LMFDB - Embedded newform 224.3.n.a.17.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(17,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("224.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.n (of order $6$, 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:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.9
Character	$\chi$	$=$	224.17
Dual form			224.3.n.a.145.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.455431 - 0.788830i) q^{3} +(3.17251 + 5.49495i) q^{5} +(-3.79106 + 5.88455i) q^{7} +(4.08516 + 7.07571i) q^{9} +O(q^{10})$	\(q+(0.455431 - 0.788830i) q^{3} +(3.17251 + 5.49495i) q^{5} +(-3.79106 + 5.88455i) q^{7} +(4.08516 + 7.07571i) q^{9} +(-11.4442 - 6.60732i) q^{11} -19.4243 q^{13} +5.77945 q^{15} +(13.7930 + 7.96338i) q^{17} +(8.22725 + 14.2500i) q^{19} +(2.91534 + 5.67051i) q^{21} +(11.9607 + 20.7166i) q^{23} +(-7.62967 + 13.2150i) q^{25} +15.6398 q^{27} -16.6618i q^{29} +(11.1360 + 6.42939i) q^{31} +(-10.4241 + 6.01837i) q^{33} +(-44.3625 - 2.16288i) q^{35} +(41.1844 - 23.7778i) q^{37} +(-8.84646 + 15.3225i) q^{39} +6.49499i q^{41} +33.2928i q^{43} +(-25.9205 + 44.8956i) q^{45} +(18.9713 - 10.9531i) q^{47} +(-20.2558 - 44.6173i) q^{49} +(12.5635 - 7.25355i) q^{51} +(-32.2028 - 18.5923i) q^{53} -83.8473i q^{55} +14.9878 q^{57} +(27.3428 - 47.3591i) q^{59} +(-5.12340 - 8.87399i) q^{61} +(-57.1245 - 2.78508i) q^{63} +(-61.6240 - 106.736i) q^{65} +(14.8386 + 8.56706i) q^{67} +21.7892 q^{69} -32.0568 q^{71} +(92.8082 + 53.5828i) q^{73} +(6.94958 + 12.0370i) q^{75} +(82.2668 - 42.2953i) q^{77} +(-29.1542 - 50.4965i) q^{79} +(-29.6436 + 51.3443i) q^{81} +36.3441 q^{83} +101.056i q^{85} +(-13.1433 - 7.58829i) q^{87} +(0.929882 - 0.536867i) q^{89} +(73.6388 - 114.303i) q^{91} +(10.1434 - 5.85629i) q^{93} +(-52.2021 + 90.4167i) q^{95} -169.517i q^{97} -107.968i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{7} - 32 q^{9}+O(q^{10}) $ 28 * q + 4 * q^7 - 32 * q^9	$ 28 q + 4 q^{7} - 32 q^{9} - 28 q^{15} - 6 q^{17} - 30 q^{23} - 32 q^{25} + 6 q^{31} - 6 q^{33} + 20 q^{39} + 294 q^{47} - 20 q^{49} + 124 q^{57} - 432 q^{63} - 52 q^{65} + 136 q^{71} + 234 q^{73} + 162 q^{79} - 18 q^{81} - 48 q^{87} - 150 q^{89} - 290 q^{95}+O(q^{100}) $ 28 * q + 4 * q^7 - 32 * q^9 - 28 * q^15 - 6 * q^17 - 30 * q^23 - 32 * q^25 + 6 * q^31 - 6 * q^33 + 20 * q^39 + 294 * q^47 - 20 * q^49 + 124 * q^57 - 432 * q^63 - 52 * q^65 + 136 * q^71 + 234 * q^73 + 162 * q^79 - 18 * q^81 - 48 * q^87 - 150 * q^89 - 290 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.455431	−	0.788830i	0.151810	−	0.262943i	−0.780083	−	0.625677i	$-0.784823\pi$
$3$	0.455431	−	0.788830i	0.151810	−	0.262943i	0.931893	+	0.362733i	$0.118156\pi$
$4$		0			0
$5$	3.17251	+	5.49495i	0.634503	+	1.09899i	0.986620	+	0.163035i	$0.0521283\pi$
$5$	3.17251	+	5.49495i	0.634503	+	1.09899i	−0.352118	+	0.935956i	$0.614538\pi$
$6$		0			0
$7$	−3.79106	+	5.88455i	−0.541579	+	0.840650i
$7$	−3.79106	+	5.88455i	−0.541579	+	0.840650i
$8$		0			0
$9$	4.08516	+	7.07571i	0.453907	+	0.786190i
$10$		0			0
$11$	−11.4442	−	6.60732i	−1.04038	−	0.600666i	−0.120442	−	0.992720i	$-0.538431\pi$
$11$	−11.4442	−	6.60732i	−1.04038	−	0.600666i	−0.919942	+	0.392054i	$0.871764\pi$
$12$		0			0
$13$	−19.4243			−1.49418			−0.747090	−	0.664723i	$-0.768550\pi$
$13$	−19.4243			−1.49418			−0.747090	+	0.664723i	$0.768550\pi$
$14$		0			0
$15$	5.77945			0.385296
$16$		0			0
$17$	13.7930	+	7.96338i	0.811352	+	0.468434i	0.847425	−	0.530915i	$-0.178152\pi$
$17$	13.7930	+	7.96338i	0.811352	+	0.468434i	−0.0360732	+	0.999349i	$0.511485\pi$
$18$		0			0
$19$	8.22725	+	14.2500i	0.433013	+	0.750001i	0.997131	−	0.0756934i	$-0.0241170\pi$
$19$	8.22725	+	14.2500i	0.433013	+	0.750001i	−0.564118	+	0.825694i	$0.690784\pi$
$20$		0			0
$21$	2.91534	+	5.67051i	0.138826	+	0.270024i
$22$		0			0
$23$	11.9607	+	20.7166i	0.520032	+	0.900721i	0.999729	+	0.0232870i	$0.00741316\pi$
$23$	11.9607	+	20.7166i	0.520032	+	0.900721i	−0.479697	+	0.877434i	$0.659254\pi$
$24$		0			0
$25$	−7.62967	+	13.2150i	−0.305187	+	0.528599i
$26$		0			0
$27$	15.6398			0.579252
$28$		0			0
$29$		−	16.6618i		−	0.574544i	−0.957849	−	0.287272i	$-0.907252\pi$
$29$		−	16.6618i		−	0.574544i	0.957849	−	0.287272i	$-0.0927483\pi$
$30$		0			0
$31$	11.1360	+	6.42939i	0.359227	+	0.207400i	0.668741	−	0.743495i	$-0.266833\pi$
$31$	11.1360	+	6.42939i	0.359227	+	0.207400i	−0.309515	+	0.950895i	$0.600167\pi$
$32$		0			0
$33$	−10.4241	+	6.01837i	−0.315882	+	0.182375i
$34$		0			0
$35$	−44.3625	−	2.16288i	−1.26750	−	0.0617964i
$36$		0			0
$37$	41.1844	−	23.7778i	1.11309	−	0.642644i	0.173463	−	0.984840i	$-0.444504\pi$
$37$	41.1844	−	23.7778i	1.11309	−	0.642644i	0.939628	+	0.342196i	$0.111171\pi$
$38$		0			0
$39$	−8.84646	+	15.3225i	−0.226832	+	0.392885i
$40$		0			0
$41$			6.49499i			0.158415i	0.996858	+	0.0792073i	$0.0252389\pi$
$41$			6.49499i			0.158415i	−0.996858	+	0.0792073i	$0.974761\pi$
$42$		0			0
$43$			33.2928i			0.774252i	0.922027	+	0.387126i	$0.126532\pi$
$43$			33.2928i			0.774252i	−0.922027	+	0.387126i	$0.873468\pi$
$44$		0			0
$45$	−25.9205	+	44.8956i	−0.576010	+	0.997679i
$46$		0			0
$47$	18.9713	−	10.9531i	0.403645	−	0.233045i	−0.284411	−	0.958703i	$-0.591798\pi$
$47$	18.9713	−	10.9531i	0.403645	−	0.233045i	0.688056	+	0.725658i	$0.258465\pi$
$48$		0			0
$49$	−20.2558	−	44.6173i	−0.413383	−	0.910557i
$50$		0			0
$51$	12.5635	−	7.25355i	0.246343	−	0.142226i
$52$		0			0
$53$	−32.2028	−	18.5923i	−0.607601	−	0.350798i	0.164425	−	0.986390i	$-0.447423\pi$
$53$	−32.2028	−	18.5923i	−0.607601	−	0.350798i	−0.772026	+	0.635591i	$0.780756\pi$
$54$		0			0
$55$		−	83.8473i		−	1.52450i
$56$		0			0
$57$	14.9878			0.262944
$58$		0			0
$59$	27.3428	−	47.3591i	0.463437	−	0.802696i	−0.535693	−	0.844413i	$-0.679949\pi$
$59$	27.3428	−	47.3591i	0.463437	−	0.802696i	0.999129	+	0.0417169i	$0.0132827\pi$
$60$		0			0
$61$	−5.12340	−	8.87399i	−0.0839902	−	0.145475i	0.820970	−	0.570971i	$-0.193433\pi$
$61$	−5.12340	−	8.87399i	−0.0839902	−	0.145475i	−0.904960	+	0.425496i	$0.860100\pi$
$62$		0			0
$63$	−57.1245	−	2.78508i	−0.906737	−	0.0442076i
$64$		0			0
$65$	−61.6240	−	106.736i	−0.948061	−	1.64209i
$66$		0			0
$67$	14.8386	+	8.56706i	0.221471	+	0.127867i	0.606631	−	0.794983i	$-0.292520\pi$
$67$	14.8386	+	8.56706i	0.221471	+	0.127867i	−0.385160	+	0.922850i	$0.625854\pi$
$68$		0			0
$69$	21.7892			0.315785
$70$		0			0
$71$	−32.0568			−0.451505			−0.225752	−	0.974185i	$-0.572484\pi$
$71$	−32.0568			−0.451505			−0.225752	+	0.974185i	$0.572484\pi$
$72$		0			0
$73$	92.8082	+	53.5828i	1.27135	+	0.734011i	0.975241	−	0.221144i	$-0.0709792\pi$
$73$	92.8082	+	53.5828i	1.27135	+	0.734011i	0.296104	+	0.955156i	$0.404313\pi$
$74$		0			0
$75$	6.94958	+	12.0370i	0.0926611	+	0.160494i
$76$		0			0
$77$	82.2668	−	42.2953i	1.06840	−	0.549290i
$78$		0			0
$79$	−29.1542	−	50.4965i	−0.369040	−	0.639196i	0.620376	−	0.784305i	$-0.286980\pi$
$79$	−29.1542	−	50.4965i	−0.369040	−	0.639196i	−0.989416	+	0.145109i	$0.953647\pi$
$80$		0			0
$81$	−29.6436	+	51.3443i	−0.365971	+	0.633880i
$82$		0			0
$83$	36.3441			0.437880			0.218940	−	0.975738i	$-0.429740\pi$
$83$	36.3441			0.437880			0.218940	+	0.975738i	$0.429740\pi$
$84$		0			0
$85$			101.056i			1.18889i
$86$		0			0
$87$	−13.1433	−	7.58829i	−0.151072	−	0.0872217i
$88$		0			0
$89$	0.929882	−	0.536867i	0.0104481	−	0.00603222i	−0.494767	−	0.869026i	$-0.664747\pi$
$89$	0.929882	−	0.536867i	0.0104481	−	0.00603222i	0.505215	+	0.862994i	$0.331413\pi$
$90$		0			0
$91$	73.6388	−	114.303i	0.809217	−	1.25608i
$92$		0			0
$93$	10.1434	−	5.85629i	0.109069	−	0.0629709i
$94$		0			0
$95$	−52.2021	+	90.4167i	−0.549496	+	0.951755i
$96$		0			0
$97$		−	169.517i		−	1.74760i	−0.486286	−	0.873799i	$-0.661649\pi$
$97$		−	169.517i		−	1.74760i	0.486286	−	0.873799i	$-0.338351\pi$
$98$		0			0
$99$		−	107.968i		−	1.09059i
$100$		0			0
$101$	−14.0630	+	24.3579i	−0.139238	+	0.241167i	−0.927208	−	0.374546i	$-0.877799\pi$
$101$	−14.0630	+	24.3579i	−0.139238	+	0.241167i	0.787971	+	0.615713i	$0.211132\pi$
$102$		0			0
$103$	144.029	−	83.1551i	1.39834	−	0.807331i	0.404120	−	0.914706i	$-0.367578\pi$
$103$	144.029	−	83.1551i	1.39834	−	0.807331i	0.994219	+	0.107374i	$0.0342444\pi$
$104$		0			0
$105$	−21.9102	+	34.0094i	−0.208669	+	0.323899i
$106$		0			0
$107$	−171.112	+	98.7918i	−1.59918	+	0.923288i	−0.607536	+	0.794292i	$0.707842\pi$
$107$	−171.112	+	98.7918i	−1.59918	+	0.923288i	−0.991645	+	0.128996i	$0.958825\pi$
$108$		0			0
$109$	9.97643	+	5.75990i	0.0915269	+	0.0528431i	0.545065	−	0.838394i	$-0.316505\pi$
$109$	9.97643	+	5.75990i	0.0915269	+	0.0528431i	−0.453538	+	0.891237i	$0.649838\pi$
$110$		0			0
$111$		−	43.3167i		−	0.390240i
$112$		0			0
$113$	−14.7908			−0.130892			−0.0654460	−	0.997856i	$-0.520847\pi$
$113$	−14.7908			−0.130892			−0.0654460	+	0.997856i	$0.520847\pi$
$114$		0			0
$115$	−75.8911	+	131.447i	−0.659923	+	1.14302i
$116$		0			0
$117$	−79.3516	−	137.441i	−0.678219	−	1.17471i
$118$		0			0
$119$	−99.1509	+	50.9758i	−0.833201	+	0.428368i
$120$		0			0
$121$	26.8135	+	46.4423i	0.221599	+	0.383821i
$122$		0			0
$123$	5.12345	+	2.95802i	0.0416541	+	0.0240490i
$124$		0			0
$125$	61.8047			0.494438
$126$		0			0
$127$	70.2656			0.553272			0.276636	−	0.960975i	$-0.410780\pi$
$127$	70.2656			0.553272			0.276636	+	0.960975i	$0.410780\pi$
$128$		0			0
$129$	26.2624	+	15.1626i	0.203584	+	0.117540i
$130$		0			0
$131$	71.0646	+	123.088i	0.542478	+	0.939600i	0.998761	+	0.0497649i	$0.0158472\pi$
$131$	71.0646	+	123.088i	0.542478	+	0.939600i	−0.456283	+	0.889835i	$0.650819\pi$
$132$		0			0
$133$	−115.045	−	5.60897i	−0.864999	−	0.0421727i
$134$		0			0
$135$	49.6175	+	85.9400i	0.367537	+	0.636593i
$136$		0			0
$137$	−126.537	+	219.168i	−0.923626	+	1.59977i	−0.129870	+	0.991531i	$0.541456\pi$
$137$	−126.537	+	219.168i	−0.923626	+	1.59977i	−0.793756	+	0.608236i	$0.791877\pi$
$138$		0			0
$139$	49.1909			0.353892			0.176946	−	0.984221i	$-0.443378\pi$
$139$	49.1909			0.353892			0.176946	+	0.984221i	$0.443378\pi$
$140$		0			0
$141$		−	19.9535i		−	0.141514i
$142$		0			0
$143$	222.296	+	128.343i	1.55452	+	0.897503i
$144$		0			0
$145$	91.5556	−	52.8597i	0.631418	−	0.364549i
$146$		0			0
$147$	−44.4206	−	4.34174i	−0.302181	−	0.0295356i
$148$		0			0
$149$	−36.1077	+	20.8468i	−0.242334	+	0.139911i	−0.616249	−	0.787551i	$-0.711348\pi$
$149$	−36.1077	+	20.8468i	−0.242334	+	0.139911i	0.373915	+	0.927463i	$0.378015\pi$
$150$		0			0
$151$	−48.8145	+	84.5492i	−0.323275	+	0.559928i	−0.981162	−	0.193188i	$-0.938117\pi$
$151$	−48.8145	+	84.5492i	−0.323275	+	0.559928i	0.657887	+	0.753117i	$0.271450\pi$
$152$		0			0
$153$			130.127i			0.850503i
$154$		0			0
$155$			81.5892i			0.526382i
$156$		0			0
$157$	−14.0827	+	24.3919i	−0.0896986	+	0.155363i	−0.907384	−	0.420303i	$-0.861924\pi$
$157$	−14.0827	+	24.3919i	−0.0896986	+	0.155363i	0.817685	+	0.575666i	$0.195257\pi$
$158$		0			0
$159$	−29.3324	+	16.9350i	−0.184480	+	0.106510i
$160$		0			0
$161$	−167.251	−	8.15428i	−1.03883	−	0.0506477i
$162$		0			0
$163$	209.952	−	121.216i	1.28805	−	0.743655i	0.309743	−	0.950820i	$-0.399757\pi$
$163$	209.952	−	121.216i	1.28805	−	0.743655i	0.978306	+	0.207165i	$0.0664237\pi$
$164$		0			0
$165$	−66.1413	−	38.1867i	−0.400856	−	0.231434i
$166$		0			0
$167$			60.1108i			0.359945i	0.983672	+	0.179972i	$0.0576008\pi$
$167$			60.1108i			0.359945i	−0.983672	+	0.179972i	$0.942399\pi$
$168$		0			0
$169$	208.305			1.23257
$170$		0			0
$171$	−67.2193	+	116.427i	−0.393096	+	0.680861i
$172$		0			0
$173$	69.6820	+	120.693i	0.402786	+	0.697646i	0.994061	−	0.108824i	$-0.0347085\pi$
$173$	69.6820	+	120.693i	0.402786	+	0.697646i	−0.591275	+	0.806470i	$0.701375\pi$
$174$		0			0
$175$	−48.8397	−	94.9959i	−0.279084	−	0.542834i
$176$		0			0
$177$	−24.9055	−	43.1376i	−0.140709	−	0.243715i
$178$		0			0
$179$	−252.643	−	145.863i	−1.41141	−	0.814879i	−0.415891	−	0.909415i	$-0.636530\pi$
$179$	−252.643	−	145.863i	−1.41141	−	0.814879i	−0.995522	+	0.0945354i	$0.969863\pi$
$180$		0			0
$181$	166.844			0.921791			0.460895	−	0.887455i	$-0.347528\pi$
$181$	166.844			0.921791			0.460895	+	0.887455i	$0.347528\pi$
$182$		0			0
$183$	−9.33343			−0.0510024
$184$		0			0
$185$	261.316	+	150.871i	1.41252	+	0.815518i
$186$		0			0
$187$	−105.233	−	182.269i	−0.562745	−	0.974703i
$188$		0			0
$189$	−59.2914	+	92.0332i	−0.313711	+	0.486948i
$190$		0			0
$191$	−65.6781	−	113.758i	−0.343864	−	0.595590i	0.641283	−	0.767305i	$-0.278403\pi$
$191$	−65.6781	−	113.758i	−0.343864	−	0.595590i	−0.985147	+	0.171715i	$0.945069\pi$
$192$		0			0
$193$	40.7196	−	70.5284i	0.210982	−	0.365432i	−0.741040	−	0.671461i	$-0.765667\pi$
$193$	40.7196	−	70.5284i	0.210982	−	0.365432i	0.952022	+	0.306029i	$0.0990004\pi$
$194$		0			0
$195$	−112.262			−0.575702
$196$		0			0
$197$		−	2.09549i		−	0.0106370i	−0.999986	−	0.00531851i	$-0.998307\pi$
$197$		−	2.09549i		−	0.0106370i	0.999986	−	0.00531851i	$-0.00169294\pi$
$198$		0			0
$199$	109.937	+	63.4721i	0.552447	+	0.318955i	0.750108	−	0.661315i	$-0.230001\pi$
$199$	109.937	+	63.4721i	0.552447	+	0.318955i	−0.197662	+	0.980270i	$0.563335\pi$
$200$		0			0
$201$	13.5159	−	7.80341i	0.0672433	−	0.0388230i
$202$		0			0
$203$	98.0469	+	63.1657i	0.482990	+	0.311161i
$204$		0			0
$205$	−35.6897	+	20.6055i	−0.174096	+	0.100514i
$206$		0			0
$207$	−97.7231	+	169.261i	−0.472092	+	0.817687i
$208$		0			0
$209$		−	217.440i		−	1.04038i
$210$		0			0
$211$		−	7.16822i		−	0.0339726i	−0.999856	−	0.0169863i	$-0.994593\pi$
$211$		−	7.16822i		−	0.0339726i	0.999856	−	0.0169863i	$-0.00540717\pi$
$212$		0			0
$213$	−14.5997	+	25.2874i	−0.0685432	+	0.118720i
$214$		0			0
$215$	−182.943	+	105.622i	−0.850896	+	0.491265i
$216$		0			0
$217$	−80.0513	+	41.1563i	−0.368900	+	0.189660i
$218$		0			0
$219$	84.5355	−	48.8066i	0.386007	−	0.222861i
$220$		0			0
$221$	−267.920	−	154.683i	−1.21231	−	0.699925i
$222$		0			0
$223$		−	279.720i		−	1.25435i	−0.778878	−	0.627175i	$-0.784211\pi$
$223$		−	279.720i		−	1.25435i	0.778878	−	0.627175i	$-0.215789\pi$
$224$		0			0
$225$	−124.674			−0.554106
$226$		0			0
$227$	152.392	−	263.950i	0.671330	−	1.16278i	−0.306198	−	0.951968i	$-0.599057\pi$
$227$	152.392	−	263.950i	0.671330	−	1.16278i	0.977527	−	0.210809i	$-0.0676098\pi$
$228$		0			0
$229$	207.344	+	359.130i	0.905433	+	1.56826i	0.820335	+	0.571883i	$0.193787\pi$
$229$	207.344	+	359.130i	0.905433	+	1.56826i	0.0850971	+	0.996373i	$0.472880\pi$
$230$		0			0
$231$	4.10305	−	84.1572i	0.0177621	−	0.364317i
$232$		0			0
$233$	82.4628	+	142.830i	0.353918	+	0.613004i	0.986932	−	0.161136i	$-0.0515159\pi$
$233$	82.4628	+	142.830i	0.353918	+	0.613004i	−0.633014	+	0.774140i	$0.718183\pi$
$234$		0			0
$235$	120.373	+	69.4976i	0.512227	+	0.295735i
$236$		0			0
$237$	−53.1109			−0.224097
$238$		0			0
$239$	19.1182			0.0799926			0.0399963	−	0.999200i	$-0.487265\pi$
$239$	19.1182			0.0799926			0.0399963	+	0.999200i	$0.487265\pi$
$240$		0			0
$241$	−303.376	−	175.154i	−1.25882	−	0.726780i	−0.285975	−	0.958237i	$-0.592317\pi$
$241$	−303.376	−	175.154i	−1.25882	−	0.726780i	−0.972845	+	0.231457i	$0.925651\pi$
$242$		0			0
$243$	97.3804	+	168.668i	0.400743	+	0.694106i
$244$		0			0
$245$	180.908	−	252.854i	0.738401	−	1.03206i
$246$		0			0
$247$	−159.809	−	276.797i	−0.647000	−	1.12064i
$248$		0			0
$249$	16.5522	−	28.6693i	0.0664748	−	0.115138i
$250$		0			0
$251$	88.3204			0.351874			0.175937	−	0.984401i	$-0.443704\pi$
$251$	88.3204			0.351874			0.175937	+	0.984401i	$0.443704\pi$
$252$		0			0
$253$		−	316.114i		−	1.24946i
$254$		0			0
$255$	79.7158	+	46.0240i	0.312611	+	0.180486i
$256$		0			0
$257$	74.5499	−	43.0414i	0.290077	−	0.167476i	−0.347899	−	0.937532i	$-0.613105\pi$
$257$	74.5499	−	43.0414i	0.290077	−	0.167476i	0.637977	+	0.770056i	$0.279772\pi$
$258$		0			0
$259$	−16.2106	+	332.495i	−0.0625893	+	1.28376i
$260$		0			0
$261$	117.894	−	68.0661i	0.451701	−	0.260789i
$262$		0			0
$263$	159.605	−	276.444i	0.606863	−	1.05112i	−0.384891	−	0.922962i	$-0.625761\pi$
$263$	159.605	−	276.444i	0.606863	−	1.05112i	0.991754	−	0.128156i	$-0.0409057\pi$
$264$		0			0
$265$		−	235.937i		−	0.890330i
$266$		0			0
$267$		−	0.978025i		−	0.00366302i
$268$		0			0
$269$	28.7340	−	49.7687i	0.106818	−	0.185014i	−0.807662	−	0.589646i	$-0.799267\pi$
$269$	28.7340	−	49.7687i	0.106818	−	0.185014i	0.914479	+	0.404632i	$0.132601\pi$
$270$		0			0
$271$	−26.7398	+	15.4382i	−0.0986709	+	0.0569677i	−0.548523	−	0.836135i	$-0.684810\pi$
$271$	−26.7398	+	15.4382i	−0.0986709	+	0.0569677i	0.449853	+	0.893103i	$0.351477\pi$
$272$		0			0
$273$	−56.6286	−	110.146i	−0.207431	−	0.403465i
$274$		0			0
$275$	174.631	−	100.823i	0.635023	−	0.366631i
$276$		0			0
$277$	308.465	+	178.092i	1.11359	+	0.642933i	0.939757	−	0.341842i	$-0.111051\pi$
$277$	308.465	+	178.092i	1.11359	+	0.642933i	0.173834	+	0.984775i	$0.444384\pi$
$278$		0			0
$279$			105.060i			0.376561i
$280$		0			0
$281$	−294.160			−1.04683			−0.523416	−	0.852077i	$-0.675343\pi$
$281$	−294.160			−1.04683			−0.523416	+	0.852077i	$0.675343\pi$
$282$		0			0
$283$	−207.501	+	359.402i	−0.733219	+	1.26997i	0.222282	+	0.974982i	$0.428649\pi$
$283$	−207.501	+	359.402i	−0.733219	+	1.26997i	−0.955501	+	0.294989i	$0.904684\pi$
$284$		0			0
$285$	47.5490	+	82.3572i	0.166838	+	0.288973i
$286$		0			0
$287$	−38.2201	−	24.6229i	−0.133171	−	0.0857940i
$288$		0			0
$289$	−17.6691	−	30.6037i	−0.0611386	−	0.105895i
$290$		0			0
$291$	−133.720	−	77.2034i	−0.459520	−	0.265304i
$292$		0			0
$293$	−370.564			−1.26472			−0.632362	−	0.774673i	$-0.717915\pi$
$293$	−370.564			−1.26472			−0.632362	+	0.774673i	$0.717915\pi$
$294$		0			0
$295$	346.981			1.17621
$296$		0			0
$297$	−178.986	−	103.337i	−0.602645	−	0.347937i
$298$		0			0
$299$	−232.329	−	402.406i	−0.777021	−	1.34584i
$300$		0			0
$301$	−195.913	−	126.215i	−0.650875	−	0.419319i
$302$		0			0
$303$	12.8095	+	22.1867i	0.0422755	+	0.0732233i
$304$		0			0
$305$	32.5081	−	56.3057i	0.106584	−	0.184609i
$306$		0			0
$307$	160.327			0.522239			0.261120	−	0.965306i	$-0.415908\pi$
$307$	160.327			0.522239			0.261120	+	0.965306i	$0.415908\pi$
$308$		0			0
$309$		−	151.486i		−	0.490245i
$310$		0			0
$311$	−409.490	−	236.419i	−1.31669	−	0.760191i	−0.333495	−	0.942752i	$-0.608228\pi$
$311$	−409.490	−	236.419i	−1.31669	−	0.760191i	−0.983195	+	0.182561i	$0.941561\pi$
$312$		0			0
$313$	200.063	−	115.506i	0.639179	−	0.369030i	−0.145119	−	0.989414i	$-0.546357\pi$
$313$	200.063	−	115.506i	0.639179	−	0.369030i	0.784298	+	0.620384i	$0.213023\pi$
$314$		0			0
$315$	−165.924	−	322.732i	−0.526743	−	1.02455i
$316$		0			0
$317$	−195.132	+	112.659i	−0.615557	+	0.355392i	−0.775137	−	0.631793i	$-0.782319\pi$
$317$	−195.132	+	112.659i	−0.615557	+	0.355392i	0.159580	+	0.987185i	$0.448986\pi$
$318$		0			0
$319$	−110.090	+	190.681i	−0.345109	+	0.597746i
$320$		0			0
$321$			179.972i			0.560659i
$322$		0			0
$323$			262.067i			0.811353i
$324$		0			0
$325$	148.201	−	256.692i	0.456004	−	0.789822i
$326$		0			0
$327$	9.08716	−	5.24648i	0.0277895	−	0.0160443i
$328$		0			0
$329$	−7.46732	+	153.161i	−0.0226970	+	0.465536i
$330$		0			0
$331$	−17.9257	+	10.3494i	−0.0541561	+	0.0312671i	−0.526834	−	0.849968i	$-0.676621\pi$
$331$	−17.9257	+	10.3494i	−0.0541561	+	0.0312671i	0.472677	+	0.881236i	$0.343288\pi$
$332$		0			0
$333$	336.490	+	194.273i	1.01048	+	0.583401i
$334$		0			0
$335$			108.716i			0.324527i
$336$		0			0
$337$	34.9645			0.103752			0.0518762	−	0.998654i	$-0.483480\pi$
$337$	34.9645			0.103752			0.0518762	+	0.998654i	$0.483480\pi$
$338$		0			0
$339$	−6.73619	+	11.6674i	−0.0198708	+	0.0344172i
$340$		0			0
$341$	−84.9621	−	147.159i	−0.249156	−	0.431550i
$342$		0			0
$343$	339.343	+	49.9505i	0.989339	+	0.145628i
$344$		0			0
$345$	69.1264	+	119.730i	0.200366	+	0.347045i
$346$		0			0
$347$	379.958	+	219.369i	1.09498	+	0.632188i	0.934898	−	0.354916i	$-0.115491\pi$
$347$	379.958	+	219.369i	1.09498	+	0.632188i	0.160083	+	0.987104i	$0.448824\pi$
$348$		0			0
$349$	435.121			1.24677			0.623383	−	0.781917i	$-0.285758\pi$
$349$	435.121			1.24677			0.623383	+	0.781917i	$0.285758\pi$
$350$		0			0
$351$	−303.793			−0.865507
$352$		0			0
$353$	243.447	+	140.554i	0.689653	+	0.398171i	0.803482	−	0.595329i	$-0.202978\pi$
$353$	243.447	+	140.554i	0.689653	+	0.398171i	−0.113829	+	0.993500i	$0.536312\pi$
$354$		0			0
$355$	−101.701	−	176.151i	−0.286481	−	0.496200i
$356$		0			0
$357$	−4.94514	+	101.429i	−0.0138519	+	0.284115i
$358$		0			0
$359$	131.965	+	228.570i	0.367590	+	0.636685i	0.989188	−	0.146652i	$-0.0468497\pi$
$359$	131.965	+	228.570i	0.367590	+	0.636685i	−0.621598	+	0.783336i	$0.713516\pi$
$360$		0			0
$361$	45.1247	−	78.1583i	0.124999	−	0.216505i
$362$		0			0
$363$	48.8468			0.134564
$364$		0			0
$365$			679.969i			1.86293i
$366$		0			0
$367$	134.181	+	77.4694i	0.365615	+	0.211088i	0.671541	−	0.740967i	$-0.265633\pi$
$367$	134.181	+	77.4694i	0.365615	+	0.211088i	−0.305926	+	0.952055i	$0.598966\pi$
$368$		0			0
$369$	−45.9567	+	26.5331i	−0.124544	+	0.0719055i
$370$		0			0
$371$	231.490	−	119.015i	0.623962	−	0.320794i
$372$		0			0
$373$	−506.505	+	292.431i	−1.35792	+	0.783997i	−0.989344	−	0.145600i	$-0.953489\pi$
$373$	−506.505	+	292.431i	−1.35792	+	0.783997i	−0.368579	+	0.929597i	$0.620155\pi$
$374$		0			0
$375$	28.1478	−	48.7534i	0.0750608	−	0.130009i
$376$		0			0
$377$			323.644i			0.858472i
$378$		0			0
$379$			128.176i			0.338195i	0.985599	+	0.169098i	$0.0540853\pi$
$379$			128.176i			0.338195i	−0.985599	+	0.169098i	$0.945915\pi$
$380$		0			0
$381$	32.0011	−	55.4276i	0.0839925	−	0.145479i
$382$		0			0
$383$	216.437	−	124.960i	0.565110	−	0.326266i	−0.190084	−	0.981768i	$-0.560876\pi$
$383$	216.437	−	124.960i	0.565110	−	0.326266i	0.755194	+	0.655502i	$0.227543\pi$
$384$		0			0
$385$	493.403	+	317.870i	1.28157	+	0.825636i
$386$		0			0
$387$	−235.571	+	136.007i	−0.608709	+	0.351439i
$388$		0			0
$389$	−187.428	−	108.212i	−0.481821	−	0.278179i	0.239354	−	0.970932i	$-0.423064\pi$
$389$	−187.428	−	108.212i	−0.481821	−	0.278179i	−0.721175	+	0.692753i	$0.756398\pi$
$390$		0			0
$391$			380.991i			0.974402i
$392$		0			0
$393$	129.460			0.329415
$394$		0			0
$395$	184.984	−	320.401i	0.468314	−	0.811143i
$396$		0			0
$397$	−349.941	−	606.116i	−0.881463	−	1.52674i	−0.849714	−	0.527244i	$-0.823226\pi$
$397$	−349.941	−	606.116i	−0.881463	−	1.52674i	−0.0317493	−	0.999496i	$-0.510108\pi$
$398$		0			0
$399$	−56.8196	+	88.1964i	−0.142405	+	0.221044i
$400$		0			0
$401$	90.4903	+	156.734i	0.225662	+	0.390858i	0.956518	−	0.291674i	$-0.0942123\pi$
$401$	90.4903	+	156.734i	0.225662	+	0.390858i	−0.730856	+	0.682532i	$0.760879\pi$
$402$		0			0
$403$	−216.310	−	124.887i	−0.536749	−	0.309892i
$404$		0			0
$405$	−376.179			−0.928837
$406$		0			0
$407$	−628.431			−1.54406
$408$		0			0
$409$	−310.767	−	179.421i	−0.759821	−	0.438683i	0.0694104	−	0.997588i	$-0.477888\pi$
$409$	−310.767	−	179.421i	−0.759821	−	0.438683i	−0.829232	+	0.558905i	$0.811222\pi$
$410$		0			0
$411$	115.258	+	199.632i	0.280432	+	0.485723i
$412$		0			0
$413$	175.029	+	340.441i	0.423798	+	0.824312i
$414$		0			0
$415$	115.302	+	199.709i	0.277836	+	0.481226i
$416$		0			0
$417$	22.4031	−	38.8033i	0.0537245	−	0.0930535i
$418$		0			0
$419$	−780.890			−1.86370			−0.931849	−	0.362846i	$-0.881805\pi$
$419$	−780.890			−1.86370			−0.931849	+	0.362846i	$0.881805\pi$
$420$		0			0
$421$			114.961i			0.273068i	0.990635	+	0.136534i	$0.0435962\pi$
$421$			114.961i			0.273068i	−0.990635	+	0.136534i	$0.956404\pi$
$422$		0			0
$423$	155.002	+	89.4904i	0.366435	+	0.211561i
$424$		0			0
$425$	−210.472	+	121.516i	−0.495228	+	0.285920i
$426$		0			0
$427$	71.6425	+	3.49290i	0.167781	+	0.00818010i
$428$		0			0
$429$	202.482	−	116.903i	0.471985	−	0.272501i
$430$		0			0
$431$	154.856	−	268.219i	0.359295	−	0.622317i	−0.628548	−	0.777771i	$-0.716351\pi$
$431$	154.856	−	268.219i	0.359295	−	0.622317i	0.987843	+	0.155453i	$0.0496838\pi$
$432$		0			0
$433$			595.775i			1.37592i	0.725747	+	0.687962i	$0.241494\pi$
$433$			595.775i			1.37592i	−0.725747	+	0.687962i	$0.758506\pi$
$434$		0			0
$435$		−	96.2958i		−	0.221370i
$436$		0			0
$437$	−196.808	+	340.881i	−0.450361	+	0.780048i
$438$		0			0
$439$	−698.796	+	403.450i	−1.59179	+	0.919020i	−0.598789	+	0.800907i	$0.704351\pi$
$439$	−698.796	+	403.450i	−1.59179	+	0.919020i	−0.993000	+	0.118113i	$0.962315\pi$
$440$		0			0
$441$	232.951	−	325.593i	0.528233	−	0.738306i
$442$		0			0
$443$	−385.214	+	222.403i	−0.869557	+	0.502039i	−0.867201	−	0.497958i	$-0.834083\pi$
$443$	−385.214	+	222.403i	−0.869557	+	0.502039i	−0.00235617	+	0.999997i	$0.500750\pi$
$444$		0			0
$445$	5.90012	+	3.40644i	0.0132587	+	0.00765491i
$446$		0			0
$447$			37.9772i			0.0849601i
$448$		0			0
$449$	262.420			0.584455			0.292228	−	0.956349i	$-0.405604\pi$
$449$	262.420			0.584455			0.292228	+	0.956349i	$0.405604\pi$
$450$		0			0
$451$	42.9145	−	74.3302i	0.0951542	−	0.164812i
$452$		0			0
$453$	44.4633	+	77.0127i	0.0981530	+	0.170006i
$454$		0			0
$455$	861.712	+	42.0124i	1.89387	+	0.0923350i
$456$		0			0
$457$	−194.738	−	337.296i	−0.426122	−	0.738065i	0.570403	−	0.821365i	$-0.306787\pi$
$457$	−194.738	−	337.296i	−0.426122	−	0.738065i	−0.996524	+	0.0833004i	$0.973454\pi$
$458$		0			0
$459$	215.720	+	124.546i	0.469978	+	0.271342i
$460$		0			0
$461$	158.714			0.344283			0.172141	−	0.985072i	$-0.444931\pi$
$461$	158.714			0.344283			0.172141	+	0.985072i	$0.444931\pi$
$462$		0			0
$463$	528.844			1.14221			0.571106	−	0.820877i	$-0.306515\pi$
$463$	528.844			1.14221			0.571106	+	0.820877i	$0.306515\pi$
$464$		0			0
$465$	64.3601	+	37.1583i	0.138409	+	0.0799103i
$466$		0			0
$467$	218.449	+	378.365i	0.467771	+	0.810203i	0.999322	−	0.0368236i	$-0.0117240\pi$
$467$	218.449	+	378.365i	0.467771	+	0.810203i	−0.531551	+	0.847026i	$0.678391\pi$
$468$		0			0
$469$	−106.667	+	54.8401i	−0.227435	+	0.116930i
$470$		0			0
$471$	12.8274	+	22.2177i	0.0272344	+	0.0471713i
$472$		0			0
$473$	219.977	−	381.011i	0.465067	−	0.805519i
$474$		0			0
$475$	−251.085			−0.528600
$476$		0			0
$477$		−	303.811i		−	0.636920i
$478$		0			0
$479$	−472.737	−	272.935i	−0.986925	−	0.569802i	−0.0825716	−	0.996585i	$-0.526313\pi$
$479$	−472.737	−	272.935i	−0.986925	−	0.569802i	−0.904354	+	0.426783i	$0.859647\pi$
$480$		0			0
$481$	−799.980	+	461.869i	−1.66316	+	0.960226i
$482$		0			0
$483$	−82.6039	+	128.219i	−0.171023	+	0.265464i
$484$		0			0
$485$	931.488	−	537.795i	1.92059	−	1.10886i
$486$		0			0
$487$	324.115	−	561.384i	0.665534	−	1.15274i	−0.313606	−	0.949553i	$-0.601537\pi$
$487$	324.115	−	561.384i	0.665534	−	1.15274i	0.979140	−	0.203185i	$-0.0651294\pi$
$488$		0			0
$489$		−	220.822i		−	0.451579i
$490$		0			0
$491$		−	732.074i		−	1.49098i	−0.666514	−	0.745492i	$-0.732214\pi$
$491$		−	732.074i		−	1.49098i	0.666514	−	0.745492i	$-0.267786\pi$
$492$		0			0
$493$	132.684	−	229.815i	0.269136	−	0.466157i
$494$		0			0
$495$	593.279	−	342.530i	1.19854	−	0.691980i
$496$		0			0
$497$	121.529	−	188.640i	0.244526	−	0.379557i
$498$		0			0
$499$	−23.1264	+	13.3520i	−0.0463454	+	0.0267575i	−0.522994	−	0.852337i	$-0.675185\pi$
$499$	−23.1264	+	13.3520i	−0.0463454	+	0.0267575i	0.476648	+	0.879094i	$0.341852\pi$
$500$		0			0
$501$	47.4172	+	27.3763i	0.0946451	+	0.0546434i
$502$		0			0
$503$			616.414i			1.22548i	0.790286	+	0.612738i	$0.209932\pi$
$503$			616.414i			1.22548i	−0.790286	+	0.612738i	$0.790068\pi$
$504$		0			0
$505$	−178.460			−0.353387
$506$		0			0
$507$	94.8687	−	164.317i	0.187118	−	0.324097i
$508$		0			0
$509$	−66.3763	−	114.967i	−0.130405	−	0.225869i	0.793428	−	0.608665i	$-0.208295\pi$
$509$	−66.3763	−	114.967i	−0.130405	−	0.225869i	−0.923833	+	0.382796i	$0.874961\pi$
$510$		0			0
$511$	−667.152	+	342.999i	−1.30558	+	0.671230i
$512$		0			0
$513$	128.673	+	222.868i	0.250824	+	0.434440i
$514$		0			0
$515$	913.867	+	527.621i	1.77450	+	1.02451i
$516$		0			0
$517$	−289.483			−0.559928
$518$		0			0
$519$	126.942			0.244589
$520$		0			0
$521$	−585.480	−	338.027i	−1.12376	−	0.648804i	−0.181403	−	0.983409i	$-0.558064\pi$
$521$	−585.480	−	338.027i	−1.12376	−	0.648804i	−0.942359	+	0.334605i	$0.891397\pi$
$522$		0			0
$523$	186.224	+	322.550i	0.356069	+	0.616730i	0.987300	−	0.158865i	$-0.0507833\pi$
$523$	186.224	+	322.550i	0.356069	+	0.616730i	−0.631231	+	0.775595i	$0.717450\pi$
$524$		0			0
$525$	−97.1787	−	4.73791i	−0.185102	−	0.00902459i
$526$		0			0
$527$	102.399	+	177.361i	0.194306	+	0.336548i
$528$		0			0
$529$	−21.6179	+	37.4433i	−0.0408656	+	0.0707813i
$530$		0			0
$531$	446.799			0.841429
$532$		0			0
$533$		−	126.161i		−	0.236700i
$534$		0			0
$535$	−1085.71	−	626.836i	−2.02937	−	1.17166i
$536$		0			0
$537$	−230.123	+	132.862i	−0.428534	+	0.247414i
$538$		0			0
$539$	−62.9892	+	644.447i	−0.116863	+	1.19563i
$540$		0			0
$541$	−60.3373	+	34.8357i	−0.111529	+	0.0643914i	−0.554727	−	0.832032i	$-0.687177\pi$
$541$	−60.3373	+	34.8357i	−0.111529	+	0.0643914i	0.443198	+	0.896424i	$0.353844\pi$
$542$		0			0
$543$	75.9860	−	131.612i	0.139937	−	0.242379i
$544$		0			0
$545$			73.0934i			0.134116i
$546$		0			0
$547$		−	466.463i		−	0.852765i	−0.904543	−	0.426383i	$-0.859788\pi$
$547$		−	466.463i		−	0.852765i	0.904543	−	0.426383i	$-0.140212\pi$
$548$		0			0
$549$	41.8599	−	72.5034i	0.0762475	−	0.132065i
$550$		0			0
$551$	237.430	−	137.081i	0.430908	−	0.248785i
$552$		0			0
$553$	407.674	+	19.8760i	0.737204	+	0.0359421i
$554$		0			0
$555$	238.023	−	137.423i	0.428870	−	0.247608i
$556$		0			0
$557$	−118.835	−	68.6094i	−0.213348	−	0.123177i	0.389518	−	0.921019i	$-0.372642\pi$
$557$	−118.835	−	68.6094i	−0.213348	−	0.123177i	−0.602866	+	0.797842i	$0.705975\pi$
$558$		0			0
$559$		−	646.692i		−	1.15687i
$560$		0			0
$561$	−191.706			−0.341722
$562$		0			0
$563$	84.5632	−	146.468i	0.150201	−	0.260156i	−0.781100	−	0.624406i	$-0.785341\pi$
$563$	84.5632	−	146.468i	0.150201	−	0.260156i	0.931301	+	0.364250i	$0.118675\pi$
$564$		0			0
$565$	−46.9240	−	81.2747i	−0.0830513	−	0.143849i
$566$		0			0
$567$	−189.757	−	369.088i	−0.334669	−	0.650949i
$568$		0			0
$569$	−372.466	−	645.129i	−0.654597	−	1.13379i	−0.981995	−	0.188908i	$-0.939505\pi$
$569$	−372.466	−	645.129i	−0.654597	−	1.13379i	0.327398	−	0.944887i	$-0.393828\pi$
$570$		0			0
$571$	−767.828	−	443.306i	−1.34471	−	0.776367i	−0.357213	−	0.934023i	$-0.616273\pi$
$571$	−767.828	−	443.306i	−1.34471	−	0.776367i	−0.987494	+	0.157655i	$0.949606\pi$
$572$		0			0
$573$	−119.647			−0.208809
$574$		0			0
$575$	−365.026			−0.634827
$576$		0			0
$577$	−207.900	−	120.031i	−0.360311	−	0.208026i	0.308906	−	0.951093i	$-0.400037\pi$
$577$	−207.900	−	120.031i	−0.360311	−	0.208026i	−0.669217	+	0.743067i	$0.733370\pi$
$578$		0			0
$579$	−37.0900	−	64.2417i	−0.0640586	−	0.110953i
$580$		0			0
$581$	−137.782	+	213.868i	−0.237147	+	0.368104i
$582$		0			0
$583$	245.691	+	425.549i	0.421425	+	0.729930i
$584$		0			0
$585$	503.488	−	872.067i	0.860663	−	1.49071i
$586$		0			0
$587$	−190.873			−0.325168			−0.162584	−	0.986695i	$-0.551983\pi$
$587$	−190.873			−0.325168			−0.162584	+	0.986695i	$0.551983\pi$
$588$		0			0
$589$			211.585i			0.359227i
$590$		0			0
$591$	−1.65299	−	0.954353i	−0.00279693	−	0.00161481i
$592$		0			0
$593$	637.548	−	368.089i	1.07512	−	0.620723i	0.145547	−	0.989351i	$-0.453506\pi$
$593$	637.548	−	368.089i	1.07512	−	0.620723i	0.929577	+	0.368629i	$0.120173\pi$
$594$		0			0
$595$	−594.667	−	383.108i	−0.999441	−	0.643879i
$596$		0			0
$597$	100.137	−	57.8144i	0.167734	−	0.0968415i
$598$		0			0
$599$	558.330	−	967.057i	0.932104	−	1.61445i	0.152386	−	0.988321i	$-0.451304\pi$
$599$	558.330	−	967.057i	0.932104	−	1.61445i	0.779718	−	0.626131i	$-0.215362\pi$
$600$		0			0
$601$		−	183.100i		−	0.304659i	−0.988330	−	0.152329i	$-0.951323\pi$
$601$		−	183.100i		−	0.304659i	0.988330	−	0.152329i	$-0.0486774\pi$
$602$		0			0
$603$			139.991i			0.232158i
$604$		0			0
$605$	−170.132	+	294.678i	−0.281210	+	0.487071i
$606$		0			0
$607$	−394.026	+	227.491i	−0.649136	+	0.374779i	−0.788125	−	0.615515i	$-0.788948\pi$
$607$	−394.026	+	227.491i	−0.649136	+	0.374779i	0.138989	+	0.990294i	$0.455615\pi$
$608$		0			0
$609$	94.4807	−	48.5748i	0.155141	−	0.0797615i
$610$		0			0
$611$	−368.505	+	212.757i	−0.603118	+	0.348211i
$612$		0			0
$613$	232.853	+	134.438i	0.379859	+	0.219312i	0.677757	−	0.735286i	$-0.262952\pi$
$613$	232.853	+	134.438i	0.379859	+	0.219312i	−0.297898	+	0.954598i	$0.596286\pi$
$614$		0			0
$615$			37.5375i			0.0610366i
$616$		0			0
$617$	−184.934			−0.299731			−0.149866	−	0.988706i	$-0.547884\pi$
$617$	−184.934			−0.299731			−0.149866	+	0.988706i	$0.547884\pi$
$618$		0			0
$619$	496.809	−	860.498i	0.802599	−	1.39014i	−0.115301	−	0.993331i	$-0.536783\pi$
$619$	496.809	−	860.498i	0.802599	−	1.39014i	0.917900	−	0.396812i	$-0.129884\pi$
$620$		0			0
$621$	187.064	+	324.004i	0.301229	+	0.521745i
$622$		0			0
$623$	−0.366012	+	7.50723i	−0.000587499	+	0.0120501i
$624$		0			0
$625$	386.818	+	669.988i	0.618909	+	1.07198i
$626$		0			0
$627$	−171.524	−	99.0292i	−0.273562	−	0.157941i
$628$		0			0
$629$	757.408			1.20415
$630$		0			0
$631$	−805.857			−1.27711			−0.638555	−	0.769576i	$-0.720468\pi$
$631$	−805.857			−1.27711			−0.638555	+	0.769576i	$0.720468\pi$
$632$		0			0
$633$	−5.65451	−	3.26463i	−0.00893287	−	0.00515740i
$634$		0			0
$635$	222.918	+	386.106i	0.351053	+	0.608041i
$636$		0			0
$637$	393.455	+	866.662i	0.617669	+	1.36054i
$638$		0			0
$639$	−130.957	−	226.825i	−0.204941	−	0.354969i
$640$		0			0
$641$	−2.75221	+	4.76696i	−0.00429361	+	0.00743676i	−0.868164	−	0.496277i	$-0.834700\pi$
$641$	−2.75221	+	4.76696i	−0.00429361	+	0.00743676i	0.863871	+	0.503714i	$0.168033\pi$
$642$		0			0
$643$	1024.08			1.59266			0.796331	−	0.604861i	$-0.206771\pi$
$643$	1024.08			1.59266			0.796331	+	0.604861i	$0.206771\pi$
$644$		0			0
$645$			192.414i			0.298317i
$646$		0			0
$647$	−395.404	−	228.287i	−0.611134	−	0.352839i	0.162275	−	0.986746i	$-0.448117\pi$
$647$	−395.404	−	228.287i	−0.611134	−	0.352839i	−0.773409	+	0.633907i	$0.781450\pi$
$648$		0			0
$649$	−625.834	+	361.325i	−0.964304	+	0.556741i
$650$		0			0
$651$	−3.99255	+	81.8908i	−0.00613295	+	0.125792i
$652$		0			0
$653$	−24.4603	+	14.1222i	−0.0374584	+	0.0216266i	−0.518612	−	0.855010i	$-0.673551\pi$
$653$	−24.4603	+	14.1222i	−0.0374584	+	0.0216266i	0.481154	+	0.876636i	$0.340218\pi$
$654$		0			0
$655$	−450.907	+	780.994i	−0.688407	+	1.19236i
$656$		0			0
$657$			875.579i			1.33269i
$658$		0			0
$659$			132.188i			0.200589i	0.994958	+	0.100295i	$0.0319785\pi$
$659$			132.188i			0.200589i	−0.994958	+	0.100295i	$0.968021\pi$
$660$		0			0
$661$	346.924	−	600.889i	0.524847	−	0.909061i	−0.474735	−	0.880129i	$-0.657456\pi$
$661$	346.924	−	600.889i	0.524847	−	0.909061i	0.999581	−	0.0289321i	$-0.00921065\pi$
$662$		0			0
$663$	−244.038	+	140.895i	−0.368082	+	0.212512i
$664$		0			0
$665$	−334.160	−	649.960i	−0.502497	−	0.977384i
$666$		0			0
$667$	345.175	−	199.287i	0.517504	−	0.298781i
$668$		0			0
$669$	−220.652	−	127.393i	−0.329823	−	0.190424i
$670$		0			0
$671$			135.408i			0.201800i
$672$		0			0
$673$	532.137			0.790694			0.395347	−	0.918532i	$-0.370624\pi$
$673$	532.137			0.790694			0.395347	+	0.918532i	$0.370624\pi$
$674$		0			0
$675$	−119.327	+	206.680i	−0.176780	+	0.306192i
$676$		0			0
$677$	−143.115	−	247.883i	−0.211396	−	0.366149i	0.740756	−	0.671775i	$-0.234468\pi$
$677$	−143.115	−	247.883i	−0.211396	−	0.366149i	−0.952152	+	0.305626i	$0.901134\pi$
$678$		0			0
$679$	997.531	+	642.649i	1.46912	+	0.946464i
$680$		0			0
$681$	−138.808	−	240.423i	−0.203830	−	0.353043i
$682$		0			0
$683$	−387.838	−	223.918i	−0.567844	−	0.327845i	0.188443	−	0.982084i	$-0.439656\pi$
$683$	−387.838	−	223.918i	−0.567844	−	0.327845i	−0.756288	+	0.654239i	$0.772989\pi$
$684$		0			0
$685$	−1605.76			−2.34417
$686$		0			0
$687$	377.724			0.549817
$688$		0			0
$689$	625.519	+	361.143i	0.907865	+	0.524156i
$690$		0			0
$691$	−510.366	−	883.980i	−0.738591	−	1.27928i	−0.953130	−	0.302561i	$-0.902158\pi$
$691$	−510.366	−	883.980i	−0.738591	−	1.27928i	0.214539	−	0.976715i	$-0.431175\pi$
$692$		0			0
$693$	635.343	+	409.313i	0.916801	+	0.590639i
$694$		0			0
$695$	156.059	+	270.302i	0.224545	+	0.388924i
$696$		0			0
$697$	−51.7221	+	89.5854i	−0.0742068	+	0.128530i
$698$		0			0
$699$	150.225			0.214914
$700$		0			0
$701$		−	1311.02i		−	1.87021i	−0.354369	−	0.935106i	$-0.615304\pi$
$701$		−	1311.02i		−	1.87021i	0.354369	−	0.935106i	$-0.384696\pi$
$702$		0			0
$703$	677.669	+	391.252i	0.963967	+	0.556546i
$704$		0			0
$705$	109.644	−	63.3028i	0.155523	−	0.0897912i
$706$		0			0
$707$	−90.0213	−	175.096i	−0.127329	−	0.247661i
$708$		0			0
$709$	−465.495	+	268.754i	−0.656552	+	0.379061i	−0.790962	−	0.611865i	$-0.790419\pi$
$709$	−465.495	+	268.754i	−0.656552	+	0.379061i	0.134410	+	0.990926i	$0.457086\pi$
$710$		0			0
$711$	238.199	−	412.573i	0.335020	−	0.580271i
$712$		0			0
$713$			307.601i			0.431417i
$714$		0			0
$715$			1628.68i			2.27787i
$716$		0			0
$717$	8.70704	−	15.0810i	0.0121437	−	0.0210335i
$718$		0			0
$719$	233.275	−	134.681i	0.324443	−	0.187318i	−0.328928	−	0.944355i	$-0.606687\pi$
$719$	233.275	−	134.681i	0.324443	−	0.187318i	0.653371	+	0.757037i	$0.273354\pi$
$720$		0			0
$721$	−56.6914	+	1162.79i	−0.0786288	+	1.61275i
$722$		0			0
$723$	−276.334	+	159.541i	−0.382204	+	0.220666i
$724$		0			0
$725$	220.185	+	127.124i	0.303703	+	0.175343i
$726$		0			0
$727$			460.316i			0.633172i	0.948564	+	0.316586i	$0.102537\pi$
$727$			460.316i			0.633172i	−0.948564	+	0.316586i	$0.897463\pi$
$728$		0			0
$729$	−356.185			−0.488594
$730$		0			0
$731$	−265.124	+	459.208i	−0.362686	+	0.628191i
$732$		0			0
$733$	−33.3410	−	57.7484i	−0.0454857	−	0.0787836i	0.842386	−	0.538874i	$-0.181150\pi$
$733$	−33.3410	−	57.7484i	−0.0454857	−	0.0787836i	−0.887872	+	0.460091i	$0.847817\pi$
$734$		0			0
$735$	−117.067	−	257.863i	−0.159275	−	0.350834i
$736$		0			0
$737$	−113.211	−	196.087i	−0.153610	−	0.266061i
$738$		0			0
$739$	808.772	+	466.944i	1.09441	+	0.631860i	0.934748	−	0.355311i	$-0.115625\pi$
$739$	808.772	+	466.944i	1.09441	+	0.631860i	0.159665	+	0.987171i	$0.448958\pi$
$740$		0			0
$741$	−291.128			−0.392885
$742$		0			0
$743$	1198.23			1.61269			0.806345	−	0.591446i	$-0.201443\pi$
$743$	1198.23			1.61269			0.806345	+	0.591446i	$0.201443\pi$
$744$		0			0
$745$	−229.104	−	132.273i	−0.307523	−	0.177548i
$746$		0			0
$747$	148.471	+	257.160i	0.198757	+	0.344257i
$748$		0			0
$749$	67.3518	−	1381.44i	0.0899222	−	1.84438i
$750$		0			0
$751$	−84.2993	−	146.011i	−0.112249	−	0.194422i	0.804427	−	0.594051i	$-0.202472\pi$
$751$	−84.2993	−	146.011i	−0.112249	−	0.194422i	−0.916677	+	0.399629i	$0.869139\pi$
$752$		0			0
$753$	40.2239	−	69.6698i	0.0534182	−	0.0925230i
$754$		0			0
$755$	−619.458			−0.820474
$756$		0			0
$757$			209.207i			0.276364i	0.990407	+	0.138182i	$0.0441259\pi$
$757$			209.207i			0.276364i	−0.990407	+	0.138182i	$0.955874\pi$
$758$		0			0
$759$	−249.360	−	143.968i	−0.328538	−	0.189681i
$760$		0			0
$761$	479.127	−	276.624i	0.629602	−	0.363501i	−0.150996	−	0.988534i	$-0.548248\pi$
$761$	479.127	−	276.624i	0.629602	−	0.363501i	0.780598	+	0.625033i	$0.214915\pi$
$762$		0			0
$763$	−71.7156	+	36.8707i	−0.0939916	+	0.0483233i
$764$		0			0
$765$	−715.041	+	412.829i	−0.934695	+	0.539646i
$766$		0			0
$767$	−531.115	+	919.919i	−0.692458	+	1.19937i
$768$		0			0
$769$			219.524i			0.285467i	0.989761	+	0.142734i	$0.0455892\pi$
$769$			219.524i			0.285467i	−0.989761	+	0.142734i	$0.954411\pi$
$770$		0			0
$771$		−	78.4096i		−	0.101699i
$772$		0			0
$773$	−333.337	+	577.357i	−0.431225	+	0.746904i	−0.996979	−	0.0776701i	$-0.975252\pi$
$773$	−333.337	+	577.357i	−0.431225	+	0.746904i	0.565754	+	0.824574i	$0.308585\pi$
$774$		0			0
$775$	−169.928	+	98.1082i	−0.219262	+	0.126591i
$776$		0			0
$777$	254.899	+	164.216i	0.328055	+	0.211346i
$778$		0			0
$779$	−92.5538	+	53.4359i	−0.118811	+	0.0685956i
$780$		0			0
$781$	366.866	+	211.810i	0.469738	+	0.271204i
$782$		0			0
$783$		−	260.587i		−	0.332806i
$784$		0			0
$785$	−178.710			−0.227656
$786$		0			0
$787$	−459.932	+	796.626i	−0.584412	+	1.01223i	0.410536	+	0.911844i	$0.365341\pi$
$787$	−459.932	+	796.626i	−0.584412	+	1.01223i	−0.994948	+	0.100387i	$0.967992\pi$
$788$		0			0
$789$	−145.378	−	251.803i	−0.184256	−	0.319141i
$790$		0			0
$791$	56.0727	−	87.0371i	0.0708884	−	0.110034i
$792$		0			0
$793$	99.5187	+	172.371i	0.125496	+	0.217366i
$794$		0			0
$795$	−186.115	−	107.453i	−0.234106	−	0.135161i
$796$		0			0
$797$	1016.13			1.27494			0.637470	−	0.770476i	$-0.279981\pi$
$797$	1016.13			1.27494			0.637470	+	0.770476i	$0.279981\pi$
$798$		0			0
$799$	348.895			0.436664
$800$		0			0
$801$	7.59744	+	4.38638i	0.00948494	+	0.00547613i
$802$		0			0
$803$	−708.078	−	1226.43i	−0.881791	−	1.52731i
$804$		0			0
$805$	−485.800	−	944.909i	−0.603478	−	1.17380i
$806$		0			0
$807$	−26.1727	−	45.3325i	−0.0324321	−	0.0561741i
$808$		0			0
$809$	−565.950	+	980.254i	−0.699567	+	1.21169i	0.269049	+	0.963126i	$0.413291\pi$
$809$	−565.950	+	980.254i	−0.699567	+	1.21169i	−0.968617	+	0.248560i	$0.920043\pi$
$810$		0			0
$811$	−481.066			−0.593176			−0.296588	−	0.955006i	$-0.595849\pi$
$811$	−481.066			−0.593176			−0.296588	+	0.955006i	$0.595849\pi$
$812$		0			0
$813$			28.1242i			0.0345931i
$814$		0			0
$815$	1332.15	+	769.117i	1.63454	+	0.943702i
$816$		0			0
$817$	−474.423	+	273.908i	−0.580690	+	0.335261i
$818$		0			0
$819$	1109.60	+	54.0983i	1.35483	+	0.0660541i
$820$		0			0
$821$	−630.185	+	363.838i	−0.767582	+	0.443164i	−0.832011	−	0.554758i	$-0.812811\pi$
$821$	−630.185	+	363.838i	−0.767582	+	0.443164i	0.0644292	+	0.997922i	$0.479477\pi$
$822$		0			0
$823$	−313.323	+	542.692i	−0.380709	+	0.659407i	−0.991164	−	0.132644i	$-0.957653\pi$
$823$	−313.323	+	542.692i	−0.380709	+	0.659407i	0.610455	+	0.792051i	$0.290987\pi$
$824$		0			0
$825$		−	183.673i		−	0.222633i
$826$		0			0
$827$		−	1468.52i		−	1.77572i	−0.460116	−	0.887859i	$-0.652192\pi$
$827$		−	1468.52i		−	1.77572i	0.460116	−	0.887859i	$-0.347808\pi$
$828$		0			0
$829$	−409.352	+	709.019i	−0.493790	+	0.855270i	−0.999974	−	0.00715566i	$-0.997722\pi$
$829$	−409.352	+	709.019i	−0.493790	+	0.855270i	0.506184	+	0.862425i	$0.331056\pi$
$830$		0			0
$831$	280.969	−	162.218i	0.338110	−	0.195208i
$832$		0			0
$833$	75.9169	−	776.710i	0.0911367	−	0.932425i
$834$		0			0
$835$	−330.306	+	190.702i	−0.395576	+	0.228386i
$836$		0			0
$837$	174.165	+	100.554i	0.208083	+	0.120137i
$838$		0			0
$839$			1108.84i			1.32162i	0.750555	+	0.660808i	$0.229786\pi$
$839$			1108.84i			1.32162i	−0.750555	+	0.660808i	$0.770214\pi$
$840$		0			0
$841$	563.386			0.669900
$842$		0			0
$843$	−133.970	+	232.042i	−0.158920	+	0.275258i
$844$		0			0
$845$	660.850	+	1144.63i	0.782072	+	1.35459i
$846$		0			0
$847$	−374.943	−	18.2802i	−0.442672	−	0.0215823i
$848$		0			0
$849$	189.005	+	327.366i	0.222621	+	0.385590i
$850$		0			0
$851$	985.191	+	568.800i	1.15769	+	0.668390i
$852$		0			0
$853$	610.400			0.715592			0.357796	−	0.933800i	$-0.383528\pi$
$853$	610.400			0.715592			0.357796	+	0.933800i	$0.383528\pi$
$854$		0			0
$855$	−853.017			−0.997680
$856$		0			0
$857$	384.614	+	222.057i	0.448791	+	0.259110i	0.707319	−	0.706894i	$-0.249904\pi$
$857$	384.614	+	222.057i	0.448791	+	0.259110i	−0.258529	+	0.966004i	$0.583238\pi$
$858$		0			0
$859$	−40.7547	−	70.5892i	−0.0474443	−	0.0821760i	0.841328	−	0.540525i	$-0.181774\pi$
$859$	−40.7547	−	70.5892i	−0.0474443	−	0.0821760i	−0.888772	+	0.458349i	$0.848441\pi$
$860$		0			0
$861$	−36.8299	+	18.9351i	−0.0427757	+	0.0219920i
$862$		0			0
$863$	−525.730	−	910.592i	−0.609189	−	1.05515i	−0.991374	−	0.131061i	$-0.958162\pi$
$863$	−525.730	−	910.592i	−0.609189	−	1.05515i	0.382185	−	0.924086i	$-0.375172\pi$
$864$		0			0
$865$	−442.134	+	765.799i	−0.511138	+	0.885317i
$866$		0			0
$867$	−32.1882			−0.0371259
$868$		0			0
$869$			770.524i			0.886679i
$870$		0			0
$871$	−288.230	−	166.409i	−0.330918	−	0.191056i
$872$		0			0
$873$	1199.45	−	692.505i	1.37395	−	0.793248i
$874$		0			0
$875$	−234.305	+	363.693i	−0.267777	+	0.415649i
$876$		0			0
$877$	1350.68	−	779.814i	1.54011	−	0.889183i	0.541280	−	0.840842i	$-0.317940\pi$
$877$	1350.68	−	779.814i	1.54011	−	0.889183i	0.998831	−	0.0483410i	$-0.0153934\pi$
$878$		0			0
$879$	−168.767	+	292.312i	−0.191998	+	0.332551i
$880$		0			0
$881$		−	1515.22i		−	1.71989i	−0.510389	−	0.859944i	$-0.670499\pi$
$881$		−	1515.22i		−	1.71989i	0.510389	−	0.859944i	$-0.329501\pi$
$882$		0			0
$883$			763.828i			0.865037i	0.901625	+	0.432519i	$0.142375\pi$
$883$			763.828i			0.865037i	−0.901625	+	0.432519i	$0.857625\pi$
$884$		0			0
$885$	158.026	−	273.709i	0.178561	−	0.309276i
$886$		0			0
$887$	−496.554	+	286.686i	−0.559813	+	0.323208i	−0.753070	−	0.657940i	$-0.771428\pi$
$887$	−496.554	+	286.686i	−0.559813	+	0.323208i	0.193258	+	0.981148i	$0.438095\pi$
$888$		0			0
$889$	−266.381	+	413.481i	−0.299641	+	0.465108i
$890$		0			0
$891$	678.496	−	391.730i	0.761500	−	0.439652i
$892$		0			0
$893$	312.163	+	180.228i	0.349567	+	0.201823i
$894$		0			0
$895$		−	1851.01i		−	2.06817i
$896$		0			0
$897$	−423.240			−0.471840
$898$		0			0
$899$	107.125	−	185.546i	0.119160	−	0.206391i
$900$		0			0
$901$	−296.115	−	512.887i	−0.328652	−	0.569242i
$902$		0			0
$903$	−188.787	+	97.0600i	−0.209067	+	0.107486i
$904$		0			0
$905$	529.315	+	916.800i	0.584878	+	1.01304i
$906$		0			0
$907$	−885.036	−	510.976i	−0.975784	−	0.563369i	−0.0747894	−	0.997199i	$-0.523828\pi$
$907$	−885.036	−	510.976i	−0.975784	−	0.563369i	−0.900995	+	0.433830i	$0.857162\pi$
$908$		0			0
$909$	−229.799			−0.252804
$910$		0			0
$911$	−630.111			−0.691669			−0.345835	−	0.938295i	$-0.612404\pi$
$911$	−630.111			−0.691669			−0.345835	+	0.938295i	$0.612404\pi$
$912$		0			0
$913$	−415.930	−	240.137i	−0.455564	−	0.263020i
$914$		0			0
$915$	−29.6104	−	51.2868i	−0.0323611	−	0.0560511i
$916$		0			0
$917$	−993.725	−	48.4486i	−1.08367	−	0.0528339i
$918$		0			0
$919$	−421.489	−	730.041i	−0.458639	−	0.794386i	0.540250	−	0.841504i	$-0.318330\pi$
$919$	−421.489	−	730.041i	−0.458639	−	0.794386i	−0.998889	+	0.0471182i	$0.984996\pi$
$920$		0			0
$921$	73.0182	−	126.471i	0.0792814	−	0.137319i
$922$		0			0
$923$	622.683			0.674630
$924$		0			0
$925$			725.668i			0.784506i
$926$		0			0
$927$	1176.76	+	679.405i	1.26943	+	0.732907i
$928$		0			0
$929$	670.867	−	387.325i	0.722139	−	0.416927i	−0.0934003	−	0.995629i	$-0.529774\pi$
$929$	670.867	−	387.325i	0.722139	−	0.416927i	0.815540	+	0.578701i	$0.196440\pi$
$930$		0			0
$931$	469.148	−	655.723i	0.503918	−	0.704321i
$932$		0			0
$933$	−372.990	+	215.346i	−0.399774	+	0.230810i
$934$		0			0
$935$	667.708	−	1156.50i	0.714126	−	1.23690i
$936$		0			0
$937$		−	1586.27i		−	1.69293i	−0.532447	−	0.846463i	$-0.678727\pi$
$937$		−	1586.27i		−	1.69293i	0.532447	−	0.846463i	$-0.321273\pi$
$938$		0			0
$939$		−	210.421i		−	0.224090i
$940$		0			0
$941$	410.023	−	710.181i	0.435731	−	0.754708i	−0.561624	−	0.827393i	$-0.689823\pi$
$941$	410.023	−	710.181i	0.435731	−	0.754708i	0.997355	+	0.0726842i	$0.0231565\pi$
$942$		0			0
$943$	−134.554	+	77.6849i	−0.142687	+	0.0823805i
$944$		0			0
$945$	−693.821	−	33.8270i	−0.734202	−	0.0357957i
$946$		0			0
$947$	551.949	−	318.668i	0.582839	−	0.336502i	−0.179422	−	0.983772i	$-0.557423\pi$
$947$	551.949	−	318.668i	0.582839	−	0.336502i	0.762261	+	0.647270i	$0.224089\pi$
$948$		0			0
$949$	−1802.74	−	1040.81i	−1.89962	−	1.09675i
$950$		0			0
$951$			205.234i			0.215809i
$952$		0			0
$953$	−350.626			−0.367918			−0.183959	−	0.982934i	$-0.558891\pi$
$953$	−350.626			−0.367918			−0.183959	+	0.982934i	$0.558891\pi$
$954$		0			0
$955$	416.729	−	721.796i	0.436365	−	0.755807i
$956$		0			0
$957$	100.277	+	173.684i	0.104782	+	0.181488i
$958$		0			0
$959$	−809.997	−	1575.49i	−0.844627	−	1.64285i
$960$		0			0
$961$	−397.826	−	689.055i	−0.413971	−	0.717019i
$962$		0			0
$963$	−1398.04	−	807.161i	−1.45176	−	0.838174i
$964$		0			0
$965$	516.734			0.535475
$966$		0			0
$967$	649.816			0.671992			0.335996	−	0.941863i	$-0.390927\pi$
$967$	649.816			0.671992			0.335996	+	0.941863i	$0.390927\pi$
$968$		0			0
$969$	206.726	+	119.354i	0.213340	+	0.123172i
$970$		0			0
$971$	485.305	+	840.573i	0.499799	+	0.865677i	1.00000		0.000232071i	$-7.38706e-5\pi$
$971$	485.305	+	840.573i	0.499799	+	0.865677i	−0.500201	+	0.865909i	$0.666741\pi$
$972$		0			0
$973$	−186.486	+	289.466i	−0.191660	+	0.297499i
$974$		0			0
$975$	−134.991	−	233.811i	−0.138452	−	0.239807i
$976$		0			0
$977$	300.437	−	520.373i	0.307510	−	0.532623i	−0.670307	−	0.742084i	$-0.733838\pi$
$977$	300.437	−	520.373i	0.307510	−	0.532623i	0.977817	+	0.209461i	$0.0671709\pi$
$978$		0			0
$979$	−14.1890			−0.0144934
$980$		0			0
$981$			94.1205i			0.0959434i
$982$		0			0
$983$	−1098.66	−	634.311i	−1.11766	−	0.645281i	−0.176857	−	0.984236i	$-0.556593\pi$
$983$	−1098.66	−	634.311i	−1.11766	−	0.645281i	−0.940802	+	0.338955i	$0.889926\pi$
$984$		0			0
$985$	11.5146	−	6.64797i	0.0116900	−	0.00674921i
$986$		0			0
$987$	117.417	+	75.6449i	0.118964	+	0.0766413i
$988$		0			0
$989$	−689.714	+	398.207i	−0.697385	+	0.402636i
$990$		0			0
$991$	−774.555	+	1341.57i	−0.781590	+	1.35375i	0.149426	+	0.988773i	$0.452258\pi$
$991$	−774.555	+	1341.57i	−0.781590	+	1.35375i	−0.931015	+	0.364980i	$0.881076\pi$
$992$		0			0
$993$			18.8538i			0.0189867i
$994$		0			0
$995$			805.464i			0.809512i
$996$		0			0
$997$	470.469	−	814.876i	0.471885	−	0.817328i	−0.527598	−	0.849494i	$-0.676907\pi$
$997$	470.469	−	814.876i	0.471885	−	0.817328i	0.999483	+	0.0321661i	$0.0102406\pi$
$998$		0			0
$999$	644.116	−	371.881i	0.644761	−	0.372253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.n.a.17.9		28
4.3	odd	2		56.3.j.a.45.4	yes	28
7.3	odd	6		1568.3.h.a.881.17		28
7.4	even	3		1568.3.h.a.881.11		28
7.5	odd	6	inner	224.3.n.a.145.6		28
8.3	odd	2		56.3.j.a.45.6	yes	28
8.5	even	2	inner	224.3.n.a.17.6		28
28.3	even	6		392.3.h.a.293.25		28
28.11	odd	6		392.3.h.a.293.26		28
28.19	even	6		56.3.j.a.5.6	yes	28
28.23	odd	6		392.3.j.e.117.6		28
28.27	even	2		392.3.j.e.325.4		28
56.3	even	6		392.3.h.a.293.28		28
56.5	odd	6	inner	224.3.n.a.145.9		28
56.11	odd	6		392.3.h.a.293.27		28
56.19	even	6		56.3.j.a.5.4	✓	28
56.27	even	2		392.3.j.e.325.6		28
56.45	odd	6		1568.3.h.a.881.12		28
56.51	odd	6		392.3.j.e.117.4		28
56.53	even	6		1568.3.h.a.881.18		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.4	✓	28	56.19	even	6
56.3.j.a.5.6	yes	28	28.19	even	6
56.3.j.a.45.4	yes	28	4.3	odd	2
56.3.j.a.45.6	yes	28	8.3	odd	2
224.3.n.a.17.6		28	8.5	even	2	inner
224.3.n.a.17.9		28	1.1	even	1	trivial
224.3.n.a.145.6		28	7.5	odd	6	inner
224.3.n.a.145.9		28	56.5	odd	6	inner
392.3.h.a.293.25		28	28.3	even	6
392.3.h.a.293.26		28	28.11	odd	6
392.3.h.a.293.27		28	56.11	odd	6
392.3.h.a.293.28		28	56.3	even	6
392.3.j.e.117.4		28	56.51	odd	6
392.3.j.e.117.6		28	28.23	odd	6
392.3.j.e.325.4		28	28.27	even	2
392.3.j.e.325.6		28	56.27	even	2
1568.3.h.a.881.11		28	7.4	even	3
1568.3.h.a.881.12		28	56.45	odd	6
1568.3.h.a.881.17		28	7.3	odd	6
1568.3.h.a.881.18		28	56.53	even	6

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.455431 - 0.788830i) q^{3} +(3.17251 + 5.49495i) q^{5} +(-3.79106 + 5.88455i) q^{7} +(4.08516 + 7.07571i) q^{9} +O(q^{10})\)	\(q+(0.455431 - 0.788830i) q^{3} +(3.17251 + 5.49495i) q^{5} +(-3.79106 + 5.88455i) q^{7} +(4.08516 + 7.07571i) q^{9} +(-11.4442 - 6.60732i) q^{11} -19.4243 q^{13} +5.77945 q^{15} +(13.7930 + 7.96338i) q^{17} +(8.22725 + 14.2500i) q^{19} +(2.91534 + 5.67051i) q^{21} +(11.9607 + 20.7166i) q^{23} +(-7.62967 + 13.2150i) q^{25} +15.6398 q^{27} -16.6618i q^{29} +(11.1360 + 6.42939i) q^{31} +(-10.4241 + 6.01837i) q^{33} +(-44.3625 - 2.16288i) q^{35} +(41.1844 - 23.7778i) q^{37} +(-8.84646 + 15.3225i) q^{39} +6.49499i q^{41} +33.2928i q^{43} +(-25.9205 + 44.8956i) q^{45} +(18.9713 - 10.9531i) q^{47} +(-20.2558 - 44.6173i) q^{49} +(12.5635 - 7.25355i) q^{51} +(-32.2028 - 18.5923i) q^{53} -83.8473i q^{55} +14.9878 q^{57} +(27.3428 - 47.3591i) q^{59} +(-5.12340 - 8.87399i) q^{61} +(-57.1245 - 2.78508i) q^{63} +(-61.6240 - 106.736i) q^{65} +(14.8386 + 8.56706i) q^{67} +21.7892 q^{69} -32.0568 q^{71} +(92.8082 + 53.5828i) q^{73} +(6.94958 + 12.0370i) q^{75} +(82.2668 - 42.2953i) q^{77} +(-29.1542 - 50.4965i) q^{79} +(-29.6436 + 51.3443i) q^{81} +36.3441 q^{83} +101.056i q^{85} +(-13.1433 - 7.58829i) q^{87} +(0.929882 - 0.536867i) q^{89} +(73.6388 - 114.303i) q^{91} +(10.1434 - 5.85629i) q^{93} +(-52.2021 + 90.4167i) q^{95} -169.517i q^{97} -107.968i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{7} - 32 q^{9}+O(q^{10}) \) 28 * q + 4 * q^7 - 32 * q^9	\( 28 q + 4 q^{7} - 32 q^{9} - 28 q^{15} - 6 q^{17} - 30 q^{23} - 32 q^{25} + 6 q^{31} - 6 q^{33} + 20 q^{39} + 294 q^{47} - 20 q^{49} + 124 q^{57} - 432 q^{63} - 52 q^{65} + 136 q^{71} + 234 q^{73} + 162 q^{79} - 18 q^{81} - 48 q^{87} - 150 q^{89} - 290 q^{95}+O(q^{100}) \) 28 * q + 4 * q^7 - 32 * q^9 - 28 * q^15 - 6 * q^17 - 30 * q^23 - 32 * q^25 + 6 * q^31 - 6 * q^33 + 20 * q^39 + 294 * q^47 - 20 * q^49 + 124 * q^57 - 432 * q^63 - 52 * q^65 + 136 * q^71 + 234 * q^73 + 162 * q^79 - 18 * q^81 - 48 * q^87 - 150 * q^89 - 290 * q^95

Introduction

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