LMFDB - Embedded newform 936.2.q.g.313.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(313,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.313"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22,0,0,0,-3,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			313.7
Character	$\chi$	$=$	936.313
Dual form			936.2.q.g.625.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.400278 + 1.68516i) q^{3} +(0.618351 + 1.07102i) q^{5} +(2.31092 - 4.00263i) q^{7} +(-2.67955 + 1.34907i) q^{9} +(-0.517400 + 0.896163i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-1.55732 + 1.47073i) q^{15} +7.43820 q^{17} +4.41618 q^{19} +(7.67010 + 2.29211i) q^{21} +(2.42822 + 4.20580i) q^{23} +(1.73528 - 3.00560i) q^{25} +(-3.34597 - 3.97549i) q^{27} +(-3.04612 + 5.27603i) q^{29} +(3.58751 + 6.21374i) q^{31} +(-1.71728 - 0.513189i) q^{33} +5.71584 q^{35} -8.61130 q^{37} +(1.25926 - 1.18923i) q^{39} +(-0.532259 - 0.921899i) q^{41} +(1.34187 - 2.32419i) q^{43} +(-3.10178 - 2.03565i) q^{45} +(4.00605 - 6.93867i) q^{47} +(-7.18071 - 12.4374i) q^{49} +(2.97735 + 12.5346i) q^{51} -10.4399 q^{53} -1.27974 q^{55} +(1.76770 + 7.44199i) q^{57} +(4.04267 + 7.00211i) q^{59} +(-5.92025 + 10.2542i) q^{61} +(-0.792412 + 13.8429i) q^{63} +(0.618351 - 1.07102i) q^{65} +(-0.406963 - 0.704881i) q^{67} +(-6.11549 + 5.77543i) q^{69} +10.3144 q^{71} +8.15391 q^{73} +(5.75953 + 1.72116i) q^{75} +(2.39134 + 4.14192i) q^{77} +(-3.78968 + 6.56392i) q^{79} +(5.36003 - 7.22981i) q^{81} +(2.56200 - 4.43752i) q^{83} +(4.59942 + 7.96643i) q^{85} +(-10.1103 - 3.02133i) q^{87} -3.37420 q^{89} -4.62184 q^{91} +(-9.03518 + 8.53276i) q^{93} +(2.73075 + 4.72980i) q^{95} +(4.96536 - 8.60025i) q^{97} +(0.177416 - 3.09932i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{5} - 4 q^{7} - 4 q^{9} + 5 q^{11} - 11 q^{13} + 5 q^{15} + 8 q^{17} + 10 q^{19} + 4 q^{21} + 9 q^{23} - 24 q^{25} - 12 q^{27} - 16 q^{29} - q^{31} + 9 q^{33} + 18 q^{37} + 3 q^{39} - 6 q^{41}+ \cdots - 109 q^{99}+O(q^{100}) $ 22 * q - 3 * q^5 - 4 * q^7 - 4 * q^9 + 5 * q^11 - 11 * q^13 + 5 * q^15 + 8 * q^17 + 10 * q^19 + 4 * q^21 + 9 * q^23 - 24 * q^25 - 12 * q^27 - 16 * q^29 - q^31 + 9 * q^33 + 18 * q^37 + 3 * q^39 - 6 * q^41 - 7 * q^43 - 21 * q^45 + 21 * q^47 - 27 * q^49 - 11 * q^51 + 32 * q^53 + 34 * q^55 + 2 * q^57 + 11 * q^59 - 2 * q^61 - 27 * q^63 - 3 * q^65 - 18 * q^67 + 7 * q^69 - 30 * q^71 + 18 * q^73 + 62 * q^75 - 9 * q^77 - 30 * q^79 + 4 * q^81 - 16 * q^83 - 32 * q^85 + 33 * q^87 + 26 * q^89 + 8 * q^91 + 20 * q^95 - 10 * q^97 - 109 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.400278	+	1.68516i	0.231101	+	0.972930i
$3$	0.400278	+	1.68516i	0.231101	+	0.972930i
$4$		0			0
$5$	0.618351	+	1.07102i	0.276535	+	0.478973i	0.970521	−	0.241016i	$-0.0774805\pi$
$5$	0.618351	+	1.07102i	0.276535	+	0.478973i	−0.693986	+	0.719988i	$0.744147\pi$
$6$		0			0
$7$	2.31092	−	4.00263i	0.873446	−	1.51285i	0.0150373	−	0.999887i	$-0.495213\pi$
$7$	2.31092	−	4.00263i	0.873446	−	1.51285i	0.858409	−	0.512966i	$-0.171453\pi$
$8$		0			0
$9$	−2.67955	+	1.34907i	−0.893185	+	0.449690i
$10$		0			0
$11$	−0.517400	+	0.896163i	−0.156002	+	0.270203i	−0.933423	−	0.358777i	$-0.883194\pi$
$11$	−0.517400	+	0.896163i	−0.156002	+	0.270203i	0.777422	+	0.628980i	$0.216527\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$		0			0
$15$	−1.55732	+	1.47073i	−0.402099	+	0.379740i
$16$		0			0
$17$	7.43820			1.80403			0.902015	−	0.431705i	$-0.142088\pi$
$17$	7.43820			1.80403			0.902015	+	0.431705i	$0.142088\pi$
$18$		0			0
$19$	4.41618			1.01314			0.506571	−	0.862198i	$-0.330913\pi$
$19$	4.41618			1.01314			0.506571	+	0.862198i	$0.330913\pi$
$20$		0			0
$21$	7.67010	+	2.29211i	1.67375	+	0.500180i
$22$		0			0
$23$	2.42822	+	4.20580i	0.506318	+	0.876969i	0.999973	+	0.00731127i	$0.00232727\pi$
$23$	2.42822	+	4.20580i	0.506318	+	0.876969i	−0.493655	+	0.869658i	$0.664339\pi$
$24$		0			0
$25$	1.73528	−	3.00560i	0.347057	−	0.601120i
$26$		0			0
$27$	−3.34597	−	3.97549i	−0.643932	−	0.765083i
$28$		0			0
$29$	−3.04612	+	5.27603i	−0.565650	+	0.979734i	0.431339	+	0.902190i	$0.358041\pi$
$29$	−3.04612	+	5.27603i	−0.565650	+	0.979734i	−0.996989	+	0.0775442i	$0.975292\pi$
$30$		0			0
$31$	3.58751	+	6.21374i	0.644335	+	1.11602i	0.984455	+	0.175639i	$0.0561992\pi$
$31$	3.58751	+	6.21374i	0.644335	+	1.11602i	−0.340119	+	0.940382i	$0.610467\pi$
$32$		0			0
$33$	−1.71728	−	0.513189i	−0.298941	−	0.0893347i
$34$		0			0
$35$	5.71584			0.966154
$36$		0			0
$37$	−8.61130			−1.41569			−0.707844	−	0.706368i	$-0.750332\pi$
$37$	−8.61130			−1.41569			−0.707844	+	0.706368i	$0.750332\pi$
$38$		0			0
$39$	1.25926	−	1.18923i	0.201642	−	0.190430i
$40$		0			0
$41$	−0.532259	−	0.921899i	−0.0831249	−	0.143976i	0.821466	−	0.570258i	$-0.193157\pi$
$41$	−0.532259	−	0.921899i	−0.0831249	−	0.143976i	−0.904591	+	0.426281i	$0.859823\pi$
$42$		0			0
$43$	1.34187	−	2.32419i	0.204634	−	0.354436i	−0.745382	−	0.666637i	$-0.767733\pi$
$43$	1.34187	−	2.32419i	0.204634	−	0.354436i	0.950016	+	0.312201i	$0.101066\pi$
$44$		0			0
$45$	−3.10178	−	2.03565i	−0.462386	−	0.303456i
$46$		0			0
$47$	4.00605	−	6.93867i	0.584342	−	1.01211i	−0.410615	−	0.911809i	$-0.634686\pi$
$47$	4.00605	−	6.93867i	0.584342	−	1.01211i	0.994957	−	0.100301i	$-0.0319806\pi$
$48$		0			0
$49$	−7.18071	−	12.4374i	−1.02582	−	1.77677i
$50$		0			0
$51$	2.97735	+	12.5346i	0.416913	+	1.75519i
$52$		0			0
$53$	−10.4399			−1.43403			−0.717017	−	0.697056i	$-0.754493\pi$
$53$	−10.4399			−1.43403			−0.717017	+	0.697056i	$0.754493\pi$
$54$		0			0
$55$	−1.27974			−0.172560
$56$		0			0
$57$	1.76770	+	7.44199i	0.234138	+	0.985716i
$58$		0			0
$59$	4.04267	+	7.00211i	0.526311	+	0.911597i	0.999530	+	0.0306521i	$0.00975841\pi$
$59$	4.04267	+	7.00211i	0.526311	+	0.911597i	−0.473220	+	0.880945i	$0.656908\pi$
$60$		0			0
$61$	−5.92025	+	10.2542i	−0.758011	+	1.31291i	0.185853	+	0.982578i	$0.440495\pi$
$61$	−5.92025	+	10.2542i	−0.758011	+	1.31291i	−0.943864	+	0.330335i	$0.892838\pi$
$62$		0			0
$63$	−0.792412	+	13.8429i	−0.0998345	+	1.74404i
$64$		0			0
$65$	0.618351	−	1.07102i	0.0766970	−	0.132843i
$66$		0			0
$67$	−0.406963	−	0.704881i	−0.0497185	−	0.0861149i	0.840095	−	0.542439i	$-0.182499\pi$
$67$	−0.406963	−	0.704881i	−0.0497185	−	0.0861149i	−0.889814	+	0.456324i	$0.849166\pi$
$68$		0			0
$69$	−6.11549	+	5.77543i	−0.736219	+	0.695280i
$70$		0			0
$71$	10.3144			1.22409			0.612044	−	0.790824i	$-0.290347\pi$
$71$	10.3144			1.22409			0.612044	+	0.790824i	$0.290347\pi$
$72$		0			0
$73$	8.15391			0.954343			0.477171	−	0.878810i	$-0.341662\pi$
$73$	8.15391			0.954343			0.477171	+	0.878810i	$0.341662\pi$
$74$		0			0
$75$	5.75953	+	1.72116i	0.665053	+	0.198743i
$76$		0			0
$77$	2.39134	+	4.14192i	0.272518	+	0.472016i
$78$		0			0
$79$	−3.78968	+	6.56392i	−0.426373	+	0.738499i	−0.996548	−	0.0830244i	$-0.973542\pi$
$79$	−3.78968	+	6.56392i	−0.426373	+	0.738499i	0.570175	+	0.821523i	$0.306875\pi$
$80$		0			0
$81$	5.36003	−	7.22981i	0.595558	−	0.803312i
$82$		0			0
$83$	2.56200	−	4.43752i	0.281216	−	0.487081i	−0.690468	−	0.723363i	$-0.742595\pi$
$83$	2.56200	−	4.43752i	0.281216	−	0.487081i	0.971685	+	0.236282i	$0.0759288\pi$
$84$		0			0
$85$	4.59942	+	7.96643i	0.498877	+	0.864081i
$86$		0			0
$87$	−10.1103	−	3.02133i	−1.08393	−	0.323920i
$88$		0			0
$89$	−3.37420			−0.357665			−0.178832	−	0.983880i	$-0.557232\pi$
$89$	−3.37420			−0.357665			−0.178832	+	0.983880i	$0.557232\pi$
$90$		0			0
$91$	−4.62184			−0.484501
$92$		0			0
$93$	−9.03518	+	8.53276i	−0.936904	+	0.884806i
$94$		0			0
$95$	2.73075	+	4.72980i	0.280169	+	0.485267i
$96$		0			0
$97$	4.96536	−	8.60025i	0.504156	−	0.873223i	−0.495833	−	0.868418i	$-0.665137\pi$
$97$	4.96536	−	8.60025i	0.504156	−	0.873223i	0.999988	−	0.00480529i	$-0.00152958\pi$
$98$		0			0
$99$	0.177416	−	3.09932i	0.0178310	−	0.311494i
$100$		0			0
$101$	2.98103	−	5.16330i	0.296624	−	0.513768i	−0.678737	−	0.734381i	$-0.737473\pi$
$101$	2.98103	−	5.16330i	0.296624	−	0.513768i	0.975361	+	0.220613i	$0.0708059\pi$
$102$		0			0
$103$	−2.65513	−	4.59883i	−0.261618	−	0.453136i	0.705054	−	0.709154i	$-0.250923\pi$
$103$	−2.65513	−	4.59883i	−0.261618	−	0.453136i	−0.966672	+	0.256018i	$0.917589\pi$
$104$		0			0
$105$	2.28793	+	9.63213i	0.223279	+	0.940000i
$106$		0			0
$107$	−2.79266			−0.269977			−0.134988	−	0.990847i	$-0.543100\pi$
$107$	−2.79266			−0.269977			−0.134988	+	0.990847i	$0.543100\pi$
$108$		0			0
$109$	−11.3696			−1.08901			−0.544507	−	0.838756i	$-0.683283\pi$
$109$	−11.3696			−1.08901			−0.544507	+	0.838756i	$0.683283\pi$
$110$		0			0
$111$	−3.44692	−	14.5114i	−0.327167	−	1.37737i
$112$		0			0
$113$	−8.99219	−	15.5749i	−0.845914	−	1.46517i	−0.884825	−	0.465924i	$-0.845722\pi$
$113$	−8.99219	−	15.5749i	−0.845914	−	1.46517i	0.0389108	−	0.999243i	$-0.487611\pi$
$114$		0			0
$115$	−3.00298	+	5.20132i	−0.280029	+	0.485025i
$116$		0			0
$117$	2.50811	+	1.64603i	0.231874	+	0.152175i
$118$		0			0
$119$	17.1891	−	29.7724i	1.57572	−	2.72923i
$120$		0			0
$121$	4.96460	+	8.59893i	0.451327	+	0.781721i
$122$		0			0
$123$	1.34050	−	1.26596i	0.120869	−	0.114148i
$124$		0			0
$125$	10.4756			0.936963
$126$		0			0
$127$	−8.20363			−0.727954			−0.363977	−	0.931408i	$-0.618581\pi$
$127$	−8.20363			−0.727954			−0.363977	+	0.931408i	$0.618581\pi$
$128$		0			0
$129$	4.45376	+	1.33095i	0.392132	+	0.117184i
$130$		0			0
$131$	5.73112	+	9.92658i	0.500730	+	0.867290i	1.00000		0.000843000i	$0.000268335\pi$
$131$	5.73112	+	9.92658i	0.500730	+	0.867290i	−0.499270	+	0.866447i	$0.666398\pi$
$132$		0			0
$133$	10.2055	−	17.6764i	0.884925	−	1.53274i
$134$		0			0
$135$	2.18882	−	6.04183i	0.188384	−	0.519998i
$136$		0			0
$137$	−10.5319	+	18.2418i	−0.899800	+	1.55850i	−0.0720520	+	0.997401i	$0.522955\pi$
$137$	−10.5319	+	18.2418i	−0.899800	+	1.55850i	−0.827749	+	0.561099i	$0.810379\pi$
$138$		0			0
$139$	−11.7804	−	20.4042i	−0.999200	−	1.73067i	−0.534227	−	0.845341i	$-0.679397\pi$
$139$	−11.7804	−	20.4042i	−0.999200	−	1.73067i	−0.464973	−	0.885325i	$-0.653936\pi$
$140$		0			0
$141$	13.2963	+	3.97344i	1.11975	+	0.334624i
$142$		0			0
$143$	1.03480			0.0865343
$144$		0			0
$145$	−7.53428			−0.625688
$146$		0			0
$147$	18.0847	−	17.0791i	1.49160	−	1.40866i
$148$		0			0
$149$	1.17486	+	2.03492i	0.0962485	+	0.166707i	0.910129	−	0.414325i	$-0.135982\pi$
$149$	1.17486	+	2.03492i	0.0962485	+	0.166707i	−0.813880	+	0.581032i	$0.802649\pi$
$150$		0			0
$151$	0.914469	−	1.58391i	0.0744184	−	0.128896i	−0.826415	−	0.563062i	$-0.809623\pi$
$151$	0.914469	−	1.58391i	0.0744184	−	0.128896i	0.900833	+	0.434165i	$0.142957\pi$
$152$		0			0
$153$	−19.9311	+	10.0346i	−1.61133	+	0.811253i
$154$		0			0
$155$	−4.43668	+	7.68455i	−0.356363	+	0.617238i
$156$		0			0
$157$	−9.53466	−	16.5145i	−0.760948	−	1.31800i	−0.942362	−	0.334594i	$-0.891401\pi$
$157$	−9.53466	−	16.5145i	−0.760948	−	1.31800i	0.181414	−	0.983407i	$-0.441933\pi$
$158$		0			0
$159$	−4.17887	−	17.5930i	−0.331406	−	1.39521i
$160$		0			0
$161$	22.4457			1.76897
$162$		0			0
$163$	5.40033			0.422986			0.211493	−	0.977379i	$-0.432167\pi$
$163$	5.40033			0.422986			0.211493	+	0.977379i	$0.432167\pi$
$164$		0			0
$165$	−0.512251	−	2.15657i	−0.0398787	−	0.167889i
$166$		0			0
$167$	4.80911	+	8.32963i	0.372140	+	0.644566i	0.989895	−	0.141805i	$-0.0452907\pi$
$167$	4.80911	+	8.32963i	0.372140	+	0.644566i	−0.617754	+	0.786371i	$0.711957\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$	−11.8334	+	5.95774i	−0.904923	+	0.455600i
$172$		0			0
$173$	−0.182732	+	0.316501i	−0.0138929	+	0.0240632i	−0.872888	−	0.487920i	$-0.837756\pi$
$173$	−0.182732	+	0.316501i	−0.0138929	+	0.0240632i	0.858995	+	0.511983i	$0.171089\pi$
$174$		0			0
$175$	−8.02021	−	13.8914i	−0.606271	−	1.05009i
$176$		0			0
$177$	−10.1815	+	9.61535i	−0.765289	+	0.722734i
$178$		0			0
$179$	3.94330			0.294736			0.147368	−	0.989082i	$-0.452920\pi$
$179$	3.94330			0.294736			0.147368	+	0.989082i	$0.452920\pi$
$180$		0			0
$181$	5.11469			0.380172			0.190086	−	0.981767i	$-0.439123\pi$
$181$	5.11469			0.380172			0.190086	+	0.981767i	$0.439123\pi$
$182$		0			0
$183$	−19.6497	−	5.87207i	−1.45255	−	0.434076i
$184$		0			0
$185$	−5.32481	−	9.22283i	−0.391487	−	0.678076i
$186$		0			0
$187$	−3.84852	+	6.66584i	−0.281432	+	0.487454i
$188$		0			0
$189$	−23.6447	+	4.20565i	−1.71990	+	0.305916i
$190$		0			0
$191$	−0.217758	+	0.377168i	−0.0157564	+	0.0272909i	−0.873796	−	0.486292i	$-0.838349\pi$
$191$	−0.217758	+	0.377168i	−0.0157564	+	0.0272909i	0.858040	+	0.513583i	$0.171682\pi$
$192$		0			0
$193$	−8.14261	−	14.1034i	−0.586118	−	1.01519i	−0.994735	−	0.102480i	$-0.967322\pi$
$193$	−8.14261	−	14.1034i	−0.586118	−	1.01519i	0.408617	−	0.912706i	$-0.366011\pi$
$194$		0			0
$195$	2.05235	+	0.613319i	0.146972	+	0.0439207i
$196$		0			0
$197$	−15.9126			−1.13373			−0.566863	−	0.823812i	$-0.691843\pi$
$197$	−15.9126			−1.13373			−0.566863	+	0.823812i	$0.691843\pi$
$198$		0			0
$199$	13.8785			0.983822			0.491911	−	0.870646i	$-0.336299\pi$
$199$	13.8785			0.983822			0.491911	+	0.870646i	$0.336299\pi$
$200$		0			0
$201$	1.02494	−	0.967948i	0.0722938	−	0.0682738i
$202$		0			0
$203$	14.0787	+	24.3850i	0.988129	+	1.71149i
$204$		0			0
$205$	0.658245	−	1.14011i	0.0459739	−	0.0796291i
$206$		0			0
$207$	−12.1805	−	7.99383i	−0.846600	−	0.555609i
$208$		0			0
$209$	−2.28493	+	3.95762i	−0.158052	+	0.273754i
$210$		0			0
$211$	−4.72422	−	8.18259i	−0.325229	−	0.563313i	0.656330	−	0.754474i	$-0.272108\pi$
$211$	−4.72422	−	8.18259i	−0.325229	−	0.563313i	−0.981559	+	0.191161i	$0.938775\pi$
$212$		0			0
$213$	4.12861	+	17.3814i	0.282888	+	1.19095i
$214$		0			0
$215$	3.31899			0.226353
$216$		0			0
$217$	33.1618			2.25117
$218$		0			0
$219$	3.26383	+	13.7407i	0.220549	+	0.928509i
$220$		0			0
$221$	−3.71910	−	6.44167i	−0.250174	−	0.433314i
$222$		0			0
$223$	−4.44932	+	7.70644i	−0.297948	+	0.516062i	−0.975666	−	0.219260i	$-0.929636\pi$
$223$	−4.44932	+	7.70644i	−0.297948	+	0.516062i	0.677718	+	0.735322i	$0.262969\pi$
$224$		0			0
$225$	−0.595027	+	10.3947i	−0.0396685	+	0.692979i
$226$		0			0
$227$	9.10801	−	15.7755i	0.604520	−	1.04706i	−0.387607	−	0.921825i	$-0.626698\pi$
$227$	9.10801	−	15.7755i	0.604520	−	1.04706i	0.992127	−	0.125235i	$-0.0399684\pi$
$228$		0			0
$229$	−11.8921	−	20.5977i	−0.785852	−	1.36113i	−0.928489	−	0.371360i	$-0.878892\pi$
$229$	−11.8921	−	20.5977i	−0.785852	−	1.36113i	0.142638	−	0.989775i	$-0.454442\pi$
$230$		0			0
$231$	−6.02262	+	5.68772i	−0.396259	+	0.374225i
$232$		0			0
$233$	−8.70410			−0.570225			−0.285112	−	0.958494i	$-0.592031\pi$
$233$	−8.70410			−0.570225			−0.285112	+	0.958494i	$0.592031\pi$
$234$		0			0
$235$	9.90857			0.646364
$236$		0			0
$237$	−12.5782	−	3.75884i	−0.817043	−	0.244163i
$238$		0			0
$239$	−8.28917	−	14.3573i	−0.536182	−	0.928694i	−0.999105	−	0.0422959i	$-0.986533\pi$
$239$	−8.28917	−	14.3573i	−0.536182	−	0.928694i	0.462923	−	0.886398i	$-0.346801\pi$
$240$		0			0
$241$	−5.97432	+	10.3478i	−0.384839	+	0.666562i	−0.991747	−	0.128211i	$-0.959077\pi$
$241$	−5.97432	+	10.3478i	−0.384839	+	0.666562i	0.606907	+	0.794773i	$0.292410\pi$
$242$		0			0
$243$	14.3289	+	6.13859i	0.919200	+	0.393791i
$244$		0			0
$245$	8.88040	−	15.3813i	0.567348	−	0.982676i
$246$		0			0
$247$	−2.20809	−	3.82453i	−0.140498	−	0.243349i
$248$		0			0
$249$	8.50346	+	2.54115i	0.538885	+	0.161039i
$250$		0			0
$251$	−1.09870			−0.0693495			−0.0346748	−	0.999399i	$-0.511040\pi$
$251$	−1.09870			−0.0693495			−0.0346748	+	0.999399i	$0.511040\pi$
$252$		0			0
$253$	−5.02544			−0.315946
$254$		0			0
$255$	−11.5837	+	10.9396i	−0.725399	+	0.685062i
$256$		0			0
$257$	−5.63626	−	9.76229i	−0.351580	−	0.608955i	0.634946	−	0.772556i	$-0.281022\pi$
$257$	−5.63626	−	9.76229i	−0.351580	−	0.608955i	−0.986526	+	0.163602i	$0.947689\pi$
$258$		0			0
$259$	−19.9000	+	34.4679i	−1.23653	+	2.14173i
$260$		0			0
$261$	1.04451	−	18.2468i	0.0646535	−	1.12945i
$262$		0			0
$263$	−9.05973	+	15.6919i	−0.558647	+	0.967605i	0.438963	+	0.898505i	$0.355346\pi$
$263$	−9.05973	+	15.6919i	−0.558647	+	0.967605i	−0.997610	+	0.0690994i	$0.977987\pi$
$264$		0			0
$265$	−6.45554	−	11.1813i	−0.396561	−	0.686863i
$266$		0			0
$267$	−1.35062	−	5.68608i	−0.0826566	−	0.347983i
$268$		0			0
$269$	8.69587			0.530197			0.265098	−	0.964221i	$-0.414596\pi$
$269$	8.69587			0.530197			0.265098	+	0.964221i	$0.414596\pi$
$270$		0			0
$271$	−2.47019			−0.150053			−0.0750266	−	0.997182i	$-0.523904\pi$
$271$	−2.47019			−0.150053			−0.0750266	+	0.997182i	$0.523904\pi$
$272$		0			0
$273$	−1.85002	−	7.78856i	−0.111968	−	0.471385i
$274$		0			0
$275$	1.79567	+	3.11019i	0.108283	+	0.187552i
$276$		0			0
$277$	16.0775	−	27.8470i	0.966002	−	1.67316i	0.259103	−	0.965850i	$-0.416573\pi$
$277$	16.0775	−	27.8470i	0.966002	−	1.67316i	0.706899	−	0.707315i	$-0.250094\pi$
$278$		0			0
$279$	−17.9957	−	11.8103i	−1.07737	−	0.707063i
$280$		0			0
$281$	−6.02312	+	10.4323i	−0.359309	+	0.622342i	−0.987846	−	0.155438i	$-0.950321\pi$
$281$	−6.02312	+	10.4323i	−0.359309	+	0.622342i	0.628536	+	0.777780i	$0.283654\pi$
$282$		0			0
$283$	−8.39750	−	14.5449i	−0.499180	−	0.864605i	0.500820	−	0.865552i	$-0.333032\pi$
$283$	−8.39750	−	14.5449i	−0.499180	−	0.864605i	−1.00000		0.000946989i	$0.999699\pi$
$284$		0			0
$285$	−6.87743	+	6.49500i	−0.407384	+	0.384731i
$286$		0			0
$287$	−4.92003			−0.290420
$288$		0			0
$289$	38.3269			2.25452
$290$		0			0
$291$	16.4804	+	4.92495i	0.966096	+	0.288706i
$292$		0			0
$293$	5.95928	+	10.3218i	0.348145	+	0.603004i	0.985920	−	0.167218i	$-0.0534785\pi$
$293$	5.95928	+	10.3218i	0.348145	+	0.603004i	−0.637775	+	0.770223i	$0.720145\pi$
$294$		0			0
$295$	−4.99958	+	8.65952i	−0.291087	+	0.504177i
$296$		0			0
$297$	5.29389	−	0.941618i	0.307182	−	0.0546382i
$298$		0			0
$299$	2.42822	−	4.20580i	0.140427	−	0.243227i
$300$		0			0
$301$	−6.20192	−	10.7420i	−0.357473	−	0.619161i
$302$		0			0
$303$	9.89425	+	2.95677i	0.568410	+	0.169862i
$304$		0			0
$305$	−14.6432			−0.838466
$306$		0			0
$307$	2.39507			0.136694			0.0683469	−	0.997662i	$-0.478228\pi$
$307$	2.39507			0.136694			0.0683469	+	0.997662i	$0.478228\pi$
$308$		0			0
$309$	6.68698	−	6.31515i	0.380409	−	0.359256i
$310$		0			0
$311$	−12.2622	−	21.2388i	−0.695327	−	1.20434i	−0.970070	−	0.242824i	$-0.921926\pi$
$311$	−12.2622	−	21.2388i	−0.695327	−	1.20434i	0.274743	−	0.961518i	$-0.411407\pi$
$312$		0			0
$313$	4.17269	−	7.22731i	0.235854	−	0.408512i	−0.723666	−	0.690150i	$-0.757545\pi$
$313$	4.17269	−	7.22731i	0.235854	−	0.408512i	0.959521	+	0.281638i	$0.0908779\pi$
$314$		0			0
$315$	−15.3159	+	7.71106i	−0.862954	+	0.434469i
$316$		0			0
$317$	−2.35033	+	4.07089i	−0.132008	+	0.228644i	−0.924450	−	0.381302i	$-0.875476\pi$
$317$	−2.35033	+	4.07089i	−0.132008	+	0.228644i	0.792443	+	0.609946i	$0.208809\pi$
$318$		0			0
$319$	−3.15212	−	5.45963i	−0.176485	−	0.305681i
$320$		0			0
$321$	−1.11784	−	4.70610i	−0.0623919	−	0.262669i
$322$		0			0
$323$	32.8485			1.82774
$324$		0			0
$325$	−3.47057			−0.192512
$326$		0			0
$327$	−4.55102	−	19.1597i	−0.251672	−	1.05953i
$328$		0			0
$329$	−18.5153	−	32.0695i	−1.02078	−	1.76805i
$330$		0			0
$331$	−7.41963	+	12.8512i	−0.407820	+	0.706364i	−0.994645	−	0.103349i	$-0.967044\pi$
$331$	−7.41963	+	12.8512i	−0.407820	+	0.706364i	0.586826	+	0.809713i	$0.300377\pi$
$332$		0			0
$333$	23.0744	−	11.6172i	1.26447	−	0.636621i
$334$		0			0
$335$	0.503292	−	0.871727i	0.0274978	−	0.0476276i
$336$		0			0
$337$	14.4755	+	25.0722i	0.788529	+	1.36577i	0.926868	+	0.375387i	$0.122490\pi$
$337$	14.4755	+	25.0722i	0.788529	+	1.36577i	−0.138339	+	0.990385i	$0.544176\pi$
$338$		0			0
$339$	22.6469	−	21.3876i	1.23001	−	1.16162i
$340$		0			0
$341$	−7.42470			−0.402070
$342$		0			0
$343$	−34.0234			−1.83709
$344$		0			0
$345$	−9.96710	−	2.97854i	−0.536611	−	0.160359i
$346$		0			0
$347$	−2.47367	−	4.28452i	−0.132793	−	0.230005i	0.791959	−	0.610574i	$-0.209061\pi$
$347$	−2.47367	−	4.28452i	−0.132793	−	0.230005i	−0.924752	+	0.380569i	$0.875728\pi$
$348$		0			0
$349$	−13.0836	+	22.6615i	−0.700351	+	1.21304i	0.267993	+	0.963421i	$0.413640\pi$
$349$	−13.0836	+	22.6615i	−0.700351	+	1.21304i	−0.968343	+	0.249622i	$0.919694\pi$
$350$		0			0
$351$	−1.76989	+	4.88544i	−0.0944696	+	0.260765i
$352$		0			0
$353$	−17.0625	+	29.5531i	−0.908143	+	1.57295i	−0.0915021	+	0.995805i	$0.529167\pi$
$353$	−17.0625	+	29.5531i	−0.908143	+	1.57295i	−0.816641	+	0.577146i	$0.804167\pi$
$354$		0			0
$355$	6.37789	+	11.0468i	0.338503	+	0.586305i
$356$		0			0
$357$	57.0518	+	17.0492i	3.01950	+	0.902340i
$358$		0			0
$359$	−31.0572			−1.63914			−0.819569	−	0.572980i	$-0.805787\pi$
$359$	−31.0572			−1.63914			−0.819569	+	0.572980i	$0.805787\pi$
$360$		0			0
$361$	0.502686			0.0264572
$362$		0			0
$363$	−12.5034	+	11.8081i	−0.656258	+	0.619766i
$364$		0			0
$365$	5.04198	+	8.73296i	0.263909	+	0.457104i
$366$		0			0
$367$	−13.3961	+	23.2027i	−0.699271	+	1.21117i	0.269449	+	0.963015i	$0.413158\pi$
$367$	−13.3961	+	23.2027i	−0.699271	+	1.21117i	−0.968720	+	0.248158i	$0.920175\pi$
$368$		0			0
$369$	2.66992	+	1.75223i	0.138991	+	0.0912172i
$370$		0			0
$371$	−24.1258	+	41.7872i	−1.25255	+	2.16948i
$372$		0			0
$373$	−9.69162	−	16.7864i	−0.501813	−	0.869166i	−0.999998	−	0.00209477i	$-0.999333\pi$
$373$	−9.69162	−	16.7864i	−0.501813	−	0.869166i	0.498185	−	0.867071i	$-0.334000\pi$
$374$		0			0
$375$	4.19314	+	17.6531i	0.216533	+	0.911600i
$376$		0			0
$377$	6.09223			0.313766
$378$		0			0
$379$	9.40917			0.483317			0.241658	−	0.970361i	$-0.422309\pi$
$379$	9.40917			0.483317			0.241658	+	0.970361i	$0.422309\pi$
$380$		0			0
$381$	−3.28373	−	13.8245i	−0.168231	−	0.708248i
$382$		0			0
$383$	−6.66805	−	11.5494i	−0.340721	−	0.590147i	0.643845	−	0.765156i	$-0.277338\pi$
$383$	−6.66805	−	11.5494i	−0.340721	−	0.590147i	−0.984567	+	0.175009i	$0.944005\pi$
$384$		0			0
$385$	−2.95737	+	5.12232i	−0.150722	+	0.261058i
$386$		0			0
$387$	−0.460126	+	8.03807i	−0.0233895	+	0.408598i
$388$		0			0
$389$	−1.51890	+	2.63081i	−0.0770112	+	0.133387i	−0.901959	−	0.431821i	$-0.857871\pi$
$389$	−1.51890	+	2.63081i	−0.0770112	+	0.133387i	0.824948	+	0.565209i	$0.191204\pi$
$390$		0			0
$391$	18.0616	+	31.2836i	0.913413	+	1.58208i
$392$		0			0
$393$	−14.4339	+	13.6313i	−0.728093	+	0.687606i
$394$		0			0
$395$	−9.37341			−0.471628
$396$		0			0
$397$	26.4484			1.32741			0.663703	−	0.747997i	$-0.268984\pi$
$397$	26.4484			1.32741			0.663703	+	0.747997i	$0.268984\pi$
$398$		0			0
$399$	33.8726	+	10.1224i	1.69575	+	0.506754i
$400$		0			0
$401$	5.85782	+	10.1460i	0.292525	+	0.506669i	0.974406	−	0.224794i	$-0.0721710\pi$
$401$	5.85782	+	10.1460i	0.292525	+	0.506669i	−0.681881	+	0.731463i	$0.738838\pi$
$402$		0			0
$403$	3.58751	−	6.21374i	0.178706	−	0.309529i
$404$		0			0
$405$	11.0576	+	1.27011i	0.549457	+	0.0631124i
$406$		0			0
$407$	4.45548	−	7.71712i	0.220850	−	0.382524i
$408$		0			0
$409$	−1.53325	−	2.65567i	−0.0758144	−	0.131314i	0.825626	−	0.564218i	$-0.190822\pi$
$409$	−1.53325	−	2.65567i	−0.0758144	−	0.131314i	−0.901440	+	0.432904i	$0.857489\pi$
$410$		0			0
$411$	−34.9561	−	10.4462i	−1.72426	−	0.515272i
$412$		0			0
$413$	37.3692			1.83882
$414$		0			0
$415$	6.33687			0.311065
$416$		0			0
$417$	29.6691	−	28.0193i	1.45290	−	1.37211i
$418$		0			0
$419$	−2.61427	−	4.52805i	−0.127715	−	0.221209i	0.795076	−	0.606510i	$-0.207431\pi$
$419$	−2.61427	−	4.52805i	−0.127715	−	0.221209i	−0.922791	+	0.385301i	$0.874098\pi$
$420$		0			0
$421$	−18.4928	+	32.0304i	−0.901283	+	1.56107i	−0.0754524	+	0.997149i	$0.524040\pi$
$421$	−18.4928	+	32.0304i	−0.901283	+	1.56107i	−0.825831	+	0.563918i	$0.809293\pi$
$422$		0			0
$423$	−1.37367	+	23.9970i	−0.0667900	+	1.16677i
$424$		0			0
$425$	12.9074	−	22.3563i	0.626101	−	1.08444i
$426$		0			0
$427$	27.3625	+	47.3932i	1.32416	+	2.29352i
$428$		0			0
$429$	0.414208	+	1.74381i	0.0199981	+	0.0841918i
$430$		0			0
$431$	0.273718			0.0131845			0.00659227	−	0.999978i	$-0.497902\pi$
$431$	0.273718			0.0131845			0.00659227	+	0.999978i	$0.497902\pi$
$432$		0			0
$433$	−14.2228			−0.683504			−0.341752	−	0.939790i	$-0.611020\pi$
$433$	−14.2228			−0.683504			−0.341752	+	0.939790i	$0.611020\pi$
$434$		0			0
$435$	−3.01581	−	12.6965i	−0.144597	−	0.608750i
$436$		0			0
$437$	10.7235	+	18.5736i	0.512973	+	0.888494i
$438$		0			0
$439$	1.86696	−	3.23366i	0.0891049	−	0.154334i	−0.818028	−	0.575178i	$-0.804933\pi$
$439$	1.86696	−	3.23366i	0.0891049	−	0.154334i	0.907133	+	0.420844i	$0.138266\pi$
$440$		0			0
$441$	36.0200	+	23.6393i	1.71524	+	1.12568i
$442$		0			0
$443$	19.2608	−	33.3606i	0.915107	−	1.58501i	0.108363	−	0.994111i	$-0.465439\pi$
$443$	19.2608	−	33.3606i	0.915107	−	1.58501i	0.806744	−	0.590901i	$-0.201228\pi$
$444$		0			0
$445$	−2.08644	−	3.61382i	−0.0989068	−	0.171312i
$446$		0			0
$447$	−2.95890	+	2.79437i	−0.139951	+	0.132169i
$448$		0			0
$449$	−11.4384			−0.539813			−0.269907	−	0.962887i	$-0.586993\pi$
$449$	−11.4384			−0.539813			−0.269907	+	0.962887i	$0.586993\pi$
$450$		0			0
$451$	1.10156			0.0518705
$452$		0			0
$453$	3.03518	+	0.907026i	0.142605	+	0.0426158i
$454$		0			0
$455$	−2.85792	−	4.95006i	−0.133981	−	0.232063i
$456$		0			0
$457$	11.8697	−	20.5589i	0.555240	−	0.961704i	−0.442644	−	0.896697i	$-0.645960\pi$
$457$	11.8697	−	20.5589i	0.555240	−	0.961704i	0.997885	−	0.0650072i	$-0.0207070\pi$
$458$		0			0
$459$	−24.8880	−	29.5705i	−1.16167	−	1.38023i
$460$		0			0
$461$	−7.04097	+	12.1953i	−0.327931	+	0.567993i	−0.982101	−	0.188355i	$-0.939685\pi$
$461$	−7.04097	+	12.1953i	−0.327931	+	0.567993i	0.654170	+	0.756347i	$0.273018\pi$
$462$		0			0
$463$	−5.80139	−	10.0483i	−0.269613	−	0.466984i	0.699149	−	0.714976i	$-0.253563\pi$
$463$	−5.80139	−	10.0483i	−0.269613	−	0.466984i	−0.968762	+	0.247992i	$0.920229\pi$
$464$		0			0
$465$	−14.7256	−	4.40057i	−0.682885	−	0.204072i
$466$		0			0
$467$	−15.2384			−0.705150			−0.352575	−	0.935784i	$-0.614694\pi$
$467$	−15.2384			−0.705150			−0.352575	+	0.935784i	$0.614694\pi$
$468$		0			0
$469$	−3.76184			−0.173706
$470$		0			0
$471$	24.0131	−	22.6779i	1.10647	−	1.04494i
$472$		0			0
$473$	1.38857	+	2.40507i	0.0638465	+	0.110585i
$474$		0			0
$475$	7.66333	−	13.2733i	0.351618	−	0.609020i
$476$		0			0
$477$	27.9743	−	14.0842i	1.28086	−	0.644870i
$478$		0			0
$479$	3.21975	−	5.57676i	0.147114	−	0.254809i	−0.783046	−	0.621964i	$-0.786335\pi$
$479$	3.21975	−	5.57676i	0.147114	−	0.254809i	0.930160	+	0.367155i	$0.119668\pi$
$480$		0			0
$481$	4.30565	+	7.45760i	0.196321	+	0.340037i
$482$		0			0
$483$	8.98452	+	37.8246i	0.408810	+	1.72108i
$484$		0			0
$485$	12.2813			0.557667
$486$		0			0
$487$	11.6913			0.529783			0.264891	−	0.964278i	$-0.414664\pi$
$487$	11.6913			0.529783			0.264891	+	0.964278i	$0.414664\pi$
$488$		0			0
$489$	2.16163	+	9.10044i	0.0977525	+	0.411536i
$490$		0			0
$491$	−6.94879	−	12.0357i	−0.313595	−	0.543162i	0.665543	−	0.746359i	$-0.268200\pi$
$491$	−6.94879	−	12.0357i	−0.313595	−	0.543162i	−0.979138	+	0.203198i	$0.934867\pi$
$492$		0			0
$493$	−22.6576	+	39.2442i	−1.02045	+	1.76747i
$494$		0			0
$495$	3.42913	−	1.72646i	0.154128	−	0.0775984i
$496$		0			0
$497$	23.8357	−	41.2846i	1.06918	−	1.85187i
$498$		0			0
$499$	−2.21828	−	3.84217i	−0.0993036	−	0.171999i	0.812093	−	0.583528i	$-0.198328\pi$
$499$	−2.21828	−	3.84217i	−0.0993036	−	0.171999i	−0.911397	+	0.411529i	$0.864995\pi$
$500$		0			0
$501$	−12.1118	+	11.4383i	−0.541115	+	0.511026i
$502$		0			0
$503$	−18.6182			−0.830144			−0.415072	−	0.909788i	$-0.636244\pi$
$503$	−18.6182			−0.830144			−0.415072	+	0.909788i	$0.636244\pi$
$504$		0			0
$505$	7.37330			0.328107
$506$		0			0
$507$	−1.65953	−	0.495931i	−0.0737025	−	0.0220251i
$508$		0			0
$509$	6.60765	+	11.4448i	0.292879	+	0.507281i	0.974489	−	0.224434i	$-0.0720534\pi$
$509$	6.60765	+	11.4448i	0.292879	+	0.507281i	−0.681610	+	0.731715i	$0.738720\pi$
$510$		0			0
$511$	18.8430	−	32.6371i	0.833567	−	1.44378i
$512$		0			0
$513$	−14.7764	−	17.5565i	−0.652395	−	0.775137i
$514$		0			0
$515$	3.28361	−	5.68738i	0.144693	−	0.250616i
$516$		0			0
$517$	4.14545	+	7.18014i	0.182317	+	0.315782i
$518$		0			0
$519$	−0.606500	−	0.181245i	−0.0266224	−	0.00795577i
$520$		0			0
$521$	−24.3997			−1.06897			−0.534486	−	0.845177i	$-0.679495\pi$
$521$	−24.3997			−1.06897			−0.534486	+	0.845177i	$0.679495\pi$
$522$		0			0
$523$	29.2553			1.27924			0.639622	−	0.768690i	$-0.279091\pi$
$523$	29.2553			1.27924			0.639622	+	0.768690i	$0.279091\pi$
$524$		0			0
$525$	20.1990	−	19.0758i	0.881556	−	0.832536i
$526$		0			0
$527$	26.6846	+	46.2191i	1.16240	+	2.01334i
$528$		0			0
$529$	−0.292482	+	0.506593i	−0.0127166	+	0.0220258i
$530$		0			0
$531$	−20.2789	−	13.3087i	−0.880028	−	0.577548i
$532$		0			0
$533$	−0.532259	+	0.921899i	−0.0230547	+	0.0399319i
$534$		0			0
$535$	−1.72685	−	2.99099i	−0.0746581	−	0.129312i
$536$		0			0
$537$	1.57842	+	6.64510i	0.0681137	+	0.286757i
$538$		0			0
$539$	14.8612			0.640117
$540$		0			0
$541$	29.9138			1.28609			0.643047	−	0.765827i	$-0.277670\pi$
$541$	29.9138			1.28609			0.643047	+	0.765827i	$0.277670\pi$
$542$		0			0
$543$	2.04730	+	8.61910i	0.0878581	+	0.369881i
$544$		0			0
$545$	−7.03043	−	12.1771i	−0.301150	−	0.521608i
$546$		0			0
$547$	−10.4275	+	18.0610i	−0.445848	+	0.772231i	−0.998111	−	0.0614391i	$-0.980431\pi$
$547$	−10.4275	+	18.0610i	−0.445848	+	0.772231i	0.552263	+	0.833670i	$0.313764\pi$
$548$		0			0
$549$	2.03005	−	35.4635i	0.0866403	−	1.51354i
$550$		0			0
$551$	−13.4522	+	23.2999i	−0.573084	+	0.992610i
$552$		0			0
$553$	17.5153	+	30.3374i	0.744827	+	1.29008i
$554$		0			0
$555$	13.4106	−	12.6649i	0.569247	−	0.537594i
$556$		0			0
$557$	−21.9289			−0.929158			−0.464579	−	0.885532i	$-0.653794\pi$
$557$	−21.9289			−0.929158			−0.464579	+	0.885532i	$0.653794\pi$
$558$		0			0
$559$	−2.68374			−0.113510
$560$		0			0
$561$	−12.7735	−	3.81720i	−0.539298	−	0.161162i
$562$		0			0
$563$	9.14597	+	15.8413i	0.385457	+	0.667631i	0.991832	−	0.127548i	$-0.0407105\pi$
$563$	9.14597	+	15.8413i	0.385457	+	0.667631i	−0.606376	+	0.795178i	$0.707377\pi$
$564$		0			0
$565$	11.1207	−	19.2615i	0.467850	−	0.810339i
$566$		0			0
$567$	−16.5517	−	38.1617i	−0.695105	−	1.60264i
$568$		0			0
$569$	−16.9632	+	29.3811i	−0.711135	+	1.23172i	0.253297	+	0.967389i	$0.418485\pi$
$569$	−16.9632	+	29.3811i	−0.711135	+	1.23172i	−0.964432	+	0.264333i	$0.914848\pi$
$570$		0			0
$571$	−2.01975	−	3.49830i	−0.0845237	−	0.146399i	0.820664	−	0.571410i	$-0.193604\pi$
$571$	−2.01975	−	3.49830i	−0.0845237	−	0.146399i	−0.905188	+	0.425011i	$0.860270\pi$
$572$		0			0
$573$	−0.722754	−	0.215986i	−0.0301935	−	0.00902294i
$574$		0			0
$575$	16.8546			0.702885
$576$		0			0
$577$	25.7179			1.07065			0.535325	−	0.844646i	$-0.320189\pi$
$577$	25.7179			1.07065			0.535325	+	0.844646i	$0.320189\pi$
$578$		0			0
$579$	20.5073	−	19.3669i	0.852253	−	0.804862i
$580$		0			0
$581$	−11.8412	−	20.5095i	−0.491255	−	0.850878i
$582$		0			0
$583$	5.40161	−	9.35587i	0.223712	−	0.387481i
$584$		0			0
$585$	−0.212032	+	3.70404i	−0.00876644	+	0.153143i
$586$		0			0
$587$	−4.65906	+	8.06972i	−0.192300	+	0.333073i	−0.946012	−	0.324132i	$-0.894928\pi$
$587$	−4.65906	+	8.06972i	−0.192300	+	0.333073i	0.753712	+	0.657205i	$0.228261\pi$
$588$		0			0
$589$	15.8431	+	27.4410i	0.652803	+	1.13069i
$590$		0			0
$591$	−6.36946	−	26.8153i	−0.262005	−	1.10304i
$592$		0			0
$593$	21.3998			0.878786			0.439393	−	0.898295i	$-0.355194\pi$
$593$	21.3998			0.878786			0.439393	+	0.898295i	$0.355194\pi$
$594$		0			0
$595$	42.5156			1.74297
$596$		0			0
$597$	5.55527	+	23.3876i	0.227362	+	0.957189i
$598$		0			0
$599$	10.5949	+	18.3510i	0.432898	+	0.749801i	0.997121	−	0.0758212i	$-0.0241578\pi$
$599$	10.5949	+	18.3510i	0.432898	+	0.749801i	−0.564224	+	0.825622i	$0.690825\pi$
$600$		0			0
$601$	−11.7940	+	20.4278i	−0.481088	+	0.833268i	−0.999764	−	0.0217021i	$-0.993091\pi$
$601$	−11.7940	+	20.4278i	−0.481088	+	0.833268i	0.518677	+	0.854970i	$0.326425\pi$
$602$		0			0
$603$	2.04141	+	1.33975i	0.0831327	+	0.0545586i
$604$		0			0
$605$	−6.13972	+	10.6343i	−0.249615	+	0.432346i
$606$		0			0
$607$	7.90602	+	13.6936i	0.320895	+	0.555807i	0.980673	−	0.195654i	$-0.0626829\pi$
$607$	7.90602	+	13.6936i	0.320895	+	0.555807i	−0.659778	+	0.751461i	$0.729350\pi$
$608$		0			0
$609$	−35.4573	+	33.4856i	−1.43680	+	1.35691i
$610$		0			0
$611$	−8.01209			−0.324134
$612$		0			0
$613$	−1.30853			−0.0528510			−0.0264255	−	0.999651i	$-0.508412\pi$
$613$	−1.30853			−0.0528510			−0.0264255	+	0.999651i	$0.508412\pi$
$614$		0			0
$615$	2.18476	+	0.652888i	0.0880981	+	0.0263270i
$616$		0			0
$617$	−0.543935	−	0.942123i	−0.0218980	−	0.0379285i	0.854869	−	0.518844i	$-0.173638\pi$
$617$	−0.543935	−	0.942123i	−0.0218980	−	0.0379285i	−0.876767	+	0.480916i	$0.840304\pi$
$618$		0			0
$619$	−7.24611	+	12.5506i	−0.291246	+	0.504453i	−0.974105	−	0.226098i	$-0.927403\pi$
$619$	−7.24611	+	12.5506i	−0.291246	+	0.504453i	0.682859	+	0.730550i	$0.260736\pi$
$620$		0			0
$621$	8.59534	−	23.7258i	0.344919	−	0.952084i
$622$		0			0
$623$	−7.79751	+	13.5057i	−0.312401	+	0.541094i
$624$		0			0
$625$	−2.19884	−	3.80851i	−0.0879537	−	0.152340i
$626$		0			0
$627$	−7.58385	−	2.26634i	−0.302870	−	0.0905088i
$628$		0			0
$629$	−64.0526			−2.55394
$630$		0			0
$631$	−41.4115			−1.64856			−0.824282	−	0.566179i	$-0.808421\pi$
$631$	−41.4115			−1.64856			−0.824282	+	0.566179i	$0.808421\pi$
$632$		0			0
$633$	11.8980	−	11.2364i	0.472903	−	0.446607i
$634$		0			0
$635$	−5.07272	−	8.78621i	−0.201305	−	0.348670i
$636$		0			0
$637$	−7.18071	+	12.4374i	−0.284510	+	0.492786i
$638$		0			0
$639$	−27.6379	+	13.9148i	−1.09334	+	0.550460i
$640$		0			0
$641$	12.0907	−	20.9416i	0.477553	−	0.827145i	−0.522116	−	0.852874i	$-0.674857\pi$
$641$	12.0907	−	20.9416i	0.477553	−	0.827145i	0.999669	+	0.0257289i	$0.00819068\pi$
$642$		0			0
$643$	18.6005	+	32.2169i	0.733530	+	1.27051i	0.955365	+	0.295428i	$0.0954621\pi$
$643$	18.6005	+	32.2169i	0.733530	+	1.27051i	−0.221835	+	0.975084i	$0.571205\pi$
$644$		0			0
$645$	1.32852	+	5.59305i	0.0523104	+	0.220226i
$646$		0			0
$647$	9.31675			0.366279			0.183140	−	0.983087i	$-0.441374\pi$
$647$	9.31675			0.366279			0.183140	+	0.983087i	$0.441374\pi$
$648$		0			0
$649$	−8.36670			−0.328422
$650$		0			0
$651$	13.2739	+	55.8830i	0.520247	+	2.19023i
$652$		0			0
$653$	9.51790	+	16.4855i	0.372464	+	0.645127i	0.989944	−	0.141460i	$-0.0451796\pi$
$653$	9.51790	+	16.4855i	0.372464	+	0.645127i	−0.617480	+	0.786587i	$0.711846\pi$
$654$		0			0
$655$	−7.08768	+	12.2762i	−0.276939	+	0.479672i
$656$		0			0
$657$	−21.8488	+	11.0002i	−0.852405	+	0.429158i
$658$		0			0
$659$	−20.1576	+	34.9140i	−0.785228	+	1.36006i	0.143634	+	0.989631i	$0.454121\pi$
$659$	−20.1576	+	34.9140i	−0.785228	+	1.36006i	−0.928863	+	0.370424i	$0.879212\pi$
$660$		0			0
$661$	−2.06589	−	3.57822i	−0.0803537	−	0.139177i	0.823048	−	0.567972i	$-0.192272\pi$
$661$	−2.06589	−	3.57822i	−0.0803537	−	0.139177i	−0.903402	+	0.428795i	$0.858938\pi$
$662$		0			0
$663$	9.36660	−	8.84576i	0.363769	−	0.343541i
$664$		0			0
$665$	25.2422			0.978851
$666$		0			0
$667$	−29.5865			−1.14560
$668$		0			0
$669$	−14.7676	−	4.41311i	−0.570948	−	0.170621i
$670$		0			0
$671$	−6.12627	−	10.6110i	−0.236502	−	0.409634i
$672$		0			0
$673$	6.07150	−	10.5162i	0.234039	−	0.405368i	−0.724954	−	0.688798i	$-0.758139\pi$
$673$	6.07150	−	10.5162i	0.234039	−	0.405368i	0.958993	+	0.283430i	$0.0914722\pi$
$674$		0			0
$675$	−17.7549	+	3.15805i	−0.683388	+	0.121553i
$676$		0			0
$677$	−20.5796	+	35.6449i	−0.790937	+	1.36994i	0.134450	+	0.990920i	$0.457073\pi$
$677$	−20.5796	+	35.6449i	−0.790937	+	1.36994i	−0.925387	+	0.379023i	$0.876260\pi$
$678$		0			0
$679$	−22.9491	−	39.7490i	−0.880706	−	1.52543i
$680$		0			0
$681$	30.2301	+	9.03389i	1.15842	+	0.346179i
$682$		0			0
$683$	1.71255			0.0655290			0.0327645	−	0.999463i	$-0.489569\pi$
$683$	1.71255			0.0655290			0.0327645	+	0.999463i	$0.489569\pi$
$684$		0			0
$685$	−26.0496			−0.995305
$686$		0			0
$687$	29.9504	−	28.2849i	1.14268	−	1.07914i
$688$		0			0
$689$	5.21996	+	9.04124i	0.198865	+	0.344444i
$690$		0			0
$691$	15.6971	−	27.1881i	0.597145	−	1.03429i	−0.396095	−	0.918209i	$-0.629635\pi$
$691$	15.6971	−	27.1881i	0.597145	−	1.03429i	0.993240	−	0.116076i	$-0.0370317\pi$
$692$		0			0
$693$	−11.9955	−	7.87242i	−0.455670	−	0.299049i
$694$		0			0
$695$	14.5688	−	25.2340i	0.552628	−	0.957179i
$696$		0			0
$697$	−3.95905	−	6.85727i	−0.149960	−	0.259738i
$698$		0			0
$699$	−3.48406	−	14.6678i	−0.131779	−	0.554788i
$700$		0			0
$701$	5.17150			0.195325			0.0976625	−	0.995220i	$-0.468863\pi$
$701$	5.17150			0.195325			0.0976625	+	0.995220i	$0.468863\pi$
$702$		0			0
$703$	−38.0291			−1.43429
$704$		0			0
$705$	3.96618	+	16.6976i	0.149375	+	0.628867i
$706$		0			0
$707$	−13.7779	−	23.8640i	−0.518170	−	0.897497i
$708$		0			0
$709$	12.3700	−	21.4255i	0.464565	−	0.804650i	−0.534617	−	0.845095i	$-0.679544\pi$
$709$	12.3700	−	21.4255i	0.464565	−	0.804650i	0.999182	+	0.0404443i	$0.0128773\pi$
$710$		0			0
$711$	1.29948	−	22.7009i	0.0487342	−	0.851351i
$712$		0			0
$713$	−17.4225	+	30.1766i	−0.652478	+	1.13012i
$714$		0			0
$715$	0.639869	+	1.10829i	0.0239298	+	0.0414475i
$716$		0			0
$717$	20.8764	−	19.7155i	0.779642	−	0.736289i
$718$		0			0
$719$	−48.5746			−1.81153			−0.905764	−	0.423783i	$-0.860702\pi$
$719$	−48.5746			−1.81153			−0.905764	+	0.423783i	$0.860702\pi$
$720$		0			0
$721$	−24.5432			−0.914037
$722$		0			0
$723$	−19.8292	−	5.92569i	−0.737454	−	0.220379i
$724$		0			0
$725$	10.5718	+	18.3108i	0.392625	+	0.680047i
$726$		0			0
$727$	−15.1119	+	26.1745i	−0.560469	+	0.970760i	0.436987	+	0.899468i	$0.356046\pi$
$727$	−15.1119	+	26.1745i	−0.560469	+	0.970760i	−0.997455	+	0.0712923i	$0.977288\pi$
$728$		0			0
$729$	−4.60897	+	26.6037i	−0.170703	+	0.985323i
$730$		0			0
$731$	9.98112	−	17.2878i	0.369165	−	0.639413i
$732$		0			0
$733$	6.25615	+	10.8360i	0.231076	+	0.400236i	0.958125	−	0.286350i	$-0.0924420\pi$
$733$	6.25615	+	10.8360i	0.231076	+	0.400236i	−0.727049	+	0.686586i	$0.759109\pi$
$734$		0			0
$735$	29.4747	+	8.80813i	1.08719	+	0.324893i
$736$		0			0
$737$	0.842250			0.0310247
$738$		0			0
$739$	1.67848			0.0617439			0.0308720	−	0.999523i	$-0.490172\pi$
$739$	1.67848			0.0617439			0.0308720	+	0.999523i	$0.490172\pi$
$740$		0			0
$741$	5.56111	−	5.25187i	0.204292	−	0.192932i
$742$		0			0
$743$	5.53968	+	9.59501i	0.203231	+	0.352007i	0.949568	−	0.313562i	$-0.101522\pi$
$743$	5.53968	+	9.59501i	0.203231	+	0.352007i	−0.746337	+	0.665569i	$0.768189\pi$
$744$		0			0
$745$	−1.45296	+	2.51659i	−0.0532322	+	0.0922008i
$746$		0			0
$747$	−0.878508	+	15.3469i	−0.0321429	+	0.561513i
$748$		0			0
$749$	−6.45363	+	11.1780i	−0.235810	+	0.408435i
$750$		0			0
$751$	−4.76341	−	8.25046i	−0.173819	−	0.301064i	0.765933	−	0.642921i	$-0.222277\pi$
$751$	−4.76341	−	8.25046i	−0.173819	−	0.301064i	−0.939752	+	0.341857i	$0.888944\pi$
$752$		0			0
$753$	−0.439787	−	1.85150i	−0.0160267	−	0.0674722i
$754$		0			0
$755$	2.26185			0.0823172
$756$		0			0
$757$	20.1215			0.731329			0.365664	−	0.930747i	$-0.380842\pi$
$757$	20.1215			0.731329			0.365664	+	0.930747i	$0.380842\pi$
$758$		0			0
$759$	−2.01157	−	8.46868i	−0.0730155	−	0.307394i
$760$		0			0
$761$	−25.5920	−	44.3267i	−0.927711	−	1.60684i	−0.787142	−	0.616772i	$-0.788440\pi$
$761$	−25.5920	−	44.3267i	−0.927711	−	1.60684i	−0.140569	−	0.990071i	$-0.544893\pi$
$762$		0			0
$763$	−26.2743	+	45.5085i	−0.951195	+	1.64752i
$764$		0			0
$765$	−23.0717	−	15.1415i	−0.834158	−	0.547444i
$766$		0			0
$767$	4.04267	−	7.00211i	0.145972	−	0.252831i
$768$		0			0
$769$	4.27904	+	7.41152i	0.154306	+	0.267266i	0.932806	−	0.360378i	$-0.117352\pi$
$769$	4.27904	+	7.41152i	0.154306	+	0.267266i	−0.778500	+	0.627645i	$0.784019\pi$
$770$		0			0
$771$	14.1950	−	13.4056i	0.511220	−	0.482793i
$772$		0			0
$773$	19.6620			0.707194			0.353597	−	0.935398i	$-0.384959\pi$
$773$	19.6620			0.707194			0.353597	+	0.935398i	$0.384959\pi$
$774$		0			0
$775$	24.9014			0.894484
$776$		0			0
$777$	−66.0496	−	19.7381i	−2.36951	−	0.708100i
$778$		0			0
$779$	−2.35055	−	4.07128i	−0.0842173	−	0.145869i
$780$		0			0
$781$	−5.33664	+	9.24333i	−0.190960	+	0.330753i
$782$		0			0
$783$	31.1670	−	5.54364i	1.11382	−	0.198113i
$784$		0			0
$785$	11.7915	−	20.4235i	0.420858	−	0.728947i
$786$		0			0
$787$	6.31421	+	10.9365i	0.225077	+	0.389845i	0.956343	−	0.292248i	$-0.0944032\pi$
$787$	6.31421	+	10.9365i	0.225077	+	0.389845i	−0.731265	+	0.682093i	$0.761070\pi$
$788$		0			0
$789$	−30.0699	−	8.98600i	−1.07052	−	0.319910i
$790$		0			0
$791$	−83.1210			−2.95544
$792$		0			0
$793$	11.8405			0.420469
$794$		0			0
$795$	16.2583	−	15.3543i	0.576624	−	0.544560i
$796$		0			0
$797$	−21.8643	−	37.8700i	−0.774472	−	1.34142i	−0.935091	−	0.354408i	$-0.884682\pi$
$797$	−21.8643	−	37.8700i	−0.774472	−	1.34142i	0.160619	−	0.987016i	$-0.448651\pi$
$798$		0			0
$799$	29.7978	−	51.6113i	1.05417	−	1.82588i
$800$		0			0
$801$	9.04136	−	4.55203i	0.319461	−	0.160838i
$802$		0			0
$803$	−4.21883	+	7.30723i	−0.148879	+	0.257866i
$804$		0			0
$805$	13.8793	+	24.0397i	0.489181	+	0.847287i
$806$		0			0
$807$	3.48077	+	14.6540i	0.122529	+	0.515844i
$808$		0			0
$809$	−30.7778			−1.08209			−0.541044	−	0.840994i	$-0.681971\pi$
$809$	−30.7778			−1.08209			−0.541044	+	0.840994i	$0.681971\pi$
$810$		0			0
$811$	0.698137			0.0245149			0.0122575	−	0.999925i	$-0.496098\pi$
$811$	0.698137			0.0245149			0.0122575	+	0.999925i	$0.496098\pi$
$812$		0			0
$813$	−0.988762	−	4.16267i	−0.0346774	−	0.145991i
$814$		0			0
$815$	3.33930	+	5.78384i	0.116971	+	0.202599i
$816$		0			0
$817$	5.92596	−	10.2641i	0.207323	−	0.359094i
$818$		0			0
$819$	12.3845	−	6.23518i	0.432749	−	0.217875i
$820$		0			0
$821$	9.75886	−	16.9028i	0.340586	−	0.589913i	−0.643955	−	0.765063i	$-0.722708\pi$
$821$	9.75886	−	16.9028i	0.340586	−	0.589913i	0.984542	+	0.175150i	$0.0560411\pi$
$822$		0			0
$823$	−21.2528	−	36.8109i	−0.740825	−	1.28315i	−0.952120	−	0.305725i	$-0.901101\pi$
$823$	−21.2528	−	36.8109i	−0.740825	−	1.28315i	0.211295	−	0.977422i	$-0.432232\pi$
$824$		0			0
$825$	−4.52242	+	4.27094i	−0.157450	+	0.148695i
$826$		0			0
$827$	32.1362			1.11749			0.558743	−	0.829341i	$-0.311284\pi$
$827$	32.1362			1.11749			0.558743	+	0.829341i	$0.311284\pi$
$828$		0			0
$829$	35.4543			1.23138			0.615690	−	0.787989i	$-0.288878\pi$
$829$	35.4543			1.23138			0.615690	+	0.787989i	$0.288878\pi$
$830$		0			0
$831$	53.3622	+	15.9466i	1.85112	+	0.553183i
$832$		0			0
$833$	−53.4116	−	92.5116i	−1.85060	−	3.20534i
$834$		0			0
$835$	−5.94744	+	10.3013i	−0.205820	+	0.356490i
$836$		0			0
$837$	12.6990	−	35.0531i	0.438940	−	1.21161i
$838$		0			0
$839$	−2.46587	+	4.27100i	−0.0851311	+	0.147451i	−0.905447	−	0.424459i	$-0.860464\pi$
$839$	−2.46587	+	4.27100i	−0.0851311	+	0.147451i	0.820316	+	0.571911i	$0.193798\pi$
$840$		0			0
$841$	−4.05765	−	7.02806i	−0.139919	−	0.242347i
$842$		0			0
$843$	−19.9911	−	5.97410i	−0.688532	−	0.205759i
$844$		0			0
$845$	−1.23670			−0.0425438
$846$		0			0
$847$	45.8912			1.57684
$848$		0			0
$849$	21.1492	−	19.9732i	0.725839	−	0.685478i
$850$		0			0
$851$	−20.9101	−	36.2174i	−0.716789	−	1.24152i
$852$		0			0
$853$	7.44717	−	12.8989i	0.254986	−	0.441649i	−0.709906	−	0.704297i	$-0.751262\pi$
$853$	7.44717	−	12.8989i	0.254986	−	0.441649i	0.964892	+	0.262648i	$0.0845957\pi$
$854$		0			0
$855$	−13.6980	−	8.98979i	−0.468463	−	0.307444i
$856$		0			0
$857$	−10.0396	+	17.3891i	−0.342946	+	0.593999i	−0.984978	−	0.172678i	$-0.944758\pi$
$857$	−10.0396	+	17.3891i	−0.342946	+	0.593999i	0.642033	+	0.766677i	$0.278091\pi$
$858$		0			0
$859$	6.62665	+	11.4777i	0.226098	+	0.391614i	0.956648	−	0.291245i	$-0.0940696\pi$
$859$	6.62665	+	11.4777i	0.226098	+	0.391614i	−0.730550	+	0.682859i	$0.760736\pi$
$860$		0			0
$861$	−1.96938	−	8.29106i	−0.0671164	−	0.282559i
$862$		0			0
$863$	10.8734			0.370135			0.185068	−	0.982726i	$-0.440750\pi$
$863$	10.8734			0.370135			0.185068	+	0.982726i	$0.440750\pi$
$864$		0			0
$865$	−0.451971			−0.0153675
$866$		0			0
$867$	15.3414	+	64.5871i	0.521022	+	2.19349i
$868$		0			0
$869$	−3.92156	−	6.79234i	−0.133030	−	0.230414i
$870$		0			0
$871$	−0.406963	+	0.704881i	−0.0137894	+	0.0238840i
$872$		0			0
$873$	−1.70262	+	29.7435i	−0.0576248	+	1.00666i
$874$		0			0
$875$	24.2082	−	41.9299i	0.818387	−	1.41749i
$876$		0			0
$877$	−6.24563	−	10.8178i	−0.210900	−	0.365289i	0.741096	−	0.671399i	$-0.234306\pi$
$877$	−6.24563	−	10.8178i	−0.210900	−	0.365289i	−0.951996	+	0.306109i	$0.900973\pi$
$878$		0			0
$879$	−15.0085	+	14.1739i	−0.506224	+	0.478075i
$880$		0			0
$881$	−1.28015			−0.0431293			−0.0215646	−	0.999767i	$-0.506865\pi$
$881$	−1.28015			−0.0431293			−0.0215646	+	0.999767i	$0.506865\pi$
$882$		0			0
$883$	−7.14883			−0.240577			−0.120289	−	0.992739i	$-0.538382\pi$
$883$	−7.14883			−0.240577			−0.120289	+	0.992739i	$0.538382\pi$
$884$		0			0
$885$	−16.5939	−	4.95889i	−0.557799	−	0.166691i
$886$		0			0
$887$	−6.25551	−	10.8349i	−0.210039	−	0.363799i	0.741687	−	0.670746i	$-0.234026\pi$
$887$	−6.25551	−	10.8349i	−0.210039	−	0.363799i	−0.951727	+	0.306947i	$0.900693\pi$
$888$		0			0
$889$	−18.9579	+	32.8361i	−0.635829	+	1.10129i
$890$		0			0
$891$	3.70581	+	8.54416i	0.124149	+	0.286240i
$892$		0			0
$893$	17.6914	−	30.6425i	0.592021	−	1.02541i
$894$		0			0
$895$	2.43834	+	4.22333i	0.0815047	+	0.141170i
$896$		0			0
$897$	8.05942	+	2.40846i	0.269096	+	0.0804160i
$898$		0			0
$899$	−43.7119			−1.45787
$900$		0			0
$901$	−77.6543			−2.58704
$902$		0			0
$903$	15.6196	−	14.7511i	0.519788	−	0.490885i
$904$		0			0
$905$	3.16268	+	5.47792i	0.105131	+	0.182092i
$906$		0			0
$907$	26.0188	−	45.0659i	0.863940	−	1.49639i	−0.00415607	−	0.999991i	$-0.501323\pi$
$907$	26.0188	−	45.0659i	0.863940	−	1.49639i	0.868096	−	0.496396i	$-0.165344\pi$
$908$		0			0
$909$	−1.02219	+	17.8570i	−0.0339040	+	0.592278i
$910$		0			0
$911$	25.0479	−	43.3842i	0.829873	−	1.43738i	−0.0682636	−	0.997667i	$-0.521746\pi$
$911$	25.0479	−	43.3842i	0.829873	−	1.43738i	0.898137	−	0.439716i	$-0.144921\pi$
$912$		0			0
$913$	2.65116	+	4.59194i	0.0877406	+	0.151971i
$914$		0			0
$915$	−5.86135	−	24.6762i	−0.193770	−	0.815768i
$916$		0			0
$917$	52.9766			1.74944
$918$		0			0
$919$	31.9154			1.05279			0.526396	−	0.850240i	$-0.323543\pi$
$919$	31.9154			1.05279			0.526396	+	0.850240i	$0.323543\pi$
$920$		0			0
$921$	0.958693	+	4.03608i	0.0315900	+	0.132993i
$922$		0			0
$923$	−5.15718	−	8.93249i	−0.169750	−	0.294016i
$924$		0			0
$925$	−14.9430	+	25.8821i	−0.491324	+	0.850999i
$926$		0			0
$927$	13.3187	+	8.74085i	0.437444	+	0.287087i
$928$		0			0
$929$	−0.968674	+	1.67779i	−0.0317812	+	0.0550466i	−0.881479	−	0.472224i	$-0.843451\pi$
$929$	−0.968674	+	1.67779i	−0.0317812	+	0.0550466i	0.849697	+	0.527271i	$0.176785\pi$
$930$		0			0
$931$	−31.7114	−	54.9257i	−1.03930	−	1.80012i
$932$		0			0
$933$	30.8825	−	29.1653i	1.01105	−	0.954829i
$934$		0			0
$935$	−9.51896			−0.311303
$936$		0			0
$937$	12.4448			0.406553			0.203277	−	0.979121i	$-0.434841\pi$
$937$	12.4448			0.406553			0.203277	+	0.979121i	$0.434841\pi$
$938$		0			0
$939$	13.8494	+	4.13873i	0.451959	+	0.135062i
$940$		0			0
$941$	14.0002	+	24.2490i	0.456393	+	0.790496i	0.998767	−	0.0496411i	$-0.0158078\pi$
$941$	14.0002	+	24.2490i	0.456393	+	0.790496i	−0.542374	+	0.840137i	$0.682474\pi$
$942$		0			0
$943$	2.58488	−	4.47714i	0.0841753	−	0.145796i
$944$		0			0
$945$	−19.1250	−	22.7232i	−0.622137	−	0.739187i
$946$		0			0
$947$	−24.2126	+	41.9375i	−0.786804	+	1.36278i	0.141111	+	0.989994i	$0.454932\pi$
$947$	−24.2126	+	41.9375i	−0.786804	+	1.36278i	−0.927915	+	0.372791i	$0.878401\pi$
$948$		0			0
$949$	−4.07695	−	7.06149i	−0.132344	−	0.229226i
$950$		0			0
$951$	−7.80089	−	2.33120i	−0.252961	−	0.0755943i
$952$		0			0
$953$	−19.9083			−0.644894			−0.322447	−	0.946588i	$-0.604505\pi$
$953$	−19.9083			−0.644894			−0.322447	+	0.946588i	$0.604505\pi$
$954$		0			0
$955$	−0.538604			−0.0174288
$956$		0			0
$957$	7.93865	−	7.49721i	0.256620	−	0.242350i
$958$		0			0
$959$	48.6768	+	84.3106i	1.57185	+	2.72253i
$960$		0			0
$961$	−10.2404	+	17.7369i	−0.330336	+	0.572159i
$962$		0			0
$963$	7.48309	−	3.76750i	0.241139	−	0.121406i
$964$		0			0
$965$	10.0700	−	17.4417i	0.324164	−	0.561469i
$966$		0			0
$967$	24.5219	+	42.4732i	0.788572	+	1.36585i	0.926842	+	0.375452i	$0.122512\pi$
$967$	24.5219	+	42.4732i	0.788572	+	1.36585i	−0.138270	+	0.990395i	$0.544154\pi$
$968$		0			0
$969$	13.1485	+	55.3551i	0.422392	+	1.77826i
$970$		0			0
$971$	−8.47587			−0.272004			−0.136002	−	0.990709i	$-0.543425\pi$
$971$	−8.47587			−0.272004			−0.136002	+	0.990709i	$0.543425\pi$
$972$		0			0
$973$	−108.894			−3.49099
$974$		0			0
$975$	−1.38919	−	5.84848i	−0.0444898	−	0.187301i
$976$		0			0
$977$	8.15362	+	14.1225i	0.260857	+	0.451818i	0.966470	−	0.256780i	$-0.0826615\pi$
$977$	8.15362	+	14.1225i	0.260857	+	0.451818i	−0.705613	+	0.708598i	$0.749328\pi$
$978$		0			0
$979$	1.74581	−	3.02383i	0.0557964	−	0.0966421i
$980$		0			0
$981$	30.4656	−	15.3384i	0.972691	−	0.489718i
$982$		0			0
$983$	−16.8494	+	29.1840i	−0.537411	+	0.930824i	0.461631	+	0.887072i	$0.347264\pi$
$983$	−16.8494	+	29.1840i	−0.537411	+	0.930824i	−0.999042	+	0.0437519i	$0.986069\pi$
$984$		0			0
$985$	−9.83957	−	17.0426i	−0.313515	−	0.543023i
$986$		0			0
$987$	46.6310	−	44.0380i	1.48428	−	1.40175i
$988$		0			0
$989$	13.0334			0.414439
$990$		0			0
$991$	−15.0990			−0.479634			−0.239817	−	0.970818i	$-0.577087\pi$
$991$	−15.0990			−0.479634			−0.239817	+	0.970818i	$0.577087\pi$
$992$		0			0
$993$	−24.6262	−	7.35924i	−0.781490	−	0.233538i
$994$		0			0
$995$	8.58179	+	14.8641i	0.272061	+	0.471224i
$996$		0			0
$997$	−7.49064	+	12.9742i	−0.237231	+	0.410896i	−0.959919	−	0.280279i	$-0.909573\pi$
$997$	−7.49064	+	12.9742i	−0.237231	+	0.410896i	0.722688	+	0.691175i	$0.242906\pi$
$998$		0			0
$999$	28.8131	+	34.2341i	0.911608	+	1.08312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.q.g.313.7	✓	22
3.2	odd	2		2808.2.q.g.937.4		22
9.2	odd	6		8424.2.a.be.1.8		11
9.4	even	3	inner	936.2.q.g.625.7	yes	22
9.5	odd	6		2808.2.q.g.1873.4		22
9.7	even	3		8424.2.a.bf.1.4		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.q.g.313.7	✓	22	1.1	even	1	trivial
936.2.q.g.625.7	yes	22	9.4	even	3	inner
2808.2.q.g.937.4		22	3.2	odd	2
2808.2.q.g.1873.4		22	9.5	odd	6
8424.2.a.be.1.8		11	9.2	odd	6
8424.2.a.bf.1.4		11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.400278 + 1.68516i) q^{3} +(0.618351 + 1.07102i) q^{5} +(2.31092 - 4.00263i) q^{7} +(-2.67955 + 1.34907i) q^{9} +(-0.517400 + 0.896163i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-1.55732 + 1.47073i) q^{15} +7.43820 q^{17} +4.41618 q^{19} +(7.67010 + 2.29211i) q^{21} +(2.42822 + 4.20580i) q^{23} +(1.73528 - 3.00560i) q^{25} +(-3.34597 - 3.97549i) q^{27} +(-3.04612 + 5.27603i) q^{29} +(3.58751 + 6.21374i) q^{31} +(-1.71728 - 0.513189i) q^{33} +5.71584 q^{35} -8.61130 q^{37} +(1.25926 - 1.18923i) q^{39} +(-0.532259 - 0.921899i) q^{41} +(1.34187 - 2.32419i) q^{43} +(-3.10178 - 2.03565i) q^{45} +(4.00605 - 6.93867i) q^{47} +(-7.18071 - 12.4374i) q^{49} +(2.97735 + 12.5346i) q^{51} -10.4399 q^{53} -1.27974 q^{55} +(1.76770 + 7.44199i) q^{57} +(4.04267 + 7.00211i) q^{59} +(-5.92025 + 10.2542i) q^{61} +(-0.792412 + 13.8429i) q^{63} +(0.618351 - 1.07102i) q^{65} +(-0.406963 - 0.704881i) q^{67} +(-6.11549 + 5.77543i) q^{69} +10.3144 q^{71} +8.15391 q^{73} +(5.75953 + 1.72116i) q^{75} +(2.39134 + 4.14192i) q^{77} +(-3.78968 + 6.56392i) q^{79} +(5.36003 - 7.22981i) q^{81} +(2.56200 - 4.43752i) q^{83} +(4.59942 + 7.96643i) q^{85} +(-10.1103 - 3.02133i) q^{87} -3.37420 q^{89} -4.62184 q^{91} +(-9.03518 + 8.53276i) q^{93} +(2.73075 + 4.72980i) q^{95} +(4.96536 - 8.60025i) q^{97} +(0.177416 - 3.09932i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{5} - 4 q^{7} - 4 q^{9} + 5 q^{11} - 11 q^{13} + 5 q^{15} + 8 q^{17} + 10 q^{19} + 4 q^{21} + 9 q^{23} - 24 q^{25} - 12 q^{27} - 16 q^{29} - q^{31} + 9 q^{33} + 18 q^{37} + 3 q^{39} - 6 q^{41}+ \cdots - 109 q^{99}+O(q^{100}) \) 22 * q - 3 * q^5 - 4 * q^7 - 4 * q^9 + 5 * q^11 - 11 * q^13 + 5 * q^15 + 8 * q^17 + 10 * q^19 + 4 * q^21 + 9 * q^23 - 24 * q^25 - 12 * q^27 - 16 * q^29 - q^31 + 9 * q^33 + 18 * q^37 + 3 * q^39 - 6 * q^41 - 7 * q^43 - 21 * q^45 + 21 * q^47 - 27 * q^49 - 11 * q^51 + 32 * q^53 + 34 * q^55 + 2 * q^57 + 11 * q^59 - 2 * q^61 - 27 * q^63 - 3 * q^65 - 18 * q^67 + 7 * q^69 - 30 * q^71 + 18 * q^73 + 62 * q^75 - 9 * q^77 - 30 * q^79 + 4 * q^81 - 16 * q^83 - 32 * q^85 + 33 * q^87 + 26 * q^89 + 8 * q^91 + 20 * q^95 - 10 * q^97 - 109 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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