LMFDB - Embedded newform 630.3.o.b.253.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("630.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.1662566547$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.12745506816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 23x^{4} + 1 $ x^8 + 23*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.2
Root			$-0.323042 + 0.323042i$ of defining polynomial
Character	$\chi$	$=$	630.253
Dual form			630.3.o.b.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-0.578661 - 4.96640i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-0.578661 - 4.96640i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +(5.54506 + 4.38774i) q^{10} -19.5717 q^{11} +(8.03207 + 8.03207i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(2.19659 - 2.19659i) q^{17} +8.25097i q^{19} +(-9.93280 + 1.15732i) q^{20} +(19.5717 - 19.5717i) q^{22} +(17.9068 + 17.9068i) q^{23} +(-24.3303 + 5.74773i) q^{25} -16.0641 q^{26} +(3.74166 + 3.74166i) q^{28} +19.7495i q^{29} +30.0043 q^{31} +(4.00000 - 4.00000i) q^{32} +4.39319i q^{34} +(10.3739 + 8.20871i) q^{35} +(37.2346 - 37.2346i) q^{37} +(-8.25097 - 8.25097i) q^{38} +(8.77548 - 11.0901i) q^{40} +80.8620 q^{41} +(-13.6780 - 13.6780i) q^{43} +39.1434i q^{44} -35.8136 q^{46} +(8.17549 - 8.17549i) q^{47} -7.00000i q^{49} +(18.5826 - 30.0780i) q^{50} +(16.0641 - 16.0641i) q^{52} +(38.8560 + 38.8560i) q^{53} +(11.3254 + 97.2008i) q^{55} -7.48331 q^{56} +(-19.7495 - 19.7495i) q^{58} +74.3773i q^{59} +97.8414 q^{61} +(-30.0043 + 30.0043i) q^{62} +8.00000i q^{64} +(35.2426 - 44.5383i) q^{65} +(-67.1712 + 67.1712i) q^{67} +(-4.39319 - 4.39319i) q^{68} +(-18.5826 + 2.16515i) q^{70} +13.3793 q^{71} +(-48.2738 - 48.2738i) q^{73} +74.4691i q^{74} +16.5019 q^{76} +(36.6153 - 36.6153i) q^{77} +40.2089i q^{79} +(2.31464 + 19.8656i) q^{80} +(-80.8620 + 80.8620i) q^{82} +(-34.4137 - 34.4137i) q^{83} +(-12.1803 - 9.63809i) q^{85} +27.3560 q^{86} +(-39.1434 - 39.1434i) q^{88} +157.941i q^{89} -30.0532 q^{91} +(35.8136 - 35.8136i) q^{92} +16.3510i q^{94} +(40.9776 - 4.77451i) q^{95} +(-73.2856 + 73.2856i) q^{97} +(7.00000 + 7.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 16 * q^8	$ 8 q - 8 q^{2} + 16 q^{8} + 8 q^{11} + 8 q^{13} - 32 q^{16} + 32 q^{17} - 8 q^{22} + 40 q^{23} - 48 q^{25} - 16 q^{26} + 144 q^{31} + 32 q^{32} + 28 q^{35} + 160 q^{37} + 320 q^{41} - 32 q^{43} - 80 q^{46} + 144 q^{47} + 112 q^{50} + 16 q^{52} + 200 q^{53} + 184 q^{55} - 64 q^{58} + 288 q^{61} - 144 q^{62} - 24 q^{65} + 80 q^{67} - 64 q^{68} - 112 q^{70} + 280 q^{71} + 312 q^{73} + 56 q^{77} - 320 q^{82} + 320 q^{83} + 80 q^{85} + 64 q^{86} + 16 q^{88} + 80 q^{92} + 472 q^{95} - 24 q^{97} + 56 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 16 * q^8 + 8 * q^11 + 8 * q^13 - 32 * q^16 + 32 * q^17 - 8 * q^22 + 40 * q^23 - 48 * q^25 - 16 * q^26 + 144 * q^31 + 32 * q^32 + 28 * q^35 + 160 * q^37 + 320 * q^41 - 32 * q^43 - 80 * q^46 + 144 * q^47 + 112 * q^50 + 16 * q^52 + 200 * q^53 + 184 * q^55 - 64 * q^58 + 288 * q^61 - 144 * q^62 - 24 * q^65 + 80 * q^67 - 64 * q^68 - 112 * q^70 + 280 * q^71 + 312 * q^73 + 56 * q^77 - 320 * q^82 + 320 * q^83 + 80 * q^85 + 64 * q^86 + 16 * q^88 + 80 * q^92 + 472 * q^95 - 24 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	0.500000i
$5$	−0.578661	−	4.96640i	−0.115732	−	0.993280i
$5$	−0.578661	−	4.96640i	−0.115732	−	0.993280i
$6$		0			0
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$		0			0
$10$	5.54506	+	4.38774i	0.554506	+	0.438774i
$11$	−19.5717			−1.77924			−0.889622	−	0.456698i	$-0.849032\pi$
$11$	−19.5717			−1.77924			−0.889622	+	0.456698i	$0.849032\pi$
$12$		0			0
$13$	8.03207	+	8.03207i	0.617851	+	0.617851i	0.944980	−	0.327129i	$-0.106081\pi$
$13$	8.03207	+	8.03207i	0.617851	+	0.617851i	−0.327129	+	0.944980i	$0.606081\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	2.19659	−	2.19659i	0.129211	−	0.129211i	−0.639543	−	0.768755i	$-0.720877\pi$
$17$	2.19659	−	2.19659i	0.129211	−	0.129211i	0.768755	+	0.639543i	$0.220877\pi$
$18$		0			0
$19$			8.25097i			0.434261i	0.976143	+	0.217131i	$0.0696698\pi$
$19$			8.25097i			0.434261i	−0.976143	+	0.217131i	$0.930330\pi$
$20$	−9.93280	+	1.15732i	−0.496640	+	0.0578661i
$21$		0			0
$22$	19.5717	−	19.5717i	0.889622	−	0.889622i
$23$	17.9068	+	17.9068i	0.778557	+	0.778557i	0.979585	−	0.201028i	$-0.0644284\pi$
$23$	17.9068	+	17.9068i	0.778557	+	0.778557i	−0.201028	+	0.979585i	$0.564428\pi$
$24$		0			0
$25$	−24.3303	+	5.74773i	−0.973212	+	0.229909i
$26$	−16.0641			−0.617851
$27$		0			0
$28$	3.74166	+	3.74166i	0.133631	+	0.133631i
$29$			19.7495i			0.681017i	0.940241	+	0.340508i	$0.110599\pi$
$29$			19.7495i			0.681017i	−0.940241	+	0.340508i	$0.889401\pi$
$30$		0			0
$31$	30.0043			0.967881			0.483940	−	0.875101i	$-0.339205\pi$
$31$	30.0043			0.967881			0.483940	+	0.875101i	$0.339205\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$		0			0
$34$			4.39319i			0.129211i
$35$	10.3739	+	8.20871i	0.296396	+	0.234535i
$36$		0			0
$37$	37.2346	−	37.2346i	1.00634	−	1.00634i	0.00635971	−	0.999980i	$-0.497976\pi$
$37$	37.2346	−	37.2346i	1.00634	−	1.00634i	0.999980	−	0.00635971i	$-0.00202437\pi$
$38$	−8.25097	−	8.25097i	−0.217131	−	0.217131i
$39$		0			0
$40$	8.77548	−	11.0901i	0.219387	−	0.277253i
$41$	80.8620			1.97224			0.986122	−	0.166023i	$-0.0530928\pi$
$41$	80.8620			1.97224			0.986122	+	0.166023i	$0.0530928\pi$
$42$		0			0
$43$	−13.6780	−	13.6780i	−0.318093	−	0.318093i	0.529942	−	0.848034i	$-0.322214\pi$
$43$	−13.6780	−	13.6780i	−0.318093	−	0.318093i	−0.848034	+	0.529942i	$0.822214\pi$
$44$			39.1434i			0.889622i
$45$		0			0
$46$	−35.8136			−0.778557
$47$	8.17549	−	8.17549i	0.173947	−	0.173947i	−0.614764	−	0.788711i	$-0.710749\pi$
$47$	8.17549	−	8.17549i	0.173947	−	0.173947i	0.788711	+	0.614764i	$0.210749\pi$
$48$		0			0
$49$		−	7.00000i		−	0.142857i
$50$	18.5826	−	30.0780i	0.371652	−	0.601561i
$51$		0			0
$52$	16.0641	−	16.0641i	0.308926	−	0.308926i
$53$	38.8560	+	38.8560i	0.733132	+	0.733132i	0.971239	−	0.238107i	$-0.0765268\pi$
$53$	38.8560	+	38.8560i	0.733132	+	0.733132i	−0.238107	+	0.971239i	$0.576527\pi$
$54$		0			0
$55$	11.3254	+	97.2008i	0.205916	+	1.76729i
$56$	−7.48331			−0.133631
$57$		0			0
$58$	−19.7495	−	19.7495i	−0.340508	−	0.340508i
$59$			74.3773i			1.26063i	0.776339	+	0.630316i	$0.217075\pi$
$59$			74.3773i			1.26063i	−0.776339	+	0.630316i	$0.782925\pi$
$60$		0			0
$61$	97.8414			1.60396			0.801979	−	0.597352i	$-0.203781\pi$
$61$	97.8414			1.60396			0.801979	+	0.597352i	$0.203781\pi$
$62$	−30.0043	+	30.0043i	−0.483940	+	0.483940i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	35.2426	−	44.5383i	0.542194	−	0.685205i
$66$		0			0
$67$	−67.1712	+	67.1712i	−1.00255	+	1.00255i	−0.00255792	+	0.999997i	$0.500814\pi$
$67$	−67.1712	+	67.1712i	−1.00255	+	1.00255i	−0.999997	+	0.00255792i	$0.999186\pi$
$68$	−4.39319	−	4.39319i	−0.0646057	−	0.0646057i
$69$		0			0
$70$	−18.5826	+	2.16515i	−0.265465	+	0.0309307i
$71$	13.3793			0.188441			0.0942203	−	0.995551i	$-0.469964\pi$
$71$	13.3793			0.188441			0.0942203	+	0.995551i	$0.469964\pi$
$72$		0			0
$73$	−48.2738	−	48.2738i	−0.661285	−	0.661285i	0.294398	−	0.955683i	$-0.404881\pi$
$73$	−48.2738	−	48.2738i	−0.661285	−	0.661285i	−0.955683	+	0.294398i	$0.904881\pi$
$74$			74.4691i			1.00634i
$75$		0			0
$76$	16.5019			0.217131
$77$	36.6153	−	36.6153i	0.475523	−	0.475523i
$78$		0			0
$79$			40.2089i			0.508973i	0.967076	+	0.254487i	$0.0819065\pi$
$79$			40.2089i			0.508973i	−0.967076	+	0.254487i	$0.918094\pi$
$80$	2.31464	+	19.8656i	0.0289331	+	0.248320i
$81$		0			0
$82$	−80.8620	+	80.8620i	−0.986122	+	0.986122i
$83$	−34.4137	−	34.4137i	−0.414623	−	0.414623i	0.468722	−	0.883346i	$-0.344715\pi$
$83$	−34.4137	−	34.4137i	−0.414623	−	0.414623i	−0.883346	+	0.468722i	$0.844715\pi$
$84$		0			0
$85$	−12.1803	−	9.63809i	−0.143297	−	0.113389i
$86$	27.3560			0.318093
$87$		0			0
$88$	−39.1434	−	39.1434i	−0.444811	−	0.444811i
$89$			157.941i			1.77462i	0.461176	+	0.887309i	$0.347428\pi$
$89$			157.941i			1.77462i	−0.461176	+	0.887309i	$0.652572\pi$
$90$		0			0
$91$	−30.0532			−0.330255
$92$	35.8136	−	35.8136i	0.389278	−	0.389278i
$93$		0			0
$94$			16.3510i			0.173947i
$95$	40.9776	−	4.77451i	0.431343	−	0.0502580i
$96$		0			0
$97$	−73.2856	+	73.2856i	−0.755522	+	0.755522i	−0.975504	−	0.219982i	$-0.929400\pi$
$97$	−73.2856	+	73.2856i	−0.755522	+	0.755522i	0.219982	+	0.975504i	$0.429400\pi$
$98$	7.00000	+	7.00000i	0.0714286	+	0.0714286i
$99$		0			0
$100$	11.4955	+	48.6606i	0.114955	+	0.486606i
$101$	−121.236			−1.20035			−0.600176	−	0.799868i	$-0.704903\pi$
$101$	−121.236			−1.20035			−0.600176	+	0.799868i	$0.704903\pi$
$102$		0			0
$103$	23.5614	+	23.5614i	0.228751	+	0.228751i	0.812171	−	0.583419i	$-0.198286\pi$
$103$	23.5614	+	23.5614i	0.228751	+	0.228751i	−0.583419	+	0.812171i	$0.698286\pi$
$104$			32.1283i			0.308926i
$105$		0			0
$106$	−77.7120			−0.733132
$107$	14.4314	−	14.4314i	0.134873	−	0.134873i	−0.636447	−	0.771320i	$-0.719597\pi$
$107$	14.4314	−	14.4314i	0.134873	−	0.134873i	0.771320	+	0.636447i	$0.219597\pi$
$108$		0			0
$109$			34.6374i			0.317775i	0.987297	+	0.158887i	$0.0507907\pi$
$109$			34.6374i			0.317775i	−0.987297	+	0.158887i	$0.949209\pi$
$110$	−108.526	−	85.8755i	−0.986602	−	0.780686i
$111$		0			0
$112$	7.48331	−	7.48331i	0.0668153	−	0.0668153i
$113$	19.9430	+	19.9430i	0.176486	+	0.176486i	0.789822	−	0.613336i	$-0.210173\pi$
$113$	19.9430	+	19.9430i	0.176486	+	0.176486i	−0.613336	+	0.789822i	$0.710173\pi$
$114$		0			0
$115$	78.5704	−	99.2944i	0.683221	−	0.863429i
$116$	39.4990			0.340508
$117$		0			0
$118$	−74.3773	−	74.3773i	−0.630316	−	0.630316i
$119$			8.21890i			0.0690664i
$120$		0			0
$121$	262.051			2.16571
$122$	−97.8414	+	97.8414i	−0.801979	+	0.801979i
$123$		0			0
$124$		−	60.0086i		−	0.483940i
$125$	42.6245	+	117.508i	0.340996	+	0.940065i
$126$		0			0
$127$	13.8950	−	13.8950i	0.109410	−	0.109410i	−0.650283	−	0.759692i	$-0.725350\pi$
$127$	13.8950	−	13.8950i	0.109410	−	0.109410i	0.759692	+	0.650283i	$0.225350\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	9.29569	+	79.7809i	0.0715053	+	0.613700i
$131$	−161.799			−1.23511			−0.617554	−	0.786528i	$-0.711876\pi$
$131$	−161.799			−1.23511			−0.617554	+	0.786528i	$0.711876\pi$
$132$		0			0
$133$	−15.4361	−	15.4361i	−0.116061	−	0.116061i
$134$		−	134.342i		−	1.00255i
$135$		0			0
$136$	8.78638			0.0646057
$137$	35.8023	−	35.8023i	0.261331	−	0.261331i	−0.564264	−	0.825595i	$-0.690840\pi$
$137$	35.8023	−	35.8023i	0.261331	−	0.261331i	0.825595	+	0.564264i	$0.190840\pi$
$138$		0			0
$139$			89.7460i			0.645654i	0.946458	+	0.322827i	$0.104633\pi$
$139$			89.7460i			0.645654i	−0.946458	+	0.322827i	$0.895367\pi$
$140$	16.4174	−	20.7477i	0.117267	−	0.148198i
$141$		0			0
$142$	−13.3793	+	13.3793i	−0.0942203	+	0.0942203i
$143$	−157.201	−	157.201i	−1.09931	−	1.09931i
$144$		0			0
$145$	98.0839	−	11.4283i	0.676441	−	0.0788156i
$146$	96.5477			0.661285
$147$		0			0
$148$	−74.4691	−	74.4691i	−0.503170	−	0.503170i
$149$			293.641i			1.97075i	0.170408	+	0.985374i	$0.445491\pi$
$149$			293.641i			1.97075i	−0.170408	+	0.985374i	$0.554509\pi$
$150$		0			0
$151$	231.725			1.53461			0.767303	−	0.641285i	$-0.221598\pi$
$151$	231.725			1.53461			0.767303	+	0.641285i	$0.221598\pi$
$152$	−16.5019	+	16.5019i	−0.108565	+	0.108565i
$153$		0			0
$154$			73.2305i			0.475523i
$155$	−17.3623	−	149.013i	−0.112015	−	0.961377i
$156$		0			0
$157$	62.8204	−	62.8204i	0.400130	−	0.400130i	−0.478149	−	0.878279i	$-0.658692\pi$
$157$	62.8204	−	62.8204i	0.400130	−	0.400130i	0.878279	+	0.478149i	$0.158692\pi$
$158$	−40.2089	−	40.2089i	−0.254487	−	0.254487i
$159$		0			0
$160$	−22.1803	−	17.5510i	−0.138627	−	0.109694i
$161$	−67.0011			−0.416156
$162$		0			0
$163$	97.0117	+	97.0117i	0.595164	+	0.595164i	0.939022	−	0.343858i	$-0.111734\pi$
$163$	97.0117	+	97.0117i	0.595164	+	0.595164i	−0.343858	+	0.939022i	$0.611734\pi$
$164$		−	161.724i		−	0.986122i
$165$		0			0
$166$	68.8275			0.414623
$167$	135.497	−	135.497i	0.811362	−	0.811362i	−0.173476	−	0.984838i	$-0.555500\pi$
$167$	135.497	−	135.497i	0.811362	−	0.811362i	0.984838	+	0.173476i	$0.0554999\pi$
$168$		0			0
$169$		−	39.9718i		−	0.236520i
$170$	21.8183	−	2.54217i	0.128343	−	0.0149539i
$171$		0			0
$172$	−27.3560	+	27.3560i	−0.159046	+	0.159046i
$173$	66.1772	+	66.1772i	0.382527	+	0.382527i	0.872012	−	0.489485i	$-0.162815\pi$
$173$	66.1772	+	66.1772i	0.382527	+	0.382527i	−0.489485	+	0.872012i	$0.662815\pi$
$174$		0			0
$175$	34.7648	−	56.2708i	0.198656	−	0.321548i
$176$	78.2867			0.444811
$177$		0			0
$178$	−157.941	−	157.941i	−0.887309	−	0.887309i
$179$		−	274.045i		−	1.53098i	−0.643450	−	0.765488i	$-0.722497\pi$
$179$		−	274.045i		−	1.53098i	0.643450	−	0.765488i	$-0.277503\pi$
$180$		0			0
$181$	−36.0493			−0.199167			−0.0995836	−	0.995029i	$-0.531751\pi$
$181$	−36.0493			−0.199167			−0.0995836	+	0.995029i	$0.531751\pi$
$182$	30.0532	−	30.0532i	0.165128	−	0.165128i
$183$		0			0
$184$			71.6272i			0.389278i
$185$	−206.468	−	163.376i	−1.11604	−	0.883111i
$186$		0			0
$187$	−42.9910	+	42.9910i	−0.229899	+	0.229899i
$188$	−16.3510	−	16.3510i	−0.0869733	−	0.0869733i
$189$		0			0
$190$	−36.2031	+	45.7521i	−0.190543	+	0.240801i
$191$	−133.194			−0.697352			−0.348676	−	0.937243i	$-0.613369\pi$
$191$	−133.194			−0.697352			−0.348676	+	0.937243i	$0.613369\pi$
$192$		0			0
$193$	−236.565	−	236.565i	−1.22573	−	1.22573i	−0.965566	−	0.260160i	$-0.916225\pi$
$193$	−236.565	−	236.565i	−1.22573	−	1.22573i	−0.260160	−	0.965566i	$-0.583775\pi$
$194$		−	146.571i		−	0.755522i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	203.011	−	203.011i	1.03051	−	1.03051i	0.0309909	−	0.999520i	$-0.490134\pi$
$197$	203.011	−	203.011i	1.03051	−	1.03051i	0.999520	−	0.0309909i	$-0.00986629\pi$
$198$		0			0
$199$			102.932i			0.517244i	0.965979	+	0.258622i	$0.0832684\pi$
$199$			102.932i			0.517244i	−0.965979	+	0.258622i	$0.916732\pi$
$200$	−60.1561	−	37.1652i	−0.300780	−	0.185826i
$201$		0			0
$202$	121.236	−	121.236i	0.600176	−	0.600176i
$203$	−36.9479	−	36.9479i	−0.182009	−	0.182009i
$204$		0			0
$205$	−46.7917	−	401.593i	−0.228252	−	1.95899i
$206$	−47.1228			−0.228751
$207$		0			0
$208$	−32.1283	−	32.1283i	−0.154463	−	0.154463i
$209$		−	161.485i		−	0.772657i
$210$		0			0
$211$	−216.191			−1.02460			−0.512301	−	0.858806i	$-0.671207\pi$
$211$	−216.191			−1.02460			−0.512301	+	0.858806i	$0.671207\pi$
$212$	77.7120	−	77.7120i	0.366566	−	0.366566i
$213$		0			0
$214$			28.8629i			0.134873i
$215$	−60.0154	+	75.8453i	−0.279142	+	0.352769i
$216$		0			0
$217$	−56.1329	+	56.1329i	−0.258677	+	0.258677i
$218$	−34.6374	−	34.6374i	−0.158887	−	0.158887i
$219$		0			0
$220$	194.402	−	22.6507i	0.883644	−	0.102958i
$221$	35.2864			0.159667
$222$		0			0
$223$	143.253	+	143.253i	0.642390	+	0.642390i	0.951142	−	0.308752i	$-0.0999114\pi$
$223$	143.253	+	143.253i	0.642390	+	0.642390i	−0.308752	+	0.951142i	$0.599911\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	−39.8859			−0.176486
$227$	−226.766	+	226.766i	−0.998969	+	0.998969i	−0.999999	−	0.00103000i	$-0.999672\pi$
$227$	−226.766	+	226.766i	−0.998969	+	0.998969i	0.00103000	+	0.999999i	$0.499672\pi$
$228$		0			0
$229$		−	48.9068i		−	0.213567i	−0.994282	−	0.106783i	$-0.965945\pi$
$229$		−	48.9068i		−	0.213567i	0.994282	−	0.106783i	$-0.0340552\pi$
$230$	20.7239	+	177.865i	0.0901041	+	0.773325i
$231$		0			0
$232$	−39.4990	+	39.4990i	−0.170254	+	0.170254i
$233$	122.967	+	122.967i	0.527755	+	0.527755i	0.919902	−	0.392147i	$-0.128268\pi$
$233$	122.967	+	122.967i	0.527755	+	0.527755i	−0.392147	+	0.919902i	$0.628268\pi$
$234$		0			0
$235$	−45.3336	−	35.8719i	−0.192909	−	0.152647i
$236$	148.755			0.630316
$237$		0			0
$238$	−8.21890	−	8.21890i	−0.0345332	−	0.0345332i
$239$			359.392i			1.50373i	0.659317	+	0.751865i	$0.270846\pi$
$239$			359.392i			1.50373i	−0.659317	+	0.751865i	$0.729154\pi$
$240$		0			0
$241$	−96.4510			−0.400212			−0.200106	−	0.979774i	$-0.564129\pi$
$241$	−96.4510			−0.400212			−0.200106	+	0.979774i	$0.564129\pi$
$242$	−262.051	+	262.051i	−1.08285	+	1.08285i
$243$		0			0
$244$		−	195.683i		−	0.801979i
$245$	−34.7648	+	4.05063i	−0.141897	+	0.0165332i
$246$		0			0
$247$	−66.2723	+	66.2723i	−0.268309	+	0.268309i
$248$	60.0086	+	60.0086i	0.241970	+	0.241970i
$249$		0			0
$250$	−160.133	−	74.8836i	−0.640530	−	0.299534i
$251$	290.502			1.15738			0.578690	−	0.815548i	$-0.303564\pi$
$251$	290.502			1.15738			0.578690	+	0.815548i	$0.303564\pi$
$252$		0			0
$253$	−350.466	−	350.466i	−1.38524	−	1.38524i
$254$			27.7901i			0.109410i
$255$		0			0
$256$	16.0000			0.0625000
$257$	225.583	−	225.583i	0.877755	−	0.877755i	−0.115547	−	0.993302i	$-0.536862\pi$
$257$	225.583	−	225.583i	0.877755	−	0.877755i	0.993302	+	0.115547i	$0.0368620\pi$
$258$		0			0
$259$			139.319i			0.537911i
$260$	−89.0766	−	70.4852i	−0.342602	−	0.271097i
$261$		0			0
$262$	161.799	−	161.799i	0.617554	−	0.617554i
$263$	−245.931	−	245.931i	−0.935097	−	0.935097i	0.0629214	−	0.998018i	$-0.479958\pi$
$263$	−245.931	−	245.931i	−0.935097	−	0.935097i	−0.998018	+	0.0629214i	$0.979958\pi$
$264$		0			0
$265$	170.490	−	215.459i	0.643359	−	0.813053i
$266$	30.8723			0.116061
$267$		0			0
$268$	134.342	+	134.342i	0.501277	+	0.501277i
$269$		−	306.198i		−	1.13828i	−0.822240	−	0.569142i	$-0.807276\pi$
$269$		−	306.198i		−	1.13828i	0.822240	−	0.569142i	$-0.192724\pi$
$270$		0			0
$271$	−370.284			−1.36636			−0.683180	−	0.730250i	$-0.739404\pi$
$271$	−370.284			−1.36636			−0.683180	+	0.730250i	$0.739404\pi$
$272$	−8.78638	+	8.78638i	−0.0323029	+	0.0323029i
$273$		0			0
$274$			71.6046i			0.261331i
$275$	476.185	−	112.493i	1.73158	−	0.409064i
$276$		0			0
$277$	−161.817	+	161.817i	−0.584176	+	0.584176i	−0.936048	−	0.351872i	$-0.885545\pi$
$277$	−161.817	+	161.817i	−0.584176	+	0.584176i	0.351872	+	0.936048i	$0.385545\pi$
$278$	−89.7460	−	89.7460i	−0.322827	−	0.322827i
$279$		0			0
$280$	4.33030	+	37.1652i	0.0154654	+	0.132733i
$281$	235.757			0.838994			0.419497	−	0.907757i	$-0.362207\pi$
$281$	235.757			0.838994			0.419497	+	0.907757i	$0.362207\pi$
$282$		0			0
$283$	2.26750	+	2.26750i	0.00801238	+	0.00801238i	0.711102	−	0.703089i	$-0.248197\pi$
$283$	2.26750	+	2.26750i	0.00801238	+	0.00801238i	−0.703089	+	0.711102i	$0.748197\pi$
$284$		−	26.7586i		−	0.0942203i
$285$		0			0
$286$	314.402			1.09931
$287$	−151.279	+	151.279i	−0.527104	+	0.527104i
$288$		0			0
$289$			279.350i			0.966609i
$290$	−86.6556	+	109.512i	−0.298813	+	0.377628i
$291$		0			0
$292$	−96.5477	+	96.5477i	−0.330643	+	0.330643i
$293$	−199.403	−	199.403i	−0.680556	−	0.680556i	0.279570	−	0.960125i	$-0.409808\pi$
$293$	−199.403	−	199.403i	−0.680556	−	0.680556i	−0.960125	+	0.279570i	$0.909808\pi$
$294$		0			0
$295$	369.387	−	43.0392i	1.25216	−	0.145896i
$296$	148.938			0.503170
$297$		0			0
$298$	−293.641	−	293.641i	−0.985374	−	0.985374i
$299$			287.657i			0.962065i
$300$		0			0
$301$	51.1783			0.170028
$302$	−231.725	+	231.725i	−0.767303	+	0.767303i
$303$		0			0
$304$		−	33.0039i		−	0.108565i
$305$	−56.6170	−	485.920i	−0.185630	−	1.59318i
$306$		0			0
$307$	−381.514	+	381.514i	−1.24272	+	1.24272i	−0.283847	+	0.958870i	$0.591611\pi$
$307$	−381.514	+	381.514i	−1.24272	+	1.24272i	−0.958870	+	0.283847i	$0.908389\pi$
$308$	−73.2305	−	73.2305i	−0.237761	−	0.237761i
$309$		0			0
$310$	166.376	+	131.651i	0.536696	+	0.424681i
$311$	388.702			1.24985			0.624923	−	0.780686i	$-0.285130\pi$
$311$	388.702			1.24985			0.624923	+	0.780686i	$0.285130\pi$
$312$		0			0
$313$	−50.5806	−	50.5806i	−0.161599	−	0.161599i	0.621675	−	0.783275i	$-0.286452\pi$
$313$	−50.5806	−	50.5806i	−0.161599	−	0.161599i	−0.783275	+	0.621675i	$0.786452\pi$
$314$			125.641i			0.400130i
$315$		0			0
$316$	80.4178			0.254487
$317$	−54.9675	+	54.9675i	−0.173399	+	0.173399i	−0.788471	−	0.615072i	$-0.789127\pi$
$317$	−54.9675	+	54.9675i	−0.173399	+	0.173399i	0.615072	+	0.788471i	$0.289127\pi$
$318$		0			0
$319$		−	386.531i		−	1.21169i
$320$	39.7312	−	4.62929i	0.124160	−	0.0144665i
$321$		0			0
$322$	67.0011	−	67.0011i	0.208078	−	0.208078i
$323$	18.1240	+	18.1240i	0.0561115	+	0.0561115i
$324$		0			0
$325$	−241.589	−	149.256i	−0.743350	−	0.459251i
$326$	−194.023			−0.595164
$327$		0			0
$328$	161.724	+	161.724i	0.493061	+	0.493061i
$329$			30.5899i			0.0929783i
$330$		0			0
$331$	195.576			0.590865			0.295433	−	0.955364i	$-0.404536\pi$
$331$	195.576			0.590865			0.295433	+	0.955364i	$0.404536\pi$
$332$	−68.8275	+	68.8275i	−0.207312	+	0.207312i
$333$		0			0
$334$			270.995i			0.811362i
$335$	372.468	+	294.730i	1.11185	+	0.879790i
$336$		0			0
$337$	420.206	−	420.206i	1.24690	−	1.24690i	0.289822	−	0.957081i	$-0.406404\pi$
$337$	420.206	−	420.206i	1.24690	−	1.24690i	0.957081	−	0.289822i	$-0.0935961\pi$
$338$	39.9718	+	39.9718i	0.118260	+	0.118260i
$339$		0			0
$340$	−19.2762	+	24.3605i	−0.0566946	+	0.0716485i
$341$	−587.235			−1.72210
$342$		0			0
$343$	13.0958	+	13.0958i	0.0381802	+	0.0381802i
$344$		−	54.7119i		−	0.159046i
$345$		0			0
$346$	−132.354			−0.382527
$347$	−21.4182	+	21.4182i	−0.0617238	+	0.0617238i	−0.737295	−	0.675571i	$-0.763897\pi$
$347$	−21.4182	+	21.4182i	−0.0617238	+	0.0617238i	0.675571	+	0.737295i	$0.263897\pi$
$348$		0			0
$349$			244.156i			0.699588i	0.936827	+	0.349794i	$0.113748\pi$
$349$			244.156i			0.699588i	−0.936827	+	0.349794i	$0.886252\pi$
$350$	21.5060	+	91.0357i	0.0614458	+	0.260102i
$351$		0			0
$352$	−78.2867	+	78.2867i	−0.222405	+	0.222405i
$353$	−228.969	−	228.969i	−0.648637	−	0.648637i	0.304026	−	0.952664i	$-0.401669\pi$
$353$	−228.969	−	228.969i	−0.648637	−	0.648637i	−0.952664	+	0.304026i	$0.901669\pi$
$354$		0			0
$355$	−7.74207	−	66.4469i	−0.0218087	−	0.187174i
$356$	315.882			0.887309
$357$		0			0
$358$	274.045	+	274.045i	0.765488	+	0.765488i
$359$			165.483i			0.460956i	0.973078	+	0.230478i	$0.0740290\pi$
$359$			165.483i			0.460956i	−0.973078	+	0.230478i	$0.925971\pi$
$360$		0			0
$361$	292.922			0.811417
$362$	36.0493	−	36.0493i	0.0995836	−	0.0995836i
$363$		0			0
$364$			60.1065i			0.165128i
$365$	−211.813	+	267.681i	−0.580310	+	0.733374i
$366$		0			0
$367$	−225.601	+	225.601i	−0.614715	+	0.614715i	−0.944171	−	0.329456i	$-0.893135\pi$
$367$	−225.601	+	225.601i	−0.614715	+	0.614715i	0.329456	+	0.944171i	$0.393135\pi$
$368$	−71.6272	−	71.6272i	−0.194639	−	0.194639i
$369$		0			0
$370$	369.844	−	43.0924i	0.999577	−	0.116466i
$371$	−145.386			−0.391876
$372$		0			0
$373$	279.406	+	279.406i	0.749078	+	0.749078i	0.974306	−	0.225228i	$-0.0723128\pi$
$373$	279.406	+	279.406i	0.749078	+	0.749078i	−0.225228	+	0.974306i	$0.572313\pi$
$374$		−	85.9821i		−	0.229899i
$375$		0			0
$376$	32.7020			0.0869733
$377$	−158.629	+	158.629i	−0.420767	+	0.420767i
$378$		0			0
$379$			746.946i			1.97083i	0.170158	+	0.985417i	$0.445572\pi$
$379$			746.946i			1.97083i	−0.170158	+	0.985417i	$0.554428\pi$
$380$	−9.54903	−	81.9553i	−0.0251290	−	0.215672i
$381$		0			0
$382$	133.194	−	133.194i	0.348676	−	0.348676i
$383$	−359.176	−	359.176i	−0.937797	−	0.937797i	0.0603788	−	0.998176i	$-0.480769\pi$
$383$	−359.176	−	359.176i	−0.937797	−	0.937797i	−0.998176	+	0.0603788i	$0.980769\pi$
$384$		0			0
$385$	−203.034	−	160.658i	−0.527361	−	0.417294i
$386$	473.130			1.22573
$387$		0			0
$388$	146.571	+	146.571i	0.377761	+	0.377761i
$389$			476.719i			1.22550i	0.790278	+	0.612749i	$0.209936\pi$
$389$			476.719i			1.22550i	−0.790278	+	0.612749i	$0.790064\pi$
$390$		0			0
$391$	78.6680			0.201197
$392$	14.0000	−	14.0000i	0.0357143	−	0.0357143i
$393$		0			0
$394$			406.021i			1.03051i
$395$	199.693	−	23.2673i	0.505553	−	0.0589046i
$396$		0			0
$397$	−137.315	+	137.315i	−0.345883	+	0.345883i	−0.858573	−	0.512691i	$-0.828649\pi$
$397$	−137.315	+	137.315i	−0.345883	+	0.345883i	0.512691	+	0.858573i	$0.328649\pi$
$398$	−102.932	−	102.932i	−0.258622	−	0.258622i
$399$		0			0
$400$	97.3212	−	22.9909i	0.243303	−	0.0574773i
$401$	691.294			1.72392			0.861962	−	0.506973i	$-0.169235\pi$
$401$	691.294			1.72392			0.861962	+	0.506973i	$0.169235\pi$
$402$		0			0
$403$	240.997	+	240.997i	0.598006	+	0.598006i
$404$			242.471i			0.600176i
$405$		0			0
$406$	73.8958			0.182009
$407$	−728.743	+	728.743i	−1.79052	+	1.79052i
$408$		0			0
$409$			146.348i			0.357818i	0.983866	+	0.178909i	$0.0572568\pi$
$409$			146.348i			0.357818i	−0.983866	+	0.178909i	$0.942743\pi$
$410$	448.385	+	354.801i	1.09362	+	0.865369i
$411$		0			0
$412$	47.1228	−	47.1228i	0.114376	−	0.114376i
$413$	−139.147	−	139.147i	−0.336918	−	0.336918i
$414$		0			0
$415$	−150.999	+	190.826i	−0.363852	+	0.459823i
$416$	64.2565			0.154463
$417$		0			0
$418$	161.485	+	161.485i	0.386329	+	0.386329i
$419$			19.1814i			0.0457790i	0.999738	+	0.0228895i	$0.00728659\pi$
$419$			19.1814i			0.0457790i	−0.999738	+	0.0228895i	$0.992713\pi$
$420$		0			0
$421$	−343.060			−0.814870			−0.407435	−	0.913234i	$-0.633577\pi$
$421$	−343.060			−0.814870			−0.407435	+	0.913234i	$0.633577\pi$
$422$	216.191	−	216.191i	0.512301	−	0.512301i
$423$		0			0
$424$			155.424i			0.366566i
$425$	−40.8184	+	66.0692i	−0.0960432	+	0.155457i
$426$		0			0
$427$	−183.045	+	183.045i	−0.428676	+	0.428676i
$428$	−28.8629	−	28.8629i	−0.0674366	−	0.0674366i
$429$		0			0
$430$	−15.8298	−	135.861i	−0.0368136	−	0.315955i
$431$	−251.794			−0.584210			−0.292105	−	0.956386i	$-0.594356\pi$
$431$	−251.794			−0.584210			−0.292105	+	0.956386i	$0.594356\pi$
$432$		0			0
$433$	−125.195	−	125.195i	−0.289133	−	0.289133i	0.547604	−	0.836737i	$-0.315540\pi$
$433$	−125.195	−	125.195i	−0.289133	−	0.289133i	−0.836737	+	0.547604i	$0.815540\pi$
$434$		−	112.266i		−	0.258677i
$435$		0			0
$436$	69.2749			0.158887
$437$	−147.749	+	147.749i	−0.338097	+	0.338097i
$438$		0			0
$439$		−	37.5609i		−	0.0855601i	−0.999085	−	0.0427801i	$-0.986379\pi$
$439$		−	37.5609i		−	0.0855601i	0.999085	−	0.0427801i	$-0.0136215\pi$
$440$	−171.751	+	217.052i	−0.390343	+	0.493301i
$441$		0			0
$442$	−35.2864	+	35.2864i	−0.0798334	+	0.0798334i
$443$	583.967	+	583.967i	1.31821	+	1.31821i	0.915192	+	0.403019i	$0.132039\pi$
$443$	583.967	+	583.967i	1.31821	+	1.31821i	0.403019	+	0.915192i	$0.367961\pi$
$444$		0			0
$445$	784.398	−	91.3943i	1.76269	−	0.205380i
$446$	−286.506			−0.642390
$447$		0			0
$448$	−14.9666	−	14.9666i	−0.0334077	−	0.0334077i
$449$		−	595.556i		−	1.32640i	−0.748440	−	0.663202i	$-0.769197\pi$
$449$		−	595.556i		−	1.32640i	0.748440	−	0.663202i	$-0.230803\pi$
$450$		0			0
$451$	−1582.61			−3.50910
$452$	39.8859	−	39.8859i	0.0882432	−	0.0882432i
$453$		0			0
$454$		−	453.532i		−	0.998969i
$455$	17.3906	+	149.256i	0.0382212	+	0.328036i
$456$		0			0
$457$	300.505	−	300.505i	0.657560	−	0.657560i	−0.297242	−	0.954802i	$-0.596067\pi$
$457$	300.505	−	300.505i	0.657560	−	0.657560i	0.954802	+	0.297242i	$0.0960668\pi$
$458$	48.9068	+	48.9068i	0.106783	+	0.106783i
$459$		0			0
$460$	−198.589	−	157.141i	−0.431715	−	0.341611i
$461$	−565.424			−1.22652			−0.613258	−	0.789883i	$-0.710141\pi$
$461$	−565.424			−1.22652			−0.613258	+	0.789883i	$0.710141\pi$
$462$		0			0
$463$	−247.619	−	247.619i	−0.534815	−	0.534815i	0.387186	−	0.922001i	$-0.373447\pi$
$463$	−247.619	−	247.619i	−0.534815	−	0.534815i	−0.922001	+	0.387186i	$0.873447\pi$
$464$		−	78.9979i		−	0.170254i
$465$		0			0
$466$	−245.934			−0.527755
$467$	310.936	−	310.936i	0.665816	−	0.665816i	−0.290929	−	0.956745i	$-0.593964\pi$
$467$	310.936	−	310.936i	0.665816	−	0.665816i	0.956745	+	0.290929i	$0.0939643\pi$
$468$		0			0
$469$		−	251.331i		−	0.535888i
$470$	81.2055	−	9.46167i	0.172778	−	0.0201312i
$471$		0			0
$472$	−148.755	+	148.755i	−0.315158	+	0.315158i
$473$	267.701	+	267.701i	0.565964	+	0.565964i
$474$		0			0
$475$	−47.4243	−	200.749i	−0.0998407	−	0.422629i
$476$	16.4378			0.0345332
$477$		0			0
$478$	−359.392	−	359.392i	−0.751865	−	0.751865i
$479$			337.547i			0.704692i	0.935870	+	0.352346i	$0.114616\pi$
$479$			337.547i			0.704692i	−0.935870	+	0.352346i	$0.885384\pi$
$480$		0			0
$481$	598.141			1.24354
$482$	96.4510	−	96.4510i	0.200106	−	0.200106i
$483$		0			0
$484$		−	524.101i		−	1.08285i
$485$	406.373	+	321.558i	0.837883	+	0.663007i
$486$		0			0
$487$	153.784	−	153.784i	0.315778	−	0.315778i	−0.531365	−	0.847143i	$-0.678321\pi$
$487$	153.784	−	153.784i	0.315778	−	0.315778i	0.847143	+	0.531365i	$0.178321\pi$
$488$	195.683	+	195.683i	0.400989	+	0.400989i
$489$		0			0
$490$	30.7142	−	38.8154i	0.0626820	−	0.0792152i
$491$	−320.910			−0.653585			−0.326792	−	0.945096i	$-0.605968\pi$
$491$	−320.910			−0.653585			−0.326792	+	0.945096i	$0.605968\pi$
$492$		0			0
$493$	43.3816	+	43.3816i	0.0879951	+	0.0879951i
$494$		−	132.545i		−	0.268309i
$495$		0			0
$496$	−120.017			−0.241970
$497$	−25.0304	+	25.0304i	−0.0503629	+	0.0503629i
$498$		0			0
$499$		−	284.928i		−	0.570997i	−0.958379	−	0.285499i	$-0.907841\pi$
$499$		−	284.928i		−	0.570997i	0.958379	−	0.285499i	$-0.0921592\pi$
$500$	235.016	−	85.2490i	0.470032	−	0.170498i
$501$		0			0
$502$	−290.502	+	290.502i	−0.578690	+	0.578690i
$503$	548.564	+	548.564i	1.09058	+	1.09058i	0.995466	+	0.0951181i	$0.0303229\pi$
$503$	548.564	+	548.564i	1.09058	+	1.09058i	0.0951181	+	0.995466i	$0.469677\pi$
$504$		0			0
$505$	70.1543	+	602.105i	0.138919	+	1.19229i
$506$	700.933			1.38524
$507$		0			0
$508$	−27.7901	−	27.7901i	−0.0547049	−	0.0547049i
$509$		−	558.480i		−	1.09721i	−0.836081	−	0.548606i	$-0.815159\pi$
$509$		−	558.480i		−	1.09721i	0.836081	−	0.548606i	$-0.184841\pi$
$510$		0			0
$511$	180.624			0.353472
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			451.166i			0.877755i
$515$	103.381	−	130.649i	0.200740	−	0.253688i
$516$		0			0
$517$	−160.008	+	160.008i	−0.309493	+	0.309493i
$518$	−139.319	−	139.319i	−0.268956	−	0.268956i
$519$		0			0
$520$	159.562	−	18.5914i	0.306850	−	0.0357526i
$521$	−455.328			−0.873949			−0.436975	−	0.899474i	$-0.643950\pi$
$521$	−455.328			−0.873949			−0.436975	+	0.899474i	$0.643950\pi$
$522$		0			0
$523$	37.6920	+	37.6920i	0.0720687	+	0.0720687i	0.742222	−	0.670154i	$-0.233772\pi$
$523$	37.6920	+	37.6920i	0.0720687	+	0.0720687i	−0.670154	+	0.742222i	$0.733772\pi$
$524$			323.598i			0.617554i
$525$		0			0
$526$	491.861			0.935097
$527$	65.9073	−	65.9073i	0.125061	−	0.125061i
$528$		0			0
$529$			112.308i			0.212302i
$530$	44.9689	+	385.949i	0.0848470	+	0.728206i
$531$		0			0
$532$	−30.8723	+	30.8723i	−0.0580306	+	0.0580306i
$533$	649.489	+	649.489i	1.21855	+	1.21855i
$534$		0			0
$535$	−80.0233	−	63.3214i	−0.149576	−	0.118358i
$536$	−268.685			−0.501277
$537$		0			0
$538$	306.198	+	306.198i	0.569142	+	0.569142i
$539$			137.002i			0.254178i
$540$		0			0
$541$	122.456			0.226352			0.113176	−	0.993575i	$-0.463898\pi$
$541$	122.456			0.226352			0.113176	+	0.993575i	$0.463898\pi$
$542$	370.284	−	370.284i	0.683180	−	0.683180i
$543$		0			0
$544$		−	17.5728i		−	0.0323029i
$545$	172.023	−	20.0433i	0.315639	−	0.0367768i
$546$		0			0
$547$	630.975	−	630.975i	1.15352	−	1.15352i	0.167676	−	0.985842i	$-0.446374\pi$
$547$	630.975	−	630.975i	1.15352	−	1.15352i	0.985842	−	0.167676i	$-0.0536264\pi$
$548$	−71.6046	−	71.6046i	−0.130665	−	0.130665i
$549$		0			0
$550$	−363.692	+	588.678i	−0.661259	+	1.07032i
$551$	−162.952			−0.295739
$552$		0			0
$553$	−75.2239	−	75.2239i	−0.136029	−	0.136029i
$554$		−	323.634i		−	0.584176i
$555$		0			0
$556$	179.492			0.322827
$557$	−89.6207	+	89.6207i	−0.160899	+	0.160899i	−0.782965	−	0.622066i	$-0.786294\pi$
$557$	−89.6207	+	89.6207i	−0.160899	+	0.160899i	0.622066	+	0.782965i	$0.286294\pi$
$558$		0			0
$559$		−	219.725i		−	0.393068i
$560$	−41.4955	−	32.8348i	−0.0740990	−	0.0586337i
$561$		0			0
$562$	−235.757	+	235.757i	−0.419497	+	0.419497i
$563$	268.774	+	268.774i	0.477396	+	0.477396i	0.904298	−	0.426902i	$-0.140395\pi$
$563$	268.774	+	268.774i	0.477396	+	0.477396i	−0.426902	+	0.904298i	$0.640395\pi$
$564$		0			0
$565$	87.5046	−	110.585i	0.154875	−	0.195726i
$566$	−4.53501			−0.00801238
$567$		0			0
$568$	26.7586	+	26.7586i	0.0471102	+	0.0471102i
$569$		−	373.315i		−	0.656089i	−0.944662	−	0.328045i	$-0.893610\pi$
$569$		−	373.315i		−	0.656089i	0.944662	−	0.328045i	$-0.106390\pi$
$570$		0			0
$571$	93.3963			0.163566			0.0817831	−	0.996650i	$-0.473939\pi$
$571$	93.3963			0.163566			0.0817831	+	0.996650i	$0.473939\pi$
$572$	−314.402	+	314.402i	−0.549654	+	0.549654i
$573$		0			0
$574$		−	302.558i		−	0.527104i
$575$	−538.602	−	332.755i	−0.936698	−	0.578704i
$576$		0			0
$577$	−356.401	+	356.401i	−0.617679	+	0.617679i	−0.944936	−	0.327257i	$-0.893876\pi$
$577$	−356.401	+	356.401i	−0.617679	+	0.617679i	0.327257	+	0.944936i	$0.393876\pi$
$578$	−279.350	−	279.350i	−0.483304	−	0.483304i
$579$		0			0
$580$	−22.8565	−	196.168i	−0.0394078	−	0.338220i
$581$	128.764			0.221626
$582$		0			0
$583$	−760.478	−	760.478i	−1.30442	−	1.30442i
$584$		−	193.095i		−	0.330643i
$585$		0			0
$586$	398.806			0.680556
$587$	213.286	−	213.286i	0.363349	−	0.363349i	−0.501695	−	0.865044i	$-0.667290\pi$
$587$	213.286	−	213.286i	0.363349	−	0.363349i	0.865044	+	0.501695i	$0.167290\pi$
$588$		0			0
$589$			247.565i			0.420313i
$590$	−326.348	+	412.427i	−0.553133	+	0.699028i
$591$		0			0
$592$	−148.938	+	148.938i	−0.251585	+	0.251585i
$593$	−118.172	−	118.172i	−0.199279	−	0.199279i	0.600412	−	0.799691i	$-0.295003\pi$
$593$	−118.172	−	118.172i	−0.199279	−	0.199279i	−0.799691	+	0.600412i	$0.795003\pi$
$594$		0			0
$595$	40.8184	−	4.75596i	0.0686023	−	0.00799321i
$596$	587.283			0.985374
$597$		0			0
$598$	−287.657	−	287.657i	−0.481032	−	0.481032i
$599$			210.890i			0.352071i	0.984384	+	0.176035i	$0.0563273\pi$
$599$			210.890i			0.352071i	−0.984384	+	0.176035i	$0.943673\pi$
$600$		0			0
$601$	−238.143			−0.396244			−0.198122	−	0.980177i	$-0.563484\pi$
$601$	−238.143			−0.396244			−0.198122	+	0.980177i	$0.563484\pi$
$602$	−51.1783	+	51.1783i	−0.0850138	+	0.0850138i
$603$		0			0
$604$		−	463.451i		−	0.767303i
$605$	−151.639	−	1301.45i	−0.250642	−	2.15116i
$606$		0			0
$607$	617.412	−	617.412i	1.01715	−	1.01715i	0.0173035	−	0.999850i	$-0.494492\pi$
$607$	617.412	−	617.412i	1.01715	−	1.01715i	0.999850	−	0.0173035i	$-0.00550814\pi$
$608$	33.0039	+	33.0039i	0.0542827	+	0.0542827i
$609$		0			0
$610$	542.537	+	429.303i	0.889405	+	0.703775i
$611$	131.332			0.214946
$612$		0			0
$613$	−765.627	−	765.627i	−1.24898	−	1.24898i	−0.956169	−	0.292816i	$-0.905408\pi$
$613$	−765.627	−	765.627i	−1.24898	−	1.24898i	−0.292816	−	0.956169i	$-0.594592\pi$
$614$		−	763.028i		−	1.24272i
$615$		0			0
$616$	146.461			0.237761
$617$	−42.0185	+	42.0185i	−0.0681012	+	0.0681012i	−0.740337	−	0.672236i	$-0.765334\pi$
$617$	−42.0185	+	42.0185i	−0.0681012	+	0.0681012i	0.672236	+	0.740337i	$0.265334\pi$
$618$		0			0
$619$			564.440i			0.911858i	0.890016	+	0.455929i	$0.150693\pi$
$619$			564.440i			0.911858i	−0.890016	+	0.455929i	$0.849307\pi$
$620$	−298.027	+	34.7247i	−0.480689	+	0.0560075i
$621$		0			0
$622$	−388.702	+	388.702i	−0.624923	+	0.624923i
$623$	−295.480	−	295.480i	−0.474287	−	0.474287i
$624$		0			0
$625$	558.927	−	279.688i	0.894284	−	0.447501i
$626$	101.161			0.161599
$627$		0			0
$628$	−125.641	−	125.641i	−0.200065	−	0.200065i
$629$		−	163.578i		−	0.260061i
$630$		0			0
$631$	498.286			0.789676			0.394838	−	0.918751i	$-0.370801\pi$
$631$	498.286			0.789676			0.394838	+	0.918751i	$0.370801\pi$
$632$	−80.4178	+	80.4178i	−0.127243	+	0.127243i
$633$		0			0
$634$		−	109.935i		−	0.173399i
$635$	−77.0489	−	60.9678i	−0.121337	−	0.0960123i
$636$		0			0
$637$	56.2245	−	56.2245i	0.0882645	−	0.0882645i
$638$	386.531	+	386.531i	0.605847	+	0.605847i
$639$		0			0
$640$	−35.1019	+	44.3605i	−0.0548468	+	0.0693133i
$641$	−145.183			−0.226494			−0.113247	−	0.993567i	$-0.536125\pi$
$641$	−145.183			−0.226494			−0.113247	+	0.993567i	$0.536125\pi$
$642$		0			0
$643$	646.724	+	646.724i	1.00579	+	1.00579i	0.999983	+	0.00580843i	$0.00184889\pi$
$643$	646.724	+	646.724i	1.00579	+	1.00579i	0.00580843	+	0.999983i	$0.498151\pi$
$644$			134.002i			0.208078i
$645$		0			0
$646$	−36.2481			−0.0561115
$647$	−190.030	+	190.030i	−0.293710	+	0.293710i	−0.838544	−	0.544834i	$-0.816593\pi$
$647$	−190.030	+	190.030i	−0.293710	+	0.293710i	0.544834	+	0.838544i	$0.316593\pi$
$648$		0			0
$649$		−	1455.69i		−	2.24297i
$650$	390.845	−	92.3322i	0.601300	−	0.142050i
$651$		0			0
$652$	194.023	−	194.023i	0.297582	−	0.297582i
$653$	−416.099	−	416.099i	−0.637212	−	0.637212i	0.312655	−	0.949867i	$-0.398782\pi$
$653$	−416.099	−	416.099i	−0.637212	−	0.637212i	−0.949867	+	0.312655i	$0.898782\pi$
$654$		0			0
$655$	93.6269	+	803.560i	0.142942	+	1.22681i
$656$	−323.448			−0.493061
$657$		0			0
$658$	−30.5899	−	30.5899i	−0.0464892	−	0.0464892i
$659$		−	615.296i		−	0.933682i	−0.884341	−	0.466841i	$-0.845392\pi$
$659$		−	615.296i		−	0.933682i	0.884341	−	0.466841i	$-0.154608\pi$
$660$		0			0
$661$	−455.425			−0.688994			−0.344497	−	0.938787i	$-0.611951\pi$
$661$	−455.425			−0.688994			−0.344497	+	0.938787i	$0.611951\pi$
$662$	−195.576	+	195.576i	−0.295433	+	0.295433i
$663$		0			0
$664$		−	137.655i		−	0.207312i
$665$	−67.7298	+	85.5944i	−0.101849	+	0.128713i
$666$		0			0
$667$	−353.650	+	353.650i	−0.530210	+	0.530210i
$668$	−270.995	−	270.995i	−0.405681	−	0.405681i
$669$		0			0
$670$	−667.198	+	77.7387i	−0.995818	+	0.116028i
$671$	−1914.92			−2.85383
$672$		0			0
$673$	156.161	+	156.161i	0.232037	+	0.232037i	0.813543	−	0.581505i	$-0.197536\pi$
$673$	156.161	+	156.161i	0.232037	+	0.232037i	−0.581505	+	0.813543i	$0.697536\pi$
$674$			840.412i			1.24690i
$675$		0			0
$676$	−79.9437			−0.118260
$677$	567.709	−	567.709i	0.838566	−	0.838566i	−0.150104	−	0.988670i	$-0.547961\pi$
$677$	567.709	−	567.709i	0.838566	−	0.838566i	0.988670	+	0.150104i	$0.0479610\pi$
$678$		0			0
$679$		−	274.210i		−	0.403843i
$680$	−5.08433	−	43.6367i	−0.00747696	−	0.0641716i
$681$		0			0
$682$	587.235	−	587.235i	0.861048	−	0.861048i
$683$	124.523	+	124.523i	0.182317	+	0.182317i	0.792365	−	0.610047i	$-0.208850\pi$
$683$	124.523	+	124.523i	0.182317	+	0.182317i	−0.610047	+	0.792365i	$0.708850\pi$
$684$		0			0
$685$	−198.526	−	157.091i	−0.289819	−	0.229330i
$686$	−26.1916			−0.0381802
$687$		0			0
$688$	54.7119	+	54.7119i	0.0795231	+	0.0795231i
$689$			624.188i			0.905934i
$690$		0			0
$691$	−1214.16			−1.75710			−0.878551	−	0.477648i	$-0.841489\pi$
$691$	−1214.16			−1.75710			−0.878551	+	0.477648i	$0.841489\pi$
$692$	132.354	−	132.354i	0.191263	−	0.191263i
$693$		0			0
$694$		−	42.8363i		−	0.0617238i
$695$	445.715	−	51.9325i	0.641316	−	0.0747230i
$696$		0			0
$697$	177.621	−	177.621i	0.254836	−	0.254836i
$698$	−244.156	−	244.156i	−0.349794	−	0.349794i
$699$		0			0
$700$	−112.542	−	69.5296i	−0.160774	−	0.0993280i
$701$	788.147			1.12432			0.562159	−	0.827029i	$-0.309971\pi$
$701$	788.147			1.12432			0.562159	+	0.827029i	$0.309971\pi$
$702$		0			0
$703$	307.221	+	307.221i	0.437014	+	0.437014i
$704$		−	156.573i		−	0.222405i
$705$		0			0
$706$	457.938			0.648637
$707$	226.811	−	226.811i	0.320808	−	0.320808i
$708$		0			0
$709$			1230.75i			1.73589i	0.496660	+	0.867945i	$0.334560\pi$
$709$			1230.75i			1.73589i	−0.496660	+	0.867945i	$0.665440\pi$
$710$	74.1890	+	58.7049i	0.104492	+	0.0826829i
$711$		0			0
$712$	−315.882	+	315.882i	−0.443654	+	0.443654i
$713$	537.281	+	537.281i	0.753550	+	0.753550i
$714$		0			0
$715$	−689.757	+	871.690i	−0.964696	+	1.21915i
$716$	−548.090			−0.765488
$717$		0			0
$718$	−165.483	−	165.483i	−0.230478	−	0.230478i
$719$		−	251.624i		−	0.349963i	−0.984572	−	0.174982i	$-0.944013\pi$
$719$		−	251.624i		−	0.349963i	0.984572	−	0.174982i	$-0.0559866\pi$
$720$		0			0
$721$	−88.1587			−0.122273
$722$	−292.922	+	292.922i	−0.405708	+	0.405708i
$723$		0			0
$724$			72.0985i			0.0995836i
$725$	−113.515	−	480.511i	−0.156572	−	0.662774i
$726$		0			0
$727$	254.322	−	254.322i	0.349824	−	0.349824i	−0.510220	−	0.860044i	$-0.670436\pi$
$727$	254.322	−	254.322i	0.349824	−	0.349824i	0.860044	+	0.510220i	$0.170436\pi$
$728$	−60.1065	−	60.1065i	−0.0825638	−	0.0825638i
$729$		0			0
$730$	−55.8684	−	479.495i	−0.0765320	−	0.656842i
$731$	−60.0899			−0.0822024
$732$		0			0
$733$	−27.6831	−	27.6831i	−0.0377668	−	0.0377668i	0.687971	−	0.725738i	$-0.258502\pi$
$733$	−27.6831	−	27.6831i	−0.0377668	−	0.0377668i	−0.725738	+	0.687971i	$0.758502\pi$
$734$		−	451.201i		−	0.614715i
$735$		0			0
$736$	143.254			0.194639
$737$	1314.65	−	1314.65i	1.78379	−	1.78379i
$738$		0			0
$739$		−	434.621i		−	0.588121i	−0.955787	−	0.294060i	$-0.904993\pi$
$739$		−	434.621i		−	0.588121i	0.955787	−	0.294060i	$-0.0950066\pi$
$740$	−326.751	+	412.936i	−0.441556	+	0.558022i
$741$		0			0
$742$	145.386	−	145.386i	0.195938	−	0.195938i
$743$	−126.704	−	126.704i	−0.170530	−	0.170530i	0.616682	−	0.787212i	$-0.288476\pi$
$743$	−126.704	−	126.704i	−0.170530	−	0.170530i	−0.787212	+	0.616682i	$0.788476\pi$
$744$		0			0
$745$	1458.34	−	169.919i	1.95750	−	0.228079i
$746$	−558.812			−0.749078
$747$		0			0
$748$	85.9821	+	85.9821i	0.114949	+	0.114949i
$749$			53.9975i			0.0720928i
$750$		0			0
$751$	735.755			0.979701			0.489851	−	0.871806i	$-0.337051\pi$
$751$	735.755			0.979701			0.489851	+	0.871806i	$0.337051\pi$
$752$	−32.7020	+	32.7020i	−0.0434866	+	0.0434866i
$753$		0			0
$754$		−	317.258i		−	0.420767i
$755$	−134.090	−	1150.84i	−0.177603	−	1.52429i
$756$		0			0
$757$	−255.322	+	255.322i	−0.337281	+	0.337281i	−0.855343	−	0.518062i	$-0.826654\pi$
$757$	−255.322	+	255.322i	−0.337281	+	0.337281i	0.518062	+	0.855343i	$0.326654\pi$
$758$	−746.946	−	746.946i	−0.985417	−	0.985417i
$759$		0			0
$760$	91.5043	+	72.4062i	0.120400	+	0.0952713i
$761$	−783.231			−1.02921			−0.514606	−	0.857427i	$-0.672062\pi$
$761$	−783.231			−1.02921			−0.514606	+	0.857427i	$0.672062\pi$
$762$		0			0
$763$	−64.8007	−	64.8007i	−0.0849289	−	0.0849289i
$764$			266.389i			0.348676i
$765$		0			0
$766$	718.352			0.937797
$767$	−597.403	+	597.403i	−0.778883	+	0.778883i
$768$		0			0
$769$			186.068i			0.241961i	0.992655	+	0.120980i	$0.0386038\pi$
$769$			186.068i			0.241961i	−0.992655	+	0.120980i	$0.961396\pi$
$770$	363.692	−	42.3757i	0.472328	−	0.0550333i
$771$		0			0
$772$	−473.130	+	473.130i	−0.612863	+	0.612863i
$773$	333.576	+	333.576i	0.431534	+	0.431534i	0.889150	−	0.457616i	$-0.151297\pi$
$773$	333.576	+	333.576i	0.431534	+	0.431534i	−0.457616	+	0.889150i	$0.651297\pi$
$774$		0			0
$775$	−730.014	+	172.457i	−0.941953	+	0.222525i
$776$	−293.143			−0.377761
$777$		0			0
$778$	−476.719	−	476.719i	−0.612749	−	0.612749i
$779$			667.190i			0.856469i
$780$		0			0
$781$	−261.855			−0.335282
$782$	−78.6680	+	78.6680i	−0.100598	+	0.100598i
$783$		0			0
$784$			28.0000i			0.0357143i
$785$	−348.343	−	275.639i	−0.443749	−	0.351133i
$786$		0			0
$787$	431.752	−	431.752i	0.548605	−	0.548605i	−0.377432	−	0.926037i	$-0.623193\pi$
$787$	431.752	−	431.752i	0.548605	−	0.548605i	0.926037	+	0.377432i	$0.123193\pi$
$788$	−406.021	−	406.021i	−0.515255	−	0.515255i
$789$		0			0
$790$	−176.426	+	222.961i	−0.223324	+	0.282229i
$791$	−74.6197			−0.0943360
$792$		0			0
$793$	785.869	+	785.869i	0.991007	+	0.991007i
$794$		−	274.631i		−	0.345883i
$795$		0			0
$796$	205.863			0.258622
$797$	67.9296	−	67.9296i	0.0852316	−	0.0852316i	−0.663206	−	0.748437i	$-0.730805\pi$
$797$	67.9296	−	67.9296i	0.0852316	−	0.0852316i	0.748437	+	0.663206i	$0.230805\pi$
$798$		0			0
$799$		−	35.9165i		−	0.0449518i
$800$	−74.3303	+	120.312i	−0.0929129	+	0.150390i
$801$		0			0
$802$	−691.294	+	691.294i	−0.861962	+	0.861962i
$803$	944.800	+	944.800i	1.17659	+	1.17659i
$804$		0			0
$805$	38.7710	+	332.755i	0.0481627	+	0.413360i
$806$	−481.993			−0.598006
$807$		0			0
$808$	−242.471	−	242.471i	−0.300088	−	0.300088i
$809$			375.281i			0.463883i	0.972730	+	0.231941i	$0.0745078\pi$
$809$			375.281i			0.463883i	−0.972730	+	0.231941i	$0.925492\pi$
$810$		0			0
$811$	283.093			0.349066			0.174533	−	0.984651i	$-0.444158\pi$
$811$	283.093			0.349066			0.174533	+	0.984651i	$0.444158\pi$
$812$	−73.8958	+	73.8958i	−0.0910047	+	0.0910047i
$813$		0			0
$814$		−	1457.49i		−	1.79052i
$815$	425.662	−	537.936i	0.522285	−	0.660044i
$816$		0			0
$817$	112.857	−	112.857i	0.138135	−	0.138135i
$818$	−146.348	−	146.348i	−0.178909	−	0.178909i
$819$		0			0
$820$	−803.186	+	93.5834i	−0.979496	+	0.114126i
$821$	−1325.60			−1.61462			−0.807308	−	0.590131i	$-0.799076\pi$
$821$	−1325.60			−1.61462			−0.807308	+	0.590131i	$0.799076\pi$
$822$		0			0
$823$	794.494	+	794.494i	0.965363	+	0.965363i	0.999420	−	0.0340566i	$-0.0108427\pi$
$823$	794.494	+	794.494i	0.965363	+	0.965363i	−0.0340566	+	0.999420i	$0.510843\pi$
$824$			94.2456i			0.114376i
$825$		0			0
$826$	278.294			0.336918
$827$	−361.128	+	361.128i	−0.436672	+	0.436672i	−0.890890	−	0.454218i	$-0.849919\pi$
$827$	−361.128	+	361.128i	−0.436672	+	0.436672i	0.454218	+	0.890890i	$0.349919\pi$
$828$		0			0
$829$		−	195.726i		−	0.236099i	−0.993008	−	0.118049i	$-0.962336\pi$
$829$		−	195.726i		−	0.236099i	0.993008	−	0.118049i	$-0.0376641\pi$
$830$	−39.8278	−	341.825i	−0.0479853	−	0.411837i
$831$		0			0
$832$	−64.2565	+	64.2565i	−0.0772314	+	0.0772314i
$833$	−15.3762	−	15.3762i	−0.0184588	−	0.0184588i
$834$		0			0
$835$	−751.342	−	594.528i	−0.899811	−	0.712009i
$836$	−322.971			−0.386329
$837$		0			0
$838$	−19.1814	−	19.1814i	−0.0228895	−	0.0228895i
$839$		−	10.5401i		−	0.0125627i	−0.999980	−	0.00628133i	$-0.998001\pi$
$839$		−	10.5401i		−	0.0125627i	0.999980	−	0.00628133i	$-0.00199942\pi$
$840$		0			0
$841$	450.958			0.536216
$842$	343.060	−	343.060i	0.407435	−	0.407435i
$843$		0			0
$844$			432.382i			0.512301i
$845$	−198.516	+	23.1302i	−0.234931	+	0.0273730i
$846$		0			0
$847$	−490.252	+	490.252i	−0.578810	+	0.578810i
$848$	−155.424	−	155.424i	−0.183283	−	0.183283i
$849$		0			0
$850$	−25.2508	−	106.888i	−0.0297069	−	0.125750i
$851$	1333.50			1.56699
$852$		0			0
$853$	−950.696	−	950.696i	−1.11453	−	1.11453i	−0.992530	−	0.122002i	$-0.961068\pi$
$853$	−950.696	−	950.696i	−1.11453	−	1.11453i	−0.122002	−	0.992530i	$-0.538932\pi$
$854$		−	366.089i		−	0.428676i
$855$		0			0
$856$	57.7258			0.0674366
$857$	−628.392	+	628.392i	−0.733246	+	0.733246i	−0.971261	−	0.238016i	$-0.923503\pi$
$857$	−628.392	+	628.392i	−0.733246	+	0.733246i	0.238016	+	0.971261i	$0.423503\pi$
$858$		0			0
$859$			832.998i			0.969730i	0.874589	+	0.484865i	$0.161131\pi$
$859$			832.998i			0.969730i	−0.874589	+	0.484865i	$0.838869\pi$
$860$	151.691	+	120.031i	0.176384	+	0.139571i
$861$		0			0
$862$	251.794	−	251.794i	0.292105	−	0.292105i
$863$	−802.913	−	802.913i	−0.930374	−	0.930374i	0.0673547	−	0.997729i	$-0.478544\pi$
$863$	−802.913	−	802.913i	−0.930374	−	0.930374i	−0.997729	+	0.0673547i	$0.978544\pi$
$864$		0			0
$865$	290.368	−	366.957i	0.335686	−	0.424227i
$866$	250.389			0.289133
$867$		0			0
$868$	112.266	+	112.266i	0.129339	+	0.129339i
$869$		−	786.955i		−	0.905587i
$870$		0			0
$871$	−1079.05			−1.23886
$872$	−69.2749	+	69.2749i	−0.0794437	+	0.0794437i
$873$		0			0
$874$		−	295.497i		−	0.338097i
$875$	−299.581	−	140.094i	−0.342378	−	0.160108i
$876$		0			0
$877$	483.085	−	483.085i	0.550838	−	0.550838i	−0.375845	−	0.926683i	$-0.622647\pi$
$877$	483.085	−	483.085i	0.550838	−	0.550838i	0.926683	+	0.375845i	$0.122647\pi$
$878$	37.5609	+	37.5609i	0.0427801	+	0.0427801i
$879$		0			0
$880$	−45.3015	−	388.803i	−0.0514790	−	0.441822i
$881$	1190.88			1.35174			0.675868	−	0.737023i	$-0.263769\pi$
$881$	1190.88			1.35174			0.675868	+	0.737023i	$0.263769\pi$
$882$		0			0
$883$	−52.9133	−	52.9133i	−0.0599245	−	0.0599245i	0.676509	−	0.736434i	$-0.263492\pi$
$883$	−52.9133	−	52.9133i	−0.0599245	−	0.0599245i	−0.736434	+	0.676509i	$0.763492\pi$
$884$		−	70.5727i		−	0.0798334i
$885$		0			0
$886$	−1167.93			−1.31821
$887$	393.366	−	393.366i	0.443479	−	0.443479i	−0.449700	−	0.893180i	$-0.648469\pi$
$887$	393.366	−	393.366i	0.443479	−	0.443479i	0.893180	+	0.449700i	$0.148469\pi$
$888$		0			0
$889$			51.9905i			0.0584820i
$890$	−693.004	+	875.793i	−0.778656	+	0.984037i
$891$		0			0
$892$	286.506	−	286.506i	0.321195	−	0.321195i
$893$	67.4557	+	67.4557i	0.0755383	+	0.0755383i
$894$		0			0
$895$	−1361.02	+	158.579i	−1.52069	+	0.177183i
$896$	29.9333			0.0334077
$897$		0			0
$898$	595.556	+	595.556i	0.663202	+	0.663202i
$899$			592.570i			0.659143i
$900$		0			0
$901$	170.702			0.189458
$902$	1582.61	−	1582.61i	1.75455	−	1.75455i
$903$		0			0
$904$			79.7719i			0.0882432i
$905$	20.8603	+	179.035i	0.0230501	+	0.197829i
$906$		0			0
$907$	715.081	−	715.081i	0.788403	−	0.788403i	−0.192829	−	0.981232i	$-0.561766\pi$
$907$	715.081	−	715.081i	0.788403	−	0.788403i	0.981232	+	0.192829i	$0.0617664\pi$
$908$	453.532	+	453.532i	0.499485	+	0.499485i
$909$		0			0
$910$	−166.647	−	131.866i	−0.183129	−	0.144908i
$911$	1440.70			1.58145			0.790727	−	0.612169i	$-0.209703\pi$
$911$	1440.70			1.58145			0.790727	+	0.612169i	$0.209703\pi$
$912$		0			0
$913$	673.535	+	673.535i	0.737716	+	0.737716i
$914$			601.010i			0.657560i
$915$		0			0
$916$	−97.8136			−0.106783
$917$	302.699	−	302.699i	0.330097	−	0.330097i
$918$		0			0
$919$			139.961i			0.152297i	0.997096	+	0.0761485i	$0.0242623\pi$
$919$			139.961i			0.152297i	−0.997096	+	0.0761485i	$0.975738\pi$
$920$	355.730	−	41.4479i	0.386663	−	0.0450521i
$921$		0			0
$922$	565.424	−	565.424i	0.613258	−	0.613258i
$923$	107.463	+	107.463i	0.116428	+	0.116428i
$924$		0			0
$925$	−691.914	+	1119.94i	−0.748015	+	1.21075i
$926$	495.239			0.534815
$927$		0			0
$928$	78.9979	+	78.9979i	0.0851271	+	0.0851271i
$929$			268.303i			0.288808i	0.989519	+	0.144404i	$0.0461265\pi$
$929$			268.303i			0.288808i	−0.989519	+	0.144404i	$0.953874\pi$
$930$		0			0
$931$	57.7568			0.0620374
$932$	245.934	−	245.934i	0.263878	−	0.263878i
$933$		0			0
$934$			621.872i			0.665816i
$935$	238.388	+	188.634i	0.254960	+	0.201747i
$936$		0			0
$937$	−750.288	+	750.288i	−0.800734	+	0.800734i	−0.983210	−	0.182476i	$-0.941589\pi$
$937$	−750.288	+	750.288i	−0.800734	+	0.800734i	0.182476	+	0.983210i	$0.441589\pi$
$938$	251.331	+	251.331i	0.267944	+	0.267944i
$939$		0			0
$940$	−71.7439	+	90.6672i	−0.0763233	+	0.0964545i
$941$	−858.370			−0.912189			−0.456095	−	0.889931i	$-0.650752\pi$
$941$	−858.370			−0.912189			−0.456095	+	0.889931i	$0.650752\pi$
$942$		0			0
$943$	1447.98	+	1447.98i	1.53550	+	1.53550i
$944$		−	297.509i		−	0.315158i
$945$		0			0
$946$	−535.402			−0.565964
$947$	−1103.38	+	1103.38i	−1.16513	+	1.16513i	−0.181798	+	0.983336i	$0.558192\pi$
$947$	−1103.38	+	1103.38i	−1.16513	+	1.16513i	−0.983336	+	0.181798i	$0.941808\pi$
$948$		0			0
$949$		−	775.477i		−	0.817152i
$950$	248.173	+	153.324i	0.261235	+	0.161394i
$951$		0			0
$952$	−16.4378	+	16.4378i	−0.0172666	+	0.0172666i
$953$	1277.56	+	1277.56i	1.34056	+	1.34056i	0.895499	+	0.445064i	$0.146819\pi$
$953$	1277.56	+	1277.56i	1.34056	+	1.34056i	0.445064	+	0.895499i	$0.353181\pi$
$954$		0			0
$955$	77.0743	+	661.496i	0.0807061	+	0.692666i
$956$	718.783			0.751865
$957$		0			0
$958$	−337.547	−	337.547i	−0.352346	−	0.352346i
$959$			133.960i			0.139687i
$960$		0			0
$961$	−60.7414			−0.0632064
$962$	−598.141	+	598.141i	−0.621768	+	0.621768i
$963$		0			0
$964$			192.902i			0.200106i
$965$	−1037.99	+	1311.77i	−1.07563	+	1.35935i
$966$		0			0
$967$	−478.601	+	478.601i	−0.494933	+	0.494933i	−0.909857	−	0.414923i	$-0.863808\pi$
$967$	−478.601	+	478.601i	−0.494933	+	0.494933i	0.414923	+	0.909857i	$0.363808\pi$
$968$	524.101	+	524.101i	0.541427	+	0.541427i
$969$		0			0
$970$	−727.932	+	84.8151i	−0.750445	+	0.0874382i
$971$	−97.1677			−0.100070			−0.0500349	−	0.998747i	$-0.515933\pi$
$971$	−97.1677			−0.100070			−0.0500349	+	0.998747i	$0.515933\pi$
$972$		0			0
$973$	−167.899	−	167.899i	−0.172558	−	0.172558i
$974$			307.568i			0.315778i
$975$		0			0
$976$	−391.366			−0.400989
$977$	711.442	−	711.442i	0.728191	−	0.728191i	−0.242068	−	0.970259i	$-0.577826\pi$
$977$	711.442	−	711.442i	0.728191	−	0.728191i	0.970259	+	0.242068i	$0.0778259\pi$
$978$		0			0
$979$		−	3091.17i		−	3.15748i
$980$	8.10125	+	69.5296i	0.00826659	+	0.0709486i
$981$		0			0
$982$	320.910	−	320.910i	0.326792	−	0.326792i
$983$	443.320	+	443.320i	0.450986	+	0.450986i	0.895682	−	0.444695i	$-0.146688\pi$
$983$	443.320	+	443.320i	0.450986	+	0.450986i	−0.444695	+	0.895682i	$0.646688\pi$
$984$		0			0
$985$	−1125.71	−	890.758i	−1.14285	−	0.904323i
$986$	−86.7632			−0.0879951
$987$		0			0
$988$	132.545	+	132.545i	0.134154	+	0.134154i
$989$		−	489.858i		−	0.495306i
$990$		0			0
$991$	1708.27			1.72378			0.861890	−	0.507095i	$-0.169281\pi$
$991$	1708.27			1.72378			0.861890	+	0.507095i	$0.169281\pi$
$992$	120.017	−	120.017i	0.120985	−	0.120985i
$993$		0			0
$994$		−	50.0607i		−	0.0503629i
$995$	511.200	−	59.5625i	0.513768	−	0.0598618i
$996$		0			0
$997$	1363.41	−	1363.41i	1.36752	−	1.36752i	0.503548	−	0.863967i	$-0.332028\pi$
$997$	1363.41	−	1363.41i	1.36752	−	1.36752i	0.863967	−	0.503548i	$-0.167972\pi$
$998$	284.928	+	284.928i	0.285499	+	0.285499i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.o.b.253.2		8
3.2	odd	2		210.3.l.a.43.3	✓	8
5.2	odd	4	inner	630.3.o.b.127.2		8
15.2	even	4		210.3.l.a.127.3	yes	8
15.8	even	4		1050.3.l.b.757.2		8
15.14	odd	2		1050.3.l.b.43.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.a.43.3	✓	8	3.2	odd	2
210.3.l.a.127.3	yes	8	15.2	even	4
630.3.o.b.127.2		8	5.2	odd	4	inner
630.3.o.b.253.2		8	1.1	even	1	trivial
1050.3.l.b.43.2		8	15.14	odd	2
1050.3.l.b.757.2		8	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-0.578661 - 4.96640i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-0.578661 - 4.96640i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +(5.54506 + 4.38774i) q^{10} -19.5717 q^{11} +(8.03207 + 8.03207i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(2.19659 - 2.19659i) q^{17} +8.25097i q^{19} +(-9.93280 + 1.15732i) q^{20} +(19.5717 - 19.5717i) q^{22} +(17.9068 + 17.9068i) q^{23} +(-24.3303 + 5.74773i) q^{25} -16.0641 q^{26} +(3.74166 + 3.74166i) q^{28} +19.7495i q^{29} +30.0043 q^{31} +(4.00000 - 4.00000i) q^{32} +4.39319i q^{34} +(10.3739 + 8.20871i) q^{35} +(37.2346 - 37.2346i) q^{37} +(-8.25097 - 8.25097i) q^{38} +(8.77548 - 11.0901i) q^{40} +80.8620 q^{41} +(-13.6780 - 13.6780i) q^{43} +39.1434i q^{44} -35.8136 q^{46} +(8.17549 - 8.17549i) q^{47} -7.00000i q^{49} +(18.5826 - 30.0780i) q^{50} +(16.0641 - 16.0641i) q^{52} +(38.8560 + 38.8560i) q^{53} +(11.3254 + 97.2008i) q^{55} -7.48331 q^{56} +(-19.7495 - 19.7495i) q^{58} +74.3773i q^{59} +97.8414 q^{61} +(-30.0043 + 30.0043i) q^{62} +8.00000i q^{64} +(35.2426 - 44.5383i) q^{65} +(-67.1712 + 67.1712i) q^{67} +(-4.39319 - 4.39319i) q^{68} +(-18.5826 + 2.16515i) q^{70} +13.3793 q^{71} +(-48.2738 - 48.2738i) q^{73} +74.4691i q^{74} +16.5019 q^{76} +(36.6153 - 36.6153i) q^{77} +40.2089i q^{79} +(2.31464 + 19.8656i) q^{80} +(-80.8620 + 80.8620i) q^{82} +(-34.4137 - 34.4137i) q^{83} +(-12.1803 - 9.63809i) q^{85} +27.3560 q^{86} +(-39.1434 - 39.1434i) q^{88} +157.941i q^{89} -30.0532 q^{91} +(35.8136 - 35.8136i) q^{92} +16.3510i q^{94} +(40.9776 - 4.77451i) q^{95} +(-73.2856 + 73.2856i) q^{97} +(7.00000 + 7.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 16 * q^8	\( 8 q - 8 q^{2} + 16 q^{8} + 8 q^{11} + 8 q^{13} - 32 q^{16} + 32 q^{17} - 8 q^{22} + 40 q^{23} - 48 q^{25} - 16 q^{26} + 144 q^{31} + 32 q^{32} + 28 q^{35} + 160 q^{37} + 320 q^{41} - 32 q^{43} - 80 q^{46} + 144 q^{47} + 112 q^{50} + 16 q^{52} + 200 q^{53} + 184 q^{55} - 64 q^{58} + 288 q^{61} - 144 q^{62} - 24 q^{65} + 80 q^{67} - 64 q^{68} - 112 q^{70} + 280 q^{71} + 312 q^{73} + 56 q^{77} - 320 q^{82} + 320 q^{83} + 80 q^{85} + 64 q^{86} + 16 q^{88} + 80 q^{92} + 472 q^{95} - 24 q^{97} + 56 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 16 * q^8 + 8 * q^11 + 8 * q^13 - 32 * q^16 + 32 * q^17 - 8 * q^22 + 40 * q^23 - 48 * q^25 - 16 * q^26 + 144 * q^31 + 32 * q^32 + 28 * q^35 + 160 * q^37 + 320 * q^41 - 32 * q^43 - 80 * q^46 + 144 * q^47 + 112 * q^50 + 16 * q^52 + 200 * q^53 + 184 * q^55 - 64 * q^58 + 288 * q^61 - 144 * q^62 - 24 * q^65 + 80 * q^67 - 64 * q^68 - 112 * q^70 + 280 * q^71 + 312 * q^73 + 56 * q^77 - 320 * q^82 + 320 * q^83 + 80 * q^85 + 64 * q^86 + 16 * q^88 + 80 * q^92 + 472 * q^95 - 24 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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