LMFDB - Embedded newform 630.3.o.f.253.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("630.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			253.1
Root			$-0.394902 + 0.394902i$ of defining polynomial
Character	$\chi$	$=$	630.253
Dual form			630.3.o.f.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-4.80148 + 1.39490i) q^{5} +(1.87083 - 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-4.80148 + 1.39490i) q^{5} +(1.87083 - 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-3.40658 + 6.19639i) q^{10} +11.5078 q^{11} +(-7.70521 - 7.70521i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(-21.0749 + 21.0749i) q^{17} -24.1173i q^{19} +(2.78980 + 9.60297i) q^{20} +(11.5078 - 11.5078i) q^{22} +(-30.1762 - 30.1762i) q^{23} +(21.1085 - 13.3952i) q^{25} -15.4104 q^{26} +(-3.74166 - 3.74166i) q^{28} +51.1392i q^{29} -46.9852 q^{31} +(-4.00000 + 4.00000i) q^{32} +42.1499i q^{34} +(-6.37313 + 11.5924i) q^{35} +(-8.50020 + 8.50020i) q^{37} +(-24.1173 - 24.1173i) q^{38} +(12.3928 + 6.81316i) q^{40} -18.6089 q^{41} +(-26.1383 - 26.1383i) q^{43} -23.0156i q^{44} -60.3523 q^{46} +(-50.1311 + 50.1311i) q^{47} -7.00000i q^{49} +(7.71330 - 34.5037i) q^{50} +(-15.4104 + 15.4104i) q^{52} +(-7.08527 - 7.08527i) q^{53} +(-55.2546 + 16.0523i) q^{55} -7.48331 q^{56} +(51.1392 + 51.1392i) q^{58} -94.3487i q^{59} +8.09003 q^{61} +(-46.9852 + 46.9852i) q^{62} +8.00000i q^{64} +(47.7445 + 26.2484i) q^{65} +(-20.6469 + 20.6469i) q^{67} +(42.1499 + 42.1499i) q^{68} +(5.21925 + 17.9655i) q^{70} +63.7595 q^{71} +(50.1883 + 50.1883i) q^{73} +17.0004i q^{74} -48.2346 q^{76} +(21.5292 - 21.5292i) q^{77} -1.06121i q^{79} +(19.2059 - 5.57961i) q^{80} +(-18.6089 + 18.6089i) q^{82} +(-53.6243 - 53.6243i) q^{83} +(71.7935 - 130.588i) q^{85} -52.2765 q^{86} +(-23.0156 - 23.0156i) q^{88} -145.154i q^{89} -28.8303 q^{91} +(-60.3523 + 60.3523i) q^{92} +100.262i q^{94} +(33.6413 + 115.799i) q^{95} +(23.7872 - 23.7872i) q^{97} +(-7.00000 - 7.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8	$ 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8} + 24 q^{10} - 8 q^{11} - 32 q^{13} - 64 q^{16} - 56 q^{17} + 16 q^{20} - 8 q^{22} - 24 q^{23} + 40 q^{25} - 64 q^{26} - 112 q^{31} - 64 q^{32} - 28 q^{35} - 152 q^{37} - 16 q^{40} - 48 q^{46} - 80 q^{47} + 72 q^{50} - 64 q^{52} - 48 q^{53} - 24 q^{55} + 96 q^{58} + 96 q^{61} - 112 q^{62} - 16 q^{65} - 80 q^{67} + 112 q^{68} - 536 q^{71} + 168 q^{77} - 64 q^{80} + 256 q^{83} + 40 q^{85} + 16 q^{88} - 48 q^{92} - 360 q^{95} + 688 q^{97} - 112 q^{98}+O(q^{100}) $ 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8 + 24 * q^10 - 8 * q^11 - 32 * q^13 - 64 * q^16 - 56 * q^17 + 16 * q^20 - 8 * q^22 - 24 * q^23 + 40 * q^25 - 64 * q^26 - 112 * q^31 - 64 * q^32 - 28 * q^35 - 152 * q^37 - 16 * q^40 - 48 * q^46 - 80 * q^47 + 72 * q^50 - 64 * q^52 - 48 * q^53 - 24 * q^55 + 96 * q^58 + 96 * q^61 - 112 * q^62 - 16 * q^65 - 80 * q^67 + 112 * q^68 - 536 * q^71 + 168 * q^77 - 64 * q^80 + 256 * q^83 + 40 * q^85 + 16 * q^88 - 48 * q^92 - 360 * q^95 + 688 * q^97 - 112 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−4.80148	+	1.39490i	−0.960297	+	0.278980i
$5$	−4.80148	+	1.39490i	−0.960297	+	0.278980i
$6$		0			0
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$		0			0
$10$	−3.40658	+	6.19639i	−0.340658	+	0.619639i
$11$	11.5078			1.04617			0.523083	−	0.852282i	$-0.324782\pi$
$11$	11.5078			1.04617			0.523083	+	0.852282i	$0.324782\pi$
$12$		0			0
$13$	−7.70521	−	7.70521i	−0.592708	−	0.592708i	0.345654	−	0.938362i	$-0.387657\pi$
$13$	−7.70521	−	7.70521i	−0.592708	−	0.592708i	−0.938362	+	0.345654i	$0.887657\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−21.0749	+	21.0749i	−1.23970	+	1.23970i	−0.279579	+	0.960123i	$0.590195\pi$
$17$	−21.0749	+	21.0749i	−1.23970	+	1.23970i	−0.960123	+	0.279579i	$0.909805\pi$
$18$		0			0
$19$		−	24.1173i		−	1.26933i	−0.772786	−	0.634666i	$-0.781138\pi$
$19$		−	24.1173i		−	1.26933i	0.772786	−	0.634666i	$-0.218862\pi$
$20$	2.78980	+	9.60297i	0.139490	+	0.480148i
$21$		0			0
$22$	11.5078	−	11.5078i	0.523083	−	0.523083i
$23$	−30.1762	−	30.1762i	−1.31201	−	1.31201i	−0.919934	−	0.392073i	$-0.871758\pi$
$23$	−30.1762	−	30.1762i	−1.31201	−	1.31201i	−0.392073	−	0.919934i	$-0.628242\pi$
$24$		0			0
$25$	21.1085	−	13.3952i	0.844340	−	0.535808i
$26$	−15.4104			−0.592708
$27$		0			0
$28$	−3.74166	−	3.74166i	−0.133631	−	0.133631i
$29$			51.1392i			1.76342i	0.471790	+	0.881711i	$0.343608\pi$
$29$			51.1392i			1.76342i	−0.471790	+	0.881711i	$0.656392\pi$
$30$		0			0
$31$	−46.9852			−1.51565			−0.757826	−	0.652457i	$-0.773738\pi$
$31$	−46.9852			−1.51565			−0.757826	+	0.652457i	$0.773738\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$		0			0
$34$			42.1499i			1.23970i
$35$	−6.37313	+	11.5924i	−0.182089	+	0.331211i
$36$		0			0
$37$	−8.50020	+	8.50020i	−0.229735	+	0.229735i	−0.812582	−	0.582847i	$-0.801939\pi$
$37$	−8.50020	+	8.50020i	−0.229735	+	0.229735i	0.582847	+	0.812582i	$0.301939\pi$
$38$	−24.1173	−	24.1173i	−0.634666	−	0.634666i
$39$		0			0
$40$	12.3928	+	6.81316i	0.309819	+	0.170329i
$41$	−18.6089			−0.453875			−0.226937	−	0.973909i	$-0.572871\pi$
$41$	−18.6089			−0.453875			−0.226937	+	0.973909i	$0.572871\pi$
$42$		0			0
$43$	−26.1383	−	26.1383i	−0.607867	−	0.607867i	0.334522	−	0.942388i	$-0.391425\pi$
$43$	−26.1383	−	26.1383i	−0.607867	−	0.607867i	−0.942388	+	0.334522i	$0.891425\pi$
$44$		−	23.0156i		−	0.523083i
$45$		0			0
$46$	−60.3523			−1.31201
$47$	−50.1311	+	50.1311i	−1.06662	+	1.06662i	−0.0690016	+	0.997617i	$0.521981\pi$
$47$	−50.1311	+	50.1311i	−1.06662	+	1.06662i	−0.997617	+	0.0690016i	$0.978019\pi$
$48$		0			0
$49$		−	7.00000i		−	0.142857i
$50$	7.71330	−	34.5037i	0.154266	−	0.690074i
$51$		0			0
$52$	−15.4104	+	15.4104i	−0.296354	+	0.296354i
$53$	−7.08527	−	7.08527i	−0.133684	−	0.133684i	0.637098	−	0.770783i	$-0.280135\pi$
$53$	−7.08527	−	7.08527i	−0.133684	−	0.133684i	−0.770783	+	0.637098i	$0.780135\pi$
$54$		0			0
$55$	−55.2546	+	16.0523i	−1.00463	+	0.291860i
$56$	−7.48331			−0.133631
$57$		0			0
$58$	51.1392	+	51.1392i	0.881711	+	0.881711i
$59$		−	94.3487i		−	1.59913i	−0.600579	−	0.799565i	$-0.705063\pi$
$59$		−	94.3487i		−	1.59913i	0.600579	−	0.799565i	$-0.294937\pi$
$60$		0			0
$61$	8.09003			0.132623			0.0663117	−	0.997799i	$-0.478877\pi$
$61$	8.09003			0.132623			0.0663117	+	0.997799i	$0.478877\pi$
$62$	−46.9852	+	46.9852i	−0.757826	+	0.757826i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	47.7445	+	26.2484i	0.734530	+	0.403822i
$66$		0			0
$67$	−20.6469	+	20.6469i	−0.308163	+	0.308163i	−0.844197	−	0.536034i	$-0.819922\pi$
$67$	−20.6469	+	20.6469i	−0.308163	+	0.308163i	0.536034	+	0.844197i	$0.319922\pi$
$68$	42.1499	+	42.1499i	0.619851	+	0.619851i
$69$		0			0
$70$	5.21925	+	17.9655i	0.0745607	+	0.256650i
$71$	63.7595			0.898021			0.449011	−	0.893526i	$-0.351777\pi$
$71$	63.7595			0.898021			0.449011	+	0.893526i	$0.351777\pi$
$72$		0			0
$73$	50.1883	+	50.1883i	0.687511	+	0.687511i	0.961681	−	0.274170i	$-0.0884031\pi$
$73$	50.1883	+	50.1883i	0.687511	+	0.687511i	−0.274170	+	0.961681i	$0.588403\pi$
$74$			17.0004i			0.229735i
$75$		0			0
$76$	−48.2346			−0.634666
$77$	21.5292	−	21.5292i	0.279599	−	0.279599i
$78$		0			0
$79$		−	1.06121i		−	0.0134331i	−0.999977	−	0.00671653i	$-0.997862\pi$
$79$		−	1.06121i		−	0.0134331i	0.999977	−	0.00671653i	$-0.00213796\pi$
$80$	19.2059	−	5.57961i	0.240074	−	0.0697451i
$81$		0			0
$82$	−18.6089	+	18.6089i	−0.226937	+	0.226937i
$83$	−53.6243	−	53.6243i	−0.646075	−	0.646075i	0.305967	−	0.952042i	$-0.401020\pi$
$83$	−53.6243	−	53.6243i	−0.646075	−	0.646075i	−0.952042	+	0.305967i	$0.901020\pi$
$84$		0			0
$85$	71.7935	−	130.588i	0.844629	−	1.53633i
$86$	−52.2765			−0.607867
$87$		0			0
$88$	−23.0156	−	23.0156i	−0.261541	−	0.261541i
$89$		−	145.154i		−	1.63095i	−0.578794	−	0.815473i	$-0.696477\pi$
$89$		−	145.154i		−	1.63095i	0.578794	−	0.815473i	$-0.303523\pi$
$90$		0			0
$91$	−28.8303			−0.316816
$92$	−60.3523	+	60.3523i	−0.656003	+	0.656003i
$93$		0			0
$94$			100.262i			1.06662i
$95$	33.6413	+	115.799i	0.354119	+	1.21894i
$96$		0			0
$97$	23.7872	−	23.7872i	0.245229	−	0.245229i	−0.573780	−	0.819009i	$-0.694524\pi$
$97$	23.7872	−	23.7872i	0.245229	−	0.245229i	0.819009	+	0.573780i	$0.194524\pi$
$98$	−7.00000	−	7.00000i	−0.0714286	−	0.0714286i
$99$		0			0
$100$	−26.7904	−	42.2170i	−0.267904	−	0.422170i
$101$	−50.1467			−0.496502			−0.248251	−	0.968696i	$-0.579856\pi$
$101$	−50.1467			−0.496502			−0.248251	+	0.968696i	$0.579856\pi$
$102$		0			0
$103$	56.3876	+	56.3876i	0.547453	+	0.547453i	0.925703	−	0.378251i	$-0.123474\pi$
$103$	56.3876	+	56.3876i	0.547453	+	0.547453i	−0.378251	+	0.925703i	$0.623474\pi$
$104$			30.8208i			0.296354i
$105$		0			0
$106$	−14.1705			−0.133684
$107$	135.365	−	135.365i	1.26510	−	1.26510i	0.316506	−	0.948590i	$-0.397490\pi$
$107$	135.365	−	135.365i	1.26510	−	1.26510i	0.948590	−	0.316506i	$-0.102510\pi$
$108$		0			0
$109$			100.934i			0.926001i	0.886358	+	0.463001i	$0.153227\pi$
$109$			100.934i			0.926001i	−0.886358	+	0.463001i	$0.846773\pi$
$110$	−39.2023	+	71.3069i	−0.356385	+	0.648245i
$111$		0			0
$112$	−7.48331	+	7.48331i	−0.0668153	+	0.0668153i
$113$	−25.3174	−	25.3174i	−0.224048	−	0.224048i	0.586153	−	0.810201i	$-0.300642\pi$
$113$	−25.3174	−	25.3174i	−0.224048	−	0.224048i	−0.810201	+	0.586153i	$0.800642\pi$
$114$		0			0
$115$	186.983	+	102.798i	1.62594	+	0.893892i
$116$	102.278			0.881711
$117$		0			0
$118$	−94.3487	−	94.3487i	−0.799565	−	0.799565i
$119$			78.8552i			0.662649i
$120$		0			0
$121$	11.4299			0.0944623
$122$	8.09003	−	8.09003i	0.0663117	−	0.0663117i
$123$		0			0
$124$			93.9704i			0.757826i
$125$	−82.6671	+	93.7611i	−0.661337	+	0.750089i
$126$		0			0
$127$	116.746	−	116.746i	0.919262	−	0.919262i	−0.0777140	−	0.996976i	$-0.524762\pi$
$127$	116.746	−	116.746i	0.919262	−	0.919262i	0.996976	+	0.0777140i	$0.0247621\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		0			0
$130$	73.9929	−	21.4960i	0.569176	−	0.165354i
$131$	−34.8004			−0.265652			−0.132826	−	0.991139i	$-0.542405\pi$
$131$	−34.8004			−0.265652			−0.132826	+	0.991139i	$0.542405\pi$
$132$		0			0
$133$	−45.1194	−	45.1194i	−0.339243	−	0.339243i
$134$			41.2938i			0.308163i
$135$		0			0
$136$	84.2997			0.619851
$137$	−131.552	+	131.552i	−0.960235	+	0.960235i	−0.999239	−	0.0390044i	$-0.987581\pi$
$137$	−131.552	+	131.552i	−0.960235	+	0.960235i	0.0390044	+	0.999239i	$0.487581\pi$
$138$		0			0
$139$		−	89.4407i		−	0.643458i	−0.946832	−	0.321729i	$-0.895736\pi$
$139$		−	89.4407i		−	0.643458i	0.946832	−	0.321729i	$-0.104264\pi$
$140$	23.1848	+	12.7463i	0.165605	+	0.0910447i
$141$		0			0
$142$	63.7595	−	63.7595i	0.449011	−	0.449011i
$143$	−88.6702	−	88.6702i	−0.620071	−	0.620071i
$144$		0			0
$145$	−71.3342	−	245.544i	−0.491960	−	1.69341i
$146$	100.377			0.687511
$147$		0			0
$148$	17.0004	+	17.0004i	0.114868	+	0.114868i
$149$		−	55.7399i		−	0.374093i	−0.982351	−	0.187047i	$-0.940108\pi$
$149$		−	55.7399i		−	0.374093i	0.982351	−	0.187047i	$-0.0598915\pi$
$150$		0			0
$151$	82.9665			0.549447			0.274724	−	0.961523i	$-0.411414\pi$
$151$	82.9665			0.549447			0.274724	+	0.961523i	$0.411414\pi$
$152$	−48.2346	+	48.2346i	−0.317333	+	0.317333i
$153$		0			0
$154$		−	43.0583i		−	0.279599i
$155$	225.599	−	65.5398i	1.45548	−	0.422837i
$156$		0			0
$157$	−99.7950	+	99.7950i	−0.635637	+	0.635637i	−0.949476	−	0.313839i	$-0.898385\pi$
$157$	−99.7950	+	99.7950i	−0.635637	+	0.635637i	0.313839	+	0.949476i	$0.398385\pi$
$158$	−1.06121	−	1.06121i	−0.00671653	−	0.00671653i
$159$		0			0
$160$	13.6263	−	24.7855i	0.0851645	−	0.154910i
$161$	−112.909			−0.701297
$162$		0			0
$163$	−45.3884	−	45.3884i	−0.278457	−	0.278457i	0.554036	−	0.832493i	$-0.313087\pi$
$163$	−45.3884	−	45.3884i	−0.278457	−	0.278457i	−0.832493	+	0.554036i	$0.813087\pi$
$164$			37.2177i			0.226937i
$165$		0			0
$166$	−107.249			−0.646075
$167$	99.2501	−	99.2501i	0.594312	−	0.594312i	−0.344481	−	0.938793i	$-0.611945\pi$
$167$	99.2501	−	99.2501i	0.594312	−	0.594312i	0.938793	+	0.344481i	$0.111945\pi$
$168$		0			0
$169$		−	50.2595i		−	0.297393i
$170$	−58.7949	−	202.382i	−0.345853	−	1.19048i
$171$		0			0
$172$	−52.2765	+	52.2765i	−0.303933	+	0.303933i
$173$	80.5404	+	80.5404i	0.465551	+	0.465551i	0.900470	−	0.434919i	$-0.143223\pi$
$173$	80.5404	+	80.5404i	0.465551	+	0.465551i	−0.434919	+	0.900470i	$0.643223\pi$
$174$		0			0
$175$	14.4303	−	64.5505i	0.0824586	−	0.368860i
$176$	−46.0313			−0.261541
$177$		0			0
$178$	−145.154	−	145.154i	−0.815473	−	0.815473i
$179$			154.267i			0.861824i	0.902394	+	0.430912i	$0.141808\pi$
$179$			154.267i			0.861824i	−0.902394	+	0.430912i	$0.858192\pi$
$180$		0			0
$181$	166.548			0.920155			0.460078	−	0.887879i	$-0.347822\pi$
$181$	166.548			0.920155			0.460078	+	0.887879i	$0.347822\pi$
$182$	−28.8303	+	28.8303i	−0.158408	+	0.158408i
$183$		0			0
$184$			120.705i			0.656003i
$185$	28.9566	−	52.6705i	0.156522	−	0.284705i
$186$		0			0
$187$	−242.527	+	242.527i	−1.29693	+	1.29693i
$188$	100.262	+	100.262i	0.533309	+	0.533309i
$189$		0			0
$190$	149.440	+	82.1576i	0.786528	+	0.432409i
$191$	235.646			1.23375			0.616873	−	0.787063i	$-0.288399\pi$
$191$	235.646			1.23375			0.616873	+	0.787063i	$0.288399\pi$
$192$		0			0
$193$	−16.2211	−	16.2211i	−0.0840471	−	0.0840471i	0.663833	−	0.747880i	$-0.268928\pi$
$193$	−16.2211	−	16.2211i	−0.0840471	−	0.0840471i	−0.747880	+	0.663833i	$0.768928\pi$
$194$		−	47.5744i		−	0.245229i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	6.68134	−	6.68134i	0.0339154	−	0.0339154i	−0.689946	−	0.723861i	$-0.742366\pi$
$197$	6.68134	−	6.68134i	0.0339154	−	0.0339154i	0.723861	+	0.689946i	$0.242366\pi$
$198$		0			0
$199$			32.0712i			0.161162i	0.996748	+	0.0805808i	$0.0256775\pi$
$199$			32.0712i			0.161162i	−0.996748	+	0.0805808i	$0.974322\pi$
$200$	−69.0074	−	15.4266i	−0.345037	−	0.0771330i
$201$		0			0
$202$	−50.1467	+	50.1467i	−0.248251	+	0.248251i
$203$	95.6728	+	95.6728i	0.471294	+	0.471294i
$204$		0			0
$205$	89.3502	−	25.9575i	0.435855	−	0.126622i
$206$	112.775			0.547453
$207$		0			0
$208$	30.8208	+	30.8208i	0.148177	+	0.148177i
$209$		−	277.538i		−	1.32793i
$210$		0			0
$211$	123.531			0.585457			0.292728	−	0.956196i	$-0.405437\pi$
$211$	123.531			0.585457			0.292728	+	0.956196i	$0.405437\pi$
$212$	−14.1705	+	14.1705i	−0.0668422	+	0.0668422i
$213$		0			0
$214$		−	270.731i		−	1.26510i
$215$	161.963	+	89.0421i	0.753315	+	0.414149i
$216$		0			0
$217$	−87.9013	+	87.9013i	−0.405075	+	0.405075i
$218$	100.934	+	100.934i	0.463001	+	0.463001i
$219$		0			0
$220$	32.1046	+	110.509i	0.145930	+	0.502315i
$221$	324.774			1.46956
$222$		0			0
$223$	−81.9590	−	81.9590i	−0.367529	−	0.367529i	0.499046	−	0.866575i	$-0.333684\pi$
$223$	−81.9590	−	81.9590i	−0.367529	−	0.367529i	−0.866575	+	0.499046i	$0.833684\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	−50.6348			−0.224048
$227$	−93.6089	+	93.6089i	−0.412374	+	0.412374i	−0.882565	−	0.470191i	$-0.844185\pi$
$227$	−93.6089	+	93.6089i	−0.412374	+	0.412374i	0.470191	+	0.882565i	$0.344185\pi$
$228$		0			0
$229$			348.973i			1.52390i	0.647635	+	0.761950i	$0.275758\pi$
$229$			348.973i			1.52390i	−0.647635	+	0.761950i	$0.724242\pi$
$230$	289.781	−	84.1856i	1.25992	−	0.366024i
$231$		0			0
$232$	102.278	−	102.278i	0.440856	−	0.440856i
$233$	−208.319	−	208.319i	−0.894074	−	0.894074i	0.100829	−	0.994904i	$-0.467850\pi$
$233$	−208.319	−	208.319i	−0.894074	−	0.894074i	−0.994904	+	0.100829i	$0.967850\pi$
$234$		0			0
$235$	170.776	−	310.631i	0.726704	−	1.32184i
$236$	−188.697			−0.799565
$237$		0			0
$238$	78.8552	+	78.8552i	0.331324	+	0.331324i
$239$		−	330.793i		−	1.38407i	−0.721864	−	0.692035i	$-0.756715\pi$
$239$		−	330.793i		−	1.38407i	0.721864	−	0.692035i	$-0.243285\pi$
$240$		0			0
$241$	375.584			1.55844			0.779221	−	0.626749i	$-0.215615\pi$
$241$	375.584			1.55844			0.779221	+	0.626749i	$0.215615\pi$
$242$	11.4299	−	11.4299i	0.0472312	−	0.0472312i
$243$		0			0
$244$		−	16.1801i		−	0.0663117i
$245$	9.76432	+	33.6104i	0.0398543	+	0.137185i
$246$		0			0
$247$	−185.829	+	185.829i	−0.752344	+	0.752344i
$248$	93.9704	+	93.9704i	0.378913	+	0.378913i
$249$		0			0
$250$	11.0940	+	176.428i	0.0443761	+	0.705713i
$251$	−41.2876			−0.164493			−0.0822463	−	0.996612i	$-0.526209\pi$
$251$	−41.2876			−0.164493			−0.0822463	+	0.996612i	$0.526209\pi$
$252$		0			0
$253$	−347.262	−	347.262i	−1.37258	−	1.37258i
$254$		−	233.492i		−	0.919262i
$255$		0			0
$256$	16.0000			0.0625000
$257$	101.370	−	101.370i	0.394437	−	0.394437i	−0.481828	−	0.876266i	$-0.660027\pi$
$257$	101.370	−	101.370i	0.394437	−	0.394437i	0.876266	+	0.481828i	$0.160027\pi$
$258$		0			0
$259$			31.8048i			0.122799i
$260$	52.4969	−	95.4889i	0.201911	−	0.367265i
$261$		0			0
$262$	−34.8004	+	34.8004i	−0.132826	+	0.132826i
$263$	−164.594	−	164.594i	−0.625833	−	0.625833i	0.321184	−	0.947017i	$-0.395919\pi$
$263$	−164.594	−	164.594i	−0.625833	−	0.625833i	−0.947017	+	0.321184i	$0.895919\pi$
$264$		0			0
$265$	43.9031	+	24.1366i	0.165672	+	0.0910813i
$266$	−90.2387			−0.339243
$267$		0			0
$268$	41.2938	+	41.2938i	0.154081	+	0.154081i
$269$			254.148i			0.944788i	0.881387	+	0.472394i	$0.156610\pi$
$269$			254.148i			0.944788i	−0.881387	+	0.472394i	$0.843390\pi$
$270$		0			0
$271$	22.4723			0.0829237			0.0414619	−	0.999140i	$-0.486798\pi$
$271$	22.4723			0.0829237			0.0414619	+	0.999140i	$0.486798\pi$
$272$	84.2997	−	84.2997i	0.309925	−	0.309925i
$273$		0			0
$274$			263.104i			0.960235i
$275$	242.913	−	154.150i	0.883319	−	0.560544i
$276$		0			0
$277$	47.3949	−	47.3949i	0.171101	−	0.171101i	−0.616362	−	0.787463i	$-0.711394\pi$
$277$	47.3949	−	47.3949i	0.171101	−	0.171101i	0.787463	+	0.616362i	$0.211394\pi$
$278$	−89.4407	−	89.4407i	−0.321729	−	0.321729i
$279$		0			0
$280$	35.9310	−	10.4385i	0.128325	−	0.0372803i
$281$	18.8810			0.0671920			0.0335960	−	0.999435i	$-0.489304\pi$
$281$	18.8810			0.0671920			0.0335960	+	0.999435i	$0.489304\pi$
$282$		0			0
$283$	−115.825	−	115.825i	−0.409277	−	0.409277i	0.472209	−	0.881486i	$-0.343457\pi$
$283$	−115.825	−	115.825i	−0.409277	−	0.409277i	−0.881486	+	0.472209i	$0.843457\pi$
$284$		−	127.519i		−	0.449011i
$285$		0			0
$286$	−177.340			−0.620071
$287$	−34.8140	+	34.8140i	−0.121303	+	0.121303i
$288$		0			0
$289$		−	599.306i		−	2.07372i
$290$	−316.879	−	174.210i	−1.09268	−	0.600724i
$291$		0			0
$292$	100.377	−	100.377i	0.343756	−	0.343756i
$293$	−224.451	−	224.451i	−0.766043	−	0.766043i	0.211364	−	0.977407i	$-0.432209\pi$
$293$	−224.451	−	224.451i	−0.766043	−	0.766043i	−0.977407	+	0.211364i	$0.932209\pi$
$294$		0			0
$295$	131.607	+	453.014i	0.446126	+	1.53564i
$296$	34.0008			0.114868
$297$		0			0
$298$	−55.7399	−	55.7399i	−0.187047	−	0.187047i
$299$			465.027i			1.55528i
$300$		0			0
$301$	−97.8004			−0.324918
$302$	82.9665	−	82.9665i	0.274724	−	0.274724i
$303$		0			0
$304$			96.4693i			0.317333i
$305$	−38.8441	+	11.2848i	−0.127358	+	0.0369993i
$306$		0			0
$307$	−42.5120	+	42.5120i	−0.138476	+	0.138476i	−0.772947	−	0.634471i	$-0.781218\pi$
$307$	−42.5120	+	42.5120i	−0.138476	+	0.138476i	0.634471	+	0.772947i	$0.281218\pi$
$308$	−43.0583	−	43.0583i	−0.139800	−	0.139800i
$309$		0			0
$310$	160.059	−	291.139i	0.516319	−	0.939157i
$311$	97.1353			0.312332			0.156166	−	0.987731i	$-0.450086\pi$
$311$	97.1353			0.312332			0.156166	+	0.987731i	$0.450086\pi$
$312$		0			0
$313$	−94.4913	−	94.4913i	−0.301889	−	0.301889i	0.539863	−	0.841753i	$-0.318476\pi$
$313$	−94.4913	−	94.4913i	−0.301889	−	0.301889i	−0.841753	+	0.539863i	$0.818476\pi$
$314$			199.590i			0.635637i
$315$		0			0
$316$	−2.12242			−0.00671653
$317$	−146.150	+	146.150i	−0.461040	+	0.461040i	−0.898996	−	0.437956i	$-0.855703\pi$
$317$	−146.150	+	146.150i	−0.461040	+	0.461040i	0.437956	+	0.898996i	$0.355703\pi$
$318$		0			0
$319$			588.501i			1.84483i
$320$	−11.1592	−	38.4119i	−0.0348726	−	0.120037i
$321$		0			0
$322$	−112.909	+	112.909i	−0.350649	+	0.350649i
$323$	508.271	+	508.271i	1.57359	+	1.57359i
$324$		0			0
$325$	−265.858	−	59.4326i	−0.818025	−	0.182869i
$326$	−90.7768			−0.278457
$327$		0			0
$328$	37.2177	+	37.2177i	0.113469	+	0.113469i
$329$			187.573i			0.570131i
$330$		0			0
$331$	223.981			0.676679			0.338339	−	0.941024i	$-0.390135\pi$
$331$	223.981			0.676679			0.338339	+	0.941024i	$0.390135\pi$
$332$	−107.249	+	107.249i	−0.323038	+	0.323038i
$333$		0			0
$334$		−	198.500i		−	0.594312i
$335$	70.3354	−	127.936i	0.209956	−	0.381899i
$336$		0			0
$337$	−41.7444	+	41.7444i	−0.123871	+	0.123871i	−0.766324	−	0.642454i	$-0.777916\pi$
$337$	−41.7444	+	41.7444i	−0.123871	+	0.123871i	0.642454	+	0.766324i	$0.277916\pi$
$338$	−50.2595	−	50.2595i	−0.148697	−	0.148697i
$339$		0			0
$340$	−261.177	−	143.587i	−0.768167	−	0.422315i
$341$	−540.697			−1.58562
$342$		0			0
$343$	−13.0958	−	13.0958i	−0.0381802	−	0.0381802i
$344$			104.553i			0.303933i
$345$		0			0
$346$	161.081			0.465551
$347$	−283.163	+	283.163i	−0.816031	+	0.816031i	−0.985530	−	0.169500i	$-0.945785\pi$
$347$	−283.163	+	283.163i	−0.816031	+	0.816031i	0.169500	+	0.985530i	$0.445785\pi$
$348$		0			0
$349$		−	73.8529i		−	0.211613i	−0.994387	−	0.105807i	$-0.966258\pi$
$349$		−	73.8529i		−	0.211613i	0.994387	−	0.105807i	$-0.0337424\pi$
$350$	−50.1203	−	78.9808i	−0.143201	−	0.225659i
$351$		0			0
$352$	−46.0313	+	46.0313i	−0.130771	+	0.130771i
$353$	221.700	+	221.700i	0.628047	+	0.628047i	0.947576	−	0.319530i	$-0.103525\pi$
$353$	221.700	+	221.700i	0.628047	+	0.628047i	−0.319530	+	0.947576i	$0.603525\pi$
$354$		0			0
$355$	−306.140	+	88.9383i	−0.862367	+	0.250530i
$356$	−290.309			−0.815473
$357$		0			0
$358$	154.267	+	154.267i	0.430912	+	0.430912i
$359$			351.735i			0.979764i	0.871789	+	0.489882i	$0.162960\pi$
$359$			351.735i			0.979764i	−0.871789	+	0.489882i	$0.837040\pi$
$360$		0			0
$361$	−220.645			−0.611205
$362$	166.548	−	166.548i	0.460078	−	0.460078i
$363$		0			0
$364$			57.6605i			0.158408i
$365$	−310.986	−	170.971i	−0.852017	−	0.468413i
$366$		0			0
$367$	9.03767	−	9.03767i	0.0246258	−	0.0246258i	−0.694687	−	0.719312i	$-0.744457\pi$
$367$	9.03767	−	9.03767i	0.0246258	−	0.0246258i	0.719312	+	0.694687i	$0.244457\pi$
$368$	120.705	+	120.705i	0.328002	+	0.328002i
$369$		0			0
$370$	−23.7139	−	81.6271i	−0.0640916	−	0.220614i
$371$	−26.5107			−0.0714573
$372$		0			0
$373$	−151.095	−	151.095i	−0.405079	−	0.405079i	0.474939	−	0.880019i	$-0.342470\pi$
$373$	−151.095	−	151.095i	−0.405079	−	0.405079i	−0.880019	+	0.474939i	$0.842470\pi$
$374$			485.053i			1.29693i
$375$		0			0
$376$	200.524			0.533309
$377$	394.039	−	394.039i	1.04520	−	1.04520i
$378$		0			0
$379$		−	268.787i		−	0.709201i	−0.935018	−	0.354601i	$-0.884617\pi$
$379$		−	268.787i		−	0.709201i	0.935018	−	0.354601i	$-0.115383\pi$
$380$	231.598	−	67.2826i	0.609468	−	0.177059i
$381$		0			0
$382$	235.646	−	235.646i	0.616873	−	0.616873i
$383$	−304.341	−	304.341i	−0.794625	−	0.794625i	0.187618	−	0.982242i	$-0.439923\pi$
$383$	−304.341	−	304.341i	−0.794625	−	0.794625i	−0.982242	+	0.187618i	$0.939923\pi$
$384$		0			0
$385$	−73.3408	+	133.403i	−0.190496	+	0.346501i
$386$	−32.4422			−0.0840471
$387$		0			0
$388$	−47.5744	−	47.5744i	−0.122614	−	0.122614i
$389$		−	50.0127i		−	0.128567i	−0.997932	−	0.0642837i	$-0.979524\pi$
$389$		−	50.0127i		−	0.128567i	0.997932	−	0.0642837i	$-0.0204763\pi$
$390$		0			0
$391$	1271.92			3.25299
$392$	−14.0000	+	14.0000i	−0.0357143	+	0.0357143i
$393$		0			0
$394$		−	13.3627i		−	0.0339154i
$395$	1.48029	+	5.09539i	0.00374756	+	0.0128997i
$396$		0			0
$397$	−325.002	+	325.002i	−0.818644	+	0.818644i	−0.985912	−	0.167268i	$-0.946506\pi$
$397$	−325.002	+	325.002i	−0.818644	+	0.818644i	0.167268	+	0.985912i	$0.446506\pi$
$398$	32.0712	+	32.0712i	0.0805808	+	0.0805808i
$399$		0			0
$400$	−84.4340	+	53.5808i	−0.211085	+	0.133952i
$401$	462.981			1.15457			0.577283	−	0.816544i	$-0.304113\pi$
$401$	462.981			1.15457			0.577283	+	0.816544i	$0.304113\pi$
$402$		0			0
$403$	362.031	+	362.031i	0.898340	+	0.898340i
$404$			100.293i			0.248251i
$405$		0			0
$406$	191.346			0.471294
$407$	−97.8188	+	97.8188i	−0.240341	+	0.240341i
$408$		0			0
$409$		−	131.630i		−	0.321834i	−0.986968	−	0.160917i	$-0.948555\pi$
$409$		−	131.630i		−	0.321834i	0.986968	−	0.160917i	$-0.0514451\pi$
$410$	63.3926	−	115.308i	0.154616	−	0.281238i
$411$		0			0
$412$	112.775	−	112.775i	0.273726	−	0.273726i
$413$	−176.510	−	176.510i	−0.427386	−	0.427386i
$414$		0			0
$415$	332.277	+	182.675i	0.800667	+	0.440182i
$416$	61.6417			0.148177
$417$		0			0
$418$	−277.538	−	277.538i	−0.663966	−	0.663966i
$419$			536.418i			1.28023i	0.768277	+	0.640117i	$0.221114\pi$
$419$			536.418i			1.28023i	−0.768277	+	0.640117i	$0.778886\pi$
$420$		0			0
$421$	−508.770			−1.20848			−0.604240	−	0.796803i	$-0.706523\pi$
$421$	−508.770			−1.20848			−0.604240	+	0.796803i	$0.706523\pi$
$422$	123.531	−	123.531i	0.292728	−	0.292728i
$423$		0			0
$424$			28.3411i			0.0668422i
$425$	−162.557	+	727.163i	−0.382487	+	1.71097i
$426$		0			0
$427$	15.1351	−	15.1351i	0.0354451	−	0.0354451i
$428$	−270.731	−	270.731i	−0.632548	−	0.632548i
$429$		0			0
$430$	251.005	−	72.9206i	0.583732	−	0.169583i
$431$	−467.561			−1.08483			−0.542414	−	0.840111i	$-0.682490\pi$
$431$	−467.561			−1.08483			−0.542414	+	0.840111i	$0.682490\pi$
$432$		0			0
$433$	−129.391	−	129.391i	−0.298825	−	0.298825i	0.541729	−	0.840554i	$-0.317770\pi$
$433$	−129.391	−	129.391i	−0.298825	−	0.298825i	−0.840554	+	0.541729i	$0.817770\pi$
$434$			175.803i			0.405075i
$435$		0			0
$436$	201.868			0.463001
$437$	−727.768	+	727.768i	−1.66537	+	1.66537i
$438$		0			0
$439$			51.7818i			0.117954i	0.998259	+	0.0589770i	$0.0187839\pi$
$439$			51.7818i			0.117954i	−0.998259	+	0.0589770i	$0.981216\pi$
$440$	142.614	+	78.4047i	0.324122	+	0.178192i
$441$		0			0
$442$	324.774	−	324.774i	0.734782	−	0.734782i
$443$	−357.514	−	357.514i	−0.807029	−	0.807029i	0.177154	−	0.984183i	$-0.443311\pi$
$443$	−357.514	−	357.514i	−0.807029	−	0.807029i	−0.984183	+	0.177154i	$0.943311\pi$
$444$		0			0
$445$	202.476	+	696.956i	0.455002	+	1.56619i
$446$	−163.918			−0.367529
$447$		0			0
$448$	14.9666	+	14.9666i	0.0334077	+	0.0334077i
$449$		−	615.742i		−	1.37136i	−0.727902	−	0.685681i	$-0.759504\pi$
$449$		−	615.742i		−	1.37136i	0.727902	−	0.685681i	$-0.240496\pi$
$450$		0			0
$451$	−214.148			−0.474828
$452$	−50.6348	+	50.6348i	−0.112024	+	0.112024i
$453$		0			0
$454$			187.218i			0.412374i
$455$	138.428	−	40.2154i	0.304237	−	0.0883855i
$456$		0			0
$457$	−502.144	+	502.144i	−1.09878	+	1.09878i	−0.104230	+	0.994553i	$0.533238\pi$
$457$	−502.144	+	502.144i	−1.09878	+	1.09878i	−0.994553	+	0.104230i	$0.966762\pi$
$458$	348.973	+	348.973i	0.761950	+	0.761950i
$459$		0			0
$460$	205.595	−	373.966i	0.446946	−	0.812970i
$461$	−100.965			−0.219012			−0.109506	−	0.993986i	$-0.534927\pi$
$461$	−100.965			−0.219012			−0.109506	+	0.993986i	$0.534927\pi$
$462$		0			0
$463$	312.235	+	312.235i	0.674374	+	0.674374i	0.958721	−	0.284347i	$-0.0917768\pi$
$463$	312.235	+	312.235i	0.674374	+	0.674374i	−0.284347	+	0.958721i	$0.591777\pi$
$464$		−	204.557i		−	0.440856i
$465$		0			0
$466$	−416.639			−0.894074
$467$	−502.571	+	502.571i	−1.07617	+	1.07617i	−0.0793198	+	0.996849i	$0.525275\pi$
$467$	−502.571	+	502.571i	−1.07617	+	1.07617i	−0.996849	+	0.0793198i	$0.974725\pi$
$468$		0			0
$469$			77.2537i			0.164720i
$470$	−139.856	−	481.407i	−0.297566	−	1.02427i
$471$		0			0
$472$	−188.697	+	188.697i	−0.399783	+	0.399783i
$473$	−300.794	−	300.794i	−0.635929	−	0.635929i
$474$		0			0
$475$	−323.056	−	509.080i	−0.680119	−	1.07175i
$476$	157.710			0.331324
$477$		0			0
$478$	−330.793	−	330.793i	−0.692035	−	0.692035i
$479$			270.133i			0.563952i	0.959421	+	0.281976i	$0.0909899\pi$
$479$			270.133i			0.563952i	−0.959421	+	0.281976i	$0.909010\pi$
$480$		0			0
$481$	130.992			0.272332
$482$	375.584	−	375.584i	0.779221	−	0.779221i
$483$		0			0
$484$		−	22.8599i		−	0.0472312i
$485$	−81.0330	+	147.395i	−0.167078	+	0.303906i
$486$		0			0
$487$	−227.632	+	227.632i	−0.467417	+	0.467417i	−0.901077	−	0.433660i	$-0.857222\pi$
$487$	−227.632	+	227.632i	−0.467417	+	0.467417i	0.433660	+	0.901077i	$0.357222\pi$
$488$	−16.1801	−	16.1801i	−0.0331559	−	0.0331559i
$489$		0			0
$490$	43.3747	+	23.8461i	0.0885198	+	0.0486655i
$491$	23.2563			0.0473652			0.0236826	−	0.999720i	$-0.492461\pi$
$491$	23.2563			0.0473652			0.0236826	+	0.999720i	$0.492461\pi$
$492$		0			0
$493$	−1077.76	−	1077.76i	−2.18612	−	2.18612i
$494$			371.658i			0.752344i
$495$		0			0
$496$	187.941			0.378913
$497$	119.283	−	119.283i	0.240006	−	0.240006i
$498$		0			0
$499$		−	319.077i		−	0.639433i	−0.947513	−	0.319717i	$-0.896412\pi$
$499$		−	319.077i		−	0.639433i	0.947513	−	0.319717i	$-0.103588\pi$
$500$	187.522	+	165.334i	0.375045	+	0.330668i
$501$		0			0
$502$	−41.2876	+	41.2876i	−0.0822463	+	0.0822463i
$503$	−585.731	−	585.731i	−1.16448	−	1.16448i	−0.983485	−	0.180990i	$-0.942070\pi$
$503$	−585.731	−	585.731i	−1.16448	−	1.16448i	−0.180990	−	0.983485i	$-0.557930\pi$
$504$		0			0
$505$	240.779	−	69.9498i	0.476789	−	0.138514i
$506$	−694.524			−1.37258
$507$		0			0
$508$	−233.492	−	233.492i	−0.459631	−	0.459631i
$509$			266.157i			0.522902i	0.965217	+	0.261451i	$0.0842009\pi$
$509$			266.157i			0.522902i	−0.965217	+	0.261451i	$0.915799\pi$
$510$		0			0
$511$	187.787			0.367490
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	202.741i		−	0.394437i
$515$	−349.399	−	192.089i	−0.678446	−	0.372988i
$516$		0			0
$517$	−576.899	+	576.899i	−1.11586	+	1.11586i
$518$	31.8048	+	31.8048i	0.0613993	+	0.0613993i
$519$		0			0
$520$	−42.9921	−	147.986i	−0.0826770	−	0.284588i
$521$	1.52542			0.00292786			0.00146393	−	0.999999i	$-0.499534\pi$
$521$	1.52542			0.00292786			0.00146393	+	0.999999i	$0.499534\pi$
$522$		0			0
$523$	260.120	+	260.120i	0.497362	+	0.497362i	0.910616	−	0.413254i	$-0.135608\pi$
$523$	260.120	+	260.120i	0.497362	+	0.497362i	−0.413254	+	0.910616i	$0.635608\pi$
$524$			69.6007i			0.132826i
$525$		0			0
$526$	−329.188			−0.625833
$527$	990.210	−	990.210i	1.87896	−	1.87896i
$528$		0			0
$529$			1292.20i			2.44272i
$530$	68.0396	−	19.7665i	0.128377	−	0.0372953i
$531$		0			0
$532$	−90.2387	+	90.2387i	−0.169622	+	0.169622i
$533$	143.385	+	143.385i	0.269015	+	0.269015i
$534$		0			0
$535$	−461.133	+	838.776i	−0.861931	+	1.56781i
$536$	82.5877			0.154081
$537$		0			0
$538$	254.148	+	254.148i	0.472394	+	0.472394i
$539$		−	80.5547i		−	0.149452i
$540$		0			0
$541$	−273.648			−0.505820			−0.252910	−	0.967490i	$-0.581388\pi$
$541$	−273.648			−0.505820			−0.252910	+	0.967490i	$0.581388\pi$
$542$	22.4723	−	22.4723i	0.0414619	−	0.0414619i
$543$		0			0
$544$		−	168.599i		−	0.309925i
$545$	−140.793	−	484.634i	−0.258336	−	0.889236i
$546$		0			0
$547$	355.490	−	355.490i	0.649890	−	0.649890i	−0.303077	−	0.952966i	$-0.598014\pi$
$547$	355.490	−	355.490i	0.649890	−	0.649890i	0.952966	+	0.303077i	$0.0980138\pi$
$548$	263.104	+	263.104i	0.480117	+	0.480117i
$549$		0			0
$550$	88.7632	−	397.062i	0.161388	−	0.721932i
$551$	1233.34			2.23837
$552$		0			0
$553$	−1.98535	−	1.98535i	−0.00359014	−	0.00359014i
$554$		−	94.7898i		−	0.171101i
$555$		0			0
$556$	−178.881			−0.321729
$557$	270.897	−	270.897i	0.486350	−	0.486350i	−0.420802	−	0.907152i	$-0.638251\pi$
$557$	270.897	−	270.897i	0.486350	−	0.486350i	0.907152	+	0.420802i	$0.138251\pi$
$558$		0			0
$559$			402.802i			0.720575i
$560$	25.4925	−	46.3695i	0.0455224	−	0.0828027i
$561$		0			0
$562$	18.8810	−	18.8810i	0.0335960	−	0.0335960i
$563$	−73.1143	−	73.1143i	−0.129866	−	0.129866i	0.639186	−	0.769052i	$-0.279271\pi$
$563$	−73.1143	−	73.1143i	−0.129866	−	0.129866i	−0.769052	+	0.639186i	$0.779271\pi$
$564$		0			0
$565$	156.876	+	86.2458i	0.277657	+	0.152647i
$566$	−231.651			−0.409277
$567$		0			0
$568$	−127.519	−	127.519i	−0.224505	−	0.224505i
$569$		−	1018.55i		−	1.79007i	−0.445992	−	0.895037i	$-0.647149\pi$
$569$		−	1018.55i		−	1.79007i	0.445992	−	0.895037i	$-0.352851\pi$
$570$		0			0
$571$	−621.517			−1.08847			−0.544236	−	0.838932i	$-0.683180\pi$
$571$	−621.517			−1.08847			−0.544236	+	0.838932i	$0.683180\pi$
$572$	−177.340	+	177.340i	−0.310036	+	0.310036i
$573$		0			0
$574$			69.6280i			0.121303i
$575$	−1041.19	−	232.758i	−1.81076	−	0.404796i
$576$		0			0
$577$	760.301	−	760.301i	1.31768	−	1.31768i	0.402071	−	0.915608i	$-0.368290\pi$
$577$	760.301	−	760.301i	1.31768	−	1.31768i	0.915608	−	0.402071i	$-0.131710\pi$
$578$	−599.306	−	599.306i	−1.03686	−	1.03686i
$579$		0			0
$580$	−491.089	+	142.668i	−0.846704	+	0.245980i
$581$	−200.644			−0.345342
$582$		0			0
$583$	−81.5360	−	81.5360i	−0.139856	−	0.139856i
$584$		−	200.753i		−	0.343756i
$585$		0			0
$586$	−448.901			−0.766043
$587$	−5.94607	+	5.94607i	−0.0101296	+	0.0101296i	−0.712153	−	0.702024i	$-0.752280\pi$
$587$	−5.94607	+	5.94607i	−0.0101296	+	0.0101296i	0.702024	+	0.712153i	$0.252280\pi$
$588$		0			0
$589$			1133.16i			1.92387i
$590$	584.621	+	321.407i	0.990883	+	0.544757i
$591$		0			0
$592$	34.0008	−	34.0008i	0.0574338	−	0.0574338i
$593$	463.916	+	463.916i	0.782320	+	0.782320i	0.980222	−	0.197902i	$-0.0634127\pi$
$593$	463.916	+	463.916i	0.782320	+	0.782320i	−0.197902	+	0.980222i	$0.563413\pi$
$594$		0			0
$595$	−109.995	−	378.622i	−0.184866	−	0.636339i
$596$	−111.480			−0.187047
$597$		0			0
$598$	465.027	+	465.027i	0.777638	+	0.777638i
$599$			660.745i			1.10308i	0.834148	+	0.551540i	$0.185960\pi$
$599$			660.745i			1.10308i	−0.834148	+	0.551540i	$0.814040\pi$
$600$		0			0
$601$	−905.439			−1.50655			−0.753277	−	0.657704i	$-0.771528\pi$
$601$	−905.439			−1.50655			−0.753277	+	0.657704i	$0.771528\pi$
$602$	−97.8004	+	97.8004i	−0.162459	+	0.162459i
$603$		0			0
$604$		−	165.933i		−	0.274724i
$605$	−54.8807	+	15.9436i	−0.0907119	+	0.0263531i
$606$		0			0
$607$	518.514	−	518.514i	0.854224	−	0.854224i	−0.136426	−	0.990650i	$-0.543562\pi$
$607$	518.514	−	518.514i	0.854224	−	0.854224i	0.990650	+	0.136426i	$0.0435615\pi$
$608$	96.4693	+	96.4693i	0.158667	+	0.158667i
$609$		0			0
$610$	−27.5593	+	50.1289i	−0.0451792	+	0.0821786i
$611$	772.541			1.26439
$612$		0			0
$613$	−500.739	−	500.739i	−0.816867	−	0.816867i	0.168786	−	0.985653i	$-0.446015\pi$
$613$	−500.739	−	500.739i	−0.816867	−	0.816867i	−0.985653	+	0.168786i	$0.946015\pi$
$614$			85.0240i			0.138476i
$615$		0			0
$616$	−86.1166			−0.139800
$617$	−122.242	+	122.242i	−0.198123	+	0.198123i	−0.799195	−	0.601072i	$-0.794740\pi$
$617$	−122.242	+	122.242i	−0.198123	+	0.198123i	0.601072	+	0.799195i	$0.294740\pi$
$618$		0			0
$619$			320.914i			0.518440i	0.965818	+	0.259220i	$0.0834655\pi$
$619$			320.914i			0.518440i	−0.965818	+	0.259220i	$0.916534\pi$
$620$	−131.080	−	451.198i	−0.211419	−	0.727738i
$621$		0			0
$622$	97.1353	−	97.1353i	0.156166	−	0.156166i
$623$	−271.559	−	271.559i	−0.435889	−	0.435889i
$624$		0			0
$625$	266.137	−	565.505i	0.425820	−	0.904808i
$626$	−188.983			−0.301889
$627$		0			0
$628$	199.590	+	199.590i	0.317818	+	0.317818i
$629$		−	358.282i		−	0.569606i
$630$		0			0
$631$	−636.141			−1.00815			−0.504074	−	0.863661i	$-0.668166\pi$
$631$	−636.141			−1.00815			−0.504074	+	0.863661i	$0.668166\pi$
$632$	−2.12242	+	2.12242i	−0.00335827	+	0.00335827i
$633$		0			0
$634$			292.300i			0.461040i
$635$	−397.706	+	723.405i	−0.626308	+	1.13922i
$636$		0			0
$637$	−53.9365	+	53.9365i	−0.0846726	+	0.0846726i
$638$	588.501	+	588.501i	0.922416	+	0.922416i
$639$		0			0
$640$	−49.5711	−	27.2527i	−0.0774548	−	0.0425823i
$641$	682.051			1.06404			0.532021	−	0.846731i	$-0.321433\pi$
$641$	682.051			1.06404			0.532021	+	0.846731i	$0.321433\pi$
$642$		0			0
$643$	−5.33298	−	5.33298i	−0.00829390	−	0.00829390i	0.702948	−	0.711242i	$-0.251867\pi$
$643$	−5.33298	−	5.33298i	−0.00829390	−	0.00829390i	−0.711242	+	0.702948i	$0.751867\pi$
$644$			225.818i			0.350649i
$645$		0			0
$646$	1016.54			1.57359
$647$	−285.931	+	285.931i	−0.441933	+	0.441933i	−0.892661	−	0.450728i	$-0.851164\pi$
$647$	−285.931	+	285.931i	−0.441933	+	0.441933i	0.450728	+	0.892661i	$0.351164\pi$
$648$		0			0
$649$		−	1085.75i		−	1.67296i
$650$	−325.291	+	206.426i	−0.500447	+	0.317578i
$651$		0			0
$652$	−90.7768	+	90.7768i	−0.139228	+	0.139228i
$653$	−199.462	−	199.462i	−0.305455	−	0.305455i	0.537689	−	0.843144i	$-0.319298\pi$
$653$	−199.462	−	199.462i	−0.305455	−	0.305455i	−0.843144	+	0.537689i	$0.819298\pi$
$654$		0			0
$655$	167.093	−	48.5431i	0.255104	−	0.0741116i
$656$	74.4355			0.113469
$657$		0			0
$658$	187.573	+	187.573i	0.285066	+	0.285066i
$659$		−	204.685i		−	0.310599i	−0.987867	−	0.155300i	$-0.950366\pi$
$659$		−	204.685i		−	0.310599i	0.987867	−	0.155300i	$-0.0496343\pi$
$660$		0			0
$661$	143.044			0.216406			0.108203	−	0.994129i	$-0.465490\pi$
$661$	143.044			0.216406			0.108203	+	0.994129i	$0.465490\pi$
$662$	223.981	−	223.981i	0.338339	−	0.338339i
$663$		0			0
$664$			214.497i			0.323038i
$665$	279.577	+	153.703i	0.420417	+	0.231132i
$666$		0			0
$667$	1543.19	−	1543.19i	2.31362	−	2.31362i
$668$	−198.500	−	198.500i	−0.297156	−	0.297156i
$669$		0			0
$670$	−57.6008	−	198.272i	−0.0859714	−	0.295928i
$671$	93.0986			0.138746
$672$		0			0
$673$	−317.527	−	317.527i	−0.471808	−	0.471808i	0.430691	−	0.902499i	$-0.358270\pi$
$673$	−317.527	−	317.527i	−0.471808	−	0.471808i	−0.902499	+	0.430691i	$0.858270\pi$
$674$			83.4888i			0.123871i
$675$		0			0
$676$	−100.519			−0.148697
$677$	272.663	−	272.663i	0.402752	−	0.402752i	−0.476450	−	0.879202i	$-0.658077\pi$
$677$	272.663	−	272.663i	0.402752	−	0.402752i	0.879202	+	0.476450i	$0.158077\pi$
$678$		0			0
$679$		−	89.0035i		−	0.131080i
$680$	−404.764	+	117.590i	−0.595241	+	0.172926i
$681$		0			0
$682$	−540.697	+	540.697i	−0.792812	+	0.792812i
$683$	449.231	+	449.231i	0.657732	+	0.657732i	0.954843	−	0.297111i	$-0.0960232\pi$
$683$	449.231	+	449.231i	0.657732	+	0.657732i	−0.297111	+	0.954843i	$0.596023\pi$
$684$		0			0
$685$	448.143	−	815.148i	0.654224	−	1.19000i
$686$	−26.1916			−0.0381802
$687$		0			0
$688$	104.553	+	104.553i	0.151967	+	0.151967i
$689$			109.187i			0.158472i
$690$		0			0
$691$	1004.13			1.45316			0.726578	−	0.687084i	$-0.241109\pi$
$691$	1004.13			1.45316			0.726578	+	0.687084i	$0.241109\pi$
$692$	161.081	−	161.081i	0.232776	−	0.232776i
$693$		0			0
$694$			566.325i			0.816031i
$695$	124.761	+	429.448i	0.179512	+	0.617911i
$696$		0			0
$697$	392.181	−	392.181i	0.562669	−	0.562669i
$698$	−73.8529	−	73.8529i	−0.105807	−	0.105807i
$699$		0			0
$700$	−129.101	−	28.8605i	−0.184430	−	0.0412293i
$701$	869.248			1.24001			0.620006	−	0.784597i	$-0.287130\pi$
$701$	869.248			1.24001			0.620006	+	0.784597i	$0.287130\pi$
$702$		0			0
$703$	205.002	+	205.002i	0.291610	+	0.291610i
$704$			92.0626i			0.130771i
$705$		0			0
$706$	443.401			0.628047
$707$	−93.8159	+	93.8159i	−0.132696	+	0.132696i
$708$		0			0
$709$			79.6980i			0.112409i	0.998419	+	0.0562045i	$0.0178999\pi$
$709$			79.6980i			0.112409i	−0.998419	+	0.0562045i	$0.982100\pi$
$710$	−217.202	+	395.078i	−0.305918	+	0.556449i
$711$		0			0
$712$	−290.309	+	290.309i	−0.407737	+	0.407737i
$713$	1417.83	+	1417.83i	1.98855	+	1.98855i
$714$		0			0
$715$	549.435	+	302.062i	0.768440	+	0.422465i
$716$	308.533			0.430912
$717$		0			0
$718$	351.735	+	351.735i	0.489882	+	0.489882i
$719$		−	1081.03i		−	1.50351i	−0.659440	−	0.751757i	$-0.729207\pi$
$719$		−	1081.03i		−	1.50351i	0.659440	−	0.751757i	$-0.270793\pi$
$720$		0			0
$721$	210.983			0.292626
$722$	−220.645	+	220.645i	−0.305603	+	0.305603i
$723$		0			0
$724$		−	333.096i		−	0.460078i
$725$	685.020	+	1079.47i	0.944856	+	1.48893i
$726$		0			0
$727$	281.701	−	281.701i	0.387484	−	0.387484i	−0.486305	−	0.873789i	$-0.661656\pi$
$727$	281.701	−	281.701i	0.387484	−	0.387484i	0.873789	+	0.486305i	$0.161656\pi$
$728$	57.6605	+	57.6605i	0.0792040	+	0.0792040i
$729$		0			0
$730$	−481.957	+	140.016i	−0.660215	+	0.191802i
$731$	1101.72			1.50715
$732$		0			0
$733$	1016.28	+	1016.28i	1.38647	+	1.38647i	0.832611	+	0.553858i	$0.186845\pi$
$733$	1016.28	+	1016.28i	1.38647	+	1.38647i	0.553858	+	0.832611i	$0.313155\pi$
$734$		−	18.0753i		−	0.0246258i
$735$		0			0
$736$	241.409			0.328002
$737$	−237.601	+	237.601i	−0.322389	+	0.322389i
$738$		0			0
$739$			289.140i			0.391258i	0.980678	+	0.195629i	$0.0626749\pi$
$739$			289.140i			0.391258i	−0.980678	+	0.195629i	$0.937325\pi$
$740$	−105.341	−	57.9132i	−0.142353	−	0.0782611i
$741$		0			0
$742$	−26.5107	+	26.5107i	−0.0357286	+	0.0357286i
$743$	−290.501	−	290.501i	−0.390984	−	0.390984i	0.484054	−	0.875038i	$-0.339164\pi$
$743$	−290.501	−	290.501i	−0.390984	−	0.390984i	−0.875038	+	0.484054i	$0.839164\pi$
$744$		0			0
$745$	77.7517	+	267.634i	0.104365	+	0.359240i
$746$	−302.189			−0.405079
$747$		0			0
$748$	485.053	+	485.053i	0.648467	+	0.648467i
$749$		−	506.491i		−	0.676223i
$750$		0			0
$751$	688.089			0.916231			0.458115	−	0.888893i	$-0.348525\pi$
$751$	688.089			0.916231			0.458115	+	0.888893i	$0.348525\pi$
$752$	200.524	−	200.524i	0.266655	−	0.266655i
$753$		0			0
$754$		−	788.077i		−	1.04520i
$755$	−398.363	+	115.730i	−0.527632	+	0.153285i
$756$		0			0
$757$	180.960	−	180.960i	0.239049	−	0.239049i	−0.577408	−	0.816456i	$-0.695936\pi$
$757$	180.960	−	180.960i	0.239049	−	0.239049i	0.816456	+	0.577408i	$0.195936\pi$
$758$	−268.787	−	268.787i	−0.354601	−	0.354601i
$759$		0			0
$760$	164.315	−	298.880i	0.216204	−	0.393264i
$761$	−1096.09			−1.44033			−0.720163	−	0.693805i	$-0.755933\pi$
$761$	−1096.09			−1.44033			−0.720163	+	0.693805i	$0.755933\pi$
$762$		0			0
$763$	188.831	+	188.831i	0.247484	+	0.247484i
$764$		−	471.291i		−	0.616873i
$765$		0			0
$766$	−608.682			−0.794625
$767$	−726.977	+	726.977i	−0.947818	+	0.947818i
$768$		0			0
$769$		−	892.540i		−	1.16065i	−0.814385	−	0.580325i	$-0.802925\pi$
$769$		−	892.540i		−	1.16065i	0.814385	−	0.580325i	$-0.197075\pi$
$770$	60.0621	+	206.744i	0.0780028	+	0.268499i
$771$		0			0
$772$	−32.4422	+	32.4422i	−0.0420235	+	0.0420235i
$773$	−836.773	−	836.773i	−1.08250	−	1.08250i	−0.996276	−	0.0862244i	$-0.972520\pi$
$773$	−836.773	−	836.773i	−1.08250	−	1.08250i	−0.0862244	−	0.996276i	$-0.527480\pi$
$774$		0			0
$775$	−991.787	+	629.376i	−1.27973	+	0.812099i
$776$	−95.1487			−0.122614
$777$		0			0
$778$	−50.0127	−	50.0127i	−0.0642837	−	0.0642837i
$779$			448.796i			0.576118i
$780$		0			0
$781$	733.733			0.939479
$782$	1271.92	−	1271.92i	1.62650	−	1.62650i
$783$		0			0
$784$			28.0000i			0.0357143i
$785$	339.960	−	618.368i	0.433070	−	0.787730i
$786$		0			0
$787$	−226.485	+	226.485i	−0.287782	+	0.287782i	−0.836203	−	0.548420i	$-0.815229\pi$
$787$	−226.485	+	226.485i	−0.287782	+	0.287782i	0.548420	+	0.836203i	$0.315229\pi$
$788$	−13.3627	−	13.3627i	−0.0169577	−	0.0169577i
$789$		0			0
$790$	6.57568	+	3.61511i	0.00832365	+	0.00457608i
$791$	−94.7290			−0.119759
$792$		0			0
$793$	−62.3354	−	62.3354i	−0.0786070	−	0.0786070i
$794$			650.003i			0.818644i
$795$		0			0
$796$	64.1423			0.0805808
$797$	728.914	−	728.914i	0.914572	−	0.914572i	−0.0820555	−	0.996628i	$-0.526148\pi$
$797$	728.914	−	728.914i	0.914572	−	0.914572i	0.996628	+	0.0820555i	$0.0261485\pi$
$798$		0			0
$799$		−	2113.02i		−	2.64458i
$800$	−30.8532	+	138.015i	−0.0385665	+	0.172518i
$801$		0			0
$802$	462.981	−	462.981i	0.577283	−	0.577283i
$803$	577.558	+	577.558i	0.719250	+	0.719250i
$804$		0			0
$805$	542.130	−	157.497i	0.673453	−	0.195648i
$806$	724.062			0.898340
$807$		0			0
$808$	100.293	+	100.293i	0.124126	+	0.124126i
$809$		−	1196.38i		−	1.47884i	−0.673247	−	0.739418i	$-0.735101\pi$
$809$		−	1196.38i		−	1.47884i	0.673247	−	0.739418i	$-0.264899\pi$
$810$		0			0
$811$	−1180.03			−1.45503			−0.727513	−	0.686094i	$-0.759324\pi$
$811$	−1180.03			−1.45503			−0.727513	+	0.686094i	$0.759324\pi$
$812$	191.346	−	191.346i	0.235647	−	0.235647i
$813$		0			0
$814$			195.638i			0.240341i
$815$	281.244	+	154.619i	0.345085	+	0.189717i
$816$		0			0
$817$	−630.385	+	630.385i	−0.771585	+	0.771585i
$818$	−131.630	−	131.630i	−0.160917	−	0.160917i
$819$		0			0
$820$	−51.9151	−	178.700i	−0.0633111	−	0.217927i
$821$	−35.8305			−0.0436425			−0.0218212	−	0.999762i	$-0.506946\pi$
$821$	−35.8305			−0.0436425			−0.0218212	+	0.999762i	$0.506946\pi$
$822$		0			0
$823$	448.829	+	448.829i	0.545357	+	0.545357i	0.925094	−	0.379737i	$-0.123986\pi$
$823$	448.829	+	448.829i	0.545357	+	0.545357i	−0.379737	+	0.925094i	$0.623986\pi$
$824$		−	225.550i		−	0.273726i
$825$		0			0
$826$	−353.021			−0.427386
$827$	−874.926	+	874.926i	−1.05795	+	1.05795i	−0.0597373	+	0.998214i	$0.519026\pi$
$827$	−874.926	+	874.926i	−1.05795	+	1.05795i	−0.998214	+	0.0597373i	$0.980974\pi$
$828$		0			0
$829$		−	934.022i		−	1.12669i	−0.826223	−	0.563343i	$-0.809515\pi$
$829$		−	934.022i		−	1.12669i	0.826223	−	0.563343i	$-0.190485\pi$
$830$	514.952	−	149.601i	0.620424	−	0.180242i
$831$		0			0
$832$	61.6417	−	61.6417i	0.0740886	−	0.0740886i
$833$	147.525	+	147.525i	0.177100	+	0.177100i
$834$		0			0
$835$	−338.104	+	614.992i	−0.404915	+	0.736517i
$836$	−555.076			−0.663966
$837$		0			0
$838$	536.418	+	536.418i	0.640117	+	0.640117i
$839$		−	10.5147i		−	0.0125324i	−0.999980	−	0.00626621i	$-0.998005\pi$
$839$		−	10.5147i		−	0.0125324i	0.999980	−	0.00626621i	$-0.00199461\pi$
$840$		0			0
$841$	−1774.22			−2.10966
$842$	−508.770	+	508.770i	−0.604240	+	0.604240i
$843$		0			0
$844$		−	247.063i		−	0.292728i
$845$	70.1071	+	241.320i	0.0829670	+	0.285586i
$846$		0			0
$847$	21.3835	−	21.3835i	0.0252461	−	0.0252461i
$848$	28.3411	+	28.3411i	0.0334211	+	0.0334211i
$849$		0			0
$850$	564.606	+	889.720i	0.664242	+	1.04673i
$851$	513.007			0.602828
$852$		0			0
$853$	1082.57	+	1082.57i	1.26914	+	1.26914i	0.946534	+	0.322603i	$0.104558\pi$
$853$	1082.57	+	1082.57i	1.26914	+	1.26914i	0.322603	+	0.946534i	$0.395442\pi$
$854$		−	30.2701i		−	0.0354451i
$855$		0			0
$856$	−541.461			−0.632548
$857$	−506.843	+	506.843i	−0.591416	+	0.591416i	−0.938014	−	0.346598i	$-0.887337\pi$
$857$	−506.843	+	506.843i	−0.591416	+	0.591416i	0.346598	+	0.938014i	$0.387337\pi$
$858$		0			0
$859$			471.172i			0.548512i	0.961657	+	0.274256i	$0.0884315\pi$
$859$			471.172i			0.548512i	−0.961657	+	0.274256i	$0.911568\pi$
$860$	178.084	−	323.926i	0.207075	−	0.376658i
$861$		0			0
$862$	−467.561	+	467.561i	−0.542414	+	0.542414i
$863$	−352.570	−	352.570i	−0.408540	−	0.408540i	0.472689	−	0.881229i	$-0.343283\pi$
$863$	−352.570	−	352.570i	−0.408540	−	0.408540i	−0.881229	+	0.472689i	$0.843283\pi$
$864$		0			0
$865$	−499.059	−	274.367i	−0.576947	−	0.317188i
$866$	−258.782			−0.298825
$867$		0			0
$868$	175.803	+	175.803i	0.202538	+	0.202538i
$869$		−	12.2122i		−	0.0140532i
$870$		0			0
$871$	318.178			0.365301
$872$	201.868	−	201.868i	0.231500	−	0.231500i
$873$		0			0
$874$			1455.54i			1.66537i
$875$	20.7550	+	330.067i	0.0237200	+	0.377219i
$876$		0			0
$877$	−1223.94	+	1223.94i	−1.39560	+	1.39560i	−0.583467	+	0.812137i	$0.698304\pi$
$877$	−1223.94	+	1223.94i	−1.39560	+	1.39560i	−0.812137	+	0.583467i	$0.801696\pi$
$878$	51.7818	+	51.7818i	0.0589770	+	0.0589770i
$879$		0			0
$880$	221.018	−	64.2091i	0.251157	−	0.0729649i
$881$	635.103			0.720889			0.360444	−	0.932781i	$-0.382625\pi$
$881$	635.103			0.720889			0.360444	+	0.932781i	$0.382625\pi$
$882$		0			0
$883$	−230.546	−	230.546i	−0.261094	−	0.261094i	0.564405	−	0.825498i	$-0.309106\pi$
$883$	−230.546	−	230.546i	−0.261094	−	0.261094i	−0.825498	+	0.564405i	$0.809106\pi$
$884$		−	649.547i		−	0.734782i
$885$		0			0
$886$	−715.028			−0.807029
$887$	1224.61	−	1224.61i	1.38062	−	1.38062i	0.537101	−	0.843518i	$-0.319520\pi$
$887$	1224.61	−	1224.61i	1.38062	−	1.38062i	0.843518	−	0.537101i	$-0.180480\pi$
$888$		0			0
$889$		−	436.824i		−	0.491366i
$890$	899.432	+	494.480i	1.01060	+	0.555595i
$891$		0			0
$892$	−163.918	+	163.918i	−0.183765	+	0.183765i
$893$	1209.03	+	1209.03i	1.35389	+	1.35389i
$894$		0			0
$895$	−215.187	−	740.708i	−0.240432	−	0.827607i
$896$	29.9333			0.0334077
$897$		0			0
$898$	−615.742	−	615.742i	−0.685681	−	0.685681i
$899$		−	2402.79i		−	2.67273i
$900$		0			0
$901$	298.643			0.331457
$902$	−214.148	+	214.148i	−0.237414	+	0.237414i
$903$		0			0
$904$			101.270i			0.112024i
$905$	−799.678	+	232.318i	−0.883622	+	0.256705i
$906$		0			0
$907$	766.713	−	766.713i	0.845329	−	0.845329i	−0.144217	−	0.989546i	$-0.546066\pi$
$907$	766.713	−	766.713i	0.845329	−	0.845329i	0.989546	+	0.144217i	$0.0460664\pi$
$908$	187.218	+	187.218i	0.206187	+	0.206187i
$909$		0			0
$910$	98.2126	−	178.643i	0.107926	−	0.196311i
$911$	754.441			0.828146			0.414073	−	0.910244i	$-0.364106\pi$
$911$	754.441			0.828146			0.414073	+	0.910244i	$0.364106\pi$
$912$		0			0
$913$	−617.098	−	617.098i	−0.675902	−	0.675902i
$914$			1004.29i			1.09878i
$915$		0			0
$916$	697.947			0.761950
$917$	−65.1055	+	65.1055i	−0.0709984	+	0.0709984i
$918$		0			0
$919$			858.117i			0.933750i	0.884323	+	0.466875i	$0.154620\pi$
$919$			858.117i			0.933750i	−0.884323	+	0.466875i	$0.845380\pi$
$920$	−168.371	−	579.561i	−0.183012	−	0.629958i
$921$		0			0
$922$	−100.965	+	100.965i	−0.109506	+	0.109506i
$923$	−491.280	−	491.280i	−0.532265	−	0.532265i
$924$		0			0
$925$	−65.5645	+	293.288i	−0.0708806	+	0.317068i
$926$	624.471			0.674374
$927$		0			0
$928$	−204.557	−	204.557i	−0.220428	−	0.220428i
$929$		−	631.542i		−	0.679809i	−0.940460	−	0.339904i	$-0.889605\pi$
$929$		−	631.542i		−	0.679809i	0.940460	−	0.339904i	$-0.110395\pi$
$930$		0			0
$931$	−168.821			−0.181333
$932$	−416.639	+	416.639i	−0.447037	+	0.447037i
$933$		0			0
$934$			1005.14i			1.07617i
$935$	826.186	−	1502.79i	0.883622	−	1.60726i
$936$		0			0
$937$	1167.50	−	1167.50i	1.24599	−	1.24599i	0.288519	−	0.957474i	$-0.406837\pi$
$937$	1167.50	−	1167.50i	1.24599	−	1.24599i	0.957474	−	0.288519i	$-0.0931630\pi$
$938$	77.2537	+	77.2537i	0.0823600	+	0.0823600i
$939$		0			0
$940$	−621.263	−	341.551i	−0.660918	−	0.363352i
$941$	614.550			0.653082			0.326541	−	0.945183i	$-0.394117\pi$
$941$	614.550			0.653082			0.326541	+	0.945183i	$0.394117\pi$
$942$		0			0
$943$	561.544	+	561.544i	0.595487	+	0.595487i
$944$			377.395i			0.399783i
$945$		0			0
$946$	−601.589			−0.635929
$947$	635.282	−	635.282i	0.670837	−	0.670837i	−0.287072	−	0.957909i	$-0.592682\pi$
$947$	635.282	−	635.282i	0.670837	−	0.670837i	0.957909	+	0.287072i	$0.0926820\pi$
$948$		0			0
$949$		−	773.423i		−	0.814987i
$950$	−832.137	−	186.024i	−0.875933	−	0.195815i
$951$		0			0
$952$	157.710	−	157.710i	0.165662	−	0.165662i
$953$	−350.517	−	350.517i	−0.367803	−	0.367803i	0.498872	−	0.866676i	$-0.333748\pi$
$953$	−350.517	−	350.517i	−0.367803	−	0.367803i	−0.866676	+	0.498872i	$0.833748\pi$
$954$		0			0
$955$	−1131.45	+	328.703i	−1.18476	+	0.344191i
$956$	−661.585			−0.692035
$957$		0			0
$958$	270.133	+	270.133i	0.281976	+	0.281976i
$959$			492.223i			0.513267i
$960$		0			0
$961$	1246.61			1.29720
$962$	130.992	−	130.992i	0.136166	−	0.136166i
$963$		0			0
$964$		−	751.169i		−	0.779221i
$965$	100.512	+	55.2585i	0.104158	+	0.0572627i
$966$		0			0
$967$	435.204	−	435.204i	0.450056	−	0.450056i	−0.445317	−	0.895373i	$-0.646909\pi$
$967$	435.204	−	435.204i	0.450056	−	0.450056i	0.895373	+	0.445317i	$0.146909\pi$
$968$	−22.8599	−	22.8599i	−0.0236156	−	0.0236156i
$969$		0			0
$970$	66.3616	+	228.428i	0.0684140	+	0.235492i
$971$	−218.866			−0.225403			−0.112701	−	0.993629i	$-0.535950\pi$
$971$	−218.866			−0.225403			−0.112701	+	0.993629i	$0.535950\pi$
$972$		0			0
$973$	−167.328	−	167.328i	−0.171971	−	0.171971i
$974$			455.264i			0.467417i
$975$		0			0
$976$	−32.3601			−0.0331559
$977$	−1000.73	+	1000.73i	−1.02429	+	1.02429i	−0.0245886	+	0.999698i	$0.507828\pi$
$977$	−1000.73	+	1000.73i	−1.02429	+	1.02429i	−0.999698	+	0.0245886i	$0.992172\pi$
$978$		0			0
$979$		−	1670.41i		−	1.70624i
$980$	67.2208	−	19.5286i	0.0685926	−	0.0199272i
$981$		0			0
$982$	23.2563	−	23.2563i	0.0236826	−	0.0236826i
$983$	−915.596	−	915.596i	−0.931431	−	0.931431i	0.0663648	−	0.997795i	$-0.478860\pi$
$983$	−915.596	−	915.596i	−0.931431	−	0.931431i	−0.997795	+	0.0663648i	$0.978860\pi$
$984$		0			0
$985$	−22.7605	+	41.4001i	−0.0231071	+	0.0420306i
$986$	−2155.51			−2.18612
$987$		0			0
$988$	371.658	+	371.658i	0.376172	+	0.376172i
$989$			1577.50i			1.59505i
$990$		0			0
$991$	−437.633			−0.441608			−0.220804	−	0.975318i	$-0.570868\pi$
$991$	−437.633			−0.441608			−0.220804	+	0.975318i	$0.570868\pi$
$992$	187.941	−	187.941i	0.189457	−	0.189457i
$993$		0			0
$994$		−	238.566i		−	0.240006i
$995$	−44.7361	−	153.989i	−0.0449609	−	0.154763i
$996$		0			0
$997$	180.748	−	180.748i	0.181292	−	0.181292i	−0.610627	−	0.791919i	$-0.709082\pi$
$997$	180.748	−	180.748i	0.181292	−	0.181292i	0.791919	+	0.610627i	$0.209082\pi$
$998$	−319.077	−	319.077i	−0.319717	−	0.319717i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.o.f.253.1		16
3.2	odd	2		210.3.l.b.43.4	✓	16
5.2	odd	4	inner	630.3.o.f.127.1		16
15.2	even	4		210.3.l.b.127.4	yes	16
15.8	even	4		1050.3.l.h.757.5		16
15.14	odd	2		1050.3.l.h.43.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.4	✓	16	3.2	odd	2
210.3.l.b.127.4	yes	16	15.2	even	4
630.3.o.f.127.1		16	5.2	odd	4	inner
630.3.o.f.253.1		16	1.1	even	1	trivial
1050.3.l.h.43.5		16	15.14	odd	2
1050.3.l.h.757.5		16	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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-4.80148 + 1.39490i) q^{5} +(1.87083 - 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-4.80148 + 1.39490i) q^{5} +(1.87083 - 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-3.40658 + 6.19639i) q^{10} +11.5078 q^{11} +(-7.70521 - 7.70521i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(-21.0749 + 21.0749i) q^{17} -24.1173i q^{19} +(2.78980 + 9.60297i) q^{20} +(11.5078 - 11.5078i) q^{22} +(-30.1762 - 30.1762i) q^{23} +(21.1085 - 13.3952i) q^{25} -15.4104 q^{26} +(-3.74166 - 3.74166i) q^{28} +51.1392i q^{29} -46.9852 q^{31} +(-4.00000 + 4.00000i) q^{32} +42.1499i q^{34} +(-6.37313 + 11.5924i) q^{35} +(-8.50020 + 8.50020i) q^{37} +(-24.1173 - 24.1173i) q^{38} +(12.3928 + 6.81316i) q^{40} -18.6089 q^{41} +(-26.1383 - 26.1383i) q^{43} -23.0156i q^{44} -60.3523 q^{46} +(-50.1311 + 50.1311i) q^{47} -7.00000i q^{49} +(7.71330 - 34.5037i) q^{50} +(-15.4104 + 15.4104i) q^{52} +(-7.08527 - 7.08527i) q^{53} +(-55.2546 + 16.0523i) q^{55} -7.48331 q^{56} +(51.1392 + 51.1392i) q^{58} -94.3487i q^{59} +8.09003 q^{61} +(-46.9852 + 46.9852i) q^{62} +8.00000i q^{64} +(47.7445 + 26.2484i) q^{65} +(-20.6469 + 20.6469i) q^{67} +(42.1499 + 42.1499i) q^{68} +(5.21925 + 17.9655i) q^{70} +63.7595 q^{71} +(50.1883 + 50.1883i) q^{73} +17.0004i q^{74} -48.2346 q^{76} +(21.5292 - 21.5292i) q^{77} -1.06121i q^{79} +(19.2059 - 5.57961i) q^{80} +(-18.6089 + 18.6089i) q^{82} +(-53.6243 - 53.6243i) q^{83} +(71.7935 - 130.588i) q^{85} -52.2765 q^{86} +(-23.0156 - 23.0156i) q^{88} -145.154i q^{89} -28.8303 q^{91} +(-60.3523 + 60.3523i) q^{92} +100.262i q^{94} +(33.6413 + 115.799i) q^{95} +(23.7872 - 23.7872i) q^{97} +(-7.00000 - 7.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8	\( 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8} + 24 q^{10} - 8 q^{11} - 32 q^{13} - 64 q^{16} - 56 q^{17} + 16 q^{20} - 8 q^{22} - 24 q^{23} + 40 q^{25} - 64 q^{26} - 112 q^{31} - 64 q^{32} - 28 q^{35} - 152 q^{37} - 16 q^{40} - 48 q^{46} - 80 q^{47} + 72 q^{50} - 64 q^{52} - 48 q^{53} - 24 q^{55} + 96 q^{58} + 96 q^{61} - 112 q^{62} - 16 q^{65} - 80 q^{67} + 112 q^{68} - 536 q^{71} + 168 q^{77} - 64 q^{80} + 256 q^{83} + 40 q^{85} + 16 q^{88} - 48 q^{92} - 360 q^{95} + 688 q^{97} - 112 q^{98}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8 + 24 * q^10 - 8 * q^11 - 32 * q^13 - 64 * q^16 - 56 * q^17 + 16 * q^20 - 8 * q^22 - 24 * q^23 + 40 * q^25 - 64 * q^26 - 112 * q^31 - 64 * q^32 - 28 * q^35 - 152 * q^37 - 16 * q^40 - 48 * q^46 - 80 * q^47 + 72 * q^50 - 64 * q^52 - 48 * q^53 - 24 * q^55 + 96 * q^58 + 96 * q^61 - 112 * q^62 - 16 * q^65 - 80 * q^67 + 112 * q^68 - 536 * q^71 + 168 * q^77 - 64 * q^80 + 256 * q^83 + 40 * q^85 + 16 * q^88 - 48 * q^92 - 360 * q^95 + 688 * q^97 - 112 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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