LMFDB - Embedded newform 675.2.k.c.199.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(199,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("675.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.k (of order $6$, degree $2$, not 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 102x^{12} - 406x^{10} + 1167x^{8} - 1842x^{6} + 2023x^{4} - 441x^{2} + 81 $ x^16 - 12x^14 + 102x^12 - 406x^10 + 1167x^8 - 1842x^6 + 2023x^4 - 441*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.8
Root			$2.28087 - 1.31686i$ of defining polynomial
Character	$\chi$	$=$	675.199
Dual form			675.2.k.c.424.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.28087 - 1.31686i) q^{2} +(2.46825 - 4.27513i) q^{4} +(1.55662 - 0.898714i) q^{7} -7.73393i q^{8} +O(q^{10})$	\(q+(2.28087 - 1.31686i) q^{2} +(2.46825 - 4.27513i) q^{4} +(1.55662 - 0.898714i) q^{7} -7.73393i q^{8} +(0.904062 + 1.56588i) q^{11} +(-1.70765 - 0.985914i) q^{13} +(2.36696 - 4.09970i) q^{14} +(-5.24801 - 9.08982i) q^{16} +4.80812i q^{17} -2.96467 q^{19} +(4.12410 + 2.38105i) q^{22} +(-1.50162 - 0.866963i) q^{23} -5.19325 q^{26} -8.87300i q^{28} +(3.68382 + 6.38057i) q^{29} +(1.31151 - 2.27161i) q^{31} +(-10.5445 - 6.08789i) q^{32} +(6.33163 + 10.9667i) q^{34} -11.6351i q^{37} +(-6.76203 + 3.90406i) q^{38} +(-1.23324 + 2.13603i) q^{41} +(-6.30306 + 3.63907i) q^{43} +8.92580 q^{44} -4.56668 q^{46} +(5.44910 - 3.14604i) q^{47} +(-1.88463 + 3.26427i) q^{49} +(-8.42983 + 4.86696i) q^{52} -1.72540i q^{53} +(-6.95059 - 12.0388i) q^{56} +(16.8047 + 9.70218i) q^{58} +(-5.51300 + 9.54880i) q^{59} +(6.33521 + 10.9729i) q^{61} -6.90833i q^{62} -11.0756 q^{64} +(7.88407 + 4.55187i) q^{67} +(20.5554 + 11.8676i) q^{68} -1.27460 q^{71} -3.58770i q^{73} +(-15.3218 - 26.5382i) q^{74} +(-7.31755 + 12.6744i) q^{76} +(2.81456 + 1.62499i) q^{77} +(1.05545 + 1.82809i) q^{79} +6.49602i q^{82} +(-0.951614 + 0.549415i) q^{83} +(-9.58431 + 16.6005i) q^{86} +(12.1104 - 6.99195i) q^{88} -13.2935 q^{89} -3.54422 q^{91} +(-7.41277 + 4.27976i) q^{92} +(8.28580 - 14.3514i) q^{94} +(3.31926 - 1.91638i) q^{97} +9.92718i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} - 2 q^{11} - 6 q^{14} - 8 q^{16} - 8 q^{19} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 18 q^{34} - 10 q^{41} + 88 q^{44} - 6 q^{49} - 60 q^{56} - 34 q^{59} + 26 q^{61} - 76 q^{64} + 32 q^{71} - 80 q^{74} - 22 q^{76} - 14 q^{79} - 68 q^{86} - 36 q^{89} - 68 q^{91} + 6 q^{94}+O(q^{100}) $ 16 * q + 8 * q^4 - 2 * q^11 - 6 * q^14 - 8 * q^16 - 8 * q^19 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 18 * q^34 - 10 * q^41 + 88 * q^44 - 6 * q^49 - 60 * q^56 - 34 * q^59 + 26 * q^61 - 76 * q^64 + 32 * q^71 - 80 * q^74 - 22 * q^76 - 14 * q^79 - 68 * q^86 - 36 * q^89 - 68 * q^91 + 6 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	2.28087	−	1.31686i	1.61282	−	0.931162i	0.624107	−	0.781339i	$-0.285463\pi$
$2$	2.28087	−	1.31686i	1.61282	−	0.931162i	0.988713	−	0.149823i	$-0.0478703\pi$
$3$		0			0
$3$		0			0
$4$	2.46825	−	4.27513i	1.23412	−	2.13757i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.55662	−	0.898714i	0.588346	−	0.339682i	−0.176097	−	0.984373i	$-0.556347\pi$
$7$	1.55662	−	0.898714i	0.588346	−	0.339682i	0.764443	+	0.644691i	$0.223014\pi$
$8$		−	7.73393i		−	2.73436i
$9$		0			0
$10$		0			0
$11$	0.904062	+	1.56588i	0.272585	+	0.472131i	0.969523	−	0.245000i	$-0.0787881\pi$
$11$	0.904062	+	1.56588i	0.272585	+	0.472131i	−0.696938	+	0.717131i	$0.745455\pi$
$12$		0			0
$13$	−1.70765	−	0.985914i	−0.473618	−	0.273443i	0.244135	−	0.969741i	$-0.421496\pi$
$13$	−1.70765	−	0.985914i	−0.473618	−	0.273443i	−0.717753	+	0.696298i	$0.754829\pi$
$14$	2.36696	−	4.09970i	0.632598	−	1.09569i
$15$		0			0
$16$	−5.24801	−	9.08982i	−1.31200	−	2.27246i
$17$			4.80812i			1.16614i	0.812421	+	0.583071i	$0.198149\pi$
$17$			4.80812i			1.16614i	−0.812421	+	0.583071i	$0.801851\pi$
$18$		0			0
$19$	−2.96467			−0.680142			−0.340071	−	0.940400i	$-0.610451\pi$
$19$	−2.96467			−0.680142			−0.340071	+	0.940400i	$0.610451\pi$
$20$		0			0
$21$		0			0
$22$	4.12410	+	2.38105i	0.879261	+	0.507641i
$23$	−1.50162	−	0.866963i	−0.313110	−	0.180774i	0.335207	−	0.942144i	$-0.391194\pi$
$23$	−1.50162	−	0.866963i	−0.313110	−	0.180774i	−0.648317	+	0.761370i	$0.724527\pi$
$24$		0			0
$25$		0			0
$26$	−5.19325			−1.01848
$27$		0			0
$28$		−	8.87300i		−	1.67684i
$29$	3.68382	+	6.38057i	0.684069	+	1.18484i	0.973728	+	0.227713i	$0.0731247\pi$
$29$	3.68382	+	6.38057i	0.684069	+	1.18484i	−0.289659	+	0.957130i	$0.593542\pi$
$30$		0			0
$31$	1.31151	−	2.27161i	0.235555	−	0.407993i	−0.723879	−	0.689927i	$-0.757643\pi$
$31$	1.31151	−	2.27161i	0.235555	−	0.407993i	0.959434	+	0.281934i	$0.0909760\pi$
$32$	−10.5445	−	6.08789i	−1.86403	−	1.07620i
$33$		0			0
$34$	6.33163	+	10.9667i	1.08587	+	1.88078i
$35$		0			0
$36$		0			0
$37$		−	11.6351i		−	1.91280i	−0.292063	−	0.956399i	$-0.594342\pi$
$37$		−	11.6351i		−	1.91280i	0.292063	−	0.956399i	$-0.405658\pi$
$38$	−6.76203	+	3.90406i	−1.09695	+	0.633322i
$39$		0			0
$40$		0			0
$41$	−1.23324	+	2.13603i	−0.192600	+	0.333592i	−0.946111	−	0.323842i	$-0.895025\pi$
$41$	−1.23324	+	2.13603i	−0.192600	+	0.333592i	0.753511	+	0.657435i	$0.228359\pi$
$42$		0			0
$43$	−6.30306	+	3.63907i	−0.961207	+	0.554953i	−0.896544	−	0.442954i	$-0.853931\pi$
$43$	−6.30306	+	3.63907i	−0.961207	+	0.554953i	−0.0646628	+	0.997907i	$0.520597\pi$
$44$	8.92580			1.34562
$45$		0			0
$46$	−4.56668			−0.673321
$47$	5.44910	−	3.14604i	0.794833	−	0.458897i	−0.0468283	−	0.998903i	$-0.514911\pi$
$47$	5.44910	−	3.14604i	0.794833	−	0.458897i	0.841661	+	0.540006i	$0.181578\pi$
$48$		0			0
$49$	−1.88463	+	3.26427i	−0.269233	+	0.466324i
$50$		0			0
$51$		0			0
$52$	−8.42983	+	4.86696i	−1.16901	+	0.674926i
$53$		−	1.72540i		−	0.237001i	−0.992954	−	0.118501i	$-0.962191\pi$
$53$		−	1.72540i		−	0.237001i	0.992954	−	0.118501i	$-0.0378088\pi$
$54$		0			0
$55$		0			0
$56$	−6.95059	−	12.0388i	−0.928811	−	1.60875i
$57$		0			0
$58$	16.8047	+	9.70218i	2.20656	+	1.27396i
$59$	−5.51300	+	9.54880i	−0.717732	+	1.24315i	0.244165	+	0.969734i	$0.421486\pi$
$59$	−5.51300	+	9.54880i	−0.717732	+	1.24315i	−0.961896	+	0.273414i	$0.911847\pi$
$60$		0			0
$61$	6.33521	+	10.9729i	0.811141	+	1.40494i	0.912066	+	0.410043i	$0.134486\pi$
$61$	6.33521	+	10.9729i	0.811141	+	1.40494i	−0.100925	+	0.994894i	$0.532180\pi$
$62$		−	6.90833i		−	0.877358i
$63$		0			0
$64$	−11.0756			−1.38445
$65$		0			0
$66$		0			0
$67$	7.88407	+	4.55187i	0.963193	+	0.556100i	0.897154	−	0.441717i	$-0.145631\pi$
$67$	7.88407	+	4.55187i	0.963193	+	0.556100i	0.0660386	+	0.997817i	$0.478964\pi$
$68$	20.5554	+	11.8676i	2.49271	+	1.43916i
$69$		0			0
$70$		0			0
$71$	−1.27460			−0.151268			−0.0756338	−	0.997136i	$-0.524098\pi$
$71$	−1.27460			−0.151268			−0.0756338	+	0.997136i	$0.524098\pi$
$72$		0			0
$73$		−	3.58770i		−	0.419908i	−0.977711	−	0.209954i	$-0.932669\pi$
$73$		−	3.58770i		−	0.419908i	0.977711	−	0.209954i	$-0.0673315\pi$
$74$	−15.3218	−	26.5382i	−1.78112	−	3.08500i
$75$		0			0
$76$	−7.31755	+	12.6744i	−0.839380	+	1.45385i
$77$	2.81456	+	1.62499i	0.320749	+	0.185184i
$78$		0			0
$79$	1.05545	+	1.82809i	0.118747	+	0.205676i	0.919272	−	0.393624i	$-0.128779\pi$
$79$	1.05545	+	1.82809i	0.118747	+	0.205676i	−0.800524	+	0.599300i	$0.795445\pi$
$80$		0			0
$81$		0			0
$82$			6.49602i			0.717366i
$83$	−0.951614	+	0.549415i	−0.104453	+	0.0603061i	−0.551317	−	0.834296i	$-0.685874\pi$
$83$	−0.951614	+	0.549415i	−0.104453	+	0.0603061i	0.446863	+	0.894602i	$0.352541\pi$
$84$		0			0
$85$		0			0
$86$	−9.58431	+	16.6005i	−1.03350	+	1.79008i
$87$		0			0
$88$	12.1104	−	6.99195i	1.29097	−	0.745344i
$89$	−13.2935			−1.40910			−0.704552	−	0.709653i	$-0.748852\pi$
$89$	−13.2935			−1.40910			−0.704552	+	0.709653i	$0.748852\pi$
$90$		0			0
$91$	−3.54422			−0.371535
$92$	−7.41277	+	4.27976i	−0.772834	+	0.446196i
$93$		0			0
$94$	8.28580	−	14.3514i	0.854615	−	1.48024i
$95$		0			0
$96$		0			0
$97$	3.31926	−	1.91638i	0.337020	−	0.194579i	−0.321933	−	0.946762i	$-0.604333\pi$
$97$	3.31926	−	1.91638i	0.337020	−	0.194579i	0.658954	+	0.752184i	$0.270999\pi$
$98$			9.92718i			1.00280i
$99$		0			0
$100$		0			0
$101$	3.27618	+	5.67452i	0.325993	+	0.564636i	0.981713	−	0.190368i	$-0.0609682\pi$
$101$	3.27618	+	5.67452i	0.325993	+	0.564636i	−0.655720	+	0.755004i	$0.727635\pi$
$102$		0			0
$103$	6.99365	+	4.03779i	0.689105	+	0.397855i	0.803277	−	0.595606i	$-0.203088\pi$
$103$	6.99365	+	4.03779i	0.689105	+	0.397855i	−0.114172	+	0.993461i	$0.536421\pi$
$104$	−7.62499	+	13.2069i	−0.747691	+	1.29504i
$105$		0			0
$106$	−2.27211	−	3.93541i	−0.220687	−	0.382241i
$107$		−	8.97674i		−	0.867814i	−0.900958	−	0.433907i	$-0.857135\pi$
$107$		−	8.97674i		−	0.867814i	0.900958	−	0.433907i	$-0.142865\pi$
$108$		0			0
$109$	6.34164			0.607419			0.303710	−	0.952765i	$-0.401775\pi$
$109$	6.34164			0.607419			0.303710	+	0.952765i	$0.401775\pi$
$110$		0			0
$111$		0			0
$112$	−16.3383	−	9.43292i	−1.54382	−	0.891327i
$113$	−12.9060	−	7.45127i	−1.21409	−	0.700957i	−0.250444	−	0.968131i	$-0.580577\pi$
$113$	−12.9060	−	7.45127i	−1.21409	−	0.700957i	−0.963648	+	0.267174i	$0.913910\pi$
$114$		0			0
$115$		0			0
$116$	36.3704			3.37691
$117$		0			0
$118$			29.0394i			2.67330i
$119$	4.32113	+	7.48441i	0.396117	+	0.686095i
$120$		0			0
$121$	3.86534	−	6.69497i	0.351395	−	0.608634i
$122$	28.8996	+	16.6852i	2.61645	+	1.51061i
$123$		0			0
$124$	−6.47428	−	11.2138i	−0.581408	−	1.00703i
$125$		0			0
$126$		0			0
$127$		−	3.62303i		−	0.321492i	−0.986996	−	0.160746i	$-0.948610\pi$
$127$		−	3.62303i		−	0.321492i	0.986996	−	0.160746i	$-0.0513899\pi$
$128$	−4.17289	+	2.40922i	−0.368835	+	0.212947i
$129$		0			0
$130$		0			0
$131$	3.64673	−	6.31631i	0.318616	−	0.551859i	−0.661584	−	0.749871i	$-0.730115\pi$
$131$	3.64673	−	6.31631i	0.318616	−	0.551859i	0.980200	+	0.198012i	$0.0634486\pi$
$132$		0			0
$133$	−4.61486	+	2.66439i	−0.400159	+	0.231032i
$134$	23.9767			2.07127
$135$		0			0
$136$	37.1857			3.18865
$137$	−6.17148	+	3.56310i	−0.527265	+	0.304417i	−0.739902	−	0.672715i	$-0.765128\pi$
$137$	−6.17148	+	3.56310i	−0.527265	+	0.304417i	0.212637	+	0.977131i	$0.431795\pi$
$138$		0			0
$139$	−7.35533	+	12.7398i	−0.623871	+	1.08058i	0.364887	+	0.931052i	$0.381108\pi$
$139$	−7.35533	+	12.7398i	−0.623871	+	1.08058i	−0.988758	+	0.149525i	$0.952226\pi$
$140$		0			0
$141$		0			0
$142$	−2.90721	+	1.67848i	−0.243967	+	0.140855i
$143$		−	3.56531i		−	0.298146i
$144$		0			0
$145$		0			0
$146$	−4.72450	−	8.18308i	−0.391003	−	0.677236i
$147$		0			0
$148$	−49.7416	−	28.7183i	−4.08873	−	2.36063i
$149$	0.282655	−	0.489572i	0.0231560	−	0.0401073i	−0.854215	−	0.519920i	$-0.825962\pi$
$149$	0.282655	−	0.489572i	0.0231560	−	0.0401073i	0.877371	+	0.479812i	$0.159295\pi$
$150$		0			0
$151$	−0.0766925	−	0.132835i	−0.00624115	−	0.0108100i	0.862888	−	0.505395i	$-0.168653\pi$
$151$	−0.0766925	−	0.132835i	−0.00624115	−	0.0108100i	−0.869129	+	0.494585i	$0.835320\pi$
$152$			22.9285i			1.85975i
$153$		0			0
$154$	8.55953			0.689746
$155$		0			0
$156$		0			0
$157$	−9.92525	−	5.73035i	−0.792121	−	0.457332i	0.0485874	−	0.998819i	$-0.484528\pi$
$157$	−9.92525	−	5.73035i	−0.792121	−	0.457332i	−0.840709	+	0.541487i	$0.817861\pi$
$158$	4.81469	+	2.77976i	0.383036	+	0.221146i
$159$		0			0
$160$		0			0
$161$	−3.11661			−0.245623
$162$		0			0
$163$		−	22.0595i		−	1.72783i	−0.503637	−	0.863915i	$-0.668005\pi$
$163$		−	22.0595i		−	1.72783i	0.503637	−	0.863915i	$-0.331995\pi$
$164$	6.08789	+	10.5445i	0.475384	+	0.823389i
$165$		0			0
$166$	−1.44701	+	2.50629i	−0.112310	+	0.194526i
$167$	−14.7817	−	8.53421i	−1.14384	−	0.660397i	−0.196462	−	0.980511i	$-0.562945\pi$
$167$	−14.7817	−	8.53421i	−1.14384	−	0.660397i	−0.947379	+	0.320115i	$0.896279\pi$
$168$		0			0
$169$	−4.55595	−	7.89113i	−0.350457	−	0.607010i
$170$		0			0
$171$		0			0
$172$			35.9285i			2.73953i
$173$	−10.3444	+	5.97233i	−0.786468	+	0.454067i	−0.838718	−	0.544567i	$-0.816694\pi$
$173$	−10.3444	+	5.97233i	−0.786468	+	0.454067i	0.0522497	+	0.998634i	$0.483361\pi$
$174$		0			0
$175$		0			0
$176$	9.48906	−	16.4355i	0.715265	−	1.23887i
$177$		0			0
$178$	−30.3207	+	17.5056i	−2.27263	+	1.31210i
$179$	8.54921			0.638998			0.319499	−	0.947587i	$-0.396485\pi$
$179$	8.54921			0.638998			0.319499	+	0.947587i	$0.396485\pi$
$180$		0			0
$181$	−10.5524			−0.784351			−0.392176	−	0.919890i	$-0.628277\pi$
$181$	−10.5524			−0.784351			−0.392176	+	0.919890i	$0.628277\pi$
$182$	−8.08390	+	4.66724i	−0.599219	+	0.345959i
$183$		0			0
$184$	−6.70503	+	11.6135i	−0.494301	+	0.856155i
$185$		0			0
$186$		0			0
$187$	−7.52895	+	4.34684i	−0.550571	+	0.317873i
$188$		−	31.0608i		−	2.26534i
$189$		0			0
$190$		0			0
$191$	−8.66862	−	15.0145i	−0.627239	−	1.08641i	−0.988103	−	0.153792i	$-0.950852\pi$
$191$	−8.66862	−	15.0145i	−0.627239	−	1.08641i	0.360864	−	0.932618i	$-0.382482\pi$
$192$		0			0
$193$	−1.35059	−	0.779763i	−0.0972175	−	0.0561286i	0.450603	−	0.892724i	$-0.351209\pi$
$193$	−1.35059	−	0.779763i	−0.0972175	−	0.0561286i	−0.547821	+	0.836596i	$0.684542\pi$
$194$	5.04721	−	8.74202i	0.362369	−	0.627641i
$195$		0			0
$196$	9.30346	+	16.1141i	0.664533	+	1.15100i
$197$			17.9767i			1.28079i	0.768046	+	0.640395i	$0.221229\pi$
$197$			17.9767i			1.28079i	−0.768046	+	0.640395i	$0.778771\pi$
$198$		0			0
$199$	−11.0225			−0.781362			−0.390681	−	0.920526i	$-0.627760\pi$
$199$	−11.0225			−0.781362			−0.390681	+	0.920526i	$0.627760\pi$
$200$		0			0
$201$		0			0
$202$	14.9451	+	8.62856i	1.05153	+	0.607104i
$203$	11.4686	+	6.62141i	0.804939	+	0.464732i
$204$		0			0
$205$		0			0
$206$	21.2688			1.48187
$207$		0			0
$208$			20.6964i			1.43503i
$209$	−2.68025	−	4.64232i	−0.185397	−	0.321116i
$210$		0			0
$211$	11.9643	−	20.7227i	0.823655	−	1.42661i	−0.0792886	−	0.996852i	$-0.525265\pi$
$211$	11.9643	−	20.7227i	0.823655	−	1.42661i	0.902943	−	0.429760i	$-0.141402\pi$
$212$	−7.37630	−	4.25871i	−0.506606	−	0.292489i
$213$		0			0
$214$	−11.8211	−	20.4748i	−0.808076	−	1.39963i
$215$		0			0
$216$		0			0
$217$		−	4.71470i		−	0.320055i
$218$	14.4645	−	8.35107i	0.979658	−	0.565606i
$219$		0			0
$220$		0			0
$221$	4.74040	−	8.21061i	0.318874	−	0.552305i
$222$		0			0
$223$	18.8020	−	10.8553i	1.25907	−	0.726927i	0.286180	−	0.958176i	$-0.407615\pi$
$223$	18.8020	−	10.8553i	1.25907	−	0.726927i	0.972895	+	0.231249i	$0.0742812\pi$
$224$	−21.8851			−1.46226
$225$		0			0
$226$	−39.2492			−2.61082
$227$	12.2111	−	7.05010i	0.810481	−	0.467932i	−0.0366416	−	0.999328i	$-0.511666\pi$
$227$	12.2111	−	7.05010i	0.810481	−	0.467932i	0.847123	+	0.531397i	$0.178333\pi$
$228$		0			0
$229$	1.83879	−	3.18488i	0.121511	−	0.210463i	−0.798853	−	0.601526i	$-0.794559\pi$
$229$	1.83879	−	3.18488i	0.121511	−	0.210463i	0.920364	+	0.391064i	$0.127893\pi$
$230$		0			0
$231$		0			0
$232$	49.3469	−	28.4904i	3.23978	−	1.87049i
$233$			5.34164i			0.349943i	0.984574	+	0.174971i	$0.0559833\pi$
$233$			5.34164i			0.349943i	−0.984574	+	0.174971i	$0.944017\pi$
$234$		0			0
$235$		0			0
$236$	27.2149	+	47.1376i	1.77154	+	3.06840i
$237$		0			0
$238$	19.7119	+	11.3807i	1.27773	+	0.737698i
$239$	11.0167	−	19.0815i	0.712613	−	1.23428i	−0.251260	−	0.967920i	$-0.580845\pi$
$239$	11.0167	−	19.0815i	0.712613	−	1.23428i	0.963873	−	0.266362i	$-0.0858218\pi$
$240$		0			0
$241$	9.32358	+	16.1489i	0.600585	+	1.04024i	0.992733	+	0.120341i	$0.0383988\pi$
$241$	9.32358	+	16.1489i	0.600585	+	1.04024i	−0.392148	+	0.919902i	$0.628268\pi$
$242$		−	20.3605i		−	1.30882i
$243$		0			0
$244$	62.5475			4.00420
$245$		0			0
$246$		0			0
$247$	5.06263	+	2.92291i	0.322127	+	0.185980i
$248$	−17.5684	−	10.1431i	−1.11560	−	0.644091i
$249$		0			0
$250$		0			0
$251$	−14.6929			−0.927407			−0.463704	−	0.885990i	$-0.653480\pi$
$251$	−14.6929			−0.927407			−0.463704	+	0.885990i	$0.653480\pi$
$252$		0			0
$253$		−	3.13515i		−	0.197105i
$254$	−4.77103	−	8.26366i	−0.299361	−	0.518508i
$255$		0			0
$256$	4.73035	−	8.19320i	0.295647	−	0.512075i
$257$	−19.2335	−	11.1045i	−1.19975	−	0.692678i	−0.239253	−	0.970957i	$-0.576902\pi$
$257$	−19.2335	−	11.1045i	−1.19975	−	0.692678i	−0.960500	+	0.278280i	$0.910236\pi$
$258$		0			0
$259$	−10.4566	−	18.1114i	−0.649743	−	1.12539i
$260$		0			0
$261$		0			0
$262$		−	19.2089i		−	1.18673i
$263$	−4.97100	+	2.87001i	−0.306525	+	0.176972i	−0.645370	−	0.763870i	$-0.723297\pi$
$263$	−4.97100	+	2.87001i	−0.306525	+	0.176972i	0.338846	+	0.940842i	$0.389964\pi$
$264$		0			0
$265$		0			0
$266$	−7.01727	+	12.1543i	−0.430256	+	0.745226i
$267$		0			0
$268$	38.9197	−	22.4703i	2.37740	−	1.37259i
$269$	−15.6162			−0.952139			−0.476070	−	0.879408i	$-0.657939\pi$
$269$	−15.6162			−0.952139			−0.476070	+	0.879408i	$0.657939\pi$
$270$		0			0
$271$	−6.75315			−0.410225			−0.205112	−	0.978738i	$-0.565756\pi$
$271$	−6.75315			−0.410225			−0.205112	+	0.978738i	$0.565756\pi$
$272$	43.7050	−	25.2331i	2.65000	−	1.52998i
$273$		0			0
$274$	−9.38423	+	16.2540i	−0.566922	+	0.981938i
$275$		0			0
$276$		0			0
$277$	−26.2376	+	15.1483i	−1.57646	+	0.910172i	−0.581118	+	0.813820i	$0.697384\pi$
$277$	−26.2376	+	15.1483i	−1.57646	+	0.910172i	−0.995347	+	0.0963529i	$0.969282\pi$
$278$			38.7438i			2.32370i
$279$		0			0
$280$		0			0
$281$	9.31755	+	16.1385i	0.555838	+	0.962740i	0.997838	+	0.0657249i	$0.0209360\pi$
$281$	9.31755	+	16.1385i	0.555838	+	0.962740i	−0.441999	+	0.897015i	$0.645731\pi$
$282$		0			0
$283$	4.91354	+	2.83683i	0.292079	+	0.168632i	0.638879	−	0.769307i	$-0.279398\pi$
$283$	4.91354	+	2.83683i	0.292079	+	0.168632i	−0.346800	+	0.937939i	$0.612732\pi$
$284$	−3.14604	+	5.44910i	−0.186683	+	0.323345i
$285$		0			0
$286$	−4.69502	−	8.13201i	−0.277622	−	0.480856i
$287$			4.43332i			0.261690i
$288$		0			0
$289$	−6.11806			−0.359886
$290$		0			0
$291$		0			0
$292$	−15.3379	−	8.85533i	−0.897582	−	0.518219i
$293$	15.8286	+	9.13867i	0.924720	+	0.533887i	0.885138	−	0.465329i	$-0.154064\pi$
$293$	15.8286	+	9.13867i	0.924720	+	0.533887i	0.0395819	+	0.999216i	$0.487397\pi$
$294$		0			0
$295$		0			0
$296$	−89.9850			−5.23027
$297$		0			0
$298$		−	1.48887i		−	0.0862478i
$299$	1.70950	+	2.96094i	0.0988631	+	0.171236i
$300$		0			0
$301$	−6.54097	+	11.3293i	−0.377015	+	0.653009i
$302$	−0.349852	−	0.201987i	−0.0201317	−	0.0116230i
$303$		0			0
$304$	15.5586	+	26.9483i	0.892349	+	1.54559i
$305$		0			0
$306$		0			0
$307$			15.5050i			0.884915i	0.896789	+	0.442458i	$0.145893\pi$
$307$			15.5050i			0.884915i	−0.896789	+	0.442458i	$0.854107\pi$
$308$	13.8941	−	8.02174i	0.791688	−	0.457081i
$309$		0			0
$310$		0			0
$311$	15.2232	−	26.3673i	0.863228	−	1.49515i	−0.00556798	−	0.999984i	$-0.501772\pi$
$311$	15.2232	−	26.3673i	0.863228	−	1.49515i	0.868796	−	0.495170i	$-0.164894\pi$
$312$		0			0
$313$	−6.01832	+	3.47468i	−0.340176	+	0.196401i	−0.660350	−	0.750958i	$-0.729592\pi$
$313$	−6.01832	+	3.47468i	−0.340176	+	0.196401i	0.320174	+	0.947359i	$0.396259\pi$
$314$	−30.1843			−1.70340
$315$		0			0
$316$	10.4205			0.586196
$317$	−13.9820	+	8.07253i	−0.785309	+	0.453398i	−0.838308	−	0.545196i	$-0.816455\pi$
$317$	−13.9820	+	8.07253i	−0.785309	+	0.453398i	0.0529995	+	0.998595i	$0.483122\pi$
$318$		0			0
$319$	−6.66081	+	11.5369i	−0.372934	+	0.645940i
$320$		0			0
$321$		0			0
$322$	−7.10858	+	4.10414i	−0.396146	+	0.228715i
$323$		−	14.2545i		−	0.793142i
$324$		0			0
$325$		0			0
$326$	−29.0493	−	50.3148i	−1.60889	−	2.78668i
$327$		0			0
$328$	16.5199	+	9.53779i	0.912160	+	0.526636i
$329$	5.65478	−	9.79436i	0.311758	−	0.539981i
$330$		0			0
$331$	−6.31112	−	10.9312i	−0.346890	−	0.600832i	0.638805	−	0.769369i	$-0.279429\pi$
$331$	−6.31112	−	10.9312i	−0.346890	−	0.600832i	−0.985695	+	0.168537i	$0.946096\pi$
$332$			5.42437i			0.297701i
$333$		0			0
$334$	−44.9535			−2.45975
$335$		0			0
$336$		0			0
$337$	−5.99324	−	3.46020i	−0.326473	−	0.188489i	0.327801	−	0.944747i	$-0.393692\pi$
$337$	−5.99324	−	3.46020i	−0.326473	−	0.188489i	−0.654274	+	0.756258i	$0.727026\pi$
$338$	−20.7831	−	11.9991i	−1.13045	−	0.652665i
$339$		0			0
$340$		0			0
$341$	4.74276			0.256835
$342$		0			0
$343$			19.3570i			1.04518i
$344$	28.1443	+	48.7474i	1.51744	+	2.62828i
$345$		0			0
$346$	−15.7295	+	27.2442i	−0.845621	+	1.46466i
$347$	−11.9566	−	6.90317i	−0.641866	−	0.370581i	0.143467	−	0.989655i	$-0.454175\pi$
$347$	−11.9566	−	6.90317i	−0.641866	−	0.370581i	−0.785333	+	0.619074i	$0.787508\pi$
$348$		0			0
$349$	3.28384	+	5.68778i	0.175780	+	0.304460i	0.940431	−	0.339985i	$-0.110422\pi$
$349$	3.28384	+	5.68778i	0.175780	+	0.304460i	−0.764651	+	0.644445i	$0.777089\pi$
$350$		0			0
$351$		0			0
$352$		−	22.0153i		−	1.17342i
$353$	3.05273	−	1.76250i	0.162481	−	0.0938082i	−0.416555	−	0.909111i	$-0.636763\pi$
$353$	3.05273	−	1.76250i	0.162481	−	0.0938082i	0.579035	+	0.815302i	$0.303429\pi$
$354$		0			0
$355$		0			0
$356$	−32.8116	+	56.8313i	−1.73901	+	3.01205i
$357$		0			0
$358$	19.4996	−	11.2581i	1.03059	−	0.595010i
$359$	22.9285			1.21012			0.605061	−	0.796179i	$-0.293149\pi$
$359$	22.9285			1.21012			0.605061	+	0.796179i	$0.293149\pi$
$360$		0			0
$361$	−10.2107			−0.537407
$362$	−24.0686	+	13.8960i	−1.26502	+	0.730358i
$363$		0			0
$364$	−8.74801	+	15.1520i	−0.458520	+	0.794181i
$365$		0			0
$366$		0			0
$367$	−3.61939	+	2.08966i	−0.188931	+	0.109079i	−0.591482	−	0.806318i	$-0.701457\pi$
$367$	−3.61939	+	2.08966i	−0.188931	+	0.109079i	0.402551	+	0.915397i	$0.368124\pi$
$368$			18.1993i			0.948706i
$369$		0			0
$370$		0			0
$371$	−1.55064	−	2.68578i	−0.0805051	−	0.139439i
$372$		0			0
$373$	−5.92440	−	3.42045i	−0.306754	−	0.177104i	0.338719	−	0.940888i	$-0.390006\pi$
$373$	−5.92440	−	3.42045i	−0.306754	−	0.177104i	−0.645473	+	0.763783i	$0.723340\pi$
$374$	−11.4484	+	19.8292i	−0.591982	+	1.02534i
$375$		0			0
$376$	−24.3312	−	42.1429i	−1.25479	−	2.17336i
$377$		−	14.5277i		−	0.748217i
$378$		0			0
$379$	12.7764			0.656280			0.328140	−	0.944629i	$-0.393578\pi$
$379$	12.7764			0.656280			0.328140	+	0.944629i	$0.393578\pi$
$380$		0			0
$381$		0			0
$382$	−39.5440	−	22.8307i	−2.02325	−	1.16812i
$383$	6.52515	+	3.76730i	0.333420	+	0.192500i	0.657358	−	0.753578i	$-0.271674\pi$
$383$	6.52515	+	3.76730i	0.333420	+	0.192500i	−0.323939	+	0.946078i	$0.605007\pi$
$384$		0			0
$385$		0			0
$386$	−4.10736			−0.209059
$387$		0			0
$388$		−	18.9204i		−	0.960538i
$389$	−2.72588	−	4.72135i	−0.138207	−	0.239382i	0.788611	−	0.614893i	$-0.210801\pi$
$389$	−2.72588	−	4.72135i	−0.138207	−	0.239382i	−0.926818	+	0.375511i	$0.877467\pi$
$390$		0			0
$391$	4.16847	−	7.22000i	0.210808	−	0.365131i
$392$	25.2456	+	14.5756i	1.27510	+	0.736177i
$393$		0			0
$394$	23.6729	+	41.0026i	1.19262	+	2.06568i
$395$		0			0
$396$		0			0
$397$			5.64549i			0.283339i	0.989914	+	0.141670i	$0.0452470\pi$
$397$			5.64549i			0.283339i	−0.989914	+	0.141670i	$0.954753\pi$
$398$	−25.1408	+	14.5151i	−1.26020	+	0.727574i
$399$		0			0
$400$		0			0
$401$	−2.75209	+	4.76676i	−0.137433	+	0.238040i	−0.926524	−	0.376235i	$-0.877218\pi$
$401$	−2.75209	+	4.76676i	−0.137433	+	0.238040i	0.789091	+	0.614276i	$0.210552\pi$
$402$		0			0
$403$	−4.47922	+	2.58608i	−0.223126	+	0.128822i
$404$	32.3458			1.60926
$405$		0			0
$406$	34.8779			1.73096
$407$	18.2192	−	10.5188i	0.903091	−	0.521400i
$408$		0			0
$409$	16.4265	−	28.4515i	0.812238	−	1.40684i	−0.0990570	−	0.995082i	$-0.531583\pi$
$409$	16.4265	−	28.4515i	0.812238	−	1.40684i	0.911295	−	0.411755i	$-0.135084\pi$
$410$		0			0
$411$		0			0
$412$	34.5241	−	19.9325i	1.70088	−	0.982005i
$413$			19.8184i			0.975202i
$414$		0			0
$415$		0			0
$416$	12.0043	+	20.7920i	0.588558	+	1.01941i
$417$		0			0
$418$	−12.2266	−	7.05903i	−0.598022	−	0.345268i
$419$	−11.4295	+	19.7965i	−0.558369	+	0.967124i	0.439264	+	0.898358i	$0.355239\pi$
$419$	−11.4295	+	19.7965i	−0.558369	+	0.967124i	−0.997633	+	0.0687656i	$0.978094\pi$
$420$		0			0
$421$	−8.97071	−	15.5377i	−0.437205	−	0.757262i	0.560267	−	0.828312i	$-0.310698\pi$
$421$	−8.97071	−	15.5377i	−0.437205	−	0.757262i	−0.997473	+	0.0710498i	$0.977365\pi$
$422$		−	63.0212i		−	3.06782i
$423$		0			0
$424$	−13.3441			−0.648046
$425$		0			0
$426$		0			0
$427$	19.7230	+	11.3871i	0.954463	+	0.551060i
$428$	−38.3768	−	22.1568i	−1.85501	−	1.07099i
$429$		0			0
$430$		0			0
$431$	6.18871			0.298100			0.149050	−	0.988830i	$-0.452378\pi$
$431$	6.18871			0.298100			0.149050	+	0.988830i	$0.452378\pi$
$432$		0			0
$433$		−	3.11806i		−	0.149844i	−0.997189	−	0.0749221i	$-0.976129\pi$
$433$		−	3.11806i		−	0.149844i	0.997189	−	0.0749221i	$-0.0238708\pi$
$434$	−6.20861	−	10.7536i	−0.298023	−	0.516190i
$435$		0			0
$436$	15.6528	−	27.1114i	0.749631	−	1.29840i
$437$	4.45182	+	2.57026i	0.212960	+	0.122952i
$438$		0			0
$439$	6.75494	+	11.6999i	0.322396	+	0.558406i	0.980982	−	0.194100i	$-0.0621785\pi$
$439$	6.75494	+	11.6999i	0.322396	+	0.558406i	−0.658586	+	0.752505i	$0.728845\pi$
$440$		0			0
$441$		0			0
$442$		−	24.9698i		−	1.18769i
$443$	21.0248	−	12.1387i	0.998918	−	0.576726i	0.0909904	−	0.995852i	$-0.470997\pi$
$443$	21.0248	−	12.1387i	0.998918	−	0.576726i	0.907928	+	0.419126i	$0.137663\pi$
$444$		0			0
$445$		0			0
$446$	28.5899	−	49.5192i	1.35377	−	2.34480i
$447$		0			0
$448$	−17.2404	+	9.95377i	−0.814534	+	0.470271i
$449$	−24.1437			−1.13941			−0.569705	−	0.821849i	$-0.692943\pi$
$449$	−24.1437			−1.13941			−0.569705	+	0.821849i	$0.692943\pi$
$450$		0			0
$451$	−4.45970			−0.209999
$452$	−63.7104	+	36.7832i	−2.99668	+	1.73014i
$453$		0			0
$454$	18.5680	−	32.1607i	0.871440	−	1.50938i
$455$		0			0
$456$		0			0
$457$	2.44355	−	1.41078i	0.114304	−	0.0659937i	−0.441758	−	0.897134i	$-0.645645\pi$
$457$	2.44355	−	1.41078i	0.114304	−	0.0659937i	0.556062	+	0.831141i	$0.312312\pi$
$458$		−	9.68573i		−	0.452585i
$459$		0			0
$460$		0			0
$461$	10.7286	+	18.5825i	0.499681	+	0.865474i	1.00000		0.000367761i	$-0.000117062\pi$
$461$	10.7286	+	18.5825i	0.499681	+	0.865474i	−0.500318	+	0.865841i	$0.666784\pi$
$462$		0			0
$463$	17.1502	+	9.90167i	0.797037	+	0.460170i	0.842434	−	0.538799i	$-0.181122\pi$
$463$	17.1502	+	9.90167i	0.797037	+	0.460170i	−0.0453970	+	0.998969i	$0.514455\pi$
$464$	38.6655	−	66.9706i	1.79500	−	3.10903i
$465$		0			0
$466$	7.03421	+	12.1836i	0.325853	+	0.564395i
$467$			22.7210i			1.05140i	0.850669	+	0.525701i	$0.176197\pi$
$467$			22.7210i			1.05140i	−0.850669	+	0.525701i	$0.823803\pi$
$468$		0			0
$469$	16.3633			0.755588
$470$		0			0
$471$		0			0
$472$	73.8497	+	42.6372i	3.39921	+	1.96253i
$473$	−11.3967	−	6.57989i	−0.524021	−	0.302544i
$474$		0			0
$475$		0			0
$476$	42.6625			1.95543
$477$		0			0
$478$		−	58.0300i		−	2.65423i
$479$	−10.6440	−	18.4359i	−0.486336	−	0.842359i	0.513541	−	0.858065i	$-0.328334\pi$
$479$	−10.6440	−	18.4359i	−0.486336	−	0.842359i	−0.999877	+	0.0157065i	$0.995000\pi$
$480$		0			0
$481$	−11.4712	+	19.8687i	−0.523042	+	0.905935i
$482$	42.5318	+	24.5557i	1.93727	+	1.11848i
$483$		0			0
$484$	−19.0813	−	33.0497i	−0.867330	−	1.50226i
$485$		0			0
$486$		0			0
$487$			9.58690i			0.434424i	0.976124	+	0.217212i	$0.0696963\pi$
$487$			9.58690i			0.434424i	−0.976124	+	0.217212i	$0.930304\pi$
$488$	84.8637	−	48.9961i	3.84160	−	2.21795i
$489$		0			0
$490$		0			0
$491$	−18.9222	+	32.7742i	−0.853945	+	1.47908i	0.0236745	+	0.999720i	$0.492463\pi$
$491$	−18.9222	+	32.7742i	−0.853945	+	1.47908i	−0.877620	+	0.479357i	$0.840870\pi$
$492$		0			0
$493$	−30.6786	+	17.7123i	−1.38169	+	0.797721i
$494$	15.3963			0.692711
$495$		0			0
$496$	−27.5314			−1.23619
$497$	−1.98407	+	1.14550i	−0.0889977	+	0.0513829i
$498$		0			0
$499$	8.46266	−	14.6577i	0.378840	−	0.656171i	−0.612053	−	0.790816i	$-0.709656\pi$
$499$	8.46266	−	14.6577i	0.378840	−	0.656171i	0.990894	+	0.134646i	$0.0429896\pi$
$500$		0			0
$501$		0			0
$502$	−33.5126	+	19.3485i	−1.49574	+	0.863566i
$503$		−	40.4168i		−	1.80210i	−0.433719	−	0.901048i	$-0.642799\pi$
$503$		−	40.4168i		−	1.80210i	0.433719	−	0.901048i	$-0.357201\pi$
$504$		0			0
$505$		0			0
$506$	−4.12856	−	7.15088i	−0.183537	−	0.317896i
$507$		0			0
$508$	−15.4889	−	8.94253i	−0.687210	−	0.396761i
$509$	20.7034	−	35.8593i	0.917660	−	1.58943i	0.114701	−	0.993400i	$-0.463409\pi$
$509$	20.7034	−	35.8593i	0.917660	−	1.58943i	0.802959	−	0.596034i	$-0.203258\pi$
$510$		0			0
$511$	−3.22431	−	5.58467i	−0.142635	−	0.247051i
$512$		−	34.5537i		−	1.52707i
$513$		0			0
$514$	−58.4922			−2.57998
$515$		0			0
$516$		0			0
$517$	9.85265	+	5.68843i	0.433319	+	0.250177i
$518$	−47.7004	−	27.5398i	−2.09584	−	1.21003i
$519$		0			0
$520$		0			0
$521$	17.0301			0.746103			0.373052	−	0.927811i	$-0.378311\pi$
$521$	17.0301			0.746103			0.373052	+	0.927811i	$0.378311\pi$
$522$		0			0
$523$			9.57651i			0.418751i	0.977835	+	0.209376i	$0.0671432\pi$
$523$			9.57651i			0.418751i	−0.977835	+	0.209376i	$0.932857\pi$
$524$	−18.0021	−	31.1805i	−0.786424	−	1.36213i
$525$		0			0
$526$	−7.55880	+	13.0922i	−0.329579	+	0.570848i
$527$	10.9222	+	6.30592i	0.475777	+	0.274690i
$528$		0			0
$529$	−9.99675	−	17.3149i	−0.434641	−	0.752821i
$530$		0			0
$531$		0			0
$532$			26.3055i			1.14049i
$533$	4.21189	−	2.43174i	0.182437	−	0.105330i
$534$		0			0
$535$		0			0
$536$	35.2038	−	60.9748i	1.52057	−	2.63371i
$537$		0			0
$538$	−35.6187	+	20.5644i	−1.53563	+	0.886596i
$539$	−6.81528			−0.293555
$540$		0			0
$541$	−0.833751			−0.0358458			−0.0179229	−	0.999839i	$-0.505705\pi$
$541$	−0.833751			−0.0358458			−0.0179229	+	0.999839i	$0.505705\pi$
$542$	−15.4031	+	8.89297i	−0.661619	+	0.381986i
$543$		0			0
$544$	29.2713	−	50.6994i	1.25500	−	2.17372i
$545$		0			0
$546$		0			0
$547$	24.5319	−	14.1635i	1.04891	−	0.605587i	0.126565	−	0.991958i	$-0.459605\pi$
$547$	24.5319	−	14.1635i	1.04891	−	0.605587i	0.922343	+	0.386371i	$0.126272\pi$
$548$			35.1785i			1.50275i
$549$		0			0
$550$		0			0
$551$	−10.9213	−	18.9163i	−0.465264	−	0.805861i
$552$		0			0
$553$	3.28586	+	1.89709i	0.139729	+	0.0806727i
$554$	−39.8964	+	69.1026i	−1.69504	+	2.93589i
$555$		0			0
$556$	36.3096	+	62.8901i	1.53987	+	2.66713i
$557$			11.5042i			0.487448i	0.969845	+	0.243724i	$0.0783690\pi$
$557$			11.5042i			0.487448i	−0.969845	+	0.243724i	$0.921631\pi$
$558$		0			0
$559$	14.3512			0.606993
$560$		0			0
$561$		0			0
$562$	42.5043	+	24.5398i	1.79293	+	1.03515i
$563$	28.5840	+	16.5030i	1.20467	+	0.695517i	0.961590	−	0.274490i	$-0.0885089\pi$
$563$	28.5840	+	16.5030i	1.20467	+	0.695517i	0.243080	+	0.970006i	$0.421842\pi$
$564$		0			0
$565$		0			0
$566$	14.9429			0.628095
$567$		0			0
$568$			9.85769i			0.413619i
$569$	13.5044	+	23.3903i	0.566135	+	0.980574i	0.996943	+	0.0781305i	$0.0248951\pi$
$569$	13.5044	+	23.3903i	0.566135	+	0.980574i	−0.430809	+	0.902443i	$0.641772\pi$
$570$		0			0
$571$	12.2122	−	21.1521i	0.511064	−	0.885189i	−0.488854	−	0.872366i	$-0.662585\pi$
$571$	12.2122	−	21.1521i	0.511064	−	0.885189i	0.999918	−	0.0128232i	$-0.00408185\pi$
$572$	−15.2422	−	8.80007i	−0.637307	−	0.367950i
$573$		0			0
$574$	5.83807	+	10.1118i	0.243676	+	0.422060i
$575$		0			0
$576$		0			0
$577$		−	14.7976i		−	0.616033i	−0.951381	−	0.308017i	$-0.900335\pi$
$577$		−	14.7976i		−	0.616033i	0.951381	−	0.308017i	$-0.0996653\pi$
$578$	−13.9545	+	8.05663i	−0.580431	+	0.335112i
$579$		0			0
$580$		0			0
$581$	−0.987533	+	1.71046i	−0.0409698	+	0.0709617i
$582$		0			0
$583$	2.70177	−	1.55987i	0.111896	−	0.0646030i
$584$	−27.7470			−1.14818
$585$		0			0
$586$	48.1375			1.98854
$587$	26.4813	−	15.2890i	1.09300	−	0.631044i	0.158626	−	0.987339i	$-0.449294\pi$
$587$	26.4813	−	15.2890i	1.09300	−	0.631044i	0.934374	+	0.356295i	$0.115960\pi$
$588$		0			0
$589$	−3.88821	+	6.73457i	−0.160211	+	0.277493i
$590$		0			0
$591$		0			0
$592$	−105.761	+	61.0611i	−4.34675	+	2.50960i
$593$			5.09990i			0.209428i	0.994502	+	0.104714i	$0.0333927\pi$
$593$			5.09990i			0.209428i	−0.994502	+	0.104714i	$0.966607\pi$
$594$		0			0
$595$		0			0
$596$	−1.39532	−	2.41677i	−0.0571547	−	0.0989949i
$597$		0			0
$598$	7.79831	+	4.50236i	0.318897	+	0.184115i
$599$	0.282655	−	0.489572i	0.0115490	−	0.0200034i	−0.860193	−	0.509968i	$-0.829657\pi$
$599$	0.282655	−	0.489572i	0.0115490	−	0.0200034i	0.871742	+	0.489965i	$0.162990\pi$
$600$		0			0
$601$	5.50480	+	9.53459i	0.224546	+	0.388924i	0.956183	−	0.292770i	$-0.0945769\pi$
$601$	5.50480	+	9.53459i	0.224546	+	0.388924i	−0.731637	+	0.681694i	$0.761244\pi$
$602$			34.4542i			1.40425i
$603$		0			0
$604$	−0.757185			−0.0308094
$605$		0			0
$606$		0			0
$607$	−16.5396	−	9.54913i	−0.671321	−	0.387587i	0.125256	−	0.992124i	$-0.460025\pi$
$607$	−16.5396	−	9.54913i	−0.671321	−	0.387587i	−0.796577	+	0.604537i	$0.793358\pi$
$608$	31.2611	+	18.0486i	1.26780	+	0.731967i
$609$		0			0
$610$		0			0
$611$	−12.4069			−0.501929
$612$		0			0
$613$			9.33918i			0.377206i	0.982053	+	0.188603i	$0.0603959\pi$
$613$			9.33918i			0.377206i	−0.982053	+	0.188603i	$0.939604\pi$
$614$	20.4179	+	35.3648i	0.823999	+	1.42721i
$615$		0			0
$616$	12.5675	−	21.7676i	0.506360	−	0.877041i
$617$	21.1444	+	12.2077i	0.851241	+	0.491464i	0.861069	−	0.508488i	$-0.169795\pi$
$617$	21.1444	+	12.2077i	0.851241	+	0.491464i	−0.00982861	+	0.999952i	$0.503129\pi$
$618$		0			0
$619$	19.7431	+	34.1961i	0.793544	+	1.37446i	0.923760	+	0.382973i	$0.125100\pi$
$619$	19.7431	+	34.1961i	0.793544	+	1.37446i	−0.130216	+	0.991486i	$0.541567\pi$
$620$		0			0
$621$		0			0
$622$		−	80.1874i		−	3.21522i
$623$	−20.6928	+	11.9470i	−0.829040	+	0.478647i
$624$		0			0
$625$		0			0
$626$	−9.15135	+	15.8506i	−0.365761	+	0.633517i
$627$		0			0
$628$	−48.9960	+	28.2879i	−1.95515	+	1.12881i
$629$	55.9430			2.23059
$630$		0			0
$631$	42.1634			1.67850			0.839249	−	0.543747i	$-0.182995\pi$
$631$	42.1634			1.67850			0.839249	+	0.543747i	$0.182995\pi$
$632$	14.1383	−	8.16277i	0.562393	−	0.324698i
$633$		0			0
$634$	−21.2608	+	36.8248i	−0.844375	+	1.46250i
$635$		0			0
$636$		0			0
$637$	6.43658	−	3.71616i	0.255027	−	0.147240i
$638$			35.0855i			1.38905i
$639$		0			0
$640$		0			0
$641$	17.6577	+	30.5841i	0.697438	+	1.20800i	0.969352	+	0.245677i	$0.0790103\pi$
$641$	17.6577	+	30.5841i	0.697438	+	1.20800i	−0.271913	+	0.962322i	$0.587656\pi$
$642$		0			0
$643$	−12.2936	−	7.09771i	−0.484812	−	0.279906i	0.237608	−	0.971361i	$-0.423637\pi$
$643$	−12.2936	−	7.09771i	−0.484812	−	0.279906i	−0.722420	+	0.691455i	$0.756970\pi$
$644$	−7.69256	+	13.3239i	−0.303129	+	0.525036i
$645$		0			0
$646$	−18.7712	−	32.5127i	−0.738544	−	1.27919i
$647$			17.4897i			0.687593i	0.939044	+	0.343796i	$0.111713\pi$
$647$			17.4897i			0.687593i	−0.939044	+	0.343796i	$0.888287\pi$
$648$		0			0
$649$	−19.9364			−0.782572
$650$		0			0
$651$		0			0
$652$	−94.3072	−	54.4483i	−3.69335	−	2.13236i
$653$	−9.50650	−	5.48858i	−0.372018	−	0.214785i	0.302322	−	0.953206i	$-0.402238\pi$
$653$	−9.50650	−	5.48858i	−0.372018	−	0.214785i	−0.674340	+	0.738421i	$0.735572\pi$
$654$		0			0
$655$		0			0
$656$	25.8882			1.01077
$657$		0			0
$658$		−	29.7862i		−	1.16119i
$659$	7.89381	+	13.6725i	0.307499	+	0.532604i	0.977815	−	0.209472i	$-0.0671746\pi$
$659$	7.89381	+	13.6725i	0.307499	+	0.532604i	−0.670316	+	0.742076i	$0.733841\pi$
$660$		0			0
$661$	−24.9466	+	43.2088i	−0.970311	+	1.68063i	−0.275697	+	0.961245i	$0.588909\pi$
$661$	−24.9466	+	43.2088i	−0.970311	+	1.68063i	−0.694614	+	0.719383i	$0.744425\pi$
$662$	−28.7897	−	16.6217i	−1.11894	−	0.646022i
$663$		0			0
$664$	4.24913	+	7.35972i	0.164898	+	0.285612i
$665$		0			0
$666$		0			0
$667$		−	12.7750i		−	0.494649i
$668$	−72.9698	+	42.1291i	−2.82328	+	1.63002i
$669$		0			0
$670$		0			0
$671$	−11.4549	+	19.8404i	−0.442210	+	0.765929i
$672$		0			0
$673$	24.9757	−	14.4197i	0.962743	−	0.555840i	0.0657266	−	0.997838i	$-0.479063\pi$
$673$	24.9757	−	14.4197i	0.962743	−	0.555840i	0.897016	+	0.441998i	$0.145730\pi$
$674$	−18.2264			−0.702055
$675$		0			0
$676$	−44.9809			−1.73003
$677$	9.06176	−	5.23181i	0.348272	−	0.201075i	−0.315652	−	0.948875i	$-0.602223\pi$
$677$	9.06176	−	5.23181i	0.348272	−	0.201075i	0.663924	+	0.747800i	$0.268890\pi$
$678$		0			0
$679$	3.44455	−	5.96614i	0.132190	−	0.228959i
$680$		0			0
$681$		0			0
$682$	10.8176	−	6.24556i	0.414228	−	0.239155i
$683$			16.1875i			0.619396i	0.950835	+	0.309698i	$0.100228\pi$
$683$			16.1875i			0.619396i	−0.950835	+	0.309698i	$0.899772\pi$
$684$		0			0
$685$		0			0
$686$	25.4904	+	44.1507i	0.973229	+	1.68568i
$687$		0			0
$688$	66.1570	+	38.1958i	2.52221	+	1.45620i
$689$	−1.70109	+	2.94638i	−0.0648065	+	0.112248i
$690$		0			0
$691$	−4.94181	−	8.55946i	−0.187995	−	0.325617i	0.756586	−	0.653894i	$-0.226866\pi$
$691$	−4.94181	−	8.55946i	−0.187995	−	0.325617i	−0.944582	+	0.328276i	$0.893532\pi$
$692$			58.9648i			2.24150i
$693$		0			0
$694$	−36.3621			−1.38029
$695$		0			0
$696$		0			0
$697$	−10.2703	−	5.92957i	−0.389016	−	0.224598i
$698$	14.9800	+	8.64872i	0.567002	+	0.327359i
$699$		0			0
$700$		0			0
$701$	−43.9692			−1.66069			−0.830346	−	0.557248i	$-0.811857\pi$
$701$	−43.9692			−1.66069			−0.830346	+	0.557248i	$0.811857\pi$
$702$		0			0
$703$			34.4942i			1.30097i
$704$	−10.0130	−	17.3430i	−0.377379	−	0.653640i
$705$		0			0
$706$	4.64193	−	8.04005i	0.174701	−	0.302591i
$707$	10.1995	+	5.88870i	0.383593	+	0.221467i
$708$		0			0
$709$	12.6130	+	21.8464i	0.473692	+	0.820458i	0.999546	−	0.0301162i	$-0.00958774\pi$
$709$	12.6130	+	21.8464i	0.473692	+	0.820458i	−0.525855	+	0.850574i	$0.676254\pi$
$710$		0			0
$711$		0			0
$712$			102.811i			3.85299i
$713$	−3.93880	+	2.27407i	−0.147509	+	0.0851645i
$714$		0			0
$715$		0			0
$716$	21.1016	−	36.5490i	0.788603	−	1.36590i
$717$		0			0
$718$	52.2971	−	30.1937i	1.95171	−	1.12682i
$719$	−36.8600			−1.37465			−0.687323	−	0.726352i	$-0.741214\pi$
$719$	−36.8600			−1.37465			−0.687323	+	0.726352i	$0.741214\pi$
$720$		0			0
$721$	14.5153			0.540576
$722$	−23.2893	+	13.4461i	−0.866740	+	0.500412i
$723$		0			0
$724$	−26.0459	+	45.1128i	−0.967988	+	1.67660i
$725$		0			0
$726$		0			0
$727$	33.1213	−	19.1226i	1.22840	−	0.709217i	0.261705	−	0.965148i	$-0.415715\pi$
$727$	33.1213	−	19.1226i	1.22840	−	0.709217i	0.966695	+	0.255931i	$0.0823820\pi$
$728$			27.4107i			1.01591i
$729$		0			0
$730$		0			0
$731$	−17.4971	−	30.3059i	−0.647154	−	1.12090i
$732$		0			0
$733$	−34.2801	−	19.7916i	−1.26616	−	0.731020i	−0.291903	−	0.956448i	$-0.594289\pi$
$733$	−34.2801	−	19.7916i	−1.26616	−	0.731020i	−0.974260	+	0.225428i	$0.927622\pi$
$734$	−5.50358	+	9.53248i	−0.203141	+	0.351850i
$735$		0			0
$736$	10.5559	+	18.2834i	0.389097	+	0.673936i
$737$			16.4607i			0.606338i
$738$		0			0
$739$	8.24773			0.303398			0.151699	−	0.988427i	$-0.451526\pi$
$739$	8.24773			0.303398			0.151699	+	0.988427i	$0.451526\pi$
$740$		0			0
$741$		0			0
$742$	−7.07361	−	4.08395i	−0.259680	−	0.149927i
$743$	1.13292	+	0.654091i	0.0415627	+	0.0239963i	0.520637	−	0.853778i	$-0.325694\pi$
$743$	1.13292	+	0.654091i	0.0415627	+	0.0239963i	−0.479075	+	0.877774i	$0.659028\pi$
$744$		0			0
$745$		0			0
$746$	−18.0171			−0.659651
$747$		0			0
$748$			42.9164i			1.56918i
$749$	−8.06752	−	13.9734i	−0.294781	−	0.510575i
$750$		0			0
$751$	−14.2234	+	24.6357i	−0.519020	+	0.898969i	0.480736	+	0.876866i	$0.340370\pi$
$751$	−14.2234	+	24.6357i	−0.519020	+	0.898969i	−0.999756	+	0.0221034i	$0.992964\pi$
$752$	−57.1939	−	33.0209i	−2.08565	−	1.20415i
$753$		0			0
$754$	−19.1310	−	33.1359i	−0.696711	−	1.20674i
$755$		0			0
$756$		0			0
$757$			38.2012i			1.38845i	0.719760	+	0.694223i	$0.244252\pi$
$757$			38.2012i			1.38845i	−0.719760	+	0.694223i	$0.755748\pi$
$758$	29.1414	−	16.8248i	1.05846	−	0.611103i
$759$		0			0
$760$		0			0
$761$	11.0952	−	19.2174i	0.402200	−	0.696632i	−0.591791	−	0.806092i	$-0.701579\pi$
$761$	11.0952	−	19.2174i	0.402200	−	0.696632i	0.993991	+	0.109460i	$0.0349121\pi$
$762$		0			0
$763$	9.87152	−	5.69932i	0.357373	−	0.206329i
$764$	−85.5852			−3.09637
$765$		0			0
$766$	19.8440			0.716994
$767$	18.8286	−	10.8707i	0.679861	−	0.392518i
$768$		0			0
$769$	−8.45652	+	14.6471i	−0.304950	+	0.528189i	−0.977250	−	0.212090i	$-0.931973\pi$
$769$	−8.45652	+	14.6471i	−0.304950	+	0.528189i	0.672300	+	0.740279i	$0.265306\pi$
$770$		0			0
$771$		0			0
$772$	−6.66718	+	3.84930i	−0.239957	+	0.138539i
$773$			38.6464i			1.39001i	0.719003	+	0.695007i	$0.244599\pi$
$773$			38.6464i			1.39001i	−0.719003	+	0.695007i	$0.755401\pi$
$774$		0			0
$775$		0			0
$776$	−14.8211	−	25.6709i	−0.532047	−	0.921533i
$777$		0			0
$778$	−12.4347	−	7.17920i	−0.445807	−	0.257387i
$779$	3.65615	−	6.33264i	0.130995	−	0.226890i
$780$		0			0
$781$	−1.15232	−	1.99588i	−0.0412333	−	0.0714181i
$782$		−	21.9572i		−	0.785187i
$783$		0			0
$784$	39.5622			1.41294
$785$		0			0
$786$		0			0
$787$	9.45240	+	5.45734i	0.336942	+	0.194533i	0.658919	−	0.752214i	$-0.271014\pi$
$787$	9.45240	+	5.45734i	0.336942	+	0.194533i	−0.321977	+	0.946747i	$0.604347\pi$
$788$	76.8530	+	44.3711i	2.73777	+	1.58065i
$789$		0			0
$790$		0			0
$791$	−26.7862			−0.952409
$792$		0			0
$793$		−	24.9839i		−	0.887204i
$794$	7.43433	+	12.8766i	0.263835	+	0.456975i
$795$		0			0
$796$	−27.2062	+	47.1225i	−0.964298	+	1.67021i
$797$	2.53356	+	1.46275i	0.0897432	+	0.0518133i	0.544200	−	0.838956i	$-0.316833\pi$
$797$	2.53356	+	1.46275i	0.0897432	+	0.0518133i	−0.454457	+	0.890769i	$0.650167\pi$
$798$		0			0
$799$	15.1265	+	26.1999i	0.535139	+	0.926888i
$800$		0			0
$801$		0			0
$802$			14.4965i			0.511888i
$803$	5.61791	−	3.24350i	0.198252	−	0.114461i
$804$		0			0
$805$		0			0
$806$	−6.81102	+	11.7970i	−0.239908	+	0.415532i
$807$		0			0
$808$	43.8863	−	25.3378i	1.54391	−	0.891380i
$809$	−37.9241			−1.33334			−0.666671	−	0.745352i	$-0.732281\pi$
$809$	−37.9241			−1.33334			−0.666671	+	0.745352i	$0.732281\pi$
$810$		0			0
$811$	19.5050			0.684912			0.342456	−	0.939534i	$-0.388741\pi$
$811$	19.5050			0.684912			0.342456	+	0.939534i	$0.388741\pi$
$812$	56.6148	−	32.6866i	1.98679	−	1.14707i
$813$		0			0
$814$	27.7037	−	47.9843i	0.971016	−	1.68185i
$815$		0			0
$816$		0			0
$817$	18.6865	−	10.7887i	0.653758	−	0.377447i
$818$		−	86.5257i		−	3.02530i
$819$		0			0
$820$		0			0
$821$	22.3762	+	38.7567i	0.780934	+	1.35262i	0.931398	+	0.364002i	$0.118590\pi$
$821$	22.3762	+	38.7567i	0.780934	+	1.35262i	−0.150464	+	0.988615i	$0.548077\pi$
$822$		0			0
$823$	31.0898	+	17.9497i	1.08372	+	0.625687i	0.931898	−	0.362721i	$-0.118152\pi$
$823$	31.0898	+	17.9497i	1.08372	+	0.625687i	0.151824	+	0.988408i	$0.451485\pi$
$824$	31.2279	−	54.0884i	1.08788	−	1.88426i
$825$		0			0
$826$	26.0981	+	45.2033i	0.908071	+	1.57282i
$827$		−	16.2717i		−	0.565822i	−0.959146	−	0.282911i	$-0.908700\pi$
$827$		−	16.2717i		−	0.565822i	0.959146	−	0.282911i	$-0.0913001\pi$
$828$		0			0
$829$	20.6592			0.717525			0.358762	−	0.933429i	$-0.383199\pi$
$829$	20.6592			0.717525			0.358762	+	0.933429i	$0.383199\pi$
$830$		0			0
$831$		0			0
$832$	18.9132	+	10.9196i	0.655698	+	0.378568i
$833$	−15.6950	−	9.06152i	−0.543800	−	0.313963i
$834$		0			0
$835$		0			0
$836$	−26.4621			−0.915210
$837$		0			0
$838$			60.2044i			2.07973i
$839$	6.11836	+	10.5973i	0.211229	+	0.365860i	0.952100	−	0.305788i	$-0.0989200\pi$
$839$	6.11836	+	10.5973i	0.211229	+	0.365860i	−0.740870	+	0.671648i	$0.765587\pi$
$840$		0			0
$841$	−12.6411	+	21.8951i	−0.435901	+	0.755003i
$842$	−40.9221	−	23.6264i	−1.41027	−	0.814218i
$843$		0			0
$844$	−59.0616	−	102.298i	−2.03299	−	3.52123i
$845$		0			0
$846$		0			0
$847$		−	13.8953i		−	0.477450i
$848$	−15.6836	+	9.05490i	−0.538575	+	0.310947i
$849$		0			0
$850$		0			0
$851$	−10.0872	+	17.4715i	−0.345785	+	0.598917i
$852$		0			0
$853$	14.2282	−	8.21464i	0.487164	−	0.281264i	−0.236233	−	0.971696i	$-0.575913\pi$
$853$	14.2282	−	8.21464i	0.487164	−	0.281264i	0.723397	+	0.690432i	$0.242580\pi$
$854$	59.9809			2.05250
$855$		0			0
$856$	−69.4255			−2.37291
$857$	42.5129	−	24.5449i	1.45221	−	0.838436i	0.453607	−	0.891202i	$-0.350137\pi$
$857$	42.5129	−	24.5449i	1.45221	−	0.838436i	0.998607	+	0.0527655i	$0.0168036\pi$
$858$		0			0
$859$	20.5454	−	35.5856i	0.700999	−	1.21417i	−0.267117	−	0.963664i	$-0.586071\pi$
$859$	20.5454	−	35.5856i	0.700999	−	1.21417i	0.968116	−	0.250502i	$-0.0805958\pi$
$860$		0			0
$861$		0			0
$862$	14.1157	−	8.14968i	0.480781	−	0.277579i
$863$		−	47.8366i		−	1.62838i	−0.580601	−	0.814188i	$-0.697183\pi$
$863$		−	47.8366i		−	1.62838i	0.580601	−	0.814188i	$-0.302817\pi$
$864$		0			0
$865$		0			0
$866$	−4.10605	−	7.11189i	−0.139529	−	0.241672i
$867$		0			0
$868$	−20.1560	−	11.6371i	−0.684138	−	0.394987i
$869$	−1.90838	+	3.30542i	−0.0647375	+	0.112129i
$870$		0			0
$871$	−8.97551	−	15.5460i	−0.304123	−	0.526757i
$872$		−	49.0458i		−	1.66090i
$873$		0			0
$874$	13.5387			0.457954
$875$		0			0
$876$		0			0
$877$	−9.85292	−	5.68859i	−0.332710	−	0.192090i	0.324334	−	0.945943i	$-0.394860\pi$
$877$	−9.85292	−	5.68859i	−0.332710	−	0.192090i	−0.657043	+	0.753853i	$0.728193\pi$
$878$	30.8143	+	17.7906i	1.03993	+	0.600405i
$879$		0			0
$880$		0			0
$881$	43.9924			1.48214			0.741071	−	0.671426i	$-0.234318\pi$
$881$	43.9924			1.48214			0.741071	+	0.671426i	$0.234318\pi$
$882$		0			0
$883$			37.6820i			1.26810i	0.773291	+	0.634051i	$0.218609\pi$
$883$			37.6820i			1.26810i	−0.773291	+	0.634051i	$0.781391\pi$
$884$	−23.4010	−	40.5317i	−0.787060	−	1.36323i
$885$		0			0
$886$	31.9699	−	55.3735i	1.07405	−	1.86031i
$887$	28.8241	+	16.6416i	0.967820	+	0.558771i	0.898571	−	0.438828i	$-0.144606\pi$
$887$	28.8241	+	16.6416i	0.967820	+	0.558771i	0.0692492	+	0.997599i	$0.477940\pi$
$888$		0			0
$889$	−3.25606	−	5.63967i	−0.109205	−	0.189148i
$890$		0			0
$891$		0			0
$892$		−	107.175i		−	3.58847i
$893$	−16.1548	+	9.32697i	−0.540599	+	0.312115i
$894$		0			0
$895$		0			0
$896$	−4.33040	+	7.50047i	−0.144669	+	0.250573i
$897$		0			0
$898$	−55.0686	+	31.7939i	−1.83766	+	1.06098i
$899$	19.3255			0.644543
$900$		0			0
$901$	8.29592			0.276377
$902$	−10.1720	+	5.87281i	−0.338691	+	0.195543i
$903$		0			0
$904$	−57.6276	+	99.8139i	−1.91667	+	3.31976i
$905$		0			0
$906$		0			0
$907$	12.1922	−	7.03918i	0.404836	−	0.233732i	−0.283733	−	0.958903i	$-0.591573\pi$
$907$	12.1922	−	7.03918i	0.404836	−	0.233732i	0.688568	+	0.725171i	$0.258239\pi$
$908$		−	69.6056i		−	2.30994i
$909$		0			0
$910$		0			0
$911$	3.65761	+	6.33517i	0.121182	+	0.209894i	0.920234	−	0.391368i	$-0.127998\pi$
$911$	3.65761	+	6.33517i	0.121182	+	0.209894i	−0.799052	+	0.601262i	$0.794665\pi$
$912$		0			0
$913$	−1.72064	−	0.993410i	−0.0569448	−	0.0328771i
$914$	3.71561	−	6.43563i	0.122902	−	0.212872i
$915$		0			0
$916$	−9.07719	−	15.7222i	−0.299919	−	0.519475i
$917$		−	13.1094i		−	0.432912i
$918$		0			0
$919$	−4.44684			−0.146688			−0.0733438	−	0.997307i	$-0.523367\pi$
$919$	−4.44684			−0.146688			−0.0733438	+	0.997307i	$0.523367\pi$
$920$		0			0
$921$		0			0
$922$	48.9412	+	28.2562i	1.61179	+	0.930569i
$923$	2.17658	+	1.25665i	0.0716430	+	0.0413631i
$924$		0			0
$925$		0			0
$926$	52.1565			1.71397
$927$		0			0
$928$		−	89.7068i		−	2.94477i
$929$	−6.55663	−	11.3564i	−0.215116	−	0.372592i	0.738192	−	0.674590i	$-0.235680\pi$
$929$	−6.55663	−	11.3564i	−0.215116	−	0.372592i	−0.953309	+	0.301998i	$0.902346\pi$
$930$		0			0
$931$	5.58730	−	9.67749i	0.183116	−	0.317167i
$932$	22.8362	+	13.1845i	0.748026	+	0.431873i
$933$		0			0
$934$	29.9204	+	51.8236i	0.979025	+	1.69572i
$935$		0			0
$936$		0			0
$937$			33.5187i			1.09501i	0.836803	+	0.547504i	$0.184422\pi$
$937$			33.5187i			1.09501i	−0.836803	+	0.547504i	$0.815578\pi$
$938$	37.3226	−	21.5482i	1.21863	−	0.703574i
$939$		0			0
$940$		0			0
$941$	0.895381	−	1.55085i	0.0291886	−	0.0505561i	−0.851062	−	0.525065i	$-0.824041\pi$
$941$	0.895381	−	1.55085i	0.0291886	−	0.0505561i	0.880251	+	0.474509i	$0.157374\pi$
$942$		0			0
$943$	3.70373	−	2.13835i	0.120610	−	0.0696342i
$944$	115.729			3.76667
$945$		0			0
$946$	−34.6592			−1.12687
$947$	−45.5832	+	26.3175i	−1.48126	+	0.855204i	−0.999774	−	0.0212525i	$-0.993235\pi$
$947$	−45.5832	+	26.3175i	−1.48126	+	0.855204i	−0.481482	+	0.876456i	$0.659901\pi$
$948$		0			0
$949$	−3.53716	+	6.12654i	−0.114821	+	0.198876i
$950$		0			0
$951$		0			0
$952$	57.8839	−	33.4193i	1.87603	−	1.08312i
$953$			18.4072i			0.596268i	0.954524	+	0.298134i	$0.0963642\pi$
$953$			18.4072i			0.596268i	−0.954524	+	0.298134i	$0.903636\pi$
$954$		0			0
$955$		0			0
$956$	−54.3841	−	94.1960i	−1.75891	−	3.04652i
$957$		0			0
$958$	−48.5551	−	28.0333i	−1.56874	−	0.905715i
$959$	−6.40442	+	11.0928i	−0.206810	+	0.358205i
$960$		0			0
$961$	12.0599	+	20.8883i	0.389028	+	0.673816i
$962$			60.4240i			1.94815i
$963$		0			0
$964$	92.0517			2.96479
$965$		0			0
$966$		0			0
$967$	−5.27911	−	3.04790i	−0.169765	−	0.0980137i	0.412710	−	0.910862i	$-0.364582\pi$
$967$	−5.27911	−	3.04790i	−0.169765	−	0.0980137i	−0.582475	+	0.812849i	$0.697916\pi$
$968$	−51.7784	−	29.8943i	−1.66422	−	0.960839i
$969$		0			0
$970$		0			0
$971$	34.1077			1.09457			0.547283	−	0.836947i	$-0.315662\pi$
$971$	34.1077			1.09457			0.547283	+	0.836947i	$0.315662\pi$
$972$		0			0
$973$			26.4414i			0.847671i
$974$	12.6246	+	21.8665i	0.404519	+	0.700648i
$975$		0			0
$976$	66.4945	−	115.172i	2.12844	−	3.68656i
$977$	−42.2546	−	24.3957i	−1.35184	−	0.780488i	−0.363337	−	0.931658i	$-0.618363\pi$
$977$	−42.2546	−	24.3957i	−1.35184	−	0.780488i	−0.988508	+	0.151170i	$0.951696\pi$
$978$		0			0
$979$	−12.0181	−	20.8160i	−0.384100	−	0.665281i
$980$		0			0
$981$		0			0
$982$			99.6715i			3.18065i
$983$	−28.9402	+	16.7086i	−0.923048	+	0.532922i	−0.884606	−	0.466339i	$-0.845573\pi$
$983$	−28.9402	+	16.7086i	−0.923048	+	0.532922i	−0.0384416	+	0.999261i	$0.512239\pi$
$984$		0			0
$985$		0			0
$986$	−46.6493	+	80.7989i	−1.48562	+	2.57316i
$987$		0			0
$988$	24.9917	−	14.4289i	0.795091	−	0.459046i
$989$	12.6198			0.401285
$990$		0			0
$991$	−19.3512			−0.614713			−0.307356	−	0.951595i	$-0.599444\pi$
$991$	−19.3512			−0.614713			−0.307356	+	0.951595i	$0.599444\pi$
$992$	−27.6586	+	15.9687i	−0.878161	+	0.507006i
$993$		0			0
$994$	−3.01694	+	5.22549i	−0.0956915	+	0.165743i
$995$		0			0
$996$		0			0
$997$	−34.2463	+	19.7721i	−1.08459	+	0.626189i	−0.932131	−	0.362121i	$-0.882053\pi$
$997$	−34.2463	+	19.7721i	−1.08459	+	0.626189i	−0.152460	+	0.988310i	$0.548719\pi$
$998$		−	44.5766i		−	1.41105i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.k.c.199.8		16
3.2	odd	2		225.2.k.c.49.1		16
5.2	odd	4		675.2.e.e.226.4		8
5.3	odd	4		675.2.e.c.226.1		8
5.4	even	2	inner	675.2.k.c.199.1		16
9.2	odd	6		225.2.k.c.124.8		16
9.4	even	3		2025.2.b.o.649.8		8
9.5	odd	6		2025.2.b.n.649.1		8
9.7	even	3	inner	675.2.k.c.424.1		16
15.2	even	4		225.2.e.c.76.1	✓	8
15.8	even	4		225.2.e.e.76.4	yes	8
15.14	odd	2		225.2.k.c.49.8		16
45.2	even	12		225.2.e.c.151.1	yes	8
45.4	even	6		2025.2.b.o.649.1		8
45.7	odd	12		675.2.e.e.451.4		8
45.13	odd	12		2025.2.a.z.1.4		4
45.14	odd	6		2025.2.b.n.649.8		8
45.22	odd	12		2025.2.a.p.1.1		4
45.23	even	12		2025.2.a.q.1.1		4
45.29	odd	6		225.2.k.c.124.1		16
45.32	even	12		2025.2.a.y.1.4		4
45.34	even	6	inner	675.2.k.c.424.8		16
45.38	even	12		225.2.e.e.151.4	yes	8
45.43	odd	12		675.2.e.c.451.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.e.c.76.1	✓	8	15.2	even	4
225.2.e.c.151.1	yes	8	45.2	even	12
225.2.e.e.76.4	yes	8	15.8	even	4
225.2.e.e.151.4	yes	8	45.38	even	12
225.2.k.c.49.1		16	3.2	odd	2
225.2.k.c.49.8		16	15.14	odd	2
225.2.k.c.124.1		16	45.29	odd	6
225.2.k.c.124.8		16	9.2	odd	6
675.2.e.c.226.1		8	5.3	odd	4
675.2.e.c.451.1		8	45.43	odd	12
675.2.e.e.226.4		8	5.2	odd	4
675.2.e.e.451.4		8	45.7	odd	12
675.2.k.c.199.1		16	5.4	even	2	inner
675.2.k.c.199.8		16	1.1	even	1	trivial
675.2.k.c.424.1		16	9.7	even	3	inner
675.2.k.c.424.8		16	45.34	even	6	inner
2025.2.a.p.1.1		4	45.22	odd	12
2025.2.a.q.1.1		4	45.23	even	12
2025.2.a.y.1.4		4	45.32	even	12
2025.2.a.z.1.4		4	45.13	odd	12
2025.2.b.n.649.1		8	9.5	odd	6
2025.2.b.n.649.8		8	45.14	odd	6
2025.2.b.o.649.1		8	45.4	even	6
2025.2.b.o.649.8		8	9.4	even	3

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.28087 - 1.31686i) q^{2} +(2.46825 - 4.27513i) q^{4} +(1.55662 - 0.898714i) q^{7} -7.73393i q^{8} +O(q^{10})\)	\(q+(2.28087 - 1.31686i) q^{2} +(2.46825 - 4.27513i) q^{4} +(1.55662 - 0.898714i) q^{7} -7.73393i q^{8} +(0.904062 + 1.56588i) q^{11} +(-1.70765 - 0.985914i) q^{13} +(2.36696 - 4.09970i) q^{14} +(-5.24801 - 9.08982i) q^{16} +4.80812i q^{17} -2.96467 q^{19} +(4.12410 + 2.38105i) q^{22} +(-1.50162 - 0.866963i) q^{23} -5.19325 q^{26} -8.87300i q^{28} +(3.68382 + 6.38057i) q^{29} +(1.31151 - 2.27161i) q^{31} +(-10.5445 - 6.08789i) q^{32} +(6.33163 + 10.9667i) q^{34} -11.6351i q^{37} +(-6.76203 + 3.90406i) q^{38} +(-1.23324 + 2.13603i) q^{41} +(-6.30306 + 3.63907i) q^{43} +8.92580 q^{44} -4.56668 q^{46} +(5.44910 - 3.14604i) q^{47} +(-1.88463 + 3.26427i) q^{49} +(-8.42983 + 4.86696i) q^{52} -1.72540i q^{53} +(-6.95059 - 12.0388i) q^{56} +(16.8047 + 9.70218i) q^{58} +(-5.51300 + 9.54880i) q^{59} +(6.33521 + 10.9729i) q^{61} -6.90833i q^{62} -11.0756 q^{64} +(7.88407 + 4.55187i) q^{67} +(20.5554 + 11.8676i) q^{68} -1.27460 q^{71} -3.58770i q^{73} +(-15.3218 - 26.5382i) q^{74} +(-7.31755 + 12.6744i) q^{76} +(2.81456 + 1.62499i) q^{77} +(1.05545 + 1.82809i) q^{79} +6.49602i q^{82} +(-0.951614 + 0.549415i) q^{83} +(-9.58431 + 16.6005i) q^{86} +(12.1104 - 6.99195i) q^{88} -13.2935 q^{89} -3.54422 q^{91} +(-7.41277 + 4.27976i) q^{92} +(8.28580 - 14.3514i) q^{94} +(3.31926 - 1.91638i) q^{97} +9.92718i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} - 2 q^{11} - 6 q^{14} - 8 q^{16} - 8 q^{19} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 18 q^{34} - 10 q^{41} + 88 q^{44} - 6 q^{49} - 60 q^{56} - 34 q^{59} + 26 q^{61} - 76 q^{64} + 32 q^{71} - 80 q^{74} - 22 q^{76} - 14 q^{79} - 68 q^{86} - 36 q^{89} - 68 q^{91} + 6 q^{94}+O(q^{100}) \) 16 * q + 8 * q^4 - 2 * q^11 - 6 * q^14 - 8 * q^16 - 8 * q^19 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 18 * q^34 - 10 * q^41 + 88 * q^44 - 6 * q^49 - 60 * q^56 - 34 * q^59 + 26 * q^61 - 76 * q^64 + 32 * q^71 - 80 * q^74 - 22 * q^76 - 14 * q^79 - 68 * q^86 - 36 * q^89 - 68 * q^91 + 6 * q^94

Introduction

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