LMFDB - Embedded newform 644.4.i.b.93.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,4,Mod(93,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("644.93");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	644.i (of order $3$, degree $2$, 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:	$37.9972300437$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.3
Character	$\chi$	$=$	644.93
Dual form			644.4.i.b.277.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.96641 - 6.87002i) q^{3} +(-0.583194 + 1.01012i) q^{5} +(-10.1039 - 15.5213i) q^{7} +(-17.9648 + 31.1159i) q^{9} +O(q^{10})$	\(q+(-3.96641 - 6.87002i) q^{3} +(-0.583194 + 1.01012i) q^{5} +(-10.1039 - 15.5213i) q^{7} +(-17.9648 + 31.1159i) q^{9} +(16.2140 + 28.0836i) q^{11} +55.4395 q^{13} +9.25274 q^{15} +(33.7439 + 58.4462i) q^{17} +(47.6230 - 82.4854i) q^{19} +(-66.5553 + 130.978i) q^{21} +(11.5000 - 19.9186i) q^{23} +(61.8198 + 107.075i) q^{25} +70.8367 q^{27} +160.296 q^{29} +(52.4314 + 90.8139i) q^{31} +(128.623 - 222.782i) q^{33} +(21.5709 - 1.15428i) q^{35} +(-20.5917 + 35.6658i) q^{37} +(-219.896 - 380.870i) q^{39} +499.448 q^{41} -95.3681 q^{43} +(-20.9539 - 36.2932i) q^{45} +(68.4586 - 118.574i) q^{47} +(-138.821 + 313.652i) q^{49} +(267.684 - 463.643i) q^{51} +(-308.917 - 535.060i) q^{53} -37.8237 q^{55} -755.568 q^{57} +(-96.0380 - 166.343i) q^{59} +(-290.411 + 503.007i) q^{61} +(664.474 - 35.5565i) q^{63} +(-32.3320 + 56.0006i) q^{65} +(286.662 + 496.513i) q^{67} -182.455 q^{69} -458.662 q^{71} +(65.8721 + 114.094i) q^{73} +(490.405 - 849.406i) q^{75} +(272.067 - 535.417i) q^{77} +(173.703 - 300.863i) q^{79} +(204.082 + 353.481i) q^{81} -621.128 q^{83} -78.7170 q^{85} +(-635.798 - 1101.23i) q^{87} +(649.483 - 1124.94i) q^{89} +(-560.157 - 860.493i) q^{91} +(415.929 - 720.410i) q^{93} +(55.5468 + 96.2099i) q^{95} -0.172727 q^{97} -1165.13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9}+O(q^{10}) $ 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9	$ 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9} + 28 q^{11} - 152 q^{13} + 208 q^{15} - 52 q^{17} + 38 q^{19} - 10 q^{21} + 506 q^{23} - 516 q^{25} - 876 q^{27} - 100 q^{29} + 230 q^{31} + 424 q^{33} + 98 q^{35} + 18 q^{37} - 350 q^{39} + 784 q^{41} - 336 q^{43} + 1156 q^{45} + 452 q^{47} + 546 q^{49} - 498 q^{51} - 508 q^{53} - 3084 q^{55} - 1916 q^{57} + 508 q^{59} + 1386 q^{61} + 1290 q^{63} + 360 q^{65} - 1896 q^{67} + 552 q^{69} - 3352 q^{71} + 990 q^{73} + 3328 q^{75} + 1328 q^{77} + 524 q^{79} - 4486 q^{81} - 1120 q^{83} - 5296 q^{85} + 3700 q^{87} + 1216 q^{89} + 1438 q^{91} + 366 q^{93} + 90 q^{95} + 716 q^{97} + 5716 q^{99}+O(q^{100}) $ 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9 + 28 * q^11 - 152 * q^13 + 208 * q^15 - 52 * q^17 + 38 * q^19 - 10 * q^21 + 506 * q^23 - 516 * q^25 - 876 * q^27 - 100 * q^29 + 230 * q^31 + 424 * q^33 + 98 * q^35 + 18 * q^37 - 350 * q^39 + 784 * q^41 - 336 * q^43 + 1156 * q^45 + 452 * q^47 + 546 * q^49 - 498 * q^51 - 508 * q^53 - 3084 * q^55 - 1916 * q^57 + 508 * q^59 + 1386 * q^61 + 1290 * q^63 + 360 * q^65 - 1896 * q^67 + 552 * q^69 - 3352 * q^71 + 990 * q^73 + 3328 * q^75 + 1328 * q^77 + 524 * q^79 - 4486 * q^81 - 1120 * q^83 - 5296 * q^85 + 3700 * q^87 + 1216 * q^89 + 1438 * q^91 + 366 * q^93 + 90 * q^95 + 716 * q^97 + 5716 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.96641	−	6.87002i	−0.763336	−	1.32214i	−0.941122	−	0.338067i	$-0.890227\pi$
$3$	−3.96641	−	6.87002i	−0.763336	−	1.32214i	0.177786	−	0.984069i	$-0.443106\pi$
$4$		0			0
$5$	−0.583194	+	1.01012i	−0.0521624	+	0.0903480i	−0.890928	−	0.454145i	$-0.849945\pi$
$5$	−0.583194	+	1.01012i	−0.0521624	+	0.0903480i	0.838765	+	0.544493i	$0.183278\pi$
$6$		0			0
$7$	−10.1039	−	15.5213i	−0.545561	−	0.838071i
$7$	−10.1039	−	15.5213i	−0.545561	−	0.838071i
$8$		0			0
$9$	−17.9648	+	31.1159i	−0.665362	+	1.15244i
$10$		0			0
$11$	16.2140	+	28.0836i	0.444429	+	0.769774i	0.998012	−	0.0630202i	$-0.0200732\pi$
$11$	16.2140	+	28.0836i	0.444429	+	0.769774i	−0.553583	+	0.832794i	$0.686740\pi$
$12$		0			0
$13$	55.4395			1.18278			0.591390	−	0.806385i	$-0.298579\pi$
$13$	55.4395			1.18278			0.591390	+	0.806385i	$0.298579\pi$
$14$		0			0
$15$	9.25274			0.159270
$16$		0			0
$17$	33.7439	+	58.4462i	0.481418	+	0.833840i	0.999773	−	0.0213253i	$-0.00678858\pi$
$17$	33.7439	+	58.4462i	0.481418	+	0.833840i	−0.518355	+	0.855166i	$0.673455\pi$
$18$		0			0
$19$	47.6230	−	82.4854i	0.575024	−	0.995971i	−0.421015	−	0.907054i	$-0.638326\pi$
$19$	47.6230	−	82.4854i	0.575024	−	0.995971i	0.996039	−	0.0889172i	$-0.0283407\pi$
$20$		0			0
$21$	−66.5553	+	130.978i	−0.691598	+	1.36104i
$22$		0			0
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$24$		0			0
$25$	61.8198	+	107.075i	0.494558	+	0.856600i
$26$		0			0
$27$	70.8367			0.504908
$28$		0			0
$29$	160.296			1.02642			0.513209	−	0.858263i	$-0.328456\pi$
$29$	160.296			1.02642			0.513209	+	0.858263i	$0.328456\pi$
$30$		0			0
$31$	52.4314	+	90.8139i	0.303773	+	0.526150i	0.976987	−	0.213297i	$-0.0684202\pi$
$31$	52.4314	+	90.8139i	0.303773	+	0.526150i	−0.673214	+	0.739447i	$0.735087\pi$
$32$		0			0
$33$	128.623	−	222.782i	0.678497	−	1.17519i
$34$		0			0
$35$	21.5709	−	1.15428i	0.104176	−	0.00557453i
$36$		0			0
$37$	−20.5917	+	35.6658i	−0.0914933	+	0.158471i	−0.908140	−	0.418667i	$-0.862497\pi$
$37$	−20.5917	+	35.6658i	−0.0914933	+	0.158471i	0.816646	+	0.577138i	$0.195831\pi$
$38$		0			0
$39$	−219.896	−	380.870i	−0.902859	−	1.56380i
$40$		0			0
$41$	499.448			1.90245			0.951227	−	0.308492i	$-0.0998242\pi$
$41$	499.448			1.90245			0.951227	+	0.308492i	$0.0998242\pi$
$42$		0			0
$43$	−95.3681			−0.338221			−0.169110	−	0.985597i	$-0.554089\pi$
$43$	−95.3681			−0.338221			−0.169110	+	0.985597i	$0.554089\pi$
$44$		0			0
$45$	−20.9539	−	36.2932i	−0.0694138	−	0.120228i
$46$		0			0
$47$	68.4586	−	118.574i	0.212462	−	0.367995i	−0.740022	−	0.672582i	$-0.765185\pi$
$47$	68.4586	−	118.574i	0.212462	−	0.367995i	0.952484	+	0.304587i	$0.0985185\pi$
$48$		0			0
$49$	−138.821	+	313.652i	−0.404726	+	0.914438i
$50$		0			0
$51$	267.684	−	463.643i	0.734967	−	1.27300i
$52$		0			0
$53$	−308.917	−	535.060i	−0.800623	−	1.38672i	−0.919207	−	0.393775i	$-0.871169\pi$
$53$	−308.917	−	535.060i	−0.800623	−	1.38672i	0.118584	−	0.992944i	$-0.462165\pi$
$54$		0			0
$55$	−37.8237			−0.0927300
$56$		0			0
$57$	−755.568			−1.75575
$58$		0			0
$59$	−96.0380	−	166.343i	−0.211917	−	0.367051i	0.740398	−	0.672169i	$-0.234637\pi$
$59$	−96.0380	−	166.343i	−0.211917	−	0.367051i	−0.952314	+	0.305119i	$0.901304\pi$
$60$		0			0
$61$	−290.411	+	503.007i	−0.609563	+	1.05579i	0.381750	+	0.924266i	$0.375322\pi$
$61$	−290.411	+	503.007i	−0.609563	+	1.05579i	−0.991312	+	0.131528i	$0.958012\pi$
$62$		0			0
$63$	664.474	−	35.5565i	1.32882	−	0.0711064i
$64$		0			0
$65$	−32.3320	+	56.0006i	−0.0616967	+	0.106862i
$66$		0			0
$67$	286.662	+	496.513i	0.522707	+	0.905354i	0.999651	+	0.0264208i	$0.00841097\pi$
$67$	286.662	+	496.513i	0.522707	+	0.905354i	−0.476944	+	0.878933i	$0.658256\pi$
$68$		0			0
$69$	−182.455			−0.318333
$70$		0			0
$71$	−458.662			−0.766665			−0.383332	−	0.923610i	$-0.625224\pi$
$71$	−458.662			−0.766665			−0.383332	+	0.923610i	$0.625224\pi$
$72$		0			0
$73$	65.8721	+	114.094i	0.105613	+	0.182927i	0.913988	−	0.405740i	$-0.132986\pi$
$73$	65.8721	+	114.094i	0.105613	+	0.182927i	−0.808376	+	0.588667i	$0.799653\pi$
$74$		0			0
$75$	490.405	−	849.406i	0.755028	−	1.30775i
$76$		0			0
$77$	272.067	−	535.417i	0.402662	−	0.792422i
$78$		0			0
$79$	173.703	−	300.863i	0.247381	−	0.428477i	−0.715417	−	0.698698i	$-0.753763\pi$
$79$	173.703	−	300.863i	0.247381	−	0.428477i	0.962798	+	0.270220i	$0.0870966\pi$
$80$		0			0
$81$	204.082	+	353.481i	0.279948	+	0.484884i
$82$		0			0
$83$	−621.128			−0.821418			−0.410709	−	0.911767i	$-0.634719\pi$
$83$	−621.128			−0.821418			−0.410709	+	0.911767i	$0.634719\pi$
$84$		0			0
$85$	−78.7170			−0.100448
$86$		0			0
$87$	−635.798	−	1101.23i	−0.783502	−	1.35707i
$88$		0			0
$89$	649.483	−	1124.94i	0.773541	−	1.33981i	−0.162071	−	0.986779i	$-0.551817\pi$
$89$	649.483	−	1124.94i	0.773541	−	1.33981i	0.935611	−	0.353032i	$-0.114849\pi$
$90$		0			0
$91$	−560.157	−	860.493i	−0.645279	−	0.991254i
$92$		0			0
$93$	415.929	−	720.410i	0.463762	−	0.803259i
$94$		0			0
$95$	55.5468	+	96.2099i	0.0599893	+	0.103905i
$96$		0			0
$97$	−0.172727			−0.000180802			−9.04009e−5	−	1.00000i	$-0.500029\pi$
$97$	−0.172727			−0.000180802			−9.04009e−5		1.00000i	$0.500029\pi$
$98$		0			0
$99$	−1165.13			−1.18283
$100$		0			0
$101$	778.597	+	1348.57i	0.767062	+	1.32859i	0.939149	+	0.343509i	$0.111616\pi$
$101$	778.597	+	1348.57i	0.767062	+	1.32859i	−0.172087	+	0.985082i	$0.555051\pi$
$102$		0			0
$103$	479.632	−	830.746i	0.458830	−	0.794717i	−0.540069	−	0.841621i	$-0.681602\pi$
$103$	479.632	−	830.746i	0.458830	−	0.794717i	0.998899	+	0.0469035i	$0.0149353\pi$
$104$		0			0
$105$	−93.4890	−	143.614i	−0.0868914	−	0.133479i
$106$		0			0
$107$	862.359	−	1493.65i	0.779135	−	1.34950i	−0.153307	−	0.988179i	$-0.548992\pi$
$107$	862.359	−	1493.65i	0.779135	−	1.34950i	0.932441	−	0.361322i	$-0.117674\pi$
$108$		0			0
$109$	−673.641	−	1166.78i	−0.591955	−	1.02530i	−0.993969	−	0.109663i	$-0.965023\pi$
$109$	−673.641	−	1166.78i	−0.591955	−	1.02530i	0.402014	−	0.915634i	$-0.368310\pi$
$110$		0			0
$111$	326.700			0.279360
$112$		0			0
$113$	−1037.34			−0.863585			−0.431792	−	0.901973i	$-0.642119\pi$
$113$	−1037.34			−0.863585			−0.431792	+	0.901973i	$0.642119\pi$
$114$		0			0
$115$	13.4135	+	23.2328i	0.0108766	+	0.0188389i
$116$		0			0
$117$	−995.959	+	1725.05i	−0.786978	+	1.36309i
$118$		0			0
$119$	566.214	−	1114.29i	0.436175	−	0.858373i
$120$		0			0
$121$	139.709	−	241.984i	0.104966	−	0.181806i
$122$		0			0
$123$	−1981.01	−	3431.22i	−1.45221	−	2.51530i
$124$		0			0
$125$	−290.010			−0.207514
$126$		0			0
$127$	−688.809			−0.481275			−0.240638	−	0.970615i	$-0.577357\pi$
$127$	−688.809			−0.481275			−0.240638	+	0.970615i	$0.577357\pi$
$128$		0			0
$129$	378.269	+	655.181i	0.258176	+	0.447174i
$130$		0			0
$131$	982.539	−	1701.81i	0.655304	−	1.13502i	−0.326514	−	0.945192i	$-0.605874\pi$
$131$	982.539	−	1701.81i	0.655304	−	1.13502i	0.981818	−	0.189827i	$-0.0607928\pi$
$132$		0			0
$133$	−1761.46	+	94.2571i	−1.14841	+	0.0614521i
$134$		0			0
$135$	−41.3115	+	71.5536i	−0.0263372	+	0.0456174i
$136$		0			0
$137$	419.746	+	727.021i	0.261761	+	0.453384i	0.966710	−	0.255874i	$-0.0823633\pi$
$137$	419.746	+	727.021i	0.261761	+	0.453384i	−0.704949	+	0.709258i	$0.749030\pi$
$138$		0			0
$139$	0.619327			0.000377918			0.000188959	−	1.00000i	$-0.499940\pi$
$139$	0.619327			0.000377918			0.000188959		1.00000i	$0.499940\pi$
$140$		0			0
$141$	−1086.14			−0.648720
$142$		0			0
$143$	898.899	+	1556.94i	0.525662	+	0.910474i
$144$		0			0
$145$	−93.4834	+	161.918i	−0.0535405	+	0.0927349i
$146$		0			0
$147$	2705.42	−	290.369i	1.51795	−	0.162920i
$148$		0			0
$149$	930.863	−	1612.30i	0.511807	−	0.886476i	−0.488099	−	0.872788i	$-0.662310\pi$
$149$	930.863	−	1612.30i	0.511807	−	0.886476i	0.999906	−	0.0136880i	$-0.00435716\pi$
$150$		0			0
$151$	701.651	+	1215.29i	0.378143	+	0.654962i	0.990792	−	0.135393i	$-0.0432296\pi$
$151$	701.651	+	1215.29i	0.378143	+	0.654962i	−0.612649	+	0.790355i	$0.709896\pi$
$152$		0			0
$153$	−2424.81			−1.28127
$154$		0			0
$155$	−122.311			−0.0633822
$156$		0			0
$157$	−815.745	−	1412.91i	−0.414672	−	0.718233i	0.580722	−	0.814102i	$-0.302770\pi$
$157$	−815.745	−	1412.91i	−0.414672	−	0.718233i	−0.995394	+	0.0958690i	$0.969437\pi$
$158$		0			0
$159$	−2450.58	+	4244.53i	−1.22229	+	2.11706i
$160$		0			0
$161$	−425.357	+	22.7612i	−0.208217	+	0.0111418i
$162$		0			0
$163$	1455.22	−	2520.52i	0.699276	−	1.21118i	−0.269442	−	0.963017i	$-0.586839\pi$
$163$	1455.22	−	2520.52i	0.699276	−	1.21118i	0.968718	−	0.248165i	$-0.0798275\pi$
$164$		0			0
$165$	150.024	+	259.850i	0.0707841	+	0.122602i
$166$		0			0
$167$	787.863			0.365070			0.182535	−	0.983199i	$-0.441570\pi$
$167$	787.863			0.365070			0.182535	+	0.983199i	$0.441570\pi$
$168$		0			0
$169$	876.538			0.398970
$170$		0			0
$171$	1711.07	+	2963.67i	0.765199	+	1.32536i
$172$		0			0
$173$	−1566.30	+	2712.91i	−0.688345	+	1.19225i	0.284028	+	0.958816i	$0.408329\pi$
$173$	−1566.30	+	2712.91i	−0.688345	+	1.19225i	−0.972373	+	0.233433i	$0.925004\pi$
$174$		0			0
$175$	1037.32	−	2041.40i	0.448080	−	0.881802i
$176$		0			0
$177$	−761.852	+	1319.57i	−0.323527	+	0.560366i
$178$		0			0
$179$	1151.52	+	1994.49i	0.480830	+	0.832822i	0.999758	−	0.0219959i	$-0.00700207\pi$
$179$	1151.52	+	1994.49i	0.480830	+	0.832822i	−0.518928	+	0.854818i	$0.673669\pi$
$180$		0			0
$181$	4822.71			1.98049			0.990246	−	0.139330i	$-0.0444949\pi$
$181$	4822.71			1.98049			0.990246	+	0.139330i	$0.0444949\pi$
$182$		0			0
$183$	4607.56			1.86120
$184$		0			0
$185$	−24.0179	−	41.6002i	−0.00954502	−	0.0165325i
$186$		0			0
$187$	−1094.25	+	1895.30i	−0.427912	+	0.741166i
$188$		0			0
$189$	−715.729	−	1099.48i	−0.275458	−	0.423149i
$190$		0			0
$191$	675.921	−	1170.73i	0.256063	−	0.443513i	−0.709121	−	0.705087i	$-0.750908\pi$
$191$	675.921	−	1170.73i	0.256063	−	0.443513i	0.965184	+	0.261573i	$0.0842414\pi$
$192$		0			0
$193$	499.265	+	864.753i	0.186207	+	0.322520i	0.943983	−	0.329995i	$-0.107047\pi$
$193$	499.265	+	864.753i	0.186207	+	0.322520i	−0.757776	+	0.652515i	$0.773714\pi$
$194$		0			0
$195$	512.967			0.188381
$196$		0			0
$197$	−1675.16			−0.605838			−0.302919	−	0.953016i	$-0.597961\pi$
$197$	−1675.16			−0.605838			−0.302919	+	0.953016i	$0.597961\pi$
$198$		0			0
$199$	2448.96	+	4241.72i	0.872372	+	1.51099i	0.859536	+	0.511074i	$0.170752\pi$
$199$	2448.96	+	4241.72i	0.872372	+	1.51099i	0.0128352	+	0.999918i	$0.495914\pi$
$200$		0			0
$201$	2274.04	−	3938.75i	0.798001	−	1.38218i
$202$		0			0
$203$	−1619.62	−	2487.99i	−0.559974	−	0.860212i
$204$		0			0
$205$	−291.275	+	504.503i	−0.0992366	+	0.171883i
$206$		0			0
$207$	413.190	+	715.666i	0.138738	+	0.240301i
$208$		0			0
$209$	3088.64			1.02223
$210$		0			0
$211$	3430.05			1.11912			0.559560	−	0.828790i	$-0.310970\pi$
$211$	3430.05			1.11912			0.559560	+	0.828790i	$0.310970\pi$
$212$		0			0
$213$	1819.24	+	3151.02i	0.585223	+	1.01364i
$214$		0			0
$215$	55.6181	−	96.3334i	0.0176424	−	0.0305576i
$216$		0			0
$217$	879.786	−	1731.38i	0.275225	−	0.541631i
$218$		0			0
$219$	522.551	−	905.085i	0.161236	−	0.279269i
$220$		0			0
$221$	1870.75	+	3240.23i	0.569412	+	0.986250i
$222$		0			0
$223$	−2438.69			−0.732319			−0.366159	−	0.930552i	$-0.619328\pi$
$223$	−2438.69			−0.732319			−0.366159	+	0.930552i	$0.619328\pi$
$224$		0			0
$225$	−4442.32			−1.31624
$226$		0			0
$227$	1020.09	+	1766.85i	0.298264	+	0.516608i	0.975739	−	0.218938i	$-0.0702592\pi$
$227$	1020.09	+	1766.85i	0.298264	+	0.516608i	−0.677475	+	0.735546i	$0.736926\pi$
$228$		0			0
$229$	−2990.60	+	5179.87i	−0.862988	+	1.49474i	0.00604239	+	0.999982i	$0.498077\pi$
$229$	−2990.60	+	5179.87i	−0.862988	+	1.49474i	−0.869031	+	0.494758i	$0.835257\pi$
$230$		0			0
$231$	−4757.46	+	254.575i	−1.35506	+	0.0725101i
$232$		0			0
$233$	−1010.35	+	1749.98i	−0.284079	+	0.492040i	−0.972386	−	0.233380i	$-0.925021\pi$
$233$	−1010.35	+	1749.98i	−0.284079	+	0.492040i	0.688306	+	0.725420i	$0.258355\pi$
$234$		0			0
$235$	79.8493	+	138.303i	0.0221651	+	0.0383910i
$236$		0			0
$237$	−2755.91			−0.755340
$238$		0			0
$239$	331.454			0.0897069			0.0448535	−	0.998994i	$-0.485718\pi$
$239$	331.454			0.0897069			0.0448535	+	0.998994i	$0.485718\pi$
$240$		0			0
$241$	−773.285	−	1339.37i	−0.206688	−	0.357993i	0.743982	−	0.668200i	$-0.232935\pi$
$241$	−773.285	−	1339.37i	−0.206688	−	0.357993i	−0.950669	+	0.310207i	$0.899602\pi$
$242$		0			0
$243$	2575.24	−	4460.45i	0.679843	−	1.17752i
$244$		0			0
$245$	−235.867	−	323.146i	−0.0615061	−	0.0842655i
$246$		0			0
$247$	2640.19	−	4572.95i	0.680127	−	1.17802i
$248$		0			0
$249$	2463.65	+	4267.16i	0.627017	+	1.08603i
$250$		0			0
$251$	−4115.99			−1.03505			−0.517527	−	0.855667i	$-0.673147\pi$
$251$	−4115.99			−1.03505			−0.517527	+	0.855667i	$0.673147\pi$
$252$		0			0
$253$	745.846			0.185340
$254$		0			0
$255$	312.224	+	540.787i	0.0766753	+	0.132806i
$256$		0			0
$257$	−889.649	+	1540.92i	−0.215933	+	0.374007i	−0.953561	−	0.301201i	$-0.902613\pi$
$257$	−889.649	+	1540.92i	−0.215933	+	0.374007i	0.737628	+	0.675207i	$0.235946\pi$
$258$		0			0
$259$	761.637	−	40.7558i	0.182725	−	0.00977776i
$260$		0			0
$261$	−2879.68	+	4987.75i	−0.682941	+	1.18289i
$262$		0			0
$263$	426.676	+	739.025i	0.100038	+	0.173271i	0.911700	−	0.410856i	$-0.134770\pi$
$263$	426.676	+	739.025i	0.100038	+	0.173271i	−0.811662	+	0.584127i	$0.801437\pi$
$264$		0			0
$265$	720.634			0.167050
$266$		0			0
$267$	−10304.5			−2.36188
$268$		0			0
$269$	−1680.47	−	2910.66i	−0.380893	−	0.659725i	0.610297	−	0.792172i	$-0.291050\pi$
$269$	−1680.47	−	2910.66i	−0.380893	−	0.659725i	−0.991190	+	0.132447i	$0.957717\pi$
$270$		0			0
$271$	−3926.00	+	6800.03i	−0.880027	+	1.52425i	−0.0287182	+	0.999588i	$0.509143\pi$
$271$	−3926.00	+	6800.03i	−0.880027	+	1.52425i	−0.851309	+	0.524664i	$0.824191\pi$
$272$		0			0
$273$	−3689.79	+	7261.35i	−0.818008	+	1.60981i
$274$		0			0
$275$	−2004.70	+	3472.24i	−0.439592	+	0.761396i
$276$		0			0
$277$	−3371.81	−	5840.14i	−0.731380	−	1.26679i	−0.956294	−	0.292408i	$-0.905543\pi$
$277$	−3371.81	−	5840.14i	−0.731380	−	1.26679i	0.224914	−	0.974379i	$-0.427790\pi$
$278$		0			0
$279$	−3767.68			−0.808477
$280$		0			0
$281$	2052.66			0.435771			0.217886	−	0.975974i	$-0.430084\pi$
$281$	2052.66			0.435771			0.217886	+	0.975974i	$0.430084\pi$
$282$		0			0
$283$	4201.76	+	7277.66i	0.882574	+	1.52866i	0.848469	+	0.529245i	$0.177525\pi$
$283$	4201.76	+	7277.66i	0.882574	+	1.52866i	0.0341055	+	0.999418i	$0.489142\pi$
$284$		0			0
$285$	440.643	−	763.216i	0.0915839	−	0.158628i
$286$		0			0
$287$	−5046.39	−	7752.07i	−1.03791	−	1.59439i
$288$		0			0
$289$	179.194	−	310.373i	0.0364734	−	0.0631737i
$290$		0			0
$291$	0.685106	+	1.18664i	0.000138012	+	0.000239044i
$292$		0			0
$293$	7610.84			1.51751			0.758755	−	0.651377i	$-0.225808\pi$
$293$	7610.84			1.51751			0.758755	+	0.651377i	$0.225808\pi$
$294$		0			0
$295$	224.035			0.0442164
$296$		0			0
$297$	1148.55	+	1989.35i	0.224396	+	0.388665i
$298$		0			0
$299$	637.554	−	1104.28i	0.123313	−	0.213585i
$300$		0			0
$301$	963.593	+	1480.24i	0.184520	+	0.283453i
$302$		0			0
$303$	6176.47	−	10698.0i	1.17105	−	2.02832i
$304$		0			0
$305$	−338.732	−	586.701i	−0.0635926	−	0.110146i
$306$		0			0
$307$	−725.958			−0.134960			−0.0674798	−	0.997721i	$-0.521496\pi$
$307$	−725.958			−0.134960			−0.0674798	+	0.997721i	$0.521496\pi$
$308$		0			0
$309$	−7609.66			−1.40097
$310$		0			0
$311$	−1423.32	−	2465.25i	−0.259514	−	0.449491i	0.706598	−	0.707615i	$-0.250229\pi$
$311$	−1423.32	−	2465.25i	−0.259514	−	0.449491i	−0.966112	+	0.258124i	$0.916896\pi$
$312$		0			0
$313$	3207.12	−	5554.89i	0.579159	−	1.00313i	−0.416417	−	0.909174i	$-0.636714\pi$
$313$	3207.12	−	5554.89i	0.579159	−	1.00313i	0.995576	−	0.0939596i	$-0.0299524\pi$
$314$		0			0
$315$	−351.601	+	691.936i	−0.0628904	+	0.123766i
$316$		0			0
$317$	2365.11	−	4096.49i	0.419046	−	0.725809i	−0.576798	−	0.816887i	$-0.695698\pi$
$317$	2365.11	−	4096.49i	0.419046	−	0.725809i	0.995844	+	0.0910778i	$0.0290312\pi$
$318$		0			0
$319$	2599.04	+	4501.67i	0.456170	+	0.790110i
$320$		0			0
$321$	−13681.9			−2.37896
$322$		0			0
$323$	6427.95			1.10731
$324$		0			0
$325$	3427.26	+	5936.18i	0.584954	+	1.01317i
$326$		0			0
$327$	−5343.87	+	9255.86i	−0.903721	+	1.56529i
$328$		0			0
$329$	−2532.12	+	135.496i	−0.424317	+	0.0227055i
$330$		0			0
$331$	1033.25	−	1789.64i	0.171579	−	0.297183i	−0.767393	−	0.641177i	$-0.778447\pi$
$331$	1033.25	−	1789.64i	0.171579	−	0.297183i	0.938972	+	0.343994i	$0.111780\pi$
$332$		0			0
$333$	−739.850	−	1281.46i	−0.121752	−	0.210881i
$334$		0			0
$335$	−668.718			−0.109063
$336$		0			0
$337$	−11249.4			−1.81838			−0.909189	−	0.416383i	$-0.863298\pi$
$337$	−11249.4			−1.81838			−0.909189	+	0.416383i	$0.863298\pi$
$338$		0			0
$339$	4114.53	+	7126.57i	0.659205	+	1.14178i
$340$		0			0
$341$	−1700.25	+	2944.92i	−0.270011	+	0.467673i
$342$		0			0
$343$	6270.93	−	1014.44i	0.987167	−	0.159693i
$344$		0			0
$345$	106.406	−	184.301i	0.0166050	−	0.0287607i
$346$		0			0
$347$	−1324.97	−	2294.91i	−0.204980	−	0.355036i	0.745146	−	0.666901i	$-0.232380\pi$
$347$	−1324.97	−	2294.91i	−0.204980	−	0.355036i	−0.950126	+	0.311865i	$0.899046\pi$
$348$		0			0
$349$	10334.2			1.58503			0.792517	−	0.609850i	$-0.208770\pi$
$349$	10334.2			1.58503			0.792517	+	0.609850i	$0.208770\pi$
$350$		0			0
$351$	3927.15			0.597196
$352$		0			0
$353$	−1219.09	−	2111.52i	−0.183811	−	0.318370i	0.759364	−	0.650666i	$-0.225510\pi$
$353$	−1219.09	−	2111.52i	−0.183811	−	0.318370i	−0.943175	+	0.332296i	$0.892177\pi$
$354$		0			0
$355$	267.489	−	463.304i	0.0399911	−	0.0692666i
$356$		0			0
$357$	−9901.01	+	529.810i	−1.46783	+	0.0785449i
$358$		0			0
$359$	1822.73	−	3157.07i	0.267967	−	0.464133i	−0.700370	−	0.713780i	$-0.746982\pi$
$359$	1822.73	−	3157.07i	0.267967	−	0.464133i	0.968337	+	0.249648i	$0.0803148\pi$
$360$		0			0
$361$	−1106.39	−	1916.33i	−0.161305	−	0.279389i
$362$		0			0
$363$	−2216.58			−0.320496
$364$		0			0
$365$	−153.665			−0.0220361
$366$		0			0
$367$	2130.61	+	3690.32i	0.303043	+	0.524887i	0.976824	−	0.214045i	$-0.0686639\pi$
$367$	2130.61	+	3690.32i	0.303043	+	0.524887i	−0.673780	+	0.738932i	$0.735331\pi$
$368$		0			0
$369$	−8972.47	+	15540.8i	−1.26582	+	2.19247i
$370$		0			0
$371$	−5183.54	+	10201.0i	−0.725381	+	1.42752i
$372$		0			0
$373$	2975.54	−	5153.79i	0.413050	−	0.715424i	−0.582172	−	0.813066i	$-0.697797\pi$
$373$	2975.54	−	5153.79i	0.413050	−	0.715424i	0.995222	+	0.0976424i	$0.0311301\pi$
$374$		0			0
$375$	1150.30	+	1992.37i	0.158403	+	0.274362i
$376$		0			0
$377$	8886.71			1.21403
$378$		0			0
$379$	7909.04			1.07193			0.535963	−	0.844241i	$-0.319949\pi$
$379$	7909.04			1.07193			0.535963	+	0.844241i	$0.319949\pi$
$380$		0			0
$381$	2732.10	+	4732.14i	0.367375	+	0.636311i
$382$		0			0
$383$	7379.31	−	12781.3i	0.984504	−	1.70521i	0.340382	−	0.940287i	$-0.389444\pi$
$383$	7379.31	−	12781.3i	0.984504	−	1.70521i	0.644121	−	0.764923i	$-0.277223\pi$
$384$		0			0
$385$	382.168	+	587.073i	0.0505899	+	0.0777143i
$386$		0			0
$387$	1713.27	−	2967.47i	0.225040	−	0.389780i
$388$		0			0
$389$	−3091.07	−	5353.89i	−0.402888	−	0.697822i	0.591185	−	0.806536i	$-0.298660\pi$
$389$	−3091.07	−	5353.89i	−0.402888	−	0.697822i	−0.994073	+	0.108714i	$0.965327\pi$
$390$		0			0
$391$	1552.22			0.200765
$392$		0			0
$393$	−15588.6			−2.00087
$394$		0			0
$395$	202.605	+	350.923i	0.0258080	+	0.0447008i
$396$		0			0
$397$	5563.25	−	9635.83i	0.703303	−	1.21816i	−0.263997	−	0.964523i	$-0.585041\pi$
$397$	5563.25	−	9635.83i	0.703303	−	1.21816i	0.967300	−	0.253634i	$-0.0816257\pi$
$398$		0			0
$399$	7634.21	+	11727.4i	0.957867	+	1.47144i
$400$		0			0
$401$	−2919.41	+	5056.57i	−0.363562	+	0.629708i	−0.988544	−	0.150931i	$-0.951773\pi$
$401$	−2919.41	+	5056.57i	−0.363562	+	0.629708i	0.624982	+	0.780639i	$0.285106\pi$
$402$		0			0
$403$	2906.77	+	5034.68i	0.359297	+	0.622321i
$404$		0			0
$405$	−476.078			−0.0584111
$406$		0			0
$407$	−1335.50			−0.162649
$408$		0			0
$409$	3349.88	+	5802.17i	0.404990	+	0.701464i	0.994320	−	0.106429i	$-0.0339416\pi$
$409$	3349.88	+	5802.17i	0.404990	+	0.701464i	−0.589330	+	0.807892i	$0.700608\pi$
$410$		0			0
$411$	3329.77	−	5767.33i	0.399624	−	0.692168i
$412$		0			0
$413$	−1611.49	+	3171.35i	−0.192001	+	0.377850i
$414$		0			0
$415$	362.238	−	627.415i	0.0428471	−	0.0742134i
$416$		0			0
$417$	−2.45650	−	4.25479i	−0.000288478	−	0.000499659i
$418$		0			0
$419$	3977.40			0.463744			0.231872	−	0.972746i	$-0.425515\pi$
$419$	3977.40			0.463744			0.231872	+	0.972746i	$0.425515\pi$
$420$		0			0
$421$	4536.02			0.525112			0.262556	−	0.964917i	$-0.415435\pi$
$421$	4536.02			0.525112			0.262556	+	0.964917i	$0.415435\pi$
$422$		0			0
$423$	2459.69	+	4260.31i	0.282729	+	0.489700i
$424$		0			0
$425$	−4172.08	+	7226.26i	−0.476178	+	0.824765i
$426$		0			0
$427$	10741.6	−	574.792i	1.21738	−	0.0651432i
$428$		0			0
$429$	7130.80	−	12350.9i	0.802513	−	1.38999i
$430$		0			0
$431$	−3614.29	−	6260.13i	−0.403930	−	0.699628i	0.590266	−	0.807209i	$-0.299023\pi$
$431$	−3614.29	−	6260.13i	−0.403930	−	0.699628i	−0.994196	+	0.107581i	$0.965690\pi$
$432$		0			0
$433$	−1456.11			−0.161608			−0.0808041	−	0.996730i	$-0.525749\pi$
$433$	−1456.11			−0.161608			−0.0808041	+	0.996730i	$0.525749\pi$
$434$		0			0
$435$	1483.17			0.163477
$436$		0			0
$437$	−1095.33	−	1897.16i	−0.119901	−	0.207674i
$438$		0			0
$439$	−24.3594	+	42.1917i	−0.00264831	+	0.00458701i	−0.867347	−	0.497705i	$-0.834176\pi$
$439$	−24.3594	+	42.1917i	−0.00264831	+	0.00458701i	0.864698	+	0.502292i	$0.167510\pi$
$440$		0			0
$441$	−7265.69	−	9954.24i	−0.784547	−	1.07486i
$442$		0			0
$443$	−5048.16	+	8743.66i	−0.541411	+	0.937752i	0.457412	+	0.889255i	$0.348776\pi$
$443$	−5048.16	+	8743.66i	−0.541411	+	0.937752i	−0.998823	+	0.0484967i	$0.984557\pi$
$444$		0			0
$445$	757.549	+	1312.11i	0.0806995	+	0.139776i
$446$		0			0
$447$	−14768.7			−1.56272
$448$		0			0
$449$	−8937.89			−0.939433			−0.469716	−	0.882817i	$-0.655644\pi$
$449$	−8937.89			−0.939433			−0.469716	+	0.882817i	$0.655644\pi$
$450$		0			0
$451$	8098.07	+	14026.3i	0.845506	+	1.46446i
$452$		0			0
$453$	5566.07	−	9640.71i	0.577299	−	0.999912i
$454$		0			0
$455$	1195.88	−	63.9926i	0.123217	−	0.00659345i
$456$		0			0
$457$	7437.87	−	12882.8i	0.761333	−	1.31867i	−0.180831	−	0.983514i	$-0.557879\pi$
$457$	7437.87	−	12882.8i	0.761333	−	1.31867i	0.942164	−	0.335153i	$-0.108788\pi$
$458$		0			0
$459$	2390.31	+	4140.13i	0.243072	+	0.421013i
$460$		0			0
$461$	−10868.1			−1.09800			−0.549000	−	0.835822i	$-0.684991\pi$
$461$	−10868.1			−1.09800			−0.549000	+	0.835822i	$0.684991\pi$
$462$		0			0
$463$	−9139.99			−0.917433			−0.458717	−	0.888583i	$-0.651691\pi$
$463$	−9139.99			−0.917433			−0.458717	+	0.888583i	$0.651691\pi$
$464$		0			0
$465$	485.134	+	840.277i	0.0483819	+	0.0837998i
$466$		0			0
$467$	1505.09	−	2606.90i	0.149138	−	0.258315i	−0.781771	−	0.623565i	$-0.785683\pi$
$467$	1505.09	−	2606.90i	0.149138	−	0.258315i	0.930909	+	0.365251i	$0.119017\pi$
$468$		0			0
$469$	4810.11	−	9466.10i	0.473583	−	0.931991i
$470$		0			0
$471$	−6471.15	+	11208.4i	−0.633068	+	1.09651i
$472$		0			0
$473$	−1546.30	−	2678.28i	−0.150315	−	0.260354i
$474$		0			0
$475$	11776.2			1.13753
$476$		0			0
$477$	22198.5			2.13082
$478$		0			0
$479$	−3553.00	−	6153.97i	−0.338916	−	0.587019i	0.645313	−	0.763918i	$-0.276727\pi$
$479$	−3553.00	−	6153.97i	−0.338916	−	0.587019i	−0.984229	+	0.176899i	$0.943393\pi$
$480$		0			0
$481$	−1141.59	+	1977.30i	−0.108216	+	0.187436i
$482$		0			0
$483$	1843.51	+	2831.93i	0.173670	+	0.266786i
$484$		0			0
$485$	0.100733	−	0.174475i	9.43106e−6	−	1.63351e-5i
$486$		0			0
$487$	−7500.94	−	12992.0i	−0.697947	−	1.20888i	−0.969177	−	0.246365i	$-0.920764\pi$
$487$	−7500.94	−	12992.0i	−0.697947	−	1.20888i	0.271231	−	0.962514i	$-0.412569\pi$
$488$		0			0
$489$	−23088.1			−2.13513
$490$		0			0
$491$	13089.9			1.20313			0.601566	−	0.798823i	$-0.294544\pi$
$491$	13089.9			1.20313			0.601566	+	0.798823i	$0.294544\pi$
$492$		0			0
$493$	5409.00	+	9368.67i	0.494137	+	0.855870i
$494$		0			0
$495$	679.495	−	1176.92i	0.0616991	−	0.106866i
$496$		0			0
$497$	4634.29	+	7119.03i	0.418263	+	0.642520i
$498$		0			0
$499$	−7990.05	+	13839.2i	−0.716801	+	1.24154i	0.245459	+	0.969407i	$0.421061\pi$
$499$	−7990.05	+	13839.2i	−0.716801	+	1.24154i	−0.962261	+	0.272130i	$0.912272\pi$
$500$		0			0
$501$	−3124.99	−	5412.63i	−0.278671	−	0.482672i
$502$		0			0
$503$	−1301.28			−0.115350			−0.0576752	−	0.998335i	$-0.518369\pi$
$503$	−1301.28			−0.115350			−0.0576752	+	0.998335i	$0.518369\pi$
$504$		0			0
$505$	−1816.29			−0.160047
$506$		0			0
$507$	−3476.71	−	6021.83i	−0.304548	−	0.527493i
$508$		0			0
$509$	6098.96	−	10563.7i	0.531103	−	0.919898i	−0.468238	−	0.883602i	$-0.655111\pi$
$509$	6098.96	−	10563.7i	0.531103	−	0.919898i	0.999341	−	0.0362953i	$-0.0115557\pi$
$510$		0			0
$511$	1105.32	−	2175.22i	0.0956875	−	0.188309i
$512$		0			0
$513$	3373.45	−	5842.99i	0.290334	−	0.502874i
$514$		0			0
$515$	559.436	+	968.972i	0.0478674	+	0.0829087i
$516$		0			0
$517$	4439.97			0.377697
$518$		0			0
$519$	24850.4			2.10175
$520$		0			0
$521$	5640.64	+	9769.87i	0.474320	+	0.821547i	0.999568	−	0.0294027i	$-0.00936052\pi$
$521$	5640.64	+	9769.87i	0.474320	+	0.821547i	−0.525247	+	0.850950i	$0.676027\pi$
$522$		0			0
$523$	2220.26	−	3845.61i	0.185631	−	0.321523i	−0.758158	−	0.652071i	$-0.773900\pi$
$523$	2220.26	−	3845.61i	0.185631	−	0.321523i	0.943789	+	0.330548i	$0.107234\pi$
$524$		0			0
$525$	−18138.9	+	970.627i	−1.50790	+	0.0806888i
$526$		0			0
$527$	−3538.49	+	6128.84i	−0.292484	+	0.506597i
$528$		0			0
$529$	−264.500	−	458.127i	−0.0217391	−	0.0376533i
$530$		0			0
$531$	6901.21			0.564006
$532$		0			0
$533$	27689.1			2.25019
$534$		0			0
$535$	1005.84	+	1742.17i	0.0812831	+	0.140786i
$536$		0			0
$537$	9134.79	−	15821.9i	0.734069	−	1.27145i
$538$		0			0
$539$	−11059.3	+	1186.98i	−0.883782	+	0.0948554i
$540$		0			0
$541$	−8249.48	+	14288.5i	−0.655588	+	1.13551i	0.326158	+	0.945315i	$0.394246\pi$
$541$	−8249.48	+	14288.5i	−0.655588	+	1.13551i	−0.981746	+	0.190196i	$0.939088\pi$
$542$		0			0
$543$	−19128.8	−	33132.1i	−1.51178	−	2.61848i
$544$		0			0
$545$	1571.45			0.123511
$546$		0			0
$547$	20371.0			1.59233			0.796163	−	0.605082i	$-0.206860\pi$
$547$	20371.0			1.59233			0.796163	+	0.605082i	$0.206860\pi$
$548$		0			0
$549$	−10434.3	−	18072.8i	−0.811161	−	1.40497i
$550$		0			0
$551$	7633.75	−	13222.0i	0.590216	−	1.02228i
$552$		0			0
$553$	−6424.86	+	343.799i	−0.494056	+	0.0264373i
$554$		0			0
$555$	−190.529	+	330.007i	−0.0145721	+	0.0252396i
$556$		0			0
$557$	−7467.14	−	12933.5i	−0.568030	−	0.983857i	−0.996761	−	0.0804248i	$-0.974372\pi$
$557$	−7467.14	−	12933.5i	−0.568030	−	0.983857i	0.428730	−	0.903432i	$-0.358961\pi$
$558$		0			0
$559$	−5287.16			−0.400041
$560$		0			0
$561$	17361.0			1.30656
$562$		0			0
$563$	1706.39	+	2955.56i	0.127737	+	0.221247i	0.922799	−	0.385281i	$-0.125895\pi$
$563$	1706.39	+	2955.56i	0.127737	+	0.221247i	−0.795062	+	0.606528i	$0.792562\pi$
$564$		0			0
$565$	604.972	−	1047.84i	0.0450467	−	0.0780231i
$566$		0			0
$567$	3424.44	−	6739.16i	0.253639	−	0.499150i
$568$		0			0
$569$	1033.63	−	1790.30i	0.0761546	−	0.131904i	−0.825433	−	0.564500i	$-0.809069\pi$
$569$	1033.63	−	1790.30i	0.0761546	−	0.131904i	0.901588	+	0.432596i	$0.142402\pi$
$570$		0			0
$571$	4997.92	+	8656.66i	0.366299	+	0.634448i	0.988984	−	0.148025i	$-0.0472915\pi$
$571$	4997.92	+	8656.66i	0.366299	+	0.634448i	−0.622685	+	0.782473i	$0.713958\pi$
$572$		0			0
$573$	−10723.9			−0.781846
$574$		0			0
$575$	2843.71			0.206245
$576$		0			0
$577$	−986.496	−	1708.66i	−0.0711757	−	0.123280i	0.828241	−	0.560372i	$-0.189342\pi$
$577$	−986.496	−	1708.66i	−0.0711757	−	0.123280i	−0.899417	+	0.437092i	$0.856008\pi$
$578$		0			0
$579$	3960.58	−	6859.93i	0.284277	−	0.492381i
$580$		0			0
$581$	6275.84	+	9640.71i	0.448134	+	0.688406i
$582$		0			0
$583$	10017.6	−	17351.0i	0.711640	−	1.23260i
$584$		0			0
$585$	−1161.67	−	2012.08i	−0.0821014	−	0.142204i
$586$		0			0
$587$	−20139.7			−1.41611			−0.708053	−	0.706159i	$-0.750426\pi$
$587$	−20139.7			−1.41611			−0.708053	+	0.706159i	$0.750426\pi$
$588$		0			0
$589$	9987.76			0.698707
$590$		0			0
$591$	6644.37	+	11508.4i	0.462458	+	0.801001i
$592$		0			0
$593$	−8041.42	+	13928.1i	−0.556866	+	0.964520i	0.440890	+	0.897561i	$0.354663\pi$
$593$	−8041.42	+	13928.1i	−0.556866	+	0.964520i	−0.997756	+	0.0669589i	$0.978670\pi$
$594$		0			0
$595$	795.351	+	1221.79i	0.0548004	+	0.0841823i
$596$		0			0
$597$	19427.1	−	33648.8i	1.33182	−	2.30679i
$598$		0			0
$599$	−8738.83	−	15136.1i	−0.596092	−	1.03246i	−0.993392	−	0.114772i	$-0.963386\pi$
$599$	−8738.83	−	15136.1i	−0.596092	−	1.03246i	0.397300	−	0.917689i	$-0.369947\pi$
$600$		0			0
$601$	−28447.6			−1.93078			−0.965392	−	0.260804i	$-0.916012\pi$
$601$	−28447.6			−1.93078			−0.965392	+	0.260804i	$0.916012\pi$
$602$		0			0
$603$	−20599.3			−1.39116
$604$		0			0
$605$	162.955	+	282.247i	0.0109505	+	0.0189669i
$606$		0			0
$607$	984.455	−	1705.13i	0.0658283	−	0.114018i	−0.831233	−	0.555924i	$-0.812364\pi$
$607$	984.455	−	1705.13i	0.0658283	−	0.114018i	0.897061	+	0.441906i	$0.145698\pi$
$608$		0			0
$609$	−10668.5	+	20995.2i	−0.709869	+	1.39699i
$610$		0			0
$611$	3795.31	−	6573.67i	0.251296	−	0.435258i
$612$		0			0
$613$	10914.5	+	18904.5i	0.719141	+	1.24559i	0.961341	+	0.275362i	$0.0887978\pi$
$613$	10914.5	+	18904.5i	0.719141	+	1.24559i	−0.242200	+	0.970226i	$0.577869\pi$
$614$		0			0
$615$	4621.26			0.303003
$616$		0			0
$617$	−13971.9			−0.911652			−0.455826	−	0.890069i	$-0.650656\pi$
$617$	−13971.9			−0.911652			−0.455826	+	0.890069i	$0.650656\pi$
$618$		0			0
$619$	−9088.21	−	15741.2i	−0.590123	−	1.02212i	−0.994215	−	0.107405i	$-0.965746\pi$
$619$	−9088.21	−	15741.2i	−0.590123	−	1.02212i	0.404093	−	0.914718i	$-0.367587\pi$
$620$		0			0
$621$	814.622	−	1410.97i	0.0526403	−	0.0911757i
$622$		0			0
$623$	−24022.8	+	1285.48i	−1.54487	+	0.0826672i
$624$		0			0
$625$	−7558.34	+	13091.4i	−0.483734	+	0.837851i
$626$		0			0
$627$	−12250.8	−	21219.0i	−0.780304	−	1.35153i
$628$		0			0
$629$	−2779.38			−0.176186
$630$		0			0
$631$	−21951.0			−1.38488			−0.692438	−	0.721477i	$-0.743464\pi$
$631$	−21951.0			−1.38488			−0.692438	+	0.721477i	$0.743464\pi$
$632$		0			0
$633$	−13605.0	−	23564.5i	−0.854265	−	1.47963i
$634$		0			0
$635$	401.709	−	695.781i	0.0251045	−	0.0434822i
$636$		0			0
$637$	−7696.17	+	17388.7i	−0.478702	+	1.08158i
$638$		0			0
$639$	8239.77	−	14271.7i	0.510110	−	0.883536i
$640$		0			0
$641$	−2258.92	−	3912.56i	−0.139192	−	0.241087i	0.787999	−	0.615676i	$-0.211117\pi$
$641$	−2258.92	−	3912.56i	−0.139192	−	0.241087i	−0.927191	+	0.374589i	$0.877784\pi$
$642$		0			0
$643$	−17209.8			−1.05550			−0.527750	−	0.849400i	$-0.676964\pi$
$643$	−17209.8			−1.05550			−0.527750	+	0.849400i	$0.676964\pi$
$644$		0			0
$645$	−882.416			−0.0538684
$646$		0			0
$647$	−4747.63	−	8223.14i	−0.288483	−	0.499668i	0.684965	−	0.728576i	$-0.259818\pi$
$647$	−4747.63	−	8223.14i	−0.288483	−	0.499668i	−0.973448	+	0.228908i	$0.926484\pi$
$648$		0			0
$649$	3114.33	−	5394.18i	0.188364	−	0.326256i
$650$		0			0
$651$	−15384.2	+	823.221i	−0.926198	+	0.0495616i
$652$		0			0
$653$	6660.21	−	11535.8i	0.399134	−	0.691320i	−0.594486	−	0.804106i	$-0.702644\pi$
$653$	6660.21	−	11535.8i	0.399134	−	0.691320i	0.993619	+	0.112787i	$0.0359776\pi$
$654$		0			0
$655$	1146.02	+	1984.97i	0.0683645	+	0.118411i
$656$		0			0
$657$	−4733.51			−0.281083
$658$		0			0
$659$	21226.1			1.25470			0.627352	−	0.778736i	$-0.284139\pi$
$659$	21226.1			1.25470			0.627352	+	0.778736i	$0.284139\pi$
$660$		0			0
$661$	1244.26	+	2155.13i	0.0732168	+	0.126815i	0.900309	−	0.435250i	$-0.143340\pi$
$661$	1244.26	+	2155.13i	0.0732168	+	0.126815i	−0.827093	+	0.562066i	$0.810007\pi$
$662$		0			0
$663$	14840.3	−	25704.1i	0.869305	−	1.50568i
$664$		0			0
$665$	932.061	−	1834.26i	0.0543515	−	0.106962i
$666$		0			0
$667$	1843.40	−	3192.86i	0.107012	−	0.185349i
$668$		0			0
$669$	9672.86	+	16753.9i	0.559005	+	0.968225i
$670$		0			0
$671$	−18835.0			−1.08363
$672$		0			0
$673$	4345.20			0.248879			0.124439	−	0.992227i	$-0.460287\pi$
$673$	4345.20			0.248879			0.124439	+	0.992227i	$0.460287\pi$
$674$		0			0
$675$	4379.11	+	7584.83i	0.249706	+	0.432504i
$676$		0			0
$677$	5941.27	−	10290.6i	0.337284	−	0.584193i	−0.646637	−	0.762798i	$-0.723825\pi$
$677$	5941.27	−	10290.6i	0.337284	−	0.584193i	0.983921	+	0.178605i	$0.0571584\pi$
$678$		0			0
$679$	1.74522	+	2.68095i	9.86384e−5	+	0.000151525i
$680$		0			0
$681$	8092.20	−	14016.1i	0.455351	−	0.788690i
$682$		0			0
$683$	−2357.98	−	4084.14i	−0.132102	−	0.228807i	0.792385	−	0.610022i	$-0.208839\pi$
$683$	−2357.98	−	4084.14i	−0.132102	−	0.228807i	−0.924487	+	0.381215i	$0.875506\pi$
$684$		0			0
$685$	−979.173			−0.0546164
$686$		0			0
$687$	47447.7			2.63500
$688$		0			0
$689$	−17126.2	−	29663.5i	−0.946961	−	1.64018i
$690$		0			0
$691$	−7478.04	+	12952.4i	−0.411691	+	0.713069i	−0.995075	−	0.0991273i	$-0.968395\pi$
$691$	−7478.04	+	12952.4i	−0.411691	+	0.713069i	0.583384	+	0.812196i	$0.301728\pi$
$692$		0			0
$693$	11772.4	+	18084.3i	0.645304	+	0.991292i
$694$		0			0
$695$	−0.361187	+	0.625595i	−1.97131e−5	+	3.41441e-5i
$696$		0			0
$697$	16853.3	+	29190.8i	0.915876	+	1.58634i
$698$		0			0
$699$	16029.9			0.867392
$700$		0			0
$701$	−11789.9			−0.635235			−0.317617	−	0.948219i	$-0.602883\pi$
$701$	−11789.9			−0.635235			−0.317617	+	0.948219i	$0.602883\pi$
$702$		0			0
$703$	1961.27	+	3397.03i	0.105222	+	0.182249i
$704$		0			0
$705$	633.430	−	1097.13i	0.0338388	−	0.0586105i
$706$		0			0
$707$	13064.7	−	25710.7i	0.694974	−	1.36768i
$708$		0			0
$709$	1737.81	−	3009.98i	0.0920522	−	0.159439i	−0.816322	−	0.577597i	$-0.803991\pi$
$709$	1737.81	−	3009.98i	0.0920522	−	0.159439i	0.908375	+	0.418158i	$0.137324\pi$
$710$		0			0
$711$	6241.08	+	10809.9i	0.329197	+	0.570185i
$712$		0			0
$713$	2411.85			0.126682
$714$		0			0
$715$	−2096.93			−0.109679
$716$		0			0
$717$	−1314.68	−	2277.09i	−0.0684765	−	0.118605i
$718$		0			0
$719$	−13094.8	+	22680.9i	−0.679213	+	1.17643i	0.296006	+	0.955186i	$0.404345\pi$
$719$	−13094.8	+	22680.9i	−0.679213	+	1.17643i	−0.975218	+	0.221245i	$0.928988\pi$
$720$		0			0
$721$	−17740.4	+	949.304i	−0.916349	+	0.0490346i
$722$		0			0
$723$	−6134.33	+	10625.0i	−0.315544	+	0.546538i
$724$		0			0
$725$	9909.44	+	17163.6i	0.507624	+	0.879230i
$726$		0			0
$727$	−986.540			−0.0503284			−0.0251642	−	0.999683i	$-0.508011\pi$
$727$	−986.540			−0.0503284			−0.0251642	+	0.999683i	$0.508011\pi$
$728$		0			0
$729$	−29837.4			−1.51590
$730$		0			0
$731$	−3218.10	−	5573.91i	−0.162826	−	0.282022i
$732$		0			0
$733$	10795.9	−	18699.0i	0.544003	−	0.942241i	−0.454666	−	0.890662i	$-0.650241\pi$
$733$	10795.9	−	18699.0i	0.544003	−	0.942241i	0.998669	−	0.0515788i	$-0.0164253\pi$
$734$		0			0
$735$	−1284.47	+	2902.14i	−0.0644606	+	0.145642i
$736$		0			0
$737$	−9295.90	+	16101.0i	−0.464612	+	0.804731i
$738$		0			0
$739$	−17824.9	−	30873.6i	−0.887280	−	1.53681i	−0.843078	−	0.537791i	$-0.819259\pi$
$739$	−17824.9	−	30873.6i	−0.887280	−	1.53681i	−0.0442013	−	0.999023i	$-0.514074\pi$
$740$		0			0
$741$	−41888.3			−2.07666
$742$		0			0
$743$	22629.2			1.11734			0.558670	−	0.829390i	$-0.311312\pi$
$743$	22629.2			1.11734			0.558670	+	0.829390i	$0.311312\pi$
$744$		0			0
$745$	1085.75	+	1880.57i	0.0533942	+	0.0924815i
$746$		0			0
$747$	11158.4	−	19327.0i	0.546540	−	0.946636i
$748$		0			0
$749$	−31896.6	+	1706.81i	−1.55604	+	0.0832651i
$750$		0			0
$751$	6559.42	−	11361.3i	0.318717	−	0.552034i	−0.661503	−	0.749942i	$-0.730081\pi$
$751$	6559.42	−	11361.3i	0.318717	−	0.552034i	0.980221	+	0.197908i	$0.0634146\pi$
$752$		0			0
$753$	16325.7	+	28276.9i	0.790094	+	1.36848i
$754$		0			0
$755$	−1636.79			−0.0788993
$756$		0			0
$757$	36572.2			1.75593			0.877966	−	0.478723i	$-0.158900\pi$
$757$	36572.2			1.75593			0.877966	+	0.478723i	$0.158900\pi$
$758$		0			0
$759$	−2958.33	−	5123.98i	−0.141476	−	0.245044i
$760$		0			0
$761$	−15903.8	+	27546.1i	−0.757570	+	1.31215i	0.186517	+	0.982452i	$0.440280\pi$
$761$	−15903.8	+	27546.1i	−0.757570	+	1.31215i	−0.944087	+	0.329698i	$0.893053\pi$
$762$		0			0
$763$	−11303.5	+	22244.9i	−0.536323	+	1.05546i
$764$		0			0
$765$	1414.13	−	2449.35i	0.0668342	−	0.115760i
$766$		0			0
$767$	−5324.30	−	9221.96i	−0.250651	−	0.434140i
$768$		0			0
$769$	4081.87			0.191412			0.0957062	−	0.995410i	$-0.469489\pi$
$769$	4081.87			0.191412			0.0957062	+	0.995410i	$0.469489\pi$
$770$		0			0
$771$	14114.8			0.659317
$772$		0			0
$773$	3994.71	+	6919.04i	0.185873	+	0.321941i	0.943870	−	0.330316i	$-0.107155\pi$
$773$	3994.71	+	6919.04i	0.185873	+	0.321941i	−0.757997	+	0.652258i	$0.773822\pi$
$774$		0			0
$775$	−6482.60	+	11228.2i	−0.300467	+	0.520424i
$776$		0			0
$777$	−3300.95	−	5070.81i	−0.152408	−	0.234124i
$778$		0			0
$779$	23785.2	−	41197.1i	1.09396	−	1.89479i
$780$		0			0
$781$	−7436.77	−	12880.9i	−0.340728	−	0.590158i
$782$		0			0
$783$	11354.8			0.518247
$784$		0			0
$785$	1902.95			0.0865212
$786$		0			0
$787$	12616.3	+	21852.1i	0.571440	+	0.989762i	0.996418	+	0.0845592i	$0.0269482\pi$
$787$	12616.3	+	21852.1i	0.571440	+	0.989762i	−0.424979	+	0.905203i	$0.639718\pi$
$788$		0			0
$789$	3384.74	−	5862.55i	0.152725	−	0.264527i
$790$		0			0
$791$	10481.2	+	16100.9i	0.471138	+	0.723745i
$792$		0			0
$793$	−16100.2	+	27886.4i	−0.720979	+	1.24877i
$794$		0			0
$795$	−2858.33	−	4950.77i	−0.127515	−	0.220862i
$796$		0			0
$797$	37222.9			1.65433			0.827166	−	0.561958i	$-0.189952\pi$
$797$	37222.9			1.65433			0.827166	+	0.561958i	$0.189952\pi$
$798$		0			0
$799$	9240.26			0.409132
$800$		0			0
$801$	23335.7	+	40418.6i	1.02937	+	1.78292i
$802$		0			0
$803$	−2136.11	+	3699.84i	−0.0938749	+	0.162596i
$804$		0			0
$805$	225.074	−	442.937i	0.00985444	−	0.0193931i
$806$		0			0
$807$	−13330.9	+	23089.7i	−0.581498	+	1.00718i
$808$		0			0
$809$	6854.20	+	11871.8i	0.297875	+	0.515935i	0.975650	−	0.219335i	$-0.0703888\pi$
$809$	6854.20	+	11871.8i	0.297875	+	0.515935i	−0.677775	+	0.735270i	$0.737055\pi$
$810$		0			0
$811$	28549.4			1.23614			0.618068	−	0.786125i	$-0.287916\pi$
$811$	28549.4			1.23614			0.618068	+	0.786125i	$0.287916\pi$
$812$		0			0
$813$	62288.4			2.68702
$814$		0			0
$815$	1697.36	+	2939.91i	0.0729519	+	0.126356i
$816$		0			0
$817$	−4541.71	+	7866.48i	−0.194485	+	0.336858i
$818$		0			0
$819$	36838.1	−	1971.24i	1.57171	−	0.0841033i
$820$		0			0
$821$	−9395.00	+	16272.6i	−0.399376	+	0.691740i	−0.993649	−	0.112524i	$-0.964107\pi$
$821$	−9395.00	+	16272.6i	−0.399376	+	0.691740i	0.594273	+	0.804263i	$0.297440\pi$
$822$		0			0
$823$	3476.88	+	6022.14i	0.147262	+	0.255065i	0.930215	−	0.367016i	$-0.119621\pi$
$823$	3476.88	+	6022.14i	0.147262	+	0.255065i	−0.782953	+	0.622081i	$0.786287\pi$
$824$		0			0
$825$	31805.8			1.34222
$826$		0			0
$827$	−22006.5			−0.925321			−0.462660	−	0.886536i	$-0.653105\pi$
$827$	−22006.5			−0.925321			−0.462660	+	0.886536i	$0.653105\pi$
$828$		0			0
$829$	17304.7	+	29972.7i	0.724991	+	1.25572i	0.958978	+	0.283482i	$0.0914897\pi$
$829$	17304.7	+	29972.7i	0.724991	+	1.25572i	−0.233986	+	0.972240i	$0.575177\pi$
$830$		0			0
$831$	−26747.9	+	46328.7i	−1.11658	+	1.93397i
$832$		0			0
$833$	−23016.2	+	2470.30i	−0.957338	+	0.102750i
$834$		0			0
$835$	−459.477	+	795.837i	−0.0190429	+	0.0329833i
$836$		0			0
$837$	3714.07	+	6432.96i	0.153378	+	0.265658i
$838$		0			0
$839$	−6120.79			−0.251863			−0.125932	−	0.992039i	$-0.540192\pi$
$839$	−6120.79			−0.251863			−0.125932	+	0.992039i	$0.540192\pi$
$840$		0			0
$841$	1305.68			0.0535357
$842$		0			0
$843$	−8141.71	−	14101.8i	−0.332640	−	0.576149i
$844$		0			0
$845$	−511.191	+	885.409i	−0.0208113	+	0.0360462i
$846$		0			0
$847$	−5167.51	+	276.517i	−0.209631	+	0.0112175i
$848$		0			0
$849$	33331.8	−	57732.3i	1.34740	−	2.33377i
$850$		0			0
$851$	473.609	+	820.314i	0.0190777	+	0.0330435i
$852$		0			0
$853$	−18360.2			−0.736977			−0.368489	−	0.929632i	$-0.620125\pi$
$853$	−18360.2			−0.736977			−0.368489	+	0.929632i	$0.620125\pi$
$854$		0			0
$855$	−3991.55			−0.159659
$856$		0			0
$857$	18004.7	+	31185.0i	0.717653	+	1.24301i	0.961927	+	0.273305i	$0.0881169\pi$
$857$	18004.7	+	31185.0i	0.717653	+	1.24301i	−0.244275	+	0.969706i	$0.578550\pi$
$858$		0			0
$859$	−1241.30	+	2149.99i	−0.0493045	+	0.0853980i	−0.889624	−	0.456693i	$-0.849034\pi$
$859$	−1241.30	+	2149.99i	−0.0493045	+	0.0853980i	0.840320	+	0.542091i	$0.182367\pi$
$860$		0			0
$861$	−33240.9	+	65416.7i	−1.31573	+	2.58931i
$862$		0			0
$863$	−4028.04	+	6976.77i	−0.158883	+	0.275194i	−0.934466	−	0.356052i	$-0.884123\pi$
$863$	−4028.04	+	6976.77i	−0.158883	+	0.275194i	0.775583	+	0.631245i	$0.217456\pi$
$864$		0			0
$865$	−1826.91	−	3164.31i	−0.0718115	−	0.124381i
$866$		0			0
$867$	−2843.02			−0.111366
$868$		0			0
$869$	11265.7			0.439774
$870$		0			0
$871$	15892.4	+	27526.4i	0.618247	+	1.07084i
$872$		0			0
$873$	3.10300	−	5.37456i	0.000120299	−	0.000208363i
$874$		0			0
$875$	2930.24	+	4501.33i	0.113212	+	0.173912i
$876$		0			0
$877$	−20912.4	+	36221.4i	−0.805202	+	1.39465i	0.110953	+	0.993826i	$0.464610\pi$
$877$	−20912.4	+	36221.4i	−0.805202	+	1.39465i	−0.916155	+	0.400825i	$0.868724\pi$
$878$		0			0
$879$	−30187.7	−	52286.6i	−1.15837	−	2.00635i
$880$		0			0
$881$	3653.15			0.139702			0.0698512	−	0.997557i	$-0.477748\pi$
$881$	3653.15			0.139702			0.0698512	+	0.997557i	$0.477748\pi$
$882$		0			0
$883$	24364.7			0.928582			0.464291	−	0.885683i	$-0.346309\pi$
$883$	24364.7			0.928582			0.464291	+	0.885683i	$0.346309\pi$
$884$		0			0
$885$	−888.615	−	1539.13i	−0.0337519	−	0.0584601i
$886$		0			0
$887$	−19361.8	+	33535.6i	−0.732927	+	1.26947i	0.222700	+	0.974887i	$0.428513\pi$
$887$	−19361.8	+	33535.6i	−0.732927	+	1.26947i	−0.955627	+	0.294580i	$0.904820\pi$
$888$		0			0
$889$	6959.69	+	10691.2i	0.262565	+	0.403343i
$890$		0			0
$891$	−6617.99	+	11462.7i	−0.248834	+	0.430993i
$892$		0			0
$893$	−6520.41	−	11293.7i	−0.244342	−	0.423212i
$894$		0			0
$895$	−2686.23			−0.100325
$896$		0			0
$897$	−10115.2			−0.376518
$898$		0			0
$899$	8404.53	+	14557.1i	0.311798	+	0.540051i
$900$		0			0
$901$	20848.1	−	36110.1i	0.770869	−	1.33518i
$902$		0			0
$903$	6347.25	−	12491.1i	0.233913	−	0.460331i
$904$		0			0
$905$	−2812.57	+	4871.52i	−0.103307	+	0.178933i
$906$		0			0
$907$	5387.02	+	9330.59i	0.197214	+	0.341584i	0.947624	−	0.319388i	$-0.103477\pi$
$907$	5387.02	+	9330.59i	0.197214	+	0.341584i	−0.750410	+	0.660972i	$0.770144\pi$
$908$		0			0
$909$	−55949.3			−2.04150
$910$		0			0
$911$	−14632.0			−0.532140			−0.266070	−	0.963954i	$-0.585725\pi$
$911$	−14632.0			−0.532140			−0.266070	+	0.963954i	$0.585725\pi$
$912$		0			0
$913$	−10071.0	−	17443.5i	−0.365062	−	0.632306i
$914$		0			0
$915$	−2687.10	+	4654.19i	−0.0970849	+	0.168156i
$916$		0			0
$917$	−36341.8	+	1944.68i	−1.30874	+	0.0700314i
$918$		0			0
$919$	−13396.6	+	23203.6i	−0.480864	+	0.832881i	−0.999759	−	0.0219571i	$-0.993010\pi$
$919$	−13396.6	+	23203.6i	−0.480864	+	0.832881i	0.518895	+	0.854838i	$0.326344\pi$
$920$		0			0
$921$	2879.45	+	4987.35i	0.103019	+	0.178435i
$922$		0			0
$923$	−25428.0			−0.906796
$924$		0			0
$925$	−5091.89			−0.180995
$926$		0			0
$927$	17233.0	+	29848.4i	0.610577	+	1.05755i
$928$		0			0
$929$	14489.6	−	25096.7i	0.511721	−	0.886326i	−0.488187	−	0.872739i	$-0.662342\pi$
$929$	14489.6	−	25096.7i	0.511721	−	0.886326i	0.999908	−	0.0135873i	$-0.00432510\pi$
$930$		0			0
$931$	19260.7	+	26387.8i	0.678026	+	0.928919i
$932$		0			0
$933$	−11290.9	+	19556.4i	−0.396192	+	0.686225i
$934$		0			0
$935$	−1276.32	−	2210.65i	−0.0446419	−	0.0773220i
$936$		0			0
$937$	24910.9			0.868522			0.434261	−	0.900787i	$-0.357010\pi$
$937$	24910.9			0.868522			0.434261	+	0.900787i	$0.357010\pi$
$938$		0			0
$939$	−50882.9			−1.76837
$940$		0			0
$941$	−22827.5	−	39538.5i	−0.790814	−	1.36973i	−0.925463	−	0.378837i	$-0.876324\pi$
$941$	−22827.5	−	39538.5i	−0.790814	−	1.36973i	0.134649	−	0.990893i	$-0.457009\pi$
$942$		0			0
$943$	5743.65	−	9948.29i	0.198345	−	0.343543i
$944$		0			0
$945$	1528.01	−	81.7652i	0.0525992	−	0.00281463i
$946$		0			0
$947$	−17596.2	+	30477.5i	−0.603800	+	1.04581i	0.388440	+	0.921474i	$0.373014\pi$
$947$	−17596.2	+	30477.5i	−0.603800	+	1.04581i	−0.992240	+	0.124338i	$0.960319\pi$
$948$		0			0
$949$	3651.91	+	6325.30i	0.124917	+	0.216362i
$950$		0			0
$951$	−37523.9			−1.27949
$952$		0			0
$953$	54.1573			0.00184085			0.000920423	−	1.00000i	$-0.499707\pi$
$953$	54.1573			0.00184085			0.000920423		1.00000i	$0.499707\pi$
$954$		0			0
$955$	788.386	+	1365.52i	0.0267137	+	0.0462695i
$956$		0			0
$957$	20617.7	−	35710.9i	0.696422	−	1.20624i
$958$		0			0
$959$	7043.22	−	13860.8i	0.237161	−	0.466723i
$960$		0			0
$961$	9397.39	−	16276.8i	0.315444	−	0.546365i
$962$		0			0
$963$	30984.2	+	53666.2i	1.03681	+	1.79581i
$964$		0			0
$965$	−1164.67			−0.0388520
$966$		0			0
$967$	−28374.1			−0.943588			−0.471794	−	0.881709i	$-0.656393\pi$
$967$	−28374.1			−0.943588			−0.471794	+	0.881709i	$0.656393\pi$
$968$		0			0
$969$	−25495.9	−	44160.1i	−0.845248	−	1.46401i
$970$		0			0
$971$	−7894.22	+	13673.2i	−0.260904	+	0.451899i	−0.966482	−	0.256733i	$-0.917354\pi$
$971$	−7894.22	+	13673.2i	−0.260904	+	0.451899i	0.705578	+	0.708632i	$0.250687\pi$
$972$		0			0
$973$	−6.25763	−	9.61275i	−0.000206177	−	0.000316722i
$974$		0			0
$975$	27187.8	−	47090.6i	0.893032	−	1.54678i
$976$		0			0
$977$	−25176.9	−	43607.7i	−0.824444	−	1.42798i	−0.902344	−	0.431018i	$-0.858155\pi$
$977$	−25176.9	−	43607.7i	−0.824444	−	1.42798i	0.0778995	−	0.996961i	$-0.475179\pi$
$978$		0			0
$979$	42123.0			1.37514
$980$		0			0
$981$	48407.3			1.57546
$982$		0			0
$983$	−19283.8	−	33400.6i	−0.625695	−	1.08374i	−0.988406	−	0.151834i	$-0.951482\pi$
$983$	−19283.8	−	33400.6i	−0.625695	−	1.08374i	0.362711	−	0.931902i	$-0.381851\pi$
$984$		0			0
$985$	976.943	−	1692.11i	0.0316020	−	0.0547363i
$986$		0			0
$987$	10974.3	+	16858.3i	0.353916	+	0.543673i
$988$		0			0
$989$	−1096.73	+	1899.60i	−0.0352620	+	0.0610755i
$990$		0			0
$991$	−7663.22	−	13273.1i	−0.245641	−	0.425463i	0.716671	−	0.697412i	$-0.245665\pi$
$991$	−7663.22	−	13273.1i	−0.245641	−	0.425463i	−0.962312	+	0.271949i	$0.912332\pi$
$992$		0			0
$993$	−16393.1			−0.523888
$994$		0			0
$995$	−5712.87			−0.182020
$996$		0			0
$997$	25002.8	+	43306.1i	0.794229	+	1.37565i	0.923328	+	0.384013i	$0.125458\pi$
$997$	25002.8	+	43306.1i	0.794229	+	1.37565i	−0.129099	+	0.991632i	$0.541208\pi$
$998$		0			0
$999$	−1458.65	+	2526.45i	−0.0461957	+	0.0800133i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.4.i.b.93.3	✓	44
7.4	even	3	inner	644.4.i.b.277.3	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.4.i.b.93.3	✓	44	1.1	even	1	trivial
644.4.i.b.277.3	yes	44	7.4	even	3	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	644.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.96641 - 6.87002i) q^{3} +(-0.583194 + 1.01012i) q^{5} +(-10.1039 - 15.5213i) q^{7} +(-17.9648 + 31.1159i) q^{9} +O(q^{10})\)	\(q+(-3.96641 - 6.87002i) q^{3} +(-0.583194 + 1.01012i) q^{5} +(-10.1039 - 15.5213i) q^{7} +(-17.9648 + 31.1159i) q^{9} +(16.2140 + 28.0836i) q^{11} +55.4395 q^{13} +9.25274 q^{15} +(33.7439 + 58.4462i) q^{17} +(47.6230 - 82.4854i) q^{19} +(-66.5553 + 130.978i) q^{21} +(11.5000 - 19.9186i) q^{23} +(61.8198 + 107.075i) q^{25} +70.8367 q^{27} +160.296 q^{29} +(52.4314 + 90.8139i) q^{31} +(128.623 - 222.782i) q^{33} +(21.5709 - 1.15428i) q^{35} +(-20.5917 + 35.6658i) q^{37} +(-219.896 - 380.870i) q^{39} +499.448 q^{41} -95.3681 q^{43} +(-20.9539 - 36.2932i) q^{45} +(68.4586 - 118.574i) q^{47} +(-138.821 + 313.652i) q^{49} +(267.684 - 463.643i) q^{51} +(-308.917 - 535.060i) q^{53} -37.8237 q^{55} -755.568 q^{57} +(-96.0380 - 166.343i) q^{59} +(-290.411 + 503.007i) q^{61} +(664.474 - 35.5565i) q^{63} +(-32.3320 + 56.0006i) q^{65} +(286.662 + 496.513i) q^{67} -182.455 q^{69} -458.662 q^{71} +(65.8721 + 114.094i) q^{73} +(490.405 - 849.406i) q^{75} +(272.067 - 535.417i) q^{77} +(173.703 - 300.863i) q^{79} +(204.082 + 353.481i) q^{81} -621.128 q^{83} -78.7170 q^{85} +(-635.798 - 1101.23i) q^{87} +(649.483 - 1124.94i) q^{89} +(-560.157 - 860.493i) q^{91} +(415.929 - 720.410i) q^{93} +(55.5468 + 96.2099i) q^{95} -0.172727 q^{97} -1165.13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9}+O(q^{10}) \) 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9	\( 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9} + 28 q^{11} - 152 q^{13} + 208 q^{15} - 52 q^{17} + 38 q^{19} - 10 q^{21} + 506 q^{23} - 516 q^{25} - 876 q^{27} - 100 q^{29} + 230 q^{31} + 424 q^{33} + 98 q^{35} + 18 q^{37} - 350 q^{39} + 784 q^{41} - 336 q^{43} + 1156 q^{45} + 452 q^{47} + 546 q^{49} - 498 q^{51} - 508 q^{53} - 3084 q^{55} - 1916 q^{57} + 508 q^{59} + 1386 q^{61} + 1290 q^{63} + 360 q^{65} - 1896 q^{67} + 552 q^{69} - 3352 q^{71} + 990 q^{73} + 3328 q^{75} + 1328 q^{77} + 524 q^{79} - 4486 q^{81} - 1120 q^{83} - 5296 q^{85} + 3700 q^{87} + 1216 q^{89} + 1438 q^{91} + 366 q^{93} + 90 q^{95} + 716 q^{97} + 5716 q^{99}+O(q^{100}) \) 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9 + 28 * q^11 - 152 * q^13 + 208 * q^15 - 52 * q^17 + 38 * q^19 - 10 * q^21 + 506 * q^23 - 516 * q^25 - 876 * q^27 - 100 * q^29 + 230 * q^31 + 424 * q^33 + 98 * q^35 + 18 * q^37 - 350 * q^39 + 784 * q^41 - 336 * q^43 + 1156 * q^45 + 452 * q^47 + 546 * q^49 - 498 * q^51 - 508 * q^53 - 3084 * q^55 - 1916 * q^57 + 508 * q^59 + 1386 * q^61 + 1290 * q^63 + 360 * q^65 - 1896 * q^67 + 552 * q^69 - 3352 * q^71 + 990 * q^73 + 3328 * q^75 + 1328 * q^77 + 524 * q^79 - 4486 * q^81 - 1120 * q^83 - 5296 * q^85 + 3700 * q^87 + 1216 * q^89 + 1438 * q^91 + 366 * q^93 + 90 * q^95 + 716 * q^97 + 5716 * q^99

Introduction

L-functions

Modular forms

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Database

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