LMFDB - Embedded newform 270.3.l.a.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,3,Mod(37,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("270.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	270.l (of order $12$, degree $4$, 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:	$7.35696713773$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			127.1
Character	$\chi$	$=$	270.127
Dual form			270.3.l.a.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(-4.17929 + 2.74473i) q^{5} +(8.06163 - 2.16011i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(4.70437 - 5.27910i) q^{10} +(2.87538 - 4.98030i) q^{11} +(-6.01206 - 1.61093i) q^{13} +(-10.2217 + 5.90153i) q^{14} +(2.00000 - 3.46410i) q^{16} +(7.29884 + 7.29884i) q^{17} +30.1705i q^{19} +(-4.49400 + 8.93331i) q^{20} +(-2.10492 + 7.85567i) q^{22} +(38.1793 + 10.2301i) q^{23} +(9.93287 - 22.9421i) q^{25} +8.80226 q^{26} +(11.8031 - 11.8031i) q^{28} +(-13.3150 - 7.68744i) q^{29} +(19.4198 + 33.6360i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(-12.6420 - 7.29884i) q^{34} +(-27.7630 + 31.1548i) q^{35} +(23.3594 + 23.3594i) q^{37} +(-11.0432 - 41.2136i) q^{38} +(2.86910 - 13.8480i) q^{40} +(23.6254 + 40.9204i) q^{41} +(2.80496 + 10.4683i) q^{43} -11.5015i q^{44} -55.8984 q^{46} +(63.8022 - 17.0957i) q^{47} +(17.8886 - 10.3280i) q^{49} +(-5.17117 + 34.9751i) q^{50} +(-12.0241 + 3.22185i) q^{52} +(-0.227111 + 0.227111i) q^{53} +(1.65257 + 28.7062i) q^{55} +(-11.8031 + 20.4435i) q^{56} +(21.0025 + 5.62760i) q^{58} +(-11.0663 + 6.38914i) q^{59} +(-41.0215 + 71.0513i) q^{61} +(-38.8395 - 38.8395i) q^{62} -8.00000i q^{64} +(29.5477 - 9.76898i) q^{65} +(28.5011 - 106.367i) q^{67} +(19.9408 + 5.34312i) q^{68} +(26.5215 - 52.7201i) q^{70} -87.7370 q^{71} +(15.8257 - 15.8257i) q^{73} +(-40.4597 - 23.3594i) q^{74} +(30.1705 + 52.2568i) q^{76} +(12.4222 - 46.3604i) q^{77} +(-72.6039 - 41.9179i) q^{79} +(1.14947 + 19.9669i) q^{80} +(-47.2508 - 47.2508i) q^{82} +(-3.11595 - 11.6289i) q^{83} +(-50.5373 - 10.4706i) q^{85} +(-7.66330 - 13.2732i) q^{86} +(4.20984 + 15.7113i) q^{88} -59.4813i q^{89} -51.9468 q^{91} +(76.3586 - 20.4602i) q^{92} +(-80.8979 + 46.7064i) q^{94} +(-82.8099 - 126.091i) q^{95} +(107.430 - 28.7859i) q^{97} +(-20.6560 + 20.6560i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} + 6 q^{7} - 48 q^{8} + 12 q^{10} + 12 q^{11} + 48 q^{16} + 36 q^{17} - 12 q^{20} + 12 q^{22} + 66 q^{23} - 42 q^{25} + 24 q^{28} + 72 q^{31} + 48 q^{32} + 240 q^{35} + 36 q^{37} + 36 q^{38}+ \cdots - 264 q^{98}+O(q^{100}) $ 24 * q - 12 * q^2 + 6 * q^7 - 48 * q^8 + 12 * q^10 + 12 * q^11 + 48 * q^16 + 36 * q^17 - 12 * q^20 + 12 * q^22 + 66 * q^23 - 42 * q^25 + 24 * q^28 + 72 * q^31 + 48 * q^32 + 240 * q^35 + 36 * q^37 + 36 * q^38 - 12 * q^40 + 24 * q^41 - 108 * q^43 - 264 * q^46 + 36 * q^47 - 42 * q^50 - 384 * q^53 + 288 * q^55 - 24 * q^56 - 108 * q^58 + 360 * q^61 - 144 * q^62 - 144 * q^65 + 144 * q^67 + 36 * q^68 - 174 * q^70 - 216 * q^71 + 432 * q^73 + 72 * q^76 + 48 * q^77 - 48 * q^82 + 378 * q^83 - 228 * q^85 - 216 * q^86 - 24 * q^88 - 1560 * q^91 + 132 * q^92 - 264 * q^95 - 294 * q^97 - 264 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.36603	+	0.366025i	−0.683013	+	0.183013i
$2$	−1.36603	+	0.366025i	−0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	1.73205	−	1.00000i	0.433013	−	0.250000i
$5$	−4.17929	+	2.74473i	−0.835857	+	0.548947i
$5$	−4.17929	+	2.74473i	−0.835857	+	0.548947i
$6$		0			0
$7$	8.06163	−	2.16011i	1.15166	−	0.308587i	0.368031	−	0.929814i	$-0.380032\pi$
$7$	8.06163	−	2.16011i	1.15166	−	0.308587i	0.783631	+	0.621227i	$0.213365\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		0			0
$10$	4.70437	−	5.27910i	0.470437	−	0.527910i
$11$	2.87538	−	4.98030i	0.261398	−	0.452754i	−0.705216	−	0.708993i	$-0.749150\pi$
$11$	2.87538	−	4.98030i	0.261398	−	0.452754i	0.966614	+	0.256239i	$0.0824833\pi$
$12$		0			0
$13$	−6.01206	−	1.61093i	−0.462466	−	0.123917i	0.0200606	−	0.999799i	$-0.493614\pi$
$13$	−6.01206	−	1.61093i	−0.462466	−	0.123917i	−0.482526	+	0.875881i	$0.660281\pi$
$14$	−10.2217	+	5.90153i	−0.730124	+	0.421538i
$15$		0			0
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	7.29884	+	7.29884i	0.429343	+	0.429343i	0.888405	−	0.459061i	$-0.151814\pi$
$17$	7.29884	+	7.29884i	0.429343	+	0.429343i	−0.459061	+	0.888405i	$0.651814\pi$
$18$		0			0
$19$			30.1705i			1.58792i	0.607971	+	0.793959i	$0.291984\pi$
$19$			30.1705i			1.58792i	−0.607971	+	0.793959i	$0.708016\pi$
$20$	−4.49400	+	8.93331i	−0.224700	+	0.446665i
$21$		0			0
$22$	−2.10492	+	7.85567i	−0.0956782	+	0.357076i
$23$	38.1793	+	10.2301i	1.65997	+	0.444788i	0.962379	−	0.271709i	$-0.0875890\pi$
$23$	38.1793	+	10.2301i	1.65997	+	0.444788i	0.697590	+	0.716497i	$0.254256\pi$
$24$		0			0
$25$	9.93287	−	22.9421i	0.397315	−	0.917682i
$26$	8.80226			0.338548
$27$		0			0
$28$	11.8031	−	11.8031i	0.421538	−	0.421538i
$29$	−13.3150	−	7.68744i	−0.459139	−	0.265084i	0.252543	−	0.967586i	$-0.418733\pi$
$29$	−13.3150	−	7.68744i	−0.459139	−	0.265084i	−0.711682	+	0.702501i	$0.752066\pi$
$30$		0			0
$31$	19.4198	+	33.6360i	0.626444	+	1.08503i	0.988260	+	0.152783i	$0.0488236\pi$
$31$	19.4198	+	33.6360i	0.626444	+	1.08503i	−0.361816	+	0.932250i	$0.617843\pi$
$32$	−1.46410	+	5.46410i	−0.0457532	+	0.170753i
$33$		0			0
$34$	−12.6420	−	7.29884i	−0.371822	−	0.214672i
$35$	−27.7630	+	31.1548i	−0.793227	+	0.890136i
$36$		0			0
$37$	23.3594	+	23.3594i	0.631336	+	0.631336i	0.948403	−	0.317067i	$-0.102698\pi$
$37$	23.3594	+	23.3594i	0.631336	+	0.631336i	−0.317067	+	0.948403i	$0.602698\pi$
$38$	−11.0432	−	41.2136i	−0.290609	−	1.08457i
$39$		0			0
$40$	2.86910	−	13.8480i	0.0717276	−	0.346201i
$41$	23.6254	+	40.9204i	0.576229	+	0.998058i	0.995907	+	0.0903851i	$0.0288098\pi$
$41$	23.6254	+	40.9204i	0.576229	+	0.998058i	−0.419678	+	0.907673i	$0.637857\pi$
$42$		0			0
$43$	2.80496	+	10.4683i	0.0652317	+	0.243448i	0.990841	−	0.135032i	$-0.0431137\pi$
$43$	2.80496	+	10.4683i	0.0652317	+	0.243448i	−0.925610	+	0.378480i	$0.876447\pi$
$44$		−	11.5015i		−	0.261398i
$45$		0			0
$46$	−55.8984			−1.21518
$47$	63.8022	−	17.0957i	1.35749	−	0.363739i	0.494598	−	0.869122i	$-0.335315\pi$
$47$	63.8022	−	17.0957i	1.35749	−	0.363739i	0.862895	+	0.505383i	$0.168649\pi$
$48$		0			0
$49$	17.8886	−	10.3280i	0.365074	−	0.210776i
$50$	−5.17117	+	34.9751i	−0.103423	+	0.699502i
$51$		0			0
$52$	−12.0241	+	3.22185i	−0.231233	+	0.0619587i
$53$	−0.227111	+	0.227111i	−0.00428512	+	0.00428512i	−0.709246	−	0.704961i	$-0.750964\pi$
$53$	−0.227111	+	0.227111i	−0.00428512	+	0.00428512i	0.704961	+	0.709246i	$0.250964\pi$
$54$		0			0
$55$	1.65257	+	28.7062i	0.0300468	+	0.521931i
$56$	−11.8031	+	20.4435i	−0.210769	+	0.365062i
$57$		0			0
$58$	21.0025	+	5.62760i	0.362112	+	0.0970276i
$59$	−11.0663	+	6.38914i	−0.187565	+	0.108291i	−0.590842	−	0.806787i	$-0.701204\pi$
$59$	−11.0663	+	6.38914i	−0.187565	+	0.108291i	0.403277	+	0.915078i	$0.367871\pi$
$60$		0			0
$61$	−41.0215	+	71.0513i	−0.672483	+	1.16478i	0.304714	+	0.952444i	$0.401439\pi$
$61$	−41.0215	+	71.0513i	−0.672483	+	1.16478i	−0.977198	+	0.212332i	$0.931894\pi$
$62$	−38.8395	−	38.8395i	−0.626444	−	0.626444i
$63$		0			0
$64$		−	8.00000i		−	0.125000i
$65$	29.5477	−	9.76898i	0.454579	−	0.150292i
$66$		0			0
$67$	28.5011	−	106.367i	0.425389	−	1.58757i	−0.337683	−	0.941260i	$-0.609643\pi$
$67$	28.5011	−	106.367i	0.425389	−	1.58757i	0.763072	−	0.646314i	$-0.223690\pi$
$68$	19.9408	+	5.34312i	0.293247	+	0.0785753i
$69$		0			0
$70$	26.5215	−	52.7201i	0.378878	−	0.753145i
$71$	−87.7370			−1.23573			−0.617866	−	0.786283i	$-0.712003\pi$
$71$	−87.7370			−1.23573			−0.617866	+	0.786283i	$0.712003\pi$
$72$		0			0
$73$	15.8257	−	15.8257i	0.216791	−	0.216791i	−0.590354	−	0.807145i	$-0.701012\pi$
$73$	15.8257	−	15.8257i	0.216791	−	0.216791i	0.807145	+	0.590354i	$0.201012\pi$
$74$	−40.4597	−	23.3594i	−0.546753	−	0.315668i
$75$		0			0
$76$	30.1705	+	52.2568i	0.396980	+	0.687589i
$77$	12.4222	−	46.3604i	0.161328	−	0.602084i
$78$		0			0
$79$	−72.6039	−	41.9179i	−0.919037	−	0.530606i	−0.0357094	−	0.999362i	$-0.511369\pi$
$79$	−72.6039	−	41.9179i	−0.919037	−	0.530606i	−0.883328	+	0.468756i	$0.844702\pi$
$80$	1.14947	+	19.9669i	0.0143683	+	0.249587i
$81$		0			0
$82$	−47.2508	−	47.2508i	−0.576229	−	0.576229i
$83$	−3.11595	−	11.6289i	−0.0375416	−	0.140107i	0.944611	−	0.328191i	$-0.106439\pi$
$83$	−3.11595	−	11.6289i	−0.0375416	−	0.140107i	−0.982153	+	0.188084i	$0.939772\pi$
$84$		0			0
$85$	−50.5373	−	10.4706i	−0.594556	−	0.123183i
$86$	−7.66330	−	13.2732i	−0.0891081	−	0.154340i
$87$		0			0
$88$	4.20984	+	15.7113i	0.0478391	+	0.178538i
$89$		−	59.4813i		−	0.668330i	−0.942515	−	0.334165i	$-0.891546\pi$
$89$		−	59.4813i		−	0.668330i	0.942515	−	0.334165i	$-0.108454\pi$
$90$		0			0
$91$	−51.9468			−0.570844
$92$	76.3586	−	20.4602i	0.829985	−	0.222394i
$93$		0			0
$94$	−80.8979	+	46.7064i	−0.860616	+	0.496877i
$95$	−82.8099	−	126.091i	−0.871683	−	1.32727i
$96$		0			0
$97$	107.430	−	28.7859i	1.10753	−	0.296762i	0.341703	−	0.939808i	$-0.388996\pi$
$97$	107.430	−	28.7859i	1.10753	−	0.296762i	0.765827	+	0.643046i	$0.222330\pi$
$98$	−20.6560	+	20.6560i	−0.210776	+	0.210776i
$99$		0			0
$100$	−5.73783	−	49.6697i	−0.0573783	−	0.496697i
$101$	46.1762	−	79.9796i	0.457191	−	0.791877i	−0.541621	−	0.840623i	$-0.682189\pi$
$101$	46.1762	−	79.9796i	0.457191	−	0.791877i	0.998811	+	0.0487458i	$0.0155224\pi$
$102$		0			0
$103$	−127.449	−	34.1499i	−1.23737	−	0.331553i	−0.419926	−	0.907558i	$-0.637944\pi$
$103$	−127.449	−	34.1499i	−1.23737	−	0.331553i	−0.817446	+	0.576006i	$0.804611\pi$
$104$	15.2460	−	8.80226i	0.146596	−	0.0846371i
$105$		0			0
$106$	0.227111	−	0.393368i	0.00214256	−	0.00371102i
$107$	−106.237	−	106.237i	−0.992872	−	0.992872i	0.00710243	−	0.999975i	$-0.497739\pi$
$107$	−106.237	−	106.237i	−0.992872	−	0.992872i	−0.999975	+	0.00710243i	$0.997739\pi$
$108$		0			0
$109$		−	138.393i		−	1.26966i	−0.772653	−	0.634829i	$-0.781071\pi$
$109$		−	138.393i		−	1.26966i	0.772653	−	0.634829i	$-0.218929\pi$
$110$	−12.7647	−	38.6085i	−0.116042	−	0.350987i
$111$		0			0
$112$	8.64043	−	32.2465i	0.0771467	−	0.287915i
$113$	134.628	+	36.0734i	1.19140	+	0.319234i	0.799437	−	0.600749i	$-0.205131\pi$
$113$	134.628	+	36.0734i	1.19140	+	0.319234i	0.391958	+	0.919983i	$0.371798\pi$
$114$		0			0
$115$	−187.641	+	62.0375i	−1.63166	+	0.539456i
$116$	−30.7498			−0.265084
$117$		0			0
$118$	12.7783	−	12.7783i	0.108291	−	0.108291i
$119$	74.6068	+	43.0743i	0.626948	+	0.361969i
$120$		0			0
$121$	43.9644	+	76.1486i	0.363342	+	0.629328i
$122$	30.0298	−	112.073i	0.246146	−	0.918629i
$123$		0			0
$124$	67.2720	+	38.8395i	0.542516	+	0.313222i
$125$	21.4576	+	123.145i	0.171661	+	0.985156i
$126$		0			0
$127$	66.9076	+	66.9076i	0.526832	+	0.526832i	0.919626	−	0.392795i	$-0.128492\pi$
$127$	66.9076	+	66.9076i	0.526832	+	0.526832i	−0.392795	+	0.919626i	$0.628492\pi$
$128$	2.92820	+	10.9282i	0.0228766	+	0.0853766i
$129$		0			0
$130$	−36.7872	+	24.1599i	−0.282978	+	0.185845i
$131$	92.0091	+	159.364i	0.702360	+	1.21652i	0.967636	+	0.252350i	$0.0812035\pi$
$131$	92.0091	+	159.364i	0.702360	+	1.21652i	−0.265276	+	0.964172i	$0.585463\pi$
$132$		0			0
$133$	65.1714	+	243.223i	0.490011	+	1.82875i
$134$			155.733i			1.16218i
$135$		0			0
$136$	−29.1953			−0.214672
$137$	−147.628	+	39.5568i	−1.07758	+	0.288736i	−0.753603	−	0.657330i	$-0.771686\pi$
$137$	−147.628	+	39.5568i	−1.07758	+	0.288736i	−0.323974	+	0.946066i	$0.605019\pi$
$138$		0			0
$139$	3.48356	−	2.01123i	0.0250616	−	0.0144693i	−0.487417	−	0.873169i	$-0.662061\pi$
$139$	3.48356	−	2.01123i	0.0250616	−	0.0144693i	0.512478	+	0.858700i	$0.328727\pi$
$140$	−16.9321	+	81.7246i	−0.120943	+	0.583747i
$141$		0			0
$142$	119.851	−	32.1140i	0.844021	−	0.226155i
$143$	−25.3098	+	25.3098i	−0.176992	+	0.176992i
$144$		0			0
$145$	76.7474	−	4.41823i	0.529292	−	0.0304705i
$146$	−15.8257	+	27.4110i	−0.108395	+	0.187746i
$147$		0			0
$148$	63.8191	+	17.1003i	0.431210	+	0.115542i
$149$	−89.1479	+	51.4696i	−0.598308	+	0.345433i	−0.768376	−	0.639999i	$-0.778935\pi$
$149$	−89.1479	+	51.4696i	−0.598308	+	0.345433i	0.170068	+	0.985432i	$0.445601\pi$
$150$		0			0
$151$	73.5398	−	127.375i	0.487019	−	0.843541i	−0.512870	−	0.858466i	$-0.671418\pi$
$151$	73.5398	−	127.375i	0.487019	−	0.843541i	0.999889	+	0.0149251i	$0.00475098\pi$
$152$	−60.3409	−	60.3409i	−0.396980	−	0.396980i
$153$		0			0
$154$			67.8764i			0.440756i
$155$	−173.483	−	87.2725i	−1.11924	−	0.563048i
$156$		0			0
$157$	5.66833	−	21.1545i	0.0361040	−	0.134742i	−0.945521	−	0.325560i	$-0.894447\pi$
$157$	5.66833	−	21.1545i	0.0361040	−	0.134742i	0.981625	+	0.190818i	$0.0611139\pi$
$158$	114.522	+	30.6860i	0.724822	+	0.194215i
$159$		0			0
$160$	−8.87861	−	26.8546i	−0.0554913	−	0.167841i
$161$	329.886			2.04898
$162$		0			0
$163$	−51.4648	+	51.4648i	−0.315735	+	0.315735i	−0.847127	−	0.531391i	$-0.821669\pi$
$163$	−51.4648	+	51.4648i	−0.315735	+	0.315735i	0.531391	+	0.847127i	$0.321669\pi$
$164$	81.8408	+	47.2508i	0.499029	+	0.288115i
$165$		0			0
$166$	8.51293	+	14.7448i	0.0512827	+	0.0888243i
$167$	−35.4672	+	132.365i	−0.212378	+	0.792607i	0.774695	+	0.632335i	$0.217904\pi$
$167$	−35.4672	+	132.365i	−0.212378	+	0.792607i	−0.987073	+	0.160271i	$0.948763\pi$
$168$		0			0
$169$	−112.809	−	65.1301i	−0.667506	−	0.385385i
$170$	72.8677	−	4.19488i	0.428634	−	0.0246758i
$171$		0			0
$172$	15.3266	+	15.3266i	0.0891081	+	0.0891081i
$173$	−46.6155	−	173.971i	−0.269454	−	1.00562i	−0.959468	−	0.281819i	$-0.909062\pi$
$173$	−46.6155	−	173.971i	−0.269454	−	1.00562i	0.690014	−	0.723796i	$-0.257604\pi$
$174$		0			0
$175$	30.5178	−	206.407i	0.174387	−	1.17947i
$176$	−11.5015	−	19.9212i	−0.0653494	−	0.113189i
$177$		0			0
$178$	21.7717	+	81.2530i	0.122313	+	0.456478i
$179$		−	6.72775i		−	0.0375852i	−0.999823	−	0.0187926i	$-0.994018\pi$
$179$		−	6.72775i		−	0.0375852i	0.999823	−	0.0187926i	$-0.00598222\pi$
$180$		0			0
$181$	153.631			0.848789			0.424395	−	0.905477i	$-0.360487\pi$
$181$	153.631			0.848789			0.424395	+	0.905477i	$0.360487\pi$
$182$	70.9606	−	19.0138i	0.389893	−	0.104472i
$183$		0			0
$184$	−96.8188	+	55.8984i	−0.526189	+	0.303796i
$185$	−161.741	−	33.5103i	−0.874276	−	0.181137i
$186$		0			0
$187$	57.3373	−	15.3635i	0.306616	−	0.0821576i
$188$	93.4129	−	93.4129i	0.496877	−	0.496877i
$189$		0			0
$190$	159.273	+	141.933i	0.838278	+	0.747015i
$191$	−180.317	+	312.319i	−0.944070	+	1.63518i	−0.186468	+	0.982461i	$0.559704\pi$
$191$	−180.317	+	312.319i	−0.944070	+	1.63518i	−0.757602	+	0.652717i	$0.773629\pi$
$192$		0			0
$193$	226.571	+	60.7095i	1.17394	+	0.314557i	0.792522	−	0.609844i	$-0.208768\pi$
$193$	226.571	+	60.7095i	1.17394	+	0.314557i	0.381422	+	0.924401i	$0.375435\pi$
$194$	−136.216	+	78.6446i	−0.702146	+	0.405384i
$195$		0			0
$196$	20.6560	−	35.7773i	0.105388	−	0.182537i
$197$	54.2664	+	54.2664i	0.275464	+	0.275464i	0.831295	−	0.555831i	$-0.187600\pi$
$197$	54.2664	+	54.2664i	0.275464	+	0.275464i	−0.555831	+	0.831295i	$0.687600\pi$
$198$		0			0
$199$		−	205.980i		−	1.03507i	−0.855661	−	0.517537i	$-0.826849\pi$
$199$		−	205.980i		−	1.03507i	0.855661	−	0.517537i	$-0.173151\pi$
$200$	26.0184	+	65.7499i	0.130092	+	0.328749i
$201$		0			0
$202$	−33.8034	+	126.156i	−0.167343	+	0.624534i
$203$	−123.947	−	33.2114i	−0.610575	−	0.163603i
$204$		0			0
$205$	−211.053	−	106.173i	−1.02953	−	0.517915i
$206$	186.599			0.905819
$207$		0			0
$208$	−17.6045	+	17.6045i	−0.0846371	+	0.0846371i
$209$	150.258	+	86.7514i	0.718937	+	0.415078i
$210$		0			0
$211$	−3.70438	−	6.41617i	−0.0175563	−	0.0304084i	0.857114	−	0.515127i	$-0.172255\pi$
$211$	−3.70438	−	6.41617i	−0.0175563	−	0.0304084i	−0.874670	+	0.484719i	$0.838922\pi$
$212$	−0.166257	+	0.620479i	−0.000784231	+	0.00292679i
$213$		0			0
$214$	184.008	+	106.237i	0.859853	+	0.496436i
$215$	−40.4553	−	36.0510i	−0.188164	−	0.167679i
$216$		0			0
$217$	229.212	+	229.212i	1.05628	+	1.05628i
$218$	50.6552	+	189.048i	0.232363	+	0.867192i
$219$		0			0
$220$	31.5686	+	48.0681i	0.143493	+	0.218491i
$221$	−32.1231	−	55.6389i	−0.145354	−	0.251760i
$222$		0			0
$223$	−35.7743	−	133.511i	−0.160423	−	0.598705i	−0.998580	−	0.0532767i	$-0.983033\pi$
$223$	−35.7743	−	133.511i	−0.160423	−	0.598705i	0.838157	−	0.545429i	$-0.183633\pi$
$224$			47.2122i			0.210769i
$225$		0			0
$226$	−197.109			−0.872162
$227$	65.8723	−	17.6504i	0.290186	−	0.0777552i	−0.110789	−	0.993844i	$-0.535338\pi$
$227$	65.8723	−	17.6504i	0.290186	−	0.0777552i	0.400976	+	0.916089i	$0.368671\pi$
$228$		0			0
$229$	−170.779	+	98.5996i	−0.745762	+	0.430566i	−0.824161	−	0.566356i	$-0.808353\pi$
$229$	−170.779	+	98.5996i	−0.745762	+	0.430566i	0.0783986	+	0.996922i	$0.475019\pi$
$230$	233.615	−	153.426i	1.01572	−	0.667070i
$231$		0			0
$232$	42.0050	−	11.2552i	0.181056	−	0.0485138i
$233$	−47.1109	+	47.1109i	−0.202193	+	0.202193i	−0.800939	−	0.598746i	$-0.795666\pi$
$233$	−47.1109	+	47.1109i	−0.202193	+	0.202193i	0.598746	+	0.800939i	$0.295666\pi$
$234$		0			0
$235$	−219.724	+	246.568i	−0.934997	+	1.04923i
$236$	−12.7783	+	22.1326i	−0.0541453	+	0.0937824i
$237$		0			0
$238$	−117.681	−	31.5326i	−0.494458	−	0.132490i
$239$	−3.11197	+	1.79669i	−0.0130208	+	0.00751755i	−0.506496	−	0.862242i	$-0.669060\pi$
$239$	−3.11197	+	1.79669i	−0.0130208	+	0.00751755i	0.493475	+	0.869760i	$0.335726\pi$
$240$		0			0
$241$	33.8177	−	58.5741i	0.140323	−	0.243046i	−0.787296	−	0.616576i	$-0.788519\pi$
$241$	33.8177	−	58.5741i	0.140323	−	0.243046i	0.927618	+	0.373530i	$0.121853\pi$
$242$	−87.9289	−	87.9289i	−0.363342	−	0.363342i
$243$		0			0
$244$			164.086i			0.672483i
$245$	−46.4141	+	92.2632i	−0.189445	+	0.376585i
$246$		0			0
$247$	48.6023	−	181.386i	0.196771	−	0.734358i
$248$	−106.112	−	28.4325i	−0.427869	−	0.114647i
$249$		0			0
$250$	−74.3856	−	160.365i	−0.297542	−	0.641458i
$251$	−15.9799			−0.0636649			−0.0318324	−	0.999493i	$-0.510134\pi$
$251$	−15.9799			−0.0636649			−0.0318324	+	0.999493i	$0.510134\pi$
$252$		0			0
$253$	160.729	−	160.729i	0.635292	−	0.635292i
$254$	−115.887	−	66.9076i	−0.456249	−	0.263416i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	45.7242	−	170.645i	0.177915	−	0.663989i	−0.818122	−	0.575045i	$-0.804984\pi$
$257$	45.7242	−	170.645i	0.177915	−	0.663989i	0.996037	−	0.0889431i	$-0.0283489\pi$
$258$		0			0
$259$	238.774	+	137.856i	0.921907	+	0.532263i
$260$	41.4091	−	46.4680i	0.159266	−	0.178723i
$261$		0			0
$262$	−184.018	−	184.018i	−0.702360	−	0.702360i
$263$	45.3709	+	169.327i	0.172513	+	0.643827i	0.996962	+	0.0778908i	$0.0248185\pi$
$263$	45.3709	+	169.327i	0.172513	+	0.643827i	−0.824449	+	0.565936i	$0.808515\pi$
$264$		0			0
$265$	0.325803	−	1.57252i	0.00122944	−	0.00593405i
$266$	−178.052	−	308.395i	−0.669367	−	1.15938i
$267$		0			0
$268$	−57.0021	−	212.735i	−0.212695	−	0.793787i
$269$		−	245.869i		−	0.914011i	−0.889464	−	0.457006i	$-0.848922\pi$
$269$		−	245.869i		−	0.914011i	0.889464	−	0.457006i	$-0.151078\pi$
$270$		0			0
$271$	−120.153			−0.443371			−0.221685	−	0.975118i	$-0.571156\pi$
$271$	−120.153			−0.443371			−0.221685	+	0.975118i	$0.571156\pi$
$272$	39.8816	−	10.6862i	0.146623	−	0.0392876i
$273$		0			0
$274$	187.185	−	108.071i	0.683156	−	0.394421i
$275$	−85.6975	−	115.436i	−0.311627	−	0.419766i
$276$		0			0
$277$	−427.888	+	114.652i	−1.54472	+	0.413907i	−0.927788	−	0.373107i	$-0.878293\pi$
$277$	−427.888	+	114.652i	−1.54472	+	0.413907i	−0.616935	+	0.787014i	$0.711626\pi$
$278$	−4.02247	+	4.02247i	−0.0144693	+	0.0144693i
$279$		0			0
$280$	−6.78361	−	117.835i	−0.0242272	−	0.420841i
$281$	133.612	−	231.422i	0.475486	−	0.823566i	−0.524120	−	0.851645i	$-0.675606\pi$
$281$	133.612	−	231.422i	0.475486	−	0.823566i	0.999606	+	0.0280785i	$0.00893884\pi$
$282$		0			0
$283$	−4.65544	−	1.24742i	−0.0164503	−	0.00440785i	0.250585	−	0.968095i	$-0.419377\pi$
$283$	−4.65544	−	1.24742i	−0.0164503	−	0.00440785i	−0.267035	+	0.963687i	$0.586044\pi$
$284$	−151.965	+	87.7370i	−0.535088	+	0.308933i
$285$		0			0
$286$	25.3098	−	43.8379i	0.0884958	−	0.153279i
$287$	278.852	+	278.852i	0.971609	+	0.971609i
$288$		0			0
$289$		−	182.454i		−	0.631329i
$290$	−103.222	+	34.1269i	−0.355937	+	0.117679i
$291$		0			0
$292$	11.5852	−	43.2367i	0.0396755	−	0.148071i
$293$	−74.9920	−	20.0940i	−0.255945	−	0.0685804i	0.128565	−	0.991701i	$-0.458963\pi$
$293$	−74.9920	−	20.0940i	−0.255945	−	0.0685804i	−0.384510	+	0.923121i	$0.625630\pi$
$294$		0			0
$295$	28.7128	−	57.0762i	0.0973316	−	0.193479i
$296$	−93.4377			−0.315668
$297$		0			0
$298$	102.939	−	102.939i	0.345433	−	0.345433i
$299$	−213.056	−	123.008i	−0.712562	−	0.411398i
$300$		0			0
$301$	45.2251	+	78.3323i	0.150250	+	0.260240i
$302$	−53.8349	+	200.915i	−0.178261	+	0.665280i
$303$		0			0
$304$	104.514	+	60.3409i	0.343794	+	0.198490i
$305$	−23.5764	−	409.537i	−0.0772997	−	1.34274i
$306$		0			0
$307$	−214.620	−	214.620i	−0.699088	−	0.699088i	0.265126	−	0.964214i	$-0.414586\pi$
$307$	−214.620	−	214.620i	−0.699088	−	0.699088i	−0.964214	+	0.265126i	$0.914586\pi$
$308$	−24.8445	−	92.7209i	−0.0806639	−	0.301042i
$309$		0			0
$310$	268.926	+	55.7173i	0.867502	+	0.179733i
$311$	−47.5516	−	82.3617i	−0.152899	−	0.264829i	0.779393	−	0.626535i	$-0.215528\pi$
$311$	−47.5516	−	82.3617i	−0.152899	−	0.264829i	−0.932292	+	0.361707i	$0.882194\pi$
$312$		0			0
$313$	120.559	+	449.931i	0.385172	+	1.43748i	0.837896	+	0.545830i	$0.183786\pi$
$313$	120.559	+	449.931i	0.385172	+	1.43748i	−0.452724	+	0.891651i	$0.649548\pi$
$314$			30.9723i			0.0986380i
$315$		0			0
$316$	−167.672			−0.530606
$317$	−140.067	+	37.5308i	−0.441852	+	0.118394i	−0.472884	−	0.881125i	$-0.656787\pi$
$317$	−140.067	+	37.5308i	−0.441852	+	0.118394i	0.0310325	+	0.999518i	$0.490120\pi$
$318$		0			0
$319$	−76.5715	+	44.2086i	−0.240036	+	0.138585i
$320$	21.9579	+	33.4343i	0.0686184	+	0.104482i
$321$		0			0
$322$	−450.632	+	120.747i	−1.39948	+	0.374989i
$323$	−220.209	+	220.209i	−0.681762	+	0.681762i
$324$		0			0
$325$	−96.6749	+	121.928i	−0.297461	+	0.375163i
$326$	51.4648	−	89.1397i	0.157868	−	0.273435i
$327$		0			0
$328$	−129.092	−	34.5900i	−0.393572	−	0.105457i
$329$	477.421	−	275.639i	1.45113	−	0.837809i
$330$		0			0
$331$	221.369	−	383.422i	0.668788	−	1.15838i	−0.309455	−	0.950914i	$-0.600147\pi$
$331$	221.369	−	383.422i	0.668788	−	1.15838i	0.978243	−	0.207461i	$-0.0665200\pi$
$332$	−17.0259	−	17.0259i	−0.0512827	−	0.0512827i
$333$		0			0
$334$		−	193.796i		−	0.580228i
$335$	172.836	+	522.768i	0.515929	+	1.56050i
$336$		0			0
$337$	−35.0491	+	130.805i	−0.104003	+	0.388145i	−0.998230	−	0.0594686i	$-0.981059\pi$
$337$	−35.0491	+	130.805i	−0.104003	+	0.388145i	0.894227	+	0.447614i	$0.147726\pi$
$338$	177.939	+	47.6785i	0.526446	+	0.141061i
$339$		0			0
$340$	−98.0037	+	32.4018i	−0.288246	+	0.0952993i
$341$	223.356			0.655004
$342$		0			0
$343$	−167.273	+	167.273i	−0.487676	+	0.487676i
$344$	−26.5464	−	15.3266i	−0.0771699	−	0.0445541i
$345$		0			0
$346$	127.356	+	220.587i	0.368081	+	0.637535i
$347$	108.480	−	404.853i	0.312623	−	1.16672i	−0.613560	−	0.789648i	$-0.710263\pi$
$347$	108.480	−	404.853i	0.312623	−	1.16672i	0.926182	−	0.377076i	$-0.123070\pi$
$348$		0			0
$349$	206.863	+	119.432i	0.592731	+	0.342213i	0.766176	−	0.642630i	$-0.222157\pi$
$349$	206.863	+	119.432i	0.592731	+	0.342213i	−0.173446	+	0.984843i	$0.555490\pi$
$350$	33.8620	+	293.127i	0.0967485	+	0.837505i
$351$		0			0
$352$	23.0030	+	23.0030i	0.0653494	+	0.0653494i
$353$	−16.9753	−	63.3528i	−0.0480887	−	0.179470i	0.937704	−	0.347435i	$-0.112947\pi$
$353$	−16.9753	−	63.3528i	−0.0480887	−	0.179470i	−0.985793	+	0.167965i	$0.946280\pi$
$354$		0			0
$355$	366.678	−	240.815i	1.03290	−	0.678351i
$356$	−59.4813	−	103.025i	−0.167082	−	0.289395i
$357$		0			0
$358$	2.46253	+	9.19028i	0.00687857	+	0.0256712i
$359$		−	269.424i		−	0.750484i	−0.926927	−	0.375242i	$-0.877560\pi$
$359$		−	269.424i		−	0.750484i	0.926927	−	0.375242i	$-0.122440\pi$
$360$		0			0
$361$	−549.256			−1.52149
$362$	−209.864	+	56.2328i	−0.579734	+	0.155339i
$363$		0			0
$364$	−89.9744	+	51.9468i	−0.247183	+	0.142711i
$365$	−22.7028	+	109.578i	−0.0621995	+	0.300213i
$366$		0			0
$367$	−437.004	+	117.095i	−1.19075	+	0.319059i	−0.799181	−	0.601091i	$-0.794733\pi$
$367$	−437.004	+	117.095i	−1.19075	+	0.319059i	−0.391565	+	0.920150i	$0.628066\pi$
$368$	111.797	−	111.797i	0.303796	−	0.303796i
$369$		0			0
$370$	233.208	−	13.4254i	0.630292	−	0.0362850i
$371$	−1.34030	+	2.32147i	−0.00361268	+	0.00625734i
$372$		0			0
$373$	−589.150	−	157.862i	−1.57949	−	0.423224i	−0.640723	−	0.767772i	$-0.721365\pi$
$373$	−589.150	−	157.862i	−1.57949	−	0.423224i	−0.938769	+	0.344548i	$0.888032\pi$
$374$	−72.7007	+	41.9738i	−0.194387	+	0.112229i
$375$		0			0
$376$	−93.4129	+	161.796i	−0.248439	+	0.430308i
$377$	67.6669	+	67.6669i	0.179488	+	0.179488i
$378$		0			0
$379$			444.508i			1.17284i	0.810006	+	0.586422i	$0.199464\pi$
$379$			444.508i			1.17284i	−0.810006	+	0.586422i	$0.800536\pi$
$380$	−269.522	−	135.586i	−0.709268	−	0.356805i
$381$		0			0
$382$	132.002	−	492.636i	0.345554	−	1.28962i
$383$	−234.373	−	62.8001i	−0.611940	−	0.163969i	−0.0604790	−	0.998169i	$-0.519263\pi$
$383$	−234.373	−	62.8001i	−0.611940	−	0.163969i	−0.551461	+	0.834201i	$0.685929\pi$
$384$		0			0
$385$	75.3310	+	227.849i	0.195665	+	0.591816i
$386$	−331.723			−0.859386
$387$		0			0
$388$	157.289	−	157.289i	0.405384	−	0.405384i
$389$	565.614	+	326.557i	1.45402	+	0.839479i	0.998706	−	0.0508516i	$-0.0161935\pi$
$389$	565.614	+	326.557i	1.45402	+	0.839479i	0.455314	+	0.890331i	$0.349527\pi$
$390$		0			0
$391$	203.997	+	353.332i	0.521730	+	0.903663i
$392$	−15.1212	+	56.4333i	−0.0385746	+	0.143962i
$393$		0			0
$394$	−93.9921	−	54.2664i	−0.238559	−	0.137732i
$395$	418.486	−	24.0916i	1.05946	−	0.0609914i
$396$		0			0
$397$	362.820	+	362.820i	0.913903	+	0.913903i	0.996577	−	0.0826735i	$-0.0263458\pi$
$397$	362.820	+	362.820i	0.913903	+	0.913903i	−0.0826735	+	0.996577i	$0.526346\pi$
$398$	75.3938	+	281.373i	0.189432	+	0.706968i
$399$		0			0
$400$	−59.6079	−	80.2926i	−0.149020	−	0.200731i
$401$	−130.663	−	226.315i	−0.325842	−	0.564375i	0.655840	−	0.754900i	$-0.272315\pi$
$401$	−130.663	−	226.315i	−0.325842	−	0.564375i	−0.981682	+	0.190524i	$0.938981\pi$
$402$		0			0
$403$	−62.5676	−	233.505i	−0.155255	−	0.579418i
$404$		−	184.705i		−	0.457191i
$405$		0			0
$406$	181.471			0.446972
$407$	183.504	−	49.1697i	0.450869	−	0.120810i
$408$		0			0
$409$	248.853	−	143.675i	0.608442	−	0.351284i	−0.163913	−	0.986475i	$-0.552412\pi$
$409$	248.853	−	143.675i	0.608442	−	0.351284i	0.772355	+	0.635191i	$0.219078\pi$
$410$	327.166	+	67.7837i	0.797965	+	0.165326i
$411$		0			0
$412$	−254.899	+	68.2999i	−0.618686	+	0.165776i
$413$	−75.4114	+	75.4114i	−0.182594	+	0.182594i
$414$		0			0
$415$	44.9406	+	40.0480i	0.108291	+	0.0965011i
$416$	17.6045	−	30.4919i	0.0423186	−	0.0732979i
$417$		0			0
$418$	−237.009	−	63.5064i	−0.567007	−	0.151929i
$419$	172.948	−	99.8517i	0.412764	−	0.238310i	−0.279212	−	0.960229i	$-0.590073\pi$
$419$	172.948	−	99.8517i	0.412764	−	0.238310i	0.691977	+	0.721920i	$0.256740\pi$
$420$		0			0
$421$	244.456	−	423.411i	0.580656	−	1.00573i	−0.414745	−	0.909937i	$-0.636129\pi$
$421$	244.456	−	423.411i	0.580656	−	1.00573i	0.995402	−	0.0957886i	$-0.0305373\pi$
$422$	7.40876	+	7.40876i	0.0175563	+	0.0175563i
$423$		0			0
$424$		−	0.908445i		−	0.00214256i
$425$	239.949	−	94.9520i	0.564585	−	0.223416i
$426$		0			0
$427$	−177.222	+	661.400i	−0.415039	+	1.54895i
$428$	−290.246	−	77.7711i	−0.678144	−	0.181708i
$429$		0			0
$430$	68.4586	+	34.4389i	0.159206	+	0.0800904i
$431$	−504.045			−1.16948			−0.584739	−	0.811221i	$-0.698803\pi$
$431$	−504.045			−1.16948			−0.584739	+	0.811221i	$0.698803\pi$
$432$		0			0
$433$	379.677	−	379.677i	0.876851	−	0.876851i	−0.116356	−	0.993208i	$-0.537121\pi$
$433$	379.677	−	379.677i	0.876851	−	0.876851i	0.993208	+	0.116356i	$0.0371214\pi$
$434$	−397.008	−	229.212i	−0.914764	−	0.528139i
$435$		0			0
$436$	−138.393	−	239.703i	−0.317414	−	0.549778i
$437$	−308.647	+	1151.89i	−0.706286	+	2.63590i
$438$		0			0
$439$	−285.924	−	165.078i	−0.651308	−	0.376033i	0.137649	−	0.990481i	$-0.456045\pi$
$439$	−285.924	−	165.078i	−0.651308	−	0.376033i	−0.788957	+	0.614448i	$0.789379\pi$
$440$	−60.7176	−	54.1073i	−0.137995	−	0.122971i
$441$		0			0
$442$	64.2463	+	64.2463i	0.145354	+	0.145354i
$443$	−109.435	−	408.416i	−0.247031	−	0.921932i	−0.972352	−	0.233521i	$-0.924975\pi$
$443$	−109.435	−	408.416i	−0.247031	−	0.921932i	0.725321	−	0.688411i	$-0.241692\pi$
$444$		0			0
$445$	163.261	+	248.590i	0.366878	+	0.558628i
$446$	97.7371	+	169.286i	0.219141	+	0.379564i
$447$		0			0
$448$	−17.2809	−	64.4931i	−0.0385734	−	0.143958i
$449$			177.792i			0.395972i	0.980205	+	0.197986i	$0.0634401\pi$
$449$			177.792i			0.395972i	−0.980205	+	0.197986i	$0.936560\pi$
$450$		0			0
$451$	271.728			0.602500
$452$	269.255	−	72.1468i	0.595698	−	0.159617i
$453$		0			0
$454$	−83.5227	+	48.2219i	−0.183971	+	0.106216i
$455$	217.100	−	142.580i	0.477144	−	0.313363i
$456$		0			0
$457$	831.978	−	222.928i	1.82052	−	0.487807i	0.823666	−	0.567075i	$-0.191925\pi$
$457$	831.978	−	222.928i	1.82052	−	0.487807i	0.996853	+	0.0792678i	$0.0252582\pi$
$458$	197.199	−	197.199i	0.430566	−	0.430566i
$459$		0			0
$460$	−262.967	+	295.093i	−0.571666	+	0.641507i
$461$	−59.9057	+	103.760i	−0.129947	+	0.225075i	−0.923656	−	0.383223i	$-0.874814\pi$
$461$	−59.9057	+	103.760i	−0.129947	+	0.225075i	0.793709	+	0.608298i	$0.208147\pi$
$462$		0			0
$463$	−358.368	−	96.0243i	−0.774012	−	0.207396i	−0.149869	−	0.988706i	$-0.547885\pi$
$463$	−358.368	−	96.0243i	−0.774012	−	0.207396i	−0.624143	+	0.781310i	$0.714552\pi$
$464$	−53.2602	+	30.7498i	−0.114785	+	0.0662711i
$465$		0			0
$466$	47.1109	−	81.5984i	0.101096	−	0.175104i
$467$	221.252	+	221.252i	0.473772	+	0.473772i	0.903133	−	0.429361i	$-0.141261\pi$
$467$	221.252	+	221.252i	0.473772	+	0.473772i	−0.429361	+	0.903133i	$0.641261\pi$
$468$		0			0
$469$		−	919.061i		−	1.95962i
$470$	209.899	−	417.243i	0.446593	−	0.887751i
$471$		0			0
$472$	9.35435	−	34.9109i	0.0198185	−	0.0739638i
$473$	60.2003	+	16.1306i	0.127273	+	0.0341028i
$474$		0			0
$475$	692.172	+	299.679i	1.45720	+	0.630903i
$476$	172.297			0.361969
$477$		0			0
$478$	3.59339	−	3.59339i	0.00751755	−	0.00751755i
$479$	−466.040	−	269.068i	−0.972943	−	0.561729i	−0.0728106	−	0.997346i	$-0.523197\pi$
$479$	−466.040	−	269.068i	−0.972943	−	0.561729i	−0.900132	+	0.435617i	$0.856530\pi$
$480$		0			0
$481$	−102.808	−	178.068i	−0.213738	−	0.370205i
$482$	−24.7563	+	92.3918i	−0.0513616	+	0.191684i
$483$		0			0
$484$	152.297	+	87.9289i	0.314664	+	0.181671i
$485$	−369.973	+	415.173i	−0.762831	+	0.856026i
$486$		0			0
$487$	142.335	+	142.335i	0.292268	+	0.292268i	0.837976	−	0.545708i	$-0.183739\pi$
$487$	142.335	+	142.335i	0.292268	+	0.292268i	−0.545708	+	0.837976i	$0.683739\pi$
$488$	−60.0596	−	224.146i	−0.123073	−	0.459315i
$489$		0			0
$490$	29.6321	−	143.023i	0.0604737	−	0.291883i
$491$	235.845	+	408.495i	0.480335	+	0.831965i	0.999745	−	0.0225601i	$-0.00718170\pi$
$491$	235.845	+	408.495i	0.480335	+	0.831965i	−0.519410	+	0.854525i	$0.673848\pi$
$492$		0			0
$493$	−41.0749	−	153.294i	−0.0833163	−	0.310941i
$494$			265.568i			0.537587i
$495$		0			0
$496$	155.358			0.313222
$497$	−707.303	+	189.521i	−1.42315	+	0.381331i
$498$		0			0
$499$	−227.181	+	131.163i	−0.455273	+	0.262852i	−0.710055	−	0.704147i	$-0.751330\pi$
$499$	−227.181	+	131.163i	−0.455273	+	0.262852i	0.254782	+	0.966999i	$0.417996\pi$
$500$	160.310	+	191.835i	0.320620	+	0.383670i
$501$		0			0
$502$	21.8289	−	5.84904i	0.0434839	−	0.0116515i
$503$	−92.4744	+	92.4744i	−0.183846	+	0.183846i	−0.793029	−	0.609184i	$-0.791497\pi$
$503$	−92.4744	+	92.4744i	−0.183846	+	0.183846i	0.609184	+	0.793029i	$0.291497\pi$
$504$		0			0
$505$	26.5390	+	460.999i	0.0525525	+	0.912870i
$506$	−160.729	+	278.390i	−0.317646	+	0.550179i
$507$		0			0
$508$	182.795	+	48.9798i	0.359833	+	0.0964169i
$509$	−379.182	+	218.921i	−0.744955	+	0.430100i	−0.823868	−	0.566781i	$-0.808188\pi$
$509$	−379.182	+	218.921i	−0.744955	+	0.430100i	0.0789130	+	0.996882i	$0.474855\pi$
$510$		0			0
$511$	93.3959	−	161.766i	0.182771	−	0.316568i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$		0			0
$514$			249.842i			0.486073i
$515$	626.380	−	207.092i	1.21627	−	0.402121i
$516$		0			0
$517$	98.3134	−	366.910i	0.190161	−	0.709691i
$518$	−376.630	−	100.918i	−0.727085	−	0.194822i
$519$		0			0
$520$	−39.5574	+	78.6333i	−0.0760719	+	0.151218i
$521$	−943.155			−1.81028			−0.905139	−	0.425115i	$-0.860234\pi$
$521$	−943.155			−1.81028			−0.905139	+	0.425115i	$0.860234\pi$
$522$		0			0
$523$	217.654	−	217.654i	0.416165	−	0.416165i	−0.467715	−	0.883879i	$-0.654923\pi$
$523$	217.654	−	217.654i	0.416165	−	0.416165i	0.883879	+	0.467715i	$0.154923\pi$
$524$	318.729	+	184.018i	0.608261	+	0.351180i
$525$		0			0
$526$	−123.956	−	214.697i	−0.235657	−	0.408170i
$527$	−103.762	+	387.245i	−0.196892	+	0.734811i
$528$		0			0
$529$	894.876	+	516.657i	1.69164	+	0.976667i
$530$	0.130528	+	2.26736i	0.000246280	+	0.00427803i
$531$		0			0
$532$	356.103	+	356.103i	0.669367	+	0.669367i
$533$	−76.1175	−	284.074i	−0.142810	−	0.532973i
$534$		0			0
$535$	735.590	+	152.403i	1.37493	+	0.284865i
$536$	155.733	+	269.737i	0.290546	+	0.503241i
$537$		0			0
$538$	89.9943	+	335.863i	0.167276	+	0.624281i
$539$		−	118.788i		−	0.220385i
$540$		0			0
$541$	−249.489			−0.461162			−0.230581	−	0.973053i	$-0.574063\pi$
$541$	−249.489			−0.461162			−0.230581	+	0.973053i	$0.574063\pi$
$542$	164.133	−	43.9792i	0.302828	−	0.0811424i
$543$		0			0
$544$	−50.5678	+	29.1953i	−0.0929555	+	0.0536679i
$545$	379.851	+	578.383i	0.696975	+	1.06125i
$546$		0			0
$547$	−543.268	+	145.568i	−0.993178	+	0.266121i	−0.718585	−	0.695439i	$-0.755210\pi$
$547$	−543.268	+	145.568i	−0.993178	+	0.266121i	−0.274593	+	0.961561i	$0.588543\pi$
$548$	−216.142	+	216.142i	−0.394421	+	0.394421i
$549$		0			0
$550$	159.317	+	126.321i	0.289668	+	0.229674i
$551$	231.934	−	401.721i	0.420932	−	0.729076i
$552$		0			0
$553$	−675.854	−	181.094i	−1.22216	−	0.327476i
$554$	542.541	−	313.236i	0.979316	−	0.565408i
$555$		0			0
$556$	4.02247	−	6.96711i	0.00723465	−	0.0125308i
$557$	268.053	+	268.053i	0.481244	+	0.481244i	0.905529	−	0.424285i	$-0.139475\pi$
$557$	268.053	+	268.053i	0.481244	+	0.481244i	−0.424285	+	0.905529i	$0.639475\pi$
$558$		0			0
$559$		−	67.4543i		−	0.120670i
$560$	52.3973	+	158.483i	0.0935667	+	0.283006i
$561$		0			0
$562$	−97.8105	+	365.034i	−0.174040	+	0.649526i
$563$	644.580	+	172.715i	1.14490	+	0.306776i	0.780920	−	0.624630i	$-0.214750\pi$
$563$	644.580	+	172.715i	1.14490	+	0.306776i	0.363982	+	0.931406i	$0.381417\pi$
$564$		0			0
$565$	−661.660	+	218.756i	−1.17108	+	0.387179i
$566$	6.81604			0.0120425
$567$		0			0
$568$	175.474	−	175.474i	0.308933	−	0.308933i
$569$	222.641	+	128.542i	0.391284	+	0.225908i	0.682716	−	0.730684i	$-0.260799\pi$
$569$	222.641	+	128.542i	0.391284	+	0.225908i	−0.291432	+	0.956591i	$0.594132\pi$
$570$		0			0
$571$	438.771	+	759.974i	0.768426	+	1.33095i	0.938416	+	0.345507i	$0.112293\pi$
$571$	438.771	+	759.974i	0.768426	+	1.33095i	−0.169991	+	0.985446i	$0.554374\pi$
$572$	−18.5281	+	69.1477i	−0.0323917	+	0.120888i
$573$		0			0
$574$	−482.985	−	278.852i	−0.841438	−	0.485805i
$575$	613.930	−	774.297i	1.06770	−	1.34660i
$576$		0			0
$577$	−687.574	−	687.574i	−1.19164	−	1.19164i	−0.976608	−	0.215027i	$-0.931016\pi$
$577$	−687.574	−	687.574i	−1.19164	−	1.19164i	−0.215027	−	0.976608i	$-0.568984\pi$
$578$	66.7828	+	249.237i	0.115541	+	0.431206i
$579$		0			0
$580$	128.512	−	84.4000i	0.221573	−	0.145517i
$581$	−50.2393	−	87.0170i	−0.0864704	−	0.149771i
$582$		0			0
$583$	0.478051	+	1.78411i	0.000819985	+	0.00306023i
$584$			63.3029i			0.108395i
$585$		0			0
$586$	109.796			0.187365
$587$	−93.9197	+	25.1657i	−0.159999	+	0.0428717i	−0.337930	−	0.941171i	$-0.609727\pi$
$587$	−93.9197	+	25.1657i	−0.159999	+	0.0428717i	0.177930	+	0.984043i	$0.443060\pi$
$588$		0			0
$589$	−1014.81	+	585.903i	−1.72294	+	0.994742i
$590$	−18.3311	+	88.4771i	−0.0310697	+	0.149961i
$591$		0			0
$592$	127.638	−	34.2006i	0.215605	−	0.0577712i
$593$	196.612	−	196.612i	0.331555	−	0.331555i	−0.521622	−	0.853177i	$-0.674673\pi$
$593$	196.612	−	196.612i	0.331555	−	0.331555i	0.853177	+	0.521622i	$0.174673\pi$
$594$		0			0
$595$	−430.031	+	24.7562i	−0.722741	+	0.0416071i
$596$	−102.939	+	178.296i	−0.172717	+	0.299154i
$597$		0			0
$598$	336.064	+	90.0481i	0.561980	+	0.150582i
$599$	95.2202	−	54.9754i	0.158965	−	0.0917787i	−0.418407	−	0.908260i	$-0.637411\pi$
$599$	95.2202	−	54.9754i	0.158965	−	0.0917787i	0.577372	+	0.816481i	$0.304078\pi$
$600$		0			0
$601$	24.2179	−	41.9466i	0.0402960	−	0.0697946i	−0.845174	−	0.534491i	$-0.820503\pi$
$601$	24.2179	−	41.9466i	0.0402960	−	0.0697946i	0.885470	+	0.464697i	$0.153837\pi$
$602$	−90.4503	−	90.4503i	−0.150250	−	0.150250i
$603$		0			0
$604$		−	294.159i		−	0.487019i
$605$	−392.748	−	197.576i	−0.649170	−	0.326572i
$606$		0			0
$607$	33.6276	−	125.500i	0.0553997	−	0.206754i	−0.932678	−	0.360710i	$-0.882535\pi$
$607$	33.6276	−	125.500i	0.0553997	−	0.206754i	0.988078	+	0.153955i	$0.0492012\pi$
$608$	−164.854	−	44.1726i	−0.271142	−	0.0726523i
$609$		0			0
$610$	182.107	+	550.808i	0.298536	+	0.902964i
$611$	−411.122			−0.672868
$612$		0			0
$613$	68.4305	−	68.4305i	0.111632	−	0.111632i	−0.649084	−	0.760716i	$-0.724848\pi$
$613$	68.4305	−	68.4305i	0.111632	−	0.111632i	0.760716	+	0.649084i	$0.224848\pi$
$614$	371.733	+	214.620i	0.605428	+	0.349544i
$615$		0			0
$616$	67.8764	+	117.565i	0.110189	+	0.190853i
$617$	239.548	−	894.007i	0.388247	−	1.44896i	−0.444737	−	0.895661i	$-0.646703\pi$
$617$	239.548	−	894.007i	0.388247	−	1.44896i	0.832984	−	0.553297i	$-0.186630\pi$
$618$		0			0
$619$	−352.357	−	203.433i	−0.569235	−	0.328648i	0.187609	−	0.982244i	$-0.439926\pi$
$619$	−352.357	−	203.433i	−0.569235	−	0.328648i	−0.756844	+	0.653596i	$0.773260\pi$
$620$	−387.753	+	22.3224i	−0.625409	+	0.0360038i
$621$		0			0
$622$	95.1032	+	95.1032i	0.152899	+	0.152899i
$623$	−128.486	−	479.517i	−0.206238	−	0.769690i
$624$		0			0
$625$	−427.676	−	455.761i	−0.684282	−	0.729217i
$626$	−329.373	−	570.490i	−0.526154	−	0.911326i
$627$		0			0
$628$	−11.3367	−	42.3090i	−0.0180520	−	0.0673710i
$629$			340.993i			0.542119i
$630$		0			0
$631$	39.5574			0.0626900			0.0313450	−	0.999509i	$-0.490021\pi$
$631$	39.5574			0.0626900			0.0313450	+	0.999509i	$0.490021\pi$
$632$	229.044	−	61.3721i	0.362411	−	0.0971077i
$633$		0			0
$634$	177.598	−	102.536i	0.280123	−	0.161729i
$635$	−463.270	−	95.9824i	−0.729558	−	0.151153i
$636$		0			0
$637$	−124.185	+	33.2753i	−0.194953	+	0.0522375i
$638$	88.4171	−	88.4171i	0.138585	−	0.138585i
$639$		0			0
$640$	−42.2328	−	37.6349i	−0.0659888	−	0.0588046i
$641$	416.098	−	720.703i	0.649139	−	1.12434i	−0.334190	−	0.942506i	$-0.608463\pi$
$641$	416.098	−	720.703i	0.649139	−	1.12434i	0.983329	−	0.181836i	$-0.0582040\pi$
$642$		0			0
$643$	892.066	+	239.028i	1.38735	+	0.371739i	0.873785	−	0.486312i	$-0.161658\pi$
$643$	892.066	+	239.028i	1.38735	+	0.371739i	0.513564	+	0.858051i	$0.328325\pi$
$644$	571.379	−	329.886i	0.887234	−	0.512245i
$645$		0			0
$646$	220.209	−	381.413i	0.340881	−	0.590423i
$647$	4.82533	+	4.82533i	0.00745800	+	0.00745800i	0.710826	−	0.703368i	$-0.248321\pi$
$647$	4.82533	+	4.82533i	0.00745800	+	0.00745800i	−0.703368	+	0.710826i	$0.748321\pi$
$648$		0			0
$649$			73.4847i			0.113228i
$650$	87.4317	−	201.942i	0.134510	−	0.310680i
$651$		0			0
$652$	−37.6749	+	140.605i	−0.0577836	+	0.215651i
$653$	179.600	+	48.1238i	0.275039	+	0.0736965i	0.393702	−	0.919238i	$-0.371194\pi$
$653$	179.600	+	48.1238i	0.275039	+	0.0736965i	−0.118663	+	0.992935i	$0.537861\pi$
$654$		0			0
$655$	−821.946	−	413.489i	−1.25488	−	0.631281i
$656$	189.003			0.288115
$657$		0			0
$658$	−551.279	+	551.279i	−0.837809	+	0.837809i
$659$	−274.113	−	158.259i	−0.415953	−	0.240151i	0.277391	−	0.960757i	$-0.410530\pi$
$659$	−274.113	−	158.259i	−0.415953	−	0.240151i	−0.693344	+	0.720606i	$0.743863\pi$
$660$		0			0
$661$	−435.173	−	753.742i	−0.658356	−	1.14031i	−0.981041	−	0.193800i	$-0.937919\pi$
$661$	−435.173	−	753.742i	−0.658356	−	1.14031i	0.322685	−	0.946506i	$-0.395414\pi$
$662$	−162.053	+	604.791i	−0.244793	+	0.913582i
$663$		0			0
$664$	29.4897	+	17.0259i	0.0444121	+	0.0256414i
$665$	−939.953	−	837.621i	−1.41346	−	1.25958i
$666$		0			0
$667$	−429.716	−	429.716i	−0.644251	−	0.644251i
$668$	70.9344	+	264.731i	0.106189	+	0.396303i
$669$		0			0
$670$	−427.445	−	650.852i	−0.637978	−	0.971420i
$671$	235.904	+	408.598i	0.351571	+	0.608939i
$672$		0			0
$673$	65.2386	+	243.474i	0.0969371	+	0.361774i	0.997306	−	0.0733532i	$-0.0233700\pi$
$673$	65.2386	+	243.474i	0.0969371	+	0.361774i	−0.900369	+	0.435127i	$0.856703\pi$
$674$		−	191.512i		−	0.284142i
$675$		0			0
$676$	−260.520			−0.385385
$677$	−291.869	+	78.2062i	−0.431122	+	0.115519i	−0.467853	−	0.883806i	$-0.654972\pi$
$677$	−291.869	+	78.2062i	−0.431122	+	0.115519i	0.0367309	+	0.999325i	$0.488306\pi$
$678$		0			0
$679$	803.884	−	464.123i	1.18392	−	0.683539i
$680$	122.016	−	80.1335i	0.179435	−	0.117843i
$681$		0			0
$682$	−305.111	+	81.7541i	−0.447376	+	0.119874i
$683$	56.0495	−	56.0495i	0.0820637	−	0.0820637i	−0.664883	−	0.746947i	$-0.731519\pi$
$683$	56.0495	−	56.0495i	0.0820637	−	0.0820637i	0.746947	+	0.664883i	$0.231519\pi$
$684$		0			0
$685$	508.407	−	570.519i	0.742200	−	0.832874i
$686$	167.273	−	289.725i	0.243838	−	0.422340i
$687$		0			0
$688$	41.8730	+	11.2198i	0.0608620	+	0.0163079i
$689$	1.73126	−	0.999546i	0.00251272	−	0.00145072i
$690$		0			0
$691$	−15.4812	+	26.8142i	−0.0224041	+	0.0388050i	−0.877010	−	0.480472i	$-0.840465\pi$
$691$	−15.4812	+	26.8142i	−0.0224041	+	0.0388050i	0.854606	+	0.519277i	$0.173799\pi$
$692$	−254.712	−	254.712i	−0.368081	−	0.368081i
$693$		0			0
$694$			592.746i			0.854101i
$695$	−9.03848	+	17.9670i	−0.0130050	+	0.0258517i
$696$		0			0
$697$	−126.233	+	471.109i	−0.181109	+	0.675910i
$698$	−326.295	−	87.4306i	−0.467472	−	0.125259i
$699$		0			0
$700$	−153.548	−	388.024i	−0.219355	−	0.554321i
$701$	−395.892			−0.564753			−0.282376	−	0.959304i	$-0.591123\pi$
$701$	−395.892			−0.564753			−0.282376	+	0.959304i	$0.591123\pi$
$702$		0			0
$703$	−704.764	+	704.764i	−1.00251	+	1.00251i
$704$	−39.8424	−	23.0030i	−0.0565943	−	0.0326747i
$705$		0			0
$706$	46.3775	+	80.3281i	0.0656904	+	0.113779i
$707$	199.491	−	744.512i	0.282166	−	1.05306i
$708$		0			0
$709$	−315.081	−	181.912i	−0.444403	−	0.256576i	0.261061	−	0.965322i	$-0.415928\pi$
$709$	−315.081	−	181.912i	−0.444403	−	0.256576i	−0.705463	+	0.708746i	$0.749261\pi$
$710$	−412.747	+	463.172i	−0.581334	+	0.652355i
$711$		0			0
$712$	118.963	+	118.963i	0.167082	+	0.167082i
$713$	397.333	+	1482.87i	0.557269	+	2.07976i
$714$		0			0
$715$	36.3082	−	175.246i	0.0507807	−	0.245099i
$716$	−6.72775	−	11.6528i	−0.00939630	−	0.0162749i
$717$		0			0
$718$	98.6160	+	368.040i	0.137348	+	0.512590i
$719$			509.086i			0.708048i	0.935236	+	0.354024i	$0.115187\pi$
$719$			509.086i			0.708048i	−0.935236	+	0.354024i	$0.884813\pi$
$720$		0			0
$721$	−1101.22			−1.52735
$722$	750.298	−	201.042i	1.03919	−	0.278451i
$723$		0			0
$724$	266.096	−	153.631i	0.367536	−	0.212197i
$725$	−308.622	+	229.116i	−0.425686	+	0.316022i
$726$		0			0
$727$	407.908	−	109.299i	0.561084	−	0.150342i	0.0328794	−	0.999459i	$-0.489532\pi$
$727$	407.908	−	109.299i	0.561084	−	0.150342i	0.528204	+	0.849117i	$0.322866\pi$
$728$	103.894	−	103.894i	0.142711	−	0.142711i
$729$		0			0
$730$	−9.09557	−	157.996i	−0.0124597	−	0.216432i
$731$	−55.9332	+	96.8791i	−0.0765159	+	0.132529i
$732$		0			0
$733$	750.335	+	201.052i	1.02365	+	0.274286i	0.731322	−	0.682032i	$-0.238904\pi$
$733$	750.335	+	201.052i	1.02365	+	0.274286i	0.292328	+	0.956318i	$0.405570\pi$
$734$	554.099	−	319.909i	0.754903	−	0.435843i
$735$		0			0
$736$	−111.797	+	193.638i	−0.151898	+	0.263095i
$737$	−447.790	−	447.790i	−0.607585	−	0.607585i
$738$		0			0
$739$			365.394i			0.494444i	0.968959	+	0.247222i	$0.0795176\pi$
$739$			365.394i			0.494444i	−0.968959	+	0.247222i	$0.920482\pi$
$740$	−313.654	+	103.700i	−0.423857	+	0.140135i
$741$		0			0
$742$	0.981170	−	3.66178i	0.00132233	−	0.00493501i
$743$	−587.633	−	157.456i	−0.790892	−	0.211919i	−0.159311	−	0.987229i	$-0.550927\pi$
$743$	−587.633	−	157.456i	−0.790892	−	0.211919i	−0.631581	+	0.775310i	$0.717594\pi$
$744$		0			0
$745$	231.304	−	459.793i	0.310476	−	0.617172i
$746$	862.576			1.15627
$747$		0			0
$748$	83.9476	−	83.9476i	0.112229	−	0.112229i
$749$	−1085.93	−	626.962i	−1.44984	−	0.837066i
$750$		0			0
$751$	404.776	+	701.092i	0.538983	+	0.933545i	0.998959	+	0.0456141i	$0.0145245\pi$
$751$	404.776	+	701.092i	0.538983	+	0.933545i	−0.459977	+	0.887931i	$0.652142\pi$
$752$	68.3830	−	255.209i	0.0909348	−	0.339373i
$753$		0			0
$754$	−117.202	−	67.6669i	−0.155441	−	0.0897439i
$755$	42.2658	+	734.183i	0.0559812	+	0.972428i
$756$		0			0
$757$	−491.291	−	491.291i	−0.648997	−	0.648997i	0.303753	−	0.952751i	$-0.401760\pi$
$757$	−491.291	−	491.291i	−0.648997	−	0.648997i	−0.952751	+	0.303753i	$0.901760\pi$
$758$	−162.701	−	607.209i	−0.214645	−	0.801068i
$759$		0			0
$760$	417.802	+	86.5621i	0.549739	+	0.113898i
$761$	−188.782	−	326.981i	−0.248072	−	0.429673i	0.714919	−	0.699207i	$-0.246463\pi$
$761$	−188.782	−	326.981i	−0.248072	−	0.429673i	−0.962991	+	0.269535i	$0.913130\pi$
$762$		0			0
$763$	−298.943	−	1115.67i	−0.391800	−	1.46222i
$764$			721.270i			0.944070i
$765$		0			0
$766$	343.146			0.447971
$767$	76.8238	−	20.5849i	0.100161	−	0.0268382i
$768$		0			0
$769$	1249.73	−	721.531i	1.62513	−	0.938271i	0.639617	−	0.768694i	$-0.279093\pi$
$769$	1249.73	−	721.531i	1.62513	−	0.938271i	0.985517	−	0.169577i	$-0.0542402\pi$
$770$	−186.303	−	283.675i	−0.241952	−	0.368409i
$771$		0			0
$772$	453.142	−	121.419i	0.586972	−	0.157279i
$773$	−369.006	+	369.006i	−0.477369	+	0.477369i	−0.904289	−	0.426920i	$-0.859598\pi$
$773$	−369.006	+	369.006i	−0.477369	+	0.477369i	0.426920	+	0.904289i	$0.359598\pi$
$774$		0			0
$775$	964.574	−	111.427i	1.24461	−	0.143777i
$776$	−157.289	+	272.433i	−0.202692	+	0.351073i
$777$		0			0
$778$	−892.171	−	239.057i	−1.14675	−	0.307271i
$779$	−1234.59	+	712.789i	−1.58484	+	0.915005i
$780$		0			0
$781$	−252.277	+	436.956i	−0.323017	+	0.559483i
$782$	−407.993	−	407.993i	−0.521730	−	0.521730i
$783$		0			0
$784$		−	82.6240i		−	0.105388i
$785$	34.3739	+	103.969i	0.0437884	+	0.132444i
$786$		0			0
$787$	298.330	−	1113.38i	0.379072	−	1.41472i	−0.468230	−	0.883607i	$-0.655108\pi$
$787$	298.330	−	1113.38i	0.379072	−	1.41472i	0.847302	−	0.531111i	$-0.178225\pi$
$788$	148.259	+	39.7258i	0.188145	+	0.0504134i
$789$		0			0
$790$	−562.845	+	186.086i	−0.712461	+	0.235552i
$791$	1163.24			1.47060
$792$		0			0
$793$	361.082	−	361.082i	0.455336	−	0.455336i
$794$	−628.422	−	362.820i	−0.791463	−	0.456952i
$795$		0			0
$796$	−205.980	−	356.767i	−0.258768	−	0.448200i
$797$	400.142	−	1493.35i	0.502061	−	1.87372i	0.0158493	−	0.999874i	$-0.494955\pi$
$797$	400.142	−	1493.35i	0.502061	−	1.87372i	0.486211	−	0.873841i	$-0.338379\pi$
$798$		0			0
$799$	590.461	+	340.903i	0.739000	+	0.426662i
$800$	110.815	+	87.8637i	0.138519	+	0.109830i
$801$		0			0
$802$	261.326	+	261.326i	0.325842	+	0.325842i
$803$	−33.3119	−	124.322i	−0.0414843	−	0.154822i
$804$		0			0
$805$	−1378.69	+	905.449i	−1.71265	+	1.12478i
$806$	170.938	+	296.073i	0.212082	+	0.367336i
$807$		0			0
$808$	67.6067	+	252.312i	0.0836717	+	0.312267i
$809$			132.217i			0.163433i	0.996656	+	0.0817163i	$0.0260401\pi$
$809$			132.217i			0.163433i	−0.996656	+	0.0817163i	$0.973960\pi$
$810$		0			0
$811$	99.9069			0.123190			0.0615949	−	0.998101i	$-0.480381\pi$
$811$	99.9069			0.123190			0.0615949	+	0.998101i	$0.480381\pi$
$812$	−247.893	+	66.4228i	−0.305287	+	0.0818015i
$813$		0			0
$814$	−232.674	+	134.334i	−0.285840	+	0.165030i
$815$	73.8290	−	356.344i	0.0905877	−	0.437231i
$816$		0			0
$817$	−315.832	+	84.6270i	−0.386575	+	0.103583i
$818$	−287.350	+	287.350i	−0.351284	+	0.351284i
$819$		0			0
$820$	−471.727	+	27.1566i	−0.575277	+	0.0331178i
$821$	300.172	−	519.913i	0.365618	−	0.633268i	−0.623257	−	0.782017i	$-0.714191\pi$
$821$	300.172	−	519.913i	0.365618	−	0.633268i	0.988875	+	0.148748i	$0.0475244\pi$
$822$		0			0
$823$	101.960	+	27.3202i	0.123889	+	0.0331959i	0.320231	−	0.947340i	$-0.396240\pi$
$823$	101.960	+	27.3202i	0.123889	+	0.0331959i	−0.196342	+	0.980535i	$0.562906\pi$
$824$	323.198	−	186.599i	0.392231	−	0.226455i
$825$		0			0
$826$	75.4114	−	130.616i	0.0912971	−	0.158131i
$827$	−199.922	−	199.922i	−0.241743	−	0.241743i	0.575828	−	0.817571i	$-0.304680\pi$
$827$	−199.922	−	199.922i	−0.241743	−	0.241743i	−0.817571	+	0.575828i	$0.804680\pi$
$828$		0			0
$829$			444.676i			0.536400i	0.963363	+	0.268200i	$0.0864288\pi$
$829$			444.676i			0.536400i	−0.963363	+	0.268200i	$0.913571\pi$
$830$	−76.0486	−	38.2571i	−0.0916248	−	0.0460929i
$831$		0			0
$832$	−12.8874	+	48.0964i	−0.0154897	+	0.0578082i
$833$	205.949	+	55.1837i	0.247237	+	0.0662470i
$834$		0			0
$835$	−215.080	−	650.541i	−0.257581	−	0.779091i
$836$	347.005			0.415078
$837$		0			0
$838$	−199.703	+	199.703i	−0.238310	+	0.238310i
$839$	795.475	+	459.268i	0.948123	+	0.547399i	0.892497	−	0.451053i	$-0.148951\pi$
$839$	795.475	+	459.268i	0.948123	+	0.547399i	0.0556257	+	0.998452i	$0.482285\pi$
$840$		0			0
$841$	−302.306	−	523.610i	−0.359461	−	0.622604i
$842$	−178.954	+	667.867i	−0.212535	+	0.793191i
$843$		0			0
$844$	−12.8323	−	7.40876i	−0.0152042	−	0.00877815i
$845$	650.224	−	37.4324i	0.769496	−	0.0442987i
$846$		0			0
$847$	518.914	+	518.914i	0.612650	+	0.612650i
$848$	0.332514	+	1.24096i	0.000392116	+	0.00146339i
$849$		0			0
$850$	−293.021	+	217.534i	−0.344731	+	0.255923i
$851$	652.877	+	1130.82i	0.767188	+	1.32881i
$852$		0			0
$853$	10.2946	+	38.4199i	0.0120687	+	0.0450409i	0.971698	−	0.236228i	$-0.0759113\pi$
$853$	10.2946	+	38.4199i	0.0120687	+	0.0450409i	−0.959629	+	0.281269i	$0.909245\pi$
$854$		−	968.357i		−	1.13391i
$855$		0			0
$856$	424.949			0.496436
$857$	−168.243	+	45.0806i	−0.196316	+	0.0526028i	−0.355637	−	0.934624i	$-0.615736\pi$
$857$	−168.243	+	45.0806i	−0.196316	+	0.0526028i	0.159321	+	0.987227i	$0.449070\pi$
$858$		0			0
$859$	−1152.81	+	665.578i	−1.34204	+	0.774829i	−0.987107	−	0.160062i	$-0.948831\pi$
$859$	−1152.81	+	665.578i	−1.34204	+	0.774829i	−0.354936	+	0.934891i	$0.615497\pi$
$860$	−106.122	−	21.9868i	−0.123397	−	0.0255660i
$861$		0			0
$862$	688.539	−	184.493i	0.798769	−	0.214029i
$863$	980.185	−	980.185i	1.13579	−	1.13579i	0.146591	−	0.989197i	$-0.453170\pi$
$863$	980.185	−	980.185i	1.13579	−	1.13579i	0.989197	−	0.146591i	$-0.0468302\pi$
$864$		0			0
$865$	672.325	+	599.129i	0.777254	+	0.692635i
$866$	−379.677	+	657.619i	−0.438426	+	0.759376i
$867$		0			0
$868$	626.220	+	167.795i	0.721452	+	0.193312i
$869$	−417.527	+	241.059i	−0.480468	+	0.277399i
$870$		0			0
$871$	−342.700	+	593.574i	−0.393456	+	0.681486i
$872$	276.785	+	276.785i	0.317414	+	0.317414i
$873$		0			0
$874$		−	1686.48i		−	1.92961i
$875$	438.989	+	946.395i	0.501701	+	1.08159i
$876$		0			0
$877$	−326.118	+	1217.09i	−0.371856	+	1.38779i	0.486027	+	0.873944i	$0.338446\pi$
$877$	−326.118	+	1217.09i	−0.371856	+	1.38779i	−0.857884	+	0.513844i	$0.828221\pi$
$878$	451.003	+	120.846i	0.513670	+	0.137638i
$879$		0			0
$880$	102.746	+	51.6878i	0.116757	+	0.0587361i
$881$	482.151			0.547277			0.273639	−	0.961833i	$-0.411773\pi$
$881$	482.151			0.547277			0.273639	+	0.961833i	$0.411773\pi$
$882$		0			0
$883$	−20.8159	+	20.8159i	−0.0235740	+	0.0235740i	−0.718796	−	0.695222i	$-0.755306\pi$
$883$	−20.8159	+	20.8159i	−0.0235740	+	0.0235740i	0.695222	+	0.718796i	$0.255306\pi$
$884$	−111.278	−	64.2463i	−0.125880	−	0.0726768i
$885$		0			0
$886$	298.981	+	517.851i	0.337451	+	0.584482i
$887$	31.4487	−	117.368i	0.0354552	−	0.132320i	−0.945930	−	0.324371i	$-0.894847\pi$
$887$	31.4487	−	117.368i	0.0354552	−	0.132320i	0.981385	+	0.192051i	$0.0615139\pi$
$888$		0			0
$889$	683.912	+	394.857i	0.769305	+	0.444159i
$890$	−314.008	−	279.822i	−0.352818	−	0.314407i
$891$		0			0
$892$	−195.474	−	195.474i	−0.219141	−	0.219141i
$893$	515.786	+	1924.94i	0.577588	+	2.15559i
$894$		0			0
$895$	18.4659	+	28.1172i	0.0206323	+	0.0314159i
$896$	47.2122	+	81.7739i	0.0526922	+	0.0912656i
$897$		0			0
$898$	−65.0762	−	242.868i	−0.0724679	−	0.270454i
$899$		−	597.153i		−	0.664242i
$900$		0			0
$901$	−3.31530			−0.00367957
$902$	−371.187	+	99.4592i	−0.411515	+	0.110265i
$903$		0			0
$904$	−341.402	+	197.109i	−0.377657	+	0.218041i
$905$	−642.067	+	421.676i	−0.709466	+	0.465940i
$906$		0			0
$907$	1106.27	−	296.423i	1.21970	−	0.326817i	0.409138	−	0.912472i	$-0.365829\pi$
$907$	1106.27	−	296.423i	1.21970	−	0.326817i	0.810560	+	0.585655i	$0.199163\pi$
$908$	96.4437	−	96.4437i	0.106216	−	0.106216i
$909$		0			0
$910$	−244.377	+	274.232i	−0.268546	+	0.301354i
$911$	−33.3225	+	57.7163i	−0.0365780	+	0.0633549i	−0.883735	−	0.467988i	$-0.844979\pi$
$911$	−33.3225	+	57.7163i	−0.0365780	+	0.0633549i	0.847157	+	0.531343i	$0.178312\pi$
$912$		0			0
$913$	−66.8748	−	17.9190i	−0.0732473	−	0.0196266i
$914$	−1054.91	+	609.050i	−1.15416	+	0.666356i
$915$		0			0
$916$	−197.199	+	341.559i	−0.215283	+	0.372881i
$917$	1085.99	+	1085.99i	1.18428	+	1.18428i
$918$		0			0
$919$			1575.30i			1.71415i	0.515194	+	0.857074i	$0.327720\pi$
$919$			1575.30i			1.71415i	−0.515194	+	0.857074i	$0.672280\pi$
$920$	251.207	−	499.357i	0.273052	−	0.542780i
$921$		0			0
$922$	43.8540	−	163.665i	0.0475640	−	0.177511i
$923$	527.479	+	141.338i	0.571484	+	0.153129i
$924$		0			0
$925$	767.939	−	303.887i	0.830204	−	0.328527i
$926$	524.687			0.566616
$927$		0			0
$928$	61.4995	−	61.4995i	0.0662711	−	0.0662711i
$929$	614.392	+	354.719i	0.661348	+	0.381829i	0.792790	−	0.609494i	$-0.208628\pi$
$929$	614.392	+	354.719i	0.661348	+	0.381829i	−0.131443	+	0.991324i	$0.541961\pi$
$930$		0			0
$931$	311.601	+	539.708i	0.334694	+	0.579708i
$932$	−34.4876	+	128.709i	−0.0370038	+	0.138100i
$933$		0			0
$934$	−383.219	−	221.252i	−0.410299	−	0.236886i
$935$	−197.460	+	221.584i	−0.211187	+	0.236988i
$936$		0			0
$937$	716.809	+	716.809i	0.765004	+	0.765004i	0.977222	−	0.212218i	$-0.0680688\pi$
$937$	716.809	+	716.809i	0.765004	+	0.765004i	−0.212218	+	0.977222i	$0.568069\pi$
$938$	336.400	+	1255.46i	0.358635	+	1.33844i
$939$		0			0
$940$	−134.006	+	646.793i	−0.142559	+	0.688077i
$941$	137.643	+	238.405i	0.146273	+	0.253353i	0.929847	−	0.367946i	$-0.119939\pi$
$941$	137.643	+	238.405i	0.146273	+	0.253353i	−0.783574	+	0.621298i	$0.786605\pi$
$942$		0			0
$943$	483.381	+	1804.00i	0.512599	+	1.91305i
$944$			51.1131i			0.0541453i
$945$		0			0
$946$	−88.1394			−0.0931706
$947$	−61.8292	+	16.5671i	−0.0652896	+	0.0174943i	−0.291316	−	0.956627i	$-0.594093\pi$
$947$	−61.8292	+	16.5671i	−0.0652896	+	0.0174943i	0.226026	+	0.974121i	$0.427426\pi$
$948$		0			0
$949$	−120.639	+	69.6511i	−0.127122	+	0.0733942i
$950$	−1055.22	−	156.017i	−1.11075	−	0.164228i
$951$		0			0
$952$	−235.362	+	63.0651i	−0.247229	+	0.0662449i
$953$	578.229	−	578.229i	0.606746	−	0.606746i	−0.335348	−	0.942094i	$-0.608854\pi$
$953$	578.229	−	578.229i	0.606746	−	0.606746i	0.942094	+	0.335348i	$0.108854\pi$
$954$		0			0
$955$	−103.634	−	1800.19i	−0.108518	−	1.88502i
$956$	−3.59339	+	6.22393i	−0.00375877	+	0.00651039i
$957$		0			0
$958$	735.108	+	196.971i	0.767336	+	0.205607i
$959$	−1104.68	+	637.785i	−1.15190	+	0.665052i
$960$		0			0
$961$	−273.754	+	474.157i	−0.284864	+	0.493399i
$962$	205.616	+	205.616i	0.213738	+	0.213738i
$963$		0			0
$964$		−	135.271i		−	0.140323i
$965$	−1113.54	+	368.155i	−1.15392	+	0.381508i
$966$		0			0
$967$	370.649	−	1383.28i	0.383298	−	1.43049i	−0.457535	−	0.889192i	$-0.651267\pi$
$967$	370.649	−	1383.28i	0.383298	−	1.43049i	0.840833	−	0.541295i	$-0.182066\pi$
$968$	−240.226	−	64.3684i	−0.248168	−	0.0664963i
$969$		0			0
$970$	353.429	−	702.556i	0.364360	−	0.724284i
$971$	435.010			0.448002			0.224001	−	0.974589i	$-0.428088\pi$
$971$	435.010			0.448002			0.224001	+	0.974589i	$0.428088\pi$
$972$		0			0
$973$	23.7387	−	23.7387i	0.0243974	−	0.0243974i
$974$	−246.531	−	142.335i	−0.253112	−	0.146134i
$975$		0			0
$976$	164.086	+	284.205i	0.168121	+	0.291194i
$977$	446.328	−	1665.72i	0.456835	−	1.70493i	−0.225801	−	0.974173i	$-0.572500\pi$
$977$	446.328	−	1665.72i	0.456835	−	1.70493i	0.682636	−	0.730759i	$-0.260833\pi$
$978$		0			0
$979$	−296.235	−	171.031i	−0.302589	−	0.174700i
$980$	11.8717	+	206.219i	0.0121140	+	0.210427i
$981$		0			0
$982$	−471.689	−	471.689i	−0.480335	−	0.480335i
$983$	−380.122	−	1418.63i	−0.386696	−	1.44317i	−0.835476	−	0.549526i	$-0.814808\pi$
$983$	−380.122	−	1418.63i	−0.386696	−	1.44317i	0.448781	−	0.893642i	$-0.351858\pi$
$984$		0			0
$985$	−375.742	−	77.8479i	−0.381464	−	0.0790334i
$986$	112.219	+	194.369i	0.113812	+	0.197128i
$987$		0			0
$988$	−97.2047	−	362.773i	−0.0983853	−	0.367179i
$989$			428.366i			0.433130i
$990$		0			0
$991$	877.590			0.885560			0.442780	−	0.896630i	$-0.353992\pi$
$991$	877.590			0.885560			0.442780	+	0.896630i	$0.353992\pi$
$992$	−212.223	+	56.8650i	−0.213935	+	0.0573236i
$993$		0			0
$994$	896.825	−	517.782i	0.902238	−	0.520907i
$995$	565.359	+	860.848i	0.568200	+	0.865174i
$996$		0			0
$997$	−274.662	+	73.5956i	−0.275489	+	0.0738170i	−0.393918	−	0.919145i	$-0.628881\pi$
$997$	−274.662	+	73.5956i	−0.275489	+	0.0738170i	0.118429	+	0.992962i	$0.462214\pi$
$998$	262.326	−	262.326i	0.262852	−	0.262852i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.3.l.a.127.1		24
3.2	odd	2		90.3.k.b.7.1	✓	24
5.3	odd	4	inner	270.3.l.a.73.5		24
9.2	odd	6		810.3.g.h.487.3		12
9.4	even	3	inner	270.3.l.a.37.5		24
9.5	odd	6		90.3.k.b.67.3	yes	24
9.7	even	3		810.3.g.j.487.4		12
15.8	even	4		90.3.k.b.43.3	yes	24
45.13	odd	12	inner	270.3.l.a.253.1		24
45.23	even	12		90.3.k.b.13.1	yes	24
45.38	even	12		810.3.g.h.163.3		12
45.43	odd	12		810.3.g.j.163.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.k.b.7.1	✓	24	3.2	odd	2
90.3.k.b.13.1	yes	24	45.23	even	12
90.3.k.b.43.3	yes	24	15.8	even	4
90.3.k.b.67.3	yes	24	9.5	odd	6
270.3.l.a.37.5		24	9.4	even	3	inner
270.3.l.a.73.5		24	5.3	odd	4	inner
270.3.l.a.127.1		24	1.1	even	1	trivial
270.3.l.a.253.1		24	45.13	odd	12	inner
810.3.g.h.163.3		12	45.38	even	12
810.3.g.h.487.3		12	9.2	odd	6
810.3.g.j.163.4		12	45.43	odd	12
810.3.g.j.487.4		12	9.7	even	3

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	270.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(-4.17929 + 2.74473i) q^{5} +(8.06163 - 2.16011i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(4.70437 - 5.27910i) q^{10} +(2.87538 - 4.98030i) q^{11} +(-6.01206 - 1.61093i) q^{13} +(-10.2217 + 5.90153i) q^{14} +(2.00000 - 3.46410i) q^{16} +(7.29884 + 7.29884i) q^{17} +30.1705i q^{19} +(-4.49400 + 8.93331i) q^{20} +(-2.10492 + 7.85567i) q^{22} +(38.1793 + 10.2301i) q^{23} +(9.93287 - 22.9421i) q^{25} +8.80226 q^{26} +(11.8031 - 11.8031i) q^{28} +(-13.3150 - 7.68744i) q^{29} +(19.4198 + 33.6360i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(-12.6420 - 7.29884i) q^{34} +(-27.7630 + 31.1548i) q^{35} +(23.3594 + 23.3594i) q^{37} +(-11.0432 - 41.2136i) q^{38} +(2.86910 - 13.8480i) q^{40} +(23.6254 + 40.9204i) q^{41} +(2.80496 + 10.4683i) q^{43} -11.5015i q^{44} -55.8984 q^{46} +(63.8022 - 17.0957i) q^{47} +(17.8886 - 10.3280i) q^{49} +(-5.17117 + 34.9751i) q^{50} +(-12.0241 + 3.22185i) q^{52} +(-0.227111 + 0.227111i) q^{53} +(1.65257 + 28.7062i) q^{55} +(-11.8031 + 20.4435i) q^{56} +(21.0025 + 5.62760i) q^{58} +(-11.0663 + 6.38914i) q^{59} +(-41.0215 + 71.0513i) q^{61} +(-38.8395 - 38.8395i) q^{62} -8.00000i q^{64} +(29.5477 - 9.76898i) q^{65} +(28.5011 - 106.367i) q^{67} +(19.9408 + 5.34312i) q^{68} +(26.5215 - 52.7201i) q^{70} -87.7370 q^{71} +(15.8257 - 15.8257i) q^{73} +(-40.4597 - 23.3594i) q^{74} +(30.1705 + 52.2568i) q^{76} +(12.4222 - 46.3604i) q^{77} +(-72.6039 - 41.9179i) q^{79} +(1.14947 + 19.9669i) q^{80} +(-47.2508 - 47.2508i) q^{82} +(-3.11595 - 11.6289i) q^{83} +(-50.5373 - 10.4706i) q^{85} +(-7.66330 - 13.2732i) q^{86} +(4.20984 + 15.7113i) q^{88} -59.4813i q^{89} -51.9468 q^{91} +(76.3586 - 20.4602i) q^{92} +(-80.8979 + 46.7064i) q^{94} +(-82.8099 - 126.091i) q^{95} +(107.430 - 28.7859i) q^{97} +(-20.6560 + 20.6560i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} + 6 q^{7} - 48 q^{8} + 12 q^{10} + 12 q^{11} + 48 q^{16} + 36 q^{17} - 12 q^{20} + 12 q^{22} + 66 q^{23} - 42 q^{25} + 24 q^{28} + 72 q^{31} + 48 q^{32} + 240 q^{35} + 36 q^{37} + 36 q^{38}+ \cdots - 264 q^{98}+O(q^{100}) \) 24 * q - 12 * q^2 + 6 * q^7 - 48 * q^8 + 12 * q^10 + 12 * q^11 + 48 * q^16 + 36 * q^17 - 12 * q^20 + 12 * q^22 + 66 * q^23 - 42 * q^25 + 24 * q^28 + 72 * q^31 + 48 * q^32 + 240 * q^35 + 36 * q^37 + 36 * q^38 - 12 * q^40 + 24 * q^41 - 108 * q^43 - 264 * q^46 + 36 * q^47 - 42 * q^50 - 384 * q^53 + 288 * q^55 - 24 * q^56 - 108 * q^58 + 360 * q^61 - 144 * q^62 - 144 * q^65 + 144 * q^67 + 36 * q^68 - 174 * q^70 - 216 * q^71 + 432 * q^73 + 72 * q^76 + 48 * q^77 - 48 * q^82 + 378 * q^83 - 228 * q^85 - 216 * q^86 - 24 * q^88 - 1560 * q^91 + 132 * q^92 - 264 * q^95 - 294 * q^97 - 264 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more