LMFDB - Embedded newform 756.2.ca.a.173.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(173,756)]

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, 13, 15]))

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

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

chi := DirichletCharacter("756.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ca (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			173.12
Character	$\chi$	$=$	756.173
Dual form			756.2.ca.a.437.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.267657 + 1.71125i) q^{3} +(0.977821 - 0.820489i) q^{5} +(-2.63440 - 0.244842i) q^{7} +(-2.85672 - 0.916052i) q^{9} +O(q^{10})$	\(q+(-0.267657 + 1.71125i) q^{3} +(0.977821 - 0.820489i) q^{5} +(-2.63440 - 0.244842i) q^{7} +(-2.85672 - 0.916052i) q^{9} +(3.70397 - 4.41422i) q^{11} +(-3.02767 - 3.60823i) q^{13} +(1.14234 + 1.89290i) q^{15} +(0.171047 - 0.296263i) q^{17} +(7.09541 - 4.09654i) q^{19} +(1.12410 - 4.44257i) q^{21} +(0.177071 - 0.486499i) q^{23} +(-0.585309 + 3.31946i) q^{25} +(2.33221 - 4.64336i) q^{27} +(0.622374 - 0.741717i) q^{29} +(-2.73487 - 3.25929i) q^{31} +(6.56243 + 7.51990i) q^{33} +(-2.77686 + 1.92208i) q^{35} +2.37862 q^{37} +(6.98495 - 4.21531i) q^{39} +(-7.78109 + 6.52911i) q^{41} +(4.17869 - 1.52092i) q^{43} +(-3.54497 + 1.44817i) q^{45} +(2.38242 + 1.99909i) q^{47} +(6.88011 + 1.29002i) q^{49} +(0.461196 + 0.372001i) q^{51} +(-5.32288 + 3.07317i) q^{53} -7.35539i q^{55} +(5.11105 + 13.2385i) q^{57} +(-2.19088 - 12.4251i) q^{59} +(4.38098 - 5.22105i) q^{61} +(7.30145 + 3.11269i) q^{63} +(-5.92103 - 1.04404i) q^{65} +(3.70049 + 1.34687i) q^{67} +(0.785125 + 0.433227i) q^{69} +(-2.19597 + 1.26784i) q^{71} -12.0632i q^{73} +(-5.52374 - 1.89008i) q^{75} +(-10.8385 + 10.7219i) q^{77} +(4.86198 - 1.76962i) q^{79} +(7.32170 + 5.23381i) q^{81} +(0.555623 + 0.466223i) q^{83} +(-0.0758267 - 0.430035i) q^{85} +(1.10268 + 1.26356i) q^{87} +(-5.12067 - 8.86926i) q^{89} +(7.09264 + 10.2468i) q^{91} +(6.30946 - 3.80767i) q^{93} +(3.57688 - 9.82739i) q^{95} +(3.14019 + 8.62759i) q^{97} +(-14.6249 + 9.21717i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 12 q^{15} - 3 q^{21} - 15 q^{23} - 6 q^{29} - 42 q^{39} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 18 q^{51} + 45 q^{53} + 3 q^{57} + 54 q^{61} + 39 q^{63} - 3 q^{65} + 36 q^{69} + 36 q^{71} + 93 q^{77} - 18 q^{79} - 36 q^{81} + 36 q^{85} - 18 q^{91} + 60 q^{93} + 6 q^{95}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 12 * q^15 - 3 * q^21 - 15 * q^23 - 6 * q^29 - 42 * q^39 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 18 * q^51 + 45 * q^53 + 3 * q^57 + 54 * q^61 + 39 * q^63 - 3 * q^65 + 36 * q^69 + 36 * q^71 + 93 * q^77 - 18 * q^79 - 36 * q^81 + 36 * q^85 - 18 * q^91 + 60 * q^93 + 6 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−0.267657	+	1.71125i	−0.154532	+	0.987988i
$3$	−0.267657	+	1.71125i	−0.154532	+	0.987988i
$4$		0			0
$5$	0.977821	−	0.820489i	0.437295	−	0.366934i	−0.397401	−	0.917645i	$-0.630088\pi$
$5$	0.977821	−	0.820489i	0.437295	−	0.366934i	0.834696	+	0.550711i	$0.185643\pi$
$6$		0			0
$7$	−2.63440	−	0.244842i	−0.995709	−	0.0925414i
$7$	−2.63440	−	0.244842i	−0.995709	−	0.0925414i
$8$		0			0
$9$	−2.85672	−	0.916052i	−0.952240	−	0.305351i
$10$		0			0
$11$	3.70397	−	4.41422i	1.11679	−	1.33094i	0.178955	−	0.983857i	$-0.442728\pi$
$11$	3.70397	−	4.41422i	1.11679	−	1.33094i	0.937835	−	0.347081i	$-0.112827\pi$
$12$		0			0
$13$	−3.02767	−	3.60823i	−0.839724	−	1.00074i	−0.999907	−	0.0136566i	$-0.995653\pi$
$13$	−3.02767	−	3.60823i	−0.839724	−	1.00074i	0.160183	−	0.987087i	$-0.448792\pi$
$14$		0			0
$15$	1.14234	+	1.89290i	0.294950	+	0.488745i
$16$		0			0
$17$	0.171047	−	0.296263i	0.0414851	−	0.0718543i	−0.844537	−	0.535497i	$-0.820124\pi$
$17$	0.171047	−	0.296263i	0.0414851	−	0.0718543i	0.886022	+	0.463642i	$0.153458\pi$
$18$		0			0
$19$	7.09541	−	4.09654i	1.62780	−	0.939810i	0.643051	−	0.765823i	$-0.277668\pi$
$19$	7.09541	−	4.09654i	1.62780	−	0.939810i	0.984748	−	0.173987i	$-0.0556650\pi$
$20$		0			0
$21$	1.12410	−	4.44257i	0.245298	−	0.969448i
$22$		0			0
$23$	0.177071	−	0.486499i	0.0369219	−	0.101442i	−0.919862	−	0.392243i	$-0.871699\pi$
$23$	0.177071	−	0.486499i	0.0369219	−	0.101442i	0.956784	+	0.290801i	$0.0939216\pi$
$24$		0			0
$25$	−0.585309	+	3.31946i	−0.117062	+	0.663891i
$26$		0			0
$27$	2.33221	−	4.64336i	0.448834	−	0.893615i
$28$		0			0
$29$	0.622374	−	0.741717i	0.115572	−	0.137733i	−0.705157	−	0.709052i	$-0.749123\pi$
$29$	0.622374	−	0.741717i	0.115572	−	0.137733i	0.820729	+	0.571318i	$0.193568\pi$
$30$		0			0
$31$	−2.73487	−	3.25929i	−0.491198	−	0.585386i	0.462324	−	0.886711i	$-0.347016\pi$
$31$	−2.73487	−	3.25929i	−0.491198	−	0.585386i	−0.953522	+	0.301325i	$0.902571\pi$
$32$		0			0
$33$	6.56243	+	7.51990i	1.14237	+	1.30905i
$34$		0			0
$35$	−2.77686	+	1.92208i	−0.469375	+	0.324892i
$36$		0			0
$37$	2.37862			0.391043			0.195522	−	0.980699i	$-0.437360\pi$
$37$	2.37862			0.391043			0.195522	+	0.980699i	$0.437360\pi$
$38$		0			0
$39$	6.98495	−	4.21531i	1.11849	−	0.674990i
$40$		0			0
$41$	−7.78109	+	6.52911i	−1.21520	+	1.01968i	−0.216140	+	0.976362i	$0.569347\pi$
$41$	−7.78109	+	6.52911i	−1.21520	+	1.01968i	−0.999062	+	0.0433131i	$0.986209\pi$
$42$		0			0
$43$	4.17869	−	1.52092i	0.637245	−	0.231938i	−0.00313689	−	0.999995i	$-0.500999\pi$
$43$	4.17869	−	1.52092i	0.637245	−	0.231938i	0.640381	+	0.768057i	$0.278776\pi$
$44$		0			0
$45$	−3.54497	+	1.44817i	−0.528453	+	0.215881i
$46$		0			0
$47$	2.38242	+	1.99909i	0.347512	+	0.291597i	0.799790	−	0.600280i	$-0.204944\pi$
$47$	2.38242	+	1.99909i	0.347512	+	0.291597i	−0.452278	+	0.891877i	$0.649389\pi$
$48$		0			0
$49$	6.88011	+	1.29002i	0.982872	+	0.184289i
$50$		0			0
$51$	0.461196	+	0.372001i	0.0645804	+	0.0520905i
$52$		0			0
$53$	−5.32288	+	3.07317i	−0.731154	+	0.422132i	−0.818844	−	0.574016i	$-0.805385\pi$
$53$	−5.32288	+	3.07317i	−0.731154	+	0.422132i	0.0876903	+	0.996148i	$0.472051\pi$
$54$		0			0
$55$		−	7.35539i		−	0.991801i
$56$		0			0
$57$	5.11105	+	13.2385i	0.676975	+	1.75348i
$58$		0			0
$59$	−2.19088	−	12.4251i	−0.285229	−	1.61761i	−0.704468	−	0.709736i	$-0.748814\pi$
$59$	−2.19088	−	12.4251i	−0.285229	−	1.61761i	0.419240	−	0.907876i	$-0.362297\pi$
$60$		0			0
$61$	4.38098	−	5.22105i	0.560927	−	0.668486i	−0.408816	−	0.912617i	$-0.634058\pi$
$61$	4.38098	−	5.22105i	0.560927	−	0.668486i	0.969742	+	0.244131i	$0.0785025\pi$
$62$		0			0
$63$	7.30145	+	3.11269i	0.919896	+	0.392162i
$64$		0			0
$65$	−5.92103	−	1.04404i	−0.734414	−	0.129497i
$66$		0			0
$67$	3.70049	+	1.34687i	0.452087	+	0.164546i	0.558021	−	0.829827i	$-0.311561\pi$
$67$	3.70049	+	1.34687i	0.452087	+	0.164546i	−0.105934	+	0.994373i	$0.533783\pi$
$68$		0			0
$69$	0.785125	+	0.433227i	0.0945180	+	0.0521544i
$70$		0			0
$71$	−2.19597	+	1.26784i	−0.260614	+	0.150465i	−0.624614	−	0.780933i	$-0.714744\pi$
$71$	−2.19597	+	1.26784i	−0.260614	+	0.150465i	0.364001	+	0.931399i	$0.381411\pi$
$72$		0			0
$73$		−	12.0632i		−	1.41189i	−0.708267	−	0.705945i	$-0.750523\pi$
$73$		−	12.0632i		−	1.41189i	0.708267	−	0.705945i	$-0.249477\pi$
$74$		0			0
$75$	−5.52374	−	1.89008i	−0.637826	−	0.218248i
$76$		0			0
$77$	−10.8385	+	10.7219i	−1.23516	+	1.22188i
$78$		0			0
$79$	4.86198	−	1.76962i	0.547016	−	0.199097i	−0.0537044	−	0.998557i	$-0.517103\pi$
$79$	4.86198	−	1.76962i	0.547016	−	0.199097i	0.600720	+	0.799459i	$0.294881\pi$
$80$		0			0
$81$	7.32170	+	5.23381i	0.813522	+	0.581534i
$82$		0			0
$83$	0.555623	+	0.466223i	0.0609875	+	0.0511746i	0.672772	−	0.739850i	$-0.265104\pi$
$83$	0.555623	+	0.466223i	0.0609875	+	0.0511746i	−0.611784	+	0.791025i	$0.709548\pi$
$84$		0			0
$85$	−0.0758267	−	0.430035i	−0.00822456	−	0.0466438i
$86$		0			0
$87$	1.10268	+	1.26356i	0.118219	+	0.135468i
$88$		0			0
$89$	−5.12067	−	8.86926i	−0.542790	−	0.940140i	−0.998742	−	0.0501357i	$-0.984035\pi$
$89$	−5.12067	−	8.86926i	−0.542790	−	0.940140i	0.455952	−	0.890004i	$-0.349299\pi$
$90$		0			0
$91$	7.09264	+	10.2468i	0.743510	+	1.07416i
$92$		0			0
$93$	6.30946	−	3.80767i	0.654260	−	0.394836i
$94$		0			0
$95$	3.57688	−	9.82739i	0.366980	−	1.00827i
$96$		0			0
$97$	3.14019	+	8.62759i	0.318838	+	0.875999i	0.990790	+	0.135405i	$0.0432336\pi$
$97$	3.14019	+	8.62759i	0.318838	+	0.875999i	−0.671953	+	0.740594i	$0.734544\pi$
$98$		0			0
$99$	−14.6249	+	9.21717i	−1.46985	+	0.926360i
$100$		0			0
$101$	1.51066	−	0.549834i	0.150316	−	0.0547105i	−0.265766	−	0.964037i	$-0.585625\pi$
$101$	1.51066	−	0.549834i	0.150316	−	0.0547105i	0.416082	+	0.909327i	$0.363403\pi$
$102$		0			0
$103$	−2.00897	−	2.39420i	−0.197950	−	0.235908i	0.657934	−	0.753076i	$-0.271431\pi$
$103$	−2.00897	−	2.39420i	−0.197950	−	0.235908i	−0.855884	+	0.517168i	$0.826986\pi$
$104$		0			0
$105$	−2.54591	−	5.26635i	−0.248456	−	0.513943i
$106$		0			0
$107$	15.1503	+	8.74701i	1.46463	+	0.845605i	0.999220	−	0.0394897i	$-0.0125732\pi$
$107$	15.1503	+	8.74701i	1.46463	+	0.845605i	0.465411	+	0.885095i	$0.345907\pi$
$108$		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	−0.964839	−	0.262843i	$-0.915340\pi$
$113$	−0.603550	+	1.65824i	−0.0567772	+	0.155994i	0.908061	+	0.418837i	$0.137562\pi$
$114$		0			0
$115$	−0.226023	−	0.620994i	−0.0210768	−	0.0579080i
$116$		0			0
$117$	5.34387	+	13.0812i	0.494041	+	1.20936i
$118$		0			0
$119$	−0.523144	+	0.738595i	−0.0479566	+	0.0677069i
$120$		0			0
$121$	−3.85582	−	21.8674i	−0.350529	−	1.98795i
$122$		0			0
$123$	−9.09025	−	15.0629i	−0.819640	−	1.35818i
$124$		0			0
$125$	5.34239	+	9.25329i	0.477838	+	0.827639i
$126$		0			0
$127$	−7.47580	+	12.9485i	−0.663370	+	1.14899i	0.316355	+	0.948641i	$0.397541\pi$
$127$	−7.47580	+	12.9485i	−0.663370	+	1.14899i	−0.979725	+	0.200349i	$0.935792\pi$
$128$		0			0
$129$	1.48421	+	7.55785i	0.130678	+	0.665432i
$130$		0			0
$131$	−11.5476	−	4.20298i	−1.00892	−	0.367216i	−0.215900	−	0.976415i	$-0.569269\pi$
$131$	−11.5476	−	4.20298i	−1.00892	−	0.367216i	−0.793017	+	0.609200i	$0.791491\pi$
$132$		0			0
$133$	−19.6951	+	9.05466i	−1.70779	+	0.785138i
$134$		0			0
$135$	−1.52934	−	6.45393i	−0.131625	−	0.555466i
$136$		0			0
$137$	1.26504	+	0.223061i	0.108080	+	0.0190574i	0.227426	−	0.973795i	$-0.426969\pi$
$137$	1.26504	+	0.223061i	0.108080	+	0.0190574i	−0.119347	+	0.992853i	$0.538080\pi$
$138$		0			0
$139$	0.844510	−	0.148910i	0.0716304	−	0.0126304i	−0.137718	−	0.990471i	$-0.543977\pi$
$139$	0.844510	−	0.148910i	0.0716304	−	0.0126304i	0.209349	+	0.977841i	$0.432866\pi$
$140$		0			0
$141$	−4.05861	+	3.54184i	−0.341796	+	0.298277i
$142$		0			0
$143$	−27.1419			−2.26972
$144$		0			0
$145$		−	1.23592i		−	0.102637i
$146$		0			0
$147$	−4.04905	+	11.4283i	−0.333960	+	0.942587i
$148$		0			0
$149$	−18.5366	+	3.26851i	−1.51858	+	0.267766i	−0.869874	−	0.493274i	$-0.835800\pi$
$149$	−18.5366	+	3.26851i	−1.51858	+	0.267766i	−0.648705	+	0.761040i	$0.724689\pi$
$150$		0			0
$151$	−0.788995	−	0.662045i	−0.0642075	−	0.0538765i	0.610119	−	0.792310i	$-0.291122\pi$
$151$	−0.788995	−	0.662045i	−0.0642075	−	0.0538765i	−0.674327	+	0.738433i	$0.735566\pi$
$152$		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
$157$	−6.54443	+	1.15396i	−0.522303	+	0.0920960i	−0.428583	−	0.903503i	$-0.640987\pi$
$157$	−6.54443	+	1.15396i	−0.522303	+	0.0920960i	−0.0937199	+	0.995599i	$0.529876\pi$
$158$		0			0
$159$	−3.83424	−	9.93131i	−0.304075	−	0.787604i
$160$		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
$165$	12.5869	+	1.96872i	0.979887	+	0.153265i
$166$		0			0
$167$	−19.3814	−	7.05424i	−1.49977	−	0.545873i	−0.543773	−	0.839233i	$-0.683005\pi$
$167$	−19.3814	−	7.05424i	−1.49977	−	0.545873i	−0.956002	+	0.293359i	$0.905227\pi$
$168$		0			0
$169$	−1.59515	+	9.04656i	−0.122704	+	0.695889i
$170$		0			0
$171$	−24.0222	+	5.20289i	−1.83703	+	0.397875i
$172$		0			0
$173$	−3.66651	+	20.7938i	−0.278759	+	1.58092i	0.448002	+	0.894033i	$0.352136\pi$
$173$	−3.66651	+	20.7938i	−0.278759	+	1.58092i	−0.726761	+	0.686890i	$0.758975\pi$
$174$		0			0
$175$	2.35468	−	8.60146i	0.177997	−	0.650209i
$176$		0			0
$177$	21.8488	−	0.423473i	1.64226	−	0.0318302i
$178$		0			0
$179$	10.0679	+	5.81270i	0.752510	+	0.434462i	0.826600	−	0.562790i	$-0.190272\pi$
$179$	10.0679	+	5.81270i	0.752510	+	0.434462i	−0.0740901	+	0.997252i	$0.523605\pi$
$180$		0			0
$181$	7.09964	+	4.09898i	0.527712	+	0.304675i	0.740084	−	0.672514i	$-0.234786\pi$
$181$	7.09964	+	4.09898i	0.527712	+	0.304675i	−0.212372	+	0.977189i	$0.568119\pi$
$182$		0			0
$183$	7.76189	+	8.89437i	0.573776	+	0.657491i
$184$		0			0
$185$	2.32587	−	1.95164i	0.171001	−	0.143487i
$186$		0			0
$187$	−0.674215	−	1.85239i	−0.0493035	−	0.135460i
$188$		0			0
$189$	−7.28086	+	11.6614i	−0.529604	+	0.848245i
$190$		0			0
$191$	6.36294	+	17.4820i	0.460406	+	1.26496i	0.925181	+	0.379527i	$0.123913\pi$
$191$	6.36294	+	17.4820i	0.460406	+	1.26496i	−0.464775	+	0.885429i	$0.653865\pi$
$192$		0			0
$193$	13.1823	−	11.0613i	0.948884	−	0.796208i	−0.0302252	−	0.999543i	$-0.509622\pi$
$193$	13.1823	−	11.0613i	0.948884	−	0.796208i	0.979109	+	0.203335i	$0.0651780\pi$
$194$		0			0
$195$	3.37141	−	9.85290i	0.241432	−	0.705581i
$196$		0			0
$197$	8.64136	+	4.98909i	0.615671	+	0.355458i	0.775182	−	0.631738i	$-0.217658\pi$
$197$	8.64136	+	4.98909i	0.615671	+	0.355458i	−0.159510	+	0.987196i	$0.550992\pi$
$198$		0			0
$199$	14.8387	+	8.56712i	1.05189	+	0.607307i	0.923177	−	0.384375i	$-0.125583\pi$
$199$	14.8387	+	8.56712i	1.05189	+	0.607307i	0.128710	+	0.991682i	$0.458916\pi$
$200$		0			0
$201$	−3.29528	+	5.97195i	−0.232431	+	0.421229i
$202$		0			0
$203$	−1.82118	+	1.80159i	−0.127822	+	0.126447i
$204$		0			0
$205$	−2.25145	+	12.7686i	−0.157248	+	0.891798i
$206$		0			0
$207$	−0.951502	+	1.22759i	−0.0661339	+	0.0853231i
$208$		0			0
$209$	8.19818	−	46.4942i	0.567080	−	3.21607i
$210$		0			0
$211$	18.9938	+	6.91319i	1.30759	+	0.475923i	0.899461	−	0.437001i	$-0.143960\pi$
$211$	18.9938	+	6.91319i	1.30759	+	0.475923i	0.408128	+	0.912925i	$0.366182\pi$
$212$		0			0
$213$	−1.58182	−	4.09719i	−0.108385	−	0.280735i
$214$		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
$219$	20.6431	+	3.22879i	1.39493	+	0.218182i
$220$		0			0
$221$	−1.58686	+	0.279806i	−0.106744	+	0.0188218i
$222$		0			0
$223$	−6.90013	−	1.21668i	−0.462067	−	0.0814749i	−0.0622313	−	0.998062i	$-0.519822\pi$
$223$	−6.90013	−	1.21668i	−0.462067	−	0.0814749i	−0.399836	+	0.916587i	$0.630933\pi$
$224$		0			0
$225$	4.71286	−	8.94658i	0.314191	−	0.596439i
$226$		0			0
$227$	−10.5335	−	8.83862i	−0.699130	−	0.586640i	0.222396	−	0.974956i	$-0.428612\pi$
$227$	−10.5335	−	8.83862i	−0.699130	−	0.586640i	−0.921526	+	0.388317i	$0.873057\pi$
$228$		0			0
$229$	−20.3247	+	3.58380i	−1.34310	+	0.236824i	−0.798561	−	0.601914i	$-0.794405\pi$
$229$	−20.3247	+	3.58380i	−1.34310	+	0.236824i	−0.544535	+	0.838738i	$0.683294\pi$
$230$		0			0
$231$	−15.4469	−	21.4172i	−1.01633	−	1.40915i
$232$		0			0
$233$			27.8824i			1.82663i	0.407250	+	0.913317i	$0.366488\pi$
$233$			27.8824i			1.82663i	−0.407250	+	0.913317i	$0.633512\pi$
$234$		0			0
$235$	3.96982			0.258962
$236$		0			0
$237$	1.72691	+	8.79369i	0.112175	+	0.571212i
$238$		0			0
$239$	23.7274	−	4.18378i	1.53480	−	0.270626i	0.658569	−	0.752520i	$-0.271162\pi$
$239$	23.7274	−	4.18378i	1.53480	−	0.270626i	0.876229	+	0.481894i	$0.160051\pi$
$240$		0			0
$241$	1.69617	+	0.299080i	0.109260	+	0.0192655i	0.228011	−	0.973659i	$-0.426778\pi$
$241$	1.69617	+	0.299080i	0.109260	+	0.0192655i	−0.118751	+	0.992924i	$0.537889\pi$
$242$		0			0
$243$	−10.9160	+	11.1284i	−0.700264	+	0.713884i
$244$		0			0
$245$	7.78596	−	4.38364i	0.497427	−	0.280061i
$246$		0			0
$247$	−36.2638	−	13.1989i	−2.30741	−	0.839829i
$248$		0			0
$249$	−0.946538	+	0.826019i	−0.0599844	+	0.0523468i
$250$		0			0
$251$	−1.34720	+	2.33342i	−0.0850344	+	0.147284i	−0.905406	−	0.424547i	$-0.860433\pi$
$251$	−1.34720	+	2.33342i	−0.0850344	+	0.147284i	0.820371	+	0.571831i	$0.193767\pi$
$252$		0			0
$253$	−1.49165	−	2.58361i	−0.0937792	−	0.162430i
$254$		0			0
$255$	0.756190	−	0.0146565i	0.0473545	−	0.000917824i
$256$		0			0
$257$	3.30432	+	18.7397i	0.206118	+	1.16895i	0.895671	+	0.444718i	$0.146696\pi$
$257$	3.30432	+	18.7397i	0.206118	+	1.16895i	−0.689553	+	0.724235i	$0.742193\pi$
$258$		0			0
$259$	−6.26624	−	0.582386i	−0.389365	−	0.0361877i
$260$		0			0
$261$	−2.45740	+	1.54875i	−0.152109	+	0.0958652i
$262$		0			0
$263$	−9.85248	−	27.0695i	−0.607530	−	1.66918i	−0.735605	−	0.677411i	$-0.763102\pi$
$263$	−9.85248	−	27.0695i	−0.607530	−	1.66918i	0.128075	−	0.991765i	$-0.459120\pi$
$264$		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	0.999943	−	0.0106885i	$-0.00340232\pi$
$269$	8.04832	+	13.9401i	0.490715	+	0.849943i	−0.509228	+	0.860632i	$0.670069\pi$
$270$		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
$273$	−19.4332	+	9.39461i	−1.17615	+	0.568588i
$274$		0			0
$275$	12.4848	+	14.8789i	0.752864	+	0.897229i
$276$		0			0
$277$	11.5898	−	4.21833i	0.696361	−	0.253455i	0.0305048	−	0.999535i	$-0.490289\pi$
$277$	11.5898	−	4.21833i	0.696361	−	0.253455i	0.665856	+	0.746080i	$0.268066\pi$
$278$		0			0
$279$	4.82708	+	11.8162i	0.288990	+	0.707416i
$280$		0			0
$281$	3.46150	+	9.51038i	0.206496	+	0.567342i	0.999101	−	0.0423930i	$-0.0134982\pi$
$281$	3.46150	+	9.51038i	0.206496	+	0.567342i	−0.792606	+	0.609735i	$0.791276\pi$
$282$		0			0
$283$	3.32761	−	9.14252i	0.197806	−	0.543466i	−0.800643	−	0.599141i	$-0.795509\pi$
$283$	3.32761	−	9.14252i	0.197806	−	0.543466i	0.998449	+	0.0556748i	$0.0177310\pi$
$284$		0			0
$285$	15.8597	+	8.75128i	0.939447	+	0.518381i
$286$		0			0
$287$	22.0971	−	15.2951i	1.30435	−	0.902843i
$288$		0			0
$289$	8.44149	+	14.6211i	0.496558	+	0.860064i
$290$		0			0
$291$	−15.6044	+	3.06440i	−0.914747	+	0.179638i
$292$		0			0
$293$	0.111390	+	0.631726i	0.00650749	+	0.0369058i	0.987889	−	0.155165i	$-0.0495908\pi$
$293$	0.111390	+	0.631726i	0.00650749	+	0.0369058i	−0.981381	+	0.192071i	$0.938480\pi$
$294$		0			0
$295$	−12.3370	−	10.3519i	−0.718286	−	0.602713i
$296$		0			0
$297$	−11.8584	−	27.4938i	−0.688093	−	1.59535i
$298$		0			0
$299$	−2.29152	+	0.834043i	−0.132522	+	0.0482340i
$300$		0			0
$301$	−11.3807	+	2.98359i	−0.655974	+	0.171971i
$302$		0			0
$303$	0.536564	+	2.73227i	0.0308248	+	0.156965i
$304$		0			0
$305$		−	8.69980i		−	0.498149i
$306$		0			0
$307$	7.14240	−	4.12367i	0.407638	−	0.235350i	−0.282136	−	0.959374i	$-0.591043\pi$
$307$	7.14240	−	4.12367i	0.407638	−	0.235350i	0.689774	+	0.724024i	$0.257710\pi$
$308$		0			0
$309$	4.63478	−	2.79702i	0.263664	−	0.159117i
$310$		0			0
$311$	−16.5392	−	6.01976i	−0.937850	−	0.341349i	−0.172533	−	0.985004i	$-0.555195\pi$
$311$	−16.5392	−	6.01976i	−0.937850	−	0.341349i	−0.765316	+	0.643654i	$0.777417\pi$
$312$		0			0
$313$	−19.8192	−	3.49465i	−1.12025	−	0.197529i	−0.417297	−	0.908770i	$-0.637022\pi$
$313$	−19.8192	−	3.49465i	−1.12025	−	0.197529i	−0.702949	+	0.711241i	$0.748134\pi$
$314$		0			0
$315$	9.69344	−	2.94711i	0.546163	−	0.166051i
$316$		0			0
$317$	10.1383	−	12.0823i	0.569422	−	0.678611i	−0.402090	−	0.915600i	$-0.631716\pi$
$317$	10.1383	−	12.0823i	0.569422	−	0.678611i	0.971512	+	0.236989i	$0.0761606\pi$
$318$		0			0
$319$	−0.968846	−	5.49460i	−0.0542450	−	0.307638i
$320$		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
$327$	26.7001	−	10.3083i	1.47652	−	0.570049i
$328$		0			0
$329$	−5.78679	−	5.84972i	−0.319036	−	0.322505i
$330$		0			0
$331$	3.60732	+	3.02690i	0.198276	+	0.166374i	0.736520	−	0.676416i	$-0.236468\pi$
$331$	3.60732	+	3.02690i	0.198276	+	0.166374i	−0.538244	+	0.842789i	$0.680912\pi$
$332$		0			0
$333$	−6.79506	−	2.17894i	−0.372367	−	0.119405i
$334$		0			0
$335$	4.72351	−	1.71922i	0.258073	−	0.0939308i
$336$		0			0
$337$	2.80872	−	2.35680i	0.153001	−	0.128383i	−0.563074	−	0.826407i	$-0.690381\pi$
$337$	2.80872	−	2.35680i	0.153001	−	0.128383i	0.716075	+	0.698024i	$0.245937\pi$
$338$		0			0
$339$	−2.67611	−	1.47666i	−0.145346	−	0.0802011i
$340$		0			0
$341$	−24.5171			−1.32768
$342$		0			0
$343$	−17.8091	−	5.08296i	−0.961600	−	0.274454i
$344$		0			0
$345$	1.12317	−	0.220568i	0.0604694	−	0.0118750i
$346$		0			0
$347$	19.4067	+	23.1280i	1.04181	+	1.24158i	0.969730	+	0.244180i	$0.0785187\pi$
$347$	19.4067	+	23.1280i	1.04181	+	1.24158i	0.0720783	+	0.997399i	$0.477037\pi$
$348$		0			0
$349$	18.5777	−	22.1400i	0.994441	−	1.18513i	0.0117402	−	0.999931i	$-0.496263\pi$
$349$	18.5777	−	22.1400i	0.994441	−	1.18513i	0.982701	−	0.185198i	$-0.0592927\pi$
$350$		0			0
$351$	−23.8155	+	5.64339i	−1.27118	+	0.301222i
$352$		0			0
$353$	3.65450	−	20.7257i	0.194509	−	1.10312i	−0.718606	−	0.695417i	$-0.755220\pi$
$353$	3.65450	−	20.7257i	0.194509	−	1.10312i	0.913116	−	0.407700i	$-0.133669\pi$
$354$		0			0
$355$	−1.10701	+	3.04149i	−0.0587541	+	0.161426i
$356$		0			0
$357$	−1.12389	−	1.09292i	−0.0594827	−	0.0578434i
$358$		0			0
$359$	11.0480	−	6.37857i	0.583091	−	0.336648i	−0.179270	−	0.983800i	$-0.557373\pi$
$359$	11.0480	−	6.37857i	0.583091	−	0.336648i	0.762361	+	0.647152i	$0.224040\pi$
$360$		0			0
$361$	24.0632	−	41.6788i	1.26649	−	2.19362i
$362$		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
$367$	−20.4669	+	24.3915i	−1.06836	+	1.27323i	−0.108098	+	0.994140i	$0.534476\pi$
$367$	−20.4669	+	24.3915i	−1.06836	+	1.27323i	−0.960266	+	0.279087i	$0.909968\pi$
$368$		0			0
$369$	28.2094	−	11.5240i	1.46852	−	0.599913i
$370$		0			0
$371$	14.7750	−	6.79268i	0.767081	−	0.352658i
$372$		0			0
$373$	−4.66185	+	3.91176i	−0.241381	+	0.202543i	−0.755451	−	0.655206i	$-0.772582\pi$
$373$	−4.66185	+	3.91176i	−0.241381	+	0.202543i	0.514069	+	0.857749i	$0.328137\pi$
$374$		0			0
$375$	−17.2646	+	6.66543i	−0.891538	+	0.344201i
$376$		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
$381$	−20.1570	−	16.2587i	−1.03268	−	0.832957i
$382$		0			0
$383$	−4.08949	+	3.43149i	−0.208963	+	0.175341i	−0.741262	−	0.671215i	$-0.765773\pi$
$383$	−4.08949	+	3.43149i	−0.208963	+	0.175341i	0.532299	+	0.846556i	$0.321328\pi$
$384$		0			0
$385$	−1.80091	+	19.3770i	−0.0917827	+	0.987545i
$386$		0			0
$387$	−13.3306	+	0.516941i	−0.677632	+	0.0262776i
$388$		0			0
$389$	−15.8623	+	18.9039i	−0.804250	+	0.958468i	−0.999753	−	0.0222351i	$-0.992922\pi$
$389$	−15.8623	+	18.9039i	−0.804250	+	0.958468i	0.195503	+	0.980703i	$0.437366\pi$
$390$		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
$395$	3.30220	−	5.71957i	0.166152	−	0.287783i
$396$		0			0
$397$	8.32850	−	4.80846i	0.417996	−	0.241330i	−0.276224	−	0.961093i	$-0.589083\pi$
$397$	8.32850	−	4.80846i	0.417996	−	0.241330i	0.694219	+	0.719763i	$0.255750\pi$
$398$		0			0
$399$	−10.2232	−	36.1268i	−0.511800	−	1.80860i
$400$		0			0
$401$	11.1532	−	30.6432i	0.556965	−	1.53025i	−0.267052	−	0.963682i	$-0.586050\pi$
$401$	11.1532	−	30.6432i	0.556965	−	1.53025i	0.824017	−	0.566566i	$-0.191728\pi$
$402$		0			0
$403$	−3.48001	+	19.7361i	−0.173352	+	0.983126i
$404$		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
$409$	0.524590	+	0.625182i	0.0259393	+	0.0309133i	0.778858	−	0.627200i	$-0.215799\pi$
$409$	0.524590	+	0.625182i	0.0259393	+	0.0309133i	−0.752919	+	0.658113i	$0.771355\pi$
$410$		0			0
$411$	−0.720308	+	2.10509i	−0.0355302	+	0.103837i
$412$		0			0
$413$	2.72947	+	33.2691i	0.134308	+	1.63707i
$414$		0			0
$415$	0.925831			0.0454472
$416$		0			0
$417$	0.0287827	+	1.48502i	0.00140949	+	0.0727218i
$418$		0			0
$419$	−0.632382	+	0.530632i	−0.0308939	+	0.0259231i	−0.658104	−	0.752927i	$-0.728641\pi$
$419$	−0.632382	+	0.530632i	−0.0308939	+	0.0259231i	0.627210	+	0.778850i	$0.284197\pi$
$420$		0			0
$421$	32.9353	−	11.9875i	1.60517	−	0.584233i	0.624690	−	0.780873i	$-0.285225\pi$
$421$	32.9353	−	11.9875i	1.60517	−	0.584233i	0.980476	+	0.196640i	$0.0630030\pi$
$422$		0			0
$423$	−4.97465	−	7.89327i	−0.241876	−	0.383784i
$424$		0			0
$425$	0.883315	+	0.741190i	0.0428471	+	0.0359530i
$426$		0			0
$427$	−12.8196	+	12.6817i	−0.620382	+	0.613709i
$428$		0			0
$429$	7.26472	−	46.4465i	0.350744	−	2.24246i
$430$		0			0
$431$	1.84508	−	1.06526i	0.0888745	−	0.0513117i	−0.454904	−	0.890540i	$-0.650326\pi$
$431$	1.84508	−	1.06526i	0.0888745	−	0.0513117i	0.543779	+	0.839229i	$0.316993\pi$
$432$		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
$437$	−0.736569	−	4.17729i	−0.0352349	−	0.199827i
$438$		0			0
$439$	18.9518	−	22.5859i	0.904521	−	1.07797i	−0.0920930	−	0.995750i	$-0.529356\pi$
$439$	18.9518	−	22.5859i	0.904521	−	1.07797i	0.996615	−	0.0822163i	$-0.0261998\pi$
$440$		0			0
$441$	−18.4728	−	9.98776i	−0.879657	−	0.475608i
$442$		0			0
$443$	8.10940	+	1.42991i	0.385289	+	0.0679369i	0.362938	−	0.931813i	$-0.381774\pi$
$443$	8.10940	+	1.42991i	0.385289	+	0.0679369i	0.0223512	+	0.999750i	$0.492885\pi$
$444$		0			0
$445$	−12.2842	−	4.47110i	−0.582329	−	0.211950i
$446$		0			0
$447$	−0.631766	−	32.5955i	−0.0298815	−	1.54172i
$448$		0			0
$449$	−31.8671	+	18.3985i	−1.50390	+	0.868278i	−0.503911	+	0.863755i	$0.668106\pi$
$449$	−31.8671	+	18.3985i	−1.50390	+	0.868278i	−0.999990	+	0.00452223i	$0.998561\pi$
$450$		0			0
$451$			58.5311i			2.75612i
$452$		0			0
$453$	1.34410	−	1.17296i	0.0631514	−	0.0551106i
$454$		0			0
$455$	15.3427	+	4.20013i	0.719279	+	0.196905i
$456$		0			0
$457$	−30.7830	+	11.2041i	−1.43997	+	0.524106i	−0.939771	−	0.341805i	$-0.888962\pi$
$457$	−30.7830	+	11.2041i	−1.43997	+	0.524106i	−0.500199	+	0.865911i	$0.666740\pi$
$458$		0			0
$459$	−0.976737	−	1.48518i	−0.0455902	−	0.0693223i
$460$		0			0
$461$	28.7198	+	24.0988i	1.33762	+	1.12239i	0.982231	+	0.187674i	$0.0600948\pi$
$461$	28.7198	+	24.0988i	1.33762	+	1.12239i	0.355385	+	0.934720i	$0.384350\pi$
$462$		0			0
$463$	4.27116	+	24.2230i	0.198498	+	1.12574i	0.907349	+	0.420379i	$0.138103\pi$
$463$	4.27116	+	24.2230i	0.198498	+	1.12574i	−0.708851	+	0.705358i	$0.750786\pi$
$464$		0			0
$465$	3.04537	−	8.90006i	0.141226	−	0.412730i
$466$		0			0
$467$	10.3865	+	17.9899i	0.480628	+	0.832473i	0.999753	−	0.0222258i	$-0.00707528\pi$
$467$	10.3865	+	17.9899i	0.480628	+	0.832473i	−0.519125	+	0.854699i	$0.673742\pi$
$468$		0			0
$469$	−9.41879	−	4.45422i	−0.434919	−	0.205677i
$470$		0			0
$471$	−0.223048	−	11.5080i	−0.0102775	−	0.530260i
$472$		0			0
$473$	8.76408	−	24.0791i	0.402973	−	1.10716i
$474$		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
$479$	36.8175	−	13.4005i	1.68224	−	0.612284i	0.688623	−	0.725120i	$-0.258216\pi$
$479$	36.8175	−	13.4005i	1.68224	−	0.612284i	0.993614	+	0.112836i	$0.0359933\pi$
$480$		0			0
$481$	−7.20168	−	8.58263i	−0.328368	−	0.391334i
$482$		0			0
$483$	−1.96226	−	1.33352i	−0.0892859	−	0.0606774i
$484$		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	−0.498353	−	0.866974i	$-0.666061\pi$
$491$	9.76500	−	26.8291i	0.440688	−	1.21078i	0.939041	−	0.343806i	$-0.111716\pi$
$492$		0			0
$493$	−0.113288	−	0.311255i	−0.00510222	−	0.0140182i
$494$		0			0
$495$	−6.73792	+	21.0123i	−0.302847	+	0.944432i
$496$		0			0
$497$	6.09548	−	2.80234i	0.273419	−	0.125702i
$498$		0			0
$499$	−0.399077	−	2.26328i	−0.0178651	−	0.101318i	0.974571	−	0.224077i	$-0.0719368\pi$
$499$	−0.399077	−	2.26328i	−0.0178651	−	0.101318i	−0.992436	+	0.122759i	$0.960826\pi$
$500$		0			0
$501$	17.2591	−	31.2782i	0.771079	−	1.39740i
$502$		0			0
$503$	7.80677	+	13.5217i	0.348087	+	0.602904i	0.985910	−	0.167279i	$-0.0534981\pi$
$503$	7.80677	+	13.5217i	0.348087	+	0.602904i	−0.637823	+	0.770183i	$0.720165\pi$
$504$		0			0
$505$	1.02602	−	1.77712i	0.0456572	−	0.0790807i
$506$		0			0
$507$	−15.0539	−	5.15107i	−0.668569	−	0.228767i
$508$		0			0
$509$	−40.3584	−	14.6893i	−1.78886	−	0.651090i	−0.999300	−	0.0374109i	$-0.988089\pi$
$509$	−40.3584	−	14.6893i	−1.78886	−	0.651090i	−0.789555	−	0.613679i	$-0.789689\pi$
$510$		0			0
$511$	−2.95357	+	31.7792i	−0.130658	+	1.40583i
$512$		0			0
$513$	−2.47371	−	42.5005i	−0.109217	−	1.87644i
$514$		0			0
$515$	−3.92883	−	0.692760i	−0.173125	−	0.0305266i
$516$		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
$521$	27.5273			1.20599			0.602997	−	0.797743i	$-0.293973\pi$
$521$	27.5273			1.20599			0.602997	+	0.797743i	$0.293973\pi$
$522$		0			0
$523$		−	9.36228i		−	0.409384i	−0.978826	−	0.204692i	$-0.934381\pi$
$523$		−	9.36228i		−	0.409384i	0.978826	−	0.204692i	$-0.0656192\pi$
$524$		0			0
$525$	14.0890	+	6.33167i	0.614892	+	0.276337i
$526$		0			0
$527$	−1.43340	+	0.252747i	−0.0624399	+	0.0110098i
$528$		0			0
$529$	17.4137	+	14.6118i	0.757117	+	0.635297i
$530$		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
$535$	21.9911	−	3.87762i	0.950757	−	0.167644i
$536$		0			0
$537$	−12.6417	+	15.6728i	−0.545530	+	0.676333i
$538$		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
$543$	−8.91463	+	11.0521i	−0.382563	+	0.474291i
$544$		0			0
$545$	−19.8205	−	7.21407i	−0.849017	−	0.309017i
$546$		0			0
$547$	−4.56791	+	25.9059i	−0.195310	+	1.10766i	0.716667	+	0.697415i	$0.245667\pi$
$547$	−4.56791	+	25.9059i	−0.195310	+	1.10766i	−0.911977	+	0.410241i	$0.865444\pi$
$548$		0			0
$549$	−17.2980	+	10.9019i	−0.738260	+	0.465280i
$550$		0			0
$551$	1.37753	−	7.81237i	0.0586848	−	0.332818i
$552$		0			0
$553$	−13.2417	+	3.47146i	−0.563093	+	0.147621i
$554$		0			0
$555$	2.71719	+	4.50250i	0.115338	+	0.191120i
$556$		0			0
$557$	7.26996	+	4.19731i	0.308038	+	0.177846i	0.646048	−	0.763297i	$-0.276420\pi$
$557$	7.26996	+	4.19731i	0.308038	+	0.177846i	−0.338010	+	0.941142i	$0.609754\pi$
$558$		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
$563$	4.05104	−	3.39922i	0.170731	−	0.143260i	−0.553419	−	0.832903i	$-0.686677\pi$
$563$	4.05104	−	3.39922i	0.170731	−	0.143260i	0.724149	+	0.689643i	$0.242233\pi$
$564$		0			0
$565$	0.770404	+	2.11667i	0.0324111	+	0.0890488i
$566$		0			0
$567$	−18.0068	−	15.5806i	−0.756215	−	0.654323i
$568$		0			0
$569$	4.55216	+	12.5070i	0.190837	+	0.524319i	0.997801	−	0.0662809i	$-0.0211134\pi$
$569$	4.55216	+	12.5070i	0.190837	+	0.524319i	−0.806964	+	0.590600i	$0.798891\pi$
$570$		0			0
$571$	−15.5496	+	13.0477i	−0.650732	+	0.546029i	−0.907293	−	0.420499i	$-0.861855\pi$
$571$	−15.5496	+	13.0477i	−0.650732	+	0.546029i	0.256561	+	0.966528i	$0.417411\pi$
$572$		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
$577$	9.02134	+	5.20847i	0.375563	+	0.216832i	0.675886	−	0.737006i	$-0.263761\pi$
$577$	9.02134	+	5.20847i	0.375563	+	0.216832i	−0.300323	+	0.953838i	$0.597094\pi$
$578$		0			0
$579$	15.4002	+	25.5188i	0.640011	+	1.06053i
$580$		0			0
$581$	−1.34958	−	1.36426i	−0.0559901	−	0.0565989i
$582$		0			0
$583$	−6.15016	+	34.8793i	−0.254714	+	1.44455i
$584$		0			0
$585$	15.9583	+	8.40650i	0.659796	+	0.347566i
$586$		0			0
$587$	0.0514158	−	0.291593i	0.00212216	−	0.0120354i	−0.983728	−	0.179663i	$-0.942499\pi$
$587$	0.0514158	−	0.291593i	0.00212216	−	0.0120354i	0.985850	+	0.167627i	$0.0536105\pi$
$588$		0			0
$589$	−32.7569	−	11.9225i	−1.34972	−	0.491259i
$590$		0			0
$591$	−10.8505	+	13.4521i	−0.446329	+	0.553346i
$592$		0			0
$593$	−15.3529	+	26.5920i	−0.630467	+	1.09200i	0.356989	+	0.934109i	$0.383803\pi$
$593$	−15.3529	+	26.5920i	−0.630467	+	1.09200i	−0.987456	+	0.157893i	$0.949530\pi$
$594$		0			0
$595$	0.0944673	+	1.15145i	0.00387278	+	0.0472048i
$596$		0			0
$597$	−18.6321	+	23.0996i	−0.762562	+	0.945403i
$598$		0			0
$599$	−29.4307	+	5.18942i	−1.20250	+	0.212034i	−0.738781	−	0.673946i	$-0.764598\pi$
$599$	−29.4307	+	5.18942i	−1.20250	+	0.212034i	−0.463724	+	0.885980i	$0.653487\pi$
$600$		0			0
$601$	−7.31717	−	1.29022i	−0.298474	−	0.0526290i	0.0224059	−	0.999749i	$-0.492867\pi$
$601$	−7.31717	−	1.29022i	−0.298474	−	0.0526290i	−0.320880	+	0.947120i	$0.603979\pi$
$602$		0			0
$603$	−9.33746	−	7.23747i	−0.380251	−	0.294732i
$604$		0			0
$605$	−21.7123	−	18.2188i	−0.882731	−	0.740699i
$606$		0			0
$607$	35.1166	−	6.19200i	1.42534	−	0.251325i	0.592824	−	0.805332i	$-0.298013\pi$
$607$	35.1166	−	6.19200i	1.42534	−	0.251325i	0.832512	+	0.554006i	$0.186902\pi$
$608$		0			0
$609$	−2.59552	−	3.59870i	−0.105176	−	0.145827i
$610$		0			0
$611$		−	14.6489i		−	0.592632i
$612$		0			0
$613$	−14.9929			−0.605558			−0.302779	−	0.953061i	$-0.597914\pi$
$613$	−14.9929			−0.605558			−0.302779	+	0.953061i	$0.597914\pi$
$614$		0			0
$615$	−21.2476	−	7.27038i	−0.856786	−	0.293170i
$616$		0			0
$617$	−14.8177	+	2.61276i	−0.596537	+	0.105186i	−0.463761	−	0.885960i	$-0.653500\pi$
$617$	−14.8177	+	2.61276i	−0.596537	+	0.105186i	−0.132776	+	0.991146i	$0.542389\pi$
$618$		0			0
$619$	−20.5453	−	3.62268i	−0.825784	−	0.145608i	−0.255243	−	0.966877i	$-0.582155\pi$
$619$	−20.5453	−	3.62268i	−0.825784	−	0.145608i	−0.570541	+	0.821269i	$0.693267\pi$
$620$		0			0
$621$	−1.84602	−	1.95682i	−0.0740784	−	0.0785246i
$622$		0			0
$623$	11.3183	+	24.6189i	0.453459	+	0.986336i
$624$		0			0
$625$	−3.02081	−	1.09949i	−0.120833	−	0.0439795i
$626$		0			0
$627$	77.3687	+	26.4736i	3.08981	+	1.05725i
$628$		0			0
$629$	0.406857	−	0.704698i	0.0162225	−	0.0280981i
$630$		0			0
$631$	6.15238	+	10.6562i	0.244923	+	0.424218i	0.962110	−	0.272662i	$-0.0879041\pi$
$631$	6.15238	+	10.6562i	0.244923	+	0.424218i	−0.717187	+	0.696880i	$0.754571\pi$
$632$		0			0
$633$	−16.9140	+	30.6527i	−0.672270	+	1.21834i
$634$		0			0
$635$	3.31408	+	18.7951i	0.131515	+	0.745861i
$636$		0			0
$637$	−16.1760	−	28.7308i	−0.640915	−	1.13835i
$638$		0			0
$639$	7.43468	−	1.61025i	0.294111	−	0.0637005i
$640$		0			0
$641$	−1.77221	−	4.86910i	−0.0699981	−	0.192318i	0.899761	−	0.436384i	$-0.143741\pi$
$641$	−1.77221	−	4.86910i	−0.0699981	−	0.192318i	−0.969759	+	0.244066i	$0.921519\pi$
$642$		0			0
$643$	15.2007	−	41.7635i	0.599457	−	1.64699i	−0.152903	−	0.988241i	$-0.548862\pi$
$643$	15.2007	−	41.7635i	0.599457	−	1.64699i	0.752360	−	0.658752i	$-0.228915\pi$
$644$		0			0
$645$	7.65243	+	6.17245i	0.301314	+	0.243040i
$646$		0			0
$647$	0.558967	+	0.968159i	0.0219753	+	0.0380623i	0.876804	−	0.480848i	$-0.159671\pi$
$647$	0.558967	+	0.968159i	0.0219753	+	0.0380623i	−0.854829	+	0.518910i	$0.826338\pi$
$648$		0			0
$649$	−62.9622	−	36.3512i	−2.47148	−	1.42691i
$650$		0			0
$651$	−17.5539	+	8.48609i	−0.687991	+	0.332596i
$652$		0			0
$653$	19.8654	+	23.6746i	0.777392	+	0.926460i	0.998813	−	0.0487185i	$-0.0155137\pi$
$653$	19.8654	+	23.6746i	0.777392	+	0.926460i	−0.221420	+	0.975178i	$0.571069\pi$
$654$		0			0
$655$	−14.7400	+	5.36491i	−0.575938	+	0.209624i
$656$		0			0
$657$	−11.0505	+	34.4612i	−0.431122	+	1.34446i
$658$		0			0
$659$	12.4980	+	34.3381i	0.486855	+	1.33762i	0.903514	+	0.428559i	$0.140979\pi$
$659$	12.4980	+	34.3381i	0.486855	+	1.33762i	−0.416659	+	0.909063i	$0.636799\pi$
$660$		0			0
$661$	−8.38100	+	23.0266i	−0.325983	+	0.895631i	0.663134	+	0.748501i	$0.269226\pi$
$661$	−8.38100	+	23.0266i	−0.325983	+	0.895631i	−0.989117	+	0.147130i	$0.952996\pi$
$662$		0			0
$663$	−0.0540835	−	2.79040i	−0.00210043	−	0.108370i
$664$		0			0
$665$	−11.8291	+	25.0135i	−0.458712	+	0.969981i
$666$		0			0
$667$	−0.250640	−	0.434121i	−0.00970482	−	0.0168092i
$668$		0			0
$669$	3.92890	−	11.4822i	0.151900	−	0.443926i
$670$		0			0
$671$	−6.81984	−	38.6772i	−0.263277	−	1.49312i
$672$		0			0
$673$	4.11606	+	3.45379i	0.158663	+	0.133134i	0.718663	−	0.695359i	$-0.244755\pi$
$673$	4.11606	+	3.45379i	0.158663	+	0.133134i	−0.560000	+	0.828492i	$0.689199\pi$
$674$		0			0
$675$	14.0484	+	10.4595i	0.540722	+	0.402585i
$676$		0			0
$677$	−11.9724	+	4.35758i	−0.460135	+	0.167475i	−0.561678	−	0.827356i	$-0.689844\pi$
$677$	−11.9724	+	4.35758i	−0.460135	+	0.167475i	0.101543	+	0.994831i	$0.467622\pi$
$678$		0			0
$679$	−6.16011	−	23.4974i	−0.236403	−	0.901746i
$680$		0			0
$681$	17.9444	−	15.6596i	0.687631	−	0.600078i
$682$		0			0
$683$		−	35.7951i		−	1.36966i	−0.728703	−	0.684830i	$-0.759876\pi$
$683$		−	35.7951i		−	1.36966i	0.728703	−	0.684830i	$-0.240124\pi$
$684$		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
$689$	27.2046	+	9.90167i	1.03641	+	0.377224i
$690$		0			0
$691$	0.975763	+	0.172053i	0.0371198	+	0.00654521i	0.192177	−	0.981360i	$-0.438445\pi$
$691$	0.975763	+	0.172053i	0.0371198	+	0.00654521i	−0.155057	+	0.987905i	$0.549556\pi$
$692$		0			0
$693$	40.7845	−	20.7009i	1.54927	−	0.786362i
$694$		0			0
$695$	0.703601	−	0.838519i	0.0266891	−	0.0318068i
$696$		0			0
$697$	0.603397	+	3.42203i	0.0228553	+	0.129619i
$698$		0			0
$699$	−47.7135	−	7.46290i	−1.80469	−	0.282273i
$700$		0			0
$701$		−	21.7180i		−	0.820277i	−0.912023	−	0.410139i	$-0.865480\pi$
$701$		−	21.7180i		−	0.820277i	0.912023	−	0.410139i	$-0.134520\pi$
$702$		0			0
$703$	16.8773	−	9.74412i	0.636540	−	0.367506i
$704$		0			0
$705$	−1.06255	+	6.79333i	−0.0400179	+	0.255852i
$706$		0			0
$707$	−4.11429	+	1.07861i	−0.154734	+	0.0405653i
$708$		0			0
$709$	−10.3982	−	8.72509i	−0.390511	−	0.327677i	0.426301	−	0.904581i	$-0.359816\pi$
$709$	−10.3982	−	8.72509i	−0.390511	−	0.327677i	−0.816812	+	0.576904i	$0.804261\pi$
$710$		0			0
$711$	−15.5104	+	0.601470i	−0.581685	+	0.0225569i
$712$		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
$717$	0.808679	+	41.7232i	0.0302007	+	1.55818i
$718$		0			0
$719$	−12.0457			−0.449229			−0.224614	−	0.974448i	$-0.572112\pi$
$719$	−12.0457			−0.449229			−0.224614	+	0.974448i	$0.572112\pi$
$720$		0			0
$721$	4.70624	+	6.79916i	0.175269	+	0.253214i
$722$		0			0
$723$	−0.965791	+	2.82251i	−0.0359181	+	0.104970i
$724$		0			0
$725$	2.09781	+	2.50008i	0.0779109	+	0.0928505i
$726$		0			0
$727$	29.9518	−	35.6951i	1.11085	−	1.32386i	0.169842	−	0.985471i	$-0.445674\pi$
$727$	29.9518	−	35.6951i	1.11085	−	1.32386i	0.941007	−	0.338387i	$-0.109881\pi$
$728$		0			0
$729$	−16.1216	−	21.6586i	−0.597096	−	0.802170i
$730$		0			0
$731$	0.264163	−	1.49814i	0.00977041	−	0.0554107i
$732$		0			0
$733$	11.5490	−	31.7305i	0.426571	−	1.17199i	−0.521310	−	0.853368i	$-0.674556\pi$
$733$	11.5490	−	31.7305i	0.426571	−	1.17199i	0.947880	−	0.318626i	$-0.103221\pi$
$734$		0			0
$735$	5.41753	+	14.4970i	0.199828	+	0.534730i
$736$		0			0
$737$	19.6519	−	11.3460i	0.723887	−	0.417936i
$738$		0			0
$739$	−5.67407	+	9.82777i	−0.208724	+	0.361520i	−0.951313	−	0.308227i	$-0.900264\pi$
$739$	−5.67407	+	9.82777i	−0.208724	+	0.361520i	0.742589	+	0.669748i	$0.233598\pi$
$740$		0			0
$741$	32.2929	−	58.5235i	1.18631	−	2.14991i
$742$		0			0
$743$	19.8314	+	23.6342i	0.727544	+	0.867053i	0.995341	−	0.0964222i	$-0.0307399\pi$
$743$	19.8314	+	23.6342i	0.727544	+	0.867053i	−0.267796	+	0.963476i	$0.586295\pi$
$744$		0			0
$745$	−15.4437	+	18.4051i	−0.565814	+	0.674311i
$746$		0			0
$747$	−1.16017	−	1.84085i	−0.0424486	−	0.0673531i
$748$		0			0
$749$	−37.7702	−	26.7525i	−1.38009	−	0.977515i
$750$		0			0
$751$	−18.6268	+	15.6297i	−0.679701	+	0.570337i	−0.915919	−	0.401363i	$-0.868537\pi$
$751$	−18.6268	+	15.6297i	−0.679701	+	0.570337i	0.236218	+	0.971700i	$0.424092\pi$
$752$		0			0
$753$	−3.63246	−	2.92994i	−0.132374	−	0.106773i
$754$		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
$759$	4.82044	−	1.86106i	0.174971	−	0.0675521i
$760$		0			0
$761$	11.1068	−	9.31970i	0.402620	−	0.337839i	−0.418885	−	0.908039i	$-0.637579\pi$
$761$	11.1068	−	9.31970i	0.402620	−	0.337839i	0.821506	+	0.570201i	$0.193135\pi$
$762$		0			0
$763$	18.2620	+	39.7224i	0.661129	+	1.43805i
$764$		0			0
$765$	−0.177318	+	1.29795i	−0.00641096	+	0.0469275i
$766$		0			0
$767$	−38.1994	+	45.5243i	−1.37930	+	1.64379i
$768$		0			0
$769$	22.5194	+	26.8375i	0.812069	+	0.967786i	0.999896	−	0.0144157i	$-0.00458883\pi$
$769$	22.5194	+	26.8375i	0.812069	+	0.967786i	−0.187827	+	0.982202i	$0.560144\pi$
$770$		0			0
$771$	−32.9527	+	0.638689i	−1.18676	+	0.0230018i
$772$		0			0
$773$	19.4202	−	33.6368i	0.698496	−	1.20983i	−0.270492	−	0.962722i	$-0.587186\pi$
$773$	19.4202	−	33.6368i	0.698496	−	1.20983i	0.968988	−	0.247108i	$-0.0794802\pi$
$774$		0			0
$775$	12.4198	−	7.17059i	0.446133	−	0.257575i
$776$		0			0
$777$	2.67381	−	10.5672i	0.0959223	−	0.379096i
$778$		0			0
$779$	−28.4633	+	78.2022i	−1.01980	+	2.80189i
$780$		0			0
$781$	−2.53727	+	14.3896i	−0.0907905	+	0.514899i
$782$		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
$787$	8.19195	+	9.76279i	0.292012	+	0.348006i	0.892027	−	0.451983i	$-0.149283\pi$
$787$	8.19195	+	9.76279i	0.292012	+	0.348006i	−0.600015	+	0.799989i	$0.704839\pi$
$788$		0			0
$789$	48.9596	−	9.61469i	1.74301	−	0.342292i
$790$		0			0
$791$	1.99600	−	4.22069i	0.0709694	−	0.150070i
$792$		0			0
$793$	−32.1029			−1.14001
$794$		0			0
$795$	−11.8977	−	6.56509i	−0.421969	−	0.232840i
$796$		0			0
$797$	−26.9959	+	22.6523i	−0.956245	+	0.802385i	−0.980338	−	0.197325i	$-0.936775\pi$
$797$	−26.9959	+	22.6523i	−0.956245	+	0.802385i	0.0240929	+	0.999710i	$0.492330\pi$
$798$		0			0
$799$	0.999764	−	0.363884i	0.0353691	−	0.0128733i
$800$		0			0
$801$	6.50362	+	30.0278i	0.229794	+	1.06098i
$802$		0			0
$803$	−53.2496	−	44.6817i	−1.87914	−	1.57678i
$804$		0			0
$805$	0.443390	+	1.69129i	0.0156275	+	0.0596100i
$806$		0			0
$807$	−26.0091	+	10.0415i	−0.915565	+	0.353477i
$808$		0			0
$809$	−1.66941	+	0.963835i	−0.0586934	+	0.0338866i	−0.529060	−	0.848585i	$-0.677455\pi$
$809$	−1.66941	+	0.963835i	−0.0586934	+	0.0338866i	0.470366	+	0.882471i	$0.344122\pi$
$810$		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
$815$	−0.708993	−	4.02090i	−0.0248349	−	0.140846i
$816$		0			0
$817$	23.4190	−	27.9097i	0.819328	−	0.976437i
$818$		0			0
$819$	−10.8750	−	35.7695i	−0.380005	−	1.24989i
$820$		0			0
$821$	−29.8176	−	5.25764i	−1.04064	−	0.183493i	−0.372888	−	0.927876i	$-0.621633\pi$
$821$	−29.8176	−	5.25764i	−1.04064	−	0.183493i	−0.667753	+	0.744383i	$0.732744\pi$
$822$		0			0
$823$	−3.13774	−	1.14204i	−0.109375	−	0.0398092i	0.286753	−	0.958005i	$-0.407424\pi$
$823$	−3.13774	−	1.14204i	−0.109375	−	0.0398092i	−0.396128	+	0.918195i	$0.629646\pi$
$824$		0			0
$825$	−28.8030	+	17.3822i	−1.00279	+	0.605171i
$826$		0			0
$827$	−18.2554	+	10.5397i	−0.634801	+	0.366503i	−0.782609	−	0.622513i	$-0.786112\pi$
$827$	−18.2554	+	10.5397i	−0.634801	+	0.366503i	0.147808	+	0.989016i	$0.452778\pi$
$828$		0			0
$829$		−	29.6628i		−	1.03023i	−0.857121	−	0.515115i	$-0.827749\pi$
$829$		−	29.6628i		−	1.03023i	0.857121	−	0.515115i	$-0.172251\pi$
$830$		0			0
$831$	4.11652	+	20.9620i	0.142800	+	0.727163i
$832$		0			0
$833$	1.55901	−	1.81766i	0.0540165	−	0.0629783i
$834$		0			0
$835$	−24.7394	+	9.00442i	−0.856143	+	0.311611i
$836$		0			0
$837$	−21.5124	+	5.09764i	−0.743576	+	0.176200i
$838$		0			0
$839$	13.0322	+	10.9353i	0.449921	+	0.377529i	0.839407	−	0.543504i	$-0.182903\pi$
$839$	13.0322	+	10.9353i	0.449921	+	0.377529i	−0.389485	+	0.921033i	$0.627347\pi$
$840$		0			0
$841$	4.87300	+	27.6362i	0.168035	+	0.952972i
$842$		0			0
$843$	−17.2011	+	3.37795i	−0.592437	+	0.116343i
$844$		0			0
$845$	5.86283	+	10.1547i	0.201688	+	0.349333i
$846$		0			0
$847$	4.80370	+	58.5516i	0.165057	+	2.01186i
$848$		0			0
$849$	14.7544	+	8.14140i	0.506371	+	0.279412i
$850$		0			0
$851$	0.421186	−	1.15720i	0.0144381	−	0.0396683i
$852$		0			0
$853$	−16.4221	−	45.1192i	−0.562281	−	1.54485i	−0.816285	−	0.577650i	$-0.803970\pi$
$853$	−16.4221	−	45.1192i	−0.562281	−	1.54485i	0.254004	−	0.967203i	$-0.418252\pi$
$854$		0			0
$855$	−19.2205	+	24.7975i	−0.657329	+	0.848056i
$856$		0			0
$857$	8.84986	−	3.22109i	0.302305	−	0.110030i	−0.186414	−	0.982471i	$-0.559686\pi$
$857$	8.84986	−	3.22109i	0.302305	−	0.110030i	0.488719	+	0.872441i	$0.337464\pi$
$858$		0			0
$859$	7.27186	+	8.66627i	0.248113	+	0.295689i	0.875699	−	0.482858i	$-0.160401\pi$
$859$	7.27186	+	8.66627i	0.248113	+	0.295689i	−0.627586	+	0.778547i	$0.715957\pi$
$860$		0			0
$861$	20.2593	+	41.9074i	0.690435	+	1.42820i
$862$		0			0
$863$	−45.3985	−	26.2109i	−1.54538	−	0.892228i	−0.998485	−	0.0550294i	$-0.982475\pi$
$863$	−45.3985	−	26.2109i	−1.54538	−	0.892228i	−0.546899	−	0.837198i	$-0.684192\pi$
$864$		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
$871$	−6.34404	−	17.4301i	−0.214960	−	0.590596i
$872$		0			0
$873$	−1.06731	−	27.5232i	−0.0361229	−	0.931519i
$874$		0			0
$875$	−11.8084	−	25.6849i	−0.399196	−	0.868307i
$876$		0			0
$877$	−0.346610	−	1.96572i	−0.0117042	−	0.0663777i	0.978396	−	0.206738i	$-0.0662849\pi$
$877$	−0.346610	−	1.96572i	−0.0117042	−	0.0663777i	−0.990100	+	0.140361i	$0.955174\pi$
$878$		0			0
$879$	−1.11085	+	0.0215305i	−0.0374681	+	0.000726207i
$880$		0			0
$881$	−9.50503	−	16.4632i	−0.320233	−	0.554659i	0.660303	−	0.750999i	$-0.270428\pi$
$881$	−9.50503	−	16.4632i	−0.320233	−	0.554659i	−0.980536	+	0.196340i	$0.937094\pi$
$882$		0			0
$883$	15.4288	−	26.7235i	0.519221	−	0.899317i	−0.480529	−	0.876979i	$-0.659555\pi$
$883$	15.4288	−	26.7235i	0.519221	−	0.899317i	0.999750	−	0.0223387i	$-0.00711123\pi$
$884$		0			0
$885$	21.0168	−	18.3408i	0.706471	−	0.616519i
$886$		0			0
$887$	39.1613	+	14.2536i	1.31491	+	0.478587i	0.901823	−	0.432105i	$-0.142229\pi$
$887$	39.1613	+	14.2536i	1.31491	+	0.478587i	0.413085	+	0.910692i	$0.364451\pi$
$888$		0			0
$889$	22.8646	−	32.2810i	0.766852	−	1.08267i
$890$		0			0
$891$	50.2226	−	12.9337i	1.68252	−	0.433296i
$892$		0			0
$893$	25.0936	+	4.42468i	0.839726	+	0.148066i
$894$		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
$899$	−4.11959			−0.137396
$900$		0			0
$901$			2.10263i			0.0700487i
$902$		0			0
$903$	−2.05953	−	20.2738i	−0.0685368	−	0.674669i
$904$		0			0
$905$	10.3053	−	1.81711i	0.342561	−	0.0604028i
$906$		0			0
$907$	−20.2780	−	17.0153i	−0.673320	−	0.564983i	0.240726	−	0.970593i	$-0.422615\pi$
$907$	−20.2780	−	17.0153i	−0.673320	−	0.564983i	−0.914046	+	0.405610i	$0.867059\pi$
$908$		0			0
$909$	−4.81920	+	0.186882i	−0.159843	+	0.00619847i
$910$		0			0
$911$	−16.8822	−	2.97679i	−0.559333	−	0.0986255i	−0.113167	−	0.993576i	$-0.536100\pi$
$911$	−16.8822	−	2.97679i	−0.559333	−	0.0986255i	−0.446166	+	0.894950i	$0.647211\pi$
$912$		0			0
$913$	4.11602	−	0.725766i	0.136221	−	0.0240194i
$914$		0			0
$915$	14.8875	+	2.32856i	0.492165	+	0.0769797i
$916$		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
$921$	5.14489	+	13.3261i	0.169530	+	0.439111i
$922$		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
$927$	3.54586	+	8.67989i	0.116461	+	0.285085i
$928$		0			0
$929$	−1.28499	+	7.28755i	−0.0421592	+	0.239097i	−0.998604	−	0.0528155i	$-0.983180\pi$
$929$	−1.28499	+	7.28755i	−0.0421592	+	0.239097i	0.956445	+	0.291912i	$0.0942916\pi$
$930$		0			0
$931$	54.1018	−	19.0314i	1.77311	−	0.623728i
$932$		0			0
$933$	14.7281	−	26.6913i	0.482176	−	0.873835i
$934$		0			0
$935$	−2.17913	−	1.25812i	−0.0712651	−	0.0411449i
$936$		0			0
$937$	36.6771	+	21.1756i	1.19819	+	0.691775i	0.960151	−	0.279480i	$-0.0901622\pi$
$937$	36.6771	+	21.1756i	1.19819	+	0.691775i	0.238039	+	0.971256i	$0.423496\pi$
$938$		0			0
$939$	11.2849	−	32.9801i	0.368270	−	1.07626i
$940$		0			0
$941$	−10.3319	+	8.66953i	−0.336812	+	0.282619i	−0.795469	−	0.605995i	$-0.792775\pi$
$941$	−10.3319	+	8.66953i	−0.336812	+	0.282619i	0.458657	+	0.888613i	$0.348331\pi$
$942$		0			0
$943$	1.79860	+	4.94161i	0.0585705	+	0.160921i
$944$		0			0
$945$	2.44871	+	17.3767i	0.0796565	+	0.565263i
$946$		0			0
$947$	15.6107	+	42.8902i	0.507281	+	1.39374i	0.884031	+	0.467428i	$0.154819\pi$
$947$	15.6107	+	42.8902i	0.507281	+	1.39374i	−0.376750	+	0.926315i	$0.622958\pi$
$948$		0			0
$949$	−43.5268	+	36.5233i	−1.41294	+	1.18560i
$950$		0			0
$951$	17.9622	+	20.5830i	0.582466	+	0.667449i
$952$		0			0
$953$	−39.3815	−	22.7369i	−1.27569	−	0.736522i	−0.299640	−	0.954052i	$-0.596867\pi$
$953$	−39.3815	−	22.7369i	−1.27569	−	0.736522i	−0.976054	+	0.217530i	$0.930200\pi$
$954$		0			0
$955$	20.5656	+	11.8736i	0.665489	+	0.384220i
$956$		0			0
$957$	9.66192	−	0.187267i	0.312326	−	0.00605349i
$958$		0			0
$959$	−3.27801	−	0.897366i	−0.105852	−	0.0289775i
$960$		0			0
$961$	2.23962	−	12.7015i	0.0722459	−	0.409727i
$962$		0			0
$963$	−35.2673	−	38.8662i	−1.13647	−	1.25244i
$964$		0			0
$965$	3.81429	−	21.6319i	0.122786	−	0.696356i
$966$		0			0
$967$	20.8633	+	7.59361i	0.670918	+	0.244194i	0.654943	−	0.755678i	$-0.272693\pi$
$967$	20.8633	+	7.59361i	0.670918	+	0.244194i	0.0159747	+	0.999872i	$0.494915\pi$
$968$		0			0
$969$	4.79629	+	0.750190i	0.154079	+	0.0240996i
$970$		0			0
$971$	6.22659	−	10.7848i	0.199821	−	0.346100i	−0.748649	−	0.662966i	$-0.769297\pi$
$971$	6.22659	−	10.7848i	0.199821	−	0.346100i	0.948470	+	0.316866i	$0.102631\pi$
$972$		0			0
$973$	−2.26123	+	0.185517i	−0.0724919	+	0.00594739i
$974$		0			0
$975$	9.90419	+	25.6535i	0.317188	+	0.821569i
$976$		0			0
$977$	−10.9722	+	1.93470i	−0.351033	+	0.0618966i	−0.346385	−	0.938093i	$-0.612591\pi$
$977$	−10.9722	+	1.93470i	−0.351033	+	0.0618966i	−0.00464859	+	0.999989i	$0.501480\pi$
$978$		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
$983$	−15.6099	−	13.0983i	−0.497878	−	0.417770i	0.358961	−	0.933352i	$-0.383131\pi$
$983$	−15.6099	−	13.0983i	−0.497878	−	0.417770i	−0.856840	+	0.515583i	$0.827575\pi$
$984$		0			0
$985$	12.5432	−	2.21170i	0.399660	−	0.0704708i
$986$		0			0
$987$	11.5592	−	8.33690i	0.367933	−	0.265367i
$988$		0			0
$989$		−	2.30224i		−	0.0732070i
$990$		0			0
$991$	7.09184			0.225280			0.112640	−	0.993636i	$-0.464069\pi$
$991$	7.09184			0.225280			0.112640	+	0.993636i	$0.464069\pi$
$992$		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
$997$	52.5960	+	9.27409i	1.66573	+	0.293713i	0.925531	−	0.378672i	$-0.123619\pi$
$997$	52.5960	+	9.27409i	1.66573	+	0.293713i	0.740201	+	0.672386i	$0.234730\pi$
$998$		0			0
$999$	5.54745	−	11.0448i	0.175514	−	0.349442i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.12	✓	144	1.1	even	1	trivial
756.2.ca.a.437.12	yes	144	189.59	even	18	inner
756.2.ck.a.5.5	yes	144	27.5	odd	18
756.2.ck.a.605.5	yes	144	7.3	odd	6

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.ca (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.267657 + 1.71125i) q^{3} +(0.977821 - 0.820489i) q^{5} +(-2.63440 - 0.244842i) q^{7} +(-2.85672 - 0.916052i) q^{9} +O(q^{10})\)	\(q+(-0.267657 + 1.71125i) q^{3} +(0.977821 - 0.820489i) q^{5} +(-2.63440 - 0.244842i) q^{7} +(-2.85672 - 0.916052i) q^{9} +(3.70397 - 4.41422i) q^{11} +(-3.02767 - 3.60823i) q^{13} +(1.14234 + 1.89290i) q^{15} +(0.171047 - 0.296263i) q^{17} +(7.09541 - 4.09654i) q^{19} +(1.12410 - 4.44257i) q^{21} +(0.177071 - 0.486499i) q^{23} +(-0.585309 + 3.31946i) q^{25} +(2.33221 - 4.64336i) q^{27} +(0.622374 - 0.741717i) q^{29} +(-2.73487 - 3.25929i) q^{31} +(6.56243 + 7.51990i) q^{33} +(-2.77686 + 1.92208i) q^{35} +2.37862 q^{37} +(6.98495 - 4.21531i) q^{39} +(-7.78109 + 6.52911i) q^{41} +(4.17869 - 1.52092i) q^{43} +(-3.54497 + 1.44817i) q^{45} +(2.38242 + 1.99909i) q^{47} +(6.88011 + 1.29002i) q^{49} +(0.461196 + 0.372001i) q^{51} +(-5.32288 + 3.07317i) q^{53} -7.35539i q^{55} +(5.11105 + 13.2385i) q^{57} +(-2.19088 - 12.4251i) q^{59} +(4.38098 - 5.22105i) q^{61} +(7.30145 + 3.11269i) q^{63} +(-5.92103 - 1.04404i) q^{65} +(3.70049 + 1.34687i) q^{67} +(0.785125 + 0.433227i) q^{69} +(-2.19597 + 1.26784i) q^{71} -12.0632i q^{73} +(-5.52374 - 1.89008i) q^{75} +(-10.8385 + 10.7219i) q^{77} +(4.86198 - 1.76962i) q^{79} +(7.32170 + 5.23381i) q^{81} +(0.555623 + 0.466223i) q^{83} +(-0.0758267 - 0.430035i) q^{85} +(1.10268 + 1.26356i) q^{87} +(-5.12067 - 8.86926i) q^{89} +(7.09264 + 10.2468i) q^{91} +(6.30946 - 3.80767i) q^{93} +(3.57688 - 9.82739i) q^{95} +(3.14019 + 8.62759i) q^{97} +(-14.6249 + 9.21717i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 12 q^{15} - 3 q^{21} - 15 q^{23} - 6 q^{29} - 42 q^{39} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 18 q^{51} + 45 q^{53} + 3 q^{57} + 54 q^{61} + 39 q^{63} - 3 q^{65} + 36 q^{69} + 36 q^{71} + 93 q^{77} - 18 q^{79} - 36 q^{81} + 36 q^{85} - 18 q^{91} + 60 q^{93} + 6 q^{95}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 12 * q^15 - 3 * q^21 - 15 * q^23 - 6 * q^29 - 42 * q^39 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 18 * q^51 + 45 * q^53 + 3 * q^57 + 54 * q^61 + 39 * q^63 - 3 * q^65 + 36 * q^69 + 36 * q^71 + 93 * q^77 - 18 * q^79 - 36 * q^81 + 36 * q^85 - 18 * q^91 + 60 * q^93 + 6 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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