LMFDB - Embedded newform 273.2.r.b.68.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(68,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 2]))

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

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

chi := DirichletCharacter("273.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.4
Character	$\chi$	$=$	273.68
Dual form			273.2.r.b.269.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.39579i q^{2} +(0.452516 + 1.67189i) q^{3} -3.73983 q^{4} +(-1.50632 + 2.60901i) q^{5} +(4.00551 - 1.08414i) q^{6} +(2.64172 - 0.145950i) q^{7} +4.16828i q^{8} +(-2.59046 + 1.51312i) q^{9} +(6.25066 + 3.60882i) q^{10} +(2.03299 + 1.17375i) q^{11} +(-1.69233 - 6.25260i) q^{12} +(1.38026 + 3.33090i) q^{13} +(-0.349666 - 6.32902i) q^{14} +(-5.04363 - 1.33778i) q^{15} +2.50668 q^{16} +7.57477 q^{17} +(3.62512 + 6.20621i) q^{18} +(-0.990209 + 0.571698i) q^{19} +(5.63336 - 9.75727i) q^{20} +(1.43944 + 4.35064i) q^{21} +(2.81206 - 4.87063i) q^{22} -2.98207i q^{23} +(-6.96892 + 1.88621i) q^{24} +(-2.03797 - 3.52987i) q^{25} +(7.98015 - 3.30681i) q^{26} +(-3.70200 - 3.64626i) q^{27} +(-9.87960 + 0.545828i) q^{28} +(-3.46295 + 1.99933i) q^{29} +(-3.20504 + 12.0835i) q^{30} +(-6.93264 + 4.00256i) q^{31} +2.33108i q^{32} +(-1.04242 + 3.93009i) q^{33} -18.1476i q^{34} +(-3.59848 + 7.11214i) q^{35} +(9.68788 - 5.65881i) q^{36} -4.43428 q^{37} +(1.36967 + 2.37234i) q^{38} +(-4.94432 + 3.81493i) q^{39} +(-10.8751 - 6.27874i) q^{40} +(-2.44169 - 4.22913i) q^{41} +(10.4232 - 3.44859i) q^{42} +(1.21160 - 2.09856i) q^{43} +(-7.60305 - 4.38962i) q^{44} +(-0.0457018 - 9.03778i) q^{45} -7.14444 q^{46} +(5.09681 - 8.82793i) q^{47} +(1.13431 + 4.19090i) q^{48} +(6.95740 - 0.771118i) q^{49} +(-8.45684 + 4.88256i) q^{50} +(3.42771 + 12.6642i) q^{51} +(-5.16193 - 12.4570i) q^{52} +(3.05667 - 1.76477i) q^{53} +(-8.73569 + 8.86923i) q^{54} +(-6.12466 + 3.53607i) q^{55} +(0.608360 + 11.0114i) q^{56} +(-1.40390 - 1.39682i) q^{57} +(4.78999 + 8.29651i) q^{58} -0.573777 q^{59} +(18.8623 + 5.00306i) q^{60} +(7.66197 - 4.42364i) q^{61} +(9.58931 + 16.6092i) q^{62} +(-6.62243 + 4.37532i) q^{63} +10.5981 q^{64} +(-10.7695 - 1.41628i) q^{65} +(9.41569 + 2.49743i) q^{66} +(1.13672 - 1.96886i) q^{67} -28.3284 q^{68} +(4.98571 - 1.34944i) q^{69} +(17.0392 + 8.62122i) q^{70} +(-1.96371 - 1.13375i) q^{71} +(-6.30710 - 10.7978i) q^{72} +(0.346827 - 0.200241i) q^{73} +10.6236i q^{74} +(4.97935 - 5.00459i) q^{75} +(3.70322 - 2.13805i) q^{76} +(5.54191 + 2.80400i) q^{77} +(9.13978 + 11.8456i) q^{78} +(6.63110 - 11.4854i) q^{79} +(-3.77584 + 6.53995i) q^{80} +(4.42094 - 7.83934i) q^{81} +(-10.1321 + 5.84978i) q^{82} +9.96949 q^{83} +(-5.38325 - 16.2706i) q^{84} +(-11.4100 + 19.7627i) q^{85} +(-5.02771 - 2.90275i) q^{86} +(-4.90971 - 4.88495i) q^{87} +(-4.89251 + 8.47408i) q^{88} -2.75244 q^{89} +(-21.6527 + 0.109492i) q^{90} +(4.13240 + 8.59786i) q^{91} +11.1525i q^{92} +(-9.82899 - 9.77941i) q^{93} +(-21.1499 - 12.2109i) q^{94} -3.44463i q^{95} +(-3.89731 + 1.05485i) q^{96} +(-7.47021 - 4.31293i) q^{97} +(-1.84744 - 16.6685i) q^{98} +(-7.04240 + 0.0356117i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{12} + 12 q^{13} - 9 q^{15} + 32 q^{16} + 2 q^{18} - 36 q^{19} + 10 q^{21} + 10 q^{22} - 18 q^{24} - 24 q^{25} - 14 q^{28} + 8 q^{30} - 24 q^{31}+ \cdots + 22 q^{99}+O(q^{100}) $ 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^12 + 12 * q^13 - 9 * q^15 + 32 * q^16 + 2 * q^18 - 36 * q^19 + 10 * q^21 + 10 * q^22 - 18 * q^24 - 24 * q^25 - 14 * q^28 + 8 * q^30 - 24 * q^31 - 45 * q^33 + 33 * q^39 + 90 * q^40 + 3 * q^42 - 20 * q^43 - 6 * q^48 - 6 * q^49 - 10 * q^51 - 48 * q^52 - 18 * q^55 + 4 * q^57 + 30 * q^58 + 55 * q^60 - 18 * q^61 + 31 * q^63 - 84 * q^64 + 75 * q^66 + 44 * q^67 + 33 * q^69 + 20 * q^70 + 17 * q^72 + 84 * q^73 - 18 * q^76 - 71 * q^78 + 20 * q^79 + 16 * q^81 - 18 * q^82 - 135 * q^84 - 2 * q^85 - 46 * q^88 - 10 * q^91 - 56 * q^93 + 36 * q^94 + 30 * q^96 - 24 * q^97 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	2.39579i		−	1.69408i	−0.531527	−	0.847041i	$-0.678382\pi$
$2$		−	2.39579i		−	1.69408i	0.531527	−	0.847041i	$-0.321618\pi$
$3$	0.452516	+	1.67189i	0.261260	+	0.965268i
$3$	0.452516	+	1.67189i	0.261260	+	0.965268i
$4$	−3.73983			−1.86992
$5$	−1.50632	+	2.60901i	−0.673645	+	1.16679i	0.303218	+	0.952921i	$0.401939\pi$
$5$	−1.50632	+	2.60901i	−0.673645	+	1.16679i	−0.976863	+	0.213866i	$0.931395\pi$
$6$	4.00551	−	1.08414i	1.63524	−	0.442597i
$7$	2.64172	−	0.145950i	0.998477	−	0.0551639i
$7$	2.64172	−	0.145950i	0.998477	−	0.0551639i
$8$			4.16828i			1.47371i
$9$	−2.59046	+	1.51312i	−0.863486	+	0.504373i
$10$	6.25066	+	3.60882i	1.97663	+	1.14121i
$11$	2.03299	+	1.17375i	0.612970	+	0.353899i	0.774127	−	0.633030i	$-0.218189\pi$
$11$	2.03299	+	1.17375i	0.612970	+	0.353899i	−0.161157	+	0.986929i	$0.551522\pi$
$12$	−1.69233	−	6.25260i	−0.488535	−	1.80497i
$13$	1.38026	+	3.33090i	0.382814	+	0.923825i
$13$	1.38026	+	3.33090i	0.382814	+	0.923825i
$14$	−0.349666	−	6.32902i	−0.0934521	−	1.69150i
$15$	−5.04363	−	1.33778i	−1.30226	−	0.345413i
$16$	2.50668			0.626669
$17$	7.57477			1.83715			0.918575	−	0.395246i	$-0.129341\pi$
$17$	7.57477			1.83715			0.918575	+	0.395246i	$0.129341\pi$
$18$	3.62512	+	6.20621i	0.854449	+	1.46282i
$19$	−0.990209	+	0.571698i	−0.227170	+	0.131156i	−0.609266	−	0.792966i	$-0.708536\pi$
$19$	−0.990209	+	0.571698i	−0.227170	+	0.131156i	0.382096	+	0.924123i	$0.375202\pi$
$20$	5.63336	−	9.75727i	1.25966	−	2.18179i
$21$	1.43944	+	4.35064i	0.314111	+	0.949386i
$22$	2.81206	−	4.87063i	0.599534	−	1.03842i
$23$		−	2.98207i		−	0.621806i	−0.950442	−	0.310903i	$-0.899369\pi$
$23$		−	2.98207i		−	0.621806i	0.950442	−	0.310903i	$-0.100631\pi$
$24$	−6.96892	+	1.88621i	−1.42252	+	0.385022i
$25$	−2.03797	−	3.52987i	−0.407594	−	0.705974i
$26$	7.98015	−	3.30681i	1.56504	−	0.648519i
$27$	−3.70200	−	3.64626i	−0.712450	−	0.701723i
$28$	−9.87960	+	0.545828i	−1.86707	+	0.103152i
$29$	−3.46295	+	1.99933i	−0.643053	+	0.371267i	−0.785790	−	0.618494i	$-0.787743\pi$
$29$	−3.46295	+	1.99933i	−0.643053	+	0.371267i	0.142737	+	0.989761i	$0.454410\pi$
$30$	−3.20504	+	12.0835i	−0.585158	+	2.20613i
$31$	−6.93264	+	4.00256i	−1.24514	+	0.718881i	−0.970136	−	0.242562i	$-0.922012\pi$
$31$	−6.93264	+	4.00256i	−1.24514	+	0.718881i	−0.275003	+	0.961443i	$0.588679\pi$
$32$			2.33108i			0.412080i
$33$	−1.04242	+	3.93009i	−0.181462	+	0.684141i
$34$		−	18.1476i		−	3.11229i
$35$	−3.59848	+	7.11214i	−0.608254	+	1.20217i
$36$	9.68788	−	5.65881i	1.61465	−	0.943135i
$37$	−4.43428			−0.728991			−0.364495	−	0.931205i	$-0.618758\pi$
$37$	−4.43428			−0.728991			−0.364495	+	0.931205i	$0.618758\pi$
$38$	1.36967	+	2.37234i	0.222190	+	0.384844i
$39$	−4.94432	+	3.81493i	−0.791725	+	0.610877i
$40$	−10.8751	−	6.27874i	−1.71950	−	0.992756i
$41$	−2.44169	−	4.22913i	−0.381327	−	0.660478i	0.609925	−	0.792459i	$-0.291200\pi$
$41$	−2.44169	−	4.22913i	−0.381327	−	0.660478i	−0.991252	+	0.131981i	$0.957866\pi$
$42$	10.4232	−	3.44859i	1.60834	−	0.532129i
$43$	1.21160	−	2.09856i	0.184768	−	0.320027i	−0.758731	−	0.651405i	$-0.774180\pi$
$43$	1.21160	−	2.09856i	0.184768	−	0.320027i	0.943498	+	0.331378i	$0.107513\pi$
$44$	−7.60305	−	4.38962i	−1.14620	−	0.661761i
$45$	−0.0457018	−	9.03778i	−0.00681282	−	1.34727i
$46$	−7.14444			−1.05339
$47$	5.09681	−	8.82793i	0.743445	−	1.28769i	−0.207472	−	0.978241i	$-0.566524\pi$
$47$	5.09681	−	8.82793i	0.743445	−	1.28769i	0.950918	−	0.309444i	$-0.100143\pi$
$48$	1.13431	+	4.19090i	0.163724	+	0.604904i
$49$	6.95740	−	0.771118i	0.993914	−	0.110160i
$50$	−8.45684	+	4.88256i	−1.19598	+	0.690498i
$51$	3.42771	+	12.6642i	0.479975	+	1.77334i
$52$	−5.16193	−	12.4570i	−0.715830	−	1.72748i
$53$	3.05667	−	1.76477i	0.419866	−	0.242410i	−0.275154	−	0.961400i	$-0.588729\pi$
$53$	3.05667	−	1.76477i	0.419866	−	0.242410i	0.695020	+	0.718990i	$0.255396\pi$
$54$	−8.73569	+	8.86923i	−1.18878	+	1.20695i
$55$	−6.12466	+	3.53607i	−0.825849	+	0.476804i
$56$	0.608360	+	11.0114i	0.0812955	+	1.47146i
$57$	−1.40390	−	1.39682i	−0.185952	−	0.185014i
$58$	4.78999	+	8.29651i	0.628956	+	1.08938i
$59$	−0.573777			−0.0746994			−0.0373497	−	0.999302i	$-0.511892\pi$
$59$	−0.573777			−0.0746994			−0.0373497	+	0.999302i	$0.511892\pi$
$60$	18.8623	+	5.00306i	2.43511	+	0.645893i
$61$	7.66197	−	4.42364i	0.981015	−	0.566389i	0.0784387	−	0.996919i	$-0.475006\pi$
$61$	7.66197	−	4.42364i	0.981015	−	0.566389i	0.902576	+	0.430530i	$0.141673\pi$
$62$	9.58931	+	16.6092i	1.21784	+	2.10937i
$63$	−6.62243	+	4.37532i	−0.834348	+	0.551238i
$64$	10.5981			1.32477
$65$	−10.7695	−	1.41628i	−1.33579	−	0.175667i
$66$	9.41569	+	2.49743i	1.15899	+	0.307412i
$67$	1.13672	−	1.96886i	0.138873	−	0.240535i	−0.788197	−	0.615422i	$-0.788985\pi$
$67$	1.13672	−	1.96886i	0.138873	−	0.240535i	0.927070	+	0.374888i	$0.122319\pi$
$68$	−28.3284			−3.43532
$69$	4.98571	−	1.34944i	0.600209	−	0.162453i
$70$	17.0392	+	8.62122i	2.03658	+	1.03043i
$71$	−1.96371	−	1.13375i	−0.233050	−	0.134551i	0.378929	−	0.925426i	$-0.376293\pi$
$71$	−1.96371	−	1.13375i	−0.233050	−	0.134551i	−0.611978	+	0.790875i	$0.709626\pi$
$72$	−6.30710	−	10.7978i	−0.743299	−	1.27253i
$73$	0.346827	−	0.200241i	0.0405930	−	0.0234364i	−0.479566	−	0.877506i	$-0.659206\pi$
$73$	0.346827	−	0.200241i	0.0405930	−	0.0234364i	0.520159	+	0.854069i	$0.325873\pi$
$74$			10.6236i			1.23497i
$75$	4.97935	−	5.00459i	0.574966	−	0.577881i
$76$	3.70322	−	2.13805i	0.424788	−	0.245251i
$77$	5.54191	+	2.80400i	0.631560	+	0.319546i
$78$	9.13978	+	11.8456i	1.03488	+	1.34125i
$79$	6.63110	−	11.4854i	0.746057	−	1.29221i	−0.203642	−	0.979045i	$-0.565278\pi$
$79$	6.63110	−	11.4854i	0.746057	−	1.29221i	0.949699	−	0.313163i	$-0.101389\pi$
$80$	−3.77584	+	6.53995i	−0.422152	+	0.731189i
$81$	4.42094	−	7.83934i	0.491216	−	0.871038i
$82$	−10.1321	+	5.84978i	−1.11891	+	0.646000i
$83$	9.96949			1.09429			0.547147	−	0.837037i	$-0.315714\pi$
$83$	9.96949			1.09429			0.547147	+	0.837037i	$0.315714\pi$
$84$	−5.38325	−	16.2706i	−0.587360	−	1.77527i
$85$	−11.4100	+	19.7627i	−1.23759	+	2.14356i
$86$	−5.02771	−	2.90275i	−0.542152	−	0.313012i
$87$	−4.90971	−	4.88495i	−0.526376	−	0.523721i
$88$	−4.89251	+	8.47408i	−0.521544	+	0.903340i
$89$	−2.75244			−0.291758			−0.145879	−	0.989302i	$-0.546601\pi$
$89$	−2.75244			−0.291758			−0.145879	+	0.989302i	$0.546601\pi$
$90$	−21.6527	+	0.109492i	−2.28239	+	0.0115415i
$91$	4.13240	+	8.59786i	0.433193	+	0.901301i
$92$			11.1525i			1.16272i
$93$	−9.82899	−	9.77941i	−1.01922	−	1.01408i
$94$	−21.1499	−	12.2109i	−2.18145	−	1.25946i
$95$		−	3.44463i		−	0.353411i
$96$	−3.89731	+	1.05485i	−0.397768	+	0.107660i
$97$	−7.47021	−	4.31293i	−0.758484	−	0.437911i	0.0702669	−	0.997528i	$-0.477615\pi$
$97$	−7.47021	−	4.31293i	−0.758484	−	0.437911i	−0.828751	+	0.559617i	$0.810948\pi$
$98$	−1.84744	−	16.6685i	−0.186620	−	1.68377i
$99$	−7.04240	+	0.0356117i	−0.707788	+	0.00357911i
$100$	7.62167	+	13.2011i	0.762167	+	1.32011i
$101$	−7.46597	+	12.9314i	−0.742891	+	1.28673i	0.208282	+	0.978069i	$0.433213\pi$
$101$	−7.46597	+	12.9314i	−0.742891	+	1.28673i	−0.951173	+	0.308657i	$0.900120\pi$
$102$	30.3408	−	8.21208i	3.00419	−	0.813117i
$103$	8.34410	+	4.81747i	0.822169	+	0.474679i	0.851164	−	0.524900i	$-0.175897\pi$
$103$	8.34410	+	4.81747i	0.822169	+	0.474679i	−0.0289949	+	0.999580i	$0.509231\pi$
$104$	−13.8841	+	5.75329i	−1.36145	+	0.564157i
$105$	−13.5191	−	2.79792i	−1.31933	−	0.273049i
$106$	−4.22803	−	7.32316i	−0.410662	−	0.711288i
$107$			0.881311i			0.0851996i	0.999092	+	0.0425998i	$0.0135640\pi$
$107$			0.881311i			0.0851996i	−0.999092	+	0.0425998i	$0.986436\pi$
$108$	13.8448	+	13.6364i	1.33222	+	1.31216i
$109$	−5.12018	−	8.86840i	−0.490424	−	0.849439i	0.509515	−	0.860462i	$-0.329825\pi$
$109$	−5.12018	−	8.86840i	−0.490424	−	0.849439i	−0.999939	+	0.0110224i	$0.996491\pi$
$110$	8.47170	+	14.6734i	0.807745	+	1.39906i
$111$	−2.00658	−	7.41364i	−0.190456	−	0.703672i
$112$	6.62194	−	0.365849i	0.625715	−	0.0345695i
$113$	2.35913	+	1.36205i	0.221929	+	0.128131i	0.606843	−	0.794822i	$-0.292436\pi$
$113$	2.35913	+	1.36205i	0.221929	+	0.128131i	−0.384914	+	0.922952i	$0.625769\pi$
$114$	−3.34650	+	3.36346i	−0.313428	+	0.315017i
$115$	7.78028	+	4.49194i	0.725514	+	0.418876i
$116$	12.9508	−	7.47717i	1.20245	−	0.694237i
$117$	−8.61554	−	6.54006i	−0.796507	−	0.604629i
$118$			1.37465i			0.126547i
$119$	20.0104	−	1.10554i	1.83435	−	0.101344i
$120$	5.57623	−	21.0232i	0.509038	−	1.91915i
$121$	−2.74463	−	4.75383i	−0.249511	−	0.432167i
$122$	−10.5981	−	18.3565i	−0.959510	−	1.66192i
$123$	5.96575	−	5.99599i	0.537913	−	0.540640i
$124$	25.9269	−	14.9689i	2.32830	−	1.34425i
$125$	−2.78385			−0.248995
$126$	10.4824	+	15.8660i	0.933843	+	1.41345i
$127$	−2.28093	−	3.95069i	−0.202400	−	0.350567i	0.746901	−	0.664935i	$-0.231541\pi$
$127$	−2.28093	−	3.95069i	−0.202400	−	0.350567i	−0.949301	+	0.314368i	$0.898207\pi$
$128$		−	20.7288i		−	1.83218i
$129$	4.05683	+	1.07604i	0.357184	+	0.0947400i
$130$	−3.39311	+	25.8014i	−0.297595	+	2.26293i
$131$	3.29835	−	5.71291i	0.288178	−	0.499139i	−0.685197	−	0.728358i	$-0.740284\pi$
$131$	3.29835	−	5.71291i	0.288178	−	0.499139i	0.973375	+	0.229219i	$0.0736172\pi$
$132$	3.89848	−	14.6979i	0.339319	−	1.27929i
$133$	−2.53242	+	1.65479i	−0.219589	+	0.143488i
$134$	−4.71699	−	2.72335i	−0.407486	−	0.235262i
$135$	15.0895	−	4.16615i	1.29870	−	0.358565i
$136$			31.5737i			2.70743i
$137$		−	3.02636i		−	0.258559i	−0.991608	−	0.129280i	$-0.958734\pi$
$137$		−	3.02636i		−	0.258559i	0.991608	−	0.129280i	$-0.0412665\pi$
$138$	−3.23297	−	11.9447i	−0.275209	−	1.01680i
$139$	13.5658	+	7.83223i	1.15064	+	0.664321i	0.949042	−	0.315148i	$-0.102054\pi$
$139$	13.5658	+	7.83223i	1.15064	+	0.664321i	0.201595	+	0.979469i	$0.435388\pi$
$140$	13.4577	−	26.5982i	1.13738	−	2.24796i
$141$	17.0657	+	4.52654i	1.43719	+	0.381203i
$142$	−2.71623	+	4.70465i	−0.227941	+	0.394805i
$143$	−1.10359	+	8.39177i	−0.0922867	+	0.701755i
$144$	−6.49344	+	3.79290i	−0.541120	+	0.316075i
$145$		−	12.0465i		−	1.00041i
$146$	−0.479735	−	0.830926i	−0.0397032	−	0.0687679i
$147$	4.43756	+	11.2831i	0.366004	+	0.930613i
$148$	16.5834			1.36315
$149$	6.10792	−	3.52641i	0.500380	−	0.288895i	−0.228490	−	0.973546i	$-0.573379\pi$
$149$	6.10792	−	3.52641i	0.500380	−	0.288895i	0.728871	+	0.684652i	$0.240046\pi$
$150$	−11.9900	−	11.9295i	−0.978978	−	0.974040i
$151$	3.71789	+	6.43958i	0.302558	+	0.524046i	0.976715	−	0.214543i	$-0.0688261\pi$
$151$	3.71789	+	6.43958i	0.302558	+	0.524046i	−0.674157	+	0.738588i	$0.735493\pi$
$152$	−2.38299	−	4.12747i	−0.193286	−	0.334782i
$153$	−19.6221	+	11.4615i	−1.58635	+	0.926609i
$154$	6.71782	−	13.2773i	0.541337	−	1.06991i
$155$		−	24.1165i		−	1.93708i
$156$	18.4909	−	14.2672i	1.48046	−	1.14229i
$157$	−17.9506	+	10.3638i	−1.43261	+	0.827120i	−0.997320	−	0.0731686i	$-0.976689\pi$
$157$	−17.9506	+	10.3638i	−1.43261	+	0.827120i	−0.435294	+	0.900288i	$0.643356\pi$
$158$	−27.5167	−	15.8867i	−2.18911	−	1.26388i
$159$	4.33370	+	4.31184i	0.343685	+	0.341951i
$160$	−6.08181	−	3.51134i	−0.480809	−	0.277595i
$161$	−0.435233	−	7.87781i	−0.0343012	−	0.620859i
$162$	−18.7814	−	10.5917i	−1.47561	−	0.832161i
$163$	−1.58512	−	2.74550i	−0.124156	−	0.215044i	0.797247	−	0.603653i	$-0.206289\pi$
$163$	−1.58512	−	2.74550i	−0.124156	−	0.215044i	−0.921403	+	0.388609i	$0.872956\pi$
$164$	9.13150	+	15.8162i	0.713050	+	1.23504i
$165$	−8.68344	−	8.63965i	−0.676005	−	0.672595i
$166$		−	23.8848i		−	1.85382i
$167$	−2.15047	−	3.72473i	−0.166409	−	0.288228i	0.770746	−	0.637142i	$-0.219884\pi$
$167$	−2.15047	−	3.72473i	−0.166409	−	0.288228i	−0.937155	+	0.348914i	$0.886550\pi$
$168$	−18.1347	+	5.99997i	−1.39912	+	0.462908i
$169$	−9.18978	+	9.19499i	−0.706907	+	0.707307i
$170$	47.3473	+	27.3360i	3.63137	+	2.09657i
$171$	1.70005	−	2.97926i	0.130006	−	0.227830i
$172$	−4.53119	+	7.84825i	−0.345500	+	0.598423i
$173$	9.80920	+	16.9900i	0.745780	+	1.29173i	0.949829	+	0.312768i	$0.101256\pi$
$173$	9.80920	+	16.9900i	0.745780	+	1.29173i	−0.204050	+	0.978961i	$0.565410\pi$
$174$	−11.7033	+	11.7627i	−0.887227	+	0.891725i
$175$	−5.89894	−	9.02749i	−0.445918	−	0.682414i
$176$	5.09605	+	2.94221i	0.384130	+	0.221777i
$177$	−0.259644	−	0.959295i	−0.0195160	−	0.0721050i
$178$			6.59429i			0.494263i
$179$	−8.80695	−	5.08469i	−0.658262	−	0.380048i	0.133352	−	0.991069i	$-0.457426\pi$
$179$	−8.80695	−	5.08469i	−0.658262	−	0.380048i	−0.791614	+	0.611021i	$0.790759\pi$
$180$	0.170917	+	33.7998i	0.0127394	+	2.51929i
$181$		−	17.9244i		−	1.33231i	−0.745813	−	0.666155i	$-0.767939\pi$
$181$		−	17.9244i		−	1.33231i	0.745813	−	0.666155i	$-0.232061\pi$
$182$	20.5987	−	9.90038i	1.52688	−	0.733865i
$183$	10.8630	+	10.8082i	0.803018	+	0.798968i
$184$	12.4301			0.916360
$185$	6.67942	−	11.5691i	0.491081	−	0.850577i
$186$	−23.4295	+	23.5482i	−1.71793	+	1.72664i
$187$	15.3994	+	8.89088i	1.12612	+	0.650165i
$188$	−19.0612	+	33.0150i	−1.39018	+	2.40786i
$189$	−10.3118	−	9.09210i	−0.750075	−	0.661353i
$190$	−8.25262			−0.598708
$191$	3.02197	−	1.74474i	0.218662	−	0.126245i	−0.386669	−	0.922219i	$-0.626374\pi$
$191$	3.02197	−	1.74474i	0.218662	−	0.126245i	0.605331	+	0.795974i	$0.293041\pi$
$192$	4.79583	+	17.7190i	0.346109	+	1.27876i
$193$	3.29537	−	5.70775i	0.237206	−	0.410853i	−0.722705	−	0.691156i	$-0.757102\pi$
$193$	3.29537	−	5.70775i	0.237206	−	0.410853i	0.959912	+	0.280303i	$0.0904350\pi$
$194$	−10.3329	+	17.8971i	−0.741858	+	1.28494i
$195$	−2.50550	−	18.6463i	−0.179422	−	1.33529i
$196$	−26.0195	+	2.88385i	−1.85854	+	0.205989i
$197$	−18.2907	+	10.5602i	−1.30316	+	0.752380i	−0.980945	−	0.194286i	$-0.937761\pi$
$197$	−18.2907	+	10.5602i	−1.30316	+	0.752380i	−0.322216	+	0.946666i	$0.604428\pi$
$198$	0.0853183	+	16.8722i	0.00606330	+	1.19905i
$199$			1.73731i			0.123155i	0.998102	+	0.0615775i	$0.0196131\pi$
$199$			1.73731i			0.123155i	−0.998102	+	0.0615775i	$0.980387\pi$
$200$	14.7135	−	8.49483i	1.04040	−	0.600675i
$201$	3.80611	+	1.00954i	0.268463	+	0.0712073i
$202$	30.9811	+	17.8869i	2.17982	+	1.25852i
$203$	−8.85634	+	5.78710i	−0.621593	+	0.406175i
$204$	−12.8190	−	47.3620i	−0.897512	−	3.31600i
$205$	14.7118			1.02752
$206$	11.5417	−	19.9908i	0.804146	−	1.39282i
$207$	4.51223	+	7.72494i	0.313622	+	0.536920i
$208$	3.45986	+	8.34949i	0.239898	+	0.578933i
$209$	−2.68412			−0.185664
$210$	−6.70324	+	32.3890i	−0.462568	+	2.23505i
$211$	2.76341	+	4.78637i	0.190241	+	0.329507i	0.945330	−	0.326115i	$-0.105740\pi$
$211$	2.76341	+	4.78637i	0.190241	+	0.329507i	−0.755089	+	0.655622i	$0.772406\pi$
$212$	−11.4314	+	6.59994i	−0.785114	+	0.453286i
$213$	1.00690	−	3.79616i	0.0689914	−	0.260108i
$214$	2.11144			0.144335
$215$	3.65011	+	6.32218i	0.248935	+	0.431169i
$216$	15.1986	−	15.4310i	1.03414	−	1.04994i
$217$	−17.7299	+	11.5855i	−1.20359	+	0.786473i
$218$	−21.2469	+	12.2669i	−1.43902	+	0.830819i
$219$	0.491726	+	0.489245i	0.0332277	+	0.0330601i
$220$	22.9052	−	13.2243i	1.54427	−	0.891583i
$221$	10.4551	+	25.2308i	0.703288	+	1.69721i
$222$	−17.7616	+	4.80736i	−1.19208	+	0.322649i
$223$	−12.4756	+	7.20276i	−0.835425	+	0.482333i	−0.855706	−	0.517462i	$-0.826877\pi$
$223$	−12.4756	+	7.20276i	−0.835425	+	0.482333i	0.0202817	+	0.999794i	$0.493544\pi$
$224$	0.340220	+	6.15806i	0.0227319	+	0.411453i
$225$	10.6204	+	6.06029i	0.708026	+	0.404019i
$226$	3.26318	−	5.65200i	0.217064	−	0.375965i
$227$	0.136345			0.00904957			0.00452478	−	0.999990i	$-0.498560\pi$
$227$	0.136345			0.00904957			0.00452478	+	0.999990i	$0.498560\pi$
$228$	5.25036	+	5.22388i	0.347714	+	0.345960i
$229$	0.521290	+	0.300967i	0.0344478	+	0.0198885i	0.517125	−	0.855910i	$-0.327002\pi$
$229$	0.521290	+	0.300967i	0.0344478	+	0.0198885i	−0.482677	+	0.875798i	$0.660336\pi$
$230$	10.7618	−	18.6399i	0.709610	−	1.22908i
$231$	−2.18019	+	10.5343i	−0.143446	+	0.693109i
$232$	−8.33377	−	14.4345i	−0.547139	−	0.947673i
$233$	−12.3805	−	7.14790i	−0.811076	−	0.468275i	0.0362537	−	0.999343i	$-0.488458\pi$
$233$	−12.3805	−	7.14790i	−0.811076	−	0.468275i	−0.847329	+	0.531068i	$0.821791\pi$
$234$	−15.6686	+	20.6411i	−1.02429	+	1.34935i
$235$	15.3548	+	26.5953i	1.00164	+	1.73488i
$236$	2.14583			0.139682
$237$	22.2030	+	5.88916i	1.44224	+	0.382542i
$238$	−2.64864	−	47.9409i	−0.171686	−	3.10755i
$239$			17.4646i			1.12969i	0.825197	+	0.564846i	$0.191064\pi$
$239$			17.4646i			1.12969i	−0.825197	+	0.564846i	$0.808936\pi$
$240$	−12.6427	−	3.35337i	−0.816085	−	0.216459i
$241$		−	13.7346i		−	0.884722i	−0.896837	−	0.442361i	$-0.854141\pi$
$241$		−	13.7346i		−	0.884722i	0.896837	−	0.442361i	$-0.145859\pi$
$242$	−11.3892	+	6.57556i	−0.732126	+	0.422693i
$243$	15.1071	+	3.84392i	0.969120	+	0.246588i
$244$	−28.6545	+	16.5437i	−1.83442	+	1.05910i
$245$	−8.46817	+	19.3135i	−0.541012	+	1.23389i
$246$	−14.3652	−	14.2927i	−0.915889	−	0.911269i
$247$	−3.27101	−	2.50920i	−0.208129	−	0.159656i
$248$	−16.6838	−	28.8972i	−1.05942	−	1.83497i
$249$	4.51136	+	16.6679i	0.285896	+	1.05629i
$250$			6.66953i			0.421818i
$251$	14.5439	−	25.1908i	0.918003	−	1.59003i	0.115559	−	0.993301i	$-0.463134\pi$
$251$	14.5439	−	25.1908i	0.918003	−	1.59003i	0.802444	−	0.596727i	$-0.203533\pi$
$252$	24.7668	−	16.3629i	1.56016	−	1.03077i
$253$	3.50021	−	6.06254i	0.220056	−	0.381148i
$254$	−9.46503	+	5.46464i	−0.593889	+	0.342882i
$255$	−38.2043	−	10.1334i	−2.39245	−	0.634575i
$256$	−28.4657			−1.77910
$257$	0.564893			0.0352370			0.0176185	−	0.999845i	$-0.494392\pi$
$257$	0.564893			0.0352370			0.0176185	+	0.999845i	$0.494392\pi$
$258$	2.57797	−	9.71934i	0.160497	−	0.605100i
$259$	−11.7141	+	0.647182i	−0.727881	+	0.0402139i
$260$	40.2760	+	5.29663i	2.49781	+	0.328483i
$261$	5.94539	−	10.4190i	0.368010	−	0.644922i
$262$	−13.6870	−	7.90216i	−0.845583	−	0.488197i
$263$	−18.1106	−	10.4562i	−1.11675	−	0.644756i	−0.176181	−	0.984358i	$-0.556374\pi$
$263$	−18.1106	−	10.4562i	−1.11675	−	0.644756i	−0.940569	+	0.339602i	$0.889708\pi$
$264$	−16.3817	−	4.34510i	−1.00822	−	0.267423i
$265$			10.6332i			0.653192i
$266$	3.96453	+	6.06716i	0.243081	+	0.372001i
$267$	−1.24553	−	4.60179i	−0.0762249	−	0.281625i
$268$	−4.25115	+	7.36321i	−0.259680	+	0.449780i
$269$	15.8796			0.968199			0.484099	−	0.875013i	$-0.339147\pi$
$269$	15.8796			0.968199			0.484099	+	0.875013i	$0.339147\pi$
$270$	−9.98124	−	36.1514i	−0.607439	−	2.20010i
$271$			5.99130i			0.363945i	0.983304	+	0.181973i	$0.0582483\pi$
$271$			5.99130i			0.363945i	−0.983304	+	0.181973i	$0.941752\pi$
$272$	18.9875			1.15129
$273$	−12.5047	+	10.7996i	−0.756821	+	0.653622i
$274$	−7.25053			−0.438020
$275$		−	9.56826i		−	0.576988i
$276$	−18.6457	+	5.04667i	−1.12234	+	0.303774i
$277$	28.7317			1.72632			0.863160	−	0.504930i	$-0.168482\pi$
$277$	28.7317			1.72632			0.863160	+	0.504930i	$0.168482\pi$
$278$	18.7644	−	32.5009i	1.12541	−	1.94927i
$279$	11.9024	−	20.8584i	0.712576	−	1.24876i
$280$	−29.6454	−	14.9995i	−1.77165	−	0.896390i
$281$		−	13.6303i		−	0.813117i	−0.913625	−	0.406558i	$-0.866729\pi$
$281$		−	13.6303i		−	0.813117i	0.913625	−	0.406558i	$-0.133271\pi$
$282$	10.8447	−	40.8860i	0.645790	−	2.43473i
$283$	24.0386	+	13.8787i	1.42895	+	0.825003i	0.997038	−	0.0769133i	$-0.0245065\pi$
$283$	24.0386	+	13.8787i	1.42895	+	0.825003i	0.431910	+	0.901917i	$0.357840\pi$
$284$	7.34395	+	4.24003i	0.435783	+	0.251599i
$285$	5.75905	−	1.55875i	0.341137	−	0.0923324i
$286$	20.1050	+	2.64397i	1.18883	+	0.156341i
$287$	−7.06750	−	10.8158i	−0.417181	−	0.638437i
$288$	−3.52719	−	6.03856i	−0.207842	−	0.355825i
$289$	40.3771			2.37512
$290$	−28.8609			−1.69477
$291$	3.83036	−	14.4411i	0.224540	−	0.846550i
$292$	−1.29707	+	0.748866i	−0.0759055	+	0.0438241i
$293$	−4.84856	+	8.39795i	−0.283256	+	0.490614i	−0.972185	−	0.234215i	$-0.924748\pi$
$293$	−4.84856	+	8.39795i	−0.283256	+	0.490614i	0.688929	+	0.724829i	$0.258081\pi$
$294$	27.0320	−	10.6315i	1.57654	−	0.620041i
$295$	0.864289	−	1.49699i	0.0503209	−	0.0871583i
$296$		−	18.4833i		−	1.07432i
$297$	−3.24634	−	11.7580i	−0.188372	−	0.682271i
$298$	−8.44855	−	14.6333i	−0.489411	−	0.847685i
$299$	9.93299	−	4.11603i	0.574440	−	0.238036i
$300$	−18.6219	+	18.7163i	−1.07514	+	1.08059i
$301$	2.89443	−	5.72064i	0.166832	−	0.329732i
$302$	15.4279	−	8.90731i	0.887777	−	0.512558i
$303$	−24.9985	−	6.63062i	−1.43612	−	0.380919i
$304$	−2.48213	+	1.43306i	−0.142360	+	0.0821917i
$305$			26.6536i			1.52618i
$306$	27.4594	+	47.0106i	1.56975	+	2.68741i
$307$			31.6343i			1.80546i	0.430203	+	0.902732i	$0.358442\pi$
$307$			31.6343i			1.80546i	−0.430203	+	0.902732i	$0.641558\pi$
$308$	−20.7258	−	10.4865i	−1.18096	−	0.597524i
$309$	−4.27846	+	16.1304i	−0.243393	+	0.917629i
$310$	−57.7781			−3.28158
$311$	7.62664	+	13.2097i	0.432467	+	0.749055i	0.997085	−	0.0762977i	$-0.0243099\pi$
$311$	7.62664	+	13.2097i	0.432467	+	0.749055i	−0.564618	+	0.825352i	$0.690977\pi$
$312$	−15.9017	−	20.6093i	−0.900256	−	1.16677i
$313$	−10.5870	−	6.11243i	−0.598414	−	0.345495i	0.170003	−	0.985444i	$-0.445622\pi$
$313$	−10.5870	−	6.11243i	−0.598414	−	0.345495i	−0.768418	+	0.639949i	$0.778956\pi$
$314$	24.8295	+	43.0059i	1.40121	+	2.42697i
$315$	−1.43979	−	23.8686i	−0.0811232	−	1.34484i
$316$	−24.7992	+	42.9535i	−1.39506	+	2.41632i
$317$	−26.5252	−	15.3144i	−1.48981	−	0.860140i	−0.489874	−	0.871793i	$-0.662957\pi$
$317$	−26.5252	−	15.3144i	−1.48981	−	0.860140i	−0.999932	+	0.0116535i	$0.996291\pi$
$318$	10.3303	−	10.3827i	0.579294	−	0.582230i
$319$	−9.38686			−0.525563
$320$	−15.9641	+	27.6507i	−0.892422	+	1.54572i
$321$	−1.47346	+	0.398808i	−0.0822404	+	0.0222593i
$322$	−18.8736	+	1.04273i	−1.05179	+	0.0581091i
$323$	−7.50060	+	4.33048i	−0.417345	+	0.240954i
$324$	−16.5336	+	29.3178i	−0.918533	+	1.62877i
$325$	8.94472	−	11.6604i	0.496164	−	0.646803i
$326$	−6.57766	+	3.79761i	−0.364303	+	0.210330i
$327$	12.5101	−	12.5735i	0.691808	−	0.695316i
$328$	17.6282	−	10.1776i	0.973353	−	0.561966i
$329$	12.1759	−	24.0648i	0.671280	−	1.32674i
$330$	−20.6988	+	20.8037i	−1.13943	+	1.14521i
$331$	8.70725	+	15.0814i	0.478594	+	0.828948i	0.999699	−	0.0245441i	$-0.00781342\pi$
$331$	8.70725	+	15.0814i	0.478594	+	0.828948i	−0.521105	+	0.853492i	$0.674480\pi$
$332$	−37.2842			−2.04624
$333$	11.4868	−	6.70959i	0.629473	−	0.367683i
$334$	−8.92368	+	5.15209i	−0.488282	+	0.281910i
$335$	3.42453	+	5.93145i	0.187102	+	0.324070i
$336$	3.60820	+	10.9056i	0.196843	+	0.594951i
$337$	19.3854			1.05599			0.527996	−	0.849247i	$-0.322944\pi$
$337$	19.3854			1.05599			0.527996	+	0.849247i	$0.322944\pi$
$338$	22.0293	+	22.0168i	1.19824	+	1.19756i
$339$	−1.20965	+	4.56057i	−0.0656992	+	0.247696i
$340$	42.6714	−	73.9091i	2.31418	−	4.00828i
$341$	−18.7920			−1.01764
$342$	−7.13770	−	4.07297i	−0.385963	−	0.220241i
$343$	18.2670	−	3.05251i	0.986324	−	0.164820i
$344$	8.74737	+	5.05030i	0.471627	+	0.272294i
$345$	−3.98935	+	15.0405i	−0.214779	+	0.809752i
$346$	40.7046	−	23.5008i	2.18830	−	1.26341i
$347$			0.0971993i			0.00521793i	0.999997	+	0.00260897i	$0.000830460\pi$
$347$			0.0971993i			0.00521793i	−0.999997	+	0.00260897i	$0.999170\pi$
$348$	18.3615	+	18.2689i	0.984279	+	0.979315i
$349$	−16.6421	+	9.60835i	−0.890834	+	0.514323i	−0.874215	−	0.485539i	$-0.838623\pi$
$349$	−16.6421	+	9.60835i	−0.890834	+	0.514323i	−0.0166187	+	0.999862i	$0.505290\pi$
$350$	−21.6280	+	14.1326i	−1.15607	+	0.755421i
$351$	7.03562	−	17.3638i	0.375534	−	0.926809i
$352$	−2.73610	+	4.73906i	−0.145835	+	0.252593i
$353$	−1.17384	+	2.03315i	−0.0624773	+	0.108214i	−0.895572	−	0.444916i	$-0.853233\pi$
$353$	−1.17384	+	2.03315i	−0.0624773	+	0.108214i	0.833095	+	0.553130i	$0.186567\pi$
$354$	−2.29827	+	0.622053i	−0.122152	+	0.0330617i
$355$	5.91593	−	3.41557i	0.313985	−	0.181279i
$356$	10.2937			0.545564
$357$	10.9034	+	32.9550i	0.577068	+	1.74417i
$358$	−12.1819	+	21.0996i	−0.643832	+	1.11515i
$359$	4.25959	+	2.45928i	0.224813	+	0.129796i	0.608177	−	0.793802i	$-0.291901\pi$
$359$	4.25959	+	2.45928i	0.224813	+	0.129796i	−0.383364	+	0.923597i	$0.625235\pi$
$360$	37.6720	−	0.190498i	1.98549	−	0.0100401i
$361$	−8.84632	+	15.3223i	−0.465596	+	0.806436i
$362$	−42.9432			−2.25704
$363$	6.70591	−	6.73991i	0.351969	−	0.353754i
$364$	−15.4545	−	32.1546i	−0.810035	−	1.68536i
$365$			1.20650i			0.0631512i
$366$	25.8943	−	26.0256i	1.35352	−	1.36038i
$367$	4.54478	+	2.62393i	0.237235	+	0.136968i	0.613905	−	0.789380i	$-0.289598\pi$
$367$	4.54478	+	2.62393i	0.237235	+	0.136968i	−0.376670	+	0.926348i	$0.622931\pi$
$368$		−	7.47509i		−	0.389666i
$369$	12.7243	+	7.26081i	0.662398	+	0.377983i
$370$	−27.7172	−	16.0025i	−1.44095	−	0.831931i
$371$	7.81731	−	5.10815i	0.405854	−	0.265202i
$372$	36.7588	+	36.5733i	1.90585	+	1.89624i
$373$	−16.1661	−	28.0005i	−0.837050	−	1.44981i	−0.892351	−	0.451343i	$-0.850945\pi$
$373$	−16.1661	−	28.0005i	−0.837050	−	1.44981i	0.0553011	−	0.998470i	$-0.482388\pi$
$374$	21.3007	−	36.8939i	1.10143	−	1.90774i
$375$	−1.25974	−	4.65430i	−0.0650525	−	0.240347i
$376$	36.7973	+	21.2449i	1.89767	+	1.09562i
$377$	−11.4393	−	8.77513i	−0.589155	−	0.451942i
$378$	−21.7828	+	24.7050i	−1.12039	+	1.27069i
$379$	2.14418	+	3.71383i	0.110139	+	0.190766i	0.915826	−	0.401575i	$-0.131537\pi$
$379$	2.14418	+	3.71383i	0.110139	+	0.190766i	−0.805687	+	0.592341i	$0.798204\pi$
$380$			12.8823i			0.660849i
$381$	5.57297	−	5.60122i	0.285512	−	0.286959i
$382$	−4.18003	−	7.24002i	−0.213869	−	0.370432i
$383$	−8.12508	−	14.0730i	−0.415172	−	0.719099i	0.580274	−	0.814421i	$-0.302945\pi$
$383$	−8.12508	−	14.0730i	−0.415172	−	0.719099i	−0.995446	+	0.0953219i	$0.969612\pi$
$384$	34.6563	−	9.38012i	1.76855	−	0.478677i
$385$	−15.6636	+	10.2352i	−0.798289	+	0.521635i
$386$	−13.6746	−	7.89504i	−0.696019	−	0.401847i
$387$	0.0367602	+	7.26952i	0.00186862	+	0.369531i
$388$	27.9373	+	16.1296i	1.41830	+	0.818857i
$389$	−8.08628	+	4.66861i	−0.409990	+	0.236708i	−0.690786	−	0.723060i	$-0.742735\pi$
$389$	−8.08628	+	4.66861i	−0.409990	+	0.236708i	0.280795	+	0.959768i	$0.409402\pi$
$390$	−44.6727	+	6.00265i	−2.26209	+	0.303956i
$391$		−	22.5885i		−	1.14235i
$392$	3.21423	+	29.0004i	0.162343	+	1.46474i
$393$	11.0439	+	2.92930i	0.557093	+	0.147764i
$394$	25.3000	+	43.8208i	1.27459	+	2.20766i
$395$	19.9770	+	34.6013i	1.00515	+	1.74098i
$396$	26.3374	−	0.133182i	1.32350	−	0.00669263i
$397$	−0.218983	+	0.126430i	−0.0109904	+	0.00634534i	−0.505485	−	0.862835i	$-0.668686\pi$
$397$	−0.218983	+	0.126430i	−0.0109904	+	0.00634534i	0.494495	+	0.869181i	$0.335353\pi$
$398$	4.16225			0.208635
$399$	−3.91259	−	3.48512i	−0.195874	−	0.174474i
$400$	−5.10853	−	8.84824i	−0.255427	−	0.442412i
$401$			18.8656i			0.942104i	0.882105	+	0.471052i	$0.156126\pi$
$401$			18.8656i			0.942104i	−0.882105	+	0.471052i	$0.843874\pi$
$402$	2.41865	−	9.11867i	0.120631	−	0.454798i
$403$	−22.9009	−	17.5674i	−1.14078	−	0.875093i
$404$	27.9215	−	48.3614i	1.38914	−	2.40607i
$405$	13.7936	+	23.3428i	0.685410	+	1.15991i
$406$	13.8647	+	21.2180i	0.688093	+	1.05303i
$407$	−9.01485	−	5.20473i	−0.446850	−	0.257989i
$408$	−52.7879	+	14.2876i	−2.61339	+	0.707343i
$409$		−	7.91197i		−	0.391221i	−0.980682	−	0.195611i	$-0.937331\pi$
$409$		−	7.91197i		−	0.391221i	0.980682	−	0.195611i	$-0.0626689\pi$
$410$		−	35.2464i		−	1.74070i
$411$	5.05975	−	1.36948i	0.249579	−	0.0675513i
$412$	−31.2055	−	18.0165i	−1.53739	−	0.887611i
$413$	−1.51576	+	0.0837427i	−0.0745857	+	0.00412071i
$414$	18.5074	−	10.8104i	0.909587	−	0.531301i
$415$	−15.0172	+	26.0105i	−0.737165	+	1.27681i
$416$	−7.76458	+	3.21748i	−0.380690	+	0.157750i
$417$	−6.95590	+	26.2248i	−0.340632	+	1.28423i
$418$			6.43060i			0.314531i
$419$	−3.20858	−	5.55742i	−0.156749	−	0.271498i	0.776945	−	0.629568i	$-0.216768\pi$
$419$	−3.20858	−	5.55742i	−0.156749	−	0.271498i	−0.933695	+	0.358070i	$0.883435\pi$
$420$	50.5592	+	10.4638i	2.46704	+	0.510579i
$421$	−27.2075			−1.32601			−0.663007	−	0.748614i	$-0.730720\pi$
$421$	−27.2075			−1.32601			−0.663007	+	0.748614i	$0.730720\pi$
$422$	11.4672	−	6.62056i	0.558212	−	0.322284i
$423$	0.154638	+	30.5804i	0.00751874	+	1.48687i
$424$	7.35605	+	12.7411i	0.357241	+	0.618760i
$425$	−15.4372	−	26.7379i	−0.748812	−	1.29698i
$426$	−9.09481	−	2.41232i	−0.440645	−	0.116877i
$427$	19.5952	−	12.8043i	0.948277	−	0.619644i
$428$		−	3.29595i		−	0.159316i
$429$	−14.5295	+	1.95233i	−0.701493	+	0.0942594i
$430$	15.1466	−	8.74491i	0.730436	−	0.421717i
$431$	19.5603	+	11.2931i	0.942185	+	0.543971i	0.890645	−	0.454700i	$-0.150254\pi$
$431$	19.5603	+	11.2931i	0.942185	+	0.543971i	0.0515405	+	0.998671i	$0.483587\pi$
$432$	−9.27971	−	9.13999i	−0.446470	−	0.439748i
$433$	−23.8203	−	13.7527i	−1.14473	−	0.660910i	−0.197133	−	0.980377i	$-0.563163\pi$
$433$	−23.8203	−	13.7527i	−1.14473	−	0.660910i	−0.947598	+	0.319466i	$0.896496\pi$
$434$	27.7564	+	42.4773i	1.33235	+	2.03897i
$435$	20.1405	−	5.45124i	0.965662	−	0.261367i
$436$	19.1486	+	33.1663i	0.917051	+	1.58838i
$437$	1.70484	+	2.95288i	0.0815538	+	0.141255i
$438$	1.17213	−	1.17807i	0.0560066	−	0.0562905i
$439$		−	26.9564i		−	1.28656i	−0.765631	−	0.643280i	$-0.777573\pi$
$439$		−	26.9564i		−	1.28656i	0.765631	−	0.643280i	$-0.222427\pi$
$440$	−14.7393	−	25.5293i	−0.702670	−	1.21706i
$441$	−16.8561	+	12.5249i	−0.802669	+	0.596425i
$442$	60.4478	−	25.0483i	2.87521	−	1.19143i
$443$	−11.1645	−	6.44581i	−0.530440	−	0.306250i	0.210756	−	0.977539i	$-0.432408\pi$
$443$	−11.1645	−	6.44581i	−0.530440	−	0.306250i	−0.741196	+	0.671289i	$0.765741\pi$
$444$	7.50428	+	27.7258i	0.356137	+	1.31581i
$445$	4.14605	−	7.18116i	0.196542	−	0.340420i
$446$	17.2563	+	29.8889i	0.817111	+	1.41528i
$447$	8.65971	+	8.61603i	0.409590	+	0.407524i
$448$	27.9973	−	1.54680i	1.32275	−	0.0730792i
$449$	15.3399	+	8.85649i	0.723934	+	0.417964i	0.816199	−	0.577771i	$-0.196077\pi$
$449$	15.3399	+	8.85649i	0.723934	+	0.417964i	−0.0922648	+	0.995735i	$0.529411\pi$
$450$	14.5192	−	25.4443i	0.684442	−	1.19945i
$451$		−	11.4637i		−	0.539805i
$452$	−8.82276	−	5.09382i	−0.414988	−	0.239593i
$453$	−9.08389	+	9.12994i	−0.426798	+	0.428962i
$454$		−	0.326656i		−	0.0153307i
$455$	−28.6566	−	2.16961i	−1.34344	−	0.101713i
$456$	5.82234	−	5.85186i	0.272656	−	0.274038i
$457$	−26.9925			−1.26266			−0.631329	−	0.775515i	$-0.717490\pi$
$457$	−26.9925			−1.26266			−0.631329	+	0.775515i	$0.717490\pi$
$458$	0.721055	−	1.24890i	0.0336927	−	0.0583575i
$459$	−28.0418	−	27.6196i	−1.30888	−	1.28917i
$460$	−29.0969	−	16.7991i	−1.35665	−	0.783263i
$461$	−9.02803	+	15.6370i	−0.420477	+	0.728288i	−0.995986	−	0.0895077i	$-0.971471\pi$
$461$	−9.02803	+	15.6370i	−0.420477	+	0.728288i	0.575509	+	0.817795i	$0.304804\pi$
$462$	25.2381	+	5.22329i	1.17418	+	0.243010i
$463$	−7.75112			−0.360225			−0.180113	−	0.983646i	$-0.557646\pi$
$463$	−7.75112			−0.360225			−0.180113	+	0.983646i	$0.557646\pi$
$464$	−8.68048	+	5.01168i	−0.402981	+	0.232661i
$465$	40.3202	−	10.9131i	1.86980	−	0.506083i
$466$	−17.1249	+	29.6612i	−0.793296	+	1.37403i
$467$	9.49821	−	16.4514i	0.439525	−	0.761279i	−0.558128	−	0.829755i	$-0.688480\pi$
$467$	9.49821	−	16.4514i	0.439525	−	0.761279i	0.997653	+	0.0684756i	$0.0218135\pi$
$468$	32.2207	+	24.4587i	1.48940	+	1.13061i
$469$	2.71555	−	5.36709i	0.125393	−	0.247829i
$470$	63.7168	−	36.7869i	2.93904	−	1.69685i
$471$	−25.4501	−	25.3217i	−1.17268	−	1.16676i
$472$		−	2.39166i		−	0.110085i
$473$	4.92636	−	2.84423i	0.226514	−	0.130778i
$474$	14.1092	−	53.1939i	0.648058	−	2.44328i
$475$	4.03603	+	2.33021i	0.185186	+	0.106917i
$476$	−74.8357	+	4.13452i	−3.43009	+	0.189505i
$477$	−5.24787	+	9.19667i	−0.240284	+	0.421086i
$478$	41.8416			1.91379
$479$	5.30499	−	9.18852i	0.242391	−	0.419834i	−0.719004	−	0.695006i	$-0.755402\pi$
$479$	5.30499	−	9.18852i	0.242391	−	0.419834i	0.961395	+	0.275172i	$0.0887349\pi$
$480$	3.11846	−	11.7571i	0.142338	−	0.536635i
$481$	−6.12044	−	14.7701i	−0.279068	−	0.673460i
$482$	−32.9052			−1.49879
$483$	12.9739	−	4.29250i	0.590334	−	0.195316i
$484$	10.2644	+	17.7785i	0.466565	+	0.808115i
$485$	22.5050	−	12.9932i	1.02190	−	0.589993i
$486$	9.20925	−	36.1935i	0.417740	−	1.64177i
$487$	−34.2992			−1.55425			−0.777124	−	0.629348i	$-0.783322\pi$
$487$	−34.2992			−1.55425			−0.777124	+	0.629348i	$0.783322\pi$
$488$	18.4390	+	31.9372i	0.834693	+	1.44573i
$489$	3.87290	−	3.89253i	0.175138	−	0.176026i
$490$	46.2712	+	20.2880i	2.09032	+	0.916519i
$491$	−13.6044	+	7.85449i	−0.613957	+	0.354468i	−0.774512	−	0.632559i	$-0.782005\pi$
$491$	−13.6044	+	7.85449i	−0.613957	+	0.354468i	0.160556	+	0.987027i	$0.448671\pi$
$492$	−22.3109	+	22.4240i	−1.00585	+	1.01095i
$493$	−26.2310	+	15.1445i	−1.18139	+	0.682073i
$494$	−6.01152	+	7.83667i	−0.270471	+	0.352588i
$495$	10.5152	−	18.4274i	0.472622	−	0.828249i
$496$	−17.3779	+	10.0331i	−0.780290	+	0.450500i
$497$	−5.35305	−	2.70845i	−0.240117	−	0.121490i
$498$	39.9329	−	10.8083i	1.78944	−	0.484331i
$499$	14.6954	−	25.4532i	0.657856	−	1.13944i	−0.323313	−	0.946292i	$-0.604797\pi$
$499$	14.6954	−	25.4532i	0.657856	−	1.13944i	0.981170	−	0.193149i	$-0.0618700\pi$
$500$	10.4111			0.465599
$501$	5.25422	−	5.28086i	0.234741	−	0.235931i
$502$	−60.3519	−	34.8442i	−2.69364	−	1.55517i
$503$	−7.24340	+	12.5459i	−0.322967	+	0.559396i	−0.981099	−	0.193507i	$-0.938014\pi$
$503$	−7.24340	+	12.5459i	−0.322967	+	0.559396i	0.658132	+	0.752903i	$0.271347\pi$
$504$	−18.2375	−	27.6041i	−0.812364	−	1.22959i
$505$	−22.4922	−	38.9576i	−1.00089	−	1.73359i
$506$	−14.5246	−	8.38578i	−0.645697	−	0.372793i
$507$	−19.5316	−	11.2035i	−0.867428	−	0.497563i
$508$	8.53029	+	14.7749i	0.378470	+	0.655530i
$509$	−19.2843			−0.854762			−0.427381	−	0.904072i	$-0.640564\pi$
$509$	−19.2843			−0.854762			−0.427381	+	0.904072i	$0.640564\pi$
$510$	−24.2774	+	91.5297i	−1.07502	+	4.05300i
$511$	0.886995	−	0.579599i	0.0392383	−	0.0256400i
$512$			26.7403i			1.18177i
$513$	5.75031	+	1.49414i	0.253882	+	0.0659678i
$514$		−	1.35337i		−	0.0596944i
$515$	−25.1377	+	14.5133i	−1.10770	+	0.639530i
$516$	−15.1719	−	4.02421i	−0.667905	−	0.177156i
$517$	20.7235	−	11.9647i	0.911420	−	0.526209i
$518$	1.55052	+	28.0647i	0.0681257	+	1.23309i
$519$	−23.9667	+	24.0882i	−1.05202	+	1.05736i
$520$	5.90343	−	44.8901i	0.258883	−	1.96856i
$521$	1.83171	+	3.17261i	0.0802486	+	0.138995i	0.903357	−	0.428890i	$-0.141095\pi$
$521$	1.83171	+	3.17261i	0.0802486	+	0.138995i	−0.823108	+	0.567885i	$0.807762\pi$
$522$	−24.9619	−	14.2439i	−1.09255	−	0.623440i
$523$		−	1.22628i		−	0.0536214i	−0.999641	−	0.0268107i	$-0.991465\pi$
$523$		−	1.22628i		−	0.0536214i	0.999641	−	0.0268107i	$-0.00853513\pi$
$524$	−12.3353	+	21.3653i	−0.538869	+	0.933348i
$525$	12.4236	−	13.9475i	0.542212	−	0.608718i
$526$	−25.0509	+	43.3894i	−1.09227	+	1.89187i
$527$	−52.5131	+	30.3185i	−2.28751	+	1.32069i
$528$	−2.61301	+	9.85146i	−0.113717	+	0.428730i
$529$	14.1072			0.613358
$530$	25.4750			1.10656
$531$	1.48635	−	0.868193i	0.0645019	−	0.0376764i
$532$	9.47082	−	6.18863i	0.410612	−	0.268311i
$533$	10.7166	−	13.9703i	0.464189	−	0.605120i
$534$	−11.0250	+	2.98402i	−0.477096	+	0.129131i
$535$	−2.29935	−	1.32753i	−0.0994097	−	0.0573942i
$536$	8.20676	+	4.73818i	0.354478	+	0.204658i
$537$	4.51578	−	17.0252i	0.194870	−	0.734691i
$538$		−	38.0444i		−	1.64021i
$539$	15.0494	+	6.59856i	0.648225	+	0.284220i
$540$	−56.4323	+	15.5807i	−2.42846	+	0.670486i
$541$	−19.9675	+	34.5848i	−0.858472	+	1.48692i	0.0149143	+	0.999889i	$0.495252\pi$
$541$	−19.9675	+	34.5848i	−0.858472	+	1.48692i	−0.873386	+	0.487028i	$0.838081\pi$
$542$	14.3539			0.616554
$543$	29.9677	−	8.11109i	1.28604	−	0.348080i
$544$			17.6574i			0.757053i
$545$	30.8504			1.32149
$546$	25.8736	+	29.9588i	1.10729	+	1.28212i
$547$	9.62236			0.411422			0.205711	−	0.978613i	$-0.434049\pi$
$547$	9.62236			0.411422			0.205711	+	0.978613i	$0.434049\pi$
$548$			11.3181i			0.483484i
$549$	−13.1545	+	23.0527i	−0.561421	+	0.983867i
$550$	−22.9236			−0.977465
$551$	2.28603	−	3.95952i	0.0973880	−	0.168681i
$552$	5.62483	+	20.7818i	0.239409	+	0.884534i
$553$	15.8412	−	31.3090i	0.673638	−	1.33140i
$554$		−	68.8353i		−	2.92453i
$555$	22.3648	+	5.93208i	0.949335	+	0.251803i
$556$	−50.7339	−	29.2912i	−2.15159	−	1.24222i
$557$	4.00214	+	2.31063i	0.169576	+	0.0979047i	0.582386	−	0.812912i	$-0.302119\pi$
$557$	4.00214	+	2.31063i	0.169576	+	0.0979047i	−0.412810	+	0.910817i	$0.635453\pi$
$558$	−49.9724	−	28.5156i	−2.11550	−	1.20716i
$559$	8.66241	+	1.13918i	0.366381	+	0.0481822i
$560$	−9.02023	+	17.8278i	−0.381174	+	0.753363i
$561$	−7.89610	+	29.7695i	−0.333374	+	1.25687i
$562$	−32.6555			−1.37749
$563$	31.4988			1.32752			0.663759	−	0.747947i	$-0.268960\pi$
$563$	31.4988			1.32752			0.663759	+	0.747947i	$0.268960\pi$
$564$	−63.8230	−	16.9285i	−2.68743	−	0.712818i
$565$	−7.10720	+	4.10334i	−0.299002	+	0.172629i
$566$	33.2505	−	57.5916i	1.39762	−	2.42076i
$567$	10.5348	−	21.3546i	0.442418	−	0.896809i
$568$	4.72578	−	8.18529i	0.198289	−	0.343447i
$569$			29.6621i			1.24350i	0.783215	+	0.621750i	$0.213578\pi$
$569$			29.6621i			1.24350i	−0.783215	+	0.621750i	$0.786422\pi$
$570$	−3.73444	−	13.7975i	−0.156419	−	0.577914i
$571$	−0.414519	−	0.717968i	−0.0173471	−	0.0300460i	0.857222	−	0.514948i	$-0.172189\pi$
$571$	−0.414519	−	0.717968i	−0.0173471	−	0.0300460i	−0.874569	+	0.484902i	$0.838855\pi$
$572$	4.12724	−	31.3838i	0.172568	−	1.31222i
$573$	4.28450	+	4.26289i	0.178988	+	0.178085i
$574$	−25.9125	+	16.9323i	−1.08157	+	0.706740i
$575$	−10.5263	+	6.07738i	−0.438978	+	0.253444i
$576$	−27.4540	+	16.0362i	−1.14392	+	0.668176i
$577$	−5.14146	+	2.96842i	−0.214042	+	0.123577i	−0.603188	−	0.797599i	$-0.706103\pi$
$577$	−5.14146	+	2.96842i	−0.214042	+	0.123577i	0.389147	+	0.921176i	$0.372770\pi$
$578$		−	96.7352i		−	4.02366i
$579$	11.0340	+	2.92666i	0.458556	+	0.121628i
$580$			45.0519i			1.87068i
$581$	26.3366	−	1.45505i	1.09263	−	0.0603654i
$582$	−34.5978	−	9.17676i	−1.43413	−	0.380389i
$583$	8.28559			0.343154
$584$	0.834658	+	1.44567i	0.0345384	+	0.0598223i
$585$	30.0408	−	12.6267i	1.24204	−	0.522049i
$586$	20.1198	+	11.6162i	0.831140	+	0.479859i
$587$	−13.8587	−	24.0040i	−0.572012	−	0.990753i	−0.996359	−	0.0852537i	$-0.972830\pi$
$587$	−13.8587	−	24.0040i	−0.572012	−	0.990753i	0.424348	−	0.905499i	$-0.360503\pi$
$588$	−16.5957	−	42.1968i	−0.684397	−	1.74017i
$589$	4.57651	−	7.92674i	0.188572	−	0.326616i
$590$	−3.58649	−	2.07066i	−0.147653	−	0.0852477i
$591$	−25.9323	−	25.8015i	−1.06671	−	1.06133i
$592$	−11.1153			−0.456836
$593$	15.6217	−	27.0576i	0.641507	−	1.11112i	−0.343589	−	0.939120i	$-0.611643\pi$
$593$	15.6217	−	27.0576i	0.641507	−	1.11112i	0.985096	−	0.172003i	$-0.0550240\pi$
$594$	−28.1698	+	7.77757i	−1.15582	+	0.319117i
$595$	−27.2577	+	53.8728i	−1.11746	+	2.20857i
$596$	−22.8426	+	13.1882i	−0.935669	+	0.540209i
$597$	−2.90461	+	0.786163i	−0.118878	+	0.0321755i
$598$	−9.86116	−	23.7974i	−0.403253	−	0.973148i
$599$	−0.638289	+	0.368516i	−0.0260798	+	0.0150572i	−0.512983	−	0.858399i	$-0.671460\pi$
$599$	−0.638289	+	0.368516i	−0.0260798	+	0.0150572i	0.486903	+	0.873456i	$0.338126\pi$
$600$	20.8605	+	20.7553i	0.851628	+	0.847332i
$601$	7.40310	−	4.27418i	0.301979	−	0.174348i	−0.341353	−	0.939935i	$-0.610885\pi$
$601$	7.40310	−	4.27418i	0.301979	−	0.174348i	0.643332	+	0.765588i	$0.277552\pi$
$602$	−13.7055	−	6.93447i	−0.558593	−	0.282628i
$603$	0.0344883	+	6.82025i	0.00140447	+	0.277742i
$604$	−13.9043	−	24.0829i	−0.565758	−	0.979921i
$605$	16.5371			0.672328
$606$	−15.8856	+	59.8912i	−0.645308	+	2.43291i
$607$	−39.0905	+	22.5689i	−1.58663	+	0.916043i	−0.592776	+	0.805367i	$0.701968\pi$
$607$	−39.0905	+	22.5689i	−1.58663	+	0.916043i	−0.993857	+	0.110675i	$0.964699\pi$
$608$	−1.33267	−	2.30825i	−0.0540469	−	0.0936120i
$609$	−13.6831	−	12.1881i	−0.554465	−	0.493887i
$610$	63.8565			2.58548
$611$	36.4398	+	4.79215i	1.47420	+	0.193869i
$612$	73.3834	−	42.8642i	2.96635	−	1.73268i
$613$	12.0863	−	20.9342i	0.488163	−	0.845523i	−0.511745	−	0.859138i	$-0.671001\pi$
$613$	12.0863	−	20.9342i	0.488163	−	0.845523i	0.999907	+	0.0136150i	$0.00433392\pi$
$614$	75.7893			3.05861
$615$	6.65733	+	24.5966i	0.268449	+	0.991829i
$616$	−11.6879	+	23.1002i	−0.470918	+	0.930735i
$617$	24.4243	+	14.1014i	0.983286	+	0.567700i	0.903261	−	0.429092i	$-0.141167\pi$
$617$	24.4243	+	14.1014i	0.983286	+	0.567700i	0.0800253	+	0.996793i	$0.474500\pi$
$618$	38.6452	+	10.2503i	1.55454	+	0.412328i
$619$	11.2287	−	6.48287i	0.451318	−	0.260568i	−0.257069	−	0.966393i	$-0.582757\pi$
$619$	11.2287	−	6.48287i	0.451318	−	0.260568i	0.708387	+	0.705825i	$0.249423\pi$
$620$			90.1915i			3.62218i
$621$	−10.8734	+	11.0396i	−0.436335	+	0.443005i
$622$	31.6478	−	18.2719i	1.26896	−	0.732635i
$623$	−7.27119	+	0.401719i	−0.291314	+	0.0160945i
$624$	−12.3938	+	9.56279i	−0.496150	+	0.382818i
$625$	14.3832	−	24.9124i	0.575328	−	0.996498i
$626$	−14.6441	+	25.3644i	−0.585297	+	1.01376i
$627$	−1.21461	−	4.48756i	−0.0485067	−	0.179216i
$628$	67.1322	−	38.7588i	2.67887	−	1.54664i
$629$	−33.5886			−1.33927
$630$	−57.1843	+	3.44945i	−2.27828	+	0.137429i
$631$	3.84197	−	6.65449i	0.152947	−	0.264911i	−0.779363	−	0.626573i	$-0.784457\pi$
$631$	3.84197	−	6.65449i	0.152947	−	0.264911i	0.932309	+	0.361662i	$0.117790\pi$
$632$	47.8743	+	27.6403i	1.90434	+	1.09947i
$633$	−6.75181	+	6.78604i	−0.268360	+	0.269721i
$634$	−36.6900	+	63.5490i	−1.45715	+	2.52385i
$635$	13.7432			0.545382
$636$	−16.2073	−	16.1256i	−0.642662	−	0.639420i
$637$	12.1715	+	22.1101i	0.482253	+	0.876032i
$638$			22.4890i			0.890347i
$639$	6.80241	−	0.0343981i	0.269099	−	0.00136077i
$640$	54.0817	+	31.2241i	2.13777	+	1.23424i
$641$		−	22.8500i		−	0.902520i	−0.892393	−	0.451260i	$-0.850975\pi$
$641$		−	22.8500i		−	0.902520i	0.892393	−	0.451260i	$-0.149025\pi$
$642$	0.955461	+	3.53010i	0.0377090	+	0.139322i
$643$	2.15372	+	1.24345i	0.0849343	+	0.0490368i	0.541866	−	0.840465i	$-0.317718\pi$
$643$	2.15372	+	1.24345i	0.0849343	+	0.0490368i	−0.456931	+	0.889502i	$0.651051\pi$
$644$	1.62770	+	29.4617i	0.0641403	+	1.16095i
$645$	−8.91827	+	8.96349i	−0.351157	+	0.352937i
$646$	10.3749	+	17.9699i	0.408196	+	0.707017i
$647$	−16.2720	+	28.1839i	−0.639718	+	1.10802i	0.345777	+	0.938317i	$0.387615\pi$
$647$	−16.2720	+	28.1839i	−0.639718	+	1.10802i	−0.985495	+	0.169707i	$0.945718\pi$
$648$	32.6766	+	18.4277i	1.28366	+	0.723910i
$649$	−1.16649	−	0.673471i	−0.0457885	−	0.0264360i
$650$	−27.9359	−	21.4297i	−1.09574	−	0.840542i
$651$	−27.3928	−	24.4000i	−1.07361	−	0.956309i
$652$	5.92807	+	10.2677i	0.232161	+	0.402115i
$653$			0.0139052i			0.000544151i	1.00000		0.000272075i	$8.66043e-5\pi$
$653$			0.0139052i			0.000544151i	−1.00000		0.000272075i	$0.999913\pi$
$654$	−30.1235	−	29.9716i	−1.17792	−	1.17198i
$655$	9.93670	+	17.2109i	0.388259	+	0.672485i
$656$	−6.12052	−	10.6010i	−0.238966	−	0.413901i
$657$	−0.595452	+	1.04350i	−0.0232308	+	0.0407110i
$658$	−57.6543	−	29.1710i	−2.24760	−	1.13720i
$659$	−22.5680	−	13.0297i	−0.879126	−	0.507564i	−0.00875579	−	0.999962i	$-0.502787\pi$
$659$	−22.5680	−	13.0297i	−0.879126	−	0.507564i	−0.870370	+	0.492398i	$0.836120\pi$
$660$	32.4746	+	32.3108i	1.26407	+	1.25770i
$661$	−5.89003	−	3.40061i	−0.229096	−	0.132268i	0.381059	−	0.924551i	$-0.375559\pi$
$661$	−5.89003	−	3.40061i	−0.229096	−	0.132268i	−0.610155	+	0.792282i	$0.708893\pi$
$662$	36.1319	−	20.8608i	1.40431	−	0.810777i
$663$	−37.4521	+	28.8972i	−1.45452	+	1.12227i
$664$			41.5556i			1.61267i
$665$	−0.502743	−	9.09975i	−0.0194955	−	0.352873i
$666$	−16.0748	−	27.5200i	−0.622886	−	1.06638i
$667$	5.96216	+	10.3268i	0.230856	+	0.399854i
$668$	8.04240	+	13.9299i	0.311170	+	0.538962i
$669$	−17.6876	−	17.5984i	−0.683844	−	0.680395i
$670$	14.2105	−	8.20446i	0.549001	−	0.316966i
$671$	20.7690			0.801778
$672$	−10.1417	+	3.35543i	−0.391223	+	0.129439i
$673$	−2.26755	−	3.92750i	−0.0874075	−	0.151394i	0.819007	−	0.573783i	$-0.194525\pi$
$673$	−2.26755	−	3.92750i	−0.0874075	−	0.151394i	−0.906415	+	0.422389i	$0.861192\pi$
$674$		−	46.4435i		−	1.78894i
$675$	−5.32626	+	20.4985i	−0.205008	+	0.788989i
$676$	34.3682	−	34.3877i	1.32186	−	1.32260i
$677$	−15.3870	+	26.6510i	−0.591369	+	1.02428i	0.402679	+	0.915341i	$0.368079\pi$
$677$	−15.3870	+	26.6510i	−0.591369	+	1.02428i	−0.994048	+	0.108940i	$0.965254\pi$
$678$	10.9262	+	2.89807i	0.419618	+	0.111300i
$679$	−20.3637	−	10.3033i	−0.781486	−	0.395403i
$680$	−82.3763	−	47.5600i	−3.15899	−	1.82384i
$681$	0.0616986	+	0.227955i	0.00236429	+	0.00873526i
$682$			45.0218i			1.72397i
$683$		−	2.02544i		−	0.0775015i	−0.999249	−	0.0387507i	$-0.987662\pi$
$683$		−	2.02544i		−	0.0775015i	0.999249	−	0.0387507i	$-0.0123378\pi$
$684$	−6.35790	+	11.1419i	−0.243100	+	0.426023i
$685$	7.89581	+	4.55865i	0.301683	+	0.174177i
$686$	−7.31319	−	43.7639i	−0.279219	−	1.67091i
$687$	−0.267293	+	1.00773i	−0.0101978	+	0.0384475i
$688$	3.03709	−	5.26040i	0.115788	−	0.200551i
$689$	10.0973	+	7.74563i	0.384675	+	0.295085i
$690$	36.0339	+	9.55767i	1.37179	+	0.363854i
$691$			51.9477i			1.97618i	0.153864	+	0.988092i	$0.450828\pi$
$691$			51.9477i			1.97618i	−0.153864	+	0.988092i	$0.549172\pi$
$692$	−36.6848	−	63.5399i	−1.39455	−	2.41542i
$693$	−18.5989	+	1.12191i	−0.706513	+	0.0426180i
$694$	0.232870			0.00883961
$695$	−40.8688	+	23.5956i	−1.55024	+	0.895032i
$696$	20.3618	−	20.4650i	0.771813	−	0.775725i
$697$	−18.4952	−	32.0346i	−0.700556	−	1.21340i
$698$	23.0196	+	39.8712i	0.871306	+	1.50915i
$699$	6.34814	−	23.9335i	0.240109	−	0.905247i
$700$	22.0610	+	33.7613i	0.833829	+	1.27606i
$701$		−	32.3744i		−	1.22276i	−0.791335	−	0.611382i	$-0.790614\pi$
$701$		−	32.3744i		−	1.22276i	0.791335	−	0.611382i	$-0.209386\pi$
$702$	−41.6000	−	16.8559i	−1.57009	−	0.636185i
$703$	4.39086	−	2.53507i	0.165605	−	0.0956118i
$704$	21.5459	+	12.4395i	0.812043	+	0.468833i
$705$	−37.5162	+	37.7064i	−1.41294	+	1.42010i
$706$	4.87102	+	2.81228i	0.183323	+	0.105842i
$707$	−17.8357	+	35.2509i	−0.670780	+	1.32575i
$708$	0.971023	+	3.58760i	0.0364933	+	0.134830i
$709$	−16.7039	−	28.9320i	−0.627329	−	1.08657i	−0.988086	−	0.153905i	$-0.950815\pi$
$709$	−16.7039	−	28.9320i	−0.627329	−	1.08657i	0.360757	−	0.932660i	$-0.382518\pi$
$710$	−8.18300	−	14.1734i	−0.307102	−	0.531917i
$711$	0.201188	+	39.7861i	0.00754515	+	1.49209i
$712$		−	11.4730i		−	0.429967i
$713$	11.9359	+	20.6736i	0.447004	+	0.774234i
$714$	78.9535	−	26.1223i	2.95476	−	0.977602i
$715$	−20.2319	−	15.5199i	−0.756630	−	0.580412i
$716$	32.9365	+	19.0159i	1.23089	+	0.710657i
$717$	−29.1990	+	7.90302i	−1.09045	+	0.295144i
$718$	5.89192	−	10.2051i	0.219884	−	0.380851i
$719$	7.03132	+	12.1786i	0.262224	+	0.454185i	0.966833	−	0.255411i	$-0.0822107\pi$
$719$	7.03132	+	12.1786i	0.262224	+	0.454185i	−0.704609	+	0.709596i	$0.748877\pi$
$720$	−0.114560	−	22.6548i	−0.00426938	−	0.844294i
$721$	22.7459	+	11.5086i	0.847102	+	0.428603i
$722$	36.7090	+	21.1940i	1.36617	+	0.788758i
$723$	22.9627	−	6.21512i	0.853994	−	0.231143i
$724$			67.0343i			2.49131i
$725$	14.1148	+	8.14916i	0.524209	+	0.302652i
$726$	−16.1474	−	16.0660i	−0.599288	−	0.596265i
$727$			24.2189i			0.898230i	0.893474	+	0.449115i	$0.148261\pi$
$727$			24.2189i			0.898230i	−0.893474	+	0.449115i	$0.851739\pi$
$728$	−35.8383	+	17.2250i	−1.32826	+	0.638401i
$729$	0.409577	+	26.9969i	0.0151695	+	0.999885i
$730$	2.89053			0.106983
$731$	9.17761	−	15.8961i	0.339446	−	0.587938i
$732$	−40.6259	−	40.4210i	−1.50158	−	1.49400i
$733$	34.5195	+	19.9298i	1.27501	+	0.736125i	0.975926	−	0.218103i	$-0.0699867\pi$
$733$	34.5195	+	19.9298i	1.27501	+	0.736125i	0.299081	+	0.954228i	$0.403320\pi$
$734$	6.28639	−	10.8884i	0.232035	−	0.401896i
$735$	−36.1221	−	5.41822i	−1.33238	−	0.199854i
$736$	6.95144			0.256234
$737$	4.62190	−	2.66845i	0.170250	−	0.0982938i
$738$	17.3954	−	30.4847i	0.640334	−	1.12216i
$739$	22.3798	−	38.7629i	0.823254	−	1.42592i	−0.0799921	−	0.996795i	$-0.525490\pi$
$739$	22.3798	−	38.7629i	0.823254	−	1.42592i	0.903246	−	0.429123i	$-0.141177\pi$
$740$	−24.9799	+	43.2665i	−0.918279	+	1.59051i
$741$	2.71493	−	6.60423i	0.0997354	−	0.242613i
$742$	−12.2381	−	18.7287i	−0.449274	−	0.687551i
$743$	32.0510	−	18.5047i	1.17584	−	0.678870i	0.220790	−	0.975321i	$-0.429137\pi$
$743$	32.0510	−	18.5047i	1.17584	−	0.678870i	0.955048	+	0.296451i	$0.0958033\pi$
$744$	40.7633	−	40.9700i	1.49446	−	1.50203i
$745$			21.2475i			0.778449i
$746$	−67.0835	+	38.7307i	−2.45610	+	1.41803i
$747$	−25.8255	+	15.0850i	−0.944907	+	0.551932i
$748$	−57.5913	−	33.2504i	−2.10575	−	1.21575i
$749$	0.128627	+	2.32818i	0.00469994	+	0.0850698i
$750$	−11.1507	+	3.01807i	−0.407167	+	0.110204i
$751$	−17.5397			−0.640032			−0.320016	−	0.947412i	$-0.603688\pi$
$751$	−17.5397			−0.640032			−0.320016	+	0.947412i	$0.603688\pi$
$752$	12.7760	−	22.1288i	0.465894	−	0.806952i
$753$	48.6977	+	12.9166i	1.77464	+	0.470708i
$754$	−21.0234	+	27.4063i	−0.765628	+	0.998078i
$755$	−22.4013			−0.815266
$756$	38.5645	+	34.0029i	1.40258	+	1.23667i
$757$	−3.24870	−	5.62691i	−0.118076	−	0.204514i	0.800929	−	0.598759i	$-0.204339\pi$
$757$	−3.24870	−	5.62691i	−0.118076	−	0.204514i	−0.919005	+	0.394245i	$0.871006\pi$
$758$	8.89756	−	5.13701i	0.323174	−	0.186585i
$759$	11.7198	+	3.10858i	0.425402	+	0.112834i
$760$	14.3582			0.520825
$761$	−2.70659	−	4.68795i	−0.0981138	−	0.169938i	0.812790	−	0.582557i	$-0.197948\pi$
$761$	−2.70659	−	4.68795i	−0.0981138	−	0.169938i	−0.910904	+	0.412619i	$0.864614\pi$
$762$	−13.4194	−	13.3517i	−0.486133	−	0.483681i
$763$	−14.8204	−	22.6806i	−0.536535	−	0.821092i
$764$	−11.3017	+	6.52502i	−0.408880	+	0.236067i
$765$	−0.346180	−	68.4590i	−0.0125162	−	2.47514i
$766$	−33.7161	+	19.4660i	−1.21821	+	0.703336i
$767$	−0.791960	−	1.91119i	−0.0285960	−	0.0690092i
$768$	−12.8812	−	47.5916i	−0.464809	−	1.71731i
$769$	−6.05121	+	3.49367i	−0.218212	+	0.125985i	−0.605122	−	0.796133i	$-0.706876\pi$
$769$	−6.05121	+	3.49367i	−0.218212	+	0.125985i	0.386910	+	0.922118i	$0.373542\pi$
$770$	24.5215	+	37.5267i	0.883692	+	1.35237i
$771$	0.255623	+	0.944441i	0.00920604	+	0.0340132i
$772$	−12.3241	+	21.3460i	−0.443556	+	0.768261i
$773$	−42.2660			−1.52020			−0.760101	−	0.649805i	$-0.774851\pi$
$773$	−42.2660			−1.52020			−0.760101	+	0.649805i	$0.774851\pi$
$774$	17.4163	−	0.0880698i	0.626015	−	0.00316560i
$775$	28.2570	+	16.3142i	1.01502	+	0.586023i
$776$	17.9775	−	31.1379i	0.645354	−	1.11779i
$777$	−6.38286	−	19.2919i	−0.228984	−	0.692094i
$778$	11.1850	+	19.3731i	0.401003	+	0.694558i
$779$	4.83556	+	2.79181i	0.173252	+	0.100027i
$780$	9.37013	+	69.7340i	0.335505	+	2.49688i
$781$	−2.66147	−	4.60981i	−0.0952350	−	0.164952i
$782$	−54.1175			−1.93524
$783$	20.1099	+	5.22527i	0.718669	+	0.186736i
$784$	17.4399	−	1.93294i	0.622855	−	0.0690337i
$785$		−	62.4445i		−	2.22874i
$786$	7.01801	−	26.4590i	0.250324	−	0.943761i
$787$		−	6.35416i		−	0.226501i	−0.993566	−	0.113251i	$-0.963874\pi$
$787$		−	6.35416i		−	0.226501i	0.993566	−	0.113251i	$-0.0361263\pi$
$788$	68.4043	−	39.4932i	2.43680	−	1.40689i
$789$	9.28627	−	35.0107i	0.330600	−	1.24641i
$790$	82.8975	−	47.8609i	2.94936	−	1.70281i
$791$	6.43097	+	3.25383i	0.228659	+	0.115693i
$792$	−0.148439	−	29.3547i	−0.00527456	−	1.04307i
$793$	25.3102	+	19.4155i	0.898791	+	0.689465i
$794$	0.302900	+	0.524639i	0.0107495	+	0.0186187i
$795$	−17.7776	+	4.81170i	−0.630506	+	0.170653i
$796$		−	6.49726i		−	0.230289i
$797$	2.27331	−	3.93749i	0.0805247	−	0.139473i	−0.822951	−	0.568113i	$-0.807674\pi$
$797$	2.27331	−	3.93749i	0.0805247	−	0.139473i	0.903475	+	0.428640i	$0.141007\pi$
$798$	−8.34963	+	9.37376i	−0.295574	+	0.331828i
$799$	38.6071	−	66.8695i	1.36582	−	2.36567i
$800$	8.22839	−	4.75067i	0.290918	−	0.167961i
$801$	7.13009	−	4.16477i	0.251929	−	0.147155i
$802$	45.1982			1.59600
$803$	0.940128			0.0331764
$804$	−14.2342	−	3.77550i	−0.502002	−	0.133152i
$805$	21.2089	+	10.7309i	0.747516	+	0.378216i
$806$	−42.0878	+	54.8660i	−1.48248	+	1.93257i
$807$	7.18580	+	26.5491i	0.252952	+	0.934572i
$808$	−53.9018	−	31.1202i	−1.89626	−	1.09481i
$809$	−21.5666	−	12.4515i	−0.758242	−	0.437771i	0.0704220	−	0.997517i	$-0.477565\pi$
$809$	−21.5666	−	12.4515i	−0.758242	−	0.437771i	−0.828664	+	0.559746i	$0.810899\pi$
$810$	55.9246	−	33.0467i	1.96499	−	1.16114i
$811$			5.09180i			0.178797i	0.995996	+	0.0893986i	$0.0284945\pi$
$811$			5.09180i			0.178797i	−0.995996	+	0.0893986i	$0.971506\pi$
$812$	33.1212	−	21.6428i	1.16233	−	0.759512i
$813$	−10.0168	+	2.71116i	−0.351305	+	0.0950845i
$814$	−12.4695	+	21.5977i	−0.437054	+	0.757000i
$815$	9.55074			0.334548
$816$	8.59215	+	31.7451i	0.300785	+	1.11130i
$817$			2.77068i			0.0969339i
$818$	−18.9554			−0.662762
$819$	−23.7144	−	16.0196i	−0.828648	−	0.559770i
$820$	−55.0196			−1.92137
$821$		−	35.6798i		−	1.24523i	−0.782527	−	0.622617i	$-0.786070\pi$
$821$		−	35.6798i		−	1.24523i	0.782527	−	0.622617i	$-0.213930\pi$
$822$	−3.28098	−	12.1221i	−0.114437	−	0.422807i
$823$	34.9399			1.21793			0.608964	−	0.793198i	$-0.291585\pi$
$823$	34.9399			1.21793			0.608964	+	0.793198i	$0.291585\pi$
$824$	−20.0806	+	34.7805i	−0.699539	+	1.21164i
$825$	15.9971	−	4.32980i	0.556948	−	0.150744i
$826$	0.200630	+	3.63145i	0.00698082	+	0.126354i
$827$			1.15820i			0.0402746i	0.999797	+	0.0201373i	$0.00641033\pi$
$827$			1.15820i			0.0402746i	−0.999797	+	0.0201373i	$0.993590\pi$
$828$	−16.8750	−	28.8900i	−0.586446	−	1.00400i
$829$	−33.9561	−	19.6046i	−1.17934	−	0.680895i	−0.223481	−	0.974708i	$-0.571742\pi$
$829$	−33.9561	−	19.6046i	−1.17934	−	0.680895i	−0.955863	+	0.293814i	$0.905076\pi$
$830$	62.3159	+	35.9781i	2.16302	+	1.24882i
$831$	13.0016	+	48.0364i	0.451019	+	1.66636i
$832$	14.6281	+	35.3013i	0.507139	+	1.22385i
$833$	52.7007	−	5.84104i	1.82597	−	0.202380i
$834$	62.8293	+	16.6649i	2.17560	+	0.577058i
$835$	12.9572			0.448401
$836$	10.0381			0.347177
$837$	40.2590	+	10.4607i	1.39155	+	0.361576i
$838$	−13.3144	+	7.68710i	−0.459940	+	0.265546i
$839$	−24.1607	+	41.8475i	−0.834119	+	1.44474i	0.0606274	+	0.998160i	$0.480690\pi$
$839$	−24.1607	+	41.8475i	−0.834119	+	1.44474i	−0.894746	+	0.446575i	$0.852643\pi$
$840$	11.6625	−	56.3514i	0.402395	−	1.94431i
$841$	−6.50534	+	11.2676i	−0.224322	+	0.388537i
$842$			65.1836i			2.24638i
$843$	22.7885	−	6.16794i	0.784876	−	0.212435i
$844$	−10.3347	−	17.9002i	−0.355735	−	0.616151i
$845$	−10.1472	−	37.8268i	−0.349073	−	1.30128i
$846$	73.2645	−	0.370480i	2.51888	−	0.0127374i
$847$	−7.94436	−	12.1577i	−0.272972	−	0.417744i
$848$	7.66208	−	4.42371i	0.263117	−	0.151911i
$849$	−12.3259	+	46.4704i	−0.423022	+	1.59486i
$850$	−64.0586	+	36.9842i	−2.19719	+	1.26855i
$851$			13.2233i			0.453290i
$852$	−3.76562	+	14.1970i	−0.129008	+	0.486381i
$853$			40.9592i			1.40242i	0.712956	+	0.701209i	$0.247356\pi$
$853$			40.9592i			1.40242i	−0.712956	+	0.701209i	$0.752644\pi$
$854$	−30.6765	−	46.9460i	−1.04973	−	1.60646i
$855$	5.21213	+	8.92316i	0.178251	+	0.305166i
$856$	−3.67355			−0.125559
$857$	−25.1618	−	43.5814i	−0.859509	−	1.48871i	−0.872398	−	0.488797i	$-0.837436\pi$
$857$	−25.1618	−	43.5814i	−0.859509	−	1.48871i	0.0128882	−	0.999917i	$-0.495897\pi$
$858$	4.67738	+	34.8098i	0.159683	+	1.18839i
$859$	−28.0631	−	16.2022i	−0.957499	−	0.552812i	−0.0620968	−	0.998070i	$-0.519779\pi$
$859$	−28.0631	−	16.2022i	−0.957499	−	0.552812i	−0.895402	+	0.445258i	$0.853112\pi$
$860$	−13.6508	−	23.6439i	−0.465488	−	0.806249i
$861$	14.8847	−	16.7104i	0.507270	−	0.569490i
$862$	27.0560	−	46.8624i	0.921532	−	1.59614i
$863$	14.0230	+	8.09617i	0.477348	+	0.275597i	0.719311	−	0.694689i	$-0.244458\pi$
$863$	14.0230	+	8.09617i	0.477348	+	0.275597i	−0.241963	+	0.970286i	$0.577791\pi$
$864$	8.49971	−	8.62964i	0.289166	−	0.293586i
$865$	−59.1030			−2.00956
$866$	−32.9485	+	57.0685i	−1.11964	+	1.93927i
$867$	18.2713	+	67.5062i	0.620526	+	2.29263i
$868$	66.3070	−	43.3277i	2.25060	−	1.47064i
$869$	26.9620	−	15.5665i	0.914622	−	0.528057i
$870$	−13.0600	−	48.2524i	−0.442777	−	1.63591i
$871$	8.12705	+	1.06878i	0.275375	+	0.0362141i
$872$	36.9660	−	21.3423i	1.25183	−	0.722742i
$873$	25.8772	−	0.130855i	0.875811	−	0.00442876i
$874$	7.07449	−	4.08446i	0.239298	−	0.138159i
$875$	−7.35415	+	0.406302i	−0.248616	+	0.0137355i
$876$	−1.83897	−	1.82970i	−0.0621331	−	0.0618197i
$877$	9.65237	+	16.7184i	0.325937	+	0.564540i	0.981702	−	0.190426i	$-0.0609869\pi$
$877$	9.65237	+	16.7184i	0.325937	+	0.564540i	−0.655764	+	0.754966i	$0.727654\pi$
$878$	−64.5821			−2.17954
$879$	−16.2345	−	4.30607i	−0.547577	−	0.145240i
$880$	−15.3525	+	8.86379i	−0.517534	+	0.298798i
$881$	13.8104	+	23.9203i	0.465285	+	0.805897i	0.999214	−	0.0396322i	$-0.0126186\pi$
$881$	13.8104	+	23.9203i	0.465285	+	0.805897i	−0.533930	+	0.845529i	$0.679285\pi$
$882$	30.0071	+	40.3836i	1.01039	+	1.35979i
$883$	−46.7289			−1.57255			−0.786276	−	0.617876i	$-0.787994\pi$
$883$	−46.7289			−1.57255			−0.786276	+	0.617876i	$0.787994\pi$
$884$	−39.1004	−	94.3589i	−1.31509	−	3.17363i
$885$	2.89392	+	0.767586i	0.0972780	+	0.0258021i
$886$	−15.4428	+	26.7478i	−0.518812	+	0.898609i
$887$	39.9198			1.34038			0.670189	−	0.742191i	$-0.266213\pi$
$887$	39.9198			1.34038			0.670189	+	0.742191i	$0.266213\pi$
$888$	30.9021	−	8.36400i	1.03701	−	0.280677i
$889$	−6.60218	−	10.1037i	−0.221430	−	0.338868i
$890$	−17.2046	−	9.93308i	−0.576699	−	0.332958i
$891$	18.1892	−	10.7482i	0.609360	−	0.360080i
$892$	46.6565	−	26.9371i	1.56217	−	0.901922i
$893$			11.6553i			0.390031i
$894$	20.6422	−	20.7469i	0.690380	−	0.693880i
$895$	26.5321	−	15.3183i	0.886869	−	0.512034i
$896$	−3.02536	−	54.7597i	−0.101070	−	1.82939i
$897$	11.3764	+	14.7443i	0.379847	+	0.492299i
$898$	21.2183	−	36.7512i	0.708065	−	1.22640i
$899$	16.0049	−	27.7213i	0.533793	−	0.924557i
$900$	−39.7185	−	22.6644i	−1.32395	−	0.755482i
$901$	23.1536	−	13.3677i	0.771357	−	0.445343i
$902$	−27.4647			−0.914474
$903$	10.8741	+	2.25050i	0.361867	+	0.0748921i
$904$	−5.67739	+	9.83352i	−0.188827	+	0.327058i
$905$	46.7650	+	26.9998i	1.55452	+	0.897504i
$906$	21.8735	+	21.7631i	0.726697	+	0.723031i
$907$	−9.15805	+	15.8622i	−0.304088	+	0.526696i	−0.977058	−	0.212974i	$-0.931685\pi$
$907$	−9.15805	+	15.8622i	−0.304088	+	0.526696i	0.672970	+	0.739670i	$0.265018\pi$
$908$	−0.509909			−0.0169219
$909$	−0.226518	−	44.7952i	−0.00751314	−	1.48576i
$910$	−5.19793	+	68.6554i	−0.172310	+	2.27591i
$911$			31.3937i			1.04012i	0.854130	+	0.520060i	$0.174090\pi$
$911$			31.3937i			1.04012i	−0.854130	+	0.520060i	$0.825910\pi$
$912$	−3.51913	−	3.50138i	−0.116530	−	0.115942i
$913$	20.2679	+	11.7017i	0.670770	+	0.387269i
$914$			64.6686i			2.13905i
$915$	−44.5620	+	12.0612i	−1.47317	+	0.398731i
$916$	−1.94954	−	1.12557i	−0.0644145	−	0.0371897i
$917$	7.87952	−	15.5733i	0.260205	−	0.514276i
$918$	−66.1708	+	67.1823i	−2.18396	+	2.21735i
$919$	−22.8453	−	39.5692i	−0.753597	−	1.30527i	−0.946069	−	0.323966i	$-0.894984\pi$
$919$	−22.8453	−	39.5692i	−0.753597	−	1.30527i	0.192472	−	0.981303i	$-0.438350\pi$
$920$	−18.7237	+	32.4304i	−0.617301	+	1.06920i
$921$	−52.8892	+	14.3150i	−1.74276	+	0.471696i
$922$	37.4630	+	21.6293i	1.23378	+	0.712323i
$923$	1.06598	−	8.10579i	0.0350871	−	0.266805i
$924$	8.15355	−	39.3967i	0.268232	−	1.29606i
$925$	9.03693	+	15.6524i	0.297132	+	0.514648i
$926$			18.5701i			0.610251i
$927$	−28.9045	+	0.146163i	−0.949347	+	0.00480061i
$928$	−4.66060	−	8.07239i	−0.152992	−	0.264989i
$929$	−1.89892	−	3.28903i	−0.0623017	−	0.107910i	0.833192	−	0.552984i	$-0.186511\pi$
$929$	−1.89892	−	3.28903i	−0.0623017	−	0.107910i	−0.895494	+	0.445074i	$0.853177\pi$
$930$	−26.1455	−	96.5989i	−0.857346	−	3.16760i
$931$	−6.44843	+	4.74110i	−0.211339	+	0.155383i
$932$	46.3011	+	26.7320i	1.51664	+	0.875634i
$933$	−18.6341	+	18.7285i	−0.610052	+	0.613145i
$934$	−39.4141	−	22.7558i	−1.28967	−	0.744591i
$935$	−46.3928	+	26.7849i	−1.51721	+	0.875961i
$936$	27.2608	−	35.9120i	0.891047	−	1.17382i
$937$			39.4934i			1.29019i	0.764101	+	0.645096i	$0.223183\pi$
$937$			39.4934i			1.29019i	−0.764101	+	0.645096i	$0.776817\pi$
$938$	−12.8584	−	6.50590i	−0.419843	−	0.212425i
$939$	5.42852	−	20.4664i	0.177153	−	0.667895i
$940$	−57.4243	−	99.4619i	−1.87298	−	3.24409i
$941$	−9.67541	−	16.7583i	−0.315409	−	0.546305i	0.664115	−	0.747630i	$-0.268809\pi$
$941$	−9.67541	−	16.7583i	−0.315409	−	0.546305i	−0.979524	+	0.201325i	$0.935475\pi$
$942$	−60.6656	+	60.9732i	−1.97659	+	1.98661i
$943$	−12.6116	+	7.28129i	−0.410689	+	0.237111i
$944$	−1.43827			−0.0468118
$945$	39.2543	−	13.2081i	1.27694	−	0.429660i
$946$	−6.81420	−	11.8025i	−0.221549	−	0.383734i
$947$		−	13.0602i		−	0.424398i	−0.977226	−	0.212199i	$-0.931937\pi$
$947$		−	13.0602i		−	0.424398i	0.977226	−	0.212199i	$-0.0680625\pi$
$948$	−83.0357	−	22.0245i	−2.69687	−	0.715322i
$949$	1.14569	+	0.878862i	0.0371907	+	0.0285291i
$950$	5.58269	−	9.66951i	0.181127	−	0.313720i
$951$	13.6009	−	51.2774i	0.441038	−	1.66278i
$952$	4.60818	+	83.4091i	0.149352	+	2.70330i
$953$	6.45680	+	3.72784i	0.209156	+	0.120756i	0.600919	−	0.799310i	$-0.294801\pi$
$953$	6.45680	+	3.72784i	0.209156	+	0.120756i	−0.391763	+	0.920066i	$0.628135\pi$
$954$	22.0333	+	12.5728i	0.713355	+	0.407060i
$955$			10.5125i			0.340176i
$956$		−	65.3147i		−	2.11243i
$957$	−4.24771	−	15.6938i	−0.137309	−	0.507310i
$958$	−22.0138	−	12.7097i	−0.711234	−	0.410631i
$959$	−0.441696	−	7.99479i	−0.0142631	−	0.258165i
$960$	−53.4530	−	14.1779i	−1.72519	−	0.457591i
$961$	16.5410	−	28.6498i	0.533580	−	0.924187i
$962$	−35.3862	+	14.6633i	−1.14090	+	0.472764i
$963$	−1.33353	−	2.28300i	−0.0429723	−	0.0735686i
$964$			51.3650i			1.65435i
$965$	9.92774	+	17.1954i	0.319585	+	0.553538i
$966$	−10.2840	−	31.0828i	−0.330881	−	1.00007i
$967$	−28.3666			−0.912210			−0.456105	−	0.889926i	$-0.650756\pi$
$967$	−28.3666			−0.912210			−0.456105	+	0.889926i	$0.650756\pi$
$968$	19.8153	−	11.4404i	0.636888	−	0.367707i
$969$	−10.6342	−	10.5806i	−0.341621	−	0.339898i
$970$	−31.1292	−	53.9173i	−0.999497	−	1.73118i
$971$	−5.99215	−	10.3787i	−0.192297	−	0.333069i	0.753714	−	0.657203i	$-0.228260\pi$
$971$	−5.99215	−	10.3787i	−0.192297	−	0.333069i	−0.946011	+	0.324134i	$0.894927\pi$
$972$	−56.4980	−	14.3756i	−1.81217	−	0.461098i
$973$	36.9802	+	18.7106i	1.18553	+	0.599836i
$974$			82.1739i			2.63302i
$975$	23.5426	+	9.67810i	0.753966	+	0.309947i
$976$	19.2061	−	11.0886i	0.614772	−	0.354939i
$977$	−26.9739	−	15.5734i	−0.862973	−	0.498238i	0.00203369	−	0.999998i	$-0.499353\pi$
$977$	−26.9739	−	15.5734i	−0.862973	−	0.498238i	−0.865007	+	0.501760i	$0.832686\pi$
$978$	−9.32570	−	9.27866i	−0.298203	−	0.296699i
$979$	−5.59570	−	3.23068i	−0.178839	−	0.103253i
$980$	31.6695	−	72.2292i	1.01165	−	2.30728i
$981$	26.6825	+	15.2258i	0.851908	+	0.486122i
$982$	18.8177	+	32.5933i	0.600498	+	1.04009i
$983$	15.5338	+	26.9053i	0.495451	+	0.858146i	0.999986	−	0.00524482i	$-0.00166949\pi$
$983$	15.5338	+	26.9053i	0.495451	+	0.858146i	−0.504535	+	0.863391i	$0.668336\pi$
$984$	24.9930	+	24.8669i	0.796746	+	0.792728i
$985$		−	63.6277i		−	2.02735i
$986$	36.2831	+	62.8441i	1.15549	+	2.00136i
$987$	45.7436	+	9.46711i	1.45604	+	0.301342i
$988$	12.2330	+	9.38398i	0.389184	+	0.298544i
$989$	−6.25805	−	3.61309i	−0.198995	−	0.114890i
$990$	−44.1482	−	25.1922i	−1.40312	−	0.800660i
$991$	−22.6698	+	39.2652i	−0.720130	+	1.24730i	0.240818	+	0.970570i	$0.422584\pi$
$991$	−22.6698	+	39.2652i	−0.720130	+	1.24730i	−0.960947	+	0.276731i	$0.910749\pi$
$992$	−9.33027	−	16.1605i	−0.296236	−	0.513097i
$993$	−21.2743	+	21.3822i	−0.675120	+	0.678543i
$994$	−6.48888	+	12.8248i	−0.205815	+	0.406778i
$995$	−4.53268	−	2.61694i	−0.143696	−	0.0829627i
$996$	−16.8717	−	62.3352i	−0.534601	−	1.97517i
$997$			59.8681i			1.89604i	0.318208	+	0.948021i	$0.396919\pi$
$997$			59.8681i			1.89604i	−0.318208	+	0.948021i	$0.603081\pi$
$998$	−60.9806	−	35.2072i	−1.93031	−	1.11446i
$999$	16.4157	+	16.1685i	0.519369	+	0.511550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.r.b.68.4	✓	64
3.2	odd	2	inner	273.2.r.b.68.29	yes	64
7.3	odd	6		273.2.bf.b.185.29	yes	64
13.9	even	3		273.2.bf.b.152.4	yes	64
21.17	even	6		273.2.bf.b.185.4	yes	64
39.35	odd	6		273.2.bf.b.152.29	yes	64
91.87	odd	6	inner	273.2.r.b.269.4	yes	64
273.269	even	6	inner	273.2.r.b.269.29	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.r.b.68.4	✓	64	1.1	even	1	trivial
273.2.r.b.68.29	yes	64	3.2	odd	2	inner
273.2.r.b.269.4	yes	64	91.87	odd	6	inner
273.2.r.b.269.29	yes	64	273.269	even	6	inner
273.2.bf.b.152.4	yes	64	13.9	even	3
273.2.bf.b.152.29	yes	64	39.35	odd	6
273.2.bf.b.185.4	yes	64	21.17	even	6
273.2.bf.b.185.29	yes	64	7.3	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.39579i q^{2} +(0.452516 + 1.67189i) q^{3} -3.73983 q^{4} +(-1.50632 + 2.60901i) q^{5} +(4.00551 - 1.08414i) q^{6} +(2.64172 - 0.145950i) q^{7} +4.16828i q^{8} +(-2.59046 + 1.51312i) q^{9} +(6.25066 + 3.60882i) q^{10} +(2.03299 + 1.17375i) q^{11} +(-1.69233 - 6.25260i) q^{12} +(1.38026 + 3.33090i) q^{13} +(-0.349666 - 6.32902i) q^{14} +(-5.04363 - 1.33778i) q^{15} +2.50668 q^{16} +7.57477 q^{17} +(3.62512 + 6.20621i) q^{18} +(-0.990209 + 0.571698i) q^{19} +(5.63336 - 9.75727i) q^{20} +(1.43944 + 4.35064i) q^{21} +(2.81206 - 4.87063i) q^{22} -2.98207i q^{23} +(-6.96892 + 1.88621i) q^{24} +(-2.03797 - 3.52987i) q^{25} +(7.98015 - 3.30681i) q^{26} +(-3.70200 - 3.64626i) q^{27} +(-9.87960 + 0.545828i) q^{28} +(-3.46295 + 1.99933i) q^{29} +(-3.20504 + 12.0835i) q^{30} +(-6.93264 + 4.00256i) q^{31} +2.33108i q^{32} +(-1.04242 + 3.93009i) q^{33} -18.1476i q^{34} +(-3.59848 + 7.11214i) q^{35} +(9.68788 - 5.65881i) q^{36} -4.43428 q^{37} +(1.36967 + 2.37234i) q^{38} +(-4.94432 + 3.81493i) q^{39} +(-10.8751 - 6.27874i) q^{40} +(-2.44169 - 4.22913i) q^{41} +(10.4232 - 3.44859i) q^{42} +(1.21160 - 2.09856i) q^{43} +(-7.60305 - 4.38962i) q^{44} +(-0.0457018 - 9.03778i) q^{45} -7.14444 q^{46} +(5.09681 - 8.82793i) q^{47} +(1.13431 + 4.19090i) q^{48} +(6.95740 - 0.771118i) q^{49} +(-8.45684 + 4.88256i) q^{50} +(3.42771 + 12.6642i) q^{51} +(-5.16193 - 12.4570i) q^{52} +(3.05667 - 1.76477i) q^{53} +(-8.73569 + 8.86923i) q^{54} +(-6.12466 + 3.53607i) q^{55} +(0.608360 + 11.0114i) q^{56} +(-1.40390 - 1.39682i) q^{57} +(4.78999 + 8.29651i) q^{58} -0.573777 q^{59} +(18.8623 + 5.00306i) q^{60} +(7.66197 - 4.42364i) q^{61} +(9.58931 + 16.6092i) q^{62} +(-6.62243 + 4.37532i) q^{63} +10.5981 q^{64} +(-10.7695 - 1.41628i) q^{65} +(9.41569 + 2.49743i) q^{66} +(1.13672 - 1.96886i) q^{67} -28.3284 q^{68} +(4.98571 - 1.34944i) q^{69} +(17.0392 + 8.62122i) q^{70} +(-1.96371 - 1.13375i) q^{71} +(-6.30710 - 10.7978i) q^{72} +(0.346827 - 0.200241i) q^{73} +10.6236i q^{74} +(4.97935 - 5.00459i) q^{75} +(3.70322 - 2.13805i) q^{76} +(5.54191 + 2.80400i) q^{77} +(9.13978 + 11.8456i) q^{78} +(6.63110 - 11.4854i) q^{79} +(-3.77584 + 6.53995i) q^{80} +(4.42094 - 7.83934i) q^{81} +(-10.1321 + 5.84978i) q^{82} +9.96949 q^{83} +(-5.38325 - 16.2706i) q^{84} +(-11.4100 + 19.7627i) q^{85} +(-5.02771 - 2.90275i) q^{86} +(-4.90971 - 4.88495i) q^{87} +(-4.89251 + 8.47408i) q^{88} -2.75244 q^{89} +(-21.6527 + 0.109492i) q^{90} +(4.13240 + 8.59786i) q^{91} +11.1525i q^{92} +(-9.82899 - 9.77941i) q^{93} +(-21.1499 - 12.2109i) q^{94} -3.44463i q^{95} +(-3.89731 + 1.05485i) q^{96} +(-7.47021 - 4.31293i) q^{97} +(-1.84744 - 16.6685i) q^{98} +(-7.04240 + 0.0356117i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{12} + 12 q^{13} - 9 q^{15} + 32 q^{16} + 2 q^{18} - 36 q^{19} + 10 q^{21} + 10 q^{22} - 18 q^{24} - 24 q^{25} - 14 q^{28} + 8 q^{30} - 24 q^{31}+ \cdots + 22 q^{99}+O(q^{100}) \) 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^12 + 12 * q^13 - 9 * q^15 + 32 * q^16 + 2 * q^18 - 36 * q^19 + 10 * q^21 + 10 * q^22 - 18 * q^24 - 24 * q^25 - 14 * q^28 + 8 * q^30 - 24 * q^31 - 45 * q^33 + 33 * q^39 + 90 * q^40 + 3 * q^42 - 20 * q^43 - 6 * q^48 - 6 * q^49 - 10 * q^51 - 48 * q^52 - 18 * q^55 + 4 * q^57 + 30 * q^58 + 55 * q^60 - 18 * q^61 + 31 * q^63 - 84 * q^64 + 75 * q^66 + 44 * q^67 + 33 * q^69 + 20 * q^70 + 17 * q^72 + 84 * q^73 - 18 * q^76 - 71 * q^78 + 20 * q^79 + 16 * q^81 - 18 * q^82 - 135 * q^84 - 2 * q^85 - 46 * q^88 - 10 * q^91 - 56 * q^93 + 36 * q^94 + 30 * q^96 - 24 * q^97 + 22 * q^99

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