LMFDB - Embedded newform 756.2.ck.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5, 15]))

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

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

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.5
Character	$\chi$	$=$	756.5
Dual form			756.2.ck.a.605.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61581 - 0.623825i) q^{3} +(-0.221654 + 1.25706i) q^{5} +(2.55927 - 0.670941i) q^{7} +(2.22168 + 2.01597i) q^{9} +O(q^{10})$	\(q+(-1.61581 - 0.623825i) q^{3} +(-0.221654 + 1.25706i) q^{5} +(2.55927 - 0.670941i) q^{7} +(2.22168 + 2.01597i) q^{9} +(-5.67482 + 1.00062i) q^{11} +(3.02767 - 3.60823i) q^{13} +(1.14234 - 1.89290i) q^{15} +0.342095 q^{17} +8.19307i q^{19} +(-4.55384 - 0.512420i) q^{21} +(0.332785 - 0.396598i) q^{23} +(3.16739 + 1.15283i) q^{25} +(-2.33221 - 4.64336i) q^{27} +(0.622374 + 0.741717i) q^{29} +(1.45520 + 3.99812i) q^{31} +(9.79364 + 1.92328i) q^{33} +(0.276144 + 3.36587i) q^{35} +(-1.18931 - 2.05995i) q^{37} +(-7.14304 + 3.94148i) q^{39} +(7.78109 + 6.52911i) q^{41} +(4.17869 + 1.52092i) q^{43} +(-3.02664 + 2.34595i) q^{45} +(2.92248 + 1.06369i) q^{47} +(6.09968 - 3.43423i) q^{49} +(-0.552760 - 0.213407i) q^{51} +(5.32288 - 3.07317i) q^{53} -7.35539i q^{55} +(5.11105 - 13.2385i) q^{57} +(9.66502 + 8.10991i) q^{59} +(-2.33107 + 6.40456i) q^{61} +(7.03847 + 3.66877i) q^{63} +(3.86468 + 4.60575i) q^{65} +(-0.683823 + 3.87815i) q^{67} +(-0.785125 + 0.433227i) q^{69} +(-2.19597 - 1.26784i) q^{71} +(10.4470 + 6.03160i) q^{73} +(-4.39873 - 3.83866i) q^{75} +(-13.8520 + 6.36833i) q^{77} +(-0.898458 - 5.09541i) q^{79} +(0.871763 + 8.95768i) q^{81} +(-0.555623 + 0.466223i) q^{83} +(-0.0758267 + 0.430035i) q^{85} +(-0.542937 - 1.58673i) q^{87} -10.2413 q^{89} +(5.32769 - 11.2658i) q^{91} +(0.142806 - 7.36798i) q^{93} +(-10.2992 - 1.81603i) q^{95} +(-3.14019 + 8.62759i) q^{97} +(-14.6249 - 9.21717i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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			0
$2$		0			0
$3$	−1.61581	−	0.623825i	−0.932888	−	0.360166i
$3$	−1.61581	−	0.623825i	−0.932888	−	0.360166i
$4$		0			0
$5$	−0.221654	+	1.25706i	−0.0991267	+	0.562176i	0.894278	+	0.447512i	$0.147690\pi$
$5$	−0.221654	+	1.25706i	−0.0991267	+	0.562176i	−0.993404	+	0.114663i	$0.963421\pi$
$6$		0			0
$7$	2.55927	−	0.670941i	0.967311	−	0.253592i
$7$	2.55927	−	0.670941i	0.967311	−	0.253592i
$8$		0			0
$9$	2.22168	+	2.01597i	0.740561	+	0.671989i
$10$		0			0
$11$	−5.67482	+	1.00062i	−1.71102	+	0.301699i	−0.941523	−	0.336949i	$-0.890605\pi$
$11$	−5.67482	+	1.00062i	−1.71102	+	0.301699i	−0.769499	+	0.638648i	$0.779494\pi$
$12$		0			0
$13$	3.02767	−	3.60823i	0.839724	−	1.00074i	−0.160183	−	0.987087i	$-0.551208\pi$
$13$	3.02767	−	3.60823i	0.839724	−	1.00074i	0.999907	−	0.0136566i	$-0.00434715\pi$
$14$		0			0
$15$	1.14234	−	1.89290i	0.294950	−	0.488745i
$16$		0			0
$17$	0.342095			0.0829702			0.0414851	−	0.999139i	$-0.486791\pi$
$17$	0.342095			0.0829702			0.0414851	+	0.999139i	$0.486791\pi$
$18$		0			0
$19$			8.19307i			1.87962i	0.341697	+	0.939810i	$0.388998\pi$
$19$			8.19307i			1.87962i	−0.341697	+	0.939810i	$0.611002\pi$
$20$		0			0
$21$	−4.55384	−	0.512420i	−0.993729	−	0.111819i
$22$		0			0
$23$	0.332785	−	0.396598i	0.0693905	−	0.0826964i	−0.730232	−	0.683199i	$-0.760588\pi$
$23$	0.332785	−	0.396598i	0.0693905	−	0.0826964i	0.799623	+	0.600502i	$0.205033\pi$
$24$		0			0
$25$	3.16739	+	1.15283i	0.633477	+	0.230567i
$26$		0			0
$27$	−2.33221	−	4.64336i	−0.448834	−	0.893615i
$28$		0			0
$29$	0.622374	+	0.741717i	0.115572	+	0.137733i	0.820729	−	0.571318i	$-0.193568\pi$
$29$	0.622374	+	0.741717i	0.115572	+	0.137733i	−0.705157	+	0.709052i	$0.749123\pi$
$30$		0			0
$31$	1.45520	+	3.99812i	0.261361	+	0.718083i	0.999076	+	0.0429711i	$0.0136823\pi$
$31$	1.45520	+	3.99812i	0.261361	+	0.718083i	−0.737716	+	0.675112i	$0.764095\pi$
$32$		0			0
$33$	9.79364	+	1.92328i	1.70485	+	0.334799i
$34$		0			0
$35$	0.276144	+	3.36587i	0.0466768	+	0.568936i
$36$		0			0
$37$	−1.18931	−	2.05995i	−0.195522	−	0.338653i	0.751550	−	0.659676i	$-0.229307\pi$
$37$	−1.18931	−	2.05995i	−0.195522	−	0.338653i	−0.947071	+	0.321023i	$0.895973\pi$
$38$		0			0
$39$	−7.14304	+	3.94148i	−1.14380	+	0.631143i
$40$		0			0
$41$	7.78109	+	6.52911i	1.21520	+	1.01968i	0.999062	+	0.0433131i	$0.0137913\pi$
$41$	7.78109	+	6.52911i	1.21520	+	1.01968i	0.216140	+	0.976362i	$0.430653\pi$
$42$		0			0
$43$	4.17869	+	1.52092i	0.637245	+	0.231938i	0.640381	−	0.768057i	$-0.278776\pi$
$43$	4.17869	+	1.52092i	0.637245	+	0.231938i	−0.00313689	+	0.999995i	$0.500999\pi$
$44$		0			0
$45$	−3.02664	+	2.34595i	−0.451185	+	0.349713i
$46$		0			0
$47$	2.92248	+	1.06369i	0.426287	+	0.155156i	0.546249	−	0.837623i	$-0.316055\pi$
$47$	2.92248	+	1.06369i	0.426287	+	0.155156i	−0.119962	+	0.992778i	$0.538277\pi$
$48$		0			0
$49$	6.09968	−	3.43423i	0.871382	−	0.490605i
$50$		0			0
$51$	−0.552760	−	0.213407i	−0.0774019	−	0.0298830i
$52$		0			0
$53$	5.32288	−	3.07317i	0.731154	−	0.422132i	−0.0876903	−	0.996148i	$-0.527949\pi$
$53$	5.32288	−	3.07317i	0.731154	−	0.422132i	0.818844	+	0.574016i	$0.194615\pi$
$54$		0			0
$55$		−	7.35539i		−	0.991801i
$56$		0			0
$57$	5.11105	−	13.2385i	0.676975	−	1.75348i
$58$		0			0
$59$	9.66502	+	8.10991i	1.25828	+	1.05582i	0.995863	+	0.0908657i	$0.0289634\pi$
$59$	9.66502	+	8.10991i	1.25828	+	1.05582i	0.262415	+	0.964955i	$0.415481\pi$
$60$		0			0
$61$	−2.33107	+	6.40456i	−0.298463	+	0.820020i	0.696294	+	0.717756i	$0.254831\pi$
$61$	−2.33107	+	6.40456i	−0.298463	+	0.820020i	−0.994757	+	0.102264i	$0.967391\pi$
$62$		0			0
$63$	7.03847	+	3.66877i	0.886764	+	0.462222i
$64$		0			0
$65$	3.86468	+	4.60575i	0.479355	+	0.571273i
$66$		0			0
$67$	−0.683823	+	3.87815i	−0.0835423	+	0.473792i	0.914119	+	0.405445i	$0.132883\pi$
$67$	−0.683823	+	3.87815i	−0.0835423	+	0.473792i	−0.997662	+	0.0683466i	$0.978228\pi$
$68$		0			0
$69$	−0.785125	+	0.433227i	−0.0945180	+	0.0521544i
$70$		0			0
$71$	−2.19597	−	1.26784i	−0.260614	−	0.150465i	0.364001	−	0.931399i	$-0.381411\pi$
$71$	−2.19597	−	1.26784i	−0.260614	−	0.150465i	−0.624614	+	0.780933i	$0.714744\pi$
$72$		0			0
$73$	10.4470	+	6.03160i	1.22273	+	0.705945i	0.965500	−	0.260404i	$-0.0838559\pi$
$73$	10.4470	+	6.03160i	1.22273	+	0.705945i	0.257233	+	0.966349i	$0.417189\pi$
$74$		0			0
$75$	−4.39873	−	3.83866i	−0.507921	−	0.443250i
$76$		0			0
$77$	−13.8520	+	6.36833i	−1.57858	+	0.725738i
$78$		0			0
$79$	−0.898458	−	5.09541i	−0.101084	−	0.573278i	−0.992712	−	0.120509i	$-0.961547\pi$
$79$	−0.898458	−	5.09541i	−0.101084	−	0.573278i	0.891628	−	0.452769i	$-0.149564\pi$
$80$		0			0
$81$	0.871763	+	8.95768i	0.0968626	+	0.995298i
$82$		0			0
$83$	−0.555623	+	0.466223i	−0.0609875	+	0.0511746i	−0.672772	−	0.739850i	$-0.734896\pi$
$83$	−0.555623	+	0.466223i	−0.0609875	+	0.0511746i	0.611784	+	0.791025i	$0.290452\pi$
$84$		0			0
$85$	−0.0758267	+	0.430035i	−0.00822456	+	0.0466438i
$86$		0			0
$87$	−0.542937	−	1.58673i	−0.0582090	−	0.170115i
$88$		0			0
$89$	−10.2413			−1.08558			−0.542790	−	0.839868i	$-0.682632\pi$
$89$	−10.2413			−1.08558			−0.542790	+	0.839868i	$0.682632\pi$
$90$		0			0
$91$	5.32769	−	11.2658i	0.558494	−	1.18098i
$92$		0			0
$93$	0.142806	−	7.36798i	0.0148083	−	0.764024i
$94$		0			0
$95$	−10.2992	−	1.81603i	−1.05668	−	0.186321i
$96$		0			0
$97$	−3.14019	+	8.62759i	−0.318838	+	0.875999i	0.671953	+	0.740594i	$0.265456\pi$
$97$	−3.14019	+	8.62759i	−0.318838	+	0.875999i	−0.990790	+	0.135405i	$0.956766\pi$
$98$		0			0
$99$	−14.6249	−	9.21717i	−1.46985	−	0.926360i
$100$		0			0
$101$	1.23150	−	1.03335i	0.122539	−	0.102822i	−0.579459	−	0.815001i	$-0.696736\pi$
$101$	1.23150	−	1.03335i	0.122539	−	0.102822i	0.701998	+	0.712179i	$0.252292\pi$
$102$		0			0
$103$	−3.07793	−	0.542722i	−0.303277	−	0.0534759i	0.0199387	−	0.999801i	$-0.493653\pi$
$103$	−3.07793	−	0.542722i	−0.303277	−	0.0534759i	−0.323216	+	0.946325i	$0.604764\pi$
$104$		0			0
$105$	1.65352	−	5.61088i	0.161367	−	0.547566i
$106$		0			0
$107$	−15.1503	−	8.74701i	−1.46463	−	0.845605i	−0.465411	−	0.885095i	$-0.654093\pi$
$107$	−15.1503	−	8.74701i	−1.46463	−	0.845605i	−0.999220	+	0.0394897i	$0.987427\pi$
$108$		0			0
$109$	−8.26215	−	14.3105i	−0.791371	−	1.37069i	−0.925118	−	0.379679i	$-0.876034\pi$
$109$	−8.26215	−	14.3105i	−0.791371	−	1.37069i	0.133748	−	0.991015i	$-0.457299\pi$
$110$		0			0
$111$	0.636654	+	4.07041i	0.0604286	+	0.386346i
$112$		0			0
$113$	−0.603550	−	1.65824i	−0.0567772	−	0.155994i	0.908061	−	0.418837i	$-0.137562\pi$
$113$	−0.603550	−	1.65824i	−0.0567772	−	0.155994i	−0.964839	+	0.262843i	$0.915340\pi$
$114$		0			0
$115$	0.424785	+	0.506239i	0.0396114	+	0.0472070i
$116$		0			0
$117$	14.0006	−	1.91268i	1.29436	−	0.176827i
$118$		0			0
$119$	0.875511	−	0.229526i	0.0802580	−	0.0210406i
$120$		0			0
$121$	20.8657	−	7.59448i	1.89688	−	0.690408i
$122$		0			0
$123$	−8.49974	−	15.4038i	−0.766396	−	1.38892i
$124$		0			0
$125$	−5.34239	+	9.25329i	−0.477838	+	0.827639i
$126$		0			0
$127$	−7.47580	−	12.9485i	−0.663370	−	1.14899i	−0.979725	−	0.200349i	$-0.935792\pi$
$127$	−7.47580	−	12.9485i	−0.663370	−	1.14899i	0.316355	−	0.948641i	$-0.397541\pi$
$128$		0			0
$129$	−5.80318	−	5.06429i	−0.510942	−	0.445886i
$130$		0			0
$131$	−9.41368	−	7.89901i	−0.822477	−	0.690140i	0.131074	−	0.991373i	$-0.458158\pi$
$131$	−9.41368	−	7.89901i	−0.822477	−	0.690140i	−0.953551	+	0.301232i	$0.902602\pi$
$132$		0			0
$133$	5.49707	+	20.9683i	0.476657	+	1.81818i
$134$		0			0
$135$	6.35394	−	1.90251i	0.546860	−	0.163742i
$136$		0			0
$137$	−0.439344	+	1.20709i	−0.0375357	+	0.103128i	−0.957045	−	0.289941i	$-0.906364\pi$
$137$	−0.439344	+	1.20709i	−0.0375357	+	0.103128i	0.919509	+	0.393069i	$0.128587\pi$
$138$		0			0
$139$	−0.844510	−	0.148910i	−0.0716304	−	0.0126304i	0.137718	−	0.990471i	$-0.456023\pi$
$139$	−0.844510	−	0.148910i	−0.0716304	−	0.0126304i	−0.209349	+	0.977841i	$0.567134\pi$
$140$		0			0
$141$	−4.05861	−	3.54184i	−0.341796	−	0.298277i
$142$		0			0
$143$	−13.5710	+	23.5056i	−1.13486	+	1.96564i
$144$		0			0
$145$	−1.07034	+	0.617959i	−0.0888866	+	0.0513187i
$146$		0			0
$147$	−11.9983	+	1.74394i	−0.989601	+	0.143838i
$148$		0			0
$149$	6.43770	+	17.6874i	0.527397	+	1.44901i	0.862125	+	0.506696i	$0.169133\pi$
$149$	6.43770	+	17.6874i	0.527397	+	1.44901i	−0.334728	+	0.942315i	$0.608644\pi$
$150$		0			0
$151$	−0.178851	−	1.01431i	−0.0145547	−	0.0825435i	0.976665	−	0.214767i	$-0.0688993\pi$
$151$	−0.178851	−	1.01431i	−0.0145547	−	0.0825435i	−0.991220	+	0.132224i	$0.957788\pi$
$152$		0			0
$153$	0.760027	+	0.689651i	0.0614445	+	0.0557550i
$154$		0			0
$155$	−5.34843	+	0.943073i	−0.429596	+	0.0757494i
$156$		0			0
$157$	−4.27157	+	5.09066i	−0.340909	+	0.406279i	−0.909074	−	0.416636i	$-0.863209\pi$
$157$	−4.27157	+	5.09066i	−0.340909	+	0.406279i	0.568165	+	0.822915i	$0.307654\pi$
$158$		0			0
$159$	−10.5179	+	1.64511i	−0.834122	+	0.130465i
$160$		0			0
$161$	0.585591	−	1.23828i	0.0461511	−	0.0975900i
$162$		0			0
$163$	1.59932	−	2.77011i	0.125269	−	0.216972i	−0.796569	−	0.604547i	$-0.793354\pi$
$163$	1.59932	−	2.77011i	0.125269	−	0.216972i	0.921838	+	0.387576i	$0.126687\pi$
$164$		0			0
$165$	−4.58848	+	11.8849i	−0.357213	+	0.925239i
$166$		0			0
$167$	19.3814	−	7.05424i	1.49977	−	0.545873i	0.543773	−	0.839233i	$-0.316995\pi$
$167$	19.3814	−	7.05424i	1.49977	−	0.545873i	0.956002	+	0.293359i	$0.0947732\pi$
$168$		0			0
$169$	−1.59515	−	9.04656i	−0.122704	−	0.695889i
$170$		0			0
$171$	−16.5170	+	18.2024i	−1.26308	+	1.39197i
$172$		0			0
$173$	16.1747	−	13.5722i	1.22974	−	1.03187i	0.231484	−	0.972839i	$-0.425642\pi$
$173$	16.1747	−	13.5722i	1.22974	−	1.03187i	0.998256	−	0.0590352i	$-0.0188024\pi$
$174$		0			0
$175$	8.87967	+	0.825279i	0.671240	+	0.0623852i
$176$		0			0
$177$	−10.5577	−	19.1334i	−0.793563	−	1.43815i
$178$		0			0
$179$			11.6254i			0.868924i	0.900690	+	0.434462i	$0.143061\pi$
$179$			11.6254i			0.868924i	−0.900690	+	0.434462i	$0.856939\pi$
$180$		0			0
$181$	−7.09964	+	4.09898i	−0.527712	+	0.304675i	−0.740084	−	0.672514i	$-0.765214\pi$
$181$	−7.09964	+	4.09898i	−0.527712	+	0.304675i	0.212372	+	0.977189i	$0.431881\pi$
$182$		0			0
$183$	7.76189	−	8.89437i	0.573776	−	0.657491i
$184$		0			0
$185$	2.85310	−	1.03844i	0.209764	−	0.0763479i
$186$		0			0
$187$	−1.94133	+	0.342308i	−0.141964	+	0.0250320i
$188$		0			0
$189$	−9.08417	−	10.3188i	−0.660776	−	0.750583i
$190$		0			0
$191$	−18.3214	+	3.23055i	−1.32569	+	0.233754i	−0.791270	−	0.611467i	$-0.790580\pi$
$191$	−18.3214	+	3.23055i	−1.32569	+	0.233754i	−0.534417	+	0.845221i	$0.679469\pi$
$192$		0			0
$193$	−16.1705	+	5.88558i	−1.16398	+	0.423654i	−0.850517	−	0.525947i	$-0.823711\pi$
$193$	−16.1705	+	5.88558i	−1.16398	+	0.423654i	−0.313461	+	0.949601i	$0.601489\pi$
$194$		0			0
$195$	−3.37141	−	9.85290i	−0.241432	−	0.705581i
$196$		0			0
$197$	8.64136	−	4.98909i	0.615671	−	0.355458i	−0.159510	−	0.987196i	$-0.550992\pi$
$197$	8.64136	−	4.98909i	0.615671	−	0.355458i	0.775182	+	0.631738i	$0.217658\pi$
$198$		0			0
$199$		−	17.1342i		−	1.21461i	−0.794467	−	0.607307i	$-0.792250\pi$
$199$		−	17.1342i		−	1.21461i	0.794467	−	0.607307i	$-0.207750\pi$
$200$		0			0
$201$	3.52422	−	5.83977i	0.248579	−	0.411906i
$202$		0			0
$203$	2.09047	+	1.48067i	0.146722	+	0.103923i
$204$		0			0
$205$	−9.93221	+	8.33411i	−0.693696	+	0.582080i
$206$		0			0
$207$	1.53887	−	0.210232i	0.106959	−	0.0146121i
$208$		0			0
$209$	−8.19818	−	46.4942i	−0.567080	−	3.21607i
$210$		0			0
$211$	18.9938	−	6.91319i	1.30759	−	0.475923i	0.408128	−	0.912925i	$-0.366182\pi$
$211$	18.9938	−	6.91319i	1.30759	−	0.475923i	0.899461	+	0.437001i	$0.143960\pi$
$212$		0			0
$213$	2.75736	+	3.41849i	0.188931	+	0.234231i
$214$		0			0
$215$	−2.83812	+	4.91576i	−0.193558	+	0.335252i
$216$		0			0
$217$	6.40673	+	9.25589i	0.434917	+	0.628331i
$218$		0			0
$219$	−13.1178	−	16.2630i	−0.886416	−	1.09895i
$220$		0			0
$221$	1.03575	−	1.23436i	0.0696720	−	0.0830319i
$222$		0			0
$223$	6.90013	−	1.21668i	0.462067	−	0.0814749i	0.0622313	−	0.998062i	$-0.480178\pi$
$223$	6.90013	−	1.21668i	0.462067	−	0.0814749i	0.399836	+	0.916587i	$0.369067\pi$
$224$		0			0
$225$	4.71286	+	8.94658i	0.314191	+	0.596439i
$226$		0			0
$227$	2.38774	+	13.5416i	0.158480	+	0.898784i	0.955535	+	0.294878i	$0.0952789\pi$
$227$	2.38774	+	13.5416i	0.158480	+	0.898784i	−0.797055	+	0.603907i	$0.793610\pi$
$228$		0			0
$229$	−7.05870	−	19.3936i	−0.466452	−	1.28157i	−0.920553	−	0.390617i	$-0.872262\pi$
$229$	−7.05870	−	19.3936i	−0.466452	−	1.28157i	0.454101	−	0.890950i	$-0.349960\pi$
$230$		0			0
$231$	26.3549	−	1.64878i	1.73403	−	0.108482i
$232$		0			0
$233$	−24.1468	+	13.9412i	−1.58191	+	0.913317i	−0.587331	+	0.809347i	$0.699821\pi$
$233$	−24.1468	+	13.9412i	−1.58191	+	0.913317i	−0.994580	+	0.103970i	$0.966846\pi$
$234$		0			0
$235$	−1.98491	+	3.43796i	−0.129481	+	0.224268i
$236$		0			0
$237$	−1.72691	+	8.79369i	−0.112175	+	0.571212i
$238$		0			0
$239$	23.7274	+	4.18378i	1.53480	+	0.270626i	0.876229	−	0.481894i	$-0.160051\pi$
$239$	23.7274	+	4.18378i	1.53480	+	0.270626i	0.658569	+	0.752520i	$0.271162\pi$
$240$		0			0
$241$	0.589073	−	1.61847i	0.0379455	−	0.104255i	−0.919273	−	0.393621i	$-0.871222\pi$
$241$	0.589073	−	1.61847i	0.0379455	−	0.104255i	0.957218	+	0.289366i	$0.0934445\pi$
$242$		0			0
$243$	4.17942	−	15.0177i	0.268110	−	0.963388i
$244$		0			0
$245$	2.96503	+	8.42889i	0.189429	+	0.538502i
$246$		0			0
$247$	29.5625	+	24.8059i	1.88102	+	1.57836i
$248$		0			0
$249$	1.18862	−	0.406716i	0.0753259	−	0.0257746i
$250$		0			0
$251$	1.34720	+	2.33342i	0.0850344	+	0.147284i	0.905406	−	0.424547i	$-0.139567\pi$
$251$	1.34720	+	2.33342i	0.0850344	+	0.147284i	−0.820371	+	0.571831i	$0.806233\pi$
$252$		0			0
$253$	−1.49165	+	2.58361i	−0.0937792	+	0.162430i
$254$		0			0
$255$	0.390788	−	0.647552i	0.0244721	−	0.0405513i
$256$		0			0
$257$	17.8813	−	6.50824i	1.11540	−	0.405973i	0.282430	−	0.959288i	$-0.408860\pi$
$257$	17.8813	−	6.50824i	1.11540	−	0.405973i	0.832972	+	0.553315i	$0.186637\pi$
$258$		0			0
$259$	−4.42587	−	4.47400i	−0.275010	−	0.278001i
$260$		0			0
$261$	−0.112557	+	2.90255i	−0.00696707	+	0.179663i
$262$		0			0
$263$	−18.5166	−	22.0672i	−1.14178	−	1.36072i	−0.922931	−	0.384966i	$-0.874213\pi$
$263$	−18.5166	−	22.0672i	−1.14178	−	1.36072i	−0.218853	−	0.975758i	$-0.570231\pi$
$264$		0			0
$265$	2.68332	+	7.37237i	0.164835	+	0.452881i
$266$		0			0
$267$	16.5481	+	6.38881i	1.01272	+	0.390989i
$268$		0			0
$269$	−8.04832	−	13.9401i	−0.490715	−	0.849943i	0.509228	−	0.860632i	$-0.329931\pi$
$269$	−8.04832	−	13.9401i	−0.490715	−	0.849943i	−0.999943	+	0.0106885i	$0.996598\pi$
$270$		0			0
$271$	16.2246	+	9.36726i	0.985572	+	0.569020i	0.903948	−	0.427643i	$-0.140656\pi$
$271$	16.2246	+	9.36726i	0.985572	+	0.569020i	0.0816245	+	0.996663i	$0.473989\pi$
$272$		0			0
$273$	−15.6364	+	14.8799i	−0.946360	+	0.900571i
$274$		0			0
$275$	−19.1279	−	3.37276i	−1.15346	−	0.203385i
$276$		0			0
$277$	−9.44806	+	7.92786i	−0.567679	+	0.476339i	−0.880875	−	0.473349i	$-0.843045\pi$
$277$	−9.44806	+	7.92786i	−0.567679	+	0.476339i	0.313196	+	0.949689i	$0.398600\pi$
$278$		0			0
$279$	−4.82708	+	11.8162i	−0.288990	+	0.707416i
$280$		0			0
$281$	3.46150	−	9.51038i	0.206496	−	0.567342i	−0.792606	−	0.609735i	$-0.791276\pi$
$281$	3.46150	−	9.51038i	0.206496	−	0.567342i	0.999101	+	0.0423930i	$0.0134982\pi$
$282$		0			0
$283$	9.58146	+	1.68947i	0.569559	+	0.100429i	0.451009	−	0.892520i	$-0.351064\pi$
$283$	9.58146	+	1.68947i	0.569559	+	0.100429i	0.118550	+	0.992948i	$0.462175\pi$
$284$		0			0
$285$	15.5087	+	9.35926i	0.918655	+	0.554395i
$286$		0			0
$287$	24.2945	+	11.4891i	1.43406	+	0.678178i
$288$		0			0
$289$	−16.8830			−0.993116
$290$		0			0
$291$	10.4561	−	11.9816i	0.612945	−	0.702375i
$292$		0			0
$293$	−0.111390	+	0.631726i	−0.00650749	+	0.0369058i	−0.987889	−	0.155165i	$-0.950409\pi$
$293$	−0.111390	+	0.631726i	−0.00650749	+	0.0369058i	0.981381	+	0.192071i	$0.0615203\pi$
$294$		0			0
$295$	−12.3370	+	10.3519i	−0.718286	+	0.602713i
$296$		0			0
$297$	17.8811	+	24.0166i	1.03757	+	1.39358i
$298$		0			0
$299$	−0.423455	−	2.40153i	−0.0244890	−	0.138884i
$300$		0			0
$301$	11.7148	+	1.08878i	0.675231	+	0.0627562i
$302$		0			0
$303$	−2.63450	+	0.901457i	−0.151348	+	0.0517874i
$304$		0			0
$305$	−7.53424	−	4.34990i	−0.431410	−	0.249074i
$306$		0			0
$307$	−7.14240	−	4.12367i	−0.407638	−	0.235350i	0.282136	−	0.959374i	$-0.408957\pi$
$307$	−7.14240	−	4.12367i	−0.407638	−	0.235350i	−0.689774	+	0.724024i	$0.742290\pi$
$308$		0			0
$309$	4.63478	+	2.79702i	0.263664	+	0.159117i
$310$		0			0
$311$	−3.05631	+	17.3332i	−0.173308	+	0.982876i	0.766772	+	0.641920i	$0.221862\pi$
$311$	−3.05631	+	17.3332i	−0.173308	+	0.982876i	−0.940079	+	0.340956i	$0.889249\pi$
$312$		0			0
$313$	−12.9360	−	15.4166i	−0.731188	−	0.871396i	0.264478	−	0.964392i	$-0.414800\pi$
$313$	−12.9360	−	15.4166i	−0.731188	−	0.871396i	−0.995667	+	0.0929954i	$0.970356\pi$
$314$		0			0
$315$	−6.17198	+	8.03460i	−0.347752	+	0.452699i
$316$		0			0
$317$	5.39446	−	14.8212i	0.302983	−	0.832440i	−0.690995	−	0.722860i	$-0.742827\pi$
$317$	5.39446	−	14.8212i	0.302983	−	0.832440i	0.993978	−	0.109580i	$-0.0349505\pi$
$318$		0			0
$319$	−4.27404	−	3.58634i	−0.239300	−	0.200797i
$320$		0			0
$321$	19.0233	+	23.5846i	1.06178	+	1.31636i
$322$		0			0
$323$			2.80281i			0.155952i
$324$		0			0
$325$	13.7495	−	7.93827i	0.762685	−	0.440336i
$326$		0			0
$327$	4.42284	+	28.2771i	0.244584	+	1.56373i
$328$		0			0
$329$	8.19306	+	0.761466i	0.451698	+	0.0419810i
$330$		0			0
$331$	−4.42503	−	1.61058i	−0.243222	−	0.0885255i	0.217533	−	0.976053i	$-0.430199\pi$
$331$	−4.42503	−	1.61058i	−0.243222	−	0.0885255i	−0.460755	+	0.887527i	$0.652421\pi$
$332$		0			0
$333$	1.51051	−	6.97417i	0.0827755	−	0.382182i
$334$		0			0
$335$	−4.72351	−	1.71922i	−0.258073	−	0.0939308i
$336$		0			0
$337$	2.80872	+	2.35680i	0.153001	+	0.128383i	0.716075	−	0.698024i	$-0.245937\pi$
$337$	2.80872	+	2.35680i	0.153001	+	0.128383i	−0.563074	+	0.826407i	$0.690381\pi$
$338$		0			0
$339$	−0.0592296	+	3.05591i	−0.00321691	+	0.165974i
$340$		0			0
$341$	−12.2586	−	21.2325i	−0.663839	−	1.14980i
$342$		0			0
$343$	13.3065	−	12.8816i	0.718484	−	0.695543i
$344$		0			0
$345$	−0.370567	−	1.08298i	−0.0199507	−	0.0583056i
$346$		0			0
$347$	10.3261	+	28.3708i	0.554335	+	1.52302i	0.827734	+	0.561121i	$0.189630\pi$
$347$	10.3261	+	28.3708i	0.554335	+	1.52302i	−0.273399	+	0.961901i	$0.588148\pi$
$348$		0			0
$349$	−18.5777	−	22.1400i	−0.994441	−	1.18513i	−0.982701	−	0.185198i	$-0.940707\pi$
$349$	−18.5777	−	22.1400i	−0.994441	−	1.18513i	−0.0117402	−	0.999931i	$-0.503737\pi$
$350$		0			0
$351$	−23.8155	−	5.64339i	−1.27118	−	0.301222i
$352$		0			0
$353$	19.7762	+	7.19796i	1.05258	+	0.383109i	0.809637	−	0.586931i	$-0.199664\pi$
$353$	19.7762	+	7.19796i	1.05258	+	0.383109i	0.242946	+	0.970040i	$0.421886\pi$
$354$		0			0
$355$	2.08050	−	2.47945i	0.110422	−	0.131595i
$356$		0			0
$357$	−1.55784	−	0.175296i	−0.0824498	−	0.00927766i
$358$		0			0
$359$		−	12.7571i		−	0.673296i	−0.941631	−	0.336648i	$-0.890707\pi$
$359$		−	12.7571i		−	0.673296i	0.941631	−	0.336648i	$-0.109293\pi$
$360$		0			0
$361$	−48.1265			−2.53297
$362$		0			0
$363$	−38.4526	−	0.745288i	−2.01824	−	0.0391175i
$364$		0			0
$365$	−9.89772	+	11.7956i	−0.518070	+	0.617412i
$366$		0			0
$367$	−31.3571	+	5.52911i	−1.63683	+	0.288617i	−0.915000	−	0.403454i	$-0.867809\pi$
$367$	−31.3571	+	5.52911i	−1.63683	+	0.288617i	−0.721829	+	0.692071i	$0.756698\pi$
$368$		0			0
$369$	4.12466	+	30.1920i	0.214721	+	1.57173i
$370$		0			0
$371$	11.5607	−	11.4364i	0.600204	−	0.593748i
$372$		0			0
$373$	−1.05676	+	5.99316i	−0.0547167	+	0.310314i	−0.999867	−	0.0163225i	$-0.994804\pi$
$373$	−1.05676	+	5.99316i	−0.0547167	+	0.310314i	0.945150	+	0.326636i	$0.105915\pi$
$374$		0			0
$375$	14.4047	−	11.6188i	0.743856	−	0.599994i
$376$		0			0
$377$	4.56063			0.234884
$378$		0			0
$379$	−2.73209			−0.140338			−0.0701690	−	0.997535i	$-0.522354\pi$
$379$	−2.73209			−0.140338			−0.0701690	+	0.997535i	$0.522354\pi$
$380$		0			0
$381$	4.00189	+	25.5858i	0.205023	+	1.31080i
$382$		0			0
$383$	0.927013	−	5.25735i	0.0473681	−	0.268638i	−0.951921	−	0.306344i	$-0.900894\pi$
$383$	0.927013	−	5.25735i	0.0473681	−	0.268638i	0.999289	+	0.0377064i	$0.0120052\pi$
$384$		0			0
$385$	−4.93504	−	18.8244i	−0.251513	−	0.959380i
$386$		0			0
$387$	6.21761	+	11.8031i	0.316059	+	0.599985i
$388$		0			0
$389$	24.3024	−	4.28518i	1.23218	−	0.217267i	0.480620	−	0.876929i	$-0.340412\pi$
$389$	24.3024	−	4.28518i	1.23218	−	0.217267i	0.751563	+	0.659662i	$0.229300\pi$
$390$		0			0
$391$	0.113844	−	0.135674i	0.00575734	−	0.00686133i
$392$		0			0
$393$	10.2831	+	18.6358i	0.518714	+	0.940052i
$394$		0			0
$395$	6.60439			0.332303
$396$		0			0
$397$			9.61693i			0.482660i	0.970443	+	0.241330i	$0.0775836\pi$
$397$			9.61693i			0.482660i	−0.970443	+	0.241330i	$0.922416\pi$
$398$		0			0
$399$	4.19830	−	37.3099i	0.210178	−	1.86783i
$400$		0			0
$401$	20.9612	−	24.9806i	1.04675	−	1.24747i	0.0786520	−	0.996902i	$-0.474938\pi$
$401$	20.9612	−	24.9806i	1.04675	−	1.24747i	0.968099	−	0.250567i	$-0.0806172\pi$
$402$		0			0
$403$	18.8320	+	6.85428i	0.938088	+	0.341436i
$404$		0			0
$405$	−11.4536	−	0.889645i	−0.569134	−	0.0442068i
$406$		0			0
$407$	8.81036	+	10.4998i	0.436713	+	0.520455i
$408$		0			0
$409$	−0.279129	−	0.766899i	−0.0138020	−	0.0379207i	0.932600	−	0.360911i	$-0.117534\pi$
$409$	−0.279129	−	0.766899i	−0.0138020	−	0.0379207i	−0.946402	+	0.322990i	$0.895312\pi$
$410$		0			0
$411$	1.46291	−	1.67635i	0.0721600	−	0.0826883i
$412$		0			0
$413$	30.1766	+	14.2708i	1.48489	+	0.702218i
$414$		0			0
$415$	−0.462915	−	0.801793i	−0.0227236	−	0.0393585i
$416$		0			0
$417$	1.27167	+	0.767437i	0.0622741	+	0.0375815i
$418$		0			0
$419$	0.632382	+	0.530632i	0.0308939	+	0.0259231i	0.658104	−	0.752927i	$-0.271359\pi$
$419$	0.632382	+	0.530632i	0.0308939	+	0.0259231i	−0.627210	+	0.778850i	$0.715803\pi$
$420$		0			0
$421$	32.9353	+	11.9875i	1.60517	+	0.584233i	0.980476	−	0.196640i	$-0.0630030\pi$
$421$	32.9353	+	11.9875i	1.60517	+	0.584233i	0.624690	+	0.780873i	$0.285225\pi$
$422$		0			0
$423$	4.34845	+	8.25480i	0.211429	+	0.401362i
$424$		0			0
$425$	1.08355	+	0.394379i	0.0525597	+	0.0191302i
$426$		0			0
$427$	−1.66874	+	17.9550i	−0.0807560	+	0.868902i
$428$		0			0
$429$	36.5915	−	29.5147i	1.76665	−	1.42498i
$430$		0			0
$431$	−1.84508	+	1.06526i	−0.0888745	+	0.0513117i	−0.543779	−	0.839229i	$-0.683007\pi$
$431$	−1.84508	+	1.06526i	−0.0888745	+	0.0513117i	0.454904	+	0.890540i	$0.349674\pi$
$432$		0			0
$433$			24.2310i			1.16447i	0.813022	+	0.582233i	$0.197821\pi$
$433$			24.2310i			1.16447i	−0.813022	+	0.582233i	$0.802179\pi$
$434$		0			0
$435$	2.11496	−	0.330802i	0.101404	−	0.0158607i
$436$		0			0
$437$	3.24936	+	2.72653i	0.155438	+	0.130428i
$438$		0			0
$439$	−10.0841	+	27.7057i	−0.481286	+	1.32232i	0.427106	+	0.904202i	$0.359533\pi$
$439$	−10.0841	+	27.7057i	−0.481286	+	1.32232i	−0.908392	+	0.418120i	$0.862689\pi$
$440$		0			0
$441$	20.4749	+	4.66696i	0.974993	+	0.222236i
$442$		0			0
$443$	−5.29303	−	6.30799i	−0.251480	−	0.299702i	0.625505	−	0.780220i	$-0.284893\pi$
$443$	−5.29303	−	6.30799i	−0.251480	−	0.299702i	−0.876985	+	0.480518i	$0.840449\pi$
$444$		0			0
$445$	2.27003	−	12.8740i	0.107610	−	0.610286i
$446$		0			0
$447$	0.631766	−	32.5955i	0.0298815	−	1.54172i
$448$		0			0
$449$	−31.8671	−	18.3985i	−1.50390	−	0.868278i	−0.999990	−	0.00452223i	$-0.998561\pi$
$449$	−31.8671	−	18.3985i	−1.50390	−	0.868278i	−0.503911	−	0.863755i	$-0.668106\pi$
$450$		0			0
$451$	−50.6894	−	29.2656i	−2.38687	−	1.37806i
$452$		0			0
$453$	−0.343765	+	1.75051i	−0.0161515	+	0.0822460i
$454$		0			0
$455$	12.9809	+	9.19435i	0.608555	+	0.431038i
$456$		0			0
$457$	5.68848	+	32.2609i	0.266096	+	1.50910i	0.765897	+	0.642963i	$0.222295\pi$
$457$	5.68848	+	32.2609i	0.266096	+	1.50910i	−0.499801	+	0.866140i	$0.666594\pi$
$458$		0			0
$459$	−0.797837	−	1.58847i	−0.0372398	−	0.0741434i
$460$		0			0
$461$	−28.7198	+	24.0988i	−1.33762	+	1.12239i	−0.355385	+	0.934720i	$0.615650\pi$
$461$	−28.7198	+	24.0988i	−1.33762	+	1.12239i	−0.982231	+	0.187674i	$0.939905\pi$
$462$		0			0
$463$	4.27116	−	24.2230i	0.198498	−	1.12574i	−0.708851	−	0.705358i	$-0.750786\pi$
$463$	4.27116	−	24.2230i	0.198498	−	1.12574i	0.907349	−	0.420379i	$-0.138103\pi$
$464$		0			0
$465$	9.23036	+	1.81266i	0.428048	+	0.0840601i
$466$		0			0
$467$	20.7729			0.961257			0.480628	−	0.876924i	$-0.340409\pi$
$467$	20.7729			0.961257			0.480628	+	0.876924i	$0.340409\pi$
$468$		0			0
$469$	0.851928	+	10.3840i	0.0393384	+	0.479490i
$470$		0			0
$471$	10.0777	−	5.56083i	0.464358	−	0.256230i
$472$		0			0
$473$	−25.2352	−	4.44964i	−1.16031	−	0.204595i
$474$		0			0
$475$	−9.44526	+	25.9506i	−0.433378	+	1.19070i
$476$		0			0
$477$	18.0212	+	3.90314i	0.825132	+	0.178712i
$478$		0			0
$479$	30.0139	−	25.1847i	1.37137	−	1.15072i	0.399088	−	0.916912i	$-0.369327\pi$
$479$	30.0139	−	25.1847i	1.37137	−	1.15072i	0.972283	−	0.233805i	$-0.0751178\pi$
$480$		0			0
$481$	−11.0336	−	1.94552i	−0.503090	−	0.0887083i
$482$		0			0
$483$	−1.71867	+	1.63552i	−0.0782024	+	0.0744185i
$484$		0			0
$485$	−10.1494	−	5.85975i	−0.460860	−	0.266078i
$486$		0			0
$487$	0.541148	+	0.937296i	0.0245218	+	0.0424729i	0.878026	−	0.478613i	$-0.158860\pi$
$487$	0.541148	+	0.937296i	0.0245218	+	0.0424729i	−0.853504	+	0.521086i	$0.825527\pi$
$488$		0			0
$489$	−4.31227	+	3.47827i	−0.195007	+	0.157293i
$490$		0			0
$491$	9.76500	+	26.8291i	0.440688	+	1.21078i	0.939041	+	0.343806i	$0.111716\pi$
$491$	9.76500	+	26.8291i	0.440688	+	1.21078i	−0.498353	+	0.866974i	$0.666061\pi$
$492$		0			0
$493$	0.212911	+	0.253737i	0.00958903	+	0.0114278i
$494$		0			0
$495$	14.8282	−	16.3414i	0.666479	−	0.734489i
$496$		0			0
$497$	−6.47071	−	1.77138i	−0.290251	−	0.0794573i
$498$		0			0
$499$	2.15959	−	0.786028i	0.0966767	−	0.0351874i	−0.293229	−	0.956042i	$-0.594730\pi$
$499$	2.15959	−	0.786028i	0.0966767	−	0.0351874i	0.389906	+	0.920855i	$0.372508\pi$
$500$		0			0
$501$	−35.7172	−	0.692271i	−1.59573	−	0.0309284i
$502$		0			0
$503$	−7.80677	+	13.5217i	−0.348087	+	0.602904i	−0.985910	−	0.167279i	$-0.946502\pi$
$503$	−7.80677	+	13.5217i	−0.348087	+	0.602904i	0.637823	+	0.770183i	$0.279835\pi$
$504$		0			0
$505$	1.02602	+	1.77712i	0.0456572	+	0.0790807i
$506$		0			0
$507$	−3.06601	+	15.6126i	−0.136166	+	0.693381i
$508$		0			0
$509$	−32.9005	−	27.6068i	−1.45829	−	1.22365i	−0.926240	−	0.376935i	$-0.876978\pi$
$509$	−32.9005	−	27.6068i	−1.45829	−	1.22365i	−0.532049	−	0.846714i	$-0.678578\pi$
$510$		0			0
$511$	30.7836	+	8.42711i	1.36178	+	0.372793i
$512$		0			0
$513$	38.0434	−	19.1080i	1.67966	−	0.843637i
$514$		0			0
$515$	1.36447	−	3.74885i	0.0601257	−	0.165194i
$516$		0			0
$517$	−17.6489	−	3.11197i	−0.776196	−	0.136864i
$518$		0			0
$519$	−34.6019	+	11.8399i	−1.51886	+	0.519713i
$520$		0			0
$521$	13.7637	−	23.8394i	0.602997	−	1.04442i	−0.389367	−	0.921083i	$-0.627306\pi$
$521$	13.7637	−	23.8394i	0.602997	−	1.04442i	0.992365	−	0.123339i	$-0.0393604\pi$
$522$		0			0
$523$	−8.10797	+	4.68114i	−0.354537	+	0.204692i	−0.666682	−	0.745343i	$-0.732286\pi$
$523$	−8.10797	+	4.68114i	−0.354537	+	0.204692i	0.312145	+	0.950035i	$0.398953\pi$
$524$		0			0
$525$	−13.8330	−	6.87285i	−0.603723	−	0.299956i
$526$		0			0
$527$	0.497815	+	1.36773i	0.0216851	+	0.0595795i
$528$		0			0
$529$	3.94736	+	22.3866i	0.171625	+	0.973331i
$530$		0			0
$531$	5.12331	+	37.5020i	0.222333	+	1.62745i
$532$		0			0
$533$	47.1171	−	8.30802i	2.04087	−	0.359860i
$534$		0			0
$535$	14.3537	−	17.1060i	0.620562	−	0.739558i
$536$		0			0
$537$	7.25222	−	18.7844i	0.312956	−	0.810609i
$538$		0			0
$539$	−31.1782	+	25.5921i	−1.34294	+	1.10233i
$540$		0			0
$541$	6.19661	−	10.7328i	0.266413	−	0.461441i	−0.701520	−	0.712650i	$-0.747495\pi$
$541$	6.19661	−	10.7328i	0.266413	−	0.461441i	0.967933	+	0.251209i	$0.0808281\pi$
$542$		0			0
$543$	14.0287	−	2.19424i	0.602030	−	0.0941638i
$544$		0			0
$545$	19.8205	−	7.21407i	0.849017	−	0.309017i
$546$		0			0
$547$	−4.56791	−	25.9059i	−0.195310	−	1.10766i	−0.911977	−	0.410241i	$-0.865444\pi$
$547$	−4.56791	−	25.9059i	−0.195310	−	1.10766i	0.716667	−	0.697415i	$-0.245667\pi$
$548$		0			0
$549$	−18.0903	+	9.52956i	−0.772074	+	0.406712i
$550$		0			0
$551$	−6.07694	+	5.09916i	−0.258886	+	0.217231i
$552$		0			0
$553$	−5.71811	−	12.4377i	−0.243159	−	0.528904i
$554$		0			0
$555$	−5.25788	−	0.101908i	−0.223184	−	0.00432576i
$556$		0			0
$557$			8.39463i			0.355692i	0.984058	+	0.177846i	$0.0569129\pi$
$557$			8.39463i			0.355692i	−0.984058	+	0.177846i	$0.943087\pi$
$558$		0			0
$559$	18.1395	−	10.4729i	0.767220	−	0.442955i
$560$		0			0
$561$	3.35035	+	0.657943i	0.141452	+	0.0277784i
$562$		0			0
$563$	4.96933	−	1.80869i	0.209432	−	0.0762271i	−0.235174	−	0.971953i	$-0.575566\pi$
$563$	4.96933	−	1.80869i	0.209432	−	0.0762271i	0.444606	+	0.895726i	$0.353344\pi$
$564$		0			0
$565$	2.21829	−	0.391144i	0.0933241	−	0.0164556i
$566$		0			0
$567$	8.24115	+	22.3402i	0.346096	+	0.938199i
$568$		0			0
$569$	−13.1074	+	2.31119i	−0.549492	+	0.0968902i	−0.441500	−	0.897261i	$-0.645553\pi$
$569$	−13.1074	+	2.31119i	−0.549492	+	0.0968902i	−0.107992	+	0.994152i	$0.534442\pi$
$570$		0			0
$571$	19.0745	−	6.94253i	0.798241	−	0.290536i	0.0894837	−	0.995988i	$-0.471478\pi$
$571$	19.0745	−	6.94253i	0.798241	−	0.290536i	0.708757	+	0.705452i	$0.249256\pi$
$572$		0			0
$573$	31.6191	+	6.20937i	1.32091	+	0.259400i
$574$		0			0
$575$	1.51127	−	0.872533i	0.0630244	−	0.0363871i
$576$		0			0
$577$		−	10.4169i		−	0.433663i	−0.976209	−	0.216832i	$-0.930428\pi$
$577$		−	10.4169i		−	0.433663i	0.976209	−	0.216832i	$-0.0695723\pi$
$578$		0			0
$579$	29.8000	+	0.577584i	1.23845	+	0.0240036i
$580$		0			0
$581$	−1.10918	+	1.56598i	−0.0460165	+	0.0649677i
$582$		0			0
$583$	−27.1313	+	22.7658i	−1.12366	+	0.942865i
$584$		0			0
$585$	−0.698928	+	18.0236i	−0.0288971	+	0.745183i
$586$		0			0
$587$	−0.0514158	−	0.291593i	−0.00212216	−	0.0120354i	0.983728	−	0.179663i	$-0.0575006\pi$
$587$	−0.0514158	−	0.291593i	−0.00212216	−	0.0120354i	−0.985850	+	0.167627i	$0.946389\pi$
$588$		0			0
$589$	−32.7569	+	11.9225i	−1.34972	+	0.491259i
$590$		0			0
$591$	−17.0751	+	2.67073i	−0.702376	+	0.109859i
$592$		0			0
$593$	15.3529	−	26.5920i	0.630467	−	1.09200i	−0.356989	−	0.934109i	$-0.616197\pi$
$593$	15.3529	−	26.5920i	0.630467	−	1.09200i	0.987456	−	0.157893i	$-0.0504701\pi$
$594$		0			0
$595$	0.0944673	+	1.15145i	0.00387278	+	0.0472048i
$596$		0			0
$597$	−10.6888	+	27.6857i	−0.437462	+	1.13310i
$598$		0			0
$599$	19.2095	−	22.8930i	0.784879	−	0.935382i	−0.214264	−	0.976776i	$-0.568735\pi$
$599$	19.2095	−	22.8930i	0.784879	−	0.935382i	0.999143	+	0.0413935i	$0.0131797\pi$
$600$		0			0
$601$	7.31717	−	1.29022i	0.298474	−	0.0526290i	−0.0224059	−	0.999749i	$-0.507133\pi$
$601$	7.31717	−	1.29022i	0.298474	−	0.0526290i	0.320880	+	0.947120i	$0.396021\pi$
$602$		0			0
$603$	−9.33746	+	7.23747i	−0.380251	+	0.294732i
$604$		0			0
$605$	4.92178	+	27.9128i	0.200099	+	1.13482i
$606$		0			0
$607$	12.1959	+	33.5078i	0.495014	+	1.36004i	0.896040	+	0.443974i	$0.146432\pi$
$607$	12.1959	+	33.5078i	0.495014	+	1.36004i	−0.401025	+	0.916067i	$0.631346\pi$
$608$		0			0
$609$	−2.45412	−	3.69657i	−0.0994460	−	0.149793i
$610$		0			0
$611$	12.6863	−	7.32446i	0.513234	−	0.296316i
$612$		0			0
$613$	7.49646	−	12.9843i	0.302779	−	0.524429i	−0.673985	−	0.738745i	$-0.735419\pi$
$613$	7.49646	−	12.9843i	0.302779	−	0.524429i	0.976764	+	0.214316i	$0.0687522\pi$
$614$		0			0
$615$	21.2476	−	7.27038i	0.856786	−	0.293170i
$616$		0			0
$617$	−14.8177	−	2.61276i	−0.596537	−	0.105186i	−0.132776	−	0.991146i	$-0.542389\pi$
$617$	−14.8177	−	2.61276i	−0.596537	−	0.105186i	−0.463761	+	0.885960i	$0.653500\pi$
$618$		0			0
$619$	−7.13530	+	19.6041i	−0.286792	+	0.787954i	0.709719	+	0.704485i	$0.248822\pi$
$619$	−7.13530	+	19.6041i	−0.286792	+	0.787954i	−0.996510	+	0.0834686i	$0.973400\pi$
$620$		0			0
$621$	−2.61767	−	0.620292i	−0.105044	−	0.0248915i
$622$		0			0
$623$	−26.2103	+	6.87134i	−1.05009	+	0.275294i
$624$		0			0
$625$	2.46259	+	2.06636i	0.0985036	+	0.0826544i
$626$		0			0
$627$	−15.7575	+	80.2400i	−0.629296	+	3.20448i
$628$		0			0
$629$	−0.406857	−	0.704698i	−0.0162225	−	0.0280981i
$630$		0			0
$631$	6.15238	−	10.6562i	0.244923	−	0.424218i	−0.717187	−	0.696880i	$-0.754571\pi$
$631$	6.15238	−	10.6562i	0.244923	−	0.424218i	0.962110	+	0.272662i	$0.0879041\pi$
$632$		0			0
$633$	−35.0030	−	0.678428i	−1.39125	−	0.0269651i
$634$		0			0
$635$	17.9341	−	6.52747i	0.711692	−	0.259035i
$636$		0			0
$637$	6.07627	−	32.4068i	0.240751	−	1.28400i
$638$		0			0
$639$	−2.32282	−	7.24374i	−0.0918894	−	0.286558i
$640$		0			0
$641$	−3.33066	−	3.96933i	−0.131553	−	0.156779i	0.696246	−	0.717803i	$-0.254852\pi$
$641$	−3.33066	−	3.96933i	−0.131553	−	0.156779i	−0.827800	+	0.561024i	$0.810408\pi$
$642$		0			0
$643$	−15.2007	−	41.7635i	−0.599457	−	1.64699i	−0.752360	−	0.658752i	$-0.771085\pi$
$643$	−15.2007	−	41.7635i	−0.599457	−	1.64699i	0.152903	−	0.988241i	$-0.451138\pi$
$644$		0			0
$645$	7.65243	−	6.17245i	0.301314	−	0.243040i
$646$		0			0
$647$	−0.558967	−	0.968159i	−0.0219753	−	0.0380623i	0.854829	−	0.518910i	$-0.173662\pi$
$647$	−0.558967	−	0.968159i	−0.0219753	−	0.0380623i	−0.876804	+	0.480848i	$0.840329\pi$
$648$		0			0
$649$	−62.9622	−	36.3512i	−2.47148	−	1.42691i
$650$		0			0
$651$	−4.57801	−	18.9524i	−0.179426	−	0.742805i
$652$		0			0
$653$	−30.4355	−	5.36660i	−1.19103	−	0.210011i	−0.457215	−	0.889356i	$-0.651153\pi$
$653$	−30.4355	−	5.36660i	−1.19103	−	0.210011i	−0.733819	+	0.679345i	$0.762264\pi$
$654$		0			0
$655$	12.0161	−	10.0827i	0.469509	−	0.393965i
$656$		0			0
$657$	11.0505	+	34.4612i	0.431122	+	1.34446i
$658$		0			0
$659$	12.4980	−	34.3381i	0.486855	−	1.33762i	−0.416659	−	0.909063i	$-0.636799\pi$
$659$	12.4980	−	34.3381i	0.486855	−	1.33762i	0.903514	−	0.428559i	$-0.140979\pi$
$660$		0			0
$661$	−24.1321	−	4.25514i	−0.938631	−	0.165506i	−0.316654	−	0.948541i	$-0.602559\pi$
$661$	−24.1321	−	4.25514i	−0.938631	−	0.165506i	−0.621977	+	0.783035i	$0.713670\pi$
$662$		0			0
$663$	−2.44360	+	1.34836i	−0.0949015	+	0.0523660i
$664$		0			0
$665$	−27.5769	+	2.26247i	−1.06938	+	0.0877347i
$666$		0			0
$667$	0.501280			0.0194096
$668$		0			0
$669$	−11.9083	−	2.33855i	−0.460401	−	0.0904136i
$670$		0			0
$671$	6.81984	−	38.6772i	0.263277	−	1.49312i
$672$		0			0
$673$	4.11606	−	3.45379i	0.158663	−	0.133134i	−0.560000	−	0.828492i	$-0.689199\pi$
$673$	4.11606	−	3.45379i	0.158663	−	0.133134i	0.718663	+	0.695359i	$0.244755\pi$
$674$		0			0
$675$	−2.03398	−	17.3960i	−0.0782881	−	0.669571i
$676$		0			0
$677$	−2.21240	−	12.5472i	−0.0850295	−	0.482226i	−0.997350	−	0.0727498i	$-0.976823\pi$
$677$	−2.21240	−	12.5472i	−0.0850295	−	0.482226i	0.912321	−	0.409476i	$-0.134289\pi$
$678$		0			0
$679$	−2.24796	+	24.1872i	−0.0862689	+	0.928219i
$680$		0			0
$681$	4.58942	−	23.3701i	0.175867	−	0.895545i
$682$		0			0
$683$	−30.9994	−	17.8975i	−1.18616	−	0.684830i	−0.228729	−	0.973490i	$-0.573457\pi$
$683$	−30.9994	−	17.8975i	−1.18616	−	0.684830i	−0.957432	+	0.288660i	$0.906790\pi$
$684$		0			0
$685$	−1.42000	−	0.819839i	−0.0542555	−	0.0313244i
$686$		0			0
$687$	−0.692709	+	35.7398i	−0.0264285	+	1.36356i
$688$		0			0
$689$	5.02721	−	28.5107i	0.191521	−	1.08617i
$690$		0			0
$691$	0.636884	+	0.759009i	0.0242282	+	0.0288740i	0.778022	−	0.628236i	$-0.216223\pi$
$691$	0.636884	+	0.759009i	0.0242282	+	0.0288740i	−0.753794	+	0.657110i	$0.771778\pi$
$692$		0			0
$693$	−43.6131	−	13.7767i	−1.65672	−	0.523335i
$694$		0			0
$695$	0.374378	−	1.02860i	0.0142010	−	0.0390169i
$696$		0			0
$697$	2.66187	+	2.23357i	0.100826	+	0.0846027i
$698$		0			0
$699$	47.7135	−	7.46290i	1.80469	−	0.282273i
$700$		0			0
$701$			21.7180i			0.820277i	0.912023	+	0.410139i	$0.134520\pi$
$701$			21.7180i			0.820277i	−0.912023	+	0.410139i	$0.865480\pi$
$702$		0			0
$703$	16.8773	−	9.74412i	0.636540	−	0.367506i
$704$		0			0
$705$	5.35192	−	4.31686i	0.201565	−	0.162582i
$706$		0			0
$707$	2.45841	−	3.47088i	0.0924582	−	0.130536i
$708$		0			0
$709$	12.7552	+	4.64252i	0.479032	+	0.174354i	0.570240	−	0.821478i	$-0.306850\pi$
$709$	12.7552	+	4.64252i	0.479032	+	0.174354i	−0.0912072	+	0.995832i	$0.529073\pi$
$710$		0			0
$711$	8.27608	−	13.1316i	0.310377	−	0.492475i
$712$		0			0
$713$	2.06991	+	0.753386i	0.0775188	+	0.0282145i
$714$		0			0
$715$	−26.5400	−	22.2697i	−0.992539	−	0.832839i
$716$		0			0
$717$	−35.7290	−	21.5620i	−1.33433	−	0.805246i
$718$		0			0
$719$	−6.02285	−	10.4319i	−0.224614	−	0.389044i	0.731589	−	0.681746i	$-0.238779\pi$
$719$	−6.02285	−	10.4319i	−0.224614	−	0.389044i	−0.956204	+	0.292702i	$0.905446\pi$
$720$		0			0
$721$	−8.24137	+	0.676140i	−0.306924	+	0.0251808i
$722$		0			0
$723$	−1.96147	+	2.24765i	−0.0729479	+	0.0835912i
$724$		0			0
$725$	1.11622	+	3.06680i	0.0414555	+	0.113898i
$726$		0			0
$727$	−29.9518	−	35.6951i	−1.11085	−	1.32386i	−0.941007	−	0.338387i	$-0.890119\pi$
$727$	−29.9518	−	35.6951i	−1.11085	−	1.32386i	−0.169842	−	0.985471i	$-0.554326\pi$
$728$		0			0
$729$	−16.1216	+	21.6586i	−0.597096	+	0.802170i
$730$		0			0
$731$	1.42951	+	0.520299i	0.0528723	+	0.0192439i
$732$		0			0
$733$	−21.7050	+	25.8670i	−0.801691	+	0.955418i	−0.999693	−	0.0247835i	$-0.992110\pi$
$733$	−21.7050	+	25.8670i	−0.801691	+	0.955418i	0.198002	+	0.980202i	$0.436555\pi$
$734$		0			0
$735$	0.467228	−	15.4691i	0.0172340	−	0.570588i
$736$		0			0
$737$		−	22.6920i		−	0.835872i
$738$		0			0
$739$	11.3481			0.417448			0.208724	−	0.977975i	$-0.433069\pi$
$739$	11.3481			0.417448			0.208724	+	0.977975i	$0.433069\pi$
$740$		0			0
$741$	−32.2929	−	58.5235i	−1.18631	−	2.14991i
$742$		0			0
$743$	19.8314	−	23.6342i	0.727544	−	0.867053i	−0.267796	−	0.963476i	$-0.586295\pi$
$743$	19.8314	−	23.6342i	0.727544	−	0.867053i	0.995341	+	0.0964222i	$0.0307399\pi$
$744$		0			0
$745$	−23.6612	+	4.17210i	−0.866878	+	0.152854i
$746$		0			0
$747$	−2.17431	−	0.0843165i	−0.0795538	−	0.00308498i
$748$		0			0
$749$	−44.6423	−	12.2210i	−1.63119	−	0.446545i
$750$		0			0
$751$	−4.22235	+	23.9461i	−0.154076	+	0.873807i	0.805550	+	0.592528i	$0.201870\pi$
$751$	−4.22235	+	23.9461i	−0.154076	+	0.873807i	−0.959626	+	0.281279i	$0.909241\pi$
$752$		0			0
$753$	−0.721173	−	4.61077i	−0.0262810	−	0.168026i
$754$		0			0
$755$	1.31470			0.0478467
$756$		0			0
$757$	−6.10213			−0.221786			−0.110893	−	0.993832i	$-0.535371\pi$
$757$	−6.10213			−0.221786			−0.110893	+	0.993832i	$0.535371\pi$
$758$		0			0
$759$	4.02194	−	3.24410i	0.145987	−	0.117753i
$760$		0			0
$761$	−2.51770	+	14.2786i	−0.0912667	+	0.517599i	0.904561	+	0.426344i	$0.140199\pi$
$761$	−2.51770	+	14.2786i	−0.0912667	+	0.517599i	−0.995828	+	0.0912546i	$0.970912\pi$
$762$		0			0
$763$	−30.7465	−	31.0809i	−1.11310	−	1.12520i
$764$		0			0
$765$	−1.03540	+	0.802537i	−0.0374349	+	0.0290158i
$766$		0			0
$767$	58.5249	−	10.3195i	2.11321	−	0.372616i
$768$		0			0
$769$	−22.5194	+	26.8375i	−0.812069	+	0.967786i	−0.999896	−	0.0144157i	$-0.995411\pi$
$769$	−22.5194	+	26.8375i	−0.812069	+	0.967786i	0.187827	+	0.982202i	$0.439856\pi$
$770$		0			0
$771$	−32.9527	−	0.638689i	−1.18676	−	0.0230018i
$772$		0			0
$773$	38.8404			1.39699			0.698496	−	0.715614i	$-0.253853\pi$
$773$	38.8404			1.39699			0.698496	+	0.715614i	$0.253853\pi$
$774$		0			0
$775$			14.3412i			0.515150i
$776$		0			0
$777$	4.36037	+	9.99010i	0.156427	+	0.358393i
$778$		0			0
$779$	−53.4935	+	63.7510i	−1.91660	+	2.28412i
$780$		0			0
$781$	13.7304	+	4.99744i	0.491311	+	0.178822i
$782$		0			0
$783$	1.99255	−	4.61975i	0.0712080	−	0.165096i
$784$		0			0
$785$	−5.45247	−	6.49800i	−0.194607	−	0.231924i
$786$		0			0
$787$	−4.35885	−	11.9758i	−0.155376	−	0.426892i	0.837442	−	0.546526i	$-0.184050\pi$
$787$	−4.35885	−	11.9758i	−0.155376	−	0.426892i	−0.992818	+	0.119634i	$0.961828\pi$
$788$		0			0
$789$	16.1532	+	47.2076i	0.575070	+	1.68063i
$790$		0			0
$791$	−2.65722	−	3.83893i	−0.0944800	−	0.136496i
$792$		0			0
$793$	16.0514	+	27.8019i	0.570004	+	0.987275i
$794$		0			0
$795$	0.263329	−	13.5863i	0.00933932	−	0.481856i
$796$		0			0
$797$	26.9959	+	22.6523i	0.956245	+	0.802385i	0.980338	−	0.197325i	$-0.0632253\pi$
$797$	26.9959	+	22.6523i	0.956245	+	0.802385i	−0.0240929	+	0.999710i	$0.507670\pi$
$798$		0			0
$799$	0.999764	+	0.363884i	0.0353691	+	0.0128733i
$800$		0			0
$801$	−22.7530	−	20.6462i	−0.803939	−	0.729497i
$802$		0			0
$803$	−65.3203	−	23.7747i	−2.30510	−	0.838989i
$804$		0			0
$805$	1.42679	+	1.01059i	0.0502879	+	0.0356188i
$806$		0			0
$807$	4.30837	+	27.5453i	0.151662	+	0.969641i
$808$		0			0
$809$	1.66941	−	0.963835i	0.0586934	−	0.0338866i	−0.470366	−	0.882471i	$-0.655878\pi$
$809$	1.66941	−	0.963835i	0.0586934	−	0.0338866i	0.529060	+	0.848585i	$0.322545\pi$
$810$		0			0
$811$			28.0560i			0.985179i	0.870262	+	0.492589i	$0.163950\pi$
$811$			28.0560i			0.985179i	−0.870262	+	0.492589i	$0.836050\pi$
$812$		0			0
$813$	−20.3723	−	25.2570i	−0.714487	−	0.885802i
$814$		0			0
$815$	3.12770	+	2.62445i	0.109559	+	0.0919306i
$816$		0			0
$817$	−12.4610	+	34.2363i	−0.435955	+	1.19778i
$818$		0			0
$819$	34.5479	−	14.2886i	1.20720	−	0.499285i
$820$		0			0
$821$	19.4620	+	23.1940i	0.679230	+	0.809475i	0.990009	−	0.141007i	$-0.0450342\pi$
$821$	19.4620	+	23.1940i	0.679230	+	0.809475i	−0.310778	+	0.950482i	$0.600590\pi$
$822$		0			0
$823$	0.579831	−	3.28839i	0.0202116	−	0.114626i	−0.973033	−	0.230667i	$-0.925909\pi$
$823$	0.579831	−	3.28839i	0.0202116	−	0.114626i	0.993244	+	0.116041i	$0.0370204\pi$
$824$		0			0
$825$	28.8030	+	17.3822i	1.00279	+	0.605171i
$826$		0			0
$827$	−18.2554	−	10.5397i	−0.634801	−	0.366503i	0.147808	−	0.989016i	$-0.452778\pi$
$827$	−18.2554	−	10.5397i	−0.634801	−	0.366503i	−0.782609	+	0.622513i	$0.786112\pi$
$828$		0			0
$829$	25.6887	+	14.8314i	0.892206	+	0.515115i	0.874663	−	0.484731i	$-0.161082\pi$
$829$	25.6887	+	14.8314i	0.892206	+	0.515115i	0.0175426	+	0.999846i	$0.494416\pi$
$830$		0			0
$831$	20.2119	−	6.91598i	0.701142	−	0.239913i
$832$		0			0
$833$	2.08667	−	1.17483i	0.0722987	−	0.0407056i
$834$		0			0
$835$	4.57166	+	25.9272i	0.158209	+	0.897247i
$836$		0			0
$837$	15.1709	−	16.0814i	0.524382	−	0.555856i
$838$		0			0
$839$	−13.0322	+	10.9353i	−0.449921	+	0.377529i	−0.839407	−	0.543504i	$-0.817097\pi$
$839$	−13.0322	+	10.9353i	−0.449921	+	0.377529i	0.389485	+	0.921033i	$0.372653\pi$
$840$		0			0
$841$	4.87300	−	27.6362i	0.168035	−	0.952972i
$842$		0			0
$843$	−11.5259	+	13.2076i	−0.396974	+	0.454894i
$844$		0			0
$845$	11.7257			0.403375
$846$		0			0
$847$	48.3053	−	33.4359i	1.65979	−	1.14887i
$848$		0			0
$849$	−14.4279	−	8.70702i	−0.495164	−	0.298824i
$850$		0			0
$851$	−1.21276	−	0.213842i	−0.0415728	−	0.00733040i
$852$		0			0
$853$	16.4221	−	45.1192i	0.562281	−	1.54485i	−0.254004	−	0.967203i	$-0.581748\pi$
$853$	16.4221	−	45.1192i	0.562281	−	1.54485i	0.816285	−	0.577650i	$-0.196030\pi$
$854$		0			0
$855$	−19.2205	−	24.7975i	−0.657329	−	0.848056i
$856$		0			0
$857$	7.21447	−	6.05366i	0.246442	−	0.206789i	−0.511197	−	0.859464i	$-0.670798\pi$
$857$	7.21447	−	6.05366i	0.246442	−	0.206789i	0.757638	+	0.652675i	$0.226353\pi$
$858$		0			0
$859$	11.1411	+	1.96448i	0.380131	+	0.0670273i	0.360449	−	0.932779i	$-0.382624\pi$
$859$	11.1411	+	1.96448i	0.380131	+	0.0670273i	0.0196820	+	0.999806i	$0.493735\pi$
$860$		0			0
$861$	−32.0882	−	33.7197i	−1.09356	−	1.14916i
$862$		0			0
$863$	45.3985	+	26.2109i	1.54538	+	0.892228i	0.998485	+	0.0550294i	$0.0175253\pi$
$863$	45.3985	+	26.2109i	1.54538	+	0.892228i	0.546899	+	0.837198i	$0.315808\pi$
$864$		0			0
$865$	13.4759	+	23.3409i	0.458194	+	0.793616i
$866$		0			0
$867$	27.2797	+	10.5320i	0.926466	+	0.357686i
$868$		0			0
$869$	10.1972	+	28.0165i	0.345915	+	0.950394i
$870$		0			0
$871$	11.9229	+	14.2091i	0.403992	+	0.481459i
$872$		0			0
$873$	−24.3694	+	12.8373i	−0.824780	+	0.434476i
$874$		0			0
$875$	−7.46417	+	27.2660i	−0.252335	+	0.921760i
$876$		0			0
$877$	1.87567	−	0.682688i	0.0633369	−	0.0230527i	−0.310157	−	0.950685i	$-0.600382\pi$
$877$	1.87567	−	0.682688i	0.0633369	−	0.0230527i	0.373494	+	0.927632i	$0.378160\pi$
$878$		0			0
$879$	0.574072	−	0.951261i	0.0193630	−	0.0320852i
$880$		0			0
$881$	9.50503	−	16.4632i	0.320233	−	0.554659i	−0.660303	−	0.750999i	$-0.729572\pi$
$881$	9.50503	−	16.4632i	0.320233	−	0.554659i	0.980536	+	0.196340i	$0.0629056\pi$
$882$		0			0
$883$	15.4288	+	26.7235i	0.519221	+	0.899317i	0.999750	+	0.0223387i	$0.00711123\pi$
$883$	15.4288	+	26.7235i	0.519221	+	0.899317i	−0.480529	+	0.876979i	$0.659555\pi$
$884$		0			0
$885$	26.3920	−	9.03066i	0.887157	−	0.303562i
$886$		0			0
$887$	31.9246	+	26.7879i	1.07192	+	0.899450i	0.995225	−	0.0976041i	$-0.0311179\pi$
$887$	31.9246	+	26.7879i	1.07192	+	0.899450i	0.0766978	+	0.997054i	$0.475562\pi$
$888$		0			0
$889$	−27.8202	−	28.1227i	−0.933060	−	0.943206i
$890$		0			0
$891$	−13.9104	−	49.9609i	−0.466014	−	1.67375i
$892$		0			0
$893$	−8.71492	+	23.9441i	−0.291634	+	0.801257i
$894$		0			0
$895$	−14.6139	−	2.57682i	−0.488488	−	0.0861335i
$896$		0			0
$897$	−0.813914	+	4.14458i	−0.0271758	+	0.138384i
$898$		0			0
$899$	−2.05979	+	3.56767i	−0.0686980	+	0.118988i
$900$		0			0
$901$	1.82093	−	1.05131i	0.0606640	−	0.0350244i
$902$		0			0
$903$	−18.2497	−	9.06726i	−0.607313	−	0.301740i
$904$		0			0
$905$	−3.57901	−	9.83325i	−0.118970	−	0.326868i
$906$		0			0
$907$	−4.59665	−	26.0689i	−0.152629	−	0.865604i	−0.960921	−	0.276822i	$-0.910719\pi$
$907$	−4.59665	−	26.0689i	−0.152629	−	0.865604i	0.808292	−	0.588782i	$-0.200392\pi$
$908$		0			0
$909$	4.81920	+	0.186882i	0.159843	+	0.00619847i
$910$		0			0
$911$	−16.8822	+	2.97679i	−0.559333	+	0.0986255i	−0.446166	−	0.894950i	$-0.647211\pi$
$911$	−16.8822	+	2.97679i	−0.559333	+	0.0986255i	−0.113167	+	0.993576i	$0.536100\pi$
$912$		0			0
$913$	2.68654	−	3.20170i	0.0889116	−	0.105961i
$914$		0			0
$915$	9.46033	+	11.7287i	0.312749	+	0.387738i
$916$		0			0
$917$	−29.3919	−	13.8996i	−0.970605	−	0.459007i
$918$		0			0
$919$	11.8096	−	20.4549i	0.389564	−	0.674745i	−0.602827	−	0.797872i	$-0.705959\pi$
$919$	11.8096	−	20.4549i	0.389564	−	0.674745i	0.992391	+	0.123127i	$0.0392924\pi$
$920$		0			0
$921$	8.96832	+	11.1187i	0.295516	+	0.366373i
$922$		0			0
$923$	−11.2233	+	4.08496i	−0.369421	+	0.134458i
$924$		0			0
$925$	−1.39223	−	7.89573i	−0.0457763	−	0.259610i
$926$		0			0
$927$	−5.74407	−	7.41075i	−0.188660	−	0.243401i
$928$		0			0
$929$	5.66871	−	4.75661i	0.185984	−	0.156059i	−0.545042	−	0.838409i	$-0.683486\pi$
$929$	5.66871	−	4.75661i	0.185984	−	0.156059i	0.731026	+	0.682350i	$0.239042\pi$
$930$		0			0
$931$	28.1369	+	49.9751i	0.922151	+	1.63787i
$932$		0			0
$933$	15.7513	−	26.1006i	0.515675	−	0.854494i
$934$		0			0
$935$		−	2.51624i		−	0.0822899i
$936$		0			0
$937$	−36.6771	+	21.1756i	−1.19819	+	0.691775i	−0.960151	−	0.279480i	$-0.909838\pi$
$937$	−36.6771	+	21.1756i	−1.19819	+	0.691775i	−0.238039	+	0.971256i	$0.576504\pi$
$938$		0			0
$939$	11.2849	+	32.9801i	0.368270	+	1.07626i
$940$		0			0
$941$	−12.6740	+	4.61296i	−0.413161	+	0.150378i	−0.540233	−	0.841515i	$-0.681664\pi$
$941$	−12.6740	+	4.61296i	−0.413161	+	0.150378i	0.127073	+	0.991893i	$0.459442\pi$
$942$		0			0
$943$	5.17886	−	0.913173i	0.168647	−	0.0297370i
$944$		0			0
$945$	14.9849	−	9.13216i	0.487460	−	0.297069i
$946$		0			0
$947$	−44.9493	+	7.92578i	−1.46066	+	0.257553i	−0.846820	−	0.531879i	$-0.821486\pi$
$947$	−44.9493	+	7.92578i	−1.46066	+	0.257553i	−0.613837	+	0.789433i	$0.710375\pi$
$948$		0			0
$949$	53.3935	−	19.4337i	1.73323	−	0.630843i
$950$		0			0
$951$	−17.9622	+	20.5830i	−0.582466	+	0.667449i
$952$		0			0
$953$	−39.3815	+	22.7369i	−1.27569	+	0.736522i	−0.976054	−	0.217530i	$-0.930200\pi$
$953$	−39.3815	+	22.7369i	−1.27569	+	0.736522i	−0.299640	+	0.954052i	$0.596867\pi$
$954$		0			0
$955$		−	23.7472i		−	0.768440i
$956$		0			0
$957$	4.66878	+	8.46110i	0.150920	+	0.273509i
$958$		0			0
$959$	−0.314513	+	3.38403i	−0.0101561	+	0.109276i
$960$		0			0
$961$	9.88004	−	8.29034i	0.318711	−	0.267430i
$962$		0			0
$963$	−16.0254	−	49.9755i	−0.516412	−	1.61044i
$964$		0			0
$965$	−3.81429	−	21.6319i	−0.122786	−	0.696356i
$966$		0			0
$967$	20.8633	−	7.59361i	0.670918	−	0.244194i	0.0159747	−	0.999872i	$-0.494915\pi$
$967$	20.8633	−	7.59361i	0.670918	−	0.244194i	0.654943	+	0.755678i	$0.272693\pi$
$968$		0			0
$969$	1.74846	−	4.52881i	0.0561687	−	0.145486i
$970$		0			0
$971$	−6.22659	+	10.7848i	−0.199821	+	0.346100i	−0.948470	−	0.316866i	$-0.897369\pi$
$971$	−6.22659	+	10.7848i	−0.199821	+	0.346100i	0.748649	+	0.662966i	$0.230703\pi$
$972$		0			0
$973$	−2.26123	+	0.185517i	−0.0724919	+	0.00594739i
$974$		0			0
$975$	−27.1687	+	4.24946i	−0.870093	+	0.136092i
$976$		0			0
$977$	7.16163	−	8.53489i	0.229121	−	0.273055i	−0.639220	−	0.769024i	$-0.720743\pi$
$977$	7.16163	−	8.53489i	0.229121	−	0.273055i	0.868340	+	0.495969i	$0.165187\pi$
$978$		0			0
$979$	58.1177	−	10.2477i	1.85745	−	0.327519i
$980$		0			0
$981$	10.4935	−	48.4496i	0.335032	−	1.54688i
$982$		0			0
$983$	3.53848	+	20.0677i	0.112860	+	0.640060i	0.987788	+	0.155807i	$0.0497977\pi$
$983$	3.53848	+	20.0677i	0.112860	+	0.640060i	−0.874928	+	0.484254i	$0.839091\pi$
$984$		0			0
$985$	4.35621	+	11.9686i	0.138800	+	0.381351i
$986$		0			0
$987$	−12.7634	−	6.34142i	−0.406264	−	0.201850i
$988$		0			0
$989$	1.99380	−	1.15112i	0.0633991	−	0.0366035i
$990$		0			0
$991$	−3.54592	+	6.14172i	−0.112640	+	0.195098i	−0.916834	−	0.399269i	$-0.869264\pi$
$991$	−3.54592	+	6.14172i	−0.112640	+	0.195098i	0.804194	+	0.594367i	$0.202597\pi$
$992$		0			0
$993$	6.14529	+	5.36284i	0.195015	+	0.170185i
$994$		0			0
$995$	21.5388	+	3.79787i	0.682826	+	0.120401i
$996$		0			0
$997$	18.2664	−	50.1865i	0.578503	−	1.58942i	−0.212203	−	0.977226i	$-0.568064\pi$
$997$	18.2664	−	50.1865i	0.578503	−	1.58942i	0.790705	−	0.612197i	$-0.209714\pi$
$998$		0			0
$999$	−6.79136	+	10.3266i	−0.214869	+	0.326720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.5.5	yes	144
7.3	odd	6		756.2.ca.a.437.12	yes	144
27.11	odd	18		756.2.ca.a.173.12	✓	144
189.38	even	18	inner	756.2.ck.a.605.5	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.12	✓	144	27.11	odd	18
756.2.ca.a.437.12	yes	144	7.3	odd	6
756.2.ck.a.5.5	yes	144	1.1	even	1	trivial
756.2.ck.a.605.5	yes	144	189.38	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.61581 - 0.623825i) q^{3} +(-0.221654 + 1.25706i) q^{5} +(2.55927 - 0.670941i) q^{7} +(2.22168 + 2.01597i) q^{9} +O(q^{10})\)	\(q+(-1.61581 - 0.623825i) q^{3} +(-0.221654 + 1.25706i) q^{5} +(2.55927 - 0.670941i) q^{7} +(2.22168 + 2.01597i) q^{9} +(-5.67482 + 1.00062i) q^{11} +(3.02767 - 3.60823i) q^{13} +(1.14234 - 1.89290i) q^{15} +0.342095 q^{17} +8.19307i q^{19} +(-4.55384 - 0.512420i) q^{21} +(0.332785 - 0.396598i) q^{23} +(3.16739 + 1.15283i) q^{25} +(-2.33221 - 4.64336i) q^{27} +(0.622374 + 0.741717i) q^{29} +(1.45520 + 3.99812i) q^{31} +(9.79364 + 1.92328i) q^{33} +(0.276144 + 3.36587i) q^{35} +(-1.18931 - 2.05995i) q^{37} +(-7.14304 + 3.94148i) q^{39} +(7.78109 + 6.52911i) q^{41} +(4.17869 + 1.52092i) q^{43} +(-3.02664 + 2.34595i) q^{45} +(2.92248 + 1.06369i) q^{47} +(6.09968 - 3.43423i) q^{49} +(-0.552760 - 0.213407i) q^{51} +(5.32288 - 3.07317i) q^{53} -7.35539i q^{55} +(5.11105 - 13.2385i) q^{57} +(9.66502 + 8.10991i) q^{59} +(-2.33107 + 6.40456i) q^{61} +(7.03847 + 3.66877i) q^{63} +(3.86468 + 4.60575i) q^{65} +(-0.683823 + 3.87815i) q^{67} +(-0.785125 + 0.433227i) q^{69} +(-2.19597 - 1.26784i) q^{71} +(10.4470 + 6.03160i) q^{73} +(-4.39873 - 3.83866i) q^{75} +(-13.8520 + 6.36833i) q^{77} +(-0.898458 - 5.09541i) q^{79} +(0.871763 + 8.95768i) q^{81} +(-0.555623 + 0.466223i) q^{83} +(-0.0758267 + 0.430035i) q^{85} +(-0.542937 - 1.58673i) q^{87} -10.2413 q^{89} +(5.32769 - 11.2658i) q^{91} +(0.142806 - 7.36798i) q^{93} +(-10.2992 - 1.81603i) q^{95} +(-3.14019 + 8.62759i) q^{97} +(-14.6249 - 9.21717i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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