LMFDB - Embedded newform 644.2.bc.a.425.6

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			425.6
Character	$\chi$	$=$	644.425
Dual form			644.2.bc.a.297.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.548786 - 1.37080i) q^{3} +(0.0440940 - 0.181758i) q^{5} +(1.60642 - 2.10224i) q^{7} +(0.593270 - 0.565681i) q^{9} +O(q^{10})$	\(q+(-0.548786 - 1.37080i) q^{3} +(0.0440940 - 0.181758i) q^{5} +(1.60642 - 2.10224i) q^{7} +(0.593270 - 0.565681i) q^{9} +(-5.75170 - 0.273987i) q^{11} +(-0.543947 - 0.471333i) q^{13} +(-0.273352 + 0.0393021i) q^{15} +(2.18446 - 3.06764i) q^{17} +(-0.00719054 - 0.0100977i) q^{19} +(-3.76334 - 1.04841i) q^{21} +(-0.696512 + 4.74498i) q^{23} +(4.41309 + 2.27510i) q^{25} +(-5.13043 - 2.34299i) q^{27} +(-3.60596 - 7.89596i) q^{29} +(-1.42832 - 1.81626i) q^{31} +(2.78087 + 8.03481i) q^{33} +(-0.311265 - 0.384676i) q^{35} +(1.09032 + 1.14349i) q^{37} +(-0.347593 + 1.00431i) q^{39} +(-1.29661 - 4.41586i) q^{41} +(-5.05078 - 0.726193i) q^{43} +(-0.0766574 - 0.132775i) q^{45} +(-4.15451 - 2.39861i) q^{47} +(-1.83882 - 6.75416i) q^{49} +(-5.40393 - 1.31098i) q^{51} +(-9.92446 - 3.43489i) q^{53} +(-0.303415 + 1.03334i) q^{55} +(-0.00989589 + 0.0153983i) q^{57} +(0.0414137 - 0.214875i) q^{59} +(8.68512 + 3.47700i) q^{61} +(-0.236157 - 2.15592i) q^{63} +(-0.109653 + 0.0780837i) q^{65} +(2.85550 - 5.53889i) q^{67} +(6.88667 - 1.64920i) q^{69} +(0.637435 - 0.409655i) q^{71} +(1.16679 + 12.2192i) q^{73} +(0.696876 - 7.29801i) q^{75} +(-9.81565 + 11.6513i) q^{77} +(-0.308341 + 0.106718i) q^{79} +(-0.279250 + 5.86219i) q^{81} +(14.8144 + 4.34991i) q^{83} +(-0.461247 - 0.532307i) q^{85} +(-8.84490 + 9.27626i) q^{87} +(10.2698 + 8.07627i) q^{89} +(-1.86466 + 0.386348i) q^{91} +(-1.70589 + 2.95469i) q^{93} +(-0.00215240 + 0.000861690i) q^{95} +(11.4577 - 3.36428i) q^{97} +(-3.56730 + 3.09108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{22}\right)$	$1$

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
$3$	−0.548786	−	1.37080i	−0.316842	−	0.791433i	−0.998228	−	0.0595086i	$-0.981047\pi$
$3$	−0.548786	−	1.37080i	−0.316842	−	0.791433i	0.681386	−	0.731924i	$-0.261378\pi$
$4$		0			0
$5$	0.0440940	−	0.181758i	0.0197194	−	0.0812846i	−0.961102	−	0.276195i	$-0.910926\pi$
$5$	0.0440940	−	0.181758i	0.0197194	−	0.0812846i	0.980821	+	0.194910i	$0.0624416\pi$
$6$		0			0
$7$	1.60642	−	2.10224i	0.607170	−	0.794572i
$7$	1.60642	−	2.10224i	0.607170	−	0.794572i
$8$		0			0
$9$	0.593270	−	0.565681i	0.197757	−	0.188560i
$10$		0			0
$11$	−5.75170	−	0.273987i	−1.73420	−	0.0826103i	−0.843482	−	0.537158i	$-0.819498\pi$
$11$	−5.75170	−	0.273987i	−1.73420	−	0.0826103i	−0.890722	+	0.454548i	$0.849801\pi$
$12$		0			0
$13$	−0.543947	−	0.471333i	−0.150864	−	0.130724i	0.576159	−	0.817338i	$-0.304551\pi$
$13$	−0.543947	−	0.471333i	−0.150864	−	0.130724i	−0.727023	+	0.686614i	$0.759096\pi$
$14$		0			0
$15$	−0.273352	+	0.0393021i	−0.0705793	+	0.0101478i
$16$		0			0
$17$	2.18446	−	3.06764i	0.529809	−	0.744013i	−0.459765	−	0.888041i	$-0.652066\pi$
$17$	2.18446	−	3.06764i	0.529809	−	0.744013i	0.989574	+	0.144028i	$0.0460056\pi$
$18$		0			0
$19$	−0.00719054	−	0.0100977i	−0.00164962	−	0.00231657i	0.813750	−	0.581215i	$-0.197422\pi$
$19$	−0.00719054	−	0.0100977i	−0.00164962	−	0.00231657i	−0.815400	+	0.578898i	$0.803483\pi$
$20$		0			0
$21$	−3.76334	−	1.04841i	−0.821227	−	0.228781i
$22$		0			0
$23$	−0.696512	+	4.74498i	−0.145233	+	0.989398i
$23$	−0.696512	+	4.74498i	−0.145233	+	0.989398i
$24$		0			0
$25$	4.41309	+	2.27510i	0.882617	+	0.455021i
$26$		0			0
$27$	−5.13043	−	2.34299i	−0.987351	−	0.450908i
$28$		0			0
$29$	−3.60596	−	7.89596i	−0.669611	−	1.46624i	−0.873288	−	0.487205i	$-0.838017\pi$
$29$	−3.60596	−	7.89596i	−0.669611	−	1.46624i	0.203677	−	0.979038i	$-0.434711\pi$
$30$		0			0
$31$	−1.42832	−	1.81626i	−0.256535	−	0.326210i	0.640678	−	0.767810i	$-0.278654\pi$
$31$	−1.42832	−	1.81626i	−0.256535	−	0.326210i	−0.897212	+	0.441600i	$0.854411\pi$
$32$		0			0
$33$	2.78087	+	8.03481i	0.484088	+	1.39868i
$34$		0			0
$35$	−0.311265	−	0.384676i	−0.0526134	−	0.0650221i
$36$		0			0
$37$	1.09032	+	1.14349i	0.179247	+	0.187989i	0.807228	−	0.590240i	$-0.200967\pi$
$37$	1.09032	+	1.14349i	0.179247	+	0.187989i	−0.627981	+	0.778229i	$0.716118\pi$
$38$		0			0
$39$	−0.347593	+	1.00431i	−0.0556595	+	0.160818i
$40$		0			0
$41$	−1.29661	−	4.41586i	−0.202497	−	0.689642i	−0.996640	−	0.0819102i	$-0.973898\pi$
$41$	−1.29661	−	4.41586i	−0.202497	−	0.689642i	0.794143	−	0.607731i	$-0.207920\pi$
$42$		0			0
$43$	−5.05078	−	0.726193i	−0.770237	−	0.110743i	−0.254017	−	0.967200i	$-0.581752\pi$
$43$	−5.05078	−	0.726193i	−0.770237	−	0.110743i	−0.516219	+	0.856456i	$0.672661\pi$
$44$		0			0
$45$	−0.0766574	−	0.132775i	−0.0114274	−	0.0197929i
$46$		0			0
$47$	−4.15451	−	2.39861i	−0.605998	−	0.349873i	0.165400	−	0.986227i	$-0.447109\pi$
$47$	−4.15451	−	2.39861i	−0.605998	−	0.349873i	−0.771397	+	0.636354i	$0.780442\pi$
$48$		0			0
$49$	−1.83882	−	6.75416i	−0.262688	−	0.964881i
$50$		0			0
$51$	−5.40393	−	1.31098i	−0.756702	−	0.183574i
$52$		0			0
$53$	−9.92446	−	3.43489i	−1.36323	−	0.471818i	−0.455074	−	0.890453i	$-0.650387\pi$
$53$	−9.92446	−	3.43489i	−1.36323	−	0.471818i	−0.908154	+	0.418635i	$0.862509\pi$
$54$		0			0
$55$	−0.303415	+	1.03334i	−0.0409125	+	0.139335i
$56$		0			0
$57$	−0.00989589	+	0.0153983i	−0.00131074	+	0.00203955i
$58$		0			0
$59$	0.0414137	−	0.214875i	0.00539160	−	0.0279743i	−0.979133	−	0.203219i	$-0.934860\pi$
$59$	0.0414137	−	0.214875i	0.00539160	−	0.0279743i	0.984525	+	0.175245i	$0.0560717\pi$
$60$		0			0
$61$	8.68512	+	3.47700i	1.11202	+	0.445184i	0.853642	−	0.520861i	$-0.174389\pi$
$61$	8.68512	+	3.47700i	1.11202	+	0.445184i	0.258374	+	0.966045i	$0.416813\pi$
$62$		0			0
$63$	−0.236157	−	2.15592i	−0.0297529	−	0.271620i
$64$		0			0
$65$	−0.109653	+	0.0780837i	−0.0136008	+	0.00968509i
$66$		0			0
$67$	2.85550	−	5.53889i	0.348854	−	0.676683i	−0.647493	−	0.762071i	$-0.724183\pi$
$67$	2.85550	−	5.53889i	0.348854	−	0.676683i	0.996348	+	0.0853879i	$0.0272130\pi$
$68$		0			0
$69$	6.88667	−	1.64920i	0.829058	−	0.198541i
$70$		0			0
$71$	0.637435	−	0.409655i	0.0756496	−	0.0486171i	−0.502269	−	0.864711i	$-0.667501\pi$
$71$	0.637435	−	0.409655i	0.0756496	−	0.0486171i	0.577919	+	0.816094i	$0.303865\pi$
$72$		0			0
$73$	1.16679	+	12.2192i	0.136563	+	1.43015i	0.760837	+	0.648943i	$0.224789\pi$
$73$	1.16679	+	12.2192i	0.136563	+	1.43015i	−0.624274	+	0.781205i	$0.714605\pi$
$74$		0			0
$75$	0.696876	−	7.29801i	0.0804683	−	0.842702i
$76$		0			0
$77$	−9.81565	+	11.6513i	−1.11860	+	1.32779i
$78$		0			0
$79$	−0.308341	+	0.106718i	−0.0346910	+	0.0120067i	−0.344358	−	0.938838i	$-0.611904\pi$
$79$	−0.308341	+	0.106718i	−0.0346910	+	0.0120067i	0.309667	+	0.950845i	$0.399782\pi$
$80$		0			0
$81$	−0.279250	+	5.86219i	−0.0310278	+	0.651354i
$82$		0			0
$83$	14.8144	+	4.34991i	1.62609	+	0.477464i	0.962647	−	0.270759i	$-0.0872746\pi$
$83$	14.8144	+	4.34991i	1.62609	+	0.477464i	0.663447	+	0.748223i	$0.269093\pi$
$84$		0			0
$85$	−0.461247	−	0.532307i	−0.0500292	−	0.0577368i
$86$		0			0
$87$	−8.84490	+	9.27626i	−0.948272	+	0.994519i
$88$		0			0
$89$	10.2698	+	8.07627i	1.08860	+	0.856083i	0.990282	−	0.139072i	$-0.0444120\pi$
$89$	10.2698	+	8.07627i	1.08860	+	0.856083i	0.0983158	+	0.995155i	$0.468654\pi$
$90$		0			0
$91$	−1.86466	+	0.386348i	−0.195470	+	0.0405002i
$92$		0			0
$93$	−1.70589	+	2.95469i	−0.176893	+	0.306387i
$94$		0			0
$95$	−0.00215240		0.000861690i	−0.000220831		8.84075e-5i
$96$		0			0
$97$	11.4577	−	3.36428i	1.16335	−	0.341591i	0.357618	−	0.933868i	$-0.383589\pi$
$97$	11.4577	−	3.36428i	1.16335	−	0.341591i	0.805735	+	0.592277i	$0.201771\pi$
$98$		0			0
$99$	−3.56730	+	3.09108i	−0.358527	+	0.310666i
$100$		0			0
$101$	17.9872	−	4.36365i	1.78980	−	0.434200i	0.802975	−	0.596013i	$-0.203249\pi$
$101$	17.9872	−	4.36365i	1.78980	−	0.434200i	0.986821	+	0.161813i	$0.0517342\pi$
$102$		0			0
$103$	4.67705	−	2.41119i	0.460844	−	0.237581i	−0.212139	−	0.977239i	$-0.568043\pi$
$103$	4.67705	−	2.41119i	0.460844	−	0.237581i	0.672983	+	0.739658i	$0.265013\pi$
$104$		0			0
$105$	−0.356497	+	0.637788i	−0.0347905	+	0.0622417i
$106$		0			0
$107$	2.71142	−	6.77279i	0.262123	−	0.654751i	−0.737669	−	0.675162i	$-0.764074\pi$
$107$	2.71142	−	6.77279i	0.262123	−	0.654751i	0.999792	+	0.0204119i	$0.00649775\pi$
$108$		0			0
$109$	2.26845	+	1.61535i	0.217278	+	0.154723i	0.683514	−	0.729938i	$-0.260451\pi$
$109$	2.26845	+	1.61535i	0.217278	+	0.154723i	−0.466236	+	0.884660i	$0.654390\pi$
$110$		0			0
$111$	0.969151	−	2.12214i	0.0919877	−	0.201425i
$112$		0			0
$113$	−3.86140	−	6.00845i	−0.363250	−	0.565227i	0.610737	−	0.791834i	$-0.290873\pi$
$113$	−3.86140	−	6.00845i	−0.363250	−	0.565227i	−0.973986	+	0.226606i	$0.927237\pi$
$114$		0			0
$115$	0.831726	+	0.335822i	0.0775589	+	0.0313155i
$116$		0			0
$117$	−0.589332	+	0.0280733i	−0.0544837	+	0.00259538i
$118$		0			0
$119$	−2.93976	−	9.52018i	−0.269487	−	0.872714i
$120$		0			0
$121$	22.0568	+	2.10617i	2.00517	+	0.191470i
$122$		0			0
$123$	−5.34171	+	4.20077i	−0.481646	+	0.378770i
$124$		0			0
$125$	1.22050	−	1.40853i	0.109165	−	0.125983i
$126$		0			0
$127$	−7.98602	−	5.13230i	−0.708645	−	0.455418i	0.136025	−	0.990705i	$-0.456567\pi$
$127$	−7.98602	−	5.13230i	−0.708645	−	0.455418i	−0.844670	+	0.535287i	$0.820203\pi$
$128$		0			0
$129$	1.77633	+	7.32215i	0.156397	+	0.644679i
$130$		0			0
$131$	0.309176	+	1.60416i	0.0270129	+	0.140156i	0.992931	−	0.118691i	$-0.0378697\pi$
$131$	0.309176	+	1.60416i	0.0270129	+	0.140156i	−0.965918	+	0.258847i	$0.916658\pi$
$132$		0			0
$133$	−0.0327788	−	0.00110493i	−0.00284229	−	9.58096e-5i
$134$		0			0
$135$	−0.652078	+	0.829184i	−0.0561219	+	0.0713648i
$136$		0			0
$137$	−12.8989	+	7.44716i	−1.10202	+	0.636253i	−0.936752	−	0.349995i	$-0.886183\pi$
$137$	−12.8989	+	7.44716i	−1.10202	+	0.636253i	−0.165272	+	0.986248i	$0.552850\pi$
$138$		0			0
$139$		−	17.8814i		−	1.51668i	−0.651857	−	0.758342i	$-0.726010\pi$
$139$		−	17.8814i		−	1.51668i	0.651857	−	0.758342i	$-0.273990\pi$
$140$		0			0
$141$	−1.00808	+	7.01134i	−0.0848955	+	0.590461i
$142$		0			0
$143$	2.99948	+	2.86000i	0.250829	+	0.239165i
$144$		0			0
$145$	−1.59415	+	0.307248i	−0.132387	+	0.0255156i
$146$		0			0
$147$	−8.24951	+	6.22725i	−0.680408	+	0.513615i
$148$		0			0
$149$	4.86306	+	9.43303i	0.398398	+	0.772784i	0.999655	−	0.0262718i	$-0.00836353\pi$
$149$	4.86306	+	9.43303i	0.398398	+	0.772784i	−0.601257	+	0.799056i	$0.705333\pi$
$150$		0			0
$151$	19.6535	+	3.78790i	1.59938	+	0.308255i	0.909510	−	0.415682i	$-0.136457\pi$
$151$	19.6535	+	3.78790i	1.59938	+	0.308255i	0.689867	+	0.723936i	$0.257669\pi$
$152$		0			0
$153$	−0.439336	−	3.05565i	−0.0355182	−	0.247034i
$154$		0			0
$155$	−0.393100	+	0.179523i	−0.0315746	+	0.0144196i
$156$		0			0
$157$	10.5565	−	1.00802i	0.842501	−	0.0804491i	0.335125	−	0.942174i	$-0.391222\pi$
$157$	10.5565	−	1.00802i	0.842501	−	0.0804491i	0.507376	+	0.861725i	$0.330616\pi$
$158$		0			0
$159$	0.737855	+	15.4895i	0.0585157	+	1.22840i
$160$		0			0
$161$	8.85620	+	9.08668i	0.697966	+	0.716131i
$162$		0			0
$163$	0.452314	+	9.49524i	0.0354280	+	0.743725i	0.944782	+	0.327701i	$0.106274\pi$
$163$	0.452314	+	9.49524i	0.0354280	+	0.743725i	−0.909354	+	0.416024i	$0.863423\pi$
$164$		0			0
$165$	1.58301	−	0.151159i	0.123237	−	0.0117677i
$166$		0			0
$167$	17.2190	−	7.86364i	1.33244	−	0.608506i	0.383380	−	0.923591i	$-0.374760\pi$
$167$	17.2190	−	7.86364i	1.33244	−	0.608506i	0.949064	+	0.315084i	$0.102033\pi$
$168$		0			0
$169$	−1.77637	−	12.3549i	−0.136644	−	0.950378i
$170$		0			0
$171$	−0.00997802	−	0.00192311i	−0.000763038	−	0.000147064i
$172$		0			0
$173$	−0.221020	−	0.428718i	−0.0168038	−	0.0325948i	0.880284	−	0.474447i	$-0.157352\pi$
$173$	−0.221020	−	0.428718i	−0.0168038	−	0.0325948i	−0.897088	+	0.441852i	$0.854322\pi$
$174$		0			0
$175$	11.8721	−	5.62259i	0.897446	−	0.425028i
$176$		0			0
$177$	−0.317278	+	0.0611503i	−0.0238481	+	0.00459634i
$178$		0			0
$179$	−0.676469	−	0.645012i	−0.0505617	−	0.0482105i	0.664377	−	0.747398i	$-0.268697\pi$
$179$	−0.676469	−	0.645012i	−0.0505617	−	0.0482105i	−0.714939	+	0.699187i	$0.753545\pi$
$180$		0			0
$181$	−3.31863	+	23.0816i	−0.246672	+	1.71564i	0.370518	+	0.928825i	$0.379180\pi$
$181$	−3.31863	+	23.0816i	−0.246672	+	1.71564i	−0.617190	+	0.786815i	$0.711729\pi$
$182$		0			0
$183$		−	13.8137i		−	1.02114i
$184$		0			0
$185$	0.255915	−	0.147753i	0.0188153	−	0.0108630i
$186$		0			0
$187$	−13.4049	+	17.0457i	−0.980260	+	1.24650i
$188$		0			0
$189$	−13.1672	+	7.02156i	−0.957769	+	0.510743i
$190$		0			0
$191$	2.24913	+	11.6696i	0.162742	+	0.844384i	0.967902	+	0.251327i	$0.0808669\pi$
$191$	2.24913	+	11.6696i	0.162742	+	0.844384i	−0.805161	+	0.593057i	$0.797921\pi$
$192$		0			0
$193$	−4.06858	−	16.7709i	−0.292863	−	1.20720i	−0.908066	−	0.418827i	$-0.862441\pi$
$193$	−4.06858	−	16.7709i	−0.292863	−	1.20720i	0.615203	−	0.788369i	$-0.289074\pi$
$194$		0			0
$195$	0.167214	+	0.107462i	0.0119744	+	0.00769549i
$196$		0			0
$197$	−2.85363	+	3.29327i	−0.203313	+	0.234636i	−0.848245	−	0.529605i	$-0.822340\pi$
$197$	−2.85363	+	3.29327i	−0.203313	+	0.234636i	0.644932	+	0.764240i	$0.276886\pi$
$198$		0			0
$199$	−12.2861	+	9.66191i	−0.870939	+	0.684914i	−0.950099	−	0.311948i	$-0.899019\pi$
$199$	−12.2861	+	9.66191i	−0.870939	+	0.684914i	0.0791599	+	0.996862i	$0.474776\pi$
$200$		0			0
$201$	−9.15978	−	0.874653i	−0.646081	−	0.0616933i
$202$		0			0
$203$	−22.3919	−	5.10364i	−1.57160	−	0.358205i
$204$		0			0
$205$	−0.859790	+	0.0409569i	−0.0600504	+	0.00286055i
$206$		0			0
$207$	2.27093	+	3.20906i	0.157841	+	0.223045i
$208$		0			0
$209$	0.0385912	+	0.0600491i	0.00266941	+	0.00415369i
$210$		0			0
$211$	−3.15191	+	6.90171i	−0.216986	+	0.475134i	−0.986555	−	0.163431i	$-0.947744\pi$
$211$	−3.15191	+	6.90171i	−0.216986	+	0.475134i	0.769569	+	0.638564i	$0.220471\pi$
$212$		0			0
$213$	−0.911372	−	0.648985i	−0.0624462	−	0.0444677i
$214$		0			0
$215$	−0.354700	+	0.885998i	−0.0241904	+	0.0604246i
$216$		0			0
$217$	−6.11271	+	0.0849966i	−0.414958	+	0.00576994i
$218$		0			0
$219$	16.1098	−	8.30517i	1.08860	−	0.561211i
$220$		0			0
$221$	−2.63411	+	0.639028i	−0.177189	+	0.0429857i
$222$		0			0
$223$	18.3896	−	15.9347i	1.23146	−	1.06706i	0.236011	−	0.971750i	$-0.424160\pi$
$223$	18.3896	−	15.9347i	1.23146	−	1.06706i	0.995447	−	0.0953139i	$-0.0303855\pi$
$224$		0			0
$225$	3.90513	−	1.14665i	0.260342	−	0.0764434i
$226$		0			0
$227$	−4.47738	+	1.79247i	−0.297174	+	0.118970i	−0.515458	−	0.856915i	$-0.672378\pi$
$227$	−4.47738	+	1.79247i	−0.297174	+	0.118970i	0.218284	+	0.975885i	$0.429954\pi$
$228$		0			0
$229$	−9.12980	+	15.8133i	−0.603314	+	1.04497i	0.389001	+	0.921237i	$0.372820\pi$
$229$	−9.12980	+	15.8133i	−0.603314	+	1.04497i	−0.992315	+	0.123734i	$0.960513\pi$
$230$		0			0
$231$	21.3583	+	7.06123i	1.40528	+	0.464595i
$232$		0			0
$233$	−6.67188	−	5.24683i	−0.437090	−	0.343731i	0.375242	−	0.926927i	$-0.377560\pi$
$233$	−6.67188	−	5.24683i	−0.437090	−	0.343731i	−0.812332	+	0.583196i	$0.801802\pi$
$234$		0			0
$235$	−0.619155	+	0.649351i	−0.0403892	+	0.0423590i
$236$		0			0
$237$	0.315502	+	0.364109i	0.0204941	+	0.0236514i
$238$		0			0
$239$	−9.65271	−	2.83429i	−0.624382	−	0.183335i	−0.0457885	−	0.998951i	$-0.514580\pi$
$239$	−9.65271	−	2.83429i	−0.624382	−	0.183335i	−0.578594	+	0.815616i	$0.696398\pi$
$240$		0			0
$241$	0.980649	−	20.5863i	0.0631691	−	1.32608i	−0.715484	−	0.698629i	$-0.753794\pi$
$241$	0.980649	−	20.5863i	0.0631691	−	1.32608i	0.778653	−	0.627454i	$-0.215903\pi$
$242$		0			0
$243$	−7.80059	+	2.69981i	−0.500408	+	0.173193i
$244$		0			0
$245$	−1.30870	+	0.0364018i	−0.0836100	+	0.00232563i
$246$		0			0
$247$	−0.000848105		0.00888176i	−5.39636e−5		0.000565133i
$248$		0			0
$249$	−2.16709	−	22.6948i	−0.137334	−	1.43823i
$250$		0			0
$251$	−7.23184	+	4.64762i	−0.456470	+	0.293355i	−0.748598	−	0.663024i	$-0.769273\pi$
$251$	−7.23184	+	4.64762i	−0.456470	+	0.293355i	0.292129	+	0.956379i	$0.405636\pi$
$252$		0			0
$253$	5.30620	−	27.1009i	0.333598	−	1.70382i
$254$		0			0
$255$	−0.476562	+	0.924401i	−0.0298435	+	0.0578882i
$256$		0			0
$257$	−14.4120	+	10.2627i	−0.898996	+	0.640172i	−0.933245	−	0.359241i	$-0.883036\pi$
$257$	−14.4120	+	10.2627i	−0.898996	+	0.640172i	0.0342488	+	0.999413i	$0.489096\pi$
$258$		0			0
$259$	4.15541	−	0.455178i	0.258204	−	0.0282834i
$260$		0			0
$261$	−6.60591	−	2.64461i	−0.408895	−	0.163697i
$262$		0			0
$263$	−3.94536	+	20.4705i	−0.243281	+	1.26226i	0.630594	+	0.776113i	$0.282811\pi$
$263$	−3.94536	+	20.4705i	−0.243281	+	1.26226i	−0.873876	+	0.486150i	$0.838401\pi$
$264$		0			0
$265$	−1.06193	+	1.65239i	−0.0652336	+	0.101506i
$266$		0			0
$267$	5.43504	−	18.5100i	0.332619	−	1.13280i
$268$		0			0
$269$	1.20645	+	0.417556i	0.0735585	+	0.0254589i	0.363599	−	0.931555i	$-0.381548\pi$
$269$	1.20645	+	0.417556i	0.0735585	+	0.0254589i	−0.290041	+	0.957014i	$0.593669\pi$
$270$		0			0
$271$	5.45408	+	1.32315i	0.331312	+	0.0803753i	0.397964	−	0.917401i	$-0.369717\pi$
$271$	5.45408	+	1.32315i	0.331312	+	0.0803753i	−0.0666526	+	0.997776i	$0.521232\pi$
$272$		0			0
$273$	1.55291	+	2.34406i	0.0939863	+	0.141869i
$274$		0			0
$275$	−24.7594	−	14.2949i	−1.49305	−	0.862012i
$276$		0			0
$277$	15.9476	+	27.6220i	0.958196	+	1.65964i	0.726878	+	0.686767i	$0.240971\pi$
$277$	15.9476	+	27.6220i	0.958196	+	1.65964i	0.231318	+	0.972878i	$0.425696\pi$
$278$		0			0
$279$	−1.87481	−	0.269557i	−0.112242	−	0.0161379i
$280$		0			0
$281$	−0.549365	−	1.87096i	−0.0327724	−	0.111612i	0.941483	−	0.337062i	$-0.109433\pi$
$281$	−0.549365	−	1.87096i	−0.0327724	−	0.111612i	−0.974255	+	0.225449i	$0.927615\pi$
$282$		0			0
$283$	9.81977	−	28.3724i	0.583725	−	1.68656i	−0.134638	−	0.990895i	$-0.542987\pi$
$283$	9.81977	−	28.3724i	0.583725	−	1.68656i	0.718364	−	0.695668i	$-0.244891\pi$
$284$		0			0
$285$	0.00236241	+	0.00247763i	0.000139937	+	0.000146762i
$286$		0			0
$287$	−11.3661	−	4.36794i	−0.670920	−	0.257831i
$288$		0			0
$289$	0.921584	+	2.66274i	0.0542108	+	0.156632i
$290$		0			0
$291$	−10.8996	−	13.8600i	−0.638946	−	0.812485i
$292$		0			0
$293$	−2.01948	−	4.42205i	−0.117979	−	0.258339i	0.841424	−	0.540375i	$-0.181718\pi$
$293$	−2.01948	−	4.42205i	−0.117979	−	0.258339i	−0.959404	+	0.282036i	$0.908990\pi$
$294$		0			0
$295$	−0.0372291	−	0.0170019i	−0.00216756	−	0.000989891i
$296$		0			0
$297$	28.8668	+	14.8818i	1.67502	+	0.863532i
$298$		0			0
$299$	2.61533	−	2.25273i	0.151249	−	0.130279i
$300$		0			0
$301$	−9.64031	+	9.45138i	−0.555658	+	0.544768i
$302$		0			0
$303$	−15.8529	−	22.2622i	−0.910723	−	1.27893i
$304$		0			0
$305$	1.01493	−	1.42527i	0.0581149	−	0.0816110i
$306$		0			0
$307$	27.1598	−	3.90499i	1.55009	−	0.222870i	0.686526	−	0.727105i	$-0.259135\pi$
$307$	27.1598	−	3.90499i	1.55009	−	0.222870i	0.863566	+	0.504236i	$0.168226\pi$
$308$		0			0
$309$	−5.87197	−	5.08809i	−0.334045	−	0.289451i
$310$		0			0
$311$	4.50521	+	0.214610i	0.255467	+	0.0121694i	0.174925	−	0.984582i	$-0.444032\pi$
$311$	4.50521	+	0.214610i	0.255467	+	0.0121694i	0.0805423	+	0.996751i	$0.474335\pi$
$312$		0			0
$313$	11.7840	−	11.2360i	0.666072	−	0.635099i	−0.279639	−	0.960105i	$-0.590215\pi$
$313$	11.7840	−	11.2360i	0.666072	−	0.635099i	0.945712	+	0.325006i	$0.105366\pi$
$314$		0			0
$315$	−0.402268	−	0.0521397i	−0.0226652	−	0.00293774i
$316$		0			0
$317$	5.93075	−	24.4469i	0.333104	−	1.37307i	−0.521259	−	0.853398i	$-0.674538\pi$
$317$	5.93075	−	24.4469i	0.333104	−	1.37307i	0.854363	−	0.519676i	$-0.173947\pi$
$318$		0			0
$319$	18.5770	+	46.4032i	1.04011	+	2.59808i
$320$		0			0
$321$	−10.7722			−0.601243
$322$		0			0
$323$	−0.0466836			−0.00259755
$324$		0			0
$325$	−1.32815	−	3.31757i	−0.0736727	−	0.184026i
$326$		0			0
$327$	0.969437	−	3.99607i	0.0536100	−	0.220983i
$328$		0			0
$329$	−11.7163	+	4.88060i	−0.645943	+	0.269076i
$330$		0			0
$331$	5.54811	−	5.29011i	0.304952	−	0.290771i	−0.522115	−	0.852875i	$-0.674857\pi$
$331$	5.54811	−	5.29011i	0.304952	−	0.290771i	0.827066	+	0.562105i	$0.190008\pi$
$332$		0			0
$333$	1.29371	+	0.0616268i	0.0708946	+	0.00337713i
$334$		0			0
$335$	−0.880827	−	0.763241i	−0.0481247	−	0.0417003i
$336$		0			0
$337$	−3.03818	+	0.436825i	−0.165500	+	0.0237954i	−0.224567	−	0.974459i	$-0.572097\pi$
$337$	−3.03818	+	0.436825i	−0.165500	+	0.0237954i	0.0590664	+	0.998254i	$0.481188\pi$
$338$		0			0
$339$	−6.11732	+	8.59057i	−0.332247	+	0.466576i
$340$		0			0
$341$	7.71766	+	10.8379i	0.417935	+	0.586907i
$342$		0			0
$343$	−17.1528	−	6.98440i	−0.926164	−	0.377122i
$344$		0			0
$345$	0.00390520	−	1.32443i	0.000210249	−	0.0713047i
$346$		0			0
$347$	−21.4572	−	11.0619i	−1.15188	−	0.593836i	−0.226926	−	0.973912i	$-0.572867\pi$
$347$	−21.4572	−	11.0619i	−1.15188	−	0.593836i	−0.924955	+	0.380076i	$0.875898\pi$
$348$		0			0
$349$	−7.57175	−	3.45790i	−0.405306	−	0.185097i	0.202321	−	0.979319i	$-0.435151\pi$
$349$	−7.57175	−	3.45790i	−0.405306	−	0.185097i	−0.607628	+	0.794222i	$0.707879\pi$
$350$		0			0
$351$	1.68635	+	3.69260i	0.0900109	+	0.197096i
$352$		0			0
$353$	−21.7290	−	27.6306i	−1.15652	−	1.47063i	−0.856092	−	0.516824i	$-0.827114\pi$
$353$	−21.7290	−	27.6306i	−1.15652	−	1.47063i	−0.300425	−	0.953806i	$-0.597128\pi$
$354$		0			0
$355$	−0.0463509	−	0.133922i	−0.00246005	−	0.00710785i
$356$		0			0
$357$	−11.4370	+	9.25437i	−0.605310	+	0.489793i
$358$		0			0
$359$	−1.62663	−	1.70596i	−0.0858503	−	0.0900372i	0.679407	−	0.733761i	$-0.262237\pi$
$359$	−1.62663	−	1.70596i	−0.0858503	−	0.0900372i	−0.765258	+	0.643724i	$0.777388\pi$
$360$		0			0
$361$	6.21424	−	17.9549i	0.327065	−	0.944993i
$362$		0			0
$363$	−9.21735	−	31.3914i	−0.483785	−	1.64762i
$364$		0			0
$365$	2.27238	+	0.326719i	0.118942	+	0.0171013i
$366$		0			0
$367$	3.57970	+	6.20022i	0.186859	+	0.323649i	0.944201	−	0.329369i	$-0.106836\pi$
$367$	3.57970	+	6.20022i	0.186859	+	0.323649i	−0.757343	+	0.653018i	$0.773503\pi$
$368$		0			0
$369$	−3.26721	−	1.88633i	−0.170084	−	0.0981982i
$370$		0			0
$371$	−23.1638	+	15.3457i	−1.20261	+	0.796709i
$372$		0			0
$373$	−5.73554	−	1.39143i	−0.296975	−	0.0720454i	0.0845031	−	0.996423i	$-0.473070\pi$
$373$	−5.73554	−	1.39143i	−0.296975	−	0.0720454i	−0.381478	+	0.924378i	$0.624585\pi$
$374$		0			0
$375$	−2.60062	−	0.900082i	−0.134295	−	0.0464800i
$376$		0			0
$377$	−1.76017	+	5.99459i	−0.0906535	+	0.308737i
$378$		0			0
$379$	6.92430	−	10.7744i	0.355678	−	0.553445i	−0.616599	−	0.787277i	$-0.711490\pi$
$379$	6.92430	−	10.7744i	0.355678	−	0.553445i	0.972277	+	0.233832i	$0.0751265\pi$
$380$		0			0
$381$	−2.65275	+	13.7638i	−0.135905	+	0.705141i
$382$		0			0
$383$	−5.73565	−	2.29621i	−0.293078	−	0.117331i	0.220464	−	0.975395i	$-0.429243\pi$
$383$	−5.73565	−	2.29621i	−0.293078	−	0.117331i	−0.513542	+	0.858064i	$0.671667\pi$
$384$		0			0
$385$	1.68491	+	2.29782i	0.0858708	+	0.117108i
$386$		0			0
$387$	−3.40727	+	2.42630i	−0.173201	+	0.123336i
$388$		0			0
$389$	13.6094	−	26.3985i	0.690022	−	1.33846i	−0.239936	−	0.970789i	$-0.577126\pi$
$389$	13.6094	−	26.3985i	0.690022	−	1.33846i	0.929958	−	0.367667i	$-0.119843\pi$
$390$		0			0
$391$	13.0344	+	12.5019i	0.659179	+	0.632247i
$392$		0			0
$393$	2.02931	−	1.30416i	0.102365	−	0.0657862i
$394$		0			0
$395$	0.00580082	+	0.0607490i	0.000291871	+	0.00305661i
$396$		0			0
$397$	−0.257778	+	2.69957i	−0.0129375	+	0.135488i	−0.999633	−	0.0270919i	$-0.991375\pi$
$397$	−0.257778	+	2.69957i	−0.0129375	+	0.135488i	0.986695	+	0.162579i	$0.0519814\pi$
$398$		0			0
$399$	0.0164739	+	0.0455397i	0.000824729	+	0.00227984i
$400$		0			0
$401$	15.8310	−	5.47917i	0.790563	−	0.273617i	0.0982008	−	0.995167i	$-0.468691\pi$
$401$	15.8310	−	5.47917i	0.790563	−	0.273617i	0.692362	+	0.721550i	$0.256570\pi$
$402$		0			0
$403$	−0.0791311	+	1.66117i	−0.00394180	+	0.0827486i
$404$		0			0
$405$	1.05319	+	0.309243i	0.0523332	+	0.0153664i
$406$		0			0
$407$	−5.95788	−	6.87576i	−0.295321	−	0.340819i
$408$		0			0
$409$	−3.31069	+	3.47215i	−0.163703	+	0.171687i	−0.800477	−	0.599364i	$-0.795420\pi$
$409$	−3.31069	+	3.47215i	−0.163703	+	0.171687i	0.636773	+	0.771051i	$0.280269\pi$
$410$		0			0
$411$	17.2873	+	13.5949i	0.852719	+	0.670586i
$412$		0			0
$413$	−0.385190	−	0.432241i	−0.0189540	−	0.0212692i
$414$		0			0
$415$	1.44386	−	2.50083i	0.0708761	−	0.122761i
$416$		0			0
$417$	−24.5119	+	9.81310i	−1.20035	+	0.480549i
$418$		0			0
$419$	−12.9501	+	3.80249i	−0.632653	+	0.185764i	−0.582308	−	0.812968i	$-0.697850\pi$
$419$	−12.9501	+	3.80249i	−0.632653	+	0.185764i	−0.0503451	+	0.998732i	$0.516032\pi$
$420$		0			0
$421$	3.27200	−	2.83520i	0.159467	−	0.138179i	−0.571472	−	0.820621i	$-0.693628\pi$
$421$	3.27200	−	2.83520i	0.159467	−	0.138179i	0.730940	+	0.682442i	$0.239082\pi$
$422$		0			0
$423$	−3.82159	+	0.927109i	−0.185812	+	0.0450776i
$424$		0			0
$425$	16.6194	−	8.56790i	0.806160	−	0.415604i
$426$		0			0
$427$	21.2614	−	12.6727i	1.02891	−	0.613274i
$428$		0			0
$429$	2.27442	−	5.68123i	0.109810	−	0.274292i
$430$		0			0
$431$	33.0979	+	23.5689i	1.59427	+	1.13528i	0.916523	+	0.399981i	$0.130983\pi$
$431$	33.0979	+	23.5689i	1.59427	+	1.13528i	0.677748	+	0.735294i	$0.262956\pi$
$432$		0			0
$433$	−12.1713	+	26.6515i	−0.584917	+	1.28079i	0.353548	+	0.935416i	$0.384975\pi$
$433$	−12.1713	+	26.6515i	−0.584917	+	1.28079i	−0.938465	+	0.345374i	$0.887752\pi$
$434$		0			0
$435$	1.29603	+	2.01666i	0.0621397	+	0.0966913i
$436$		0			0
$437$	0.0529218	−	0.0270858i	0.00253159	−	0.00129569i
$438$		0			0
$439$	−23.9257	+	1.13972i	−1.14191	+	0.0543959i	−0.609998	−	0.792403i	$-0.708830\pi$
$439$	−23.9257	+	1.13972i	−1.14191	+	0.0543959i	−0.531913	+	0.846799i	$0.678527\pi$
$440$		0			0
$441$	−4.91162	−	2.96686i	−0.233887	−	0.141279i
$442$		0			0
$443$	−7.29329	−	0.696425i	−0.346515	−	0.0330882i	−0.0796522	−	0.996823i	$-0.525381\pi$
$443$	−7.29329	−	0.696425i	−0.346515	−	0.0330882i	−0.266863	+	0.963735i	$0.585987\pi$
$444$		0			0
$445$	1.92076	−	1.51050i	0.0910529	−	0.0716048i
$446$		0			0
$447$	10.2620	−	11.8430i	0.485378	−	0.560156i
$448$		0			0
$449$	−3.95497	−	2.54170i	−0.186646	−	0.119950i	0.443981	−	0.896036i	$-0.353566\pi$
$449$	−3.95497	−	2.54170i	−0.186646	−	0.119950i	−0.630627	+	0.776086i	$0.717202\pi$
$450$		0			0
$451$	6.24785	+	25.7540i	0.294200	+	1.21271i
$452$		0			0
$453$	−5.59310	−	29.0198i	−0.262787	−	1.36347i
$454$		0			0
$455$	−0.0119987	+	0.355953i	−0.000562507	+	0.0166873i
$456$		0			0
$457$	−16.9510	+	21.5550i	−0.792937	+	1.00830i	0.206617	+	0.978422i	$0.433755\pi$
$457$	−16.9510	+	21.5550i	−0.792937	+	1.00830i	−0.999554	+	0.0298790i	$0.990488\pi$
$458$		0			0
$459$	−18.3947	+	10.6202i	−0.858589	+	0.495707i
$460$		0			0
$461$			9.23097i			0.429929i	0.976622	+	0.214964i	$0.0689636\pi$
$461$			9.23097i			0.429929i	−0.976622	+	0.214964i	$0.931036\pi$
$462$		0			0
$463$	−0.508287	+	3.53521i	−0.0236221	+	0.164295i	−0.998218	−	0.0596763i	$-0.980993\pi$
$463$	−0.508287	+	3.53521i	−0.0236221	+	0.164295i	0.974596	+	0.223971i	$0.0719023\pi$
$464$		0			0
$465$	0.461819	+	0.440343i	0.0214163	+	0.0204204i
$466$		0			0
$467$	−32.2047	+	6.20695i	−1.49026	+	0.287224i	−0.868383	−	0.495894i	$-0.834841\pi$
$467$	−32.2047	+	6.20695i	−1.49026	+	0.287224i	−0.621874	+	0.783117i	$0.713628\pi$
$468$		0			0
$469$	−7.05694	−	14.9007i	−0.325859	−	0.688052i
$470$		0			0
$471$	−7.17507	−	13.9177i	−0.330610	−	0.641293i
$472$		0			0
$473$	28.8516	+	5.56069i	1.32660	+	0.255681i
$474$		0			0
$475$	−0.00875916	−	0.0609213i	−0.000401898	−	0.00279526i
$476$		0			0
$477$	−7.83093	+	3.57627i	−0.358554	+	0.163746i
$478$		0			0
$479$	20.9898	−	2.00428i	0.959049	−	0.0915781i	0.396224	−	0.918154i	$-0.370320\pi$
$479$	20.9898	−	2.00428i	0.959049	−	0.0915781i	0.562825	+	0.826576i	$0.309714\pi$
$480$		0			0
$481$	−0.0541097	−	1.13590i	−0.00246719	−	0.0517927i
$482$		0			0
$483$	7.59588	−	17.1267i	0.345624	−	0.779294i
$484$		0			0
$485$	−0.106269	−	2.23087i	−0.00482545	−	0.101299i
$486$		0			0
$487$	−7.34576	+	0.701435i	−0.332868	+	0.0317850i	−0.260152	−	0.965568i	$-0.583773\pi$
$487$	−7.34576	+	0.701435i	−0.332868	+	0.0317850i	−0.0727159	+	0.997353i	$0.523167\pi$
$488$		0			0
$489$	12.7679	−	5.83090i	0.577383	−	0.263682i
$490$		0			0
$491$	4.50562	+	31.3373i	0.203336	+	1.41423i	0.794295	+	0.607532i	$0.207840\pi$
$491$	4.50562	+	31.3373i	0.203336	+	1.41423i	−0.590959	+	0.806701i	$0.701251\pi$
$492$		0			0
$493$	−32.0991	−	6.18659i	−1.44567	−	0.278630i
$494$		0			0
$495$	0.404532	+	0.784683i	0.0181824	+	0.0352689i
$496$		0			0
$497$	0.162797	−	1.99812i	0.00730247	−	0.0896279i
$498$		0			0
$499$	23.1382	−	4.45951i	1.03581	−	0.199635i	0.357116	−	0.934060i	$-0.383760\pi$
$499$	23.1382	−	4.45951i	1.03581	−	0.199635i	0.678690	+	0.734425i	$0.262548\pi$
$500$		0			0
$501$	−20.2290	−	19.2883i	−0.903766	−	0.861739i
$502$		0			0
$503$	−1.21950	+	8.48181i	−0.0543748	+	0.378185i	0.944404	+	0.328786i	$0.106640\pi$
$503$	−1.21950	+	8.48181i	−0.0543748	+	0.378185i	−0.998779	+	0.0493987i	$0.984269\pi$
$504$		0			0
$505$		−	3.46173i		−	0.154045i
$506$		0			0
$507$	−15.9613	+	9.21526i	−0.708866	+	0.409264i
$508$		0			0
$509$	9.03696	−	11.4914i	0.400556	−	0.509349i	−0.543375	−	0.839490i	$-0.682854\pi$
$509$	9.03696	−	11.4914i	0.400556	−	0.509349i	0.943932	+	0.330141i	$0.107096\pi$
$510$		0			0
$511$	27.5620	+	17.1763i	1.21927	+	0.759835i
$512$		0			0
$513$	0.0132318	+	0.0686529i	0.000584197	+	0.00303110i
$514$		0			0
$515$	−0.232023	−	0.956410i	−0.0102241	−	0.0421445i
$516$		0			0
$517$	23.2383	+	14.9344i	1.02202	+	0.656813i
$518$		0			0
$519$	−0.466395	+	0.538249i	−0.0204725	+	0.0236265i
$520$		0			0
$521$	13.3086	−	10.4660i	0.583062	−	0.458525i	−0.282541	−	0.959255i	$-0.591177\pi$
$521$	13.3086	−	10.4660i	0.583062	−	0.458525i	0.865604	+	0.500730i	$0.166935\pi$
$522$		0			0
$523$	17.3715	+	1.65878i	0.759602	+	0.0725332i	0.467667	−	0.883905i	$-0.345095\pi$
$523$	17.3715	+	1.65878i	0.759602	+	0.0725332i	0.291935	+	0.956438i	$0.405701\pi$
$524$		0			0
$525$	−14.2227	−	13.1887i	−0.620729	−	0.575602i
$526$		0			0
$527$	−8.69176	+	0.414039i	−0.378619	+	0.0180358i
$528$		0			0
$529$	−22.0297	−	6.60988i	−0.957815	−	0.287386i
$530$		0			0
$531$	−0.0969811	−	0.150906i	−0.00420862	−	0.00654874i
$532$		0			0
$533$	−1.37605	+	3.01313i	−0.0596034	+	0.130513i
$534$		0			0
$535$	−1.11145	−	0.791461i	−0.0480522	−	0.0342178i
$536$		0			0
$537$	−0.512947	+	1.28128i	−0.0221353	+	0.0552913i
$538$		0			0
$539$	8.72579	+	39.3518i	0.375846	+	1.69500i
$540$		0			0
$541$	−31.7334	+	16.3597i	−1.36432	+	0.703358i	−0.975919	−	0.218131i	$-0.930004\pi$
$541$	−31.7334	+	16.3597i	−1.36432	+	0.703358i	−0.388404	+	0.921489i	$0.626974\pi$
$542$		0			0
$543$	33.4615	−	8.11767i	1.43597	−	0.348363i
$544$		0			0
$545$	0.393628	−	0.341080i	0.0168612	−	0.0146103i
$546$		0			0
$547$	−25.0826	+	7.36492i	−1.07246	+	0.314901i	−0.769857	−	0.638217i	$-0.779672\pi$
$547$	−25.0826	+	7.36492i	−1.07246	+	0.314901i	−0.302599	+	0.953118i	$0.597854\pi$
$548$		0			0
$549$	7.11949	−	2.85021i	0.303852	−	0.121644i
$550$		0			0
$551$	−0.0538022	+	0.0931882i	−0.00229205	+	0.00396995i
$552$		0			0
$553$	−0.270979	+	0.819640i	−0.0115232	+	0.0348546i
$554$		0			0
$555$	−0.342983	−	0.269725i	−0.0145588	−	0.0114492i
$556$		0			0
$557$	−0.210176	+	0.220426i	−0.00890544	+	0.00933976i	−0.728172	−	0.685395i	$-0.759630\pi$
$557$	−0.210176	+	0.220426i	−0.00890544	+	0.00933976i	0.719266	+	0.694735i	$0.244478\pi$
$558$		0			0
$559$	2.40508	+	2.77561i	0.101724	+	0.117396i
$560$		0			0
$561$	30.7226	+	9.02098i	1.29711	+	0.380866i
$562$		0			0
$563$	−0.904098	+	18.9793i	−0.0381032	+	0.799884i	0.896253	+	0.443543i	$0.146279\pi$
$563$	−0.904098	+	18.9793i	−0.0381032	+	0.799884i	−0.934356	+	0.356341i	$0.884024\pi$
$564$		0			0
$565$	−1.26235	+	0.436903i	−0.0531074	+	0.0183806i
$566$		0			0
$567$	11.8751	+	10.0042i	0.498708	+	0.420137i
$568$		0			0
$569$	−2.58913	+	27.1146i	−0.108542	+	1.13670i	0.763005	+	0.646393i	$0.223723\pi$
$569$	−2.58913	+	27.1146i	−0.108542	+	1.13670i	−0.871547	+	0.490312i	$0.836883\pi$
$570$		0			0
$571$	−1.24887	−	13.0788i	−0.0522636	−	0.547329i	−0.983248	−	0.182271i	$-0.941655\pi$
$571$	−1.24887	−	13.0788i	−0.0522636	−	0.547329i	0.930985	−	0.365058i	$-0.118951\pi$
$572$		0			0
$573$	14.7624	−	9.48724i	0.616710	−	0.396335i
$574$		0			0
$575$	−13.8691	+	19.3554i	−0.578381	+	0.807175i
$576$		0			0
$577$	14.0241	−	27.2030i	0.583831	−	1.13247i	−0.393215	−	0.919446i	$-0.628637\pi$
$577$	14.0241	−	27.2030i	0.583831	−	1.13247i	0.977046	−	0.213027i	$-0.0683323\pi$
$578$		0			0
$579$	−20.7568	+	14.7809i	−0.862624	+	0.614272i
$580$		0			0
$581$	32.9428	−	24.1557i	1.36670	−	1.00215i
$582$		0			0
$583$	56.1414	+	22.4756i	2.32514	+	0.930846i
$584$		0			0
$585$	−0.0208834	+	0.108354i	−0.000863424	+	0.00447987i
$586$		0			0
$587$	10.6715	−	16.6052i	0.440461	−	0.685371i	−0.548063	−	0.836437i	$-0.684634\pi$
$587$	10.6715	−	16.6052i	0.440461	−	0.685371i	0.988524	+	0.151067i	$0.0482708\pi$
$588$		0			0
$589$	−0.00806965	+	0.0274827i	−0.000332504	+	0.00113241i
$590$		0			0
$591$	6.08045	+	2.10447i	0.250116	+	0.0865662i
$592$		0			0
$593$	−22.7915	−	5.52916i	−0.935935	−	0.227055i	−0.261343	−	0.965246i	$-0.584165\pi$
$593$	−22.7915	−	5.52916i	−0.935935	−	0.227055i	−0.674592	+	0.738191i	$0.735680\pi$
$594$		0			0
$595$	−1.85999	+	0.114541i	−0.0762523	+	0.00469574i
$596$		0			0
$597$	19.9870	+	11.5395i	0.818014	+	0.472281i
$598$		0			0
$599$	21.4027	+	37.0705i	0.874490	+	1.51466i	0.857305	+	0.514809i	$0.172137\pi$
$599$	21.4027	+	37.0705i	0.874490	+	1.51466i	0.0171847	+	0.999852i	$0.494530\pi$
$600$		0			0
$601$	−30.6954	−	4.41333i	−1.25209	−	0.180023i	−0.515811	−	0.856702i	$-0.672509\pi$
$601$	−30.6954	−	4.41333i	−1.25209	−	0.180023i	−0.736278	+	0.676679i	$0.763419\pi$
$602$		0			0
$603$	−1.43917	−	4.90136i	−0.0586075	−	0.199599i
$604$		0			0
$605$	1.35539	−	3.91613i	0.0551043	−	0.159213i
$606$		0			0
$607$	21.4180	+	22.4625i	0.869329	+	0.911726i	0.996785	−	0.0801183i	$-0.0255298\pi$
$607$	21.4180	+	22.4625i	0.869329	+	0.911726i	−0.127457	+	0.991844i	$0.540681\pi$
$608$		0			0
$609$	5.29229	+	33.4957i	0.214454	+	1.35731i
$610$		0			0
$611$	1.12929	+	3.26287i	0.0456863	+	0.132002i
$612$		0			0
$613$	−6.57438	−	8.36000i	−0.265537	−	0.337657i	0.634940	−	0.772561i	$-0.281025\pi$
$613$	−6.57438	−	8.36000i	−0.265537	−	0.337657i	−0.900477	+	0.434904i	$0.856782\pi$
$614$		0			0
$615$	0.527985	+	1.15613i	0.0212904	+	0.0466195i
$616$		0			0
$617$	−12.6390	−	5.77204i	−0.508827	−	0.232373i	0.144423	−	0.989516i	$-0.453867\pi$
$617$	−12.6390	−	5.77204i	−0.508827	−	0.232373i	−0.653250	+	0.757143i	$0.726595\pi$
$618$		0			0
$619$	−15.5981	−	8.04138i	−0.626940	−	0.323210i	0.115313	−	0.993329i	$-0.463213\pi$
$619$	−15.5981	−	8.04138i	−0.626940	−	0.323210i	−0.742254	+	0.670119i	$0.766243\pi$
$620$		0			0
$621$	14.6908	−	22.7119i	0.589523	−	0.911396i
$622$		0			0
$623$	33.4759	−	8.61571i	1.34118	−	0.345181i
$624$		0			0
$625$	14.1978	+	19.9380i	0.567911	+	0.797519i
$626$		0			0
$627$	0.0611372	−	0.0858551i	0.00244158	−	0.00342872i
$628$		0			0
$629$	5.88958	−	0.846794i	0.234833	−	0.0337639i
$630$		0			0
$631$	23.3742	+	20.2538i	0.930510	+	0.806292i	0.981313	−	0.192417i	$-0.0616326\pi$
$631$	23.3742	+	20.2538i	0.930510	+	0.806292i	−0.0508029	+	0.998709i	$0.516178\pi$
$632$		0			0
$633$	11.1906	+	0.533074i	0.444787	+	0.0211878i
$634$		0			0
$635$	−1.28497	+	1.22522i	−0.0509926	+	0.0486213i
$636$		0			0
$637$	−2.18324	+	4.54060i	−0.0865031	+	0.179905i
$638$		0			0
$639$	0.146437	−	0.603621i	0.00579295	−	0.0238789i
$640$		0			0
$641$	4.29598	+	10.7308i	0.169681	+	0.423843i	0.988697	−	0.149928i	$-0.0479042\pi$
$641$	4.29598	+	10.7308i	0.169681	+	0.423843i	−0.819016	+	0.573771i	$0.805480\pi$
$642$		0			0
$643$	−14.4354			−0.569275			−0.284638	−	0.958635i	$-0.591873\pi$
$643$	−14.4354			−0.569275			−0.284638	+	0.958635i	$0.591873\pi$
$644$		0			0
$645$	1.40918			0.0554865
$646$		0			0
$647$	4.08828	+	10.2120i	0.160727	+	0.401476i	0.986769	−	0.162132i	$-0.0518370\pi$
$647$	4.08828	+	10.2120i	0.160727	+	0.401476i	−0.826042	+	0.563608i	$0.809413\pi$
$648$		0			0
$649$	−0.297072	+	1.22455i	−0.0116611	+	0.0480677i
$650$		0			0
$651$	3.47108	+	8.33267i	0.136043	+	0.326583i
$652$		0			0
$653$	−8.90413	+	8.49007i	−0.348445	+	0.332242i	−0.844008	−	0.536330i	$-0.819810\pi$
$653$	−8.90413	+	8.49007i	−0.348445	+	0.332242i	0.495563	+	0.868572i	$0.334962\pi$
$654$		0			0
$655$	0.305201	+	0.0145385i	0.0119252	+	0.000568068i
$656$		0			0
$657$	7.60439	+	6.58925i	0.296676	+	0.257071i
$658$		0			0
$659$	39.1632	−	5.63081i	1.52558	−	0.219345i	0.672096	−	0.740464i	$-0.265394\pi$
$659$	39.1632	−	5.63081i	1.52558	−	0.219345i	0.853484	+	0.521119i	$0.174485\pi$
$660$		0			0
$661$	4.26038	−	5.98287i	0.165710	−	0.232707i	−0.723368	−	0.690462i	$-0.757407\pi$
$661$	4.26038	−	5.98287i	0.165710	−	0.232707i	0.889078	+	0.457756i	$0.151347\pi$
$662$		0			0
$663$	2.32155	+	3.26015i	0.0901614	+	0.126614i
$664$		0			0
$665$	−0.00164618	+	0.00590909i	−6.38361e−5	+	0.000229145i
$666$		0			0
$667$	39.9778	−	11.6106i	1.54795	−	0.449565i
$668$		0			0
$669$	−31.9352	−	16.4638i	−1.23469	−	0.636526i
$670$		0			0
$671$	−49.0016	−	22.3783i	−1.89169	−	0.863904i
$672$		0			0
$673$	−17.8460	−	39.0774i	−0.687914	−	1.50632i	−0.854034	−	0.520217i	$-0.825851\pi$
$673$	−17.8460	−	39.0774i	−0.687914	−	1.50632i	0.166120	−	0.986106i	$-0.446876\pi$
$674$		0			0
$675$	−17.3105	−	22.0121i	−0.666281	−	0.847245i
$676$		0			0
$677$	9.58603	+	27.6970i	0.368421	+	1.06448i	0.965073	+	0.261983i	$0.0843763\pi$
$677$	9.58603	+	27.6970i	0.368421	+	1.06448i	−0.596651	+	0.802501i	$0.703502\pi$
$678$		0			0
$679$	11.3334	−	29.4913i	0.434934	−	1.13177i
$680$		0			0
$681$	4.91425	+	5.15391i	0.188314	+	0.197498i
$682$		0			0
$683$	11.7707	−	34.0092i	0.450394	−	1.30133i	−0.460123	−	0.887855i	$-0.652195\pi$
$683$	11.7707	−	34.0092i	0.450394	−	1.30133i	0.910517	−	0.413472i	$-0.135684\pi$
$684$		0			0
$685$	0.784817	+	2.67284i	0.0299863	+	0.102124i
$686$		0			0
$687$	26.6872	+	3.83704i	1.01818	+	0.146392i
$688$		0			0
$689$	3.77940	+	6.54612i	0.143984	+	0.249387i
$690$		0			0
$691$	12.4921	+	7.21231i	0.475221	+	0.274369i	0.718423	−	0.695607i	$-0.244864\pi$
$691$	12.4921	+	7.21231i	0.475221	+	0.274369i	−0.243202	+	0.969976i	$0.578198\pi$
$692$		0			0
$693$	0.767608	+	12.4649i	0.0291590	+	0.473503i
$694$		0			0
$695$	−3.25009	−	0.788464i	−0.123283	−	0.0299081i
$696$		0			0
$697$	−16.3787	−	5.66872i	−0.620387	−	0.214718i
$698$		0			0
$699$	−3.53092	+	12.0252i	−0.133552	+	0.454836i
$700$		0			0
$701$	−18.0107	+	28.0252i	−0.680256	+	1.05850i	0.313786	+	0.949494i	$0.398403\pi$
$701$	−18.0107	+	28.0252i	−0.680256	+	1.05850i	−0.994041	+	0.109004i	$0.965234\pi$
$702$		0			0
$703$	0.00370667	−	0.0192320i	0.000139800	−	0.000725350i
$704$		0			0
$705$	1.22992	+	0.492384i	0.0463213	+	0.0185443i
$706$		0			0
$707$	19.7216	−	44.8233i	0.741708	−	1.68575i
$708$		0			0
$709$	27.8309	−	19.8183i	1.04521	−	0.744292i	0.0776640	−	0.996980i	$-0.475254\pi$
$709$	27.8309	−	19.8183i	1.04521	−	0.744292i	0.967548	+	0.252688i	$0.0813145\pi$
$710$		0			0
$711$	−0.122561	+	0.237735i	−0.00459639	+	0.00891576i
$712$		0			0
$713$	9.61298	−	5.51233i	0.360009	−	0.206438i
$714$		0			0
$715$	0.652087	−	0.419071i	0.0243867	−	0.0156724i
$716$		0			0
$717$	1.41202	+	14.7874i	0.0527330	+	0.552245i
$718$		0			0
$719$	4.38538	−	45.9258i	0.163547	−	1.71274i	−0.425762	−	0.904835i	$-0.639994\pi$
$719$	4.38538	−	45.9258i	0.163547	−	1.71274i	0.589309	−	0.807908i	$-0.299400\pi$
$720$		0			0
$721$	2.44442	−	13.7057i	0.0910351	−	0.510426i
$722$		0			0
$723$	−28.7580	+	9.95323i	−1.06952	+	0.370165i
$724$		0			0
$725$	2.05070	−	43.0495i	0.0761611	−	1.59882i
$726$		0			0
$727$	−38.4383	−	11.2865i	−1.42560	−	0.418593i	−0.524203	−	0.851594i	$-0.675637\pi$
$727$	−38.4383	−	11.2865i	−1.42560	−	0.418593i	−0.901394	+	0.433001i	$0.857455\pi$
$728$		0			0
$729$	19.5116	+	22.5176i	0.722651	+	0.833983i
$730$		0			0
$731$	−13.2609	+	13.9077i	−0.490473	+	0.514393i
$732$		0			0
$733$	−10.3982	−	8.17720i	−0.384065	−	0.302032i	0.407396	−	0.913251i	$-0.366437\pi$
$733$	−10.3982	−	8.17720i	−0.384065	−	0.302032i	−0.791461	+	0.611220i	$0.790679\pi$
$734$		0			0
$735$	0.768098	+	1.77400i	0.0283317	+	0.0654349i
$736$		0			0
$737$	−17.9416	+	31.0757i	−0.660886	+	1.14469i
$738$		0			0
$739$	−8.72096	+	3.49134i	−0.320806	+	0.128431i	−0.526476	−	0.850190i	$-0.676487\pi$
$739$	−8.72096	+	3.49134i	−0.320806	+	0.128431i	0.205670	+	0.978621i	$0.434063\pi$
$740$		0			0
$741$	0.0126406	−	0.00371160i	0.000464363	−	0.000136349i
$742$		0			0
$743$	−18.3848	+	15.9305i	−0.674474	+	0.584435i	−0.923284	−	0.384117i	$-0.874506\pi$
$743$	−18.3848	+	15.9305i	−0.674474	+	0.584435i	0.248811	+	0.968552i	$0.419960\pi$
$744$		0			0
$745$	1.92896	−	0.467960i	0.0706716	−	0.0171447i
$746$		0			0
$747$	11.2496	−	5.79958i	0.411602	−	0.212195i
$748$		0			0
$749$	−9.88235	−	16.5800i	−0.361093	−	0.605820i
$750$		0			0
$751$	−11.8126	+	29.5065i	−0.431048	+	1.07671i	0.540811	+	0.841144i	$0.318117\pi$
$751$	−11.8126	+	29.5065i	−0.431048	+	1.07671i	−0.971859	+	0.235562i	$0.924307\pi$
$752$		0			0
$753$	10.3397	+	7.36287i	0.376800	+	0.268318i
$754$		0			0
$755$	1.55508	−	3.40515i	0.0565952	−	0.123926i
$756$		0			0
$757$	15.1470	+	23.5693i	0.550529	+	0.856639i	0.999315	−	0.0369995i	$-0.0117800\pi$
$757$	15.1470	+	23.5693i	0.550529	+	0.856639i	−0.448787	+	0.893639i	$0.648144\pi$
$758$		0			0
$759$	−40.0620	+	7.59886i	−1.45416	+	0.275821i
$760$		0			0
$761$	−7.84512	+	0.373709i	−0.284385	+	0.0135469i	−0.189290	−	0.981921i	$-0.560619\pi$
$761$	−7.84512	+	0.373709i	−0.284385	+	0.0135469i	−0.0950953	+	0.995468i	$0.530316\pi$
$762$		0			0
$763$	7.03994	−	2.17388i	0.254863	−	0.0786996i
$764$		0			0
$765$	−0.574760	−	0.0548829i	−0.0207805	−	0.00198430i
$766$		0			0
$767$	−0.123804	+	0.0973608i	−0.00447031	+	0.00351549i
$768$		0			0
$769$	−25.9431	+	29.9399i	−0.935530	+	1.07966i	0.0611405	+	0.998129i	$0.480526\pi$
$769$	−25.9431	+	29.9399i	−0.935530	+	1.07966i	−0.996671	+	0.0815304i	$0.974019\pi$
$770$		0			0
$771$	21.9773	+	14.1240i	0.791493	+	0.508662i
$772$		0			0
$773$	8.96557	+	36.9566i	0.322469	+	1.32924i	0.870249	+	0.492613i	$0.163958\pi$
$773$	8.96557	+	36.9566i	0.322469	+	1.32924i	−0.547779	+	0.836623i	$0.684527\pi$
$774$		0			0
$775$	−2.17113	−	11.2649i	−0.0779894	−	0.404647i
$776$		0			0
$777$	−2.90439	−	5.44644i	−0.104194	−	0.195390i
$778$		0			0
$779$	−0.0352667	+	0.0448453i	−0.00126356	+	0.00160675i
$780$		0			0
$781$	−3.77858	+	2.18156i	−0.135208	+	0.0780625i
$782$		0			0
$783$			48.9584i			1.74963i
$784$		0			0
$785$	0.282262	−	1.96318i	0.0100744	−	0.0700687i
$786$		0			0
$787$	−5.77146	−	5.50308i	−0.205730	−	0.196164i	0.580208	−	0.814468i	$-0.302971\pi$
$787$	−5.77146	−	5.50308i	−0.205730	−	0.196164i	−0.785938	+	0.618305i	$0.787820\pi$
$788$		0			0
$789$	30.2261	−	5.82560i	1.07608	−	0.207397i
$790$		0			0
$791$	−18.8342	−	1.53453i	−0.669668	−	0.0545614i
$792$		0			0
$793$	−3.08542	−	5.98489i	−0.109567	−	0.212530i
$794$		0			0
$795$	2.84787	+	0.548882i	0.101004	+	0.0194668i
$796$		0			0
$797$	3.68808	+	25.6512i	0.130638	+	0.908610i	0.944724	+	0.327866i	$0.106329\pi$
$797$	3.68808	+	25.6512i	0.130638	+	0.908610i	−0.814086	+	0.580745i	$0.802762\pi$
$798$		0			0
$799$	−16.4334	+	7.50490i	−0.581373	+	0.265504i
$800$		0			0
$801$	10.6614	−	1.01804i	0.376701	−	0.0359706i
$802$		0			0
$803$	−3.36313	−	70.6009i	−0.118682	−	2.49145i
$804$		0			0
$805$	2.04208	−	1.20902i	0.0719739	−	0.0426122i
$806$		0			0
$807$	−0.0896961	−	1.88295i	−0.00315745	−	0.0662831i
$808$		0			0
$809$	−10.0582	+	0.960440i	−0.353627	+	0.0337673i	−0.270358	−	0.962760i	$-0.587142\pi$
$809$	−10.0582	+	0.960440i	−0.353627	+	0.0337673i	−0.0832689	+	0.996527i	$0.526536\pi$
$810$		0			0
$811$	−6.65993	+	3.04149i	−0.233862	+	0.106801i	−0.528899	−	0.848685i	$-0.677395\pi$
$811$	−6.65993	+	3.04149i	−0.233862	+	0.106801i	0.295038	+	0.955486i	$0.404668\pi$
$812$		0			0
$813$	−1.17935	−	8.20259i	−0.0413618	−	0.287677i
$814$		0			0
$815$	1.74578	+	0.336471i	0.0611520	+	0.0117861i
$816$		0			0
$817$	0.0289850	+	0.0562230i	0.00101406	+	0.00196699i
$818$		0			0
$819$	−0.887698	+	1.28401i	−0.0310187	+	0.0448671i
$820$		0			0
$821$	−1.76453	+	0.340086i	−0.0615826	+	0.0118691i	−0.219949	−	0.975511i	$-0.570589\pi$
$821$	−1.76453	+	0.340086i	−0.0615826	+	0.0118691i	0.158367	+	0.987380i	$0.449377\pi$
$822$		0			0
$823$	−0.626522	−	0.597388i	−0.0218392	−	0.0208236i	0.679081	−	0.734063i	$-0.262379\pi$
$823$	−0.626522	−	0.597388i	−0.0218392	−	0.0208236i	−0.700920	+	0.713240i	$0.747227\pi$
$824$		0			0
$825$	−6.00779	+	41.7851i	−0.209164	+	1.45477i
$826$		0			0
$827$			29.9526i			1.04155i	0.853693	+	0.520777i	$0.174358\pi$
$827$			29.9526i			1.04155i	−0.853693	+	0.520777i	$0.825642\pi$
$828$		0			0
$829$	32.9169	−	19.0046i	1.14325	−	0.660057i	0.196018	−	0.980600i	$-0.437199\pi$
$829$	32.9169	−	19.0046i	1.14325	−	0.660057i	0.947234	+	0.320543i	$0.103866\pi$
$830$		0			0
$831$	29.1125	−	37.0195i	1.00990	−	1.28419i
$832$		0			0
$833$	−24.7362	−	9.11335i	−0.857058	−	0.315759i
$834$		0			0
$835$	−0.670025	−	3.47642i	−0.0231872	−	0.120306i
$836$		0			0
$837$	3.07243	+	12.6647i	0.106199	+	0.437758i
$838$		0			0
$839$	24.2054	+	15.5558i	0.835662	+	0.537048i	0.887073	−	0.461630i	$-0.152735\pi$
$839$	24.2054	+	15.5558i	0.835662	+	0.537048i	−0.0514103	+	0.998678i	$0.516372\pi$
$840$		0			0
$841$	−30.3522	+	35.0284i	−1.04663	+	1.20787i
$842$		0			0
$843$	−2.26324	+	1.77983i	−0.0779501	+	0.0613006i
$844$		0			0
$845$	−2.32393	−	0.221908i	−0.0799457	−	0.00763388i
$846$		0			0
$847$	39.8603	−	42.9853i	1.36961	−	1.47699i
$848$		0			0
$849$	−44.2819	+	2.10941i	−1.51975	+	0.0723946i
$850$		0			0
$851$	−6.18527	+	4.37709i	−0.212028	+	0.150045i
$852$		0			0
$853$	−20.0643	−	31.2207i	−0.686989	−	1.06898i	−0.993133	−	0.116990i	$-0.962675\pi$
$853$	−20.0643	−	31.2207i	−0.686989	−	1.06898i	0.306144	−	0.951985i	$-0.400961\pi$
$854$		0			0
$855$	−0.000789510		0.00172879i	−2.70007e−5		5.91232e-5i
$856$		0			0
$857$	−18.7726	−	13.3679i	−0.641260	−	0.456639i	0.212602	−	0.977139i	$-0.431806\pi$
$857$	−18.7726	−	13.3679i	−0.641260	−	0.456639i	−0.853862	+	0.520500i	$0.825746\pi$
$858$		0			0
$859$	−7.31593	+	18.2743i	−0.249616	+	0.623511i	−0.999265	−	0.0383241i	$-0.987798\pi$
$859$	−7.31593	+	18.2743i	−0.249616	+	0.623511i	0.749649	+	0.661836i	$0.230222\pi$
$860$		0			0
$861$	0.249979	+	17.9777i	0.00851925	+	0.612680i
$862$		0			0
$863$	−17.6030	+	9.07498i	−0.599213	+	0.308916i	−0.731016	−	0.682360i	$-0.760954\pi$
$863$	−17.6030	+	9.07498i	−0.599213	+	0.308916i	0.131803	+	0.991276i	$0.457923\pi$
$864$		0			0
$865$	−0.0876685	+	0.0212682i	−0.00298082	+	0.000723139i
$866$		0			0
$867$	3.14434	−	2.72459i	0.106787	−	0.0925318i
$868$		0			0
$869$	1.80272	−	0.529327i	0.0611532	−	0.0179562i
$870$		0			0
$871$	−4.16390	+	1.66697i	−0.141088	+	0.0564833i
$872$		0			0
$873$	4.89439	−	8.47733i	0.165650	−	0.286914i
$874$		0			0
$875$	−1.00043	−	4.82848i	−0.0338209	−	0.163233i
$876$		0			0
$877$	−38.4354	−	30.2260i	−1.29787	−	1.02066i	−0.997770	−	0.0667511i	$-0.978737\pi$
$877$	−38.4354	−	30.2260i	−1.29787	−	1.02066i	−0.300103	−	0.953907i	$-0.597021\pi$
$878$		0			0
$879$	−4.95349	+	5.19507i	−0.167077	+	0.175225i
$880$		0			0
$881$	−32.3449	−	37.3280i	−1.08973	−	1.25761i	−0.964101	−	0.265535i	$-0.914451\pi$
$881$	−32.3449	−	37.3280i	−1.08973	−	1.25761i	−0.125626	−	0.992078i	$-0.540094\pi$
$882$		0			0
$883$	5.92167	+	1.73876i	0.199280	+	0.0585140i	0.379849	−	0.925048i	$-0.375976\pi$
$883$	5.92167	+	1.73876i	0.199280	+	0.0585140i	−0.180569	+	0.983562i	$0.557794\pi$
$884$		0			0
$885$	−0.00287550	+	0.0603641i	−9.66588e−5	+	0.00202912i
$886$		0			0
$887$	24.1655	−	8.36375i	0.811397	−	0.280827i	0.110305	−	0.993898i	$-0.464817\pi$
$887$	24.1655	−	8.36375i	0.811397	−	0.280827i	0.701092	+	0.713071i	$0.252696\pi$
$888$		0			0
$889$	−23.6182	+	8.54388i	−0.792131	+	0.286553i
$890$		0			0
$891$	3.21233	−	33.6410i	0.107617	−	1.12702i
$892$		0			0
$893$	0.00565276	+	0.0591983i	0.000189162	+	0.00198100i
$894$		0			0
$895$	−0.147064	+	0.0945124i	−0.00491581	+	0.00315920i
$896$		0			0
$897$	−4.52331	−	2.34884i	−0.151029	−	0.0784253i
$898$		0			0
$899$	−9.19065	+	17.8274i	−0.306525	+	0.594576i
$900$		0			0
$901$	−32.2166	+	22.9413i	−1.07329	+	0.764286i
$902$		0			0
$903$	18.2464	+	8.02818i	0.607204	+	0.267161i
$904$		0			0
$905$	4.04893	+	1.62095i	0.134591	+	0.0538821i
$906$		0			0
$907$	−2.82105	+	14.6370i	−0.0936713	+	0.486013i	0.904548	+	0.426371i	$0.140208\pi$
$907$	−2.82105	+	14.6370i	−0.0936713	+	0.486013i	−0.998220	+	0.0596423i	$0.981004\pi$
$908$		0			0
$909$	8.20284	−	12.7639i	0.272071	−	0.423351i
$910$		0			0
$911$	9.04125	−	30.7917i	0.299550	−	1.02017i	−0.662898	−	0.748709i	$-0.730674\pi$
$911$	9.04125	−	30.7917i	0.299550	−	1.02017i	0.962448	−	0.271464i	$-0.0875079\pi$
$912$		0			0
$913$	−84.0163	−	29.0783i	−2.78054	−	0.962353i
$914$		0			0
$915$	−2.51075	−	0.609102i	−0.0830029	−	0.0201363i
$916$		0			0
$917$	3.86899	+	1.92699i	0.127765	+	0.0636349i
$918$		0			0
$919$	1.24936	+	0.721320i	0.0412127	+	0.0237942i	0.520465	−	0.853883i	$-0.325759\pi$
$919$	1.24936	+	0.721320i	0.0412127	+	0.0237942i	−0.479252	+	0.877677i	$0.659092\pi$
$920$		0			0
$921$	−20.2579	−	35.0877i	−0.667521	−	1.15618i
$922$		0			0
$923$	−0.539815	−	0.0776137i	−0.0177682	−	0.00255468i
$924$		0			0
$925$	2.21010	+	7.52692i	0.0726677	+	0.247484i
$926$		0			0
$927$	1.41079	−	4.07621i	0.0463364	−	0.133880i
$928$		0			0
$929$	4.44593	+	4.66275i	0.145866	+	0.152980i	0.792614	−	0.609724i	$-0.208720\pi$
$929$	4.44593	+	4.66275i	0.145866	+	0.152980i	−0.646748	+	0.762704i	$0.723871\pi$
$930$		0			0
$931$	−0.0549795	+	0.0671340i	−0.00180188	+	0.00220023i
$932$		0			0
$933$	−2.17821	−	6.29353i	−0.0713114	−	0.206041i
$934$		0			0
$935$	2.50711	+	3.18805i	0.0819912	+	0.104260i
$936$		0			0
$937$	6.40168	+	14.0177i	0.209134	+	0.457939i	0.984910	−	0.173070i	$-0.0553686\pi$
$937$	6.40168	+	14.0177i	0.209134	+	0.457939i	−0.775776	+	0.631008i	$0.782641\pi$
$938$		0			0
$939$	−21.8693	−	9.98738i	−0.713678	−	0.325926i
$940$		0			0
$941$	30.0157	+	15.4742i	0.978485	+	0.504444i	0.871807	−	0.489850i	$-0.162948\pi$
$941$	30.0157	+	15.4742i	0.978485	+	0.504444i	0.106678	+	0.994294i	$0.465979\pi$
$942$		0			0
$943$	21.8563	−	3.07671i	0.711739	−	0.100191i
$944$		0			0
$945$	0.695632	+	2.70284i	0.0226289	+	0.0879235i
$946$		0			0
$947$	−17.4193	−	24.4619i	−0.566050	−	0.794906i	0.428006	−	0.903776i	$-0.359216\pi$
$947$	−17.4193	−	24.4619i	−0.566050	−	0.794906i	−0.994056	+	0.108870i	$0.965277\pi$
$948$		0			0
$949$	5.12464	−	7.19654i	0.166353	−	0.233610i
$950$		0			0
$951$	−36.7666	+	5.28624i	−1.19224	+	0.171418i
$952$		0			0
$953$	21.4850	+	18.6169i	0.695968	+	0.603060i	0.929295	−	0.369339i	$-0.120416\pi$
$953$	21.4850	+	18.6169i	0.695968	+	0.603060i	−0.233327	+	0.972398i	$0.574961\pi$
$954$		0			0
$955$	2.22022	+	0.105762i	0.0718446	+	0.00342238i
$956$		0			0
$957$	53.4148	−	50.9309i	1.72666	−	1.64636i
$958$		0			0
$959$	−5.06529	+	39.0797i	−0.163567	+	1.26195i
$960$		0			0
$961$	6.04983	−	24.9377i	0.195156	−	0.804443i
$962$		0			0
$963$	−2.22264	−	5.55189i	−0.0716236	−	0.178907i
$964$		0			0
$965$	−3.22764			−0.103902
$966$		0			0
$967$	−4.29051			−0.137973			−0.0689867	−	0.997618i	$-0.521977\pi$
$967$	−4.29051			−0.137973			−0.0689867	+	0.997618i	$0.521977\pi$
$968$		0			0
$969$	0.0256193	+	0.0639940i	0.000823011	+	0.00205578i
$970$		0			0
$971$	7.40586	−	30.5274i	0.237665	−	0.979670i	−0.720500	−	0.693455i	$-0.756088\pi$
$971$	7.40586	−	30.5274i	0.237665	−	0.979670i	0.958165	−	0.286215i	$-0.0923973\pi$
$972$		0			0
$973$	−37.5911	−	28.7251i	−1.20511	−	0.920886i
$974$		0			0
$975$	−3.81886	+	3.64127i	−0.122301	+	0.116614i
$976$		0			0
$977$	6.44003	+	0.306776i	0.206035	+	0.00981464i	0.150346	−	0.988634i	$-0.451961\pi$
$977$	6.44003	+	0.306776i	0.206035	+	0.00981464i	0.0556892	+	0.998448i	$0.482264\pi$
$978$		0			0
$979$	−56.8561	−	49.2661i	−1.81713	−	1.57455i
$980$		0			0
$981$	2.25957	−	0.324878i	0.0721427	−	0.0103726i
$982$		0			0
$983$	12.8477	−	18.0421i	0.409779	−	0.575454i	−0.557178	−	0.830393i	$-0.688116\pi$
$983$	12.8477	−	18.0421i	0.409779	−	0.575454i	0.966957	+	0.254939i	$0.0820554\pi$
$984$		0			0
$985$	0.472749	+	0.663884i	0.0150630	+	0.0211531i
$986$		0			0
$987$	13.1201	+	13.3824i	0.417618	+	0.425966i
$988$		0			0
$989$	6.96370	−	23.4601i	0.221433	−	0.745987i
$990$		0			0
$991$	−33.9180	−	17.4859i	−1.07744	−	0.555459i	−0.174251	−	0.984701i	$-0.555751\pi$
$991$	−33.9180	−	17.4859i	−1.07744	−	0.555459i	−0.903190	+	0.429242i	$0.858781\pi$
$992$		0			0
$993$	−10.2964	−	4.70222i	−0.326747	−	0.149220i
$994$		0			0
$995$	1.21438	+	2.65913i	0.0384986	+	0.0843001i
$996$		0			0
$997$	−8.64226	−	10.9895i	−0.273703	−	0.348042i	0.629697	−	0.776841i	$-0.283179\pi$
$997$	−8.64226	−	10.9895i	−0.273703	−	0.348042i	−0.903400	+	0.428799i	$0.858937\pi$
$998$		0			0
$999$	−2.91461	−	8.42121i	−0.0922141	−	0.266435i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.bc.a.425.6	yes	320
7.3	odd	6	inner	644.2.bc.a.241.11	✓	320
23.21	odd	22	inner	644.2.bc.a.481.11	yes	320
161.136	even	66	inner	644.2.bc.a.297.6	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.bc.a.241.11	✓	320	7.3	odd	6	inner
644.2.bc.a.297.6	yes	320	161.136	even	66	inner
644.2.bc.a.425.6	yes	320	1.1	even	1	trivial
644.2.bc.a.481.11	yes	320	23.21	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)

\(f(q)\)	\(=\)	\(q+(-0.548786 - 1.37080i) q^{3} +(0.0440940 - 0.181758i) q^{5} +(1.60642 - 2.10224i) q^{7} +(0.593270 - 0.565681i) q^{9} +O(q^{10})\)	\(q+(-0.548786 - 1.37080i) q^{3} +(0.0440940 - 0.181758i) q^{5} +(1.60642 - 2.10224i) q^{7} +(0.593270 - 0.565681i) q^{9} +(-5.75170 - 0.273987i) q^{11} +(-0.543947 - 0.471333i) q^{13} +(-0.273352 + 0.0393021i) q^{15} +(2.18446 - 3.06764i) q^{17} +(-0.00719054 - 0.0100977i) q^{19} +(-3.76334 - 1.04841i) q^{21} +(-0.696512 + 4.74498i) q^{23} +(4.41309 + 2.27510i) q^{25} +(-5.13043 - 2.34299i) q^{27} +(-3.60596 - 7.89596i) q^{29} +(-1.42832 - 1.81626i) q^{31} +(2.78087 + 8.03481i) q^{33} +(-0.311265 - 0.384676i) q^{35} +(1.09032 + 1.14349i) q^{37} +(-0.347593 + 1.00431i) q^{39} +(-1.29661 - 4.41586i) q^{41} +(-5.05078 - 0.726193i) q^{43} +(-0.0766574 - 0.132775i) q^{45} +(-4.15451 - 2.39861i) q^{47} +(-1.83882 - 6.75416i) q^{49} +(-5.40393 - 1.31098i) q^{51} +(-9.92446 - 3.43489i) q^{53} +(-0.303415 + 1.03334i) q^{55} +(-0.00989589 + 0.0153983i) q^{57} +(0.0414137 - 0.214875i) q^{59} +(8.68512 + 3.47700i) q^{61} +(-0.236157 - 2.15592i) q^{63} +(-0.109653 + 0.0780837i) q^{65} +(2.85550 - 5.53889i) q^{67} +(6.88667 - 1.64920i) q^{69} +(0.637435 - 0.409655i) q^{71} +(1.16679 + 12.2192i) q^{73} +(0.696876 - 7.29801i) q^{75} +(-9.81565 + 11.6513i) q^{77} +(-0.308341 + 0.106718i) q^{79} +(-0.279250 + 5.86219i) q^{81} +(14.8144 + 4.34991i) q^{83} +(-0.461247 - 0.532307i) q^{85} +(-8.84490 + 9.27626i) q^{87} +(10.2698 + 8.07627i) q^{89} +(-1.86466 + 0.386348i) q^{91} +(-1.70589 + 2.95469i) q^{93} +(-0.00215240 + 0.000861690i) q^{95} +(11.4577 - 3.36428i) q^{97} +(-3.56730 + 3.09108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 20 q^{9}+O(q^{10}) \) 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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