LMFDB - Embedded newform 1008.2.cj.c.527.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(527,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5, 2]))

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

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

chi := DirichletCharacter("1008.527");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cj (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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			527.5
Character	$\chi$	$=$	1008.527
Dual form			1008.2.cj.c.767.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02952 + 1.39287i) q^{3} +(-2.34742 + 1.35528i) q^{5} +(-2.57527 + 0.606609i) q^{7} +(-0.880179 - 2.86798i) q^{9} +O(q^{10})$	\(q+(-1.02952 + 1.39287i) q^{3} +(-2.34742 + 1.35528i) q^{5} +(-2.57527 + 0.606609i) q^{7} +(-0.880179 - 2.86798i) q^{9} +(0.711483 - 1.23232i) q^{11} +(2.56378 - 4.44059i) q^{13} +(0.528979 - 4.66494i) q^{15} +(-1.04103 + 0.601041i) q^{17} +(-6.15547 - 3.55386i) q^{19} +(1.80636 - 4.21154i) q^{21} +(3.74811 + 6.49192i) q^{23} +(1.17357 - 2.03269i) q^{25} +(4.90088 + 1.72666i) q^{27} +(6.90901 - 3.98892i) q^{29} +7.34842i q^{31} +(0.983983 + 2.25971i) q^{33} +(5.22311 - 4.91418i) q^{35} +(-0.194581 + 0.337025i) q^{37} +(3.54572 + 8.14269i) q^{39} +(-1.52819 - 0.882303i) q^{41} +(0.214184 - 0.123659i) q^{43} +(5.95306 + 5.53944i) q^{45} +6.80343 q^{47} +(6.26405 - 3.12437i) q^{49} +(0.234592 - 2.06881i) q^{51} +(10.7865 - 6.22758i) q^{53} +3.85704i q^{55} +(11.2873 - 4.91501i) q^{57} -4.75647 q^{59} -0.204627 q^{61} +(4.00644 + 6.85189i) q^{63} +13.8986i q^{65} -5.33812i q^{67} +(-12.9012 - 1.46292i) q^{69} -2.22420 q^{71} +(-7.54731 - 13.0723i) q^{73} +(1.62306 + 3.72733i) q^{75} +(-1.08472 + 3.60516i) q^{77} -9.62145i q^{79} +(-7.45057 + 5.04866i) q^{81} +(-2.59188 - 4.48927i) q^{83} +(1.62916 - 2.82179i) q^{85} +(-1.55691 + 13.7300i) q^{87} +(-4.17410 - 2.40992i) q^{89} +(-3.90872 + 12.9910i) q^{91} +(-10.2354 - 7.56534i) q^{93} +19.2659 q^{95} +(2.40373 + 4.16339i) q^{97} +(-4.16051 - 0.955849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{5} - 7 q^{7} + 8 q^{9}+O(q^{10}) $ 30 * q + 3 * q^5 - 7 * q^7 + 8 * q^9	$ 30 q + 3 q^{5} - 7 q^{7} + 8 q^{9} - 3 q^{11} - 12 q^{17} - 9 q^{19} + 2 q^{21} + 12 q^{23} + 18 q^{25} + 27 q^{27} + 27 q^{29} + 13 q^{33} - 6 q^{35} + 6 q^{37} + 12 q^{39} + 9 q^{41} - 21 q^{43} + 13 q^{45} - 3 q^{49} + 12 q^{51} + 3 q^{53} + 20 q^{57} - 6 q^{59} + 6 q^{61} + 51 q^{63} + 10 q^{69} + 18 q^{71} + 21 q^{73} - 3 q^{75} + 72 q^{77} - 20 q^{81} - 15 q^{83} - 3 q^{85} - 57 q^{87} - 6 q^{89} + 26 q^{91} + 9 q^{93} + 54 q^{95} - 6 q^{97} - 48 q^{99}+O(q^{100}) $ 30 * q + 3 * q^5 - 7 * q^7 + 8 * q^9 - 3 * q^11 - 12 * q^17 - 9 * q^19 + 2 * q^21 + 12 * q^23 + 18 * q^25 + 27 * q^27 + 27 * q^29 + 13 * q^33 - 6 * q^35 + 6 * q^37 + 12 * q^39 + 9 * q^41 - 21 * q^43 + 13 * q^45 - 3 * q^49 + 12 * q^51 + 3 * q^53 + 20 * q^57 - 6 * q^59 + 6 * q^61 + 51 * q^63 + 10 * q^69 + 18 * q^71 + 21 * q^73 - 3 * q^75 + 72 * q^77 - 20 * q^81 - 15 * q^83 - 3 * q^85 - 57 * q^87 - 6 * q^89 + 26 * q^91 + 9 * q^93 + 54 * q^95 - 6 * q^97 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−1.02952	+	1.39287i	−0.594393	+	0.804174i
$3$	−1.02952	+	1.39287i	−0.594393	+	0.804174i
$4$		0			0
$5$	−2.34742	+	1.35528i	−1.04980	+	0.606100i	−0.922592	−	0.385776i	$-0.873934\pi$
$5$	−2.34742	+	1.35528i	−1.04980	+	0.606100i	−0.127204	+	0.991877i	$0.540600\pi$
$6$		0			0
$7$	−2.57527	+	0.606609i	−0.973361	+	0.229277i
$7$	−2.57527	+	0.606609i	−0.973361	+	0.229277i
$8$		0			0
$9$	−0.880179	−	2.86798i	−0.293393	−	0.955992i
$10$		0			0
$11$	0.711483	−	1.23232i	0.214520	−	0.371560i	−0.738604	−	0.674140i	$-0.764515\pi$
$11$	0.711483	−	1.23232i	0.214520	−	0.371560i	0.953124	+	0.302580i	$0.0978479\pi$
$12$		0			0
$13$	2.56378	−	4.44059i	0.711064	−	1.23160i	−0.253394	−	0.967363i	$-0.581547\pi$
$13$	2.56378	−	4.44059i	0.711064	−	1.23160i	0.964458	−	0.264236i	$-0.0851198\pi$
$14$		0			0
$15$	0.528979	−	4.66494i	0.136582	−	1.20448i
$16$		0			0
$17$	−1.04103	+	0.601041i	−0.252488	+	0.145774i	−0.620903	−	0.783887i	$-0.713234\pi$
$17$	−1.04103	+	0.601041i	−0.252488	+	0.145774i	0.368415	+	0.929661i	$0.379901\pi$
$18$		0			0
$19$	−6.15547	−	3.55386i	−1.41216	−	0.815312i	−0.416570	−	0.909104i	$-0.636768\pi$
$19$	−6.15547	−	3.55386i	−1.41216	−	0.815312i	−0.995592	+	0.0937915i	$0.970101\pi$
$20$		0			0
$21$	1.80636	−	4.21154i	0.394181	−	0.919033i
$22$		0			0
$23$	3.74811	+	6.49192i	0.781535	+	1.35366i	0.931047	+	0.364899i	$0.118896\pi$
$23$	3.74811	+	6.49192i	0.781535	+	1.35366i	−0.149512	+	0.988760i	$0.547770\pi$
$24$		0			0
$25$	1.17357	−	2.03269i	0.234715	−	0.406538i
$26$		0			0
$27$	4.90088	+	1.72666i	0.943175	+	0.332296i
$28$		0			0
$29$	6.90901	−	3.98892i	1.28297	−	0.740724i	0.305581	−	0.952166i	$-0.401149\pi$
$29$	6.90901	−	3.98892i	1.28297	−	0.740724i	0.977390	+	0.211443i	$0.0678161\pi$
$30$		0			0
$31$			7.34842i			1.31982i	0.751347	+	0.659908i	$0.229405\pi$
$31$			7.34842i			1.31982i	−0.751347	+	0.659908i	$0.770595\pi$
$32$		0			0
$33$	0.983983	+	2.25971i	0.171290	+	0.393364i
$34$		0			0
$35$	5.22311	−	4.91418i	0.882866	−	0.830648i
$36$		0			0
$37$	−0.194581	+	0.337025i	−0.0319890	+	0.0554065i	−0.881577	−	0.472041i	$-0.843517\pi$
$37$	−0.194581	+	0.337025i	−0.0319890	+	0.0554065i	0.849588	+	0.527447i	$0.176851\pi$
$38$		0			0
$39$	3.54572	+	8.14269i	0.567769	+	1.30387i
$40$		0			0
$41$	−1.52819	−	0.882303i	−0.238664	−	0.137793i	0.375899	−	0.926661i	$-0.377334\pi$
$41$	−1.52819	−	0.882303i	−0.238664	−	0.137793i	−0.614562	+	0.788868i	$0.710667\pi$
$42$		0			0
$43$	0.214184	−	0.123659i	0.0326628	−	0.0188579i	−0.483580	−	0.875300i	$-0.660664\pi$
$43$	0.214184	−	0.123659i	0.0326628	−	0.0188579i	0.516242	+	0.856442i	$0.327330\pi$
$44$		0			0
$45$	5.95306	+	5.53944i	0.887430	+	0.825771i
$46$		0			0
$47$	6.80343			0.992382			0.496191	−	0.868213i	$-0.334732\pi$
$47$	6.80343			0.992382			0.496191	+	0.868213i	$0.334732\pi$
$48$		0			0
$49$	6.26405	−	3.12437i	0.894864	−	0.446338i
$50$		0			0
$51$	0.234592	−	2.06881i	0.0328494	−	0.289691i
$52$		0			0
$53$	10.7865	−	6.22758i	1.48164	−	0.855423i	0.481853	−	0.876252i	$-0.339964\pi$
$53$	10.7865	−	6.22758i	1.48164	−	0.855423i	0.999783	+	0.0208286i	$0.00663044\pi$
$54$		0			0
$55$			3.85704i			0.520083i
$56$		0			0
$57$	11.2873	−	4.91501i	1.49503	−	0.651008i
$58$		0			0
$59$	−4.75647			−0.619240			−0.309620	−	0.950860i	$-0.600202\pi$
$59$	−4.75647			−0.619240			−0.309620	+	0.950860i	$0.600202\pi$
$60$		0			0
$61$	−0.204627			−0.0261998			−0.0130999	−	0.999914i	$-0.504170\pi$
$61$	−0.204627			−0.0261998			−0.0130999	+	0.999914i	$0.504170\pi$
$62$		0			0
$63$	4.00644	+	6.85189i	0.504764	+	0.863257i
$64$		0			0
$65$			13.8986i			1.72390i
$66$		0			0
$67$		−	5.33812i		−	0.652155i	−0.945343	−	0.326077i	$-0.894273\pi$
$67$		−	5.33812i		−	0.652155i	0.945343	−	0.326077i	$-0.105727\pi$
$68$		0			0
$69$	−12.9012	−	1.46292i	−1.55312	−	0.176115i
$70$		0			0
$71$	−2.22420			−0.263964			−0.131982	−	0.991252i	$-0.542134\pi$
$71$	−2.22420			−0.263964			−0.131982	+	0.991252i	$0.542134\pi$
$72$		0			0
$73$	−7.54731	−	13.0723i	−0.883345	−	1.53000i	−0.847598	−	0.530638i	$-0.821952\pi$
$73$	−7.54731	−	13.0723i	−0.883345	−	1.53000i	−0.0357471	−	0.999361i	$-0.511381\pi$
$74$		0			0
$75$	1.62306	+	3.72733i	0.187414	+	0.430395i
$76$		0			0
$77$	−1.08472	+	3.60516i	−0.123616	+	0.410846i
$78$		0			0
$79$		−	9.62145i		−	1.08250i	−0.840863	−	0.541249i	$-0.817952\pi$
$79$		−	9.62145i		−	1.08250i	0.840863	−	0.541249i	$-0.182048\pi$
$80$		0			0
$81$	−7.45057	+	5.04866i	−0.827841	+	0.560963i
$82$		0			0
$83$	−2.59188	−	4.48927i	−0.284496	−	0.492761i	0.687991	−	0.725719i	$-0.258493\pi$
$83$	−2.59188	−	4.48927i	−0.284496	−	0.492761i	−0.972487	+	0.232958i	$0.925159\pi$
$84$		0			0
$85$	1.62916	−	2.82179i	0.176707	−	0.306066i
$86$		0			0
$87$	−1.55691	+	13.7300i	−0.166918	+	1.47201i
$88$		0			0
$89$	−4.17410	−	2.40992i	−0.442454	−	0.255451i	0.262184	−	0.965018i	$-0.415557\pi$
$89$	−4.17410	−	2.40992i	−0.442454	−	0.255451i	−0.704638	+	0.709567i	$0.748891\pi$
$90$		0			0
$91$	−3.90872	+	12.9910i	−0.409745	+	1.36182i
$92$		0			0
$93$	−10.2354	−	7.56534i	−1.06136	−	0.784490i
$94$		0			0
$95$	19.2659			1.97664
$96$		0			0
$97$	2.40373	+	4.16339i	0.244062	+	0.422728i	0.961868	−	0.273516i	$-0.0881865\pi$
$97$	2.40373	+	4.16339i	0.244062	+	0.422728i	−0.717805	+	0.696244i	$0.754853\pi$
$98$		0			0
$99$	−4.16051	−	0.955849i	−0.418147	−	0.0960665i
$100$		0			0
$101$	3.36507	+	1.94282i	0.334837	+	0.193318i	0.657987	−	0.753030i	$-0.271408\pi$
$101$	3.36507	+	1.94282i	0.334837	+	0.193318i	−0.323150	+	0.946348i	$0.604742\pi$
$102$		0			0
$103$	11.0608	−	6.38595i	1.08985	−	0.629226i	0.156315	−	0.987707i	$-0.450039\pi$
$103$	11.0608	−	6.38595i	1.08985	−	0.629226i	0.933537	+	0.358481i	$0.116705\pi$
$104$		0			0
$105$	1.46753	+	12.3344i	0.143216	+	1.20371i
$106$		0			0
$107$	6.20389	−	10.7455i	0.599753	−	1.03880i	−0.393104	−	0.919494i	$-0.628599\pi$
$107$	6.20389	−	10.7455i	0.599753	−	1.03880i	0.992857	−	0.119309i	$-0.0380679\pi$
$108$		0			0
$109$	−6.14048	−	10.6356i	−0.588152	−	1.01871i	−0.994474	−	0.104979i	$-0.966523\pi$
$109$	−6.14048	−	10.6356i	−0.588152	−	1.01871i	0.406323	−	0.913730i	$-0.366811\pi$
$110$		0			0
$111$	−0.269107	−	0.618000i	−0.0255425	−	0.0586579i
$112$		0			0
$113$	13.2555	+	7.65305i	1.24697	+	0.719938i	0.970504	−	0.241086i	$-0.0775035\pi$
$113$	13.2555	+	7.65305i	1.24697	+	0.719938i	0.276465	+	0.961024i	$0.410837\pi$
$114$		0			0
$115$	−17.5968	−	10.1595i	−1.64091	−	0.947377i
$116$		0			0
$117$	−14.9921	−	3.44434i	−1.38602	−	0.318429i
$118$		0			0
$119$	2.31635	−	2.17935i	0.212339	−	0.199780i
$120$		0			0
$121$	4.48758	+	7.77272i	0.407962	+	0.706611i
$122$		0			0
$123$	2.80224	−	1.22023i	0.252669	−	0.110024i
$124$		0			0
$125$		−	7.19072i		−	0.643158i
$126$		0			0
$127$		−	15.1494i		−	1.34429i	−0.740418	−	0.672147i	$-0.765372\pi$
$127$		−	15.1494i		−	1.34429i	0.740418	−	0.672147i	$-0.234628\pi$
$128$		0			0
$129$	−0.0482654	+	0.425641i	−0.00424953	+	0.0374756i
$130$		0			0
$131$	4.62022	+	8.00246i	0.403671	+	0.699178i	0.994166	−	0.107863i	$-0.0344008\pi$
$131$	4.62022	+	8.00246i	0.403671	+	0.699178i	−0.590495	+	0.807041i	$0.701068\pi$
$132$		0			0
$133$	18.0078	+	5.41820i	1.56148	+	0.469817i
$134$		0			0
$135$	−13.8445	+	2.58888i	−1.19155	+	0.222815i
$136$		0			0
$137$	−3.57002	−	2.06115i	−0.305008	−	0.176096i	0.339683	−	0.940540i	$-0.389680\pi$
$137$	−3.57002	−	2.06115i	−0.305008	−	0.176096i	−0.644690	+	0.764444i	$0.723014\pi$
$138$		0			0
$139$	3.87372	+	2.23649i	0.328564	+	0.189697i	0.655204	−	0.755452i	$-0.272583\pi$
$139$	3.87372	+	2.23649i	0.328564	+	0.189697i	−0.326639	+	0.945149i	$0.605916\pi$
$140$		0			0
$141$	−7.00426	+	9.47630i	−0.589865	+	0.798048i
$142$		0			0
$143$	−3.64817	−	6.31881i	−0.305075	−	0.528406i
$144$		0			0
$145$	−10.8122	+	18.7273i	−0.897905	+	1.55522i
$146$		0			0
$147$	−2.09712	+	11.9416i	−0.172968	+	0.984927i
$148$		0			0
$149$	17.5491	−	10.1320i	1.43768	−	0.830045i	0.439992	−	0.898002i	$-0.354981\pi$
$149$	17.5491	−	10.1320i	1.43768	−	0.830045i	0.997688	+	0.0679562i	$0.0216478\pi$
$150$		0			0
$151$	−6.44512	−	3.72109i	−0.524497	−	0.302818i	0.214276	−	0.976773i	$-0.431261\pi$
$151$	−6.44512	−	3.72109i	−0.524497	−	0.302818i	−0.738772	+	0.673955i	$0.764594\pi$
$152$		0			0
$153$	2.64007	+	2.45664i	0.213437	+	0.198607i
$154$		0			0
$155$	−9.95918	−	17.2498i	−0.799940	−	1.38554i
$156$		0			0
$157$	−14.9414			−1.19245			−0.596226	−	0.802816i	$-0.703334\pi$
$157$	−14.9414			−1.19245			−0.596226	+	0.802816i	$0.703334\pi$
$158$		0			0
$159$	−2.43068	+	21.4356i	−0.192765	+	1.69995i
$160$		0			0
$161$	−13.5905	−	14.4448i	−1.07108	−	1.13841i
$162$		0			0
$163$	−10.3855	−	5.99605i	−0.813453	−	0.469647i	0.0347008	−	0.999398i	$-0.488952\pi$
$163$	−10.3855	−	5.99605i	−0.813453	−	0.469647i	−0.848153	+	0.529751i	$0.822286\pi$
$164$		0			0
$165$	−5.37235	−	3.97090i	−0.418237	−	0.309134i
$166$		0			0
$167$	8.91245	−	15.4368i	0.689666	−	1.19454i	−0.282280	−	0.959332i	$-0.591091\pi$
$167$	8.91245	−	15.4368i	0.689666	−	1.19454i	0.971946	−	0.235205i	$-0.0755760\pi$
$168$		0			0
$169$	−6.64592	−	11.5111i	−0.511225	−	0.885467i
$170$		0			0
$171$	−4.77448	+	20.7818i	−0.365113	+	1.58922i
$172$		0			0
$173$			25.2496i			1.91969i	0.280526	+	0.959847i	$0.409491\pi$
$173$			25.2496i			1.91969i	−0.280526	+	0.959847i	$0.590509\pi$
$174$		0			0
$175$	−1.78922	+	5.94663i	−0.135253	+	0.449523i
$176$		0			0
$177$	4.89688	−	6.62515i	0.368072	−	0.497977i
$178$		0			0
$179$	−4.16327	−	7.21099i	−0.311177	−	0.538975i	0.667440	−	0.744663i	$-0.267390\pi$
$179$	−4.16327	−	7.21099i	−0.311177	−	0.538975i	−0.978617	+	0.205689i	$0.934057\pi$
$180$		0			0
$181$	15.6017			1.15967			0.579833	−	0.814735i	$-0.303118\pi$
$181$	15.6017			1.15967			0.579833	+	0.814735i	$0.303118\pi$
$182$		0			0
$183$	0.210667	−	0.285018i	0.0155730	−	0.0210692i
$184$		0			0
$185$		−	1.05485i		−	0.0775540i
$186$		0			0
$187$			1.71052i			0.125086i
$188$		0			0
$189$	−13.6685	−	1.47370i	−0.994238	−	0.107196i
$190$		0			0
$191$	−10.8565			−0.785552			−0.392776	−	0.919634i	$-0.628485\pi$
$191$	−10.8565			−0.785552			−0.392776	+	0.919634i	$0.628485\pi$
$192$		0			0
$193$	5.20956			0.374992			0.187496	−	0.982265i	$-0.439963\pi$
$193$	5.20956			0.374992			0.187496	+	0.982265i	$0.439963\pi$
$194$		0			0
$195$	−19.3589	−	14.3088i	−1.38632	−	1.02468i
$196$		0			0
$197$			20.7479i			1.47823i	0.673582	+	0.739113i	$0.264755\pi$
$197$			20.7479i			1.47823i	−0.673582	+	0.739113i	$0.735245\pi$
$198$		0			0
$199$	−1.76108	+	1.01676i	−0.124839	+	0.0720760i	−0.561119	−	0.827735i	$-0.689629\pi$
$199$	−1.76108	+	1.01676i	−0.124839	+	0.0720760i	0.436280	+	0.899811i	$0.356296\pi$
$200$		0			0
$201$	7.43531	+	5.49570i	0.524446	+	0.387636i
$202$		0			0
$203$	−15.3729	+	14.4636i	−1.07896	+	1.01515i
$204$		0			0
$205$	4.78307			0.334064
$206$		0			0
$207$	15.3197	−	16.4635i	1.06479	−	1.14430i
$208$		0			0
$209$	−8.75902	+	5.05702i	−0.605874	+	0.349802i
$210$		0			0
$211$	0.705274	+	0.407190i	0.0485531	+	0.0280321i	0.524080	−	0.851669i	$-0.324409\pi$
$211$	0.705274	+	0.407190i	0.0485531	+	0.0280321i	−0.475527	+	0.879701i	$0.657743\pi$
$212$		0			0
$213$	2.28986	−	3.09802i	0.156898	−	0.212273i
$214$		0			0
$215$	−0.335187	+	0.580560i	−0.0228595	+	0.0395939i
$216$		0			0
$217$	−4.45762	−	18.9242i	−0.302603	−	1.28466i
$218$		0			0
$219$	25.9782	+	2.94578i	1.75544	+	0.199058i
$220$		0			0
$221$			6.16375i			0.414619i
$222$		0			0
$223$	−9.40736	+	5.43134i	−0.629963	+	0.363709i	−0.780738	−	0.624859i	$-0.785157\pi$
$223$	−9.40736	+	5.43134i	−0.629963	+	0.363709i	0.150775	+	0.988568i	$0.451823\pi$
$224$		0			0
$225$	−6.86266	−	1.57665i	−0.457511	−	0.105110i
$226$		0			0
$227$	10.1494	−	17.5792i	0.673638	−	1.16677i	−0.303227	−	0.952918i	$-0.598064\pi$
$227$	10.1494	−	17.5792i	0.673638	−	1.16677i	0.976865	−	0.213857i	$-0.0686025\pi$
$228$		0			0
$229$	−2.51141	−	4.34989i	−0.165959	−	0.287449i	0.771037	−	0.636791i	$-0.219738\pi$
$229$	−2.51141	−	4.34989i	−0.165959	−	0.287449i	−0.936995	+	0.349342i	$0.886405\pi$
$230$		0			0
$231$	−3.90478	−	5.22246i	−0.256916	−	0.343613i
$232$		0			0
$233$	−12.4121	−	7.16616i	−0.813147	−	0.469470i	0.0349007	−	0.999391i	$-0.488889\pi$
$233$	−12.4121	−	7.16616i	−0.813147	−	0.469470i	−0.848047	+	0.529920i	$0.822222\pi$
$234$		0			0
$235$	−15.9705	+	9.22056i	−1.04180	+	0.601483i
$236$		0			0
$237$	13.4014	+	9.90547i	0.870517	+	0.643429i
$238$		0			0
$239$	−9.71239	+	16.8224i	−0.628242	+	1.08815i	0.359662	+	0.933083i	$0.382892\pi$
$239$	−9.71239	+	16.8224i	−0.628242	+	1.08815i	−0.987904	+	0.155065i	$0.950441\pi$
$240$		0			0
$241$	3.05881	−	5.29801i	0.197035	−	0.341275i	−0.750531	−	0.660836i	$-0.770202\pi$
$241$	3.05881	−	5.29801i	0.197035	−	0.341275i	0.947566	+	0.319561i	$0.103535\pi$
$242$		0			0
$243$	0.638369	−	15.5754i	0.0409514	−	0.999161i
$244$		0			0
$245$	−10.4699	+	15.8237i	−0.668900	+	1.01094i
$246$		0			0
$247$	−31.5625	+	18.2226i	−2.00828	+	1.15948i
$248$		0			0
$249$	8.92136	+	1.01163i	0.565368	+	0.0641097i
$250$		0			0
$251$	−2.54044			−0.160351			−0.0801757	−	0.996781i	$-0.525548\pi$
$251$	−2.54044			−0.160351			−0.0801757	+	0.996781i	$0.525548\pi$
$252$		0			0
$253$	10.6669			0.670620
$254$		0			0
$255$	2.25313	+	5.17430i	0.141097	+	0.324027i
$256$		0			0
$257$	16.0461	−	9.26423i	1.00093	−	0.577886i	0.0924058	−	0.995721i	$-0.470544\pi$
$257$	16.0461	−	9.26423i	1.00093	−	0.577886i	0.908523	+	0.417835i	$0.137211\pi$
$258$		0			0
$259$	0.296657	−	0.985964i	0.0184334	−	0.0612649i
$260$		0			0
$261$	−17.5213	−	16.3039i	−1.08454	−	1.00919i
$262$		0			0
$263$	6.21852	−	10.7708i	0.383451	−	0.664156i	−0.608102	−	0.793859i	$-0.708069\pi$
$263$	6.21852	−	10.7708i	0.383451	−	0.664156i	0.991553	+	0.129703i	$0.0414023\pi$
$264$		0			0
$265$	−16.8802	+	29.2374i	−1.03694	+	1.79604i
$266$		0			0
$267$	7.65402	−	3.33292i	0.468418	−	0.203972i
$268$		0			0
$269$	−21.0139	+	12.1324i	−1.28124	+	0.739723i	−0.977075	−	0.212897i	$-0.931710\pi$
$269$	−21.0139	+	12.1324i	−1.28124	+	0.739723i	−0.304163	+	0.952620i	$0.598377\pi$
$270$		0			0
$271$	17.6964	+	10.2170i	1.07498	+	0.620638i	0.929537	−	0.368729i	$-0.120207\pi$
$271$	17.6964	+	10.2170i	1.07498	+	0.620638i	0.145440	+	0.989367i	$0.453540\pi$
$272$		0			0
$273$	−14.0706	−	18.8188i	−0.851592	−	1.13896i
$274$		0			0
$275$	−1.66996	−	2.89245i	−0.100702	−	0.174421i
$276$		0			0
$277$	−6.63541	+	11.4929i	−0.398683	+	0.690539i	−0.993564	−	0.113275i	$-0.963866\pi$
$277$	−6.63541	+	11.4929i	−0.398683	+	0.690539i	0.594881	+	0.803814i	$0.297199\pi$
$278$		0			0
$279$	21.0751	−	6.46793i	1.26173	−	0.387225i
$280$		0			0
$281$	1.56448	−	0.903251i	0.0933289	−	0.0538835i	−0.452609	−	0.891709i	$-0.649507\pi$
$281$	1.56448	−	0.903251i	0.0933289	−	0.0538835i	0.545938	+	0.837826i	$0.316173\pi$
$282$		0			0
$283$		−	28.1885i		−	1.67563i	−0.545953	−	0.837816i	$-0.683832\pi$
$283$		−	28.1885i		−	1.67563i	0.545953	−	0.837816i	$-0.316168\pi$
$284$		0			0
$285$	−19.8347	+	26.8350i	−1.17490	+	1.58957i
$286$		0			0
$287$	4.47073	+	1.34515i	0.263899	+	0.0794019i
$288$		0			0
$289$	−7.77750	+	13.4710i	−0.457500	+	0.792413i
$290$		0			0
$291$	−8.27376	−	0.938200i	−0.485016	−	0.0549982i
$292$		0			0
$293$	−8.28005	−	4.78049i	−0.483726	−	0.279279i	0.238242	−	0.971206i	$-0.423429\pi$
$293$	−8.28005	−	4.78049i	−0.483726	−	0.279279i	−0.721968	+	0.691927i	$0.756762\pi$
$294$		0			0
$295$	11.1654	−	6.44636i	0.650076	−	0.375322i
$296$		0			0
$297$	5.61470	−	4.81099i	0.325798	−	0.279162i
$298$		0			0
$299$	38.4373			2.22289
$300$		0			0
$301$	−0.476570	+	0.448383i	−0.0274690	+	0.0258444i
$302$		0			0
$303$	−6.17051	+	2.68693i	−0.354486	+	0.154360i
$304$		0			0
$305$	0.480344	−	0.277327i	0.0275044	−	0.0158797i
$306$		0			0
$307$		−	19.8578i		−	1.13334i	−0.823944	−	0.566671i	$-0.808231\pi$
$307$		−	19.8578i		−	1.13334i	0.823944	−	0.566671i	$-0.191769\pi$
$308$		0			0
$309$	−2.49249	+	21.9807i	−0.141793	+	1.25044i
$310$		0			0
$311$	0.757772			0.0429693			0.0214846	−	0.999769i	$-0.493161\pi$
$311$	0.757772			0.0429693			0.0214846	+	0.999769i	$0.493161\pi$
$312$		0			0
$313$	−7.95282			−0.449520			−0.224760	−	0.974414i	$-0.572160\pi$
$313$	−7.95282			−0.449520			−0.224760	+	0.974414i	$0.572160\pi$
$314$		0			0
$315$	−18.6910	−	10.6544i	−1.05312	−	0.600307i
$316$		0			0
$317$			14.1843i			0.796667i	0.917241	+	0.398334i	$0.130411\pi$
$317$			14.1843i			0.796667i	−0.917241	+	0.398334i	$0.869589\pi$
$318$		0			0
$319$		−	11.3522i		−	0.635601i
$320$		0			0
$321$	8.58001	+	19.7039i	0.478889	+	1.09976i
$322$		0			0
$323$	8.54408			0.475405
$324$		0			0
$325$	−6.01757	−	10.4227i	−0.333795	−	0.578149i
$326$		0			0
$327$	21.1358	+	2.39669i	1.16881	+	0.132537i
$328$		0			0
$329$	−17.5207	+	4.12702i	−0.965946	+	0.227530i
$330$		0			0
$331$		−	8.43888i		−	0.463843i	−0.972735	−	0.231921i	$-0.925499\pi$
$331$		−	8.43888i		−	0.463843i	0.972735	−	0.231921i	$-0.0745012\pi$
$332$		0			0
$333$	1.13784	+	0.261412i	0.0623535	+	0.0143253i
$334$		0			0
$335$	7.23465	+	12.5308i	0.395271	+	0.684630i
$336$		0			0
$337$	6.41921	−	11.1184i	0.349677	−	0.605658i	−0.636515	−	0.771264i	$-0.719625\pi$
$337$	6.41921	−	11.1184i	0.349677	−	0.605658i	0.986192	+	0.165606i	$0.0529582\pi$
$338$		0			0
$339$	−24.3065	+	10.5842i	−1.32015	+	0.574854i
$340$		0			0
$341$	9.05564	+	5.22828i	0.490390	+	0.283127i
$342$		0			0
$343$	−14.2364	+	11.8459i	−0.768691	+	0.639620i
$344$		0			0
$345$	32.2671	−	14.0506i	1.73720	−	0.756459i
$346$		0			0
$347$	10.5540			0.566567			0.283283	−	0.959036i	$-0.408576\pi$
$347$	10.5540			0.566567			0.283283	+	0.959036i	$0.408576\pi$
$348$		0			0
$349$	−7.84572	−	13.5892i	−0.419972	−	0.727412i	0.575964	−	0.817475i	$-0.304627\pi$
$349$	−7.84572	−	13.5892i	−0.419972	−	0.727412i	−0.995936	+	0.0900624i	$0.971293\pi$
$350$		0			0
$351$	20.2322	−	17.3361i	1.07991	−	0.925330i
$352$		0			0
$353$	0.0186821	+	0.0107861i	0.000994348	+	0.000574087i	0.500497	−	0.865738i	$-0.333151\pi$
$353$	0.0186821	+	0.0107861i	0.000994348	+	0.000574087i	−0.499503	+	0.866312i	$0.666484\pi$
$354$		0			0
$355$	5.22112	−	3.01442i	0.277108	−	0.159989i
$356$		0			0
$357$	0.650821	+	5.47005i	0.0344451	+	0.289506i
$358$		0			0
$359$	−3.41437	+	5.91386i	−0.180203	+	0.312121i	−0.941950	−	0.335754i	$-0.891009\pi$
$359$	−3.41437	+	5.91386i	−0.180203	+	0.312121i	0.761746	+	0.647875i	$0.224342\pi$
$360$		0			0
$361$	15.7599	+	27.2969i	0.829468	+	1.43668i
$362$		0			0
$363$	−15.4465	−	1.75155i	−0.810729	−	0.0919323i
$364$		0			0
$365$	35.4333	+	20.4574i	1.85467	+	1.07079i
$366$		0			0
$367$	2.99931	+	1.73165i	0.156563	+	0.0903916i	0.576235	−	0.817284i	$-0.304521\pi$
$367$	2.99931	+	1.73165i	0.156563	+	0.0903916i	−0.419672	+	0.907676i	$0.637855\pi$
$368$		0			0
$369$	−1.18534	+	5.15941i	−0.0617063	+	0.268588i
$370$		0			0
$371$	−24.0004	+	22.5809i	−1.24604	+	1.17234i
$372$		0			0
$373$	−4.26770	−	7.39187i	−0.220973	−	0.382736i	0.734131	−	0.679008i	$-0.237590\pi$
$373$	−4.26770	−	7.39187i	−0.220973	−	0.382736i	−0.955104	+	0.296272i	$0.904257\pi$
$374$		0			0
$375$	10.0157	+	7.40299i	0.517211	+	0.382289i
$376$		0			0
$377$		−	40.9068i		−	2.10681i
$378$		0			0
$379$			6.38671i			0.328063i	0.986455	+	0.164032i	$0.0524499\pi$
$379$			6.38671i			0.328063i	−0.986455	+	0.164032i	$0.947550\pi$
$380$		0			0
$381$	21.1012	+	15.5966i	1.08105	+	0.799039i
$382$		0			0
$383$	13.2604	+	22.9677i	0.677575	+	1.17359i	0.975709	+	0.219070i	$0.0703023\pi$
$383$	13.2604	+	22.9677i	0.677575	+	1.17359i	−0.298135	+	0.954524i	$0.596364\pi$
$384$		0			0
$385$	−2.33971	−	9.93292i	−0.119243	−	0.506228i
$386$		0			0
$387$	−0.543173	−	0.505433i	−0.0276110	−	0.0256926i
$388$		0			0
$389$	0.247789	+	0.143061i	0.0125634	+	0.00725347i	0.506269	−	0.862376i	$-0.331024\pi$
$389$	0.247789	+	0.143061i	0.0125634	+	0.00725347i	−0.493705	+	0.869629i	$0.664358\pi$
$390$		0			0
$391$	−7.80382	−	4.50554i	−0.394656	−	0.227855i
$392$		0			0
$393$	−15.9030	−	1.80331i	−0.802200	−	0.0909652i
$394$		0			0
$395$	13.0398	+	22.5855i	0.656102	+	1.13640i
$396$		0			0
$397$	15.6448	−	27.0975i	0.785188	−	1.35998i	−0.143699	−	0.989621i	$-0.545900\pi$
$397$	15.6448	−	27.0975i	0.785188	−	1.35998i	0.928887	−	0.370363i	$-0.120767\pi$
$398$		0			0
$399$	−26.0863	+	19.5044i	−1.30595	+	0.976443i
$400$		0			0
$401$	−12.5838	+	7.26527i	−0.628406	+	0.362810i	−0.780135	−	0.625612i	$-0.784849\pi$
$401$	−12.5838	+	7.26527i	−0.628406	+	0.362810i	0.151728	+	0.988422i	$0.451516\pi$
$402$		0			0
$403$	32.6314	+	18.8397i	1.62548	+	0.938474i
$404$		0			0
$405$	10.6472	−	21.9489i	0.529065	−	1.09065i
$406$		0			0
$407$	0.276882	+	0.479574i	0.0137245	+	0.0237716i
$408$		0			0
$409$	−18.6983			−0.924573			−0.462286	−	0.886731i	$-0.652971\pi$
$409$	−18.6983			−0.924573			−0.462286	+	0.886731i	$0.652971\pi$
$410$		0			0
$411$	6.54633	−	2.85058i	0.322907	−	0.140609i
$412$		0			0
$413$	12.2492	−	2.88532i	0.602744	−	0.141977i
$414$		0			0
$415$	12.1684	+	7.02545i	0.597325	+	0.344866i
$416$		0			0
$417$	−7.10321	+	3.09308i	−0.347846	+	0.151469i
$418$		0			0
$419$	0.0728005	−	0.126094i	0.00355653	−	0.00616010i	−0.864242	−	0.503077i	$-0.832201\pi$
$419$	0.0728005	−	0.126094i	0.00355653	−	0.00616010i	0.867798	+	0.496917i	$0.165535\pi$
$420$		0			0
$421$	−10.4460	−	18.0930i	−0.509107	−	0.881799i	−0.999944	−	0.0105480i	$-0.996642\pi$
$421$	−10.4460	−	18.0930i	−0.509107	−	0.881799i	0.490837	−	0.871251i	$-0.336691\pi$
$422$		0			0
$423$	−5.98823	−	19.5121i	−0.291158	−	0.948709i
$424$		0			0
$425$			2.82147i			0.136861i
$426$		0			0
$427$	0.526969	−	0.124128i	0.0255018	−	0.00600699i
$428$		0			0
$429$	12.5572	+	1.42391i	0.606265	+	0.0687472i
$430$		0			0
$431$	−10.5495	−	18.2723i	−0.508151	−	0.880144i	−0.999955	−	0.00943786i	$-0.996996\pi$
$431$	−10.5495	−	18.2723i	−0.508151	−	0.880144i	0.491804	−	0.870706i	$-0.336338\pi$
$432$		0			0
$433$	9.19616			0.441939			0.220970	−	0.975281i	$-0.429078\pi$
$433$	9.19616			0.441939			0.220970	+	0.975281i	$0.429078\pi$
$434$		0			0
$435$	−14.9533	−	34.3401i	−0.716957	−	1.64648i
$436$		0			0
$437$		−	53.2811i		−	2.54878i
$438$		0			0
$439$			11.3238i			0.540456i	0.962796	+	0.270228i	$0.0870991\pi$
$439$			11.3238i			0.540456i	−0.962796	+	0.270228i	$0.912901\pi$
$440$		0			0
$441$	−14.4741	−	15.2151i	−0.689243	−	0.724531i
$442$		0			0
$443$	−34.8943			−1.65788			−0.828940	−	0.559338i	$-0.811055\pi$
$443$	−34.8943			−1.65788			−0.828940	+	0.559338i	$0.811055\pi$
$444$		0			0
$445$	13.0645			0.619315
$446$		0			0
$447$	−3.95461	+	34.8748i	−0.187047	+	1.64952i
$448$		0			0
$449$		−	24.4981i		−	1.15614i	−0.815988	−	0.578069i	$-0.803806\pi$
$449$		−	24.4981i		−	1.15614i	0.815988	−	0.578069i	$-0.196194\pi$
$450$		0			0
$451$	−2.17457	+	1.25549i	−0.102396	+	0.0591186i
$452$		0			0
$453$	11.8184	−	5.14629i	0.555276	−	0.241794i
$454$		0			0
$455$	−8.43100	−	35.7926i	−0.395251	−	1.67798i
$456$		0			0
$457$	33.8516			1.58351			0.791756	−	0.610838i	$-0.209167\pi$
$457$	33.8516			1.58351			0.791756	+	0.610838i	$0.209167\pi$
$458$		0			0
$459$	−6.13978	+	1.14812i	−0.286580	+	0.0535896i
$460$		0			0
$461$	0.526552	−	0.304005i	0.0245240	−	0.0141589i	−0.487688	−	0.873018i	$-0.662160\pi$
$461$	0.526552	−	0.304005i	0.0245240	−	0.0141589i	0.512212	+	0.858859i	$0.328826\pi$
$462$		0			0
$463$	13.6357	+	7.87260i	0.633707	+	0.365871i	0.782186	−	0.623045i	$-0.214105\pi$
$463$	13.6357	+	7.87260i	0.633707	+	0.365871i	−0.148479	+	0.988915i	$0.547438\pi$
$464$		0			0
$465$	34.2799	+	3.88716i	1.58969	+	0.180263i
$466$		0			0
$467$	−3.73247	+	6.46483i	−0.172718	+	0.299156i	−0.939369	−	0.342907i	$-0.888588\pi$
$467$	−3.73247	+	6.46483i	−0.172718	+	0.299156i	0.766651	+	0.642064i	$0.221922\pi$
$468$		0			0
$469$	3.23815	+	13.7471i	0.149524	+	0.634782i
$470$		0			0
$471$	15.3825	−	20.8114i	0.708786	−	0.958940i
$472$		0			0
$473$		−	0.351926i		−	0.0161816i
$474$		0			0
$475$	−14.4478	+	8.34144i	−0.662910	+	0.382732i
$476$		0			0
$477$	−27.3546	−	25.4540i	−1.25248	−	1.16546i
$478$		0			0
$479$	−14.0468	+	24.3297i	−0.641813	+	1.11165i	0.343215	+	0.939257i	$0.388484\pi$
$479$	−14.0468	+	24.3297i	−0.641813	+	1.11165i	−0.985028	+	0.172395i	$0.944849\pi$
$480$		0			0
$481$	0.997726	+	1.72811i	0.0454924	+	0.0787951i
$482$		0			0
$483$	34.1114	−	4.05854i	1.55212	−	0.184670i
$484$		0			0
$485$	−11.2851	−	6.51547i	−0.512431	−	0.295852i
$486$		0			0
$487$	23.2895	−	13.4462i	1.05535	−	0.609305i	0.131205	−	0.991355i	$-0.458115\pi$
$487$	23.2895	−	13.4462i	1.05535	−	0.609305i	0.924141	+	0.382051i	$0.124782\pi$
$488$		0			0
$489$	19.0438	−	8.29256i	0.861189	−	0.375003i
$490$		0			0
$491$	−0.958840	+	1.66076i	−0.0432719	+	0.0749491i	−0.886850	−	0.462057i	$-0.847111\pi$
$491$	−0.958840	+	1.66076i	−0.0432719	+	0.0749491i	0.843578	+	0.537006i	$0.180445\pi$
$492$		0			0
$493$	−4.79501	+	8.30520i	−0.215956	+	0.374048i
$494$		0			0
$495$	11.0619	−	3.39488i	0.497195	−	0.152589i
$496$		0			0
$497$	5.72792	−	1.34922i	0.256932	−	0.0605208i
$498$		0			0
$499$	−5.08439	+	2.93547i	−0.227608	+	0.131410i	−0.609468	−	0.792810i	$-0.708617\pi$
$499$	−5.08439	+	2.93547i	−0.227608	+	0.131410i	0.381860	+	0.924220i	$0.375284\pi$
$500$		0			0
$501$	12.3260	+	28.3064i	0.550683	+	1.26464i
$502$		0			0
$503$	10.9558			0.488495			0.244248	−	0.969713i	$-0.421459\pi$
$503$	10.9558			0.488495			0.244248	+	0.969713i	$0.421459\pi$
$504$		0			0
$505$	−10.5323			−0.468681
$506$		0			0
$507$	22.8755	+	2.59396i	1.01594	+	0.115202i
$508$		0			0
$509$	33.3859	−	19.2753i	1.47980	−	0.854364i	0.480064	−	0.877234i	$-0.340614\pi$
$509$	33.3859	−	19.2753i	1.47980	−	0.854364i	0.999738	+	0.0228696i	$0.00728024\pi$
$510$		0			0
$511$	27.3662	+	29.0865i	1.21061	+	1.28671i
$512$		0			0
$513$	−24.0309	−	28.0455i	−1.06099	−	1.23824i
$514$		0			0
$515$	−17.3095	+	29.9810i	−0.762748	+	1.32112i
$516$		0			0
$517$	4.84052	−	8.38403i	0.212886	−	0.368729i
$518$		0			0
$519$	−35.1695	−	25.9950i	−1.54377	−	1.14105i
$520$		0			0
$521$	16.6259	−	9.59898i	0.728395	−	0.420539i	−0.0894400	−	0.995992i	$-0.528508\pi$
$521$	16.6259	−	9.59898i	0.728395	−	0.420539i	0.817835	+	0.575453i	$0.195174\pi$
$522$		0			0
$523$	12.6079	+	7.27919i	0.551306	+	0.318297i	0.749649	−	0.661836i	$-0.230222\pi$
$523$	12.6079	+	7.27919i	0.551306	+	0.318297i	−0.198343	+	0.980133i	$0.563556\pi$
$524$		0			0
$525$	−6.44085	−	8.61433i	−0.281102	−	0.375960i
$526$		0			0
$527$	−4.41671	−	7.64996i	−0.192395	−	0.333237i
$528$		0			0
$529$	−16.5967	+	28.7463i	−0.721595	+	1.24984i
$530$		0			0
$531$	4.18655	+	13.6415i	0.181681	+	0.591989i
$532$		0			0
$533$	−7.83590	+	4.52406i	−0.339410	+	0.195959i
$534$		0			0
$535$			33.6321i			1.45404i
$536$		0			0
$537$	14.3301	+	1.62496i	0.618391	+	0.0701223i
$538$		0			0
$539$	0.606531	−	9.94228i	0.0261251	−	0.428244i
$540$		0			0
$541$	−2.33531	+	4.04487i	−0.100403	+	0.173903i	−0.911851	−	0.410522i	$-0.865346\pi$
$541$	−2.33531	+	4.04487i	−0.100403	+	0.173903i	0.811448	+	0.584425i	$0.198680\pi$
$542$		0			0
$543$	−16.0623	+	21.7312i	−0.689298	+	0.932574i
$544$		0			0
$545$	28.8285	+	16.6442i	1.23488	+	0.712957i
$546$		0			0
$547$	30.6708	−	17.7078i	1.31139	−	0.757130i	0.329062	−	0.944308i	$-0.393267\pi$
$547$	30.6708	−	17.7078i	1.31139	−	0.757130i	0.982326	+	0.187178i	$0.0599341\pi$
$548$		0			0
$549$	0.180108	+	0.586864i	0.00768683	+	0.0250468i
$550$		0			0
$551$	−56.7043			−2.41568
$552$		0			0
$553$	5.83646	+	24.7778i	0.248191	+	1.05366i
$554$		0			0
$555$	1.46927	+	1.08599i	0.0623670	+	0.0460976i
$556$		0			0
$557$	−19.7408	+	11.3974i	−0.836446	+	0.482922i	−0.856054	−	0.516886i	$-0.827091\pi$
$557$	−19.7408	+	11.3974i	−0.836446	+	0.482922i	0.0196089	+	0.999808i	$0.493758\pi$
$558$		0			0
$559$		−	1.26814i		−	0.0536367i
$560$		0			0
$561$	−2.38254	−	1.76102i	−0.100591	−	0.0743502i
$562$		0			0
$563$	−30.6920			−1.29351			−0.646756	−	0.762697i	$-0.723875\pi$
$563$	−30.6920			−1.29351			−0.646756	+	0.762697i	$0.723875\pi$
$564$		0			0
$565$	−41.4881			−1.74542
$566$		0			0
$567$	16.1247	−	17.5213i	0.677173	−	0.735824i
$568$		0			0
$569$		−	39.2328i		−	1.64472i	−0.568965	−	0.822362i	$-0.692656\pi$
$569$		−	39.2328i		−	1.64472i	0.568965	−	0.822362i	$-0.307344\pi$
$570$		0			0
$571$		−	1.86834i		−	0.0781877i	−0.999236	−	0.0390938i	$-0.987553\pi$
$571$		−	1.86834i		−	0.0781877i	0.999236	−	0.0390938i	$-0.0124471\pi$
$572$		0			0
$573$	11.1770	−	15.1218i	0.466927	−	0.631721i
$574$		0			0
$575$	17.5947			0.733751
$576$		0			0
$577$	20.6560	+	35.7773i	0.859921	+	1.48943i	0.872003	+	0.489500i	$0.162821\pi$
$577$	20.6560	+	35.7773i	0.859921	+	1.48943i	−0.0120819	+	0.999927i	$0.503846\pi$
$578$		0			0
$579$	−5.36334	+	7.25624i	−0.222893	+	0.301559i
$580$		0			0
$581$	9.39802	+	9.98882i	0.389896	+	0.414406i
$582$		0			0
$583$		−	17.7233i		−	0.734022i
$584$		0			0
$585$	39.8607	−	12.2332i	1.64804	−	0.505782i
$586$		0			0
$587$	−7.03460	−	12.1843i	−0.290349	−	0.502899i	0.683543	−	0.729910i	$-0.260438\pi$
$587$	−7.03460	−	12.1843i	−0.290349	−	0.502899i	−0.973892	+	0.227011i	$0.927105\pi$
$588$		0			0
$589$	26.1153	−	45.2330i	1.07606	−	1.86379i
$590$		0			0
$591$	−28.8991	−	21.3603i	−1.18875	−	0.878647i
$592$		0			0
$593$	−36.5014	−	21.0741i	−1.49893	−	0.865410i	−0.498935	−	0.866639i	$-0.666275\pi$
$593$	−36.5014	−	21.0741i	−1.49893	−	0.865410i	−0.999999	+	0.00122942i	$0.999609\pi$
$594$		0			0
$595$	−2.48381	+	8.25514i	−0.101826	+	0.338428i
$596$		0			0
$597$	0.396850	−	3.49972i	0.0162420	−	0.143234i
$598$		0			0
$599$	−16.3701			−0.668865			−0.334432	−	0.942420i	$-0.608545\pi$
$599$	−16.3701			−0.668865			−0.334432	+	0.942420i	$0.608545\pi$
$600$		0			0
$601$	3.42868	+	5.93864i	0.139859	+	0.242242i	0.927443	−	0.373965i	$-0.122002\pi$
$601$	3.42868	+	5.93864i	0.139859	+	0.242242i	−0.787584	+	0.616207i	$0.788669\pi$
$602$		0			0
$603$	−15.3096	+	4.69850i	−0.623455	+	0.191338i
$604$		0			0
$605$	−21.0685	−	12.1639i	−0.856554	−	0.494532i
$606$		0			0
$607$	36.5705	−	21.1140i	1.48435	−	0.856989i	0.484508	−	0.874787i	$-0.338999\pi$
$607$	36.5705	−	21.1140i	1.48435	−	0.856989i	0.999842	+	0.0177977i	$0.00566548\pi$
$608$		0			0
$609$	−4.31929	−	36.3030i	−0.175026	−	1.47107i
$610$		0			0
$611$	17.4425	−	30.2113i	0.705647	−	1.22222i
$612$		0			0
$613$	3.14051	+	5.43953i	0.126844	+	0.219700i	0.922452	−	0.386111i	$-0.126182\pi$
$613$	3.14051	+	5.43953i	0.126844	+	0.219700i	−0.795608	+	0.605812i	$0.792849\pi$
$614$		0			0
$615$	−4.92427	+	6.66220i	−0.198566	+	0.268646i
$616$		0			0
$617$	22.8749	+	13.2068i	0.920910	+	0.531688i	0.883925	−	0.467628i	$-0.154891\pi$
$617$	22.8749	+	13.2068i	0.920910	+	0.531688i	0.0369847	+	0.999316i	$0.488225\pi$
$618$		0			0
$619$	6.91891	+	3.99463i	0.278094	+	0.160558i	0.632560	−	0.774511i	$-0.282004\pi$
$619$	6.91891	+	3.99463i	0.278094	+	0.160558i	−0.354466	+	0.935069i	$0.615337\pi$
$620$		0			0
$621$	7.15970	+	38.2878i	0.287309	+	1.53644i
$622$		0			0
$623$	12.2113	+	3.67415i	0.489236	+	0.147202i
$624$		0			0
$625$	15.6133	+	27.0431i	0.624533	+	1.08172i
$626$		0			0
$627$	1.97380	−	17.4065i	0.0788261	−	0.695149i
$628$		0			0
$629$		−	0.467805i		−	0.0186526i
$630$		0			0
$631$		−	28.8074i		−	1.14681i	−0.819274	−	0.573403i	$-0.805623\pi$
$631$		−	28.8074i		−	1.14681i	0.819274	−	0.573403i	$-0.194377\pi$
$632$		0			0
$633$	−1.29326	+	0.563145i	−0.0514023	+	0.0223830i
$634$		0			0
$635$	20.5317	+	35.5620i	0.814777	+	1.41123i
$636$		0			0
$637$	2.18559	−	35.8263i	0.0865963	−	1.41949i
$638$		0			0
$639$	1.95769	+	6.37895i	0.0774452	+	0.252347i
$640$		0			0
$641$	26.0963	+	15.0667i	1.03074	+	0.595099i	0.917197	−	0.398434i	$-0.130446\pi$
$641$	26.0963	+	15.0667i	1.03074	+	0.595099i	0.113544	+	0.993533i	$0.463780\pi$
$642$		0			0
$643$	13.6075	+	7.85629i	0.536627	+	0.309822i	0.743711	−	0.668501i	$-0.233064\pi$
$643$	13.6075	+	7.85629i	0.536627	+	0.309822i	−0.207084	+	0.978323i	$0.566397\pi$
$644$		0			0
$645$	−0.463564	−	1.06457i	−0.0182528	−	0.0419174i
$646$		0			0
$647$	11.3703	+	19.6939i	0.447012	+	0.774248i	0.998190	−	0.0601397i	$-0.0191546\pi$
$647$	11.3703	+	19.6939i	0.447012	+	0.774248i	−0.551177	+	0.834388i	$0.685821\pi$
$648$		0			0
$649$	−3.38415	+	5.86152i	−0.132839	+	0.230085i
$650$		0			0
$651$	30.9482	+	13.2739i	1.21295	+	0.520246i
$652$		0			0
$653$	−35.2807	+	20.3693i	−1.38064	+	0.797114i	−0.992235	−	0.124374i	$-0.960308\pi$
$653$	−35.2807	+	20.3693i	−1.38064	+	0.797114i	−0.388407	+	0.921488i	$0.626974\pi$
$654$		0			0
$655$	−21.6912	−	12.5234i	−0.847544	−	0.489330i
$656$		0			0
$657$	−30.8481	+	33.1515i	−1.20350	+	1.29336i
$658$		0			0
$659$	−15.8968	−	27.5340i	−0.619251	−	1.07257i	−0.989623	−	0.143690i	$-0.954103\pi$
$659$	−15.8968	−	27.5340i	−0.619251	−	1.07257i	0.370372	−	0.928884i	$-0.379230\pi$
$660$		0			0
$661$	−39.4918			−1.53605			−0.768026	−	0.640419i	$-0.778761\pi$
$661$	−39.4918			−1.53605			−0.768026	+	0.640419i	$0.778761\pi$
$662$		0			0
$663$	−8.58531	−	6.34570i	−0.333426	−	0.246447i
$664$		0			0
$665$	−49.6150	+	11.6869i	−1.92399	+	0.453198i
$666$		0			0
$667$	51.7915	+	29.9018i	2.00537	+	1.15780i
$668$		0			0
$669$	2.11990	−	18.6949i	0.0819601	−	0.722787i
$670$		0			0
$671$	−0.145588	+	0.252166i	−0.00562038	+	0.00973478i
$672$		0			0
$673$	−6.03747	−	10.4572i	−0.232727	−	0.403095i	0.725883	−	0.687819i	$-0.241432\pi$
$673$	−6.03747	−	10.4572i	−0.232727	−	0.403095i	−0.958610	+	0.284723i	$0.908098\pi$
$674$		0			0
$675$	9.26131	−	7.93561i	0.356468	−	0.305442i
$676$		0			0
$677$		−	9.43834i		−	0.362745i	−0.983414	−	0.181373i	$-0.941946\pi$
$677$		−	9.43834i		−	0.362745i	0.983414	−	0.181373i	$-0.0580540\pi$
$678$		0			0
$679$	−8.71582	−	9.26373i	−0.334482	−	0.355509i
$680$		0			0
$681$	14.0366	+	32.2349i	0.537885	+	1.23525i
$682$		0			0
$683$	18.4219	+	31.9076i	0.704893	+	1.22091i	0.966730	+	0.255799i	$0.0823384\pi$
$683$	18.4219	+	31.9076i	0.704893	+	1.22091i	−0.261837	+	0.965112i	$0.584328\pi$
$684$		0			0
$685$	11.1738			0.426928
$686$		0			0
$687$	8.64437	+	0.980226i	0.329803	+	0.0373979i
$688$		0			0
$689$		−	63.8645i		−	2.43304i
$690$		0			0
$691$			16.4596i			0.626152i	0.949728	+	0.313076i	$0.101359\pi$
$691$			16.4596i			0.626152i	−0.949728	+	0.313076i	$0.898641\pi$
$692$		0			0
$693$	11.2943	−	0.0622307i	0.429034	−	0.00236395i
$694$		0			0
$695$	−12.1243			−0.459901
$696$		0			0
$697$	2.12120			0.0803463
$698$		0			0
$699$	22.7601	−	9.91082i	0.860865	−	0.374862i
$700$		0			0
$701$			23.7098i			0.895506i	0.894157	+	0.447753i	$0.147776\pi$
$701$			23.7098i			0.895506i	−0.894157	+	0.447753i	$0.852224\pi$
$702$		0			0
$703$	2.39548	−	1.38303i	0.0903472	−	0.0521620i
$704$		0			0
$705$	3.59887	−	31.7376i	0.135541	−	1.19531i
$706$		0			0
$707$	−9.84450	−	2.96202i	−0.370241	−	0.111398i
$708$		0			0
$709$	37.5648			1.41077			0.705387	−	0.708822i	$-0.250773\pi$
$709$	37.5648			1.41077			0.705387	+	0.708822i	$0.250773\pi$
$710$		0			0
$711$	−27.5941	+	8.46859i	−1.03486	+	0.317597i
$712$		0			0
$713$	−47.7054	+	27.5427i	−1.78658	+	1.03148i
$714$		0			0
$715$	17.1275	+	9.88859i	0.640534	+	0.369812i
$716$		0			0
$717$	−13.4323	−	30.8470i	−0.501637	−	1.15200i
$718$		0			0
$719$	13.5085	−	23.3975i	0.503783	−	0.872578i	−0.496207	−	0.868204i	$-0.665274\pi$
$719$	13.5085	−	23.3975i	0.503783	−	0.872578i	0.999990	−	0.00437396i	$-0.00139228\pi$
$720$		0			0
$721$	−24.6108	+	23.1551i	−0.916553	+	0.862342i
$722$		0			0
$723$	4.23034	+	9.71493i	0.157328	+	0.361302i
$724$		0			0
$725$		−	18.7252i		−	0.695435i
$726$		0			0
$727$	−6.96075	+	4.01879i	−0.258160	+	0.149049i	−0.623495	−	0.781827i	$-0.714288\pi$
$727$	−6.96075	+	4.01879i	−0.258160	+	0.149049i	0.365335	+	0.930876i	$0.380954\pi$
$728$		0			0
$729$	21.0373	+	16.9243i	0.779159	+	0.626827i
$730$		0			0
$731$	−0.148649	+	0.257467i	−0.00549798	+	0.00952278i
$732$		0			0
$733$	4.87974	+	8.45196i	0.180237	+	0.312180i	0.941961	−	0.335721i	$-0.108980\pi$
$733$	4.87974	+	8.45196i	0.180237	+	0.312180i	−0.761724	+	0.647902i	$0.775647\pi$
$734$		0			0
$735$	−11.2614	−	30.8741i	−0.415384	−	1.13881i
$736$		0			0
$737$	−6.57829	−	3.79798i	−0.242314	−	0.139900i
$738$		0			0
$739$	8.20806	−	4.73893i	0.301938	−	0.174324i	−0.341375	−	0.939927i	$-0.610893\pi$
$739$	8.20806	−	4.73893i	0.301938	−	0.174324i	0.643313	+	0.765603i	$0.277559\pi$
$740$		0			0
$741$	7.11246	−	62.7231i	0.261283	−	2.30419i
$742$		0			0
$743$	−23.9246	+	41.4386i	−0.877709	+	1.52024i	−0.0238602	+	0.999715i	$0.507596\pi$
$743$	−23.9246	+	41.4386i	−0.877709	+	1.52024i	−0.853849	+	0.520521i	$0.825738\pi$
$744$		0			0
$745$	−27.4634	+	47.5680i	−1.00618	+	1.74276i
$746$		0			0
$747$	−10.5938	+	11.3848i	−0.387607	+	0.416548i
$748$		0			0
$749$	−9.45842	+	31.4358i	−0.345603	+	1.14864i
$750$		0			0
$751$	−18.8378	+	10.8760i	−0.687399	+	0.396870i	−0.802637	−	0.596468i	$-0.796570\pi$
$751$	−18.8378	+	10.8760i	−0.687399	+	0.396870i	0.115238	+	0.993338i	$0.463237\pi$
$752$		0			0
$753$	2.61544	−	3.53851i	0.0953118	−	0.128951i
$754$		0			0
$755$	20.1725			0.734153
$756$		0			0
$757$	18.2247			0.662390			0.331195	−	0.943562i	$-0.392548\pi$
$757$	18.2247			0.662390			0.331195	+	0.943562i	$0.392548\pi$
$758$		0			0
$759$	−10.9817	+	14.8576i	−0.398612	+	0.539296i
$760$		0			0
$761$	−6.47507	+	3.73838i	−0.234721	+	0.135516i	−0.612748	−	0.790278i	$-0.709936\pi$
$761$	−6.47507	+	3.73838i	−0.234721	+	0.135516i	0.378027	+	0.925795i	$0.376603\pi$
$762$		0			0
$763$	22.2651	+	23.6648i	0.806050	+	0.856722i
$764$		0			0
$765$	−9.52677	−	2.18871i	−0.344441	−	0.0791331i
$766$		0			0
$767$	−12.1945	+	21.1216i	−0.440319	+	0.762656i
$768$		0			0
$769$	−11.1663	+	19.3406i	−0.402666	+	0.697439i	−0.994047	−	0.108954i	$-0.965250\pi$
$769$	−11.1663	+	19.3406i	−0.402666	+	0.697439i	0.591380	+	0.806393i	$0.298583\pi$
$770$		0			0
$771$	−3.61591	+	31.8879i	−0.130224	+	1.14841i
$772$		0			0
$773$	41.7168	−	24.0852i	1.50045	−	0.866285i	0.500450	−	0.865766i	$-0.333168\pi$
$773$	41.7168	−	24.0852i	1.50045	−	0.866285i	1.00000		0.000519449i	$-0.000165346\pi$
$774$		0			0
$775$	14.9371	+	8.62391i	0.536555	+	0.309780i
$776$		0			0
$777$	1.06791	+	1.42828i	0.0383109	+	0.0512391i
$778$		0			0
$779$	6.27117	+	10.8620i	0.224688	+	0.389171i
$780$		0			0
$781$	−1.58248	+	2.74094i	−0.0566256	+	0.0980784i
$782$		0			0
$783$	40.7478	−	7.61970i	1.45621	−	0.272306i
$784$		0			0
$785$	35.0737	−	20.2498i	1.25183	−	0.722746i
$786$		0			0
$787$		−	4.18145i		−	0.149053i	−0.997219	−	0.0745263i	$-0.976256\pi$
$787$		−	4.18145i		−	0.149053i	0.997219	−	0.0745263i	$-0.0237445\pi$
$788$		0			0
$789$	8.60024	+	19.7503i	0.306177	+	0.703131i
$790$		0			0
$791$	−38.7788	−	11.6678i	−1.37882	−	0.414859i
$792$		0			0
$793$	−0.524617	+	0.908664i	−0.0186297	+	0.0322676i
$794$		0			0
$795$	−23.3454	−	53.6125i	−0.827977	−	1.90144i
$796$		0			0
$797$	28.4260	+	16.4118i	1.00690	+	0.581335i	0.910283	−	0.413986i	$-0.135864\pi$
$797$	28.4260	+	16.4118i	1.00690	+	0.581335i	0.0966189	+	0.995321i	$0.469197\pi$
$798$		0			0
$799$	−7.08260	+	4.08914i	−0.250564	+	0.144663i
$800$		0			0
$801$	−3.23763	+	14.0924i	−0.114396	+	0.497930i
$802$		0			0
$803$	−21.4791			−0.757982
$804$		0			0
$805$	51.4793	+	15.4891i	1.81441	+	0.545919i
$806$		0			0
$807$	4.73537	−	41.7601i	0.166693	−	1.47003i
$808$		0			0
$809$	3.93633	−	2.27264i	0.138394	−	0.0799018i	−0.429204	−	0.903207i	$-0.641206\pi$
$809$	3.93633	−	2.27264i	0.138394	−	0.0799018i	0.567598	+	0.823306i	$0.307873\pi$
$810$		0			0
$811$		−	31.5008i		−	1.10614i	−0.833133	−	0.553072i	$-0.813455\pi$
$811$		−	31.5008i		−	1.10614i	0.833133	−	0.553072i	$-0.186545\pi$
$812$		0			0
$813$	−32.4497	+	14.1301i	−1.13806	+	0.495566i
$814$		0			0
$815$	32.5053			1.13861
$816$		0			0
$817$	−1.75787			−0.0615003
$818$		0			0
$819$	40.6981	−	0.224244i	1.42211	−	0.00783572i
$820$		0			0
$821$			28.2584i			0.986223i	0.869966	+	0.493112i	$0.164141\pi$
$821$			28.2584i			0.986223i	−0.869966	+	0.493112i	$0.835859\pi$
$822$		0			0
$823$		−	15.0066i		−	0.523096i	−0.965190	−	0.261548i	$-0.915767\pi$
$823$		−	15.0066i		−	0.523096i	0.965190	−	0.261548i	$-0.0842329\pi$
$824$		0			0
$825$	5.74806	+	0.651799i	0.200122	+	0.0226927i
$826$		0			0
$827$	−24.7519			−0.860709			−0.430354	−	0.902660i	$-0.641611\pi$
$827$	−24.7519			−0.860709			−0.430354	+	0.902660i	$0.641611\pi$
$828$		0			0
$829$	−1.67861	−	2.90744i	−0.0583005	−	0.100979i	0.835402	−	0.549639i	$-0.185235\pi$
$829$	−1.67861	−	2.90744i	−0.0583005	−	0.100979i	−0.893703	+	0.448660i	$0.851901\pi$
$830$		0			0
$831$	−9.17679	−	21.0744i	−0.318339	−	0.731063i
$832$		0			0
$833$	−4.64322	+	7.01753i	−0.160878	+	0.243143i
$834$		0			0
$835$			48.3155i			1.67203i
$836$		0			0
$837$	−12.6882	+	36.0137i	−0.438570	+	1.24482i
$838$		0			0
$839$	2.54338	+	4.40526i	0.0878073	+	0.152087i	0.906584	−	0.422025i	$-0.138681\pi$
$839$	2.54338	+	4.40526i	0.0878073	+	0.152087i	−0.818777	+	0.574112i	$0.805347\pi$
$840$		0			0
$841$	17.3229	−	30.0042i	0.597343	−	1.03463i
$842$		0			0
$843$	−0.352547	+	3.10903i	−0.0121424	+	0.107081i
$844$		0			0
$845$	31.2015	+	18.0142i	1.07336	+	0.619707i
$846$		0			0
$847$	−16.2718	−	17.2947i	−0.559104	−	0.594252i
$848$		0			0
$849$	39.2629	+	29.0206i	1.34750	+	0.995984i
$850$		0			0
$851$	−2.91725			−0.100002
$852$		0			0
$853$	20.5066	+	35.5185i	0.702134	+	1.21613i	0.967716	+	0.252043i	$0.0811024\pi$
$853$	20.5066	+	35.5185i	0.702134	+	1.21613i	−0.265582	+	0.964088i	$0.585564\pi$
$854$		0			0
$855$	−16.9575	−	55.2542i	−0.579933	−	1.88965i
$856$		0			0
$857$	−27.1819	−	15.6935i	−0.928515	−	0.536078i	−0.0421734	−	0.999110i	$-0.513428\pi$
$857$	−27.1819	−	15.6935i	−0.928515	−	0.536078i	−0.886342	+	0.463032i	$0.846762\pi$
$858$		0			0
$859$	−47.9116	+	27.6618i	−1.63472	+	0.943807i	−0.652113	+	0.758121i	$0.726117\pi$
$859$	−47.9116	+	27.6618i	−1.63472	+	0.943807i	−0.982609	+	0.185686i	$0.940549\pi$
$860$		0			0
$861$	−6.47633	+	4.84228i	−0.220713	+	0.165025i
$862$		0			0
$863$	7.18055	−	12.4371i	0.244429	−	0.423363i	−0.717542	−	0.696515i	$-0.754733\pi$
$863$	7.18055	−	12.4371i	0.244429	−	0.423363i	0.961971	+	0.273152i	$0.0880662\pi$
$864$		0			0
$865$	−34.2203	−	59.2714i	−1.16353	−	2.01529i
$866$		0			0
$867$	−10.7563	−	24.7017i	−0.365303	−	0.838915i
$868$		0			0
$869$	−11.8567	−	6.84549i	−0.402212	−	0.232217i
$870$		0			0
$871$	−23.7044	−	13.6857i	−0.803193	−	0.463724i
$872$		0			0
$873$	9.82478	−	10.5584i	0.332519	−	0.357347i
$874$		0			0
$875$	4.36196	+	18.5181i	0.147461	+	0.626025i
$876$		0			0
$877$	−25.5368	−	44.2310i	−0.862316	−	1.49358i	−0.869687	−	0.493603i	$-0.835680\pi$
$877$	−25.5368	−	44.2310i	−0.862316	−	1.49358i	0.00737111	−	0.999973i	$-0.497654\pi$
$878$		0			0
$879$	15.1831	−	6.61143i	0.512112	−	0.222998i
$880$		0			0
$881$			38.4851i			1.29660i	0.761387	+	0.648298i	$0.224519\pi$
$881$			38.4851i			1.29660i	−0.761387	+	0.648298i	$0.775481\pi$
$882$		0			0
$883$		−	16.7854i		−	0.564872i	−0.959286	−	0.282436i	$-0.908857\pi$
$883$		−	16.7854i		−	0.564872i	0.959286	−	0.282436i	$-0.0911425\pi$
$884$		0			0
$885$	−2.51607	+	22.1886i	−0.0845769	+	0.745863i
$886$		0			0
$887$	−17.1564	−	29.7157i	−0.576054	−	0.997755i	−0.995926	−	0.0901717i	$-0.971258\pi$
$887$	−17.1564	−	29.7157i	−0.576054	−	0.997755i	0.419872	−	0.907583i	$-0.362075\pi$
$888$		0			0
$889$	9.18978	+	39.0139i	0.308215	+	1.30848i
$890$		0			0
$891$	0.920640	+	12.7736i	0.0308426	+	0.427930i
$892$		0			0
$893$	−41.8783	−	24.1785i	−1.40140	−	0.809101i
$894$		0			0
$895$	19.5458	+	11.2848i	0.653345	+	0.377209i
$896$		0			0
$897$	−39.5720	+	53.5382i	−1.32127	+	1.78759i
$898$		0			0
$899$	29.3123	+	50.7703i	0.977618	+	1.69328i
$900$		0			0
$901$	−7.48606	+	12.9662i	−0.249397	+	0.431968i
$902$		0			0
$903$	−0.133901	−	1.12542i	−0.00445595	−	0.0374516i
$904$		0			0
$905$	−36.6237	+	21.1447i	−1.21741	+	0.702874i
$906$		0			0
$907$	26.2030	+	15.1283i	0.870058	+	0.502328i	0.867367	−	0.497668i	$-0.165810\pi$
$907$	26.2030	+	15.1283i	0.870058	+	0.502328i	0.00269031	+	0.999996i	$0.499144\pi$
$908$		0			0
$909$	2.61011	−	11.3610i	0.0865718	−	0.376820i
$910$		0			0
$911$	22.9890	+	39.8181i	0.761660	+	1.31923i	0.941995	+	0.335628i	$0.108948\pi$
$911$	22.9890	+	39.8181i	0.761660	+	1.31923i	−0.180335	+	0.983605i	$0.557718\pi$
$912$		0			0
$913$	−7.37631			−0.244120
$914$		0			0
$915$	−0.108243	+	0.954570i	−0.00357841	+	0.0315571i
$916$		0			0
$917$	−16.7527	−	17.8058i	−0.553223	−	0.588001i
$918$		0			0
$919$	6.58006	+	3.79900i	0.217056	+	0.125317i	0.604586	−	0.796540i	$-0.293338\pi$
$919$	6.58006	+	3.79900i	0.217056	+	0.125317i	−0.387530	+	0.921857i	$0.626672\pi$
$920$		0			0
$921$	27.6593	+	20.4440i	0.911405	+	0.673651i
$922$		0			0
$923$	−5.70235	+	9.87677i	−0.187695	+	0.325098i
$924$		0			0
$925$	0.456711	+	0.791046i	0.0150166	+	0.0260094i
$926$		0			0
$927$	−28.0502	−	26.1013i	−0.921290	−	0.857279i
$928$		0			0
$929$		−	38.0118i		−	1.24713i	−0.781773	−	0.623564i	$-0.785684\pi$
$929$		−	38.0118i		−	1.24713i	0.781773	−	0.623564i	$-0.214316\pi$
$930$		0			0
$931$	−49.6618	−	3.02963i	−1.62760	−	0.0992920i
$932$		0			0
$933$	−0.780141	+	1.05548i	−0.0255407	+	0.0345548i
$934$		0			0
$935$	−2.31824	−	4.01531i	−0.0758145	−	0.131315i
$936$		0			0
$937$	−53.0882			−1.73431			−0.867157	−	0.498034i	$-0.834055\pi$
$937$	−53.0882			−1.73431			−0.867157	+	0.498034i	$0.834055\pi$
$938$		0			0
$939$	8.18759	−	11.0773i	0.267192	−	0.361493i
$940$		0			0
$941$			9.52665i			0.310560i	0.987871	+	0.155280i	$0.0496280\pi$
$941$			9.52665i			0.310560i	−0.987871	+	0.155280i	$0.950372\pi$
$942$		0			0
$943$		−	13.2279i		−	0.430759i
$944$		0			0
$945$	34.0830	−	15.0653i	1.10872	−	0.490074i
$946$		0			0
$947$	−7.61009			−0.247295			−0.123647	−	0.992326i	$-0.539459\pi$
$947$	−7.61009			−0.247295			−0.123647	+	0.992326i	$0.539459\pi$
$948$		0			0
$949$	−77.3985			−2.51246
$950$		0			0
$951$	−19.7568	−	14.6030i	−0.640659	−	0.473534i
$952$		0			0
$953$			8.51742i			0.275906i	0.990439	+	0.137953i	$0.0440524\pi$
$953$			8.51742i			0.275906i	−0.990439	+	0.137953i	$0.955948\pi$
$954$		0			0
$955$	25.4848	−	14.7137i	0.824669	−	0.476123i
$956$		0			0
$957$	15.8121	+	11.6873i	0.511134	+	0.377797i
$958$		0			0
$959$	10.4441	+	3.14242i	0.337257	+	0.101474i
$960$		0			0
$961$	−22.9993			−0.741913
$962$		0			0
$963$	−36.2783	−	8.33469i	−1.16905	−	0.268582i
$964$		0			0
$965$	−12.2290	+	7.06042i	−0.393666	+	0.227283i
$966$		0			0
$967$	−13.0326	−	7.52437i	−0.419100	−	0.241967i	0.275592	−	0.961275i	$-0.411126\pi$
$967$	−13.0326	−	7.52437i	−0.419100	−	0.241967i	−0.694692	+	0.719307i	$0.744459\pi$
$968$		0			0
$969$	−8.79629	+	11.9008i	−0.282578	+	0.382309i
$970$		0			0
$971$	13.1706	−	22.8121i	0.422664	−	0.732076i	−0.573535	−	0.819181i	$-0.694428\pi$
$971$	13.1706	−	22.8121i	0.422664	−	0.732076i	0.996199	+	0.0871050i	$0.0277616\pi$
$972$		0			0
$973$	−11.3325	−	3.40974i	−0.363305	−	0.109311i
$974$		0			0
$975$	20.7127	+	2.34871i	0.663338	+	0.0752190i
$976$		0			0
$977$		−	27.2504i		−	0.871818i	−0.899991	−	0.435909i	$-0.856427\pi$
$977$		−	27.2504i		−	0.871818i	0.899991	−	0.435909i	$-0.143573\pi$
$978$		0			0
$979$	−5.93960	+	3.42923i	−0.189830	+	0.109599i
$980$		0			0
$981$	−25.0980	+	26.9720i	−0.801317	+	0.861150i
$982$		0			0
$983$	20.1791	−	34.9511i	0.643612	−	1.11477i	−0.341008	−	0.940060i	$-0.610768\pi$
$983$	20.1791	−	34.9511i	0.643612	−	1.11477i	0.984620	−	0.174708i	$-0.0558982\pi$
$984$		0			0
$985$	−28.1192	−	48.7039i	−0.895953	−	1.55184i
$986$		0			0
$987$	12.2895	−	28.6529i	0.391178	−	0.912032i
$988$		0			0
$989$	1.60557	+	0.926979i	0.0510543	+	0.0294762i
$990$		0			0
$991$	−24.0823	+	13.9039i	−0.765000	+	0.441673i	−0.831088	−	0.556141i	$-0.812282\pi$
$991$	−24.0823	+	13.9039i	−0.765000	+	0.441673i	0.0660879	+	0.997814i	$0.478948\pi$
$992$		0			0
$993$	11.7543	+	8.68799i	0.373010	+	0.275705i
$994$		0			0
$995$	2.75598	−	4.77350i	0.0873706	−	0.151330i
$996$		0			0
$997$	−23.1178	+	40.0413i	−0.732149	+	1.26812i	0.223813	+	0.974632i	$0.428149\pi$
$997$	−23.1178	+	40.0413i	−0.732149	+	1.26812i	−0.955963	+	0.293488i	$0.905184\pi$
$998$		0			0
$999$	−1.53555	+	1.31574i	−0.0485825	+	0.0416282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cj.c.527.5	yes	30
3.2	odd	2		3024.2.cj.c.2879.13		30
4.3	odd	2		1008.2.cj.d.527.11	yes	30
7.4	even	3		1008.2.bh.c.95.15	✓	30
9.2	odd	6		1008.2.bh.d.191.1	yes	30
9.7	even	3		3024.2.bh.d.1871.3		30
12.11	even	2		3024.2.cj.d.2879.13		30
21.11	odd	6		3024.2.bh.c.2447.13		30
28.11	odd	6		1008.2.bh.d.95.1	yes	30
36.7	odd	6		3024.2.bh.c.1871.3		30
36.11	even	6		1008.2.bh.c.191.15	yes	30
63.11	odd	6		1008.2.cj.d.767.11	yes	30
63.25	even	3		3024.2.cj.d.1439.13		30
84.11	even	6		3024.2.bh.d.2447.13		30
252.11	even	6	inner	1008.2.cj.c.767.5	yes	30
252.151	odd	6		3024.2.cj.c.1439.13		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bh.c.95.15	✓	30	7.4	even	3
1008.2.bh.c.191.15	yes	30	36.11	even	6
1008.2.bh.d.95.1	yes	30	28.11	odd	6
1008.2.bh.d.191.1	yes	30	9.2	odd	6
1008.2.cj.c.527.5	yes	30	1.1	even	1	trivial
1008.2.cj.c.767.5	yes	30	252.11	even	6	inner
1008.2.cj.d.527.11	yes	30	4.3	odd	2
1008.2.cj.d.767.11	yes	30	63.11	odd	6
3024.2.bh.c.1871.3		30	36.7	odd	6
3024.2.bh.c.2447.13		30	21.11	odd	6
3024.2.bh.d.1871.3		30	9.7	even	3
3024.2.bh.d.2447.13		30	84.11	even	6
3024.2.cj.c.1439.13		30	252.151	odd	6
3024.2.cj.c.2879.13		30	3.2	odd	2
3024.2.cj.d.1439.13		30	63.25	even	3
3024.2.cj.d.2879.13		30	12.11	even	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02952 + 1.39287i) q^{3} +(-2.34742 + 1.35528i) q^{5} +(-2.57527 + 0.606609i) q^{7} +(-0.880179 - 2.86798i) q^{9} +O(q^{10})\)	\(q+(-1.02952 + 1.39287i) q^{3} +(-2.34742 + 1.35528i) q^{5} +(-2.57527 + 0.606609i) q^{7} +(-0.880179 - 2.86798i) q^{9} +(0.711483 - 1.23232i) q^{11} +(2.56378 - 4.44059i) q^{13} +(0.528979 - 4.66494i) q^{15} +(-1.04103 + 0.601041i) q^{17} +(-6.15547 - 3.55386i) q^{19} +(1.80636 - 4.21154i) q^{21} +(3.74811 + 6.49192i) q^{23} +(1.17357 - 2.03269i) q^{25} +(4.90088 + 1.72666i) q^{27} +(6.90901 - 3.98892i) q^{29} +7.34842i q^{31} +(0.983983 + 2.25971i) q^{33} +(5.22311 - 4.91418i) q^{35} +(-0.194581 + 0.337025i) q^{37} +(3.54572 + 8.14269i) q^{39} +(-1.52819 - 0.882303i) q^{41} +(0.214184 - 0.123659i) q^{43} +(5.95306 + 5.53944i) q^{45} +6.80343 q^{47} +(6.26405 - 3.12437i) q^{49} +(0.234592 - 2.06881i) q^{51} +(10.7865 - 6.22758i) q^{53} +3.85704i q^{55} +(11.2873 - 4.91501i) q^{57} -4.75647 q^{59} -0.204627 q^{61} +(4.00644 + 6.85189i) q^{63} +13.8986i q^{65} -5.33812i q^{67} +(-12.9012 - 1.46292i) q^{69} -2.22420 q^{71} +(-7.54731 - 13.0723i) q^{73} +(1.62306 + 3.72733i) q^{75} +(-1.08472 + 3.60516i) q^{77} -9.62145i q^{79} +(-7.45057 + 5.04866i) q^{81} +(-2.59188 - 4.48927i) q^{83} +(1.62916 - 2.82179i) q^{85} +(-1.55691 + 13.7300i) q^{87} +(-4.17410 - 2.40992i) q^{89} +(-3.90872 + 12.9910i) q^{91} +(-10.2354 - 7.56534i) q^{93} +19.2659 q^{95} +(2.40373 + 4.16339i) q^{97} +(-4.16051 - 0.955849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{5} - 7 q^{7} + 8 q^{9}+O(q^{10}) \) 30 * q + 3 * q^5 - 7 * q^7 + 8 * q^9	\( 30 q + 3 q^{5} - 7 q^{7} + 8 q^{9} - 3 q^{11} - 12 q^{17} - 9 q^{19} + 2 q^{21} + 12 q^{23} + 18 q^{25} + 27 q^{27} + 27 q^{29} + 13 q^{33} - 6 q^{35} + 6 q^{37} + 12 q^{39} + 9 q^{41} - 21 q^{43} + 13 q^{45} - 3 q^{49} + 12 q^{51} + 3 q^{53} + 20 q^{57} - 6 q^{59} + 6 q^{61} + 51 q^{63} + 10 q^{69} + 18 q^{71} + 21 q^{73} - 3 q^{75} + 72 q^{77} - 20 q^{81} - 15 q^{83} - 3 q^{85} - 57 q^{87} - 6 q^{89} + 26 q^{91} + 9 q^{93} + 54 q^{95} - 6 q^{97} - 48 q^{99}+O(q^{100}) \) 30 * q + 3 * q^5 - 7 * q^7 + 8 * q^9 - 3 * q^11 - 12 * q^17 - 9 * q^19 + 2 * q^21 + 12 * q^23 + 18 * q^25 + 27 * q^27 + 27 * q^29 + 13 * q^33 - 6 * q^35 + 6 * q^37 + 12 * q^39 + 9 * q^41 - 21 * q^43 + 13 * q^45 - 3 * q^49 + 12 * q^51 + 3 * q^53 + 20 * q^57 - 6 * q^59 + 6 * q^61 + 51 * q^63 + 10 * q^69 + 18 * q^71 + 21 * q^73 - 3 * q^75 + 72 * q^77 - 20 * q^81 - 15 * q^83 - 3 * q^85 - 57 * q^87 - 6 * q^89 + 26 * q^91 + 9 * q^93 + 54 * q^95 - 6 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

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Database

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