LMFDB - Embedded newform 756.2.cf.a.659.31

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			659.31
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.870500 + 1.11455i) q^{2} +(-0.977433 - 1.42990i) q^{3} +(-0.484459 - 1.94044i) q^{4} +(0.0906174 - 0.248969i) q^{5} +(2.44456 + 0.155330i) q^{6} +(0.984808 + 0.173648i) q^{7} +(2.58444 + 1.14920i) q^{8} +(-1.08925 + 2.79527i) q^{9} +(0.198607 + 0.317726i) q^{10} +(-5.73024 + 2.08564i) q^{11} +(-2.30111 + 2.58938i) q^{12} +(1.01491 - 0.851609i) q^{13} +(-1.05082 + 0.946460i) q^{14} +(-0.444574 + 0.113777i) q^{15} +(-3.53060 + 1.88013i) q^{16} +(2.19650 - 1.26815i) q^{17} +(-2.16729 - 3.64731i) q^{18} +(-2.96118 - 1.70964i) q^{19} +(-0.527010 - 0.0552219i) q^{20} +(-0.714283 - 1.57791i) q^{21} +(2.66362 - 8.20220i) q^{22} +(0.696333 + 3.94910i) q^{23} +(-0.882882 - 4.81877i) 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} +(0.260192 - 0.594545i) q^{30} +(2.67023 - 0.470833i) q^{31} +(0.977883 - 5.57169i) q^{32} +(8.58318 + 6.15512i) q^{33} +(-0.498631 + 3.55203i) q^{34} +(0.132474 - 0.229451i) q^{35} +(5.95175 + 0.759426i) q^{36} +(3.66294 + 6.34440i) q^{37} +(4.48319 - 1.81215i) q^{38} +(-2.20972 - 0.618830i) q^{39} +(0.520310 - 0.539310i) q^{40} +(1.34043 + 1.59747i) q^{41} +(2.38045 + 0.577463i) q^{42} +(-1.74088 - 4.78302i) q^{43} +(6.82312 + 10.1088i) q^{44} +(0.597231 + 0.524490i) q^{45} +(-5.00764 - 2.66159i) q^{46} +(-1.79913 + 10.2033i) q^{47} +(6.13932 + 3.21072i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-6.81921 + 1.45060i) q^{50} +(-3.96026 - 1.90125i) q^{51} +(-2.14418 - 1.55680i) q^{52} +7.06881i q^{53} +(-3.09692 + 6.66401i) q^{54} +1.61565i q^{55} +(2.34562 + 1.58052i) q^{56} +(0.449737 + 5.90526i) q^{57} +(-1.31940 - 6.20247i) q^{58} +(-1.92884 - 0.702041i) q^{59} +(0.436155 + 0.807549i) q^{60} +(-1.40863 + 7.98872i) q^{61} +(-1.79966 + 3.38597i) q^{62} +(-1.55810 + 2.56366i) q^{63} +(5.35870 + 5.94006i) q^{64} +(-0.120056 - 0.329851i) q^{65} +(-14.3319 + 4.20839i) q^{66} +(3.41998 + 4.07577i) q^{67} +(-3.52487 - 3.64780i) q^{68} +(4.96621 - 4.85567i) q^{69} +(0.140417 + 0.347386i) q^{70} +(3.68578 + 6.38396i) q^{71} +(-6.02742 + 5.97246i) q^{72} +(3.77756 - 6.54292i) q^{73} +(-10.2598 - 1.44026i) q^{74} +(0.839877 - 8.49726i) q^{75} +(-1.88287 + 6.57423i) q^{76} +(-6.00535 + 1.05891i) q^{77} +(2.61328 - 1.92416i) 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} +(-2.71579 + 2.15046i) q^{84} +(-0.116689 - 0.661776i) q^{85} +(6.84637 + 2.22332i) q^{86} +(7.72875 + 0.763917i) q^{87} +(-17.2063 - 1.19495i) q^{88} +(7.43301 + 4.29145i) q^{89} +(-1.10446 + 0.209078i) q^{90} +(1.14737 - 0.662434i) q^{91} +(7.32564 - 3.26437i) q^{92} +(-3.28321 - 3.35796i) q^{93} +(-9.80604 - 10.8872i) q^{94} +(-0.693982 + 0.582320i) q^{95} +(-8.92280 + 4.04768i) q^{96} +(-16.7870 + 6.10996i) q^{97} +(-1.19920 + 0.749609i) 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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$-1$

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 $

$2$	−0.870500	+	1.11455i	−0.615536	+	0.788108i
$2$	−0.870500	+	1.11455i	−0.615536	+	0.788108i
$3$	−0.977433	−	1.42990i	−0.564321	−	0.825555i
$3$	−0.977433	−	1.42990i	−0.564321	−	0.825555i
$4$	−0.484459	−	1.94044i	−0.242230	−	0.970219i
$5$	0.0906174	−	0.248969i	0.0405253	−	0.111342i	−0.917779	−	0.397091i	$-0.870020\pi$
$5$	0.0906174	−	0.248969i	0.0405253	−	0.111342i	0.958305	+	0.285748i	$0.0922421\pi$
$6$	2.44456	+	0.155330i	0.997987	+	0.0634131i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$8$	2.58444	+	1.14920i	0.913739	+	0.406302i
$9$	−1.08925	+	2.79527i	−0.363083	+	0.931757i
$10$	0.198607	+	0.317726i	0.0628051	+	0.100474i
$11$	−5.73024	+	2.08564i	−1.72773	+	0.628843i	−0.998465	−	0.0553862i	$-0.982361\pi$
$11$	−5.73024	+	2.08564i	−1.72773	+	0.628843i	−0.729267	+	0.684229i	$0.760139\pi$
$12$	−2.30111	+	2.58938i	−0.664274	+	0.747489i
$13$	1.01491	−	0.851609i	0.281485	−	0.236194i	−0.491103	−	0.871101i	$-0.663406\pi$
$13$	1.01491	−	0.851609i	0.281485	−	0.236194i	0.772588	+	0.634908i	$0.218962\pi$
$14$	−1.05082	+	0.946460i	−0.280842	+	0.252952i
$15$	−0.444574	+	0.113777i	−0.114789	+	0.0293770i
$16$	−3.53060	+	1.88013i	−0.882650	+	0.470032i
$17$	2.19650	−	1.26815i	0.532728	−	0.307571i	−0.209398	−	0.977830i	$-0.567151\pi$
$17$	2.19650	−	1.26815i	0.532728	−	0.307571i	0.742127	+	0.670260i	$0.233817\pi$
$18$	−2.16729	−	3.64731i	−0.510834	−	0.859679i
$19$	−2.96118	−	1.70964i	−0.679341	−	0.392218i	0.120266	−	0.992742i	$-0.461625\pi$
$19$	−2.96118	−	1.70964i	−0.679341	−	0.392218i	−0.799607	+	0.600524i	$0.794959\pi$
$20$	−0.527010	−	0.0552219i	−0.117843	−	0.0123480i
$21$	−0.714283	−	1.57791i	−0.155869	−	0.344328i
$22$	2.66362	−	8.20220i	0.567886	−	1.74872i
$23$	0.696333	+	3.94910i	0.145195	+	0.823444i	0.967210	+	0.253978i	$0.0817390\pi$
$23$	0.696333	+	3.94910i	0.145195	+	0.823444i	−0.822015	+	0.569466i	$0.807150\pi$
$24$	−0.882882	−	4.81877i	−0.180218	−	0.983627i
$25$	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	−0.964108	−	0.265511i	$-0.914459\pi$
$29$	−2.88222	+	3.43490i	−0.535215	+	0.637845i	0.428893	+	0.903355i	$0.358904\pi$
$30$	0.260192	−	0.594545i	0.0475043	−	0.108548i
$31$	2.67023	−	0.470833i	0.479587	−	0.0845641i	0.0713716	−	0.997450i	$-0.477262\pi$
$31$	2.67023	−	0.470833i	0.479587	−	0.0845641i	0.408215	+	0.912886i	$0.366151\pi$
$32$	0.977883	−	5.57169i	0.172867	−	0.984945i
$33$	8.58318	+	6.15512i	1.49414	+	1.07147i
$34$	−0.498631	+	3.55203i	−0.0855146	+	0.609169i
$35$	0.132474	−	0.229451i	0.0223922	−	0.0387843i
$36$	5.95175	+	0.759426i	0.991958	+	0.126571i
$37$	3.66294	+	6.34440i	0.602184	+	1.04301i	0.992490	+	0.122328i	$0.0390358\pi$
$37$	3.66294	+	6.34440i	0.602184	+	1.04301i	−0.390306	+	0.920685i	$0.627631\pi$
$38$	4.48319	−	1.81215i	0.727269	−	0.293970i
$39$	−2.20972	−	0.618830i	−0.353839	−	0.0990921i
$40$	0.520310	−	0.539310i	0.0822682	−	0.0852724i
$41$	1.34043	+	1.59747i	0.209341	+	0.249482i	0.860490	−	0.509467i	$-0.170157\pi$
$41$	1.34043	+	1.59747i	0.209341	+	0.249482i	−0.651150	+	0.758949i	$0.725713\pi$
$42$	2.38045	+	0.577463i	0.367311	+	0.0891045i
$43$	−1.74088	−	4.78302i	−0.265481	−	0.729404i	−0.998775	−	0.0494915i	$-0.984240\pi$
$43$	−1.74088	−	4.78302i	−0.265481	−	0.729404i	0.733293	−	0.679913i	$-0.237982\pi$
$44$	6.82312	+	10.1088i	1.02862	+	1.52395i
$45$	0.597231	+	0.524490i	0.0890300	+	0.0781863i
$46$	−5.00764	−	2.66159i	−0.738336	−	0.392430i
$47$	−1.79913	+	10.2033i	−0.262429	+	1.48831i	0.513827	+	0.857894i	$0.328227\pi$
$47$	−1.79913	+	10.2033i	−0.262429	+	1.48831i	−0.776256	+	0.630418i	$0.782884\pi$
$48$	6.13932	+	3.21072i	0.886135	+	0.463427i
$49$	0.939693	+	0.342020i	0.134242	+	0.0488600i
$50$	−6.81921	+	1.45060i	−0.964382	+	0.205146i
$51$	−3.96026	−	1.90125i	−0.554547	−	0.266228i
$52$	−2.14418	−	1.55680i	−0.297344	−	0.215889i
$53$			7.06881i			0.970976i	0.874243	+	0.485488i	$0.161358\pi$
$53$			7.06881i			0.970976i	−0.874243	+	0.485488i	$0.838642\pi$
$54$	−3.09692	+	6.66401i	−0.421438	+	0.906857i
$55$			1.61565i			0.217854i
$56$	2.34562	+	1.58052i	0.313447	+	0.211206i
$57$	0.449737	+	5.90526i	0.0595691	+	0.782170i
$58$	−1.31940	−	6.20247i	−0.173246	−	0.814424i
$59$	−1.92884	−	0.702041i	−0.251114	−	0.0913980i	0.213396	−	0.976966i	$-0.431547\pi$
$59$	−1.92884	−	0.702041i	−0.251114	−	0.0913980i	−0.464510	+	0.885568i	$0.653770\pi$
$60$	0.436155	+	0.807549i	0.0563073	+	0.104254i
$61$	−1.40863	+	7.98872i	−0.180356	+	1.02285i	0.751422	+	0.659822i	$0.229368\pi$
$61$	−1.40863	+	7.98872i	−0.180356	+	1.02285i	−0.931778	+	0.363029i	$0.881743\pi$
$62$	−1.79966	+	3.38597i	−0.228557	+	0.430019i
$63$	−1.55810	+	2.56366i	−0.196302	+	0.322990i
$64$	5.35870	+	5.94006i	0.669838	+	0.742508i
$65$	−0.120056	−	0.329851i	−0.0148911	−	0.0409130i
$66$	−14.3319	+	4.20839i	−1.76413	+	0.518016i
$67$	3.41998	+	4.07577i	0.417817	+	0.497935i	0.933366	−	0.358925i	$-0.116857\pi$
$67$	3.41998	+	4.07577i	0.417817	+	0.497935i	−0.515550	+	0.856860i	$0.672412\pi$
$68$	−3.52487	−	3.64780i	−0.427454	−	0.442360i
$69$	4.96621	−	4.85567i	0.597862	−	0.584554i
$70$	0.140417	+	0.347386i	0.0167831	+	0.0415206i
$71$	3.68578	+	6.38396i	0.437422	+	0.757636i	0.997490	−	0.0708101i	$-0.0225584\pi$
$71$	3.68578	+	6.38396i	0.437422	+	0.757636i	−0.560068	+	0.828446i	$0.689225\pi$
$72$	−6.02742	+	5.97246i	−0.710338	+	0.703861i
$73$	3.77756	−	6.54292i	0.442130	−	0.765791i	−0.555717	−	0.831371i	$-0.687556\pi$
$73$	3.77756	−	6.54292i	0.442130	−	0.765791i	0.997847	+	0.0655798i	$0.0208897\pi$
$74$	−10.2598	−	1.44026i	−1.19267	−	0.167426i
$75$	0.839877	−	8.49726i	0.0969807	−	0.981179i
$76$	−1.88287	+	6.57423i	−0.215980	+	0.754116i
$77$	−6.00535	+	1.05891i	−0.684373	+	0.120673i
$78$	2.61328	−	1.92416i	0.295896	−	0.217869i
$79$	6.83234	−	8.14247i	0.768699	−	0.916099i	−0.229666	−	0.973270i	$-0.573763\pi$
$79$	6.83234	−	8.14247i	0.768699	−	0.916099i	0.998364	+	0.0571703i	$0.0182078\pi$
$80$	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	$-0.230565\pi$
$83$	2.06272	+	1.73083i	0.226413	+	0.189983i	−0.522523	+	0.852625i	$0.675009\pi$
$84$	−2.71579	+	2.15046i	−0.296317	+	0.234634i
$85$	−0.116689	−	0.661776i	−0.0126567	−	0.0717797i
$86$	6.84637	+	2.22332i	0.738263	+	0.239747i
$87$	7.72875	+	0.763917i	0.828609	+	0.0819005i
$88$	−17.2063	−	1.19495i	−1.83420	−	0.127382i
$89$	7.43301	+	4.29145i	0.787898	+	0.454893i	0.839222	−	0.543789i	$-0.183011\pi$
$89$	7.43301	+	4.29145i	0.787898	+	0.454893i	−0.0513240	+	0.998682i	$0.516344\pi$
$90$	−1.10446	+	0.209078i	−0.116420	+	0.0220388i
$91$	1.14737	−	0.662434i	0.120277	−	0.0694419i
$92$	7.32564	−	3.26437i	0.763750	−	0.340334i
$93$	−3.28321	−	3.35796i	−0.340453	−	0.348204i
$94$	−9.80604	−	10.8872i	−1.01142	−	1.12293i
$95$	−0.693982	+	0.582320i	−0.0712010	+	0.0597447i
$96$	−8.92280	+	4.04768i	−0.910679	+	0.413114i
$97$	−16.7870	+	6.10996i	−1.70446	+	0.620372i	−0.996321	−	0.0857023i	$-0.972687\pi$
$97$	−16.7870	+	6.10996i	−1.70446	+	0.620372i	−0.708138	+	0.706074i	$0.750464\pi$
$98$	−1.19920	+	0.749609i	−0.121138	+	0.0757220i
$99$	0.411744	−	18.2893i	0.0413818	−	1.83815i
$100$	4.31935	−	8.86313i	0.431935	−	0.886313i
$101$	14.2433	+	2.51147i	1.41726	+	0.249901i	0.829216	−	0.558928i	$-0.188787\pi$
$101$	14.2433	+	2.51147i	1.41726	+	0.249901i	0.588044	+	0.808829i	$0.299898\pi$
$102$	5.56645	−	2.75888i	0.551160	−	0.273170i
$103$	−1.63360	+	4.48829i	−0.160964	+	0.442244i	−0.993788	−	0.111294i	$-0.964500\pi$
$103$	−1.63360	+	4.48829i	−0.160964	+	0.442244i	0.832824	+	0.553538i	$0.186723\pi$
$104$	3.60164	−	1.03461i	0.353169	−	0.101452i
$105$	−0.457577	+	0.0348485i	−0.0446550	+	0.00340087i
$106$	−7.87857	−	6.15340i	−0.765234	−	0.597671i
$107$	−6.40420			−0.619117			−0.309559	−	0.950880i	$-0.600181\pi$
$107$	−6.40420			−0.619117			−0.309559	+	0.950880i	$0.600181\pi$
$108$	−4.73153	−	9.25271i	−0.455291	−	0.890343i
$109$	−13.9221			−1.33349			−0.666746	−	0.745285i	$-0.732314\pi$
$109$	−13.9221			−1.33349			−0.666746	+	0.745285i	$0.732314\pi$
$110$	−1.80073	−	1.40642i	−0.171693	−	0.134097i
$111$	5.49160	−	11.4389i	0.521240	−	1.08573i
$112$	−3.80344	+	1.23848i	−0.359391	+	0.117026i
$113$	0.359261	−	0.987062i	0.0337965	−	0.0928550i	−0.921647	−	0.388030i	$-0.873156\pi$
$113$	0.359261	−	0.987062i	0.0337965	−	0.0928550i	0.955443	+	0.295175i	$0.0953779\pi$
$114$	−6.97322	−	4.63927i	−0.653102	−	0.434508i
$115$	1.04630	+	0.184492i	0.0975684	+	0.0172039i
$116$	8.06153	+	3.92870i	0.748494	+	0.364771i
$117$	1.27499	+	3.76456i	0.117873	+	0.348033i
$118$	2.46152	−	1.53867i	0.226601	−	0.141646i
$119$	2.38334	−	0.867464i	0.218480	−	0.0795203i
$120$	−1.27973	−	0.216854i	−0.116823	−	0.0197959i
$121$	20.0593	−	16.8317i	1.82357	−	1.53016i
$122$	−7.67765	−	8.52417i	−0.695102	−	0.771742i
$123$	0.974040	−	3.47811i	0.0878262	−	0.313610i
$124$	−2.20724	−	4.95331i	−0.198216	−	0.444820i
$125$	2.27841	−	1.31544i	0.203787	−	0.117656i
$126$	−1.50101	−	3.96824i	−0.133721	−	0.353519i
$127$	−0.641968	−	0.370640i	−0.0569654	−	0.0328890i	0.471247	−	0.882001i	$-0.343804\pi$
$127$	−0.641968	−	0.370640i	−0.0569654	−	0.0328890i	−0.528212	+	0.849112i	$0.677137\pi$
$128$	−11.2853	+	0.801737i	−0.997486	+	0.0708642i
$129$	−5.13767	+	7.16437i	−0.452347	+	0.630788i
$130$	0.472146	+	0.153327i	0.0414099	+	0.0134476i
$131$	3.94355	+	22.3650i	0.344550	+	1.95404i	0.295880	+	0.955225i	$0.404387\pi$
$131$	3.94355	+	22.3650i	0.344550	+	1.95404i	0.0486698	+	0.998815i	$0.484502\pi$
$132$	7.78542	−	19.6370i	0.677634	−	1.70918i
$133$	−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	−0.763083	−	0.646301i	$-0.776315\pi$
$137$	0.0691415	−	0.0823996i	0.00590715	−	0.00703987i	0.768990	+	0.639261i	$0.220760\pi$
$138$	1.08881	+	9.76197i	0.0926860	+	0.830994i
$139$	−9.62962	+	1.69796i	−0.816774	+	0.144019i	−0.566400	−	0.824130i	$-0.691664\pi$
$139$	−9.62962	+	1.69796i	−0.816774	+	0.144019i	−0.250373	+	0.968149i	$0.580553\pi$
$140$	−0.509414	−	0.145897i	−0.0430534	−	0.0123306i
$141$	16.3483	−	7.40051i	1.37678	−	0.623236i
$142$	−10.3237	−	1.44924i	−0.866349	−	0.121617i
$143$	−4.03952	+	6.99665i	−0.337801	+	0.585089i
$144$	−1.40976	−	11.9169i	−0.117480	−	0.993075i
$145$	0.594005	+	1.02885i	0.0493294	+	0.0854410i
$146$	4.00408	+	9.90591i	0.331380	+	0.819819i
$147$	−0.429431	−	1.67797i	−0.0354188	−	0.138397i
$148$	10.5364	−	10.1813i	0.866084	−	0.836899i
$149$	−4.32275	−	5.15165i	−0.354133	−	0.422039i	0.559340	−	0.828938i	$-0.311055\pi$
$149$	−4.32275	−	5.15165i	−0.354133	−	0.422039i	−0.913473	+	0.406899i	$0.866610\pi$
$150$	8.73954	+	8.33296i	0.713581	+	0.680383i
$151$	3.51465	+	9.65641i	0.286018	+	0.785827i	0.996614	+	0.0822270i	$0.0262033\pi$
$151$	3.51465	+	9.65641i	0.286018	+	0.785827i	−0.710596	+	0.703600i	$0.751575\pi$
$152$	−5.68829	−	7.82144i	−0.461382	−	0.634402i
$153$	1.15228	+	7.52113i	0.0931565	+	0.608047i
$154$	4.04745	−	7.61506i	0.326153	−	0.613639i
$155$	0.124746	−	0.707470i	0.0100198	−	0.0568253i
$156$	−0.130280	+	4.58763i	−0.0104308	+	0.367304i
$157$	6.22305	+	2.26501i	0.496654	+	0.180767i	0.578188	−	0.815903i	$-0.303760\pi$
$157$	6.22305	+	2.26501i	0.496654	+	0.180767i	−0.0815346	+	0.996671i	$0.525982\pi$
$158$	3.12766	+	14.7030i	0.248824	+	1.16971i
$159$	10.1077	−	6.90929i	0.801594	−	0.547942i
$160$	−1.29857	−	0.748355i	−0.102661	−	0.0591627i
$161$			4.01002i			0.316034i
$162$	12.5559	−	2.08532i	0.986487	−	0.163838i
$163$			14.2845i			1.11884i	0.828883	+	0.559422i	$0.188977\pi$
$163$			14.2845i			1.11884i	−0.828883	+	0.559422i	$0.811023\pi$
$164$	2.45040	−	3.37494i	0.191344	−	0.263538i
$165$	2.31022	−	1.57919i	0.179850	−	0.122940i
$166$	−3.72470	+	0.792327i	−0.289093	+	0.0614965i
$167$	−7.08519	−	2.57880i	−0.548269	−	0.199553i	0.0530084	−	0.998594i	$-0.483119\pi$
$167$	−7.08519	−	2.57880i	−0.548269	−	0.199553i	−0.601277	+	0.799041i	$0.705341\pi$
$168$	−0.0326991	−	4.89887i	−0.00252279	−	0.377956i
$169$	−1.95263	+	11.0739i	−0.150202	+	0.851838i
$170$	0.839163	+	0.446020i	0.0643608	+	0.0342082i
$171$	8.00436	−	6.41507i	0.612109	−	0.490573i
$172$	−8.43777	+	5.69525i	−0.643374	+	0.434258i
$173$	−8.45513	−	23.2303i	−0.642832	−	1.76617i	−0.642643	−	0.766165i	$-0.722162\pi$
$173$	−8.45513	−	23.2303i	−0.642832	−	1.76617i	−0.000188152	−	1.00000i	$-0.500060\pi$
$174$	−7.57931	+	7.94912i	−0.574586	+	0.602621i
$175$	3.16882	+	3.77645i	0.239540	+	0.285473i
$176$	16.3099	−	18.1371i	1.22941	−	1.36714i
$177$	0.881463	+	3.44426i	0.0662548	+	0.258886i
$178$	−11.2535	+	4.54878i	−0.843485	+	0.340946i
$179$	−6.16081	−	10.6708i	−0.460481	−	0.797576i	0.538504	−	0.842623i	$-0.318990\pi$
$179$	−6.16081	−	10.6708i	−0.460481	−	0.797576i	−0.998985	+	0.0450470i	$0.985656\pi$
$180$	0.728405	−	1.41298i	0.0542921	−	0.105318i
$181$	−0.977001	+	1.69222i	−0.0726199	+	0.125781i	−0.900049	−	0.435789i	$-0.856469\pi$
$181$	−0.977001	+	1.69222i	−0.0726199	+	0.125781i	0.827429	+	0.561571i	$0.189803\pi$
$182$	−0.260467	+	1.85545i	−0.0193071	+	0.137535i
$183$	12.7999	−	5.79424i	0.946199	−	0.428322i
$184$	−2.73865	+	11.0064i	−0.201896	+	0.811406i
$185$	1.91149	−	0.337047i	0.140535	−	0.0247802i
$186$	6.60066	−	0.736213i	0.483984	−	0.0539818i
$187$	−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	$-0.502504\pi$
$191$	−13.7375	−	11.5271i	−0.994011	−	0.834074i	−0.986143	+	0.165895i	$0.946949\pi$
$192$	3.25594	−	13.4684i	0.234978	−	0.972001i
$193$	−3.94897	−	22.3957i	−0.284253	−	1.61208i	−0.707940	−	0.706272i	$-0.750375\pi$
$193$	−3.94897	−	22.3957i	−0.284253	−	1.61208i	0.423687	−	0.905809i	$-0.360736\pi$
$194$	7.80318	−	24.0287i	0.560236	−	1.72516i
$195$	−0.354309	+	0.494076i	−0.0253726	+	0.0353815i
$196$	0.208426	−	1.98911i	0.0148876	−	0.142079i
$197$	−21.5813	−	12.4600i	−1.53760	−	0.887736i	−0.998978	−	0.0451897i	$-0.985611\pi$
$197$	−21.5813	−	12.4600i	−1.53760	−	0.887736i	−0.538625	−	0.842546i	$-0.681056\pi$
$198$	20.0260	+	16.3798i	1.42319	+	1.16406i
$199$	12.9243	−	7.46182i	0.916176	−	0.528955i	0.0337630	−	0.999430i	$-0.489251\pi$
$199$	12.9243	−	7.46182i	0.916176	−	0.528955i	0.882413	+	0.470475i	$0.155918\pi$
$200$	6.11843	+	12.5295i	0.432638	+	0.885970i
$201$	2.48516	−	8.87403i	0.175290	−	0.625926i
$202$	−15.1980	+	13.6887i	−1.06932	+	0.963131i
$203$	−3.43490	+	2.88222i	−0.241083	+	0.202292i
$204$	−1.77067	+	8.60571i	−0.123972	+	0.602520i
$205$	0.519187	−	0.188968i	0.0362616	−	0.0131981i
$206$	−3.58038	−	5.72779i	−0.249457	−	0.399074i
$207$	−11.7973	−	2.35512i	−0.819968	−	0.163692i
$208$	−1.98210	+	4.91484i	−0.137434	+	0.340783i
$209$	20.5339	+	3.62069i	1.42036	+	0.250448i
$210$	0.359481	−	0.540330i	0.0248065	−	0.0372863i
$211$	3.39710	−	9.33345i	0.233866	−	0.642541i	−0.766134	−	0.642681i	$-0.777822\pi$
$211$	3.39710	−	9.33345i	0.233866	−	0.642541i	1.00000		0.000139562i	$4.44240e-5\pi$
$212$	13.7166	−	3.42455i	0.942059	−	0.235199i
$213$	5.52584	−	11.5102i	0.378624	−	0.788666i
$214$	5.57485	−	7.13782i	0.381089	−	0.487931i
$215$	−1.34858			−0.0919723
$216$	14.4314	+	2.78095i	0.981935	+	0.189219i
$217$	2.71142			0.184063
$218$	12.1192	−	15.5169i	0.820814	−	1.05094i
$219$	−13.0481	+	0.993724i	−0.881706	+	0.0671496i
$220$	3.13506	−	0.782716i	0.211366	−	0.0527707i
$221$	1.14927	−	3.15761i	0.0773086	−	0.212404i
$222$	7.96880	+	16.0782i	0.534831	+	1.07910i
$223$	0.325443	+	0.0573844i	0.0217933	+	0.00384274i	0.184534	−	0.982826i	$-0.440922\pi$
$223$	0.325443	+	0.0573844i	0.0217933	+	0.00384274i	−0.162741	+	0.986669i	$0.552033\pi$
$224$	1.93054	−	5.31724i	0.128990	−	0.355273i
$225$	−12.9712	+	7.10456i	−0.864746	+	0.473637i
$226$	0.787397	+	1.25965i	0.0523769	+	0.0837909i
$227$	7.43425	−	2.70584i	0.493428	−	0.179593i	−0.0833076	−	0.996524i	$-0.526548\pi$
$227$	7.43425	−	2.70584i	0.493428	−	0.179593i	0.576736	+	0.816931i	$0.304326\pi$
$228$	11.2409	−	3.73354i	0.744447	−	0.247260i
$229$	13.3833	−	11.2300i	0.884396	−	0.742096i	−0.0826823	−	0.996576i	$-0.526349\pi$
$229$	13.3833	−	11.2300i	0.884396	−	0.742096i	0.967078	+	0.254480i	$0.0819042\pi$
$230$	−1.11643	+	1.00556i	−0.0736155	+	0.0663048i
$231$	7.38396	+	7.55206i	0.485829	+	0.496889i
$232$	−11.3963	+	5.56507i	−0.748204	+	0.365365i
$233$	−8.64256	+	4.98978i	−0.566193	+	0.326892i	−0.755627	−	0.655002i	$-0.772668\pi$
$233$	−8.64256	+	4.98978i	−0.566193	+	0.326892i	0.189434	+	0.981893i	$0.439335\pi$
$234$	−5.30568	−	1.85600i	−0.346843	−	0.121331i
$235$	2.37729	+	1.37253i	0.155077	+	0.0895339i
$236$	−0.427821	+	4.08291i	−0.0278488	+	0.265775i
$237$	−18.3211	−	1.81087i	−1.19008	−	0.117629i
$238$	−1.10786	+	3.41148i	−0.0718119	+	0.221134i
$239$	−4.46340	−	25.3132i	−0.288713	−	1.63737i	−0.691711	−	0.722174i	$-0.743143\pi$
$239$	−4.46340	−	25.3132i	−0.288713	−	1.63737i	0.402998	−	0.915201i	$-0.367968\pi$
$240$	1.35570	−	1.23756i	0.0875100	−	0.0798839i
$241$	15.9103	+	13.3503i	1.02487	+	0.859971i	0.990232	−	0.139429i	$-0.0445267\pi$
$241$	15.9103	+	13.3503i	1.02487	+	0.859971i	0.0346411	+	0.999400i	$0.488971\pi$
$242$	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
$246$	3.02864	+	4.11331i	0.193099	+	0.262255i
$247$	−4.46127	+	0.786641i	−0.283864	+	0.0500528i
$248$	7.44213	+	1.85177i	0.472576	+	0.117587i
$249$	0.458747	−	4.64126i	0.0290719	−	0.294128i
$250$	−0.517226	+	3.68449i	−0.0327122	+	0.233028i
$251$	−11.8373	+	20.5028i	−0.747162	+	1.29412i	0.202016	+	0.979382i	$0.435251\pi$
$251$	−11.8373	+	20.5028i	−0.747162	+	1.29412i	−0.949178	+	0.314740i	$0.898083\pi$
$252$	5.72945	+	1.78140i	0.360922	+	0.112218i
$253$	−12.2265	−	21.1770i	−0.768676	−	1.33139i
$254$	0.971931	−	0.392865i	0.0609844	−	0.0246505i
$255$	−0.832220	+	0.813696i	−0.0521157	+	0.0509556i
$256$	8.93025	−	13.2759i	0.558140	−	0.829747i
$257$	−15.4657	−	18.4313i	−0.964724	−	1.14971i	−0.988686	−	0.150001i	$-0.952072\pi$
$257$	−15.4657	−	18.4313i	−0.964724	−	1.14971i	0.0239616	−	0.999713i	$-0.492372\pi$
$258$	−3.51273	−	11.9628i	−0.218693	−	0.744771i
$259$	2.50560	+	6.88408i	0.155690	+	0.427756i
$260$	−0.581894	+	0.392761i	−0.0360875	+	0.0243580i
$261$	−6.46201	−	11.7981i	−0.399988	−	0.730281i
$262$	−28.3599	−	15.0734i	−1.75208	−	0.931240i
$263$	−2.46725	+	13.9925i	−0.152137	+	0.862814i	0.809219	+	0.587507i	$0.199891\pi$
$263$	−2.46725	+	13.9925i	−0.152137	+	0.862814i	−0.961356	+	0.275307i	$0.911220\pi$
$264$	15.1093	+	25.7713i	0.929914	+	1.58611i
$265$	1.75992	+	0.640557i	0.108111	+	0.0393491i
$266$	4.72976	−	1.00613i	0.290000	−	0.0616895i
$267$	−1.12891	−	14.8231i	−0.0690881	−	0.907159i
$268$	6.25194	−	8.61080i	0.381898	−	0.525988i
$269$		−	14.3360i		−	0.874081i	−0.899442	−	0.437041i	$-0.856027\pi$
$269$		−	14.3360i		−	0.874081i	0.899442	−	0.437041i	$-0.143973\pi$
$270$	1.37850	+	1.37491i	0.0838928	+	0.0836746i
$271$			18.9316i			1.15001i	0.818149	+	0.575007i	$0.195001\pi$
$271$			18.9316i			1.15001i	−0.818149	+	0.575007i	$0.804999\pi$
$272$	−5.37066	+	8.60701i	−0.325644	+	0.521877i
$273$	−2.06869	−	0.993143i	−0.125203	−	0.0601077i
$274$	0.0316511	+	0.148791i	0.00191211	+	0.00898878i
$275$	−28.2489	−	10.2818i	−1.70348	−	0.620014i
$276$	−11.8281	−	7.28425i	−0.711965	−	0.438461i
$277$	−1.18175	+	6.70204i	−0.0710045	+	0.402687i	0.928504	+	0.371324i	$0.121096\pi$
$277$	−1.18175	+	6.70204i	−0.0710045	+	0.402687i	−0.999508	+	0.0313631i	$0.990015\pi$
$278$	6.49011	−	12.2108i	0.389251	−	0.732355i
$279$	−1.59244	+	7.97686i	−0.0953368	+	0.477562i
$280$	0.606055	−	0.440766i	0.0362187	−	0.0263408i
$281$	6.97569	+	19.1656i	0.416135	+	1.14332i	0.953873	+	0.300210i	$0.0970566\pi$
$281$	6.97569	+	19.1656i	0.416135	+	1.14332i	−0.537738	+	0.843112i	$0.680721\pi$
$282$	−5.98296	+	24.6632i	−0.356280	+	1.46867i
$283$	9.28422	+	11.0645i	0.551889	+	0.657716i	0.967809	−	0.251685i	$-0.0809847\pi$
$283$	9.28422	+	11.0645i	0.551889	+	0.657716i	−0.415920	+	0.909401i	$0.636540\pi$
$284$	10.6021	−	10.2448i	0.629117	−	0.607917i
$285$	1.51098	+	0.423148i	0.0895028	+	0.0250651i
$286$	−4.28174	−	10.5928i	−0.253185	−	0.626368i
$287$	1.04267	+	1.80596i	0.0615470	+	0.106603i
$288$	14.5092	+	8.80241i	0.854964	+	0.518687i
$289$	−5.28361	+	9.15147i	−0.310800	+	0.538322i
$290$	−1.66379	−	0.233561i	−0.0977008	−	0.0137152i
$291$	25.1448	+	18.0317i	1.47401	+	1.05704i
$292$	−14.5262	−	4.16034i	−0.850082	−	0.243465i
$293$	−7.72115	+	1.36145i	−0.451075	+	0.0795366i	−0.394570	−	0.918866i	$-0.629107\pi$
$293$	−7.72115	+	1.36145i	−0.451075	+	0.0795366i	−0.0565043	+	0.998402i	$0.517995\pi$
$294$	2.24401	+	0.982051i	0.130873	+	0.0572744i
$295$	−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
$300$	−16.8953	+	2.48685i	−0.975450	+	0.143578i
$301$	−0.883867	−	5.01266i	−0.0509452	−	0.288925i
$302$	−13.8221	−	4.48864i	−0.795372	−	0.258292i
$303$	−10.3307	−	22.8213i	−0.593482	−	1.31105i
$304$	13.6691	+	0.468650i	0.783975	+	0.0268789i
$305$	1.86130	+	1.07462i	0.106578	+	0.0615327i
$306$	−9.38576	−	5.26286i	−0.536548	−	0.300858i
$307$	15.1078	−	8.72250i	0.862248	−	0.497819i	−0.00251619	−	0.999997i	$-0.500801\pi$
$307$	15.1078	−	8.72250i	0.862248	−	0.497819i	0.864765	+	0.502177i	$0.167468\pi$
$308$	4.96409	+	11.1400i	0.282855	+	0.634761i
$309$	8.01455	−	2.05110i	0.455932	−	0.116683i
$310$	0.679922	+	0.754889i	0.0386170	+	0.0428748i
$311$	13.1215	−	11.0102i	0.744051	−	0.624333i	−0.189872	−	0.981809i	$-0.560807\pi$
$311$	13.1215	−	11.0102i	0.744051	−	0.624333i	0.933922	+	0.357476i	$0.116363\pi$
$312$	−4.99975	−	4.13873i	−0.283055	−	0.234310i
$313$	−18.0562	+	6.57190i	−1.02059	+	0.371466i	−0.797492	−	0.603329i	$-0.793840\pi$
$313$	−18.0562	+	6.57190i	−1.02059	+	0.371466i	−0.223102	+	0.974795i	$0.571618\pi$
$314$	−7.94164	+	4.96424i	−0.448173	+	0.280148i
$315$	0.497081	+	0.620230i	0.0280074	+	0.0349460i
$316$	−19.1099	−	9.31304i	−1.07502	−	0.523899i
$317$	10.2751	+	1.81177i	0.577106	+	0.101759i	0.454580	−	0.890706i	$-0.349789\pi$
$317$	10.2751	+	1.81177i	0.577106	+	0.101759i	0.122526	+	0.992465i	$0.460900\pi$
$318$	−1.09800	+	17.2801i	−0.0615726	+	0.969022i
$319$	9.35187	−	25.6941i	0.523604	−	1.43859i
$320$	1.96448	−	0.795879i	0.109818	−	0.0444910i
$321$	6.25967	+	9.15739i	0.349381	+	0.511116i
$322$	−4.46938	−	3.49072i	−0.249069	−	0.194530i
$323$	−8.67229			−0.482539
$324$	−8.60574	+	15.8095i	−0.478097	+	0.878307i
$325$	6.53134			0.362293
$326$	−15.9208	−	12.4346i	−0.881771	−	0.688690i
$327$	13.6079	+	19.9072i	0.752518	+	1.10087i
$328$	1.62847	+	5.66898i	0.0899175	+	0.313017i
$329$	−3.54359	+	9.73592i	−0.195364	+	0.536759i
$330$	−0.250958	+	3.94955i	−0.0138148	+	0.217415i
$331$	−26.9120	−	4.74531i	−1.47922	−	0.260826i	−0.624952	−	0.780663i	$-0.714882\pi$
$331$	−26.9120	−	4.74531i	−1.47922	−	0.260826i	−0.854266	+	0.519837i	$0.825993\pi$
$332$	2.35926	−	4.84110i	0.129481	−	0.265690i
$333$	−21.7242	+	3.32827i	−1.19048	+	0.182388i
$334$	9.04187	−	5.65198i	0.494749	−	0.309263i
$335$	1.32465	−	0.482134i	0.0723734	−	0.0263418i
$336$	5.48852	+	4.22802i	0.299423	+	0.230658i
$337$	−11.9661	+	10.0408i	−0.651835	+	0.546955i	−0.907627	−	0.419777i	$-0.862108\pi$
$337$	−11.9661	+	10.0408i	−0.651835	+	0.546955i	0.255792	+	0.966732i	$0.417664\pi$
$338$	−10.6427	−	11.8161i	−0.578886	−	0.642713i
$339$	−1.76256	+	0.451078i	−0.0957290	+	0.0244992i
$340$	−1.22760	+	0.547031i	−0.0665762	+	0.0296669i
$341$	−14.3190	+	8.26711i	−0.775420	+	0.447689i
$342$	0.182146	+	14.5056i	0.00984932	+	0.784374i
$343$	0.866025	+	0.500000i	0.0467610	+	0.0269975i
$344$	0.997425	−	14.3621i	0.0537776	−	0.774350i
$345$	−0.758887	−	1.67644i	−0.0408571	−	0.0902566i
$346$	33.2516	+	10.7983i	1.78762	+	0.580518i
$347$	0.759626	+	4.30805i	0.0407789	+	0.231268i	0.998385	−	0.0568127i	$-0.0180938\pi$
$347$	0.759626	+	4.30805i	0.0407789	+	0.231268i	−0.957606	+	0.288081i	$0.906983\pi$
$348$	−2.26193	−	15.3673i	−0.121252	−	0.823771i
$349$	−19.1646	−	16.0810i	−1.02586	−	0.860799i	−0.0355075	−	0.999369i	$-0.511305\pi$
$349$	−19.1646	−	16.0810i	−1.02586	−	0.860799i	−0.990353	+	0.138571i	$0.955749\pi$
$350$	−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	−0.675987	−	0.736913i	$-0.736283\pi$
$353$	3.13979	−	3.74186i	0.167114	−	0.199159i	0.843102	+	0.537754i	$0.180727\pi$
$354$	−4.60612	−	2.01579i	−0.244813	−	0.107138i
$355$	1.92340	−	0.339148i	0.102084	−	0.0180001i
$356$	4.72630	−	16.5023i	0.250494	−	0.874622i
$357$	−3.56994	−	2.56006i	−0.188941	−	0.135492i
$358$	17.2562	+	2.42241i	0.912019	+	0.128028i
$359$	3.44207	−	5.96183i	0.181665	−	0.314654i	−0.760782	−	0.649007i	$-0.775185\pi$
$359$	3.44207	−	5.96183i	0.181665	−	0.314654i	0.942448	+	0.334353i	$0.108518\pi$
$360$	0.940770	+	2.04185i	0.0495829	+	0.107615i
$361$	−3.65428	−	6.32940i	−0.192330	−	0.333126i
$362$	−1.03559	−	2.56199i	−0.0544292	−	0.134655i
$363$	−43.6743	−	12.2309i	−2.29231	−	0.641958i
$364$	−1.84127	−	1.90548i	−0.0965085	−	0.0998741i
$365$	−1.28667	−	1.53340i	−0.0673476	−	0.0802618i
$366$	−4.68436	+	19.3101i	−0.244855	+	1.00936i
$367$	11.5429	+	31.7138i	0.602533	+	1.65544i	0.746124	+	0.665808i	$0.231913\pi$
$367$	11.5429	+	31.7138i	0.602533	+	1.65544i	−0.143591	+	0.989637i	$0.545865\pi$
$368$	−9.88328	−	12.6335i	−0.515202	−	0.658566i
$369$	−5.92542	+	2.00683i	−0.308465	+	0.104472i
$370$	−1.28829	+	2.42385i	−0.0669751	+	0.126010i
$371$	−1.22749	+	6.96142i	−0.0637279	+	0.361419i
$372$	−4.92533	+	7.99767i	−0.255366	+	0.414660i
$373$	2.63950	+	0.960699i	0.136668	+	0.0497431i	0.409449	−	0.912333i	$-0.365721\pi$
$373$	2.63950	+	0.960699i	0.136668	+	0.0497431i	−0.272781	+	0.962076i	$0.587943\pi$
$374$	−4.55098	−	21.3940i	−0.235325	−	1.10626i
$375$	−4.10794	−	1.97215i	−0.212133	−	0.101841i
$376$	−16.3754	+	24.3024i	−0.844496	+	1.25330i
$377$			5.94063i			0.305958i
$378$	−4.20707	+	6.02500i	−0.216388	+	0.309892i
$379$		−	12.9476i		−	0.665074i	−0.943090	−	0.332537i	$-0.892095\pi$
$379$		−	12.9476i		−	0.665074i	0.943090	−	0.332537i	$-0.107905\pi$
$380$	1.46616	+	1.06452i	0.0752125	+	0.0546086i
$381$	0.0975005	+	1.28023i	0.00499510	+	0.0655881i
$382$	24.8061	−	5.27681i	1.26919	−	0.269985i
$383$	−11.1971	−	4.07539i	−0.572143	−	0.208243i	0.0397146	−	0.999211i	$-0.487355\pi$
$383$	−11.1971	−	4.07539i	−0.572143	−	0.208243i	−0.611857	+	0.790968i	$0.709577\pi$
$384$	12.1770	+	15.3532i	0.621405	+	0.783490i
$385$	−0.280554	+	1.59110i	−0.0142984	+	0.0810901i
$386$	28.3988	+	15.0942i	1.44546	+	0.768272i
$387$	15.2661	+	0.343682i	0.776019	+	0.0174703i
$388$	19.9886	+	29.6140i	1.01477	+	1.50343i
$389$	8.44612	+	23.2055i	0.428235	+	1.17657i	0.946883	+	0.321578i	$0.104213\pi$
$389$	8.44612	+	23.2055i	0.428235	+	1.17657i	−0.518648	+	0.854988i	$0.673564\pi$
$390$	−0.242248	−	0.824990i	−0.0122667	−	0.0417750i
$391$	6.53753	+	7.79113i	0.330617	+	0.394014i
$392$	2.03554	+	1.96382i	0.102810	+	0.0991880i
$393$	28.1253	−	27.4992i	1.41873	−	1.38715i
$394$	32.6738	−	13.2071i	1.64608	−	0.665364i
$395$	−1.40810	−	2.43889i	−0.0708490	−	0.122714i
$396$	−35.6888	+	8.06148i	−1.79343	+	0.405105i
$397$	−17.8150	+	30.8565i	−0.894110	+	1.54864i	−0.0592070	+	0.998246i	$0.518857\pi$
$397$	−17.8150	+	30.8565i	−0.894110	+	1.54864i	−0.834903	+	0.550398i	$0.814476\pi$
$398$	−2.93396	+	20.9003i	−0.147066	+	1.04764i
$399$	−0.582533	+	5.89364i	−0.0291631	+	0.295051i
$400$	−19.2909	−	4.08761i	−0.964545	−	0.204381i
$401$	−20.7094	+	3.65163i	−1.03418	+	0.182354i	−0.664875	−	0.746954i	$-0.731515\pi$
$401$	−20.7094	+	3.65163i	−1.03418	+	0.182354i	−0.369305	+	0.929308i	$0.620404\pi$
$402$	7.72725	+	10.4947i	0.385400	+	0.523428i
$403$	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
$408$	−8.05015	−	9.46478i	−0.398542	−	0.468576i
$409$	0.530601	+	3.00919i	0.0262365	+	0.148795i	0.995112	−	0.0987546i	$-0.0314859\pi$
$409$	0.530601	+	3.00919i	0.0262365	+	0.148795i	−0.968875	+	0.247549i	$0.920375\pi$
$410$	−0.241336	+	0.743158i	−0.0119188	+	0.0367020i
$411$	−0.185405	−	0.0183256i	−0.00914534	−	0.000903934i
$412$	9.50065	+	0.995512i	0.468064	+	0.0490453i
$413$	−1.77763	−	1.02632i	−0.0874715	−	0.0505017i
$414$	12.8944	−	11.0986i	0.633727	−	0.545465i
$415$	0.617842	−	0.356711i	0.0303287	−	0.0175103i
$416$	−3.75244	−	6.48753i	−0.183978	−	0.318077i
$417$	11.8402	+	12.1098i	0.579818	+	0.593019i
$418$	−21.9103	+	19.7344i	−1.07167	+	0.965240i
$419$	−5.30321	+	4.44992i	−0.259079	+	0.217393i	−0.763070	−	0.646316i	$-0.776309\pi$
$419$	−5.30321	+	4.44992i	−0.259079	+	0.217393i	0.503991	+	0.863709i	$0.331864\pi$
$420$	0.289299	+	0.871018i	0.0141164	+	0.0425013i
$421$	3.73412	−	1.35911i	0.181990	−	0.0662389i	−0.249418	−	0.968396i	$-0.580239\pi$
$421$	3.73412	−	1.35911i	0.181990	−	0.0662389i	0.431408	+	0.902157i	$0.358017\pi$
$422$	7.44546	+	11.9110i	0.362439	+	0.579819i
$423$	−26.5614	−	16.1430i	−1.29146	−	0.784901i
$424$	−8.12344	+	18.2689i	−0.394509	+	0.887219i
$425$	12.3135	+	2.17120i	0.597291	+	0.105319i
$426$	8.01849	+	16.1785i	0.388497	+	0.783850i
$427$	−2.77445	+	7.62275i	−0.134265	+	0.368891i
$428$	3.10257	+	12.4269i	0.149969	+	0.600679i
$429$	13.9529	−	1.06263i	0.673652	−	0.0513045i
$430$	1.17394	−	1.50306i	0.0566123	−	0.0724842i
$431$	15.4450			0.743958			0.371979	−	0.928241i	$-0.378679\pi$
$431$	15.4450			0.743958			0.371979	+	0.928241i	$0.378679\pi$
$432$	−15.6621	+	13.6638i	−0.753542	+	0.657400i
$433$	−32.8075			−1.57663			−0.788315	−	0.615272i	$-0.789046\pi$
$433$	−32.8075			−1.57663			−0.788315	+	0.615272i	$0.789046\pi$
$434$	−2.36029	+	3.02202i	−0.113298	+	0.145062i
$435$	0.890551	−	1.85500i	0.0426987	−	0.0889403i
$436$	6.74468	+	27.0149i	0.323012	+	1.29378i
$437$	4.68956	−	12.8845i	0.224332	−	0.616348i
$438$	10.2508	−	15.4078i	0.489801	−	0.736213i
$439$	36.4354	+	6.42454i	1.73897	+	0.306627i	0.951023	−	0.309121i	$-0.100035\pi$
$439$	36.4354	+	6.42454i	1.73897	+	0.306627i	0.787943	+	0.615748i	$0.211146\pi$
$440$	−1.85669	+	4.17555i	−0.0885145	+	0.199062i
$441$	−1.97960	+	2.25415i	−0.0942666	+	0.107340i
$442$	2.51888	+	4.02963i	0.119811	+	0.191670i
$443$	15.7559	−	5.73469i	0.748587	−	0.272464i	0.0605762	−	0.998164i	$-0.480706\pi$
$443$	15.7559	−	5.73469i	0.748587	−	0.272464i	0.688011	+	0.725700i	$0.258484\pi$
$444$	−24.8569	−	5.11444i	−1.17966	−	0.242721i
$445$	1.74200	−	1.46171i	0.0825787	−	0.0692918i
$446$	−0.347256	+	0.312770i	−0.0164430	+	0.0148101i
$447$	−3.14117	+	11.2165i	−0.148572	+	0.530522i
$448$	4.24581	+	6.78035i	0.200596	+	0.320341i
$449$	−26.0115	+	15.0177i	−1.22756	+	0.708731i	−0.966519	−	0.256597i	$-0.917399\pi$
$449$	−26.0115	+	15.0177i	−1.22756	+	0.708731i	−0.261040	+	0.965328i	$0.584065\pi$
$450$	3.37301	−	20.6416i	0.159005	−	0.973055i
$451$	−11.0127	−	6.35821i	−0.518570	−	0.299396i
$452$	−2.08938	−	0.218933i	−0.0982762	−	0.0102977i
$453$	10.3724	−	14.4641i	0.487338	−	0.679583i
$454$	−3.45570	+	10.6413i	−0.162184	+	0.499421i
$455$	−0.0609541	−	0.345688i	−0.00285757	−	0.0162061i
$456$	−5.62397	+	15.7786i	−0.263367	+	0.738903i
$457$	27.4429	+	23.0274i	1.28373	+	1.07717i	0.992719	+	0.120454i	$0.0384351\pi$
$457$	27.4429	+	23.0274i	1.28373	+	1.07717i	0.291008	+	0.956721i	$0.406009\pi$
$458$	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	0.300030	−	0.953930i	$-0.403003\pi$
$461$	25.4939	−	30.3824i	1.18737	−	1.41505i	0.887338	−	0.461120i	$-0.152552\pi$
$462$	−14.8449	+	1.65575i	−0.690648	+	0.0770323i
$463$	3.78973	−	0.668232i	0.176124	−	0.0310554i	−0.0848906	−	0.996390i	$-0.527054\pi$
$463$	3.78973	−	0.668232i	0.176124	−	0.0310554i	0.261014	+	0.965335i	$0.415943\pi$
$464$	3.71792	−	17.5462i	0.172600	−	0.814561i
$465$	−1.13354	+	0.513130i	−0.0525669	+	0.0237958i
$466$	1.96197	−	13.9762i	0.0908863	−	0.647435i
$467$	16.7389	−	28.9926i	0.774584	−	1.34162i	−0.160445	−	0.987045i	$-0.551293\pi$
$467$	16.7389	−	28.9926i	0.774584	−	1.34162i	0.935028	−	0.354573i	$-0.115374\pi$
$468$	6.68721	−	4.29781i	0.309116	−	0.198666i
$469$	2.66027	+	4.60772i	0.122840	+	0.212765i
$470$	−3.59919	+	1.45483i	−0.166018	+	0.0671063i
$471$	−2.84388	−	11.1123i	−0.131039	−	0.512026i
$472$	−4.17820	−	4.03100i	−0.192317	−	0.185542i
$473$	19.9513	+	23.7770i	0.917361	+	1.09327i
$474$	17.9668	−	18.8435i	0.825244	−	0.865510i
$475$	−5.76521	−	15.8398i	−0.264526	−	0.726779i
$476$	−2.83789	−	4.20447i	−0.130074	−	0.192711i
$477$	−19.7592	−	7.69970i	−0.904713	−	0.352545i
$478$	32.0983	+	17.0604i	1.46814	+	0.780327i
$479$	−2.28613	+	12.9653i	−0.104456	+	0.592400i	0.886980	+	0.461808i	$0.152799\pi$
$479$	−2.28613	+	12.9653i	−0.104456	+	0.592400i	−0.991436	+	0.130592i	$0.958312\pi$
$480$	0.199186	+	2.58829i	0.00909156	+	0.118139i
$481$	9.12049	+	3.31959i	0.415859	+	0.151360i
$482$	−28.7296	+	6.11143i	−1.30860	+	0.278368i
$483$	5.73394	−	3.91953i	0.260903	−	0.178345i
$484$	−42.3788	−	30.7695i	−1.92631	−	1.39861i
$485$			4.73311i			0.214919i
$486$	−15.2544	−	15.9155i	−0.691953	−	0.721942i
$487$			25.5869i			1.15945i	0.814811	+	0.579727i	$0.196841\pi$
$487$			25.5869i			1.15945i	−0.814811	+	0.579727i	$0.803159\pi$
$488$	−12.8211	+	19.0276i	−0.580385	+	0.861340i
$489$	20.4254	−	13.9621i	0.923668	−	0.631388i
$490$	0.0779611	+	0.366492i	0.00352192	+	0.0165564i
$491$	32.0106	+	11.6509i	1.44462	+	0.525798i	0.941083	−	0.338176i	$-0.109810\pi$
$491$	32.0106	+	11.6509i	1.44462	+	0.525798i	0.503536	+	0.863974i	$0.332032\pi$
$492$	−7.22093	−	0.205061i	−0.325545	−	0.00924487i
$493$	−1.97483	+	11.1998i	−0.0889419	+	0.504415i
$494$	3.00678	−	5.65709i	0.135281	−	0.254525i
$495$	−4.51617	−	1.75984i	−0.202987	−	0.0790991i
$496$	−8.54227	+	6.68269i	−0.383559	+	0.300061i
$497$	2.52122	+	6.92700i	0.113092	+	0.310718i
$498$	4.77360	+	4.55152i	0.213910	+	0.203958i
$499$	10.8209	+	12.8959i	0.484411	+	0.577299i	0.951787	−	0.306760i	$-0.0992448\pi$
$499$	10.8209	+	12.8959i	0.484411	+	0.577299i	−0.467376	+	0.884059i	$0.654800\pi$
$500$	−3.65632	−	3.78383i	−0.163516	−	0.169218i
$501$	3.23787	+	12.6517i	0.144657	+	0.565238i
$502$	−12.5471	−	31.0409i	−0.560003	−	1.38542i
$503$	−4.15479	−	7.19631i	−0.185253	−	0.320868i	0.758409	−	0.651779i	$-0.225977\pi$
$503$	−4.15479	−	7.19631i	−0.185253	−	0.320868i	−0.943662	+	0.330912i	$0.892644\pi$
$504$	−6.97295	+	4.83507i	−0.310600	+	0.215371i
$505$	1.91597	−	3.31856i	0.0852595	−	0.147674i
$506$	34.2461	+	4.80743i	1.52242	+	0.213717i
$507$	17.7432	−	8.03192i	0.788001	−	0.356710i
$508$	−0.408197	+	1.42526i	−0.0181108	+	0.0632356i
$509$	−12.8218	+	2.26082i	−0.568315	+	0.100209i	−0.450420	−	0.892817i	$-0.648726\pi$
$509$	−12.8218	+	2.26082i	−0.568315	+	0.100209i	−0.117895	+	0.993026i	$0.537615\pi$
$510$	−0.182460	−	1.63588i	−0.00807945	−	0.0724378i
$511$	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
$516$	16.3910	+	6.49848i	0.721574	+	0.286080i
$517$	−10.9711	−	62.2200i	−0.482507	−	2.73643i
$518$	−9.85380	−	3.19996i	−0.432951	−	0.140598i
$519$	−24.9527	+	34.7961i	−1.09530	+	1.52738i
$520$	0.0687854	−	0.990450i	0.00301644	−	0.0434341i
$521$	−36.1611	−	20.8776i	−1.58425	−	0.914666i	−0.994229	−	0.107277i	$-0.965787\pi$
$521$	−36.1611	−	20.8776i	−1.58425	−	0.914666i	−0.590019	−	0.807389i	$-0.700880\pi$
$522$	18.7747	+	3.06795i	0.821748	+	0.134280i
$523$	24.8984	−	14.3751i	1.08873	−	0.628578i	0.155492	−	0.987837i	$-0.450304\pi$
$523$	24.8984	−	14.3751i	1.08873	−	0.628578i	0.933238	+	0.359259i	$0.116970\pi$
$524$	41.4874	−	18.4872i	1.81239	−	0.807615i
$525$	2.30265	−	8.22233i	0.100496	−	0.358852i
$526$	−13.4476	−	14.9304i	−0.586345	−	0.650994i
$527$	5.26805	−	4.42042i	0.229480	−	0.192557i
$528$	−41.8762	−	5.59378i	−1.82243	−	0.243438i
$529$	6.50242	−	2.36669i	0.282714	−	0.102899i
$530$	−2.24594	+	1.40392i	−0.0975575	+	0.0609822i
$531$	4.06339	−	4.62694i	0.176336	−	0.200792i
$532$	−2.99587	+	6.14740i	−0.129888	+	0.266524i
$533$	2.72083	+	0.479756i	0.117852	+	0.0207805i
$534$	17.5039	+	11.6453i	0.757466	+	0.503941i
$535$	−0.580332	+	1.59445i	−0.0250899	+	0.0689340i
$536$	4.15489	+	14.4638i	0.179464	+	0.624742i
$537$	−9.23649	+	19.2394i	−0.398584	+	0.830241i
$538$	15.9782	+	12.4795i	0.688871	+	0.538029i
$539$	−6.09799			−0.262659
$540$	−2.73240	+	0.339548i	−0.117584	+	0.0146118i
$541$	16.1185			0.692990			0.346495	−	0.938052i	$-0.387372\pi$
$541$	16.1185			0.692990			0.346495	+	0.938052i	$0.387372\pi$
$542$	−21.1003	−	16.4800i	−0.906335	−	0.707875i
$543$	3.37466	−	0.257010i	0.144820	−	0.0110293i
$544$	−4.91781	−	13.4783i	−0.210849	−	0.577877i
$545$	−1.26158	+	3.46617i	−0.0540402	+	0.148474i
$546$	2.90771	−	1.44114i	0.124438	−	0.0616750i
$547$	27.6779	+	4.88035i	1.18342	+	0.208669i	0.730519	−	0.682892i	$-0.239278\pi$
$547$	27.6779	+	4.88035i	1.18342	+	0.208669i	0.452901	+	0.891561i	$0.350389\pi$
$548$	−0.193388	−	0.0942455i	−0.00826111	−	0.00402597i
$549$	−20.7963	−	12.6392i	−0.887564	−	0.539428i
$550$	36.0503	−	22.5347i	1.53719	−	0.960882i
$551$	14.4072	−	5.24380i	0.613768	−	0.223393i
$552$	18.4150	−	6.84206i	0.783795	−	0.291217i
$553$	8.14247	−	6.83234i	0.346253	−	0.290541i
$554$	−6.44107	−	7.15125i	−0.273655	−	0.303828i
$555$	−2.35029	−	2.40380i	−0.0997644	−	0.102036i
$556$	7.95995	+	17.8631i	0.337577	+	0.757563i
$557$	−1.80737	+	1.04349i	−0.0765807	+	0.0442139i	−0.537801	−	0.843072i	$-0.680745\pi$
$557$	−1.80737	+	1.04349i	−0.0765807	+	0.0442139i	0.461221	+	0.887285i	$0.347412\pi$
$558$	−7.50442	−	8.71871i	−0.317687	−	0.369093i
$559$	−5.84009	−	3.37178i	−0.247010	−	0.142611i
$560$	−0.0363141	+	1.05917i	−0.00153455	+	0.0447580i
$561$	26.6585	+	2.63495i	1.12552	+	0.111248i
$562$	−27.4334	−	8.90884i	−1.15721	−	0.375797i
$563$	6.88053	+	39.0214i	0.289980	+	1.64456i	0.686935	+	0.726719i	$0.258956\pi$
$563$	6.88053	+	39.0214i	0.289980	+	1.64456i	−0.396955	+	0.917838i	$0.629933\pi$
$564$	−22.2803	−	28.1377i	−0.938172	−	1.18481i
$565$	−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	−0.456996	−	0.889469i	$-0.651075\pi$
$569$	11.8867	−	14.1660i	0.498316	−	0.593870i	0.955312	+	0.295599i	$0.0955192\pi$
$570$	−1.78693	+	1.31572i	−0.0748463	+	0.0551094i
$571$	12.1340	−	2.13955i	0.507793	−	0.0895375i	0.0861183	−	0.996285i	$-0.472554\pi$
$571$	12.1340	−	2.13955i	0.507793	−	0.0895375i	0.421674	+	0.906747i	$0.361443\pi$
$572$	15.5335	+	4.44884i	0.649490	+	0.186015i
$573$	−3.05520	+	30.9103i	−0.127633	+	1.29130i
$574$	−2.92049	−	0.409975i	−0.121899	−	0.0171120i
$575$	−9.88431	+	17.1201i	−0.412204	+	0.713958i
$576$	−22.4410	+	8.50881i	−0.935043	+	0.354534i
$577$	6.34486	+	10.9896i	0.264140	+	0.457504i	0.967338	−	0.253490i	$-0.0815786\pi$
$577$	6.34486	+	10.9896i	0.264140	+	0.457504i	−0.703198	+	0.710994i	$0.748245\pi$
$578$	−5.60043	−	13.8552i	−0.232947	−	0.576301i
$579$	−28.1639	+	27.5370i	−1.17045	+	1.14440i
$580$	1.70864	−	1.65106i	0.0709475	−	0.0685567i
$581$	1.73083	+	2.06272i	0.0718069	+	0.0855761i
$582$	−41.9858	+	12.3286i	−1.74037	+	0.511038i
$583$	−14.7430	−	40.5060i	−0.610591	−	1.67759i
$584$	17.2820	−	12.5687i	0.715134	−	0.520095i
$585$	1.05279	+	0.0237013i	0.0435277	+	0.000979929i
$586$	5.20386	−	9.79078i	0.214969	−	0.404453i
$587$	2.08154	−	11.8050i	0.0859142	−	0.487244i	−0.911241	−	0.411873i	$-0.864875\pi$
$587$	2.08154	−	11.8050i	0.0859142	−	0.487244i	0.997156	−	0.0753709i	$-0.0240141\pi$
$588$	−3.04796	+	1.64619i	−0.125696	+	0.0678878i
$589$	−8.71197	−	3.17090i	−0.358971	−	0.130655i
$590$	−0.160025	−	0.752273i	−0.00658814	−	0.0309706i
$591$	3.27771	+	43.0379i	0.134827	+	1.77034i
$592$	−24.8606	−	15.5127i	−1.02177	−	0.637569i
$593$		−	40.6594i		−	1.66968i	−0.550491	−	0.834841i	$-0.685560\pi$
$593$		−	40.6594i		−	1.66968i	0.550491	−	0.834841i	$-0.314440\pi$
$594$	3.84741	−	44.6454i	0.157861	−	1.83182i
$595$		−	0.671985i		−	0.0275487i
$596$	−7.90226	+	10.8838i	−0.323689	+	0.445817i
$597$	−23.3023	−	11.1870i	−0.953699	−	0.457854i
$598$	−7.34893	+	1.56328i	−0.300520	+	0.0639273i
$599$	28.5266	+	10.3828i	1.16556	+	0.424231i	0.851082	−	0.525033i	$-0.175947\pi$
$599$	28.5266	+	10.3828i	1.16556	+	0.424231i	0.314482	+	0.949263i	$0.398169\pi$
$600$	11.9356	−	20.9955i	0.487270	−	0.857138i
$601$	0.780474	−	4.42629i	0.0318362	−	0.180552i	−0.964743	−	0.263193i	$-0.915224\pi$
$601$	0.780474	−	4.42629i	0.0318362	−	0.180552i	0.996579	+	0.0826411i	$0.0263355\pi$
$602$	6.35628	+	3.37840i	0.259063	+	0.137693i
$603$	−15.1181	+	5.12023i	−0.615656	+	0.208512i
$604$	17.0350	−	11.4981i	0.693143	−	0.467851i
$605$	−2.37286	−	6.51939i	−0.0964706	−	0.265051i
$606$	34.4284	+	8.35186i	1.39856	+	0.339271i
$607$	16.8343	+	20.0623i	0.683283	+	0.814305i	0.990526	−	0.137326i	$-0.0438508\pi$
$607$	16.8343	+	20.0623i	0.683283	+	0.814305i	−0.307243	+	0.951631i	$0.599406\pi$
$608$	−12.4213	+	14.8270i	−0.503749	+	0.601312i
$609$	7.47868	+	2.09440i	0.303052	+	0.0848692i
$610$	−2.81799	+	1.13906i	−0.114097	+	0.0461192i
$611$	6.86331	+	11.8876i	0.277660	+	0.480921i
$612$	14.0360	−	5.87961i	0.567374	−	0.237669i
$613$	10.5256	−	18.2308i	0.425124	−	0.736336i	−0.571308	−	0.820735i	$-0.693564\pi$
$613$	10.5256	−	18.2308i	0.425124	−	0.736336i	0.996432	+	0.0843998i	$0.0268973\pi$
$614$	−3.42966	+	24.4314i	−0.138410	+	0.985971i
$615$	−0.777677	−	0.557683i	−0.0313590	−	0.0224879i
$616$	−16.7374	−	4.16464i	−0.674368	−	0.167798i
$617$	25.0600	−	4.41876i	1.00888	−	0.177893i	0.355301	−	0.934752i	$-0.384378\pi$
$617$	25.0600	−	4.41876i	1.00888	−	0.177893i	0.653578	+	0.756859i	$0.273267\pi$
$618$	−4.69060	+	10.7181i	−0.188684	+	0.431147i
$619$	−2.18822	+	2.60782i	−0.0879521	+	0.104817i	−0.808226	−	0.588873i	$-0.799572\pi$
$619$	−2.18822	+	2.60782i	−0.0879521	+	0.104817i	0.720274	+	0.693690i	$0.244016\pi$
$620$	−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
$624$	8.96512	−	1.96972i	0.358892	−	0.0788519i
$625$	4.15922	+	23.5881i	0.166369	+	0.943523i
$626$	8.39314	−	25.8454i	0.335457	−	1.03299i
$627$	−14.8933	−	32.9005i	−0.594782	−	1.31392i
$628$	1.38029	−	13.1728i	0.0550794	−	0.525650i
$629$	16.0913	+	9.29029i	0.641601	+	0.370428i
$630$	−1.12399	+	0.0141138i	−0.0447808	+	0.000562309i
$631$	−21.6819	+	12.5180i	−0.863142	+	0.498335i	−0.865063	−	0.501663i	$-0.832722\pi$
$631$	−21.6819	+	12.5180i	−0.863142	+	0.498335i	0.00192146	+	0.999998i	$0.499388\pi$
$632$	27.0151	−	13.1921i	1.07460	−	0.524752i
$633$	−16.6664	+	4.26530i	−0.662429	+	0.169530i
$634$	−10.9638	+	9.87498i	−0.435427	+	0.392186i
$635$	−0.150451	+	0.126244i	−0.00597048	+	0.00500983i
$636$	−18.3038	−	16.2661i	−0.725794	−	0.644994i
$637$	1.24497	−	0.453131i	0.0493274	−	0.0179537i
$638$	20.4966	+	32.7898i	0.811468	+	1.29816i
$639$	−21.8596	+	3.34903i	−0.864753	+	0.132485i
$640$	−0.823034	+	2.88234i	−0.0325333	+	0.113934i
$641$	24.2742	+	4.28020i	0.958773	+	0.169058i	0.631072	−	0.775724i	$-0.282615\pi$
$641$	24.2742	+	4.28020i	0.958773	+	0.169058i	0.327701	+	0.944781i	$0.393726\pi$
$642$	−15.6554	−	0.994763i	−0.617871	−	0.0392602i
$643$	−7.65457	+	21.0308i	−0.301867	+	0.829372i	0.692309	+	0.721601i	$0.256594\pi$
$643$	−7.65457	+	21.0308i	−0.301867	+	0.829372i	−0.994176	+	0.107771i	$0.965629\pi$
$644$	7.78120	−	1.94269i	0.306622	−	0.0765528i
$645$	1.31815	+	1.92834i	0.0519019	+	0.0759283i
$646$	7.54923	−	9.66573i	0.297020	−	0.380293i
$647$	−8.04045			−0.316103			−0.158051	−	0.987431i	$-0.550521\pi$
$647$	−8.04045			−0.316103			−0.158051	+	0.987431i	$0.550521\pi$
$648$	−10.1293	−	23.3538i	−0.397915	−	0.917422i
$649$	12.5169			0.491333
$650$	−5.68553	+	7.27953i	−0.223005	+	0.285526i
$651$	−2.65023	−	3.87707i	−0.103871	−	0.151954i
$652$	27.7181	−	6.92024i	1.08552	−	0.271017i
$653$	−9.14893	+	25.1365i	−0.358025	+	0.983667i	0.621688	+	0.783265i	$0.286447\pi$
$653$	−9.14893	+	25.1365i	−0.358025	+	0.983667i	−0.979714	+	0.200402i	$0.935775\pi$
$654$	−34.0333	−	2.16251i	−1.33081	−	0.0845610i
$655$	5.92555	+	1.04484i	0.231531	+	0.0408251i
$656$	−7.73597	−	3.11983i	−0.302039	−	0.121809i
$657$	14.1745	+	17.6862i	0.553001	+	0.690004i
$658$	−7.76652	−	12.4246i	−0.302770	−	0.484363i
$659$	14.9464	−	5.44006i	0.582230	−	0.211915i	−0.0340784	−	0.999419i	$-0.510850\pi$
$659$	14.9464	−	5.44006i	0.582230	−	0.211915i	0.616309	+	0.787505i	$0.288627\pi$
$660$	−4.18352	−	3.71779i	−0.162843	−	0.144715i
$661$	21.5030	−	18.0432i	0.836371	−	0.701798i	−0.120374	−	0.992729i	$-0.538409\pi$
$661$	21.5030	−	18.0432i	0.836371	−	0.701798i	0.956744	+	0.290930i	$0.0939648\pi$
$662$	28.7158	−	25.8641i	1.11607	−	1.00524i
$663$	−5.63841	+	1.44300i	−0.218978	+	0.0560413i
$664$	3.34193	+	6.84370i	0.129692	+	0.265587i
$665$	−0.784557	+	0.452964i	−0.0304238	+	0.0175652i
$666$	15.2013	−	27.1100i	0.589040	−	1.05049i
$667$	−15.5717	−	8.99035i	−0.602940	−	0.348108i
$668$	−1.57151	+	14.9977i	−0.0608036	+	0.580278i
$669$	−0.236045	−	0.521441i	−0.00912601	−	0.0201601i
$670$	−0.615745	+	1.89609i	−0.0237883	+	0.0732524i
$671$	−8.58980	−	48.7152i	−0.331605	−	1.88063i
$672$	−9.49011	+	2.43675i	−0.366089	+	0.0939998i
$673$	23.4607	+	19.6859i	0.904343	+	0.758834i	0.971034	−	0.238939i	$-0.0767998\pi$
$673$	23.4607	+	19.6859i	0.904343	+	0.758834i	−0.0666911	+	0.997774i	$0.521244\pi$
$674$	−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	−0.206688	−	0.978407i	$-0.566268\pi$
$677$	20.6266	−	24.5819i	0.792746	−	0.944758i	0.999434	+	0.0336493i	$0.0107129\pi$
$678$	1.03156	−	2.35713i	0.0396167	−	0.0905250i
$679$	−17.5929	+	3.10211i	−0.675154	+	0.119048i
$680$	0.458934	−	1.84442i	0.0175993	−	0.0707303i
$681$	−11.1356	−	7.98548i	−0.426716	−	0.306004i
$682$	3.25060	−	23.1559i	0.124472	−	0.886684i
$683$	16.9029	−	29.2766i	0.646770	−	1.12024i	−0.337120	−	0.941462i	$-0.609453\pi$
$683$	16.9029	−	29.2766i	0.646770	−	1.12024i	0.983890	−	0.178776i	$-0.0572138\pi$
$684$	−16.3258	−	12.4241i	−0.624234	−	0.475048i
$685$	−0.0142495	−	0.0246809i	−0.000544447	−	0.000943010i
$686$	−1.31115	+	0.529982i	−0.0500600	+	0.0202348i
$687$	−29.1391	−	8.16036i	−1.11172	−	0.311337i
$688$	15.1390	+	13.6139i	0.577170	+	0.519023i
$689$	6.01986	+	7.17419i	0.229338	+	0.273315i
$690$	2.52910	+	0.613523i	0.0962810	+	0.0233564i
$691$	−14.5733	−	40.0399i	−0.554396	−	1.52319i	−0.827648	−	0.561247i	$-0.810322\pi$
$691$	−14.5733	−	40.0399i	−0.554396	−	1.52319i	0.273253	−	0.961942i	$-0.411901\pi$
$692$	−40.9807	+	27.6608i	−1.55785	+	1.05151i
$693$	3.58140	−	17.9400i	0.136046	−	0.681484i
$694$	−5.46281	−	2.90352i	−0.207366	−	0.110216i
$695$	−0.449871	+	2.55134i	−0.0170646	+	0.0967780i
$696$	19.0966	+	10.8561i	0.723856	+	0.411501i
$697$	4.97008	+	1.80896i	0.188255	+	0.0685193i
$698$	34.6060	−	7.36147i	1.30986	−	0.278636i
$699$	15.5824	+	7.48085i	0.589382	+	0.282952i
$700$	5.79280	−	7.97843i	0.218947	−	0.301556i
$701$		−	16.4373i		−	0.620827i	−0.950602	−	0.310413i	$-0.899533\pi$
$701$		−	16.4373i		−	0.620827i	0.950602	−	0.310413i	$-0.100467\pi$
$702$	2.53204	+	9.40072i	0.0955656	+	0.354807i
$703$		−	25.0492i		−	0.944749i
$704$	−43.0954	−	22.8617i	−1.62422	−	0.861631i
$705$	−0.361057	−	4.74085i	−0.0135982	−	0.178551i
$706$	1.43731	+	6.75676i	0.0540940	+	0.254294i
$707$	13.5908	+	4.94664i	0.511134	+	0.186038i
$708$	6.25634	−	3.37903i	0.235127	−	0.126992i
$709$	−0.119477	+	0.677587i	−0.00448705	+	0.0254473i	−0.986969	−	0.160910i	$-0.948557\pi$
$709$	−0.119477	+	0.677587i	−0.00448705	+	0.0254473i	0.982482	+	0.186357i	$0.0596682\pi$
$710$	−1.29633	+	2.43897i	−0.0486502	+	0.0915328i
$711$	15.3183	+	27.9674i	0.574480	+	1.04886i
$712$	14.2785	+	19.6330i	0.535109	+	0.735778i
$713$	3.71873	+	10.2171i	0.139268	+	0.382635i
$714$	5.96095	−	1.75036i	0.223083	−	0.0655057i
$715$	1.37590	+	1.63973i	0.0514557	+	0.0613226i
$716$	−17.7214	+	17.1243i	−0.662281	+	0.639963i
$717$	−31.8328	+	31.1242i	−1.18882	+	1.16235i
$718$	3.64846	+	9.02614i	0.136159	+	0.336853i
$719$	−20.4826	−	35.4769i	−0.763871	−	1.32306i	−0.940841	−	0.338848i	$-0.889963\pi$
$719$	−20.4826	−	35.4769i	−0.763871	−	1.32306i	0.176970	−	0.984216i	$-0.443370\pi$
$720$	−3.09469	−	0.728892i	−0.115332	−	0.0271642i
$721$	−2.38817	+	4.13643i	−0.0889400	+	0.154049i
$722$	10.2355	+	1.43685i	0.380926	+	0.0534740i
$723$	3.53843	−	35.7993i	0.131596	−	1.33139i
$724$	3.75696	+	1.07600i	0.139626	+	0.0399892i
$725$	−21.7691	+	3.83848i	−0.808485	+	0.142558i
$726$	51.6505	−	38.0304i	1.91693	−	1.41144i
$727$	−0.296828	+	0.353746i	−0.0110087	+	0.0131197i	−0.771521	−	0.636204i	$-0.780504\pi$
$727$	−0.296828	+	0.353746i	−0.0110087	+	0.0131197i	0.760512	+	0.649324i	$0.224948\pi$
$728$	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
$732$	−17.4444	−	22.0304i	−0.644764	−	0.814268i
$733$	1.18163	+	6.70137i	0.0436446	+	0.247521i	0.998823	−	0.0485111i	$-0.0154476\pi$
$733$	1.18163	+	6.70137i	0.0436446	+	0.247521i	−0.955178	+	0.296032i	$0.904337\pi$
$734$	−45.3947	−	14.7417i	−1.67555	−	0.544126i
$735$	−0.456677	−	0.0451384i	−0.0168448	−	0.00166496i
$736$	22.6841	−	0.0179924i	0.836147	−	0.000663209i
$737$	−28.0979	−	16.2223i	−1.03500	−	0.597557i
$738$	2.92135	−	8.35115i	0.107536	−	0.307410i
$739$	−31.0508	+	17.9272i	−1.14222	+	0.659462i	−0.946980	−	0.321293i	$-0.895882\pi$
$739$	−31.0508	+	17.9272i	−1.14222	+	0.659462i	−0.195242	+	0.980755i	$0.562549\pi$
$740$	−1.58006	−	3.54583i	−0.0580840	−	0.130347i
$741$	5.48541	+	5.61029i	0.201512	+	0.206099i
$742$	−6.69035	−	7.42802i	−0.245610	−	0.272691i
$743$	−9.19653	+	7.71681i	−0.337388	+	0.283102i	−0.795702	−	0.605688i	$-0.792898\pi$
$743$	−9.19653	+	7.71681i	−0.337388	+	0.283102i	0.458314	+	0.888790i	$0.348453\pi$
$744$	−4.62633	−	12.4515i	−0.169609	−	0.456494i
$745$	−1.67432	+	0.609402i	−0.0613423	+	0.0223268i
$746$	−3.36843	+	2.10557i	−0.123327	+	0.0770905i
$747$	−7.08495	+	3.88056i	−0.259225	+	0.141982i
$748$	27.8063	+	13.5511i	1.01670	+	0.495479i
$749$	−6.30690	−	1.11208i	−0.230449	−	0.0406344i
$750$	5.77403	−	2.86176i	0.210838	−	0.104497i
$751$	18.1675	−	49.9147i	0.662940	−	1.82141i	0.0998762	−	0.995000i	$-0.468155\pi$
$751$	18.1675	−	49.9147i	0.662940	−	1.82141i	0.563064	−	0.826413i	$-0.309622\pi$
$752$	−12.8316	−	39.4065i	−0.467920	−	1.43701i
$753$	40.8871	−	3.11391i	1.49001	−	0.113477i
$754$	−6.62115	−	5.17132i	−0.241128	−	0.188328i
$755$	2.72264			0.0990869
$756$	−3.05293	−	9.93376i	−0.111034	−	0.361287i
$757$	−17.8443			−0.648563			−0.324282	−	0.945961i	$-0.605123\pi$
$757$	−17.8443			−0.648563			−0.324282	+	0.945961i	$0.605123\pi$
$758$	14.4308	+	11.2709i	0.524151	+	0.409377i
$759$	−18.3304	+	38.1819i	−0.665353	+	1.38591i
$760$	−2.46276	+	0.707452i	−0.0893335	+	0.0256620i
$761$	−11.7016	+	32.1500i	−0.424184	+	1.16544i	0.525107	+	0.851036i	$0.324025\pi$
$761$	−11.7016	+	32.1500i	−0.424184	+	1.16544i	−0.949291	+	0.314399i	$0.898197\pi$
$762$	−1.51176	−	1.00577i	−0.0547652	−	0.0364352i
$763$	−13.7106	−	2.41754i	−0.496356	−	0.0875209i
$764$	−15.7124	+	32.2412i	−0.568456	+	1.16645i
$765$	1.97695	+	0.394662i	0.0714766	+	0.0142690i
$766$	14.2893	−	8.93209i	0.516293	−	0.322729i
$767$	−2.55546	+	0.930112i	−0.0922724	+	0.0335844i
$768$	−27.7120	+	0.206954i	−0.999972	+	0.00746782i
$769$	−3.72512	+	3.12575i	−0.134331	+	0.112717i	−0.707478	−	0.706736i	$-0.750167\pi$
$769$	−3.72512	+	3.12575i	−0.134331	+	0.112717i	0.573146	+	0.819453i	$0.305723\pi$
$770$	−1.52915	−	1.69775i	−0.0551066	−	0.0611826i
$771$	−11.2383	+	40.1298i	−0.404738	+	1.44524i
$772$	−41.5444	+	18.5126i	−1.49522	+	0.666282i
$773$	14.8042	−	8.54720i	0.532470	−	0.307421i	−0.209552	−	0.977798i	$-0.567201\pi$
$773$	14.8042	−	8.54720i	0.532470	−	0.307421i	0.742022	+	0.670376i	$0.233867\pi$
$774$	−13.6722	+	16.7157i	−0.491436	+	0.600833i
$775$	11.5760	+	6.68338i	0.415821	+	0.240074i
$776$	−50.4065	−	3.50066i	−1.80949	−	0.125666i
$777$	7.39451	−	10.3115i	0.265277	−	0.369923i
$778$	−33.2161	−	10.7868i	−1.19086	−	0.386724i
$779$	−1.23818	−	7.02204i	−0.0443622	−	0.251591i
$780$	1.13037	+	0.448155i	0.0404738	+	0.0160465i
$781$	−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
$786$	6.16630	+	55.2852i	0.219945	+	1.97196i
$787$	−53.9190	+	9.50737i	−1.92200	+	0.338901i	−0.998952	−	0.0457725i	$-0.985425\pi$
$787$	−53.9190	+	9.50737i	−1.92200	+	0.338901i	−0.923053	+	0.384674i	$0.874314\pi$
$788$	−13.7225	+	47.9135i	−0.488845	+	1.70685i
$789$	22.4195	−	10.1488i	0.798155	−	0.361306i
$790$	3.94402	+	0.553658i	0.140322	+	0.0196983i
$791$	0.525205	−	0.909682i	0.0186741	−	0.0323446i
$792$	22.0822	−	46.7946i	0.784655	−	1.66277i
$793$	5.37364	+	9.30741i	0.190823	+	0.330516i
$794$	−18.8833	−	46.7164i	−0.670142	−	1.65790i
$795$	−0.804265	−	3.14261i	−0.0285244	−	0.111457i
$796$	−20.7405	−	21.4638i	−0.735127	−	0.760763i
$797$	14.0696	+	16.7675i	0.498372	+	0.593936i	0.955326	−	0.295554i	$-0.0955041\pi$
$797$	14.0696	+	16.7675i	0.498372	+	0.593936i	−0.456954	+	0.889490i	$0.651060\pi$
$798$	−6.06168	−	5.77968i	−0.214581	−	0.204598i
$799$	8.98758	+	24.6932i	0.317958	+	0.873581i
$800$	21.3486	−	17.9425i	0.754787	−	0.634362i
$801$	−20.0922	+	16.1028i	−0.709922	+	0.568965i
$802$	13.9576	−	26.2605i	0.492861	−	0.927292i
$803$	−8.00016	+	45.3711i	−0.282319	+	1.60111i
$804$	−18.4235	−	0.523192i	−0.649746	−	0.0184516i
$805$	0.998372	+	0.363378i	0.0351880	+	0.0128074i
$806$	1.05703	+	4.96906i	0.0372323	+	0.175028i
$807$	−20.4991	+	14.0125i	−0.721602	+	0.493262i
$808$	33.9248	+	22.8591i	1.19347	+	0.804180i
$809$		−	15.5284i		−	0.545951i	−0.962021	−	0.272975i	$-0.911992\pi$
$809$		−	15.5284i		−	0.545951i	0.962021	−	0.272975i	$-0.0880077\pi$
$810$	0.618605	−	3.31501i	0.0217356	−	0.116477i
$811$		−	5.33197i		−	0.187231i	−0.995608	−	0.0936155i	$-0.970158\pi$
$811$		−	5.33197i		−	0.187231i	0.995608	−	0.0936155i	$-0.0298424\pi$
$812$	7.25684	+	5.26889i	0.254665	+	0.184902i
$813$	27.0704	−	18.5044i	0.949400	−	0.648977i
$814$	61.7947	−	13.1451i	2.16590	−	0.460736i
$815$	3.55639	+	1.29442i	0.124575	+	0.0453415i
$816$	17.5567	−	0.733240i	0.614606	−	0.0256685i
$817$	−3.02218	+	17.1397i	−0.105733	+	0.599641i
$818$	−3.81579	−	2.02811i	−0.133416	−	0.0709113i
$819$	0.601910	+	3.92876i	0.0210324	+	0.137282i
$820$	−0.618207	−	0.915902i	−0.0215887	−	0.0319847i
$821$	−3.58463	−	9.84870i	−0.125105	−	0.343722i	0.861291	−	0.508112i	$-0.169657\pi$
$821$	−3.58463	−	9.84870i	−0.125105	−	0.343722i	−0.986395	+	0.164390i	$0.947434\pi$
$822$	0.181820	−	0.190691i	0.00634169	−	0.00665111i
$823$	−15.1205	−	18.0199i	−0.527067	−	0.628134i	0.435170	−	0.900348i	$-0.356688\pi$
$823$	−15.1205	−	18.0199i	−0.527067	−	0.628134i	−0.962237	+	0.272215i	$0.912244\pi$
$824$	−9.37987	+	9.72240i	−0.326763	+	0.338696i
$825$	12.9095	+	50.4430i	0.449451	+	1.75620i
$826$	2.69131	−	1.08786i	0.0936427	−	0.0378514i
$827$	11.5041	+	19.9257i	0.400038	+	0.692886i	0.993730	−	0.111806i	$-0.0356636\pi$
$827$	11.5041	+	19.9257i	0.400038	+	0.692886i	−0.593692	+	0.804692i	$0.702330\pi$
$828$	1.14535	+	24.0328i	0.0398035	+	0.835199i
$829$	−2.04046	+	3.53418i	−0.0708682	+	0.122747i	−0.899282	−	0.437369i	$-0.855910\pi$
$829$	−2.04046	+	3.53418i	−0.0708682	+	0.122747i	0.828414	+	0.560116i	$0.189244\pi$
$830$	−0.140258	+	0.999135i	−0.00486841	+	0.0346805i
$831$	10.7384	−	4.86101i	0.372510	−	0.168626i
$832$	10.4972	+	1.46510i	0.363925	+	0.0507931i
$833$	2.49776	−	0.440423i	0.0865423	−	0.0152597i
$834$	−23.8039	+	2.65500i	−0.824262	+	0.0919352i
$835$	−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	$-0.332458\pi$
$839$	−7.58588	−	6.36531i	−0.261894	−	0.219755i	−0.764274	+	0.644892i	$0.776902\pi$
$840$	−1.22263	−	0.435782i	−0.0421848	−	0.0150359i
$841$	1.54447	+	8.75914i	0.0532577	+	0.302039i
$842$	−1.73575	+	5.34498i	−0.0598180	+	0.184200i
$843$	20.5866	−	28.7076i	0.709041	−	0.988743i
$844$	−19.7567	−	2.07018i	−0.680055	−	0.0712585i
$845$	2.58012	+	1.48963i	0.0887587	+	0.0512449i
$846$	41.1140	−	15.5516i	1.41353	−	0.534675i
$847$	22.6773	−	13.0928i	0.779202	−	0.449872i
$848$	−13.2903	−	24.9571i	−0.456390	−	0.857032i
$849$	6.74647	−	24.0903i	0.231538	−	0.826778i
$850$	−13.1388	+	11.8340i	−0.450657	+	0.405903i
$851$	−22.5040	+	18.8831i	−0.771428	+	0.647305i
$852$	−25.0119	−	5.14633i	−0.856893	−	0.176310i
$853$	20.8062	−	7.57282i	0.712389	−	0.259288i	0.0396978	−	0.999212i	$-0.487360\pi$
$853$	20.8062	−	7.57282i	0.712389	−	0.259288i	0.672691	+	0.739923i	$0.265138\pi$
$854$	−6.08080	−	9.72788i	−0.208081	−	0.332881i
$855$	−0.871822	−	2.57416i	−0.0298157	−	0.0880343i
$856$	−16.5513	−	7.35967i	−0.565711	−	0.251548i
$857$	−0.893421	−	0.157534i	−0.0305187	−	0.00538126i	0.158368	−	0.987380i	$-0.449377\pi$
$857$	−0.893421	−	0.157534i	−0.0305187	−	0.00538126i	−0.188887	+	0.981999i	$0.560488\pi$
$858$	−10.9616	+	16.4763i	−0.374224	+	0.562491i
$859$	5.78403	−	15.8915i	0.197349	−	0.542211i	−0.801061	−	0.598582i	$-0.795731\pi$
$859$	5.78403	−	15.8915i	0.197349	−	0.542211i	0.998410	+	0.0563717i	$0.0179532\pi$
$860$	0.653332	+	2.61683i	0.0222784	+	0.0892333i
$861$	1.56321	−	3.25613i	0.0532740	−	0.110969i
$862$	−13.4448	+	17.2142i	−0.457933	+	0.586320i
$863$	15.5633			0.529780			0.264890	−	0.964279i	$-0.414664\pi$
$863$	15.5633			0.529780			0.264890	+	0.964279i	$0.414664\pi$
$864$	−1.59519	−	29.3506i	−0.0542695	−	0.998526i
$865$	−6.54981			−0.222700
$866$	28.5590	−	36.5657i	0.970473	−	1.24255i
$867$	18.2501	−	1.38990i	0.619806	−	0.0472036i
$868$	−1.31357	−	5.26134i	−0.0445856	−	0.178582i
$869$	−22.1687	+	60.9081i	−0.752022	+	2.06616i
$870$	1.29227	+	2.60734i	0.0438120	+	0.0883972i
$871$	6.94192	+	1.22405i	0.235218	+	0.0414753i
$872$	−35.9808	−	15.9992i	−1.21846	−	0.541801i
$873$	1.20622	−	53.5794i	0.0408244	−	1.81339i
$874$	10.2782	+	16.4427i	0.347664	+	0.556183i
$875$	2.47222	−	0.899813i	0.0835761	−	0.0304192i
$876$	8.24952	+	24.8375i	0.278725	+	0.839183i
$877$	2.29157	−	1.92285i	0.0773807	−	0.0649302i	−0.603277	−	0.797532i	$-0.706139\pi$
$877$	2.29157	−	1.92285i	0.0773807	−	0.0649302i	0.680658	+	0.732602i	$0.261694\pi$
$878$	−38.8775	+	35.0166i	−1.31205	+	1.18175i
$879$	9.49365	+	9.70978i	0.320213	+	0.327503i
$880$	−3.03762	−	5.70420i	−0.102398	−	0.192289i
$881$	24.2603	−	14.0067i	0.817349	−	0.471897i	−0.0321525	−	0.999483i	$-0.510236\pi$
$881$	24.2603	−	14.0067i	0.817349	−	0.471897i	0.849501	+	0.527586i	$0.176903\pi$
$882$	−0.789130	−	4.16861i	−0.0265714	−	0.140364i
$883$	−33.6102	−	19.4048i	−1.13107	−	0.653025i	−0.186868	−	0.982385i	$-0.559834\pi$
$883$	−33.6102	−	19.4048i	−1.13107	−	0.653025i	−0.944204	+	0.329360i	$0.893167\pi$
$884$	−6.68392	−	0.700364i	−0.224804	−	0.0235558i
$885$	0.937390	+	0.0926525i	0.0315100	+	0.00311448i
$886$	−7.32392	+	22.5529i	−0.246052	+	0.757679i
$887$	−2.39941	−	13.6077i	−0.0805644	−	0.456903i	−0.998226	−	0.0595402i	$-0.981037\pi$
$887$	−2.39941	−	13.6077i	−0.0805644	−	0.456903i	0.917662	−	0.397363i	$-0.130075\pi$
$888$	27.3382	−	23.2522i	0.917411	−	0.780293i
$889$	−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
$894$	−9.76701	−	13.2650i	−0.326658	−	0.443647i
$895$	−3.21499	+	0.566889i	−0.107465	+	0.0189490i
$896$	−11.2530	−	1.17011i	−0.375938	−	0.0390906i
$897$	0.905119	−	9.15733i	0.0302210	−	0.305754i
$898$	5.90493	−	42.0642i	0.197050	−	1.40370i
$899$	−6.07892	+	10.5290i	−0.202743	+	0.351162i
$900$	20.0700	+	21.7279i	0.668999	+	0.724264i
$901$	8.96429	+	15.5266i	0.298644	+	0.517266i
$902$	16.6732	−	6.73947i	0.555155	−	0.224400i
$903$	−6.30370	+	6.16338i	−0.209774	+	0.205104i
$904$	2.06282	−	2.13815i	0.0686083	−	0.0711137i
$905$	0.332776	+	0.396587i	0.0110619	+	0.0131830i
$906$	7.09183	+	24.1516i	0.235610	+	0.802383i
$907$	7.17006	+	19.6996i	0.238078	+	0.654113i	0.999979	+	0.00642053i	$0.00204373\pi$
$907$	7.17006	+	19.6996i	0.238078	+	0.654113i	−0.761902	+	0.647693i	$0.775734\pi$
$908$	−8.85212	−	13.1148i	−0.293768	−	0.435231i
$909$	−22.5347	+	37.0782i	−0.747430	+	1.22981i
$910$	0.438348	+	0.232985i	0.0145311	+	0.00772336i
$911$	4.85601	−	27.5398i	0.160887	−	0.912435i	−0.792318	−	0.610109i	$-0.791126\pi$
$911$	4.85601	−	27.5398i	0.160887	−	0.912435i	0.953205	−	0.302326i	$-0.0977631\pi$
$912$	−12.6905	−	20.0035i	−0.420224	−	0.662383i
$913$	−15.4298	−	5.61598i	−0.510651	−	0.185862i
$914$	−49.5543	+	10.5413i	−1.63911	+	0.348676i
$915$	−0.282690	−	3.71185i	−0.00934544	−	0.122710i
$916$	−28.2747	−	20.5291i	−0.934223	−	0.678300i
$917$			22.7100i			0.749951i
$918$	1.64857	+	18.5648i	0.0544108	+	0.612731i
$919$			25.1415i			0.829342i	0.909971	+	0.414671i	$0.136103\pi$
$919$			25.1415i			0.829342i	−0.909971	+	0.414671i	$0.863897\pi$
$920$	2.49210	+	1.67922i	0.0821620	+	0.0553621i
$921$	−27.2392	−	13.0771i	−0.897562	−	0.430904i
$922$	11.6704	+	54.8622i	0.384344	+	1.80679i
$923$	9.17736	+	3.34029i	0.302076	+	0.109947i
$924$	11.0771	−	17.9868i	0.364409	−	0.591722i
$925$	−6.27133	+	35.5665i	−0.206200	+	1.16942i
$926$	−2.55418	+	4.80556i	−0.0839356	+	0.157920i
$927$	−10.7666	−	9.45522i	−0.353621	−	0.310550i
$928$	16.3197	+	19.4178i	0.535721	+	0.637420i
$929$	14.0294	+	38.5454i	0.460289	+	1.26463i	0.925268	+	0.379313i	$0.123840\pi$
$929$	14.0294	+	38.5454i	0.460289	+	1.26463i	−0.464979	+	0.885322i	$0.653938\pi$
$930$	0.414840	−	1.71008i	0.0136031	−	0.0560756i
$931$	−2.19787	−	2.61932i	−0.0720322	−	0.0858446i
$932$	13.8693	+	14.3530i	0.454305	+	0.470148i
$933$	−28.5689	−	8.00069i	−0.935305	−	0.261931i
$934$	17.7426	+	43.8945i	0.580556	+	1.43627i
$935$	2.04888	+	3.54876i	0.0670055	+	0.116057i
$936$	−1.03107	+	11.1945i	−0.0337017	+	0.365903i
$937$	7.36995	−	12.7651i	0.240766	−	0.417019i	−0.720167	−	0.693801i	$-0.755935\pi$
$937$	7.36995	−	12.7651i	0.240766	−	0.417019i	0.960933	+	0.276782i	$0.0892681\pi$
$938$	−7.45132	−	1.04601i	−0.243294	−	0.0341534i
$939$	27.0459	+	19.3950i	0.882608	+	0.632931i
$940$	1.51161	−	5.27791i	0.0493031	−	0.172147i
$941$	−5.58566	+	0.984902i	−0.182087	+	0.0321069i	−0.263948	−	0.964537i	$-0.585025\pi$
$941$	−5.58566	+	0.984902i	−0.182087	+	0.0321069i	0.0818609	+	0.996644i	$0.473914\pi$
$942$	14.8608	+	6.50357i	0.484191	+	0.211898i
$943$	−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	$-0.213111\pi$
$947$	9.51257	+	7.98199i	0.309117	+	0.259380i	−0.475010	+	0.879980i	$0.657556\pi$
$948$	5.36194	+	36.4283i	0.174148	+	1.18313i
$949$	−1.73814	−	9.85747i	−0.0564223	−	0.319987i
$950$	22.6729	+	7.36290i	0.735606	+	0.238884i
$951$	−7.45254	−	16.4633i	−0.241665	−	0.533858i
$952$	7.15649	+	0.497008i	0.231943	+	0.0161081i
$953$	1.74515	+	1.00756i	0.0565310	+	0.0326382i	0.527999	−	0.849245i	$-0.322942\pi$
$953$	1.74515	+	1.00756i	0.0565310	+	0.0326382i	−0.471468	+	0.881883i	$0.656276\pi$
$954$	25.7821	−	15.3201i	0.834728	−	0.496008i
$955$	−4.11476	+	2.37566i	−0.133150	+	0.0768745i
$956$	−46.9564	+	20.9242i	−1.51868	+	0.676736i
$957$	−45.8809	+	11.7419i	−1.48312	+	0.379563i
$958$	−12.4605	−	13.8343i	−0.402579	−	0.446967i
$959$	0.0823996	−	0.0691415i	0.00266082	−	0.00223269i
$960$	−3.05818	−	2.03110i	−0.0987024	−	0.0655536i
$961$	−22.2220	+	8.08816i	−0.716840	+	0.260908i
$962$	−11.6392	+	7.27557i	−0.375264	+	0.234574i
$963$	6.97577	−	17.9015i	0.224791	−	0.576867i
$964$	18.1976	−	37.3407i	0.586105	−	1.20266i
$965$	−5.93370	−	1.04627i	−0.191013	−	0.0336807i
$966$	−0.622876	+	9.80274i	−0.0200407	+	0.315398i
$967$	13.2658	−	36.4474i	0.426599	−	1.17207i	−0.521265	−	0.853395i	$-0.674540\pi$
$967$	13.2658	−	36.4474i	0.426599	−	1.17207i	0.947864	−	0.318675i	$-0.103238\pi$
$968$	71.1850	−	20.4486i	2.28797	−	0.657244i
$969$	8.47658	+	12.4005i	0.272307	+	0.398363i
$970$	−5.27530	−	4.12017i	−0.169380	−	0.132291i
$971$	48.6895			1.56252			0.781260	−	0.624205i	$-0.214577\pi$
$971$	48.6895			1.56252			0.781260	+	0.624205i	$0.214577\pi$
$972$	31.0176	−	3.14738i	0.994891	−	0.100952i
$973$	−9.77817			−0.313474
$974$	−28.5180	−	22.2734i	−0.913775	−	0.713686i
$975$	−6.38394	−	9.33918i	−0.204450	−	0.299093i
$976$	−10.0465	−	30.8534i	−0.321581	−	0.987592i
$977$	−11.5820	+	31.8214i	−0.370542	+	1.01806i	0.604610	+	0.796522i	$0.293329\pi$
$977$	−11.5820	+	31.8214i	−0.370542	+	1.01806i	−0.975152	+	0.221535i	$0.928893\pi$
$978$	−2.21880	+	34.9192i	−0.0709494	+	1.11659i
$979$	−51.5434	−	9.08849i	−1.64733	−	0.290469i
$980$	−0.476340	−	0.232140i	−0.0152161	−	0.00741543i
$981$	15.1646	−	38.9160i	0.484169	−	1.24249i
$982$	−40.8508	+	25.5354i	−1.30360	+	0.814868i
$983$	−1.27889	+	0.465478i	−0.0407903	+	0.0148464i	−0.362335	−	0.932048i	$-0.618020\pi$
$983$	−1.27889	+	0.465478i	−0.0407903	+	0.0148464i	0.321544	+	0.946894i	$0.395798\pi$
$984$	6.51438	−	7.86961i	0.207671	−	0.250874i
$985$	−5.05779	+	4.24399i	−0.161155	+	0.135225i
$986$	−10.7637	−	11.9505i	−0.342786	−	0.380581i
$987$	17.3851	−	4.44922i	0.553372	−	0.141620i
$988$	3.68773	+	8.27571i	0.117322	+	0.263285i
$989$	17.6764	−	10.2055i	0.562077	−	0.324515i
$990$	5.89277	−	3.50157i	0.187284	−	0.111287i
$991$	−15.9836	−	9.22812i	−0.507735	−	0.293141i	0.224167	−	0.974551i	$-0.428034\pi$
$991$	−15.9836	−	9.22812i	−0.507735	−	0.293141i	−0.731902	+	0.681410i	$0.761367\pi$
$992$	−0.0121658	−	15.3381i	−0.000386263	−	0.486985i
$993$	19.5193	+	43.1198i	0.619428	+	1.36837i
$994$	−9.91524	−	3.21992i	−0.314492	−	0.102130i
$995$	−0.686602	−	3.89391i	−0.0217667	−	0.123445i
$996$	−9.22833	+	1.35833i	−0.292411	+	0.0430405i
$997$	27.1086	+	22.7468i	0.858539	+	0.720400i	0.961653	−	0.274270i	$-0.0884361\pi$
$997$	27.1086	+	22.7468i	0.858539	+	0.720400i	−0.103114	+	0.994670i	$0.532881\pi$
$998$	−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.659.31	yes	648
4.3	odd	2	inner	756.2.cf.a.659.30	yes	648
27.5	odd	18	inner	756.2.cf.a.491.30	✓	648
108.59	even	18	inner	756.2.cf.a.491.31	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.30	✓	648	27.5	odd	18	inner
756.2.cf.a.491.31	yes	648	108.59	even	18	inner
756.2.cf.a.659.30	yes	648	4.3	odd	2	inner
756.2.cf.a.659.31	yes	648	1.1	even	1	trivial

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+(-0.870500 + 1.11455i) q^{2} +(-0.977433 - 1.42990i) q^{3} +(-0.484459 - 1.94044i) q^{4} +(0.0906174 - 0.248969i) q^{5} +(2.44456 + 0.155330i) q^{6} +(0.984808 + 0.173648i) q^{7} +(2.58444 + 1.14920i) q^{8} +(-1.08925 + 2.79527i) q^{9} +(0.198607 + 0.317726i) q^{10} +(-5.73024 + 2.08564i) q^{11} +(-2.30111 + 2.58938i) q^{12} +(1.01491 - 0.851609i) q^{13} +(-1.05082 + 0.946460i) q^{14} +(-0.444574 + 0.113777i) q^{15} +(-3.53060 + 1.88013i) q^{16} +(2.19650 - 1.26815i) q^{17} +(-2.16729 - 3.64731i) q^{18} +(-2.96118 - 1.70964i) q^{19} +(-0.527010 - 0.0552219i) q^{20} +(-0.714283 - 1.57791i) q^{21} +(2.66362 - 8.20220i) q^{22} +(0.696333 + 3.94910i) q^{23} +(-0.882882 - 4.81877i) 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} +(0.260192 - 0.594545i) q^{30} +(2.67023 - 0.470833i) q^{31} +(0.977883 - 5.57169i) q^{32} +(8.58318 + 6.15512i) q^{33} +(-0.498631 + 3.55203i) q^{34} +(0.132474 - 0.229451i) q^{35} +(5.95175 + 0.759426i) q^{36} +(3.66294 + 6.34440i) q^{37} +(4.48319 - 1.81215i) q^{38} +(-2.20972 - 0.618830i) q^{39} +(0.520310 - 0.539310i) q^{40} +(1.34043 + 1.59747i) q^{41} +(2.38045 + 0.577463i) q^{42} +(-1.74088 - 4.78302i) q^{43} +(6.82312 + 10.1088i) q^{44} +(0.597231 + 0.524490i) q^{45} +(-5.00764 - 2.66159i) q^{46} +(-1.79913 + 10.2033i) q^{47} +(6.13932 + 3.21072i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-6.81921 + 1.45060i) q^{50} +(-3.96026 - 1.90125i) q^{51} +(-2.14418 - 1.55680i) q^{52} +7.06881i q^{53} +(-3.09692 + 6.66401i) q^{54} +1.61565i q^{55} +(2.34562 + 1.58052i) q^{56} +(0.449737 + 5.90526i) q^{57} +(-1.31940 - 6.20247i) q^{58} +(-1.92884 - 0.702041i) q^{59} +(0.436155 + 0.807549i) q^{60} +(-1.40863 + 7.98872i) q^{61} +(-1.79966 + 3.38597i) q^{62} +(-1.55810 + 2.56366i) q^{63} +(5.35870 + 5.94006i) q^{64} +(-0.120056 - 0.329851i) q^{65} +(-14.3319 + 4.20839i) q^{66} +(3.41998 + 4.07577i) q^{67} +(-3.52487 - 3.64780i) q^{68} +(4.96621 - 4.85567i) q^{69} +(0.140417 + 0.347386i) q^{70} +(3.68578 + 6.38396i) q^{71} +(-6.02742 + 5.97246i) q^{72} +(3.77756 - 6.54292i) q^{73} +(-10.2598 - 1.44026i) q^{74} +(0.839877 - 8.49726i) q^{75} +(-1.88287 + 6.57423i) q^{76} +(-6.00535 + 1.05891i) q^{77} +(2.61328 - 1.92416i) 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} +(-2.71579 + 2.15046i) q^{84} +(-0.116689 - 0.661776i) q^{85} +(6.84637 + 2.22332i) q^{86} +(7.72875 + 0.763917i) q^{87} +(-17.2063 - 1.19495i) q^{88} +(7.43301 + 4.29145i) q^{89} +(-1.10446 + 0.209078i) q^{90} +(1.14737 - 0.662434i) q^{91} +(7.32564 - 3.26437i) q^{92} +(-3.28321 - 3.35796i) q^{93} +(-9.80604 - 10.8872i) q^{94} +(-0.693982 + 0.582320i) q^{95} +(-8.92280 + 4.04768i) q^{96} +(-16.7870 + 6.10996i) q^{97} +(-1.19920 + 0.749609i) 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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