LMFDB - Embedded newform 435.2.bm.a.247.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(37,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([0, 7, 3]))

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

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

chi := DirichletCharacter("435.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$435 = 3 \cdot 5 \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	435.bm (of order $28$ , degree $12$ , 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:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$15$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			247.4
Character	$\chi$	$=$	435.247
Dual form			435.2.bm.a.118.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41179 - 1.12587i) q^{2} +(-0.222521 + 0.974928i) q^{3} +(0.280537 + 1.22911i) q^{4} +(0.462326 + 2.18775i) q^{5} +(1.41179 - 1.12587i) q^{6} +(-1.19153 + 0.748687i) q^{7} +(-0.579211 + 1.20274i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(1.81040 - 3.60916i) q^{10} +(1.85612 + 0.649486i) q^{11} -1.26072 q^{12} +(-5.28445 - 1.84911i) q^{13} +(2.52511 + 0.284512i) q^{14} +(-2.23578 - 0.0360856i) q^{15} +(4.44360 - 2.13992i) q^{16} -1.11616i q^{17} +(0.783484 + 1.62692i) q^{18} +(-6.53617 - 4.10695i) q^{19} +(-2.55930 + 1.18200i) q^{20} +(-0.464776 - 1.32825i) q^{21} +(-1.88922 - 3.00668i) q^{22} +(0.157748 + 0.0177739i) q^{23} +(-1.04370 - 0.832325i) q^{24} +(-4.57251 + 2.02291i) q^{25} +(5.37869 + 8.56014i) q^{26} +(0.623490 - 0.781831i) q^{27} +(-1.25449 - 1.25449i) q^{28} +(1.76897 - 5.08633i) q^{29} +(3.11582 + 2.56813i) q^{30} +(-2.39611 + 0.269977i) q^{31} +(-6.07974 - 1.38766i) q^{32} +(-1.04623 + 1.66506i) q^{33} +(-1.25664 + 1.57578i) q^{34} +(-2.18882 - 2.26063i) q^{35} +(0.280537 - 1.22911i) q^{36} +(-1.41705 - 0.682413i) q^{37} +(4.60383 + 13.1570i) q^{38} +(2.97865 - 4.74050i) q^{39} +(-2.89909 - 0.711110i) q^{40} +(-3.98328 + 3.98328i) q^{41} +(-0.839268 + 2.39849i) q^{42} +(0.585191 + 0.733807i) q^{43} +(-0.277580 + 2.46359i) q^{44} +(0.532688 - 2.17169i) q^{45} +(-0.202696 - 0.202696i) q^{46} +(-10.8499 + 5.22505i) q^{47} +(1.09748 + 4.80837i) q^{48} +(-2.17798 + 4.52262i) q^{49} +(8.73295 + 2.29210i) q^{50} +(1.08817 + 0.248368i) q^{51} +(0.790282 - 7.01395i) q^{52} +(0.871687 + 7.73644i) q^{53} +(-1.76047 + 0.401817i) q^{54} +(-0.562778 + 4.36101i) q^{55} +(-0.210333 - 1.86675i) q^{56} +(5.45841 - 5.45841i) q^{57} +(-8.22393 + 5.18921i) q^{58} +3.64885i q^{59} +(-0.582866 - 2.75815i) q^{60} +(9.64032 - 6.05742i) q^{61} +(3.68677 + 2.31655i) q^{62} +(1.39837 - 0.157559i) q^{63} +(0.870871 + 1.09204i) q^{64} +(1.60225 - 12.4160i) q^{65} +(3.35169 - 1.17281i) q^{66} +(-4.98362 + 1.74384i) q^{67} +(1.37188 - 0.313124i) q^{68} +(-0.0524306 + 0.149838i) q^{69} +(0.544984 + 5.65585i) q^{70} +(0.723391 + 1.50214i) q^{71} +(1.04370 - 0.832325i) q^{72} +(3.75632 - 2.99557i) q^{73} +(1.23227 + 2.55883i) q^{74} +(-0.954712 - 4.90801i) q^{75} +(3.21427 - 9.18586i) q^{76} +(-2.69789 + 0.615775i) q^{77} +(-9.54239 + 3.33903i) q^{78} +(2.74883 - 0.961856i) q^{79} +(6.73602 + 8.73215i) q^{80} +(0.623490 + 0.781831i) q^{81} +(10.1082 - 1.13892i) q^{82} +(-9.61890 - 6.04396i) q^{83} +(1.50219 - 0.943888i) q^{84} +(2.44187 - 0.516028i) q^{85} -1.69483i q^{86} +(4.56517 + 2.85643i) q^{87} +(-1.85625 + 1.85625i) q^{88} +(0.801017 + 7.10922i) q^{89} +(-3.19708 + 2.46624i) q^{90} +(7.68099 - 1.75313i) q^{91} +(0.0224080 + 0.198877i) q^{92} +(0.269977 - 2.39611i) q^{93} +(21.2005 + 4.83888i) q^{94} +(5.96314 - 16.1983i) q^{95} +(2.70574 - 5.61853i) q^{96} +(-3.42177 - 14.9918i) q^{97} +(8.16670 - 3.93288i) q^{98} +(-1.39051 - 1.39051i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$180 q - 30 q^{3} + 30 q^{4} + 10 q^{5} - 30 q^{9} - 4 q^{10} - 30 q^{11} - 180 q^{12} - 20 q^{13} - 10 q^{14} - 4 q^{15} - 14 q^{16} + 8 q^{19} + 2 q^{20} + 36 q^{22} + 64 q^{25} - 36 q^{26} - 30 q^{27}+ \cdots + 12 q^{99}+O(q^{100})$ 180 * q - 30 * q^3 + 30 * q^4 + 10 * q^5 - 30 * q^9 - 4 * q^10 - 30 * q^11 - 180 * q^12 - 20 * q^13 - 10 * q^14 - 4 * q^15 - 14 * q^16 + 8 * q^19 + 2 * q^20 + 36 * q^22 + 64 * q^25 - 36 * q^26 - 30 * q^27 + 72 * q^28 + 12 * q^29 - 4 * q^30 - 20 * q^31 + 12 * q^33 + 40 * q^34 - 6 * q^35 + 30 * q^36 + 42 * q^37 + 16 * q^38 + 22 * q^39 + 18 * q^40 - 10 * q^41 + 4 * q^42 + 26 * q^43 + 4 * q^44 - 4 * q^45 + 12 * q^46 - 20 * q^47 - 70 * q^48 + 8 * q^50 + 12 * q^52 - 82 * q^53 + 48 * q^55 + 6 * q^56 + 8 * q^57 - 70 * q^58 - 40 * q^60 + 14 * q^61 + 110 * q^62 - 14 * q^63 - 74 * q^64 + 42 * q^65 + 22 * q^66 - 20 * q^67 - 98 * q^68 + 28 * q^69 + 8 * q^70 + 140 * q^71 + 98 * q^73 + 22 * q^75 - 4 * q^76 - 42 * q^77 + 34 * q^78 - 24 * q^79 - 62 * q^80 - 30 * q^81 + 6 * q^82 - 60 * q^83 - 68 * q^84 - 178 * q^85 - 44 * q^87 - 156 * q^88 - 12 * q^89 - 4 * q^90 - 56 * q^91 - 8 * q^92 + 8 * q^93 + 4 * q^95 - 42 * q^97 + 194 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$ .

$n$	$31$	$146$	$262$
$\chi(n)$	$e\left(\frac{27}{28}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.41179	−	1.12587i	−0.998286	−	0.796107i	−0.0192547	−	0.999815i	$-0.506129\pi$
$2$	−1.41179	−	1.12587i	−0.998286	−	0.796107i	−0.979032	+	0.203708i	$0.934701\pi$
$3$	−0.222521	+	0.974928i	−0.128473	+	0.562875i
$3$	−0.222521	+	0.974928i	−0.128473	+	0.562875i
$4$	0.280537	+	1.22911i	0.140269	+	0.614557i
$5$	0.462326	+	2.18775i	0.206759	+	0.978392i
$5$	0.462326	+	2.18775i	0.206759	+	0.978392i
$6$	1.41179	−	1.12587i	0.576361	−	0.459633i
$7$	−1.19153	+	0.748687i	−0.450356	+	0.282977i	−0.738051	−	0.674745i	$-0.764254\pi$
$7$	−1.19153	+	0.748687i	−0.450356	+	0.282977i	0.287696	+	0.957722i	$0.407111\pi$
$8$	−0.579211	+	1.20274i	−0.204782	+	0.425235i
$9$	−0.900969	−	0.433884i	−0.300323	−	0.144628i
$10$	1.81040	−	3.60916i	0.572500	−	1.14132i
$11$	1.85612	+	0.649486i	0.559643	+	0.195827i	0.595253	−	0.803538i	$-0.297052\pi$
$11$	1.85612	+	0.649486i	0.559643	+	0.195827i	−0.0356105	+	0.999366i	$0.511338\pi$
$12$	−1.26072			−0.363940
$13$	−5.28445	−	1.84911i	−1.46564	−	0.512851i	−0.524663	−	0.851310i	$-0.675809\pi$
$13$	−5.28445	−	1.84911i	−1.46564	−	0.512851i	−0.940981	+	0.338459i	$0.890094\pi$
$14$	2.52511	+	0.284512i	0.674864	+	0.0760389i
$15$	−2.23578	−	0.0360856i	−0.577275	−	0.00931725i
$16$	4.44360	−	2.13992i	1.11090	−	0.534981i
$17$		−	1.11616i		−	0.270708i	−0.990797	−	0.135354i	$-0.956783\pi$
$17$		−	1.11616i		−	0.270708i	0.990797	−	0.135354i	$-0.0432171\pi$
$18$	0.783484	+	1.62692i	0.184669	+	0.383469i
$19$	−6.53617	−	4.10695i	−1.49950	−	0.942199i	−0.996982	−	0.0776322i	$-0.975264\pi$
$19$	−6.53617	−	4.10695i	−1.49950	−	0.942199i	−0.502518	−	0.864566i	$-0.667593\pi$
$20$	−2.55930	+	1.18200i	−0.572276	+	0.264303i
$21$	−0.464776	−	1.32825i	−0.101422	−	0.289849i
$22$	−1.88922	−	3.00668i	−0.402784	−	0.641027i
$23$	0.157748	+	0.0177739i	0.0328928	+	0.00370612i	0.128396	−	0.991723i	$-0.459017\pi$
$23$	0.157748	+	0.0177739i	0.0328928	+	0.00370612i	−0.0955028	+	0.995429i	$0.530446\pi$
$24$	−1.04370	−	0.832325i	−0.213045	−	0.169898i
$25$	−4.57251	+	2.02291i	−0.914502	+	0.404582i
$26$	5.37869	+	8.56014i	1.05485	+	1.67878i
$27$	0.623490	−	0.781831i	0.119991	−	0.150464i
$28$	−1.25449	−	1.25449i	−0.237077	−	0.237077i
$29$	1.76897	−	5.08633i	0.328489	−	0.944508i
$29$	1.76897	−	5.08633i	0.328489	−	0.944508i
$30$	3.11582	+	2.56813i	0.568868	+	0.468874i
$31$	−2.39611	+	0.269977i	−0.430355	+	0.0484893i	−0.324485	−	0.945891i	$-0.605191\pi$
$31$	−2.39611	+	0.269977i	−0.430355	+	0.0484893i	−0.105869	+	0.994380i	$0.533763\pi$
$32$	−6.07974	−	1.38766i	−1.07476	−	0.245306i
$33$	−1.04623	+	1.66506i	−0.182125	+	0.289850i
$34$	−1.25664	+	1.57578i	−0.215512	+	0.270244i
$35$	−2.18882	−	2.26063i	−0.369977	−	0.382116i
$36$	0.280537	−	1.22911i	0.0467562	−	0.204852i
$37$	−1.41705	−	0.682413i	−0.232961	−	0.112188i	0.313762	−	0.949502i	$-0.398411\pi$
$37$	−1.41705	−	0.682413i	−0.232961	−	0.112188i	−0.546723	+	0.837314i	$0.684125\pi$
$38$	4.60383	+	13.1570i	0.746840	+	2.13435i
$39$	2.97865	−	4.74050i	0.476966	−	0.759087i
$40$	−2.89909	−	0.711110i	−0.458387	−	0.112436i
$41$	−3.98328	+	3.98328i	−0.622084	+	0.622084i	−0.946064	−	0.323980i	$-0.894979\pi$
$41$	−3.98328	+	3.98328i	−0.622084	+	0.622084i	0.323980	+	0.946064i	$0.394979\pi$
$42$	−0.839268	+	2.39849i	−0.129502	+	0.370095i
$43$	0.585191	+	0.733807i	0.0892408	+	0.111904i	0.824447	−	0.565939i	$-0.191486\pi$
$43$	0.585191	+	0.733807i	0.0892408	+	0.111904i	−0.735206	+	0.677843i	$0.762915\pi$
$44$	−0.277580	+	2.46359i	−0.0418468	+	0.371401i
$45$	0.532688	−	2.17169i	0.0794084	−	0.323737i
$46$	−0.202696	−	0.202696i	−0.0298859	−	0.0298859i
$47$	−10.8499	+	5.22505i	−1.58263	+	0.762152i	−0.998764	−	0.0497008i	$-0.984173\pi$
$47$	−10.8499	+	5.22505i	−1.58263	+	0.762152i	−0.583862	+	0.811853i	$0.698459\pi$
$48$	1.09748	+	4.80837i	0.158407	+	0.694028i
$49$	−2.17798	+	4.52262i	−0.311140	+	0.646088i
$50$	8.73295	+	2.29210i	1.23503	+	0.324152i
$51$	1.08817	+	0.248368i	0.152375	+	0.0347785i
$52$	0.790282	−	7.01395i	0.109592	−	0.972659i
$53$	0.871687	+	7.73644i	0.119735	+	1.06268i	0.899594	+	0.436726i	$0.143862\pi$
$53$	0.871687	+	7.73644i	0.119735	+	1.06268i	−0.779859	+	0.625955i	$0.784709\pi$
$54$	−1.76047	+	0.401817i	−0.239570	+	0.0546803i
$55$	−0.562778	+	4.36101i	−0.0758850	+	0.588039i
$56$	−0.210333	−	1.86675i	−0.0281069	−	0.249455i
$57$	5.45841	−	5.45841i	0.722985	−	0.722985i
$58$	−8.22393	+	5.18921i	−1.07986	+	0.681377i
$59$			3.64885i			0.475040i	0.971383	+	0.237520i	$0.0763346\pi$
$59$			3.64885i			0.475040i	−0.971383	+	0.237520i	$0.923665\pi$
$60$	−0.582866	−	2.75815i	−0.0752477	−	0.356076i
$61$	9.64032	−	6.05742i	1.23432	−	0.775573i	0.252906	−	0.967491i	$-0.418614\pi$
$61$	9.64032	−	6.05742i	1.23432	−	0.775573i	0.981411	+	0.191918i	$0.0614708\pi$
$62$	3.68677	+	2.31655i	0.468220	+	0.294202i
$63$	1.39837	−	0.157559i	0.176179	−	0.0198506i
$64$	0.870871	+	1.09204i	0.108859	+	0.136505i
$65$	1.60225	−	12.4160i	0.198735	−	1.54001i
$66$	3.35169	−	1.17281i	0.412565	−	0.144363i
$67$	−4.98362	+	1.74384i	−0.608846	+	0.213044i	−0.617053	−	0.786922i	$-0.711673\pi$
$67$	−4.98362	+	1.74384i	−0.608846	+	0.213044i	0.00820668	+	0.999966i	$0.497388\pi$
$68$	1.37188	−	0.313124i	0.166365	−	0.0379718i
$69$	−0.0524306	+	0.149838i	−0.00631190	+	0.0180384i
$70$	0.544984	+	5.65585i	0.0651381	+	0.676003i
$71$	0.723391	+	1.50214i	0.0858507	+	0.178271i	0.939474	−	0.342620i	$-0.111314\pi$
$71$	0.723391	+	1.50214i	0.0858507	+	0.178271i	−0.853623	+	0.520891i	$0.825600\pi$
$72$	1.04370	−	0.832325i	0.123002	−	0.0980905i
$73$	3.75632	−	2.99557i	0.439644	−	0.350605i	−0.378516	−	0.925595i	$-0.623566\pi$
$73$	3.75632	−	2.99557i	0.439644	−	0.350605i	0.818160	+	0.574990i	$0.194994\pi$
$74$	1.23227	+	2.55883i	0.143248	+	0.297457i
$75$	−0.954712	−	4.90801i	−0.110241	−	0.566728i
$76$	3.21427	−	9.18586i	0.368702	−	1.05369i
$77$	−2.69789	+	0.615775i	−0.307453	+	0.0701741i
$78$	−9.54239	+	3.33903i	−1.08046	+	0.378070i
$79$	2.74883	−	0.961856i	0.309267	−	0.108217i	−0.171183	−	0.985239i	$-0.554759\pi$
$79$	2.74883	−	0.961856i	0.309267	−	0.108217i	0.480450	+	0.877022i	$0.340473\pi$
$80$	6.73602	+	8.73215i	0.753109	+	0.976284i
$81$	0.623490	+	0.781831i	0.0692766	+	0.0868702i
$82$	10.1082	−	1.13892i	1.11626	−	0.125773i
$83$	−9.61890	−	6.04396i	−1.05581	−	0.663410i	−0.111937	−	0.993715i	$-0.535706\pi$
$83$	−9.61890	−	6.04396i	−1.05581	−	0.663410i	−0.943874	+	0.330305i	$0.892848\pi$
$84$	1.50219	−	0.943888i	0.163902	−	0.102987i
$85$	2.44187	−	0.516028i	0.264858	−	0.0559711i
$86$		−	1.69483i		−	0.182758i
$87$	4.56517	+	2.85643i	0.489438	+	0.306242i
$88$	−1.85625	+	1.85625i	−0.197877	+	0.197877i
$89$	0.801017	+	7.10922i	0.0849077	+	0.753576i	0.961962	+	0.273185i	$0.0880770\pi$
$89$	0.801017	+	7.10922i	0.0849077	+	0.753576i	−0.877054	+	0.480392i	$0.840494\pi$
$90$	−3.19708	+	2.46624i	−0.337001	+	0.259964i
$91$	7.68099	−	1.75313i	0.805186	−	0.183778i
$92$	0.0224080	+	0.198877i	0.00233620	+	0.0207343i
$93$	0.269977	−	2.39611i	0.0279953	−	0.248466i
$94$	21.2005	+	4.83888i	2.18667	+	0.499093i
$95$	5.96314	−	16.1983i	0.611805	−	1.66191i
$96$	2.70574	−	5.61853i	0.276153	−	0.573439i
$97$	−3.42177	−	14.9918i	−0.347428	−	1.52218i	−0.782996	−	0.622027i	$-0.786309\pi$
$97$	−3.42177	−	14.9918i	−0.347428	−	1.52218i	0.435567	−	0.900156i	$-0.356548\pi$
$98$	8.16670	−	3.93288i	0.824962	−	0.397281i
$99$	−1.39051	−	1.39051i	−0.139751	−	0.139751i
$100$	−3.76915	−	5.05264i	−0.376915	−	0.505264i
$101$	0.544876	−	4.83591i	0.0542172	−	0.481191i	−0.937038	−	0.349228i	$-0.886444\pi$
$101$	0.544876	−	4.83591i	0.0542172	−	0.481191i	0.991255	−	0.131962i	$-0.0421277\pi$
$102$	−1.25664	−	1.57578i	−0.124426	−	0.156025i
$103$	−0.642751	+	1.83688i	−0.0633321	+	0.180993i	−0.971201	−	0.238261i	$-0.923423\pi$
$103$	−0.642751	+	1.83688i	−0.0633321	+	0.180993i	0.907869	+	0.419254i	$0.137708\pi$
$104$	5.28482	−	5.28482i	0.518220	−	0.518220i
$105$	2.69101	−	1.63090i	0.262616	−	0.159160i
$106$	7.47955	−	11.9036i	0.726478	−	1.15618i
$107$	3.84291	+	10.9824i	0.371508	+	1.06171i	0.966208	+	0.257762i	$0.0829851\pi$
$107$	3.84291	+	10.9824i	0.371508	+	1.06171i	−0.594700	+	0.803948i	$0.702729\pi$
$108$	1.13587	+	0.547008i	0.109299	+	0.0526358i
$109$	0.587414	−	2.57363i	0.0562640	−	0.246509i	−0.938973	−	0.343990i	$-0.888221\pi$
$109$	0.587414	−	2.57363i	0.0562640	−	0.246509i	0.995237	+	0.0974811i	$0.0310786\pi$
$110$	5.70444	−	5.52322i	0.543897	−	0.526618i
$111$	0.980626	−	1.22967i	0.0930769	−	0.116715i
$112$	−3.69254	+	5.87665i	−0.348912	+	0.555291i
$113$	−8.06339	−	1.84042i	−0.758539	−	0.173132i	−0.174277	−	0.984697i	$-0.555759\pi$
$113$	−8.06339	−	1.84042i	−0.758539	−	0.173132i	−0.584262	+	0.811565i	$0.698616\pi$
$114$	−13.8516	+	1.56070i	−1.29732	+	0.146173i
$115$	0.0340461	+	0.353331i	0.00317482	+	0.0329483i
$116$	6.74795	+	0.747359i	0.626531	+	0.0693905i
$117$	3.95883	+	3.95883i	0.365994	+	0.365994i
$118$	4.10812	−	5.15142i	0.378183	−	0.474226i
$119$	0.835652	+	1.32993i	0.0766041	+	0.121915i
$120$	1.33839	−	2.66817i	0.122178	−	0.243569i
$121$	−5.57678	−	4.44733i	−0.506980	−	0.404303i
$122$	−20.4300	−	2.30190i	−1.84964	−	0.208404i
$123$	−2.99705	−	4.76978i	−0.270235	−	0.430076i
$124$	−1.00403	−	2.86936i	−0.0901648	−	0.257676i
$125$	−6.53961	−	9.06827i	−0.584921	−	0.811090i
$126$	−2.15160	−	1.35194i	−0.191680	−	0.120440i
$127$	6.93205	+	14.3945i	0.615120	+	1.27731i	0.943064	+	0.332612i	$0.107930\pi$
$127$	6.93205	+	14.3945i	0.615120	+	1.27731i	−0.327944	+	0.944697i	$0.606356\pi$
$128$			9.94998i			0.879462i
$129$	−0.845626	+	0.407232i	−0.0744532	+	0.0358548i
$130$	−16.2407	+	15.7248i	−1.42441	+	1.37916i
$131$	3.03347	+	0.341790i	0.265035	+	0.0298623i	0.243482	−	0.969905i	$-0.421710\pi$
$131$	3.03347	+	0.341790i	0.265035	+	0.0298623i	0.0215532	+	0.999768i	$0.493139\pi$
$132$	−2.34006	−	0.818822i	−0.203676	−	0.0712693i
$133$	10.8629			0.941929
$134$	8.99916	+	3.14894i	0.777409	+	0.272027i
$135$	1.99871	+	1.00258i	0.172021	+	0.0862883i
$136$	1.34245	+	0.646490i	0.115114	+	0.0554361i
$137$	9.21583	−	19.1369i	0.787362	−	1.63497i	0.0149188	−	0.999889i	$-0.495251\pi$
$137$	9.21583	−	19.1369i	0.787362	−	1.63497i	0.772443	−	0.635084i	$-0.219035\pi$
$138$	0.242718	−	0.152510i	0.0206616	−	0.0129825i
$139$	−5.76354	+	4.59627i	−0.488857	+	0.389851i	−0.836665	−	0.547715i	$-0.815498\pi$
$139$	−5.76354	+	4.59627i	−0.488857	+	0.389851i	0.347807	+	0.937566i	$0.386926\pi$
$140$	2.16453	−	3.32450i	0.182936	−	0.280971i
$141$	−2.67971	−	11.7406i	−0.225673	−	0.988736i
$142$	0.669927	−	2.93514i	0.0562190	−	0.246312i
$143$	−8.60763	−	6.86436i	−0.719806	−	0.574026i
$144$	−4.93202			−0.411002
$145$	11.9455	+	1.51852i	0.992017	+	0.126106i
$146$	−8.67575			−0.718010
$147$	−3.92458	−	3.12975i	−0.323694	−	0.258137i
$148$	0.441230	−	1.93315i	0.0362689	−	0.158904i
$149$	3.48570	+	15.2718i	0.285560	+	1.25112i	0.890550	+	0.454885i	$0.150320\pi$
$149$	3.48570	+	15.2718i	0.285560	+	1.25112i	−0.604991	+	0.796233i	$0.706823\pi$
$150$	−4.17790	+	8.00395i	−0.341124	+	0.653520i
$151$	−15.3886	+	12.2720i	−1.25231	+	0.998682i	−0.252794	+	0.967520i	$0.581349\pi$
$151$	−15.3886	+	12.2720i	−1.25231	+	0.998682i	−0.999514	+	0.0311621i	$0.990079\pi$
$152$	8.72544	−	5.48255i	0.707726	−	0.444694i
$153$	−0.484282	+	1.00562i	−0.0391519	+	0.0812997i
$154$	4.50213	+	2.16811i	0.362792	+	0.174711i
$155$	−1.69843	−	5.11728i	−0.136421	−	0.411030i
$156$	6.66224	+	2.33122i	0.533406	+	0.186647i
$157$	22.5292			1.79802			0.899011	−	0.437925i	$-0.144287\pi$
$157$	22.5292			1.79802			0.899011	+	0.437925i	$0.144287\pi$
$158$	−4.96369	−	1.73687i	−0.394890	−	0.138178i
$159$	−7.73644	−	0.871687i	−0.613539	−	0.0691293i
$160$	0.225033	−	13.9425i	0.0177904	−	1.10225i
$161$	−0.201269	+	0.0969258i	−0.0158622	+	0.00763882i
$162$		−	1.80575i		−	0.141873i
$163$	8.22830	+	17.0862i	0.644490	+	1.33830i	0.925556	+	0.378610i	$0.123598\pi$
$163$	8.22830	+	17.0862i	0.644490	+	1.33830i	−0.281066	+	0.959688i	$0.590688\pi$
$164$	−6.01337	−	3.77845i	−0.469566	−	0.295048i
$165$	−4.12644	−	1.51908i	−0.321243	−	0.118261i
$166$	6.77519	+	19.3624i	0.525857	+	1.50281i
$167$	−3.25923	−	5.18703i	−0.252207	−	0.401384i	0.696493	−	0.717564i	$-0.254743\pi$
$167$	−3.25923	−	5.18703i	−0.252207	−	0.401384i	−0.948699	+	0.316179i	$0.897600\pi$
$168$	1.86675	+	0.210333i	0.144023	+	0.0162275i
$169$	14.3424	+	11.4377i	1.10326	+	0.879824i
$170$	−4.02839	−	2.02069i	−0.308963	−	0.154980i
$171$	4.10695	+	6.53617i	0.314066	+	0.499834i
$172$	−0.737765	+	0.925128i	−0.0562540	+	0.0705403i
$173$	13.8835	+	13.8835i	1.05554	+	1.05554i	0.998364	+	0.0571753i	$0.0182094\pi$
$173$	13.8835	+	13.8835i	1.05554	+	1.05554i	0.0571753	+	0.998364i	$0.481791\pi$
$174$	−3.22911	−	9.17245i	−0.244798	−	0.695362i
$175$	3.93375	−	5.83373i	0.297364	−	0.440989i
$176$	9.63772	−	1.08591i	0.726471	−	0.0818536i
$177$	−3.55737	−	0.811947i	−0.267388	−	0.0610296i
$178$	6.87316	−	10.9386i	0.515165	−	0.819881i
$179$	−7.66883	+	9.61641i	−0.573195	+	0.718764i	−0.980935	−	0.194334i	$-0.937746\pi$
$179$	−7.66883	+	9.61641i	−0.573195	+	0.718764i	0.407740	+	0.913098i	$0.366317\pi$
$180$	2.81870	+	0.0454939i	0.210093	+	0.00339092i
$181$	−4.77751	+	20.9316i	−0.355110	+	1.55584i	0.410091	+	0.912045i	$0.365497\pi$
$181$	−4.77751	+	20.9316i	−0.355110	+	1.55584i	−0.765201	+	0.643792i	$0.777360\pi$
$182$	−12.8177	−	6.17269i	−0.950114	−	0.457551i
$183$	3.76037	+	10.7465i	0.277975	+	0.794406i
$184$	−0.112747	+	0.179436i	−0.00831182	+	0.0132282i
$185$	0.837813	−	3.41564i	0.0615972	−	0.251123i
$186$	−3.07885	+	3.07885i	−0.225752	+	0.225752i
$187$	0.724928	−	2.07172i	0.0530120	−	0.151500i
$188$	−9.46600	−	11.8700i	−0.690379	−	0.865708i
$189$	−0.157559	+	1.39837i	−0.0114607	+	0.101717i
$190$	−26.6558	+	16.1549i	−1.93381	+	1.17200i
$191$	−7.12550	−	7.12550i	−0.515583	−	0.515583i	0.400649	−	0.916232i	$-0.368785\pi$
$191$	−7.12550	−	7.12550i	−0.515583	−	0.515583i	−0.916232	+	0.400649i	$0.868785\pi$
$192$	−1.25844	+	0.606035i	−0.0908204	+	0.0437368i
$193$	−5.27201	−	23.0982i	−0.379488	−	1.66264i	−0.699046	−	0.715077i	$-0.746392\pi$
$193$	−5.27201	−	23.0982i	−0.379488	−	1.66264i	0.319558	−	0.947567i	$-0.396466\pi$
$194$	−12.0479	+	25.0177i	−0.864987	+	1.79616i
$195$	11.7481	+	4.32489i	0.841301	+	0.309712i
$196$	−6.16982	−	1.40822i	−0.440701	−	0.100587i
$197$	−2.24883	+	19.9589i	−0.160222	+	1.42201i	0.614104	+	0.789225i	$0.289517\pi$
$197$	−2.24883	+	19.9589i	−0.160222	+	1.42201i	−0.774326	+	0.632786i	$0.781911\pi$
$198$	0.397581	+	3.52863i	0.0282549	+	0.250769i
$199$	−6.97985	+	1.59311i	−0.494789	+	0.112932i	−0.462632	−	0.886551i	$-0.653095\pi$
$199$	−6.97985	+	1.59311i	−0.494789	+	0.112932i	−0.0321569	+	0.999483i	$0.510238\pi$
$200$	0.215405	−	6.67125i	0.0152314	−	0.471729i
$201$	−0.591162	−	5.24671i	−0.0416974	−	0.370074i
$202$	−6.21383	+	6.21383i	−0.437203	+	0.437203i
$203$	1.70029	+	7.38491i	0.119337	+	0.518319i
$204$			1.40716i			0.0985212i
$205$	−10.5560	−	6.87286i	−0.737264	−	0.480021i
$206$	2.97550	−	1.86963i	0.207313	−	0.130264i
$207$	−0.134414	−	0.0844581i	−0.00934244	−	0.00587024i
$208$	−27.4390	+	3.09163i	−1.90255	+	0.214366i
$209$	−9.46454	−	11.8682i	−0.654676	−	0.820938i
$210$	−5.63531	−	0.727224i	−0.388874	−	0.0501832i
$211$	−21.8798	+	7.65608i	−1.50627	+	0.527066i	−0.952219	−	0.305418i	$-0.901204\pi$
$211$	−21.8798	+	7.65608i	−1.50627	+	0.527066i	−0.554050	+	0.832484i	$0.686918\pi$
$212$	−9.26443	+	3.24176i	−0.636284	+	0.222645i
$213$	−1.62544	+	0.370997i	−0.111374	+	0.0254203i
$214$	6.93933	−	19.8315i	0.474363	−	1.35565i
$215$	−1.33484	+	1.61951i	−0.0910351	+	0.110450i
$216$	0.579211	+	1.20274i	0.0394103	+	0.0818364i
$217$	2.65291	−	2.11563i	0.180091	−	0.143618i
$218$	−3.72686	+	2.97207i	−0.252415	+	0.201294i
$219$	2.08460	+	4.32872i	0.140864	+	0.292508i
$220$	−5.51807	+	0.531708i	−0.372028	+	0.0358477i
$221$	−2.06390	+	5.89828i	−0.138833	+	0.396761i
$222$	−2.76888	+	0.631978i	−0.185835	+	0.0424156i
$223$	−5.29821	+	1.85392i	−0.354794	+	0.124148i	−0.501790	−	0.864989i	$-0.667325\pi$
$223$	−5.29821	+	1.85392i	−0.354794	+	0.124148i	0.146996	+	0.989137i	$0.453039\pi$
$224$	8.28311	−	2.89839i	0.553439	−	0.193657i
$225$	4.99740	+	0.161359i	0.333160	+	0.0107572i
$226$	9.31175	+	11.6766i	0.619408	+	0.776713i
$227$	−20.1085	+	2.26568i	−1.33464	+	0.150378i	−0.750284	−	0.661116i	$-0.770083\pi$
$227$	−20.1085	+	2.26568i	−1.33464	+	0.150378i	−0.584361	+	0.811494i	$0.698655\pi$
$228$	8.24031	+	5.17773i	0.545728	+	0.342903i
$229$	−0.120917	+	0.0759774i	−0.00799044	+	0.00502073i	−0.536021	−	0.844204i	$-0.680073\pi$
$229$	−0.120917	+	0.0759774i	−0.00799044	+	0.00502073i	0.528031	+	0.849225i	$0.322931\pi$
$230$	0.349737	−	0.537161i	0.0230610	−	0.0354193i
$231$		−	2.76727i		−	0.182073i
$232$	5.09295	+	5.07368i	0.334369	+	0.333103i
$233$	5.51014	−	5.51014i	0.360981	−	0.360981i	−0.503193	−	0.864174i	$-0.667841\pi$
$233$	5.51014	−	5.51014i	0.360981	−	0.360981i	0.864174	+	0.503193i	$0.167841\pi$
$234$	−1.13193	−	10.0461i	−0.0739965	−	0.656737i
$235$	−16.4473	−	21.3213i	−1.07291	−	1.39085i
$236$	−4.48486	+	1.02364i	−0.291940	+	0.0666333i
$237$	0.326069	+	2.89394i	0.0211805	+	0.187982i
$238$	0.317559	−	2.81842i	0.0205843	−	0.182691i
$239$	25.1239	+	5.73436i	1.62513	+	0.370925i	0.935524	−	0.353263i	$-0.114928\pi$
$239$	25.1239	+	5.73436i	1.62513	+	0.370925i	0.689603	+	0.724187i	$0.257785\pi$
$240$	−10.0121	+	4.62404i	−0.646279	+	0.298481i
$241$	1.90061	−	3.94665i	0.122429	−	0.254226i	−0.830743	−	0.556657i	$-0.812084\pi$
$241$	1.90061	−	3.94665i	0.122429	−	0.254226i	0.953171	+	0.302431i	$0.0977981\pi$
$242$	2.86615	+	12.5574i	0.184243	+	0.807221i
$243$	−0.900969	+	0.433884i	−0.0577972	+	0.0278337i
$244$	10.1497	+	10.1497i	0.649770	+	0.649770i
$245$	−10.9013	−	2.67395i	−0.696458	−	0.170832i
$246$	−1.13892	+	10.1082i	−0.0726149	+	0.644475i
$247$	26.9459	+	33.7891i	1.71453	+	2.14995i
$248$	1.06314	−	3.03829i	0.0675097	−	0.192931i
$249$	8.03283	−	8.03283i	0.509060	−	0.509060i
$250$	−0.977082	+	20.1652i	−0.0617961	+	1.27536i
$251$	−2.68632	+	4.27526i	−0.169559	+	0.269852i	−0.920684	−	0.390308i	$-0.872369\pi$
$251$	−2.68632	+	4.27526i	−0.169559	+	0.269852i	0.751125	+	0.660160i	$0.229511\pi$
$252$	0.585954	+	1.67456i	0.0369116	+	0.105487i
$253$	0.281256	+	0.135446i	0.0176824	+	0.00851541i
$254$	6.41972	−	28.1266i	0.402809	−	1.76482i
$255$	−0.0402771	+	2.49548i	−0.00252225	+	0.156273i
$256$	12.9441	−	16.2314i	0.809005	−	1.01446i
$257$	−4.88619	+	7.77632i	−0.304792	+	0.485074i	−0.963641	−	0.267202i	$-0.913901\pi$
$257$	−4.88619	+	7.77632i	−0.304792	+	0.485074i	0.658849	+	0.752276i	$0.271044\pi$
$258$	1.65233	+	0.377135i	0.102870	+	0.0234794i
$259$	2.19936	−	0.247809i	0.136662	−	0.0153981i
$260$	15.7101	−	1.51379i	0.974301	−	0.0938814i
$261$	−3.80066	+	3.81510i	−0.235255	+	0.236149i
$262$	−3.89781	−	3.89781i	−0.240808	−	0.240808i
$263$	14.2337	−	17.8484i	0.877685	−	1.10058i	−0.116532	−	0.993187i	$-0.537178\pi$
$263$	14.2337	−	17.8484i	0.877685	−	1.10058i	0.994216	−	0.107395i	$-0.0342509\pi$
$264$	−1.39666	−	2.22277i	−0.0859584	−	0.136802i
$265$	−16.5224	+	5.48379i	−1.01496	+	0.336867i
$266$	−15.3361	−	12.2301i	−0.940315	−	0.749876i
$267$	−7.10922	−	0.801017i	−0.435077	−	0.0490215i
$268$	−3.54148	−	5.63623i	−0.216330	−	0.344287i
$269$	4.50848	+	12.8845i	0.274887	+	0.785582i	0.995716	+	0.0924684i	$0.0294757\pi$
$269$	4.50848	+	12.8845i	0.274887	+	0.785582i	−0.720829	+	0.693113i	$0.756239\pi$
$270$	−1.69299	−	3.66571i	−0.103032	−	0.223088i
$271$	−14.1688	−	8.90285i	−0.860694	−	0.540810i	0.0278445	−	0.999612i	$-0.491136\pi$
$271$	−14.1688	−	8.90285i	−0.860694	−	0.540810i	−0.888538	+	0.458802i	$0.848279\pi$
$272$	−2.38849	−	4.95975i	−0.144823	−	0.300729i
$273$			7.87852i			0.476829i
$274$	−34.5564	+	16.6415i	−2.08763	+	1.00535i
$275$	−9.80100	+	0.784991i	−0.591022	+	0.0473368i
$276$	−0.198877	−	0.0224080i	−0.0119710	−	0.00134881i
$277$	−5.38368	−	1.88383i	−0.323474	−	0.113188i	0.163657	−	0.986517i	$-0.447671\pi$
$277$	−5.38368	−	1.88383i	−0.323474	−	0.113188i	−0.487131	+	0.873329i	$0.661957\pi$
$278$	13.3117			0.798383
$279$	2.27596	+	0.796394i	0.136258	+	0.0476789i
$280$	3.98675	−	1.32320i	0.238254	−	0.0790766i
$281$	0.379586	+	0.182799i	0.0226442	+	0.0109049i	0.445172	−	0.895445i	$-0.353143\pi$
$281$	0.379586	+	0.182799i	0.0226442	+	0.0109049i	−0.422527	+	0.906350i	$0.638857\pi$
$282$	−9.43513	+	19.5922i	−0.561854	+	1.16670i
$283$	11.1430	−	7.00161i	0.662382	−	0.416202i	−0.158454	−	0.987366i	$-0.550651\pi$
$283$	11.1430	−	7.00161i	0.662382	−	0.416202i	0.820836	+	0.571164i	$0.193508\pi$
$284$	−1.64336	+	1.31054i	−0.0975155	+	0.0777660i
$285$	14.4652	+	9.41808i	0.856846	+	0.557879i
$286$	4.42383	+	19.3821i	0.261587	+	1.14609i
$287$	1.76396	−	7.72843i	0.104123	−	0.456195i
$288$	4.87558	+	3.88814i	0.287296	+	0.229111i
$289$	15.7542			0.926717
$290$	−15.1548	−	15.5928i	−0.889923	−	0.915641i
$291$	15.3773			0.901434
$292$	4.73569	+	3.77658i	0.277135	+	0.221008i
$293$	0.977886	−	4.28440i	0.0571287	−	0.250297i	−0.938298	−	0.345829i	$-0.887598\pi$
$293$	0.977886	−	4.28440i	0.0571287	−	0.250297i	0.995426	+	0.0955313i	$0.0304550\pi$
$294$	2.01701	+	8.83710i	0.117634	+	0.515390i
$295$	−7.98279	+	1.68696i	−0.464776	+	0.0982187i
$296$	1.64154	−	1.30908i	0.0954124	−	0.0760889i
$297$	1.66506	−	1.04623i	0.0966168	−	0.0607083i
$298$	12.2730	−	25.4851i	0.710953	−	1.47631i
$299$	−0.800747	−	0.385619i	−0.0463084	−	0.0223009i
$300$	5.76467	−	2.55033i	0.332823	−	0.147243i
$301$	−1.24666	−	0.436227i	−0.0718565	−	0.0251437i
$302$	35.5421			2.04522
$303$	4.59341	+	1.60730i	0.263885	+	0.0923372i
$304$	−37.8327	−	4.26272i	−2.16985	−	0.244484i
$305$	17.7091	+	18.2901i	1.01402	+	1.04729i
$306$	1.81590	−	0.874491i	0.103808	−	0.0499913i
$307$		−	25.0399i		−	1.42910i	−0.699584	−	0.714550i	$-0.746631\pi$
$307$		−	25.0399i		−	1.42910i	0.699584	−	0.714550i	$-0.253369\pi$
$308$	−1.51372	−	3.14327i	−0.0862520	−	0.179104i
$309$	−1.64780	−	1.03538i	−0.0937399	−	0.0589007i
$310$	−3.36355	+	9.13673i	−0.191037	+	0.518932i
$311$	−1.08819	−	3.10986i	−0.0617054	−	0.176344i	0.908903	−	0.417007i	$-0.136921\pi$
$311$	−1.08819	−	3.10986i	−0.0617054	−	0.176344i	−0.970609	+	0.240663i	$0.922635\pi$
$312$	3.97634	+	6.32831i	0.225116	+	0.358270i
$313$	−14.0982	−	1.58848i	−0.796875	−	0.0897863i	−0.295867	−	0.955229i	$-0.595609\pi$
$313$	−14.0982	−	1.58848i	−0.796875	−	0.0897863i	−0.501008	+	0.865443i	$0.667037\pi$
$314$	−31.8064	−	25.3648i	−1.79494	−	1.43142i
$315$	0.991204	+	2.98645i	0.0558480	+	0.168267i
$316$	1.95338	+	3.10879i	0.109886	+	0.174883i
$317$	1.53639	−	1.92657i	0.0862921	−	0.108207i	−0.736811	−	0.676099i	$-0.763669\pi$
$317$	1.53639	−	1.92657i	0.0862921	−	0.108207i	0.823103	+	0.567892i	$0.192241\pi$
$318$	9.94082	+	9.94082i	0.557454	+	0.557454i
$319$	6.58692	−	8.29194i	0.368797	−	0.464260i
$320$	−1.98648	+	2.41013i	−0.111048	+	0.134730i
$321$	−11.5622	+	1.30275i	−0.645338	+	0.0727122i
$322$	0.393274	+	0.0897623i	0.0219163	+	0.00500226i
$323$	−4.58400	+	7.29539i	−0.255060	+	0.405926i
$324$	−0.786048	+	0.985674i	−0.0436694	+	0.0547596i
$325$	27.9038	−	2.23490i	1.54782	−	0.123970i
$326$	7.62017	−	33.3862i	0.422042	−	1.84909i
$327$	2.37839	+	1.14537i	0.131525	+	0.0633392i
$328$	−2.48371	−	7.09804i	−0.137140	−	0.391923i
$329$	9.01608	−	14.3490i	0.497073	−	0.791086i
$330$	4.11539	+	6.79045i	0.226545	+	0.373802i
$331$	−14.5500	+	14.5500i	−0.799741	+	0.799741i	−0.983055	−	0.183313i	$-0.941318\pi$
$331$	−14.5500	+	14.5500i	−0.799741	+	0.799741i	0.183313	+	0.983055i	$0.441318\pi$
$332$	4.73025	−	13.5183i	0.259606	−	0.741913i
$333$	0.980626	+	1.22967i	0.0537380	+	0.0673853i
$334$	−1.23855	+	10.9924i	−0.0677705	+	0.601480i
$335$	−6.11915	−	10.0967i	−0.334325	−	0.551641i
$336$	−4.90764	−	4.90764i	−0.267734	−	0.267734i
$337$	29.8695	−	14.3844i	1.62710	−	0.783568i	0.627106	−	0.778934i	$-0.284239\pi$
$337$	29.8695	−	14.3844i	1.62710	−	0.783568i	0.999989	−	0.00463366i	$-0.00147495\pi$
$338$	−7.37119	−	32.2953i	−0.400940	−	1.75663i
$339$	3.58854	−	7.45169i	0.194903	−	0.404720i
$340$	1.31929	+	2.85658i	0.0715488	+	0.154920i
$341$	−4.62283	−	1.05513i	−0.250340	−	0.0571386i
$342$	1.56070	−	13.8516i	0.0843929	−	0.749007i
$343$	−1.89381	−	16.8081i	−0.102256	−	0.907550i
$344$	−1.22153	+	0.278807i	−0.0658606	+	0.0150322i
$345$	−0.352048	−	0.0454310i	−0.0189536	−	0.00244592i
$346$	−3.96963	−	35.2314i	−0.213409	−	1.89405i
$347$	4.80559	−	4.80559i	0.257978	−	0.257978i	−0.566254	−	0.824231i	$-0.691608\pi$
$347$	4.80559	−	4.80559i	0.257978	−	0.257978i	0.824231	+	0.566254i	$0.191608\pi$
$348$	−2.23018	+	6.41246i	−0.119550	+	0.343744i
$349$		−	13.0039i		−	0.696085i	−0.937479	−	0.348043i	$-0.886846\pi$
$349$		−	13.0039i		−	0.696085i	0.937479	−	0.348043i	$-0.113154\pi$
$350$	−12.1216	+	3.80714i	−0.647928	+	0.203500i
$351$	−4.74050	+	2.97865i	−0.253029	+	0.158989i
$352$	−10.3835	−	6.52438i	−0.553442	−	0.347751i
$353$	−6.86271	+	0.773242i	−0.365265	+	0.0411555i	−0.292690	−	0.956207i	$-0.594550\pi$
$353$	−6.86271	+	0.773242i	−0.365265	+	0.0411555i	−0.0725754	+	0.997363i	$0.523122\pi$
$354$	4.10812	+	5.15142i	0.218344	+	0.273795i
$355$	−2.95186	+	2.27708i	−0.156668	+	0.120855i
$356$	−8.51334	+	2.97895i	−0.451206	+	0.157884i
$357$	−1.48254	+	0.518763i	−0.0784642	+	0.0274558i
$358$	21.6536	−	4.94229i	1.14443	−	0.261208i
$359$	−8.69119	+	24.8380i	−0.458703	+	1.31090i	0.449840	+	0.893109i	$0.351481\pi$
$359$	−8.69119	+	24.8380i	−0.458703	+	1.31090i	−0.908544	+	0.417790i	$0.862805\pi$
$360$	2.30345	+	1.89856i	0.121403	+	0.100063i
$361$	17.6107	+	36.5690i	0.926880	+	1.92469i
$362$	30.3110	−	24.1723i	1.59311	−	1.27047i
$363$	5.57678	−	4.44733i	0.292705	−	0.233425i
$364$	4.30961	+	8.94899i	0.225885	+	0.469055i
$365$	8.29020	+	6.83297i	0.433929	+	0.357654i
$366$	6.79028	−	19.4055i	0.354934	−	1.01434i
$367$	0.953832	−	0.217706i	0.0497896	−	0.0113642i	−0.197554	−	0.980292i	$-0.563300\pi$
$367$	0.953832	−	0.217706i	0.0497896	−	0.0113642i	0.247343	+	0.968928i	$0.420442\pi$
$368$	0.739004	−	0.258589i	0.0385233	−	0.0134799i
$369$	5.31710	−	1.86053i	0.276797	−	0.0968554i
$370$	−5.02837	+	3.87890i	−0.261412	+	0.201655i
$371$	−6.83081	−	8.56557i	−0.354638	−	0.444702i
$372$	3.02084	−	0.340367i	0.156623	−	0.0176472i
$373$	3.51759	+	2.21025i	0.182134	+	0.114442i	0.620013	−	0.784592i	$-0.287127\pi$
$373$	3.51759	+	2.21025i	0.182134	+	0.114442i	−0.437879	+	0.899034i	$0.644270\pi$
$374$	−3.35593	+	2.10867i	−0.173531	+	0.109037i
$375$	10.2961	−	4.35777i	0.531689	−	0.225034i
$376$		−	16.0761i		−	0.829062i
$377$	−18.7532	+	23.6075i	−0.965840	+	1.21585i
$378$	1.79682	−	1.79682i	0.0924185	−	0.0924185i
$379$	0.672735	+	5.97069i	0.0345561	+	0.306694i	0.999087	+	0.0427236i	$0.0136035\pi$
$379$	0.672735	+	5.97069i	0.0345561	+	0.306694i	−0.964531	+	0.263970i	$0.914968\pi$
$380$	21.5824	+	2.78516i	1.10715	+	0.142876i
$381$	−15.5762	+	3.55516i	−0.797992	+	0.182136i
$382$	2.03736	+	18.0821i	0.104240	+	0.925159i
$383$	0.535387	−	4.75169i	0.0273570	−	0.242800i	−0.972590	−	0.232526i	$-0.925301\pi$
$383$	0.535387	−	4.75169i	0.0273570	−	0.242800i	0.999947	−	0.0102742i	$-0.00327044\pi$
$384$	−9.70051	−	2.21408i	−0.495027	−	0.112987i
$385$	−2.59447	−	5.61762i	−0.132226	−	0.286300i
$386$	−18.5625	+	38.5454i	−0.944805	+	1.96191i
$387$	−0.208852	−	0.915042i	−0.0106166	−	0.0465142i
$388$	17.4667	−	8.41150i	0.886736	−	0.427029i
$389$	21.9500	+	21.9500i	1.11291	+	1.11291i	0.992755	+	0.120157i	$0.0383397\pi$
$389$	21.9500	+	21.9500i	1.11291	+	1.11291i	0.120157	+	0.992755i	$0.461660\pi$
$390$	−11.7167	−	19.3327i	−0.593296	−	0.978947i
$391$	0.0198385	−	0.176072i	0.00100328	−	0.00890432i
$392$	−4.17805	−	5.23910i	−0.211023	−	0.264615i
$393$	−1.00823	+	2.88136i	−0.0508585	+	0.145345i
$394$	25.6459	−	25.6459i	1.29202	−	1.29202i
$395$	3.37516	+	5.56906i	0.169823	+	0.280210i
$396$	1.31901	−	2.09918i	0.0662825	−	0.105488i
$397$	−6.05176	−	17.2949i	−0.303729	−	0.868009i	−0.990051	−	0.140710i	$-0.955061\pi$
$397$	−6.05176	−	17.2949i	−0.303729	−	0.868009i	0.686321	−	0.727298i	$-0.259224\pi$
$398$	11.6477	+	5.60924i	0.583847	+	0.281166i
$399$	−2.41721	+	10.5905i	−0.121012	+	0.530188i
$400$	−15.9895	+	18.7738i	−0.799476	+	0.938691i
$401$	6.21527	−	7.79370i	0.310376	−	0.389199i	−0.602038	−	0.798467i	$-0.705645\pi$
$401$	6.21527	−	7.79370i	0.310376	−	0.389199i	0.912414	+	0.409268i	$0.134216\pi$
$402$	−5.07249	+	8.07282i	−0.252993	+	0.402636i
$403$	13.1614	+	3.00400i	0.655615	+	0.149640i
$404$	6.09674	−	0.686938i	0.303324	−	0.0341764i
$405$	−1.42220	+	1.72550i	−0.0706695	+	0.0857409i
$406$	5.91396	−	12.3402i	0.293505	−	0.612436i
$407$	−2.18699	−	2.18699i	−0.108405	−	0.108405i
$408$	−0.929005	+	1.16494i	−0.0459926	+	0.0576729i
$409$	−8.59821	−	13.6840i	−0.425154	−	0.676629i	0.563622	−	0.826033i	$-0.309407\pi$
$409$	−8.59821	−	13.6840i	−0.425154	−	0.676629i	−0.988776	+	0.149404i	$0.952265\pi$
$410$	7.16496	+	21.5877i	0.353852	+	1.06614i
$411$	16.6064	+	13.2431i	0.819131	+	0.653235i
$412$	−2.43805	−	0.274702i	−0.120114	−	0.0135336i
$413$	−2.73185	−	4.34772i	−0.134426	−	0.213937i
$414$	0.0946764	+	0.270570i	0.00465309	+	0.0132978i
$415$	8.77560	−	23.8380i	0.430777	−	1.17016i
$416$	29.5622	+	18.5752i	1.44941	+	0.910722i
$417$	−3.19853	−	6.64181i	−0.156632	−	0.325251i
$418$			27.4111i			1.34072i
$419$	−16.7853	+	8.08336i	−0.820015	+	0.394898i	−0.796361	−	0.604822i	$-0.793244\pi$
$419$	−16.7853	+	8.08336i	−0.820015	+	0.394898i	−0.0236539	+	0.999720i	$0.507530\pi$
$420$	2.75949	+	2.85003i	0.134649	+	0.139067i
$421$	−21.4969	−	2.42212i	−1.04770	−	0.118047i	−0.428704	−	0.903445i	$-0.641030\pi$
$421$	−21.4969	−	2.42212i	−1.04770	−	0.118047i	−0.618991	+	0.785398i	$0.712458\pi$
$422$	39.5094	+	13.8249i	1.92329	+	0.672988i
$423$	12.0425			0.585527
$424$	−9.80985	−	3.43262i	−0.476408	−	0.166703i
$425$	2.25788	+	5.10363i	0.109523	+	0.247563i
$426$	2.71248	+	1.30626i	0.131420	+	0.0632886i
$427$	−6.95161	+	14.4352i	−0.336412	+	0.698567i
$428$	−12.4206	+	7.80436i	−0.600371	+	0.377238i
$429$	8.60763	−	6.86436i	0.415580	−	0.331414i
$430$	3.70786	−	0.783563i	0.178809	−	0.0377868i
$431$	−6.08540	−	26.6619i	−0.293124	−	1.28426i	−0.880152	−	0.474692i	$-0.842559\pi$
$431$	−6.08540	−	26.6619i	−0.293124	−	1.28426i	0.587028	−	0.809566i	$-0.300298\pi$
$432$	1.09748	−	4.80837i	0.0528025	−	0.231343i
$433$	−15.6081	−	12.4471i	−0.750078	−	0.598167i	0.172033	−	0.985091i	$-0.444966\pi$
$433$	−15.6081	−	12.4471i	−0.750078	−	0.598167i	−0.922112	+	0.386924i	$0.873538\pi$
$434$	−6.12726			−0.294118
$435$	−4.13856	+	11.3081i	−0.198429	+	0.542180i
$436$	3.32807			0.159386
$437$	−0.958072	−	0.764037i	−0.0458308	−	0.0365488i
$438$	1.93054	−	8.45823i	0.0922445	−	0.404150i
$439$	4.82227	+	21.1277i	0.230154	+	1.00837i	0.949512	+	0.313732i	$0.101579\pi$
$439$	4.82227	+	21.1277i	0.230154	+	1.00837i	−0.719357	+	0.694640i	$0.755564\pi$
$440$	−4.91922	−	3.20283i	−0.234514	−	0.152689i
$441$	3.92458	−	3.12975i	0.186885	−	0.149036i
$442$	9.55445	−	6.00346i	0.454459	−	0.285555i
$443$	−11.7461	+	24.3911i	−0.558075	+	1.15886i	0.410896	+	0.911682i	$0.365216\pi$
$443$	−11.7461	+	24.3911i	−0.558075	+	1.15886i	−0.968971	+	0.247173i	$0.920498\pi$
$444$	1.78650	+	0.860334i	0.0847837	+	0.0408297i
$445$	−15.1829	+	5.03921i	−0.719738	+	0.238881i
$446$	9.56722	+	3.34772i	0.453021	+	0.158519i
$447$	−15.6646			−0.740909
$448$	−1.85526	−	0.649184i	−0.0876529	−	0.0306711i
$449$	0.816966	+	0.0920500i	0.0385550	+	0.00434411i	0.131221	−	0.991353i	$-0.458110\pi$
$449$	0.816966	+	0.0920500i	0.0385550	+	0.00434411i	−0.0926659	+	0.995697i	$0.529539\pi$
$450$	−6.87361	−	5.85420i	−0.324025	−	0.275970i
$451$	−9.98055	+	4.80638i	−0.469966	+	0.226324i
$452$		−	10.4271i		−	0.490451i
$453$	−8.54004	−	17.7336i	−0.401246	−	0.833196i
$454$	30.9398	+	19.4407i	1.45208	+	0.912399i
$455$	7.38654	+	15.9936i	0.346287	+	0.749790i
$456$	3.40350	+	9.72665i	0.159384	+	0.455492i
$457$	10.7477	+	17.1048i	0.502755	+	0.800130i	0.997628	−	0.0688353i	$-0.0219283\pi$
$457$	10.7477	+	17.1048i	0.502755	+	0.800130i	−0.494873	+	0.868965i	$0.664785\pi$
$458$	0.256250	+	0.0288725i	0.0119738	+	0.00134912i
$459$	−0.872646	−	0.695912i	−0.0407316	−	0.0324824i
$460$	−0.424733	+	0.140969i	−0.0198033	+	0.00657272i
$461$	6.35146	+	10.1083i	0.295817	+	0.470790i	0.961254	−	0.275664i	$-0.0888977\pi$
$461$	6.35146	+	10.1083i	0.295817	+	0.470790i	−0.665437	+	0.746454i	$0.731755\pi$
$462$	−3.11557	+	3.90680i	−0.144949	+	0.181761i
$463$	16.6601	+	16.6601i	0.774261	+	0.774261i	0.978848	−	0.204587i	$-0.0655851\pi$
$463$	16.6601	+	16.6601i	0.774261	+	0.774261i	−0.204587	+	0.978848i	$0.565585\pi$
$464$	−3.02378	−	26.3871i	−0.140375	−	1.22499i
$465$	5.36692	−	0.517144i	0.248885	−	0.0239820i
$466$	−13.9828	+	1.57549i	−0.647742	+	0.0729830i
$467$	−25.2320	−	5.75903i	−1.16760	−	0.266496i	−0.405583	−	0.914058i	$-0.632932\pi$
$467$	−25.2320	−	5.75903i	−1.16760	−	0.266496i	−0.762013	+	0.647562i	$0.775789\pi$
$468$	−3.75526	+	5.97646i	−0.173587	+	0.276262i
$469$	4.63253	−	5.80901i	0.213910	−	0.268235i
$470$	−0.784708	+	48.6186i	−0.0361959	+	2.24261i
$471$	−5.01321	+	21.9643i	−0.230997	+	1.01206i
$472$	−4.38864	−	2.11346i	−0.202004	−	0.0972798i
$473$	0.609591	+	1.74211i	0.0280290	+	0.0801023i
$474$	2.79785	−	4.45275i	0.128509	−	0.204521i
$475$	38.1947	+	5.55697i	1.75249	+	0.254971i
$476$	−1.40021	+	1.40021i	−0.0641784	+	0.0641784i
$477$	2.57135	−	7.34850i	0.117734	−	0.336465i
$478$	−29.0135	−	36.3818i	−1.32705	−	1.66406i
$479$	3.45247	−	30.6415i	0.157747	−	1.40005i	−0.626415	−	0.779490i	$-0.715479\pi$
$479$	3.45247	−	30.6415i	0.157747	−	1.40005i	0.784162	−	0.620556i	$-0.213093\pi$
$480$	13.5429	+	3.32189i	0.618145	+	0.151623i
$481$	6.22645	+	6.22645i	0.283902	+	0.283902i
$482$	−7.12665	+	3.43201i	−0.324610	+	0.156324i
$483$	−0.0497092	−	0.217790i	−0.00226185	−	0.00990980i
$484$	3.90179	−	8.10215i	0.177354	−	0.368279i
$485$	31.2163	−	14.4171i	1.41746	−	0.654646i
$486$	1.76047	+	0.401817i	0.0798567	+	0.0182268i
$487$	1.82887	−	16.2317i	0.0828740	−	0.735527i	−0.881717	−	0.471778i	$-0.843612\pi$
$487$	1.82887	−	16.2317i	0.0828740	−	0.735527i	0.964591	−	0.263749i	$-0.0849591\pi$
$488$	1.70174	+	15.1034i	0.0770342	+	0.683698i
$489$	−18.4888	+	4.21995i	−0.836094	+	0.190833i
$490$	12.3798	+	16.0484i	0.559264	+	0.724995i
$491$	−0.414893	−	3.68228i	−0.0187239	−	0.166179i	0.980870	−	0.194662i	$-0.0623610\pi$
$491$	−0.414893	−	3.68228i	−0.0187239	−	0.166179i	−0.999594	+	0.0284829i	$0.990932\pi$
$492$	5.02182	−	5.02182i	0.226401	−	0.226401i
$493$	−5.67714	−	1.97444i	−0.255685	−	0.0889245i
$494$		−	78.0405i		−	3.51121i
$495$	2.39922	−	3.68496i	0.107837	−	0.165626i
$496$	−10.0696	+	6.32718i	−0.452140	+	0.284099i
$497$	−1.98657	−	1.24825i	−0.0891099	−	0.0559915i
$498$	−20.3845	+	2.29679i	−0.913453	+	0.102921i
$499$	13.1792	+	16.5262i	0.589982	+	0.739814i	0.983779	−	0.179384i	$-0.0574103\pi$
$499$	13.1792	+	16.5262i	0.589982	+	0.739814i	−0.393798	+	0.919197i	$0.628839\pi$
$500$	9.31133	−	10.5819i	0.416416	−	0.473238i
$501$	5.78223	−	2.02329i	0.258331	−	0.0903939i
$502$	8.60589	−	3.01133i	0.384100	−	0.134402i
$503$	−13.0051	+	2.96832i	−0.579867	+	0.132351i	−0.502387	−	0.864643i	$-0.667545\pi$
$503$	−13.0051	+	2.96832i	−0.579867	+	0.132351i	−0.0774802	+	0.996994i	$0.524687\pi$
$504$	−0.620451	+	1.77315i	−0.0276371	+	0.0789822i
$505$	10.8317	−	1.04371i	0.482003	−	0.0464447i
$506$	−0.244581	−	0.507878i	−0.0108729	−	0.0225779i
$507$	−14.3424	+	11.4377i	−0.636970	+	0.507967i
$508$	−15.7479	+	12.5585i	−0.698698	+	0.557193i
$509$	−0.0370946	−	0.0770276i	−0.00164419	−	0.00341419i	0.900145	−	0.435590i	$-0.143460\pi$
$509$	−0.0370946	−	0.0770276i	−0.00164419	−	0.00341419i	−0.901789	+	0.432176i	$0.857746\pi$
$510$	2.86643	−	3.47774i	0.126928	−	0.153997i
$511$	−2.23302	+	6.38162i	−0.0987832	+	0.282306i
$512$	−17.1476	+	3.91383i	−0.757825	+	0.172969i
$513$	−7.28618	+	2.54954i	−0.321693	+	0.112565i
$514$	15.6534	−	5.47735i	0.690440	−	0.241595i
$515$	−4.31579	−	0.556942i	−0.190176	−	0.0245418i
$516$	−0.737765	−	0.925128i	−0.0324783	−	0.0407265i
$517$	−23.5324	+	2.65147i	−1.03495	+	0.116611i
$518$	−3.38404	−	2.12633i	−0.148686	−	0.0934257i
$519$	−16.6247	+	10.4460i	−0.729744	+	0.458529i
$520$	14.0052	+	9.11857i	0.614168	+	0.399876i
$521$		−	14.9112i		−	0.653272i	−0.945150	−	0.326636i	$-0.894085\pi$
$521$		−	14.9112i		−	0.653272i	0.945150	−	0.326636i	$-0.105915\pi$
$522$	9.66102	−	1.10709i	0.422851	−	0.0484559i
$523$	−9.27322	+	9.27322i	−0.405490	+	0.405490i	−0.880162	−	0.474673i	$-0.842566\pi$
$523$	−9.27322	+	9.27322i	−0.405490	+	0.405490i	0.474673	+	0.880162i	$0.342566\pi$
$524$	0.430902	+	3.82436i	0.0188241	+	0.167068i
$525$	4.81213	+	5.13325i	0.210018	+	0.224033i
$526$	−40.1899	+	9.17308i	−1.75236	+	0.399965i
$527$	0.301337	+	2.67444i	0.0131264	+	0.116500i
$528$	−1.08591	+	9.63772i	−0.0472582	+	0.419428i
$529$	−22.3988	−	5.11237i	−0.973860	−	0.222277i
$530$	29.5002	+	10.8600i	1.28141	+	0.471729i
$531$	1.58318	−	3.28750i	0.0687041	−	0.142666i
$532$	3.04744	+	13.3517i	0.132123	+	0.578870i
$533$	28.4150	−	13.6839i	1.23079	−	0.592718i
$534$	9.13490	+	9.13490i	0.395306	+	0.395306i
$535$	−22.2501	+	13.4848i	−0.961956	+	0.582998i
$536$	0.789170	−	7.00408i	0.0340869	−	0.302530i
$537$	−7.66883	−	9.61641i	−0.330935	−	0.414979i
$538$	8.14118	−	23.2661i	0.350991	−	1.00307i
$539$	−6.97997	+	6.97997i	−0.300649	+	0.300649i
$540$	−0.671572	+	2.73790i	−0.0288999	+	0.117821i
$541$	−9.82246	+	15.6324i	−0.422301	+	0.672088i	−0.988335	−	0.152294i	$-0.951334\pi$
$541$	−9.82246	+	15.6324i	−0.422301	+	0.672088i	0.566035	+	0.824381i	$0.308477\pi$
$542$	9.97997	+	28.5211i	0.428677	+	1.22509i
$543$	−19.3437	−	9.31546i	−0.830120	−	0.399764i
$544$	−1.54885	+	6.78594i	−0.0664063	+	0.290945i
$545$	5.90203	+	0.0952591i	0.252815	+	0.00408045i
$546$	8.87015	−	11.1228i	0.379607	−	0.476012i
$547$	9.24316	−	14.7104i	0.395209	−	0.628971i	−0.588551	−	0.808460i	$-0.700301\pi$
$547$	9.24316	−	14.7104i	0.395209	−	0.628971i	0.983760	+	0.179489i	$0.0574443\pi$
$548$	26.1068	+	5.95871i	1.11523	+	0.254543i
$549$	−11.3138	+	1.27476i	−0.482863	+	0.0544056i
$550$	14.7207	+	9.92636i	0.627695	+	0.423261i
$551$	−32.4516	+	25.9801i	−1.38248	+	1.10679i
$552$	−0.149848	−	0.149848i	−0.00637797	−	0.00637797i
$553$	−2.55518	+	3.20409i	−0.108657	+	0.136252i
$554$	5.47968	+	8.72087i	0.232809	+	0.370514i
$555$	3.14357	+	1.57686i	0.133437	+	0.0669339i
$556$	−7.26624	−	5.79463i	−0.308157	−	0.245747i
$557$	−37.4437	−	4.21889i	−1.58654	−	0.178760i	−0.725836	−	0.687867i	$-0.758547\pi$
$557$	−37.4437	−	4.21889i	−1.58654	−	0.178760i	−0.860703	+	0.509107i	$0.829976\pi$
$558$	−2.31655	−	3.68677i	−0.0980674	−	0.156073i
$559$	−1.73553	−	4.95985i	−0.0734050	−	0.209779i
$560$	−14.5638	−	5.36143i	−0.615433	−	0.226562i
$561$	1.85847	+	1.16775i	0.0784647	+	0.0493026i
$562$	−0.330089	−	0.685437i	−0.0139240	−	0.0289134i
$563$			41.0633i			1.73061i	0.501246	+	0.865305i	$0.332875\pi$
$563$			41.0633i			1.73061i	−0.501246	+	0.865305i	$0.667125\pi$
$564$	13.6788	−	6.58735i	0.575980	−	0.277377i
$565$	0.298455	−	18.4916i	0.0125561	−	0.777945i
$566$	−23.6144	−	2.66071i	−0.992589	−	0.111838i
$567$	−1.32825	−	0.464776i	−0.0557814	−	0.0195188i
$568$	−2.22568			−0.0933876
$569$	−31.1140	−	10.8873i	−1.30437	−	0.456418i	−0.413427	−	0.910537i	$-0.635668\pi$
$569$	−31.1140	−	10.8873i	−1.30437	−	0.456418i	−0.890941	+	0.454120i	$0.849954\pi$
$570$	−9.81836	−	29.5822i	−0.411246	−	1.23906i
$571$	−9.39901	−	4.52632i	−0.393336	−	0.189421i	0.226752	−	0.973952i	$-0.427189\pi$
$571$	−9.39901	−	4.52632i	−0.393336	−	0.189421i	−0.620089	+	0.784532i	$0.712903\pi$
$572$	6.02232	−	12.5055i	0.251806	−	0.522880i
$573$	8.53242	−	5.36128i	0.356447	−	0.223971i
$574$	−11.1915	+	8.92494i	−0.467125	+	0.372520i
$575$	−0.757260	+	0.237839i	−0.0315799	+	0.00991856i
$576$	−0.310810	−	1.36175i	−0.0129504	−	0.0567395i
$577$	5.23705	−	22.9450i	0.218021	−	0.955213i	−0.740917	−	0.671597i	$-0.765609\pi$
$577$	5.23705	−	22.9450i	0.218021	−	0.955213i	0.958938	−	0.283616i	$-0.0915342\pi$
$578$	−22.2416	−	17.7371i	−0.925129	−	0.737766i
$579$	23.6922			0.984614
$580$	1.48472	+	15.1083i	0.0616495	+	0.627340i
$581$	15.9862			0.663221
$582$	−21.7095	−	17.3128i	−0.899889	−	0.717638i
$583$	−3.40675	+	14.9259i	−0.141093	+	0.618169i
$584$	1.42720	+	6.25297i	0.0590579	+	0.258750i
$585$	−6.83066	+	10.4912i	−0.282413	+	0.433758i
$586$	−6.20423	+	4.94771i	−0.256294	+	0.204388i
$587$	6.03796	−	3.79390i	0.249213	−	0.156591i	−0.401633	−	0.915801i	$-0.631557\pi$
$587$	6.03796	−	3.79390i	0.249213	−	0.156591i	0.650846	+	0.759210i	$0.274414\pi$
$588$	2.74583	−	5.70177i	0.113236	−	0.235137i
$589$	16.7702	+	8.07610i	0.691004	+	0.332770i
$590$	13.1693	+	6.60590i	0.542172	+	0.271961i
$591$	−18.9581	−	6.63371i	−0.779830	−	0.272874i
$592$	−7.75709			−0.318815
$593$	8.04074	+	2.81358i	0.330194	+	0.115540i	0.490284	−	0.871563i	$-0.336893\pi$
$593$	8.04074	+	2.81358i	0.330194	+	0.115540i	−0.160091	+	0.987102i	$0.551179\pi$
$594$	−3.52863	−	0.397581i	−0.144782	−	0.0163130i
$595$	−2.52322	+	2.44306i	−0.103442	+	0.100156i
$596$	−17.7930	+	8.56865i	−0.728829	+	0.350985i
$597$		−	7.15935i		−	0.293013i
$598$	0.696331	+	1.44595i	0.0284751	+	0.0591291i
$599$	−28.0229	−	17.6080i	−1.14499	−	0.719443i	−0.180500	−	0.983575i	$-0.557772\pi$
$599$	−28.0229	−	17.6080i	−1.14499	−	0.719443i	−0.964486	+	0.264132i	$0.914914\pi$
$600$	6.45606	+	1.69450i	0.263568	+	0.0691776i
$601$	−9.38994	−	26.8349i	−0.383024	−	1.09462i	−0.960516	−	0.278223i	$-0.910255\pi$
$601$	−9.38994	−	26.8349i	−0.383024	−	1.09462i	0.577493	−	0.816396i	$-0.304031\pi$
$602$	1.26890	+	2.01944i	0.0517163	+	0.0823061i
$603$	5.24671	+	0.591162i	0.213663	+	0.0240740i
$604$	−19.4008	−	15.4716i	−0.789407	−	0.629531i
$605$	7.15137	−	14.2567i	0.290744	−	0.579618i
$606$	−4.67533	−	7.44074i	−0.189922	−	0.302259i
$607$	−16.1334	+	20.2307i	−0.654835	+	0.821137i	−0.992770	−	0.120032i	$-0.961700\pi$
$607$	−16.1334	+	20.2307i	−0.654835	+	0.821137i	0.337935	+	0.941170i	$0.390272\pi$
$608$	34.0392	+	34.0392i	1.38047	+	1.38047i
$609$	−7.57811	+	0.0143660i	−0.307080	+	0.000582138i
$610$	−4.40931	−	45.7599i	−0.178528	−	1.85276i
$611$	66.9977	−	7.54883i	2.71044	−	0.305393i
$612$	−1.37188	−	0.313124i	−0.0554551	−	0.0126573i
$613$	9.79994	−	15.5965i	0.395816	−	0.629937i	−0.588054	−	0.808821i	$-0.700106\pi$
$613$	9.79994	−	15.5965i	0.395816	−	0.629937i	0.983870	+	0.178884i	$0.0572487\pi$
$614$	−28.1915	+	35.3510i	−1.13772	+	1.42665i
$615$	9.04947	−	8.76199i	0.364910	−	0.353318i
$616$	0.822027	−	3.60153i	0.0331204	−	0.145110i
$617$	2.45698	+	1.18322i	0.0989144	+	0.0476347i	0.482687	−	0.875793i	$-0.339661\pi$
$617$	2.45698	+	1.18322i	0.0989144	+	0.0476347i	−0.383772	+	0.923428i	$0.625375\pi$
$618$	1.16065	+	3.31693i	0.0466880	+	0.133427i
$619$	16.8221	−	26.7722i	0.676137	−	1.07607i	−0.315738	−	0.948846i	$-0.602252\pi$
$619$	16.8221	−	26.7722i	0.676137	−	1.07607i	0.991875	−	0.127219i	$-0.0406050\pi$
$620$	5.81326	−	3.52316i	0.233466	−	0.141493i
$621$	0.112251	−	0.112251i	0.00450446	−	0.00450446i
$622$	−1.96499	+	5.61562i	−0.0787889	+	0.225166i
$623$	−6.27702	−	7.87113i	−0.251484	−	0.315350i
$624$	3.09163	−	27.4390i	0.123764	−	1.09844i
$625$	16.8157	−	18.4995i	0.672627	−	0.739982i
$626$	18.1152	+	18.1152i	0.724030	+	0.724030i
$627$	13.6767	−	6.58633i	0.546193	−	0.263033i
$628$	6.32027	+	27.6909i	0.252206	+	1.10499i
$629$	−0.761680	+	1.58164i	−0.0303702	+	0.0630643i
$630$	1.96297	−	5.33220i	0.0782065	−	0.212440i
$631$	43.8862	+	10.0167i	1.74708	+	0.398760i	0.972350	−	0.233530i	$-0.0750277\pi$
$631$	43.8862	+	10.0167i	1.74708	+	0.398760i	0.774732	+	0.632290i	$0.217885\pi$
$632$	−0.435284	+	3.86326i	−0.0173147	+	0.153672i
$633$	−2.59541	−	23.0349i	−0.103158	−	0.915554i
$634$	−4.33811	+	0.990146i	−0.172289	+	0.0393237i
$635$	−28.2868	+	21.8206i	−1.12253	+	0.865923i
$636$	−1.09896	−	9.75351i	−0.0435765	−	0.386752i
$637$	19.8722	−	19.8722i	0.787367	−	0.787367i
$638$	−18.6350	+	4.29049i	−0.737765	+	0.169862i
$639$		−	1.66725i		−	0.0659552i
$640$	−21.7681	+	4.60014i	−0.860459	+	0.181836i
$641$	15.2607	−	9.58892i	0.602761	−	0.378740i	−0.195809	−	0.980642i	$-0.562733\pi$
$641$	15.2607	−	9.58892i	0.602761	−	0.378740i	0.798570	+	0.601902i	$0.205590\pi$
$642$	17.7901	+	11.1783i	0.702119	+	0.441171i
$643$	10.0075	−	1.12757i	0.394657	−	0.0444671i	0.0875935	−	0.996156i	$-0.472082\pi$
$643$	10.0075	−	1.12757i	0.394657	−	0.0444671i	0.307063	+	0.951689i	$0.400654\pi$
$644$	−0.175596	−	0.220191i	−0.00691946	−	0.00867673i
$645$	−1.28188	−	1.66175i	−0.0504739	−	0.0654311i
$646$	14.6853	−	5.13860i	0.577784	−	0.202175i
$647$	−11.7388	+	4.10757i	−0.461498	+	0.161485i	−0.551007	−	0.834501i	$-0.685756\pi$
$647$	−11.7388	+	4.10757i	−0.461498	+	0.161485i	0.0895084	+	0.995986i	$0.471470\pi$
$648$	−1.30148	+	0.297053i	−0.0511268	+	0.0116694i
$649$	−2.36988	+	6.77273i	−0.0930259	+	0.265853i
$650$	−41.9105	−	28.2607i	−1.64387	−	1.10848i
$651$	1.47225	+	3.05717i	0.0577022	+	0.119820i
$652$	−18.6926	+	14.9069i	−0.732059	+	0.583798i
$653$	3.26618	−	2.60470i	0.127816	−	0.101930i	−0.557496	−	0.830180i	$-0.688238\pi$
$653$	3.26618	−	2.60470i	0.127816	−	0.101930i	0.685311	+	0.728250i	$0.259666\pi$
$654$	−2.06825	−	4.29477i	−0.0808751	−	0.167939i
$655$	0.654701	+	6.79449i	0.0255813	+	0.265483i
$656$	−9.17619	+	26.2240i	−0.358270	+	1.02388i
$657$	−4.68406	+	1.06911i	−0.182743	+	0.0417098i
$658$	−28.8839	+	10.1069i	−1.12601	+	0.394008i
$659$	−6.05292	+	2.11801i	−0.235788	+	0.0825059i	−0.445587	−	0.895239i	$-0.647005\pi$
$659$	−6.05292	+	2.11801i	−0.235788	+	0.0825059i	0.209798	+	0.977745i	$0.432719\pi$
$660$	0.709508	−	5.49803i	0.0276176	−	0.214011i
$661$	1.88830	+	2.36786i	0.0734465	+	0.0920990i	0.817197	−	0.576358i	$-0.195527\pi$
$661$	1.88830	+	2.36786i	0.0734465	+	0.0920990i	−0.743751	+	0.668457i	$0.766955\pi$
$662$	36.9229	−	4.16022i	1.43505	−	0.161691i
$663$	−5.29113	−	3.32464i	−0.205491	−	0.129118i
$664$	12.8407	−	8.06836i	0.498316	−	0.313113i
$665$	5.02218	+	23.7652i	0.194752	+	0.921576i
$666$		−	2.84008i		−	0.110051i
$667$	0.369456	−	0.770917i	0.0143054	−	0.0298500i
$668$	5.46112	−	5.46112i	0.211297	−	0.211297i
$669$	−0.628479	−	5.57791i	−0.0242984	−	0.215654i
$670$	−2.72855	+	21.1438i	−0.105413	+	0.816854i
$671$	21.8278	−	4.98206i	0.842655	−	0.192330i
$672$	0.982552	+	8.72039i	0.0379028	+	0.336396i
$673$	2.88162	−	25.5751i	0.111078	−	0.985848i	−0.807299	−	0.590142i	$-0.799072\pi$
$673$	2.88162	−	25.5751i	0.111078	−	0.985848i	0.918378	−	0.395705i	$-0.129500\pi$
$674$	−58.3643	−	13.3213i	−2.24811	−	0.513117i
$675$	−1.26934	+	4.83619i	−0.0488568	+	0.186145i
$676$	−10.0347	+	20.8372i	−0.385949	+	0.801431i
$677$	8.96098	+	39.2606i	0.344398	+	1.50891i	0.789681	+	0.613518i	$0.210246\pi$
$677$	8.96098	+	39.2606i	0.344398	+	1.50891i	−0.445282	+	0.895390i	$0.646897\pi$
$678$	−13.4559	+	6.48000i	−0.516769	+	0.248863i
$679$	15.3013	+	15.3013i	0.587209	+	0.587209i
$680$	−0.793710	+	3.23584i	−0.0304374	+	0.124089i
$681$	2.26568	−	20.1085i	0.0868210	−	0.770558i
$682$	5.33853	+	6.69431i	0.204423	+	0.256338i
$683$	−10.2031	+	29.1588i	−0.390411	+	1.11573i	0.566176	+	0.824285i	$0.308422\pi$
$683$	−10.2031	+	29.1588i	−0.390411	+	1.11573i	−0.956587	+	0.291447i	$0.905863\pi$
$684$	−6.88155	+	6.88155i	−0.263123	+	0.263123i
$685$	46.1274	+	11.3145i	1.76244	+	0.432303i
$686$	−16.2499	+	25.8616i	−0.620426	+	0.987402i
$687$	−0.0471658	−	0.134792i	−0.00179949	−	0.00514264i
$688$	4.17065	+	2.00848i	0.159004	+	0.0765725i
$689$	9.69914	−	42.4947i	0.369508	−	1.61892i
$690$	0.445869	+	0.460498i	0.0169739	+	0.0175309i
$691$	3.43398	−	4.30607i	0.130635	−	0.163811i	−0.712212	−	0.701964i	$-0.752307\pi$
$691$	3.43398	−	4.30607i	0.130635	−	0.163811i	0.842847	+	0.538154i	$0.180878\pi$
$692$	−13.1695	+	20.9592i	−0.500630	+	0.796749i
$693$	2.69789	+	0.615775i	0.102484	+	0.0233914i
$694$	−12.1949	+	1.37404i	−0.462913	+	0.0521578i
$695$	−12.7201	−	10.4842i	−0.482502	−	0.397689i
$696$	−6.07976	+	3.83626i	−0.230453	+	0.145413i
$697$	4.44597	+	4.44597i	0.168403	+	0.168403i
$698$	−14.6407	+	18.3588i	−0.554158	+	0.694892i
$699$	4.14587	+	6.59811i	0.156811	+	0.249563i
$700$	8.27389	+	3.19845i	0.312724	+	0.120890i
$701$	−38.3479	−	30.5814i	−1.44838	−	1.15505i	−0.959152	−	0.282890i	$-0.908707\pi$
$701$	−38.3479	−	30.5814i	−1.44838	−	1.15505i	−0.489229	−	0.872156i	$-0.662722\pi$
$702$	10.0461	+	1.13193i	0.379167	+	0.0427219i
$703$	6.45942	+	10.2801i	0.243621	+	0.387721i
$704$	0.907181	+	2.59258i	0.0341907	+	0.0977114i
$705$	24.4466	−	11.2905i	0.920712	−	0.425226i
$706$	10.5593	+	6.63483i	0.397404	+	0.249705i
$707$	2.97135	+	6.17006i	0.111749	+	0.232049i
$708$		−	4.60020i		−	0.172886i
$709$	15.6836	−	7.55282i	0.589010	−	0.283652i	−0.115544	−	0.993302i	$-0.536861\pi$
$709$	15.6836	−	7.55282i	0.589010	−	0.283652i	0.704554	+	0.709650i	$0.251147\pi$
$710$	6.73109	+	0.108640i	0.252613	+	0.00407719i
$711$	−2.89394	−	0.326069i	−0.108531	−	0.0122285i
$712$	−9.01454	−	3.15432i	−0.337834	−	0.118213i
$713$	−0.382781			−0.0143353
$714$	2.67709	+	0.936754i	0.100188	+	0.0350571i
$715$	11.0380	−	22.0049i	0.412797	−	0.822938i
$716$	−13.9711	−	6.72811i	−0.522123	−	0.251441i
$717$	−11.1812	+	23.2179i	−0.417568	+	0.867090i
$718$	40.2344	−	25.2809i	1.50153	−	0.943476i
$719$	31.0735	−	24.7803i	1.15884	−	0.924148i	0.160821	−	0.986984i	$-0.448586\pi$
$719$	31.0735	−	24.7803i	1.15884	−	0.924148i	0.998024	+	0.0628356i	$0.0200144\pi$
$720$	−2.28020	−	10.7900i	−0.0849782	−	0.402121i
$721$	−0.609390	−	2.66991i	−0.0226949	−	0.0994326i
$722$	16.3092	−	71.4551i	0.606964	−	2.65928i
$723$	3.42477	+	2.73117i	0.127369	+	0.101573i
$724$	−27.0677			−1.00596
$725$	2.20056	+	26.8358i	0.0817269	+	0.996655i
$726$	−12.8803			−0.478034
$727$	−22.5350	−	17.9711i	−0.835777	−	0.666510i	0.109065	−	0.994035i	$-0.465214\pi$
$727$	−22.5350	−	17.9711i	−0.835777	−	0.666510i	−0.944843	+	0.327524i	$0.893786\pi$
$728$	−2.34034	+	10.2537i	−0.0867388	+	0.380027i
$729$	−0.222521	−	0.974928i	−0.00824152	−	0.0361084i
$730$	−4.01103	−	18.9804i	−0.148455	−	0.702495i
$731$	0.819043	−	0.653165i	0.0302934	−	0.0241582i
$732$	−12.1538	+	7.63673i	−0.449217	+	0.282262i
$733$	−13.7159	+	28.4814i	−0.506609	+	1.05198i	0.478185	+	0.878259i	$0.341295\pi$
$733$	−13.7159	+	28.4814i	−0.506609	+	1.05198i	−0.984794	+	0.173725i	$0.944420\pi$
$734$	−1.59172	−	0.766531i	−0.0587514	−	0.0282932i
$735$	5.03267	−	10.0330i	0.185633	−	0.370072i
$736$	−0.934404	−	0.326962i	−0.0344426	−	0.0120520i
$737$	−10.3828			−0.382456
$738$	−9.60133	−	3.35965i	−0.353430	−	0.123670i
$739$	−43.1915	−	4.86651i	−1.58882	−	0.179018i	−0.727150	−	0.686479i	$-0.759156\pi$
$739$	−43.1915	−	4.86651i	−1.58882	−	0.179018i	−0.861675	+	0.507461i	$0.830584\pi$
$740$	4.43325	+	0.0715529i	0.162970	+	0.00263034i
$741$	−38.9380	+	18.7515i	−1.43042	+	0.688855i
$742$			19.7834i			0.726270i
$743$	−6.98154	−	14.4973i	−0.256128	−	0.531855i	0.732765	−	0.680481i	$-0.238229\pi$
$743$	−6.98154	−	14.4973i	−0.256128	−	0.531855i	−0.988893	+	0.148626i	$0.952515\pi$
$744$	2.72554	+	1.71257i	0.0999232	+	0.0627859i
$745$	−31.7995	+	14.6864i	−1.16504	+	0.538069i
$746$	−2.47766	−	7.08074i	−0.0907135	−	0.259244i
$747$	6.04396	+	9.61890i	0.221137	+	0.351937i
$748$	2.74976	+	0.309823i	0.100541	+	0.0113283i
$749$	−12.8013	−	10.2087i	−0.467750	−	0.373019i
$750$	−19.4422	−	5.43977i	−0.709929	−	0.198632i
$751$	8.30173	+	13.2121i	0.302934	+	0.482117i	0.963152	−	0.268957i	$-0.0866789\pi$
$751$	8.30173	+	13.2121i	0.302934	+	0.482117i	−0.660218	+	0.751074i	$0.729536\pi$
$752$	−37.0315	+	46.4361i	−1.35040	+	1.69335i
$753$	−3.57031	−	3.57031i	−0.130109	−	0.130109i
$754$	53.0544	−	12.2152i	1.93213	−	0.444851i
$755$	−33.9627	−	27.9928i	−1.23603	−	1.01876i
$756$	−1.76296	+	0.198638i	−0.0641183	+	0.00722440i
$757$	8.03336	+	1.83356i	0.291977	+	0.0666420i	0.366001	−	0.930615i	$-0.380727\pi$
$757$	8.03336	+	1.83356i	0.291977	+	0.0666420i	−0.0740233	+	0.997257i	$0.523584\pi$
$758$	5.77243	−	9.18677i	0.209664	−	0.333679i
$759$	−0.194635	+	0.244065i	−0.00706481	+	0.00885900i
$760$	16.0285	+	16.5544i	0.581413	+	0.600489i
$761$	−5.80089	+	25.4153i	−0.210282	+	0.921306i	0.754093	+	0.656767i	$0.228077\pi$
$761$	−5.80089	+	25.4153i	−0.210282	+	0.921306i	−0.964375	+	0.264538i	$0.914780\pi$
$762$	25.9929	+	12.5175i	0.941624	+	0.453462i
$763$	1.22692	+	3.50634i	0.0444175	+	0.126938i
$764$	6.75909	−	10.7570i	0.244535	−	0.389176i
$765$	−2.42395	−	0.594563i	−0.0876380	−	0.0214965i
$766$	−6.10562	+	6.10562i	−0.220605	+	0.220605i
$767$	6.74714	−	19.2822i	0.243625	−	0.696240i
$768$	12.9441	+	16.2314i	0.467079	+	0.585699i
$769$	−0.343647	+	3.04995i	−0.0123922	+	0.109984i	−0.998386	−	0.0568009i	$-0.981910\pi$
$769$	−0.343647	+	3.04995i	−0.0123922	+	0.109984i	0.985993	+	0.166785i	$0.0533385\pi$
$770$	−2.66184	+	10.8519i	−0.0959259	+	0.391076i
$771$	−6.49408	−	6.49408i	−0.233878	−	0.233878i
$772$	26.9113	−	12.9598i	0.968560	−	0.466434i
$773$	−2.59530	−	11.3707i	−0.0933464	−	0.408977i	0.906568	−	0.422060i	$-0.138693\pi$
$773$	−2.59530	−	11.3707i	−0.0933464	−	0.408977i	−0.999914	+	0.0130824i	$0.995836\pi$
$774$	−0.735358	+	1.52699i	−0.0264319	+	0.0548864i
$775$	10.4101	−	6.08160i	0.373942	−	0.218457i
$776$	20.0132	+	4.56788i	0.718432	+	0.163977i
$777$	−0.247809	+	2.19936i	−0.00889009	+	0.0789018i
$778$	−6.27607	−	55.7017i	−0.225008	−	1.99700i
$779$	42.3946	−	9.67628i	1.51894	−	0.346689i
$780$	−2.02000	+	15.6531i	−0.0723275	+	0.560471i
$781$	0.367087	+	3.25798i	0.0131354	+	0.116580i
$782$	−0.226241	+	0.226241i	−0.00809035	+	0.00809035i
$783$	−2.87372	−	4.55431i	−0.102698	−	0.162758i
$784$			24.7574i			0.884193i
$785$	10.4158	+	49.2882i	0.371757	+	1.75917i
$786$	4.66743	−	2.93274i	0.166482	−	0.104607i
$787$	−29.7763	−	18.7097i	−1.06141	−	0.666928i	−0.116145	−	0.993232i	$-0.537054\pi$
$787$	−29.7763	−	18.7097i	−1.06141	−	0.666928i	−0.945265	+	0.326304i	$0.894197\pi$
$788$	−25.1626	+	2.83515i	−0.896382	+	0.100998i
$789$	14.2337	+	17.8484i	0.506732	+	0.635421i
$790$	1.50499	−	11.6623i	0.0535453	−	0.414926i
$791$	10.9857	−	3.84405i	0.390605	−	0.136679i
$792$	2.47783	−	0.867029i	0.0880457	−	0.0308085i
$793$	−62.1447	+	14.1841i	−2.20682	+	0.503693i
$794$	−10.9280	+	31.2303i	−0.387819	+	1.10832i
$795$	−1.66972	−	17.3284i	−0.0592190	−	0.614575i
$796$	−3.91622	−	8.13211i	−0.138807	−	0.288235i
$797$	31.2695	−	24.9366i	1.10762	−	0.883299i	0.113714	−	0.993514i	$-0.463725\pi$
$797$	31.2695	−	24.9366i	1.10762	−	0.883299i	0.993908	+	0.110214i	$0.0351537\pi$
$798$	15.3361	−	12.2301i	0.542891	−	0.432941i
$799$	5.83198	+	12.1102i	0.206320	+	0.428429i
$800$	30.6068	−	5.95368i	1.08211	−	0.210494i
$801$	2.36289	−	6.75274i	0.0834885	−	0.238596i
$802$	−17.5493	+	4.00551i	−0.619687	+	0.141440i
$803$	8.91778	−	3.12047i	0.314702	−	0.110119i
$804$	6.28297	−	2.19851i	0.221583	−	0.0775353i
$805$	−0.305101	−	0.395514i	−0.0107534	−	0.0139400i
$806$	−15.1990	−	19.0589i	−0.535362	−	0.671323i
$807$	−13.5647	+	1.52837i	−0.477500	+	0.0538013i
$808$	5.50076	+	3.45636i	0.193516	+	0.121594i
$809$	−10.3682	+	6.51476i	−0.364526	+	0.229047i	−0.701823	−	0.712351i	$-0.747630\pi$
$809$	−10.3682	+	6.51476i	−0.364526	+	0.229047i	0.337297	+	0.941398i	$0.390487\pi$
$810$	3.95053	−	0.834845i	0.138807	−	0.0293334i
$811$			3.03664i			0.106631i	0.998578	+	0.0533154i	$0.0169789\pi$
$811$			3.03664i			0.106631i	−0.998578	+	0.0533154i	$0.983021\pi$
$812$	−8.59991	+	4.16160i	−0.301798	+	0.146044i
$813$	11.8325	−	11.8325i	0.414984	−	0.414984i
$814$	0.625317	+	5.54984i	0.0219173	+	0.194522i
$815$	−33.5763	+	25.9009i	−1.17613	+	0.907269i
$816$	5.36689	−	1.22496i	0.187879	−	0.0428821i
$817$	−0.811204	−	7.19964i	−0.0283804	−	0.251883i
$818$	−3.26744	+	28.9993i	−0.114243	+	1.01394i
$819$	−7.68099	−	1.75313i	−0.268395	−	0.0612595i
$820$	5.48617	−	14.9026i	0.191585	−	0.520423i
$821$	−1.15002	+	2.38804i	−0.0401359	+	0.0833431i	−0.920073	−	0.391748i	$-0.871871\pi$
$821$	−1.15002	+	2.38804i	−0.0401359	+	0.0833431i	0.879937	+	0.475091i	$0.157585\pi$
$822$	−8.53471	−	37.3930i	−0.297682	−	1.30423i
$823$	25.0177	−	12.0479i	0.872062	−	0.419963i	0.0563429	−	0.998411i	$-0.482056\pi$
$823$	25.0177	−	12.0479i	0.872062	−	0.419963i	0.815719	+	0.578449i	$0.196342\pi$
$824$	−1.83700	−	1.83700i	−0.0639951	−	0.0639951i
$825$	1.41562	−	9.72994i	0.0492854	−	0.338753i
$826$	−1.03814	+	9.21376i	−0.0361216	+	0.320588i
$827$	34.4086	+	43.1470i	1.19650	+	1.50037i	0.818443	+	0.574588i	$0.194838\pi$
$827$	34.4086	+	43.1470i	1.19650	+	1.50037i	0.378061	+	0.925781i	$0.376591\pi$
$828$	0.0661005	−	0.188904i	0.00229715	−	0.00656488i
$829$	−16.6461	+	16.6461i	−0.578141	+	0.578141i	−0.934391	−	0.356249i	$-0.884055\pi$
$829$	−16.6461	+	16.6461i	−0.578141	+	0.578141i	0.356249	+	0.934391i	$0.384055\pi$
$830$	−39.2277	+	23.7742i	−1.36161	+	0.825213i
$831$	3.03458	−	4.82951i	0.105268	−	0.167534i
$832$	−2.58278	−	7.38116i	−0.0895417	−	0.255896i
$833$	5.04795	+	2.43096i	0.174901	+	0.0842279i
$834$	−2.96213	+	12.9779i	−0.102570	+	0.449390i
$835$	9.84110	−	9.52848i	0.340565	−	0.329747i
$836$	11.9322	−	14.9625i	0.412683	−	0.517488i
$837$	−1.28288	+	2.04169i	−0.0443427	+	0.0705710i
$838$	32.7981	+	7.48595i	1.13299	+	0.258598i
$839$	20.3695	−	2.29509i	0.703234	−	0.0792354i	0.246896	−	0.969042i	$-0.420589\pi$
$839$	20.3695	−	2.29509i	0.703234	−	0.0792354i	0.456338	+	0.889807i	$0.349161\pi$
$840$	0.402894	+	4.18123i	0.0139012	+	0.144266i
$841$	−22.7415	−	17.9951i	−0.784190	−	0.620521i
$842$	27.6222	+	27.6222i	0.951922	+	0.951922i
$843$	−0.262682	+	0.329392i	−0.00904724	+	0.0113449i
$844$	−15.5483	−	24.7450i	−0.535195	−	0.851757i
$845$	−18.3920	+	36.6656i	−0.632703	+	1.26134i
$846$	−17.0015	−	13.5583i	−0.584524	−	0.466142i
$847$	9.97456	+	1.12386i	0.342730	+	0.0386164i
$848$	20.4288	+	32.5123i	0.701529	+	1.11648i
$849$	4.34651	+	12.4216i	0.149172	+	0.426309i
$850$	2.55835	−	9.74733i	0.0877506	−	0.334331i
$851$	−0.211407	−	0.132836i	−0.00724694	−	0.00455355i
$852$	−0.911996	−	1.89378i	−0.0312445	−	0.0648798i
$853$		−	6.09039i		−	0.208531i	−0.994550	−	0.104265i	$-0.966751\pi$
$853$		−	6.09039i		−	0.208531i	0.994550	−	0.104265i	$-0.0332492\pi$
$854$	26.0663	−	12.5529i	0.891970	−	0.429550i
$855$	−12.4008	+	12.0068i	−0.424097	+	0.410625i
$856$	−15.4349	−	1.73910i	−0.527554	−	0.0594410i
$857$	−11.7998	−	4.12891i	−0.403072	−	0.141041i	0.121127	−	0.992637i	$-0.461349\pi$
$857$	−11.7998	−	4.12891i	−0.403072	−	0.141041i	−0.524199	+	0.851596i	$0.675635\pi$
$858$	−19.8805			−0.678709
$859$	29.3860	+	10.2826i	1.00264	+	0.350838i	0.781163	−	0.624327i	$-0.214627\pi$
$859$	29.3860	+	10.2826i	1.00264	+	0.350838i	0.221476	+	0.975166i	$0.428913\pi$
$860$	−2.36504	−	1.18633i	−0.0806471	−	0.0404537i
$861$	7.14214	+	3.43947i	0.243404	+	0.117217i
$862$	−21.4264	+	44.4923i	−0.729786	+	1.51542i
$863$	−19.0845	+	11.9916i	−0.649645	+	0.408199i	−0.816149	−	0.577842i	$-0.803895\pi$
$863$	−19.0845	+	11.9916i	−0.649645	+	0.408199i	0.166504	+	0.986041i	$0.446752\pi$
$864$	−4.87558	+	3.88814i	−0.165870	+	0.132277i
$865$	−23.9549	+	36.7922i	−0.814489	+	1.25097i
$866$	8.02168	+	35.1453i	0.272588	+	1.19428i
$867$	−3.50564	+	15.3592i	−0.119058	+	0.521626i
$868$	3.34459	+	2.66722i	0.113523	+	0.0905313i
$869$	5.72688			0.194271
$870$	18.5741	−	11.3052i	0.629722	−	0.383281i
$871$	29.5603			1.00161
$872$	2.75518	+	2.19718i	0.0933022	+	0.0744060i
$873$	−3.42177	+	14.9918i	−0.115809	+	0.507394i
$874$	0.492394	+	2.15732i	0.0166555	+	0.0729724i
$875$	14.5814	+	5.90898i	0.492942	+	0.199760i
$876$	−4.73569	+	3.77658i	−0.160004	+	0.127599i
$877$	−29.9045	+	18.7902i	−1.00980	+	0.634501i	−0.931996	−	0.362467i	$-0.881934\pi$
$877$	−29.9045	+	18.7902i	−1.00980	+	0.634501i	−0.0778063	+	0.996968i	$0.524792\pi$
$878$	16.9790	−	35.2572i	0.573012	−	1.18987i
$879$	3.95938	+	1.90674i	0.133547	+	0.0643127i
$880$	6.83147	+	20.5829i	0.230289	+	0.693849i
$881$	−29.2037	−	10.2188i	−0.983897	−	0.344280i	−0.210076	−	0.977685i	$-0.567371\pi$
$881$	−29.2037	−	10.2188i	−0.983897	−	0.344280i	−0.773821	+	0.633405i	$0.781657\pi$
$882$	−9.06436			−0.305213
$883$	−2.88407	−	1.00918i	−0.0970566	−	0.0339616i	0.281314	−	0.959616i	$-0.409230\pi$
$883$	−2.88407	−	1.00918i	−0.0970566	−	0.0339616i	−0.378371	+	0.925654i	$0.623515\pi$
$884$	−7.82866	−	0.882078i	−0.263306	−	0.0296675i
$885$	0.131671	−	8.15803i	0.00442607	−	0.274229i
$886$	44.0442	−	21.2105i	1.47969	−	0.712582i
$887$		−	19.4845i		−	0.654224i	−0.944986	−	0.327112i	$-0.893925\pi$
$887$		−	19.4845i		−	0.654224i	0.944986	−	0.327112i	$-0.106075\pi$
$888$	0.910985	+	1.89168i	0.0305706	+	0.0634806i
$889$	−19.0368	−	11.9616i	−0.638472	−	0.401179i
$890$	27.1085	+	9.97957i	0.908679	+	0.334516i
$891$	0.649486	+	1.85612i	0.0217586	+	0.0621825i
$892$	−3.76503	−	5.99201i	−0.126062	−	0.200627i
$893$	92.3761	+	10.4083i	3.09125	+	0.348300i
$894$	22.1151	+	17.6362i	0.739640	+	0.589843i
$895$	−24.5838	−	12.3316i	−0.821746	−	0.412199i
$896$	−7.44942	−	11.8557i	−0.248868	−	0.396071i
$897$	0.554134	−	0.694862i	0.0185020	−	0.0232008i
$898$	−1.04975	−	1.04975i	−0.0350306	−	0.0350306i
$899$	−2.86546	+	12.6650i	−0.0955683	+	0.422402i
$900$	1.20363	+	6.18764i	0.0401209	+	0.206255i
$901$	8.63507	−	0.972939i	0.287676	−	0.0324133i
$902$	19.5018	+	4.45116i	0.649338	+	0.148207i
$903$	0.702698	−	1.11834i	0.0233843	−	0.0372160i
$904$	6.88395	−	8.63221i	0.228957	−	0.287103i
$905$	−48.0020	−	0.774755i	−1.59564	−	0.0257537i
$906$	−7.90887	+	34.6510i	−0.262755	+	1.15120i
$907$	−27.6026	−	13.2927i	−0.916530	−	0.441377i	−0.0846987	−	0.996407i	$-0.526993\pi$
$907$	−27.6026	−	13.2927i	−0.916530	−	0.441377i	−0.831831	+	0.555029i	$0.812707\pi$
$908$	−8.42595	−	24.0800i	−0.279625	−	0.799123i
$909$	−2.58914	+	4.12059i	−0.0858762	+	0.136671i
$910$	7.57834	−	30.8958i	0.251220	−	1.02419i
$911$	28.0295	−	28.0295i	0.928660	−	0.928660i	−0.0689591	−	0.997619i	$-0.521968\pi$
$911$	28.0295	−	28.0295i	0.928660	−	0.928660i	0.997619	+	0.0689591i	$0.0219678\pi$
$912$	12.5744	−	35.9356i	0.416380	−	1.18995i
$913$	−13.9284	−	17.4657i	−0.460963	−	0.578029i
$914$	4.08426	−	36.2489i	0.135095	−	1.19901i
$915$	−21.7722	+	13.1952i	−0.719767	+	0.436218i
$916$	−0.127307	−	0.127307i	−0.00420633	−	0.00420633i
$917$	−3.87036	+	1.86387i	−0.127810	+	0.0615503i
$918$	0.448490	+	1.96496i	0.0148024	+	0.0648535i
$919$	21.5911	−	44.8343i	0.712224	−	1.47895i	−0.158595	−	0.987344i	$-0.550696\pi$
$919$	21.5911	−	44.8343i	0.712224	−	1.47895i	0.870819	−	0.491604i	$-0.163589\pi$
$920$	−0.444687	−	0.163704i	−0.0146609	−	0.00539718i
$921$	24.4121	+	5.57189i	0.804405	+	0.183600i
$922$	2.41364	−	21.4217i	0.0794891	−	0.705485i
$923$	−1.04511	−	9.27560i	−0.0344002	−	0.305310i
$924$	3.40129	−	0.776322i	0.111894	−	0.0255391i
$925$	7.85991	+	0.253785i	0.258432	+	0.00834440i
$926$	−4.76355	−	42.2776i	−0.156540	−	1.38933i
$927$	1.37609	−	1.37609i	0.0451967	−	0.0451967i
$928$	−17.8130	+	28.4689i	−0.584740	+	0.934536i
$929$			46.0203i			1.50988i	0.655796	+	0.754938i	$0.272333\pi$
$929$			46.0203i			1.50988i	−0.655796	+	0.754938i	$0.727667\pi$
$930$	−8.15920	−	5.31233i	−0.267551	−	0.174198i
$931$	32.8098	−	20.6158i	1.07530	−	0.675654i
$932$	8.31839	+	5.22679i	0.272478	+	0.171209i
$933$	3.27403	−	0.368895i	0.107187	−	0.0120771i
$934$	29.1383	+	36.5383i	0.953436	+	1.19557i
$935$	4.86757	+	0.628149i	0.159187	+	0.0205427i
$936$	−7.05446	+	2.46846i	−0.230582	+	0.0806842i
$937$	42.9319	−	15.0225i	1.40253	−	0.490765i	0.480193	−	0.877163i	$-0.340567\pi$
$937$	42.9319	−	15.0225i	1.40253	−	0.490765i	0.922332	+	0.386398i	$0.126281\pi$
$938$	−13.0803	+	2.98550i	−0.427088	+	0.0974800i
$939$	4.68579	−	13.3912i	0.152915	−	0.437006i
$940$	21.5922	−	26.1971i	0.704260	−	0.854454i
$941$	20.8817	+	43.3614i	0.680725	+	1.41354i	0.899130	+	0.437682i	$0.144200\pi$
$941$	20.8817	+	43.3614i	0.680725	+	1.41354i	−0.218405	+	0.975858i	$0.570085\pi$
$942$	31.8064	−	25.3648i	1.03631	−	0.826430i
$943$	−0.699154	+	0.557557i	−0.0227676	+	0.0181565i
$944$	7.80827	+	16.2140i	0.254138	+	0.527722i
$945$	−3.13214	+	0.301805i	−0.101888	+	0.00981773i
$946$	1.10077	−	3.14581i	0.0357890	−	0.102279i
$947$	19.3983	−	4.42754i	0.630360	−	0.143876i	0.104608	−	0.994514i	$-0.466641\pi$
$947$	19.3983	−	4.42754i	0.630360	−	0.143876i	0.525752	+	0.850638i	$0.323784\pi$
$948$	−3.46551	+	1.21264i	−0.112555	+	0.0393846i
$949$	−25.3893	+	8.88408i	−0.824170	+	0.288390i
$950$	−47.6665	−	50.8473i	−1.54650	−	1.64971i
$951$	1.53639	+	1.92657i	0.0498208	+	0.0624733i
$952$	−2.08359	+	0.234764i	−0.0675295	+	0.00760875i
$953$	−13.9279	−	8.75148i	−0.451169	−	0.283488i	0.287218	−	0.957865i	$-0.407270\pi$
$953$	−13.9279	−	8.75148i	−0.451169	−	0.283488i	−0.738387	+	0.674377i	$0.764412\pi$
$954$	−11.9036	+	7.47955i	−0.385394	+	0.242159i
$955$	12.2945	−	18.8831i	0.397841	−	0.611044i
$956$			32.4888i			1.05076i
$957$	6.61832	+	8.26691i	0.213940	+	0.267231i
$958$	−39.3723	+	39.3723i	−1.27206	+	1.27206i
$959$	3.34660	+	29.7019i	0.108067	+	0.959125i
$960$	−1.90767	−	2.47298i	−0.0615696	−	0.0798150i
$961$	−24.5543	+	5.60436i	−0.792074	+	0.180786i
$962$	−1.78030	−	15.8006i	−0.0573992	−	0.509432i
$963$	1.30275	−	11.5622i	0.0419804	−	0.372586i
$964$	5.38407	+	1.22888i	0.173409	+	0.0395796i
$965$	48.0957	−	22.2127i	1.54825	−	0.715053i
$966$	−0.175024	+	0.363440i	−0.00563129	+	0.0116935i
$967$	11.2618	+	49.3412i	0.362155	+	1.58671i	0.747712	+	0.664023i	$0.231152\pi$
$967$	11.2618	+	49.3412i	0.362155	+	1.58671i	−0.385557	+	0.922684i	$0.625991\pi$
$968$	8.57914	−	4.13150i	0.275744	−	0.132791i
$969$	−6.09244	−	6.09244i	−0.195717	−	0.195717i
$970$	−60.3025	−	14.7914i	−1.93620	−	0.474924i
$971$	6.53206	−	57.9737i	0.209624	−	1.86046i	−0.244664	−	0.969608i	$-0.578678\pi$
$971$	6.53206	−	57.9737i	0.209624	−	1.86046i	0.454288	−	0.890855i	$-0.349894\pi$
$972$	−0.786048	−	0.985674i	−0.0252125	−	0.0316155i
$973$	3.42626	−	9.79168i	0.109841	−	0.313907i
$974$	−20.8567	+	20.8567i	−0.668290	+	0.668290i
$975$	−4.03031	+	27.7015i	−0.129073	+	0.887158i
$976$	29.8753	−	47.5463i	0.956286	−	1.52192i
$977$	−1.30544	−	3.73073i	−0.0417647	−	0.119357i	0.921112	−	0.389297i	$-0.127282\pi$
$977$	−1.30544	−	3.73073i	−0.0417647	−	0.119357i	−0.962877	+	0.269940i	$0.912996\pi$
$978$	30.8534	+	14.8582i	0.986584	+	0.475114i
$979$	−3.13055	+	13.7159i	−0.100053	+	0.438361i
$980$	0.228367	−	14.1491i	0.00729492	−	0.451976i
$981$	−1.64590	+	2.06389i	−0.0525494	+	0.0658949i
$982$	−3.56001	+	5.66572i	−0.113604	+	0.180800i
$983$	−0.543105	−	0.123960i	−0.0173224	−	0.00395372i	0.213851	−	0.976866i	$-0.431399\pi$
$983$	−0.543105	−	0.123960i	−0.0173224	−	0.00395372i	−0.231173	+	0.972913i	$0.574256\pi$
$984$	7.47275	−	0.841977i	0.238223	−	0.0268412i
$985$	−44.7047	+	4.30764i	−1.42441	+	0.137253i
$986$	5.79197	+	9.17919i	0.184454	+	0.292325i
$987$	11.9830	+	11.9830i	0.381423	+	0.381423i
$988$	−33.9713	+	42.5987i	−1.08077	+	1.35525i
$989$	0.0792702	+	0.126158i	0.00252065	+	0.00401158i
$990$	−7.53596	+	2.50119i	−0.239508	+	0.0794930i
$991$	−0.497982	−	0.397128i	−0.0158189	−	0.0126152i	0.615548	−	0.788099i	$-0.288935\pi$
$991$	−0.497982	−	0.397128i	−0.0158189	−	0.0126152i	−0.631367	+	0.775484i	$0.717506\pi$
$992$	14.9424	+	1.68360i	0.474422	+	0.0534545i
$993$	−10.9475	−	17.4229i	−0.347410	−	0.552899i
$994$	1.39927	+	3.99887i	0.0443820	+	0.126837i
$995$	−6.71229	−	14.5336i	−0.212794	−	0.460747i
$996$	12.1268	+	7.61976i	0.384252	+	0.241441i
$997$	−18.0413	−	37.4632i	−0.571374	−	1.18647i	−0.963785	−	0.266681i	$-0.914073\pi$
$997$	−18.0413	−	37.4632i	−0.571374	−	1.18647i	0.392411	−	0.919790i	$-0.371641\pi$
$998$		−	38.1695i		−	1.20823i
$999$	−1.41705	+	0.682413i	−0.0448333	+	0.0215906i

Display

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a_n

instead) (See

a_n

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a_n

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.bm.a.247.4	yes	180
5.3	odd	4		435.2.bd.b.73.4	✓	180
29.2	odd	28		435.2.bd.b.292.4	yes	180
145.118	even	28	inner	435.2.bm.a.118.4	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.bd.b.73.4	✓	180	5.3	odd	4
435.2.bd.b.292.4	yes	180	29.2	odd	28
435.2.bm.a.118.4	yes	180	145.118	even	28	inner
435.2.bm.a.247.4	yes	180	1.1	even	1	trivial

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

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	435.2.bm.a.247.4

Level	$435$
Weight	$2$
Character	435.247
Analytic conductor	$3.473$
Analytic rank	$0$
Dimension	$180$
Inner twists	$2$