LMFDB - Embedded newform 441.2.i.d.68.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(68,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

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

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

chi := DirichletCharacter("441.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.i (of order $6$, degree $2$, not 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.8
Character	$\chi$	$=$	441.68
Dual form			441.2.i.d.227.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.17820i q^{2} +(0.278055 + 1.70959i) q^{3} +0.611843 q^{4} +(2.16601 + 3.75164i) q^{5} +(2.01424 - 0.327604i) q^{6} -3.07728i q^{8} +(-2.84537 + 0.950717i) q^{9} +O(q^{10})$	\(q-1.17820i q^{2} +(0.278055 + 1.70959i) q^{3} +0.611843 q^{4} +(2.16601 + 3.75164i) q^{5} +(2.01424 - 0.327604i) q^{6} -3.07728i q^{8} +(-2.84537 + 0.950717i) q^{9} +(4.42019 - 2.55200i) q^{10} +(1.87238 + 1.08102i) q^{11} +(0.170126 + 1.04600i) q^{12} +(-2.25256 - 1.30052i) q^{13} +(-5.81148 + 4.74614i) q^{15} -2.40196 q^{16} +(-0.585576 - 1.01425i) q^{17} +(1.12014 + 3.35242i) q^{18} +(-2.09282 - 1.20829i) q^{19} +(1.32526 + 2.29541i) q^{20} +(1.27366 - 2.20604i) q^{22} +(3.16186 - 1.82550i) q^{23} +(5.26087 - 0.855651i) q^{24} +(-6.88321 + 11.9221i) q^{25} +(-1.53227 + 2.65397i) q^{26} +(-2.41650 - 4.60006i) q^{27} +(0.589262 - 0.340210i) q^{29} +(5.59191 + 6.84710i) q^{30} +6.55550i q^{31} -3.32456i q^{32} +(-1.32747 + 3.50158i) q^{33} +(-1.19499 + 0.689926i) q^{34} +(-1.74092 + 0.581689i) q^{36} +(2.55346 - 4.42272i) q^{37} +(-1.42361 + 2.46576i) q^{38} +(1.59701 - 4.21256i) q^{39} +(11.5448 - 6.66541i) q^{40} +(3.68473 - 6.38214i) q^{41} +(-2.12577 - 3.68194i) q^{43} +(1.14560 + 0.661414i) q^{44} +(-9.72985 - 8.61555i) q^{45} +(-2.15081 - 3.72531i) q^{46} +7.14314 q^{47} +(-0.667877 - 4.10636i) q^{48} +(14.0466 + 8.10980i) q^{50} +(1.57112 - 1.28311i) q^{51} +(-1.37821 - 0.795711i) q^{52} +(2.79976 - 1.61644i) q^{53} +(-5.41979 + 2.84713i) q^{54} +9.36601i q^{55} +(1.48376 - 3.91383i) q^{57} +(-0.400836 - 0.694269i) q^{58} +5.83621 q^{59} +(-3.55571 + 2.90389i) q^{60} -7.17805i q^{61} +7.72370 q^{62} -8.72092 q^{64} -11.2677i q^{65} +(4.12557 + 1.56403i) q^{66} +6.65363 q^{67} +(-0.358281 - 0.620560i) q^{68} +(4.00003 + 4.89789i) q^{69} +1.95976i q^{71} +(2.92562 + 8.75599i) q^{72} +(-10.3117 + 5.95345i) q^{73} +(-5.21085 - 3.00849i) q^{74} +(-22.2957 - 8.45245i) q^{75} +(-1.28048 - 0.739283i) q^{76} +(-4.96324 - 1.88160i) q^{78} -9.75404 q^{79} +(-5.20268 - 9.01130i) q^{80} +(7.19227 - 5.41029i) q^{81} +(-7.51944 - 4.34135i) q^{82} +(-0.796736 - 1.37999i) q^{83} +(2.53673 - 4.39374i) q^{85} +(-4.33806 + 2.50458i) q^{86} +(0.745466 + 0.912797i) q^{87} +(3.32660 - 5.76184i) q^{88} +(-3.04961 + 5.28207i) q^{89} +(-10.1508 + 11.4637i) q^{90} +(1.93456 - 1.11692i) q^{92} +(-11.2072 + 1.82279i) q^{93} -8.41605i q^{94} -10.4687i q^{95} +(5.68361 - 0.924409i) q^{96} +(2.36387 - 1.36478i) q^{97} +(-6.35537 - 1.29580i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) $ 48 * q - 48 * q^4 - 8 * q^9	$ 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.17820i		−	0.833114i	−0.909110	−	0.416557i	$-0.863237\pi$
$2$		−	1.17820i		−	0.833114i	0.909110	−	0.416557i	$-0.136763\pi$
$3$	0.278055	+	1.70959i	0.160535	+	0.987030i
$3$	0.278055	+	1.70959i	0.160535	+	0.987030i
$4$	0.611843			0.305921
$5$	2.16601	+	3.75164i	0.968670	+	1.67778i	0.699415	+	0.714716i	$0.253444\pi$
$5$	2.16601	+	3.75164i	0.968670	+	1.67778i	0.269254	+	0.963069i	$0.413223\pi$
$6$	2.01424	−	0.327604i	0.822308	−	0.133744i
$7$		0			0
$7$		0			0
$8$		−	3.07728i		−	1.08798i
$9$	−2.84537	+	0.950717i	−0.948457	+	0.316906i
$10$	4.42019	−	2.55200i	1.39779	−	0.807012i
$11$	1.87238	+	1.08102i	0.564545	+	0.325940i	0.754968	−	0.655762i	$-0.227653\pi$
$11$	1.87238	+	1.08102i	0.564545	+	0.325940i	−0.190423	+	0.981702i	$0.560986\pi$
$12$	0.170126	+	1.04600i	0.0491111	+	0.301954i
$13$	−2.25256	−	1.30052i	−0.624748	−	0.360698i	0.153967	−	0.988076i	$-0.450795\pi$
$13$	−2.25256	−	1.30052i	−0.624748	−	0.360698i	−0.778715	+	0.627378i	$0.784128\pi$
$14$		0			0
$15$	−5.81148	+	4.74614i	−1.50052	+	1.22545i
$16$	−2.40196			−0.600491
$17$	−0.585576	−	1.01425i	−0.142023	−	0.245991i	0.786235	−	0.617927i	$-0.212027\pi$
$17$	−0.585576	−	1.01425i	−0.142023	−	0.245991i	−0.928258	+	0.371936i	$0.878694\pi$
$18$	1.12014	+	3.35242i	0.264019	+	0.790173i
$19$	−2.09282	−	1.20829i	−0.480126	−	0.277201i	0.240343	−	0.970688i	$-0.422740\pi$
$19$	−2.09282	−	1.20829i	−0.480126	−	0.277201i	−0.720469	+	0.693487i	$0.756073\pi$
$20$	1.32526	+	2.29541i	0.296337	+	0.513270i
$21$		0			0
$22$	1.27366	−	2.20604i	0.271545	−	0.470330i
$23$	3.16186	−	1.82550i	0.659294	−	0.380644i	−0.132714	−	0.991154i	$-0.542369\pi$
$23$	3.16186	−	1.82550i	0.659294	−	0.380644i	0.792008	+	0.610511i	$0.209036\pi$
$24$	5.26087	−	0.855651i	1.07387	−	0.174659i
$25$	−6.88321	+	11.9221i	−1.37664	+	2.38441i
$26$	−1.53227	+	2.65397i	−0.300503	+	0.520486i
$27$	−2.41650	−	4.60006i	−0.465056	−	0.885281i
$28$		0			0
$29$	0.589262	−	0.340210i	0.109423	−	0.0631755i	−0.444290	−	0.895883i	$-0.646544\pi$
$29$	0.589262	−	0.340210i	0.109423	−	0.0631755i	0.553713	+	0.832708i	$0.313211\pi$
$30$	5.59191	+	6.84710i	1.02094	+	1.25010i
$31$			6.55550i			1.17740i	0.808350	+	0.588702i	$0.200361\pi$
$31$			6.55550i			1.17740i	−0.808350	+	0.588702i	$0.799639\pi$
$32$		−	3.32456i		−	0.587704i
$33$	−1.32747	+	3.50158i	−0.231083	+	0.609547i
$34$	−1.19499	+	0.689926i	−0.204939	+	0.118321i
$35$		0			0
$36$	−1.74092	+	0.581689i	−0.290153	+	0.0969482i
$37$	2.55346	−	4.42272i	0.419786	−	0.727090i	−0.576132	−	0.817357i	$-0.695439\pi$
$37$	2.55346	−	4.42272i	0.419786	−	0.727090i	0.995918	+	0.0902663i	$0.0287718\pi$
$38$	−1.42361	+	2.46576i	−0.230940	+	0.399999i
$39$	1.59701	−	4.21256i	0.255726	−	0.674550i
$40$	11.5448	−	6.66541i	1.82540	−	1.05389i
$41$	3.68473	−	6.38214i	0.575458	−	0.996723i	−0.420534	−	0.907277i	$-0.638157\pi$
$41$	3.68473	−	6.38214i	0.575458	−	0.996723i	0.995992	−	0.0894458i	$-0.0285096\pi$
$42$		0			0
$43$	−2.12577	−	3.68194i	−0.324176	−	0.561490i	0.657169	−	0.753743i	$-0.271754\pi$
$43$	−2.12577	−	3.68194i	−0.324176	−	0.561490i	−0.981345	+	0.192253i	$0.938420\pi$
$44$	1.14560	+	0.661414i	0.172706	+	0.0997120i
$45$	−9.72985	−	8.61555i	−1.45044	−	1.28433i
$46$	−2.15081	−	3.72531i	−0.317120	−	0.549267i
$47$	7.14314			1.04193			0.520967	−	0.853577i	$-0.325572\pi$
$47$	7.14314			1.04193			0.520967	+	0.853577i	$0.325572\pi$
$48$	−0.667877	−	4.10636i	−0.0963998	−	0.592703i
$49$		0			0
$50$	14.0466	+	8.10980i	1.98649	+	1.14690i
$51$	1.57112	−	1.28311i	0.220001	−	0.179671i
$52$	−1.37821	−	0.795711i	−0.191124	−	0.110345i
$53$	2.79976	−	1.61644i	0.384577	−	0.222036i	−0.295231	−	0.955426i	$-0.595397\pi$
$53$	2.79976	−	1.61644i	0.384577	−	0.222036i	0.679808	+	0.733390i	$0.262063\pi$
$54$	−5.41979	+	2.84713i	−0.737540	+	0.387445i
$55$			9.36601i			1.26291i
$56$		0			0
$57$	1.48376	−	3.91383i	0.196528	−	0.518399i
$58$	−0.400836	−	0.694269i	−0.0526324	−	0.0911619i
$59$	5.83621			0.759810			0.379905	−	0.925026i	$-0.375957\pi$
$59$	5.83621			0.759810			0.379905	+	0.925026i	$0.375957\pi$
$60$	−3.55571	+	2.90389i	−0.459041	+	0.374891i
$61$		−	7.17805i		−	0.919055i	−0.888163	−	0.459528i	$-0.848019\pi$
$61$		−	7.17805i		−	0.919055i	0.888163	−	0.459528i	$-0.151981\pi$
$62$	7.72370			0.980911
$63$		0			0
$64$	−8.72092			−1.09012
$65$		−	11.2677i		−	1.39759i
$66$	4.12557	+	1.56403i	0.507822	+	0.192519i
$67$	6.65363			0.812870			0.406435	−	0.913680i	$-0.366772\pi$
$67$	6.65363			0.812870			0.406435	+	0.913680i	$0.366772\pi$
$68$	−0.358281	−	0.620560i	−0.0434479	−	0.0752540i
$69$	4.00003	+	4.89789i	0.481547	+	0.589637i
$70$		0			0
$71$			1.95976i			0.232580i	0.993215	+	0.116290i	$0.0371003\pi$
$71$			1.95976i			0.232580i	−0.993215	+	0.116290i	$0.962900\pi$
$72$	2.92562	+	8.75599i	0.344788	+	1.03190i
$73$	−10.3117	+	5.95345i	−1.20689	+	0.696799i	−0.962079	−	0.272771i	$-0.912060\pi$
$73$	−10.3117	+	5.95345i	−1.20689	+	0.696799i	−0.244812	+	0.969570i	$0.578726\pi$
$74$	−5.21085	−	3.00849i	−0.605749	−	0.349729i
$75$	−22.2957	−	8.45245i	−2.57449	−	0.976005i
$76$	−1.28048	−	0.739283i	−0.146881	−	0.0848016i
$77$		0			0
$78$	−4.96324	−	1.88160i	−0.561977	−	0.213049i
$79$	−9.75404			−1.09742			−0.548708	−	0.836014i	$-0.684880\pi$
$79$	−9.75404			−1.09742			−0.548708	+	0.836014i	$0.684880\pi$
$80$	−5.20268	−	9.01130i	−0.581677	−	1.00749i
$81$	7.19227	−	5.41029i	0.799141	−	0.601143i
$82$	−7.51944	−	4.34135i	−0.830384	−	0.479422i
$83$	−0.796736	−	1.37999i	−0.0874531	−	0.151473i	0.818981	−	0.573821i	$-0.194539\pi$
$83$	−0.796736	−	1.37999i	−0.0874531	−	0.151473i	−0.906434	+	0.422348i	$0.861206\pi$
$84$		0			0
$85$	2.53673	−	4.39374i	0.275147	−	0.476568i
$86$	−4.33806	+	2.50458i	−0.467785	+	0.270076i
$87$	0.745466	+	0.912797i	0.0799224	+	0.0978621i
$88$	3.32660	−	5.76184i	0.354617	−	0.614214i
$89$	−3.04961	+	5.28207i	−0.323258	+	0.559899i	−0.981158	−	0.193206i	$-0.938111\pi$
$89$	−3.04961	+	5.28207i	−0.323258	+	0.559899i	0.657901	+	0.753105i	$0.271445\pi$
$90$	−10.1508	+	11.4637i	−1.06999	+	1.20838i
$91$		0			0
$92$	1.93456	−	1.11692i	0.201692	−	0.116447i
$93$	−11.2072	+	1.82279i	−1.16213	+	0.189014i
$94$		−	8.41605i		−	0.868049i
$95$		−	10.4687i		−	1.07406i
$96$	5.68361	−	0.924409i	0.580081	−	0.0943471i
$97$	2.36387	−	1.36478i	0.240014	−	0.138572i	−0.375169	−	0.926956i	$-0.622415\pi$
$97$	2.36387	−	1.36478i	0.240014	−	0.138572i	0.615183	+	0.788384i	$0.289082\pi$
$98$		0			0
$99$	−6.35537	−	1.29580i	−0.638738	−	0.130233i
$100$	−4.21144	+	7.29443i	−0.421144	+	0.729443i
$101$	−7.99849	+	13.8538i	−0.795880	+	1.37850i	0.126400	+	0.991979i	$0.459658\pi$
$101$	−7.99849	+	13.8538i	−0.795880	+	1.37850i	−0.922279	+	0.386524i	$0.873676\pi$
$102$	−1.51176	−	1.85110i	−0.149687	−	0.183286i
$103$	−2.61251	+	1.50834i	−0.257419	+	0.148621i	−0.623156	−	0.782097i	$-0.714150\pi$
$103$	−2.61251	+	1.50834i	−0.257419	+	0.148621i	0.365738	+	0.930718i	$0.380817\pi$
$104$	−4.00205	+	6.93175i	−0.392433	+	0.679714i
$105$		0			0
$106$	−1.90450	−	3.29868i	−0.184981	−	0.320397i
$107$	10.2611	+	5.92422i	0.991973	+	0.572716i	0.905864	−	0.423569i	$-0.139223\pi$
$107$	10.2611	+	5.92422i	0.991973	+	0.572716i	0.0861099	+	0.996286i	$0.472556\pi$
$108$	−1.47852	−	2.81451i	−0.142271	−	0.270826i
$109$	−3.58078	−	6.20210i	−0.342977	−	0.594053i	0.642007	−	0.766699i	$-0.278102\pi$
$109$	−3.58078	−	6.20210i	−0.342977	−	0.594053i	−0.984984	+	0.172645i	$0.944769\pi$
$110$	11.0350			1.05215
$111$	8.27102	+	3.13560i	0.785051	+	0.297618i
$112$		0			0
$113$	2.46102	+	1.42087i	0.231514	+	0.133664i	0.611270	−	0.791422i	$-0.290659\pi$
$113$	2.46102	+	1.42087i	0.231514	+	0.133664i	−0.379756	+	0.925086i	$0.623992\pi$
$114$	−4.61127	−	1.74816i	−0.431885	−	0.163731i
$115$	13.6973	+	7.90812i	1.27728	+	0.737436i
$116$	0.360535	−	0.208155i	0.0334749	−	0.0193267i
$117$	7.64579	+	1.55890i	0.706854	+	0.144121i
$118$		−	6.87623i		−	0.633008i
$119$		0			0
$120$	14.6052	+	17.8835i	1.33327	+	1.63254i
$121$	−3.16279	−	5.47811i	−0.287526	−	0.498010i
$122$	−8.45719			−0.765678
$123$	11.9354	+	4.52478i	1.07618	+	0.407986i
$124$			4.01094i			0.360193i
$125$	−37.9763			−3.39670
$126$		0			0
$127$	18.5344			1.64466			0.822332	−	0.569009i	$-0.192673\pi$
$127$	18.5344			1.64466			0.822332	+	0.569009i	$0.192673\pi$
$128$			3.62589i			0.320486i
$129$	5.70351	−	4.65796i	0.502166	−	0.410111i
$130$	−13.2757			−1.16435
$131$	−3.35221	−	5.80619i	−0.292884	−	0.507289i	0.681607	−	0.731719i	$-0.261282\pi$
$131$	−3.35221	−	5.80619i	−0.292884	−	0.507289i	−0.974490	+	0.224429i	$0.927948\pi$
$132$	−0.812205	+	2.14242i	−0.0706933	+	0.186474i
$133$		0			0
$134$		−	7.83931i		−	0.677214i
$135$	12.0236	−	19.0296i	1.03483	−	1.63781i
$136$	−3.12112	+	1.80198i	−0.267634	+	0.154518i
$137$	−11.8181	−	6.82316i	−1.00969	−	0.582942i	−0.0985856	−	0.995129i	$-0.531432\pi$
$137$	−11.8181	−	6.82316i	−1.00969	−	0.582942i	−0.911099	+	0.412187i	$0.864765\pi$
$138$	5.77070	−	4.71284i	0.491234	−	0.401183i
$139$	−7.74126	−	4.46942i	−0.656605	−	0.379091i	0.134377	−	0.990930i	$-0.457097\pi$
$139$	−7.74126	−	4.46942i	−0.656605	−	0.379091i	−0.790982	+	0.611839i	$0.790430\pi$
$140$		0			0
$141$	1.98618	+	12.2118i	0.167267	+	1.02842i
$142$	2.30899			0.193766
$143$	−2.81177	−	4.87013i	−0.235132	−	0.407261i
$144$	6.83448	−	2.28359i	0.569540	−	0.190299i
$145$	2.55269	+	1.47380i	0.211990	+	0.122392i
$146$	7.01436	+	12.1492i	0.580513	+	1.00548i
$147$		0			0
$148$	1.56231	−	2.70601i	0.128421	−	0.222432i
$149$	3.29003	−	1.89950i	0.269530	−	0.155613i	−0.359144	−	0.933282i	$-0.616931\pi$
$149$	3.29003	−	1.89950i	0.269530	−	0.155613i	0.628674	+	0.777669i	$0.283598\pi$
$150$	−9.95868	+	26.2688i	−0.813123	+	2.14484i
$151$	1.91083	−	3.30965i	0.155501	−	0.269336i	−0.777740	−	0.628586i	$-0.783634\pi$
$151$	1.91083	−	3.30965i	0.155501	−	0.269336i	0.933241	+	0.359250i	$0.116967\pi$
$152$	−3.71824	+	6.44018i	−0.301589	+	0.522368i
$153$	2.63044	+	2.32919i	0.212659	+	0.188304i
$154$		0			0
$155$	−24.5939	+	14.1993i	−1.97543	+	1.14051i
$156$	0.977119	−	2.57742i	0.0782321	−	0.206359i
$157$		−	21.4868i		−	1.71483i	−0.514622	−	0.857417i	$-0.672068\pi$
$157$		−	21.4868i		−	1.71483i	0.514622	−	0.857417i	$-0.327932\pi$
$158$			11.4922i			0.914272i
$159$	3.54194	+	4.33698i	0.280894	+	0.343945i
$160$	12.4725	−	7.20102i	0.986041	−	0.569291i
$161$		0			0
$162$	−6.37441	−	8.47394i	−0.500821	−	0.665776i
$163$	−6.25875	+	10.8405i	−0.490223	+	0.849092i	−0.999937	−	0.0112525i	$-0.996418\pi$
$163$	−6.25875	+	10.8405i	−0.490223	+	0.849092i	0.509713	+	0.860344i	$0.329751\pi$
$164$	2.25448	−	3.90487i	0.176045	−	0.304919i
$165$	−16.0120	+	2.60426i	−1.24653	+	0.202742i
$166$	−1.62590	+	0.938715i	−0.126194	+	0.0728584i
$167$	7.70819	−	13.3510i	0.596477	−	1.03313i	−0.396859	−	0.917880i	$-0.629900\pi$
$167$	7.70819	−	13.3510i	0.596477	−	1.03313i	0.993337	−	0.115250i	$-0.0367668\pi$
$168$		0			0
$169$	−3.11731	−	5.39935i	−0.239793	−	0.415334i
$170$	−5.17671	−	2.98878i	−0.397036	−	0.229229i
$171$	7.10359	+	1.44835i	0.543225	+	0.110758i
$172$	−1.30063	−	2.25277i	−0.0991725	−	0.171772i
$173$	−8.61474			−0.654967			−0.327483	−	0.944857i	$-0.606201\pi$
$173$	−8.61474			−0.654967			−0.327483	+	0.944857i	$0.606201\pi$
$174$	1.07546	−	0.878309i	0.0815302	−	0.0665844i
$175$		0			0
$176$	−4.49739	−	2.59657i	−0.339004	−	0.195724i
$177$	1.62279	+	9.97750i	0.121976	+	0.749955i
$178$	6.22334	+	3.59305i	0.466459	+	0.269310i
$179$	−16.5744	+	9.56922i	−1.23883	+	0.715237i	−0.968854	−	0.247631i	$-0.920348\pi$
$179$	−16.5744	+	9.56922i	−1.23883	+	0.715237i	−0.269972	+	0.962868i	$0.587015\pi$
$180$	−5.95314	−	5.27136i	−0.443721	−	0.392904i
$181$		−	7.69817i		−	0.572200i	−0.958200	−	0.286100i	$-0.907641\pi$
$181$		−	7.69817i		−	0.572200i	0.958200	−	0.286100i	$-0.0923590\pi$
$182$		0			0
$183$	12.2715	−	1.99589i	0.907135	−	0.147541i
$184$	−5.61758	−	9.72993i	−0.414133	−	0.717300i
$185$	22.1233			1.62654
$186$	2.14761	+	13.2043i	0.157471	+	0.968189i
$187$		−	2.53208i		−	0.185164i
$188$	4.37047			0.318750
$189$		0			0
$190$	−12.3342			−0.894817
$191$			18.6141i			1.34687i	0.739248	+	0.673433i	$0.235181\pi$
$191$			18.6141i			1.34687i	−0.739248	+	0.673433i	$0.764819\pi$
$192$	−2.42489	−	14.9092i	−0.175002	−	1.07598i
$193$	18.1144			1.30390			0.651952	−	0.758260i	$-0.273950\pi$
$193$	18.1144			1.30390			0.651952	+	0.758260i	$0.273950\pi$
$194$	−1.60799	−	2.78511i	−0.115447	−	0.199959i
$195$	19.2632	−	3.13305i	1.37946	−	0.224362i
$196$		0			0
$197$		−	16.5945i		−	1.18231i	−0.806559	−	0.591154i	$-0.798672\pi$
$197$		−	16.5945i		−	1.18231i	0.806559	−	0.591154i	$-0.201328\pi$
$198$	−1.52671	+	7.48790i	−0.108499	+	0.532142i
$199$	−2.35461	+	1.35943i	−0.166914	+	0.0963677i	−0.581130	−	0.813811i	$-0.697389\pi$
$199$	−2.35461	+	1.35943i	−0.166914	+	0.0963677i	0.414216	+	0.910179i	$0.364056\pi$
$200$	36.6875	+	21.1815i	2.59420	+	1.49776i
$201$	1.85007	+	11.3750i	0.130494	+	0.802328i
$202$	16.3225	+	9.42383i	1.14845	+	0.663058i
$203$		0			0
$204$	0.961279	−	0.785061i	0.0673030	−	0.0549653i
$205$	31.9247			2.22972
$206$	1.77712	+	3.07807i	0.123818	+	0.214459i
$207$	−7.26114	+	8.20027i	−0.504684	+	0.569958i
$208$	5.41057	+	3.12379i	0.375155	+	0.216596i
$209$	−2.61237	−	4.52476i	−0.180702	−	0.312984i
$210$		0			0
$211$	−13.9445	+	24.1526i	−0.959979	+	1.66273i	−0.237440	+	0.971402i	$0.576308\pi$
$211$	−13.9445	+	24.1526i	−0.959979	+	1.66273i	−0.722539	+	0.691330i	$0.757025\pi$
$212$	1.71301	−	0.989010i	0.117650	−	0.0679255i
$213$	−3.35037	+	0.544920i	−0.229564	+	0.0373373i
$214$	6.97992	−	12.0896i	0.477138	−	0.826427i
$215$	9.20887	−	15.9502i	0.628040	−	1.08780i
$216$	−14.1556	+	7.43624i	−0.963169	+	0.505972i
$217$		0			0
$218$	−7.30732	+	4.21888i	−0.494914	+	0.285739i
$219$	−13.0452	−	15.9733i	−0.881510	−	1.07938i
$220$			5.73052i			0.386352i
$221$			3.04621i			0.204910i
$222$	3.69436	−	9.74492i	0.247950	−	0.654036i
$223$	−6.64349	+	3.83562i	−0.444881	+	0.256852i	−0.705666	−	0.708545i	$-0.749352\pi$
$223$	−6.64349	+	3.83562i	−0.444881	+	0.256852i	0.260785	+	0.965397i	$0.416019\pi$
$224$		0			0
$225$	8.25076	−	40.4667i	0.550051	−	2.69778i
$226$	1.67407	−	2.89958i	0.111358	−	0.192877i
$227$	−1.16439	+	2.01677i	−0.0772829	+	0.133858i	−0.902077	−	0.431576i	$-0.857958\pi$
$227$	−1.16439	+	2.01677i	−0.0772829	+	0.133858i	0.824794	+	0.565434i	$0.191291\pi$
$228$	0.907826	−	2.39465i	0.0601223	−	0.158589i
$229$	−10.3653	+	5.98443i	−0.684961	+	0.395463i	−0.801722	−	0.597698i	$-0.796082\pi$
$229$	−10.3653	+	5.98443i	−0.684961	+	0.395463i	0.116760	+	0.993160i	$0.462749\pi$
$230$	9.31735	−	16.1381i	0.614368	−	1.06412i
$231$		0			0
$232$	−1.04692	−	1.81332i	−0.0687337	−	0.119050i
$233$	2.18913	+	1.26390i	0.143415	+	0.0828007i	0.569991	−	0.821651i	$-0.306947\pi$
$233$	2.18913	+	1.26390i	0.143415	+	0.0828007i	−0.426576	+	0.904452i	$0.640280\pi$
$234$	1.83670	−	9.00828i	0.120069	−	0.588890i
$235$	15.4721	+	26.7985i	1.00929	+	1.74814i
$236$	3.57084			0.232442
$237$	−2.71216	−	16.6754i	−0.176174	−	1.08318i
$238$		0			0
$239$	17.4587	+	10.0798i	1.12931	+	0.652006i	0.943761	−	0.330630i	$-0.107261\pi$
$239$	17.4587	+	10.0798i	1.12931	+	0.652006i	0.185546	+	0.982636i	$0.440595\pi$
$240$	13.9590	−	11.4001i	0.901048	−	0.735871i
$241$	−18.1254	−	10.4647i	−1.16756	−	0.674091i	−0.214455	−	0.976734i	$-0.568798\pi$
$241$	−18.1254	−	10.4647i	−1.16756	−	0.674091i	−0.953104	+	0.302643i	$0.902131\pi$
$242$	−6.45432	+	3.72640i	−0.414899	+	0.239542i
$243$	11.2492	+	10.7915i	0.721636	+	0.692272i
$244$		−	4.39184i		−	0.281159i
$245$		0			0
$246$	5.33110	−	14.0623i	0.339899	−	0.896578i
$247$	3.14280	+	5.44349i	0.199972	+	0.346361i
$248$	20.1731			1.28099
$249$	2.13767	−	1.74580i	0.135469	−	0.110636i
$250$			44.7437i			2.82984i
$251$	25.5747			1.61426			0.807130	−	0.590374i	$-0.201020\pi$
$251$	25.5747			1.61426			0.807130	+	0.590374i	$0.201020\pi$
$252$		0			0
$253$	7.89363			0.496268
$254$		−	21.8373i		−	1.37019i
$255$	8.21683	+	3.11506i	0.514558	+	0.195072i
$256$	−13.1698			−0.823114
$257$	−5.93725	−	10.2836i	−0.370355	−	0.641474i	0.619265	−	0.785182i	$-0.287431\pi$
$257$	−5.93725	−	10.2836i	−0.370355	−	0.641474i	−0.989620	+	0.143708i	$0.954097\pi$
$258$	−5.48801	−	6.71988i	−0.341669	−	0.418361i
$259$		0			0
$260$		−	6.89408i		−	0.427553i
$261$	−1.35322	+	1.52825i	−0.0837625	+	0.0945961i
$262$	−6.84086	+	3.94957i	−0.422630	+	0.244005i
$263$	−19.3705	−	11.1836i	−1.19444	−	0.689608i	−0.235127	−	0.971965i	$-0.575550\pi$
$263$	−19.3705	−	11.1836i	−1.19444	−	0.689608i	−0.959309	+	0.282357i	$0.908884\pi$
$264$	10.7753	+	4.08500i	0.663176	+	0.251414i
$265$	12.1286	+	7.00247i	0.745056	+	0.430158i
$266$		0			0
$267$	−9.87812	−	3.74486i	−0.604531	−	0.229182i
$268$	4.07098			0.248674
$269$	2.11335	+	3.66043i	0.128853	+	0.223180i	0.923232	−	0.384242i	$-0.125537\pi$
$269$	2.11335	+	3.66043i	0.128853	+	0.223180i	−0.794379	+	0.607422i	$0.792204\pi$
$270$	−22.4207	−	14.1662i	−1.36448	−	0.862128i
$271$	19.3941	+	11.1972i	1.17811	+	0.680179i	0.955576	−	0.294746i	$-0.0952352\pi$
$271$	19.3941	+	11.1972i	1.17811	+	0.680179i	0.222530	+	0.974926i	$0.428568\pi$
$272$	1.40653	+	2.43619i	0.0852836	+	0.147715i
$273$		0			0
$274$	−8.03905	+	13.9240i	−0.485657	+	0.841183i
$275$	−25.7760	+	14.8818i	−1.55435	+	0.897405i
$276$	2.44739	+	2.99674i	0.147315	+	0.180382i
$277$	−5.69230	+	9.85935i	−0.342017	+	0.592391i	−0.984807	−	0.173651i	$-0.944443\pi$
$277$	−5.69230	+	9.85935i	−0.342017	+	0.592391i	0.642790	+	0.766042i	$0.277777\pi$
$278$	−5.26587	+	9.12076i	−0.315826	+	0.547027i
$279$	−6.23243	−	18.6528i	−0.373126	−	1.11672i
$280$		0			0
$281$	−0.702700	+	0.405704i	−0.0419196	+	0.0242023i	−0.520813	−	0.853671i	$-0.674371\pi$
$281$	−0.702700	+	0.405704i	−0.0419196	+	0.0242023i	0.478894	+	0.877873i	$0.341038\pi$
$282$	14.3880	−	2.34012i	0.856791	−	0.139352i
$283$			18.3297i			1.08959i	0.838570	+	0.544794i	$0.183392\pi$
$283$			18.3297i			1.08959i	−0.838570	+	0.544794i	$0.816608\pi$
$284$			1.19906i			0.0711513i
$285$	17.8971	−	2.91087i	1.06013	−	0.172425i
$286$	−5.73799	+	3.31283i	−0.339294	+	0.195892i
$287$		0			0
$288$	3.16071	+	9.45959i	0.186247	+	0.557412i
$289$	7.81420	−	13.5346i	0.459659	−	0.796153i
$290$	1.73643	−	3.00759i	0.101967	−	0.176612i
$291$	2.99049	+	3.66175i	0.175306	+	0.214656i
$292$	−6.30913	+	3.64258i	−0.369214	+	0.213166i
$293$	−6.23639	+	10.8017i	−0.364334	+	0.631044i	−0.988669	−	0.150112i	$-0.952037\pi$
$293$	−6.23639	+	10.8017i	−0.364334	+	0.631044i	0.624335	+	0.781156i	$0.285370\pi$
$294$		0			0
$295$	12.6413	+	21.8954i	0.736004	+	1.27480i
$296$	−13.6099	−	7.85769i	−0.791061	−	0.456719i
$297$	0.448138	−	11.2254i	0.0260036	−	0.651361i
$298$	−2.23800	−	3.87632i	−0.129644	−	0.224549i
$299$	−9.49639			−0.549190
$300$	−13.6415	−	5.17157i	−0.787590	−	0.298581i
$301$		0			0
$302$	−3.89943	−	2.25134i	−0.224387	−	0.129550i
$303$	−25.9083	−	9.82200i	−1.48839	−	0.564259i
$304$	5.02688	+	2.90227i	0.288311	+	0.166457i
$305$	26.9295	−	15.5477i	1.54198	−	0.890261i
$306$	2.74426	−	3.09919i	0.156879	−	0.177169i
$307$			21.3241i			1.21703i	0.793543	+	0.608514i	$0.208234\pi$
$307$			21.3241i			1.21703i	−0.793543	+	0.608514i	$0.791766\pi$
$308$		0			0
$309$	−3.30505	−	4.04692i	−0.188018	−	0.230221i
$310$	16.7296	+	28.9765i	0.950178	+	1.64576i
$311$	−7.84187			−0.444672			−0.222336	−	0.974970i	$-0.571368\pi$
$311$	−7.84187			−0.444672			−0.222336	+	0.974970i	$0.571368\pi$
$312$	−12.9632	−	4.91444i	−0.733897	−	0.278225i
$313$		−	9.90263i		−	0.559730i	−0.960039	−	0.279865i	$-0.909710\pi$
$313$		−	9.90263i		−	0.559730i	0.960039	−	0.279865i	$-0.0902897\pi$
$314$	−25.3158			−1.42865
$315$		0			0
$316$	−5.96794			−0.335723
$317$			24.0591i			1.35129i	0.737225	+	0.675647i	$0.236136\pi$
$317$			24.0591i			1.35129i	−0.737225	+	0.675647i	$0.763864\pi$
$318$	5.10983	−	4.17312i	0.286545	−	0.234017i
$319$	1.47110			0.0823657
$320$	−18.8896	−	32.7178i	−1.05596	−	1.82898i
$321$	−7.27483	+	19.1894i	−0.406042	+	1.07105i
$322$		0			0
$323$			2.83018i			0.157476i
$324$	4.40054	−	3.31024i	0.244474	−	0.183902i
$325$	31.0097	−	17.9034i	1.72011	−	0.993104i
$326$	12.7723	+	7.37407i	0.707390	+	0.408412i
$327$	9.60737	−	7.84618i	0.531289	−	0.433895i
$328$	−19.6396	−	11.3389i	−1.08442	−	0.626088i
$329$		0			0
$330$	3.06835	+	18.8654i	0.168907	+	1.03850i
$331$	−9.07371			−0.498736			−0.249368	−	0.968409i	$-0.580223\pi$
$331$	−9.07371			−0.498736			−0.249368	+	0.968409i	$0.580223\pi$
$332$	−0.487477	−	0.844335i	−0.0267538	−	0.0463389i
$333$	−3.06078	+	15.0119i	−0.167730	+	0.822647i
$334$	−15.7301	−	9.08179i	−0.860714	−	0.496934i
$335$	14.4118	+	24.9620i	0.787403	+	1.36382i
$336$		0			0
$337$	4.02012	−	6.96304i	0.218990	−	0.379301i	−0.735510	−	0.677514i	$-0.763057\pi$
$337$	4.02012	−	6.96304i	0.218990	−	0.379301i	0.954499	+	0.298213i	$0.0963906\pi$
$338$	−6.36152	+	3.67282i	−0.346021	+	0.199775i
$339$	−1.74481	+	4.60241i	−0.0947648	+	0.249969i
$340$	1.55208	−	2.68828i	0.0841733	−	0.145792i
$341$	−7.08663	+	12.2744i	−0.383763	+	0.664696i
$342$	1.70645	−	8.36946i	0.0922743	−	0.452568i
$343$		0			0
$344$	−11.3303	+	6.54157i	−0.610891	+	0.352698i
$345$	−9.71102	+	25.6155i	−0.522824	+	1.37909i
$346$			10.1499i			0.545662i
$347$			35.3736i			1.89896i	0.313832	+	0.949478i	$0.398387\pi$
$347$			35.3736i			1.89896i	−0.313832	+	0.949478i	$0.601613\pi$
$348$	0.456108	+	0.558488i	0.0244500	+	0.0299381i
$349$	−21.1868	+	12.2322i	−1.13411	+	0.654776i	−0.944964	−	0.327174i	$-0.893904\pi$
$349$	−21.1868	+	12.2322i	−1.13411	+	0.654776i	−0.189141	+	0.981950i	$0.560570\pi$
$350$		0			0
$351$	−0.539130	+	13.5046i	−0.0287766	+	0.720823i
$352$	3.59391	−	6.22484i	0.191556	−	0.331785i
$353$	0.485949	−	0.841688i	0.0258644	−	0.0447985i	−0.852803	−	0.522232i	$-0.825100\pi$
$353$	0.485949	−	0.841688i	0.0258644	−	0.0447985i	0.878668	+	0.477433i	$0.158433\pi$
$354$	11.7555	−	1.91197i	0.624798	−	0.101620i
$355$	−7.35231	+	4.24486i	−0.390220	+	0.225294i
$356$	−1.86588	+	3.23180i	−0.0988914	+	0.171285i
$357$		0			0
$358$	11.2745	+	19.5279i	0.595874	+	1.03208i
$359$	−13.7879	−	7.96048i	−0.727700	−	0.420138i	0.0898801	−	0.995953i	$-0.471352\pi$
$359$	−13.7879	−	7.96048i	−0.727700	−	0.420138i	−0.817580	+	0.575815i	$0.804685\pi$
$360$	−26.5124	+	29.9414i	−1.39733	+	1.57805i
$361$	−6.58007	−	11.3970i	−0.346319	−	0.599843i
$362$	−9.06999			−0.476708
$363$	8.48588	−	6.93028i	0.445393	−	0.363745i
$364$		0			0
$365$	−44.6704	−	25.7905i	−2.33816	−	1.34994i
$366$	−2.35156	−	14.4583i	−0.122918	−	0.755747i
$367$	−21.3983	−	12.3543i	−1.11698	−	0.644891i	−0.176355	−	0.984327i	$-0.556431\pi$
$367$	−21.3983	−	12.3543i	−1.11698	−	0.644891i	−0.940629	+	0.339435i	$0.889764\pi$
$368$	−7.59468	+	4.38479i	−0.395900	+	0.228573i
$369$	−4.41681	+	21.6627i	−0.229930	+	1.12771i
$370$		−	26.0657i		−	1.35509i
$371$		0			0
$372$	−6.85704	+	1.11526i	−0.355521	+	0.0578235i
$373$	4.71810	+	8.17200i	0.244294	+	0.423130i	0.961933	−	0.273286i	$-0.0881104\pi$
$373$	4.71810	+	8.17200i	0.244294	+	0.423130i	−0.717639	+	0.696416i	$0.754777\pi$
$374$	−2.98330			−0.154263
$375$	−10.5595	−	64.9237i	−0.545290	−	3.35265i
$376$		−	21.9814i		−	1.13360i
$377$	−1.76980			−0.0911492
$378$		0			0
$379$	20.8031			1.06858			0.534292	−	0.845300i	$-0.320578\pi$
$379$	20.8031			1.06858			0.534292	+	0.845300i	$0.320578\pi$
$380$		−	6.40518i		−	0.328579i
$381$	5.15358	+	31.6862i	0.264026	+	1.62333i
$382$	21.9311			1.12209
$383$	3.23008	+	5.59467i	0.165050	+	0.285874i	0.936673	−	0.350205i	$-0.113888\pi$
$383$	3.23008	+	5.59467i	0.165050	+	0.285874i	−0.771623	+	0.636080i	$0.780555\pi$
$384$	−6.19876	+	1.00819i	−0.316329	+	0.0514492i
$385$		0			0
$386$		−	21.3424i		−	1.08630i
$387$	9.54908	+	8.45547i	0.485407	+	0.429816i
$388$	1.44632	−	0.835031i	0.0734255	−	0.0423923i
$389$	0.0445846	+	0.0257409i	0.00226053	+	0.00130512i	0.501130	−	0.865372i	$-0.332918\pi$
$389$	0.0445846	+	0.0257409i	0.00226053	+	0.00130512i	−0.498869	+	0.866677i	$0.666251\pi$
$390$	−3.69136	−	22.6959i	−0.186919	−	1.14925i
$391$	−3.70303	−	2.13794i	−0.187270	−	0.108120i
$392$		0			0
$393$	8.99409	−	7.34533i	0.453692	−	0.370523i
$394$	−19.5516			−0.984997
$395$	−21.1274	−	36.5937i	−1.06303	−	1.84123i
$396$	−3.88849	−	0.792824i	−0.195404	−	0.0398409i
$397$	−11.0099	−	6.35655i	−0.552569	−	0.319026i	0.197588	−	0.980285i	$-0.436689\pi$
$397$	−11.0099	−	6.35655i	−0.552569	−	0.319026i	−0.750158	+	0.661259i	$0.770022\pi$
$398$	1.60169	+	2.77420i	0.0802853	+	0.139058i
$399$		0			0
$400$	16.5332	−	28.6364i	0.826660	−	1.43182i
$401$	2.19725	−	1.26858i	0.109725	−	0.0633500i	−0.444133	−	0.895961i	$-0.646488\pi$
$401$	2.19725	−	1.26858i	0.109725	−	0.0633500i	0.553858	+	0.832611i	$0.313155\pi$
$402$	13.4020	−	2.17976i	0.668430	−	0.108716i
$403$	8.52554	−	14.7667i	0.424687	−	0.735580i
$404$	−4.89382	+	8.47634i	−0.243477	+	0.421714i
$405$	35.8760	+	15.2641i	1.78269	+	0.758478i
$406$		0			0
$407$	9.56210	−	5.52068i	0.473976	−	0.273650i
$408$	−3.94848	−	4.83478i	−0.195479	−	0.239357i
$409$		−	0.0572333i		−	0.00283000i	−0.999999	−	0.00141500i	$-0.999550\pi$
$409$		−	0.0572333i		−	0.00283000i	0.999999	−	0.00141500i	$-0.000450409\pi$
$410$		−	37.6137i		−	1.85761i
$411$	8.37871	−	22.1012i	0.413291	−	1.09017i
$412$	−1.59845	+	0.922864i	−0.0787499	+	0.0454663i
$413$		0			0
$414$	9.66157	+	8.55508i	0.474840	+	0.420459i
$415$	3.45148	−	5.97813i	0.169426	−	0.293455i
$416$	−4.32364	+	7.48876i	−0.211984	+	0.367167i
$417$	5.48836	−	14.4771i	0.268766	−	0.708947i
$418$	−5.33108	+	3.07790i	−0.260752	+	0.150545i
$419$	−3.08007	+	5.33484i	−0.150471	+	0.260624i	−0.931401	−	0.363995i	$-0.881412\pi$
$419$	−3.08007	+	5.33484i	−0.150471	+	0.260624i	0.780930	+	0.624619i	$0.214746\pi$
$420$		0			0
$421$	15.0693	+	26.1007i	0.734431	+	1.27207i	0.954973	+	0.296694i	$0.0958842\pi$
$421$	15.0693	+	26.1007i	0.734431	+	1.27207i	−0.220542	+	0.975378i	$0.570783\pi$
$422$	28.4566	+	16.4294i	1.38525	+	0.799772i
$423$	−20.3249	+	6.79110i	−0.988229	+	0.330195i
$424$	−4.97424	−	8.61564i	−0.241571	−	0.418413i
$425$	16.1226			0.782059
$426$	0.642025	+	3.94741i	0.0311062	+	0.191253i
$427$		0			0
$428$	6.27815	+	3.62469i	0.303466	+	0.175206i
$429$	7.54408	−	6.16113i	0.364232	−	0.297462i
$430$	−18.7926	−	10.8499i	−0.906258	−	0.523228i
$431$	6.99003	−	4.03570i	0.336698	−	0.194393i	−0.322113	−	0.946701i	$-0.604393\pi$
$431$	6.99003	−	4.03570i	0.336698	−	0.194393i	0.658811	+	0.752309i	$0.271060\pi$
$432$	5.80435	+	11.0492i	0.279262	+	0.531603i
$433$			28.4938i			1.36933i	0.728860	+	0.684663i	$0.240051\pi$
$433$			28.4938i			1.36933i	−0.728860	+	0.684663i	$0.759949\pi$
$434$		0			0
$435$	−1.80980	+	4.77385i	−0.0867731	+	0.228889i
$436$	−2.19088	−	3.79471i	−0.104924	−	0.181734i
$437$	−8.82295			−0.422059
$438$	−18.8198	+	15.3698i	−0.899244	+	0.734398i
$439$		−	2.04460i		−	0.0975832i	−0.998809	−	0.0487916i	$-0.984463\pi$
$439$		−	2.04460i		−	0.0975832i	0.998809	−	0.0487916i	$-0.0155370\pi$
$440$	28.8218			1.37402
$441$		0			0
$442$	3.58904			0.170713
$443$		−	24.4016i		−	1.15935i	−0.814846	−	0.579677i	$-0.803179\pi$
$443$		−	24.4016i		−	1.15935i	0.814846	−	0.579677i	$-0.196821\pi$
$444$	5.06056	+	1.91849i	0.240164	+	0.0910476i
$445$	−26.4219			−1.25252
$446$	4.51913	+	7.82737i	0.213987	+	0.370637i
$447$	4.16217	+	5.09643i	0.196864	+	0.241053i
$448$		0			0
$449$			0.293539i			0.0138529i	0.999976	+	0.00692647i	$0.00220478\pi$
$449$			0.293539i			0.0138529i	−0.999976	+	0.00692647i	$0.997795\pi$
$450$	−47.6779	−	9.72106i	−2.24756	−	0.458255i
$451$	13.7984	−	7.96654i	0.649744	−	0.375130i
$452$	1.50576	+	0.869351i	0.0708250	+	0.0408908i
$453$	6.18945	+	2.34646i	0.290806	+	0.110246i
$454$	2.37616	+	1.37188i	0.111519	+	0.0643855i
$455$		0			0
$456$	−12.0439	−	4.56593i	−0.564008	−	0.213819i
$457$	16.5494			0.774148			0.387074	−	0.922049i	$-0.373486\pi$
$457$	16.5494			0.774148			0.387074	+	0.922049i	$0.373486\pi$
$458$	7.05087	+	12.2125i	0.329465	+	0.570651i
$459$	−3.25055	+	5.14462i	−0.151723	+	0.240130i
$460$	8.38057	+	4.83852i	0.390746	+	0.225597i
$461$	−10.0560	−	17.4175i	−0.468354	−	0.811213i	0.530992	−	0.847377i	$-0.321820\pi$
$461$	−10.0560	−	17.4175i	−0.468354	−	0.811213i	−0.999346	+	0.0361638i	$0.988486\pi$
$462$		0			0
$463$	9.34602	−	16.1878i	0.434346	−	0.752310i	−0.562896	−	0.826528i	$-0.690313\pi$
$463$	9.34602	−	16.1878i	0.434346	−	0.752310i	0.997242	+	0.0742181i	$0.0236461\pi$
$464$	−1.41538	+	0.817173i	−0.0657076	+	0.0379363i
$465$	−31.1134	−	38.0972i	−1.44285	−	1.76672i
$466$	1.48912	−	2.57924i	0.0689824	−	0.119481i
$467$	14.6803	−	25.4270i	0.679322	−	1.17662i	−0.295864	−	0.955230i	$-0.595607\pi$
$467$	14.6803	−	25.4270i	0.679322	−	1.17662i	0.975185	−	0.221390i	$-0.0710593\pi$
$468$	4.67802	+	0.953804i	0.216242	+	0.0440896i
$469$		0			0
$470$	31.5740	−	18.2293i	1.45640	−	0.840853i
$471$	36.7336	−	5.97451i	1.69259	−	0.275291i
$472$		−	17.9596i		−	0.826659i
$473$		−	9.19199i		−	0.422648i
$474$	−19.6469	+	3.19547i	−0.902414	+	0.146773i
$475$	28.8106	−	16.6338i	1.32192	−	0.763212i
$476$		0			0
$477$	−6.42958	+	7.26117i	−0.294390	+	0.332466i
$478$	11.8760	−	20.5698i	0.543195	−	0.940841i
$479$	−10.9660	+	18.9938i	−0.501051	+	0.867847i	0.498948	+	0.866632i	$0.333720\pi$
$479$	−10.9660	+	18.9938i	−0.501051	+	0.867847i	−0.999999	+	0.00121455i	$0.999613\pi$
$480$	15.7788	+	19.3206i	0.720201	+	0.881861i
$481$	−11.5036	+	6.64163i	−0.524521	+	0.302832i
$482$	−12.3295	+	21.3554i	−0.561594	+	0.972710i
$483$		0			0
$484$	−1.93513	−	3.35174i	−0.0879604	−	0.152352i
$485$	10.2403	+	5.91226i	0.464989	+	0.268462i
$486$	12.7145	−	13.2538i	0.576742	−	0.601205i
$487$	−0.538896	−	0.933395i	−0.0244197	−	0.0422962i	0.853557	−	0.520999i	$-0.174440\pi$
$487$	−0.538896	−	0.933395i	−0.0244197	−	0.0422962i	−0.877977	+	0.478703i	$0.841107\pi$
$488$	−22.0888			−0.999915
$489$	−20.2730	−	7.68563i	−0.916777	−	0.347556i
$490$		0			0
$491$	16.3708	+	9.45168i	0.738804	+	0.426549i	0.821634	−	0.570015i	$-0.193063\pi$
$491$	16.3708	+	9.45168i	0.738804	+	0.426549i	−0.0828305	+	0.996564i	$0.526396\pi$
$492$	7.30257	+	2.76845i	0.329225	+	0.124812i
$493$	−0.690115	−	0.398438i	−0.0310812	−	0.0179448i
$494$	6.41353	−	3.70285i	0.288558	−	0.166599i
$495$	−8.90443	−	26.6498i	−0.400224	−	1.19782i
$496$		−	15.7461i		−	0.707020i
$497$		0			0
$498$	−2.05690	−	2.51860i	−0.0921721	−	0.112861i
$499$	8.34290	+	14.4503i	0.373479	+	0.646885i	0.990098	−	0.140377i	$-0.0448314\pi$
$499$	8.34290	+	14.4503i	0.373479	+	0.646885i	−0.616619	+	0.787262i	$0.711498\pi$
$500$	−23.2355			−1.03912
$501$	24.9679	+	9.46551i	1.11549	+	0.422888i
$502$		−	30.1321i		−	1.34486i
$503$	−21.2386			−0.946981			−0.473491	−	0.880799i	$-0.657006\pi$
$503$	−21.2386			−0.946981			−0.473491	+	0.880799i	$0.657006\pi$
$504$		0			0
$505$	−69.2993			−3.08378
$506$		−	9.30028i		−	0.413448i
$507$	8.36387	−	6.83063i	0.371452	−	0.303359i
$508$	11.3401			0.503138
$509$	5.72252	+	9.91170i	0.253646	+	0.439328i	0.964527	−	0.263984i	$-0.0850367\pi$
$509$	5.72252	+	9.91170i	0.253646	+	0.439328i	−0.710881	+	0.703313i	$0.751703\pi$
$510$	3.67016	−	9.68108i	0.162517	−	0.428685i
$511$		0			0
$512$			22.7685i			1.00623i
$513$	−0.500898	+	12.5469i	−0.0221152	+	0.553960i
$514$	−12.1162	+	6.99527i	−0.534421	+	0.308548i
$515$	−11.3175	−	6.53414i	−0.498707	−	0.287929i
$516$	3.48965	−	2.84994i	0.153623	−	0.125462i
$517$	13.3747	+	7.72188i	0.588218	+	0.339608i
$518$		0			0
$519$	−2.39537	−	14.7276i	−0.105145	−	0.646472i
$520$	−34.6739			−1.52055
$521$	10.3999	+	18.0131i	0.455627	+	0.789169i	0.998724	−	0.0505007i	$-0.0160817\pi$
$521$	10.3999	+	18.0131i	0.455627	+	0.789169i	−0.543097	+	0.839670i	$0.682748\pi$
$522$	1.80058	+	1.59437i	0.0788093	+	0.0697837i
$523$	12.9330	+	7.46690i	0.565523	+	0.326505i	0.755359	−	0.655311i	$-0.227462\pi$
$523$	12.9330	+	7.46690i	0.565523	+	0.326505i	−0.189836	+	0.981816i	$0.560796\pi$
$524$	−2.05102	−	3.55248i	−0.0895994	−	0.155191i
$525$		0			0
$526$	−13.1765	+	22.8223i	−0.574522	+	0.995101i
$527$	6.64890	−	3.83875i	0.289631	−	0.167218i
$528$	3.18854	−	8.41067i	0.138763	−	0.366028i
$529$	−4.83508	+	8.37460i	−0.210221	+	0.364113i
$530$	8.25032	−	14.2900i	0.358371	−	0.620717i
$531$	−16.6062	+	5.54858i	−0.720647	+	0.240788i
$532$		0			0
$533$	−16.6002	+	9.58410i	−0.719033	+	0.415134i
$534$	−4.41220	+	11.6384i	−0.190934	+	0.503643i
$535$			51.3277i			2.21909i
$536$		−	20.4751i		−	0.884388i
$537$	−20.9680	−	25.6746i	−0.904835	−	1.10794i
$538$	4.31272	−	2.48995i	0.185934	−	0.107349i
$539$		0			0
$540$	7.35654	−	11.6431i	0.316575	−	0.501041i
$541$	−15.5838	+	26.9920i	−0.670002	+	1.16048i	0.307902	+	0.951418i	$0.400373\pi$
$541$	−15.5838	+	26.9920i	−0.670002	+	1.16048i	−0.977903	+	0.209058i	$0.932960\pi$
$542$	13.1925	−	22.8501i	0.566667	−	0.981496i
$543$	13.1607	−	2.14051i	0.564779	−	0.0918582i
$544$	−3.37192	+	1.94678i	−0.144570	+	0.0834675i
$545$	15.5120	−	26.8676i	0.664462	−	1.15088i
$546$		0			0
$547$	−15.7410	−	27.2642i	−0.673035	−	1.16573i	−0.977039	−	0.213061i	$-0.931657\pi$
$547$	−15.7410	−	27.2642i	−0.673035	−	1.16573i	0.304004	−	0.952671i	$-0.401677\pi$
$548$	−7.23079	−	4.17470i	−0.308884	−	0.178334i
$549$	6.82430	+	20.4242i	0.291254	+	0.871685i
$550$	17.5337	+	30.3693i	0.747640	+	1.29495i
$551$	−1.64429			−0.0700492
$552$	15.0722	−	12.3092i	0.641514	−	0.523914i
$553$		0			0
$554$	11.6163	+	6.70667i	0.493529	+	0.284939i
$555$	6.15148	+	37.8216i	0.261116	+	1.60544i
$556$	−4.73643	−	2.73458i	−0.200870	−	0.115972i
$557$	−23.5896	+	13.6194i	−0.999522	+	0.577074i	−0.908107	−	0.418738i	$-0.862472\pi$
$557$	−23.5896	+	13.6194i	−0.999522	+	0.577074i	−0.0914153	+	0.995813i	$0.529139\pi$
$558$	−21.9768	+	7.34306i	−0.930352	+	0.310856i
$559$			11.0584i			0.467720i
$560$		0			0
$561$	4.32881	−	0.704057i	0.182762	−	0.0297253i
$562$	0.478001	+	0.827922i	0.0201633	+	0.0349238i
$563$	28.3743			1.19583			0.597916	−	0.801559i	$-0.295996\pi$
$563$	28.3743			1.19583			0.597916	+	0.801559i	$0.295996\pi$
$564$	1.21523	+	7.47170i	0.0511705	+	0.314615i
$565$			12.3105i			0.517907i
$566$	21.5961			0.907751
$567$		0			0
$568$	6.03071			0.253043
$569$			34.0193i			1.42616i	0.701081	+	0.713082i	$0.252701\pi$
$569$			34.0193i			1.42616i	−0.701081	+	0.713082i	$0.747299\pi$
$570$	−3.42958	−	21.0864i	−0.143650	−	0.883212i
$571$	−44.6910			−1.87026			−0.935130	−	0.354305i	$-0.884717\pi$
$571$	−44.6910			−1.87026			−0.935130	+	0.354305i	$0.884717\pi$
$572$	−1.72036	−	2.97975i	−0.0719319	−	0.124590i
$573$	−31.8224	+	5.17573i	−1.32940	+	0.216219i
$574$		0			0
$575$			50.2613i			2.09604i
$576$	24.8143	−	8.29113i	1.03393	−	0.345464i
$577$	6.36301	−	3.67369i	0.264896	−	0.152938i	−0.361670	−	0.932306i	$-0.617793\pi$
$577$	6.36301	−	3.67369i	0.264896	−	0.152938i	0.626566	+	0.779369i	$0.284460\pi$
$578$	−15.9465	−	9.20670i	−0.663286	−	0.382948i
$579$	5.03680	+	30.9682i	0.209322	+	1.28699i
$580$	1.56185	+	0.901733i	0.0648522	+	0.0374424i
$581$		0			0
$582$	4.31428	−	3.52340i	0.178833	−	0.146050i
$583$	6.98964			0.289481
$584$	18.3204	+	31.7319i	0.758104	+	1.31307i
$585$	10.7124	+	32.0609i	0.442904	+	1.32555i
$586$	12.7266	+	7.34772i	0.525732	+	0.303531i
$587$	−13.1328	−	22.7466i	−0.542048	−	0.938855i	−0.998786	−	0.0492535i	$-0.984316\pi$
$587$	−13.1328	−	22.7466i	−0.542048	−	0.938855i	0.456738	−	0.889601i	$-0.349018\pi$
$588$		0			0
$589$	7.92095	−	13.7195i	0.326377	−	0.565302i
$590$	25.7971	−	14.8940i	1.06205	−	0.613175i
$591$	28.3697	−	4.61418i	1.16697	−	0.189802i
$592$	−6.13331	+	10.6232i	−0.252078	+	0.436611i
$593$	4.56209	−	7.90178i	0.187343	−	0.324487i	−0.757021	−	0.653391i	$-0.773346\pi$
$593$	4.56209	−	7.90178i	0.187343	−	0.324487i	0.944363	+	0.328904i	$0.106679\pi$
$594$	−13.2257	−	0.527997i	−0.542658	−	0.0216640i
$595$		0			0
$596$	2.01298	−	1.16220i	0.0824550	−	0.0476054i
$597$	−2.97878	−	3.64741i	−0.121913	−	0.149279i
$598$			11.1887i			0.457538i
$599$			23.2080i			0.948252i	0.880457	+	0.474126i	$0.157236\pi$
$599$			23.2080i			0.948252i	−0.880457	+	0.474126i	$0.842764\pi$
$600$	−26.0105	+	68.6100i	−1.06187	+	2.80099i
$601$	−19.0021	+	10.9709i	−0.775111	+	0.447510i	−0.834695	−	0.550713i	$-0.814356\pi$
$601$	−19.0021	+	10.9709i	−0.775111	+	0.447510i	0.0595840	+	0.998223i	$0.481023\pi$
$602$		0			0
$603$	−18.9320	+	6.32572i	−0.770973	+	0.257603i
$604$	1.16913	−	2.02499i	0.0475711	−	0.0823955i
$605$	13.7013	−	23.7313i	0.557036	−	0.964815i
$606$	−11.5723	+	30.5251i	−0.470092	+	1.24000i
$607$	38.6289	−	22.3024i	1.56790	−	0.905226i	0.571484	−	0.820613i	$-0.306368\pi$
$607$	38.6289	−	22.3024i	1.56790	−	0.905226i	0.996414	−	0.0846136i	$-0.0269656\pi$
$608$	−4.01703	+	6.95770i	−0.162912	+	0.282172i
$609$		0			0
$610$	−18.3184	−	31.7283i	−0.741689	−	1.28464i
$611$	−16.0903	−	9.28976i	−0.650946	−	0.375824i
$612$	1.60942	+	1.42510i	0.0650569	+	0.0576063i
$613$	−5.82799	−	10.0944i	−0.235390	−	0.407708i	0.723996	−	0.689804i	$-0.242303\pi$
$613$	−5.82799	−	10.0944i	−0.235390	−	0.407708i	−0.959386	+	0.282097i	$0.908970\pi$
$614$	25.1240			1.01392
$615$	8.87681	+	54.5780i	0.357947	+	2.20080i
$616$		0			0
$617$	36.6143	+	21.1393i	1.47403	+	0.851034i	0.999572	−	0.0292416i	$-0.00930923\pi$
$617$	36.6143	+	21.1393i	1.47403	+	0.851034i	0.474462	+	0.880276i	$0.342643\pi$
$618$	−4.76808	+	3.89402i	−0.191800	+	0.156640i
$619$	30.0633	+	17.3571i	1.20835	+	0.697640i	0.962398	−	0.271643i	$-0.0875670\pi$
$619$	30.0633	+	17.3571i	1.20835	+	0.697640i	0.245949	+	0.969283i	$0.420900\pi$
$620$	−15.0476	+	8.68773i	−0.604326	+	0.348908i
$621$	−16.0381	−	10.1334i	−0.643586	−	0.406640i
$622$			9.23930i			0.370462i
$623$		0			0
$624$	−3.83596	+	10.1184i	−0.153561	+	0.405061i
$625$	−47.8410	−	82.8631i	−1.91364	−	3.31452i
$626$	−11.6673			−0.466319
$627$	7.00909	−	5.72421i	0.279916	−	0.228603i
$628$		−	13.1465i		−	0.524604i
$629$	−5.98098			−0.238477
$630$		0			0
$631$	−12.8860			−0.512982			−0.256491	−	0.966547i	$-0.582566\pi$
$631$	−12.8860			−0.512982			−0.256491	+	0.966547i	$0.582566\pi$
$632$			30.0159i			1.19397i
$633$	−45.1683	−	17.1236i	−1.79528	−	0.680601i
$634$	28.3465			1.12578
$635$	40.1457	+	69.5345i	1.59314	+	2.75939i
$636$	2.16711	+	2.65355i	0.0859315	+	0.105220i
$637$		0			0
$638$		−	1.73325i		−	0.0686200i
$639$	−1.86318	−	5.57624i	−0.0737061	−	0.220593i
$640$	−13.6030	+	7.85371i	−0.537707	+	0.310445i
$641$	16.5666	+	9.56474i	0.654342	+	0.377785i	0.790118	−	0.612955i	$-0.210019\pi$
$641$	16.5666	+	9.56474i	0.654342	+	0.377785i	−0.135776	+	0.990740i	$0.543353\pi$
$642$	22.6090	+	8.57122i	0.892306	+	0.338279i
$643$	−9.77521	−	5.64372i	−0.385497	−	0.222567i	0.294710	−	0.955587i	$-0.404777\pi$
$643$	−9.77521	−	5.64372i	−0.385497	−	0.222567i	−0.680207	+	0.733020i	$0.738110\pi$
$644$		0			0
$645$	29.8289	+	11.3083i	1.17451	+	0.445265i
$646$	3.33453			0.131195
$647$	2.54339	+	4.40528i	0.0999909	+	0.173189i	0.911681	−	0.410900i	$-0.134785\pi$
$647$	2.54339	+	4.40528i	0.0999909	+	0.173189i	−0.811690	+	0.584089i	$0.801452\pi$
$648$	−16.6489	−	22.1326i	−0.654032	−	0.869451i
$649$	10.9276	+	6.30906i	0.428946	+	0.247652i
$650$	−21.0939	−	36.5356i	−0.827369	−	1.43305i
$651$		0			0
$652$	−3.82937	+	6.63267i	−0.149970	+	0.259755i
$653$	32.9044	−	18.9974i	1.28765	−	0.743424i	0.309414	−	0.950927i	$-0.399867\pi$
$653$	32.9044	−	18.9974i	1.28765	−	0.743424i	0.978234	+	0.207503i	$0.0665338\pi$
$654$	−9.24438	−	11.3194i	−0.361484	−	0.442624i
$655$	14.5218	−	25.1526i	0.567415	−	0.982792i
$656$	−8.85059	+	15.3297i	−0.345557	+	0.598523i
$657$	23.6805	−	26.7433i	0.923865	−	1.04335i
$658$		0			0
$659$	9.97949	−	5.76166i	0.388746	−	0.224442i	−0.292871	−	0.956152i	$-0.594611\pi$
$659$	9.97949	−	5.76166i	0.388746	−	0.224442i	0.681617	+	0.731710i	$0.261277\pi$
$660$	−9.79683	+	1.59340i	−0.381341	+	0.0620230i
$661$		−	43.9858i		−	1.71085i	−0.517929	−	0.855424i	$-0.673297\pi$
$661$		−	43.9858i		−	1.71085i	0.517929	−	0.855424i	$-0.326703\pi$
$662$			10.6907i			0.415504i
$663$	−5.20775	+	0.847012i	−0.202252	+	0.0328952i
$664$	−4.24660	+	2.45178i	−0.164800	+	0.0951473i
$665$		0			0
$666$	17.6870	+	3.60621i	0.685358	+	0.139738i
$667$	1.24211	−	2.15140i	0.0480947	−	0.0833025i
$668$	4.71620	−	8.16869i	0.182475	−	0.316056i
$669$	−8.40458	−	10.2911i	−0.324940	−	0.397877i
$670$	29.4103	−	16.9800i	1.13622	−	0.655996i
$671$	7.75962	−	13.4401i	0.299557	−	0.518848i
$672$		0			0
$673$	−21.9316	−	37.9866i	−0.845400	−	1.46428i	−0.885273	−	0.465071i	$-0.846029\pi$
$673$	−21.9316	−	37.9866i	−0.845400	−	1.46428i	0.0398735	−	0.999205i	$-0.487305\pi$
$674$	−8.20387	−	4.73650i	−0.316001	−	0.182443i
$675$	71.4754	+	2.85344i	2.75109	+	0.109829i
$676$	−1.90731	−	3.30355i	−0.0733579	−	0.127060i
$677$	1.47800			0.0568041			0.0284020	−	0.999597i	$-0.490958\pi$
$677$	1.47800			0.0568041			0.0284020	+	0.999597i	$0.490958\pi$
$678$	5.42257	+	2.05573i	0.208252	+	0.0789499i
$679$		0			0
$680$	−13.5208	−	7.80621i	−0.518497	−	0.299355i
$681$	−3.77161	−	1.42984i	−0.144528	−	0.0547917i
$682$	14.4617	+	8.34948i	0.553768	+	0.319718i
$683$	8.94252	−	5.16296i	0.342176	−	0.197555i	−0.319058	−	0.947735i	$-0.603366\pi$
$683$	8.94252	−	5.16296i	0.342176	−	0.197555i	0.661234	+	0.750180i	$0.270033\pi$
$684$	4.34628	+	0.886164i	0.166184	+	0.0338833i
$685$		−	59.1162i		−	2.25871i
$686$		0			0
$687$	−13.1130	−	16.0565i	−0.500294	−	0.612592i
$688$	5.10601	+	8.84388i	0.194665	+	0.337170i
$689$	−8.40885			−0.320352
$690$	30.1803	+	11.4415i	1.14894	+	0.435572i
$691$		−	7.59984i		−	0.289112i	−0.989497	−	0.144556i	$-0.953825\pi$
$691$		−	7.59984i		−	0.289112i	0.989497	−	0.144556i	$-0.0461753\pi$
$692$	−5.27087			−0.200368
$693$		0			0
$694$	41.6773			1.58205
$695$		−	38.7232i		−	1.46886i
$696$	2.80893	−	2.29400i	0.106472	−	0.0869540i
$697$	−8.63076			−0.326913
$698$	14.4120	+	24.9624i	0.545503	+	0.944839i
$699$	−1.55204	+	4.09395i	−0.0587036	+	0.154847i
$700$		0			0
$701$		−	6.35907i		−	0.240179i	−0.992763	−	0.120089i	$-0.961682\pi$
$701$		−	6.35907i		−	0.240179i	0.992763	−	0.120089i	$-0.0383181\pi$
$702$	15.9111	+	0.635204i	0.600527	+	0.0239742i
$703$	−10.6879	+	6.17064i	−0.403100	+	0.232730i
$704$	−16.3289	−	9.42749i	−0.615419	−	0.355312i
$705$	−41.5122	+	33.9024i	−1.56344	+	1.27684i
$706$	−0.991677	−	0.572545i	−0.0373223	−	0.0215480i
$707$		0			0
$708$	0.992890	+	6.10466i	0.0373151	+	0.229427i
$709$	−47.6095			−1.78801			−0.894007	−	0.448054i	$-0.852117\pi$
$709$	−47.6095			−1.78801			−0.894007	+	0.448054i	$0.852117\pi$
$710$	5.00129	+	8.66249i	0.187695	+	0.325098i
$711$	27.7539	−	9.27334i	1.04085	−	0.347777i
$712$	16.2544	+	9.38448i	0.609159	+	0.351698i
$713$	11.9671	+	20.7276i	0.448171	+	0.776255i
$714$		0			0
$715$	12.1806	−	21.0975i	0.455530	−	0.789002i
$716$	−10.1409	+	5.85486i	−0.378983	+	0.218806i
$717$	−12.3778	+	32.6498i	−0.462256	+	1.21933i
$718$	−9.37904	+	16.2450i	−0.350023	+	0.606257i
$719$	−7.07350	+	12.2517i	−0.263797	+	0.456910i	−0.967248	−	0.253834i	$-0.918308\pi$
$719$	−7.07350	+	12.2517i	−0.263797	+	0.456910i	0.703451	+	0.710744i	$0.251642\pi$
$720$	23.3708	+	20.6942i	0.870977	+	0.771228i
$721$		0			0
$722$	−13.4280	+	7.75264i	−0.499737	+	0.288524i
$723$	12.8505	−	33.8967i	0.477914	−	1.26063i
$724$		−	4.71007i		−	0.175048i
$725$			9.36695i			0.347880i
$726$	−8.16526	−	9.99807i	−0.303041	−	0.371063i
$727$	40.1828	−	23.1996i	1.49030	−	0.860424i	0.490360	−	0.871520i	$-0.336865\pi$
$727$	40.1828	−	23.1996i	1.49030	−	0.860424i	0.999938	+	0.0110955i	$0.00353187\pi$
$728$		0			0
$729$	−15.3210	+	22.2321i	−0.567446	+	0.823411i
$730$	−30.3864	+	52.6307i	−1.12465	+	1.94795i
$731$	−2.48960	+	4.31211i	−0.0920811	+	0.159489i
$732$	7.50823	−	1.22117i	0.277512	−	0.0451358i
$733$	−22.8893	+	13.2151i	−0.845436	+	0.488112i	−0.859108	−	0.511794i	$-0.828981\pi$
$733$	−22.8893	+	13.2151i	−0.845436	+	0.488112i	0.0136726	+	0.999907i	$0.495648\pi$
$734$	−14.5559	+	25.2115i	−0.537268	+	0.930575i
$735$		0			0
$736$	−6.06899	−	10.5118i	−0.223706	−	0.387470i
$737$	12.4581	+	7.19271i	0.458902	+	0.264947i
$738$	25.5230	+	5.20389i	0.939515	+	0.191558i
$739$	23.1335	+	40.0684i	0.850979	+	1.47394i	0.880326	+	0.474370i	$0.157324\pi$
$739$	23.1335	+	40.0684i	0.850979	+	1.47394i	−0.0293467	+	0.999569i	$0.509343\pi$
$740$	13.5360			0.497592
$741$	−8.43225	+	6.88648i	−0.309766	+	0.252981i
$742$		0			0
$743$	−36.5640	−	21.1102i	−1.34140	−	0.774458i	−0.354388	−	0.935098i	$-0.615311\pi$
$743$	−36.5640	−	21.1102i	−1.34140	−	0.774458i	−0.987013	+	0.160640i	$0.948644\pi$
$744$	5.60922	+	34.4876i	0.205644	+	1.26438i
$745$	14.2525	+	8.22868i	0.522171	+	0.301476i
$746$	9.62825	−	5.55887i	0.352515	−	0.203525i
$747$	3.57899	+	3.16910i	0.130948	+	0.115951i
$748$		−	1.54923i		−	0.0566456i
$749$		0			0
$750$	−76.4932	+	12.4412i	−2.79314	+	0.454288i
$751$	8.02320	+	13.8966i	0.292771	+	0.507094i	0.974464	−	0.224544i	$-0.0720894\pi$
$751$	8.02320	+	13.8966i	0.292771	+	0.507094i	−0.681693	+	0.731638i	$0.738756\pi$
$752$	−17.1575			−0.625671
$753$	7.11116	+	43.7221i	0.259145	+	1.59332i
$754$			2.08518i			0.0759376i
$755$	16.5555			0.602516
$756$		0			0
$757$	25.0149			0.909183			0.454591	−	0.890700i	$-0.349785\pi$
$757$	25.0149			0.909183			0.454591	+	0.890700i	$0.349785\pi$
$758$		−	24.5102i		−	0.890252i
$759$	2.19486	+	13.4948i	0.0796684	+	0.489831i
$760$	−32.2150			−1.16856
$761$	3.00365	+	5.20247i	0.108882	+	0.188589i	0.915318	−	0.402733i	$-0.131940\pi$
$761$	3.00365	+	5.20247i	0.108882	+	0.188589i	−0.806436	+	0.591322i	$0.798606\pi$
$762$	37.3327	−	6.07196i	1.35242	−	0.219964i
$763$		0			0
$764$			11.3889i			0.412035i
$765$	−3.04073	+	14.9135i	−0.109938	+	0.539200i
$766$	6.59165	−	3.80569i	0.238166	−	0.137505i
$767$	−13.1464	−	7.59008i	−0.474689	−	0.274062i
$768$	−3.66193	−	22.5149i	−0.132139	−	0.812438i
$769$	28.9946	+	16.7400i	1.04557	+	0.603661i	0.921406	−	0.388600i	$-0.127041\pi$
$769$	28.9946	+	16.7400i	1.04557	+	0.603661i	0.124166	+	0.992262i	$0.460375\pi$
$770$		0			0
$771$	15.9298	−	13.0096i	0.573699	−	0.468531i
$772$	11.0832			0.398892
$773$	−18.1008	−	31.3515i	−0.651040	−	1.12763i	−0.982871	−	0.184296i	$-0.941000\pi$
$773$	−18.1008	−	31.3515i	−0.651040	−	1.12763i	0.331831	−	0.943339i	$-0.392334\pi$
$774$	9.96224	−	11.2507i	0.358085	−	0.404399i
$775$	−78.1551	−	45.1229i	−2.80741	−	1.62086i
$776$	−4.19980	−	7.27427i	−0.150764	−	0.261131i
$777$		0			0
$778$	0.0303280	−	0.0525296i	0.00108731	−	0.00188328i
$779$	−15.4230	+	8.90445i	−0.552585	+	0.319035i
$780$	11.7860	−	1.91693i	0.422007	−	0.0686372i
$781$	−2.11854	+	3.66942i	−0.0758073	+	0.131302i
$782$	−2.51893	+	4.36291i	−0.0900766	+	0.156017i
$783$	−2.98894	−	1.88852i	−0.106816	−	0.0674901i
$784$		0			0
$785$	80.6108	−	46.5407i	2.87712	−	1.66111i
$786$	−8.65427	−	10.5968i	−0.308688	−	0.377977i
$787$		−	16.3887i		−	0.584193i	−0.956389	−	0.292096i	$-0.905647\pi$
$787$		−	16.3887i		−	0.584193i	0.956389	−	0.292096i	$-0.0943528\pi$
$788$		−	10.1532i		−	0.361693i
$789$	13.7332	−	36.2252i	0.488915	−	1.28965i
$790$	−43.1147	+	24.8923i	−1.53395	+	0.885628i
$791$		0			0
$792$	−3.98753	+	19.5572i	−0.141691	+	0.694935i
$793$	−9.33517	+	16.1690i	−0.331502	+	0.574178i
$794$	−7.48929	+	12.9718i	−0.265785	+	0.460353i
$795$	−8.59890	+	22.6820i	−0.304972	+	0.804448i
$796$	−1.44065	+	0.831760i	−0.0510625	+	0.0294809i
$797$	−23.3328	+	40.4137i	−0.826492	+	1.43153i	0.0742821	+	0.997237i	$0.476333\pi$
$797$	−23.3328	+	40.4137i	−0.826492	+	1.43153i	−0.900774	+	0.434288i	$0.857000\pi$
$798$		0			0
$799$	−4.18285	−	7.24491i	−0.147979	−	0.256306i
$800$	39.6356	+	22.8836i	1.40133	+	0.809057i
$801$	3.65550	−	17.9288i	0.129161	−	0.633482i
$802$	−1.49464	−	2.58880i	−0.0527777	−	0.0914137i
$803$	−25.7432			−0.908459
$804$	1.13195	+	6.95968i	0.0399209	+	0.245449i
$805$		0			0
$806$	−17.3981	−	10.0448i	−0.612822	−	0.353813i
$807$	−5.67019	+	4.63075i	−0.199600	+	0.163010i
$808$	42.6319	+	24.6136i	1.49979	+	0.865902i
$809$	25.8925	−	14.9490i	0.910330	−	0.525580i	0.0297930	−	0.999556i	$-0.490515\pi$
$809$	25.8925	−	14.9490i	0.910330	−	0.525580i	0.880537	+	0.473977i	$0.157182\pi$
$810$	17.9842	−	42.2691i	0.631899	−	1.48519i
$811$		−	25.3404i		−	0.889821i	−0.895575	−	0.444911i	$-0.853235\pi$
$811$		−	25.3404i		−	0.889821i	0.895575	−	0.444911i	$-0.146765\pi$
$812$		0			0
$813$	−13.7499	+	36.2693i	−0.482230	+	1.27202i
$814$	−6.50447	−	11.2661i	−0.227982	−	0.394876i
$815$	−54.2261			−1.89946
$816$	−3.77378	+	3.08198i	−0.132109	+	0.107891i
$817$			10.2742i			0.359448i
$818$	−0.0674323			−0.00235772
$819$		0			0
$820$	19.5329			0.682117
$821$			10.6580i			0.371968i	0.982553	+	0.185984i	$0.0595472\pi$
$821$			10.6580i			0.371968i	−0.982553	+	0.185984i	$0.940453\pi$
$822$	−26.0397	−	9.87181i	−0.908238	−	0.344319i
$823$	17.1048			0.596235			0.298118	−	0.954529i	$-0.403641\pi$
$823$	17.1048			0.596235			0.298118	+	0.954529i	$0.403641\pi$
$824$	4.64156	+	8.03943i	0.161697	+	0.280067i
$825$	−32.6088	−	39.9283i	−1.13529	−	1.39013i
$826$		0			0
$827$			18.3221i			0.637121i	0.947903	+	0.318560i	$0.103199\pi$
$827$			18.3221i			0.637121i	−0.947903	+	0.318560i	$0.896801\pi$
$828$	−4.44267	+	5.01728i	−0.154394	+	0.174362i
$829$	6.69733	−	3.86670i	0.232608	−	0.134296i	−0.379167	−	0.925328i	$-0.623789\pi$
$829$	6.69733	−	3.86670i	0.232608	−	0.134296i	0.611775	+	0.791032i	$0.290456\pi$
$830$	−7.04344	−	4.06653i	−0.244481	−	0.141151i
$831$	−18.4382	−	6.99004i	−0.639613	−	0.242482i
$832$	19.6444	+	11.3417i	0.681047	+	0.393203i
$833$		0			0
$834$	−17.0569	−	6.46639i	−0.590633	−	0.223913i
$835$	66.7841			2.31116
$836$	−1.59836	−	2.76844i	−0.0552805	−	0.0957486i
$837$	30.1557	−	15.8414i	1.04233	−	0.547559i
$838$	6.28551	+	3.62894i	0.217129	+	0.125360i
$839$	−9.73588	−	16.8630i	−0.336120	−	0.582177i	0.647579	−	0.761998i	$-0.275781\pi$
$839$	−9.73588	−	16.8630i	−0.336120	−	0.582177i	−0.983699	+	0.179821i	$0.942448\pi$
$840$		0			0
$841$	−14.2685	+	24.7138i	−0.492018	+	0.852200i
$842$	30.7519	−	17.7546i	1.05978	−	0.611865i
$843$	−0.888976	−	1.08852i	−0.0306179	−	0.0374906i
$844$	−8.53184	+	14.7776i	−0.293678	+	0.508665i
$845$	13.5043	−	23.3901i	0.464561	−	0.804643i
$846$	8.00128	+	23.9468i	0.275090	+	0.823307i
$847$		0			0
$848$	−6.72493	+	3.88264i	−0.230935	+	0.133330i
$849$	−31.3362	+	5.09666i	−1.07546	+	0.174917i
$850$		−	18.9956i		−	0.651545i
$851$		−	18.6454i		−	0.639155i
$852$	−2.04990	+	0.333405i	−0.0702285	+	0.0114223i
$853$	−0.812274	+	0.468967i	−0.0278117	+	0.0160571i	−0.513841	−	0.857885i	$-0.671778\pi$
$853$	−0.812274	+	0.468967i	−0.0278117	+	0.0160571i	0.486030	+	0.873942i	$0.338445\pi$
$854$		0			0
$855$	9.95275	+	29.7873i	0.340377	+	1.01870i
$856$	18.2305	−	31.5761i	0.623104	−	1.07925i
$857$	−9.00087	+	15.5900i	−0.307464	+	0.532543i	−0.977807	−	0.209509i	$-0.932814\pi$
$857$	−9.00087	+	15.5900i	−0.307464	+	0.532543i	0.670343	+	0.742051i	$0.266147\pi$
$858$	−7.25904	−	8.88844i	−0.247820	−	0.303446i
$859$	23.1160	−	13.3460i	0.788709	−	0.455361i	−0.0507989	−	0.998709i	$-0.516177\pi$
$859$	23.1160	−	13.3460i	0.788709	−	0.455361i	0.839508	+	0.543348i	$0.182843\pi$
$860$	5.63438	−	9.75903i	0.192131	−	0.332780i
$861$		0			0
$862$	−4.75486	−	8.23566i	−0.161951	−	0.280508i
$863$	−24.0405	−	13.8798i	−0.818348	−	0.472473i	0.0314987	−	0.999504i	$-0.489972\pi$
$863$	−24.0405	−	13.8798i	−0.818348	−	0.472473i	−0.849846	+	0.527031i	$0.823305\pi$
$864$	−15.2931	+	8.03380i	−0.520283	+	0.273315i
$865$	−18.6596	−	32.3194i	−0.634446	−	1.09889i
$866$	33.5715			1.14080
$867$	25.3113	+	9.59569i	0.859618	+	0.325887i
$868$		0			0
$869$	−18.2633	−	10.5443i	−0.619540	−	0.357692i
$870$	5.62455	+	2.13231i	0.190690	+	0.0722919i
$871$	−14.9877	−	8.65316i	−0.507839	−	0.293201i
$872$	−19.0856	+	11.0191i	−0.646319	+	0.373152i
$873$	−5.42856	+	6.13068i	−0.183729	+	0.207492i
$874$			10.3952i			0.351623i
$875$		0			0
$876$	−7.98158	−	9.77316i	−0.269673	−	0.330205i
$877$	−6.90978	−	11.9681i	−0.233327	−	0.404134i	0.725458	−	0.688266i	$-0.241628\pi$
$877$	−6.90978	−	11.9681i	−0.233327	−	0.404134i	−0.958785	+	0.284132i	$0.908295\pi$
$878$	−2.40894			−0.0812979
$879$	−20.2006	−	7.65817i	−0.681348	−	0.258304i
$880$		−	22.4968i		−	0.758367i
$881$	43.9006			1.47905			0.739525	−	0.673129i	$-0.235050\pi$
$881$	43.9006			1.47905			0.739525	+	0.673129i	$0.235050\pi$
$882$		0			0
$883$	7.96743			0.268125			0.134063	−	0.990973i	$-0.457198\pi$
$883$	7.96743			0.268125			0.134063	+	0.990973i	$0.457198\pi$
$884$			1.86380i			0.0626863i
$885$	−33.9170	+	27.6995i	−1.14011	+	0.931108i
$886$	−28.7500			−0.965875
$887$	−10.6080	−	18.3736i	−0.356181	−	0.616924i	0.631138	−	0.775670i	$-0.282588\pi$
$887$	−10.6080	−	18.3736i	−0.356181	−	0.616924i	−0.987319	+	0.158747i	$0.949255\pi$
$888$	9.64910	−	25.4522i	0.323803	−	0.854120i
$889$		0			0
$890$			31.1303i			1.04349i
$891$	19.3153	−	2.35513i	0.647087	−	0.0788999i
$892$	−4.06477	+	2.34680i	−0.136099	+	0.0785766i
$893$	−14.9493	−	8.63098i	−0.500259	−	0.288825i
$894$	6.00462	−	4.90388i	0.200825	−	0.164010i
$895$	−71.8005	−	41.4541i	−2.40003	−	1.38566i
$896$		0			0
$897$	−2.64052	−	16.2349i	−0.0881643	−	0.542067i
$898$	0.345848			0.0115411
$899$	2.23025	+	3.86291i	0.0743830	+	0.128835i
$900$	5.04817	−	24.7592i	0.168272	−	0.825308i
$901$	−3.27895	−	1.89310i	−0.109238	−	0.0630684i
$902$	−9.38618	−	16.2573i	−0.312526	−	0.541310i
$903$		0			0
$904$	4.37242	−	7.57325i	0.145424	−	0.251883i
$905$	28.8808	−	16.6743i	0.960029	−	0.554273i
$906$	2.76460	−	7.29241i	0.0918478	−	0.242274i
$907$	−1.88344	+	3.26221i	−0.0625385	+	0.108320i	−0.895599	−	0.444861i	$-0.853253\pi$
$907$	−1.88344	+	3.26221i	−0.0625385	+	0.108320i	0.833061	+	0.553181i	$0.186586\pi$
$908$	−0.712420	+	1.23395i	−0.0236425	+	0.0409500i
$909$	9.58763	−	47.0235i	0.318002	−	1.55967i
$910$		0			0
$911$	40.0013	−	23.0947i	1.32530	−	0.765163i	0.340732	−	0.940160i	$-0.389325\pi$
$911$	40.0013	−	23.0947i	1.32530	−	0.765163i	0.984569	+	0.174998i	$0.0559917\pi$
$912$	−3.56393	+	9.40087i	−0.118014	+	0.311294i
$913$		−	3.44515i		−	0.114018i
$914$		−	19.4985i		−	0.644953i
$915$	34.0681	+	41.7151i	1.12626	+	1.37906i
$916$	−6.34196	+	3.66153i	−0.209544	+	0.120980i
$917$		0			0
$918$	6.06139	+	3.82980i	0.200056	+	0.126402i
$919$	−0.607610	+	1.05241i	−0.0200432	+	0.0347158i	−0.875873	−	0.482542i	$-0.839714\pi$
$919$	−0.607610	+	1.05241i	−0.0200432	+	0.0347158i	0.855830	+	0.517257i	$0.173047\pi$
$920$	24.3355	−	42.1503i	0.802316	−	1.38965i
$921$	−36.4553	+	5.92926i	−1.20124	+	0.195376i
$922$	−20.5213	+	11.8480i	−0.675833	+	0.390192i
$923$	2.54870	−	4.41447i	0.0838914	−	0.145304i
$924$		0			0
$925$	35.1520	+	60.8850i	1.15579	+	2.00189i
$926$	−19.0725	−	11.0115i	−0.626760	−	0.361860i
$927$	5.99957	−	6.77554i	0.197052	−	0.222538i
$928$	−1.13105	−	1.95903i	−0.0371285	−	0.0643084i
$929$	−18.8903			−0.619771			−0.309886	−	0.950774i	$-0.600291\pi$
$929$	−18.8903			−0.619771			−0.309886	+	0.950774i	$0.600291\pi$
$930$	−44.8862	+	36.6578i	−1.47188	+	1.20206i
$931$		0			0
$932$	1.33941	+	0.773306i	0.0438737	+	0.0253305i
$933$	−2.18047	−	13.4064i	−0.0713854	−	0.438905i
$934$	−29.9581	−	17.2963i	−0.980258	−	0.565952i
$935$	9.49945	−	5.48451i	0.310665	−	0.179363i
$936$	4.79717	−	23.5282i	0.156801	−	0.769044i
$937$			27.0448i			0.883516i	0.897134	+	0.441758i	$0.145645\pi$
$937$			27.0448i			0.883516i	−0.897134	+	0.441758i	$0.854355\pi$
$938$		0			0
$939$	16.9294	−	2.75347i	0.552470	−	0.0898562i
$940$	9.46650	+	16.3965i	0.308763	+	0.534793i
$941$	−16.3205			−0.532032			−0.266016	−	0.963969i	$-0.585707\pi$
$941$	−16.3205			−0.532032			−0.266016	+	0.963969i	$0.585707\pi$
$942$	−7.03917	−	43.2795i	−0.229349	−	1.41012i
$943$		−	26.9059i		−	0.876178i
$944$	−14.0184			−0.456259
$945$		0			0
$946$	−10.8300			−0.352114
$947$		−	28.7020i		−	0.932691i	−0.884603	−	0.466345i	$-0.845570\pi$
$947$		−	28.7020i		−	0.932691i	0.884603	−	0.466345i	$-0.154430\pi$
$948$	−1.65941	−	10.2027i	−0.0538953	−	0.331369i
$949$	30.9703			1.00534
$950$	−19.5980	−	33.9447i	−0.635842	−	1.10131i
$951$	−41.1311	+	6.68975i	−1.33377	+	0.216930i
$952$		0			0
$953$			34.5757i			1.12002i	0.828486	+	0.560009i	$0.189202\pi$
$953$			34.5757i			1.12002i	−0.828486	+	0.560009i	$0.810798\pi$
$954$	8.55511	+	7.57534i	0.276982	+	0.245261i
$955$	−69.8333	+	40.3183i	−2.25975	+	1.30467i
$956$	10.6820	+	6.16723i	0.345479	+	0.199462i
$957$	0.409046	+	2.51497i	0.0132226	+	0.0812974i
$958$	22.3785	+	12.9202i	0.723015	+	0.417433i
$959$		0			0
$960$	50.6815	−	41.3907i	1.63574	−	1.33588i
$961$	−11.9746			−0.386278
$962$	7.82517	+	13.5536i	0.252294	+	0.436985i
$963$	−34.8288	−	7.10125i	−1.12234	−	0.228835i
$964$	−11.0899	−	6.40275i	−0.357181	−	0.206219i
$965$	39.2360	+	67.9588i	1.26305	+	2.18767i
$966$		0			0
$967$	−5.25000	+	9.09327i	−0.168829	+	0.292420i	−0.938008	−	0.346613i	$-0.887332\pi$
$967$	−5.25000	+	9.09327i	−0.168829	+	0.292420i	0.769180	+	0.639033i	$0.220665\pi$
$968$	−16.8577	+	9.73277i	−0.541826	+	0.312823i
$969$	−4.83844	+	0.786946i	−0.155433	+	0.0252804i
$970$	6.96583	−	12.0652i	0.223659	−	0.387389i
$971$	−11.4156	+	19.7724i	−0.366345	+	0.634527i	−0.988991	−	0.147976i	$-0.952724\pi$
$971$	−11.4156	+	19.7724i	−0.366345	+	0.634527i	0.622646	+	0.782503i	$0.286058\pi$
$972$	6.88274	+	6.60267i	0.220764	+	0.211781i
$973$		0			0
$974$	−1.09973	+	0.634927i	−0.0352375	+	0.0203444i
$975$	39.2299	+	48.0356i	1.25636	+	1.53837i
$976$			17.2414i			0.551884i
$977$			10.2601i			0.328250i	0.986440	+	0.164125i	$0.0524800\pi$
$977$			10.2601i			0.328250i	−0.986440	+	0.164125i	$0.947520\pi$
$978$	−9.05522	+	23.8857i	−0.289554	+	0.763780i
$979$	−11.4201	+	6.59337i	−0.364987	+	0.210725i
$980$		0			0
$981$	16.0851	+	14.2430i	0.513558	+	0.454743i
$982$	11.1360	−	19.2881i	0.355363	−	0.615508i
$983$	16.9599	−	29.3754i	0.540937	−	0.936930i	−0.457913	−	0.888997i	$-0.651403\pi$
$983$	16.9599	−	29.3754i	0.540937	−	0.936930i	0.998851	−	0.0479337i	$-0.0152636\pi$
$984$	13.9240	−	36.7284i	0.443881	−	1.17086i
$985$	62.2566	−	35.9438i	1.98366	−	1.14527i
$986$	−0.469440	+	0.813095i	−0.0149500	+	0.0258942i
$987$		0			0
$988$	1.92290	+	3.33056i	0.0611756	+	0.105959i
$989$	−13.4428	−	7.76119i	−0.427455	−	0.246791i
$990$	−31.3988	+	10.4912i	−0.997919	+	0.333432i
$991$	−11.4278	−	19.7935i	−0.363015	−	0.628761i	0.625440	−	0.780272i	$-0.284919\pi$
$991$	−11.4278	−	19.7935i	−0.363015	−	0.628761i	−0.988456	+	0.151511i	$0.951586\pi$
$992$	21.7941			0.691964
$993$	−2.52299	−	15.5123i	−0.0800647	−	0.492268i
$994$		0			0
$995$	−10.2002	−	5.88910i	−0.323369	−	0.186697i
$996$	1.30792	−	1.06816i	0.0414430	−	0.0338458i
$997$	−5.65867	−	3.26704i	−0.179212	−	0.103468i	0.407710	−	0.913111i	$-0.366327\pi$
$997$	−5.65867	−	3.26704i	−0.179212	−	0.103468i	−0.586922	+	0.809643i	$0.699661\pi$
$998$	17.0254	−	9.82961i	0.538929	−	0.311151i
$999$	−26.5152	−	1.05854i	−0.838904	−	0.0334907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.i.d.68.8		48
3.2	odd	2		1323.2.i.d.1097.20		48
7.2	even	3		441.2.o.e.293.7	yes	48
7.3	odd	6		441.2.s.d.374.17		48
7.4	even	3		441.2.s.d.374.18		48
7.5	odd	6		441.2.o.e.293.8	yes	48
7.6	odd	2	inner	441.2.i.d.68.7		48
9.2	odd	6		441.2.s.d.362.17		48
9.7	even	3		1323.2.s.d.656.7		48
21.2	odd	6		1323.2.o.e.881.17		48
21.5	even	6		1323.2.o.e.881.18		48
21.11	odd	6		1323.2.s.d.962.8		48
21.17	even	6		1323.2.s.d.962.7		48
21.20	even	2		1323.2.i.d.1097.1		48
63.2	odd	6		441.2.o.e.146.8	yes	48
63.11	odd	6	inner	441.2.i.d.227.17		48
63.16	even	3		1323.2.o.e.440.18		48
63.20	even	6		441.2.s.d.362.18		48
63.25	even	3		1323.2.i.d.521.1		48
63.34	odd	6		1323.2.s.d.656.8		48
63.38	even	6	inner	441.2.i.d.227.18		48
63.47	even	6		441.2.o.e.146.7	✓	48
63.52	odd	6		1323.2.i.d.521.20		48
63.61	odd	6		1323.2.o.e.440.17		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.7		48	7.6	odd	2	inner
441.2.i.d.68.8		48	1.1	even	1	trivial
441.2.i.d.227.17		48	63.11	odd	6	inner
441.2.i.d.227.18		48	63.38	even	6	inner
441.2.o.e.146.7	✓	48	63.47	even	6
441.2.o.e.146.8	yes	48	63.2	odd	6
441.2.o.e.293.7	yes	48	7.2	even	3
441.2.o.e.293.8	yes	48	7.5	odd	6
441.2.s.d.362.17		48	9.2	odd	6
441.2.s.d.362.18		48	63.20	even	6
441.2.s.d.374.17		48	7.3	odd	6
441.2.s.d.374.18		48	7.4	even	3
1323.2.i.d.521.1		48	63.25	even	3
1323.2.i.d.521.20		48	63.52	odd	6
1323.2.i.d.1097.1		48	21.20	even	2
1323.2.i.d.1097.20		48	3.2	odd	2
1323.2.o.e.440.17		48	63.61	odd	6
1323.2.o.e.440.18		48	63.16	even	3
1323.2.o.e.881.17		48	21.2	odd	6
1323.2.o.e.881.18		48	21.5	even	6
1323.2.s.d.656.7		48	9.7	even	3
1323.2.s.d.656.8		48	63.34	odd	6
1323.2.s.d.962.7		48	21.17	even	6
1323.2.s.d.962.8		48	21.11	odd	6

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.17820i q^{2} +(0.278055 + 1.70959i) q^{3} +0.611843 q^{4} +(2.16601 + 3.75164i) q^{5} +(2.01424 - 0.327604i) q^{6} -3.07728i q^{8} +(-2.84537 + 0.950717i) q^{9} +O(q^{10})\)	\(q-1.17820i q^{2} +(0.278055 + 1.70959i) q^{3} +0.611843 q^{4} +(2.16601 + 3.75164i) q^{5} +(2.01424 - 0.327604i) q^{6} -3.07728i q^{8} +(-2.84537 + 0.950717i) q^{9} +(4.42019 - 2.55200i) q^{10} +(1.87238 + 1.08102i) q^{11} +(0.170126 + 1.04600i) q^{12} +(-2.25256 - 1.30052i) q^{13} +(-5.81148 + 4.74614i) q^{15} -2.40196 q^{16} +(-0.585576 - 1.01425i) q^{17} +(1.12014 + 3.35242i) q^{18} +(-2.09282 - 1.20829i) q^{19} +(1.32526 + 2.29541i) q^{20} +(1.27366 - 2.20604i) q^{22} +(3.16186 - 1.82550i) q^{23} +(5.26087 - 0.855651i) q^{24} +(-6.88321 + 11.9221i) q^{25} +(-1.53227 + 2.65397i) q^{26} +(-2.41650 - 4.60006i) q^{27} +(0.589262 - 0.340210i) q^{29} +(5.59191 + 6.84710i) q^{30} +6.55550i q^{31} -3.32456i q^{32} +(-1.32747 + 3.50158i) q^{33} +(-1.19499 + 0.689926i) q^{34} +(-1.74092 + 0.581689i) q^{36} +(2.55346 - 4.42272i) q^{37} +(-1.42361 + 2.46576i) q^{38} +(1.59701 - 4.21256i) q^{39} +(11.5448 - 6.66541i) q^{40} +(3.68473 - 6.38214i) q^{41} +(-2.12577 - 3.68194i) q^{43} +(1.14560 + 0.661414i) q^{44} +(-9.72985 - 8.61555i) q^{45} +(-2.15081 - 3.72531i) q^{46} +7.14314 q^{47} +(-0.667877 - 4.10636i) q^{48} +(14.0466 + 8.10980i) q^{50} +(1.57112 - 1.28311i) q^{51} +(-1.37821 - 0.795711i) q^{52} +(2.79976 - 1.61644i) q^{53} +(-5.41979 + 2.84713i) q^{54} +9.36601i q^{55} +(1.48376 - 3.91383i) q^{57} +(-0.400836 - 0.694269i) q^{58} +5.83621 q^{59} +(-3.55571 + 2.90389i) q^{60} -7.17805i q^{61} +7.72370 q^{62} -8.72092 q^{64} -11.2677i q^{65} +(4.12557 + 1.56403i) q^{66} +6.65363 q^{67} +(-0.358281 - 0.620560i) q^{68} +(4.00003 + 4.89789i) q^{69} +1.95976i q^{71} +(2.92562 + 8.75599i) q^{72} +(-10.3117 + 5.95345i) q^{73} +(-5.21085 - 3.00849i) q^{74} +(-22.2957 - 8.45245i) q^{75} +(-1.28048 - 0.739283i) q^{76} +(-4.96324 - 1.88160i) q^{78} -9.75404 q^{79} +(-5.20268 - 9.01130i) q^{80} +(7.19227 - 5.41029i) q^{81} +(-7.51944 - 4.34135i) q^{82} +(-0.796736 - 1.37999i) q^{83} +(2.53673 - 4.39374i) q^{85} +(-4.33806 + 2.50458i) q^{86} +(0.745466 + 0.912797i) q^{87} +(3.32660 - 5.76184i) q^{88} +(-3.04961 + 5.28207i) q^{89} +(-10.1508 + 11.4637i) q^{90} +(1.93456 - 1.11692i) q^{92} +(-11.2072 + 1.82279i) q^{93} -8.41605i q^{94} -10.4687i q^{95} +(5.68361 - 0.924409i) q^{96} +(2.36387 - 1.36478i) q^{97} +(-6.35537 - 1.29580i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) \) 48 * q - 48 * q^4 - 8 * q^9	\( 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Introduction

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