LMFDB - Embedded newform 364.2.u.a.309.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [364,2,Mod(225,364)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(364, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("364.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 364 = 2^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	364.u (of order $6$, degree $2$, 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:	$2.90655463357$
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} + 38x^{14} + 587x^{12} + 4762x^{10} + 21849x^{8} + 56552x^{6} + 76456x^{4} + 42624x^{2} + 2704 $ x^16 + 38x^14 + 587x^12 + 4762x^10 + 21849x^8 + 56552x^6 + 76456x^4 + 42624*x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			309.1
Root			$3.23100i$ of defining polynomial
Character	$\chi$	$=$	364.309
Dual form			364.2.u.a.225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61550 - 2.79813i) q^{3} +3.14769i q^{5} +(0.866025 + 0.500000i) q^{7} +(-3.71968 + 6.44268i) q^{9} +(-3.33264 + 1.92410i) q^{11} +(1.38576 + 3.32861i) q^{13} +(8.80765 - 5.08510i) q^{15} +(0.0971843 - 0.168328i) q^{17} +(5.33141 + 3.07809i) q^{19} -3.23100i q^{21} +(-4.01081 - 6.94693i) q^{23} -4.90796 q^{25} +14.3436 q^{27} +(1.35952 + 2.35475i) q^{29} +8.51671i q^{31} +(10.7678 + 6.21677i) q^{33} +(-1.57385 + 2.72598i) q^{35} +(3.10928 - 1.79515i) q^{37} +(7.07520 - 9.25491i) q^{39} +(-3.44934 + 1.99148i) q^{41} +(-5.74755 + 9.95506i) q^{43} +(-20.2796 - 11.7084i) q^{45} -4.35126i q^{47} +(0.500000 + 0.866025i) q^{49} -0.628005 q^{51} -0.576803 q^{53} +(-6.05647 - 10.4901i) q^{55} -19.8906i q^{57} +(1.80715 + 1.04336i) q^{59} +(-1.70255 + 2.94891i) q^{61} +(-6.44268 + 3.71968i) q^{63} +(-10.4775 + 4.36194i) q^{65} +(4.69408 - 2.71013i) q^{67} +(-12.9589 + 22.4456i) q^{69} +(-7.92574 - 4.57593i) q^{71} -3.31209i q^{73} +(7.92882 + 13.7331i) q^{75} -3.84820 q^{77} -8.98752 q^{79} +(-12.0130 - 20.8072i) q^{81} +7.66353i q^{83} +(0.529845 + 0.305906i) q^{85} +(4.39260 - 7.60821i) q^{87} +(4.42996 - 2.55764i) q^{89} +(-0.464204 + 3.57554i) q^{91} +(23.8309 - 13.7588i) q^{93} +(-9.68888 + 16.7816i) q^{95} +(8.33696 + 4.81334i) q^{97} -28.6282i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 14 q^{9} + 6 q^{11} + 10 q^{13} + 6 q^{15} + 2 q^{17} - 44 q^{25} - 12 q^{27} - 22 q^{29} + 42 q^{33} - 6 q^{35} + 12 q^{37} + 24 q^{39} + 36 q^{41} + 6 q^{43} - 30 q^{45} + 8 q^{49} - 4 q^{51} + 8 q^{53}+ \cdots - 42 q^{97}+O(q^{100}) $ 16 * q - 14 * q^9 + 6 * q^11 + 10 * q^13 + 6 * q^15 + 2 * q^17 - 44 * q^25 - 12 * q^27 - 22 * q^29 + 42 * q^33 - 6 * q^35 + 12 * q^37 + 24 * q^39 + 36 * q^41 + 6 * q^43 - 30 * q^45 + 8 * q^49 - 4 * q^51 + 8 * q^53 + 2 * q^55 - 18 * q^59 + 4 * q^61 - 12 * q^63 - 30 * q^65 + 24 * q^67 - 52 * q^69 + 36 * q^71 - 10 * q^75 - 24 * q^77 + 8 * q^79 + 42 * q^85 + 26 * q^87 - 36 * q^89 - 2 * q^91 - 42 * q^93 - 30 * q^95 - 42 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/364\mathbb{Z}\right)^\times$.

$n$	$157$	$183$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.61550	−	2.79813i	−0.932710	−	1.61550i	−0.778668	−	0.627436i	$-0.784104\pi$
$3$	−1.61550	−	2.79813i	−0.932710	−	1.61550i	−0.154042	−	0.988064i	$-0.549229\pi$
$4$		0			0
$5$			3.14769i			1.40769i	0.710353	+	0.703845i	$0.248535\pi$
$5$			3.14769i			1.40769i	−0.710353	+	0.703845i	$0.751465\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		0			0
$9$	−3.71968	+	6.44268i	−1.23989	+	2.14756i
$10$		0			0
$11$	−3.33264	+	1.92410i	−1.00483	+	0.580138i	−0.909673	−	0.415324i	$-0.863668\pi$
$11$	−3.33264	+	1.92410i	−1.00483	+	0.580138i	−0.0951552	+	0.995462i	$0.530335\pi$
$12$		0			0
$13$	1.38576	+	3.32861i	0.384340	+	0.923191i
$13$	1.38576	+	3.32861i	0.384340	+	0.923191i
$14$		0			0
$15$	8.80765	−	5.08510i	2.27412	−	1.31297i
$16$		0			0
$17$	0.0971843	−	0.168328i	0.0235707	−	0.0408256i	−0.853999	−	0.520274i	$-0.825830\pi$
$17$	0.0971843	−	0.168328i	0.0235707	−	0.0408256i	0.877570	+	0.479448i	$0.159163\pi$
$18$		0			0
$19$	5.33141	+	3.07809i	1.22311	+	0.706162i	0.965579	−	0.260108i	$-0.0837583\pi$
$19$	5.33141	+	3.07809i	1.22311	+	0.706162i	0.257529	+	0.966271i	$0.417092\pi$
$20$		0			0
$21$		−	3.23100i		−	0.705062i
$22$		0			0
$23$	−4.01081	−	6.94693i	−0.836313	−	1.44854i	−0.892957	−	0.450141i	$-0.851374\pi$
$23$	−4.01081	−	6.94693i	−0.836313	−	1.44854i	0.0566448	−	0.998394i	$-0.481960\pi$
$24$		0			0
$25$	−4.90796			−0.981593
$26$		0			0
$27$	14.3436			2.76043
$28$		0			0
$29$	1.35952	+	2.35475i	0.252456	+	0.437267i	0.964201	−	0.265171i	$-0.0854283\pi$
$29$	1.35952	+	2.35475i	0.252456	+	0.437267i	−0.711745	+	0.702438i	$0.752095\pi$
$30$		0			0
$31$			8.51671i			1.52965i	0.644240	+	0.764823i	$0.277174\pi$
$31$			8.51671i			1.52965i	−0.644240	+	0.764823i	$0.722826\pi$
$32$		0			0
$33$	10.7678	+	6.21677i	1.87443	+	1.08220i
$34$		0			0
$35$	−1.57385	+	2.72598i	−0.266029	+	0.460775i
$36$		0			0
$37$	3.10928	−	1.79515i	0.511163	−	0.295120i	−0.222149	−	0.975013i	$-0.571307\pi$
$37$	3.10928	−	1.79515i	0.511163	−	0.295120i	0.733312	+	0.679893i	$0.237974\pi$
$38$		0			0
$39$	7.07520	−	9.25491i	1.13294	−	1.48197i
$40$		0			0
$41$	−3.44934	+	1.99148i	−0.538696	+	0.311016i	−0.744550	−	0.667566i	$-0.767336\pi$
$41$	−3.44934	+	1.99148i	−0.538696	+	0.311016i	0.205854	+	0.978583i	$0.434003\pi$
$42$		0			0
$43$	−5.74755	+	9.95506i	−0.876494	+	1.51813i	−0.0213310	+	0.999772i	$0.506790\pi$
$43$	−5.74755	+	9.95506i	−0.876494	+	1.51813i	−0.855163	+	0.518359i	$0.826543\pi$
$44$		0			0
$45$	−20.2796	−	11.7084i	−3.02310	−	1.74539i
$46$		0			0
$47$		−	4.35126i		−	0.634696i	−0.948309	−	0.317348i	$-0.897208\pi$
$47$		−	4.35126i		−	0.634696i	0.948309	−	0.317348i	$-0.102792\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	−0.628005			−0.0879383
$52$		0			0
$53$	−0.576803			−0.0792300			−0.0396150	−	0.999215i	$-0.512613\pi$
$53$	−0.576803			−0.0792300			−0.0396150	+	0.999215i	$0.512613\pi$
$54$		0			0
$55$	−6.05647	−	10.4901i	−0.816655	−	1.41449i
$56$		0			0
$57$		−	19.8906i		−	2.63458i
$58$		0			0
$59$	1.80715	+	1.04336i	0.235271	+	0.135834i	0.613002	−	0.790082i	$-0.289962\pi$
$59$	1.80715	+	1.04336i	0.235271	+	0.135834i	−0.377730	+	0.925916i	$0.623295\pi$
$60$		0			0
$61$	−1.70255	+	2.94891i	−0.217989	+	0.377569i	−0.954193	−	0.299191i	$-0.903283\pi$
$61$	−1.70255	+	2.94891i	−0.217989	+	0.377569i	0.736204	+	0.676760i	$0.236617\pi$
$62$		0			0
$63$	−6.44268	+	3.71968i	−0.811702	+	0.468636i
$64$		0			0
$65$	−10.4775	+	4.36194i	−1.29957	+	0.541032i
$66$		0			0
$67$	4.69408	−	2.71013i	0.573474	−	0.331095i	−0.185062	−	0.982727i	$-0.559249\pi$
$67$	4.69408	−	2.71013i	0.573474	−	0.331095i	0.758535	+	0.651632i	$0.225915\pi$
$68$		0			0
$69$	−12.9589	+	22.4456i	−1.56007	+	2.70213i
$70$		0			0
$71$	−7.92574	−	4.57593i	−0.940612	−	0.543063i	−0.0504599	−	0.998726i	$-0.516069\pi$
$71$	−7.92574	−	4.57593i	−0.940612	−	0.543063i	−0.890152	+	0.455663i	$0.849402\pi$
$72$		0			0
$73$		−	3.31209i		−	0.387650i	−0.981036	−	0.193825i	$-0.937911\pi$
$73$		−	3.31209i		−	0.387650i	0.981036	−	0.193825i	$-0.0620894\pi$
$74$		0			0
$75$	7.92882	+	13.7331i	0.915541	+	1.58576i
$76$		0			0
$77$	−3.84820			−0.438543
$78$		0			0
$79$	−8.98752			−1.01117			−0.505587	−	0.862775i	$-0.668724\pi$
$79$	−8.98752			−1.01117			−0.505587	+	0.862775i	$0.668724\pi$
$80$		0			0
$81$	−12.0130	−	20.8072i	−1.33478	−	2.31191i
$82$		0			0
$83$			7.66353i			0.841181i	0.907251	+	0.420591i	$0.138177\pi$
$83$			7.66353i			0.841181i	−0.907251	+	0.420591i	$0.861823\pi$
$84$		0			0
$85$	0.529845	+	0.305906i	0.0574698	+	0.0331802i
$86$		0			0
$87$	4.39260	−	7.60821i	0.470936	−	0.815686i
$88$		0			0
$89$	4.42996	−	2.55764i	0.469574	−	0.271109i	−0.246487	−	0.969146i	$-0.579276\pi$
$89$	4.42996	−	2.55764i	0.469574	−	0.271109i	0.716062	+	0.698037i	$0.245943\pi$
$90$		0			0
$91$	−0.464204	+	3.57554i	−0.0486618	+	0.374819i
$92$		0			0
$93$	23.8309	−	13.7588i	2.47114	−	1.42672i
$94$		0			0
$95$	−9.68888	+	16.7816i	−0.994058	+	1.72176i
$96$		0			0
$97$	8.33696	+	4.81334i	0.846490	+	0.488721i	0.859465	−	0.511195i	$-0.170797\pi$
$97$	8.33696	+	4.81334i	0.846490	+	0.488721i	−0.0129752	+	0.999916i	$0.504130\pi$
$98$		0			0
$99$		−	28.6282i		−	2.87724i
$100$		0			0
$101$	−1.27079	−	2.20107i	−0.126448	−	0.219015i	0.795850	−	0.605494i	$-0.207024\pi$
$101$	−1.27079	−	2.20107i	−0.126448	−	0.219015i	−0.922298	+	0.386479i	$0.873691\pi$
$102$		0			0
$103$	3.35392			0.330471			0.165236	−	0.986254i	$-0.447162\pi$
$103$	3.35392			0.330471			0.165236	+	0.986254i	$0.447162\pi$
$104$		0			0
$105$	10.1702			0.992510
$106$		0			0
$107$	6.45650	+	11.1830i	0.624174	+	1.08110i	0.988700	+	0.149907i	$0.0478975\pi$
$107$	6.45650	+	11.1830i	0.624174	+	1.08110i	−0.364526	+	0.931193i	$0.618769\pi$
$108$		0			0
$109$		−	8.04268i		−	0.770349i	−0.922844	−	0.385174i	$-0.874141\pi$
$109$		−	8.04268i		−	0.770349i	0.922844	−	0.385174i	$-0.125859\pi$
$110$		0			0
$111$	−10.0461	−	5.80012i	−0.953534	−	0.550523i
$112$		0			0
$113$	4.00235	−	6.93227i	0.376509	−	0.652133i	−0.614043	−	0.789273i	$-0.710458\pi$
$113$	4.00235	−	6.93227i	0.376509	−	0.652133i	0.990552	+	0.137140i	$0.0437910\pi$
$114$		0			0
$115$	21.8668	−	12.6248i	2.03909	−	1.17727i
$116$		0			0
$117$	−26.5998	−	3.45339i	−2.45915	−	0.319266i
$118$		0			0
$119$	0.168328	−	0.0971843i	0.0154306	−	0.00890887i
$120$		0			0
$121$	1.90432	−	3.29839i	0.173120	−	0.299853i
$122$		0			0
$123$	11.1448	+	6.43446i	1.00489	+	0.580176i
$124$		0			0
$125$			0.289701i			0.0259116i
$126$		0			0
$127$	0.664383	+	1.15075i	0.0589545	+	0.102112i	0.893996	−	0.448074i	$-0.147890\pi$
$127$	0.664383	+	1.15075i	0.0589545	+	0.102112i	−0.835042	+	0.550186i	$0.814557\pi$
$128$		0			0
$129$	37.1407			3.27006
$130$		0			0
$131$	−0.592761			−0.0517897			−0.0258949	−	0.999665i	$-0.508244\pi$
$131$	−0.592761			−0.0517897			−0.0258949	+	0.999665i	$0.508244\pi$
$132$		0			0
$133$	3.07809	+	5.33141i	0.266904	+	0.462292i
$134$		0			0
$135$			45.1492i			3.88583i
$136$		0			0
$137$	−2.21732	−	1.28017i	−0.189439	−	0.109372i	0.402281	−	0.915516i	$-0.368217\pi$
$137$	−2.21732	−	1.28017i	−0.189439	−	0.109372i	−0.591720	+	0.806144i	$0.701551\pi$
$138$		0			0
$139$	9.01150	−	15.6084i	0.764345	−	1.32388i	−0.176247	−	0.984346i	$-0.556396\pi$
$139$	9.01150	−	15.6084i	0.764345	−	1.32388i	0.940592	−	0.339538i	$-0.110271\pi$
$140$		0			0
$141$	−12.1754	+	7.02946i	−1.02535	+	0.591987i
$142$		0			0
$143$	−11.0228	−	8.42673i	−0.921775	−	0.704679i
$144$		0			0
$145$	−7.41204	+	4.27934i	−0.615536	+	0.355380i
$146$		0			0
$147$	1.61550	−	2.79813i	0.133244	−	0.230786i
$148$		0			0
$149$	7.02164	+	4.05394i	0.575235	+	0.332112i	0.759237	−	0.650814i	$-0.225572\pi$
$149$	7.02164	+	4.05394i	0.575235	+	0.332112i	−0.184002	+	0.982926i	$0.558905\pi$
$150$		0			0
$151$		−	3.58804i		−	0.291991i	−0.989285	−	0.145995i	$-0.953362\pi$
$151$		−	3.58804i		−	0.291991i	0.989285	−	0.145995i	$-0.0466385\pi$
$152$		0			0
$153$	0.722990	+	1.25226i	0.0584503	+	0.101239i
$154$		0			0
$155$	−26.8080			−2.15327
$156$		0			0
$157$	14.3447			1.14483			0.572417	−	0.819963i	$-0.306006\pi$
$157$	14.3447			1.14483			0.572417	+	0.819963i	$0.306006\pi$
$158$		0			0
$159$	0.931826	+	1.61397i	0.0738986	+	0.127996i
$160$		0			0
$161$		−	8.02163i		−	0.632193i
$162$		0			0
$163$	0.213164	+	0.123070i	0.0166963	+	0.00963961i	0.508325	−	0.861165i	$-0.330265\pi$
$163$	0.213164	+	0.123070i	0.0166963	+	0.00963961i	−0.491629	+	0.870805i	$0.663598\pi$
$164$		0			0
$165$	−19.5685	+	33.8936i	−1.52340	+	2.63861i
$166$		0			0
$167$	1.56604	−	0.904156i	0.121184	−	0.0699657i	−0.438183	−	0.898886i	$-0.644378\pi$
$167$	1.56604	−	0.904156i	0.121184	−	0.0699657i	0.559367	+	0.828920i	$0.311044\pi$
$168$		0			0
$169$	−9.15934	+	9.22532i	−0.704565	+	0.709640i
$170$		0			0
$171$	−39.6623	+	22.8990i	−3.03305	+	1.75113i
$172$		0			0
$173$	−5.39981	+	9.35275i	−0.410540	+	0.711076i	−0.994949	−	0.100383i	$-0.967993\pi$
$173$	−5.39981	+	9.35275i	−0.410540	+	0.711076i	0.584409	+	0.811459i	$0.301326\pi$
$174$		0			0
$175$	−4.25042	−	2.45398i	−0.321302	−	0.185504i
$176$		0			0
$177$		−	6.74220i		−	0.506775i
$178$		0			0
$179$	4.33823	+	7.51404i	0.324255	+	0.561626i	0.981361	−	0.192172i	$-0.0615532\pi$
$179$	4.33823	+	7.51404i	0.324255	+	0.561626i	−0.657106	+	0.753798i	$0.728220\pi$
$180$		0			0
$181$	−10.0087			−0.743940			−0.371970	−	0.928245i	$-0.621318\pi$
$181$	−10.0087			−0.743940			−0.371970	+	0.928245i	$0.621318\pi$
$182$		0			0
$183$	11.0019			0.813283
$184$		0			0
$185$	5.65057	+	9.78707i	0.415438	+	0.719559i
$186$		0			0
$187$			0.747970i			0.0546970i
$188$		0			0
$189$	12.4219	+	7.17180i	0.903562	+	0.521672i
$190$		0			0
$191$	12.0156	−	20.8117i	0.869420	−	1.50588i	0.00682903	−	0.999977i	$-0.497826\pi$
$191$	12.0156	−	20.8117i	0.869420	−	1.50588i	0.862591	−	0.505902i	$-0.168840\pi$
$192$		0			0
$193$	−2.83457	+	1.63654i	−0.204037	+	0.117801i	−0.598537	−	0.801095i	$-0.704251\pi$
$193$	−2.83457	+	1.63654i	−0.204037	+	0.117801i	0.394500	+	0.918896i	$0.370918\pi$
$194$		0			0
$195$	29.1316	+	22.2705i	2.08616	+	1.59483i
$196$		0			0
$197$	11.0439	−	6.37619i	0.786844	−	0.454285i	−0.0520061	−	0.998647i	$-0.516562\pi$
$197$	11.0439	−	6.37619i	0.786844	−	0.454285i	0.838850	+	0.544362i	$0.183228\pi$
$198$		0			0
$199$	13.6616	−	23.6625i	0.968442	−	1.67739i	0.268373	−	0.963315i	$-0.413514\pi$
$199$	13.6616	−	23.6625i	0.968442	−	1.67739i	0.700069	−	0.714076i	$-0.253153\pi$
$200$		0			0
$201$	−15.1666	−	8.75643i	−1.06977	−	0.617631i
$202$		0			0
$203$			2.71904i			0.190839i
$204$		0			0
$205$	−6.26855	−	10.8575i	−0.437815	−	0.758317i
$206$		0			0
$207$	59.6758			4.14776
$208$		0			0
$209$	−23.6902			−1.63869
$210$		0			0
$211$	−13.2929	−	23.0239i	−0.915118	−	1.58503i	−0.806728	−	0.590923i	$-0.798764\pi$
$211$	−13.2929	−	23.0239i	−0.915118	−	1.58503i	−0.108390	−	0.994108i	$-0.534570\pi$
$212$		0			0
$213$			29.5696i			2.02608i
$214$		0			0
$215$	−31.3355	−	18.0915i	−2.13706	−	1.23383i
$216$		0			0
$217$	−4.25836	+	7.37569i	−0.289076	+	0.500694i
$218$		0			0
$219$	−9.26764	+	5.35068i	−0.626249	+	0.361565i
$220$		0			0
$221$	0.694974	+	0.0902268i	0.0467490	+	0.00606931i
$222$		0			0
$223$	13.1063	−	7.56691i	0.877661	−	0.506718i	0.00777474	−	0.999970i	$-0.497525\pi$
$223$	13.1063	−	7.56691i	0.877661	−	0.506718i	0.869887	+	0.493252i	$0.164192\pi$
$224$		0			0
$225$	18.2561	−	31.6205i	1.21707	−	2.10803i
$226$		0			0
$227$	−18.5376	−	10.7027i	−1.23038	−	0.710362i	−0.263274	−	0.964721i	$-0.584802\pi$
$227$	−18.5376	−	10.7027i	−1.23038	−	0.710362i	−0.967110	+	0.254359i	$0.918136\pi$
$228$		0			0
$229$		−	8.36123i		−	0.552526i	−0.961082	−	0.276263i	$-0.910904\pi$
$229$		−	8.36123i		−	0.552526i	0.961082	−	0.276263i	$-0.0890961\pi$
$230$		0			0
$231$	6.21677	+	10.7678i	0.409033	+	0.708467i
$232$		0			0
$233$	26.1663			1.71421			0.857107	−	0.515138i	$-0.172260\pi$
$233$	26.1663			1.71421			0.857107	+	0.515138i	$0.172260\pi$
$234$		0			0
$235$	13.6964			0.893456
$236$		0			0
$237$	14.5193	+	25.1482i	0.943132	+	1.63355i
$238$		0			0
$239$			18.3562i			1.18736i	0.804700	+	0.593682i	$0.202326\pi$
$239$			18.3562i			1.18736i	−0.804700	+	0.593682i	$0.797674\pi$
$240$		0			0
$241$	−2.88804	−	1.66741i	−0.186035	−	0.107407i	0.404090	−	0.914719i	$-0.367588\pi$
$241$	−2.88804	−	1.66741i	−0.186035	−	0.107407i	−0.590125	+	0.807312i	$0.700922\pi$
$242$		0			0
$243$	−17.2988	+	29.9623i	−1.10972	+	1.92209i
$244$		0			0
$245$	−2.72598	+	1.57385i	−0.174157	+	0.100549i
$246$		0			0
$247$	−2.85772	+	22.0117i	−0.181833	+	1.40057i
$248$		0			0
$249$	21.4435	−	12.3804i	1.35893	−	0.784578i
$250$		0			0
$251$	−6.09884	+	10.5635i	−0.384956	+	0.666763i	−0.991763	−	0.128086i	$-0.959117\pi$
$251$	−6.09884	+	10.5635i	−0.384956	+	0.666763i	0.606807	+	0.794849i	$0.292450\pi$
$252$		0			0
$253$	26.7332	+	15.4344i	1.68070	+	0.970353i
$254$		0			0
$255$		−	1.97677i		−	0.123790i
$256$		0			0
$257$	7.63648	+	13.2268i	0.476350	+	0.825063i	0.999633	−	0.0270962i	$-0.00862605\pi$
$257$	7.63648	+	13.2268i	0.476350	+	0.825063i	−0.523282	+	0.852159i	$0.675293\pi$
$258$		0			0
$259$	3.59029			0.223090
$260$		0			0
$261$	−20.2279			−1.25208
$262$		0			0
$263$	−12.4495	−	21.5631i	−0.767666	−	1.32964i	−0.938825	−	0.344394i	$-0.888085\pi$
$263$	−12.4495	−	21.5631i	−0.767666	−	1.32964i	0.171159	−	0.985243i	$-0.445249\pi$
$264$		0			0
$265$		−	1.81560i		−	0.111531i
$266$		0			0
$267$	−14.3132	−	8.26373i	−0.875953	−	0.505732i
$268$		0			0
$269$	3.92836	−	6.80413i	0.239517	−	0.414855i	−0.721059	−	0.692874i	$-0.756344\pi$
$269$	3.92836	−	6.80413i	0.239517	−	0.414855i	0.960576	+	0.278019i	$0.0896777\pi$
$270$		0			0
$271$	2.28514	−	1.31933i	0.138812	−	0.0801433i	−0.428986	−	0.903311i	$-0.641129\pi$
$271$	2.28514	−	1.31933i	0.138812	−	0.0801433i	0.567798	+	0.823168i	$0.307796\pi$
$272$		0			0
$273$	10.7548	−	4.47739i	0.650907	−	0.270984i
$274$		0			0
$275$	16.3565	−	9.44342i	0.986333	−	0.569459i
$276$		0			0
$277$	5.82743	−	10.0934i	0.350136	−	0.606454i	−0.636137	−	0.771576i	$-0.719469\pi$
$277$	5.82743	−	10.0934i	0.350136	−	0.606454i	0.986273	+	0.165122i	$0.0528019\pi$
$278$		0			0
$279$	−54.8705	−	31.6795i	−3.28501	−	1.89660i
$280$		0			0
$281$			3.86501i			0.230567i	0.993333	+	0.115283i	$0.0367776\pi$
$281$			3.86501i			0.230567i	−0.993333	+	0.115283i	$0.963222\pi$
$282$		0			0
$283$	3.42431	+	5.93109i	0.203554	+	0.352566i	0.949671	−	0.313249i	$-0.101417\pi$
$283$	3.42431	+	5.93109i	0.203554	+	0.352566i	−0.746117	+	0.665815i	$0.768084\pi$
$284$		0			0
$285$	62.6095			3.70867
$286$		0			0
$287$	−3.98295			−0.235106
$288$		0			0
$289$	8.48111	+	14.6897i	0.498889	+	0.864101i
$290$		0			0
$291$		−	31.1038i		−	1.82334i
$292$		0			0
$293$	1.28946	+	0.744468i	0.0753309	+	0.0434923i	0.537192	−	0.843460i	$-0.319485\pi$
$293$	1.28946	+	0.744468i	0.0753309	+	0.0434923i	−0.461861	+	0.886952i	$0.652818\pi$
$294$		0			0
$295$	−3.28418	+	5.68836i	−0.191212	+	0.331189i
$296$		0			0
$297$	−47.8021	+	27.5985i	−2.77376	+	1.60143i
$298$		0			0
$299$	17.5656	−	22.9772i	1.01585	−	1.32881i
$300$		0			0
$301$	−9.95506	+	5.74755i	−0.573800	+	0.331284i
$302$		0			0
$303$	−4.10592	+	7.11166i	−0.235879	+	0.408554i
$304$		0			0
$305$	−9.28225	−	5.35911i	−0.531500	−	0.306862i
$306$		0			0
$307$			2.33128i			0.133053i	0.997785	+	0.0665265i	$0.0211917\pi$
$307$			2.33128i			0.133053i	−0.997785	+	0.0665265i	$0.978808\pi$
$308$		0			0
$309$	−5.41826	−	9.38470i	−0.308234	−	0.533877i
$310$		0			0
$311$	11.8244			0.670502			0.335251	−	0.942129i	$-0.391179\pi$
$311$	11.8244			0.670502			0.335251	+	0.942129i	$0.391179\pi$
$312$		0			0
$313$	−18.4087			−1.04052			−0.520260	−	0.854008i	$-0.674165\pi$
$313$	−18.4087			−1.04052			−0.520260	+	0.854008i	$0.674165\pi$
$314$		0			0
$315$	−11.7084	−	20.2796i	−0.659695	−	1.14262i
$316$		0			0
$317$		−	8.42274i		−	0.473068i	−0.971623	−	0.236534i	$-0.923988\pi$
$317$		−	8.42274i		−	0.473068i	0.971623	−	0.236534i	$-0.0760115\pi$
$318$		0			0
$319$	−9.06156	−	5.23170i	−0.507350	−	0.292919i
$320$		0			0
$321$	20.8610	−	36.1323i	1.16435	−	2.01671i
$322$		0			0
$323$	1.03626	−	0.598284i	0.0576590	−	0.0332894i
$324$		0			0
$325$	−6.80126	−	16.3367i	−0.377266	−	0.906198i
$326$		0			0
$327$	−22.5044	+	12.9929i	−1.24450	+	0.718512i
$328$		0			0
$329$	2.17563	−	3.76830i	0.119946	−	0.207753i
$330$		0			0
$331$	15.6375	+	9.02830i	0.859513	+	0.496240i	0.863849	−	0.503750i	$-0.168047\pi$
$331$	15.6375	+	9.02830i	0.859513	+	0.496240i	−0.00433587	+	0.999991i	$0.501380\pi$
$332$		0			0
$333$			26.7095i			1.46367i
$334$		0			0
$335$	8.53065	+	14.7755i	0.466079	+	0.807273i
$336$		0			0
$337$	−3.64765			−0.198700			−0.0993500	−	0.995053i	$-0.531676\pi$
$337$	−3.64765			−0.198700			−0.0993500	+	0.995053i	$0.531676\pi$
$338$		0			0
$339$	−25.8632			−1.40469
$340$		0			0
$341$	−16.3870	−	28.3831i	−0.887406	−	1.53703i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$	−70.6517	−	40.7908i	−3.80376	−	2.19610i
$346$		0			0
$347$	−7.29727	+	12.6392i	−0.391738	+	0.678510i	−0.992679	−	0.120783i	$-0.961459\pi$
$347$	−7.29727	+	12.6392i	−0.391738	+	0.678510i	0.600941	+	0.799294i	$0.294793\pi$
$348$		0			0
$349$	−15.4877	+	8.94182i	−0.829037	+	0.478645i	−0.853523	−	0.521056i	$-0.825538\pi$
$349$	−15.4877	+	8.94182i	−0.829037	+	0.478645i	0.0244861	+	0.999700i	$0.492205\pi$
$350$		0			0
$351$	19.8768	+	47.7443i	1.06094	+	2.54840i
$352$		0			0
$353$	5.52760	−	3.19136i	0.294204	−	0.169859i	−0.345632	−	0.938370i	$-0.612335\pi$
$353$	5.52760	−	3.19136i	0.294204	−	0.169859i	0.639836	+	0.768511i	$0.279002\pi$
$354$		0			0
$355$	14.4036	−	24.9478i	0.764464	−	1.32409i
$356$		0			0
$357$	−0.543869	−	0.314003i	−0.0287846	−	0.0166188i
$358$		0			0
$359$			30.4944i			1.60943i	0.593659	+	0.804717i	$0.297683\pi$
$359$			30.4944i			1.60943i	−0.593659	+	0.804717i	$0.702317\pi$
$360$		0			0
$361$	9.44927	+	16.3666i	0.497330	+	0.861400i
$362$		0			0
$363$	−12.3057			−0.645884
$364$		0			0
$365$	10.4254			0.545692
$366$		0			0
$367$	3.58169	+	6.20366i	0.186962	+	0.323829i	0.944236	−	0.329269i	$-0.106802\pi$
$367$	3.58169	+	6.20366i	0.186962	+	0.323829i	−0.757274	+	0.653098i	$0.773469\pi$
$368$		0			0
$369$		−	29.6306i		−	1.54251i
$370$		0			0
$371$	−0.499526	−	0.288402i	−0.0259341	−	0.0149731i
$372$		0			0
$373$	0.582337	−	1.00864i	0.0301523	−	0.0522252i	−0.850556	−	0.525885i	$-0.823734\pi$
$373$	0.582337	−	1.00864i	0.0301523	−	0.0522252i	0.880708	+	0.473660i	$0.157067\pi$
$374$		0			0
$375$	0.810620	−	0.468011i	0.0418602	−	0.0241680i
$376$		0			0
$377$	−5.95410	+	7.78843i	−0.306652	+	0.401125i
$378$		0			0
$379$	−25.1318	+	14.5099i	−1.29093	+	0.745322i	−0.978820	−	0.204723i	$-0.934371\pi$
$379$	−25.1318	+	14.5099i	−1.29093	+	0.745322i	−0.312115	+	0.950044i	$0.601037\pi$
$380$		0			0
$381$	2.14662	−	3.71806i	0.109975	−	0.190482i
$382$		0			0
$383$	19.0154	+	10.9786i	0.971642	+	0.560978i	0.899737	−	0.436433i	$-0.143759\pi$
$383$	19.0154	+	10.9786i	0.971642	+	0.560978i	0.0719059	+	0.997411i	$0.477092\pi$
$384$		0			0
$385$		−	12.1129i		−	0.617333i
$386$		0			0
$387$	−42.7582	−	74.0593i	−2.17352	−	3.76465i
$388$		0			0
$389$	−29.1973			−1.48036			−0.740180	−	0.672409i	$-0.765260\pi$
$389$	−29.1973			−1.48036			−0.740180	+	0.672409i	$0.765260\pi$
$390$		0			0
$391$	−1.55915			−0.0788498
$392$		0			0
$393$	0.957605	+	1.65862i	0.0483048	+	0.0836664i
$394$		0			0
$395$		−	28.2899i		−	1.42342i
$396$		0			0
$397$	27.6698	+	15.9752i	1.38871	+	0.801771i	0.993170	−	0.116679i	$-0.0372248\pi$
$397$	27.6698	+	15.9752i	1.38871	+	0.801771i	0.395538	+	0.918450i	$0.370558\pi$
$398$		0			0
$399$	9.94531	−	17.2258i	0.497888	−	0.862368i
$400$		0			0
$401$	31.9176	−	18.4276i	1.59389	−	0.920232i	0.601257	−	0.799056i	$-0.294667\pi$
$401$	31.9176	−	18.4276i	1.59389	−	0.920232i	0.992631	−	0.121176i	$-0.0386664\pi$
$402$		0			0
$403$	−28.3488	+	11.8021i	−1.41216	+	0.587905i
$404$		0			0
$405$	65.4947	−	37.8134i	3.25446	−	1.87896i
$406$		0			0
$407$	−6.90808	+	11.9651i	−0.342421	+	0.593090i
$408$		0			0
$409$	4.89732	+	2.82747i	0.242157	+	0.139809i	0.616168	−	0.787615i	$-0.288684\pi$
$409$	4.89732	+	2.82747i	0.242157	+	0.139809i	−0.374011	+	0.927424i	$0.622018\pi$
$410$		0			0
$411$			8.27247i			0.408051i
$412$		0			0
$413$	1.04336	+	1.80715i	0.0513404	+	0.0889242i
$414$		0			0
$415$	−24.1224			−1.18412
$416$		0			0
$417$	−58.2323			−2.85165
$418$		0			0
$419$	12.9031	+	22.3488i	0.630358	+	1.09181i	0.987478	+	0.157754i	$0.0504254\pi$
$419$	12.9031	+	22.3488i	0.630358	+	1.09181i	−0.357120	+	0.934059i	$0.616241\pi$
$420$		0			0
$421$			28.8606i			1.40658i	0.710903	+	0.703290i	$0.248286\pi$
$421$			28.8606i			1.40658i	−0.710903	+	0.703290i	$0.751714\pi$
$422$		0			0
$423$	28.0338	+	16.1853i	1.36305	+	0.786957i
$424$		0			0
$425$	−0.476977	+	0.826149i	−0.0231368	+	0.0400741i
$426$		0			0
$427$	−2.94891	+	1.70255i	−0.142708	+	0.0823923i
$428$		0			0
$429$	−5.77170	+	44.4567i	−0.278660	+	2.14639i
$430$		0			0
$431$	−27.4281	+	15.8356i	−1.32116	+	0.762774i	−0.983914	−	0.178641i	$-0.942830\pi$
$431$	−27.4281	+	15.8356i	−1.32116	+	0.762774i	−0.337249	+	0.941415i	$0.609496\pi$
$432$		0			0
$433$	15.6517	−	27.1095i	0.752172	−	1.30280i	−0.194597	−	0.980883i	$-0.562340\pi$
$433$	15.6517	−	27.1095i	0.752172	−	1.30280i	0.946768	−	0.321916i	$-0.104327\pi$
$434$		0			0
$435$	23.9483	+	13.8266i	1.14823	+	0.662933i
$436$		0			0
$437$		−	49.3826i		−	2.36229i
$438$		0			0
$439$	18.4786	+	32.0059i	0.881935	+	1.52756i	0.849187	+	0.528092i	$0.177093\pi$
$439$	18.4786	+	32.0059i	0.881935	+	1.52756i	0.0327479	+	0.999464i	$0.489574\pi$
$440$		0			0
$441$	−7.43937			−0.354256
$442$		0			0
$443$	28.2871			1.34396			0.671981	−	0.740568i	$-0.265444\pi$
$443$	28.2871			1.34396			0.671981	+	0.740568i	$0.265444\pi$
$444$		0			0
$445$	8.05065	+	13.9441i	0.381638	+	0.661016i
$446$		0			0
$447$		−	26.1966i		−	1.23906i
$448$		0			0
$449$	21.0690	+	12.1642i	0.994308	+	0.574064i	0.906559	−	0.422079i	$-0.138699\pi$
$449$	21.0690	+	12.1642i	0.994308	+	0.574064i	0.0877485	+	0.996143i	$0.472033\pi$
$450$		0			0
$451$	7.66360	−	13.2737i	0.360865	−	0.625036i
$452$		0			0
$453$	−10.0398	+	5.79649i	−0.471712	+	0.272343i
$454$		0			0
$455$	−11.2547	−	1.46117i	−0.527629	−	0.0685008i
$456$		0			0
$457$	−1.34199	+	0.774798i	−0.0627756	+	0.0362435i	−0.531059	−	0.847335i	$-0.678206\pi$
$457$	−1.34199	+	0.774798i	−0.0627756	+	0.0362435i	0.468284	+	0.883578i	$0.344873\pi$
$458$		0			0
$459$	1.39397	−	2.41443i	0.0650651	−	0.112696i
$460$		0			0
$461$	11.2195	+	6.47760i	0.522545	+	0.301692i	0.737975	−	0.674828i	$-0.235782\pi$
$461$	11.2195	+	6.47760i	0.522545	+	0.301692i	−0.215430	+	0.976519i	$0.569115\pi$
$462$		0			0
$463$		−	28.1690i		−	1.30912i	−0.756008	−	0.654562i	$-0.772853\pi$
$463$		−	28.1690i		−	1.30912i	0.756008	−	0.654562i	$-0.227147\pi$
$464$		0			0
$465$	43.3083	+	75.0122i	2.00837	+	3.47861i
$466$		0			0
$467$	−29.2908			−1.35542			−0.677709	−	0.735330i	$-0.737027\pi$
$467$	−29.2908			−1.35542			−0.677709	+	0.735330i	$0.737027\pi$
$468$		0			0
$469$	5.42026			0.250284
$470$		0			0
$471$	−23.1739	−	40.1384i	−1.06780	−	1.84948i
$472$		0			0
$473$		−	44.2355i		−	2.03395i
$474$		0			0
$475$	−26.1664	−	15.1072i	−1.20059	−	0.693164i
$476$		0			0
$477$	2.14553	−	3.71616i	0.0982369	−	0.170151i
$478$		0			0
$479$	−16.8625	+	9.73555i	−0.770466	+	0.444829i	−0.833041	−	0.553211i	$-0.813402\pi$
$479$	−16.8625	+	9.73555i	−0.770466	+	0.444829i	0.0625747	+	0.998040i	$0.480069\pi$
$480$		0			0
$481$	10.2841	+	7.86197i	0.468913	+	0.358475i
$482$		0			0
$483$	−22.4456	+	12.9589i	−1.02131	+	0.589652i
$484$		0			0
$485$	−15.1509	+	26.2422i	−0.687968	+	1.19160i
$486$		0			0
$487$	3.92783	+	2.26773i	0.177987	+	0.102761i	0.586346	−	0.810060i	$-0.300566\pi$
$487$	3.92783	+	2.26773i	0.177987	+	0.102761i	−0.408360	+	0.912821i	$0.633899\pi$
$488$		0			0
$489$		−	0.795281i		−	0.0359638i
$490$		0			0
$491$	9.07433	+	15.7172i	0.409519	+	0.709307i	0.994836	−	0.101497i	$-0.0323633\pi$
$491$	9.07433	+	15.7172i	0.409519	+	0.709307i	−0.585317	+	0.810804i	$0.699030\pi$
$492$		0			0
$493$	0.528495			0.0238022
$494$		0			0
$495$	90.1127			4.05026
$496$		0			0
$497$	−4.57593	−	7.92574i	−0.205258	−	0.355518i
$498$		0			0
$499$		−	6.65532i		−	0.297933i	−0.988842	−	0.148967i	$-0.952405\pi$
$499$		−	6.65532i		−	0.297933i	0.988842	−	0.148967i	$-0.0475947\pi$
$500$		0			0
$501$	−5.05989	−	2.92133i	−0.226059	−	0.130515i
$502$		0			0
$503$	−7.45978	+	12.9207i	−0.332615	+	0.576106i	−0.983024	−	0.183478i	$-0.941264\pi$
$503$	−7.45978	+	12.9207i	−0.332615	+	0.576106i	0.650409	+	0.759584i	$0.274598\pi$
$504$		0			0
$505$	6.92829	−	4.00005i	0.308305	−	0.178000i
$506$		0			0
$507$	40.6105	+	10.7255i	1.80358	+	0.476337i
$508$		0			0
$509$	−15.3869	+	8.88365i	−0.682014	+	0.393761i	−0.800613	−	0.599181i	$-0.795493\pi$
$509$	−15.3869	+	8.88365i	−0.682014	+	0.393761i	0.118599	+	0.992942i	$0.462160\pi$
$510$		0			0
$511$	1.65604	−	2.86835i	0.0732590	−	0.126888i
$512$		0			0
$513$	76.4716	+	44.1509i	3.37630	+	1.94931i
$514$		0			0
$515$			10.5571i			0.465201i
$516$		0			0
$517$	8.37226	+	14.5012i	0.368211	+	0.637761i
$518$		0			0
$519$	34.8936			1.53166
$520$		0			0
$521$	38.0579			1.66735			0.833673	−	0.552258i	$-0.186234\pi$
$521$	38.0579			1.66735			0.833673	+	0.552258i	$0.186234\pi$
$522$		0			0
$523$	−6.94526	−	12.0295i	−0.303695	−	0.526015i	0.673275	−	0.739392i	$-0.264887\pi$
$523$	−6.94526	−	12.0295i	−0.303695	−	0.526015i	−0.976970	+	0.213377i	$0.931554\pi$
$524$		0			0
$525$			15.8576i			0.692084i
$526$		0			0
$527$	1.43360	+	0.827691i	0.0624487	+	0.0360548i
$528$		0			0
$529$	−20.6733	+	35.8071i	−0.898837	+	1.55683i
$530$		0			0
$531$	−13.4441	+	7.76195i	−0.583424	+	0.336840i
$532$		0			0
$533$	−11.4088	−	8.72181i	−0.494170	−	0.377783i
$534$		0			0
$535$	−35.2006	+	20.3231i	−1.52185	+	0.878643i
$536$		0			0
$537$	14.0168	−	24.2779i	0.604871	−	1.04767i
$538$		0			0
$539$	−3.33264	−	1.92410i	−0.143547	−	0.0828769i
$540$		0			0
$541$		−	41.8453i		−	1.79907i	−0.436850	−	0.899535i	$-0.643906\pi$
$541$		−	41.8453i		−	1.79907i	0.436850	−	0.899535i	$-0.356094\pi$
$542$		0			0
$543$	16.1690	+	28.0056i	0.693880	+	1.20184i
$544$		0			0
$545$	25.3159			1.08441
$546$		0			0
$547$	−22.3475			−0.955509			−0.477754	−	0.878493i	$-0.658549\pi$
$547$	−22.3475			−0.955509			−0.477754	+	0.878493i	$0.658549\pi$
$548$		0			0
$549$	−12.6659	−	21.9380i	−0.540568	−	0.936291i
$550$		0			0
$551$			16.7389i			0.713100i
$552$		0			0
$553$	−7.78342	−	4.49376i	−0.330985	−	0.191094i
$554$		0			0
$555$	18.2570	−	31.6220i	0.774966	−	1.34228i
$556$		0			0
$557$	26.5499	−	15.3286i	1.12495	−	0.649493i	0.182293	−	0.983244i	$-0.441648\pi$
$557$	26.5499	−	15.3286i	1.12495	−	0.649493i	0.942661	+	0.333752i	$0.108315\pi$
$558$		0			0
$559$	−41.1013	−	5.33608i	−1.73840	−	0.225692i
$560$		0			0
$561$	2.09292	−	1.20835i	0.0883630	−	0.0510164i
$562$		0			0
$563$	−16.6237	+	28.7930i	−0.700604	+	1.21348i	0.267651	+	0.963516i	$0.413753\pi$
$563$	−16.6237	+	28.7930i	−0.700604	+	1.21348i	−0.968255	+	0.249966i	$0.919581\pi$
$564$		0			0
$565$	21.8206	+	12.5982i	0.918001	+	0.530008i
$566$		0			0
$567$		−	24.0261i		−	1.00900i
$568$		0			0
$569$	5.80511	+	10.0547i	0.243363	+	0.421517i	0.961670	−	0.274209i	$-0.0884161\pi$
$569$	5.80511	+	10.0547i	0.243363	+	0.421517i	−0.718307	+	0.695726i	$0.755083\pi$
$570$		0			0
$571$	16.6994			0.698847			0.349423	−	0.936965i	$-0.386377\pi$
$571$	16.6994			0.698847			0.349423	+	0.936965i	$0.386377\pi$
$572$		0			0
$573$	−77.6450			−3.24366
$574$		0			0
$575$	19.6849	+	34.0953i	0.820918	+	1.42187i
$576$		0			0
$577$		−	37.2583i		−	1.55108i	−0.631297	−	0.775541i	$-0.717477\pi$
$577$		−	37.2583i		−	1.55108i	0.631297	−	0.775541i	$-0.282523\pi$
$578$		0			0
$579$	9.15849	+	5.28765i	0.380614	+	0.219747i
$580$		0			0
$581$	−3.83176	+	6.63681i	−0.158968	+	0.275341i
$582$		0			0
$583$	1.92228	−	1.10983i	0.0796126	−	0.0459643i
$584$		0			0
$585$	10.8702	−	83.7279i	0.449427	−	3.46172i
$586$		0			0
$587$	36.1912	−	20.8950i	1.49377	−	0.862429i	0.493796	−	0.869578i	$-0.335609\pi$
$587$	36.1912	−	20.8950i	1.49377	−	0.862429i	0.999974	+	0.00714861i	$0.00227549\pi$
$588$		0			0
$589$	−26.2152	+	45.4061i	−1.08018	+	1.87092i
$590$		0			0
$591$	−35.6828	−	20.6015i	−1.46779	−	0.847432i
$592$		0			0
$593$		−	4.33672i		−	0.178088i	−0.996028	−	0.0890438i	$-0.971619\pi$
$593$		−	4.33672i		−	0.178088i	0.996028	−	0.0890438i	$-0.0283811\pi$
$594$		0			0
$595$	0.305906	+	0.529845i	0.0125409	+	0.0217215i
$596$		0			0
$597$	−88.2810			−3.61310
$598$		0			0
$599$	22.7578			0.929858			0.464929	−	0.885348i	$-0.346080\pi$
$599$	22.7578			0.929858			0.464929	+	0.885348i	$0.346080\pi$
$600$		0			0
$601$	13.7634	+	23.8389i	0.561421	+	0.972410i	0.997373	+	0.0724402i	$0.0230786\pi$
$601$	13.7634	+	23.8389i	0.561421	+	0.972410i	−0.435951	+	0.899970i	$0.643588\pi$
$602$		0			0
$603$			40.3233i			1.64209i
$604$		0			0
$605$	10.3823	+	5.99423i	0.422101	+	0.243700i
$606$		0			0
$607$	4.53483	−	7.85456i	0.184063	−	0.318807i	−0.759197	−	0.650861i	$-0.774408\pi$
$607$	4.53483	−	7.85456i	0.184063	−	0.318807i	0.943260	+	0.332054i	$0.107742\pi$
$608$		0			0
$609$	7.60821	−	4.39260i	0.308300	−	0.177997i
$610$		0			0
$611$	14.4837	−	6.02980i	0.585946	−	0.243939i
$612$		0			0
$613$	−8.12241	+	4.68947i	−0.328061	+	0.189406i	−0.654980	−	0.755646i	$-0.727323\pi$
$613$	−8.12241	+	4.68947i	−0.328061	+	0.189406i	0.326919	+	0.945052i	$0.393990\pi$
$614$		0			0
$615$	−20.2537	+	35.0804i	−0.816708	+	1.41458i
$616$		0			0
$617$	−26.0786	−	15.0565i	−1.04988	−	0.606151i	−0.127267	−	0.991869i	$-0.540620\pi$
$617$	−26.0786	−	15.0565i	−1.04988	−	0.606151i	−0.922617	+	0.385718i	$0.873954\pi$
$618$		0			0
$619$			39.8942i			1.60348i	0.597671	+	0.801742i	$0.296093\pi$
$619$			39.8942i			1.60348i	−0.597671	+	0.801742i	$0.703907\pi$
$620$		0			0
$621$	−57.5295	−	99.6441i	−2.30858	−	3.99858i
$622$		0			0
$623$	5.11527			0.204939
$624$		0			0
$625$	−25.4517			−1.01807
$626$		0			0
$627$	38.2715	+	66.2883i	1.52842	+	2.64730i
$628$		0			0
$629$		−	0.697840i		−	0.0278247i
$630$		0			0
$631$	−21.3804	−	12.3440i	−0.851140	−	0.491406i	0.00989522	−	0.999951i	$-0.496850\pi$
$631$	−21.3804	−	12.3440i	−0.851140	−	0.491406i	−0.861035	+	0.508545i	$0.830184\pi$
$632$		0			0
$633$	−42.9492	+	74.3903i	−1.70708	+	2.95675i
$634$		0			0
$635$	−3.62219	+	2.09127i	−0.143742	+	0.0829896i
$636$		0			0
$637$	−2.18978	+	2.86441i	−0.0867624	+	0.113492i
$638$		0			0
$639$	58.9625	−	34.0420i	2.33252	−	1.34668i
$640$		0			0
$641$	−9.30883	+	16.1234i	−0.367677	+	0.636834i	−0.989202	−	0.146560i	$-0.953180\pi$
$641$	−9.30883	+	16.1234i	−0.367677	+	0.636834i	0.621525	+	0.783394i	$0.286513\pi$
$642$		0			0
$643$	−27.4384	−	15.8415i	−1.08206	−	0.624729i	−0.150611	−	0.988593i	$-0.548124\pi$
$643$	−27.4384	−	15.8415i	−1.08206	−	0.624729i	−0.931452	+	0.363864i	$0.881457\pi$
$644$		0			0
$645$			116.908i			4.60323i
$646$		0			0
$647$	14.8291	+	25.6848i	0.582994	+	1.00977i	0.995122	+	0.0986488i	$0.0314521\pi$
$647$	14.8291	+	25.6848i	0.582994	+	1.00977i	−0.412129	+	0.911126i	$0.635215\pi$
$648$		0			0
$649$	−8.03013			−0.315210
$650$		0			0
$651$	27.5175			1.07850
$652$		0			0
$653$	−6.34483	−	10.9896i	−0.248292	−	0.430055i	0.714760	−	0.699370i	$-0.246536\pi$
$653$	−6.34483	−	10.9896i	−0.248292	−	0.430055i	−0.963052	+	0.269315i	$0.913203\pi$
$654$		0			0
$655$		−	1.86583i		−	0.0729039i
$656$		0			0
$657$	21.3387	+	12.3199i	0.832502	+	0.480645i
$658$		0			0
$659$	12.2763	−	21.2632i	0.478217	−	0.828296i	−0.521471	−	0.853269i	$-0.674617\pi$
$659$	12.2763	−	21.2632i	0.478217	−	0.828296i	0.999688	+	0.0249730i	$0.00794998\pi$
$660$		0			0
$661$	22.1333	−	12.7787i	0.860887	−	0.497033i	−0.00342228	−	0.999994i	$-0.501089\pi$
$661$	22.1333	−	12.7787i	0.860887	−	0.497033i	0.864309	+	0.502961i	$0.167756\pi$
$662$		0			0
$663$	−0.870264	−	2.09039i	−0.0337983	−	0.0811839i
$664$		0			0
$665$	−16.7816	+	9.68888i	−0.650764	+	0.375719i
$666$		0			0
$667$	10.9055	−	18.8890i	0.422264	−	0.731383i
$668$		0			0
$669$	−42.3464	−	24.4487i	−1.63721	−	0.945242i
$670$		0			0
$671$		−	13.1035i		−	0.505856i
$672$		0			0
$673$	−3.39829	−	5.88601i	−0.130994	−	0.226889i	0.793066	−	0.609136i	$-0.208484\pi$
$673$	−3.39829	−	5.88601i	−0.130994	−	0.226889i	−0.924060	+	0.382247i	$0.875150\pi$
$674$		0			0
$675$	−70.3979			−2.70962
$676$		0			0
$677$	−26.0956			−1.00294			−0.501468	−	0.865176i	$-0.667207\pi$
$677$	−26.0956			−1.00294			−0.501468	+	0.865176i	$0.667207\pi$
$678$		0			0
$679$	4.81334	+	8.33696i	0.184719	+	0.319943i
$680$		0			0
$681$			69.1608i			2.65025i
$682$		0			0
$683$	42.1666	+	24.3449i	1.61346	+	0.931532i	0.988560	+	0.150827i	$0.0481936\pi$
$683$	42.1666	+	24.3449i	1.61346	+	0.931532i	0.624900	+	0.780705i	$0.285140\pi$
$684$		0			0
$685$	4.02958	−	6.97944i	0.153962	−	0.266671i
$686$		0			0
$687$	−23.3958	+	13.5076i	−0.892606	+	0.515346i
$688$		0			0
$689$	−0.799310	−	1.91995i	−0.0304513	−	0.0731445i
$690$		0			0
$691$	−3.10942	+	1.79522i	−0.118288	+	0.0682935i	−0.557977	−	0.829857i	$-0.688422\pi$
$691$	−3.10942	+	1.79522i	−0.118288	+	0.0682935i	0.439689	+	0.898150i	$0.355089\pi$
$692$		0			0
$693$	14.3141	−	24.7927i	0.543747	−	0.941798i
$694$		0			0
$695$	49.1303	+	28.3654i	1.86362	+	1.07596i
$696$		0			0
$697$			0.774161i			0.0293234i
$698$		0			0
$699$	−42.2717	−	73.2168i	−1.59886	−	2.76931i
$700$		0			0
$701$	−15.8746			−0.599575			−0.299787	−	0.954006i	$-0.596916\pi$
$701$	−15.8746			−0.599575			−0.299787	+	0.954006i	$0.596916\pi$
$702$		0			0
$703$	22.1025			0.833611
$704$		0			0
$705$	−22.1266	−	38.3244i	−0.833335	−	1.44338i
$706$		0			0
$707$		−	2.54158i		−	0.0955858i
$708$		0			0
$709$	−19.6154	−	11.3250i	−0.736673	−	0.425318i	0.0841852	−	0.996450i	$-0.473171\pi$
$709$	−19.6154	−	11.3250i	−0.736673	−	0.425318i	−0.820858	+	0.571132i	$0.806505\pi$
$710$		0			0
$711$	33.4307	−	57.9037i	1.25375	−	2.17156i
$712$		0			0
$713$	59.1650	−	34.1589i	2.21575	−	1.27926i
$714$		0			0
$715$	26.5248	−	34.6965i	0.991969	−	1.29757i
$716$		0			0
$717$	51.3630	−	29.6544i	1.91819	−	1.10747i
$718$		0			0
$719$	5.12631	−	8.87903i	0.191179	−	0.331132i	−0.754462	−	0.656344i	$-0.772102\pi$
$719$	5.12631	−	8.87903i	0.191179	−	0.331132i	0.945641	+	0.325212i	$0.105436\pi$
$720$		0			0
$721$	2.90458	+	1.67696i	0.108172	+	0.0624532i
$722$		0			0
$723$			10.7748i			0.400719i
$724$		0			0
$725$	−6.67246	−	11.5570i	−0.247809	−	0.429218i
$726$		0			0
$727$	−5.60059			−0.207715			−0.103857	−	0.994592i	$-0.533119\pi$
$727$	−5.60059			−0.207715			−0.103857	+	0.994592i	$0.533119\pi$
$728$		0			0
$729$	39.7064			1.47061
$730$		0			0
$731$	1.11714	+	1.93495i	0.0413191	+	0.0715667i
$732$		0			0
$733$		−	41.1556i		−	1.52012i	−0.649855	−	0.760058i	$-0.725170\pi$
$733$		−	41.1556i		−	1.52012i	0.649855	−	0.760058i	$-0.274830\pi$
$734$		0			0
$735$	8.80765	+	5.08510i	0.324875	+	0.187567i
$736$		0			0
$737$	−10.4291	+	18.0638i	−0.384162	+	0.665388i
$738$		0			0
$739$	10.5196	−	6.07347i	0.386968	−	0.223416i	−0.293877	−	0.955843i	$-0.594946\pi$
$739$	10.5196	−	6.07347i	0.386968	−	0.223416i	0.680846	+	0.732427i	$0.261612\pi$
$740$		0			0
$741$	66.2082	−	27.5636i	2.43222	−	1.01257i
$742$		0			0
$743$	0.486744	−	0.281022i	0.0178569	−	0.0103097i	−0.491045	−	0.871134i	$-0.663385\pi$
$743$	0.486744	−	0.281022i	0.0178569	−	0.0103097i	0.508902	+	0.860825i	$0.330052\pi$
$744$		0			0
$745$	−12.7606	+	22.1020i	−0.467511	+	0.809753i
$746$		0			0
$747$	−49.3737	−	28.5059i	−1.80649	−	1.04298i
$748$		0			0
$749$			12.9130i			0.471831i
$750$		0			0
$751$	−11.3569	−	19.6707i	−0.414418	−	0.717794i	0.580949	−	0.813940i	$-0.302682\pi$
$751$	−11.3569	−	19.6707i	−0.414418	−	0.717794i	−0.995367	+	0.0961463i	$0.969348\pi$
$752$		0			0
$753$	39.4107			1.43621
$754$		0			0
$755$	11.2941			0.411033
$756$		0			0
$757$	−9.74099	−	16.8719i	−0.354042	−	0.613219i	0.632911	−	0.774224i	$-0.281860\pi$
$757$	−9.74099	−	16.8719i	−0.354042	−	0.613219i	−0.986954	+	0.161005i	$0.948526\pi$
$758$		0			0
$759$		−	99.7372i		−	3.62023i
$760$		0			0
$761$	37.0082	+	21.3667i	1.34155	+	0.774543i	0.987034	−	0.160509i	$-0.0513135\pi$
$761$	37.0082	+	21.3667i	1.34155	+	0.774543i	0.354513	+	0.935051i	$0.384647\pi$
$762$		0			0
$763$	4.02134	−	6.96516i	0.145582	−	0.252156i
$764$		0			0
$765$	−3.94171	+	2.27575i	−0.142513	+	0.0822799i
$766$		0			0
$767$	−0.968665	+	7.46117i	−0.0349765	+	0.269407i
$768$		0			0
$769$	−29.5477	+	17.0593i	−1.06552	+	0.615176i	−0.926953	−	0.375178i	$-0.877582\pi$
$769$	−29.5477	+	17.0593i	−1.06552	+	0.615176i	−0.138563	+	0.990354i	$0.544248\pi$
$770$		0			0
$771$	24.6735	−	42.7357i	0.888593	−	1.53909i
$772$		0			0
$773$	−25.0026	−	14.4353i	−0.899281	−	0.519200i	−0.0223144	−	0.999751i	$-0.507103\pi$
$773$	−25.0026	−	14.4353i	−0.899281	−	0.519200i	−0.876967	+	0.480551i	$0.840437\pi$
$774$		0			0
$775$		−	41.7997i		−	1.50149i
$776$		0			0
$777$	−5.80012	−	10.0461i	−0.208078	−	0.360402i
$778$		0			0
$779$	−24.5198			−0.878512
$780$		0			0
$781$	35.2182			1.26021
$782$		0			0
$783$	19.5004	+	33.7757i	0.696887	+	1.20704i
$784$		0			0
$785$			45.1528i			1.61157i
$786$		0			0
$787$	38.9448	+	22.4848i	1.38823	+	0.801497i	0.993116	−	0.117134i	$-0.0373706\pi$
$787$	38.9448	+	22.4848i	1.38823	+	0.801497i	0.395117	+	0.918631i	$0.370704\pi$
$788$		0			0
$789$	−40.2242	+	69.6704i	−1.43202	+	2.48033i
$790$		0			0
$791$	6.93227	−	4.00235i	0.246483	−	0.142307i
$792$		0			0
$793$	−12.1751	−	1.58066i	−0.432350	−	0.0561310i
$794$		0			0
$795$	−5.08028	+	2.93310i	−0.180179	+	0.104026i
$796$		0			0
$797$	−10.7092	+	18.5489i	−0.379340	+	0.657036i	−0.990966	−	0.134111i	$-0.957182\pi$
$797$	−10.7092	+	18.5489i	−0.379340	+	0.657036i	0.611627	+	0.791147i	$0.290515\pi$
$798$		0			0
$799$	−0.732440	−	0.422874i	−0.0259118	−	0.0149602i
$800$		0			0
$801$			38.0544i			1.34459i
$802$		0			0
$803$	6.37278	+	11.0380i	0.224891	+	0.389522i
$804$		0			0
$805$	25.2496			0.889932
$806$		0			0
$807$	−25.3851			−0.893598
$808$		0			0
$809$	4.12749	+	7.14902i	0.145115	+	0.251346i	0.929416	−	0.369034i	$-0.120312\pi$
$809$	4.12749	+	7.14902i	0.145115	+	0.251346i	−0.784301	+	0.620381i	$0.786978\pi$
$810$		0			0
$811$			43.7679i			1.53690i	0.639910	+	0.768450i	$0.278971\pi$
$811$			43.7679i			1.53690i	−0.639910	+	0.768450i	$0.721029\pi$
$812$		0			0
$813$	−7.38329	−	4.26274i	−0.258943	−	0.149501i
$814$		0			0
$815$	−0.387387	+	0.670975i	−0.0135696	+	0.0235032i
$816$		0			0
$817$	−61.2851	+	35.3830i	−2.14409	+	1.23789i
$818$		0			0
$819$	−21.3094	−	16.2906i	−0.744611	−	0.569240i
$820$		0			0
$821$	19.1465	−	11.0542i	0.668216	−	0.385795i	−0.127184	−	0.991879i	$-0.540594\pi$
$821$	19.1465	−	11.0542i	0.668216	−	0.385795i	0.795400	+	0.606084i	$0.207261\pi$
$822$		0			0
$823$	−21.0355	+	36.4346i	−0.733252	+	1.27003i	0.222234	+	0.974993i	$0.428665\pi$
$823$	−21.0355	+	36.4346i	−0.733252	+	1.27003i	−0.955486	+	0.295037i	$0.904668\pi$
$824$		0			0
$825$	−52.8478	−	30.5117i	−1.83992	−	1.06228i
$826$		0			0
$827$		−	44.4242i		−	1.54478i	−0.635148	−	0.772390i	$-0.719061\pi$
$827$		−	44.4242i		−	1.54478i	0.635148	−	0.772390i	$-0.280939\pi$
$828$		0			0
$829$	−8.97394	−	15.5433i	−0.311678	−	0.539842i	0.667048	−	0.745015i	$-0.267558\pi$
$829$	−8.97394	−	15.5433i	−0.311678	−	0.539842i	−0.978726	+	0.205173i	$0.934224\pi$
$830$		0			0
$831$	−37.6569			−1.30630
$832$		0			0
$833$	0.194369			0.00673448
$834$		0			0
$835$	2.84600	+	4.92942i	0.0984900	+	0.170590i
$836$		0			0
$837$			122.160i			4.22248i
$838$		0			0
$839$	3.09534	+	1.78709i	0.106863	+	0.0616973i	0.552479	−	0.833527i	$-0.313682\pi$
$839$	3.09534	+	1.78709i	0.106863	+	0.0616973i	−0.445616	+	0.895224i	$0.647015\pi$
$840$		0			0
$841$	10.8034	−	18.7121i	0.372532	−	0.645244i
$842$		0			0
$843$	10.8148	−	6.24392i	0.372481	−	0.215052i
$844$		0			0
$845$	−29.0385	−	28.8308i	−0.998953	−	0.991809i
$846$		0			0
$847$	3.29839	−	1.90432i	0.113334	−	0.0654334i
$848$		0			0
$849$	11.0640	−	19.1633i	0.379714	−	0.657684i
$850$		0			0
$851$	−24.9415	−	14.4000i	−0.854984	−	0.493625i
$852$		0			0
$853$			24.4780i			0.838111i	0.907961	+	0.419055i	$0.137639\pi$
$853$			24.4780i			0.838111i	−0.907961	+	0.419055i	$0.862361\pi$
$854$		0			0
$855$	−72.0791	−	124.845i	−2.46505	−	4.26960i
$856$		0			0
$857$	−26.9438			−0.920384			−0.460192	−	0.887820i	$-0.652219\pi$
$857$	−26.9438			−0.920384			−0.460192	+	0.887820i	$0.652219\pi$
$858$		0			0
$859$	−17.9537			−0.612573			−0.306287	−	0.951939i	$-0.599087\pi$
$859$	−17.9537			−0.612573			−0.306287	+	0.951939i	$0.599087\pi$
$860$		0			0
$861$	6.43446	+	11.1448i	0.219286	+	0.379814i
$862$		0			0
$863$			11.0841i			0.377308i	0.982044	+	0.188654i	$0.0604125\pi$
$863$			11.0841i			0.377308i	−0.982044	+	0.188654i	$0.939588\pi$
$864$		0			0
$865$	−29.4396	−	16.9969i	−1.00098	−	0.577913i
$866$		0			0
$867$	27.4025	−	47.4625i	0.930637	−	1.61191i
$868$		0			0
$869$	29.9521	−	17.2929i	1.01606	−	0.586621i
$870$		0			0
$871$	15.5258	+	11.8692i	0.526073	+	0.402173i
$872$		0			0
$873$	−62.0217	+	35.8082i	−2.09912	+	1.21193i
$874$		0			0
$875$	−0.144850	+	0.250888i	−0.00489683	+	0.00848156i
$876$		0			0
$877$	−3.99010	−	2.30368i	−0.134736	−	0.0777899i	0.431117	−	0.902296i	$-0.358120\pi$
$877$	−3.99010	−	2.30368i	−0.134736	−	0.0777899i	−0.565853	+	0.824506i	$0.691453\pi$
$878$		0			0
$879$		−	4.81075i		−	0.162263i
$880$		0			0
$881$	−17.1554	−	29.7140i	−0.577979	−	1.00109i	−0.995711	−	0.0925186i	$-0.970508\pi$
$881$	−17.1554	−	29.7140i	−0.577979	−	1.00109i	0.417732	−	0.908570i	$-0.362825\pi$
$882$		0			0
$883$	42.5926			1.43336			0.716678	−	0.697404i	$-0.245662\pi$
$883$	42.5926			1.43336			0.716678	+	0.697404i	$0.245662\pi$
$884$		0			0
$885$	21.2224			0.713382
$886$		0			0
$887$	−20.8026	−	36.0312i	−0.698483	−	1.20981i	−0.968992	−	0.247091i	$-0.920525\pi$
$887$	−20.8026	−	36.0312i	−0.698483	−	1.20981i	0.270509	−	0.962717i	$-0.412808\pi$
$888$		0			0
$889$			1.32877i			0.0445654i
$890$		0			0
$891$	80.0703	+	46.2286i	2.68246	+	1.54872i
$892$		0			0
$893$	13.3936	−	23.1983i	0.448198	−	0.776302i
$894$		0			0
$895$	−23.6519	+	13.6554i	−0.790595	+	0.456450i
$896$		0			0
$897$	−92.6706	−	12.0312i	−3.09418	−	0.401710i
$898$		0			0
$899$	−20.0548	+	11.5786i	−0.668864	+	0.386169i
$900$		0			0
$901$	−0.0560562	+	0.0970922i	−0.00186750	+	0.00323461i
$902$		0			0
$903$	32.1648	+	18.5704i	1.07038	+	0.617983i
$904$		0			0
$905$		−	31.5043i		−	1.04724i
$906$		0			0
$907$	7.83580	+	13.5720i	0.260183	+	0.450651i	0.966290	−	0.257454i	$-0.0828837\pi$
$907$	7.83580	+	13.5720i	0.260183	+	0.450651i	−0.706107	+	0.708105i	$0.749550\pi$
$908$		0			0
$909$	18.9077			0.627129
$910$		0			0
$911$	−33.5478			−1.11149			−0.555743	−	0.831354i	$-0.687566\pi$
$911$	−33.5478			−1.11149			−0.555743	+	0.831354i	$0.687566\pi$
$912$		0			0
$913$	−14.7454	−	25.5398i	−0.488001	−	0.845243i
$914$		0			0
$915$			34.6306i			1.14485i
$916$		0			0
$917$	−0.513346	−	0.296380i	−0.0169522	−	0.00978734i
$918$		0			0
$919$	−1.66880	+	2.89045i	−0.0550488	+	0.0953473i	−0.892237	−	0.451568i	$-0.850865\pi$
$919$	−1.66880	+	2.89045i	−0.0550488	+	0.0953473i	0.837188	+	0.546915i	$0.184198\pi$
$920$		0			0
$921$	6.52321	−	3.76618i	0.214947	−	0.124100i
$922$		0			0
$923$	4.24833	−	32.7229i	0.139835	−	1.07709i
$924$		0			0
$925$	−15.2603	+	8.81051i	−0.501754	+	0.289688i
$926$		0			0
$927$	−12.4755	+	21.6082i	−0.409750	+	0.709707i
$928$		0			0
$929$	7.87813	+	4.54844i	0.258473	+	0.149230i	0.623638	−	0.781713i	$-0.285654\pi$
$929$	7.87813	+	4.54844i	0.258473	+	0.149230i	−0.365165	+	0.930943i	$0.618987\pi$
$930$		0			0
$931$			6.15618i			0.201761i
$932$		0			0
$933$	−19.1024	−	33.0863i	−0.625384	−	1.08320i
$934$		0			0
$935$	−2.35438			−0.0769964
$936$		0			0
$937$	9.08442			0.296775			0.148388	−	0.988929i	$-0.452592\pi$
$937$	9.08442			0.296775			0.148388	+	0.988929i	$0.452592\pi$
$938$		0			0
$939$	29.7392	+	51.5099i	0.970504	+	1.68096i
$940$		0			0
$941$			8.23345i			0.268403i	0.990954	+	0.134201i	$0.0428469\pi$
$941$			8.23345i			0.268403i	−0.990954	+	0.134201i	$0.957153\pi$
$942$		0			0
$943$	27.6693	+	15.9749i	0.901036	+	0.520214i
$944$		0			0
$945$	−22.5746	+	39.1004i	−0.734353	+	1.27194i
$946$		0			0
$947$	4.37804	−	2.52766i	0.142267	−	0.0821380i	−0.427177	−	0.904168i	$-0.640492\pi$
$947$	4.37804	−	2.52766i	0.142267	−	0.0821380i	0.569444	+	0.822030i	$0.307159\pi$
$948$		0			0
$949$	11.0247	−	4.58975i	0.357875	−	0.148990i
$950$		0			0
$951$	−23.5679	+	13.6069i	−0.764242	+	0.441235i
$952$		0			0
$953$	19.6579	−	34.0485i	0.636782	−	1.10294i	−0.349352	−	0.936992i	$-0.613598\pi$
$953$	19.6579	−	34.0485i	0.636782	−	1.10294i	0.986135	−	0.165948i	$-0.0530684\pi$
$954$		0			0
$955$	65.5087	+	37.8215i	2.11981	+	1.22387i
$956$		0			0
$957$			33.8072i			1.09283i
$958$		0			0
$959$	−1.28017	−	2.21732i	−0.0413389	−	0.0716010i
$960$		0			0
$961$	−41.5344			−1.33982
$962$		0			0
$963$	−96.0646			−3.09564
$964$		0			0
$965$	−5.15132	−	8.92234i	−0.165827	−	0.287220i
$966$		0			0
$967$			21.2101i			0.682071i	0.940050	+	0.341036i	$0.110778\pi$
$967$			21.2101i			0.682071i	−0.940050	+	0.341036i	$0.889222\pi$
$968$		0			0
$969$	−3.34815	−	1.93306i	−0.107558	−	0.0620987i
$970$		0			0
$971$	11.7705	−	20.3871i	0.377733	−	0.654252i	−0.612999	−	0.790084i	$-0.710037\pi$
$971$	11.7705	−	20.3871i	0.377733	−	0.654252i	0.990732	+	0.135831i	$0.0433705\pi$
$972$		0			0
$973$	15.6084	−	9.01150i	0.500381	−	0.288895i
$974$		0			0
$975$	−34.7248	+	45.4228i	−1.11208	+	1.45469i
$976$		0			0
$977$	−10.7380	+	6.19958i	−0.343539	+	0.198342i	−0.661836	−	0.749649i	$-0.730222\pi$
$977$	−10.7380	+	6.19958i	−0.343539	+	0.198342i	0.318297	+	0.947991i	$0.396889\pi$
$978$		0			0
$979$	−9.84230	+	17.0474i	−0.314561	+	0.544836i
$980$		0			0
$981$	51.8164	+	29.9162i	1.65437	+	0.955151i
$982$		0			0
$983$		−	36.0862i		−	1.15097i	−0.817812	−	0.575486i	$-0.804813\pi$
$983$		−	36.0862i		−	1.15097i	0.817812	−	0.575486i	$-0.195187\pi$
$984$		0			0
$985$	20.0703	+	34.7628i	0.639492	+	1.10763i
$986$		0			0
$987$	−14.0589			−0.447500
$988$		0			0
$989$	92.2095			2.93209
$990$		0			0
$991$	−26.4245	−	45.7686i	−0.839403	−	1.45389i	−0.890395	−	0.455189i	$-0.849572\pi$
$991$	−26.4245	−	45.7686i	−0.839403	−	1.45389i	0.0509920	−	0.998699i	$-0.483762\pi$
$992$		0			0
$993$		−	58.3409i		−	1.85139i
$994$		0			0
$995$	74.4823	+	43.0024i	2.36125	+	1.36327i
$996$		0			0
$997$	−0.704139	+	1.21960i	−0.0223003	+	0.0386252i	−0.876960	−	0.480563i	$-0.840432\pi$
$997$	−0.704139	+	1.21960i	−0.0223003	+	0.0386252i	0.854660	+	0.519188i	$0.173766\pi$
$998$		0			0
$999$	44.5983	−	25.7489i	1.41103	−	0.814658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	364.2.u.a.309.1	yes	16
3.2	odd	2		3276.2.cf.c.1765.2		16
4.3	odd	2		1456.2.cc.f.673.8		16
7.2	even	3		2548.2.bq.e.361.8		16
7.3	odd	6		2548.2.bb.c.569.8		16
7.4	even	3		2548.2.bb.d.569.1		16
7.5	odd	6		2548.2.bq.c.361.1		16
7.6	odd	2		2548.2.u.c.1765.8		16
13.2	odd	12		4732.2.a.t.1.8		8
13.3	even	3		4732.2.g.k.337.16		16
13.4	even	6	inner	364.2.u.a.225.1	✓	16
13.10	even	6		4732.2.g.k.337.15		16
13.11	odd	12		4732.2.a.s.1.8		8
39.17	odd	6		3276.2.cf.c.2773.7		16
52.43	odd	6		1456.2.cc.f.225.8		16
91.4	even	6		2548.2.bq.e.1941.8		16
91.17	odd	6		2548.2.bq.c.1941.1		16
91.30	even	6		2548.2.bb.d.1733.1		16
91.69	odd	6		2548.2.u.c.589.8		16
91.82	odd	6		2548.2.bb.c.1733.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.u.a.225.1	✓	16	13.4	even	6	inner
364.2.u.a.309.1	yes	16	1.1	even	1	trivial
1456.2.cc.f.225.8		16	52.43	odd	6
1456.2.cc.f.673.8		16	4.3	odd	2
2548.2.u.c.589.8		16	91.69	odd	6
2548.2.u.c.1765.8		16	7.6	odd	2
2548.2.bb.c.569.8		16	7.3	odd	6
2548.2.bb.c.1733.8		16	91.82	odd	6
2548.2.bb.d.569.1		16	7.4	even	3
2548.2.bb.d.1733.1		16	91.30	even	6
2548.2.bq.c.361.1		16	7.5	odd	6
2548.2.bq.c.1941.1		16	91.17	odd	6
2548.2.bq.e.361.8		16	7.2	even	3
2548.2.bq.e.1941.8		16	91.4	even	6
3276.2.cf.c.1765.2		16	3.2	odd	2
3276.2.cf.c.2773.7		16	39.17	odd	6
4732.2.a.s.1.8		8	13.11	odd	12
4732.2.a.t.1.8		8	13.2	odd	12
4732.2.g.k.337.15		16	13.10	even	6
4732.2.g.k.337.16		16	13.3	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:	\( N \)	\(=\)	\( 364 = 2^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	364.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61550 - 2.79813i) q^{3} +3.14769i q^{5} +(0.866025 + 0.500000i) q^{7} +(-3.71968 + 6.44268i) q^{9} +(-3.33264 + 1.92410i) q^{11} +(1.38576 + 3.32861i) q^{13} +(8.80765 - 5.08510i) q^{15} +(0.0971843 - 0.168328i) q^{17} +(5.33141 + 3.07809i) q^{19} -3.23100i q^{21} +(-4.01081 - 6.94693i) q^{23} -4.90796 q^{25} +14.3436 q^{27} +(1.35952 + 2.35475i) q^{29} +8.51671i q^{31} +(10.7678 + 6.21677i) q^{33} +(-1.57385 + 2.72598i) q^{35} +(3.10928 - 1.79515i) q^{37} +(7.07520 - 9.25491i) q^{39} +(-3.44934 + 1.99148i) q^{41} +(-5.74755 + 9.95506i) q^{43} +(-20.2796 - 11.7084i) q^{45} -4.35126i q^{47} +(0.500000 + 0.866025i) q^{49} -0.628005 q^{51} -0.576803 q^{53} +(-6.05647 - 10.4901i) q^{55} -19.8906i q^{57} +(1.80715 + 1.04336i) q^{59} +(-1.70255 + 2.94891i) q^{61} +(-6.44268 + 3.71968i) q^{63} +(-10.4775 + 4.36194i) q^{65} +(4.69408 - 2.71013i) q^{67} +(-12.9589 + 22.4456i) q^{69} +(-7.92574 - 4.57593i) q^{71} -3.31209i q^{73} +(7.92882 + 13.7331i) q^{75} -3.84820 q^{77} -8.98752 q^{79} +(-12.0130 - 20.8072i) q^{81} +7.66353i q^{83} +(0.529845 + 0.305906i) q^{85} +(4.39260 - 7.60821i) q^{87} +(4.42996 - 2.55764i) q^{89} +(-0.464204 + 3.57554i) q^{91} +(23.8309 - 13.7588i) q^{93} +(-9.68888 + 16.7816i) q^{95} +(8.33696 + 4.81334i) q^{97} -28.6282i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 14 q^{9} + 6 q^{11} + 10 q^{13} + 6 q^{15} + 2 q^{17} - 44 q^{25} - 12 q^{27} - 22 q^{29} + 42 q^{33} - 6 q^{35} + 12 q^{37} + 24 q^{39} + 36 q^{41} + 6 q^{43} - 30 q^{45} + 8 q^{49} - 4 q^{51} + 8 q^{53}+ \cdots - 42 q^{97}+O(q^{100}) \) 16 * q - 14 * q^9 + 6 * q^11 + 10 * q^13 + 6 * q^15 + 2 * q^17 - 44 * q^25 - 12 * q^27 - 22 * q^29 + 42 * q^33 - 6 * q^35 + 12 * q^37 + 24 * q^39 + 36 * q^41 + 6 * q^43 - 30 * q^45 + 8 * q^49 - 4 * q^51 + 8 * q^53 + 2 * q^55 - 18 * q^59 + 4 * q^61 - 12 * q^63 - 30 * q^65 + 24 * q^67 - 52 * q^69 + 36 * q^71 - 10 * q^75 - 24 * q^77 + 8 * q^79 + 42 * q^85 + 26 * q^87 - 36 * q^89 - 2 * q^91 - 42 * q^93 - 30 * q^95 - 42 * q^97

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