LMFDB - Embedded newform 272.4.o.f.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [272,4,Mod(81,272)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(272, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("272.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	272.o (of order $4$, degree $2$, not 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:	$16.0485195216$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 119x^{12} + 5319x^{10} + 112122x^{8} + 1120191x^{6} + 4382607x^{4} + 1699337x^{2} + 2704 $ x^14 + 119x^12 + 5319x^10 + 112122x^8 + 1120191x^6 + 4382607x^4 + 1699337x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 136)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.3
Root			$3.13314i$ of defining polynomial
Character	$\chi$	$=$	272.81
Dual form			272.4.o.f.225.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.13314 - 3.13314i) q^{3} +(-13.6954 - 13.6954i) q^{5} +(0.366316 - 0.366316i) q^{7} -7.36691i q^{9} +(48.7591 - 48.7591i) q^{11} -78.1851 q^{13} +85.8194i q^{15} +(24.2962 - 65.7472i) q^{17} +20.0829i q^{19} -2.29544 q^{21} +(-76.8250 + 76.8250i) q^{23} +250.130i q^{25} +(-107.676 + 107.676i) q^{27} +(-69.3788 - 69.3788i) q^{29} +(181.264 + 181.264i) q^{31} -305.538 q^{33} -10.0337 q^{35} +(209.679 + 209.679i) q^{37} +(244.964 + 244.964i) q^{39} +(-43.1738 + 43.1738i) q^{41} -494.561i q^{43} +(-100.893 + 100.893i) q^{45} -8.61388 q^{47} +342.732i q^{49} +(-282.118 + 129.872i) q^{51} -484.077i q^{53} -1335.55 q^{55} +(62.9225 - 62.9225i) q^{57} +229.865i q^{59} +(-69.4383 + 69.4383i) q^{61} +(-2.69862 - 2.69862i) q^{63} +(1070.78 + 1070.78i) q^{65} -42.5197 q^{67} +481.407 q^{69} +(135.009 + 135.009i) q^{71} +(-579.139 - 579.139i) q^{73} +(783.692 - 783.692i) q^{75} -35.7224i q^{77} +(99.3286 - 99.3286i) q^{79} +475.822 q^{81} -108.862i q^{83} +(-1233.18 + 567.690i) q^{85} +434.747i q^{87} +150.487 q^{89} +(-28.6404 + 28.6404i) q^{91} -1135.85i q^{93} +(275.044 - 275.044i) q^{95} +(-705.497 - 705.497i) q^{97} +(-359.204 - 359.204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 6 q^{3} + 6 q^{5} - 10 q^{7} + 66 q^{11} - 124 q^{13} + 130 q^{17} - 148 q^{21} + 162 q^{23} + 204 q^{27} + 158 q^{29} + 350 q^{31} + 116 q^{33} - 236 q^{35} + 582 q^{37} + 320 q^{39} + 878 q^{41}+ \cdots - 3870 q^{99}+O(q^{100}) $ 14 * q - 6 * q^3 + 6 * q^5 - 10 * q^7 + 66 * q^11 - 124 * q^13 + 130 * q^17 - 148 * q^21 + 162 * q^23 + 204 * q^27 + 158 * q^29 + 350 * q^31 + 116 * q^33 - 236 * q^35 + 582 * q^37 + 320 * q^39 + 878 * q^41 - 26 * q^45 + 448 * q^47 + 590 * q^51 - 1460 * q^55 + 292 * q^57 - 1130 * q^61 - 114 * q^63 + 20 * q^65 + 64 * q^67 + 2076 * q^69 + 3274 * q^71 - 1426 * q^73 - 946 * q^75 - 1718 * q^79 + 166 * q^81 - 2018 * q^85 + 476 * q^89 - 2128 * q^91 + 2444 * q^95 + 1926 * q^97 - 3870 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−3.13314	−	3.13314i	−0.602972	−	0.602972i	0.338128	−	0.941100i	$-0.390206\pi$
$3$	−3.13314	−	3.13314i	−0.602972	−	0.602972i	−0.941100	+	0.338128i	$0.890206\pi$
$4$		0			0
$5$	−13.6954	−	13.6954i	−1.22496	−	1.22496i	−0.965848	−	0.259109i	$-0.916571\pi$
$5$	−13.6954	−	13.6954i	−1.22496	−	1.22496i	−0.259109	−	0.965848i	$-0.583429\pi$
$6$		0			0
$7$	0.366316	−	0.366316i	0.0197792	−	0.0197792i	−0.697148	−	0.716927i	$-0.745548\pi$
$7$	0.366316	−	0.366316i	0.0197792	−	0.0197792i	0.716927	+	0.697148i	$0.245548\pi$
$8$		0			0
$9$		−	7.36691i		−	0.272849i
$10$		0			0
$11$	48.7591	−	48.7591i	1.33649	−	1.33649i	0.437058	−	0.899433i	$-0.356020\pi$
$11$	48.7591	−	48.7591i	1.33649	−	1.33649i	0.899433	−	0.437058i	$-0.143980\pi$
$12$		0			0
$13$	−78.1851			−1.66805			−0.834025	−	0.551727i	$-0.813969\pi$
$13$	−78.1851			−1.66805			−0.834025	+	0.551727i	$0.813969\pi$
$14$		0			0
$15$			85.8194i			1.47723i
$16$		0			0
$17$	24.2962	−	65.7472i	0.346629	−	0.938002i
$17$	24.2962	−	65.7472i	0.346629	−	0.938002i
$18$		0			0
$19$			20.0829i			0.242491i	0.992623	+	0.121246i	$0.0386889\pi$
$19$			20.0829i			0.242491i	−0.992623	+	0.121246i	$0.961311\pi$
$20$		0			0
$21$	−2.29544			−0.0238526
$22$		0			0
$23$	−76.8250	+	76.8250i	−0.696484	+	0.696484i	−0.963650	−	0.267167i	$-0.913913\pi$
$23$	−76.8250	+	76.8250i	−0.696484	+	0.696484i	0.267167	+	0.963650i	$0.413913\pi$
$24$		0			0
$25$			250.130i			2.00104i
$26$		0			0
$27$	−107.676	+	107.676i	−0.767493	+	0.767493i
$28$		0			0
$29$	−69.3788	−	69.3788i	−0.444253	−	0.444253i	0.449186	−	0.893438i	$-0.351714\pi$
$29$	−69.3788	−	69.3788i	−0.444253	−	0.444253i	−0.893438	+	0.449186i	$0.851714\pi$
$30$		0			0
$31$	181.264	+	181.264i	1.05020	+	1.05020i	0.998672	+	0.0515239i	$0.0164078\pi$
$31$	181.264	+	181.264i	1.05020	+	1.05020i	0.0515239	+	0.998672i	$0.483592\pi$
$32$		0			0
$33$	−305.538			−1.61174
$34$		0			0
$35$	−10.0337			−0.0484573
$36$		0			0
$37$	209.679	+	209.679i	0.931651	+	0.931651i	0.997809	−	0.0661585i	$-0.0210743\pi$
$37$	209.679	+	209.679i	0.931651	+	0.931651i	−0.0661585	+	0.997809i	$0.521074\pi$
$38$		0			0
$39$	244.964	+	244.964i	1.00579	+	1.00579i
$40$		0			0
$41$	−43.1738	+	43.1738i	−0.164454	+	0.164454i	−0.784537	−	0.620082i	$-0.787099\pi$
$41$	−43.1738	+	43.1738i	−0.164454	+	0.164454i	0.620082	+	0.784537i	$0.287099\pi$
$42$		0			0
$43$		−	494.561i		−	1.75395i	−0.480535	−	0.876975i	$-0.659558\pi$
$43$		−	494.561i		−	1.75395i	0.480535	−	0.876975i	$-0.340442\pi$
$44$		0			0
$45$	−100.893	+	100.893i	−0.334228	+	0.334228i
$46$		0			0
$47$	−8.61388			−0.0267333			−0.0133666	−	0.999911i	$-0.504255\pi$
$47$	−8.61388			−0.0267333			−0.0133666	+	0.999911i	$0.504255\pi$
$48$		0			0
$49$			342.732i			0.999218i
$50$		0			0
$51$	−282.118	+	129.872i	−0.774597	+	0.356582i
$52$		0			0
$53$		−	484.077i		−	1.25459i	−0.778783	−	0.627293i	$-0.784163\pi$
$53$		−	484.077i		−	1.25459i	0.778783	−	0.627293i	$-0.215837\pi$
$54$		0			0
$55$	−1335.55			−3.27429
$56$		0			0
$57$	62.9225	−	62.9225i	0.146216	−	0.146216i
$58$		0			0
$59$			229.865i			0.507219i	0.967307	+	0.253609i	$0.0816178\pi$
$59$			229.865i			0.507219i	−0.967307	+	0.253609i	$0.918382\pi$
$60$		0			0
$61$	−69.4383	+	69.4383i	−0.145749	+	0.145749i	−0.776216	−	0.630467i	$-0.782863\pi$
$61$	−69.4383	+	69.4383i	−0.145749	+	0.145749i	0.630467	+	0.776216i	$0.282863\pi$
$62$		0			0
$63$	−2.69862	−	2.69862i	−0.00539673	−	0.00539673i
$64$		0			0
$65$	1070.78	+	1070.78i	2.04329	+	2.04329i
$66$		0			0
$67$	−42.5197			−0.0775314			−0.0387657	−	0.999248i	$-0.512343\pi$
$67$	−42.5197			−0.0775314			−0.0387657	+	0.999248i	$0.512343\pi$
$68$		0			0
$69$	481.407			0.839921
$70$		0			0
$71$	135.009	+	135.009i	0.225670	+	0.225670i	0.810881	−	0.585211i	$-0.198988\pi$
$71$	135.009	+	135.009i	0.225670	+	0.225670i	−0.585211	+	0.810881i	$0.698988\pi$
$72$		0			0
$73$	−579.139	−	579.139i	−0.928535	−	0.928535i	0.0690762	−	0.997611i	$-0.477995\pi$
$73$	−579.139	−	579.139i	−0.928535	−	0.928535i	−0.997611	+	0.0690762i	$0.977995\pi$
$74$		0			0
$75$	783.692	−	783.692i	1.20657	−	1.20657i
$76$		0			0
$77$		−	35.7224i		−	0.0528695i
$78$		0			0
$79$	99.3286	−	99.3286i	0.141460	−	0.141460i	−0.632830	−	0.774290i	$-0.718107\pi$
$79$	99.3286	−	99.3286i	0.141460	−	0.141460i	0.774290	+	0.632830i	$0.218107\pi$
$80$		0			0
$81$	475.822			0.652705
$82$		0			0
$83$		−	108.862i		−	0.143965i	−0.997406	−	0.0719826i	$-0.977067\pi$
$83$		−	108.862i		−	0.143965i	0.997406	−	0.0719826i	$-0.0229326\pi$
$84$		0			0
$85$	−1233.18	+	567.690i	−1.57362	+	0.724407i
$86$		0			0
$87$			434.747i			0.535744i
$88$		0			0
$89$	150.487			0.179232			0.0896158	−	0.995976i	$-0.471436\pi$
$89$	150.487			0.179232			0.0896158	+	0.995976i	$0.471436\pi$
$90$		0			0
$91$	−28.6404	+	28.6404i	−0.0329927	+	0.0329927i
$92$		0			0
$93$		−	1135.85i		−	1.26648i
$94$		0			0
$95$	275.044	−	275.044i	0.297041	−	0.297041i
$96$		0			0
$97$	−705.497	−	705.497i	−0.738478	−	0.738478i	0.233805	−	0.972283i	$-0.424882\pi$
$97$	−705.497	−	705.497i	−0.738478	−	0.738478i	−0.972283	+	0.233805i	$0.924882\pi$
$98$		0			0
$99$	−359.204	−	359.204i	−0.364660	−	0.364660i
$100$		0			0
$101$	228.629			0.225242			0.112621	−	0.993638i	$-0.464075\pi$
$101$	228.629			0.225242			0.112621	+	0.993638i	$0.464075\pi$
$102$		0			0
$103$	−479.936			−0.459121			−0.229561	−	0.973294i	$-0.573729\pi$
$103$	−479.936			−0.459121			−0.229561	+	0.973294i	$0.573729\pi$
$104$		0			0
$105$	31.4370	+	31.4370i	0.0292184	+	0.0292184i
$106$		0			0
$107$	767.152	+	767.152i	0.693116	+	0.693116i	0.962916	−	0.269801i	$-0.0869578\pi$
$107$	767.152	+	767.152i	0.693116	+	0.693116i	−0.269801	+	0.962916i	$0.586958\pi$
$108$		0			0
$109$	−165.398	+	165.398i	−0.145342	+	0.145342i	−0.776033	−	0.630692i	$-0.782771\pi$
$109$	−165.398	+	165.398i	−0.145342	+	0.145342i	0.630692	+	0.776033i	$0.282771\pi$
$110$		0			0
$111$		−	1313.91i		−	1.12352i
$112$		0			0
$113$	638.981	−	638.981i	0.531950	−	0.531950i	−0.389202	−	0.921152i	$-0.627249\pi$
$113$	638.981	−	638.981i	0.531950	−	0.531950i	0.921152	+	0.389202i	$0.127249\pi$
$114$		0			0
$115$	2104.30			1.70633
$116$		0			0
$117$			575.983i			0.455125i
$118$		0			0
$119$	−15.1842	−	32.9843i	−0.0116969	−	0.0254090i
$120$		0			0
$121$		−	3423.89i		−	2.57242i
$122$		0			0
$123$	270.539			0.198323
$124$		0			0
$125$	1713.71	−	1713.71i	1.22623	−	1.22623i
$126$		0			0
$127$		−	1701.56i		−	1.18889i	−0.804137	−	0.594444i	$-0.797372\pi$
$127$		−	1701.56i		−	1.18889i	0.804137	−	0.594444i	$-0.202628\pi$
$128$		0			0
$129$	−1549.53	+	1549.53i	−1.05758	+	1.05758i
$130$		0			0
$131$	763.277	+	763.277i	0.509068	+	0.509068i	0.914240	−	0.405173i	$-0.132789\pi$
$131$	763.277	+	763.277i	0.509068	+	0.509068i	−0.405173	+	0.914240i	$0.632789\pi$
$132$		0			0
$133$	7.35669	+	7.35669i	0.00479628	+	0.00479628i
$134$		0			0
$135$	2949.35			1.88029
$136$		0			0
$137$	−935.131			−0.583165			−0.291583	−	0.956546i	$-0.594182\pi$
$137$	−935.131			−0.583165			−0.291583	+	0.956546i	$0.594182\pi$
$138$		0			0
$139$	−377.681	−	377.681i	−0.230464	−	0.230464i	0.582422	−	0.812886i	$-0.302105\pi$
$139$	−377.681	−	377.681i	−0.230464	−	0.230464i	−0.812886	+	0.582422i	$0.802105\pi$
$140$		0			0
$141$	26.9885	+	26.9885i	0.0161194	+	0.0161194i
$142$		0			0
$143$	−3812.23	+	3812.23i	−2.22933	+	2.22933i
$144$		0			0
$145$			1900.35i			1.08838i
$146$		0			0
$147$	1073.82	−	1073.82i	0.602501	−	0.602501i
$148$		0			0
$149$	174.251			0.0958066			0.0479033	−	0.998852i	$-0.484746\pi$
$149$	174.251			0.0958066			0.0479033	+	0.998852i	$0.484746\pi$
$150$		0			0
$151$			2206.26i			1.18902i	0.804087	+	0.594512i	$0.202655\pi$
$151$			2206.26i			1.18902i	−0.804087	+	0.594512i	$0.797345\pi$
$152$		0			0
$153$	−484.354	−	178.988i	−0.255933	−	0.0945772i
$154$		0			0
$155$		−	4964.99i		−	2.57289i
$156$		0			0
$157$	−835.318			−0.424622			−0.212311	−	0.977202i	$-0.568099\pi$
$157$	−835.318			−0.424622			−0.212311	+	0.977202i	$0.568099\pi$
$158$		0			0
$159$	−1516.68	+	1516.68i	−0.756481	+	0.756481i
$160$		0			0
$161$			56.2845i			0.0275518i
$162$		0			0
$163$	−428.709	+	428.709i	−0.206007	+	0.206007i	−0.802568	−	0.596561i	$-0.796533\pi$
$163$	−428.709	+	428.709i	−0.206007	+	0.206007i	0.596561	+	0.802568i	$0.296533\pi$
$164$		0			0
$165$	4184.47	+	4184.47i	1.97431	+	1.97431i
$166$		0			0
$167$	1829.98	+	1829.98i	0.847953	+	0.847953i	0.989878	−	0.141924i	$-0.0453290\pi$
$167$	1829.98	+	1829.98i	0.847953	+	0.847953i	−0.141924	+	0.989878i	$0.545329\pi$
$168$		0			0
$169$	3915.91			1.78239
$170$		0			0
$171$	147.949			0.0661634
$172$		0			0
$173$	−2288.28	−	2288.28i	−1.00563	−	1.00563i	−0.999984	−	0.00564957i	$-0.998202\pi$
$173$	−2288.28	−	2288.28i	−1.00563	−	1.00563i	−0.00564957	−	0.999984i	$-0.501798\pi$
$174$		0			0
$175$	91.6266	+	91.6266i	0.0395790	+	0.0395790i
$176$		0			0
$177$	720.199	−	720.199i	0.305839	−	0.305839i
$178$		0			0
$179$		−	187.225i		−	0.0781781i	−0.999236	−	0.0390890i	$-0.987554\pi$
$179$		−	187.225i		−	0.0781781i	0.999236	−	0.0390890i	$-0.0124456\pi$
$180$		0			0
$181$	−1463.63	+	1463.63i	−0.601054	+	0.601054i	−0.940592	−	0.339538i	$-0.889729\pi$
$181$	−1463.63	+	1463.63i	−0.601054	+	0.601054i	0.339538	+	0.940592i	$0.389729\pi$
$182$		0			0
$183$	435.120			0.175765
$184$		0			0
$185$		−	5743.30i		−	2.28246i
$186$		0			0
$187$	−2021.11	−	4390.43i	−0.790365	−	1.71690i
$188$		0			0
$189$			78.8870i			0.0303608i
$190$		0			0
$191$	−1610.64			−0.610166			−0.305083	−	0.952326i	$-0.598684\pi$
$191$	−1610.64			−0.610166			−0.305083	+	0.952326i	$0.598684\pi$
$192$		0			0
$193$	−2937.22	+	2937.22i	−1.09547	+	1.09547i	−0.100537	+	0.994933i	$0.532056\pi$
$193$	−2937.22	+	2937.22i	−1.09547	+	1.09547i	−0.994933	+	0.100537i	$0.967944\pi$
$194$		0			0
$195$		−	6709.79i		−	2.46409i
$196$		0			0
$197$	−919.581	+	919.581i	−0.332576	+	0.332576i	−0.853564	−	0.520988i	$-0.825564\pi$
$197$	−919.581	+	919.581i	−0.332576	+	0.332576i	0.520988	+	0.853564i	$0.325564\pi$
$198$		0			0
$199$	−592.702	−	592.702i	−0.211133	−	0.211133i	0.593615	−	0.804749i	$-0.297700\pi$
$199$	−592.702	−	592.702i	−0.211133	−	0.211133i	−0.804749	+	0.593615i	$0.797700\pi$
$200$		0			0
$201$	133.220	+	133.220i	0.0467493	+	0.0467493i
$202$		0			0
$203$	−50.8291			−0.0175739
$204$		0			0
$205$	1182.57			0.402899
$206$		0			0
$207$	565.963	+	565.963i	0.190035	+	0.190035i
$208$		0			0
$209$	979.223	+	979.223i	0.324088	+	0.324088i
$210$		0			0
$211$	−244.691	+	244.691i	−0.0798353	+	0.0798353i	−0.745897	−	0.666062i	$-0.767979\pi$
$211$	−244.691	+	244.691i	−0.0798353	+	0.0798353i	0.666062	+	0.745897i	$0.267979\pi$
$212$		0			0
$213$		−	846.001i		−	0.272146i
$214$		0			0
$215$	−6773.23	+	6773.23i	−2.14851	+	2.14851i
$216$		0			0
$217$	132.800			0.0415441
$218$		0			0
$219$			3629.04i			1.11976i
$220$		0			0
$221$	−1899.60	+	5140.45i	−0.578194	+	1.56463i
$222$		0			0
$223$		−	2120.33i		−	0.636716i	−0.947970	−	0.318358i	$-0.896869\pi$
$223$		−	2120.33i		−	0.636716i	0.947970	−	0.318358i	$-0.103131\pi$
$224$		0			0
$225$	1842.69			0.545981
$226$		0			0
$227$	−1434.23	+	1434.23i	−0.419352	+	0.419352i	−0.884980	−	0.465628i	$-0.845828\pi$
$227$	−1434.23	+	1434.23i	−0.419352	+	0.419352i	0.465628	+	0.884980i	$0.345828\pi$
$228$		0			0
$229$		−	1720.34i		−	0.496432i	−0.968705	−	0.248216i	$-0.920156\pi$
$229$		−	1720.34i		−	0.496432i	0.968705	−	0.248216i	$-0.0798443\pi$
$230$		0			0
$231$	−111.923	+	111.923i	−0.0318788	+	0.0318788i
$232$		0			0
$233$	1693.58	+	1693.58i	0.476180	+	0.476180i	0.903908	−	0.427728i	$-0.140686\pi$
$233$	1693.58	+	1693.58i	0.476180	+	0.476180i	−0.427728	+	0.903908i	$0.640686\pi$
$234$		0			0
$235$	117.971	+	117.971i	0.0327471	+	0.0327471i
$236$		0			0
$237$	−622.420			−0.170593
$238$		0			0
$239$	−2646.56			−0.716284			−0.358142	−	0.933667i	$-0.616590\pi$
$239$	−2646.56			−0.716284			−0.358142	+	0.933667i	$0.616590\pi$
$240$		0			0
$241$	−2584.91	−	2584.91i	−0.690908	−	0.690908i	0.271524	−	0.962432i	$-0.412472\pi$
$241$	−2584.91	−	2584.91i	−0.690908	−	0.690908i	−0.962432	+	0.271524i	$0.912472\pi$
$242$		0			0
$243$	1416.44	+	1416.44i	0.373929	+	0.373929i
$244$		0			0
$245$	4693.86	−	4693.86i	1.22400	−	1.22400i
$246$		0			0
$247$		−	1570.18i		−	0.404487i
$248$		0			0
$249$	−341.078	+	341.078i	−0.0868071	+	0.0868071i
$250$		0			0
$251$	−2232.04			−0.561295			−0.280648	−	0.959811i	$-0.590549\pi$
$251$	−2232.04			−0.561295			−0.280648	+	0.959811i	$0.590549\pi$
$252$		0			0
$253$			7491.83i			1.86169i
$254$		0			0
$255$	5642.38	+	2085.08i	1.38565	+	0.512051i
$256$		0			0
$257$			4945.83i			1.20044i	0.799836	+	0.600219i	$0.204920\pi$
$257$			4945.83i			1.20044i	−0.799836	+	0.600219i	$0.795080\pi$
$258$		0			0
$259$	153.618			0.0368546
$260$		0			0
$261$	−511.108	+	511.108i	−0.121214	+	0.121214i
$262$		0			0
$263$			5765.09i			1.35168i	0.737051	+	0.675838i	$0.236218\pi$
$263$			5765.09i			1.35168i	−0.737051	+	0.675838i	$0.763782\pi$
$264$		0			0
$265$	−6629.65	+	6629.65i	−1.53681	+	1.53681i
$266$		0			0
$267$	−471.497	−	471.497i	−0.108072	−	0.108072i
$268$		0			0
$269$	−1769.02	−	1769.02i	−0.400962	−	0.400962i	0.477610	−	0.878572i	$-0.341503\pi$
$269$	−1769.02	−	1769.02i	−0.400962	−	0.400962i	−0.878572	+	0.477610i	$0.841503\pi$
$270$		0			0
$271$	3004.87			0.673552			0.336776	−	0.941585i	$-0.390663\pi$
$271$	3004.87			0.673552			0.336776	+	0.941585i	$0.390663\pi$
$272$		0			0
$273$	179.469			0.0397873
$274$		0			0
$275$	12196.1	+	12196.1i	2.67437	+	2.67437i
$276$		0			0
$277$	−3350.03	−	3350.03i	−0.726656	−	0.726656i	0.243296	−	0.969952i	$-0.421771\pi$
$277$	−3350.03	−	3350.03i	−0.726656	−	0.726656i	−0.969952	+	0.243296i	$0.921771\pi$
$278$		0			0
$279$	1335.36	−	1335.36i	0.286544	−	0.286544i
$280$		0			0
$281$		−	1635.27i		−	0.347161i	−0.984820	−	0.173580i	$-0.944466\pi$
$281$		−	1635.27i		−	0.347161i	0.984820	−	0.173580i	$-0.0555336\pi$
$282$		0			0
$283$	−2719.64	+	2719.64i	−0.571257	+	0.571257i	−0.932480	−	0.361222i	$-0.882359\pi$
$283$	−2719.64	+	2719.64i	−0.571257	+	0.571257i	0.361222	+	0.932480i	$0.382359\pi$
$284$		0			0
$285$	−1723.50			−0.358216
$286$		0			0
$287$			31.6305i			0.00650554i
$288$		0			0
$289$	−3732.39	−	3194.81i	−0.759697	−	0.650278i
$290$		0			0
$291$			4420.84i			0.890564i
$292$		0			0
$293$	−7075.63			−1.41080			−0.705398	−	0.708812i	$-0.749231\pi$
$293$	−7075.63			−1.41080			−0.705398	+	0.708812i	$0.749231\pi$
$294$		0			0
$295$	3148.10	−	3148.10i	0.621321	−	0.621321i
$296$		0			0
$297$			10500.4i			2.05149i
$298$		0			0
$299$	6006.57	−	6006.57i	1.16177	−	1.16177i
$300$		0			0
$301$	−181.166	−	181.166i	−0.0346917	−	0.0346917i
$302$		0			0
$303$	−716.325	−	716.325i	−0.135815	−	0.135815i
$304$		0			0
$305$	1901.98			0.357072
$306$		0			0
$307$	−8876.20			−1.65014			−0.825068	−	0.565034i	$-0.808863\pi$
$307$	−8876.20			−1.65014			−0.825068	+	0.565034i	$0.808863\pi$
$308$		0			0
$309$	1503.70	+	1503.70i	0.276837	+	0.276837i
$310$		0			0
$311$	−6123.95	−	6123.95i	−1.11658	−	1.11658i	−0.992239	−	0.124344i	$-0.960317\pi$
$311$	−6123.95	−	6123.95i	−1.11658	−	1.11658i	−0.124344	−	0.992239i	$-0.539683\pi$
$312$		0			0
$313$	5223.18	−	5223.18i	0.943233	−	0.943233i	−0.0552406	−	0.998473i	$-0.517593\pi$
$313$	5223.18	−	5223.18i	0.943233	−	0.943233i	0.998473	+	0.0552406i	$0.0175926\pi$
$314$		0			0
$315$			73.9175i			0.0132215i
$316$		0			0
$317$	683.304	−	683.304i	0.121067	−	0.121067i	−0.643978	−	0.765044i	$-0.722717\pi$
$317$	683.304	−	683.304i	0.121067	−	0.121067i	0.765044	+	0.643978i	$0.222717\pi$
$318$		0			0
$319$	−6765.69			−1.18748
$320$		0			0
$321$		−	4807.18i		−	0.835859i
$322$		0			0
$323$	1320.39	+	487.938i	0.227457	+	0.0840545i
$324$		0			0
$325$		−	19556.4i		−	3.33783i
$326$		0			0
$327$	1036.43			0.175274
$328$		0			0
$329$	−3.15540	+	3.15540i	−0.000528762	+	0.000528762i
$330$		0			0
$331$		−	4832.27i		−	0.802434i	−0.915983	−	0.401217i	$-0.868587\pi$
$331$		−	4832.27i		−	0.802434i	0.915983	−	0.401217i	$-0.131413\pi$
$332$		0			0
$333$	1544.69	−	1544.69i	0.254200	−	0.254200i
$334$		0			0
$335$	582.325	+	582.325i	0.0949726	+	0.0949726i
$336$		0			0
$337$	525.653	+	525.653i	0.0849678	+	0.0849678i	0.748313	−	0.663345i	$-0.230864\pi$
$337$	525.653	+	525.653i	0.0849678	+	0.0849678i	−0.663345	+	0.748313i	$0.730864\pi$
$338$		0			0
$339$	−4004.03			−0.641502
$340$		0			0
$341$	17676.6			2.80716
$342$		0			0
$343$	251.194	+	251.194i	0.0395429	+	0.0395429i
$344$		0			0
$345$	−6593.07	−	6593.07i	−1.02887	−	1.02887i
$346$		0			0
$347$	8737.59	−	8737.59i	1.35175	−	1.35175i	0.468053	−	0.883700i	$-0.344956\pi$
$347$	8737.59	−	8737.59i	1.35175	−	1.35175i	0.883700	−	0.468053i	$-0.155044\pi$
$348$		0			0
$349$		−	4021.47i		−	0.616803i	−0.951256	−	0.308402i	$-0.900206\pi$
$349$		−	4021.47i		−	0.616803i	0.951256	−	0.308402i	$-0.0997941\pi$
$350$		0			0
$351$	8418.67	−	8418.67i	1.28022	−	1.28022i
$352$		0			0
$353$	−1609.77			−0.242718			−0.121359	−	0.992609i	$-0.538725\pi$
$353$	−1609.77			−0.242718			−0.121359	+	0.992609i	$0.538725\pi$
$354$		0			0
$355$		−	3698.01i		−	0.552873i
$356$		0			0
$357$	−55.7703	+	150.918i	−0.00826801	+	0.0223738i
$358$		0			0
$359$		−	5346.19i		−	0.785964i	−0.919546	−	0.392982i	$-0.871443\pi$
$359$		−	5346.19i		−	0.785964i	0.919546	−	0.392982i	$-0.128557\pi$
$360$		0			0
$361$	6455.68			0.941198
$362$		0			0
$363$	−10727.5	+	10727.5i	−1.55110	+	1.55110i
$364$		0			0
$365$			15863.1i			2.27483i
$366$		0			0
$367$	3919.39	−	3919.39i	0.557468	−	0.557468i	−0.371118	−	0.928586i	$-0.621026\pi$
$367$	3919.39	−	3919.39i	0.557468	−	0.557468i	0.928586	+	0.371118i	$0.121026\pi$
$368$		0			0
$369$	318.058	+	318.058i	0.0448711	+	0.0448711i
$370$		0			0
$371$	−177.325	−	177.325i	−0.0248147	−	0.0248147i
$372$		0			0
$373$	−3949.42			−0.548240			−0.274120	−	0.961696i	$-0.588387\pi$
$373$	−3949.42			−0.548240			−0.274120	+	0.961696i	$0.588387\pi$
$374$		0			0
$375$	−10738.6			−1.47877
$376$		0			0
$377$	5424.39	+	5424.39i	0.741035	+	0.741035i
$378$		0			0
$379$	10277.5	+	10277.5i	1.39293	+	1.39293i	0.818676	+	0.574255i	$0.194708\pi$
$379$	10277.5	+	10277.5i	1.39293	+	1.39293i	0.574255	+	0.818676i	$0.305292\pi$
$380$		0			0
$381$	−5331.21	+	5331.21i	−0.716867	+	0.716867i
$382$		0			0
$383$		−	12879.2i		−	1.71827i	−0.511752	−	0.859133i	$-0.671003\pi$
$383$		−	12879.2i		−	1.71827i	0.511752	−	0.859133i	$-0.328997\pi$
$384$		0			0
$385$	−489.234	+	489.234i	−0.0647628	+	0.0647628i
$386$		0			0
$387$	−3643.39			−0.478563
$388$		0			0
$389$		−	7488.75i		−	0.976078i	−0.872822	−	0.488039i	$-0.837712\pi$
$389$		−	7488.75i		−	0.976078i	0.872822	−	0.488039i	$-0.162288\pi$
$390$		0			0
$391$	3184.47	+	6917.59i	0.411882	+	0.894725i
$392$		0			0
$393$		−	4782.90i		−	0.613907i
$394$		0			0
$395$	−2720.70			−0.346565
$396$		0			0
$397$	−8076.83	+	8076.83i	−1.02107	+	1.02107i	−0.0212958	+	0.999773i	$0.506779\pi$
$397$	−8076.83	+	8076.83i	−1.02107	+	1.02107i	−0.999773	+	0.0212958i	$0.993221\pi$
$398$		0			0
$399$		−	46.0990i		−	0.00578405i
$400$		0			0
$401$	2650.51	−	2650.51i	0.330076	−	0.330076i	−0.522539	−	0.852615i	$-0.675015\pi$
$401$	2650.51	−	2650.51i	0.330076	−	0.330076i	0.852615	+	0.522539i	$0.175015\pi$
$402$		0			0
$403$	−14172.2	−	14172.2i	−1.75178	−	1.75178i
$404$		0			0
$405$	−6516.59	−	6516.59i	−0.799536	−	0.799536i
$406$		0			0
$407$	20447.5			2.49029
$408$		0			0
$409$	9473.41			1.14531			0.572653	−	0.819798i	$-0.305914\pi$
$409$	9473.41			1.14531			0.572653	+	0.819798i	$0.305914\pi$
$410$		0			0
$411$	2929.89	+	2929.89i	0.351633	+	0.351633i
$412$		0			0
$413$	84.2033	+	84.2033i	0.0100324	+	0.0100324i
$414$		0			0
$415$	−1490.91	+	1490.91i	−0.176351	+	0.176351i
$416$		0			0
$417$			2366.65i			0.277927i
$418$		0			0
$419$	−7161.34	+	7161.34i	−0.834974	+	0.834974i	−0.988192	−	0.153218i	$-0.951036\pi$
$419$	−7161.34	+	7161.34i	−0.834974	+	0.834974i	0.153218	+	0.988192i	$0.451036\pi$
$420$		0			0
$421$	609.770			0.0705900			0.0352950	−	0.999377i	$-0.488763\pi$
$421$	609.770			0.0705900			0.0352950	+	0.999377i	$0.488763\pi$
$422$		0			0
$423$			63.4577i			0.00729413i
$424$		0			0
$425$	16445.3	+	6077.21i	1.87698	+	0.693619i
$426$		0			0
$427$			50.8727i			0.00576558i
$428$		0			0
$429$	23888.5			2.68845
$430$		0			0
$431$	969.821	−	969.821i	0.108387	−	0.108387i	−0.650834	−	0.759220i	$-0.725580\pi$
$431$	969.821	−	969.821i	0.108387	−	0.108387i	0.759220	+	0.650834i	$0.225580\pi$
$432$		0			0
$433$			9567.13i			1.06182i	0.847429	+	0.530909i	$0.178149\pi$
$433$			9567.13i			1.06182i	−0.847429	+	0.530909i	$0.821851\pi$
$434$		0			0
$435$	5954.05	−	5954.05i	0.656264	−	0.656264i
$436$		0			0
$437$	−1542.87	−	1542.87i	−0.168891	−	0.168891i
$438$		0			0
$439$	−3853.48	−	3853.48i	−0.418945	−	0.418945i	0.465895	−	0.884840i	$-0.345732\pi$
$439$	−3853.48	−	3853.48i	−0.418945	−	0.418945i	−0.884840	+	0.465895i	$0.845732\pi$
$440$		0			0
$441$	2524.87			0.272635
$442$		0			0
$443$	−1212.61			−0.130052			−0.0650260	−	0.997884i	$-0.520713\pi$
$443$	−1212.61			−0.130052			−0.0650260	+	0.997884i	$0.520713\pi$
$444$		0			0
$445$	−2060.99	−	2060.99i	−0.219551	−	0.219551i
$446$		0			0
$447$	−545.952	−	545.952i	−0.0577687	−	0.0577687i
$448$		0			0
$449$	5558.66	−	5558.66i	0.584252	−	0.584252i	−0.351817	−	0.936069i	$-0.614436\pi$
$449$	5558.66	−	5558.66i	0.584252	−	0.584252i	0.936069	+	0.351817i	$0.114436\pi$
$450$		0			0
$451$			4210.23i			0.439583i
$452$		0			0
$453$	6912.50	−	6912.50i	0.716949	−	0.716949i
$454$		0			0
$455$	784.487			0.0808292
$456$		0			0
$457$		−	1470.94i		−	0.150563i	−0.997162	−	0.0752817i	$-0.976014\pi$
$457$		−	1470.94i		−	0.150563i	0.997162	−	0.0752817i	$-0.0239856\pi$
$458$		0			0
$459$	4463.29	+	9695.53i	0.453875	+	0.985945i
$460$		0			0
$461$			3690.37i			0.372837i	0.982470	+	0.186418i	$0.0596880\pi$
$461$			3690.37i			0.372837i	−0.982470	+	0.186418i	$0.940312\pi$
$462$		0			0
$463$	−11715.3			−1.17593			−0.587967	−	0.808885i	$-0.700071\pi$
$463$	−11715.3			−1.17593			−0.587967	+	0.808885i	$0.700071\pi$
$464$		0			0
$465$	−15556.0	+	15556.0i	−1.55138	+	1.55138i
$466$		0			0
$467$		−	4167.27i		−	0.412930i	−0.978454	−	0.206465i	$-0.933804\pi$
$467$		−	4167.27i		−	0.412930i	0.978454	−	0.206465i	$-0.0661959\pi$
$468$		0			0
$469$	−15.5756	+	15.5756i	−0.00153351	+	0.00153351i
$470$		0			0
$471$	2617.16	+	2617.16i	0.256035	+	0.256035i
$472$		0			0
$473$	−24114.3	−	24114.3i	−2.34414	−	2.34414i
$474$		0			0
$475$	−5023.34			−0.485235
$476$		0			0
$477$	−3566.15			−0.342312
$478$		0			0
$479$	8784.23	+	8784.23i	0.837916	+	0.837916i	0.988584	−	0.150668i	$-0.0481426\pi$
$479$	8784.23	+	8784.23i	0.837916	+	0.837916i	−0.150668	+	0.988584i	$0.548143\pi$
$480$		0			0
$481$	−16393.8	−	16393.8i	−1.55404	−	1.55404i
$482$		0			0
$483$	176.347	−	176.347i	0.0166130	−	0.0166130i
$484$		0			0
$485$			19324.2i			1.80921i
$486$		0			0
$487$	11055.7	−	11055.7i	1.02871	−	1.02871i	0.0291339	−	0.999576i	$-0.490725\pi$
$487$	11055.7	−	11055.7i	1.02871	−	1.02871i	0.999576	−	0.0291339i	$-0.00927493\pi$
$488$		0			0
$489$	2686.41			0.248433
$490$		0			0
$491$		−	15230.5i		−	1.39988i	−0.714201	−	0.699941i	$-0.753210\pi$
$491$		−	15230.5i		−	1.39988i	0.714201	−	0.699941i	$-0.246790\pi$
$492$		0			0
$493$	−6247.11	+	2875.82i	−0.570701	+	0.262719i
$494$		0			0
$495$			9838.90i			0.893385i
$496$		0			0
$497$	98.9116			0.00892715
$498$		0			0
$499$	−7806.36	+	7806.36i	−0.700322	+	0.700322i	−0.964480	−	0.264157i	$-0.914906\pi$
$499$	−7806.36	+	7806.36i	−0.700322	+	0.700322i	0.264157	+	0.964480i	$0.414906\pi$
$500$		0			0
$501$		−	11467.2i		−	1.02258i
$502$		0			0
$503$	−3012.51	+	3012.51i	−0.267040	+	0.267040i	−0.827906	−	0.560866i	$-0.810468\pi$
$503$	−3012.51	+	3012.51i	−0.267040	+	0.267040i	0.560866	+	0.827906i	$0.310468\pi$
$504$		0			0
$505$	−3131.17	−	3131.17i	−0.275912	−	0.275912i
$506$		0			0
$507$	−12269.1	−	12269.1i	−1.07473	−	1.07473i
$508$		0			0
$509$	3001.86			0.261405			0.130703	−	0.991422i	$-0.458277\pi$
$509$	3001.86			0.261405			0.130703	+	0.991422i	$0.458277\pi$
$510$		0			0
$511$	−424.295			−0.0367314
$512$		0			0
$513$	−2162.45	−	2162.45i	−0.186110	−	0.186110i
$514$		0			0
$515$	6572.93	+	6572.93i	0.562404	+	0.562404i
$516$		0			0
$517$	−420.005	+	420.005i	−0.0357288	+	0.0357288i
$518$		0			0
$519$			14339.0i			1.21274i
$520$		0			0
$521$	−5296.86	+	5296.86i	−0.445412	+	0.445412i	−0.893826	−	0.448414i	$-0.851989\pi$
$521$	−5296.86	+	5296.86i	−0.445412	+	0.445412i	0.448414	+	0.893826i	$0.351989\pi$
$522$		0			0
$523$	−3953.10			−0.330511			−0.165255	−	0.986251i	$-0.552845\pi$
$523$	−3953.10			−0.330511			−0.165255	+	0.986251i	$0.552845\pi$
$524$		0			0
$525$		−	574.157i		−	0.0477301i
$526$		0			0
$527$	16321.7	−	7513.60i	1.34911	−	0.621058i
$528$		0			0
$529$			362.831i			0.0298209i
$530$		0			0
$531$	1693.40			0.138394
$532$		0			0
$533$	3375.55	−	3375.55i	0.274318	−	0.274318i
$534$		0			0
$535$		−	21013.0i		−	1.69807i
$536$		0			0
$537$	−586.602	+	586.602i	−0.0471392	+	0.0471392i
$538$		0			0
$539$	16711.3	+	16711.3i	1.33545	+	1.33545i
$540$		0			0
$541$	13943.1	+	13943.1i	1.10806	+	1.10806i	0.993405	+	0.114657i	$0.0365769\pi$
$541$	13943.1	+	13943.1i	1.10806	+	1.10806i	0.114657	+	0.993405i	$0.463423\pi$
$542$		0			0
$543$	9171.51			0.724838
$544$		0			0
$545$	4530.39			0.356074
$546$		0			0
$547$	12070.1	+	12070.1i	0.943473	+	0.943473i	0.998486	−	0.0550128i	$-0.0175200\pi$
$547$	12070.1	+	12070.1i	0.943473	+	0.943473i	−0.0550128	+	0.998486i	$0.517520\pi$
$548$		0			0
$549$	511.546	+	511.546i	0.0397673	+	0.0397673i
$550$		0			0
$551$	1393.33	−	1393.33i	0.107727	−	0.107727i
$552$		0			0
$553$		−	72.7713i		−	0.00559593i
$554$		0			0
$555$	−17994.5	+	17994.5i	−1.37626	+	1.37626i
$556$		0			0
$557$	−18723.9			−1.42434			−0.712171	−	0.702006i	$-0.752288\pi$
$557$	−18723.9			−1.42434			−0.712171	+	0.702006i	$0.752288\pi$
$558$		0			0
$559$			38667.3i			2.92568i
$560$		0			0
$561$	−7423.40	+	20088.2i	−0.558674	+	1.51181i
$562$		0			0
$563$		−	3287.36i		−	0.246085i	−0.992401	−	0.123043i	$-0.960735\pi$
$563$		−	3287.36i		−	0.246085i	0.992401	−	0.123043i	$-0.0392652\pi$
$564$		0			0
$565$	−17502.3			−1.30323
$566$		0			0
$567$	174.301	−	174.301i	0.0129100	−	0.0129100i
$568$		0			0
$569$		−	17433.1i		−	1.28442i	−0.766528	−	0.642210i	$-0.778018\pi$
$569$		−	17433.1i		−	1.28442i	0.766528	−	0.642210i	$-0.221982\pi$
$570$		0			0
$571$	−17336.7	+	17336.7i	−1.27061	+	1.27061i	−0.324844	+	0.945768i	$0.605312\pi$
$571$	−17336.7	+	17336.7i	−1.27061	+	1.27061i	−0.945768	+	0.324844i	$0.894688\pi$
$572$		0			0
$573$	5046.35	+	5046.35i	0.367913	+	0.367913i
$574$		0			0
$575$	−19216.2	−	19216.2i	−1.39369	−	1.39369i
$576$		0			0
$577$	2547.25			0.183784			0.0918922	−	0.995769i	$-0.470708\pi$
$577$	2547.25			0.183784			0.0918922	+	0.995769i	$0.470708\pi$
$578$		0			0
$579$	18405.4			1.32108
$580$		0			0
$581$	−39.8778	−	39.8778i	−0.00284752	−	0.00284752i
$582$		0			0
$583$	−23603.1	−	23603.1i	−1.67674	−	1.67674i
$584$		0			0
$585$	7888.33	−	7888.33i	0.557508	−	0.557508i
$586$		0			0
$587$			1606.96i			0.112992i	0.998403	+	0.0564962i	$0.0179929\pi$
$587$			1606.96i			0.112992i	−0.998403	+	0.0564962i	$0.982007\pi$
$588$		0			0
$589$	−3640.32	+	3640.32i	−0.254663	+	0.254663i
$590$		0			0
$591$	5762.35			0.401068
$592$		0			0
$593$			18908.8i			1.30943i	0.755877	+	0.654714i	$0.227211\pi$
$593$			18908.8i			1.30943i	−0.755877	+	0.654714i	$0.772789\pi$
$594$		0			0
$595$	−243.781	+	659.689i	−0.0167967	+	0.0454531i
$596$		0			0
$597$			3714.04i			0.254615i
$598$		0			0
$599$	20444.8			1.39458			0.697290	−	0.716789i	$-0.254389\pi$
$599$	20444.8			1.39458			0.697290	+	0.716789i	$0.254389\pi$
$600$		0			0
$601$	16779.3	−	16779.3i	1.13884	−	1.13884i	0.150181	−	0.988659i	$-0.452014\pi$
$601$	16779.3	−	16779.3i	1.13884	−	1.13884i	0.988659	−	0.150181i	$-0.0479856\pi$
$602$		0			0
$603$			313.239i			0.0211543i
$604$		0			0
$605$	−46891.7	+	46891.7i	−3.15110	+	3.15110i
$606$		0			0
$607$	−10839.5	−	10839.5i	−0.724815	−	0.724815i	0.244767	−	0.969582i	$-0.421289\pi$
$607$	−10839.5	−	10839.5i	−0.724815	−	0.724815i	−0.969582	+	0.244767i	$0.921289\pi$
$608$		0			0
$609$	159.255	+	159.255i	0.0105966	+	0.0105966i
$610$		0			0
$611$	673.477			0.0445924
$612$		0			0
$613$	−2760.08			−0.181858			−0.0909288	−	0.995857i	$-0.528984\pi$
$613$	−2760.08			−0.181858			−0.0909288	+	0.995857i	$0.528984\pi$
$614$		0			0
$615$	−3705.15	−	3705.15i	−0.242937	−	0.242937i
$616$		0			0
$617$	11698.3	+	11698.3i	0.763302	+	0.763302i	0.976918	−	0.213616i	$-0.0685240\pi$
$617$	11698.3	+	11698.3i	0.763302	+	0.763302i	−0.213616	+	0.976918i	$0.568524\pi$
$618$		0			0
$619$	−14914.8	+	14914.8i	−0.968459	+	0.968459i	−0.999518	−	0.0310588i	$-0.990112\pi$
$619$	−14914.8	+	14914.8i	−0.968459	+	0.968459i	0.0310588	+	0.999518i	$0.490112\pi$
$620$		0			0
$621$		−	16544.5i		−	1.06909i
$622$		0			0
$623$	55.1258	−	55.1258i	0.00354506	−	0.00354506i
$624$		0			0
$625$	−15673.8			−1.00312
$626$		0			0
$627$		−	6136.08i		−	0.390832i
$628$		0			0
$629$	18880.2	−	8691.42i	1.19683	−	0.550953i
$630$		0			0
$631$		−	17334.8i		−	1.09364i	−0.837250	−	0.546821i	$-0.815838\pi$
$631$		−	17334.8i		−	1.09364i	0.837250	−	0.546821i	$-0.184162\pi$
$632$		0			0
$633$	1533.30			0.0962769
$634$		0			0
$635$	−23303.6	+	23303.6i	−1.45634	+	1.45634i
$636$		0			0
$637$		−	26796.5i		−	1.66674i
$638$		0			0
$639$	994.597	−	994.597i	0.0615738	−	0.0615738i
$640$		0			0
$641$	1598.14	+	1598.14i	0.0984752	+	0.0984752i	0.754628	−	0.656153i	$-0.227817\pi$
$641$	1598.14	+	1598.14i	0.0984752	+	0.0984752i	−0.656153	+	0.754628i	$0.727817\pi$
$642$		0			0
$643$	19597.2	+	19597.2i	1.20193	+	1.20193i	0.973579	+	0.228349i	$0.0733328\pi$
$643$	19597.2	+	19597.2i	1.20193	+	1.20193i	0.228349	+	0.973579i	$0.426667\pi$
$644$		0			0
$645$	42442.9			2.59099
$646$		0			0
$647$	−14051.6			−0.853828			−0.426914	−	0.904292i	$-0.640399\pi$
$647$	−14051.6			−0.853828			−0.426914	+	0.904292i	$0.640399\pi$
$648$		0			0
$649$	11208.0	+	11208.0i	0.677893	+	0.677893i
$650$		0			0
$651$	−416.081	−	416.081i	−0.0250499	−	0.0250499i
$652$		0			0
$653$	11507.8	−	11507.8i	0.689642	−	0.689642i	−0.272510	−	0.962153i	$-0.587854\pi$
$653$	11507.8	−	11507.8i	0.689642	−	0.689642i	0.962153	+	0.272510i	$0.0878539\pi$
$654$		0			0
$655$		−	20906.8i		−	1.24717i
$656$		0			0
$657$	−4266.46	+	4266.46i	−0.253350	+	0.253350i
$658$		0			0
$659$	−27644.5			−1.63411			−0.817054	−	0.576561i	$-0.804394\pi$
$659$	−27644.5			−1.63411			−0.817054	+	0.576561i	$0.804394\pi$
$660$		0			0
$661$		−	2837.54i		−	0.166971i	−0.996509	−	0.0834853i	$-0.973395\pi$
$661$		−	2837.54i		−	0.166971i	0.996509	−	0.0834853i	$-0.0266052\pi$
$662$		0			0
$663$	22057.4	−	10154.0i	1.29207	−	0.594796i
$664$		0			0
$665$		−	201.506i		−	0.0117505i
$666$		0			0
$667$	10660.1			0.618829
$668$		0			0
$669$	−6643.28	+	6643.28i	−0.383922	+	0.383922i
$670$		0			0
$671$			6771.50i			0.389584i
$672$		0			0
$673$	12475.1	−	12475.1i	0.714534	−	0.714534i	−0.252947	−	0.967480i	$-0.581400\pi$
$673$	12475.1	−	12475.1i	0.714534	−	0.714534i	0.967480	+	0.252947i	$0.0813997\pi$
$674$		0			0
$675$	−26933.1	−	26933.1i	−1.53578	−	1.53578i
$676$		0			0
$677$	8632.34	+	8632.34i	0.490056	+	0.490056i	0.908324	−	0.418268i	$-0.137363\pi$
$677$	8632.34	+	8632.34i	0.490056	+	0.490056i	−0.418268	+	0.908324i	$0.637363\pi$
$678$		0			0
$679$	−516.870			−0.0292130
$680$		0			0
$681$	8987.25			0.505716
$682$		0			0
$683$	−13591.8	−	13591.8i	−0.761457	−	0.761457i	0.215129	−	0.976586i	$-0.430983\pi$
$683$	−13591.8	−	13591.8i	−0.761457	−	0.761457i	−0.976586	+	0.215129i	$0.930983\pi$
$684$		0			0
$685$	12807.0	+	12807.0i	0.714352	+	0.714352i
$686$		0			0
$687$	−5390.05	+	5390.05i	−0.299335	+	0.299335i
$688$		0			0
$689$			37847.6i			2.09271i
$690$		0			0
$691$	−5194.46	+	5194.46i	−0.285972	+	0.285972i	−0.835485	−	0.549513i	$-0.814813\pi$
$691$	−5194.46	+	5194.46i	−0.285972	+	0.285972i	0.549513	+	0.835485i	$0.314813\pi$
$692$		0			0
$693$	−263.164			−0.0144254
$694$		0			0
$695$			10345.0i			0.564617i
$696$		0			0
$697$	1789.60	+	3887.52i	0.0972538	+	0.211263i
$698$		0			0
$699$		−	10612.4i		−	0.574247i
$700$		0			0
$701$	−30765.7			−1.65764			−0.828819	−	0.559517i	$-0.810987\pi$
$701$	−30765.7			−1.65764			−0.828819	+	0.559517i	$0.810987\pi$
$702$		0			0
$703$	−4210.97	+	4210.97i	−0.225917	+	0.225917i
$704$		0			0
$705$		−	739.237i		−	0.0394912i
$706$		0			0
$707$	83.7504	−	83.7504i	0.00445510	−	0.00445510i
$708$		0			0
$709$	−7349.12	−	7349.12i	−0.389283	−	0.389283i	0.485148	−	0.874432i	$-0.338766\pi$
$709$	−7349.12	−	7349.12i	−0.389283	−	0.389283i	−0.874432	+	0.485148i	$0.838766\pi$
$710$		0			0
$711$	−731.745	−	731.745i	−0.0385972	−	0.0385972i
$712$		0			0
$713$	−27851.3			−1.46289
$714$		0			0
$715$	104420.			5.46168
$716$		0			0
$717$	8292.04	+	8292.04i	0.431899	+	0.431899i
$718$		0			0
$719$	11756.7	+	11756.7i	0.609807	+	0.609807i	0.942895	−	0.333089i	$-0.108091\pi$
$719$	11756.7	+	11756.7i	0.609807	+	0.609807i	−0.333089	+	0.942895i	$0.608091\pi$
$720$		0			0
$721$	−175.808	+	175.808i	−0.00908105	+	0.00908105i
$722$		0			0
$723$			16197.8i			0.833197i
$724$		0			0
$725$	17353.7	−	17353.7i	0.888967	−	0.888967i
$726$		0			0
$727$	−19028.0			−0.970716			−0.485358	−	0.874315i	$-0.661311\pi$
$727$	−19028.0			−0.970716			−0.485358	+	0.874315i	$0.661311\pi$
$728$		0			0
$729$		−	21723.0i		−	1.10364i
$730$		0			0
$731$	−32516.0	−	12016.0i	−1.64521	−	0.607970i
$732$		0			0
$733$		−	27862.7i		−	1.40400i	−0.712178	−	0.701999i	$-0.752291\pi$
$733$		−	27862.7i		−	1.40400i	0.712178	−	0.701999i	$-0.247709\pi$
$734$		0			0
$735$	−29413.0			−1.47607
$736$		0			0
$737$	−2073.22	+	2073.22i	−0.103620	+	0.103620i
$738$		0			0
$739$		−	16393.5i		−	0.816030i	−0.912975	−	0.408015i	$-0.866221\pi$
$739$		−	16393.5i		−	0.816030i	0.912975	−	0.408015i	$-0.133779\pi$
$740$		0			0
$741$	−4919.60	+	4919.60i	−0.243895	+	0.243895i
$742$		0			0
$743$	10078.0	+	10078.0i	0.497610	+	0.497610i	0.910693	−	0.413083i	$-0.135548\pi$
$743$	10078.0	+	10078.0i	0.497610	+	0.497610i	−0.413083	+	0.910693i	$0.635548\pi$
$744$		0			0
$745$	−2386.44	−	2386.44i	−0.117359	−	0.117359i
$746$		0			0
$747$	−801.974			−0.0392807
$748$		0			0
$749$	562.040			0.0274185
$750$		0			0
$751$	17832.0	+	17832.0i	0.866442	+	0.866442i	0.992077	−	0.125634i	$-0.0400966\pi$
$751$	17832.0	+	17832.0i	0.866442	+	0.866442i	−0.125634	+	0.992077i	$0.540097\pi$
$752$		0			0
$753$	6993.29	+	6993.29i	0.338446	+	0.338446i
$754$		0			0
$755$	30215.7	−	30215.7i	1.45650	−	1.45650i
$756$		0			0
$757$			15778.0i			0.757544i	0.925490	+	0.378772i	$0.123653\pi$
$757$			15778.0i			0.757544i	−0.925490	+	0.378772i	$0.876347\pi$
$758$		0			0
$759$	23472.9	−	23472.9i	1.12255	−	1.12255i
$760$		0			0
$761$	−23368.6			−1.11316			−0.556578	−	0.830795i	$-0.687886\pi$
$761$	−23368.6			−1.11316			−0.556578	+	0.830795i	$0.687886\pi$
$762$		0			0
$763$			121.176i			0.00574948i
$764$		0			0
$765$	4182.12	+	9084.76i	0.197653	+	0.429360i
$766$		0			0
$767$		−	17972.0i		−	0.846065i
$768$		0			0
$769$	−14054.3			−0.659051			−0.329526	−	0.944147i	$-0.606889\pi$
$769$	−14054.3			−0.659051			−0.329526	+	0.944147i	$0.606889\pi$
$770$		0			0
$771$	15496.0	−	15496.0i	0.723831	−	0.723831i
$772$		0			0
$773$		−	23430.1i		−	1.09020i	−0.838371	−	0.545099i	$-0.816492\pi$
$773$		−	23430.1i		−	1.09020i	0.838371	−	0.545099i	$-0.183508\pi$
$774$		0			0
$775$	−45339.7	+	45339.7i	−2.10148	+	2.10148i
$776$		0			0
$777$	−481.305	−	481.305i	−0.0222223	−	0.0222223i
$778$		0			0
$779$	−867.056	−	867.056i	−0.0398787	−	0.0398787i
$780$		0			0
$781$	13165.8			0.603213
$782$		0			0
$783$	14940.9			0.681921
$784$		0			0
$785$	11440.0	+	11440.0i	0.520144	+	0.520144i
$786$		0			0
$787$	10487.9	+	10487.9i	0.475037	+	0.475037i	0.903540	−	0.428503i	$-0.140959\pi$
$787$	10487.9	+	10487.9i	0.475037	+	0.475037i	−0.428503	+	0.903540i	$0.640959\pi$
$788$		0			0
$789$	18062.8	−	18062.8i	0.815023	−	0.815023i
$790$		0			0
$791$		−	468.138i		−	0.0210431i
$792$		0			0
$793$	5429.04	−	5429.04i	0.243116	−	0.243116i
$794$		0			0
$795$	41543.2			1.85331
$796$		0			0
$797$		−	6135.55i		−	0.272688i	−0.990662	−	0.136344i	$-0.956465\pi$
$797$		−	6135.55i		−	0.272688i	0.990662	−	0.136344i	$-0.0435352\pi$
$798$		0			0
$799$	−209.284	+	566.338i	−0.00926652	+	0.0250759i
$800$		0			0
$801$		−	1108.63i		−	0.0489031i
$802$		0			0
$803$	−56476.5			−2.48196
$804$		0			0
$805$	770.840	−	770.840i	0.0337497	−	0.0337497i
$806$		0			0
$807$			11085.1i			0.483539i
$808$		0			0
$809$	10345.1	−	10345.1i	0.449587	−	0.449587i	−0.445630	−	0.895217i	$-0.647020\pi$
$809$	10345.1	−	10345.1i	0.449587	−	0.449587i	0.895217	+	0.445630i	$0.147020\pi$
$810$		0			0
$811$	−15395.4	−	15395.4i	−0.666591	−	0.666591i	0.290334	−	0.956925i	$-0.406233\pi$
$811$	−15395.4	−	15395.4i	−0.666591	−	0.666591i	−0.956925	+	0.290334i	$0.906233\pi$
$812$		0			0
$813$	−9414.65	−	9414.65i	−0.406133	−	0.406133i
$814$		0			0
$815$	11742.7			0.504698
$816$		0			0
$817$	9932.23			0.425318
$818$		0			0
$819$	210.992	+	210.992i	0.00900200	+	0.00900200i
$820$		0			0
$821$	−14235.7	−	14235.7i	−0.605151	−	0.605151i	0.336524	−	0.941675i	$-0.390749\pi$
$821$	−14235.7	−	14235.7i	−0.605151	−	0.605151i	−0.941675	+	0.336524i	$0.890749\pi$
$822$		0			0
$823$	−15061.7	+	15061.7i	−0.637933	+	0.637933i	−0.950045	−	0.312112i	$-0.898963\pi$
$823$	−15061.7	+	15061.7i	−0.637933	+	0.637933i	0.312112	+	0.950045i	$0.398963\pi$
$824$		0			0
$825$		−	76424.1i		−	3.22515i
$826$		0			0
$827$	26087.9	−	26087.9i	1.09694	−	1.09694i	0.102169	−	0.994767i	$-0.467422\pi$
$827$	26087.9	−	26087.9i	1.09694	−	1.09694i	0.994767	−	0.102169i	$-0.0325783\pi$
$828$		0			0
$829$	39084.3			1.63746			0.818730	−	0.574179i	$-0.194679\pi$
$829$	39084.3			1.63746			0.818730	+	0.574179i	$0.194679\pi$
$830$		0			0
$831$			20992.2i			0.876307i
$832$		0			0
$833$	22533.6	+	8327.07i	0.937268	+	0.346358i
$834$		0			0
$835$		−	50124.8i		−	2.07741i
$836$		0			0
$837$	−39035.8			−1.61203
$838$		0			0
$839$	24472.2	−	24472.2i	1.00700	−	1.00700i	0.00702661	−	0.999975i	$-0.497763\pi$
$839$	24472.2	−	24472.2i	1.00700	−	1.00700i	0.999975	−	0.00702661i	$-0.00223666\pi$
$840$		0			0
$841$		−	14762.2i		−	0.605279i
$842$		0			0
$843$	−5123.53	+	5123.53i	−0.209328	+	0.209328i
$844$		0			0
$845$	−53630.0	−	53630.0i	−2.18335	−	2.18335i
$846$		0			0
$847$	−1254.23	−	1254.23i	−0.0508804	−	0.0508804i
$848$		0			0
$849$	17042.0			0.688905
$850$		0			0
$851$	−32217.2			−1.29776
$852$		0			0
$853$	12611.3	+	12611.3i	0.506216	+	0.506216i	0.913363	−	0.407147i	$-0.133476\pi$
$853$	12611.3	+	12611.3i	0.506216	+	0.506216i	−0.407147	+	0.913363i	$0.633476\pi$
$854$		0			0
$855$	−2026.23	−	2026.23i	−0.0810473	−	0.0810473i
$856$		0			0
$857$	−11326.2	+	11326.2i	−0.451452	+	0.451452i	−0.895836	−	0.444384i	$-0.853422\pi$
$857$	−11326.2	+	11326.2i	−0.451452	+	0.451452i	0.444384	+	0.895836i	$0.353422\pi$
$858$		0			0
$859$		−	2024.23i		−	0.0804025i	−0.999192	−	0.0402012i	$-0.987200\pi$
$859$		−	2024.23i		−	0.0804025i	0.999192	−	0.0402012i	$-0.0127999\pi$
$860$		0			0
$861$	99.1028	−	99.1028i	0.00392266	−	0.00392266i
$862$		0			0
$863$	42859.5			1.69056			0.845280	−	0.534324i	$-0.179434\pi$
$863$	42859.5			1.69056			0.845280	+	0.534324i	$0.179434\pi$
$864$		0			0
$865$			62678.0i			2.46372i
$866$		0			0
$867$	1684.30	+	21703.9i	0.0659767	+	0.850176i
$868$		0			0
$869$		−	9686.34i		−	0.378120i
$870$		0			0
$871$	3324.40			0.129326
$872$		0			0
$873$	−5197.34	+	5197.34i	−0.201493	+	0.201493i
$874$		0			0
$875$		−	1255.52i		−	0.0485077i
$876$		0			0
$877$	−4958.50	+	4958.50i	−0.190920	+	0.190920i	−0.796093	−	0.605174i	$-0.793104\pi$
$877$	−4958.50	+	4958.50i	−0.190920	+	0.190920i	0.605174	+	0.796093i	$0.293104\pi$
$878$		0			0
$879$	22168.9	+	22168.9i	0.850670	+	0.850670i
$880$		0			0
$881$	−13945.5	−	13945.5i	−0.533299	−	0.533299i	0.388254	−	0.921552i	$-0.373078\pi$
$881$	−13945.5	−	13945.5i	−0.533299	−	0.533299i	−0.921552	+	0.388254i	$0.873078\pi$
$882$		0			0
$883$	23295.5			0.887831			0.443915	−	0.896069i	$-0.353589\pi$
$883$	23295.5			0.887831			0.443915	+	0.896069i	$0.353589\pi$
$884$		0			0
$885$	−19726.9			−0.749279
$886$		0			0
$887$	−7233.33	−	7233.33i	−0.273812	−	0.273812i	0.556821	−	0.830633i	$-0.312021\pi$
$887$	−7233.33	−	7233.33i	−0.273812	−	0.273812i	−0.830633	+	0.556821i	$0.812021\pi$
$888$		0			0
$889$	−623.307	−	623.307i	−0.0235153	−	0.0235153i
$890$		0			0
$891$	23200.6	−	23200.6i	0.872335	−	0.872335i
$892$		0			0
$893$		−	172.992i		−	0.00648258i
$894$		0			0
$895$	−2564.13	+	2564.13i	−0.0957648	+	0.0957648i
$896$		0			0
$897$	−37638.8			−1.40103
$898$		0			0
$899$		−	25151.8i		−	0.933104i
$900$		0			0
$901$	−31826.7	−	11761.2i	−1.17681	−	0.434876i
$902$		0			0
$903$			1135.23i			0.0418363i
$904$		0			0
$905$	40090.1			1.47253
$906$		0			0
$907$	10879.2	−	10879.2i	0.398277	−	0.398277i	−0.479348	−	0.877625i	$-0.659127\pi$
$907$	10879.2	−	10879.2i	0.398277	−	0.398277i	0.877625	+	0.479348i	$0.159127\pi$
$908$		0			0
$909$		−	1684.29i		−	0.0614569i
$910$		0			0
$911$	−21788.4	+	21788.4i	−0.792407	+	0.792407i	−0.981885	−	0.189478i	$-0.939321\pi$
$911$	−21788.4	+	21788.4i	−0.792407	+	0.792407i	0.189478	+	0.981885i	$0.439321\pi$
$912$		0			0
$913$	−5307.99	−	5307.99i	−0.192408	−	0.192408i
$914$		0			0
$915$	−5959.15	−	5959.15i	−0.215304	−	0.215304i
$916$		0			0
$917$	559.201			0.0201379
$918$		0			0
$919$	8011.29			0.287561			0.143780	−	0.989610i	$-0.454074\pi$
$919$	8011.29			0.287561			0.143780	+	0.989610i	$0.454074\pi$
$920$		0			0
$921$	27810.3	+	27810.3i	0.994986	+	0.994986i
$922$		0			0
$923$	−10555.7	−	10555.7i	−0.376429	−	0.376429i
$924$		0			0
$925$	−52447.1	+	52447.1i	−1.86427	+	1.86427i
$926$		0			0
$927$			3535.65i			0.125271i
$928$		0			0
$929$	9778.94	−	9778.94i	0.345357	−	0.345357i	−0.513020	−	0.858377i	$-0.671473\pi$
$929$	9778.94	−	9778.94i	0.345357	−	0.345357i	0.858377	+	0.513020i	$0.171473\pi$
$930$		0			0
$931$	−6883.05			−0.242302
$932$		0			0
$933$			38374.4i			1.34654i
$934$		0			0
$935$	−32448.9	+	87808.9i	−1.13496	+	3.07129i
$936$		0			0
$937$		−	32193.2i		−	1.12242i	−0.827674	−	0.561209i	$-0.810336\pi$
$937$		−	32193.2i		−	1.12242i	0.827674	−	0.561209i	$-0.189664\pi$
$938$		0			0
$939$	−32729.9			−1.13749
$940$		0			0
$941$	8068.16	−	8068.16i	0.279505	−	0.279505i	−0.553406	−	0.832912i	$-0.686672\pi$
$941$	8068.16	−	8068.16i	0.279505	−	0.279505i	0.832912	+	0.553406i	$0.186672\pi$
$942$		0			0
$943$		−	6633.66i		−	0.229079i
$944$		0			0
$945$	1080.39	−	1080.39i	0.0371906	−	0.0371906i
$946$		0			0
$947$	14134.1	+	14134.1i	0.485003	+	0.485003i	0.906725	−	0.421722i	$-0.138574\pi$
$947$	14134.1	+	14134.1i	0.485003	+	0.485003i	−0.421722	+	0.906725i	$0.638574\pi$
$948$		0			0
$949$	45280.0	+	45280.0i	1.54884	+	1.54884i
$950$		0			0
$951$	−4281.77			−0.146000
$952$		0			0
$953$	−4521.78			−0.153699			−0.0768493	−	0.997043i	$-0.524486\pi$
$953$	−4521.78			−0.153699			−0.0768493	+	0.997043i	$0.524486\pi$
$954$		0			0
$955$	22058.4	+	22058.4i	0.747427	+	0.747427i
$956$		0			0
$957$	21197.8	+	21197.8i	0.716018	+	0.716018i
$958$		0			0
$959$	−342.553	+	342.553i	−0.0115345	+	0.0115345i
$960$		0			0
$961$			35922.6i			1.20582i
$962$		0			0
$963$	5651.54	−	5651.54i	0.189116	−	0.189116i
$964$		0			0
$965$	80453.1			2.68381
$966$		0			0
$967$		−	34958.6i		−	1.16256i	−0.813704	−	0.581279i	$-0.802552\pi$
$967$		−	34958.6i		−	1.16256i	0.813704	−	0.581279i	$-0.197448\pi$
$968$		0			0
$969$	−2608.20	−	5665.75i	−0.0864680	−	0.187833i
$970$		0			0
$971$			37210.9i			1.22982i	0.788598	+	0.614909i	$0.210807\pi$
$971$			37210.9i			1.22982i	−0.788598	+	0.614909i	$0.789193\pi$
$972$		0			0
$973$	−276.701			−0.00911679
$974$		0			0
$975$	−61273.0	+	61273.0i	−2.01262	+	2.01262i
$976$		0			0
$977$		−	12272.8i		−	0.401886i	−0.979603	−	0.200943i	$-0.935599\pi$
$977$		−	12272.8i		−	0.401886i	0.979603	−	0.200943i	$-0.0644007\pi$
$978$		0			0
$979$	7337.61	−	7337.61i	0.239541	−	0.239541i
$980$		0			0
$981$	1218.47	+	1218.47i	0.0396563	+	0.0396563i
$982$		0			0
$983$	10806.3	+	10806.3i	0.350627	+	0.350627i	0.860343	−	0.509716i	$-0.170249\pi$
$983$	10806.3	+	10806.3i	0.350627	+	0.350627i	−0.509716	+	0.860343i	$0.670249\pi$
$984$		0			0
$985$	25188.1			0.814782
$986$		0			0
$987$	19.7726			0.000637658
$988$		0			0
$989$	37994.7	+	37994.7i	1.22160	+	1.22160i
$990$		0			0
$991$	−38811.4	−	38811.4i	−1.24408	−	1.24408i	−0.958292	−	0.285790i	$-0.907744\pi$
$991$	−38811.4	−	38811.4i	−1.24408	−	1.24408i	−0.285790	−	0.958292i	$-0.592256\pi$
$992$		0			0
$993$	−15140.2	+	15140.2i	−0.483846	+	0.483846i
$994$		0			0
$995$			16234.6i			0.517259i
$996$		0			0
$997$	−17112.5	+	17112.5i	−0.543589	+	0.543589i	−0.924579	−	0.380990i	$-0.875583\pi$
$997$	−17112.5	+	17112.5i	−0.543589	+	0.543589i	0.380990	+	0.924579i	$0.375583\pi$
$998$		0			0
$999$	−45155.0			−1.43007

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.4.o.f.81.3		14
4.3	odd	2		136.4.k.b.81.5	✓	14
17.4	even	4	inner	272.4.o.f.225.3		14
68.15	odd	8		2312.4.a.l.1.5		14
68.19	odd	8		2312.4.a.l.1.10		14
68.55	odd	4		136.4.k.b.89.5	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.k.b.81.5	✓	14	4.3	odd	2
136.4.k.b.89.5	yes	14	68.55	odd	4
272.4.o.f.81.3		14	1.1	even	1	trivial
272.4.o.f.225.3		14	17.4	even	4	inner
2312.4.a.l.1.5		14	68.15	odd	8
2312.4.a.l.1.10		14	68.19	odd	8

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:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	272.o (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.13314 - 3.13314i) q^{3} +(-13.6954 - 13.6954i) q^{5} +(0.366316 - 0.366316i) q^{7} -7.36691i q^{9} +(48.7591 - 48.7591i) q^{11} -78.1851 q^{13} +85.8194i q^{15} +(24.2962 - 65.7472i) q^{17} +20.0829i q^{19} -2.29544 q^{21} +(-76.8250 + 76.8250i) q^{23} +250.130i q^{25} +(-107.676 + 107.676i) q^{27} +(-69.3788 - 69.3788i) q^{29} +(181.264 + 181.264i) q^{31} -305.538 q^{33} -10.0337 q^{35} +(209.679 + 209.679i) q^{37} +(244.964 + 244.964i) q^{39} +(-43.1738 + 43.1738i) q^{41} -494.561i q^{43} +(-100.893 + 100.893i) q^{45} -8.61388 q^{47} +342.732i q^{49} +(-282.118 + 129.872i) q^{51} -484.077i q^{53} -1335.55 q^{55} +(62.9225 - 62.9225i) q^{57} +229.865i q^{59} +(-69.4383 + 69.4383i) q^{61} +(-2.69862 - 2.69862i) q^{63} +(1070.78 + 1070.78i) q^{65} -42.5197 q^{67} +481.407 q^{69} +(135.009 + 135.009i) q^{71} +(-579.139 - 579.139i) q^{73} +(783.692 - 783.692i) q^{75} -35.7224i q^{77} +(99.3286 - 99.3286i) q^{79} +475.822 q^{81} -108.862i q^{83} +(-1233.18 + 567.690i) q^{85} +434.747i q^{87} +150.487 q^{89} +(-28.6404 + 28.6404i) q^{91} -1135.85i q^{93} +(275.044 - 275.044i) q^{95} +(-705.497 - 705.497i) q^{97} +(-359.204 - 359.204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 6 q^{3} + 6 q^{5} - 10 q^{7} + 66 q^{11} - 124 q^{13} + 130 q^{17} - 148 q^{21} + 162 q^{23} + 204 q^{27} + 158 q^{29} + 350 q^{31} + 116 q^{33} - 236 q^{35} + 582 q^{37} + 320 q^{39} + 878 q^{41}+ \cdots - 3870 q^{99}+O(q^{100}) \) 14 * q - 6 * q^3 + 6 * q^5 - 10 * q^7 + 66 * q^11 - 124 * q^13 + 130 * q^17 - 148 * q^21 + 162 * q^23 + 204 * q^27 + 158 * q^29 + 350 * q^31 + 116 * q^33 - 236 * q^35 + 582 * q^37 + 320 * q^39 + 878 * q^41 - 26 * q^45 + 448 * q^47 + 590 * q^51 - 1460 * q^55 + 292 * q^57 - 1130 * q^61 - 114 * q^63 + 20 * q^65 + 64 * q^67 + 2076 * q^69 + 3274 * q^71 - 1426 * q^73 - 946 * q^75 - 1718 * q^79 + 166 * q^81 - 2018 * q^85 + 476 * q^89 - 2128 * q^91 + 2444 * q^95 + 1926 * q^97 - 3870 * q^99

Introduction

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