$		−	3.21957e6i		−	0.999854i	−0.866068	−	0.499927i	$-0.833360\pi$
$401$		−	3.21957e6i		−	0.999854i	0.866068	−	0.499927i	$-0.166640\pi$
$402$		0			0
$403$	−2.88530e6	+	2.88530e6i	−0.884970	+	0.884970i
$404$	−1.59258e6			−0.485455
$405$		0			0
$406$	−7.56188e6			−2.27675
$407$	−787800.	+	787800.i	−0.235738	+	0.235738i
$408$		0			0
$409$			1.50857e6i			0.445920i	0.974828	+	0.222960i	$0.0715720\pi$
$409$			1.50857e6i			0.445920i	−0.974828	+	0.222960i	$0.928428\pi$
$410$		0			0
$411$		0			0
$412$	1.30854e6	+	1.30854e6i	0.379791	+	0.379791i
$413$	1.36529e6	+	1.36529e6i	0.393868	+	0.393868i
$414$		0			0
$415$		0			0
$416$			4.86596e6i			1.37859i
$417$		0			0
$418$	−514252.	+	514252.i	−0.143958	+	0.143958i
$419$	3.75060e6			1.04368			0.521839	−	0.853044i	$-0.325246\pi$
$419$	3.75060e6			1.04368			0.521839	+	0.853044i	$0.325246\pi$
$420$		0			0
$421$	3.18867e6			0.876808			0.438404	−	0.898778i	$-0.355544\pi$
$421$	3.18867e6			0.876808			0.438404	+	0.898778i	$0.355544\pi$
$422$	−2.54664e6	+	2.54664e6i	−0.696123	+	0.696123i
$423$		0			0
$424$			33130.5i			0.00894979i
$425$		0			0
$426$		0			0
$427$	−3.91962e6	−	3.91962e6i	−1.04034	−	1.04034i
$428$	−3.51368e6	−	3.51368e6i	−0.927156	−	0.927156i
$429$		0			0
$430$		0			0
$431$		−	84499.3i		−	0.0219109i	−0.999940	−	0.0109554i	$-0.996513\pi$
$431$		−	84499.3i		−	0.0219109i	0.999940	−	0.0109554i	$-0.00348730\pi$
$432$		0			0
$433$	−1.40166e6	+	1.40166e6i	−0.359272	+	0.359272i	−0.863545	−	0.504272i	$-0.831761\pi$
$433$	−1.40166e6	+	1.40166e6i	−0.359272	+	0.359272i	0.504272	+	0.863545i	$0.331761\pi$
$434$	7.33872e6			1.87023
$435$		0			0
$436$	−2.95101e6			−0.743454
$437$	−2.13709e6	+	2.13709e6i	−0.535328	+	0.535328i
$438$		0			0
$439$		−	7.46343e6i		−	1.84832i	−0.382004	−	0.924161i	$-0.624766\pi$
$439$		−	7.46343e6i		−	1.84832i	0.382004	−	0.924161i	$-0.375234\pi$
$440$		0			0
$441$		0			0
$442$	−5.44331e6	−	5.44331e6i	−1.32528	−	1.32528i
$443$	−890872.	−	890872.i	−0.215678	−	0.215678i	0.590996	−	0.806674i	$-0.298735\pi$
$443$	−890872.	−	890872.i	−0.215678	−	0.215678i	−0.806674	+	0.590996i	$0.798735\pi$
$444$		0			0
$445$		0			0
$446$		−	6.74163e6i		−	1.60482i
$447$		0			0
$448$	3.34900e6	−	3.34900e6i	0.788353	−	0.788353i
$449$	4.23397e6			0.991134			0.495567	−	0.868570i	$-0.334960\pi$
$449$	4.23397e6			0.991134			0.495567	+	0.868570i	$0.334960\pi$
$450$		0			0
$451$	1.42957e6			0.330952
$452$	−1.82361e6	+	1.82361e6i	−0.419841	+	0.419841i
$453$		0			0
$454$		−	4.45862e6i		−	1.01522i
$455$		0			0
$456$		0			0
$457$	5.04757e6	+	5.04757e6i	1.13055	+	1.13055i	0.990085	+	0.140469i	$0.0448611\pi$
$457$	5.04757e6	+	5.04757e6i	1.13055	+	1.13055i	0.140469	+	0.990085i	$0.455139\pi$
$458$	−7.30868e6	−	7.30868e6i	−1.62808	−	1.62808i
$459$		0			0
$460$		0			0
$461$		−	2.15968e6i		−	0.473300i	−0.971595	−	0.236650i	$-0.923951\pi$
$461$		−	2.15968e6i		−	0.473300i	0.971595	−	0.236650i	$-0.0760494\pi$
$462$		0			0
$463$	−464247.	+	464247.i	−0.100646	+	0.100646i	−0.755637	−	0.654991i	$-0.772672\pi$
$463$	−464247.	+	464247.i	−0.100646	+	0.100646i	0.654991	+	0.755637i	$0.272672\pi$
$464$	−6.89032e6			−1.48574
$465$		0			0
$466$	760079.			0.162141
$467$	−1.49671e6	+	1.49671e6i	−0.317574	+	0.317574i	−0.847835	−	0.530260i	$-0.822094\pi$
$467$	−1.49671e6	+	1.49671e6i	−0.317574	+	0.317574i	0.530260	+	0.847835i	$0.322094\pi$
$468$		0			0
$469$			5.04680e6i			1.05946i
$470$		0			0
$471$		0			0
$472$	−153260.	−	153260.i	−0.0316646	−	0.0316646i
$473$	1.64374e6	+	1.64374e6i	0.337816	+	0.337816i
$474$		0			0
$475$		0			0
$476$			7.11216e6i			1.43875i
$477$		0			0
$478$	−4.44187e6	+	4.44187e6i	−0.889194	+	0.889194i
$479$	−6.98129e6			−1.39026			−0.695131	−	0.718883i	$-0.744654\pi$
$479$	−6.98129e6			−1.39026			−0.695131	+	0.718883i	$0.744654\pi$
$480$		0			0
$481$	−5.19136e6			−1.02310
$482$	−2.31522e6	+	2.31522e6i	−0.453915	+	0.453915i
$483$		0			0
$484$		−	4.90635e6i		−	0.952017i
$485$		0			0
$486$		0			0
$487$	3.84567e6	+	3.84567e6i	0.734767	+	0.734767i	0.971560	−	0.236793i	$-0.0760965\pi$
$487$	3.84567e6	+	3.84567e6i	0.734767	+	0.734767i	−0.236793	+	0.971560i	$0.576096\pi$
$488$	439994.	+	439994.i	0.0836368	+	0.0836368i
$489$		0			0
$490$		0			0
$491$			6.37323e6i			1.19304i	0.802597	+	0.596521i	$0.203451\pi$
$491$			6.37323e6i			1.19304i	−0.802597	+	0.596521i	$0.796549\pi$
$492$		0			0
$493$	8.16963e6	−	8.16963e6i	1.51386	−	1.51386i
$494$	−3.38876e6			−0.624776
$495$		0			0
$496$	6.68697e6			1.22046
$497$	2.73844e6	−	2.73844e6i	0.497293	−	0.497293i
$498$		0			0
$499$		−	689634.i		−	0.123984i	−0.998077	−	0.0619922i	$-0.980255\pi$
$499$		−	689634.i		−	0.123984i	0.998077	−	0.0619922i	$-0.0197454\pi$
$500$		0			0
$501$		0			0
$502$	−3.97084e6	−	3.97084e6i	−0.703272	−	0.703272i
$503$	−3.68739e6	−	3.68739e6i	−0.649829	−	0.649829i	0.303123	−	0.952952i	$-0.401971\pi$
$503$	−3.68739e6	−	3.68739e6i	−0.649829	−	0.649829i	−0.952952	+	0.303123i	$0.901971\pi$
$504$		0			0
$505$		0			0
$506$			4.34957e6i			0.755214i
$507$		0			0
$508$	−93135.3	+	93135.3i	−0.0160123	+	0.0160123i
$509$	−1.82009e6			−0.311385			−0.155693	−	0.987806i	$-0.549761\pi$
$509$	−1.82009e6			−0.311385			−0.155693	+	0.987806i	$0.549761\pi$
$510$		0			0
$511$	−5.78529e6			−0.980105
$512$	5.95739e6	−	5.95739e6i	1.00434	−	1.00434i
$513$		0			0
$514$		−	1.88615e6i		−	0.314897i
$515$		0			0
$516$		0			0
$517$	15833.7	+	15833.7i	0.00260529	+	0.00260529i
$518$	6.60208e6	+	6.60208e6i	1.08108	+	1.08108i
$519$		0			0
$520$		0			0
$521$			2.81731e6i			0.454717i	0.973811	+	0.227358i	$0.0730088\pi$
$521$			2.81731e6i			0.454717i	−0.973811	+	0.227358i	$0.926991\pi$
$522$		0			0
$523$	219790.	−	219790.i	0.0351361	−	0.0351361i	−0.689320	−	0.724457i	$-0.742091\pi$
$523$	219790.	−	219790.i	0.0351361	−	0.0351361i	0.724457	+	0.689320i	$0.242091\pi$
$524$	−4.07159e6			−0.647792
$525$		0			0
$526$	1.31211e7			2.06778
$527$	−7.92853e6	+	7.92853e6i	−1.24356	+	1.24356i
$528$		0			0
$529$			1.16393e7i			1.80837i
$530$		0			0
$531$		0			0
$532$	2.21386e6	+	2.21386e6i	0.339134	+	0.339134i
$533$	4.71023e6	+	4.71023e6i	0.718164	+	0.718164i
$534$		0			0
$535$		0			0
$536$		−	566525.i		−	0.0851739i
$537$		0			0
$538$	1.33990e7	−	1.33990e7i	1.99581	−	1.99581i
$539$	−21318.2			−0.00316066
$540$		0			0
$541$	−3.73308e6			−0.548370			−0.274185	−	0.961677i	$-0.588408\pi$
$541$	−3.73308e6			−0.548370			−0.274185	+	0.961677i	$0.588408\pi$
$542$	2.96215e6	−	2.96215e6i	0.433121	−	0.433121i
$543$		0			0
$544$			1.33712e7i			1.93719i
$545$		0			0
$546$		0			0
$547$	3.83801e6	+	3.83801e6i	0.548451	+	0.548451i	0.925992	−	0.377542i	$-0.123231\pi$
$547$	3.83801e6	+	3.83801e6i	0.548451	+	0.548451i	−0.377542	+	0.925992i	$0.623231\pi$
$548$	6.13241e6	+	6.13241e6i	0.872328	+	0.872328i
$549$		0			0
$550$		0			0
$551$		−	5.08605e6i		−	0.713677i
$552$		0			0
$553$	−6.43698e6	+	6.43698e6i	−0.895096	+	0.895096i
$554$	4.02280e6			0.556871
$555$		0			0
$556$	1.46565e7			2.01069
$557$	−2.11338e6	+	2.11338e6i	−0.288628	+	0.288628i	−0.836538	−	0.547909i	$-0.815424\pi$
$557$	−2.11338e6	+	2.11338e6i	−0.288628	+	0.288628i	0.547909	+	0.836538i	$0.315424\pi$
$558$		0			0
$559$			1.08317e7i			1.46612i
$560$		0			0
$561$		0			0
$562$	−2.59742e6	−	2.59742e6i	−0.346898	−	0.346898i
$563$	1.12294e6	+	1.12294e6i	0.149309	+	0.149309i	0.777810	−	0.628500i	$-0.216331\pi$
$563$	1.12294e6	+	1.12294e6i	0.149309	+	0.149309i	−0.628500	+	0.777810i	$0.716331\pi$
$564$		0			0
$565$		0			0
$566$		−	6.16763e6i		−	0.809240i
$567$		0			0
$568$	−307401.	+	307401.i	−0.0399793	+	0.0399793i
$569$	6.07129e6			0.786141			0.393071	−	0.919508i	$-0.371413\pi$
$569$	6.07129e6			0.786141			0.393071	+	0.919508i	$0.371413\pi$
$570$		0			0
$571$	7.10133e6			0.911484			0.455742	−	0.890112i	$-0.349374\pi$
$571$	7.10133e6			0.911484			0.455742	+	0.890112i	$0.349374\pi$
$572$	−1.77151e6	+	1.77151e6i	−0.226388	+	0.226388i
$573$		0			0
$574$		−	1.19804e7i		−	1.51772i
$575$		0			0
$576$		0			0
$577$	−8.96551e6	−	8.96551e6i	−1.12108	−	1.12108i	−0.991580	−	0.129498i	$-0.958664\pi$
$577$	−8.96551e6	−	8.96551e6i	−1.12108	−	1.12108i	−0.129498	−	0.991580i	$-0.541336\pi$
$578$	−6.81340e6	−	6.81340e6i	−0.848290	−	0.848290i
$579$		0			0
$580$		0			0
$581$		−	1.82855e6i		−	0.224733i
$582$		0			0
$583$	202008.	−	202008.i	0.0246149	−	0.0246149i
$584$	649422.			0.0787943
$585$		0			0
$586$	−9.51673e6			−1.14484
$587$	354204.	−	354204.i	0.0424285	−	0.0424285i	−0.685574	−	0.728003i	$-0.740449\pi$
$587$	354204.	−	354204.i	0.0424285	−	0.0424285i	0.728003	+	0.685574i	$0.240449\pi$
$588$		0			0
$589$			4.93595e6i			0.586250i
$590$		0			0
$591$		0			0
$592$	6.01575e6	+	6.01575e6i	0.705481	+	0.705481i
$593$	5.94681e6	+	5.94681e6i	0.694460	+	0.694460i	0.963210	−	0.268750i	$-0.0866105\pi$
$593$	5.94681e6	+	5.94681e6i	0.694460	+	0.694460i	−0.268750	+	0.963210i	$0.586611\pi$
$594$		0			0
$595$		0			0
$596$			1.04422e7i			1.20413i
$597$		0			0
$598$	−1.43312e7	+	1.43312e7i	−1.63881	+	1.63881i
$599$	3.80854e6			0.433702			0.216851	−	0.976205i	$-0.430421\pi$
$599$	3.80854e6			0.433702			0.216851	+	0.976205i	$0.430421\pi$
$600$		0			0
$601$	−2.21664e6			−0.250328			−0.125164	−	0.992136i	$-0.539946\pi$
$601$	−2.21664e6			−0.250328			−0.125164	+	0.992136i	$0.539946\pi$
$602$	1.37752e7	−	1.37752e7i	1.54919	−	1.54919i
$603$		0			0
$604$		−	7.58354e6i		−	0.845823i
$605$		0			0
$606$		0			0
$607$	1.19106e7	+	1.19106e7i	1.31208	+	1.31208i	0.919877	+	0.392208i	$0.128289\pi$
$607$	1.19106e7	+	1.19106e7i	1.31208	+	1.31208i	0.392208	+	0.919877i	$0.371711\pi$
$608$	4.16216e6	+	4.16216e6i	0.456625	+	0.456625i
$609$		0			0
$610$		0			0
$611$			104339.i			0.0113069i
$612$		0			0
$613$	−5.33619e6	+	5.33619e6i	−0.573561	+	0.573561i	−0.933122	−	0.359560i	$-0.882927\pi$
$613$	−5.33619e6	+	5.33619e6i	−0.573561	+	0.573561i	0.359560	+	0.933122i	$0.382927\pi$
$614$	1.17851e7			1.26157
$615$		0			0
$616$	240334.			0.0255190
$617$	5.89511e6	−	5.89511e6i	0.623418	−	0.623418i	−0.322986	−	0.946404i	$-0.604687\pi$
$617$	5.89511e6	−	5.89511e6i	0.623418	−	0.623418i	0.946404	+	0.322986i	$0.104687\pi$
$618$		0			0
$619$		−	1.12433e7i		−	1.17942i	−0.807615	−	0.589710i	$-0.799242\pi$
$619$		−	1.12433e7i		−	1.17942i	0.807615	−	0.589710i	$-0.200758\pi$
$620$		0			0
$621$		0			0
$622$	1.69883e7	+	1.69883e7i	1.76066	+	1.76066i
$623$	304192.	+	304192.i	0.0313999	+	0.0313999i
$624$		0			0
$625$		0			0
$626$		−	1.56560e7i		−	1.59678i
$627$		0			0
$628$	5.84776e6	−	5.84776e6i	0.591685	−	0.591685i
$629$	−1.42654e7			−1.43766
$630$		0			0
$631$	−2.29941e6			−0.229902			−0.114951	−	0.993371i	$-0.536671\pi$
$631$	−2.29941e6			−0.229902			−0.114951	+	0.993371i	$0.536671\pi$
$632$	722578.	−	722578.i	0.0719601	−	0.0719601i
$633$		0			0
$634$		−	7.47769e6i		−	0.738829i
$635$		0			0
$636$		0			0
$637$	−70240.1	−	70240.1i	−0.00685862	−	0.00685862i
$638$	−5.17575e6	−	5.17575e6i	−0.503410	−	0.503410i
$639$		0			0
$640$		0			0
$641$		−	2.31083e6i		−	0.222138i	−0.993813	−	0.111069i	$-0.964573\pi$
$641$		−	2.31083e6i		−	0.222138i	0.993813	−	0.111069i	$-0.0354275\pi$
$642$		0			0
$643$	−9.10207e6	+	9.10207e6i	−0.868186	+	0.868186i	−0.992272	−	0.124086i	$-0.960400\pi$
$643$	−9.10207e6	+	9.10207e6i	−0.868186	+	0.868186i	0.124086	+	0.992272i	$0.460400\pi$
$644$	1.87249e7			1.77912
$645$		0			0
$646$	−9.31199e6			−0.877933
$647$	−1.44863e7	+	1.44863e7i	−1.36049	+	1.36049i	−0.487203	+	0.873289i	$0.661983\pi$
$647$	−1.44863e7	+	1.44863e7i	−1.36049	+	1.36049i	−0.873289	+	0.487203i	$0.838017\pi$
$648$		0			0
$649$			1.86896e6i			0.174176i
$650$		0			0
$651$		0			0
$652$	−1.25309e7	−	1.25309e7i	−1.15442	−	1.15442i
$653$	−1.84964e6	−	1.84964e6i	−0.169748	−	0.169748i	0.617120	−	0.786869i	$-0.288299\pi$
$653$	−1.84964e6	−	1.84964e6i	−0.169748	−	0.169748i	−0.786869	+	0.617120i	$0.788299\pi$
$654$		0			0
$655$		0			0
$656$		−	1.09164e7i		−	0.990422i
$657$		0			0
$658$	132693.	−	132693.i	0.0119476	−	0.0119476i
$659$	3.73930e6			0.335410			0.167705	−	0.985837i	$-0.446364\pi$
$659$	3.73930e6			0.335410			0.167705	+	0.985837i	$0.446364\pi$
$660$		0			0
$661$	5.61689e6			0.500026			0.250013	−	0.968243i	$-0.419565\pi$
$661$	5.61689e6			0.500026			0.250013	+	0.968243i	$0.419565\pi$
$662$	1.97685e7	−	1.97685e7i	1.75319	−	1.75319i
$663$		0			0
$664$			205262.i			0.0180671i
$665$		0			0
$666$		0			0
$667$	−2.15090e7	−	2.15090e7i	−1.87200	−	1.87200i
$668$	4.31124e6	+	4.31124e6i	0.373819	+	0.373819i
$669$		0			0
$670$		0			0
$671$		−	5.36559e6i		−	0.460057i
$672$		0			0
$673$	−9.85678e6	+	9.85678e6i	−0.838876	+	0.838876i	−0.988711	−	0.149835i	$-0.952126\pi$
$673$	−9.85678e6	+	9.85678e6i	−0.838876	+	0.838876i	0.149835	+	0.988711i	$0.452126\pi$
$674$	−1.30003e7			−1.10231
$675$		0			0
$676$	877099.			0.0738214
$677$	1.13727e7	−	1.13727e7i	0.953656	−	0.953656i	−0.0453170	−	0.998973i	$-0.514430\pi$
$677$	1.13727e7	−	1.13727e7i	0.953656	−	0.953656i	0.998973	+	0.0453170i	$0.0144298\pi$
$678$		0			0
$679$			5.64939e6i			0.470248i
$680$		0			0
$681$		0			0
$682$	5.02301e6	+	5.02301e6i	0.413526	+	0.413526i
$683$	−1.44662e7	−	1.44662e7i	−1.18660	−	1.18660i	−0.978002	−	0.208596i	$-0.933111\pi$
$683$	−1.44662e7	−	1.44662e7i	−1.18660	−	1.18660i	−0.208596	−	0.978002i	$-0.566889\pi$
$684$		0			0
$685$		0			0
$686$		−	1.75850e7i		−	1.42669i
$687$		0			0
$688$	1.25518e7	−	1.25518e7i	1.01096	−	1.01096i
$689$	1.33117e6			0.106828
$690$		0			0
$691$	−365135.			−0.0290909			−0.0145455	−	0.999894i	$-0.504630\pi$
$691$	−365135.			−0.0290909			−0.0145455	+	0.999894i	$0.504630\pi$
$692$	−1.03837e7	+	1.03837e7i	−0.824306	+	0.824306i
$693$		0			0
$694$			658930.i			0.0519327i
$695$		0			0
$696$		0			0
$697$	1.29432e7	+	1.29432e7i	1.00916	+	1.00916i
$698$	−1.07564e7	−	1.07564e7i	−0.835659	−	0.835659i
$699$		0			0
$700$		0			0
$701$		−	1.76534e7i		−	1.35685i	−0.734668	−	0.678427i	$-0.762662\pi$
$701$		−	1.76534e7i		−	1.35685i	0.734668	−	0.678427i	$-0.237338\pi$
$702$		0			0
$703$	−4.44049e6	+	4.44049e6i	−0.338878	+	0.338878i
$704$	4.58447e6			0.348624
$705$		0			0
$706$	−2.08606e7			−1.57512
$707$	4.34060e6	−	4.34060e6i	0.326589	−	0.326589i
$708$		0			0
$709$		−	4.50263e6i		−	0.336396i	−0.985753	−	0.168198i	$-0.946205\pi$
$709$		−	4.50263e6i		−	0.336396i	0.985753	−	0.168198i	$-0.0537947\pi$
$710$		0			0
$711$		0			0
$712$	−34146.8	−	34146.8i	−0.00252435	−	0.00252435i
$713$	2.08743e7	+	2.08743e7i	1.53776	+	1.53776i
$714$		0			0
$715$		0			0
$716$			7.75964e6i			0.565664i
$717$		0			0
$718$	1.63437e7	−	1.63437e7i	1.18315	−	1.18315i
$719$	4.18770e6			0.302101			0.151051	−	0.988526i	$-0.451734\pi$
$719$	4.18770e6			0.302101			0.151051	+	0.988526i	$0.451734\pi$
$720$		0			0
$721$	−7.13289e6			−0.511007
$722$	1.13042e7	−	1.13042e7i	0.807046	−	0.807046i
$723$		0			0
$724$			1.56695e7i			1.11099i
$725$		0			0
$726$		0			0
$727$	−2.93326e6	−	2.93326e6i	−0.205832	−	0.205832i	0.596661	−	0.802493i	$-0.296494\pi$
$727$	−2.93326e6	−	2.93326e6i	−0.205832	−	0.205832i	−0.802493	+	0.596661i	$0.796494\pi$
$728$	791864.	+	791864.i	0.0553761	+	0.0553761i
$729$		0			0
$730$		0			0
$731$			2.97645e7i			2.06018i
$732$		0			0
$733$	−4.22829e6	+	4.22829e6i	−0.290673	+	0.290673i	−0.837346	−	0.546673i	$-0.815894\pi$
$733$	−4.22829e6	+	4.22829e6i	−0.290673	+	0.290673i	0.546673	+	0.837346i	$0.315894\pi$
$734$	−2.15462e7			−1.47615
$735$		0			0
$736$	3.52037e7			2.39549
$737$	−3.45430e6	+	3.45430e6i	−0.234256	+	0.234256i
$738$		0			0
$739$			1.01894e7i			0.686335i	0.939274	+	0.343168i	$0.111500\pi$
$739$			1.01894e7i			0.686335i	−0.939274	+	0.343168i	$0.888500\pi$
$740$		0			0
$741$		0			0
$742$	−1.69291e6	−	1.69291e6i	−0.112882	−	0.112882i
$743$	1.18237e7	+	1.18237e7i	0.785744	+	0.785744i	0.980793	−	0.195050i	$-0.0624868\pi$
$743$	1.18237e7	+	1.18237e7i	0.785744	+	0.785744i	−0.195050	+	0.980793i	$0.562487\pi$
$744$		0			0
$745$		0			0
$746$		−	3.51729e6i		−	0.231399i
$747$		0			0
$748$	−4.86794e6	+	4.86794e6i	−0.318120	+	0.318120i
$749$	1.91531e7			1.24749
$750$		0			0
$751$	−1.57471e7			−1.01883			−0.509415	−	0.860521i	$-0.670138\pi$
$751$	−1.57471e7			−1.01883			−0.509415	+	0.860521i	$0.670138\pi$
$752$	120908.	−	120908.i	0.00779671	−	0.00779671i
$753$		0			0
$754$		−	3.41066e7i		−	2.18479i
$755$		0			0
$756$		0			0
$757$	−374181.	−	374181.i	−0.0237324	−	0.0237324i	0.695141	−	0.718873i	$-0.255342\pi$
$757$	−374181.	−	374181.i	−0.0237324	−	0.0237324i	−0.718873	+	0.695141i	$0.755342\pi$
$758$	−9.70075e6	−	9.70075e6i	−0.613243	−	0.613243i
$759$		0			0
$760$		0			0
$761$			2.96991e7i			1.85901i	0.368811	+	0.929504i	$0.379765\pi$
$761$			2.96991e7i			1.85901i	−0.368811	+	0.929504i	$0.620235\pi$
$762$		0			0
$763$	8.04301e6	−	8.04301e6i	0.500158	−	0.500158i
$764$	−1.74143e7			−1.07937
$765$		0			0
$766$	−805044.			−0.0495733
$767$	−6.15793e6	+	6.15793e6i	−0.377961	+	0.377961i
$768$		0			0
$769$			1.54556e7i			0.942477i	0.882006	+	0.471239i	$0.156193\pi$
$769$			1.54556e7i			0.942477i	−0.882006	+	0.471239i	$0.843807\pi$
$770$		0			0
$771$		0			0
$772$	8.71291e6	+	8.71291e6i	0.526163	+	0.526163i
$773$	−2.74275e6	−	2.74275e6i	−0.165096	−	0.165096i	0.619724	−	0.784820i	$-0.287245\pi$
$773$	−2.74275e6	−	2.74275e6i	−0.165096	−	0.165096i	−0.784820	+	0.619724i	$0.787245\pi$
$774$		0			0
$775$		0			0
$776$		−	634168.i		−	0.0378051i
$777$		0			0
$778$	−2.92317e7	+	2.92317e7i	−1.73143	+	1.73143i
$779$	8.05789e6			0.475749
$780$		0			0
$781$	3.74867e6			0.219912
$782$	−3.93806e7	+	3.93806e7i	−2.30285	+	2.30285i
$783$		0			0
$784$			162788.i			0.00945874i
$785$		0			0
$786$		0			0
$787$	−1.73678e7	−	1.73678e7i	−0.999556	−	0.999556i	0.000444176	−	1.00000i	$-0.499859\pi$
$787$	−1.73678e7	−	1.73678e7i	−0.999556	−	0.999556i	−1.00000		0.000444176i	$0.999859\pi$
$788$	−2.56522e6	−	2.56522e6i	−0.147166	−	0.147166i
$789$		0			0
$790$		0			0
$791$		−	9.94052e6i		−	0.564895i
$792$		0			0
$793$	1.76788e7	−	1.76788e7i	0.998321	−	0.998321i
$794$	−7.43821e6			−0.418714
$795$		0			0
$796$	−9.27341e6			−0.518749
$797$	−1.69545e7	+	1.69545e7i	−0.945453	+	0.945453i	−0.998587	−	0.0531345i	$-0.983079\pi$
$797$	−1.69545e7	+	1.69545e7i	−0.945453	+	0.945453i	0.0531345	+	0.998587i	$0.483079\pi$
$798$		0			0
$799$			286714.i			0.0158885i
$800$		0			0
$801$		0			0
$802$	−1.84674e7	−	1.84674e7i	−1.01384	−	1.01384i
$803$	−3.95975e6	−	3.95975e6i	−0.216710	−	0.216710i
$804$		0			0
$805$		0			0
$806$			3.31001e7i			1.79470i
$807$		0			0
$808$	−487251.	+	487251.i	−0.0262557	+	0.0262557i
$809$	7.99865e6			0.429680			0.214840	−	0.976649i	$-0.431077\pi$
$809$	7.99865e6			0.429680			0.214840	+	0.976649i	$0.431077\pi$
$810$		0			0
$811$	7.05559e6			0.376687			0.188344	−	0.982103i	$-0.439688\pi$
$811$	7.05559e6			0.376687			0.188344	+	0.982103i	$0.439688\pi$
$812$	−2.22817e7	+	2.22817e7i	−1.18593	+	1.18593i
$813$		0			0
$814$			9.03762e6i			0.478072i
$815$		0			0
$816$		0			0
$817$	9.26505e6	+	9.26505e6i	0.485615	+	0.485615i
$818$	8.65313e6	+	8.65313e6i	0.452158	+	0.452158i
$819$		0			0
$820$		0			0
$821$			5.48109e6i			0.283798i	0.989881	+	0.141899i	$0.0453208\pi$
$821$			5.48109e6i			0.283798i	−0.989881	+	0.141899i	$0.954679\pi$
$822$		0			0
$823$	2.05839e7	−	2.05839e7i	1.05932	−	1.05932i	0.0611965	−	0.998126i	$-0.480508\pi$
$823$	2.05839e7	−	2.05839e7i	1.05932	−	1.05932i	0.998126	−	0.0611965i	$-0.0194916\pi$
$824$	800696.			0.0410818
$825$		0			0
$826$	1.56626e7			0.798756
$827$	8.71932e6	−	8.71932e6i	0.443321	−	0.443321i	−0.449805	−	0.893127i	$-0.648507\pi$
$827$	8.71932e6	−	8.71932e6i	0.443321	−	0.443321i	0.893127	+	0.449805i	$0.148507\pi$
$828$		0			0
$829$		−	2.48546e7i		−	1.25609i	−0.778178	−	0.628044i	$-0.783856\pi$
$829$		−	2.48546e7i		−	1.25609i	0.778178	−	0.628044i	$-0.216144\pi$
$830$		0			0
$831$		0			0
$832$	1.51051e7	+	1.51051e7i	0.756512	+	0.756512i
$833$	−193013.	−	193013.i	−0.00963771	−	0.00963771i
$834$		0			0
$835$		0			0
$836$			3.03056e6i			0.149971i
$837$		0			0
$838$	2.15134e7	−	2.15134e7i	1.05828	−	1.05828i
$839$	8.64274e6			0.423884			0.211942	−	0.977282i	$-0.432021\pi$
$839$	8.64274e6			0.423884			0.211942	+	0.977282i	$0.432021\pi$
$840$		0			0
$841$	3.06780e7			1.49568
$842$	1.82902e7	−	1.82902e7i	0.889073	−	0.889073i
$843$		0			0
$844$			1.50077e7i			0.725202i
$845$		0			0
$846$		0			0
$847$	1.33723e7	+	1.33723e7i	0.640468	+	0.640468i
$848$	−1.54256e6	−	1.54256e6i	−0.0736636	−	0.0736636i
$849$		0			0
$850$		0			0
$851$			3.75579e7i			1.77778i
$852$		0			0
$853$	−1.52468e7	+	1.52468e7i	−0.717474	+	0.717474i	−0.968087	−	0.250613i	$-0.919368\pi$
$853$	−1.52468e7	+	1.52468e7i	−0.717474	+	0.717474i	0.250613	+	0.968087i	$0.419368\pi$
$854$	−4.49658e7			−2.10978
$855$		0			0
$856$	−2.15002e6			−0.100290
$857$	4.83516e6	−	4.83516e6i	0.224884	−	0.224884i	−0.585667	−	0.810552i	$-0.699167\pi$
$857$	4.83516e6	−	4.83516e6i	0.224884	−	0.224884i	0.810552	+	0.585667i	$0.199167\pi$
$858$		0			0
$859$		−	8.47794e6i		−	0.392019i	−0.980602	−	0.196010i	$-0.937202\pi$
$859$		−	8.47794e6i		−	0.392019i	0.980602	−	0.196010i	$-0.0627984\pi$
$860$		0			0
$861$		0			0
$862$	−484687.	−	484687.i	−0.0222174	−	0.0222174i
$863$	6.89866e6	+	6.89866e6i	0.315310	+	0.315310i	0.846962	−	0.531653i	$-0.178429\pi$
$863$	6.89866e6	+	6.89866e6i	0.315310	+	0.315310i	−0.531653	+	0.846962i	$0.678429\pi$
$864$		0			0
$865$		0			0
$866$			1.60798e7i			0.728596i
$867$		0			0
$868$	2.16241e7	−	2.16241e7i	0.974178	−	0.974178i
$869$	−8.81162e6			−0.395828
$870$		0			0
$871$	−2.27628e7			−1.01667
$872$	−902861.	+	902861.i	−0.0402096	+	0.0402096i
$873$		0			0
$874$			2.45167e7i			1.08563i
$875$		0			0
$876$		0			0
$877$	−1.19156e7	−	1.19156e7i	−0.523139	−	0.523139i	0.395379	−	0.918518i	$-0.370613\pi$
$877$	−1.19156e7	−	1.19156e7i	−0.523139	−	0.523139i	−0.918518	+	0.395379i	$0.870613\pi$
$878$	−4.28101e7	−	4.28101e7i	−1.87418	−	1.87418i
$879$		0			0
$880$		0			0
$881$		−	4.15756e7i		−	1.80467i	−0.431031	−	0.902337i	$-0.641850\pi$
$881$		−	4.15756e7i		−	1.80467i	0.431031	−	0.902337i	$-0.358150\pi$
$882$		0			0
$883$	215530.	−	215530.i	0.00930264	−	0.00930264i	−0.702440	−	0.711743i	$-0.747906\pi$
$883$	215530.	−	215530.i	0.00930264	−	0.00930264i	0.711743	+	0.702440i	$0.247906\pi$
$884$	−3.20782e7			−1.38064
$885$		0			0
$886$	−1.02201e7			−0.437390
$887$	−8.10371e6	+	8.10371e6i	−0.345840	+	0.345840i	−0.858557	−	0.512718i	$-0.828639\pi$
$887$	−8.10371e6	+	8.10371e6i	−0.345840	+	0.345840i	0.512718	+	0.858557i	$0.328639\pi$
$888$		0			0
$889$		−	507682.i		−	0.0215446i
$890$		0			0
$891$		0			0
$892$	−1.98647e7	−	1.98647e7i	−0.835930	−	0.835930i
$893$	89247.8	+	89247.8i	0.00374515	+	0.00374515i
$894$		0			0
$895$		0			0
$896$		−	3.89653e6i		−	0.162147i
$897$		0			0
$898$	2.42860e7	−	2.42860e7i	1.00500	−	1.00500i
$899$	−4.96785e7			−2.05007
$900$		0			0
$901$	3.65793e6			0.150115
$902$	8.20000e6	−	8.20000e6i	0.335581	−	0.335581i
$903$		0			0
$904$			1.11586e6i			0.0454140i
$905$		0			0
$906$		0			0
$907$	−1.11090e7	−	1.11090e7i	−0.448392	−	0.448392i	0.446428	−	0.894820i	$-0.352696\pi$
$907$	−1.11090e7	−	1.11090e7i	−0.448392	−	0.448392i	−0.894820	+	0.446428i	$0.852696\pi$
$908$	−1.31377e7	−	1.31377e7i	−0.528815	−	0.528815i
$909$		0			0
$910$		0			0
$911$		−	3.62514e7i		−	1.44720i	−0.690220	−	0.723599i	$-0.742486\pi$
$911$		−	3.62514e7i		−	1.44720i	0.690220	−	0.723599i	$-0.257514\pi$
$912$		0			0
$913$	1.25155e6	−	1.25155e6i	0.0496904	−	0.0496904i
$914$	5.79055e7			2.29274
$915$		0			0
$916$	−4.30712e7			−1.69609
$917$	1.10971e7	−	1.10971e7i	0.435801	−	0.435801i
$918$		0			0
$919$		−	2.57259e7i		−	1.00481i	−0.864634	−	0.502403i	$-0.832450\pi$
$919$		−	2.57259e7i		−	1.00481i	0.864634	−	0.502403i	$-0.167550\pi$
$920$		0			0
$921$		0			0
$922$	−1.23879e7	−	1.23879e7i	−0.479920	−	0.479920i
$923$	1.23513e7	+	1.23513e7i	0.477208	+	0.477208i
$924$		0			0
$925$		0			0
$926$			5.32582e6i			0.204108i
$927$		0			0
$928$	−4.18905e7	+	4.18905e7i	−1.59678	+	1.59678i
$929$	3.54934e7			1.34930			0.674650	−	0.738137i	$-0.264294\pi$
$929$	3.54934e7			1.34930			0.674650	+	0.738137i	$0.264294\pi$
$930$		0			0
$931$	−120161.			−0.00454350
$932$	2.23963e6	−	2.23963e6i	0.0844572	−	0.0844572i
$933$		0			0
$934$			1.71702e7i			0.644033i
$935$		0			0
$936$		0			0
$937$	1.37732e7	+	1.37732e7i	0.512490	+	0.512490i	0.915289	−	0.402798i	$-0.131962\pi$
$937$	1.37732e7	+	1.37732e7i	0.512490	+	0.512490i	−0.402798	+	0.915289i	$0.631962\pi$
$938$	2.89484e7	+	2.89484e7i	1.07428	+	1.07428i
$939$		0			0
$940$		0			0
$941$		−	4.69622e6i		−	0.172892i	−0.996257	−	0.0864458i	$-0.972449\pi$
$941$		−	4.69622e6i		−	0.172892i	0.996257	−	0.0864458i	$-0.0275510\pi$
$942$		0			0
$943$	3.40770e7	−	3.40770e7i	1.24791	−	1.24791i
$944$	1.42716e7			0.521247
$945$		0			0
$946$	1.88569e7			0.685082
$947$	−2.94353e7	+	2.94353e7i	−1.06658	+	1.06658i	−0.0689613	+	0.997619i	$0.521968\pi$
$947$	−2.94353e7	+	2.94353e7i	−1.06658	+	1.06658i	−0.997619	+	0.0689613i	$0.978032\pi$
$948$		0			0
$949$		−	2.60936e7i		−	0.940520i
$950$		0			0
$951$		0			0
$952$	2.17596e6	+	2.17596e6i	0.0778143	+	0.0778143i
$953$	−6.43420e6	−	6.43420e6i	−0.229489	−	0.229489i	0.582990	−	0.812479i	$-0.301883\pi$
$953$	−6.43420e6	−	6.43420e6i	−0.229489	−	0.229489i	−0.812479	+	0.582990i	$0.801883\pi$
$954$		0			0
$955$		0			0
$956$			2.61766e7i			0.926337i
$957$		0			0
$958$	−4.00445e7	+	4.00445e7i	−1.40971	+	1.40971i
$959$	−3.34279e7			−1.17371
$960$		0			0
$961$	1.95832e7			0.684031
$962$	−2.97776e7	+	2.97776e7i	−1.03741	+	1.03741i
$963$		0			0
$964$			1.36439e7i			0.472875i
$965$		0			0
$966$		0			0
$967$	−3.97838e7	−	3.97838e7i	−1.36817	−	1.36817i	−0.863050	−	0.505119i	$-0.831449\pi$
$967$	−3.97838e7	−	3.97838e7i	−1.36817	−	1.36817i	−0.505119	−	0.863050i	$-0.668551\pi$
$968$	−1.50110e6	−	1.50110e6i	−0.0514897	−	0.0514897i
$969$		0			0
$970$		0			0
$971$			3.23036e7i			1.09952i	0.835323	+	0.549760i	$0.185281\pi$
$971$			3.23036e7i			1.09952i	−0.835323	+	0.549760i	$0.814719\pi$
$972$		0			0
$973$	−3.99466e7	+	3.99466e7i	−1.35269	+	1.35269i
$974$	4.41174e7			1.49009
$975$		0			0
$976$	−4.09724e7			−1.37679
$977$	3.27323e7	−	3.27323e7i	1.09709	−	1.09709i	0.102335	−	0.994750i	$-0.467369\pi$
$977$	3.27323e7	−	3.27323e7i	1.09709	−	1.09709i	0.994750	−	0.102335i	$-0.0326315\pi$
$978$		0			0
$979$			416410.i			0.0138856i
$980$		0			0
$981$		0			0
$982$	3.65567e7	+	3.65567e7i	1.20973	+	1.20973i
$983$	−1.23155e7	−	1.23155e7i	−0.406509	−	0.406509i	0.474010	−	0.880519i	$-0.342806\pi$
$983$	−1.23155e7	−	1.23155e7i	−0.406509	−	0.406509i	−0.880519	+	0.474010i	$0.842806\pi$
$984$		0			0
$985$		0			0
$986$		−	9.37217e7i		−	3.07007i
$987$		0			0
$988$	−9.98525e6	+	9.98525e6i	−0.325437	+	0.325437i
$989$	7.83642e7			2.54758
$990$		0			0
$991$	−3.98494e7			−1.28896			−0.644478	−	0.764623i	$-0.722925\pi$
$991$	−3.98494e7			−1.28896			−0.644478	+	0.764623i	$0.722925\pi$
$992$	4.06543e7	−	4.06543e7i	1.31168	−	1.31168i
$993$		0			0
$994$		−	3.14153e7i		−	1.00850i
$995$		0			0
$996$		0			0
$997$	2.38488e7	+	2.38488e7i	0.759851	+	0.759851i	0.976295	−	0.216444i	$-0.0694459\pi$
$997$	2.38488e7	+	2.38488e7i	0.759851	+	0.759851i	−0.216444	+	0.976295i	$0.569446\pi$
$998$	−3.95573e6	−	3.95573e6i	−0.125719	−	0.125719i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.6.f.b.107.9		20
3.2	odd	2	inner	225.6.f.b.107.2		20
5.2	odd	4		45.6.f.a.8.9	yes	20
5.3	odd	4	inner	225.6.f.b.143.2		20
5.4	even	2		45.6.f.a.17.2	yes	20
15.2	even	4		45.6.f.a.8.2	✓	20
15.8	even	4	inner	225.6.f.b.143.9		20
15.14	odd	2		45.6.f.a.17.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.6.f.a.8.2	✓	20	15.2	even	4
45.6.f.a.8.9	yes	20	5.2	odd	4
45.6.f.a.17.2	yes	20	5.4	even	2
45.6.f.a.17.9	yes	20	15.14	odd	2
225.6.f.b.107.2		20	3.2	odd	2	inner
225.6.f.b.107.9		20	1.1	even	1	trivial
225.6.f.b.143.2		20	5.3	odd	4	inner
225.6.f.b.143.9		20	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	225.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.73598 - 5.73598i) q^{2} -33.8030i q^{4} +(92.1304 + 92.1304i) q^{7} +(-10.3420 - 10.3420i) q^{8} +O(q^{10})\)	\(q+(5.73598 - 5.73598i) q^{2} -33.8030i q^{4} +(92.1304 + 92.1304i) q^{7} +(-10.3420 - 10.3420i) q^{8} +126.118i q^{11} +(-415.539 + 415.539i) q^{13} +1056.92 q^{14} +963.053 q^{16} +(-1141.86 + 1141.86i) q^{17} +710.872i q^{19} +(723.410 + 723.410i) q^{22} +(3006.30 + 3006.30i) q^{23} +4767.05i q^{26} +(3114.29 - 3114.29i) q^{28} -7154.66 q^{29} +6943.51 q^{31} +(5855.00 - 5855.00i) q^{32} +13099.4i q^{34} +(6246.54 + 6246.54i) q^{37} +(4077.55 + 4077.55i) q^{38} -11335.2i q^{41} +(13033.3 - 13033.3i) q^{43} +4263.16 q^{44} +34488.1 q^{46} +(125.547 - 125.547i) q^{47} +169.034i q^{49} +(14046.5 + 14046.5i) q^{52} +(-1601.74 - 1601.74i) q^{53} -1905.63i q^{56} +(-41039.0 + 41039.0i) q^{58} +14819.1 q^{59} -42544.3 q^{61} +(39827.9 - 39827.9i) q^{62} -36350.7i q^{64} +(27389.5 + 27389.5i) q^{67} +(38598.3 + 38598.3i) q^{68} -29723.5i q^{71} +(-31397.3 + 31397.3i) q^{73} +71660.1 q^{74} +24029.6 q^{76} +(-11619.3 + 11619.3i) q^{77} +69868.2i q^{79} +(-65018.6 - 65018.6i) q^{82} +(-9923.69 - 9923.69i) q^{83} -149518. i q^{86} +(1304.31 - 1304.31i) q^{88} +3301.75 q^{89} -76567.6 q^{91} +(101622. - 101622. i) q^{92} -1440.27i q^{94} +(30659.8 + 30659.8i) q^{97} +(969.574 + 969.574i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 152 q^{7}+O(q^{10}) \) 20 * q - 152 * q^7	\( 20 q - 152 q^{7} - 1844 q^{13} - 6280 q^{16} + 6512 q^{22} - 29728 q^{28} + 43120 q^{31} + 37516 q^{37} - 5408 q^{43} + 118720 q^{46} + 285256 q^{52} - 274752 q^{58} + 163360 q^{61} + 302704 q^{67} - 146324 q^{73} + 760800 q^{76} + 305744 q^{82} - 355296 q^{88} + 499120 q^{91} + 362524 q^{97}+O(q^{100}) \) 20 * q - 152 * q^7 - 1844 * q^13 - 6280 * q^16 + 6512 * q^22 - 29728 * q^28 + 43120 * q^31 + 37516 * q^37 - 5408 * q^43 + 118720 * q^46 + 285256 * q^52 - 274752 * q^58 + 163360 * q^61 + 302704 * q^67 - 146324 * q^73 + 760800 * q^76 + 305744 * q^82 - 355296 * q^88 + 499120 * q^91 + 362524 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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