LMFDB - Embedded newform 1216.2.s.i.31.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(31,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1216.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.s (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:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.11
Character	$\chi$	$=$	1216.31
Dual form			1216.2.s.i.863.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22910 - 0.709622i) q^{3} +(2.34387 - 1.35323i) q^{5} +4.52840i q^{7} +(-0.492874 + 0.853683i) q^{9} +O(q^{10})$	\(q+(1.22910 - 0.709622i) q^{3} +(2.34387 - 1.35323i) q^{5} +4.52840i q^{7} +(-0.492874 + 0.853683i) q^{9} -4.04042 q^{11} +(1.51867 - 2.63041i) q^{13} +(1.92057 - 3.32652i) q^{15} +(2.88017 + 4.98860i) q^{17} +(4.10778 + 1.45813i) q^{19} +(3.21345 + 5.56586i) q^{21} +(1.92057 + 1.10884i) q^{23} +(1.16249 - 2.01348i) q^{25} +5.65675i q^{27} +(3.96196 - 6.86232i) q^{29} +7.84342 q^{31} +(-4.96608 + 2.86717i) q^{33} +(6.12799 + 10.6140i) q^{35} -6.02920 q^{37} -4.31072i q^{39} +(2.97862 - 1.71971i) q^{41} +(2.63041 + 4.55601i) q^{43} +2.66790i q^{45} +(-8.05662 - 4.65149i) q^{47} -13.5064 q^{49} +(7.08003 + 4.08766i) q^{51} +(2.93791 - 5.08861i) q^{53} +(-9.47021 + 5.46763i) q^{55} +(6.08360 - 1.12277i) q^{57} +(-0.972014 + 0.561192i) q^{59} +(9.77209 + 5.64192i) q^{61} +(-3.86582 - 2.23193i) q^{63} -8.22046i q^{65} +(-8.69104 - 5.01777i) q^{67} +3.14743 q^{69} +(-0.269091 - 0.466080i) q^{71} +(-3.22481 - 5.58553i) q^{73} -3.29970i q^{75} -18.2966i q^{77} +(2.40286 + 4.16188i) q^{79} +(2.53553 + 4.39166i) q^{81} -10.6912 q^{83} +(13.5015 + 7.79508i) q^{85} -11.2460i q^{87} +(-14.5977 - 8.42801i) q^{89} +(11.9116 + 6.87714i) q^{91} +(9.64035 - 5.56586i) q^{93} +(11.6013 - 2.14111i) q^{95} +(12.0852 - 6.97740i) q^{97} +(1.99142 - 3.44924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 24 q^{9}+O(q^{10}) $ 32 * q + 24 * q^9	$ 32 q + 24 q^{9} + 20 q^{17} + 44 q^{25} - 60 q^{33} - 24 q^{41} - 64 q^{49} - 36 q^{57} - 64 q^{73} - 24 q^{81} - 12 q^{89} - 48 q^{97}+O(q^{100}) $ 32 * q + 24 * q^9 + 20 * q^17 + 44 * q^25 - 60 * q^33 - 24 * q^41 - 64 * q^49 - 36 * q^57 - 64 * q^73 - 24 * q^81 - 12 * q^89 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.22910	−	0.709622i	0.709622	−	0.409700i	−0.101299	−	0.994856i	$-0.532300\pi$
$3$	1.22910	−	0.709622i	0.709622	−	0.409700i	0.810921	+	0.585156i	$0.198967\pi$
$4$		0			0
$5$	2.34387	−	1.35323i	1.04821	−	0.605185i	0.126063	−	0.992022i	$-0.459766\pi$
$5$	2.34387	−	1.35323i	1.04821	−	0.605185i	0.922148	+	0.386838i	$0.126433\pi$
$6$		0			0
$7$			4.52840i			1.71157i	0.517328	+	0.855787i	$0.326927\pi$
$7$			4.52840i			1.71157i	−0.517328	+	0.855787i	$0.673073\pi$
$8$		0			0
$9$	−0.492874	+	0.853683i	−0.164291	+	0.284561i
$10$		0			0
$11$	−4.04042			−1.21823			−0.609116	−	0.793081i	$-0.708476\pi$
$11$	−4.04042			−1.21823			−0.609116	+	0.793081i	$0.708476\pi$
$12$		0			0
$13$	1.51867	−	2.63041i	0.421203	−	0.729545i	−0.574855	−	0.818256i	$-0.694941\pi$
$13$	1.51867	−	2.63041i	0.421203	−	0.729545i	0.996057	+	0.0887109i	$0.0282747\pi$
$14$		0			0
$15$	1.92057	−	3.32652i	0.495889	−	0.858904i
$16$		0			0
$17$	2.88017	+	4.98860i	0.698543	+	1.20991i	0.968972	+	0.247172i	$0.0795013\pi$
$17$	2.88017	+	4.98860i	0.698543	+	1.20991i	−0.270429	+	0.962740i	$0.587165\pi$
$18$		0			0
$19$	4.10778	+	1.45813i	0.942389	+	0.334519i
$19$	4.10778	+	1.45813i	0.942389	+	0.334519i
$20$		0			0
$21$	3.21345	+	5.56586i	0.701233	+	1.21457i
$22$		0			0
$23$	1.92057	+	1.10884i	0.400466	+	0.231209i	0.686685	−	0.726955i	$-0.259065\pi$
$23$	1.92057	+	1.10884i	0.400466	+	0.231209i	−0.286219	+	0.958164i	$0.592398\pi$
$24$		0			0
$25$	1.16249	−	2.01348i	0.232497	−	0.402697i
$26$		0			0
$27$			5.65675i			1.08864i
$28$		0			0
$29$	3.96196	−	6.86232i	0.735718	−	1.27430i	−0.218689	−	0.975795i	$-0.570178\pi$
$29$	3.96196	−	6.86232i	0.735718	−	1.27430i	0.954408	−	0.298507i	$-0.0964886\pi$
$30$		0			0
$31$	7.84342			1.40872			0.704360	−	0.709843i	$-0.251234\pi$
$31$	7.84342			1.40872			0.704360	+	0.709843i	$0.251234\pi$
$32$		0			0
$33$	−4.96608	+	2.86717i	−0.864483	+	0.499110i
$34$		0			0
$35$	6.12799	+	10.6140i	1.03582	+	1.79409i
$36$		0			0
$37$	−6.02920			−0.991195			−0.495597	−	0.868552i	$-0.665051\pi$
$37$	−6.02920			−0.991195			−0.495597	+	0.868552i	$0.665051\pi$
$38$		0			0
$39$		−	4.31072i		−	0.690268i
$40$		0			0
$41$	2.97862	−	1.71971i	0.465183	−	0.268573i	−0.249038	−	0.968494i	$-0.580114\pi$
$41$	2.97862	−	1.71971i	0.465183	−	0.268573i	0.714221	+	0.699920i	$0.246781\pi$
$42$		0			0
$43$	2.63041	+	4.55601i	0.401134	+	0.694784i	0.993863	−	0.110618i	$-0.0352829\pi$
$43$	2.63041	+	4.55601i	0.401134	+	0.694784i	−0.592729	+	0.805402i	$0.701950\pi$
$44$		0			0
$45$			2.66790i			0.397707i
$46$		0			0
$47$	−8.05662	−	4.65149i	−1.17518	−	0.678490i	−0.220285	−	0.975436i	$-0.570699\pi$
$47$	−8.05662	−	4.65149i	−1.17518	−	0.678490i	−0.954894	+	0.296946i	$0.904032\pi$
$48$		0			0
$49$	−13.5064			−1.92949
$50$		0			0
$51$	7.08003	+	4.08766i	0.991403	+	0.572387i
$52$		0			0
$53$	2.93791	−	5.08861i	0.403553	−	0.698975i	−0.590599	−	0.806965i	$-0.701108\pi$
$53$	2.93791	−	5.08861i	0.403553	−	0.698975i	0.994152	+	0.107991i	$0.0344417\pi$
$54$		0			0
$55$	−9.47021	+	5.46763i	−1.27696	+	0.737255i
$56$		0			0
$57$	6.08360	−	1.12277i	0.805792	−	0.148715i
$58$		0			0
$59$	−0.972014	+	0.561192i	−0.126545	+	0.0730610i	−0.561936	−	0.827180i	$-0.689943\pi$
$59$	−0.972014	+	0.561192i	−0.126545	+	0.0730610i	0.435391	+	0.900241i	$0.356610\pi$
$60$		0			0
$61$	9.77209	+	5.64192i	1.25119	+	0.722374i	0.971345	−	0.237672i	$-0.0763844\pi$
$61$	9.77209	+	5.64192i	1.25119	+	0.722374i	0.279842	+	0.960046i	$0.409718\pi$
$62$		0			0
$63$	−3.86582	−	2.23193i	−0.487048	−	0.281197i
$64$		0			0
$65$		−	8.22046i		−	1.01962i
$66$		0			0
$67$	−8.69104	−	5.01777i	−1.06178	−	0.613018i	−0.135855	−	0.990729i	$-0.543378\pi$
$67$	−8.69104	−	5.01777i	−1.06178	−	0.613018i	−0.925924	+	0.377710i	$0.876712\pi$
$68$		0			0
$69$	3.14743			0.378906
$70$		0			0
$71$	−0.269091	−	0.466080i	−0.0319352	−	0.0553135i	0.849616	−	0.527402i	$-0.176834\pi$
$71$	−0.269091	−	0.466080i	−0.0319352	−	0.0553135i	−0.881551	+	0.472088i	$0.843500\pi$
$72$		0			0
$73$	−3.22481	−	5.58553i	−0.377435	−	0.653737i	0.613253	−	0.789886i	$-0.289861\pi$
$73$	−3.22481	−	5.58553i	−0.377435	−	0.653737i	−0.990688	+	0.136150i	$0.956527\pi$
$74$		0			0
$75$		−	3.29970i		−	0.381016i
$76$		0			0
$77$		−	18.2966i		−	2.08509i
$78$		0			0
$79$	2.40286	+	4.16188i	0.270343	+	0.468248i	0.968950	−	0.247258i	$-0.0795296\pi$
$79$	2.40286	+	4.16188i	0.270343	+	0.468248i	−0.698607	+	0.715506i	$0.746196\pi$
$80$		0			0
$81$	2.53553	+	4.39166i	0.281725	+	0.487962i
$82$		0			0
$83$	−10.6912			−1.17351			−0.586753	−	0.809766i	$-0.699594\pi$
$83$	−10.6912			−1.17351			−0.586753	+	0.809766i	$0.699594\pi$
$84$		0			0
$85$	13.5015	+	7.79508i	1.46444	+	0.845495i
$86$		0			0
$87$		−	11.2460i		−	1.20570i
$88$		0			0
$89$	−14.5977	−	8.42801i	−1.54736	−	0.893368i	−0.998342	−	0.0575556i	$-0.981669\pi$
$89$	−14.5977	−	8.42801i	−1.54736	−	0.893368i	−0.549016	−	0.835812i	$-0.684997\pi$
$90$		0			0
$91$	11.9116	+	6.87714i	1.24867	+	0.720920i
$92$		0			0
$93$	9.64035	−	5.56586i	0.999658	−	0.577153i
$94$		0			0
$95$	11.6013	−	2.14111i	1.19027	−	0.219673i
$96$		0			0
$97$	12.0852	−	6.97740i	1.22707	−	0.708447i	0.260651	−	0.965433i	$-0.416063\pi$
$97$	12.0852	−	6.97740i	1.22707	−	0.708447i	0.966415	+	0.256986i	$0.0827294\pi$
$98$		0			0
$99$	1.99142	−	3.44924i	0.200145	−	0.346661i
$100$		0			0
$101$	−2.34387	−	1.35323i	−0.233224	−	0.134652i	0.378835	−	0.925464i	$-0.376325\pi$
$101$	−2.34387	−	1.35323i	−0.233224	−	0.134652i	−0.612058	+	0.790813i	$0.709658\pi$
$102$		0			0
$103$	6.92820			0.682656			0.341328	−	0.939944i	$-0.389123\pi$
$103$	6.92820			0.682656			0.341328	+	0.939944i	$0.389123\pi$
$104$		0			0
$105$	15.0638	+	8.69710i	1.47008	+	0.848750i
$106$		0			0
$107$		−	6.13929i		−	0.593508i	−0.954954	−	0.296754i	$-0.904096\pi$
$107$		−	6.13929i		−	0.593508i	0.954954	−	0.296754i	$-0.0959041\pi$
$108$		0			0
$109$	−6.20641	−	10.7498i	−0.594466	−	1.02965i	−0.993622	−	0.112763i	$-0.964030\pi$
$109$	−6.20641	−	10.7498i	−0.594466	−	1.02965i	0.399156	−	0.916883i	$-0.369303\pi$
$110$		0			0
$111$	−7.41050	+	4.27845i	−0.703373	+	0.406093i
$112$		0			0
$113$			13.4166i			1.26213i	0.775731	+	0.631064i	$0.217382\pi$
$113$			13.4166i			1.26213i	−0.775731	+	0.631064i	$0.782618\pi$
$114$		0			0
$115$	6.00208			0.559697
$116$		0			0
$117$	1.49703	+	2.59292i	0.138400	+	0.239716i
$118$		0			0
$119$	−22.5904	+	13.0426i	−2.07085	+	1.19561i
$120$		0			0
$121$	5.32497			0.484088
$122$		0			0
$123$	2.44069	−	4.22739i	0.220069	−	0.381171i
$124$		0			0
$125$			7.23988i			0.647555i
$126$		0			0
$127$	0.670810	−	1.16188i	0.0595248	−	0.103100i	−0.834727	−	0.550663i	$-0.814375\pi$
$127$	0.670810	−	1.16188i	0.0595248	−	0.103100i	0.894252	+	0.447563i	$0.147708\pi$
$128$		0			0
$129$	6.46608	+	3.73319i	0.569307	+	0.328689i
$130$		0			0
$131$	3.05958	+	5.29935i	0.267317	+	0.463007i	0.968168	−	0.250301i	$-0.0805296\pi$
$131$	3.05958	+	5.29935i	0.267317	+	0.463007i	−0.700851	+	0.713308i	$0.747196\pi$
$132$		0			0
$133$	−6.60302	+	18.6017i	−0.572554	+	1.61297i
$134$		0			0
$135$	7.65490	+	13.2587i	0.658829	+	1.14113i
$136$		0			0
$137$	0.717681	−	1.24306i	0.0613157	−	0.106202i	−0.833738	−	0.552160i	$-0.813804\pi$
$137$	0.717681	−	1.24306i	0.0613157	−	0.106202i	0.895054	+	0.445958i	$0.147137\pi$
$138$		0			0
$139$	−10.0636	+	17.4306i	−0.853580	+	1.47844i	0.0243767	+	0.999703i	$0.492240\pi$
$139$	−10.0636	+	17.4306i	−0.853580	+	1.47844i	−0.877956	+	0.478741i	$0.841093\pi$
$140$		0			0
$141$	−13.2032			−1.11191
$142$		0			0
$143$	−6.13605	+	10.6280i	−0.513123	+	0.888754i
$144$		0			0
$145$		−	21.4459i		−	1.78098i
$146$		0			0
$147$	−16.6007	+	9.58444i	−1.36921	+	0.790512i
$148$		0			0
$149$	4.65434	−	2.68718i	0.381298	−	0.220143i	−0.297085	−	0.954851i	$-0.596014\pi$
$149$	4.65434	−	2.68718i	0.381298	−	0.220143i	0.678383	+	0.734709i	$0.262681\pi$
$150$		0			0
$151$	−4.37932			−0.356384			−0.178192	−	0.983996i	$-0.557025\pi$
$151$	−4.37932			−0.356384			−0.178192	+	0.983996i	$0.557025\pi$
$152$		0			0
$153$	−5.67824			−0.459059
$154$		0			0
$155$	18.3840	−	10.6140i	1.47664	−	0.852536i
$156$		0			0
$157$	4.38947	−	2.53426i	0.350317	−	0.202256i	−0.314508	−	0.949255i	$-0.601839\pi$
$157$	4.38947	−	2.53426i	0.350317	−	0.202256i	0.664825	+	0.746999i	$0.268506\pi$
$158$		0			0
$159$		−	8.33922i		−	0.661343i
$160$		0			0
$161$	−5.02128	+	8.69710i	−0.395732	+	0.685428i
$162$		0			0
$163$	−5.79239			−0.453695			−0.226847	−	0.973930i	$-0.572842\pi$
$163$	−5.79239			−0.453695			−0.226847	+	0.973930i	$0.572842\pi$
$164$		0			0
$165$	−7.75990	+	13.4405i	−0.604107	+	1.04634i
$166$		0			0
$167$	5.46524	−	9.46608i	0.422913	−	0.732507i	−0.573310	−	0.819339i	$-0.694341\pi$
$167$	5.46524	−	9.46608i	0.422913	−	0.732507i	0.996223	+	0.0868315i	$0.0276742\pi$
$168$		0			0
$169$	1.88729	+	3.26889i	0.145176	+	0.251453i
$170$		0			0
$171$	−3.26940	+	2.78807i	−0.250018	+	0.213209i
$172$		0			0
$173$	−9.24375	−	16.0106i	−0.702789	−	1.21727i	−0.967484	−	0.252934i	$-0.918604\pi$
$173$	−9.24375	−	16.0106i	−0.702789	−	1.21727i	0.264695	−	0.964332i	$-0.414729\pi$
$174$		0			0
$175$	9.11786	+	5.26420i	0.689246	+	0.397936i
$176$		0			0
$177$	−0.796468	+	1.37952i	−0.0598662	+	0.103691i
$178$		0			0
$179$		−	13.3697i		−	0.999301i	−0.866227	−	0.499651i	$-0.833462\pi$
$179$		−	13.3697i		−	0.999301i	0.866227	−	0.499651i	$-0.166538\pi$
$180$		0			0
$181$	−13.2274	+	22.9104i	−0.983181	+	1.70292i	−0.333427	+	0.942776i	$0.608205\pi$
$181$	−13.2274	+	22.9104i	−0.983181	+	1.70292i	−0.649754	+	0.760144i	$0.725128\pi$
$182$		0			0
$183$	16.0145			1.18383
$184$		0			0
$185$	−14.1317	+	8.15892i	−1.03898	+	0.599856i
$186$		0			0
$187$	−11.6371	−	20.1560i	−0.850987	−	1.47395i
$188$		0			0
$189$	−25.6160			−1.86329
$190$		0			0
$191$		−	16.4354i		−	1.18922i	−0.804014	−	0.594611i	$-0.797306\pi$
$191$		−	16.4354i		−	1.18922i	0.804014	−	0.594611i	$-0.202694\pi$
$192$		0			0
$193$	20.5977	−	11.8921i	1.48266	−	0.856013i	0.482852	−	0.875702i	$-0.339601\pi$
$193$	20.5977	−	11.8921i	1.48266	−	0.856013i	0.999806	+	0.0196888i	$0.00626754\pi$
$194$		0			0
$195$	−5.83341	−	10.1038i	−0.417739	−	0.723546i
$196$		0			0
$197$		−	6.02302i		−	0.429122i	−0.976711	−	0.214561i	$-0.931168\pi$
$197$		−	6.02302i		−	0.429122i	0.976711	−	0.214561i	$-0.0688321\pi$
$198$		0			0
$199$	4.13491	+	2.38729i	0.293116	+	0.169231i	0.639346	−	0.768919i	$-0.279205\pi$
$199$	4.13491	+	2.38729i	0.293116	+	0.169231i	−0.346230	+	0.938150i	$0.612538\pi$
$200$		0			0
$201$	−14.2429			−1.00462
$202$		0			0
$203$	31.0754	+	17.9414i	2.18106	+	1.25924i
$204$		0			0
$205$	4.65434	−	8.06155i	0.325073	−	0.563043i
$206$		0			0
$207$	−1.89320	+	1.09304i	−0.131586	+	0.0759714i
$208$		0			0
$209$	−16.5971	−	5.89147i	−1.14805	−	0.407522i
$210$		0			0
$211$	4.48711	−	2.59063i	0.308905	−	0.178346i	−0.337531	−	0.941314i	$-0.609592\pi$
$211$	4.48711	−	2.59063i	0.308905	−	0.178346i	0.646436	+	0.762968i	$0.276259\pi$
$212$		0			0
$213$	−0.661480	−	0.381906i	−0.0453239	−	0.0261678i
$214$		0			0
$215$	12.3307	+	7.11912i	0.840946	+	0.485520i
$216$		0			0
$217$			35.5182i			2.41113i
$218$		0			0
$219$	−7.92723	−	4.57679i	−0.535672	−	0.309271i
$220$		0			0
$221$	17.4961			1.17691
$222$		0			0
$223$	−4.59252	−	7.95448i	−0.307538	−	0.532671i	0.670285	−	0.742104i	$-0.266172\pi$
$223$	−4.59252	−	7.95448i	−0.307538	−	0.532671i	−0.977823	+	0.209432i	$0.932838\pi$
$224$		0			0
$225$	1.14592	+	1.98479i	0.0763946	+	0.132319i
$226$		0			0
$227$		−	10.1336i		−	0.672588i	−0.941757	−	0.336294i	$-0.890826\pi$
$227$		−	10.1336i		−	0.672588i	0.941757	−	0.336294i	$-0.109174\pi$
$228$		0			0
$229$		−	7.39200i		−	0.488477i	−0.969715	−	0.244238i	$-0.921462\pi$
$229$		−	7.39200i		−	0.488477i	0.969715	−	0.244238i	$-0.0785380\pi$
$230$		0			0
$231$	−12.9837	−	22.4884i	−0.854264	−	1.47963i
$232$		0			0
$233$	6.28161	+	10.8801i	0.411522	+	0.712777i	0.995056	−	0.0993115i	$-0.0316640\pi$
$233$	6.28161	+	10.8801i	0.411522	+	0.712777i	−0.583534	+	0.812088i	$0.698331\pi$
$234$		0			0
$235$	−25.1782			−1.64245
$236$		0			0
$237$	5.90672	+	3.41024i	0.383682	+	0.221519i
$238$		0			0
$239$		−	3.73525i		−	0.241613i	−0.992676	−	0.120807i	$-0.961452\pi$
$239$		−	3.73525i		−	0.241613i	0.992676	−	0.120807i	$-0.0385481\pi$
$240$		0			0
$241$	−2.32558	−	1.34267i	−0.149804	−	0.0864892i	0.423225	−	0.906025i	$-0.360898\pi$
$241$	−2.32558	−	1.34267i	−0.149804	−	0.0864892i	−0.573028	+	0.819536i	$0.694231\pi$
$242$		0			0
$243$	−8.46382	−	4.88659i	−0.542955	−	0.313475i
$244$		0			0
$245$	−31.6573	+	18.2773i	−2.02251	+	1.16770i
$246$		0			0
$247$	10.0738	−	8.59072i	0.640983	−	0.546615i
$248$		0			0
$249$	−13.1405	+	7.58667i	−0.832745	+	0.480786i
$250$		0			0
$251$	11.9029	−	20.6164i	0.751302	−	1.30129i	−0.195890	−	0.980626i	$-0.562760\pi$
$251$	11.9029	−	20.6164i	0.751302	−	1.30129i	0.947192	−	0.320667i	$-0.103907\pi$
$252$		0			0
$253$	−7.75990	−	4.48018i	−0.487861	−	0.281666i
$254$		0			0
$255$	22.1262			1.38560
$256$		0			0
$257$	−13.6066	−	7.85576i	−0.848755	−	0.490029i	0.0114755	−	0.999934i	$-0.496347\pi$
$257$	−13.6066	−	7.85576i	−0.848755	−	0.490029i	−0.860231	+	0.509905i	$0.829680\pi$
$258$		0			0
$259$		−	27.3026i		−	1.69650i
$260$		0			0
$261$	3.90550	+	6.76453i	0.241744	+	0.418714i
$262$		0			0
$263$	−2.33568	+	1.34851i	−0.144024	+	0.0831525i	−0.570281	−	0.821450i	$-0.693166\pi$
$263$	−2.33568	+	1.34851i	−0.144024	+	0.0831525i	0.426256	+	0.904602i	$0.359832\pi$
$264$		0			0
$265$		−	15.9027i		−	0.976897i
$266$		0			0
$267$	−23.9228			−1.46405
$268$		0			0
$269$	2.44220	+	4.23002i	0.148904	+	0.257909i	0.930823	−	0.365471i	$-0.119092\pi$
$269$	2.44220	+	4.23002i	0.148904	+	0.257909i	−0.781919	+	0.623380i	$0.785759\pi$
$270$		0			0
$271$	−5.40935	+	3.12309i	−0.328595	+	0.189714i	−0.655217	−	0.755441i	$-0.727423\pi$
$271$	−5.40935	+	3.12309i	−0.328595	+	0.189714i	0.326622	+	0.945155i	$0.394090\pi$
$272$		0			0
$273$	19.5207			1.18144
$274$		0			0
$275$	−4.69693	+	8.13532i	−0.283235	+	0.490578i
$276$		0			0
$277$			13.1531i			0.790295i	0.918618	+	0.395148i	$0.129307\pi$
$277$			13.1531i			0.790295i	−0.918618	+	0.395148i	$0.870693\pi$
$278$		0			0
$279$	−3.86582	+	6.69580i	−0.231441	+	0.400867i
$280$		0			0
$281$	2.04646	+	1.18153i	0.122082	+	0.0704840i	0.559797	−	0.828630i	$-0.310879\pi$
$281$	2.04646	+	1.18153i	0.122082	+	0.0704840i	−0.437716	+	0.899114i	$0.644212\pi$
$282$		0			0
$283$	−11.8067	−	20.4498i	−0.701836	−	1.21562i	−0.967821	−	0.251638i	$-0.919031\pi$
$283$	−11.8067	−	20.4498i	−0.701836	−	1.21562i	0.265985	−	0.963977i	$-0.414303\pi$
$284$		0			0
$285$	12.7398	−	10.8642i	0.754640	−	0.643538i
$286$		0			0
$287$	7.78753	+	13.4884i	0.459683	+	0.796195i
$288$		0			0
$289$	−8.09072	+	14.0135i	−0.475925	+	0.824326i
$290$		0			0
$291$	9.90262	−	17.1518i	0.580502	−	1.00546i
$292$		0			0
$293$	6.66904			0.389609			0.194805	−	0.980842i	$-0.437593\pi$
$293$	6.66904			0.389609			0.194805	+	0.980842i	$0.437593\pi$
$294$		0			0
$295$	−1.51885	+	2.63072i	−0.0884308	+	0.153167i
$296$		0			0
$297$		−	22.8556i		−	1.32622i
$298$		0			0
$299$	5.83341	−	3.36792i	0.337355	−	0.194772i
$300$		0			0
$301$	−20.6314	+	11.9116i	−1.18918	+	0.686571i
$302$		0			0
$303$	−3.84114			−0.220668
$304$		0			0
$305$	30.5393			1.74868
$306$		0			0
$307$	−10.8836	+	6.28364i	−0.621159	+	0.358626i	−0.777320	−	0.629105i	$-0.783421\pi$
$307$	−10.8836	+	6.28364i	−0.621159	+	0.358626i	0.156161	+	0.987732i	$0.450088\pi$
$308$		0			0
$309$	8.51546	−	4.91640i	0.484428	−	0.279684i
$310$		0			0
$311$			9.14984i			0.518840i	0.965765	+	0.259420i	$0.0835314\pi$
$311$			9.14984i			0.518840i	−0.965765	+	0.259420i	$0.916469\pi$
$312$		0			0
$313$	−9.07818	+	15.7239i	−0.513129	+	0.888766i	0.486755	+	0.873539i	$0.338180\pi$
$313$	−9.07818	+	15.7239i	−0.513129	+	0.888766i	−0.999884	+	0.0152270i	$0.995153\pi$
$314$		0			0
$315$	−12.0813			−0.680705
$316$		0			0
$317$	−1.74983	+	3.03079i	−0.0982802	+	0.170226i	−0.910973	−	0.412466i	$-0.864667\pi$
$317$	−1.74983	+	3.03079i	−0.0982802	+	0.170226i	0.812693	+	0.582693i	$0.198001\pi$
$318$		0			0
$319$	−16.0080	+	27.7266i	−0.896275	+	1.55239i
$320$		0			0
$321$	−4.35658	−	7.54581i	−0.243160	−	0.421166i
$322$		0			0
$323$	4.55705	+	24.6917i	0.253561	+	1.37388i
$324$		0			0
$325$	−3.53086	−	6.11563i	−0.195857	−	0.339234i
$326$		0			0
$327$	−15.2566	−	8.80840i	−0.843692	−	0.487106i
$328$		0			0
$329$	21.0638	−	36.4836i	1.16129	−	2.01141i
$330$		0			0
$331$		−	15.2168i		−	0.836391i	−0.908357	−	0.418196i	$-0.862663\pi$
$331$		−	15.2168i		−	0.836391i	0.908357	−	0.418196i	$-0.137337\pi$
$332$		0			0
$333$	2.97164	−	5.14703i	0.162845	−	0.282055i
$334$		0			0
$335$	−27.1609			−1.48396
$336$		0			0
$337$	−27.0852	+	15.6376i	−1.47543	+	0.851837i	−0.999616	−	0.0277116i	$-0.991178\pi$
$337$	−27.0852	+	15.6376i	−1.47543	+	0.851837i	−0.475809	+	0.879549i	$0.657845\pi$
$338$		0			0
$339$	9.52072	+	16.4904i	0.517094	+	0.895634i
$340$		0			0
$341$	−31.6907			−1.71615
$342$		0			0
$343$		−	29.4637i		−	1.59089i
$344$		0			0
$345$	7.37717	−	4.25921i	0.397173	−	0.229308i
$346$		0			0
$347$	−5.87102	−	10.1689i	−0.315173	−	0.545896i	0.664301	−	0.747465i	$-0.268729\pi$
$347$	−5.87102	−	10.1689i	−0.315173	−	0.545896i	−0.979474	+	0.201569i	$0.935396\pi$
$348$		0			0
$349$		−	19.5955i		−	1.04893i	−0.851433	−	0.524463i	$-0.824266\pi$
$349$		−	19.5955i		−	1.04893i	0.851433	−	0.524463i	$-0.175734\pi$
$350$		0			0
$351$	14.8796	+	8.59072i	0.794213	+	0.458539i
$352$		0			0
$353$	20.9735			1.11631			0.558153	−	0.829738i	$-0.311510\pi$
$353$	20.9735			1.11631			0.558153	+	0.829738i	$0.311510\pi$
$354$		0			0
$355$	−1.26143	−	0.728287i	−0.0669497	−	0.0386534i
$356$		0			0
$357$	−18.5106	+	32.0612i	−0.979682	+	1.69686i
$358$		0			0
$359$	−4.21549	+	2.43381i	−0.222485	+	0.128452i	−0.607100	−	0.794625i	$-0.707667\pi$
$359$	−4.21549	+	2.43381i	−0.222485	+	0.128452i	0.384615	+	0.923077i	$0.374334\pi$
$360$		0			0
$361$	14.7477	+	11.9794i	0.776194	+	0.630494i
$362$		0			0
$363$	6.54493	−	3.77871i	0.343519	−	0.198331i
$364$		0			0
$365$	−15.1171	−	8.72784i	−0.791263	−	0.456836i
$366$		0			0
$367$	−13.7797	−	7.95569i	−0.719293	−	0.415284i	0.0951995	−	0.995458i	$-0.469651\pi$
$367$	−13.7797	−	7.95569i	−0.719293	−	0.415284i	−0.814492	+	0.580174i	$0.802984\pi$
$368$		0			0
$369$			3.39040i			0.176497i
$370$		0			0
$371$	23.0433	+	13.3040i	1.19635	+	0.690711i
$372$		0			0
$373$	−7.92174			−0.410172			−0.205086	−	0.978744i	$-0.565747\pi$
$373$	−7.92174			−0.410172			−0.205086	+	0.978744i	$0.565747\pi$
$374$		0			0
$375$	5.13758	+	8.89854i	0.265303	+	0.459519i
$376$		0			0
$377$	−12.0338	−	20.8432i	−0.619773	−	1.07348i
$378$		0			0
$379$			23.0750i			1.18529i	0.805466	+	0.592643i	$0.201915\pi$
$379$			23.0750i			1.18529i	−0.805466	+	0.592643i	$0.798085\pi$
$380$		0			0
$381$		−	1.90409i		−	0.0975493i
$382$		0			0
$383$	−7.11672	−	12.3265i	−0.363647	−	0.629856i	0.624911	−	0.780696i	$-0.285135\pi$
$383$	−7.11672	−	12.3265i	−0.363647	−	0.629856i	−0.988558	+	0.150840i	$0.951802\pi$
$384$		0			0
$385$	−24.7596	−	42.8849i	−1.26187	−	2.18562i
$386$		0			0
$387$	−5.18585			−0.263611
$388$		0			0
$389$	13.1016	+	7.56421i	0.664277	+	0.383520i	0.793905	−	0.608042i	$-0.208045\pi$
$389$	13.1016	+	7.56421i	0.664277	+	0.383520i	−0.129628	+	0.991563i	$0.541378\pi$
$390$		0			0
$391$			12.7746i			0.646039i
$392$		0			0
$393$	7.52107	+	4.34229i	0.379388	+	0.219040i
$394$		0			0
$395$	11.2640	+	6.50327i	0.566753	+	0.327215i
$396$		0			0
$397$	−9.93863	+	5.73807i	−0.498806	+	0.287985i	−0.728220	−	0.685343i	$-0.759652\pi$
$397$	−9.93863	+	5.73807i	−0.498806	+	0.287985i	0.229415	+	0.973329i	$0.426319\pi$
$398$		0			0
$399$	5.08437	+	27.5490i	0.254537	+	1.37917i
$400$		0			0
$401$	2.15304	−	1.24306i	0.107518	−	0.0620755i	−0.445277	−	0.895393i	$-0.646895\pi$
$401$	2.15304	−	1.24306i	0.107518	−	0.0620755i	0.552795	+	0.833317i	$0.313561\pi$
$402$		0			0
$403$	11.9116	−	20.6314i	0.593357	−	1.02772i
$404$		0			0
$405$	11.8859	+	6.86232i	0.590615	+	0.340992i
$406$		0			0
$407$	24.3605			1.20750
$408$		0			0
$409$	7.64933	+	4.41635i	0.378235	+	0.218374i	0.677050	−	0.735937i	$-0.263258\pi$
$409$	7.64933	+	4.41635i	0.378235	+	0.218374i	−0.298815	+	0.954311i	$0.596591\pi$
$410$		0			0
$411$		−	2.03713i		−	0.100484i
$412$		0			0
$413$	−2.54130	−	4.40167i	−0.125049	−	0.216592i
$414$		0			0
$415$	−25.0587	+	14.4676i	−1.23008	+	0.710188i
$416$		0			0
$417$			28.5653i			1.39885i
$418$		0			0
$419$	34.1177			1.66676			0.833379	−	0.552703i	$-0.186403\pi$
$419$	34.1177			1.66676			0.833379	+	0.552703i	$0.186403\pi$
$420$		0			0
$421$	8.25200	+	14.2929i	0.402178	+	0.696593i	0.993989	−	0.109484i	$-0.0349199\pi$
$421$	8.25200	+	14.2929i	0.402178	+	0.696593i	−0.591810	+	0.806077i	$0.701587\pi$
$422$		0			0
$423$	7.94180	−	4.58520i	0.386144	−	0.222940i
$424$		0			0
$425$	13.3926			0.649637
$426$		0			0
$427$	−25.5489	+	44.2519i	−1.23640	+	2.14150i
$428$		0			0
$429$			17.4171i			0.840906i
$430$		0			0
$431$	−10.1232	+	17.5339i	−0.487618	+	0.844579i	−0.999899	−	0.0142389i	$-0.995467\pi$
$431$	−10.1232	+	17.5339i	−0.487618	+	0.844579i	0.512281	+	0.858818i	$0.328801\pi$
$432$		0			0
$433$	1.01254	+	0.584592i	0.0486597	+	0.0280937i	0.524133	−	0.851637i	$-0.324390\pi$
$433$	1.01254	+	0.584592i	0.0486597	+	0.0280937i	−0.475473	+	0.879730i	$0.657723\pi$
$434$		0			0
$435$	−15.2184	−	26.3591i	−0.729669	−	1.26382i
$436$		0			0
$437$	6.27243	+	7.35532i	0.300051	+	0.351853i
$438$		0			0
$439$	−6.88744	−	11.9294i	−0.328719	−	0.569359i	0.653539	−	0.756893i	$-0.273284\pi$
$439$	−6.88744	−	11.9294i	−0.328719	−	0.569359i	−0.982258	+	0.187534i	$0.939950\pi$
$440$		0			0
$441$	6.65697	−	11.5302i	0.316998	−	0.549057i
$442$		0			0
$443$	7.86244	−	13.6181i	0.373556	−	0.647018i	−0.616554	−	0.787313i	$-0.711472\pi$
$443$	7.86244	−	13.6181i	0.373556	−	0.647018i	0.990110	+	0.140295i	$0.0448051\pi$
$444$		0			0
$445$	−45.6203			−2.16261
$446$		0			0
$447$	3.81377	−	6.60564i	0.180385	−	0.312436i
$448$		0			0
$449$			36.2041i			1.70858i	0.519799	+	0.854288i	$0.326007\pi$
$449$			36.2041i			1.70858i	−0.519799	+	0.854288i	$0.673993\pi$
$450$		0			0
$451$	−12.0349	+	6.94834i	−0.566700	+	0.327185i
$452$		0			0
$453$	−5.38262	+	3.10766i	−0.252898	+	0.146011i
$454$		0			0
$455$	37.2255			1.74516
$456$		0			0
$457$	4.21137			0.196999			0.0984997	−	0.995137i	$-0.468596\pi$
$457$	4.21137			0.196999			0.0984997	+	0.995137i	$0.468596\pi$
$458$		0			0
$459$	−28.2192	+	16.2924i	−1.31716	+	0.760463i
$460$		0			0
$461$	30.2082	−	17.4407i	1.40694	−	0.812296i	0.411847	−	0.911253i	$-0.364884\pi$
$461$	30.2082	−	17.4407i	1.40694	−	0.812296i	0.995092	+	0.0989571i	$0.0315506\pi$
$462$		0			0
$463$		−	41.8705i		−	1.94589i	−0.231041	−	0.972944i	$-0.574213\pi$
$463$		−	41.8705i		−	1.94589i	0.231041	−	0.972944i	$-0.425787\pi$
$464$		0			0
$465$	15.0638	−	26.0913i	0.698568	−	1.20996i
$466$		0			0
$467$	−4.04042			−0.186968			−0.0934841	−	0.995621i	$-0.529800\pi$
$467$	−4.04042			−0.186968			−0.0934841	+	0.995621i	$0.529800\pi$
$468$		0			0
$469$	22.7225	−	39.3565i	1.04923	−	1.81731i
$470$		0			0
$471$	3.59673	−	6.22972i	0.165729	−	0.287050i
$472$		0			0
$473$	−10.6280	−	18.4082i	−0.488674	−	0.846408i
$474$		0			0
$475$	7.71116	−	6.57589i	0.353812	−	0.301722i
$476$		0			0
$477$	2.89604	+	5.01609i	0.132601	+	0.229671i
$478$		0			0
$479$	−4.23330	−	2.44409i	−0.193424	−	0.111674i	0.400160	−	0.916445i	$-0.368954\pi$
$479$	−4.23330	−	2.44409i	−0.193424	−	0.111674i	−0.593585	+	0.804772i	$0.702288\pi$
$480$		0			0
$481$	−9.15636	+	15.8593i	−0.417494	+	0.723121i
$482$		0			0
$483$			14.2528i			0.648526i
$484$		0			0
$485$	18.8841	−	32.7082i	0.857483	−	1.48520i
$486$		0			0
$487$	−25.1639			−1.14029			−0.570143	−	0.821545i	$-0.693112\pi$
$487$	−25.1639			−1.14029			−0.570143	+	0.821545i	$0.693112\pi$
$488$		0			0
$489$	−7.11943	+	4.11040i	−0.321952	+	0.185879i
$490$		0			0
$491$	−6.23026	−	10.7911i	−0.281168	−	0.486997i	0.690505	−	0.723328i	$-0.257388\pi$
$491$	−6.23026	−	10.7911i	−0.281168	−	0.486997i	−0.971673	+	0.236331i	$0.924055\pi$
$492$		0			0
$493$	45.6445			2.05572
$494$		0			0
$495$		−	10.7794i		−	0.484499i
$496$		0			0
$497$	2.11059	−	1.21855i	0.0946731	−	0.0546596i
$498$		0			0
$499$	−0.00869618	−	0.0150622i	−0.000389295	−	0.000674278i	0.865831	−	0.500337i	$-0.166791\pi$
$499$	−0.00869618	−	0.0150622i	−0.000389295	−	0.000674278i	−0.866220	+	0.499663i	$0.833457\pi$
$500$		0			0
$501$		−	15.5130i		−	0.693071i
$502$		0			0
$503$	−19.7299	−	11.3911i	−0.879712	−	0.507902i	−0.00914879	−	0.999958i	$-0.502912\pi$
$503$	−19.7299	−	11.3911i	−0.879712	−	0.507902i	−0.870564	+	0.492056i	$0.836246\pi$
$504$		0			0
$505$	−7.32497			−0.325957
$506$		0			0
$507$	4.63935	+	2.67853i	0.206041	+	0.118958i
$508$		0			0
$509$	9.67376	−	16.7554i	0.428782	−	0.742672i	−0.567984	−	0.823040i	$-0.692276\pi$
$509$	9.67376	−	16.7554i	0.428782	−	0.742672i	0.996765	+	0.0803682i	$0.0256096\pi$
$510$		0			0
$511$	25.2935	−	14.6032i	1.11892	−	0.646008i
$512$		0			0
$513$	−8.24830	+	23.2367i	−0.364171	+	1.02592i
$514$		0			0
$515$	16.2388	−	9.37548i	0.715567	−	0.413133i
$516$		0			0
$517$	32.5521	+	18.7940i	1.43164	+	0.826558i
$518$		0			0
$519$	−22.7230	−	13.1191i	−0.997429	−	0.575866i
$520$		0			0
$521$			37.5666i			1.64582i	0.568170	+	0.822911i	$0.307651\pi$
$521$			37.5666i			1.64582i	−0.568170	+	0.822911i	$0.692349\pi$
$522$		0			0
$523$	−27.6177	−	15.9451i	−1.20764	−	0.697230i	−0.245396	−	0.969423i	$-0.578918\pi$
$523$	−27.6177	−	15.9451i	−1.20764	−	0.697230i	−0.962243	+	0.272193i	$0.912251\pi$
$524$		0			0
$525$	14.9424			0.652138
$526$		0			0
$527$	22.5904	+	39.1277i	0.984052	+	1.70443i
$528$		0			0
$529$	−9.04094	−	15.6594i	−0.393085	−	0.680842i
$530$		0			0
$531$		−	1.10639i		−	0.0480132i
$532$		0			0
$533$		−	10.4467i		−	0.452495i
$534$		0			0
$535$	−8.30790	−	14.3897i	−0.359182	−	0.622121i
$536$		0			0
$537$	−9.48746	−	16.4328i	−0.409414	−	0.709126i
$538$		0			0
$539$	54.5716			2.35056
$540$		0			0
$541$	−3.30222	−	1.90654i	−0.141974	−	0.0819686i	0.427331	−	0.904095i	$-0.359454\pi$
$541$	−3.30222	−	1.90654i	−0.141974	−	0.0819686i	−0.569304	+	0.822127i	$0.692787\pi$
$542$		0			0
$543$			37.5457i			1.61124i
$544$		0			0
$545$	−29.0940	−	16.7974i	−1.24625	−	0.719524i
$546$		0			0
$547$	−1.90654	−	1.10074i	−0.0815178	−	0.0470643i	0.458687	−	0.888598i	$-0.348320\pi$
$547$	−1.90654	−	1.10074i	−0.0815178	−	0.0470643i	−0.540205	+	0.841534i	$0.681653\pi$
$548$		0			0
$549$	−9.63282	+	5.56151i	−0.411119	+	0.237360i
$550$		0			0
$551$	26.2811	−	22.4118i	1.11961	−	0.954776i
$552$		0			0
$553$	−18.8467	+	10.8811i	−0.801441	+	0.462712i
$554$		0			0
$555$	−11.5795	+	20.0563i	−0.491522	+	0.851341i
$556$		0			0
$557$	11.1910	+	6.46113i	0.474178	+	0.273767i	0.717987	−	0.696056i	$-0.245064\pi$
$557$	11.1910	+	6.46113i	0.474178	+	0.273767i	−0.243809	+	0.969823i	$0.578397\pi$
$558$		0			0
$559$	15.9789			0.675835
$560$		0			0
$561$	−28.6063	−	16.5158i	−1.20776	−	0.697299i
$562$		0			0
$563$			29.0862i			1.22584i	0.790146	+	0.612919i	$0.210005\pi$
$563$			29.0862i			1.22584i	−0.790146	+	0.612919i	$0.789995\pi$
$564$		0			0
$565$	18.1558	+	31.4468i	0.763821	+	1.32298i
$566$		0			0
$567$	−19.8872	+	11.4819i	−0.835184	+	0.482194i
$568$		0			0
$569$		−	38.4250i		−	1.61086i	−0.592692	−	0.805429i	$-0.701935\pi$
$569$		−	38.4250i		−	1.61086i	0.592692	−	0.805429i	$-0.298065\pi$
$570$		0			0
$571$	29.2936			1.22590			0.612950	−	0.790122i	$-0.289983\pi$
$571$	29.2936			1.22590			0.612950	+	0.790122i	$0.289983\pi$
$572$		0			0
$573$	−11.6629	−	20.2007i	−0.487224	−	0.843897i
$574$		0			0
$575$	4.46527	−	2.57802i	0.186214	−	0.107511i
$576$		0			0
$577$	−8.38056			−0.348887			−0.174444	−	0.984667i	$-0.555813\pi$
$577$	−8.38056			−0.348887			−0.174444	+	0.984667i	$0.555813\pi$
$578$		0			0
$579$	16.8778	−	29.2332i	0.701418	−	1.21489i
$580$		0			0
$581$		−	48.4138i		−	2.00854i
$582$		0			0
$583$	−11.8704	+	20.5601i	−0.491621	+	0.851513i
$584$		0			0
$585$	7.01767	+	4.05165i	0.290145	+	0.167515i
$586$		0			0
$587$	12.0664	+	20.8996i	0.498032	+	0.862618i	0.999997	−	0.00227040i	$-0.000722691\pi$
$587$	12.0664	+	20.8996i	0.498032	+	0.862618i	−0.501965	+	0.864888i	$0.667389\pi$
$588$		0			0
$589$	32.2190	+	11.4368i	1.32756	+	0.471244i
$590$		0			0
$591$	−4.27406	−	7.40289i	−0.175811	−	0.304514i
$592$		0			0
$593$	−20.8888	+	36.1805i	−0.857800	+	1.48575i	0.0162227	+	0.999868i	$0.494836\pi$
$593$	−20.8888	+	36.1805i	−0.857800	+	1.48575i	−0.874023	+	0.485885i	$0.838497\pi$
$594$		0			0
$595$	−35.2993	+	61.1401i	−1.44713	+	2.50650i
$596$		0			0
$597$	6.77630			0.277335
$598$		0			0
$599$	4.61720	−	7.99723i	0.188654	−	0.326758i	−0.756148	−	0.654401i	$-0.772921\pi$
$599$	4.61720	−	7.99723i	0.188654	−	0.326758i	0.944802	+	0.327643i	$0.106254\pi$
$600$		0			0
$601$			17.8072i			0.726372i	0.931717	+	0.363186i	$0.118311\pi$
$601$			17.8072i			0.726372i	−0.931717	+	0.363186i	$0.881689\pi$
$602$		0			0
$603$	8.56718	−	4.94626i	0.348882	−	0.201427i
$604$		0			0
$605$	12.4810	−	7.20593i	0.507426	−	0.292963i
$606$		0			0
$607$	−3.67462			−0.149148			−0.0745740	−	0.997215i	$-0.523760\pi$
$607$	−3.67462			−0.149148			−0.0745740	+	0.997215i	$0.523760\pi$
$608$		0			0
$609$	50.9263			2.06364
$610$		0			0
$611$	−24.4707	+	14.1282i	−0.989978	+	0.571564i
$612$		0			0
$613$	−22.8102	+	13.1694i	−0.921293	+	0.531909i	−0.884047	−	0.467397i	$-0.845192\pi$
$613$	−22.8102	+	13.1694i	−0.921293	+	0.531909i	−0.0372459	+	0.999306i	$0.511858\pi$
$614$		0			0
$615$		−	13.2113i		−	0.532730i
$616$		0			0
$617$	5.82497	−	10.0891i	0.234505	−	0.406174i	−0.724624	−	0.689144i	$-0.757987\pi$
$617$	5.82497	−	10.0891i	0.234505	−	0.406174i	0.959129	+	0.282971i	$0.0913199\pi$
$618$		0			0
$619$	20.6587			0.830342			0.415171	−	0.909743i	$-0.363722\pi$
$619$	20.6587			0.830342			0.415171	+	0.909743i	$0.363722\pi$
$620$		0			0
$621$	−6.27243	+	10.8642i	−0.251704	+	0.435964i
$622$		0			0
$623$	38.1654	−	66.1045i	1.52907	−	2.64842i
$624$		0			0
$625$	15.6097	+	27.0368i	0.624387	+	1.08147i
$626$		0			0
$627$	−24.5803	+	4.53648i	−0.981641	+	0.181169i
$628$		0			0
$629$	−17.3651	−	30.0772i	−0.692392	−	1.19926i
$630$		0			0
$631$	36.1821	+	20.8897i	1.44039	+	0.831607i	0.997875	−	0.0651555i	$-0.0207544\pi$
$631$	36.1821	+	20.8897i	1.44039	+	0.831607i	0.442511	+	0.896763i	$0.354088\pi$
$632$		0			0
$633$	3.67674	−	6.36829i	0.146137	−	0.253117i
$634$		0			0
$635$		−	3.63105i		−	0.144094i
$636$		0			0
$637$	−20.5118	+	35.5274i	−0.812706	+	1.40765i
$638$		0			0
$639$	0.530512			0.0209867
$640$		0			0
$641$	35.4300	−	20.4555i	1.39940	−	0.807945i	0.405072	−	0.914285i	$-0.367246\pi$
$641$	35.4300	−	20.4555i	1.39940	−	0.807945i	0.994330	+	0.106340i	$0.0339130\pi$
$642$		0			0
$643$	8.01456	+	13.8816i	0.316063	+	0.547438i	0.979663	−	0.200650i	$-0.0643055\pi$
$643$	8.01456	+	13.8816i	0.316063	+	0.547438i	−0.663600	+	0.748088i	$0.730972\pi$
$644$		0			0
$645$	20.2075			0.795671
$646$		0			0
$647$			24.9057i			0.979142i	0.871963	+	0.489571i	$0.162847\pi$
$647$			24.9057i			0.979142i	−0.871963	+	0.489571i	$0.837153\pi$
$648$		0			0
$649$	3.92734	−	2.26745i	0.154162	−	0.0890052i
$650$		0			0
$651$	25.2045	+	43.6554i	0.987840	+	1.71099i
$652$		0			0
$653$			35.2607i			1.37986i	0.723877	+	0.689929i	$0.242358\pi$
$653$			35.2607i			1.37986i	−0.723877	+	0.689929i	$0.757642\pi$
$654$		0			0
$655$	14.3425	+	8.28067i	0.560409	+	0.323552i
$656$		0			0
$657$	6.35770			0.248037
$658$		0			0
$659$	1.37522	+	0.793985i	0.0535710	+	0.0309292i	0.526546	−	0.850146i	$-0.323487\pi$
$659$	1.37522	+	0.793985i	0.0535710	+	0.0309292i	−0.472975	+	0.881076i	$0.656820\pi$
$660$		0			0
$661$	9.93580	−	17.2093i	0.386458	−	0.669364i	−0.605513	−	0.795836i	$-0.707032\pi$
$661$	9.93580	−	17.2093i	0.386458	−	0.669364i	0.991970	+	0.126471i	$0.0403652\pi$
$662$		0			0
$663$	21.5044	−	12.4156i	0.835163	−	0.482182i
$664$		0			0
$665$	9.69580	+	52.5353i	0.375987	+	2.03723i
$666$		0			0
$667$	15.2184	−	8.78637i	0.589261	−	0.340210i
$668$		0			0
$669$	−11.2893	−	6.51790i	−0.436471	−	0.251997i
$670$		0			0
$671$	−39.4833	−	22.7957i	−1.52424	−	0.880018i
$672$		0			0
$673$			32.8349i			1.26569i	0.774277	+	0.632846i	$0.218114\pi$
$673$			32.8349i			1.26569i	−0.774277	+	0.632846i	$0.781886\pi$
$674$		0			0
$675$	11.3898	+	6.57589i	0.438392	+	0.253106i
$676$		0			0
$677$	−24.3633			−0.936358			−0.468179	−	0.883634i	$-0.655090\pi$
$677$	−24.3633			−0.936358			−0.468179	+	0.883634i	$0.655090\pi$
$678$		0			0
$679$	31.5964	+	54.7266i	1.21256	+	2.10022i
$680$		0			0
$681$	−7.19099	−	12.4552i	−0.275559	−	0.477283i
$682$		0			0
$683$			0.860022i			0.0329078i	0.999865	+	0.0164539i	$0.00523768\pi$
$683$			0.860022i			0.0329078i	−0.999865	+	0.0164539i	$0.994762\pi$
$684$		0			0
$685$		−	3.88476i		−	0.148429i
$686$		0			0
$687$	−5.24552	−	9.08551i	−0.200129	−	0.346634i
$688$		0			0
$689$	−8.92343	−	15.4558i	−0.339955	−	0.588820i
$690$		0			0
$691$		0			0			−	1.00000i	$-0.5\pi$
$691$		0			0				1.00000i	$0.5\pi$
$692$		0			0
$693$	15.6195	+	9.01794i	0.593337	+	0.342563i
$694$		0			0
$695$			54.4734i			2.06629i
$696$		0			0
$697$	17.1579	+	9.90610i	0.649900	+	0.375220i
$698$		0			0
$699$	15.4415	+	8.91513i	0.584050	+	0.337201i
$700$		0			0
$701$	29.3468	−	16.9434i	1.10841	−	0.639943i	0.169996	−	0.985445i	$-0.445625\pi$
$701$	29.3468	−	16.9434i	1.10841	−	0.639943i	0.938418	+	0.345502i	$0.112291\pi$
$702$		0			0
$703$	−24.7666	−	8.79139i	−0.934091	−	0.331573i
$704$		0			0
$705$	−30.9466	+	17.8670i	−1.16552	+	0.672911i
$706$		0			0
$707$	6.12799	−	10.6140i	0.230467	−	0.399180i
$708$		0			0
$709$	−7.92219	−	4.57388i	−0.297524	−	0.171776i	0.343806	−	0.939041i	$-0.388284\pi$
$709$	−7.92219	−	4.57388i	−0.297524	−	0.171776i	−0.641330	+	0.767265i	$0.721617\pi$
$710$		0			0
$711$	−4.73723			−0.177660
$712$		0			0
$713$	15.0638	+	8.69710i	0.564145	+	0.325709i
$714$		0			0
$715$			33.2141i			1.24214i
$716$		0			0
$717$	−2.65061	−	4.59099i	−0.0989889	−	0.171454i
$718$		0			0
$719$	1.52327	−	0.879457i	0.0568082	−	0.0327982i	−0.471327	−	0.881959i	$-0.656225\pi$
$719$	1.52327	−	0.879457i	0.0568082	−	0.0327982i	0.528135	+	0.849160i	$0.322891\pi$
$720$		0			0
$721$			31.3737i			1.16842i
$722$		0			0
$723$	−3.81116			−0.141739
$724$		0			0
$725$	−9.21145	−	15.9547i	−0.342105	−	0.592543i
$726$		0			0
$727$	−28.1731	+	16.2658i	−1.04488	+	0.603263i	−0.921212	−	0.389060i	$-0.872800\pi$
$727$	−28.1731	+	16.2658i	−1.04488	+	0.603263i	−0.123670	+	0.992323i	$0.539467\pi$
$728$		0			0
$729$	−29.0837			−1.07717
$730$		0			0
$731$	−15.1520	+	26.2441i	−0.560419	+	0.970674i
$732$		0			0
$733$			10.0235i			0.370226i	0.982717	+	0.185113i	$0.0592651\pi$
$733$			10.0235i			0.370226i	−0.982717	+	0.185113i	$0.940735\pi$
$734$		0			0
$735$	−25.9400	+	44.9294i	−0.956811	+	1.65725i
$736$		0			0
$737$	35.1154	+	20.2739i	1.29349	+	0.746798i
$738$		0			0
$739$	8.80458	+	15.2500i	0.323882	+	0.560980i	0.981285	−	0.192559i	$-0.0616787\pi$
$739$	8.80458	+	15.2500i	0.323882	+	0.560980i	−0.657404	+	0.753539i	$0.728345\pi$
$740$		0			0
$741$	6.28561	−	17.7075i	0.230908	−	0.650501i
$742$		0			0
$743$	5.35999	+	9.28377i	0.196639	+	0.340588i	0.947437	−	0.319944i	$-0.103664\pi$
$743$	5.35999	+	9.28377i	0.196639	+	0.340588i	−0.750798	+	0.660532i	$0.770331\pi$
$744$		0			0
$745$	7.27278	−	12.5968i	0.266454	−	0.461512i
$746$		0			0
$747$	5.26939	−	9.12686i	0.192797	−	0.333934i
$748$		0			0
$749$	27.8012			1.01583
$750$		0			0
$751$	19.2589	−	33.3574i	0.702767	−	1.21723i	−0.264725	−	0.964324i	$-0.585281\pi$
$751$	19.2589	−	33.3574i	0.702767	−	1.21723i	0.967491	−	0.252904i	$-0.0813856\pi$
$752$		0			0
$753$		−	33.7861i		−	1.23123i
$754$		0			0
$755$	−10.2646	+	5.92624i	−0.373565	+	0.215678i
$756$		0			0
$757$	22.6135	−	13.0559i	0.821901	−	0.474525i	−0.0291705	−	0.999574i	$-0.509287\pi$
$757$	22.6135	−	13.0559i	0.821901	−	0.474525i	0.851072	+	0.525050i	$0.175953\pi$
$758$		0			0
$759$	−12.7169			−0.461595
$760$		0			0
$761$	38.2820			1.38772			0.693861	−	0.720109i	$-0.255908\pi$
$761$	38.2820			1.38772			0.693861	+	0.720109i	$0.255908\pi$
$762$		0			0
$763$	48.6795	−	28.1051i	1.76232	−	1.01747i
$764$		0			0
$765$	−13.3091	+	7.68399i	−0.481190	+	0.277815i
$766$		0			0
$767$			3.40906i			0.123094i
$768$		0			0
$769$	25.2825	−	43.7906i	0.911710	−	1.57913i	0.100063	−	0.994981i	$-0.468096\pi$
$769$	25.2825	−	43.7906i	0.911710	−	1.57913i	0.811647	−	0.584148i	$-0.198571\pi$
$770$		0			0
$771$	−22.2985			−0.803060
$772$		0			0
$773$	26.2115	−	45.3996i	0.942761	−	1.63291i	0.182589	−	0.983189i	$-0.441552\pi$
$773$	26.2115	−	45.3996i	0.942761	−	1.63291i	0.760173	−	0.649721i	$-0.225114\pi$
$774$		0			0
$775$	9.11786	−	15.7926i	0.327523	−	0.567287i
$776$		0			0
$777$	−19.3745	−	33.5577i	−0.695058	−	1.20388i
$778$		0			0
$779$	14.7431	−	2.72095i	0.528226	−	0.0974882i
$780$		0			0
$781$	1.08724	+	1.88316i	0.0389045	+	0.0673846i
$782$		0			0
$783$	38.8184	+	22.4118i	1.38726	+	0.800933i
$784$		0			0
$785$	6.85889	−	11.8799i	0.244804	−	0.424014i
$786$		0			0
$787$		−	17.9239i		−	0.638918i	−0.947600	−	0.319459i	$-0.896499\pi$
$787$		−	17.9239i		−	0.638918i	0.947600	−	0.319459i	$-0.103501\pi$
$788$		0			0
$789$	−1.91386	+	3.31490i	−0.0681352	+	0.118014i
$790$		0			0
$791$	−60.7558			−2.16023
$792$		0			0
$793$	29.6811	−	17.1364i	1.05401	−	0.608532i
$794$		0			0
$795$	−11.2849	−	19.5461i	−0.400235	−	0.693227i
$796$		0			0
$797$	6.07403			0.215153			0.107577	−	0.994197i	$-0.465691\pi$
$797$	6.07403			0.215153			0.107577	+	0.994197i	$0.465691\pi$
$798$		0			0
$799$		−	53.5883i		−	1.89582i
$800$		0			0
$801$	14.3897	−	8.30790i	0.508435	−	0.293545i
$802$		0			0
$803$	13.0296	+	22.5679i	0.459803	+	0.796403i
$804$		0			0
$805$			27.1798i			0.957964i
$806$		0			0
$807$	6.00343	+	3.46608i	0.211331	+	0.122012i
$808$		0			0
$809$	−48.6309			−1.70977			−0.854885	−	0.518818i	$-0.826372\pi$
$809$	−48.6309			−1.70977			−0.854885	+	0.518818i	$0.826372\pi$
$810$		0			0
$811$	−33.8491	−	19.5428i	−1.18860	−	0.686239i	−0.230613	−	0.973046i	$-0.574073\pi$
$811$	−33.8491	−	19.5428i	−1.18860	−	0.686239i	−0.957989	+	0.286806i	$0.907406\pi$
$812$		0			0
$813$	−4.43243	+	7.67719i	−0.155452	+	0.269251i
$814$		0			0
$815$	−13.5766	+	7.83846i	−0.475568	+	0.274569i
$816$		0			0
$817$	4.16188	+	22.5506i	0.145606	+	0.788944i
$818$		0			0
$819$	−11.7418	+	6.77913i	−0.410292	+	0.236882i
$820$		0			0
$821$	−23.2768	−	13.4389i	−0.812367	−	0.469021i	0.0354099	−	0.999373i	$-0.488726\pi$
$821$	−23.2768	−	13.4389i	−0.812367	−	0.469021i	−0.847777	+	0.530352i	$0.822060\pi$
$822$		0			0
$823$	−9.68342	−	5.59072i	−0.337543	−	0.194880i	0.321642	−	0.946861i	$-0.395765\pi$
$823$	−9.68342	−	5.59072i	−0.337543	−	0.194880i	−0.659185	+	0.751981i	$0.729099\pi$
$824$		0			0
$825$			13.3322i			0.464166i
$826$		0			0
$827$	−13.4101	−	7.74233i	−0.466315	−	0.269227i	0.248381	−	0.968662i	$-0.420102\pi$
$827$	−13.4101	−	7.74233i	−0.466315	−	0.269227i	−0.714696	+	0.699435i	$0.753435\pi$
$828$		0			0
$829$	−30.5672			−1.06164			−0.530822	−	0.847483i	$-0.678117\pi$
$829$	−30.5672			−1.06164			−0.530822	+	0.847483i	$0.678117\pi$
$830$		0			0
$831$	9.33375	+	16.1665i	0.323784	+	0.560811i
$832$		0			0
$833$	−38.9007	−	67.3780i	−1.34783	−	2.33451i
$834$		0			0
$835$		−	29.5830i		−	1.02376i
$836$		0			0
$837$			44.3682i			1.53359i
$838$		0			0
$839$	−15.8888	−	27.5201i	−0.548541	−	0.950100i	−0.998375	−	0.0569883i	$-0.981850\pi$
$839$	−15.8888	−	27.5201i	−0.548541	−	0.950100i	0.449834	−	0.893112i	$-0.351483\pi$
$840$		0			0
$841$	−16.8943	−	29.2618i	−0.582563	−	1.00903i
$842$		0			0
$843$	3.35375			0.115509
$844$		0			0
$845$	8.84714	+	5.10790i	0.304351	+	0.175717i
$846$		0			0
$847$			24.1136i			0.828553i
$848$		0			0
$849$	−29.0233	−	16.7566i	−0.996076	−	0.575085i
$850$		0			0
$851$	−11.5795	−	6.68542i	−0.396940	−	0.229173i
$852$		0			0
$853$	40.9039	−	23.6159i	1.40052	−	0.808592i	0.406076	−	0.913839i	$-0.366897\pi$
$853$	40.9039	−	23.6159i	1.40052	−	0.808592i	0.994446	+	0.105247i	$0.0335634\pi$
$854$		0			0
$855$	−3.89015	+	10.9591i	−0.133040	+	0.374794i
$856$		0			0
$857$	−25.7559	+	14.8702i	−0.879805	+	0.507956i	−0.870594	−	0.492002i	$-0.836265\pi$
$857$	−25.7559	+	14.8702i	−0.879805	+	0.507956i	−0.00921107	+	0.999958i	$0.502932\pi$
$858$		0			0
$859$	−26.8827	+	46.5622i	−0.917226	+	1.58868i	−0.113616	+	0.993525i	$0.536243\pi$
$859$	−26.8827	+	46.5622i	−0.917226	+	1.58868i	−0.803610	+	0.595157i	$0.797090\pi$
$860$		0			0
$861$	19.1433	+	11.0524i	0.652403	+	0.376665i
$862$		0			0
$863$	2.49952			0.0850845			0.0425423	−	0.999095i	$-0.486454\pi$
$863$	2.49952			0.0850845			0.0425423	+	0.999095i	$0.486454\pi$
$864$		0			0
$865$	−43.3323	−	25.0179i	−1.47334	−	0.850634i
$866$		0			0
$867$			22.9654i			0.779946i
$868$		0			0
$869$	−9.70856	−	16.8157i	−0.329340	−	0.570434i
$870$		0			0
$871$	−26.3976	+	15.2407i	−0.894449	+	0.516410i
$872$		0			0
$873$			13.7559i			0.465567i
$874$		0			0
$875$	−32.7851			−1.10834
$876$		0			0
$877$	26.2460	+	45.4594i	0.886264	+	1.53505i	0.844259	+	0.535936i	$0.180041\pi$
$877$	26.2460	+	45.4594i	0.886264	+	1.53505i	0.0420049	+	0.999117i	$0.486625\pi$
$878$		0			0
$879$	8.19692	−	4.73249i	0.276475	−	0.159623i
$880$		0			0
$881$	31.4954			1.06111			0.530553	−	0.847652i	$-0.321984\pi$
$881$	31.4954			1.06111			0.530553	+	0.847652i	$0.321984\pi$
$882$		0			0
$883$	12.2087	−	21.1461i	0.410856	−	0.711623i	−0.584128	−	0.811662i	$-0.698563\pi$
$883$	12.2087	−	21.1461i	0.410856	−	0.711623i	0.994984	+	0.100039i	$0.0318967\pi$
$884$		0			0
$885$			4.31123i			0.144921i
$886$		0			0
$887$	29.3972	−	50.9175i	0.987062	−	1.70964i	0.354675	−	0.934990i	$-0.384592\pi$
$887$	29.3972	−	50.9175i	0.987062	−	1.70964i	0.632388	−	0.774652i	$-0.282075\pi$
$888$		0			0
$889$	5.26145	+	3.03770i	0.176463	+	0.101881i
$890$		0			0
$891$	−10.2446	−	17.7441i	−0.343207	−	0.594451i
$892$		0			0
$893$	−26.3123	−	30.8549i	−0.880508	−	1.03252i
$894$		0			0
$895$	−18.0924	−	31.3369i	−0.604762	−	1.04748i
$896$		0			0
$897$	4.77990	−	8.27903i	0.159596	−	0.276429i
$898$		0			0
$899$	31.0754	−	53.8241i	1.03642	−	1.79513i
$900$		0			0
$901$	33.8467			1.12760
$902$		0			0
$903$	−16.9054	+	29.2810i	−0.562576	+	0.974411i
$904$		0			0
$905$			71.5988i			2.38003i
$906$		0			0
$907$	21.2686	−	12.2795i	0.706213	−	0.407732i	−0.103444	−	0.994635i	$-0.532986\pi$
$907$	21.2686	−	12.2795i	0.706213	−	0.407732i	0.809657	+	0.586903i	$0.199653\pi$
$908$		0			0
$909$	2.31047	−	1.33395i	0.0766334	−	0.0442443i
$910$		0			0
$911$	24.6066			0.815254			0.407627	−	0.913149i	$-0.366356\pi$
$911$	24.6066			0.815254			0.407627	+	0.913149i	$0.366356\pi$
$912$		0			0
$913$	43.1967			1.42960
$914$		0			0
$915$	37.5359	−	21.6714i	1.24090	−	0.716434i
$916$		0			0
$917$	−23.9976	+	13.8550i	−0.792471	+	0.457533i
$918$		0			0
$919$		−	43.6188i		−	1.43885i	−0.694569	−	0.719426i	$-0.744405\pi$
$919$		−	43.6188i		−	1.43885i	0.694569	−	0.719426i	$-0.255595\pi$
$920$		0			0
$921$	−8.91801	+	15.4464i	−0.293858	+	0.508978i
$922$		0			0
$923$	−1.63464			−0.0538049
$924$		0			0
$925$	−7.00886	+	12.1397i	−0.230450	+	0.399151i
$926$		0			0
$927$	−3.41473	+	5.91449i	−0.112155	+	0.194257i
$928$		0			0
$929$	2.93536	+	5.08420i	0.0963061	+	0.166807i	0.910153	−	0.414272i	$-0.135964\pi$
$929$	2.93536	+	5.08420i	0.0963061	+	0.166807i	−0.813847	+	0.581079i	$0.802631\pi$
$930$		0			0
$931$	−55.4814	−	19.6942i	−1.81833	−	0.645450i
$932$		0			0
$933$	6.49292	+	11.2461i	0.212569	+	0.368180i
$934$		0			0
$935$	−54.5516	−	31.4954i	−1.78403	−	1.03001i
$936$		0			0
$937$	10.0574	−	17.4199i	0.328561	−	0.569085i	−0.653665	−	0.756784i	$-0.726770\pi$
$937$	10.0574	−	17.4199i	0.328561	−	0.569085i	0.982227	+	0.187699i	$0.0601029\pi$
$938$		0			0
$939$			25.7683i			0.840916i
$940$		0			0
$941$	9.83528	−	17.0352i	0.320621	−	0.555332i	−0.659995	−	0.751270i	$-0.729442\pi$
$941$	9.83528	−	17.0352i	0.320621	−	0.555332i	0.980616	+	0.195938i	$0.0627751\pi$
$942$		0			0
$943$	7.62753			0.248387
$944$		0			0
$945$	−60.0406	+	34.6645i	−1.95312	+	1.12764i
$946$		0			0
$947$	−6.02572	−	10.4368i	−0.195809	−	0.339152i	0.751356	−	0.659897i	$-0.229400\pi$
$947$	−6.02572	−	10.4368i	−0.195809	−	0.339152i	−0.947166	+	0.320745i	$0.896067\pi$
$948$		0			0
$949$	−19.5897			−0.635907
$950$		0			0
$951$			4.96687i			0.161062i
$952$		0			0
$953$	24.5889	−	14.1964i	0.796513	−	0.459867i	−0.0457374	−	0.998953i	$-0.514564\pi$
$953$	24.5889	−	14.1964i	0.796513	−	0.459867i	0.842250	+	0.539086i	$0.181230\pi$
$954$		0			0
$955$	−22.2409	−	38.5224i	−0.719698	−	1.24655i
$956$		0			0
$957$			45.4385i			1.46882i
$958$		0			0
$959$	5.62908	+	3.24995i	0.181772	+	0.104946i
$960$		0			0
$961$	30.5192			0.984492
$962$		0			0
$963$	5.24101	+	3.02590i	0.168889	+	0.0975083i
$964$		0			0
$965$	32.1856	−	55.7471i	1.03609	−	1.79456i
$966$		0			0
$967$	−15.7588	+	9.09835i	−0.506769	+	0.292583i	−0.731505	−	0.681836i	$-0.761182\pi$
$967$	−15.7588	+	9.09835i	−0.506769	+	0.292583i	0.224735	+	0.974420i	$0.427848\pi$
$968$		0			0
$969$	23.1228	+	27.1148i	0.742813	+	0.871054i
$970$		0			0
$971$	−48.9417	+	28.2565i	−1.57061	+	0.906795i	−0.574521	+	0.818490i	$0.694812\pi$
$971$	−48.9417	+	28.2565i	−1.57061	+	0.906795i	−0.996093	+	0.0883051i	$0.971855\pi$
$972$		0			0
$973$	−78.9327	−	45.5718i	−2.53047	−	1.46097i
$974$		0			0
$975$	−8.67956	−	5.01115i	−0.277969	−	0.160485i
$976$		0			0
$977$		−	4.10067i		−	0.131192i	−0.997846	−	0.0655960i	$-0.979105\pi$
$977$		−	4.10067i		−	0.131192i	0.997846	−	0.0655960i	$-0.0208949\pi$
$978$		0			0
$979$	58.9810	+	34.0527i	1.88504	+	1.08833i
$980$		0			0
$981$	12.2359			0.390663
$982$		0			0
$983$	22.7364	+	39.3806i	0.725178	+	1.25605i	0.958901	+	0.283742i	$0.0915759\pi$
$983$	22.7364	+	39.3806i	0.725178	+	1.25605i	−0.233723	+	0.972303i	$0.575091\pi$
$984$		0			0
$985$	−8.15055	−	14.1172i	−0.259698	−	0.449810i
$986$		0			0
$987$		−	59.7894i		−	1.90312i
$988$		0			0
$989$			11.6668i			0.370983i
$990$		0			0
$991$	−12.3688	−	21.4233i	−0.392907	−	0.680534i	0.599925	−	0.800056i	$-0.295197\pi$
$991$	−12.3688	−	21.4233i	−0.392907	−	0.680534i	−0.992832	+	0.119522i	$0.961864\pi$
$992$		0			0
$993$	−10.7982	−	18.7030i	−0.342670	−	0.593521i
$994$		0			0
$995$	12.9223			0.409663
$996$		0			0
$997$	−47.2072	−	27.2551i	−1.49507	−	0.863178i	−0.495083	−	0.868845i	$-0.664862\pi$
$997$	−47.2072	−	27.2551i	−1.49507	−	0.863178i	−0.999984	+	0.00566798i	$0.998196\pi$
$998$		0			0
$999$		−	34.1057i		−	1.07906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.s.i.31.11	yes	32
4.3	odd	2	inner	1216.2.s.i.31.5	✓	32
8.3	odd	2	inner	1216.2.s.i.31.12	yes	32
8.5	even	2	inner	1216.2.s.i.31.6	yes	32
19.8	odd	6	inner	1216.2.s.i.863.12	yes	32
76.27	even	6	inner	1216.2.s.i.863.6	yes	32
152.27	even	6	inner	1216.2.s.i.863.11	yes	32
152.141	odd	6	inner	1216.2.s.i.863.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1216.2.s.i.31.5	✓	32	4.3	odd	2	inner
1216.2.s.i.31.6	yes	32	8.5	even	2	inner
1216.2.s.i.31.11	yes	32	1.1	even	1	trivial
1216.2.s.i.31.12	yes	32	8.3	odd	2	inner
1216.2.s.i.863.5	yes	32	152.141	odd	6	inner
1216.2.s.i.863.6	yes	32	76.27	even	6	inner
1216.2.s.i.863.11	yes	32	152.27	even	6	inner
1216.2.s.i.863.12	yes	32	19.8	odd	6	inner

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:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22910 - 0.709622i) q^{3} +(2.34387 - 1.35323i) q^{5} +4.52840i q^{7} +(-0.492874 + 0.853683i) q^{9} +O(q^{10})\)	\(q+(1.22910 - 0.709622i) q^{3} +(2.34387 - 1.35323i) q^{5} +4.52840i q^{7} +(-0.492874 + 0.853683i) q^{9} -4.04042 q^{11} +(1.51867 - 2.63041i) q^{13} +(1.92057 - 3.32652i) q^{15} +(2.88017 + 4.98860i) q^{17} +(4.10778 + 1.45813i) q^{19} +(3.21345 + 5.56586i) q^{21} +(1.92057 + 1.10884i) q^{23} +(1.16249 - 2.01348i) q^{25} +5.65675i q^{27} +(3.96196 - 6.86232i) q^{29} +7.84342 q^{31} +(-4.96608 + 2.86717i) q^{33} +(6.12799 + 10.6140i) q^{35} -6.02920 q^{37} -4.31072i q^{39} +(2.97862 - 1.71971i) q^{41} +(2.63041 + 4.55601i) q^{43} +2.66790i q^{45} +(-8.05662 - 4.65149i) q^{47} -13.5064 q^{49} +(7.08003 + 4.08766i) q^{51} +(2.93791 - 5.08861i) q^{53} +(-9.47021 + 5.46763i) q^{55} +(6.08360 - 1.12277i) q^{57} +(-0.972014 + 0.561192i) q^{59} +(9.77209 + 5.64192i) q^{61} +(-3.86582 - 2.23193i) q^{63} -8.22046i q^{65} +(-8.69104 - 5.01777i) q^{67} +3.14743 q^{69} +(-0.269091 - 0.466080i) q^{71} +(-3.22481 - 5.58553i) q^{73} -3.29970i q^{75} -18.2966i q^{77} +(2.40286 + 4.16188i) q^{79} +(2.53553 + 4.39166i) q^{81} -10.6912 q^{83} +(13.5015 + 7.79508i) q^{85} -11.2460i q^{87} +(-14.5977 - 8.42801i) q^{89} +(11.9116 + 6.87714i) q^{91} +(9.64035 - 5.56586i) q^{93} +(11.6013 - 2.14111i) q^{95} +(12.0852 - 6.97740i) q^{97} +(1.99142 - 3.44924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 24 q^{9}+O(q^{10}) \) 32 * q + 24 * q^9	\( 32 q + 24 q^{9} + 20 q^{17} + 44 q^{25} - 60 q^{33} - 24 q^{41} - 64 q^{49} - 36 q^{57} - 64 q^{73} - 24 q^{81} - 12 q^{89} - 48 q^{97}+O(q^{100}) \) 32 * q + 24 * q^9 + 20 * q^17 + 44 * q^25 - 60 * q^33 - 24 * q^41 - 64 * q^49 - 36 * q^57 - 64 * q^73 - 24 * q^81 - 12 * q^89 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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