LMFDB - Embedded newform 624.2.bz.g.335.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(95,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 3, 1]))

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

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

chi := DirichletCharacter("624.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.bz (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:	$4.98266508613$
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} - 3 x^{15} + 5 x^{14} - 6 x^{13} + 9 x^{12} + 3 x^{11} - 46 x^{10} + 141 x^{9} - 266 x^{8} + \cdots + 6561 $ x^16 - 3x^15 + 5x^14 - 6x^13 + 9x^12 + 3x^11 - 46x^10 + 141x^9 - 266x^8 + 423x^7 - 414x^6 + 81x^5 + 729x^4 - 1458x^3 + 3645x^2 - 6561*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			335.2
Root			$1.46152 + 0.929486i$ of defining polynomial
Character	$\chi$	$=$	624.335
Dual form			624.2.bz.g.95.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46152 - 0.929486i) q^{3} +1.88845 q^{5} +(-0.897962 + 1.55532i) q^{7} +(1.27211 + 2.71693i) q^{9} +O(q^{10})$	\(q+(-1.46152 - 0.929486i) q^{3} +1.88845 q^{5} +(-0.897962 + 1.55532i) q^{7} +(1.27211 + 2.71693i) q^{9} +(-2.56534 + 1.48110i) q^{11} +(-3.29809 + 1.45691i) q^{13} +(-2.76002 - 1.75529i) q^{15} +(2.00651 + 1.15846i) q^{17} +(-0.897962 + 1.55532i) q^{19} +(2.75804 - 1.43849i) q^{21} +(2.56534 + 4.44331i) q^{23} -1.43376 q^{25} +(0.666132 - 5.15328i) q^{27} +(1.08236 - 0.624903i) q^{29} -2.65910 q^{31} +(5.12598 + 0.219784i) q^{33} +(-1.69576 + 2.93714i) q^{35} +(-5.01497 + 2.89540i) q^{37} +(6.17442 + 0.936227i) q^{39} +(5.74408 + 9.94904i) q^{41} +(9.00651 + 5.19991i) q^{43} +(2.40232 + 5.13079i) q^{45} +0.667511i q^{47} +(1.88733 + 3.26895i) q^{49} +(-1.85579 - 3.55814i) q^{51} -3.67049i q^{53} +(-4.84452 + 2.79699i) q^{55} +(2.75804 - 1.43849i) q^{57} +(-3.14343 - 1.81486i) q^{59} +(-4.68542 + 8.11539i) q^{61} +(-5.36800 - 0.461171i) q^{63} +(-6.22828 + 2.75129i) q^{65} +(-0.306114 - 0.530205i) q^{67} +(0.380678 - 8.87846i) q^{69} +(8.23069 + 4.75199i) q^{71} -8.90142i q^{73} +(2.09547 + 1.33266i) q^{75} -5.31989i q^{77} +6.22126i q^{79} +(-5.76347 + 6.91248i) q^{81} -17.7231i q^{83} +(3.78919 + 2.18769i) q^{85} +(-2.16274 - 0.0927308i) q^{87} +(-2.75804 - 4.77706i) q^{89} +(0.695613 - 6.43782i) q^{91} +(3.88634 + 2.47160i) q^{93} +(-1.69576 + 2.93714i) q^{95} +(-9.54976 - 5.51356i) q^{97} +(-7.28746 - 5.08575i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{3} - 6 q^{7} - q^{9}+O(q^{10}) $ 16 * q - 3 * q^3 - 6 * q^7 - q^9	$ 16 q - 3 q^{3} - 6 q^{7} - q^{9} + 14 q^{13} + 6 q^{15} - 6 q^{19} + 28 q^{25} - 24 q^{31} + 9 q^{33} + 12 q^{37} + 27 q^{39} - 6 q^{43} + 30 q^{45} + 14 q^{49} + 24 q^{55} + 8 q^{61} + 21 q^{63} - 30 q^{67} + 9 q^{69} - 15 q^{75} - 13 q^{81} - 30 q^{85} + 39 q^{87} - 30 q^{91} - 72 q^{93} - 54 q^{97} - 42 q^{99}+O(q^{100}) $ 16 * q - 3 * q^3 - 6 * q^7 - q^9 + 14 * q^13 + 6 * q^15 - 6 * q^19 + 28 * q^25 - 24 * q^31 + 9 * q^33 + 12 * q^37 + 27 * q^39 - 6 * q^43 + 30 * q^45 + 14 * q^49 + 24 * q^55 + 8 * q^61 + 21 * q^63 - 30 * q^67 + 9 * q^69 - 15 * q^75 - 13 * q^81 - 30 * q^85 + 39 * q^87 - 30 * q^91 - 72 * q^93 - 54 * q^97 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.46152	−	0.929486i	−0.843812	−	0.536639i
$3$	−1.46152	−	0.929486i	−0.843812	−	0.536639i
$4$		0			0
$5$	1.88845			0.844540			0.422270	−	0.906470i	$-0.361233\pi$
$5$	1.88845			0.844540			0.422270	+	0.906470i	$0.361233\pi$
$6$		0			0
$7$	−0.897962	+	1.55532i	−0.339398	+	0.587854i	−0.984320	−	0.176394i	$-0.943557\pi$
$7$	−0.897962	+	1.55532i	−0.339398	+	0.587854i	0.644922	+	0.764249i	$0.276890\pi$
$8$		0			0
$9$	1.27211	+	2.71693i	0.424037	+	0.905645i
$10$		0			0
$11$	−2.56534	+	1.48110i	−0.773481	+	0.446569i	−0.834115	−	0.551591i	$-0.814021\pi$
$11$	−2.56534	+	1.48110i	−0.773481	+	0.446569i	0.0606343	+	0.998160i	$0.480688\pi$
$12$		0			0
$13$	−3.29809	+	1.45691i	−0.914727	+	0.404073i
$13$	−3.29809	+	1.45691i	−0.914727	+	0.404073i
$14$		0			0
$15$	−2.76002	−	1.75529i	−0.712633	−	0.453213i
$16$		0			0
$17$	2.00651	+	1.15846i	0.486650	+	0.280967i	0.723183	−	0.690656i	$-0.242678\pi$
$17$	2.00651	+	1.15846i	0.486650	+	0.280967i	−0.236534	+	0.971623i	$0.576011\pi$
$18$		0			0
$19$	−0.897962	+	1.55532i	−0.206007	+	0.356814i	−0.950453	−	0.310868i	$-0.899380\pi$
$19$	−0.897962	+	1.55532i	−0.206007	+	0.356814i	0.744446	+	0.667682i	$0.232714\pi$
$20$		0			0
$21$	2.75804	−	1.43849i	0.601853	−	0.313904i
$22$		0			0
$23$	2.56534	+	4.44331i	0.534911	+	0.926494i	0.999168	+	0.0407927i	$0.0129883\pi$
$23$	2.56534	+	4.44331i	0.534911	+	0.926494i	−0.464256	+	0.885701i	$0.653678\pi$
$24$		0			0
$25$	−1.43376			−0.286752
$26$		0			0
$27$	0.666132	−	5.15328i	0.128197	−	0.991749i
$28$		0			0
$29$	1.08236	−	0.624903i	0.200990	−	0.116041i	−0.396127	−	0.918196i	$-0.629646\pi$
$29$	1.08236	−	0.624903i	0.200990	−	0.116041i	0.597117	+	0.802154i	$0.296313\pi$
$30$		0			0
$31$	−2.65910			−0.477589			−0.238794	−	0.971070i	$-0.576752\pi$
$31$	−2.65910			−0.477589			−0.238794	+	0.971070i	$0.576752\pi$
$32$		0			0
$33$	5.12598	+	0.219784i	0.892319	+	0.0382596i
$34$		0			0
$35$	−1.69576	+	2.93714i	−0.286635	+	0.496466i
$36$		0			0
$37$	−5.01497	+	2.89540i	−0.824457	+	0.476000i	−0.851951	−	0.523622i	$-0.824581\pi$
$37$	−5.01497	+	2.89540i	−0.824457	+	0.476000i	0.0274943	+	0.999622i	$0.491247\pi$
$38$		0			0
$39$	6.17442	+	0.936227i	0.988699	+	0.149916i
$40$		0			0
$41$	5.74408	+	9.94904i	0.897075	+	1.55378i	0.831215	+	0.555950i	$0.187646\pi$
$41$	5.74408	+	9.94904i	0.897075	+	1.55378i	0.0658595	+	0.997829i	$0.479021\pi$
$42$		0			0
$43$	9.00651	+	5.19991i	1.37348	+	0.792979i	0.991364	−	0.131136i	$-0.0418623\pi$
$43$	9.00651	+	5.19991i	1.37348	+	0.792979i	0.382115	+	0.924115i	$0.375196\pi$
$44$		0			0
$45$	2.40232	+	5.13079i	0.358116	+	0.764854i
$46$		0			0
$47$			0.667511i			0.0973664i	0.998814	+	0.0486832i	$0.0155025\pi$
$47$			0.667511i			0.0973664i	−0.998814	+	0.0486832i	$0.984498\pi$
$48$		0			0
$49$	1.88733	+	3.26895i	0.269618	+	0.466993i
$50$		0			0
$51$	−1.85579	−	3.55814i	−0.259863	−	0.498239i
$52$		0			0
$53$		−	3.67049i		−	0.504181i	−0.967704	−	0.252090i	$-0.918882\pi$
$53$		−	3.67049i		−	0.504181i	0.967704	−	0.252090i	$-0.0811180\pi$
$54$		0			0
$55$	−4.84452	+	2.79699i	−0.653235	+	0.377146i
$56$		0			0
$57$	2.75804	−	1.43849i	0.365311	−	0.190533i
$58$		0			0
$59$	−3.14343	−	1.81486i	−0.409239	−	0.236274i	0.281224	−	0.959642i	$-0.409260\pi$
$59$	−3.14343	−	1.81486i	−0.409239	−	0.236274i	−0.690463	+	0.723368i	$0.742593\pi$
$60$		0			0
$61$	−4.68542	+	8.11539i	−0.599907	+	1.03907i	0.392927	+	0.919570i	$0.371462\pi$
$61$	−4.68542	+	8.11539i	−0.599907	+	1.03907i	−0.992834	+	0.119500i	$0.961871\pi$
$62$		0			0
$63$	−5.36800	−	0.461171i	−0.676304	−	0.0581020i
$64$		0			0
$65$	−6.22828	+	2.75129i	−0.772523	+	0.341256i
$66$		0			0
$67$	−0.306114	−	0.530205i	−0.0373978	−	0.0647749i	0.846721	−	0.532038i	$-0.178574\pi$
$67$	−0.306114	−	0.530205i	−0.0373978	−	0.0647749i	−0.884118	+	0.467263i	$0.845240\pi$
$68$		0			0
$69$	0.380678	−	8.87846i	0.0458282	−	1.06884i
$70$		0			0
$71$	8.23069	+	4.75199i	0.976804	+	0.563958i	0.901304	−	0.433188i	$-0.142611\pi$
$71$	8.23069	+	4.75199i	0.976804	+	0.563958i	0.0755000	+	0.997146i	$0.475945\pi$
$72$		0			0
$73$		−	8.90142i		−	1.04183i	−0.853608	−	0.520916i	$-0.825590\pi$
$73$		−	8.90142i		−	1.04183i	0.853608	−	0.520916i	$-0.174410\pi$
$74$		0			0
$75$	2.09547	+	1.33266i	0.241964	+	0.153882i
$76$		0			0
$77$		−	5.31989i		−	0.606258i
$78$		0			0
$79$			6.22126i			0.699947i	0.936760	+	0.349973i	$0.113809\pi$
$79$			6.22126i			0.699947i	−0.936760	+	0.349973i	$0.886191\pi$
$80$		0			0
$81$	−5.76347	+	6.91248i	−0.640386	+	0.768054i
$82$		0			0
$83$		−	17.7231i		−	1.94536i	−0.232146	−	0.972681i	$-0.574575\pi$
$83$		−	17.7231i		−	1.94536i	0.232146	−	0.972681i	$-0.425425\pi$
$84$		0			0
$85$	3.78919	+	2.18769i	0.410995	+	0.237288i
$86$		0			0
$87$	−2.16274	−	0.0927308i	−0.231870	−	0.00994179i
$88$		0			0
$89$	−2.75804	−	4.77706i	−0.292351	−	0.506368i	0.682014	−	0.731339i	$-0.261104\pi$
$89$	−2.75804	−	4.77706i	−0.292351	−	0.506368i	−0.974365	+	0.224972i	$0.927771\pi$
$90$		0			0
$91$	0.695613	−	6.43782i	0.0729200	−	0.674867i
$92$		0			0
$93$	3.88634	+	2.47160i	0.402995	+	0.256293i
$94$		0			0
$95$	−1.69576	+	2.93714i	−0.173981	+	0.301344i
$96$		0			0
$97$	−9.54976	−	5.51356i	−0.969631	−	0.559817i	−0.0705073	−	0.997511i	$-0.522462\pi$
$97$	−9.54976	−	5.51356i	−0.969631	−	0.559817i	−0.899124	+	0.437695i	$0.855795\pi$
$98$		0			0
$99$	−7.28746	−	5.08575i	−0.732417	−	0.511137i
$100$		0			0
$101$	10.6428	−	6.14460i	1.05899	−	0.611410i	0.133840	−	0.991003i	$-0.457269\pi$
$101$	10.6428	−	6.14460i	1.05899	−	0.611410i	0.925154	+	0.379593i	$0.123936\pi$
$102$		0			0
$103$			19.1044i			1.88242i	0.337829	+	0.941208i	$0.390308\pi$
$103$			19.1044i			1.88242i	−0.337829	+	0.941208i	$0.609692\pi$
$104$		0			0
$105$	5.20842	−	2.71651i	0.508289	−	0.265105i
$106$		0			0
$107$	−8.57676	−	14.8554i	−0.829146	−	1.43612i	−0.898709	−	0.438546i	$-0.855494\pi$
$107$	−8.57676	−	14.8554i	−0.829146	−	1.43612i	0.0695624	−	0.997578i	$-0.477840\pi$
$108$		0			0
$109$		−	12.2885i		−	1.17703i	−0.808487	−	0.588514i	$-0.799713\pi$
$109$		−	12.2885i		−	1.17703i	0.808487	−	0.588514i	$-0.200287\pi$
$110$		0			0
$111$	10.0207	+	0.429655i	0.951126	+	0.0407810i
$112$		0			0
$113$	−7.32579	−	4.22955i	−0.689153	−	0.397882i	0.114142	−	0.993464i	$-0.463588\pi$
$113$	−7.32579	−	4.22955i	−0.689153	−	0.397882i	−0.803295	+	0.595582i	$0.796921\pi$
$114$		0			0
$115$	4.84452	+	8.39096i	0.451754	+	0.782461i
$116$		0			0
$117$	−8.15386	−	7.10736i	−0.753825	−	0.657076i
$118$		0			0
$119$	−3.60353	+	2.08050i	−0.330335	+	0.190719i
$120$		0			0
$121$	−1.11267	+	1.92720i	−0.101152	+	0.175200i
$122$		0			0
$123$	0.852379	−	19.8798i	0.0768564	−	1.79250i
$124$		0			0
$125$	−12.1498			−1.08671
$126$		0			0
$127$	−3.54976	+	2.04945i	−0.314990	+	0.181860i	−0.649157	−	0.760654i	$-0.724878\pi$
$127$	−3.54976	+	2.04945i	−0.314990	+	0.181860i	0.334167	+	0.942514i	$0.391545\pi$
$128$		0			0
$129$	−8.32999	−	15.9712i	−0.733415	−	1.40619i
$130$		0			0
$131$	10.9535			0.957012			0.478506	−	0.878084i	$-0.341178\pi$
$131$	10.9535			0.957012			0.478506	+	0.878084i	$0.341178\pi$
$132$		0			0
$133$	−1.61267	−	2.79323i	−0.139836	−	0.242204i
$134$		0			0
$135$	1.25796	−	9.73170i	0.108268	−	0.837572i
$136$		0			0
$137$	5.35869	−	9.28153i	0.457824	−	0.792975i	−0.541022	−	0.841009i	$-0.681962\pi$
$137$	5.35869	−	9.28153i	0.457824	−	0.792975i	0.998846	+	0.0480340i	$0.0152956\pi$
$138$		0			0
$139$	−0.849362	−	0.490379i	−0.0720420	−	0.0415934i	0.463546	−	0.886073i	$-0.346577\pi$
$139$	−0.849362	−	0.490379i	−0.0720420	−	0.0415934i	−0.535588	+	0.844479i	$0.679910\pi$
$140$		0			0
$141$	0.620442	−	0.975584i	0.0522506	−	0.0821590i
$142$		0			0
$143$	6.30292	−	8.62228i	0.527077	−	0.721031i
$144$		0			0
$145$	2.04399	−	1.18010i	0.169744	−	0.0980017i
$146$		0			0
$147$	0.280065	−	6.53190i	0.0230994	−	0.538742i
$148$		0			0
$149$	−8.94290	+	15.4896i	−0.732631	+	1.26895i	0.223124	+	0.974790i	$0.428374\pi$
$149$	−8.94290	+	15.4896i	−0.732631	+	1.26895i	−0.955755	+	0.294164i	$0.904959\pi$
$150$		0			0
$151$	17.3036			1.40815			0.704073	−	0.710127i	$-0.251363\pi$
$151$	17.3036			1.40815			0.704073	+	0.710127i	$0.251363\pi$
$152$		0			0
$153$	−0.594955	+	6.92524i	−0.0480992	+	0.559872i
$154$		0			0
$155$	−5.02158			−0.403343
$156$		0			0
$157$	−7.04687			−0.562402			−0.281201	−	0.959649i	$-0.590733\pi$
$157$	−7.04687			−0.562402			−0.281201	+	0.959649i	$0.590733\pi$
$158$		0			0
$159$	−3.41167	+	5.36451i	−0.270563	+	0.425434i
$160$		0			0
$161$	−9.21433			−0.726191
$162$		0			0
$163$	−2.49154	+	4.31547i	−0.195152	+	0.338014i	−0.946950	−	0.321380i	$-0.895853\pi$
$163$	−2.49154	+	4.31547i	−0.195152	+	0.338014i	0.751798	+	0.659393i	$0.229187\pi$
$164$		0			0
$165$	9.68015	+	0.415052i	0.753599	+	0.0323117i
$166$		0			0
$167$	3.14343	−	1.81486i	0.243246	−	0.140438i	−0.373422	−	0.927662i	$-0.621816\pi$
$167$	3.14343	−	1.81486i	0.243246	−	0.140438i	0.616668	+	0.787224i	$0.288482\pi$
$168$		0			0
$169$	8.75485	−	9.61003i	0.673450	−	0.739233i
$170$		0			0
$171$	−5.36800	−	0.461171i	−0.410501	−	0.0352666i
$172$		0			0
$173$	−17.1424	−	9.89716i	−1.30331	−	0.752467i	−0.322340	−	0.946624i	$-0.604470\pi$
$173$	−17.1424	−	9.89716i	−1.30331	−	0.752467i	−0.980970	+	0.194157i	$0.937803\pi$
$174$		0			0
$175$	1.28746	−	2.22995i	0.0973229	−	0.168568i
$176$		0			0
$177$	2.90731	+	5.57423i	0.218527	+	0.418985i
$178$		0			0
$179$	6.64898	+	11.5164i	0.496968	+	0.860774i	0.999994	−	0.00349718i	$-0.00111319\pi$
$179$	6.64898	+	11.5164i	0.496968	+	0.860774i	−0.503026	+	0.864272i	$0.667780\pi$
$180$		0			0
$181$	11.9371			0.887277			0.443638	−	0.896206i	$-0.353687\pi$
$181$	11.9371			0.887277			0.443638	+	0.896206i	$0.353687\pi$
$182$		0			0
$183$	14.3910	−	7.50581i	1.06381	−	0.554845i
$184$		0			0
$185$	−9.47052	+	5.46781i	−0.696287	+	0.402001i
$186$		0			0
$187$	−6.86318			−0.501885
$188$		0			0
$189$	7.41681	+	5.66349i	0.539494	+	0.411958i
$190$		0			0
$191$	−10.2725	+	17.7925i	−0.743293	+	1.28742i	0.207695	+	0.978194i	$0.433404\pi$
$191$	−10.2725	+	17.7925i	−0.743293	+	1.28742i	−0.950988	+	0.309227i	$0.899930\pi$
$192$		0			0
$193$	−1.84090	+	1.06284i	−0.132511	+	0.0765051i	−0.564790	−	0.825235i	$-0.691043\pi$
$193$	−1.84090	+	1.06284i	−0.132511	+	0.0765051i	0.432279	+	0.901740i	$0.357709\pi$
$194$		0			0
$195$	11.6601	+	1.76802i	0.834996	+	0.126610i
$196$		0			0
$197$	11.5870	+	20.0692i	0.825538	+	1.42987i	0.901507	+	0.432764i	$0.142462\pi$
$197$	11.5870	+	20.0692i	0.825538	+	1.42987i	−0.0759694	+	0.997110i	$0.524205\pi$
$198$		0			0
$199$	−2.39428	−	1.38234i	−0.169726	−	0.0979914i	0.412731	−	0.910853i	$-0.364575\pi$
$199$	−2.39428	−	1.38234i	−0.169726	−	0.0979914i	−0.582457	+	0.812862i	$0.697908\pi$
$200$		0			0
$201$	−0.0454250	+	1.05944i	−0.00320404	+	0.0747269i
$202$		0			0
$203$			2.24455i			0.157537i
$204$		0			0
$205$	10.8474	+	18.7883i	0.757616	+	1.31223i
$206$		0			0
$207$	−8.80877	+	12.6223i	−0.612252	+	0.877307i
$208$		0			0
$209$		−	5.31989i		−	0.367985i
$210$		0			0
$211$	12.5498	−	7.24561i	0.863961	−	0.498808i	−0.00137575	−	0.999999i	$-0.500438\pi$
$211$	12.5498	−	7.24561i	0.863961	−	0.498808i	0.865337	+	0.501191i	$0.167105\pi$
$212$		0			0
$213$	−7.61245	−	14.5955i	−0.521597	−	1.00007i
$214$		0			0
$215$	17.0083	+	9.81977i	1.15996	+	0.669703i
$216$		0			0
$217$	2.38777	−	4.13574i	0.162092	−	0.280752i
$218$		0			0
$219$	−8.27375	+	13.0097i	−0.559088	+	0.879111i
$220$		0			0
$221$	−8.30541	−	0.897408i	−0.558683	−	0.0603662i
$222$		0			0
$223$	−5.36606	−	9.29429i	−0.359338	−	0.622392i	0.628512	−	0.777800i	$-0.283664\pi$
$223$	−5.36606	−	9.29429i	−0.359338	−	0.622392i	−0.987850	+	0.155408i	$0.950331\pi$
$224$		0			0
$225$	−1.82390	−	3.89543i	−0.121593	−	0.259695i
$226$		0			0
$227$	−3.60353	−	2.08050i	−0.239175	−	0.138088i	0.375623	−	0.926773i	$-0.377429\pi$
$227$	−3.60353	−	2.08050i	−0.239175	−	0.138088i	−0.614797	+	0.788685i	$0.710762\pi$
$228$		0			0
$229$			16.5809i			1.09570i	0.836577	+	0.547849i	$0.184553\pi$
$229$			16.5809i			1.09570i	−0.836577	+	0.547849i	$0.815447\pi$
$230$		0			0
$231$	−4.94477	+	7.77516i	−0.325342	+	0.511568i
$232$		0			0
$233$		−	13.9386i		−	0.913148i	−0.889685	−	0.456574i	$-0.849076\pi$
$233$		−	13.9386i		−	0.913148i	0.889685	−	0.456574i	$-0.150924\pi$
$234$		0			0
$235$			1.26056i			0.0822299i
$236$		0			0
$237$	5.78258	−	9.09253i	0.375619	−	0.590623i
$238$		0			0
$239$		−	7.69044i		−	0.497453i	−0.968574	−	0.248727i	$-0.919988\pi$
$239$		−	7.69044i		−	0.497453i	0.968574	−	0.248727i	$-0.0800121\pi$
$240$		0			0
$241$	−7.13083	−	4.11698i	−0.459337	−	0.265198i	0.252428	−	0.967616i	$-0.418771\pi$
$241$	−7.13083	−	4.11698i	−0.459337	−	0.265198i	−0.711765	+	0.702417i	$0.752104\pi$
$242$		0			0
$243$	14.8485	−	4.74570i	0.952533	−	0.304437i
$244$		0			0
$245$	3.56412	+	6.17325i	0.227704	+	0.394394i
$246$		0			0
$247$	0.695613	−	6.43782i	0.0442608	−	0.409629i
$248$		0			0
$249$	−16.4734	+	25.9027i	−1.04396	+	1.64152i
$250$		0			0
$251$	−2.79736	+	4.84517i	−0.176568	+	0.305825i	−0.940703	−	0.339232i	$-0.889833\pi$
$251$	−2.79736	+	4.84517i	−0.176568	+	0.305825i	0.764135	+	0.645057i	$0.223166\pi$
$252$		0			0
$253$	−13.1620	−	7.59908i	−0.827487	−	0.477750i
$254$		0			0
$255$	−3.50457	−	6.71936i	−0.219464	−	0.420783i
$256$		0			0
$257$	26.1005	−	15.0691i	1.62811	−	0.939987i	0.643447	−	0.765490i	$-0.277504\pi$
$257$	26.1005	−	15.0691i	1.62811	−	0.939987i	0.984658	−	0.174497i	$-0.0558298\pi$
$258$		0			0
$259$		−	10.3998i		−	0.646213i
$260$		0			0
$261$	3.07470	+	2.14576i	0.190319	+	0.132819i
$262$		0			0
$263$	0.0545556	+	0.0944930i	0.00336404	+	0.00582669i	0.867703	−	0.497084i	$-0.165596\pi$
$263$	0.0545556	+	0.0944930i	0.00336404	+	0.00582669i	−0.864338	+	0.502911i	$0.832263\pi$
$264$		0			0
$265$		−	6.93153i		−	0.425801i
$266$		0			0
$267$	−0.409272	+	9.54536i	−0.0250470	+	0.584166i
$268$		0			0
$269$	26.3567	+	15.2171i	1.60700	+	0.927800i	0.990037	+	0.140805i	$0.0449691\pi$
$269$	26.3567	+	15.2171i	1.60700	+	0.927800i	0.616959	+	0.786995i	$0.288364\pi$
$270$		0			0
$271$	−9.33433	−	16.1675i	−0.567020	−	0.982108i	−0.996859	−	0.0792022i	$-0.974763\pi$
$271$	−9.33433	−	16.1675i	−0.567020	−	0.982108i	0.429838	−	0.902906i	$-0.358571\pi$
$272$		0			0
$273$	−7.00052	+	8.76248i	−0.423691	+	0.530329i
$274$		0			0
$275$	3.67808	−	2.12354i	0.221797	−	0.128054i
$276$		0			0
$277$	−9.95764	+	17.2471i	−0.598296	+	1.03628i	0.394776	+	0.918777i	$0.370822\pi$
$277$	−9.95764	+	17.2471i	−0.598296	+	1.03628i	−0.993073	+	0.117503i	$0.962511\pi$
$278$		0			0
$279$	−3.38267	−	7.22460i	−0.202515	−	0.432526i
$280$		0			0
$281$	14.5507			0.868020			0.434010	−	0.900908i	$-0.357098\pi$
$281$	14.5507			0.868020			0.434010	+	0.900908i	$0.357098\pi$
$282$		0			0
$283$	0.682537	−	0.394063i	0.0405726	−	0.0234246i	−0.479576	−	0.877500i	$-0.659210\pi$
$283$	0.682537	−	0.394063i	0.0405726	−	0.0234246i	0.520149	+	0.854075i	$0.325876\pi$
$284$		0			0
$285$	5.20842	−	2.71651i	0.308520	−	0.160912i
$286$		0			0
$287$	−20.6319			−1.21786
$288$		0			0
$289$	−5.81595	−	10.0735i	−0.342115	−	0.592560i
$290$		0			0
$291$	8.83244	+	16.9346i	0.517767	+	0.992722i
$292$		0			0
$293$	6.28284	−	10.8822i	0.367047	−	0.635745i	−0.622055	−	0.782973i	$-0.713702\pi$
$293$	6.28284	−	10.8822i	0.367047	−	0.635745i	0.989102	+	0.147229i	$0.0470354\pi$
$294$		0			0
$295$	−5.93620	−	3.42727i	−0.345619	−	0.199543i
$296$		0			0
$297$	5.92367	+	14.2065i	0.343726	+	0.824347i
$298$		0			0
$299$	−14.9342	−	10.9170i	−0.863669	−	0.631345i
$300$		0			0
$301$	−16.1750	+	9.33864i	−0.932312	+	0.538270i
$302$		0			0
$303$	−21.2660	−	0.911812i	−1.22170	−	0.0523822i
$304$		0			0
$305$	−8.84818	+	15.3255i	−0.506646	+	0.877536i
$306$		0			0
$307$	−19.1125			−1.09081			−0.545405	−	0.838173i	$-0.683624\pi$
$307$	−19.1125			−1.09081			−0.545405	+	0.838173i	$0.683624\pi$
$308$		0			0
$309$	17.7573	−	27.9216i	1.01018	−	1.58840i
$310$		0			0
$311$	15.8882			0.900939			0.450470	−	0.892792i	$-0.351257\pi$
$311$	15.8882			0.900939			0.450470	+	0.892792i	$0.351257\pi$
$312$		0			0
$313$	21.4008			1.20964			0.604822	−	0.796361i	$-0.293244\pi$
$313$	21.4008			1.20964			0.604822	+	0.796361i	$0.293244\pi$
$314$		0			0
$315$	−10.1372	−	0.870897i	−0.571166	−	0.0490695i
$316$		0			0
$317$	0.504196			0.0283185			0.0141592	−	0.999900i	$-0.495493\pi$
$317$	0.504196			0.0283185			0.0141592	+	0.999900i	$0.495493\pi$
$318$		0			0
$319$	−1.85109	+	3.20618i	−0.103641	+	0.179512i
$320$		0			0
$321$	−1.27273	+	29.6835i	−0.0710366	+	1.65677i
$322$		0			0
$323$	−3.60353	+	2.08050i	−0.200506	+	0.115762i
$324$		0			0
$325$	4.72867	−	2.08885i	0.262299	−	0.115869i
$326$		0			0
$327$	−11.4220	+	17.9600i	−0.631639	+	0.993189i
$328$		0			0
$329$	−1.03819	−	0.599399i	−0.0572373	−	0.0330459i
$330$		0			0
$331$	−6.50846	+	11.2730i	−0.357737	+	0.619620i	−0.987582	−	0.157101i	$-0.949785\pi$
$331$	−6.50846	+	11.2730i	−0.357737	+	0.619620i	0.629845	+	0.776721i	$0.283118\pi$
$332$		0			0
$333$	−14.2462	−	9.94209i	−0.780687	−	0.544823i
$334$		0			0
$335$	−0.578081	−	1.00127i	−0.0315840	−	0.0547050i
$336$		0			0
$337$	20.0995			1.09489			0.547445	−	0.836842i	$-0.315600\pi$
$337$	20.0995			1.09489			0.547445	+	0.836842i	$0.315600\pi$
$338$		0			0
$339$	6.77552	+	12.9908i	0.367996	+	0.705564i
$340$		0			0
$341$	6.82151	−	3.93840i	0.369406	−	0.213276i
$342$		0			0
$343$	−19.3505			−1.04483
$344$		0			0
$345$	0.718891	−	16.7665i	0.0387038	−	0.902679i
$346$		0			0
$347$	−12.5898	+	21.8061i	−0.675854	+	1.17061i	0.300364	+	0.953825i	$0.402892\pi$
$347$	−12.5898	+	21.8061i	−0.675854	+	1.17061i	−0.976218	+	0.216789i	$0.930442\pi$
$348$		0			0
$349$	0.849362	−	0.490379i	0.0454653	−	0.0262494i	−0.477095	−	0.878852i	$-0.658310\pi$
$349$	0.849362	−	0.490379i	0.0454653	−	0.0262494i	0.522560	+	0.852602i	$0.324977\pi$
$350$		0			0
$351$	5.31088	+	17.9665i	0.283474	+	0.958980i
$352$		0			0
$353$	15.7300	+	27.2452i	0.837225	+	1.45012i	0.892206	+	0.451628i	$0.149157\pi$
$353$	15.7300	+	27.2452i	0.837225	+	1.45012i	−0.0549818	+	0.998487i	$0.517510\pi$
$354$		0			0
$355$	15.5432	+	8.97390i	0.824950	+	0.476285i
$356$		0			0
$357$	7.20045	+	0.308731i	0.381088	+	0.0163398i
$358$		0			0
$359$		−	18.3045i		−	0.966075i	−0.875600	−	0.483038i	$-0.839533\pi$
$359$		−	18.3045i		−	0.966075i	0.875600	−	0.483038i	$-0.160467\pi$
$360$		0			0
$361$	7.88733	+	13.6613i	0.415123	+	0.719013i
$362$		0			0
$363$	3.41751	−	1.78244i	0.179373	−	0.0935540i
$364$		0			0
$365$		−	16.8099i		−	0.879870i
$366$		0			0
$367$	21.6956	−	12.5259i	1.13250	−	0.653849i	0.187937	−	0.982181i	$-0.439820\pi$
$367$	21.6956	−	12.5259i	1.13250	−	0.653849i	0.944562	+	0.328333i	$0.106487\pi$
$368$		0			0
$369$	−19.7238	+	28.2626i	−1.02678	+	1.47129i
$370$		0			0
$371$	5.70877	+	3.29596i	0.296385	+	0.171118i
$372$		0			0
$373$	2.18209	−	3.77950i	0.112985	−	0.195695i	−0.803988	−	0.594646i	$-0.797292\pi$
$373$	2.18209	−	3.77950i	0.112985	−	0.195695i	0.916972	+	0.398951i	$0.130626\pi$
$374$		0			0
$375$	17.7573	+	11.2931i	0.916982	+	0.583173i
$376$		0			0
$377$	−2.65931	+	3.63789i	−0.136961	+	0.187361i
$378$		0			0
$379$	−18.3756	−	31.8275i	−0.943893	−	1.63487i	−0.757953	−	0.652309i	$-0.773801\pi$
$379$	−18.3756	−	31.8275i	−0.943893	−	1.63487i	−0.185939	−	0.982561i	$-0.559533\pi$
$380$		0			0
$381$	7.09300	+	0.304123i	0.363385	+	0.0155807i
$382$		0			0
$383$	−12.2486	−	7.07176i	−0.625876	−	0.361350i	0.153277	−	0.988183i	$-0.451017\pi$
$383$	−12.2486	−	7.07176i	−0.625876	−	0.361350i	−0.779153	+	0.626833i	$0.784351\pi$
$384$		0			0
$385$		−	10.0464i		−	0.512009i
$386$		0			0
$387$	−2.67054	+	31.0850i	−0.135751	+	1.58014i
$388$		0			0
$389$			10.8039i			0.547781i	0.961761	+	0.273891i	$0.0883106\pi$
$389$			10.8039i			0.547781i	−0.961761	+	0.273891i	$0.911689\pi$
$390$		0			0
$391$			11.8874i			0.601170i
$392$		0			0
$393$	−16.0088	−	10.1811i	−0.807538	−	0.513570i
$394$		0			0
$395$			11.7485i			0.591133i
$396$		0			0
$397$	18.7928	+	10.8500i	0.943184	+	0.544548i	0.890957	−	0.454088i	$-0.150035\pi$
$397$	18.7928	+	10.8500i	0.943184	+	0.544548i	0.0522272	+	0.998635i	$0.483368\pi$
$398$		0			0
$399$	−0.239308	+	5.58133i	−0.0119804	+	0.279416i
$400$		0			0
$401$	14.1170	+	24.4514i	0.704970	+	1.22104i	0.966702	+	0.255903i	$0.0823728\pi$
$401$	14.1170	+	24.4514i	0.704970	+	1.22104i	−0.261733	+	0.965140i	$0.584294\pi$
$402$		0			0
$403$	8.76997	−	3.87406i	0.436863	−	0.192981i
$404$		0			0
$405$	−10.8840	+	13.0539i	−0.540831	+	0.648652i
$406$		0			0
$407$	8.57676	−	14.8554i	0.425134	−	0.736354i
$408$		0			0
$409$	5.32242	+	3.07290i	0.263177	+	0.151945i	0.625783	−	0.779997i	$-0.284780\pi$
$409$	5.32242	+	3.07290i	0.263177	+	0.151945i	−0.362606	+	0.931942i	$0.618113\pi$
$410$		0			0
$411$	−16.4589	+	8.58436i	−0.811859	+	0.423435i
$412$		0			0
$413$	5.64535	−	3.25935i	0.277790	−	0.160382i
$414$		0			0
$415$		−	33.4692i		−	1.64294i
$416$		0			0
$417$	0.785563	+	1.50617i	0.0384692	+	0.0737576i
$418$		0			0
$419$	2.79736	+	4.84517i	0.136660	+	0.236702i	0.926230	−	0.376958i	$-0.123030\pi$
$419$	2.79736	+	4.84517i	0.136660	+	0.236702i	−0.789570	+	0.613660i	$0.789697\pi$
$420$		0			0
$421$			19.6161i			0.956029i	0.878352	+	0.478015i	$0.158643\pi$
$421$			19.6161i			0.956029i	−0.878352	+	0.478015i	$0.841357\pi$
$422$		0			0
$423$	−1.81358	+	0.849147i	−0.0881794	+	0.0412870i
$424$		0			0
$425$	−2.87685	−	1.66095i	−0.139548	−	0.0805678i
$426$		0			0
$427$	−8.41466	−	14.5746i	−0.407214	−	0.705315i
$428$		0			0
$429$	−17.2262	+	6.74320i	−0.831687	+	0.325565i
$430$		0			0
$431$	−34.8355	+	20.1123i	−1.67797	+	0.968774i	−0.715011	+	0.699113i	$0.753578\pi$
$431$	−34.8355	+	20.1123i	−1.67797	+	0.968774i	−0.962955	+	0.269661i	$0.913088\pi$
$432$		0			0
$433$	11.2473	−	19.4808i	0.540509	−	0.936189i	−0.458366	−	0.888764i	$-0.651565\pi$
$433$	11.2473	−	19.4808i	0.540509	−	0.936189i	0.998875	−	0.0474257i	$-0.0151017\pi$
$434$		0			0
$435$	−4.08422	−	0.175117i	−0.195823	−	0.00839624i
$436$		0			0
$437$	−9.21433			−0.440781
$438$		0			0
$439$	19.4694	−	11.2407i	0.929225	−	0.536488i	0.0426587	−	0.999090i	$-0.486417\pi$
$439$	19.4694	−	11.2407i	0.929225	−	0.536488i	0.886566	+	0.462601i	$0.153084\pi$
$440$		0			0
$441$	−6.48063	+	9.28621i	−0.308601	+	0.442201i
$442$		0			0
$443$	24.1424			1.14704			0.573519	−	0.819192i	$-0.305578\pi$
$443$	24.1424			1.14704			0.573519	+	0.819192i	$0.305578\pi$
$444$		0			0
$445$	−5.20842	−	9.02124i	−0.246903	−	0.427648i
$446$		0			0
$447$	27.4676	−	14.3261i	1.29917	−	0.677600i
$448$		0			0
$449$	16.8669	−	29.2144i	0.796000	−	1.37871i	−0.126202	−	0.992005i	$-0.540279\pi$
$449$	16.8669	−	29.2144i	0.796000	−	1.37871i	0.922202	−	0.386708i	$-0.126388\pi$
$450$		0			0
$451$	−29.4711	−	17.0151i	−1.38774	−	0.801212i
$452$		0			0
$453$	−25.2896	−	16.0835i	−1.18821	−	0.755666i
$454$		0			0
$455$	1.31363	−	12.1575i	0.0615839	−	0.569953i
$456$		0			0
$457$	−15.7957	+	9.11965i	−0.738892	+	0.426599i	−0.821666	−	0.569969i	$-0.806955\pi$
$457$	−15.7957	+	9.11965i	−0.738892	+	0.426599i	0.0827746	+	0.996568i	$0.473622\pi$
$458$		0			0
$459$	7.30645	−	9.56840i	0.341036	−	0.446615i
$460$		0			0
$461$	−4.04833	+	7.01191i	−0.188549	+	0.326577i	−0.944767	−	0.327743i	$-0.893712\pi$
$461$	−4.04833	+	7.01191i	−0.188549	+	0.326577i	0.756217	+	0.654320i	$0.227045\pi$
$462$		0			0
$463$	41.2470			1.91691			0.958456	−	0.285239i	$-0.0920731\pi$
$463$	41.2470			1.91691			0.958456	+	0.285239i	$0.0920731\pi$
$464$		0			0
$465$	7.33916	+	4.66749i	0.340345	+	0.216450i
$466$		0			0
$467$	38.7233			1.79190			0.895951	−	0.444153i	$-0.146495\pi$
$467$	38.7233			1.79190			0.895951	+	0.444153i	$0.146495\pi$
$468$		0			0
$469$	1.09952			0.0507709
$470$		0			0
$471$	10.2992	+	6.54997i	0.474561	+	0.301807i
$472$		0			0
$473$	−30.8064			−1.41648
$474$		0			0
$475$	1.28746	−	2.22995i	0.0590727	−	0.102317i
$476$		0			0
$477$	9.97248	−	4.66927i	0.456609	−	0.213791i
$478$		0			0
$479$	3.56011	−	2.05543i	0.162666	−	0.0939151i	−0.416457	−	0.909155i	$-0.636728\pi$
$479$	3.56011	−	2.05543i	0.162666	−	0.0939151i	0.579123	+	0.815240i	$0.303395\pi$
$480$		0			0
$481$	12.3215	−	16.8556i	0.561813	−	0.768551i
$482$		0			0
$483$	13.4670	+	8.56459i	0.612768	+	0.389702i
$484$		0			0
$485$	−18.0342	−	10.4121i	−0.818892	−	0.472788i
$486$		0			0
$487$	−12.4933	+	21.6390i	−0.566124	+	0.980555i	0.430820	+	0.902438i	$0.358224\pi$
$487$	−12.4933	+	21.6390i	−0.566124	+	0.980555i	−0.996944	+	0.0781175i	$0.975109\pi$
$488$		0			0
$489$	7.65261	−	3.99132i	0.346063	−	0.180494i
$490$		0			0
$491$	5.53131	+	9.58051i	0.249624	+	0.432362i	0.963422	−	0.267990i	$-0.0863595\pi$
$491$	5.53131	+	9.58051i	0.249624	+	0.432362i	−0.713797	+	0.700352i	$0.753026\pi$
$492$		0			0
$493$	2.89569			0.130415
$494$		0			0
$495$	−13.7620	−	9.60418i	−0.618556	−	0.431676i
$496$		0			0
$497$	−14.7817	+	8.53422i	−0.663050	+	0.382812i
$498$		0			0
$499$	26.3108			1.17784			0.588918	−	0.808193i	$-0.299554\pi$
$499$	26.3108			1.17784			0.588918	+	0.808193i	$0.299554\pi$
$500$		0			0
$501$	−6.28108	−	0.269311i	−0.280618	−	0.0120319i
$502$		0			0
$503$	6.76696	−	11.7207i	0.301724	−	0.522601i	−0.674803	−	0.737998i	$-0.735771\pi$
$503$	6.76696	−	11.7207i	0.301724	−	0.522601i	0.976526	+	0.215397i	$0.0691047\pi$
$504$		0			0
$505$	20.0983	−	11.6038i	0.894363	−	0.516361i
$506$		0			0
$507$	−21.7278	+	5.90779i	−0.964966	+	0.262374i
$508$		0			0
$509$	−8.14083	−	14.1003i	−0.360836	−	0.624986i	0.627263	−	0.778808i	$-0.284175\pi$
$509$	−8.14083	−	14.1003i	−0.360836	−	0.624986i	−0.988099	+	0.153822i	$0.950842\pi$
$510$		0			0
$511$	13.8445	+	7.99314i	0.612446	+	0.353596i
$512$		0			0
$513$	7.41681	+	5.66349i	0.327460	+	0.250049i
$514$		0			0
$515$			36.0777i			1.58978i
$516$		0			0
$517$	−0.988652	−	1.71239i	−0.0434809	−	0.0753110i
$518$		0			0
$519$	15.8547	+	30.3985i	0.695946	+	1.33435i
$520$		0			0
$521$		−	3.40258i		−	0.149070i	−0.997218	−	0.0745348i	$-0.976253\pi$
$521$		−	3.40258i		−	0.149070i	0.997218	−	0.0745348i	$-0.0237472\pi$
$522$		0			0
$523$	0.605718	−	0.349712i	0.0264862	−	0.0152918i	−0.486698	−	0.873570i	$-0.661799\pi$
$523$	0.605718	−	0.349712i	0.0264862	−	0.0152918i	0.513185	+	0.858278i	$0.328466\pi$
$524$		0			0
$525$	−3.95436	+	2.06245i	−0.172582	+	0.0900126i
$526$		0			0
$527$	−5.33551	−	3.08046i	−0.232418	−	0.134187i
$528$		0			0
$529$	−1.66199	+	2.87864i	−0.0722603	+	0.125158i
$530$		0			0
$531$	0.932065	−	10.8492i	0.0404482	−	0.470814i
$532$		0			0
$533$	−33.4393	−	24.4443i	−1.44842	−	1.05880i
$534$		0			0
$535$	−16.1968	−	28.0536i	−0.700247	−	1.21286i
$536$		0			0
$537$	0.986659	−	23.0116i	0.0425775	−	0.993024i
$538$		0			0
$539$	−9.68330	−	5.59065i	−0.417089	−	0.240807i
$540$		0			0
$541$			3.25977i			0.140148i	0.997542	+	0.0700742i	$0.0223236\pi$
$541$			3.25977i			0.140148i	−0.997542	+	0.0700742i	$0.977676\pi$
$542$		0			0
$543$	−17.4464	−	11.0954i	−0.748695	−	0.476147i
$544$		0			0
$545$		−	23.2063i		−	0.994047i
$546$		0			0
$547$			26.3786i			1.12787i	0.825820	+	0.563933i	$0.190713\pi$
$547$			26.3786i			1.12787i	−0.825820	+	0.563933i	$0.809287\pi$
$548$		0			0
$549$	−28.0094	−	2.40631i	−1.19541	−	0.102699i
$550$		0			0
$551$			2.24455i			0.0956212i
$552$		0			0
$553$	−9.67603	−	5.58646i	−0.411467	−	0.237560i
$554$		0			0
$555$	18.9237	+	0.811382i	0.803265	+	0.0344412i
$556$		0			0
$557$	8.59684	+	14.8902i	0.364260	+	0.630916i	0.988657	−	0.150191i	$-0.0479887\pi$
$557$	8.59684	+	14.8902i	0.364260	+	0.630916i	−0.624397	+	0.781107i	$0.714655\pi$
$558$		0			0
$559$	−37.2801	−	4.02815i	−1.57678	−	0.170373i
$560$		0			0
$561$	10.0307	+	6.37923i	0.423497	+	0.269331i
$562$		0			0
$563$	16.7963	−	29.0921i	0.707880	−	1.22608i	−0.257762	−	0.966209i	$-0.582985\pi$
$563$	16.7963	−	29.0921i	0.707880	−	1.22608i	0.965642	−	0.259876i	$-0.0836817\pi$
$564$		0			0
$565$	−13.8344	−	7.98729i	−0.582017	−	0.336028i
$566$		0			0
$567$	−5.57572	−	15.1712i	−0.234158	−	0.637129i
$568$		0			0
$569$	−4.42743	+	2.55618i	−0.185607	+	0.107161i	−0.589925	−	0.807458i	$-0.700843\pi$
$569$	−4.42743	+	2.55618i	−0.185607	+	0.107161i	0.404317	+	0.914619i	$0.367509\pi$
$570$		0			0
$571$		−	13.5901i		−	0.568728i	−0.958716	−	0.284364i	$-0.908218\pi$
$571$		−	13.5901i		−	0.568728i	0.958716	−	0.284364i	$-0.0917825\pi$
$572$		0			0
$573$	31.5514	−	16.4560i	1.31808	−	0.687461i
$574$		0			0
$575$	−3.67808	−	6.37063i	−0.153387	−	0.265674i
$576$		0			0
$577$		−	24.8884i		−	1.03612i	−0.855345	−	0.518058i	$-0.826655\pi$
$577$		−	24.8884i		−	1.03612i	0.855345	−	0.518058i	$-0.173345\pi$
$578$		0			0
$579$	3.67842	+	0.157718i	0.152870	+	0.00655454i
$580$		0			0
$581$	27.5650	+	15.9147i	1.14359	+	0.660251i
$582$		0			0
$583$	5.43637	+	9.41607i	0.225151	+	0.389974i
$584$		0			0
$585$	−15.3982	−	13.4219i	−0.636635	−	0.554927i
$586$		0			0
$587$	−7.11795	+	4.10955i	−0.293789	+	0.169619i	−0.639650	−	0.768667i	$-0.720920\pi$
$587$	−7.11795	+	4.10955i	−0.293789	+	0.169619i	0.345860	+	0.938286i	$0.387587\pi$
$588$		0			0
$589$	2.38777	−	4.13574i	0.0983864	−	0.170410i
$590$		0			0
$591$	1.71942	−	40.1016i	0.0707275	−	1.64956i
$592$		0			0
$593$	−40.6118			−1.66773			−0.833863	−	0.551972i	$-0.813876\pi$
$593$	−40.6118			−1.66773			−0.833863	+	0.551972i	$0.813876\pi$
$594$		0			0
$595$	−6.80509	+	3.92892i	−0.278982	+	0.161070i
$596$		0			0
$597$	2.21444	+	4.24577i	0.0906309	+	0.173768i
$598$		0			0
$599$	−19.9719			−0.816029			−0.408014	−	0.912975i	$-0.633779\pi$
$599$	−19.9719			−0.816029			−0.408014	+	0.912975i	$0.633779\pi$
$600$		0			0
$601$	15.5299	+	26.8987i	0.633480	+	1.09722i	0.986835	+	0.161730i	$0.0517073\pi$
$601$	15.5299	+	26.8987i	0.633480	+	1.09722i	−0.353355	+	0.935489i	$0.614959\pi$
$602$		0			0
$603$	1.05112	−	1.50617i	0.0428050	−	0.0613361i
$604$		0			0
$605$	−2.10122	+	3.63943i	−0.0854269	+	0.147964i
$606$		0			0
$607$	−11.3864	−	6.57397i	−0.462161	−	0.266829i	0.250791	−	0.968041i	$-0.419309\pi$
$607$	−11.3864	−	6.57397i	−0.462161	−	0.266829i	−0.712953	+	0.701212i	$0.752643\pi$
$608$		0			0
$609$	2.08628	−	3.28047i	0.0845404	−	0.132931i
$610$		0			0
$611$	−0.972501	−	2.20151i	−0.0393432	−	0.0890637i
$612$		0			0
$613$	−1.05460	+	0.608871i	−0.0425947	+	0.0245921i	−0.521146	−	0.853467i	$-0.674495\pi$
$613$	−1.05460	+	0.608871i	−0.0425947	+	0.0245921i	0.478551	+	0.878060i	$0.341162\pi$
$614$		0			0
$615$	1.60967	−	37.5420i	0.0649083	−	1.51384i
$616$		0			0
$617$	4.04423	−	7.00481i	0.162815	−	0.282003i	−0.773063	−	0.634330i	$-0.781276\pi$
$617$	4.04423	−	7.00481i	0.162815	−	0.282003i	0.935877	+	0.352327i	$0.114609\pi$
$618$		0			0
$619$	12.5019			0.502494			0.251247	−	0.967923i	$-0.419159\pi$
$619$	12.5019			0.502494			0.251247	+	0.967923i	$0.419159\pi$
$620$		0			0
$621$	24.6065	−	10.2601i	0.987423	−	0.411724i
$622$		0			0
$623$	9.90645			0.396894
$624$		0			0
$625$	−15.7755			−0.631022
$626$		0			0
$627$	−4.94477	+	7.77516i	−0.197475	+	0.310510i
$628$		0			0
$629$	−13.4168			−0.534962
$630$		0			0
$631$	−4.62836	+	8.01655i	−0.184252	+	0.319134i	−0.943324	−	0.331873i	$-0.892320\pi$
$631$	−4.62836	+	8.01655i	−0.184252	+	0.319134i	0.759072	+	0.651006i	$0.225653\pi$
$632$		0			0
$633$	−25.0765	−	1.07519i	−0.996700	−	0.0427351i
$634$		0			0
$635$	−6.70354	+	3.87029i	−0.266022	+	0.153588i
$636$		0			0
$637$	−10.9871	−	8.03164i	−0.435326	−	0.318225i
$638$		0			0
$639$	−2.44050	+	28.4073i	−0.0965448	+	1.12378i
$640$		0			0
$641$	10.8264	+	6.25063i	0.427618	+	0.246885i	0.698331	−	0.715775i	$-0.253926\pi$
$641$	10.8264	+	6.25063i	0.427618	+	0.246885i	−0.270714	+	0.962660i	$0.587260\pi$
$642$		0			0
$643$	−19.7894	+	34.2762i	−0.780416	+	1.35172i	0.151283	+	0.988490i	$0.451659\pi$
$643$	−19.7894	+	34.2762i	−0.780416	+	1.35172i	−0.931700	+	0.363230i	$0.881674\pi$
$644$		0			0
$645$	−15.7308	−	30.1609i	−0.619399	−	1.18758i
$646$		0			0
$647$	−13.1294	−	22.7407i	−0.516169	−	0.894030i	−0.999824	−	0.0187716i	$-0.994024\pi$
$647$	−13.1294	−	22.7407i	−0.516169	−	0.894030i	0.483655	−	0.875259i	$-0.339309\pi$
$648$		0			0
$649$	10.7520			0.422051
$650$		0			0
$651$	−7.33390	+	3.82509i	−0.287438	+	0.149917i
$652$		0			0
$653$	−23.9639	+	13.8356i	−0.937779	+	0.541427i	−0.889264	−	0.457395i	$-0.848782\pi$
$653$	−23.9639	+	13.8356i	−0.937779	+	0.541427i	−0.0485159	+	0.998822i	$0.515449\pi$
$654$		0			0
$655$	20.6851			0.808235
$656$		0			0
$657$	24.1846	−	11.3236i	0.943531	−	0.441776i
$658$		0			0
$659$	19.7623	−	34.2293i	0.769829	−	1.33338i	−0.167826	−	0.985817i	$-0.553675\pi$
$659$	19.7623	−	34.2293i	0.769829	−	1.33338i	0.937655	−	0.347567i	$-0.112992\pi$
$660$		0			0
$661$	5.92681	−	3.42184i	0.230526	−	0.133094i	−0.380289	−	0.924868i	$-0.624175\pi$
$661$	5.92681	−	3.42184i	0.230526	−	0.133094i	0.610815	+	0.791774i	$0.290842\pi$
$662$		0			0
$663$	11.3044	+	9.03135i	0.439028	+	0.350749i
$664$		0			0
$665$	−3.04545	−	5.27487i	−0.118097	−	0.204551i
$666$		0			0
$667$	5.55327	+	3.20618i	0.215023	+	0.124144i
$668$		0			0
$669$	−0.796283	+	18.5715i	−0.0307861	+	0.718017i
$670$		0			0
$671$		−	27.7584i		−	1.07160i
$672$		0			0
$673$	−9.60509	−	16.6365i	−0.370249	−	0.641290i	0.619355	−	0.785111i	$-0.287394\pi$
$673$	−9.60509	−	16.6365i	−0.370249	−	0.641290i	−0.989604	+	0.143821i	$0.954061\pi$
$674$		0			0
$675$	−0.955073	+	7.38856i	−0.0367608	+	0.284386i
$676$		0			0
$677$		−	31.2564i		−	1.20128i	−0.799519	−	0.600640i	$-0.794912\pi$
$677$		−	31.2564i		−	1.20128i	0.799519	−	0.600640i	$-0.205088\pi$
$678$		0			0
$679$	17.1506	−	9.90193i	0.658181	−	0.380001i
$680$		0			0
$681$	3.33286	+	6.39014i	0.127715	+	0.244871i
$682$		0			0
$683$	−25.1522	−	14.5216i	−0.962422	−	0.555654i	−0.0655042	−	0.997852i	$-0.520866\pi$
$683$	−25.1522	−	14.5216i	−0.962422	−	0.555654i	−0.896918	+	0.442198i	$0.854199\pi$
$684$		0			0
$685$	10.1196	−	17.5277i	0.386651	−	0.669699i
$686$		0			0
$687$	15.4117	−	24.2334i	0.587994	−	0.924563i
$688$		0			0
$689$	5.34756	+	12.1056i	0.203726	+	0.461187i
$690$		0			0
$691$	23.2202	+	40.2185i	0.883336	+	1.52998i	0.847609	+	0.530622i	$0.178041\pi$
$691$	23.2202	+	40.2185i	0.883336	+	1.52998i	0.0357274	+	0.999362i	$0.488625\pi$
$692$		0			0
$693$	14.4538	−	6.76749i	0.549055	−	0.257076i
$694$		0			0
$695$	−1.60398	−	0.926057i	−0.0608423	−	0.0351273i
$696$		0			0
$697$			26.6171i			1.00819i
$698$		0			0
$699$	−12.9557	+	20.3716i	−0.490031	+	0.770525i
$700$		0			0
$701$		−	5.03343i		−	0.190110i	−0.995472	−	0.0950550i	$-0.969697\pi$
$701$		−	5.03343i		−	0.190110i	0.995472	−	0.0950550i	$-0.0303027\pi$
$702$		0			0
$703$		−	10.3998i		−	0.392237i
$704$		0			0
$705$	1.17167	−	1.84234i	0.0441278	−	0.0693865i
$706$		0			0
$707$			22.0705i			0.830045i
$708$		0			0
$709$	36.8731	+	21.2887i	1.38480	+	0.799514i	0.992723	−	0.120419i	$-0.0384239\pi$
$709$	36.8731	+	21.2887i	1.38480	+	0.799514i	0.392075	+	0.919933i	$0.371757\pi$
$710$		0			0
$711$	−16.9028	+	7.91413i	−0.633903	+	0.296803i
$712$		0			0
$713$	−6.82151	−	11.8152i	−0.255468	−	0.442483i
$714$		0			0
$715$	11.9027	−	16.2827i	0.445137	−	0.608940i
$716$		0			0
$717$	−7.14816	+	11.2398i	−0.266953	+	0.419757i
$718$		0			0
$719$	−5.48789	+	9.50530i	−0.204664	+	0.354488i	−0.950026	−	0.312172i	$-0.898943\pi$
$719$	−5.48789	+	9.50530i	−0.204664	+	0.354488i	0.745362	+	0.666660i	$0.232277\pi$
$720$		0			0
$721$	−29.7134	−	17.1550i	−1.10659	−	0.638887i
$722$		0			0
$723$	6.59520	+	12.6451i	0.245278	+	0.470276i
$724$		0			0
$725$	−1.55185	+	0.895959i	−0.0576342	+	0.0332751i
$726$		0			0
$727$			0.642323i			0.0238224i	0.999929	+	0.0119112i	$0.00379155\pi$
$727$			0.642323i			0.0238224i	−0.999929	+	0.0119112i	$0.996208\pi$
$728$		0			0
$729$	−26.1125	−	6.86553i	−0.967131	−	0.254279i
$730$		0			0
$731$	12.0478	+	20.8673i	0.445602	+	0.771806i
$732$		0			0
$733$		−	28.1122i		−	1.03835i	−0.854669	−	0.519173i	$-0.826240\pi$
$733$		−	28.1122i		−	1.03835i	0.854669	−	0.519173i	$-0.173760\pi$
$734$		0			0
$735$	0.528889	−	12.3352i	0.0195084	−	0.454989i
$736$		0			0
$737$	1.57058	+	0.906773i	0.0578529	+	0.0334014i
$738$		0			0
$739$	−18.7724	−	32.5148i	−0.690555	−	1.19608i	−0.971656	−	0.236398i	$-0.924033\pi$
$739$	−18.7724	−	32.5148i	−0.690555	−	1.19608i	0.281101	−	0.959678i	$-0.409300\pi$
$740$		0			0
$741$	−7.00052	+	8.76248i	−0.257171	+	0.321898i
$742$		0			0
$743$	−10.2637	+	5.92572i	−0.376537	+	0.217394i	−0.676310	−	0.736617i	$-0.736422\pi$
$743$	−10.2637	+	5.92572i	−0.376537	+	0.217394i	0.299774	+	0.954010i	$0.403089\pi$
$744$		0			0
$745$	−16.8882	+	29.2512i	−0.618736	+	1.07168i
$746$		0			0
$747$	48.1525	−	22.5457i	1.76181	−	0.824905i
$748$		0			0
$749$	30.8064			1.12564
$750$		0			0
$751$	−18.4467	+	10.6502i	−0.673131	+	0.388632i	−0.797262	−	0.603634i	$-0.793719\pi$
$751$	−18.4467	+	10.6502i	−0.673131	+	0.388632i	0.124131	+	0.992266i	$0.460386\pi$
$752$		0			0
$753$	8.59194	−	4.48123i	0.313108	−	0.163305i
$754$		0			0
$755$	32.6770			1.18924
$756$		0			0
$757$	11.7008	+	20.2664i	0.425274	+	0.736597i	0.996446	−	0.0842340i	$-0.0268443\pi$
$757$	11.7008	+	20.2664i	0.425274	+	0.736597i	−0.571172	+	0.820831i	$0.693511\pi$
$758$		0			0
$759$	12.1733	+	23.3401i	0.441864	+	0.847193i
$760$		0			0
$761$	−1.86026	+	3.22206i	−0.0674343	+	0.116800i	−0.897771	−	0.440462i	$-0.854815\pi$
$761$	−1.86026	+	3.22206i	−0.0674343	+	0.116800i	0.830337	+	0.557262i	$0.188148\pi$
$762$		0			0
$763$	19.1125	+	11.0346i	0.691920	+	0.399480i
$764$		0			0
$765$	−1.12354	+	13.0780i	−0.0406217	+	0.472835i
$766$		0			0
$767$	13.0114	+	1.40589i	0.469814	+	0.0507639i
$768$		0			0
$769$	25.4463	−	14.6914i	0.917618	−	0.529787i	0.0347439	−	0.999396i	$-0.488938\pi$
$769$	25.4463	−	14.6914i	0.917618	−	0.529787i	0.882874	+	0.469609i	$0.155605\pi$
$770$		0			0
$771$	−52.1531	−	2.23615i	−1.87825	−	0.0805328i
$772$		0			0
$773$	−0.287410	+	0.497808i	−0.0103374	+	0.0179049i	−0.871148	−	0.491021i	$-0.836624\pi$
$773$	−0.287410	+	0.497808i	−0.0103374	+	0.0179049i	0.860810	+	0.508926i	$0.169957\pi$
$774$		0			0
$775$	3.81251			0.136949
$776$		0			0
$777$	−9.66649	+	15.1996i	−0.346783	+	0.545283i
$778$		0			0
$779$	−20.6319			−0.739213
$780$		0			0
$781$	−28.1528			−1.00738
$782$		0			0
$783$	−2.49930	−	5.99398i	−0.0893177	−	0.214208i
$784$		0			0
$785$	−13.3077			−0.474971
$786$		0			0
$787$	−3.29304	+	5.70371i	−0.117384	+	0.203315i	−0.918730	−	0.394886i	$-0.870784\pi$
$787$	−3.29304	+	5.70371i	−0.117384	+	0.203315i	0.801346	+	0.598201i	$0.204118\pi$
$788$		0			0
$789$	0.00809564	−	0.188813i	0.000288212	−	0.00672191i
$790$		0			0
$791$	13.1566	−	7.59595i	0.467794	−	0.270081i
$792$		0			0
$793$	3.62960	−	33.5915i	0.128891	−	1.19287i
$794$		0			0
$795$	−6.44277	+	10.1306i	−0.228501	+	0.359296i
$796$		0			0
$797$	25.0021	+	14.4350i	0.885619	+	0.511312i	0.872507	−	0.488602i	$-0.162493\pi$
$797$	25.0021	+	14.4350i	0.885619	+	0.511312i	0.0131121	+	0.999914i	$0.495826\pi$
$798$		0			0
$799$	−0.773283	+	1.33937i	−0.0273568	+	0.0473833i
$800$		0			0
$801$	9.47044	−	13.5704i	0.334621	−	0.479485i
$802$		0			0
$803$	13.1839	+	22.8352i	0.465250	+	0.805837i
$804$		0			0
$805$	−17.4008			−0.613297
$806$		0			0
$807$	−24.3769	−	46.7383i	−0.858109	−	1.64527i
$808$		0			0
$809$	5.13144	−	2.96264i	0.180412	−	0.104161i	−0.407074	−	0.913395i	$-0.633451\pi$
$809$	5.13144	−	2.96264i	0.180412	−	0.104161i	0.587486	+	0.809234i	$0.300118\pi$
$810$		0			0
$811$	−42.5845			−1.49534			−0.747672	−	0.664068i	$-0.768828\pi$
$811$	−42.5845			−1.49534			−0.747672	+	0.664068i	$0.768828\pi$
$812$		0			0
$813$	−1.38514	+	32.3054i	−0.0485791	+	1.13300i
$814$		0			0
$815$	−4.70514	+	8.14954i	−0.164814	+	0.285466i
$816$		0			0
$817$	−16.1750	+	9.33864i	−0.565892	+	0.326718i
$818$		0			0
$819$	18.3760	−	6.29969i	0.642111	−	0.220129i
$820$		0			0
$821$	16.4101	+	28.4231i	0.572716	+	0.991973i	0.996286	+	0.0861099i	$0.0274436\pi$
$821$	16.4101	+	28.4231i	0.572716	+	0.991973i	−0.423569	+	0.905864i	$0.639223\pi$
$822$		0			0
$823$	46.4135	+	26.7968i	1.61787	+	0.934079i	0.987469	+	0.157810i	$0.0504434\pi$
$823$	46.4135	+	26.7968i	1.61787	+	0.934079i	0.630402	+	0.776269i	$0.282890\pi$
$824$		0			0
$825$	−7.34942	−	0.315118i	−0.255874	−	0.0109710i
$826$		0			0
$827$			34.5894i			1.20279i	0.798951	+	0.601396i	$0.205388\pi$
$827$			34.5894i			1.20279i	−0.798951	+	0.601396i	$0.794612\pi$
$828$		0			0
$829$	8.41879	+	14.5818i	0.292397	+	0.506446i	0.974376	−	0.224926i	$-0.0722140\pi$
$829$	8.41879	+	14.5818i	0.292397	+	0.506446i	−0.681979	+	0.731371i	$0.738881\pi$
$830$		0			0
$831$	30.5843	−	15.9516i	1.06096	−	0.553356i
$832$		0			0
$833$			8.74556i			0.303016i
$834$		0			0
$835$	5.93620	−	3.42727i	0.205431	−	0.118605i
$836$		0			0
$837$	−1.77131	+	13.7031i	−0.0612255	+	0.473648i
$838$		0			0
$839$	40.5443	+	23.4082i	1.39974	+	0.808142i	0.994365	−	0.106007i	$-0.0338066\pi$
$839$	40.5443	+	23.4082i	1.39974	+	0.808142i	0.405378	+	0.914149i	$0.367140\pi$
$840$		0			0
$841$	−13.7190	+	23.7620i	−0.473069	+	0.819379i
$842$		0			0
$843$	−21.2662	−	13.5246i	−0.732446	−	0.465814i
$844$		0			0
$845$	16.5331	−	18.1481i	0.568755	−	0.624312i
$846$		0			0
$847$	−1.99827	−	3.46111i	−0.0686615	−	0.118925i
$848$		0			0
$849$	−1.36382	−	0.0584760i	−0.0468062	−	0.00200689i
$850$		0			0
$851$	−25.7303	−	14.8554i	−0.882022	−	0.509236i
$852$		0			0
$853$			50.6867i			1.73548i	0.497019	+	0.867739i	$0.334428\pi$
$853$			50.6867i			1.73548i	−0.497019	+	0.867739i	$0.665572\pi$
$854$		0			0
$855$	−10.1372	−	0.870897i	−0.346685	−	0.0297841i
$856$		0			0
$857$			37.9765i			1.29725i	0.761107	+	0.648626i	$0.224656\pi$
$857$			37.9765i			1.29725i	−0.761107	+	0.648626i	$0.775344\pi$
$858$		0			0
$859$			38.6738i			1.31953i	0.751471	+	0.659766i	$0.229345\pi$
$859$			38.6738i			1.31953i	−0.751471	+	0.659766i	$0.770655\pi$
$860$		0			0
$861$	30.1540	+	19.1770i	1.02765	+	0.653552i
$862$		0			0
$863$			0.0860835i			0.00293032i	0.999999	+	0.00146516i	$0.000466374\pi$
$863$			0.0860835i			0.00293032i	−0.999999	+	0.00146516i	$0.999534\pi$
$864$		0			0
$865$	−32.3725	−	18.6903i	−1.10070	−	0.635489i
$866$		0			0
$867$	−0.863044	+	20.1286i	−0.0293105	+	0.683602i
$868$		0			0
$869$	−9.21433	−	15.9597i	−0.312575	−	0.541395i
$870$		0			0
$871$	1.78205	+	1.30269i	0.0603826	+	0.0441399i
$872$		0			0
$873$	2.83162	−	32.9599i	0.0958359	−	1.11552i
$874$		0			0
$875$	10.9101	−	18.8968i	0.368828	−	0.638829i
$876$		0			0
$877$	−32.4044	−	18.7087i	−1.09422	−	0.631748i	−0.159523	−	0.987194i	$-0.550996\pi$
$877$	−32.4044	−	18.7087i	−1.09422	−	0.631748i	−0.934697	+	0.355446i	$0.884329\pi$
$878$		0			0
$879$	−19.2974	+	10.0648i	−0.650884	+	0.339477i
$880$		0			0
$881$	29.6895	−	17.1412i	1.00026	−	0.577503i	0.0919376	−	0.995765i	$-0.470694\pi$
$881$	29.6895	−	17.1412i	1.00026	−	0.577503i	0.908326	+	0.418262i	$0.137361\pi$
$882$		0			0
$883$			7.37789i			0.248286i	0.992264	+	0.124143i	$0.0396181\pi$
$883$			7.37789i			0.248286i	−0.992264	+	0.124143i	$0.960382\pi$
$884$		0			0
$885$	5.49031	+	10.5267i	0.184555	+	0.353850i
$886$		0			0
$887$	4.79576	+	8.30650i	0.161026	+	0.278905i	0.935237	−	0.354023i	$-0.115186\pi$
$887$	4.79576	+	8.30650i	0.161026	+	0.278905i	−0.774211	+	0.632928i	$0.781853\pi$
$888$		0			0
$889$		−	7.36133i		−	0.246891i
$890$		0			0
$891$	4.54719	−	26.2692i	0.152337	−	0.880051i
$892$		0			0
$893$	−1.03819	−	0.599399i	−0.0347417	−	0.0200581i
$894$		0			0
$895$	12.5563	+	21.7481i	0.419710	+	0.726959i
$896$		0			0
$897$	11.6796	+	29.8366i	0.389970	+	0.996215i
$898$		0			0
$899$	−2.87811	+	1.66168i	−0.0959904	+	0.0554201i
$900$		0			0
$901$	4.25211	−	7.36487i	0.141658	−	0.245359i
$902$		0			0
$903$	32.3203	+	1.38578i	1.07555	+	0.0461160i
$904$		0			0
$905$	22.5426			0.749341
$906$		0			0
$907$	21.8624	−	12.6223i	0.725928	−	0.419115i	−0.0910023	−	0.995851i	$-0.529007\pi$
$907$	21.8624	−	12.6223i	0.725928	−	0.419115i	0.816931	+	0.576736i	$0.195674\pi$
$908$		0			0
$909$	30.2332	+	21.0991i	1.00277	+	0.699812i
$910$		0			0
$911$	−43.6403			−1.44587			−0.722934	−	0.690917i	$-0.757207\pi$
$911$	−43.6403			−1.44587			−0.722934	+	0.690917i	$0.757207\pi$
$912$		0			0
$913$	26.2497	+	45.4658i	0.868739	+	1.50470i
$914$		0			0
$915$	27.1767	−	14.1743i	0.898434	−	0.468589i
$916$		0			0
$917$	−9.83583	+	17.0362i	−0.324808	+	0.562584i
$918$		0			0
$919$	−23.9505	−	13.8279i	−0.790056	−	0.456139i	0.0499264	−	0.998753i	$-0.484101\pi$
$919$	−23.9505	−	13.8279i	−0.790056	−	0.456139i	−0.839982	+	0.542614i	$0.817435\pi$
$920$		0			0
$921$	27.9334	+	17.7648i	0.920438	+	0.585371i
$922$		0			0
$923$	−34.0688	−	3.68117i	−1.12139	−	0.121167i
$924$		0			0
$925$	7.19026	−	4.15130i	0.236414	−	0.136494i
$926$		0			0
$927$	−51.9055	+	24.3029i	−1.70480	+	0.798213i
$928$		0			0
$929$	13.5733	−	23.5097i	0.445326	−	0.771328i	−0.552749	−	0.833348i	$-0.686421\pi$
$929$	13.5733	−	23.5097i	0.445326	−	0.771328i	0.998075	+	0.0620204i	$0.0197544\pi$
$930$		0			0
$931$	−6.77900			−0.222173
$932$		0			0
$933$	−23.2211	−	14.7679i	−0.760223	−	0.483479i
$934$		0			0
$935$	−12.9608			−0.423862
$936$		0			0
$937$	−12.5163			−0.408891			−0.204446	−	0.978878i	$-0.565539\pi$
$937$	−12.5163			−0.408891			−0.204446	+	0.978878i	$0.565539\pi$
$938$		0			0
$939$	−31.2778	−	19.8917i	−1.02071	−	0.649142i
$940$		0			0
$941$	46.8824			1.52832			0.764161	−	0.645025i	$-0.223153\pi$
$941$	46.8824			1.52832			0.764161	+	0.645025i	$0.223153\pi$
$942$		0			0
$943$	−29.4711	+	51.0454i	−0.959711	+	1.66227i
$944$		0			0
$945$	14.0063	+	10.6952i	0.455624	+	0.347916i
$946$		0			0
$947$	−14.2693	+	8.23839i	−0.463690	+	0.267712i	−0.713595	−	0.700559i	$-0.752934\pi$
$947$	−14.2693	+	8.23839i	−0.463690	+	0.267712i	0.249904	+	0.968270i	$0.419601\pi$
$948$		0			0
$949$	12.9685	+	29.3577i	0.420977	+	0.952992i
$950$		0			0
$951$	−0.736896	−	0.468644i	−0.0238955	−	0.0151968i
$952$		0			0
$953$	11.4608	+	6.61690i	0.371252	+	0.214342i	0.674005	−	0.738727i	$-0.264572\pi$
$953$	11.4608	+	6.61690i	0.371252	+	0.214342i	−0.302753	+	0.953069i	$0.597906\pi$
$954$		0			0
$955$	−19.3991	+	33.6003i	−0.627741	+	1.08728i
$956$		0			0
$957$	5.68551	−	2.96535i	0.183787	−	0.0958562i
$958$		0			0
$959$	9.62381	+	16.6689i	0.310769	+	0.538268i
$960$		0			0
$961$	−23.9292			−0.771909
$962$		0			0
$963$	29.4505	−	42.2002i	0.949029	−	1.35988i
$964$		0			0
$965$	−3.47644	+	2.00713i	−0.111911	+	0.0646117i
$966$		0			0
$967$	2.89544			0.0931111			0.0465555	−	0.998916i	$-0.485176\pi$
$967$	2.89544			0.0931111			0.0465555	+	0.998916i	$0.485176\pi$
$968$		0			0
$969$	7.20045	+	0.308731i	0.231312	+	0.00991786i
$970$		0			0
$971$	10.8072	−	18.7186i	0.346819	−	0.600707i	−0.638864	−	0.769320i	$-0.720595\pi$
$971$	10.8072	−	18.7186i	0.346819	−	0.600707i	0.985682	+	0.168612i	$0.0539286\pi$
$972$		0			0
$973$	1.52539	−	0.880684i	0.0489017	−	0.0282334i
$974$		0			0
$975$	−8.85263	−	1.34232i	−0.283511	−	0.0429888i
$976$		0			0
$977$	7.32579	+	12.6886i	0.234373	+	0.405946i	0.959090	−	0.283101i	$-0.0913630\pi$
$977$	7.32579	+	12.6886i	0.234373	+	0.405946i	−0.724717	+	0.689046i	$0.758030\pi$
$978$		0			0
$979$	14.1506	+	8.16987i	0.452256	+	0.261110i
$980$		0			0
$981$	33.3871	−	15.6324i	1.06597	−	0.499103i
$982$		0			0
$983$		−	41.6123i		−	1.32723i	−0.748075	−	0.663614i	$-0.769022\pi$
$983$		−	41.6123i		−	1.32723i	0.748075	−	0.663614i	$-0.230978\pi$
$984$		0			0
$985$	21.8814	+	37.8997i	0.697200	+	1.20759i
$986$		0			0
$987$	0.960207	+	1.84102i	0.0305637	+	0.0586003i
$988$		0			0
$989$			53.3583i			1.69669i
$990$		0			0
$991$	−44.8946	+	25.9199i	−1.42612	+	0.823373i	−0.996812	−	0.0797837i	$-0.974577\pi$
$991$	−44.8946	+	25.9199i	−1.42612	+	0.823373i	−0.429311	+	0.903157i	$0.641244\pi$
$992$		0			0
$993$	19.9904	−	10.4262i	0.634375	−	0.330866i
$994$		0			0
$995$	−4.52148	−	2.61048i	−0.143341	−	0.0827577i
$996$		0			0
$997$	0.909879	−	1.57596i	0.0288162	−	0.0499111i	−0.851258	−	0.524748i	$-0.824160\pi$
$997$	0.909879	−	1.57596i	0.0288162	−	0.0499111i	0.880074	+	0.474837i	$0.157493\pi$
$998$		0			0
$999$	11.5801	+	27.7723i	0.366380	+	0.878676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.bz.g.335.2	yes	16
3.2	odd	2	inner	624.2.bz.g.335.5	yes	16
4.3	odd	2		624.2.bz.h.335.7	yes	16
12.11	even	2		624.2.bz.h.335.4	yes	16
13.4	even	6		624.2.bz.h.95.4	yes	16
39.17	odd	6		624.2.bz.h.95.7	yes	16
52.43	odd	6	inner	624.2.bz.g.95.5	yes	16
156.95	even	6	inner	624.2.bz.g.95.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
624.2.bz.g.95.2	✓	16	156.95	even	6	inner
624.2.bz.g.95.5	yes	16	52.43	odd	6	inner
624.2.bz.g.335.2	yes	16	1.1	even	1	trivial
624.2.bz.g.335.5	yes	16	3.2	odd	2	inner
624.2.bz.h.95.4	yes	16	13.4	even	6
624.2.bz.h.95.7	yes	16	39.17	odd	6
624.2.bz.h.335.4	yes	16	12.11	even	2
624.2.bz.h.335.7	yes	16	4.3	odd	2

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.bz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46152 - 0.929486i) q^{3} +1.88845 q^{5} +(-0.897962 + 1.55532i) q^{7} +(1.27211 + 2.71693i) q^{9} +O(q^{10})\)	\(q+(-1.46152 - 0.929486i) q^{3} +1.88845 q^{5} +(-0.897962 + 1.55532i) q^{7} +(1.27211 + 2.71693i) q^{9} +(-2.56534 + 1.48110i) q^{11} +(-3.29809 + 1.45691i) q^{13} +(-2.76002 - 1.75529i) q^{15} +(2.00651 + 1.15846i) q^{17} +(-0.897962 + 1.55532i) q^{19} +(2.75804 - 1.43849i) q^{21} +(2.56534 + 4.44331i) q^{23} -1.43376 q^{25} +(0.666132 - 5.15328i) q^{27} +(1.08236 - 0.624903i) q^{29} -2.65910 q^{31} +(5.12598 + 0.219784i) q^{33} +(-1.69576 + 2.93714i) q^{35} +(-5.01497 + 2.89540i) q^{37} +(6.17442 + 0.936227i) q^{39} +(5.74408 + 9.94904i) q^{41} +(9.00651 + 5.19991i) q^{43} +(2.40232 + 5.13079i) q^{45} +0.667511i q^{47} +(1.88733 + 3.26895i) q^{49} +(-1.85579 - 3.55814i) q^{51} -3.67049i q^{53} +(-4.84452 + 2.79699i) q^{55} +(2.75804 - 1.43849i) q^{57} +(-3.14343 - 1.81486i) q^{59} +(-4.68542 + 8.11539i) q^{61} +(-5.36800 - 0.461171i) q^{63} +(-6.22828 + 2.75129i) q^{65} +(-0.306114 - 0.530205i) q^{67} +(0.380678 - 8.87846i) q^{69} +(8.23069 + 4.75199i) q^{71} -8.90142i q^{73} +(2.09547 + 1.33266i) q^{75} -5.31989i q^{77} +6.22126i q^{79} +(-5.76347 + 6.91248i) q^{81} -17.7231i q^{83} +(3.78919 + 2.18769i) q^{85} +(-2.16274 - 0.0927308i) q^{87} +(-2.75804 - 4.77706i) q^{89} +(0.695613 - 6.43782i) q^{91} +(3.88634 + 2.47160i) q^{93} +(-1.69576 + 2.93714i) q^{95} +(-9.54976 - 5.51356i) q^{97} +(-7.28746 - 5.08575i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{3} - 6 q^{7} - q^{9}+O(q^{10}) \) 16 * q - 3 * q^3 - 6 * q^7 - q^9	\( 16 q - 3 q^{3} - 6 q^{7} - q^{9} + 14 q^{13} + 6 q^{15} - 6 q^{19} + 28 q^{25} - 24 q^{31} + 9 q^{33} + 12 q^{37} + 27 q^{39} - 6 q^{43} + 30 q^{45} + 14 q^{49} + 24 q^{55} + 8 q^{61} + 21 q^{63} - 30 q^{67} + 9 q^{69} - 15 q^{75} - 13 q^{81} - 30 q^{85} + 39 q^{87} - 30 q^{91} - 72 q^{93} - 54 q^{97} - 42 q^{99}+O(q^{100}) \) 16 * q - 3 * q^3 - 6 * q^7 - q^9 + 14 * q^13 + 6 * q^15 - 6 * q^19 + 28 * q^25 - 24 * q^31 + 9 * q^33 + 12 * q^37 + 27 * q^39 - 6 * q^43 + 30 * q^45 + 14 * q^49 + 24 * q^55 + 8 * q^61 + 21 * q^63 - 30 * q^67 + 9 * q^69 - 15 * q^75 - 13 * q^81 - 30 * q^85 + 39 * q^87 - 30 * q^91 - 72 * q^93 - 54 * q^97 - 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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