LMFDB - Embedded newform 630.4.m.a.323.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,4,Mod(197,630)]

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([2, 1, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("630.197");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	630.m (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:	$37.1712033036$
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} - 62 x^{14} + 184 x^{13} + 5442 x^{12} + 68448 x^{11} + 1829094 x^{10} + \cdots + 101023536964 $ x^16 - 8x^15 - 62x^14 + 184x^13 + 5442x^12 + 68448x^11 + 1829094x^10 - 45903568x^9 + 994701932x^8 - 9338829780x^7 + 56019913036x^6 - 164275655480x^5 - 103469892238x^4 + 1441603925160x^3 + 2253271661956x^2 + 418235574120*x + 101023536964
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.2
Root			$3.04417 - 7.34926i$ of defining polynomial
Character	$\chi$	$=$	630.323
Dual form			630.4.m.a.197.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 - 1.41421i) q^{2} +4.00000i q^{4} +(-4.93229 - 10.0336i) q^{5} +(-4.94975 + 4.94975i) q^{7} +(5.65685 - 5.65685i) q^{8} +(-7.21430 + 21.1649i) q^{10} -50.0412i q^{11} +(-53.8210 - 53.8210i) q^{13} +14.0000 q^{14} -16.0000 q^{16} +(79.2489 + 79.2489i) q^{17} -53.7189i q^{19} +(40.1343 - 19.7292i) q^{20} +(-70.7689 + 70.7689i) q^{22} +(136.901 - 136.901i) q^{23} +(-76.3450 + 98.9769i) q^{25} +152.229i q^{26} +(-19.7990 - 19.7990i) q^{28} -254.335 q^{29} +128.624 q^{31} +(22.6274 + 22.6274i) q^{32} -224.150i q^{34} +(74.0772 + 25.2500i) q^{35} +(11.7935 - 11.7935i) q^{37} +(-75.9700 + 75.9700i) q^{38} +(-84.6597 - 28.8572i) q^{40} +319.078i q^{41} +(-193.204 - 193.204i) q^{43} +200.165 q^{44} -387.216 q^{46} +(-263.998 - 263.998i) q^{47} -49.0000i q^{49} +(247.943 - 32.0064i) q^{50} +(215.284 - 215.284i) q^{52} +(145.779 - 145.779i) q^{53} +(-502.091 + 246.817i) q^{55} +56.0000i q^{56} +(359.684 + 359.684i) q^{58} +429.023 q^{59} -146.439 q^{61} +(-181.902 - 181.902i) q^{62} -64.0000i q^{64} +(-274.556 + 805.477i) q^{65} +(-656.932 + 656.932i) q^{67} +(-316.996 + 316.996i) q^{68} +(-69.0521 - 140.470i) q^{70} +731.101i q^{71} +(-464.640 - 464.640i) q^{73} -33.3571 q^{74} +214.876 q^{76} +(247.691 + 247.691i) q^{77} +449.741i q^{79} +(78.9166 + 160.537i) q^{80} +(451.244 - 451.244i) q^{82} +(-338.503 + 338.503i) q^{83} +(404.271 - 1186.03i) q^{85} +546.462i q^{86} +(-283.076 - 283.076i) q^{88} +251.633 q^{89} +532.800 q^{91} +(547.605 + 547.605i) q^{92} +746.700i q^{94} +(-538.992 + 264.957i) q^{95} +(-942.169 + 942.169i) q^{97} +(-69.2965 + 69.2965i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 44 q^{5} - 24 q^{10} - 212 q^{13} + 224 q^{14} - 256 q^{16} + 32 q^{17} + 32 q^{20} + 72 q^{22} - 128 q^{23} - 268 q^{25} + 232 q^{29} - 200 q^{31} + 112 q^{35} + 900 q^{37} - 368 q^{38} - 128 q^{40}+ \cdots - 2668 q^{97}+O(q^{100}) $ 16 * q - 44 * q^5 - 24 * q^10 - 212 * q^13 + 224 * q^14 - 256 * q^16 + 32 * q^17 + 32 * q^20 + 72 * q^22 - 128 * q^23 - 268 * q^25 + 232 * q^29 - 200 * q^31 + 112 * q^35 + 900 * q^37 - 368 * q^38 - 128 * q^40 - 908 * q^43 + 352 * q^44 + 208 * q^46 - 604 * q^47 + 896 * q^50 + 848 * q^52 - 440 * q^53 - 1232 * q^55 + 536 * q^58 + 224 * q^59 + 1200 * q^61 - 1304 * q^62 + 1936 * q^65 + 652 * q^67 - 128 * q^68 - 616 * q^70 - 2148 * q^73 + 1328 * q^74 - 252 * q^77 + 704 * q^80 + 616 * q^82 - 2624 * q^83 - 1712 * q^85 + 288 * q^88 + 2400 * q^89 - 512 * q^92 + 4200 * q^95 - 2668 * q^97

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			4.00000i			0.500000i
$5$	−4.93229	−	10.0336i	−0.441157	−	0.897430i
$5$	−4.93229	−	10.0336i	−0.441157	−	0.897430i
$6$		0			0
$7$	−4.94975	+	4.94975i	−0.267261	+	0.267261i
$7$	−4.94975	+	4.94975i	−0.267261	+	0.267261i
$8$	5.65685	−	5.65685i	0.250000	−	0.250000i
$9$		0			0
$10$	−7.21430	+	21.1649i	−0.228136	+	0.669294i
$11$		−	50.0412i		−	1.37163i	−0.727774	−	0.685817i	$-0.759445\pi$
$11$		−	50.0412i		−	1.37163i	0.727774	−	0.685817i	$-0.240555\pi$
$12$		0			0
$13$	−53.8210	−	53.8210i	−1.14825	−	1.14825i	−0.986897	−	0.161353i	$-0.948414\pi$
$13$	−53.8210	−	53.8210i	−1.14825	−	1.14825i	−0.161353	−	0.986897i	$-0.551586\pi$
$14$	14.0000			0.267261
$15$		0			0
$16$	−16.0000			−0.250000
$17$	79.2489	+	79.2489i	1.13063	+	1.13063i	0.990073	+	0.140556i	$0.0448890\pi$
$17$	79.2489	+	79.2489i	1.13063	+	1.13063i	0.140556	+	0.990073i	$0.455111\pi$
$18$		0			0
$19$		−	53.7189i		−	0.648630i	−0.945949	−	0.324315i	$-0.894866\pi$
$19$		−	53.7189i		−	0.648630i	0.945949	−	0.324315i	$-0.105134\pi$
$20$	40.1343	−	19.7292i	0.448715	−	0.220579i
$21$		0			0
$22$	−70.7689	+	70.7689i	−0.685817	+	0.685817i
$23$	136.901	−	136.901i	1.24113	−	1.24113i	0.281592	−	0.959534i	$-0.409137\pi$
$23$	136.901	−	136.901i	1.24113	−	1.24113i	0.959534	−	0.281592i	$-0.0908625\pi$
$24$		0			0
$25$	−76.3450	+	98.9769i	−0.610760	+	0.791816i
$26$			152.229i			1.14825i
$27$		0			0
$28$	−19.7990	−	19.7990i	−0.133631	−	0.133631i
$29$	−254.335			−1.62858			−0.814291	−	0.580457i	$-0.802874\pi$
$29$	−254.335			−1.62858			−0.814291	+	0.580457i	$0.802874\pi$
$30$		0			0
$31$	128.624			0.745211			0.372605	−	0.927990i	$-0.378464\pi$
$31$	128.624			0.745211			0.372605	+	0.927990i	$0.378464\pi$
$32$	22.6274	+	22.6274i	0.125000	+	0.125000i
$33$		0			0
$34$		−	224.150i		−	1.13063i
$35$	74.0772	+	25.2500i	0.357752	+	0.121944i
$36$		0			0
$37$	11.7935	−	11.7935i	0.0524012	−	0.0524012i	−0.680421	−	0.732822i	$-0.738203\pi$
$37$	11.7935	−	11.7935i	0.0524012	−	0.0524012i	0.732822	+	0.680421i	$0.238203\pi$
$38$	−75.9700	+	75.9700i	−0.324315	+	0.324315i
$39$		0			0
$40$	−84.6597	−	28.8572i	−0.334647	−	0.114068i
$41$			319.078i			1.21540i	0.794165	+	0.607702i	$0.207909\pi$
$41$			319.078i			1.21540i	−0.794165	+	0.607702i	$0.792091\pi$
$42$		0			0
$43$	−193.204	−	193.204i	−0.685192	−	0.685192i	0.275973	−	0.961165i	$-0.411000\pi$
$43$	−193.204	−	193.204i	−0.685192	−	0.685192i	−0.961165	+	0.275973i	$0.911000\pi$
$44$	200.165			0.685817
$45$		0			0
$46$	−387.216			−1.24113
$47$	−263.998	−	263.998i	−0.819321	−	0.819321i	0.166689	−	0.986010i	$-0.446693\pi$
$47$	−263.998	−	263.998i	−0.819321	−	0.819321i	−0.986010	+	0.166689i	$0.946693\pi$
$48$		0			0
$49$		−	49.0000i		−	0.142857i
$50$	247.943	−	32.0064i	0.701288	−	0.0905276i
$51$		0			0
$52$	215.284	−	215.284i	0.574125	−	0.574125i
$53$	145.779	−	145.779i	0.377816	−	0.377816i	−0.492498	−	0.870314i	$-0.663916\pi$
$53$	145.779	−	145.779i	0.377816	−	0.377816i	0.870314	+	0.492498i	$0.163916\pi$
$54$		0			0
$55$	−502.091	+	246.817i	−1.23095	+	0.605107i
$56$			56.0000i			0.133631i
$57$		0			0
$58$	359.684	+	359.684i	0.814291	+	0.814291i
$59$	429.023			0.946680			0.473340	−	0.880880i	$-0.343048\pi$
$59$	429.023			0.946680			0.473340	+	0.880880i	$0.343048\pi$
$60$		0			0
$61$	−146.439			−0.307370			−0.153685	−	0.988120i	$-0.549114\pi$
$61$	−146.439			−0.307370			−0.153685	+	0.988120i	$0.549114\pi$
$62$	−181.902	−	181.902i	−0.372605	−	0.372605i
$63$		0			0
$64$		−	64.0000i		−	0.125000i
$65$	−274.556	+	805.477i	−0.523915	+	1.53703i
$66$		0			0
$67$	−656.932	+	656.932i	−1.19787	+	1.19787i	−0.223062	+	0.974804i	$0.571605\pi$
$67$	−656.932	+	656.932i	−1.19787	+	1.19787i	−0.974804	+	0.223062i	$0.928395\pi$
$68$	−316.996	+	316.996i	−0.565314	+	0.565314i
$69$		0			0
$70$	−69.0521	−	140.470i	−0.117904	−	0.239848i
$71$			731.101i			1.22205i	0.791610	+	0.611026i	$0.209243\pi$
$71$			731.101i			1.22205i	−0.791610	+	0.611026i	$0.790757\pi$
$72$		0			0
$73$	−464.640	−	464.640i	−0.744958	−	0.744958i	0.228569	−	0.973528i	$-0.426595\pi$
$73$	−464.640	−	464.640i	−0.744958	−	0.744958i	−0.973528	+	0.228569i	$0.926595\pi$
$74$	−33.3571			−0.0524012
$75$		0			0
$76$	214.876			0.324315
$77$	247.691	+	247.691i	0.366585	+	0.366585i
$78$		0			0
$79$			449.741i			0.640504i	0.947332	+	0.320252i	$0.103768\pi$
$79$			449.741i			0.640504i	−0.947332	+	0.320252i	$0.896232\pi$
$80$	78.9166	+	160.537i	0.110289	+	0.224357i
$81$		0			0
$82$	451.244	−	451.244i	0.607702	−	0.607702i
$83$	−338.503	+	338.503i	−0.447657	+	0.447657i	−0.894575	−	0.446918i	$-0.852522\pi$
$83$	−338.503	+	338.503i	−0.447657	+	0.447657i	0.446918	+	0.894575i	$0.352522\pi$
$84$		0			0
$85$	404.271	−	1186.03i	0.515875	−	1.51345i
$86$			546.462i			0.685192i
$87$		0			0
$88$	−283.076	−	283.076i	−0.342909	−	0.342909i
$89$	251.633			0.299697			0.149848	−	0.988709i	$-0.452121\pi$
$89$	251.633			0.299697			0.149848	+	0.988709i	$0.452121\pi$
$90$		0			0
$91$	532.800			0.613765
$92$	547.605	+	547.605i	0.620563	+	0.620563i
$93$		0			0
$94$			746.700i			0.819321i
$95$	−538.992	+	264.957i	−0.582099	+	0.286148i
$96$		0			0
$97$	−942.169	+	942.169i	−0.986214	+	0.986214i	−0.999906	−	0.0136920i	$-0.995642\pi$
$97$	−942.169	+	942.169i	−0.986214	+	0.986214i	0.0136920	+	0.999906i	$0.495642\pi$
$98$	−69.2965	+	69.2965i	−0.0714286	+	0.0714286i
$99$		0			0
$100$	−395.908	−	305.380i	−0.395908	−	0.305380i
$101$		−	1796.02i		−	1.76941i	−0.466147	−	0.884707i	$-0.654358\pi$
$101$		−	1796.02i		−	1.76941i	0.466147	−	0.884707i	$-0.345642\pi$
$102$		0			0
$103$	−361.347	−	361.347i	−0.345675	−	0.345675i	0.512821	−	0.858496i	$-0.328601\pi$
$103$	−361.347	−	361.347i	−0.345675	−	0.345675i	−0.858496	+	0.512821i	$0.828601\pi$
$104$	−608.915			−0.574125
$105$		0			0
$106$	−412.324			−0.377816
$107$	31.5227	+	31.5227i	0.0284805	+	0.0284805i	0.721204	−	0.692723i	$-0.243589\pi$
$107$	31.5227	+	31.5227i	0.0284805	+	0.0284805i	−0.692723	+	0.721204i	$0.743589\pi$
$108$		0			0
$109$			841.974i			0.739876i	0.929056	+	0.369938i	$0.120621\pi$
$109$			841.974i			0.739876i	−0.929056	+	0.369938i	$0.879379\pi$
$110$	1059.12	+	361.012i	0.918026	+	0.312919i
$111$		0			0
$112$	79.1960	−	79.1960i	0.0668153	−	0.0668153i
$113$	−1061.14	+	1061.14i	−0.883393	+	0.883393i	−0.993878	−	0.110485i	$-0.964760\pi$
$113$	−1061.14	+	1061.14i	−0.883393	+	0.883393i	0.110485	+	0.993878i	$0.464760\pi$
$114$		0			0
$115$	−2048.85	−	698.372i	−1.66136	−	0.566292i
$116$		−	1017.34i		−	0.814291i
$117$		0			0
$118$	−606.731	−	606.731i	−0.473340	−	0.473340i
$119$	−784.524			−0.604346
$120$		0			0
$121$	−1173.12			−0.881380
$122$	207.096	+	207.096i	0.153685	+	0.153685i
$123$		0			0
$124$			514.496i			0.372605i
$125$	1369.65	+	277.830i	0.980040	+	0.198799i
$126$		0			0
$127$	−1108.69	+	1108.69i	−0.774647	+	0.774647i	−0.978915	−	0.204268i	$-0.934519\pi$
$127$	−1108.69	+	1108.69i	−0.774647	+	0.774647i	0.204268	+	0.978915i	$0.434519\pi$
$128$	−90.5097	+	90.5097i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	1527.40	−	750.836i	1.03047	−	0.506559i
$131$			1495.11i			0.997165i	0.866842	+	0.498582i	$0.166146\pi$
$131$			1495.11i			0.997165i	−0.866842	+	0.498582i	$0.833854\pi$
$132$		0			0
$133$	265.895	+	265.895i	0.173354	+	0.173354i
$134$	1858.09			1.19787
$135$		0			0
$136$	896.599			0.565314
$137$	1081.55	+	1081.55i	0.674477	+	0.674477i	0.958745	−	0.284268i	$-0.0917504\pi$
$137$	1081.55	+	1081.55i	0.674477	+	0.674477i	−0.284268	+	0.958745i	$0.591750\pi$
$138$		0			0
$139$			920.420i			0.561648i	0.959759	+	0.280824i	$0.0906077\pi$
$139$			920.420i			0.561648i	−0.959759	+	0.280824i	$0.909392\pi$
$140$	−101.000	+	296.309i	−0.0609720	+	0.178876i
$141$		0			0
$142$	1033.93	−	1033.93i	0.611026	−	0.611026i
$143$	−2693.26	+	2693.26i	−1.57498	+	1.57498i
$144$		0			0
$145$	1254.45	+	2551.89i	0.718461	+	1.46154i
$146$			1314.20i			0.744958i
$147$		0			0
$148$	47.1741	+	47.1741i	0.0262006	+	0.0262006i
$149$	2676.61			1.47165			0.735827	−	0.677169i	$-0.236794\pi$
$149$	2676.61			1.47165			0.735827	+	0.677169i	$0.236794\pi$
$150$		0			0
$151$	1383.90			0.745830			0.372915	−	0.927866i	$-0.378358\pi$
$151$	1383.90			0.745830			0.372915	+	0.927866i	$0.378358\pi$
$152$	−303.880	−	303.880i	−0.162157	−	0.162157i
$153$		0			0
$154$		−	700.576i		−	0.366585i
$155$	−634.410	−	1290.56i	−0.328755	−	0.668774i
$156$		0			0
$157$	−2110.89	+	2110.89i	−1.07304	+	1.07304i	−0.0759270	+	0.997113i	$0.524192\pi$
$157$	−2110.89	+	2110.89i	−1.07304	+	1.07304i	−0.997113	+	0.0759270i	$0.975808\pi$
$158$	636.030	−	636.030i	0.320252	−	0.320252i
$159$		0			0
$160$	115.429	−	338.639i	0.0570340	−	0.167323i
$161$			1355.25i			0.663410i
$162$		0			0
$163$	1530.70	+	1530.70i	0.735543	+	0.735543i	0.971712	−	0.236169i	$-0.0758919\pi$
$163$	1530.70	+	1530.70i	0.735543	+	0.735543i	−0.236169	+	0.971712i	$0.575892\pi$
$164$	−1276.31			−0.607702
$165$		0			0
$166$	957.432			0.447657
$167$	−1215.99	−	1215.99i	−0.563451	−	0.563451i	0.366835	−	0.930286i	$-0.380441\pi$
$167$	−1215.99	−	1215.99i	−0.563451	−	0.563451i	−0.930286	+	0.366835i	$0.880441\pi$
$168$		0			0
$169$			3596.39i			1.63696i
$170$	−2249.02	+	1105.57i	−1.01466	+	0.498785i
$171$		0			0
$172$	772.814	−	772.814i	0.342596	−	0.342596i
$173$	1696.87	−	1696.87i	0.745727	−	0.745727i	−0.227947	−	0.973674i	$-0.573201\pi$
$173$	1696.87	−	1696.87i	0.745727	−	0.745727i	0.973674	+	0.227947i	$0.0732012\pi$
$174$		0			0
$175$	−112.022	−	867.800i	−0.0483891	−	0.374854i
$176$			800.658i			0.342909i
$177$		0			0
$178$	−355.862	−	355.862i	−0.149848	−	0.149848i
$179$	−2294.83			−0.958234			−0.479117	−	0.877751i	$-0.659043\pi$
$179$	−2294.83			−0.958234			−0.479117	+	0.877751i	$0.659043\pi$
$180$		0			0
$181$	−94.7403			−0.0389060			−0.0194530	−	0.999811i	$-0.506192\pi$
$181$	−94.7403			−0.0389060			−0.0194530	+	0.999811i	$0.506192\pi$
$182$	−753.493	−	753.493i	−0.306883	−	0.306883i
$183$		0			0
$184$		−	1548.86i		−	0.620563i
$185$	−176.500	−	60.1621i	−0.0701435	−	0.0239092i
$186$		0			0
$187$	3965.71	−	3965.71i	1.55081	−	1.55081i
$188$	1055.99	−	1055.99i	0.409661	−	0.409661i
$189$		0			0
$190$	1136.96	+	387.544i	0.434124	+	0.147976i
$191$			2981.63i			1.12955i	0.825246	+	0.564774i	$0.191037\pi$
$191$			2981.63i			1.12955i	−0.825246	+	0.564774i	$0.808963\pi$
$192$		0			0
$193$	−2295.50	−	2295.50i	−0.856132	−	0.856132i	0.134748	−	0.990880i	$-0.456977\pi$
$193$	−2295.50	−	2295.50i	−0.856132	−	0.856132i	−0.990880	+	0.134748i	$0.956977\pi$
$194$	2664.86			0.986214
$195$		0			0
$196$	196.000			0.0714286
$197$	−3248.66	−	3248.66i	−1.17491	−	1.17491i	−0.981024	−	0.193888i	$-0.937890\pi$
$197$	−3248.66	−	3248.66i	−1.17491	−	1.17491i	−0.193888	−	0.981024i	$-0.562110\pi$
$198$		0			0
$199$		−	1023.17i		−	0.364475i	−0.983255	−	0.182238i	$-0.941666\pi$
$199$		−	1023.17i		−	0.364475i	0.983255	−	0.182238i	$-0.0583340\pi$
$200$	128.025	+	991.771i	0.0452638	+	0.350644i
$201$		0			0
$202$	−2539.96	+	2539.96i	−0.884707	+	0.884707i
$203$	1258.89	−	1258.89i	0.435257	−	0.435257i
$204$		0			0
$205$	3201.49	−	1573.78i	1.09074	−	0.536185i
$206$			1022.04i			0.345675i
$207$		0			0
$208$	861.135	+	861.135i	0.287062	+	0.287062i
$209$	−2688.16			−0.889682
$210$		0			0
$211$	−275.984			−0.0900450			−0.0450225	−	0.998986i	$-0.514336\pi$
$211$	−275.984			−0.0900450			−0.0450225	+	0.998986i	$0.514336\pi$
$212$	583.115	+	583.115i	0.188908	+	0.188908i
$213$		0			0
$214$		−	89.1595i		−	0.0284805i
$215$	−985.585	+	2891.46i	−0.312634	+	0.917189i
$216$		0			0
$217$	−636.656	+	636.656i	−0.199166	+	0.199166i
$218$	1190.73	−	1190.73i	0.369938	−	0.369938i
$219$		0			0
$220$	−987.270	−	2008.37i	−0.302553	−	0.615473i
$221$		−	8530.51i		−	2.59649i
$222$		0			0
$223$	442.803	+	442.803i	0.132970	+	0.132970i	0.770459	−	0.637489i	$-0.220027\pi$
$223$	442.803	+	442.803i	0.132970	+	0.132970i	−0.637489	+	0.770459i	$0.720027\pi$
$224$	−224.000			−0.0668153
$225$		0			0
$226$	3001.35			0.883393
$227$	−4734.13	−	4734.13i	−1.38421	−	1.38421i	−0.836990	−	0.547218i	$-0.815687\pi$
$227$	−4734.13	−	4734.13i	−1.38421	−	1.38421i	−0.547218	−	0.836990i	$-0.684313\pi$
$228$		0			0
$229$			242.150i			0.0698764i	0.999389	+	0.0349382i	$0.0111234\pi$
$229$			242.150i			0.0698764i	−0.999389	+	0.0349382i	$0.988877\pi$
$230$	1909.86	+	3885.15i	0.547532	+	1.11382i
$231$		0			0
$232$	−1438.74	+	1438.74i	−0.407145	+	0.407145i
$233$	2074.96	−	2074.96i	0.583412	−	0.583412i	−0.352427	−	0.935839i	$-0.614644\pi$
$233$	2074.96	−	2074.96i	0.583412	−	0.583412i	0.935839	+	0.352427i	$0.114644\pi$
$234$		0			0
$235$	−1346.73	+	3950.96i	−0.373834	+	1.09673i
$236$			1716.09i			0.473340i
$237$		0			0
$238$	1109.49	+	1109.49i	0.302173	+	0.302173i
$239$	5538.03			1.49885			0.749425	−	0.662089i	$-0.230330\pi$
$239$	5538.03			1.49885			0.749425	+	0.662089i	$0.230330\pi$
$240$		0			0
$241$	1842.19			0.492390			0.246195	−	0.969220i	$-0.420820\pi$
$241$	1842.19			0.492390			0.246195	+	0.969220i	$0.420820\pi$
$242$	1659.04	+	1659.04i	0.440690	+	0.440690i
$243$		0			0
$244$		−	585.755i		−	0.153685i
$245$	−491.645	+	241.682i	−0.128204	+	0.0630225i
$246$		0			0
$247$	−2891.20	+	2891.20i	−0.744789	+	0.744789i
$248$	727.607	−	727.607i	0.186303	−	0.186303i
$249$		0			0
$250$	−1544.06	−	2329.89i	−0.390621	−	0.589420i
$251$		−	4808.65i		−	1.20924i	−0.796514	−	0.604620i	$-0.793325\pi$
$251$		−	4808.65i		−	1.20924i	0.796514	−	0.604620i	$-0.206675\pi$
$252$		0			0
$253$	−6850.70	−	6850.70i	−1.70237	−	1.70237i
$254$	3135.84			0.774647
$255$		0			0
$256$	256.000			0.0625000
$257$	−5130.50	−	5130.50i	−1.24526	−	1.24526i	−0.957790	−	0.287469i	$-0.907186\pi$
$257$	−5130.50	−	5130.50i	−1.24526	−	1.24526i	−0.287469	−	0.957790i	$-0.592814\pi$
$258$		0			0
$259$			116.750i			0.0280096i
$260$	−3221.91	−	1098.22i	−0.768516	−	0.261957i
$261$		0			0
$262$	2114.41	−	2114.41i	0.498582	−	0.498582i
$263$	3399.42	−	3399.42i	0.797023	−	0.797023i	−0.185602	−	0.982625i	$-0.559423\pi$
$263$	3399.42	−	3399.42i	0.797023	−	0.797023i	0.982625	+	0.185602i	$0.0594235\pi$
$264$		0			0
$265$	−2181.70	−	743.658i	−0.505739	−	0.172387i
$266$		−	752.065i		−	0.173354i
$267$		0			0
$268$	−2627.73	−	2627.73i	−0.598933	−	0.598933i
$269$	3096.54			0.701857			0.350928	−	0.936402i	$-0.385866\pi$
$269$	3096.54			0.701857			0.350928	+	0.936402i	$0.385866\pi$
$270$		0			0
$271$	3315.54			0.743190			0.371595	−	0.928395i	$-0.378811\pi$
$271$	3315.54			0.743190			0.371595	+	0.928395i	$0.378811\pi$
$272$	−1267.98	−	1267.98i	−0.282657	−	0.282657i
$273$		0			0
$274$		−	3059.10i		−	0.674477i
$275$	4952.92	+	3820.39i	1.08608	+	0.837740i
$276$		0			0
$277$	3973.23	−	3973.23i	0.861834	−	0.861834i	−0.129717	−	0.991551i	$-0.541407\pi$
$277$	3973.23	−	3973.23i	0.861834	−	0.861834i	0.991551	+	0.129717i	$0.0414068\pi$
$278$	1301.67	−	1301.67i	0.280824	−	0.280824i
$279$		0			0
$280$	561.880	−	276.208i	0.119924	−	0.0589521i
$281$		−	6226.68i		−	1.32190i	−0.750432	−	0.660948i	$-0.770154\pi$
$281$		−	6226.68i		−	1.32190i	0.750432	−	0.660948i	$-0.229846\pi$
$282$		0			0
$283$	49.7888	+	49.7888i	0.0104581	+	0.0104581i	0.712316	−	0.701858i	$-0.247646\pi$
$283$	49.7888	+	49.7888i	0.0104581	+	0.0104581i	−0.701858	+	0.712316i	$0.747646\pi$
$284$	−2924.40			−0.611026
$285$		0			0
$286$	7617.70			1.57498
$287$	−1579.35	−	1579.35i	−0.324830	−	0.324830i
$288$		0			0
$289$			7647.79i			1.55664i
$290$	1834.85	−	5382.98i	0.371538	−	1.09000i
$291$		0			0
$292$	1858.56	−	1858.56i	0.372479	−	0.372479i
$293$	−4162.42	+	4162.42i	−0.829935	+	0.829935i	−0.987507	−	0.157572i	$-0.949633\pi$
$293$	−4162.42	+	4162.42i	−0.829935	+	0.829935i	0.157572	+	0.987507i	$0.449633\pi$
$294$		0			0
$295$	−2116.07	−	4304.64i	−0.417635	−	0.849578i
$296$		−	133.428i		−	0.0262006i
$297$		0			0
$298$	−3785.30	−	3785.30i	−0.735827	−	0.735827i
$299$	−14736.3			−2.85025
$300$		0			0
$301$	1912.62			0.366251
$302$	−1957.13	−	1957.13i	−0.372915	−	0.372915i
$303$		0			0
$304$			859.502i			0.162157i
$305$	722.278	+	1469.30i	0.135598	+	0.275843i
$306$		0			0
$307$	3575.70	−	3575.70i	0.664743	−	0.664743i	−0.291751	−	0.956494i	$-0.594238\pi$
$307$	3575.70	−	3575.70i	0.664743	−	0.664743i	0.956494	+	0.291751i	$0.0942380\pi$
$308$	−990.764	+	990.764i	−0.183292	+	0.183292i
$309$		0			0
$310$	−927.931	+	2722.32i	−0.170010	+	0.498765i
$311$		−	1755.61i		−	0.320102i	−0.987109	−	0.160051i	$-0.948834\pi$
$311$		−	1755.61i		−	0.320102i	0.987109	−	0.160051i	$-0.0511658\pi$
$312$		0			0
$313$	−1945.93	−	1945.93i	−0.351407	−	0.351407i	0.509226	−	0.860633i	$-0.329932\pi$
$313$	−1945.93	−	1945.93i	−0.351407	−	0.351407i	−0.860633	+	0.509226i	$0.829932\pi$
$314$	5970.50			1.07304
$315$		0			0
$316$	−1798.96			−0.320252
$317$	2326.21	+	2326.21i	0.412155	+	0.412155i	0.882489	−	0.470334i	$-0.155866\pi$
$317$	2326.21	+	2326.21i	0.412155	+	0.412155i	−0.470334	+	0.882489i	$0.655866\pi$
$318$		0			0
$319$			12727.2i			2.23382i
$320$	−642.148	+	315.667i	−0.112179	+	0.0551447i
$321$		0			0
$322$	1916.62	−	1916.62i	0.331705	−	0.331705i
$323$	4257.17	−	4257.17i	0.733359	−	0.733359i
$324$		0			0
$325$	9436.00	−	1218.07i	1.61051	−	0.207897i
$326$		−	4329.47i		−	0.735543i
$327$		0			0
$328$	1804.98	+	1804.98i	0.303851	+	0.303851i
$329$	2613.45			0.437946
$330$		0			0
$331$	−10635.1			−1.76603			−0.883017	−	0.469341i	$-0.844491\pi$
$331$	−10635.1			−1.76603			−0.883017	+	0.469341i	$0.844491\pi$
$332$	−1354.01	−	1354.01i	−0.223829	−	0.223829i
$333$		0			0
$334$			3439.35i			0.563451i
$335$	9831.56	+	3351.20i	1.60345	+	0.546553i
$336$		0			0
$337$	−5154.26	+	5154.26i	−0.833147	+	0.833147i	−0.987946	−	0.154799i	$-0.950527\pi$
$337$	−5154.26	+	5154.26i	−0.833147	+	0.833147i	0.154799	+	0.987946i	$0.450527\pi$
$338$	5086.07	−	5086.07i	0.818478	−	0.818478i
$339$		0			0
$340$	4744.11	+	1617.08i	0.756723	+	0.257937i
$341$		−	6436.49i		−	1.02216i
$342$		0			0
$343$	242.538	+	242.538i	0.0381802	+	0.0381802i
$344$	−2185.85			−0.342596
$345$		0			0
$346$	−4799.48			−0.745727
$347$	−2956.45	−	2956.45i	−0.457380	−	0.457380i	0.440415	−	0.897794i	$-0.354831\pi$
$347$	−2956.45	−	2956.45i	−0.457380	−	0.457380i	−0.897794	+	0.440415i	$0.854831\pi$
$348$		0			0
$349$		−	6561.02i		−	1.00631i	−0.864195	−	0.503157i	$-0.832172\pi$
$349$		−	6561.02i		−	1.00631i	0.864195	−	0.503157i	$-0.167828\pi$
$350$	−1068.83	+	1385.68i	−0.163233	+	0.211622i
$351$		0			0
$352$	1132.30	−	1132.30i	0.171454	−	0.171454i
$353$	4459.98	−	4459.98i	0.672467	−	0.672467i	−0.285817	−	0.958284i	$-0.592265\pi$
$353$	4459.98	−	4459.98i	0.672467	−	0.672467i	0.958284	+	0.285817i	$0.0922651\pi$
$354$		0			0
$355$	7335.55	−	3606.00i	1.09671	−	0.539117i
$356$			1006.53i			0.149848i
$357$		0			0
$358$	3245.39	+	3245.39i	0.479117	+	0.479117i
$359$	−1916.27			−0.281718			−0.140859	−	0.990030i	$-0.544986\pi$
$359$	−1916.27			−0.281718			−0.140859	+	0.990030i	$0.544986\pi$
$360$		0			0
$361$	3973.28			0.579280
$362$	133.983	+	133.983i	0.0194530	+	0.0194530i
$363$		0			0
$364$			2131.20i			0.306883i
$365$	−2370.26	+	6953.73i	−0.339904	+	0.997191i
$366$		0			0
$367$	−3806.35	+	3806.35i	−0.541389	+	0.541389i	−0.923936	−	0.382547i	$-0.875047\pi$
$367$	−3806.35	+	3806.35i	−0.541389	+	0.541389i	0.382547	+	0.923936i	$0.375047\pi$
$368$	−2190.42	+	2190.42i	−0.310282	+	0.310282i
$369$		0			0
$370$	164.527	+	334.691i	0.0231172	+	0.0470264i
$371$			1443.13i			0.201951i
$372$		0			0
$373$	1131.80	+	1131.80i	0.157111	+	0.157111i	0.781285	−	0.624174i	$-0.214564\pi$
$373$	1131.80	+	1131.80i	0.157111	+	0.157111i	−0.624174	+	0.781285i	$0.714564\pi$
$374$	−11216.7			−1.55081
$375$		0			0
$376$	−2986.80			−0.409661
$377$	13688.6	+	13688.6i	1.87002	+	1.87002i
$378$		0			0
$379$			8534.48i			1.15669i	0.815791	+	0.578347i	$0.196302\pi$
$379$			8534.48i			1.15669i	−0.815791	+	0.578347i	$0.803698\pi$
$380$	−1059.83	−	2155.97i	−0.143074	−	0.291050i
$381$		0			0
$382$	4216.67	−	4216.67i	0.564774	−	0.564774i
$383$	5183.36	−	5183.36i	0.691533	−	0.691533i	−0.271036	−	0.962569i	$-0.587366\pi$
$383$	5183.36	−	5183.36i	0.691533	−	0.691533i	0.962569	+	0.271036i	$0.0873662\pi$
$384$		0			0
$385$	1263.54	−	3706.91i	0.167262	−	0.490705i
$386$			6492.64i			0.856132i
$387$		0			0
$388$	−3768.68	−	3768.68i	−0.493107	−	0.493107i
$389$	−3462.83			−0.451343			−0.225672	−	0.974203i	$-0.572458\pi$
$389$	−3462.83			−0.451343			−0.225672	+	0.974203i	$0.572458\pi$
$390$		0			0
$391$	21698.6			2.80651
$392$	−277.186	−	277.186i	−0.0357143	−	0.0357143i
$393$		0			0
$394$			9188.60i			1.17491i
$395$	4512.51	−	2218.25i	0.574807	−	0.282563i
$396$		0			0
$397$	−1021.59	+	1021.59i	−0.129148	+	0.129148i	−0.768726	−	0.639578i	$-0.779109\pi$
$397$	−1021.59	+	1021.59i	−0.129148	+	0.129148i	0.639578	+	0.768726i	$0.279109\pi$
$398$	−1446.98	+	1446.98i	−0.182238	+	0.182238i
$399$		0			0
$400$	1221.52	−	1583.63i	0.152690	−	0.197954i
$401$			1485.73i			0.185022i	0.995712	+	0.0925110i	$0.0294893\pi$
$401$			1485.73i			0.185022i	−0.995712	+	0.0925110i	$0.970511\pi$
$402$		0			0
$403$	−6922.66	−	6922.66i	−0.855688	−	0.855688i
$404$	7184.09			0.884707
$405$		0			0
$406$	−3560.69			−0.435257
$407$	−590.161	−	590.161i	−0.0718752	−	0.0718752i
$408$		0			0
$409$		−	1933.47i		−	0.233750i	−0.993147	−	0.116875i	$-0.962712\pi$
$409$		−	1933.47i		−	0.233750i	0.993147	−	0.116875i	$-0.0372877\pi$
$410$	−6753.26	−	2301.92i	−0.813462	−	0.277278i
$411$		0			0
$412$	1445.39	−	1445.39i	0.172838	−	0.172838i
$413$	−2123.56	+	2123.56i	−0.253011	+	0.253011i
$414$		0			0
$415$	5065.99	+	1726.80i	0.599229	+	0.204254i
$416$		−	2435.66i		−	0.287062i
$417$		0			0
$418$	3801.63	+	3801.63i	0.444841	+	0.444841i
$419$	−5825.91			−0.679271			−0.339635	−	0.940557i	$-0.610304\pi$
$419$	−5825.91			−0.679271			−0.339635	+	0.940557i	$0.610304\pi$
$420$		0			0
$421$	−1576.13			−0.182461			−0.0912304	−	0.995830i	$-0.529080\pi$
$421$	−1576.13			−0.182461			−0.0912304	+	0.995830i	$0.529080\pi$
$422$	390.300	+	390.300i	0.0450225	+	0.0450225i
$423$		0			0
$424$		−	1649.30i		−	0.188908i
$425$	−13894.1	+	1793.55i	−1.58579	+	0.204706i
$426$		0			0
$427$	724.835	−	724.835i	0.0821480	−	0.0821480i
$428$	−126.091	+	126.091i	−0.0142402	+	0.0142402i
$429$		0			0
$430$	5482.97	−	2695.31i	0.614912	−	0.302278i
$431$			14248.8i			1.59244i	0.605007	+	0.796220i	$0.293170\pi$
$431$			14248.8i			1.59244i	−0.605007	+	0.796220i	$0.706830\pi$
$432$		0			0
$433$	−6575.28	−	6575.28i	−0.729764	−	0.729764i	0.240808	−	0.970573i	$-0.422587\pi$
$433$	−6575.28	−	6575.28i	−0.729764	−	0.729764i	−0.970573	+	0.240808i	$0.922587\pi$
$434$	1800.73			0.199166
$435$		0			0
$436$	−3367.90			−0.369938
$437$	−7354.19	−	7354.19i	−0.805031	−	0.805031i
$438$		0			0
$439$		−	4976.57i		−	0.541045i	−0.962714	−	0.270522i	$-0.912804\pi$
$439$		−	4976.57i		−	0.541045i	0.962714	−	0.270522i	$-0.0871964\pi$
$440$	−1444.05	+	4236.47i	−0.156460	+	0.459013i
$441$		0			0
$442$	−12064.0	+	12064.0i	−1.29824	+	1.29824i
$443$	−8182.61	+	8182.61i	−0.877579	+	0.877579i	−0.993284	−	0.115704i	$-0.963087\pi$
$443$	−8182.61	+	8182.61i	−0.877579	+	0.877579i	0.115704	+	0.993284i	$0.463087\pi$
$444$		0			0
$445$	−1241.12	−	2524.77i	−0.132213	−	0.268957i
$446$		−	1252.44i		−	0.132970i
$447$		0			0
$448$	316.784	+	316.784i	0.0334077	+	0.0334077i
$449$	116.512			0.0122462			0.00612308	−	0.999981i	$-0.498051\pi$
$449$	116.512			0.0122462			0.00612308	+	0.999981i	$0.498051\pi$
$450$		0			0
$451$	15967.0			1.66709
$452$	−4244.55	−	4244.55i	−0.441696	−	0.441696i
$453$		0			0
$454$			13390.1i			1.38421i
$455$	−2627.93	−	5345.89i	−0.270767	−	0.550811i
$456$		0			0
$457$	−5744.50	+	5744.50i	−0.588001	+	0.588001i	−0.937090	−	0.349089i	$-0.886491\pi$
$457$	−5744.50	+	5744.50i	−0.588001	+	0.588001i	0.349089	+	0.937090i	$0.386491\pi$
$458$	342.451	−	342.451i	0.0349382	−	0.0349382i
$459$		0			0
$460$	2793.49	−	8195.39i	0.283146	−	0.830678i
$461$			14172.1i			1.43180i	0.698203	+	0.715899i	$0.253983\pi$
$461$			14172.1i			1.43180i	−0.698203	+	0.715899i	$0.746017\pi$
$462$		0			0
$463$	2176.56	+	2176.56i	0.218474	+	0.218474i	0.807855	−	0.589381i	$-0.200628\pi$
$463$	2176.56	+	2176.56i	0.218474	+	0.218474i	−0.589381	+	0.807855i	$0.700628\pi$
$464$	4069.36			0.407145
$465$		0			0
$466$	−5868.87			−0.583412
$467$	8344.13	+	8344.13i	0.826810	+	0.826810i	0.987074	−	0.160264i	$-0.0512347\pi$
$467$	8344.13	+	8344.13i	0.826810	+	0.826810i	−0.160264	+	0.987074i	$0.551235\pi$
$468$		0			0
$469$		−	6503.30i		−	0.640287i
$470$	7492.06	−	3682.94i	0.735283	−	0.361450i
$471$		0			0
$472$	2426.92	−	2426.92i	0.236670	−	0.236670i
$473$	−9668.13	+	9668.13i	−0.939833	+	0.939833i
$474$		0			0
$475$	5316.93	+	4101.17i	0.513595	+	0.396157i
$476$		−	3138.10i		−	0.302173i
$477$		0			0
$478$	−7831.95	−	7831.95i	−0.749425	−	0.749425i
$479$	−5643.81			−0.538356			−0.269178	−	0.963090i	$-0.586752\pi$
$479$	−5643.81			−0.538356			−0.269178	+	0.963090i	$0.586752\pi$
$480$		0			0
$481$	−1269.48			−0.120339
$482$	−2605.25	−	2605.25i	−0.246195	−	0.246195i
$483$		0			0
$484$		−	4692.47i		−	0.440690i
$485$	14100.4	+	4806.27i	1.32013	+	0.449982i
$486$		0			0
$487$	−5851.74	+	5851.74i	−0.544492	+	0.544492i	−0.924843	−	0.380350i	$-0.875803\pi$
$487$	−5851.74	+	5851.74i	−0.544492	+	0.544492i	0.380350	+	0.924843i	$0.375803\pi$
$488$	−828.382	+	828.382i	−0.0768424	+	0.0768424i
$489$		0			0
$490$	1037.08	+	353.501i	0.0956134	+	0.0325909i
$491$		−	8977.31i		−	0.825133i	−0.910927	−	0.412567i	$-0.864632\pi$
$491$		−	8977.31i		−	0.825133i	0.910927	−	0.412567i	$-0.135368\pi$
$492$		0			0
$493$	−20155.8	−	20155.8i	−1.84132	−	1.84132i
$494$	8177.56			0.744789
$495$		0			0
$496$	−2057.98			−0.186303
$497$	−3618.76	−	3618.76i	−0.326607	−	0.326607i
$498$		0			0
$499$			11113.0i			0.996962i	0.866901	+	0.498481i	$0.166109\pi$
$499$			11113.0i			0.996962i	−0.866901	+	0.498481i	$0.833891\pi$
$500$	−1111.32	+	5478.59i	−0.0993996	+	0.490020i
$501$		0			0
$502$	−6800.45	+	6800.45i	−0.604620	+	0.604620i
$503$	7844.62	−	7844.62i	0.695376	−	0.695376i	−0.268033	−	0.963410i	$-0.586374\pi$
$503$	7844.62	−	7844.62i	0.695376	−	0.695376i	0.963410	+	0.268033i	$0.0863737\pi$
$504$		0			0
$505$	−18020.5	+	8858.50i	−1.58793	+	0.780590i
$506$			19376.7i			1.70237i
$507$		0			0
$508$	−4434.75	−	4434.75i	−0.387323	−	0.387323i
$509$	−5411.99			−0.471281			−0.235641	−	0.971840i	$-0.575719\pi$
$509$	−5411.99			−0.471281			−0.235641	+	0.971840i	$0.575719\pi$
$510$		0			0
$511$	4599.70			0.398197
$512$	−362.039	−	362.039i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			14511.2i			1.24526i
$515$	−1843.33	+	5407.86i	−0.157722	+	0.462716i
$516$		0			0
$517$	−13210.8	+	13210.8i	−1.12381	+	1.12381i
$518$	165.109	−	165.109i	0.0140048	−	0.0140048i
$519$		0			0
$520$	3003.34	+	6109.59i	0.253279	+	0.515237i
$521$		−	811.829i		−	0.0682666i	−0.999417	−	0.0341333i	$-0.989133\pi$
$521$		−	811.829i		−	0.0682666i	0.999417	−	0.0341333i	$-0.0108671\pi$
$522$		0			0
$523$	−624.754	−	624.754i	−0.0522344	−	0.0522344i	0.680507	−	0.732741i	$-0.261760\pi$
$523$	−624.754	−	624.754i	−0.0522344	−	0.0522344i	−0.732741	+	0.680507i	$0.761760\pi$
$524$	−5980.45			−0.498582
$525$		0			0
$526$	−9615.01			−0.797023
$527$	10193.3	+	10193.3i	0.842557	+	0.842557i
$528$		0			0
$529$		−	25317.0i		−	2.08079i
$530$	2033.70	+	4137.08i	0.166676	+	0.339063i
$531$		0			0
$532$	−1063.58	+	1063.58i	−0.0866768	+	0.0866768i
$533$	17173.1	−	17173.1i	1.39559	−	1.39559i
$534$		0			0
$535$	160.806	−	471.764i	0.0129949	−	0.0381236i
$536$			7432.34i			0.598933i
$537$		0			0
$538$	−4379.17	−	4379.17i	−0.350928	−	0.350928i
$539$	−2452.02			−0.195948
$540$		0			0
$541$	1928.13			0.153228			0.0766142	−	0.997061i	$-0.475589\pi$
$541$	1928.13			0.153228			0.0766142	+	0.997061i	$0.475589\pi$
$542$	−4688.88	−	4688.88i	−0.371595	−	0.371595i
$543$		0			0
$544$			3586.40i			0.282657i
$545$	8448.01	−	4152.86i	0.663987	−	0.326402i
$546$		0			0
$547$	9490.21	−	9490.21i	0.741814	−	0.741814i	−0.231113	−	0.972927i	$-0.574237\pi$
$547$	9490.21	−	9490.21i	0.741814	−	0.741814i	0.972927	+	0.231113i	$0.0742368\pi$
$548$	−4326.22	+	4326.22i	−0.337239	+	0.337239i
$549$		0			0
$550$	−1601.63	−	12407.3i	−0.124171	−	0.961910i
$551$			13662.6i			1.05635i
$552$		0			0
$553$	−2226.10	−	2226.10i	−0.171182	−	0.171182i
$554$	−11238.0			−0.861834
$555$		0			0
$556$	−3681.68			−0.280824
$557$	−8850.91	−	8850.91i	−0.673295	−	0.673295i	0.285179	−	0.958474i	$-0.407947\pi$
$557$	−8850.91	−	8850.91i	−0.673295	−	0.673295i	−0.958474	+	0.285179i	$0.907947\pi$
$558$		0			0
$559$			20796.8i			1.57354i
$560$	−1185.24	−	404.001i	−0.0894381	−	0.0304860i
$561$		0			0
$562$	−8805.86	+	8805.86i	−0.660948	+	0.660948i
$563$	−2719.96	+	2719.96i	−0.203610	+	0.203610i	−0.801545	−	0.597935i	$-0.795988\pi$
$563$	−2719.96	+	2719.96i	−0.203610	+	0.203610i	0.597935	+	0.801545i	$0.295988\pi$
$564$		0			0
$565$	15880.8	+	5413.16i	1.18250	+	0.403068i
$566$		−	140.824i		−	0.0104581i
$567$		0			0
$568$	4135.73	+	4135.73i	0.305513	+	0.305513i
$569$	20169.8			1.48605			0.743023	−	0.669266i	$-0.233391\pi$
$569$	20169.8			1.48605			0.743023	+	0.669266i	$0.233391\pi$
$570$		0			0
$571$	17518.3			1.28392			0.641961	−	0.766737i	$-0.278121\pi$
$571$	17518.3			1.28392			0.641961	+	0.766737i	$0.278121\pi$
$572$	−10773.1	−	10773.1i	−0.787489	−	0.787489i
$573$		0			0
$574$			4467.09i			0.324830i
$575$	3098.34	+	24001.8i	0.224712	+	1.74077i
$576$		0			0
$577$	16545.2	−	16545.2i	1.19374	−	1.19374i	0.217730	−	0.976009i	$-0.430135\pi$
$577$	16545.2	−	16545.2i	1.19374	−	1.19374i	0.976009	−	0.217730i	$-0.0698653\pi$
$578$	10815.6	−	10815.6i	0.778321	−	0.778321i
$579$		0			0
$580$	−10207.6	+	5017.82i	−0.730769	+	0.359230i
$581$		−	3351.01i		−	0.239283i
$582$		0			0
$583$	−7294.93	−	7294.93i	−0.518225	−	0.518225i
$584$	−5256.80			−0.372479
$585$		0			0
$586$	11773.1			0.829935
$587$	17588.7	+	17588.7i	1.23674	+	1.23674i	0.961327	+	0.275410i	$0.0888137\pi$
$587$	17588.7	+	17588.7i	1.23674	+	1.23674i	0.275410	+	0.961327i	$0.411186\pi$
$588$		0			0
$589$		−	6909.54i		−	0.483366i
$590$	−3095.10	+	9080.25i	−0.215972	+	0.633607i
$591$		0			0
$592$	−188.696	+	188.696i	−0.0131003	+	0.0131003i
$593$	2495.82	−	2495.82i	0.172835	−	0.172835i	−0.615389	−	0.788224i	$-0.711001\pi$
$593$	2495.82	−	2495.82i	0.172835	−	0.172835i	0.788224	+	0.615389i	$0.211001\pi$
$594$		0			0
$595$	3869.50	+	7871.58i	0.266612	+	0.542359i
$596$			10706.4i			0.735827i
$597$		0			0
$598$	20840.3	+	20840.3i	1.42512	+	1.42512i
$599$	−14590.2			−0.995222			−0.497611	−	0.867400i	$-0.665789\pi$
$599$	−14590.2			−0.995222			−0.497611	+	0.867400i	$0.665789\pi$
$600$		0			0
$601$	−12899.3			−0.875498			−0.437749	−	0.899097i	$-0.644224\pi$
$601$	−12899.3			−0.875498			−0.437749	+	0.899097i	$0.644224\pi$
$602$	−2704.85	−	2704.85i	−0.183125	−	0.183125i
$603$		0			0
$604$			5535.60i			0.372915i
$605$	5786.15	+	11770.5i	0.388827	+	0.790977i
$606$		0			0
$607$	4187.38	−	4187.38i	0.280001	−	0.280001i	−0.553108	−	0.833109i	$-0.686558\pi$
$607$	4187.38	−	4187.38i	0.280001	−	0.280001i	0.833109	+	0.553108i	$0.186558\pi$
$608$	1215.52	−	1215.52i	0.0810787	−	0.0810787i
$609$		0			0
$610$	1056.45	−	3099.36i	0.0701222	−	0.205721i
$611$			28417.3i			1.88157i
$612$		0			0
$613$	11263.3	+	11263.3i	0.742123	+	0.742123i	0.972986	−	0.230863i	$-0.0741549\pi$
$613$	11263.3	+	11263.3i	0.742123	+	0.742123i	−0.230863	+	0.972986i	$0.574155\pi$
$614$	−10113.6			−0.664743
$615$		0			0
$616$	2802.30			0.183292
$617$	8548.13	+	8548.13i	0.557755	+	0.557755i	0.928668	−	0.370913i	$-0.120955\pi$
$617$	8548.13	+	8548.13i	0.557755	+	0.557755i	−0.370913	+	0.928668i	$0.620955\pi$
$618$		0			0
$619$		−	9303.95i		−	0.604131i	−0.953287	−	0.302066i	$-0.902324\pi$
$619$		−	9303.95i		−	0.604131i	0.953287	−	0.302066i	$-0.0976762\pi$
$620$	5162.23	−	2537.64i	0.334387	−	0.164378i
$621$		0			0
$622$	−2482.81	+	2482.81i	−0.160051	+	0.160051i
$623$	−1245.52	+	1245.52i	−0.0800973	+	0.0800973i
$624$		0			0
$625$	−3967.87	−	15112.8i	−0.253944	−	0.967219i
$626$			5503.92i			0.351407i
$627$		0			0
$628$	−8443.56	−	8443.56i	−0.536520	−	0.536520i
$629$	1869.25			0.118493
$630$		0			0
$631$	−14580.9			−0.919896			−0.459948	−	0.887946i	$-0.652132\pi$
$631$	−14580.9			−0.919896			−0.459948	+	0.887946i	$0.652132\pi$
$632$	2544.12	+	2544.12i	0.160126	+	0.160126i
$633$		0			0
$634$		−	6579.52i		−	0.412155i
$635$	16592.5	+	5655.73i	1.03693	+	0.353450i
$636$		0			0
$637$	−2637.23	+	2637.23i	−0.164036	+	0.164036i
$638$	17999.0	−	17999.0i	1.11691	−	1.11691i
$639$		0			0
$640$	1354.55	+	461.715i	0.0836617	+	0.0285170i
$641$		−	4094.31i		−	0.252286i	−0.992012	−	0.126143i	$-0.959740\pi$
$641$		−	4094.31i		−	0.252286i	0.992012	−	0.126143i	$-0.0402598\pi$
$642$		0			0
$643$	−9405.18	−	9405.18i	−0.576834	−	0.576834i	0.357196	−	0.934030i	$-0.383733\pi$
$643$	−9405.18	−	9405.18i	−0.576834	−	0.576834i	−0.934030	+	0.357196i	$0.883733\pi$
$644$	−5421.02			−0.331705
$645$		0			0
$646$	−12041.1			−0.733359
$647$	−11841.8	−	11841.8i	−0.719548	−	0.719548i	0.248964	−	0.968513i	$-0.419910\pi$
$647$	−11841.8	−	11841.8i	−0.719548	−	0.719548i	−0.968513	+	0.248964i	$0.919910\pi$
$648$		0			0
$649$		−	21468.8i		−	1.29850i
$650$	−15067.1	−	11621.9i	−0.909202	−	0.701305i
$651$		0			0
$652$	−6122.79	+	6122.79i	−0.367771	+	0.367771i
$653$	1134.32	−	1134.32i	0.0679778	−	0.0679778i	−0.672301	−	0.740278i	$-0.734694\pi$
$653$	1134.32	−	1134.32i	0.0679778	−	0.0679778i	0.740278	+	0.672301i	$0.234694\pi$
$654$		0			0
$655$	15001.3	−	7374.33i	0.894885	−	0.439907i
$656$		−	5105.24i		−	0.303851i
$657$		0			0
$658$	−3695.97	−	3695.97i	−0.218973	−	0.218973i
$659$	−10897.4			−0.644161			−0.322081	−	0.946712i	$-0.604382\pi$
$659$	−10897.4			−0.644161			−0.322081	+	0.946712i	$0.604382\pi$
$660$		0			0
$661$	−25208.4			−1.48335			−0.741673	−	0.670761i	$-0.765967\pi$
$661$	−25208.4			−1.48335			−0.741673	+	0.670761i	$0.765967\pi$
$662$	15040.3	+	15040.3i	0.883017	+	0.883017i
$663$		0			0
$664$			3829.73i			0.223829i
$665$	1356.40	−	3979.35i	0.0790964	−	0.232049i
$666$		0			0
$667$	−34818.8	+	34818.8i	−2.02128	+	2.02128i
$668$	4863.97	−	4863.97i	0.281726	−	0.281726i
$669$		0			0
$670$	−9164.61	−	18643.2i	−0.528448	−	1.07500i
$671$			7327.96i			0.421599i
$672$		0			0
$673$	−2811.39	−	2811.39i	−0.161027	−	0.161027i	0.621995	−	0.783022i	$-0.286323\pi$
$673$	−2811.39	−	2811.39i	−0.161027	−	0.161027i	−0.783022	+	0.621995i	$0.786323\pi$
$674$	14578.4			0.833147
$675$		0			0
$676$	−14385.6			−0.818478
$677$	−17846.8	−	17846.8i	−1.01316	−	1.01316i	−0.999912	−	0.0132440i	$-0.995784\pi$
$677$	−17846.8	−	17846.8i	−1.01316	−	1.01316i	−0.0132440	−	0.999912i	$-0.504216\pi$
$678$		0			0
$679$		−	9327.00i		−	0.527154i
$680$	−4422.29	−	8996.09i	−0.249393	−	0.507330i
$681$		0			0
$682$	−9102.57	+	9102.57i	−0.511078	+	0.511078i
$683$	−4610.86	+	4610.86i	−0.258316	+	0.258316i	−0.824369	−	0.566053i	$-0.808470\pi$
$683$	−4610.86	+	4610.86i	−0.258316	+	0.258316i	0.566053	+	0.824369i	$0.308470\pi$
$684$		0			0
$685$	5517.31	−	16186.4i	0.307745	−	0.902847i
$686$		−	686.000i		−	0.0381802i
$687$		0			0
$688$	3091.26	+	3091.26i	0.171298	+	0.171298i
$689$	−15691.9			−0.867654
$690$		0			0
$691$	−1414.28			−0.0778605			−0.0389302	−	0.999242i	$-0.512395\pi$
$691$	−1414.28			−0.0778605			−0.0389302	+	0.999242i	$0.512395\pi$
$692$	6787.49	+	6787.49i	0.372864	+	0.372864i
$693$		0			0
$694$			8362.11i			0.457380i
$695$	9235.10	−	4539.78i	0.504039	−	0.247775i
$696$		0			0
$697$	−25286.6	+	25286.6i	−1.37417	+	1.37417i
$698$	−9278.69	+	9278.69i	−0.503157	+	0.503157i
$699$		0			0
$700$	3471.20	−	448.089i	0.187427	−	0.0241945i
$701$			20378.1i			1.09796i	0.835836	+	0.548979i	$0.184983\pi$
$701$			20378.1i			1.09796i	−0.835836	+	0.548979i	$0.815017\pi$
$702$		0			0
$703$	−633.535	−	633.535i	−0.0339889	−	0.0339889i
$704$	−3202.63			−0.171454
$705$		0			0
$706$	−12614.7			−0.672467
$707$	8889.86	+	8889.86i	0.472896	+	0.472896i
$708$		0			0
$709$			2551.74i			0.135166i	0.997714	+	0.0675831i	$0.0215288\pi$
$709$			2551.74i			0.135166i	−0.997714	+	0.0675831i	$0.978471\pi$
$710$	−15473.7	−	5274.38i	−0.817912	−	0.278794i
$711$		0			0
$712$	1423.45	−	1423.45i	0.0749242	−	0.0749242i
$713$	17608.8	−	17608.8i	0.924901	−	0.924901i
$714$		0			0
$715$	40307.0	+	13739.1i	2.10825	+	0.718619i
$716$		−	9179.34i		−	0.479117i
$717$		0			0
$718$	2710.01	+	2710.01i	0.140859	+	0.140859i
$719$	−14660.4			−0.760416			−0.380208	−	0.924901i	$-0.624148\pi$
$719$	−14660.4			−0.760416			−0.380208	+	0.924901i	$0.624148\pi$
$720$		0			0
$721$	3577.15			0.184771
$722$	−5619.07	−	5619.07i	−0.289640	−	0.289640i
$723$		0			0
$724$		−	378.961i		−	0.0194530i
$725$	19417.2	−	25173.3i	0.994673	−	1.28954i
$726$		0			0
$727$	9221.73	−	9221.73i	0.470447	−	0.470447i	−0.431612	−	0.902059i	$-0.642055\pi$
$727$	9221.73	−	9221.73i	0.470447	−	0.470447i	0.902059	+	0.431612i	$0.142055\pi$
$728$	3013.97	−	3013.97i	0.153441	−	0.153441i
$729$		0			0
$730$	13186.1	−	6482.01i	0.668548	−	0.328644i
$731$		−	30622.3i		−	1.54940i
$732$		0			0
$733$	−5953.45	−	5953.45i	−0.299994	−	0.299994i	0.541017	−	0.841012i	$-0.318039\pi$
$733$	−5953.45	−	5953.45i	−0.299994	−	0.299994i	−0.841012	+	0.541017i	$0.818039\pi$
$734$	10766.0			0.541389
$735$		0			0
$736$	6195.45			0.310282
$737$	32873.6	+	32873.6i	1.64303	+	1.64303i
$738$		0			0
$739$			10358.0i			0.515596i	0.966199	+	0.257798i	$0.0829968\pi$
$739$			10358.0i			0.515596i	−0.966199	+	0.257798i	$0.917003\pi$
$740$	240.648	−	706.001i	0.0119546	−	0.0350718i
$741$		0			0
$742$	2040.90	−	2040.90i	0.100976	−	0.100976i
$743$	−25378.8	+	25378.8i	−1.25311	+	1.25311i	−0.298786	+	0.954320i	$0.596582\pi$
$743$	−25378.8	+	25378.8i	−1.25311	+	1.25311i	−0.954320	+	0.298786i	$0.903418\pi$
$744$		0			0
$745$	−13201.8	−	26856.0i	−0.649231	−	1.32071i
$746$		−	3201.22i		−	0.157111i
$747$		0			0
$748$	15862.8	+	15862.8i	0.775404	+	0.775404i
$749$	−312.058			−0.0152235
$750$		0			0
$751$	14724.1			0.715432			0.357716	−	0.933830i	$-0.383556\pi$
$751$	14724.1			0.715432			0.357716	+	0.933830i	$0.383556\pi$
$752$	4223.97	+	4223.97i	0.204830	+	0.204830i
$753$		0			0
$754$		−	38717.1i		−	1.87002i
$755$	−6825.80	−	13885.5i	−0.329028	−	0.669330i
$756$		0			0
$757$	7636.45	−	7636.45i	0.366647	−	0.366647i	−0.499606	−	0.866253i	$-0.666522\pi$
$757$	7636.45	−	7636.45i	0.366647	−	0.366647i	0.866253	+	0.499606i	$0.166522\pi$
$758$	12069.6	−	12069.6i	0.578347	−	0.578347i
$759$		0			0
$760$	−1550.18	+	4547.83i	−0.0739879	+	0.217062i
$761$		−	27010.6i		−	1.28664i	−0.765597	−	0.643321i	$-0.777556\pi$
$761$		−	27010.6i		−	1.28664i	0.765597	−	0.643321i	$-0.222444\pi$
$762$		0			0
$763$	−4167.56	−	4167.56i	−0.197740	−	0.197740i
$764$	−11926.5			−0.564774
$765$		0			0
$766$	−14660.8			−0.691533
$767$	−23090.5	−	23090.5i	−1.08702	−	1.08702i
$768$		0			0
$769$			18288.0i			0.857582i	0.903404	+	0.428791i	$0.141060\pi$
$769$			18288.0i			0.857582i	−0.903404	+	0.428791i	$0.858940\pi$
$770$	−7029.28	+	3455.44i	−0.328984	+	0.161722i
$771$		0			0
$772$	9181.98	−	9181.98i	0.428066	−	0.428066i
$773$	−1643.27	+	1643.27i	−0.0764611	+	0.0764611i	−0.744303	−	0.667842i	$-0.767218\pi$
$773$	−1643.27	+	1643.27i	−0.0764611	+	0.0764611i	0.667842	+	0.744303i	$0.267218\pi$
$774$		0			0
$775$	−9819.80	+	12730.8i	−0.455145	+	0.590070i
$776$			10659.4i			0.493107i
$777$		0			0
$778$	4897.18	+	4897.18i	0.225672	+	0.225672i
$779$	17140.5			0.788347
$780$		0			0
$781$	36585.1			1.67621
$782$	−30686.4	−	30686.4i	−1.40325	−	1.40325i
$783$		0			0
$784$			784.000i			0.0357143i
$785$	31591.3	+	10768.2i	1.43636	+	0.489599i
$786$		0			0
$787$	17422.9	−	17422.9i	0.789150	−	0.789150i	−0.192205	−	0.981355i	$-0.561564\pi$
$787$	17422.9	−	17422.9i	0.789150	−	0.789150i	0.981355	+	0.192205i	$0.0615639\pi$
$788$	12994.6	−	12994.6i	0.587456	−	0.587456i
$789$		0			0
$790$	−9518.73	−	3244.57i	−0.428685	−	0.146122i
$791$		−	10504.7i		−	0.472193i
$792$		0			0
$793$	7881.47	+	7881.47i	0.352937	+	0.352937i
$794$	2889.48			0.129148
$795$		0			0
$796$	4092.68			0.182238
$797$	−8434.48	−	8434.48i	−0.374861	−	0.374861i	0.494383	−	0.869244i	$-0.335394\pi$
$797$	−8434.48	−	8434.48i	−0.374861	−	0.374861i	−0.869244	+	0.494383i	$0.835394\pi$
$798$		0			0
$799$		−	41843.1i		−	1.85270i
$800$	−3967.08	+	512.102i	−0.175322	+	0.0226319i
$801$		0			0
$802$	2101.14	−	2101.14i	0.0925110	−	0.0925110i
$803$	−23251.1	+	23251.1i	−1.02181	+	1.02181i
$804$		0			0
$805$	13598.0	−	6684.51i	0.595364	−	0.292668i
$806$			19580.2i			0.855688i
$807$		0			0
$808$	−10159.8	−	10159.8i	−0.442354	−	0.442354i
$809$	−34990.7			−1.52065			−0.760327	−	0.649540i	$-0.774961\pi$
$809$	−34990.7			−1.52065			−0.760327	+	0.649540i	$0.774961\pi$
$810$		0			0
$811$	−44670.0			−1.93413			−0.967063	−	0.254537i	$-0.918077\pi$
$811$	−44670.0			−1.93413			−0.967063	+	0.254537i	$0.918077\pi$
$812$	5035.58	+	5035.58i	0.217628	+	0.217628i
$813$		0			0
$814$			1669.23i			0.0718752i
$815$	7808.52	−	22908.2i	0.335608	−	0.984588i
$816$		0			0
$817$	−10378.7	+	10378.7i	−0.444436	+	0.444436i
$818$	−2734.34	+	2734.34i	−0.116875	+	0.116875i
$819$		0			0
$820$	6295.14	+	12806.0i	0.268092	+	0.545370i
$821$		−	31375.0i		−	1.33373i	−0.745177	−	0.666866i	$-0.767635\pi$
$821$		−	31375.0i		−	1.33373i	0.745177	−	0.666866i	$-0.232365\pi$
$822$		0			0
$823$	−4697.73	−	4697.73i	−0.198970	−	0.198970i	0.600588	−	0.799558i	$-0.294933\pi$
$823$	−4697.73	−	4697.73i	−0.198970	−	0.198970i	−0.799558	+	0.600588i	$0.794933\pi$
$824$	−4088.17			−0.172838
$825$		0			0
$826$	6006.33			0.253011
$827$	8084.35	+	8084.35i	0.339928	+	0.339928i	0.856340	−	0.516412i	$-0.172733\pi$
$827$	8084.35	+	8084.35i	0.339928	+	0.339928i	−0.516412	+	0.856340i	$0.672733\pi$
$828$		0			0
$829$			19624.9i			0.822196i	0.911591	+	0.411098i	$0.134855\pi$
$829$			19624.9i			0.822196i	−0.911591	+	0.411098i	$0.865145\pi$
$830$	−4722.33	−	9606.46i	−0.197487	−	0.401741i
$831$		0			0
$832$	−3444.54	+	3444.54i	−0.143531	+	0.143531i
$833$	3883.20	−	3883.20i	0.161518	−	0.161518i
$834$		0			0
$835$	−6203.12	+	18198.4i	−0.257087	+	0.754229i
$836$		−	10752.6i		−	0.444841i
$837$		0			0
$838$	8239.08	+	8239.08i	0.339635	+	0.339635i
$839$	−1357.49			−0.0558590			−0.0279295	−	0.999610i	$-0.508891\pi$
$839$	−1357.49			−0.0558590			−0.0279295	+	0.999610i	$0.508891\pi$
$840$		0			0
$841$	40297.4			1.65228
$842$	2228.99	+	2228.99i	0.0912304	+	0.0912304i
$843$		0			0
$844$		−	1103.93i		−	0.0450225i
$845$	36084.6	−	17738.4i	1.46905	−	0.722155i
$846$		0			0
$847$	5806.63	−	5806.63i	0.235559	−	0.235559i
$848$	−2332.46	+	2332.46i	−0.0944539	+	0.0944539i
$849$		0			0
$850$	22185.7	+	17112.7i	0.895249	+	0.690543i
$851$		−	3229.10i		−	0.130073i
$852$		0			0
$853$	−29496.2	−	29496.2i	−1.18398	−	1.18398i	−0.978705	−	0.205272i	$-0.934192\pi$
$853$	−29496.2	−	29496.2i	−1.18398	−	1.18398i	−0.205272	−	0.978705i	$-0.565808\pi$
$854$	−2050.14			−0.0821480
$855$		0			0
$856$	356.638			0.0142402
$857$	12080.3	+	12080.3i	0.481510	+	0.481510i	0.905614	−	0.424104i	$-0.139411\pi$
$857$	12080.3	+	12080.3i	0.481510	+	0.481510i	−0.424104	+	0.905614i	$0.639411\pi$
$858$		0			0
$859$			38185.8i			1.51674i	0.651822	+	0.758372i	$0.274005\pi$
$859$			38185.8i			1.51674i	−0.651822	+	0.758372i	$0.725995\pi$
$860$	−11565.8	−	3942.34i	−0.458595	−	0.156317i
$861$		0			0
$862$	20150.9	−	20150.9i	0.796220	−	0.796220i
$863$	−17934.6	+	17934.6i	−0.707416	+	0.707416i	−0.965991	−	0.258575i	$-0.916747\pi$
$863$	−17934.6	+	17934.6i	−0.707416	+	0.707416i	0.258575	+	0.965991i	$0.416747\pi$
$864$		0			0
$865$	−25395.1	−	8656.22i	−0.998221	−	0.340255i
$866$			18597.7i			0.729764i
$867$		0			0
$868$	−2546.62	−	2546.62i	−0.0995830	−	0.0995830i
$869$	22505.6			0.878537
$870$		0			0
$871$	70713.5			2.75090
$872$	4762.92	+	4762.92i	0.184969	+	0.184969i
$873$		0			0
$874$			20800.8i			0.805031i
$875$	−8154.60	+	5404.22i	−0.315058	+	0.208795i
$876$		0			0
$877$	−10265.9	+	10265.9i	−0.395272	+	0.395272i	−0.876562	−	0.481290i	$-0.840168\pi$
$877$	−10265.9	+	10265.9i	−0.395272	+	0.395272i	0.481290	+	0.876562i	$0.340168\pi$
$878$	−7037.93	+	7037.93i	−0.270522	+	0.270522i
$879$		0			0
$880$	8033.46	−	3949.08i	0.307736	−	0.151277i
$881$			13503.1i			0.516381i	0.966094	+	0.258190i	$0.0831262\pi$
$881$			13503.1i			0.516381i	−0.966094	+	0.258190i	$0.916874\pi$
$882$		0			0
$883$	−3590.04	−	3590.04i	−0.136823	−	0.136823i	0.635378	−	0.772201i	$-0.280844\pi$
$883$	−3590.04	−	3590.04i	−0.136823	−	0.136823i	−0.772201	+	0.635378i	$0.780844\pi$
$884$	34122.0			1.29824
$885$		0			0
$886$	23143.9			0.877579
$887$	−5217.72	−	5217.72i	−0.197513	−	0.197513i	0.601420	−	0.798933i	$-0.294602\pi$
$887$	−5217.72	−	5217.72i	−0.197513	−	0.197513i	−0.798933	+	0.601420i	$0.794602\pi$
$888$		0			0
$889$		−	10975.5i		−	0.414066i
$890$	−1815.35	+	5325.78i	−0.0683716	+	0.200585i
$891$		0			0
$892$	−1771.21	+	1771.21i	−0.0664849	+	0.0664849i
$893$	−14181.7	+	14181.7i	−0.531436	+	0.531436i
$894$		0			0
$895$	11318.8	+	23025.4i	0.422732	+	0.859948i
$896$		−	896.000i		−	0.0334077i
$897$		0			0
$898$	−164.772	−	164.772i	−0.00612308	−	0.00612308i
$899$	−32713.6			−1.21364
$900$		0			0
$901$	23105.6			0.854339
$902$	−22580.8	−	22580.8i	−0.833545	−	0.833545i
$903$		0			0
$904$			12005.4i			0.441696i
$905$	467.287	+	950.583i	0.0171637	+	0.0349154i
$906$		0			0
$907$	−23419.2	+	23419.2i	−0.857357	+	0.857357i	−0.991026	−	0.133669i	$-0.957324\pi$
$907$	−23419.2	+	23419.2i	−0.857357	+	0.857357i	0.133669	+	0.991026i	$0.457324\pi$
$908$	18936.5	−	18936.5i	0.692104	−	0.692104i
$909$		0			0
$910$	−3843.78	+	11276.7i	−0.140022	+	0.410789i
$911$		−	4729.94i		−	0.172020i	−0.996294	−	0.0860098i	$-0.972588\pi$
$911$		−	4729.94i		−	0.172020i	0.996294	−	0.0860098i	$-0.0274116\pi$
$912$		0			0
$913$	16939.1	+	16939.1i	0.614022	+	0.614022i
$914$	16247.9			0.588001
$915$		0			0
$916$	−968.599			−0.0349382
$917$	−7400.43	−	7400.43i	−0.266503	−	0.266503i
$918$		0			0
$919$		−	26469.5i		−	0.950108i	−0.879957	−	0.475054i	$-0.842429\pi$
$919$		−	26469.5i		−	0.950108i	0.879957	−	0.475054i	$-0.157571\pi$
$920$	−15540.6	+	7639.44i	−0.556912	+	0.273766i
$921$		0			0
$922$	20042.3	−	20042.3i	0.715899	−	0.715899i
$923$	39348.5	−	39348.5i	1.40322	−	1.40322i
$924$		0			0
$925$	266.910	+	2067.66i	0.00948751	+	0.0734966i
$926$		−	6156.25i		−	0.218474i
$927$		0			0
$928$	−5754.95	−	5754.95i	−0.203573	−	0.203573i
$929$	−25871.8			−0.913697			−0.456849	−	0.889544i	$-0.651022\pi$
$929$	−25871.8			−0.913697			−0.456849	+	0.889544i	$0.651022\pi$
$930$		0			0
$931$	−2632.23			−0.0926614
$932$	8299.83	+	8299.83i	0.291706	+	0.291706i
$933$		0			0
$934$		−	23600.8i		−	0.826810i
$935$	−59350.2	−	20230.2i	−2.07589	−	0.707591i
$936$		0			0
$937$	10302.9	−	10302.9i	0.359211	−	0.359211i	−0.504311	−	0.863522i	$-0.668253\pi$
$937$	10302.9	−	10302.9i	0.359211	−	0.359211i	0.863522	+	0.504311i	$0.168253\pi$
$938$	−9197.05	+	9197.05i	−0.320143	+	0.320143i
$939$		0			0
$940$	−15803.8	−	5386.91i	−0.548366	−	0.186917i
$941$		−	19838.5i		−	0.687264i	−0.939104	−	0.343632i	$-0.888343\pi$
$941$		−	19838.5i		−	0.687264i	0.939104	−	0.343632i	$-0.111657\pi$
$942$		0			0
$943$	43682.2	+	43682.2i	1.50847	+	1.50847i
$944$	−6864.38			−0.236670
$945$		0			0
$946$	27345.6			0.939833
$947$	8536.06	+	8536.06i	0.292909	+	0.292909i	0.838228	−	0.545319i	$-0.183592\pi$
$947$	8536.06	+	8536.06i	0.292909	+	0.292909i	−0.545319	+	0.838228i	$0.683592\pi$
$948$		0			0
$949$			50014.7i			1.71080i
$950$	−1719.35	−	13319.2i	−0.0587189	−	0.454876i
$951$		0			0
$952$	−4437.94	+	4437.94i	−0.151087	+	0.151087i
$953$	25950.7	−	25950.7i	0.882085	−	0.882085i	−0.111661	−	0.993746i	$-0.535617\pi$
$953$	25950.7	−	25950.7i	0.882085	−	0.882085i	0.993746	+	0.111661i	$0.0356171\pi$
$954$		0			0
$955$	29916.4	−	14706.3i	1.01369	−	0.498308i
$956$			22152.1i			0.749425i
$957$		0			0
$958$	7981.56	+	7981.56i	0.269178	+	0.269178i
$959$	−10706.8			−0.360523
$960$		0			0
$961$	−13246.9			−0.444661
$962$	1795.31	+	1795.31i	0.0601696	+	0.0601696i
$963$		0			0
$964$			7368.77i			0.246195i
$965$	−11710.0	+	34354.1i	−0.390629	+	1.14601i
$966$		0			0
$967$	−22719.0	+	22719.0i	−0.755525	+	0.755525i	−0.975505	−	0.219979i	$-0.929401\pi$
$967$	−22719.0	+	22719.0i	−0.755525	+	0.755525i	0.219979	+	0.975505i	$0.429401\pi$
$968$	−6636.15	+	6636.15i	−0.220345	+	0.220345i
$969$		0			0
$970$	−13143.8	−	26738.0i	−0.435076	−	0.885058i
$971$		−	43649.4i		−	1.44261i	−0.692617	−	0.721306i	$-0.743542\pi$
$971$		−	43649.4i		−	1.44261i	0.692617	−	0.721306i	$-0.256458\pi$
$972$		0			0
$973$	−4555.85	−	4555.85i	−0.150107	−	0.150107i
$974$	16551.2			0.544492
$975$		0			0
$976$	2343.02			0.0768424
$977$	−16833.7	−	16833.7i	−0.551235	−	0.551235i	0.375562	−	0.926797i	$-0.377450\pi$
$977$	−16833.7	−	16833.7i	−0.551235	−	0.551235i	−0.926797	+	0.375562i	$0.877450\pi$
$978$		0			0
$979$		−	12592.0i		−	0.411074i
$980$	−966.729	−	1966.58i	−0.0315112	−	0.0641021i
$981$		0			0
$982$	−12695.8	+	12695.8i	−0.412567	+	0.412567i
$983$	−21752.1	+	21752.1i	−0.705784	+	0.705784i	−0.965646	−	0.259862i	$-0.916323\pi$
$983$	−21752.1	+	21752.1i	−0.705784	+	0.705784i	0.259862	+	0.965646i	$0.416323\pi$
$984$		0			0
$985$	−16572.3	+	48619.0i	−0.536080	+	1.57272i
$986$			57009.2i			1.84132i
$987$		0			0
$988$	−11564.8	−	11564.8i	−0.372394	−	0.372394i
$989$	−52899.7			−1.70082
$990$		0			0
$991$	46742.8			1.49832			0.749159	−	0.662390i	$-0.230458\pi$
$991$	46742.8			1.49832			0.749159	+	0.662390i	$0.230458\pi$
$992$	2910.43	+	2910.43i	0.0931514	+	0.0931514i
$993$		0			0
$994$			10235.4i			0.326607i
$995$	−10266.0	+	5046.57i	−0.327091	+	0.160791i
$996$		0			0
$997$	43984.5	−	43984.5i	1.39720	−	1.39720i	0.589232	−	0.807964i	$-0.299431\pi$
$997$	43984.5	−	43984.5i	1.39720	−	1.39720i	0.807964	−	0.589232i	$-0.200569\pi$
$998$	15716.1	−	15716.1i	0.498481	−	0.498481i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.4.m.a.323.2	yes	16
3.2	odd	2		630.4.m.b.323.7	yes	16
5.2	odd	4		630.4.m.b.197.7	yes	16
15.2	even	4	inner	630.4.m.a.197.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.4.m.a.197.2	✓	16	15.2	even	4	inner
630.4.m.a.323.2	yes	16	1.1	even	1	trivial
630.4.m.b.197.7	yes	16	5.2	odd	4
630.4.m.b.323.7	yes	16	3.2	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	630.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +4.00000i q^{4} +(-4.93229 - 10.0336i) q^{5} +(-4.94975 + 4.94975i) q^{7} +(5.65685 - 5.65685i) q^{8} +(-7.21430 + 21.1649i) q^{10} -50.0412i q^{11} +(-53.8210 - 53.8210i) q^{13} +14.0000 q^{14} -16.0000 q^{16} +(79.2489 + 79.2489i) q^{17} -53.7189i q^{19} +(40.1343 - 19.7292i) q^{20} +(-70.7689 + 70.7689i) q^{22} +(136.901 - 136.901i) q^{23} +(-76.3450 + 98.9769i) q^{25} +152.229i q^{26} +(-19.7990 - 19.7990i) q^{28} -254.335 q^{29} +128.624 q^{31} +(22.6274 + 22.6274i) q^{32} -224.150i q^{34} +(74.0772 + 25.2500i) q^{35} +(11.7935 - 11.7935i) q^{37} +(-75.9700 + 75.9700i) q^{38} +(-84.6597 - 28.8572i) q^{40} +319.078i q^{41} +(-193.204 - 193.204i) q^{43} +200.165 q^{44} -387.216 q^{46} +(-263.998 - 263.998i) q^{47} -49.0000i q^{49} +(247.943 - 32.0064i) q^{50} +(215.284 - 215.284i) q^{52} +(145.779 - 145.779i) q^{53} +(-502.091 + 246.817i) q^{55} +56.0000i q^{56} +(359.684 + 359.684i) q^{58} +429.023 q^{59} -146.439 q^{61} +(-181.902 - 181.902i) q^{62} -64.0000i q^{64} +(-274.556 + 805.477i) q^{65} +(-656.932 + 656.932i) q^{67} +(-316.996 + 316.996i) q^{68} +(-69.0521 - 140.470i) q^{70} +731.101i q^{71} +(-464.640 - 464.640i) q^{73} -33.3571 q^{74} +214.876 q^{76} +(247.691 + 247.691i) q^{77} +449.741i q^{79} +(78.9166 + 160.537i) q^{80} +(451.244 - 451.244i) q^{82} +(-338.503 + 338.503i) q^{83} +(404.271 - 1186.03i) q^{85} +546.462i q^{86} +(-283.076 - 283.076i) q^{88} +251.633 q^{89} +532.800 q^{91} +(547.605 + 547.605i) q^{92} +746.700i q^{94} +(-538.992 + 264.957i) q^{95} +(-942.169 + 942.169i) q^{97} +(-69.2965 + 69.2965i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 44 q^{5} - 24 q^{10} - 212 q^{13} + 224 q^{14} - 256 q^{16} + 32 q^{17} + 32 q^{20} + 72 q^{22} - 128 q^{23} - 268 q^{25} + 232 q^{29} - 200 q^{31} + 112 q^{35} + 900 q^{37} - 368 q^{38} - 128 q^{40}+ \cdots - 2668 q^{97}+O(q^{100}) \) 16 * q - 44 * q^5 - 24 * q^10 - 212 * q^13 + 224 * q^14 - 256 * q^16 + 32 * q^17 + 32 * q^20 + 72 * q^22 - 128 * q^23 - 268 * q^25 + 232 * q^29 - 200 * q^31 + 112 * q^35 + 900 * q^37 - 368 * q^38 - 128 * q^40 - 908 * q^43 + 352 * q^44 + 208 * q^46 - 604 * q^47 + 896 * q^50 + 848 * q^52 - 440 * q^53 - 1232 * q^55 + 536 * q^58 + 224 * q^59 + 1200 * q^61 - 1304 * q^62 + 1936 * q^65 + 652 * q^67 - 128 * q^68 - 616 * q^70 - 2148 * q^73 + 1328 * q^74 - 252 * q^77 + 704 * q^80 + 616 * q^82 - 2624 * q^83 - 1712 * q^85 + 288 * q^88 + 2400 * q^89 - 512 * q^92 + 4200 * q^95 - 2668 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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