LMFDB - Embedded newform 756.2.cf.a.491.30

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(155,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 7, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.cf (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$108$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			491.30
Character	$\chi$	$=$	756.491
Dual form			756.2.cf.a.659.30

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.946460 - 1.05082i) q^{2} +(0.977433 - 1.42990i) q^{3} +(-0.208426 + 1.98911i) q^{4} +(0.0906174 + 0.248969i) q^{5} +(-2.42767 + 0.326246i) q^{6} +(-0.984808 + 0.173648i) q^{7} +(2.28745 - 1.66360i) q^{8} +(-1.08925 - 2.79527i) q^{9} +(0.175855 - 0.330862i) q^{10} +(5.73024 + 2.08564i) q^{11} +(2.64051 + 2.24225i) q^{12} +(1.01491 + 0.851609i) q^{13} +(1.11455 + 0.870500i) q^{14} +(0.444574 + 0.113777i) q^{15} +(-3.91312 - 0.829164i) q^{16} +(2.19650 + 1.26815i) q^{17} +(-1.90638 + 3.79021i) q^{18} +(2.96118 - 1.70964i) q^{19} +(-0.514114 + 0.128356i) q^{20} +(-0.714283 + 1.57791i) q^{21} +(-3.23182 - 7.99539i) q^{22} +(-0.696333 + 3.94910i) q^{23} +(-0.142950 - 4.89689i) q^{24} +(3.77645 - 3.16882i) q^{25} +(-0.0656863 - 1.87249i) q^{26} +(-5.06164 - 1.17467i) q^{27} +(-0.140146 - 1.99508i) q^{28} +(-2.88222 - 3.43490i) q^{29} +(-0.301214 - 0.574851i) q^{30} +(-2.67023 - 0.470833i) q^{31} +(2.83231 + 4.89673i) q^{32} +(8.58318 - 6.15512i) q^{33} +(-0.746307 - 3.50836i) q^{34} +(-0.132474 - 0.229451i) q^{35} +(5.78713 - 1.58403i) q^{36} +(3.66294 - 6.34440i) q^{37} +(-4.59915 - 1.49355i) q^{38} +(2.20972 - 0.618830i) q^{39} +(0.621467 + 0.418755i) q^{40} +(1.34043 - 1.59747i) q^{41} +(2.33413 - 0.742849i) q^{42} +(1.74088 - 4.78302i) q^{43} +(-5.34289 + 10.9634i) q^{44} +(0.597231 - 0.524490i) q^{45} +(4.80883 - 3.00595i) q^{46} +(1.79913 + 10.2033i) q^{47} +(-5.01043 + 4.78493i) q^{48} +(0.939693 - 0.342020i) q^{49} +(-6.90410 - 0.969191i) q^{50} +(3.96026 - 1.90125i) q^{51} +(-1.90548 + 1.84127i) q^{52} -7.06881i q^{53} +(3.55628 + 6.43062i) q^{54} +1.61565i q^{55} +(-1.96382 + 2.03554i) q^{56} +(0.449737 - 5.90526i) q^{57} +(-0.881535 + 6.27968i) q^{58} +(1.92884 - 0.702041i) q^{59} +(-0.318975 + 0.860594i) q^{60} +(-1.40863 - 7.98872i) q^{61} +(2.03250 + 3.25154i) q^{62} +(1.55810 + 2.56366i) q^{63} +(2.46489 - 7.61080i) q^{64} +(-0.120056 + 0.329851i) q^{65} +(-14.5915 - 3.19376i) q^{66} +(-3.41998 + 4.07577i) q^{67} +(-2.98029 + 4.10476i) q^{68} +(4.96621 + 4.85567i) q^{69} +(-0.115730 + 0.356372i) q^{70} +(-3.68578 + 6.38396i) q^{71} +(-7.14181 - 4.58198i) q^{72} +(3.77756 + 6.54292i) q^{73} +(-10.1336 + 2.15565i) q^{74} +(-0.839877 - 8.49726i) q^{75} +(2.78347 + 6.24644i) q^{76} +(-6.00535 - 1.05891i) q^{77} +(-2.74169 - 1.73631i) q^{78} +(-6.83234 - 8.14247i) q^{79} +(-0.148160 - 1.04938i) q^{80} +(-6.62707 + 6.08949i) q^{81} +(-2.94731 + 0.103390i) q^{82} +(-2.06272 + 1.73083i) q^{83} +(-2.98976 - 1.74967i) q^{84} +(-0.116689 + 0.661776i) q^{85} +(-6.67374 + 2.69760i) q^{86} +(-7.72875 + 0.763917i) q^{87} +(16.5773 - 4.76201i) q^{88} +(7.43301 - 4.29145i) q^{89} +(-1.11640 - 0.131171i) q^{90} +(-1.14737 - 0.662434i) q^{91} +(-7.71006 - 2.20818i) q^{92} +(-3.28321 + 3.35796i) q^{93} +(9.01904 - 11.5476i) q^{94} +(0.693982 + 0.582320i) q^{95} +(9.77025 + 0.736296i) q^{96} +(-16.7870 - 6.10996i) q^{97} +(-1.24878 - 0.663735i) q^{98} +(-0.411744 - 18.2893i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$

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 $

$2$	−0.946460	−	1.05082i	−0.669248	−	0.743039i
$2$	−0.946460	−	1.05082i	−0.669248	−	0.743039i
$3$	0.977433	−	1.42990i	0.564321	−	0.825555i
$3$	0.977433	−	1.42990i	0.564321	−	0.825555i
$4$	−0.208426	+	1.98911i	−0.104213	+	0.994555i
$5$	0.0906174	+	0.248969i	0.0405253	+	0.111342i	0.958305	−	0.285748i	$-0.0922421\pi$
$5$	0.0906174	+	0.248969i	0.0405253	+	0.111342i	−0.917779	+	0.397091i	$0.870020\pi$
$6$	−2.42767	+	0.326246i	−0.991091	+	0.133189i
$7$	−0.984808	+	0.173648i	−0.372222	+	0.0656328i
$7$	−0.984808	+	0.173648i	−0.372222	+	0.0656328i
$8$	2.28745	−	1.66360i	0.808737	−	0.588170i
$9$	−1.08925	−	2.79527i	−0.363083	−	0.931757i
$10$	0.175855	−	0.330862i	0.0556102	−	0.104628i
$11$	5.73024	+	2.08564i	1.72773	+	0.628843i	0.998465	−	0.0553862i	$-0.0176390\pi$
$11$	5.73024	+	2.08564i	1.72773	+	0.628843i	0.729267	+	0.684229i	$0.239861\pi$
$12$	2.64051	+	2.24225i	0.762251	+	0.647282i
$13$	1.01491	+	0.851609i	0.281485	+	0.236194i	0.772588	−	0.634908i	$-0.218962\pi$
$13$	1.01491	+	0.851609i	0.281485	+	0.236194i	−0.491103	+	0.871101i	$0.663406\pi$
$14$	1.11455	+	0.870500i	0.297877	+	0.232651i
$15$	0.444574	+	0.113777i	0.114789	+	0.0293770i
$16$	−3.91312	−	0.829164i	−0.978279	−	0.207291i
$17$	2.19650	+	1.26815i	0.532728	+	0.307571i	0.742127	−	0.670260i	$-0.233817\pi$
$17$	2.19650	+	1.26815i	0.532728	+	0.307571i	−0.209398	+	0.977830i	$0.567151\pi$
$18$	−1.90638	+	3.79021i	−0.449338	+	0.893362i
$19$	2.96118	−	1.70964i	0.679341	−	0.392218i	−0.120266	−	0.992742i	$-0.538375\pi$
$19$	2.96118	−	1.70964i	0.679341	−	0.392218i	0.799607	+	0.600524i	$0.205041\pi$
$20$	−0.514114	+	0.128356i	−0.114959	+	0.0287013i
$21$	−0.714283	+	1.57791i	−0.155869	+	0.344328i
$22$	−3.23182	−	7.99539i	−0.689027	−	1.70462i
$23$	−0.696333	+	3.94910i	−0.145195	+	0.823444i	0.822015	+	0.569466i	$0.192850\pi$
$23$	−0.696333	+	3.94910i	−0.145195	+	0.823444i	−0.967210	+	0.253978i	$0.918261\pi$
$24$	−0.142950	−	4.89689i	−0.0291795	−	0.999574i
$25$	3.77645	−	3.16882i	0.755290	−	0.633763i
$26$	−0.0656863	−	1.87249i	−0.0128822	−	0.367226i
$27$	−5.06164	−	1.17467i	−0.974112	−	0.226065i
$28$	−0.140146	−	1.99508i	−0.0264851	−	0.377035i
$29$	−2.88222	−	3.43490i	−0.535215	−	0.637845i	0.428893	−	0.903355i	$-0.358904\pi$
$29$	−2.88222	−	3.43490i	−0.535215	−	0.637845i	−0.964108	+	0.265511i	$0.914459\pi$
$30$	−0.301214	−	0.574851i	−0.0549939	−	0.104953i
$31$	−2.67023	−	0.470833i	−0.479587	−	0.0845641i	−0.0713716	−	0.997450i	$-0.522738\pi$
$31$	−2.67023	−	0.470833i	−0.479587	−	0.0845641i	−0.408215	+	0.912886i	$0.633849\pi$
$32$	2.83231	+	4.89673i	0.500687	+	0.865629i
$33$	8.58318	−	6.15512i	1.49414	−	1.07147i
$34$	−0.746307	−	3.50836i	−0.127991	−	0.601679i
$35$	−0.132474	−	0.229451i	−0.0223922	−	0.0387843i
$36$	5.78713	−	1.58403i	0.964521	−	0.264005i
$37$	3.66294	−	6.34440i	0.602184	−	1.04301i	−0.390306	−	0.920685i	$-0.627631\pi$
$37$	3.66294	−	6.34440i	0.602184	−	1.04301i	0.992490	−	0.122328i	$-0.0390358\pi$
$38$	−4.59915	−	1.49355i	−0.746081	−	0.242286i
$39$	2.20972	−	0.618830i	0.353839	−	0.0990921i
$40$	0.621467	+	0.418755i	0.0982626	+	0.0662110i
$41$	1.34043	−	1.59747i	0.209341	−	0.249482i	−0.651150	−	0.758949i	$-0.725713\pi$
$41$	1.34043	−	1.59747i	0.209341	−	0.249482i	0.860490	+	0.509467i	$0.170157\pi$
$42$	2.33413	−	0.742849i	0.360164	−	0.114624i
$43$	1.74088	−	4.78302i	0.265481	−	0.729404i	−0.733293	−	0.679913i	$-0.762018\pi$
$43$	1.74088	−	4.78302i	0.265481	−	0.729404i	0.998775	−	0.0494915i	$-0.0157601\pi$
$44$	−5.34289	+	10.9634i	−0.805471	+	1.65279i
$45$	0.597231	−	0.524490i	0.0890300	−	0.0781863i
$46$	4.80883	−	3.00595i	0.709023	−	0.443203i
$47$	1.79913	+	10.2033i	0.262429	+	1.48831i	0.776256	+	0.630418i	$0.217116\pi$
$47$	1.79913	+	10.2033i	0.262429	+	1.48831i	−0.513827	+	0.857894i	$0.671773\pi$
$48$	−5.01043	+	4.78493i	−0.723194	+	0.690645i
$49$	0.939693	−	0.342020i	0.134242	−	0.0488600i
$50$	−6.90410	−	0.969191i	−0.976387	−	0.137064i
$51$	3.96026	−	1.90125i	0.554547	−	0.266228i
$52$	−1.90548	+	1.84127i	−0.264242	+	0.255338i
$53$		−	7.06881i		−	0.970976i	−0.874243	−	0.485488i	$-0.838642\pi$
$53$		−	7.06881i		−	0.970976i	0.874243	−	0.485488i	$-0.161358\pi$
$54$	3.55628	+	6.43062i	0.483948	+	0.875097i
$55$			1.61565i			0.217854i
$56$	−1.96382	+	2.03554i	−0.262427	+	0.272010i
$57$	0.449737	−	5.90526i	0.0595691	−	0.782170i
$58$	−0.881535	+	6.27968i	−0.115751	+	0.824562i
$59$	1.92884	−	0.702041i	0.251114	−	0.0913980i	−0.213396	−	0.976966i	$-0.568453\pi$
$59$	1.92884	−	0.702041i	0.251114	−	0.0913980i	0.464510	+	0.885568i	$0.346230\pi$
$60$	−0.318975	+	0.860594i	−0.0411795	+	0.111102i
$61$	−1.40863	−	7.98872i	−0.180356	−	1.02285i	−0.931778	−	0.363029i	$-0.881743\pi$
$61$	−1.40863	−	7.98872i	−0.180356	−	1.02285i	0.751422	−	0.659822i	$-0.229368\pi$
$62$	2.03250	+	3.25154i	0.258128	+	0.412946i
$63$	1.55810	+	2.56366i	0.196302	+	0.322990i
$64$	2.46489	−	7.61080i	0.308112	−	0.951350i
$65$	−0.120056	+	0.329851i	−0.0148911	+	0.0409130i
$66$	−14.5915	−	3.19376i	−1.79609	−	0.393125i
$67$	−3.41998	+	4.07577i	−0.417817	+	0.497935i	−0.933366	−	0.358925i	$-0.883143\pi$
$67$	−3.41998	+	4.07577i	−0.417817	+	0.497935i	0.515550	+	0.856860i	$0.327588\pi$
$68$	−2.98029	+	4.10476i	−0.361413	+	0.497775i
$69$	4.96621	+	4.85567i	0.597862	+	0.584554i
$70$	−0.115730	+	0.356372i	−0.0138324	+	0.0425946i
$71$	−3.68578	+	6.38396i	−0.437422	+	0.757636i	−0.997490	−	0.0708101i	$-0.977442\pi$
$71$	−3.68578	+	6.38396i	−0.437422	+	0.757636i	0.560068	+	0.828446i	$0.310775\pi$
$72$	−7.14181	−	4.58198i	−0.841670	−	0.539992i
$73$	3.77756	+	6.54292i	0.442130	+	0.765791i	0.997847	−	0.0655798i	$-0.0208897\pi$
$73$	3.77756	+	6.54292i	0.442130	+	0.765791i	−0.555717	+	0.831371i	$0.687556\pi$
$74$	−10.1336	+	2.15565i	−1.17801	+	0.250589i
$75$	−0.839877	−	8.49726i	−0.0969807	−	0.981179i
$76$	2.78347	+	6.24644i	0.319286	+	0.716516i
$77$	−6.00535	−	1.05891i	−0.684373	−	0.120673i
$78$	−2.74169	−	1.73631i	−0.310435	−	0.196599i
$79$	−6.83234	−	8.14247i	−0.768699	−	0.916099i	0.229666	−	0.973270i	$-0.426237\pi$
$79$	−6.83234	−	8.14247i	−0.768699	−	0.916099i	−0.998364	+	0.0571703i	$0.981792\pi$
$80$	−0.148160	−	1.04938i	−0.0165648	−	0.117325i
$81$	−6.62707	+	6.08949i	−0.736341	+	0.676610i
$82$	−2.94731	+	0.103390i	−0.325476	+	0.0114176i
$83$	−2.06272	+	1.73083i	−0.226413	+	0.189983i	−0.748936	−	0.662642i	$-0.769435\pi$
$83$	−2.06272	+	1.73083i	−0.226413	+	0.189983i	0.522523	+	0.852625i	$0.324991\pi$
$84$	−2.98976	−	1.74967i	−0.326210	−	0.190904i
$85$	−0.116689	+	0.661776i	−0.0126567	+	0.0717797i
$86$	−6.67374	+	2.69760i	−0.719648	+	0.290890i
$87$	−7.72875	+	0.763917i	−0.828609	+	0.0819005i
$88$	16.5773	−	4.76201i	1.76715	−	0.507632i
$89$	7.43301	−	4.29145i	0.787898	−	0.454893i	−0.0513240	−	0.998682i	$-0.516344\pi$
$89$	7.43301	−	4.29145i	0.787898	−	0.454893i	0.839222	+	0.543789i	$0.183011\pi$
$90$	−1.11640	−	0.131171i	−0.117679	−	0.0138267i
$91$	−1.14737	−	0.662434i	−0.120277	−	0.0694419i
$92$	−7.71006	−	2.20818i	−0.803829	−	0.230218i
$93$	−3.28321	+	3.35796i	−0.340453	+	0.348204i
$94$	9.01904	−	11.5476i	0.930242	−	1.19105i
$95$	0.693982	+	0.582320i	0.0712010	+	0.0597447i
$96$	9.77025	+	0.736296i	0.997172	+	0.0751479i
$97$	−16.7870	−	6.10996i	−1.70446	−	0.620372i	−0.708138	−	0.706074i	$-0.750464\pi$
$97$	−16.7870	−	6.10996i	−1.70446	−	0.620372i	−0.996321	+	0.0857023i	$0.972687\pi$
$98$	−1.24878	−	0.663735i	−0.126146	−	0.0670474i
$99$	−0.411744	−	18.2893i	−0.0413818	−	1.83815i
$100$	5.51601	+	8.17223i	0.551601	+	0.817223i
$101$	14.2433	−	2.51147i	1.41726	−	0.249901i	0.588044	−	0.808829i	$-0.299898\pi$
$101$	14.2433	−	2.51147i	1.41726	−	0.249901i	0.829216	+	0.558928i	$0.188787\pi$
$102$	−5.74609	−	2.36204i	−0.568947	−	0.233877i
$103$	1.63360	+	4.48829i	0.160964	+	0.442244i	0.993788	−	0.111294i	$-0.0354996\pi$
$103$	1.63360	+	4.48829i	0.160964	+	0.442244i	−0.832824	+	0.553538i	$0.813277\pi$
$104$	3.73829	+	0.259619i	0.366569	+	0.0254577i
$105$	−0.457577	−	0.0348485i	−0.0446550	−	0.00340087i
$106$	−7.42802	+	6.69035i	−0.721473	+	0.649824i
$107$	6.40420			0.619117			0.309559	−	0.950880i	$-0.399819\pi$
$107$	6.40420			0.619117			0.309559	+	0.950880i	$0.399819\pi$
$108$	3.39152	−	9.82332i	0.326349	−	0.945249i
$109$	−13.9221			−1.33349			−0.666746	−	0.745285i	$-0.732314\pi$
$109$	−13.9221			−1.33349			−0.666746	+	0.745285i	$0.732314\pi$
$110$	1.69775	−	1.52915i	0.161874	−	0.145798i
$111$	−5.49160	−	11.4389i	−0.521240	−	1.08573i
$112$	3.99765	+	0.137061i	0.377743	+	0.0129511i
$113$	0.359261	+	0.987062i	0.0337965	+	0.0928550i	0.955443	−	0.295175i	$-0.0953779\pi$
$113$	0.359261	+	0.987062i	0.0337965	+	0.0928550i	−0.921647	+	0.388030i	$0.873156\pi$
$114$	−6.63099	+	5.11650i	−0.621049	+	0.479204i
$115$	−1.04630	+	0.184492i	−0.0975684	+	0.0172039i
$116$	7.43312	−	5.01714i	0.690148	−	0.465829i
$117$	1.27499	−	3.76456i	0.117873	−	0.348033i
$118$	−2.56329	−	1.36240i	−0.235970	−	0.125419i
$119$	−2.38334	−	0.867464i	−0.218480	−	0.0795203i
$120$	1.20622	−	0.479334i	0.110113	−	0.0437570i
$121$	20.0593	+	16.8317i	1.82357	+	1.53016i
$122$	−7.06146	+	9.04121i	−0.639315	+	0.818553i
$123$	−0.974040	−	3.47811i	−0.0878262	−	0.313610i
$124$	1.49308	−	5.21324i	0.134083	−	0.468163i
$125$	2.27841	+	1.31544i	0.203787	+	0.117656i
$126$	1.21926	−	4.06367i	0.108620	−	0.362021i
$127$	0.641968	−	0.370640i	0.0569654	−	0.0328890i	−0.471247	−	0.882001i	$-0.656196\pi$
$127$	0.641968	−	0.370640i	0.0569654	−	0.0328890i	0.528212	+	0.849112i	$0.322863\pi$
$128$	−10.3305	+	4.61317i	−0.913093	+	0.407751i
$129$	−5.13767	−	7.16437i	−0.452347	−	0.630788i
$130$	0.460241	−	0.186034i	0.0403658	−	0.0163163i
$131$	−3.94355	+	22.3650i	−0.344550	+	1.95404i	−0.0486698	+	0.998815i	$0.515498\pi$
$131$	−3.94355	+	22.3650i	−0.344550	+	1.95404i	−0.295880	+	0.955225i	$0.595613\pi$
$132$	10.4543	+	18.3558i	0.909926	+	1.59767i
$133$	−2.61932	+	2.19787i	−0.227124	+	0.190579i
$134$	7.51976	−	0.263790i	0.649608	−	0.0227880i
$135$	−0.166216	−	1.36664i	−0.0143056	−	0.117621i
$136$	7.13407	−	0.753254i	0.611741	−	0.0645910i
$137$	0.0691415	+	0.0823996i	0.00590715	+	0.00703987i	0.768990	−	0.639261i	$-0.220760\pi$
$137$	0.0691415	+	0.0823996i	0.00590715	+	0.00703987i	−0.763083	+	0.646301i	$0.776315\pi$
$138$	0.402087	−	9.81427i	0.0342280	−	0.835446i
$139$	9.62962	+	1.69796i	0.816774	+	0.144019i	0.566400	−	0.824130i	$-0.308336\pi$
$139$	9.62962	+	1.69796i	0.816774	+	0.144019i	0.250373	+	0.968149i	$0.419447\pi$
$140$	0.484015	−	0.215681i	0.0409067	−	0.0182284i
$141$	16.3483	+	7.40051i	1.37678	+	0.623236i
$142$	10.1968	−	2.16909i	0.855697	−	0.182026i
$143$	4.03952	+	6.99665i	0.337801	+	0.585089i
$144$	1.94462	+	11.8414i	0.162052	+	0.986782i
$145$	0.594005	−	1.02885i	0.0493294	−	0.0854410i
$146$	3.30010	−	10.1621i	0.273118	−	0.841024i
$147$	0.429431	−	1.67797i	0.0354188	−	0.138397i
$148$	11.8563	+	8.60833i	0.974578	+	0.707600i
$149$	−4.32275	+	5.15165i	−0.354133	+	0.422039i	−0.913473	−	0.406899i	$-0.866610\pi$
$149$	−4.32275	+	5.15165i	−0.354133	+	0.422039i	0.559340	+	0.828938i	$0.311055\pi$
$150$	−8.13414	+	8.92488i	−0.664150	+	0.728713i
$151$	−3.51465	+	9.65641i	−0.286018	+	0.785827i	0.710596	+	0.703600i	$0.248425\pi$
$151$	−3.51465	+	9.65641i	−0.286018	+	0.785827i	−0.996614	+	0.0822270i	$0.973797\pi$
$152$	3.92941	−	8.83693i	0.318718	−	0.716769i
$153$	1.15228	−	7.52113i	0.0931565	−	0.608047i
$154$	4.57111	+	7.31273i	0.368351	+	0.589276i
$155$	−0.124746	−	0.707470i	−0.0100198	−	0.0568253i
$156$	0.770358	+	4.52436i	0.0616780	+	0.362239i
$157$	6.22305	−	2.26501i	0.496654	−	0.180767i	−0.0815346	−	0.996671i	$-0.525982\pi$
$157$	6.22305	−	2.26501i	0.496654	−	0.180767i	0.578188	+	0.815903i	$0.303760\pi$
$158$	−2.08969	+	14.8861i	−0.166247	+	1.18427i
$159$	−10.1077	−	6.90929i	−0.801594	−	0.547942i
$160$	−0.962480	+	1.14889i	−0.0760907	+	0.0908276i
$161$		−	4.01002i		−	0.316034i
$162$	12.6712	+	1.20036i	0.995543	+	0.0943094i
$163$			14.2845i			1.11884i	0.828883	+	0.559422i	$0.188977\pi$
$163$			14.2845i			1.11884i	−0.828883	+	0.559422i	$0.811023\pi$
$164$	2.89816	+	2.99922i	0.226308	+	0.234200i
$165$	2.31022	+	1.57919i	0.179850	+	0.122940i
$166$	3.77107	+	0.529379i	0.292691	+	0.0410878i
$167$	7.08519	−	2.57880i	0.548269	−	0.199553i	−0.0530084	−	0.998594i	$-0.516881\pi$
$167$	7.08519	−	2.57880i	0.548269	−	0.199553i	0.601277	+	0.799041i	$0.294659\pi$
$168$	0.991115	+	4.79768i	0.0764662	+	0.370149i
$169$	−1.95263	−	11.0739i	−0.150202	−	0.851838i
$170$	0.805846	−	0.503726i	0.0618056	−	0.0386340i
$171$	−8.00436	−	6.41507i	−0.612109	−	0.490573i
$172$	9.15111	+	4.45970i	0.697766	+	0.340049i
$173$	−8.45513	+	23.2303i	−0.642832	+	1.76617i	−0.000188152		1.00000i	$0.500060\pi$
$173$	−8.45513	+	23.2303i	−0.642832	+	1.76617i	−0.642643	+	0.766165i	$0.722162\pi$
$174$	8.11769	+	7.39848i	0.615401	+	0.560877i
$175$	−3.16882	+	3.77645i	−0.239540	+	0.285473i
$176$	−20.6938	−	12.9126i	−1.55985	−	0.973327i
$177$	0.881463	−	3.44426i	0.0662548	−	0.258886i
$178$	−11.5446	−	3.74904i	−0.865303	−	0.281002i
$179$	6.16081	−	10.6708i	0.460481	−	0.797576i	−0.538504	−	0.842623i	$-0.681010\pi$
$179$	6.16081	−	10.6708i	0.460481	−	0.797576i	0.998985	+	0.0450470i	$0.0143438\pi$
$180$	0.918789	+	1.29728i	0.0684825	+	0.0966932i
$181$	−0.977001	−	1.69222i	−0.0726199	−	0.125781i	0.827429	−	0.561571i	$-0.189803\pi$
$181$	−0.977001	−	1.69222i	−0.0726199	−	0.125781i	−0.900049	+	0.435789i	$0.856469\pi$
$182$	0.389844	+	1.83264i	0.0288971	+	0.135844i
$183$	−12.7999	−	5.79424i	−0.946199	−	0.428322i
$184$	4.97688	+	10.1918i	0.366900	+	0.751350i
$185$	1.91149	+	0.337047i	0.140535	+	0.0247802i
$186$	6.63603	+	0.271876i	0.486577	+	0.0199349i
$187$	9.94155	+	11.8479i	0.726998	+	0.866403i
$188$	−20.6706	+	1.45202i	−1.50756	+	0.105899i
$189$	5.18872	+	0.277877i	0.377424	+	0.0202126i
$190$	−0.0449155	−	1.28039i	−0.00325851	−	0.0928892i
$191$	13.7375	−	11.5271i	0.994011	−	0.834074i	0.00786756	−	0.999969i	$-0.497496\pi$
$191$	13.7375	−	11.5271i	0.994011	−	0.834074i	0.986143	+	0.165895i	$0.0530512\pi$
$192$	−8.47345	−	10.9636i	−0.611518	−	0.791230i
$193$	−3.94897	+	22.3957i	−0.284253	+	1.61208i	0.423687	+	0.905809i	$0.360736\pi$
$193$	−3.94897	+	22.3957i	−0.284253	+	1.61208i	−0.707940	+	0.706272i	$0.750375\pi$
$194$	9.46776	+	23.4228i	0.679746	+	1.68166i
$195$	0.354309	+	0.494076i	0.0253726	+	0.0353815i
$196$	0.484459	+	1.94044i	0.0346042	+	0.138603i
$197$	−21.5813	+	12.4600i	−1.53760	+	0.887736i	−0.538625	+	0.842546i	$0.681056\pi$
$197$	−21.5813	+	12.4600i	−1.53760	+	0.887736i	−0.998978	+	0.0451897i	$0.985611\pi$
$198$	−18.8290	+	17.7428i	−1.33812	+	1.26093i
$199$	−12.9243	−	7.46182i	−0.916176	−	0.528955i	−0.0337630	−	0.999430i	$-0.510749\pi$
$199$	−12.9243	−	7.46182i	−0.916176	−	0.528955i	−0.882413	+	0.470475i	$0.844082\pi$
$200$	3.36682	−	13.5310i	0.238070	−	0.956787i
$201$	2.48516	+	8.87403i	0.175290	+	0.625926i
$202$	−16.1198	−	12.5900i	−1.13419	−	0.885833i
$203$	3.43490	+	2.88222i	0.241083	+	0.202292i
$204$	2.95637	+	8.27365i	0.206987	+	0.579272i
$205$	0.519187	+	0.188968i	0.0362616	+	0.0131981i
$206$	3.17022	−	5.96460i	0.220880	−	0.415573i
$207$	11.7973	−	2.35512i	0.819968	−	0.163692i
$208$	−3.26533	−	4.17397i	−0.226410	−	0.289413i
$209$	20.5339	−	3.62069i	1.42036	−	0.250448i
$210$	0.396460	+	0.513812i	0.0273583	+	0.0354564i
$211$	−3.39710	−	9.33345i	−0.233866	−	0.642541i	0.766134	−	0.642681i	$-0.222178\pi$
$211$	−3.39710	−	9.33345i	−0.233866	−	0.642541i	−1.00000		0.000139562i	$0.999956\pi$
$212$	14.0606	+	1.47332i	0.965689	+	0.101188i
$213$	5.52584	+	11.5102i	0.378624	+	0.788666i
$214$	−6.06132	−	6.72963i	−0.414343	−	0.460028i
$215$	1.34858			0.0919723
$216$	−13.5324	+	5.73352i	−0.920765	+	0.390117i
$217$	2.71142			0.184063
$218$	13.1767	+	14.6295i	0.892438	+	0.990837i
$219$	13.0481	+	0.993724i	0.881706	+	0.0671496i
$220$	−3.21370	−	0.336743i	−0.216668	−	0.0227032i
$221$	1.14927	+	3.15761i	0.0773086	+	0.212404i
$222$	−6.82256	+	16.5971i	−0.457901	+	1.11392i
$223$	−0.325443	+	0.0573844i	−0.0217933	+	0.00384274i	−0.184534	−	0.982826i	$-0.559078\pi$
$223$	−0.325443	+	0.0573844i	−0.0217933	+	0.00384274i	0.162741	+	0.986669i	$0.447967\pi$
$224$	−3.63959	−	4.33052i	−0.243180	−	0.289345i
$225$	−12.9712	−	7.10456i	−0.864746	−	0.473637i
$226$	0.697194	−	1.31173i	0.0463766	−	0.0872552i
$227$	−7.43425	−	2.70584i	−0.493428	−	0.179593i	0.0833076	−	0.996524i	$-0.473452\pi$
$227$	−7.43425	−	2.70584i	−0.493428	−	0.179593i	−0.576736	+	0.816931i	$0.695674\pi$
$228$	11.6525	+	2.12538i	0.771704	+	0.140757i
$229$	13.3833	+	11.2300i	0.884396	+	0.742096i	0.967078	−	0.254480i	$-0.0819042\pi$
$229$	13.3833	+	11.2300i	0.884396	+	0.742096i	−0.0826823	+	0.996576i	$0.526349\pi$
$230$	1.18415	+	0.924858i	0.0780807	+	0.0609834i
$231$	−7.38396	+	7.55206i	−0.485829	+	0.496889i
$232$	−12.3072	−	3.06232i	−0.808010	−	0.201051i
$233$	−8.64256	−	4.98978i	−0.566193	−	0.326892i	0.189434	−	0.981893i	$-0.439335\pi$
$233$	−8.64256	−	4.98978i	−0.566193	−	0.326892i	−0.755627	+	0.655002i	$0.772668\pi$
$234$	−5.16258	+	2.22322i	−0.337488	+	0.145337i
$235$	−2.37729	+	1.37253i	−0.155077	+	0.0895339i
$236$	0.994417	+	3.98300i	0.0647310	+	0.259271i
$237$	−18.3211	+	1.81087i	−1.19008	+	0.117629i
$238$	1.34419	+	3.32547i	0.0871309	+	0.215558i
$239$	4.46340	−	25.3132i	0.288713	−	1.63737i	−0.402998	−	0.915201i	$-0.632032\pi$
$239$	4.46340	−	25.3132i	0.288713	−	1.63737i	0.691711	−	0.722174i	$-0.256857\pi$
$240$	−1.64533	−	0.813846i	−0.106206	−	0.0525335i
$241$	15.9103	−	13.3503i	1.02487	−	0.859971i	0.0346411	−	0.999400i	$-0.488971\pi$
$241$	15.9103	−	13.3503i	1.02487	−	0.859971i	0.990232	+	0.139429i	$0.0445267\pi$
$242$	−1.29827	−	37.0091i	−0.0834557	−	2.37904i
$243$	2.22987	+	15.4281i	0.143046	+	0.989716i
$244$	16.1840	−	1.13686i	1.03608	−	0.0727799i
$245$	0.170305	+	0.202962i	0.0108804	+	0.0129667i
$246$	−2.73296	+	4.31543i	−0.174247	+	0.275142i
$247$	4.46127	+	0.786641i	0.283864	+	0.0500528i
$248$	−6.89130	+	3.36517i	−0.437598	+	0.213689i
$249$	0.458747	+	4.64126i	0.0290719	+	0.294128i
$250$	−0.774138	−	3.63919i	−0.0489608	−	0.230163i
$251$	11.8373	+	20.5028i	0.747162	+	1.29412i	0.949178	+	0.314740i	$0.101917\pi$
$251$	11.8373	+	20.5028i	0.747162	+	1.29412i	−0.202016	+	0.979382i	$0.564749\pi$
$252$	−5.42414	+	2.56489i	−0.341689	+	0.161573i
$253$	−12.2265	+	21.1770i	−0.768676	+	1.33139i
$254$	−0.997071	−	0.323793i	−0.0625618	−	0.0203166i
$255$	0.832220	+	0.813696i	0.0521157	+	0.0509556i
$256$	14.6250	+	6.48923i	0.914061	+	0.405577i
$257$	−15.4657	+	18.4313i	−0.964724	+	1.14971i	0.0239616	+	0.999713i	$0.492372\pi$
$257$	−15.4657	+	18.4313i	−0.964724	+	1.14971i	−0.988686	+	0.150001i	$0.952072\pi$
$258$	−2.66583	+	12.1795i	−0.165967	+	0.758265i
$259$	−2.50560	+	6.88408i	−0.155690	+	0.427756i
$260$	−0.631088	−	0.307554i	−0.0391384	−	0.0190737i
$261$	−6.46201	+	11.7981i	−0.399988	+	0.730281i
$262$	27.2339	−	17.0236i	1.68252	−	1.05172i
$263$	2.46725	+	13.9925i	0.152137	+	0.862814i	0.961356	+	0.275307i	$0.0887795\pi$
$263$	2.46725	+	13.9925i	0.152137	+	0.862814i	−0.809219	+	0.587507i	$0.800109\pi$
$264$	9.39400	−	28.3585i	0.578161	−	1.74535i
$265$	1.75992	−	0.640557i	0.108111	−	0.0393491i
$266$	4.78863	+	0.672224i	0.293610	+	0.0412167i
$267$	1.12891	−	14.8231i	0.0690881	−	0.907159i
$268$	−7.39435	−	7.65221i	−0.451682	−	0.467433i
$269$			14.3360i			0.874081i	0.899442	+	0.437041i	$0.143973\pi$
$269$			14.3360i			0.874081i	−0.899442	+	0.437041i	$0.856027\pi$
$270$	−1.27877	+	1.46813i	−0.0778232	+	0.0893476i
$271$			18.9316i			1.15001i	0.818149	+	0.575007i	$0.195001\pi$
$271$			18.9316i			1.15001i	−0.818149	+	0.575007i	$0.804999\pi$
$272$	−7.54364	−	6.78366i	−0.457401	−	0.411320i
$273$	−2.06869	+	0.993143i	−0.125203	+	0.0601077i
$274$	0.0211471	−	0.150643i	0.00127754	−	0.00910067i
$275$	28.2489	−	10.2818i	1.70348	−	0.620014i
$276$	−10.6935	+	8.86630i	−0.643676	+	0.533688i
$277$	−1.18175	−	6.70204i	−0.0710045	−	0.402687i	−0.999508	−	0.0313631i	$-0.990015\pi$
$277$	−1.18175	−	6.70204i	−0.0710045	−	0.402687i	0.928504	−	0.371324i	$-0.121096\pi$
$278$	−7.32981	−	11.7260i	−0.439613	−	0.703279i
$279$	1.59244	+	7.97686i	0.0953368	+	0.477562i
$280$	−0.684742	−	0.304476i	−0.0409212	−	0.0181959i
$281$	6.97569	−	19.1656i	0.416135	−	1.14332i	−0.537738	−	0.843112i	$-0.680721\pi$
$281$	6.97569	−	19.1656i	0.416135	−	1.14332i	0.953873	−	0.300210i	$-0.0970566\pi$
$282$	−7.69648	−	24.1834i	−0.458318	−	1.44010i
$283$	−9.28422	+	11.0645i	−0.551889	+	0.657716i	−0.967809	−	0.251685i	$-0.919015\pi$
$283$	−9.28422	+	11.0645i	−0.551889	+	0.657716i	0.415920	+	0.909401i	$0.363460\pi$
$284$	−11.9302	−	8.66200i	−0.707926	−	0.513995i
$285$	1.51098	−	0.423148i	0.0895028	−	0.0250651i
$286$	3.52894	−	10.8668i	0.208671	−	0.642570i
$287$	−1.04267	+	1.80596i	−0.0615470	+	0.106603i
$288$	10.6026	−	13.2508i	0.624764	−	0.780813i
$289$	−5.28361	−	9.15147i	−0.310800	−	0.538322i
$290$	−1.64333	+	0.349573i	−0.0964996	+	0.0205276i
$291$	−25.1448	+	18.0317i	−1.47401	+	1.05704i
$292$	−13.8019	+	6.15027i	−0.807697	+	0.359917i
$293$	−7.72115	−	1.36145i	−0.451075	−	0.0795366i	−0.0565043	−	0.998402i	$-0.517995\pi$
$293$	−7.72115	−	1.36145i	−0.451075	−	0.0795366i	−0.394570	+	0.918866i	$0.629107\pi$
$294$	−2.16968	+	1.13688i	−0.126538	+	0.0663043i
$295$	0.349573	+	0.416605i	0.0203529	+	0.0242557i
$296$	−2.17571	−	20.6062i	−0.126461	−	1.19771i
$297$	−26.5545	−	17.2879i	−1.54085	−	1.00314i
$298$	9.50474	−	0.333422i	0.550595	−	0.0193146i
$299$	−4.06980	+	3.41497i	−0.235363	+	0.197493i
$300$	17.0770	+	0.100441i	0.985944	+	0.00579894i
$301$	−0.883867	+	5.01266i	−0.0509452	+	0.288925i
$302$	13.4736	−	5.44616i	0.775317	−	0.313392i
$303$	10.3307	−	22.8213i	0.593482	−	1.31105i
$304$	−13.0050	+	4.23471i	−0.745889	+	0.242877i
$305$	1.86130	−	1.07462i	0.106578	−	0.0615327i
$306$	−8.99391	+	5.90761i	−0.514147	+	0.337716i
$307$	−15.1078	−	8.72250i	−0.862248	−	0.497819i	0.00251619	−	0.999997i	$-0.499199\pi$
$307$	−15.1078	−	8.72250i	−0.862248	−	0.497819i	−0.864765	+	0.502177i	$0.832532\pi$
$308$	3.35795	−	11.7246i	0.191337	−	0.668071i
$309$	8.01455	+	2.05110i	0.455932	+	0.116683i
$310$	−0.625353	+	0.800677i	−0.0355177	+	0.0454754i
$311$	−13.1215	−	11.0102i	−0.744051	−	0.624333i	0.189872	−	0.981809i	$-0.439193\pi$
$311$	−13.1215	−	11.0102i	−0.744051	−	0.624333i	−0.933922	+	0.357476i	$0.883637\pi$
$312$	4.02516	−	5.09163i	0.227880	−	0.288257i
$313$	−18.0562	−	6.57190i	−1.02059	−	0.371466i	−0.223102	−	0.974795i	$-0.571618\pi$
$313$	−18.0562	−	6.57190i	−1.02059	−	0.371466i	−0.797492	+	0.603329i	$0.793840\pi$
$314$	−8.26998	−	4.39554i	−0.466702	−	0.248055i
$315$	−0.497081	+	0.620230i	−0.0280074	+	0.0349460i
$316$	17.6203	−	11.8932i	0.991219	−	0.669044i
$317$	10.2751	−	1.81177i	0.577106	−	0.101759i	0.122526	−	0.992465i	$-0.460900\pi$
$317$	10.2751	−	1.81177i	0.577106	−	0.101759i	0.454580	+	0.890706i	$0.349789\pi$
$318$	2.30617	+	17.1607i	0.129324	+	0.962325i
$319$	−9.35187	−	25.6941i	−0.523604	−	1.43859i
$320$	2.11822	−	0.0759885i	0.118412	−	0.00424788i
$321$	6.25967	−	9.15739i	0.349381	−	0.511116i
$322$	−4.21379	+	3.79533i	−0.234825	+	0.211505i
$323$	8.67229			0.482539
$324$	−10.7314	−	14.4512i	−0.596190	−	0.802843i
$325$	6.53134			0.362293
$326$	15.0103	−	13.5197i	0.831345	−	0.748785i
$327$	−13.6079	+	19.9072i	−0.752518	+	1.10087i
$328$	0.408641	−	5.88407i	0.0225634	−	0.324894i
$329$	−3.54359	−	9.73592i	−0.195364	−	0.536759i
$330$	−0.527098	−	3.92225i	−0.0290158	−	0.215913i
$331$	26.9120	−	4.74531i	1.47922	−	0.260826i	0.624952	−	0.780663i	$-0.285118\pi$
$331$	26.9120	−	4.74531i	1.47922	−	0.260826i	0.854266	+	0.519837i	$0.174007\pi$
$332$	−3.01288	−	4.46373i	−0.165354	−	0.244979i
$333$	−21.7242	−	3.32827i	−1.19048	−	0.182388i
$334$	−9.41570	−	5.00450i	−0.515204	−	0.273834i
$335$	−1.32465	−	0.482134i	−0.0723734	−	0.0263418i
$336$	4.10342	−	5.58229i	0.223860	−	0.304539i
$337$	−11.9661	−	10.0408i	−0.651835	−	0.546955i	0.255792	−	0.966732i	$-0.417664\pi$
$337$	−11.9661	−	10.0408i	−0.651835	−	0.546955i	−0.907627	+	0.419777i	$0.862108\pi$
$338$	−9.78853	+	12.5328i	−0.532426	+	0.681697i
$339$	1.76256	+	0.451078i	0.0957290	+	0.0244992i
$340$	−1.29202	−	0.370038i	−0.0700699	−	0.0200682i
$341$	−14.3190	−	8.26711i	−0.775420	−	0.447689i
$342$	0.834753	+	14.4827i	0.0451383	+	0.783136i
$343$	−0.866025	+	0.500000i	−0.0467610	+	0.0269975i
$344$	−3.97484	−	13.8371i	−0.214309	−	0.746044i
$345$	−0.758887	+	1.67644i	−0.0408571	+	0.0902566i
$346$	32.4132	−	13.1018i	1.74254	−	0.704355i
$347$	−0.759626	+	4.30805i	−0.0407789	+	0.231268i	−0.998385	−	0.0568127i	$-0.981906\pi$
$347$	−0.759626	+	4.30805i	−0.0407789	+	0.231268i	0.957606	+	0.288081i	$0.0930173\pi$
$348$	0.0913565	−	15.5326i	0.00489722	−	0.832633i
$349$	−19.1646	+	16.0810i	−1.02586	+	0.860799i	−0.990353	−	0.138571i	$-0.955749\pi$
$349$	−19.1646	+	16.0810i	−1.02586	+	0.860799i	−0.0355075	+	0.999369i	$0.511305\pi$
$350$	6.96751	−	0.244417i	0.372429	−	0.0130647i
$351$	−4.13674	−	5.50271i	−0.220803	−	0.293713i
$352$	6.01702	+	33.9666i	0.320708	+	1.81043i
$353$	3.13979	+	3.74186i	0.167114	+	0.199159i	0.843102	−	0.537754i	$-0.180727\pi$
$353$	3.13979	+	3.74186i	0.167114	+	0.199159i	−0.675987	+	0.736913i	$0.736283\pi$
$354$	−4.45355	+	2.33360i	−0.236703	+	0.124029i
$355$	−1.92340	−	0.339148i	−0.102084	−	0.0180001i
$356$	6.98694	+	15.6795i	0.370307	+	0.831014i
$357$	−3.56994	+	2.56006i	−0.188941	+	0.135492i
$358$	−17.0440	+	3.62565i	−0.900805	+	0.191621i
$359$	−3.44207	−	5.96183i	−0.181665	−	0.314654i	0.760782	−	0.649007i	$-0.224815\pi$
$359$	−3.44207	−	5.96183i	−0.181665	−	0.314654i	−0.942448	+	0.334353i	$0.891482\pi$
$360$	0.493600	−	2.19330i	0.0260150	−	0.115597i
$361$	−3.65428	+	6.32940i	−0.192330	+	0.333126i
$362$	−0.853513	+	2.62826i	−0.0448597	+	0.138138i
$363$	43.6743	−	12.2309i	2.29231	−	0.641958i
$364$	1.55680	−	2.14418i	0.0815982	−	0.112385i
$365$	−1.28667	+	1.53340i	−0.0673476	+	0.0802618i
$366$	6.02596	+	18.9344i	0.314982	+	0.989717i
$367$	−11.5429	+	31.7138i	−0.602533	+	1.65544i	0.143591	+	0.989637i	$0.454135\pi$
$367$	−11.5429	+	31.7138i	−0.602533	+	1.65544i	−0.746124	+	0.665808i	$0.768087\pi$
$368$	5.99928	−	14.8759i	0.312734	−	0.775461i
$369$	−5.92542	−	2.00683i	−0.308465	−	0.104472i
$370$	−1.45497	−	2.32762i	−0.0756404	−	0.121007i
$371$	1.22749	+	6.96142i	0.0637279	+	0.361419i
$372$	−5.99504	−	7.23056i	−0.310829	−	0.374887i
$373$	2.63950	−	0.960699i	0.136668	−	0.0497431i	−0.272781	−	0.962076i	$-0.587943\pi$
$373$	2.63950	−	0.960699i	0.136668	−	0.0497431i	0.409449	+	0.912333i	$0.365721\pi$
$374$	3.04065	−	21.6603i	0.157228	−	1.12003i
$375$	4.10794	−	1.97215i	0.212133	−	0.101841i
$376$	21.0897	+	20.3467i	1.08762	+	1.04930i
$377$		−	5.94063i		−	0.305958i
$378$	−4.61892	−	5.71538i	−0.237571	−	0.293968i
$379$		−	12.9476i		−	0.665074i	−0.943090	−	0.332537i	$-0.892095\pi$
$379$		−	12.9476i		−	0.665074i	0.943090	−	0.332537i	$-0.107905\pi$
$380$	−1.30294	+	1.25904i	−0.0668395	+	0.0645871i
$381$	0.0975005	−	1.28023i	0.00499510	−	0.0655881i
$382$	−25.1149	−	3.52561i	−1.28499	−	0.180386i
$383$	11.1971	−	4.07539i	0.572143	−	0.208243i	−0.0397146	−	0.999211i	$-0.512645\pi$
$383$	11.1971	−	4.07539i	0.572143	−	0.208243i	0.611857	+	0.790968i	$0.290423\pi$
$384$	−3.50095	+	19.2806i	−0.178657	+	0.983911i
$385$	−0.280554	−	1.59110i	−0.0142984	−	0.0810901i
$386$	27.2713	−	17.0470i	1.38807	−	0.867672i
$387$	−15.2661	+	0.343682i	−0.776019	+	0.0174703i
$388$	15.6522	−	32.1177i	0.794621	−	1.63053i
$389$	8.44612	−	23.2055i	0.428235	−	1.17657i	−0.518648	−	0.854988i	$-0.673564\pi$
$389$	8.44612	−	23.2055i	0.428235	−	1.17657i	0.946883	−	0.321578i	$-0.104213\pi$
$390$	0.183844	−	0.839937i	0.00930928	−	0.0425318i
$391$	−6.53753	+	7.79113i	−0.330617	+	0.394014i
$392$	1.58052	−	2.34562i	0.0798283	−	0.118472i
$393$	28.1253	+	27.4992i	1.41873	+	1.38715i
$394$	33.5190	+	10.8851i	1.68866	+	0.548383i
$395$	1.40810	−	2.43889i	0.0708490	−	0.122714i
$396$	36.4653	+	2.99297i	1.83245	+	0.150402i
$397$	−17.8150	−	30.8565i	−0.894110	−	1.54864i	−0.834903	−	0.550398i	$-0.814476\pi$
$397$	−17.8150	−	30.8565i	−0.894110	−	1.54864i	−0.0592070	−	0.998246i	$-0.518857\pi$
$398$	4.39130	+	20.6433i	0.220116	+	1.03476i
$399$	0.582533	+	5.89364i	0.0291631	+	0.295051i
$400$	−17.4052	+	9.26866i	−0.870258	+	0.463433i
$401$	−20.7094	−	3.65163i	−1.03418	−	0.182354i	−0.369305	−	0.929308i	$-0.620404\pi$
$401$	−20.7094	−	3.65163i	−1.03418	−	0.182354i	−0.664875	+	0.746954i	$0.731515\pi$
$402$	6.97286	−	11.0104i	0.347775	−	0.549147i
$403$	−2.30907	−	2.75184i	−0.115023	−	0.137079i
$404$	2.02693	+	28.8549i	0.100844	+	1.43559i
$405$	−2.11662	−	1.09812i	−0.105176	−	0.0545662i
$406$	−0.222312	−	6.33735i	−0.0110331	−	0.314518i
$407$	34.2216	−	28.7154i	1.69630	−	1.42337i
$408$	5.89599	−	10.9373i	0.291895	−	0.541476i
$409$	0.530601	−	3.00919i	0.0262365	−	0.148795i	−0.968875	−	0.247549i	$-0.920375\pi$
$409$	0.530601	−	3.00919i	0.0262365	−	0.148795i	0.995112	+	0.0987546i	$0.0314859\pi$
$410$	−0.292819	−	0.724421i	−0.0144613	−	0.0357766i
$411$	0.185405	−	0.0183256i	0.00914534	−	0.000903934i
$412$	−9.26818	+	2.31394i	−0.456610	+	0.114000i
$413$	−1.77763	+	1.02632i	−0.0874715	+	0.0505017i
$414$	−13.6405	−	10.1677i	−0.670392	−	0.499717i
$415$	−0.617842	−	0.356711i	−0.0303287	−	0.0175103i
$416$	−1.29557	+	7.38175i	−0.0635204	+	0.361920i
$417$	11.8402	−	12.1098i	0.579818	−	0.593019i
$418$	−23.2392	−	18.1505i	−1.13667	−	0.887772i
$419$	5.30321	+	4.44992i	0.259079	+	0.217393i	0.763070	−	0.646316i	$-0.223691\pi$
$419$	5.30321	+	4.44992i	0.259079	+	0.217393i	−0.503991	+	0.863709i	$0.668136\pi$
$420$	0.164689	−	0.902909i	0.00803598	−	0.0440574i
$421$	3.73412	+	1.35911i	0.181990	+	0.0662389i	0.431408	−	0.902157i	$-0.358017\pi$
$421$	3.73412	+	1.35911i	0.181990	+	0.0662389i	−0.249418	+	0.968396i	$0.580239\pi$
$422$	−6.59251	+	12.4035i	−0.320919	+	0.603791i
$423$	26.5614	−	16.1430i	1.29146	−	0.784901i
$424$	−11.7597	−	16.1696i	−0.571099	−	0.785264i
$425$	12.3135	−	2.17120i	0.597291	−	0.105319i
$426$	6.86510	−	16.7006i	0.332615	−	0.809146i
$427$	2.77445	+	7.62275i	0.134265	+	0.368891i
$428$	−1.33480	+	12.7387i	−0.0645200	+	0.615746i
$429$	13.9529	+	1.06263i	0.673652	+	0.0513045i
$430$	−1.27638	−	1.41711i	−0.0615523	−	0.0683390i
$431$	−15.4450			−0.743958			−0.371979	−	0.928241i	$-0.621321\pi$
$431$	−15.4450			−0.743958			−0.371979	+	0.928241i	$0.621321\pi$
$432$	18.8328	+	8.79354i	0.906093	+	0.423079i
$433$	−32.8075			−1.57663			−0.788315	−	0.615272i	$-0.789046\pi$
$433$	−32.8075			−1.57663			−0.788315	+	0.615272i	$0.789046\pi$
$434$	−2.56625	−	2.84920i	−0.123184	−	0.136766i
$435$	−0.890551	−	1.85500i	−0.0426987	−	0.0889403i
$436$	2.90172	−	27.6925i	0.138967	−	1.32623i
$437$	4.68956	+	12.8845i	0.224332	+	0.616348i
$438$	−11.3053	−	14.6516i	−0.540186	−	0.700082i
$439$	−36.4354	+	6.42454i	−1.73897	+	0.306627i	−0.951023	−	0.309121i	$-0.899965\pi$
$439$	−36.4354	+	6.42454i	−1.73897	+	0.306627i	−0.787943	+	0.615748i	$0.788854\pi$
$440$	2.68779	+	3.69572i	0.128135	+	0.176187i
$441$	−1.97960	−	2.25415i	−0.0942666	−	0.107340i
$442$	2.23032	−	4.19622i	0.106085	−	0.199594i
$443$	−15.7559	−	5.73469i	−0.748587	−	0.272464i	−0.0605762	−	0.998164i	$-0.519294\pi$
$443$	−15.7559	−	5.73469i	−0.748587	−	0.272464i	−0.688011	+	0.725700i	$0.741516\pi$
$444$	23.8978	−	8.53924i	1.13414	−	0.405254i
$445$	1.74200	+	1.46171i	0.0825787	+	0.0692918i
$446$	0.368319	+	0.287668i	0.0174404	+	0.0136215i
$447$	3.14117	+	11.2165i	0.148572	+	0.530522i
$448$	−1.10584	+	7.92320i	−0.0522462	+	0.374336i
$449$	−26.0115	−	15.0177i	−1.22756	−	0.708731i	−0.261040	−	0.965328i	$-0.584065\pi$
$449$	−26.0115	−	15.0177i	−1.22756	−	0.708731i	−0.966519	+	0.256597i	$0.917399\pi$
$450$	4.81114	+	20.3545i	0.226799	+	0.959521i
$451$	11.0127	−	6.35821i	0.518570	−	0.299396i
$452$	−2.03825	+	0.508881i	−0.0958714	+	0.0239357i
$453$	10.3724	+	14.4641i	0.487338	+	0.679583i
$454$	4.19288	+	10.3730i	0.196781	+	0.486829i
$455$	0.0609541	−	0.345688i	0.00285757	−	0.0162061i
$456$	−8.79521	−	14.2562i	−0.411874	−	0.667607i
$457$	27.4429	−	23.0274i	1.28373	−	1.07717i	0.291008	−	0.956721i	$-0.406009\pi$
$457$	27.4429	−	23.0274i	1.28373	−	1.07717i	0.992719	−	0.120454i	$-0.0384351\pi$
$458$	−0.866190	−	24.6921i	−0.0404744	−	1.15379i
$459$	−9.62821	−	8.99905i	−0.449406	−	0.420040i
$460$	−0.148897	−	2.11967i	−0.00694238	−	0.0988300i
$461$	25.4939	+	30.3824i	1.18737	+	1.41505i	0.887338	+	0.461120i	$0.152552\pi$
$461$	25.4939	+	30.3824i	1.18737	+	1.41505i	0.300030	+	0.953930i	$0.403003\pi$
$462$	14.9245	+	0.611450i	0.694348	+	0.0284472i
$463$	−3.78973	−	0.668232i	−0.176124	−	0.0310554i	0.0848906	−	0.996390i	$-0.472946\pi$
$463$	−3.78973	−	0.668232i	−0.176124	−	0.0310554i	−0.261014	+	0.965335i	$0.584057\pi$
$464$	8.43038	+	15.8310i	0.391371	+	0.734936i
$465$	−1.13354	−	0.513130i	−0.0525669	−	0.0237958i
$466$	2.93650	+	13.8044i	0.136031	+	0.639475i
$467$	−16.7389	−	28.9926i	−0.774584	−	1.34162i	−0.935028	−	0.354573i	$-0.884626\pi$
$467$	−16.7389	−	28.9926i	−0.774584	−	1.34162i	0.160445	−	0.987045i	$-0.448707\pi$
$468$	7.22237	+	3.32072i	0.333854	+	0.153500i
$469$	2.66027	−	4.60772i	0.122840	−	0.212765i
$470$	3.69228	+	1.19905i	0.170312	+	0.0553079i
$471$	2.84388	−	11.1123i	0.131039	−	0.512026i
$472$	3.24423	−	4.81470i	0.149328	−	0.221615i
$473$	19.9513	−	23.7770i	0.917361	−	1.09327i
$474$	19.2431	+	17.5382i	0.883864	+	0.805555i
$475$	5.76521	−	15.8398i	0.264526	−	0.726779i
$476$	2.22223	−	4.55992i	0.101856	−	0.209003i
$477$	−19.7592	+	7.69970i	−0.904713	+	0.352545i
$478$	−30.8239	+	19.2677i	−1.40985	+	0.881285i
$479$	2.28613	+	12.9653i	0.104456	+	0.592400i	0.991436	+	0.130592i	$0.0416879\pi$
$479$	2.28613	+	12.9653i	0.104456	+	0.592400i	−0.886980	+	0.461808i	$0.847201\pi$
$480$	0.702040	+	2.49921i	0.0320436	+	0.114073i
$481$	9.12049	−	3.31959i	0.415859	−	0.151360i
$482$	−29.0872	−	4.08324i	−1.32489	−	0.185986i
$483$	−5.73394	−	3.91953i	−0.260903	−	0.178345i
$484$	−37.6610	+	36.3919i	−1.71186	+	1.65418i
$485$		−	4.73311i		−	0.214919i
$486$	14.1016	−	16.9453i	0.639664	−	0.768655i
$487$			25.5869i			1.15945i	0.814811	+	0.579727i	$0.196841\pi$
$487$			25.5869i			1.15945i	−0.814811	+	0.579727i	$0.803159\pi$
$488$	−16.5122	−	15.9304i	−0.747471	−	0.721137i
$489$	20.4254	+	13.9621i	0.923668	+	0.631388i
$490$	0.0520882	−	0.371054i	0.00235311	−	0.0167625i
$491$	−32.0106	+	11.6509i	−1.44462	+	0.525798i	−0.941083	−	0.338176i	$-0.890190\pi$
$491$	−32.0106	+	11.6509i	−1.44462	+	0.525798i	−0.503536	+	0.863974i	$0.667968\pi$
$492$	7.12135	−	1.21254i	0.321055	−	0.0546657i
$493$	−1.97483	−	11.1998i	−0.0889419	−	0.504415i
$494$	−3.39580	−	5.43249i	−0.152784	−	0.244419i
$495$	4.51617	−	1.75984i	0.202987	−	0.0790991i
$496$	10.0585	+	4.05648i	0.451640	+	0.182141i
$497$	2.52122	−	6.92700i	0.113092	−	0.310718i
$498$	4.44292	−	4.87483i	0.199092	−	0.218446i
$499$	−10.8209	+	12.8959i	−0.484411	+	0.577299i	−0.951787	−	0.306760i	$-0.900755\pi$
$499$	−10.8209	+	12.8959i	−0.484411	+	0.577299i	0.467376	+	0.884059i	$0.345200\pi$
$500$	−3.09143	+	4.25783i	−0.138253	+	0.190416i
$501$	3.23787	−	12.6517i	0.144657	−	0.565238i
$502$	10.3411	−	31.8438i	0.461546	−	1.42126i
$503$	4.15479	−	7.19631i	0.185253	−	0.320868i	−0.758409	−	0.651779i	$-0.774023\pi$
$503$	4.15479	−	7.19631i	0.185253	−	0.320868i	0.943662	+	0.330912i	$0.107356\pi$
$504$	7.82896	+	3.27221i	0.348730	+	0.145756i
$505$	1.91597	+	3.31856i	0.0852595	+	0.147674i
$506$	33.8250	−	7.19534i	1.50371	−	0.319872i
$507$	−17.7432	−	8.03192i	−0.788001	−	0.356710i
$508$	0.603441	+	1.35420i	0.0267734	+	0.0600827i
$509$	−12.8218	−	2.26082i	−0.568315	−	0.100209i	−0.117895	−	0.993026i	$-0.537615\pi$
$509$	−12.8218	−	2.26082i	−0.568315	−	0.100209i	−0.450420	+	0.892817i	$0.648726\pi$
$510$	0.0673804	−	1.64464i	0.00298365	−	0.0728259i
$511$	−4.85634	−	5.78756i	−0.214832	−	0.256026i
$512$	−7.02297	−	21.5099i	−0.310375	−	0.950614i
$513$	−16.9967	+	5.17516i	−0.750421	+	0.228489i
$514$	34.0056	−	1.19290i	1.49992	−	0.0526167i
$515$	−0.969412	+	0.813434i	−0.0427174	+	0.0358442i
$516$	15.3215	−	8.72615i	0.674493	−	0.384147i
$517$	−10.9711	+	62.2200i	−0.482507	+	2.73643i
$518$	9.60534	−	3.88258i	0.422035	−	0.170591i
$519$	24.9527	+	34.7961i	1.09530	+	1.52738i
$520$	0.274117	+	0.954245i	0.0120208	+	0.0418464i
$521$	−36.1611	+	20.8776i	−1.58425	+	0.914666i	−0.590019	+	0.807389i	$0.700880\pi$
$521$	−36.1611	+	20.8776i	−1.58425	+	0.914666i	−0.994229	+	0.107277i	$0.965787\pi$
$522$	18.5136	−	4.37601i	0.810319	−	0.191533i
$523$	−24.8984	−	14.3751i	−1.08873	−	0.628578i	−0.155492	−	0.987837i	$-0.549696\pi$
$523$	−24.8984	−	14.3751i	−1.08873	−	0.628578i	−0.933238	+	0.359259i	$0.883030\pi$
$524$	−43.6645	−	12.5056i	−1.90749	−	0.546310i
$525$	2.30265	+	8.22233i	0.100496	+	0.358852i
$526$	12.3684	−	15.8360i	0.539287	−	0.690481i
$527$	−5.26805	−	4.42042i	−0.229480	−	0.192557i
$528$	−38.6906	+	16.9688i	−1.68379	+	0.738474i
$529$	6.50242	+	2.36669i	0.282714	+	0.102899i
$530$	−2.33880	−	1.24309i	−0.101591	−	0.0539962i
$531$	−4.06339	−	4.62694i	−0.176336	−	0.200792i
$532$	−3.82587	−	5.66820i	−0.165872	−	0.245748i
$533$	2.72083	−	0.479756i	0.117852	−	0.0207805i
$534$	−16.6448	+	12.8432i	−0.720291	+	0.555780i
$535$	0.580332	+	1.59445i	0.0250899	+	0.0689340i
$536$	−1.04260	+	15.0126i	−0.0450336	+	0.648446i
$537$	−9.23649	−	19.2394i	−0.398584	−	0.830241i
$538$	15.0645	−	13.5684i	0.649476	−	0.584977i
$539$	6.09799			0.262659
$540$	2.75303	−	0.0457801i	0.118472	−	0.00197006i
$541$	16.1185			0.692990			0.346495	−	0.938052i	$-0.387372\pi$
$541$	16.1185			0.692990			0.346495	+	0.938052i	$0.387372\pi$
$542$	19.8936	−	17.9180i	0.854504	−	0.769645i
$543$	−3.37466	−	0.257010i	−0.144820	−	0.0110293i
$544$	0.0113800	+	14.3474i	0.000487913	+	0.615142i
$545$	−1.26158	−	3.46617i	−0.0540402	−	0.148474i
$546$	3.00155	+	1.23384i	0.128454	+	0.0528037i
$547$	−27.6779	+	4.88035i	−1.18342	+	0.208669i	−0.730519	−	0.682892i	$-0.760722\pi$
$547$	−27.6779	+	4.88035i	−1.18342	+	0.208669i	−0.452901	+	0.891561i	$0.649611\pi$
$548$	−0.178313	+	0.120356i	−0.00761714	+	0.00514134i
$549$	−20.7963	+	12.6392i	−0.887564	+	0.539428i
$550$	−37.5408	−	19.9531i	−1.60074	−	0.850805i
$551$	−14.4072	−	5.24380i	−0.613768	−	0.223393i
$552$	19.4379	+	2.84534i	0.827330	+	0.121106i
$553$	8.14247	+	6.83234i	0.346253	+	0.290541i
$554$	−5.92413	+	7.58502i	−0.251692	+	0.322257i
$555$	2.35029	−	2.40380i	0.0997644	−	0.102036i
$556$	−5.38449	+	18.8005i	−0.228353	+	0.797318i
$557$	−1.80737	−	1.04349i	−0.0765807	−	0.0442139i	0.461221	−	0.887285i	$-0.347412\pi$
$557$	−1.80737	−	1.04349i	−0.0765807	−	0.0442139i	−0.537801	+	0.843072i	$0.680745\pi$
$558$	6.87503	−	9.22314i	0.291043	−	0.390447i
$559$	5.84009	−	3.37178i	0.247010	−	0.142611i
$560$	0.328133	+	1.00771i	0.0138661	+	0.0425836i
$561$	26.6585	−	2.63495i	1.12552	−	0.111248i
$562$	−26.7417	+	10.8093i	−1.12803	+	0.455962i
$563$	−6.88053	+	39.0214i	−0.289980	+	1.64456i	0.396955	+	0.917838i	$0.370067\pi$
$563$	−6.88053	+	39.0214i	−0.289980	+	1.64456i	−0.686935	+	0.726719i	$0.741044\pi$
$564$	−18.1279	+	30.9762i	−0.763320	+	1.30433i
$565$	−0.213193	+	0.178890i	−0.00896909	+	0.00752596i
$566$	20.4139	−	0.716111i	0.858060	−	0.0301004i
$567$	5.46896	−	7.14776i	0.229675	−	0.300178i
$568$	2.18928	+	20.7347i	0.0918601	+	0.870007i
$569$	11.8867	+	14.1660i	0.498316	+	0.593870i	0.955312	−	0.295599i	$-0.0955192\pi$
$569$	11.8867	+	14.1660i	0.498316	+	0.593870i	−0.456996	+	0.889469i	$0.651075\pi$
$570$	−1.87473	−	1.18727i	−0.0785240	−	0.0497292i
$571$	−12.1340	−	2.13955i	−0.507793	−	0.0895375i	−0.0861183	−	0.996285i	$-0.527446\pi$
$571$	−12.1340	−	2.13955i	−0.507793	−	0.0895375i	−0.421674	+	0.906747i	$0.638557\pi$
$572$	−14.7590	+	6.57676i	−0.617107	+	0.274988i
$573$	−3.05520	−	30.9103i	−0.127633	−	1.29130i
$574$	2.88458	−	0.613615i	0.120400	−	0.0256118i
$575$	9.88431	+	17.1201i	0.412204	+	0.713958i
$576$	−23.9591	+	1.40002i	−0.998297	+	0.0583342i
$577$	6.34486	−	10.9896i	0.264140	−	0.457504i	−0.703198	−	0.710994i	$-0.748245\pi$
$577$	6.34486	−	10.9896i	0.264140	−	0.457504i	0.967338	+	0.253490i	$0.0815786\pi$
$578$	−4.61579	+	14.2136i	−0.191991	+	0.591208i
$579$	28.1639	+	27.5370i	1.17045	+	1.14440i
$580$	1.92268	+	1.39598i	0.0798350	+	0.0579649i
$581$	1.73083	−	2.06272i	0.0718069	−	0.0855761i
$582$	42.7465	+	9.35626i	1.77190	+	0.387830i
$583$	14.7430	−	40.5060i	0.610591	−	1.67759i
$584$	19.5258	+	8.68231i	0.807983	+	0.359276i
$585$	1.05279	−	0.0237013i	0.0435277	−	0.000979929i
$586$	5.87714	+	9.40206i	0.242782	+	0.388396i
$587$	−2.08154	−	11.8050i	−0.0859142	−	0.487244i	−0.997156	−	0.0753709i	$-0.975986\pi$
$587$	−2.08154	−	11.8050i	−0.0859142	−	0.487244i	0.911241	−	0.411873i	$-0.135125\pi$
$588$	3.24817	+	1.20392i	0.133952	+	0.0496487i
$589$	−8.71197	+	3.17090i	−0.358971	+	0.130655i
$590$	0.106918	−	0.761638i	0.00440174	−	0.0313561i
$591$	−3.27771	+	43.0379i	−0.134827	+	1.77034i
$592$	−19.5941	+	21.7892i	−0.805311	+	0.895531i
$593$			40.6594i			1.66968i	0.550491	+	0.834841i	$0.314440\pi$
$593$			40.6594i			1.66968i	−0.550491	+	0.834841i	$0.685560\pi$
$594$	6.96639	+	44.2661i	0.285835	+	1.81626i
$595$		−	0.671985i		−	0.0275487i
$596$	−9.34622	−	9.67215i	−0.382836	−	0.396187i
$597$	−23.3023	+	11.1870i	−0.953699	+	0.457854i
$598$	7.44041	+	1.04448i	0.304261	+	0.0427119i
$599$	−28.5266	+	10.3828i	−1.16556	+	0.424231i	−0.851082	−	0.525033i	$-0.824053\pi$
$599$	−28.5266	+	10.3828i	−1.16556	+	0.424231i	−0.314482	+	0.949263i	$0.601831\pi$
$600$	−16.0572	−	18.0399i	−0.655532	−	0.736475i
$601$	0.780474	+	4.42629i	0.0318362	+	0.180552i	0.996579	−	0.0826411i	$-0.0263355\pi$
$601$	0.780474	+	4.42629i	0.0318362	+	0.180552i	−0.964743	+	0.263193i	$0.915224\pi$
$602$	6.10392	−	3.81550i	0.248777	−	0.155508i
$603$	15.1181	+	5.12023i	0.615656	+	0.208512i
$604$	−18.4751	−	9.00366i	−0.751742	−	0.366354i
$605$	−2.37286	+	6.51939i	−0.0964706	+	0.265051i
$606$	−33.7586	+	10.7438i	−1.37135	+	0.436438i
$607$	−16.8343	+	20.0623i	−0.683283	+	0.814305i	−0.990526	−	0.137326i	$-0.956149\pi$
$607$	−16.8343	+	20.0623i	−0.683283	+	0.814305i	0.307243	+	0.951631i	$0.400594\pi$
$608$	16.7586	+	9.65788i	0.679652	+	0.391679i
$609$	7.47868	−	2.09440i	0.303052	−	0.0848692i
$610$	−2.89088	−	0.938795i	−0.117048	−	0.0380107i
$611$	−6.86331	+	11.8876i	−0.277660	+	0.480921i
$612$	14.7202	+	3.85961i	0.595028	+	0.156016i
$613$	10.5256	+	18.2308i	0.425124	+	0.736336i	0.996432	−	0.0843998i	$-0.0268973\pi$
$613$	10.5256	+	18.2308i	0.425124	+	0.736336i	−0.571308	+	0.820735i	$0.693564\pi$
$614$	5.13321	+	24.1310i	0.207159	+	0.973849i
$615$	0.777677	−	0.557683i	0.0313590	−	0.0224879i
$616$	−15.4986	+	7.56828i	−0.624455	+	0.304935i
$617$	25.0600	+	4.41876i	1.00888	+	0.177893i	0.653578	−	0.756859i	$-0.273267\pi$
$617$	25.0600	+	4.41876i	1.00888	+	0.177893i	0.355301	+	0.934752i	$0.384378\pi$
$618$	−5.43013	−	10.3631i	−0.218432	−	0.416865i
$619$	2.18822	+	2.60782i	0.0879521	+	0.104817i	0.808226	−	0.588873i	$-0.200428\pi$
$619$	2.18822	+	2.60782i	0.0879521	+	0.104817i	−0.720274	+	0.693690i	$0.755984\pi$
$620$	1.43324	−	0.100679i	0.0575601	−	0.00404335i
$621$	8.16346	−	19.1709i	0.327588	−	0.769304i
$622$	0.849242	+	24.2090i	0.0340515	+	0.970692i
$623$	−6.57489	+	5.51699i	−0.263417	+	0.221033i
$624$	−9.16001	+	0.589332i	−0.366694	+	0.0235922i
$625$	4.15922	−	23.5881i	0.166369	−	0.943523i
$626$	10.1836	+	25.1937i	0.407017	+	1.00694i
$627$	14.8933	−	32.9005i	0.594782	−	1.31392i
$628$	3.20830	+	12.8504i	0.128025	+	0.512788i
$629$	16.0913	−	9.29029i	0.641601	−	0.370428i
$630$	1.12221	−	0.0646821i	0.0447101	−	0.00257700i
$631$	21.6819	+	12.5180i	0.863142	+	0.498335i	0.865063	−	0.501663i	$-0.167278\pi$
$631$	21.6819	+	12.5180i	0.863142	+	0.498335i	−0.00192146	+	0.999998i	$0.500612\pi$
$632$	−29.1745	−	7.25926i	−1.16050	−	0.288758i
$633$	−16.6664	−	4.26530i	−0.662429	−	0.169530i
$634$	−11.6288	−	9.08244i	−0.461839	−	0.360710i
$635$	0.150451	+	0.126244i	0.00597048	+	0.00500983i
$636$	15.8500	−	18.6653i	0.628495	−	0.740127i
$637$	1.24497	+	0.453131i	0.0493274	+	0.0179537i
$638$	−18.1485	+	34.1455i	−0.718507	+	1.35183i
$639$	21.8596	+	3.34903i	0.864753	+	0.132485i
$640$	−2.08466	−	2.15394i	−0.0824034	−	0.0851418i
$641$	24.2742	−	4.28020i	0.958773	−	0.169058i	0.327701	−	0.944781i	$-0.393726\pi$
$641$	24.2742	−	4.28020i	0.958773	−	0.169058i	0.631072	+	0.775724i	$0.282615\pi$
$642$	−15.5473	+	2.08934i	−0.613601	+	0.0824597i
$643$	7.65457	+	21.0308i	0.301867	+	0.829372i	0.994176	+	0.107771i	$0.0343713\pi$
$643$	7.65457	+	21.0308i	0.301867	+	0.829372i	−0.692309	+	0.721601i	$0.743406\pi$
$644$	7.97637	+	0.835792i	0.314313	+	0.0329348i
$645$	1.31815	−	1.92834i	0.0519019	−	0.0759283i
$646$	−8.20798	−	9.11297i	−0.322939	−	0.358545i
$647$	8.04045			0.316103			0.158051	−	0.987431i	$-0.449479\pi$
$647$	8.04045			0.316103			0.158051	+	0.987431i	$0.449479\pi$
$648$	−5.02866	+	24.9542i	−0.197544	+	0.980294i
$649$	12.5169			0.491333
$650$	−6.18165	−	6.86323i	−0.242464	−	0.269198i
$651$	2.65023	−	3.87707i	0.103871	−	0.151954i
$652$	−28.4133	−	2.97725i	−1.11275	−	0.116598i
$653$	−9.14893	−	25.1365i	−0.358025	−	0.983667i	−0.979714	−	0.200402i	$-0.935775\pi$
$653$	−9.14893	−	25.1365i	−0.358025	−	0.983667i	0.621688	−	0.783265i	$-0.286447\pi$
$654$	33.7982	−	4.54202i	1.32161	−	0.177607i
$655$	−5.92555	+	1.04484i	−0.231531	+	0.0408251i
$656$	−6.56984	+	5.13964i	−0.256509	+	0.200669i
$657$	14.1745	−	17.6862i	0.553001	−	0.690004i
$658$	−6.87679	+	12.9383i	−0.268085	+	0.504388i
$659$	−14.9464	−	5.44006i	−0.582230	−	0.211915i	0.0340784	−	0.999419i	$-0.489150\pi$
$659$	−14.9464	−	5.44006i	−0.582230	−	0.211915i	−0.616309	+	0.787505i	$0.711373\pi$
$660$	−3.62269	+	4.26614i	−0.141013	+	0.166059i
$661$	21.5030	+	18.0432i	0.836371	+	0.701798i	0.956744	−	0.290930i	$-0.0939648\pi$
$661$	21.5030	+	18.0432i	0.836371	+	0.701798i	−0.120374	+	0.992729i	$0.538409\pi$
$662$	−30.4576	−	23.7883i	−1.18377	−	0.924559i
$663$	5.63841	+	1.44300i	0.218978	+	0.0560413i
$664$	−1.83898	+	7.39073i	−0.0713663	+	0.286816i
$665$	−0.784557	−	0.452964i	−0.0304238	−	0.0175652i
$666$	17.0637	+	25.9782i	0.661203	+	1.00663i
$667$	15.5717	−	8.99035i	0.602940	−	0.348108i
$668$	3.65278	+	14.6307i	0.141330	+	0.566079i
$669$	−0.236045	+	0.521441i	−0.00912601	+	0.0201601i
$670$	0.747096	+	1.84828i	0.0288629	+	0.0714054i
$671$	8.58980	−	48.7152i	0.331605	−	1.88063i
$672$	−9.74968	+	0.971477i	−0.376102	+	0.0374755i
$673$	23.4607	−	19.6859i	0.904343	−	0.758834i	−0.0666911	−	0.997774i	$-0.521244\pi$
$673$	23.4607	−	19.6859i	0.904343	−	0.758834i	0.971034	+	0.238939i	$0.0767998\pi$
$674$	0.774464	+	22.0773i	0.0298313	+	0.850388i
$675$	−22.8373	+	11.6033i	−0.879008	+	0.446612i
$676$	22.4342	−	1.57590i	0.862853	−	0.0606116i
$677$	20.6266	+	24.5819i	0.792746	+	0.944758i	0.999434	−	0.0336493i	$-0.0107129\pi$
$677$	20.6266	+	24.5819i	0.792746	+	0.944758i	−0.206688	+	0.978407i	$0.566268\pi$
$678$	−1.19419	−	2.27905i	−0.0458626	−	0.0875264i
$679$	17.5929	+	3.10211i	0.675154	+	0.119048i
$680$	0.834008	+	1.70791i	0.0319827	+	0.0654952i
$681$	−11.1356	+	7.98548i	−0.426716	+	0.306004i
$682$	4.86521	+	22.8712i	0.186298	+	0.875782i
$683$	−16.9029	−	29.2766i	−0.646770	−	1.12024i	−0.983890	−	0.178776i	$-0.942786\pi$
$683$	−16.9029	−	29.2766i	−0.646770	−	1.12024i	0.337120	−	0.941462i	$-0.390547\pi$
$684$	14.4286	−	14.5845i	0.551691	−	0.557652i
$685$	−0.0142495	+	0.0246809i	−0.000544447	+	0.000943010i
$686$	1.34507	+	0.436803i	0.0513549	+	0.0166772i
$687$	29.1391	−	8.16036i	1.11172	−	0.311337i
$688$	−10.7782	+	17.2731i	−0.410914	+	0.658529i
$689$	6.01986	−	7.17419i	0.229338	−	0.273315i
$690$	2.47989	−	0.789236i	0.0944077	−	0.0300457i
$691$	14.5733	−	40.0399i	0.554396	−	1.52319i	−0.273253	−	0.961942i	$-0.588099\pi$
$691$	14.5733	−	40.0399i	0.554396	−	1.52319i	0.827648	−	0.561247i	$-0.189678\pi$
$692$	−44.4453	−	21.6600i	−1.68956	−	0.823389i
$693$	3.58140	+	17.9400i	0.136046	+	0.681484i
$694$	5.24593	−	3.27918i	0.199133	−	0.124476i
$695$	0.449871	+	2.55134i	0.0170646	+	0.0967780i
$696$	−16.4083	+	14.6050i	−0.621956	+	0.553599i
$697$	4.97008	−	1.80896i	0.188255	−	0.0685193i
$698$	35.0368	+	4.91843i	1.32616	+	0.186165i
$699$	−15.5824	+	7.48085i	−0.589382	+	0.282952i
$700$	−6.85131	−	7.09023i	−0.258955	−	0.267986i
$701$			16.4373i			0.620827i	0.950602	+	0.310413i	$0.100467\pi$
$701$			16.4373i			0.620827i	−0.950602	+	0.310413i	$0.899533\pi$
$702$	−1.86708	+	9.55504i	−0.0704683	+	0.360632i
$703$		−	25.0492i		−	0.944749i
$704$	29.9978	−	38.4708i	1.13058	−	1.44992i
$705$	−0.361057	+	4.74085i	−0.0135982	+	0.178551i
$706$	0.960314	−	6.84087i	0.0361419	−	0.257459i
$707$	−13.5908	+	4.94664i	−0.511134	+	0.186038i
$708$	6.66729	+	2.47120i	0.250572	+	0.0928733i
$709$	−0.119477	−	0.677587i	−0.00448705	−	0.0254473i	0.982482	−	0.186357i	$-0.0596682\pi$
$709$	−0.119477	−	0.677587i	−0.00448705	−	0.0254473i	−0.986969	+	0.160910i	$0.948557\pi$
$710$	1.46404	+	2.34213i	0.0549446	+	0.0878987i
$711$	−15.3183	+	27.9674i	−0.574480	+	1.04886i
$712$	9.86343	−	22.1820i	0.369648	−	0.831307i
$713$	3.71873	−	10.2171i	0.139268	−	0.382635i
$714$	6.06895	+	1.32836i	0.227125	+	0.0497126i
$715$	−1.37590	+	1.63973i	−0.0514557	+	0.0613226i
$716$	19.9414	+	14.4786i	0.745245	+	0.541091i
$717$	−31.8328	−	31.1242i	−1.18882	−	1.16235i
$718$	−3.00701	+	9.25961i	−0.112221	+	0.345566i
$719$	20.4826	−	35.4769i	0.763871	−	1.32306i	−0.176970	−	0.984216i	$-0.556630\pi$
$719$	20.4826	−	35.4769i	0.763871	−	1.32306i	0.940841	−	0.338848i	$-0.110037\pi$
$720$	−2.77192	+	1.55719i	−0.103304	+	0.0580329i
$721$	−2.38817	−	4.13643i	−0.0889400	−	0.154049i
$722$	10.1097	−	2.15055i	0.376242	−	0.0800352i
$723$	−3.53843	−	35.7993i	−0.131596	−	1.33139i
$724$	3.56963	−	1.59066i	0.132664	−	0.0591165i
$725$	−21.7691	−	3.83848i	−0.808485	−	0.142558i
$726$	−54.1885	−	34.3176i	−2.01112	−	1.27364i
$727$	0.296828	+	0.353746i	0.0110087	+	0.0131197i	0.771521	−	0.636204i	$-0.219496\pi$
$727$	0.296828	+	0.353746i	0.0110087	+	0.0131197i	−0.760512	+	0.649324i	$0.775052\pi$
$728$	−3.72658	+	0.393472i	−0.138116	+	0.0145831i
$729$	24.2403	+	11.8915i	0.897789	+	0.440425i
$730$	2.82911	−	0.0992439i	0.104710	−	0.00367318i
$731$	9.88941	−	8.29820i	0.365773	−	0.306920i
$732$	14.1932	−	24.2528i	0.524596	−	0.896410i
$733$	1.18163	−	6.70137i	0.0436446	−	0.247521i	−0.955178	−	0.296032i	$-0.904337\pi$
$733$	1.18163	−	6.70137i	0.0436446	−	0.247521i	0.998823	+	0.0485111i	$0.0154476\pi$
$734$	44.2502	−	17.8864i	1.63330	−	0.660199i
$735$	0.456677	−	0.0451384i	0.0168448	−	0.00166496i
$736$	−21.3099	+	7.77533i	−0.785494	+	0.286602i
$737$	−28.0979	+	16.2223i	−1.03500	+	0.597557i
$738$	3.49936	+	8.12591i	0.128813	+	0.299119i
$739$	31.0508	+	17.9272i	1.14222	+	0.659462i	0.946980	−	0.321293i	$-0.104118\pi$
$739$	31.0508	+	17.9272i	1.14222	+	0.659462i	0.195242	+	0.980755i	$0.437451\pi$
$740$	−1.06883	+	3.73191i	−0.0392908	+	0.137188i
$741$	5.48541	−	5.61029i	0.201512	−	0.206099i
$742$	6.15340	−	7.87857i	0.225898	−	0.289231i
$743$	9.19653	+	7.71681i	0.337388	+	0.283102i	0.795702	−	0.605688i	$-0.207102\pi$
$743$	9.19653	+	7.71681i	0.337388	+	0.283102i	−0.458314	+	0.888790i	$0.651547\pi$
$744$	−1.92391	+	13.1431i	−0.0705340	+	0.481850i
$745$	−1.67432	−	0.609402i	−0.0613423	−	0.0223268i
$746$	−3.50770	−	1.86436i	−0.128426	−	0.0682591i
$747$	7.08495	+	3.88056i	0.259225	+	0.141982i
$748$	−25.6388	+	17.3054i	−0.937448	+	0.632749i
$749$	−6.30690	+	1.11208i	−0.230449	+	0.0406344i
$750$	−5.96037	−	2.45013i	−0.217642	−	0.0894659i
$751$	−18.1675	−	49.9147i	−0.662940	−	1.82141i	−0.563064	−	0.826413i	$-0.690378\pi$
$751$	−18.1675	−	49.9147i	−0.662940	−	1.82141i	−0.0998762	−	0.995000i	$-0.531845\pi$
$752$	1.42006	−	41.4187i	0.0517842	−	1.51038i
$753$	40.8871	+	3.11391i	1.49001	+	0.113477i
$754$	−6.24251	+	5.62257i	−0.227339	+	0.204762i
$755$	−2.72264			−0.0990869
$756$	−1.63419	+	10.2630i	−0.0594350	+	0.373262i
$757$	−17.8443			−0.648563			−0.324282	−	0.945961i	$-0.605123\pi$
$757$	−17.8443			−0.648563			−0.324282	+	0.945961i	$0.605123\pi$
$758$	−13.6056	+	12.2544i	−0.494176	+	0.445100i
$759$	18.3304	+	38.1819i	0.665353	+	1.38591i
$760$	2.55620	+	0.177524i	0.0927230	+	0.00643948i
$761$	−11.7016	−	32.1500i	−0.424184	−	1.16544i	−0.949291	−	0.314399i	$-0.898197\pi$
$761$	−11.7016	−	32.1500i	−0.424184	−	1.16544i	0.525107	−	0.851036i	$-0.324025\pi$
$762$	−1.43756	+	1.10923i	−0.0520774	+	0.0401831i
$763$	13.7106	−	2.41754i	0.496356	−	0.0875209i
$764$	20.0655	+	29.7280i	0.725944	+	1.07552i
$765$	1.97695	−	0.394662i	0.0714766	−	0.0142690i
$766$	−14.8801	−	7.90884i	−0.537638	−	0.285758i
$767$	2.55546	+	0.930112i	0.0922724	+	0.0335844i
$768$	23.5739	−	14.5695i	0.850650	−	0.525732i
$769$	−3.72512	−	3.12575i	−0.134331	−	0.112717i	0.573146	−	0.819453i	$-0.305723\pi$
$769$	−3.72512	−	3.12575i	−0.134331	−	0.112717i	−0.707478	+	0.706736i	$0.750167\pi$
$770$	−1.40642	+	1.80073i	−0.0506839	+	0.0648937i
$771$	11.2383	+	40.1298i	0.404738	+	1.44524i
$772$	−43.7245	−	12.5228i	−1.57368	−	0.450705i
$773$	14.8042	+	8.54720i	0.532470	+	0.307421i	0.742022	−	0.670376i	$-0.233867\pi$
$773$	14.8042	+	8.54720i	0.532470	+	0.307421i	−0.209552	+	0.977798i	$0.567201\pi$
$774$	14.8099	+	15.7166i	0.532331	+	0.564920i
$775$	−11.5760	+	6.68338i	−0.415821	+	0.240074i
$776$	−48.5639	+	13.9505i	−1.74334	+	0.500794i
$777$	7.39451	+	10.3115i	0.265277	+	0.369923i
$778$	−32.3786	+	13.0878i	−1.16083	+	0.469220i
$779$	1.23818	−	7.02204i	0.0443622	−	0.251591i
$780$	−1.05662	+	0.601781i	−0.0378330	+	0.0215472i
$781$	−34.4350	+	28.8944i	−1.23218	+	1.03392i
$782$	14.3745	−	0.504253i	0.514033	−	0.0180321i
$783$	10.5539	+	20.7719i	0.377166	+	0.742326i
$784$	−3.96072	+	0.559206i	−0.141454	+	0.0199716i
$785$	1.12783	+	1.34410i	0.0402541	+	0.0479730i
$786$	2.27715	−	55.5813i	0.0812232	−	1.98252i
$787$	53.9190	+	9.50737i	1.92200	+	0.338901i	0.998952	−	0.0457725i	$-0.0145749\pi$
$787$	53.9190	+	9.50737i	1.92200	+	0.338901i	0.923053	+	0.384674i	$0.125686\pi$
$788$	−20.2861	−	45.5245i	−0.722664	−	1.62174i
$789$	22.4195	+	10.1488i	0.798155	+	0.361306i
$790$	−3.89553	+	0.828667i	−0.138597	+	0.0294826i
$791$	−0.525205	−	0.909682i	−0.0186741	−	0.0323446i
$792$	−31.3679	−	41.1511i	−1.11461	−	1.46224i
$793$	5.37364	−	9.30741i	0.190823	−	0.330516i
$794$	−15.5633	+	47.9247i	−0.552320	+	1.70079i
$795$	0.804265	−	3.14261i	0.0285244	−	0.111457i
$796$	17.5361	−	24.1525i	0.621552	−	0.856064i
$797$	14.0696	−	16.7675i	0.498372	−	0.593936i	−0.456954	−	0.889490i	$-0.651060\pi$
$797$	14.0696	−	16.7675i	0.498372	−	0.593936i	0.955326	+	0.295554i	$0.0955041\pi$
$798$	5.64178	−	6.19023i	0.199717	−	0.219132i
$799$	−8.98758	+	24.6932i	−0.317958	+	0.873581i
$800$	26.2129	+	9.51719i	0.926767	+	0.336483i
$801$	−20.0922	−	16.1028i	−0.709922	−	0.568965i
$802$	15.7635	+	25.2179i	0.556628	+	0.890476i
$803$	8.00016	+	45.3711i	0.282319	+	1.60111i
$804$	−18.1694	+	3.09368i	−0.640785	+	0.109106i
$805$	0.998372	−	0.363378i	0.0351880	−	0.0128074i
$806$	−0.706235	+	5.03091i	−0.0248761	+	0.177206i
$807$	20.4991	+	14.0125i	0.721602	+	0.493262i
$808$	28.4028	−	29.4400i	0.999206	−	1.03569i
$809$			15.5284i			0.545951i	0.962021	+	0.272975i	$0.0880077\pi$
$809$			15.5284i			0.545951i	−0.962021	+	0.272975i	$0.911992\pi$
$810$	0.849377	+	3.26351i	0.0298441	+	0.114668i
$811$		−	5.33197i		−	0.187231i	−0.995608	−	0.0936155i	$-0.970158\pi$
$811$		−	5.33197i		−	0.187231i	0.995608	−	0.0936155i	$-0.0298424\pi$
$812$	−6.44898	+	6.23166i	−0.226315	+	0.218688i
$813$	27.0704	+	18.5044i	0.949400	+	0.648977i
$814$	−62.5640	−	8.78267i	−2.19287	−	0.307832i
$815$	−3.55639	+	1.29442i	−0.124575	+	0.0453415i
$816$	−17.0734	+	4.15611i	−0.597688	+	0.145493i
$817$	−3.02218	−	17.1397i	−0.105733	−	0.599641i
$818$	−3.66429	+	2.29051i	−0.128119	+	0.0800858i
$819$	−0.601910	+	3.92876i	−0.0210324	+	0.137282i
$820$	−0.484091	+	0.993333i	−0.0169052	+	0.0346887i
$821$	−3.58463	+	9.84870i	−0.125105	+	0.343722i	−0.986395	−	0.164390i	$-0.947434\pi$
$821$	−3.58463	+	9.84870i	−0.125105	+	0.343722i	0.861291	+	0.508112i	$0.169657\pi$
$822$	−0.194735	−	0.177482i	−0.00679216	−	0.00619038i
$823$	15.1205	−	18.0199i	0.527067	−	0.628134i	−0.435170	−	0.900348i	$-0.643312\pi$
$823$	15.1205	−	18.0199i	0.527067	−	0.628134i	0.962237	+	0.272215i	$0.0877561\pi$
$824$	11.2035	+	7.54909i	0.390292	+	0.262985i
$825$	12.9095	−	50.4430i	0.449451	−	1.75620i
$826$	2.76093	+	0.896595i	0.0960649	+	0.0311965i
$827$	−11.5041	+	19.9257i	−0.400038	+	0.692886i	−0.993730	−	0.111806i	$-0.964336\pi$
$827$	−11.5041	+	19.9257i	−0.400038	+	0.692886i	0.593692	+	0.804692i	$0.297670\pi$
$828$	2.22573	+	23.9570i	0.0773494	+	0.832562i
$829$	−2.04046	−	3.53418i	−0.0708682	−	0.122747i	0.828414	−	0.560116i	$-0.189244\pi$
$829$	−2.04046	−	3.53418i	−0.0708682	−	0.122747i	−0.899282	+	0.437369i	$0.855910\pi$
$830$	0.209925	+	0.986850i	0.00728661	+	0.0342541i
$831$	−10.7384	−	4.86101i	−0.372510	−	0.168626i
$832$	8.98306	−	5.62514i	0.311432	−	0.195017i
$833$	2.49776	+	0.440423i	0.0865423	+	0.0152597i
$834$	−23.9315	−	0.980464i	−0.828678	−	0.0339507i
$835$	1.28408	+	1.53031i	0.0444375	+	0.0529586i
$836$	2.92214	+	41.5989i	0.101064	+	1.43873i
$837$	12.9626	+	5.51981i	0.448054	+	0.190793i
$838$	−0.343232	−	9.78437i	−0.0118567	−	0.337995i
$839$	7.58588	−	6.36531i	0.261894	−	0.219755i	−0.502380	−	0.864647i	$-0.667542\pi$
$839$	7.58588	−	6.36531i	0.261894	−	0.219755i	0.764274	+	0.644892i	$0.223098\pi$
$840$	−1.10466	+	0.681510i	−0.0381144	+	0.0235143i
$841$	1.54447	−	8.75914i	0.0532577	−	0.302039i
$842$	−2.10603	−	5.21022i	−0.0725784	−	0.179556i
$843$	−20.5866	−	28.7076i	−0.709041	−	0.988743i
$844$	19.2733	−	4.81187i	0.663414	−	0.165631i
$845$	2.58012	−	1.48963i	0.0887587	−	0.0512449i
$846$	−42.1027	−	12.6324i	−1.44752	−	0.434311i
$847$	−22.6773	−	13.0928i	−0.779202	−	0.449872i
$848$	−5.86120	+	27.6611i	−0.201275	+	0.949886i
$849$	6.74647	+	24.0903i	0.231538	+	0.826778i
$850$	−13.9357	−	10.8842i	−0.477992	−	0.373326i
$851$	22.5040	+	18.8831i	0.771428	+	0.647305i
$852$	−24.0468	+	8.59249i	−0.823829	+	0.294374i
$853$	20.8062	+	7.57282i	0.712389	+	0.259288i	0.672691	−	0.739923i	$-0.265138\pi$
$853$	20.8062	+	7.57282i	0.712389	+	0.259288i	0.0396978	+	0.999212i	$0.487360\pi$
$854$	5.38419	−	10.1301i	0.184243	−	0.346644i
$855$	0.871822	−	2.57416i	0.0298157	−	0.0880343i
$856$	14.6493	−	10.6540i	0.500703	−	0.364146i
$857$	−0.893421	+	0.157534i	−0.0305187	+	0.00538126i	−0.188887	−	0.981999i	$-0.560488\pi$
$857$	−0.893421	+	0.157534i	−0.0305187	+	0.00538126i	0.158368	+	0.987380i	$0.449377\pi$
$858$	−12.0892	−	15.6677i	−0.412719	−	0.534885i
$859$	−5.78403	−	15.8915i	−0.197349	−	0.542211i	0.801061	−	0.598582i	$-0.204269\pi$
$859$	−5.78403	−	15.8915i	−0.197349	−	0.542211i	−0.998410	+	0.0563717i	$0.982047\pi$
$860$	−0.281079	+	2.68247i	−0.00958471	+	0.0914715i
$861$	1.56321	+	3.25613i	0.0532740	+	0.110969i
$862$	14.6181	+	16.2298i	0.497893	+	0.552790i
$863$	−15.5633			−0.529780			−0.264890	−	0.964279i	$-0.585336\pi$
$863$	−15.5633			−0.529780			−0.264890	+	0.964279i	$0.585336\pi$
$864$	−8.58410	−	28.1125i	−0.292037	−	0.956407i
$865$	−6.54981			−0.222700
$866$	31.0510	+	34.4747i	1.05516	+	1.17150i
$867$	−18.2501	−	1.38990i	−0.619806	−	0.0472036i
$868$	−0.565130	+	5.39331i	−0.0191818	+	0.183061i
$869$	−22.1687	−	60.9081i	−0.752022	−	2.06616i
$870$	−1.10639	+	2.69149i	−0.0375101	+	0.0912499i
$871$	−6.94192	+	1.22405i	−0.235218	+	0.0414753i
$872$	−31.8461	+	23.1607i	−1.07845	+	0.784321i
$873$	1.20622	+	53.5794i	0.0408244	+	1.81339i
$874$	9.10071	−	17.1225i	0.307836	−	0.579177i
$875$	−2.47222	−	0.899813i	−0.0835761	−	0.0304192i
$876$	−4.69618	+	25.7469i	−0.158669	+	0.869908i
$877$	2.29157	+	1.92285i	0.0773807	+	0.0649302i	0.680658	−	0.732602i	$-0.261694\pi$
$877$	2.29157	+	1.92285i	0.0773807	+	0.0649302i	−0.603277	+	0.797532i	$0.706139\pi$
$878$	41.2357	+	32.2063i	1.39164	+	1.08691i
$879$	−9.49365	+	9.70978i	−0.320213	+	0.327503i
$880$	1.33964	−	6.32222i	0.0451592	−	0.213122i
$881$	24.2603	+	14.0067i	0.817349	+	0.471897i	0.849501	−	0.527586i	$-0.176903\pi$
$881$	24.2603	+	14.0067i	0.817349	+	0.471897i	−0.0321525	+	0.999483i	$0.510236\pi$
$882$	−0.495083	+	4.21366i	−0.0166703	+	0.141881i
$883$	33.6102	−	19.4048i	1.13107	−	0.653025i	0.186868	−	0.982385i	$-0.440166\pi$
$883$	33.6102	−	19.4048i	1.13107	−	0.653025i	0.944204	+	0.329360i	$0.106833\pi$
$884$	−6.52037	+	1.62791i	−0.219304	+	0.0547524i
$885$	0.937390	−	0.0926525i	0.0315100	−	0.00311448i
$886$	8.88627	+	21.9842i	0.298540	+	0.738575i
$887$	2.39941	−	13.6077i	0.0805644	−	0.456903i	−0.917662	−	0.397363i	$-0.869925\pi$
$887$	2.39941	−	13.6077i	0.0805644	−	0.456903i	0.998226	−	0.0595402i	$-0.0189635\pi$
$888$	−31.5915	−	17.0301i	−1.06014	−	0.571493i
$889$	−0.567854	+	0.476486i	−0.0190452	+	0.0159808i
$890$	−0.112745	−	3.21397i	−0.00377922	−	0.107733i
$891$	−50.6752	+	21.0726i	−1.69768	+	0.705959i
$892$	−0.0463131	−	0.659302i	−0.00155068	−	0.0220751i
$893$	22.7716	+	27.1381i	0.762021	+	0.908142i
$894$	8.81348	−	13.9168i	0.294767	−	0.465446i
$895$	3.21499	+	0.566889i	0.107465	+	0.0189490i
$896$	9.37246	−	6.33696i	0.313112	−	0.211703i
$897$	0.905119	+	9.15733i	0.0302210	+	0.305754i
$898$	8.83797	+	41.5470i	0.294927	+	1.38644i
$899$	6.07892	+	10.5290i	0.202743	+	0.351162i
$900$	16.8353	−	24.3204i	0.561176	−	0.810678i
$901$	8.96429	−	15.5266i	0.298644	−	0.517266i
$902$	−17.1044	−	5.55456i	−0.569515	−	0.184947i
$903$	6.30370	+	6.16338i	0.209774	+	0.205104i
$904$	2.46387	+	1.66019i	0.0819470	+	0.0552172i
$905$	0.332776	−	0.396587i	0.0110619	−	0.0131830i
$906$	5.38203	−	24.5892i	0.178806	−	0.816921i
$907$	−7.17006	+	19.6996i	−0.238078	+	0.654113i	0.761902	+	0.647693i	$0.224266\pi$
$907$	−7.17006	+	19.6996i	−0.238078	+	0.654113i	−0.999979	+	0.00642053i	$0.997956\pi$
$908$	6.93171	−	14.2236i	0.230037	−	0.472026i
$909$	−22.5347	−	37.0782i	−0.747430	−	1.22981i
$910$	−0.420945	+	0.263128i	−0.0139542	+	0.00872261i
$911$	−4.85601	−	27.5398i	−0.160887	−	0.912435i	−0.953205	−	0.302326i	$-0.902237\pi$
$911$	−4.85601	−	27.5398i	−0.160887	−	0.912435i	0.792318	−	0.610109i	$-0.208874\pi$
$912$	−6.65630	+	22.7351i	−0.220412	+	0.752833i
$913$	−15.4298	+	5.61598i	−0.510651	+	0.185862i
$914$	−50.1712	−	7.04298i	−1.65951	−	0.232961i
$915$	0.282690	−	3.71185i	0.00934544	−	0.122710i
$916$	−25.1270	+	24.2803i	−0.830221	+	0.802244i
$917$		−	22.7100i		−	0.749951i
$918$	−0.343622	+	18.6347i	−0.0113412	+	0.615037i
$919$			25.1415i			0.829342i	0.909971	+	0.414671i	$0.136103\pi$
$919$			25.1415i			0.829342i	−0.909971	+	0.414671i	$0.863897\pi$
$920$	−2.08645	+	2.16264i	−0.0687883	+	0.0713003i
$921$	−27.2392	+	13.0771i	−0.897562	+	0.430904i
$922$	7.79737	−	55.5451i	0.256793	−	1.82928i
$923$	−9.17736	+	3.34029i	−0.302076	+	0.109947i
$924$	−13.4829	−	16.2616i	−0.443554	−	0.534966i
$925$	−6.27133	−	35.5665i	−0.206200	−	1.16942i
$926$	2.88464	+	4.61476i	0.0947953	+	0.151651i
$927$	10.7666	−	9.45522i	0.353621	−	0.310550i
$928$	8.65643	−	23.8422i	0.284161	−	0.782658i
$929$	14.0294	−	38.5454i	0.460289	−	1.26463i	−0.464979	−	0.885322i	$-0.653938\pi$
$929$	14.0294	−	38.5454i	0.460289	−	1.26463i	0.925268	−	0.379313i	$-0.123840\pi$
$930$	0.533651	+	1.67680i	0.0174991	+	0.0549845i
$931$	2.19787	−	2.61932i	0.0720322	−	0.0858446i
$932$	11.7266	−	16.1510i	0.384116	−	0.529044i
$933$	−28.5689	+	8.00069i	−0.935305	+	0.261931i
$934$	−14.6232	+	45.0298i	−0.478485	+	1.47342i
$935$	−2.04888	+	3.54876i	−0.0670055	+	0.116057i
$936$	−3.34622	−	10.7323i	−0.109375	−	0.350797i
$937$	7.36995	+	12.7651i	0.240766	+	0.417019i	0.960933	−	0.276782i	$-0.0892681\pi$
$937$	7.36995	+	12.7651i	0.240766	+	0.417019i	−0.720167	+	0.693801i	$0.755935\pi$
$938$	−7.35971	+	1.56557i	−0.240303	+	0.0511178i
$939$	−27.0459	+	19.3950i	−0.882608	+	0.632931i
$940$	−2.23462	−	5.01476i	−0.0728853	−	0.163563i
$941$	−5.58566	−	0.984902i	−0.182087	−	0.0321069i	0.0818609	−	0.996644i	$-0.473914\pi$
$941$	−5.58566	−	0.984902i	−0.182087	−	0.0321069i	−0.263948	+	0.964537i	$0.585025\pi$
$942$	−14.3686	+	7.52892i	−0.468153	+	0.245306i
$943$	5.37517	+	6.40587i	0.175040	+	0.208604i
$944$	−8.12990	+	1.14784i	−0.264606	+	0.0373591i
$945$	0.401005	+	1.31701i	0.0130447	+	0.0428424i
$946$	−43.8684	+	1.53888i	−1.42628	+	0.0500335i
$947$	−9.51257	+	7.98199i	−0.309117	+	0.259380i	−0.784127	−	0.620601i	$-0.786889\pi$
$947$	−9.51257	+	7.98199i	−0.309117	+	0.259380i	0.475010	+	0.879980i	$0.342444\pi$
$948$	0.216562	−	36.8201i	0.00703360	−	1.19586i
$949$	−1.73814	+	9.85747i	−0.0564223	+	0.319987i
$950$	−22.1012	+	8.93356i	−0.717059	+	0.289843i
$951$	7.45254	−	16.4633i	0.241665	−	0.533858i
$952$	−6.89488	+	1.98063i	−0.223464	+	0.0641925i
$953$	1.74515	−	1.00756i	0.0565310	−	0.0326382i	−0.471468	−	0.881883i	$-0.656276\pi$
$953$	1.74515	−	1.00756i	0.0565310	−	0.0326382i	0.527999	+	0.849245i	$0.322942\pi$
$954$	26.7923	+	13.4759i	0.867433	+	0.436297i
$955$	4.11476	+	2.37566i	0.133150	+	0.0768745i
$956$	49.4205	+	14.1541i	1.59837	+	0.457777i
$957$	−45.8809	−	11.7419i	−1.48312	−	0.379563i
$958$	11.4604	−	14.6735i	0.370269	−	0.474078i
$959$	−0.0823996	−	0.0691415i	−0.00266082	−	0.00223269i
$960$	1.96176	−	3.10312i	0.0633155	−	0.100153i
$961$	−22.2220	−	8.08816i	−0.716840	−	0.260908i
$962$	−12.1205	−	6.44209i	−0.390779	−	0.207701i
$963$	−6.97577	−	17.9015i	−0.224791	−	0.576867i
$964$	23.2392	+	34.4299i	0.748483	+	1.10891i
$965$	−5.93370	+	1.04627i	−0.191013	+	0.0336807i
$966$	1.30825	+	9.73499i	0.0420923	+	0.313218i
$967$	−13.2658	−	36.4474i	−0.426599	−	1.17207i	−0.947864	−	0.318675i	$-0.896762\pi$
$967$	−13.2658	−	36.4474i	−0.426599	−	1.17207i	0.521265	−	0.853395i	$-0.325460\pi$
$968$	73.8859	+	5.13127i	2.37478	+	0.164925i
$969$	8.47658	−	12.4005i	0.272307	−	0.398363i
$970$	−4.97362	+	4.47970i	−0.159693	+	0.143834i
$971$	−48.6895			−1.56252			−0.781260	−	0.624205i	$-0.785423\pi$
$971$	−48.6895			−1.56252			−0.781260	+	0.624205i	$0.785423\pi$
$972$	−31.1530	+	1.21984i	−0.999234	+	0.0391264i
$973$	−9.77817			−0.313474
$974$	26.8871	−	24.2170i	0.861519	−	0.775963i
$975$	6.38394	−	9.33918i	0.204450	−	0.299093i
$976$	−1.11184	+	32.4288i	−0.0355890	+	1.03802i
$977$	−11.5820	−	31.8214i	−0.370542	−	1.01806i	−0.975152	−	0.221535i	$-0.928893\pi$
$977$	−11.5820	−	31.8214i	−0.370542	−	1.01806i	0.604610	−	0.796522i	$-0.293329\pi$
$978$	−4.66024	−	34.6779i	−0.149018	−	1.10888i
$979$	51.5434	−	9.08849i	1.64733	−	0.290469i
$980$	−0.439209	+	0.296453i	−0.0140300	+	0.00946984i
$981$	15.1646	+	38.9160i	0.484169	+	1.24249i
$982$	42.5397	+	22.6101i	1.35750	+	0.721518i
$983$	1.27889	+	0.465478i	0.0407903	+	0.0148464i	0.362335	−	0.932048i	$-0.381980\pi$
$983$	1.27889	+	0.465478i	0.0407903	+	0.0148464i	−0.321544	+	0.946894i	$0.604202\pi$
$984$	−8.01424	−	6.33560i	−0.255485	−	0.201972i
$985$	−5.05779	−	4.24399i	−0.161155	−	0.135225i
$986$	−9.89985	+	12.6754i	−0.315275	+	0.403666i
$987$	−17.3851	−	4.44922i	−0.553372	−	0.141620i
$988$	−2.49456	+	8.70999i	−0.0793625	+	0.277102i
$989$	17.6764	+	10.2055i	0.562077	+	0.324515i
$990$	−6.12365	−	3.08004i	−0.194622	−	0.0978901i
$991$	15.9836	−	9.22812i	0.507735	−	0.293141i	−0.224167	−	0.974551i	$-0.571966\pi$
$991$	15.9836	−	9.22812i	0.507735	−	0.293141i	0.731902	+	0.681410i	$0.238633\pi$
$992$	−5.25737	−	14.4089i	−0.166922	−	0.457484i
$993$	19.5193	−	43.1198i	0.619428	−	1.36837i
$994$	−9.66523	+	3.90679i	−0.306563	+	0.123916i
$995$	0.686602	−	3.89391i	0.0217667	−	0.123445i
$996$	−9.32760	−	0.0548613i	−0.295556	−	0.00173835i
$997$	27.1086	−	22.7468i	0.858539	−	0.720400i	−0.103114	−	0.994670i	$-0.532881\pi$
$997$	27.1086	−	22.7468i	0.858539	−	0.720400i	0.961653	+	0.274270i	$0.0884361\pi$
$998$	23.7928	−	0.834641i	0.753147	−	0.0264201i
$999$	−25.9930	+	27.8103i	−0.822383	+	0.879879i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.491.30	✓	648
4.3	odd	2	inner	756.2.cf.a.491.31	yes	648
27.11	odd	18	inner	756.2.cf.a.659.31	yes	648
108.11	even	18	inner	756.2.cf.a.659.30	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.30	✓	648	1.1	even	1	trivial
756.2.cf.a.491.31	yes	648	4.3	odd	2	inner
756.2.cf.a.659.30	yes	648	108.11	even	18	inner
756.2.cf.a.659.31	yes	648	27.11	odd	18	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.946460 - 1.05082i) q^{2} +(0.977433 - 1.42990i) q^{3} +(-0.208426 + 1.98911i) q^{4} +(0.0906174 + 0.248969i) q^{5} +(-2.42767 + 0.326246i) q^{6} +(-0.984808 + 0.173648i) q^{7} +(2.28745 - 1.66360i) q^{8} +(-1.08925 - 2.79527i) q^{9} +(0.175855 - 0.330862i) q^{10} +(5.73024 + 2.08564i) q^{11} +(2.64051 + 2.24225i) q^{12} +(1.01491 + 0.851609i) q^{13} +(1.11455 + 0.870500i) q^{14} +(0.444574 + 0.113777i) q^{15} +(-3.91312 - 0.829164i) q^{16} +(2.19650 + 1.26815i) q^{17} +(-1.90638 + 3.79021i) q^{18} +(2.96118 - 1.70964i) q^{19} +(-0.514114 + 0.128356i) q^{20} +(-0.714283 + 1.57791i) q^{21} +(-3.23182 - 7.99539i) q^{22} +(-0.696333 + 3.94910i) q^{23} +(-0.142950 - 4.89689i) q^{24} +(3.77645 - 3.16882i) q^{25} +(-0.0656863 - 1.87249i) q^{26} +(-5.06164 - 1.17467i) q^{27} +(-0.140146 - 1.99508i) q^{28} +(-2.88222 - 3.43490i) q^{29} +(-0.301214 - 0.574851i) q^{30} +(-2.67023 - 0.470833i) q^{31} +(2.83231 + 4.89673i) q^{32} +(8.58318 - 6.15512i) q^{33} +(-0.746307 - 3.50836i) q^{34} +(-0.132474 - 0.229451i) q^{35} +(5.78713 - 1.58403i) q^{36} +(3.66294 - 6.34440i) q^{37} +(-4.59915 - 1.49355i) q^{38} +(2.20972 - 0.618830i) q^{39} +(0.621467 + 0.418755i) q^{40} +(1.34043 - 1.59747i) q^{41} +(2.33413 - 0.742849i) q^{42} +(1.74088 - 4.78302i) q^{43} +(-5.34289 + 10.9634i) q^{44} +(0.597231 - 0.524490i) q^{45} +(4.80883 - 3.00595i) q^{46} +(1.79913 + 10.2033i) q^{47} +(-5.01043 + 4.78493i) q^{48} +(0.939693 - 0.342020i) q^{49} +(-6.90410 - 0.969191i) q^{50} +(3.96026 - 1.90125i) q^{51} +(-1.90548 + 1.84127i) q^{52} -7.06881i q^{53} +(3.55628 + 6.43062i) q^{54} +1.61565i q^{55} +(-1.96382 + 2.03554i) q^{56} +(0.449737 - 5.90526i) q^{57} +(-0.881535 + 6.27968i) q^{58} +(1.92884 - 0.702041i) q^{59} +(-0.318975 + 0.860594i) q^{60} +(-1.40863 - 7.98872i) q^{61} +(2.03250 + 3.25154i) q^{62} +(1.55810 + 2.56366i) q^{63} +(2.46489 - 7.61080i) q^{64} +(-0.120056 + 0.329851i) q^{65} +(-14.5915 - 3.19376i) q^{66} +(-3.41998 + 4.07577i) q^{67} +(-2.98029 + 4.10476i) q^{68} +(4.96621 + 4.85567i) q^{69} +(-0.115730 + 0.356372i) q^{70} +(-3.68578 + 6.38396i) q^{71} +(-7.14181 - 4.58198i) q^{72} +(3.77756 + 6.54292i) q^{73} +(-10.1336 + 2.15565i) q^{74} +(-0.839877 - 8.49726i) q^{75} +(2.78347 + 6.24644i) q^{76} +(-6.00535 - 1.05891i) q^{77} +(-2.74169 - 1.73631i) q^{78} +(-6.83234 - 8.14247i) q^{79} +(-0.148160 - 1.04938i) q^{80} +(-6.62707 + 6.08949i) q^{81} +(-2.94731 + 0.103390i) q^{82} +(-2.06272 + 1.73083i) q^{83} +(-2.98976 - 1.74967i) q^{84} +(-0.116689 + 0.661776i) q^{85} +(-6.67374 + 2.69760i) q^{86} +(-7.72875 + 0.763917i) q^{87} +(16.5773 - 4.76201i) q^{88} +(7.43301 - 4.29145i) q^{89} +(-1.11640 - 0.131171i) q^{90} +(-1.14737 - 0.662434i) q^{91} +(-7.71006 - 2.20818i) q^{92} +(-3.28321 + 3.35796i) q^{93} +(9.01904 - 11.5476i) q^{94} +(0.693982 + 0.582320i) q^{95} +(9.77025 + 0.736296i) q^{96} +(-16.7870 - 6.10996i) q^{97} +(-1.24878 - 0.663735i) q^{98} +(-0.411744 - 18.2893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) \) 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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