LMFDB - Embedded newform 1386.2.bu.b.701.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(701,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("1386.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bu (of order $10$, degree $4$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			701.12
Character	$\chi$	$=$	1386.701
Dual form			1386.2.bu.b.953.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(2.53437 - 3.48826i) q^{5} +(0.951057 + 0.309017i) q^{7} +(-0.309017 - 0.951057i) q^{8} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(2.53437 - 3.48826i) q^{5} +(0.951057 + 0.309017i) q^{7} +(-0.309017 - 0.951057i) q^{8} -4.31173i q^{10} +(-2.59917 + 2.06017i) q^{11} +(-3.41320 - 4.69786i) q^{13} +(0.951057 - 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(3.36138 + 2.44219i) q^{17} +(2.74131 - 0.890705i) q^{19} +(-2.53437 - 3.48826i) q^{20} +(-0.891833 + 3.19447i) q^{22} -5.92718i q^{23} +(-4.19986 - 12.9258i) q^{25} +(-5.52267 - 1.79442i) q^{26} +(0.587785 - 0.809017i) q^{28} +(-2.53329 + 7.79665i) q^{29} +(5.02066 - 3.64772i) q^{31} -1.00000 q^{32} +4.15490 q^{34} +(3.48826 - 2.53437i) q^{35} +(-2.74015 + 8.43333i) q^{37} +(1.69422 - 2.33190i) q^{38} +(-4.10070 - 1.33240i) q^{40} +(1.31016 + 4.03225i) q^{41} -2.81396i q^{43} +(1.15615 + 3.10859i) q^{44} +(-3.48391 - 4.79519i) q^{46} +(-3.74057 + 1.21539i) q^{47} +(0.809017 + 0.587785i) q^{49} +(-10.9954 - 7.98861i) q^{50} +(-5.52267 + 1.79442i) q^{52} +(-5.28579 - 7.27526i) q^{53} +(0.599164 + 14.2878i) q^{55} -1.00000i q^{56} +(2.53329 + 7.79665i) q^{58} +(6.92609 + 2.25042i) q^{59} +(0.553996 - 0.762510i) q^{61} +(1.91772 - 5.90213i) q^{62} +(-0.809017 + 0.587785i) q^{64} -25.0377 q^{65} +15.2881 q^{67} +(3.36138 - 2.44219i) q^{68} +(1.33240 - 4.10070i) q^{70} +(-0.423833 + 0.583357i) q^{71} +(-5.71280 - 1.85620i) q^{73} +(2.74015 + 8.43333i) q^{74} -2.88238i q^{76} +(-3.10859 + 1.15615i) q^{77} +(8.25094 + 11.3564i) q^{79} +(-4.10070 + 1.33240i) q^{80} +(3.43004 + 2.49207i) q^{82} +(4.38705 + 3.18738i) q^{83} +(17.0380 - 5.53598i) q^{85} +(-1.65400 - 2.27654i) q^{86} +(2.76253 + 1.83533i) q^{88} +4.27098i q^{89} +(-1.79442 - 5.52267i) q^{91} +(-5.63708 - 1.83160i) q^{92} +(-2.31180 + 3.18192i) q^{94} +(3.84048 - 11.8198i) q^{95} +(-0.399891 + 0.290538i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8}+O(q^{10}) $ 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8	$ 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8} - 4 q^{11} - 12 q^{16} - 24 q^{17} + 4 q^{22} + 24 q^{25} - 40 q^{26} + 16 q^{29} + 40 q^{31} - 48 q^{32} - 16 q^{34} + 12 q^{35} + 16 q^{37} + 40 q^{38} - 24 q^{41} - 4 q^{44} - 40 q^{46} + 40 q^{47} + 12 q^{49} - 4 q^{50} - 40 q^{52} + 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} + 40 q^{62} - 12 q^{64} + 48 q^{67} - 24 q^{68} + 8 q^{70} + 40 q^{73} - 16 q^{74} - 32 q^{77} + 40 q^{79} - 16 q^{82} + 16 q^{83} - 20 q^{85} + 4 q^{88} + 20 q^{92} + 52 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) $ 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8 - 4 * q^11 - 12 * q^16 - 24 * q^17 + 4 * q^22 + 24 * q^25 - 40 * q^26 + 16 * q^29 + 40 * q^31 - 48 * q^32 - 16 * q^34 + 12 * q^35 + 16 * q^37 + 40 * q^38 - 24 * q^41 - 4 * q^44 - 40 * q^46 + 40 * q^47 + 12 * q^49 - 4 * q^50 - 40 * q^52 + 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 + 40 * q^62 - 12 * q^64 + 48 * q^67 - 24 * q^68 + 8 * q^70 + 40 * q^73 - 16 * q^74 - 32 * q^77 + 40 * q^79 - 16 * q^82 + 16 * q^83 - 20 * q^85 + 4 * q^88 + 20 * q^92 + 52 * q^95 - 8 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	2.53437	−	3.48826i	1.13341	−	1.56000i	0.351972	−	0.936010i	$-0.385511\pi$
$5$	2.53437	−	3.48826i	1.13341	−	1.56000i	0.781433	−	0.623989i	$-0.214489\pi$
$6$		0			0
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$		0			0
$10$		−	4.31173i		−	1.36349i
$11$	−2.59917	+	2.06017i	−0.783679	+	0.621166i
$11$	−2.59917	+	2.06017i	−0.783679	+	0.621166i
$12$		0			0
$13$	−3.41320	−	4.69786i	−0.946651	−	1.30295i	−0.952999	−	0.302973i	$-0.902021\pi$
$13$	−3.41320	−	4.69786i	−0.946651	−	1.30295i	0.00634847	−	0.999980i	$-0.497979\pi$
$14$	0.951057	−	0.309017i	0.254181	−	0.0825883i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	3.36138	+	2.44219i	0.815255	+	0.592318i	0.915349	−	0.402660i	$-0.131914\pi$
$17$	3.36138	+	2.44219i	0.815255	+	0.592318i	−0.100094	+	0.994978i	$0.531914\pi$
$18$		0			0
$19$	2.74131	−	0.890705i	0.628899	−	0.204342i	0.0228117	−	0.999740i	$-0.492738\pi$
$19$	2.74131	−	0.890705i	0.628899	−	0.204342i	0.606087	+	0.795398i	$0.292738\pi$
$20$	−2.53437	−	3.48826i	−0.566703	−	0.780000i
$21$		0			0
$22$	−0.891833	+	3.19447i	−0.190140	+	0.681063i
$23$		−	5.92718i		−	1.23590i	−0.786216	−	0.617951i	$-0.787963\pi$
$23$		−	5.92718i		−	1.23590i	0.786216	−	0.617951i	$-0.212037\pi$
$24$		0			0
$25$	−4.19986	−	12.9258i	−0.839972	−	2.58517i
$26$	−5.52267	−	1.79442i	−1.08308	−	0.351916i
$27$		0			0
$28$	0.587785	−	0.809017i	0.111081	−	0.152890i
$29$	−2.53329	+	7.79665i	−0.470419	+	1.44780i	0.381618	+	0.924320i	$0.375367\pi$
$29$	−2.53329	+	7.79665i	−0.470419	+	1.44780i	−0.852037	+	0.523482i	$0.824633\pi$
$30$		0			0
$31$	5.02066	−	3.64772i	0.901736	−	0.655150i	−0.0371750	−	0.999309i	$-0.511836\pi$
$31$	5.02066	−	3.64772i	0.901736	−	0.655150i	0.938911	+	0.344159i	$0.111836\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	4.15490			0.712559
$35$	3.48826	−	2.53437i	0.589624	−	0.428387i
$36$		0			0
$37$	−2.74015	+	8.43333i	−0.450479	+	1.38643i	0.425884	+	0.904778i	$0.359963\pi$
$37$	−2.74015	+	8.43333i	−0.450479	+	1.38643i	−0.876362	+	0.481653i	$0.840037\pi$
$38$	1.69422	−	2.33190i	0.274839	−	0.378283i
$39$		0			0
$40$	−4.10070	−	1.33240i	−0.648378	−	0.210671i
$41$	1.31016	+	4.03225i	0.204612	+	0.629731i	0.999729	+	0.0232753i	$0.00740943\pi$
$41$	1.31016	+	4.03225i	0.204612	+	0.629731i	−0.795117	+	0.606456i	$0.792591\pi$
$42$		0			0
$43$		−	2.81396i		−	0.429125i	−0.976710	−	0.214562i	$-0.931167\pi$
$43$		−	2.81396i		−	0.429125i	0.976710	−	0.214562i	$-0.0688325\pi$
$44$	1.15615	+	3.10859i	0.174297	+	0.468637i
$45$		0			0
$46$	−3.48391	−	4.79519i	−0.513674	−	0.707012i
$47$	−3.74057	+	1.21539i	−0.545618	+	0.177282i	−0.568840	−	0.822448i	$-0.692608\pi$
$47$	−3.74057	+	1.21539i	−0.545618	+	0.177282i	0.0232216	+	0.999730i	$0.492608\pi$
$48$		0			0
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	−10.9954	−	7.98861i	−1.55498	−	1.12976i
$51$		0			0
$52$	−5.52267	+	1.79442i	−0.765856	+	0.248842i
$53$	−5.28579	−	7.27526i	−0.726059	−	0.999334i	−0.999301	−	0.0373890i	$-0.988096\pi$
$53$	−5.28579	−	7.27526i	−0.726059	−	0.999334i	0.273242	−	0.961945i	$-0.411904\pi$
$54$		0			0
$55$	0.599164	+	14.2878i	0.0807913	+	1.92657i
$56$		−	1.00000i		−	0.133631i
$57$		0			0
$58$	2.53329	+	7.79665i	0.332637	+	1.02375i
$59$	6.92609	+	2.25042i	0.901700	+	0.292980i	0.722938	−	0.690913i	$-0.242791\pi$
$59$	6.92609	+	2.25042i	0.901700	+	0.292980i	0.178761	+	0.983892i	$0.442791\pi$
$60$		0			0
$61$	0.553996	−	0.762510i	0.0709319	−	0.0976293i	−0.772077	−	0.635529i	$-0.780782\pi$
$61$	0.553996	−	0.762510i	0.0709319	−	0.0976293i	0.843009	+	0.537900i	$0.180782\pi$
$62$	1.91772	−	5.90213i	0.243551	−	0.749572i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−25.0377			−3.10554
$66$		0			0
$67$	15.2881			1.86774			0.933869	−	0.357615i	$-0.116410\pi$
$67$	15.2881			1.86774			0.933869	+	0.357615i	$0.116410\pi$
$68$	3.36138	−	2.44219i	0.407628	−	0.296159i
$69$		0			0
$70$	1.33240	−	4.10070i	0.159252	−	0.490127i
$71$	−0.423833	+	0.583357i	−0.0502998	+	0.0692317i	−0.833426	−	0.552631i	$-0.813624\pi$
$71$	−0.423833	+	0.583357i	−0.0502998	+	0.0692317i	0.783126	+	0.621863i	$0.213624\pi$
$72$		0			0
$73$	−5.71280	−	1.85620i	−0.668632	−	0.217252i	−0.0450206	−	0.998986i	$-0.514335\pi$
$73$	−5.71280	−	1.85620i	−0.668632	−	0.217252i	−0.623612	+	0.781734i	$0.714335\pi$
$74$	2.74015	+	8.43333i	0.318536	+	0.980354i
$75$		0			0
$76$		−	2.88238i		−	0.330632i
$77$	−3.10859	+	1.15615i	−0.354256	+	0.131756i
$78$		0			0
$79$	8.25094	+	11.3564i	0.928303	+	1.27770i	0.960518	+	0.278219i	$0.0897440\pi$
$79$	8.25094	+	11.3564i	0.928303	+	1.27770i	−0.0322147	+	0.999481i	$0.510256\pi$
$80$	−4.10070	+	1.33240i	−0.458472	+	0.148967i
$81$		0			0
$82$	3.43004	+	2.49207i	0.378784	+	0.275203i
$83$	4.38705	+	3.18738i	0.481541	+	0.349860i	0.801922	−	0.597429i	$-0.203811\pi$
$83$	4.38705	+	3.18738i	0.481541	+	0.349860i	−0.320381	+	0.947289i	$0.603811\pi$
$84$		0			0
$85$	17.0380	−	5.53598i	1.84803	−	0.600461i
$86$	−1.65400	−	2.27654i	−0.178356	−	0.245486i
$87$		0			0
$88$	2.76253	+	1.83533i	0.294487	+	0.195647i
$89$			4.27098i			0.452723i	0.974043	+	0.226362i	$0.0726831\pi$
$89$			4.27098i			0.452723i	−0.974043	+	0.226362i	$0.927317\pi$
$90$		0			0
$91$	−1.79442	−	5.52267i	−0.188107	−	0.578933i
$92$	−5.63708	−	1.83160i	−0.587707	−	0.190957i
$93$		0			0
$94$	−2.31180	+	3.18192i	−0.238444	+	0.328190i
$95$	3.84048	−	11.8198i	0.394025	−	1.21268i
$96$		0			0
$97$	−0.399891	+	0.290538i	−0.0406028	+	0.0294997i	−0.607902	−	0.794012i	$-0.707988\pi$
$97$	−0.399891	+	0.290538i	−0.0406028	+	0.0294997i	0.567299	+	0.823512i	$0.307988\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	−13.5910			−1.35910
$101$	−2.96053	+	2.15095i	−0.294583	+	0.214027i	−0.725253	−	0.688482i	$-0.758277\pi$
$101$	−2.96053	+	2.15095i	−0.294583	+	0.214027i	0.430670	+	0.902510i	$0.358277\pi$
$102$		0			0
$103$	3.66357	−	11.2753i	0.360983	−	1.11099i	−0.591476	−	0.806323i	$-0.701455\pi$
$103$	3.66357	−	11.2753i	0.360983	−	1.11099i	0.952459	−	0.304668i	$-0.0985454\pi$
$104$	−3.41320	+	4.69786i	−0.334692	+	0.460663i
$105$		0			0
$106$	−8.55259	−	2.77890i	−0.830701	−	0.269911i
$107$	0.0559276	+	0.172127i	0.00540672	+	0.0166402i	0.953723	−	0.300685i	$-0.0972153\pi$
$107$	0.0559276	+	0.172127i	0.00540672	+	0.0166402i	−0.948317	+	0.317325i	$0.897215\pi$
$108$		0			0
$109$		−	18.4311i		−	1.76538i	−0.469957	−	0.882689i	$-0.655731\pi$
$109$		−	18.4311i		−	1.76538i	0.469957	−	0.882689i	$-0.344269\pi$
$110$	8.88291	+	11.2069i	0.846953	+	1.06854i
$111$		0			0
$112$	−0.587785	−	0.809017i	−0.0555405	−	0.0764449i
$113$	−16.2117	+	5.26751i	−1.52507	+	0.495525i	−0.947211	−	0.320611i	$-0.896112\pi$
$113$	−16.2117	+	5.26751i	−1.52507	+	0.495525i	−0.577859	+	0.816136i	$0.696112\pi$
$114$		0			0
$115$	−20.6756	−	15.0217i	−1.92801	−	1.40078i
$116$	6.63223	+	4.81860i	0.615787	+	0.447395i
$117$		0			0
$118$	6.92609	−	2.25042i	0.637598	−	0.207168i
$119$	2.44219	+	3.36138i	0.223875	+	0.308137i
$120$		0			0
$121$	2.51137	−	10.7095i	0.228306	−	0.973589i
$122$		−	0.942514i		−	0.0853312i
$123$		0			0
$124$	−1.91772	−	5.90213i	−0.172216	−	0.530027i
$125$	−35.2292	−	11.4467i	−3.15100	−	1.02382i
$126$		0			0
$127$	−2.49397	+	3.43265i	−0.221304	+	0.304599i	−0.905204	−	0.424977i	$-0.860282\pi$
$127$	−2.49397	+	3.43265i	−0.221304	+	0.304599i	0.683900	+	0.729575i	$0.260282\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$		0			0
$130$	−20.2559	+	14.7168i	−1.77656	+	1.29075i
$131$	3.42886			0.299581			0.149791	−	0.988718i	$-0.452140\pi$
$131$	3.42886			0.299581			0.149791	+	0.988718i	$0.452140\pi$
$132$		0			0
$133$	2.88238			0.249934
$134$	12.3683	−	8.98612i	1.06846	−	0.776282i
$135$		0			0
$136$	1.28393	−	3.95154i	0.110096	−	0.338842i
$137$	2.78447	−	3.83250i	0.237894	−	0.327432i	−0.673332	−	0.739340i	$-0.735137\pi$
$137$	2.78447	−	3.83250i	0.237894	−	0.327432i	0.911225	+	0.411908i	$0.135137\pi$
$138$		0			0
$139$	−2.41957	−	0.786167i	−0.205225	−	0.0666818i	0.204600	−	0.978846i	$-0.434411\pi$
$139$	−2.41957	−	0.786167i	−0.205225	−	0.0666818i	−0.409826	+	0.912164i	$0.634411\pi$
$140$	−1.33240	−	4.10070i	−0.112608	−	0.346572i
$141$		0			0
$142$			0.721068i			0.0605107i
$143$	18.5499	+	5.17877i	1.55122	+	0.433070i
$144$		0			0
$145$	20.7765	+	28.5964i	1.72539	+	2.37480i
$146$	−5.71280	+	1.85620i	−0.472794	+	0.153620i
$147$		0			0
$148$	7.17382	+	5.21208i	0.589684	+	0.428431i
$149$	13.6305	+	9.90317i	1.11666	+	0.811299i	0.983699	−	0.179822i	$-0.0575522\pi$
$149$	13.6305	+	9.90317i	1.11666	+	0.811299i	0.132959	+	0.991122i	$0.457552\pi$
$150$		0			0
$151$	18.4946	−	6.00925i	1.50507	−	0.489026i	0.563576	−	0.826064i	$-0.309425\pi$
$151$	18.4946	−	6.00925i	1.50507	−	0.489026i	0.941491	+	0.337038i	$0.109425\pi$
$152$	−1.69422	−	2.33190i	−0.137420	−	0.189142i
$153$		0			0
$154$	−1.83533	+	2.76253i	−0.147895	+	0.222611i
$155$		−	26.7581i		−	2.14926i
$156$		0			0
$157$	1.04760	+	3.22419i	0.0836079	+	0.257319i	0.984118	−	0.177517i	$-0.0568065\pi$
$157$	1.04760	+	3.22419i	0.0836079	+	0.257319i	−0.900510	+	0.434836i	$0.856806\pi$
$158$	13.3503	+	4.33778i	1.06209	+	0.345095i
$159$		0			0
$160$	−2.53437	+	3.48826i	−0.200360	+	0.275771i
$161$	1.83160	−	5.63708i	0.144350	−	0.444264i
$162$		0			0
$163$	0.987582	−	0.717521i	0.0773534	−	0.0562006i	−0.548436	−	0.836192i	$-0.684777\pi$
$163$	0.987582	−	0.717521i	0.0773534	−	0.0562006i	0.625790	+	0.779992i	$0.284777\pi$
$164$	4.23976			0.331069
$165$		0			0
$166$	5.42269			0.420883
$167$	−5.10188	+	3.70673i	−0.394795	+	0.286836i	−0.767418	−	0.641147i	$-0.778459\pi$
$167$	−5.10188	+	3.70673i	−0.394795	+	0.286836i	0.372622	+	0.927983i	$0.378459\pi$
$168$		0			0
$169$	−6.40278	+	19.7057i	−0.492522	+	1.51583i
$170$	10.5301	−	14.4934i	0.807619	−	1.11159i
$171$		0			0
$172$	−2.67623	−	0.869561i	−0.204061	−	0.0663034i
$173$	1.76290	+	5.42564i	0.134031	+	0.412504i	0.995438	−	0.0954109i	$-0.0304165\pi$
$173$	1.76290	+	5.42564i	0.134031	+	0.412504i	−0.861407	+	0.507915i	$0.830417\pi$
$174$		0			0
$175$		−	13.5910i		−	1.02739i
$176$	3.31371	−	0.138961i	0.249780	−	0.0104746i
$177$		0			0
$178$	2.51042	+	3.45530i	0.188164	+	0.258986i
$179$	−9.25347	+	3.00663i	−0.691636	+	0.224726i	−0.633683	−	0.773593i	$-0.718458\pi$
$179$	−9.25347	+	3.00663i	−0.691636	+	0.224726i	−0.0579536	+	0.998319i	$0.518458\pi$
$180$		0			0
$181$	0.120760	+	0.0877375i	0.00897604	+	0.00652148i	0.592264	−	0.805744i	$-0.298234\pi$
$181$	0.120760	+	0.0877375i	0.00897604	+	0.00652148i	−0.583288	+	0.812265i	$0.698234\pi$
$182$	−4.69786	−	3.41320i	−0.348229	−	0.253003i
$183$		0			0
$184$	−5.63708	+	1.83160i	−0.415571	+	0.135027i
$185$	22.4731	+	30.9316i	1.65226	+	2.27413i
$186$		0			0
$187$	−13.7681	+	0.577370i	−1.00683	+	0.0422215i
$188$			3.93307i			0.286849i
$189$		0			0
$190$	−3.84048	−	11.8198i	−0.278618	−	0.857497i
$191$	16.8555	+	5.47668i	1.21962	+	0.396279i	0.846944	−	0.531682i	$-0.178440\pi$
$191$	16.8555	+	5.47668i	1.21962	+	0.396279i	0.372677	+	0.927961i	$0.378440\pi$
$192$		0			0
$193$	1.90354	−	2.62000i	0.137020	−	0.188592i	−0.734993	−	0.678075i	$-0.762814\pi$
$193$	1.90354	−	2.62000i	0.137020	−	0.188592i	0.872013	+	0.489483i	$0.162814\pi$
$194$	−0.152745	+	0.470101i	−0.0109664	+	0.0337513i
$195$		0			0
$196$	0.809017	−	0.587785i	0.0577869	−	0.0419847i
$197$	7.60665			0.541951			0.270976	−	0.962586i	$-0.412654\pi$
$197$	7.60665			0.541951			0.270976	+	0.962586i	$0.412654\pi$
$198$		0			0
$199$	21.3449			1.51310			0.756549	−	0.653937i	$-0.226884\pi$
$199$	21.3449			1.51310			0.756549	+	0.653937i	$0.226884\pi$
$200$	−10.9954	+	7.98861i	−0.777490	+	0.564880i
$201$		0			0
$202$	−1.13082	+	3.48031i	−0.0795642	+	0.244874i
$203$	−4.81860	+	6.63223i	−0.338199	+	0.465491i
$204$		0			0
$205$	17.3860	+	5.64905i	1.21429	+	0.394546i
$206$	−3.66357	−	11.2753i	−0.255253	−	0.785589i
$207$		0			0
$208$			5.80688i			0.402635i
$209$	−5.29012	+	7.96266i	−0.365925	+	0.550789i
$210$		0			0
$211$	3.06556	+	4.21938i	0.211042	+	0.290474i	0.901394	−	0.432999i	$-0.142545\pi$
$211$	3.06556	+	4.21938i	0.211042	+	0.290474i	−0.690353	+	0.723473i	$0.742545\pi$
$212$	−8.55259	+	2.77890i	−0.587394	+	0.190856i
$213$		0			0
$214$	0.146420	+	0.106381i	0.0100091	+	0.00727202i
$215$	−9.81583	−	7.13162i	−0.669434	−	0.486372i
$216$		0			0
$217$	5.90213	−	1.91772i	0.400663	−	0.130183i
$218$	−10.8335	−	14.9111i	−0.733739	−	1.00990i
$219$		0			0
$220$	13.7737	+	3.84535i	0.928622	+	0.259253i
$221$		−	24.1270i		−	1.62296i
$222$		0			0
$223$	−0.994548	−	3.06090i	−0.0665999	−	0.204973i	0.912218	−	0.409704i	$-0.134368\pi$
$223$	−0.994548	−	3.06090i	−0.0665999	−	0.204973i	−0.978818	+	0.204731i	$0.934368\pi$
$224$	−0.951057	−	0.309017i	−0.0635451	−	0.0206471i
$225$		0			0
$226$	−10.0194	+	13.7905i	−0.666480	+	0.917331i
$227$	−6.35431	+	19.5566i	−0.421751	+	1.29802i	0.484321	+	0.874890i	$0.339067\pi$
$227$	−6.35431	+	19.5566i	−0.421751	+	1.29802i	−0.906071	+	0.423125i	$0.860933\pi$
$228$		0			0
$229$	−16.4333	+	11.9395i	−1.08594	+	0.788984i	−0.978710	−	0.205250i	$-0.934199\pi$
$229$	−16.4333	+	11.9395i	−1.08594	+	0.788984i	−0.107234	+	0.994234i	$0.534199\pi$
$230$	−25.5564			−1.68514
$231$		0			0
$232$	8.19788			0.538217
$233$	12.4662	−	9.05721i	0.816686	−	0.593357i	−0.0990751	−	0.995080i	$-0.531588\pi$
$233$	12.4662	−	9.05721i	0.816686	−	0.593357i	0.915761	+	0.401723i	$0.131588\pi$
$234$		0			0
$235$	−5.24041	+	16.1283i	−0.341847	+	1.05210i
$236$	4.28056	−	5.89168i	0.278640	−	0.383516i
$237$		0			0
$238$	3.95154	+	1.28393i	0.256140	+	0.0832251i
$239$	1.40187	+	4.31452i	0.0906796	+	0.279083i	0.986104	−	0.166131i	$-0.0531275\pi$
$239$	1.40187	+	4.31452i	0.0906796	+	0.279083i	−0.895424	+	0.445214i	$0.853128\pi$
$240$		0			0
$241$			16.2792i			1.04863i	0.851523	+	0.524317i	$0.175679\pi$
$241$			16.2792i			1.04863i	−0.851523	+	0.524317i	$0.824321\pi$
$242$	−4.26313	−	10.1403i	−0.274045	−	0.651843i
$243$		0			0
$244$	−0.553996	−	0.762510i	−0.0354659	−	0.0488147i
$245$	4.10070	−	1.33240i	0.261984	−	0.0851238i
$246$		0			0
$247$	−13.5410	−	9.83814i	−0.861595	−	0.625986i
$248$	−5.02066	−	3.64772i	−0.318812	−	0.231630i
$249$		0			0
$250$	−35.2292	+	11.4467i	−2.22809	+	0.723951i
$251$	15.6171	+	21.4951i	0.985745	+	1.35676i	0.933676	+	0.358118i	$0.116581\pi$
$251$	15.6171	+	21.4951i	0.985745	+	1.35676i	0.0520684	+	0.998644i	$0.483419\pi$
$252$		0			0
$253$	12.2110	+	15.4057i	0.767700	+	0.968551i
$254$			4.24299i			0.266229i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−0.165234	−	0.0536878i	−0.0103070	−	0.00334895i	0.303859	−	0.952717i	$-0.401725\pi$
$257$	−0.165234	−	0.0536878i	−0.0103070	−	0.00334895i	−0.314166	+	0.949368i	$0.601725\pi$
$258$		0			0
$259$	−5.21208	+	7.17382i	−0.323863	+	0.445759i
$260$	−7.73707	+	23.8123i	−0.479833	+	1.47677i
$261$		0			0
$262$	2.77401	−	2.01544i	0.171379	−	0.124514i
$263$	6.71198			0.413878			0.206939	−	0.978354i	$-0.433650\pi$
$263$	6.71198			0.413878			0.206939	+	0.978354i	$0.433650\pi$
$264$		0			0
$265$	−38.7742			−2.38188
$266$	2.33190	−	1.69422i	0.142978	−	0.103879i
$267$		0			0
$268$	4.72428	−	14.5398i	0.288581	−	0.888162i
$269$	15.3811	−	21.1702i	0.937801	−	1.29077i	−0.0189362	−	0.999821i	$-0.506028\pi$
$269$	15.3811	−	21.1702i	0.937801	−	1.29077i	0.956738	−	0.290952i	$-0.0939721\pi$
$270$		0			0
$271$	24.9997	+	8.12288i	1.51862	+	0.493430i	0.945384	−	0.325960i	$-0.105687\pi$
$271$	24.9997	+	8.12288i	1.51862	+	0.493430i	0.573237	+	0.819390i	$0.305687\pi$
$272$	−1.28393	−	3.95154i	−0.0778499	−	0.239597i
$273$		0			0
$274$		−	4.73723i		−	0.286186i
$275$	37.5456	+	24.9440i	2.26409	+	1.50418i
$276$		0			0
$277$	3.25366	+	4.47828i	0.195493	+	0.269074i	0.895499	−	0.445064i	$-0.146819\pi$
$277$	3.25366	+	4.47828i	0.195493	+	0.269074i	−0.700005	+	0.714138i	$0.746819\pi$
$278$	−2.41957	+	0.786167i	−0.145116	+	0.0471511i
$279$		0			0
$280$	−3.48826	−	2.53437i	−0.208464	−	0.151458i
$281$	1.65661	+	1.20360i	0.0988251	+	0.0718007i	0.636100	−	0.771606i	$-0.280546\pi$
$281$	1.65661	+	1.20360i	0.0988251	+	0.0718007i	−0.537275	+	0.843407i	$0.680546\pi$
$282$		0			0
$283$	−25.9077	+	8.41792i	−1.54005	+	0.500393i	−0.951391	−	0.307987i	$-0.900345\pi$
$283$	−25.9077	+	8.41792i	−1.54005	+	0.500393i	−0.588661	+	0.808380i	$0.700345\pi$
$284$	0.423833	+	0.583357i	0.0251499	+	0.0346158i
$285$		0			0
$286$	18.0512	−	6.71364i	1.06739	−	0.396986i
$287$			4.23976i			0.250265i
$288$		0			0
$289$	0.0813269	+	0.250298i	0.00478393	+	0.0147234i
$290$	33.6171	+	10.9228i	1.97406	+	0.641412i
$291$		0			0
$292$	−3.53070	+	4.85960i	−0.206619	+	0.284386i
$293$	−4.48755	+	13.8113i	−0.262166	+	0.806862i	0.730167	+	0.683268i	$0.239442\pi$
$293$	−4.48755	+	13.8113i	−0.262166	+	0.806862i	−0.992333	+	0.123594i	$0.960558\pi$
$294$		0			0
$295$	25.4033	−	18.4566i	1.47904	−	1.07459i
$296$	8.86733			0.515403
$297$		0			0
$298$	16.8483			0.975995
$299$	−27.8451	+	20.2306i	−1.61032	+	1.16997i
$300$		0			0
$301$	0.869561	−	2.67623i	0.0501207	−	0.154256i
$302$	11.4303	−	15.7324i	0.657738	−	0.905299i
$303$		0			0
$304$	−2.74131	−	0.890705i	−0.157225	−	0.0510854i
$305$	−1.25580	−	3.86497i	−0.0719071	−	0.221307i
$306$		0			0
$307$			8.78840i			0.501581i	0.968041	+	0.250790i	$0.0806905\pi$
$307$			8.78840i			0.501581i	−0.968041	+	0.250790i	$0.919310\pi$
$308$	0.138961	+	3.31371i	0.00791806	+	0.188816i
$309$		0			0
$310$	−15.7280	−	21.6477i	−0.893290	−	1.22951i
$311$	−15.6852	+	5.09644i	−0.889428	+	0.288993i	−0.717866	−	0.696181i	$-0.754881\pi$
$311$	−15.6852	+	5.09644i	−0.889428	+	0.288993i	−0.171561	+	0.985173i	$0.554881\pi$
$312$		0			0
$313$	−0.263884	−	0.191723i	−0.0149156	−	0.0108368i	0.580302	−	0.814401i	$-0.302934\pi$
$313$	−0.263884	−	0.191723i	−0.0149156	−	0.0108368i	−0.595218	+	0.803564i	$0.702934\pi$
$314$	2.74266	+	1.99266i	0.154777	+	0.112452i
$315$		0			0
$316$	13.3503	−	4.33778i	0.751013	−	0.244019i
$317$	2.74807	+	3.78240i	0.154347	+	0.212441i	0.879187	−	0.476477i	$-0.158086\pi$
$317$	2.74807	+	3.78240i	0.154347	+	0.212441i	−0.724840	+	0.688917i	$0.758086\pi$
$318$		0			0
$319$	−9.47801	−	25.4838i	−0.530667	−	1.42682i
$320$			4.31173i			0.241033i
$321$		0			0
$322$	−1.83160	−	5.63708i	−0.102071	−	0.314142i
$323$	11.3899	+	3.70079i	0.633748	+	0.205917i
$324$		0			0
$325$	−46.3889	+	63.8488i	−2.57319	+	3.54169i
$326$	0.377223	−	1.16097i	0.0208924	−	0.0643003i
$327$		0			0
$328$	3.43004	−	2.49207i	0.189392	−	0.137601i
$329$	−3.93307			−0.216837
$330$		0			0
$331$	−29.4642			−1.61950			−0.809749	−	0.586777i	$-0.800397\pi$
$331$	−29.4642			−1.61950			−0.809749	+	0.586777i	$0.800397\pi$
$332$	4.38705	−	3.18738i	0.240771	−	0.174930i
$333$		0			0
$334$	−1.94875	+	5.99762i	−0.106631	+	0.328175i
$335$	38.7457	−	53.3289i	2.11690	−	2.91367i
$336$		0			0
$337$	−4.48179	−	1.45622i	−0.244138	−	0.0793254i	0.184392	−	0.982853i	$-0.440968\pi$
$337$	−4.48179	−	1.45622i	−0.244138	−	0.0793254i	−0.428530	+	0.903527i	$0.640968\pi$
$338$	6.40278	+	19.7057i	0.348265	+	1.07185i
$339$		0			0
$340$		−	17.9148i		−	0.971567i
$341$	−5.53460	+	19.8245i	−0.299716	+	1.07356i
$342$		0			0
$343$	0.587785	+	0.809017i	0.0317374	+	0.0436828i
$344$	−2.67623	+	0.869561i	−0.144293	+	0.0468836i
$345$		0			0
$346$	4.61533	+	3.35323i	0.248121	+	0.180271i
$347$	−19.3628	−	14.0679i	−1.03945	−	0.755204i	−0.0692715	−	0.997598i	$-0.522067\pi$
$347$	−19.3628	−	14.0679i	−1.03945	−	0.755204i	−0.970178	+	0.242394i	$0.922067\pi$
$348$		0			0
$349$	11.9738	−	3.89054i	0.640945	−	0.208256i	0.0295278	−	0.999564i	$-0.490600\pi$
$349$	11.9738	−	3.89054i	0.640945	−	0.208256i	0.611417	+	0.791308i	$0.290600\pi$
$350$	−7.98861	−	10.9954i	−0.427009	−	0.587727i
$351$		0			0
$352$	2.59917	−	2.06017i	0.138536	−	0.109808i
$353$			21.7996i			1.16028i	0.814518	+	0.580138i	$0.197002\pi$
$353$			21.7996i			1.16028i	−0.814518	+	0.580138i	$0.802998\pi$
$354$		0			0
$355$	0.960750	+	2.95688i	0.0509913	+	0.156935i
$356$	4.06195	+	1.31981i	0.215283	+	0.0699496i
$357$		0			0
$358$	−5.71896	+	7.87147i	−0.302256	+	0.416020i
$359$	−2.50360	+	7.70528i	−0.132135	+	0.406669i	−0.995133	−	0.0985372i	$-0.968584\pi$
$359$	−2.50360	+	7.70528i	−0.132135	+	0.406669i	0.862999	+	0.505206i	$0.168584\pi$
$360$		0			0
$361$	−8.64991	+	6.28453i	−0.455258	+	0.330765i
$362$	0.149268			0.00784535
$363$		0			0
$364$	−5.80688			−0.304363
$365$	−20.9533	+	15.2234i	−1.09674	+	0.796831i
$366$		0			0
$367$	2.51094	−	7.72788i	0.131070	−	0.403392i	−0.863888	−	0.503684i	$-0.831978\pi$
$367$	2.51094	−	7.72788i	0.131070	−	0.403392i	0.994958	+	0.100292i	$0.0319776\pi$
$368$	−3.48391	+	4.79519i	−0.181611	+	0.249967i
$369$		0			0
$370$	36.3622	+	11.8148i	1.89038	+	0.614223i
$371$	−2.77890	−	8.55259i	−0.144273	−	0.444028i
$372$		0			0
$373$		−	17.3374i		−	0.897697i	−0.893608	−	0.448848i	$-0.851834\pi$
$373$		−	17.3374i		−	0.897697i	0.893608	−	0.448848i	$-0.148166\pi$
$374$	−10.7993	+	8.55981i	−0.558418	+	0.442617i
$375$		0			0
$376$	2.31180	+	3.18192i	0.119222	+	0.164095i
$377$	45.2742	−	14.7105i	2.33174	−	0.757628i
$378$		0			0
$379$	−17.8523	−	12.9705i	−0.917011	−	0.666247i	0.0257674	−	0.999668i	$-0.491797\pi$
$379$	−17.8523	−	12.9705i	−0.917011	−	0.666247i	−0.942778	+	0.333421i	$0.891797\pi$
$380$	−10.0545	−	7.30503i	−0.515785	−	0.374740i
$381$		0			0
$382$	16.8555	−	5.47668i	0.862402	−	0.280211i
$383$	10.2721	+	14.1383i	0.524878	+	0.722432i	0.986339	−	0.164728i	$-0.0526747\pi$
$383$	10.2721	+	14.1383i	0.524878	+	0.722432i	−0.461461	+	0.887160i	$0.652675\pi$
$384$		0			0
$385$	−3.84535	+	13.7737i	−0.195977	+	0.701972i
$386$		−	3.23850i		−	0.164835i
$387$		0			0
$388$	0.152745	+	0.470101i	0.00775445	+	0.0238657i
$389$	−1.82783	−	0.593900i	−0.0926749	−	0.0301119i	0.262313	−	0.964983i	$-0.415515\pi$
$389$	−1.82783	−	0.593900i	−0.0926749	−	0.0301119i	−0.354987	+	0.934871i	$0.615515\pi$
$390$		0			0
$391$	14.4753	−	19.9235i	0.732047	−	1.00758i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$		0			0
$394$	6.15391	−	4.47108i	0.310029	−	0.225250i
$395$	60.5252			3.04535
$396$		0			0
$397$	−13.9716			−0.701213			−0.350607	−	0.936523i	$-0.614025\pi$
$397$	−13.9716			−0.701213			−0.350607	+	0.936523i	$0.614025\pi$
$398$	17.2684	−	12.5462i	0.865585	−	0.628884i
$399$		0			0
$400$	−4.19986	+	12.9258i	−0.209993	+	0.646292i
$401$	−11.0247	+	15.1743i	−0.550549	+	0.757766i	−0.990087	−	0.140458i	$-0.955142\pi$
$401$	−11.0247	+	15.1743i	−0.550549	+	0.757766i	0.439537	+	0.898224i	$0.355142\pi$
$402$		0			0
$403$	−34.2730	−	11.1360i	−1.70726	−	0.554722i
$404$	1.13082	+	3.48031i	0.0562604	+	0.173152i
$405$		0			0
$406$			8.19788i			0.406854i
$407$	−10.2520	−	27.5648i	−0.508172	−	1.36634i
$408$		0			0
$409$	10.6801	+	14.6999i	0.528095	+	0.726861i	0.986839	−	0.161708i	$-0.0517003\pi$
$409$	10.6801	+	14.6999i	0.528095	+	0.726861i	−0.458743	+	0.888569i	$0.651700\pi$
$410$	17.3860	−	5.64905i	0.858632	−	0.278986i
$411$		0			0
$412$	−9.59136	−	6.96853i	−0.472532	−	0.343315i
$413$	5.89168	+	4.28056i	0.289911	+	0.210632i
$414$		0			0
$415$	22.2368	−	7.22519i	1.09156	−	0.354671i
$416$	3.41320	+	4.69786i	0.167346	+	0.230332i
$417$		0			0
$418$	0.400540	+	9.55138i	0.0195910	+	0.467173i
$419$		−	8.56411i		−	0.418384i	−0.977875	−	0.209192i	$-0.932917\pi$
$419$		−	8.56411i		−	0.418384i	0.977875	−	0.209192i	$-0.0670834\pi$
$420$		0			0
$421$	−9.42213	−	28.9983i	−0.459207	−	1.41329i	−0.866125	−	0.499828i	$-0.833396\pi$
$421$	−9.42213	−	28.9983i	−0.459207	−	1.41329i	0.406918	−	0.913465i	$-0.366604\pi$
$422$	4.96017	+	1.61166i	0.241457	+	0.0784543i
$423$		0			0
$424$	−5.28579	+	7.27526i	−0.256701	+	0.353318i
$425$	17.4500	−	53.7055i	0.846449	−	2.60510i
$426$		0			0
$427$	0.762510	−	0.553996i	0.0369004	−	0.0268097i
$428$	0.180985			0.00874826
$429$		0			0
$430$	−12.1330			−0.585107
$431$	−14.9504	+	10.8621i	−0.720136	+	0.523209i	−0.886428	−	0.462867i	$-0.846821\pi$
$431$	−14.9504	+	10.8621i	−0.720136	+	0.523209i	0.166292	+	0.986077i	$0.446821\pi$
$432$		0			0
$433$	3.08751	−	9.50239i	0.148376	−	0.456656i	−0.849053	−	0.528307i	$-0.822827\pi$
$433$	3.08751	−	9.50239i	0.148376	−	0.456656i	0.997430	+	0.0716515i	$0.0228269\pi$
$434$	3.64772	−	5.02066i	0.175096	−	0.240999i
$435$		0			0
$436$	−17.5290	−	5.69552i	−0.839487	−	0.272766i
$437$	−5.27937	−	16.2482i	−0.252546	−	0.777258i
$438$		0			0
$439$		−	25.1676i		−	1.20118i	−0.799556	−	0.600592i	$-0.794932\pi$
$439$		−	25.1676i		−	1.20118i	0.799556	−	0.600592i	$-0.205068\pi$
$440$	13.4034	−	4.98502i	0.638982	−	0.237652i
$441$		0			0
$442$	−14.1815	−	19.5191i	−0.674545	−	0.928431i
$443$	21.8740	−	7.10729i	1.03926	−	0.337678i	0.260818	−	0.965388i	$-0.416008\pi$
$443$	21.8740	−	7.10729i	1.03926	−	0.337678i	0.778447	+	0.627711i	$0.216008\pi$
$444$		0			0
$445$	14.8983	+	10.8243i	0.706248	+	0.513119i
$446$	−2.60376	−	1.89174i	−0.123292	−	0.0895766i
$447$		0			0
$448$	−0.951057	+	0.309017i	−0.0449332	+	0.0145997i
$449$	−12.2420	−	16.8497i	−0.577737	−	0.795187i	0.415708	−	0.909498i	$-0.363534\pi$
$449$	−12.2420	−	16.8497i	−0.577737	−	0.795187i	−0.993445	+	0.114311i	$0.963534\pi$
$450$		0			0
$451$	−11.7125	−	7.78135i	−0.551518	−	0.366409i
$452$			17.0460i			0.801777i
$453$		0			0
$454$	6.35431	+	19.5566i	0.298223	+	0.917835i
$455$	−23.8123	−	7.73707i	−1.11634	−	0.362720i
$456$		0			0
$457$	18.2635	−	25.1375i	0.854329	−	1.17588i	−0.128563	−	0.991701i	$-0.541037\pi$
$457$	18.2635	−	25.1375i	0.854329	−	1.17588i	0.982892	−	0.184181i	$-0.0589634\pi$
$458$	−6.27696	+	19.3185i	−0.293303	+	0.902695i
$459$		0			0
$460$	−20.6756	+	15.0217i	−0.964003	+	0.700389i
$461$	11.3136			0.526925			0.263463	−	0.964670i	$-0.415135\pi$
$461$	11.3136			0.526925			0.263463	+	0.964670i	$0.415135\pi$
$462$		0			0
$463$	8.00572			0.372057			0.186029	−	0.982544i	$-0.440438\pi$
$463$	8.00572			0.372057			0.186029	+	0.982544i	$0.440438\pi$
$464$	6.63223	−	4.81860i	0.307893	−	0.223698i
$465$		0			0
$466$	4.76166	−	14.6549i	0.220579	−	0.678874i
$467$	−4.56259	+	6.27987i	−0.211132	+	0.290598i	−0.901428	−	0.432929i	$-0.857480\pi$
$467$	−4.56259	+	6.27987i	−0.211132	+	0.290598i	0.690296	+	0.723527i	$0.257480\pi$
$468$		0			0
$469$	14.5398	+	4.72428i	0.671388	+	0.218147i
$470$	5.24041	+	16.1283i	0.241722	+	0.743945i
$471$		0			0
$472$		−	7.28252i		−	0.335205i
$473$	5.79724	+	7.31396i	0.266558	+	0.336296i
$474$		0			0
$475$	−23.0262	−	31.6929i	−1.05651	−	1.45417i
$476$	3.95154	−	1.28393i	0.181119	−	0.0588490i
$477$		0			0
$478$	3.67015	+	2.66652i	0.167869	+	0.121964i
$479$	8.24807	+	5.99257i	0.376864	+	0.273808i	0.760051	−	0.649863i	$-0.225174\pi$
$479$	8.24807	+	5.99257i	0.376864	+	0.273808i	−0.383188	+	0.923671i	$0.625174\pi$
$480$		0			0
$481$	48.9713	−	15.9117i	2.23290	−	0.725513i
$482$	9.56866	+	13.1701i	0.435840	+	0.599883i
$483$		0			0
$484$	−9.40927	−	5.69787i	−0.427694	−	0.258994i
$485$			2.13126i			0.0967755i
$486$		0			0
$487$	6.83010	+	21.0209i	0.309501	+	0.952547i	0.977959	+	0.208797i	$0.0669547\pi$
$487$	6.83010	+	21.0209i	0.309501	+	0.952547i	−0.668458	+	0.743750i	$0.733045\pi$
$488$	−0.896384	−	0.291253i	−0.0405774	−	0.0131844i
$489$		0			0
$490$	2.53437	−	3.48826i	0.114491	−	0.157584i
$491$	−11.4726	+	35.3091i	−0.517752	+	1.59348i	0.260467	+	0.965483i	$0.416123\pi$
$491$	−11.4726	+	35.3091i	−0.517752	+	1.59348i	−0.778219	+	0.627993i	$0.783877\pi$
$492$		0			0
$493$	−27.5562	+	20.0208i	−1.24107	+	0.901690i
$494$	−16.7376			−0.753062
$495$		0			0
$496$	−6.20587			−0.278652
$497$	−0.583357	+	0.423833i	−0.0261671	+	0.0190115i
$498$		0			0
$499$	0.160809	−	0.494920i	0.00719881	−	0.0221557i	−0.947393	−	0.320074i	$-0.896292\pi$
$499$	0.160809	−	0.494920i	0.00719881	−	0.0221557i	0.954591	+	0.297918i	$0.0962923\pi$
$500$	−21.7729	+	29.9678i	−0.973712	+	1.34020i
$501$		0			0
$502$	25.2691	+	8.21041i	1.12781	+	0.366449i
$503$	−7.72337	−	23.7701i	−0.344368	−	1.05986i	−0.961921	−	0.273327i	$-0.911876\pi$
$503$	−7.72337	−	23.7701i	−0.344368	−	1.05986i	0.617553	−	0.786529i	$-0.288124\pi$
$504$		0			0
$505$			15.7784i			0.702130i
$506$	18.9342	+	5.28606i	0.841728	+	0.234994i
$507$		0			0
$508$	2.49397	+	3.43265i	0.110652	+	0.152299i
$509$	10.7315	−	3.48687i	0.475664	−	0.154553i	−0.0613665	−	0.998115i	$-0.519546\pi$
$509$	10.7315	−	3.48687i	0.475664	−	0.154553i	0.537031	+	0.843563i	$0.319546\pi$
$510$		0			0
$511$	−4.85960	−	3.53070i	−0.214976	−	0.156189i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$		0			0
$514$	−0.165234	+	0.0536878i	−0.00728816	+	0.00236807i
$515$	−30.0464	−	41.3554i	−1.32400	−	1.82234i
$516$		0			0
$517$	7.21848	−	10.8652i	0.317468	−	0.477852i
$518$			8.86733i			0.389608i
$519$		0			0
$520$	7.73707	+	23.8123i	0.339293	+	1.04424i
$521$	4.69525	+	1.52558i	0.205703	+	0.0668369i	0.410056	−	0.912060i	$-0.365509\pi$
$521$	4.69525	+	1.52558i	0.205703	+	0.0668369i	−0.204353	+	0.978897i	$0.565509\pi$
$522$		0			0
$523$	−11.5961	+	15.9606i	−0.507061	+	0.697910i	−0.983420	−	0.181341i	$-0.941956\pi$
$523$	−11.5961	+	15.9606i	−0.507061	+	0.697910i	0.476359	+	0.879251i	$0.341956\pi$
$524$	1.05958	−	3.26104i	0.0462878	−	0.142459i
$525$		0			0
$526$	5.43010	−	3.94520i	0.236764	−	0.172019i
$527$	25.7848			1.12320
$528$		0			0
$529$	−12.1315			−0.527455
$530$	−31.3690	+	22.7909i	−1.36258	+	0.989974i
$531$		0			0
$532$	0.890705	−	2.74131i	0.0386170	−	0.118851i
$533$	14.4711	−	19.9178i	0.626814	−	0.862736i
$534$		0			0
$535$	0.742167	+	0.241145i	0.0320867	+	0.0104256i
$536$	−4.72428	−	14.5398i	−0.204058	−	0.628026i
$537$		0			0
$538$		−	26.1679i		−	1.12818i
$539$	−3.31371	+	0.138961i	−0.142732	+	0.00598549i
$540$		0			0
$541$	−14.2223	−	19.5753i	−0.611463	−	0.841607i	0.385234	−	0.922819i	$-0.374121\pi$
$541$	−14.2223	−	19.5753i	−0.611463	−	0.841607i	−0.996697	+	0.0812120i	$0.974121\pi$
$542$	24.9997	−	8.12288i	1.07383	−	0.348908i
$543$		0			0
$544$	−3.36138	−	2.44219i	−0.144118	−	0.104708i
$545$	−64.2925	−	46.7112i	−2.75399	−	2.00089i
$546$		0			0
$547$	6.60428	−	2.14586i	0.282379	−	0.0917504i	−0.164403	−	0.986393i	$-0.552570\pi$
$547$	6.60428	−	2.14586i	0.282379	−	0.0917504i	0.446782	+	0.894643i	$0.352570\pi$
$548$	−2.78447	−	3.83250i	−0.118947	−	0.163716i
$549$		0			0
$550$	45.0368	−	1.88863i	1.92037	−	0.0805314i
$551$			23.6294i			1.00665i
$552$		0			0
$553$	4.33778	+	13.3503i	0.184461	+	0.567712i
$554$	5.26453	+	1.71055i	0.223669	+	0.0726743i
$555$		0			0
$556$	−1.49538	+	2.05821i	−0.0634182	+	0.0872876i
$557$	1.21155	−	3.72875i	0.0513348	−	0.157992i	−0.922103	−	0.386945i	$-0.873530\pi$
$557$	1.21155	−	3.72875i	0.0513348	−	0.157992i	0.973437	+	0.228953i	$0.0735302\pi$
$558$		0			0
$559$	−13.2196	+	9.60460i	−0.559129	+	0.406231i
$560$	−4.31173			−0.182204
$561$		0			0
$562$	2.04768			0.0863763
$563$	−23.7099	+	17.2263i	−0.999254	+	0.726000i	−0.961928	−	0.273303i	$-0.911884\pi$
$563$	−23.7099	+	17.2263i	−0.999254	+	0.726000i	−0.0373255	+	0.999303i	$0.511884\pi$
$564$		0			0
$565$	−22.7121	+	69.9006i	−0.955504	+	2.94074i
$566$	−16.0118	+	22.0384i	−0.673027	+	0.926343i
$567$		0			0
$568$	0.685777	+	0.222822i	0.0287746	+	0.00934942i
$569$	2.10077	+	6.46550i	0.0880687	+	0.271048i	0.985385	−	0.170340i	$-0.0544865\pi$
$569$	2.10077	+	6.46550i	0.0880687	+	0.271048i	−0.897317	+	0.441387i	$0.854486\pi$
$570$		0			0
$571$		−	20.7010i		−	0.866311i	−0.901319	−	0.433155i	$-0.857400\pi$
$571$		−	20.7010i		−	0.866311i	0.901319	−	0.433155i	$-0.142600\pi$
$572$	10.6575	−	16.0417i	0.445614	−	0.670736i
$573$		0			0
$574$	2.49207	+	3.43004i	0.104017	+	0.143167i
$575$	−76.6138	+	24.8933i	−3.19501	+	1.03812i
$576$		0			0
$577$	13.0964	+	9.51509i	0.545210	+	0.396118i	0.826016	−	0.563646i	$-0.190602\pi$
$577$	13.0964	+	9.51509i	0.545210	+	0.396118i	−0.280806	+	0.959764i	$0.590602\pi$
$578$	0.212916	+	0.154693i	0.00885616	+	0.00643438i
$579$		0			0
$580$	33.6171	−	10.9228i	1.39587	−	0.453547i
$581$	3.18738	+	4.38705i	0.132235	+	0.182006i
$582$		0			0
$583$	28.7270	+	8.02001i	1.18975	+	0.332155i
$584$			6.00679i			0.248563i
$585$		0			0
$586$	4.48755	+	13.8113i	0.185379	+	0.570538i
$587$	−13.3028	−	4.32234i	−0.549065	−	0.178402i	0.0213302	−	0.999772i	$-0.493210\pi$
$587$	−13.3028	−	4.32234i	−0.549065	−	0.178402i	−0.570395	+	0.821371i	$0.693210\pi$
$588$		0			0
$589$	10.5141	−	14.4714i	0.433227	−	0.596286i
$590$	9.70321	−	29.8634i	0.399475	−	1.22946i
$591$		0			0
$592$	7.17382	−	5.21208i	0.294842	−	0.214215i
$593$	−4.92979			−0.202442			−0.101221	−	0.994864i	$-0.532275\pi$
$593$	−4.92979			−0.202442			−0.101221	+	0.994864i	$0.532275\pi$
$594$		0			0
$595$	17.9148			0.734435
$596$	13.6305	−	9.90317i	0.558329	−	0.405650i
$597$		0			0
$598$	−10.6359	+	32.7339i	−0.434933	+	1.33859i
$599$	8.89523	−	12.2432i	0.363449	−	0.500245i	−0.587656	−	0.809111i	$-0.699949\pi$
$599$	8.89523	−	12.2432i	0.363449	−	0.500245i	0.951106	+	0.308866i	$0.0999493\pi$
$600$		0			0
$601$	45.9857	+	14.9417i	1.87580	+	0.609483i	0.989123	+	0.147088i	$0.0469901\pi$
$601$	45.9857	+	14.9417i	1.87580	+	0.609483i	0.886674	+	0.462395i	$0.153010\pi$
$602$	−0.869561	−	2.67623i	−0.0354407	−	0.109075i
$603$		0			0
$604$		−	19.4463i		−	0.791260i
$605$	−30.9928	−	35.9021i	−1.26003	−	1.45963i
$606$		0			0
$607$	20.1998	+	27.8026i	0.819884	+	1.12847i	0.989722	+	0.143002i	$0.0456755\pi$
$607$	20.1998	+	27.8026i	0.819884	+	1.12847i	−0.169838	+	0.985472i	$0.554325\pi$
$608$	−2.74131	+	0.890705i	−0.111175	+	0.0361229i
$609$		0			0
$610$	−3.28774	−	2.38868i	−0.133117	−	0.0967148i
$611$	18.4770	+	13.4243i	0.747500	+	0.543091i
$612$		0			0
$613$	−8.33637	+	2.70865i	−0.336703	+	0.109401i	−0.472488	−	0.881337i	$-0.656644\pi$
$613$	−8.33637	+	2.70865i	−0.336703	+	0.109401i	0.135786	+	0.990738i	$0.456644\pi$
$614$	5.16569	+	7.10997i	0.208470	+	0.286935i
$615$		0			0
$616$	2.06017	+	2.59917i	0.0830068	+	0.104724i
$617$		−	16.7658i		−	0.674967i	−0.941331	−	0.337484i	$-0.890424\pi$
$617$		−	16.7658i		−	0.674967i	0.941331	−	0.337484i	$-0.109576\pi$
$618$		0			0
$619$	−12.9885	−	39.9744i	−0.522050	−	1.60671i	−0.770076	−	0.637952i	$-0.779782\pi$
$619$	−12.9885	−	39.9744i	−0.522050	−	1.60671i	0.248026	−	0.968753i	$-0.420218\pi$
$620$	−25.4484	−	8.26869i	−1.02203	−	0.332079i
$621$		0			0
$622$	−9.69400	+	13.3427i	−0.388694	+	0.534992i
$623$	−1.31981	+	4.06195i	−0.0528769	+	0.162738i
$624$		0			0
$625$	−74.2361	+	53.9357i	−2.96945	+	2.15743i
$626$	−0.326179			−0.0130367
$627$		0			0
$628$	3.39012			0.135280
$629$	−29.8065	+	21.6557i	−1.18846	+	0.863468i
$630$		0			0
$631$	−8.92497	+	27.4682i	−0.355297	+	1.09349i	0.600540	+	0.799595i	$0.294953\pi$
$631$	−8.92497	+	27.4682i	−0.355297	+	1.09349i	−0.955837	+	0.293898i	$0.905047\pi$
$632$	8.25094	−	11.3564i	0.328205	−	0.451735i
$633$		0			0
$634$	4.44648	+	1.44475i	0.176592	+	0.0573783i
$635$	5.65335	+	17.3992i	0.224346	+	0.690467i
$636$		0			0
$637$		−	5.80688i		−	0.230077i
$638$	−22.6469	−	15.0458i	−0.896599	−	0.595670i
$639$		0			0
$640$	2.53437	+	3.48826i	0.100180	+	0.137886i
$641$	−35.5933	+	11.5650i	−1.40585	+	0.456789i	−0.911078	−	0.412234i	$-0.864749\pi$
$641$	−35.5933	+	11.5650i	−1.40585	+	0.456789i	−0.494773	+	0.869022i	$0.664749\pi$
$642$		0			0
$643$	−26.5942	−	19.3219i	−1.04877	−	0.761979i	−0.0767956	−	0.997047i	$-0.524469\pi$
$643$	−26.5942	−	19.3219i	−1.04877	−	0.761979i	−0.971979	+	0.235067i	$0.924469\pi$
$644$	−4.79519	−	3.48391i	−0.188957	−	0.137285i
$645$		0			0
$646$	11.3899	−	3.70079i	0.448128	−	0.145606i
$647$	−22.5532	−	31.0418i	−0.886657	−	1.22038i	−0.974532	−	0.224247i	$-0.928008\pi$
$647$	−22.5532	−	31.0418i	−0.886657	−	1.22038i	0.0878751	−	0.996131i	$-0.471992\pi$
$648$		0			0
$649$	−22.6383	+	8.41971i	−0.888632	+	0.330502i
$650$			78.9214i			3.09555i
$651$		0			0
$652$	−0.377223	−	1.16097i	−0.0147732	−	0.0454672i
$653$	−45.4277	−	14.7604i	−1.77772	−	0.577617i	−0.778948	−	0.627088i	$-0.784246\pi$
$653$	−45.4277	−	14.7604i	−1.77772	−	0.577617i	−0.998776	+	0.0494709i	$0.984246\pi$
$654$		0			0
$655$	8.69002	−	11.9608i	0.339547	−	0.467346i
$656$	1.31016	−	4.03225i	0.0511530	−	0.157433i
$657$		0			0
$658$	−3.18192	+	2.31180i	−0.124044	+	0.0901234i
$659$	6.89197			0.268473			0.134237	−	0.990949i	$-0.457142\pi$
$659$	6.89197			0.268473			0.134237	+	0.990949i	$0.457142\pi$
$660$		0			0
$661$	−13.4149			−0.521781			−0.260890	−	0.965368i	$-0.584016\pi$
$661$	−13.4149			−0.521781			−0.260890	+	0.965368i	$0.584016\pi$
$662$	−23.8370	+	17.3186i	−0.926452	+	0.673107i
$663$		0			0
$664$	1.67570	−	5.15729i	0.0650299	−	0.200142i
$665$	7.30503	−	10.0545i	0.283277	−	0.389897i
$666$		0			0
$667$	46.2122	+	15.0152i	1.78934	+	0.581392i
$668$	1.94875	+	5.99762i	0.0753992	+	0.232055i
$669$		0			0
$670$		−	65.9182i		−	2.54664i
$671$	0.130973	+	3.12322i	0.00505616	+	0.120571i
$672$		0			0
$673$	−9.10918	−	12.5377i	−0.351133	−	0.483293i	0.596519	−	0.802599i	$-0.296550\pi$
$673$	−9.10918	−	12.5377i	−0.351133	−	0.483293i	−0.947652	+	0.319306i	$0.896550\pi$
$674$	−4.48179	+	1.45622i	−0.172632	+	0.0560915i
$675$		0			0
$676$	16.7627	+	12.1788i	0.644719	+	0.468416i
$677$	−21.8579	−	15.8807i	−0.840067	−	0.610344i	0.0823225	−	0.996606i	$-0.473766\pi$
$677$	−21.8579	−	15.8807i	−0.840067	−	0.610344i	−0.922389	+	0.386262i	$0.873766\pi$
$678$		0			0
$679$	−0.470101	+	0.152745i	−0.0180408	+	0.00586181i
$680$	−10.5301	−	14.4934i	−0.403809	−	0.555796i
$681$		0			0
$682$	7.17494	+	19.2915i	0.274743	+	0.738709i
$683$			35.1229i			1.34394i	0.740577	+	0.671971i	$0.234552\pi$
$683$			35.1229i			1.34394i	−0.740577	+	0.671971i	$0.765448\pi$
$684$		0			0
$685$	−6.31187	−	19.4260i	−0.241164	−	0.742228i
$686$	0.951057	+	0.309017i	0.0363115	+	0.0117983i
$687$		0			0
$688$	−1.65400	+	2.27654i	−0.0630583	+	0.0867923i
$689$	−16.1368	+	49.6638i	−0.614761	+	1.89204i
$690$		0			0
$691$	4.46454	−	3.24368i	0.169839	−	0.123395i	−0.499619	−	0.866245i	$-0.666527\pi$
$691$	4.46454	−	3.24368i	0.169839	−	0.123395i	0.669458	+	0.742850i	$0.266527\pi$
$692$	5.70486			0.216866
$693$		0			0
$694$	−23.9337			−0.908512
$695$	−8.87445	+	6.44767i	−0.336627	+	0.244574i
$696$		0			0
$697$	−5.44357	+	16.7536i	−0.206190	+	0.634587i
$698$	7.40024	−	10.1856i	0.280103	−	0.385529i
$699$		0			0
$700$	−12.9258	−	4.19986i	−0.488551	−	0.158740i
$701$	−7.57827	−	23.3235i	−0.286227	−	0.880918i	−0.986028	−	0.166579i	$-0.946728\pi$
$701$	−7.57827	−	23.3235i	−0.286227	−	0.880918i	0.699801	−	0.714338i	$-0.253272\pi$
$702$		0			0
$703$			25.5590i			0.963977i
$704$	0.891833	−	3.19447i	0.0336122	−	0.120396i
$705$		0			0
$706$	12.8135	+	17.6363i	0.482242	+	0.663750i
$707$	−3.48031	+	1.13082i	−0.130890	+	0.0425289i
$708$		0			0
$709$	1.70097	+	1.23583i	0.0638814	+	0.0464126i	0.619268	−	0.785180i	$-0.287430\pi$
$709$	1.70097	+	1.23583i	0.0638814	+	0.0464126i	−0.555386	+	0.831593i	$0.687430\pi$
$710$	2.51528	+	1.82746i	0.0943966	+	0.0685832i
$711$		0			0
$712$	4.06195	−	1.31981i	0.152228	−	0.0494618i
$713$	−21.6207	−	29.7583i	−0.809701	−	1.11446i
$714$		0			0
$715$	65.0772	−	51.5820i	2.43375	−	1.92906i
$716$			9.72967i			0.363615i
$717$		0			0
$718$	2.50360	+	7.70528i	0.0934334	+	0.287559i
$719$	−34.6050	−	11.2439i	−1.29055	−	0.419325i	−0.418266	−	0.908325i	$-0.637362\pi$
$719$	−34.6050	−	11.2439i	−1.29055	−	0.419325i	−0.872284	+	0.489000i	$0.837362\pi$
$720$		0			0
$721$	6.96853	−	9.59136i	0.259522	−	0.357201i
$722$	−3.30397	+	10.1686i	−0.122961	+	0.378435i
$723$		0			0
$724$	0.120760	−	0.0877375i	0.00448802	−	0.00326074i
$725$	111.418			4.13795
$726$		0			0
$727$	−2.11541			−0.0784563			−0.0392282	−	0.999230i	$-0.512490\pi$
$727$	−2.11541			−0.0784563			−0.0392282	+	0.999230i	$0.512490\pi$
$728$	−4.69786	+	3.41320i	−0.174114	+	0.126502i
$729$		0			0
$730$	−8.00344	+	24.6320i	−0.296221	+	0.911673i
$731$	6.87222	−	9.45880i	0.254178	−	0.349846i
$732$		0			0
$733$	−21.9856	−	7.14355i	−0.812056	−	0.263853i	−0.126588	−	0.991955i	$-0.540403\pi$
$733$	−21.9856	−	7.14355i	−0.812056	−	0.263853i	−0.685468	+	0.728102i	$0.740403\pi$
$734$	−2.51094	−	7.72788i	−0.0926805	−	0.285241i
$735$		0			0
$736$			5.92718i			0.218479i
$737$	−39.7364	+	31.4961i	−1.46371	+	1.16017i
$738$		0			0
$739$	0.132523	+	0.182402i	0.00487494	+	0.00670978i	0.811448	−	0.584425i	$-0.198680\pi$
$739$	0.132523	+	0.182402i	0.00487494	+	0.00670978i	−0.806573	+	0.591135i	$0.798680\pi$
$740$	36.3622	−	11.8148i	1.33670	−	0.434321i
$741$		0			0
$742$	−7.27526	−	5.28579i	−0.267083	−	0.194047i
$743$	31.8197	+	23.1184i	1.16735	+	0.848132i	0.990690	−	0.136140i	$-0.0434696\pi$
$743$	31.8197	+	23.1184i	1.16735	+	0.848132i	0.176663	+	0.984271i	$0.443470\pi$
$744$		0			0
$745$	69.0898	−	22.4486i	2.53125	−	0.822454i
$746$	−10.1907	−	14.0263i	−0.373107	−	0.513538i
$747$		0			0
$748$	−3.70548	+	13.2727i	−0.135486	+	0.485298i
$749$			0.180985i			0.00661306i
$750$		0			0
$751$	−3.57775	−	11.0112i	−0.130554	−	0.401804i	0.864318	−	0.502946i	$-0.167750\pi$
$751$	−3.57775	−	11.0112i	−0.130554	−	0.401804i	−0.994872	+	0.101142i	$0.967750\pi$
$752$	3.74057	+	1.21539i	0.136405	+	0.0443205i
$753$		0			0
$754$	27.9810	−	38.5125i	1.01901	−	1.40254i
$755$	25.9103	−	79.7436i	0.942971	−	2.90217i
$756$		0			0
$757$	27.9566	−	20.3116i	1.01610	−	0.738239i	0.0506190	−	0.998718i	$-0.483881\pi$
$757$	27.9566	−	20.3116i	1.01610	−	0.738239i	0.965479	+	0.260479i	$0.0838806\pi$
$758$	−22.0666			−0.801497
$759$		0			0
$760$	−12.4281			−0.450813
$761$	34.0967	−	24.7727i	1.23601	−	0.898011i	0.238680	−	0.971098i	$-0.423285\pi$
$761$	34.0967	−	24.7727i	1.23601	−	0.898011i	0.997326	+	0.0730876i	$0.0232853\pi$
$762$		0			0
$763$	5.69552	−	17.5290i	0.206192	−	0.634593i
$764$	10.4173	−	14.3381i	0.376884	−	0.518736i
$765$		0			0
$766$	16.6205	+	5.40034i	0.600525	+	0.195122i
$767$	−13.0679	−	40.2189i	−0.471855	−	1.45222i
$768$		0			0
$769$			26.7836i			0.965841i	0.875664	+	0.482921i	$0.160424\pi$
$769$			26.7836i			0.965841i	−0.875664	+	0.482921i	$0.839576\pi$
$770$	4.98502	+	13.4034i	0.179648	+	0.483025i
$771$		0			0
$772$	−1.90354	−	2.62000i	−0.0685100	−	0.0942960i
$773$	39.8783	−	12.9573i	1.43432	−	0.466040i	0.514201	−	0.857670i	$-0.328089\pi$
$773$	39.8783	−	12.9573i	1.43432	−	0.466040i	0.920123	+	0.391630i	$0.128089\pi$
$774$		0			0
$775$	−68.2359	−	49.5763i	−2.45110	−	1.78083i
$776$	0.399891	+	0.290538i	0.0143553	+	0.0104297i
$777$		0			0
$778$	−1.82783	+	0.593900i	−0.0655311	+	0.0212923i
$779$	7.18309	+	9.88667i	0.257361	+	0.354227i
$780$		0			0
$781$	−0.100201	−	2.38941i	−0.00358546	−	0.0854999i
$782$		−	24.6268i		−	0.880654i
$783$		0			0
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	13.9019	+	4.51699i	0.496178	+	0.161218i
$786$		0			0
$787$	−8.73635	+	12.0245i	−0.311417	+	0.428629i	−0.935823	−	0.352472i	$-0.885341\pi$
$787$	−8.73635	+	12.0245i	−0.311417	+	0.428629i	0.624405	+	0.781100i	$0.285341\pi$
$788$	2.35058	−	7.23435i	0.0837361	−	0.257713i
$789$		0			0
$790$	48.9659	−	35.5758i	1.74213	−	1.26573i
$791$	−17.0460			−0.606086
$792$		0			0
$793$	−5.47306			−0.194354
$794$	−11.3032	+	8.21228i	−0.401137	+	0.291443i
$795$		0			0
$796$	6.59593	−	20.3002i	0.233786	−	0.719521i
$797$	−24.0827	+	33.1470i	−0.853053	+	1.17413i	0.130128	+	0.991497i	$0.458461\pi$
$797$	−24.0827	+	33.1470i	−0.853053	+	1.17413i	−0.983182	+	0.182630i	$0.941539\pi$
$798$		0			0
$799$	−15.5417	−	5.04980i	−0.549826	−	0.178649i
$800$	4.19986	+	12.9258i	0.148487	+	0.456997i
$801$		0			0
$802$			18.7564i			0.662312i
$803$	18.6726	−	6.94477i	0.658943	−	0.245076i
$804$		0			0
$805$	−15.0217	−	20.6756i	−0.529445	−	0.728718i
$806$	−34.2730	+	11.1360i	−1.20721	+	0.392248i
$807$		0			0
$808$	2.96053	+	2.15095i	0.104151	+	0.0756701i
$809$	−25.0597	−	18.2069i	−0.881051	−	0.640121i	0.0524781	−	0.998622i	$-0.483288\pi$
$809$	−25.0597	−	18.2069i	−0.881051	−	0.640121i	−0.933529	+	0.358501i	$0.883288\pi$
$810$		0			0
$811$	−30.2775	+	9.83777i	−1.06319	+	0.345451i	−0.787831	−	0.615891i	$-0.788796\pi$
$811$	−30.2775	+	9.83777i	−1.06319	+	0.345451i	−0.275357	+	0.961342i	$0.588796\pi$
$812$	4.81860	+	6.63223i	0.169100	+	0.232746i
$813$		0			0
$814$	−24.4962	−	16.2745i	−0.858593	−	0.570420i
$815$		−	5.26341i		−	0.184369i
$816$		0			0
$817$	−2.50641	−	7.71393i	−0.0876881	−	0.269876i
$818$	17.2807	+	5.61484i	0.604206	+	0.196318i
$819$		0			0
$820$	10.7451	−	14.7894i	0.375236	−	0.516468i
$821$	−11.3088	+	34.8049i	−0.394680	+	1.21470i	0.534530	+	0.845149i	$0.320489\pi$
$821$	−11.3088	+	34.8049i	−0.394680	+	1.21470i	−0.929210	+	0.369551i	$0.879511\pi$
$822$		0			0
$823$	−15.5717	+	11.3135i	−0.542794	+	0.394363i	−0.825122	−	0.564955i	$-0.808893\pi$
$823$	−15.5717	+	11.3135i	−0.542794	+	0.394363i	0.282328	+	0.959318i	$0.408893\pi$
$824$	−11.8556			−0.413009
$825$		0			0
$826$	7.28252			0.253391
$827$	10.8600	−	7.89027i	0.377640	−	0.274371i	−0.382732	−	0.923859i	$-0.625017\pi$
$827$	10.8600	−	7.89027i	0.377640	−	0.274371i	0.760372	+	0.649488i	$0.225017\pi$
$828$		0			0
$829$	−12.8705	+	39.6112i	−0.447010	+	1.37576i	0.433254	+	0.901272i	$0.357365\pi$
$829$	−12.8705	+	39.6112i	−0.447010	+	1.37576i	−0.880264	+	0.474484i	$0.842635\pi$
$830$	13.7431	−	18.9158i	0.477031	−	0.656577i
$831$		0			0
$832$	5.52267	+	1.79442i	0.191464	+	0.0622105i
$833$	1.28393	+	3.95154i	0.0444857	+	0.136913i
$834$		0			0
$835$			27.1910i			0.940982i
$836$	5.93821	+	7.49180i	0.205377	+	0.259109i
$837$		0			0
$838$	−5.03386	−	6.92851i	−0.173892	−	0.239341i
$839$	0.657040	−	0.213485i	0.0226835	−	0.00737033i	−0.297653	−	0.954674i	$-0.596204\pi$
$839$	0.657040	−	0.213485i	0.0226835	−	0.00737033i	0.320337	+	0.947304i	$0.396204\pi$
$840$		0			0
$841$	−30.9087	−	22.4565i	−1.06582	−	0.774363i
$842$	−24.6675	−	17.9220i	−0.850097	−	0.617632i
$843$		0			0
$844$	4.96017	−	1.61166i	0.170736	−	0.0554756i
$845$	52.5118	+	72.2763i	1.80646	+	2.48638i
$846$		0			0
$847$	5.69787	−	9.40927i	0.195781	−	0.323306i
$848$			8.99272i			0.308811i
$849$		0			0
$850$	−17.4500	−	53.7055i	−0.598530	−	1.84208i
$851$	49.9859	+	16.2414i	1.71349	+	0.556748i
$852$		0			0
$853$	−0.731623	+	1.00699i	−0.0250503	+	0.0344788i	−0.821358	−	0.570412i	$-0.806783\pi$
$853$	−0.731623	+	1.00699i	−0.0250503	+	0.0344788i	0.796308	+	0.604891i	$0.206783\pi$
$854$	0.291253	−	0.896384i	0.00996646	−	0.0306736i
$855$		0			0
$856$	0.146420	−	0.106381i	0.00500454	−	0.00363601i
$857$	29.2600			0.999504			0.499752	−	0.866169i	$-0.333424\pi$
$857$	29.2600			0.999504			0.499752	+	0.866169i	$0.333424\pi$
$858$		0			0
$859$	−15.4472			−0.527051			−0.263525	−	0.964652i	$-0.584885\pi$
$859$	−15.4472			−0.527051			−0.263525	+	0.964652i	$0.584885\pi$
$860$	−9.81583	+	7.13162i	−0.334717	+	0.243186i
$861$		0			0
$862$	−5.71055	+	17.5753i	−0.194502	+	0.598616i
$863$	−1.17852	+	1.62209i	−0.0401172	+	0.0552166i	−0.828604	−	0.559835i	$-0.810865\pi$
$863$	−1.17852	+	1.62209i	−0.0401172	+	0.0552166i	0.788487	+	0.615051i	$0.210865\pi$
$864$		0			0
$865$	23.3939	+	7.60114i	0.795417	+	0.258447i
$866$	−3.08751	−	9.50239i	−0.104918	−	0.322904i
$867$		0			0
$868$		−	6.20587i		−	0.210641i
$869$	−44.8418	−	12.5190i	−1.52116	−	0.424677i
$870$		0			0
$871$	−52.1813	−	71.8214i	−1.76810	−	2.43357i
$872$	−17.5290	+	5.69552i	−0.593607	+	0.192875i
$873$		0			0
$874$	−13.8216	−	10.0420i	−0.467521	−	0.339674i
$875$	−29.9678	−	21.7729i	−1.01310	−	0.736057i
$876$		0			0
$877$	−7.38900	+	2.40083i	−0.249509	+	0.0810703i	−0.431101	−	0.902304i	$-0.641875\pi$
$877$	−7.38900	+	2.40083i	−0.249509	+	0.0810703i	0.181593	+	0.983374i	$0.441875\pi$
$878$	−14.7931	−	20.3610i	−0.499244	−	0.687151i
$879$		0			0
$880$	7.91345	−	11.9113i	0.266762	−	0.401529i
$881$		−	11.5224i		−	0.388200i	−0.980982	−	0.194100i	$-0.937821\pi$
$881$		−	11.5224i		−	0.388200i	0.980982	−	0.194100i	$-0.0621786\pi$
$882$		0			0
$883$	−3.74522	−	11.5266i	−0.126037	−	0.387901i	0.868052	−	0.496474i	$-0.165372\pi$
$883$	−3.74522	−	11.5266i	−0.126037	−	0.387901i	−0.994089	+	0.108572i	$0.965372\pi$
$884$	−22.9461	−	7.45565i	−0.771762	−	0.250761i
$885$		0			0
$886$	13.5189	−	18.6071i	0.454175	−	0.625119i
$887$	3.93187	−	12.1010i	0.132019	−	0.406313i	−0.863095	−	0.505041i	$-0.831477\pi$
$887$	3.93187	−	12.1010i	0.132019	−	0.406313i	0.995114	+	0.0987277i	$0.0314773\pi$
$888$		0			0
$889$	−3.43265	+	2.49397i	−0.115127	+	0.0836450i
$890$	18.4153			0.617284
$891$		0			0
$892$	−3.21843			−0.107761
$893$	−9.17151	+	6.66349i	−0.306913	+	0.222985i
$894$		0			0
$895$	−12.9638	+	39.8985i	−0.433332	+	1.33366i
$896$	−0.587785	+	0.809017i	−0.0196365	+	0.0270274i
$897$		0			0
$898$	−19.8080	−	6.43602i	−0.661002	−	0.214773i
$899$	15.7212	+	48.3850i	0.524333	+	1.61373i
$900$		0			0
$901$		−	37.3638i		−	1.24477i
$902$	−14.0493	+	0.589162i	−0.467792	+	0.0196170i
$903$		0			0
$904$	10.0194	+	13.7905i	0.333240	+	0.458666i
$905$	0.612103	−	0.198884i	0.0203470	−	0.00661114i
$906$		0			0
$907$	−36.1553	−	26.2683i	−1.20052	−	0.872226i	−0.206180	−	0.978514i	$-0.566103\pi$
$907$	−36.1553	−	26.2683i	−1.20052	−	0.872226i	−0.994335	+	0.106288i	$0.966103\pi$
$908$	16.6358	+	12.0866i	0.552079	+	0.401109i
$909$		0			0
$910$	−23.8123	+	7.73707i	−0.789369	+	0.256482i
$911$	17.5727	+	24.1868i	0.582210	+	0.801343i	0.993936	−	0.109965i	$-0.0350737\pi$
$911$	17.5727	+	24.1868i	0.582210	+	0.801343i	−0.411725	+	0.911308i	$0.635074\pi$
$912$		0			0
$913$	−17.9692	+	0.753545i	−0.594695	+	0.0249387i
$914$		−	31.0717i		−	1.02776i
$915$		0			0
$916$	6.27696	+	19.3185i	0.207397	+	0.638302i
$917$	3.26104	+	1.05958i	0.107689	+	0.0349903i
$918$		0			0
$919$	−23.5387	+	32.3982i	−0.776469	+	1.06872i	0.219194	+	0.975681i	$0.429657\pi$
$919$	−23.5387	+	32.3982i	−0.776469	+	1.06872i	−0.995663	+	0.0930364i	$0.970343\pi$
$920$	−7.89736	+	24.3056i	−0.260368	+	0.801331i
$921$		0			0
$922$	9.15287	−	6.64995i	0.301434	−	0.219004i
$923$	4.18716			0.137822
$924$		0			0
$925$	120.516			3.96254
$926$	6.47677	−	4.70565i	0.212840	−	0.154637i
$927$		0			0
$928$	2.53329	−	7.79665i	0.0831592	−	0.255938i
$929$	−25.4578	+	35.0396i	−0.835242	+	1.14961i	0.151682	+	0.988429i	$0.451531\pi$
$929$	−25.4578	+	35.0396i	−0.835242	+	1.14961i	−0.986925	+	0.161183i	$0.948469\pi$
$930$		0			0
$931$	2.74131	+	0.890705i	0.0898427	+	0.0291917i
$932$	−4.76166	−	14.6549i	−0.155973	−	0.480036i
$933$		0			0
$934$			7.76235i			0.253992i
$935$	−32.8796	+	49.4902i	−1.07528	+	1.61850i
$936$		0			0
$937$	−11.7242	−	16.1369i	−0.383012	−	0.527171i	0.573367	−	0.819299i	$-0.305637\pi$
$937$	−11.7242	−	16.1369i	−0.383012	−	0.527171i	−0.956379	+	0.292127i	$0.905637\pi$
$938$	14.5398	−	4.72428i	0.474743	−	0.154253i
$939$		0			0
$940$	13.7196	+	9.96786i	0.447484	+	0.325116i
$941$	−40.3582	−	29.3219i	−1.31564	−	0.955868i	−0.999976	−	0.00699647i	$-0.997773\pi$
$941$	−40.3582	−	29.3219i	−1.31564	−	0.955868i	−0.315663	−	0.948871i	$-0.602227\pi$
$942$		0			0
$943$	23.8999	−	7.76554i	0.778287	−	0.252881i
$944$	−4.28056	−	5.89168i	−0.139320	−	0.191758i
$945$		0			0
$946$	8.98911	+	2.50958i	0.292261	+	0.0815936i
$947$		−	16.3466i		−	0.531194i	−0.964084	−	0.265597i	$-0.914431\pi$
$947$		−	16.3466i		−	0.531194i	0.964084	−	0.265597i	$-0.0855691\pi$
$948$		0			0
$949$	10.7787	+	33.1735i	0.349892	+	1.07686i
$950$	−37.2572	−	12.1056i	−1.20878	−	0.392757i
$951$		0			0
$952$	2.44219	−	3.36138i	0.0791518	−	0.108943i
$953$	−6.01142	+	18.5013i	−0.194729	+	0.599315i	0.805251	+	0.592935i	$0.202031\pi$
$953$	−6.01142	+	18.5013i	−0.194729	+	0.599315i	−0.999980	+	0.00637986i	$0.997969\pi$
$954$		0			0
$955$	61.8222	−	44.9165i	2.00052	−	1.45346i
$956$	4.53655			0.146723
$957$		0			0
$958$	10.1952			0.329391
$959$	3.83250	−	2.78447i	0.123758	−	0.0899153i
$960$		0			0
$961$	2.32160	−	7.14514i	0.0748902	−	0.230488i
$962$	30.2659	−	41.6575i	0.975813	−	1.34309i
$963$		0			0
$964$	15.4824	+	5.03054i	0.498655	+	0.162023i
$965$	−4.31497	−	13.2801i	−0.138904	−	0.427502i
$966$		0			0
$967$			30.6704i			0.986292i	0.869947	+	0.493146i	$0.164153\pi$
$967$			30.6704i			0.986292i	−0.869947	+	0.493146i	$0.835847\pi$
$968$	−10.9614	+	0.920956i	−0.352312	+	0.0296006i
$969$		0			0
$970$	1.25272	+	1.72422i	0.0402225	+	0.0553615i
$971$	27.2080	−	8.84043i	0.873148	−	0.283703i	0.162038	−	0.986784i	$-0.448193\pi$
$971$	27.2080	−	8.84043i	0.873148	−	0.283703i	0.711109	+	0.703082i	$0.248193\pi$
$972$		0			0
$973$	−2.05821	−	1.49538i	−0.0659832	−	0.0479396i
$974$	17.8814	+	12.9916i	0.572958	+	0.416278i
$975$		0			0
$976$	−0.896384	+	0.291253i	−0.0286925	+	0.00932277i
$977$	−19.2143	−	26.4462i	−0.614721	−	0.846090i	0.382235	−	0.924065i	$-0.375155\pi$
$977$	−19.2143	−	26.4462i	−0.614721	−	0.846090i	−0.996955	+	0.0779750i	$0.975155\pi$
$978$		0			0
$979$	−8.79897	−	11.1010i	−0.281216	−	0.354790i
$980$		−	4.31173i		−	0.137733i
$981$		0			0
$982$	11.4726	+	35.3091i	0.366106	+	1.12676i
$983$	14.1730	+	4.60509i	0.452048	+	0.146879i	0.526188	−	0.850368i	$-0.323621\pi$
$983$	14.1730	+	4.60509i	0.452048	+	0.146879i	−0.0741393	+	0.997248i	$0.523621\pi$
$984$		0			0
$985$	19.2781	−	26.5340i	0.614251	−	0.845444i
$986$	−10.5255	+	32.3943i	−0.335202	+	1.03164i
$987$		0			0
$988$	−13.5410	+	9.83814i	−0.430798	+	0.312993i
$989$	−16.6788			−0.530356
$990$		0			0
$991$	15.6110			0.495901			0.247951	−	0.968773i	$-0.420243\pi$
$991$	15.6110			0.495901			0.247951	+	0.968773i	$0.420243\pi$
$992$	−5.02066	+	3.64772i	−0.159406	+	0.115815i
$993$		0			0
$994$	−0.222822	+	0.685777i	−0.00706750	+	0.0217515i
$995$	54.0958	−	74.4565i	1.71495	−	2.36043i
$996$		0			0
$997$	−0.947568	−	0.307883i	−0.0300098	−	0.00975077i	0.293974	−	0.955814i	$-0.405022\pi$
$997$	−0.947568	−	0.307883i	−0.0300098	−	0.00975077i	−0.323983	+	0.946063i	$0.605022\pi$
$998$	−0.160809	−	0.494920i	−0.00509033	−	0.0156664i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.b.701.12	yes	48
3.2	odd	2		1386.2.bu.a.701.1	✓	48
11.7	odd	10		1386.2.bu.a.953.1	yes	48
33.29	even	10	inner	1386.2.bu.b.953.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.701.1	✓	48	3.2	odd	2
1386.2.bu.a.953.1	yes	48	11.7	odd	10
1386.2.bu.b.701.12	yes	48	1.1	even	1	trivial
1386.2.bu.b.953.12	yes	48	33.29	even	10	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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(2.53437 - 3.48826i) q^{5} +(0.951057 + 0.309017i) q^{7} +(-0.309017 - 0.951057i) q^{8} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(2.53437 - 3.48826i) q^{5} +(0.951057 + 0.309017i) q^{7} +(-0.309017 - 0.951057i) q^{8} -4.31173i q^{10} +(-2.59917 + 2.06017i) q^{11} +(-3.41320 - 4.69786i) q^{13} +(0.951057 - 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(3.36138 + 2.44219i) q^{17} +(2.74131 - 0.890705i) q^{19} +(-2.53437 - 3.48826i) q^{20} +(-0.891833 + 3.19447i) q^{22} -5.92718i q^{23} +(-4.19986 - 12.9258i) q^{25} +(-5.52267 - 1.79442i) q^{26} +(0.587785 - 0.809017i) q^{28} +(-2.53329 + 7.79665i) q^{29} +(5.02066 - 3.64772i) q^{31} -1.00000 q^{32} +4.15490 q^{34} +(3.48826 - 2.53437i) q^{35} +(-2.74015 + 8.43333i) q^{37} +(1.69422 - 2.33190i) q^{38} +(-4.10070 - 1.33240i) q^{40} +(1.31016 + 4.03225i) q^{41} -2.81396i q^{43} +(1.15615 + 3.10859i) q^{44} +(-3.48391 - 4.79519i) q^{46} +(-3.74057 + 1.21539i) q^{47} +(0.809017 + 0.587785i) q^{49} +(-10.9954 - 7.98861i) q^{50} +(-5.52267 + 1.79442i) q^{52} +(-5.28579 - 7.27526i) q^{53} +(0.599164 + 14.2878i) q^{55} -1.00000i q^{56} +(2.53329 + 7.79665i) q^{58} +(6.92609 + 2.25042i) q^{59} +(0.553996 - 0.762510i) q^{61} +(1.91772 - 5.90213i) q^{62} +(-0.809017 + 0.587785i) q^{64} -25.0377 q^{65} +15.2881 q^{67} +(3.36138 - 2.44219i) q^{68} +(1.33240 - 4.10070i) q^{70} +(-0.423833 + 0.583357i) q^{71} +(-5.71280 - 1.85620i) q^{73} +(2.74015 + 8.43333i) q^{74} -2.88238i q^{76} +(-3.10859 + 1.15615i) q^{77} +(8.25094 + 11.3564i) q^{79} +(-4.10070 + 1.33240i) q^{80} +(3.43004 + 2.49207i) q^{82} +(4.38705 + 3.18738i) q^{83} +(17.0380 - 5.53598i) q^{85} +(-1.65400 - 2.27654i) q^{86} +(2.76253 + 1.83533i) q^{88} +4.27098i q^{89} +(-1.79442 - 5.52267i) q^{91} +(-5.63708 - 1.83160i) q^{92} +(-2.31180 + 3.18192i) q^{94} +(3.84048 - 11.8198i) q^{95} +(-0.399891 + 0.290538i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8}+O(q^{10}) \) 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8	\( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8} - 4 q^{11} - 12 q^{16} - 24 q^{17} + 4 q^{22} + 24 q^{25} - 40 q^{26} + 16 q^{29} + 40 q^{31} - 48 q^{32} - 16 q^{34} + 12 q^{35} + 16 q^{37} + 40 q^{38} - 24 q^{41} - 4 q^{44} - 40 q^{46} + 40 q^{47} + 12 q^{49} - 4 q^{50} - 40 q^{52} + 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} + 40 q^{62} - 12 q^{64} + 48 q^{67} - 24 q^{68} + 8 q^{70} + 40 q^{73} - 16 q^{74} - 32 q^{77} + 40 q^{79} - 16 q^{82} + 16 q^{83} - 20 q^{85} + 4 q^{88} + 20 q^{92} + 52 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) \) 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8 - 4 * q^11 - 12 * q^16 - 24 * q^17 + 4 * q^22 + 24 * q^25 - 40 * q^26 + 16 * q^29 + 40 * q^31 - 48 * q^32 - 16 * q^34 + 12 * q^35 + 16 * q^37 + 40 * q^38 - 24 * q^41 - 4 * q^44 - 40 * q^46 + 40 * q^47 + 12 * q^49 - 4 * q^50 - 40 * q^52 + 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 + 40 * q^62 - 12 * q^64 + 48 * q^67 - 24 * q^68 + 8 * q^70 + 40 * q^73 - 16 * q^74 - 32 * q^77 + 40 * q^79 - 16 * q^82 + 16 * q^83 - 20 * q^85 + 4 * q^88 + 20 * q^92 + 52 * q^95 - 8 * q^97 + 48 * q^98

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