LMFDB - Embedded newform 224.6.p.a.31.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,6,Mod(31,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("224.31");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	224.p (of order $6$, 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:	$35.9259756381$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.11
Character	$\chi$	$=$	224.31
Dual form			224.6.p.a.159.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.16376 + 14.1401i) q^{3} +(19.2452 - 11.1112i) q^{5} +(103.004 - 78.7217i) q^{7} +(-11.7941 - 20.4280i) q^{9} +(-230.097 - 132.846i) q^{11} -31.5899i q^{13} +362.837i q^{15} +(110.876 + 64.0143i) q^{17} +(-1375.26 - 2382.02i) q^{19} +(272.226 + 2099.15i) q^{21} +(-2222.74 + 1283.30i) q^{23} +(-1315.58 + 2278.66i) q^{25} -3582.45 q^{27} +1603.73 q^{29} +(-349.938 + 606.110i) q^{31} +(3756.91 - 2169.05i) q^{33} +(1107.64 - 2659.51i) q^{35} +(-2421.84 - 4194.76i) q^{37} +(446.683 + 257.893i) q^{39} -5910.34i q^{41} -15217.5i q^{43} +(-453.959 - 262.093i) q^{45} +(-49.5838 - 85.8817i) q^{47} +(4412.79 - 16217.4i) q^{49} +(-1810.33 + 1045.20i) q^{51} +(17857.4 - 30929.9i) q^{53} -5904.34 q^{55} +44909.2 q^{57} +(3443.80 - 5964.84i) q^{59} +(-3111.85 + 1796.62i) q^{61} +(-2822.97 - 1175.72i) q^{63} +(-351.002 - 607.953i) q^{65} +(-42290.4 - 24416.4i) q^{67} -41906.2i q^{69} -31698.2i q^{71} +(27063.6 + 15625.2i) q^{73} +(-21480.2 - 37204.8i) q^{75} +(-34158.9 + 4429.84i) q^{77} +(-20637.0 + 11914.8i) q^{79} +(32112.3 - 55620.1i) q^{81} +18288.6 q^{83} +2845.11 q^{85} +(-13092.5 + 22676.8i) q^{87} +(60686.8 - 35037.5i) q^{89} +(-2486.81 - 3253.90i) q^{91} +(-5713.62 - 9896.28i) q^{93} +(-52934.2 - 30561.6i) q^{95} +122256. i q^{97} +6267.22i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 3240 q^{9} + 6856 q^{21} + 27728 q^{25} - 15920 q^{29} - 28296 q^{33} - 2152 q^{37} + 35400 q^{45} + 29280 q^{49} - 17512 q^{53} - 108368 q^{57} + 37704 q^{61} + 18216 q^{65} + 157704 q^{73} + 28224 q^{77}+ \cdots + 39400 q^{93}+O(q^{100}) $ 80 * q - 3240 * q^9 + 6856 * q^21 + 27728 * q^25 - 15920 * q^29 - 28296 * q^33 - 2152 * q^37 + 35400 * q^45 + 29280 * q^49 - 17512 * q^53 - 108368 * q^57 + 37704 * q^61 + 18216 * q^65 + 157704 * q^73 + 28224 * q^77 - 273136 * q^81 + 230704 * q^85 + 28440 * q^89 + 39400 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−8.16376	+	14.1401i	−0.523706	+	0.907085i	0.475913	+	0.879492i	$0.342118\pi$
$3$	−8.16376	+	14.1401i	−0.523706	+	0.907085i	−0.999619	+	0.0275929i	$0.991216\pi$
$4$		0			0
$5$	19.2452	−	11.1112i	0.344268	−	0.198763i	−0.317890	−	0.948128i	$-0.602974\pi$
$5$	19.2452	−	11.1112i	0.344268	−	0.198763i	0.662158	+	0.749364i	$0.269641\pi$
$6$		0			0
$7$	103.004	−	78.7217i	0.794530	−	0.607224i
$7$	103.004	−	78.7217i	0.794530	−	0.607224i
$8$		0			0
$9$	−11.7941	−	20.4280i	−0.0485354	−	0.0840658i
$10$		0			0
$11$	−230.097	−	132.846i	−0.573362	−	0.331031i	0.185129	−	0.982714i	$-0.440730\pi$
$11$	−230.097	−	132.846i	−0.573362	−	0.331031i	−0.758491	+	0.651684i	$0.774063\pi$
$12$		0			0
$13$		−	31.5899i		−	0.0518430i	−0.999664	−	0.0259215i	$-0.991748\pi$
$13$		−	31.5899i		−	0.0518430i	0.999664	−	0.0259215i	$-0.00825199\pi$
$14$		0			0
$15$			362.837i			0.416374i
$16$		0			0
$17$	110.876	+	64.0143i	0.0930498	+	0.0537223i	0.545803	−	0.837914i	$-0.316225\pi$
$17$	110.876	+	64.0143i	0.0930498	+	0.0537223i	−0.452753	+	0.891636i	$0.649558\pi$
$18$		0			0
$19$	−1375.26	−	2382.02i	−0.873979	−	1.51378i	−0.857847	−	0.513905i	$-0.828198\pi$
$19$	−1375.26	−	2382.02i	−0.873979	−	1.51378i	−0.0161318	−	0.999870i	$-0.505135\pi$
$20$		0			0
$21$	272.226	+	2099.15i	0.134704	+	1.03871i
$22$		0			0
$23$	−2222.74	+	1283.30i	−0.876130	+	0.505834i	−0.869381	−	0.494143i	$-0.835482\pi$
$23$	−2222.74	+	1283.30i	−0.876130	+	0.505834i	−0.00674965	+	0.999977i	$0.502148\pi$
$24$		0			0
$25$	−1315.58	+	2278.66i	−0.420986	+	0.729170i
$26$		0			0
$27$	−3582.45			−0.945738
$28$		0			0
$29$	1603.73			0.354108			0.177054	−	0.984201i	$-0.443343\pi$
$29$	1603.73			0.354108			0.177054	+	0.984201i	$0.443343\pi$
$30$		0			0
$31$	−349.938	+	606.110i	−0.0654014	+	0.113278i	−0.896872	−	0.442290i	$-0.854166\pi$
$31$	−349.938	+	606.110i	−0.0654014	+	0.113278i	0.831471	+	0.555569i	$0.187499\pi$
$32$		0			0
$33$	3756.91	−	2169.05i	0.600546	−	0.346725i
$34$		0			0
$35$	1107.64	−	2659.51i	0.152838	−	0.366971i
$36$		0			0
$37$	−2421.84	−	4194.76i	−0.290832	−	0.503735i	0.683175	−	0.730255i	$-0.260599\pi$
$37$	−2421.84	−	4194.76i	−0.290832	−	0.503735i	−0.974007	+	0.226519i	$0.927265\pi$
$38$		0			0
$39$	446.683	+	257.893i	0.0470260	+	0.0271505i
$40$		0			0
$41$		−	5910.34i		−	0.549101i	−0.961573	−	0.274551i	$-0.911471\pi$
$41$		−	5910.34i		−	0.549101i	0.961573	−	0.274551i	$-0.0885291\pi$
$42$		0			0
$43$		−	15217.5i		−	1.25508i	−0.778585	−	0.627540i	$-0.784062\pi$
$43$		−	15217.5i		−	1.25508i	0.778585	−	0.627540i	$-0.215938\pi$
$44$		0			0
$45$	−453.959	−	262.093i	−0.0334184	−	0.0192941i
$46$		0			0
$47$	−49.5838	−	85.8817i	−0.00327413	−	0.00567095i	0.864384	−	0.502833i	$-0.167709\pi$
$47$	−49.5838	−	85.8817i	−0.00327413	−	0.00567095i	−0.867658	+	0.497162i	$0.834376\pi$
$48$		0			0
$49$	4412.79	−	16217.4i	0.262557	−	0.964916i
$50$		0			0
$51$	−1810.33	+	1045.20i	−0.0974614	+	0.0562694i
$52$		0			0
$53$	17857.4	−	30929.9i	0.873228	−	1.51248i	0.0145896	−	0.999894i	$-0.495356\pi$
$53$	17857.4	−	30929.9i	0.873228	−	1.51248i	0.858638	−	0.512582i	$-0.171311\pi$
$54$		0			0
$55$	−5904.34			−0.263187
$56$		0			0
$57$	44909.2			1.83083
$58$		0			0
$59$	3443.80	−	5964.84i	0.128798	−	0.223084i	−0.794413	−	0.607378i	$-0.792222\pi$
$59$	3443.80	−	5964.84i	0.128798	−	0.223084i	0.923211	+	0.384293i	$0.125555\pi$
$60$		0			0
$61$	−3111.85	+	1796.62i	−0.107076	+	0.0618205i	−0.552582	−	0.833459i	$-0.686357\pi$
$61$	−3111.85	+	1796.62i	−0.107076	+	0.0618205i	0.445505	+	0.895279i	$0.353024\pi$
$62$		0			0
$63$	−2822.97	−	1175.72i	−0.0896097	−	0.0373209i
$64$		0			0
$65$	−351.002	−	607.953i	−0.0103045	−	0.0178479i
$66$		0			0
$67$	−42290.4	−	24416.4i	−1.15095	−	0.664499i	−0.201829	−	0.979421i	$-0.564689\pi$
$67$	−42290.4	−	24416.4i	−1.15095	−	0.664499i	−0.949118	+	0.314921i	$0.898022\pi$
$68$		0			0
$69$		−	41906.2i		−	1.05963i
$70$		0			0
$71$		−	31698.2i		−	0.746257i	−0.927780	−	0.373128i	$-0.878285\pi$
$71$		−	31698.2i		−	0.746257i	0.927780	−	0.373128i	$-0.121715\pi$
$72$		0			0
$73$	27063.6	+	15625.2i	0.594399	+	0.343176i	0.766835	−	0.641844i	$-0.221831\pi$
$73$	27063.6	+	15625.2i	0.594399	+	0.343176i	−0.172436	+	0.985021i	$0.555164\pi$
$74$		0			0
$75$	−21480.2	−	37204.8i	−0.440946	−	0.763741i
$76$		0			0
$77$	−34158.9	+	4429.84i	−0.656563	+	0.0851455i
$78$		0			0
$79$	−20637.0	+	11914.8i	−0.372031	+	0.214792i	−0.674345	−	0.738416i	$-0.735574\pi$
$79$	−20637.0	+	11914.8i	−0.372031	+	0.214792i	0.302314	+	0.953208i	$0.402241\pi$
$80$		0			0
$81$	32112.3	−	55620.1i	0.543824	−	0.941931i
$82$		0			0
$83$	18288.6			0.291398			0.145699	−	0.989329i	$-0.453457\pi$
$83$	18288.6			0.291398			0.145699	+	0.989329i	$0.453457\pi$
$84$		0			0
$85$	2845.11			0.0427121
$86$		0			0
$87$	−13092.5	+	22676.8i	−0.185449	+	0.321206i
$88$		0			0
$89$	60686.8	−	35037.5i	0.812118	−	0.468876i	−0.0355730	−	0.999367i	$-0.511326\pi$
$89$	60686.8	−	35037.5i	0.812118	−	0.468876i	0.847691	+	0.530491i	$0.177992\pi$
$90$		0			0
$91$	−2486.81	−	3253.90i	−0.0314803	−	0.0411908i
$92$		0			0
$93$	−5713.62	−	9896.28i	−0.0685021	−	0.118649i
$94$		0			0
$95$	−52934.2	−	30561.6i	−0.601766	−	0.347430i
$96$		0			0
$97$			122256.i			1.31929i	0.751579	+	0.659644i	$0.229293\pi$
$97$			122256.i			1.31929i	−0.751579	+	0.659644i	$0.770707\pi$
$98$		0			0
$99$			6267.22i			0.0642668i
$100$		0			0
$101$	−91505.7	−	52830.9i	−0.892575	−	0.515329i	−0.0177913	−	0.999842i	$-0.505663\pi$
$101$	−91505.7	−	52830.9i	−0.892575	−	0.515329i	−0.874784	+	0.484513i	$0.838997\pi$
$102$		0			0
$103$	−90044.5	−	155962.i	−0.836304	−	1.44852i	−0.892964	−	0.450127i	$-0.851379\pi$
$103$	−90044.5	−	155962.i	−0.836304	−	1.44852i	0.0566605	−	0.998394i	$-0.481955\pi$
$104$		0			0
$105$	28563.1	+	37373.8i	0.252832	+	0.330822i
$106$		0			0
$107$	−130537.	+	75365.5i	−1.10223	+	0.636375i	−0.936807	−	0.349847i	$-0.886234\pi$
$107$	−130537.	+	75365.5i	−1.10223	+	0.636375i	−0.165427	+	0.986222i	$0.552900\pi$
$108$		0			0
$109$	−39532.1	+	68471.7i	−0.318701	+	0.552007i	−0.980217	−	0.197924i	$-0.936580\pi$
$109$	−39532.1	+	68471.7i	−0.318701	+	0.552007i	0.661516	+	0.749931i	$0.269913\pi$
$110$		0			0
$111$	79085.5			0.609241
$112$		0			0
$113$	100179.			0.738040			0.369020	−	0.929421i	$-0.379693\pi$
$113$	100179.			0.738040			0.369020	+	0.929421i	$0.379693\pi$
$114$		0			0
$115$	−28518.0	+	49394.6i	−0.201082	+	0.348285i
$116$		0			0
$117$	−645.318	+	372.575i	−0.00435822	+	0.00251622i
$118$		0			0
$119$	16460.0	−	2134.60i	0.106552	−	0.0138181i
$120$		0			0
$121$	−45229.2	−	78339.2i	−0.280837	−	0.486425i
$122$		0			0
$123$	83572.5	+	48250.6i	0.498082	+	0.287568i
$124$		0			0
$125$			127916.i			0.732233i
$126$		0			0
$127$		−	133657.i		−	0.735329i	−0.929959	−	0.367664i	$-0.880158\pi$
$127$		−	133657.i		−	0.735329i	0.929959	−	0.367664i	$-0.119842\pi$
$128$		0			0
$129$	215176.	+	124232.i	1.13846	+	0.657292i
$130$		0			0
$131$	64841.1	+	112308.i	0.330120	+	0.571785i	0.982535	−	0.186077i	$-0.0595773\pi$
$131$	64841.1	+	112308.i	0.330120	+	0.571785i	−0.652415	+	0.757862i	$0.726244\pi$
$132$		0			0
$133$	−329174.	−	137096.i	−1.61360	−	0.672039i
$134$		0			0
$135$	−68944.9	+	39805.4i	−0.325588	+	0.187978i
$136$		0			0
$137$	23507.7	−	40716.5i	0.107006	−	0.185340i	−0.807550	−	0.589799i	$-0.799207\pi$
$137$	23507.7	−	40716.5i	0.107006	−	0.185340i	0.914556	+	0.404459i	$0.132540\pi$
$138$		0			0
$139$	323808.			1.42151			0.710756	−	0.703439i	$-0.248353\pi$
$139$	323808.			1.42151			0.710756	+	0.703439i	$0.248353\pi$
$140$		0			0
$141$	1619.16			0.00685871
$142$		0			0
$143$	−4196.61	+	7268.73i	−0.0171616	+	0.0297248i
$144$		0			0
$145$	30864.0	−	17819.4i	0.121908	−	0.0703837i
$146$		0			0
$147$	193289.	+	194792.i	0.737759	+	0.743494i
$148$		0			0
$149$	−88736.6	−	153696.i	−0.327444	−	0.567150i	0.654560	−	0.756010i	$-0.272854\pi$
$149$	−88736.6	−	153696.i	−0.327444	−	0.567150i	−0.982004	+	0.188860i	$0.939521\pi$
$150$		0			0
$151$	132002.	+	76211.4i	0.471128	+	0.272006i	0.716712	−	0.697370i	$-0.245646\pi$
$151$	132002.	+	76211.4i	0.471128	+	0.272006i	−0.245584	+	0.969375i	$0.578980\pi$
$152$		0			0
$153$		−	3019.97i		−	0.0104297i
$154$		0			0
$155$			15552.9i			0.0519976i
$156$		0			0
$157$	−269397.	−	155536.i	−0.872254	−	0.503596i	−0.00415732	−	0.999991i	$-0.501323\pi$
$157$	−269397.	−	155536.i	−0.872254	−	0.503596i	−0.868097	+	0.496395i	$0.834657\pi$
$158$		0			0
$159$	291567.	+	505008.i	0.914629	+	1.58418i
$160$		0			0
$161$	−127928.	+	307163.i	−0.388957	+	0.933908i
$162$		0			0
$163$	152716.	−	88170.5i	0.450210	−	0.259929i	−0.257709	−	0.966223i	$-0.582968\pi$
$163$	152716.	−	88170.5i	0.450210	−	0.259929i	0.707919	+	0.706294i	$0.249634\pi$
$164$		0			0
$165$	48201.6	−	83487.6i	0.137832	−	0.238733i
$166$		0			0
$167$	469993.			1.30407			0.652035	−	0.758189i	$-0.273916\pi$
$167$	469993.			1.30407			0.652035	+	0.758189i	$0.273916\pi$
$168$		0			0
$169$	370295.			0.997312
$170$		0			0
$171$	−32439.9	+	56187.6i	−0.0848378	+	0.146943i
$172$		0			0
$173$	−674698.	+	389537.i	−1.71393	+	0.989540i	−0.784839	+	0.619700i	$0.787254\pi$
$173$	−674698.	+	389537.i	−1.71393	+	0.989540i	−0.929095	+	0.369841i	$0.879412\pi$
$174$		0			0
$175$	43868.9	+	338276.i	0.108283	+	0.834981i
$176$		0			0
$177$	56228.8	+	97391.1i	0.134904	+	0.233661i
$178$		0			0
$179$	−535593.	−	309225.i	−1.24940	−	0.721343i	−0.278412	−	0.960462i	$-0.589808\pi$
$179$	−535593.	−	309225.i	−1.24940	−	0.721343i	−0.970990	+	0.239119i	$0.923141\pi$
$180$		0			0
$181$			178785.i			0.405635i	0.979217	+	0.202818i	$0.0650098\pi$
$181$			178785.i			0.405635i	−0.979217	+	0.202818i	$0.934990\pi$
$182$		0			0
$183$		−	58668.9i		−	0.129503i
$184$		0			0
$185$	−93217.6	−	53819.2i	−0.200248	−	0.115613i
$186$		0			0
$187$	−17008.1	−	29459.0i	−0.0355675	−	0.0616047i
$188$		0			0
$189$	−369008.	+	282017.i	−0.751418	+	0.574275i
$190$		0			0
$191$	9396.44	−	5425.04i	0.0186372	−	0.0107602i	−0.490652	−	0.871355i	$-0.663242\pi$
$191$	9396.44	−	5425.04i	0.0186372	−	0.0107602i	0.509290	+	0.860595i	$0.329908\pi$
$192$		0			0
$193$	−473563.	+	820235.i	−0.915133	+	1.58506i	−0.108427	+	0.994104i	$0.534581\pi$
$193$	−473563.	+	820235.i	−0.915133	+	1.58506i	−0.806706	+	0.590953i	$0.798752\pi$
$194$		0			0
$195$	11462.0			0.0215861
$196$		0			0
$197$	−81454.8			−0.149538			−0.0747689	−	0.997201i	$-0.523822\pi$
$197$	−81454.8			−0.149538			−0.0747689	+	0.997201i	$0.523822\pi$
$198$		0			0
$199$	−491764.	+	851761.i	−0.880287	+	1.52470i	−0.0292649	+	0.999572i	$0.509317\pi$
$199$	−491764.	+	851761.i	−0.880287	+	1.52470i	−0.851022	+	0.525130i	$0.824017\pi$
$200$		0			0
$201$	690498.	−	398659.i	1.20551	−	0.696004i
$202$		0			0
$203$	165191.	−	126248.i	0.281350	−	0.215023i
$204$		0			0
$205$	−65671.0	−	113745.i	−0.109141	−	0.189038i
$206$		0			0
$207$	52430.4	+	30270.7i	0.0850467	+	0.0491017i
$208$		0			0
$209$			730793.i			1.15725i
$210$		0			0
$211$		−	427608.i		−	0.661210i	−0.943769	−	0.330605i	$-0.892747\pi$
$211$		−	427608.i		−	0.661210i	0.943769	−	0.330605i	$-0.107253\pi$
$212$		0			0
$213$	448214.	+	258776.i	0.676918	+	0.390819i
$214$		0			0
$215$	−169084.	−	292863.i	−0.249464	−	0.432084i
$216$		0			0
$217$	11668.9	+	89979.7i	0.0168221	+	0.129716i
$218$		0			0
$219$	−441881.	+	255120.i	−0.622580	+	0.359447i
$220$		0			0
$221$	2022.21	−	3502.56i	0.00278513	−	0.00482398i
$222$		0			0
$223$	60238.8			0.0811174			0.0405587	−	0.999177i	$-0.487086\pi$
$223$	60238.8			0.0811174			0.0405587	+	0.999177i	$0.487086\pi$
$224$		0			0
$225$	62064.5			0.0817310
$226$		0			0
$227$	27615.1	−	47830.8i	0.0355699	−	0.0616088i	−0.847692	−	0.530488i	$-0.822009\pi$
$227$	27615.1	−	47830.8i	0.0355699	−	0.0616088i	0.883262	+	0.468879i	$0.155342\pi$
$228$		0			0
$229$	−3063.24	+	1768.56i	−0.00386004	+	0.00222859i	−0.501929	−	0.864909i	$-0.667376\pi$
$229$	−3063.24	+	1768.56i	−0.00386004	+	0.00222859i	0.498069	+	0.867138i	$0.334043\pi$
$230$		0			0
$231$	216227.	−	519172.i	0.266612	−	0.640150i
$232$		0			0
$233$	−599259.	−	1.03795e6i	−0.723143	−	1.25252i	−0.959734	−	0.280912i	$-0.909363\pi$
$233$	−599259.	−	1.03795e6i	−0.723143	−	1.25252i	0.236590	−	0.971610i	$-0.423970\pi$
$234$		0			0
$235$	−1908.50	−	1101.87i	−0.00225435	−	0.00130155i
$236$		0			0
$237$		−	389078.i		−	0.449952i
$238$		0			0
$239$		−	531464.i		−	0.601837i	−0.953650	−	0.300918i	$-0.902707\pi$
$239$		−	531464.i		−	0.601837i	0.953650	−	0.300918i	$-0.0972932\pi$
$240$		0			0
$241$	−487249.	−	281313.i	−0.540391	−	0.311995i	0.204846	−	0.978794i	$-0.434331\pi$
$241$	−487249.	−	281313.i	−0.540391	−	0.311995i	−0.745237	+	0.666799i	$0.767664\pi$
$242$		0			0
$243$	89046.0	+	154232.i	0.0967384	+	0.167556i
$244$		0			0
$245$	−95269.3	−	361137.i	−0.101400	−	0.384377i
$246$		0			0
$247$	−75247.8	+	43444.3i	−0.0784786	+	0.0453096i
$248$		0			0
$249$	−149304.	+	258602.i	−0.152607	+	0.264323i
$250$		0			0
$251$	1.06837e6			1.07037			0.535187	−	0.844734i	$-0.320241\pi$
$251$	1.06837e6			1.07037			0.535187	+	0.844734i	$0.320241\pi$
$252$		0			0
$253$	681926.			0.669786
$254$		0			0
$255$	−23226.8	+	40229.9i	−0.0223686	+	0.0387435i
$256$		0			0
$257$	1.16285e6	−	671372.i	1.09822	−	0.634060i	0.162470	−	0.986714i	$-0.448054\pi$
$257$	1.16285e6	−	671372.i	1.09822	−	0.634060i	0.935754	+	0.352654i	$0.114721\pi$
$258$		0			0
$259$	−579679.	−	241427.i	−0.536955	−	0.223633i
$260$		0			0
$261$	−18914.6	−	32761.0i	−0.0171868	−	0.0297684i
$262$		0			0
$263$	−1.39724e6	−	806697.i	−1.24561	−	0.719153i	−0.275378	−	0.961336i	$-0.588803\pi$
$263$	−1.39724e6	−	806697.i	−1.24561	−	0.719153i	−0.970231	+	0.242183i	$0.922136\pi$
$264$		0			0
$265$		−	793667.i		−	0.694263i
$266$		0			0
$267$			1.14415e6i			0.982213i
$268$		0			0
$269$	1.89088e6	+	1.09170e6i	1.59325	+	0.919864i	0.992744	+	0.120245i	$0.0383679\pi$
$269$	1.89088e6	+	1.09170e6i	1.59325	+	0.919864i	0.600507	+	0.799619i	$0.294965\pi$
$270$		0			0
$271$	203437.	+	352363.i	0.168270	+	0.291452i	0.937812	−	0.347144i	$-0.112849\pi$
$271$	203437.	+	352363.i	0.168270	+	0.291452i	−0.769542	+	0.638597i	$0.779515\pi$
$272$		0			0
$273$	66312.0	−	8599.58i	0.0538500	−	0.00698346i
$274$		0			0
$275$	605422.	−	349541.i	0.482755	−	0.278719i
$276$		0			0
$277$	254717.	−	441182.i	0.199461	−	0.345477i	−0.748893	−	0.662691i	$-0.769414\pi$
$277$	254717.	−	441182.i	0.199461	−	0.345477i	0.948354	+	0.317215i	$0.102748\pi$
$278$		0			0
$279$	16508.8			0.0126971
$280$		0			0
$281$	−1.11878e6			−0.845240			−0.422620	−	0.906307i	$-0.638889\pi$
$281$	−1.11878e6			−0.845240			−0.422620	+	0.906307i	$0.638889\pi$
$282$		0			0
$283$	−134959.	+	233755.i	−0.100169	+	0.173498i	−0.911754	−	0.410736i	$-0.865272\pi$
$283$	−134959.	+	233755.i	−0.100169	+	0.173498i	0.811585	+	0.584234i	$0.198605\pi$
$284$		0			0
$285$	864285.	−	498995.i	0.630296	−	0.363902i
$286$		0			0
$287$	−465272.	−	608790.i	−0.333428	−	0.436278i
$288$		0			0
$289$	−701733.	−	1.21544e6i	−0.494228	−	0.856028i
$290$		0			0
$291$	−1.72870e6	−	998066.i	−1.19671	−	0.690918i
$292$		0			0
$293$		−	1.92194e6i		−	1.30789i	−0.756542	−	0.653945i	$-0.773113\pi$
$293$		−	1.92194e6i		−	1.30789i	0.756542	−	0.653945i	$-0.226887\pi$
$294$		0			0
$295$		−	153059.i		−	0.102401i
$296$		0			0
$297$	824311.	+	475916.i	0.542250	+	0.313068i
$298$		0			0
$299$	40539.3	+	70216.1i	0.0262239	+	0.0454212i
$300$		0			0
$301$	−1.19794e6	−	1.56747e6i	−0.762115	−	0.997199i
$302$		0			0
$303$	1.49406e6	−	862597.i	0.934894	−	0.539761i
$304$		0			0
$305$	−39925.3	+	69152.7i	−0.0245753	+	0.0425657i
$306$		0			0
$307$	−940708.			−0.569651			−0.284825	−	0.958579i	$-0.591936\pi$
$307$	−940708.			−0.569651			−0.284825	+	0.958579i	$0.591936\pi$
$308$		0			0
$309$	2.94041e6			1.75191
$310$		0			0
$311$	365640.	−	633306.i	0.214364	−	0.371290i	−0.738712	−	0.674022i	$-0.764565\pi$
$311$	365640.	−	633306.i	0.214364	−	0.371290i	0.953076	+	0.302732i	$0.0978987\pi$
$312$		0			0
$313$	271139.	−	156542.i	0.156434	−	0.0903171i	−0.419740	−	0.907645i	$-0.637879\pi$
$313$	271139.	−	156542.i	0.156434	−	0.0903171i	0.576173	+	0.817327i	$0.304545\pi$
$314$		0			0
$315$	−67392.2	+	8739.66i	−0.0382678	+	0.00496270i
$316$		0			0
$317$	1.65827e6	+	2.87221e6i	0.926846	+	1.60534i	0.788565	+	0.614951i	$0.210824\pi$
$317$	1.65827e6	+	2.87221e6i	0.926846	+	1.60534i	0.138281	+	0.990393i	$0.455842\pi$
$318$		0			0
$319$	−369013.	−	213050.i	−0.203032	−	0.117221i
$320$		0			0
$321$		−	2.46107e6i		−	1.33309i
$322$		0			0
$323$		−	352145.i		−	0.187809i
$324$		0			0
$325$	71982.5	+	41559.1i	0.0378023	+	0.0218252i
$326$		0			0
$327$	−645462.	−	1.11797e6i	−0.333812	−	0.578179i
$328$		0			0
$329$	−11868.1	−	4942.87i	−0.00604493	−	0.00251761i
$330$		0			0
$331$	908606.	−	524584.i	0.455833	−	0.263175i	−0.254458	−	0.967084i	$-0.581897\pi$
$331$	908606.	−	524584.i	0.455833	−	0.263175i	0.710290	+	0.703909i	$0.248564\pi$
$332$		0			0
$333$	−57127.0	+	98946.8i	−0.0282313	+	0.0488980i
$334$		0			0
$335$	−1.08518e6			−0.528312
$336$		0			0
$337$	−2.90507e6			−1.39342			−0.696710	−	0.717353i	$-0.745353\pi$
$337$	−2.90507e6			−1.39342			−0.696710	+	0.717353i	$0.745353\pi$
$338$		0			0
$339$	−817837.	+	1.41653e6i	−0.386516	+	0.669465i
$340$		0			0
$341$	161039.	−	92976.0i	0.0749973	−	0.0432997i
$342$		0			0
$343$	−822120.	−	2.01784e6i	−0.377311	−	0.926086i
$344$		0			0
$345$	−465628.	−	806492.i	−0.210616	−	0.364798i
$346$		0			0
$347$	−391122.	−	225815.i	−0.174377	−	0.100677i	0.410271	−	0.911964i	$-0.365434\pi$
$347$	−391122.	−	225815.i	−0.174377	−	0.100677i	−0.584648	+	0.811287i	$0.698767\pi$
$348$		0			0
$349$		−	1.27258e6i		−	0.559269i	−0.960107	−	0.279634i	$-0.909787\pi$
$349$		−	1.27258e6i		−	0.559269i	0.960107	−	0.279634i	$-0.0902132\pi$
$350$		0			0
$351$			113169.i			0.0490299i
$352$		0			0
$353$	1.73409e6	+	1.00118e6i	0.740686	+	0.427636i	0.822319	−	0.569027i	$-0.192680\pi$
$353$	1.73409e6	+	1.00118e6i	0.740686	+	0.427636i	−0.0816324	+	0.996663i	$0.526013\pi$
$354$		0			0
$355$	−352205.	−	610037.i	−0.148328	−	0.256912i
$356$		0			0
$357$	−104193.	+	250172.i	−0.0432679	+	0.103889i
$358$		0			0
$359$	−1.09761e6	+	633703.i	−0.449480	+	0.259507i	−0.707610	−	0.706603i	$-0.750227\pi$
$359$	−1.09761e6	+	633703.i	−0.449480	+	0.259507i	0.258131	+	0.966110i	$0.416893\pi$
$360$		0			0
$361$	−2.54463e6	+	4.40743e6i	−1.02768	+	1.77999i
$362$		0			0
$363$	1.47696e6			0.588305
$364$		0			0
$365$	694457.			0.272843
$366$		0			0
$367$	−2.18287e6	+	3.78084e6i	−0.845985	+	1.46529i	0.0387779	+	0.999248i	$0.487654\pi$
$367$	−2.18287e6	+	3.78084e6i	−0.845985	+	1.46529i	−0.884763	+	0.466041i	$0.845680\pi$
$368$		0			0
$369$	−120736.	+	69707.1i	−0.0461607	+	0.0266509i
$370$		0			0
$371$	−595464.	−	4.59167e6i	−0.224606	−	1.73195i
$372$		0			0
$373$	1.74926e6	+	3.02980e6i	0.651001	+	1.12757i	0.982880	+	0.184245i	$0.0589840\pi$
$373$	1.74926e6	+	3.02980e6i	0.651001	+	1.12757i	−0.331879	+	0.943322i	$0.607683\pi$
$374$		0			0
$375$	−1.80874e6	−	1.04427e6i	−0.664198	−	0.383475i
$376$		0			0
$377$		−	50661.7i		−	0.0183580i
$378$		0			0
$379$			4.42455e6i			1.58224i	0.611663	+	0.791118i	$0.290501\pi$
$379$			4.42455e6i			1.58224i	−0.611663	+	0.791118i	$0.709499\pi$
$380$		0			0
$381$	1.88991e6	+	1.09114e6i	0.667006	+	0.385096i
$382$		0			0
$383$	2.38842e6	+	4.13686e6i	0.831980	+	1.44103i	0.896466	+	0.443113i	$0.146126\pi$
$383$	2.38842e6	+	4.13686e6i	0.831980	+	1.44103i	−0.0644852	+	0.997919i	$0.520541\pi$
$384$		0			0
$385$	−608172.	+	464799.i	−0.209110	+	0.159814i
$386$		0			0
$387$	−310862.	+	179476.i	−0.105509	+	0.0609158i
$388$		0			0
$389$	−1.27234e6	+	2.20375e6i	−0.426312	+	0.738395i	−0.996542	−	0.0830906i	$-0.973521\pi$
$389$	−1.27234e6	+	2.20375e6i	−0.426312	+	0.738395i	0.570230	+	0.821485i	$0.306854\pi$
$390$		0			0
$391$	−328598.			−0.108698
$392$		0			0
$393$	−2.11739e6			−0.691544
$394$		0			0
$395$	−264775.	+	458604.i	−0.0853856	+	0.147892i
$396$		0			0
$397$	−988211.	+	570544.i	−0.314683	+	0.181682i	−0.649020	−	0.760771i	$-0.724821\pi$
$397$	−988211.	+	570544.i	−0.314683	+	0.181682i	0.334337	+	0.942454i	$0.391488\pi$
$398$		0			0
$399$	4.62584e6	−	3.53533e6i	1.45465	−	1.11173i
$400$		0			0
$401$	−2.23541e6	−	3.87184e6i	−0.694217	−	1.20242i	−0.970444	−	0.241327i	$-0.922417\pi$
$401$	−2.23541e6	−	3.87184e6i	−0.694217	−	1.20242i	0.276227	−	0.961093i	$-0.410916\pi$
$402$		0			0
$403$	19147.0	+	11054.5i	0.00587269	+	0.00339060i
$404$		0			0
$405$		−	1.42722e6i		−	0.432369i
$406$		0			0
$407$			1.28693e6i			0.385097i
$408$		0			0
$409$	−497871.	−	287446.i	−0.147167	−	0.0849666i	0.424609	−	0.905377i	$-0.360412\pi$
$409$	−497871.	−	287446.i	−0.147167	−	0.0849666i	−0.571775	+	0.820410i	$0.693745\pi$
$410$		0			0
$411$	383823.	+	664801.i	0.112080	+	0.194127i
$412$		0			0
$413$	−114836.	−	885507.i	−0.0331285	−	0.255456i
$414$		0			0
$415$	351968.	−	203209.i	0.100319	−	0.0579192i
$416$		0			0
$417$	−2.64349e6	+	4.57866e6i	−0.744454	+	1.28943i
$418$		0			0
$419$	2.06791e6			0.575434			0.287717	−	0.957715i	$-0.407104\pi$
$419$	2.06791e6			0.575434			0.287717	+	0.957715i	$0.407104\pi$
$420$		0			0
$421$	−4.36685e6			−1.20078			−0.600390	−	0.799708i	$-0.704988\pi$
$421$	−4.36685e6			−1.20078			−0.600390	+	0.799708i	$0.704988\pi$
$422$		0			0
$423$	−1169.59	+	2025.80i	−0.000317822	+	0.000550484i
$424$		0			0
$425$	−291733.	+	168432.i	−0.0783454	+	0.0452327i
$426$		0			0
$427$	−179100.	+	430030.i	−0.0475364	+	0.114138i
$428$		0			0
$429$	−68520.2	−	118680.i	−0.0179753	−	0.0311341i
$430$		0			0
$431$	5.19547e6	+	2.99961e6i	1.34720	+	0.777806i	0.987852	−	0.155398i	$-0.0496659\pi$
$431$	5.19547e6	+	2.99961e6i	1.34720	+	0.777806i	0.359348	+	0.933204i	$0.382999\pi$
$432$		0			0
$433$		−	5.69706e6i		−	1.46026i	−0.683307	−	0.730131i	$-0.739459\pi$
$433$		−	5.69706e6i		−	1.46026i	0.683307	−	0.730131i	$-0.260541\pi$
$434$		0			0
$435$			581892.i			0.147441i
$436$		0			0
$437$	6.11368e6	+	3.52974e6i	1.53144	+	0.884176i
$438$		0			0
$439$	2.73386e6	+	4.73519e6i	0.677042	+	1.17267i	0.975867	+	0.218364i	$0.0700718\pi$
$439$	2.73386e6	+	4.73519e6i	0.677042	+	1.17267i	−0.298825	+	0.954308i	$0.596595\pi$
$440$		0			0
$441$	−383333.	+	101125.i	−0.0938598	+	0.0247606i
$442$		0			0
$443$	5.51411e6	−	3.18357e6i	1.33495	−	0.770735i	0.348898	−	0.937161i	$-0.386556\pi$
$443$	5.51411e6	−	3.18357e6i	1.33495	−	0.770735i	0.986054	+	0.166426i	$0.0532225\pi$
$444$		0			0
$445$	778618.	−	1.34861e6i	0.186391	−	0.322838i
$446$		0			0
$447$	2.89770e6			0.685938
$448$		0			0
$449$	4.50171e6			1.05381			0.526904	−	0.849925i	$-0.323353\pi$
$449$	4.50171e6			1.05381			0.526904	+	0.849925i	$0.323353\pi$
$450$		0			0
$451$	−785167.	+	1.35995e6i	−0.181769	+	0.314834i
$452$		0			0
$453$	−2.15527e6	+	1.24434e6i	−0.493464	+	0.284902i
$454$		0			0
$455$	−84013.8	−	34990.4i	−0.0190249	−	0.00792355i
$456$		0			0
$457$	718680.	+	1.24479e6i	0.160970	+	0.278808i	0.935217	−	0.354075i	$-0.115204\pi$
$457$	718680.	+	1.24479e6i	0.160970	+	0.278808i	−0.774247	+	0.632884i	$0.781871\pi$
$458$		0			0
$459$	−397208.	−	229328.i	−0.0880008	−	0.0508073i
$460$		0			0
$461$		−	6.30635e6i		−	1.38206i	−0.722828	−	0.691028i	$-0.757158\pi$
$461$		−	6.30635e6i		−	1.38206i	0.722828	−	0.691028i	$-0.242842\pi$
$462$		0			0
$463$			9.12301e6i			1.97782i	0.148531	+	0.988908i	$0.452545\pi$
$463$			9.12301e6i			1.97782i	−0.148531	+	0.988908i	$0.547455\pi$
$464$		0			0
$465$	−219919.	−	126970.i	−0.0471662	−	0.0272314i
$466$		0			0
$467$	−664462.	−	1.15088e6i	−0.140987	−	0.244196i	0.786882	−	0.617104i	$-0.211694\pi$
$467$	−664462.	−	1.15088e6i	−0.140987	−	0.244196i	−0.927868	+	0.372908i	$0.878361\pi$
$468$		0			0
$469$	−6.27820e6	+	814179.i	−1.31796	+	0.170918i
$470$		0			0
$471$	4.39858e6	−	2.53952e6i	0.913609	−	0.527472i
$472$		0			0
$473$	−2.02159e6	+	3.50149e6i	−0.415470	+	0.719615i
$474$		0			0
$475$	7.23707e6			1.47173
$476$		0			0
$477$	−842447.			−0.169530
$478$		0			0
$479$	−2.00910e6	+	3.47987e6i	−0.400095	+	0.692985i	−0.993737	−	0.111744i	$-0.964356\pi$
$479$	−2.00910e6	+	3.47987e6i	−0.400095	+	0.692985i	0.593642	+	0.804729i	$0.297690\pi$
$480$		0			0
$481$	−132512.	+	76505.8i	−0.0261151	+	0.0150776i
$482$		0			0
$483$	−3.29892e6	−	4.31652e6i	−0.643435	−	0.841910i
$484$		0			0
$485$	1.35841e6	+	2.35283e6i	0.262226	+	0.454188i
$486$		0			0
$487$	−7.43986e6	−	4.29540e6i	−1.42148	−	0.820695i	−0.425059	−	0.905166i	$-0.639747\pi$
$487$	−7.43986e6	−	4.29540e6i	−1.42148	−	0.820695i	−0.996426	+	0.0844709i	$0.973080\pi$
$488$		0			0
$489$			2.87921e6i			0.544505i
$490$		0			0
$491$			1.57232e6i			0.294332i	0.989112	+	0.147166i	$0.0470151\pi$
$491$			1.57232e6i			0.294332i	−0.989112	+	0.147166i	$0.952985\pi$
$492$		0			0
$493$	177815.	+	102662.i	0.0329497	+	0.0190235i
$494$		0			0
$495$	69636.4	+	120614.i	0.0127739	+	0.0221250i
$496$		0			0
$497$	−2.49533e6	−	3.26505e6i	−0.453145	−	0.592924i
$498$		0			0
$499$	−1.25743e6	+	725978.i	−0.226065	+	0.130518i	−0.608755	−	0.793358i	$-0.708331\pi$
$499$	−1.25743e6	+	725978.i	−0.226065	+	0.130518i	0.382691	+	0.923877i	$0.374998\pi$
$500$		0			0
$501$	−3.83692e6	+	6.64573e6i	−0.682948	+	1.18290i
$502$		0			0
$503$	−3.59897e6			−0.634247			−0.317123	−	0.948384i	$-0.602717\pi$
$503$	−3.59897e6			−0.634247			−0.317123	+	0.948384i	$0.602717\pi$
$504$		0			0
$505$	−2.34806e6			−0.409714
$506$		0			0
$507$	−3.02300e6	+	5.23599e6i	−0.522298	+	0.904647i
$508$		0			0
$509$	−1.76938e6	+	1.02155e6i	−0.302711	+	0.174770i	−0.643660	−	0.765312i	$-0.722585\pi$
$509$	−1.76938e6	+	1.02155e6i	−0.302711	+	0.174770i	0.340949	+	0.940082i	$0.389252\pi$
$510$		0			0
$511$	4.01770e6	−	521030.i	0.680653	−	0.0882695i
$512$		0			0
$513$	4.92680e6	+	8.53347e6i	0.826555	+	1.43164i
$514$		0			0
$515$	−3.46584e6	−	2.00101e6i	−0.575825	−	0.332453i
$516$		0			0
$517$			26348.1i			0.00433534i
$518$		0			0
$519$		−	1.27204e7i		−	2.07291i
$520$		0			0
$521$	6.36726e6	+	3.67614e6i	1.02768	+	0.593332i	0.916320	−	0.400448i	$-0.131145\pi$
$521$	6.36726e6	+	3.67614e6i	1.02768	+	0.593332i	0.111362	+	0.993780i	$0.464479\pi$
$522$		0			0
$523$	4.56417e6	+	7.90537e6i	0.729638	+	1.26377i	0.957036	+	0.289968i	$0.0936445\pi$
$523$	4.56417e6	+	7.90537e6i	0.729638	+	1.26377i	−0.227399	+	0.973802i	$0.573022\pi$
$524$		0			0
$525$	−5.14138e6	−	2.14130e6i	−0.814107	−	0.339062i
$526$		0			0
$527$	−77599.5	+	44802.1i	−0.0121712	+	0.00702703i
$528$		0			0
$529$	75537.1	−	130834.i	0.0117360	−	0.0203274i
$530$		0			0
$531$	−162466.			−0.0250050
$532$		0			0
$533$	−186707.			−0.0284670
$534$		0			0
$535$	−1.67480e6	+	2.90085e6i	−0.252976	+	0.438167i
$536$		0			0
$537$	8.74491e6	−	5.04887e6i	1.30864	−	0.755542i
$538$		0			0
$539$	−3.16979e6	+	3.14534e6i	−0.469957	+	0.466332i
$540$		0			0
$541$	−5.66666e6	−	9.81493e6i	−0.832403	−	1.44176i	−0.896128	−	0.443797i	$-0.853631\pi$
$541$	−5.66666e6	−	9.81493e6i	−0.832403	−	1.44176i	0.0637246	−	0.997968i	$-0.479702\pi$
$542$		0			0
$543$	−2.52804e6	−	1.45956e6i	−0.367946	−	0.212433i
$544$		0			0
$545$			1.75700e6i			0.253385i
$546$		0			0
$547$			9.79610e6i			1.39986i	0.714211	+	0.699930i	$0.246786\pi$
$547$			9.79610e6i			1.39986i	−0.714211	+	0.699930i	$0.753214\pi$
$548$		0			0
$549$	73402.9	+	42379.2i	0.0103940	+	0.00600097i
$550$		0			0
$551$	−2.20555e6	−	3.82012e6i	−0.309483	−	0.536040i
$552$		0			0
$553$	−1.18775e6	+	2.85186e6i	−0.165163	+	0.396565i
$554$		0			0
$555$	1.52201e6	−	878735.i	0.209742	−	0.121095i
$556$		0			0
$557$	−3.23228e6	+	5.59847e6i	−0.441439	+	0.764595i	−0.997797	−	0.0663481i	$-0.978865\pi$
$557$	−3.23228e6	+	5.59847e6i	−0.441439	+	0.764595i	0.556357	+	0.830943i	$0.312199\pi$
$558$		0			0
$559$	−480718.			−0.0650670
$560$		0			0
$561$	555402.			0.0745076
$562$		0			0
$563$	627220.	−	1.08638e6i	0.0833967	−	0.144447i	−0.821310	−	0.570482i	$-0.806756\pi$
$563$	627220.	−	1.08638e6i	0.0833967	−	0.144447i	0.904707	+	0.426035i	$0.140090\pi$
$564$		0			0
$565$	1.92796e6	−	1.11311e6i	0.254084	−	0.146695i
$566$		0			0
$567$	−1.07080e6	−	8.25704e6i	−0.139879	−	1.07862i
$568$		0			0
$569$	−2.77361e6	−	4.80403e6i	−0.359140	−	0.622050i	0.628677	−	0.777667i	$-0.283597\pi$
$569$	−2.77361e6	−	4.80403e6i	−0.359140	−	0.622050i	−0.987817	+	0.155617i	$0.950263\pi$
$570$		0			0
$571$	−5.57019e6	−	3.21595e6i	−0.714956	−	0.412780i	0.0979373	−	0.995193i	$-0.468776\pi$
$571$	−5.57019e6	−	3.21595e6i	−0.714956	−	0.412780i	−0.812893	+	0.582412i	$0.802109\pi$
$572$		0			0
$573$			177155.i			0.0225407i
$574$		0			0
$575$		−	6.75314e6i		−	0.851797i
$576$		0			0
$577$	9.92482e6	+	5.73010e6i	1.24103	+	0.716510i	0.969304	−	0.245864i	$-0.0790715\pi$
$577$	9.92482e6	+	5.73010e6i	1.24103	+	0.716510i	0.271728	+	0.962374i	$0.412405\pi$
$578$		0			0
$579$	−7.73211e6	−	1.33924e7i	−0.958521	−	1.66021i
$580$		0			0
$581$	1.88381e6	−	1.43971e6i	0.231524	−	0.176944i
$582$		0			0
$583$	−8.21784e6	+	4.74457e6i	−1.00135	+	0.578130i
$584$		0			0
$585$	−8279.51	+	14340.5i	−0.00100026	+	0.00173251i
$586$		0			0
$587$	1.54952e7			1.85610			0.928052	−	0.372451i	$-0.121483\pi$
$587$	1.54952e7			1.85610			0.928052	+	0.372451i	$0.121483\pi$
$588$		0			0
$589$	1.92502e6			0.228638
$590$		0			0
$591$	664978.	−	1.15178e6i	0.0783138	−	0.135644i
$592$		0			0
$593$	7.54037e6	−	4.35344e6i	0.880554	−	0.508388i	0.00971325	−	0.999953i	$-0.496908\pi$
$593$	7.54037e6	−	4.35344e6i	0.880554	−	0.508388i	0.870841	+	0.491564i	$0.163575\pi$
$594$		0			0
$595$	293058.	−	223971.i	0.0339361	−	0.0259358i
$596$		0			0
$597$	−8.02929e6	−	1.39071e7i	−0.922023	−	1.59699i
$598$		0			0
$599$	−9.92434e6	−	5.72982e6i	−1.13015	−	0.652490i	−0.186175	−	0.982517i	$-0.559609\pi$
$599$	−9.92434e6	−	5.72982e6i	−1.13015	−	0.652490i	−0.943972	+	0.330026i	$0.892942\pi$
$600$		0			0
$601$		−	9.83228e6i		−	1.11037i	−0.831727	−	0.555185i	$-0.812647\pi$
$601$		−	9.83228e6i		−	1.11037i	0.831727	−	0.555185i	$-0.187353\pi$
$602$		0			0
$603$			1.15188e6i			0.129007i
$604$		0			0
$605$	−1.74089e6	−	1.00510e6i	−0.193367	−	0.111640i
$606$		0			0
$607$	6.70187e6	+	1.16080e7i	0.738286	+	1.27875i	0.953267	+	0.302130i	$0.0976977\pi$
$607$	6.70187e6	+	1.16080e7i	0.738286	+	1.27875i	−0.214981	+	0.976618i	$0.568969\pi$
$608$		0			0
$609$	436576.	+	3.36647e6i	0.0476998	+	0.367817i
$610$		0			0
$611$	−2712.99	+	1566.35i	−0.000293999	+	0.000169740i
$612$		0			0
$613$	−838947.	+	1.45310e6i	−0.0901744	+	0.156187i	−0.907584	−	0.419870i	$-0.862076\pi$
$613$	−838947.	+	1.45310e6i	−0.0901744	+	0.156187i	0.817410	+	0.576056i	$0.195409\pi$
$614$		0			0
$615$	2.14449e6			0.228631
$616$		0			0
$617$	1.48745e7			1.57300			0.786499	−	0.617592i	$-0.211891\pi$
$617$	1.48745e7			1.57300			0.786499	+	0.617592i	$0.211891\pi$
$618$		0			0
$619$	−3.56661e6	+	6.17755e6i	−0.374136	+	0.648022i	−0.990197	−	0.139676i	$-0.955394\pi$
$619$	−3.56661e6	+	6.17755e6i	−0.374136	+	0.648022i	0.616061	+	0.787698i	$0.288727\pi$
$620$		0			0
$621$	7.96285e6	−	4.59735e6i	0.828590	−	0.478387i
$622$		0			0
$623$	3.49279e6	−	8.38638e6i	0.360539	−	0.865674i
$624$		0			0
$625$	−2.68990e6	−	4.65904e6i	−0.275445	−	0.477085i
$626$		0			0
$627$	−1.03335e7	−	5.96603e6i	−1.04973	−	0.606061i
$628$		0			0
$629$		−	620131.i		−	0.0624967i
$630$		0			0
$631$		−	9.49875e6i		−	0.949715i	−0.880063	−	0.474857i	$-0.842500\pi$
$631$		−	9.49875e6i		−	0.949715i	0.880063	−	0.474857i	$-0.157500\pi$
$632$		0			0
$633$	6.04639e6	+	3.49089e6i	0.599773	+	0.346279i
$634$		0			0
$635$	−1.48509e6	−	2.57225e6i	−0.146156	−	0.253150i
$636$		0			0
$637$	−512305.	−	139400.i	−0.0500241	−	0.0136117i
$638$		0			0
$639$	−647530.	+	373852.i	−0.0627347	+	0.0362199i
$640$		0			0
$641$	7.67359e6	−	1.32910e7i	0.737655	−	1.27766i	−0.215894	−	0.976417i	$-0.569266\pi$
$641$	7.67359e6	−	1.32910e7i	0.737655	−	1.27766i	0.953549	−	0.301239i	$-0.0974002\pi$
$642$		0			0
$643$	−988668.			−0.0943025			−0.0471512	−	0.998888i	$-0.515014\pi$
$643$	−988668.			−0.0943025			−0.0471512	+	0.998888i	$0.515014\pi$
$644$		0			0
$645$	5.52146e6			0.522582
$646$		0			0
$647$	−5.51747e6	+	9.55655e6i	−0.518179	+	0.897512i	0.481598	+	0.876392i	$0.340056\pi$
$647$	−5.51747e6	+	9.55655e6i	−0.518179	+	0.897512i	−0.999777	+	0.0211198i	$0.993277\pi$
$648$		0			0
$649$	−1.58482e6	+	914994.i	−0.147695	+	0.0852720i
$650$		0			0
$651$	−1.36758e6	−	569574.i	−0.126474	−	0.0526742i
$652$		0			0
$653$	2.55762e6	+	4.42993e6i	0.234722	+	0.406550i	0.959192	−	0.282756i	$-0.0912488\pi$
$653$	2.55762e6	+	4.42993e6i	0.234722	+	0.406550i	−0.724470	+	0.689306i	$0.757915\pi$
$654$		0			0
$655$	2.49576e6	+	1.44093e6i	0.227300	+	0.131232i
$656$		0			0
$657$		−	737139.i		−	0.0666248i
$658$		0			0
$659$		−	1.13694e7i		−	1.01982i	−0.860227	−	0.509911i	$-0.829678\pi$
$659$		−	1.13694e7i		−	1.01982i	0.860227	−	0.509911i	$-0.170322\pi$
$660$		0			0
$661$	−1.41836e7	−	8.18893e6i	−1.26265	−	0.728993i	−0.289066	−	0.957309i	$-0.593345\pi$
$661$	−1.41836e7	−	8.18893e6i	−1.26265	−	0.728993i	−0.973587	+	0.228316i	$0.926678\pi$
$662$		0			0
$663$	33017.6	+	57188.2i	0.00291717	+	0.00505269i
$664$		0			0
$665$	−7.85832e6	+	1.01909e6i	−0.689089	+	0.0893635i
$666$		0			0
$667$	−3.56467e6	+	2.05806e6i	−0.310245	+	0.179120i
$668$		0			0
$669$	−491775.	+	851779.i	−0.0424816	+	0.0735803i
$670$		0			0
$671$	954701.			0.0818580
$672$		0			0
$673$	9.53588e6			0.811564			0.405782	−	0.913970i	$-0.366999\pi$
$673$	9.53588e6			0.811564			0.405782	+	0.913970i	$0.366999\pi$
$674$		0			0
$675$	4.71301e6	−	8.16317e6i	0.398143	−	0.689604i
$676$		0			0
$677$	1.06224e7	−	6.13284e6i	0.890740	−	0.514269i	0.0165554	−	0.999863i	$-0.494730\pi$
$677$	1.06224e7	−	6.13284e6i	0.890740	−	0.514269i	0.874184	+	0.485594i	$0.161397\pi$
$678$		0			0
$679$	9.62416e6	+	1.25929e7i	0.801103	+	1.04821i
$680$		0			0
$681$	450887.	+	780959.i	0.0372563	+	0.0645298i
$682$		0			0
$683$	−2.91586e6	−	1.68347e6i	−0.239175	−	0.138088i	0.375623	−	0.926773i	$-0.377429\pi$
$683$	−2.91586e6	−	1.68347e6i	−0.239175	−	0.138088i	−0.614797	+	0.788685i	$0.710762\pi$
$684$		0			0
$685$		−	1.04480e6i		−	0.0850756i
$686$		0			0
$687$		−	57752.4i		−	0.00466851i
$688$		0			0
$689$	−977071.	−	564112.i	−0.0784112	−	0.0452707i
$690$		0			0
$691$	−2.65246e6	−	4.59420e6i	−0.211327	−	0.366028i	0.740803	−	0.671722i	$-0.234445\pi$
$691$	−2.65246e6	−	4.59420e6i	−0.211327	−	0.366028i	−0.952130	+	0.305694i	$0.901112\pi$
$692$		0			0
$693$	493366.	+	645551.i	0.0390244	+	0.0510620i
$694$		0			0
$695$	6.23174e6	−	3.59789e6i	0.489381	−	0.282544i
$696$		0			0
$697$	378346.	−	655315.i	0.0294990	−	0.0510938i
$698$		0			0
$699$	1.95688e7			1.51486
$700$		0			0
$701$	3.03260e6			0.233088			0.116544	−	0.993186i	$-0.462818\pi$
$701$	3.03260e6			0.233088			0.116544	+	0.993186i	$0.462818\pi$
$702$		0			0
$703$	−6.66133e6	+	1.15378e7i	−0.508362	+	0.880508i
$704$		0			0
$705$	31161.1	−	17990.8i	0.00236124	−	0.00136326i
$706$		0			0
$707$	−1.35844e7	+	1.76168e6i	−1.02210	+	0.132549i
$708$		0			0
$709$	−7.72319e6	−	1.33770e7i	−0.577007	−	0.999406i	−0.995820	−	0.0913332i	$-0.970887\pi$
$709$	−7.72319e6	−	1.33770e7i	−0.577007	−	0.999406i	0.418813	−	0.908072i	$-0.362446\pi$
$710$		0			0
$711$	486790.	+	281049.i	0.0361134	+	0.0208501i
$712$		0			0
$713$		−	1.79630e6i		−	0.132329i
$714$		0			0
$715$			186517.i			0.0136444i
$716$		0			0
$717$	7.51492e6	+	4.33874e6i	0.545917	+	0.315185i
$718$		0			0
$719$	8.99286e6	+	1.55761e7i	0.648748	+	1.12366i	0.983422	+	0.181330i	$0.0580402\pi$
$719$	8.99286e6	+	1.55761e7i	0.648748	+	1.12366i	−0.334675	+	0.942334i	$0.608626\pi$
$720$		0			0
$721$	−2.15525e7	−	8.97627e6i	−1.54405	−	0.643070i
$722$		0			0
$723$	7.95557e6	−	4.59315e6i	0.566012	−	0.326787i
$724$		0			0
$725$	−2.10984e6	+	3.65435e6i	−0.149075	+	0.258205i
$726$		0			0
$727$	−1.55969e7			−1.09447			−0.547234	−	0.836980i	$-0.684319\pi$
$727$	−1.55969e7			−1.09447			−0.547234	+	0.836980i	$0.684319\pi$
$728$		0			0
$729$	1.26988e7			0.884998
$730$		0			0
$731$	974136.	−	1.68725e6i	0.0674258	−	0.116785i
$732$		0			0
$733$	−1.11442e7	+	6.43409e6i	−0.766104	+	0.442310i	−0.831483	−	0.555550i	$-0.812508\pi$
$733$	−1.11442e7	+	6.43409e6i	−0.766104	+	0.442310i	0.0653790	+	0.997861i	$0.479174\pi$
$734$		0			0
$735$	5.88426e6	+	1.60113e6i	0.401766	+	0.109322i
$736$		0			0
$737$	6.48726e6	+	1.12363e7i	0.439939	+	0.761997i
$738$		0			0
$739$	−1.72415e7	−	9.95440e6i	−1.16135	−	0.670508i	−0.209726	−	0.977760i	$-0.567257\pi$
$739$	−1.72415e7	−	9.95440e6i	−1.16135	−	0.670508i	−0.951628	+	0.307252i	$0.900591\pi$
$740$		0			0
$741$		−	1.41868e6i		−	0.0949157i
$742$		0			0
$743$		−	2.89554e7i		−	1.92423i	−0.272640	−	0.962116i	$-0.587897\pi$
$743$		−	2.89554e7i		−	1.92423i	0.272640	−	0.962116i	$-0.412103\pi$
$744$		0			0
$745$	−3.41550e6	−	1.97194e6i	−0.225457	−	0.130168i
$746$		0			0
$747$	−215698.	−	373600.i	−0.0141431	−	0.0244966i
$748$		0			0
$749$	−7.51297e6	+	1.80391e7i	−0.489336	+	1.17492i
$750$		0			0
$751$	56095.8	−	32386.9i	0.00362936	−	0.00209541i	−0.498184	−	0.867071i	$-0.666000\pi$
$751$	56095.8	−	32386.9i	0.00362936	−	0.00209541i	0.501814	+	0.864976i	$0.332666\pi$
$752$		0			0
$753$	−8.72188e6	+	1.51067e7i	−0.560561	+	0.970920i
$754$		0			0
$755$	3.38720e6			0.216259
$756$		0			0
$757$	−1.28686e7			−0.816190			−0.408095	−	0.912940i	$-0.633807\pi$
$757$	−1.28686e7			−0.816190			−0.408095	+	0.912940i	$0.633807\pi$
$758$		0			0
$759$	−5.56709e6	+	9.64248e6i	−0.350771	+	0.607553i
$760$		0			0
$761$	−1.58510e7	+	9.15160e6i	−0.992193	+	0.572843i	−0.905929	−	0.423429i	$-0.860826\pi$
$761$	−1.58510e7	+	9.15160e6i	−0.992193	+	0.572843i	−0.0862641	+	0.996272i	$0.527493\pi$
$762$		0			0
$763$	1.31822e6	+	1.01649e7i	0.0819742	+	0.632110i
$764$		0			0
$765$	−33555.5	−	58119.8i	−0.00207305	−	0.00359063i
$766$		0			0
$767$	−188429.	−	108789.i	−0.0115654	−	0.00667726i
$768$		0			0
$769$			1.68118e7i			1.02518i	0.858634	+	0.512589i	$0.171314\pi$
$769$			1.68118e7i			1.02518i	−0.858634	+	0.512589i	$0.828686\pi$
$770$		0			0
$771$			2.19237e7i			1.32824i
$772$		0			0
$773$	2.16919e7	+	1.25238e7i	1.30571	+	0.753854i	0.981378	−	0.192088i	$-0.0615259\pi$
$773$	2.16919e7	+	1.25238e7i	1.30571	+	0.753854i	0.324336	+	0.945942i	$0.394859\pi$
$774$		0			0
$775$	−920744.	−	1.59478e6i	−0.0550662	−	0.0953774i
$776$		0			0
$777$	8.14615e6	−	6.22574e6i	0.484061	−	0.369946i
$778$		0			0
$779$	−1.40785e7	+	8.12825e6i	−0.831216	+	0.479903i
$780$		0			0
$781$	−4.21099e6	+	7.29365e6i	−0.247034	+	0.427875i
$782$		0			0
$783$	−5.74528e6			−0.334894
$784$		0			0
$785$	−6.91278e6			−0.400386
$786$		0			0
$787$	1.99502e6	−	3.45547e6i	0.114818	−	0.198870i	−0.802889	−	0.596128i	$-0.796705\pi$
$787$	1.99502e6	−	3.45547e6i	0.114818	−	0.198870i	0.917707	+	0.397258i	$0.130038\pi$
$788$		0			0
$789$	2.28135e7	−	1.31714e7i	1.30467	−	0.753249i
$790$		0			0
$791$	1.03189e7	−	7.88625e6i	0.586395	−	0.448156i
$792$		0			0
$793$	56755.2	+	98302.9i	0.00320496	+	0.00555115i
$794$		0			0
$795$	1.12225e7	+	6.47931e6i	0.629755	+	0.363589i
$796$		0			0
$797$			2.69992e7i			1.50558i	0.658259	+	0.752792i	$0.271293\pi$
$797$			2.69992e7i			1.50558i	−0.658259	+	0.752792i	$0.728707\pi$
$798$		0			0
$799$		−	12696.3i		−	0.000703575i
$800$		0			0
$801$	−1.43149e6	−	826473.i	−0.0788330	−	0.0455142i
$802$		0			0
$803$	−4.15149e6	−	7.19060e6i	−0.227204	−	0.393528i
$804$		0			0
$805$	950949.	+	7.33284e6i	0.0517211	+	0.398825i
$806$		0			0
$807$	−3.08735e7	+	1.78248e7i	−1.66879	+	0.963476i
$808$		0			0
$809$	8.61028e6	−	1.49134e7i	0.462536	−	0.801136i	−0.536550	−	0.843868i	$-0.680273\pi$
$809$	8.61028e6	−	1.49134e7i	0.462536	−	0.801136i	0.999087	+	0.0427321i	$0.0136062\pi$
$810$		0			0
$811$	1.90148e7			1.01517			0.507587	−	0.861601i	$-0.330538\pi$
$811$	1.90148e7			1.01517			0.507587	+	0.861601i	$0.330538\pi$
$812$		0			0
$813$	−6.64325e6			−0.352496
$814$		0			0
$815$	1.95936e6	−	3.39371e6i	0.103329	−	0.178970i
$816$		0			0
$817$	−3.62483e7	+	2.09280e7i	−1.89991	+	1.09691i
$818$		0			0
$819$	−37140.9	+	89177.3i	−0.00193483	+	0.00464563i
$820$		0			0
$821$	−1.54355e6	−	2.67352e6i	−0.0799216	−	0.138428i	0.823294	−	0.567615i	$-0.192134\pi$
$821$	−1.54355e6	−	2.67352e6i	−0.0799216	−	0.138428i	−0.903216	+	0.429186i	$0.858800\pi$
$822$		0			0
$823$	2.03659e7	+	1.17582e7i	1.04810	+	0.605122i	0.922117	−	0.386910i	$-0.126458\pi$
$823$	2.03659e7	+	1.17582e7i	1.04810	+	0.605122i	0.125984	+	0.992032i	$0.459791\pi$
$824$		0			0
$825$			1.14143e7i			0.583866i
$826$		0			0
$827$			2.15389e7i			1.09512i	0.836767	+	0.547559i	$0.184443\pi$
$827$			2.15389e7i			1.09512i	−0.836767	+	0.547559i	$0.815557\pi$
$828$		0			0
$829$	−1.14533e7	−	6.61258e6i	−0.578823	−	0.334183i	0.181843	−	0.983328i	$-0.441794\pi$
$829$	−1.14533e7	−	6.61258e6i	−0.578823	−	0.334183i	−0.760665	+	0.649144i	$0.775127\pi$
$830$		0			0
$831$	4.15889e6	+	7.20342e6i	0.208918	+	0.361856i
$832$		0			0
$833$	1.52742e6	−	1.51563e6i	0.0762684	−	0.0756801i
$834$		0			0
$835$	9.04510e6	−	5.22219e6i	0.448949	−	0.259201i
$836$		0			0
$837$	1.25364e6	−	2.17136e6i	0.0618526	−	0.107132i
$838$		0			0
$839$	1.67107e7			0.819575			0.409788	−	0.912181i	$-0.365603\pi$
$839$	1.67107e7			0.819575			0.409788	+	0.912181i	$0.365603\pi$
$840$		0			0
$841$	−1.79392e7			−0.874607
$842$		0			0
$843$	9.13348e6	−	1.58196e7i	0.442657	−	0.766704i
$844$		0			0
$845$	7.12639e6	−	4.11442e6i	0.343343	−	0.198229i
$846$		0			0
$847$	−1.08258e7	−	4.50876e6i	−0.518503	−	0.215948i
$848$		0			0
$849$	−2.20354e6	−	3.81664e6i	−0.104918	−	0.181724i
$850$		0			0
$851$	1.07662e7	+	6.21590e6i	0.509613	+	0.294225i
$852$		0			0
$853$			484559.i			0.0228020i	0.999935	+	0.0114010i	$0.00362914\pi$
$853$			484559.i			0.0228020i	−0.999935	+	0.0114010i	$0.996371\pi$
$854$		0			0
$855$			1.44179e6i			0.0674506i
$856$		0			0
$857$	−2.82629e7	−	1.63176e7i	−1.31451	−	0.758935i	−0.331674	−	0.943394i	$-0.607613\pi$
$857$	−2.82629e7	−	1.63176e7i	−1.31451	−	0.758935i	−0.982840	+	0.184459i	$0.940947\pi$
$858$		0			0
$859$	−5.10980e6	−	8.85044e6i	−0.236277	−	0.409243i	0.723366	−	0.690465i	$-0.242594\pi$
$859$	−5.10980e6	−	8.85044e6i	−0.236277	−	0.409243i	−0.959643	+	0.281221i	$0.909261\pi$
$860$		0			0
$861$	1.24067e7	−	1.60894e6i	0.570359	−	0.0739662i
$862$		0			0
$863$	2.91512e7	−	1.68305e7i	1.33239	−	0.769253i	0.346721	−	0.937968i	$-0.387295\pi$
$863$	2.91512e7	−	1.68305e7i	1.33239	−	0.769253i	0.985665	+	0.168715i	$0.0539617\pi$
$864$		0			0
$865$	−8.65645e6	+	1.49934e7i	−0.393369	+	0.681334i
$866$		0			0
$867$	2.29151e7			1.03532
$868$		0			0
$869$	6.33135e6			0.284411
$870$		0			0
$871$	−771312.	+	1.33595e6i	−0.0344496	+	0.0596685i
$872$		0			0
$873$	2.49744e6	−	1.44190e6i	0.110907	−	0.0640322i
$874$		0			0
$875$	1.00697e7	+	1.31759e7i	0.444630	+	0.581781i
$876$		0			0
$877$	3.88346e6	+	6.72635e6i	0.170498	+	0.295311i	0.938594	−	0.345023i	$-0.112129\pi$
$877$	3.88346e6	+	6.72635e6i	0.170498	+	0.295311i	−0.768096	+	0.640335i	$0.778796\pi$
$878$		0			0
$879$	2.71764e7	+	1.56903e7i	1.18637	+	0.684950i
$880$		0			0
$881$		−	3.44116e7i		−	1.49370i	−0.664990	−	0.746852i	$-0.731564\pi$
$881$		−	3.44116e7i		−	1.49370i	0.664990	−	0.746852i	$-0.268436\pi$
$882$		0			0
$883$			4.33214e7i			1.86982i	0.354880	+	0.934912i	$0.384522\pi$
$883$			4.33214e7i			1.86982i	−0.354880	+	0.934912i	$0.615478\pi$
$884$		0			0
$885$	2.16427e6	+	1.24954e6i	0.0928865	+	0.0536280i
$886$		0			0
$887$	−40392.9	−	69962.6i	−0.00172384	−	0.00298577i	0.865162	−	0.501492i	$-0.167215\pi$
$887$	−40392.9	−	69962.6i	−0.00172384	−	0.00298577i	−0.866886	+	0.498506i	$0.833882\pi$
$888$		0			0
$889$	−1.05217e7	−	1.37672e7i	−0.446510	−	0.584241i
$890$		0			0
$891$	−1.47779e7	+	8.53200e6i	−0.623616	+	0.360045i
$892$		0			0
$893$	−136381.	+	236219.i	−0.00572303	+	0.00991258i
$894$		0			0
$895$	−1.37434e7			−0.573506
$896$		0			0
$897$	−1.32381e6			−0.0549345
$898$		0			0
$899$	−561206.	+	972037.i	−0.0231592	+	0.0401129i
$900$		0			0
$901$	3.95991e6	−	2.28625e6i	0.162507	−	0.0938237i
$902$		0			0
$903$	3.19438e7	−	4.14258e6i	1.30367	−	0.169064i
$904$		0			0
$905$	1.98652e6	+	3.44076e6i	0.0806254	+	0.139647i
$906$		0			0
$907$	9.05859e6	+	5.22998e6i	0.365630	+	0.211097i	0.671548	−	0.740961i	$-0.265630\pi$
$907$	9.05859e6	+	5.22998e6i	0.365630	+	0.211097i	−0.305917	+	0.952058i	$0.598963\pi$
$908$		0			0
$909$			2.49237e6i			0.100047i
$910$		0			0
$911$		−	1.12503e7i		−	0.449127i	−0.974459	−	0.224563i	$-0.927904\pi$
$911$		−	1.12503e7i		−	0.449127i	0.974459	−	0.224563i	$-0.0720956\pi$
$912$		0			0
$913$	−4.20816e6	−	2.42958e6i	−0.167076	−	0.0964616i
$914$		0			0
$915$	−651882.	−	1.12909e6i	−0.0257405	−	0.0445838i
$916$		0			0
$917$	1.55200e7	+	6.46383e6i	0.609493	+	0.253844i
$918$		0			0
$919$	−4.64723e6	+	2.68308e6i	−0.181512	+	0.104796i	−0.588003	−	0.808859i	$-0.700086\pi$
$919$	−4.64723e6	+	2.68308e6i	−0.181512	+	0.104796i	0.406491	+	0.913655i	$0.366752\pi$
$920$		0			0
$921$	7.67972e6	−	1.33017e7i	0.298329	−	0.516722i
$922$		0			0
$923$	−1.00134e6			−0.0386882
$924$		0			0
$925$	1.27445e7			0.489745
$926$		0			0
$927$	−2.12399e6	+	3.67886e6i	−0.0811807	+	0.140609i
$928$		0			0
$929$	−2.14406e7	+	1.23787e7i	−0.815074	+	0.470583i	−0.848715	−	0.528851i	$-0.822623\pi$
$929$	−2.14406e7	+	1.23787e7i	−0.815074	+	0.470583i	0.0336410	+	0.999434i	$0.489290\pi$
$930$		0			0
$931$	−4.46988e7	+	1.17917e7i	−1.69014	+	0.445864i
$932$		0			0
$933$	5.96999e6	+	1.03403e7i	0.224527	+	0.388893i
$934$		0			0
$935$	−654649.	−	377962.i	−0.0244895	−	0.0141390i
$936$		0			0
$937$			1.46850e6i			0.0546419i	0.999627	+	0.0273210i	$0.00869762\pi$
$937$			1.46850e6i			0.0546419i	−0.999627	+	0.0273210i	$0.991302\pi$
$938$		0			0
$939$			5.11189e6i			0.189198i
$940$		0			0
$941$	5.16498e6	+	2.98200e6i	0.190149	+	0.109783i	0.592052	−	0.805899i	$-0.298318\pi$
$941$	5.16498e6	+	2.98200e6i	0.190149	+	0.109783i	−0.401903	+	0.915682i	$0.631651\pi$
$942$		0			0
$943$	7.58472e6	+	1.31371e7i	0.277754	+	0.481084i
$944$		0			0
$945$	−3.96808e6	+	9.52758e6i	−0.144544	+	0.347059i
$946$		0			0
$947$	4.13119e7	−	2.38514e7i	1.49692	−	0.864250i	0.496931	−	0.867790i	$-0.334460\pi$
$947$	4.13119e7	−	2.38514e7i	1.49692	−	0.864250i	0.999994	+	0.00353991i	$0.00112679\pi$
$948$		0			0
$949$	493597.	−	854935.i	0.0177913	−	0.0308154i
$950$		0			0
$951$	−5.41510e7			−1.94158
$952$		0			0
$953$	−4.82889e7			−1.72232			−0.861162	−	0.508330i	$-0.830263\pi$
$953$	−4.82889e7			−1.72232			−0.861162	+	0.508330i	$0.830263\pi$
$954$		0			0
$955$	120557.	−	208812.i	0.00427746	−	0.00740877i
$956$		0			0
$957$	6.02507e6	−	3.47858e6i	0.212658	−	0.122778i
$958$		0			0
$959$	−783878.	−	6.04455e6i	−0.0275234	−	0.212235i
$960$		0			0
$961$	1.40697e7	+	2.43694e7i	0.491445	+	0.851208i
$962$		0			0
$963$	3.07913e6	+	1.77774e6i	0.106995	+	0.0617735i
$964$		0			0
$965$			2.10474e7i			0.727580i
$966$		0			0
$967$		−	5.23912e7i		−	1.80174i	−0.434089	−	0.900870i	$-0.642930\pi$
$967$		−	5.23912e7i		−	1.80174i	0.434089	−	0.900870i	$-0.357070\pi$
$968$		0			0
$969$	4.97935e6	+	2.87483e6i	0.170358	+	0.0983565i
$970$		0			0
$971$	−1.39434e7	−	2.41507e7i	−0.474592	−	0.822017i	0.524985	−	0.851112i	$-0.324071\pi$
$971$	−1.39434e7	−	2.41507e7i	−0.474592	−	0.822017i	−0.999577	+	0.0290944i	$0.990738\pi$
$972$		0			0
$973$	3.33536e7	−	2.54907e7i	1.12943	−	0.863176i
$974$		0			0
$975$	−1.17530e6	+	678558.i	−0.0395946	+	0.0228599i
$976$		0			0
$977$	2.87737e7	−	4.98375e7i	0.964405	−	1.67040i	0.253201	−	0.967414i	$-0.418517\pi$
$977$	2.87737e7	−	4.98375e7i	0.964405	−	1.67040i	0.711204	−	0.702985i	$-0.248150\pi$
$978$		0			0
$979$	−1.86184e7			−0.620850
$980$		0			0
$981$	1.86499e6			0.0618732
$982$		0			0
$983$	5.32884e6	−	9.22981e6i	0.175893	−	0.304656i	−0.764577	−	0.644532i	$-0.777052\pi$
$983$	5.32884e6	−	9.22981e6i	0.175893	−	0.304656i	0.940470	+	0.339877i	$0.110385\pi$
$984$		0			0
$985$	−1.56761e6	+	905061.i	−0.0514811	+	0.0297226i
$986$		0			0
$987$	166781.	−	127463.i	0.00544946	−	0.00416478i
$988$		0			0
$989$	1.95285e7	+	3.38244e7i	0.634862	+	1.09961i
$990$		0			0
$991$	−5.15687e6	−	2.97732e6i	−0.166802	−	0.0963034i	0.414275	−	0.910152i	$-0.364035\pi$
$991$	−5.15687e6	−	2.97732e6i	−0.166802	−	0.0963034i	−0.581077	+	0.813848i	$0.697369\pi$
$992$		0			0
$993$			1.71303e7i			0.551306i
$994$		0			0
$995$			2.18564e7i			0.699875i
$996$		0			0
$997$	−3.30824e7	−	1.91001e7i	−1.05404	−	0.608552i	−0.130265	−	0.991479i	$-0.541583\pi$
$997$	−3.30824e7	−	1.91001e7i	−1.05404	−	0.608552i	−0.923779	+	0.382927i	$0.874916\pi$
$998$		0			0
$999$	8.67614e6	+	1.50275e7i	0.275051	+	0.476402i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.6.p.a.31.11	✓	80
4.3	odd	2	inner	224.6.p.a.31.30	yes	80
7.5	odd	6	inner	224.6.p.a.159.30	yes	80
28.19	even	6	inner	224.6.p.a.159.11	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.6.p.a.31.11	✓	80	1.1	even	1	trivial
224.6.p.a.31.30	yes	80	4.3	odd	2	inner
224.6.p.a.159.11	yes	80	28.19	even	6	inner
224.6.p.a.159.30	yes	80	7.5	odd	6	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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	224.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.16376 + 14.1401i) q^{3} +(19.2452 - 11.1112i) q^{5} +(103.004 - 78.7217i) q^{7} +(-11.7941 - 20.4280i) q^{9} +(-230.097 - 132.846i) q^{11} -31.5899i q^{13} +362.837i q^{15} +(110.876 + 64.0143i) q^{17} +(-1375.26 - 2382.02i) q^{19} +(272.226 + 2099.15i) q^{21} +(-2222.74 + 1283.30i) q^{23} +(-1315.58 + 2278.66i) q^{25} -3582.45 q^{27} +1603.73 q^{29} +(-349.938 + 606.110i) q^{31} +(3756.91 - 2169.05i) q^{33} +(1107.64 - 2659.51i) q^{35} +(-2421.84 - 4194.76i) q^{37} +(446.683 + 257.893i) q^{39} -5910.34i q^{41} -15217.5i q^{43} +(-453.959 - 262.093i) q^{45} +(-49.5838 - 85.8817i) q^{47} +(4412.79 - 16217.4i) q^{49} +(-1810.33 + 1045.20i) q^{51} +(17857.4 - 30929.9i) q^{53} -5904.34 q^{55} +44909.2 q^{57} +(3443.80 - 5964.84i) q^{59} +(-3111.85 + 1796.62i) q^{61} +(-2822.97 - 1175.72i) q^{63} +(-351.002 - 607.953i) q^{65} +(-42290.4 - 24416.4i) q^{67} -41906.2i q^{69} -31698.2i q^{71} +(27063.6 + 15625.2i) q^{73} +(-21480.2 - 37204.8i) q^{75} +(-34158.9 + 4429.84i) q^{77} +(-20637.0 + 11914.8i) q^{79} +(32112.3 - 55620.1i) q^{81} +18288.6 q^{83} +2845.11 q^{85} +(-13092.5 + 22676.8i) q^{87} +(60686.8 - 35037.5i) q^{89} +(-2486.81 - 3253.90i) q^{91} +(-5713.62 - 9896.28i) q^{93} +(-52934.2 - 30561.6i) q^{95} +122256. i q^{97} +6267.22i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 3240 q^{9} + 6856 q^{21} + 27728 q^{25} - 15920 q^{29} - 28296 q^{33} - 2152 q^{37} + 35400 q^{45} + 29280 q^{49} - 17512 q^{53} - 108368 q^{57} + 37704 q^{61} + 18216 q^{65} + 157704 q^{73} + 28224 q^{77}+ \cdots + 39400 q^{93}+O(q^{100}) \) 80 * q - 3240 * q^9 + 6856 * q^21 + 27728 * q^25 - 15920 * q^29 - 28296 * q^33 - 2152 * q^37 + 35400 * q^45 + 29280 * q^49 - 17512 * q^53 - 108368 * q^57 + 37704 * q^61 + 18216 * q^65 + 157704 * q^73 + 28224 * q^77 - 273136 * q^81 + 230704 * q^85 + 28440 * q^89 + 39400 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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