LMFDB - Embedded newform 672.3.bh.a.577.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [672,3,Mod(481,672)] 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("672.481"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(672, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	672.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,-24,0,0,0,-12,0,24,0,-12,0,0,0,0,0,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$18.3106737650$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 76 x^{14} - 392 x^{13} + 1982 x^{12} - 7160 x^{11} + 23796 x^{10} - 61736 x^{9} + \cdots + 16807 $ x^16 - 8x^15 + 76x^14 - 392x^13 + 1982x^12 - 7160x^11 + 23796x^10 - 61736x^9 + 141869x^8 - 261520x^7 + 411696x^6 - 515296x^5 + 526280x^4 - 407176x^3 + 235396x^2 - 87808*x + 16807
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{18}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			577.1
Root			$0.500000 - 3.21278i$ of defining polynomial
Character	$\chi$	$=$	672.577
Dual form			672.3.bh.a.481.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 - 0.866025i) q^{3} +(-7.21243 + 4.16410i) q^{5} +(-5.15876 + 4.73151i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-7.36661 + 12.7593i) q^{11} +8.49148i q^{13} +14.4249 q^{15} +(17.8626 + 10.3130i) q^{17} +(9.53028 - 5.50231i) q^{19} +(11.8357 - 2.62965i) q^{21} +(-15.4788 - 26.8101i) q^{23} +(22.1794 - 38.4158i) q^{25} -5.19615i q^{27} -47.0132 q^{29} +(-38.7720 - 22.3850i) q^{31} +(22.0998 - 12.7593i) q^{33} +(17.5047 - 55.6072i) q^{35} +(4.49322 + 7.78248i) q^{37} +(7.35384 - 12.7372i) q^{39} +60.5425i q^{41} -1.11577 q^{43} +(-21.6373 - 12.4923i) q^{45} +(66.1896 - 38.2146i) q^{47} +(4.22557 - 48.8175i) q^{49} +(-17.8626 - 30.9389i) q^{51} +(-52.4136 + 90.7831i) q^{53} -122.701i q^{55} -19.0606 q^{57} +(-42.3384 - 24.4441i) q^{59} +(88.9552 - 51.3583i) q^{61} +(-20.0310 - 6.30558i) q^{63} +(-35.3594 - 61.2442i) q^{65} +(10.2674 - 17.7837i) q^{67} +53.6203i q^{69} -8.79832 q^{71} +(17.1084 + 9.87756i) q^{73} +(-66.5382 + 38.4158i) q^{75} +(-22.3684 - 100.678i) q^{77} +(17.9401 + 31.0731i) q^{79} +(-4.50000 + 7.79423i) q^{81} +4.30830i q^{83} -171.777 q^{85} +(70.5198 + 40.7147i) q^{87} +(70.8903 - 40.9286i) q^{89} +(-40.1776 - 43.8055i) q^{91} +(38.7720 + 67.1551i) q^{93} +(-45.8243 + 79.3700i) q^{95} -62.7407i q^{97} -44.1997 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{3} - 12 q^{7} + 24 q^{9} - 12 q^{11} - 48 q^{17} - 60 q^{19} + 24 q^{21} - 48 q^{23} + 52 q^{25} - 64 q^{29} - 60 q^{31} + 36 q^{33} - 4 q^{37} + 12 q^{39} + 72 q^{43} + 120 q^{47} - 8 q^{49}+ \cdots - 72 q^{99}+O(q^{100}) $ 16 * q - 24 * q^3 - 12 * q^7 + 24 * q^9 - 12 * q^11 - 48 * q^17 - 60 * q^19 + 24 * q^21 - 48 * q^23 + 52 * q^25 - 64 * q^29 - 60 * q^31 + 36 * q^33 - 4 * q^37 + 12 * q^39 + 72 * q^43 + 120 * q^47 - 8 * q^49 + 48 * q^51 - 72 * q^53 + 120 * q^57 - 228 * q^59 + 72 * q^61 - 36 * q^63 - 40 * q^65 + 12 * q^67 - 528 * q^71 - 36 * q^73 - 156 * q^75 - 96 * q^77 - 204 * q^79 - 72 * q^81 - 480 * q^85 + 96 * q^87 - 192 * q^89 - 276 * q^91 + 60 * q^93 - 48 * q^95 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$		0			0
$5$	−7.21243	+	4.16410i	−1.44249	+	0.832819i	−0.998015	−	0.0629746i	$-0.979941\pi$
$5$	−7.21243	+	4.16410i	−1.44249	+	0.832819i	−0.444470	+	0.895794i	$0.646608\pi$
$6$		0			0
$7$	−5.15876	+	4.73151i	−0.736965	+	0.675930i
$7$	−5.15876	+	4.73151i	−0.736965	+	0.675930i
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	−7.36661	+	12.7593i	−0.669692	+	1.15994i	0.308298	+	0.951290i	$0.400240\pi$
$11$	−7.36661	+	12.7593i	−0.669692	+	1.15994i	−0.977990	+	0.208651i	$0.933093\pi$
$12$		0			0
$13$			8.49148i			0.653191i	0.945164	+	0.326596i	$0.105901\pi$
$13$			8.49148i			0.653191i	−0.945164	+	0.326596i	$0.894099\pi$
$14$		0			0
$15$	14.4249			0.961657
$16$		0			0
$17$	17.8626	+	10.3130i	1.05074	+	0.606646i	0.922857	−	0.385143i	$-0.125848\pi$
$17$	17.8626	+	10.3130i	1.05074	+	0.606646i	0.127885	+	0.991789i	$0.459181\pi$
$18$		0			0
$19$	9.53028	−	5.50231i	0.501594	−	0.289595i	−0.227778	−	0.973713i	$-0.573146\pi$
$19$	9.53028	−	5.50231i	0.501594	−	0.289595i	0.729371	+	0.684118i	$0.239813\pi$
$20$		0			0
$21$	11.8357	−	2.62965i	0.563607	−	0.125222i
$22$		0			0
$23$	−15.4788	−	26.8101i	−0.672993	−	1.16566i	−0.977051	−	0.213004i	$-0.931675\pi$
$23$	−15.4788	−	26.8101i	−0.672993	−	1.16566i	0.304058	−	0.952653i	$-0.401658\pi$
$24$		0			0
$25$	22.1794	−	38.4158i	0.887175	−	1.53663i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	−47.0132			−1.62115			−0.810573	−	0.585638i	$-0.800844\pi$
$29$	−47.0132			−1.62115			−0.810573	+	0.585638i	$0.800844\pi$
$30$		0			0
$31$	−38.7720	−	22.3850i	−1.25071	−	0.722097i	−0.279459	−	0.960158i	$-0.590155\pi$
$31$	−38.7720	−	22.3850i	−1.25071	−	0.722097i	−0.971250	+	0.238060i	$0.923488\pi$
$32$		0			0
$33$	22.0998	−	12.7593i	0.669692	−	0.386647i
$34$		0			0
$35$	17.5047	−	55.6072i	0.500134	−	1.58878i
$36$		0			0
$37$	4.49322	+	7.78248i	0.121438	+	0.210337i	0.920335	−	0.391131i	$-0.127916\pi$
$37$	4.49322	+	7.78248i	0.121438	+	0.210337i	−0.798897	+	0.601468i	$0.794583\pi$
$38$		0			0
$39$	7.35384	−	12.7372i	0.188560	−	0.326596i
$40$		0			0
$41$			60.5425i			1.47665i	0.674447	+	0.738323i	$0.264382\pi$
$41$			60.5425i			1.47665i	−0.674447	+	0.738323i	$0.735618\pi$
$42$		0			0
$43$	−1.11577			−0.0259481			−0.0129740	−	0.999916i	$-0.504130\pi$
$43$	−1.11577			−0.0259481			−0.0129740	+	0.999916i	$0.504130\pi$
$44$		0			0
$45$	−21.6373	−	12.4923i	−0.480828	−	0.277606i
$46$		0			0
$47$	66.1896	−	38.2146i	1.40829	−	0.813076i	0.413065	−	0.910701i	$-0.364458\pi$
$47$	66.1896	−	38.2146i	1.40829	−	0.813076i	0.995223	+	0.0976256i	$0.0311248\pi$
$48$		0			0
$49$	4.22557	−	48.8175i	0.0862362	−	0.996275i
$50$		0			0
$51$	−17.8626	−	30.9389i	−0.350247	−	0.606646i
$52$		0			0
$53$	−52.4136	+	90.7831i	−0.988936	+	1.71289i	−0.366002	+	0.930614i	$0.619274\pi$
$53$	−52.4136	+	90.7831i	−0.988936	+	1.71289i	−0.622934	+	0.782274i	$0.714060\pi$
$54$		0			0
$55$		−	122.701i		−	2.23093i
$56$		0			0
$57$	−19.0606			−0.334396
$58$		0			0
$59$	−42.3384	−	24.4441i	−0.717600	−	0.414307i	0.0962686	−	0.995355i	$-0.469309\pi$
$59$	−42.3384	−	24.4441i	−0.717600	−	0.414307i	−0.813869	+	0.581049i	$0.802643\pi$
$60$		0			0
$61$	88.9552	−	51.3583i	1.45828	−	0.841939i	0.459354	−	0.888253i	$-0.348081\pi$
$61$	88.9552	−	51.3583i	1.45828	−	0.841939i	0.998927	+	0.0463140i	$0.0147475\pi$
$62$		0			0
$63$	−20.0310	−	6.30558i	−0.317952	−	0.100089i
$64$		0			0
$65$	−35.3594	−	61.2442i	−0.543990	−	0.942218i
$66$		0			0
$67$	10.2674	−	17.7837i	0.153245	−	0.265428i	−0.779174	−	0.626808i	$-0.784361\pi$
$67$	10.2674	−	17.7837i	0.153245	−	0.265428i	0.932419	+	0.361380i	$0.117694\pi$
$68$		0			0
$69$			53.6203i			0.777105i
$70$		0			0
$71$	−8.79832			−0.123920			−0.0619600	−	0.998079i	$-0.519735\pi$
$71$	−8.79832			−0.123920			−0.0619600	+	0.998079i	$0.519735\pi$
$72$		0			0
$73$	17.1084	+	9.87756i	0.234362	+	0.135309i	0.612583	−	0.790406i	$-0.290131\pi$
$73$	17.1084	+	9.87756i	0.234362	+	0.135309i	−0.378221	+	0.925715i	$0.623464\pi$
$74$		0			0
$75$	−66.5382	+	38.4158i	−0.887175	+	0.512211i
$76$		0			0
$77$	−22.3684	−	100.678i	−0.290499	−	1.30750i
$78$		0			0
$79$	17.9401	+	31.0731i	0.227089	+	0.393330i	0.956944	−	0.290272i	$-0.0937457\pi$
$79$	17.9401	+	31.0731i	0.227089	+	0.393330i	−0.729855	+	0.683602i	$0.760412\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			4.30830i			0.0519072i	0.999663	+	0.0259536i	$0.00826221\pi$
$83$			4.30830i			0.0519072i	−0.999663	+	0.0259536i	$0.991738\pi$
$84$		0			0
$85$	−171.777			−2.02090
$86$		0			0
$87$	70.5198	+	40.7147i	0.810573	+	0.467984i
$88$		0			0
$89$	70.8903	−	40.9286i	0.796521	−	0.459871i	−0.0457323	−	0.998954i	$-0.514562\pi$
$89$	70.8903	−	40.9286i	0.796521	−	0.459871i	0.842253	+	0.539082i	$0.181229\pi$
$90$		0			0
$91$	−40.1776	−	43.8055i	−0.441512	−	0.481379i
$92$		0			0
$93$	38.7720	+	67.1551i	0.416903	+	0.722097i
$94$		0			0
$95$	−45.8243	+	79.3700i	−0.482361	+	0.835474i
$96$		0			0
$97$		−	62.7407i		−	0.646812i	−0.946260	−	0.323406i	$-0.895172\pi$
$97$		−	62.7407i		−	0.646812i	0.946260	−	0.323406i	$-0.104828\pi$
$98$		0			0
$99$	−44.1997			−0.446461
$100$		0			0
$101$	113.394	+	65.4682i	1.12272	+	0.648200i	0.942093	−	0.335353i	$-0.108855\pi$
$101$	113.394	+	65.4682i	1.12272	+	0.648200i	0.180622	+	0.983553i	$0.442189\pi$
$102$		0			0
$103$	−6.51425	+	3.76101i	−0.0632452	+	0.0365146i	−0.531289	−	0.847191i	$-0.678292\pi$
$103$	−6.51425	+	3.76101i	−0.0632452	+	0.0365146i	0.468044	+	0.883705i	$0.344959\pi$
$104$		0			0
$105$	−74.4143	+	68.2514i	−0.708708	+	0.650013i
$106$		0			0
$107$	−38.8373	−	67.2683i	−0.362966	−	0.628675i	0.625482	−	0.780239i	$-0.284903\pi$
$107$	−38.8373	−	67.2683i	−0.362966	−	0.628675i	−0.988448	+	0.151564i	$0.951569\pi$
$108$		0			0
$109$	50.7763	−	87.9471i	0.465837	−	0.806854i	−0.533402	−	0.845862i	$-0.679087\pi$
$109$	50.7763	−	87.9471i	0.465837	−	0.806854i	0.999239	+	0.0390082i	$0.0124199\pi$
$110$		0			0
$111$		−	15.5650i		−	0.140225i
$112$		0			0
$113$	6.89019			0.0609751			0.0304876	−	0.999535i	$-0.490294\pi$
$113$	6.89019			0.0609751			0.0304876	+	0.999535i	$0.490294\pi$
$114$		0			0
$115$	223.280	+	128.911i	1.94156	+	1.12096i
$116$		0			0
$117$	−22.0615	+	12.7372i	−0.188560	+	0.108865i
$118$		0			0
$119$	−140.945	+	31.3150i	−1.18441	+	0.263151i
$120$		0			0
$121$	−48.0339	−	83.1971i	−0.396974	−	0.687580i
$122$		0			0
$123$	52.4313	−	90.8138i	0.426271	−	0.738323i
$124$		0			0
$125$			161.224i			1.28979i
$126$		0			0
$127$	−104.898			−0.825970			−0.412985	−	0.910738i	$-0.635514\pi$
$127$	−104.898			−0.825970			−0.412985	+	0.910738i	$0.635514\pi$
$128$		0			0
$129$	1.67365	+	0.966282i	0.0129740	+	0.00749056i
$130$		0			0
$131$	20.8066	−	12.0127i	0.158829	−	0.0917000i	−0.418479	−	0.908227i	$-0.637437\pi$
$131$	20.8066	−	12.0127i	0.158829	−	0.0917000i	0.577308	+	0.816527i	$0.304103\pi$
$132$		0			0
$133$	−23.1302	+	73.4777i	−0.173911	+	0.552464i
$134$		0			0
$135$	21.6373	+	37.4769i	0.160276	+	0.277606i
$136$		0			0
$137$	40.8638	−	70.7782i	0.298276	−	0.516630i	−0.677465	−	0.735555i	$-0.736922\pi$
$137$	40.8638	−	70.7782i	0.298276	−	0.516630i	0.975742	+	0.218925i	$0.0702550\pi$
$138$		0			0
$139$		−	57.8997i		−	0.416544i	−0.978071	−	0.208272i	$-0.933216\pi$
$139$		−	57.8997i		−	0.416544i	0.978071	−	0.208272i	$-0.0667840\pi$
$140$		0			0
$141$	−132.379			−0.938859
$142$		0			0
$143$	−108.346	−	62.5535i	−0.757663	−	0.437437i
$144$		0			0
$145$	339.079	−	195.768i	2.33848	−	1.35012i
$146$		0			0
$147$	−48.6155	+	69.5667i	−0.330718	+	0.473243i
$148$		0			0
$149$	−1.29307	−	2.23966i	−0.00867830	−	0.0150313i	0.861654	−	0.507497i	$-0.169429\pi$
$149$	−1.29307	−	2.23966i	−0.00867830	−	0.0150313i	−0.870332	+	0.492466i	$0.836096\pi$
$150$		0			0
$151$	72.2937	−	125.216i	0.478766	−	0.829247i	−0.520938	−	0.853595i	$-0.674418\pi$
$151$	72.2937	−	125.216i	0.478766	−	0.829247i	0.999704	+	0.0243477i	$0.00775089\pi$
$152$		0			0
$153$			61.8779i			0.404431i
$154$		0			0
$155$	372.853			2.40551
$156$		0			0
$157$	−108.354	−	62.5579i	−0.690150	−	0.398458i	0.113518	−	0.993536i	$-0.463788\pi$
$157$	−108.354	−	62.5579i	−0.690150	−	0.398458i	−0.803668	+	0.595078i	$0.797121\pi$
$158$		0			0
$159$	157.241	−	90.7831i	0.988936	−	0.570963i
$160$		0			0
$161$	206.704	+	65.0687i	1.28388	+	0.404153i
$162$		0			0
$163$	−107.403	−	186.028i	−0.658915	−	1.14128i	−0.980897	−	0.194529i	$-0.937682\pi$
$163$	−107.403	−	186.028i	−0.658915	−	1.14128i	0.321981	−	0.946746i	$-0.395651\pi$
$164$		0			0
$165$	−106.262	+	184.052i	−0.644014	+	1.11546i
$166$		0			0
$167$		−	15.6536i		−	0.0937341i	−0.998901	−	0.0468670i	$-0.985076\pi$
$167$		−	15.6536i		−	0.0937341i	0.998901	−	0.0468670i	$-0.0149237\pi$
$168$		0			0
$169$	96.8947			0.573341
$170$		0			0
$171$	28.5908	+	16.5069i	0.167198	+	0.0965317i
$172$		0			0
$173$	−71.2931	+	41.1611i	−0.412099	+	0.237925i	−0.691691	−	0.722193i	$-0.743134\pi$
$173$	−71.2931	+	41.1611i	−0.412099	+	0.237925i	0.279592	+	0.960119i	$0.409801\pi$
$174$		0			0
$175$	67.3469	+	303.120i	0.384839	+	1.73211i
$176$		0			0
$177$	42.3384	+	73.3323i	0.239200	+	0.414307i
$178$		0			0
$179$	−149.734	+	259.347i	−0.836504	+	1.44887i	0.0562959	+	0.998414i	$0.482071\pi$
$179$	−149.734	+	259.347i	−0.836504	+	1.44887i	−0.892800	+	0.450453i	$0.851262\pi$
$180$		0			0
$181$			144.379i			0.797672i	0.917022	+	0.398836i	$0.130586\pi$
$181$			144.379i			0.797672i	−0.917022	+	0.398836i	$0.869414\pi$
$182$		0			0
$183$	−177.910			−0.972188
$184$		0			0
$185$	−64.8140	−	37.4204i	−0.350346	−	0.202272i
$186$		0			0
$187$	−263.174	+	151.943i	−1.40735	+	0.812531i
$188$		0			0
$189$	24.5857	+	26.8057i	0.130083	+	0.141829i
$190$		0			0
$191$	151.589	+	262.559i	0.793658	+	1.37466i	0.923688	+	0.383146i	$0.125159\pi$
$191$	151.589	+	262.559i	0.793658	+	1.37466i	−0.130030	+	0.991510i	$0.541507\pi$
$192$		0			0
$193$	−95.3663	+	165.179i	−0.494126	+	0.855851i	−0.999977	−	0.00676941i	$-0.997845\pi$
$193$	−95.3663	+	165.179i	−0.494126	+	0.855851i	0.505851	+	0.862621i	$0.331179\pi$
$194$		0			0
$195$			122.488i			0.628146i
$196$		0			0
$197$	−155.533			−0.789509			−0.394754	−	0.918787i	$-0.629170\pi$
$197$	−155.533			−0.789509			−0.394754	+	0.918787i	$0.629170\pi$
$198$		0			0
$199$	198.410	+	114.552i	0.997037	+	0.575640i	0.907370	−	0.420332i	$-0.138086\pi$
$199$	198.410	+	114.552i	0.997037	+	0.575640i	0.0896670	+	0.995972i	$0.471420\pi$
$200$		0			0
$201$	−30.8022	+	17.7837i	−0.153245	+	0.0884759i
$202$		0			0
$203$	242.530	−	222.444i	1.19473	−	1.09578i
$204$		0			0
$205$	−252.105	−	436.658i	−1.22978	−	2.13004i
$206$		0			0
$207$	46.4365	−	80.4304i	0.224331	−	0.388553i
$208$		0			0
$209$			162.133i			0.775758i
$210$		0			0
$211$	−35.4502			−0.168011			−0.0840053	−	0.996465i	$-0.526771\pi$
$211$	−35.4502			−0.168011			−0.0840053	+	0.996465i	$0.526771\pi$
$212$		0			0
$213$	13.1975	+	7.61957i	0.0619600	+	0.0357726i
$214$		0			0
$215$	8.04738	−	4.64616i	0.0374297	−	0.0216100i
$216$		0			0
$217$	305.930	−	67.9713i	1.40982	−	0.313232i
$218$		0			0
$219$	−17.1084	−	29.6327i	−0.0781207	−	0.135309i
$220$		0			0
$221$	−87.5725	+	151.680i	−0.396256	+	0.686335i
$222$		0			0
$223$			246.335i			1.10464i	0.833631	+	0.552322i	$0.186258\pi$
$223$			246.335i			1.10464i	−0.833631	+	0.552322i	$0.813742\pi$
$224$		0			0
$225$	133.076			0.591450
$226$		0			0
$227$	54.0164	+	31.1864i	0.237958	+	0.137385i	0.614238	−	0.789121i	$-0.289464\pi$
$227$	54.0164	+	31.1864i	0.237958	+	0.137385i	−0.376280	+	0.926506i	$0.622797\pi$
$228$		0			0
$229$	176.412	−	101.851i	0.770356	−	0.444765i	−0.0626456	−	0.998036i	$-0.519954\pi$
$229$	176.412	−	101.851i	0.770356	−	0.444765i	0.833002	+	0.553271i	$0.186620\pi$
$230$		0			0
$231$	−53.6367	+	170.388i	−0.232193	+	0.737610i
$232$		0			0
$233$	−174.464	−	302.181i	−0.748774	−	1.29691i	−0.948411	−	0.317044i	$-0.897310\pi$
$233$	−174.464	−	302.181i	−0.748774	−	1.29691i	0.199637	−	0.979870i	$-0.436024\pi$
$234$		0			0
$235$	−318.258	+	551.239i	−1.35429	+	2.34570i
$236$		0			0
$237$		−	62.1462i		−	0.262220i
$238$		0			0
$239$	−137.867			−0.576850			−0.288425	−	0.957503i	$-0.593132\pi$
$239$	−137.867			−0.576850			−0.288425	+	0.957503i	$0.593132\pi$
$240$		0			0
$241$	−231.221	−	133.496i	−0.959425	−	0.553924i	−0.0634289	−	0.997986i	$-0.520204\pi$
$241$	−231.221	−	133.496i	−0.959425	−	0.553924i	−0.895996	+	0.444062i	$0.853537\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		0			0
$245$	172.804	+	369.688i	0.705322	+	1.50893i
$246$		0			0
$247$	46.7228	+	80.9262i	0.189161	+	0.327636i
$248$		0			0
$249$	3.73109	−	6.46244i	0.0149843	−	0.0259536i
$250$		0			0
$251$			175.586i			0.699548i	0.936834	+	0.349774i	$0.113742\pi$
$251$			175.586i			0.699548i	−0.936834	+	0.349774i	$0.886258\pi$
$252$		0			0
$253$	456.106			1.80279
$254$		0			0
$255$	257.665	+	148.763i	1.01045	+	0.583385i
$256$		0			0
$257$	−222.197	+	128.285i	−0.864579	+	0.499165i	−0.865543	−	0.500835i	$-0.833026\pi$
$257$	−222.197	+	128.285i	−0.864579	+	0.499165i	0.000964281		1.00000i	$0.499693\pi$
$258$		0			0
$259$	−60.0024	−	18.8882i	−0.231669	−	0.0729275i
$260$		0			0
$261$	−70.5198	−	122.144i	−0.270191	−	0.467984i
$262$		0			0
$263$	−224.162	+	388.259i	−0.852326	+	1.47627i	0.0267784	+	0.999641i	$0.491475\pi$
$263$	−224.162	+	388.259i	−0.852326	+	1.47627i	−0.879104	+	0.476630i	$0.841858\pi$
$264$		0			0
$265$		−	873.021i		−	3.29442i
$266$		0			0
$267$	−141.781			−0.531014
$268$		0			0
$269$	−291.914	−	168.537i	−1.08518	−	0.626530i	−0.152892	−	0.988243i	$-0.548859\pi$
$269$	−291.914	−	168.537i	−1.08518	−	0.626530i	−0.932290	+	0.361713i	$0.882192\pi$
$270$		0			0
$271$	148.371	−	85.6621i	0.547495	−	0.316096i	−0.200616	−	0.979670i	$-0.564294\pi$
$271$	148.371	−	85.6621i	0.547495	−	0.316096i	0.748111	+	0.663574i	$0.230961\pi$
$272$		0			0
$273$	22.3297	+	100.503i	0.0817936	+	0.368143i
$274$		0			0
$275$	326.774	+	565.989i	1.18827	+	2.05814i
$276$		0			0
$277$	48.6768	−	84.3106i	0.175728	−	0.304370i	−0.764685	−	0.644405i	$-0.777105\pi$
$277$	48.6768	−	84.3106i	0.175728	−	0.304370i	0.940413	+	0.340034i	$0.110439\pi$
$278$		0			0
$279$		−	134.310i		−	0.481398i
$280$		0			0
$281$	76.4885			0.272201			0.136101	−	0.990695i	$-0.456543\pi$
$281$	76.4885			0.272201			0.136101	+	0.990695i	$0.456543\pi$
$282$		0			0
$283$	−189.018	−	109.129i	−0.667906	−	0.385616i	0.127376	−	0.991854i	$-0.459344\pi$
$283$	−189.018	−	109.129i	−0.667906	−	0.385616i	−0.795283	+	0.606238i	$0.792678\pi$
$284$		0			0
$285$	137.473	−	79.3700i	0.482361	−	0.278491i
$286$		0			0
$287$	−286.458	−	312.324i	−0.998110	−	1.08824i
$288$		0			0
$289$	68.2151	+	118.152i	0.236038	+	0.408830i
$290$		0			0
$291$	−54.3351	+	94.1111i	−0.186718	+	0.323406i
$292$		0			0
$293$		−	85.1258i		−	0.290532i	−0.989393	−	0.145266i	$-0.953596\pi$
$293$		−	85.1258i		−	0.290532i	0.989393	−	0.145266i	$-0.0464038\pi$
$294$		0			0
$295$	407.150			1.38017
$296$		0			0
$297$	66.2995	+	38.2780i	0.223231	+	0.128882i
$298$		0			0
$299$	227.658	−	131.438i	0.761397	−	0.439593i
$300$		0			0
$301$	5.75597	−	5.27926i	0.0191228	−	0.0175391i
$302$		0			0
$303$	−113.394	−	196.405i	−0.374238	−	0.648200i
$304$		0			0
$305$	−427.722	+	740.836i	−1.40237	+	2.42897i
$306$		0			0
$307$		−	153.436i		−	0.499793i	−0.968273	−	0.249896i	$-0.919603\pi$
$307$		−	153.436i		−	0.499793i	0.968273	−	0.249896i	$-0.0803965\pi$
$308$		0			0
$309$	13.0285			0.0421635
$310$		0			0
$311$	−492.222	−	284.184i	−1.58271	−	0.913776i	−0.994462	−	0.105093i	$-0.966486\pi$
$311$	−492.222	−	284.184i	−1.58271	−	0.913776i	−0.588244	−	0.808683i	$-0.700181\pi$
$312$		0			0
$313$	−332.299	+	191.853i	−1.06166	+	0.612949i	−0.925891	−	0.377792i	$-0.876684\pi$
$313$	−332.299	+	191.853i	−1.06166	+	0.612949i	−0.135768	+	0.990741i	$0.543350\pi$
$314$		0			0
$315$	170.729	−	37.9324i	0.541996	−	0.120420i
$316$		0			0
$317$	−7.71140	−	13.3565i	−0.0243262	−	0.0421342i	0.853606	−	0.520919i	$-0.174411\pi$
$317$	−7.71140	−	13.3565i	−0.0243262	−	0.0421342i	−0.877932	+	0.478785i	$0.841077\pi$
$318$		0			0
$319$	346.328	−	599.858i	1.08567	−	1.88043i
$320$		0			0
$321$			134.537i			0.419117i
$322$		0			0
$323$	226.981			0.702727
$324$		0			0
$325$	326.207	+	188.336i	1.00371	+	0.579495i
$326$		0			0
$327$	−152.329	+	87.9471i	−0.465837	+	0.268951i
$328$		0			0
$329$	−160.643	+	510.316i	−0.488277	+	1.55111i
$330$		0			0
$331$	−108.876	−	188.579i	−0.328930	−	0.569724i	0.653370	−	0.757039i	$-0.273355\pi$
$331$	−108.876	−	188.579i	−0.328930	−	0.569724i	−0.982300	+	0.187315i	$0.940021\pi$
$332$		0			0
$333$	−13.4797	+	23.3475i	−0.0404795	+	0.0701125i
$334$		0			0
$335$			171.018i			0.510501i
$336$		0			0
$337$	−421.037			−1.24937			−0.624683	−	0.780878i	$-0.714772\pi$
$337$	−421.037			−1.24937			−0.624683	+	0.780878i	$0.714772\pi$
$338$		0			0
$339$	−10.3353	−	5.96708i	−0.0304876	−	0.0176020i
$340$		0			0
$341$	571.236	−	329.803i	1.67518	−	0.967165i
$342$		0			0
$343$	209.182	+	271.831i	0.609859	+	0.792510i
$344$		0			0
$345$	−223.280	−	386.732i	−0.647188	−	1.12096i
$346$		0			0
$347$	146.946	−	254.519i	0.423477	−	0.733484i	−0.572800	−	0.819695i	$-0.694143\pi$
$347$	146.946	−	254.519i	0.423477	−	0.733484i	0.996277	+	0.0862116i	$0.0274761\pi$
$348$		0			0
$349$			142.089i			0.407132i	0.979061	+	0.203566i	$0.0652532\pi$
$349$			142.089i			0.407132i	−0.979061	+	0.203566i	$0.934747\pi$
$350$		0			0
$351$	44.1230			0.125707
$352$		0			0
$353$	36.2907	+	20.9524i	0.102806	+	0.0593553i	0.550522	−	0.834821i	$-0.314429\pi$
$353$	36.2907	+	20.9524i	0.102806	+	0.0593553i	−0.447715	+	0.894176i	$0.647762\pi$
$354$		0			0
$355$	63.4572	−	36.6370i	0.178753	−	0.103203i
$356$		0			0
$357$	238.537	+	75.0894i	0.668170	+	0.210334i
$358$		0			0
$359$	−110.578	−	191.527i	−0.308017	−	0.533501i	0.669911	−	0.742441i	$-0.266332\pi$
$359$	−110.578	−	191.527i	−0.308017	−	0.533501i	−0.977929	+	0.208940i	$0.932999\pi$
$360$		0			0
$361$	−119.949	+	207.758i	−0.332269	+	0.575507i
$362$		0			0
$363$			166.394i			0.458386i
$364$		0			0
$365$	−164.524			−0.450752
$366$		0			0
$367$	−58.9333	−	34.0252i	−0.160581	−	0.0927117i	0.417556	−	0.908651i	$-0.362887\pi$
$367$	−58.9333	−	34.0252i	−0.160581	−	0.0927117i	−0.578137	+	0.815940i	$0.696220\pi$
$368$		0			0
$369$	−157.294	+	90.8138i	−0.426271	+	0.246108i
$370$		0			0
$371$	−159.152	−	716.324i	−0.428981	−	1.93079i
$372$		0			0
$373$	−357.885	−	619.875i	−0.959478	−	1.66186i	−0.723771	−	0.690040i	$-0.757593\pi$
$373$	−357.885	−	619.875i	−0.959478	−	1.66186i	−0.235707	−	0.971824i	$-0.575740\pi$
$374$		0			0
$375$	139.624	−	241.835i	0.372330	−	0.644894i
$376$		0			0
$377$		−	399.212i		−	1.05892i
$378$		0			0
$379$	386.176			1.01893			0.509467	−	0.860490i	$-0.329843\pi$
$379$	386.176			1.01893			0.509467	+	0.860490i	$0.329843\pi$
$380$		0			0
$381$	157.347	+	90.8445i	0.412985	+	0.238437i
$382$		0			0
$383$	−308.271	+	177.980i	−0.804886	+	0.464701i	−0.845177	−	0.534487i	$-0.820505\pi$
$383$	−308.271	+	177.980i	−0.804886	+	0.464701i	0.0402911	+	0.999188i	$0.487171\pi$
$384$		0			0
$385$	580.562	+	632.985i	1.50795	+	1.64412i
$386$		0			0
$387$	−1.67365	−	2.89885i	−0.00432468	−	0.00749056i
$388$		0			0
$389$	1.73326	−	3.00210i	0.00445569	−	0.00771748i	−0.863789	−	0.503854i	$-0.831915\pi$
$389$	1.73326	−	3.00210i	0.00445569	−	0.00771748i	0.868245	+	0.496136i	$0.165248\pi$
$390$		0			0
$391$		−	638.532i		−	1.63307i
$392$		0			0
$393$	−41.6132			−0.105886
$394$		0			0
$395$	−258.783	−	149.408i	−0.655146	−	0.378249i
$396$		0			0
$397$	434.505	−	250.861i	1.09447	−	0.631893i	0.159707	−	0.987164i	$-0.448945\pi$
$397$	434.505	−	250.861i	1.09447	−	0.631893i	0.934763	+	0.355272i	$0.115612\pi$
$398$		0			0
$399$	98.3288	−	90.1853i	0.246438	−	0.226028i
$400$		0			0
$401$	−128.281	−	222.189i	−0.319903	−	0.554088i	0.660565	−	0.750769i	$-0.270317\pi$
$401$	−128.281	−	222.189i	−0.319903	−	0.554088i	−0.980468	+	0.196681i	$0.936984\pi$
$402$		0			0
$403$	190.082	−	329.232i	0.471668	−	0.816952i
$404$		0			0
$405$		−	74.9537i		−	0.185071i
$406$		0			0
$407$	−132.399			−0.325305
$408$		0			0
$409$	−59.6169	−	34.4198i	−0.145763	−	0.0841561i	0.425345	−	0.905031i	$-0.360153\pi$
$409$	−59.6169	−	34.4198i	−0.145763	−	0.0841561i	−0.571108	+	0.820875i	$0.693486\pi$
$410$		0			0
$411$	−122.592	+	70.7782i	−0.298276	+	0.172210i
$412$		0			0
$413$	334.071	−	74.2236i	0.808889	−	0.179718i
$414$		0			0
$415$	−17.9402	−	31.0733i	−0.0432293	−	0.0748753i
$416$		0			0
$417$	−50.1426	+	86.8495i	−0.120246	+	0.208272i
$418$		0			0
$419$			494.854i			1.18103i	0.807025	+	0.590517i	$0.201076\pi$
$419$			494.854i			1.18103i	−0.807025	+	0.590517i	$0.798924\pi$
$420$		0			0
$421$	405.990			0.964347			0.482173	−	0.876076i	$-0.339847\pi$
$421$	405.990			0.964347			0.482173	+	0.876076i	$0.339847\pi$
$422$		0			0
$423$	198.569	+	114.644i	0.469430	+	0.271025i
$424$		0			0
$425$	792.363	−	457.471i	1.86438	−	1.07640i
$426$		0			0
$427$	−215.896	+	685.837i	−0.505611	+	1.60618i
$428$		0			0
$429$	108.346	+	187.660i	0.252554	+	0.437437i
$430$		0			0
$431$	91.4270	−	158.356i	0.212128	−	0.367416i	−0.740253	−	0.672329i	$-0.765294\pi$
$431$	91.4270	−	158.356i	0.212128	−	0.367416i	0.952380	+	0.304913i	$0.0986274\pi$
$432$		0			0
$433$			731.022i			1.68827i	0.536129	+	0.844136i	$0.319886\pi$
$433$			731.022i			1.68827i	−0.536129	+	0.844136i	$0.680114\pi$
$434$		0			0
$435$	−678.159			−1.55899
$436$		0			0
$437$	−295.035	−	170.339i	−0.675138	−	0.389791i
$438$		0			0
$439$	−568.087	+	327.985i	−1.29405	+	0.747119i	−0.979369	−	0.202080i	$-0.935230\pi$
$439$	−568.087	+	327.985i	−1.29405	+	0.747119i	−0.314678	+	0.949198i	$0.601897\pi$
$440$		0			0
$441$	133.170	−	62.2478i	0.301972	−	0.141152i
$442$		0			0
$443$	−206.680	−	357.980i	−0.466545	−	0.808080i	0.532724	−	0.846289i	$-0.321168\pi$
$443$	−206.680	−	357.980i	−0.466545	−	0.808080i	−0.999270	+	0.0382085i	$0.987835\pi$
$444$		0			0
$445$	−340.861	+	590.388i	−0.765980	+	1.32672i
$446$		0			0
$447$			4.47932i			0.0100208i
$448$		0			0
$449$	372.607			0.829860			0.414930	−	0.909853i	$-0.363806\pi$
$449$	372.607			0.829860			0.414930	+	0.909853i	$0.363806\pi$
$450$		0			0
$451$	−772.483	−	445.993i	−1.71282	−	0.988898i
$452$		0			0
$453$	−216.881	+	125.216i	−0.478766	+	0.276416i
$454$		0			0
$455$	472.188	+	148.641i	1.03778	+	0.326683i
$456$		0			0
$457$	−13.3793	−	23.1737i	−0.0292764	−	0.0507082i	0.851016	−	0.525140i	$-0.175987\pi$
$457$	−13.3793	−	23.1737i	−0.0292764	−	0.0507082i	−0.880292	+	0.474432i	$0.842654\pi$
$458$		0			0
$459$	53.5878	−	92.8168i	0.116749	−	0.202215i
$460$		0			0
$461$		−	679.215i		−	1.47335i	−0.676246	−	0.736676i	$-0.736394\pi$
$461$		−	679.215i		−	1.47335i	0.676246	−	0.736676i	$-0.263606\pi$
$462$		0			0
$463$	−761.698			−1.64514			−0.822568	−	0.568666i	$-0.807460\pi$
$463$	−761.698			−1.64514			−0.822568	+	0.568666i	$0.807460\pi$
$464$		0			0
$465$	−559.280	−	322.901i	−1.20275	−	0.694410i
$466$		0			0
$467$	650.561	−	375.602i	1.39306	−	0.804286i	0.399412	−	0.916772i	$-0.369214\pi$
$467$	650.561	−	375.602i	1.39306	−	0.804286i	0.993653	+	0.112485i	$0.0358811\pi$
$468$		0			0
$469$	31.1766	+	140.322i	0.0664746	+	0.299194i
$470$		0			0
$471$	108.354	+	187.674i	0.230050	+	0.398458i
$472$		0			0
$473$	8.21941	−	14.2364i	0.0173772	−	0.0300982i
$474$		0			0
$475$		−	488.151i		−	1.02769i
$476$		0			0
$477$	−314.482			−0.659291
$478$		0			0
$479$	703.994	+	406.451i	1.46972	+	0.848541i	0.999423	−	0.0339692i	$-0.0108148\pi$
$479$	703.994	+	406.451i	1.46972	+	0.848541i	0.470293	+	0.882510i	$0.344148\pi$
$480$		0			0
$481$	−66.0848	+	38.1541i	−0.137391	+	0.0793225i
$482$		0			0
$483$	−253.705	−	276.614i	−0.525269	−	0.572700i
$484$		0			0
$485$	261.258	+	452.513i	0.538677	+	0.933016i
$486$		0			0
$487$	67.8036	−	117.439i	0.139227	−	0.241149i	−0.787977	−	0.615705i	$-0.788872\pi$
$487$	67.8036	−	117.439i	0.139227	−	0.241149i	0.927204	+	0.374556i	$0.122205\pi$
$488$		0			0
$489$			372.056i			0.760850i
$490$		0			0
$491$	157.798			0.321380			0.160690	−	0.987005i	$-0.448628\pi$
$491$	157.798			0.321380			0.160690	+	0.987005i	$0.448628\pi$
$492$		0			0
$493$	−839.779	−	484.846i	−1.70340	−	0.983461i
$494$		0			0
$495$	318.787	−	184.052i	0.644014	−	0.371821i
$496$		0			0
$497$	45.3884	−	41.6294i	0.0913247	−	0.0837613i
$498$		0			0
$499$	178.980	+	310.002i	0.358677	+	0.621247i	0.987740	−	0.156107i	$-0.0498946\pi$
$499$	178.980	+	310.002i	0.358677	+	0.621247i	−0.629063	+	0.777354i	$0.716561\pi$
$500$		0			0
$501$	−13.5564	+	23.4804i	−0.0270587	+	0.0468670i
$502$		0			0
$503$		−	423.704i		−	0.842353i	−0.906979	−	0.421176i	$-0.861617\pi$
$503$		−	423.704i		−	0.842353i	0.906979	−	0.421176i	$-0.138383\pi$
$504$		0			0
$505$	−1090.46			−2.15933
$506$		0			0
$507$	−145.342	−	83.9133i	−0.286671	−	0.165509i
$508$		0			0
$509$	716.114	−	413.449i	1.40690	−	0.812277i	0.411816	−	0.911267i	$-0.364895\pi$
$509$	716.114	−	413.449i	1.40690	−	0.812277i	0.995088	+	0.0989903i	$0.0315613\pi$
$510$		0			0
$511$	−134.994	+	29.9928i	−0.264176	+	0.0586944i
$512$		0			0
$513$	−28.5908	−	49.5208i	−0.0557326	−	0.0965317i
$514$		0			0
$515$	31.3224	−	54.2520i	0.0608202	−	0.105344i
$516$		0			0
$517$			1126.05i			2.17804i
$518$		0			0
$519$	142.586			0.274733
$520$		0			0
$521$	−86.7574	−	50.0894i	−0.166521	−	0.0961409i	0.414423	−	0.910084i	$-0.363983\pi$
$521$	−86.7574	−	50.0894i	−0.166521	−	0.0961409i	−0.580944	+	0.813943i	$0.697317\pi$
$522$		0			0
$523$	−72.5028	+	41.8595i	−0.138629	+	0.0800373i	−0.567710	−	0.823228i	$-0.692171\pi$
$523$	−72.5028	+	41.8595i	−0.138629	+	0.0800373i	0.429082	+	0.903266i	$0.358837\pi$
$524$		0			0
$525$	161.489	−	513.004i	0.307599	−	0.977151i
$526$		0			0
$527$	−461.712	−	799.709i	−0.876115	−	1.51748i
$528$		0			0
$529$	−214.689	+	371.852i	−0.405839	+	0.702933i
$530$		0			0
$531$		−	146.665i		−	0.276204i
$532$		0			0
$533$	−514.096			−0.964532
$534$		0			0
$535$	560.223	+	323.445i	1.04715	+	0.604570i
$536$		0			0
$537$	449.203	−	259.347i	0.836504	−	0.482956i
$538$		0			0
$539$	591.751	+	413.535i	1.09787	+	0.767226i
$540$		0			0
$541$	−138.738	−	240.301i	−0.256447	−	0.444179i	0.708841	−	0.705369i	$-0.249218\pi$
$541$	−138.738	−	240.301i	−0.256447	−	0.444179i	−0.965287	+	0.261190i	$0.915885\pi$
$542$		0			0
$543$	125.036	−	216.568i	0.230268	−	0.398836i
$544$		0			0
$545$			845.749i			1.55183i
$546$		0			0
$547$	477.875			0.873629			0.436815	−	0.899552i	$-0.356107\pi$
$547$	477.875			0.873629			0.436815	+	0.899552i	$0.356107\pi$
$548$		0			0
$549$	266.865	+	154.075i	0.486094	+	0.280646i
$550$		0			0
$551$	−448.049	+	258.681i	−0.813156	+	0.469476i
$552$		0			0
$553$	−239.571	−	75.4150i	−0.433221	−	0.136374i
$554$		0			0
$555$	64.8140	+	112.261i	0.116782	+	0.202272i
$556$		0			0
$557$	383.386	−	664.045i	0.688306	−	1.19218i	−0.284080	−	0.958801i	$-0.591688\pi$
$557$	383.386	−	664.045i	0.688306	−	1.19218i	0.972386	−	0.233380i	$-0.0749786\pi$
$558$		0			0
$559$		−	9.47451i		−	0.0169490i
$560$		0			0
$561$	526.347			0.938231
$562$		0			0
$563$	−850.985	−	491.316i	−1.51152	−	0.872675i	−0.999909	−	0.0134564i	$-0.995717\pi$
$563$	−850.985	−	491.316i	−1.51152	−	0.872675i	−0.511608	−	0.859219i	$-0.670950\pi$
$564$		0			0
$565$	−49.6950	+	28.6914i	−0.0879557	+	0.0507813i
$566$		0			0
$567$	−13.6641	−	61.5003i	−0.0240989	−	0.108466i
$568$		0			0
$569$	−420.773	−	728.800i	−0.739495	−	1.28084i	−0.952723	−	0.303841i	$-0.901731\pi$
$569$	−420.773	−	728.800i	−0.739495	−	1.28084i	0.213227	−	0.977003i	$-0.431602\pi$
$570$		0			0
$571$	−100.734	+	174.477i	−0.176417	+	0.305564i	−0.940651	−	0.339376i	$-0.889784\pi$
$571$	−100.734	+	174.477i	−0.176417	+	0.305564i	0.764234	+	0.644940i	$0.223117\pi$
$572$		0			0
$573$		−	525.118i		−	0.916437i
$574$		0			0
$575$	−1373.24			−2.38825
$576$		0			0
$577$	837.034	+	483.262i	1.45067	+	0.837542i	0.998519	−	0.0544018i	$-0.0173252\pi$
$577$	837.034	+	483.262i	1.45067	+	0.837542i	0.452146	+	0.891944i	$0.350659\pi$
$578$		0			0
$579$	286.099	−	165.179i	0.494126	−	0.285284i
$580$		0			0
$581$	−20.3848	−	22.2255i	−0.0350856	−	0.0382538i
$582$		0			0
$583$	−772.222	−	1337.53i	−1.32457	−	2.29421i
$584$		0			0
$585$	106.078	−	183.733i	0.181330	−	0.314073i
$586$		0			0
$587$		−	824.078i		−	1.40388i	−0.712236	−	0.701940i	$-0.752317\pi$
$587$		−	824.078i		−	1.40388i	0.712236	−	0.701940i	$-0.247683\pi$
$588$		0			0
$589$	−492.677			−0.836464
$590$		0			0
$591$	233.300	+	134.696i	0.394754	+	0.227911i
$592$		0			0
$593$	−29.3431	+	16.9413i	−0.0494825	+	0.0285687i	−0.524537	−	0.851388i	$-0.675762\pi$
$593$	−29.3431	+	16.9413i	−0.0494825	+	0.0285687i	0.475055	+	0.879956i	$0.342428\pi$
$594$		0			0
$595$	886.156	−	812.765i	1.48934	−	1.36599i
$596$		0			0
$597$	−198.410	−	343.657i	−0.332346	−	0.575640i
$598$		0			0
$599$	529.215	−	916.627i	0.883497	−	1.53026i	0.0360702	−	0.999349i	$-0.488516\pi$
$599$	529.215	−	916.627i	0.883497	−	1.53026i	0.847427	−	0.530912i	$-0.178151\pi$
$600$		0			0
$601$			162.013i			0.269572i	0.990875	+	0.134786i	$0.0430347\pi$
$601$			162.013i			0.269572i	−0.990875	+	0.134786i	$0.956965\pi$
$602$		0			0
$603$	61.6044			0.102163
$604$		0			0
$605$	692.882	+	400.035i	1.14526	+	0.661216i
$606$		0			0
$607$	−205.690	+	118.755i	−0.338863	+	0.195643i	−0.659769	−	0.751468i	$-0.729346\pi$
$607$	−205.690	+	118.755i	−0.338863	+	0.195643i	0.320906	+	0.947111i	$0.396013\pi$
$608$		0			0
$609$	−556.437	+	123.629i	−0.913689	+	0.203002i
$610$		0			0
$611$	324.498	+	562.048i	0.531094	+	0.919882i
$612$		0			0
$613$	−20.5512	+	35.5957i	−0.0335255	+	0.0580680i	−0.882301	−	0.470685i	$-0.844007\pi$
$613$	−20.5512	+	35.5957i	−0.0335255	+	0.0580680i	0.848776	+	0.528753i	$0.177340\pi$
$614$		0			0
$615$			873.317i			1.42003i
$616$		0			0
$617$	−707.669			−1.14695			−0.573476	−	0.819222i	$-0.694405\pi$
$617$	−707.669			−1.14695			−0.573476	+	0.819222i	$0.694405\pi$
$618$		0			0
$619$	−689.396	−	398.023i	−1.11373	−	0.643010i	−0.173934	−	0.984757i	$-0.555648\pi$
$619$	−689.396	−	398.023i	−1.11373	−	0.643010i	−0.939792	+	0.341748i	$0.888981\pi$
$620$		0			0
$621$	−139.310	+	80.4304i	−0.224331	+	0.129518i
$622$		0			0
$623$	−172.052	+	546.559i	−0.276167	+	0.877302i
$624$		0			0
$625$	−116.866	−	202.417i	−0.186985	−	0.323868i
$626$		0			0
$627$	140.412	−	243.200i	0.223942	−	0.387879i
$628$		0			0
$629$			185.354i			0.294680i
$630$		0			0
$631$	925.600			1.46688			0.733439	−	0.679755i	$-0.237914\pi$
$631$	925.600			1.46688			0.733439	+	0.679755i	$0.237914\pi$
$632$		0			0
$633$	53.1753	+	30.7008i	0.0840053	+	0.0485005i
$634$		0			0
$635$	756.570	−	436.806i	1.19145	−	0.687884i
$636$		0			0
$637$	414.533	+	35.8814i	0.650758	+	0.0563287i
$638$		0			0
$639$	−13.1975	−	22.8587i	−0.0206533	−	0.0357726i
$640$		0			0
$641$	315.870	−	547.102i	0.492776	−	0.853514i	−0.507189	−	0.861835i	$-0.669315\pi$
$641$	315.870	−	547.102i	0.492776	−	0.853514i	0.999965	+	0.00832113i	$0.00264873\pi$
$642$		0			0
$643$			270.185i			0.420194i	0.977681	+	0.210097i	$0.0673780\pi$
$643$			270.185i			0.420194i	−0.977681	+	0.210097i	$0.932622\pi$
$644$		0			0
$645$	−16.0948			−0.0249531
$646$		0			0
$647$	556.635	+	321.373i	0.860332	+	0.496713i	0.864124	−	0.503280i	$-0.167873\pi$
$647$	556.635	+	321.373i	0.860332	+	0.496713i	−0.00379117	+	0.999993i	$0.501207\pi$
$648$		0			0
$649$	623.781	−	360.140i	0.961142	−	0.554915i
$650$		0			0
$651$	−517.760	−	162.987i	−0.795331	−	0.250363i
$652$		0			0
$653$	−575.070	−	996.050i	−0.880658	−	1.52534i	−0.850611	−	0.525796i	$-0.823767\pi$
$653$	−575.070	−	996.050i	−0.880658	−	1.52534i	−0.0300475	−	0.999548i	$-0.509566\pi$
$654$		0			0
$655$	−100.044	+	173.281i	−0.152739	+	0.264552i
$656$		0			0
$657$			59.2653i			0.0902060i
$658$		0			0
$659$	−350.787			−0.532303			−0.266151	−	0.963931i	$-0.585752\pi$
$659$	−350.787			−0.532303			−0.266151	+	0.963931i	$0.585752\pi$
$660$		0			0
$661$	1061.60	+	612.918i	1.60606	+	0.927258i	0.990240	+	0.139370i	$0.0445078\pi$
$661$	1061.60	+	612.918i	1.60606	+	0.927258i	0.615818	+	0.787888i	$0.288826\pi$
$662$		0			0
$663$	262.717	−	151.680i	0.396256	−	0.228778i
$664$		0			0
$665$	−139.144	−	626.269i	−0.209239	−	0.941757i
$666$		0			0
$667$	727.710	+	1260.43i	1.09102	+	1.88970i
$668$		0			0
$669$	213.333	−	369.503i	0.318883	−	0.552322i
$670$		0			0
$671$			1513.35i			2.25536i
$672$		0			0
$673$	−885.582			−1.31587			−0.657936	−	0.753074i	$-0.728570\pi$
$673$	−885.582			−1.31587			−0.657936	+	0.753074i	$0.728570\pi$
$674$		0			0
$675$	−199.614	−	115.247i	−0.295725	−	0.170737i
$676$		0			0
$677$	627.726	−	362.418i	0.927218	−	0.535329i	0.0412871	−	0.999147i	$-0.486854\pi$
$677$	627.726	−	362.418i	0.927218	−	0.535329i	0.885931	+	0.463818i	$0.153521\pi$
$678$		0			0
$679$	296.859	+	323.664i	0.437200	+	0.476678i
$680$		0			0
$681$	−54.0164	−	93.5591i	−0.0793192	−	0.137385i
$682$		0			0
$683$	−454.674	+	787.518i	−0.665701	+	1.15303i	0.313393	+	0.949623i	$0.398534\pi$
$683$	−454.674	+	787.518i	−0.665701	+	1.15303i	−0.979095	+	0.203405i	$0.934799\pi$
$684$		0			0
$685$			680.644i			0.993640i
$686$		0			0
$687$	−352.823			−0.513571
$688$		0			0
$689$	−770.883	−	445.070i	−1.11884	−	0.645964i
$690$		0			0
$691$	−595.946	+	344.070i	−0.862440	+	0.497930i	−0.864829	−	0.502067i	$-0.832573\pi$
$691$	−595.946	+	344.070i	−0.862440	+	0.497930i	0.00238851	+	0.999997i	$0.499240\pi$
$692$		0			0
$693$	228.015	−	209.131i	0.329026	−	0.301777i
$694$		0			0
$695$	241.100	+	417.597i	0.346906	+	0.600859i
$696$		0			0
$697$	−624.374	+	1081.45i	−0.895801	+	1.55157i
$698$		0			0
$699$			604.362i			0.864609i
$700$		0			0
$701$	−689.466			−0.983546			−0.491773	−	0.870723i	$-0.663651\pi$
$701$	−689.466			−0.983546			−0.491773	+	0.870723i	$0.663651\pi$
$702$		0			0
$703$	85.6433	+	49.4462i	0.121825	+	0.0703359i
$704$		0			0
$705$	954.775	−	551.239i	1.35429	−	0.781900i
$706$		0			0
$707$	−894.737	+	198.792i	−1.26554	+	0.281176i
$708$		0			0
$709$	334.179	+	578.814i	0.471338	+	0.816381i	0.999462	−	0.0327858i	$-0.0104379\pi$
$709$	334.179	+	578.814i	0.471338	+	0.816381i	−0.528125	+	0.849167i	$0.677105\pi$
$710$		0			0
$711$	−53.8202	+	93.2193i	−0.0756965	+	0.131110i
$712$		0			0
$713$			1385.98i			1.94387i
$714$		0			0
$715$	1041.91			1.45722
$716$		0			0
$717$	206.801	+	119.396i	0.288425	+	0.166522i
$718$		0			0
$719$	164.703	−	95.0912i	0.229072	−	0.132255i	−0.381072	−	0.924545i	$-0.624445\pi$
$719$	164.703	−	95.0912i	0.229072	−	0.132255i	0.610144	+	0.792291i	$0.291112\pi$
$720$		0			0
$721$	15.8102	−	50.2244i	0.0219282	−	0.0696594i
$722$		0			0
$723$	231.221	+	400.487i	0.319808	+	0.553924i
$724$		0			0
$725$	−1042.72	+	1806.05i	−1.43824	+	2.49111i
$726$		0			0
$727$			95.5969i			0.131495i	0.997836	+	0.0657475i	$0.0209432\pi$
$727$			95.5969i			0.131495i	−0.997836	+	0.0657475i	$0.979057\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−19.9305	−	11.5069i	−0.0272647	−	0.0157413i
$732$		0			0
$733$	497.529	−	287.249i	0.678758	−	0.391881i	−0.120629	−	0.992698i	$-0.538491\pi$
$733$	497.529	−	287.249i	0.678758	−	0.391881i	0.799387	+	0.600817i	$0.205158\pi$
$734$		0			0
$735$	60.9532	−	704.185i	0.0829296	−	0.958074i
$736$		0			0
$737$	151.272	+	262.011i	0.205254	+	0.355510i
$738$		0			0
$739$	−442.421	+	766.296i	−0.598676	+	1.03694i	0.394341	+	0.918964i	$0.370973\pi$
$739$	−442.421	+	766.296i	−0.598676	+	1.03694i	−0.993017	+	0.117973i	$0.962360\pi$
$740$		0			0
$741$		−	161.852i		−	0.218424i
$742$		0			0
$743$	−245.958			−0.331033			−0.165517	−	0.986207i	$-0.552929\pi$
$743$	−245.958			−0.331033			−0.165517	+	0.986207i	$0.552929\pi$
$744$		0			0
$745$	18.6523	+	10.7689i	0.0250366	+	0.0144549i
$746$		0			0
$747$	−11.1933	+	6.46244i	−0.0149843	+	0.00865120i
$748$		0			0
$749$	518.633	+	163.261i	0.692434	+	0.217972i
$750$		0			0
$751$	−7.33995	−	12.7132i	−0.00977357	−	0.0169283i	0.861097	−	0.508440i	$-0.169778\pi$
$751$	−7.33995	−	12.7132i	−0.00977357	−	0.0169283i	−0.870871	+	0.491512i	$0.836444\pi$
$752$		0			0
$753$	152.062	−	263.380i	0.201942	−	0.349774i
$754$		0			0
$755$			1204.15i			1.59490i
$756$		0			0
$757$	41.6269			0.0549893			0.0274947	−	0.999622i	$-0.491247\pi$
$757$	41.6269			0.0549893			0.0274947	+	0.999622i	$0.491247\pi$
$758$		0			0
$759$	−684.159	−	395.000i	−0.901396	−	0.520421i
$760$		0			0
$761$	−626.101	+	361.479i	−0.822734	+	0.475006i	−0.851358	−	0.524584i	$-0.824221\pi$
$761$	−626.101	+	361.479i	−0.822734	+	0.475006i	0.0286243	+	0.999590i	$0.490887\pi$
$762$		0			0
$763$	154.180	+	693.946i	0.202071	+	0.909497i
$764$		0			0
$765$	−257.665	−	446.290i	−0.336817	−	0.583385i
$766$		0			0
$767$	207.567	−	359.516i	0.270621	−	0.468730i
$768$		0			0
$769$		−	298.436i		−	0.388083i	−0.980993	−	0.194042i	$-0.937840\pi$
$769$		−	298.436i		−	0.388083i	0.980993	−	0.194042i	$-0.0621597\pi$
$770$		0			0
$771$	444.393			0.576386
$772$		0			0
$773$	53.9583	+	31.1529i	0.0698038	+	0.0403013i	0.534496	−	0.845171i	$-0.320502\pi$
$773$	53.9583	+	31.1529i	0.0698038	+	0.0403013i	−0.464692	+	0.885472i	$0.653835\pi$
$774$		0			0
$775$	−1719.88	+	992.972i	−2.21920	+	1.28125i
$776$		0			0
$777$	73.6458	+	80.2959i	0.0947823	+	0.103341i
$778$		0			0
$779$	333.124	+	576.987i	0.427630	+	0.740676i
$780$		0			0
$781$	64.8138	−	112.261i	0.0829882	−	0.143740i
$782$		0			0
$783$			244.288i			0.311990i
$784$		0			0
$785$	1041.99			1.32737
$786$		0			0
$787$	−276.770	−	159.793i	−0.351678	−	0.203041i	0.313746	−	0.949507i	$-0.398416\pi$
$787$	−276.770	−	159.793i	−0.351678	−	0.203041i	−0.665424	+	0.746466i	$0.731749\pi$
$788$		0			0
$789$	672.485	−	388.259i	0.852326	−	0.492090i
$790$		0			0
$791$	−35.5448	+	32.6010i	−0.0449366	+	0.0412150i
$792$		0			0
$793$	436.108	+	755.361i	0.549947	+	0.952536i
$794$		0			0
$795$	−756.059	+	1309.53i	−0.951017	+	1.64721i
$796$		0			0
$797$			267.732i			0.335924i	0.985793	+	0.167962i	$0.0537186\pi$
$797$			267.732i			0.335924i	−0.985793	+	0.167962i	$0.946281\pi$
$798$		0			0
$799$	1576.42			1.97300
$800$		0			0
$801$	212.671	+	122.786i	0.265507	+	0.153290i
$802$		0			0
$803$	−252.062	+	145.528i	−0.313901	+	0.181231i
$804$		0			0
$805$	−1761.79	+	391.433i	−2.18856	+	0.486252i
$806$		0			0
$807$	291.914	+	505.610i	0.361727	+	0.626530i
$808$		0			0
$809$	280.552	−	485.930i	0.346788	−	0.600655i	−0.638889	−	0.769299i	$-0.720606\pi$
$809$	280.552	−	485.930i	0.346788	−	0.600655i	0.985677	+	0.168644i	$0.0539390\pi$
$810$		0			0
$811$		−	1190.74i		−	1.46824i	−0.679018	−	0.734121i	$-0.737594\pi$
$811$		−	1190.74i		−	1.46824i	0.679018	−	0.734121i	$-0.262406\pi$
$812$		0			0
$813$	−296.742			−0.364997
$814$		0			0
$815$	1549.28	+	894.475i	1.90095	+	1.09751i
$816$		0			0
$817$	−10.6336	+	6.13929i	−0.0130154	+	0.00751443i
$818$		0			0
$819$	53.5437	−	170.093i	0.0653769	−	0.207683i
$820$		0			0
$821$	307.564	+	532.716i	0.374621	+	0.648862i	0.990270	−	0.139158i	$-0.0444396\pi$
$821$	307.564	+	532.716i	0.374621	+	0.648862i	−0.615649	+	0.788020i	$0.711106\pi$
$822$		0			0
$823$	−635.998	+	1101.58i	−0.772780	+	1.33849i	0.163254	+	0.986584i	$0.447801\pi$
$823$	−635.998	+	1101.58i	−0.772780	+	1.33849i	−0.936034	+	0.351910i	$0.885532\pi$
$824$		0			0
$825$		−	1131.98i		−	1.37209i
$826$		0			0
$827$	598.318			0.723480			0.361740	−	0.932279i	$-0.382183\pi$
$827$	598.318			0.723480			0.361740	+	0.932279i	$0.382183\pi$
$828$		0			0
$829$	−1264.54	−	730.085i	−1.52538	−	0.880681i	−0.999547	−	0.0300958i	$-0.990419\pi$
$829$	−1264.54	−	730.085i	−1.52538	−	0.880681i	−0.525837	−	0.850585i	$-0.676248\pi$
$830$		0			0
$831$	−146.030	+	84.3106i	−0.175728	+	0.101457i
$832$		0			0
$833$	578.933	−	828.429i	0.694998	−	0.994512i
$834$		0			0
$835$	65.1831	+	112.900i	0.0780635	+	0.135210i
$836$		0			0
$837$	−116.316	+	201.465i	−0.138968	+	0.240699i
$838$		0			0
$839$		−	189.331i		−	0.225663i	−0.993614	−	0.112832i	$-0.964008\pi$
$839$		−	189.331i		−	0.225663i	0.993614	−	0.112832i	$-0.0359921\pi$
$840$		0			0
$841$	1369.24			1.62811
$842$		0			0
$843$	−114.733	−	66.2410i	−0.136101	−	0.0785777i
$844$		0			0
$845$	−698.846	+	403.479i	−0.827036	+	0.477490i
$846$		0			0
$847$	641.444	+	201.921i	0.757312	+	0.238395i
$848$		0			0
$849$	189.018	+	327.388i	0.222635	+	0.385616i
$850$		0			0
$851$	139.100	−	240.928i	0.163454	−	0.283111i
$852$		0			0
$853$			426.767i			0.500313i	0.968205	+	0.250157i	$0.0804821\pi$
$853$			426.767i			0.500313i	−0.968205	+	0.250157i	$0.919518\pi$
$854$		0			0
$855$	−274.946			−0.321574
$856$		0			0
$857$	764.302	+	441.270i	0.891834	+	0.514900i	0.874542	−	0.484950i	$-0.161162\pi$
$857$	764.302	+	441.270i	0.891834	+	0.514900i	0.0172919	+	0.999850i	$0.494496\pi$
$858$		0			0
$859$	346.399	−	199.994i	0.403259	−	0.232822i	−0.284630	−	0.958637i	$-0.591871\pi$
$859$	346.399	−	199.994i	0.403259	−	0.232822i	0.687889	+	0.725816i	$0.258538\pi$
$860$		0			0
$861$	159.206	+	716.566i	0.184908	+	0.832248i
$862$		0			0
$863$	−469.793	−	813.706i	−0.544372	−	0.942880i	−0.998646	−	0.0520183i	$-0.983435\pi$
$863$	−469.793	−	813.706i	−0.544372	−	0.942880i	0.454274	−	0.890862i	$-0.349899\pi$
$864$		0			0
$865$	342.797	−	593.743i	0.396298	−	0.686408i
$866$		0			0
$867$		−	236.304i		−	0.272554i
$868$		0			0
$869$	−528.630			−0.608320
$870$		0			0
$871$	151.010	+	87.1855i	0.173375	+	0.100098i
$872$		0			0
$873$	163.005	−	94.1111i	0.186718	−	0.107802i
$874$		0			0
$875$	−762.831	−	831.713i	−0.871807	−	0.950529i
$876$		0			0
$877$	162.256	+	281.036i	0.185013	+	0.320451i	0.943581	−	0.331142i	$-0.107434\pi$
$877$	162.256	+	281.036i	0.185013	+	0.320451i	−0.758568	+	0.651594i	$0.774101\pi$
$878$		0			0
$879$	−73.7211	+	127.689i	−0.0838693	+	0.145266i
$880$		0			0
$881$		−	810.382i		−	0.919844i	−0.887959	−	0.459922i	$-0.847877\pi$
$881$		−	810.382i		−	0.919844i	0.887959	−	0.459922i	$-0.152123\pi$
$882$		0			0
$883$	−225.207			−0.255048			−0.127524	−	0.991835i	$-0.540703\pi$
$883$	−225.207			−0.255048			−0.127524	+	0.991835i	$0.540703\pi$
$884$		0			0
$885$	−610.725	−	352.602i	−0.690085	−	0.398421i
$886$		0			0
$887$	−111.660	+	64.4668i	−0.125885	+	0.0726796i	−0.561620	−	0.827395i	$-0.689822\pi$
$887$	−111.660	+	64.4668i	−0.125885	+	0.0726796i	0.435735	+	0.900075i	$0.356488\pi$
$888$		0			0
$889$	541.144	−	496.327i	0.608711	−	0.558298i
$890$		0			0
$891$	−66.2995	−	114.834i	−0.0744102	−	0.128882i
$892$		0			0
$893$	420.537	−	728.391i	0.470926	−	0.815667i
$894$		0			0
$895$		−	2494.03i		−	2.78663i
$896$		0			0
$897$	−455.316			−0.507598
$898$		0			0
$899$	1822.80	+	1052.39i	2.02758	+	1.17063i
$900$		0			0
$901$	−1872.49	+	1081.08i	−2.07823	+	1.19987i
$902$		0			0
$903$	−13.2059	+	2.93408i	−0.0146245	+	0.00324926i
$904$		0			0
$905$	−601.206	−	1041.32i	−0.664316	−	1.15063i
$906$		0			0
$907$	−656.138	+	1136.46i	−0.723415	+	1.25299i	0.236208	+	0.971703i	$0.424095\pi$
$907$	−656.138	+	1136.46i	−0.723415	+	1.25299i	−0.959623	+	0.281289i	$0.909238\pi$
$908$		0			0
$909$			392.809i			0.432133i
$910$		0			0
$911$	−1496.33			−1.64251			−0.821256	−	0.570559i	$-0.806727\pi$
$911$	−1496.33			−1.64251			−0.821256	+	0.570559i	$0.806727\pi$
$912$		0			0
$913$	−54.9710	−	31.7375i	−0.0602092	−	0.0347618i
$914$		0			0
$915$	1283.16	−	740.836i	1.40237	−	0.809656i
$916$		0			0
$917$	−50.4980	+	160.417i	−0.0550687	+	0.174937i
$918$		0			0
$919$	897.082	+	1553.79i	0.976150	+	1.69074i	0.676086	+	0.736822i	$0.263675\pi$
$919$	897.082	+	1553.79i	0.976150	+	1.69074i	0.300064	+	0.953919i	$0.402992\pi$
$920$		0			0
$921$	−132.880	+	230.154i	−0.144278	+	0.249896i
$922$		0			0
$923$		−	74.7108i		−	0.0809434i
$924$		0			0
$925$	398.627			0.430949
$926$		0			0
$927$	−19.5428	−	11.2830i	−0.0210817	−	0.0121715i
$928$		0			0
$929$	192.764	−	111.292i	0.207496	−	0.119798i	−0.392651	−	0.919688i	$-0.628442\pi$
$929$	192.764	−	111.292i	0.207496	−	0.119798i	0.600147	+	0.799890i	$0.295109\pi$
$930$		0			0
$931$	−228.338	−	488.494i	−0.245261	−	0.524699i
$932$		0			0
$933$	492.222	+	852.553i	0.527569	+	0.913776i
$934$		0			0
$935$	1265.41	−	2191.76i	1.35338	−	2.34413i
$936$		0			0
$937$		−	276.806i		−	0.295418i	−0.989031	−	0.147709i	$-0.952810\pi$
$937$		−	276.806i		−	0.295418i	0.989031	−	0.147709i	$-0.0471898\pi$
$938$		0			0
$939$	664.598			0.707772
$940$		0			0
$941$	−1025.60	−	592.133i	−1.08991	−	0.629259i	−0.156356	−	0.987701i	$-0.549975\pi$
$941$	−1025.60	−	592.133i	−1.08991	−	0.629259i	−0.933552	+	0.358442i	$0.883308\pi$
$942$		0			0
$943$	1623.15	−	937.127i	1.72126	−	0.993772i
$944$		0			0
$945$	−288.944	−	90.9570i	−0.305761	−	0.0962508i
$946$		0			0
$947$	23.0435	+	39.9124i	0.0243331	+	0.0421462i	0.877936	−	0.478779i	$-0.158920\pi$
$947$	23.0435	+	39.9124i	0.0243331	+	0.0421462i	−0.853602	+	0.520925i	$0.825587\pi$
$948$		0			0
$949$	−83.8751	+	145.276i	−0.0883826	+	0.153083i
$950$		0			0
$951$			26.7131i			0.0280894i
$952$		0			0
$953$	245.731			0.257850			0.128925	−	0.991654i	$-0.458847\pi$
$953$	245.731			0.257850			0.128925	+	0.991654i	$0.458847\pi$
$954$		0			0
$955$	−2186.64	−	1262.46i	−2.28968	−	1.32195i
$956$		0			0
$957$	−1038.98	+	599.858i	−1.08567	+	0.626811i
$958$		0			0
$959$	124.082	+	558.476i	0.129386	+	0.582352i
$960$		0			0
$961$	521.678	+	903.573i	0.542849	+	0.940242i
$962$		0			0
$963$	116.512	−	201.805i	0.120989	−	0.209558i
$964$		0			0
$965$		−	1588.46i		−	1.64607i
$966$		0			0
$967$	−199.613			−0.206425			−0.103213	−	0.994659i	$-0.532912\pi$
$967$	−199.613			−0.206425			−0.103213	+	0.994659i	$0.532912\pi$
$968$		0			0
$969$	−340.471	−	196.571i	−0.351363	−	0.202860i
$970$		0			0
$971$	−1001.62	+	578.285i	−1.03153	+	0.595556i	−0.917424	−	0.397912i	$-0.869735\pi$
$971$	−1001.62	+	578.285i	−1.03153	+	0.595556i	−0.114110	+	0.993468i	$0.536402\pi$
$972$		0			0
$973$	273.953	+	298.690i	0.281555	+	0.306979i
$974$		0			0
$975$	−326.207	−	565.008i	−0.334572	−	0.579495i
$976$		0			0
$977$	551.486	−	955.202i	0.564469	−	0.977689i	−0.432630	−	0.901572i	$-0.642414\pi$
$977$	551.486	−	955.202i	0.564469	−	0.977689i	0.997099	−	0.0761175i	$-0.0242524\pi$
$978$		0			0
$979$			1206.02i			1.23189i
$980$		0			0
$981$	304.658			0.310558
$982$		0			0
$983$	425.583	+	245.710i	0.432943	+	0.249960i	0.700600	−	0.713555i	$-0.252916\pi$
$983$	425.583	+	245.710i	0.432943	+	0.249960i	−0.267657	+	0.963514i	$0.586249\pi$
$984$		0			0
$985$	1121.77	−	647.655i	1.13885	−	0.657518i
$986$		0			0
$987$	682.912	−	626.354i	0.691907	−	0.634603i
$988$		0			0
$989$	17.2708	+	29.9138i	0.0174629	+	0.0302466i
$990$		0			0
$991$	−401.403	+	695.251i	−0.405049	+	0.701565i	−0.994327	−	0.106365i	$-0.966079\pi$
$991$	−401.403	+	695.251i	−0.405049	+	0.701565i	0.589279	+	0.807930i	$0.299412\pi$
$992$		0			0
$993$			377.157i			0.379816i
$994$		0			0
$995$	−1908.03			−1.91762
$996$		0			0
$997$	−425.562	−	245.698i	−0.426842	−	0.246437i	0.271158	−	0.962535i	$-0.412593\pi$
$997$	−425.562	−	245.698i	−0.426842	−	0.246437i	−0.698000	+	0.716097i	$0.745927\pi$
$998$		0			0
$999$	40.4390	−	23.3475i	0.0404795	−	0.0233708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.3.bh.a.577.1	yes	16
4.3	odd	2		672.3.bh.c.577.1	yes	16
7.5	odd	6	inner	672.3.bh.a.481.1	✓	16
28.19	even	6		672.3.bh.c.481.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.3.bh.a.481.1	✓	16	7.5	odd	6	inner
672.3.bh.a.577.1	yes	16	1.1	even	1	trivial
672.3.bh.c.481.1	yes	16	28.19	even	6
672.3.bh.c.577.1	yes	16	4.3	odd	2

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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	672.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-7.21243 + 4.16410i) q^{5} +(-5.15876 + 4.73151i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-7.36661 + 12.7593i) q^{11} +8.49148i q^{13} +14.4249 q^{15} +(17.8626 + 10.3130i) q^{17} +(9.53028 - 5.50231i) q^{19} +(11.8357 - 2.62965i) q^{21} +(-15.4788 - 26.8101i) q^{23} +(22.1794 - 38.4158i) q^{25} -5.19615i q^{27} -47.0132 q^{29} +(-38.7720 - 22.3850i) q^{31} +(22.0998 - 12.7593i) q^{33} +(17.5047 - 55.6072i) q^{35} +(4.49322 + 7.78248i) q^{37} +(7.35384 - 12.7372i) q^{39} +60.5425i q^{41} -1.11577 q^{43} +(-21.6373 - 12.4923i) q^{45} +(66.1896 - 38.2146i) q^{47} +(4.22557 - 48.8175i) q^{49} +(-17.8626 - 30.9389i) q^{51} +(-52.4136 + 90.7831i) q^{53} -122.701i q^{55} -19.0606 q^{57} +(-42.3384 - 24.4441i) q^{59} +(88.9552 - 51.3583i) q^{61} +(-20.0310 - 6.30558i) q^{63} +(-35.3594 - 61.2442i) q^{65} +(10.2674 - 17.7837i) q^{67} +53.6203i q^{69} -8.79832 q^{71} +(17.1084 + 9.87756i) q^{73} +(-66.5382 + 38.4158i) q^{75} +(-22.3684 - 100.678i) q^{77} +(17.9401 + 31.0731i) q^{79} +(-4.50000 + 7.79423i) q^{81} +4.30830i q^{83} -171.777 q^{85} +(70.5198 + 40.7147i) q^{87} +(70.8903 - 40.9286i) q^{89} +(-40.1776 - 43.8055i) q^{91} +(38.7720 + 67.1551i) q^{93} +(-45.8243 + 79.3700i) q^{95} -62.7407i q^{97} -44.1997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{3} - 12 q^{7} + 24 q^{9} - 12 q^{11} - 48 q^{17} - 60 q^{19} + 24 q^{21} - 48 q^{23} + 52 q^{25} - 64 q^{29} - 60 q^{31} + 36 q^{33} - 4 q^{37} + 12 q^{39} + 72 q^{43} + 120 q^{47} - 8 q^{49}+ \cdots - 72 q^{99}+O(q^{100}) \) 16 * q - 24 * q^3 - 12 * q^7 + 24 * q^9 - 12 * q^11 - 48 * q^17 - 60 * q^19 + 24 * q^21 - 48 * q^23 + 52 * q^25 - 64 * q^29 - 60 * q^31 + 36 * q^33 - 4 * q^37 + 12 * q^39 + 72 * q^43 + 120 * q^47 - 8 * q^49 + 48 * q^51 - 72 * q^53 + 120 * q^57 - 228 * q^59 + 72 * q^61 - 36 * q^63 - 40 * q^65 + 12 * q^67 - 528 * q^71 - 36 * q^73 - 156 * q^75 - 96 * q^77 - 204 * q^79 - 72 * q^81 - 480 * q^85 + 96 * q^87 - 192 * q^89 - 276 * q^91 + 60 * q^93 - 48 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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