LMFDB - Embedded newform 220.3.x.a.37.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(37,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("220.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.x (of order $20$, degree $8$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.9
Character	$\chi$	$=$	220.37
Dual form			220.3.x.a.113.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34992 + 2.64938i) q^{3} +(-3.11539 + 3.91080i) q^{5} +(-3.58267 + 7.03139i) q^{7} +(0.0931732 - 0.128242i) q^{9} +(-6.18826 - 9.09425i) q^{11} +(-15.0235 + 2.37948i) q^{13} +(-14.5667 - 2.97454i) q^{15} +(2.16631 + 0.343110i) q^{17} +(19.4291 + 6.31290i) q^{19} -23.4651 q^{21} +(-26.5643 + 26.5643i) q^{23} +(-5.58873 - 24.3673i) q^{25} +(26.8972 + 4.26010i) q^{27} +(7.54043 - 2.45004i) q^{29} +(19.0407 + 13.8339i) q^{31} +(15.7404 - 28.6716i) q^{33} +(-16.3370 - 35.9166i) q^{35} +(-23.1073 + 45.3507i) q^{37} +(-26.5847 - 36.5906i) q^{39} +(-16.8469 + 51.8496i) q^{41} +(-37.5264 + 37.5264i) q^{43} +(0.211258 + 0.763905i) q^{45} +(64.1840 - 32.7034i) q^{47} +(-7.80344 - 10.7405i) q^{49} +(2.01533 + 6.20255i) q^{51} +(32.7376 - 5.18513i) q^{53} +(54.8446 + 4.13103i) q^{55} +(9.50259 + 59.9970i) q^{57} +(68.0751 - 22.1189i) q^{59} +(-43.1118 + 31.3225i) q^{61} +(0.567910 + 1.11459i) q^{63} +(37.4982 - 66.1667i) q^{65} +(2.89959 + 2.89959i) q^{67} +(-106.238 - 34.5190i) q^{69} +(44.2385 - 32.1412i) q^{71} +(2.08514 + 1.06243i) q^{73} +(57.0138 - 47.7007i) q^{75} +(86.1158 - 10.9304i) q^{77} +(52.5752 - 72.3635i) q^{79} +(24.5818 + 75.6549i) q^{81} +(9.81477 - 61.9680i) q^{83} +(-8.09074 + 7.40310i) q^{85} +(16.6701 + 16.6701i) q^{87} -36.0140i q^{89} +(37.0931 - 114.161i) q^{91} +(-10.9476 + 69.1207i) q^{93} +(-85.2177 + 56.3163i) q^{95} +(1.24843 + 7.88225i) q^{97} +(-1.74284 - 0.0537454i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{3} + 4 q^{5} - 2 q^{7} - 20 q^{11} - 8 q^{13} + 88 q^{15} + 42 q^{17} + 56 q^{21} - 104 q^{23} - 126 q^{25} - 14 q^{27} - 32 q^{31} + 52 q^{33} + 56 q^{35} - 134 q^{37} + 24 q^{41} + 332 q^{43}+ \cdots - 310 q^{97}+O(q^{100}) $ 96 * q - 2 * q^3 + 4 * q^5 - 2 * q^7 - 20 * q^11 - 8 * q^13 + 88 * q^15 + 42 * q^17 + 56 * q^21 - 104 * q^23 - 126 * q^25 - 14 * q^27 - 32 * q^31 + 52 * q^33 + 56 * q^35 - 134 * q^37 + 24 * q^41 + 332 * q^43 + 344 * q^45 + 258 * q^47 - 320 * q^51 + 222 * q^53 - 46 * q^55 + 504 * q^57 - 168 * q^61 - 298 * q^63 - 416 * q^65 - 632 * q^67 - 252 * q^71 + 56 * q^73 - 352 * q^75 - 820 * q^77 + 336 * q^81 + 236 * q^83 + 88 * q^85 - 176 * q^87 - 756 * q^91 - 770 * q^93 - 334 * q^95 - 310 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	1.34992	+	2.64938i	0.449975	+	0.883125i	0.998883	+	0.0472428i	$0.0150434\pi$
$3$	1.34992	+	2.64938i	0.449975	+	0.883125i	−0.548909	+	0.835882i	$0.684957\pi$
$4$		0			0
$5$	−3.11539	+	3.91080i	−0.623077	+	0.782160i
$5$	−3.11539	+	3.91080i	−0.623077	+	0.782160i
$6$		0			0
$7$	−3.58267	+	7.03139i	−0.511810	+	1.00448i	0.480060	+	0.877235i	$0.340615\pi$
$7$	−3.58267	+	7.03139i	−0.511810	+	1.00448i	−0.991871	+	0.127249i	$0.959385\pi$
$8$		0			0
$9$	0.0931732	−	0.128242i	0.0103526	−	0.0142491i
$10$		0			0
$11$	−6.18826	−	9.09425i	−0.562570	−	0.826750i
$11$	−6.18826	−	9.09425i	−0.562570	−	0.826750i
$12$		0			0
$13$	−15.0235	+	2.37948i	−1.15565	+	0.183037i	−0.704696	−	0.709510i	$-0.748916\pi$
$13$	−15.0235	+	2.37948i	−1.15565	+	0.183037i	−0.450955	+	0.892547i	$0.648916\pi$
$14$		0			0
$15$	−14.5667	−	2.97454i	−0.971114	−	0.198303i
$16$		0			0
$17$	2.16631	+	0.343110i	0.127430	+	0.0201830i	0.219824	−	0.975540i	$-0.429452\pi$
$17$	2.16631	+	0.343110i	0.127430	+	0.0201830i	−0.0923935	+	0.995723i	$0.529452\pi$
$18$		0			0
$19$	19.4291	+	6.31290i	1.02259	+	0.332258i	0.771855	−	0.635799i	$-0.219329\pi$
$19$	19.4291	+	6.31290i	1.02259	+	0.332258i	0.250730	+	0.968057i	$0.419329\pi$
$20$		0			0
$21$	−23.4651			−1.11739
$22$		0			0
$23$	−26.5643	+	26.5643i	−1.15497	+	1.15497i	−0.169425	+	0.985543i	$0.554191\pi$
$23$	−26.5643	+	26.5643i	−1.15497	+	1.15497i	−0.985543	+	0.169425i	$0.945809\pi$
$24$		0			0
$25$	−5.58873	−	24.3673i	−0.223549	−	0.974693i
$26$		0			0
$27$	26.8972	+	4.26010i	0.996194	+	0.157782i
$28$		0			0
$29$	7.54043	−	2.45004i	0.260015	−	0.0844840i	−0.176109	−	0.984371i	$-0.556351\pi$
$29$	7.54043	−	2.45004i	0.260015	−	0.0844840i	0.436124	+	0.899887i	$0.356351\pi$
$30$		0			0
$31$	19.0407	+	13.8339i	0.614217	+	0.446255i	0.850897	−	0.525333i	$-0.176059\pi$
$31$	19.0407	+	13.8339i	0.614217	+	0.446255i	−0.236680	+	0.971588i	$0.576059\pi$
$32$		0			0
$33$	15.7404	−	28.6716i	0.476982	−	0.868836i
$34$		0			0
$35$	−16.3370	−	35.9166i	−0.466770	−	1.02619i
$36$		0			0
$37$	−23.1073	+	45.3507i	−0.624522	+	1.22569i	0.334509	+	0.942393i	$0.391430\pi$
$37$	−23.1073	+	45.3507i	−0.624522	+	1.22569i	−0.959031	+	0.283301i	$0.908570\pi$
$38$		0			0
$39$	−26.5847	−	36.5906i	−0.681658	−	0.938222i
$40$		0			0
$41$	−16.8469	+	51.8496i	−0.410901	+	1.26462i	0.504965	+	0.863140i	$0.331505\pi$
$41$	−16.8469	+	51.8496i	−0.410901	+	1.26462i	−0.915866	+	0.401484i	$0.868495\pi$
$42$		0			0
$43$	−37.5264	+	37.5264i	−0.872707	+	0.872707i	−0.992767	−	0.120060i	$-0.961691\pi$
$43$	−37.5264	+	37.5264i	−0.872707	+	0.872707i	0.120060	+	0.992767i	$0.461691\pi$
$44$		0			0
$45$	0.211258	+	0.763905i	0.00469462	+	0.0169757i
$46$		0			0
$47$	64.1840	−	32.7034i	1.36562	−	0.695816i	0.391145	−	0.920329i	$-0.372079\pi$
$47$	64.1840	−	32.7034i	1.36562	−	0.695816i	0.974471	+	0.224513i	$0.0720790\pi$
$48$		0			0
$49$	−7.80344	−	10.7405i	−0.159254	−	0.219194i
$50$		0			0
$51$	2.01533	+	6.20255i	0.0395163	+	0.121619i
$52$		0			0
$53$	32.7376	−	5.18513i	0.617690	−	0.0978326i	0.160255	−	0.987076i	$-0.448768\pi$
$53$	32.7376	−	5.18513i	0.617690	−	0.0978326i	0.457435	+	0.889243i	$0.348768\pi$
$54$		0			0
$55$	54.8446	+	4.13103i	0.997175	+	0.0751096i
$56$		0			0
$57$	9.50259	+	59.9970i	0.166712	+	1.05258i
$58$		0			0
$59$	68.0751	−	22.1189i	1.15382	−	0.374897i	0.331236	−	0.943548i	$-0.392534\pi$
$59$	68.0751	−	22.1189i	1.15382	−	0.374897i	0.822579	+	0.568651i	$0.192534\pi$
$60$		0			0
$61$	−43.1118	+	31.3225i	−0.706750	+	0.513484i	−0.882124	−	0.471018i	$-0.843887\pi$
$61$	−43.1118	+	31.3225i	−0.706750	+	0.513484i	0.175374	+	0.984502i	$0.443887\pi$
$62$		0			0
$63$	0.567910	+	1.11459i	0.00901444	+	0.0176918i
$64$		0			0
$65$	37.4982	−	66.1667i	0.576895	−	1.01795i
$66$		0			0
$67$	2.89959	+	2.89959i	0.0432774	+	0.0432774i	0.728414	−	0.685137i	$-0.240258\pi$
$67$	2.89959	+	2.89959i	0.0432774	+	0.0432774i	−0.685137	+	0.728414i	$0.740258\pi$
$68$		0			0
$69$	−106.238	−	34.5190i	−1.53969	−	0.500275i
$70$		0			0
$71$	44.2385	−	32.1412i	0.623078	−	0.452693i	−0.230917	−	0.972973i	$-0.574173\pi$
$71$	44.2385	−	32.1412i	0.623078	−	0.452693i	0.853995	+	0.520281i	$0.174173\pi$
$72$		0			0
$73$	2.08514	+	1.06243i	0.0285636	+	0.0145539i	0.468214	−	0.883615i	$-0.344898\pi$
$73$	2.08514	+	1.06243i	0.0285636	+	0.0145539i	−0.439650	+	0.898169i	$0.644898\pi$
$74$		0			0
$75$	57.0138	−	47.7007i	0.760184	−	0.636009i
$76$		0			0
$77$	86.1158	−	10.9304i	1.11839	−	0.141953i
$78$		0			0
$79$	52.5752	−	72.3635i	0.665508	−	0.915994i	−0.334140	−	0.942524i	$-0.608446\pi$
$79$	52.5752	−	72.3635i	0.665508	−	0.915994i	0.999648	+	0.0265298i	$0.00844568\pi$
$80$		0			0
$81$	24.5818	+	75.6549i	0.303478	+	0.934011i
$82$		0			0
$83$	9.81477	−	61.9680i	0.118250	−	0.746602i	−0.855301	−	0.518132i	$-0.826628\pi$
$83$	9.81477	−	61.9680i	0.118250	−	0.746602i	0.973551	−	0.228470i	$-0.0733724\pi$
$84$		0			0
$85$	−8.09074	+	7.40310i	−0.0951852	+	0.0870953i
$86$		0			0
$87$	16.6701	+	16.6701i	0.191610	+	0.191610i
$88$		0			0
$89$		−	36.0140i		−	0.404652i	−0.979318	−	0.202326i	$-0.935150\pi$
$89$		−	36.0140i		−	0.404652i	0.979318	−	0.202326i	$-0.0648501\pi$
$90$		0			0
$91$	37.0931	−	114.161i	0.407616	−	1.25451i
$92$		0			0
$93$	−10.9476	+	69.1207i	−0.117717	+	0.743234i
$94$		0			0
$95$	−85.2177	+	56.3163i	−0.897029	+	0.592803i
$96$		0			0
$97$	1.24843	+	7.88225i	0.0128704	+	0.0812603i	0.993287	−	0.115672i	$-0.0369021\pi$
$97$	1.24843	+	7.88225i	0.0128704	+	0.0812603i	−0.980417	+	0.196932i	$0.936902\pi$
$98$		0			0
$99$	−1.74284	−	0.0537454i	−0.0176045	−	0.000542883i
$100$		0			0
$101$	−149.483	−	108.606i	−1.48003	−	1.07531i	−0.977546	−	0.210722i	$-0.932419\pi$
$101$	−149.483	−	108.606i	−1.48003	−	1.07531i	−0.502487	−	0.864585i	$-0.667581\pi$
$102$		0			0
$103$	150.810	+	76.8415i	1.46417	+	0.746034i	0.990864	−	0.134862i	$-0.0430592\pi$
$103$	150.810	+	76.8415i	1.46417	+	0.746034i	0.473310	+	0.880896i	$0.343059\pi$
$104$		0			0
$105$	73.1029	−	91.7675i	0.696219	−	0.873976i
$106$		0			0
$107$	40.7795	−	20.7782i	0.381117	−	0.194189i	−0.252928	−	0.967485i	$-0.581394\pi$
$107$	40.7795	−	20.7782i	0.381117	−	0.194189i	0.634045	+	0.773296i	$0.281394\pi$
$108$		0			0
$109$			208.005i			1.90830i	0.299322	+	0.954152i	$0.403240\pi$
$109$			208.005i			1.90830i	−0.299322	+	0.954152i	$0.596760\pi$
$110$		0			0
$111$	−151.344			−1.36346
$112$		0			0
$113$	19.2153	+	37.7122i	0.170047	+	0.333736i	0.960265	−	0.279090i	$-0.0900327\pi$
$113$	19.2153	+	37.7122i	0.170047	+	0.333736i	−0.790218	+	0.612826i	$0.790033\pi$
$114$		0			0
$115$	−21.1296	−	186.646i	−0.183736	−	1.62300i
$116$		0			0
$117$	−1.09463	+	2.14834i	−0.00935584	+	0.0183619i
$118$		0			0
$119$	−10.1737	+	14.0029i	−0.0854936	+	0.117672i
$120$		0			0
$121$	−44.4108	+	112.555i	−0.367031	+	0.930209i
$122$		0			0
$123$	−160.111	+	25.3591i	−1.30172	+	0.206172i
$124$		0			0
$125$	112.707	+	54.0572i	0.901654	+	0.432457i
$126$		0			0
$127$	89.7535	+	14.2156i	0.706721	+	0.111934i	0.499441	−	0.866348i	$-0.333539\pi$
$127$	89.7535	+	14.2156i	0.706721	+	0.111934i	0.207280	+	0.978282i	$0.433539\pi$
$128$		0			0
$129$	−150.079	−	48.7637i	−1.16341	−	0.378013i
$130$		0			0
$131$	−177.199			−1.35267			−0.676333	−	0.736596i	$-0.736432\pi$
$131$	−177.199			−1.35267			−0.676333	+	0.736596i	$0.736432\pi$
$132$		0			0
$133$	−113.997	+	113.997i	−0.857118	+	0.857118i
$134$		0			0
$135$	−100.456	+	91.9179i	−0.744116	+	0.680873i
$136$		0			0
$137$	94.2000	+	14.9198i	0.687592	+	0.108904i	0.490448	−	0.871471i	$-0.336833\pi$
$137$	94.2000	+	14.9198i	0.687592	+	0.108904i	0.197144	+	0.980375i	$0.436833\pi$
$138$		0			0
$139$	−65.8473	+	21.3951i	−0.473722	+	0.153922i	−0.536141	−	0.844128i	$-0.680118\pi$
$139$	−65.8473	+	21.3951i	−0.473722	+	0.153922i	0.0624192	+	0.998050i	$0.480118\pi$
$140$		0			0
$141$	173.287	+	125.900i	1.22899	+	0.892910i
$142$		0			0
$143$	114.609	+	121.902i	0.801459	+	0.852463i
$144$		0			0
$145$	−13.9098	+	37.1219i	−0.0959294	+	0.256013i
$146$		0			0
$147$	17.9216	−	35.1731i	0.121916	−	0.239273i
$148$		0			0
$149$	−91.5925	−	126.066i	−0.614715	−	0.846083i	0.382240	−	0.924063i	$-0.375153\pi$
$149$	−91.5925	−	126.066i	−0.614715	−	0.846083i	−0.996955	+	0.0779806i	$0.975153\pi$
$150$		0			0
$151$	7.29942	−	22.4653i	0.0483405	−	0.148777i	−0.923973	−	0.382459i	$-0.875077\pi$
$151$	7.29942	−	22.4653i	0.0483405	−	0.148777i	0.972313	+	0.233682i	$0.0750774\pi$
$152$		0			0
$153$	0.245843	−	0.245843i	0.00160682	−	0.00160682i
$154$		0			0
$155$	−113.421	+	31.3665i	−0.731747	+	0.202365i
$156$		0			0
$157$	−28.1663	+	14.3514i	−0.179403	+	0.0914104i	−0.541385	−	0.840774i	$-0.682100\pi$
$157$	−28.1663	+	14.3514i	−0.179403	+	0.0914104i	0.361982	+	0.932185i	$0.382100\pi$
$158$		0			0
$159$	57.9306	+	79.7346i	0.364343	+	0.501476i
$160$		0			0
$161$	−91.6127	−	281.955i	−0.569023	−	1.75127i
$162$		0			0
$163$	−227.560	+	36.0420i	−1.39607	+	0.221116i	−0.808710	−	0.588207i	$-0.799834\pi$
$163$	−227.560	+	36.0420i	−1.39607	+	0.221116i	−0.587363	+	0.809323i	$0.699834\pi$
$164$		0			0
$165$	63.0915	+	150.881i	0.382372	+	0.914428i
$166$		0			0
$167$	−12.6224	−	79.6950i	−0.0755835	−	0.477216i	−0.996225	−	0.0868069i	$-0.972334\pi$
$167$	−12.6224	−	79.6950i	−0.0755835	−	0.477216i	0.920642	−	0.390409i	$-0.127666\pi$
$168$		0			0
$169$	59.3137	−	19.2722i	0.350969	−	0.114037i
$170$		0			0
$171$	2.61985	−	1.90343i	0.0153208	−	0.0111312i
$172$		0			0
$173$	−41.4799	−	81.4089i	−0.239768	−	0.470572i	0.739495	−	0.673162i	$-0.235064\pi$
$173$	−41.4799	−	81.4089i	−0.239768	−	0.470572i	−0.979264	+	0.202590i	$0.935064\pi$
$174$		0			0
$175$	191.359	+	48.0035i	1.09348	+	0.274306i
$176$		0			0
$177$	150.498	+	150.498i	0.850269	+	0.850269i
$178$		0			0
$179$	56.9862	+	18.5159i	0.318359	+	0.103441i	0.463837	−	0.885920i	$-0.346472\pi$
$179$	56.9862	+	18.5159i	0.318359	+	0.103441i	−0.145479	+	0.989361i	$0.546472\pi$
$180$		0			0
$181$	−168.899	+	122.712i	−0.933143	+	0.677968i	−0.946760	−	0.321939i	$-0.895665\pi$
$181$	−168.899	+	122.712i	−0.933143	+	0.677968i	0.0136175	+	0.999907i	$0.495665\pi$
$182$		0			0
$183$	−141.183	−	71.9362i	−0.771490	−	0.393094i
$184$		0			0
$185$	−105.369	−	231.653i	−0.569563	−	1.25218i
$186$		0			0
$187$	−10.2854	−	21.8243i	−0.0550021	−	0.116707i
$188$		0			0
$189$	−126.318	+	173.862i	−0.668351	+	0.919907i
$190$		0			0
$191$	−19.9880	−	61.5168i	−0.104649	−	0.322078i	0.884999	−	0.465594i	$-0.154159\pi$
$191$	−19.9880	−	61.5168i	−0.104649	−	0.322078i	−0.989648	+	0.143516i	$0.954159\pi$
$192$		0			0
$193$	42.5384	−	268.577i	0.220406	−	1.39159i	−0.590794	−	0.806823i	$-0.701185\pi$
$193$	42.5384	−	268.577i	0.220406	−	1.39159i	0.811200	−	0.584769i	$-0.198815\pi$
$194$		0			0
$195$	225.920	+	10.0267i	1.15857	+	0.0514189i
$196$		0			0
$197$	−152.219	−	152.219i	−0.772686	−	0.772686i	0.205890	−	0.978575i	$-0.433991\pi$
$197$	−152.219	−	152.219i	−0.772686	−	0.772686i	−0.978575	+	0.205890i	$0.933991\pi$
$198$		0			0
$199$			150.100i			0.754269i	0.926159	+	0.377135i	$0.123091\pi$
$199$			150.100i			0.754269i	−0.926159	+	0.377135i	$0.876909\pi$
$200$		0			0
$201$	−3.76787	+	11.5963i	−0.0187456	+	0.0576931i
$202$		0			0
$203$	−9.78775	+	61.7974i	−0.0482155	+	0.304421i
$204$		0			0
$205$	−150.289	−	227.416i	−0.733115	−	1.10935i
$206$		0			0
$207$	0.931574	+	5.88173i	0.00450036	+	0.0284141i
$208$		0			0
$209$	−62.8214	−	215.759i	−0.300581	−	1.03234i
$210$		0			0
$211$	249.829	+	181.511i	1.18402	+	0.860244i	0.992620	−	0.121267i	$-0.0386958\pi$
$211$	249.829	+	181.511i	1.18402	+	0.860244i	0.191404	+	0.981511i	$0.438696\pi$
$212$		0			0
$213$	144.873	+	73.8163i	0.680154	+	0.346556i
$214$		0			0
$215$	−29.8490	−	263.668i	−0.138833	−	1.22636i
$216$		0			0
$217$	−165.488	+	84.3204i	−0.762618	+	0.388573i
$218$		0			0
$219$			6.95853i			0.0317741i
$220$		0			0
$221$	−33.3619			−0.150959
$222$		0			0
$223$	−54.1939	−	106.362i	−0.243022	−	0.476958i	0.736988	−	0.675906i	$-0.236247\pi$
$223$	−54.1939	−	106.362i	−0.243022	−	0.476958i	−0.980010	+	0.198948i	$0.936247\pi$
$224$		0			0
$225$	−3.64563	−	1.55367i	−0.0162028	−	0.00690520i
$226$		0			0
$227$	−95.9036	+	188.221i	−0.422483	+	0.829169i	0.577436	+	0.816436i	$0.304053\pi$
$227$	−95.9036	+	188.221i	−0.422483	+	0.829169i	−0.999919	+	0.0127332i	$0.995947\pi$
$228$		0			0
$229$	251.849	−	346.641i	1.09978	−	1.51371i	0.264100	−	0.964495i	$-0.414925\pi$
$229$	251.849	−	346.641i	1.09978	−	1.51371i	0.835678	−	0.549219i	$-0.185075\pi$
$230$		0			0
$231$	145.208	+	213.398i	0.628608	+	0.923800i
$232$		0			0
$233$	101.586	−	16.0897i	0.435994	−	0.0690546i	0.0654202	−	0.997858i	$-0.479161\pi$
$233$	101.586	−	16.0897i	0.435994	−	0.0690546i	0.370573	+	0.928803i	$0.379161\pi$
$234$		0			0
$235$	−72.0615	+	352.894i	−0.306645	+	1.50168i
$236$		0			0
$237$	262.691	+	41.6061i	1.10840	+	0.175553i
$238$		0			0
$239$	407.279	+	132.333i	1.70410	+	0.553695i	0.989333	−	0.145672i	$-0.0465343\pi$
$239$	407.279	+	132.333i	1.70410	+	0.553695i	0.714764	+	0.699366i	$0.246534\pi$
$240$		0			0
$241$	60.3944			0.250599			0.125300	−	0.992119i	$-0.460011\pi$
$241$	60.3944			0.250599			0.125300	+	0.992119i	$0.460011\pi$
$242$		0			0
$243$	6.05202	−	6.05202i	0.0249054	−	0.0249054i
$244$		0			0
$245$	66.3147	+	2.94315i	0.270672	+	0.0120129i
$246$		0			0
$247$	−306.914	−	48.6104i	−1.24257	−	0.196803i
$248$		0			0
$249$	177.426	−	57.6491i	0.712553	−	0.231522i
$250$		0			0
$251$	368.024	+	267.385i	1.46623	+	1.06528i	0.981685	+	0.190513i	$0.0610150\pi$
$251$	368.024	+	267.385i	1.46623	+	1.06528i	0.484545	+	0.874766i	$0.338985\pi$
$252$		0			0
$253$	405.969	+	77.1954i	1.60462	+	0.305120i
$254$		0			0
$255$	−30.5355	−	11.4418i	−0.119747	−	0.0448697i
$256$		0			0
$257$	34.3916	−	67.4972i	0.133819	−	0.262635i	−0.814367	−	0.580350i	$-0.802916\pi$
$257$	34.3916	−	67.4972i	0.133819	−	0.262635i	0.948186	+	0.317715i	$0.102916\pi$
$258$		0			0
$259$	−236.092	−	324.953i	−0.911553	−	1.25465i
$260$		0			0
$261$	0.388369	−	1.19528i	0.00148800	−	0.00457960i
$262$		0			0
$263$	−101.777	+	101.777i	−0.386984	+	0.386984i	−0.873610	−	0.486626i	$-0.838227\pi$
$263$	−101.777	+	101.777i	−0.386984	+	0.386984i	0.486626	+	0.873610i	$0.338227\pi$
$264$		0			0
$265$	−81.7123	+	144.184i	−0.308348	+	0.544090i
$266$		0			0
$267$	95.4147	−	48.6162i	0.357358	−	0.182083i
$268$		0			0
$269$	83.8954	+	115.472i	0.311879	+	0.429265i	0.935966	−	0.352090i	$-0.114529\pi$
$269$	83.8954	+	115.472i	0.311879	+	0.429265i	−0.624087	+	0.781355i	$0.714529\pi$
$270$		0			0
$271$	−20.0339	−	61.6580i	−0.0739258	−	0.227520i	0.907265	−	0.420559i	$-0.138166\pi$
$271$	−20.0339	−	61.6580i	−0.0739258	−	0.227520i	−0.981191	+	0.193038i	$0.938166\pi$
$272$		0			0
$273$	352.527	−	55.8348i	1.29131	−	0.204523i
$274$		0			0
$275$	−187.018	+	201.617i	−0.680065	+	0.733152i
$276$		0			0
$277$	79.6156	+	502.673i	0.287421	+	1.81470i	0.533891	+	0.845553i	$0.320729\pi$
$277$	79.6156	+	502.673i	0.287421	+	1.81470i	−0.246470	+	0.969150i	$0.579271\pi$
$278$		0			0
$279$	3.54817	−	1.15287i	0.0127174	−	0.00413215i
$280$		0			0
$281$	427.771	−	310.794i	1.52232	−	1.10603i	0.561992	−	0.827143i	$-0.310035\pi$
$281$	427.771	−	310.794i	1.52232	−	1.10603i	0.960324	−	0.278885i	$-0.0899649\pi$
$282$		0			0
$283$	−59.2646	−	116.313i	−0.209415	−	0.411001i	0.762277	−	0.647251i	$-0.224081\pi$
$283$	−59.2646	−	116.313i	−0.209415	−	0.411001i	−0.971692	+	0.236250i	$0.924081\pi$
$284$		0			0
$285$	−264.240	−	149.751i	−0.927160	−	0.525442i
$286$		0			0
$287$	−304.217	−	304.217i	−1.05999	−	1.05999i
$288$		0			0
$289$	−270.280	−	87.8193i	−0.935225	−	0.303873i
$290$		0			0
$291$	−19.1977	+	13.9480i	−0.0659716	+	0.0479312i
$292$		0			0
$293$	−116.074	−	59.1428i	−0.396158	−	0.201853i	0.244551	−	0.969636i	$-0.421359\pi$
$293$	−116.074	−	59.1428i	−0.396158	−	0.201853i	−0.640709	+	0.767784i	$0.721359\pi$
$294$		0			0
$295$	−125.577	+	335.137i	−0.425686	+	1.13606i
$296$		0			0
$297$	−127.705	−	270.973i	−0.429982	−	0.912366i
$298$		0			0
$299$	335.878	−	462.296i	1.12334	−	1.54614i
$300$		0			0
$301$	−129.418	−	398.308i	−0.429960	−	1.32328i
$302$		0			0
$303$	85.9469	−	542.647i	0.283653	−	1.79091i
$304$		0			0
$305$	11.8136	−	266.183i	0.0387332	−	0.872732i
$306$		0			0
$307$	−53.8112	−	53.8112i	−0.175281	−	0.175281i	0.614014	−	0.789295i	$-0.289554\pi$
$307$	−53.8112	−	53.8112i	−0.175281	−	0.175281i	−0.789295	+	0.614014i	$0.789554\pi$
$308$		0			0
$309$			503.282i			1.62875i
$310$		0			0
$311$	55.3408	−	170.321i	0.177945	−	0.547657i	−0.821811	−	0.569760i	$-0.807036\pi$
$311$	55.3408	−	170.321i	0.177945	−	0.547657i	0.999756	+	0.0221029i	$0.00703613\pi$
$312$		0			0
$313$	−20.3142	+	128.259i	−0.0649016	+	0.409772i	0.933753	+	0.357918i	$0.116513\pi$
$313$	−20.3142	+	128.259i	−0.0649016	+	0.409772i	−0.998655	+	0.0518545i	$0.983487\pi$
$314$		0			0
$315$	−6.12818	−	1.25138i	−0.0194545	−	0.00397264i
$316$		0			0
$317$	−17.0787	−	107.830i	−0.0538759	−	0.340159i	−0.999872	−	0.0159819i	$-0.994913\pi$
$317$	−17.0787	−	107.830i	−0.0538759	−	0.340159i	0.945996	−	0.324177i	$-0.105087\pi$
$318$		0			0
$319$	−68.9434	−	53.4131i	−0.216124	−	0.167439i
$320$		0			0
$321$	110.098	+	79.9912i	0.342986	+	0.249194i
$322$		0			0
$323$	39.9235	+	20.3421i	0.123602	+	0.0629785i
$324$		0			0
$325$	141.944	+	352.783i	0.436750	+	1.08549i
$326$		0			0
$327$	−551.084	+	280.791i	−1.68527	+	0.858689i
$328$		0			0
$329$			568.468i			1.72787i
$330$		0			0
$331$	292.474			0.883607			0.441804	−	0.897112i	$-0.354339\pi$
$331$	292.474			0.883607			0.441804	+	0.897112i	$0.354339\pi$
$332$		0			0
$333$	3.66287	+	7.18879i	0.0109996	+	0.0215880i
$334$		0			0
$335$	−20.3730	+	2.30637i	−0.0608151	+	0.00688470i
$336$		0			0
$337$	101.753	−	199.701i	0.301937	−	0.592584i	−0.689331	−	0.724446i	$-0.742096\pi$
$337$	101.753	−	199.701i	0.301937	−	0.592584i	0.991268	+	0.131862i	$0.0420956\pi$
$338$		0			0
$339$	−73.9745	+	101.817i	−0.218214	+	0.300346i
$340$		0			0
$341$	7.97986	−	258.769i	0.0234013	−	0.758853i
$342$		0			0
$343$	−278.446	+	44.1014i	−0.811795	+	0.128576i
$344$		0			0
$345$	465.971	−	307.938i	1.35064	−	0.892573i
$346$		0			0
$347$	−157.118	−	24.8851i	−0.452791	−	0.0717150i	−0.0741260	−	0.997249i	$-0.523617\pi$
$347$	−157.118	−	24.8851i	−0.452791	−	0.0717150i	−0.378665	+	0.925534i	$0.623617\pi$
$348$		0			0
$349$	623.519	+	202.593i	1.78659	+	0.580497i	0.999346	−	0.0361497i	$-0.0115093\pi$
$349$	623.519	+	202.593i	1.78659	+	0.580497i	0.787240	+	0.616647i	$0.211509\pi$
$350$		0			0
$351$	−414.226			−1.18013
$352$		0			0
$353$	240.681	−	240.681i	0.681817	−	0.681817i	−0.278593	−	0.960409i	$-0.589868\pi$
$353$	240.681	−	240.681i	0.681817	−	0.681817i	0.960409	+	0.278593i	$0.0898679\pi$
$354$		0			0
$355$	−12.1224	+	273.140i	−0.0341476	+	0.769410i
$356$		0			0
$357$	−50.8328	−	8.05113i	−0.142389	−	0.0225522i
$358$		0			0
$359$	−332.050	+	107.889i	−0.924930	+	0.300528i	−0.732487	−	0.680780i	$-0.761641\pi$
$359$	−332.050	+	107.889i	−0.924930	+	0.300528i	−0.192442	+	0.981308i	$0.561641\pi$
$360$		0			0
$361$	45.5828	+	33.1179i	0.126268	+	0.0917392i
$362$		0			0
$363$	−358.152	+	34.2803i	−0.986645	+	0.0944361i
$364$		0			0
$365$	−10.6510	+	4.84469i	−0.0291808	+	0.0132731i
$366$		0			0
$367$	79.5195	−	156.066i	0.216674	−	0.425247i	−0.756928	−	0.653498i	$-0.773301\pi$
$367$	79.5195	−	156.066i	0.216674	−	0.425247i	0.973602	+	0.228251i	$0.0733007\pi$
$368$		0			0
$369$	5.07960	+	6.99147i	0.0137659	+	0.0189471i
$370$		0			0
$371$	−80.8294	+	248.767i	−0.217869	+	0.670532i
$372$		0			0
$373$	−207.975	+	207.975i	−0.557573	+	0.557573i	−0.928616	−	0.371042i	$-0.879000\pi$
$373$	−207.975	+	207.975i	−0.557573	+	0.557573i	0.371042	+	0.928616i	$0.379000\pi$
$374$		0			0
$375$	8.92785	+	371.576i	0.0238076	+	0.990868i
$376$		0			0
$377$	−107.454	+	54.7503i	−0.285023	+	0.145226i
$378$		0			0
$379$	66.0392	+	90.8951i	0.174246	+	0.239829i	0.887204	−	0.461378i	$-0.152645\pi$
$379$	66.0392	+	90.8951i	0.174246	+	0.239829i	−0.712958	+	0.701207i	$0.752645\pi$
$380$		0			0
$381$	83.4981	+	256.981i	0.219155	+	0.674490i
$382$		0			0
$383$	488.900	−	77.4342i	1.27650	−	0.202178i	0.518866	−	0.854856i	$-0.326354\pi$
$383$	488.900	−	77.4342i	1.27650	−	0.202178i	0.757636	+	0.652678i	$0.226354\pi$
$384$		0			0
$385$	−225.537	+	370.834i	−0.585811	+	0.963205i
$386$		0			0
$387$	1.31600	+	8.30891i	0.00340052	+	0.0214700i
$388$		0			0
$389$	−426.589	+	138.607i	−1.09663	+	0.356316i	−0.800804	−	0.598926i	$-0.795594\pi$
$389$	−426.589	+	138.607i	−1.09663	+	0.356316i	−0.295824	+	0.955242i	$0.595594\pi$
$390$		0			0
$391$	−66.6610	+	48.4321i	−0.170489	+	0.123867i
$392$		0			0
$393$	−239.205	−	469.467i	−0.608665	−	1.19457i
$394$		0			0
$395$	119.207	+	431.051i	0.301791	+	1.09127i
$396$		0			0
$397$	−510.808	−	510.808i	−1.28667	−	1.28667i	−0.936798	−	0.349872i	$-0.886225\pi$
$397$	−510.808	−	510.808i	−1.28667	−	1.28667i	−0.349872	−	0.936798i	$-0.613775\pi$
$398$		0			0
$399$	−455.907	−	148.133i	−1.14262	−	0.371261i
$400$		0			0
$401$	−117.926	+	85.6783i	−0.294080	+	0.213662i	−0.725035	−	0.688712i	$-0.758177\pi$
$401$	−117.926	+	85.6783i	−0.294080	+	0.213662i	0.430955	+	0.902373i	$0.358177\pi$
$402$		0			0
$403$	−318.975	−	162.526i	−0.791501	−	0.403290i
$404$		0			0
$405$	−372.453	−	139.560i	−0.919637	−	0.344592i
$406$		0			0
$407$	555.425	−	70.4982i	1.36468	−	0.173214i
$408$		0			0
$409$	−107.001	+	147.274i	−0.261615	+	0.360083i	−0.919537	−	0.393004i	$-0.871436\pi$
$409$	−107.001	+	147.274i	−0.261615	+	0.360083i	0.657921	+	0.753087i	$0.271436\pi$
$410$		0			0
$411$	87.6347	+	269.712i	0.213223	+	0.656233i
$412$		0			0
$413$	−88.3639	+	557.907i	−0.213956	+	1.35087i
$414$		0			0
$415$	211.768	+	231.438i	0.510284	+	0.557682i
$416$		0			0
$417$	−145.573	−	145.573i	−0.349095	−	0.349095i
$418$		0			0
$419$			33.8672i			0.0808286i	0.999183	+	0.0404143i	$0.0128678\pi$
$419$			33.8672i			0.0808286i	−0.999183	+	0.0404143i	$0.987132\pi$
$420$		0			0
$421$	92.2752	−	283.994i	0.219181	−	0.674570i	−0.779649	−	0.626216i	$-0.784603\pi$
$421$	92.2752	−	283.994i	0.219181	−	0.674570i	0.998830	−	0.0483532i	$-0.0153973\pi$
$422$		0			0
$423$	1.78628	−	11.2781i	0.00422289	−	0.0266623i
$424$		0			0
$425$	−3.74627	−	54.7048i	−0.00881475	−	0.128717i
$426$		0			0
$427$	−65.7856	−	415.354i	−0.154065	−	0.972726i
$428$		0			0
$429$	−168.252	+	468.200i	−0.392195	+	1.09138i
$430$		0			0
$431$	−470.349	−	341.729i	−1.09130	−	0.792874i	−0.111679	−	0.993744i	$-0.535623\pi$
$431$	−470.349	−	341.729i	−1.09130	−	0.792874i	−0.979618	+	0.200871i	$0.935623\pi$
$432$		0			0
$433$	175.140	+	89.2385i	0.404481	+	0.206093i	0.644382	−	0.764704i	$-0.277115\pi$
$433$	175.140	+	89.2385i	0.404481	+	0.206093i	−0.239901	+	0.970797i	$0.577115\pi$
$434$		0			0
$435$	−117.127	+	13.2596i	−0.269258	+	0.0304819i
$436$		0			0
$437$	−683.818	+	348.423i	−1.56480	+	0.797306i
$438$		0			0
$439$			116.632i			0.265676i	0.991138	+	0.132838i	$0.0424091\pi$
$439$			116.632i			0.265676i	−0.991138	+	0.132838i	$0.957591\pi$
$440$		0			0
$441$	−2.10445			−0.00477200
$442$		0			0
$443$	−15.9495	−	31.3026i	−0.0360033	−	0.0706605i	0.872304	−	0.488964i	$-0.162625\pi$
$443$	−15.9495	−	31.3026i	−0.0360033	−	0.0706605i	−0.908307	+	0.418303i	$0.862625\pi$
$444$		0			0
$445$	140.844	+	112.198i	0.316503	+	0.252129i
$446$		0			0
$447$	210.354	−	412.843i	0.470591	−	0.923586i
$448$		0			0
$449$	−248.055	+	341.418i	−0.552460	+	0.760396i	−0.990343	−	0.138635i	$-0.955728\pi$
$449$	−248.055	+	341.418i	−0.552460	+	0.760396i	0.437883	+	0.899032i	$0.355728\pi$
$450$		0			0
$451$	575.786	−	167.649i	1.27669	−	0.371726i
$452$		0			0
$453$	69.3727	−	10.9875i	0.153141	−	0.0242551i
$454$		0			0
$455$	330.901	+	500.718i	0.727254	+	1.10048i
$456$		0			0
$457$	51.6963	+	8.18788i	0.113121	+	0.0179166i	0.212738	−	0.977109i	$-0.431762\pi$
$457$	51.6963	+	8.18788i	0.113121	+	0.0179166i	−0.0996173	+	0.995026i	$0.531762\pi$
$458$		0			0
$459$	56.8062	+	18.4574i	0.123761	+	0.0402123i
$460$		0			0
$461$	−360.723			−0.782479			−0.391240	−	0.920289i	$-0.627954\pi$
$461$	−360.723			−0.782479			−0.391240	+	0.920289i	$0.627954\pi$
$462$		0			0
$463$	−221.558	+	221.558i	−0.478526	+	0.478526i	−0.904660	−	0.426134i	$-0.859875\pi$
$463$	−221.558	+	221.558i	−0.478526	+	0.478526i	0.426134	+	0.904660i	$0.359875\pi$
$464$		0			0
$465$	−236.211	−	258.152i	−0.507981	−	0.555165i
$466$		0			0
$467$	291.930	+	46.2371i	0.625117	+	0.0990089i	0.460954	−	0.887424i	$-0.347507\pi$
$467$	291.930	+	46.2371i	0.625117	+	0.0990089i	0.164164	+	0.986433i	$0.447507\pi$
$468$		0			0
$469$	−30.7764	+	9.99986i	−0.0656213	+	0.0213217i
$470$		0			0
$471$	−76.0447	−	55.2497i	−0.161454	−	0.117303i
$472$		0			0
$473$	573.498	+	109.051i	1.21247	+	0.230552i
$474$		0			0
$475$	45.2444	−	508.717i	0.0952513	−	1.07098i
$476$		0			0
$477$	2.38532	−	4.68144i	0.00500066	−	0.00981435i
$478$		0			0
$479$	150.645	+	207.345i	0.314499	+	0.432871i	0.936778	−	0.349925i	$-0.113793\pi$
$479$	150.645	+	207.345i	0.314499	+	0.432871i	−0.622279	+	0.782796i	$0.713793\pi$
$480$		0			0
$481$	239.241	−	736.307i	0.497382	−	1.53078i
$482$		0			0
$483$	623.334	−	623.334i	1.29055	−	1.29055i
$484$		0			0
$485$	−34.7152	−	19.6739i	−0.0715778	−	0.0405647i
$486$		0			0
$487$	603.175	−	307.333i	1.23855	−	0.631074i	0.292865	−	0.956154i	$-0.405391\pi$
$487$	603.175	−	307.333i	1.23855	−	0.631074i	0.945686	+	0.325080i	$0.105391\pi$
$488$		0			0
$489$	−402.678	−	554.238i	−0.823471	−	1.13341i
$490$		0			0
$491$	133.739	+	411.608i	0.272382	+	0.838305i	0.989900	+	0.141766i	$0.0452779\pi$
$491$	133.739	+	411.608i	0.272382	+	0.838305i	−0.717518	+	0.696540i	$0.754722\pi$
$492$		0			0
$493$	17.1756	−	2.72034i	0.0348389	−	0.00551794i
$494$		0			0
$495$	5.63982	−	6.64848i	0.0113936	−	0.0134313i
$496$		0			0
$497$	67.5050	+	426.210i	0.135825	+	0.857565i
$498$		0			0
$499$	230.428	−	74.8705i	0.461779	−	0.150041i	−0.0688828	−	0.997625i	$-0.521943\pi$
$499$	230.428	−	74.8705i	0.461779	−	0.150041i	0.530662	+	0.847584i	$0.321943\pi$
$500$		0			0
$501$	194.103	−	141.024i	0.387430	−	0.281485i
$502$		0			0
$503$	−184.621	−	362.339i	−0.367039	−	0.720356i	0.631443	−	0.775422i	$-0.282463\pi$
$503$	−184.621	−	362.339i	−0.367039	−	0.720356i	−0.998483	+	0.0550666i	$0.982463\pi$
$504$		0			0
$505$	890.435	−	246.250i	1.76324	−	0.487624i
$506$		0			0
$507$	131.128	+	131.128i	0.258636	+	0.258636i
$508$		0			0
$509$	297.341	+	96.6120i	0.584168	+	0.189808i	0.586167	−	0.810190i	$-0.300636\pi$
$509$	297.341	+	96.6120i	0.584168	+	0.189808i	−0.00199918	+	0.999998i	$0.500636\pi$
$510$		0			0
$511$	−14.9408	+	10.8551i	−0.0292383	+	0.0212429i
$512$		0			0
$513$	495.696	+	252.570i	0.966269	+	0.492339i
$514$		0			0
$515$	−770.343	+	350.397i	−1.49581	+	0.680382i
$516$		0			0
$517$	−694.600	−	381.328i	−1.34352	−	0.737578i
$518$		0			0
$519$	159.688	−	219.792i	0.307684	−	0.423491i
$520$		0			0
$521$	−33.9003	−	104.335i	−0.0650678	−	0.200258i	0.913237	−	0.407429i	$-0.133575\pi$
$521$	−33.9003	−	104.335i	−0.0650678	−	0.200258i	−0.978305	+	0.207171i	$0.933575\pi$
$522$		0			0
$523$	−125.718	+	793.754i	−0.240379	+	1.51769i	0.512012	+	0.858978i	$0.328900\pi$
$523$	−125.718	+	793.754i	−0.240379	+	1.51769i	−0.752391	+	0.658716i	$0.771100\pi$
$524$		0			0
$525$	131.140	+	571.782i	0.249791	+	1.08911i
$526$		0			0
$527$	36.5016	+	36.5016i	0.0692630	+	0.0692630i
$528$		0			0
$529$		−	882.321i		−	1.66790i
$530$		0			0
$531$	3.50620	−	10.7910i	0.00660301	−	0.0203220i
$532$		0			0
$533$	129.724	−	819.046i	0.243385	−	1.53667i
$534$		0			0
$535$	−45.7845	+	224.213i	−0.0855786	+	0.419089i
$536$		0			0
$537$	27.8714	+	175.973i	0.0519020	+	0.327696i
$538$		0			0
$539$	−49.3871	+	137.432i	−0.0916274	+	0.254975i
$540$		0			0
$541$	−79.5754	−	57.8149i	−0.147089	−	0.106867i	0.511807	−	0.859101i	$-0.328976\pi$
$541$	−79.5754	−	57.8149i	−0.147089	−	0.106867i	−0.658896	+	0.752234i	$0.728976\pi$
$542$		0			0
$543$	−553.111	−	281.824i	−1.01862	−	0.519013i
$544$		0			0
$545$	−813.467	−	648.017i	−1.49260	−	1.18902i
$546$		0			0
$547$	41.9672	−	21.3834i	0.0767225	−	0.0390921i	−0.415208	−	0.909726i	$-0.636291\pi$
$547$	41.9672	−	21.3834i	0.0767225	−	0.0390921i	0.491931	+	0.870634i	$0.336291\pi$
$548$		0			0
$549$			8.44715i			0.0153864i
$550$		0			0
$551$	161.971			0.293958
$552$		0			0
$553$	320.457	+	628.931i	0.579487	+	1.13731i
$554$		0			0
$555$	471.495	−	591.877i	0.849541	−	1.06644i
$556$		0			0
$557$	−368.928	+	724.062i	−0.662348	+	1.29993i	0.278282	+	0.960499i	$0.410235\pi$
$557$	−368.928	+	724.062i	−0.662348	+	1.29993i	−0.940630	+	0.339433i	$0.889765\pi$
$558$		0			0
$559$	474.483	−	653.069i	0.848806	−	1.16828i
$560$		0			0
$561$	43.9361	−	56.7110i	0.0783176	−	0.101089i
$562$		0			0
$563$	−274.336	+	43.4505i	−0.487275	+	0.0771767i	−0.395238	−	0.918579i	$-0.629338\pi$
$563$	−274.336	+	43.4505i	−0.487275	+	0.0771767i	−0.0920370	+	0.995756i	$0.529338\pi$
$564$		0			0
$565$	−207.348	−	42.3407i	−0.366988	−	0.0749394i
$566$		0			0
$567$	−620.027	−	98.2027i	−1.09352	−	0.173197i
$568$		0			0
$569$	151.476	+	49.2175i	0.266214	+	0.0864983i	0.439083	−	0.898447i	$-0.355304\pi$
$569$	151.476	+	49.2175i	0.266214	+	0.0864983i	−0.172868	+	0.984945i	$0.555304\pi$
$570$		0			0
$571$	514.236			0.900588			0.450294	−	0.892880i	$-0.351319\pi$
$571$	514.236			0.900588			0.450294	+	0.892880i	$0.351319\pi$
$572$		0			0
$573$	135.999	−	135.999i	0.237345	−	0.237345i
$574$		0			0
$575$	795.761	+	498.839i	1.38393	+	0.867547i
$576$		0			0
$577$	948.349	+	150.204i	1.64359	+	0.260319i	0.908571	−	0.417731i	$-0.137175\pi$
$577$	948.349	+	150.204i	1.64359	+	0.260319i	0.735016	+	0.678050i	$0.237175\pi$
$578$		0			0
$579$	768.985	−	249.858i	1.32813	−	0.431534i
$580$		0			0
$581$	400.558	+	291.023i	0.689429	+	0.500899i
$582$		0			0
$583$	−249.744	−	265.637i	−0.428377	−	0.455638i
$584$		0			0
$585$	−4.99152	−	10.9738i	−0.00853252	−	0.0187586i
$586$		0			0
$587$	−393.300	+	771.894i	−0.670016	+	1.31498i	0.266323	+	0.963884i	$0.414191\pi$
$587$	−393.300	+	771.894i	−0.670016	+	1.31498i	−0.936339	+	0.351097i	$0.885809\pi$
$588$		0			0
$589$	282.612	+	388.983i	0.479817	+	0.660412i
$590$		0			0
$591$	197.801	−	608.770i	0.334689	−	1.03007i
$592$		0			0
$593$	649.577	−	649.577i	1.09541	−	1.09541i	0.100468	−	0.994940i	$-0.467966\pi$
$593$	649.577	−	649.577i	1.09541	−	1.09541i	0.994940	−	0.100468i	$-0.0320341\pi$
$594$		0			0
$595$	−23.0676	−	83.4121i	−0.0387691	−	0.140188i
$596$		0			0
$597$	−397.670	+	202.623i	−0.666114	+	0.339402i
$598$		0			0
$599$	356.047	+	490.056i	0.594402	+	0.818124i	0.995181	−	0.0980508i	$-0.0312608\pi$
$599$	356.047	+	490.056i	0.594402	+	0.818124i	−0.400780	+	0.916174i	$0.631261\pi$
$600$		0			0
$601$	142.502	+	438.575i	0.237108	+	0.729742i	0.996835	+	0.0795001i	$0.0253324\pi$
$601$	142.502	+	438.575i	0.237108	+	0.729742i	−0.759727	+	0.650242i	$0.774668\pi$
$602$		0			0
$603$	0.642012	−	0.101685i	0.00106470	−	0.000168631i
$604$		0			0
$605$	−301.825	−	524.335i	−0.498884	−	0.866669i
$606$		0			0
$607$	−109.412	−	690.800i	−0.180250	−	1.13806i	−0.897426	−	0.441164i	$-0.854566\pi$
$607$	−109.412	−	690.800i	−0.180250	−	1.13806i	0.717176	−	0.696892i	$-0.245434\pi$
$608$		0			0
$609$	−176.937	+	57.4904i	−0.290537	+	0.0944013i
$610$		0			0
$611$	−886.448	+	644.042i	−1.45081	+	1.05408i
$612$		0			0
$613$	187.006	+	367.019i	0.305066	+	0.598726i	0.991744	−	0.128236i	$-0.0409315\pi$
$613$	187.006	+	367.019i	0.305066	+	0.598726i	−0.686677	+	0.726962i	$0.740932\pi$
$614$		0			0
$615$	399.633	−	705.166i	0.649810	−	1.14661i
$616$		0			0
$617$	418.073	+	418.073i	0.677590	+	0.677590i	0.959454	−	0.281864i	$-0.0909527\pi$
$617$	418.073	+	418.073i	0.677590	+	0.677590i	−0.281864	+	0.959454i	$0.590953\pi$
$618$		0			0
$619$	−523.296	−	170.029i	−0.845390	−	0.274684i	−0.145876	−	0.989303i	$-0.546600\pi$
$619$	−523.296	−	170.029i	−0.845390	−	0.274684i	−0.699514	+	0.714619i	$0.746600\pi$
$620$		0			0
$621$	−827.672	+	601.339i	−1.33280	+	0.968339i
$622$		0			0
$623$	253.229	+	129.026i	0.406467	+	0.207105i
$624$		0			0
$625$	−562.532	+	272.365i	−0.900051	+	0.435784i
$626$		0			0
$627$	486.823	−	457.696i	0.776432	−	0.729978i
$628$		0			0
$629$	−65.6180	+	90.3154i	−0.104321	+	0.143586i
$630$		0			0
$631$	254.599	+	783.575i	0.403485	+	1.24180i	0.922154	+	0.386823i	$0.126428\pi$
$631$	254.599	+	783.575i	0.403485	+	1.24180i	−0.518669	+	0.854975i	$0.673572\pi$
$632$		0			0
$633$	−143.642	+	906.918i	−0.226922	+	1.43273i
$634$		0			0
$635$	−335.211	+	306.721i	−0.527892	+	0.483026i
$636$		0			0
$637$	142.791	+	142.791i	0.224162	+	0.224162i
$638$		0			0
$639$		−	8.66793i		−	0.0135648i
$640$		0			0
$641$	−199.661	+	614.494i	−0.311484	+	0.958649i	0.665694	+	0.746225i	$0.268136\pi$
$641$	−199.661	+	614.494i	−0.311484	+	0.958649i	−0.977178	+	0.212424i	$0.931864\pi$
$642$		0			0
$643$	−32.3568	+	204.293i	−0.0503217	+	0.317719i	0.949668	+	0.313257i	$0.101420\pi$
$643$	−32.3568	+	204.293i	−0.0503217	+	0.317719i	−0.999990	+	0.00446153i	$0.998580\pi$
$644$		0			0
$645$	658.260	−	435.012i	1.02056	−	0.674438i
$646$		0			0
$647$	56.9385	+	359.495i	0.0880038	+	0.555634i	0.991813	+	0.127699i	$0.0407590\pi$
$647$	56.9385	+	359.495i	0.0880038	+	0.555634i	−0.903809	+	0.427936i	$0.859241\pi$
$648$		0			0
$649$	−622.422	−	482.214i	−0.959048	−	0.743011i
$650$		0			0
$651$	−446.793	−	324.614i	−0.686318	−	0.498639i
$652$		0			0
$653$	−348.656	−	177.649i	−0.533929	−	0.272050i	0.166169	−	0.986097i	$-0.446860\pi$
$653$	−348.656	−	177.649i	−0.533929	−	0.272050i	−0.700098	+	0.714047i	$0.746860\pi$
$654$		0			0
$655$	552.044	−	692.991i	0.842815	−	1.05800i
$656$		0			0
$657$	0.330528	−	0.168412i	0.000503087	−	0.000256335i
$658$		0			0
$659$		−	1045.08i		−	1.58586i	−0.609312	−	0.792931i	$-0.708554\pi$
$659$		−	1045.08i		−	1.58586i	0.609312	−	0.792931i	$-0.291446\pi$
$660$		0			0
$661$	908.162			1.37392			0.686960	−	0.726695i	$-0.258945\pi$
$661$	908.162			1.37392			0.686960	+	0.726695i	$0.258945\pi$
$662$		0			0
$663$	−45.0361	−	88.3883i	−0.0679277	−	0.133316i
$664$		0			0
$665$	−90.6746	−	800.962i	−0.136353	−	1.20445i
$666$		0			0
$667$	−135.223	+	265.389i	−0.202733	+	0.397885i
$668$		0			0
$669$	208.634	−	287.160i	0.311860	−	0.429238i
$670$		0			0
$671$	551.642	+	198.237i	0.822119	+	0.295435i
$672$		0			0
$673$	−1251.10	+	198.155i	−1.85899	+	0.294435i	−0.982398	−	0.186798i	$-0.940189\pi$
$673$	−1251.10	+	198.155i	−1.85899	+	0.294435i	−0.876593	+	0.481233i	$0.840189\pi$
$674$		0			0
$675$	−46.5142	−	679.222i	−0.0689099	−	1.00625i
$676$		0			0
$677$	1250.03	+	197.985i	1.84642	+	0.292444i	0.978806	−	0.204791i	$-0.0656515\pi$
$677$	1250.03	+	197.985i	1.84642	+	0.292444i	0.867616	+	0.497235i	$0.165651\pi$
$678$		0			0
$679$	−59.8959	−	19.4613i	−0.0882119	−	0.0286618i
$680$		0			0
$681$	−628.132			−0.922367
$682$		0			0
$683$	295.545	−	295.545i	0.432715	−	0.432715i	−0.456836	−	0.889551i	$-0.651017\pi$
$683$	295.545	−	295.545i	0.432715	−	0.432715i	0.889551	+	0.456836i	$0.151017\pi$
$684$		0			0
$685$	−351.818	+	321.917i	−0.513603	+	0.469951i
$686$		0			0
$687$	1258.36	+	199.304i	1.83167	+	0.290108i
$688$		0			0
$689$	−479.494	+	155.797i	−0.695927	+	0.226120i
$690$		0			0
$691$	−1042.47	−	757.400i	−1.50864	−	1.09609i	−0.966775	−	0.255628i	$-0.917718\pi$
$691$	−1042.47	−	757.400i	−1.50864	−	1.09609i	−0.541867	−	0.840464i	$-0.682282\pi$
$692$		0			0
$693$	6.62194	−	12.0621i	0.00955547	−	0.0174056i
$694$		0			0
$695$	121.468	−	324.170i	0.174774	−	0.466431i
$696$		0			0
$697$	−54.2859	+	106.542i	−0.0778851	+	0.152858i
$698$		0			0
$699$	179.762	+	247.421i	0.257170	+	0.353964i
$700$		0			0
$701$	169.091	−	520.409i	0.241214	−	0.742382i	−0.755022	−	0.655700i	$-0.772374\pi$
$701$	169.091	−	520.409i	0.241214	−	0.742382i	0.996236	−	0.0866817i	$-0.0276263\pi$
$702$		0			0
$703$	−735.249	+	735.249i	−1.04587	+	1.04587i
$704$		0			0
$705$	−1032.23	+	285.463i	−1.46415	+	0.404912i
$706$		0			0
$707$	1299.20	−	661.976i	1.83762	−	0.936317i
$708$		0			0
$709$	−698.138	−	960.905i	−0.984680	−	1.35530i	−0.934270	−	0.356567i	$-0.883947\pi$
$709$	−698.138	−	960.905i	−0.984680	−	1.35530i	−0.0504104	−	0.998729i	$-0.516053\pi$
$710$		0			0
$711$	−4.38144	−	13.4847i	−0.00616236	−	0.0189658i
$712$		0			0
$713$	−873.290	+	138.316i	−1.22481	+	0.193991i
$714$		0			0
$715$	−833.786	+	68.4395i	−1.16613	+	0.0957195i
$716$		0			0
$717$	199.196	+	1257.67i	0.277819	+	1.75408i
$718$		0			0
$719$	−760.081	+	246.965i	−1.05714	+	0.343485i	−0.785466	−	0.618905i	$-0.787576\pi$
$719$	−760.081	+	246.965i	−1.05714	+	0.343485i	−0.271671	+	0.962390i	$0.587576\pi$
$720$		0			0
$721$	−1080.61	+	785.106i	−1.49876	+	1.08891i
$722$		0			0
$723$	81.5278	+	160.007i	0.112763	+	0.221310i
$724$		0			0
$725$	−101.842	−	170.048i	−0.140472	−	0.234548i
$726$		0			0
$727$	−365.797	−	365.797i	−0.503160	−	0.503160i	0.409258	−	0.912419i	$-0.365787\pi$
$727$	−365.797	−	365.797i	−0.503160	−	0.503160i	−0.912419	+	0.409258i	$0.865787\pi$
$728$		0			0
$729$	705.098	+	229.100i	0.967212	+	0.314266i
$730$		0			0
$731$	−94.1696	+	68.4183i	−0.128823	+	0.0935954i
$732$		0			0
$733$	−414.599	−	211.249i	−0.565620	−	0.288198i	0.147705	−	0.989032i	$-0.452811\pi$
$733$	−414.599	−	211.249i	−0.565620	−	0.288198i	−0.713325	+	0.700834i	$0.752811\pi$
$734$		0			0
$735$	81.7223	+	179.666i	0.111187	+	0.244443i
$736$		0			0
$737$	8.42616	−	44.3130i	0.0114331	−	0.0601262i
$738$		0			0
$739$	803.504	−	1105.93i	1.08729	−	1.49652i	0.236046	−	0.971742i	$-0.424148\pi$
$739$	803.504	−	1105.93i	1.08729	−	1.49652i	0.851239	−	0.524778i	$-0.175852\pi$
$740$		0			0
$741$	−285.523	−	878.750i	−0.385322	−	1.18590i
$742$		0			0
$743$	−126.259	+	797.167i	−0.169931	+	1.07290i	0.744340	+	0.667800i	$0.232764\pi$
$743$	−126.259	+	797.167i	−0.169931	+	1.07290i	−0.914271	+	0.405102i	$0.867236\pi$
$744$		0			0
$745$	778.366	+	34.5451i	1.04479	+	0.0463692i
$746$		0			0
$747$	−7.03242	−	7.03242i	−0.00941422	−	0.00941422i
$748$		0			0
$749$			361.178i			0.482214i
$750$		0			0
$751$	−162.000	+	498.585i	−0.215712	+	0.663894i	0.783390	+	0.621531i	$0.213489\pi$
$751$	−162.000	+	498.585i	−0.215712	+	0.663894i	−0.999102	+	0.0423638i	$0.986511\pi$
$752$		0			0
$753$	−211.599	+	1335.98i	−0.281008	+	1.77421i
$754$		0			0
$755$	65.1168	+	98.5346i	0.0862474	+	0.130509i
$756$		0			0
$757$	−64.3815	−	406.489i	−0.0850482	−	0.536973i	−0.993020	−	0.117943i	$-0.962370\pi$
$757$	−64.3815	−	406.489i	−0.0850482	−	0.536973i	0.907972	−	0.419030i	$-0.137630\pi$
$758$		0			0
$759$	343.508	+	1179.77i	0.452579	+	1.55438i
$760$		0			0
$761$	442.423	+	321.439i	0.581371	+	0.422391i	0.839218	−	0.543795i	$-0.183013\pi$
$761$	442.423	+	321.439i	0.581371	+	0.422391i	−0.257847	+	0.966186i	$0.583013\pi$
$762$		0			0
$763$	−1462.57	−	745.214i	−1.91686	−	0.976690i
$764$		0			0
$765$	0.195547	+	1.72734i	0.000255618	+	0.00225796i
$766$		0			0
$767$	−970.091	+	494.286i	−1.26479	+	0.644441i
$768$		0			0
$769$			662.450i			0.861443i	0.902485	+	0.430722i	$0.141741\pi$
$769$			662.450i			0.861443i	−0.902485	+	0.430722i	$0.858259\pi$
$770$		0			0
$771$	225.251			0.292155
$772$		0			0
$773$	−173.487	−	340.487i	−0.224433	−	0.440475i	0.751142	−	0.660141i	$-0.229503\pi$
$773$	−173.487	−	340.487i	−0.224433	−	0.440475i	−0.975575	+	0.219666i	$0.929503\pi$
$774$		0			0
$775$	230.681	−	541.285i	0.297653	−	0.698432i
$776$		0			0
$777$	542.216	−	1064.16i	0.697833	−	1.36957i
$778$		0			0
$779$	−654.643	+	901.038i	−0.840363	+	1.15666i
$780$		0			0
$781$	−566.060	−	203.418i	−0.724788	−	0.260459i
$782$		0			0
$783$	213.254	−	33.7761i	0.272355	−	0.0431368i
$784$		0			0
$785$	31.6232	−	154.863i	0.0402844	−	0.197278i
$786$		0			0
$787$	355.100	+	56.2423i	0.451207	+	0.0714641i	0.377902	−	0.925845i	$-0.376646\pi$
$787$	355.100	+	56.2423i	0.451207	+	0.0714641i	0.0733045	+	0.997310i	$0.476646\pi$
$788$		0			0
$789$	−407.036	−	132.254i	−0.515889	−	0.167622i
$790$		0			0
$791$	−334.011			−0.422265
$792$		0			0
$793$	573.156	−	573.156i	0.722769	−	0.722769i
$794$		0			0
$795$	−492.303	−	21.8491i	−0.619249	−	0.0274832i
$796$		0			0
$797$	−932.508	−	147.695i	−1.17002	−	0.185313i	−0.458970	−	0.888452i	$-0.651781\pi$
$797$	−932.508	−	147.695i	−1.17002	−	0.185313i	−0.711053	+	0.703138i	$0.751781\pi$
$798$		0			0
$799$	150.263	−	48.8236i	0.188064	−	0.0611058i
$800$		0			0
$801$	−4.61851	−	3.35554i	−0.00576592	−	0.00418919i
$802$		0			0
$803$	−3.24138	−	25.5374i	−0.00403659	−	0.0318025i
$804$		0			0
$805$	1388.08	+	520.119i	1.72432	+	0.646111i
$806$		0			0
$807$	−192.677	+	378.149i	−0.238757	+	0.468586i
$808$		0			0
$809$	148.538	+	204.445i	0.183607	+	0.252713i	0.890892	−	0.454215i	$-0.150080\pi$
$809$	148.538	+	204.445i	0.183607	+	0.252713i	−0.707285	+	0.706929i	$0.750080\pi$
$810$		0			0
$811$	16.5757	−	51.0148i	0.0204386	−	0.0629035i	−0.940317	−	0.340300i	$-0.889471\pi$
$811$	16.5757	−	51.0148i	0.0204386	−	0.0629035i	0.960756	+	0.277396i	$0.0894715\pi$
$812$		0			0
$813$	136.311	−	136.311i	0.167664	−	0.167664i
$814$		0			0
$815$	567.985	−	1002.23i	0.696914	−	1.22973i
$816$		0			0
$817$	−966.005	+	492.204i	−1.18238	+	0.602453i
$818$		0			0
$819$	−11.1841	−	15.3936i	−0.0136558	−	0.0187956i
$820$		0			0
$821$	269.289	+	828.788i	0.328002	+	1.00949i	0.970067	+	0.242836i	$0.0780777\pi$
$821$	269.289	+	828.788i	0.328002	+	1.00949i	−0.642066	+	0.766650i	$0.721922\pi$
$822$		0			0
$823$	580.731	−	91.9788i	0.705628	−	0.111760i	0.206700	−	0.978404i	$-0.433727\pi$
$823$	580.731	−	91.9788i	0.705628	−	0.111760i	0.498927	+	0.866644i	$0.333727\pi$
$824$		0			0
$825$	−786.618	−	223.313i	−0.953477	−	0.270683i
$826$		0			0
$827$	225.805	+	1425.68i	0.273042	+	1.72392i	0.618761	+	0.785579i	$0.287635\pi$
$827$	225.805	+	1425.68i	0.273042	+	1.72392i	−0.345719	+	0.938338i	$0.612365\pi$
$828$		0			0
$829$	1263.48	−	410.531i	1.52411	−	0.495212i	0.577167	−	0.816626i	$-0.304158\pi$
$829$	1263.48	−	410.531i	1.52411	−	0.495212i	0.946939	+	0.321414i	$0.104158\pi$
$830$		0			0
$831$	−1224.29	+	889.502i	−1.47328	+	1.07040i
$832$		0			0
$833$	−13.2195	−	25.9448i	−0.0158698	−	0.0311462i
$834$		0			0
$835$	350.995	+	198.917i	0.420353	+	0.238224i
$836$		0			0
$837$	453.209	+	453.209i	0.541468	+	0.541468i
$838$		0			0
$839$	−216.137	−	70.2272i	−0.257613	−	0.0837035i	0.177363	−	0.984145i	$-0.443243\pi$
$839$	−216.137	−	70.2272i	−0.257613	−	0.0837035i	−0.434976	+	0.900442i	$0.643243\pi$
$840$		0			0
$841$	−629.528	+	457.379i	−0.748547	+	0.543851i
$842$		0			0
$843$	1400.87	+	713.778i	1.66176	+	0.846711i
$844$		0			0
$845$	−109.415	+	292.004i	−0.129486	+	0.345567i
$846$		0			0
$847$	−632.311	−	715.518i	−0.746530	−	0.844767i
$848$		0			0
$849$	228.155	−	314.028i	0.268734	−	0.369880i
$850$		0			0
$851$	−590.878	−	1818.54i	−0.694334	−	2.13694i
$852$		0			0
$853$	−93.0977	+	587.796i	−0.109142	+	0.689093i	0.871073	+	0.491154i	$0.163425\pi$
$853$	−93.0977	+	587.796i	−0.109142	+	0.689093i	−0.980214	+	0.197939i	$0.936575\pi$
$854$		0			0
$855$	−0.717900	+	16.1756i	−0.000839649	+	0.0189189i
$856$		0			0
$857$	1137.02	+	1137.02i	1.32674	+	1.32674i	0.908196	+	0.418544i	$0.137460\pi$
$857$	1137.02	+	1137.02i	1.32674	+	1.32674i	0.418544	+	0.908196i	$0.362540\pi$
$858$		0			0
$859$		−	678.461i		−	0.789827i	−0.918718	−	0.394914i	$-0.870775\pi$
$859$		−	678.461i		−	0.789827i	0.918718	−	0.394914i	$-0.129225\pi$
$860$		0			0
$861$	395.316	−	1216.66i	0.459136	−	1.41307i
$862$		0			0
$863$	−218.128	+	1377.20i	−0.252755	+	1.59583i	0.455737	+	0.890114i	$0.349376\pi$
$863$	−218.128	+	1377.20i	−0.252755	+	1.59583i	−0.708492	+	0.705718i	$0.750624\pi$
$864$		0			0
$865$	447.600	+	91.4005i	0.517457	+	0.105665i
$866$		0			0
$867$	−132.191	−	834.623i	−0.152470	−	0.962656i
$868$		0			0
$869$	−983.441	−	30.3271i	−1.13169	−	0.0348989i
$870$		0			0
$871$	−50.4613	−	36.6623i	−0.0579349	−	0.0420922i
$872$		0			0
$873$	1.12715	+	0.574313i	0.00129113	+	0.000657862i
$874$		0			0
$875$	−783.889	+	598.816i	−0.895873	+	0.684362i
$876$		0			0
$877$	−116.459	+	59.3387i	−0.132792	+	0.0676610i	−0.519124	−	0.854699i	$-0.673742\pi$
$877$	−116.459	+	59.3387i	−0.132792	+	0.0676610i	0.386332	+	0.922360i	$0.373742\pi$
$878$		0			0
$879$		−	387.363i		−	0.440685i
$880$		0			0
$881$	−211.392			−0.239946			−0.119973	−	0.992777i	$-0.538281\pi$
$881$	−211.392			−0.239946			−0.119973	+	0.992777i	$0.538281\pi$
$882$		0			0
$883$	246.556	+	483.894i	0.279226	+	0.548011i	0.987442	−	0.157985i	$-0.0504997\pi$
$883$	246.556	+	483.894i	0.279226	+	0.548011i	−0.708216	+	0.705996i	$0.750500\pi$
$884$		0			0
$885$	−1057.42	+	119.708i	−1.19483	+	0.135263i
$886$		0			0
$887$	−142.193	+	279.069i	−0.160307	+	0.314621i	−0.957163	−	0.289548i	$-0.906495\pi$
$887$	−142.193	+	279.069i	−0.160307	+	0.314621i	0.796856	+	0.604169i	$0.206495\pi$
$888$		0			0
$889$	−421.513	+	580.162i	−0.474142	+	0.652601i
$890$		0			0
$891$	535.906	−	691.725i	0.601466	−	0.776347i
$892$		0			0
$893$	1453.49	−	230.210i	1.62765	−	0.257794i
$894$		0			0
$895$	−249.946	+	165.177i	−0.279269	+	0.184556i
$896$		0			0
$897$	1678.21	+	265.802i	1.87091	+	0.296323i
$898$		0			0
$899$	177.469	+	57.6631i	0.197407	+	0.0641414i
$900$		0			0
$901$	72.6990			0.0806870
$902$		0			0
$903$	880.562	−	880.562i	0.975151	−	0.975151i
$904$		0			0
$905$	46.2822	−	1042.83i	0.0511405	−	1.15229i
$906$		0			0
$907$	1506.41	+	238.592i	1.66087	+	0.263056i	0.915124	−	0.403173i	$-0.132093\pi$
$907$	1506.41	+	238.592i	1.66087	+	0.263056i	0.745747	+	0.666229i	$0.232093\pi$
$908$		0			0
$909$	−27.8557	+	9.05085i	−0.0306443	+	0.00995694i
$910$		0			0
$911$	771.138	+	560.264i	0.846474	+	0.614999i	0.924172	−	0.381978i	$-0.124757\pi$
$911$	771.138	+	560.264i	0.846474	+	0.614999i	−0.0776975	+	0.996977i	$0.524757\pi$
$912$		0			0
$913$	−624.289	+	294.216i	−0.683777	+	0.322252i
$914$		0			0
$915$	721.167	−	328.029i	0.788161	−	0.358501i
$916$		0			0
$917$	634.847	−	1245.96i	0.692308	−	1.35873i
$918$		0			0
$919$	−258.510	−	355.809i	−0.281295	−	0.387170i	0.644867	−	0.764295i	$-0.276913\pi$
$919$	−258.510	−	355.809i	−0.281295	−	0.387170i	−0.926162	+	0.377125i	$0.876913\pi$
$920$		0			0
$921$	69.9250	−	215.207i	0.0759229	−	0.233667i
$922$		0			0
$923$	−588.136	+	588.136i	−0.637201	+	0.637201i
$924$		0			0
$925$	1234.21	+	309.611i	1.33429	+	0.334714i
$926$		0			0
$927$	23.9057	−	12.1806i	0.0257883	−	0.0131398i
$928$		0			0
$929$	−585.018	−	805.208i	−0.629729	−	0.866747i	0.368287	−	0.929712i	$-0.379944\pi$
$929$	−585.018	−	805.208i	−0.629729	−	0.866747i	−0.998016	+	0.0629648i	$0.979944\pi$
$930$		0			0
$931$	−83.8101	−	257.941i	−0.0900216	−	0.277058i
$932$		0			0
$933$	525.951	−	83.3025i	0.563720	−	0.0892845i
$934$		0			0
$935$	117.393	+	27.7669i	0.125554	+	0.0296972i
$936$		0			0
$937$	−169.215	−	1068.38i	−0.180593	−	1.14022i	−0.896835	−	0.442365i	$-0.854140\pi$
$937$	−169.215	−	1068.38i	−0.180593	−	1.14022i	0.716243	−	0.697851i	$-0.245860\pi$
$938$		0			0
$939$	−367.228	+	119.320i	−0.391084	+	0.127071i
$940$		0			0
$941$	871.044	−	632.850i	0.925657	−	0.672529i	−0.0192683	−	0.999814i	$-0.506134\pi$
$941$	871.044	−	632.850i	0.925657	−	0.672529i	0.944926	+	0.327285i	$0.106134\pi$
$942$		0			0
$943$	−929.819	−	1824.87i	−0.986022	−	1.93518i
$944$		0			0
$945$	−286.411	−	1035.65i	−0.303080	−	1.09593i
$946$		0			0
$947$	−1103.75	−	1103.75i	−1.16552	−	1.16552i	−0.983248	−	0.182275i	$-0.941654\pi$
$947$	−1103.75	−	1103.75i	−1.16552	−	1.16552i	−0.182275	−	0.983248i	$-0.558346\pi$
$948$		0			0
$949$	−33.8541	−	10.9999i	−0.0356734	−	0.0115910i
$950$		0			0
$951$	262.628	−	190.811i	0.276160	−	0.200642i
$952$		0			0
$953$	−648.844	−	330.603i	−0.680844	−	0.346907i	0.0791267	−	0.996865i	$-0.474787\pi$
$953$	−648.844	−	330.603i	−0.680844	−	0.346907i	−0.759971	+	0.649957i	$0.774787\pi$
$954$		0			0
$955$	302.851	+	113.480i	0.317121	+	0.118827i
$956$		0			0
$957$	48.4430	−	254.761i	0.0506196	−	0.266208i
$958$		0			0
$959$	−442.395	+	608.904i	−0.461309	+	0.634937i
$960$		0			0
$961$	−125.793	−	387.151i	−0.130898	−	0.402862i
$962$		0			0
$963$	1.13492	−	7.16561i	0.00117853	−	0.00744093i
$964$		0			0
$965$	917.828	+	1003.08i	0.951117	+	1.03946i
$966$		0			0
$967$	485.778	+	485.778i	0.502355	+	0.502355i	0.912169	−	0.409814i	$-0.134406\pi$
$967$	485.778	+	485.778i	0.502355	+	0.502355i	−0.409814	+	0.912169i	$0.634406\pi$
$968$		0			0
$969$			133.233i			0.137495i
$970$		0			0
$971$	−501.435	+	1543.26i	−0.516411	+	1.58935i	0.264289	+	0.964444i	$0.414863\pi$
$971$	−501.435	+	1543.26i	−0.516411	+	1.58935i	−0.780700	+	0.624906i	$0.785137\pi$
$972$		0			0
$973$	85.4721	−	539.650i	0.0878439	−	0.554625i
$974$		0			0
$975$	−743.041	+	852.292i	−0.762094	+	0.874146i
$976$		0			0
$977$	−285.484	−	1802.47i	−0.292205	−	1.84491i	−0.499101	−	0.866544i	$-0.666336\pi$
$977$	−285.484	−	1802.47i	−0.292205	−	1.84491i	0.206897	−	0.978363i	$-0.433664\pi$
$978$		0			0
$979$	−327.521	+	222.864i	−0.334546	+	0.227645i
$980$		0			0
$981$	26.6750	+	19.3805i	0.0271916	+	0.0197559i
$982$		0			0
$983$	504.570	+	257.091i	0.513296	+	0.261537i	0.691397	−	0.722475i	$-0.256995\pi$
$983$	504.570	+	257.091i	0.513296	+	0.261537i	−0.178101	+	0.984012i	$0.556995\pi$
$984$		0			0
$985$	1069.52	−	121.077i	1.08581	−	0.122921i
$986$		0			0
$987$	−1506.09	+	767.389i	−1.52592	+	0.777496i
$988$		0			0
$989$		−	1993.72i		−	2.01590i
$990$		0			0
$991$	765.723			0.772677			0.386339	−	0.922357i	$-0.373740\pi$
$991$	765.723			0.772677			0.386339	+	0.922357i	$0.373740\pi$
$992$		0			0
$993$	394.818	+	774.873i	0.397601	+	0.780336i
$994$		0			0
$995$	−587.009	−	467.618i	−0.589959	−	0.469968i
$996$		0			0
$997$	523.420	−	1027.27i	0.524995	−	1.03036i	−0.464471	−	0.885589i	$-0.653755\pi$
$997$	523.420	−	1027.27i	0.524995	−	1.03036i	0.989465	−	0.144771i	$-0.0462446\pi$
$998$		0			0
$999$	−814.722	+	1121.37i	−0.815537	+	1.12249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.x.a.37.9	✓	96
5.3	odd	4	inner	220.3.x.a.213.4	yes	96
11.3	even	5	inner	220.3.x.a.157.4	yes	96
55.3	odd	20	inner	220.3.x.a.113.9	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.x.a.37.9	✓	96	1.1	even	1	trivial
220.3.x.a.113.9	yes	96	55.3	odd	20	inner
220.3.x.a.157.4	yes	96	11.3	even	5	inner
220.3.x.a.213.4	yes	96	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34992 + 2.64938i) q^{3} +(-3.11539 + 3.91080i) q^{5} +(-3.58267 + 7.03139i) q^{7} +(0.0931732 - 0.128242i) q^{9} +(-6.18826 - 9.09425i) q^{11} +(-15.0235 + 2.37948i) q^{13} +(-14.5667 - 2.97454i) q^{15} +(2.16631 + 0.343110i) q^{17} +(19.4291 + 6.31290i) q^{19} -23.4651 q^{21} +(-26.5643 + 26.5643i) q^{23} +(-5.58873 - 24.3673i) q^{25} +(26.8972 + 4.26010i) q^{27} +(7.54043 - 2.45004i) q^{29} +(19.0407 + 13.8339i) q^{31} +(15.7404 - 28.6716i) q^{33} +(-16.3370 - 35.9166i) q^{35} +(-23.1073 + 45.3507i) q^{37} +(-26.5847 - 36.5906i) q^{39} +(-16.8469 + 51.8496i) q^{41} +(-37.5264 + 37.5264i) q^{43} +(0.211258 + 0.763905i) q^{45} +(64.1840 - 32.7034i) q^{47} +(-7.80344 - 10.7405i) q^{49} +(2.01533 + 6.20255i) q^{51} +(32.7376 - 5.18513i) q^{53} +(54.8446 + 4.13103i) q^{55} +(9.50259 + 59.9970i) q^{57} +(68.0751 - 22.1189i) q^{59} +(-43.1118 + 31.3225i) q^{61} +(0.567910 + 1.11459i) q^{63} +(37.4982 - 66.1667i) q^{65} +(2.89959 + 2.89959i) q^{67} +(-106.238 - 34.5190i) q^{69} +(44.2385 - 32.1412i) q^{71} +(2.08514 + 1.06243i) q^{73} +(57.0138 - 47.7007i) q^{75} +(86.1158 - 10.9304i) q^{77} +(52.5752 - 72.3635i) q^{79} +(24.5818 + 75.6549i) q^{81} +(9.81477 - 61.9680i) q^{83} +(-8.09074 + 7.40310i) q^{85} +(16.6701 + 16.6701i) q^{87} -36.0140i q^{89} +(37.0931 - 114.161i) q^{91} +(-10.9476 + 69.1207i) q^{93} +(-85.2177 + 56.3163i) q^{95} +(1.24843 + 7.88225i) q^{97} +(-1.74284 - 0.0537454i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{3} + 4 q^{5} - 2 q^{7} - 20 q^{11} - 8 q^{13} + 88 q^{15} + 42 q^{17} + 56 q^{21} - 104 q^{23} - 126 q^{25} - 14 q^{27} - 32 q^{31} + 52 q^{33} + 56 q^{35} - 134 q^{37} + 24 q^{41} + 332 q^{43}+ \cdots - 310 q^{97}+O(q^{100}) \) 96 * q - 2 * q^3 + 4 * q^5 - 2 * q^7 - 20 * q^11 - 8 * q^13 + 88 * q^15 + 42 * q^17 + 56 * q^21 - 104 * q^23 - 126 * q^25 - 14 * q^27 - 32 * q^31 + 52 * q^33 + 56 * q^35 - 134 * q^37 + 24 * q^41 + 332 * q^43 + 344 * q^45 + 258 * q^47 - 320 * q^51 + 222 * q^53 - 46 * q^55 + 504 * q^57 - 168 * q^61 - 298 * q^63 - 416 * q^65 - 632 * q^67 - 252 * q^71 + 56 * q^73 - 352 * q^75 - 820 * q^77 + 336 * q^81 + 236 * q^83 + 88 * q^85 - 176 * q^87 - 756 * q^91 - 770 * q^93 - 334 * q^95 - 310 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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