LMFDB - Embedded newform 644.2.bc.a.493.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(5,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("644.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.bc (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			493.3
Character	$\chi$	$=$	644.493
Dual form			644.2.bc.a.145.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09494 - 2.12389i) q^{3} +(2.52091 - 0.240718i) q^{5} +(-2.14090 + 1.55452i) q^{7} +(-1.57183 + 2.20732i) q^{9} +O(q^{10})$	\(q+(-1.09494 - 2.12389i) q^{3} +(2.52091 - 0.240718i) q^{5} +(-2.14090 + 1.55452i) q^{7} +(-1.57183 + 2.20732i) q^{9} +(-5.71879 + 1.97929i) q^{11} +(-1.22317 - 4.16575i) q^{13} +(-3.27150 - 5.09056i) q^{15} +(-4.08981 - 1.63731i) q^{17} +(0.372753 - 0.149228i) q^{19} +(5.64578 + 2.84493i) q^{21} +(-0.206485 - 4.79138i) q^{23} +(1.38741 - 0.267401i) q^{25} +(-0.686426 - 0.0986931i) q^{27} +(0.406193 + 2.82514i) q^{29} +(0.742215 - 0.0353561i) q^{31} +(10.4655 + 9.97885i) q^{33} +(-5.02283 + 4.43416i) q^{35} +(-6.59484 - 4.69616i) q^{37} +(-7.50828 + 7.15913i) q^{39} +(2.52275 + 1.15210i) q^{41} +(-5.13520 + 7.99052i) q^{43} +(-3.43110 + 5.94283i) q^{45} +(7.24098 - 4.18058i) q^{47} +(2.16693 - 6.65616i) q^{49} +(1.00063 + 10.4790i) q^{51} +(-0.276713 - 0.290208i) q^{53} +(-13.9401 + 6.36624i) q^{55} +(-0.725084 - 0.628289i) q^{57} +(-6.06424 - 1.47117i) q^{59} +(5.65126 + 2.91343i) q^{61} +(-0.0661981 - 7.16910i) q^{63} +(-4.08629 - 10.2071i) q^{65} +(-0.116259 - 0.603208i) q^{67} +(-9.95026 + 5.68482i) q^{69} +(-2.71359 - 3.13165i) q^{71} +(3.50157 - 4.45261i) q^{73} +(-2.08706 - 2.65391i) q^{75} +(9.16652 - 13.1274i) q^{77} +(5.46537 - 5.73191i) q^{79} +(3.20083 + 9.24819i) q^{81} +(2.93845 + 6.43430i) q^{83} +(-10.7042 - 3.14303i) q^{85} +(5.55551 - 3.95606i) q^{87} +(0.0246673 - 0.517829i) q^{89} +(9.09444 + 7.01702i) q^{91} +(-0.887773 - 1.53767i) q^{93} +(0.903755 - 0.465918i) q^{95} +(-3.94799 + 8.64489i) q^{97} +(4.62001 - 15.7343i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 20 q^{9}+O(q^{10}) $ 320 * q - 20 * q^9	$ 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) $ 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.09494	−	2.12389i	−0.632163	−	1.22623i	−0.959604	−	0.281354i	$-0.909216\pi$
$3$	−1.09494	−	2.12389i	−0.632163	−	1.22623i	0.327441	−	0.944872i	$-0.393814\pi$
$4$		0			0
$5$	2.52091	−	0.240718i	1.12739	−	0.107652i	0.485345	−	0.874323i	$-0.338694\pi$
$5$	2.52091	−	0.240718i	1.12739	−	0.107652i	0.642041	+	0.766670i	$0.278088\pi$
$6$		0			0
$7$	−2.14090	+	1.55452i	−0.809185	+	0.587554i
$7$	−2.14090	+	1.55452i	−0.809185	+	0.587554i
$8$		0			0
$9$	−1.57183	+	2.20732i	−0.523942	+	0.735774i
$10$		0			0
$11$	−5.71879	+	1.97929i	−1.72428	+	0.596779i	−0.996070	−	0.0885744i	$-0.971769\pi$
$11$	−5.71879	+	1.97929i	−1.72428	+	0.596779i	−0.728211	+	0.685353i	$0.759648\pi$
$12$		0			0
$13$	−1.22317	−	4.16575i	−0.339248	−	1.15537i	−0.935722	−	0.352739i	$-0.885250\pi$
$13$	−1.22317	−	4.16575i	−0.339248	−	1.15537i	0.596474	−	0.802632i	$-0.296568\pi$
$14$		0			0
$15$	−3.27150	−	5.09056i	−0.844698	−	1.31438i
$16$		0			0
$17$	−4.08981	−	1.63731i	−0.991924	−	0.397106i	−0.181781	−	0.983339i	$-0.558186\pi$
$17$	−4.08981	−	1.63731i	−0.991924	−	0.397106i	−0.810143	+	0.586233i	$0.800611\pi$
$18$		0			0
$19$	0.372753	−	0.149228i	0.0855153	−	0.0342352i	−0.328510	−	0.944500i	$-0.606547\pi$
$19$	0.372753	−	0.149228i	0.0855153	−	0.0342352i	0.414026	+	0.910265i	$0.364122\pi$
$20$		0			0
$21$	5.64578	+	2.84493i	1.23201	+	0.620814i
$22$		0			0
$23$	−0.206485	−	4.79138i	−0.0430550	−	0.999073i
$23$	−0.206485	−	4.79138i	−0.0430550	−	0.999073i
$24$		0			0
$25$	1.38741	−	0.267401i	0.277482	−	0.0534803i
$26$		0			0
$27$	−0.686426	−	0.0986931i	−0.132103	−	0.0189935i
$28$		0			0
$29$	0.406193	+	2.82514i	0.0754282	+	0.524615i	0.992147	+	0.125081i	$0.0399189\pi$
$29$	0.406193	+	2.82514i	0.0754282	+	0.524615i	−0.916718	+	0.399534i	$0.869172\pi$
$30$		0			0
$31$	0.742215	−	0.0353561i	0.133306	−	0.00635014i	0.0191770	−	0.999816i	$-0.493895\pi$
$31$	0.742215	−	0.0353561i	0.133306	−	0.00635014i	0.114129	+	0.993466i	$0.463592\pi$
$32$		0			0
$33$	10.4655	+	9.97885i	1.82181	+	1.73709i
$34$		0			0
$35$	−5.02283	+	4.43416i	−0.849013	+	0.749510i
$36$		0			0
$37$	−6.59484	−	4.69616i	−1.08418	−	0.772045i	−0.109134	−	0.994027i	$-0.534808\pi$
$37$	−6.59484	−	4.69616i	−1.08418	−	0.772045i	−0.975051	+	0.221982i	$0.928747\pi$
$38$		0			0
$39$	−7.50828	+	7.15913i	−1.20229	+	1.14638i
$40$		0			0
$41$	2.52275	+	1.15210i	0.393988	+	0.179928i	0.602550	−	0.798081i	$-0.294151\pi$
$41$	2.52275	+	1.15210i	0.393988	+	0.179928i	−0.208563	+	0.978009i	$0.566879\pi$
$42$		0			0
$43$	−5.13520	+	7.99052i	−0.783110	+	1.21854i	0.188527	+	0.982068i	$0.439629\pi$
$43$	−5.13520	+	7.99052i	−0.783110	+	1.21854i	−0.971637	+	0.236475i	$0.924008\pi$
$44$		0			0
$45$	−3.43110	+	5.94283i	−0.511478	+	0.885905i
$46$		0			0
$47$	7.24098	−	4.18058i	1.05621	−	0.609801i	0.131825	−	0.991273i	$-0.457916\pi$
$47$	7.24098	−	4.18058i	1.05621	−	0.609801i	0.924380	+	0.381472i	$0.124583\pi$
$48$		0			0
$49$	2.16693	−	6.65616i	0.309562	−	0.950879i
$50$		0			0
$51$	1.00063	+	10.4790i	0.140116	+	1.46736i
$52$		0			0
$53$	−0.276713	−	0.290208i	−0.0380094	−	0.0398631i	0.704455	−	0.709749i	$-0.251192\pi$
$53$	−0.276713	−	0.290208i	−0.0380094	−	0.0398631i	−0.742464	+	0.669886i	$0.766343\pi$
$54$		0			0
$55$	−13.9401	+	6.36624i	−1.87968	+	0.858423i
$56$		0			0
$57$	−0.725084	−	0.628289i	−0.0960397	−	0.0832189i
$58$		0			0
$59$	−6.06424	−	1.47117i	−0.789497	−	0.191530i	−0.179315	−	0.983792i	$-0.557388\pi$
$59$	−6.06424	−	1.47117i	−0.789497	−	0.191530i	−0.610181	+	0.792262i	$0.708903\pi$
$60$		0			0
$61$	5.65126	+	2.91343i	0.723570	+	0.373026i	0.780335	−	0.625361i	$-0.215048\pi$
$61$	5.65126	+	2.91343i	0.723570	+	0.373026i	−0.0567654	+	0.998388i	$0.518079\pi$
$62$		0			0
$63$	−0.0661981	−	7.16910i	−0.00834018	−	0.903222i
$64$		0			0
$65$	−4.08629	−	10.2071i	−0.506842	−	1.26603i
$66$		0			0
$67$	−0.116259	−	0.603208i	−0.0142033	−	0.0736936i	0.974135	−	0.225965i	$-0.0725534\pi$
$67$	−0.116259	−	0.603208i	−0.0142033	−	0.0736936i	−0.988339	+	0.152271i	$0.951341\pi$
$68$		0			0
$69$	−9.95026	+	5.68482i	−1.19787	+	0.684372i
$70$		0			0
$71$	−2.71359	−	3.13165i	−0.322044	−	0.371659i	0.571525	−	0.820585i	$-0.306352\pi$
$71$	−2.71359	−	3.13165i	−0.322044	−	0.371659i	−0.893569	+	0.448926i	$0.851807\pi$
$72$		0			0
$73$	3.50157	−	4.45261i	0.409828	−	0.521139i	−0.536695	−	0.843777i	$-0.680327\pi$
$73$	3.50157	−	4.45261i	0.409828	−	0.521139i	0.946522	+	0.322638i	$0.104570\pi$
$74$		0			0
$75$	−2.08706	−	2.65391i	−0.240993	−	0.306447i
$76$		0			0
$77$	9.16652	−	13.1274i	1.04462	−	1.49601i
$78$		0			0
$79$	5.46537	−	5.73191i	0.614902	−	0.644891i	−0.340484	−	0.940250i	$-0.610591\pi$
$79$	5.46537	−	5.73191i	0.614902	−	0.644891i	0.955386	+	0.295360i	$0.0954395\pi$
$80$		0			0
$81$	3.20083	+	9.24819i	0.355648	+	1.02758i
$82$		0			0
$83$	2.93845	+	6.43430i	0.322537	+	0.706256i	0.999559	−	0.0297062i	$-0.00945716\pi$
$83$	2.93845	+	6.43430i	0.322537	+	0.706256i	−0.677022	+	0.735963i	$0.736730\pi$
$84$		0			0
$85$	−10.7042	−	3.14303i	−1.16103	−	0.340909i
$86$		0			0
$87$	5.55551	−	3.95606i	0.595613	−	0.424134i
$88$		0			0
$89$	0.0246673	−	0.517829i	0.00261472	−	0.0548898i	−0.997183	−	0.0750089i	$-0.976101\pi$
$89$	0.0246673	−	0.517829i	0.00261472	−	0.0548898i	0.999798	+	0.0201190i	$0.00640452\pi$
$90$		0			0
$91$	9.09444	+	7.01702i	0.953357	+	0.735583i
$92$		0			0
$93$	−0.887773	−	1.53767i	−0.0920577	−	0.159449i
$94$		0			0
$95$	0.903755	−	0.465918i	0.0927233	−	0.0478022i
$96$		0			0
$97$	−3.94799	+	8.64489i	−0.400857	+	0.877755i	0.596325	+	0.802743i	$0.296627\pi$
$97$	−3.94799	+	8.64489i	−0.400857	+	0.877755i	−0.997183	+	0.0750123i	$0.976100\pi$
$98$		0			0
$99$	4.62001	−	15.7343i	0.464329	−	1.58136i
$100$		0			0
$101$	−1.39777	+	14.6381i	−0.139083	+	1.45655i	0.609121	+	0.793077i	$0.291522\pi$
$101$	−1.39777	+	14.6381i	−0.139083	+	1.45655i	−0.748204	+	0.663468i	$0.769084\pi$
$102$		0			0
$103$	−4.87750	−	0.940060i	−0.480594	−	0.0926269i	−0.0568001	−	0.998386i	$-0.518090\pi$
$103$	−4.87750	−	0.940060i	−0.480594	−	0.0926269i	−0.423794	+	0.905759i	$0.639302\pi$
$104$		0			0
$105$	14.9173	+	5.81277i	1.45578	+	0.567268i
$106$		0			0
$107$	5.53591	−	10.7382i	0.535177	−	1.03810i	−0.453949	−	0.891027i	$-0.649985\pi$
$107$	5.53591	−	10.7382i	0.535177	−	1.03810i	0.989126	−	0.147070i	$-0.0469844\pi$
$108$		0			0
$109$	4.25413	−	10.6263i	0.407472	−	1.01782i	−0.572717	−	0.819753i	$-0.694111\pi$
$109$	4.25413	−	10.6263i	0.407472	−	1.01782i	0.980189	−	0.198063i	$-0.0634650\pi$
$110$		0			0
$111$	−2.75317	+	19.1487i	−0.261319	+	1.81751i
$112$		0			0
$113$	10.1774	−	8.81878i	0.957411	−	0.829601i	−0.0280325	−	0.999607i	$-0.508924\pi$
$113$	10.1774	−	8.81878i	0.957411	−	0.829601i	0.985443	+	0.170006i	$0.0543787\pi$
$114$		0			0
$115$	−1.67390	−	12.0290i	−0.156092	−	1.12171i
$116$		0			0
$117$	11.1178	+	3.84790i	1.02784	+	0.355738i
$118$		0			0
$119$	11.3011	−	2.85236i	1.03597	−	0.261476i
$120$		0			0
$121$	20.1404	−	15.8386i	1.83094	−	1.43987i
$122$		0			0
$123$	−0.315326	−	6.61952i	−0.0284320	−	0.596862i
$124$		0			0
$125$	−8.71583	+	2.55920i	−0.779567	+	0.228902i
$126$		0			0
$127$	10.1136	−	11.6717i	0.897435	−	1.03569i	−0.101729	−	0.994812i	$-0.532438\pi$
$127$	10.1136	−	11.6717i	0.897435	−	1.03569i	0.999164	−	0.0408827i	$-0.0130170\pi$
$128$		0			0
$129$	22.5937	+	2.15744i	1.98926	+	0.189952i
$130$		0			0
$131$	−0.500154	+	0.121336i	−0.0436987	+	0.0106012i	−0.257549	−	0.966265i	$-0.582915\pi$
$131$	−0.500154	+	0.121336i	−0.0436987	+	0.0106012i	0.213850	+	0.976867i	$0.431400\pi$
$132$		0			0
$133$	−0.566050	+	0.898934i	−0.0490828	+	0.0779474i
$134$		0			0
$135$	−1.75418	−	0.0835617i	−0.150975	−	0.00719184i
$136$		0			0
$137$	−17.7623	−	10.2551i	−1.51754	−	0.876150i	−0.999787	−	0.0206174i	$-0.993437\pi$
$137$	−17.7623	−	10.2551i	−1.51754	−	0.876150i	−0.517749	−	0.855533i	$-0.673230\pi$
$138$		0			0
$139$		−	22.3561i		−	1.89622i	−0.317948	−	0.948108i	$-0.602994\pi$
$139$		−	22.3561i		−	1.89622i	0.317948	−	0.948108i	$-0.397006\pi$
$140$		0			0
$141$	−16.8075	−	10.8015i	−1.41545	−	0.909653i
$142$		0			0
$143$	15.2403	+	21.4020i	1.27446	+	1.78973i
$144$		0			0
$145$	1.70404	+	7.02414i	0.141513	+	0.583323i
$146$		0			0
$147$	−16.5096	+	2.68577i	−1.36169	+	0.221518i
$148$		0			0
$149$	−4.14678	+	21.5155i	−0.339718	+	1.76262i	0.263125	+	0.964762i	$0.415247\pi$
$149$	−4.14678	+	21.5155i	−0.339718	+	1.76262i	−0.602842	+	0.797860i	$0.705965\pi$
$150$		0			0
$151$	1.02681	−	4.23258i	0.0835607	−	0.344442i	−0.914649	−	0.404248i	$-0.867533\pi$
$151$	1.02681	−	4.23258i	0.0835607	−	0.344442i	0.998210	+	0.0598063i	$0.0190483\pi$
$152$		0			0
$153$	10.0425	−	6.45395i	0.811892	−	0.521771i
$154$		0			0
$155$	1.86255	−	0.267794i	0.149603	−	0.0215097i
$156$		0			0
$157$	−12.3122	−	9.68243i	−0.982621	−	0.772742i	−0.00877766	−	0.999961i	$-0.502794\pi$
$157$	−12.3122	−	9.68243i	−0.982621	−	0.772742i	−0.973844	+	0.227220i	$0.927036\pi$
$158$		0			0
$159$	−0.313385	+	0.905466i	−0.0248530	+	0.0718081i
$160$		0			0
$161$	7.89037	+	9.93691i	0.621848	+	0.783138i
$162$		0			0
$163$	−2.48346	+	7.17549i	−0.194520	+	0.562028i	−0.999511	−	0.0312582i	$-0.990049\pi$
$163$	−2.48346	+	7.17549i	−0.194520	+	0.562028i	0.804992	+	0.593286i	$0.202170\pi$
$164$		0			0
$165$	28.7847	+	22.6366i	2.24089	+	1.76225i
$166$		0			0
$167$	16.5393	−	2.37799i	1.27985	−	0.184014i	0.531351	−	0.847152i	$-0.321685\pi$
$167$	16.5393	−	2.37799i	1.27985	−	0.184014i	0.748498	+	0.663137i	$0.230775\pi$
$168$		0			0
$169$	−4.92103	+	3.16255i	−0.378541	+	0.243273i
$170$		0			0
$171$	−0.256509	+	1.05735i	−0.0196157	+	0.0808572i
$172$		0			0
$173$	0.444274	−	2.30511i	0.0337776	−	0.175255i	−0.961122	−	0.276123i	$-0.910950\pi$
$173$	0.444274	−	2.30511i	0.0337776	−	0.175255i	0.994900	+	0.100869i	$0.0321623\pi$
$174$		0			0
$175$	−2.55463	+	2.72924i	−0.193112	+	0.206311i
$176$		0			0
$177$	3.51538	+	14.4906i	0.264232	+	1.08918i
$178$		0			0
$179$	−5.57980	−	7.83574i	−0.417054	−	0.585671i	0.551592	−	0.834114i	$-0.314020\pi$
$179$	−5.57980	−	7.83574i	−0.417054	−	0.585671i	−0.968646	+	0.248443i	$0.920081\pi$
$180$		0			0
$181$	−10.9744	−	7.05282i	−0.815721	−	0.524232i	0.0649900	−	0.997886i	$-0.479298\pi$
$181$	−10.9744	−	7.05282i	−0.815721	−	0.524232i	−0.880711	+	0.473654i	$0.842935\pi$
$182$		0			0
$183$		−	15.1927i		−	1.12307i
$184$		0			0
$185$	−17.7555	−	10.2511i	−1.30541	−	0.753677i
$186$		0			0
$187$	26.6295	+	1.26852i	1.94734	+	0.0927632i
$188$		0			0
$189$	1.62299	−	0.855770i	0.118055	−	0.0622481i
$190$		0			0
$191$	−14.4404	+	3.50320i	−1.04487	+	0.253482i	−0.721228	−	0.692698i	$-0.756422\pi$
$191$	−14.4404	+	3.50320i	−1.04487	+	0.253482i	−0.323641	+	0.946180i	$0.604907\pi$
$192$		0			0
$193$	10.2551	+	0.979243i	0.738178	+	0.0704874i	0.457370	−	0.889277i	$-0.348792\pi$
$193$	10.2551	+	0.979243i	0.738178	+	0.0704874i	0.280808	+	0.959764i	$0.409398\pi$
$194$		0			0
$195$	−17.2044	+	19.8549i	−1.23203	+	1.42184i
$196$		0			0
$197$	−13.0047	+	3.81854i	−0.926550	+	0.272060i	−0.709992	−	0.704210i	$-0.751301\pi$
$197$	−13.0047	+	3.81854i	−0.926550	+	0.272060i	−0.216558	+	0.976270i	$0.569483\pi$
$198$		0			0
$199$	0.941947	+	19.7739i	0.0667728	+	1.40173i	0.745089	+	0.666965i	$0.232407\pi$
$199$	0.941947	+	19.7739i	0.0667728	+	1.40173i	−0.678317	+	0.734770i	$0.737290\pi$
$200$		0			0
$201$	−1.15385	+	0.907397i	−0.0813863	+	0.0640029i
$202$		0			0
$203$	−5.26135	−	5.41691i	−0.369275	−	0.380192i
$204$		0			0
$205$	6.63697	+	2.29708i	0.463546	+	0.160435i
$206$		0			0
$207$	10.9007	+	7.07545i	0.757650	+	0.491778i
$208$		0			0
$209$	−1.83633	+	1.59119i	−0.127022	+	0.110065i
$210$		0			0
$211$	3.28334	−	22.8361i	0.226035	−	1.57211i	−0.488537	−	0.872543i	$-0.662469\pi$
$211$	3.28334	−	22.8361i	0.226035	−	1.57211i	0.714572	−	0.699562i	$-0.246622\pi$
$212$		0			0
$213$	−3.68005	+	9.19232i	−0.252153	+	0.629848i
$214$		0			0
$215$	−11.0219	+	21.3795i	−0.751689	+	1.45807i
$216$		0			0
$217$	−1.53405	+	1.22948i	−0.104138	+	0.0834627i
$218$		0			0
$219$	−13.2908	−	2.56160i	−0.898112	−	0.173097i
$220$		0			0
$221$	−1.81808	+	19.0398i	−0.122298	+	1.28076i
$222$		0			0
$223$	6.80351	−	23.1706i	0.455597	−	1.55162i	−0.336777	−	0.941584i	$-0.609337\pi$
$223$	6.80351	−	23.1706i	0.455597	−	1.55162i	0.792374	−	0.610035i	$-0.208845\pi$
$224$		0			0
$225$	−1.59053	+	3.48277i	−0.106035	+	0.232185i
$226$		0			0
$227$	−13.5285	+	6.97441i	−0.897917	+	0.462908i	−0.844433	−	0.535661i	$-0.820063\pi$
$227$	−13.5285	+	6.97441i	−0.897917	+	0.462908i	−0.0534831	+	0.998569i	$0.517032\pi$
$228$		0			0
$229$	−7.85664	−	13.6081i	−0.519181	−	0.899248i	−0.999752	−	0.0222920i	$-0.992904\pi$
$229$	−7.85664	−	13.6081i	−0.519181	−	0.899248i	0.480570	−	0.876956i	$-0.340430\pi$
$230$		0			0
$231$	−37.9180	−	5.09489i	−2.49482	−	0.335219i
$232$		0			0
$233$	−1.26307	+	26.5151i	−0.0827464	+	1.73706i	0.451974	+	0.892031i	$0.350720\pi$
$233$	−1.26307	+	26.5151i	−0.0827464	+	1.73706i	−0.534720	+	0.845029i	$0.679583\pi$
$234$		0			0
$235$	17.2475	−	12.2819i	1.12511	−	0.801184i
$236$		0			0
$237$	−18.1582	−	5.33172i	−1.17950	−	0.346332i
$238$		0			0
$239$	−4.41673	−	9.67129i	−0.285694	−	0.625584i	0.711314	−	0.702874i	$-0.248100\pi$
$239$	−4.41673	−	9.67129i	−0.285694	−	0.625584i	−0.997009	+	0.0772906i	$0.975373\pi$
$240$		0			0
$241$	1.57038	+	4.53731i	0.101157	+	0.292274i	0.984211	−	0.176996i	$-0.0566381\pi$
$241$	1.57038	+	4.53731i	0.101157	+	0.292274i	−0.883054	+	0.469271i	$0.844517\pi$
$242$		0			0
$243$	14.7017	−	15.4187i	0.943114	−	0.989110i
$244$		0			0
$245$	3.86039	−	17.3012i	0.246631	−	1.10533i
$246$		0			0
$247$	−1.07759	−	1.37026i	−0.0685652	−	0.0871878i
$248$		0			0
$249$	10.4483	−	13.2861i	0.662134	−	0.841972i
$250$		0			0
$251$	13.9457	+	16.0942i	0.880246	+	1.01586i	0.999735	+	0.0230223i	$0.00732886\pi$
$251$	13.9457	+	16.0942i	0.880246	+	1.01586i	−0.119489	+	0.992836i	$0.538126\pi$
$252$		0			0
$253$	10.6644	+	26.9922i	0.670465	+	1.69699i
$254$		0			0
$255$	5.04499	+	26.1759i	0.315929	+	1.63920i
$256$		0			0
$257$	0.271053	+	0.677057i	0.0169078	+	0.0422337i	0.936582	−	0.350449i	$-0.113971\pi$
$257$	0.271053	+	0.677057i	0.0169078	+	0.0422337i	−0.919674	+	0.392683i	$0.871547\pi$
$258$		0			0
$259$	21.4192	−	0.197781i	1.33092	−	0.0122895i
$260$		0			0
$261$	−6.87445	−	3.54403i	−0.425518	−	0.219370i
$262$		0			0
$263$	−20.7843	−	5.04222i	−1.28162	−	0.310917i	−0.463565	−	0.886063i	$-0.653430\pi$
$263$	−20.7843	−	5.04222i	−1.28162	−	0.310917i	−0.818051	+	0.575146i	$0.804945\pi$
$264$		0			0
$265$	−0.767427	−	0.664979i	−0.0471427	−	0.0408493i
$266$		0			0
$267$	−1.12682	+	0.514601i	−0.0689602	+	0.0314931i
$268$		0			0
$269$	12.6628	+	13.2804i	0.772067	+	0.809721i	0.985933	−	0.167142i	$-0.0534539\pi$
$269$	12.6628	+	13.2804i	0.772067	+	0.809721i	−0.213866	+	0.976863i	$0.568605\pi$
$270$		0			0
$271$	1.21548	+	12.7291i	0.0738354	+	0.773239i	0.954245	+	0.299026i	$0.0966616\pi$
$271$	1.21548	+	12.7291i	0.0738354	+	0.773239i	−0.880410	+	0.474214i	$0.842732\pi$
$272$		0			0
$273$	4.94548	−	26.9988i	0.299314	−	1.63404i
$274$		0			0
$275$	−7.40504	+	4.27530i	−0.446541	+	0.257810i
$276$		0			0
$277$	5.88164	−	10.1873i	0.353394	−	0.612096i	−0.633448	−	0.773785i	$-0.718361\pi$
$277$	5.88164	−	10.1873i	0.353394	−	0.612096i	0.986842	+	0.161690i	$0.0516943\pi$
$278$		0			0
$279$	−1.08859	+	1.69388i	−0.0651723	+	0.101410i
$280$		0			0
$281$	−27.1346	−	12.3920i	−1.61872	−	0.739243i	−0.619755	−	0.784795i	$-0.712768\pi$
$281$	−27.1346	−	12.3920i	−1.61872	−	0.739243i	−0.998962	+	0.0455516i	$0.985495\pi$
$282$		0			0
$283$	22.8233	−	21.7620i	1.35671	−	1.29362i	0.437838	−	0.899054i	$-0.355744\pi$
$283$	22.8233	−	21.7620i	1.35671	−	1.29362i	0.918869	−	0.394563i	$-0.129104\pi$
$284$		0			0
$285$	−1.97911	−	1.40932i	−0.117233	−	0.0834809i
$286$		0			0
$287$	−7.19193	+	1.45513i	−0.424526	+	0.0858936i
$288$		0			0
$289$	1.74226	+	1.66124i	0.102486	+	0.0977200i
$290$		0			0
$291$	22.6836	−	1.08055i	1.32973	−	0.0633430i
$292$		0			0
$293$	2.78222	+	19.3508i	0.162539	+	1.13048i	0.893826	+	0.448414i	$0.148011\pi$
$293$	2.78222	+	19.3508i	0.162539	+	1.13048i	−0.731287	+	0.682070i	$0.761080\pi$
$294$		0			0
$295$	−15.6415	−	2.24892i	−0.910686	−	0.130937i
$296$		0			0
$297$	4.12087	−	0.794232i	0.239117	−	0.0460860i
$298$		0			0
$299$	−19.7071	+	6.72086i	−1.13969	+	0.388678i
$300$		0			0
$301$	−1.42747	−	25.0897i	−0.0822781	−	1.44615i
$302$		0			0
$303$	32.6201	−	13.0591i	1.87398	−	0.750227i
$304$		0			0
$305$	14.9476	+	5.98414i	0.855900	+	0.342651i
$306$		0			0
$307$	−7.13618	−	11.1041i	−0.407284	−	0.633746i	0.575652	−	0.817695i	$-0.304748\pi$
$307$	−7.13618	−	11.1041i	−0.407284	−	0.633746i	−0.982936	+	0.183949i	$0.941112\pi$
$308$		0			0
$309$	3.34398	+	11.3885i	0.190232	+	0.647872i
$310$		0			0
$311$	13.9079	−	4.81358i	0.788646	−	0.272953i	0.0970898	−	0.995276i	$-0.469047\pi$
$311$	13.9079	−	4.81358i	0.788646	−	0.272953i	0.691556	+	0.722323i	$0.256925\pi$
$312$		0			0
$313$	1.61686	−	2.27057i	0.0913905	−	0.128340i	−0.766349	−	0.642424i	$-0.777929\pi$
$313$	1.61686	−	2.27057i	0.0913905	−	0.128340i	0.857740	+	0.514084i	$0.171868\pi$
$314$		0			0
$315$	−1.89261	−	18.0567i	−0.106637	−	1.01738i
$316$		0			0
$317$	10.6129	−	1.01341i	0.596078	−	0.0569186i	0.207343	−	0.978268i	$-0.433518\pi$
$317$	10.6129	−	1.01341i	0.596078	−	0.0569186i	0.388735	+	0.921350i	$0.372912\pi$
$318$		0			0
$319$	−7.91470	−	15.3524i	−0.443138	−	0.859568i
$320$		0			0
$321$	−28.8681			−1.61126
$322$		0			0
$323$	−1.76882			−0.0984197
$324$		0			0
$325$	−2.81097	−	5.45252i	−0.155925	−	0.302452i
$326$		0			0
$327$	−27.2271	+	2.59987i	−1.50566	+	0.143773i
$328$		0			0
$329$	−9.00344	+	20.2065i	−0.496376	+	1.11402i
$330$		0			0
$331$	−14.8137	+	20.8030i	−0.814236	+	1.14343i	0.173117	+	0.984901i	$0.444616\pi$
$331$	−14.8137	+	20.8030i	−0.814236	+	1.14343i	−0.987354	+	0.158534i	$0.949323\pi$
$332$		0			0
$333$	20.7319	−	7.17538i	1.13610	−	0.393208i
$334$		0			0
$335$	−0.438282	−	1.49265i	−0.0239459	−	0.0815522i
$336$		0			0
$337$	1.34860	+	2.09846i	0.0734627	+	0.114310i	0.876041	−	0.482237i	$-0.160175\pi$
$337$	1.34860	+	2.09846i	0.0734627	+	0.114310i	−0.802578	+	0.596547i	$0.796539\pi$
$338$		0			0
$339$	−29.8737	−	11.9596i	−1.62252	−	0.649558i
$340$		0			0
$341$	−4.17459	+	1.67125i	−0.226067	+	0.0905035i
$342$		0			0
$343$	5.70794	+	17.6187i	0.308200	+	0.951322i
$344$		0			0
$345$	−23.7153	+	16.7261i	−1.27679	+	0.900505i
$346$		0			0
$347$	−10.8646	+	2.09399i	−0.583244	+	0.112411i	−0.472334	−	0.881420i	$-0.656588\pi$
$347$	−10.8646	+	2.09399i	−0.583244	+	0.112411i	−0.110909	+	0.993831i	$0.535376\pi$
$348$		0			0
$349$	5.90503	+	0.849015i	0.316089	+	0.0454467i	0.298533	−	0.954399i	$-0.403503\pi$
$349$	5.90503	+	0.849015i	0.316089	+	0.0454467i	0.0175555	+	0.999846i	$0.494412\pi$
$350$		0			0
$351$	0.428488	+	2.98020i	0.0228710	+	0.159071i
$352$		0			0
$353$	8.51150	−	0.405453i	0.453022	−	0.0215801i	0.180168	−	0.983636i	$-0.442336\pi$
$353$	8.51150	−	0.405453i	0.453022	−	0.0215801i	0.272853	+	0.962056i	$0.412033\pi$
$354$		0			0
$355$	−7.59457	−	7.24141i	−0.403078	−	0.384334i
$356$		0			0
$357$	−18.4321	−	20.8791i	−0.975532	−	1.10504i
$358$		0			0
$359$	−11.8539	−	8.44111i	−0.625624	−	0.445505i	0.222769	−	0.974871i	$-0.428490\pi$
$359$	−11.8539	−	8.44111i	−0.625624	−	0.445505i	−0.848393	+	0.529366i	$0.822430\pi$
$360$		0			0
$361$	−13.6343	+	13.0003i	−0.717593	+	0.684224i
$362$		0			0
$363$	−55.6918	−	25.4336i	−2.92306	−	1.33492i
$364$		0			0
$365$	7.75533	−	12.0675i	0.405933	−	0.631643i
$366$		0			0
$367$	−11.1097	+	19.2426i	−0.579923	+	1.00446i	0.415565	+	0.909563i	$0.363584\pi$
$367$	−11.1097	+	19.2426i	−0.579923	+	1.00446i	−0.995488	+	0.0948918i	$0.969749\pi$
$368$		0			0
$369$	−6.50839	+	3.75762i	−0.338813	+	0.195614i
$370$		0			0
$371$	1.04355	+	0.191152i	0.0541784	+	0.00992409i
$372$		0			0
$373$	−0.442213	−	4.63107i	−0.0228969	−	0.239788i	−0.999674	−	0.0255297i	$-0.991873\pi$
$373$	−0.442213	−	4.63107i	−0.0228969	−	0.239788i	0.976777	−	0.214258i	$-0.0687333\pi$
$374$		0			0
$375$	14.9787	+	15.7093i	0.773499	+	0.811223i
$376$		0			0
$377$	11.2720	−	5.14773i	0.580536	−	0.265122i
$378$		0			0
$379$	6.93873	+	6.01244i	0.356419	+	0.308838i	0.814603	−	0.580019i	$-0.196955\pi$
$379$	6.93873	+	6.01244i	0.356419	+	0.308838i	−0.458185	+	0.888857i	$0.651500\pi$
$380$		0			0
$381$	−35.8631	−	8.70029i	−1.83732	−	0.445729i
$382$		0			0
$383$	31.5801	+	16.2807i	1.61367	+	0.831905i	0.999072	+	0.0430641i	$0.0137120\pi$
$383$	31.5801	+	16.2807i	1.61367	+	0.831905i	0.614598	+	0.788841i	$0.289318\pi$
$384$		0			0
$385$	19.9480	−	35.2997i	1.01664	−	1.79904i
$386$		0			0
$387$	−9.56602	−	23.8948i	−0.486268	−	1.21464i
$388$		0			0
$389$	−3.99626	−	20.7346i	−0.202619	−	1.05128i	−0.930697	−	0.365791i	$-0.880799\pi$
$389$	−3.99626	−	20.7346i	−0.202619	−	1.05128i	0.728079	−	0.685494i	$-0.240414\pi$
$390$		0			0
$391$	−7.00051	+	19.9339i	−0.354031	+	1.00810i
$392$		0			0
$393$	0.805342	+	0.929414i	0.0406241	+	0.0468827i
$394$		0			0
$395$	12.3979	−	15.7653i	0.623808	−	0.793236i
$396$		0			0
$397$	−17.0961	−	21.7395i	−0.858030	−	1.09107i	−0.994938	−	0.100490i	$-0.967959\pi$
$397$	−17.0961	−	21.7395i	−0.858030	−	1.09107i	0.136908	−	0.990584i	$-0.456284\pi$
$398$		0			0
$399$	2.52902	+	0.217948i	0.126609	+	0.0109110i
$400$		0			0
$401$	−7.21640	+	7.56834i	−0.360370	+	0.377945i	−0.878812	−	0.477168i	$-0.841663\pi$
$401$	−7.21640	+	7.56834i	−0.360370	+	0.377945i	0.518443	+	0.855112i	$0.326512\pi$
$402$		0			0
$403$	−1.05514	−	3.04864i	−0.0525604	−	0.151863i
$404$		0			0
$405$	10.2952	+	22.5434i	0.511573	+	1.12019i
$406$		0			0
$407$	47.0096	+	13.8033i	2.33018	+	0.684202i
$408$		0			0
$409$	−16.0826	+	11.4524i	−0.795233	+	0.566283i	−0.903874	−	0.427798i	$-0.859289\pi$
$409$	−16.0826	+	11.4524i	−0.795233	+	0.566283i	0.108642	+	0.994081i	$0.465350\pi$
$410$		0			0
$411$	−2.33196	+	48.9538i	−0.115027	+	2.41471i
$412$		0			0
$413$	15.2699	−	6.27735i	0.751383	−	0.308888i
$414$		0			0
$415$	8.95642	+	15.5130i	0.439653	+	0.761502i
$416$		0			0
$417$	−47.4817	+	24.4785i	−2.32519	+	1.19872i
$418$		0			0
$419$	−6.06408	+	13.2785i	−0.296250	+	0.648697i	−0.997965	−	0.0637607i	$-0.979691\pi$
$419$	−6.06408	+	13.2785i	−0.296250	+	0.648697i	0.701715	+	0.712457i	$0.252418\pi$
$420$		0			0
$421$	−8.47983	+	28.8796i	−0.413281	+	1.40751i	0.445554	+	0.895255i	$0.353007\pi$
$421$	−8.47983	+	28.8796i	−0.413281	+	1.40751i	−0.858835	+	0.512252i	$0.828811\pi$
$422$		0			0
$423$	−2.15368	+	22.5543i	−0.104715	+	1.09663i
$424$		0			0
$425$	−6.11206	−	1.17800i	−0.296478	−	0.0571415i
$426$		0			0
$427$	−16.6278	+	2.54764i	−0.804675	+	0.123289i
$428$		0			0
$429$	28.7682	−	55.8026i	1.38894	−	2.69418i
$430$		0			0
$431$	−11.7364	+	29.3160i	−0.565320	+	1.41210i	0.320132	+	0.947373i	$0.396273\pi$
$431$	−11.7364	+	29.3160i	−0.565320	+	1.41210i	−0.885453	+	0.464729i	$0.846152\pi$
$432$		0			0
$433$	4.56773	−	31.7692i	0.219511	−	1.52673i	−0.520339	−	0.853960i	$-0.674194\pi$
$433$	4.56773	−	31.7692i	0.219511	−	1.52673i	0.739850	−	0.672772i	$-0.234896\pi$
$434$		0			0
$435$	13.0527	−	11.3102i	0.625827	−	0.542282i
$436$		0			0
$437$	−0.791975	−	1.75519i	−0.0378853	−	0.0839620i
$438$		0			0
$439$	−14.3199	−	4.95615i	−0.683449	−	0.236544i	−0.0367900	−	0.999323i	$-0.511713\pi$
$439$	−14.3199	−	4.95615i	−0.683449	−	0.236544i	−0.646659	+	0.762779i	$0.723834\pi$
$440$		0			0
$441$	11.2862	+	15.2454i	0.537440	+	0.725973i
$442$		0			0
$443$	−28.9415	+	22.7598i	−1.37505	+	1.08135i	−0.387877	+	0.921711i	$0.626791\pi$
$443$	−28.9415	+	22.7598i	−1.37505	+	1.08135i	−0.987175	+	0.159642i	$0.948966\pi$
$444$		0			0
$445$	−0.0624668	−	1.31134i	−0.00296121	−	0.0621635i
$446$		0			0
$447$	50.2370	−	14.7509i	2.37613	−	0.697695i
$448$		0			0
$449$	0.159439	−	0.184003i	0.00752441	−	0.00868363i	−0.751975	−	0.659192i	$-0.770899\pi$
$449$	0.159439	−	0.184003i	0.00752441	−	0.00868363i	0.759499	+	0.650508i	$0.225444\pi$
$450$		0			0
$451$	−16.7074	−	1.59537i	−0.786722	−	0.0751229i
$452$		0			0
$453$	−10.1138	+	2.45358i	−0.475188	+	0.115279i
$454$		0			0
$455$	24.6154	+	15.5001i	1.15399	+	0.726656i
$456$		0			0
$457$	24.6112	+	1.17238i	1.15127	+	0.0548415i	0.614519	−	0.788902i	$-0.289350\pi$
$457$	24.6112	+	1.17238i	1.15127	+	0.0548415i	0.536746	+	0.843744i	$0.319653\pi$
$458$		0			0
$459$	2.64576	+	1.52753i	0.123493	+	0.0712989i
$460$		0			0
$461$			6.65742i			0.310067i	0.987909	+	0.155033i	$0.0495485\pi$
$461$			6.65742i			0.310067i	−0.987909	+	0.155033i	$0.950451\pi$
$462$		0			0
$463$	1.04175	+	0.669494i	0.0484144	+	0.0311140i	0.564624	−	0.825348i	$-0.309021\pi$
$463$	1.04175	+	0.669494i	0.0484144	+	0.0311140i	−0.516210	+	0.856462i	$0.672658\pi$
$464$		0			0
$465$	−2.60814	−	3.66262i	−0.120950	−	0.169850i
$466$		0			0
$467$	1.60801	+	6.62829i	0.0744096	+	0.306721i	0.996839	−	0.0794445i	$-0.0253147\pi$
$467$	1.60801	+	6.62829i	0.0744096	+	0.306721i	−0.922430	+	0.386165i	$0.873800\pi$
$468$		0			0
$469$	1.18660	+	1.11068i	0.0547921	+	0.0512866i
$470$		0			0
$471$	−7.08325	+	36.7514i	−0.326379	+	1.69341i
$472$		0			0
$473$	13.5515	−	55.8602i	0.623100	−	2.56845i
$474$		0			0
$475$	0.477257	−	0.306714i	0.0218981	−	0.0140730i
$476$		0			0
$477$	1.07553	−	0.154637i	0.0492450	−	0.00708036i
$478$		0			0
$479$	20.1153	+	15.8188i	0.919090	+	0.722780i	0.961060	−	0.276339i	$-0.0891211\pi$
$479$	20.1153	+	15.8188i	0.919090	+	0.722780i	−0.0419706	+	0.999119i	$0.513364\pi$
$480$		0			0
$481$	−11.4964	+	33.2167i	−0.524191	+	1.51455i
$482$		0			0
$483$	12.4654	−	27.6385i	0.567194	−	1.25760i
$484$		0			0
$485$	−7.87155	+	22.7434i	−0.357429	+	1.03272i
$486$		0			0
$487$	31.1576	+	24.5026i	1.41188	+	1.11032i	0.977823	+	0.209434i	$0.0671622\pi$
$487$	31.1576	+	24.5026i	1.41188	+	1.11032i	0.434061	+	0.900883i	$0.357080\pi$
$488$		0			0
$489$	17.9592	−	2.58214i	0.812142	−	0.116768i
$490$		0			0
$491$	14.1445	−	9.09011i	0.638332	−	0.410231i	−0.181054	−	0.983473i	$-0.557951\pi$
$491$	14.1445	−	9.09011i	0.638332	−	0.410231i	0.819386	+	0.573242i	$0.194315\pi$
$492$		0			0
$493$	2.96438	−	12.2193i	0.133509	−	0.550331i
$494$		0			0
$495$	7.85911	−	40.7769i	0.353241	−	1.83279i
$496$		0			0
$497$	10.6777	+	2.48623i	0.478963	+	0.111523i
$498$		0			0
$499$	−5.27153	−	21.7295i	−0.235986	−	0.972748i	−0.959336	−	0.282266i	$-0.908914\pi$
$499$	−5.27153	−	21.7295i	−0.235986	−	0.972748i	0.723350	−	0.690482i	$-0.242601\pi$
$500$		0			0
$501$	−23.1601	−	32.5238i	−1.03472	−	1.45306i
$502$		0			0
$503$	−0.00920957	−	0.00591863i	−0.000410634	−	0.000263899i	0.540435	−	0.841385i	$-0.318260\pi$
$503$	−0.00920957	−	0.00591863i	−0.000410634	−	0.000263899i	−0.540846	+	0.841122i	$0.681896\pi$
$504$		0			0
$505$			37.2378i			1.65706i
$506$		0			0
$507$	12.1051	+	6.98890i	0.537608	+	0.310388i
$508$		0			0
$509$	−6.56228	−	0.312600i	−0.290868	−	0.0138557i	−0.0983591	−	0.995151i	$-0.531359\pi$
$509$	−6.56228	−	0.312600i	−0.290868	−	0.0138557i	−0.192509	+	0.981295i	$0.561662\pi$
$510$		0			0
$511$	−0.574851	+	14.9759i	−0.0254299	+	0.662493i
$512$		0			0
$513$	−0.270595	+	0.0656456i	−0.0119470	+	0.00289832i
$514$		0			0
$515$	−12.5220	−	1.19571i	−0.551786	−	0.0526892i
$516$		0			0
$517$	−33.1350	+	38.2399i	−1.45728	+	1.68179i
$518$		0			0
$519$	−5.38225	+	1.58037i	−0.236255	+	0.0693706i
$520$		0			0
$521$	−1.32443	−	27.8032i	−0.0580242	−	1.21808i	−0.820724	−	0.571325i	$-0.806429\pi$
$521$	−1.32443	−	27.8032i	−0.0580242	−	1.21808i	0.762700	−	0.646753i	$-0.223874\pi$
$522$		0			0
$523$	32.7124	−	25.7253i	1.43041	−	1.12489i	0.458735	−	0.888573i	$-0.348303\pi$
$523$	32.7124	−	25.7253i	1.43041	−	1.12489i	0.971677	−	0.236315i	$-0.0759397\pi$
$524$		0			0
$525$	8.59375	+	2.43739i	0.375062	+	0.106376i
$526$		0			0
$527$	−3.09341	−	1.07064i	−0.134751	−	0.0466377i
$528$		0			0
$529$	−22.9147	+	1.97869i	−0.996293	+	0.0860302i
$530$		0			0
$531$	12.7793	−	11.0733i	0.554573	−	0.480540i
$532$		0			0
$533$	1.71360	−	11.9184i	0.0742244	−	0.516242i
$534$		0			0
$535$	11.3707	−	28.4026i	0.491597	−	1.22795i
$536$		0			0
$537$	−10.5327	+	20.4305i	−0.454518	+	0.881642i
$538$		0			0
$539$	0.782248	+	42.3541i	0.0336938	+	1.82432i
$540$		0			0
$541$	16.0437	+	3.09216i	0.689771	+	0.132942i	0.522079	−	0.852897i	$-0.325157\pi$
$541$	16.0437	+	3.09216i	0.689771	+	0.132942i	0.167692	+	0.985839i	$0.446369\pi$
$542$		0			0
$543$	−2.96308	+	31.0308i	−0.127158	+	1.33166i
$544$		0			0
$545$	8.16635	−	27.8120i	0.349808	−	1.19134i
$546$		0			0
$547$	−10.6778	+	23.3812i	−0.456551	+	0.999708i	0.531709	+	0.846927i	$0.321550\pi$
$547$	−10.6778	+	23.3812i	−0.456551	+	0.999708i	−0.988260	+	0.152781i	$0.951177\pi$
$548$		0			0
$549$	−15.3137	+	7.89475i	−0.653572	+	0.336940i
$550$		0			0
$551$	0.572998	+	0.992462i	0.0244105	+	0.0422803i
$552$		0			0
$553$	−2.79045	+	20.7675i	−0.118662	+	0.883124i
$554$		0			0
$555$	−2.33106	+	48.9349i	−0.0989479	+	2.07717i
$556$		0			0
$557$	33.0002	−	23.4993i	1.39826	−	0.995698i	0.401453	−	0.915880i	$-0.368505\pi$
$557$	33.0002	−	23.4993i	1.39826	−	0.995698i	0.996809	−	0.0798187i	$-0.0254341\pi$
$558$		0			0
$559$	39.5678	+	11.6181i	1.67354	+	0.491395i
$560$		0			0
$561$	−26.4635	−	57.9469i	−1.11729	−	2.44652i
$562$		0			0
$563$	−12.0424	−	34.7941i	−0.507525	−	1.46640i	−0.849956	−	0.526854i	$-0.823371\pi$
$563$	−12.0424	−	34.7941i	−0.507525	−	1.46640i	0.342431	−	0.939543i	$-0.388750\pi$
$564$		0			0
$565$	23.5335	−	24.6813i	0.990063	−	1.03835i
$566$		0			0
$567$	−21.2292	−	14.8237i	−0.891541	−	0.622538i
$568$		0			0
$569$	13.6830	+	17.3993i	0.573619	+	0.729416i	0.983134	−	0.182887i	$-0.0585443\pi$
$569$	13.6830	+	17.3993i	0.573619	+	0.729416i	−0.409515	+	0.912304i	$0.634302\pi$
$570$		0			0
$571$	3.16045	−	4.01884i	0.132261	−	0.168183i	−0.715412	−	0.698703i	$-0.753761\pi$
$571$	3.16045	−	4.01884i	0.132261	−	0.168183i	0.847672	+	0.530520i	$0.178003\pi$
$572$		0			0
$573$	23.2517	+	26.8339i	0.971354	+	1.12100i
$574$		0			0
$575$	−1.56770	−	6.59240i	−0.0653777	−	0.274922i
$576$		0			0
$577$	−5.53597	−	28.7233i	−0.230465	−	1.19577i	−0.894154	−	0.447759i	$-0.852222\pi$
$577$	−5.53597	−	28.7233i	−0.230465	−	1.19577i	0.663689	−	0.748009i	$-0.268990\pi$
$578$		0			0
$579$	−9.14890	−	22.8529i	−0.380215	−	0.949732i
$580$		0			0
$581$	−16.2932	−	9.20734i	−0.675955	−	0.381985i
$582$		0			0
$583$	2.15687	+	1.11194i	0.0893284	+	0.0460520i
$584$		0			0
$585$	28.9532	+	7.02397i	1.19707	+	0.290405i
$586$		0			0
$587$	−26.3259	−	22.8115i	−1.08658	−	0.941531i	−0.0880757	−	0.996114i	$-0.528072\pi$
$587$	−26.3259	−	22.8115i	−1.08658	−	0.941531i	−0.998509	+	0.0545825i	$0.982617\pi$
$588$		0			0
$589$	0.271387	−	0.123938i	0.0111823	−	0.00510678i
$590$		0			0
$591$	22.3495	+	23.4395i	0.919337	+	0.964173i
$592$		0			0
$593$	0.629680	+	6.59431i	0.0258579	+	0.270796i	0.999150	+	0.0412252i	$0.0131261\pi$
$593$	0.629680	+	6.59431i	0.0258579	+	0.270796i	−0.973292	+	0.229571i	$0.926268\pi$
$594$		0			0
$595$	27.8025	−	9.91094i	1.13979	−	0.406309i
$596$		0			0
$597$	40.9661	−	23.6518i	1.67663	−	0.968004i
$598$		0			0
$599$	−2.18200	+	3.77933i	−0.0891541	+	0.154419i	−0.907154	−	0.420799i	$-0.861750\pi$
$599$	−2.18200	+	3.77933i	−0.0891541	+	0.154419i	0.818000	+	0.575219i	$0.195083\pi$
$600$		0			0
$601$	−5.40816	+	8.41526i	−0.220603	+	0.343266i	−0.933861	−	0.357637i	$-0.883583\pi$
$601$	−5.40816	+	8.41526i	−0.220603	+	0.343266i	0.713257	+	0.700902i	$0.247219\pi$
$602$		0			0
$603$	1.51421	+	0.691518i	0.0616636	+	0.0281608i
$604$		0			0
$605$	46.9595	−	44.7758i	1.90918	−	1.82039i
$606$		0			0
$607$	−7.03463	−	5.00934i	−0.285527	−	0.203323i	0.428315	−	0.903629i	$-0.359107\pi$
$607$	−7.03463	−	5.00934i	−0.285527	−	0.203323i	−0.713842	+	0.700307i	$0.753047\pi$
$608$		0			0
$609$	−5.74403	+	17.1057i	−0.232760	+	0.693158i
$610$		0			0
$611$	−26.2722	−	25.0505i	−1.06286	−	1.01344i
$612$		0			0
$613$	−29.7695	+	1.41810i	−1.20238	+	0.0572764i	−0.639188	−	0.769050i	$-0.720730\pi$
$613$	−29.7695	+	1.41810i	−1.20238	+	0.0572764i	−0.563191	+	0.826327i	$0.690427\pi$
$614$		0			0
$615$	−2.38835	−	16.6113i	−0.0963074	−	0.669833i
$616$		0			0
$617$	9.84749	+	1.41586i	0.396445	+	0.0570002i	0.337654	−	0.941270i	$-0.390366\pi$
$617$	9.84749	+	1.41586i	0.396445	+	0.0570002i	0.0587906	+	0.998270i	$0.481276\pi$
$618$		0			0
$619$	14.4188	−	2.77899i	0.579540	−	0.111697i	0.108947	−	0.994048i	$-0.465252\pi$
$619$	14.4188	−	2.77899i	0.579540	−	0.111697i	0.470593	+	0.882350i	$0.344040\pi$
$620$		0			0
$621$	−0.331140	+	3.30931i	−0.0132882	+	0.132798i
$622$		0			0
$623$	0.752166	+	1.14697i	0.0301349	+	0.0459523i
$624$		0			0
$625$	−27.9145	+	11.1753i	−1.11658	+	0.447010i
$626$		0			0
$627$	5.39017	+	2.15790i	0.215263	+	0.0861782i
$628$		0			0
$629$	19.2825	+	30.0042i	0.768845	+	1.19635i
$630$		0			0
$631$	−13.2627	−	45.1686i	−0.527980	−	1.79813i	−0.599110	−	0.800666i	$-0.704479\pi$
$631$	−13.2627	−	45.1686i	−0.527980	−	1.79813i	0.0711308	−	0.997467i	$-0.477339\pi$
$632$		0			0
$633$	−52.0964	+	18.0307i	−2.07065	+	0.716658i
$634$		0			0
$635$	22.6858	−	31.8578i	0.900260	−	1.26424i
$636$		0			0
$637$	−30.3784	−	0.885258i	−1.20364	−	0.0350752i
$638$		0			0
$639$	11.1779	−	1.06736i	0.442189	−	0.0422239i
$640$		0			0
$641$	1.21326	+	2.35339i	0.0479208	+	0.0929533i	0.911580	−	0.411123i	$-0.134863\pi$
$641$	1.21326	+	2.35339i	0.0479208	+	0.0929533i	−0.863659	+	0.504076i	$0.831833\pi$
$642$		0			0
$643$	5.17906			0.204242			0.102121	−	0.994772i	$-0.467437\pi$
$643$	5.17906			0.204242			0.102121	+	0.994772i	$0.467437\pi$
$644$		0			0
$645$	57.4760			2.26312
$646$		0			0
$647$	0.313296	+	0.607710i	0.0123169	+	0.0238915i	0.894914	−	0.446239i	$-0.147237\pi$
$647$	0.313296	+	0.607710i	0.0123169	+	0.0238915i	−0.882597	+	0.470131i	$0.844207\pi$
$648$		0			0
$649$	37.5920	−	3.58960i	1.47561	−	0.140904i
$650$		0			0
$651$	4.29097	+	1.91194i	0.168176	+	0.0749347i
$652$		0			0
$653$	−1.73883	+	2.44184i	−0.0680456	+	0.0955567i	−0.847196	−	0.531280i	$-0.821711\pi$
$653$	−1.73883	+	2.44184i	−0.0680456	+	0.0955567i	0.779151	+	0.626837i	$0.215651\pi$
$654$		0			0
$655$	−1.23164	+	0.426274i	−0.0481240	+	0.0166559i
$656$		0			0
$657$	4.32448	+	14.7278i	0.168714	+	0.574587i
$658$		0			0
$659$	3.50373	+	5.45191i	0.136486	+	0.212376i	0.902768	−	0.430128i	$-0.141532\pi$
$659$	3.50373	+	5.45191i	0.136486	+	0.212376i	−0.766282	+	0.642505i	$0.777895\pi$
$660$		0			0
$661$	20.1145	+	8.05264i	0.782364	+	0.313211i	0.728239	−	0.685323i	$-0.240339\pi$
$661$	20.1145	+	8.05264i	0.782364	+	0.313211i	0.0541246	+	0.998534i	$0.482763\pi$
$662$		0			0
$663$	42.4291	−	16.9861i	1.64781	−	0.659684i
$664$		0			0
$665$	−1.21057	+	2.40239i	−0.0469440	+	0.0931607i
$666$		0			0
$667$	13.4524	−	2.52957i	0.520881	−	0.0979455i
$668$		0			0
$669$	−56.6612	+	10.9205i	−2.19065	+	0.422213i
$670$		0			0
$671$	−38.0849	−	5.47578i	−1.47025	−	0.211390i
$672$		0			0
$673$	−2.92975	−	20.3768i	−0.112934	−	0.785470i	−0.965040	−	0.262102i	$-0.915584\pi$
$673$	−2.92975	−	20.3768i	−0.112934	−	0.785470i	0.852107	−	0.523368i	$-0.175325\pi$
$674$		0			0
$675$	−0.978744	+	0.0466233i	−0.0376719	+	0.00179453i
$676$		0			0
$677$	−11.4090	−	10.8784i	−0.438482	−	0.418091i	0.438413	−	0.898774i	$-0.355541\pi$
$677$	−11.4090	−	10.8784i	−0.438482	−	0.418091i	−0.876895	+	0.480682i	$0.840389\pi$
$678$		0			0
$679$	−4.98639	−	24.6451i	−0.191360	−	0.945792i
$680$		0			0
$681$	29.6257	+	21.0964i	1.13526	+	0.808415i
$682$		0			0
$683$	−9.27764	+	8.84621i	−0.354999	+	0.338491i	−0.846502	−	0.532385i	$-0.821296\pi$
$683$	−9.27764	+	8.84621i	−0.354999	+	0.338491i	0.491504	+	0.870876i	$0.336447\pi$
$684$		0			0
$685$	−47.2458	−	21.5764i	−1.80517	−	0.824393i
$686$		0			0
$687$	−20.2995	+	31.5866i	−0.774474	+	1.20511i
$688$		0			0
$689$	−0.870466	+	1.50769i	−0.0331621	+	0.0574385i
$690$		0			0
$691$	42.2051	−	24.3671i	1.60556	−	0.926968i	0.615209	−	0.788364i	$-0.289072\pi$
$691$	42.2051	−	24.3671i	1.60556	−	0.926968i	0.990348	−	0.138604i	$-0.0442615\pi$
$692$		0			0
$693$	14.5683	+	40.8675i	0.553405	+	1.55243i
$694$		0			0
$695$	−5.38150	−	56.3577i	−0.204132	−	2.13777i
$696$		0			0
$697$	−8.43122	−	8.84241i	−0.319355	−	0.334930i
$698$		0			0
$699$	57.6980	−	26.3498i	2.18234	−	0.996640i
$700$		0			0
$701$	−0.834732	−	0.723299i	−0.0315274	−	0.0273186i	0.638955	−	0.769244i	$-0.279367\pi$
$701$	−0.834732	−	0.723299i	−0.0315274	−	0.0273186i	−0.670482	+	0.741926i	$0.733913\pi$
$702$		0			0
$703$	−3.15904	−	0.766375i	−0.119146	−	0.0289044i
$704$		0			0
$705$	−44.9704	−	23.1838i	−1.69368	−	0.873154i
$706$		0			0
$707$	−19.7627	−	33.5116i	−0.743254	−	1.26033i
$708$		0			0
$709$	0.473378	+	1.18244i	0.0177781	+	0.0444075i	0.936991	−	0.349352i	$-0.113598\pi$
$709$	0.473378	+	1.18244i	0.0177781	+	0.0444075i	−0.919213	+	0.393760i	$0.871174\pi$
$710$		0			0
$711$	4.06157	+	21.0734i	0.152321	+	0.790314i
$712$		0			0
$713$	−0.322660	−	3.54894i	−0.0120837	−	0.132909i
$714$		0			0
$715$	43.5714	+	50.2840i	1.62948	+	1.88052i
$716$		0			0
$717$	−15.7047	+	19.9701i	−0.586501	+	0.745797i
$718$		0			0
$719$	19.2903	+	24.5296i	0.719406	+	0.914799i	0.998972	−	0.0453273i	$-0.0144331\pi$
$719$	19.2903	+	24.5296i	0.719406	+	0.914799i	−0.279566	+	0.960126i	$0.590191\pi$
$720$		0			0
$721$	11.9036	−	5.56959i	0.443313	−	0.207422i
$722$		0			0
$723$	7.91726	−	8.30339i	0.294446	−	0.308806i
$724$		0			0
$725$	1.31900	+	3.81100i	0.0489865	+	0.141537i
$726$		0			0
$727$	13.8120	+	30.2440i	0.512258	+	1.12169i	0.972288	+	0.233786i	$0.0751115\pi$
$727$	13.8120	+	30.2440i	0.512258	+	1.12169i	−0.460030	+	0.887904i	$0.652161\pi$
$728$		0			0
$729$	−20.6750	−	6.07072i	−0.765740	−	0.224841i
$730$		0			0
$731$	34.0850	−	24.2718i	1.26068	−	0.897724i
$732$		0			0
$733$	−0.367918	+	7.72355i	−0.0135894	+	0.285276i	0.981836	+	0.189732i	$0.0607620\pi$
$733$	−0.367918	+	7.72355i	−0.0135894	+	0.285276i	−0.995425	+	0.0955436i	$0.969541\pi$
$734$		0			0
$735$	−40.9727	+	10.7447i	−1.51130	+	0.396326i
$736$		0			0
$737$	1.85879	+	3.21951i	0.0684693	+	0.118592i
$738$		0			0
$739$	−44.8450	+	23.1192i	−1.64965	+	0.850454i	−0.654081	+	0.756424i	$0.726945\pi$
$739$	−44.8450	+	23.1192i	−1.64965	+	0.850454i	−0.995569	+	0.0940296i	$0.970025\pi$
$740$		0			0
$741$	−1.73039	+	3.78903i	−0.0635675	+	0.139193i
$742$		0			0
$743$	−8.45330	+	28.7893i	−0.310122	+	1.05618i	0.646032	+	0.763311i	$0.276427\pi$
$743$	−8.45330	+	28.7893i	−0.310122	+	1.05618i	−0.956153	+	0.292867i	$0.905391\pi$
$744$		0			0
$745$	−5.27449	+	55.2370i	−0.193243	+	2.02373i
$746$		0			0
$747$	−18.8213	−	3.62751i	−0.688636	−	0.132724i
$748$		0			0
$749$	4.84085	+	31.5951i	0.176881	+	1.15446i
$750$		0			0
$751$	18.1850	−	35.2740i	0.663580	−	1.28717i	−0.281259	−	0.959632i	$-0.590752\pi$
$751$	18.1850	−	35.2740i	0.663580	−	1.28717i	0.944839	−	0.327534i	$-0.106218\pi$
$752$		0			0
$753$	18.9126	−	47.2413i	0.689212	−	1.72157i
$754$		0			0
$755$	1.56965	−	10.9171i	0.0571252	−	0.397315i
$756$		0			0
$757$	−25.8256	+	22.3780i	−0.938646	+	0.813341i	−0.982608	−	0.185692i	$-0.940547\pi$
$757$	−25.8256	+	22.3780i	−0.938646	+	0.813341i	0.0439621	+	0.999033i	$0.486002\pi$
$758$		0			0
$759$	45.6515	−	52.2048i	1.65705	−	1.89491i
$760$		0			0
$761$	8.66283	+	2.99824i	0.314027	+	0.108686i	0.479536	−	0.877522i	$-0.340805\pi$
$761$	8.66283	+	2.99824i	0.314027	+	0.108686i	−0.165508	+	0.986208i	$0.552926\pi$
$762$		0			0
$763$	7.41113	+	29.3630i	0.268301	+	1.06301i
$764$		0			0
$765$	23.7628	−	18.6873i	0.859145	−	0.675639i
$766$		0			0
$767$	1.28910	+	27.0616i	0.0465468	+	0.977138i
$768$		0			0
$769$	26.7534	−	7.85550i	0.964752	−	0.283277i	0.238836	−	0.971060i	$-0.423234\pi$
$769$	26.7534	−	7.85550i	0.964752	−	0.283277i	0.725916	+	0.687783i	$0.241416\pi$
$770$		0			0
$771$	1.14121	−	1.31702i	0.0410995	−	0.0474314i
$772$		0			0
$773$	11.5397	+	1.10191i	0.415054	+	0.0396329i	0.300495	−	0.953784i	$-0.402848\pi$
$773$	11.5397	+	1.10191i	0.415054	+	0.0396329i	0.114559	+	0.993416i	$0.463454\pi$
$774$		0			0
$775$	1.02030	−	0.247523i	0.0366503	−	0.00889128i
$776$		0			0
$777$	−23.8728	−	45.2754i	−0.856431	−	1.62424i
$778$		0			0
$779$	1.11229	+	0.0529848i	0.0398518	+	0.00189838i
$780$		0			0
$781$	21.7169	+	12.5383i	0.777092	+	0.448654i
$782$		0			0
$783$		−	1.97933i		−	0.0707356i
$784$		0			0
$785$	−33.3687	−	21.4448i	−1.19098	−	0.765397i
$786$		0			0
$787$	0.672025	+	0.943727i	0.0239551	+	0.0336402i	0.826380	−	0.563113i	$-0.190396\pi$
$787$	0.672025	+	0.943727i	0.0239551	+	0.0336402i	−0.802425	+	0.596753i	$0.796457\pi$
$788$		0			0
$789$	12.0485	+	49.6644i	0.428937	+	1.76810i
$790$		0			0
$791$	−8.07988	+	34.7011i	−0.287288	+	1.23383i
$792$		0			0
$793$	5.22413	−	27.1054i	0.185514	−	0.962540i
$794$		0			0
$795$	−0.572054	+	2.35804i	−0.0202887	+	0.0836310i
$796$		0			0
$797$	9.35234	−	6.01039i	0.331277	−	0.212899i	−0.364419	−	0.931235i	$-0.618732\pi$
$797$	9.35234	−	6.01039i	0.331277	−	0.212899i	0.695696	+	0.718336i	$0.255096\pi$
$798$		0			0
$799$	−36.4591	+	5.24203i	−1.28983	+	0.185450i
$800$		0			0
$801$	1.10424	+	0.868387i	0.0390165	+	0.0306829i
$802$		0			0
$803$	−11.2117	+	32.3942i	−0.395653	+	1.14317i
$804$		0			0
$805$	22.2829	+	23.1507i	0.785370	+	0.815955i
$806$		0			0
$807$	14.3410	−	41.4357i	0.504828	−	1.45860i
$808$		0			0
$809$	−8.18530	−	6.43699i	−0.287780	−	0.226313i	0.463824	−	0.885927i	$-0.346477\pi$
$809$	−8.18530	−	6.43699i	−0.287780	−	0.226313i	−0.751604	+	0.659615i	$0.770719\pi$
$810$		0			0
$811$	−6.04469	+	0.869095i	−0.212258	+	0.0305181i	−0.247623	−	0.968856i	$-0.579650\pi$
$811$	−6.04469	+	0.869095i	−0.212258	+	0.0305181i	0.0353656	+	0.999374i	$0.488740\pi$
$812$		0			0
$813$	25.7043	−	16.5192i	0.901490	−	0.579352i
$814$		0			0
$815$	−4.53332	+	18.6866i	−0.158795	+	0.654563i
$816$		0			0
$817$	−0.721752	+	3.74480i	−0.0252509	+	0.131014i
$818$		0			0
$819$	−29.7837	+	9.04483i	−1.04073	+	0.316052i
$820$		0			0
$821$	−8.43232	−	34.7585i	−0.294290	−	1.21308i	−0.906439	−	0.422338i	$-0.861210\pi$
$821$	−8.43232	−	34.7585i	−0.294290	−	1.21308i	0.612148	−	0.790743i	$-0.290305\pi$
$822$		0			0
$823$	−2.10514	−	2.95626i	−0.0733806	−	0.103049i	0.776254	−	0.630420i	$-0.217117\pi$
$823$	−2.10514	−	2.95626i	−0.0733806	−	0.103049i	−0.849635	+	0.527371i	$0.823178\pi$
$824$		0			0
$825$	17.1883	+	11.0463i	0.598420	+	0.384581i
$826$		0			0
$827$			40.0457i			1.39253i	0.717787	+	0.696263i	$0.245155\pi$
$827$			40.0457i			1.39253i	−0.717787	+	0.696263i	$0.754845\pi$
$828$		0			0
$829$	−30.9039	−	17.8424i	−1.07334	−	0.619692i	−0.144247	−	0.989542i	$-0.546076\pi$
$829$	−30.9039	−	17.8424i	−1.07334	−	0.619692i	−0.929092	+	0.369849i	$0.879409\pi$
$830$		0			0
$831$	−28.0767	−	1.33746i	−0.973970	−	0.0463959i
$832$		0			0
$833$	−19.7605	+	23.6745i	−0.684662	+	0.820271i
$834$		0			0
$835$	41.1217	−	9.97601i	1.42307	−	0.345234i
$836$		0			0
$837$	−0.512965	−	0.0489822i	−0.0177307	−	0.00169307i
$838$		0			0
$839$	5.99899	−	6.92320i	0.207108	−	0.239015i	−0.642687	−	0.766129i	$-0.722180\pi$
$839$	5.99899	−	6.92320i	0.207108	−	0.239015i	0.849795	+	0.527114i	$0.176726\pi$
$840$		0			0
$841$	20.0089	−	5.87514i	0.689962	−	0.202591i
$842$		0			0
$843$	3.39164	+	71.1993i	0.116814	+	2.45224i
$844$		0			0
$845$	−11.6442	+	9.15710i	−0.400573	+	0.315014i
$846$		0			0
$847$	−18.4972	+	65.2175i	−0.635572	+	2.24090i
$848$		0			0
$849$	−71.2102	−	24.6461i	−2.44393	−	0.845851i
$850$		0			0
$851$	−21.1394	+	32.5681i	−0.724649	+	1.11642i
$852$		0			0
$853$	19.8002	−	17.1569i	0.677945	−	0.587443i	−0.246323	−	0.969188i	$-0.579222\pi$
$853$	19.8002	−	17.1569i	0.677945	−	0.587443i	0.924268	+	0.381745i	$0.124677\pi$
$854$		0			0
$855$	−0.392115	+	2.72722i	−0.0134101	+	0.0932690i
$856$		0			0
$857$	3.15595	−	7.88317i	0.107805	−	0.269284i	−0.864650	−	0.502375i	$-0.832460\pi$
$857$	3.15595	−	7.88317i	0.107805	−	0.269284i	0.972455	+	0.233091i	$0.0748840\pi$
$858$		0			0
$859$	2.96033	−	5.74225i	0.101005	−	0.195923i	−0.832918	−	0.553396i	$-0.813331\pi$
$859$	2.96033	−	5.74225i	0.101005	−	0.195923i	0.933923	+	0.357474i	$0.116362\pi$
$860$		0			0
$861$	10.9653	+	13.6816i	0.373695	+	0.466266i
$862$		0			0
$863$	−39.2489	−	7.56460i	−1.33605	−	0.257502i	−0.529319	−	0.848423i	$-0.677552\pi$
$863$	−39.2489	−	7.56460i	−1.33605	−	0.257502i	−0.806729	+	0.590921i	$0.798764\pi$
$864$		0			0
$865$	0.565094	−	5.91794i	0.0192138	−	0.201216i
$866$		0			0
$867$	1.62062	−	5.51931i	0.0550390	−	0.187446i
$868$		0			0
$869$	−19.9102	+	43.5972i	−0.675406	+	1.47893i
$870$		0			0
$871$	−2.37061	+	1.22214i	−0.0803251	+	0.0414105i
$872$		0			0
$873$	−12.8765	−	22.3027i	−0.435803	−	0.754834i
$874$		0			0
$875$	14.6814	−	19.0279i	0.496323	−	0.643261i
$876$		0			0
$877$	−0.958073	+	20.1124i	−0.0323518	+	0.679148i	0.923199	+	0.384322i	$0.125565\pi$
$877$	−0.958073	+	20.1124i	−0.0323518	+	0.679148i	−0.955551	+	0.294826i	$0.904738\pi$
$878$		0			0
$879$	38.0525	−	27.0970i	1.28348	−	0.913960i
$880$		0			0
$881$	−8.93894	−	2.62471i	−0.301161	−	0.0884287i	0.127661	−	0.991818i	$-0.459253\pi$
$881$	−8.93894	−	2.62471i	−0.301161	−	0.0884287i	−0.428822	+	0.903389i	$0.641071\pi$
$882$		0			0
$883$	−3.75457	−	8.22136i	−0.126351	−	0.276671i	0.835876	−	0.548918i	$-0.184960\pi$
$883$	−3.75457	−	8.22136i	−0.126351	−	0.276671i	−0.962227	+	0.272248i	$0.912233\pi$
$884$		0			0
$885$	12.3501	+	35.6833i	0.415144	+	1.19948i
$886$		0			0
$887$	−13.1399	+	13.7807i	−0.441194	+	0.462711i	−0.906356	−	0.422515i	$-0.861148\pi$
$887$	−13.1399	+	13.7807i	−0.441194	+	0.462711i	0.465162	+	0.885225i	$0.345996\pi$
$888$		0			0
$889$	−3.50831	+	40.7097i	−0.117665	+	1.36536i
$890$		0			0
$891$	−36.6097	−	46.5531i	−1.22647	−	1.55959i
$892$		0			0
$893$	2.07524	−	2.63888i	0.0694451	−	0.0883067i
$894$		0			0
$895$	−15.9524	−	18.4101i	−0.533230	−	0.615380i
$896$		0			0
$897$	35.8525	+	34.4968i	1.19708	+	1.15181i
$898$		0			0
$899$	0.401368	+	2.08250i	0.0133864	+	0.0694552i
$900$		0			0
$901$	0.656541	+	1.63996i	0.0218726	+	0.0546350i
$902$		0			0
$903$	−51.7247	+	30.5035i	−1.72129	+	1.01509i
$904$		0			0
$905$	−29.3633	−	15.1378i	−0.976068	−	0.503198i
$906$		0			0
$907$	−46.0747	−	11.1776i	−1.52988	−	0.371146i	−0.619529	−	0.784974i	$-0.712676\pi$
$907$	−46.0747	−	11.1776i	−1.52988	−	0.371146i	−0.910355	+	0.413828i	$0.864191\pi$
$908$		0			0
$909$	−30.1139	−	26.0939i	−0.998817	−	0.865480i
$910$		0			0
$911$	10.8987	−	4.97725i	0.361089	−	0.164904i	−0.226606	−	0.973987i	$-0.572763\pi$
$911$	10.8987	−	4.97725i	0.361089	−	0.164904i	0.587695	+	0.809083i	$0.300036\pi$
$912$		0			0
$913$	−29.5397	−	30.9804i	−0.977622	−	1.02530i
$914$		0			0
$915$	−3.65715	−	38.2994i	−0.120901	−	1.26614i
$916$		0			0
$917$	0.882162	−	1.03727i	0.0291316	−	0.0342536i
$918$		0			0
$919$	7.62790	−	4.40397i	0.251621	−	0.145273i	−0.368885	−	0.929475i	$-0.620260\pi$
$919$	7.62790	−	4.40397i	0.251621	−	0.145273i	0.620506	+	0.784201i	$0.286927\pi$
$920$		0			0
$921$	−15.7702	+	27.3148i	−0.519645	+	0.900052i
$922$		0			0
$923$	−9.72648	+	15.1347i	−0.320151	+	0.498165i
$924$		0			0
$925$	−10.4055	−	4.75203i	−0.342131	−	0.156246i
$926$		0			0
$927$	9.74159	−	9.28859i	0.319956	−	0.305077i
$928$		0			0
$929$	−20.1038	−	14.3158i	−0.659584	−	0.469687i	0.200599	−	0.979673i	$-0.435711\pi$
$929$	−20.1038	−	14.3158i	−0.659584	−	0.469687i	−0.860183	+	0.509986i	$0.829651\pi$
$930$		0			0
$931$	−0.185553	−	2.80447i	−0.00608124	−	0.0919127i
$932$		0			0
$933$	−25.4518	−	24.2683i	−0.833255	−	0.794507i
$934$		0			0
$935$	67.4359	−	3.21237i	2.20539	−	0.105056i
$936$		0			0
$937$	−3.38564	−	23.5477i	−0.110604	−	0.769269i	−0.967334	−	0.253504i	$-0.918417\pi$
$937$	−3.38564	−	23.5477i	−0.110604	−	0.769269i	0.856730	−	0.515765i	$-0.172492\pi$
$938$		0			0
$939$	−6.59279	−	0.947899i	−0.215147	−	0.0309335i
$940$		0			0
$941$	−16.3549	+	3.15216i	−0.533156	+	0.102757i	−0.448721	−	0.893672i	$-0.648120\pi$
$941$	−16.3549	+	3.15216i	−0.533156	+	0.102757i	−0.0844343	+	0.996429i	$0.526908\pi$
$942$		0			0
$943$	4.99925	−	12.3254i	0.162798	−	0.401369i
$944$		0			0
$945$	3.88542	−	2.54800i	0.126393	−	0.0828866i
$946$		0			0
$947$	2.25337	−	0.902113i	0.0732247	−	0.0293147i	−0.334761	−	0.942303i	$-0.608656\pi$
$947$	2.25337	−	0.902113i	0.0732247	−	0.0293147i	0.407986	+	0.912988i	$0.366231\pi$
$948$		0			0
$949$	−22.8315	−	9.14035i	−0.741142	−	0.296708i
$950$		0			0
$951$	−13.7728	−	21.4309i	−0.446614	−	0.694944i
$952$		0			0
$953$	−5.46081	−	18.5978i	−0.176893	−	0.602442i	−0.999431	−	0.0337317i	$-0.989261\pi$
$953$	−5.46081	−	18.5978i	−0.176893	−	0.602442i	0.822538	−	0.568710i	$-0.192557\pi$
$954$		0			0
$955$	−35.5596	+	12.3073i	−1.15068	+	0.398255i
$956$		0			0
$957$	−23.9406	+	33.6198i	−0.773889	+	1.08678i
$958$		0			0
$959$	53.9691	−	5.65675i	1.74275	−	0.182666i
$960$		0			0
$961$	−30.3100	+	2.89425i	−0.977742	+	0.0933630i
$962$		0			0
$963$	15.0011	+	29.0981i	0.483404	+	0.937672i
$964$		0			0
$965$	26.0879			0.839800
$966$		0			0
$967$	13.4056			0.431095			0.215548	−	0.976493i	$-0.430846\pi$
$967$	13.4056			0.431095			0.215548	+	0.976493i	$0.430846\pi$
$968$		0			0
$969$	1.93675	+	3.75677i	0.0622173	+	0.120685i
$970$		0			0
$971$	−37.9630	+	3.62503i	−1.21829	+	0.116333i	−0.684327	−	0.729175i	$-0.739904\pi$
$971$	−37.9630	+	3.62503i	−1.21829	+	0.116333i	−0.533963	+	0.845508i	$0.679298\pi$
$972$		0			0
$973$	34.7529	+	47.8622i	1.11413	+	1.53439i
$974$		0			0
$975$	−8.50269	+	11.9404i	−0.272304	+	0.382398i
$976$		0			0
$977$	−3.55705	+	1.23111i	−0.113800	+	0.0393867i	−0.383375	−	0.923593i	$-0.625238\pi$
$977$	−3.55705	+	1.23111i	−0.113800	+	0.0393867i	0.269574	+	0.962980i	$0.413117\pi$
$978$		0			0
$979$	0.883869	+	3.01018i	0.0282486	+	0.0962058i
$980$		0			0
$981$	16.7689	+	26.0930i	0.535391	+	0.833084i
$982$		0			0
$983$	−32.7135	−	13.0965i	−1.04340	−	0.417714i	−0.214271	−	0.976774i	$-0.568738\pi$
$983$	−32.7135	−	13.0965i	−1.04340	−	0.417714i	−0.829127	+	0.559060i	$0.811162\pi$
$984$		0			0
$985$	−31.8646	+	12.7567i	−1.01529	+	0.406461i
$986$		0			0
$987$	52.7744	−	3.00259i	1.67983	−	0.0955734i
$988$		0			0
$989$	39.3460	+	22.9548i	1.25113	+	0.729920i
$990$		0			0
$991$	−8.05628	+	1.55272i	−0.255916	+	0.0493238i	−0.315596	−	0.948894i	$-0.602204\pi$
$991$	−8.05628	+	1.55272i	−0.255916	+	0.0493238i	0.0596795	+	0.998218i	$0.480992\pi$
$992$		0			0
$993$	60.4033	+	8.68468i	1.91684	+	0.275600i
$994$		0			0
$995$	7.13450	+	49.6215i	0.226179	+	1.57311i
$996$		0			0
$997$	−25.4916	+	1.21431i	−0.807327	+	0.0384577i	−0.447187	−	0.894441i	$-0.647574\pi$
$997$	−25.4916	+	1.21431i	−0.807327	+	0.0384577i	−0.360140	+	0.932898i	$0.617271\pi$
$998$		0			0
$999$	4.06339	+	3.87443i	0.128560	+	0.122582i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.bc.a.493.3	yes	320
7.5	odd	6	inner	644.2.bc.a.33.3	✓	320
23.7	odd	22	inner	644.2.bc.a.605.3	yes	320
161.145	even	66	inner	644.2.bc.a.145.3	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.bc.a.33.3	✓	320	7.5	odd	6	inner
644.2.bc.a.145.3	yes	320	161.145	even	66	inner
644.2.bc.a.493.3	yes	320	1.1	even	1	trivial
644.2.bc.a.605.3	yes	320	23.7	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09494 - 2.12389i) q^{3} +(2.52091 - 0.240718i) q^{5} +(-2.14090 + 1.55452i) q^{7} +(-1.57183 + 2.20732i) q^{9} +O(q^{10})\)	\(q+(-1.09494 - 2.12389i) q^{3} +(2.52091 - 0.240718i) q^{5} +(-2.14090 + 1.55452i) q^{7} +(-1.57183 + 2.20732i) q^{9} +(-5.71879 + 1.97929i) q^{11} +(-1.22317 - 4.16575i) q^{13} +(-3.27150 - 5.09056i) q^{15} +(-4.08981 - 1.63731i) q^{17} +(0.372753 - 0.149228i) q^{19} +(5.64578 + 2.84493i) q^{21} +(-0.206485 - 4.79138i) q^{23} +(1.38741 - 0.267401i) q^{25} +(-0.686426 - 0.0986931i) q^{27} +(0.406193 + 2.82514i) q^{29} +(0.742215 - 0.0353561i) q^{31} +(10.4655 + 9.97885i) q^{33} +(-5.02283 + 4.43416i) q^{35} +(-6.59484 - 4.69616i) q^{37} +(-7.50828 + 7.15913i) q^{39} +(2.52275 + 1.15210i) q^{41} +(-5.13520 + 7.99052i) q^{43} +(-3.43110 + 5.94283i) q^{45} +(7.24098 - 4.18058i) q^{47} +(2.16693 - 6.65616i) q^{49} +(1.00063 + 10.4790i) q^{51} +(-0.276713 - 0.290208i) q^{53} +(-13.9401 + 6.36624i) q^{55} +(-0.725084 - 0.628289i) q^{57} +(-6.06424 - 1.47117i) q^{59} +(5.65126 + 2.91343i) q^{61} +(-0.0661981 - 7.16910i) q^{63} +(-4.08629 - 10.2071i) q^{65} +(-0.116259 - 0.603208i) q^{67} +(-9.95026 + 5.68482i) q^{69} +(-2.71359 - 3.13165i) q^{71} +(3.50157 - 4.45261i) q^{73} +(-2.08706 - 2.65391i) q^{75} +(9.16652 - 13.1274i) q^{77} +(5.46537 - 5.73191i) q^{79} +(3.20083 + 9.24819i) q^{81} +(2.93845 + 6.43430i) q^{83} +(-10.7042 - 3.14303i) q^{85} +(5.55551 - 3.95606i) q^{87} +(0.0246673 - 0.517829i) q^{89} +(9.09444 + 7.01702i) q^{91} +(-0.887773 - 1.53767i) q^{93} +(0.903755 - 0.465918i) q^{95} +(-3.94799 + 8.64489i) q^{97} +(4.62001 - 15.7343i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 20 q^{9}+O(q^{10}) \) 320 * q - 20 * q^9	\( 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) \) 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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