LMFDB - Embedded newform 429.2.j.a.122.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(122,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("429.122");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.j (of order $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			122.2
Character	$\chi$	$=$	429.122
Dual form			429.2.j.a.320.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.89533 - 1.89533i) q^{2} +(-0.602141 + 1.62402i) q^{3} +5.18453i q^{4} +(1.30667 + 1.30667i) q^{5} +(4.21929 - 1.93679i) q^{6} +(3.41860 + 3.41860i) q^{7} +(6.03572 - 6.03572i) q^{8} +(-2.27485 - 1.95577i) q^{9} +O(q^{10})$	\(q+(-1.89533 - 1.89533i) q^{2} +(-0.602141 + 1.62402i) q^{3} +5.18453i q^{4} +(1.30667 + 1.30667i) q^{5} +(4.21929 - 1.93679i) q^{6} +(3.41860 + 3.41860i) q^{7} +(6.03572 - 6.03572i) q^{8} +(-2.27485 - 1.95577i) q^{9} -4.95311i q^{10} +(-0.707107 + 0.707107i) q^{11} +(-8.41975 - 3.12182i) q^{12} +(1.44865 + 3.30173i) q^{13} -12.9587i q^{14} +(-2.90884 + 1.33525i) q^{15} -12.5103 q^{16} -2.79234 q^{17} +(0.604761 + 8.01842i) q^{18} +(0.627072 - 0.627072i) q^{19} +(-6.77444 + 6.77444i) q^{20} +(-7.61034 + 3.49338i) q^{21} +2.68040 q^{22} +1.68238 q^{23} +(6.16774 + 13.4364i) q^{24} -1.58525i q^{25} +(3.51218 - 9.00352i) q^{26} +(4.54599 - 2.51674i) q^{27} +(-17.7238 + 17.7238i) q^{28} +5.88397i q^{29} +(8.04393 + 2.98247i) q^{30} +(0.384185 - 0.384185i) q^{31} +(11.6396 + 11.6396i) q^{32} +(-0.722574 - 1.57413i) q^{33} +(5.29240 + 5.29240i) q^{34} +8.93394i q^{35} +(10.1398 - 11.7940i) q^{36} +(-7.72211 - 7.72211i) q^{37} -2.37701 q^{38} +(-6.23435 + 0.364532i) q^{39} +15.7733 q^{40} +(1.99641 + 1.99641i) q^{41} +(21.0452 + 7.80299i) q^{42} -4.66697i q^{43} +(-3.66601 - 3.66601i) q^{44} +(-0.416931 - 5.52801i) q^{45} +(-3.18865 - 3.18865i) q^{46} +(1.55759 - 1.55759i) q^{47} +(7.53293 - 20.3168i) q^{48} +16.3737i q^{49} +(-3.00457 + 3.00457i) q^{50} +(1.68138 - 4.53481i) q^{51} +(-17.1179 + 7.51059i) q^{52} +4.74240i q^{53} +(-13.3862 - 3.84608i) q^{54} -1.84790 q^{55} +41.2674 q^{56} +(0.640789 + 1.39596i) q^{57} +(11.1521 - 11.1521i) q^{58} +(-3.62235 + 3.62235i) q^{59} +(-6.92263 - 15.0810i) q^{60} +11.1461 q^{61} -1.45631 q^{62} +(-1.09081 - 14.4628i) q^{63} -19.1011i q^{64} +(-2.42134 + 6.20716i) q^{65} +(-1.61398 + 4.35301i) q^{66} +(-0.402962 + 0.402962i) q^{67} -14.4770i q^{68} +(-1.01303 + 2.73220i) q^{69} +(16.9327 - 16.9327i) q^{70} +(-6.95962 - 6.95962i) q^{71} +(-25.5348 + 1.92588i) q^{72} +(2.36351 + 2.36351i) q^{73} +29.2719i q^{74} +(2.57448 + 0.954546i) q^{75} +(3.25107 + 3.25107i) q^{76} -4.83463 q^{77} +(12.5070 + 11.1252i) q^{78} +2.38657 q^{79} +(-16.3467 - 16.3467i) q^{80} +(1.34991 + 8.89819i) q^{81} -7.56770i q^{82} +(9.01316 + 9.01316i) q^{83} +(-18.1115 - 39.4560i) q^{84} +(-3.64865 - 3.64865i) q^{85} +(-8.84544 + 8.84544i) q^{86} +(-9.55567 - 3.54298i) q^{87} +8.53579i q^{88} +(-7.68759 + 7.68759i) q^{89} +(-9.68716 + 11.2676i) q^{90} +(-6.33492 + 16.2397i) q^{91} +8.72232i q^{92} +(0.392589 + 0.855257i) q^{93} -5.90429 q^{94} +1.63875 q^{95} +(-25.9115 + 11.8942i) q^{96} +(-9.77544 + 9.77544i) q^{97} +(31.0335 - 31.0335i) q^{98} +(2.99150 - 0.225624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) $ 96 * q + 12 * q^6 - 16 * q^7	$ 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) $ 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.89533	−	1.89533i	−1.34020	−	1.34020i	−0.895858	−	0.444340i	$-0.853438\pi$
$2$	−1.89533	−	1.89533i	−1.34020	−	1.34020i	−0.444340	−	0.895858i	$-0.646562\pi$
$3$	−0.602141	+	1.62402i	−0.347646	+	0.937626i
$3$	−0.602141	+	1.62402i	−0.347646	+	0.937626i
$4$			5.18453i			2.59226i
$5$	1.30667	+	1.30667i	0.584358	+	0.584358i	0.936098	−	0.351740i	$-0.114410\pi$
$5$	1.30667	+	1.30667i	0.584358	+	0.584358i	−0.351740	+	0.936098i	$0.614410\pi$
$6$	4.21929	−	1.93679i	1.72252	−	0.790690i
$7$	3.41860	+	3.41860i	1.29211	+	1.29211i	0.933479	+	0.358631i	$0.116756\pi$
$7$	3.41860	+	3.41860i	1.29211	+	1.29211i	0.358631	+	0.933479i	$0.383244\pi$
$8$	6.03572	−	6.03572i	2.13395	−	2.13395i
$9$	−2.27485	−	1.95577i	−0.758284	−	0.651924i
$10$		−	4.95311i		−	1.56631i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	−8.41975	−	3.12182i	−2.43057	−	0.901190i
$13$	1.44865	+	3.30173i	0.401784	+	0.915734i
$13$	1.44865	+	3.30173i	0.401784	+	0.915734i
$14$		−	12.9587i		−	3.46337i
$15$	−2.90884	+	1.33525i	−0.751059	+	0.344759i
$16$	−12.5103			−3.12756
$17$	−2.79234			−0.677242			−0.338621	−	0.940923i	$-0.609960\pi$
$17$	−2.79234			−0.677242			−0.338621	+	0.940923i	$0.609960\pi$
$18$	0.604761	+	8.01842i	0.142543	+	1.88996i
$19$	0.627072	−	0.627072i	0.143860	−	0.143860i	−0.631509	−	0.775369i	$-0.717564\pi$
$19$	0.627072	−	0.627072i	0.143860	−	0.143860i	0.775369	+	0.631509i	$0.217564\pi$
$20$	−6.77444	+	6.77444i	−1.51481	+	1.51481i
$21$	−7.61034	+	3.49338i	−1.66071	+	0.762319i
$22$	2.68040			0.571462
$23$	1.68238			0.350800			0.175400	−	0.984497i	$-0.443878\pi$
$23$	1.68238			0.350800			0.175400	+	0.984497i	$0.443878\pi$
$24$	6.16774	+	13.4364i	1.25899	+	2.74270i
$25$		−	1.58525i		−	0.317051i
$26$	3.51218	−	9.00352i	0.688795	−	1.76574i
$27$	4.54599	−	2.51674i	0.874876	−	0.484348i
$28$	−17.7238	+	17.7238i	−3.34949	+	3.34949i
$29$			5.88397i			1.09263i	0.837581	+	0.546313i	$0.183969\pi$
$29$			5.88397i			1.09263i	−0.837581	+	0.546313i	$0.816031\pi$
$30$	8.04393	+	2.98247i	1.46861	+	0.544523i
$31$	0.384185	−	0.384185i	0.0690017	−	0.0690017i	−0.671764	−	0.740765i	$-0.734463\pi$
$31$	0.384185	−	0.384185i	0.0690017	−	0.0690017i	0.740765	+	0.671764i	$0.234463\pi$
$32$	11.6396	+	11.6396i	2.05761	+	2.05761i
$33$	−0.722574	−	1.57413i	−0.125784	−	0.274021i
$34$	5.29240	+	5.29240i	0.907639	+	0.907639i
$35$			8.93394i			1.51011i
$36$	10.1398	−	11.7940i	1.68996	−	1.96567i
$37$	−7.72211	−	7.72211i	−1.26951	−	1.26951i	−0.946343	−	0.323165i	$-0.895253\pi$
$37$	−7.72211	−	7.72211i	−1.26951	−	1.26951i	−0.323165	−	0.946343i	$-0.604747\pi$
$38$	−2.37701			−0.385602
$39$	−6.23435	+	0.364532i	−0.998295	+	0.0583719i
$40$	15.7733			2.49398
$41$	1.99641	+	1.99641i	0.311787	+	0.311787i	0.845602	−	0.533815i	$-0.179242\pi$
$41$	1.99641	+	1.99641i	0.311787	+	0.311787i	−0.533815	+	0.845602i	$0.679242\pi$
$42$	21.0452	+	7.80299i	3.24734	+	1.20403i
$43$		−	4.66697i		−	0.711707i	−0.934542	−	0.355853i	$-0.884190\pi$
$43$		−	4.66697i		−	0.711707i	0.934542	−	0.355853i	$-0.115810\pi$
$44$	−3.66601	−	3.66601i	−0.552672	−	0.552672i
$45$	−0.416931	−	5.52801i	−0.0621524	−	0.824067i
$46$	−3.18865	−	3.18865i	−0.470141	−	0.470141i
$47$	1.55759	−	1.55759i	0.227198	−	0.227198i	−0.584323	−	0.811521i	$-0.698640\pi$
$47$	1.55759	−	1.55759i	0.227198	−	0.227198i	0.811521	+	0.584323i	$0.198640\pi$
$48$	7.53293	−	20.3168i	1.08729	−	2.93248i
$49$			16.3737i			2.33910i
$50$	−3.00457	+	3.00457i	−0.424911	+	0.424911i
$51$	1.68138	−	4.53481i	0.235441	−	0.635000i
$52$	−17.1179	+	7.51059i	−2.37382	+	1.04153i
$53$			4.74240i			0.651419i	0.945470	+	0.325709i	$0.105603\pi$
$53$			4.74240i			0.651419i	−0.945470	+	0.325709i	$0.894397\pi$
$54$	−13.3862	−	3.84608i	−1.82163	−	0.523385i
$55$	−1.84790			−0.249171
$56$	41.2674			5.51459
$57$	0.640789	+	1.39596i	0.0848745	+	0.184899i
$58$	11.1521	−	11.1521i	1.46434	−	1.46434i
$59$	−3.62235	+	3.62235i	−0.471590	+	0.471590i	−0.902429	−	0.430839i	$-0.858218\pi$
$59$	−3.62235	+	3.62235i	−0.471590	+	0.471590i	0.430839	+	0.902429i	$0.358218\pi$
$60$	−6.92263	−	15.0810i	−0.893707	−	1.94694i
$61$	11.1461			1.42711			0.713553	−	0.700601i	$-0.247085\pi$
$61$	11.1461			1.42711			0.713553	+	0.700601i	$0.247085\pi$
$62$	−1.45631			−0.184952
$63$	−1.09081	−	14.4628i	−0.137429	−	1.82214i
$64$		−	19.1011i		−	2.38764i
$65$	−2.42134	+	6.20716i	−0.300331	+	0.769903i
$66$	−1.61398	+	4.35301i	−0.198667	+	0.535818i
$67$	−0.402962	+	0.402962i	−0.0492297	+	0.0492297i	−0.731293	−	0.682063i	$-0.761083\pi$
$67$	−0.402962	+	0.402962i	−0.0492297	+	0.0492297i	0.682063	+	0.731293i	$0.261083\pi$
$68$		−	14.4770i		−	1.75559i
$69$	−1.01303	+	2.73220i	−0.121954	+	0.328919i
$70$	16.9327	−	16.9327i	2.02385	−	2.02385i
$71$	−6.95962	−	6.95962i	−0.825955	−	0.825955i	0.161000	−	0.986954i	$-0.448528\pi$
$71$	−6.95962	−	6.95962i	−0.825955	−	0.825955i	−0.986954	+	0.161000i	$0.948528\pi$
$72$	−25.5348	+	1.92588i	−3.00931	+	0.226967i
$73$	2.36351	+	2.36351i	0.276628	+	0.276628i	0.831761	−	0.555134i	$-0.187333\pi$
$73$	2.36351	+	2.36351i	0.276628	+	0.276628i	−0.555134	+	0.831761i	$0.687333\pi$
$74$			29.2719i			3.40278i
$75$	2.57448	+	0.954546i	0.297275	+	0.110221i
$76$	3.25107	+	3.25107i	0.372923	+	0.372923i
$77$	−4.83463			−0.550958
$78$	12.5070	+	11.1252i	1.41614	+	1.25968i
$79$	2.38657			0.268510			0.134255	−	0.990947i	$-0.457136\pi$
$79$	2.38657			0.268510			0.134255	+	0.990947i	$0.457136\pi$
$80$	−16.3467	−	16.3467i	−1.82762	−	1.82762i
$81$	1.34991	+	8.89819i	0.149990	+	0.988688i
$82$		−	7.56770i		−	0.835712i
$83$	9.01316	+	9.01316i	0.989323	+	0.989323i	0.999944	−	0.0106209i	$-0.00338081\pi$
$83$	9.01316	+	9.01316i	0.989323	+	0.989323i	−0.0106209	+	0.999944i	$0.503381\pi$
$84$	−18.1115	−	39.4560i	−1.97613	−	4.30500i
$85$	−3.64865	−	3.64865i	−0.395752	−	0.395752i
$86$	−8.84544	+	8.84544i	−0.953828	+	0.953828i
$87$	−9.55567	−	3.54298i	−1.02447	−	0.379848i
$88$			8.53579i			0.909918i
$89$	−7.68759	+	7.68759i	−0.814883	+	0.814883i	−0.985361	−	0.170478i	$-0.945469\pi$
$89$	−7.68759	+	7.68759i	−0.814883	+	0.814883i	0.170478	+	0.985361i	$0.445469\pi$
$90$	−9.68716	+	11.2676i	−1.02112	+	1.18771i
$91$	−6.33492	+	16.2397i	−0.664080	+	1.70238i
$92$			8.72232i			0.909365i
$93$	0.392589	+	0.855257i	0.0407096	+	0.0886860i
$94$	−5.90429			−0.608981
$95$	1.63875			0.168132
$96$	−25.9115	+	11.8942i	−2.64458	+	1.21395i
$97$	−9.77544	+	9.77544i	−0.992546	+	0.992546i	−0.999972	−	0.00742656i	$-0.997636\pi$
$97$	−9.77544	+	9.77544i	−0.992546	+	0.992546i	0.00742656	+	0.999972i	$0.497636\pi$
$98$	31.0335	−	31.0335i	3.13485	−	3.13485i
$99$	2.99150	−	0.225624i	0.300657	−	0.0226760i
$100$	8.21878			0.821878
$101$	−3.14180			−0.312621			−0.156311	−	0.987708i	$-0.549960\pi$
$101$	−3.14180			−0.312621			−0.156311	+	0.987708i	$0.549960\pi$
$102$	−11.7817	+	5.40817i	−1.16656	+	0.535488i
$103$		−	6.88498i		−	0.678397i	−0.940715	−	0.339199i	$-0.889844\pi$
$103$		−	6.88498i		−	0.678397i	0.940715	−	0.339199i	$-0.110156\pi$
$104$	28.6719	+	11.1846i	2.81152	+	1.09674i
$105$	−14.5089	−	5.37949i	−1.41592	−	0.524984i
$106$	8.98839	−	8.98839i	0.873030	−	0.873030i
$107$		−	7.80811i		−	0.754838i	−0.926043	−	0.377419i	$-0.876812\pi$
$107$		−	7.80811i		−	0.754838i	0.926043	−	0.377419i	$-0.123188\pi$
$108$	13.0481	+	23.5688i	1.25556	+	2.26791i
$109$	−9.16865	+	9.16865i	−0.878198	+	0.878198i	−0.993348	−	0.115151i	$-0.963265\pi$
$109$	−9.16865	+	9.16865i	−0.878198	+	0.878198i	0.115151	+	0.993348i	$0.463265\pi$
$110$	3.50238	+	3.50238i	0.333939	+	0.333939i
$111$	17.1906	−	7.89103i	1.63166	−	0.748984i
$112$	−42.7676	−	42.7676i	−4.04116	−	4.04116i
$113$		−	18.7930i		−	1.76790i	−0.467584	−	0.883949i	$-0.654875\pi$
$113$		−	18.7930i		−	1.76790i	0.467584	−	0.883949i	$-0.345125\pi$
$114$	1.43130	−	3.86030i	0.134053	−	0.361551i
$115$	2.19830	+	2.19830i	0.204993	+	0.204993i
$116$	−30.5056			−2.83238
$117$	3.16195	−	10.3442i	0.292323	−	0.956320i
$118$	13.7311			1.26405
$119$	−9.54590	−	9.54590i	−0.875072	−	0.875072i
$120$	−9.49776	+	25.6161i	−0.867023	+	2.33842i
$121$		−	1.00000i		−	0.0909091i
$122$	−21.1254	−	21.1254i	−1.91261	−	1.91261i
$123$	−4.44432	+	2.04008i	−0.400731	+	0.183948i
$124$	1.99182	+	1.99182i	0.178871	+	0.178871i
$125$	8.60472	−	8.60472i	0.769630	−	0.769630i
$126$	−25.3443	+	29.4792i	−2.25785	+	2.62622i
$127$		−	18.0698i		−	1.60343i	−0.597706	−	0.801716i	$-0.703921\pi$
$127$		−	18.0698i		−	1.60343i	0.597706	−	0.801716i	$-0.296079\pi$
$128$	−12.9237	+	12.9237i	−1.14230	+	1.14230i
$129$	7.57924	+	2.81018i	0.667314	+	0.247422i
$130$	16.3538	−	7.17535i	1.43433	−	0.629320i
$131$			6.77252i			0.591718i	0.955232	+	0.295859i	$0.0956058\pi$
$131$			6.77252i			0.591718i	−0.955232	+	0.295859i	$0.904394\pi$
$132$	8.16112	−	3.74621i	0.710334	−	0.326065i
$133$	4.28742			0.371766
$134$	1.52749			0.131955
$135$	9.22862	+	2.65154i	0.794274	+	0.228208i
$136$	−16.8538	+	16.8538i	−1.44520	+	1.44520i
$137$	7.66209	−	7.66209i	0.654617	−	0.654617i	−0.299485	−	0.954101i	$-0.596815\pi$
$137$	7.66209	−	7.66209i	0.654617	−	0.654617i	0.954101	+	0.299485i	$0.0968147\pi$
$138$	7.09844	−	3.25840i	0.604259	−	0.277374i
$139$	6.45291			0.547329			0.273664	−	0.961825i	$-0.411764\pi$
$139$	6.45291			0.547329			0.273664	+	0.961825i	$0.411764\pi$
$140$	−46.3182			−3.91460
$141$	1.59166	+	3.46744i	0.134042	+	0.292011i
$142$			26.3815i			2.21389i
$143$	−3.35903	−	1.31032i	−0.280896	−	0.109574i
$144$	28.4590	+	24.4672i	2.37158	+	2.03893i
$145$	−7.68838	+	7.68838i	−0.638485	+	0.638485i
$146$		−	8.95924i		−	0.741472i
$147$	−26.5911	−	9.85927i	−2.19320	−	0.813179i
$148$	40.0355	−	40.0355i	3.29090	−	3.29090i
$149$	3.28073	+	3.28073i	0.268768	+	0.268768i	0.828603	−	0.559836i	$-0.189136\pi$
$149$	3.28073	+	3.28073i	0.268768	+	0.268768i	−0.559836	+	0.828603i	$0.689136\pi$
$150$	−3.07030	−	6.68865i	−0.250689	−	0.546126i
$151$	−4.30136	−	4.30136i	−0.350039	−	0.350039i	0.510085	−	0.860124i	$-0.329614\pi$
$151$	−4.30136	−	4.30136i	−0.350039	−	0.350039i	−0.860124	+	0.510085i	$0.829614\pi$
$152$		−	7.56965i		−	0.613980i
$153$	6.35216	+	5.46118i	0.513542	+	0.441511i
$154$	9.16321	+	9.16321i	0.738392	+	0.738392i
$155$	1.00400			0.0806435
$156$	−1.88993	−	32.3221i	−0.151315	−	2.58784i
$157$	21.1532			1.68821			0.844105	−	0.536179i	$-0.180133\pi$
$157$	21.1532			1.68821			0.844105	+	0.536179i	$0.180133\pi$
$158$	−4.52332	−	4.52332i	−0.359856	−	0.359856i
$159$	−7.70173	−	2.85559i	−0.610787	−	0.226463i
$160$			30.4181i			2.40476i
$161$	5.75137	+	5.75137i	0.453272	+	0.453272i
$162$	14.3065	−	19.4235i	1.12402	−	1.52605i
$163$	−4.60218	−	4.60218i	−0.360471	−	0.360471i	0.503516	−	0.863986i	$-0.332040\pi$
$163$	−4.60218	−	4.60218i	−0.360471	−	0.360471i	−0.863986	+	0.503516i	$0.832040\pi$
$164$	−10.3504	+	10.3504i	−0.808233	+	0.808233i
$165$	1.11270	−	3.00102i	0.0866234	−	0.233629i
$166$		−	34.1658i		−	2.65178i
$167$	−2.42871	+	2.42871i	−0.187939	+	0.187939i	−0.794805	−	0.606866i	$-0.792427\pi$
$167$	−2.42871	+	2.42871i	−0.187939	+	0.187939i	0.606866	+	0.794805i	$0.292427\pi$
$168$	−24.8488	+	67.0189i	−1.91713	+	5.17062i
$169$	−8.80280	+	9.56612i	−0.677139	+	0.735856i
$170$			13.8308i			1.06077i
$171$	−2.65291	+	0.200086i	−0.202873	+	0.0153010i
$172$	24.1960			1.84493
$173$	3.67199			0.279176			0.139588	−	0.990210i	$-0.455422\pi$
$173$	3.67199			0.279176			0.139588	+	0.990210i	$0.455422\pi$
$174$	11.3960	+	24.8262i	0.863928	+	1.88207i
$175$	5.41935	−	5.41935i	0.409664	−	0.409664i
$176$	8.84608	−	8.84608i	0.666799	−	0.666799i
$177$	−3.70159	−	8.06393i	−0.278229	−	0.606122i
$178$	29.1410			2.18421
$179$	22.1473			1.65536			0.827682	−	0.561198i	$-0.189659\pi$
$179$	22.1473			1.65536			0.827682	+	0.561198i	$0.189659\pi$
$180$	28.6601	−	2.16159i	2.13620	−	0.161115i
$181$			4.57033i			0.339710i	0.985469	+	0.169855i	$0.0543300\pi$
$181$			4.57033i			0.339710i	−0.985469	+	0.169855i	$0.945670\pi$
$182$	42.7862	−	18.7727i	3.17152	−	1.39153i
$183$	−6.71150	+	18.1014i	−0.496128	+	1.33809i
$184$	10.1543	−	10.1543i	0.748588	−	0.748588i
$185$		−	20.1804i		−	1.48369i
$186$	0.876906	−	2.36508i	0.0642979	−	0.173416i
$187$	1.97448	−	1.97448i	0.144389	−	0.144389i
$188$	8.07537	+	8.07537i	0.588957	+	0.588957i
$189$	24.1447	+	6.93717i	1.75627	+	0.504605i
$190$	−3.10596	−	3.10596i	−0.225330	−	0.225330i
$191$			16.8392i			1.21844i	0.793000	+	0.609221i	$0.208518\pi$
$191$			16.8392i			1.21844i	−0.793000	+	0.609221i	$0.791482\pi$
$192$	31.0205	+	11.5016i	2.23871	+	0.830054i
$193$	5.33472	+	5.33472i	0.384002	+	0.384002i	0.872542	−	0.488540i	$-0.162470\pi$
$193$	5.33472	+	5.33472i	0.384002	+	0.384002i	−0.488540	+	0.872542i	$0.662470\pi$
$194$	37.0553			2.66042
$195$	−8.62253	−	7.66989i	−0.617472	−	0.549252i
$196$	−84.8898			−6.06356
$197$	0.531359	+	0.531359i	0.0378577	+	0.0378577i	0.725782	−	0.687925i	$-0.241478\pi$
$197$	0.531359	+	0.531359i	0.0378577	+	0.0378577i	−0.687925	+	0.725782i	$0.741478\pi$
$198$	−6.09751	−	5.24225i	−0.433331	−	0.372550i
$199$		−	24.8357i		−	1.76056i	−0.474455	−	0.880280i	$-0.657355\pi$
$199$		−	24.8357i		−	1.76056i	0.474455	−	0.880280i	$-0.342645\pi$
$200$	−9.56814	−	9.56814i	−0.676569	−	0.676569i
$201$	−0.411777	−	0.897057i	−0.0290445	−	0.0632735i
$202$	5.95474	+	5.95474i	0.418974	+	0.418974i
$203$	−20.1150	+	20.1150i	−1.41179	+	1.41179i
$204$	23.5108	+	8.71717i	1.64609	+	0.610324i
$205$			5.21728i			0.364390i
$206$	−13.0493	+	13.0493i	−0.909187	+	0.909187i
$207$	−3.82716	−	3.29034i	−0.266006	−	0.228695i
$208$	−18.1230	−	41.3054i	−1.25661	−	2.86402i
$209$			0.886813i			0.0613422i
$210$	17.3031	+	37.6949i	1.19403	+	2.60120i
$211$	1.78461			0.122858			0.0614288	−	0.998111i	$-0.480434\pi$
$211$	1.78461			0.122858			0.0614288	+	0.998111i	$0.480434\pi$
$212$	−24.5871			−1.68865
$213$	15.4932	−	7.11186i	1.06158	−	0.487296i
$214$	−14.7989	+	14.7989i	−1.01163	+	1.01163i
$215$	6.09817	−	6.09817i	0.415892	−	0.415892i
$216$	12.2479	−	42.6286i	0.833366	−	2.90051i
$217$	2.62675			0.178316
$218$	34.7552			2.35392
$219$	−5.26154	+	2.41521i	−0.355542	+	0.163205i
$220$		−	9.58050i		−	0.645917i
$221$	−4.04514	−	9.21955i	−0.272105	−	0.620174i
$222$	−47.5379	−	17.6258i	−3.19054	−	1.18297i
$223$	5.35986	−	5.35986i	0.358922	−	0.358922i	−0.504493	−	0.863416i	$-0.668321\pi$
$223$	5.35986	−	5.35986i	0.358922	−	0.358922i	0.863416	+	0.504493i	$0.168321\pi$
$224$			79.5822i			5.31731i
$225$	−3.10039	+	3.60622i	−0.206693	+	0.240414i
$226$	−35.6189	+	35.6189i	−2.36933	+	2.36933i
$227$	−14.7810	−	14.7810i	−0.981048	−	0.981048i	0.0187761	−	0.999824i	$-0.494023\pi$
$227$	−14.7810	−	14.7810i	−0.981048	−	0.981048i	−0.999824	+	0.0187761i	$0.994023\pi$
$228$	−7.23739	+	3.32218i	−0.479308	+	0.220017i
$229$	0.516380	+	0.516380i	0.0341233	+	0.0341233i	0.723963	−	0.689839i	$-0.242319\pi$
$229$	0.516380	+	0.516380i	0.0341233	+	0.0341233i	−0.689839	+	0.723963i	$0.742319\pi$
$230$		−	8.33300i		−	0.549462i
$231$	2.91113	−	7.85152i	0.191538	−	0.516592i
$232$	35.5140	+	35.5140i	2.33161	+	2.33161i
$233$	24.7902			1.62406			0.812031	−	0.583614i	$-0.198362\pi$
$233$	24.7902			1.62406			0.812031	+	0.583614i	$0.198362\pi$
$234$	−25.5985	+	13.6127i	−1.67343	+	0.889888i
$235$	4.07050			0.265530
$236$	−18.7802	−	18.7802i	−1.22249	−	1.22249i
$237$	−1.43705	+	3.87582i	−0.0933464	+	0.251762i
$238$			36.1852i			2.34554i
$239$	6.20775	+	6.20775i	0.401546	+	0.401546i	0.878778	−	0.477231i	$-0.158360\pi$
$239$	6.20775	+	6.20775i	0.401546	+	0.401546i	−0.477231	+	0.878778i	$0.658360\pi$
$240$	36.3903	−	16.7043i	2.34899	−	1.07826i
$241$	20.6791	+	20.6791i	1.33206	+	1.33206i	0.903527	+	0.428532i	$0.140969\pi$
$241$	20.6791	+	20.6791i	1.33206	+	1.33206i	0.428532	+	0.903527i	$0.359031\pi$
$242$	−1.89533	+	1.89533i	−0.121836	+	0.121836i
$243$	−15.2636	−	3.16569i	−0.979162	−	0.203079i
$244$			57.7870i			3.69944i
$245$	−21.3949	+	21.3949i	−1.36687	+	1.36687i
$246$	12.2901	+	4.55682i	0.783585	+	0.290532i
$247$	2.97883	+	1.16201i	0.189538	+	0.0739369i
$248$		−	4.63767i		−	0.294492i
$249$	−20.0647	+	9.21032i	−1.27155	+	0.583680i
$250$	−32.6175			−2.06291
$251$	18.6493			1.17714			0.588568	−	0.808448i	$-0.299692\pi$
$251$	18.6493			1.17714			0.588568	+	0.808448i	$0.299692\pi$
$252$	74.9829	−	5.65532i	4.72348	−	0.356252i
$253$	−1.18962	+	1.18962i	−0.0747907	+	0.0747907i
$254$	−34.2481	+	34.2481i	−2.14892	+	2.14892i
$255$	8.12248	−	3.72847i	0.508649	−	0.233486i
$256$	10.7870			0.674185
$257$	−11.0519			−0.689400			−0.344700	−	0.938713i	$-0.612019\pi$
$257$	−11.0519			−0.689400			−0.344700	+	0.938713i	$0.612019\pi$
$258$	−9.03893	−	19.6913i	−0.562739	−	1.22593i
$259$		−	52.7977i		−	3.28069i
$260$	−32.1812	−	12.5535i	−1.99579	−	0.778537i
$261$	11.5077	−	13.3852i	0.712310	−	0.828521i
$262$	12.8361	−	12.8361i	0.793019	−	0.793019i
$263$		−	18.5585i		−	1.14436i	−0.820127	−	0.572182i	$-0.806097\pi$
$263$		−	18.5585i		−	1.14436i	0.820127	−	0.572182i	$-0.193903\pi$
$264$	−13.8623	−	5.13975i	−0.853163	−	0.316330i
$265$	−6.19673	+	6.19673i	−0.380662	+	0.380662i
$266$	−8.12606	−	8.12606i	−0.498240	−	0.498240i
$267$	−7.85575	−	17.1138i	−0.480764	−	1.04735i
$268$	−2.08917	−	2.08917i	−0.127616	−	0.127616i
$269$			0.771591i			0.0470447i	0.999723	+	0.0235224i	$0.00748809\pi$
$269$			0.771591i			0.0470447i	−0.999723	+	0.0235224i	$0.992512\pi$
$270$	−12.4657	−	22.5168i	−0.758640	−	1.37033i
$271$	4.23476	+	4.23476i	0.257243	+	0.257243i	0.823932	−	0.566689i	$-0.191776\pi$
$271$	4.23476	+	4.23476i	0.257243	+	0.257243i	−0.566689	+	0.823932i	$0.691776\pi$
$272$	34.9329			2.11812
$273$	−22.5590	−	20.0666i	−1.36533	−	1.21448i
$274$	−29.0443			−1.75463
$275$	1.12094	+	1.12094i	0.0675954	+	0.0675954i
$276$	−14.1652	−	5.25207i	−0.852644	−	0.316137i
$277$		−	5.72097i		−	0.343740i	−0.985120	−	0.171870i	$-0.945019\pi$
$277$		−	5.72097i		−	0.343740i	0.985120	−	0.171870i	$-0.0549809\pi$
$278$	−12.2304	−	12.2304i	−0.733529	−	0.733529i
$279$	−1.62534	+	0.122586i	−0.0973068	+	0.00733902i
$280$	53.9227	+	53.9227i	3.22250	+	3.22250i
$281$	7.75727	−	7.75727i	0.462760	−	0.462760i	−0.436799	−	0.899559i	$-0.643888\pi$
$281$	7.75727	−	7.75727i	0.462760	−	0.462760i	0.899559	+	0.436799i	$0.143888\pi$
$282$	3.55521	−	9.58865i	0.211710	−	0.570996i
$283$			12.0670i			0.717308i	0.933471	+	0.358654i	$0.116764\pi$
$283$			12.0670i			0.717308i	−0.933471	+	0.358654i	$0.883236\pi$
$284$	36.0823	−	36.0823i	2.14109	−	2.14109i
$285$	−0.986756	+	2.66135i	−0.0584504	+	0.157645i
$286$	3.88297	+	8.84994i	0.229605	+	0.523308i
$287$			13.6499i			0.805726i
$288$	−3.71396	−	49.2427i	−0.218847	−	2.90165i
$289$	−9.20283			−0.541343
$290$	29.1440			1.71139
$291$	−9.98928	−	21.7617i	−0.585582	−	1.27569i
$292$	−12.2537	+	12.2537i	−0.717092	+	0.717092i
$293$	3.77888	−	3.77888i	0.220765	−	0.220765i	−0.588056	−	0.808820i	$-0.700106\pi$
$293$	3.77888	−	3.77888i	0.220765	−	0.220765i	0.808820	+	0.588056i	$0.200106\pi$
$294$	31.7123	+	69.0854i	1.84950	+	4.02914i
$295$	−9.46641			−0.551155
$296$	−93.2170			−5.41813
$297$	−1.43489	+	4.99411i	−0.0832608	+	0.289787i
$298$		−	12.4361i		−	0.720404i
$299$	2.43718	+	5.55475i	0.140946	+	0.321239i
$300$	−4.94887	+	13.3474i	−0.285723	+	0.770614i
$301$	15.9545	−	15.9545i	0.919603	−	0.919603i
$302$			16.3049i			0.938244i
$303$	1.89181	−	5.10234i	0.108682	−	0.293122i
$304$	−7.84482	+	7.84482i	−0.449932	+	0.449932i
$305$	14.5642	+	14.5642i	0.833942	+	0.833942i
$306$	−1.68870	−	22.3902i	−0.0965365	−	1.27996i
$307$	4.95125	+	4.95125i	0.282583	+	0.282583i	0.834138	−	0.551555i	$-0.185966\pi$
$307$	4.95125	+	4.95125i	0.282583	+	0.282583i	−0.551555	+	0.834138i	$0.685966\pi$
$308$		−	25.0653i		−	1.42823i
$309$	11.1813	+	4.14573i	0.636083	+	0.235842i
$310$	−1.90291	−	1.90291i	−0.108078	−	0.108078i
$311$	16.3060			0.924629			0.462315	−	0.886716i	$-0.347019\pi$
$311$	16.3060			0.924629			0.462315	+	0.886716i	$0.347019\pi$
$312$	−35.4285	+	39.8290i	−2.00575	+	2.25487i
$313$	−19.3263			−1.09239			−0.546193	−	0.837659i	$-0.683924\pi$
$313$	−19.3263			−1.09239			−0.546193	+	0.837659i	$0.683924\pi$
$314$	−40.0922	−	40.0922i	−2.26253	−	2.26253i
$315$	17.4727	−	20.3234i	0.984478	−	1.14509i
$316$			12.3732i			0.696048i
$317$	0.990325	+	0.990325i	0.0556222	+	0.0556222i	0.734371	−	0.678749i	$-0.237477\pi$
$317$	0.990325	+	0.990325i	0.0556222	+	0.0556222i	−0.678749	+	0.734371i	$0.737477\pi$
$318$	9.18501	+	20.0096i	0.515070	+	1.12208i
$319$	−4.16060	−	4.16060i	−0.232949	−	0.232949i
$320$	24.9588	−	24.9588i	1.39524	−	1.39524i
$321$	12.6805	+	4.70158i	0.707756	+	0.262417i
$322$		−	21.8015i		−	1.21495i
$323$	−1.75100	+	1.75100i	−0.0974281	+	0.0974281i
$324$	−46.1329	+	6.99863i	−2.56294	+	0.388813i
$325$	5.23407	−	2.29648i	0.290334	−	0.127386i
$326$			17.4453i			0.966204i
$327$	−9.36921	−	20.4109i	−0.518119	−	1.12872i
$328$	24.0995			1.33067
$329$	10.6496			0.587130
$330$	−7.79685	+	3.57899i	−0.429202	+	0.197017i
$331$	0.792245	−	0.792245i	0.0435457	−	0.0435457i	−0.684999	−	0.728544i	$-0.740197\pi$
$331$	0.792245	−	0.792245i	0.0435457	−	0.0435457i	0.728544	+	0.684999i	$0.240197\pi$
$332$	−46.7289	+	46.7289i	−2.56458	+	2.56458i
$333$	2.46397	+	32.6694i	0.135025	+	1.79027i
$334$	9.20639			0.503751
$335$	−1.05307			−0.0575355
$336$	95.2073	−	43.7031i	5.19398	−	2.38420i
$337$			13.9988i			0.762564i	0.924459	+	0.381282i	$0.124517\pi$
$337$			13.9988i			0.762564i	−0.924459	+	0.381282i	$0.875483\pi$
$338$	34.8151	−	1.44674i	1.89369	−	0.0786925i
$339$	30.5201	+	11.3160i	1.65763	+	0.614603i
$340$	18.9165	−	18.9165i	1.02589	−	1.02589i
$341$			0.543320i			0.0294224i
$342$	5.40735	+	4.64889i	0.292396	+	0.251383i
$343$	−32.0449	+	32.0449i	−1.73026	+	1.73026i
$344$	−28.1685	−	28.1685i	−1.51874	−	1.51874i
$345$	−4.89376	+	2.24639i	−0.263471	+	0.120941i
$346$	−6.95961	−	6.95961i	−0.374151	−	0.374151i
$347$			16.3069i			0.875399i	0.899121	+	0.437700i	$0.144207\pi$
$347$			16.3069i			0.875399i	−0.899121	+	0.437700i	$0.855793\pi$
$348$	18.3687	−	49.5416i	0.984665	−	2.65571i
$349$	−1.06296	−	1.06296i	−0.0568990	−	0.0568990i	0.678085	−	0.734984i	$-0.262810\pi$
$349$	−1.06296	−	1.06296i	−0.0568990	−	0.0568990i	−0.734984	+	0.678085i	$0.762810\pi$
$350$	−20.5429			−1.09806
$351$	14.8952	+	11.3637i	0.795045	+	0.606550i
$352$	−16.4609			−0.877366
$353$	−5.93764	−	5.93764i	−0.316028	−	0.316028i	0.531211	−	0.847240i	$-0.321737\pi$
$353$	−5.93764	−	5.93764i	−0.316028	−	0.316028i	−0.847240	+	0.531211i	$0.821737\pi$
$354$	−8.26805	+	22.2995i	−0.439442	+	1.18520i
$355$		−	18.1878i		−	0.965307i
$356$	−39.8565	−	39.8565i	−2.11239	−	2.11239i
$357$	21.2507	−	9.75472i	1.12471	−	0.516274i
$358$	−41.9763	−	41.9763i	−2.21852	−	2.21852i
$359$	−11.6304	+	11.6304i	−0.613831	+	0.613831i	−0.943942	−	0.330111i	$-0.892914\pi$
$359$	−11.6304	+	11.6304i	−0.613831	+	0.613831i	0.330111	+	0.943942i	$0.392914\pi$
$360$	−35.8820	−	30.8490i	−1.89115	−	1.62589i
$361$			18.2136i			0.958609i
$362$	8.66227	−	8.66227i	0.455279	−	0.455279i
$363$	1.62402	+	0.602141i	0.0852387	+	0.0316042i
$364$	−84.1950	−	32.8435i	−4.41301	−	1.72147i
$365$			6.17663i			0.323299i
$366$	47.0285	−	21.5875i	2.45822	−	1.12840i
$367$	−10.8920			−0.568556			−0.284278	−	0.958742i	$-0.591754\pi$
$367$	−10.8920			−0.568556			−0.284278	+	0.958742i	$0.591754\pi$
$368$	−21.0469			−1.09715
$369$	−0.637015	−	8.44606i	−0.0331617	−	0.439684i
$370$	−38.2485	+	38.2485i	−1.98845	+	1.98845i
$371$	−16.2124	+	16.2124i	−0.841705	+	0.841705i
$372$	−4.43410	+	2.03539i	−0.229897	+	0.105530i
$373$	8.35991			0.432860			0.216430	−	0.976298i	$-0.430559\pi$
$373$	8.35991			0.432860			0.216430	+	0.976298i	$0.430559\pi$
$374$	−7.48458			−0.387019
$375$	8.79294	+	19.1555i	0.454066	+	0.989183i
$376$		−	18.8023i		−	0.969657i
$377$	−19.4273	+	8.52385i	−1.00056	+	0.439000i
$378$	−32.6138	−	58.9102i	−1.67747	−	3.03002i
$379$	14.4603	−	14.4603i	0.742774	−	0.742774i	−0.230337	−	0.973111i	$-0.573983\pi$
$379$	14.4603	−	14.4603i	0.742774	−	0.742774i	0.973111	+	0.230337i	$0.0739828\pi$
$380$			8.49612i			0.435842i
$381$	29.3456	+	10.8805i	1.50342	+	0.557427i
$382$	31.9158	−	31.9158i	1.63295	−	1.63295i
$383$	17.2691	+	17.2691i	0.882409	+	0.882409i	0.993779	−	0.111370i	$-0.0355240\pi$
$383$	17.2691	+	17.2691i	0.882409	+	0.882409i	−0.111370	+	0.993779i	$0.535524\pi$
$384$	−13.2064	−	28.7701i	−0.673935	−	1.46817i
$385$	−6.31725	−	6.31725i	−0.321957	−	0.321957i
$386$		−	20.2221i		−	1.02928i
$387$	−9.12754	+	10.6167i	−0.463979	+	0.539676i
$388$	−50.6810	−	50.6810i	−2.57294	−	2.57294i
$389$	−13.1649			−0.667489			−0.333745	−	0.942664i	$-0.608312\pi$
$389$	−13.1649			−0.667489			−0.333745	+	0.942664i	$0.608312\pi$
$390$	1.80557	+	30.8794i	0.0914286	+	1.56364i
$391$	−4.69777			−0.237576
$392$	98.8269	+	98.8269i	4.99151	+	4.99151i
$393$	−10.9987	−	4.07801i	−0.554810	−	0.205708i
$394$		−	2.01420i		−	0.101474i
$395$	3.11844	+	3.11844i	0.156906	+	0.156906i
$396$	1.16975	+	15.5095i	0.0587822	+	0.779383i
$397$	13.0124	+	13.0124i	0.653075	+	0.653075i	0.953732	−	0.300657i	$-0.0972061\pi$
$397$	13.0124	+	13.0124i	0.653075	+	0.653075i	−0.300657	+	0.953732i	$0.597206\pi$
$398$	−47.0718	+	47.0718i	−2.35950	+	2.35950i
$399$	−2.58163	+	6.96283i	−0.129243	+	0.348578i
$400$			19.8319i			0.991596i
$401$	13.5035	−	13.5035i	0.674331	−	0.674331i	−0.284380	−	0.958712i	$-0.591788\pi$
$401$	13.5035	−	13.5035i	0.674331	−	0.674331i	0.958712	+	0.284380i	$0.0917878\pi$
$402$	−0.919764	+	2.48067i	−0.0458737	+	0.123724i
$403$	1.82503	+	0.711923i	0.0909111	+	0.0354634i
$404$		−	16.2888i		−	0.810396i
$405$	−9.86307	+	13.3908i	−0.490100	+	0.665396i
$406$	76.2489			3.78417
$407$	10.9207			0.541320
$408$	−17.2224	−	37.5191i	−0.852638	−	1.85747i
$409$	13.1597	−	13.1597i	0.650706	−	0.650706i	−0.302457	−	0.953163i	$-0.597807\pi$
$409$	13.1597	−	13.1597i	0.650706	−	0.650706i	0.953163	+	0.302457i	$0.0978068\pi$
$410$	9.88845	−	9.88845i	0.488356	−	0.488356i
$411$	7.82970	+	17.0570i	0.386210	+	0.841360i
$412$	35.6953			1.75858
$413$	−24.7668			−1.21869
$414$	1.01744	+	13.4900i	0.0500042	+	0.662997i
$415$			23.5544i			1.15624i
$416$	−21.5690	+	55.2924i	−1.05751	+	2.71094i
$417$	−3.88556	+	10.4796i	−0.190277	+	0.513189i
$418$	1.68080	−	1.68080i	0.0822107	−	0.0822107i
$419$		−	17.1256i		−	0.836638i	−0.908300	−	0.418319i	$-0.862619\pi$
$419$		−	17.1256i		−	0.836638i	0.908300	−	0.418319i	$-0.137381\pi$
$420$	27.8901	−	75.2215i	1.36090	−	3.67043i
$421$	−10.4333	+	10.4333i	−0.508489	+	0.508489i	−0.914063	−	0.405573i	$-0.867072\pi$
$421$	−10.4333	+	10.4333i	−0.508489	+	0.508489i	0.405573	+	0.914063i	$0.367072\pi$
$422$	−3.38242	−	3.38242i	−0.164654	−	0.164654i
$423$	−6.58958	+	0.496996i	−0.320396	+	0.0241648i
$424$	28.6238	+	28.6238i	1.39009	+	1.39009i
$425$			4.42657i			0.214720i
$426$	−42.8440	−	15.8854i	−2.07580	−	0.769649i
$427$	38.1039	+	38.1039i	1.84398	+	1.84398i
$428$	40.4813			1.95674
$429$	4.15059	−	4.66611i	0.200392	−	0.225282i
$430$	−23.1160			−1.11475
$431$	−9.34849	−	9.34849i	−0.450301	−	0.450301i	0.445153	−	0.895454i	$-0.353149\pi$
$431$	−9.34849	−	9.34849i	−0.450301	−	0.450301i	−0.895454	+	0.445153i	$0.853149\pi$
$432$	−56.8714	+	31.4851i	−2.73623	+	1.51483i
$433$		−	20.0063i		−	0.961440i	−0.876874	−	0.480720i	$-0.840375\pi$
$433$		−	20.0063i		−	0.961440i	0.876874	−	0.480720i	$-0.159625\pi$
$434$	−4.97856	−	4.97856i	−0.238978	−	0.238978i
$435$	−7.85656	−	17.1155i	−0.376693	−	0.820628i
$436$	−47.5351	−	47.5351i	−2.27652	−	2.27652i
$437$	1.05497	−	1.05497i	0.0504661	−	0.0504661i
$438$	14.5499	+	5.39472i	0.695223	+	0.257770i
$439$		−	24.1856i		−	1.15432i	−0.816633	−	0.577158i	$-0.804162\pi$
$439$		−	24.1856i		−	1.15432i	0.816633	−	0.577158i	$-0.195838\pi$
$440$	−11.1534	+	11.1534i	−0.531718	+	0.531718i
$441$	32.0232	−	37.2477i	1.52491	−	1.77370i
$442$	−9.80720	+	25.1409i	−0.466481	+	1.19583i
$443$			8.49229i			0.403481i	0.979439	+	0.201741i	$0.0646598\pi$
$443$			8.49229i			0.403481i	−0.979439	+	0.201741i	$0.935340\pi$
$444$	40.9113	+	89.1253i	1.94156	+	4.22970i
$445$	−20.0902			−0.952367
$446$	−20.3174			−0.962055
$447$	−7.30341	+	3.35249i	−0.345439	+	0.158567i
$448$	65.2991	−	65.2991i	3.08509	−	3.08509i
$449$	−8.36231	+	8.36231i	−0.394642	+	0.394642i	−0.876338	−	0.481696i	$-0.840021\pi$
$449$	−8.36231	+	8.36231i	−0.394642	+	0.394642i	0.481696	+	0.876338i	$0.340021\pi$
$450$	12.7112	−	0.958699i	0.599213	−	0.0451935i
$451$	−2.82335			−0.132946
$452$	97.4328			4.58286
$453$	9.57549	−	4.39545i	0.449896	−	0.206516i
$454$			56.0295i			2.62960i
$455$	−29.4974	+	12.9422i	−1.38286	+	0.606739i
$456$	12.2932	+	4.55800i	0.575683	+	0.213448i
$457$	−20.5772	+	20.5772i	−0.962562	+	0.962562i	−0.999324	−	0.0367617i	$-0.988296\pi$
$457$	−20.5772	+	20.5772i	−0.962562	+	0.962562i	0.0367617	+	0.999324i	$0.488296\pi$
$458$		−	1.95742i		−	0.0914641i
$459$	−12.6939	+	7.02761i	−0.592503	+	0.328021i
$460$	−11.3972	+	11.3972i	−0.531395	+	0.531395i
$461$	−2.27085	−	2.27085i	−0.105764	−	0.105764i	0.652245	−	0.758009i	$-0.273828\pi$
$461$	−2.27085	−	2.27085i	−0.105764	−	0.105764i	−0.758009	+	0.652245i	$0.773828\pi$
$462$	−20.3987	+	9.36365i	−0.949035	+	0.435636i
$463$	5.51740	+	5.51740i	0.256415	+	0.256415i	0.823594	−	0.567179i	$-0.191965\pi$
$463$	5.51740	+	5.51740i	0.256415	+	0.256415i	−0.567179	+	0.823594i	$0.691965\pi$
$464$		−	73.6100i		−	3.41726i
$465$	−0.604551	+	1.63052i	−0.0280354	+	0.0756134i
$466$	−46.9856	−	46.9856i	−2.17657	−	2.17657i
$467$	39.5286			1.82916			0.914582	−	0.404400i	$-0.132519\pi$
$467$	39.5286			1.82916			0.914582	+	0.404400i	$0.132519\pi$
$468$	53.6297	+	16.3932i	2.47903	+	0.757777i
$469$	−2.75514			−0.127220
$470$	−7.71492	−	7.71492i	−0.355863	−	0.355863i
$471$	−12.7372	+	34.3531i	−0.586900	+	1.58291i
$472$			43.7270i			2.01270i
$473$	3.30005	+	3.30005i	0.151736	+	0.151736i
$474$	10.0696	−	4.62227i	0.462513	−	0.212308i
$475$	−0.994067	−	0.994067i	−0.0456109	−	0.0456109i
$476$	49.4910	−	49.4910i	2.26842	−	2.26842i
$477$	9.27505	−	10.7883i	0.424675	−	0.493960i
$478$		−	23.5314i		−	1.07630i
$479$	17.1899	−	17.1899i	0.785426	−	0.785426i	−0.195315	−	0.980741i	$-0.562573\pi$
$479$	17.1899	−	17.1899i	0.785426	−	0.785426i	0.980741	+	0.195315i	$0.0625729\pi$
$480$	−49.3994	−	18.3160i	−2.25476	−	0.836006i
$481$	14.3096	−	36.6830i	0.652463	−	1.67260i
$482$		−	78.3873i		−	3.57044i
$483$	−12.8035	+	5.87718i	−0.582578	+	0.267421i
$484$	5.18453			0.235660
$485$	−25.5465			−1.16000
$486$	22.9295	+	34.9296i	1.04011	+	1.58444i
$487$	−8.47156	+	8.47156i	−0.383883	+	0.383883i	−0.872499	−	0.488616i	$-0.837502\pi$
$487$	−8.47156	+	8.47156i	−0.383883	+	0.383883i	0.488616	+	0.872499i	$0.337502\pi$
$488$	67.2744	−	67.2744i	3.04537	−	3.04537i
$489$	10.2452	−	4.70285i	0.463303	−	0.212670i
$490$	81.1007			3.66376
$491$	−10.7207			−0.483817			−0.241909	−	0.970299i	$-0.577773\pi$
$491$	−10.7207			−0.483817			−0.241909	+	0.970299i	$0.577773\pi$
$492$	−10.5768	−	23.0417i	−0.476841	−	1.03880i
$493$		−	16.4301i		−	0.739973i
$494$	−3.44347	−	7.84824i	−0.154929	−	0.353109i
$495$	4.20371	+	3.61408i	0.188943	+	0.162441i
$496$	−4.80625	+	4.80625i	−0.215807	+	0.215807i
$497$		−	47.5843i		−	2.13445i
$498$	55.4857	+	20.5726i	2.48637	+	0.921880i
$499$	0.529191	−	0.529191i	0.0236899	−	0.0236899i	−0.695163	−	0.718852i	$-0.744668\pi$
$499$	0.529191	−	0.529191i	0.0236899	−	0.0236899i	0.718852	+	0.695163i	$0.244668\pi$
$500$	44.6114	+	44.6114i	1.99508	+	1.99508i
$501$	−2.48183	−	5.40668i	−0.110880	−	0.241553i
$502$	−35.3466	−	35.3466i	−1.57760	−	1.57760i
$503$		−	28.0727i		−	1.25170i	−0.779944	−	0.625849i	$-0.784753\pi$
$503$		−	28.0727i		−	1.25170i	0.779944	−	0.625849i	$-0.215247\pi$
$504$	−93.8773	−	80.7097i	−4.18163	−	3.59510i
$505$	−4.10528	−	4.10528i	−0.182683	−	0.182683i
$506$	4.50943			0.200469
$507$	−10.2350	−	20.0560i	−0.454552	−	0.890720i
$508$	93.6831			4.15652
$509$	9.82813	+	9.82813i	0.435624	+	0.435624i	0.890536	−	0.454912i	$-0.150329\pi$
$509$	9.82813	+	9.82813i	0.435624	+	0.435624i	−0.454912	+	0.890536i	$0.650329\pi$
$510$	−22.4614	−	8.32808i	−0.994608	−	0.368774i
$511$			16.1598i			0.714867i
$512$	5.40254	+	5.40254i	0.238761	+	0.238761i
$513$	1.27248	−	4.42884i	0.0561814	−	0.195538i
$514$	20.9470	+	20.9470i	0.923932	+	0.923932i
$515$	8.99636	−	8.99636i	0.396427	−	0.396427i
$516$	−14.5694	+	39.2947i	−0.641383	+	1.72985i
$517$			2.20277i			0.0968775i
$518$	−100.069	+	100.069i	−4.39677	+	4.39677i
$519$	−2.21105	+	5.96336i	−0.0970545	+	0.261763i
$520$	22.8501	+	52.0792i	1.00204	+	2.28382i
$521$			28.1147i			1.23173i	0.787854	+	0.615863i	$0.211192\pi$
$521$			28.1147i			1.23173i	−0.787854	+	0.615863i	$0.788808\pi$
$522$	−47.1802	+	3.55840i	−2.06502	+	0.155747i
$523$	39.8655			1.74320			0.871599	−	0.490219i	$-0.163083\pi$
$523$	39.8655			1.74320			0.871599	+	0.490219i	$0.163083\pi$
$524$	−35.1123			−1.53389
$525$	5.53790	+	12.0643i	0.241694	+	0.526530i
$526$	−35.1743	+	35.1743i	−1.53367	+	1.53367i
$527$	−1.07278	+	1.07278i	−0.0467309	+	0.0467309i
$528$	9.03959	+	19.6928i	0.393398	+	0.857018i
$529$	−20.1696			−0.876940
$530$	23.4896			1.02032
$531$	15.3248	−	1.15582i	0.665041	−	0.0501583i
$532$			22.2282i			0.963716i
$533$	−3.69949	+	9.48371i	−0.160243	+	0.410785i
$534$	−17.5470	+	47.3254i	−0.759332	+	2.04797i
$535$	10.2026	−	10.2026i	0.441096	−	0.441096i
$536$			4.86433i			0.210107i
$537$	−13.3358	+	35.9675i	−0.575481	+	1.55211i
$538$	1.46242	−	1.46242i	0.0630492	−	0.0630492i
$539$	−11.5779	−	11.5779i	−0.498697	−	0.498697i
$540$	−13.7470	+	47.8460i	−0.591575	+	2.05897i
$541$	6.49337	+	6.49337i	0.279172	+	0.279172i	0.832778	−	0.553607i	$-0.186749\pi$
$541$	6.49337	+	6.49337i	0.279172	+	0.279172i	−0.553607	+	0.832778i	$0.686749\pi$
$542$		−	16.0525i		−	0.689513i
$543$	−7.42229	−	2.75198i	−0.318521	−	0.118099i
$544$	−32.5017	−	32.5017i	−1.39350	−	1.39350i
$545$	−23.9607			−1.02636
$546$	4.72388	+	80.7893i	0.202163	+	3.45746i
$547$	33.5803			1.43579			0.717895	−	0.696151i	$-0.245106\pi$
$547$	33.5803			1.43579			0.717895	+	0.696151i	$0.245106\pi$
$548$	39.7243	+	39.7243i	1.69694	+	1.69694i
$549$	−25.3556	−	21.7992i	−1.08215	−	0.930365i
$550$		−	4.24911i		−	0.181183i
$551$	3.68967	+	3.68967i	0.157185	+	0.157185i
$552$	10.3765	+	22.6052i	0.441652	+	0.962139i
$553$	8.15872	+	8.15872i	0.346944	+	0.346944i
$554$	−10.8431	+	10.8431i	−0.460680	+	0.460680i
$555$	32.7733	+	12.1515i	1.39115	+	0.515801i
$556$			33.4553i			1.41882i
$557$	−16.1261	+	16.1261i	−0.683284	+	0.683284i	−0.960739	−	0.277455i	$-0.910509\pi$
$557$	−16.1261	+	16.1261i	−0.683284	+	0.683284i	0.277455	+	0.960739i	$0.410509\pi$
$558$	3.31290	+	2.84822i	0.140246	+	0.120575i
$559$	15.4091	−	6.76083i	0.651734	−	0.285953i
$560$		−	111.766i		−	4.72297i
$561$	2.01767	+	4.39551i	0.0851863	+	0.185579i
$562$	−29.4051			−1.24038
$563$	2.27036			0.0956841			0.0478421	−	0.998855i	$-0.484766\pi$
$563$	2.27036			0.0956841			0.0478421	+	0.998855i	$0.484766\pi$
$564$	−17.9770	+	8.25201i	−0.756970	+	0.347472i
$565$	24.5562	−	24.5562i	1.03309	−	1.03309i
$566$	22.8709	−	22.8709i	0.961335	−	0.961335i
$567$	−25.8046	+	35.0342i	−1.08369	+	1.47130i
$568$	−84.0125			−3.52509
$569$	14.1138			0.591682			0.295841	−	0.955237i	$-0.404400\pi$
$569$	14.1138			0.591682			0.295841	+	0.955237i	$0.404400\pi$
$570$	6.91435	−	3.17390i	0.289610	−	0.132940i
$571$		−	16.4646i		−	0.689020i	−0.938783	−	0.344510i	$-0.888045\pi$
$571$		−	16.4646i		−	0.689020i	0.938783	−	0.344510i	$-0.111955\pi$
$572$	6.79339	−	17.4150i	0.284046	−	0.728156i
$573$	−27.3471	−	10.1396i	−1.14244	−	0.423587i
$574$	25.8709	−	25.8709i	1.07983	−	1.07983i
$575$		−	2.66699i		−	0.111221i
$576$	−37.3574	+	43.4522i	−1.55656	+	1.81051i
$577$	21.2999	−	21.2999i	0.886727	−	0.886727i	−0.107481	−	0.994207i	$-0.534278\pi$
$577$	21.2999	−	21.2999i	0.886727	−	0.886727i	0.994207	+	0.107481i	$0.0342784\pi$
$578$	17.4424	+	17.4424i	0.725507	+	0.725507i
$579$	−11.8759	+	5.45141i	−0.493546	+	0.226553i
$580$	−39.8606	−	39.8606i	−1.65512	−	1.65512i
$581$			61.6248i			2.55663i
$582$	−22.3125	+	60.1784i	−0.924884	+	2.49447i
$583$	−3.35338	−	3.35338i	−0.138883	−	0.138883i
$584$	28.5309			1.18062
$585$	17.6480	−	9.38477i	0.729655	−	0.388012i
$586$	−14.3244			−0.591737
$587$	−12.1763	−	12.1763i	−0.502568	−	0.502568i	0.409667	−	0.912235i	$-0.365645\pi$
$587$	−12.1763	−	12.1763i	−0.502568	−	0.502568i	−0.912235	+	0.409667i	$0.865645\pi$
$588$	51.1156	−	137.862i	2.10797	−	5.68535i
$589$		−	0.481823i		−	0.0198532i
$590$	17.9419	+	17.9419i	0.738658	+	0.738658i
$591$	−1.18289	+	0.542982i	−0.0486575	+	0.0223353i
$592$	96.6056	+	96.6056i	3.97047	+	3.97047i
$593$	−13.6551	+	13.6551i	−0.560748	+	0.560748i	−0.929520	−	0.368772i	$-0.879778\pi$
$593$	−13.6551	+	13.6551i	−0.560748	+	0.560748i	0.368772	+	0.929520i	$0.379778\pi$
$594$	12.1850	−	6.74587i	0.499959	−	0.276787i
$595$		−	24.9466i		−	1.02271i
$596$	−17.0090	+	17.0090i	−0.696716	+	0.696716i
$597$	40.3336	+	14.9546i	1.65075	+	0.612052i
$598$	5.90880	−	15.1473i	0.241629	−	0.619420i
$599$		−	30.5672i		−	1.24894i	−0.781049	−	0.624470i	$-0.785315\pi$
$599$		−	30.5672i		−	1.24894i	0.781049	−	0.624470i	$-0.214685\pi$
$600$	21.3002	−	9.77743i	0.869576	−	0.399162i
$601$	−20.1686			−0.822693			−0.411347	−	0.911479i	$-0.634941\pi$
$601$	−20.1686			−0.822693			−0.411347	+	0.911479i	$0.634941\pi$
$602$	−60.4781			−2.46490
$603$	1.70478	−	0.128577i	0.0694241	−	0.00523607i
$604$	22.3005	−	22.3005i	0.907394	−	0.907394i
$605$	1.30667	−	1.30667i	0.0531235	−	0.0531235i
$606$	−13.2562	+	6.08500i	−0.538496	+	0.247186i
$607$	−26.0626			−1.05785			−0.528924	−	0.848669i	$-0.677404\pi$
$607$	−26.0626			−1.05785			−0.528924	+	0.848669i	$0.677404\pi$
$608$	14.5977			0.592015
$609$	−20.5550	−	44.7791i	−0.832930	−	1.81454i
$610$		−	55.2077i		−	2.23529i
$611$	7.39915	+	2.88633i	0.299338	+	0.116768i
$612$	−28.3136	+	32.9330i	−1.14451	+	1.33124i
$613$	−2.20802	+	2.20802i	−0.0891810	+	0.0891810i	−0.750290	−	0.661109i	$-0.770086\pi$
$613$	−2.20802	+	2.20802i	−0.0891810	+	0.0891810i	0.661109	+	0.750290i	$0.270086\pi$
$614$		−	18.7685i		−	0.757434i
$615$	−8.47294	−	3.14154i	−0.341662	−	0.126679i
$616$	−29.1805	+	29.1805i	−1.17571	+	1.17571i
$617$	−17.7733	−	17.7733i	−0.715527	−	0.715527i	0.252159	−	0.967686i	$-0.418860\pi$
$617$	−17.7733	−	17.7733i	−0.715527	−	0.715527i	−0.967686	+	0.252159i	$0.918860\pi$
$618$	−13.3347	−	29.0497i	−0.536401	−	1.16855i
$619$	−0.706567	−	0.706567i	−0.0283993	−	0.0283993i	0.692765	−	0.721164i	$-0.256393\pi$
$619$	−0.706567	−	0.706567i	−0.0283993	−	0.0283993i	−0.721164	+	0.692765i	$0.756393\pi$
$620$			5.20528i			0.209049i
$621$	7.64806	−	4.23411i	0.306906	−	0.169909i
$622$	−30.9052	−	30.9052i	−1.23919	−	1.23919i
$623$	−52.5616			−2.10584
$624$	77.9933	−	4.56039i	3.12223	−	0.182562i
$625$	14.5607			0.582428
$626$	36.6296	+	36.6296i	1.46401	+	1.46401i
$627$	−1.44020	−	0.533987i	−0.0575160	−	0.0213254i
$628$			109.669i			4.37628i
$629$	21.5628	+	21.5628i	0.859764	+	0.859764i
$630$	−71.6360	+	5.40289i	−2.85405	+	0.215256i
$631$	−28.3534	−	28.3534i	−1.12873	−	1.12873i	−0.990384	−	0.138347i	$-0.955821\pi$
$631$	−28.3534	−	28.3534i	−1.12873	−	1.12873i	−0.138347	−	0.990384i	$-0.544179\pi$
$632$	14.4046	−	14.4046i	0.572986	−	0.572986i
$633$	−1.07459	+	2.89824i	−0.0427110	+	0.115195i
$634$		−	3.75398i		−	0.149090i
$635$	23.6111	−	23.6111i	0.936979	−	0.936979i
$636$	14.8049	−	39.9298i	0.587052	−	1.58332i
$637$	−54.0614	+	23.7198i	−2.14199	+	0.939813i
$638$			15.7714i			0.624395i
$639$	2.22068	+	29.4435i	0.0878485	+	1.16477i
$640$	−33.7738			−1.33503
$641$	−28.9141			−1.14204			−0.571020	−	0.820936i	$-0.693452\pi$
$641$	−28.9141			−1.14204			−0.571020	+	0.820936i	$0.693452\pi$
$642$	−15.1226	−	32.9447i	−0.596843	−	1.30022i
$643$	−16.3189	+	16.3189i	−0.643553	+	0.643553i	−0.951427	−	0.307874i	$-0.900382\pi$
$643$	−16.3189	+	16.3189i	−0.643553	+	0.643553i	0.307874	+	0.951427i	$0.400382\pi$
$644$	−29.8181	+	29.8181i	−1.17500	+	1.17500i
$645$	6.23156	+	13.5755i	0.245368	+	0.534534i
$646$	6.63743			0.261146
$647$	16.6406			0.654208			0.327104	−	0.944988i	$-0.393927\pi$
$647$	16.6406			0.654208			0.327104	+	0.944988i	$0.393927\pi$
$648$	61.8546	+	45.5593i	2.42988	+	1.78974i
$649$		−	5.12278i		−	0.201087i
$650$	−14.2729	−	5.56769i	−0.559828	−	0.218383i
$651$	−1.58168	+	4.26589i	−0.0619908	+	0.167193i
$652$	23.8601	−	23.8601i	0.934434	−	0.934434i
$653$		−	4.98811i		−	0.195200i	−0.995226	−	0.0975999i	$-0.968883\pi$
$653$		−	4.98811i		−	0.195200i	0.995226	−	0.0975999i	$-0.0311166\pi$
$654$	−20.9275	+	56.4429i	−0.818331	+	2.20709i
$655$	−8.84941	+	8.84941i	−0.345775	+	0.345775i
$656$	−24.9756	−	24.9756i	−0.975133	−	0.975133i
$657$	−0.754148	−	9.99912i	−0.0294221	−	0.390103i
$658$	−20.1844	−	20.1844i	−0.786870	−	0.786870i
$659$			19.6243i			0.764453i	0.924069	+	0.382226i	$0.124843\pi$
$659$			19.6243i			0.764453i	−0.924069	+	0.382226i	$0.875157\pi$
$660$	15.5589	+	5.76881i	0.605629	+	0.224551i
$661$	−3.37488	−	3.37488i	−0.131268	−	0.131268i	0.638420	−	0.769688i	$-0.279588\pi$
$661$	−3.37488	−	3.37488i	−0.131268	−	0.131268i	−0.769688	+	0.638420i	$0.779588\pi$
$662$	−3.00313			−0.116720
$663$	17.4084	−	1.01790i	0.676087	−	0.0395319i
$664$	108.802			4.22233
$665$	5.60222	+	5.60222i	0.217245	+	0.217245i
$666$	57.2491	−	66.5892i	2.21836	−	2.58028i
$667$			9.89906i			0.383293i
$668$	−12.5917	−	12.5917i	−0.487187	−	0.487187i
$669$	5.47710	+	11.9319i	0.211757	+	0.461313i
$670$	1.99592	+	1.99592i	0.0771090	+	0.0771090i
$671$	−7.88145	+	7.88145i	−0.304260	+	0.304260i
$672$	−129.243	−	47.9197i	−4.98565	−	1.84854i
$673$		−	14.2191i		−	0.548106i	−0.961715	−	0.274053i	$-0.911636\pi$
$673$		−	14.2191i		−	0.548106i	0.961715	−	0.274053i	$-0.0883644\pi$
$674$	26.5323	−	26.5323i	1.02199	−	1.02199i
$675$	−3.98968	−	7.20654i	−0.153563	−	0.277380i
$676$	−49.5958	−	45.6383i	−1.90753	−	1.75532i
$677$		−	36.1578i		−	1.38966i	−0.719176	−	0.694828i	$-0.755481\pi$
$677$		−	36.1578i		−	1.38966i	0.719176	−	0.694828i	$-0.244519\pi$
$678$	−36.3980	−	79.2932i	−1.39786	−	3.04524i
$679$	−66.8367			−2.56496
$680$	−44.0445			−1.68903
$681$	32.9048	−	15.1043i	1.26091	−	0.578798i
$682$	1.02977	−	1.02977i	0.0394319	−	0.0394319i
$683$	22.2875	−	22.2875i	0.852809	−	0.852809i	−0.137669	−	0.990478i	$-0.543961\pi$
$683$	22.2875	−	22.2875i	0.852809	−	0.852809i	0.990478	+	0.137669i	$0.0439611\pi$
$684$	−1.03735	−	13.7541i	−0.0396641	−	0.525899i
$685$	20.0236			0.765061
$686$	121.471			4.63779
$687$	−1.14954	+	0.527675i	−0.0438578	+	0.0201321i
$688$			58.3850i			2.22591i
$689$	−15.6581	+	6.87010i	−0.596526	+	0.261730i
$690$	13.5329	+	5.01764i	0.515189	+	0.191018i
$691$	−16.0780	+	16.0780i	−0.611636	+	0.611636i	−0.943372	−	0.331736i	$-0.892366\pi$
$691$	−16.0780	+	16.0780i	−0.611636	+	0.611636i	0.331736	+	0.943372i	$0.392366\pi$
$692$			19.0375i			0.723697i
$693$	10.9981	+	9.45544i	0.417782	+	0.359183i
$694$	30.9069	−	30.9069i	1.17321	−	1.17321i
$695$	8.43179	+	8.43179i	0.319836	+	0.319836i
$696$	−79.0597	+	36.2908i	−2.99675	+	1.37560i
$697$	−5.57466	−	5.57466i	−0.211155	−	0.211155i
$698$			4.02932i			0.152512i
$699$	−14.9272	+	40.2597i	−0.564599	+	1.52276i
$700$	28.0968	+	28.0968i	1.06196	+	1.06196i
$701$	35.3906			1.33668			0.668342	−	0.743854i	$-0.267004\pi$
$701$	35.3906			1.33668			0.668342	+	0.743854i	$0.267004\pi$
$702$	−6.69326	−	49.7692i	−0.252621	−	1.87842i
$703$	−9.68464			−0.365263
$704$	13.5065	+	13.5065i	0.509046	+	0.509046i
$705$	−2.45101	+	6.61055i	−0.0923105	+	0.248968i
$706$			22.5075i			0.847082i
$707$	−10.7406	−	10.7406i	−0.403941	−	0.403941i
$708$	41.8076	−	19.1910i	1.57123	−	0.721242i
$709$	−26.0214	−	26.0214i	−0.977255	−	0.977255i	0.0224916	−	0.999747i	$-0.492840\pi$
$709$	−26.0214	−	26.0214i	−0.977255	−	0.977255i	−0.999747	+	0.0224916i	$0.992840\pi$
$710$	−34.4718	+	34.4718i	−1.29370	+	1.29370i
$711$	−5.42909	−	4.66758i	−0.203607	−	0.175048i
$712$			92.8002i			3.47784i
$713$	0.646344	−	0.646344i	0.0242058	−	0.0242058i
$714$	−58.7653	−	21.7886i	−2.19924	−	0.815418i
$715$	−2.67697	−	6.10127i	−0.100113	−	0.228175i
$716$			114.823i			4.29114i
$717$	−13.8194	+	6.34355i	−0.516096	+	0.236904i
$718$	44.0869			1.64531
$719$	−6.96460			−0.259736			−0.129868	−	0.991531i	$-0.541455\pi$
$719$	−6.96460			−0.259736			−0.129868	+	0.991531i	$0.541455\pi$
$720$	5.21591	+	69.1568i	0.194385	+	2.57732i
$721$	23.5370	−	23.5370i	0.876564	−	0.876564i
$722$	34.5206	−	34.5206i	1.28473	−	1.28473i
$723$	−46.0349	+	21.1315i	−1.71206	+	0.785887i
$724$	−23.6950			−0.880618
$725$	9.32759			0.346418
$726$	−1.93679	−	4.21929i	−0.0718809	−	0.156593i
$727$		−	26.3904i		−	0.978767i	−0.872069	−	0.489383i	$-0.837222\pi$
$727$		−	26.3904i		−	0.978767i	0.872069	−	0.489383i	$-0.162778\pi$
$728$	59.7822	+	136.254i	2.21568	+	5.04990i
$729$	14.3320	−	22.8822i	0.530814	−	0.847488i
$730$	11.7067	−	11.7067i	0.433285	−	0.433285i
$731$			13.0318i			0.481998i
$732$	−93.8470	−	34.7959i	−3.46869	−	1.28609i
$733$	−0.322264	+	0.322264i	−0.0119031	+	0.0119031i	−0.713033	−	0.701130i	$-0.752679\pi$
$733$	−0.322264	+	0.322264i	−0.0119031	+	0.0119031i	0.701130	+	0.713033i	$0.252679\pi$
$734$	20.6438	+	20.6438i	0.761978	+	0.761978i
$735$	−21.8629	−	47.6284i	−0.806426	−	1.75680i
$736$	19.5821	+	19.5821i	0.721808	+	0.721808i
$737$		−	0.569875i		−	0.0209916i
$738$	−14.8007	+	17.2154i	−0.544821	+	0.633707i
$739$	1.49338	+	1.49338i	0.0549347	+	0.0549347i	0.734040	−	0.679106i	$-0.237632\pi$
$739$	1.49338	+	1.49338i	0.0549347	+	0.0549347i	−0.679106	+	0.734040i	$0.737632\pi$
$740$	104.626			3.84613
$741$	−3.68080	+	4.13797i	−0.135217	+	0.152012i
$742$	61.4555			2.25610
$743$	−21.2476	−	21.2476i	−0.779498	−	0.779498i	0.200247	−	0.979745i	$-0.435825\pi$
$743$	−21.2476	−	21.2476i	−0.779498	−	0.779498i	−0.979745	+	0.200247i	$0.935825\pi$
$744$	7.53164	+	2.79253i	0.276123	+	0.102379i
$745$			8.57362i			0.314113i
$746$	−15.8448	−	15.8448i	−0.580118	−	0.580118i
$747$	−2.87592	−	38.1313i	−0.105224	−	1.39515i
$748$	10.2368	+	10.2368i	0.374293	+	0.374293i
$749$	26.6928	−	26.6928i	0.975334	−	0.975334i
$750$	19.6403	−	52.9713i	0.717164	−	1.93424i
$751$			29.2210i			1.06629i	0.846024	+	0.533145i	$0.178990\pi$
$751$			29.2210i			1.06629i	−0.846024	+	0.533145i	$0.821010\pi$
$752$	−19.4858	+	19.4858i	−0.710576	+	0.710576i
$753$	−11.2295	+	30.2868i	−0.409227	+	1.10371i
$754$	52.9765	+	20.6656i	1.92929	+	0.752595i
$755$		−	11.2409i		−	0.409097i
$756$	−35.9659	+	125.179i	−1.30807	+	4.55270i
$757$	−4.48566			−0.163034			−0.0815170	−	0.996672i	$-0.525977\pi$
$757$	−4.48566			−0.163034			−0.0815170	+	0.996672i	$0.525977\pi$
$758$	−54.8139			−1.99093
$759$	−1.21564	−	2.64828i	−0.0441250	−	0.0961264i
$760$	9.89100	−	9.89100i	0.358784	−	0.358784i
$761$	18.4110	−	18.4110i	0.667398	−	0.667398i	−0.289715	−	0.957113i	$-0.593560\pi$
$761$	18.4110	−	18.4110i	0.667398	−	0.667398i	0.957113	+	0.289715i	$0.0935604\pi$
$762$	−34.9972	−	76.2416i	−1.26782	−	2.76194i
$763$	−62.6879			−2.26946
$764$	−87.3033			−3.15852
$765$	1.16421	+	15.4361i	0.0420922	+	0.558093i
$766$		−	65.4611i		−	2.36521i
$767$	−17.2076	−	6.71248i	−0.621329	−	0.242374i
$768$	−6.49527	+	17.5182i	−0.234378	+	0.632133i
$769$	−18.1887	+	18.1887i	−0.655903	+	0.655903i	−0.954408	−	0.298505i	$-0.903512\pi$
$769$	−18.1887	+	18.1887i	−0.655903	+	0.655903i	0.298505	+	0.954408i	$0.403512\pi$
$770$			23.9465i			0.862972i
$771$	6.65481	−	17.9485i	0.239667	−	0.646399i
$772$	−27.6580	+	27.6580i	−0.995433	+	0.995433i
$773$	−31.0150	−	31.0150i	−1.11553	−	1.11553i	−0.992389	−	0.123143i	$-0.960703\pi$
$773$	−31.0150	−	31.0150i	−1.11553	−	1.11553i	−0.123143	−	0.992389i	$-0.539297\pi$
$774$	37.4217	−	2.82240i	1.34510	−	0.101449i
$775$	−0.609031	−	0.609031i	−0.0218770	−	0.0218770i
$776$			118.004i			4.23608i
$777$	85.7442	+	31.7916i	3.07606	+	1.14052i
$778$	24.9519	+	24.9519i	0.894568	+	0.894568i
$779$	2.50378			0.0897074
$780$	39.7647	−	44.7037i	1.42381	−	1.60065i
$781$	9.84239			0.352188
$782$	8.90380	+	8.90380i	0.318399	+	0.318399i
$783$	14.8085	+	26.7485i	0.529211	+	0.955912i
$784$		−	204.839i		−	7.31568i
$785$	27.6401	+	27.6401i	0.986519	+	0.986519i
$786$	13.1169	+	28.5752i	0.467865	+	1.01925i
$787$	5.15022	+	5.15022i	0.183585	+	0.183585i	0.792916	−	0.609331i	$-0.208562\pi$
$787$	5.15022	+	5.15022i	0.183585	+	0.183585i	−0.609331	+	0.792916i	$0.708562\pi$
$788$	−2.75484	+	2.75484i	−0.0981372	+	0.0981372i
$789$	30.1392	+	11.1748i	1.07298	+	0.397834i
$790$		−	11.8209i		−	0.420570i
$791$	64.2458	−	64.2458i	2.28432	−	2.28432i
$792$	16.6941	−	19.4177i	0.593198	−	0.689977i
$793$	16.1468	+	36.8012i	0.573389	+	1.30685i
$794$		−	49.3256i		−	1.75050i
$795$	−6.33228	−	13.7949i	−0.224583	−	0.489254i
$796$	128.762			4.56383
$797$	31.7286			1.12389			0.561943	−	0.827176i	$-0.310054\pi$
$797$	31.7286			1.12389			0.561943	+	0.827176i	$0.310054\pi$
$798$	18.0899	−	8.30381i	0.640375	−	0.293952i
$799$	−4.34932	+	4.34932i	−0.153868	+	0.153868i
$800$	18.4517	−	18.4517i	0.652365	−	0.652365i
$801$	32.5233	−	2.45296i	1.14915	−	0.0866710i
$802$	−51.1870			−1.80748
$803$	−3.34251			−0.117954
$804$	4.65081	−	2.13487i	0.164022	−	0.0752910i
$805$			15.0302i			0.529746i
$806$	−2.10969	−	4.80835i	−0.0743108	−	0.169367i
$807$	−1.25308	−	0.464606i	−0.0441103	−	0.0163549i
$808$	−18.9630	+	18.9630i	−0.667117	+	0.667117i
$809$			40.5571i			1.42591i	0.701210	+	0.712955i	$0.252644\pi$
$809$			40.5571i			1.42591i	−0.701210	+	0.712955i	$0.747356\pi$
$810$	44.0737	−	6.68625i	1.54859	−	0.234931i
$811$	13.6479	−	13.6479i	0.479242	−	0.479242i	−0.425647	−	0.904889i	$-0.639954\pi$
$811$	13.6479	−	13.6479i	0.479242	−	0.479242i	0.904889	+	0.425647i	$0.139954\pi$
$812$	−104.287	−	104.287i	−3.65974	−	3.65974i
$813$	−9.42723	+	4.32739i	−0.330627	+	0.151768i
$814$	−20.6983	−	20.6983i	−0.725476	−	0.725476i
$815$		−	12.0270i		−	0.421288i
$816$	−21.0345	+	56.7316i	−0.736356	+	1.98600i
$817$	−2.92653	−	2.92653i	−0.102386	−	0.102386i
$818$	−49.8839			−1.74415
$819$	46.1721	−	24.5532i	1.61338	−	0.857958i
$820$	−27.0491			−0.944596
$821$	33.1393	+	33.1393i	1.15657	+	1.15657i	0.985208	+	0.171360i	$0.0548161\pi$
$821$	33.1393	+	33.1393i	1.15657	+	1.15657i	0.171360	+	0.985208i	$0.445184\pi$
$822$	17.4888	−	47.1684i	0.609991	−	1.64519i
$823$			39.2471i			1.36807i	0.729451	+	0.684033i	$0.239776\pi$
$823$			39.2471i			1.36807i	−0.729451	+	0.684033i	$0.760224\pi$
$824$	−41.5558	−	41.5558i	−1.44766	−	1.44766i
$825$	−2.49539	+	1.14546i	−0.0868785	+	0.0398799i
$826$	46.9411	+	46.9411i	1.63329	+	1.63329i
$827$	24.2132	−	24.2132i	0.841975	−	0.841975i	−0.147140	−	0.989116i	$-0.547007\pi$
$827$	24.2132	−	24.2132i	0.841975	−	0.841975i	0.989116	+	0.147140i	$0.0470069\pi$
$828$	17.0589	−	19.8420i	0.592837	−	0.689557i
$829$			4.61152i			0.160165i	0.996788	+	0.0800823i	$0.0255183\pi$
$829$			4.61152i			0.160165i	−0.996788	+	0.0800823i	$0.974482\pi$
$830$	44.6432	−	44.6432i	1.54959	−	1.54959i
$831$	9.29095	+	3.44483i	0.322299	+	0.119500i
$832$	63.0666	−	27.6709i	2.18644	−	0.959316i
$833$		−	45.7209i		−	1.58414i
$834$	27.2267	−	12.4979i	0.942784	−	0.432767i
$835$	−6.34701			−0.219647
$836$	−4.59771			−0.159015
$837$	0.779605	−	2.71340i	0.0269471	−	0.0937887i
$838$	−32.4585	+	32.4585i	−1.12126	+	1.12126i
$839$	−38.4838	+	38.4838i	−1.32861	+	1.32861i	−0.422023	+	0.906585i	$0.638680\pi$
$839$	−38.4838	+	38.4838i	−1.32861	+	1.32861i	−0.906585	+	0.422023i	$0.861320\pi$
$840$	−120.040	+	55.1022i	−4.14179	+	1.90121i
$841$	−5.62115			−0.193833
$842$	39.5491			1.36295
$843$	7.92696	+	17.2689i	0.273019	+	0.594773i
$844$			9.25236i			0.318479i
$845$	−24.0020	+	0.997406i	−0.825695	+	0.0343118i
$846$	13.4314	+	11.5474i	0.461780	+	0.397009i
$847$	3.41860	−	3.41860i	0.117465	−	0.117465i
$848$		−	59.3286i		−	2.03735i
$849$	−19.5970	−	7.26603i	−0.672567	−	0.249369i
$850$	8.38979	−	8.38979i	0.287767	−	0.287767i
$851$	−12.9915	−	12.9915i	−0.445343	−	0.445343i
$852$	36.8716	+	80.3249i	1.26320	+	2.75189i
$853$	−16.8372	−	16.8372i	−0.576496	−	0.576496i	0.357440	−	0.933936i	$-0.383650\pi$
$853$	−16.8372	−	16.8372i	−0.576496	−	0.576496i	−0.933936	+	0.357440i	$0.883650\pi$
$854$		−	144.439i		−	4.94260i
$855$	−3.72790	−	3.20501i	−0.127492	−	0.109609i
$856$	−47.1275	−	47.1275i	−1.61079	−	1.61079i
$857$	−15.8594			−0.541747			−0.270873	−	0.962615i	$-0.587312\pi$
$857$	−15.8594			−0.541747			−0.270873	+	0.962615i	$0.587312\pi$
$858$	−16.7105	+	0.977091i	−0.570488	+	0.0333573i
$859$	25.3651			0.865446			0.432723	−	0.901527i	$-0.357553\pi$
$859$	25.3651			0.865446			0.432723	+	0.901527i	$0.357553\pi$
$860$	31.6161	+	31.6161i	1.07810	+	1.07810i
$861$	−22.1676	−	8.21914i	−0.755469	−	0.280108i
$862$			35.4369i			1.20698i
$863$	14.2177	+	14.2177i	0.483975	+	0.483975i	0.906399	−	0.422423i	$-0.138820\pi$
$863$	14.2177	+	14.2177i	0.483975	+	0.483975i	−0.422423	+	0.906399i	$0.638820\pi$
$864$	82.2072	+	23.6195i	2.79675	+	0.803552i
$865$	4.79806	+	4.79806i	0.163139	+	0.163139i
$866$	−37.9184	+	37.9184i	−1.28852	+	1.28852i
$867$	5.54140	−	14.9455i	0.188196	−	0.507577i
$868$			13.6185i			0.462241i
$869$	−1.68756	+	1.68756i	−0.0572465	+	0.0572465i
$870$	−17.5488	+	47.3303i	−0.594960	+	1.60465i
$871$	−1.91422	−	0.746718i	−0.0648610	−	0.0253016i
$872$			110.679i			3.74805i
$873$	41.3562	−	3.11915i	1.39970	−	0.105567i
$874$	−3.99903			−0.135269
$875$	58.8322			1.98889
$876$	−12.5217	−	27.2786i	−0.423069	−	0.921658i
$877$	−10.3362	+	10.3362i	−0.349030	+	0.349030i	−0.859748	−	0.510718i	$-0.829379\pi$
$877$	−10.3362	+	10.3362i	−0.349030	+	0.349030i	0.510718	+	0.859748i	$0.329379\pi$
$878$	−45.8396	+	45.8396i	−1.54701	+	1.54701i
$879$	3.86155	+	8.41239i	0.130247	+	0.283743i
$880$	23.1177			0.779299
$881$	−23.0970			−0.778158			−0.389079	−	0.921204i	$-0.627207\pi$
$881$	−23.0970			−0.778158			−0.389079	+	0.921204i	$0.627207\pi$
$882$	−131.291	+	9.90216i	−4.42080	+	0.333423i
$883$		−	44.9309i		−	1.51204i	−0.654546	−	0.756022i	$-0.727140\pi$
$883$		−	44.9309i		−	1.51204i	0.654546	−	0.756022i	$-0.272860\pi$
$884$	47.7990	−	20.9721i	1.60765	−	0.705369i
$885$	5.70011	−	15.3736i	0.191607	−	0.516778i
$886$	16.0957	−	16.0957i	0.540745	−	0.540745i
$887$			52.0142i			1.74647i	0.487303	+	0.873233i	$0.337981\pi$
$887$			52.0142i			1.74647i	−0.487303	+	0.873233i	$0.662019\pi$
$888$	56.1298	−	151.386i	1.88359	−	5.08017i
$889$	61.7733	−	61.7733i	2.07181	−	2.07181i
$890$	38.0775	+	38.0775i	1.27636	+	1.27636i
$891$	−7.24650	−	5.33744i	−0.242767	−	0.178811i
$892$	27.7883	+	27.7883i	0.930421	+	0.930421i
$893$		−	1.95344i		−	0.0653694i
$894$	20.1964	+	7.48828i	0.675469	+	0.250446i
$895$	28.9390	+	28.9390i	0.967325	+	0.967325i
$896$	−88.3618			−2.95196
$897$	−10.4885	+	0.613280i	−0.350201	+	0.0204768i
$898$	31.6986			1.05780
$899$	2.26054	+	2.26054i	0.0753931	+	0.0753931i
$900$	−18.6965	−	16.0741i	−0.623217	−	0.535802i
$901$		−	13.2424i		−	0.441168i
$902$	5.35117	+	5.35117i	0.178174	+	0.178174i
$903$	16.3035	+	35.5173i	0.542547	+	1.18194i
$904$	−113.429	−	113.429i	−3.77260	−	3.77260i
$905$	−5.97189	+	5.97189i	−0.198512	+	0.198512i
$906$	−26.4795	−	9.81788i	−0.879722	−	0.326177i
$907$		−	19.9131i		−	0.661202i	−0.943771	−	0.330601i	$-0.892749\pi$
$907$		−	19.9131i		−	0.661202i	0.943771	−	0.330601i	$-0.107251\pi$
$908$	76.6323	−	76.6323i	2.54313	−	2.54313i
$909$	7.14714	+	6.14465i	0.237056	+	0.203805i
$910$	80.4369	+	31.3776i	2.66646	+	1.04016i
$911$			15.5962i			0.516725i	0.966048	+	0.258363i	$0.0831829\pi$
$911$			15.5962i			0.516725i	−0.966048	+	0.258363i	$0.916817\pi$
$912$	−8.01643	−	17.4638i	−0.265450	−	0.578284i
$913$	−12.7465			−0.421849
$914$	78.0012			2.58005
$915$	−32.4221	+	14.8828i	−1.07184	+	0.492009i
$916$	−2.67718	+	2.67718i	−0.0884567	+	0.0884567i
$917$	−23.1525	+	23.1525i	−0.764564	+	0.764564i
$918$	37.3788	+	10.7396i	1.23368	+	0.354458i
$919$	−35.0128			−1.15497			−0.577483	−	0.816403i	$-0.695965\pi$
$919$	−35.0128			−1.15497			−0.577483	+	0.816403i	$0.695965\pi$
$920$	26.5366			0.874887
$921$	−11.0223	+	5.05956i	−0.363196	+	0.166718i
$922$			8.60801i			0.283490i
$923$	12.8967	−	33.0608i	0.424499	−	1.08821i
$924$	40.7064	+	15.0928i	1.33914	+	0.496518i
$925$	−12.2415	+	12.2415i	−0.402498	+	0.402498i
$926$		−	20.9145i		−	0.687295i
$927$	−13.4655	+	15.6623i	−0.442263	+	0.514418i
$928$	−68.4870	+	68.4870i	−2.24820	+	2.24820i
$929$	−31.0177	−	31.0177i	−1.01766	−	1.01766i	−0.999841	−	0.0178163i	$-0.994329\pi$
$929$	−31.0177	−	31.0177i	−1.01766	−	1.01766i	−0.0178163	−	0.999841i	$-0.505671\pi$
$930$	4.23618	−	1.94454i	0.138910	−	0.0637639i
$931$	10.2675	+	10.2675i	0.336503	+	0.336503i
$932$			128.526i			4.21000i
$933$	−9.81852	+	26.4812i	−0.321444	+	0.866956i
$934$	−74.9196	−	74.9196i	−2.45144	−	2.45144i
$935$	5.15998			0.168749
$936$	−43.3499	−	81.5192i	−1.41694	−	2.66454i
$937$	0.568918			0.0185857			0.00929287	−	0.999957i	$-0.497042\pi$
$937$	0.568918			0.0185857			0.00929287	+	0.999957i	$0.497042\pi$
$938$	5.22188	+	5.22188i	0.170500	+	0.170500i
$939$	11.6371	−	31.3862i	0.379764	−	1.02425i
$940$			21.1036i			0.688324i
$941$	4.27191	+	4.27191i	0.139260	+	0.139260i	0.773300	−	0.634040i	$-0.218605\pi$
$941$	4.27191	+	4.27191i	0.139260	+	0.139260i	−0.634040	+	0.773300i	$0.718605\pi$
$942$	89.2516	−	40.9692i	2.90797	−	1.33485i
$943$	3.35871	+	3.35871i	0.109375	+	0.109375i
$944$	45.3166	−	45.3166i	1.47493	−	1.47493i
$945$	22.4844	+	40.6136i	0.731419	+	1.32116i
$946$		−	12.5093i		−	0.406714i
$947$	17.1876	−	17.1876i	0.558522	−	0.558522i	−0.370364	−	0.928887i	$-0.620767\pi$
$947$	17.1876	−	17.1876i	0.558522	−	0.558522i	0.928887	+	0.370364i	$0.120767\pi$
$948$	−20.0943	−	7.45042i	−0.652632	−	0.241978i
$949$	−4.37975	+	11.2276i	−0.142173	+	0.364462i
$950$			3.76816i			0.122255i
$951$	−2.20462	+	1.01199i	−0.0714896	+	0.0328160i
$952$	−115.233			−3.73471
$953$	−5.75923			−0.186560			−0.0932798	−	0.995640i	$-0.529735\pi$
$953$	−5.75923			−0.186560			−0.0932798	+	0.995640i	$0.529735\pi$
$954$	−38.0265	+	2.86802i	−1.23115	+	0.0928555i
$955$	−22.0032	+	22.0032i	−0.712007	+	0.712007i
$956$	−32.1843	+	32.1843i	−1.04091	+	1.04091i
$957$	9.26214	−	4.25161i	0.299403	−	0.137435i
$958$	−65.1609			−2.10525
$959$	52.3873			1.69167
$960$	25.5047	+	55.5621i	0.823161	+	1.79326i
$961$			30.7048i			0.990478i
$962$	−96.6477	+	42.4048i	−3.11605	+	1.36719i
$963$	−15.2709	+	17.7623i	−0.492097	+	0.572382i
$964$	−107.211	+	107.211i	−3.45305	+	3.45305i
$965$			13.9414i			0.448789i
$966$	35.4059	+	13.1276i	1.13917	+	0.422372i
$967$	−13.5174	+	13.5174i	−0.434691	+	0.434691i	−0.890220	−	0.455530i	$-0.849450\pi$
$967$	−13.5174	+	13.5174i	−0.434691	+	0.434691i	0.455530	+	0.890220i	$0.349450\pi$
$968$	−6.03572	−	6.03572i	−0.193995	−	0.193995i
$969$	−1.78930	−	3.89800i	−0.0574806	−	0.125222i
$970$	48.4189	+	48.4189i	1.55464	+	1.55464i
$971$			29.1219i			0.934565i	0.884108	+	0.467282i	$0.154767\pi$
$971$			29.1219i			0.934565i	−0.884108	+	0.467282i	$0.845233\pi$
$972$	16.4126	−	79.1347i	0.526435	−	2.53825i
$973$	22.0599	+	22.0599i	0.707209	+	0.707209i
$974$	32.1127			1.02896
$975$	0.577876	+	9.88302i	0.0185068	+	0.316510i
$976$	−139.440			−4.46337
$977$	−38.3398	−	38.3398i	−1.22660	−	1.22660i	−0.965242	−	0.261356i	$-0.915830\pi$
$977$	−38.3398	−	38.3398i	−1.22660	−	1.22660i	−0.261356	−	0.965242i	$-0.584170\pi$
$978$	−28.3314	−	10.5045i	−0.905938	−	0.335897i
$979$		−	10.8719i		−	0.347467i
$980$	−110.923	−	110.923i	−3.54329	−	3.54329i
$981$	38.7891	−	2.92553i	1.23844	−	0.0934051i
$982$	20.3192	+	20.3192i	0.648411	+	0.648411i
$983$	−22.6843	+	22.6843i	−0.723516	+	0.723516i	−0.969320	−	0.245804i	$-0.920948\pi$
$983$	−22.6843	+	22.6843i	−0.723516	+	0.723516i	0.245804	+	0.969320i	$0.420948\pi$
$984$	−14.5113	+	39.1380i	−0.462604	+	1.24767i
$985$			1.38862i			0.0442450i
$986$	−31.1403	+	31.1403i	−0.991710	+	0.991710i
$987$	−6.41254	+	17.2951i	−0.204113	+	0.550508i
$988$	−6.02447	+	15.4438i	−0.191664	+	0.491333i
$989$		−	7.85160i		−	0.249666i
$990$	−1.11754	−	14.8173i	−0.0355177	−	0.470923i
$991$	7.04821			0.223894			0.111947	−	0.993714i	$-0.464291\pi$
$991$	7.04821			0.223894			0.111947	+	0.993714i	$0.464291\pi$
$992$	8.94351			0.283957
$993$	0.809575	+	1.76366i	0.0256911	+	0.0559681i
$994$	−90.1879	+	90.1879i	−2.86058	+	2.86058i
$995$	32.4520	−	32.4520i	1.02880	−	1.02880i
$996$	−47.7511	−	104.026i	−1.51305	−	3.29619i
$997$	−15.9013			−0.503599			−0.251799	−	0.967779i	$-0.581022\pi$
$997$	−15.9013			−0.503599			−0.251799	+	0.967779i	$0.581022\pi$
$998$	−2.00598			−0.0634982
$999$	−54.5392	−	15.6700i	−1.72554	−	0.495778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.j.a.122.2	✓	96
3.2	odd	2	inner	429.2.j.a.122.47	yes	96
13.8	odd	4	inner	429.2.j.a.320.47	yes	96
39.8	even	4	inner	429.2.j.a.320.2	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.j.a.122.2	✓	96	1.1	even	1	trivial
429.2.j.a.122.47	yes	96	3.2	odd	2	inner
429.2.j.a.320.2	yes	96	39.8	even	4	inner
429.2.j.a.320.47	yes	96	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89533 - 1.89533i) q^{2} +(-0.602141 + 1.62402i) q^{3} +5.18453i q^{4} +(1.30667 + 1.30667i) q^{5} +(4.21929 - 1.93679i) q^{6} +(3.41860 + 3.41860i) q^{7} +(6.03572 - 6.03572i) q^{8} +(-2.27485 - 1.95577i) q^{9} +O(q^{10})\)	\(q+(-1.89533 - 1.89533i) q^{2} +(-0.602141 + 1.62402i) q^{3} +5.18453i q^{4} +(1.30667 + 1.30667i) q^{5} +(4.21929 - 1.93679i) q^{6} +(3.41860 + 3.41860i) q^{7} +(6.03572 - 6.03572i) q^{8} +(-2.27485 - 1.95577i) q^{9} -4.95311i q^{10} +(-0.707107 + 0.707107i) q^{11} +(-8.41975 - 3.12182i) q^{12} +(1.44865 + 3.30173i) q^{13} -12.9587i q^{14} +(-2.90884 + 1.33525i) q^{15} -12.5103 q^{16} -2.79234 q^{17} +(0.604761 + 8.01842i) q^{18} +(0.627072 - 0.627072i) q^{19} +(-6.77444 + 6.77444i) q^{20} +(-7.61034 + 3.49338i) q^{21} +2.68040 q^{22} +1.68238 q^{23} +(6.16774 + 13.4364i) q^{24} -1.58525i q^{25} +(3.51218 - 9.00352i) q^{26} +(4.54599 - 2.51674i) q^{27} +(-17.7238 + 17.7238i) q^{28} +5.88397i q^{29} +(8.04393 + 2.98247i) q^{30} +(0.384185 - 0.384185i) q^{31} +(11.6396 + 11.6396i) q^{32} +(-0.722574 - 1.57413i) q^{33} +(5.29240 + 5.29240i) q^{34} +8.93394i q^{35} +(10.1398 - 11.7940i) q^{36} +(-7.72211 - 7.72211i) q^{37} -2.37701 q^{38} +(-6.23435 + 0.364532i) q^{39} +15.7733 q^{40} +(1.99641 + 1.99641i) q^{41} +(21.0452 + 7.80299i) q^{42} -4.66697i q^{43} +(-3.66601 - 3.66601i) q^{44} +(-0.416931 - 5.52801i) q^{45} +(-3.18865 - 3.18865i) q^{46} +(1.55759 - 1.55759i) q^{47} +(7.53293 - 20.3168i) q^{48} +16.3737i q^{49} +(-3.00457 + 3.00457i) q^{50} +(1.68138 - 4.53481i) q^{51} +(-17.1179 + 7.51059i) q^{52} +4.74240i q^{53} +(-13.3862 - 3.84608i) q^{54} -1.84790 q^{55} +41.2674 q^{56} +(0.640789 + 1.39596i) q^{57} +(11.1521 - 11.1521i) q^{58} +(-3.62235 + 3.62235i) q^{59} +(-6.92263 - 15.0810i) q^{60} +11.1461 q^{61} -1.45631 q^{62} +(-1.09081 - 14.4628i) q^{63} -19.1011i q^{64} +(-2.42134 + 6.20716i) q^{65} +(-1.61398 + 4.35301i) q^{66} +(-0.402962 + 0.402962i) q^{67} -14.4770i q^{68} +(-1.01303 + 2.73220i) q^{69} +(16.9327 - 16.9327i) q^{70} +(-6.95962 - 6.95962i) q^{71} +(-25.5348 + 1.92588i) q^{72} +(2.36351 + 2.36351i) q^{73} +29.2719i q^{74} +(2.57448 + 0.954546i) q^{75} +(3.25107 + 3.25107i) q^{76} -4.83463 q^{77} +(12.5070 + 11.1252i) q^{78} +2.38657 q^{79} +(-16.3467 - 16.3467i) q^{80} +(1.34991 + 8.89819i) q^{81} -7.56770i q^{82} +(9.01316 + 9.01316i) q^{83} +(-18.1115 - 39.4560i) q^{84} +(-3.64865 - 3.64865i) q^{85} +(-8.84544 + 8.84544i) q^{86} +(-9.55567 - 3.54298i) q^{87} +8.53579i q^{88} +(-7.68759 + 7.68759i) q^{89} +(-9.68716 + 11.2676i) q^{90} +(-6.33492 + 16.2397i) q^{91} +8.72232i q^{92} +(0.392589 + 0.855257i) q^{93} -5.90429 q^{94} +1.63875 q^{95} +(-25.9115 + 11.8942i) q^{96} +(-9.77544 + 9.77544i) q^{97} +(31.0335 - 31.0335i) q^{98} +(2.99150 - 0.225624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \) 96 * q + 12 * q^6 - 16 * q^7	\( 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) \) 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more