LMFDB - Embedded newform 1110.2.x.d.751.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 60x^{14} + 1362x^{12} + 15028x^{10} + 86441x^{8} + 260376x^{6} + 382684x^{4} + 224224x^{2} + 38416 $ x^16 + 60x^14 + 1362x^12 + 15028x^10 + 86441x^8 + 260376x^6 + 382684x^4 + 224224*x^2 + 38416
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.5
Root			$3.25684i$ of defining polynomial
Character	$\chi$	$=$	1110.751
Dual form			1110.2.x.d.841.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-1.62842 + 2.82051i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-1.62842 + 2.82051i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} -5.25915 q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.16873 - 1.82947i) q^{13} +3.25684i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.95448 + 1.12842i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-3.21087 - 1.85380i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-1.62842 - 2.82051i) q^{21} +(-4.55456 + 2.62957i) q^{22} +1.92689i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -3.65894 q^{26} +1.00000 q^{27} +(1.62842 + 2.82051i) q^{28} -3.37764i q^{29} +(-0.500000 + 0.866025i) q^{30} +1.35672i q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.62957 - 4.55456i) q^{33} +(-1.12842 + 1.95448i) q^{34} +(-2.82051 + 1.62842i) q^{35} -1.00000 q^{36} +(-5.27288 - 3.03262i) q^{37} -3.70759 q^{38} +(3.16873 - 1.82947i) q^{39} +(0.500000 - 0.866025i) q^{40} +(2.73745 - 4.74141i) q^{41} +(-2.82051 - 1.62842i) q^{42} -3.28360i q^{43} +(-2.62957 + 4.55456i) q^{44} -1.00000i q^{45} +(0.963443 + 1.66873i) q^{46} +3.32765 q^{47} +1.00000 q^{48} +(-1.80351 - 3.12377i) q^{49} +(0.866025 + 0.500000i) q^{50} -2.25684i q^{51} +(-3.16873 + 1.82947i) q^{52} +(5.09487 + 8.82457i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-4.55456 - 2.62957i) q^{55} +(2.82051 + 1.62842i) q^{56} +(3.21087 - 1.85380i) q^{57} +(-1.68882 - 2.92512i) q^{58} +(-9.55745 + 5.51800i) q^{59} +1.00000i q^{60} +(-1.07094 - 0.618309i) q^{61} +(0.678359 + 1.17495i) q^{62} +3.25684 q^{63} -1.00000 q^{64} +(-1.82947 - 3.16873i) q^{65} -5.25915i q^{66} +(-6.93555 + 12.0127i) q^{67} +2.25684i q^{68} +(-1.66873 - 0.963443i) q^{69} +(-1.62842 + 2.82051i) q^{70} +(-0.215263 + 0.372847i) q^{71} +(-0.866025 + 0.500000i) q^{72} +4.23689 q^{73} +(-6.08275 + 0.0101124i) q^{74} -1.00000 q^{75} +(-3.21087 + 1.85380i) q^{76} +(8.56411 - 14.8335i) q^{77} +(1.82947 - 3.16873i) q^{78} +(6.26143 + 3.61504i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -5.47491i q^{82} +(6.83148 + 11.8325i) q^{83} -3.25684 q^{84} -2.25684 q^{85} +(-1.64180 - 2.84368i) q^{86} +(2.92512 + 1.68882i) q^{87} +5.25915i q^{88} +(-9.75521 + 5.63218i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(10.3201 - 5.95829i) q^{91} +(1.66873 + 0.963443i) q^{92} +(-1.17495 - 0.678359i) q^{93} +(2.88183 - 1.66383i) q^{94} +(-1.85380 - 3.21087i) q^{95} +(0.866025 - 0.500000i) q^{96} -4.69418i q^{97} +(-3.12377 - 1.80351i) q^{98} +(2.62957 + 4.55456i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} + 16 q^{10} - 8 q^{11} + 8 q^{12} - 6 q^{13} - 8 q^{16} + 6 q^{17} - 12 q^{19} - 2 q^{21} + 8 q^{25} + 4 q^{26} + 16 q^{27} + 2 q^{28} - 8 q^{30} + 4 q^{33} + 6 q^{34} + 6 q^{35} - 16 q^{36} + 12 q^{37} - 4 q^{38} + 6 q^{39} + 8 q^{40} + 4 q^{41} + 6 q^{42} - 4 q^{44} - 2 q^{46} + 68 q^{47} + 16 q^{48} - 4 q^{49} - 6 q^{52} - 12 q^{53} - 6 q^{56} + 12 q^{57} - 6 q^{58} + 6 q^{59} + 12 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{64} + 2 q^{65} - 36 q^{67} + 18 q^{69} - 2 q^{70} + 6 q^{71} - 16 q^{73} + 14 q^{74} - 16 q^{75} - 12 q^{76} + 26 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 12 q^{83} - 4 q^{84} + 12 q^{85} - 2 q^{86} + 24 q^{89} - 8 q^{90} + 60 q^{91} - 18 q^{92} - 30 q^{93} + 6 q^{94} - 2 q^{95} - 12 q^{98} + 4 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 + 16 * q^10 - 8 * q^11 + 8 * q^12 - 6 * q^13 - 8 * q^16 + 6 * q^17 - 12 * q^19 - 2 * q^21 + 8 * q^25 + 4 * q^26 + 16 * q^27 + 2 * q^28 - 8 * q^30 + 4 * q^33 + 6 * q^34 + 6 * q^35 - 16 * q^36 + 12 * q^37 - 4 * q^38 + 6 * q^39 + 8 * q^40 + 4 * q^41 + 6 * q^42 - 4 * q^44 - 2 * q^46 + 68 * q^47 + 16 * q^48 - 4 * q^49 - 6 * q^52 - 12 * q^53 - 6 * q^56 + 12 * q^57 - 6 * q^58 + 6 * q^59 + 12 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^64 + 2 * q^65 - 36 * q^67 + 18 * q^69 - 2 * q^70 + 6 * q^71 - 16 * q^73 + 14 * q^74 - 16 * q^75 - 12 * q^76 + 26 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 12 * q^83 - 4 * q^84 + 12 * q^85 - 2 * q^86 + 24 * q^89 - 8 * q^90 + 60 * q^91 - 18 * q^92 - 30 * q^93 + 6 * q^94 - 2 * q^95 - 12 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$			1.00000i			0.408248i
$7$	−1.62842	+	2.82051i	−0.615485	+	1.06605i	0.374814	+	0.927100i	$0.377707\pi$
$7$	−1.62842	+	2.82051i	−0.615485	+	1.06605i	−0.990299	+	0.138952i	$0.955627\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.00000			0.316228
$11$	−5.25915			−1.58569			−0.792846	−	0.609422i	$-0.791402\pi$
$11$	−5.25915			−1.58569			−0.792846	+	0.609422i	$0.791402\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−3.16873	−	1.82947i	−0.878848	−	0.507403i	−0.00856971	−	0.999963i	$-0.502728\pi$
$13$	−3.16873	−	1.82947i	−0.878848	−	0.507403i	−0.870278	+	0.492560i	$0.836061\pi$
$14$			3.25684i			0.870428i
$15$	−0.866025	+	0.500000i	−0.223607	+	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.95448	+	1.12842i	−0.474032	+	0.273682i	−0.717926	−	0.696119i	$-0.754908\pi$
$17$	−1.95448	+	1.12842i	−0.474032	+	0.273682i	0.243894	+	0.969802i	$0.421575\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−3.21087	−	1.85380i	−0.736624	−	0.425290i	0.0842164	−	0.996447i	$-0.473161\pi$
$19$	−3.21087	−	1.85380i	−0.736624	−	0.425290i	−0.820841	+	0.571157i	$0.806495\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	−1.62842	−	2.82051i	−0.355351	−	0.615485i
$22$	−4.55456	+	2.62957i	−0.971035	+	0.560627i
$23$			1.92689i			0.401783i	0.979613	+	0.200892i	$0.0643839\pi$
$23$			1.92689i			0.401783i	−0.979613	+	0.200892i	$0.935616\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−3.65894			−0.717577
$27$	1.00000			0.192450
$28$	1.62842	+	2.82051i	0.307743	+	0.533026i
$29$		−	3.37764i		−	0.627212i	−0.949553	−	0.313606i	$-0.898463\pi$
$29$		−	3.37764i		−	0.627212i	0.949553	−	0.313606i	$-0.101537\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$			1.35672i			0.243674i	0.992550	+	0.121837i	$0.0388785\pi$
$31$			1.35672i			0.243674i	−0.992550	+	0.121837i	$0.961122\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	2.62957	−	4.55456i	0.457750	−	0.792846i
$34$	−1.12842	+	1.95448i	−0.193523	+	0.335191i
$35$	−2.82051	+	1.62842i	−0.476753	+	0.275253i
$36$	−1.00000			−0.166667
$37$	−5.27288	−	3.03262i	−0.866855	−	0.498560i
$37$	−5.27288	−	3.03262i	−0.866855	−	0.498560i
$38$	−3.70759			−0.601451
$39$	3.16873	−	1.82947i	0.507403	−	0.292949i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	2.73745	−	4.74141i	0.427518	−	0.740484i	−0.569133	−	0.822245i	$-0.692721\pi$
$41$	2.73745	−	4.74141i	0.427518	−	0.740484i	0.996652	+	0.0817615i	$0.0260546\pi$
$42$	−2.82051	−	1.62842i	−0.435214	−	0.251271i
$43$		−	3.28360i		−	0.500745i	−0.968150	−	0.250372i	$-0.919447\pi$
$43$		−	3.28360i		−	0.500745i	0.968150	−	0.250372i	$-0.0805531\pi$
$44$	−2.62957	+	4.55456i	−0.396423	+	0.686625i
$45$		−	1.00000i		−	0.149071i
$46$	0.963443	+	1.66873i	0.142052	+	0.246041i
$47$	3.32765			0.485388			0.242694	−	0.970103i	$-0.421969\pi$
$47$	3.32765			0.485388			0.242694	+	0.970103i	$0.421969\pi$
$48$	1.00000			0.144338
$49$	−1.80351	−	3.12377i	−0.257645	−	0.446254i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		−	2.25684i		−	0.316021i
$52$	−3.16873	+	1.82947i	−0.439424	+	0.253702i
$53$	5.09487	+	8.82457i	0.699834	+	1.21215i	0.968524	+	0.248921i	$0.0800759\pi$
$53$	5.09487	+	8.82457i	0.699834	+	1.21215i	−0.268690	+	0.963227i	$0.586591\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−4.55456	−	2.62957i	−0.614136	−	0.354572i
$56$	2.82051	+	1.62842i	0.376906	+	0.217607i
$57$	3.21087	−	1.85380i	0.425290	−	0.245541i
$58$	−1.68882	−	2.92512i	−0.221753	−	0.384087i
$59$	−9.55745	+	5.51800i	−1.24427	+	0.718382i	−0.969962	−	0.243258i	$-0.921784\pi$
$59$	−9.55745	+	5.51800i	−1.24427	+	0.718382i	−0.274313	+	0.961640i	$0.588450\pi$
$60$			1.00000i			0.129099i
$61$	−1.07094	−	0.618309i	−0.137120	−	0.0791663i	0.429871	−	0.902890i	$-0.358559\pi$
$61$	−1.07094	−	0.618309i	−0.137120	−	0.0791663i	−0.566991	+	0.823724i	$0.691892\pi$
$62$	0.678359	+	1.17495i	0.0861517	+	0.149219i
$63$	3.25684			0.410324
$64$	−1.00000			−0.125000
$65$	−1.82947	−	3.16873i	−0.226918	−	0.393033i
$66$		−	5.25915i		−	0.647356i
$67$	−6.93555	+	12.0127i	−0.847312	+	1.46759i	0.0362858	+	0.999341i	$0.488447\pi$
$67$	−6.93555	+	12.0127i	−0.847312	+	1.46759i	−0.883598	+	0.468246i	$0.844886\pi$
$68$			2.25684i			0.273682i
$69$	−1.66873	−	0.963443i	−0.200892	−	0.115985i
$70$	−1.62842	+	2.82051i	−0.194634	+	0.337115i
$71$	−0.215263	+	0.372847i	−0.0255471	+	0.0442488i	−0.878516	−	0.477712i	$-0.841466\pi$
$71$	−0.215263	+	0.372847i	−0.0255471	+	0.0442488i	0.852969	+	0.521961i	$0.174799\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	4.23689			0.495891			0.247945	−	0.968774i	$-0.420245\pi$
$73$	4.23689			0.495891			0.247945	+	0.968774i	$0.420245\pi$
$74$	−6.08275	+	0.0101124i	−0.707106	+	0.00117555i
$75$	−1.00000			−0.115470
$76$	−3.21087	+	1.85380i	−0.368312	+	0.212645i
$77$	8.56411	−	14.8335i	0.975971	−	1.69043i
$78$	1.82947	−	3.16873i	0.207147	−	0.358788i
$79$	6.26143	+	3.61504i	0.704466	+	0.406724i	0.809009	−	0.587797i	$-0.200004\pi$
$79$	6.26143	+	3.61504i	0.704466	+	0.406724i	−0.104542	+	0.994520i	$0.533338\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		−	5.47491i		−	0.604602i
$83$	6.83148	+	11.8325i	0.749853	+	1.29878i	0.947893	+	0.318589i	$0.103209\pi$
$83$	6.83148	+	11.8325i	0.749853	+	1.29878i	−0.198040	+	0.980194i	$0.563458\pi$
$84$	−3.25684			−0.355351
$85$	−2.25684			−0.244789
$86$	−1.64180	−	2.84368i	−0.177040	−	0.306642i
$87$	2.92512	+	1.68882i	0.313606	+	0.181060i
$88$			5.25915i			0.560627i
$89$	−9.75521	+	5.63218i	−1.03405	+	0.597009i	−0.918142	−	0.396251i	$-0.870311\pi$
$89$	−9.75521	+	5.63218i	−1.03405	+	0.597009i	−0.115908	+	0.993260i	$0.536978\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	10.3201	−	5.95829i	1.08184	−	0.624599i
$92$	1.66873	+	0.963443i	0.173977	+	0.100446i
$93$	−1.17495	−	0.678359i	−0.121837	−	0.0703426i
$94$	2.88183	−	1.66383i	0.297238	−	0.171611i
$95$	−1.85380	−	3.21087i	−0.190196	−	0.329428i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$		−	4.69418i		−	0.476622i	−0.971189	−	0.238311i	$-0.923406\pi$
$97$		−	4.69418i		−	0.476622i	0.971189	−	0.238311i	$-0.0765938\pi$
$98$	−3.12377	−	1.80351i	−0.315549	−	0.182182i
$99$	2.62957	+	4.55456i	0.264282	+	0.457750i
$100$	1.00000			0.100000
$101$	−9.91358			−0.986438			−0.493219	−	0.869905i	$-0.664180\pi$
$101$	−9.91358			−0.986438			−0.493219	+	0.869905i	$0.664180\pi$
$102$	−1.12842	−	1.95448i	−0.111730	−	0.193523i
$103$			11.0762i			1.09137i	0.837991	+	0.545684i	$0.183730\pi$
$103$			11.0762i			1.09137i	−0.837991	+	0.545684i	$0.816270\pi$
$104$	−1.82947	+	3.16873i	−0.179394	+	0.310720i
$105$		−	3.25684i		−	0.317835i
$106$	8.82457	+	5.09487i	0.857118	+	0.494857i
$107$	−6.80147	+	11.7805i	−0.657523	+	1.13886i	0.323732	+	0.946149i	$0.395062\pi$
$107$	−6.80147	+	11.7805i	−0.657523	+	1.13886i	−0.981255	+	0.192714i	$0.938271\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−6.42341	+	3.70856i	−0.615251	+	0.355215i	−0.775018	−	0.631939i	$-0.782259\pi$
$109$	−6.42341	+	3.70856i	−0.615251	+	0.355215i	0.159767	+	0.987155i	$0.448926\pi$
$110$	−5.25915			−0.501440
$111$	5.26276	−	3.05013i	0.499519	−	0.289506i
$112$	3.25684			0.307743
$113$	0.273291	−	0.157785i	0.0257090	−	0.0148431i	−0.487090	−	0.873352i	$-0.661942\pi$
$113$	0.273291	−	0.157785i	0.0257090	−	0.0148431i	0.512799	+	0.858508i	$0.328608\pi$
$114$	1.85380	−	3.21087i	0.173624	−	0.300726i
$115$	−0.963443	+	1.66873i	−0.0898415	+	0.155610i
$116$	−2.92512	−	1.68882i	−0.271591	−	0.156803i
$117$			3.65894i			0.338269i
$118$	−5.51800	+	9.55745i	−0.507973	+	0.879835i
$119$		−	7.35018i		−	0.673790i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	16.6586			1.51442
$122$	−1.23662			−0.111958
$123$	2.73745	+	4.74141i	0.246828	+	0.427518i
$124$	1.17495	+	0.678359i	0.105514	+	0.0609185i
$125$			1.00000i			0.0894427i
$126$	2.82051	−	1.62842i	0.251271	−	0.145071i
$127$	−7.33602	−	12.7064i	−0.650966	−	1.12751i	−0.982889	−	0.184200i	$-0.941031\pi$
$127$	−7.33602	−	12.7064i	−0.650966	−	1.12751i	0.331923	−	0.943307i	$-0.392303\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	2.84368	+	1.64180i	0.250372	+	0.144553i
$130$	−3.16873	−	1.82947i	−0.277916	−	0.160455i
$131$	−7.34599	+	4.24121i	−0.641822	+	0.370556i	−0.785316	−	0.619095i	$-0.787500\pi$
$131$	−7.34599	+	4.24121i	−0.641822	+	0.370556i	0.143494	+	0.989651i	$0.454166\pi$
$132$	−2.62957	−	4.55456i	−0.228875	−	0.396423i
$133$	10.4573	−	6.03753i	0.906763	−	0.523520i
$134$			13.8711i			1.19828i
$135$	0.866025	+	0.500000i	0.0745356	+	0.0430331i
$136$	1.12842	+	1.95448i	0.0967613	+	0.167596i
$137$	14.1845			1.21186			0.605931	−	0.795517i	$-0.292801\pi$
$137$	14.1845			1.21186			0.605931	+	0.795517i	$0.292801\pi$
$138$	−1.92689			−0.164027
$139$	−10.6538	−	18.4528i	−0.903640	−	1.56515i	−0.822733	−	0.568428i	$-0.807552\pi$
$139$	−10.6538	−	18.4528i	−0.903640	−	1.56515i	−0.0809066	−	0.996722i	$-0.525782\pi$
$140$			3.25684i			0.275253i
$141$	−1.66383	+	2.88183i	−0.140119	+	0.242694i
$142$			0.430527i			0.0361290i
$143$	16.6648	+	9.62144i	1.39358	+	0.804586i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.68882	−	2.92512i	0.140249	−	0.242918i
$146$	3.66926	−	2.11845i	0.303670	−	0.175324i
$147$	3.60702			0.297502
$148$	−5.26276	+	3.05013i	−0.432596	+	0.250720i
$149$	8.36723			0.685470			0.342735	−	0.939432i	$-0.388647\pi$
$149$	8.36723			0.685470			0.342735	+	0.939432i	$0.388647\pi$
$150$	−0.866025	+	0.500000i	−0.0707107	+	0.0408248i
$151$	6.96505	−	12.0638i	0.566808	−	0.981740i	−0.430071	−	0.902795i	$-0.641512\pi$
$151$	6.96505	−	12.0638i	0.566808	−	0.981740i	0.996879	−	0.0789449i	$-0.0251551\pi$
$152$	−1.85380	+	3.21087i	−0.150363	+	0.260436i
$153$	1.95448	+	1.12842i	0.158011	+	0.0912275i
$154$		−	17.1282i		−	1.38023i
$155$	−0.678359	+	1.17495i	−0.0544871	+	0.0943745i
$156$		−	3.65894i		−	0.292949i
$157$	−4.49155	−	7.77960i	−0.358465	−	0.620880i	0.629240	−	0.777211i	$-0.283366\pi$
$157$	−4.49155	−	7.77960i	−0.358465	−	0.620880i	−0.987705	+	0.156332i	$0.950033\pi$
$158$	7.23008			0.575194
$159$	−10.1897			−0.808098
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−5.43480	−	3.13778i	−0.428322	−	0.247292i
$162$			1.00000i			0.0785674i
$163$	17.2881	−	9.98128i	1.35411	−	0.781794i	0.365286	−	0.930895i	$-0.380971\pi$
$163$	17.2881	−	9.98128i	1.35411	−	0.781794i	0.988822	+	0.149101i	$0.0476380\pi$
$164$	−2.73745	−	4.74141i	−0.213759	−	0.370242i
$165$	4.55456	−	2.62957i	0.354572	−	0.204712i
$166$	11.8325	+	6.83148i	0.918378	+	0.530226i
$167$	−7.09782	−	4.09793i	−0.549246	−	0.317107i	0.199572	−	0.979883i	$-0.436045\pi$
$167$	−7.09782	−	4.09793i	−0.549246	−	0.317107i	−0.748818	+	0.662776i	$0.769378\pi$
$168$	−2.82051	+	1.62842i	−0.217607	+	0.125635i
$169$	0.193909	+	0.335860i	0.0149161	+	0.0258354i
$170$	−1.95448	+	1.12842i	−0.149902	+	0.0865460i
$171$			3.70759i			0.283527i
$172$	−2.84368	−	1.64180i	−0.216829	−	0.125186i
$173$	7.96169	+	13.7901i	0.605316	+	1.04844i	0.992001	+	0.126227i	$0.0402868\pi$
$173$	7.96169	+	13.7901i	0.605316	+	1.04844i	−0.386685	+	0.922212i	$0.626380\pi$
$174$	3.37764			0.256058
$175$	−3.25684			−0.246194
$176$	2.62957	+	4.55456i	0.198212	+	0.343313i
$177$		−	11.0360i		−	0.829516i
$178$	−5.63218	+	9.75521i	−0.422149	+	0.731184i
$179$		−	0.900657i		−	0.0673182i	−0.999433	−	0.0336591i	$-0.989284\pi$
$179$		−	0.900657i		−	0.0673182i	0.999433	−	0.0336591i	$-0.0107161\pi$
$180$	−0.866025	−	0.500000i	−0.0645497	−	0.0372678i
$181$	1.45760	−	2.52464i	0.108343	−	0.187655i	−0.806756	−	0.590884i	$-0.798779\pi$
$181$	1.45760	−	2.52464i	0.108343	−	0.187655i	0.915099	+	0.403229i	$0.132112\pi$
$182$	5.95829	−	10.3201i	0.441658	−	0.764974i
$183$	1.07094	−	0.618309i	0.0791663	−	0.0457067i
$184$	1.92689			0.142052
$185$	−3.05013	−	5.26276i	−0.224250	−	0.386926i
$186$	−1.35672			−0.0994794
$187$	10.2789	−	5.93453i	0.751669	−	0.433976i
$188$	1.66383	−	2.88183i	0.121347	−	0.210179i
$189$	−1.62842	+	2.82051i	−0.118450	+	0.205162i
$190$	−3.21087	−	1.85380i	−0.232941	−	0.134489i
$191$			27.0970i			1.96067i	0.197342	+	0.980335i	$0.436769\pi$
$191$			27.0970i			1.96067i	−0.197342	+	0.980335i	$0.563231\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$		−	16.6359i		−	1.19748i	−0.800943	−	0.598740i	$-0.795668\pi$
$193$		−	16.6359i		−	1.19748i	0.800943	−	0.598740i	$-0.204332\pi$
$194$	−2.34709	−	4.06528i	−0.168511	−	0.291870i
$195$	3.65894			0.262022
$196$	−3.60702			−0.257645
$197$	−8.59600	−	14.8887i	−0.612439	−	1.06078i	−0.990828	−	0.135129i	$-0.956855\pi$
$197$	−8.59600	−	14.8887i	−0.612439	−	1.06078i	0.378389	−	0.925647i	$-0.376478\pi$
$198$	4.55456	+	2.62957i	0.323678	+	0.186876i
$199$		−	2.73511i		−	0.193887i	−0.995290	−	0.0969433i	$-0.969093\pi$
$199$		−	2.73511i		−	0.193887i	0.995290	−	0.0969433i	$-0.0309066\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	−6.93555	−	12.0127i	−0.489196	−	0.847312i
$202$	−8.58541	+	4.95679i	−0.604067	+	0.348758i
$203$	9.52666	+	5.50022i	0.668640	+	0.386040i
$204$	−1.95448	−	1.12842i	−0.136841	−	0.0790053i
$205$	4.74141	−	2.73745i	0.331154	−	0.191192i
$206$	5.53809	+	9.59224i	0.385857	+	0.668323i
$207$	1.66873	−	0.963443i	0.115985	−	0.0669639i
$208$			3.65894i			0.253702i
$209$	16.8864	+	9.74939i	1.16806	+	0.674380i
$210$	−1.62842	−	2.82051i	−0.112372	−	0.194634i
$211$	−18.8199			−1.29561			−0.647807	−	0.761804i	$-0.724314\pi$
$211$	−18.8199			−1.29561			−0.647807	+	0.761804i	$0.724314\pi$
$212$	10.1897			0.699834
$213$	−0.215263	−	0.372847i	−0.0147496	−	0.0255471i
$214$			13.6029i			0.929877i
$215$	1.64180	−	2.84368i	0.111970	−	0.193938i
$216$		−	1.00000i		−	0.0680414i
$217$	−3.82664	−	2.20931i	−0.259769	−	0.149978i
$218$	−3.70856	+	6.42341i	−0.251175	+	0.435048i
$219$	−2.11845	+	3.66926i	−0.143151	+	0.247945i
$220$	−4.55456	+	2.62957i	−0.307068	+	0.177286i
$221$	8.25764			0.555469
$222$	3.03262	−	5.27288i	0.203536	−	0.353892i
$223$	25.6392			1.71693			0.858466	−	0.512871i	$-0.171418\pi$
$223$	25.6392			1.71693			0.858466	+	0.512871i	$0.171418\pi$
$224$	2.82051	−	1.62842i	0.188453	−	0.108803i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	0.157785	−	0.273291i	0.0104957	−	0.0181790i
$227$	14.0727	+	8.12488i	0.934039	+	0.539268i	0.888087	−	0.459676i	$-0.152034\pi$
$227$	14.0727	+	8.12488i	0.934039	+	0.539268i	0.0459521	+	0.998944i	$0.485368\pi$
$228$		−	3.70759i		−	0.245541i
$229$	−5.87416	+	10.1743i	−0.388176	+	0.672340i	−0.992204	−	0.124623i	$-0.960228\pi$
$229$	−5.87416	+	10.1743i	−0.388176	+	0.672340i	0.604029	+	0.796963i	$0.293561\pi$
$230$			1.92689i			0.127055i
$231$	8.56411	+	14.8335i	0.563477	+	0.975971i
$232$	−3.37764			−0.221753
$233$	10.3859			0.680403			0.340202	−	0.940353i	$-0.389505\pi$
$233$	10.3859			0.680403			0.340202	+	0.940353i	$0.389505\pi$
$234$	1.82947	+	3.16873i	0.119596	+	0.207147i
$235$	2.88183	+	1.66383i	0.187990	+	0.108536i
$236$			11.0360i			0.718382i
$237$	−6.26143	+	3.61504i	−0.406724	+	0.234822i
$238$	−3.67509	−	6.36544i	−0.238221	−	0.412610i
$239$	3.68278	−	2.12625i	0.238219	−	0.137536i	−0.376139	−	0.926563i	$-0.622748\pi$
$239$	3.68278	−	2.12625i	0.238219	−	0.137536i	0.614358	+	0.789027i	$0.289415\pi$
$240$	0.866025	+	0.500000i	0.0559017	+	0.0322749i
$241$	5.12924	+	2.96137i	0.330403	+	0.190758i	0.656020	−	0.754743i	$-0.272239\pi$
$241$	5.12924	+	2.96137i	0.330403	+	0.190758i	−0.325617	+	0.945502i	$0.605572\pi$
$242$	14.4268	−	8.32932i	0.927390	−	0.535429i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−1.07094	+	0.618309i	−0.0685601	+	0.0395832i
$245$		−	3.60702i		−	0.230444i
$246$	4.74141	+	2.73745i	0.302301	+	0.174534i
$247$	6.78293	+	11.7484i	0.431587	+	0.747531i
$248$	1.35672			0.0861517
$249$	−13.6630			−0.865856
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$			11.4250i			0.721137i	0.932733	+	0.360568i	$0.117417\pi$
$251$			11.4250i			0.721137i	−0.932733	+	0.360568i	$0.882583\pi$
$252$	1.62842	−	2.82051i	0.102581	−	0.177675i
$253$		−	10.1338i		−	0.637105i
$254$	−12.7064	−	7.33602i	−0.797267	−	0.460303i
$255$	1.12842	−	1.95448i	0.0706645	−	0.122394i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−20.3226	+	11.7333i	−1.26769	+	0.731901i	−0.974550	−	0.224169i	$-0.928033\pi$
$257$	−20.3226	+	11.7333i	−1.26769	+	0.731901i	−0.293139	+	0.956070i	$0.594700\pi$
$258$	3.28360			0.204428
$259$	17.1400	−	9.93381i	1.06503	−	0.617257i
$260$	−3.65894			−0.226918
$261$	−2.92512	+	1.68882i	−0.181060	+	0.104535i
$262$	−4.24121	+	7.34599i	−0.262023	+	0.453837i
$263$	10.3985	−	18.0108i	0.641200	−	1.11059i	−0.343965	−	0.938982i	$-0.611770\pi$
$263$	10.3985	−	18.0108i	0.641200	−	1.11059i	0.985165	−	0.171609i	$-0.0548965\pi$
$264$	−4.55456	−	2.62957i	−0.280314	−	0.161839i
$265$			10.1897i			0.625950i
$266$	6.03753	−	10.4573i	0.370184	−	0.641178i
$267$		−	11.2644i		−	0.689367i
$268$	6.93555	+	12.0127i	0.423656	+	0.733794i
$269$	20.4144			1.24469			0.622345	−	0.782743i	$-0.286180\pi$
$269$	20.4144			1.24469			0.622345	+	0.782743i	$0.286180\pi$
$270$	1.00000			0.0608581
$271$	−9.87486	−	17.1038i	−0.599855	−	1.03898i	−0.992842	−	0.119435i	$-0.961892\pi$
$271$	−9.87486	−	17.1038i	−0.599855	−	1.03898i	0.392987	−	0.919544i	$-0.371442\pi$
$272$	1.95448	+	1.12842i	0.118508	+	0.0684206i
$273$			11.9166i			0.721224i
$274$	12.2841	−	7.09224i	0.742111	−	0.428458i
$275$	−2.62957	−	4.55456i	−0.158569	−	0.274650i
$276$	−1.66873	+	0.963443i	−0.100446	+	0.0579925i
$277$	0.559700	+	0.323143i	0.0336291	+	0.0194158i	0.516720	−	0.856154i	$-0.327153\pi$
$277$	0.559700	+	0.323143i	0.0336291	+	0.0194158i	−0.483091	+	0.875570i	$0.660486\pi$
$278$	−18.4528	−	10.6538i	−1.10673	−	0.638970i
$279$	1.17495	−	0.678359i	0.0703426	−	0.0406123i
$280$	1.62842	+	2.82051i	0.0973168	+	0.168558i
$281$	−1.71343	+	0.989249i	−0.102215	+	0.0590136i	−0.550236	−	0.835009i	$-0.685462\pi$
$281$	−1.71343	+	0.989249i	−0.102215	+	0.0590136i	0.448021	+	0.894023i	$0.352129\pi$
$282$			3.32765i			0.198159i
$283$	−6.32516	−	3.65183i	−0.375992	−	0.217079i	0.300081	−	0.953914i	$-0.402986\pi$
$283$	−6.32516	−	3.65183i	−0.375992	−	0.217079i	−0.676073	+	0.736835i	$0.736320\pi$
$284$	0.215263	+	0.372847i	0.0127735	+	0.0221244i
$285$	3.70759			0.219619
$286$	19.2429			1.13786
$287$	8.91546	+	15.4420i	0.526263	+	0.911514i
$288$			1.00000i			0.0589256i
$289$	−5.95333	+	10.3115i	−0.350196	+	0.606557i
$290$		−	3.37764i		−	0.198342i
$291$	4.06528	+	2.34709i	0.238311	+	0.137589i
$292$	2.11845	−	3.66926i	0.123973	−	0.214727i
$293$	−5.66939	+	9.81967i	−0.331209	+	0.573671i	−0.982749	−	0.184943i	$-0.940790\pi$
$293$	−5.66939	+	9.81967i	−0.331209	+	0.573671i	0.651540	+	0.758614i	$0.274123\pi$
$294$	3.12377	−	1.80351i	0.182182	−	0.105183i
$295$	−11.0360			−0.642541
$296$	−3.03262	+	5.27288i	−0.176267	+	0.306480i
$297$	−5.25915			−0.305167
$298$	7.24623	−	4.18361i	0.419763	−	0.242350i
$299$	3.52518	−	6.10579i	0.203866	−	0.353107i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	9.26143	+	5.34709i	0.533820	+	0.308201i
$302$		−	13.9301i		−	0.801587i
$303$	4.95679	−	8.58541i	0.284760	−	0.493219i
$304$			3.70759i			0.212645i
$305$	−0.618309	−	1.07094i	−0.0354043	−	0.0613220i
$306$	2.25684			0.129015
$307$	−9.54245			−0.544616			−0.272308	−	0.962210i	$-0.587787\pi$
$307$	−9.54245			−0.544616			−0.272308	+	0.962210i	$0.587787\pi$
$308$	−8.56411	−	14.8335i	−0.487985	−	0.845215i
$309$	−9.59224	−	5.53809i	−0.545684	−	0.315051i
$310$			1.35672i			0.0770564i
$311$	−11.7442	+	6.78050i	−0.665951	+	0.384487i	−0.794541	−	0.607211i	$-0.792288\pi$
$311$	−11.7442	+	6.78050i	−0.665951	+	0.384487i	0.128590	+	0.991698i	$0.458955\pi$
$312$	−1.82947	−	3.16873i	−0.103573	−	0.179394i
$313$	2.94389	−	1.69966i	0.166399	−	0.0960703i	−0.414488	−	0.910055i	$-0.636039\pi$
$313$	2.94389	−	1.69966i	0.166399	−	0.0960703i	0.580887	+	0.813985i	$0.302706\pi$
$314$	−7.77960	−	4.49155i	−0.439028	−	0.253473i
$315$	2.82051	+	1.62842i	0.158918	+	0.0917511i
$316$	6.26143	−	3.61504i	0.352233	−	0.203362i
$317$	−9.98619	−	17.2966i	−0.560880	−	0.971473i	−0.997420	−	0.0717881i	$-0.977129\pi$
$317$	−9.98619	−	17.2966i	−0.560880	−	0.971473i	0.436540	−	0.899685i	$-0.356204\pi$
$318$	−8.82457	+	5.09487i	−0.494857	+	0.285706i
$319$			17.7635i			0.994565i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	−6.80147	−	11.7805i	−0.379621	−	0.657523i
$322$	−6.27556			−0.349724
$323$	8.36746			0.465578
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$		−	3.65894i		−	0.202961i
$326$	9.98128	−	17.2881i	0.552812	−	0.957499i
$327$		−	7.41712i		−	0.410167i
$328$	−4.74141	−	2.73745i	−0.261801	−	0.151151i
$329$	−5.41882	+	9.38567i	−0.298749	+	0.517449i
$330$	2.62957	−	4.55456i	0.144753	−	0.250720i
$331$	8.55298	−	4.93807i	0.470114	−	0.271421i	−0.246173	−	0.969226i	$-0.579173\pi$
$331$	8.55298	−	4.93807i	0.470114	−	0.271421i	0.716288	+	0.697805i	$0.245840\pi$
$332$	13.6630			0.749853
$333$	0.0101124	+	6.08275i	0.000554158	+	0.333333i
$334$	−8.19586			−0.448457
$335$	−12.0127	+	6.93555i	−0.656325	+	0.378930i
$336$	−1.62842	+	2.82051i	−0.0888377	+	0.153871i
$337$	−1.52567	+	2.64253i	−0.0831084	+	0.143948i	−0.904584	−	0.426296i	$-0.859818\pi$
$337$	−1.52567	+	2.64253i	−0.0831084	+	0.143948i	0.821475	+	0.570244i	$0.193151\pi$
$338$	0.335860	+	0.193909i	0.0182684	+	0.0105473i
$339$			0.315569i			0.0171394i
$340$	−1.12842	+	1.95448i	−0.0611972	+	0.105997i
$341$		−	7.13518i		−	0.386392i
$342$	1.85380	+	3.21087i	0.100242	+	0.173624i
$343$	−11.0504			−0.596665
$344$	−3.28360			−0.177040
$345$	−0.963443	−	1.66873i	−0.0518700	−	0.0898415i
$346$	13.7901	+	7.96169i	0.741358	+	0.428023i
$347$			26.8643i			1.44215i	0.692855	+	0.721077i	$0.256353\pi$
$347$			26.8643i			1.44215i	−0.692855	+	0.721077i	$0.743647\pi$
$348$	2.92512	−	1.68882i	0.156803	−	0.0905302i
$349$	−8.06293	−	13.9654i	−0.431599	−	0.747551i	0.565412	−	0.824808i	$-0.308717\pi$
$349$	−8.06293	−	13.9654i	−0.431599	−	0.747551i	−0.997011	+	0.0772571i	$0.975384\pi$
$350$	−2.82051	+	1.62842i	−0.150763	+	0.0870428i
$351$	−3.16873	−	1.82947i	−0.169134	−	0.0976498i
$352$	4.55456	+	2.62957i	0.242759	+	0.140157i
$353$	−15.0990	+	8.71739i	−0.803636	+	0.463980i	−0.844741	−	0.535175i	$-0.820246\pi$
$353$	−15.0990	+	8.71739i	−0.803636	+	0.463980i	0.0411047	+	0.999155i	$0.486912\pi$
$354$	−5.51800	−	9.55745i	−0.293278	−	0.507973i
$355$	−0.372847	+	0.215263i	−0.0197887	+	0.0114250i
$356$			11.2644i			0.597009i
$357$	6.36544	+	3.67509i	0.336895	+	0.194506i
$358$	−0.450328	−	0.779992i	−0.0238006	−	0.0412238i
$359$	−5.13196			−0.270854			−0.135427	−	0.990787i	$-0.543241\pi$
$359$	−5.13196			−0.270854			−0.135427	+	0.990787i	$0.543241\pi$
$360$	−1.00000			−0.0527046
$361$	−2.62687	−	4.54988i	−0.138256	−	0.239467i
$362$		−	2.91520i		−	0.153220i
$363$	−8.32932	+	14.4268i	−0.437176	+	0.757211i
$364$		−	11.9166i		−	0.624599i
$365$	3.66926	+	2.11845i	0.192058	+	0.110885i
$366$	0.618309	−	1.07094i	0.0323195	−	0.0559791i
$367$	−2.33684	+	4.04753i	−0.121982	+	0.211279i	−0.920549	−	0.390626i	$-0.872258\pi$
$367$	−2.33684	+	4.04753i	−0.121982	+	0.211279i	0.798567	+	0.601906i	$0.205592\pi$
$368$	1.66873	−	0.963443i	0.0869887	−	0.0502229i
$369$	−5.47491			−0.285012
$370$	−5.27288	−	3.03262i	−0.274124	−	0.157658i
$371$	−33.1864			−1.72295
$372$	−1.17495	+	0.678359i	−0.0609185	+	0.0351713i
$373$	13.4218	−	23.2473i	0.694956	−	1.20370i	−0.275240	−	0.961376i	$-0.588757\pi$
$373$	13.4218	−	23.2473i	0.694956	−	1.20370i	0.970196	−	0.242323i	$-0.0779093\pi$
$374$	5.93453	−	10.2789i	0.306867	−	0.531510i
$375$	−0.866025	−	0.500000i	−0.0447214	−	0.0258199i
$376$		−	3.32765i		−	0.171611i
$377$	−6.17928	+	10.7028i	−0.318249	+	0.551224i
$378$			3.25684i			0.167514i
$379$	−14.0580	−	24.3491i	−0.722109	−	1.25073i	−0.960153	−	0.279476i	$-0.909839\pi$
$379$	−14.0580	−	24.3491i	−0.722109	−	1.25073i	0.238043	−	0.971255i	$-0.423494\pi$
$380$	−3.70759			−0.190196
$381$	14.6720			0.751671
$382$	13.5485	+	23.4667i	0.693201	+	1.20066i
$383$	−22.9304	−	13.2389i	−1.17169	−	0.676474i	−0.217611	−	0.976036i	$-0.569826\pi$
$383$	−22.9304	−	13.2389i	−1.17169	−	0.676474i	−0.954077	+	0.299561i	$0.903160\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	14.8335	−	8.56411i	0.755984	−	0.436467i
$386$	−8.31797	−	14.4071i	−0.423373	−	0.733304i
$387$	−2.84368	+	1.64180i	−0.144553	+	0.0834575i
$388$	−4.06528	−	2.34709i	−0.206383	−	0.119156i
$389$	−24.6665	−	14.2412i	−1.25064	−	0.722057i	−0.279403	−	0.960174i	$-0.590136\pi$
$389$	−24.6665	−	14.2412i	−1.25064	−	0.722057i	−0.971236	+	0.238117i	$0.923470\pi$
$390$	3.16873	−	1.82947i	0.160455	−	0.0926387i
$391$	−2.17434	−	3.76607i	−0.109961	−	0.190458i
$392$	−3.12377	+	1.80351i	−0.157774	+	0.0910911i
$393$		−	8.48241i		−	0.427881i
$394$	−14.8887	−	8.59600i	−0.750082	−	0.433060i
$395$	3.61504	+	6.26143i	0.181892	+	0.315047i
$396$	5.25915			0.264282
$397$	−21.6765			−1.08791			−0.543956	−	0.839114i	$-0.683074\pi$
$397$	−21.6765			−1.08791			−0.543956	+	0.839114i	$0.683074\pi$
$398$	−1.36755	−	2.36867i	−0.0685493	−	0.118731i
$399$			12.0751i			0.604509i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$			8.46569i			0.422756i	0.977404	+	0.211378i	$0.0677951\pi$
$401$			8.46569i			0.422756i	−0.977404	+	0.211378i	$0.932205\pi$
$402$	−12.0127	−	6.93555i	−0.599140	−	0.345914i
$403$	2.48207	−	4.29908i	0.123641	−	0.214152i
$404$	−4.95679	+	8.58541i	−0.246609	+	0.427140i
$405$	−0.866025	+	0.500000i	−0.0430331	+	0.0248452i
$406$	11.0004			0.545942
$407$	27.7308	+	15.9490i	1.37457	+	0.790562i
$408$	−2.25684			−0.111730
$409$	−1.34173	+	0.774650i	−0.0663445	+	0.0383040i	−0.532805	−	0.846238i	$-0.678862\pi$
$409$	−1.34173	+	0.774650i	−0.0663445	+	0.0383040i	0.466461	+	0.884542i	$0.345529\pi$
$410$	2.73745	−	4.74141i	0.135193	−	0.234161i
$411$	−7.09224	+	12.2841i	−0.349834	+	0.605931i
$412$	9.59224	+	5.53809i	0.472576	+	0.272842i
$413$		−	35.9425i		−	1.76862i
$414$	0.963443	−	1.66873i	0.0473506	−	0.0820137i
$415$			13.6630i			0.670689i
$416$	1.82947	+	3.16873i	0.0896971	+	0.155360i
$417$	21.3075			1.04343
$418$	19.4988			0.953717
$419$	−16.3095	−	28.2489i	−0.796772	−	1.38005i	−0.921708	−	0.387884i	$-0.873206\pi$
$419$	−16.3095	−	28.2489i	−0.796772	−	1.38005i	0.124936	−	0.992165i	$-0.460127\pi$
$420$	−2.82051	−	1.62842i	−0.137627	−	0.0794588i
$421$		−	2.38884i		−	0.116425i	−0.998304	−	0.0582124i	$-0.981460\pi$
$421$		−	2.38884i		−	0.116425i	0.998304	−	0.0582124i	$-0.0185401\pi$
$422$	−16.2985	+	9.40994i	−0.793398	+	0.458069i
$423$	−1.66383	−	2.88183i	−0.0808980	−	0.140119i
$424$	8.82457	−	5.09487i	0.428559	−	0.247429i
$425$	−1.95448	−	1.12842i	−0.0948064	−	0.0547365i
$426$	−0.372847	−	0.215263i	−0.0180645	−	0.0104295i
$427$	3.48789	−	2.01373i	0.168791	−	0.0974515i
$428$	6.80147	+	11.7805i	0.328761	+	0.569431i
$429$	−16.6648	+	9.62144i	−0.804586	+	0.464528i
$430$		−	3.28360i		−	0.158349i
$431$	13.1116	+	7.56997i	0.631562	+	0.364633i	0.781357	−	0.624084i	$-0.214528\pi$
$431$	13.1116	+	7.56997i	0.631562	+	0.364633i	−0.149795	+	0.988717i	$0.547861\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	33.0099			1.58635			0.793177	−	0.608991i	$-0.208425\pi$
$433$	33.0099			1.58635			0.793177	+	0.608991i	$0.208425\pi$
$434$	−4.41862			−0.212100
$435$	1.68882	+	2.92512i	0.0809727	+	0.140249i
$436$			7.41712i			0.355215i
$437$	3.57206	−	6.18698i	0.170875	−	0.295963i
$438$			4.23689i			0.202447i
$439$	12.4278	+	7.17520i	0.593147	+	0.342454i	0.766341	−	0.642434i	$-0.222075\pi$
$439$	12.4278	+	7.17520i	0.593147	+	0.342454i	−0.173194	+	0.984888i	$0.555409\pi$
$440$	−2.62957	+	4.55456i	−0.125360	+	0.217130i
$441$	−1.80351	+	3.12377i	−0.0858815	+	0.148751i
$442$	7.15133	−	4.12882i	0.340154	−	0.196388i
$443$	2.18743			0.103928			0.0519639	−	0.998649i	$-0.483452\pi$
$443$	2.18743			0.103928			0.0519639	+	0.998649i	$0.483452\pi$
$444$	−0.0101124	−	6.08275i	−0.000479915	−	0.288675i
$445$	−11.2644			−0.533981
$446$	22.2042	−	12.8196i	1.05140	−	0.607027i
$447$	−4.18361	+	7.24623i	−0.197878	+	0.342735i
$448$	1.62842	−	2.82051i	0.0769357	−	0.133257i
$449$	−32.0199	−	18.4867i	−1.51111	−	0.872441i	−0.999916	−	0.0129764i	$-0.995869\pi$
$449$	−32.0199	−	18.4867i	−1.51111	−	0.872441i	−0.511196	−	0.859464i	$-0.670797\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	−14.3967	+	24.9358i	−0.677913	+	1.17418i
$452$		−	0.315569i		−	0.0148431i
$453$	6.96505	+	12.0638i	0.327247	+	0.566808i
$454$	16.2498			0.762639
$455$	11.9166			0.558658
$456$	−1.85380	−	3.21087i	−0.0868120	−	0.150363i
$457$	13.9843	+	8.07387i	0.654160	+	0.377679i	0.790048	−	0.613045i	$-0.210055\pi$
$457$	13.9843	+	8.07387i	0.654160	+	0.377679i	−0.135888	+	0.990724i	$0.543389\pi$
$458$			11.7483i			0.548963i
$459$	−1.95448	+	1.12842i	−0.0912275	+	0.0526702i
$460$	0.963443	+	1.66873i	0.0449208	+	0.0778050i
$461$	−18.0603	+	10.4271i	−0.841152	+	0.485639i	−0.857656	−	0.514224i	$-0.828080\pi$
$461$	−18.0603	+	10.4271i	−0.841152	+	0.485639i	0.0165035	+	0.999864i	$0.494747\pi$
$462$	14.8335	+	8.56411i	0.690116	+	0.398438i
$463$	−32.8561	−	18.9695i	−1.52695	−	0.881585i	−0.999488	−	0.0320070i	$-0.989810\pi$
$463$	−32.8561	−	18.9695i	−1.52695	−	0.881585i	−0.527463	−	0.849578i	$-0.676857\pi$
$464$	−2.92512	+	1.68882i	−0.135795	+	0.0784014i
$465$	−0.678359	−	1.17495i	−0.0314582	−	0.0544871i
$466$	8.99446	−	5.19295i	0.416660	−	0.240559i
$467$		−	11.6625i		−	0.539676i	−0.962906	−	0.269838i	$-0.913030\pi$
$467$		−	11.6625i		−	0.539676i	0.962906	−	0.269838i	$-0.0869702\pi$
$468$	3.16873	+	1.82947i	0.146475	+	0.0845672i
$469$	−22.5880	−	39.1236i	−1.04302	−	1.80656i
$470$	3.32765			0.153493
$471$	8.98311			0.413920
$472$	5.51800	+	9.55745i	0.253986	+	0.439917i
$473$			17.2690i			0.794028i
$474$	−3.61504	+	6.26143i	−0.166044	+	0.287597i
$475$		−	3.70759i		−	0.170116i
$476$	−6.36544	−	3.67509i	−0.291760	−	0.168448i
$477$	5.09487	−	8.82457i	0.233278	−	0.404049i
$478$	2.12625	−	3.68278i	0.0972526	−	0.168446i
$479$	−32.7632	+	18.9158i	−1.49699	+	0.864286i	−0.999994	−	0.00346864i	$-0.998896\pi$
$479$	−32.7632	+	18.9158i	−1.49699	+	0.864286i	−0.496993	+	0.867755i	$0.665563\pi$
$480$	1.00000			0.0456435
$481$	11.1602	+	19.2561i	0.508864	+	0.878003i
$482$	5.92273			0.269773
$483$	5.43480	−	3.13778i	0.247292	−	0.142774i
$484$	8.32932	−	14.4268i	0.378605	−	0.655764i
$485$	2.34709	−	4.06528i	0.106576	−	0.184595i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$			34.0667i			1.54371i	0.635799	+	0.771855i	$0.280671\pi$
$487$			34.0667i			1.54371i	−0.635799	+	0.771855i	$0.719329\pi$
$488$	−0.618309	+	1.07094i	−0.0279895	+	0.0484793i
$489$			19.9626i			0.902738i
$490$	−1.80351	−	3.12377i	−0.0814744	−	0.141118i
$491$	33.6933			1.52056			0.760278	−	0.649598i	$-0.225063\pi$
$491$	33.6933			1.52056			0.760278	+	0.649598i	$0.225063\pi$
$492$	5.47491			0.246828
$493$	3.81140	+	6.60154i	0.171657	+	0.297318i
$494$	11.7484	+	6.78293i	0.528584	+	0.305178i
$495$			5.25915i			0.236381i
$496$	1.17495	−	0.678359i	0.0527569	−	0.0304592i
$497$	−0.701079	−	1.21430i	−0.0314477	−	0.0544690i
$498$	−11.8325	+	6.83148i	−0.530226	+	0.306126i
$499$	−0.744312	−	0.429729i	−0.0333200	−	0.0192373i	0.483247	−	0.875484i	$-0.339457\pi$
$499$	−0.744312	−	0.429729i	−0.0333200	−	0.0192373i	−0.516567	+	0.856246i	$0.672790\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	7.09782	−	4.09793i	0.317107	−	0.183082i
$502$	5.71248	+	9.89430i	0.254960	+	0.441604i
$503$	32.4710	−	18.7472i	1.44781	−	0.835895i	0.449461	−	0.893300i	$-0.351616\pi$
$503$	32.4710	−	18.7472i	1.44781	−	0.835895i	0.998351	+	0.0574051i	$0.0182827\pi$
$504$		−	3.25684i		−	0.145071i
$505$	−8.58541	−	4.95679i	−0.382046	−	0.220574i
$506$	−5.06689	−	8.77611i	−0.225251	−	0.390146i
$507$	−0.387818			−0.0172236
$508$	−14.6720			−0.650966
$509$	13.1662	+	22.8045i	0.583580	+	1.01079i	0.995051	+	0.0993671i	$0.0316818\pi$
$509$	13.1662	+	22.8045i	0.583580	+	1.01079i	−0.411471	+	0.911423i	$0.634985\pi$
$510$		−	2.25684i		−	0.0999347i
$511$	−6.89945	+	11.9502i	−0.305214	+	0.528646i
$512$			1.00000i			0.0441942i
$513$	−3.21087	−	1.85380i	−0.141763	−	0.0818471i
$514$	−11.7333	+	20.3226i	−0.517532	+	0.896392i
$515$	−5.53809	+	9.59224i	−0.244037	+	0.422685i
$516$	2.84368	−	1.64180i	0.125186	−	0.0722763i
$517$	−17.5006			−0.769676
$518$	9.87676	−	17.1729i	0.433960	−	0.754535i
$519$	−15.9234			−0.698959
$520$	−3.16873	+	1.82947i	−0.138958	+	0.0802275i
$521$	0.172543	−	0.298854i	0.00755926	−	0.0130930i	−0.862221	−	0.506532i	$-0.830927\pi$
$521$	0.172543	−	0.298854i	0.00755926	−	0.0130930i	0.869780	+	0.493439i	$0.164260\pi$
$522$	−1.68882	+	2.92512i	−0.0739176	+	0.128029i
$523$	33.3875	+	19.2763i	1.45993	+	0.842893i	0.999007	−	0.0445455i	$-0.0141840\pi$
$523$	33.3875	+	19.2763i	1.45993	+	0.842893i	0.460926	+	0.887439i	$0.347517\pi$
$524$			8.48241i			0.370556i
$525$	1.62842	−	2.82051i	0.0710701	−	0.123097i
$526$		−	20.7970i		−	0.906794i
$527$	−1.53095	−	2.65168i	−0.0666892	−	0.115509i
$528$	−5.25915			−0.228875
$529$	19.2871			0.838570
$530$	5.09487	+	8.82457i	0.221307	+	0.383315i
$531$	9.55745	+	5.51800i	0.414758	+	0.239461i
$532$		−	12.0751i		−	0.523520i
$533$	−17.3485	+	10.0162i	−0.751448	+	0.433848i
$534$	−5.63218	−	9.75521i	−0.243728	−	0.422149i
$535$	−11.7805	+	6.80147i	−0.509315	+	0.294053i
$536$	12.0127	+	6.93555i	0.518871	+	0.299570i
$537$	0.779992	+	0.450328i	0.0336591	+	0.0194331i
$538$	17.6794	−	10.2072i	0.762214	−	0.440064i
$539$	9.48494	+	16.4284i	0.408545	+	0.707621i
$540$	0.866025	−	0.500000i	0.0372678	−	0.0215166i
$541$			0.789062i			0.0339244i	0.999856	+	0.0169622i	$0.00539950\pi$
$541$			0.789062i			0.0339244i	−0.999856	+	0.0169622i	$0.994601\pi$
$542$	−17.1038	−	9.87486i	−0.734669	−	0.424162i
$543$	1.45760	+	2.52464i	0.0625517	+	0.108343i
$544$	2.25684			0.0967613
$545$	−7.41712			−0.317714
$546$	5.95829	+	10.3201i	0.254991	+	0.441658i
$547$			27.8104i			1.18909i	0.804063	+	0.594544i	$0.202668\pi$
$547$			27.8104i			1.18909i	−0.804063	+	0.594544i	$0.797332\pi$
$548$	7.09224	−	12.2841i	0.302965	−	0.524752i
$549$			1.23662i			0.0527776i
$550$	−4.55456	−	2.62957i	−0.194207	−	0.112125i
$551$	−6.26145	+	10.8452i	−0.266747	+	0.462019i
$552$	−0.963443	+	1.66873i	−0.0410069	+	0.0710260i
$553$	−20.3925	+	11.7736i	−0.867178	+	0.500665i
$554$	0.646286			0.0274581
$555$	6.08275	−	0.0101124i	0.258199	−	0.000429249i
$556$	−21.3075			−0.903640
$557$	8.64914	−	4.99358i	0.366476	−	0.211585i	−0.305442	−	0.952211i	$-0.598804\pi$
$557$	8.64914	−	4.99358i	0.366476	−	0.211585i	0.671918	+	0.740626i	$0.265471\pi$
$558$	0.678359	−	1.17495i	0.0287172	−	0.0497397i
$559$	−6.00725	+	10.4049i	−0.254080	+	0.440079i
$560$	2.82051	+	1.62842i	0.119188	+	0.0688134i
$561$			11.8691i			0.501113i
$562$	−0.989249	+	1.71343i	−0.0417289	+	0.0722766i
$563$			35.7694i			1.50750i	0.657161	+	0.753751i	$0.271757\pi$
$563$			35.7694i			1.50750i	−0.657161	+	0.753751i	$0.728243\pi$
$564$	1.66383	+	2.88183i	0.0700597	+	0.121347i
$565$	0.315569			0.0132761
$566$	−7.30367			−0.306996
$567$	−1.62842	−	2.82051i	−0.0683873	−	0.118450i
$568$	0.372847	+	0.215263i	0.0156443	+	0.00903225i
$569$			1.94164i			0.0813977i	0.999171	+	0.0406989i	$0.0129584\pi$
$569$			1.94164i			0.0813977i	−0.999171	+	0.0406989i	$0.987042\pi$
$570$	3.21087	−	1.85380i	0.134489	−	0.0776470i
$571$	−12.2709	−	21.2539i	−0.513523	−	0.889448i	−0.999877	−	0.0156863i	$-0.995007\pi$
$571$	−12.2709	−	21.2539i	−0.513523	−	0.889448i	0.486354	−	0.873762i	$-0.338327\pi$
$572$	16.6648	−	9.62144i	0.696792	−	0.402293i
$573$	−23.4667	−	13.5485i	−0.980335	−	0.565996i
$574$	15.4420	+	8.91546i	0.644538	+	0.372124i
$575$	−1.66873	+	0.963443i	−0.0695909	+	0.0401783i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	16.6742	−	9.62685i	0.694156	−	0.400771i	−0.111011	−	0.993819i	$-0.535409\pi$
$577$	16.6742	−	9.62685i	0.694156	−	0.400771i	0.805167	+	0.593048i	$0.202076\pi$
$578$			11.9067i			0.495252i
$579$	14.4071	+	8.31797i	0.598740	+	0.345683i
$580$	−1.68882	−	2.92512i	−0.0701244	−	0.121459i
$581$	−44.4981			−1.84609
$582$	4.69418			0.194580
$583$	−26.7947	−	46.4097i	−1.10972	−	1.92209i
$584$		−	4.23689i		−	0.175324i
$585$	−1.82947	+	3.16873i	−0.0756392	+	0.131011i
$586$			11.3388i			0.468400i
$587$	−0.346155	−	0.199853i	−0.0142873	−	0.00824880i	0.492839	−	0.870120i	$-0.335959\pi$
$587$	−0.346155	−	0.199853i	−0.0142873	−	0.00824880i	−0.507127	+	0.861872i	$0.669292\pi$
$588$	1.80351	−	3.12377i	0.0743756	−	0.128822i
$589$	2.51508	−	4.35625i	0.103632	−	0.179496i
$590$	−9.55745	+	5.51800i	−0.393474	+	0.227172i
$591$	17.1920			0.707184
$592$	0.0101124	+	6.08275i	0.000415618	+	0.250000i
$593$	−14.6432			−0.601325			−0.300663	−	0.953731i	$-0.597208\pi$
$593$	−14.6432			−0.601325			−0.300663	+	0.953731i	$0.597208\pi$
$594$	−4.55456	+	2.62957i	−0.186876	+	0.107893i
$595$	3.67509	−	6.36544i	0.150664	−	0.260958i
$596$	4.18361	−	7.24623i	0.171367	−	0.296817i
$597$	2.36867	+	1.36755i	0.0969433	+	0.0559702i
$598$		−	7.05035i		−	0.288310i
$599$	6.43257	−	11.1415i	0.262828	−	0.455231i	−0.704165	−	0.710037i	$-0.748678\pi$
$599$	6.43257	−	11.1415i	0.262828	−	0.455231i	0.966992	+	0.254806i	$0.0820116\pi$
$600$			1.00000i			0.0408248i
$601$	8.59490	+	14.8868i	0.350593	+	0.607246i	0.986354	−	0.164641i	$-0.0526466\pi$
$601$	8.59490	+	14.8868i	0.350593	+	0.607246i	−0.635760	+	0.771887i	$0.719313\pi$
$602$	10.6942			0.435862
$603$	13.8711			0.564875
$604$	−6.96505	−	12.0638i	−0.283404	−	0.490870i
$605$	14.4268	+	8.32932i	0.586533	+	0.338635i
$606$		−	9.91358i		−	0.402712i
$607$	−42.1054	+	24.3095i	−1.70900	+	0.986694i	−0.773208	+	0.634152i	$0.781349\pi$
$607$	−42.1054	+	24.3095i	−1.70900	+	0.986694i	−0.935796	+	0.352542i	$0.885317\pi$
$608$	1.85380	+	3.21087i	0.0751814	+	0.130218i
$609$	−9.52666	+	5.50022i	−0.386040	+	0.222880i
$610$	−1.07094	−	0.618309i	−0.0433612	−	0.0250346i
$611$	−10.5444	−	6.08783i	−0.426582	−	0.246287i
$612$	1.95448	−	1.12842i	0.0790053	−	0.0456137i
$613$	14.6936	+	25.4501i	0.593471	+	1.02792i	0.993761	+	0.111533i	$0.0355761\pi$
$613$	14.6936	+	25.4501i	0.593471	+	1.02792i	−0.400290	+	0.916389i	$0.631091\pi$
$614$	−8.26401	+	4.77123i	−0.333508	+	0.192551i
$615$			5.47491i			0.220770i
$616$	−14.8335	−	8.56411i	−0.597658	−	0.345058i
$617$	−7.39870	−	12.8149i	−0.297860	−	0.515909i	0.677786	−	0.735259i	$-0.262940\pi$
$617$	−7.39870	−	12.8149i	−0.297860	−	0.515909i	−0.975646	+	0.219350i	$0.929606\pi$
$618$	−11.0762			−0.445549
$619$	−38.0010			−1.52739			−0.763694	−	0.645579i	$-0.776616\pi$
$619$	−38.0010			−1.52739			−0.763694	+	0.645579i	$0.776616\pi$
$620$	0.678359	+	1.17495i	0.0272436	+	0.0471872i
$621$			1.92689i			0.0773233i
$622$	−6.78050	+	11.7442i	−0.271873	+	0.470899i
$623$		−	36.6862i		−	1.46980i
$624$	−3.16873	−	1.82947i	−0.126851	−	0.0732373i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	1.69966	−	2.94389i	0.0679320	−	0.117662i
$627$	−16.8864	+	9.74939i	−0.674380	+	0.389353i
$628$	−8.98311			−0.358465
$629$	13.7278	−	0.0228222i	0.547364	−	0.000909979i
$630$	3.25684			0.129756
$631$	−42.9542	+	24.7996i	−1.70998	+	0.987258i	−0.775425	+	0.631440i	$0.782464\pi$
$631$	−42.9542	+	24.7996i	−1.70998	+	0.987258i	−0.934555	+	0.355818i	$0.884202\pi$
$632$	3.61504	−	6.26143i	0.143799	−	0.249066i
$633$	9.40994	−	16.2985i	0.374012	−	0.647807i
$634$	−17.2966	−	9.98619i	−0.686935	−	0.396602i
$635$		−	14.6720i		−	0.582242i
$636$	−5.09487	+	8.82457i	−0.202025	+	0.349917i
$637$			13.1979i			0.522919i
$638$	8.88175	+	15.3836i	0.351632	+	0.609044i
$639$	0.430527			0.0170314
$640$	−1.00000			−0.0395285
$641$	−16.7195	−	28.9590i	−0.660379	−	1.14381i	−0.980516	−	0.196439i	$-0.937062\pi$
$641$	−16.7195	−	28.9590i	−0.660379	−	1.14381i	0.320137	−	0.947371i	$-0.396271\pi$
$642$	−11.7805	−	6.80147i	−0.464939	−	0.268432i
$643$			33.3367i			1.31467i	0.753598	+	0.657336i	$0.228317\pi$
$643$			33.3367i			1.31467i	−0.753598	+	0.657336i	$0.771683\pi$
$644$	−5.43480	+	3.13778i	−0.214161	+	0.123646i
$645$	1.64180	+	2.84368i	0.0646459	+	0.111970i
$646$	7.24643	−	4.18373i	0.285107	−	0.164607i
$647$	14.3341	+	8.27578i	0.563530	+	0.325354i	0.754561	−	0.656230i	$-0.227850\pi$
$647$	14.3341	+	8.27578i	0.563530	+	0.325354i	−0.191031	+	0.981584i	$0.561183\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	50.2641	−	29.0200i	1.97304	−	1.13913i
$650$	−1.82947	−	3.16873i	−0.0717577	−	0.124288i
$651$	3.82664	−	2.20931i	0.149978	−	0.0865897i
$652$		−	19.9626i		−	0.781794i
$653$	4.84180	+	2.79541i	0.189474	+	0.109393i	0.591736	−	0.806132i	$-0.298443\pi$
$653$	4.84180	+	2.79541i	0.189474	+	0.109393i	−0.402262	+	0.915525i	$0.631776\pi$
$654$	−3.70856	−	6.42341i	−0.145016	−	0.251175i
$655$	−8.48241			−0.331435
$656$	−5.47491			−0.213759
$657$	−2.11845	−	3.66926i	−0.0826485	−	0.143151i
$658$			10.8376i			0.422495i
$659$	9.79210	−	16.9604i	0.381446	−	0.660684i	−0.609823	−	0.792538i	$-0.708759\pi$
$659$	9.79210	−	16.9604i	0.381446	−	0.660684i	0.991269	+	0.131853i	$0.0420928\pi$
$660$		−	5.25915i		−	0.204712i
$661$	−9.20675	−	5.31552i	−0.358101	−	0.206750i	0.310146	−	0.950689i	$-0.399622\pi$
$661$	−9.20675	−	5.31552i	−0.358101	−	0.206750i	−0.668248	+	0.743939i	$0.732955\pi$
$662$	4.93807	−	8.55298i	0.191923	−	0.332421i
$663$	−4.12882	+	7.15133i	−0.160350	+	0.277735i
$664$	11.8325	−	6.83148i	0.459189	−	0.265113i
$665$	12.0751			0.468250
$666$	3.05013	+	5.26276i	0.118190	+	0.203928i
$667$	6.50832			0.252003
$668$	−7.09782	+	4.09793i	−0.274623	+	0.158554i
$669$	−12.8196	+	22.2042i	−0.495635	+	0.858466i
$670$	−6.93555	+	12.0127i	−0.267944	+	0.464092i
$671$	5.63224	+	3.25178i	0.217430	+	0.125533i
$672$			3.25684i			0.125635i
$673$	−11.6444	+	20.1688i	−0.448860	+	0.777449i	−0.998312	−	0.0580767i	$-0.981503\pi$
$673$	−11.6444	+	20.1688i	−0.448860	+	0.777449i	0.549452	+	0.835525i	$0.314837\pi$
$674$			3.05134i			0.117533i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	0.387818			0.0149161
$677$	−19.3235			−0.742661			−0.371331	−	0.928501i	$-0.621098\pi$
$677$	−19.3235			−0.742661			−0.371331	+	0.928501i	$0.621098\pi$
$678$	0.157785	+	0.273291i	0.00605968	+	0.0104957i
$679$	13.2400	+	7.64411i	0.508104	+	0.293354i
$680$			2.25684i			0.0865460i
$681$	−14.0727	+	8.12488i	−0.539268	+	0.311346i
$682$	−3.56759	−	6.17925i	−0.136610	−	0.236616i
$683$	9.23123	−	5.32965i	0.353223	−	0.203933i	−0.312881	−	0.949792i	$-0.601294\pi$
$683$	9.23123	−	5.32965i	0.353223	−	0.203933i	0.666104	+	0.745859i	$0.267961\pi$
$684$	3.21087	+	1.85380i	0.122771	+	0.0708817i
$685$	12.2841	+	7.09224i	0.469352	+	0.270981i
$686$	−9.56992	+	5.52519i	−0.365381	+	0.210953i
$687$	−5.87416	−	10.1743i	−0.224113	−	0.388176i
$688$	−2.84368	+	1.64180i	−0.108414	+	0.0625931i
$689$		−	37.2836i		−	1.42039i
$690$	−1.66873	−	0.963443i	−0.0635275	−	0.0366776i
$691$	−15.6445	−	27.0971i	−0.595146	−	1.03082i	−0.993526	−	0.113603i	$-0.963761\pi$
$691$	−15.6445	−	27.0971i	−0.595146	−	1.03082i	0.398380	−	0.917220i	$-0.369572\pi$
$692$	15.9234			0.605316
$693$	−17.1282			−0.650647
$694$	13.4322	+	23.2652i	0.509878	+	0.883135i
$695$		−	21.3075i		−	0.808240i
$696$	1.68882	−	2.92512i	0.0640145	−	0.110876i
$697$			12.3560i			0.468017i
$698$	−13.9654	−	8.06293i	−0.528599	−	0.305187i
$699$	−5.19295	+	8.99446i	−0.196415	+	0.340202i
$700$	−1.62842	+	2.82051i	−0.0615485	+	0.106605i
$701$	30.0642	−	17.3576i	1.13551	−	0.655586i	0.190194	−	0.981746i	$-0.439088\pi$
$701$	30.0642	−	17.3576i	1.13551	−	0.655586i	0.945315	+	0.326160i	$0.105755\pi$
$702$	−3.65894			−0.138098
$703$	11.3087	+	19.5122i	0.426514	+	0.735916i
$704$	5.25915			0.198212
$705$	−2.88183	+	1.66383i	−0.108536	+	0.0626633i
$706$	−8.71739	+	15.0990i	−0.328083	+	0.568257i
$707$	16.1435	−	27.9613i	0.607138	−	1.05159i
$708$	−9.55745	−	5.51800i	−0.359191	−	0.207379i
$709$			14.9127i			0.560056i	0.959992	+	0.280028i	$0.0903438\pi$
$709$			14.9127i			0.560056i	−0.959992	+	0.280028i	$0.909656\pi$
$710$	−0.215263	+	0.372847i	−0.00807869	+	0.0139927i
$711$		−	7.23008i		−	0.271149i
$712$	5.63218	+	9.75521i	0.211075	+	0.365592i
$713$	−2.61424			−0.0979041
$714$	7.35018			0.275074
$715$	9.62144	+	16.6648i	0.359822	+	0.623229i
$716$	−0.779992	−	0.450328i	−0.0291497	−	0.0168296i
$717$			4.25251i			0.158813i
$718$	−4.44441	+	2.56598i	−0.165864	+	0.0957615i
$719$	24.6771	+	42.7419i	0.920300	+	1.59401i	0.798951	+	0.601396i	$0.205388\pi$
$719$	24.6771	+	42.7419i	0.920300	+	1.59401i	0.121348	+	0.992610i	$0.461278\pi$
$720$	−0.866025	+	0.500000i	−0.0322749	+	0.0186339i
$721$	−31.2404	−	18.0367i	−1.16345	−	0.671721i
$722$	−4.54988	−	2.62687i	−0.169329	−	0.0977621i
$723$	−5.12924	+	2.96137i	−0.190758	+	0.110134i
$724$	−1.45760	−	2.52464i	−0.0541713	−	0.0938275i
$725$	2.92512	−	1.68882i	0.108636	−	0.0627212i
$726$			16.6586i			0.618260i
$727$	−16.9389	−	9.77968i	−0.628229	−	0.362708i	0.151837	−	0.988406i	$-0.451481\pi$
$727$	−16.9389	−	9.77968i	−0.628229	−	0.362708i	−0.780066	+	0.625697i	$0.784815\pi$
$728$	−5.95829	−	10.3201i	−0.220829	−	0.382487i
$729$	1.00000			0.0370370
$730$	4.23689			0.156814
$731$	3.70529	+	6.41775i	0.137045	+	0.237369i
$732$		−	1.23662i		−	0.0457067i
$733$	−3.88876	+	6.73552i	−0.143635	+	0.248782i	−0.928863	−	0.370424i	$-0.879212\pi$
$733$	−3.88876	+	6.73552i	−0.143635	+	0.248782i	0.785228	+	0.619207i	$0.212546\pi$
$734$			4.67369i			0.172509i
$735$	3.12377	+	1.80351i	0.115222	+	0.0665235i
$736$	0.963443	−	1.66873i	0.0355130	−	0.0615103i
$737$	36.4751	−	63.1767i	1.34358	−	2.32714i
$738$	−4.74141	+	2.73745i	−0.174534	+	0.100767i
$739$	9.29956			0.342090			0.171045	−	0.985263i	$-0.445286\pi$
$739$	9.29956			0.342090			0.171045	+	0.985263i	$0.445286\pi$
$740$	−6.08275	+	0.0101124i	−0.223606	+	0.000371740i
$741$	−13.5659			−0.498354
$742$	−28.7402	+	16.5932i	−1.05509	+	0.609155i
$743$	6.76607	−	11.7192i	0.248223	−	0.429935i	−0.714810	−	0.699319i	$-0.753487\pi$
$743$	6.76607	−	11.7192i	0.248223	−	0.429935i	0.963033	+	0.269384i	$0.0868201\pi$
$744$	−0.678359	+	1.17495i	−0.0248699	+	0.0430759i
$745$	7.24623	+	4.18361i	0.265481	+	0.153276i
$746$		−	26.8436i		−	0.982816i
$747$	6.83148	−	11.8325i	0.249951	−	0.432928i
$748$		−	11.8691i		−	0.433976i
$749$	−22.1513	−	38.3672i	−0.809391	−	1.40191i
$750$	−1.00000			−0.0365148
$751$	−2.87915			−0.105062			−0.0525309	−	0.998619i	$-0.516729\pi$
$751$	−2.87915			−0.105062			−0.0525309	+	0.998619i	$0.516729\pi$
$752$	−1.66383	−	2.88183i	−0.0606735	−	0.105090i
$753$	−9.89430	−	5.71248i	−0.360568	−	0.208174i
$754$			12.3586i			0.450072i
$755$	12.0638	−	6.96505i	0.439047	−	0.253484i
$756$	1.62842	+	2.82051i	0.0592251	+	0.102581i
$757$	−26.6459	+	15.3840i	−0.968463	+	0.559143i	−0.898767	−	0.438426i	$-0.855536\pi$
$757$	−26.6459	+	15.3840i	−0.968463	+	0.559143i	−0.0696959	+	0.997568i	$0.522203\pi$
$758$	−24.3491	−	14.0580i	−0.884400	−	0.510608i
$759$	8.77611	+	5.06689i	0.318553	+	0.183916i
$760$	−3.21087	+	1.85380i	−0.116471	+	0.0672443i
$761$	5.21225	+	9.02789i	0.188944	+	0.327261i	0.944898	−	0.327364i	$-0.106160\pi$
$761$	5.21225	+	9.02789i	0.188944	+	0.327261i	−0.755954	+	0.654624i	$0.772827\pi$
$762$	12.7064	−	7.33602i	0.460303	−	0.265756i
$763$		−	24.1564i		−	0.874520i
$764$	23.4667	+	13.5485i	0.848995	+	0.490167i
$765$	1.12842	+	1.95448i	0.0407982	+	0.0706645i
$766$	−26.4777			−0.956679
$767$	40.3800			1.45804
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$		−	10.2078i		−	0.368104i	−0.982917	−	0.184052i	$-0.941079\pi$
$769$		−	10.2078i		−	0.368104i	0.982917	−	0.184052i	$-0.0589214\pi$
$770$	8.56411	−	14.8335i	0.308629	−	0.534561i
$771$		−	23.4665i		−	0.845126i
$772$	−14.4071	−	8.31797i	−0.518524	−	0.299370i
$773$	−15.3580	+	26.6008i	−0.552389	+	0.956765i	0.445713	+	0.895176i	$0.352950\pi$
$773$	−15.3580	+	26.6008i	−0.552389	+	0.956765i	−0.998102	+	0.0615892i	$0.980383\pi$
$774$	−1.64180	+	2.84368i	−0.0590134	+	0.102214i
$775$	−1.17495	+	0.678359i	−0.0422055	+	0.0243674i
$776$	−4.69418			−0.168511
$777$	0.0329346	+	19.8106i	0.00118152	+	0.710700i
$778$	−28.4824			−1.02114
$779$	−17.5792	+	10.1494i	−0.629841	+	0.363639i
$780$	1.82947	−	3.16873i	0.0655055	−	0.113459i
$781$	1.13210	−	1.96086i	0.0405098	−	0.0701650i
$782$	−3.76607	−	2.17434i	−0.134674	−	0.0777542i
$783$		−	3.37764i		−	0.120707i
$784$	−1.80351	+	3.12377i	−0.0644111	+	0.111563i
$785$		−	8.98311i		−	0.320621i
$786$	−4.24121	−	7.34599i	−0.151279	−	0.262023i
$787$	20.5669			0.733129			0.366565	−	0.930393i	$-0.380534\pi$
$787$	20.5669			0.733129			0.366565	+	0.930393i	$0.380534\pi$
$788$	−17.1920			−0.612439
$789$	10.3985	+	18.0108i	0.370197	+	0.641200i
$790$	6.26143	+	3.61504i	0.222772	+	0.128617i
$791$			1.02776i			0.0365429i
$792$	4.55456	−	2.62957i	0.161839	−	0.0934378i
$793$	2.26235	+	3.91851i	0.0803385	+	0.139150i
$794$	−18.7724	+	10.8382i	−0.666207	+	0.384635i
$795$	−8.82457	−	5.09487i	−0.312975	−	0.180696i
$796$	−2.36867	−	1.36755i	−0.0839554	−	0.0484717i
$797$	−13.8819	+	8.01472i	−0.491722	+	0.283896i	−0.725289	−	0.688445i	$-0.758294\pi$
$797$	−13.8819	+	8.01472i	−0.491722	+	0.283896i	0.233567	+	0.972341i	$0.424960\pi$
$798$	6.03753	+	10.4573i	0.213726	+	0.370184i
$799$	−6.50384	+	3.75499i	−0.230089	+	0.132842i
$800$		−	1.00000i		−	0.0353553i
$801$	9.75521	+	5.63218i	0.344684	+	0.199003i
$802$	4.23284	+	7.33150i	0.149467	+	0.258884i
$803$	−22.2825			−0.786331
$804$	−13.8711			−0.489196
$805$	−3.13778	−	5.43480i	−0.110592	−	0.191551i
$806$		−	4.96415i		−	0.174855i
$807$	−10.2072	+	17.6794i	−0.359311	+	0.622345i
$808$			9.91358i			0.348758i
$809$	27.9429	+	16.1329i	0.982421	+	0.567201i	0.903000	−	0.429640i	$-0.141360\pi$
$809$	27.9429	+	16.1329i	0.982421	+	0.567201i	0.0794206	+	0.996841i	$0.474693\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	−8.33138	+	14.4304i	−0.292554	+	0.506719i	−0.974413	−	0.224765i	$-0.927839\pi$
$811$	−8.33138	+	14.4304i	−0.292554	+	0.506719i	0.681859	+	0.731484i	$0.261172\pi$
$812$	9.52666	−	5.50022i	0.334320	−	0.193020i
$813$	19.7497			0.692653
$814$	31.9901	−	0.0531828i	1.12125	−	0.00186405i
$815$	19.9626			0.699258
$816$	−1.95448	+	1.12842i	−0.0684206	+	0.0395026i
$817$	−6.08714	+	10.5432i	−0.212962	+	0.368861i
$818$	−0.774650	+	1.34173i	−0.0270850	+	0.0469126i
$819$	−10.3201	−	5.95829i	−0.360612	−	0.208200i
$820$		−	5.47491i		−	0.191192i
$821$	13.8817	−	24.0439i	0.484476	−	0.839137i	−0.515365	−	0.856971i	$-0.672344\pi$
$821$	13.8817	−	24.0439i	0.484476	−	0.839137i	0.999841	+	0.0178335i	$0.00567689\pi$
$822$			14.1845i			0.494741i
$823$	16.7352	+	28.9863i	0.583353	+	1.01040i	0.995079	+	0.0990896i	$0.0315930\pi$
$823$	16.7352	+	28.9863i	0.583353	+	1.01040i	−0.411725	+	0.911308i	$0.635074\pi$
$824$	11.0762			0.385857
$825$	5.25915			0.183100
$826$	−17.9713	−	31.1271i	−0.625300	−	1.08305i
$827$	−9.46985	−	5.46742i	−0.329299	−	0.190121i	0.326231	−	0.945290i	$-0.394221\pi$
$827$	−9.46985	−	5.46742i	−0.329299	−	0.190121i	−0.655530	+	0.755169i	$0.727555\pi$
$828$		−	1.92689i		−	0.0669639i
$829$	19.8859	−	11.4811i	0.690665	−	0.398756i	−0.113196	−	0.993573i	$-0.536109\pi$
$829$	19.8859	−	11.4811i	0.690665	−	0.398756i	0.803861	+	0.594817i	$0.202776\pi$
$830$	6.83148	+	11.8325i	0.237124	+	0.410711i
$831$	−0.559700	+	0.323143i	−0.0194158	+	0.0112097i
$832$	3.16873	+	1.82947i	0.109856	+	0.0634254i
$833$	7.04987	+	4.07024i	0.244263	+	0.141026i
$834$	18.4528	−	10.6538i	0.638970	−	0.368909i
$835$	−4.09793	−	7.09782i	−0.141815	−	0.245630i
$836$	16.8864	−	9.74939i	0.584030	−	0.337190i
$837$			1.35672i			0.0468950i
$838$	−28.2489	−	16.3095i	−0.975842	−	0.563403i
$839$	−19.2123	−	33.2767i	−0.663282	−	1.14884i	−0.979748	−	0.200235i	$-0.935830\pi$
$839$	−19.2123	−	33.2767i	−0.663282	−	1.14884i	0.316466	−	0.948604i	$-0.397504\pi$
$840$	−3.25684			−0.112372
$841$	17.5916			0.606606
$842$	−1.19442	−	2.06879i	−0.0411624	−	0.0712954i
$843$		−	1.97850i		−	0.0681431i
$844$	−9.40994	+	16.2985i	−0.323904	+	0.561017i
$845$			0.387818i			0.0133413i
$846$	−2.88183	−	1.66383i	−0.0990794	−	0.0572035i
$847$	−27.1273	+	46.9858i	−0.932104	+	1.61445i
$848$	5.09487	−	8.82457i	0.174958	−	0.303037i
$849$	6.32516	−	3.65183i	0.217079	−	0.125331i
$850$	−2.25684			−0.0774091
$851$	5.84351	−	10.1602i	0.200313	−	0.348288i
$852$	−0.430527			−0.0147496
$853$	−4.33922	+	2.50525i	−0.148572	+	0.0857781i	−0.572443	−	0.819944i	$-0.694004\pi$
$853$	−4.33922	+	2.50525i	−0.148572	+	0.0857781i	0.423871	+	0.905723i	$0.360671\pi$
$854$	2.01373	−	3.48789i	0.0689086	−	0.119353i
$855$	−1.85380	+	3.21087i	−0.0633985	+	0.109809i
$856$	11.7805	+	6.80147i	0.402649	+	0.232469i
$857$			6.93762i			0.236985i	0.992955	+	0.118492i	$0.0378061\pi$
$857$			6.93762i			0.236985i	−0.992955	+	0.118492i	$0.962194\pi$
$858$	−9.62144	+	16.6648i	−0.328471	+	0.568928i
$859$		−	14.9800i		−	0.511110i	−0.966795	−	0.255555i	$-0.917742\pi$
$859$		−	14.9800i		−	0.511110i	0.966795	−	0.255555i	$-0.0822581\pi$
$860$	−1.64180	−	2.84368i	−0.0559850	−	0.0969688i
$861$	−17.8309			−0.607676
$862$	15.1399			0.515668
$863$	4.92892	+	8.53713i	0.167782	+	0.290607i	0.937640	−	0.347608i	$-0.113006\pi$
$863$	4.92892	+	8.53713i	0.167782	+	0.290607i	−0.769858	+	0.638216i	$0.779673\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$			15.9234i			0.541411i
$866$	28.5874	−	16.5049i	0.971440	−	0.560861i
$867$	−5.95333	−	10.3115i	−0.202186	−	0.350196i
$868$	−3.82664	+	2.20931i	−0.129884	+	0.0749888i
$869$	−32.9298	−	19.0120i	−1.11707	−	0.644939i
$870$	2.92512	+	1.68882i	0.0991709	+	0.0572563i
$871$	43.9538	−	25.3767i	1.48932	−	0.859858i
$872$	3.70856	+	6.42341i	0.125588	+	0.217524i
$873$	−4.06528	+	2.34709i	−0.137589	+	0.0794370i
$874$		−	7.14411i		−	0.241653i
$875$	−2.82051	−	1.62842i	−0.0953506	−	0.0550507i
$876$	2.11845	+	3.66926i	0.0715757	+	0.123973i
$877$	−51.9937			−1.75570			−0.877851	−	0.478933i	$-0.841024\pi$
$877$	−51.9937			−1.75570			−0.877851	+	0.478933i	$0.841024\pi$
$878$	14.3504			0.484302
$879$	−5.66939	−	9.81967i	−0.191224	−	0.331209i
$880$			5.25915i			0.177286i
$881$	−4.43573	+	7.68291i	−0.149444	+	0.258844i	−0.931022	−	0.364963i	$-0.881082\pi$
$881$	−4.43573	+	7.68291i	−0.149444	+	0.258844i	0.781578	+	0.623807i	$0.214415\pi$
$882$			3.60702i			0.121455i
$883$	22.0975	+	12.7580i	0.743639	+	0.429340i	0.823391	−	0.567475i	$-0.192080\pi$
$883$	22.0975	+	12.7580i	0.743639	+	0.429340i	−0.0797521	+	0.996815i	$0.525413\pi$
$884$	4.12882	−	7.15133i	0.138867	−	0.240525i
$885$	5.51800	−	9.55745i	0.185485	−	0.321270i
$886$	1.89437	−	1.09371i	0.0636425	−	0.0367440i
$887$	−6.43597			−0.216099			−0.108049	−	0.994146i	$-0.534460\pi$
$887$	−6.43597			−0.216099			−0.108049	+	0.994146i	$0.534460\pi$
$888$	−3.05013	−	5.26276i	−0.102356	−	0.176607i
$889$	47.7845			1.60264
$890$	−9.75521	+	5.63218i	−0.326995	+	0.188791i
$891$	2.62957	−	4.55456i	0.0880940	−	0.152583i
$892$	12.8196	−	22.2042i	0.429233	−	0.743453i
$893$	−10.6847	−	6.16879i	−0.357549	−	0.206431i
$894$			8.36723i			0.279842i
$895$	0.450328	−	0.779992i	0.0150528	−	0.0260722i
$896$		−	3.25684i		−	0.108803i
$897$	3.52518	+	6.10579i	0.117702	+	0.203866i
$898$	−36.9734			−1.23382
$899$	4.58250			0.152835
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−19.9157	−	11.4983i	−0.663487	−	0.383064i
$902$			28.7933i			0.958714i
$903$	−9.26143	+	5.34709i	−0.308201	+	0.177940i
$904$	−0.157785	−	0.273291i	−0.00524783	−	0.00908952i
$905$	2.52464	−	1.45760i	0.0839218	−	0.0484523i
$906$	12.0638	+	6.96505i	0.400794	+	0.231398i
$907$	−46.2924	−	26.7269i	−1.53711	−	0.887453i	−0.999006	−	0.0445775i	$-0.985806\pi$
$907$	−46.2924	−	26.7269i	−1.53711	−	0.887453i	−0.538108	−	0.842876i	$-0.680861\pi$
$908$	14.0727	−	8.12488i	0.467019	−	0.269634i
$909$	4.95679	+	8.58541i	0.164406	+	0.284760i
$910$	10.3201	−	5.95829i	0.342107	−	0.197515i
$911$		−	2.44321i		−	0.0809472i	−0.999181	−	0.0404736i	$-0.987113\pi$
$911$		−	2.44321i		−	0.0809472i	0.999181	−	0.0404736i	$-0.0128867\pi$
$912$	−3.21087	−	1.85380i	−0.106323	−	0.0613854i
$913$	−35.9278	−	62.2288i	−1.18904	−	2.05947i
$914$	16.1477			0.534119
$915$	1.23662			0.0408813
$916$	5.87416	+	10.1743i	0.194088	+	0.336170i
$917$		−	27.6259i		−	0.912287i
$918$	−1.12842	+	1.95448i	−0.0372435	+	0.0645076i
$919$		−	10.2898i		−	0.339428i	−0.985493	−	0.169714i	$-0.945716\pi$
$919$		−	10.2898i		−	0.339428i	0.985493	−	0.169714i	$-0.0542843\pi$
$920$	1.66873	+	0.963443i	0.0550165	+	0.0317638i
$921$	4.77123	−	8.26401i	0.157217	−	0.272308i
$922$	−10.4271	+	18.0603i	−0.343399	+	0.594784i
$923$	1.36422	−	0.787635i	0.0449040	−	0.0259253i
$924$	17.1282			0.563477
$925$	−0.0101124	−	6.08275i	−0.000332495	−	0.200000i
$926$	−37.9389			−1.24675
$927$	9.59224	−	5.53809i	0.315051	−	0.181895i
$928$	−1.68882	+	2.92512i	−0.0554382	+	0.0960218i
$929$	−27.0673	+	46.8819i	−0.888048	+	1.53814i	−0.0458675	+	0.998948i	$0.514605\pi$
$929$	−27.0673	+	46.8819i	−0.888048	+	1.53814i	−0.842180	+	0.539196i	$0.818728\pi$
$930$	−1.17495	−	0.678359i	−0.0385282	−	0.0222443i
$931$			13.3734i			0.438295i
$932$	5.19295	−	8.99446i	0.170101	−	0.294623i
$933$		−	13.5610i		−	0.443967i
$934$	−5.83125	−	10.1000i	−0.190804	−	0.330483i
$935$	11.8691			0.388160
$936$	3.65894			0.119596
$937$	5.26556	+	9.12022i	0.172018	+	0.297945i	0.939125	−	0.343575i	$-0.111638\pi$
$937$	5.26556	+	9.12022i	0.172018	+	0.297945i	−0.767107	+	0.641519i	$0.778304\pi$
$938$	−39.1236	−	22.5880i	−1.27743	−	0.737524i
$939$			3.39931i			0.110932i
$940$	2.88183	−	1.66383i	0.0939950	−	0.0542680i
$941$	8.95327	+	15.5075i	0.291868	+	0.505531i	0.974252	−	0.225464i	$-0.0723897\pi$
$941$	8.95327	+	15.5075i	0.291868	+	0.505531i	−0.682383	+	0.730995i	$0.739056\pi$
$942$	7.77960	−	4.49155i	0.253473	−	0.146343i
$943$	9.13615	+	5.27476i	0.297514	+	0.171770i
$944$	9.55745	+	5.51800i	0.311069	+	0.179596i
$945$	−2.82051	+	1.62842i	−0.0917511	+	0.0529726i
$946$	8.63448	+	14.9554i	0.280731	+	0.486241i
$947$	31.6666	−	18.2827i	1.02903	−	0.594109i	0.112321	−	0.993672i	$-0.464171\pi$
$947$	31.6666	−	18.2827i	1.02903	−	0.594109i	0.916706	+	0.399563i	$0.130838\pi$
$948$			7.23008i			0.234822i
$949$	−13.4256	−	7.75126i	−0.435813	−	0.251617i
$950$	−1.85380	−	3.21087i	−0.0601451	−	0.104174i
$951$	19.9724			0.647649
$952$	−7.35018			−0.238221
$953$	−8.28478	−	14.3497i	−0.268370	−	0.464831i	0.700071	−	0.714073i	$-0.253152\pi$
$953$	−8.28478	−	14.3497i	−0.268370	−	0.464831i	−0.968441	+	0.249242i	$0.919818\pi$
$954$		−	10.1897i		−	0.329905i
$955$	−13.5485	+	23.4667i	−0.438419	+	0.759364i
$956$		−	4.25251i		−	0.137536i
$957$	−15.3836	−	8.88175i	−0.497282	−	0.287106i
$958$	−18.9158	+	32.7632i	−0.611142	+	1.05853i
$959$	−23.0983	+	40.0074i	−0.745883	+	1.29191i
$960$	0.866025	−	0.500000i	0.0279508	−	0.0161374i
$961$	29.1593			0.940623
$962$	19.2931	+	11.0962i	0.622035	+	0.357755i
$963$	13.6029			0.438348
$964$	5.12924	−	2.96137i	0.165202	−	0.0953792i
$965$	8.31797	−	14.4071i	0.267765	−	0.463782i
$966$	3.13778	−	5.43480i	0.100956	−	0.174862i
$967$	−15.2004	−	8.77593i	−0.488810	−	0.282215i	0.235270	−	0.971930i	$-0.424402\pi$
$967$	−15.2004	−	8.77593i	−0.488810	−	0.282215i	−0.724081	+	0.689715i	$0.757736\pi$
$968$		−	16.6586i		−	0.535429i
$969$	−4.18373	+	7.24643i	−0.134401	+	0.232789i
$970$		−	4.69418i		−	0.150721i
$971$	−2.09429	−	3.62741i	−0.0672088	−	0.116409i	0.830463	−	0.557074i	$-0.188076\pi$
$971$	−2.09429	−	3.62741i	−0.0672088	−	0.116409i	−0.897672	+	0.440665i	$0.854743\pi$
$972$	−1.00000			−0.0320750
$973$	69.3952			2.22471
$974$	17.0334	+	29.5026i	0.545784	+	0.945325i
$975$	3.16873	+	1.82947i	0.101481	+	0.0585899i
$976$			1.23662i			0.0395832i
$977$	13.6731	−	7.89414i	0.437440	−	0.252556i	−0.265071	−	0.964229i	$-0.585395\pi$
$977$	13.6731	−	7.89414i	0.437440	−	0.252556i	0.702511	+	0.711673i	$0.252062\pi$
$978$	9.98128	+	17.2881i	0.319166	+	0.552812i
$979$	51.3041	−	29.6204i	1.63969	−	0.946673i
$980$	−3.12377	−	1.80351i	−0.0997853	−	0.0576111i
$981$	6.42341	+	3.70856i	0.205084	+	0.118405i
$982$	29.1792	−	16.8466i	0.931146	−	0.537597i
$983$	−15.4215	−	26.7108i	−0.491869	−	0.851941i	0.508088	−	0.861305i	$-0.330353\pi$
$983$	−15.4215	−	26.7108i	−0.491869	−	0.851941i	−0.999956	+	0.00936410i	$0.997019\pi$
$984$	4.74141	−	2.73745i	0.151151	−	0.0872668i
$985$		−	17.1920i		−	0.547782i
$986$	6.60154	+	3.81140i	0.210236	+	0.121380i
$987$	−5.41882	−	9.38567i	−0.172483	−	0.298749i
$988$	13.5659			0.431587
$989$	6.32713			0.201191
$990$	2.62957	+	4.55456i	0.0835733	+	0.144753i
$991$		−	43.2922i		−	1.37522i	−0.726079	−	0.687612i	$-0.758659\pi$
$991$		−	43.2922i		−	1.37522i	0.726079	−	0.687612i	$-0.241341\pi$
$992$	0.678359	−	1.17495i	0.0215379	−	0.0373048i
$993$			9.87613i			0.313410i
$994$	−1.21430	−	0.701079i	−0.0385154	−	0.0222369i
$995$	1.36755	−	2.36867i	0.0433544	−	0.0750920i
$996$	−6.83148	+	11.8325i	−0.216464	+	0.374926i
$997$	9.17242	−	5.29570i	0.290493	−	0.167716i	−0.347671	−	0.937617i	$-0.613027\pi$
$997$	9.17242	−	5.29570i	0.290493	−	0.167716i	0.638164	+	0.769900i	$0.279694\pi$
$998$	−0.859458			−0.0272057
$999$	−5.27288	−	3.03262i	−0.166826	−	0.0959478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.d.751.5	✓	16
37.27	even	6	inner	1110.2.x.d.841.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.d.751.5	✓	16	1.1	even	1	trivial
1110.2.x.d.841.5	yes	16	37.27	even	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-1.62842 + 2.82051i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-1.62842 + 2.82051i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} -5.25915 q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.16873 - 1.82947i) q^{13} +3.25684i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.95448 + 1.12842i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-3.21087 - 1.85380i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-1.62842 - 2.82051i) q^{21} +(-4.55456 + 2.62957i) q^{22} +1.92689i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -3.65894 q^{26} +1.00000 q^{27} +(1.62842 + 2.82051i) q^{28} -3.37764i q^{29} +(-0.500000 + 0.866025i) q^{30} +1.35672i q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.62957 - 4.55456i) q^{33} +(-1.12842 + 1.95448i) q^{34} +(-2.82051 + 1.62842i) q^{35} -1.00000 q^{36} +(-5.27288 - 3.03262i) q^{37} -3.70759 q^{38} +(3.16873 - 1.82947i) q^{39} +(0.500000 - 0.866025i) q^{40} +(2.73745 - 4.74141i) q^{41} +(-2.82051 - 1.62842i) q^{42} -3.28360i q^{43} +(-2.62957 + 4.55456i) q^{44} -1.00000i q^{45} +(0.963443 + 1.66873i) q^{46} +3.32765 q^{47} +1.00000 q^{48} +(-1.80351 - 3.12377i) q^{49} +(0.866025 + 0.500000i) q^{50} -2.25684i q^{51} +(-3.16873 + 1.82947i) q^{52} +(5.09487 + 8.82457i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-4.55456 - 2.62957i) q^{55} +(2.82051 + 1.62842i) q^{56} +(3.21087 - 1.85380i) q^{57} +(-1.68882 - 2.92512i) q^{58} +(-9.55745 + 5.51800i) q^{59} +1.00000i q^{60} +(-1.07094 - 0.618309i) q^{61} +(0.678359 + 1.17495i) q^{62} +3.25684 q^{63} -1.00000 q^{64} +(-1.82947 - 3.16873i) q^{65} -5.25915i q^{66} +(-6.93555 + 12.0127i) q^{67} +2.25684i q^{68} +(-1.66873 - 0.963443i) q^{69} +(-1.62842 + 2.82051i) q^{70} +(-0.215263 + 0.372847i) q^{71} +(-0.866025 + 0.500000i) q^{72} +4.23689 q^{73} +(-6.08275 + 0.0101124i) q^{74} -1.00000 q^{75} +(-3.21087 + 1.85380i) q^{76} +(8.56411 - 14.8335i) q^{77} +(1.82947 - 3.16873i) q^{78} +(6.26143 + 3.61504i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -5.47491i q^{82} +(6.83148 + 11.8325i) q^{83} -3.25684 q^{84} -2.25684 q^{85} +(-1.64180 - 2.84368i) q^{86} +(2.92512 + 1.68882i) q^{87} +5.25915i q^{88} +(-9.75521 + 5.63218i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(10.3201 - 5.95829i) q^{91} +(1.66873 + 0.963443i) q^{92} +(-1.17495 - 0.678359i) q^{93} +(2.88183 - 1.66383i) q^{94} +(-1.85380 - 3.21087i) q^{95} +(0.866025 - 0.500000i) q^{96} -4.69418i q^{97} +(-3.12377 - 1.80351i) q^{98} +(2.62957 + 4.55456i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} + 16 q^{10} - 8 q^{11} + 8 q^{12} - 6 q^{13} - 8 q^{16} + 6 q^{17} - 12 q^{19} - 2 q^{21} + 8 q^{25} + 4 q^{26} + 16 q^{27} + 2 q^{28} - 8 q^{30} + 4 q^{33} + 6 q^{34} + 6 q^{35} - 16 q^{36} + 12 q^{37} - 4 q^{38} + 6 q^{39} + 8 q^{40} + 4 q^{41} + 6 q^{42} - 4 q^{44} - 2 q^{46} + 68 q^{47} + 16 q^{48} - 4 q^{49} - 6 q^{52} - 12 q^{53} - 6 q^{56} + 12 q^{57} - 6 q^{58} + 6 q^{59} + 12 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{64} + 2 q^{65} - 36 q^{67} + 18 q^{69} - 2 q^{70} + 6 q^{71} - 16 q^{73} + 14 q^{74} - 16 q^{75} - 12 q^{76} + 26 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 12 q^{83} - 4 q^{84} + 12 q^{85} - 2 q^{86} + 24 q^{89} - 8 q^{90} + 60 q^{91} - 18 q^{92} - 30 q^{93} + 6 q^{94} - 2 q^{95} - 12 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 + 16 * q^10 - 8 * q^11 + 8 * q^12 - 6 * q^13 - 8 * q^16 + 6 * q^17 - 12 * q^19 - 2 * q^21 + 8 * q^25 + 4 * q^26 + 16 * q^27 + 2 * q^28 - 8 * q^30 + 4 * q^33 + 6 * q^34 + 6 * q^35 - 16 * q^36 + 12 * q^37 - 4 * q^38 + 6 * q^39 + 8 * q^40 + 4 * q^41 + 6 * q^42 - 4 * q^44 - 2 * q^46 + 68 * q^47 + 16 * q^48 - 4 * q^49 - 6 * q^52 - 12 * q^53 - 6 * q^56 + 12 * q^57 - 6 * q^58 + 6 * q^59 + 12 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^64 + 2 * q^65 - 36 * q^67 + 18 * q^69 - 2 * q^70 + 6 * q^71 - 16 * q^73 + 14 * q^74 - 16 * q^75 - 12 * q^76 + 26 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 12 * q^83 - 4 * q^84 + 12 * q^85 - 2 * q^86 + 24 * q^89 - 8 * q^90 + 60 * q^91 - 18 * q^92 - 30 * q^93 + 6 * q^94 - 2 * q^95 - 12 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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