LMFDB - Embedded newform 630.3.o.f.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,3,Mod(127,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("630.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.1662566547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 $ x^16 - 8x^15 + 32x^14 + 152x^13 + 1954x^12 - 12664x^11 + 50336x^10 + 231896x^9 + 1093889x^8 - 4595248x^7 + 18837632x^6 + 86081152x^5 + 178889856x^4 + 70149120x^3 + 10035200x^2 - 7168000*x + 2560000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{14}\cdot 5 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.4
Root			$5.71348 + 5.71348i$ of defining polynomial
Character	$\chi$	$=$	630.127
Dual form			630.3.o.f.253.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(1.66827 + 4.71348i) q^{5} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(1.66827 + 4.71348i) q^{5} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-3.04521 + 6.38175i) q^{10} +5.03576 q^{11} +(-2.44923 + 2.44923i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(18.2815 + 18.2815i) q^{17} +9.56449i q^{19} +(-9.42696 + 3.33654i) q^{20} +(5.03576 + 5.03576i) q^{22} +(-16.4256 + 16.4256i) q^{23} +(-19.4338 + 15.7267i) q^{25} -4.89847 q^{26} +(3.74166 - 3.74166i) q^{28} +4.18550i q^{29} -55.1410 q^{31} +(-4.00000 - 4.00000i) q^{32} +36.5631i q^{34} +(5.69707 - 11.9392i) q^{35} +(-1.23603 - 1.23603i) q^{37} +(-9.56449 + 9.56449i) q^{38} +(-12.7635 - 6.09042i) q^{40} +12.2171 q^{41} +(36.1249 - 36.1249i) q^{43} +10.0715i q^{44} -32.8512 q^{46} +(-18.6917 - 18.6917i) q^{47} +7.00000i q^{49} +(-35.1605 - 3.70706i) q^{50} +(-4.89847 - 4.89847i) q^{52} +(-37.8979 + 37.8979i) q^{53} +(8.40100 + 23.7359i) q^{55} +7.48331 q^{56} +(-4.18550 + 4.18550i) q^{58} +71.7488i q^{59} +60.8100 q^{61} +(-55.1410 - 55.1410i) q^{62} -8.00000i q^{64} +(-15.6304 - 7.45843i) q^{65} +(30.4868 + 30.4868i) q^{67} +(-36.5631 + 36.5631i) q^{68} +(17.6362 - 6.24209i) q^{70} -115.195 q^{71} +(54.8705 - 54.8705i) q^{73} -2.47206i q^{74} -19.1290 q^{76} +(-9.42104 - 9.42104i) q^{77} -62.5991i q^{79} +(-6.67307 - 18.8539i) q^{80} +(12.2171 + 12.2171i) q^{82} +(-52.8767 + 52.8767i) q^{83} +(-55.6711 + 116.668i) q^{85} +72.2499 q^{86} +(-10.0715 + 10.0715i) q^{88} +16.5994i q^{89} +9.16419 q^{91} +(-32.8512 - 32.8512i) q^{92} -37.3834i q^{94} +(-45.0820 + 15.9561i) q^{95} +(71.1722 + 71.1722i) q^{97} +(-7.00000 + 7.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8	$ 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8} + 24 q^{10} - 8 q^{11} - 32 q^{13} - 64 q^{16} - 56 q^{17} + 16 q^{20} - 8 q^{22} - 24 q^{23} + 40 q^{25} - 64 q^{26} - 112 q^{31} - 64 q^{32} - 28 q^{35} - 152 q^{37} - 16 q^{40} - 48 q^{46} - 80 q^{47} + 72 q^{50} - 64 q^{52} - 48 q^{53} - 24 q^{55} + 96 q^{58} + 96 q^{61} - 112 q^{62} - 16 q^{65} - 80 q^{67} + 112 q^{68} - 536 q^{71} + 168 q^{77} - 64 q^{80} + 256 q^{83} + 40 q^{85} + 16 q^{88} - 48 q^{92} - 360 q^{95} + 688 q^{97} - 112 q^{98}+O(q^{100}) $ 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8 + 24 * q^10 - 8 * q^11 - 32 * q^13 - 64 * q^16 - 56 * q^17 + 16 * q^20 - 8 * q^22 - 24 * q^23 + 40 * q^25 - 64 * q^26 - 112 * q^31 - 64 * q^32 - 28 * q^35 - 152 * q^37 - 16 * q^40 - 48 * q^46 - 80 * q^47 + 72 * q^50 - 64 * q^52 - 48 * q^53 - 24 * q^55 + 96 * q^58 + 96 * q^61 - 112 * q^62 - 16 * q^65 - 80 * q^67 + 112 * q^68 - 536 * q^71 + 168 * q^77 - 64 * q^80 + 256 * q^83 + 40 * q^85 + 16 * q^88 - 48 * q^92 - 360 * q^95 + 688 * q^97 - 112 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			2.00000i			0.500000i
$5$	1.66827	+	4.71348i	0.333654	+	0.942696i
$5$	1.66827	+	4.71348i	0.333654	+	0.942696i
$6$		0			0
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		0			0
$10$	−3.04521	+	6.38175i	−0.304521	+	0.638175i
$11$	5.03576			0.457796			0.228898	−	0.973450i	$-0.426488\pi$
$11$	5.03576			0.457796			0.228898	+	0.973450i	$0.426488\pi$
$12$		0			0
$13$	−2.44923	+	2.44923i	−0.188403	+	0.188403i	−0.795005	−	0.606603i	$-0.792532\pi$
$13$	−2.44923	+	2.44923i	−0.188403	+	0.188403i	0.606603	+	0.795005i	$0.292532\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	18.2815	+	18.2815i	1.07538	+	1.07538i	0.996917	+	0.0784682i	$0.0250029\pi$
$17$	18.2815	+	18.2815i	1.07538	+	1.07538i	0.0784682	+	0.996917i	$0.474997\pi$
$18$		0			0
$19$			9.56449i			0.503394i	0.967806	+	0.251697i	$0.0809887\pi$
$19$			9.56449i			0.503394i	−0.967806	+	0.251697i	$0.919011\pi$
$20$	−9.42696	+	3.33654i	−0.471348	+	0.166827i
$21$		0			0
$22$	5.03576	+	5.03576i	0.228898	+	0.228898i
$23$	−16.4256	+	16.4256i	−0.714157	+	0.714157i	−0.967402	−	0.253245i	$-0.918502\pi$
$23$	−16.4256	+	16.4256i	−0.714157	+	0.714157i	0.253245	+	0.967402i	$0.418502\pi$
$24$		0			0
$25$	−19.4338	+	15.7267i	−0.777350	+	0.629068i
$26$	−4.89847			−0.188403
$27$		0			0
$28$	3.74166	−	3.74166i	0.133631	−	0.133631i
$29$			4.18550i			0.144328i	0.997393	+	0.0721639i	$0.0229905\pi$
$29$			4.18550i			0.144328i	−0.997393	+	0.0721639i	$0.977010\pi$
$30$		0			0
$31$	−55.1410			−1.77874			−0.889370	−	0.457188i	$-0.848857\pi$
$31$	−55.1410			−1.77874			−0.889370	+	0.457188i	$0.848857\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$		0			0
$34$			36.5631i			1.07538i
$35$	5.69707	−	11.9392i	0.162773	−	0.341119i
$36$		0			0
$37$	−1.23603	−	1.23603i	−0.0334062	−	0.0334062i	0.690206	−	0.723613i	$-0.257520\pi$
$37$	−1.23603	−	1.23603i	−0.0334062	−	0.0334062i	−0.723613	+	0.690206i	$0.757520\pi$
$38$	−9.56449	+	9.56449i	−0.251697	+	0.251697i
$39$		0			0
$40$	−12.7635	−	6.09042i	−0.319087	−	0.152260i
$41$	12.2171			0.297979			0.148989	−	0.988839i	$-0.452398\pi$
$41$	12.2171			0.297979			0.148989	+	0.988839i	$0.452398\pi$
$42$		0			0
$43$	36.1249	−	36.1249i	0.840115	−	0.840115i	−0.148759	−	0.988874i	$-0.547528\pi$
$43$	36.1249	−	36.1249i	0.840115	−	0.840115i	0.988874	+	0.148759i	$0.0475278\pi$
$44$			10.0715i			0.228898i
$45$		0			0
$46$	−32.8512			−0.714157
$47$	−18.6917	−	18.6917i	−0.397696	−	0.397696i	0.479724	−	0.877419i	$-0.340737\pi$
$47$	−18.6917	−	18.6917i	−0.397696	−	0.397696i	−0.877419	+	0.479724i	$0.840737\pi$
$48$		0			0
$49$			7.00000i			0.142857i
$50$	−35.1605	−	3.70706i	−0.703209	−	0.0741412i
$51$		0			0
$52$	−4.89847	−	4.89847i	−0.0942013	−	0.0942013i
$53$	−37.8979	+	37.8979i	−0.715056	+	0.715056i	−0.967588	−	0.252533i	$-0.918736\pi$
$53$	−37.8979	+	37.8979i	−0.715056	+	0.715056i	0.252533	+	0.967588i	$0.418736\pi$
$54$		0			0
$55$	8.40100	+	23.7359i	0.152745	+	0.431562i
$56$	7.48331			0.133631
$57$		0			0
$58$	−4.18550	+	4.18550i	−0.0721639	+	0.0721639i
$59$			71.7488i			1.21608i	0.793906	+	0.608041i	$0.208044\pi$
$59$			71.7488i			1.21608i	−0.793906	+	0.608041i	$0.791956\pi$
$60$		0			0
$61$	60.8100			0.996885			0.498442	−	0.866923i	$-0.333906\pi$
$61$	60.8100			0.996885			0.498442	+	0.866923i	$0.333906\pi$
$62$	−55.1410	−	55.1410i	−0.889370	−	0.889370i
$63$		0			0
$64$		−	8.00000i		−	0.125000i
$65$	−15.6304	−	7.45843i	−0.240467	−	0.114745i
$66$		0			0
$67$	30.4868	+	30.4868i	0.455027	+	0.455027i	0.897019	−	0.441992i	$-0.145728\pi$
$67$	30.4868	+	30.4868i	0.455027	+	0.455027i	−0.441992	+	0.897019i	$0.645728\pi$
$68$	−36.5631	+	36.5631i	−0.537692	+	0.537692i
$69$		0			0
$70$	17.6362	−	6.24209i	0.251946	−	0.0891727i
$71$	−115.195			−1.62246			−0.811229	−	0.584728i	$-0.801201\pi$
$71$	−115.195			−1.62246			−0.811229	+	0.584728i	$0.801201\pi$
$72$		0			0
$73$	54.8705	−	54.8705i	0.751651	−	0.751651i	−0.223136	−	0.974787i	$-0.571629\pi$
$73$	54.8705	−	54.8705i	0.751651	−	0.751651i	0.974787	+	0.223136i	$0.0716294\pi$
$74$		−	2.47206i		−	0.0334062i
$75$		0			0
$76$	−19.1290			−0.251697
$77$	−9.42104	−	9.42104i	−0.122351	−	0.122351i
$78$		0			0
$79$		−	62.5991i		−	0.792394i	−0.918165	−	0.396197i	$-0.870330\pi$
$79$		−	62.5991i		−	0.792394i	0.918165	−	0.396197i	$-0.129670\pi$
$80$	−6.67307	−	18.8539i	−0.0834134	−	0.235674i
$81$		0			0
$82$	12.2171	+	12.2171i	0.148989	+	0.148989i
$83$	−52.8767	+	52.8767i	−0.637069	+	0.637069i	−0.949831	−	0.312762i	$-0.898746\pi$
$83$	−52.8767	+	52.8767i	−0.637069	+	0.637069i	0.312762	+	0.949831i	$0.398746\pi$
$84$		0			0
$85$	−55.6711	+	116.668i	−0.654954	+	1.37257i
$86$	72.2499			0.840115
$87$		0			0
$88$	−10.0715	+	10.0715i	−0.114449	+	0.114449i
$89$			16.5994i			0.186511i	0.995642	+	0.0932553i	$0.0297273\pi$
$89$			16.5994i			0.186511i	−0.995642	+	0.0932553i	$0.970273\pi$
$90$		0			0
$91$	9.16419			0.100705
$92$	−32.8512	−	32.8512i	−0.357079	−	0.357079i
$93$		0			0
$94$		−	37.3834i		−	0.397696i
$95$	−45.0820	+	15.9561i	−0.474548	+	0.167959i
$96$		0			0
$97$	71.1722	+	71.1722i	0.733734	+	0.733734i	0.971357	−	0.237623i	$-0.0763684\pi$
$97$	71.1722	+	71.1722i	0.733734	+	0.733734i	−0.237623	+	0.971357i	$0.576368\pi$
$98$	−7.00000	+	7.00000i	−0.0714286	+	0.0714286i
$99$		0			0
$100$	−31.4534	−	38.8675i	−0.314534	−	0.388675i
$101$	145.577			1.44136			0.720679	−	0.693269i	$-0.243830\pi$
$101$	145.577			1.44136			0.720679	+	0.693269i	$0.243830\pi$
$102$		0			0
$103$	105.102	−	105.102i	1.02041	−	1.02041i	0.0206221	−	0.999787i	$-0.493435\pi$
$103$	105.102	−	105.102i	1.02041	−	1.02041i	0.999787	−	0.0206221i	$-0.00656470\pi$
$104$		−	9.79693i		−	0.0942013i
$105$		0			0
$106$	−75.7959			−0.715056
$107$	45.6173	+	45.6173i	0.426330	+	0.426330i	0.887376	−	0.461046i	$-0.152526\pi$
$107$	45.6173	+	45.6173i	0.426330	+	0.426330i	−0.461046	+	0.887376i	$0.652526\pi$
$108$		0			0
$109$			156.303i			1.43397i	0.697087	+	0.716987i	$0.254479\pi$
$109$			156.303i			1.43397i	−0.697087	+	0.716987i	$0.745521\pi$
$110$	−15.3349	+	32.1369i	−0.139409	+	0.292154i
$111$		0			0
$112$	7.48331	+	7.48331i	0.0668153	+	0.0668153i
$113$	78.3428	−	78.3428i	0.693299	−	0.693299i	−0.269657	−	0.962956i	$-0.586910\pi$
$113$	78.3428	−	78.3428i	0.693299	−	0.693299i	0.962956	+	0.269657i	$0.0869104\pi$
$114$		0			0
$115$	−104.824	−	50.0194i	−0.911514	−	0.434952i
$116$	−8.37101			−0.0721639
$117$		0			0
$118$	−71.7488	+	71.7488i	−0.608041	+	0.608041i
$119$		−	68.4033i		−	0.574817i
$120$		0			0
$121$	−95.6411			−0.790423
$122$	60.8100	+	60.8100i	0.498442	+	0.498442i
$123$		0			0
$124$		−	110.282i		−	0.889370i
$125$	−106.548	−	65.3642i	−0.852385	−	0.522914i
$126$		0			0
$127$	84.9960	+	84.9960i	0.669260	+	0.669260i	0.957545	−	0.288285i	$-0.0930851\pi$
$127$	84.9960	+	84.9960i	0.669260	+	0.669260i	−0.288285	+	0.957545i	$0.593085\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		0			0
$130$	−8.17196	−	23.0888i	−0.0628612	−	0.177606i
$131$	220.554			1.68362			0.841808	−	0.539776i	$-0.181491\pi$
$131$	220.554			1.68362			0.841808	+	0.539776i	$0.181491\pi$
$132$		0			0
$133$	17.8935	−	17.8935i	0.134538	−	0.134538i
$134$			60.9737i			0.455027i
$135$		0			0
$136$	−73.1262			−0.537692
$137$	116.039	+	116.039i	0.846999	+	0.846999i	0.989758	−	0.142759i	$-0.0455973\pi$
$137$	116.039	+	116.039i	0.846999	+	0.846999i	−0.142759	+	0.989758i	$0.545597\pi$
$138$		0			0
$139$		−	270.544i		−	1.94636i	−0.230046	−	0.973180i	$-0.573888\pi$
$139$		−	270.544i		−	1.94636i	0.230046	−	0.973180i	$-0.426112\pi$
$140$	23.8783	+	11.3941i	0.170559	+	0.0813867i
$141$		0			0
$142$	−115.195	−	115.195i	−0.811229	−	0.811229i
$143$	−12.3337	+	12.3337i	−0.0862500	+	0.0862500i
$144$		0			0
$145$	−19.7283	+	6.98255i	−0.136057	+	0.0481555i
$146$	109.741			0.751651
$147$		0			0
$148$	2.47206	−	2.47206i	0.0167031	−	0.0167031i
$149$		−	101.794i		−	0.683184i	−0.939848	−	0.341592i	$-0.889034\pi$
$149$		−	101.794i		−	0.683184i	0.939848	−	0.341592i	$-0.110966\pi$
$150$		0			0
$151$	166.350			1.10165			0.550826	−	0.834620i	$-0.314313\pi$
$151$	166.350			1.10165			0.550826	+	0.834620i	$0.314313\pi$
$152$	−19.1290	−	19.1290i	−0.125849	−	0.125849i
$153$		0			0
$154$		−	18.8421i		−	0.122351i
$155$	−91.9899	−	259.906i	−0.593483	−	1.67681i
$156$		0			0
$157$	−106.083	−	106.083i	−0.675686	−	0.675686i	0.283335	−	0.959021i	$-0.408559\pi$
$157$	−106.083	−	106.083i	−0.675686	−	0.675686i	−0.959021	+	0.283335i	$0.908559\pi$
$158$	62.5991	−	62.5991i	0.396197	−	0.396197i
$159$		0			0
$160$	12.1808	−	25.5270i	0.0761302	−	0.159544i
$161$	61.4590			0.381733
$162$		0			0
$163$	54.7674	−	54.7674i	0.335996	−	0.335996i	−0.518862	−	0.854858i	$-0.673644\pi$
$163$	54.7674	−	54.7674i	0.335996	−	0.335996i	0.854858	+	0.518862i	$0.173644\pi$
$164$			24.4342i			0.148989i
$165$		0			0
$166$	−105.753			−0.637069
$167$	−12.2483	−	12.2483i	−0.0733432	−	0.0733432i	0.669484	−	0.742827i	$-0.266515\pi$
$167$	−12.2483	−	12.2483i	−0.0733432	−	0.0733432i	−0.742827	+	0.669484i	$0.766515\pi$
$168$		0			0
$169$			157.003i			0.929009i
$170$	−172.339	+	60.9970i	−1.01376	+	0.358806i
$171$		0			0
$172$	72.2499	+	72.2499i	0.420057	+	0.420057i
$173$	210.627	−	210.627i	1.21750	−	1.21750i	0.248992	−	0.968506i	$-0.419901\pi$
$173$	210.627	−	210.627i	1.21750	−	1.21750i	0.968506	−	0.248992i	$-0.0800993\pi$
$174$		0			0
$175$	65.7792	+	6.93528i	0.375881	+	0.0396302i
$176$	−20.1430			−0.114449
$177$		0			0
$178$	−16.5994	+	16.5994i	−0.0932553	+	0.0932553i
$179$		−	141.089i		−	0.788208i	−0.919066	−	0.394104i	$-0.871055\pi$
$179$		−	141.089i		−	0.788208i	0.919066	−	0.394104i	$-0.128945\pi$
$180$		0			0
$181$	−14.5190			−0.0802153			−0.0401077	−	0.999195i	$-0.512770\pi$
$181$	−14.5190			−0.0802153			−0.0401077	+	0.999195i	$0.512770\pi$
$182$	9.16419	+	9.16419i	0.0503527	+	0.0503527i
$183$		0			0
$184$		−	65.7025i		−	0.357079i
$185$	3.76396	−	7.88802i	0.0203458	−	0.0426379i
$186$		0			0
$187$	92.0614	+	92.0614i	0.492307	+	0.492307i
$188$	37.3834	−	37.3834i	0.198848	−	0.198848i
$189$		0			0
$190$	−61.0382	−	29.1259i	−0.321254	−	0.153294i
$191$	−336.312			−1.76080			−0.880398	−	0.474235i	$-0.842725\pi$
$191$	−336.312			−1.76080			−0.880398	+	0.474235i	$0.842725\pi$
$192$		0			0
$193$	15.7585	−	15.7585i	0.0816500	−	0.0816500i	−0.665102	−	0.746752i	$-0.731612\pi$
$193$	15.7585	−	15.7585i	0.0816500	−	0.0816500i	0.746752	+	0.665102i	$0.231612\pi$
$194$			142.344i			0.733734i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	160.208	+	160.208i	0.813239	+	0.813239i	0.985118	−	0.171879i	$-0.0549838\pi$
$197$	160.208	+	160.208i	0.813239	+	0.813239i	−0.171879	+	0.985118i	$0.554984\pi$
$198$		0			0
$199$			161.286i			0.810483i	0.914210	+	0.405242i	$0.132813\pi$
$199$			161.286i			0.810483i	−0.914210	+	0.405242i	$0.867187\pi$
$200$	7.41412	−	70.3209i	0.0370706	−	0.351605i
$201$		0			0
$202$	145.577	+	145.577i	0.720679	+	0.720679i
$203$	7.83036	−	7.83036i	0.0385732	−	0.0385732i
$204$		0			0
$205$	20.3814	+	57.5852i	0.0994217	+	0.280903i
$206$	210.204			1.02041
$207$		0			0
$208$	9.79693	−	9.79693i	0.0471006	−	0.0471006i
$209$			48.1645i			0.230452i
$210$		0			0
$211$	−76.5522			−0.362806			−0.181403	−	0.983409i	$-0.558064\pi$
$211$	−76.5522			−0.362806			−0.181403	+	0.983409i	$0.558064\pi$
$212$	−75.7959	−	75.7959i	−0.357528	−	0.357528i
$213$		0			0
$214$			91.2347i			0.426330i
$215$	230.540	+	110.008i	1.07228	+	0.511665i
$216$		0			0
$217$	103.159	+	103.159i	0.475388	+	0.475388i
$218$	−156.303	+	156.303i	−0.716987	+	0.716987i
$219$		0			0
$220$	−47.4719	+	16.8020i	−0.215781	+	0.0763727i
$221$	−89.5515			−0.405210
$222$		0			0
$223$	247.136	−	247.136i	1.10823	−	1.10823i	0.114852	−	0.993383i	$-0.463361\pi$
$223$	247.136	−	247.136i	1.10823	−	1.10823i	0.993383	−	0.114852i	$-0.0366394\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	156.686			0.693299
$227$	195.992	+	195.992i	0.863402	+	0.863402i	0.991732	−	0.128330i	$-0.0409615\pi$
$227$	195.992	+	195.992i	0.863402	+	0.863402i	−0.128330	+	0.991732i	$0.540962\pi$
$228$		0			0
$229$			70.9486i			0.309819i	0.987929	+	0.154910i	$0.0495086\pi$
$229$			70.9486i			0.309819i	−0.987929	+	0.154910i	$0.950491\pi$
$230$	−54.8047	−	154.844i	−0.238281	−	0.673233i
$231$		0			0
$232$	−8.37101	−	8.37101i	−0.0360819	−	0.0360819i
$233$	13.5120	−	13.5120i	0.0579912	−	0.0579912i	−0.677516	−	0.735508i	$-0.736944\pi$
$233$	13.5120	−	13.5120i	0.0579912	−	0.0579912i	0.735508	+	0.677516i	$0.236944\pi$
$234$		0			0
$235$	56.9201	−	119.286i	0.242213	−	0.507599i
$236$	−143.498			−0.608041
$237$		0			0
$238$	68.4033	−	68.4033i	0.287409	−	0.287409i
$239$		−	157.888i		−	0.660617i	−0.943873	−	0.330309i	$-0.892847\pi$
$239$		−	157.888i		−	0.660617i	0.943873	−	0.330309i	$-0.107153\pi$
$240$		0			0
$241$	142.701			0.592119			0.296060	−	0.955169i	$-0.404327\pi$
$241$	142.701			0.592119			0.296060	+	0.955169i	$0.404327\pi$
$242$	−95.6411	−	95.6411i	−0.395211	−	0.395211i
$243$		0			0
$244$			121.620i			0.498442i
$245$	−32.9943	+	11.6779i	−0.134671	+	0.0476648i
$246$		0			0
$247$	−23.4257	−	23.4257i	−0.0948408	−	0.0948408i
$248$	110.282	−	110.282i	0.444685	−	0.444685i
$249$		0			0
$250$	−41.1839	−	171.912i	−0.164736	−	0.687650i
$251$	−81.9263			−0.326400			−0.163200	−	0.986593i	$-0.552182\pi$
$251$	−81.9263			−0.326400			−0.163200	+	0.986593i	$0.552182\pi$
$252$		0			0
$253$	−82.7154	+	82.7154i	−0.326938	+	0.326938i
$254$			169.992i			0.669260i
$255$		0			0
$256$	16.0000			0.0625000
$257$	266.743	+	266.743i	1.03791	+	1.03791i	0.999252	+	0.0386594i	$0.0123087\pi$
$257$	266.743	+	266.743i	1.03791	+	1.03791i	0.0386594	+	0.999252i	$0.487691\pi$
$258$		0			0
$259$			4.62479i			0.0178563i
$260$	14.9169	−	31.2608i	0.0573725	−	0.120234i
$261$		0			0
$262$	220.554	+	220.554i	0.841808	+	0.841808i
$263$	77.4514	−	77.4514i	0.294492	−	0.294492i	−0.544360	−	0.838852i	$-0.683227\pi$
$263$	77.4514	−	77.4514i	0.294492	−	0.294492i	0.838852	+	0.544360i	$0.183227\pi$
$264$		0			0
$265$	−241.855	−	115.407i	−0.912661	−	0.435499i
$266$	35.7871			0.134538
$267$		0			0
$268$	−60.9737	+	60.9737i	−0.227514	+	0.227514i
$269$		−	51.5262i		−	0.191547i	−0.995403	−	0.0957737i	$-0.969467\pi$
$269$		−	51.5262i		−	0.191547i	0.995403	−	0.0957737i	$-0.0305325\pi$
$270$		0			0
$271$	143.162			0.528273			0.264137	−	0.964485i	$-0.414913\pi$
$271$	143.162			0.528273			0.264137	+	0.964485i	$0.414913\pi$
$272$	−73.1262	−	73.1262i	−0.268846	−	0.268846i
$273$		0			0
$274$			232.078i			0.846999i
$275$	−97.8637	+	79.1958i	−0.355868	+	0.287985i
$276$		0			0
$277$	−66.2523	−	66.2523i	−0.239178	−	0.239178i	0.577332	−	0.816510i	$-0.304094\pi$
$277$	−66.2523	−	66.2523i	−0.239178	−	0.239178i	−0.816510	+	0.577332i	$0.804094\pi$
$278$	270.544	−	270.544i	0.973180	−	0.973180i
$279$		0			0
$280$	12.4842	+	35.2724i	0.0445864	+	0.125973i
$281$	−484.413			−1.72389			−0.861945	−	0.507002i	$-0.830754\pi$
$281$	−484.413			−1.72389			−0.861945	+	0.507002i	$0.830754\pi$
$282$		0			0
$283$	248.349	−	248.349i	0.877559	−	0.877559i	−0.115723	−	0.993282i	$-0.536918\pi$
$283$	248.349	−	248.349i	0.877559	−	0.877559i	0.993282	+	0.115723i	$0.0369184\pi$
$284$		−	230.389i		−	0.811229i
$285$		0			0
$286$	−24.6675			−0.0862500
$287$	−22.8561	−	22.8561i	−0.0796381	−	0.0796381i
$288$		0			0
$289$			379.430i			1.31290i
$290$	−26.7108	−	12.7457i	−0.0921063	−	0.0439508i
$291$		0			0
$292$	109.741	+	109.741i	0.375826	+	0.375826i
$293$	201.337	−	201.337i	0.687158	−	0.687158i	−0.274445	−	0.961603i	$-0.588494\pi$
$293$	201.337	−	201.337i	0.687158	−	0.687158i	0.961603	+	0.274445i	$0.0884941\pi$
$294$		0			0
$295$	−338.187	+	119.696i	−1.14640	+	0.405750i
$296$	4.94411			0.0167031
$297$		0			0
$298$	101.794	−	101.794i	0.341592	−	0.341592i
$299$		−	80.4603i		−	0.269098i
$300$		0			0
$301$	−135.167			−0.449060
$302$	166.350	+	166.350i	0.550826	+	0.550826i
$303$		0			0
$304$		−	38.2580i		−	0.125849i
$305$	101.447	+	286.626i	0.332614	+	0.939759i
$306$		0			0
$307$	−2.87888	−	2.87888i	−0.00937745	−	0.00937745i	0.702403	−	0.711780i	$-0.252111\pi$
$307$	−2.87888	−	2.87888i	−0.00937745	−	0.00937745i	−0.711780	+	0.702403i	$0.752111\pi$
$308$	18.8421	−	18.8421i	0.0611756	−	0.0611756i
$309$		0			0
$310$	167.916	−	351.896i	0.541664	−	1.13515i
$311$	127.446			0.409793			0.204897	−	0.978784i	$-0.434314\pi$
$311$	127.446			0.409793			0.204897	+	0.978784i	$0.434314\pi$
$312$		0			0
$313$	−73.9562	+	73.9562i	−0.236282	+	0.236282i	−0.815309	−	0.579027i	$-0.803433\pi$
$313$	−73.9562	+	73.9562i	−0.236282	+	0.236282i	0.579027	+	0.815309i	$0.303433\pi$
$314$		−	212.165i		−	0.675686i
$315$		0			0
$316$	125.198			0.396197
$317$	−377.411	−	377.411i	−1.19057	−	1.19057i	−0.976907	−	0.213664i	$-0.931460\pi$
$317$	−377.411	−	377.411i	−1.19057	−	1.19057i	−0.213664	−	0.976907i	$-0.568540\pi$
$318$		0			0
$319$			21.0772i			0.0660727i
$320$	37.7078	−	13.3461i	0.117837	−	0.0417067i
$321$		0			0
$322$	61.4590	+	61.4590i	0.190867	+	0.190867i
$323$	−174.854	+	174.854i	−0.541343	+	0.541343i
$324$		0			0
$325$	9.07946	−	86.1162i	0.0279368	−	0.264973i
$326$	109.535			0.335996
$327$		0			0
$328$	−24.4342	+	24.4342i	−0.0744947	+	0.0744947i
$329$			69.9379i			0.212577i
$330$		0			0
$331$	−505.056			−1.52585			−0.762924	−	0.646488i	$-0.776237\pi$
$331$	−505.056			−1.52585			−0.762924	+	0.646488i	$0.776237\pi$
$332$	−105.753	−	105.753i	−0.318535	−	0.318535i
$333$		0			0
$334$		−	24.4966i		−	0.0733432i
$335$	−92.8388	+	194.559i	−0.277131	+	0.580774i
$336$		0			0
$337$	−389.840	−	389.840i	−1.15680	−	1.15680i	−0.985161	−	0.171635i	$-0.945095\pi$
$337$	−389.840	−	389.840i	−1.15680	−	1.15680i	−0.171635	−	0.985161i	$-0.554905\pi$
$338$	−157.003	+	157.003i	−0.464504	+	0.464504i
$339$		0			0
$340$	−233.336	−	111.342i	−0.686283	−	0.327477i
$341$	−277.676			−0.814300
$342$		0			0
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$			144.500i			0.420057i
$345$		0			0
$346$	421.254			1.21750
$347$	306.559	+	306.559i	0.883456	+	0.883456i	0.993884	−	0.110428i	$-0.0352223\pi$
$347$	306.559	+	306.559i	0.883456	+	0.883456i	−0.110428	+	0.993884i	$0.535222\pi$
$348$		0			0
$349$		−	509.585i		−	1.46013i	−0.683379	−	0.730064i	$-0.739490\pi$
$349$		−	509.585i		−	1.46013i	0.683379	−	0.730064i	$-0.260510\pi$
$350$	58.8439	+	72.7145i	0.168125	+	0.207756i
$351$		0			0
$352$	−20.1430	−	20.1430i	−0.0572245	−	0.0572245i
$353$	−330.387	+	330.387i	−0.935941	+	0.935941i	−0.998068	−	0.0621272i	$-0.980212\pi$
$353$	−330.387	+	330.387i	−0.935941	+	0.935941i	0.0621272	+	0.998068i	$0.480212\pi$
$354$		0			0
$355$	−192.176	−	542.967i	−0.541340	−	1.52949i
$356$	−33.1989			−0.0932553
$357$		0			0
$358$	141.089	−	141.089i	0.394104	−	0.394104i
$359$		−	152.593i		−	0.425051i	−0.977155	−	0.212526i	$-0.931831\pi$
$359$		−	152.593i		−	0.425051i	0.977155	−	0.212526i	$-0.0681689\pi$
$360$		0			0
$361$	269.520			0.746594
$362$	−14.5190	−	14.5190i	−0.0401077	−	0.0401077i
$363$		0			0
$364$			18.3284i			0.0503527i
$365$	350.170	+	167.092i	0.959370	+	0.457787i
$366$		0			0
$367$	−105.176	−	105.176i	−0.286583	−	0.286583i	0.549145	−	0.835727i	$-0.314954\pi$
$367$	−105.176	−	105.176i	−0.286583	−	0.286583i	−0.835727	+	0.549145i	$0.814954\pi$
$368$	65.7025	−	65.7025i	0.178539	−	0.178539i
$369$		0			0
$370$	11.6520	−	4.12405i	0.0314918	−	0.0111461i
$371$	141.801			0.382213
$372$		0			0
$373$	−304.851	+	304.851i	−0.817294	+	0.817294i	−0.985715	−	0.168421i	$-0.946133\pi$
$373$	−304.851	+	304.851i	−0.817294	+	0.817294i	0.168421	+	0.985715i	$0.446133\pi$
$374$			184.123i			0.492307i
$375$		0			0
$376$	74.7668			0.198848
$377$	−10.2513	−	10.2513i	−0.0271917	−	0.0271917i
$378$		0			0
$379$			157.708i			0.416117i	0.978116	+	0.208059i	$0.0667145\pi$
$379$			157.708i			0.416117i	−0.978116	+	0.208059i	$0.933286\pi$
$380$	−31.9123	−	90.1641i	−0.0839797	−	0.237274i
$381$		0			0
$382$	−336.312	−	336.312i	−0.880398	−	0.880398i
$383$	429.631	−	429.631i	1.12175	−	1.12175i	0.130275	−	0.991478i	$-0.458414\pi$
$383$	429.631	−	429.631i	1.12175	−	1.12175i	0.991478	−	0.130275i	$-0.0415861\pi$
$384$		0			0
$385$	28.6890	−	60.1227i	0.0745170	−	0.156163i
$386$	31.5169			0.0816500
$387$		0			0
$388$	−142.344	+	142.344i	−0.366867	+	0.366867i
$389$		−	168.931i		−	0.434269i	−0.976142	−	0.217135i	$-0.930329\pi$
$389$		−	168.931i		−	0.434269i	0.976142	−	0.217135i	$-0.0696711\pi$
$390$		0			0
$391$	−600.571			−1.53599
$392$	−14.0000	−	14.0000i	−0.0357143	−	0.0357143i
$393$		0			0
$394$			320.416i			0.813239i
$395$	295.060	−	104.432i	0.746987	−	0.264385i
$396$		0			0
$397$	514.413	+	514.413i	1.29575	+	1.29575i	0.931172	+	0.364579i	$0.118787\pi$
$397$	514.413	+	514.413i	1.29575	+	1.29575i	0.364579	+	0.931172i	$0.381213\pi$
$398$	−161.286	+	161.286i	−0.405242	+	0.405242i
$399$		0			0
$400$	77.7350	−	62.9068i	0.194338	−	0.157267i
$401$	−542.884			−1.35383			−0.676913	−	0.736063i	$-0.736683\pi$
$401$	−542.884			−1.35383			−0.676913	+	0.736063i	$0.736683\pi$
$402$		0			0
$403$	135.053	−	135.053i	0.335119	−	0.335119i
$404$			291.154i			0.720679i
$405$		0			0
$406$	15.6607			0.0385732
$407$	−6.22434	−	6.22434i	−0.0152932	−	0.0152932i
$408$		0			0
$409$			454.920i			1.11227i	0.831091	+	0.556137i	$0.187717\pi$
$409$			454.920i			1.11227i	−0.831091	+	0.556137i	$0.812283\pi$
$410$	−37.2037	+	77.9666i	−0.0907408	+	0.190162i
$411$		0			0
$412$	210.204	+	210.204i	0.510205	+	0.510205i
$413$	134.230	−	134.230i	0.325012	−	0.325012i
$414$		0			0
$415$	−337.446	−	161.021i	−0.813123	−	0.388002i
$416$	19.5939			0.0471006
$417$		0			0
$418$	−48.1645	+	48.1645i	−0.115226	+	0.115226i
$419$			597.925i			1.42703i	0.700641	+	0.713514i	$0.252898\pi$
$419$			597.925i			1.42703i	−0.700641	+	0.713514i	$0.747102\pi$
$420$		0			0
$421$	−607.858			−1.44384			−0.721921	−	0.691975i	$-0.756741\pi$
$421$	−607.858			−1.44384			−0.721921	+	0.691975i	$0.756741\pi$
$422$	−76.5522	−	76.5522i	−0.181403	−	0.181403i
$423$		0			0
$424$		−	151.592i		−	0.357528i
$425$	−642.787	−	67.7708i	−1.51244	−	0.159461i
$426$		0			0
$427$	−113.765	−	113.765i	−0.266429	−	0.266429i
$428$	−91.2347	+	91.2347i	−0.213165	+	0.213165i
$429$		0			0
$430$	120.532	+	340.548i	0.280307	+	0.791973i
$431$	−291.207			−0.675655			−0.337827	−	0.941208i	$-0.609692\pi$
$431$	−291.207			−0.675655			−0.337827	+	0.941208i	$0.609692\pi$
$432$		0			0
$433$	−47.9051	+	47.9051i	−0.110635	+	0.110635i	−0.760257	−	0.649622i	$-0.774927\pi$
$433$	−47.9051	+	47.9051i	−0.110635	+	0.110635i	0.649622	+	0.760257i	$0.274927\pi$
$434$			206.319i			0.475388i
$435$		0			0
$436$	−312.606			−0.716987
$437$	−157.103	−	157.103i	−0.359503	−	0.359503i
$438$		0			0
$439$			652.062i			1.48533i	0.669660	+	0.742667i	$0.266440\pi$
$439$			652.062i			1.48533i	−0.669660	+	0.742667i	$0.733560\pi$
$440$	−64.2739	−	30.6699i	−0.146077	−	0.0697043i
$441$		0			0
$442$	−89.5515	−	89.5515i	−0.202605	−	0.202605i
$443$	146.273	−	146.273i	0.330187	−	0.330187i	−0.522470	−	0.852657i	$-0.674989\pi$
$443$	146.273	−	146.273i	0.330187	−	0.330187i	0.852657	+	0.522470i	$0.174989\pi$
$444$		0			0
$445$	−78.2411	+	27.6923i	−0.175823	+	0.0622300i
$446$	494.273			1.10823
$447$		0			0
$448$	−14.9666	+	14.9666i	−0.0334077	+	0.0334077i
$449$			213.815i			0.476203i	0.971240	+	0.238101i	$0.0765251\pi$
$449$			213.815i			0.476203i	−0.971240	+	0.238101i	$0.923475\pi$
$450$		0			0
$451$	61.5225			0.136413
$452$	156.686	+	156.686i	0.346650	+	0.346650i
$453$		0			0
$454$			391.984i			0.863402i
$455$	15.2883	+	43.1952i	0.0336007	+	0.0949345i
$456$		0			0
$457$	339.531	+	339.531i	0.742956	+	0.742956i	0.973146	−	0.230189i	$-0.0739346\pi$
$457$	339.531	+	339.531i	0.742956	+	0.742956i	−0.230189	+	0.973146i	$0.573935\pi$
$458$	−70.9486	+	70.9486i	−0.154910	+	0.154910i
$459$		0			0
$460$	100.039	−	209.648i	0.217476	−	0.455757i
$461$	−580.456			−1.25912			−0.629562	−	0.776951i	$-0.716765\pi$
$461$	−580.456			−1.25912			−0.629562	+	0.776951i	$0.716765\pi$
$462$		0			0
$463$	551.037	−	551.037i	1.19014	−	1.19014i	0.213119	−	0.977026i	$-0.431638\pi$
$463$	551.037	−	551.037i	1.19014	−	1.19014i	0.977026	−	0.213119i	$-0.0683621\pi$
$464$		−	16.7420i		−	0.0360819i
$465$		0			0
$466$	27.0239			0.0579912
$467$	−293.344	−	293.344i	−0.628145	−	0.628145i	0.319456	−	0.947601i	$-0.396500\pi$
$467$	−293.344	−	293.344i	−0.628145	−	0.628145i	−0.947601	+	0.319456i	$0.896500\pi$
$468$		0			0
$469$		−	114.071i		−	0.243222i
$470$	176.206	−	62.3655i	0.374906	−	0.132693i
$471$		0			0
$472$	−143.498	−	143.498i	−0.304021	−	0.304021i
$473$	181.916	−	181.916i	0.384601	−	0.384601i
$474$		0			0
$475$	−150.418	−	185.874i	−0.316669	−	0.391314i
$476$	136.807			0.287409
$477$		0			0
$478$	157.888	−	157.888i	0.330309	−	0.330309i
$479$		−	694.462i		−	1.44982i	−0.688846	−	0.724908i	$-0.741882\pi$
$479$		−	694.462i		−	1.44982i	0.688846	−	0.724908i	$-0.258118\pi$
$480$		0			0
$481$	6.05464			0.0125876
$482$	142.701	+	142.701i	0.296060	+	0.296060i
$483$		0			0
$484$		−	191.282i		−	0.395211i
$485$	−216.734	+	454.203i	−0.446875	+	0.936501i
$486$		0			0
$487$	189.085	+	189.085i	0.388266	+	0.388266i	0.874068	−	0.485803i	$-0.161473\pi$
$487$	189.085	+	189.085i	0.388266	+	0.388266i	−0.485803	+	0.874068i	$0.661473\pi$
$488$	−121.620	+	121.620i	−0.249221	+	0.249221i
$489$		0			0
$490$	−44.6722	−	21.3165i	−0.0911678	−	0.0435030i
$491$	−587.867			−1.19729			−0.598643	−	0.801016i	$-0.704293\pi$
$491$	−587.867			−1.19729			−0.598643	+	0.801016i	$0.704293\pi$
$492$		0			0
$493$	−76.5175	+	76.5175i	−0.155208	+	0.155208i
$494$		−	46.8513i		−	0.0948408i
$495$		0			0
$496$	220.564			0.444685
$497$	215.509	+	215.509i	0.433620	+	0.433620i
$498$		0			0
$499$		−	13.5102i		−	0.0270745i	−0.999908	−	0.0135373i	$-0.995691\pi$
$499$		−	13.5102i		−	0.0270745i	0.999908	−	0.0135373i	$-0.00430918\pi$
$500$	130.728	−	213.096i	0.261457	−	0.426193i
$501$		0			0
$502$	−81.9263	−	81.9263i	−0.163200	−	0.163200i
$503$	−231.640	+	231.640i	−0.460516	+	0.460516i	−0.898825	−	0.438309i	$-0.855578\pi$
$503$	−231.640	+	231.640i	−0.460516	+	0.460516i	0.438309	+	0.898825i	$0.355578\pi$
$504$		0			0
$505$	242.862	+	686.175i	0.480914	+	1.35876i
$506$	−165.431			−0.326938
$507$		0			0
$508$	−169.992	+	169.992i	−0.334630	+	0.334630i
$509$			737.211i			1.44835i	0.689616	+	0.724176i	$0.257780\pi$
$509$			737.211i			1.44835i	−0.689616	+	0.724176i	$0.742220\pi$
$510$		0			0
$511$	−205.307			−0.401775
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$		0			0
$514$			533.487i			1.03791i
$515$	670.736	+	320.058i	1.30240	+	0.621472i
$516$		0			0
$517$	−94.1268	−	94.1268i	−0.182063	−	0.182063i
$518$	−4.62479	+	4.62479i	−0.00892817	+	0.00892817i
$519$		0			0
$520$	46.1776	−	16.3439i	0.0888031	−	0.0314306i
$521$	−209.021			−0.401191			−0.200596	−	0.979674i	$-0.564288\pi$
$521$	−209.021			−0.401191			−0.200596	+	0.979674i	$0.564288\pi$
$522$		0			0
$523$	99.0847	−	99.0847i	0.189455	−	0.189455i	−0.606006	−	0.795460i	$-0.707229\pi$
$523$	99.0847	−	99.0847i	0.189455	−	0.189455i	0.795460	+	0.606006i	$0.207229\pi$
$524$			441.108i			0.841808i
$525$		0			0
$526$	154.903			0.294492
$527$	−1008.06	−	1008.06i	−1.91283	−	1.91283i
$528$		0			0
$529$		−	10.6017i		−	0.0200410i
$530$	−126.448	−	357.262i	−0.238581	−	0.674080i
$531$		0			0
$532$	35.7871	+	35.7871i	0.0672689	+	0.0672689i
$533$	−29.9226	+	29.9226i	−0.0561399	+	0.0561399i
$534$		0			0
$535$	−138.914	+	291.118i	−0.259653	+	0.544147i
$536$	−121.947			−0.227514
$537$		0			0
$538$	51.5262	−	51.5262i	0.0957737	−	0.0957737i
$539$			35.2503i			0.0653994i
$540$		0			0
$541$	599.763			1.10862			0.554310	−	0.832311i	$-0.312982\pi$
$541$	599.763			1.10862			0.554310	+	0.832311i	$0.312982\pi$
$542$	143.162	+	143.162i	0.264137	+	0.264137i
$543$		0			0
$544$		−	146.252i		−	0.268846i
$545$	−736.731	+	260.756i	−1.35180	+	0.478451i
$546$		0			0
$547$	−332.261	−	332.261i	−0.607424	−	0.607424i	0.334848	−	0.942272i	$-0.391315\pi$
$547$	−332.261	−	332.261i	−0.607424	−	0.607424i	−0.942272	+	0.334848i	$0.891315\pi$
$548$	−232.078	+	232.078i	−0.423499	+	0.423499i
$549$		0			0
$550$	−177.060	−	18.6679i	−0.321926	−	0.0339416i
$551$	−40.0322			−0.0726538
$552$		0			0
$553$	−117.112	+	117.112i	−0.211776	+	0.211776i
$554$		−	132.505i		−	0.239178i
$555$		0			0
$556$	541.088			0.973180
$557$	624.562	+	624.562i	1.12130	+	1.12130i	0.991547	+	0.129750i	$0.0414174\pi$
$557$	624.562	+	624.562i	1.12130	+	1.12130i	0.129750	+	0.991547i	$0.458583\pi$
$558$		0			0
$559$			176.957i			0.316560i
$560$	−22.7883	+	47.7566i	−0.0406933	+	0.0852797i
$561$		0			0
$562$	−484.413	−	484.413i	−0.861945	−	0.861945i
$563$	385.579	−	385.579i	0.684865	−	0.684865i	−0.276228	−	0.961092i	$-0.589084\pi$
$563$	385.579	−	385.579i	0.684865	−	0.684865i	0.961092	+	0.276228i	$0.0890844\pi$
$564$		0			0
$565$	499.964	+	238.570i	0.884892	+	0.422248i
$566$	496.698			0.877559
$567$		0			0
$568$	230.389	−	230.389i	0.405615	−	0.405615i
$569$			578.028i			1.01587i	0.861397	+	0.507933i	$0.169590\pi$
$569$			578.028i			1.01587i	−0.861397	+	0.507933i	$0.830410\pi$
$570$		0			0
$571$	−14.7710			−0.0258687			−0.0129344	−	0.999916i	$-0.504117\pi$
$571$	−14.7710			−0.0258687			−0.0129344	+	0.999916i	$0.504117\pi$
$572$	−24.6675	−	24.6675i	−0.0431250	−	0.0431250i
$573$		0			0
$574$		−	45.7123i		−	0.0796381i
$575$	60.8908	−	577.532i	0.105897	−	1.00440i
$576$		0			0
$577$	359.827	+	359.827i	0.623617	+	0.623617i	0.946454	−	0.322838i	$-0.104637\pi$
$577$	359.827	+	359.827i	0.623617	+	0.623617i	−0.322838	+	0.946454i	$0.604637\pi$
$578$	−379.430	+	379.430i	−0.656452	+	0.656452i
$579$		0			0
$580$	−13.9651	−	39.4566i	−0.0240777	−	0.0680286i
$581$	197.847			0.340528
$582$		0			0
$583$	−190.845	+	190.845i	−0.327350	+	0.327350i
$584$			219.482i			0.375826i
$585$		0			0
$586$	402.675			0.687158
$587$	−628.762	−	628.762i	−1.07115	−	1.07115i	−0.997267	−	0.0738780i	$-0.976462\pi$
$587$	−628.762	−	628.762i	−1.07115	−	1.07115i	−0.0738780	−	0.997267i	$-0.523538\pi$
$588$		0			0
$589$		−	527.395i		−	0.895408i
$590$	−457.883	−	218.490i	−0.776073	−	0.370322i
$591$		0			0
$592$	4.94411	+	4.94411i	0.00835154	+	0.00835154i
$593$	221.183	−	221.183i	0.372991	−	0.372991i	−0.495575	−	0.868565i	$-0.665043\pi$
$593$	221.183	−	221.183i	0.372991	−	0.372991i	0.868565	+	0.495575i	$0.165043\pi$
$594$		0			0
$595$	322.417	−	114.115i	0.541878	−	0.191790i
$596$	203.589			0.341592
$597$		0			0
$598$	80.4603	−	80.4603i	0.134549	−	0.134549i
$599$			227.599i			0.379966i	0.981787	+	0.189983i	$0.0608432\pi$
$599$			227.599i			0.379966i	−0.981787	+	0.189983i	$0.939157\pi$
$600$		0			0
$601$	−772.444			−1.28527			−0.642633	−	0.766175i	$-0.722158\pi$
$601$	−772.444			−1.28527			−0.642633	+	0.766175i	$0.722158\pi$
$602$	−135.167	−	135.167i	−0.224530	−	0.224530i
$603$		0			0
$604$			332.699i			0.550826i
$605$	−159.555	−	450.802i	−0.263727	−	0.745128i
$606$		0			0
$607$	−145.543	−	145.543i	−0.239774	−	0.239774i	0.576982	−	0.816757i	$-0.304230\pi$
$607$	−145.543	−	145.543i	−0.239774	−	0.239774i	−0.816757	+	0.576982i	$0.804230\pi$
$608$	38.2580	−	38.2580i	0.0629243	−	0.0629243i
$609$		0			0
$610$	−185.179	+	388.074i	−0.303572	+	0.636187i
$611$	91.5606			0.149854
$612$		0			0
$613$	−443.832	+	443.832i	−0.724033	+	0.724033i	−0.969424	−	0.245391i	$-0.921084\pi$
$613$	−443.832	+	443.832i	−0.724033	+	0.724033i	0.245391	+	0.969424i	$0.421084\pi$
$614$		−	5.75775i		−	0.00937745i
$615$		0			0
$616$	37.6842			0.0611756
$617$	490.933	+	490.933i	0.795678	+	0.795678i	0.982411	−	0.186733i	$-0.0597899\pi$
$617$	490.933	+	490.933i	0.795678	+	0.795678i	−0.186733	+	0.982411i	$0.559790\pi$
$618$		0			0
$619$		−	570.340i		−	0.921390i	−0.887559	−	0.460695i	$-0.847600\pi$
$619$		−	570.340i		−	0.921390i	0.887559	−	0.460695i	$-0.152400\pi$
$620$	519.811	−	183.980i	0.838405	−	0.296742i
$621$		0			0
$622$	127.446	+	127.446i	0.204897	+	0.204897i
$623$	31.0547	−	31.0547i	0.0498471	−	0.0498471i
$624$		0			0
$625$	130.342	−	611.258i	0.208547	−	0.978012i
$626$	−147.912			−0.236282
$627$		0			0
$628$	212.165	−	212.165i	0.337843	−	0.337843i
$629$		−	45.1930i		−	0.0718489i
$630$		0			0
$631$	471.145			0.746665			0.373332	−	0.927698i	$-0.378215\pi$
$631$	471.145			0.746665			0.373332	+	0.927698i	$0.378215\pi$
$632$	125.198	+	125.198i	0.198099	+	0.198099i
$633$		0			0
$634$		−	754.822i		−	1.19057i
$635$	−258.831	+	542.423i	−0.407607	+	0.854209i
$636$		0			0
$637$	−17.1446	−	17.1446i	−0.0269147	−	0.0269147i
$638$	−21.0772	+	21.0772i	−0.0330363	+	0.0330363i
$639$		0			0
$640$	51.0540	+	24.3617i	0.0797718	+	0.0380651i
$641$	684.550			1.06794			0.533971	−	0.845503i	$-0.320699\pi$
$641$	684.550			1.06794			0.533971	+	0.845503i	$0.320699\pi$
$642$		0			0
$643$	−521.636	+	521.636i	−0.811253	+	0.811253i	−0.984822	−	0.173569i	$-0.944470\pi$
$643$	−521.636	+	521.636i	−0.811253	+	0.811253i	0.173569	+	0.984822i	$0.444470\pi$
$644$			122.918i			0.190867i
$645$		0			0
$646$	−349.707			−0.541343
$647$	72.9658	+	72.9658i	0.112776	+	0.112776i	0.761243	−	0.648467i	$-0.224590\pi$
$647$	72.9658	+	72.9658i	0.112776	+	0.112776i	−0.648467	+	0.761243i	$0.724590\pi$
$648$		0			0
$649$			361.310i			0.556718i
$650$	95.1956	−	77.0367i	0.146455	−	0.118518i
$651$		0			0
$652$	109.535	+	109.535i	0.167998	+	0.167998i
$653$	−334.041	+	334.041i	−0.511549	+	0.511549i	−0.915001	−	0.403452i	$-0.867810\pi$
$653$	−334.041	+	334.041i	−0.511549	+	0.511549i	0.403452	+	0.915001i	$0.367810\pi$
$654$		0			0
$655$	367.943	+	1039.58i	0.561745	+	1.58714i
$656$	−48.8685			−0.0744947
$657$		0			0
$658$	−69.9379	+	69.9379i	−0.106289	+	0.106289i
$659$		−	177.497i		−	0.269343i	−0.990890	−	0.134672i	$-0.957002\pi$
$659$		−	177.497i		−	0.269343i	0.990890	−	0.134672i	$-0.0429980\pi$
$660$		0			0
$661$	917.415			1.38792			0.693960	−	0.720013i	$-0.255864\pi$
$661$	917.415			1.38792			0.693960	+	0.720013i	$0.255864\pi$
$662$	−505.056	−	505.056i	−0.762924	−	0.762924i
$663$		0			0
$664$		−	211.507i		−	0.318535i
$665$	114.192	+	54.4895i	0.171717	+	0.0819392i
$666$		0			0
$667$	−68.7495	−	68.7495i	−0.103073	−	0.103073i
$668$	24.4966	−	24.4966i	0.0366716	−	0.0366716i
$669$		0			0
$670$	−287.398	+	101.720i	−0.428952	+	0.151822i
$671$	306.224			0.456370
$672$		0			0
$673$	725.252	−	725.252i	1.07764	−	1.07764i	0.0809191	−	0.996721i	$-0.474214\pi$
$673$	725.252	−	725.252i	1.07764	−	1.07764i	0.996721	−	0.0809191i	$-0.0257855\pi$
$674$		−	779.680i		−	1.15680i
$675$		0			0
$676$	−314.005			−0.464504
$677$	378.779	+	378.779i	0.559496	+	0.559496i	0.929164	−	0.369668i	$-0.120528\pi$
$677$	378.779	+	378.779i	0.559496	+	0.559496i	−0.369668	+	0.929164i	$0.620528\pi$
$678$		0			0
$679$		−	266.302i		−	0.392197i
$680$	−121.994	−	344.679i	−0.179403	−	0.506880i
$681$		0			0
$682$	−277.676	−	277.676i	−0.407150	−	0.407150i
$683$	−19.0537	+	19.0537i	−0.0278971	+	0.0278971i	−0.720918	−	0.693021i	$-0.756279\pi$
$683$	−19.0537	+	19.0537i	−0.0278971	+	0.0278971i	0.693021	+	0.720918i	$0.256279\pi$
$684$		0			0
$685$	−353.363	+	740.530i	−0.515858	+	1.08107i
$686$	26.1916			0.0381802
$687$		0			0
$688$	−144.500	+	144.500i	−0.210029	+	0.210029i
$689$		−	185.642i		−	0.269437i
$690$		0			0
$691$	−1010.25			−1.46202			−0.731008	−	0.682369i	$-0.760950\pi$
$691$	−1010.25			−1.46202			−0.731008	+	0.682369i	$0.760950\pi$
$692$	421.254	+	421.254i	0.608749	+	0.608749i
$693$		0			0
$694$			613.118i			0.883456i
$695$	1275.20	−	451.340i	1.83482	−	0.649410i
$696$		0			0
$697$	223.348	+	223.348i	0.320442	+	0.320442i
$698$	509.585	−	509.585i	0.730064	−	0.730064i
$699$		0			0
$700$	−13.8706	+	131.558i	−0.0198151	+	0.187941i
$701$	−80.0820			−0.114240			−0.0571198	−	0.998367i	$-0.518192\pi$
$701$	−80.0820			−0.114240			−0.0571198	+	0.998367i	$0.518192\pi$
$702$		0			0
$703$	11.8220	−	11.8220i	0.0168165	−	0.0168165i
$704$		−	40.2861i		−	0.0572245i
$705$		0			0
$706$	−660.774			−0.935941
$707$	−272.350	−	272.350i	−0.385219	−	0.385219i
$708$		0			0
$709$		−	1012.82i		−	1.42852i	−0.699879	−	0.714261i	$-0.746763\pi$
$709$		−	1012.82i		−	1.42852i	0.699879	−	0.714261i	$-0.253237\pi$
$710$	350.792	−	735.143i	0.494073	−	1.03541i
$711$		0			0
$712$	−33.1989	−	33.1989i	−0.0466277	−	0.0466277i
$713$	905.724	−	905.724i	1.27030	−	1.27030i
$714$		0			0
$715$	−78.7108	−	37.5588i	−0.110085	−	0.0525298i
$716$	282.178			0.394104
$717$		0			0
$718$	152.593	−	152.593i	0.212526	−	0.212526i
$719$			289.247i			0.402290i	0.979561	+	0.201145i	$0.0644663\pi$
$719$			289.247i			0.402290i	−0.979561	+	0.201145i	$0.935534\pi$
$720$		0			0
$721$	−393.256			−0.545432
$722$	269.520	+	269.520i	0.373297	+	0.373297i
$723$		0			0
$724$		−	29.0379i		−	0.0401077i
$725$	−65.8242	−	81.3401i	−0.0907919	−	0.112193i
$726$		0			0
$727$	444.891	+	444.891i	0.611954	+	0.611954i	0.943455	−	0.331501i	$-0.107555\pi$
$727$	444.891	+	444.891i	0.611954	+	0.611954i	−0.331501	+	0.943455i	$0.607555\pi$
$728$	−18.3284	+	18.3284i	−0.0251764	+	0.0251764i
$729$		0			0
$730$	183.078	+	517.262i	0.250791	+	0.708578i
$731$	1320.84			1.80689
$732$		0			0
$733$	−169.024	+	169.024i	−0.230592	+	0.230592i	−0.812940	−	0.582348i	$-0.802134\pi$
$733$	−169.024	+	169.024i	−0.230592	+	0.230592i	0.582348	+	0.812940i	$0.302134\pi$
$734$		−	210.352i		−	0.286583i
$735$		0			0
$736$	131.405			0.178539
$737$	153.524	+	153.524i	0.208310	+	0.208310i
$738$		0			0
$739$		−	153.342i		−	0.207499i	−0.994603	−	0.103749i	$-0.966916\pi$
$739$		−	153.342i		−	0.207499i	0.994603	−	0.103749i	$-0.0330840\pi$
$740$	15.7760	+	7.52793i	0.0213190	+	0.0101729i
$741$		0			0
$742$	141.801	+	141.801i	0.191107	+	0.191107i
$743$	402.717	−	402.717i	0.542015	−	0.542015i	−0.382104	−	0.924119i	$-0.624800\pi$
$743$	402.717	−	402.717i	0.542015	−	0.542015i	0.924119	+	0.382104i	$0.124800\pi$
$744$		0			0
$745$	479.806	−	169.821i	0.644035	−	0.227947i
$746$	−609.701			−0.817294
$747$		0			0
$748$	−184.123	+	184.123i	−0.246153	+	0.246153i
$749$		−	170.684i		−	0.227883i
$750$		0			0
$751$	−549.263			−0.731376			−0.365688	−	0.930738i	$-0.619166\pi$
$751$	−549.263			−0.731376			−0.365688	+	0.930738i	$0.619166\pi$
$752$	74.7668	+	74.7668i	0.0994239	+	0.0994239i
$753$		0			0
$754$		−	20.5026i		−	0.0271917i
$755$	277.516	+	784.085i	0.367571	+	1.03852i
$756$		0			0
$757$	−838.559	−	838.559i	−1.10774	−	1.10774i	−0.993447	−	0.114292i	$-0.963540\pi$
$757$	−838.559	−	838.559i	−1.10774	−	1.10774i	−0.114292	−	0.993447i	$-0.536460\pi$
$758$	−157.708	+	157.708i	−0.208059	+	0.208059i
$759$		0			0
$760$	58.2518	−	122.076i	0.0766471	−	0.160627i
$761$	1207.74			1.58705			0.793524	−	0.608538i	$-0.208244\pi$
$761$	1207.74			1.58705			0.793524	+	0.608538i	$0.208244\pi$
$762$		0			0
$763$	292.416	−	292.416i	0.383246	−	0.383246i
$764$		−	672.624i		−	0.880398i
$765$		0			0
$766$	859.263			1.12175
$767$	−175.730	−	175.730i	−0.229113	−	0.229113i
$768$		0			0
$769$		−	1284.27i		−	1.67006i	−0.550206	−	0.835029i	$-0.685451\pi$
$769$		−	1284.27i		−	1.67006i	0.550206	−	0.835029i	$-0.314549\pi$
$770$	88.8117	−	31.4336i	0.115340	−	0.0408229i
$771$		0			0
$772$	31.5169	+	31.5169i	0.0408250	+	0.0408250i
$773$	−321.946	+	321.946i	−0.416489	+	0.416489i	−0.883992	−	0.467503i	$-0.845154\pi$
$773$	−321.946	+	321.946i	−0.416489	+	0.416489i	0.467503	+	0.883992i	$0.345154\pi$
$774$		0			0
$775$	1071.60	−	867.185i	1.38270	−	1.11895i
$776$	−284.689			−0.366867
$777$		0			0
$778$	168.931	−	168.931i	0.217135	−	0.217135i
$779$			116.851i			0.150001i
$780$		0			0
$781$	−580.092			−0.742755
$782$	−600.571	−	600.571i	−0.767994	−	0.767994i
$783$		0			0
$784$		−	28.0000i		−	0.0357143i
$785$	323.044	−	676.992i	0.411521	−	0.862411i
$786$		0			0
$787$	−792.563	−	792.563i	−1.00707	−	1.00707i	−0.999975	−	0.00709380i	$-0.997742\pi$
$787$	−792.563	−	792.563i	−1.00707	−	1.00707i	−0.00709380	−	0.999975i	$-0.502258\pi$
$788$	−320.416	+	320.416i	−0.406620	+	0.406620i
$789$		0			0
$790$	399.492	+	190.628i	0.505686	+	0.241301i
$791$	−293.132			−0.370584
$792$		0			0
$793$	−148.938	+	148.938i	−0.187816	+	0.187816i
$794$			1028.83i			1.29575i
$795$		0			0
$796$	−322.572			−0.405242
$797$	−754.256	−	754.256i	−0.946369	−	0.946369i	0.0522640	−	0.998633i	$-0.483356\pi$
$797$	−754.256	−	754.256i	−0.946369	−	0.946369i	−0.998633	+	0.0522640i	$0.983356\pi$
$798$		0			0
$799$		−	683.426i		−	0.855352i
$800$	140.642	+	14.8282i	0.175802	+	0.0185353i
$801$		0			0
$802$	−542.884	−	542.884i	−0.676913	−	0.676913i
$803$	276.315	−	276.315i	0.344103	−	0.344103i
$804$		0			0
$805$	102.530	+	289.686i	0.127367	+	0.359858i
$806$	270.106			0.335119
$807$		0			0
$808$	−291.154	+	291.154i	−0.360339	+	0.360339i
$809$		−	286.564i		−	0.354220i	−0.984191	−	0.177110i	$-0.943325\pi$
$809$		−	286.564i		−	0.354220i	0.984191	−	0.177110i	$-0.0566749\pi$
$810$		0			0
$811$	130.099			0.160418			0.0802091	−	0.996778i	$-0.474441\pi$
$811$	130.099			0.160418			0.0802091	+	0.996778i	$0.474441\pi$
$812$	15.6607	+	15.6607i	0.0192866	+	0.0192866i
$813$		0			0
$814$		−	12.4487i		−	0.0152932i
$815$	349.512	+	166.778i	0.428849	+	0.204636i
$816$		0			0
$817$	345.517	+	345.517i	0.422909	+	0.422909i
$818$	−454.920	+	454.920i	−0.556137	+	0.556137i
$819$		0			0
$820$	−115.170	+	40.7629i	−0.140452	+	0.0497108i
$821$	647.519			0.788695			0.394348	−	0.918961i	$-0.370971\pi$
$821$	647.519			0.788695			0.394348	+	0.918961i	$0.370971\pi$
$822$		0			0
$823$	1076.83	−	1076.83i	1.30842	−	1.30842i	0.385863	−	0.922556i	$-0.373904\pi$
$823$	1076.83	−	1076.83i	1.30842	−	1.30842i	0.922556	−	0.385863i	$-0.126096\pi$
$824$			420.409i			0.510205i
$825$		0			0
$826$	268.460			0.325012
$827$	201.783	+	201.783i	0.243994	+	0.243994i	0.818500	−	0.574506i	$-0.194806\pi$
$827$	201.783	+	201.783i	0.243994	+	0.243994i	−0.574506	+	0.818500i	$0.694806\pi$
$828$		0			0
$829$		−	33.3580i		−	0.0402388i	−0.999798	−	0.0201194i	$-0.993595\pi$
$829$		−	33.3580i		−	0.0402388i	0.999798	−	0.0201194i	$-0.00640464\pi$
$830$	−176.425	−	498.467i	−0.212561	−	0.600562i
$831$		0			0
$832$	19.5939	+	19.5939i	0.0235503	+	0.0235503i
$833$	−127.971	+	127.971i	−0.153626	+	0.153626i
$834$		0			0
$835$	37.2987	−	78.1657i	0.0446691	−	0.0936116i
$836$	−96.3289			−0.115226
$837$		0			0
$838$	−597.925	+	597.925i	−0.713514	+	0.713514i
$839$		−	1231.60i		−	1.46794i	−0.679181	−	0.733971i	$-0.737665\pi$
$839$		−	1231.60i		−	1.46794i	0.679181	−	0.733971i	$-0.262335\pi$
$840$		0			0
$841$	823.482			0.979170
$842$	−607.858	−	607.858i	−0.721921	−	0.721921i
$843$		0			0
$844$		−	153.104i		−	0.181403i
$845$	−740.028	+	261.922i	−0.875773	+	0.309967i
$846$		0			0
$847$	178.928	+	178.928i	0.211249	+	0.211249i
$848$	151.592	−	151.592i	0.178764	−	0.178764i
$849$		0			0
$850$	−575.017	−	710.558i	−0.676490	−	0.835951i
$851$	40.6050			0.0477145
$852$		0			0
$853$	134.357	−	134.357i	0.157511	−	0.157511i	−0.623952	−	0.781463i	$-0.714474\pi$
$853$	134.357	−	134.357i	0.157511	−	0.157511i	0.781463	+	0.623952i	$0.214474\pi$
$854$		−	227.530i		−	0.266429i
$855$		0			0
$856$	−182.469			−0.213165
$857$	271.551	+	271.551i	0.316862	+	0.316862i	0.847561	−	0.530698i	$-0.178070\pi$
$857$	271.551	+	271.551i	0.316862	+	0.316862i	−0.530698	+	0.847561i	$0.678070\pi$
$858$		0			0
$859$			93.6478i			0.109020i	0.998513	+	0.0545098i	$0.0173596\pi$
$859$			93.6478i			0.109020i	−0.998513	+	0.0545098i	$0.982640\pi$
$860$	−220.016	+	461.080i	−0.255833	+	0.536140i
$861$		0			0
$862$	−291.207	−	291.207i	−0.337827	−	0.337827i
$863$	−1072.78	+	1072.78i	−1.24308	+	1.24308i	−0.284361	+	0.958717i	$0.591781\pi$
$863$	−1072.78	+	1072.78i	−1.24308	+	1.24308i	−0.958717	+	0.284361i	$0.908219\pi$
$864$		0			0
$865$	1344.17	+	641.404i	1.55395	+	0.741507i
$866$	−95.8102			−0.110635
$867$		0			0
$868$	−206.319	+	206.319i	−0.237694	+	0.237694i
$869$		−	315.234i		−	0.362755i
$870$		0			0
$871$	−149.339			−0.171457
$872$	−312.606	−	312.606i	−0.358493	−	0.358493i
$873$		0			0
$874$		−	314.205i		−	0.359503i
$875$	77.0481	+	321.619i	0.0880550	+	0.367564i
$876$		0			0
$877$	797.374	+	797.374i	0.909206	+	0.909206i	0.996208	−	0.0870020i	$-0.0277287\pi$
$877$	797.374	+	797.374i	0.909206	+	0.909206i	−0.0870020	+	0.996208i	$0.527729\pi$
$878$	−652.062	+	652.062i	−0.742667	+	0.742667i
$879$		0			0
$880$	−33.6040	−	94.9437i	−0.0381863	−	0.107891i
$881$	808.680			0.917911			0.458956	−	0.888459i	$-0.348224\pi$
$881$	808.680			0.917911			0.458956	+	0.888459i	$0.348224\pi$
$882$		0			0
$883$	619.669	−	619.669i	0.701777	−	0.701777i	−0.263015	−	0.964792i	$-0.584717\pi$
$883$	619.669	−	619.669i	0.701777	−	0.701777i	0.964792	+	0.263015i	$0.0847168\pi$
$884$		−	179.103i		−	0.202605i
$885$		0			0
$886$	292.546			0.330187
$887$	339.213	+	339.213i	0.382428	+	0.382428i	0.871976	−	0.489549i	$-0.162838\pi$
$887$	339.213	+	339.213i	0.382428	+	0.382428i	−0.489549	+	0.871976i	$0.662838\pi$
$888$		0			0
$889$		−	318.026i		−	0.357734i
$890$	−105.933	−	50.5488i	−0.119026	−	0.0567964i
$891$		0			0
$892$	494.273	+	494.273i	0.554117	+	0.554117i
$893$	178.777	−	178.777i	0.200198	−	0.200198i
$894$		0			0
$895$	665.021	−	235.375i	0.743040	−	0.262988i
$896$	−29.9333			−0.0334077
$897$		0			0
$898$	−213.815	+	213.815i	−0.238101	+	0.238101i
$899$		−	230.793i		−	0.256722i
$900$		0			0
$901$	−1385.67			−1.53792
$902$	61.5225	+	61.5225i	0.0682067	+	0.0682067i
$903$		0			0
$904$			313.371i			0.346650i
$905$	−24.2216	−	68.4349i	−0.0267641	−	0.0756186i
$906$		0			0
$907$	1097.10	+	1097.10i	1.20959	+	1.20959i	0.971158	+	0.238436i	$0.0766346\pi$
$907$	1097.10	+	1097.10i	1.20959	+	1.20959i	0.238436	+	0.971158i	$0.423365\pi$
$908$	−391.984	+	391.984i	−0.431701	+	0.431701i
$909$		0			0
$910$	−27.9069	+	58.4836i	−0.0306669	+	0.0642676i
$911$	−1028.80			−1.12930			−0.564652	−	0.825329i	$-0.690989\pi$
$911$	−1028.80			−1.12930			−0.564652	+	0.825329i	$0.690989\pi$
$912$		0			0
$913$	−266.274	+	266.274i	−0.291648	+	0.291648i
$914$			679.062i			0.742956i
$915$		0			0
$916$	−141.897			−0.154910
$917$	−412.618	−	412.618i	−0.449966	−	0.449966i
$918$		0			0
$919$			175.940i			0.191447i	0.995408	+	0.0957237i	$0.0305165\pi$
$919$			175.940i			0.191447i	−0.995408	+	0.0957237i	$0.969483\pi$
$920$	309.687	−	109.609i	0.336616	−	0.119141i
$921$		0			0
$922$	−580.456	−	580.456i	−0.629562	−	0.629562i
$923$	282.138	−	282.138i	0.305675	−	0.305675i
$924$		0			0
$925$	43.4593	+	4.58203i	0.0469830	+	0.00495355i
$926$	1102.07			1.19014
$927$		0			0
$928$	16.7420	−	16.7420i	0.0180410	−	0.0180410i
$929$		−	745.229i		−	0.802184i	−0.916038	−	0.401092i	$-0.868631\pi$
$929$		−	745.229i		−	0.802184i	0.916038	−	0.401092i	$-0.131369\pi$
$930$		0			0
$931$	−66.9514			−0.0719135
$932$	27.0239	+	27.0239i	0.0289956	+	0.0289956i
$933$		0			0
$934$		−	586.687i		−	0.628145i
$935$	−280.346	+	587.513i	−0.299836	+	0.628356i
$936$		0			0
$937$	646.673	+	646.673i	0.690152	+	0.690152i	0.962265	−	0.272113i	$-0.0877225\pi$
$937$	646.673	+	646.673i	0.690152	+	0.690152i	−0.272113	+	0.962265i	$0.587723\pi$
$938$	114.071	−	114.071i	0.121611	−	0.121611i
$939$		0			0
$940$	238.571	+	113.840i	0.253799	+	0.121107i
$941$	−780.569			−0.829510			−0.414755	−	0.909933i	$-0.636133\pi$
$941$	−780.569			−0.829510			−0.414755	+	0.909933i	$0.636133\pi$
$942$		0			0
$943$	−200.674	+	200.674i	−0.212804	+	0.212804i
$944$		−	286.995i		−	0.304021i
$945$		0			0
$946$	363.833			0.384601
$947$	436.209	+	436.209i	0.460622	+	0.460622i	0.898859	−	0.438237i	$-0.144397\pi$
$947$	436.209	+	436.209i	0.460622	+	0.460622i	−0.438237	+	0.898859i	$0.644397\pi$
$948$		0			0
$949$			268.782i			0.283226i
$950$	35.4562	−	336.292i	0.0373223	−	0.353991i
$951$		0			0
$952$	136.807	+	136.807i	0.143704	+	0.143704i
$953$	144.567	−	144.567i	0.151697	−	0.151697i	−0.627178	−	0.778876i	$-0.715790\pi$
$953$	144.567	−	144.567i	0.151697	−	0.151697i	0.778876	+	0.627178i	$0.215790\pi$
$954$		0			0
$955$	−561.059	−	1585.20i	−0.587496	−	1.65990i
$956$	315.775			0.330309
$957$		0			0
$958$	694.462	−	694.462i	0.724908	−	0.724908i
$959$		−	434.178i		−	0.452740i
$960$		0			0
$961$	2079.52			2.16392
$962$	6.05464	+	6.05464i	0.00629381	+	0.00629381i
$963$		0			0
$964$			285.402i			0.296060i
$965$	100.567	+	47.9878i	0.104214	+	0.0497283i
$966$		0			0
$967$	896.278	+	896.278i	0.926865	+	0.926865i	0.997502	−	0.0706371i	$-0.0225032\pi$
$967$	896.278	+	896.278i	0.926865	+	0.926865i	−0.0706371	+	0.997502i	$0.522503\pi$
$968$	191.282	−	191.282i	0.197606	−	0.197606i
$969$		0			0
$970$	−670.937	+	237.469i	−0.691688	+	0.244813i
$971$	386.872			0.398426			0.199213	−	0.979956i	$-0.436161\pi$
$971$	386.872			0.398426			0.199213	+	0.979956i	$0.436161\pi$
$972$		0			0
$973$	−506.141	+	506.141i	−0.520186	+	0.520186i
$974$			378.171i			0.388266i
$975$		0			0
$976$	−243.240			−0.249221
$977$	−906.290	−	906.290i	−0.927626	−	0.927626i	0.0699265	−	0.997552i	$-0.477724\pi$
$977$	−906.290	−	906.290i	−0.927626	−	0.927626i	−0.997552	+	0.0699265i	$0.977724\pi$
$978$		0			0
$979$			83.5908i			0.0853839i
$980$	−23.3558	−	65.9887i	−0.0238324	−	0.0673354i
$981$		0			0
$982$	−587.867	−	587.867i	−0.598643	−	0.598643i
$983$	−647.728	+	647.728i	−0.658930	+	0.658930i	−0.955127	−	0.296197i	$-0.904282\pi$
$983$	−647.728	+	647.728i	−0.658930	+	0.658930i	0.296197	+	0.955127i	$0.404282\pi$
$984$		0			0
$985$	−487.867	+	1022.41i	−0.495297	+	1.03798i
$986$	−153.035			−0.155208
$987$		0			0
$988$	46.8513	−	46.8513i	0.0474204	−	0.0474204i
$989$			1186.75i			1.19995i
$990$		0			0
$991$	1308.46			1.32034			0.660169	−	0.751117i	$-0.270485\pi$
$991$	1308.46			1.32034			0.660169	+	0.751117i	$0.270485\pi$
$992$	220.564	+	220.564i	0.222343	+	0.222343i
$993$		0			0
$994$			431.019i			0.433620i
$995$	−760.219	+	269.069i	−0.764039	+	0.270421i
$996$		0			0
$997$	−1347.69	−	1347.69i	−1.35174	−	1.35174i	−0.883711	−	0.468033i	$-0.844963\pi$
$997$	−1347.69	−	1347.69i	−1.35174	−	1.35174i	−0.468033	−	0.883711i	$-0.655037\pi$
$998$	13.5102	−	13.5102i	0.0135373	−	0.0135373i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.o.f.127.4		16
3.2	odd	2		210.3.l.b.127.7	yes	16
5.3	odd	4	inner	630.3.o.f.253.4		16
15.2	even	4		1050.3.l.h.43.3		16
15.8	even	4		210.3.l.b.43.7	✓	16
15.14	odd	2		1050.3.l.h.757.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.7	✓	16	15.8	even	4
210.3.l.b.127.7	yes	16	3.2	odd	2
630.3.o.f.127.4		16	1.1	even	1	trivial
630.3.o.f.253.4		16	5.3	odd	4	inner
1050.3.l.h.43.3		16	15.2	even	4
1050.3.l.h.757.3		16	15.14	odd	2

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

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(1.66827 + 4.71348i) q^{5} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(1.66827 + 4.71348i) q^{5} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-3.04521 + 6.38175i) q^{10} +5.03576 q^{11} +(-2.44923 + 2.44923i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(18.2815 + 18.2815i) q^{17} +9.56449i q^{19} +(-9.42696 + 3.33654i) q^{20} +(5.03576 + 5.03576i) q^{22} +(-16.4256 + 16.4256i) q^{23} +(-19.4338 + 15.7267i) q^{25} -4.89847 q^{26} +(3.74166 - 3.74166i) q^{28} +4.18550i q^{29} -55.1410 q^{31} +(-4.00000 - 4.00000i) q^{32} +36.5631i q^{34} +(5.69707 - 11.9392i) q^{35} +(-1.23603 - 1.23603i) q^{37} +(-9.56449 + 9.56449i) q^{38} +(-12.7635 - 6.09042i) q^{40} +12.2171 q^{41} +(36.1249 - 36.1249i) q^{43} +10.0715i q^{44} -32.8512 q^{46} +(-18.6917 - 18.6917i) q^{47} +7.00000i q^{49} +(-35.1605 - 3.70706i) q^{50} +(-4.89847 - 4.89847i) q^{52} +(-37.8979 + 37.8979i) q^{53} +(8.40100 + 23.7359i) q^{55} +7.48331 q^{56} +(-4.18550 + 4.18550i) q^{58} +71.7488i q^{59} +60.8100 q^{61} +(-55.1410 - 55.1410i) q^{62} -8.00000i q^{64} +(-15.6304 - 7.45843i) q^{65} +(30.4868 + 30.4868i) q^{67} +(-36.5631 + 36.5631i) q^{68} +(17.6362 - 6.24209i) q^{70} -115.195 q^{71} +(54.8705 - 54.8705i) q^{73} -2.47206i q^{74} -19.1290 q^{76} +(-9.42104 - 9.42104i) q^{77} -62.5991i q^{79} +(-6.67307 - 18.8539i) q^{80} +(12.2171 + 12.2171i) q^{82} +(-52.8767 + 52.8767i) q^{83} +(-55.6711 + 116.668i) q^{85} +72.2499 q^{86} +(-10.0715 + 10.0715i) q^{88} +16.5994i q^{89} +9.16419 q^{91} +(-32.8512 - 32.8512i) q^{92} -37.3834i q^{94} +(-45.0820 + 15.9561i) q^{95} +(71.1722 + 71.1722i) q^{97} +(-7.00000 + 7.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8	\( 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8} + 24 q^{10} - 8 q^{11} - 32 q^{13} - 64 q^{16} - 56 q^{17} + 16 q^{20} - 8 q^{22} - 24 q^{23} + 40 q^{25} - 64 q^{26} - 112 q^{31} - 64 q^{32} - 28 q^{35} - 152 q^{37} - 16 q^{40} - 48 q^{46} - 80 q^{47} + 72 q^{50} - 64 q^{52} - 48 q^{53} - 24 q^{55} + 96 q^{58} + 96 q^{61} - 112 q^{62} - 16 q^{65} - 80 q^{67} + 112 q^{68} - 536 q^{71} + 168 q^{77} - 64 q^{80} + 256 q^{83} + 40 q^{85} + 16 q^{88} - 48 q^{92} - 360 q^{95} + 688 q^{97} - 112 q^{98}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8 + 24 * q^10 - 8 * q^11 - 32 * q^13 - 64 * q^16 - 56 * q^17 + 16 * q^20 - 8 * q^22 - 24 * q^23 + 40 * q^25 - 64 * q^26 - 112 * q^31 - 64 * q^32 - 28 * q^35 - 152 * q^37 - 16 * q^40 - 48 * q^46 - 80 * q^47 + 72 * q^50 - 64 * q^52 - 48 * q^53 - 24 * q^55 + 96 * q^58 + 96 * q^61 - 112 * q^62 - 16 * q^65 - 80 * q^67 + 112 * q^68 - 536 * q^71 + 168 * q^77 - 64 * q^80 + 256 * q^83 + 40 * q^85 + 16 * q^88 - 48 * q^92 - 360 * q^95 + 688 * q^97 - 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more