LMFDB - Embedded newform 224.5.o.a.207.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,5,Mod(79,224)]

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, 3, 2]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("224.79");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	224.o (of order $6$, degree $2$, not 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:	$23.1548717308$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			207.2
Character	$\chi$	$=$	224.207
Dual form			224.5.o.a.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.74459 + 13.4140i) q^{3} +(13.5276 - 7.81018i) q^{5} +(43.5544 - 22.4503i) q^{7} +(-79.4574 - 137.624i) q^{9} +O(q^{10})$	\(q+(-7.74459 + 13.4140i) q^{3} +(13.5276 - 7.81018i) q^{5} +(43.5544 - 22.4503i) q^{7} +(-79.4574 - 137.624i) q^{9} +(-81.1739 + 140.597i) q^{11} +187.067i q^{13} +241.946i q^{15} +(-128.409 + 222.411i) q^{17} +(-97.3921 - 168.688i) q^{19} +(-36.1617 + 758.108i) q^{21} +(-7.27105 + 4.19794i) q^{23} +(-190.502 + 329.960i) q^{25} +1206.84 q^{27} -1453.99i q^{29} +(-330.503 - 190.816i) q^{31} +(-1257.32 - 2177.74i) q^{33} +(413.846 - 643.867i) q^{35} +(-2295.71 + 1325.43i) q^{37} +(-2509.32 - 1448.76i) q^{39} +434.605 q^{41} -291.635 q^{43} +(-2149.74 - 1241.15i) q^{45} +(-93.1673 + 53.7902i) q^{47} +(1392.97 - 1955.62i) q^{49} +(-1988.95 - 3444.97i) q^{51} +(-1740.94 - 1005.13i) q^{53} +2535.93i q^{55} +3017.05 q^{57} +(1008.42 - 1746.64i) q^{59} +(2834.96 - 1636.76i) q^{61} +(-6550.42 - 4210.29i) q^{63} +(1461.03 + 2530.57i) q^{65} +(-2399.09 + 4155.34i) q^{67} -130.045i q^{69} +5285.79i q^{71} +(1141.45 - 1977.05i) q^{73} +(-2950.72 - 5110.80i) q^{75} +(-379.024 + 7946.01i) q^{77} +(-2590.18 + 1495.44i) q^{79} +(-2910.40 + 5040.96i) q^{81} -13164.6 q^{83} +4011.60i q^{85} +(19503.8 + 11260.5i) q^{87} +(-2624.77 - 4546.23i) q^{89} +(4199.71 + 8147.59i) q^{91} +(5119.22 - 2955.59i) q^{93} +(-2634.97 - 1521.30i) q^{95} -16262.7 q^{97} +25799.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 2 q^{3} - 704 q^{9}+O(q^{10}) $ 60 * q + 2 * q^3 - 704 * q^9	$ 60 q + 2 q^{3} - 704 q^{9} - 94 q^{11} - 2 q^{17} + 2 q^{19} + 2748 q^{25} - 316 q^{27} + 322 q^{33} + 3846 q^{35} - 8 q^{41} + 5576 q^{43} + 1500 q^{49} - 7202 q^{51} + 7804 q^{57} + 6530 q^{59} + 1248 q^{65} + 8002 q^{67} + 3678 q^{73} - 1572 q^{75} - 12898 q^{81} - 10552 q^{83} - 6818 q^{89} - 18240 q^{91} - 6984 q^{97} - 640 q^{99}+O(q^{100}) $ 60 * q + 2 * q^3 - 704 * q^9 - 94 * q^11 - 2 * q^17 + 2 * q^19 + 2748 * q^25 - 316 * q^27 + 322 * q^33 + 3846 * q^35 - 8 * q^41 + 5576 * q^43 + 1500 * q^49 - 7202 * q^51 + 7804 * q^57 + 6530 * q^59 + 1248 * q^65 + 8002 * q^67 + 3678 * q^73 - 1572 * q^75 - 12898 * q^81 - 10552 * q^83 - 6818 * q^89 - 18240 * q^91 - 6984 * q^97 - 640 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−7.74459	+	13.4140i	−0.860510	+	1.49045i	0.0109273	+	0.999940i	$0.496522\pi$
$3$	−7.74459	+	13.4140i	−0.860510	+	1.49045i	−0.871437	+	0.490507i	$0.836812\pi$
$4$		0			0
$5$	13.5276	−	7.81018i	0.541105	−	0.312407i	−0.204422	−	0.978883i	$-0.565531\pi$
$5$	13.5276	−	7.81018i	0.541105	−	0.312407i	0.745527	+	0.666476i	$0.232198\pi$
$6$		0			0
$7$	43.5544	−	22.4503i	0.888865	−	0.458170i
$7$	43.5544	−	22.4503i	0.888865	−	0.458170i
$8$		0			0
$9$	−79.4574	−	137.624i	−0.980955	−	1.69906i
$10$		0			0
$11$	−81.1739	+	140.597i	−0.670859	+	1.16196i	0.306802	+	0.951773i	$0.400741\pi$
$11$	−81.1739	+	140.597i	−0.670859	+	1.16196i	−0.977661	+	0.210188i	$0.932592\pi$
$12$		0			0
$13$			187.067i			1.10691i	0.832880	+	0.553453i	$0.186690\pi$
$13$			187.067i			1.10691i	−0.832880	+	0.553453i	$0.813310\pi$
$14$		0			0
$15$			241.946i			1.07532i
$16$		0			0
$17$	−128.409	+	222.411i	−0.444323	+	0.769589i	−0.998005	−	0.0631387i	$-0.979889\pi$
$17$	−128.409	+	222.411i	−0.444323	+	0.769589i	0.553682	+	0.832728i	$0.313222\pi$
$18$		0			0
$19$	−97.3921	−	168.688i	−0.269784	−	0.467280i	0.699022	−	0.715100i	$-0.253619\pi$
$19$	−97.3921	−	168.688i	−0.269784	−	0.467280i	−0.968806	+	0.247820i	$0.920286\pi$
$20$		0			0
$21$	−36.1617	+	758.108i	−0.0819994	+	1.71907i
$22$		0			0
$23$	−7.27105	+	4.19794i	−0.0137449	+	0.00793562i	−0.506857	−	0.862030i	$-0.669193\pi$
$23$	−7.27105	+	4.19794i	−0.0137449	+	0.00793562i	0.493112	+	0.869966i	$0.335859\pi$
$24$		0			0
$25$	−190.502	+	329.960i	−0.304804	+	0.527935i
$26$		0			0
$27$	1206.84			1.65547
$28$		0			0
$29$		−	1453.99i		−	1.72888i	−0.502736	−	0.864440i	$-0.667673\pi$
$29$		−	1453.99i		−	1.72888i	0.502736	−	0.864440i	$-0.332327\pi$
$30$		0			0
$31$	−330.503	−	190.816i	−0.343916	−	0.198560i	0.318086	−	0.948062i	$-0.396960\pi$
$31$	−330.503	−	190.816i	−0.343916	−	0.198560i	−0.662002	+	0.749502i	$0.730293\pi$
$32$		0			0
$33$	−1257.32	−	2177.74i	−1.15456	−	1.99976i
$34$		0			0
$35$	413.846	−	643.867i	0.337834	−	0.525605i
$36$		0			0
$37$	−2295.71	+	1325.43i	−1.67693	+	0.968173i	−0.713322	+	0.700836i	$0.752810\pi$
$37$	−2295.71	+	1325.43i	−1.67693	+	0.968173i	−0.963603	+	0.267337i	$0.913856\pi$
$38$		0			0
$39$	−2509.32	−	1448.76i	−1.64978	−	0.952504i
$40$		0			0
$41$	434.605			0.258539			0.129270	−	0.991609i	$-0.458737\pi$
$41$	434.605			0.258539			0.129270	+	0.991609i	$0.458737\pi$
$42$		0			0
$43$	−291.635			−0.157726			−0.0788628	−	0.996885i	$-0.525129\pi$
$43$	−291.635			−0.157726			−0.0788628	+	0.996885i	$0.525129\pi$
$44$		0			0
$45$	−2149.74	−	1241.15i	−1.06160	−	0.612915i
$46$		0			0
$47$	−93.1673	+	53.7902i	−0.0421762	+	0.0243505i	−0.520940	−	0.853593i	$-0.674418\pi$
$47$	−93.1673	+	53.7902i	−0.0421762	+	0.0243505i	0.478764	+	0.877944i	$0.341085\pi$
$48$		0			0
$49$	1392.97	−	1955.62i	0.580161	−	0.814502i
$50$		0			0
$51$	−1988.95	−	3444.97i	−0.764688	−	1.32448i
$52$		0			0
$53$	−1740.94	−	1005.13i	−0.619772	−	0.357826i	0.157008	−	0.987597i	$-0.449815\pi$
$53$	−1740.94	−	1005.13i	−0.619772	−	0.357826i	−0.776780	+	0.629772i	$0.783149\pi$
$54$		0			0
$55$			2535.93i			0.838324i
$56$		0			0
$57$	3017.05			0.928608
$58$		0			0
$59$	1008.42	−	1746.64i	0.289693	−	0.501763i	−0.684043	−	0.729441i	$-0.739780\pi$
$59$	1008.42	−	1746.64i	0.289693	−	0.501763i	0.973736	+	0.227678i	$0.0731135\pi$
$60$		0			0
$61$	2834.96	−	1636.76i	0.761881	−	0.439872i	−0.0680898	−	0.997679i	$-0.521690\pi$
$61$	2834.96	−	1636.76i	0.761881	−	0.439872i	0.829971	+	0.557807i	$0.188357\pi$
$62$		0			0
$63$	−6550.42	−	4210.29i	−1.65040	−	1.06079i
$64$		0			0
$65$	1461.03	+	2530.57i	0.345805	+	0.598952i
$66$		0			0
$67$	−2399.09	+	4155.34i	−0.534437	+	0.925672i	0.464753	+	0.885440i	$0.346143\pi$
$67$	−2399.09	+	4155.34i	−0.534437	+	0.925672i	−0.999190	+	0.0402319i	$0.987190\pi$
$68$		0			0
$69$		−	130.045i		−	0.0273147i
$70$		0			0
$71$			5285.79i			1.04856i	0.851546	+	0.524280i	$0.175666\pi$
$71$			5285.79i			1.04856i	−0.851546	+	0.524280i	$0.824334\pi$
$72$		0			0
$73$	1141.45	−	1977.05i	0.214196	−	0.370999i	−0.738827	−	0.673895i	$-0.764620\pi$
$73$	1141.45	−	1977.05i	0.214196	−	0.370999i	0.953024	+	0.302896i	$0.0979534\pi$
$74$		0			0
$75$	−2950.72	−	5110.80i	−0.524573	−	0.908587i
$76$		0			0
$77$	−379.024	+	7946.01i	−0.0639272	+	1.34019i
$78$		0			0
$79$	−2590.18	+	1495.44i	−0.415027	+	0.239616i	−0.692947	−	0.720988i	$-0.743688\pi$
$79$	−2590.18	+	1495.44i	−0.415027	+	0.239616i	0.277920	+	0.960604i	$0.410355\pi$
$80$		0			0
$81$	−2910.40	+	5040.96i	−0.443591	+	0.768321i
$82$		0			0
$83$	−13164.6			−1.91096			−0.955480	−	0.295055i	$-0.904662\pi$
$83$	−13164.6			−1.91096			−0.955480	+	0.295055i	$0.904662\pi$
$84$		0			0
$85$			4011.60i			0.555238i
$86$		0			0
$87$	19503.8	+	11260.5i	2.57680	+	1.48772i
$88$		0			0
$89$	−2624.77	−	4546.23i	−0.331368	−	0.573946i	0.651412	−	0.758724i	$-0.274177\pi$
$89$	−2624.77	−	4546.23i	−0.331368	−	0.573946i	−0.982780	+	0.184778i	$0.940844\pi$
$90$		0			0
$91$	4199.71	+	8147.59i	0.507151	+	0.983890i
$92$		0			0
$93$	5119.22	−	2955.59i	0.591886	−	0.341726i
$94$		0			0
$95$	−2634.97	−	1521.30i	−0.291963	−	0.168565i
$96$		0			0
$97$	−16262.7			−1.72842			−0.864208	−	0.503135i	$-0.832180\pi$
$97$	−16262.7			−1.72842			−0.864208	+	0.503135i	$0.832180\pi$
$98$		0			0
$99$	25799.4			2.63233
$100$		0			0
$101$	−4960.25	−	2863.80i	−0.486251	−	0.280737i	0.236767	−	0.971567i	$-0.423912\pi$
$101$	−4960.25	−	2863.80i	−0.486251	−	0.280737i	−0.723018	+	0.690829i	$0.757246\pi$
$102$		0			0
$103$	−1033.29	+	596.570i	−0.0973975	+	0.0562325i	−0.547908	−	0.836539i	$-0.684575\pi$
$103$	−1033.29	+	596.570i	−0.0973975	+	0.0562325i	0.450510	+	0.892771i	$0.351242\pi$
$104$		0			0
$105$	5431.77	+	10537.8i	0.492678	+	0.955812i
$106$		0			0
$107$	1026.05	+	1777.18i	0.0896196	+	0.155226i	0.907350	−	0.420375i	$-0.138102\pi$
$107$	1026.05	+	1777.18i	0.0896196	+	0.155226i	−0.817731	+	0.575601i	$0.804768\pi$
$108$		0			0
$109$	−5066.17	−	2924.95i	−0.426409	−	0.246187i	0.271407	−	0.962465i	$-0.412511\pi$
$109$	−5066.17	−	2924.95i	−0.426409	−	0.246187i	−0.697816	+	0.716277i	$0.745845\pi$
$110$		0			0
$111$		−	41059.6i		−	3.33249i
$112$		0			0
$113$	16771.5			1.31346			0.656729	−	0.754127i	$-0.271940\pi$
$113$	16771.5			1.31346			0.656729	+	0.754127i	$0.271940\pi$
$114$		0			0
$115$	−65.5733	+	113.576i	−0.00495829	+	0.00858800i
$116$		0			0
$117$	25745.0	−	14863.9i	1.88070	−	1.08582i
$118$		0			0
$119$	−599.580	+	12569.8i	−0.0423402	+	0.887636i
$120$		0			0
$121$	−5857.90	−	10146.2i	−0.400102	−	0.692998i
$122$		0			0
$123$	−3365.84	+	5829.80i	−0.222476	+	0.385339i
$124$		0			0
$125$			15714.1i			1.00571i
$126$		0			0
$127$			9743.20i			0.604079i	0.953295	+	0.302040i	$0.0976675\pi$
$127$			9743.20i			0.604079i	−0.953295	+	0.302040i	$0.902332\pi$
$128$		0			0
$129$	2258.59	−	3912.00i	0.135725	−	0.235082i
$130$		0			0
$131$	−5972.23	−	10344.2i	−0.348012	−	0.602774i	0.637884	−	0.770132i	$-0.279810\pi$
$131$	−5972.23	−	10344.2i	−0.348012	−	0.602774i	−0.985896	+	0.167358i	$0.946476\pi$
$132$		0			0
$133$	−8028.95	−	5160.62i	−0.453895	−	0.291742i
$134$		0			0
$135$	16325.6	−	9425.60i	0.895781	−	0.517179i
$136$		0			0
$137$	−14785.8	+	25609.7i	−0.787775	+	1.36447i	0.139552	+	0.990215i	$0.455434\pi$
$137$	−14785.8	+	25609.7i	−0.787775	+	1.36447i	−0.927327	+	0.374252i	$0.877900\pi$
$138$		0			0
$139$	6043.09			0.312773			0.156386	−	0.987696i	$-0.450015\pi$
$139$	6043.09			0.312773			0.156386	+	0.987696i	$0.450015\pi$
$140$		0			0
$141$		−	1666.33i		−	0.0838153i
$142$		0			0
$143$	−26301.1	−	15185.0i	−1.28618	−	0.742577i
$144$		0			0
$145$	−11355.9	−	19669.0i	−0.540114	−	0.935505i
$146$		0			0
$147$	15444.8	+	33830.8i	0.714737	+	1.56559i
$148$		0			0
$149$	5093.93	−	2940.98i	0.229446	−	0.132471i	−0.380871	−	0.924628i	$-0.624376\pi$
$149$	5093.93	−	2940.98i	0.229446	−	0.132471i	0.610316	+	0.792158i	$0.291042\pi$
$150$		0			0
$151$	33159.8	+	19144.8i	1.45431	+	0.839648i	0.998722	−	0.0505420i	$-0.0160949\pi$
$151$	33159.8	+	19144.8i	1.45431	+	0.839648i	0.455590	+	0.890190i	$0.349428\pi$
$152$		0			0
$153$	40812.2			1.74344
$154$		0			0
$155$	−5961.23			−0.248126
$156$		0			0
$157$	24602.2	+	14204.1i	0.998102	+	0.576254i	0.907686	−	0.419650i	$-0.137847\pi$
$157$	24602.2	+	14204.1i	0.998102	+	0.576254i	0.0904156	+	0.995904i	$0.471180\pi$
$158$		0			0
$159$	26965.7	−	15568.7i	1.06664	−	0.615825i
$160$		0			0
$161$	−222.441	+	346.076i	−0.00858149	+	0.0133512i
$162$		0			0
$163$	2832.62	+	4906.23i	0.106614	+	0.184660i	0.914396	−	0.404820i	$-0.132666\pi$
$163$	2832.62	+	4906.23i	0.106614	+	0.184660i	−0.807783	+	0.589480i	$0.799333\pi$
$164$		0			0
$165$	−34017.0	−	19639.7i	−1.24948	−	0.721386i
$166$		0			0
$167$		−	889.212i		−	0.0318840i	−0.999873	−	0.0159420i	$-0.994925\pi$
$167$		−	889.212i		−	0.0318840i	0.999873	−	0.0159420i	$-0.00507471\pi$
$168$		0			0
$169$	−6433.09			−0.225240
$170$		0			0
$171$	−15477.0	+	26807.0i	−0.529292	+	0.916761i
$172$		0			0
$173$	25091.5	−	14486.6i	0.838368	−	0.484032i	−0.0183408	−	0.999832i	$-0.505838\pi$
$173$	25091.5	−	14486.6i	0.838368	−	0.484032i	0.856709	+	0.515800i	$0.172505\pi$
$174$		0			0
$175$	−889.510	+	18648.0i	−0.0290452	+	0.608915i
$176$		0			0
$177$	15619.6	+	27054.0i	0.498567	+	0.863544i
$178$		0			0
$179$	8846.06	−	15321.8i	0.276085	−	0.478194i	−0.694323	−	0.719664i	$-0.744296\pi$
$179$	8846.06	−	15321.8i	0.276085	−	0.478194i	0.970408	+	0.241469i	$0.0776294\pi$
$180$		0			0
$181$			58888.5i			1.79752i	0.438442	+	0.898759i	$0.355530\pi$
$181$			58888.5i			1.79752i	−0.438442	+	0.898759i	$0.644470\pi$
$182$		0			0
$183$			50704.3i			1.51406i
$184$		0			0
$185$	−20703.7	+	35859.8i	−0.604928	+	1.04777i
$186$		0			0
$187$	−20847.0	−	36108.0i	−0.596155	−	1.03257i
$188$		0			0
$189$	52562.9	−	27093.8i	1.47149	−	0.758485i
$190$		0			0
$191$	−24045.3	+	13882.5i	−0.659118	+	0.380542i	−0.791941	−	0.610598i	$-0.790929\pi$
$191$	−24045.3	+	13882.5i	−0.659118	+	0.380542i	0.132823	+	0.991140i	$0.457596\pi$
$192$		0			0
$193$	−17838.3	+	30896.9i	−0.478894	+	0.829468i	−0.999707	−	0.0242025i	$-0.992295\pi$
$193$	−17838.3	+	30896.9i	−0.478894	+	0.829468i	0.520814	+	0.853670i	$0.325629\pi$
$194$		0			0
$195$	−45260.2			−1.19028
$196$		0			0
$197$			40371.3i			1.04026i	0.854088	+	0.520128i	$0.174116\pi$
$197$			40371.3i			1.04026i	−0.854088	+	0.520128i	$0.825884\pi$
$198$		0			0
$199$	−11250.3	−	6495.34i	−0.284090	−	0.164020i	0.351183	−	0.936307i	$-0.385779\pi$
$199$	−11250.3	−	6495.34i	−0.284090	−	0.164020i	−0.635274	+	0.772287i	$0.719113\pi$
$200$		0			0
$201$	−37159.9	−	64362.8i	−0.919777	−	1.59310i
$202$		0			0
$203$	−32642.5	−	63327.5i	−0.792120	−	1.53674i
$204$		0			0
$205$	5879.17	−	3394.34i	0.139897	−	0.0807695i
$206$		0			0
$207$	1155.48	+	667.115i	0.0269662	+	0.0155690i
$208$		0			0
$209$	31622.8			0.723948
$210$		0			0
$211$	7259.57			0.163059			0.0815297	−	0.996671i	$-0.474019\pi$
$211$	7259.57			0.163059			0.0815297	+	0.996671i	$0.474019\pi$
$212$		0			0
$213$	−70903.8	−	40936.3i	−1.56282	−	0.902297i
$214$		0			0
$215$	−3945.13	+	2277.72i	−0.0853461	+	0.0492746i
$216$		0			0
$217$	−18678.7	−	890.976i	−0.396669	−	0.0189211i
$218$		0			0
$219$	17680.2	+	30623.0i	0.368636	+	0.638497i
$220$		0			0
$221$	−41605.8	−	24021.1i	−0.851863	−	0.491823i
$222$		0			0
$223$			4333.96i			0.0871515i	0.999050	+	0.0435758i	$0.0138750\pi$
$223$			4333.96i			0.0871515i	−0.999050	+	0.0435758i	$0.986125\pi$
$224$		0			0
$225$	60547.2			1.19599
$226$		0			0
$227$	27713.7	−	48001.5i	0.537826	−	0.931543i	−0.461194	−	0.887299i	$-0.652579\pi$
$227$	27713.7	−	48001.5i	0.537826	−	0.931543i	0.999021	−	0.0442435i	$-0.0140877\pi$
$228$		0			0
$229$	−38433.8	+	22189.7i	−0.732895	+	0.423137i	−0.819480	−	0.573107i	$-0.805738\pi$
$229$	−38433.8	+	22189.7i	−0.732895	+	0.423137i	0.0865851	+	0.996244i	$0.472405\pi$
$230$		0			0
$231$	−103653.	−	66622.8i	−1.94248	−	1.24853i
$232$		0			0
$233$	10601.3	+	18361.9i	0.195275	+	0.338225i	0.946990	−	0.321262i	$-0.104107\pi$
$233$	10601.3	+	18361.9i	0.195275	+	0.338225i	−0.751716	+	0.659487i	$0.770774\pi$
$234$		0			0
$235$	−840.222	+	1455.31i	−0.0152145	+	0.0263523i
$236$		0			0
$237$		−	46326.4i		−	0.824768i
$238$		0			0
$239$		−	32072.9i		−	0.561491i	−0.959782	−	0.280745i	$-0.909418\pi$
$239$		−	32072.9i		−	0.561491i	0.959782	−	0.280745i	$-0.0905816\pi$
$240$		0			0
$241$	18088.8	−	31330.7i	0.311440	−	0.539430i	−0.667234	−	0.744848i	$-0.732522\pi$
$241$	18088.8	−	31330.7i	0.311440	−	0.539430i	0.978674	+	0.205418i	$0.0658553\pi$
$242$		0			0
$243$	3797.15	+	6576.86i	0.0643051	+	0.111380i
$244$		0			0
$245$	3569.80	−	37334.2i	0.0594719	−	0.621977i
$246$		0			0
$247$	31556.0	−	18218.9i	0.517235	−	0.298626i
$248$		0			0
$249$	101954.	−	176590.i	1.64440	−	2.84819i
$250$		0			0
$251$	105699.			1.67774			0.838871	−	0.544330i	$-0.183216\pi$
$251$	105699.			1.67774			0.838871	+	0.544330i	$0.183216\pi$
$252$		0			0
$253$		−	1363.05i		−	0.0212947i
$254$		0			0
$255$	−53811.6	−	31068.2i	−0.827553	−	0.477788i
$256$		0			0
$257$	−14596.5	−	25282.0i	−0.220996	−	0.382776i	0.734115	−	0.679025i	$-0.237597\pi$
$257$	−14596.5	−	25282.0i	−0.220996	−	0.382776i	−0.955111	+	0.296250i	$0.904264\pi$
$258$		0			0
$259$	−70231.9	+	109268.i	−1.04697	+	1.62889i
$260$		0			0
$261$	−200104.	+	115530.i	−2.93748	+	1.69595i
$262$		0			0
$263$	15490.4	+	8943.40i	0.223950	+	0.129298i	0.607778	−	0.794107i	$-0.292061\pi$
$263$	15490.4	+	8943.40i	0.223950	+	0.129298i	−0.383828	+	0.923405i	$0.625394\pi$
$264$		0			0
$265$	−31401.1			−0.447149
$266$		0			0
$267$	81311.0			1.14058
$268$		0			0
$269$	43097.9	+	24882.6i	0.595595	+	0.343867i	0.767307	−	0.641280i	$-0.221596\pi$
$269$	43097.9	+	24882.6i	0.595595	+	0.343867i	−0.171712	+	0.985147i	$0.554930\pi$
$270$		0			0
$271$	−93013.0	+	53701.1i	−1.26650	+	0.731214i	−0.974324	−	0.225151i	$-0.927712\pi$
$271$	−93013.0	+	53701.1i	−1.26650	+	0.731214i	−0.292175	+	0.956365i	$0.594379\pi$
$272$		0			0
$273$	−141817.	−	6764.67i	−1.90284	−	0.0907656i
$274$		0			0
$275$	−30927.6	−	53568.2i	−0.408960	−	0.708340i
$276$		0			0
$277$	59838.2	+	34547.6i	0.779864	+	0.450255i	0.836382	−	0.548147i	$-0.184666\pi$
$277$	59838.2	+	34547.6i	0.779864	+	0.450255i	−0.0565178	+	0.998402i	$0.518000\pi$
$278$		0			0
$279$			60647.0i			0.779114i
$280$		0			0
$281$	−80467.7			−1.01908			−0.509540	−	0.860447i	$-0.670185\pi$
$281$	−80467.7			−1.01908			−0.509540	+	0.860447i	$0.670185\pi$
$282$		0			0
$283$	−30267.8	+	52425.3i	−0.377927	+	0.654589i	−0.990760	−	0.135623i	$-0.956696\pi$
$283$	−30267.8	+	52425.3i	−0.377927	+	0.654589i	0.612834	+	0.790212i	$0.290030\pi$
$284$		0			0
$285$	40813.5	−	23563.7i	0.502474	−	0.290104i
$286$		0			0
$287$	18928.9	−	9757.01i	0.229807	−	0.118455i
$288$		0			0
$289$	8782.63	+	15212.0i	0.105155	+	0.182133i
$290$		0			0
$291$	125948.	−	218148.i	1.48732	−	2.57611i
$292$		0			0
$293$		−	78403.6i		−	0.913273i	−0.889653	−	0.456636i	$-0.849054\pi$
$293$		−	78403.6i		−	0.913273i	0.889653	−	0.456636i	$-0.150946\pi$
$294$		0			0
$295$		−	31503.8i		−	0.362009i
$296$		0			0
$297$	−97963.5	+	169678.i	−1.11058	+	1.92359i
$298$		0			0
$299$	−785.297	−	1360.17i	−0.00878398	−	0.0152143i
$300$		0			0
$301$	−12702.0	+	6547.29i	−0.140197	+	0.0722651i
$302$		0			0
$303$	76830.2	−	44357.9i	0.836848	−	0.483155i
$304$		0			0
$305$	25566.8	−	44283.1i	0.274838	−	0.476034i
$306$		0			0
$307$	−81991.3			−0.869944			−0.434972	−	0.900444i	$-0.643242\pi$
$307$	−81991.3			−0.869944			−0.434972	+	0.900444i	$0.643242\pi$
$308$		0			0
$309$		−	18480.8i		−	0.193554i
$310$		0			0
$311$	−74527.3	−	43028.4i	−0.770539	−	0.444871i	0.0625276	−	0.998043i	$-0.480084\pi$
$311$	−74527.3	−	43028.4i	−0.770539	−	0.444871i	−0.833067	+	0.553172i	$0.813417\pi$
$312$		0			0
$313$	66600.2	+	115355.i	0.679809	+	1.17746i	0.975038	+	0.222037i	$0.0712706\pi$
$313$	66600.2	+	115355.i	0.679809	+	1.17746i	−0.295229	+	0.955426i	$0.595396\pi$
$314$		0			0
$315$	−121495.	−	5795.30i	−1.22444	−	0.0584056i
$316$		0			0
$317$	−3544.36	+	2046.34i	−0.0352711	+	0.0203638i	−0.517532	−	0.855664i	$-0.673149\pi$
$317$	−3544.36	+	2046.34i	−0.0352711	+	0.0203638i	0.482261	+	0.876028i	$0.339816\pi$
$318$		0			0
$319$	204427.	+	118026.i	2.00889	+	1.15983i
$320$		0			0
$321$	−31785.5			−0.308474
$322$		0			0
$323$	50024.2			0.479485
$324$		0			0
$325$	−61724.6	−	35636.7i	−0.584375	−	0.337389i
$326$		0			0
$327$	78470.8	−	45305.1i	0.733858	−	0.423693i
$328$		0			0
$329$	−2850.24	+	4434.43i	−0.0263323	+	0.0409681i
$330$		0			0
$331$	37055.9	+	64182.7i	0.338222	+	0.585817i	0.984098	−	0.177625i	$-0.0568413\pi$
$331$	37055.9	+	64182.7i	0.338222	+	0.585817i	−0.645877	+	0.763442i	$0.723508\pi$
$332$		0			0
$333$	364822.	+	210630.i	3.28998	+	1.89947i
$334$		0			0
$335$			74949.2i			0.667848i
$336$		0			0
$337$	69117.3			0.608593			0.304297	−	0.952577i	$-0.401579\pi$
$337$	69117.3			0.608593			0.304297	+	0.952577i	$0.401579\pi$
$338$		0			0
$339$	−129889.	+	224974.i	−1.13024	+	1.95764i
$340$		0			0
$341$	53656.5	−	30978.6i	0.461438	−	0.266411i
$342$		0			0
$343$	16765.5	−	116448.i	0.142505	−	0.989794i
$344$		0			0
$345$	−1015.68	−	1759.20i	−0.00853331	−	0.0147801i
$346$		0			0
$347$	−13004.5	+	22524.5i	−0.108003	+	0.187066i	−0.914961	−	0.403542i	$-0.867779\pi$
$347$	−13004.5	+	22524.5i	−0.108003	+	0.187066i	0.806958	+	0.590608i	$0.201112\pi$
$348$		0			0
$349$			156809.i			1.28742i	0.765271	+	0.643709i	$0.222605\pi$
$349$			156809.i			1.28742i	−0.765271	+	0.643709i	$0.777395\pi$
$350$		0			0
$351$			225759.i			1.83245i
$352$		0			0
$353$	−9597.95	+	16624.1i	−0.0770245	+	0.133410i	−0.901965	−	0.431809i	$-0.857875\pi$
$353$	−9597.95	+	16624.1i	−0.0770245	+	0.133410i	0.824940	+	0.565220i	$0.191209\pi$
$354$		0			0
$355$	41283.0	+	71504.2i	0.327578	+	0.567381i
$356$		0			0
$357$	−163968.	−	105391.i	−1.28654	−	0.826926i
$358$		0			0
$359$	−115542.	+	66707.9i	−0.896498	+	0.517593i	−0.876062	−	0.482198i	$-0.839839\pi$
$359$	−115542.	+	66707.9i	−0.896498	+	0.517593i	−0.0204355	+	0.999791i	$0.506505\pi$
$360$		0			0
$361$	46190.1	−	80003.5i	0.354433	−	0.613896i
$362$		0			0
$363$	181468.			1.37717
$364$		0			0
$365$		−	35659.8i		−	0.267666i
$366$		0			0
$367$	160393.	+	92602.8i	1.19084	+	0.687530i	0.958497	−	0.285104i	$-0.0920282\pi$
$367$	160393.	+	92602.8i	1.19084	+	0.687530i	0.232341	+	0.972634i	$0.425362\pi$
$368$		0			0
$369$	−34532.5	−	59812.1i	−0.253616	−	0.439275i
$370$		0			0
$371$	−98391.1	−	4693.26i	−0.714839	−	0.0340978i
$372$		0			0
$373$	151411.	−	87417.2i	1.08828	−	0.628318i	0.155160	−	0.987889i	$-0.450411\pi$
$373$	151411.	−	87417.2i	1.08828	−	0.628318i	0.933117	+	0.359572i	$0.117077\pi$
$374$		0			0
$375$	−210790.	−	121700.i	−1.49895	−	0.865420i
$376$		0			0
$377$	271993.			1.91371
$378$		0			0
$379$	−191457.			−1.33289			−0.666444	−	0.745555i	$-0.732184\pi$
$379$	−191457.			−1.33289			−0.666444	+	0.745555i	$0.732184\pi$
$380$		0			0
$381$	−130695.	−	75457.1i	−0.900348	−	0.519816i
$382$		0			0
$383$	146928.	−	84828.9i	1.00163	−	0.578291i	0.0928992	−	0.995676i	$-0.470387\pi$
$383$	146928.	−	84828.9i	1.00163	−	0.578291i	0.908730	+	0.417385i	$0.137053\pi$
$384$		0			0
$385$	56932.4	+	110451.i	0.384095	+	0.745156i
$386$		0			0
$387$	23172.5	+	40136.0i	0.154722	+	0.267986i
$388$		0			0
$389$	−141675.	−	81796.3i	−0.936257	−	0.540548i	−0.0474720	−	0.998873i	$-0.515116\pi$
$389$	−141675.	−	81796.3i	−0.936257	−	0.540548i	−0.888785	+	0.458324i	$0.848450\pi$
$390$		0			0
$391$		−	2156.22i		−	0.0141039i
$392$		0			0
$393$	185010.			1.19787
$394$		0			0
$395$	−23359.4	+	40459.6i	−0.149715	+	0.259315i
$396$		0			0
$397$	244287.	−	141039.i	1.54995	−	0.894866i	0.551809	−	0.833971i	$-0.313938\pi$
$397$	244287.	−	141039.i	1.54995	−	0.894866i	0.998144	−	0.0608954i	$-0.0193956\pi$
$398$		0			0
$399$	131406.	−	67733.7i	0.825407	−	0.425460i
$400$		0			0
$401$	60334.9	+	104503.i	0.375215	+	0.649891i	0.990359	−	0.138523i	$-0.0442355\pi$
$401$	60334.9	+	104503.i	0.375215	+	0.649891i	−0.615144	+	0.788415i	$0.710902\pi$
$402$		0			0
$403$	35695.4	−	61826.3i	0.219787	−	0.380683i
$404$		0			0
$405$			90922.9i			0.554323i
$406$		0			0
$407$		−	430361.i		−	2.59803i
$408$		0			0
$409$	−70247.8	+	121673.i	−0.419939	+	0.727356i	−0.995933	−	0.0900984i	$-0.971282\pi$
$409$	−70247.8	+	121673.i	−0.419939	+	0.727356i	0.575994	+	0.817454i	$0.304615\pi$
$410$		0			0
$411$	−229019.	−	396673.i	−1.35578	−	2.34827i
$412$		0			0
$413$	4708.61	−	98713.1i	0.0276053	−	0.578728i
$414$		0			0
$415$	−178086.	+	102818.i	−1.03403	+	0.596998i
$416$		0			0
$417$	−46801.2	+	81062.1i	−0.269144	+	0.466172i
$418$		0			0
$419$	95931.3			0.546427			0.273214	−	0.961953i	$-0.411913\pi$
$419$	95931.3			0.546427			0.273214	+	0.961953i	$0.411913\pi$
$420$		0			0
$421$			89415.1i			0.504483i	0.967664	+	0.252242i	$0.0811678\pi$
$421$			89415.1i			0.504483i	−0.967664	+	0.252242i	$0.918832\pi$
$422$		0			0
$423$	14805.7	+	8548.05i	0.0827460	+	0.0477734i
$424$		0			0
$425$	−48924.5	−	84739.7i	−0.270862	−	0.469147i
$426$		0			0
$427$	86729.0	−	134934.i	0.475673	−	0.740057i
$428$		0			0
$429$	407383.	−	235203.i	2.21354	−	1.27799i
$430$		0			0
$431$	4191.55	+	2419.99i	0.0225642	+	0.0130274i	0.511240	−	0.859438i	$-0.329186\pi$
$431$	4191.55	+	2419.99i	0.0225642	+	0.0130274i	−0.488675	+	0.872466i	$0.662520\pi$
$432$		0			0
$433$	−196113.			−1.04600			−0.523000	−	0.852333i	$-0.675187\pi$
$433$	−196113.			−1.04600			−0.523000	+	0.852333i	$0.675187\pi$
$434$		0			0
$435$	351787.			1.85909
$436$		0			0
$437$	1416.29	+	817.693i	0.00741631	+	0.00428181i
$438$		0			0
$439$	196838.	−	113645.i	1.02136	−	0.589685i	0.106866	−	0.994273i	$-0.465919\pi$
$439$	196838.	−	113645.i	1.02136	−	0.589685i	0.914499	+	0.404588i	$0.132585\pi$
$440$		0			0
$441$	−379822.	−	36317.6i	−1.95300	−	0.186741i
$442$		0			0
$443$	162301.	+	281113.i	0.827015	+	1.43243i	0.900370	+	0.435126i	$0.143296\pi$
$443$	162301.	+	281113.i	0.827015	+	1.43243i	−0.0733548	+	0.997306i	$0.523371\pi$
$444$		0			0
$445$	−71013.7	−	40999.8i	−0.358610	−	0.207043i
$446$		0			0
$447$			91106.7i			0.455969i
$448$		0			0
$449$	93785.9			0.465205			0.232603	−	0.972572i	$-0.425276\pi$
$449$	93785.9			0.465205			0.232603	+	0.972572i	$0.425276\pi$
$450$		0			0
$451$	−35278.6	+	61104.2i	−0.173443	+	0.300413i
$452$		0			0
$453$	−513618.	+	296537.i	−2.50290	+	1.44505i
$454$		0			0
$455$	120446.	+	77417.0i	0.581796	+	0.373950i
$456$		0			0
$457$	53015.4	+	91825.4i	0.253846	+	0.439674i	0.964581	−	0.263786i	$-0.0849711\pi$
$457$	53015.4	+	91825.4i	0.253846	+	0.439674i	−0.710736	+	0.703459i	$0.751638\pi$
$458$		0			0
$459$	−154969.	+	268414.i	−0.735561	+	1.27403i
$460$		0			0
$461$		−	199782.i		−	0.940057i	−0.882651	−	0.470029i	$-0.844244\pi$
$461$		−	199782.i		−	0.940057i	0.882651	−	0.470029i	$-0.155756\pi$
$462$		0			0
$463$			282627.i			1.31842i	0.751961	+	0.659208i	$0.229108\pi$
$463$			282627.i			1.31842i	−0.751961	+	0.659208i	$0.770892\pi$
$464$		0			0
$465$	46167.3	−	79964.1i	0.213515	−	0.369819i
$466$		0			0
$467$	−7878.64	−	13646.2i	−0.0361258	−	0.0625717i	0.847397	−	0.530959i	$-0.178168\pi$
$467$	−7878.64	−	13646.2i	−0.0361258	−	0.0625717i	−0.883523	+	0.468388i	$0.844835\pi$
$468$		0			0
$469$	−11202.0	+	234844.i	−0.0509274	+	1.06766i
$470$		0			0
$471$	−381068.	+	220010.i	−1.71775	+	0.991745i
$472$		0			0
$473$	23673.1	−	41003.1i	0.105812	−	0.183271i
$474$		0			0
$475$	74213.7			0.328925
$476$		0			0
$477$			319461.i			1.40404i
$478$		0			0
$479$	−230398.	−	133021.i	−1.00417	−	0.579759i	−0.0946925	−	0.995507i	$-0.530187\pi$
$479$	−230398.	−	133021.i	−1.00417	−	0.579759i	−0.909480	+	0.415747i	$0.863520\pi$
$480$		0			0
$481$	−247944.	−	429452.i	−1.07168	−	1.85620i
$482$		0			0
$483$	−2919.56	−	5664.04i	−0.0125148	−	0.0242791i
$484$		0			0
$485$	−219995.	+	127014.i	−0.935254	+	0.539969i
$486$		0			0
$487$	207160.	+	119604.i	0.873471	+	0.504299i	0.868500	−	0.495689i	$-0.165084\pi$
$487$	207160.	+	119604.i	0.873471	+	0.504299i	0.00497067	+	0.999988i	$0.498418\pi$
$488$		0			0
$489$	−87749.8			−0.366968
$490$		0			0
$491$	23485.6			0.0974179			0.0487090	−	0.998813i	$-0.484489\pi$
$491$	23485.6			0.0974179			0.0487090	+	0.998813i	$0.484489\pi$
$492$		0			0
$493$	323383.	+	186705.i	1.33053	+	0.768180i
$494$		0			0
$495$	349005.	−	201498.i	1.42437	−	0.822358i
$496$		0			0
$497$	118668.	+	230219.i	0.480419	+	0.932028i
$498$		0			0
$499$	18985.5	+	32883.9i	0.0762469	+	0.132063i	0.901628	−	0.432513i	$-0.142373\pi$
$499$	18985.5	+	32883.9i	0.0762469	+	0.132063i	−0.825381	+	0.564576i	$0.809040\pi$
$500$		0			0
$501$	11927.9	+	6886.58i	0.0475214	+	0.0274365i
$502$		0			0
$503$		−	91021.5i		−	0.359756i	−0.983689	−	0.179878i	$-0.942430\pi$
$503$		−	91021.5i		−	0.359756i	0.983689	−	0.179878i	$-0.0575703\pi$
$504$		0			0
$505$	−89467.2			−0.350817
$506$		0			0
$507$	49821.7	−	86293.6i	0.193822	−	0.335709i
$508$		0			0
$509$	155182.	−	89594.2i	0.598970	−	0.345815i	−0.169666	−	0.985502i	$-0.554269\pi$
$509$	155182.	−	89594.2i	0.598970	−	0.345815i	0.768636	+	0.639686i	$0.220936\pi$
$510$		0			0
$511$	5329.77	−	111735.i	0.0204111	−	0.427906i
$512$		0			0
$513$	−117536.	−	203579.i	−0.446619	−	0.773566i
$514$		0			0
$515$	−9318.64	+	16140.3i	−0.0351348	+	0.0608553i
$516$		0			0
$517$		−	17465.4i		−	0.0653429i
$518$		0			0
$519$			448771.i			1.66606i
$520$		0			0
$521$	182567.	−	316216.i	0.672585	−	1.16495i	−0.304583	−	0.952486i	$-0.598517\pi$
$521$	182567.	−	316216.i	0.672585	−	1.16495i	0.977168	−	0.212466i	$-0.0681495\pi$
$522$		0			0
$523$	−38471.5	−	66634.6i	−0.140649	−	0.243611i	0.787092	−	0.616835i	$-0.211585\pi$
$523$	−38471.5	−	66634.6i	−0.140649	−	0.243611i	−0.927741	+	0.373224i	$0.878252\pi$
$524$		0			0
$525$	−243256.	−	156353.i	−0.882562	−	0.567268i
$526$		0			0
$527$	84879.3	−	49005.1i	0.305619	−	0.176449i
$528$		0			0
$529$	−139885.	+	242288.i	−0.499874	+	0.865807i
$530$		0			0
$531$	−320506.			−1.13670
$532$		0			0
$533$			81300.2i			0.286179i
$534$		0			0
$535$	27760.2	+	16027.3i	0.0969872	+	0.0559956i
$536$		0			0
$537$	137018.	+	237322.i	0.475149	+	0.822982i
$538$		0			0
$539$	161882.	+	354593.i	0.557213	+	1.22054i
$540$		0			0
$541$	−145244.	+	83856.5i	−0.496253	+	0.286512i	−0.727165	−	0.686463i	$-0.759162\pi$
$541$	−145244.	+	83856.5i	−0.496253	+	0.286512i	0.230912	+	0.972975i	$0.425829\pi$
$542$		0			0
$543$	−789932.	−	456067.i	−2.67911	−	1.54678i
$544$		0			0
$545$	−91377.6			−0.307643
$546$		0			0
$547$	−183927.			−0.614711			−0.307355	−	0.951595i	$-0.599444\pi$
$547$	−183927.			−0.614711			−0.307355	+	0.951595i	$0.599444\pi$
$548$		0			0
$549$	−450517.	−	260106.i	−1.49474	−	0.862989i
$550$		0			0
$551$	−245270.	+	141607.i	−0.807871	+	0.466424i
$552$		0			0
$553$	−79240.7	+	123284.i	−0.259118	+	0.403139i
$554$		0			0
$555$	−320683.	−	555439.i	−1.04109	−	1.80323i
$556$		0			0
$557$	195480.	+	112860.i	0.630074	+	0.363773i	0.780781	−	0.624805i	$-0.214822\pi$
$557$	195480.	+	112860.i	0.630074	+	0.363773i	−0.150707	+	0.988579i	$0.548155\pi$
$558$		0			0
$559$		−	54555.3i		−	0.174587i
$560$		0			0
$561$	645804.			2.05199
$562$		0			0
$563$	271813.	−	470793.i	0.857537	−	1.48530i	−0.0167340	−	0.999860i	$-0.505327\pi$
$563$	271813.	−	470793.i	0.857537	−	1.48530i	0.874271	−	0.485438i	$-0.161340\pi$
$564$		0			0
$565$	226879.	−	130989.i	0.710719	−	0.410334i
$566$		0			0
$567$	−13589.5	+	284895.i	−0.0422705	+	0.886173i
$568$		0			0
$569$	−165866.	−	287289.i	−0.512311	−	0.887348i	−0.999898	−	0.0142741i	$-0.995456\pi$
$569$	−165866.	−	287289.i	−0.512311	−	0.887348i	0.487587	−	0.873074i	$-0.337877\pi$
$570$		0			0
$571$	31259.4	−	54142.9i	0.0958757	−	0.166062i	−0.814098	−	0.580727i	$-0.802768\pi$
$571$	31259.4	−	54142.9i	0.0958757	−	0.166062i	0.909974	+	0.414666i	$0.136102\pi$
$572$		0			0
$573$		−	430059.i		−	1.30984i
$574$		0			0
$575$		−	3198.87i		−	0.00967522i
$576$		0			0
$577$	−104101.	+	180308.i	−0.312681	+	0.541580i	−0.978942	−	0.204139i	$-0.934561\pi$
$577$	−104101.	+	180308.i	−0.312681	+	0.541580i	0.666260	+	0.745719i	$0.267894\pi$
$578$		0			0
$579$	−276301.	−	478567.i	−0.824185	−	1.42753i
$580$		0			0
$581$	−573376.	+	295550.i	−1.69859	+	0.875544i
$582$		0			0
$583$	282638.	−	163181.i	0.831559	−	0.480101i
$584$		0			0
$585$	232179.	−	402145.i	0.678439	−	1.17509i
$586$		0			0
$587$	−343405.			−0.996623			−0.498312	−	0.866998i	$-0.666046\pi$
$587$	−343405.			−0.996623			−0.498312	+	0.866998i	$0.666046\pi$
$588$		0			0
$589$			74335.9i			0.214273i
$590$		0			0
$591$	−541542.	−	312659.i	−1.55045	−	0.895151i
$592$		0			0
$593$	−233299.	−	404085.i	−0.663442	−	1.14912i	−0.979705	−	0.200444i	$-0.935761\pi$
$593$	−233299.	−	404085.i	−0.663442	−	1.14912i	0.316263	−	0.948672i	$-0.397572\pi$
$594$		0			0
$595$	90061.6	+	174723.i	0.254393	+	0.493532i
$596$		0			0
$597$	174257.	−	100608.i	0.488925	−	0.282281i
$598$		0			0
$599$	35401.8	+	20439.3i	0.0986670	+	0.0569654i	0.548522	−	0.836136i	$-0.315191\pi$
$599$	35401.8	+	20439.3i	0.0986670	+	0.0569654i	−0.449855	+	0.893102i	$0.648524\pi$
$600$		0			0
$601$	−181530.			−0.502574			−0.251287	−	0.967913i	$-0.580854\pi$
$601$	−181530.			−0.502574			−0.251287	+	0.967913i	$0.580854\pi$
$602$		0			0
$603$	762501.			2.09703
$604$		0			0
$605$	−158487.	−	91502.4i	−0.432995	−	0.249990i
$606$		0			0
$607$	−510121.	+	294518.i	−1.38451	+	0.799347i	−0.992690	−	0.120696i	$-0.961487\pi$
$607$	−510121.	+	294518.i	−1.38451	+	0.799347i	−0.391819	+	0.920042i	$0.628154\pi$
$608$		0			0
$609$	1.10228e6	+	52578.7i	2.97206	+	0.141767i
$610$		0			0
$611$	−10062.4	−	17428.5i	−0.0269537	−	0.0466851i
$612$		0			0
$613$	−383478.	−	221401.i	−1.02052	−	0.589195i	−0.106262	−	0.994338i	$-0.533888\pi$
$613$	−383478.	−	221401.i	−1.02052	−	0.589195i	−0.914253	+	0.405143i	$0.867222\pi$
$614$		0			0
$615$			105151.i			0.278012i
$616$		0			0
$617$	−175865.			−0.461964			−0.230982	−	0.972958i	$-0.574194\pi$
$617$	−175865.			−0.461964			−0.230982	+	0.972958i	$0.574194\pi$
$618$		0			0
$619$	−51286.9	+	88831.5i	−0.133852	+	0.231838i	−0.925158	−	0.379581i	$-0.876068\pi$
$619$	−51286.9	+	88831.5i	−0.133852	+	0.231838i	0.791306	+	0.611420i	$0.209401\pi$
$620$		0			0
$621$	−8774.96	+	5066.22i	−0.0227542	+	0.0131372i
$622$		0			0
$623$	−216384.	−	139081.i	−0.557506	−	0.358338i
$624$		0			0
$625$	3666.33	+	6350.27i	0.00938580	+	0.0162567i
$626$		0			0
$627$	−244905.	+	424189.i	−0.622965	+	1.07901i
$628$		0			0
$629$		−	680789.i		−	1.72073i
$630$		0			0
$631$			94059.5i			0.236235i	0.993000	+	0.118117i	$0.0376859\pi$
$631$			94059.5i			0.236235i	−0.993000	+	0.118117i	$0.962314\pi$
$632$		0			0
$633$	−56222.4	+	97380.1i	−0.140314	+	0.243032i
$634$		0			0
$635$	76096.1	+	131802.i	0.188719	+	0.326870i
$636$		0			0
$637$	365832.	+	260578.i	0.901577	+	0.642184i
$638$		0			0
$639$	727453.	−	419995.i	1.78157	−	1.02859i
$640$		0			0
$641$	−179854.	+	311516.i	−0.437728	+	0.758167i	−0.997514	−	0.0704705i	$-0.977550\pi$
$641$	−179854.	+	311516.i	−0.437728	+	0.758167i	0.559786	+	0.828637i	$0.310883\pi$
$642$		0			0
$643$	560587.			1.35588			0.677940	−	0.735117i	$-0.262873\pi$
$643$	560587.			1.35588			0.677940	+	0.735117i	$0.262873\pi$
$644$		0			0
$645$		−	70560.0i		−	0.169605i
$646$		0			0
$647$	594586.	+	343284.i	1.42039	+	0.820060i	0.996332	−	0.0855772i	$-0.0272734\pi$
$647$	594586.	+	343284.i	1.42039	+	0.820060i	0.424054	+	0.905637i	$0.360607\pi$
$648$		0			0
$649$	163715.	+	283563.i	0.388686	+	0.673224i
$650$		0			0
$651$	156611.	−	243657.i	0.369538	−	0.574932i
$652$		0			0
$653$	−471693.	+	272332.i	−1.10620	+	0.638665i	−0.937842	−	0.347061i	$-0.887180\pi$
$653$	−471693.	+	272332.i	−1.10620	+	0.638665i	−0.168357	+	0.985726i	$0.553846\pi$
$654$		0			0
$655$	−161580.	−	93288.4i	−0.376622	−	0.217443i
$656$		0			0
$657$	−362787.			−0.840468
$658$		0			0
$659$	−367708.			−0.846705			−0.423352	−	0.905965i	$-0.639147\pi$
$659$	−367708.			−0.846705			−0.423352	+	0.905965i	$0.639147\pi$
$660$		0			0
$661$	607701.	+	350856.i	1.39087	+	0.803020i	0.993412	−	0.114599i	$-0.0365584\pi$
$661$	607701.	+	350856.i	1.39087	+	0.803020i	0.397460	+	0.917619i	$0.369892\pi$
$662$		0			0
$663$	644440.	−	372068.i	1.46607	−	0.846438i
$664$		0			0
$665$	−148918.	−	7103.38i	−0.336747	−	0.0160628i
$666$		0			0
$667$	6103.76	+	10572.0i	0.0137197	+	0.0237633i
$668$		0			0
$669$	−58135.8	−	33564.7i	−0.129895	−	0.0749948i
$670$		0			0
$671$			531450.i			1.18037i
$672$		0			0
$673$	−308012.			−0.680044			−0.340022	−	0.940418i	$-0.610434\pi$
$673$	−308012.			−0.680044			−0.340022	+	0.940418i	$0.610434\pi$
$674$		0			0
$675$	−229905.	+	398207.i	−0.504592	+	0.873979i
$676$		0			0
$677$	147654.	−	85248.2i	0.322158	−	0.185998i	−0.330196	−	0.943912i	$-0.607115\pi$
$677$	147654.	−	85248.2i	0.322158	−	0.185998i	0.652354	+	0.757914i	$0.273782\pi$
$678$		0			0
$679$	−708310.	+	365102.i	−1.53633	+	0.791908i
$680$		0			0
$681$	429262.	+	743503.i	0.925610	+	1.60320i
$682$		0			0
$683$	65963.0	−	114251.i	0.141403	−	0.244917i	−0.786622	−	0.617435i	$-0.788172\pi$
$683$	65963.0	−	114251.i	0.141403	−	0.244917i	0.928025	+	0.372517i	$0.121505\pi$
$684$		0			0
$685$			461917.i			0.984426i
$686$		0			0
$687$		−	687402.i		−	1.45646i
$688$		0			0
$689$	188027.	−	325673.i	0.396079	−	0.686030i
$690$		0			0
$691$	−217222.	−	376240.i	−0.454933	−	0.787968i	0.543751	−	0.839247i	$-0.317004\pi$
$691$	−217222.	−	376240.i	−0.454933	−	0.787968i	−0.998684	+	0.0512789i	$0.983670\pi$
$692$		0			0
$693$	1.12368e6	−	579206.i	2.33978	−	1.20605i
$694$		0			0
$695$	81748.6	−	47197.6i	0.169243	−	0.0977125i
$696$		0			0
$697$	−55807.3	+	96661.0i	−0.114875	+	0.198969i
$698$		0			0
$699$	−328410.			−0.672143
$700$		0			0
$701$			322397.i			0.656078i	0.944664	+	0.328039i	$0.106388\pi$
$701$			322397.i			0.656078i	−0.944664	+	0.328039i	$0.893612\pi$
$702$		0			0
$703$	447168.	+	258173.i	0.904816	+	0.522396i
$704$		0			0
$705$	−13014.3	−	22541.5i	−0.0261845	−	0.0453529i
$706$		0			0
$707$	−280334.	−	13371.9i	−0.560837	−	0.0267519i
$708$		0			0
$709$	−392850.	+	226812.i	−0.781510	+	0.451205i	−0.836965	−	0.547256i	$-0.815672\pi$
$709$	−392850.	+	226812.i	−0.781510	+	0.451205i	0.0554554	+	0.998461i	$0.482339\pi$
$710$		0			0
$711$	411618.	+	237648.i	0.814246	+	0.470105i
$712$		0			0
$713$	3204.14			0.00630278
$714$		0			0
$715$	−474389.			−0.927945
$716$		0			0
$717$	430227.	+	248392.i	0.836872	+	0.483168i
$718$		0			0
$719$	−190956.	+	110248.i	−0.369381	+	0.213262i	−0.673188	−	0.739471i	$-0.735076\pi$
$719$	−190956.	+	110248.i	−0.369381	+	0.213262i	0.303807	+	0.952734i	$0.401742\pi$
$720$		0			0
$721$	−31611.1	+	49180.9i	−0.0608092	+	0.0946076i
$722$		0			0
$723$	280180.	+	485286.i	0.535995	+	0.928371i
$724$		0			0
$725$	479757.	+	276988.i	0.912737	+	0.526969i
$726$		0			0
$727$			692116.i			1.30951i	0.755839	+	0.654757i	$0.227229\pi$
$727$			692116.i			1.30951i	−0.755839	+	0.654757i	$0.772771\pi$
$728$		0			0
$729$	−589114.			−1.10852
$730$		0			0
$731$	37448.6	−	64862.9i	0.0700811	−	0.121384i
$732$		0			0
$733$	5411.70	−	3124.45i	0.0100722	−	0.00581521i	−0.494955	−	0.868918i	$-0.664816\pi$
$733$	5411.70	−	3124.45i	0.0100722	−	0.00581521i	0.505028	+	0.863103i	$0.331482\pi$
$734$		0			0
$735$	473155.	+	337023.i	0.875848	+	0.623857i
$736$		0			0
$737$	−389487.	−	674611.i	−0.717063	−	1.24199i
$738$		0			0
$739$	−242549.	+	420107.i	−0.444130	+	0.769256i	−0.997991	−	0.0633532i	$-0.979821\pi$
$739$	−242549.	+	420107.i	−0.444130	+	0.769256i	0.553861	+	0.832609i	$0.313154\pi$
$740$		0			0
$741$			564390.i			1.02788i
$742$		0			0
$743$		−	649002.i		−	1.17562i	−0.808998	−	0.587812i	$-0.799989\pi$
$743$		−	649002.i		−	1.17562i	0.808998	−	0.587812i	$-0.200011\pi$
$744$		0			0
$745$	45939.1	−	79568.9i	0.0827695	−	0.143361i
$746$		0			0
$747$	1.04602e6	+	1.81177e6i	1.87457	+	3.24684i
$748$		0			0
$749$	84587.4	+	54368.7i	0.150779	+	0.0969136i
$750$		0			0
$751$	276574.	−	159680.i	0.490379	−	0.283121i	−0.234352	−	0.972152i	$-0.575297\pi$
$751$	276574.	−	159680.i	0.490379	−	0.283121i	0.724732	+	0.689031i	$0.241964\pi$
$752$		0			0
$753$	−818599.	+	1.41786e6i	−1.44371	+	2.50059i
$754$		0			0
$755$	598097.			1.04925
$756$		0			0
$757$		−	249555.i		−	0.435486i	−0.976006	−	0.217743i	$-0.930131\pi$
$757$		−	249555.i		−	0.435486i	0.976006	−	0.217743i	$-0.0698694\pi$
$758$		0			0
$759$	18284.0	+	10556.3i	0.0317386	+	0.0183243i
$760$		0			0
$761$	190350.	+	329696.i	0.328687	+	0.569303i	0.982252	−	0.187568i	$-0.0600604\pi$
$761$	190350.	+	329696.i	0.328687	+	0.569303i	−0.653564	+	0.756871i	$0.726727\pi$
$762$		0			0
$763$	−286320.	−	13657.4i	−0.491816	−	0.0234596i
$764$		0			0
$765$	552093.	−	318751.i	0.943385	−	0.544664i
$766$		0			0
$767$	326738.	+	188642.i	0.555404	+	0.320663i
$768$		0			0
$769$	1.00102e6			1.69274			0.846372	−	0.532592i	$-0.178782\pi$
$769$	1.00102e6			1.69274			0.846372	+	0.532592i	$0.178782\pi$
$770$		0			0
$771$	452177.			0.760676
$772$		0			0
$773$	214549.	+	123870.i	0.359061	+	0.207304i	0.668669	−	0.743560i	$-0.266864\pi$
$773$	214549.	+	123870.i	0.359061	+	0.207304i	−0.309608	+	0.950864i	$0.600198\pi$
$774$		0			0
$775$	125923.	−	72701.8i	0.209654	−	0.121044i
$776$		0			0
$777$	−921802.	−	1.78833e6i	−1.52685	−	2.96213i
$778$		0			0
$779$	−42327.1	−	73312.6i	−0.0697498	−	0.120810i
$780$		0			0
$781$	−743168.	−	429068.i	−1.21839	−	0.703436i
$782$		0			0
$783$		−	1.75472e6i		−	2.86210i
$784$		0			0
$785$	443746.			0.720104
$786$		0			0
$787$	107534.	−	186254.i	0.173618	−	0.300715i	−0.766064	−	0.642764i	$-0.777788\pi$
$787$	107534.	−	186254.i	0.173618	−	0.300715i	0.939682	+	0.342049i	$0.111121\pi$
$788$		0			0
$789$	−239934.	+	138526.i	−0.385423	+	0.222524i
$790$		0			0
$791$	730474.	−	376526.i	1.16749	−	0.601787i
$792$		0			0
$793$	306185.	+	530327.i	0.486897	+	0.843330i
$794$		0			0
$795$	243188.	−	421215.i	0.384776	−	0.666452i
$796$		0			0
$797$			159361.i			0.250879i	0.992101	+	0.125440i	$0.0400341\pi$
$797$			159361.i			0.250879i	−0.992101	+	0.125440i	$0.959966\pi$
$798$		0			0
$799$		−	27628.6i		−	0.0432779i
$800$		0			0
$801$	−417114.	+	722463.i	−0.650114	+	1.12603i
$802$		0			0
$803$	185312.	+	320970.i	0.287391	+	0.497776i
$804$		0			0
$805$	−306.181	+	6418.89i	−0.000472483	+	0.00990531i
$806$		0			0
$807$	−667551.	+	385411.i	−1.02503	+	0.591802i
$808$		0			0
$809$	600062.	−	1.03934e6i	0.916851	−	1.58803i	0.112682	−	0.993631i	$-0.464056\pi$
$809$	600062.	−	1.03934e6i	0.916851	−	1.58803i	0.804169	−	0.594401i	$-0.202611\pi$
$810$		0			0
$811$	−672707.			−1.02278			−0.511392	−	0.859347i	$-0.670870\pi$
$811$	−672707.			−1.02278			−0.511392	+	0.859347i	$0.670870\pi$
$812$		0			0
$813$		−	1.66357e6i		−	2.51687i
$814$		0			0
$815$	76637.1	+	44246.4i	0.115378	+	0.0666136i
$816$		0			0
$817$	28402.9	+	49195.3i	0.0425519	+	0.0737020i
$818$		0			0
$819$	787607.	−	1.22537e6i	1.17420	−	1.82683i
$820$		0			0
$821$	6329.92	−	3654.58i	0.00939101	−	0.00542190i	−0.495297	−	0.868724i	$-0.664941\pi$
$821$	6329.92	−	3654.58i	0.00939101	−	0.00542190i	0.504688	+	0.863302i	$0.331607\pi$
$822$		0			0
$823$	548787.	+	316842.i	0.810222	+	0.467782i	0.847033	−	0.531541i	$-0.178387\pi$
$823$	548787.	+	316842.i	0.810222	+	0.467782i	−0.0368112	+	0.999322i	$0.511720\pi$
$824$		0			0
$825$	958087.			1.40766
$826$		0			0
$827$	−729635.			−1.06683			−0.533414	−	0.845854i	$-0.679091\pi$
$827$	−729635.			−1.06683			−0.533414	+	0.845854i	$0.679091\pi$
$828$		0			0
$829$	−604502.	−	349009.i	−0.879606	−	0.507841i	−0.00907777	−	0.999959i	$-0.502890\pi$
$829$	−604502.	−	349009.i	−0.879606	−	0.507841i	−0.870529	+	0.492118i	$0.836223\pi$
$830$		0			0
$831$	−926845.	+	535114.i	−1.34216	+	0.774898i
$832$		0			0
$833$	256082.	+	560931.i	0.369053	+	0.808387i
$834$		0			0
$835$	−6944.90	−	12028.9i	−0.00996078	−	0.0172526i
$836$		0			0
$837$	−398863.	−	230284.i	−0.569341	−	0.328709i
$838$		0			0
$839$		−	875849.i		−	1.24424i	−0.782920	−	0.622122i	$-0.786271\pi$
$839$		−	875849.i		−	1.24424i	0.782920	−	0.622122i	$-0.213729\pi$
$840$		0			0
$841$	−1.40680e6			−1.98903
$842$		0			0
$843$	623189.	−	1.07940e6i	0.876929	−	1.51889i
$844$		0			0
$845$	−87024.4	+	50243.6i	−0.121879	+	0.0703667i
$846$		0			0
$847$	−482922.	−	310399.i	−0.673147	−	0.432666i
$848$		0			0
$849$	−468823.	−	812026.i	−0.650420	−	1.12656i
$850$		0			0
$851$	11128.2	−	19274.5i	0.0153661	−	0.0266149i
$852$		0			0
$853$			973220.i			1.33756i	0.743461	+	0.668780i	$0.233183\pi$
$853$			973220.i			1.33756i	−0.743461	+	0.668780i	$0.766817\pi$
$854$		0			0
$855$			483513.i			0.661419i
$856$		0			0
$857$	2804.84	−	4858.12i	0.00381897	−	0.00661465i	−0.864110	−	0.503304i	$-0.832118\pi$
$857$	2804.84	−	4858.12i	0.00381897	−	0.00661465i	0.867929	+	0.496689i	$0.165451\pi$
$858$		0			0
$859$	81820.0	+	141716.i	0.110885	+	0.192059i	0.916127	−	0.400887i	$-0.131298\pi$
$859$	81820.0	+	141716.i	0.110885	+	0.192059i	−0.805242	+	0.592946i	$0.797965\pi$
$860$		0			0
$861$	−15716.1	+	329477.i	−0.0212001	+	0.444446i
$862$		0			0
$863$	−1.17871e6	+	680527.i	−1.58265	+	0.913743i	−0.588177	+	0.808732i	$0.700154\pi$
$863$	−1.17871e6	+	680527.i	−1.58265	+	0.913743i	−0.994471	+	0.105011i	$0.966512\pi$
$864$		0			0
$865$	226286.	−	391939.i	0.302430	−	0.523824i
$866$		0			0
$867$	−272072.			−0.361947
$868$		0			0
$869$		−	485564.i		−	0.642994i
$870$		0			0
$871$	−777328.	−	448790.i	−1.02463	−	0.591571i
$872$		0			0
$873$	1.29219e6	+	2.23814e6i	1.69550	+	2.93669i
$874$		0			0
$875$	352788.	+	684420.i	0.460784	+	0.893936i
$876$		0			0
$877$	−159527.	+	92102.9i	−0.207412	+	0.119750i	−0.600108	−	0.799919i	$-0.704876\pi$
$877$	−159527.	+	92102.9i	−0.207412	+	0.119750i	0.392696	+	0.919668i	$0.371542\pi$
$878$		0			0
$879$	1.05171e6	+	607204.i	1.36119	+	0.785881i
$880$		0			0
$881$	−874348.			−1.12650			−0.563251	−	0.826286i	$-0.690450\pi$
$881$	−874348.			−1.12650			−0.563251	+	0.826286i	$0.690450\pi$
$882$		0			0
$883$	−772039.			−0.990188			−0.495094	−	0.868839i	$-0.664866\pi$
$883$	−772039.			−0.990188			−0.495094	+	0.868839i	$0.664866\pi$
$884$		0			0
$885$	422593.	+	243984.i	0.539555	+	0.311512i
$886$		0			0
$887$	−908672.	+	524622.i	−1.15494	+	0.666806i	−0.950086	−	0.311987i	$-0.899006\pi$
$887$	−908672.	+	524622.i	−1.15494	+	0.666806i	−0.204855	+	0.978792i	$0.565672\pi$
$888$		0			0
$889$	218738.	+	424359.i	0.276771	+	0.536945i
$890$		0			0
$891$	−472497.	−	818388.i	−0.595173	−	1.03087i
$892$		0			0
$893$	18147.5	+	10477.5i	0.0227570	+	0.0131387i
$894$		0			0
$895$		−	276357.i		−	0.345004i
$896$		0			0
$897$	24327.2			0.0302348
$898$		0			0
$899$	−277444.	+	480548.i	−0.343286	+	0.594589i
$900$		0			0
$901$	447106.	−	258137.i	0.550758	−	0.317980i
$902$		0			0
$903$	10546.0	−	221091.i	0.0129334	−	0.271141i
$904$		0			0
$905$	459930.	+	796622.i	0.561558	+	0.972646i
$906$		0			0
$907$	687150.	−	1.19018e6i	0.835290	−	1.44676i	−0.0585046	−	0.998287i	$-0.518633\pi$
$907$	687150.	−	1.19018e6i	0.835290	−	1.44676i	0.893794	−	0.448477i	$-0.148033\pi$
$908$		0			0
$909$			910200.i			1.10156i
$910$		0			0
$911$			578260.i			0.696766i	0.937352	+	0.348383i	$0.113269\pi$
$911$			578260.i			0.696766i	−0.937352	+	0.348383i	$0.886731\pi$
$912$		0			0
$913$	1.06862e6	−	1.85091e6i	1.28198	−	2.22046i
$914$		0			0
$915$	396009.	+	685908.i	0.473002	+	0.819264i
$916$		0			0
$917$	−492348.	−	316457.i	−0.585509	−	0.376336i
$918$		0			0
$919$	509364.	−	294081.i	0.603111	−	0.348206i	−0.167154	−	0.985931i	$-0.553458\pi$
$919$	509364.	−	294081.i	0.603111	−	0.348206i	0.770264	+	0.637725i	$0.220124\pi$
$920$		0			0
$921$	634989.	−	1.09983e6i	0.748595	−	1.29661i
$922$		0			0
$923$	−988798.			−1.16066
$924$		0			0
$925$		−	1.00999e6i		−	1.18041i
$926$		0			0
$927$	164205.	+	94803.8i	0.191085	+	0.110323i
$928$		0			0
$929$	−183283.	−	317455.i	−0.212369	−	0.367833i	0.740087	−	0.672511i	$-0.234784\pi$
$929$	−183283.	−	317455.i	−0.212369	−	0.367833i	−0.952455	+	0.304678i	$0.901451\pi$
$930$		0			0
$931$	−465553.	−	44515.1i	−0.537119	−	0.0513579i
$932$		0			0
$933$	1.15437e6	−	666474.i	1.32611	−	0.765632i
$934$		0			0
$935$	−564019.	−	325637.i	−0.645165	−	0.372486i
$936$		0			0
$937$	438510.			0.499459			0.249730	−	0.968316i	$-0.419658\pi$
$937$	438510.			0.499459			0.249730	+	0.968316i	$0.419658\pi$
$938$		0			0
$939$	−2.06316e6			−2.33993
$940$		0			0
$941$	−22926.0	−	13236.3i	−0.0258910	−	0.0149482i	0.486999	−	0.873403i	$-0.338092\pi$
$941$	−22926.0	−	13236.3i	−0.0258910	−	0.0149482i	−0.512890	+	0.858455i	$0.671425\pi$
$942$		0			0
$943$	−3160.03	+	1824.45i	−0.00355360	+	0.00205167i
$944$		0			0
$945$	499444.	−	777041.i	0.559272	−	0.870122i
$946$		0			0
$947$	−334958.	−	580165.i	−0.373500	−	0.646921i	0.616601	−	0.787276i	$-0.288509\pi$
$947$	−334958.	−	580165.i	−0.373500	−	0.646921i	−0.990101	+	0.140354i	$0.955176\pi$
$948$		0			0
$949$	369842.	+	213528.i	0.410661	+	0.237095i
$950$		0			0
$951$		−	63392.2i		−	0.0700930i
$952$		0			0
$953$	−656581.			−0.722940			−0.361470	−	0.932384i	$-0.617725\pi$
$953$	−656581.			−0.722940			−0.361470	+	0.932384i	$0.617725\pi$
$954$		0			0
$955$	−216850.	+	375596.i	−0.237768	+	0.411826i
$956$		0			0
$957$	−3.16640e6	+	1.82812e6i	−3.45734	+	1.99610i
$958$		0			0
$959$	−69039.0	+	1.44736e6i	−0.0750684	+	1.57376i
$960$		0			0
$961$	−388939.	−	673662.i	−0.421148	−	0.729450i
$962$		0			0
$963$	163055.	−	282420.i	0.175826	−	0.304539i
$964$		0			0
$965$			557281.i			0.598439i
$966$		0			0
$967$		−	1.23209e6i		−	1.31762i	−0.752311	−	0.658809i	$-0.771061\pi$
$967$		−	1.23209e6i		−	1.31762i	0.752311	−	0.658809i	$-0.228939\pi$
$968$		0			0
$969$	−387417.	+	671025.i	−0.412602	+	0.714647i
$970$		0			0
$971$	601216.	+	1.04134e6i	0.637664	+	1.10447i	0.985944	+	0.167076i	$0.0534326\pi$
$971$	601216.	+	1.04134e6i	0.637664	+	1.10447i	−0.348280	+	0.937391i	$0.613234\pi$
$972$		0			0
$973$	263203.	−	135669.i	0.278013	−	0.143303i
$974$		0			0
$975$	956063.	−	551983.i	1.00572	−	0.580653i
$976$		0			0
$977$	−647286.	+	1.12113e6i	−0.678121	+	1.17454i	0.297426	+	0.954745i	$0.403872\pi$
$977$	−647286.	+	1.12113e6i	−0.678121	+	1.17454i	−0.975546	+	0.219794i	$0.929461\pi$
$978$		0			0
$979$	852250.			0.889205
$980$		0			0
$981$			929636.i			0.965995i
$982$		0			0
$983$	895995.	+	517303.i	0.927254	+	0.535350i	0.885942	−	0.463796i	$-0.153513\pi$
$983$	895995.	+	517303.i	0.927254	+	0.535350i	0.0413117	+	0.999146i	$0.486846\pi$
$984$		0			0
$985$	315307.	+	546128.i	0.324983	+	0.562888i
$986$		0			0
$987$	−37409.7	−	72576.0i	−0.0384016	−	0.0745005i
$988$		0			0
$989$	2120.49	−	1224.27i	0.00216792	−	0.00125165i
$990$		0			0
$991$	858861.	+	495864.i	0.874532	+	0.504911i	0.868852	−	0.495073i	$-0.164859\pi$
$991$	858861.	+	495864.i	0.874532	+	0.504911i	0.00568043	+	0.999984i	$0.498192\pi$
$992$		0			0
$993$	−1.14793e6			−1.16417
$994$		0			0
$995$	−202919.			−0.204964
$996$		0			0
$997$	−819931.	−	473387.i	−0.824873	−	0.476240i	0.0272212	−	0.999629i	$-0.491334\pi$
$997$	−819931.	−	473387.i	−0.824873	−	0.476240i	−0.852094	+	0.523389i	$0.824667\pi$
$998$		0			0
$999$	−2.77054e6	+	1.59957e6i	−2.77609	+	1.60278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.5.o.a.207.2		60
4.3	odd	2		56.5.k.a.11.27	yes	60
7.2	even	3	inner	224.5.o.a.79.1		60
8.3	odd	2	inner	224.5.o.a.207.1		60
8.5	even	2		56.5.k.a.11.15	✓	60
28.23	odd	6		56.5.k.a.51.15	yes	60
56.37	even	6		56.5.k.a.51.27	yes	60
56.51	odd	6	inner	224.5.o.a.79.2		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.5.k.a.11.15	✓	60	8.5	even	2
56.5.k.a.11.27	yes	60	4.3	odd	2
56.5.k.a.51.15	yes	60	28.23	odd	6
56.5.k.a.51.27	yes	60	56.37	even	6
224.5.o.a.79.1		60	7.2	even	3	inner
224.5.o.a.79.2		60	56.51	odd	6	inner
224.5.o.a.207.1		60	8.3	odd	2	inner
224.5.o.a.207.2		60	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	224.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-7.74459 + 13.4140i) q^{3} +(13.5276 - 7.81018i) q^{5} +(43.5544 - 22.4503i) q^{7} +(-79.4574 - 137.624i) q^{9} +O(q^{10})\)	\(q+(-7.74459 + 13.4140i) q^{3} +(13.5276 - 7.81018i) q^{5} +(43.5544 - 22.4503i) q^{7} +(-79.4574 - 137.624i) q^{9} +(-81.1739 + 140.597i) q^{11} +187.067i q^{13} +241.946i q^{15} +(-128.409 + 222.411i) q^{17} +(-97.3921 - 168.688i) q^{19} +(-36.1617 + 758.108i) q^{21} +(-7.27105 + 4.19794i) q^{23} +(-190.502 + 329.960i) q^{25} +1206.84 q^{27} -1453.99i q^{29} +(-330.503 - 190.816i) q^{31} +(-1257.32 - 2177.74i) q^{33} +(413.846 - 643.867i) q^{35} +(-2295.71 + 1325.43i) q^{37} +(-2509.32 - 1448.76i) q^{39} +434.605 q^{41} -291.635 q^{43} +(-2149.74 - 1241.15i) q^{45} +(-93.1673 + 53.7902i) q^{47} +(1392.97 - 1955.62i) q^{49} +(-1988.95 - 3444.97i) q^{51} +(-1740.94 - 1005.13i) q^{53} +2535.93i q^{55} +3017.05 q^{57} +(1008.42 - 1746.64i) q^{59} +(2834.96 - 1636.76i) q^{61} +(-6550.42 - 4210.29i) q^{63} +(1461.03 + 2530.57i) q^{65} +(-2399.09 + 4155.34i) q^{67} -130.045i q^{69} +5285.79i q^{71} +(1141.45 - 1977.05i) q^{73} +(-2950.72 - 5110.80i) q^{75} +(-379.024 + 7946.01i) q^{77} +(-2590.18 + 1495.44i) q^{79} +(-2910.40 + 5040.96i) q^{81} -13164.6 q^{83} +4011.60i q^{85} +(19503.8 + 11260.5i) q^{87} +(-2624.77 - 4546.23i) q^{89} +(4199.71 + 8147.59i) q^{91} +(5119.22 - 2955.59i) q^{93} +(-2634.97 - 1521.30i) q^{95} -16262.7 q^{97} +25799.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 2 q^{3} - 704 q^{9}+O(q^{10}) \) 60 * q + 2 * q^3 - 704 * q^9	\( 60 q + 2 q^{3} - 704 q^{9} - 94 q^{11} - 2 q^{17} + 2 q^{19} + 2748 q^{25} - 316 q^{27} + 322 q^{33} + 3846 q^{35} - 8 q^{41} + 5576 q^{43} + 1500 q^{49} - 7202 q^{51} + 7804 q^{57} + 6530 q^{59} + 1248 q^{65} + 8002 q^{67} + 3678 q^{73} - 1572 q^{75} - 12898 q^{81} - 10552 q^{83} - 6818 q^{89} - 18240 q^{91} - 6984 q^{97} - 640 q^{99}+O(q^{100}) \) 60 * q + 2 * q^3 - 704 * q^9 - 94 * q^11 - 2 * q^17 + 2 * q^19 + 2748 * q^25 - 316 * q^27 + 322 * q^33 + 3846 * q^35 - 8 * q^41 + 5576 * q^43 + 1500 * q^49 - 7202 * q^51 + 7804 * q^57 + 6530 * q^59 + 1248 * q^65 + 8002 * q^67 + 3678 * q^73 - 1572 * q^75 - 12898 * q^81 - 10552 * q^83 - 6818 * q^89 - 18240 * q^91 - 6984 * q^97 - 640 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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