LMFDB - Embedded newform 630.4.m.a.323.1

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			323.1
Root			$3.20578 - 7.73944i$ of defining polynomial
Character	$\chi$	$=$	630.323
Dual form			630.4.m.a.197.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 - 1.41421i) q^{2} +4.00000i q^{4} +(-10.7228 + 3.16564i) q^{5} +(-4.94975 + 4.94975i) q^{7} +(5.65685 - 5.65685i) q^{8} +(19.6412 + 10.6875i) q^{10} +54.2140i q^{11} +(-11.6648 - 11.6648i) q^{13} +14.0000 q^{14} -16.0000 q^{16} +(55.8903 + 55.8903i) q^{17} -37.6502i q^{19} +(-12.6625 - 42.8913i) q^{20} +(76.6702 - 76.6702i) q^{22} +(-99.2115 + 99.2115i) q^{23} +(104.957 - 67.8891i) q^{25} +32.9931i q^{26} +(-19.7990 - 19.7990i) q^{28} +131.401 q^{29} +7.72550 q^{31} +(22.6274 + 22.6274i) q^{32} -158.082i q^{34} +(37.4061 - 68.7443i) q^{35} +(-103.890 + 103.890i) q^{37} +(-53.2454 + 53.2454i) q^{38} +(-42.7498 + 78.5649i) q^{40} -26.1567i q^{41} +(-189.326 - 189.326i) q^{43} -216.856 q^{44} +280.612 q^{46} +(-8.81600 - 8.81600i) q^{47} -49.0000i q^{49} +(-244.442 - 52.4226i) q^{50} +(46.6593 - 46.6593i) q^{52} +(-256.739 + 256.739i) q^{53} +(-171.622 - 581.326i) q^{55} +56.0000i q^{56} +(-185.829 - 185.829i) q^{58} -393.511 q^{59} +344.542 q^{61} +(-10.9255 - 10.9255i) q^{62} -64.0000i q^{64} +(162.006 + 88.1532i) q^{65} +(164.410 - 164.410i) q^{67} +(-223.561 + 223.561i) q^{68} +(-150.119 + 44.3189i) q^{70} -766.258i q^{71} +(-855.944 - 855.944i) q^{73} +293.846 q^{74} +150.601 q^{76} +(-268.346 - 268.346i) q^{77} -4.06706i q^{79} +(171.565 - 50.6502i) q^{80} +(-36.9912 + 36.9912i) q^{82} +(-24.6792 + 24.6792i) q^{83} +(-776.230 - 422.373i) q^{85} +535.496i q^{86} +(306.681 + 306.681i) q^{88} -603.749 q^{89} +115.476 q^{91} +(-396.846 - 396.846i) q^{92} +24.9354i q^{94} +(119.187 + 403.716i) q^{95} +(773.428 - 773.428i) q^{97} +(-69.2965 + 69.2965i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - 44 q^{5} - 24 q^{10} - 212 q^{13} + 224 q^{14} - 256 q^{16} + 32 q^{17} + 32 q^{20} + 72 q^{22} - 128 q^{23} - 268 q^{25} + 232 q^{29} - 200 q^{31} + 112 q^{35} + 900 q^{37} - 368 q^{38} - 128 q^{40}+ \cdots - 2668 q^{97}+O(q^{100})$ 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
$5$	−10.7228	+	3.16564i	−0.959078	+	0.283143i
$5$	−10.7228	+	3.16564i	−0.959078	+	0.283143i
$6$		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
$10$	19.6412	+	10.6875i	0.621110	+	0.337967i
$11$			54.2140i			1.48601i	0.669285	+	0.743006i	$0.266601\pi$
$11$			54.2140i			1.48601i	−0.669285	+	0.743006i	$0.733399\pi$
$12$		0			0
$13$	−11.6648	−	11.6648i	−0.248865	−	0.248865i	0.571640	−	0.820505i	$-0.306307\pi$
$13$	−11.6648	−	11.6648i	−0.248865	−	0.248865i	−0.820505	+	0.571640i	$0.806307\pi$
$14$	14.0000			0.267261
$15$		0			0
$16$	−16.0000			−0.250000
$17$	55.8903	+	55.8903i	0.797376	+	0.797376i	0.982681	−	0.185305i	$-0.0593273\pi$
$17$	55.8903	+	55.8903i	0.797376	+	0.797376i	−0.185305	+	0.982681i	$0.559327\pi$
$18$		0			0
$19$		−	37.6502i		−	0.454608i	−0.973824	−	0.227304i	$-0.927009\pi$
$19$		−	37.6502i		−	0.454608i	0.973824	−	0.227304i	$-0.0729911\pi$
$20$	−12.6625	−	42.8913i	−0.141572	−	0.479539i
$21$		0			0
$22$	76.6702	−	76.6702i	0.743006	−	0.743006i
$23$	−99.2115	+	99.2115i	−0.899436	+	0.899436i	−0.995386	−	0.0959503i	$-0.969411\pi$
$23$	−99.2115	+	99.2115i	−0.899436	+	0.899436i	0.0959503	+	0.995386i	$0.469411\pi$
$24$		0			0
$25$	104.957	−	67.8891i	0.839660	−	0.543113i
$26$			32.9931i			0.248865i
$27$		0			0
$28$	−19.7990	−	19.7990i	−0.133631	−	0.133631i
$29$	131.401			0.841400			0.420700	−	0.907200i	$-0.361785\pi$
$29$	131.401			0.841400			0.420700	+	0.907200i	$0.361785\pi$
$30$		0			0
$31$	7.72550			0.0447594			0.0223797	−	0.999750i	$-0.492876\pi$
$31$	7.72550			0.0447594			0.0223797	+	0.999750i	$0.492876\pi$
$32$	22.6274	+	22.6274i	0.125000	+	0.125000i
$33$		0			0
$34$		−	158.082i		−	0.797376i
$35$	37.4061	−	68.7443i	0.180651	−	0.331997i
$36$		0			0
$37$	−103.890	+	103.890i	−0.461607	+	0.461607i	−0.899182	−	0.437575i	$-0.855837\pi$
$37$	−103.890	+	103.890i	−0.461607	+	0.461607i	0.437575	+	0.899182i	$0.355837\pi$
$38$	−53.2454	+	53.2454i	−0.227304	+	0.227304i
$39$		0			0
$40$	−42.7498	+	78.5649i	−0.168984	+	0.310555i
$41$		−	26.1567i		−	0.0996340i	−0.998758	−	0.0498170i	$-0.984136\pi$
$41$		−	26.1567i		−	0.0996340i	0.998758	−	0.0498170i	$-0.0158638\pi$
$42$		0			0
$43$	−189.326	−	189.326i	−0.671442	−	0.671442i	0.286606	−	0.958048i	$-0.407473\pi$
$43$	−189.326	−	189.326i	−0.671442	−	0.671442i	−0.958048	+	0.286606i	$0.907473\pi$
$44$	−216.856			−0.743006
$45$		0			0
$46$	280.612			0.899436
$47$	−8.81600	−	8.81600i	−0.0273605	−	0.0273605i	0.693294	−	0.720655i	$-0.256159\pi$
$47$	−8.81600	−	8.81600i	−0.0273605	−	0.0273605i	−0.720655	+	0.693294i	$0.756159\pi$
$48$		0			0
$49$		−	49.0000i		−	0.142857i
$50$	−244.442	−	52.4226i	−0.691386	−	0.148274i
$51$		0			0
$52$	46.6593	−	46.6593i	0.124432	−	0.124432i
$53$	−256.739	+	256.739i	−0.665394	+	0.665394i	−0.956646	−	0.291252i	$-0.905928\pi$
$53$	−256.739	+	256.739i	−0.665394	+	0.665394i	0.291252	+	0.956646i	$0.405928\pi$
$54$		0			0
$55$	−171.622	−	581.326i	−0.420754	−	1.42520i
$56$			56.0000i			0.133631i
$57$		0			0
$58$	−185.829	−	185.829i	−0.420700	−	0.420700i
$59$	−393.511			−0.868318			−0.434159	−	0.900836i	$-0.642954\pi$
$59$	−393.511			−0.868318			−0.434159	+	0.900836i	$0.642954\pi$
$60$		0			0
$61$	344.542			0.723182			0.361591	−	0.932337i	$-0.382234\pi$
$61$	344.542			0.723182			0.361591	+	0.932337i	$0.382234\pi$
$62$	−10.9255	−	10.9255i	−0.0223797	−	0.0223797i
$63$		0			0
$64$		−	64.0000i		−	0.125000i
$65$	162.006	+	88.1532i	0.309145	+	0.168216i
$66$		0			0
$67$	164.410	−	164.410i	0.299789	−	0.299789i	−0.541142	−	0.840931i	$-0.682008\pi$
$67$	164.410	−	164.410i	0.299789	−	0.299789i	0.840931	+	0.541142i	$0.182008\pi$
$68$	−223.561	+	223.561i	−0.398688	+	0.398688i
$69$		0			0
$70$	−150.119	+	44.3189i	−0.256324	+	0.0756732i
$71$		−	766.258i		−	1.28082i	−0.768034	−	0.640409i	$-0.778765\pi$
$71$		−	766.258i		−	1.28082i	0.768034	−	0.640409i	$-0.221235\pi$
$72$		0			0
$73$	−855.944	−	855.944i	−1.37234	−	1.37234i	−0.856968	−	0.515370i	$-0.827655\pi$
$73$	−855.944	−	855.944i	−1.37234	−	1.37234i	−0.515370	−	0.856968i	$-0.672345\pi$
$74$	293.846			0.461607
$75$		0			0
$76$	150.601			0.227304
$77$	−268.346	−	268.346i	−0.397153	−	0.397153i
$78$		0			0
$79$		−	4.06706i		−	0.00579216i	−0.999996	−	0.00289608i	$-0.999078\pi$
$79$		−	4.06706i		−	0.00579216i	0.999996	−	0.00289608i	$-0.000921852\pi$
$80$	171.565	−	50.6502i	0.239769	−	0.0707858i
$81$		0			0
$82$	−36.9912	+	36.9912i	−0.0498170	+	0.0498170i
$83$	−24.6792	+	24.6792i	−0.0326373	+	0.0326373i	−0.723237	−	0.690600i	$-0.757347\pi$
$83$	−24.6792	+	24.6792i	−0.0326373	+	0.0326373i	0.690600	+	0.723237i	$0.257347\pi$
$84$		0			0
$85$	−776.230	−	422.373i	−0.990517	−	0.538974i
$86$			535.496i			0.671442i
$87$		0			0
$88$	306.681	+	306.681i	0.371503	+	0.371503i
$89$	−603.749			−0.719070			−0.359535	−	0.933132i	$-0.617065\pi$
$89$	−603.749			−0.719070			−0.359535	+	0.933132i	$0.617065\pi$
$90$		0			0
$91$	115.476			0.133024
$92$	−396.846	−	396.846i	−0.449718	−	0.449718i
$93$		0			0
$94$			24.9354i			0.0273605i
$95$	119.187	+	403.716i	0.128719	+	0.436004i
$96$		0			0
$97$	773.428	−	773.428i	0.809585	−	0.809585i	−0.174986	−	0.984571i	$-0.555988\pi$
$97$	773.428	−	773.428i	0.809585	−	0.809585i	0.984571	+	0.174986i	$0.0559880\pi$
$98$	−69.2965	+	69.2965i	−0.0714286	+	0.0714286i
$99$		0			0
$100$	271.556	+	419.830i	0.271556	+	0.419830i
$101$			808.755i			0.796774i	0.917217	+	0.398387i	$0.130430\pi$
$101$			808.755i			0.796774i	−0.917217	+	0.398387i	$0.869570\pi$
$102$		0			0
$103$	230.858	+	230.858i	0.220846	+	0.220846i	0.808854	−	0.588009i	$-0.200088\pi$
$103$	230.858	+	230.858i	0.220846	+	0.220846i	−0.588009	+	0.808854i	$0.700088\pi$
$104$	−131.973			−0.124432
$105$		0			0
$106$	726.169			0.665394
$107$	−1126.40	−	1126.40i	−1.01770	−	1.01770i	−0.999841	−	0.0178570i	$-0.994316\pi$
$107$	−1126.40	−	1126.40i	−1.01770	−	1.01770i	−0.0178570	−	0.999841i	$-0.505684\pi$
$108$		0			0
$109$		−	29.1677i		−	0.0256308i	−0.999918	−	0.0128154i	$-0.995921\pi$
$109$		−	29.1677i		−	0.0256308i	0.999918	−	0.0128154i	$-0.00407938\pi$
$110$	−579.410	+	1064.83i	−0.502223	+	0.922978i
$111$		0			0
$112$	79.1960	−	79.1960i	0.0668153	−	0.0668153i
$113$	−1052.90	+	1052.90i	−0.876532	+	0.876532i	−0.993174	−	0.116642i	$-0.962787\pi$
$113$	−1052.90	+	1052.90i	−0.876532	+	0.876532i	0.116642	+	0.993174i	$0.462787\pi$
$114$		0			0
$115$	749.759	−	1377.89i	0.607960	−	1.11730i
$116$			525.605i			0.420700i
$117$		0			0
$118$	556.509	+	556.509i	0.434159	+	0.434159i
$119$	−553.286			−0.426215
$120$		0			0
$121$	−1608.16			−1.20823
$122$	−487.256	−	487.256i	−0.361591	−	0.361591i
$123$		0			0
$124$			30.9020i			0.0223797i
$125$	−910.527	+	1060.22i	−0.651520	+	0.758631i
$126$		0			0
$127$	−1294.36	+	1294.36i	−0.904374	+	0.904374i	−0.995811	−	0.0914372i	$-0.970854\pi$
$127$	−1294.36	+	1294.36i	−0.904374	+	0.904374i	0.0914372	+	0.995811i	$0.470854\pi$
$128$	−90.5097	+	90.5097i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−104.444	−	353.779i	−0.0704644	−	0.238681i
$131$		−	977.860i		−	0.652184i	−0.945338	−	0.326092i	$-0.894268\pi$
$131$		−	977.860i		−	0.652184i	0.945338	−	0.326092i	$-0.105732\pi$
$132$		0			0
$133$	186.359	+	186.359i	0.121499	+	0.121499i
$134$	−465.022			−0.299789
$135$		0			0
$136$	632.327			0.398688
$137$	−434.579	−	434.579i	−0.271012	−	0.271012i	0.558496	−	0.829507i	$-0.311379\pi$
$137$	−434.579	−	434.579i	−0.271012	−	0.271012i	−0.829507	+	0.558496i	$0.811379\pi$
$138$		0			0
$139$			27.4511i			0.0167509i	0.999965	+	0.00837544i	$0.00266602\pi$
$139$			27.4511i			0.0167509i	−0.999965	+	0.00837544i	$0.997334\pi$
$140$	274.977	+	149.624i	0.165999	+	0.0903255i
$141$		0			0
$142$	−1083.65	+	1083.65i	−0.640409	+	0.640409i
$143$	632.397	−	632.397i	0.369816	−	0.369816i
$144$		0			0
$145$	−1408.99	+	415.969i	−0.806968	+	0.238237i
$146$			2420.97i			1.37234i
$147$		0			0
$148$	−415.561	−	415.561i	−0.230803	−	0.230803i
$149$	−1849.19			−1.01672			−0.508361	−	0.861144i	$-0.669749\pi$
$149$	−1849.19			−1.01672			−0.508361	+	0.861144i	$0.669749\pi$
$150$		0			0
$151$	−1521.10			−0.819769			−0.409885	−	0.912137i	$-0.634431\pi$
$151$	−1521.10			−0.819769			−0.409885	+	0.912137i	$0.634431\pi$
$152$	−212.982	−	212.982i	−0.113652	−	0.113652i
$153$		0			0
$154$			758.996i			0.397153i
$155$	−82.8391	+	24.4561i	−0.0429277	+	0.0126733i
$156$		0			0
$157$	683.521	−	683.521i	0.347458	−	0.347458i	−0.511704	−	0.859162i	$-0.670986\pi$
$157$	683.521	−	683.521i	0.347458	−	0.347458i	0.859162	+	0.511704i	$0.170986\pi$
$158$	−5.75170	+	5.75170i	−0.00289608	+	0.00289608i
$159$		0			0
$160$	−314.260	−	170.999i	−0.155278	−	0.0844918i
$161$		−	982.144i		−	0.480769i
$162$		0			0
$163$	−1322.21	−	1322.21i	−0.635360	−	0.635360i	0.314048	−	0.949407i	$-0.398315\pi$
$163$	−1322.21	−	1322.21i	−0.635360	−	0.635360i	−0.949407	+	0.314048i	$0.898315\pi$
$164$	104.627			0.0498170
$165$		0			0
$166$	69.8033			0.0326373
$167$	−1707.40	−	1707.40i	−0.791155	−	0.791155i	0.190527	−	0.981682i	$-0.438980\pi$
$167$	−1707.40	−	1707.40i	−0.791155	−	0.791155i	−0.981682	+	0.190527i	$0.938980\pi$
$168$		0			0
$169$		−	1924.86i		−	0.876133i
$170$	500.429	+	1695.08i	0.225772	+	0.764745i
$171$		0			0
$172$	757.306	−	757.306i	0.335721	−	0.335721i
$173$	2630.21	−	2630.21i	1.15590	−	1.15590i	0.170553	−	0.985348i	$-0.445445\pi$
$173$	2630.21	−	2630.21i	1.15590	−	1.15590i	0.985348	−	0.170553i	$-0.0545555\pi$
$174$		0			0
$175$	−183.479	+	855.547i	−0.0792556	+	0.369561i
$176$		−	867.424i		−	0.371503i
$177$		0			0
$178$	853.830	+	853.830i	0.359535	+	0.359535i
$179$	3805.30			1.58895			0.794473	−	0.607300i	$-0.207747\pi$
$179$	3805.30			1.58895			0.794473	+	0.607300i	$0.207747\pi$
$180$		0			0
$181$	1062.96			0.436514			0.218257	−	0.975891i	$-0.429963\pi$
$181$	1062.96			0.436514			0.218257	+	0.975891i	$0.429963\pi$
$182$	−163.308	−	163.308i	−0.0665119	−	0.0665119i
$183$		0			0
$184$			1122.45i			0.449718i
$185$	785.117	−	1442.88i	0.312016	−	0.573418i
$186$		0			0
$187$	−3030.04	+	3030.04i	−1.18491	+	1.18491i
$188$	35.2640	−	35.2640i	0.0136803	−	0.0136803i
$189$		0			0
$190$	402.385	−	739.497i	0.153643	−	0.282362i
$191$		−	1429.10i		−	0.541391i	−0.962665	−	0.270696i	$-0.912746\pi$
$191$		−	1429.10i		−	0.541391i	0.962665	−	0.270696i	$-0.0872537\pi$
$192$		0			0
$193$	−2870.55	−	2870.55i	−1.07060	−	1.07060i	−0.997310	−	0.0732943i	$-0.976649\pi$
$193$	−2870.55	−	2870.55i	−1.07060	−	1.07060i	−0.0732943	−	0.997310i	$-0.523351\pi$
$194$	−2187.59			−0.809585
$195$		0			0
$196$	196.000			0.0714286
$197$	2181.49	+	2181.49i	0.788959	+	0.788959i	0.981324	−	0.192365i	$-0.0616156\pi$
$197$	2181.49	+	2181.49i	0.788959	+	0.788959i	−0.192365	+	0.981324i	$0.561616\pi$
$198$		0			0
$199$			3308.91i			1.17871i	0.807876	+	0.589353i	$0.200617\pi$
$199$			3308.91i			1.17871i	−0.807876	+	0.589353i	$0.799383\pi$
$200$	209.691	−	977.768i	0.0741368	−	0.345693i
$201$		0			0
$202$	1143.75	−	1143.75i	0.398387	−	0.398387i
$203$	−650.403	+	650.403i	−0.224874	+	0.224874i
$204$		0			0
$205$	82.8027	+	280.474i	0.0282107	+	0.0955568i
$206$		−	652.965i		−	0.220846i
$207$		0			0
$208$	186.637	+	186.637i	0.0622162	+	0.0622162i
$209$	2041.17			0.675553
$210$		0			0
$211$	405.246			0.132219			0.0661097	−	0.997812i	$-0.478941\pi$
$211$	405.246			0.132219			0.0661097	+	0.997812i	$0.478941\pi$
$212$	−1026.96	−	1026.96i	−0.332697	−	0.332697i
$213$		0			0
$214$			3185.95i			1.01770i
$215$	2629.45	+	1430.77i	0.834079	+	0.453851i
$216$		0			0
$217$	−38.2393	+	38.2393i	−0.0119625	+	0.0119625i
$218$	−41.2493	+	41.2493i	−0.0128154	+	0.0128154i
$219$		0			0
$220$	2325.31	−	686.487i	0.712600	−	0.210377i
$221$		−	1303.90i		−	0.396878i
$222$		0			0
$223$	1053.51	+	1053.51i	0.316361	+	0.316361i	0.847368	−	0.531007i	$-0.178186\pi$
$223$	1053.51	+	1053.51i	0.316361	+	0.316361i	−0.531007	+	0.847368i	$0.678186\pi$
$224$	−224.000			−0.0668153
$225$		0			0
$226$	2978.04			0.876532
$227$	−2961.74	−	2961.74i	−0.865981	−	0.865981i	0.126044	−	0.992025i	$-0.459772\pi$
$227$	−2961.74	−	2961.74i	−0.865981	−	0.865981i	−0.992025	+	0.126044i	$0.959772\pi$
$228$		0			0
$229$			3642.64i			1.05114i	0.850749	+	0.525572i	$0.176149\pi$
$229$			3642.64i			1.05114i	−0.850749	+	0.525572i	$0.823851\pi$
$230$	−3008.96	+	888.317i	−0.862629	+	0.254669i
$231$		0			0
$232$	743.318	−	743.318i	0.210350	−	0.210350i
$233$	−3554.73	+	3554.73i	−0.999476	+	0.999476i	−1.00000		0.000523602i	$-0.999833\pi$
$233$	−3554.73	+	3554.73i	−0.999476	+	0.999476i	0.000523602		1.00000i	$0.499833\pi$
$234$		0			0
$235$	122.441	+	66.6241i	0.0339878	+	0.0184939i
$236$		−	1574.04i		−	0.434159i
$237$		0			0
$238$	782.464	+	782.464i	0.213108	+	0.213108i
$239$	5375.04			1.45474			0.727369	−	0.686246i	$-0.240743\pi$
$239$	5375.04			1.45474			0.727369	+	0.686246i	$0.240743\pi$
$240$		0			0
$241$	4718.81			1.26127			0.630634	−	0.776081i	$-0.282795\pi$
$241$	4718.81			1.26127			0.630634	+	0.776081i	$0.282795\pi$
$242$	2274.28	+	2274.28i	0.604116	+	0.604116i
$243$		0			0
$244$			1378.17i			0.361591i
$245$	155.116	+	525.418i	0.0404490	+	0.137011i
$246$		0			0
$247$	−439.183	+	439.183i	−0.113136	+	0.113136i
$248$	43.7020	−	43.7020i	0.0111898	−	0.0111898i
$249$		0			0
$250$	2787.06	−	211.696i	0.705076	−	0.0535554i
$251$			6606.62i			1.66138i	0.556736	+	0.830690i	$0.312054\pi$
$251$			6606.62i			1.66138i	−0.556736	+	0.830690i	$0.687946\pi$
$252$		0			0
$253$	−5378.65	−	5378.65i	−1.33657	−	1.33657i
$254$	3660.99			0.904374
$255$		0			0
$256$	256.000			0.0625000
$257$	−1202.57	−	1202.57i	−0.291883	−	0.291883i	0.545941	−	0.837824i	$-0.316172\pi$
$257$	−1202.57	−	1202.57i	−0.291883	−	0.291883i	−0.837824	+	0.545941i	$0.816172\pi$
$258$		0			0
$259$		−	1028.46i		−	0.246739i
$260$	−352.613	+	648.026i	−0.0841081	+	0.154573i
$261$		0			0
$262$	−1382.90	+	1382.90i	−0.326092	+	0.326092i
$263$	5227.37	−	5227.37i	1.22560	−	1.22560i	0.259990	−	0.965611i	$-0.416281\pi$
$263$	5227.37	−	5227.37i	1.22560	−	1.22560i	0.965611	−	0.259990i	$-0.0837194\pi$
$264$		0			0
$265$	1940.23	−	3565.71i	0.449763	−	0.826566i
$266$		−	527.103i		−	0.121499i
$267$		0			0
$268$	657.640	+	657.640i	0.149895	+	0.149895i
$269$	6984.93			1.58319			0.791596	−	0.611045i	$-0.209251\pi$
$269$	6984.93			1.58319			0.791596	+	0.611045i	$0.209251\pi$
$270$		0			0
$271$	6674.75			1.49617			0.748085	−	0.663603i	$-0.230974\pi$
$271$	6674.75			1.49617			0.748085	+	0.663603i	$0.230974\pi$
$272$	−894.245	−	894.245i	−0.199344	−	0.199344i
$273$		0			0
$274$			1229.18i			0.271012i
$275$	3680.54	+	5690.16i	0.807072	+	1.24774i
$276$		0			0
$277$	1384.01	−	1384.01i	0.300206	−	0.300206i	−0.540888	−	0.841095i	$-0.681912\pi$
$277$	1384.01	−	1384.01i	0.300206	−	0.300206i	0.841095	+	0.540888i	$0.181912\pi$
$278$	38.8217	−	38.8217i	0.00837544	−	0.00837544i
$279$		0			0
$280$	−177.276	−	600.478i	−0.0378366	−	0.128162i
$281$		−	7041.32i		−	1.49484i	−0.664351	−	0.747420i	$-0.731292\pi$
$281$		−	7041.32i		−	1.49484i	0.664351	−	0.747420i	$-0.268708\pi$
$282$		0			0
$283$	−4987.19	−	4987.19i	−1.04755	−	1.04755i	−0.998811	−	0.0487425i	$-0.984479\pi$
$283$	−4987.19	−	4987.19i	−1.04755	−	1.04755i	−0.0487425	−	0.998811i	$-0.515521\pi$
$284$	3065.03			0.640409
$285$		0			0
$286$	−1788.69			−0.369816
$287$	129.469	+	129.469i	0.0266283	+	0.0266283i
$288$		0			0
$289$			1334.45i			0.271617i
$290$	2580.88	+	1404.35i	0.522602	+	0.284366i
$291$		0			0
$292$	3423.78	−	3423.78i	0.686169	−	0.686169i
$293$	4512.34	−	4512.34i	0.899705	−	0.899705i	−0.0957045	−	0.995410i	$-0.530510\pi$
$293$	4512.34	−	4512.34i	0.899705	−	0.899705i	0.995410	+	0.0957045i	$0.0305104\pi$
$294$		0			0
$295$	4219.55	−	1245.71i	0.832785	−	0.245858i
$296$			1175.38i			0.230803i
$297$		0			0
$298$	2615.15	+	2615.15i	0.508361	+	0.508361i
$299$	2314.57			0.447676
$300$		0			0
$301$	1874.24			0.358901
$302$	2151.16	+	2151.16i	0.409885	+	0.409885i
$303$		0			0
$304$			602.403i			0.113652i
$305$	−3694.46	+	1090.70i	−0.693588	+	0.204764i
$306$		0			0
$307$	−5676.77	+	5676.77i	−1.05534	+	1.05534i	−0.0569672	+	0.998376i	$0.518143\pi$
$307$	−5676.77	+	5676.77i	−1.05534	+	1.05534i	−0.998376	+	0.0569672i	$0.981857\pi$
$308$	1073.38	−	1073.38i	0.198577	−	0.198577i
$309$		0			0
$310$	151.738	+	82.5660i	0.0278005	+	0.0151272i
$311$		−	5319.96i		−	0.969990i	−0.874517	−	0.484995i	$-0.838821\pi$
$311$		−	5319.96i		−	0.969990i	0.874517	−	0.484995i	$-0.161179\pi$
$312$		0			0
$313$	1348.56	+	1348.56i	0.243530	+	0.243530i	0.818309	−	0.574779i	$-0.194912\pi$
$313$	1348.56	+	1348.56i	0.243530	+	0.243530i	−0.574779	+	0.818309i	$0.694912\pi$
$314$	−1933.29			−0.347458
$315$		0			0
$316$	16.2683			0.00289608
$317$	5640.35	+	5640.35i	0.999349	+	0.999349i	1.00000		0.000650974i	$-0.000207212\pi$
$317$	5640.35	+	5640.35i	0.999349	+	0.999349i	−0.000650974		1.00000i	$0.500207\pi$
$318$		0			0
$319$			7123.78i			1.25033i
$320$	202.601	+	686.260i	0.0353929	+	0.119885i
$321$		0			0
$322$	−1388.96	+	1388.96i	−0.240384	+	0.240384i
$323$	2104.28	−	2104.28i	0.362493	−	0.362493i
$324$		0			0
$325$	−2016.23	−	432.397i	−0.344123	−	0.0738002i
$326$			3739.78i			0.635360i
$327$		0			0
$328$	−147.965	−	147.965i	−0.0249085	−	0.0249085i
$329$	87.2739			0.0146248
$330$		0			0
$331$	−1576.91			−0.261857			−0.130929	−	0.991392i	$-0.541796\pi$
$331$	−1576.91			−0.261857			−0.130929	+	0.991392i	$0.541796\pi$
$332$	−98.7168	−	98.7168i	−0.0163186	−	0.0163186i
$333$		0			0
$334$			4829.27i			0.791155i
$335$	−1242.48	+	2283.40i	−0.202638	+	0.372404i
$336$		0			0
$337$	−262.992	+	262.992i	−0.0425106	+	0.0425106i	−0.728043	−	0.685532i	$-0.759570\pi$
$337$	−262.992	+	262.992i	−0.0425106	+	0.0425106i	0.685532	+	0.728043i	$0.259570\pi$
$338$	−2722.17	+	2722.17i	−0.438066	+	0.438066i
$339$		0			0
$340$	1689.49	−	3104.92i	0.269487	−	0.495258i
$341$			418.830i			0.0665130i
$342$		0			0
$343$	242.538	+	242.538i	0.0381802	+	0.0381802i
$344$	−2141.98			−0.335721
$345$		0			0
$346$	−7439.35			−1.15590
$347$	−838.163	−	838.163i	−0.129668	−	0.129668i	0.639294	−	0.768962i	$-0.279227\pi$
$347$	−838.163	−	838.163i	−0.129668	−	0.129668i	−0.768962	+	0.639294i	$0.779227\pi$
$348$		0			0
$349$			12786.5i			1.96116i	0.196132	+	0.980578i	$0.437162\pi$
$349$			12786.5i			1.96116i	−0.196132	+	0.980578i	$0.562838\pi$
$350$	1469.40	−	950.447i	0.224409	−	0.145153i
$351$		0			0
$352$	−1226.72	+	1226.72i	−0.185751	+	0.185751i
$353$	5968.78	−	5968.78i	0.899961	−	0.899961i	−0.0954712	−	0.995432i	$-0.530436\pi$
$353$	5968.78	−	5968.78i	0.899961	−	0.899961i	0.995432	+	0.0954712i	$0.0304358\pi$
$354$		0			0
$355$	2425.69	+	8216.44i	0.362655	+	1.22840i
$356$		−	2415.00i		−	0.359535i
$357$		0			0
$358$	−5381.50	−	5381.50i	−0.794473	−	0.794473i
$359$	−12316.0			−1.81062			−0.905310	−	0.424752i	$-0.860361\pi$
$359$	−12316.0			−1.81062			−0.905310	+	0.424752i	$0.860361\pi$
$360$		0			0
$361$	5441.46			0.793332
$362$	−1503.25	−	1503.25i	−0.218257	−	0.218257i
$363$		0			0
$364$			461.904i			0.0665119i
$365$	11887.7	+	6468.52i	1.70475	+	0.927610i
$366$		0			0
$367$	4453.42	−	4453.42i	0.633424	−	0.633424i	−0.315501	−	0.948925i	$-0.602173\pi$
$367$	4453.42	−	4453.42i	0.633424	−	0.633424i	0.948925	+	0.315501i	$0.102173\pi$
$368$	1587.38	−	1587.38i	0.224859	−	0.224859i
$369$		0			0
$370$	−3150.86	+	930.210i	−0.442717	+	0.130701i
$371$		−	2541.59i		−	0.355668i
$372$		0			0
$373$	−8067.36	−	8067.36i	−1.11987	−	1.11987i	−0.991760	−	0.128112i	$-0.959108\pi$
$373$	−8067.36	−	8067.36i	−1.11987	−	1.11987i	−0.128112	−	0.991760i	$-0.540892\pi$
$374$	8570.24			1.18491
$375$		0			0
$376$	−99.7416			−0.0136803
$377$	−1532.77	−	1532.77i	−0.209395	−	0.209395i
$378$		0			0
$379$		−	9125.24i		−	1.23676i	−0.785879	−	0.618380i	$-0.787789\pi$
$379$		−	9125.24i		−	1.23676i	0.785879	−	0.618380i	$-0.212211\pi$
$380$	−1614.86	+	476.748i	−0.218002	+	0.0643596i
$381$		0			0
$382$	−2021.05	+	2021.05i	−0.270696	+	0.270696i
$383$	1535.54	−	1535.54i	0.204863	−	0.204863i	−0.597217	−	0.802080i	$-0.703727\pi$
$383$	1535.54	−	1535.54i	0.204863	−	0.204863i	0.802080	+	0.597217i	$0.203727\pi$
$384$		0			0
$385$	3726.90	+	2027.93i	0.493352	+	0.268450i
$386$			8119.14i			1.07060i
$387$		0			0
$388$	3093.71	+	3093.71i	0.404792	+	0.404792i
$389$	−13707.6			−1.78664			−0.893318	−	0.449425i	$-0.851629\pi$
$389$	−13707.6			−1.78664			−0.893318	+	0.449425i	$0.851629\pi$
$390$		0			0
$391$	−11089.9			−1.43438
$392$	−277.186	−	277.186i	−0.0357143	−	0.0357143i
$393$		0			0
$394$		−	6170.19i		−	0.788959i
$395$	12.8748	+	43.6104i	0.00164001	+	0.00555513i
$396$		0			0
$397$	−79.6650	+	79.6650i	−0.0100712	+	0.0100712i	−0.712124	−	0.702053i	$-0.752267\pi$
$397$	−79.6650	+	79.6650i	−0.0100712	+	0.0100712i	0.702053	+	0.712124i	$0.252267\pi$
$398$	4679.50	−	4679.50i	0.589353	−	0.589353i
$399$		0			0
$400$	−1679.32	+	1086.23i	−0.209915	+	0.135778i
$401$			3389.96i			0.422161i	0.977469	+	0.211080i	$0.0676982\pi$
$401$			3389.96i			0.422161i	−0.977469	+	0.211080i	$0.932302\pi$
$402$		0			0
$403$	−90.1167	−	90.1167i	−0.0111390	−	0.0111390i
$404$	−3235.02			−0.398387
$405$		0			0
$406$	1839.62			0.224874
$407$	−5632.31	−	5632.31i	−0.685954	−	0.685954i
$408$		0			0
$409$			5836.72i			0.705641i	0.935691	+	0.352821i	$0.114777\pi$
$409$			5836.72i			0.705641i	−0.935691	+	0.352821i	$0.885223\pi$
$410$	279.549	−	513.751i	0.0336730	−	0.0618837i
$411$		0			0
$412$	−923.431	+	923.431i	−0.110423	+	0.110423i
$413$	1947.78	−	1947.78i	0.232068	−	0.232068i
$414$		0			0
$415$	186.505	−	342.756i	0.0220607	−	0.0405427i
$416$		−	527.890i		−	0.0622162i
$417$		0			0
$418$	−2886.65	−	2886.65i	−0.337776	−	0.337776i
$419$	−14445.2			−1.68423			−0.842115	−	0.539299i	$-0.818689\pi$
$419$	−14445.2			−1.68423			−0.842115	+	0.539299i	$0.818689\pi$
$420$		0			0
$421$	11729.6			1.35787			0.678935	−	0.734198i	$-0.262442\pi$
$421$	11729.6			1.35787			0.678935	+	0.734198i	$0.262442\pi$
$422$	−573.105	−	573.105i	−0.0661097	−	0.0661097i
$423$		0			0
$424$			2904.68i			0.332697i
$425$	9660.45	+	2071.76i	1.10259	+	0.236460i
$426$		0			0
$427$	−1705.40	+	1705.40i	−0.193278	+	0.193278i
$428$	4505.62	−	4505.62i	0.508849	−	0.508849i
$429$		0			0
$430$	−1695.19	−	5742.02i	−0.190114	−	0.643965i
$431$		−	9269.94i		−	1.03600i	−0.855380	−	0.518001i	$-0.826676\pi$
$431$		−	9269.94i		−	1.03600i	0.855380	−	0.518001i	$-0.173324\pi$
$432$		0			0
$433$	−4150.08	−	4150.08i	−0.460601	−	0.460601i	0.438251	−	0.898852i	$-0.355598\pi$
$433$	−4150.08	−	4150.08i	−0.460601	−	0.460601i	−0.898852	+	0.438251i	$0.855598\pi$
$434$	108.157			0.0119625
$435$		0			0
$436$	116.671			0.0128154
$437$	3735.33	+	3735.33i	0.408891	+	0.408891i
$438$		0			0
$439$			2217.98i			0.241135i	0.992705	+	0.120568i	$0.0384714\pi$
$439$			2217.98i			0.241135i	−0.992705	+	0.120568i	$0.961529\pi$
$440$	−4259.32	−	2317.64i	−0.461489	−	0.251112i
$441$		0			0
$442$	−1844.00	+	1844.00i	−0.198439	+	0.198439i
$443$	−11599.8	+	11599.8i	−1.24408	+	1.24408i	−0.285780	+	0.958295i	$0.592253\pi$
$443$	−11599.8	+	11599.8i	−1.24408	+	1.24408i	−0.958295	+	0.285780i	$0.907747\pi$
$444$		0			0
$445$	6473.89	−	1911.25i	0.689644	−	0.203600i
$446$		−	2979.79i		−	0.316361i
$447$		0			0
$448$	316.784	+	316.784i	0.0334077	+	0.0334077i
$449$	−4439.01			−0.466570			−0.233285	−	0.972408i	$-0.574947\pi$
$449$	−4439.01			−0.466570			−0.233285	+	0.972408i	$0.574947\pi$
$450$		0			0
$451$	1418.06			0.148057
$452$	−4211.58	−	4211.58i	−0.438266	−	0.438266i
$453$		0			0
$454$			8377.07i			0.865981i
$455$	−1238.23	+	365.555i	−0.127580	+	0.0376648i
$456$		0			0
$457$	556.528	−	556.528i	0.0569656	−	0.0569656i	−0.678050	−	0.735016i	$-0.737175\pi$
$457$	556.528	−	556.528i	0.0569656	−	0.0569656i	0.735016	+	0.678050i	$0.237175\pi$
$458$	5151.46	−	5151.46i	0.525572	−	0.525572i
$459$		0			0
$460$	5511.58	+	2999.03i	0.558649	+	0.303980i
$461$			11696.4i			1.18168i	0.806788	+	0.590841i	$0.201204\pi$
$461$			11696.4i			1.18168i	−0.806788	+	0.590841i	$0.798796\pi$
$462$		0			0
$463$	−2137.16	−	2137.16i	−0.214519	−	0.214519i	0.591665	−	0.806184i	$-0.298471\pi$
$463$	−2137.16	−	2137.16i	−0.214519	−	0.214519i	−0.806184	+	0.591665i	$0.798471\pi$
$464$	−2102.42			−0.210350
$465$		0			0
$466$	10054.3			0.999476
$467$	−11302.1	−	11302.1i	−1.11991	−	1.11991i	−0.991753	−	0.128161i	$-0.959093\pi$
$467$	−11302.1	−	11302.1i	−1.11991	−	1.11991i	−0.128161	−	0.991753i	$-0.540907\pi$
$468$		0			0
$469$			1627.58i			0.160244i
$470$	−78.9365	−	267.378i	−0.00774695	−	0.0262409i
$471$		0			0
$472$	−2226.04	+	2226.04i	−0.217080	+	0.217080i
$473$	10264.1	−	10264.1i	0.997771	−	0.997771i
$474$		0			0
$475$	−2556.04	−	3951.67i	−0.246903	−	0.381716i
$476$		−	2213.14i		−	0.213108i
$477$		0			0
$478$	−7601.45	−	7601.45i	−0.727369	−	0.727369i
$479$	−10137.1			−0.966968			−0.483484	−	0.875353i	$-0.660629\pi$
$479$	−10137.1			−0.966968			−0.483484	+	0.875353i	$0.660629\pi$
$480$		0			0
$481$	2423.73			0.229755
$482$	−6673.41	−	6673.41i	−0.630634	−	0.630634i
$483$		0			0
$484$		−	6432.62i		−	0.604116i
$485$	−5844.93	+	10741.7i	−0.547226	+	1.00568i
$486$		0			0
$487$	−8360.96	+	8360.96i	−0.777969	+	0.777969i	−0.979485	−	0.201516i	$-0.935413\pi$
$487$	−8360.96	+	8360.96i	−0.777969	+	0.777969i	0.201516	+	0.979485i	$0.435413\pi$
$488$	1949.02	−	1949.02i	0.180795	−	0.180795i
$489$		0			0
$490$	523.686	−	962.421i	0.0482810	−	0.0887301i
$491$			12261.9i			1.12703i	0.826106	+	0.563515i	$0.190551\pi$
$491$			12261.9i			1.12703i	−0.826106	+	0.563515i	$0.809449\pi$
$492$		0			0
$493$	7344.06	+	7344.06i	0.670912	+	0.670912i
$494$	1242.20			0.113136
$495$		0			0
$496$	−123.608			−0.0111898
$497$	3792.78	+	3792.78i	0.342313	+	0.342313i
$498$		0			0
$499$			3741.23i			0.335632i	0.985818	+	0.167816i	$0.0536715\pi$
$499$			3741.23i			0.335632i	−0.985818	+	0.167816i	$0.946329\pi$
$500$	−4240.88	−	3642.11i	−0.379316	−	0.325760i
$501$		0			0
$502$	9343.17	−	9343.17i	0.830690	−	0.830690i
$503$	−15703.5	+	15703.5i	−1.39202	+	1.39202i	−0.571224	+	0.820794i	$0.693531\pi$
$503$	−15703.5	+	15703.5i	−1.39202	+	1.39202i	−0.820794	+	0.571224i	$0.806469\pi$
$504$		0			0
$505$	−2560.23	−	8672.13i	−0.225601	−	0.764168i
$506$			15213.1i			1.33657i
$507$		0			0
$508$	−5177.42	−	5177.42i	−0.452187	−	0.452187i
$509$	612.431			0.0533311			0.0266656	−	0.999644i	$-0.491511\pi$
$509$	612.431			0.0533311			0.0266656	+	0.999644i	$0.491511\pi$
$510$		0			0
$511$	8473.41			0.733545
$512$	−362.039	−	362.039i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			3401.37i			0.291883i
$515$	−3206.26	−	1744.63i	−0.274339	−	0.149277i
$516$		0			0
$517$	477.950	−	477.950i	0.0406581	−	0.0406581i
$518$	−1454.46	+	1454.46i	−0.123370	+	0.123370i
$519$		0			0
$520$	1415.12	−	417.777i	0.119340	−	0.0352322i
$521$			170.383i			0.0143275i	0.999974	+	0.00716374i	$0.00228031\pi$
$521$			170.383i			0.0143275i	−0.999974	+	0.00716374i	$0.997720\pi$
$522$		0			0
$523$	5837.25	+	5837.25i	0.488041	+	0.488041i	0.907687	−	0.419647i	$-0.137846\pi$
$523$	5837.25	+	5837.25i	0.488041	+	0.488041i	−0.419647	+	0.907687i	$0.637846\pi$
$524$	3911.44			0.326092
$525$		0			0
$526$	−14785.2			−1.22560
$527$	431.781	+	431.781i	0.0356901	+	0.0356901i
$528$		0			0
$529$		−	7518.84i		−	0.617970i
$530$	−7786.57	+	2298.79i	−0.638164	+	0.188402i
$531$		0			0
$532$	−745.436	+	745.436i	−0.0607495	+	0.0607495i
$533$	−305.114	+	305.114i	−0.0247954	+	0.0247954i
$534$		0			0
$535$	15644.0	+	8512.44i	1.26421	+	0.687897i
$536$		−	1860.09i		−	0.149895i
$537$		0			0
$538$	−9878.18	−	9878.18i	−0.791596	−	0.791596i
$539$	2656.49			0.212287
$540$		0			0
$541$	−9101.86			−0.723326			−0.361663	−	0.932309i	$-0.617791\pi$
$541$	−9101.86			−0.723326			−0.361663	+	0.932309i	$0.617791\pi$
$542$	−9439.52	−	9439.52i	−0.748085	−	0.748085i
$543$		0			0
$544$			2529.31i			0.199344i
$545$	92.3343	+	312.760i	0.00725718	+	0.0245819i
$546$		0			0
$547$	−4441.76	+	4441.76i	−0.347195	+	0.347195i	−0.859064	−	0.511869i	$-0.828953\pi$
$547$	−4441.76	+	4441.76i	−0.347195	+	0.347195i	0.511869	+	0.859064i	$0.328953\pi$
$548$	1738.32	−	1738.32i	0.135506	−	0.135506i
$549$		0			0
$550$	2842.04	−	13252.2i	0.220336	−	1.02741i
$551$		−	4947.28i		−	0.382507i
$552$		0			0
$553$	20.1309	+	20.1309i	0.00154802	+	0.00154802i
$554$	−3914.58			−0.300206
$555$		0			0
$556$	−109.804			−0.00837544
$557$	−5924.27	−	5924.27i	−0.450663	−	0.450663i	0.444912	−	0.895575i	$-0.353235\pi$
$557$	−5924.27	−	5924.27i	−0.450663	−	0.450663i	−0.895575	+	0.444912i	$0.853235\pi$
$558$		0			0
$559$			4416.92i			0.334197i
$560$	−598.498	+	1099.91i	−0.0451628	+	0.0829994i
$561$		0			0
$562$	−9957.94	+	9957.94i	−0.747420	+	0.747420i
$563$	−648.027	+	648.027i	−0.0485099	+	0.0485099i	−0.730946	−	0.682436i	$-0.760921\pi$
$563$	−648.027	+	648.027i	−0.0485099	+	0.0485099i	0.682436	+	0.730946i	$0.260921\pi$
$564$		0			0
$565$	7956.92	−	14623.1i	0.592478	−	1.08885i
$566$			14105.9i			1.04755i
$567$		0			0
$568$	−4334.61	−	4334.61i	−0.320204	−	0.320204i
$569$	−13712.7			−1.01031			−0.505157	−	0.863028i	$-0.668565\pi$
$569$	−13712.7			−1.01031			−0.505157	+	0.863028i	$0.668565\pi$
$570$		0			0
$571$	−8495.55			−0.622641			−0.311320	−	0.950305i	$-0.600771\pi$
$571$	−8495.55			−0.622641			−0.311320	+	0.950305i	$0.600771\pi$
$572$	2529.59	+	2529.59i	0.184908	+	0.184908i
$573$		0			0
$574$		−	366.194i		−	0.0266283i
$575$	−3677.61	+	17148.4i	−0.266725	+	1.24372i
$576$		0			0
$577$	5702.03	−	5702.03i	0.411402	−	0.411402i	−0.470825	−	0.882227i	$-0.656044\pi$
$577$	5702.03	−	5702.03i	0.411402	−	0.411402i	0.882227	+	0.470825i	$0.156044\pi$
$578$	1887.20	−	1887.20i	0.135808	−	0.135808i
$579$		0			0
$580$	−1663.87	−	5635.96i	−0.119118	−	0.403484i
$581$		−	244.312i		−	0.0174454i
$582$		0			0
$583$	−13918.9	−	13918.9i	−0.988783	−	0.988783i
$584$	−9683.90			−0.686169
$585$		0			0
$586$	−12762.8			−0.899705
$587$	11467.0	+	11467.0i	0.806293	+	0.806293i	0.984071	−	0.177778i	$-0.0568909\pi$
$587$	11467.0	+	11467.0i	0.806293	+	0.806293i	−0.177778	+	0.984071i	$0.556891\pi$
$588$		0			0
$589$		−	290.867i		−	0.0203480i
$590$	−7729.05	−	4205.64i	−0.539322	−	0.293463i
$591$		0			0
$592$	1662.24	−	1662.24i	0.115402	−	0.115402i
$593$	−7207.99	+	7207.99i	−0.499151	+	0.499151i	−0.911174	−	0.412023i	$-0.864822\pi$
$593$	−7207.99	+	7207.99i	−0.499151	+	0.499151i	0.412023	+	0.911174i	$0.364822\pi$
$594$		0			0
$595$	5932.78	−	1751.50i	0.408774	−	0.120680i
$596$		−	7396.77i		−	0.508361i
$597$		0			0
$598$	−3273.30	−	3273.30i	−0.223838	−	0.223838i
$599$	1685.56			0.114975			0.0574874	−	0.998346i	$-0.481691\pi$
$599$	1685.56			0.114975			0.0574874	+	0.998346i	$0.481691\pi$
$600$		0			0
$601$	28410.1			1.92824			0.964119	−	0.265471i	$-0.0855273\pi$
$601$	28410.1			1.92824			0.964119	+	0.265471i	$0.0855273\pi$
$602$	−2650.57	−	2650.57i	−0.179450	−	0.179450i
$603$		0			0
$604$		−	6084.39i		−	0.409885i
$605$	17244.0	−	5090.84i	1.15879	−	0.342103i
$606$		0			0
$607$	−16117.7	+	16117.7i	−1.07776	+	1.07776i	−0.0810455	+	0.996710i	$0.525826\pi$
$607$	−16117.7	+	16117.7i	−1.07776	+	1.07776i	−0.996710	+	0.0810455i	$0.974174\pi$
$608$	851.927	−	851.927i	0.0568260	−	0.0568260i
$609$		0			0
$610$	6767.23	+	3682.28i	0.449176	+	0.244412i
$611$			205.674i			0.0136182i
$612$		0			0
$613$	−19843.4	−	19843.4i	−1.30745	−	1.30745i	−0.923252	−	0.384196i	$-0.874479\pi$
$613$	−19843.4	−	19843.4i	−1.30745	−	1.30745i	−0.384196	−	0.923252i	$-0.625521\pi$
$614$	16056.3			1.05534
$615$		0			0
$616$	−3035.98			−0.198577
$617$	4141.49	+	4141.49i	0.270227	+	0.270227i	0.829192	−	0.558965i	$-0.188801\pi$
$617$	4141.49	+	4141.49i	0.270227	+	0.270227i	−0.558965	+	0.829192i	$0.688801\pi$
$618$		0			0
$619$		−	461.366i		−	0.0299578i	−0.999888	−	0.0149789i	$-0.995232\pi$
$619$		−	461.366i		−	0.0299578i	0.999888	−	0.0149789i	$-0.00476810\pi$
$620$	−97.8245	−	331.356i	−0.00633666	−	0.0214639i
$621$		0			0
$622$	−7523.55	+	7523.55i	−0.484995	+	0.484995i
$623$	2988.40	−	2988.40i	0.192180	−	0.192180i
$624$		0			0
$625$	6407.15	−	14250.9i	0.410057	−	0.912060i
$626$		−	3814.29i		−	0.243530i
$627$		0			0
$628$	2734.08	+	2734.08i	0.173729	+	0.173729i
$629$	−11612.9			−0.736149
$630$		0			0
$631$	−6086.46			−0.383991			−0.191995	−	0.981396i	$-0.561496\pi$
$631$	−6086.46			−0.383991			−0.191995	+	0.981396i	$0.561496\pi$
$632$	−23.0068	−	23.0068i	−0.00144804	−	0.00144804i
$633$		0			0
$634$		−	15953.3i		−	0.999349i
$635$	9781.67	−	17976.6i	0.611297	−	1.12343i
$636$		0			0
$637$	−571.577	+	571.577i	−0.0355521	+	0.0355521i
$638$	10074.6	−	10074.6i	0.625165	−	0.625165i
$639$		0			0
$640$	683.998	−	1257.04i	0.0422459	−	0.0776388i
$641$		−	4943.95i		−	0.304640i	−0.988331	−	0.152320i	$-0.951326\pi$
$641$		−	4943.95i		−	0.304640i	0.988331	−	0.152320i	$-0.0486744\pi$
$642$		0			0
$643$	−10018.3	−	10018.3i	−0.614438	−	0.614438i	0.329662	−	0.944099i	$-0.393065\pi$
$643$	−10018.3	−	10018.3i	−0.614438	−	0.614438i	−0.944099	+	0.329662i	$0.893065\pi$
$644$	3928.57			0.240384
$645$		0			0
$646$	−5951.81			−0.362493
$647$	8428.07	+	8428.07i	0.512120	+	0.512120i	0.915175	−	0.403056i	$-0.132052\pi$
$647$	8428.07	+	8428.07i	0.512120	+	0.512120i	−0.403056	+	0.915175i	$0.632052\pi$
$648$		0			0
$649$		−	21333.8i		−	1.29033i
$650$	2239.87	+	3462.88i	0.135162	+	0.208962i
$651$		0			0
$652$	5288.85	−	5288.85i	0.317680	−	0.317680i
$653$	−20969.5	+	20969.5i	−1.25666	+	1.25666i	−0.303981	+	0.952678i	$0.598316\pi$
$653$	−20969.5	+	20969.5i	−1.25666	+	1.25666i	−0.952678	+	0.303981i	$0.901684\pi$
$654$		0			0
$655$	3095.55	+	10485.4i	0.184661	+	0.625495i
$656$			418.508i			0.0249085i
$657$		0			0
$658$	−123.424	−	123.424i	−0.00731241	−	0.00731241i
$659$	−24703.9			−1.46029			−0.730143	−	0.683294i	$-0.760547\pi$
$659$	−24703.9			−1.46029			−0.730143	+	0.683294i	$0.760547\pi$
$660$		0			0
$661$	23680.4			1.39343			0.696716	−	0.717347i	$-0.254644\pi$
$661$	23680.4			1.39343			0.696716	+	0.717347i	$0.254644\pi$
$662$	2230.08	+	2230.08i	0.130929	+	0.130929i
$663$		0			0
$664$			279.213i			0.0163186i
$665$	−2588.24	−	1408.35i	−0.150929	−	0.0821254i
$666$		0			0
$667$	−13036.5	+	13036.5i	−0.756785	+	0.756785i
$668$	6829.62	−	6829.62i	0.395577	−	0.395577i
$669$		0			0
$670$	4986.34	−	1472.09i	0.287521	−	0.0848833i
$671$			18679.0i			1.07466i
$672$		0			0
$673$	5649.24	+	5649.24i	0.323569	+	0.323569i	0.850135	−	0.526565i	$-0.176520\pi$
$673$	5649.24	+	5649.24i	0.323569	+	0.323569i	−0.526565	+	0.850135i	$0.676520\pi$
$674$	743.853			0.0425106
$675$		0			0
$676$	7699.45			0.438066
$677$	−13080.7	−	13080.7i	−0.742588	−	0.742588i	0.230488	−	0.973075i	$-0.425968\pi$
$677$	−13080.7	−	13080.7i	−0.742588	−	0.742588i	−0.973075	+	0.230488i	$0.925968\pi$
$678$		0			0
$679$			7656.55i			0.432741i
$680$	−6780.32	+	2001.72i	−0.382373	+	0.112886i
$681$		0			0
$682$	592.315	−	592.315i	0.0332565	−	0.0332565i
$683$	−3066.87	+	3066.87i	−0.171816	+	0.171816i	−0.787777	−	0.615961i	$-0.788768\pi$
$683$	−3066.87	+	3066.87i	−0.171816	+	0.171816i	0.615961	+	0.787777i	$0.288768\pi$
$684$		0			0
$685$	6035.63	+	3284.19i	0.336656	+	0.183186i
$686$		−	686.000i		−	0.0381802i
$687$		0			0
$688$	3029.22	+	3029.22i	0.167860	+	0.167860i
$689$	5989.65			0.331186
$690$		0			0
$691$	24106.7			1.32715			0.663575	−	0.748109i	$-0.269038\pi$
$691$	24106.7			1.32715			0.663575	+	0.748109i	$0.269038\pi$
$692$	10520.8	+	10520.8i	0.577951	+	0.577951i
$693$		0			0
$694$			2370.68i			0.129668i
$695$	−86.9003	−	294.353i	−0.00474290	−	0.0160654i
$696$		0			0
$697$	1461.91	−	1461.91i	0.0794458	−	0.0794458i
$698$	18082.8	−	18082.8i	0.980578	−	0.980578i
$699$		0			0
$700$	−3422.19	−	733.917i	−0.184781	−	0.0396278i
$701$			26863.7i			1.44740i	0.690115	+	0.723700i	$0.257560\pi$
$701$			26863.7i			1.44740i	−0.690115	+	0.723700i	$0.742440\pi$
$702$		0			0
$703$	3911.49	+	3911.49i	0.209850	+	0.209850i
$704$	3469.70			0.185751
$705$		0			0
$706$	−16882.3			−0.899961
$707$	−4003.13	−	4003.13i	−0.212947	−	0.212947i
$708$		0			0
$709$		−	18712.3i		−	0.991190i	−0.868554	−	0.495595i	$-0.834950\pi$
$709$		−	18712.3i		−	0.991190i	0.868554	−	0.495595i	$-0.165050\pi$
$710$	8189.35	−	15050.2i	0.432874	−	0.795529i
$711$		0			0
$712$	−3415.32	+	3415.32i	−0.179768	+	0.179768i
$713$	−766.458	+	766.458i	−0.0402582	+	0.0402582i
$714$		0			0
$715$	−4779.14	+	8783.02i	−0.249971	+	0.459393i
$716$			15221.2i			0.794473i
$717$		0			0
$718$	17417.4	+	17417.4i	0.905310	+	0.905310i
$719$	−36706.3			−1.90391			−0.951957	−	0.306231i	$-0.900932\pi$
$719$	−36706.3			−1.90391			−0.951957	+	0.306231i	$0.900932\pi$
$720$		0			0
$721$	−2285.38			−0.118047
$722$	−7695.39	−	7695.39i	−0.396666	−	0.396666i
$723$		0			0
$724$			4251.83i			0.218257i
$725$	13791.5	−	8920.71i	0.706490	−	0.456975i
$726$		0			0
$727$	15960.5	−	15960.5i	0.814227	−	0.814227i	−0.171038	−	0.985264i	$-0.554712\pi$
$727$	15960.5	−	15960.5i	0.814227	−	0.814227i	0.985264	+	0.171038i	$0.0547120\pi$
$728$	653.231	−	653.231i	0.0332560	−	0.0332560i
$729$		0			0
$730$	−7663.93	−	25959.7i	−0.388568	−	1.31618i
$731$		−	21163.0i		−	1.07078i
$732$		0			0
$733$	8171.60	+	8171.60i	0.411767	+	0.411767i	0.882354	−	0.470587i	$-0.155958\pi$
$733$	8171.60	+	8171.60i	0.411767	+	0.411767i	−0.470587	+	0.882354i	$0.655958\pi$
$734$	−12596.2			−0.633424
$735$		0			0
$736$	−4489.80			−0.224859
$737$	8913.32	+	8913.32i	0.445490	+	0.445490i
$738$		0			0
$739$			29569.5i			1.47190i	0.677038	+	0.735948i	$0.263263\pi$
$739$			29569.5i			1.47190i	−0.677038	+	0.735948i	$0.736737\pi$
$740$	5771.50	+	3140.47i	0.286709	+	0.156008i
$741$		0			0
$742$	−3594.35	+	3594.35i	−0.177834	+	0.177834i
$743$	−2423.44	+	2423.44i	−0.119660	+	0.119660i	−0.764401	−	0.644741i	$-0.776965\pi$
$743$	−2423.44	+	2423.44i	−0.119660	+	0.119660i	0.644741	+	0.764401i	$0.276965\pi$
$744$		0			0
$745$	19828.5	−	5853.87i	0.975116	−	0.287878i
$746$			22817.9i			1.11987i
$747$		0			0
$748$	−12120.1	−	12120.1i	−0.592455	−	0.592455i
$749$	11150.8			0.543982
$750$		0			0
$751$	−34899.7			−1.69575			−0.847874	−	0.530198i	$-0.822118\pi$
$751$	−34899.7			−1.69575			−0.847874	+	0.530198i	$0.822118\pi$
$752$	141.056	+	141.056i	0.00684014	+	0.00684014i
$753$		0			0
$754$			4335.34i			0.209395i
$755$	16310.4	−	4815.24i	0.786222	−	0.232112i
$756$		0			0
$757$	−4401.67	+	4401.67i	−0.211336	+	0.211336i	−0.804835	−	0.593499i	$-0.797746\pi$
$757$	−4401.67	+	4401.67i	−0.211336	+	0.211336i	0.593499	+	0.804835i	$0.297746\pi$
$758$	−12905.0	+	12905.0i	−0.618380	+	0.618380i
$759$		0			0
$760$	2957.99	+	1609.54i	0.141181	+	0.0768213i
$761$		−	20977.3i		−	0.999246i	−0.866243	−	0.499623i	$-0.833472\pi$
$761$		−	20977.3i		−	0.999246i	0.866243	−	0.499623i	$-0.166528\pi$
$762$		0			0
$763$	144.373	+	144.373i	0.00685012	+	0.00685012i
$764$	5716.38			0.270696
$765$		0			0
$766$	−4343.16			−0.204863
$767$	4590.24	+	4590.24i	0.216094	+	0.216094i
$768$		0			0
$769$		−	37511.1i		−	1.75902i	−0.475882	−	0.879509i	$-0.657871\pi$
$769$		−	37511.1i		−	1.75902i	0.475882	−	0.879509i	$-0.342129\pi$
$770$	−2402.71	−	8138.57i	−0.112451	−	0.380901i
$771$		0			0
$772$	11482.2	−	11482.2i	0.535302	−	0.535302i
$773$	12578.8	−	12578.8i	0.585289	−	0.585289i	−0.351063	−	0.936352i	$-0.614180\pi$
$773$	12578.8	−	12578.8i	0.585289	−	0.585289i	0.936352	+	0.351063i	$0.114180\pi$
$774$		0			0
$775$	810.849	−	524.477i	0.0375827	−	0.0243094i
$776$		−	8750.34i		−	0.404792i
$777$		0			0
$778$	19385.4	+	19385.4i	0.893318	+	0.893318i
$779$	−984.806			−0.0452944
$780$		0			0
$781$	41541.9			1.90331
$782$	15683.5	+	15683.5i	0.717188	+	0.717188i
$783$		0			0
$784$			784.000i			0.0357143i
$785$	−5165.49	+	9493.05i	−0.234859	+	0.431620i
$786$		0			0
$787$	−14130.0	+	14130.0i	−0.639999	+	0.639999i	−0.950555	−	0.310556i	$-0.899485\pi$
$787$	−14130.0	+	14130.0i	−0.639999	+	0.639999i	0.310556	+	0.950555i	$0.399485\pi$
$788$	−8725.97	+	8725.97i	−0.394479	+	0.394479i
$789$		0			0
$790$	43.4666	−	79.8821i	0.00195756	−	0.00359757i
$791$		−	10423.1i		−	0.468526i
$792$		0			0
$793$	−4019.03	−	4019.03i	−0.179974	−	0.179974i
$794$	225.327			0.0100712
$795$		0			0
$796$	−13235.6			−0.589353
$797$	21453.7	+	21453.7i	0.953485	+	0.953485i	0.998965	−	0.0454803i	$-0.0144818\pi$
$797$	21453.7	+	21453.7i	0.953485	+	0.953485i	−0.0454803	+	0.998965i	$0.514482\pi$
$798$		0			0
$799$		−	985.458i		−	0.0436333i
$800$	3911.07	+	838.762i	0.172847	+	0.0370684i
$801$		0			0
$802$	4794.12	−	4794.12i	0.211080	−	0.211080i
$803$	46404.1	−	46404.1i	2.03931	−	2.03931i
$804$		0			0
$805$	3109.11	+	10531.3i	0.136126	+	0.461094i
$806$			254.888i			0.0111390i
$807$		0			0
$808$	4575.01	+	4575.01i	0.199193	+	0.199193i
$809$	20595.0			0.895033			0.447516	−	0.894276i	$-0.352309\pi$
$809$	20595.0			0.895033			0.447516	+	0.894276i	$0.352309\pi$
$810$		0			0
$811$	35781.1			1.54925			0.774627	−	0.632419i	$-0.217938\pi$
$811$	35781.1			1.54925			0.774627	+	0.632419i	$0.217938\pi$
$812$	−2601.61	−	2601.61i	−0.112437	−	0.112437i
$813$		0			0
$814$			15930.6i			0.685954i
$815$	18363.5	+	9992.19i	0.789257	+	0.429461i
$816$		0			0
$817$	−7128.18	+	7128.18i	−0.305243	+	0.305243i
$818$	8254.37	−	8254.37i	0.352821	−	0.352821i
$819$		0			0
$820$	−1121.90	+	331.211i	−0.0477784	+	0.0141053i
$821$			45257.6i			1.92388i	0.273266	+	0.961938i	$0.411896\pi$
$821$			45257.6i			1.92388i	−0.273266	+	0.961938i	$0.588104\pi$
$822$		0			0
$823$	10482.8	+	10482.8i	0.443997	+	0.443997i	0.893353	−	0.449356i	$-0.148347\pi$
$823$	10482.8	+	10482.8i	0.443997	+	0.443997i	−0.449356	+	0.893353i	$0.648347\pi$
$824$	2611.86			0.110423
$825$		0			0
$826$	−5509.16			−0.232068
$827$	−17259.5	−	17259.5i	−0.725720	−	0.725720i	0.244044	−	0.969764i	$-0.421526\pi$
$827$	−17259.5	−	17259.5i	−0.725720	−	0.725720i	−0.969764	+	0.244044i	$0.921526\pi$
$828$		0			0
$829$			5218.53i			0.218634i	0.994007	+	0.109317i	$0.0348663\pi$
$829$			5218.53i			0.218634i	−0.994007	+	0.109317i	$0.965134\pi$
$830$	−748.488	+	220.972i	−0.0313017	+	0.00924102i
$831$		0			0
$832$	−746.549	+	746.549i	−0.0311081	+	0.0311081i
$833$	2738.63	−	2738.63i	0.113911	−	0.113911i
$834$		0			0
$835$	23713.2	+	12903.2i	0.982789	+	0.534769i
$836$			8164.67i			0.337776i
$837$		0			0
$838$	20428.5	+	20428.5i	0.842115	+	0.842115i
$839$	−16315.2			−0.671353			−0.335676	−	0.941977i	$-0.608965\pi$
$839$	−16315.2			−0.671353			−0.335676	+	0.941977i	$0.608965\pi$
$840$		0			0
$841$	−7122.72			−0.292046
$842$	−16588.1	−	16588.1i	−0.678935	−	0.678935i
$843$		0			0
$844$			1620.99i			0.0661097i
$845$	6093.42	+	20640.0i	0.248071	+	0.840279i
$846$		0			0
$847$	7959.97	−	7959.97i	0.322913	−	0.322913i
$848$	4107.83	−	4107.83i	0.166348	−	0.166348i
$849$		0			0
$850$	−10732.0	−	16591.9i	−0.433065	−	0.669525i
$851$		−	20614.2i		−	0.830372i
$852$		0			0
$853$	−9227.38	−	9227.38i	−0.370386	−	0.370386i	0.497232	−	0.867618i	$-0.334350\pi$
$853$	−9227.38	−	9227.38i	−0.370386	−	0.370386i	−0.867618	+	0.497232i	$0.834350\pi$
$854$	4823.59			0.193278
$855$		0			0
$856$	−12743.8			−0.508849
$857$	−11941.6	−	11941.6i	−0.475984	−	0.475984i	0.427860	−	0.903845i	$-0.359267\pi$
$857$	−11941.6	−	11941.6i	−0.475984	−	0.475984i	−0.903845	+	0.427860i	$0.859267\pi$
$858$		0			0
$859$			9110.68i			0.361877i	0.983494	+	0.180938i	$0.0579135\pi$
$859$			9110.68i			0.361877i	−0.983494	+	0.180938i	$0.942087\pi$
$860$	−5723.09	+	10517.8i	−0.226925	+	0.417040i
$861$		0			0
$862$	−13109.7	+	13109.7i	−0.518001	+	0.518001i
$863$	11351.0	−	11351.0i	0.447730	−	0.447730i	−0.446869	−	0.894599i	$-0.647461\pi$
$863$	11351.0	−	11351.0i	0.447730	−	0.447730i	0.894599	+	0.446869i	$0.147461\pi$
$864$		0			0
$865$	−19876.9	+	36529.5i	−0.781314	+	1.43589i
$866$			11738.2i			0.460601i
$867$		0			0
$868$	−152.957	−	152.957i	−0.00598123	−	0.00598123i
$869$	220.492			0.00860721
$870$		0			0
$871$	−3835.63			−0.149214
$872$	−164.997	−	164.997i	−0.00640770	−	0.00640770i
$873$		0			0
$874$		−	10565.1i		−	0.408891i
$875$	−740.937	−	9754.70i	−0.0286265	−	0.376879i
$876$		0			0
$877$	−29540.3	+	29540.3i	−1.13741	+	1.13741i	−0.148493	+	0.988913i	$0.547442\pi$
$877$	−29540.3	+	29540.3i	−1.13741	+	1.13741i	−0.988913	+	0.148493i	$0.952558\pi$
$878$	3136.69	−	3136.69i	0.120568	−	0.120568i
$879$		0			0
$880$	2745.95	+	9301.22i	0.105189	+	0.356300i
$881$		−	37790.6i		−	1.44517i	−0.691279	−	0.722587i	$-0.742953\pi$
$881$		−	37790.6i		−	1.44517i	0.691279	−	0.722587i	$-0.257047\pi$
$882$		0			0
$883$	3902.27	+	3902.27i	0.148722	+	0.148722i	0.777547	−	0.628825i	$-0.216464\pi$
$883$	3902.27	+	3902.27i	0.148722	+	0.148722i	−0.628825	+	0.777547i	$0.716464\pi$
$884$	5215.61			0.198439
$885$		0			0
$886$	32809.3			1.24408
$887$	−1351.33	−	1351.33i	−0.0511537	−	0.0511537i	0.681067	−	0.732221i	$-0.261516\pi$
$887$	−1351.33	−	1351.33i	−0.0511537	−	0.0511537i	−0.732221	+	0.681067i	$0.761516\pi$
$888$		0			0
$889$		−	12813.5i		−	0.483408i
$890$	−11858.4	−	6452.54i	−0.446622	−	0.243022i
$891$		0			0
$892$	−4214.06	+	4214.06i	−0.158181	+	0.158181i
$893$	−331.924	+	331.924i	−0.0124383	+	0.0124383i
$894$		0			0
$895$	−40803.5	+	12046.2i	−1.52392	+	0.449899i
$896$		−	896.000i		−	0.0334077i
$897$		0			0
$898$	6277.71	+	6277.71i	0.233285	+	0.233285i
$899$	1015.14			0.0376605
$900$		0			0
$901$	−28698.5			−1.06114
$902$	−2005.44	−	2005.44i	−0.0740287	−	0.0740287i
$903$		0			0
$904$			11912.2i			0.438266i
$905$	−11397.9	+	3364.94i	−0.418651	+	0.123596i
$906$		0			0
$907$	−19128.4	+	19128.4i	−0.700272	+	0.700272i	−0.964469	−	0.264197i	$-0.914893\pi$
$907$	−19128.4	+	19128.4i	−0.700272	+	0.700272i	0.264197	+	0.964469i	$0.414893\pi$
$908$	11847.0	−	11847.0i	0.432990	−	0.432990i
$909$		0			0
$910$	2268.09	+	1234.14i	0.0826225	+	0.0449577i
$911$		−	6574.35i		−	0.239098i	−0.992828	−	0.119549i	$-0.961855\pi$
$911$		−	6574.35i		−	0.239098i	0.992828	−	0.119549i	$-0.0381448\pi$
$912$		0			0
$913$	−1337.96	−	1337.96i	−0.0484994	−	0.0484994i
$914$	−1574.10			−0.0569656
$915$		0			0
$916$	−14570.5			−0.525572
$917$	4840.16	+	4840.16i	0.174303	+	0.174303i
$918$		0			0
$919$			19281.9i			0.692114i	0.938214	+	0.346057i	$0.112480\pi$
$919$			19281.9i			0.692114i	−0.938214	+	0.346057i	$0.887520\pi$
$920$	−3553.27	−	12035.8i	−0.127335	−	0.431314i
$921$		0			0
$922$	16541.2	−	16541.2i	0.590841	−	0.590841i
$923$	−8938.27	+	8938.27i	−0.318750	+	0.318750i
$924$		0			0
$925$	−3851.05	+	17957.1i	−0.136888	+	0.638297i
$926$			6044.80i			0.214519i
$927$		0			0
$928$	2973.27	+	2973.27i	0.105175	+	0.105175i
$929$	22184.2			0.783465			0.391733	−	0.920079i	$-0.371876\pi$
$929$	22184.2			0.783465			0.391733	+	0.920079i	$0.371876\pi$
$930$		0			0
$931$	−1844.86			−0.0649440
$932$	−14218.9	−	14218.9i	−0.499738	−	0.499738i
$933$		0			0
$934$			31967.2i			1.11991i
$935$	22898.5	−	42082.5i	0.800922	−	1.47192i
$936$		0			0
$937$	10802.9	−	10802.9i	0.376642	−	0.376642i	−0.493247	−	0.869889i	$-0.664190\pi$
$937$	10802.9	−	10802.9i	0.376642	−	0.376642i	0.869889	+	0.493247i	$0.164190\pi$
$938$	2301.74	−	2301.74i	0.0801220	−	0.0801220i
$939$		0			0
$940$	−266.496	+	489.762i	−0.00924697	+	0.0169939i
$941$		−	24244.0i		−	0.839886i	−0.907551	−	0.419943i	$-0.862050\pi$
$941$		−	24244.0i		−	0.839886i	0.907551	−	0.419943i	$-0.137950\pi$
$942$		0			0
$943$	2595.05	+	2595.05i	0.0896144	+	0.0896144i
$944$	6296.18			0.217080
$945$		0			0
$946$	−29031.4			−0.997771
$947$	2897.45	+	2897.45i	0.0994240	+	0.0994240i	0.755069	−	0.655645i	$-0.227603\pi$
$947$	2897.45	+	2897.45i	0.0994240	+	0.0994240i	−0.655645	+	0.755069i	$0.727603\pi$
$948$		0			0
$949$			19968.9i			0.683053i
$950$	−1973.72	+	9203.29i	−0.0674064	+	0.314310i
$951$		0			0
$952$	−3129.86	+	3129.86i	−0.106554	+	0.106554i
$953$	−3653.29	+	3653.29i	−0.124178	+	0.124178i	−0.766465	−	0.642287i	$-0.777986\pi$
$953$	−3653.29	+	3653.29i	−0.124178	+	0.124178i	0.642287	+	0.766465i	$0.277986\pi$
$954$		0			0
$955$	4524.00	+	15323.9i	0.153291	+	0.519236i
$956$			21500.2i			0.727369i
$957$		0			0
$958$	14336.1	+	14336.1i	0.483484	+	0.483484i
$959$	4302.12			0.144862
$960$		0			0
$961$	−29731.3			−0.997997
$962$	−3427.67	−	3427.67i	−0.114878	−	0.114878i
$963$		0			0
$964$			18875.3i			0.630634i
$965$	39867.5	+	21693.3i	1.32993	+	0.723659i
$966$		0			0
$967$	−24561.4	+	24561.4i	−0.816797	+	0.816797i	−0.985643	−	0.168845i	$-0.945996\pi$
$967$	−24561.4	+	24561.4i	−0.816797	+	0.816797i	0.168845	+	0.985643i	$0.445996\pi$
$968$	−9097.11	+	9097.11i	−0.302058	+	0.302058i
$969$		0			0
$970$	23457.1	−	6925.10i	0.776455	−	0.229228i
$971$			4087.25i			0.135083i	0.997716	+	0.0675417i	$0.0215156\pi$
$971$			4087.25i			0.135083i	−0.997716	+	0.0675417i	$0.978484\pi$
$972$		0			0
$973$	−135.876	−	135.876i	−0.00447686	−	0.00447686i
$974$	23648.4			0.777969
$975$		0			0
$976$	−5512.67			−0.180795
$977$	28701.8	+	28701.8i	0.939870	+	0.939870i	0.998292	−	0.0584221i	$-0.0186069\pi$
$977$	28701.8	+	28701.8i	0.939870	+	0.939870i	−0.0584221	+	0.998292i	$0.518607\pi$
$978$		0			0
$979$		−	32731.6i		−	1.06855i
$980$	−2101.67	+	620.465i	−0.0685055	+	0.0202245i
$981$		0			0
$982$	17340.9	−	17340.9i	0.563515	−	0.563515i
$983$	−28011.0	+	28011.0i	−0.908864	+	0.908864i	−0.996181	−	0.0873162i	$-0.972171\pi$
$983$	−28011.0	+	28011.0i	−0.908864	+	0.908864i	0.0873162	+	0.996181i	$0.472171\pi$
$984$		0			0
$985$	−30297.6	−	16485.9i	−0.980061	−	0.533285i
$986$		−	20772.1i		−	0.670912i
$987$		0			0
$988$	−1756.73	−	1756.73i	−0.0565679	−	0.0565679i
$989$	37566.7			1.20784
$990$		0			0
$991$	−17487.7			−0.560560			−0.280280	−	0.959918i	$-0.590427\pi$
$991$	−17487.7			−0.560560			−0.280280	+	0.959918i	$0.590427\pi$
$992$	174.808	+	174.808i	0.00559492	+	0.00559492i
$993$		0			0
$994$		−	10727.6i		−	0.342313i
$995$	−10474.8	−	35480.8i	−0.333742	−	1.13047i
$996$		0			0
$997$	19913.9	−	19913.9i	0.632578	−	0.632578i	−0.316136	−	0.948714i	$-0.602386\pi$
$997$	19913.9	−	19913.9i	0.632578	−	0.632578i	0.948714	+	0.316136i	$0.102386\pi$
$998$	5290.90	−	5290.90i	0.167816	−	0.167816i
$999$		0			0

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.4.m.a.323.1	yes	16
3.2	odd	2		630.4.m.b.323.8	yes	16
5.2	odd	4		630.4.m.b.197.8	yes	16
15.2	even	4	inner	630.4.m.a.197.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.4.m.a.197.1	✓	16	15.2	even	4	inner
630.4.m.a.323.1	yes	16	1.1	even	1	trivial
630.4.m.b.197.8	yes	16	5.2	odd	4
630.4.m.b.323.8	yes	16	3.2	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	630.4.m.a.323.1

Level	$630$
Weight	$4$
Character	630.323
Analytic conductor	$37.171$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$